id	sid	tid	token	lemma	pos
ejpam-6834	1	1	european	european	PROPN
ejpam-6834	1	2	journal	journal	PROPN
ejpam-6834	1	3	of	of	ADP
ejpam-6834	1	4	pure	pure	ADJ
ejpam-6834	1	5	and	and	CCONJ
ejpam-6834	1	6	applied	applied	ADJ
ejpam-6834	1	7	mathematics	mathematic	NOUN
ejpam-6834	1	8	2025	2025	NUM
ejpam-6834	1	9	,	,	PUNCT
ejpam-6834	1	10	vol	vol	NOUN
ejpam-6834	1	11	.	.	PROPN
ejpam-6834	1	12	18	18	NUM
ejpam-6834	1	13	,	,	PUNCT
ejpam-6834	1	14	issue	issue	NOUN
ejpam-6834	1	15	4	4	NUM
ejpam-6834	1	16	,	,	PUNCT
ejpam-6834	1	17	article	article	NOUN
ejpam-6834	1	18	number	number	NOUN
ejpam-6834	1	19	6834	6834	NUM
ejpam-6834	1	20	issn	issn	VERB
ejpam-6834	1	21	1307	1307	NUM
ejpam-6834	1	22	-	-	SYM
ejpam-6834	1	23	5543	5543	NUM
ejpam-6834	1	24	–	–	PUNCT
ejpam-6834	1	25	ejpam.com	ejpam.com	X
ejpam-6834	1	26	published	publish	VERB
ejpam-6834	1	27	by	by	ADP
ejpam-6834	1	28	new	new	PROPN
ejpam-6834	1	29	york	york	PROPN
ejpam-6834	1	30	business	business	PROPN
ejpam-6834	1	31	global	global	ADJ
ejpam-6834	1	32	hierarchical	hierarchical	ADJ
ejpam-6834	1	33	uncertainty	uncertainty	NOUN
ejpam-6834	1	34	modeling	model	VERB
ejpam-6834	1	35	via	via	ADP
ejpam-6834	1	36	(	(	PUNCT
ejpam-6834	1	37	m	m	X
ejpam-6834	1	38	,	,	PUNCT
ejpam-6834	1	39	n)-superhyperuncertain	n)-superhyperuncertain	PUNCT
ejpam-6834	1	40	and	and	CCONJ
ejpam-6834	1	41	(	(	PUNCT
ejpam-6834	1	42	h	h	NOUN
ejpam-6834	1	43	,	,	PUNCT
ejpam-6834	1	44	k)-ary	k)-ary	X
ejpam-6834	1	45	(	(	PUNCT
ejpam-6834	1	46	m	m	PROPN
ejpam-6834	1	47	,	,	PUNCT
ejpam-6834	1	48	n)-superhyperuncertain	n)-superhyperuncertain	ADJ
ejpam-6834	1	49	sets	set	VERB
ejpam-6834	1	50	:	:	PUNCT
ejpam-6834	1	51	unified	unified	ADJ
ejpam-6834	1	52	extensions	extension	NOUN
ejpam-6834	1	53	of	of	ADP
ejpam-6834	1	54	fuzzy	fuzzy	ADJ
ejpam-6834	1	55	,	,	PUNCT
ejpam-6834	1	56	neutrosophic	neutrosophic	ADJ
ejpam-6834	1	57	,	,	PUNCT
ejpam-6834	1	58	soft	soft	ADJ
ejpam-6834	1	59	,	,	PUNCT
ejpam-6834	1	60	rough	rough	ADJ
ejpam-6834	1	61	,	,	PUNCT
ejpam-6834	1	62	and	and	CCONJ
ejpam-6834	1	63	plithogenic	plithogenic	ADJ
ejpam-6834	1	64	set	set	NOUN
ejpam-6834	1	65	theories	theory	NOUN
ejpam-6834	1	66	takaaki	takaaki	NOUN
ejpam-6834	1	67	fujita1,∗	fujita1,∗	PROPN
ejpam-6834	1	68	,	,	PUNCT
ejpam-6834	1	69	florentin	florentin	NOUN
ejpam-6834	1	70	smarandache2	smarandache2	PROPN
ejpam-6834	1	71	1	1	NUM
ejpam-6834	1	72	independent	independent	ADJ
ejpam-6834	1	73	researcher	researcher	NOUN
ejpam-6834	1	74	,	,	PUNCT
ejpam-6834	1	75	shinjuku	shinjuku	PROPN
ejpam-6834	1	76	,	,	PUNCT
ejpam-6834	1	77	shinjuku	shinjuku	PROPN
ejpam-6834	1	78	-	-	PUNCT
ejpam-6834	1	79	ku	ku	PROPN
ejpam-6834	1	80	,	,	PUNCT
ejpam-6834	1	81	tokyo	tokyo	PROPN
ejpam-6834	1	82	,	,	PUNCT
ejpam-6834	1	83	japan	japan	PROPN
ejpam-6834	1	84	.	.	PROPN
ejpam-6834	1	85	2	2	NUM
ejpam-6834	1	86	university	university	NOUN
ejpam-6834	1	87	of	of	ADP
ejpam-6834	1	88	new	new	PROPN
ejpam-6834	1	89	mexico	mexico	PROPN
ejpam-6834	1	90	,	,	PUNCT
ejpam-6834	1	91	gallup	gallup	PROPN
ejpam-6834	1	92	campus	campus	PROPN
ejpam-6834	1	93	,	,	PUNCT
ejpam-6834	1	94	nm	nm	PROPN
ejpam-6834	1	95	87301	87301	NUM
ejpam-6834	1	96	,	,	PUNCT
ejpam-6834	1	97	usa	usa	PROPN
ejpam-6834	1	98	.	.	PROPN
ejpam-6834	1	99	abstract	abstract	PROPN
ejpam-6834	1	100	.	.	PUNCT
ejpam-6834	2	1	various	various	ADJ
ejpam-6834	2	2	set	set	VERB
ejpam-6834	2	3	-	-	PUNCT
ejpam-6834	2	4	theoretic	theoretic	NOUN
ejpam-6834	2	5	frameworks	framework	NOUN
ejpam-6834	2	6	have	have	AUX
ejpam-6834	2	7	been	be	AUX
ejpam-6834	2	8	widely	widely	ADV
ejpam-6834	2	9	recognized	recognize	VERB
ejpam-6834	2	10	for	for	ADP
ejpam-6834	2	11	their	their	PRON
ejpam-6834	2	12	effectiveness	effectiveness	NOUN
ejpam-6834	2	13	in	in	ADP
ejpam-6834	2	14	handling	handle	VERB
ejpam-6834	2	15	uncertainty	uncertainty	NOUN
ejpam-6834	2	16	,	,	PUNCT
ejpam-6834	2	17	including	include	VERB
ejpam-6834	2	18	fuzzy	fuzzy	ADJ
ejpam-6834	2	19	sets	set	NOUN
ejpam-6834	2	20	,	,	PUNCT
ejpam-6834	2	21	neutrosophic	neutrosophic	ADJ
ejpam-6834	2	22	sets	set	NOUN
ejpam-6834	2	23	,	,	PUNCT
ejpam-6834	2	24	plithogenic	plithogenic	ADJ
ejpam-6834	2	25	sets	set	NOUN
ejpam-6834	2	26	,	,	PUNCT
ejpam-6834	2	27	rough	rough	ADJ
ejpam-6834	2	28	sets	set	NOUN
ejpam-6834	2	29	,	,	PUNCT
ejpam-6834	2	30	and	and	CCONJ
ejpam-6834	2	31	soft	soft	ADJ
ejpam-6834	2	32	sets	set	NOUN
ejpam-6834	2	33	.	.	PUNCT
ejpam-6834	3	1	these	these	DET
ejpam-6834	3	2	foundational	foundational	ADJ
ejpam-6834	3	3	models	model	NOUN
ejpam-6834	3	4	have	have	AUX
ejpam-6834	3	5	been	be	AUX
ejpam-6834	3	6	further	far	ADV
ejpam-6834	3	7	extended	extend	VERB
ejpam-6834	3	8	through	through	ADP
ejpam-6834	3	9	the	the	DET
ejpam-6834	3	10	use	use	NOUN
ejpam-6834	3	11	of	of	ADP
ejpam-6834	3	12	hyperstructures	hyperstructure	NOUN
ejpam-6834	3	13	—	—	PUNCT
ejpam-6834	3	14	based	base	VERB
ejpam-6834	3	15	on	on	ADP
ejpam-6834	3	16	the	the	DET
ejpam-6834	3	17	powerset	powerset	NOUN
ejpam-6834	3	18	construction	construction	NOUN
ejpam-6834	3	19	—	—	PUNCT
ejpam-6834	3	20	and	and	CCONJ
ejpam-6834	3	21	superhyperstructures	superhyperstructure	NOUN
ejpam-6834	3	22	—	—	PUNCT
ejpam-6834	3	23	based	base	VERB
ejpam-6834	3	24	on	on	ADP
ejpam-6834	3	25	the	the	DET
ejpam-6834	3	26	n	n	CCONJ
ejpam-6834	3	27	-	-	PUNCT
ejpam-6834	3	28	th	th	NOUN
ejpam-6834	3	29	-	-	PUNCT
ejpam-6834	3	30	order	order	NOUN
ejpam-6834	3	31	powerset	powerset	NOUN
ejpam-6834	3	32	,	,	PUNCT
ejpam-6834	3	33	obtained	obtain	VERB
ejpam-6834	3	34	by	by	ADP
ejpam-6834	3	35	iteratively	iteratively	ADV
ejpam-6834	3	36	applying	apply	VERB
ejpam-6834	3	37	the	the	DET
ejpam-6834	3	38	powerset	powerset	NOUN
ejpam-6834	3	39	operation	operation	NOUN
ejpam-6834	4	1	[	[	X
ejpam-6834	4	2	1	1	NUM
ejpam-6834	4	3	,	,	PUNCT
ejpam-6834	4	4	2	2	NUM
ejpam-6834	4	5	]	]	PUNCT
ejpam-6834	4	6	.	.	PUNCT
ejpam-6834	5	1	these	these	DET
ejpam-6834	5	2	extended	extend	VERB
ejpam-6834	5	3	constructs	construct	NOUN
ejpam-6834	5	4	are	be	AUX
ejpam-6834	5	5	collectively	collectively	ADV
ejpam-6834	5	6	referred	refer	VERB
ejpam-6834	5	7	to	to	ADP
ejpam-6834	5	8	as	as	ADP
ejpam-6834	5	9	hyperuncertain	hyperuncertain	NOUN
ejpam-6834	5	10	sets	set	NOUN
ejpam-6834	5	11	and	and	CCONJ
ejpam-6834	5	12	superhyperuncertain	superhyperuncertain	ADJ
ejpam-6834	5	13	sets	set	NOUN
ejpam-6834	5	14	.	.	PUNCT
ejpam-6834	6	1	research	research	NOUN
ejpam-6834	6	2	on	on	ADP
ejpam-6834	6	3	superhyperuncertain	superhyperuncertain	ADJ
ejpam-6834	6	4	sets	set	NOUN
ejpam-6834	6	5	is	be	AUX
ejpam-6834	6	6	still	still	ADV
ejpam-6834	6	7	in	in	ADP
ejpam-6834	6	8	its	its	PRON
ejpam-6834	6	9	early	early	ADJ
ejpam-6834	6	10	stages	stage	NOUN
ejpam-6834	6	11	,	,	PUNCT
ejpam-6834	6	12	and	and	CCONJ
ejpam-6834	6	13	investigations	investigation	NOUN
ejpam-6834	6	14	into	into	ADP
ejpam-6834	6	15	their	their	PRON
ejpam-6834	6	16	properties	property	NOUN
ejpam-6834	6	17	,	,	PUNCT
ejpam-6834	6	18	extended	extend	VERB
ejpam-6834	6	19	forms	form	NOUN
ejpam-6834	6	20	,	,	PUNCT
ejpam-6834	6	21	and	and	CCONJ
ejpam-6834	6	22	potential	potential	ADJ
ejpam-6834	6	23	applications	application	NOUN
ejpam-6834	6	24	are	be	AUX
ejpam-6834	6	25	expected	expect	VERB
ejpam-6834	6	26	to	to	PART
ejpam-6834	6	27	become	become	VERB
ejpam-6834	6	28	increasingly	increasingly	ADV
ejpam-6834	6	29	significant	significant	ADJ
ejpam-6834	6	30	in	in	ADP
ejpam-6834	6	31	the	the	DET
ejpam-6834	6	32	future	future	NOUN
ejpam-6834	6	33	.	.	PUNCT
ejpam-6834	7	1	in	in	ADP
ejpam-6834	7	2	this	this	DET
ejpam-6834	7	3	paper	paper	NOUN
ejpam-6834	7	4	,	,	PUNCT
ejpam-6834	7	5	we	we	PRON
ejpam-6834	7	6	propose	propose	VERB
ejpam-6834	7	7	two	two	NUM
ejpam-6834	7	8	new	new	ADJ
ejpam-6834	7	9	,	,	PUNCT
ejpam-6834	7	10	more	more	ADV
ejpam-6834	7	11	general	general	ADJ
ejpam-6834	7	12	frameworks	framework	NOUN
ejpam-6834	7	13	:	:	PUNCT
ejpam-6834	7	14	the	the	DET
ejpam-6834	7	15	(	(	PUNCT
ejpam-6834	7	16	m	m	PROPN
ejpam-6834	7	17	,	,	PUNCT
ejpam-6834	7	18	n)superhyperuncertain	n)superhyperuncertain	PROPN
ejpam-6834	7	19	set	set	NOUN
ejpam-6834	7	20	and	and	CCONJ
ejpam-6834	7	21	the	the	DET
ejpam-6834	7	22	(	(	PUNCT
ejpam-6834	7	23	h	h	NOUN
ejpam-6834	7	24	,	,	PUNCT
ejpam-6834	7	25	k)-ary	k)-ary	X
ejpam-6834	7	26	(	(	PUNCT
ejpam-6834	7	27	m	m	PROPN
ejpam-6834	7	28	,	,	PUNCT
ejpam-6834	7	29	n)-superhyperuncertain	n)-superhyperuncertain	ADV
ejpam-6834	7	30	set	set	VERB
ejpam-6834	7	31	.	.	PUNCT
ejpam-6834	8	1	these	these	DET
ejpam-6834	8	2	new	new	ADJ
ejpam-6834	8	3	structures	structure	NOUN
ejpam-6834	8	4	represent	represent	VERB
ejpam-6834	8	5	a	a	DET
ejpam-6834	8	6	concrete	concrete	ADJ
ejpam-6834	8	7	and	and	CCONJ
ejpam-6834	8	8	refined	refined	ADJ
ejpam-6834	8	9	reconsideration	reconsideration	NOUN
ejpam-6834	8	10	of	of	ADP
ejpam-6834	8	11	the	the	DET
ejpam-6834	8	12	foundational	foundational	ADJ
ejpam-6834	8	13	concepts	concept	NOUN
ejpam-6834	8	14	introduced	introduce	VERB
ejpam-6834	8	15	in	in	ADP
ejpam-6834	8	16	[	[	X
ejpam-6834	8	17	1	1	NUM
ejpam-6834	8	18	,	,	PUNCT
ejpam-6834	8	19	2	2	NUM
ejpam-6834	8	20	]	]	PUNCT
ejpam-6834	8	21	.	.	PUNCT
ejpam-6834	9	1	it	it	PRON
ejpam-6834	9	2	is	be	AUX
ejpam-6834	9	3	anticipated	anticipate	VERB
ejpam-6834	9	4	that	that	SCONJ
ejpam-6834	9	5	the	the	DET
ejpam-6834	9	6	concepts	concept	NOUN
ejpam-6834	9	7	developed	develop	VERB
ejpam-6834	9	8	in	in	ADP
ejpam-6834	9	9	this	this	DET
ejpam-6834	9	10	work	work	NOUN
ejpam-6834	9	11	can	can	AUX
ejpam-6834	9	12	be	be	AUX
ejpam-6834	9	13	effectively	effectively	ADV
ejpam-6834	9	14	applied	apply	VERB
ejpam-6834	9	15	to	to	ADP
ejpam-6834	9	16	the	the	DET
ejpam-6834	9	17	modeling	modeling	NOUN
ejpam-6834	9	18	of	of	ADP
ejpam-6834	9	19	more	more	ADV
ejpam-6834	9	20	hierarchical	hierarchical	ADJ
ejpam-6834	9	21	forms	form	NOUN
ejpam-6834	9	22	of	of	ADP
ejpam-6834	9	23	uncertainty	uncertainty	NOUN
ejpam-6834	9	24	,	,	PUNCT
ejpam-6834	9	25	as	as	ADV
ejpam-6834	9	26	well	well	ADV
ejpam-6834	9	27	as	as	ADP
ejpam-6834	9	28	to	to	ADP
ejpam-6834	9	29	scenarios	scenario	NOUN
ejpam-6834	9	30	requiring	require	VERB
ejpam-6834	9	31	complex	complex	ADJ
ejpam-6834	9	32	membership	membership	NOUN
ejpam-6834	9	33	functions	function	NOUN
ejpam-6834	9	34	.	.	PUNCT
ejpam-6834	10	1	since	since	SCONJ
ejpam-6834	10	2	this	this	DET
ejpam-6834	10	3	paper	paper	NOUN
ejpam-6834	10	4	conducts	conduct	VERB
ejpam-6834	10	5	only	only	ADV
ejpam-6834	10	6	theoretical	theoretical	ADJ
ejpam-6834	10	7	analysis	analysis	NOUN
ejpam-6834	10	8	,	,	PUNCT
ejpam-6834	10	9	we	we	PRON
ejpam-6834	10	10	also	also	ADV
ejpam-6834	10	11	hope	hope	VERB
ejpam-6834	10	12	that	that	SCONJ
ejpam-6834	10	13	quantitative	quantitative	ADJ
ejpam-6834	10	14	analysis	analysis	NOUN
ejpam-6834	10	15	using	use	VERB
ejpam-6834	10	16	computational	computational	ADJ
ejpam-6834	10	17	methods	method	NOUN
ejpam-6834	10	18	will	will	AUX
ejpam-6834	10	19	be	be	AUX
ejpam-6834	10	20	carried	carry	VERB
ejpam-6834	10	21	out	out	ADP
ejpam-6834	10	22	in	in	ADP
ejpam-6834	10	23	the	the	DET
ejpam-6834	10	24	future	future	NOUN
ejpam-6834	10	25	.	.	PUNCT
ejpam-6834	11	1	2020	2020	NUM
ejpam-6834	11	2	mathematics	mathematic	NOUN
ejpam-6834	11	3	subject	subject	NOUN
ejpam-6834	11	4	classifications	classification	NOUN
ejpam-6834	11	5	:	:	PUNCT
ejpam-6834	11	6	03e72	03e72	X
ejpam-6834	11	7	key	key	ADJ
ejpam-6834	11	8	words	word	NOUN
ejpam-6834	11	9	and	and	CCONJ
ejpam-6834	11	10	phrases	phrase	NOUN
ejpam-6834	11	11	:	:	PUNCT
ejpam-6834	11	12	hyperfuzzy	hyperfuzzy	NOUN
ejpam-6834	11	13	set	set	PROPN
ejpam-6834	11	14	,	,	PUNCT
ejpam-6834	11	15	hyperneutrosophic	hyperneutrosophic	ADJ
ejpam-6834	11	16	set	set	NOUN
ejpam-6834	11	17	,	,	PUNCT
ejpam-6834	11	18	hyperplithogenic	hyperplithogenic	ADJ
ejpam-6834	11	19	set	set	NOUN
ejpam-6834	11	20	,	,	PUNCT
ejpam-6834	11	21	hyperrough	hyperrough	NOUN
ejpam-6834	11	22	set	set	PROPN
ejpam-6834	11	23	,	,	PUNCT
ejpam-6834	11	24	hypersoft	hypersoft	NOUN
ejpam-6834	11	25	set	set	VERB
ejpam-6834	11	26	1	1	NUM
ejpam-6834	11	27	.	.	PUNCT
ejpam-6834	12	1	introduction	introduction	NOUN
ejpam-6834	12	2	set	set	NOUN
ejpam-6834	12	3	theory	theory	NOUN
ejpam-6834	12	4	is	be	AUX
ejpam-6834	12	5	one	one	NUM
ejpam-6834	12	6	of	of	ADP
ejpam-6834	12	7	the	the	DET
ejpam-6834	12	8	most	most	ADV
ejpam-6834	12	9	fundamental	fundamental	ADJ
ejpam-6834	12	10	areas	area	NOUN
ejpam-6834	12	11	of	of	ADP
ejpam-6834	12	12	mathematics[3	mathematics[3	PROPN
ejpam-6834	12	13	]	]	PUNCT
ejpam-6834	12	14	.	.	PUNCT
ejpam-6834	13	1	however	however	ADV
ejpam-6834	13	2	,	,	PUNCT
ejpam-6834	13	3	classical	classical	ADJ
ejpam-6834	13	4	sets	set	NOUN
ejpam-6834	13	5	can	can	AUX
ejpam-6834	13	6	not	not	PART
ejpam-6834	13	7	adequately	adequately	ADV
ejpam-6834	13	8	represent	represent	VERB
ejpam-6834	13	9	the	the	DET
ejpam-6834	13	10	many	many	ADJ
ejpam-6834	13	11	forms	form	NOUN
ejpam-6834	13	12	of	of	ADP
ejpam-6834	13	13	uncertainty	uncertainty	NOUN
ejpam-6834	13	14	present	present	ADJ
ejpam-6834	13	15	in	in	ADP
ejpam-6834	13	16	the	the	DET
ejpam-6834	13	17	real	real	ADJ
ejpam-6834	13	18	world	world	NOUN
ejpam-6834	13	19	.	.	PUNCT
ejpam-6834	14	1	∗corresponding	∗corresponde	VERB
ejpam-6834	14	2	author	author	NOUN
ejpam-6834	14	3	.	.	PUNCT
ejpam-6834	15	1	doi	doi	NOUN
ejpam-6834	15	2	:	:	PUNCT
ejpam-6834	15	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6834	https://doi.org/10.29020/nybg.ejpam.v18i4.6834	PROPN
ejpam-6834	15	4	email	email	NOUN
ejpam-6834	15	5	addresses	address	NOUN
ejpam-6834	15	6	:	:	PUNCT
ejpam-6834	15	7	takaaki.fujita060@gmail.com	takaaki.fujita060@gmail.com	X
ejpam-6834	15	8	(	(	PUNCT
ejpam-6834	15	9	t.fujita	t.fujita	NUM
ejpam-6834	15	10	)	)	PUNCT
ejpam-6834	15	11	,	,	PUNCT
ejpam-6834	15	12	smarand@unm.edu	smarand@unm.edu	PROPN
ejpam-6834	15	13	(	(	PUNCT
ejpam-6834	15	14	f.	f.	PROPN
ejpam-6834	15	15	smarandache	smarandache	PROPN
ejpam-6834	15	16	)	)	PUNCT
ejpam-6834	15	17	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6834	16	1	1	1	NUM
ejpam-6834	16	2	copyright	copyright	NOUN
ejpam-6834	16	3	:	:	PUNCT
ejpam-6834	16	4	©	©	PROPN
ejpam-6834	16	5	2025	2025	NUM
ejpam-6834	16	6	the	the	DET
ejpam-6834	16	7	author(s	author(s	NOUN
ejpam-6834	16	8	)	)	PUNCT
ejpam-6834	16	9	.	.	PUNCT
ejpam-6834	17	1	(	(	PUNCT
ejpam-6834	17	2	cc	cc	NOUN
ejpam-6834	17	3	by	by	ADP
ejpam-6834	17	4	-	-	PUNCT
ejpam-6834	17	5	nc	nc	PROPN
ejpam-6834	17	6	4.0	4.0	NUM
ejpam-6834	17	7	)	)	PUNCT
ejpam-6834	17	8	t.	t.	PROPN
ejpam-6834	17	9	fujita	fujita	PROPN
ejpam-6834	17	10	,	,	PUNCT
ejpam-6834	17	11	f.smarandache	f.smarandache	NOUN
ejpam-6834	17	12	/	/	SYM
ejpam-6834	17	13	eur	eur	PROPN
ejpam-6834	17	14	.	.	PUNCT
ejpam-6834	18	1	j.	j.	PROPN
ejpam-6834	18	2	pure	pure	PROPN
ejpam-6834	18	3	appl	appl	PROPN
ejpam-6834	18	4	.	.	PROPN
ejpam-6834	18	5	math	math	PROPN
ejpam-6834	18	6	,	,	PUNCT
ejpam-6834	18	7	18	18	NUM
ejpam-6834	18	8	(	(	PUNCT
ejpam-6834	18	9	4	4	NUM
ejpam-6834	18	10	)	)	PUNCT
ejpam-6834	18	11	(	(	PUNCT
ejpam-6834	18	12	2025	2025	NUM
ejpam-6834	18	13	)	)	PUNCT
ejpam-6834	18	14	,	,	PUNCT
ejpam-6834	18	15	6834	6834	NUM
ejpam-6834	18	16	2	2	NUM
ejpam-6834	18	17	of	of	ADP
ejpam-6834	18	18	69	69	NUM
ejpam-6834	18	19	reasoning	reasoning	NOUN
ejpam-6834	18	20	with	with	ADP
ejpam-6834	18	21	incomplete	incomplete	ADJ
ejpam-6834	18	22	,	,	PUNCT
ejpam-6834	18	23	vague	vague	ADJ
ejpam-6834	18	24	,	,	PUNCT
ejpam-6834	18	25	or	or	CCONJ
ejpam-6834	18	26	heterogeneous	heterogeneous	ADJ
ejpam-6834	18	27	information	information	NOUN
ejpam-6834	18	28	has	have	AUX
ejpam-6834	18	29	therefore	therefore	ADV
ejpam-6834	18	30	motivated	motivate	VERB
ejpam-6834	18	31	the	the	DET
ejpam-6834	18	32	development	development	NOUN
ejpam-6834	18	33	of	of	ADP
ejpam-6834	18	34	a	a	DET
ejpam-6834	18	35	rich	rich	ADJ
ejpam-6834	18	36	family	family	NOUN
ejpam-6834	18	37	of	of	ADP
ejpam-6834	18	38	uncertain	uncertain	ADJ
ejpam-6834	18	39	set	set	NOUN
ejpam-6834	18	40	models	model	NOUN
ejpam-6834	18	41	[	[	X
ejpam-6834	18	42	4	4	NUM
ejpam-6834	18	43	]	]	PUNCT
ejpam-6834	18	44	.	.	PUNCT
ejpam-6834	19	1	some	some	PRON
ejpam-6834	19	2	of	of	ADP
ejpam-6834	19	3	the	the	DET
ejpam-6834	19	4	most	most	ADV
ejpam-6834	19	5	widely	widely	ADV
ejpam-6834	19	6	studied	study	VERB
ejpam-6834	19	7	examples	example	NOUN
ejpam-6834	19	8	include	include	VERB
ejpam-6834	19	9	fuzzy	fuzzy	ADJ
ejpam-6834	19	10	sets	set	NOUN
ejpam-6834	19	11	[	[	X
ejpam-6834	19	12	5	5	NUM
ejpam-6834	19	13	]	]	PUNCT
ejpam-6834	19	14	,	,	PUNCT
ejpam-6834	19	15	intuitionistic	intuitionistic	ADJ
ejpam-6834	19	16	fuzzy	fuzzy	ADJ
ejpam-6834	19	17	sets	set	NOUN
ejpam-6834	19	18	[	[	X
ejpam-6834	19	19	6	6	NUM
ejpam-6834	19	20	]	]	PUNCT
ejpam-6834	19	21	,	,	PUNCT
ejpam-6834	19	22	vague	vague	ADJ
ejpam-6834	19	23	sets	set	NOUN
ejpam-6834	19	24	[	[	X
ejpam-6834	19	25	7	7	NUM
ejpam-6834	19	26	]	]	PUNCT
ejpam-6834	19	27	,	,	PUNCT
ejpam-6834	19	28	soft	soft	ADJ
ejpam-6834	19	29	sets	set	NOUN
ejpam-6834	19	30	[	[	X
ejpam-6834	19	31	8	8	NUM
ejpam-6834	19	32	]	]	PUNCT
ejpam-6834	19	33	,	,	PUNCT
ejpam-6834	19	34	rough	rough	ADJ
ejpam-6834	19	35	sets	set	NOUN
ejpam-6834	19	36	[	[	X
ejpam-6834	19	37	9	9	NUM
ejpam-6834	19	38	]	]	PUNCT
ejpam-6834	19	39	,	,	PUNCT
ejpam-6834	19	40	neutrosophic	neutrosophic	ADJ
ejpam-6834	19	41	sets	set	NOUN
ejpam-6834	19	42	[	[	X
ejpam-6834	19	43	10	10	NUM
ejpam-6834	19	44	]	]	PUNCT
ejpam-6834	19	45	,	,	PUNCT
ejpam-6834	19	46	quadripartitioned	quadripartitione	VERB
ejpam-6834	19	47	neutrosophic	neutrosophic	ADJ
ejpam-6834	19	48	sets[11	sets[11	PROPN
ejpam-6834	19	49	,	,	PUNCT
ejpam-6834	19	50	12	12	NUM
ejpam-6834	19	51	]	]	PUNCT
ejpam-6834	19	52	,	,	PUNCT
ejpam-6834	19	53	heptapartitioned	heptapartitione	VERB
ejpam-6834	19	54	neutrosophic	neutrosophic	ADJ
ejpam-6834	19	55	sets[13	sets[13	PROPN
ejpam-6834	19	56	,	,	PUNCT
ejpam-6834	19	57	14	14	NUM
ejpam-6834	19	58	]	]	PUNCT
ejpam-6834	19	59	,	,	PUNCT
ejpam-6834	19	60	and	and	CCONJ
ejpam-6834	19	61	plithogenic	plithogenic	ADJ
ejpam-6834	19	62	sets	set	NOUN
ejpam-6834	19	63	[	[	X
ejpam-6834	19	64	15	15	NUM
ejpam-6834	19	65	]	]	PUNCT
ejpam-6834	19	66	.	.	PUNCT
ejpam-6834	20	1	for	for	ADP
ejpam-6834	20	2	the	the	DET
ejpam-6834	20	3	reader	reader	NOUN
ejpam-6834	20	4	’s	’s	PART
ejpam-6834	20	5	reference	reference	NOUN
ejpam-6834	20	6	,	,	PUNCT
ejpam-6834	20	7	a	a	DET
ejpam-6834	20	8	concise	concise	ADJ
ejpam-6834	20	9	overview	overview	NOUN
ejpam-6834	20	10	of	of	ADP
ejpam-6834	20	11	common	common	ADJ
ejpam-6834	20	12	uncertain	uncertain	ADJ
ejpam-6834	20	13	–	–	PUNCT
ejpam-6834	20	14	set	set	ADJ
ejpam-6834	20	15	families	family	NOUN
ejpam-6834	20	16	is	be	AUX
ejpam-6834	20	17	provided	provide	VERB
ejpam-6834	20	18	in	in	ADP
ejpam-6834	20	19	table	table	NOUN
ejpam-6834	20	20	1	1	NUM
ejpam-6834	20	21	.	.	PUNCT
ejpam-6834	20	22	table	table	NOUN
ejpam-6834	20	23	1	1	NUM
ejpam-6834	20	24	:	:	PUNCT
ejpam-6834	20	25	concise	concise	ADJ
ejpam-6834	20	26	overview	overview	NOUN
ejpam-6834	20	27	of	of	ADP
ejpam-6834	20	28	common	common	ADJ
ejpam-6834	20	29	uncertain	uncertain	ADJ
ejpam-6834	20	30	–	–	PUNCT
ejpam-6834	20	31	set	set	ADJ
ejpam-6834	20	32	families	family	NOUN
ejpam-6834	20	33	.	.	PUNCT
ejpam-6834	21	1	family	family	NOUN
ejpam-6834	21	2	core	core	NOUN
ejpam-6834	21	3	semantics	semantic	NOUN
ejpam-6834	21	4	key	key	ADJ
ejpam-6834	21	5	ref	ref	NOUN
ejpam-6834	21	6	.	.	PUNCT
ejpam-6834	22	1	representative	representative	ADJ
ejpam-6834	22	2	extensions	extension	NOUN
ejpam-6834	22	3	fuzzy	fuzzy	ADJ
ejpam-6834	22	4	set	set	VERB
ejpam-6834	22	5	membership	membership	NOUN
ejpam-6834	22	6	µ(x)∈	µ(x)∈	PRON
ejpam-6834	22	7	[	[	X
ejpam-6834	22	8	0	0	NUM
ejpam-6834	22	9	,	,	PUNCT
ejpam-6834	22	10	1	1	NUM
ejpam-6834	22	11	]	]	PUNCT
ejpam-6834	22	12	.	.	PUNCT
ejpam-6834	23	1	[	[	X
ejpam-6834	23	2	5	5	X
ejpam-6834	23	3	]	]	X
ejpam-6834	23	4	hesitant	hesitant	PROPN
ejpam-6834	24	1	[	[	X
ejpam-6834	24	2	16	16	NUM
ejpam-6834	24	3	]	]	X
ejpam-6834	24	4	;	;	PUNCT
ejpam-6834	24	5	spherical	spherical	ADJ
ejpam-6834	24	6	[	[	X
ejpam-6834	24	7	17	17	NUM
ejpam-6834	24	8	]	]	PUNCT
ejpam-6834	24	9	.	.	PUNCT
ejpam-6834	25	1	intuitionistic	intuitionistic	ADJ
ejpam-6834	25	2	/	/	SYM
ejpam-6834	25	3	vague	vague	ADJ
ejpam-6834	25	4	set	set	VERB
ejpam-6834	25	5	two	two	NUM
ejpam-6834	25	6	degrees	degree	NOUN
ejpam-6834	25	7	(	(	PUNCT
ejpam-6834	25	8	µ	µ	NOUN
ejpam-6834	25	9	,	,	PUNCT
ejpam-6834	25	10	ν	ν	NOUN
ejpam-6834	25	11	)	)	PUNCT
ejpam-6834	25	12	for	for	ADP
ejpam-6834	25	13	membership	membership	NOUN
ejpam-6834	25	14	/	/	SYM
ejpam-6834	25	15	non	non	ADJ
ejpam-6834	25	16	–	–	NOUN
ejpam-6834	25	17	membership	membership	NOUN
ejpam-6834	25	18	.	.	PUNCT
ejpam-6834	26	1	[	[	X
ejpam-6834	26	2	7	7	NUM
ejpam-6834	26	3	,	,	PUNCT
ejpam-6834	26	4	18	18	NUM
ejpam-6834	26	5	]	]	PUNCT
ejpam-6834	26	6	—	—	PUNCT
ejpam-6834	26	7	soft	soft	ADJ
ejpam-6834	26	8	set	set	ADJ
ejpam-6834	26	9	parameterized	parameterized	ADJ
ejpam-6834	26	10	family	family	NOUN
ejpam-6834	26	11	e	e	NOUN
ejpam-6834	26	12	→	→	SYM
ejpam-6834	26	13	p(u	p(u	ADJ
ejpam-6834	26	14	)	)	PUNCT
ejpam-6834	26	15	.	.	PUNCT
ejpam-6834	27	1	[	[	X
ejpam-6834	27	2	8	8	NUM
ejpam-6834	27	3	]	]	X
ejpam-6834	27	4	—	—	PUNCT
ejpam-6834	27	5	rough	rough	ADJ
ejpam-6834	27	6	set	set	VERB
ejpam-6834	27	7	lower	low	ADJ
ejpam-6834	27	8	/	/	SYM
ejpam-6834	27	9	upper	upper	ADJ
ejpam-6834	27	10	approximations	approximation	NOUN
ejpam-6834	27	11	via	via	ADP
ejpam-6834	27	12	indiscernibility	indiscernibility	NOUN
ejpam-6834	27	13	.	.	PUNCT
ejpam-6834	28	1	[	[	X
ejpam-6834	28	2	9	9	NUM
ejpam-6834	28	3	]	]	X
ejpam-6834	28	4	granular	granular	NOUN
ejpam-6834	28	5	[	[	X
ejpam-6834	28	6	19	19	NUM
ejpam-6834	28	7	]	]	PUNCT
ejpam-6834	28	8	;	;	PUNCT
ejpam-6834	28	9	probabilistic	probabilistic	VERB
ejpam-6834	28	10	[	[	X
ejpam-6834	28	11	20	20	NUM
ejpam-6834	28	12	]	]	PUNCT
ejpam-6834	28	13	.	.	PUNCT
ejpam-6834	29	1	neutrosophic	neutrosophic	PROPN
ejpam-6834	29	2	set	set	VERB
ejpam-6834	29	3	triple	triple	ADV
ejpam-6834	29	4	(	(	PUNCT
ejpam-6834	29	5	t	t	PROPN
ejpam-6834	29	6	,	,	PUNCT
ejpam-6834	29	7	i	i	PRON
ejpam-6834	29	8	,	,	PUNCT
ejpam-6834	29	9	f	f	PROPN
ejpam-6834	29	10	)	)	PUNCT
ejpam-6834	29	11	with	with	ADP
ejpam-6834	29	12	0	0	NUM
ejpam-6834	29	13	≤	≤	NUM
ejpam-6834	29	14	t+i+f	t+i+f	NOUN
ejpam-6834	29	15	≤3	≤3	NOUN
ejpam-6834	29	16	.	.	PUNCT
ejpam-6834	30	1	[	[	X
ejpam-6834	30	2	10	10	NUM
ejpam-6834	30	3	]	]	X
ejpam-6834	30	4	bipolar	bipolar	ADJ
ejpam-6834	30	5	[	[	X
ejpam-6834	30	6	21	21	NUM
ejpam-6834	30	7	]	]	X
ejpam-6834	30	8	;	;	PUNCT
ejpam-6834	30	9	interval	interval	NOUN
ejpam-6834	30	10	–	–	PUNCT
ejpam-6834	30	11	valued	value	VERB
ejpam-6834	30	12	[	[	PUNCT
ejpam-6834	30	13	22	22	NUM
ejpam-6834	30	14	]	]	PUNCT
ejpam-6834	30	15	.	.	PUNCT
ejpam-6834	31	1	plithogenic	plithogenic	PROPN
ejpam-6834	31	2	set	set	VERB
ejpam-6834	31	3	multi	multi	ADJ
ejpam-6834	31	4	–	–	PUNCT
ejpam-6834	31	5	attribute	attribute	NOUN
ejpam-6834	31	6	appurtenance	appurtenance	NOUN
ejpam-6834	31	7	with	with	ADP
ejpam-6834	31	8	contradiction	contradiction	NOUN
ejpam-6834	31	9	degree	degree	NOUN
ejpam-6834	31	10	.	.	PUNCT
ejpam-6834	32	1	[	[	X
ejpam-6834	32	2	15	15	NUM
ejpam-6834	32	3	]	]	PUNCT
ejpam-6834	32	4	—	—	PUNCT
ejpam-6834	32	5	these	these	DET
ejpam-6834	32	6	uncertain	uncertain	ADJ
ejpam-6834	32	7	set	set	NOUN
ejpam-6834	32	8	frameworks	framework	NOUN
ejpam-6834	32	9	have	have	AUX
ejpam-6834	32	10	been	be	AUX
ejpam-6834	32	11	successfully	successfully	ADV
ejpam-6834	32	12	adapted	adapt	VERB
ejpam-6834	32	13	to	to	PART
ejpam-6834	32	14	diverse	diverse	VERB
ejpam-6834	32	15	mathematical	mathematical	ADJ
ejpam-6834	32	16	and	and	CCONJ
ejpam-6834	32	17	applied	apply	VERB
ejpam-6834	32	18	domains	domain	NOUN
ejpam-6834	32	19	—	—	PUNCT
ejpam-6834	32	20	including	include	VERB
ejpam-6834	32	21	graph	graph	NOUN
ejpam-6834	32	22	theory	theory	NOUN
ejpam-6834	32	23	,	,	PUNCT
ejpam-6834	32	24	topology	topology	NOUN
ejpam-6834	32	25	,	,	PUNCT
ejpam-6834	32	26	and	and	CCONJ
ejpam-6834	32	27	knowledge	knowledge	NOUN
ejpam-6834	32	28	representation	representation	NOUN
ejpam-6834	32	29	—	—	PUNCT
ejpam-6834	32	30	offering	offer	VERB
ejpam-6834	32	31	flexible	flexible	ADJ
ejpam-6834	32	32	abstractions	abstraction	NOUN
ejpam-6834	32	33	for	for	ADP
ejpam-6834	32	34	modeling	model	VERB
ejpam-6834	32	35	uncertainty	uncertainty	NOUN
ejpam-6834	32	36	at	at	ADP
ejpam-6834	32	37	multiple	multiple	ADJ
ejpam-6834	32	38	levels	level	NOUN
ejpam-6834	32	39	of	of	ADP
ejpam-6834	32	40	granularity	granularity	NOUN
ejpam-6834	32	41	.	.	PUNCT
ejpam-6834	33	1	these	these	DET
ejpam-6834	33	2	uncertain	uncertain	ADJ
ejpam-6834	33	3	sets	set	NOUN
ejpam-6834	33	4	are	be	AUX
ejpam-6834	33	5	studied	study	VERB
ejpam-6834	33	6	not	not	PART
ejpam-6834	33	7	only	only	ADV
ejpam-6834	33	8	in	in	ADP
ejpam-6834	33	9	mathematics	mathematic	NOUN
ejpam-6834	33	10	but	but	CCONJ
ejpam-6834	33	11	also	also	ADV
ejpam-6834	33	12	in	in	ADP
ejpam-6834	33	13	a	a	DET
ejpam-6834	33	14	wide	wide	ADJ
ejpam-6834	33	15	range	range	NOUN
ejpam-6834	33	16	of	of	ADP
ejpam-6834	33	17	applications	application	NOUN
ejpam-6834	33	18	across	across	ADP
ejpam-6834	33	19	decision	decision	NOUN
ejpam-6834	33	20	science	science	NOUN
ejpam-6834	33	21	,	,	PUNCT
ejpam-6834	33	22	engineering	engineering	NOUN
ejpam-6834	33	23	,	,	PUNCT
ejpam-6834	33	24	and	and	CCONJ
ejpam-6834	33	25	computer	computer	NOUN
ejpam-6834	33	26	science	science	NOUN
ejpam-6834	33	27	(	(	PUNCT
ejpam-6834	33	28	e.g.[23–25	e.g.[23–25	ADV
ejpam-6834	33	29	]	]	PUNCT
ejpam-6834	33	30	)	)	PUNCT
ejpam-6834	33	31	.	.	PUNCT
ejpam-6834	34	1	next	next	ADV
ejpam-6834	34	2	,	,	PUNCT
ejpam-6834	34	3	we	we	PRON
ejpam-6834	34	4	explain	explain	VERB
ejpam-6834	34	5	the	the	DET
ejpam-6834	34	6	notions	notion	NOUN
ejpam-6834	34	7	of	of	ADP
ejpam-6834	34	8	hyperstructures	hyperstructure	NOUN
ejpam-6834	34	9	,	,	PUNCT
ejpam-6834	34	10	superhyperstructures	superhyperstructure	NOUN
ejpam-6834	34	11	,	,	PUNCT
ejpam-6834	34	12	hyperuncertain	hyperuncertain	NOUN
ejpam-6834	34	13	sets	set	NOUN
ejpam-6834	34	14	,	,	PUNCT
ejpam-6834	34	15	and	and	CCONJ
ejpam-6834	34	16	superhyperuncertain	superhyperuncertain	ADJ
ejpam-6834	34	17	sets	set	NOUN
ejpam-6834	34	18	.	.	PUNCT
ejpam-6834	35	1	many	many	ADJ
ejpam-6834	35	2	classical	classical	ADJ
ejpam-6834	35	3	mathematical	mathematical	ADJ
ejpam-6834	35	4	structures	structure	NOUN
ejpam-6834	35	5	admit	admit	VERB
ejpam-6834	35	6	two	two	NUM
ejpam-6834	35	7	natural	natural	ADJ
ejpam-6834	35	8	and	and	CCONJ
ejpam-6834	35	9	systematic	systematic	ADJ
ejpam-6834	35	10	forms	form	NOUN
ejpam-6834	35	11	of	of	ADP
ejpam-6834	35	12	enrichment	enrichment	NOUN
ejpam-6834	35	13	.	.	PUNCT
ejpam-6834	36	1	the	the	DET
ejpam-6834	36	2	first	first	ADJ
ejpam-6834	36	3	replaces	replace	VERB
ejpam-6834	36	4	a	a	DET
ejpam-6834	36	5	base	base	NOUN
ejpam-6834	36	6	set	set	NOUN
ejpam-6834	36	7	s	s	NOUN
ejpam-6834	36	8	with	with	ADP
ejpam-6834	36	9	its	its	PRON
ejpam-6834	36	10	powerset	powerset	NOUN
ejpam-6834	36	11	p(s	p(s	NOUN
ejpam-6834	36	12	)	)	PUNCT
ejpam-6834	36	13	and	and	CCONJ
ejpam-6834	36	14	endows	endow	VERB
ejpam-6834	36	15	it	it	PRON
ejpam-6834	36	16	with	with	ADP
ejpam-6834	36	17	hyperoperations	hyperoperation	NOUN
ejpam-6834	36	18	,	,	PUNCT
ejpam-6834	36	19	producing	produce	VERB
ejpam-6834	36	20	what	what	PRON
ejpam-6834	36	21	are	be	AUX
ejpam-6834	36	22	called	call	VERB
ejpam-6834	36	23	hyperstructures	hyperstructure	NOUN
ejpam-6834	36	24	[	[	X
ejpam-6834	36	25	26	26	NUM
ejpam-6834	36	26	,	,	PUNCT
ejpam-6834	36	27	27	27	NUM
ejpam-6834	36	28	]	]	PUNCT
ejpam-6834	36	29	.	.	PUNCT
ejpam-6834	37	1	the	the	DET
ejpam-6834	37	2	second	second	NOUN
ejpam-6834	37	3	applies	apply	VERB
ejpam-6834	37	4	the	the	DET
ejpam-6834	37	5	powerset	powerset	NOUN
ejpam-6834	37	6	construction	construction	NOUN
ejpam-6834	37	7	iteratively	iteratively	ADV
ejpam-6834	37	8	n	n	NUM
ejpam-6834	37	9	times	time	NOUN
ejpam-6834	37	10	,	,	PUNCT
ejpam-6834	37	11	yielding	yield	VERB
ejpam-6834	37	12	superhyperstructures	superhyperstructure	NOUN
ejpam-6834	37	13	on	on	ADP
ejpam-6834	37	14	p	p	NOUN
ejpam-6834	37	15	n(s	n(s	PROPN
ejpam-6834	37	16	)	)	PUNCT
ejpam-6834	37	17	,	,	PUNCT
ejpam-6834	37	18	which	which	PRON
ejpam-6834	37	19	are	be	AUX
ejpam-6834	37	20	capable	capable	ADJ
ejpam-6834	37	21	of	of	ADP
ejpam-6834	37	22	encoding	encode	VERB
ejpam-6834	37	23	nested	nested	ADJ
ejpam-6834	37	24	or	or	CCONJ
ejpam-6834	37	25	hierarchical	hierarchical	ADJ
ejpam-6834	37	26	interactions	interaction	NOUN
ejpam-6834	37	27	[	[	X
ejpam-6834	37	28	28	28	NUM
ejpam-6834	37	29	,	,	PUNCT
ejpam-6834	37	30	29	29	NUM
ejpam-6834	37	31	]	]	PUNCT
ejpam-6834	37	32	.	.	PUNCT
ejpam-6834	38	1	this	this	DET
ejpam-6834	38	2	perspective	perspective	NOUN
ejpam-6834	38	3	is	be	AUX
ejpam-6834	38	4	closely	closely	ADV
ejpam-6834	38	5	related	relate	VERB
ejpam-6834	38	6	to	to	ADP
ejpam-6834	38	7	the	the	DET
ejpam-6834	38	8	theory	theory	NOUN
ejpam-6834	38	9	of	of	ADP
ejpam-6834	38	10	hypergraphs	hypergraph	NOUN
ejpam-6834	38	11	[	[	X
ejpam-6834	38	12	30	30	NUM
ejpam-6834	38	13	,	,	PUNCT
ejpam-6834	38	14	31	31	NUM
ejpam-6834	38	15	]	]	PUNCT
ejpam-6834	38	16	and	and	CCONJ
ejpam-6834	38	17	their	their	PRON
ejpam-6834	38	18	higher	high	ADJ
ejpam-6834	38	19	-	-	PUNCT
ejpam-6834	38	20	order	order	NOUN
ejpam-6834	38	21	analogues	analogue	NOUN
ejpam-6834	38	22	,	,	PUNCT
ejpam-6834	38	23	superhypergraphs	superhypergraph	VERB
ejpam-6834	38	24	[	[	X
ejpam-6834	38	25	32	32	NUM
ejpam-6834	38	26	,	,	PUNCT
ejpam-6834	38	27	33	33	NUM
ejpam-6834	38	28	]	]	PUNCT
ejpam-6834	38	29	,	,	PUNCT
ejpam-6834	38	30	which	which	PRON
ejpam-6834	38	31	generalize	generalize	VERB
ejpam-6834	38	32	pairwise	pairwise	NOUN
ejpam-6834	38	33	connections	connection	NOUN
ejpam-6834	38	34	to	to	PART
ejpam-6834	38	35	multiway	multiway	VERB
ejpam-6834	38	36	and	and	CCONJ
ejpam-6834	38	37	multi	multi	ADJ
ejpam-6834	38	38	-	-	ADJ
ejpam-6834	38	39	level	level	ADJ
ejpam-6834	38	40	relationships	relationship	NOUN
ejpam-6834	38	41	.	.	PUNCT
ejpam-6834	39	1	further	further	ADJ
ejpam-6834	39	2	examples	example	NOUN
ejpam-6834	39	3	of	of	ADP
ejpam-6834	39	4	superhyperstructures	superhyperstructure	NOUN
ejpam-6834	39	5	include	include	VERB
ejpam-6834	39	6	superhyperalgebra[34	superhyperalgebra[34	PROPN
ejpam-6834	39	7	,	,	PUNCT
ejpam-6834	39	8	35	35	NUM
ejpam-6834	39	9	]	]	PUNCT
ejpam-6834	39	10	and	and	CCONJ
ejpam-6834	39	11	chemical	chemical	PROPN
ejpam-6834	39	12	superhyperstructures[36	superhyperstructures[36	PROPN
ejpam-6834	39	13	,	,	PUNCT
ejpam-6834	39	14	37	37	NUM
ejpam-6834	39	15	]	]	PUNCT
ejpam-6834	39	16	.	.	PUNCT
ejpam-6834	40	1	because	because	SCONJ
ejpam-6834	40	2	of	of	ADP
ejpam-6834	40	3	their	their	PRON
ejpam-6834	40	4	ability	ability	NOUN
ejpam-6834	40	5	to	to	PART
ejpam-6834	40	6	represent	represent	VERB
ejpam-6834	40	7	hierarchical	hierarchical	ADJ
ejpam-6834	40	8	,	,	PUNCT
ejpam-6834	40	9	multi	multi	ADJ
ejpam-6834	40	10	-	-	ADJ
ejpam-6834	40	11	scale	scale	ADJ
ejpam-6834	40	12	relationships	relationship	NOUN
ejpam-6834	40	13	,	,	PUNCT
ejpam-6834	40	14	superhyperstructures	superhyperstructure	NOUN
ejpam-6834	40	15	are	be	AUX
ejpam-6834	40	16	expected	expect	VERB
ejpam-6834	40	17	to	to	PART
ejpam-6834	40	18	find	find	VERB
ejpam-6834	40	19	applications	application	NOUN
ejpam-6834	40	20	in	in	ADP
ejpam-6834	40	21	modeling	model	VERB
ejpam-6834	40	22	a	a	DET
ejpam-6834	40	23	wide	wide	ADJ
ejpam-6834	40	24	range	range	NOUN
ejpam-6834	40	25	of	of	ADP
ejpam-6834	40	26	complex	complex	ADJ
ejpam-6834	40	27	real	real	ADJ
ejpam-6834	40	28	-	-	PUNCT
ejpam-6834	40	29	world	world	NOUN
ejpam-6834	40	30	systems	system	NOUN
ejpam-6834	40	31	.	.	PUNCT
ejpam-6834	41	1	for	for	ADP
ejpam-6834	41	2	reference	reference	NOUN
ejpam-6834	41	3	,	,	PUNCT
ejpam-6834	41	4	a	a	DET
ejpam-6834	41	5	concise	concise	ADJ
ejpam-6834	41	6	overview	overview	NOUN
ejpam-6834	41	7	of	of	ADP
ejpam-6834	41	8	classical	classical	ADJ
ejpam-6834	41	9	,	,	PUNCT
ejpam-6834	41	10	hyper	hyper	ADJ
ejpam-6834	41	11	,	,	PUNCT
ejpam-6834	41	12	and	and	CCONJ
ejpam-6834	41	13	superhyper	superhyper	NOUN
ejpam-6834	41	14	structures	structure	NOUN
ejpam-6834	41	15	is	be	AUX
ejpam-6834	41	16	provided	provide	VERB
ejpam-6834	41	17	in	in	ADP
ejpam-6834	41	18	table	table	NOUN
ejpam-6834	41	19	2	2	NUM
ejpam-6834	41	20	.	.	PUNCT
ejpam-6834	42	1	unless	unless	SCONJ
ejpam-6834	42	2	otherwise	otherwise	ADV
ejpam-6834	42	3	specified	specify	VERB
ejpam-6834	42	4	,	,	PUNCT
ejpam-6834	42	5	values	value	NOUN
ejpam-6834	42	6	such	such	ADJ
ejpam-6834	42	7	as	as	ADP
ejpam-6834	42	8	n	n	PROPN
ejpam-6834	42	9	and	and	CCONJ
ejpam-6834	42	10	m	m	VERB
ejpam-6834	42	11	in	in	ADP
ejpam-6834	42	12	this	this	DET
ejpam-6834	42	13	paper	paper	NOUN
ejpam-6834	42	14	are	be	AUX
ejpam-6834	42	15	nonnegative	nonnegative	ADJ
ejpam-6834	42	16	integers	integer	NOUN
ejpam-6834	42	17	.	.	PUNCT
ejpam-6834	43	1	moreover	moreover	ADV
ejpam-6834	43	2	,	,	PUNCT
ejpam-6834	43	3	throughout	throughout	SCONJ
ejpam-6834	43	4	we	we	PRON
ejpam-6834	43	5	work	work	VERB
ejpam-6834	43	6	only	only	ADV
ejpam-6834	43	7	with	with	ADP
ejpam-6834	43	8	finite	finite	ADJ
ejpam-6834	43	9	sets	set	NOUN
ejpam-6834	43	10	;	;	PUNCT
ejpam-6834	43	11	issues	issue	NOUN
ejpam-6834	43	12	related	relate	VERB
ejpam-6834	43	13	to	to	ADP
ejpam-6834	43	14	infinity	infinity	NOUN
ejpam-6834	43	15	are	be	AUX
ejpam-6834	43	16	not	not	PART
ejpam-6834	43	17	considered	consider	VERB
ejpam-6834	43	18	.	.	PUNCT
ejpam-6834	44	1	t.	t.	PROPN
ejpam-6834	44	2	fujita	fujita	PROPN
ejpam-6834	44	3	,	,	PUNCT
ejpam-6834	44	4	f.smarandache	f.smarandache	NOUN
ejpam-6834	44	5	/	/	SYM
ejpam-6834	44	6	eur	eur	PROPN
ejpam-6834	44	7	.	.	PUNCT
ejpam-6834	45	1	j.	j.	PROPN
ejpam-6834	45	2	pure	pure	PROPN
ejpam-6834	45	3	appl	appl	PROPN
ejpam-6834	45	4	.	.	PROPN
ejpam-6834	45	5	math	math	PROPN
ejpam-6834	45	6	,	,	PUNCT
ejpam-6834	45	7	18	18	NUM
ejpam-6834	45	8	(	(	PUNCT
ejpam-6834	45	9	4	4	NUM
ejpam-6834	45	10	)	)	PUNCT
ejpam-6834	45	11	(	(	PUNCT
ejpam-6834	45	12	2025	2025	NUM
ejpam-6834	45	13	)	)	PUNCT
ejpam-6834	45	14	,	,	PUNCT
ejpam-6834	45	15	6834	6834	NUM
ejpam-6834	45	16	3	3	NUM
ejpam-6834	45	17	of	of	ADP
ejpam-6834	45	18	69	69	NUM
ejpam-6834	45	19	table	table	NOUN
ejpam-6834	45	20	2	2	NUM
ejpam-6834	45	21	:	:	PUNCT
ejpam-6834	45	22	concise	concise	ADJ
ejpam-6834	45	23	overview	overview	NOUN
ejpam-6834	45	24	of	of	ADP
ejpam-6834	45	25	classical	classical	ADJ
ejpam-6834	45	26	,	,	PUNCT
ejpam-6834	45	27	hyper	hyper	ADJ
ejpam-6834	45	28	,	,	PUNCT
ejpam-6834	45	29	and	and	CCONJ
ejpam-6834	45	30	superhyper	superhyper	NOUN
ejpam-6834	45	31	structures	structure	NOUN
ejpam-6834	45	32	.	.	PUNCT
ejpam-6834	46	1	notion	notion	NOUN
ejpam-6834	46	2	carrier	carrier	NOUN
ejpam-6834	46	3	essence	essence	NOUN
ejpam-6834	46	4	typical	typical	ADJ
ejpam-6834	46	5	instances	instance	NOUN
ejpam-6834	46	6	/	/	SYM
ejpam-6834	46	7	refs	ref	NOUN
ejpam-6834	46	8	.	.	PUNCT
ejpam-6834	47	1	classical	classical	ADJ
ejpam-6834	47	2	structure	structure	NOUN
ejpam-6834	47	3	s	s	PART
ejpam-6834	47	4	(	(	PUNCT
ejpam-6834	47	5	base	base	NOUN
ejpam-6834	47	6	set	set	NOUN
ejpam-6834	47	7	)	)	PUNCT
ejpam-6834	47	8	operations	operation	NOUN
ejpam-6834	47	9	are	be	AUX
ejpam-6834	47	10	defined	define	VERB
ejpam-6834	47	11	directly	directly	ADV
ejpam-6834	47	12	on	on	ADP
ejpam-6834	47	13	elements	element	NOUN
ejpam-6834	47	14	of	of	ADP
ejpam-6834	47	15	s	s	X
ejpam-6834	47	16	(	(	PUNCT
ejpam-6834	47	17	e.g.	e.g.	ADV
ejpam-6834	47	18	,	,	PUNCT
ejpam-6834	47	19	groups	group	NOUN
ejpam-6834	47	20	,	,	PUNCT
ejpam-6834	47	21	rings	ring	NOUN
ejpam-6834	47	22	,	,	PUNCT
ejpam-6834	47	23	topologies	topology	NOUN
ejpam-6834	47	24	)	)	PUNCT
ejpam-6834	47	25	.	.	PUNCT
ejpam-6834	48	1	classical	classical	ADJ
ejpam-6834	48	2	structures	structure	NOUN
ejpam-6834	48	3	capture	capture	VERB
ejpam-6834	48	4	pairwise	pairwise	NOUN
ejpam-6834	48	5	or	or	CCONJ
ejpam-6834	48	6	elementwise	elementwise	VERB
ejpam-6834	48	7	interactions	interaction	NOUN
ejpam-6834	48	8	without	without	ADP
ejpam-6834	48	9	higher	high	ADJ
ejpam-6834	48	10	-	-	PUNCT
ejpam-6834	48	11	level	level	NOUN
ejpam-6834	48	12	nesting	nesting	NOUN
ejpam-6834	48	13	.	.	PUNCT
ejpam-6834	49	1	groups	group	NOUN
ejpam-6834	49	2	,	,	PUNCT
ejpam-6834	49	3	rings	ring	NOUN
ejpam-6834	49	4	,	,	PUNCT
ejpam-6834	49	5	topological	topological	ADJ
ejpam-6834	49	6	spaces	space	NOUN
ejpam-6834	49	7	,	,	PUNCT
ejpam-6834	49	8	graphs	graph	NOUN
ejpam-6834	49	9	.	.	PUNCT
ejpam-6834	50	1	see	see	VERB
ejpam-6834	50	2	[	[	X
ejpam-6834	50	3	30	30	NUM
ejpam-6834	50	4	]	]	PUNCT
ejpam-6834	50	5	.	.	PUNCT
ejpam-6834	51	1	hyperstructure	hyperstructure	PROPN
ejpam-6834	51	2	p(s	p(s	PROPN
ejpam-6834	51	3	)	)	PUNCT
ejpam-6834	52	1	(	(	PUNCT
ejpam-6834	52	2	powerset	powerset	AUX
ejpam-6834	52	3	of	of	ADP
ejpam-6834	52	4	s	s	NOUN
ejpam-6834	52	5	)	)	PUNCT
ejpam-6834	52	6	replace	replace	NOUN
ejpam-6834	52	7	s	s	NOUN
ejpam-6834	52	8	with	with	ADP
ejpam-6834	52	9	p(s	p(s	NOUN
ejpam-6834	52	10	)	)	PUNCT
ejpam-6834	52	11	and	and	CCONJ
ejpam-6834	52	12	introduce	introduce	VERB
ejpam-6834	52	13	hyperoperations	hyperoperation	NOUN
ejpam-6834	52	14	acting	act	VERB
ejpam-6834	52	15	on	on	ADP
ejpam-6834	52	16	subsets	subset	NOUN
ejpam-6834	52	17	rather	rather	ADV
ejpam-6834	52	18	than	than	ADP
ejpam-6834	52	19	single	single	ADJ
ejpam-6834	52	20	elements	element	NOUN
ejpam-6834	52	21	.	.	PUNCT
ejpam-6834	53	1	this	this	PRON
ejpam-6834	53	2	enables	enable	VERB
ejpam-6834	53	3	multi	multi	ADJ
ejpam-6834	53	4	-	-	ADJ
ejpam-6834	53	5	valued	value	VERB
ejpam-6834	53	6	or	or	CCONJ
ejpam-6834	53	7	set	set	NOUN
ejpam-6834	53	8	-	-	PUNCT
ejpam-6834	53	9	valued	value	VERB
ejpam-6834	53	10	outputs	output	NOUN
ejpam-6834	53	11	,	,	PUNCT
ejpam-6834	53	12	capturing	capture	VERB
ejpam-6834	53	13	richer	rich	ADJ
ejpam-6834	53	14	interactions	interaction	NOUN
ejpam-6834	53	15	.	.	PUNCT
ejpam-6834	54	1	hypergroups	hypergroup	NOUN
ejpam-6834	54	2	,	,	PUNCT
ejpam-6834	54	3	hyperrings	hyperring	NOUN
ejpam-6834	54	4	,	,	PUNCT
ejpam-6834	54	5	hypergraphs	hypergraph	NOUN
ejpam-6834	54	6	.	.	PUNCT
ejpam-6834	55	1	see	see	VERB
ejpam-6834	55	2	[	[	X
ejpam-6834	55	3	26	26	NUM
ejpam-6834	55	4	,	,	PUNCT
ejpam-6834	55	5	27	27	NUM
ejpam-6834	55	6	,	,	PUNCT
ejpam-6834	55	7	31	31	NUM
ejpam-6834	55	8	]	]	PUNCT
ejpam-6834	55	9	.	.	PUNCT
ejpam-6834	56	1	superhyper	superhyper	PROPN
ejpam-6834	56	2	structure	structure	NOUN
ejpam-6834	56	3	p	p	PROPN
ejpam-6834	56	4	n(s	n(s	PROPN
ejpam-6834	56	5	)	)	PUNCT
ejpam-6834	57	1	(	(	PUNCT
ejpam-6834	57	2	n≥1	n≥1	NOUN
ejpam-6834	57	3	iterated	iterate	VERB
ejpam-6834	57	4	powerset	powerset	NOUN
ejpam-6834	57	5	)	)	PUNCT
ejpam-6834	57	6	extend	extend	VERB
ejpam-6834	57	7	hyperstructures	hyperstructure	NOUN
ejpam-6834	57	8	by	by	ADP
ejpam-6834	57	9	iterating	iterate	VERB
ejpam-6834	57	10	the	the	DET
ejpam-6834	57	11	powerset	powerset	NOUN
ejpam-6834	57	12	n	n	DET
ejpam-6834	57	13	times	time	NOUN
ejpam-6834	57	14	,	,	PUNCT
ejpam-6834	57	15	thereby	thereby	ADV
ejpam-6834	57	16	modeling	model	VERB
ejpam-6834	57	17	nested	nested	ADJ
ejpam-6834	57	18	and	and	CCONJ
ejpam-6834	57	19	hierarchical	hierarchical	ADJ
ejpam-6834	57	20	uncertainty	uncertainty	NOUN
ejpam-6834	57	21	and	and	CCONJ
ejpam-6834	57	22	multi	multi	ADJ
ejpam-6834	57	23	-	-	ADJ
ejpam-6834	57	24	level	level	ADJ
ejpam-6834	57	25	interactions	interaction	NOUN
ejpam-6834	57	26	.	.	PUNCT
ejpam-6834	58	1	admits	admit	VERB
ejpam-6834	58	2	multi	multi	ADJ
ejpam-6834	58	3	-	-	ADJ
ejpam-6834	58	4	ary	ary	ADJ
ejpam-6834	58	5	inputs	input	NOUN
ejpam-6834	58	6	and	and	CCONJ
ejpam-6834	58	7	multi	multi	ADJ
ejpam-6834	58	8	-	-	ADJ
ejpam-6834	58	9	layered	layered	ADJ
ejpam-6834	58	10	outputs	output	NOUN
ejpam-6834	58	11	.	.	PUNCT
ejpam-6834	59	1	superhypergraphs	superhypergraph	NOUN
ejpam-6834	59	2	[	[	X
ejpam-6834	59	3	32	32	NUM
ejpam-6834	59	4	,	,	PUNCT
ejpam-6834	59	5	33	33	NUM
ejpam-6834	59	6	]	]	PUNCT
ejpam-6834	59	7	;	;	PUNCT
ejpam-6834	59	8	superhyperalgebra	superhyperalgebra	NOUN
ejpam-6834	59	9	[	[	X
ejpam-6834	59	10	34	34	NUM
ejpam-6834	59	11	,	,	PUNCT
ejpam-6834	59	12	35	35	NUM
ejpam-6834	59	13	]	]	PUNCT
ejpam-6834	59	14	;	;	PUNCT
ejpam-6834	59	15	chemical	chemical	NOUN
ejpam-6834	59	16	superhyperstructures	superhyperstructure	NOUN
ejpam-6834	59	17	[	[	X
ejpam-6834	59	18	36	36	NUM
ejpam-6834	59	19	,	,	PUNCT
ejpam-6834	59	20	37	37	NUM
ejpam-6834	59	21	]	]	PUNCT
ejpam-6834	59	22	.	.	PUNCT
ejpam-6834	60	1	in	in	ADP
ejpam-6834	60	2	parallel	parallel	NOUN
ejpam-6834	60	3	with	with	ADP
ejpam-6834	60	4	these	these	DET
ejpam-6834	60	5	structural	structural	ADJ
ejpam-6834	60	6	enrichments	enrichment	NOUN
ejpam-6834	60	7	,	,	PUNCT
ejpam-6834	60	8	the	the	DET
ejpam-6834	60	9	notion	notion	NOUN
ejpam-6834	60	10	of	of	ADP
ejpam-6834	60	11	uncertain	uncertain	ADJ
ejpam-6834	60	12	sets	set	NOUN
ejpam-6834	60	13	has	have	AUX
ejpam-6834	60	14	itself	itself	PRON
ejpam-6834	60	15	been	be	AUX
ejpam-6834	60	16	‘	'	PUNCT
ejpam-6834	60	17	hyperized	hyperize	VERB
ejpam-6834	60	18	”	"	PUNCT
ejpam-6834	60	19	and	and	CCONJ
ejpam-6834	60	20	‘	'	PUNCT
ejpam-6834	60	21	superhyperized	superhyperize	VERB
ejpam-6834	60	22	.	.	PUNCT
ejpam-6834	60	23	”	"	PUNCT
ejpam-6834	61	1	specifically	specifically	ADV
ejpam-6834	61	2	,	,	PUNCT
ejpam-6834	61	3	hyperfuzzy	hyperfuzzy	ADJ
ejpam-6834	62	1	[	[	X
ejpam-6834	62	2	38	38	NUM
ejpam-6834	62	3	,	,	PUNCT
ejpam-6834	62	4	39	39	NUM
ejpam-6834	62	5	]	]	PUNCT
ejpam-6834	62	6	,	,	PUNCT
ejpam-6834	62	7	hypersoft	hypersoft	PROPN
ejpam-6834	62	8	[	[	X
ejpam-6834	62	9	40	40	NUM
ejpam-6834	62	10	–	–	PUNCT
ejpam-6834	62	11	42	42	NUM
ejpam-6834	62	12	]	]	PUNCT
ejpam-6834	62	13	,	,	PUNCT
ejpam-6834	62	14	hyperrough	hyperrough	PROPN
ejpam-6834	63	1	[	[	X
ejpam-6834	63	2	43	43	NUM
ejpam-6834	63	3	,	,	PUNCT
ejpam-6834	63	4	44	44	NUM
ejpam-6834	63	5	]	]	PUNCT
ejpam-6834	63	6	,	,	PUNCT
ejpam-6834	63	7	hyperneutrosophic	hyperneutrosophic	ADJ
ejpam-6834	63	8	[	[	X
ejpam-6834	63	9	45	45	NUM
ejpam-6834	63	10	]	]	PUNCT
ejpam-6834	63	11	,	,	PUNCT
ejpam-6834	63	12	and	and	CCONJ
ejpam-6834	63	13	hyperplithogenic	hyperplithogenic	ADJ
ejpam-6834	63	14	sets	set	NOUN
ejpam-6834	63	15	[	[	X
ejpam-6834	63	16	46	46	NUM
ejpam-6834	63	17	]	]	PUNCT
ejpam-6834	63	18	arise	arise	NOUN
ejpam-6834	63	19	by	by	ADP
ejpam-6834	63	20	imposing	impose	VERB
ejpam-6834	63	21	the	the	DET
ejpam-6834	63	22	corresponding	corresponding	ADJ
ejpam-6834	63	23	semantics	semantic	NOUN
ejpam-6834	63	24	on	on	ADP
ejpam-6834	63	25	the	the	DET
ejpam-6834	63	26	powerset	powerset	NOUN
ejpam-6834	63	27	p(s	p(s	NOUN
ejpam-6834	63	28	)	)	PUNCT
ejpam-6834	64	1	[	[	X
ejpam-6834	64	2	1	1	NUM
ejpam-6834	64	3	,	,	PUNCT
ejpam-6834	64	4	2	2	NUM
ejpam-6834	64	5	]	]	PUNCT
ejpam-6834	64	6	.	.	PUNCT
ejpam-6834	65	1	their	their	PRON
ejpam-6834	65	2	superhyper	superhyper	NOUN
ejpam-6834	65	3	counterparts	counterpart	NOUN
ejpam-6834	65	4	—	—	PUNCT
ejpam-6834	65	5	such	such	ADJ
ejpam-6834	65	6	as	as	ADP
ejpam-6834	65	7	superhyperfuzzy	superhyperfuzzy	ADJ
ejpam-6834	65	8	[	[	X
ejpam-6834	65	9	47	47	NUM
ejpam-6834	65	10	]	]	PUNCT
ejpam-6834	65	11	,	,	PUNCT
ejpam-6834	65	12	superhyperneutrosophic[2	superhyperneutrosophic[2	NOUN
ejpam-6834	65	13	]	]	PUNCT
ejpam-6834	65	14	,	,	PUNCT
ejpam-6834	65	15	and	and	CCONJ
ejpam-6834	65	16	related	related	ADJ
ejpam-6834	65	17	variants	variant	NOUN
ejpam-6834	65	18	—	—	PUNCT
ejpam-6834	65	19	are	be	AUX
ejpam-6834	65	20	defined	define	VERB
ejpam-6834	65	21	over	over	ADP
ejpam-6834	65	22	the	the	DET
ejpam-6834	65	23	n	n	ADV
ejpam-6834	65	24	-	-	PUNCT
ejpam-6834	65	25	th	th	X
ejpam-6834	65	26	powerset	powerset	NOUN
ejpam-6834	65	27	p	p	PROPN
ejpam-6834	65	28	n(s	n(s	PROPN
ejpam-6834	65	29	)	)	PUNCT
ejpam-6834	65	30	and	and	CCONJ
ejpam-6834	65	31	are	be	AUX
ejpam-6834	65	32	designed	design	VERB
ejpam-6834	65	33	to	to	PART
ejpam-6834	65	34	capture	capture	VERB
ejpam-6834	65	35	uncertainty	uncertainty	NOUN
ejpam-6834	65	36	at	at	ADP
ejpam-6834	65	37	multiple	multiple	ADJ
ejpam-6834	65	38	hierarchical	hierarchical	ADJ
ejpam-6834	65	39	levels	level	NOUN
ejpam-6834	65	40	[	[	X
ejpam-6834	65	41	1	1	NUM
ejpam-6834	65	42	]	]	PUNCT
ejpam-6834	65	43	.	.	PUNCT
ejpam-6834	66	1	for	for	ADP
ejpam-6834	66	2	reference	reference	NOUN
ejpam-6834	66	3	,	,	PUNCT
ejpam-6834	66	4	a	a	DET
ejpam-6834	66	5	concise	concise	ADJ
ejpam-6834	66	6	overview	overview	NOUN
ejpam-6834	66	7	of	of	ADP
ejpam-6834	66	8	uncertain	uncertain	ADJ
ejpam-6834	66	9	,	,	PUNCT
ejpam-6834	66	10	hyperuncertain	hyperuncertain	NOUN
ejpam-6834	66	11	,	,	PUNCT
ejpam-6834	66	12	and	and	CCONJ
ejpam-6834	66	13	superhyperuncertain	superhyperuncertain	ADJ
ejpam-6834	66	14	sets	set	NOUN
ejpam-6834	66	15	is	be	AUX
ejpam-6834	66	16	provided	provide	VERB
ejpam-6834	66	17	in	in	ADP
ejpam-6834	66	18	table	table	NOUN
ejpam-6834	66	19	3	3	NUM
ejpam-6834	66	20	.	.	PUNCT
ejpam-6834	67	1	needless	needless	ADJ
ejpam-6834	67	2	to	to	PART
ejpam-6834	67	3	say	say	VERB
ejpam-6834	67	4	,	,	PUNCT
ejpam-6834	67	5	these	these	DET
ejpam-6834	67	6	frameworks	framework	NOUN
ejpam-6834	67	7	are	be	AUX
ejpam-6834	67	8	expected	expect	VERB
ejpam-6834	67	9	to	to	PART
ejpam-6834	67	10	find	find	VERB
ejpam-6834	67	11	applications	application	NOUN
ejpam-6834	67	12	in	in	ADP
ejpam-6834	67	13	various	various	ADJ
ejpam-6834	67	14	fields	field	NOUN
ejpam-6834	67	15	,	,	PUNCT
ejpam-6834	67	16	such	such	ADJ
ejpam-6834	67	17	as	as	ADP
ejpam-6834	67	18	decision	decision	NOUN
ejpam-6834	67	19	–	–	PUNCT
ejpam-6834	67	20	making	making	NOUN
ejpam-6834	67	21	and	and	CCONJ
ejpam-6834	67	22	beyond	beyond	ADP
ejpam-6834	67	23	.	.	PUNCT
ejpam-6834	68	1	note	note	VERB
ejpam-6834	68	2	that	that	SCONJ
ejpam-6834	68	3	type	type	NOUN
ejpam-6834	68	4	-	-	PUNCT
ejpam-6834	68	5	n	n	CCONJ
ejpam-6834	68	6	uncertain	uncertain	ADJ
ejpam-6834	68	7	sets	set	NOUN
ejpam-6834	68	8	refine	refine	VERB
ejpam-6834	68	9	uncertainty	uncertainty	NOUN
ejpam-6834	68	10	inside	inside	ADP
ejpam-6834	68	11	membership	membership	NOUN
ejpam-6834	68	12	values	value	NOUN
ejpam-6834	68	13	—	—	PUNCT
ejpam-6834	68	14	e.g.	e.g.	ADV
ejpam-6834	68	15	,	,	PUNCT
ejpam-6834	68	16	type	type	NOUN
ejpam-6834	68	17	-	-	PUNCT
ejpam-6834	68	18	n	n	NOUN
ejpam-6834	68	19	fuzzy	fuzzy	ADJ
ejpam-6834	69	1	[	[	X
ejpam-6834	69	2	48	48	NUM
ejpam-6834	69	3	]	]	PUNCT
ejpam-6834	69	4	treats	treat	VERB
ejpam-6834	69	5	degrees	degree	NOUN
ejpam-6834	69	6	-	-	PUNCT
ejpam-6834	69	7	of	of	ADP
ejpam-6834	69	8	-	-	PUNCT
ejpam-6834	69	9	membership	membership	NOUN
ejpam-6834	69	10	as	as	ADP
ejpam-6834	69	11	higher	high	ADJ
ejpam-6834	69	12	-	-	PUNCT
ejpam-6834	69	13	order	order	NOUN
ejpam-6834	69	14	quantities	quantity	NOUN
ejpam-6834	69	15	.	.	PUNCT
ejpam-6834	70	1	superhyperuncertain	superhyperuncertain	ADJ
ejpam-6834	70	2	sets	set	NOUN
ejpam-6834	70	3	move	move	VERB
ejpam-6834	70	4	uncertainty	uncertainty	NOUN
ejpam-6834	70	5	to	to	ADP
ejpam-6834	70	6	the	the	DET
ejpam-6834	70	7	elements	element	NOUN
ejpam-6834	70	8	themselves	themselves	PRON
ejpam-6834	70	9	via	via	ADP
ejpam-6834	70	10	iterated	iterated	ADJ
ejpam-6834	70	11	powersets	powerset	NOUN
ejpam-6834	70	12	,	,	PUNCT
ejpam-6834	70	13	capturing	capture	VERB
ejpam-6834	70	14	multi	multi	ADJ
ejpam-6834	70	15	-	-	ADJ
ejpam-6834	70	16	level	level	ADJ
ejpam-6834	70	17	groupings	grouping	NOUN
ejpam-6834	70	18	and	and	CCONJ
ejpam-6834	70	19	interactions	interaction	NOUN
ejpam-6834	70	20	;	;	PUNCT
ejpam-6834	70	21	this	this	PRON
ejpam-6834	70	22	enables	enable	VERB
ejpam-6834	70	23	explicit	explicit	ADJ
ejpam-6834	70	24	hierarchical	hierarchical	ADJ
ejpam-6834	70	25	modeling	modeling	NOUN
ejpam-6834	70	26	,	,	PUNCT
ejpam-6834	70	27	compositional	compositional	ADJ
ejpam-6834	70	28	operations	operation	NOUN
ejpam-6834	70	29	,	,	PUNCT
ejpam-6834	70	30	and	and	CCONJ
ejpam-6834	70	31	scalable	scalable	ADJ
ejpam-6834	70	32	reasoning	reasoning	NOUN
ejpam-6834	70	33	across	across	ADP
ejpam-6834	70	34	nested	nested	ADJ
ejpam-6834	70	35	attributes	attribute	NOUN
ejpam-6834	70	36	and	and	CCONJ
ejpam-6834	70	37	real	real	ADJ
ejpam-6834	70	38	-	-	PUNCT
ejpam-6834	70	39	world	world	NOUN
ejpam-6834	70	40	scenarios	scenario	NOUN
ejpam-6834	70	41	.	.	PUNCT
ejpam-6834	71	1	from	from	ADP
ejpam-6834	71	2	the	the	DET
ejpam-6834	71	3	above	above	ADJ
ejpam-6834	71	4	discussion	discussion	NOUN
ejpam-6834	71	5	,	,	PUNCT
ejpam-6834	71	6	it	it	PRON
ejpam-6834	71	7	is	be	AUX
ejpam-6834	71	8	clear	clear	ADJ
ejpam-6834	71	9	that	that	SCONJ
ejpam-6834	71	10	research	research	NOUN
ejpam-6834	71	11	on	on	ADP
ejpam-6834	71	12	hyperuncertain	hyperuncertain	NOUN
ejpam-6834	71	13	sets	set	NOUN
ejpam-6834	71	14	and	and	CCONJ
ejpam-6834	71	15	superhyperuncertain	superhyperuncertain	ADJ
ejpam-6834	71	16	sets	set	NOUN
ejpam-6834	71	17	is	be	AUX
ejpam-6834	71	18	of	of	ADP
ejpam-6834	71	19	great	great	ADJ
ejpam-6834	71	20	importance	importance	NOUN
ejpam-6834	71	21	,	,	PUNCT
ejpam-6834	71	22	both	both	PRON
ejpam-6834	71	23	mathematically	mathematically	ADV
ejpam-6834	71	24	and	and	CCONJ
ejpam-6834	71	25	in	in	ADP
ejpam-6834	71	26	applied	applied	ADJ
ejpam-6834	71	27	mathematics	mathematic	NOUN
ejpam-6834	71	28	.	.	PUNCT
ejpam-6834	72	1	nevertheless	nevertheless	ADV
ejpam-6834	72	2	,	,	PUNCT
ejpam-6834	72	3	the	the	DET
ejpam-6834	72	4	systematic	systematic	ADJ
ejpam-6834	72	5	study	study	NOUN
ejpam-6834	72	6	of	of	ADP
ejpam-6834	72	7	hyperuncertain	hyperuncertain	NOUN
ejpam-6834	72	8	sets	set	NOUN
ejpam-6834	72	9	—	—	PUNCT
ejpam-6834	72	10	including	include	VERB
ejpam-6834	72	11	hyperfuzzy	hyperfuzzy	NOUN
ejpam-6834	72	12	,	,	PUNCT
ejpam-6834	72	13	hypervague	hypervague	NOUN
ejpam-6834	72	14	,	,	PUNCT
ejpam-6834	72	15	hypersoft	hypersoft	NOUN
ejpam-6834	72	16	,	,	PUNCT
ejpam-6834	72	17	hyperrough	hyperrough	NOUN
ejpam-6834	72	18	,	,	PUNCT
ejpam-6834	72	19	hyperneutrosophic	hyperneutrosophic	ADJ
ejpam-6834	72	20	,	,	PUNCT
ejpam-6834	72	21	and	and	CCONJ
ejpam-6834	72	22	hyperplithogenic	hyperplithogenic	ADJ
ejpam-6834	72	23	models	model	NOUN
ejpam-6834	72	24	—	—	PUNCT
ejpam-6834	72	25	remains	remain	VERB
ejpam-6834	72	26	comparatively	comparatively	ADV
ejpam-6834	72	27	young	young	ADJ
ejpam-6834	72	28	despite	despite	SCONJ
ejpam-6834	72	29	their	their	PRON
ejpam-6834	72	30	clear	clear	ADJ
ejpam-6834	72	31	potential	potential	NOUN
ejpam-6834	72	32	for	for	ADP
ejpam-6834	72	33	modeling	model	VERB
ejpam-6834	72	34	complex	complex	ADJ
ejpam-6834	72	35	data	datum	NOUN
ejpam-6834	72	36	.	.	PUNCT
ejpam-6834	73	1	existing	exist	VERB
ejpam-6834	73	2	frameworks	framework	NOUN
ejpam-6834	73	3	such	such	ADJ
ejpam-6834	73	4	as	as	ADP
ejpam-6834	73	5	hyperfuzzy	hyperfuzzy	NOUN
ejpam-6834	73	6	or	or	CCONJ
ejpam-6834	73	7	n	n	CCONJ
ejpam-6834	73	8	–	–	PUNCT
ejpam-6834	73	9	superhyperfuzzy	superhyperfuzzy	ADJ
ejpam-6834	73	10	can	can	AUX
ejpam-6834	73	11	not	not	PART
ejpam-6834	73	12	adequately	adequately	ADV
ejpam-6834	73	13	address	address	VERB
ejpam-6834	73	14	real	real	ADJ
ejpam-6834	73	15	–	–	PUNCT
ejpam-6834	73	16	world	world	NOUN
ejpam-6834	73	17	scenarios	scenario	NOUN
ejpam-6834	73	18	like	like	ADP
ejpam-6834	73	19	multi	multi	ADJ
ejpam-6834	73	20	–	–	PUNCT
ejpam-6834	73	21	modal	modal	ADJ
ejpam-6834	73	22	medical	medical	ADJ
ejpam-6834	73	23	diagnostics	diagnostic	NOUN
ejpam-6834	73	24	,	,	PUNCT
ejpam-6834	73	25	hierarchical	hierarchical	ADJ
ejpam-6834	73	26	iot	iot	NOUN
ejpam-6834	73	27	sensor	sensor	NOUN
ejpam-6834	73	28	fusion	fusion	NOUN
ejpam-6834	73	29	,	,	PUNCT
ejpam-6834	73	30	or	or	CCONJ
ejpam-6834	73	31	cross	cross	ADJ
ejpam-6834	73	32	–	–	PUNCT
ejpam-6834	73	33	domain	domain	ADJ
ejpam-6834	73	34	financial	financial	ADJ
ejpam-6834	73	35	risk	risk	NOUN
ejpam-6834	73	36	analysis	analysis	NOUN
ejpam-6834	73	37	involving	involve	VERB
ejpam-6834	73	38	layered	layered	ADJ
ejpam-6834	73	39	uncertainties	uncertainty	NOUN
ejpam-6834	73	40	.	.	PUNCT
ejpam-6834	74	1	to	to	PART
ejpam-6834	74	2	bridge	bridge	VERB
ejpam-6834	74	3	this	this	DET
ejpam-6834	74	4	gap	gap	NOUN
ejpam-6834	74	5	,	,	PUNCT
ejpam-6834	74	6	in	in	ADP
ejpam-6834	74	7	this	this	DET
ejpam-6834	74	8	work	work	NOUN
ejpam-6834	74	9	we	we	PRON
ejpam-6834	74	10	introduce	introduce	VERB
ejpam-6834	74	11	and	and	CCONJ
ejpam-6834	74	12	formalize	formalize	VERB
ejpam-6834	74	13	the	the	DET
ejpam-6834	74	14	(	(	PUNCT
ejpam-6834	74	15	m	m	PROPN
ejpam-6834	74	16	,	,	PUNCT
ejpam-6834	74	17	n)-superhyperuncertain	n)-superhyperuncertain	PUNCT
ejpam-6834	74	18	t.	t.	PROPN
ejpam-6834	74	19	fujita	fujita	PROPN
ejpam-6834	74	20	,	,	PUNCT
ejpam-6834	74	21	f.smarandache	f.smarandache	NOUN
ejpam-6834	74	22	/	/	SYM
ejpam-6834	74	23	eur	eur	PROPN
ejpam-6834	74	24	.	.	PUNCT
ejpam-6834	75	1	j.	j.	PROPN
ejpam-6834	75	2	pure	pure	PROPN
ejpam-6834	75	3	appl	appl	PROPN
ejpam-6834	75	4	.	.	PROPN
ejpam-6834	75	5	math	math	PROPN
ejpam-6834	75	6	,	,	PUNCT
ejpam-6834	75	7	18	18	NUM
ejpam-6834	75	8	(	(	PUNCT
ejpam-6834	75	9	4	4	NUM
ejpam-6834	75	10	)	)	PUNCT
ejpam-6834	75	11	(	(	PUNCT
ejpam-6834	75	12	2025	2025	NUM
ejpam-6834	75	13	)	)	PUNCT
ejpam-6834	75	14	,	,	PUNCT
ejpam-6834	75	15	6834	6834	NUM
ejpam-6834	75	16	4	4	NUM
ejpam-6834	75	17	of	of	ADP
ejpam-6834	75	18	69	69	NUM
ejpam-6834	75	19	table	table	NOUN
ejpam-6834	75	20	3	3	NUM
ejpam-6834	75	21	:	:	PUNCT
ejpam-6834	75	22	concise	concise	ADJ
ejpam-6834	75	23	overview	overview	NOUN
ejpam-6834	75	24	of	of	ADP
ejpam-6834	75	25	uncertain	uncertain	ADJ
ejpam-6834	75	26	,	,	PUNCT
ejpam-6834	75	27	hyperuncertain	hyperuncertain	NOUN
ejpam-6834	75	28	,	,	PUNCT
ejpam-6834	75	29	and	and	CCONJ
ejpam-6834	75	30	superhyperuncertain	superhyperuncertain	ADJ
ejpam-6834	75	31	sets	set	NOUN
ejpam-6834	75	32	.	.	PUNCT
ejpam-6834	76	1	notion	notion	NOUN
ejpam-6834	76	2	carrier	carrier	NOUN
ejpam-6834	76	3	essence	essence	NOUN
ejpam-6834	76	4	typical	typical	ADJ
ejpam-6834	76	5	instances	instance	NOUN
ejpam-6834	76	6	/	/	SYM
ejpam-6834	76	7	refs	ref	NOUN
ejpam-6834	76	8	.	.	PUNCT
ejpam-6834	77	1	uncertain	uncertain	ADJ
ejpam-6834	77	2	set	set	NOUN
ejpam-6834	77	3	s	s	PART
ejpam-6834	77	4	(	(	PUNCT
ejpam-6834	77	5	or	or	CCONJ
ejpam-6834	77	6	model	model	NOUN
ejpam-6834	77	7	-	-	PUNCT
ejpam-6834	77	8	dependent	dependent	ADJ
ejpam-6834	77	9	p(s	p(s	NOUN
ejpam-6834	77	10	)	)	PUNCT
ejpam-6834	77	11	)	)	PUNCT
ejpam-6834	77	12	attach	attach	VERB
ejpam-6834	77	13	uncertainty	uncertainty	NOUN
ejpam-6834	77	14	semantics	semantic	NOUN
ejpam-6834	77	15	to	to	ADP
ejpam-6834	77	16	elements	element	NOUN
ejpam-6834	77	17	or	or	CCONJ
ejpam-6834	77	18	subsets	subset	NOUN
ejpam-6834	77	19	,	,	PUNCT
ejpam-6834	77	20	such	such	ADJ
ejpam-6834	77	21	as	as	ADP
ejpam-6834	77	22	graded	grade	VERB
ejpam-6834	77	23	membership	membership	NOUN
ejpam-6834	77	24	,	,	PUNCT
ejpam-6834	77	25	parameterization	parameterization	NOUN
ejpam-6834	77	26	,	,	PUNCT
ejpam-6834	77	27	lower	low	ADJ
ejpam-6834	77	28	/	/	SYM
ejpam-6834	77	29	upper	upper	ADJ
ejpam-6834	77	30	approximations	approximation	NOUN
ejpam-6834	77	31	,	,	PUNCT
ejpam-6834	77	32	neutrosophic	neutrosophic	ADJ
ejpam-6834	77	33	triples	triple	NOUN
ejpam-6834	77	34	,	,	PUNCT
ejpam-6834	77	35	or	or	CCONJ
ejpam-6834	77	36	contradiction	contradiction	NOUN
ejpam-6834	77	37	degree	degree	NOUN
ejpam-6834	77	38	.	.	PUNCT
ejpam-6834	78	1	fuzzy	fuzzy	ADJ
ejpam-6834	79	1	[	[	X
ejpam-6834	79	2	5	5	NUM
ejpam-6834	79	3	]	]	PUNCT
ejpam-6834	79	4	;	;	PUNCT
ejpam-6834	79	5	soft	soft	ADJ
ejpam-6834	79	6	[	[	X
ejpam-6834	79	7	8	8	NUM
ejpam-6834	79	8	]	]	PUNCT
ejpam-6834	79	9	;	;	PUNCT
ejpam-6834	79	10	rough	rough	ADJ
ejpam-6834	79	11	[	[	X
ejpam-6834	79	12	9	9	NUM
ejpam-6834	79	13	]	]	PUNCT
ejpam-6834	79	14	;	;	PUNCT
ejpam-6834	79	15	neutrosophic	neutrosophic	ADJ
ejpam-6834	79	16	[	[	X
ejpam-6834	79	17	10	10	NUM
ejpam-6834	79	18	]	]	X
ejpam-6834	79	19	;	;	PUNCT
ejpam-6834	79	20	plithogenic	plithogenic	ADJ
ejpam-6834	79	21	[	[	X
ejpam-6834	79	22	15	15	NUM
ejpam-6834	79	23	]	]	PUNCT
ejpam-6834	79	24	.	.	PUNCT
ejpam-6834	80	1	hyperuncertain	hyperuncertain	AUX
ejpam-6834	80	2	set	set	VERB
ejpam-6834	80	3	p(s	p(s	NOUN
ejpam-6834	80	4	)	)	PUNCT
ejpam-6834	80	5	impose	impose	VERB
ejpam-6834	80	6	these	these	DET
ejpam-6834	80	7	semantics	semantic	NOUN
ejpam-6834	80	8	on	on	ADP
ejpam-6834	80	9	the	the	DET
ejpam-6834	80	10	powerset	powerset	NOUN
ejpam-6834	80	11	;	;	PUNCT
ejpam-6834	80	12	membership	membership	NOUN
ejpam-6834	80	13	values	value	NOUN
ejpam-6834	80	14	become	become	VERB
ejpam-6834	80	15	set	set	ADJ
ejpam-6834	80	16	–	–	PUNCT
ejpam-6834	80	17	valued	value	VERB
ejpam-6834	80	18	,	,	PUNCT
ejpam-6834	80	19	allowing	allow	VERB
ejpam-6834	80	20	hesitation	hesitation	NOUN
ejpam-6834	80	21	and	and	CCONJ
ejpam-6834	80	22	multi	multi	ADJ
ejpam-6834	80	23	–	–	PUNCT
ejpam-6834	80	24	valued	value	VERB
ejpam-6834	80	25	appurtenance	appurtenance	NOUN
ejpam-6834	80	26	for	for	ADP
ejpam-6834	80	27	richer	rich	ADJ
ejpam-6834	80	28	modeling	modeling	NOUN
ejpam-6834	80	29	of	of	ADP
ejpam-6834	80	30	uncertainty	uncertainty	NOUN
ejpam-6834	80	31	.	.	PUNCT
ejpam-6834	81	1	hyperfuzzy	hyperfuzzy	PROPN
ejpam-6834	82	1	[	[	X
ejpam-6834	82	2	38	38	NUM
ejpam-6834	82	3	,	,	PUNCT
ejpam-6834	82	4	39	39	NUM
ejpam-6834	82	5	]	]	PUNCT
ejpam-6834	82	6	;	;	PUNCT
ejpam-6834	82	7	hypersoft	hypersoft	PROPN
ejpam-6834	83	1	[	[	X
ejpam-6834	83	2	40	40	NUM
ejpam-6834	83	3	,	,	PUNCT
ejpam-6834	83	4	42	42	NUM
ejpam-6834	83	5	]	]	PUNCT
ejpam-6834	83	6	;	;	PUNCT
ejpam-6834	83	7	hyperrough	hyperrough	NOUN
ejpam-6834	83	8	[	[	X
ejpam-6834	83	9	43	43	NUM
ejpam-6834	83	10	,	,	PUNCT
ejpam-6834	83	11	44	44	NUM
ejpam-6834	83	12	]	]	PUNCT
ejpam-6834	83	13	;	;	PUNCT
ejpam-6834	83	14	hyperneutrosophic	hyperneutrosophic	ADJ
ejpam-6834	83	15	[	[	X
ejpam-6834	83	16	45	45	NUM
ejpam-6834	83	17	]	]	PUNCT
ejpam-6834	83	18	;	;	PUNCT
ejpam-6834	83	19	hyperplithogenic	hyperplithogenic	ADJ
ejpam-6834	83	20	[	[	X
ejpam-6834	83	21	46	46	NUM
ejpam-6834	83	22	]	]	PUNCT
ejpam-6834	83	23	.	.	PUNCT
ejpam-6834	84	1	superhyperuncertain	superhyperuncertain	PROPN
ejpam-6834	84	2	set	set	VERB
ejpam-6834	84	3	p	p	PROPN
ejpam-6834	84	4	n(s	n(s	PROPN
ejpam-6834	84	5	)	)	PUNCT
ejpam-6834	84	6	(	(	PUNCT
ejpam-6834	84	7	n≥1	n≥1	NOUN
ejpam-6834	84	8	)	)	PUNCT
ejpam-6834	84	9	lift	lift	NOUN
ejpam-6834	84	10	semantics	semantic	NOUN
ejpam-6834	84	11	to	to	ADP
ejpam-6834	84	12	the	the	DET
ejpam-6834	84	13	n	n	ADV
ejpam-6834	84	14	-	-	PUNCT
ejpam-6834	84	15	th	th	ADV
ejpam-6834	84	16	iterated	iterate	VERB
ejpam-6834	84	17	powerset	powerset	NOUN
ejpam-6834	84	18	to	to	PART
ejpam-6834	84	19	capture	capture	VERB
ejpam-6834	84	20	hierarchical	hierarchical	ADJ
ejpam-6834	84	21	and	and	CCONJ
ejpam-6834	84	22	multi	multi	ADJ
ejpam-6834	84	23	–	–	NOUN
ejpam-6834	84	24	level	level	ADJ
ejpam-6834	84	25	uncertainty	uncertainty	NOUN
ejpam-6834	84	26	,	,	PUNCT
ejpam-6834	84	27	with	with	ADP
ejpam-6834	84	28	the	the	DET
ejpam-6834	84	29	ability	ability	NOUN
ejpam-6834	84	30	to	to	PART
ejpam-6834	84	31	admit	admit	VERB
ejpam-6834	84	32	multi	multi	ADJ
ejpam-6834	84	33	–	–	NOUN
ejpam-6834	84	34	ary	ary	ADJ
ejpam-6834	84	35	inputs	input	NOUN
ejpam-6834	84	36	and	and	CCONJ
ejpam-6834	84	37	outputs	output	NOUN
ejpam-6834	84	38	simultaneously	simultaneously	ADV
ejpam-6834	84	39	.	.	PUNCT
ejpam-6834	85	1	superhyperfuzzy	superhyperfuzzy	PROPN
ejpam-6834	85	2	,	,	PUNCT
ejpam-6834	85	3	superhypervague	superhypervague	NOUN
ejpam-6834	85	4	,	,	PUNCT
ejpam-6834	85	5	and	and	CCONJ
ejpam-6834	85	6	other	other	ADJ
ejpam-6834	85	7	variants	variant	NOUN
ejpam-6834	86	1	[	[	X
ejpam-6834	86	2	1	1	NUM
ejpam-6834	86	3	]	]	PUNCT
ejpam-6834	86	4	.	.	PUNCT
ejpam-6834	87	1	set	set	PROPN
ejpam-6834	87	2	,	,	PUNCT
ejpam-6834	87	3	which	which	PRON
ejpam-6834	87	4	assigns	assign	VERB
ejpam-6834	87	5	uncertain	uncertain	ADJ
ejpam-6834	87	6	semantics	semantic	NOUN
ejpam-6834	87	7	on	on	ADP
ejpam-6834	87	8	the	the	DET
ejpam-6834	87	9	n	n	ADV
ejpam-6834	87	10	-	-	ADJ
ejpam-6834	87	11	fold	fold	ADJ
ejpam-6834	87	12	iterated	iterated	ADJ
ejpam-6834	87	13	powerset	powerset	NOUN
ejpam-6834	87	14	p	p	PROPN
ejpam-6834	87	15	n	n	CCONJ
ejpam-6834	87	16	(	(	PUNCT
ejpam-6834	87	17	·	·	PUNCT
ejpam-6834	87	18	)	)	PUNCT
ejpam-6834	87	19	and	and	CCONJ
ejpam-6834	87	20	admits	admit	VERB
ejpam-6834	87	21	m	m	PROPN
ejpam-6834	87	22	-	-	ADJ
ejpam-6834	87	23	ary	ary	PROPN
ejpam-6834	87	24	superhyperoperations	superhyperoperation	NOUN
ejpam-6834	87	25	.	.	PUNCT
ejpam-6834	88	1	we	we	PRON
ejpam-6834	88	2	further	far	ADV
ejpam-6834	88	3	develop	develop	VERB
ejpam-6834	88	4	the	the	DET
ejpam-6834	88	5	more	more	ADV
ejpam-6834	88	6	general	general	ADJ
ejpam-6834	88	7	(	(	PUNCT
ejpam-6834	88	8	h	h	NOUN
ejpam-6834	88	9	,	,	PUNCT
ejpam-6834	88	10	k)-ary	k)-ary	X
ejpam-6834	88	11	(	(	PUNCT
ejpam-6834	88	12	m	m	PROPN
ejpam-6834	88	13	,	,	PUNCT
ejpam-6834	88	14	n)superhyperuncertain	n)superhyperuncertain	PROPN
ejpam-6834	88	15	set	set	NOUN
ejpam-6834	88	16	,	,	PUNCT
ejpam-6834	88	17	enabling	enable	VERB
ejpam-6834	88	18	multiple	multiple	ADJ
ejpam-6834	88	19	input	input	NOUN
ejpam-6834	88	20	and	and	CCONJ
ejpam-6834	88	21	output	output	NOUN
ejpam-6834	88	22	arities	arity	NOUN
ejpam-6834	88	23	at	at	ADP
ejpam-6834	88	24	each	each	DET
ejpam-6834	88	25	hierarchical	hierarchical	ADJ
ejpam-6834	88	26	level	level	NOUN
ejpam-6834	88	27	.	.	PUNCT
ejpam-6834	89	1	taken	take	VERB
ejpam-6834	89	2	together	together	ADV
ejpam-6834	89	3	,	,	PUNCT
ejpam-6834	89	4	these	these	DET
ejpam-6834	89	5	constructions	construction	NOUN
ejpam-6834	89	6	unify	unify	VERB
ejpam-6834	89	7	and	and	CCONJ
ejpam-6834	89	8	extend	extend	VERB
ejpam-6834	89	9	existing	exist	VERB
ejpam-6834	89	10	uncertain	uncertain	ADJ
ejpam-6834	89	11	–	–	PUNCT
ejpam-6834	89	12	set	set	ADJ
ejpam-6834	89	13	paradigms	paradigm	NOUN
ejpam-6834	89	14	within	within	ADP
ejpam-6834	89	15	the	the	DET
ejpam-6834	89	16	framework	framework	NOUN
ejpam-6834	89	17	of	of	ADP
ejpam-6834	89	18	superhyperstructures	superhyperstructure	NOUN
ejpam-6834	89	19	,	,	PUNCT
ejpam-6834	89	20	yielding	yield	VERB
ejpam-6834	89	21	a	a	DET
ejpam-6834	89	22	scalable	scalable	ADJ
ejpam-6834	89	23	toolkit	toolkit	NOUN
ejpam-6834	89	24	for	for	ADP
ejpam-6834	89	25	hierarchical	hierarchical	ADJ
ejpam-6834	89	26	and	and	CCONJ
ejpam-6834	89	27	multi	multi	ADJ
ejpam-6834	89	28	–	–	NOUN
ejpam-6834	89	29	attribute	attribute	NOUN
ejpam-6834	89	30	uncertainty	uncertainty	NOUN
ejpam-6834	89	31	while	while	SCONJ
ejpam-6834	89	32	clarifying	clarify	VERB
ejpam-6834	89	33	how	how	SCONJ
ejpam-6834	89	34	classical	classical	ADJ
ejpam-6834	89	35	models	model	NOUN
ejpam-6834	89	36	arise	arise	VERB
ejpam-6834	89	37	via	via	ADP
ejpam-6834	89	38	restriction	restriction	NOUN
ejpam-6834	89	39	,	,	PUNCT
ejpam-6834	89	40	projection	projection	NOUN
ejpam-6834	89	41	,	,	PUNCT
ejpam-6834	89	42	and	and	CCONJ
ejpam-6834	89	43	composition	composition	NOUN
ejpam-6834	89	44	across	across	ADP
ejpam-6834	89	45	levels	level	NOUN
ejpam-6834	89	46	.	.	PUNCT
ejpam-6834	90	1	for	for	ADP
ejpam-6834	90	2	the	the	DET
ejpam-6834	90	3	reader	reader	NOUN
ejpam-6834	90	4	’s	’s	PART
ejpam-6834	90	5	reference	reference	NOUN
ejpam-6834	90	6	,	,	PUNCT
ejpam-6834	90	7	table	table	NOUN
ejpam-6834	90	8	4	4	NUM
ejpam-6834	90	9	provides	provide	VERB
ejpam-6834	90	10	a	a	DET
ejpam-6834	90	11	compact	compact	ADJ
ejpam-6834	90	12	overview	overview	NOUN
ejpam-6834	90	13	of	of	ADP
ejpam-6834	90	14	n	n	CCONJ
ejpam-6834	90	15	–	–	PUNCT
ejpam-6834	90	16	,	,	PUNCT
ejpam-6834	90	17	(	(	PUNCT
ejpam-6834	90	18	m	m	NOUN
ejpam-6834	90	19	,	,	PUNCT
ejpam-6834	90	20	n	n	CCONJ
ejpam-6834	90	21	)	)	PUNCT
ejpam-6834	90	22	–	–	PUNCT
ejpam-6834	90	23	,	,	PUNCT
ejpam-6834	90	24	and	and	CCONJ
ejpam-6834	90	25	(	(	PUNCT
ejpam-6834	90	26	h	h	NOUN
ejpam-6834	90	27	,	,	PUNCT
ejpam-6834	90	28	k)–ary	k)–ary	PROPN
ejpam-6834	90	29	(	(	PUNCT
ejpam-6834	90	30	m	m	PROPN
ejpam-6834	90	31	,	,	PUNCT
ejpam-6834	90	32	n)–superhyperuncertain	n)–superhyperuncertain	NOUN
ejpam-6834	90	33	sets	set	NOUN
ejpam-6834	90	34	.	.	PUNCT
ejpam-6834	91	1	table	table	NOUN
ejpam-6834	91	2	4	4	NUM
ejpam-6834	91	3	:	:	PUNCT
ejpam-6834	91	4	compact	compact	ADJ
ejpam-6834	91	5	overview	overview	NOUN
ejpam-6834	91	6	of	of	ADP
ejpam-6834	91	7	n	n	CCONJ
ejpam-6834	91	8	–	–	PUNCT
ejpam-6834	91	9	,	,	PUNCT
ejpam-6834	91	10	(	(	PUNCT
ejpam-6834	91	11	m	m	NOUN
ejpam-6834	91	12	,	,	PUNCT
ejpam-6834	91	13	n	n	CCONJ
ejpam-6834	91	14	)	)	PUNCT
ejpam-6834	91	15	–	–	PUNCT
ejpam-6834	91	16	,	,	PUNCT
ejpam-6834	91	17	and	and	CCONJ
ejpam-6834	91	18	(	(	PUNCT
ejpam-6834	91	19	h	h	NOUN
ejpam-6834	91	20	,	,	PUNCT
ejpam-6834	91	21	k)–ary	k)–ary	PROPN
ejpam-6834	91	22	(	(	PUNCT
ejpam-6834	91	23	m	m	PROPN
ejpam-6834	91	24	,	,	PUNCT
ejpam-6834	91	25	n)–superhyperuncertain	n)–superhyperuncertain	NOUN
ejpam-6834	91	26	sets	set	NOUN
ejpam-6834	91	27	.	.	PUNCT
ejpam-6834	92	1	notion	notion	NOUN
ejpam-6834	92	2	carrier	carrier	NOUN
ejpam-6834	92	3	/	/	SYM
ejpam-6834	92	4	signature	signature	NOUN
ejpam-6834	92	5	essence	essence	NOUN
ejpam-6834	92	6	(	(	PUNCT
ejpam-6834	92	7	very	very	ADV
ejpam-6834	92	8	brief	brief	ADJ
ejpam-6834	92	9	)	)	PUNCT
ejpam-6834	92	10	n	n	CCONJ
ejpam-6834	92	11	–	–	PUNCT
ejpam-6834	92	12	superhyperuncertain	superhyperuncertain	ADJ
ejpam-6834	92	13	set	set	NOUN
ejpam-6834	92	14	carrier	carrier	NOUN
ejpam-6834	92	15	:	:	PUNCT
ejpam-6834	92	16	p	p	PROPN
ejpam-6834	92	17	n(s	n(s	PROPN
ejpam-6834	92	18	)	)	PUNCT
ejpam-6834	92	19	sig	sig	NOUN
ejpam-6834	92	20	.	.	PUNCT
ejpam-6834	92	21	:	:	PUNCT
ejpam-6834	93	1	f	f	X
ejpam-6834	93	2	:	:	PUNCT
ejpam-6834	93	3	p	p	NOUN
ejpam-6834	93	4	n(s	n(s	PROPN
ejpam-6834	93	5	)	)	PUNCT
ejpam-6834	93	6	→	→	SYM
ejpam-6834	93	7	d(n	d(n	PROPN
ejpam-6834	93	8	)	)	PUNCT
ejpam-6834	93	9	uncertainty	uncertainty	NOUN
ejpam-6834	93	10	on	on	ADP
ejpam-6834	93	11	the	the	DET
ejpam-6834	93	12	n	n	ADV
ejpam-6834	93	13	-	-	PUNCT
ejpam-6834	93	14	th	th	X
ejpam-6834	93	15	powerset	powerset	NOUN
ejpam-6834	93	16	(	(	PUNCT
ejpam-6834	93	17	hierarchical	hierarchical	ADJ
ejpam-6834	93	18	levels	level	NOUN
ejpam-6834	93	19	)	)	PUNCT
ejpam-6834	93	20	.	.	PUNCT
ejpam-6834	94	1	recovers	recover	NOUN
ejpam-6834	94	2	classical	classical	ADJ
ejpam-6834	94	3	for	for	ADP
ejpam-6834	94	4	n=0	n=0	NUM
ejpam-6834	94	5	,	,	PUNCT
ejpam-6834	94	6	hyper	hyper	NOUN
ejpam-6834	94	7	for	for	ADP
ejpam-6834	94	8	n=1	n=1	PROPN
ejpam-6834	94	9	.	.	PUNCT
ejpam-6834	95	1	(	(	PUNCT
ejpam-6834	95	2	m	m	PROPN
ejpam-6834	95	3	,	,	PUNCT
ejpam-6834	95	4	n)–superhyperuncertain	n)–superhyperuncertain	VERB
ejpam-6834	95	5	set	set	VERB
ejpam-6834	95	6	carrier	carrier	NOUN
ejpam-6834	95	7	:	:	PUNCT
ejpam-6834	95	8	p	p	PROPN
ejpam-6834	95	9	n(s	n(s	PROPN
ejpam-6834	95	10	)	)	PUNCT
ejpam-6834	95	11	sig	sig	NOUN
ejpam-6834	95	12	.	.	PUNCT
ejpam-6834	95	13	:	:	PUNCT
ejpam-6834	96	1	f	f	X
ejpam-6834	96	2	:	:	PUNCT
ejpam-6834	96	3	(	(	PUNCT
ejpam-6834	96	4	p	p	X
ejpam-6834	96	5	n(s))m	n(s))m	PROPN
ejpam-6834	96	6	→	→	SYM
ejpam-6834	96	7	d(n	d(n	PROPN
ejpam-6834	96	8	)	)	PUNCT
ejpam-6834	96	9	adds	add	VERB
ejpam-6834	96	10	m	m	NOUN
ejpam-6834	96	11	-	-	ADJ
ejpam-6834	96	12	ary	ary	PROPN
ejpam-6834	96	13	interaction	interaction	NOUN
ejpam-6834	96	14	at	at	ADP
ejpam-6834	96	15	level	level	NOUN
ejpam-6834	96	16	n	n	CCONJ
ejpam-6834	96	17	;	;	PUNCT
ejpam-6834	96	18	m=1	m=1	X
ejpam-6834	96	19	gives	give	VERB
ejpam-6834	96	20	the	the	DET
ejpam-6834	96	21	n	n	CCONJ
ejpam-6834	96	22	–	–	PUNCT
ejpam-6834	96	23	case	case	NOUN
ejpam-6834	96	24	.	.	PUNCT
ejpam-6834	97	1	(	(	PUNCT
ejpam-6834	97	2	h	h	NOUN
ejpam-6834	97	3	,	,	PUNCT
ejpam-6834	97	4	k)–ary	k)–ary	PROPN
ejpam-6834	97	5	(	(	PUNCT
ejpam-6834	97	6	m	m	PROPN
ejpam-6834	97	7	,	,	PUNCT
ejpam-6834	97	8	n)–superhyperuncertain	n)–superhyperuncertain	VERB
ejpam-6834	97	9	set	set	VERB
ejpam-6834	97	10	carrier	carrier	NOUN
ejpam-6834	97	11	:	:	PUNCT
ejpam-6834	97	12	inputs	input	VERB
ejpam-6834	97	13	from	from	ADP
ejpam-6834	97	14	p	p	DET
ejpam-6834	97	15	n(s	n(s	PROPN
ejpam-6834	97	16	)	)	PUNCT
ejpam-6834	97	17	sig	sig	NOUN
ejpam-6834	97	18	.	.	PUNCT
ejpam-6834	97	19	:	:	PUNCT
ejpam-6834	98	1	f	f	X
ejpam-6834	98	2	:	:	PUNCT
ejpam-6834	98	3	(	(	PUNCT
ejpam-6834	98	4	p	p	X
ejpam-6834	98	5	n(s))h	n(s))h	PROPN
ejpam-6834	98	6	→	→	PUNCT
ejpam-6834	98	7	(	(	PUNCT
ejpam-6834	98	8	d(n))k	d(n))k	PROPN
ejpam-6834	98	9	most	most	ADV
ejpam-6834	98	10	general	general	ADJ
ejpam-6834	98	11	:	:	PUNCT
ejpam-6834	98	12	h	h	NOUN
ejpam-6834	98	13	inputs	input	NOUN
ejpam-6834	98	14	,	,	PUNCT
ejpam-6834	98	15	k	k	PROPN
ejpam-6834	98	16	outputs	output	NOUN
ejpam-6834	98	17	at	at	ADP
ejpam-6834	98	18	level	level	NOUN
ejpam-6834	98	19	n.	n.	NOUN
ejpam-6834	98	20	reduces	reduce	VERB
ejpam-6834	98	21	to	to	ADP
ejpam-6834	98	22	(	(	PUNCT
ejpam-6834	98	23	m	m	PROPN
ejpam-6834	98	24	,	,	PUNCT
ejpam-6834	98	25	n)–case	n)–case	NUM
ejpam-6834	98	26	when	when	SCONJ
ejpam-6834	98	27	h=1	h=1	NOUN
ejpam-6834	98	28	,	,	PUNCT
ejpam-6834	98	29	k=1	k=1	PROPN
ejpam-6834	98	30	.	.	PUNCT
ejpam-6834	99	1	note	note	NOUN
ejpam-6834	99	2	.	.	PUNCT
ejpam-6834	100	1	d(n	d(n	NOUN
ejpam-6834	100	2	)	)	PUNCT
ejpam-6834	100	3	denotes	denote	NOUN
ejpam-6834	100	4	an	an	DET
ejpam-6834	100	5	n	n	CCONJ
ejpam-6834	100	6	–	–	PUNCT
ejpam-6834	100	7	level	level	NOUN
ejpam-6834	100	8	degree	degree	NOUN
ejpam-6834	100	9	family	family	NOUN
ejpam-6834	100	10	(	(	PUNCT
ejpam-6834	100	11	e.g.	e.g.	ADV
ejpam-6834	100	12	,	,	PUNCT
ejpam-6834	100	13	p̃n([0	p̃n([0	PROPN
ejpam-6834	100	14	,	,	PUNCT
ejpam-6834	100	15	1	1	NUM
ejpam-6834	100	16	]	]	PUNCT
ejpam-6834	100	17	)	)	PUNCT
ejpam-6834	100	18	for	for	ADP
ejpam-6834	100	19	fuzzy	fuzzy	ADJ
ejpam-6834	100	20	,	,	PUNCT
ejpam-6834	100	21	p̃n([0	p̃n([0	PROPN
ejpam-6834	100	22	,	,	PUNCT
ejpam-6834	100	23	1	1	NUM
ejpam-6834	100	24	]	]	SYM
ejpam-6834	100	25	3	3	NUM
ejpam-6834	100	26	)	)	PUNCT
ejpam-6834	100	27	for	for	ADP
ejpam-6834	100	28	neutrosophic	neutrosophic	ADJ
ejpam-6834	100	29	)	)	PUNCT
ejpam-6834	100	30	.	.	PUNCT
ejpam-6834	101	1	together	together	ADV
ejpam-6834	101	2	,	,	PUNCT
ejpam-6834	101	3	these	these	DET
ejpam-6834	101	4	frameworks	framework	NOUN
ejpam-6834	101	5	capture	capture	VERB
ejpam-6834	101	6	hierarchical	hierarchical	ADJ
ejpam-6834	101	7	uncertainty	uncertainty	NOUN
ejpam-6834	101	8	by	by	ADP
ejpam-6834	101	9	assigning	assign	VERB
ejpam-6834	101	10	set	set	NOUN
ejpam-6834	101	11	-	-	PUNCT
ejpam-6834	101	12	valued	value	VERB
ejpam-6834	101	13	memberships	membership	NOUN
ejpam-6834	101	14	across	across	ADP
ejpam-6834	101	15	iterated	iterated	ADJ
ejpam-6834	101	16	powersets	powerset	NOUN
ejpam-6834	101	17	and	and	CCONJ
ejpam-6834	101	18	permitting	permit	VERB
ejpam-6834	101	19	variable	variable	ADJ
ejpam-6834	101	20	input	input	NOUN
ejpam-6834	101	21	–	–	PUNCT
ejpam-6834	101	22	output	output	NOUN
ejpam-6834	101	23	arities	arity	NOUN
ejpam-6834	101	24	.	.	PUNCT
ejpam-6834	102	1	they	they	PRON
ejpam-6834	102	2	unify	unify	VERB
ejpam-6834	102	3	fuzzy	fuzzy	ADJ
ejpam-6834	102	4	,	,	PUNCT
ejpam-6834	102	5	neutrosophic	neutrosophic	ADJ
ejpam-6834	102	6	,	,	PUNCT
ejpam-6834	102	7	soft	soft	ADJ
ejpam-6834	102	8	,	,	PUNCT
ejpam-6834	102	9	rough	rough	ADJ
ejpam-6834	102	10	,	,	PUNCT
ejpam-6834	102	11	and	and	CCONJ
ejpam-6834	102	12	plithogenic	plithogenic	ADJ
ejpam-6834	102	13	semantics	semantic	NOUN
ejpam-6834	102	14	,	,	PUNCT
ejpam-6834	102	15	support	support	VERB
ejpam-6834	102	16	compositional	compositional	ADJ
ejpam-6834	102	17	reasoning	reasoning	NOUN
ejpam-6834	102	18	,	,	PUNCT
ejpam-6834	102	19	and	and	CCONJ
ejpam-6834	102	20	scale	scale	NOUN
ejpam-6834	102	21	to	to	ADP
ejpam-6834	102	22	complex	complex	ADJ
ejpam-6834	102	23	,	,	PUNCT
ejpam-6834	102	24	nested	nest	VERB
ejpam-6834	102	25	attributes	attribute	NOUN
ejpam-6834	102	26	through	through	ADP
ejpam-6834	102	27	well	well	ADV
ejpam-6834	102	28	-	-	PUNCT
ejpam-6834	102	29	defined	define	VERB
ejpam-6834	102	30	operations	operation	NOUN
ejpam-6834	102	31	and	and	CCONJ
ejpam-6834	102	32	t.	t.	PROPN
ejpam-6834	102	33	fujita	fujita	PROPN
ejpam-6834	102	34	,	,	PUNCT
ejpam-6834	102	35	f.smarandache	f.smarandache	NOUN
ejpam-6834	102	36	/	/	SYM
ejpam-6834	102	37	eur	eur	PROPN
ejpam-6834	102	38	.	.	PUNCT
ejpam-6834	103	1	j.	j.	PROPN
ejpam-6834	103	2	pure	pure	PROPN
ejpam-6834	103	3	appl	appl	PROPN
ejpam-6834	103	4	.	.	PROPN
ejpam-6834	103	5	math	math	PROPN
ejpam-6834	103	6	,	,	PUNCT
ejpam-6834	103	7	18	18	NUM
ejpam-6834	103	8	(	(	PUNCT
ejpam-6834	103	9	4	4	NUM
ejpam-6834	103	10	)	)	PUNCT
ejpam-6834	103	11	(	(	PUNCT
ejpam-6834	103	12	2025	2025	NUM
ejpam-6834	103	13	)	)	PUNCT
ejpam-6834	103	14	,	,	PUNCT
ejpam-6834	103	15	6834	6834	NUM
ejpam-6834	103	16	5	5	NUM
ejpam-6834	103	17	of	of	ADP
ejpam-6834	103	18	69	69	NUM
ejpam-6834	103	19	cut	cut	NOUN
ejpam-6834	103	20	-	-	PUNCT
ejpam-6834	103	21	based	base	VERB
ejpam-6834	103	22	analyses	analysis	NOUN
ejpam-6834	103	23	.	.	PUNCT
ejpam-6834	104	1	since	since	SCONJ
ejpam-6834	104	2	this	this	DET
ejpam-6834	104	3	paper	paper	NOUN
ejpam-6834	104	4	conducts	conduct	VERB
ejpam-6834	104	5	only	only	ADV
ejpam-6834	104	6	theoretical	theoretical	ADJ
ejpam-6834	104	7	analysis	analysis	NOUN
ejpam-6834	104	8	,	,	PUNCT
ejpam-6834	104	9	we	we	PRON
ejpam-6834	104	10	also	also	ADV
ejpam-6834	104	11	hope	hope	VERB
ejpam-6834	104	12	that	that	SCONJ
ejpam-6834	104	13	quantitative	quantitative	ADJ
ejpam-6834	104	14	analysis	analysis	NOUN
ejpam-6834	104	15	using	use	VERB
ejpam-6834	104	16	computational	computational	ADJ
ejpam-6834	104	17	methods	method	NOUN
ejpam-6834	104	18	will	will	AUX
ejpam-6834	104	19	be	be	AUX
ejpam-6834	104	20	carried	carry	VERB
ejpam-6834	104	21	out	out	ADP
ejpam-6834	104	22	in	in	ADP
ejpam-6834	104	23	the	the	DET
ejpam-6834	104	24	future	future	NOUN
ejpam-6834	104	25	.	.	PUNCT
ejpam-6834	105	1	a	a	DET
ejpam-6834	105	2	concise	concise	ADJ
ejpam-6834	105	3	,	,	PUNCT
ejpam-6834	105	4	section	section	NOUN
ejpam-6834	105	5	-	-	PUNCT
ejpam-6834	105	6	level	level	NOUN
ejpam-6834	105	7	outline	outline	NOUN
ejpam-6834	105	8	is	be	AUX
ejpam-6834	105	9	provided	provide	VERB
ejpam-6834	105	10	in	in	ADP
ejpam-6834	105	11	table	table	NOUN
ejpam-6834	105	12	5	5	NUM
ejpam-6834	105	13	.	.	PUNCT
ejpam-6834	105	14	table	table	NOUN
ejpam-6834	105	15	5	5	NUM
ejpam-6834	105	16	:	:	PUNCT
ejpam-6834	105	17	section	section	NOUN
ejpam-6834	105	18	-	-	PUNCT
ejpam-6834	105	19	level	level	NOUN
ejpam-6834	105	20	contents	content	NOUN
ejpam-6834	105	21	(	(	PUNCT
ejpam-6834	105	22	introduction	introduction	NOUN
ejpam-6834	105	23	omitted	omit	VERB
ejpam-6834	105	24	)	)	PUNCT
ejpam-6834	105	25	.	.	PUNCT
ejpam-6834	106	1	section	section	NOUN
ejpam-6834	106	2	summary	summary	NOUN
ejpam-6834	106	3	2	2	NUM
ejpam-6834	106	4	.	.	PUNCT
ejpam-6834	106	5	preliminaries	preliminary	NOUN
ejpam-6834	106	6	notation	notation	NOUN
ejpam-6834	106	7	and	and	CCONJ
ejpam-6834	106	8	core	core	NOUN
ejpam-6834	106	9	constructions	construction	NOUN
ejpam-6834	106	10	:	:	PUNCT
ejpam-6834	106	11	powerset	powerset	NOUN
ejpam-6834	106	12	p(s	p(s	NOUN
ejpam-6834	106	13	)	)	PUNCT
ejpam-6834	106	14	and	and	CCONJ
ejpam-6834	106	15	iterates	iterate	VERB
ejpam-6834	106	16	pn(s	pn(	NOUN
ejpam-6834	106	17	)	)	PUNCT
ejpam-6834	106	18	;	;	PUNCT
ejpam-6834	106	19	hyperoperations	hyperoperation	NOUN
ejpam-6834	106	20	and	and	CCONJ
ejpam-6834	106	21	hyperstructures	hyperstructure	NOUN
ejpam-6834	106	22	;	;	PUNCT
ejpam-6834	106	23	n	n	CCONJ
ejpam-6834	106	24	-	-	PUNCT
ejpam-6834	106	25	superhyperstructures	superhyperstructure	NOUN
ejpam-6834	106	26	on	on	ADP
ejpam-6834	106	27	pn(s	pn(	NOUN
ejpam-6834	106	28	)	)	PUNCT
ejpam-6834	106	29	;	;	PUNCT
ejpam-6834	106	30	(	(	PUNCT
ejpam-6834	106	31	h	h	NOUN
ejpam-6834	106	32	,	,	PUNCT
ejpam-6834	106	33	k)-ary	k)-ary	ADJ
ejpam-6834	106	34	superhyperstructure	superhyperstructure	NOUN
ejpam-6834	106	35	;	;	PUNCT
ejpam-6834	106	36	brief	brief	ADJ
ejpam-6834	106	37	,	,	PUNCT
ejpam-6834	106	38	concrete	concrete	ADJ
ejpam-6834	106	39	examples	example	NOUN
ejpam-6834	106	40	.	.	PUNCT
ejpam-6834	107	1	3	3	X
ejpam-6834	107	2	.	.	X
ejpam-6834	107	3	main	main	ADJ
ejpam-6834	107	4	results	result	NOUN
ejpam-6834	107	5	definition	definition	NOUN
ejpam-6834	107	6	of	of	ADP
ejpam-6834	107	7	(	(	PUNCT
ejpam-6834	107	8	m	m	PROPN
ejpam-6834	107	9	,	,	PUNCT
ejpam-6834	107	10	n)–superhyperuncertain	n)–superhyperuncertain	NOUN
ejpam-6834	107	11	sets	set	NOUN
ejpam-6834	107	12	.	.	PUNCT
ejpam-6834	108	1	subsections	subsection	NOUN
ejpam-6834	108	2	:	:	PUNCT
ejpam-6834	108	3	(	(	PUNCT
ejpam-6834	108	4	i	i	NOUN
ejpam-6834	108	5	)	)	PUNCT
ejpam-6834	108	6	superhyperfuzzy	superhyperfuzzy	ADJ
ejpam-6834	108	7	—	—	PUNCT
ejpam-6834	108	8	restriction	restriction	NOUN
ejpam-6834	108	9	/	/	SYM
ejpam-6834	108	10	projection	projection	NOUN
ejpam-6834	108	11	in	in	ADP
ejpam-6834	108	12	m	m	PROPN
ejpam-6834	108	13	,	,	PUNCT
ejpam-6834	108	14	n	n	CCONJ
ejpam-6834	108	15	,	,	PUNCT
ejpam-6834	108	16	closure	closure	NOUN
ejpam-6834	108	17	(	(	PUNCT
ejpam-6834	108	18	union	union	NOUN
ejpam-6834	108	19	/	/	SYM
ejpam-6834	108	20	intersection	intersection	NOUN
ejpam-6834	108	21	)	)	PUNCT
ejpam-6834	108	22	,	,	PUNCT
ejpam-6834	108	23	nested	nest	VERB
ejpam-6834	108	24	α	α	NOUN
ejpam-6834	108	25	-	-	PUNCT
ejpam-6834	108	26	cuts	cut	NOUN
ejpam-6834	108	27	,	,	PUNCT
ejpam-6834	108	28	functoriality	functoriality	NOUN
ejpam-6834	108	29	;	;	PUNCT
ejpam-6834	108	30	(	(	PUNCT
ejpam-6834	108	31	ii	ii	NOUN
ejpam-6834	108	32	)	)	PUNCT
ejpam-6834	108	33	superhyperneutrosophic	superhyperneutrosophic	ADJ
ejpam-6834	108	34	—	—	PUNCT
ejpam-6834	108	35	recovery	recovery	NOUN
ejpam-6834	108	36	of	of	ADP
ejpam-6834	108	37	m=1	m=1	NOUN
ejpam-6834	108	38	case	case	NOUN
ejpam-6834	108	39	,	,	PUNCT
ejpam-6834	108	40	truth	truth	NOUN
ejpam-6834	108	41	-	-	PUNCT
ejpam-6834	108	42	projection	projection	NOUN
ejpam-6834	108	43	to	to	ADP
ejpam-6834	108	44	fuzzy	fuzzy	ADJ
ejpam-6834	108	45	,	,	PUNCT
ejpam-6834	108	46	λ	λ	NOUN
ejpam-6834	108	47	-	-	NOUN
ejpam-6834	108	48	cuts	cut	NOUN
ejpam-6834	108	49	,	,	PUNCT
ejpam-6834	108	50	closure	closure	NOUN
ejpam-6834	108	51	,	,	PUNCT
ejpam-6834	108	52	functoriality	functoriality	NOUN
ejpam-6834	108	53	;	;	PUNCT
ejpam-6834	108	54	(	(	PUNCT
ejpam-6834	108	55	iii	iii	X
ejpam-6834	108	56	)	)	PUNCT
ejpam-6834	108	57	superhyperplithogenic	superhyperplithogenic	NOUN
ejpam-6834	108	58	—	—	PUNCT
ejpam-6834	108	59	hdaf	hdaf	ADJ
ejpam-6834	108	60	/	/	SYM
ejpam-6834	108	61	dcf	dcf	NOUN
ejpam-6834	108	62	axioms	axiom	NOUN
ejpam-6834	108	63	and	and	CCONJ
ejpam-6834	108	64	decision	decision	NOUN
ejpam-6834	108	65	-	-	PUNCT
ejpam-6834	108	66	making	make	VERB
ejpam-6834	108	67	examples	example	NOUN
ejpam-6834	108	68	.	.	PUNCT
ejpam-6834	109	1	4	4	X
ejpam-6834	109	2	.	.	X
ejpam-6834	109	3	additional	additional	ADJ
ejpam-6834	109	4	result	result	NOUN
ejpam-6834	109	5	(	(	PUNCT
ejpam-6834	109	6	h	h	NOUN
ejpam-6834	109	7	,	,	PUNCT
ejpam-6834	109	8	k)-ary	k)-ary	X
ejpam-6834	109	9	(	(	PUNCT
ejpam-6834	109	10	m	m	PROPN
ejpam-6834	109	11	,	,	PUNCT
ejpam-6834	109	12	n)–superhypersoft	n)–superhypersoft	NOUN
ejpam-6834	109	13	and	and	CCONJ
ejpam-6834	109	14	superhyperrough	superhyperrough	ADJ
ejpam-6834	109	15	frameworks	framework	NOUN
ejpam-6834	109	16	:	:	PUNCT
ejpam-6834	109	17	formal	formal	ADJ
ejpam-6834	109	18	definitions	definition	NOUN
ejpam-6834	109	19	over	over	ADP
ejpam-6834	109	20	p̃m(s	p̃m(s	NOUN
ejpam-6834	109	21	)	)	PUNCT
ejpam-6834	109	22	and	and	CCONJ
ejpam-6834	109	23	p̃n(u)/p̃n(x	p̃n(u)/p̃n(x	PROPN
ejpam-6834	109	24	)	)	PUNCT
ejpam-6834	109	25	;	;	PUNCT
ejpam-6834	109	26	unary	unary	ADJ
ejpam-6834	109	27	reduction	reduction	NOUN
ejpam-6834	109	28	lemmas	lemmas	ADJ
ejpam-6834	109	29	;	;	PUNCT
ejpam-6834	109	30	fixing	fix	VERB
ejpam-6834	109	31	/	/	SYM
ejpam-6834	109	32	projection	projection	NOUN
ejpam-6834	109	33	of	of	ADP
ejpam-6834	109	34	inputs	input	NOUN
ejpam-6834	109	35	/	/	SYM
ejpam-6834	109	36	outputs	output	NOUN
ejpam-6834	109	37	;	;	PUNCT
ejpam-6834	109	38	closure	closure	NOUN
ejpam-6834	109	39	under	under	ADP
ejpam-6834	109	40	pointwise	pointwise	PROPN
ejpam-6834	109	41	union	union	NOUN
ejpam-6834	109	42	/	/	SYM
ejpam-6834	109	43	intersection	intersection	NOUN
ejpam-6834	109	44	;	;	PUNCT
ejpam-6834	109	45	functorial	functorial	NOUN
ejpam-6834	109	46	pushforwards	pushforward	NOUN
ejpam-6834	109	47	(	(	PUNCT
ejpam-6834	109	48	surjections	surjection	NOUN
ejpam-6834	109	49	/	/	SYM
ejpam-6834	109	50	quotients	quotient	NOUN
ejpam-6834	109	51	)	)	PUNCT
ejpam-6834	109	52	;	;	PUNCT
ejpam-6834	109	53	illustrative	illustrative	ADJ
ejpam-6834	109	54	cases	case	NOUN
ejpam-6834	109	55	(	(	PUNCT
ejpam-6834	109	56	personalized	personalized	ADJ
ejpam-6834	109	57	recommendations	recommendation	NOUN
ejpam-6834	109	58	;	;	PUNCT
ejpam-6834	109	59	medical	medical	ADJ
ejpam-6834	109	60	diagnosis	diagnosis	NOUN
ejpam-6834	109	61	)	)	PUNCT
ejpam-6834	109	62	.	.	PUNCT
ejpam-6834	110	1	5	5	X
ejpam-6834	110	2	.	.	X
ejpam-6834	110	3	conclusion	conclusion	NOUN
ejpam-6834	110	4	and	and	CCONJ
ejpam-6834	110	5	future	future	ADJ
ejpam-6834	110	6	work	work	NOUN
ejpam-6834	110	7	summary	summary	NOUN
ejpam-6834	110	8	of	of	ADP
ejpam-6834	110	9	the	the	DET
ejpam-6834	110	10	unified	unified	ADJ
ejpam-6834	110	11	superhyper	superhyper	NOUN
ejpam-6834	110	12	framework	framework	NOUN
ejpam-6834	110	13	;	;	PUNCT
ejpam-6834	110	14	prospective	prospective	ADJ
ejpam-6834	110	15	applications	application	NOUN
ejpam-6834	110	16	to	to	ADP
ejpam-6834	110	17	hierarchical	hierarchical	ADJ
ejpam-6834	110	18	uncertainty	uncertainty	NOUN
ejpam-6834	110	19	and	and	CCONJ
ejpam-6834	110	20	complex	complex	ADJ
ejpam-6834	110	21	memberships	membership	NOUN
ejpam-6834	110	22	;	;	PUNCT
ejpam-6834	110	23	outlook	outlook	NOUN
ejpam-6834	110	24	on	on	ADP
ejpam-6834	110	25	algorithms	algorithm	NOUN
ejpam-6834	110	26	and	and	CCONJ
ejpam-6834	110	27	domain	domain	NOUN
ejpam-6834	110	28	-	-	PUNCT
ejpam-6834	110	29	specific	specific	ADJ
ejpam-6834	110	30	case	case	NOUN
ejpam-6834	110	31	studies	study	NOUN
ejpam-6834	110	32	.	.	PUNCT
ejpam-6834	111	1	2	2	X
ejpam-6834	111	2	.	.	X
ejpam-6834	111	3	preliminaries	preliminary	NOUN
ejpam-6834	111	4	in	in	ADP
ejpam-6834	111	5	this	this	DET
ejpam-6834	111	6	section	section	NOUN
ejpam-6834	111	7	,	,	PUNCT
ejpam-6834	111	8	we	we	PRON
ejpam-6834	111	9	summarize	summarize	VERB
ejpam-6834	111	10	the	the	DET
ejpam-6834	111	11	basic	basic	ADJ
ejpam-6834	111	12	definitions	definition	NOUN
ejpam-6834	111	13	and	and	CCONJ
ejpam-6834	111	14	notational	notational	ADJ
ejpam-6834	111	15	conventions	convention	NOUN
ejpam-6834	111	16	used	use	VERB
ejpam-6834	111	17	in	in	ADP
ejpam-6834	111	18	the	the	DET
ejpam-6834	111	19	paper	paper	NOUN
ejpam-6834	111	20	.	.	PUNCT
ejpam-6834	112	1	throughout	throughout	ADP
ejpam-6834	112	2	,	,	PUNCT
ejpam-6834	112	3	we	we	PRON
ejpam-6834	112	4	work	work	VERB
ejpam-6834	112	5	only	only	ADV
ejpam-6834	112	6	with	with	ADP
ejpam-6834	112	7	finite	finite	ADJ
ejpam-6834	112	8	sets	set	NOUN
ejpam-6834	112	9	;	;	PUNCT
ejpam-6834	112	10	issues	issue	NOUN
ejpam-6834	112	11	related	relate	VERB
ejpam-6834	112	12	to	to	ADP
ejpam-6834	112	13	infinity	infinity	NOUN
ejpam-6834	112	14	are	be	AUX
ejpam-6834	112	15	not	not	PART
ejpam-6834	112	16	considered	consider	VERB
ejpam-6834	112	17	.	.	PUNCT
ejpam-6834	113	1	2.1	2.1	NUM
ejpam-6834	113	2	.	.	PUNCT
ejpam-6834	113	3	superhyperstructure	superhyperstructure	NOUN
ejpam-6834	113	4	in	in	ADP
ejpam-6834	113	5	this	this	DET
ejpam-6834	113	6	context	context	NOUN
ejpam-6834	113	7	,	,	PUNCT
ejpam-6834	113	8	a	a	DET
ejpam-6834	113	9	classical	classical	ADJ
ejpam-6834	113	10	structure	structure	NOUN
ejpam-6834	113	11	refers	refer	VERB
ejpam-6834	113	12	to	to	ADP
ejpam-6834	113	13	any	any	DET
ejpam-6834	113	14	mathematical	mathematical	ADJ
ejpam-6834	113	15	or	or	CCONJ
ejpam-6834	113	16	real	real	ADJ
ejpam-6834	113	17	–	–	PUNCT
ejpam-6834	113	18	world	world	NOUN
ejpam-6834	113	19	structure	structure	NOUN
ejpam-6834	113	20	or	or	CCONJ
ejpam-6834	113	21	concept	concept	NOUN
ejpam-6834	113	22	.	.	PUNCT
ejpam-6834	114	1	to	to	PART
ejpam-6834	114	2	capture	capture	VERB
ejpam-6834	114	3	such	such	ADJ
ejpam-6834	114	4	structures	structure	NOUN
ejpam-6834	114	5	in	in	ADP
ejpam-6834	114	6	a	a	DET
ejpam-6834	114	7	hierarchical	hierarchical	ADJ
ejpam-6834	114	8	manner	manner	NOUN
ejpam-6834	114	9	,	,	PUNCT
ejpam-6834	114	10	hyperstructures	hyperstructure	NOUN
ejpam-6834	114	11	are	be	AUX
ejpam-6834	114	12	introduced	introduce	VERB
ejpam-6834	114	13	.	.	PUNCT
ejpam-6834	115	1	a	a	DET
ejpam-6834	115	2	hyperstructure	hyperstructure	NOUN
ejpam-6834	115	3	is	be	AUX
ejpam-6834	115	4	a	a	DET
ejpam-6834	115	5	mathematical	mathematical	ADJ
ejpam-6834	115	6	framework	framework	NOUN
ejpam-6834	115	7	in	in	ADP
ejpam-6834	115	8	which	which	PRON
ejpam-6834	115	9	operations	operation	NOUN
ejpam-6834	115	10	on	on	ADP
ejpam-6834	115	11	elements	element	NOUN
ejpam-6834	115	12	return	return	VERB
ejpam-6834	115	13	sets	set	NOUN
ejpam-6834	115	14	rather	rather	ADV
ejpam-6834	115	15	than	than	ADP
ejpam-6834	115	16	single	single	ADJ
ejpam-6834	115	17	outcomes	outcome	NOUN
ejpam-6834	115	18	,	,	PUNCT
ejpam-6834	115	19	thereby	thereby	ADV
ejpam-6834	115	20	enabling	enable	VERB
ejpam-6834	115	21	multivalued	multivalue	VERB
ejpam-6834	115	22	algebraic	algebraic	ADJ
ejpam-6834	115	23	relations	relation	NOUN
ejpam-6834	115	24	on	on	ADP
ejpam-6834	115	25	a	a	DET
ejpam-6834	115	26	base	base	NOUN
ejpam-6834	115	27	set[28	set[28	NOUN
ejpam-6834	115	28	,	,	PUNCT
ejpam-6834	115	29	29	29	NUM
ejpam-6834	115	30	]	]	PUNCT
ejpam-6834	115	31	.	.	PUNCT
ejpam-6834	116	1	a	a	DET
ejpam-6834	116	2	superhyperstructure	superhyperstructure	NOUN
ejpam-6834	116	3	generalizes	generalize	VERB
ejpam-6834	116	4	hyperstructures	hyperstructure	NOUN
ejpam-6834	116	5	by	by	ADP
ejpam-6834	116	6	permitting	permit	VERB
ejpam-6834	116	7	operations	operation	NOUN
ejpam-6834	116	8	on	on	ADP
ejpam-6834	116	9	higher	high	ADJ
ejpam-6834	116	10	–	–	PUNCT
ejpam-6834	116	11	order	order	NOUN
ejpam-6834	116	12	collections	collection	NOUN
ejpam-6834	116	13	such	such	ADJ
ejpam-6834	116	14	as	as	ADP
ejpam-6834	116	15	iterated	iterated	ADJ
ejpam-6834	116	16	powersets	powerset	NOUN
ejpam-6834	116	17	,	,	PUNCT
ejpam-6834	116	18	supporting	support	VERB
ejpam-6834	116	19	multiple	multiple	ADJ
ejpam-6834	116	20	input	input	NOUN
ejpam-6834	116	21	and	and	CCONJ
ejpam-6834	116	22	output	output	NOUN
ejpam-6834	116	23	arities	arity	NOUN
ejpam-6834	116	24	,	,	PUNCT
ejpam-6834	116	25	and	and	CCONJ
ejpam-6834	116	26	modeling	modeling	NOUN
ejpam-6834	116	27	layered	layer	VERB
ejpam-6834	116	28	,	,	PUNCT
ejpam-6834	116	29	hierarchical	hierarchical	ADJ
ejpam-6834	116	30	uncertainty	uncertainty	NOUN
ejpam-6834	116	31	[	[	X
ejpam-6834	116	32	28	28	NUM
ejpam-6834	116	33	,	,	PUNCT
ejpam-6834	116	34	29	29	NUM
ejpam-6834	116	35	]	]	PUNCT
ejpam-6834	116	36	.	.	PUNCT
ejpam-6834	117	1	first	first	ADV
ejpam-6834	117	2	,	,	PUNCT
ejpam-6834	117	3	we	we	PRON
ejpam-6834	117	4	record	record	VERB
ejpam-6834	117	5	formal	formal	ADJ
ejpam-6834	117	6	definitions	definition	NOUN
ejpam-6834	117	7	of	of	ADP
ejpam-6834	117	8	the	the	DET
ejpam-6834	117	9	powerset	powerset	NOUN
ejpam-6834	117	10	,	,	PUNCT
ejpam-6834	117	11	the	the	DET
ejpam-6834	117	12	n	n	CCONJ
ejpam-6834	117	13	-	-	PUNCT
ejpam-6834	117	14	th	th	X
ejpam-6834	117	15	powerset	powerset	NOUN
ejpam-6834	117	16	,	,	PUNCT
ejpam-6834	117	17	and	and	CCONJ
ejpam-6834	117	18	their	their	PRON
ejpam-6834	117	19	nonempty	nonempty	ADJ
ejpam-6834	117	20	variants	variant	NOUN
ejpam-6834	117	21	,	,	PUNCT
ejpam-6834	117	22	followed	follow	VERB
ejpam-6834	117	23	by	by	ADP
ejpam-6834	117	24	an	an	DET
ejpam-6834	117	25	illustrative	illustrative	ADJ
ejpam-6834	117	26	example	example	NOUN
ejpam-6834	117	27	.	.	PUNCT
ejpam-6834	118	1	note	note	VERB
ejpam-6834	118	2	that	that	SCONJ
ejpam-6834	118	3	the	the	DET
ejpam-6834	118	4	n	n	ADV
ejpam-6834	118	5	-	-	PUNCT
ejpam-6834	118	6	th	th	VERB
ejpam-6834	118	7	powerset	powerset	NOUN
ejpam-6834	118	8	of	of	ADP
ejpam-6834	118	9	a	a	DET
ejpam-6834	118	10	set	set	NOUN
ejpam-6834	118	11	s	s	PART
ejpam-6834	118	12	is	be	AUX
ejpam-6834	118	13	obtained	obtain	VERB
ejpam-6834	118	14	by	by	ADP
ejpam-6834	118	15	iterating	iterate	VERB
ejpam-6834	118	16	the	the	DET
ejpam-6834	118	17	powerset	powerset	NOUN
ejpam-6834	118	18	operator	operator	NOUN
ejpam-6834	118	19	n	n	PRON
ejpam-6834	118	20	times	time	NOUN
ejpam-6834	118	21	,	,	PUNCT
ejpam-6834	118	22	producing	produce	VERB
ejpam-6834	118	23	pn(s	pn(s	NOUN
ejpam-6834	118	24	)	)	PUNCT
ejpam-6834	118	25	=	=	SYM
ejpam-6834	118	26	p(pn−1(s	p(pn−1(s	PROPN
ejpam-6834	118	27	)	)	PUNCT
ejpam-6834	118	28	)	)	PUNCT
ejpam-6834	118	29	,	,	PUNCT
ejpam-6834	118	30	thereby	thereby	ADV
ejpam-6834	118	31	encoding	encode	VERB
ejpam-6834	118	32	higher	high	ADJ
ejpam-6834	118	33	-	-	PUNCT
ejpam-6834	118	34	order	order	NOUN
ejpam-6834	118	35	collections	collection	NOUN
ejpam-6834	118	36	of	of	ADP
ejpam-6834	118	37	subsets	subset	NOUN
ejpam-6834	118	38	and	and	CCONJ
ejpam-6834	118	39	supporting	support	VERB
ejpam-6834	118	40	layered	layer	VERB
ejpam-6834	118	41	,	,	PUNCT
ejpam-6834	118	42	hierarchical	hierarchical	ADJ
ejpam-6834	118	43	structures	structure	NOUN
ejpam-6834	118	44	[	[	X
ejpam-6834	118	45	28	28	NUM
ejpam-6834	118	46	,	,	PUNCT
ejpam-6834	118	47	29	29	NUM
ejpam-6834	118	48	]	]	PUNCT
ejpam-6834	118	49	.	.	PUNCT
ejpam-6834	119	1	t.	t.	PROPN
ejpam-6834	119	2	fujita	fujita	PROPN
ejpam-6834	119	3	,	,	PUNCT
ejpam-6834	119	4	f.smarandache	f.smarandache	NOUN
ejpam-6834	119	5	/	/	SYM
ejpam-6834	119	6	eur	eur	PROPN
ejpam-6834	119	7	.	.	PUNCT
ejpam-6834	120	1	j.	j.	PROPN
ejpam-6834	120	2	pure	pure	PROPN
ejpam-6834	120	3	appl	appl	PROPN
ejpam-6834	120	4	.	.	PROPN
ejpam-6834	120	5	math	math	PROPN
ejpam-6834	120	6	,	,	PUNCT
ejpam-6834	120	7	18	18	NUM
ejpam-6834	120	8	(	(	PUNCT
ejpam-6834	120	9	4	4	NUM
ejpam-6834	120	10	)	)	PUNCT
ejpam-6834	120	11	(	(	PUNCT
ejpam-6834	120	12	2025	2025	NUM
ejpam-6834	120	13	)	)	PUNCT
ejpam-6834	120	14	,	,	PUNCT
ejpam-6834	120	15	6834	6834	NUM
ejpam-6834	120	16	6	6	NUM
ejpam-6834	120	17	of	of	ADP
ejpam-6834	120	18	69	69	NUM
ejpam-6834	120	19	definition	definition	NOUN
ejpam-6834	120	20	1	1	NUM
ejpam-6834	120	21	(	(	PUNCT
ejpam-6834	120	22	base	base	NOUN
ejpam-6834	120	23	set	set	NOUN
ejpam-6834	120	24	)	)	PUNCT
ejpam-6834	120	25	.	.	PUNCT
ejpam-6834	121	1	a	a	DET
ejpam-6834	121	2	base	base	NOUN
ejpam-6834	121	3	set	set	NOUN
ejpam-6834	121	4	s	s	VERB
ejpam-6834	121	5	is	be	AUX
ejpam-6834	121	6	the	the	DET
ejpam-6834	121	7	underlying	underlie	VERB
ejpam-6834	121	8	set	set	NOUN
ejpam-6834	121	9	from	from	ADP
ejpam-6834	121	10	which	which	PRON
ejpam-6834	121	11	constructions	construction	NOUN
ejpam-6834	121	12	such	such	ADJ
ejpam-6834	121	13	as	as	ADP
ejpam-6834	121	14	powersets	powerset	NOUN
ejpam-6834	121	15	,	,	PUNCT
ejpam-6834	121	16	hyperstructures	hyperstructure	NOUN
ejpam-6834	121	17	,	,	PUNCT
ejpam-6834	121	18	and	and	CCONJ
ejpam-6834	121	19	superhyperstructures	superhyperstructure	NOUN
ejpam-6834	121	20	are	be	AUX
ejpam-6834	121	21	built	build	VERB
ejpam-6834	121	22	.	.	PUNCT
ejpam-6834	122	1	formally	formally	ADV
ejpam-6834	122	2	,	,	PUNCT
ejpam-6834	122	3	s	s	VERB
ejpam-6834	122	4	=	=	PUNCT
ejpam-6834	122	5	{	{	PUNCT
ejpam-6834	122	6	x	x	INTJ
ejpam-6834	122	7	|	|	ADV
ejpam-6834	122	8	x	x	INTJ
ejpam-6834	122	9	is	be	AUX
ejpam-6834	122	10	an	an	DET
ejpam-6834	122	11	element	element	NOUN
ejpam-6834	122	12	in	in	ADP
ejpam-6834	122	13	the	the	DET
ejpam-6834	122	14	specified	specified	ADJ
ejpam-6834	122	15	domain	domain	NOUN
ejpam-6834	122	16	}	}	PUNCT
ejpam-6834	122	17	.	.	PUNCT
ejpam-6834	123	1	all	all	DET
ejpam-6834	123	2	elements	element	NOUN
ejpam-6834	123	3	of	of	ADP
ejpam-6834	123	4	objects	object	NOUN
ejpam-6834	123	5	like	like	ADP
ejpam-6834	123	6	p(s	p(s	NOUN
ejpam-6834	123	7	)	)	PUNCT
ejpam-6834	123	8	or	or	CCONJ
ejpam-6834	123	9	pn(s	pn(s	NUM
ejpam-6834	123	10	)	)	PUNCT
ejpam-6834	123	11	are	be	AUX
ejpam-6834	123	12	ultimately	ultimately	ADV
ejpam-6834	123	13	drawn	draw	VERB
ejpam-6834	123	14	from	from	ADP
ejpam-6834	123	15	s.	s.	PROPN
ejpam-6834	123	16	definition	definition	NOUN
ejpam-6834	123	17	2	2	NUM
ejpam-6834	123	18	(	(	PUNCT
ejpam-6834	123	19	powerset	powerset	NOUN
ejpam-6834	123	20	)	)	PUNCT
ejpam-6834	123	21	.	.	PUNCT
ejpam-6834	124	1	the	the	DET
ejpam-6834	124	2	powerset	powerset	NOUN
ejpam-6834	124	3	of	of	ADP
ejpam-6834	124	4	a	a	DET
ejpam-6834	124	5	set	set	NOUN
ejpam-6834	124	6	s	s	PROPN
ejpam-6834	124	7	,	,	PUNCT
ejpam-6834	124	8	denoted	denote	VERB
ejpam-6834	124	9	p(s	p(s	NOUN
ejpam-6834	124	10	)	)	PUNCT
ejpam-6834	124	11	,	,	PUNCT
ejpam-6834	124	12	is	be	AUX
ejpam-6834	124	13	the	the	DET
ejpam-6834	124	14	set	set	NOUN
ejpam-6834	124	15	of	of	ADP
ejpam-6834	124	16	all	all	DET
ejpam-6834	124	17	subsets	subset	NOUN
ejpam-6834	124	18	of	of	ADP
ejpam-6834	124	19	s	s	PRON
ejpam-6834	124	20	(	(	PUNCT
ejpam-6834	124	21	including	include	VERB
ejpam-6834	124	22	∅	∅	NOUN
ejpam-6834	124	23	and	and	CCONJ
ejpam-6834	124	24	s	s	PRON
ejpam-6834	124	25	itself	itself	PRON
ejpam-6834	124	26	):	):	PUNCT
ejpam-6834	124	27	p(s	p(s	NUM
ejpam-6834	124	28	)	)	PUNCT
ejpam-6834	125	1	=	=	PRON
ejpam-6834	125	2	{	{	PUNCT
ejpam-6834	125	3	a	a	DET
ejpam-6834	125	4	|	|	NOUN
ejpam-6834	125	5	a	a	DET
ejpam-6834	125	6	⊆	⊆	NUM
ejpam-6834	125	7	s	s	NOUN
ejpam-6834	125	8	}	}	PUNCT
ejpam-6834	125	9	.	.	PUNCT
ejpam-6834	126	1	we	we	PRON
ejpam-6834	126	2	also	also	ADV
ejpam-6834	126	3	write	write	VERB
ejpam-6834	126	4	the	the	DET
ejpam-6834	126	5	non	non	ADJ
ejpam-6834	126	6	-	-	ADJ
ejpam-6834	126	7	empty	empty	ADJ
ejpam-6834	126	8	powerset	powerset	NOUN
ejpam-6834	126	9	as	as	ADP
ejpam-6834	126	10	p∗(s	p∗(s	NOUN
ejpam-6834	126	11	)	)	PUNCT
ejpam-6834	126	12	=	=	SYM
ejpam-6834	126	13	p(s	p(s	NUM
ejpam-6834	126	14	)	)	PUNCT
ejpam-6834	126	15	\	\	NOUN
ejpam-6834	126	16	{	{	PUNCT
ejpam-6834	126	17	∅	∅	NOUN
ejpam-6834	126	18	}	}	PUNCT
ejpam-6834	126	19	.	.	PUNCT
ejpam-6834	127	1	definition	definition	NOUN
ejpam-6834	127	2	3	3	NUM
ejpam-6834	127	3	(	(	PUNCT
ejpam-6834	127	4	n	n	CCONJ
ejpam-6834	127	5	-	-	PUNCT
ejpam-6834	127	6	th	th	X
ejpam-6834	127	7	powerset	powerset	NOUN
ejpam-6834	127	8	and	and	CCONJ
ejpam-6834	127	9	n	n	CCONJ
ejpam-6834	127	10	-	-	PUNCT
ejpam-6834	127	11	th	th	X
ejpam-6834	127	12	non	non	ADJ
ejpam-6834	127	13	-	-	ADJ
ejpam-6834	127	14	empty	empty	ADJ
ejpam-6834	127	15	powerset	powerset	NOUN
ejpam-6834	127	16	)	)	PUNCT
ejpam-6834	127	17	.	.	PUNCT
ejpam-6834	128	1	(	(	PUNCT
ejpam-6834	128	2	cf	cf	AUX
ejpam-6834	128	3	.	.	NOUN
ejpam-6834	128	4	,[28	,[28	PUNCT
ejpam-6834	128	5	,	,	PUNCT
ejpam-6834	128	6	29	29	NUM
ejpam-6834	128	7	]	]	PUNCT
ejpam-6834	128	8	)	)	PUNCT
ejpam-6834	128	9	for	for	ADP
ejpam-6834	128	10	a	a	DET
ejpam-6834	128	11	set	set	ADJ
ejpam-6834	128	12	h	h	NOUN
ejpam-6834	128	13	and	and	CCONJ
ejpam-6834	128	14	an	an	DET
ejpam-6834	128	15	integer	integer	NOUN
ejpam-6834	128	16	n	n	PRON
ejpam-6834	128	17	≥	≥	NOUN
ejpam-6834	128	18	1	1	NUM
ejpam-6834	128	19	,	,	PUNCT
ejpam-6834	128	20	define	define	VERB
ejpam-6834	128	21	recursively	recursively	ADV
ejpam-6834	128	22	p1(h	p1(h	NOUN
ejpam-6834	128	23	)	)	PUNCT
ejpam-6834	128	24	=	=	SYM
ejpam-6834	128	25	p(h	p(h	PROPN
ejpam-6834	128	26	)	)	PUNCT
ejpam-6834	128	27	,	,	PUNCT
ejpam-6834	128	28	pn+1(h	pn+1(h	PROPN
ejpam-6834	128	29	)	)	PUNCT
ejpam-6834	129	1	=	=	SYM
ejpam-6834	130	1	p	p	X
ejpam-6834	130	2	(	(	PUNCT
ejpam-6834	130	3	pn(h	pn(h	NOUN
ejpam-6834	130	4	)	)	PUNCT
ejpam-6834	130	5	)	)	PUNCT
ejpam-6834	130	6	.	.	PUNCT
ejpam-6834	131	1	similarly	similarly	ADV
ejpam-6834	131	2	,	,	PUNCT
ejpam-6834	131	3	set	set	VERB
ejpam-6834	131	4	p∗	p∗	NOUN
ejpam-6834	131	5	1	1	NUM
ejpam-6834	131	6	(	(	PUNCT
ejpam-6834	131	7	h	h	NOUN
ejpam-6834	131	8	)	)	PUNCT
ejpam-6834	131	9	=	=	SYM
ejpam-6834	131	10	p∗(h	p∗(h	PROPN
ejpam-6834	131	11	)	)	PUNCT
ejpam-6834	131	12	,	,	PUNCT
ejpam-6834	131	13	p∗	p∗	PROPN
ejpam-6834	131	14	n+1(h	n+1(h	PROPN
ejpam-6834	131	15	)	)	PUNCT
ejpam-6834	131	16	=	=	SYM
ejpam-6834	131	17	p∗(p∗	p∗(p∗	NOUN
ejpam-6834	131	18	n(h	n(h	PROPN
ejpam-6834	131	19	)	)	PUNCT
ejpam-6834	131	20	)	)	PUNCT
ejpam-6834	131	21	.	.	PUNCT
ejpam-6834	132	1	thus	thus	ADV
ejpam-6834	132	2	pn(h	pn(h	NOUN
ejpam-6834	132	3	)	)	PUNCT
ejpam-6834	132	4	(	(	PUNCT
ejpam-6834	132	5	resp	resp	NOUN
ejpam-6834	132	6	.	.	PUNCT
ejpam-6834	133	1	p∗	p∗	PROPN
ejpam-6834	133	2	n(h	n(h	PROPN
ejpam-6834	133	3	)	)	PUNCT
ejpam-6834	133	4	)	)	PUNCT
ejpam-6834	133	5	is	be	AUX
ejpam-6834	133	6	obtained	obtain	VERB
ejpam-6834	133	7	by	by	ADP
ejpam-6834	133	8	iterating	iterate	VERB
ejpam-6834	133	9	the	the	DET
ejpam-6834	133	10	(	(	PUNCT
ejpam-6834	133	11	non	non	ADJ
ejpam-6834	133	12	-	-	ADJ
ejpam-6834	133	13	empty	empty	ADJ
ejpam-6834	133	14	)	)	PUNCT
ejpam-6834	133	15	powerset	powerset	NOUN
ejpam-6834	133	16	operator	operator	NOUN
ejpam-6834	133	17	n	n	PROPN
ejpam-6834	133	18	times	time	NOUN
ejpam-6834	133	19	.	.	PUNCT
ejpam-6834	134	1	example	example	NOUN
ejpam-6834	134	2	1	1	NUM
ejpam-6834	134	3	(	(	PUNCT
ejpam-6834	134	4	n	n	CCONJ
ejpam-6834	134	5	-	-	PUNCT
ejpam-6834	134	6	th	th	VERB
ejpam-6834	134	7	powerset	powerset	NOUN
ejpam-6834	134	8	:	:	PUNCT
ejpam-6834	134	9	a	a	DET
ejpam-6834	134	10	concrete	concrete	ADJ
ejpam-6834	134	11	instance	instance	NOUN
ejpam-6834	134	12	)	)	PUNCT
ejpam-6834	134	13	.	.	PUNCT
ejpam-6834	135	1	let	let	VERB
ejpam-6834	135	2	h	h	NOUN
ejpam-6834	135	3	=	=	PUNCT
ejpam-6834	135	4	{	{	PUNCT
ejpam-6834	135	5	a	a	DET
ejpam-6834	135	6	,	,	PUNCT
ejpam-6834	135	7	b	b	NOUN
ejpam-6834	135	8	}	}	PUNCT
ejpam-6834	135	9	.	.	PUNCT
ejpam-6834	136	1	then	then	ADV
ejpam-6834	136	2	p1(h	p1(h	NOUN
ejpam-6834	136	3	)	)	PUNCT
ejpam-6834	136	4	=	=	SYM
ejpam-6834	136	5	p(h	p(h	PROPN
ejpam-6834	136	6	)	)	PUNCT
ejpam-6834	137	1	=	=	SYM
ejpam-6834	137	2	{	{	PUNCT
ejpam-6834	137	3	∅	∅	NOUN
ejpam-6834	137	4	,	,	PUNCT
ejpam-6834	137	5	{	{	PUNCT
ejpam-6834	137	6	a	a	X
ejpam-6834	137	7	}	}	PUNCT
ejpam-6834	137	8	,	,	PUNCT
ejpam-6834	137	9	{	{	PUNCT
ejpam-6834	137	10	b	b	NOUN
ejpam-6834	137	11	}	}	PUNCT
ejpam-6834	137	12	,	,	PUNCT
ejpam-6834	137	13	{	{	PUNCT
ejpam-6834	137	14	a	a	DET
ejpam-6834	137	15	,	,	PUNCT
ejpam-6834	137	16	b	b	NOUN
ejpam-6834	137	17	}	}	PUNCT
ejpam-6834	137	18	}	}	PUNCT
ejpam-6834	137	19	.	.	PUNCT
ejpam-6834	138	1	the	the	DET
ejpam-6834	138	2	second	second	ADJ
ejpam-6834	138	3	powerset	powerset	NOUN
ejpam-6834	138	4	p2(h	p2(h	NOUN
ejpam-6834	138	5	)	)	PUNCT
ejpam-6834	138	6	=	=	SYM
ejpam-6834	139	1	p	p	X
ejpam-6834	139	2	(	(	PUNCT
ejpam-6834	139	3	p1(h	p1(h	PROPN
ejpam-6834	139	4	)	)	PUNCT
ejpam-6834	139	5	)	)	PUNCT
ejpam-6834	139	6	is	be	AUX
ejpam-6834	139	7	the	the	DET
ejpam-6834	139	8	set	set	NOUN
ejpam-6834	139	9	of	of	ADP
ejpam-6834	139	10	all	all	DET
ejpam-6834	139	11	subsets	subset	NOUN
ejpam-6834	139	12	of	of	ADP
ejpam-6834	139	13	p1(h	p1(h	PROPN
ejpam-6834	139	14	)	)	PUNCT
ejpam-6834	139	15	.	.	PUNCT
ejpam-6834	140	1	since	since	SCONJ
ejpam-6834	140	2	p1(h	p1(h	PROPN
ejpam-6834	140	3	)	)	PUNCT
ejpam-6834	140	4	has	have	VERB
ejpam-6834	140	5	four	four	NUM
ejpam-6834	140	6	elements	element	NOUN
ejpam-6834	140	7	,	,	PUNCT
ejpam-6834	140	8	p2(h	p2(h	NUM
ejpam-6834	140	9	)	)	PUNCT
ejpam-6834	140	10	has	have	VERB
ejpam-6834	140	11	24	24	NUM
ejpam-6834	140	12	=	=	SYM
ejpam-6834	140	13	16	16	NUM
ejpam-6834	140	14	elements	element	NOUN
ejpam-6834	140	15	,	,	PUNCT
ejpam-6834	140	16	which	which	PRON
ejpam-6834	140	17	we	we	PRON
ejpam-6834	140	18	list	list	VERB
ejpam-6834	140	19	by	by	ADP
ejpam-6834	140	20	cardinality	cardinality	NOUN
ejpam-6834	140	21	:	:	PUNCT
ejpam-6834	140	22	size	size	NOUN
ejpam-6834	140	23	0	0	NUM
ejpam-6834	140	24	:	:	PUNCT
ejpam-6834	140	25	{	{	PUNCT
ejpam-6834	140	26	∅	∅	NOUN
ejpam-6834	140	27	}	}	PUNCT
ejpam-6834	140	28	,	,	PUNCT
ejpam-6834	140	29	size	size	NOUN
ejpam-6834	140	30	1	1	NUM
ejpam-6834	140	31	:	:	PUNCT
ejpam-6834	140	32	{	{	PUNCT
ejpam-6834	140	33	{	{	PUNCT
ejpam-6834	140	34	∅	∅	NOUN
ejpam-6834	140	35	}	}	PUNCT
ejpam-6834	140	36	}	}	PUNCT
ejpam-6834	140	37	,	,	PUNCT
ejpam-6834	140	38	{	{	PUNCT
ejpam-6834	140	39	{	{	PUNCT
ejpam-6834	140	40	{	{	PUNCT
ejpam-6834	140	41	a	a	X
ejpam-6834	140	42	}	}	PUNCT
ejpam-6834	140	43	}	}	PUNCT
ejpam-6834	140	44	}	}	PUNCT
ejpam-6834	140	45	,	,	PUNCT
ejpam-6834	140	46	{	{	PUNCT
ejpam-6834	140	47	{	{	PUNCT
ejpam-6834	140	48	{	{	PUNCT
ejpam-6834	140	49	b	b	NOUN
ejpam-6834	140	50	}	}	PUNCT
ejpam-6834	140	51	}	}	PUNCT
ejpam-6834	140	52	}	}	PUNCT
ejpam-6834	140	53	,	,	PUNCT
ejpam-6834	140	54	{	{	PUNCT
ejpam-6834	140	55	{	{	PUNCT
ejpam-6834	140	56	{	{	PUNCT
ejpam-6834	140	57	a	a	PROPN
ejpam-6834	140	58	,	,	PUNCT
ejpam-6834	140	59	b	b	NOUN
ejpam-6834	140	60	}	}	PUNCT
ejpam-6834	140	61	}	}	PUNCT
ejpam-6834	140	62	}	}	PUNCT
ejpam-6834	140	63	,	,	PUNCT
ejpam-6834	140	64	size	size	NOUN
ejpam-6834	140	65	2	2	NUM
ejpam-6834	140	66	:	:	PUNCT
ejpam-6834	140	67	{	{	PUNCT
ejpam-6834	140	68	{	{	PUNCT
ejpam-6834	140	69	∅	∅	NOUN
ejpam-6834	140	70	}	}	PUNCT
ejpam-6834	140	71	,	,	PUNCT
ejpam-6834	140	72	{	{	PUNCT
ejpam-6834	140	73	{	{	PUNCT
ejpam-6834	140	74	a	a	X
ejpam-6834	140	75	}	}	PUNCT
ejpam-6834	140	76	}	}	PUNCT
ejpam-6834	140	77	}	}	PUNCT
ejpam-6834	140	78	,	,	PUNCT
ejpam-6834	140	79	{	{	PUNCT
ejpam-6834	140	80	{	{	PUNCT
ejpam-6834	140	81	∅	∅	NOUN
ejpam-6834	140	82	}	}	PUNCT
ejpam-6834	140	83	,	,	PUNCT
ejpam-6834	140	84	{	{	PUNCT
ejpam-6834	140	85	{	{	PUNCT
ejpam-6834	140	86	b	b	NOUN
ejpam-6834	140	87	}	}	PUNCT
ejpam-6834	140	88	}	}	PUNCT
ejpam-6834	140	89	}	}	PUNCT
ejpam-6834	140	90	,	,	PUNCT
ejpam-6834	140	91	{	{	PUNCT
ejpam-6834	140	92	{	{	PUNCT
ejpam-6834	140	93	∅	∅	NOUN
ejpam-6834	140	94	}	}	PUNCT
ejpam-6834	140	95	,	,	PUNCT
ejpam-6834	140	96	{	{	PUNCT
ejpam-6834	140	97	{	{	PUNCT
ejpam-6834	140	98	a	a	PROPN
ejpam-6834	140	99	,	,	PUNCT
ejpam-6834	140	100	b	b	NOUN
ejpam-6834	140	101	}	}	PUNCT
ejpam-6834	140	102	}	}	PUNCT
ejpam-6834	140	103	}	}	PUNCT
ejpam-6834	140	104	,	,	PUNCT
ejpam-6834	140	105	{	{	PUNCT
ejpam-6834	140	106	{	{	PUNCT
ejpam-6834	140	107	{	{	PUNCT
ejpam-6834	140	108	a	a	NOUN
ejpam-6834	140	109	}	}	PUNCT
ejpam-6834	140	110	}	}	PUNCT
ejpam-6834	140	111	,	,	PUNCT
ejpam-6834	140	112	{	{	PUNCT
ejpam-6834	140	113	{	{	PUNCT
ejpam-6834	140	114	b	b	NOUN
ejpam-6834	140	115	}	}	PUNCT
ejpam-6834	140	116	}	}	PUNCT
ejpam-6834	140	117	}	}	PUNCT
ejpam-6834	140	118	,	,	PUNCT
ejpam-6834	140	119	{	{	PUNCT
ejpam-6834	140	120	{	{	PUNCT
ejpam-6834	140	121	{	{	PUNCT
ejpam-6834	140	122	a	a	NOUN
ejpam-6834	140	123	}	}	PUNCT
ejpam-6834	140	124	}	}	PUNCT
ejpam-6834	140	125	,	,	PUNCT
ejpam-6834	140	126	{	{	PUNCT
ejpam-6834	140	127	{	{	PUNCT
ejpam-6834	140	128	a	a	PROPN
ejpam-6834	140	129	,	,	PUNCT
ejpam-6834	140	130	b	b	NOUN
ejpam-6834	140	131	}	}	PUNCT
ejpam-6834	140	132	}	}	PUNCT
ejpam-6834	140	133	}	}	PUNCT
ejpam-6834	140	134	,	,	PUNCT
ejpam-6834	140	135	{	{	PUNCT
ejpam-6834	140	136	{	{	PUNCT
ejpam-6834	140	137	{	{	PUNCT
ejpam-6834	140	138	b	b	NOUN
ejpam-6834	140	139	}	}	PUNCT
ejpam-6834	140	140	}	}	PUNCT
ejpam-6834	140	141	,	,	PUNCT
ejpam-6834	140	142	{	{	PUNCT
ejpam-6834	140	143	{	{	PUNCT
ejpam-6834	140	144	a	a	PROPN
ejpam-6834	140	145	,	,	PUNCT
ejpam-6834	140	146	b	b	NOUN
ejpam-6834	140	147	}	}	PUNCT
ejpam-6834	140	148	}	}	PUNCT
ejpam-6834	140	149	}	}	PUNCT
ejpam-6834	140	150	,	,	PUNCT
ejpam-6834	140	151	size	size	NOUN
ejpam-6834	140	152	3	3	NUM
ejpam-6834	140	153	:	:	PUNCT
ejpam-6834	140	154	{	{	PUNCT
ejpam-6834	140	155	{	{	PUNCT
ejpam-6834	140	156	∅	∅	NOUN
ejpam-6834	140	157	}	}	PUNCT
ejpam-6834	140	158	,	,	PUNCT
ejpam-6834	140	159	{	{	PUNCT
ejpam-6834	140	160	{	{	PUNCT
ejpam-6834	140	161	a	a	X
ejpam-6834	140	162	}	}	PUNCT
ejpam-6834	140	163	}	}	PUNCT
ejpam-6834	140	164	,	,	PUNCT
ejpam-6834	140	165	{	{	PUNCT
ejpam-6834	140	166	{	{	PUNCT
ejpam-6834	140	167	b	b	NOUN
ejpam-6834	140	168	}	}	PUNCT
ejpam-6834	140	169	}	}	PUNCT
ejpam-6834	140	170	}	}	PUNCT
ejpam-6834	140	171	,	,	PUNCT
ejpam-6834	140	172	{	{	PUNCT
ejpam-6834	140	173	{	{	PUNCT
ejpam-6834	140	174	∅	∅	NOUN
ejpam-6834	140	175	}	}	PUNCT
ejpam-6834	140	176	,	,	PUNCT
ejpam-6834	140	177	{	{	PUNCT
ejpam-6834	140	178	{	{	PUNCT
ejpam-6834	140	179	a	a	X
ejpam-6834	140	180	}	}	PUNCT
ejpam-6834	140	181	}	}	PUNCT
ejpam-6834	140	182	,	,	PUNCT
ejpam-6834	140	183	{	{	PUNCT
ejpam-6834	140	184	{	{	PUNCT
ejpam-6834	140	185	a	a	PROPN
ejpam-6834	140	186	,	,	PUNCT
ejpam-6834	140	187	b	b	NOUN
ejpam-6834	140	188	}	}	PUNCT
ejpam-6834	140	189	}	}	PUNCT
ejpam-6834	140	190	}	}	PUNCT
ejpam-6834	140	191	,	,	PUNCT
ejpam-6834	140	192	{	{	PUNCT
ejpam-6834	140	193	{	{	PUNCT
ejpam-6834	140	194	∅	∅	NOUN
ejpam-6834	140	195	}	}	PUNCT
ejpam-6834	140	196	,	,	PUNCT
ejpam-6834	140	197	{	{	PUNCT
ejpam-6834	140	198	{	{	PUNCT
ejpam-6834	140	199	b	b	NOUN
ejpam-6834	140	200	}	}	PUNCT
ejpam-6834	140	201	}	}	PUNCT
ejpam-6834	140	202	,	,	PUNCT
ejpam-6834	140	203	{	{	PUNCT
ejpam-6834	140	204	{	{	PUNCT
ejpam-6834	140	205	a	a	PROPN
ejpam-6834	140	206	,	,	PUNCT
ejpam-6834	140	207	b	b	NOUN
ejpam-6834	140	208	}	}	PUNCT
ejpam-6834	140	209	}	}	PUNCT
ejpam-6834	140	210	}	}	PUNCT
ejpam-6834	140	211	,	,	PUNCT
ejpam-6834	140	212	{	{	PUNCT
ejpam-6834	140	213	{	{	PUNCT
ejpam-6834	140	214	{	{	PUNCT
ejpam-6834	140	215	a	a	NOUN
ejpam-6834	140	216	}	}	PUNCT
ejpam-6834	140	217	}	}	PUNCT
ejpam-6834	140	218	,	,	PUNCT
ejpam-6834	140	219	{	{	PUNCT
ejpam-6834	140	220	{	{	PUNCT
ejpam-6834	140	221	b	b	NOUN
ejpam-6834	140	222	}	}	PUNCT
ejpam-6834	140	223	}	}	PUNCT
ejpam-6834	140	224	,	,	PUNCT
ejpam-6834	140	225	{	{	PUNCT
ejpam-6834	140	226	{	{	PUNCT
ejpam-6834	140	227	a	a	PROPN
ejpam-6834	140	228	,	,	PUNCT
ejpam-6834	140	229	b	b	NOUN
ejpam-6834	140	230	}	}	PUNCT
ejpam-6834	140	231	}	}	PUNCT
ejpam-6834	140	232	}	}	PUNCT
ejpam-6834	140	233	,	,	PUNCT
ejpam-6834	140	234	size	size	NOUN
ejpam-6834	140	235	4	4	NUM
ejpam-6834	140	236	:	:	PUNCT
ejpam-6834	140	237	{	{	PUNCT
ejpam-6834	140	238	{	{	PUNCT
ejpam-6834	140	239	∅	∅	NOUN
ejpam-6834	140	240	}	}	PUNCT
ejpam-6834	140	241	,	,	PUNCT
ejpam-6834	140	242	{	{	PUNCT
ejpam-6834	140	243	{	{	PUNCT
ejpam-6834	140	244	a	a	X
ejpam-6834	140	245	}	}	PUNCT
ejpam-6834	140	246	}	}	PUNCT
ejpam-6834	140	247	,	,	PUNCT
ejpam-6834	140	248	{	{	PUNCT
ejpam-6834	140	249	{	{	PUNCT
ejpam-6834	140	250	b	b	NOUN
ejpam-6834	140	251	}	}	PUNCT
ejpam-6834	140	252	}	}	PUNCT
ejpam-6834	140	253	,	,	PUNCT
ejpam-6834	140	254	{	{	PUNCT
ejpam-6834	140	255	{	{	PUNCT
ejpam-6834	140	256	a	a	PROPN
ejpam-6834	140	257	,	,	PUNCT
ejpam-6834	140	258	b	b	NOUN
ejpam-6834	140	259	}	}	PUNCT
ejpam-6834	140	260	}	}	PUNCT
ejpam-6834	140	261	}	}	PUNCT
ejpam-6834	140	262	.	.	PUNCT
ejpam-6834	141	1	in	in	ADP
ejpam-6834	141	2	particular	particular	ADJ
ejpam-6834	141	3	,	,	PUNCT
ejpam-6834	141	4	p2(h	p2(h	NUM
ejpam-6834	141	5	)	)	PUNCT
ejpam-6834	141	6	is	be	AUX
ejpam-6834	141	7	the	the	DET
ejpam-6834	141	8	boolean	boolean	ADJ
ejpam-6834	141	9	algebra	algebra	NOUN
ejpam-6834	141	10	on	on	ADP
ejpam-6834	141	11	the	the	DET
ejpam-6834	141	12	four	four	NUM
ejpam-6834	141	13	generators	generator	NOUN
ejpam-6834	141	14	∅	∅	NOUN
ejpam-6834	141	15	,	,	PUNCT
ejpam-6834	141	16	{	{	PUNCT
ejpam-6834	141	17	a	a	X
ejpam-6834	141	18	}	}	PUNCT
ejpam-6834	141	19	,	,	PUNCT
ejpam-6834	141	20	{	{	PUNCT
ejpam-6834	141	21	b	b	NOUN
ejpam-6834	141	22	}	}	PUNCT
ejpam-6834	141	23	,	,	PUNCT
ejpam-6834	141	24	{	{	PUNCT
ejpam-6834	141	25	a	a	DET
ejpam-6834	141	26	,	,	PUNCT
ejpam-6834	141	27	b	b	NOUN
ejpam-6834	141	28	}	}	PUNCT
ejpam-6834	141	29	.	.	PUNCT
ejpam-6834	142	1	higher	high	ADJ
ejpam-6834	142	2	iterations	iteration	NOUN
ejpam-6834	142	3	pn(h	pn(h	NOUN
ejpam-6834	142	4	)	)	PUNCT
ejpam-6834	142	5	are	be	AUX
ejpam-6834	142	6	obtained	obtain	VERB
ejpam-6834	142	7	by	by	ADP
ejpam-6834	142	8	repeating	repeat	VERB
ejpam-6834	142	9	this	this	DET
ejpam-6834	142	10	construction	construction	NOUN
ejpam-6834	142	11	.	.	PUNCT
ejpam-6834	143	1	t.	t.	PROPN
ejpam-6834	143	2	fujita	fujita	PROPN
ejpam-6834	143	3	,	,	PUNCT
ejpam-6834	143	4	f.smarandache	f.smarandache	NOUN
ejpam-6834	143	5	/	/	SYM
ejpam-6834	143	6	eur	eur	PROPN
ejpam-6834	143	7	.	.	PUNCT
ejpam-6834	144	1	j.	j.	PROPN
ejpam-6834	144	2	pure	pure	PROPN
ejpam-6834	144	3	appl	appl	PROPN
ejpam-6834	144	4	.	.	PROPN
ejpam-6834	144	5	math	math	PROPN
ejpam-6834	144	6	,	,	PUNCT
ejpam-6834	144	7	18	18	NUM
ejpam-6834	144	8	(	(	PUNCT
ejpam-6834	144	9	4	4	NUM
ejpam-6834	144	10	)	)	PUNCT
ejpam-6834	144	11	(	(	PUNCT
ejpam-6834	144	12	2025	2025	NUM
ejpam-6834	144	13	)	)	PUNCT
ejpam-6834	144	14	,	,	PUNCT
ejpam-6834	144	15	6834	6834	NUM
ejpam-6834	144	16	7	7	NUM
ejpam-6834	144	17	of	of	ADP
ejpam-6834	144	18	69	69	NUM
ejpam-6834	144	19	to	to	PART
ejpam-6834	144	20	establish	establish	VERB
ejpam-6834	144	21	a	a	DET
ejpam-6834	144	22	formal	formal	ADJ
ejpam-6834	144	23	foundation	foundation	NOUN
ejpam-6834	144	24	for	for	ADP
ejpam-6834	144	25	the	the	DET
ejpam-6834	144	26	concepts	concept	NOUN
ejpam-6834	144	27	of	of	ADP
ejpam-6834	144	28	hyperstructures	hyperstructure	NOUN
ejpam-6834	144	29	and	and	CCONJ
ejpam-6834	144	30	superhyperstructures	superhyperstructure	NOUN
ejpam-6834	144	31	,	,	PUNCT
ejpam-6834	144	32	we	we	PRON
ejpam-6834	144	33	present	present	VERB
ejpam-6834	144	34	the	the	DET
ejpam-6834	144	35	following	follow	VERB
ejpam-6834	144	36	definitions	definition	NOUN
ejpam-6834	144	37	and	and	CCONJ
ejpam-6834	144	38	propositions	proposition	NOUN
ejpam-6834	144	39	.	.	PUNCT
ejpam-6834	145	1	definition	definition	NOUN
ejpam-6834	145	2	4	4	NUM
ejpam-6834	145	3	(	(	PUNCT
ejpam-6834	145	4	classical	classical	ADJ
ejpam-6834	145	5	structure	structure	NOUN
ejpam-6834	145	6	)	)	PUNCT
ejpam-6834	145	7	.	.	PUNCT
ejpam-6834	146	1	(	(	PUNCT
ejpam-6834	146	2	cf.[28	cf.[28	PROPN
ejpam-6834	146	3	,	,	PUNCT
ejpam-6834	146	4	49	49	NUM
ejpam-6834	146	5	]	]	PUNCT
ejpam-6834	146	6	)	)	PUNCT
ejpam-6834	146	7	a	a	DET
ejpam-6834	146	8	classical	classical	ADJ
ejpam-6834	146	9	structure	structure	NOUN
ejpam-6834	146	10	is	be	AUX
ejpam-6834	146	11	a	a	DET
ejpam-6834	146	12	mathematical	mathematical	ADJ
ejpam-6834	146	13	framework	framework	NOUN
ejpam-6834	146	14	defined	define	VERB
ejpam-6834	146	15	on	on	ADP
ejpam-6834	146	16	a	a	DET
ejpam-6834	146	17	non	non	ADJ
ejpam-6834	146	18	-	-	ADJ
ejpam-6834	146	19	empty	empty	ADJ
ejpam-6834	146	20	set	set	ADJ
ejpam-6834	146	21	h	h	NOUN
ejpam-6834	146	22	,	,	PUNCT
ejpam-6834	146	23	equipped	equip	VERB
ejpam-6834	146	24	with	with	ADP
ejpam-6834	146	25	one	one	NUM
ejpam-6834	146	26	or	or	CCONJ
ejpam-6834	146	27	more	more	ADJ
ejpam-6834	146	28	classical	classical	ADJ
ejpam-6834	146	29	operations	operation	NOUN
ejpam-6834	146	30	that	that	PRON
ejpam-6834	146	31	satisfy	satisfy	VERB
ejpam-6834	146	32	specified	specify	VERB
ejpam-6834	146	33	classical	classical	ADJ
ejpam-6834	146	34	axioms	axiom	NOUN
ejpam-6834	146	35	.	.	PUNCT
ejpam-6834	147	1	specifically	specifically	ADV
ejpam-6834	147	2	:	:	PUNCT
ejpam-6834	147	3	a	a	DET
ejpam-6834	147	4	classical	classical	ADJ
ejpam-6834	147	5	operation	operation	NOUN
ejpam-6834	147	6	is	be	AUX
ejpam-6834	147	7	a	a	DET
ejpam-6834	147	8	function	function	NOUN
ejpam-6834	147	9	of	of	ADP
ejpam-6834	147	10	the	the	DET
ejpam-6834	147	11	form	form	NOUN
ejpam-6834	147	12	:	:	PUNCT
ejpam-6834	147	13	#	#	SYM
ejpam-6834	147	14	0	0	NUM
ejpam-6834	147	15	:	:	PUNCT
ejpam-6834	147	16	hm	hm	INTJ
ejpam-6834	147	17	→	→	SYM
ejpam-6834	147	18	h	h	NOUN
ejpam-6834	147	19	,	,	PUNCT
ejpam-6834	147	20	where	where	SCONJ
ejpam-6834	147	21	m	m	PROPN
ejpam-6834	147	22	≥	≥	NUM
ejpam-6834	147	23	1	1	NUM
ejpam-6834	147	24	is	be	AUX
ejpam-6834	147	25	a	a	DET
ejpam-6834	147	26	positive	positive	ADJ
ejpam-6834	147	27	integer	integer	NOUN
ejpam-6834	147	28	,	,	PUNCT
ejpam-6834	147	29	and	and	CCONJ
ejpam-6834	147	30	hm	hm	INTJ
ejpam-6834	147	31	denotes	denote	VERB
ejpam-6834	147	32	the	the	DET
ejpam-6834	147	33	m	m	ADJ
ejpam-6834	147	34	-	-	ADJ
ejpam-6834	147	35	fold	fold	ADJ
ejpam-6834	147	36	cartesian	cartesian	ADJ
ejpam-6834	147	37	product	product	NOUN
ejpam-6834	147	38	of	of	ADP
ejpam-6834	147	39	h.	h.	PROPN
ejpam-6834	147	40	common	common	ADJ
ejpam-6834	147	41	examples	example	NOUN
ejpam-6834	147	42	include	include	VERB
ejpam-6834	147	43	addition	addition	NOUN
ejpam-6834	147	44	and	and	CCONJ
ejpam-6834	147	45	multiplication	multiplication	NOUN
ejpam-6834	147	46	in	in	ADP
ejpam-6834	147	47	algebraic	algebraic	ADJ
ejpam-6834	147	48	structures	structure	NOUN
ejpam-6834	147	49	such	such	ADJ
ejpam-6834	147	50	as	as	ADP
ejpam-6834	147	51	groups	group	NOUN
ejpam-6834	147	52	,	,	PUNCT
ejpam-6834	147	53	rings	ring	NOUN
ejpam-6834	147	54	,	,	PUNCT
ejpam-6834	147	55	and	and	CCONJ
ejpam-6834	147	56	fields	field	NOUN
ejpam-6834	147	57	.	.	PUNCT
ejpam-6834	148	1	definition	definition	NOUN
ejpam-6834	148	2	5	5	NUM
ejpam-6834	148	3	(	(	PUNCT
ejpam-6834	148	4	hyperoperation	hyperoperation	NOUN
ejpam-6834	148	5	)	)	PUNCT
ejpam-6834	148	6	.	.	PUNCT
ejpam-6834	149	1	(	(	PUNCT
ejpam-6834	149	2	cf.[50	cf.[50	PROPN
ejpam-6834	149	3	,	,	PUNCT
ejpam-6834	149	4	51	51	NUM
ejpam-6834	149	5	]	]	PUNCT
ejpam-6834	149	6	)	)	PUNCT
ejpam-6834	149	7	a	a	DET
ejpam-6834	149	8	hyperoperation	hyperoperation	NOUN
ejpam-6834	149	9	is	be	AUX
ejpam-6834	149	10	a	a	DET
ejpam-6834	149	11	generalization	generalization	NOUN
ejpam-6834	149	12	of	of	ADP
ejpam-6834	149	13	a	a	DET
ejpam-6834	149	14	binary	binary	ADJ
ejpam-6834	149	15	operation	operation	NOUN
ejpam-6834	149	16	where	where	SCONJ
ejpam-6834	149	17	the	the	DET
ejpam-6834	149	18	result	result	NOUN
ejpam-6834	149	19	of	of	ADP
ejpam-6834	149	20	combining	combine	VERB
ejpam-6834	149	21	two	two	NUM
ejpam-6834	149	22	elements	element	NOUN
ejpam-6834	149	23	is	be	AUX
ejpam-6834	149	24	a	a	DET
ejpam-6834	149	25	set	set	NOUN
ejpam-6834	149	26	,	,	PUNCT
ejpam-6834	149	27	not	not	PART
ejpam-6834	149	28	a	a	DET
ejpam-6834	149	29	single	single	ADJ
ejpam-6834	149	30	element	element	NOUN
ejpam-6834	149	31	.	.	PUNCT
ejpam-6834	150	1	formally	formally	ADV
ejpam-6834	150	2	,	,	PUNCT
ejpam-6834	150	3	for	for	ADP
ejpam-6834	150	4	a	a	DET
ejpam-6834	150	5	set	set	NOUN
ejpam-6834	150	6	s	s	PROPN
ejpam-6834	150	7	,	,	PUNCT
ejpam-6834	150	8	a	a	DET
ejpam-6834	150	9	hyperoperation	hyperoperation	NOUN
ejpam-6834	150	10	◦	◦	NOUN
ejpam-6834	150	11	is	be	AUX
ejpam-6834	150	12	defined	define	VERB
ejpam-6834	150	13	as	as	ADP
ejpam-6834	150	14	:	:	PUNCT
ejpam-6834	150	15	◦	◦	NOUN
ejpam-6834	150	16	:	:	PUNCT
ejpam-6834	150	17	s	s	VERB
ejpam-6834	150	18	×	×	PROPN
ejpam-6834	150	19	s	s	X
ejpam-6834	150	20	→	→	SYM
ejpam-6834	150	21	p(s	p(s	NUM
ejpam-6834	150	22	)	)	PUNCT
ejpam-6834	150	23	,	,	PUNCT
ejpam-6834	150	24	where	where	SCONJ
ejpam-6834	150	25	p(s	p(s	NOUN
ejpam-6834	150	26	)	)	PUNCT
ejpam-6834	150	27	is	be	AUX
ejpam-6834	150	28	the	the	DET
ejpam-6834	150	29	powerset	powerset	NOUN
ejpam-6834	150	30	of	of	ADP
ejpam-6834	150	31	s.	s.	PROPN
ejpam-6834	150	32	definition	definition	NOUN
ejpam-6834	150	33	6	6	NUM
ejpam-6834	150	34	(	(	PUNCT
ejpam-6834	150	35	hyperstructure	hyperstructure	NOUN
ejpam-6834	150	36	)	)	PUNCT
ejpam-6834	150	37	.	.	PUNCT
ejpam-6834	151	1	(	(	PUNCT
ejpam-6834	151	2	cf.[26	cf.[26	ADJ
ejpam-6834	151	3	,	,	PUNCT
ejpam-6834	151	4	28	28	NUM
ejpam-6834	151	5	,	,	PUNCT
ejpam-6834	151	6	52	52	NUM
ejpam-6834	151	7	]	]	PUNCT
ejpam-6834	151	8	)	)	PUNCT
ejpam-6834	151	9	a	a	DET
ejpam-6834	151	10	hyperstructure	hyperstructure	NOUN
ejpam-6834	151	11	extends	extend	VERB
ejpam-6834	151	12	the	the	DET
ejpam-6834	151	13	notion	notion	NOUN
ejpam-6834	151	14	of	of	ADP
ejpam-6834	151	15	a	a	DET
ejpam-6834	151	16	classical	classical	ADJ
ejpam-6834	151	17	structure	structure	NOUN
ejpam-6834	151	18	by	by	ADP
ejpam-6834	151	19	operating	operate	VERB
ejpam-6834	151	20	on	on	ADP
ejpam-6834	151	21	the	the	DET
ejpam-6834	151	22	powerset	powerset	NOUN
ejpam-6834	151	23	of	of	ADP
ejpam-6834	151	24	a	a	DET
ejpam-6834	151	25	base	base	NOUN
ejpam-6834	151	26	set	set	NOUN
ejpam-6834	151	27	.	.	PUNCT
ejpam-6834	152	1	formally	formally	ADV
ejpam-6834	152	2	,	,	PUNCT
ejpam-6834	152	3	it	it	PRON
ejpam-6834	152	4	is	be	AUX
ejpam-6834	152	5	defined	define	VERB
ejpam-6834	152	6	as	as	ADP
ejpam-6834	152	7	:	:	PUNCT
ejpam-6834	152	8	h	h	NOUN
ejpam-6834	152	9	=	=	SYM
ejpam-6834	152	10	(	(	PUNCT
ejpam-6834	152	11	p(s	p(s	NOUN
ejpam-6834	152	12	)	)	PUNCT
ejpam-6834	152	13	,	,	PUNCT
ejpam-6834	152	14	◦	◦	NOUN
ejpam-6834	152	15	)	)	PUNCT
ejpam-6834	152	16	,	,	PUNCT
ejpam-6834	152	17	where	where	SCONJ
ejpam-6834	152	18	s	s	NOUN
ejpam-6834	152	19	is	be	AUX
ejpam-6834	152	20	the	the	DET
ejpam-6834	152	21	base	base	NOUN
ejpam-6834	152	22	set	set	NOUN
ejpam-6834	152	23	,	,	PUNCT
ejpam-6834	152	24	p(s	p(s	PROPN
ejpam-6834	152	25	)	)	PUNCT
ejpam-6834	152	26	is	be	AUX
ejpam-6834	152	27	the	the	DET
ejpam-6834	152	28	powerset	powerset	NOUN
ejpam-6834	152	29	of	of	ADP
ejpam-6834	152	30	s	s	PROPN
ejpam-6834	152	31	,	,	PUNCT
ejpam-6834	152	32	and	and	CCONJ
ejpam-6834	152	33	◦	◦	NOUN
ejpam-6834	152	34	is	be	AUX
ejpam-6834	152	35	an	an	DET
ejpam-6834	152	36	operation	operation	NOUN
ejpam-6834	152	37	defined	define	VERB
ejpam-6834	152	38	on	on	ADP
ejpam-6834	152	39	subsets	subset	NOUN
ejpam-6834	152	40	of	of	ADP
ejpam-6834	152	41	p(s	p(s	NOUN
ejpam-6834	152	42	)	)	PUNCT
ejpam-6834	152	43	.	.	PUNCT
ejpam-6834	153	1	hyperstructures	hyperstructure	NOUN
ejpam-6834	153	2	allow	allow	VERB
ejpam-6834	153	3	for	for	ADP
ejpam-6834	153	4	generalized	generalized	ADJ
ejpam-6834	153	5	operations	operation	NOUN
ejpam-6834	153	6	that	that	PRON
ejpam-6834	153	7	can	can	AUX
ejpam-6834	153	8	apply	apply	VERB
ejpam-6834	153	9	to	to	ADP
ejpam-6834	153	10	collections	collection	NOUN
ejpam-6834	153	11	of	of	ADP
ejpam-6834	153	12	elements	element	NOUN
ejpam-6834	153	13	rather	rather	ADV
ejpam-6834	153	14	than	than	ADP
ejpam-6834	153	15	single	single	ADJ
ejpam-6834	153	16	elements	element	NOUN
ejpam-6834	153	17	.	.	PUNCT
ejpam-6834	154	1	example	example	NOUN
ejpam-6834	154	2	2	2	NUM
ejpam-6834	154	3	(	(	PUNCT
ejpam-6834	154	4	grocery	grocery	NOUN
ejpam-6834	154	5	substitution	substitution	NOUN
ejpam-6834	154	6	as	as	ADP
ejpam-6834	154	7	a	a	DET
ejpam-6834	154	8	hyperstructure	hyperstructure	NOUN
ejpam-6834	154	9	)	)	PUNCT
ejpam-6834	154	10	.	.	PUNCT
ejpam-6834	155	1	let	let	VERB
ejpam-6834	155	2	s	s	PRON
ejpam-6834	155	3	=	=	NOUN
ejpam-6834	155	4	{	{	PUNCT
ejpam-6834	155	5	milk	milk	NOUN
ejpam-6834	155	6	,	,	PUNCT
ejpam-6834	155	7	soymilk	soymilk	NOUN
ejpam-6834	155	8	,	,	PUNCT
ejpam-6834	155	9	bread	bread	NOUN
ejpam-6834	155	10	,	,	PUNCT
ejpam-6834	155	11	gfbread	gfbread	ADJ
ejpam-6834	155	12	,	,	PUNCT
ejpam-6834	155	13	eggs	egg	NOUN
ejpam-6834	155	14	}	}	PUNCT
ejpam-6834	155	15	.	.	PUNCT
ejpam-6834	156	1	define	define	VERB
ejpam-6834	156	2	a	a	DET
ejpam-6834	156	3	substitution	substitution	NOUN
ejpam-6834	156	4	map	map	NOUN
ejpam-6834	156	5	σ	σ	NOUN
ejpam-6834	156	6	:	:	PUNCT
ejpam-6834	156	7	s	s	X
ejpam-6834	156	8	→	→	SYM
ejpam-6834	156	9	p(s	p(s	NUM
ejpam-6834	156	10	)	)	PUNCT
ejpam-6834	156	11	by	by	ADP
ejpam-6834	156	12	σ(milk	σ(milk	NOUN
ejpam-6834	156	13	)	)	PUNCT
ejpam-6834	156	14	=	=	PRON
ejpam-6834	156	15	{	{	PUNCT
ejpam-6834	156	16	milk	milk	NOUN
ejpam-6834	156	17	,	,	PUNCT
ejpam-6834	156	18	soymilk	soymilk	NOUN
ejpam-6834	156	19	}	}	PUNCT
ejpam-6834	156	20	,	,	PUNCT
ejpam-6834	156	21	σ(bread	σ(bread	NOUN
ejpam-6834	156	22	)	)	PUNCT
ejpam-6834	156	23	=	=	SYM
ejpam-6834	156	24	{	{	PUNCT
ejpam-6834	156	25	bread	bread	NOUN
ejpam-6834	156	26	,	,	PUNCT
ejpam-6834	156	27	gfbread	gfbread	ADJ
ejpam-6834	156	28	}	}	PUNCT
ejpam-6834	156	29	,	,	PUNCT
ejpam-6834	156	30	and	and	CCONJ
ejpam-6834	156	31	σ(x	σ(x	NOUN
ejpam-6834	156	32	)	)	PUNCT
ejpam-6834	156	33	=	=	PRON
ejpam-6834	156	34	{	{	PUNCT
ejpam-6834	156	35	x	x	NOUN
ejpam-6834	156	36	}	}	PUNCT
ejpam-6834	156	37	for	for	ADP
ejpam-6834	156	38	x	x	PROPN
ejpam-6834	156	39	∈	∈	PROPN
ejpam-6834	156	40	{	{	PUNCT
ejpam-6834	156	41	soymilk	soymilk	NOUN
ejpam-6834	156	42	,	,	PUNCT
ejpam-6834	156	43	gfbread	gfbread	NOUN
ejpam-6834	156	44	,	,	PUNCT
ejpam-6834	156	45	eggs	egg	NOUN
ejpam-6834	156	46	}	}	PUNCT
ejpam-6834	156	47	.	.	PUNCT
ejpam-6834	157	1	set	set	VERB
ejpam-6834	157	2	a	a	DET
ejpam-6834	157	3	hyperoperation	hyperoperation	NOUN
ejpam-6834	157	4	on	on	ADP
ejpam-6834	157	5	items	item	NOUN
ejpam-6834	157	6	⋆	⋆	VERB
ejpam-6834	157	7	:	:	PUNCT
ejpam-6834	157	8	s	s	VERB
ejpam-6834	157	9	×	×	PROPN
ejpam-6834	157	10	s	s	X
ejpam-6834	157	11	→	→	SYM
ejpam-6834	157	12	p(s	p(s	NUM
ejpam-6834	157	13	)	)	PUNCT
ejpam-6834	157	14	,	,	PUNCT
ejpam-6834	157	15	a	a	DET
ejpam-6834	157	16	⋆	⋆	NOUN
ejpam-6834	157	17	b	b	NOUN
ejpam-6834	157	18	=	=	SYM
ejpam-6834	157	19	σ(a	σ(a	PROPN
ejpam-6834	157	20	)	)	PUNCT
ejpam-6834	157	21	∪	∪	ADP
ejpam-6834	157	22	σ(b	σ(b	PROPN
ejpam-6834	157	23	)	)	PUNCT
ejpam-6834	157	24	,	,	PUNCT
ejpam-6834	157	25	and	and	CCONJ
ejpam-6834	157	26	induce	induce	VERB
ejpam-6834	157	27	an	an	DET
ejpam-6834	157	28	operation	operation	NOUN
ejpam-6834	157	29	on	on	ADP
ejpam-6834	157	30	baskets	basket	NOUN
ejpam-6834	157	31	(	(	PUNCT
ejpam-6834	157	32	subsets	subset	NOUN
ejpam-6834	157	33	)	)	PUNCT
ejpam-6834	157	34	by	by	ADP
ejpam-6834	157	35	⊙	⊙	NOUN
ejpam-6834	157	36	:	:	PUNCT
ejpam-6834	157	37	p(s	p(s	NUM
ejpam-6834	157	38	)	)	PUNCT
ejpam-6834	157	39	×	×	NOUN
ejpam-6834	157	40	p(s	p(s	NOUN
ejpam-6834	157	41	)	)	PUNCT
ejpam-6834	157	42	→	→	SYM
ejpam-6834	157	43	p(s	p(s	NUM
ejpam-6834	157	44	)	)	PUNCT
ejpam-6834	157	45	,	,	PUNCT
ejpam-6834	157	46	a⊙b	a⊙b	NOUN
ejpam-6834	157	47	=	=	SYM
ejpam-6834	158	1	⋃	⋃	NOUN
ejpam-6834	158	2	a∈a	a∈a	ADJ
ejpam-6834	158	3	,	,	PUNCT
ejpam-6834	158	4	b∈b	b∈b	NOUN
ejpam-6834	158	5	(	(	PUNCT
ejpam-6834	158	6	a	a	DET
ejpam-6834	158	7	⋆	⋆	NOUN
ejpam-6834	158	8	b	b	NOUN
ejpam-6834	158	9	)	)	PUNCT
ejpam-6834	158	10	.	.	PUNCT
ejpam-6834	159	1	then	then	ADV
ejpam-6834	159	2	h	h	NOUN
ejpam-6834	159	3	=	=	PUNCT
ejpam-6834	159	4	(	(	PUNCT
ejpam-6834	159	5	p(s),⊙	p(s),⊙	NOUN
ejpam-6834	159	6	)	)	PUNCT
ejpam-6834	159	7	is	be	AUX
ejpam-6834	159	8	a	a	DET
ejpam-6834	159	9	hyperstructure	hyperstructure	NOUN
ejpam-6834	159	10	modelling	model	VERB
ejpam-6834	159	11	shopping	shopping	NOUN
ejpam-6834	159	12	lists	list	NOUN
ejpam-6834	159	13	with	with	ADP
ejpam-6834	159	14	permissible	permissible	ADJ
ejpam-6834	159	15	substitutions	substitution	NOUN
ejpam-6834	159	16	.	.	PUNCT
ejpam-6834	160	1	for	for	ADP
ejpam-6834	160	2	instance	instance	NOUN
ejpam-6834	160	3	,	,	PUNCT
ejpam-6834	160	4	{	{	PUNCT
ejpam-6834	160	5	milk	milk	NOUN
ejpam-6834	160	6	,	,	PUNCT
ejpam-6834	160	7	bread	bread	NOUN
ejpam-6834	160	8	}	}	PUNCT
ejpam-6834	160	9	⊙	⊙	NOUN
ejpam-6834	160	10	{	{	PUNCT
ejpam-6834	160	11	eggs	egg	NOUN
ejpam-6834	160	12	}	}	PUNCT
ejpam-6834	160	13	=	=	SYM
ejpam-6834	160	14	{	{	PUNCT
ejpam-6834	160	15	milk	milk	NOUN
ejpam-6834	160	16	,	,	PUNCT
ejpam-6834	160	17	soymilk	soymilk	NOUN
ejpam-6834	160	18	,	,	PUNCT
ejpam-6834	160	19	bread	bread	NOUN
ejpam-6834	160	20	,	,	PUNCT
ejpam-6834	160	21	gfbread	gfbread	ADJ
ejpam-6834	160	22	,	,	PUNCT
ejpam-6834	160	23	eggs	egg	NOUN
ejpam-6834	160	24	}	}	PUNCT
ejpam-6834	160	25	.	.	PUNCT
ejpam-6834	161	1	t.	t.	PROPN
ejpam-6834	161	2	fujita	fujita	PROPN
ejpam-6834	161	3	,	,	PUNCT
ejpam-6834	161	4	f.smarandache	f.smarandache	NOUN
ejpam-6834	161	5	/	/	SYM
ejpam-6834	161	6	eur	eur	PROPN
ejpam-6834	161	7	.	.	PUNCT
ejpam-6834	162	1	j.	j.	PROPN
ejpam-6834	162	2	pure	pure	PROPN
ejpam-6834	162	3	appl	appl	PROPN
ejpam-6834	162	4	.	.	PROPN
ejpam-6834	162	5	math	math	PROPN
ejpam-6834	162	6	,	,	PUNCT
ejpam-6834	162	7	18	18	NUM
ejpam-6834	162	8	(	(	PUNCT
ejpam-6834	162	9	4	4	NUM
ejpam-6834	162	10	)	)	PUNCT
ejpam-6834	162	11	(	(	PUNCT
ejpam-6834	162	12	2025	2025	NUM
ejpam-6834	162	13	)	)	PUNCT
ejpam-6834	162	14	,	,	PUNCT
ejpam-6834	162	15	6834	6834	NUM
ejpam-6834	162	16	8	8	NUM
ejpam-6834	162	17	of	of	ADP
ejpam-6834	162	18	69	69	NUM
ejpam-6834	162	19	definition	definition	NOUN
ejpam-6834	162	20	7	7	NUM
ejpam-6834	162	21	(	(	PUNCT
ejpam-6834	162	22	superhyperoperations	superhyperoperation	NOUN
ejpam-6834	162	23	)	)	PUNCT
ejpam-6834	162	24	.	.	PUNCT
ejpam-6834	163	1	(	(	PUNCT
ejpam-6834	163	2	cf.[28	cf.[28	PROPN
ejpam-6834	163	3	]	]	PUNCT
ejpam-6834	163	4	)	)	PUNCT
ejpam-6834	163	5	let	let	VERB
ejpam-6834	163	6	h	h	PRON
ejpam-6834	163	7	be	be	AUX
ejpam-6834	163	8	a	a	DET
ejpam-6834	163	9	non	non	ADJ
ejpam-6834	163	10	-	-	ADJ
ejpam-6834	163	11	empty	empty	ADJ
ejpam-6834	163	12	set	set	NOUN
ejpam-6834	163	13	,	,	PUNCT
ejpam-6834	163	14	and	and	CCONJ
ejpam-6834	163	15	let	let	VERB
ejpam-6834	163	16	p(h	p(h	NOUN
ejpam-6834	163	17	)	)	PUNCT
ejpam-6834	163	18	denote	denote	VERB
ejpam-6834	163	19	the	the	DET
ejpam-6834	163	20	powerset	powerset	NOUN
ejpam-6834	163	21	of	of	ADP
ejpam-6834	163	22	h.	h.	PROPN
ejpam-6834	163	23	the	the	DET
ejpam-6834	163	24	n	n	ADV
ejpam-6834	163	25	-	-	PUNCT
ejpam-6834	163	26	th	th	X
ejpam-6834	163	27	powerset	powerset	NOUN
ejpam-6834	163	28	pn(h	pn(h	NOUN
ejpam-6834	163	29	)	)	PUNCT
ejpam-6834	163	30	is	be	AUX
ejpam-6834	163	31	defined	define	VERB
ejpam-6834	163	32	recursively	recursively	ADV
ejpam-6834	163	33	as	as	SCONJ
ejpam-6834	163	34	follows	follow	VERB
ejpam-6834	163	35	:	:	PUNCT
ejpam-6834	163	36	p0(h	p0(h	X
ejpam-6834	164	1	)	)	PUNCT
ejpam-6834	164	2	=	=	SYM
ejpam-6834	164	3	h	h	PROPN
ejpam-6834	164	4	,	,	PUNCT
ejpam-6834	164	5	pk+1(h	pk+1(h	PROPN
ejpam-6834	164	6	)	)	PUNCT
ejpam-6834	164	7	=	=	PUNCT
ejpam-6834	164	8	p(pk(h	p(pk(h	NOUN
ejpam-6834	164	9	)	)	PUNCT
ejpam-6834	164	10	)	)	PUNCT
ejpam-6834	164	11	,	,	PUNCT
ejpam-6834	164	12	for	for	ADP
ejpam-6834	164	13	k	k	PROPN
ejpam-6834	164	14	≥	≥	PROPN
ejpam-6834	164	15	0	0	NUM
ejpam-6834	164	16	.	.	PUNCT
ejpam-6834	165	1	a	a	DET
ejpam-6834	165	2	superhyperoperation	superhyperoperation	NOUN
ejpam-6834	165	3	of	of	ADP
ejpam-6834	165	4	order	order	NOUN
ejpam-6834	165	5	(	(	PUNCT
ejpam-6834	165	6	m	m	NOUN
ejpam-6834	165	7	,	,	PUNCT
ejpam-6834	165	8	n	n	CCONJ
ejpam-6834	165	9	)	)	PUNCT
ejpam-6834	165	10	is	be	AUX
ejpam-6834	165	11	an	an	DET
ejpam-6834	165	12	m	m	ADJ
ejpam-6834	165	13	-	-	ADJ
ejpam-6834	165	14	ary	ary	PROPN
ejpam-6834	165	15	operation	operation	NOUN
ejpam-6834	165	16	:	:	PUNCT
ejpam-6834	165	17	◦	◦	NOUN
ejpam-6834	165	18	(	(	PUNCT
ejpam-6834	165	19	m	m	PROPN
ejpam-6834	165	20	,	,	PUNCT
ejpam-6834	165	21	n	n	CCONJ
ejpam-6834	165	22	)	)	PUNCT
ejpam-6834	165	23	:	:	PUNCT
ejpam-6834	166	1	hm	hm	INTJ
ejpam-6834	166	2	→	→	SYM
ejpam-6834	166	3	pn	pn	PROPN
ejpam-6834	166	4	∗	∗	PROPN
ejpam-6834	166	5	(	(	PUNCT
ejpam-6834	166	6	h	h	NOUN
ejpam-6834	166	7	)	)	PUNCT
ejpam-6834	166	8	,	,	PUNCT
ejpam-6834	166	9	where	where	SCONJ
ejpam-6834	166	10	pn	pn	PROPN
ejpam-6834	166	11	∗	∗	X
ejpam-6834	166	12	(	(	PUNCT
ejpam-6834	166	13	h	h	NOUN
ejpam-6834	166	14	)	)	PUNCT
ejpam-6834	166	15	represents	represent	VERB
ejpam-6834	166	16	the	the	DET
ejpam-6834	166	17	n	n	ADV
ejpam-6834	166	18	-	-	PUNCT
ejpam-6834	166	19	th	th	VERB
ejpam-6834	166	20	powerset	powerset	NOUN
ejpam-6834	166	21	of	of	ADP
ejpam-6834	166	22	h	h	NOUN
ejpam-6834	166	23	,	,	PUNCT
ejpam-6834	166	24	either	either	CCONJ
ejpam-6834	166	25	excluding	exclude	VERB
ejpam-6834	166	26	or	or	CCONJ
ejpam-6834	166	27	including	include	VERB
ejpam-6834	166	28	the	the	DET
ejpam-6834	166	29	empty	empty	ADJ
ejpam-6834	166	30	set	set	NOUN
ejpam-6834	166	31	,	,	PUNCT
ejpam-6834	166	32	depending	depend	VERB
ejpam-6834	166	33	on	on	ADP
ejpam-6834	166	34	the	the	DET
ejpam-6834	166	35	type	type	NOUN
ejpam-6834	166	36	of	of	ADP
ejpam-6834	166	37	operation	operation	NOUN
ejpam-6834	166	38	:	:	PUNCT
ejpam-6834	166	39	•	•	ADP
ejpam-6834	166	40	if	if	SCONJ
ejpam-6834	166	41	the	the	DET
ejpam-6834	166	42	codomain	codomain	NOUN
ejpam-6834	166	43	is	be	AUX
ejpam-6834	166	44	pn	pn	PROPN
ejpam-6834	166	45	∗	∗	PROPN
ejpam-6834	166	46	(	(	PUNCT
ejpam-6834	166	47	h	h	NOUN
ejpam-6834	166	48	)	)	PUNCT
ejpam-6834	166	49	excluding	exclude	VERB
ejpam-6834	166	50	the	the	DET
ejpam-6834	166	51	empty	empty	ADJ
ejpam-6834	166	52	set	set	NOUN
ejpam-6834	166	53	,	,	PUNCT
ejpam-6834	166	54	it	it	PRON
ejpam-6834	166	55	is	be	AUX
ejpam-6834	166	56	called	call	VERB
ejpam-6834	166	57	a	a	DET
ejpam-6834	166	58	classical	classical	ADJ
ejpam-6834	166	59	-	-	PUNCT
ejpam-6834	166	60	type	type	NOUN
ejpam-6834	166	61	(	(	PUNCT
ejpam-6834	166	62	m	m	PROPN
ejpam-6834	166	63	,	,	PUNCT
ejpam-6834	166	64	n)superhyperoperation	n)superhyperoperation	PROPN
ejpam-6834	166	65	.	.	PUNCT
ejpam-6834	167	1	•	•	NUM
ejpam-6834	167	2	if	if	SCONJ
ejpam-6834	167	3	the	the	DET
ejpam-6834	167	4	codomain	codomain	NOUN
ejpam-6834	167	5	is	be	AUX
ejpam-6834	167	6	pn(h	pn(h	NOUN
ejpam-6834	167	7	)	)	PUNCT
ejpam-6834	167	8	including	include	VERB
ejpam-6834	167	9	the	the	DET
ejpam-6834	167	10	empty	empty	ADJ
ejpam-6834	167	11	set	set	NOUN
ejpam-6834	167	12	,	,	PUNCT
ejpam-6834	167	13	it	it	PRON
ejpam-6834	167	14	is	be	AUX
ejpam-6834	167	15	called	call	VERB
ejpam-6834	167	16	a	a	DET
ejpam-6834	167	17	neutrosophic	neutrosophic	ADJ
ejpam-6834	167	18	(	(	PUNCT
ejpam-6834	167	19	m	m	PROPN
ejpam-6834	167	20	,	,	PUNCT
ejpam-6834	167	21	n)superhyperoperation	n)superhyperoperation	NOUN
ejpam-6834	167	22	.	.	PUNCT
ejpam-6834	168	1	these	these	DET
ejpam-6834	168	2	superhyperoperations	superhyperoperation	NOUN
ejpam-6834	168	3	are	be	AUX
ejpam-6834	168	4	higher	high	ADJ
ejpam-6834	168	5	-	-	PUNCT
ejpam-6834	168	6	order	order	NOUN
ejpam-6834	168	7	generalizations	generalization	NOUN
ejpam-6834	168	8	of	of	ADP
ejpam-6834	168	9	hyperoperations	hyperoperation	NOUN
ejpam-6834	168	10	,	,	PUNCT
ejpam-6834	168	11	capturing	capture	VERB
ejpam-6834	168	12	multi	multi	ADJ
ejpam-6834	168	13	-	-	ADJ
ejpam-6834	168	14	level	level	ADJ
ejpam-6834	168	15	complexity	complexity	NOUN
ejpam-6834	168	16	through	through	ADP
ejpam-6834	168	17	the	the	DET
ejpam-6834	168	18	construction	construction	NOUN
ejpam-6834	168	19	of	of	ADP
ejpam-6834	168	20	n	n	ADV
ejpam-6834	168	21	-	-	PUNCT
ejpam-6834	168	22	th	th	VERB
ejpam-6834	168	23	powersets	powerset	NOUN
ejpam-6834	168	24	.	.	PUNCT
ejpam-6834	169	1	definition	definition	NOUN
ejpam-6834	169	2	8	8	NUM
ejpam-6834	169	3	(	(	PUNCT
ejpam-6834	169	4	n	n	CCONJ
ejpam-6834	169	5	-	-	PUNCT
ejpam-6834	169	6	superhyperstructure	superhyperstructure	NOUN
ejpam-6834	169	7	)	)	PUNCT
ejpam-6834	169	8	.	.	PUNCT
ejpam-6834	170	1	(	(	PUNCT
ejpam-6834	170	2	cf.[28	cf.[28	PROPN
ejpam-6834	170	3	,	,	PUNCT
ejpam-6834	170	4	29	29	NUM
ejpam-6834	170	5	,	,	PUNCT
ejpam-6834	170	6	49	49	NUM
ejpam-6834	170	7	,	,	PUNCT
ejpam-6834	170	8	53	53	NUM
ejpam-6834	170	9	]	]	PUNCT
ejpam-6834	170	10	)	)	PUNCT
ejpam-6834	170	11	an	an	DET
ejpam-6834	170	12	n	n	CCONJ
ejpam-6834	170	13	-	-	PUNCT
ejpam-6834	170	14	superhyperstructure	superhyperstructure	NOUN
ejpam-6834	170	15	further	far	ADV
ejpam-6834	170	16	generalizes	generalize	VERB
ejpam-6834	170	17	a	a	DET
ejpam-6834	170	18	hyperstructure	hyperstructure	NOUN
ejpam-6834	170	19	by	by	ADP
ejpam-6834	170	20	incorporating	incorporate	VERB
ejpam-6834	170	21	the	the	DET
ejpam-6834	170	22	n	n	ADV
ejpam-6834	170	23	-	-	PUNCT
ejpam-6834	170	24	th	th	VERB
ejpam-6834	170	25	powerset	powerset	NOUN
ejpam-6834	170	26	of	of	ADP
ejpam-6834	170	27	a	a	DET
ejpam-6834	170	28	base	base	NOUN
ejpam-6834	170	29	set	set	NOUN
ejpam-6834	170	30	.	.	PUNCT
ejpam-6834	171	1	it	it	PRON
ejpam-6834	171	2	is	be	AUX
ejpam-6834	171	3	formally	formally	ADV
ejpam-6834	171	4	described	describe	VERB
ejpam-6834	171	5	as	as	ADP
ejpam-6834	171	6	:	:	PUNCT
ejpam-6834	171	7	shn	shn	NOUN
ejpam-6834	171	8	=	=	SYM
ejpam-6834	171	9	(	(	PUNCT
ejpam-6834	171	10	pn(s	pn(s	X
ejpam-6834	171	11	)	)	PUNCT
ejpam-6834	171	12	,	,	PUNCT
ejpam-6834	171	13	◦	◦	NOUN
ejpam-6834	171	14	)	)	PUNCT
ejpam-6834	171	15	,	,	PUNCT
ejpam-6834	171	16	where	where	SCONJ
ejpam-6834	171	17	s	s	NOUN
ejpam-6834	171	18	is	be	AUX
ejpam-6834	171	19	the	the	DET
ejpam-6834	171	20	base	base	NOUN
ejpam-6834	171	21	set	set	NOUN
ejpam-6834	171	22	,	,	PUNCT
ejpam-6834	171	23	pn(s	pn(s	NUM
ejpam-6834	171	24	)	)	PUNCT
ejpam-6834	171	25	is	be	AUX
ejpam-6834	171	26	the	the	DET
ejpam-6834	171	27	n	n	ADV
ejpam-6834	171	28	-	-	PUNCT
ejpam-6834	171	29	th	th	VERB
ejpam-6834	171	30	powerset	powerset	NOUN
ejpam-6834	171	31	of	of	ADP
ejpam-6834	171	32	s	s	PROPN
ejpam-6834	171	33	,	,	PUNCT
ejpam-6834	171	34	and	and	CCONJ
ejpam-6834	171	35	◦	◦	NOUN
ejpam-6834	171	36	represents	represent	VERB
ejpam-6834	171	37	an	an	DET
ejpam-6834	171	38	operation	operation	NOUN
ejpam-6834	171	39	defined	define	VERB
ejpam-6834	171	40	on	on	ADP
ejpam-6834	171	41	elements	element	NOUN
ejpam-6834	171	42	of	of	ADP
ejpam-6834	171	43	pn(s	pn(	NOUN
ejpam-6834	171	44	)	)	PUNCT
ejpam-6834	171	45	.	.	PUNCT
ejpam-6834	172	1	this	this	DET
ejpam-6834	172	2	iterative	iterative	NOUN
ejpam-6834	172	3	framework	framework	NOUN
ejpam-6834	172	4	allows	allow	VERB
ejpam-6834	172	5	for	for	ADP
ejpam-6834	172	6	increasingly	increasingly	ADV
ejpam-6834	172	7	hierarchical	hierarchical	ADJ
ejpam-6834	172	8	and	and	CCONJ
ejpam-6834	172	9	complex	complex	ADJ
ejpam-6834	172	10	representations	representation	NOUN
ejpam-6834	172	11	of	of	ADP
ejpam-6834	172	12	relationships	relationship	NOUN
ejpam-6834	172	13	within	within	ADP
ejpam-6834	172	14	the	the	DET
ejpam-6834	172	15	base	base	NOUN
ejpam-6834	172	16	set	set	NOUN
ejpam-6834	172	17	.	.	PUNCT
ejpam-6834	173	1	example	example	NOUN
ejpam-6834	173	2	3	3	NUM
ejpam-6834	173	3	(	(	PUNCT
ejpam-6834	173	4	feature	feature	NOUN
ejpam-6834	173	5	-	-	PUNCT
ejpam-6834	173	6	flag	flag	NOUN
ejpam-6834	173	7	cohorts	cohort	NOUN
ejpam-6834	173	8	as	as	ADP
ejpam-6834	173	9	a	a	DET
ejpam-6834	173	10	2	2	NUM
ejpam-6834	173	11	-	-	PUNCT
ejpam-6834	173	12	superhyperstructure	superhyperstructure	NOUN
ejpam-6834	173	13	)	)	PUNCT
ejpam-6834	173	14	.	.	PUNCT
ejpam-6834	174	1	in	in	ADP
ejpam-6834	174	2	a	a	DET
ejpam-6834	174	3	modern	modern	ADJ
ejpam-6834	174	4	microservice	microservice	NOUN
ejpam-6834	174	5	architecture	architecture	NOUN
ejpam-6834	174	6	,	,	PUNCT
ejpam-6834	174	7	a	a	DET
ejpam-6834	174	8	“	"	PUNCT
ejpam-6834	174	9	feature	feature	NOUN
ejpam-6834	174	10	flag	flag	NOUN
ejpam-6834	174	11	”	"	PUNCT
ejpam-6834	174	12	system	system	NOUN
ejpam-6834	174	13	often	often	ADV
ejpam-6834	174	14	needs	need	VERB
ejpam-6834	174	15	to	to	PART
ejpam-6834	174	16	manage	manage	VERB
ejpam-6834	174	17	nested	nested	ADJ
ejpam-6834	174	18	groups	group	NOUN
ejpam-6834	174	19	of	of	ADP
ejpam-6834	174	20	users	user	NOUN
ejpam-6834	174	21	for	for	ADP
ejpam-6834	174	22	a	a	DET
ejpam-6834	174	23	/	/	SYM
ejpam-6834	174	24	b	b	NOUN
ejpam-6834	174	25	testing	testing	NOUN
ejpam-6834	174	26	and	and	CCONJ
ejpam-6834	174	27	gradual	gradual	ADJ
ejpam-6834	174	28	roll	roll	NOUN
ejpam-6834	174	29	-	-	PUNCT
ejpam-6834	174	30	outs	out	NOUN
ejpam-6834	174	31	.	.	PUNCT
ejpam-6834	175	1	let	let	VERB
ejpam-6834	175	2	s	s	PRON
ejpam-6834	175	3	=	=	NOUN
ejpam-6834	175	4	{	{	PUNCT
ejpam-6834	175	5	featurea	featurea	PROPN
ejpam-6834	175	6	,	,	PUNCT
ejpam-6834	175	7	featureb	featureb	PROPN
ejpam-6834	175	8	,	,	PUNCT
ejpam-6834	175	9	featurec	featurec	NOUN
ejpam-6834	175	10	}	}	PUNCT
ejpam-6834	175	11	be	be	VERB
ejpam-6834	175	12	the	the	DET
ejpam-6834	175	13	base	base	NOUN
ejpam-6834	175	14	set	set	NOUN
ejpam-6834	175	15	of	of	ADP
ejpam-6834	175	16	all	all	DET
ejpam-6834	175	17	flags	flag	NOUN
ejpam-6834	175	18	.	.	PUNCT
ejpam-6834	176	1	then	then	ADV
ejpam-6834	176	2	p1(s	p1(s	PROPN
ejpam-6834	176	3	)	)	PUNCT
ejpam-6834	176	4	=	=	SYM
ejpam-6834	176	5	p(s	p(s	PROPN
ejpam-6834	176	6	)	)	PUNCT
ejpam-6834	176	7	and	and	CCONJ
ejpam-6834	176	8	p2(s	p2(s	NOUN
ejpam-6834	176	9	)	)	PUNCT
ejpam-6834	177	1	=	=	SYM
ejpam-6834	177	2	p	p	X
ejpam-6834	177	3	(	(	PUNCT
ejpam-6834	177	4	p(s	p(s	PROPN
ejpam-6834	177	5	)	)	PUNCT
ejpam-6834	177	6	)	)	PUNCT
ejpam-6834	177	7	are	be	AUX
ejpam-6834	177	8	respectively	respectively	ADV
ejpam-6834	177	9	all	all	DET
ejpam-6834	177	10	subsets	subset	NOUN
ejpam-6834	177	11	of	of	ADP
ejpam-6834	177	12	flags	flag	NOUN
ejpam-6834	177	13	(	(	PUNCT
ejpam-6834	177	14	cohorts	cohort	NOUN
ejpam-6834	177	15	)	)	PUNCT
ejpam-6834	177	16	and	and	CCONJ
ejpam-6834	177	17	all	all	DET
ejpam-6834	177	18	subsets	subset	NOUN
ejpam-6834	177	19	of	of	ADP
ejpam-6834	177	20	cohorts	cohort	NOUN
ejpam-6834	177	21	(	(	PUNCT
ejpam-6834	177	22	collections	collection	NOUN
ejpam-6834	177	23	of	of	ADP
ejpam-6834	177	24	test	test	NOUN
ejpam-6834	177	25	groups	group	NOUN
ejpam-6834	177	26	)	)	PUNCT
ejpam-6834	177	27	.	.	PUNCT
ejpam-6834	178	1	define	define	VERB
ejpam-6834	178	2	a	a	DET
ejpam-6834	178	3	binary	binary	ADJ
ejpam-6834	178	4	operation	operation	NOUN
ejpam-6834	178	5	merge	merge	NOUN
ejpam-6834	178	6	:	:	PUNCT
ejpam-6834	178	7	p2(s	p2(s	NOUN
ejpam-6834	178	8	)	)	PUNCT
ejpam-6834	178	9	×	×	NOUN
ejpam-6834	178	10	p2(s	p2(s	NOUN
ejpam-6834	178	11	)	)	PUNCT
ejpam-6834	178	12	−→	−→	ADJ
ejpam-6834	178	13	p2(s	p2(s	NOUN
ejpam-6834	178	14	)	)	PUNCT
ejpam-6834	178	15	by	by	ADP
ejpam-6834	178	16	merge(c1	merge(c1	NOUN
ejpam-6834	178	17	,	,	PUNCT
ejpam-6834	178	18	c2	c2	PROPN
ejpam-6834	178	19	)	)	PUNCT
ejpam-6834	179	1	=	=	PRON
ejpam-6834	179	2	{	{	PUNCT
ejpam-6834	179	3	g1	g1	PROPN
ejpam-6834	179	4	∪	∪	ADP
ejpam-6834	179	5	g2	g2	PROPN
ejpam-6834	179	6	|	|	ADV
ejpam-6834	179	7	g1	g1	PROPN
ejpam-6834	179	8	∈	∈	PROPN
ejpam-6834	179	9	c1	c1	PROPN
ejpam-6834	179	10	,	,	PUNCT
ejpam-6834	179	11	g2	g2	PROPN
ejpam-6834	179	12	∈	∈	PROPN
ejpam-6834	179	13	c2	c2	PROPN
ejpam-6834	179	14	}	}	PUNCT
ejpam-6834	179	15	.	.	PUNCT
ejpam-6834	180	1	t.	t.	PROPN
ejpam-6834	180	2	fujita	fujita	PROPN
ejpam-6834	180	3	,	,	PUNCT
ejpam-6834	180	4	f.smarandache	f.smarandache	NOUN
ejpam-6834	180	5	/	/	SYM
ejpam-6834	180	6	eur	eur	PROPN
ejpam-6834	180	7	.	.	PUNCT
ejpam-6834	181	1	j.	j.	PROPN
ejpam-6834	181	2	pure	pure	PROPN
ejpam-6834	181	3	appl	appl	PROPN
ejpam-6834	181	4	.	.	PROPN
ejpam-6834	181	5	math	math	PROPN
ejpam-6834	181	6	,	,	PUNCT
ejpam-6834	181	7	18	18	NUM
ejpam-6834	181	8	(	(	PUNCT
ejpam-6834	181	9	4	4	NUM
ejpam-6834	181	10	)	)	PUNCT
ejpam-6834	181	11	(	(	PUNCT
ejpam-6834	181	12	2025	2025	NUM
ejpam-6834	181	13	)	)	PUNCT
ejpam-6834	181	14	,	,	PUNCT
ejpam-6834	181	15	6834	6834	NUM
ejpam-6834	181	16	9	9	NUM
ejpam-6834	181	17	of	of	ADP
ejpam-6834	181	18	69	69	NUM
ejpam-6834	181	19	then	then	ADV
ejpam-6834	181	20	sh2	sh2	PROPN
ejpam-6834	181	21	=	=	SYM
ejpam-6834	181	22	(	(	PUNCT
ejpam-6834	181	23	p2(s	p2(s	NOUN
ejpam-6834	181	24	)	)	PUNCT
ejpam-6834	181	25	,	,	PUNCT
ejpam-6834	181	26	merge	merge	NOUN
ejpam-6834	181	27	)	)	PUNCT
ejpam-6834	181	28	is	be	AUX
ejpam-6834	181	29	a	a	DET
ejpam-6834	181	30	concrete	concrete	ADJ
ejpam-6834	181	31	2	2	NUM
ejpam-6834	181	32	-	-	PUNCT
ejpam-6834	181	33	superhyperstructure	superhyperstructure	NOUN
ejpam-6834	181	34	:	:	PUNCT
ejpam-6834	181	35	each	each	DET
ejpam-6834	181	36	element	element	NOUN
ejpam-6834	181	37	is	be	AUX
ejpam-6834	181	38	a	a	DET
ejpam-6834	181	39	collection	collection	NOUN
ejpam-6834	181	40	of	of	ADP
ejpam-6834	181	41	cohorts	cohort	NOUN
ejpam-6834	181	42	,	,	PUNCT
ejpam-6834	181	43	and	and	CCONJ
ejpam-6834	181	44	merging	merge	VERB
ejpam-6834	181	45	two	two	NUM
ejpam-6834	181	46	collections	collection	NOUN
ejpam-6834	181	47	produces	produce	VERB
ejpam-6834	181	48	every	every	DET
ejpam-6834	181	49	possible	possible	ADJ
ejpam-6834	181	50	union	union	NOUN
ejpam-6834	181	51	of	of	ADP
ejpam-6834	181	52	one	one	NUM
ejpam-6834	181	53	cohort	cohort	NOUN
ejpam-6834	181	54	from	from	ADP
ejpam-6834	181	55	each	each	PRON
ejpam-6834	181	56	.	.	PUNCT
ejpam-6834	182	1	the	the	DET
ejpam-6834	182	2	definition	definition	NOUN
ejpam-6834	182	3	of	of	ADP
ejpam-6834	182	4	the	the	DET
ejpam-6834	182	5	(	(	PUNCT
ejpam-6834	182	6	h	h	NOUN
ejpam-6834	182	7	,	,	PUNCT
ejpam-6834	182	8	k)-ary	k)-ary	ADJ
ejpam-6834	182	9	superhyperstructure	superhyperstructure	NOUN
ejpam-6834	182	10	,	,	PUNCT
ejpam-6834	182	11	which	which	PRON
ejpam-6834	182	12	is	be	AUX
ejpam-6834	182	13	known	know	VERB
ejpam-6834	182	14	as	as	ADP
ejpam-6834	182	15	a	a	DET
ejpam-6834	182	16	further	further	ADJ
ejpam-6834	182	17	generalization	generalization	NOUN
ejpam-6834	182	18	of	of	ADP
ejpam-6834	182	19	the	the	DET
ejpam-6834	182	20	above	above	ADJ
ejpam-6834	182	21	superhyper	superhyper	NOUN
ejpam-6834	182	22	-	-	PUNCT
ejpam-6834	182	23	framework	framework	NOUN
ejpam-6834	182	24	,	,	PUNCT
ejpam-6834	182	25	is	be	AUX
ejpam-6834	182	26	provided	provide	VERB
ejpam-6834	182	27	below	below	ADP
ejpam-6834	182	28	.	.	PUNCT
ejpam-6834	183	1	definition	definition	NOUN
ejpam-6834	183	2	9	9	NUM
ejpam-6834	183	3	(	(	PUNCT
ejpam-6834	183	4	(	(	PUNCT
ejpam-6834	183	5	h	h	NOUN
ejpam-6834	183	6	,	,	PUNCT
ejpam-6834	183	7	k)-ary	k)-ary	ADJ
ejpam-6834	183	8	superhyperstructure	superhyperstructure	NOUN
ejpam-6834	183	9	)	)	PUNCT
ejpam-6834	183	10	.	.	PUNCT
ejpam-6834	184	1	let	let	VERB
ejpam-6834	184	2	s	s	PRON
ejpam-6834	184	3	be	be	AUX
ejpam-6834	184	4	a	a	DET
ejpam-6834	184	5	nonempty	nonempty	ADJ
ejpam-6834	184	6	base	base	NOUN
ejpam-6834	184	7	set	set	NOUN
ejpam-6834	184	8	.	.	PUNCT
ejpam-6834	185	1	for	for	ADP
ejpam-6834	185	2	each	each	DET
ejpam-6834	185	3	i	i	PRON
ejpam-6834	185	4	∈	∈	PROPN
ejpam-6834	185	5	{	{	PUNCT
ejpam-6834	185	6	1	1	NUM
ejpam-6834	185	7	,	,	PUNCT
ejpam-6834	185	8	2	2	NUM
ejpam-6834	185	9	,	,	PUNCT
ejpam-6834	185	10	.	.	PUNCT
ejpam-6834	185	11	.	.	PUNCT
ejpam-6834	185	12	.	.	PUNCT
ejpam-6834	186	1	,	,	PUNCT
ejpam-6834	186	2	h	h	X
ejpam-6834	186	3	}	}	PUNCT
ejpam-6834	186	4	choose	choose	VERB
ejpam-6834	186	5	a	a	DET
ejpam-6834	186	6	nonempty	nonempty	NOUN
ejpam-6834	186	7	subset	subset	NOUN
ejpam-6834	186	8	ai	ai	VERB
ejpam-6834	186	9	⊆	⊆	NUM
ejpam-6834	186	10	s	s	NOUN
ejpam-6834	186	11	and	and	CCONJ
ejpam-6834	186	12	fix	fix	VERB
ejpam-6834	186	13	an	an	DET
ejpam-6834	186	14	integer	integer	NOUN
ejpam-6834	186	15	mi	mi	PROPN
ejpam-6834	186	16	≥	≥	PROPN
ejpam-6834	186	17	0	0	NUM
ejpam-6834	186	18	.	.	PUNCT
ejpam-6834	187	1	denote	denote	VERB
ejpam-6834	187	2	by	by	ADP
ejpam-6834	187	3	pmi(ai	pmi(ai	NOUN
ejpam-6834	187	4	)	)	PUNCT
ejpam-6834	187	5	the	the	DET
ejpam-6834	187	6	mi	mi	PROPN
ejpam-6834	187	7	-	-	PUNCT
ejpam-6834	187	8	th	th	ADV
ejpam-6834	187	9	iterated	iterated	ADJ
ejpam-6834	187	10	powerset	powerset	NOUN
ejpam-6834	187	11	of	of	ADP
ejpam-6834	187	12	ai	ai	PROPN
ejpam-6834	187	13	.	.	PUNCT
ejpam-6834	187	14	similarly	similarly	ADV
ejpam-6834	187	15	,	,	PUNCT
ejpam-6834	187	16	for	for	ADP
ejpam-6834	187	17	each	each	DET
ejpam-6834	187	18	j	j	PROPN
ejpam-6834	187	19	∈	∈	PROPN
ejpam-6834	187	20	{	{	PUNCT
ejpam-6834	187	21	1	1	NUM
ejpam-6834	187	22	,	,	PUNCT
ejpam-6834	187	23	2	2	NUM
ejpam-6834	187	24	,	,	PUNCT
ejpam-6834	187	25	.	.	PUNCT
ejpam-6834	187	26	.	.	PUNCT
ejpam-6834	188	1	.	.	PUNCT
ejpam-6834	189	1	,	,	PUNCT
ejpam-6834	189	2	k	k	X
ejpam-6834	189	3	}	}	PUNCT
ejpam-6834	189	4	choose	choose	VERB
ejpam-6834	189	5	a	a	DET
ejpam-6834	189	6	nonempty	nonempty	NOUN
ejpam-6834	189	7	subset	subset	NOUN
ejpam-6834	189	8	bj	bj	ADP
ejpam-6834	189	9	⊆	⊆	NUM
ejpam-6834	189	10	s	s	NOUN
ejpam-6834	189	11	and	and	CCONJ
ejpam-6834	189	12	fix	fix	VERB
ejpam-6834	189	13	an	an	DET
ejpam-6834	189	14	integer	integer	NOUN
ejpam-6834	189	15	nj	nj	PROPN
ejpam-6834	189	16	≥	≥	PROPN
ejpam-6834	189	17	0	0	NUM
ejpam-6834	189	18	,	,	PUNCT
ejpam-6834	189	19	and	and	CCONJ
ejpam-6834	189	20	denote	denote	VERB
ejpam-6834	189	21	by	by	ADP
ejpam-6834	189	22	pnj	pnj	PROPN
ejpam-6834	189	23	(	(	PUNCT
ejpam-6834	189	24	bj	bj	PROPN
ejpam-6834	189	25	)	)	PUNCT
ejpam-6834	189	26	the	the	DET
ejpam-6834	189	27	nj	nj	PROPN
ejpam-6834	189	28	-	-	PUNCT
ejpam-6834	189	29	th	th	ADV
ejpam-6834	189	30	iterated	iterated	ADJ
ejpam-6834	189	31	powerset	powerset	NOUN
ejpam-6834	189	32	of	of	ADP
ejpam-6834	189	33	bj	bj	NOUN
ejpam-6834	189	34	.	.	PUNCT
ejpam-6834	190	1	define	define	VERB
ejpam-6834	190	2	the	the	DET
ejpam-6834	190	3	domain	domain	NOUN
ejpam-6834	190	4	d	d	NOUN
ejpam-6834	190	5	and	and	CCONJ
ejpam-6834	190	6	codomain	codomain	ADJ
ejpam-6834	190	7	c	c	NOUN
ejpam-6834	190	8	as	as	ADP
ejpam-6834	190	9	d	d	X
ejpam-6834	190	10	=	=	PUNCT
ejpam-6834	190	11	pm1(a1	pm1(a1	NOUN
ejpam-6834	190	12	)	)	PUNCT
ejpam-6834	190	13	×	×	NOUN
ejpam-6834	190	14	pm2(a2	pm2(a2	ADJ
ejpam-6834	190	15	)	)	PUNCT
ejpam-6834	190	16	×	×	NOUN
ejpam-6834	190	17	·	·	PUNCT
ejpam-6834	190	18	·	·	PUNCT
ejpam-6834	190	19	·	·	PUNCT
ejpam-6834	191	1	×	×	NOUN
ejpam-6834	191	2	pmh	pmh	NOUN
ejpam-6834	191	3	(	(	PUNCT
ejpam-6834	191	4	ah	ah	INTJ
ejpam-6834	191	5	)	)	PUNCT
ejpam-6834	191	6	,	,	PUNCT
ejpam-6834	191	7	c	c	NOUN
ejpam-6834	191	8	=	=	SYM
ejpam-6834	191	9	pn1(b1	pn1(b1	X
ejpam-6834	191	10	)	)	PUNCT
ejpam-6834	191	11	×	×	NOUN
ejpam-6834	191	12	pn2(b2	pn2(b2	NOUN
ejpam-6834	191	13	)	)	PUNCT
ejpam-6834	191	14	×	×	NOUN
ejpam-6834	191	15	·	·	PUNCT
ejpam-6834	191	16	·	·	PUNCT
ejpam-6834	191	17	·	·	PUNCT
ejpam-6834	191	18	×	×	NOUN
ejpam-6834	191	19	pnk	pnk	NOUN
ejpam-6834	191	20	(	(	PUNCT
ejpam-6834	191	21	bk	bk	NOUN
ejpam-6834	191	22	)	)	PUNCT
ejpam-6834	191	23	.	.	PUNCT
ejpam-6834	192	1	an	an	DET
ejpam-6834	192	2	(	(	PUNCT
ejpam-6834	192	3	h	h	NOUN
ejpam-6834	192	4	,	,	PUNCT
ejpam-6834	192	5	k)-ary	k)-ary	ADJ
ejpam-6834	192	6	superhyperstructure	superhyperstructure	NOUN
ejpam-6834	192	7	on	on	ADP
ejpam-6834	192	8	s	s	PROPN
ejpam-6834	192	9	is	be	AUX
ejpam-6834	192	10	an	an	DET
ejpam-6834	192	11	algebraic	algebraic	ADJ
ejpam-6834	192	12	system	system	NOUN
ejpam-6834	192	13	sh	sh	INTJ
ejpam-6834	192	14	=	=	PUNCT
ejpam-6834	192	15	(	(	PUNCT
ejpam-6834	192	16	d	d	X
ejpam-6834	192	17	,	,	PUNCT
ejpam-6834	192	18	c	c	NOUN
ejpam-6834	192	19	,	,	PUNCT
ejpam-6834	192	20	{	{	PUNCT
ejpam-6834	192	21	◦	◦	NOUN
ejpam-6834	192	22	α}α∈i	α}α∈i	PRON
ejpam-6834	192	23	)	)	PUNCT
ejpam-6834	192	24	,	,	PUNCT
ejpam-6834	192	25	where	where	SCONJ
ejpam-6834	192	26	{	{	PUNCT
ejpam-6834	192	27	◦	◦	NOUN
ejpam-6834	192	28	α}α∈i	α}α∈i	PRON
ejpam-6834	192	29	is	be	AUX
ejpam-6834	192	30	an	an	DET
ejpam-6834	192	31	indexed	indexed	ADJ
ejpam-6834	192	32	family	family	NOUN
ejpam-6834	192	33	of	of	ADP
ejpam-6834	192	34	superhyperoperations	superhyperoperation	NOUN
ejpam-6834	192	35	◦	◦	VERB
ejpam-6834	192	36	α	α	NOUN
ejpam-6834	192	37	:	:	PUNCT
ejpam-6834	192	38	d	d	X
ejpam-6834	192	39	−→	−→	NOUN
ejpam-6834	192	40	c	c	NOUN
ejpam-6834	192	41	,	,	PUNCT
ejpam-6834	192	42	α	α	PROPN
ejpam-6834	192	43	∈	∈	PROPN
ejpam-6834	192	44	i.	i.	NOUN
ejpam-6834	192	45	for	for	ADP
ejpam-6834	192	46	each	each	PRON
ejpam-6834	192	47	(	(	PUNCT
ejpam-6834	192	48	x1	x1	PROPN
ejpam-6834	192	49	,	,	PUNCT
ejpam-6834	192	50	.	.	PUNCT
ejpam-6834	192	51	.	.	PUNCT
ejpam-6834	193	1	.	.	PUNCT
ejpam-6834	194	1	,	,	PUNCT
ejpam-6834	194	2	xh	xh	PROPN
ejpam-6834	194	3	)	)	PUNCT
ejpam-6834	194	4	∈	∈	PROPN
ejpam-6834	195	1	d	d	NOUN
ejpam-6834	195	2	,	,	PUNCT
ejpam-6834	195	3	one	one	PRON
ejpam-6834	195	4	has	have	VERB
ejpam-6834	195	5	◦	◦	NOUN
ejpam-6834	195	6	α(x1	α(x1	ADJ
ejpam-6834	195	7	,	,	PUNCT
ejpam-6834	195	8	.	.	PUNCT
ejpam-6834	195	9	.	.	PUNCT
ejpam-6834	196	1	.	.	PUNCT
ejpam-6834	197	1	,	,	PUNCT
ejpam-6834	197	2	xh	xh	PROPN
ejpam-6834	197	3	)	)	PUNCT
ejpam-6834	198	1	=	=	PRON
ejpam-6834	198	2	(	(	PUNCT
ejpam-6834	198	3	y1	y1	INTJ
ejpam-6834	198	4	,	,	PUNCT
ejpam-6834	198	5	.	.	PUNCT
ejpam-6834	198	6	.	.	PUNCT
ejpam-6834	199	1	.	.	PUNCT
ejpam-6834	200	1	,	,	PUNCT
ejpam-6834	200	2	yk	yk	PROPN
ejpam-6834	200	3	)	)	PUNCT
ejpam-6834	200	4	∈	∈	PROPN
ejpam-6834	201	1	c	c	NOUN
ejpam-6834	201	2	,	,	PUNCT
ejpam-6834	201	3	with	with	ADP
ejpam-6834	201	4	yj	yj	PROPN
ejpam-6834	201	5	∈	∈	PROPN
ejpam-6834	201	6	pnj	pnj	PROPN
ejpam-6834	201	7	(	(	PUNCT
ejpam-6834	201	8	bj	bj	NOUN
ejpam-6834	201	9	)	)	PUNCT
ejpam-6834	201	10	for	for	ADP
ejpam-6834	201	11	all	all	DET
ejpam-6834	201	12	j.	j.	PROPN
ejpam-6834	201	13	the	the	DET
ejpam-6834	201	14	structural	structural	ADJ
ejpam-6834	201	15	properties	property	NOUN
ejpam-6834	201	16	imposed	impose	VERB
ejpam-6834	201	17	on	on	ADP
ejpam-6834	201	18	the	the	DET
ejpam-6834	201	19	maps	map	NOUN
ejpam-6834	201	20	◦	◦	NOUN
ejpam-6834	201	21	α	α	NOUN
ejpam-6834	201	22	—	—	PUNCT
ejpam-6834	201	23	such	such	ADJ
ejpam-6834	201	24	as	as	ADP
ejpam-6834	201	25	associativity	associativity	NOUN
ejpam-6834	201	26	,	,	PUNCT
ejpam-6834	201	27	commutativity	commutativity	NOUN
ejpam-6834	201	28	,	,	PUNCT
ejpam-6834	201	29	or	or	CCONJ
ejpam-6834	201	30	distributivity	distributivity	NOUN
ejpam-6834	201	31	—	—	PUNCT
ejpam-6834	201	32	are	be	AUX
ejpam-6834	201	33	specified	specify	VERB
ejpam-6834	201	34	according	accord	VERB
ejpam-6834	201	35	to	to	ADP
ejpam-6834	201	36	the	the	DET
ejpam-6834	201	37	algebraic	algebraic	ADJ
ejpam-6834	201	38	framework	framework	NOUN
ejpam-6834	201	39	adopted	adopt	VERB
ejpam-6834	201	40	,	,	PUNCT
ejpam-6834	201	41	thereby	thereby	ADV
ejpam-6834	201	42	extending	extend	VERB
ejpam-6834	201	43	classical	classical	ADJ
ejpam-6834	201	44	algebraic	algebraic	ADJ
ejpam-6834	201	45	systems	system	NOUN
ejpam-6834	201	46	into	into	ADP
ejpam-6834	201	47	a	a	DET
ejpam-6834	201	48	higher	high	ADJ
ejpam-6834	201	49	-	-	PUNCT
ejpam-6834	201	50	order	order	NOUN
ejpam-6834	201	51	superhyperstructural	superhyperstructural	ADJ
ejpam-6834	201	52	setting	setting	NOUN
ejpam-6834	201	53	.	.	PUNCT
ejpam-6834	202	1	example	example	NOUN
ejpam-6834	202	2	4	4	NUM
ejpam-6834	202	3	(	(	PUNCT
ejpam-6834	202	4	collaborative	collaborative	NOUN
ejpam-6834	202	5	-	-	PUNCT
ejpam-6834	202	6	filtering	filtering	NOUN
ejpam-6834	202	7	as	as	ADP
ejpam-6834	202	8	a	a	DET
ejpam-6834	202	9	(	(	PUNCT
ejpam-6834	202	10	2	2	NUM
ejpam-6834	202	11	,	,	PUNCT
ejpam-6834	202	12	2)-ary	2)-ary	NUM
ejpam-6834	202	13	superhyperstructure	superhyperstructure	NOUN
ejpam-6834	202	14	)	)	PUNCT
ejpam-6834	202	15	.	.	PUNCT
ejpam-6834	203	1	in	in	ADP
ejpam-6834	203	2	a	a	DET
ejpam-6834	203	3	recommendation	recommendation	NOUN
ejpam-6834	203	4	system	system	NOUN
ejpam-6834	203	5	,	,	PUNCT
ejpam-6834	203	6	one	one	PRON
ejpam-6834	203	7	often	often	ADV
ejpam-6834	203	8	fuses	fuse	VERB
ejpam-6834	203	9	information	information	NOUN
ejpam-6834	203	10	about	about	ADP
ejpam-6834	203	11	user	user	NOUN
ejpam-6834	203	12	cohorts	cohort	NOUN
ejpam-6834	203	13	and	and	CCONJ
ejpam-6834	203	14	item	item	NOUN
ejpam-6834	203	15	-	-	PUNCT
ejpam-6834	203	16	sets	set	NOUN
ejpam-6834	203	17	to	to	PART
ejpam-6834	203	18	produce	produce	VERB
ejpam-6834	203	19	both	both	DET
ejpam-6834	203	20	new	new	ADJ
ejpam-6834	203	21	item	item	NOUN
ejpam-6834	203	22	suggestions	suggestion	NOUN
ejpam-6834	203	23	and	and	CCONJ
ejpam-6834	203	24	peer	peer	NOUN
ejpam-6834	203	25	cohorts	cohort	NOUN
ejpam-6834	203	26	.	.	PUNCT
ejpam-6834	204	1	let	let	VERB
ejpam-6834	204	2	s	s	PRON
ejpam-6834	204	3	=	=	VERB
ejpam-6834	204	4	u	u	NOUN
ejpam-6834	204	5	∪	∪	NOUN
ejpam-6834	204	6	p	p	NOUN
ejpam-6834	204	7	be	be	VERB
ejpam-6834	204	8	the	the	DET
ejpam-6834	204	9	union	union	NOUN
ejpam-6834	204	10	of	of	ADP
ejpam-6834	204	11	all	all	DET
ejpam-6834	204	12	users	user	NOUN
ejpam-6834	204	13	u	u	NOUN
ejpam-6834	204	14	=	=	X
ejpam-6834	204	15	{	{	PUNCT
ejpam-6834	204	16	hiroko	hiroko	PROPN
ejpam-6834	204	17	,	,	PUNCT
ejpam-6834	204	18	masahiro	masahiro	PROPN
ejpam-6834	204	19	,	,	PUNCT
ejpam-6834	204	20	shinya	shinya	PROPN
ejpam-6834	204	21	,	,	PUNCT
ejpam-6834	204	22	.	.	PUNCT
ejpam-6834	204	23	.	.	PUNCT
ejpam-6834	204	24	.	.	PUNCT
ejpam-6834	205	1	}	}	PUNCT
ejpam-6834	205	2	and	and	CCONJ
ejpam-6834	205	3	all	all	DET
ejpam-6834	205	4	products	product	NOUN
ejpam-6834	205	5	p	p	X
ejpam-6834	205	6	=	=	X
ejpam-6834	205	7	{	{	PUNCT
ejpam-6834	205	8	iphone	iphone	NOUN
ejpam-6834	205	9	,	,	PUNCT
ejpam-6834	205	10	galaxy	galaxy	NOUN
ejpam-6834	205	11	,	,	PUNCT
ejpam-6834	205	12	pixel	pixel	PROPN
ejpam-6834	205	13	,	,	PUNCT
ejpam-6834	205	14	.	.	PUNCT
ejpam-6834	205	15	.	.	PUNCT
ejpam-6834	205	16	.	.	PUNCT
ejpam-6834	206	1	}	}	PUNCT
ejpam-6834	206	2	.	.	PUNCT
ejpam-6834	207	1	t.	t.	PROPN
ejpam-6834	207	2	fujita	fujita	PROPN
ejpam-6834	207	3	,	,	PUNCT
ejpam-6834	207	4	f.smarandache	f.smarandache	NOUN
ejpam-6834	207	5	/	/	SYM
ejpam-6834	207	6	eur	eur	PROPN
ejpam-6834	207	7	.	.	PUNCT
ejpam-6834	208	1	j.	j.	PROPN
ejpam-6834	208	2	pure	pure	PROPN
ejpam-6834	208	3	appl	appl	PROPN
ejpam-6834	208	4	.	.	PROPN
ejpam-6834	208	5	math	math	PROPN
ejpam-6834	208	6	,	,	PUNCT
ejpam-6834	208	7	18	18	NUM
ejpam-6834	208	8	(	(	PUNCT
ejpam-6834	208	9	4	4	NUM
ejpam-6834	208	10	)	)	PUNCT
ejpam-6834	208	11	(	(	PUNCT
ejpam-6834	208	12	2025	2025	NUM
ejpam-6834	208	13	)	)	PUNCT
ejpam-6834	208	14	,	,	PUNCT
ejpam-6834	208	15	6834	6834	NUM
ejpam-6834	208	16	10	10	NUM
ejpam-6834	208	17	of	of	ADP
ejpam-6834	208	18	69	69	NUM
ejpam-6834	208	19	•	•	NOUN
ejpam-6834	208	20	choose	choose	VERB
ejpam-6834	208	21	h	h	NOUN
ejpam-6834	208	22	=	=	SYM
ejpam-6834	208	23	2	2	NUM
ejpam-6834	208	24	inputs	input	NOUN
ejpam-6834	208	25	:	:	PUNCT
ejpam-6834	208	26	a1	a1	NOUN
ejpam-6834	208	27	=	=	SYM
ejpam-6834	208	28	u	u	PROPN
ejpam-6834	208	29	,	,	PUNCT
ejpam-6834	208	30	m1	m1	PROPN
ejpam-6834	208	31	=	=	SYM
ejpam-6834	208	32	1	1	NUM
ejpam-6834	208	33	,	,	PUNCT
ejpam-6834	208	34	a2	a2	PROPN
ejpam-6834	208	35	=	=	SYM
ejpam-6834	208	36	p	p	PROPN
ejpam-6834	208	37	,	,	PUNCT
ejpam-6834	208	38	m2	m2	PROPN
ejpam-6834	208	39	=	=	PROPN
ejpam-6834	208	40	1	1	X
ejpam-6834	208	41	.	.	PUNCT
ejpam-6834	208	42	then	then	ADV
ejpam-6834	208	43	pm1(a1	pm1(a1	ADV
ejpam-6834	208	44	)	)	PUNCT
ejpam-6834	208	45	=	=	SYM
ejpam-6834	209	1	p(u	p(u	X
ejpam-6834	209	2	)	)	PUNCT
ejpam-6834	209	3	is	be	AUX
ejpam-6834	209	4	the	the	DET
ejpam-6834	209	5	set	set	NOUN
ejpam-6834	209	6	of	of	ADP
ejpam-6834	209	7	all	all	DET
ejpam-6834	209	8	user	user	NOUN
ejpam-6834	209	9	-	-	PUNCT
ejpam-6834	209	10	cohorts	cohort	NOUN
ejpam-6834	209	11	,	,	PUNCT
ejpam-6834	209	12	and	and	CCONJ
ejpam-6834	209	13	pm2(a2	pm2(a2	ADJ
ejpam-6834	209	14	)	)	PUNCT
ejpam-6834	210	1	=	=	SYM
ejpam-6834	210	2	p(p	p(p	NOUN
ejpam-6834	210	3	)	)	PUNCT
ejpam-6834	210	4	is	be	AUX
ejpam-6834	210	5	the	the	DET
ejpam-6834	210	6	set	set	NOUN
ejpam-6834	210	7	of	of	ADP
ejpam-6834	210	8	all	all	DET
ejpam-6834	210	9	item	item	NOUN
ejpam-6834	210	10	-	-	PUNCT
ejpam-6834	210	11	sets	set	NOUN
ejpam-6834	210	12	.	.	PUNCT
ejpam-6834	211	1	•	•	NUM
ejpam-6834	211	2	choose	choose	VERB
ejpam-6834	211	3	k	k	NOUN
ejpam-6834	211	4	=	=	SYM
ejpam-6834	211	5	2	2	NUM
ejpam-6834	211	6	outputs	output	NOUN
ejpam-6834	211	7	:	:	PUNCT
ejpam-6834	211	8	b1	b1	NOUN
ejpam-6834	211	9	=	=	SYM
ejpam-6834	211	10	p	p	PROPN
ejpam-6834	211	11	,	,	PUNCT
ejpam-6834	211	12	n1	n1	NOUN
ejpam-6834	211	13	=	=	SYM
ejpam-6834	211	14	1	1	NUM
ejpam-6834	211	15	,	,	PUNCT
ejpam-6834	211	16	b2	b2	NOUN
ejpam-6834	211	17	=	=	SYM
ejpam-6834	211	18	u	u	NOUN
ejpam-6834	211	19	,	,	PUNCT
ejpam-6834	211	20	n2	n2	NOUN
ejpam-6834	211	21	=	=	ADJ
ejpam-6834	211	22	1	1	X
ejpam-6834	211	23	.	.	PUNCT
ejpam-6834	211	24	then	then	ADV
ejpam-6834	211	25	pn1(b1	pn1(b1	NOUN
ejpam-6834	211	26	)	)	PUNCT
ejpam-6834	212	1	=	=	SYM
ejpam-6834	212	2	p(p	p(p	NOUN
ejpam-6834	212	3	)	)	PUNCT
ejpam-6834	212	4	are	be	AUX
ejpam-6834	212	5	the	the	DET
ejpam-6834	212	6	recommended	recommend	VERB
ejpam-6834	212	7	items	item	NOUN
ejpam-6834	212	8	,	,	PUNCT
ejpam-6834	212	9	and	and	CCONJ
ejpam-6834	212	10	pn2(b2	pn2(b2	NOUN
ejpam-6834	212	11	)	)	PUNCT
ejpam-6834	212	12	=	=	SYM
ejpam-6834	213	1	p(u	p(u	X
ejpam-6834	213	2	)	)	PUNCT
ejpam-6834	213	3	are	be	AUX
ejpam-6834	213	4	the	the	DET
ejpam-6834	213	5	peer	peer	NOUN
ejpam-6834	213	6	cohorts	cohort	NOUN
ejpam-6834	213	7	.	.	PUNCT
ejpam-6834	214	1	thus	thus	ADV
ejpam-6834	214	2	the	the	DET
ejpam-6834	214	3	domain	domain	NOUN
ejpam-6834	214	4	and	and	CCONJ
ejpam-6834	214	5	codomain	codomain	NOUN
ejpam-6834	214	6	are	be	AUX
ejpam-6834	214	7	d	d	NOUN
ejpam-6834	214	8	=	=	SYM
ejpam-6834	214	9	p(u	p(u	X
ejpam-6834	214	10	)	)	PUNCT
ejpam-6834	214	11	×	×	NOUN
ejpam-6834	214	12	p(p	p(p	ADV
ejpam-6834	214	13	)	)	PUNCT
ejpam-6834	214	14	,	,	PUNCT
ejpam-6834	214	15	c	c	NOUN
ejpam-6834	214	16	=	=	SYM
ejpam-6834	214	17	p(p	p(p	NOUN
ejpam-6834	214	18	)	)	PUNCT
ejpam-6834	214	19	×	×	NOUN
ejpam-6834	214	20	p(u	p(u	NOUN
ejpam-6834	214	21	)	)	PUNCT
ejpam-6834	214	22	.	.	PUNCT
ejpam-6834	215	1	define	define	VERB
ejpam-6834	215	2	a	a	DET
ejpam-6834	215	3	single	single	ADJ
ejpam-6834	215	4	superhyperoperation	superhyperoperation	NOUN
ejpam-6834	215	5	◦	◦	NOUN
ejpam-6834	215	6	:	:	PUNCT
ejpam-6834	216	1	d	d	X
ejpam-6834	216	2	−→	−→	NOUN
ejpam-6834	216	3	c	c	NOUN
ejpam-6834	216	4	by	by	ADP
ejpam-6834	216	5	collaborative	collaborative	ADJ
ejpam-6834	216	6	-	-	PUNCT
ejpam-6834	216	7	filtering	filter	VERB
ejpam-6834	216	8	logic	logic	NOUN
ejpam-6834	216	9	,	,	PUNCT
ejpam-6834	216	10	for	for	ADP
ejpam-6834	216	11	example	example	NOUN
ejpam-6834	216	12	◦	◦	NOUN
ejpam-6834	216	13	(	(	PUNCT
ejpam-6834	216	14	x	x	X
ejpam-6834	216	15	,	,	PUNCT
ejpam-6834	216	16	y	y	PROPN
ejpam-6834	216	17	)	)	PUNCT
ejpam-6834	216	18	=	=	PUNCT
ejpam-6834	216	19	(	(	PUNCT
ejpam-6834	216	20	recitems(x	recitems(x	PROPN
ejpam-6834	216	21	,	,	PUNCT
ejpam-6834	216	22	y	y	PROPN
ejpam-6834	216	23	)	)	PUNCT
ejpam-6834	216	24	,	,	PUNCT
ejpam-6834	216	25	simusers(x	simusers(x	PROPN
ejpam-6834	216	26	,	,	PUNCT
ejpam-6834	216	27	y	y	PROPN
ejpam-6834	216	28	)	)	PUNCT
ejpam-6834	216	29	)	)	PUNCT
ejpam-6834	216	30	,	,	PUNCT
ejpam-6834	216	31	where	where	SCONJ
ejpam-6834	216	32	recitems(x	recitems(x	ADJ
ejpam-6834	216	33	,	,	PUNCT
ejpam-6834	216	34	y	y	NOUN
ejpam-6834	216	35	)	)	PUNCT
ejpam-6834	216	36	=	=	PRON
ejpam-6834	216	37	{	{	PUNCT
ejpam-6834	216	38	p	p	X
ejpam-6834	216	39	∈	∈	PROPN
ejpam-6834	216	40	p	p	NOUN
ejpam-6834	216	41	|	|	NOUN
ejpam-6834	216	42	∃u	∃u	PROPN
ejpam-6834	216	43	∈	∈	PROPN
ejpam-6834	216	44	x	x	NOUN
ejpam-6834	216	45	,	,	PUNCT
ejpam-6834	216	46	u	u	PRON
ejpam-6834	216	47	liked	like	VERB
ejpam-6834	216	48	p′	p′	PROPN
ejpam-6834	216	49	∈	∈	PROPN
ejpam-6834	216	50	y	y	PROPN
ejpam-6834	216	51	,	,	PUNCT
ejpam-6834	216	52	and	and	CCONJ
ejpam-6834	216	53	other	other	ADJ
ejpam-6834	216	54	users	user	NOUN
ejpam-6834	216	55	in	in	ADP
ejpam-6834	216	56	x	x	PUNCT
ejpam-6834	216	57	also	also	ADV
ejpam-6834	216	58	liked	like	VERB
ejpam-6834	216	59	p	p	PRON
ejpam-6834	216	60	}	}	PUNCT
ejpam-6834	216	61	,	,	PUNCT
ejpam-6834	216	62	simusers(x	simusers(x	PROPN
ejpam-6834	216	63	,	,	PUNCT
ejpam-6834	216	64	y	y	PROPN
ejpam-6834	216	65	)	)	PUNCT
ejpam-6834	217	1	=	=	PRON
ejpam-6834	217	2	{	{	PUNCT
ejpam-6834	217	3	u′	u′	PROPN
ejpam-6834	217	4	∈	∈	PROPN
ejpam-6834	217	5	u	u	NOUN
ejpam-6834	217	6	|	|	ADV
ejpam-6834	217	7	u′	u′	PROPN
ejpam-6834	217	8	/∈	/∈	PUNCT
ejpam-6834	218	1	x	x	NOUN
ejpam-6834	218	2	,	,	PUNCT
ejpam-6834	218	3	∃	∃	PROPN
ejpam-6834	218	4	p	p	PROPN
ejpam-6834	218	5	∈	∈	PROPN
ejpam-6834	218	6	y	y	PROPN
ejpam-6834	218	7	with	with	ADP
ejpam-6834	218	8	u′	u′	PROPN
ejpam-6834	218	9	liked	like	VERB
ejpam-6834	218	10	p	p	X
ejpam-6834	218	11	}	}	PUNCT
ejpam-6834	218	12	.	.	PUNCT
ejpam-6834	219	1	for	for	ADP
ejpam-6834	219	2	instance	instance	NOUN
ejpam-6834	219	3	,	,	PUNCT
ejpam-6834	219	4	◦	◦	NOUN
ejpam-6834	219	5	(	(	PUNCT
ejpam-6834	219	6	{	{	PUNCT
ejpam-6834	219	7	hiroko	hiroko	PROPN
ejpam-6834	219	8	,	,	PUNCT
ejpam-6834	219	9	masahiro	masahiro	PROPN
ejpam-6834	219	10	}	}	PUNCT
ejpam-6834	219	11	,	,	PUNCT
ejpam-6834	219	12	{	{	PUNCT
ejpam-6834	219	13	iphone	iphone	NOUN
ejpam-6834	219	14	,	,	PUNCT
ejpam-6834	219	15	galaxy	galaxy	NOUN
ejpam-6834	219	16	}	}	PUNCT
ejpam-6834	219	17	)	)	PUNCT
ejpam-6834	219	18	=	=	SYM
ejpam-6834	219	19	(	(	PUNCT
ejpam-6834	219	20	{	{	PUNCT
ejpam-6834	219	21	pixel	pixel	ADJ
ejpam-6834	219	22	,	,	PUNCT
ejpam-6834	219	23	oneplus	oneplus	ADJ
ejpam-6834	219	24	}	}	PUNCT
ejpam-6834	219	25	,	,	PUNCT
ejpam-6834	219	26	{	{	PUNCT
ejpam-6834	219	27	shinya	shinya	PROPN
ejpam-6834	219	28	,	,	PUNCT
ejpam-6834	219	29	dan	dan	PROPN
ejpam-6834	219	30	}	}	PUNCT
ejpam-6834	219	31	)	)	PUNCT
ejpam-6834	219	32	.	.	PUNCT
ejpam-6834	220	1	hence	hence	ADV
ejpam-6834	220	2	sh	sh	PROPN
ejpam-6834	220	3	=	=	PUNCT
ejpam-6834	221	1	(	(	PUNCT
ejpam-6834	221	2	d	d	X
ejpam-6834	221	3	,	,	PUNCT
ejpam-6834	221	4	c	c	NOUN
ejpam-6834	221	5	,	,	PUNCT
ejpam-6834	221	6	{	{	PUNCT
ejpam-6834	221	7	◦	◦	NOUN
ejpam-6834	221	8	}	}	PUNCT
ejpam-6834	221	9	)	)	PUNCT
ejpam-6834	221	10	is	be	AUX
ejpam-6834	221	11	a	a	DET
ejpam-6834	221	12	concrete	concrete	ADJ
ejpam-6834	221	13	(	(	PUNCT
ejpam-6834	221	14	2	2	NUM
ejpam-6834	221	15	,	,	PUNCT
ejpam-6834	221	16	2)-ary	2)-ary	NUM
ejpam-6834	221	17	superhyperstructure	superhyperstructure	NOUN
ejpam-6834	221	18	modeling	model	VERB
ejpam-6834	221	19	collaborative	collaborative	NOUN
ejpam-6834	221	20	-	-	PUNCT
ejpam-6834	221	21	filtering	filtering	NOUN
ejpam-6834	221	22	in	in	ADP
ejpam-6834	221	23	practice	practice	NOUN
ejpam-6834	221	24	.	.	PUNCT
ejpam-6834	222	1	example	example	NOUN
ejpam-6834	222	2	5	5	NUM
ejpam-6834	222	3	(	(	PUNCT
ejpam-6834	222	4	smart	smart	ADJ
ejpam-6834	222	5	home	home	NOUN
ejpam-6834	222	6	automation	automation	NOUN
ejpam-6834	222	7	as	as	ADP
ejpam-6834	222	8	a	a	DET
ejpam-6834	222	9	(	(	PUNCT
ejpam-6834	222	10	2	2	NUM
ejpam-6834	222	11	,	,	PUNCT
ejpam-6834	222	12	2)-ary	2)-ary	NUM
ejpam-6834	222	13	superhyperstructure	superhyperstructure	NOUN
ejpam-6834	222	14	)	)	PUNCT
ejpam-6834	222	15	.	.	PUNCT
ejpam-6834	223	1	consider	consider	VERB
ejpam-6834	223	2	a	a	DET
ejpam-6834	223	3	smart	smart	ADJ
ejpam-6834	223	4	home	home	NOUN
ejpam-6834	223	5	system	system	NOUN
ejpam-6834	223	6	where	where	SCONJ
ejpam-6834	223	7	sensor	sensor	NOUN
ejpam-6834	223	8	events	event	NOUN
ejpam-6834	223	9	and	and	CCONJ
ejpam-6834	223	10	notification	notification	NOUN
ejpam-6834	223	11	preferences	preference	NOUN
ejpam-6834	223	12	determine	determine	VERB
ejpam-6834	223	13	both	both	DET
ejpam-6834	223	14	device	device	NOUN
ejpam-6834	223	15	actions	action	NOUN
ejpam-6834	223	16	and	and	CCONJ
ejpam-6834	223	17	alert	alert	NOUN
ejpam-6834	223	18	recipients	recipient	NOUN
ejpam-6834	223	19	.	.	PUNCT
ejpam-6834	224	1	let	let	VERB
ejpam-6834	224	2	the	the	DET
ejpam-6834	224	3	base	base	NOUN
ejpam-6834	224	4	set	set	VERB
ejpam-6834	224	5	be	be	AUX
ejpam-6834	224	6	s	s	NOUN
ejpam-6834	224	7	=	=	PUNCT
ejpam-6834	224	8	{	{	PUNCT
ejpam-6834	224	9	motionsensor	motionsensor	NOUN
ejpam-6834	224	10	,	,	PUNCT
ejpam-6834	224	11	doorsensor	doorsensor	NOUN
ejpam-6834	224	12	,	,	PUNCT
ejpam-6834	224	13	smokesensor	smokesensor	NOUN
ejpam-6834	224	14	,	,	PUNCT
ejpam-6834	224	15	lightswitch	lightswitch	PROPN
ejpam-6834	224	16	,	,	PUNCT
ejpam-6834	224	17	alarm	alarm	NOUN
ejpam-6834	224	18	,	,	PUNCT
ejpam-6834	224	19	ownerapp	ownerapp	ADJ
ejpam-6834	224	20	,	,	PUNCT
ejpam-6834	224	21	securityservice	securityservice	NOUN
ejpam-6834	224	22	}	}	PUNCT
ejpam-6834	224	23	.	.	PUNCT
ejpam-6834	225	1	t.	t.	PROPN
ejpam-6834	225	2	fujita	fujita	PROPN
ejpam-6834	225	3	,	,	PUNCT
ejpam-6834	225	4	f.smarandache	f.smarandache	NOUN
ejpam-6834	225	5	/	/	SYM
ejpam-6834	225	6	eur	eur	PROPN
ejpam-6834	225	7	.	.	PUNCT
ejpam-6834	226	1	j.	j.	PROPN
ejpam-6834	226	2	pure	pure	PROPN
ejpam-6834	226	3	appl	appl	PROPN
ejpam-6834	226	4	.	.	PROPN
ejpam-6834	226	5	math	math	PROPN
ejpam-6834	226	6	,	,	PUNCT
ejpam-6834	226	7	18	18	NUM
ejpam-6834	226	8	(	(	PUNCT
ejpam-6834	226	9	4	4	NUM
ejpam-6834	226	10	)	)	PUNCT
ejpam-6834	226	11	(	(	PUNCT
ejpam-6834	226	12	2025	2025	NUM
ejpam-6834	226	13	)	)	PUNCT
ejpam-6834	226	14	,	,	PUNCT
ejpam-6834	226	15	6834	6834	NUM
ejpam-6834	226	16	11	11	NUM
ejpam-6834	226	17	of	of	ADP
ejpam-6834	226	18	69	69	NUM
ejpam-6834	226	19	choose	choose	VERB
ejpam-6834	226	20	two	two	NUM
ejpam-6834	226	21	input	input	NOUN
ejpam-6834	226	22	subsets	subset	NOUN
ejpam-6834	226	23	:	:	PUNCT
ejpam-6834	226	24	a1	a1	NOUN
ejpam-6834	226	25	=	=	SYM
ejpam-6834	226	26	{	{	PUNCT
ejpam-6834	226	27	motionsensor	motionsensor	NOUN
ejpam-6834	226	28	,	,	PUNCT
ejpam-6834	226	29	doorsensor	doorsensor	NOUN
ejpam-6834	226	30	,	,	PUNCT
ejpam-6834	226	31	smokesensor	smokesensor	NOUN
ejpam-6834	226	32	}	}	PUNCT
ejpam-6834	226	33	,	,	PUNCT
ejpam-6834	226	34	m1	m1	PROPN
ejpam-6834	226	35	=	=	SYM
ejpam-6834	226	36	1	1	NUM
ejpam-6834	226	37	,	,	PUNCT
ejpam-6834	226	38	a2	a2	PROPN
ejpam-6834	226	39	=	=	PUNCT
ejpam-6834	226	40	{	{	PUNCT
ejpam-6834	226	41	ownerapp	ownerapp	ADJ
ejpam-6834	226	42	,	,	PUNCT
ejpam-6834	226	43	securityservice	securityservice	PROPN
ejpam-6834	226	44	}	}	PUNCT
ejpam-6834	226	45	,	,	PUNCT
ejpam-6834	226	46	m2	m2	PROPN
ejpam-6834	226	47	=	=	PROPN
ejpam-6834	226	48	1	1	NUM
ejpam-6834	226	49	,	,	PUNCT
ejpam-6834	226	50	so	so	SCONJ
ejpam-6834	226	51	that	that	SCONJ
ejpam-6834	226	52	pm1(a1	pm1(a1	NOUN
ejpam-6834	226	53	)	)	PUNCT
ejpam-6834	226	54	=	=	SYM
ejpam-6834	226	55	p(a1	p(a1	NOUN
ejpam-6834	226	56	)	)	PUNCT
ejpam-6834	226	57	is	be	AUX
ejpam-6834	226	58	the	the	DET
ejpam-6834	226	59	set	set	NOUN
ejpam-6834	226	60	of	of	ADP
ejpam-6834	226	61	all	all	DET
ejpam-6834	226	62	active	active	ADJ
ejpam-6834	226	63	sensor	sensor	NOUN
ejpam-6834	226	64	-	-	PUNCT
ejpam-6834	226	65	subsets	subset	NOUN
ejpam-6834	226	66	,	,	PUNCT
ejpam-6834	226	67	and	and	CCONJ
ejpam-6834	226	68	pm2(a2	pm2(a2	ADJ
ejpam-6834	226	69	)	)	PUNCT
ejpam-6834	226	70	=	=	SYM
ejpam-6834	226	71	p(a2	p(a2	NOUN
ejpam-6834	226	72	)	)	PUNCT
ejpam-6834	226	73	is	be	AUX
ejpam-6834	226	74	the	the	DET
ejpam-6834	226	75	set	set	NOUN
ejpam-6834	226	76	of	of	ADP
ejpam-6834	226	77	all	all	DET
ejpam-6834	226	78	notification	notification	NOUN
ejpam-6834	226	79	-	-	PUNCT
ejpam-6834	226	80	channel	channel	NOUN
ejpam-6834	226	81	configurations	configuration	NOUN
ejpam-6834	226	82	.	.	PUNCT
ejpam-6834	227	1	similarly	similarly	ADV
ejpam-6834	227	2	,	,	PUNCT
ejpam-6834	227	3	choose	choose	VERB
ejpam-6834	227	4	two	two	NUM
ejpam-6834	227	5	output	output	NOUN
ejpam-6834	227	6	subsets	subset	NOUN
ejpam-6834	227	7	:	:	PUNCT
ejpam-6834	227	8	b1	b1	NOUN
ejpam-6834	227	9	=	=	SYM
ejpam-6834	227	10	{	{	PUNCT
ejpam-6834	227	11	lightswitch	lightswitch	PROPN
ejpam-6834	227	12	,	,	PUNCT
ejpam-6834	227	13	alarm	alarm	NOUN
ejpam-6834	227	14	}	}	PUNCT
ejpam-6834	227	15	,	,	PUNCT
ejpam-6834	227	16	n1	n1	PROPN
ejpam-6834	227	17	=	=	SYM
ejpam-6834	227	18	1	1	NUM
ejpam-6834	227	19	,	,	PUNCT
ejpam-6834	227	20	b2	b2	NOUN
ejpam-6834	227	21	=	=	SYM
ejpam-6834	227	22	{	{	PUNCT
ejpam-6834	227	23	ownerapp	ownerapp	ADJ
ejpam-6834	227	24	,	,	PUNCT
ejpam-6834	227	25	securityservice	securityservice	PROPN
ejpam-6834	227	26	}	}	PUNCT
ejpam-6834	227	27	,	,	PUNCT
ejpam-6834	227	28	n2	n2	NOUN
ejpam-6834	227	29	=	=	SYM
ejpam-6834	227	30	1	1	NUM
ejpam-6834	227	31	,	,	PUNCT
ejpam-6834	227	32	so	so	SCONJ
ejpam-6834	227	33	that	that	SCONJ
ejpam-6834	227	34	pn1(b1	pn1(b1	X
ejpam-6834	227	35	)	)	PUNCT
ejpam-6834	227	36	=	=	SYM
ejpam-6834	227	37	p(b1	p(b1	NOUN
ejpam-6834	227	38	)	)	PUNCT
ejpam-6834	227	39	are	be	AUX
ejpam-6834	227	40	possible	possible	ADJ
ejpam-6834	227	41	device	device	NOUN
ejpam-6834	227	42	-	-	PUNCT
ejpam-6834	227	43	action	action	NOUN
ejpam-6834	227	44	sets	set	NOUN
ejpam-6834	227	45	,	,	PUNCT
ejpam-6834	227	46	and	and	CCONJ
ejpam-6834	227	47	pn2(b2	pn2(b2	NOUN
ejpam-6834	227	48	)	)	PUNCT
ejpam-6834	227	49	=	=	SYM
ejpam-6834	227	50	p(b2	p(b2	NOUN
ejpam-6834	227	51	)	)	PUNCT
ejpam-6834	227	52	are	be	AUX
ejpam-6834	227	53	possible	possible	ADJ
ejpam-6834	227	54	recipient	recipient	NOUN
ejpam-6834	227	55	sets	set	NOUN
ejpam-6834	227	56	.	.	PUNCT
ejpam-6834	228	1	thus	thus	ADV
ejpam-6834	228	2	the	the	DET
ejpam-6834	228	3	domain	domain	NOUN
ejpam-6834	228	4	and	and	CCONJ
ejpam-6834	228	5	codomain	codomain	NOUN
ejpam-6834	228	6	are	be	AUX
ejpam-6834	228	7	d	d	NOUN
ejpam-6834	228	8	=	=	PUNCT
ejpam-6834	228	9	p(a1	p(a1	NOUN
ejpam-6834	228	10	)	)	PUNCT
ejpam-6834	228	11	×	×	NOUN
ejpam-6834	228	12	p(a2	p(a2	NOUN
ejpam-6834	228	13	)	)	PUNCT
ejpam-6834	228	14	,	,	PUNCT
ejpam-6834	228	15	c	c	NOUN
ejpam-6834	228	16	=	=	SYM
ejpam-6834	228	17	p(b1	p(b1	PROPN
ejpam-6834	228	18	)	)	PUNCT
ejpam-6834	228	19	×	×	PROPN
ejpam-6834	228	20	p(b2	p(b2	NOUN
ejpam-6834	228	21	)	)	PUNCT
ejpam-6834	228	22	.	.	PUNCT
ejpam-6834	229	1	define	define	VERB
ejpam-6834	229	2	a	a	DET
ejpam-6834	229	3	single	single	ADJ
ejpam-6834	229	4	superhyperoperation	superhyperoperation	NOUN
ejpam-6834	229	5	◦	◦	NOUN
ejpam-6834	229	6	:	:	PUNCT
ejpam-6834	230	1	d	d	X
ejpam-6834	230	2	−→	−→	NOUN
ejpam-6834	230	3	c	c	NOUN
ejpam-6834	230	4	by	by	ADP
ejpam-6834	230	5	◦	◦	NOUN
ejpam-6834	230	6	(	(	PUNCT
ejpam-6834	230	7	x	x	X
ejpam-6834	230	8	,	,	PUNCT
ejpam-6834	230	9	y	y	PROPN
ejpam-6834	230	10	)	)	PUNCT
ejpam-6834	230	11	=	=	PUNCT
ejpam-6834	230	12	(	(	PUNCT
ejpam-6834	230	13	actions(x	actions(x	PROPN
ejpam-6834	230	14	)	)	PUNCT
ejpam-6834	230	15	,	,	PUNCT
ejpam-6834	230	16	recipients(x	recipients(x	PROPN
ejpam-6834	230	17	,	,	PUNCT
ejpam-6834	230	18	y	y	PROPN
ejpam-6834	230	19	)	)	PUNCT
ejpam-6834	230	20	)	)	PUNCT
ejpam-6834	230	21	,	,	PUNCT
ejpam-6834	230	22	where	where	SCONJ
ejpam-6834	230	23	actions(x	actions(x	NOUN
ejpam-6834	230	24	)	)	PUNCT
ejpam-6834	231	1	=	=	SYM
ejpam-6834	231	2			PROPN
ejpam-6834	231	3	{	{	PUNCT
ejpam-6834	231	4	lightswitch	lightswitch	PROPN
ejpam-6834	231	5	}	}	PUNCT
ejpam-6834	231	6	,	,	PUNCT
ejpam-6834	231	7	if	if	SCONJ
ejpam-6834	231	8	motionsensor	motionsensor	NOUN
ejpam-6834	231	9	∈	∈	PROPN
ejpam-6834	231	10	x	x	X
ejpam-6834	231	11	,	,	PUNCT
ejpam-6834	231	12	{	{	PUNCT
ejpam-6834	231	13	alarm	alarm	NOUN
ejpam-6834	231	14	}	}	PUNCT
ejpam-6834	231	15	,	,	PUNCT
ejpam-6834	231	16	if	if	SCONJ
ejpam-6834	231	17	smokesensor	smokesensor	NOUN
ejpam-6834	231	18	∈	∈	PROPN
ejpam-6834	231	19	x	x	NOUN
ejpam-6834	231	20	,	,	PUNCT
ejpam-6834	231	21	∅	∅	NOUN
ejpam-6834	231	22	,	,	PUNCT
ejpam-6834	231	23	otherwise	otherwise	ADV
ejpam-6834	231	24	,	,	PUNCT
ejpam-6834	231	25	recipients(x	recipients(x	PROPN
ejpam-6834	231	26	,	,	PUNCT
ejpam-6834	231	27	y	y	PROPN
ejpam-6834	231	28	)	)	PUNCT
ejpam-6834	231	29	=	=	PRON
ejpam-6834	231	30	{	{	PUNCT
ejpam-6834	231	31	r	r	NOUN
ejpam-6834	231	32	∈	∈	PROPN
ejpam-6834	231	33	y	y	NOUN
ejpam-6834	232	1	|	|	ADV
ejpam-6834	232	2	r	r	NOUN
ejpam-6834	232	3	is	be	AUX
ejpam-6834	232	4	configured	configure	VERB
ejpam-6834	232	5	}	}	PUNCT
ejpam-6834	232	6	.	.	PUNCT
ejpam-6834	233	1	for	for	ADP
ejpam-6834	233	2	example	example	NOUN
ejpam-6834	233	3	,	,	PUNCT
ejpam-6834	233	4	◦	◦	NOUN
ejpam-6834	233	5	(	(	PUNCT
ejpam-6834	233	6	{	{	PUNCT
ejpam-6834	233	7	motionsensor	motionsensor	NOUN
ejpam-6834	233	8	,	,	PUNCT
ejpam-6834	233	9	smokesensor	smokesensor	NOUN
ejpam-6834	233	10	}	}	PUNCT
ejpam-6834	233	11	,	,	PUNCT
ejpam-6834	233	12	{	{	PUNCT
ejpam-6834	233	13	ownerapp	ownerapp	ADJ
ejpam-6834	233	14	}	}	PUNCT
ejpam-6834	233	15	)	)	PUNCT
ejpam-6834	234	1	=	=	SYM
ejpam-6834	234	2	(	(	PUNCT
ejpam-6834	234	3	{	{	PUNCT
ejpam-6834	234	4	lightswitch	lightswitch	NOUN
ejpam-6834	234	5	,	,	PUNCT
ejpam-6834	234	6	alarm	alarm	NOUN
ejpam-6834	234	7	}	}	PUNCT
ejpam-6834	234	8	,	,	PUNCT
ejpam-6834	234	9	{	{	PUNCT
ejpam-6834	234	10	ownerapp	ownerapp	ADJ
ejpam-6834	234	11	}	}	PUNCT
ejpam-6834	234	12	)	)	PUNCT
ejpam-6834	234	13	.	.	PUNCT
ejpam-6834	235	1	therefore	therefore	ADV
ejpam-6834	235	2	,	,	PUNCT
ejpam-6834	235	3	sh	sh	PROPN
ejpam-6834	235	4	=	=	PUNCT
ejpam-6834	235	5	(	(	PUNCT
ejpam-6834	235	6	d	d	X
ejpam-6834	235	7	,	,	PUNCT
ejpam-6834	235	8	c	c	NOUN
ejpam-6834	235	9	,	,	PUNCT
ejpam-6834	235	10	{	{	PUNCT
ejpam-6834	235	11	◦	◦	NOUN
ejpam-6834	235	12	}	}	PUNCT
ejpam-6834	235	13	)	)	PUNCT
ejpam-6834	235	14	is	be	AUX
ejpam-6834	235	15	a	a	DET
ejpam-6834	235	16	concrete	concrete	ADJ
ejpam-6834	235	17	(	(	PUNCT
ejpam-6834	235	18	2	2	NUM
ejpam-6834	235	19	,	,	PUNCT
ejpam-6834	235	20	2)-ary	2)-ary	NUM
ejpam-6834	235	21	superhyperstructure	superhyperstructure	NOUN
ejpam-6834	235	22	modeling	model	VERB
ejpam-6834	235	23	a	a	DET
ejpam-6834	235	24	real	real	ADJ
ejpam-6834	235	25	-	-	PUNCT
ejpam-6834	235	26	world	world	NOUN
ejpam-6834	235	27	smart	smart	ADJ
ejpam-6834	235	28	home	home	NOUN
ejpam-6834	235	29	automation	automation	NOUN
ejpam-6834	235	30	workflow	workflow	NOUN
ejpam-6834	235	31	.	.	PUNCT
ejpam-6834	236	1	t.	t.	PROPN
ejpam-6834	236	2	fujita	fujita	PROPN
ejpam-6834	236	3	,	,	PUNCT
ejpam-6834	236	4	f.smarandache	f.smarandache	NOUN
ejpam-6834	236	5	/	/	SYM
ejpam-6834	236	6	eur	eur	PROPN
ejpam-6834	236	7	.	.	PUNCT
ejpam-6834	237	1	j.	j.	PROPN
ejpam-6834	237	2	pure	pure	PROPN
ejpam-6834	237	3	appl	appl	PROPN
ejpam-6834	237	4	.	.	PROPN
ejpam-6834	237	5	math	math	PROPN
ejpam-6834	237	6	,	,	PUNCT
ejpam-6834	237	7	18	18	NUM
ejpam-6834	237	8	(	(	PUNCT
ejpam-6834	237	9	4	4	NUM
ejpam-6834	237	10	)	)	PUNCT
ejpam-6834	237	11	(	(	PUNCT
ejpam-6834	237	12	2025	2025	NUM
ejpam-6834	237	13	)	)	PUNCT
ejpam-6834	237	14	,	,	PUNCT
ejpam-6834	237	15	6834	6834	NUM
ejpam-6834	237	16	12	12	NUM
ejpam-6834	237	17	of	of	ADP
ejpam-6834	237	18	69	69	NUM
ejpam-6834	237	19	2.2	2.2	NUM
ejpam-6834	237	20	.	.	PUNCT
ejpam-6834	238	1	fuzzy	fuzzy	PROPN
ejpam-6834	238	2	set	set	VERB
ejpam-6834	238	3	the	the	DET
ejpam-6834	238	4	fuzzy	fuzzy	ADJ
ejpam-6834	238	5	set	set	NOUN
ejpam-6834	238	6	is	be	AUX
ejpam-6834	238	7	a	a	DET
ejpam-6834	238	8	well	well	ADV
ejpam-6834	238	9	-	-	PUNCT
ejpam-6834	238	10	known	know	VERB
ejpam-6834	238	11	concept	concept	NOUN
ejpam-6834	238	12	used	use	VERB
ejpam-6834	238	13	to	to	PART
ejpam-6834	238	14	address	address	VERB
ejpam-6834	238	15	uncertainty	uncertainty	NOUN
ejpam-6834	238	16	in	in	ADP
ejpam-6834	238	17	set	set	NOUN
ejpam-6834	238	18	theory[5	theory[5	NUM
ejpam-6834	238	19	,	,	PUNCT
ejpam-6834	238	20	54	54	NUM
ejpam-6834	238	21	,	,	PUNCT
ejpam-6834	238	22	55	55	NUM
ejpam-6834	238	23	]	]	PUNCT
ejpam-6834	238	24	.	.	PUNCT
ejpam-6834	239	1	these	these	DET
ejpam-6834	239	2	sets	set	NOUN
ejpam-6834	239	3	can	can	AUX
ejpam-6834	239	4	be	be	AUX
ejpam-6834	239	5	extended	extend	VERB
ejpam-6834	239	6	into	into	ADP
ejpam-6834	239	7	hyperfuzzy	hyperfuzzy	PROPN
ejpam-6834	239	8	sets[56	sets[56	PROPN
ejpam-6834	239	9	,	,	PUNCT
ejpam-6834	239	10	57	57	NUM
ejpam-6834	239	11	]	]	PUNCT
ejpam-6834	239	12	and	and	CCONJ
ejpam-6834	239	13	superhyperfuzzy	superhyperfuzzy	PROPN
ejpam-6834	239	14	sets[58	sets[58	NOUN
ejpam-6834	239	15	]	]	PUNCT
ejpam-6834	239	16	using	use	VERB
ejpam-6834	239	17	hyperstructures	hyperstructure	NOUN
ejpam-6834	239	18	and	and	CCONJ
ejpam-6834	239	19	superhyperstructures	superhyperstructure	NOUN
ejpam-6834	239	20	.	.	PUNCT
ejpam-6834	240	1	the	the	DET
ejpam-6834	240	2	definition	definition	NOUN
ejpam-6834	240	3	is	be	AUX
ejpam-6834	240	4	provided	provide	VERB
ejpam-6834	240	5	below	below	ADV
ejpam-6834	240	6	.	.	PUNCT
ejpam-6834	241	1	definition	definition	NOUN
ejpam-6834	241	2	10	10	NUM
ejpam-6834	241	3	(	(	PUNCT
ejpam-6834	241	4	fuzzy	fuzzy	ADJ
ejpam-6834	241	5	set	set	NOUN
ejpam-6834	241	6	)	)	PUNCT
ejpam-6834	241	7	.	.	PUNCT
ejpam-6834	242	1	[	[	X
ejpam-6834	242	2	5	5	X
ejpam-6834	242	3	]	]	PUNCT
ejpam-6834	242	4	a	a	DET
ejpam-6834	242	5	fuzzy	fuzzy	ADJ
ejpam-6834	242	6	set	set	NOUN
ejpam-6834	242	7	τ	τ	PROPN
ejpam-6834	242	8	in	in	ADP
ejpam-6834	242	9	a	a	DET
ejpam-6834	242	10	non	non	ADJ
ejpam-6834	242	11	-	-	ADJ
ejpam-6834	242	12	empty	empty	ADJ
ejpam-6834	242	13	universe	universe	NOUN
ejpam-6834	242	14	y	y	NOUN
ejpam-6834	242	15	is	be	AUX
ejpam-6834	242	16	a	a	DET
ejpam-6834	242	17	mapping	mapping	NOUN
ejpam-6834	242	18	τ	τ	X
ejpam-6834	242	19	:	:	PUNCT
ejpam-6834	242	20	y	y	PROPN
ejpam-6834	242	21	→	→	PUNCT
ejpam-6834	243	1	[	[	X
ejpam-6834	243	2	0	0	NUM
ejpam-6834	243	3	,	,	PUNCT
ejpam-6834	243	4	1	1	NUM
ejpam-6834	243	5	]	]	PUNCT
ejpam-6834	243	6	.	.	PUNCT
ejpam-6834	244	1	a	a	DET
ejpam-6834	244	2	fuzzy	fuzzy	ADJ
ejpam-6834	244	3	relation	relation	NOUN
ejpam-6834	244	4	on	on	ADP
ejpam-6834	244	5	y	y	PROPN
ejpam-6834	244	6	is	be	AUX
ejpam-6834	244	7	a	a	DET
ejpam-6834	244	8	fuzzy	fuzzy	ADJ
ejpam-6834	244	9	subset	subset	NOUN
ejpam-6834	244	10	δ	δ	PROPN
ejpam-6834	244	11	in	in	ADP
ejpam-6834	244	12	y	y	PROPN
ejpam-6834	244	13	×	×	PROPN
ejpam-6834	244	14	y	y	PROPN
ejpam-6834	244	15	.	.	PUNCT
ejpam-6834	245	1	if	if	SCONJ
ejpam-6834	245	2	τ	τ	PROPN
ejpam-6834	245	3	is	be	AUX
ejpam-6834	245	4	a	a	DET
ejpam-6834	245	5	fuzzy	fuzzy	ADJ
ejpam-6834	245	6	set	set	NOUN
ejpam-6834	245	7	in	in	ADP
ejpam-6834	245	8	y	y	PROPN
ejpam-6834	245	9	and	and	CCONJ
ejpam-6834	245	10	δ	δ	PROPN
ejpam-6834	245	11	is	be	AUX
ejpam-6834	245	12	a	a	DET
ejpam-6834	245	13	fuzzy	fuzzy	ADJ
ejpam-6834	245	14	relation	relation	NOUN
ejpam-6834	245	15	on	on	ADP
ejpam-6834	245	16	y	y	PROPN
ejpam-6834	245	17	,	,	PUNCT
ejpam-6834	245	18	then	then	ADV
ejpam-6834	245	19	δ	δ	PROPN
ejpam-6834	245	20	is	be	AUX
ejpam-6834	245	21	called	call	VERB
ejpam-6834	245	22	a	a	DET
ejpam-6834	245	23	fuzzy	fuzzy	ADJ
ejpam-6834	245	24	relation	relation	NOUN
ejpam-6834	245	25	on	on	ADP
ejpam-6834	245	26	τ	τ	PROPN
ejpam-6834	245	27	if	if	SCONJ
ejpam-6834	245	28	δ(y	δ(y	ADV
ejpam-6834	245	29	,	,	PUNCT
ejpam-6834	245	30	z	z	NOUN
ejpam-6834	245	31	)	)	PUNCT
ejpam-6834	245	32	≤	≤	NOUN
ejpam-6834	245	33	min{τ(y	min{τ(y	PROPN
ejpam-6834	245	34	)	)	PUNCT
ejpam-6834	245	35	,	,	PUNCT
ejpam-6834	245	36	τ(z	τ(z	NOUN
ejpam-6834	245	37	)	)	PUNCT
ejpam-6834	245	38	}	}	PUNCT
ejpam-6834	245	39	for	for	ADP
ejpam-6834	245	40	all	all	DET
ejpam-6834	245	41	y	y	PROPN
ejpam-6834	245	42	,	,	PUNCT
ejpam-6834	245	43	z	z	PROPN
ejpam-6834	245	44	∈	∈	PROPN
ejpam-6834	245	45	y.	y.	NOUN
ejpam-6834	245	46	definition	definition	NOUN
ejpam-6834	245	47	11	11	NUM
ejpam-6834	245	48	(	(	PUNCT
ejpam-6834	245	49	hyperfuzzy	hyperfuzzy	NOUN
ejpam-6834	245	50	set	set	NOUN
ejpam-6834	245	51	)	)	PUNCT
ejpam-6834	245	52	.	.	PUNCT
ejpam-6834	246	1	[	[	X
ejpam-6834	246	2	2	2	NUM
ejpam-6834	246	3	,	,	PUNCT
ejpam-6834	246	4	59–61	59–61	NUM
ejpam-6834	246	5	]	]	PUNCT
ejpam-6834	246	6	let	let	VERB
ejpam-6834	246	7	x	x	PRON
ejpam-6834	246	8	be	be	AUX
ejpam-6834	246	9	a	a	DET
ejpam-6834	246	10	non	non	ADJ
ejpam-6834	246	11	-	-	ADJ
ejpam-6834	246	12	empty	empty	ADJ
ejpam-6834	246	13	set	set	NOUN
ejpam-6834	246	14	.	.	PUNCT
ejpam-6834	247	1	a	a	DET
ejpam-6834	247	2	hyperfuzzy	hyperfuzzy	NOUN
ejpam-6834	247	3	set	set	VERB
ejpam-6834	247	4	over	over	ADP
ejpam-6834	247	5	x	x	PUNCT
ejpam-6834	247	6	is	be	AUX
ejpam-6834	247	7	defined	define	VERB
ejpam-6834	247	8	as	as	ADP
ejpam-6834	247	9	a	a	DET
ejpam-6834	247	10	mapping	mapping	NOUN
ejpam-6834	247	11	:	:	PUNCT
ejpam-6834	247	12	µ̃	µ̃	PROPN
ejpam-6834	247	13	:	:	PUNCT
ejpam-6834	247	14	x	x	SYM
ejpam-6834	247	15	→	→	SYM
ejpam-6834	247	16	p([0	p([0	ADJ
ejpam-6834	247	17	,	,	PUNCT
ejpam-6834	247	18	1	1	NUM
ejpam-6834	247	19	]	]	PUNCT
ejpam-6834	247	20	)	)	PUNCT
ejpam-6834	247	21	\	\	NOUN
ejpam-6834	248	1	{	{	PUNCT
ejpam-6834	248	2	∅	∅	NOUN
ejpam-6834	248	3	}	}	PUNCT
ejpam-6834	248	4	,	,	PUNCT
ejpam-6834	248	5	where	where	SCONJ
ejpam-6834	248	6	p([0	p([0	NOUN
ejpam-6834	248	7	,	,	PUNCT
ejpam-6834	248	8	1	1	NUM
ejpam-6834	248	9	]	]	PUNCT
ejpam-6834	248	10	)	)	PUNCT
ejpam-6834	248	11	\	\	NOUN
ejpam-6834	248	12	{	{	PUNCT
ejpam-6834	248	13	∅	∅	NOUN
ejpam-6834	248	14	}	}	PUNCT
ejpam-6834	248	15	represents	represent	VERB
ejpam-6834	248	16	the	the	DET
ejpam-6834	248	17	family	family	NOUN
ejpam-6834	248	18	of	of	ADP
ejpam-6834	248	19	all	all	DET
ejpam-6834	248	20	non	non	ADJ
ejpam-6834	248	21	-	-	ADJ
ejpam-6834	248	22	empty	empty	ADJ
ejpam-6834	248	23	subsets	subset	NOUN
ejpam-6834	248	24	of	of	ADP
ejpam-6834	248	25	the	the	DET
ejpam-6834	248	26	interval	interval	NOUN
ejpam-6834	248	27	[	[	X
ejpam-6834	248	28	0	0	NUM
ejpam-6834	248	29	,	,	PUNCT
ejpam-6834	248	30	1	1	NUM
ejpam-6834	248	31	]	]	PUNCT
ejpam-6834	248	32	.	.	PUNCT
ejpam-6834	249	1	for	for	ADP
ejpam-6834	249	2	each	each	DET
ejpam-6834	249	3	element	element	NOUN
ejpam-6834	249	4	x	x	SYM
ejpam-6834	249	5	∈	∈	PROPN
ejpam-6834	249	6	x	x	SYM
ejpam-6834	249	7	,	,	PUNCT
ejpam-6834	249	8	µ̃(x	µ̃(x	ADJ
ejpam-6834	249	9	)	)	PUNCT
ejpam-6834	249	10	assigns	assign	VERB
ejpam-6834	249	11	a	a	DET
ejpam-6834	249	12	non	non	ADJ
ejpam-6834	249	13	-	-	ADJ
ejpam-6834	249	14	empty	empty	ADJ
ejpam-6834	249	15	subset	subset	NOUN
ejpam-6834	249	16	of	of	ADP
ejpam-6834	249	17	[	[	X
ejpam-6834	249	18	0	0	NUM
ejpam-6834	249	19	,	,	PUNCT
ejpam-6834	249	20	1	1	NUM
ejpam-6834	249	21	]	]	PUNCT
ejpam-6834	249	22	,	,	PUNCT
ejpam-6834	249	23	representing	represent	VERB
ejpam-6834	249	24	the	the	DET
ejpam-6834	249	25	possible	possible	ADJ
ejpam-6834	249	26	membership	membership	NOUN
ejpam-6834	249	27	degrees	degree	NOUN
ejpam-6834	249	28	of	of	ADP
ejpam-6834	249	29	x	x	PUNCT
ejpam-6834	249	30	in	in	ADP
ejpam-6834	249	31	the	the	DET
ejpam-6834	249	32	hyperfuzzy	hyperfuzzy	NOUN
ejpam-6834	249	33	set	set	NOUN
ejpam-6834	249	34	.	.	PUNCT
ejpam-6834	250	1	this	this	DET
ejpam-6834	250	2	definition	definition	NOUN
ejpam-6834	250	3	generalizes	generalize	VERB
ejpam-6834	250	4	classical	classical	ADJ
ejpam-6834	250	5	fuzzy	fuzzy	ADJ
ejpam-6834	250	6	sets	set	NOUN
ejpam-6834	250	7	by	by	ADP
ejpam-6834	250	8	allowing	allow	VERB
ejpam-6834	250	9	the	the	DET
ejpam-6834	250	10	membership	membership	NOUN
ejpam-6834	250	11	degree	degree	NOUN
ejpam-6834	250	12	of	of	ADP
ejpam-6834	250	13	each	each	DET
ejpam-6834	250	14	element	element	NOUN
ejpam-6834	250	15	to	to	PART
ejpam-6834	250	16	be	be	AUX
ejpam-6834	250	17	a	a	DET
ejpam-6834	250	18	range	range	NOUN
ejpam-6834	250	19	(	(	PUNCT
ejpam-6834	250	20	set	set	NOUN
ejpam-6834	250	21	of	of	ADP
ejpam-6834	250	22	values	value	NOUN
ejpam-6834	250	23	)	)	PUNCT
ejpam-6834	250	24	instead	instead	ADV
ejpam-6834	250	25	of	of	ADP
ejpam-6834	250	26	a	a	DET
ejpam-6834	250	27	single	single	ADJ
ejpam-6834	250	28	scalar	scalar	ADJ
ejpam-6834	250	29	value	value	NOUN
ejpam-6834	250	30	.	.	PUNCT
ejpam-6834	251	1	example	example	NOUN
ejpam-6834	251	2	6	6	NUM
ejpam-6834	251	3	(	(	PUNCT
ejpam-6834	251	4	restaurant	restaurant	NOUN
ejpam-6834	251	5	customer	customer	NOUN
ejpam-6834	251	6	satisfaction	satisfaction	NOUN
ejpam-6834	251	7	)	)	PUNCT
ejpam-6834	251	8	.	.	PUNCT
ejpam-6834	252	1	let	let	VERB
ejpam-6834	252	2	x	x	PUNCT
ejpam-6834	252	3	=	=	PRON
ejpam-6834	252	4	{	{	PUNCT
ejpam-6834	252	5	r1	r1	PROPN
ejpam-6834	252	6	,	,	PUNCT
ejpam-6834	252	7	r2	r2	PROPN
ejpam-6834	252	8	,	,	PUNCT
ejpam-6834	252	9	r3	r3	PROPN
ejpam-6834	252	10	}	}	PUNCT
ejpam-6834	252	11	be	be	AUX
ejpam-6834	252	12	a	a	DET
ejpam-6834	252	13	set	set	NOUN
ejpam-6834	252	14	of	of	ADP
ejpam-6834	252	15	restaurants	restaurant	NOUN
ejpam-6834	252	16	.	.	PUNCT
ejpam-6834	253	1	we	we	PRON
ejpam-6834	253	2	define	define	VERB
ejpam-6834	253	3	a	a	DET
ejpam-6834	253	4	hyperfuzzy	hyperfuzzy	NOUN
ejpam-6834	253	5	set	set	VERB
ejpam-6834	253	6	µ̃	µ̃	PROPN
ejpam-6834	253	7	:	:	PUNCT
ejpam-6834	253	8	x	x	SYM
ejpam-6834	253	9	→	→	SYM
ejpam-6834	253	10	p([0	p([0	ADJ
ejpam-6834	253	11	,	,	PUNCT
ejpam-6834	253	12	1	1	NUM
ejpam-6834	253	13	]	]	PUNCT
ejpam-6834	253	14	)	)	PUNCT
ejpam-6834	253	15	\	\	NOUN
ejpam-6834	254	1	{	{	PUNCT
ejpam-6834	254	2	∅	∅	NOUN
ejpam-6834	254	3	}	}	PUNCT
ejpam-6834	254	4	modeling	model	VERB
ejpam-6834	254	5	customer	customer	NOUN
ejpam-6834	254	6	satisfaction	satisfaction	NOUN
ejpam-6834	254	7	as	as	SCONJ
ejpam-6834	254	8	follows	follow	VERB
ejpam-6834	254	9	:	:	PUNCT
ejpam-6834	254	10	µ̃(r1	µ̃(r1	X
ejpam-6834	254	11	)	)	PUNCT
ejpam-6834	254	12	=	=	NOUN
ejpam-6834	255	1	[	[	X
ejpam-6834	255	2	0.7	0.7	NUM
ejpam-6834	255	3	,	,	PUNCT
ejpam-6834	255	4	0.9	0.9	NUM
ejpam-6834	255	5	]	]	PUNCT
ejpam-6834	255	6	,	,	PUNCT
ejpam-6834	255	7	µ̃(r2	µ̃(r2	X
ejpam-6834	255	8	)	)	PUNCT
ejpam-6834	255	9	=	=	NOUN
ejpam-6834	255	10	{	{	PUNCT
ejpam-6834	255	11	0.5	0.5	NUM
ejpam-6834	255	12	,	,	PUNCT
ejpam-6834	255	13	0.6	0.6	NUM
ejpam-6834	255	14	,	,	PUNCT
ejpam-6834	255	15	0.7	0.7	NUM
ejpam-6834	255	16	}	}	PUNCT
ejpam-6834	255	17	,	,	PUNCT
ejpam-6834	255	18	µ̃(r3	µ̃(r3	PUNCT
ejpam-6834	255	19	)	)	PUNCT
ejpam-6834	255	20	=	=	NOUN
ejpam-6834	256	1	[	[	X
ejpam-6834	256	2	0.2	0.2	NUM
ejpam-6834	256	3	,	,	PUNCT
ejpam-6834	256	4	0.4	0.4	NUM
ejpam-6834	256	5	]	]	PUNCT
ejpam-6834	256	6	∪	∪	X
ejpam-6834	256	7	{	{	PUNCT
ejpam-6834	256	8	0.6	0.6	NUM
ejpam-6834	256	9	}	}	PUNCT
ejpam-6834	256	10	.	.	PUNCT
ejpam-6834	257	1	here	here	ADV
ejpam-6834	257	2	:	:	PUNCT
ejpam-6834	257	3	•	•	NUM
ejpam-6834	257	4	µ̃(r1	µ̃(r1	NUM
ejpam-6834	257	5	)	)	PUNCT
ejpam-6834	257	6	=	=	PUNCT
ejpam-6834	258	1	[	[	X
ejpam-6834	258	2	0.7	0.7	NUM
ejpam-6834	258	3	,	,	PUNCT
ejpam-6834	258	4	0.9	0.9	NUM
ejpam-6834	258	5	]	]	PUNCT
ejpam-6834	258	6	reflects	reflect	VERB
ejpam-6834	258	7	that	that	SCONJ
ejpam-6834	258	8	customers	customer	NOUN
ejpam-6834	258	9	’	'	PUNCT
ejpam-6834	258	10	satisfaction	satisfaction	NOUN
ejpam-6834	258	11	scores	score	NOUN
ejpam-6834	258	12	for	for	ADP
ejpam-6834	258	13	r1	r1	PROPN
ejpam-6834	258	14	range	range	NOUN
ejpam-6834	258	15	continuously	continuously	ADV
ejpam-6834	258	16	from	from	ADP
ejpam-6834	258	17	0.7	0.7	NUM
ejpam-6834	258	18	to	to	PART
ejpam-6834	258	19	0.9	0.9	NUM
ejpam-6834	258	20	.	.	PUNCT
ejpam-6834	259	1	•	•	NUM
ejpam-6834	259	2	µ̃(r2	µ̃(r2	NOUN
ejpam-6834	259	3	)	)	PUNCT
ejpam-6834	259	4	=	=	NOUN
ejpam-6834	259	5	{	{	PUNCT
ejpam-6834	259	6	0.5	0.5	NUM
ejpam-6834	259	7	,	,	PUNCT
ejpam-6834	259	8	0.6	0.6	NUM
ejpam-6834	259	9	,	,	PUNCT
ejpam-6834	259	10	0.7	0.7	NUM
ejpam-6834	259	11	}	}	PUNCT
ejpam-6834	259	12	indicates	indicate	VERB
ejpam-6834	259	13	that	that	DET
ejpam-6834	259	14	satisfaction	satisfaction	NOUN
ejpam-6834	259	15	for	for	ADP
ejpam-6834	259	16	r2	r2	NOUN
ejpam-6834	259	17	clusters	cluster	NOUN
ejpam-6834	259	18	at	at	ADP
ejpam-6834	259	19	three	three	NUM
ejpam-6834	259	20	discrete	discrete	ADJ
ejpam-6834	259	21	levels	level	NOUN
ejpam-6834	259	22	.	.	PUNCT
ejpam-6834	260	1	•	•	NUM
ejpam-6834	260	2	µ̃(r3	µ̃(r3	NUM
ejpam-6834	260	3	)	)	PUNCT
ejpam-6834	261	1	=	=	PUNCT
ejpam-6834	262	1	[	[	X
ejpam-6834	262	2	0.2	0.2	NUM
ejpam-6834	262	3	,	,	PUNCT
ejpam-6834	262	4	0.4	0.4	NUM
ejpam-6834	262	5	]	]	PUNCT
ejpam-6834	262	6	∪	∪	X
ejpam-6834	262	7	{	{	PUNCT
ejpam-6834	262	8	0.6	0.6	NUM
ejpam-6834	262	9	}	}	PUNCT
ejpam-6834	262	10	shows	show	VERB
ejpam-6834	262	11	a	a	DET
ejpam-6834	262	12	mixed	mixed	ADJ
ejpam-6834	262	13	pattern	pattern	NOUN
ejpam-6834	262	14	:	:	PUNCT
ejpam-6834	262	15	a	a	DET
ejpam-6834	262	16	continuous	continuous	ADJ
ejpam-6834	262	17	range	range	NOUN
ejpam-6834	262	18	for	for	ADP
ejpam-6834	262	19	most	most	ADJ
ejpam-6834	262	20	customers	customer	NOUN
ejpam-6834	262	21	plus	plus	CCONJ
ejpam-6834	262	22	one	one	NUM
ejpam-6834	262	23	high	high	ADJ
ejpam-6834	262	24	outlier	outlier	NOUN
ejpam-6834	262	25	at	at	ADP
ejpam-6834	262	26	0.6	0.6	NUM
ejpam-6834	262	27	.	.	PUNCT
ejpam-6834	263	1	this	this	DET
ejpam-6834	263	2	hyperfuzzy	hyperfuzzy	NOUN
ejpam-6834	263	3	set	set	NOUN
ejpam-6834	263	4	captures	capture	VERB
ejpam-6834	263	5	the	the	DET
ejpam-6834	263	6	variability	variability	NOUN
ejpam-6834	263	7	and	and	CCONJ
ejpam-6834	263	8	uncertainty	uncertainty	NOUN
ejpam-6834	263	9	in	in	ADP
ejpam-6834	263	10	customer	customer	NOUN
ejpam-6834	263	11	satisfaction	satisfaction	NOUN
ejpam-6834	263	12	across	across	ADP
ejpam-6834	263	13	different	different	ADJ
ejpam-6834	263	14	restaurants	restaurant	NOUN
ejpam-6834	263	15	.	.	PUNCT
ejpam-6834	264	1	t.	t.	PROPN
ejpam-6834	264	2	fujita	fujita	PROPN
ejpam-6834	264	3	,	,	PUNCT
ejpam-6834	264	4	f.smarandache	f.smarandache	NOUN
ejpam-6834	264	5	/	/	SYM
ejpam-6834	264	6	eur	eur	PROPN
ejpam-6834	264	7	.	.	PUNCT
ejpam-6834	265	1	j.	j.	PROPN
ejpam-6834	265	2	pure	pure	PROPN
ejpam-6834	265	3	appl	appl	PROPN
ejpam-6834	265	4	.	.	PROPN
ejpam-6834	265	5	math	math	PROPN
ejpam-6834	265	6	,	,	PUNCT
ejpam-6834	265	7	18	18	NUM
ejpam-6834	265	8	(	(	PUNCT
ejpam-6834	265	9	4	4	NUM
ejpam-6834	265	10	)	)	PUNCT
ejpam-6834	265	11	(	(	PUNCT
ejpam-6834	265	12	2025	2025	NUM
ejpam-6834	265	13	)	)	PUNCT
ejpam-6834	265	14	,	,	PUNCT
ejpam-6834	265	15	6834	6834	NUM
ejpam-6834	265	16	13	13	NUM
ejpam-6834	265	17	of	of	ADP
ejpam-6834	265	18	69	69	NUM
ejpam-6834	265	19	definition	definition	NOUN
ejpam-6834	265	20	12	12	NUM
ejpam-6834	265	21	(	(	PUNCT
ejpam-6834	265	22	n	n	CCONJ
ejpam-6834	265	23	-	-	PUNCT
ejpam-6834	265	24	superhyperfuzzy	superhyperfuzzy	NOUN
ejpam-6834	265	25	set	set	NOUN
ejpam-6834	265	26	)	)	PUNCT
ejpam-6834	265	27	.	.	PUNCT
ejpam-6834	266	1	[	[	X
ejpam-6834	266	2	1	1	NUM
ejpam-6834	266	3	,	,	PUNCT
ejpam-6834	266	4	2	2	NUM
ejpam-6834	266	5	]	]	PUNCT
ejpam-6834	266	6	let	let	VERB
ejpam-6834	266	7	x	x	PRON
ejpam-6834	266	8	be	be	AUX
ejpam-6834	266	9	a	a	DET
ejpam-6834	266	10	non	non	ADJ
ejpam-6834	266	11	-	-	ADJ
ejpam-6834	266	12	empty	empty	ADJ
ejpam-6834	266	13	set	set	NOUN
ejpam-6834	266	14	.	.	PUNCT
ejpam-6834	267	1	the	the	DET
ejpam-6834	267	2	nsuperhyperfuzzy	nsuperhyperfuzzy	ADJ
ejpam-6834	267	3	set	set	NOUN
ejpam-6834	267	4	is	be	AUX
ejpam-6834	267	5	a	a	DET
ejpam-6834	267	6	recursive	recursive	ADJ
ejpam-6834	267	7	generalization	generalization	NOUN
ejpam-6834	267	8	of	of	ADP
ejpam-6834	267	9	fuzzy	fuzzy	ADJ
ejpam-6834	267	10	sets	set	NOUN
ejpam-6834	267	11	,	,	PUNCT
ejpam-6834	267	12	hyperfuzzy	hyperfuzzy	NOUN
ejpam-6834	267	13	sets	set	NOUN
ejpam-6834	267	14	,	,	PUNCT
ejpam-6834	267	15	and	and	CCONJ
ejpam-6834	267	16	superhyperfuzzy	superhyperfuzzy	ADJ
ejpam-6834	267	17	sets	set	NOUN
ejpam-6834	267	18	.	.	PUNCT
ejpam-6834	268	1	it	it	PRON
ejpam-6834	268	2	is	be	AUX
ejpam-6834	268	3	defined	define	VERB
ejpam-6834	268	4	as	as	ADP
ejpam-6834	268	5	:	:	PUNCT
ejpam-6834	268	6	µ̃n	µ̃n	INTJ
ejpam-6834	268	7	:	:	PUNCT
ejpam-6834	268	8	p̃n(x	p̃n(x	X
ejpam-6834	268	9	)	)	PUNCT
ejpam-6834	268	10	→	→	SYM
ejpam-6834	268	11	p̃n([0	p̃n([0	PROPN
ejpam-6834	268	12	,	,	PUNCT
ejpam-6834	268	13	1	1	NUM
ejpam-6834	268	14	]	]	NUM
ejpam-6834	268	15	)	)	PUNCT
ejpam-6834	268	16	,	,	PUNCT
ejpam-6834	268	17	where	where	SCONJ
ejpam-6834	268	18	:	:	PUNCT
ejpam-6834	268	19	•	•	NUM
ejpam-6834	268	20	p̃1(x	p̃1(x	NOUN
ejpam-6834	268	21	)	)	PUNCT
ejpam-6834	268	22	=	=	PUNCT
ejpam-6834	268	23	p̃(x	p̃(x	PROPN
ejpam-6834	268	24	)	)	PUNCT
ejpam-6834	268	25	,	,	PUNCT
ejpam-6834	268	26	and	and	CCONJ
ejpam-6834	268	27	for	for	ADP
ejpam-6834	268	28	k	k	PROPN
ejpam-6834	268	29	≥	≥	NUM
ejpam-6834	268	30	2	2	NUM
ejpam-6834	268	31	,	,	PUNCT
ejpam-6834	268	32	p̃k(x	p̃k(x	X
ejpam-6834	268	33	)	)	PUNCT
ejpam-6834	268	34	=	=	SYM
ejpam-6834	268	35	p̃(p̃k−1(x	p̃(p̃k−1(x	NOUN
ejpam-6834	268	36	)	)	PUNCT
ejpam-6834	268	37	)	)	PUNCT
ejpam-6834	268	38	,	,	PUNCT
ejpam-6834	268	39	represents	represent	VERB
ejpam-6834	268	40	the	the	DET
ejpam-6834	268	41	k	k	NOUN
ejpam-6834	268	42	-	-	PUNCT
ejpam-6834	268	43	th	th	X
ejpam-6834	268	44	nested	nested	ADJ
ejpam-6834	268	45	family	family	NOUN
ejpam-6834	268	46	of	of	ADP
ejpam-6834	268	47	non	non	ADJ
ejpam-6834	268	48	-	-	ADJ
ejpam-6834	268	49	empty	empty	ADJ
ejpam-6834	268	50	subsets	subset	NOUN
ejpam-6834	268	51	of	of	ADP
ejpam-6834	268	52	x.	x.	NOUN
ejpam-6834	268	53	•	•	ADP
ejpam-6834	268	54	p̃n([0	p̃n([0	PROPN
ejpam-6834	268	55	,	,	PUNCT
ejpam-6834	268	56	1	1	NUM
ejpam-6834	268	57	]	]	PUNCT
ejpam-6834	268	58	)	)	PUNCT
ejpam-6834	268	59	is	be	AUX
ejpam-6834	268	60	similarly	similarly	ADV
ejpam-6834	268	61	defined	define	VERB
ejpam-6834	268	62	for	for	ADP
ejpam-6834	268	63	the	the	DET
ejpam-6834	268	64	interval	interval	NOUN
ejpam-6834	268	65	[	[	X
ejpam-6834	268	66	0	0	NUM
ejpam-6834	268	67	,	,	PUNCT
ejpam-6834	268	68	1	1	NUM
ejpam-6834	268	69	]	]	PUNCT
ejpam-6834	268	70	.	.	PUNCT
ejpam-6834	269	1	•	•	NUM
ejpam-6834	269	2	µ̃n	µ̃n	PROPN
ejpam-6834	269	3	assigns	assign	NOUN
ejpam-6834	269	4	to	to	ADP
ejpam-6834	269	5	each	each	DET
ejpam-6834	269	6	element	element	NOUN
ejpam-6834	269	7	a	a	DET
ejpam-6834	269	8	∈	∈	PROPN
ejpam-6834	269	9	p̃n(x	p̃n(x	NOUN
ejpam-6834	269	10	)	)	PUNCT
ejpam-6834	269	11	a	a	DET
ejpam-6834	269	12	non	non	ADJ
ejpam-6834	269	13	-	-	ADJ
ejpam-6834	269	14	empty	empty	ADJ
ejpam-6834	269	15	subset	subset	NOUN
ejpam-6834	269	16	µ̃n(a	µ̃n(a	NOUN
ejpam-6834	269	17	)	)	PUNCT
ejpam-6834	270	1	⊆	⊆	NUM
ejpam-6834	270	2	[	[	X
ejpam-6834	270	3	0	0	NUM
ejpam-6834	270	4	,	,	PUNCT
ejpam-6834	270	5	1	1	NUM
ejpam-6834	270	6	]	]	PUNCT
ejpam-6834	270	7	,	,	PUNCT
ejpam-6834	270	8	representing	represent	VERB
ejpam-6834	270	9	the	the	DET
ejpam-6834	270	10	degrees	degree	NOUN
ejpam-6834	270	11	of	of	ADP
ejpam-6834	270	12	membership	membership	NOUN
ejpam-6834	270	13	associated	associate	VERB
ejpam-6834	270	14	with	with	ADP
ejpam-6834	270	15	a	a	PRON
ejpam-6834	270	16	at	at	ADP
ejpam-6834	270	17	the	the	DET
ejpam-6834	270	18	n	n	CCONJ
ejpam-6834	270	19	-	-	PUNCT
ejpam-6834	270	20	th	th	VERB
ejpam-6834	270	21	level	level	NOUN
ejpam-6834	270	22	.	.	PUNCT
ejpam-6834	270	23	example	example	NOUN
ejpam-6834	270	24	7	7	NUM
ejpam-6834	270	25	(	(	PUNCT
ejpam-6834	270	26	2	2	NUM
ejpam-6834	270	27	-	-	PUNCT
ejpam-6834	270	28	superhyperfuzzy	superhyperfuzzy	NOUN
ejpam-6834	270	29	set	set	VERB
ejpam-6834	270	30	for	for	ADP
ejpam-6834	270	31	equipment	equipment	NOUN
ejpam-6834	270	32	reliability	reliability	NOUN
ejpam-6834	270	33	)	)	PUNCT
ejpam-6834	270	34	.	.	PUNCT
ejpam-6834	271	1	let	let	VERB
ejpam-6834	271	2	x	x	PUNCT
ejpam-6834	271	3	=	=	PRON
ejpam-6834	271	4	{	{	PUNCT
ejpam-6834	271	5	compressor	compressor	NOUN
ejpam-6834	271	6	,	,	PUNCT
ejpam-6834	271	7	pump	pump	NOUN
ejpam-6834	271	8	}	}	PUNCT
ejpam-6834	271	9	.	.	PUNCT
ejpam-6834	272	1	then	then	ADV
ejpam-6834	272	2	p̃1(x	p̃1(x	NOUN
ejpam-6834	272	3	)	)	PUNCT
ejpam-6834	273	1	=	=	PRON
ejpam-6834	273	2	{	{	PUNCT
ejpam-6834	273	3	{	{	PUNCT
ejpam-6834	273	4	compressor	compressor	NOUN
ejpam-6834	273	5	}	}	PUNCT
ejpam-6834	273	6	,	,	PUNCT
ejpam-6834	273	7	{	{	PUNCT
ejpam-6834	273	8	pump	pump	NOUN
ejpam-6834	273	9	}	}	PUNCT
ejpam-6834	273	10	,	,	PUNCT
ejpam-6834	273	11	{	{	PUNCT
ejpam-6834	273	12	compressor	compressor	NOUN
ejpam-6834	273	13	,	,	PUNCT
ejpam-6834	273	14	pump	pump	NOUN
ejpam-6834	273	15	}	}	PUNCT
ejpam-6834	273	16	}	}	PUNCT
ejpam-6834	273	17	,	,	PUNCT
ejpam-6834	273	18	and	and	CCONJ
ejpam-6834	273	19	p̃2(x	p̃2(x	PROPN
ejpam-6834	273	20	)	)	PUNCT
ejpam-6834	273	21	=	=	SYM
ejpam-6834	274	1	p̃	p̃	PROPN
ejpam-6834	274	2	(	(	PUNCT
ejpam-6834	274	3	p̃1(x	p̃1(x	NOUN
ejpam-6834	274	4	)	)	PUNCT
ejpam-6834	274	5	)	)	PUNCT
ejpam-6834	274	6	,	,	PUNCT
ejpam-6834	274	7	the	the	DET
ejpam-6834	274	8	family	family	NOUN
ejpam-6834	274	9	of	of	ADP
ejpam-6834	274	10	all	all	DET
ejpam-6834	274	11	nonempty	nonempty	ADJ
ejpam-6834	274	12	collections	collection	NOUN
ejpam-6834	274	13	of	of	ADP
ejpam-6834	274	14	nonempty	nonempty	ADJ
ejpam-6834	274	15	subsets	subset	NOUN
ejpam-6834	274	16	of	of	ADP
ejpam-6834	274	17	x.	x.	NOUN
ejpam-6834	274	18	we	we	PRON
ejpam-6834	274	19	define	define	VERB
ejpam-6834	274	20	a	a	DET
ejpam-6834	274	21	2	2	NUM
ejpam-6834	274	22	-	-	PUNCT
ejpam-6834	274	23	superhyperfuzzy	superhyperfuzzy	NOUN
ejpam-6834	274	24	set	set	NOUN
ejpam-6834	274	25	µ̃2	µ̃2	PROPN
ejpam-6834	274	26	:	:	PUNCT
ejpam-6834	274	27	p̃2(x	p̃2(x	NOUN
ejpam-6834	274	28	)	)	PUNCT
ejpam-6834	274	29	→	→	SYM
ejpam-6834	274	30	p̃2([0	p̃2([0	NOUN
ejpam-6834	274	31	,	,	PUNCT
ejpam-6834	274	32	1	1	NUM
ejpam-6834	274	33	]	]	PUNCT
ejpam-6834	274	34	)	)	PUNCT
ejpam-6834	274	35	by	by	ADP
ejpam-6834	274	36	specifying	specify	VERB
ejpam-6834	274	37	its	its	PRON
ejpam-6834	274	38	value	value	NOUN
ejpam-6834	274	39	on	on	ADP
ejpam-6834	274	40	one	one	NUM
ejpam-6834	274	41	representative	representative	ADJ
ejpam-6834	274	42	element	element	NOUN
ejpam-6834	274	43	:	:	PUNCT
ejpam-6834	274	44	a	a	DET
ejpam-6834	274	45	=	=	X
ejpam-6834	274	46	{	{	PUNCT
ejpam-6834	274	47	{	{	PUNCT
ejpam-6834	274	48	compressor	compressor	NOUN
ejpam-6834	274	49	}	}	PUNCT
ejpam-6834	274	50	,	,	PUNCT
ejpam-6834	274	51	{	{	PUNCT
ejpam-6834	274	52	pump	pump	NOUN
ejpam-6834	274	53	}	}	PUNCT
ejpam-6834	274	54	}	}	PUNCT
ejpam-6834	274	55	∈	∈	PROPN
ejpam-6834	274	56	p̃2(x	p̃2(x	NOUN
ejpam-6834	274	57	)	)	PUNCT
ejpam-6834	274	58	,	,	PUNCT
ejpam-6834	274	59	µ̃2(a	µ̃2(a	NOUN
ejpam-6834	274	60	)	)	PUNCT
ejpam-6834	274	61	=	=	PRON
ejpam-6834	274	62	{	{	PUNCT
ejpam-6834	274	63	{	{	PUNCT
ejpam-6834	274	64	0.70	0.70	NUM
ejpam-6834	274	65	,	,	PUNCT
ejpam-6834	274	66	0.75	0.75	NUM
ejpam-6834	274	67	}	}	PUNCT
ejpam-6834	274	68	,	,	PUNCT
ejpam-6834	275	1	[	[	X
ejpam-6834	275	2	0.60	0.60	NUM
ejpam-6834	275	3	,	,	PUNCT
ejpam-6834	275	4	0.65	0.65	NUM
ejpam-6834	275	5	]	]	PUNCT
ejpam-6834	275	6	,	,	PUNCT
ejpam-6834	275	7	{	{	PUNCT
ejpam-6834	275	8	0.50	0.50	NUM
ejpam-6834	275	9	,	,	PUNCT
ejpam-6834	275	10	0.55	0.55	NUM
ejpam-6834	275	11	}	}	PUNCT
ejpam-6834	275	12	}	}	PUNCT
ejpam-6834	275	13	.	.	PUNCT
ejpam-6834	276	1	here	here	ADV
ejpam-6834	276	2	each	each	DET
ejpam-6834	276	3	inner	inner	ADJ
ejpam-6834	276	4	set	set	NOUN
ejpam-6834	276	5	(	(	PUNCT
ejpam-6834	276	6	or	or	CCONJ
ejpam-6834	276	7	interval	interval	NOUN
ejpam-6834	276	8	)	)	PUNCT
ejpam-6834	276	9	is	be	AUX
ejpam-6834	276	10	a	a	DET
ejpam-6834	276	11	subset	subset	NOUN
ejpam-6834	276	12	of	of	ADP
ejpam-6834	276	13	[	[	X
ejpam-6834	276	14	0	0	NUM
ejpam-6834	276	15	,	,	PUNCT
ejpam-6834	276	16	1	1	NUM
ejpam-6834	276	17	]	]	PUNCT
ejpam-6834	276	18	,	,	PUNCT
ejpam-6834	276	19	representing	represent	VERB
ejpam-6834	276	20	possible	possible	ADJ
ejpam-6834	276	21	reliability	reliability	NOUN
ejpam-6834	276	22	scores	score	NOUN
ejpam-6834	276	23	from	from	ADP
ejpam-6834	276	24	different	different	ADJ
ejpam-6834	276	25	assessment	assessment	NOUN
ejpam-6834	276	26	methods	method	NOUN
ejpam-6834	276	27	(	(	PUNCT
ejpam-6834	276	28	e.g.	e.g.	ADV
ejpam-6834	276	29	expert	expert	ADJ
ejpam-6834	276	30	judgment	judgment	NOUN
ejpam-6834	276	31	,	,	PUNCT
ejpam-6834	276	32	sensor	sensor	NOUN
ejpam-6834	276	33	analytics	analytic	NOUN
ejpam-6834	276	34	,	,	PUNCT
ejpam-6834	276	35	historical	historical	ADJ
ejpam-6834	276	36	data	datum	NOUN
ejpam-6834	276	37	)	)	PUNCT
ejpam-6834	276	38	.	.	PUNCT
ejpam-6834	277	1	thus	thus	ADV
ejpam-6834	277	2	µ̃2(a	µ̃2(a	NOUN
ejpam-6834	277	3	)	)	PUNCT
ejpam-6834	277	4	captures	capture	VERB
ejpam-6834	277	5	the	the	DET
ejpam-6834	277	6	multi	multi	ADJ
ejpam-6834	277	7	-	-	ADJ
ejpam-6834	277	8	level	level	ADJ
ejpam-6834	277	9	uncertainty	uncertainty	NOUN
ejpam-6834	277	10	in	in	ADP
ejpam-6834	277	11	the	the	DET
ejpam-6834	277	12	joint	joint	ADJ
ejpam-6834	277	13	reliability	reliability	NOUN
ejpam-6834	277	14	evaluation	evaluation	NOUN
ejpam-6834	277	15	of	of	ADP
ejpam-6834	277	16	the	the	DET
ejpam-6834	277	17	compressor	compressor	NOUN
ejpam-6834	277	18	and	and	CCONJ
ejpam-6834	277	19	pump	pump	NOUN
ejpam-6834	277	20	.	.	PUNCT
ejpam-6834	277	21	example	example	NOUN
ejpam-6834	277	22	8	8	NUM
ejpam-6834	277	23	(	(	PUNCT
ejpam-6834	277	24	3	3	NUM
ejpam-6834	277	25	-	-	PUNCT
ejpam-6834	277	26	superhyperfuzzy	superhyperfuzzy	NOUN
ejpam-6834	277	27	set	set	NOUN
ejpam-6834	277	28	for	for	ADP
ejpam-6834	277	29	predictive	predictive	ADJ
ejpam-6834	277	30	maintenance	maintenance	NOUN
ejpam-6834	277	31	)	)	PUNCT
ejpam-6834	277	32	.	.	PUNCT
ejpam-6834	278	1	let	let	VERB
ejpam-6834	278	2	x	x	PUNCT
ejpam-6834	278	3	=	=	PRON
ejpam-6834	278	4	{	{	PUNCT
ejpam-6834	278	5	sensor1	sensor1	PROPN
ejpam-6834	278	6	,	,	PUNCT
ejpam-6834	278	7	sensor2	sensor2	PROPN
ejpam-6834	278	8	}	}	PUNCT
ejpam-6834	278	9	.	.	PUNCT
ejpam-6834	279	1	we	we	PRON
ejpam-6834	279	2	construct	construct	VERB
ejpam-6834	279	3	the	the	DET
ejpam-6834	279	4	nested	nest	VERB
ejpam-6834	279	5	powersets	powerset	NOUN
ejpam-6834	279	6	:	:	PUNCT
ejpam-6834	279	7	p̃1(x	p̃1(x	NOUN
ejpam-6834	279	8	)	)	PUNCT
ejpam-6834	279	9	=	=	PRON
ejpam-6834	279	10	{	{	PUNCT
ejpam-6834	279	11	{	{	PUNCT
ejpam-6834	279	12	sensor1	sensor1	NOUN
ejpam-6834	279	13	}	}	PUNCT
ejpam-6834	279	14	,	,	PUNCT
ejpam-6834	279	15	{	{	PUNCT
ejpam-6834	279	16	sensor2	sensor2	X
ejpam-6834	279	17	}	}	PUNCT
ejpam-6834	279	18	,	,	PUNCT
ejpam-6834	279	19	{	{	PUNCT
ejpam-6834	279	20	sensor1,sensor2	sensor1,sensor2	NOUN
ejpam-6834	279	21	}	}	PUNCT
ejpam-6834	279	22	}	}	PUNCT
ejpam-6834	279	23	,	,	PUNCT
ejpam-6834	279	24	t.	t.	PROPN
ejpam-6834	279	25	fujita	fujita	PROPN
ejpam-6834	279	26	,	,	PUNCT
ejpam-6834	279	27	f.smarandache	f.smarandache	NOUN
ejpam-6834	279	28	/	/	SYM
ejpam-6834	279	29	eur	eur	PROPN
ejpam-6834	279	30	.	.	PUNCT
ejpam-6834	280	1	j.	j.	PROPN
ejpam-6834	280	2	pure	pure	PROPN
ejpam-6834	280	3	appl	appl	PROPN
ejpam-6834	280	4	.	.	PROPN
ejpam-6834	280	5	math	math	PROPN
ejpam-6834	280	6	,	,	PUNCT
ejpam-6834	280	7	18	18	NUM
ejpam-6834	280	8	(	(	PUNCT
ejpam-6834	280	9	4	4	NUM
ejpam-6834	280	10	)	)	PUNCT
ejpam-6834	280	11	(	(	PUNCT
ejpam-6834	280	12	2025	2025	NUM
ejpam-6834	280	13	)	)	PUNCT
ejpam-6834	280	14	,	,	PUNCT
ejpam-6834	280	15	6834	6834	NUM
ejpam-6834	280	16	14	14	NUM
ejpam-6834	280	17	of	of	ADP
ejpam-6834	280	18	69	69	NUM
ejpam-6834	280	19	p̃2(x	p̃2(x	NOUN
ejpam-6834	280	20	)	)	PUNCT
ejpam-6834	280	21	=	=	SYM
ejpam-6834	281	1	p̃	p̃	PROPN
ejpam-6834	281	2	(	(	PUNCT
ejpam-6834	281	3	p̃1(x	p̃1(x	NOUN
ejpam-6834	281	4	)	)	PUNCT
ejpam-6834	281	5	)	)	PUNCT
ejpam-6834	281	6	,	,	PUNCT
ejpam-6834	281	7	p̃3(x	p̃3(x	PROPN
ejpam-6834	281	8	)	)	PUNCT
ejpam-6834	281	9	=	=	SYM
ejpam-6834	282	1	p̃	p̃	PROPN
ejpam-6834	282	2	(	(	PUNCT
ejpam-6834	282	3	p̃2(x	p̃2(x	PROPN
ejpam-6834	282	4	)	)	PUNCT
ejpam-6834	282	5	)	)	PUNCT
ejpam-6834	282	6	.	.	PUNCT
ejpam-6834	283	1	choose	choose	VERB
ejpam-6834	283	2	the	the	DET
ejpam-6834	283	3	element	element	NOUN
ejpam-6834	283	4	a	a	PRON
ejpam-6834	283	5	=	=	X
ejpam-6834	283	6	{	{	PUNCT
ejpam-6834	283	7	{	{	PUNCT
ejpam-6834	283	8	{	{	PUNCT
ejpam-6834	283	9	sensor1	sensor1	NOUN
ejpam-6834	283	10	}	}	PUNCT
ejpam-6834	283	11	,	,	PUNCT
ejpam-6834	283	12	{	{	PUNCT
ejpam-6834	283	13	sensor2	sensor2	X
ejpam-6834	283	14	}	}	PUNCT
ejpam-6834	283	15	}	}	PUNCT
ejpam-6834	283	16	,	,	PUNCT
ejpam-6834	283	17	{	{	PUNCT
ejpam-6834	283	18	{	{	PUNCT
ejpam-6834	283	19	sensor1	sensor1	PROPN
ejpam-6834	283	20	,	,	PUNCT
ejpam-6834	283	21	sensor2	sensor2	PROPN
ejpam-6834	283	22	}	}	PUNCT
ejpam-6834	283	23	}	}	PUNCT
ejpam-6834	283	24	}	}	PUNCT
ejpam-6834	283	25	∈	∈	PROPN
ejpam-6834	283	26	p̃3(x	p̃3(x	PROPN
ejpam-6834	283	27	)	)	PUNCT
ejpam-6834	283	28	.	.	PUNCT
ejpam-6834	284	1	a	a	DET
ejpam-6834	284	2	3	3	NUM
ejpam-6834	284	3	-	-	PUNCT
ejpam-6834	284	4	superhyperfuzzy	superhyperfuzzy	NOUN
ejpam-6834	284	5	set	set	NOUN
ejpam-6834	284	6	is	be	AUX
ejpam-6834	284	7	a	a	DET
ejpam-6834	284	8	mapping	mapping	NOUN
ejpam-6834	284	9	µ̃3	µ̃3	PROPN
ejpam-6834	284	10	:	:	PUNCT
ejpam-6834	284	11	p̃3(x	p̃3(x	PROPN
ejpam-6834	284	12	)	)	PUNCT
ejpam-6834	284	13	−→	−→	NOUN
ejpam-6834	284	14	p̃3([0	p̃3([0	NOUN
ejpam-6834	284	15	,	,	PUNCT
ejpam-6834	284	16	1	1	NUM
ejpam-6834	284	17	]	]	PUNCT
ejpam-6834	284	18	)	)	PUNCT
ejpam-6834	284	19	.	.	PUNCT
ejpam-6834	285	1	we	we	PRON
ejpam-6834	285	2	define	define	VERB
ejpam-6834	285	3	its	its	PRON
ejpam-6834	285	4	value	value	NOUN
ejpam-6834	285	5	on	on	ADP
ejpam-6834	285	6	a	a	PRON
ejpam-6834	285	7	by	by	ADP
ejpam-6834	285	8	µ̃3(a	µ̃3(a	ADJ
ejpam-6834	285	9	)	)	PUNCT
ejpam-6834	285	10	=	=	SYM
ejpam-6834	285	11	{	{	PUNCT
ejpam-6834	285	12	b1	b1	NOUN
ejpam-6834	285	13	,	,	PUNCT
ejpam-6834	285	14	b2	b2	NOUN
ejpam-6834	285	15	}	}	PUNCT
ejpam-6834	285	16	⊆	⊆	NUM
ejpam-6834	285	17	p̃2([0	p̃2([0	NOUN
ejpam-6834	285	18	,	,	PUNCT
ejpam-6834	285	19	1	1	NUM
ejpam-6834	285	20	]	]	NUM
ejpam-6834	285	21	)	)	PUNCT
ejpam-6834	285	22	,	,	PUNCT
ejpam-6834	285	23	where	where	SCONJ
ejpam-6834	285	24	b1	b1	NOUN
ejpam-6834	285	25	=	=	SYM
ejpam-6834	285	26	{	{	PUNCT
ejpam-6834	286	1	[	[	X
ejpam-6834	286	2	0.80	0.80	NUM
ejpam-6834	286	3	,	,	PUNCT
ejpam-6834	286	4	0.90	0.90	NUM
ejpam-6834	286	5	]	]	PUNCT
ejpam-6834	286	6	,	,	PUNCT
ejpam-6834	286	7	{	{	PUNCT
ejpam-6834	286	8	0.85	0.85	NUM
ejpam-6834	286	9	}	}	PUNCT
ejpam-6834	286	10	}	}	PUNCT
ejpam-6834	286	11	,	,	PUNCT
ejpam-6834	286	12	b2	b2	NOUN
ejpam-6834	286	13	=	=	SYM
ejpam-6834	286	14	{	{	PUNCT
ejpam-6834	287	1	[	[	X
ejpam-6834	287	2	0.60	0.60	NUM
ejpam-6834	287	3	,	,	PUNCT
ejpam-6834	287	4	0.70	0.70	NUM
ejpam-6834	287	5	]	]	X
ejpam-6834	287	6	,	,	PUNCT
ejpam-6834	287	7	{	{	PUNCT
ejpam-6834	287	8	0.65	0.65	NUM
ejpam-6834	287	9	,	,	PUNCT
ejpam-6834	287	10	0.68	0.68	NUM
ejpam-6834	287	11	}	}	PUNCT
ejpam-6834	287	12	}	}	PUNCT
ejpam-6834	287	13	.	.	PUNCT
ejpam-6834	288	1	each	each	DET
ejpam-6834	288	2	bi	bi	NOUN
ejpam-6834	288	3	is	be	AUX
ejpam-6834	288	4	a	a	DET
ejpam-6834	288	5	non	non	ADJ
ejpam-6834	288	6	-	-	ADJ
ejpam-6834	288	7	empty	empty	ADJ
ejpam-6834	288	8	subset	subset	NOUN
ejpam-6834	288	9	of	of	ADP
ejpam-6834	288	10	p̃([0	p̃([0	NUM
ejpam-6834	288	11	,	,	PUNCT
ejpam-6834	288	12	1	1	NUM
ejpam-6834	288	13	]	]	NUM
ejpam-6834	288	14	)	)	PUNCT
ejpam-6834	288	15	,	,	PUNCT
ejpam-6834	288	16	representing	represent	VERB
ejpam-6834	288	17	multiple	multiple	ADJ
ejpam-6834	288	18	reliability	reliability	NOUN
ejpam-6834	288	19	scores	score	NOUN
ejpam-6834	288	20	from	from	ADP
ejpam-6834	288	21	different	different	ADJ
ejpam-6834	288	22	diagnostic	diagnostic	ADJ
ejpam-6834	288	23	methods	method	NOUN
ejpam-6834	288	24	(	(	PUNCT
ejpam-6834	288	25	e.g.	e.g.	ADV
ejpam-6834	288	26	expert	expert	ADJ
ejpam-6834	288	27	judgment	judgment	NOUN
ejpam-6834	288	28	vs.	vs.	ADP
ejpam-6834	288	29	sensor	sensor	NOUN
ejpam-6834	288	30	analytics	analytic	NOUN
ejpam-6834	288	31	)	)	PUNCT
ejpam-6834	288	32	.	.	PUNCT
ejpam-6834	289	1	thus	thus	ADV
ejpam-6834	289	2	µ̃3(a	µ̃3(a	X
ejpam-6834	289	3	)	)	PUNCT
ejpam-6834	289	4	captures	capture	VERB
ejpam-6834	289	5	the	the	DET
ejpam-6834	289	6	third	third	ADJ
ejpam-6834	289	7	-	-	PUNCT
ejpam-6834	289	8	level	level	NOUN
ejpam-6834	289	9	,	,	PUNCT
ejpam-6834	289	10	nested	nest	VERB
ejpam-6834	289	11	uncertainty	uncertainty	NOUN
ejpam-6834	289	12	in	in	ADP
ejpam-6834	289	13	the	the	DET
ejpam-6834	289	14	combined	combined	ADJ
ejpam-6834	289	15	sensor	sensor	NOUN
ejpam-6834	289	16	evaluation	evaluation	NOUN
ejpam-6834	289	17	.	.	PUNCT
ejpam-6834	290	1	2.3	2.3	NUM
ejpam-6834	290	2	.	.	X
ejpam-6834	290	3	neutrosophic	neutrosophic	PROPN
ejpam-6834	290	4	set	set	VERB
ejpam-6834	290	5	a	a	DET
ejpam-6834	290	6	neutrosophic	neutrosophic	ADJ
ejpam-6834	290	7	set	set	NOUN
ejpam-6834	290	8	models	model	NOUN
ejpam-6834	290	9	uncertainty	uncertainty	NOUN
ejpam-6834	290	10	using	use	VERB
ejpam-6834	290	11	three	three	NUM
ejpam-6834	290	12	membership	membership	NOUN
ejpam-6834	290	13	functions	function	NOUN
ejpam-6834	290	14	:	:	PUNCT
ejpam-6834	290	15	truth	truth	NOUN
ejpam-6834	290	16	(	(	PUNCT
ejpam-6834	290	17	t	t	NOUN
ejpam-6834	290	18	)	)	PUNCT
ejpam-6834	290	19	,	,	PUNCT
ejpam-6834	290	20	indeterminacy	indeterminacy	NOUN
ejpam-6834	290	21	(	(	PUNCT
ejpam-6834	290	22	i	i	NOUN
ejpam-6834	290	23	)	)	PUNCT
ejpam-6834	290	24	,	,	PUNCT
ejpam-6834	290	25	and	and	CCONJ
ejpam-6834	290	26	falsity	falsity	NOUN
ejpam-6834	290	27	(	(	PUNCT
ejpam-6834	290	28	f	f	PROPN
ejpam-6834	290	29	)	)	PUNCT
ejpam-6834	290	30	,	,	PUNCT
ejpam-6834	290	31	which	which	PRON
ejpam-6834	290	32	satisfy	satisfy	VERB
ejpam-6834	290	33	:	:	PUNCT
ejpam-6834	291	1	0	0	NUM
ejpam-6834	291	2	≤	≤	NUM
ejpam-6834	291	3	t	t	NOUN
ejpam-6834	291	4	+	+	CCONJ
ejpam-6834	291	5	i	i	PRON
ejpam-6834	291	6	+	+	NUM
ejpam-6834	291	7	f	f	PROPN
ejpam-6834	291	8	≤	≤	ADV
ejpam-6834	291	9	3	3	NUM
ejpam-6834	291	10	.	.	PUNCT
ejpam-6834	292	1	[	[	X
ejpam-6834	292	2	62	62	NUM
ejpam-6834	292	3	,	,	PUNCT
ejpam-6834	292	4	63	63	NUM
ejpam-6834	292	5	]	]	PUNCT
ejpam-6834	292	6	.	.	PUNCT
ejpam-6834	293	1	these	these	DET
ejpam-6834	293	2	sets	set	NOUN
ejpam-6834	293	3	can	can	AUX
ejpam-6834	293	4	be	be	AUX
ejpam-6834	293	5	extended	extend	VERB
ejpam-6834	293	6	into	into	ADP
ejpam-6834	293	7	hyperneutrosophic	hyperneutrosophic	ADJ
ejpam-6834	293	8	sets	set	NOUN
ejpam-6834	293	9	[	[	X
ejpam-6834	293	10	64	64	NUM
ejpam-6834	293	11	]	]	PUNCT
ejpam-6834	293	12	and	and	CCONJ
ejpam-6834	293	13	superhyperneutrosophic	superhyperneutrosophic	ADJ
ejpam-6834	293	14	sets	set	NOUN
ejpam-6834	293	15	using	use	VERB
ejpam-6834	293	16	hyperstructures	hyperstructure	NOUN
ejpam-6834	293	17	and	and	CCONJ
ejpam-6834	293	18	superhyperstructures	superhyperstructure	NOUN
ejpam-6834	293	19	.	.	PUNCT
ejpam-6834	294	1	definition	definition	NOUN
ejpam-6834	294	2	13	13	NUM
ejpam-6834	294	3	(	(	PUNCT
ejpam-6834	294	4	neutrosophic	neutrosophic	ADJ
ejpam-6834	294	5	set	set	NOUN
ejpam-6834	294	6	)	)	PUNCT
ejpam-6834	294	7	.	.	PUNCT
ejpam-6834	295	1	[	[	X
ejpam-6834	295	2	10	10	NUM
ejpam-6834	295	3	,	,	PUNCT
ejpam-6834	295	4	63	63	NUM
ejpam-6834	295	5	]	]	PUNCT
ejpam-6834	295	6	let	let	VERB
ejpam-6834	295	7	x	x	PRON
ejpam-6834	295	8	be	be	AUX
ejpam-6834	295	9	a	a	DET
ejpam-6834	295	10	non	non	ADJ
ejpam-6834	295	11	-	-	ADJ
ejpam-6834	295	12	empty	empty	ADJ
ejpam-6834	295	13	set	set	NOUN
ejpam-6834	295	14	.	.	PUNCT
ejpam-6834	296	1	a	a	DET
ejpam-6834	296	2	neutrosophic	neutrosophic	ADJ
ejpam-6834	296	3	set	set	NOUN
ejpam-6834	296	4	(	(	PUNCT
ejpam-6834	296	5	ns	ns	INTJ
ejpam-6834	296	6	)	)	PUNCT
ejpam-6834	296	7	a	a	PRON
ejpam-6834	296	8	on	on	NOUN
ejpam-6834	296	9	x	x	SYM
ejpam-6834	296	10	is	be	AUX
ejpam-6834	296	11	characterized	characterize	VERB
ejpam-6834	296	12	by	by	ADP
ejpam-6834	296	13	three	three	NUM
ejpam-6834	296	14	membership	membership	NOUN
ejpam-6834	296	15	functions	function	NOUN
ejpam-6834	296	16	:	:	PUNCT
ejpam-6834	296	17	ta	ta	X
ejpam-6834	296	18	:	:	PUNCT
ejpam-6834	296	19	x	x	X
ejpam-6834	296	20	→	→	PUNCT
ejpam-6834	297	1	[	[	X
ejpam-6834	297	2	0	0	NUM
ejpam-6834	297	3	,	,	PUNCT
ejpam-6834	297	4	1	1	NUM
ejpam-6834	297	5	]	]	PUNCT
ejpam-6834	297	6	,	,	PUNCT
ejpam-6834	297	7	ia	ia	PROPN
ejpam-6834	297	8	:	:	PUNCT
ejpam-6834	297	9	x	x	X
ejpam-6834	297	10	→	→	PUNCT
ejpam-6834	298	1	[	[	X
ejpam-6834	298	2	0	0	NUM
ejpam-6834	298	3	,	,	PUNCT
ejpam-6834	298	4	1	1	NUM
ejpam-6834	298	5	]	]	PUNCT
ejpam-6834	298	6	,	,	PUNCT
ejpam-6834	298	7	fa	fa	INTJ
ejpam-6834	298	8	:	:	PUNCT
ejpam-6834	298	9	x	x	X
ejpam-6834	298	10	→	→	PUNCT
ejpam-6834	299	1	[	[	X
ejpam-6834	299	2	0	0	NUM
ejpam-6834	299	3	,	,	PUNCT
ejpam-6834	299	4	1	1	NUM
ejpam-6834	299	5	]	]	PUNCT
ejpam-6834	299	6	,	,	PUNCT
ejpam-6834	299	7	where	where	SCONJ
ejpam-6834	299	8	for	for	ADP
ejpam-6834	299	9	each	each	DET
ejpam-6834	299	10	x	x	SYM
ejpam-6834	299	11	∈	∈	PROPN
ejpam-6834	299	12	x	x	NOUN
ejpam-6834	299	13	,	,	PUNCT
ejpam-6834	299	14	the	the	DET
ejpam-6834	299	15	values	value	NOUN
ejpam-6834	299	16	ta(x	ta(x	NOUN
ejpam-6834	299	17	)	)	PUNCT
ejpam-6834	299	18	,	,	PUNCT
ejpam-6834	299	19	ia(x	ia(x	NOUN
ejpam-6834	299	20	)	)	PUNCT
ejpam-6834	299	21	,	,	PUNCT
ejpam-6834	299	22	and	and	CCONJ
ejpam-6834	299	23	fa(x	fa(x	PROPN
ejpam-6834	299	24	)	)	PUNCT
ejpam-6834	299	25	represent	represent	VERB
ejpam-6834	299	26	the	the	DET
ejpam-6834	299	27	degrees	degree	NOUN
ejpam-6834	299	28	of	of	ADP
ejpam-6834	299	29	truth	truth	NOUN
ejpam-6834	299	30	,	,	PUNCT
ejpam-6834	299	31	indeterminacy	indeterminacy	NOUN
ejpam-6834	299	32	,	,	PUNCT
ejpam-6834	299	33	and	and	CCONJ
ejpam-6834	299	34	falsity	falsity	NOUN
ejpam-6834	299	35	,	,	PUNCT
ejpam-6834	299	36	respectively	respectively	ADV
ejpam-6834	299	37	.	.	PUNCT
ejpam-6834	300	1	these	these	DET
ejpam-6834	300	2	values	value	NOUN
ejpam-6834	300	3	satisfy	satisfy	VERB
ejpam-6834	300	4	the	the	DET
ejpam-6834	300	5	following	follow	VERB
ejpam-6834	300	6	condition	condition	NOUN
ejpam-6834	300	7	:	:	PUNCT
ejpam-6834	300	8	0	0	NUM
ejpam-6834	300	9	≤	≤	NUM
ejpam-6834	300	10	ta(x	ta(x	NOUN
ejpam-6834	300	11	)	)	PUNCT
ejpam-6834	300	12	+	+	NUM
ejpam-6834	300	13	ia(x	ia(x	NOUN
ejpam-6834	300	14	)	)	PUNCT
ejpam-6834	300	15	+	+	CCONJ
ejpam-6834	300	16	fa(x	fa(x	NOUN
ejpam-6834	300	17	)	)	PUNCT
ejpam-6834	300	18	≤	≤	NUM
ejpam-6834	300	19	3	3	NUM
ejpam-6834	300	20	.	.	PUNCT
ejpam-6834	301	1	definition	definition	NOUN
ejpam-6834	301	2	14	14	NUM
ejpam-6834	301	3	(	(	PUNCT
ejpam-6834	301	4	hyperneutrosophic	hyperneutrosophic	ADJ
ejpam-6834	301	5	set	set	NOUN
ejpam-6834	301	6	)	)	PUNCT
ejpam-6834	301	7	.	.	PUNCT
ejpam-6834	302	1	[	[	X
ejpam-6834	302	2	1	1	NUM
ejpam-6834	302	3	,	,	PUNCT
ejpam-6834	302	4	2	2	NUM
ejpam-6834	302	5	]	]	PUNCT
ejpam-6834	302	6	let	let	VERB
ejpam-6834	302	7	x	x	PRON
ejpam-6834	302	8	be	be	AUX
ejpam-6834	302	9	a	a	DET
ejpam-6834	302	10	non	non	ADJ
ejpam-6834	302	11	-	-	ADJ
ejpam-6834	302	12	empty	empty	ADJ
ejpam-6834	302	13	set	set	NOUN
ejpam-6834	302	14	.	.	PUNCT
ejpam-6834	303	1	a	a	DET
ejpam-6834	303	2	mapping	mapping	NOUN
ejpam-6834	303	3	µ̃	µ̃	PROPN
ejpam-6834	303	4	:	:	PUNCT
ejpam-6834	303	5	x	x	X
ejpam-6834	303	6	→	→	PUNCT
ejpam-6834	303	7	p̃	p̃	PROPN
ejpam-6834	303	8	(	(	PUNCT
ejpam-6834	303	9	[	[	X
ejpam-6834	303	10	0	0	NUM
ejpam-6834	303	11	,	,	PUNCT
ejpam-6834	303	12	1]3	1]3	NUM
ejpam-6834	303	13	)	)	PUNCT
ejpam-6834	303	14	is	be	AUX
ejpam-6834	303	15	called	call	VERB
ejpam-6834	303	16	a	a	DET
ejpam-6834	303	17	hyperneutrosophic	hyperneutrosophic	ADJ
ejpam-6834	303	18	set	set	NOUN
ejpam-6834	303	19	over	over	ADP
ejpam-6834	303	20	x	x	NOUN
ejpam-6834	303	21	,	,	PUNCT
ejpam-6834	303	22	where	where	SCONJ
ejpam-6834	303	23	p̃	p̃	PROPN
ejpam-6834	303	24	(	(	PUNCT
ejpam-6834	303	25	[	[	X
ejpam-6834	303	26	0	0	NUM
ejpam-6834	303	27	,	,	PUNCT
ejpam-6834	303	28	1]3	1]3	NUM
ejpam-6834	303	29	)	)	PUNCT
ejpam-6834	303	30	denotes	denote	VERB
ejpam-6834	303	31	the	the	DET
ejpam-6834	303	32	family	family	NOUN
ejpam-6834	303	33	of	of	ADP
ejpam-6834	303	34	all	all	DET
ejpam-6834	303	35	non	non	ADJ
ejpam-6834	303	36	-	-	ADJ
ejpam-6834	303	37	empty	empty	ADJ
ejpam-6834	303	38	subsets	subset	NOUN
ejpam-6834	303	39	of	of	ADP
ejpam-6834	303	40	the	the	DET
ejpam-6834	303	41	unit	unit	NOUN
ejpam-6834	303	42	cube	cube	NOUN
ejpam-6834	303	43	[	[	X
ejpam-6834	303	44	0	0	NUM
ejpam-6834	303	45	,	,	PUNCT
ejpam-6834	303	46	1]3	1]3	NUM
ejpam-6834	303	47	.	.	PUNCT
ejpam-6834	304	1	for	for	ADP
ejpam-6834	304	2	each	each	DET
ejpam-6834	304	3	x	x	SYM
ejpam-6834	304	4	∈	∈	PROPN
ejpam-6834	304	5	x	x	PROPN
ejpam-6834	304	6	,	,	PUNCT
ejpam-6834	304	7	µ̃(x	µ̃(x	PROPN
ejpam-6834	304	8	)	)	PUNCT
ejpam-6834	304	9	⊆	⊆	NUM
ejpam-6834	304	10	[	[	X
ejpam-6834	304	11	0	0	NUM
ejpam-6834	304	12	,	,	PUNCT
ejpam-6834	304	13	1]3	1]3	NUM
ejpam-6834	304	14	represents	represent	VERB
ejpam-6834	304	15	a	a	DET
ejpam-6834	304	16	set	set	NOUN
ejpam-6834	304	17	of	of	ADP
ejpam-6834	304	18	neutrosophic	neutrosophic	ADJ
ejpam-6834	304	19	membership	membership	NOUN
ejpam-6834	304	20	degrees	degree	NOUN
ejpam-6834	304	21	,	,	PUNCT
ejpam-6834	304	22	each	each	DET
ejpam-6834	304	23	consisting	consist	VERB
ejpam-6834	304	24	of	of	ADP
ejpam-6834	304	25	truth	truth	NOUN
ejpam-6834	304	26	(	(	PUNCT
ejpam-6834	304	27	t	t	NOUN
ejpam-6834	304	28	)	)	PUNCT
ejpam-6834	304	29	,	,	PUNCT
ejpam-6834	304	30	indeterminacy	indeterminacy	NOUN
ejpam-6834	304	31	(	(	PUNCT
ejpam-6834	304	32	i	i	NOUN
ejpam-6834	304	33	)	)	PUNCT
ejpam-6834	304	34	,	,	PUNCT
ejpam-6834	304	35	and	and	CCONJ
ejpam-6834	304	36	falsity	falsity	NOUN
ejpam-6834	304	37	(	(	PUNCT
ejpam-6834	304	38	f	f	NOUN
ejpam-6834	304	39	)	)	PUNCT
ejpam-6834	304	40	components	component	NOUN
ejpam-6834	304	41	,	,	PUNCT
ejpam-6834	304	42	satisfying	satisfy	VERB
ejpam-6834	304	43	:	:	PUNCT
ejpam-6834	304	44	0	0	NUM
ejpam-6834	304	45	≤	≤	NUM
ejpam-6834	304	46	t	t	NOUN
ejpam-6834	305	1	+	+	CCONJ
ejpam-6834	305	2	i	i	PRON
ejpam-6834	305	3	+	+	NUM
ejpam-6834	305	4	f	f	PROPN
ejpam-6834	305	5	≤	≤	ADV
ejpam-6834	305	6	3	3	NUM
ejpam-6834	305	7	.	.	PUNCT
ejpam-6834	306	1	t.	t.	PROPN
ejpam-6834	306	2	fujita	fujita	PROPN
ejpam-6834	306	3	,	,	PUNCT
ejpam-6834	306	4	f.smarandache	f.smarandache	NOUN
ejpam-6834	306	5	/	/	SYM
ejpam-6834	306	6	eur	eur	PROPN
ejpam-6834	306	7	.	.	PUNCT
ejpam-6834	307	1	j.	j.	PROPN
ejpam-6834	307	2	pure	pure	PROPN
ejpam-6834	307	3	appl	appl	PROPN
ejpam-6834	307	4	.	.	PROPN
ejpam-6834	307	5	math	math	PROPN
ejpam-6834	307	6	,	,	PUNCT
ejpam-6834	307	7	18	18	NUM
ejpam-6834	307	8	(	(	PUNCT
ejpam-6834	307	9	4	4	NUM
ejpam-6834	307	10	)	)	PUNCT
ejpam-6834	307	11	(	(	PUNCT
ejpam-6834	307	12	2025	2025	NUM
ejpam-6834	307	13	)	)	PUNCT
ejpam-6834	307	14	,	,	PUNCT
ejpam-6834	307	15	6834	6834	NUM
ejpam-6834	307	16	15	15	NUM
ejpam-6834	307	17	of	of	ADP
ejpam-6834	307	18	69	69	NUM
ejpam-6834	307	19	example	example	NOUN
ejpam-6834	307	20	9	9	NUM
ejpam-6834	307	21	(	(	PUNCT
ejpam-6834	307	22	medical	medical	ADJ
ejpam-6834	307	23	diagnosis	diagnosis	NOUN
ejpam-6834	307	24	application	application	NOUN
ejpam-6834	307	25	)	)	PUNCT
ejpam-6834	307	26	.	.	PUNCT
ejpam-6834	308	1	let	let	VERB
ejpam-6834	308	2	x	x	PUNCT
ejpam-6834	308	3	=	=	PRON
ejpam-6834	308	4	{	{	PUNCT
ejpam-6834	308	5	hiroko	hiroko	PROPN
ejpam-6834	308	6	,	,	PUNCT
ejpam-6834	308	7	masahiro	masahiro	PROPN
ejpam-6834	308	8	}	}	PUNCT
ejpam-6834	308	9	be	be	AUX
ejpam-6834	308	10	a	a	DET
ejpam-6834	308	11	set	set	NOUN
ejpam-6834	308	12	of	of	ADP
ejpam-6834	308	13	patients	patient	NOUN
ejpam-6834	308	14	undergoing	undergo	VERB
ejpam-6834	308	15	diagnosis	diagnosis	NOUN
ejpam-6834	308	16	for	for	ADP
ejpam-6834	308	17	a	a	DET
ejpam-6834	308	18	particular	particular	ADJ
ejpam-6834	308	19	disease	disease	NOUN
ejpam-6834	308	20	.	.	PUNCT
ejpam-6834	309	1	we	we	PRON
ejpam-6834	309	2	model	model	VERB
ejpam-6834	309	3	the	the	DET
ejpam-6834	309	4	uncertain	uncertain	ADJ
ejpam-6834	309	5	evaluation	evaluation	NOUN
ejpam-6834	309	6	of	of	ADP
ejpam-6834	309	7	each	each	DET
ejpam-6834	309	8	patient	patient	NOUN
ejpam-6834	309	9	’s	’s	PART
ejpam-6834	309	10	condition	condition	NOUN
ejpam-6834	309	11	by	by	ADP
ejpam-6834	309	12	a	a	DET
ejpam-6834	309	13	hyperneutrosophic	hyperneutrosophic	ADJ
ejpam-6834	309	14	set	set	VERB
ejpam-6834	309	15	µ̃	µ̃	PROPN
ejpam-6834	309	16	:	:	PUNCT
ejpam-6834	309	17	x	x	PUNCT
ejpam-6834	309	18	−→	−→	PROPN
ejpam-6834	309	19	p̃	p̃	PROPN
ejpam-6834	309	20	(	(	PUNCT
ejpam-6834	309	21	[	[	X
ejpam-6834	309	22	0	0	NUM
ejpam-6834	309	23	,	,	PUNCT
ejpam-6834	309	24	1]3	1]3	NUM
ejpam-6834	309	25	)	)	PUNCT
ejpam-6834	309	26	.	.	PUNCT
ejpam-6834	310	1	here	here	ADV
ejpam-6834	310	2	each	each	DET
ejpam-6834	310	3	element	element	NOUN
ejpam-6834	310	4	of	of	ADP
ejpam-6834	310	5	µ̃(x	µ̃(x	PROPN
ejpam-6834	310	6	)	)	PUNCT
ejpam-6834	310	7	⊆	⊆	NUM
ejpam-6834	311	1	[	[	X
ejpam-6834	311	2	0	0	NUM
ejpam-6834	311	3	,	,	PUNCT
ejpam-6834	311	4	1]3	1]3	NUM
ejpam-6834	311	5	is	be	AUX
ejpam-6834	311	6	a	a	DET
ejpam-6834	311	7	triple	triple	ADJ
ejpam-6834	311	8	(	(	PUNCT
ejpam-6834	311	9	t	t	PROPN
ejpam-6834	311	10	,	,	PUNCT
ejpam-6834	311	11	i	i	PRON
ejpam-6834	311	12	,	,	PUNCT
ejpam-6834	311	13	f	f	PROPN
ejpam-6834	311	14	)	)	PUNCT
ejpam-6834	311	15	giving	give	VERB
ejpam-6834	311	16	a	a	DET
ejpam-6834	311	17	possible	possible	ADJ
ejpam-6834	311	18	assessment	assessment	NOUN
ejpam-6834	311	19	of	of	ADP
ejpam-6834	311	20	truth	truth	NOUN
ejpam-6834	311	21	(	(	PUNCT
ejpam-6834	311	22	presence	presence	NOUN
ejpam-6834	311	23	)	)	PUNCT
ejpam-6834	311	24	,	,	PUNCT
ejpam-6834	311	25	indeterminacy	indeterminacy	NOUN
ejpam-6834	311	26	,	,	PUNCT
ejpam-6834	311	27	and	and	CCONJ
ejpam-6834	311	28	falsity	falsity	NOUN
ejpam-6834	311	29	(	(	PUNCT
ejpam-6834	311	30	absence	absence	NOUN
ejpam-6834	311	31	)	)	PUNCT
ejpam-6834	311	32	of	of	ADP
ejpam-6834	311	33	the	the	DET
ejpam-6834	311	34	disease	disease	NOUN
ejpam-6834	311	35	.	.	PUNCT
ejpam-6834	312	1	for	for	ADP
ejpam-6834	312	2	example	example	NOUN
ejpam-6834	312	3	:	:	PUNCT
ejpam-6834	312	4	µ̃(hiroko	µ̃(hiroko	PROPN
ejpam-6834	312	5	)	)	PUNCT
ejpam-6834	312	6	=	=	PRON
ejpam-6834	312	7	{	{	PUNCT
ejpam-6834	312	8	(	(	PUNCT
ejpam-6834	312	9	0.85	0.85	NUM
ejpam-6834	312	10	,	,	PUNCT
ejpam-6834	312	11	0.10	0.10	NUM
ejpam-6834	312	12	,	,	PUNCT
ejpam-6834	312	13	0.05	0.05	NUM
ejpam-6834	312	14	)	)	PUNCT
ejpam-6834	312	15	,	,	PUNCT
ejpam-6834	312	16	(	(	PUNCT
ejpam-6834	312	17	0.80	0.80	NUM
ejpam-6834	312	18	,	,	PUNCT
ejpam-6834	312	19	0.15	0.15	NUM
ejpam-6834	312	20	,	,	PUNCT
ejpam-6834	312	21	0.05	0.05	NUM
ejpam-6834	312	22	)	)	PUNCT
ejpam-6834	312	23	}	}	PUNCT
ejpam-6834	312	24	,	,	PUNCT
ejpam-6834	312	25	µ̃(masahiro	µ̃(masahiro	NOUN
ejpam-6834	312	26	)	)	PUNCT
ejpam-6834	312	27	=	=	PRON
ejpam-6834	312	28	{	{	PUNCT
ejpam-6834	312	29	(	(	PUNCT
ejpam-6834	312	30	0.60	0.60	NUM
ejpam-6834	312	31	,	,	PUNCT
ejpam-6834	312	32	0.20	0.20	NUM
ejpam-6834	312	33	,	,	PUNCT
ejpam-6834	312	34	0.20	0.20	NUM
ejpam-6834	312	35	)	)	PUNCT
ejpam-6834	312	36	,	,	PUNCT
ejpam-6834	312	37	(	(	PUNCT
ejpam-6834	312	38	0.65	0.65	NUM
ejpam-6834	312	39	,	,	PUNCT
ejpam-6834	312	40	0.25	0.25	NUM
ejpam-6834	312	41	,	,	PUNCT
ejpam-6834	312	42	0.10	0.10	NUM
ejpam-6834	312	43	)	)	PUNCT
ejpam-6834	312	44	}	}	PUNCT
ejpam-6834	312	45	.	.	PUNCT
ejpam-6834	313	1	each	each	DET
ejpam-6834	313	2	triple	triple	ADJ
ejpam-6834	313	3	satisfies	satisfie	NOUN
ejpam-6834	313	4	0	0	NUM
ejpam-6834	313	5	≤	≤	NUM
ejpam-6834	313	6	t	t	NOUN
ejpam-6834	314	1	+	+	CCONJ
ejpam-6834	314	2	i	i	PRON
ejpam-6834	314	3	+	+	NUM
ejpam-6834	314	4	f	f	PROPN
ejpam-6834	314	5	≤	≤	ADV
ejpam-6834	314	6	3	3	NUM
ejpam-6834	314	7	.	.	PUNCT
ejpam-6834	315	1	the	the	DET
ejpam-6834	315	2	two	two	NUM
ejpam-6834	315	3	points	point	NOUN
ejpam-6834	315	4	in	in	ADP
ejpam-6834	315	5	µ̃(x	µ̃(x	PROPN
ejpam-6834	315	6	)	)	PUNCT
ejpam-6834	315	7	reflect	reflect	VERB
ejpam-6834	315	8	,	,	PUNCT
ejpam-6834	315	9	for	for	ADP
ejpam-6834	315	10	instance	instance	NOUN
ejpam-6834	315	11	,	,	PUNCT
ejpam-6834	315	12	two	two	NUM
ejpam-6834	315	13	independent	independent	ADJ
ejpam-6834	315	14	expert	expert	ADJ
ejpam-6834	315	15	opinions	opinion	NOUN
ejpam-6834	315	16	or	or	CCONJ
ejpam-6834	315	17	two	two	NUM
ejpam-6834	315	18	different	different	ADJ
ejpam-6834	315	19	diagnostic	diagnostic	ADJ
ejpam-6834	315	20	tests	test	NOUN
ejpam-6834	315	21	,	,	PUNCT
ejpam-6834	315	22	capturing	capture	VERB
ejpam-6834	315	23	both	both	DET
ejpam-6834	315	24	the	the	DET
ejpam-6834	315	25	variability	variability	NOUN
ejpam-6834	315	26	among	among	ADP
ejpam-6834	315	27	assessments	assessment	NOUN
ejpam-6834	315	28	and	and	CCONJ
ejpam-6834	315	29	the	the	DET
ejpam-6834	315	30	underlying	underlying	ADJ
ejpam-6834	315	31	neutrosophic	neutrosophic	ADJ
ejpam-6834	315	32	uncertainty	uncertainty	NOUN
ejpam-6834	315	33	.	.	PUNCT
ejpam-6834	316	1	definition	definition	NOUN
ejpam-6834	316	2	15	15	NUM
ejpam-6834	316	3	(	(	PUNCT
ejpam-6834	316	4	n	n	CCONJ
ejpam-6834	316	5	-	-	PUNCT
ejpam-6834	316	6	superhyperneutrosophic	superhyperneutrosophic	ADJ
ejpam-6834	316	7	set	set	NOUN
ejpam-6834	316	8	)	)	PUNCT
ejpam-6834	316	9	.	.	PUNCT
ejpam-6834	317	1	[	[	X
ejpam-6834	317	2	1	1	NUM
ejpam-6834	317	3	,	,	PUNCT
ejpam-6834	317	4	2	2	NUM
ejpam-6834	317	5	]	]	PUNCT
ejpam-6834	317	6	let	let	VERB
ejpam-6834	317	7	x	x	PRON
ejpam-6834	317	8	be	be	AUX
ejpam-6834	317	9	a	a	DET
ejpam-6834	317	10	non	non	ADJ
ejpam-6834	317	11	-	-	ADJ
ejpam-6834	317	12	empty	empty	ADJ
ejpam-6834	317	13	set	set	NOUN
ejpam-6834	317	14	.	.	PUNCT
ejpam-6834	318	1	an	an	DET
ejpam-6834	318	2	n	n	ADV
ejpam-6834	318	3	-	-	PUNCT
ejpam-6834	318	4	superhyperneutrosophic	superhyperneutrosophic	ADJ
ejpam-6834	318	5	set	set	NOUN
ejpam-6834	318	6	is	be	AUX
ejpam-6834	318	7	a	a	DET
ejpam-6834	318	8	recursive	recursive	ADJ
ejpam-6834	318	9	generalization	generalization	NOUN
ejpam-6834	318	10	of	of	ADP
ejpam-6834	318	11	neutrosophic	neutrosophic	ADJ
ejpam-6834	318	12	sets	set	NOUN
ejpam-6834	318	13	,	,	PUNCT
ejpam-6834	318	14	hyperneutrosophic	hyperneutrosophic	ADJ
ejpam-6834	318	15	sets	set	NOUN
ejpam-6834	318	16	,	,	PUNCT
ejpam-6834	318	17	and	and	CCONJ
ejpam-6834	318	18	superhyperneutrosophic	superhyperneutrosophic	ADJ
ejpam-6834	318	19	sets	set	NOUN
ejpam-6834	318	20	.	.	PUNCT
ejpam-6834	319	1	it	it	PRON
ejpam-6834	319	2	is	be	AUX
ejpam-6834	319	3	defined	define	VERB
ejpam-6834	319	4	as	as	ADP
ejpam-6834	319	5	:	:	PUNCT
ejpam-6834	319	6	ãn	ãn	NOUN
ejpam-6834	319	7	:	:	PUNCT
ejpam-6834	320	1	p̃n(x	p̃n(x	X
ejpam-6834	320	2	)	)	PUNCT
ejpam-6834	320	3	→	→	SYM
ejpam-6834	320	4	p̃n([0	p̃n([0	PROPN
ejpam-6834	320	5	,	,	PUNCT
ejpam-6834	320	6	1]3	1]3	NUM
ejpam-6834	320	7	)	)	PUNCT
ejpam-6834	320	8	,	,	PUNCT
ejpam-6834	320	9	where	where	SCONJ
ejpam-6834	320	10	:	:	PUNCT
ejpam-6834	320	11	•	•	NUM
ejpam-6834	320	12	p̃1(x	p̃1(x	NOUN
ejpam-6834	320	13	)	)	PUNCT
ejpam-6834	320	14	=	=	PUNCT
ejpam-6834	320	15	p̃(x	p̃(x	PROPN
ejpam-6834	320	16	)	)	PUNCT
ejpam-6834	320	17	,	,	PUNCT
ejpam-6834	320	18	and	and	CCONJ
ejpam-6834	320	19	for	for	ADP
ejpam-6834	320	20	k	k	PROPN
ejpam-6834	320	21	≥	≥	NUM
ejpam-6834	320	22	2	2	NUM
ejpam-6834	320	23	,	,	PUNCT
ejpam-6834	320	24	p̃k(x	p̃k(x	X
ejpam-6834	320	25	)	)	PUNCT
ejpam-6834	320	26	=	=	SYM
ejpam-6834	320	27	p̃(p̃k−1(x	p̃(p̃k−1(x	NOUN
ejpam-6834	320	28	)	)	PUNCT
ejpam-6834	320	29	)	)	PUNCT
ejpam-6834	320	30	,	,	PUNCT
ejpam-6834	320	31	represents	represent	VERB
ejpam-6834	320	32	the	the	DET
ejpam-6834	320	33	k	k	NOUN
ejpam-6834	320	34	-	-	PUNCT
ejpam-6834	320	35	th	th	X
ejpam-6834	320	36	nested	nested	ADJ
ejpam-6834	320	37	family	family	NOUN
ejpam-6834	320	38	of	of	ADP
ejpam-6834	320	39	non	non	ADJ
ejpam-6834	320	40	-	-	ADJ
ejpam-6834	320	41	empty	empty	ADJ
ejpam-6834	320	42	subsets	subset	NOUN
ejpam-6834	320	43	of	of	ADP
ejpam-6834	320	44	x.	x.	NOUN
ejpam-6834	320	45	•	•	ADP
ejpam-6834	320	46	p̃n([0	p̃n([0	PROPN
ejpam-6834	320	47	,	,	PUNCT
ejpam-6834	320	48	1]3	1]3	NUM
ejpam-6834	320	49	)	)	PUNCT
ejpam-6834	320	50	is	be	AUX
ejpam-6834	320	51	similarly	similarly	ADV
ejpam-6834	320	52	defined	define	VERB
ejpam-6834	320	53	for	for	ADP
ejpam-6834	320	54	the	the	DET
ejpam-6834	320	55	unit	unit	NOUN
ejpam-6834	320	56	cube	cube	NOUN
ejpam-6834	321	1	[	[	X
ejpam-6834	321	2	0	0	NUM
ejpam-6834	321	3	,	,	PUNCT
ejpam-6834	321	4	1]3	1]3	NUM
ejpam-6834	321	5	.	.	NOUN
ejpam-6834	322	1	•	•	NOUN
ejpam-6834	322	2	the	the	DET
ejpam-6834	322	3	mapping	mapping	NOUN
ejpam-6834	322	4	ãn	ãn	NOUN
ejpam-6834	322	5	assigns	assign	NOUN
ejpam-6834	322	6	to	to	ADP
ejpam-6834	322	7	each	each	PRON
ejpam-6834	322	8	a	a	DET
ejpam-6834	322	9	∈	∈	PROPN
ejpam-6834	322	10	p̃n(x	p̃n(x	NOUN
ejpam-6834	322	11	)	)	PUNCT
ejpam-6834	322	12	a	a	DET
ejpam-6834	322	13	subset	subset	NOUN
ejpam-6834	322	14	ãn(a	ãn(a	NOUN
ejpam-6834	322	15	)	)	PUNCT
ejpam-6834	323	1	⊆	⊆	NUM
ejpam-6834	323	2	[	[	X
ejpam-6834	323	3	0	0	NUM
ejpam-6834	323	4	,	,	PUNCT
ejpam-6834	323	5	1]3	1]3	NUM
ejpam-6834	323	6	,	,	PUNCT
ejpam-6834	323	7	representing	represent	VERB
ejpam-6834	323	8	the	the	DET
ejpam-6834	323	9	degrees	degree	NOUN
ejpam-6834	323	10	of	of	ADP
ejpam-6834	323	11	truth	truth	NOUN
ejpam-6834	323	12	(	(	PUNCT
ejpam-6834	323	13	t	t	NOUN
ejpam-6834	323	14	)	)	PUNCT
ejpam-6834	323	15	,	,	PUNCT
ejpam-6834	323	16	indeterminacy	indeterminacy	NOUN
ejpam-6834	323	17	(	(	PUNCT
ejpam-6834	323	18	i	i	NOUN
ejpam-6834	323	19	)	)	PUNCT
ejpam-6834	323	20	,	,	PUNCT
ejpam-6834	323	21	and	and	CCONJ
ejpam-6834	323	22	falsity	falsity	NOUN
ejpam-6834	323	23	(	(	PUNCT
ejpam-6834	323	24	f	f	NOUN
ejpam-6834	323	25	)	)	PUNCT
ejpam-6834	323	26	for	for	ADP
ejpam-6834	323	27	the	the	DET
ejpam-6834	323	28	n	n	CCONJ
ejpam-6834	323	29	-	-	PUNCT
ejpam-6834	323	30	th	th	VERB
ejpam-6834	323	31	level	level	NOUN
ejpam-6834	323	32	subsets	subset	NOUN
ejpam-6834	323	33	of	of	ADP
ejpam-6834	323	34	x.	x.	NOUN
ejpam-6834	323	35	for	for	ADP
ejpam-6834	323	36	each	each	DET
ejpam-6834	323	37	a	a	DET
ejpam-6834	323	38	∈	∈	PROPN
ejpam-6834	323	39	p̃n(x	p̃n(x	NOUN
ejpam-6834	323	40	)	)	PUNCT
ejpam-6834	323	41	and	and	CCONJ
ejpam-6834	323	42	(	(	PUNCT
ejpam-6834	323	43	t	t	PROPN
ejpam-6834	323	44	,	,	PUNCT
ejpam-6834	323	45	i	i	PRON
ejpam-6834	323	46	,	,	PUNCT
ejpam-6834	323	47	f	f	PROPN
ejpam-6834	323	48	)	)	PUNCT
ejpam-6834	323	49	∈	∈	PROPN
ejpam-6834	323	50	ãn(a	ãn(a	PROPN
ejpam-6834	323	51	)	)	PUNCT
ejpam-6834	323	52	,	,	PUNCT
ejpam-6834	323	53	the	the	DET
ejpam-6834	323	54	following	follow	VERB
ejpam-6834	323	55	condition	condition	NOUN
ejpam-6834	323	56	is	be	AUX
ejpam-6834	323	57	satisfied	satisfied	ADJ
ejpam-6834	323	58	:	:	PUNCT
ejpam-6834	323	59	0	0	NUM
ejpam-6834	323	60	≤	≤	NUM
ejpam-6834	323	61	t	t	NOUN
ejpam-6834	323	62	+	+	CCONJ
ejpam-6834	323	63	i	i	PRON
ejpam-6834	324	1	+	+	NUM
ejpam-6834	324	2	f	f	PROPN
ejpam-6834	324	3	≤	≤	ADV
ejpam-6834	324	4	3	3	NUM
ejpam-6834	324	5	,	,	PUNCT
ejpam-6834	324	6	where	where	SCONJ
ejpam-6834	324	7	t	t	PROPN
ejpam-6834	324	8	,	,	PUNCT
ejpam-6834	324	9	i	i	PRON
ejpam-6834	324	10	,	,	PUNCT
ejpam-6834	324	11	and	and	CCONJ
ejpam-6834	324	12	f	f	PROPN
ejpam-6834	324	13	represent	represent	VERB
ejpam-6834	324	14	the	the	DET
ejpam-6834	324	15	truth	truth	NOUN
ejpam-6834	324	16	,	,	PUNCT
ejpam-6834	324	17	indeterminacy	indeterminacy	NOUN
ejpam-6834	324	18	,	,	PUNCT
ejpam-6834	324	19	and	and	CCONJ
ejpam-6834	324	20	falsity	falsity	NOUN
ejpam-6834	324	21	degrees	degree	NOUN
ejpam-6834	324	22	,	,	PUNCT
ejpam-6834	324	23	respectively	respectively	ADV
ejpam-6834	324	24	.	.	PUNCT
ejpam-6834	324	25	example	example	NOUN
ejpam-6834	325	1	10	10	NUM
ejpam-6834	325	2	(	(	PUNCT
ejpam-6834	325	3	hierarchical	hierarchical	ADJ
ejpam-6834	325	4	fault	fault	NOUN
ejpam-6834	325	5	diagnosis	diagnosis	NOUN
ejpam-6834	325	6	in	in	ADP
ejpam-6834	325	7	an	an	DET
ejpam-6834	325	8	industrial	industrial	ADJ
ejpam-6834	325	9	system	system	NOUN
ejpam-6834	325	10	)	)	PUNCT
ejpam-6834	325	11	.	.	PUNCT
ejpam-6834	326	1	let	let	VERB
ejpam-6834	326	2	x	x	PUNCT
ejpam-6834	326	3	=	=	PRON
ejpam-6834	326	4	{	{	PUNCT
ejpam-6834	326	5	tempsensor	tempsensor	PROPN
ejpam-6834	326	6	,	,	PUNCT
ejpam-6834	326	7	pressuresensor	pressuresensor	NOUN
ejpam-6834	326	8	}	}	PUNCT
ejpam-6834	326	9	t.	t.	PROPN
ejpam-6834	326	10	fujita	fujita	PROPN
ejpam-6834	326	11	,	,	PUNCT
ejpam-6834	326	12	f.smarandache	f.smarandache	NOUN
ejpam-6834	326	13	/	/	SYM
ejpam-6834	326	14	eur	eur	PROPN
ejpam-6834	326	15	.	.	PUNCT
ejpam-6834	327	1	j.	j.	PROPN
ejpam-6834	327	2	pure	pure	PROPN
ejpam-6834	327	3	appl	appl	PROPN
ejpam-6834	327	4	.	.	PROPN
ejpam-6834	327	5	math	math	PROPN
ejpam-6834	327	6	,	,	PUNCT
ejpam-6834	327	7	18	18	NUM
ejpam-6834	327	8	(	(	PUNCT
ejpam-6834	327	9	4	4	NUM
ejpam-6834	327	10	)	)	PUNCT
ejpam-6834	327	11	(	(	PUNCT
ejpam-6834	327	12	2025	2025	NUM
ejpam-6834	327	13	)	)	PUNCT
ejpam-6834	327	14	,	,	PUNCT
ejpam-6834	327	15	6834	6834	NUM
ejpam-6834	327	16	16	16	NUM
ejpam-6834	327	17	of	of	ADP
ejpam-6834	327	18	69	69	NUM
ejpam-6834	327	19	be	be	AUX
ejpam-6834	327	20	the	the	DET
ejpam-6834	327	21	set	set	NOUN
ejpam-6834	327	22	of	of	ADP
ejpam-6834	327	23	two	two	NUM
ejpam-6834	327	24	critical	critical	ADJ
ejpam-6834	327	25	sensors	sensor	NOUN
ejpam-6834	327	26	in	in	ADP
ejpam-6834	327	27	an	an	DET
ejpam-6834	327	28	industrial	industrial	ADJ
ejpam-6834	327	29	process	process	NOUN
ejpam-6834	327	30	.	.	PUNCT
ejpam-6834	328	1	we	we	PRON
ejpam-6834	328	2	consider	consider	VERB
ejpam-6834	328	3	n	n	NOUN
ejpam-6834	328	4	=	=	SYM
ejpam-6834	328	5	2	2	NUM
ejpam-6834	328	6	,	,	PUNCT
ejpam-6834	328	7	so	so	SCONJ
ejpam-6834	328	8	that	that	DET
ejpam-6834	328	9	p̃1(x	p̃1(x	NOUN
ejpam-6834	328	10	)	)	PUNCT
ejpam-6834	329	1	=	=	PRON
ejpam-6834	329	2	{	{	PUNCT
ejpam-6834	329	3	{	{	PUNCT
ejpam-6834	329	4	tempsensor	tempsensor	NUM
ejpam-6834	329	5	}	}	PUNCT
ejpam-6834	329	6	,	,	PUNCT
ejpam-6834	329	7	{	{	PUNCT
ejpam-6834	329	8	pressuresensor	pressuresensor	NOUN
ejpam-6834	329	9	}	}	PUNCT
ejpam-6834	329	10	,	,	PUNCT
ejpam-6834	329	11	{	{	PUNCT
ejpam-6834	329	12	tempsensor	tempsensor	PROPN
ejpam-6834	329	13	,	,	PUNCT
ejpam-6834	329	14	pressuresensor	pressuresensor	NOUN
ejpam-6834	329	15	}	}	PUNCT
ejpam-6834	329	16	}	}	PUNCT
ejpam-6834	329	17	,	,	PUNCT
ejpam-6834	329	18	and	and	CCONJ
ejpam-6834	329	19	p̃2(x	p̃2(x	PROPN
ejpam-6834	329	20	)	)	PUNCT
ejpam-6834	329	21	=	=	SYM
ejpam-6834	330	1	p̃	p̃	PROPN
ejpam-6834	330	2	(	(	PUNCT
ejpam-6834	330	3	p̃1(x	p̃1(x	NOUN
ejpam-6834	330	4	)	)	PUNCT
ejpam-6834	330	5	)	)	PUNCT
ejpam-6834	330	6	,	,	PUNCT
ejpam-6834	330	7	whose	whose	DET
ejpam-6834	330	8	elements	element	NOUN
ejpam-6834	330	9	are	be	AUX
ejpam-6834	330	10	nonempty	nonempty	ADJ
ejpam-6834	330	11	collections	collection	NOUN
ejpam-6834	330	12	of	of	ADP
ejpam-6834	330	13	nonempty	nonempty	ADJ
ejpam-6834	330	14	subsets	subset	NOUN
ejpam-6834	330	15	of	of	ADP
ejpam-6834	330	16	x.	x.	NOUN
ejpam-6834	330	17	for	for	ADP
ejpam-6834	330	18	example	example	NOUN
ejpam-6834	330	19	,	,	PUNCT
ejpam-6834	330	20	choose	choose	VERB
ejpam-6834	330	21	a	a	PRON
ejpam-6834	330	22	=	=	X
ejpam-6834	330	23	{	{	PUNCT
ejpam-6834	330	24	{	{	PUNCT
ejpam-6834	330	25	tempsensor	tempsensor	PROPN
ejpam-6834	330	26	}	}	PUNCT
ejpam-6834	330	27	,	,	PUNCT
ejpam-6834	330	28	{	{	PUNCT
ejpam-6834	330	29	pressuresensor	pressuresensor	NOUN
ejpam-6834	330	30	}	}	PUNCT
ejpam-6834	330	31	}	}	PUNCT
ejpam-6834	330	32	∈	∈	PROPN
ejpam-6834	330	33	p̃2(x	p̃2(x	NOUN
ejpam-6834	330	34	)	)	PUNCT
ejpam-6834	330	35	.	.	PUNCT
ejpam-6834	331	1	a	a	DET
ejpam-6834	331	2	2	2	NUM
ejpam-6834	331	3	-	-	PUNCT
ejpam-6834	331	4	superhyperneutrosophic	superhyperneutrosophic	ADJ
ejpam-6834	331	5	set	set	NOUN
ejpam-6834	331	6	on	on	ADP
ejpam-6834	331	7	x	x	SYM
ejpam-6834	331	8	is	be	AUX
ejpam-6834	331	9	a	a	DET
ejpam-6834	331	10	mapping	mapping	NOUN
ejpam-6834	331	11	ã2	ã2	PROPN
ejpam-6834	331	12	:	:	PUNCT
ejpam-6834	331	13	p̃2(x	p̃2(x	NOUN
ejpam-6834	331	14	)	)	PUNCT
ejpam-6834	331	15	−→	−→	NOUN
ejpam-6834	331	16	p̃2	p̃2	PROPN
ejpam-6834	331	17	(	(	PUNCT
ejpam-6834	331	18	[	[	X
ejpam-6834	331	19	0	0	NUM
ejpam-6834	331	20	,	,	PUNCT
ejpam-6834	331	21	1]3	1]3	NUM
ejpam-6834	331	22	)	)	PUNCT
ejpam-6834	331	23	.	.	PUNCT
ejpam-6834	332	1	we	we	PRON
ejpam-6834	332	2	may	may	AUX
ejpam-6834	332	3	define	define	VERB
ejpam-6834	332	4	,	,	PUNCT
ejpam-6834	332	5	for	for	ADP
ejpam-6834	332	6	instance	instance	NOUN
ejpam-6834	332	7	,	,	PUNCT
ejpam-6834	332	8	ã2(a	ã2(a	PROPN
ejpam-6834	332	9	)	)	PUNCT
ejpam-6834	333	1	=	=	PRON
ejpam-6834	333	2	{	{	PUNCT
ejpam-6834	333	3	{	{	PUNCT
ejpam-6834	333	4	(	(	PUNCT
ejpam-6834	333	5	0.85	0.85	NUM
ejpam-6834	333	6	,	,	PUNCT
ejpam-6834	333	7	0.10	0.10	NUM
ejpam-6834	333	8	,	,	PUNCT
ejpam-6834	333	9	0.05	0.05	NUM
ejpam-6834	333	10	)	)	PUNCT
ejpam-6834	333	11	,	,	PUNCT
ejpam-6834	333	12	(	(	PUNCT
ejpam-6834	333	13	0.80	0.80	NUM
ejpam-6834	333	14	,	,	PUNCT
ejpam-6834	333	15	0.15	0.15	NUM
ejpam-6834	333	16	,	,	PUNCT
ejpam-6834	333	17	0.05	0.05	NUM
ejpam-6834	333	18	)	)	PUNCT
ejpam-6834	333	19	}	}	PUNCT
ejpam-6834	333	20	,	,	PUNCT
ejpam-6834	333	21	{	{	PUNCT
ejpam-6834	333	22	(	(	PUNCT
ejpam-6834	333	23	0.70	0.70	NUM
ejpam-6834	333	24	,	,	PUNCT
ejpam-6834	333	25	0.20	0.20	NUM
ejpam-6834	333	26	,	,	PUNCT
ejpam-6834	333	27	0.10	0.10	NUM
ejpam-6834	333	28	)	)	PUNCT
ejpam-6834	333	29	}	}	PUNCT
ejpam-6834	333	30	}	}	PUNCT
ejpam-6834	333	31	.	.	PUNCT
ejpam-6834	334	1	here	here	ADV
ejpam-6834	334	2	:	:	PUNCT
ejpam-6834	334	3	•	•	ADP
ejpam-6834	334	4	the	the	DET
ejpam-6834	334	5	first	first	ADJ
ejpam-6834	334	6	inner	inner	ADJ
ejpam-6834	334	7	set	set	NOUN
ejpam-6834	334	8	{	{	PUNCT
ejpam-6834	334	9	(	(	PUNCT
ejpam-6834	334	10	0.85	0.85	NUM
ejpam-6834	334	11	,	,	PUNCT
ejpam-6834	334	12	0.10	0.10	NUM
ejpam-6834	334	13	,	,	PUNCT
ejpam-6834	334	14	0.05	0.05	NUM
ejpam-6834	334	15	)	)	PUNCT
ejpam-6834	334	16	,	,	PUNCT
ejpam-6834	334	17	(	(	PUNCT
ejpam-6834	334	18	0.80	0.80	NUM
ejpam-6834	334	19	,	,	PUNCT
ejpam-6834	334	20	0.15	0.15	NUM
ejpam-6834	334	21	,	,	PUNCT
ejpam-6834	334	22	0.05	0.05	NUM
ejpam-6834	334	23	)	)	PUNCT
ejpam-6834	334	24	}	}	PUNCT
ejpam-6834	334	25	represents	represent	VERB
ejpam-6834	334	26	two	two	NUM
ejpam-6834	334	27	expert	expert	ADJ
ejpam-6834	334	28	judgments	judgment	NOUN
ejpam-6834	334	29	about	about	ADP
ejpam-6834	334	30	the	the	DET
ejpam-6834	334	31	joint	joint	ADJ
ejpam-6834	334	32	status	status	NOUN
ejpam-6834	334	33	of	of	ADP
ejpam-6834	334	34	the	the	DET
ejpam-6834	334	35	temperature	temperature	NOUN
ejpam-6834	334	36	and	and	CCONJ
ejpam-6834	334	37	pressure	pressure	NOUN
ejpam-6834	334	38	sensors	sensor	NOUN
ejpam-6834	334	39	,	,	PUNCT
ejpam-6834	334	40	each	each	PRON
ejpam-6834	334	41	triple	triple	ADJ
ejpam-6834	334	42	(	(	PUNCT
ejpam-6834	334	43	t	t	PROPN
ejpam-6834	334	44	,	,	PUNCT
ejpam-6834	334	45	i	i	PRON
ejpam-6834	334	46	,	,	PUNCT
ejpam-6834	334	47	f	f	PROPN
ejpam-6834	334	48	)	)	PUNCT
ejpam-6834	334	49	satisfying	satisfy	VERB
ejpam-6834	334	50	0	0	NUM
ejpam-6834	334	51	≤	≤	NUM
ejpam-6834	334	52	t	t	NOUN
ejpam-6834	335	1	+	+	CCONJ
ejpam-6834	335	2	i	i	PRON
ejpam-6834	335	3	+	+	NUM
ejpam-6834	336	1	f	f	PROPN
ejpam-6834	336	2	≤	≤	ADV
ejpam-6834	336	3	3	3	NUM
ejpam-6834	336	4	.	.	NOUN
ejpam-6834	336	5	•	•	NUM
ejpam-6834	336	6	the	the	DET
ejpam-6834	336	7	second	second	ADJ
ejpam-6834	336	8	inner	inner	ADJ
ejpam-6834	336	9	set	set	NOUN
ejpam-6834	336	10	{	{	PUNCT
ejpam-6834	336	11	(	(	PUNCT
ejpam-6834	336	12	0.70	0.70	NUM
ejpam-6834	336	13	,	,	PUNCT
ejpam-6834	336	14	0.20	0.20	NUM
ejpam-6834	336	15	,	,	PUNCT
ejpam-6834	336	16	0.10	0.10	NUM
ejpam-6834	336	17	)	)	PUNCT
ejpam-6834	336	18	}	}	PUNCT
ejpam-6834	336	19	could	could	AUX
ejpam-6834	336	20	correspond	correspond	VERB
ejpam-6834	336	21	to	to	ADP
ejpam-6834	336	22	an	an	DET
ejpam-6834	336	23	automated	automate	VERB
ejpam-6834	336	24	diagnostic	diagnostic	ADJ
ejpam-6834	336	25	algorithm	algorithm	NOUN
ejpam-6834	336	26	’s	’s	PART
ejpam-6834	336	27	assessment	assessment	NOUN
ejpam-6834	336	28	.	.	PUNCT
ejpam-6834	337	1	thus	thus	ADV
ejpam-6834	337	2	ã2(a	ã2(a	PROPN
ejpam-6834	337	3	)	)	PUNCT
ejpam-6834	337	4	captures	capture	VERB
ejpam-6834	337	5	the	the	DET
ejpam-6834	337	6	hierarchical	hierarchical	ADJ
ejpam-6834	337	7	uncertainty	uncertainty	NOUN
ejpam-6834	337	8	at	at	ADP
ejpam-6834	337	9	the	the	DET
ejpam-6834	337	10	second	second	ADJ
ejpam-6834	337	11	level	level	NOUN
ejpam-6834	337	12	,	,	PUNCT
ejpam-6834	337	13	aggregating	aggregate	VERB
ejpam-6834	337	14	multiple	multiple	ADJ
ejpam-6834	337	15	neutrosophic	neutrosophic	ADJ
ejpam-6834	337	16	evaluations	evaluation	NOUN
ejpam-6834	337	17	for	for	ADP
ejpam-6834	337	18	the	the	DET
ejpam-6834	337	19	group	group	NOUN
ejpam-6834	337	20	of	of	ADP
ejpam-6834	337	21	sensors	sensor	NOUN
ejpam-6834	337	22	.	.	PUNCT
ejpam-6834	338	1	2.4	2.4	NUM
ejpam-6834	338	2	.	.	X
ejpam-6834	338	3	plithogenic	plithogenic	PROPN
ejpam-6834	338	4	set	set	VERB
ejpam-6834	338	5	a	a	DET
ejpam-6834	338	6	plithogenic	plithogenic	ADJ
ejpam-6834	338	7	set	set	NOUN
ejpam-6834	338	8	is	be	AUX
ejpam-6834	338	9	a	a	DET
ejpam-6834	338	10	mathematical	mathematical	ADJ
ejpam-6834	338	11	framework	framework	NOUN
ejpam-6834	338	12	that	that	PRON
ejpam-6834	338	13	incorporates	incorporate	VERB
ejpam-6834	338	14	multi	multi	ADJ
ejpam-6834	338	15	-	-	ADJ
ejpam-6834	338	16	valued	value	VERB
ejpam-6834	338	17	degrees	degree	NOUN
ejpam-6834	338	18	of	of	ADP
ejpam-6834	338	19	appurtenance	appurtenance	NOUN
ejpam-6834	338	20	and	and	CCONJ
ejpam-6834	338	21	contradictions	contradiction	NOUN
ejpam-6834	338	22	,	,	PUNCT
ejpam-6834	338	23	making	make	VERB
ejpam-6834	338	24	it	it	PRON
ejpam-6834	338	25	suitable	suitable	ADJ
ejpam-6834	338	26	for	for	ADP
ejpam-6834	338	27	complex	complex	ADJ
ejpam-6834	338	28	decision	decision	NOUN
ejpam-6834	338	29	-	-	PUNCT
ejpam-6834	338	30	making	make	VERB
ejpam-6834	338	31	processes	process	NOUN
ejpam-6834	338	32	.	.	PUNCT
ejpam-6834	339	1	various	various	ADJ
ejpam-6834	339	2	studies	study	NOUN
ejpam-6834	339	3	have	have	AUX
ejpam-6834	339	4	been	be	AUX
ejpam-6834	339	5	conducted	conduct	VERB
ejpam-6834	339	6	on	on	ADP
ejpam-6834	339	7	plithogenic	plithogenic	ADJ
ejpam-6834	339	8	sets	set	NOUN
ejpam-6834	339	9	[	[	X
ejpam-6834	339	10	65	65	NUM
ejpam-6834	339	11	,	,	PUNCT
ejpam-6834	339	12	66	66	NUM
ejpam-6834	339	13	]	]	PUNCT
ejpam-6834	339	14	.	.	PUNCT
ejpam-6834	340	1	the	the	DET
ejpam-6834	340	2	definition	definition	NOUN
ejpam-6834	340	3	is	be	AUX
ejpam-6834	340	4	presented	present	VERB
ejpam-6834	340	5	below	below	ADV
ejpam-6834	340	6	.	.	PUNCT
ejpam-6834	341	1	definition	definition	NOUN
ejpam-6834	341	2	16	16	NUM
ejpam-6834	341	3	(	(	PUNCT
ejpam-6834	341	4	plithogenic	plithogenic	ADJ
ejpam-6834	341	5	set	set	NOUN
ejpam-6834	341	6	)	)	PUNCT
ejpam-6834	341	7	.	.	PUNCT
ejpam-6834	342	1	[	[	X
ejpam-6834	342	2	15	15	NUM
ejpam-6834	342	3	,	,	PUNCT
ejpam-6834	342	4	65	65	NUM
ejpam-6834	342	5	]	]	PUNCT
ejpam-6834	342	6	let	let	VERB
ejpam-6834	342	7	s	s	PRON
ejpam-6834	342	8	be	be	AUX
ejpam-6834	342	9	a	a	DET
ejpam-6834	342	10	universal	universal	ADJ
ejpam-6834	342	11	set	set	NOUN
ejpam-6834	342	12	,	,	PUNCT
ejpam-6834	342	13	and	and	CCONJ
ejpam-6834	342	14	p	p	AUX
ejpam-6834	342	15	⊆	⊆	NUM
ejpam-6834	342	16	s.	s.	PROPN
ejpam-6834	342	17	a	a	DET
ejpam-6834	342	18	plithogenic	plithogenic	ADJ
ejpam-6834	342	19	set	set	VERB
ejpam-6834	342	20	ps	ps	NOUN
ejpam-6834	342	21	is	be	AUX
ejpam-6834	342	22	defined	define	VERB
ejpam-6834	342	23	as	as	ADP
ejpam-6834	342	24	:	:	PUNCT
ejpam-6834	342	25	ps	ps	PROPN
ejpam-6834	342	26	=	=	SYM
ejpam-6834	342	27	(	(	PUNCT
ejpam-6834	342	28	p	p	X
ejpam-6834	342	29	,	,	PUNCT
ejpam-6834	342	30	v	v	NOUN
ejpam-6834	342	31	,	,	PUNCT
ejpam-6834	342	32	pv	pv	INTJ
ejpam-6834	342	33	,	,	PUNCT
ejpam-6834	342	34	pdf	pdf	NOUN
ejpam-6834	342	35	,	,	PUNCT
ejpam-6834	342	36	pcf	pcf	PROPN
ejpam-6834	342	37	)	)	PUNCT
ejpam-6834	342	38	where	where	SCONJ
ejpam-6834	342	39	:	:	PUNCT
ejpam-6834	342	40	•	•	NUM
ejpam-6834	342	41	v	v	NOUN
ejpam-6834	342	42	is	be	AUX
ejpam-6834	342	43	an	an	DET
ejpam-6834	342	44	attribute	attribute	NOUN
ejpam-6834	342	45	.	.	PUNCT
ejpam-6834	343	1	•	•	NUM
ejpam-6834	344	1	pv	pv	NOUN
ejpam-6834	344	2	is	be	AUX
ejpam-6834	344	3	the	the	DET
ejpam-6834	344	4	range	range	NOUN
ejpam-6834	344	5	of	of	ADP
ejpam-6834	344	6	possible	possible	ADJ
ejpam-6834	344	7	values	value	NOUN
ejpam-6834	344	8	for	for	ADP
ejpam-6834	344	9	the	the	DET
ejpam-6834	344	10	attribute	attribute	NOUN
ejpam-6834	344	11	v.	v.	ADP
ejpam-6834	344	12	t.	t.	PROPN
ejpam-6834	344	13	fujita	fujita	PROPN
ejpam-6834	344	14	,	,	PUNCT
ejpam-6834	344	15	f.smarandache	f.smarandache	NOUN
ejpam-6834	344	16	/	/	SYM
ejpam-6834	344	17	eur	eur	PROPN
ejpam-6834	344	18	.	.	PUNCT
ejpam-6834	345	1	j.	j.	PROPN
ejpam-6834	345	2	pure	pure	PROPN
ejpam-6834	345	3	appl	appl	PROPN
ejpam-6834	345	4	.	.	PROPN
ejpam-6834	345	5	math	math	PROPN
ejpam-6834	345	6	,	,	PUNCT
ejpam-6834	345	7	18	18	NUM
ejpam-6834	345	8	(	(	PUNCT
ejpam-6834	345	9	4	4	NUM
ejpam-6834	345	10	)	)	PUNCT
ejpam-6834	345	11	(	(	PUNCT
ejpam-6834	345	12	2025	2025	NUM
ejpam-6834	345	13	)	)	PUNCT
ejpam-6834	345	14	,	,	PUNCT
ejpam-6834	345	15	6834	6834	NUM
ejpam-6834	345	16	17	17	NUM
ejpam-6834	345	17	of	of	ADP
ejpam-6834	345	18	69	69	NUM
ejpam-6834	345	19	•	•	NOUN
ejpam-6834	345	20	pdf	pdf	NOUN
ejpam-6834	345	21	:	:	PUNCT
ejpam-6834	345	22	p	p	X
ejpam-6834	345	23	×	×	NOUN
ejpam-6834	345	24	pv	pv	INTJ
ejpam-6834	346	1	→	→	PUNCT
ejpam-6834	346	2	[	[	X
ejpam-6834	346	3	0	0	NUM
ejpam-6834	346	4	,	,	PUNCT
ejpam-6834	346	5	1]s	1]s	NOUN
ejpam-6834	346	6	is	be	AUX
ejpam-6834	346	7	the	the	DET
ejpam-6834	346	8	degree	degree	NOUN
ejpam-6834	346	9	of	of	ADP
ejpam-6834	346	10	appurtenance	appurtenance	NOUN
ejpam-6834	346	11	function	function	NOUN
ejpam-6834	346	12	(	(	PUNCT
ejpam-6834	346	13	daf	daf	NOUN
ejpam-6834	346	14	)	)	PUNCT
ejpam-6834	346	15	.	.	PUNCT
ejpam-6834	347	1	•	•	NUM
ejpam-6834	347	2	pcf	pcf	PROPN
ejpam-6834	347	3	:	:	PUNCT
ejpam-6834	347	4	pv	pv	INTJ
ejpam-6834	347	5	×	×	NOUN
ejpam-6834	347	6	pv	pv	INTJ
ejpam-6834	347	7	→	→	PUNCT
ejpam-6834	347	8	[	[	X
ejpam-6834	347	9	0	0	NUM
ejpam-6834	347	10	,	,	PUNCT
ejpam-6834	347	11	1]t	1]t	NUM
ejpam-6834	347	12	is	be	AUX
ejpam-6834	347	13	the	the	DET
ejpam-6834	347	14	degree	degree	NOUN
ejpam-6834	347	15	of	of	ADP
ejpam-6834	347	16	contradiction	contradiction	NOUN
ejpam-6834	347	17	function	function	NOUN
ejpam-6834	347	18	(	(	PUNCT
ejpam-6834	347	19	dcf	dcf	PROPN
ejpam-6834	347	20	)	)	PUNCT
ejpam-6834	347	21	.	.	PUNCT
ejpam-6834	348	1	these	these	DET
ejpam-6834	348	2	functions	function	NOUN
ejpam-6834	348	3	satisfy	satisfy	VERB
ejpam-6834	348	4	the	the	DET
ejpam-6834	348	5	following	following	ADJ
ejpam-6834	348	6	axioms	axiom	NOUN
ejpam-6834	348	7	for	for	ADP
ejpam-6834	348	8	all	all	DET
ejpam-6834	348	9	a	a	DET
ejpam-6834	348	10	,	,	PUNCT
ejpam-6834	348	11	b	b	X
ejpam-6834	348	12	∈	∈	PROPN
ejpam-6834	348	13	pv	pv	NOUN
ejpam-6834	348	14	:	:	PUNCT
ejpam-6834	348	15	(	(	PUNCT
ejpam-6834	348	16	i	i	NOUN
ejpam-6834	348	17	)	)	PUNCT
ejpam-6834	348	18	reflexivity	reflexivity	NOUN
ejpam-6834	348	19	of	of	ADP
ejpam-6834	348	20	contradiction	contradiction	NOUN
ejpam-6834	348	21	function	function	NOUN
ejpam-6834	348	22	:	:	PUNCT
ejpam-6834	348	23	pcf	pcf	PROPN
ejpam-6834	348	24	(	(	PUNCT
ejpam-6834	348	25	a	a	PRON
ejpam-6834	348	26	,	,	PUNCT
ejpam-6834	348	27	a	a	NOUN
ejpam-6834	348	28	)	)	PUNCT
ejpam-6834	348	29	=	=	SYM
ejpam-6834	348	30	0	0	NUM
ejpam-6834	348	31	(	(	PUNCT
ejpam-6834	348	32	ii	ii	NOUN
ejpam-6834	348	33	)	)	PUNCT
ejpam-6834	348	34	symmetry	symmetry	NOUN
ejpam-6834	348	35	of	of	ADP
ejpam-6834	348	36	contradiction	contradiction	NOUN
ejpam-6834	348	37	function	function	NOUN
ejpam-6834	348	38	:	:	PUNCT
ejpam-6834	348	39	pcf	pcf	PROPN
ejpam-6834	348	40	(	(	PUNCT
ejpam-6834	348	41	a	a	DET
ejpam-6834	348	42	,	,	PUNCT
ejpam-6834	348	43	b	b	NOUN
ejpam-6834	348	44	)	)	PUNCT
ejpam-6834	349	1	=	=	SYM
ejpam-6834	349	2	pcf	pcf	PROPN
ejpam-6834	349	3	(	(	PUNCT
ejpam-6834	349	4	b	b	PROPN
ejpam-6834	349	5	,	,	PUNCT
ejpam-6834	349	6	a	a	PRON
ejpam-6834	349	7	)	)	PUNCT
ejpam-6834	349	8	example	example	NOUN
ejpam-6834	349	9	11	11	NUM
ejpam-6834	349	10	(	(	PUNCT
ejpam-6834	349	11	job	job	NOUN
ejpam-6834	349	12	candidate	candidate	NOUN
ejpam-6834	349	13	english	english	ADJ
ejpam-6834	349	14	proficiency	proficiency	NOUN
ejpam-6834	349	15	)	)	PUNCT
ejpam-6834	349	16	.	.	PUNCT
ejpam-6834	350	1	let	let	VERB
ejpam-6834	350	2	s	s	PRON
ejpam-6834	350	3	=	=	PUNCT
ejpam-6834	350	4	{	{	PUNCT
ejpam-6834	350	5	hiroko	hiroko	PROPN
ejpam-6834	350	6	,	,	PUNCT
ejpam-6834	350	7	masahiro	masahiro	PROPN
ejpam-6834	350	8	,	,	PUNCT
ejpam-6834	350	9	shinya	shinya	PROPN
ejpam-6834	350	10	}	}	PUNCT
ejpam-6834	350	11	be	be	VERB
ejpam-6834	350	12	the	the	DET
ejpam-6834	350	13	universal	universal	ADJ
ejpam-6834	350	14	set	set	NOUN
ejpam-6834	350	15	of	of	ADP
ejpam-6834	350	16	job	job	NOUN
ejpam-6834	350	17	candidates	candidate	NOUN
ejpam-6834	350	18	,	,	PUNCT
ejpam-6834	350	19	and	and	CCONJ
ejpam-6834	350	20	set	set	VERB
ejpam-6834	350	21	p	p	PROPN
ejpam-6834	350	22	=	=	PUNCT
ejpam-6834	350	23	s.	s.	PROPN
ejpam-6834	350	24	we	we	PRON
ejpam-6834	350	25	evaluate	evaluate	VERB
ejpam-6834	350	26	each	each	DET
ejpam-6834	350	27	candidate	candidate	NOUN
ejpam-6834	350	28	’s	’s	PART
ejpam-6834	350	29	english	english	ADJ
ejpam-6834	350	30	proficiency	proficiency	NOUN
ejpam-6834	350	31	using	use	VERB
ejpam-6834	350	32	a	a	DET
ejpam-6834	350	33	plithogenic	plithogenic	ADJ
ejpam-6834	350	34	set	set	NOUN
ejpam-6834	350	35	.	.	PUNCT
ejpam-6834	351	1	ps	ps	NOUN
ejpam-6834	351	2	=	=	PUNCT
ejpam-6834	351	3	(	(	PUNCT
ejpam-6834	351	4	p	p	X
ejpam-6834	351	5	,	,	PUNCT
ejpam-6834	351	6	v	v	NOUN
ejpam-6834	351	7	,	,	PUNCT
ejpam-6834	351	8	pv	pv	INTJ
ejpam-6834	351	9	,	,	PUNCT
ejpam-6834	351	10	pdf	pdf	NOUN
ejpam-6834	351	11	,	,	PUNCT
ejpam-6834	351	12	pcf	pcf	PROPN
ejpam-6834	351	13	)	)	PUNCT
ejpam-6834	351	14	,	,	PUNCT
ejpam-6834	351	15	where	where	SCONJ
ejpam-6834	351	16	:	:	PUNCT
ejpam-6834	351	17	•	•	NUM
ejpam-6834	351	18	v	v	NOUN
ejpam-6834	351	19	is	be	AUX
ejpam-6834	351	20	the	the	DET
ejpam-6834	351	21	attribute	attribute	NOUN
ejpam-6834	351	22	“	"	PUNCT
ejpam-6834	351	23	english	english	ADJ
ejpam-6834	351	24	proficiency	proficiency	NOUN
ejpam-6834	351	25	level	level	NOUN
ejpam-6834	351	26	.	.	PUNCT
ejpam-6834	351	27	”	"	PUNCT
ejpam-6834	352	1	•	•	NUM
ejpam-6834	352	2	pv	pv	NOUN
ejpam-6834	352	3	=	=	PUNCT
ejpam-6834	352	4	{	{	PUNCT
ejpam-6834	352	5	beginner	beginner	NOUN
ejpam-6834	352	6	,	,	PUNCT
ejpam-6834	352	7	intermediate	intermediate	ADJ
ejpam-6834	352	8	,	,	PUNCT
ejpam-6834	352	9	advanced	advanced	ADJ
ejpam-6834	352	10	}	}	PUNCT
ejpam-6834	352	11	.	.	PUNCT
ejpam-6834	353	1	•	•	NUM
ejpam-6834	353	2	the	the	DET
ejpam-6834	353	3	degree	degree	NOUN
ejpam-6834	353	4	of	of	ADP
ejpam-6834	353	5	appurtenance	appurtenance	NOUN
ejpam-6834	353	6	function	function	NOUN
ejpam-6834	353	7	pdf	pdf	NOUN
ejpam-6834	353	8	:	:	PUNCT
ejpam-6834	353	9	p	p	X
ejpam-6834	353	10	×	×	NOUN
ejpam-6834	353	11	pv	pv	INTJ
ejpam-6834	354	1	→	→	PUNCT
ejpam-6834	354	2	[	[	X
ejpam-6834	354	3	0	0	NUM
ejpam-6834	354	4	,	,	PUNCT
ejpam-6834	354	5	1]3	1]3	NUM
ejpam-6834	354	6	assigns	assign	NOUN
ejpam-6834	354	7	to	to	ADP
ejpam-6834	354	8	each	each	PRON
ejpam-6834	354	9	(	(	PUNCT
ejpam-6834	354	10	x	x	X
ejpam-6834	354	11	,	,	PUNCT
ejpam-6834	354	12	ℓ	ℓ	X
ejpam-6834	354	13	)	)	PUNCT
ejpam-6834	354	14	a	a	DET
ejpam-6834	354	15	triple	triple	ADJ
ejpam-6834	354	16	(	(	PUNCT
ejpam-6834	354	17	g	g	NOUN
ejpam-6834	354	18	,	,	PUNCT
ejpam-6834	354	19	w	w	PROPN
ejpam-6834	354	20	,	,	PUNCT
ejpam-6834	354	21	f	f	NOUN
ejpam-6834	354	22	)	)	PUNCT
ejpam-6834	354	23	of	of	ADP
ejpam-6834	354	24	degrees	degree	NOUN
ejpam-6834	354	25	for	for	ADP
ejpam-6834	354	26	grammar	grammar	NOUN
ejpam-6834	354	27	(	(	PUNCT
ejpam-6834	354	28	g	g	NOUN
ejpam-6834	354	29	)	)	PUNCT
ejpam-6834	354	30	,	,	PUNCT
ejpam-6834	354	31	vocabulary	vocabulary	NOUN
ejpam-6834	354	32	(	(	PUNCT
ejpam-6834	354	33	w	w	NOUN
ejpam-6834	354	34	)	)	PUNCT
ejpam-6834	354	35	,	,	PUNCT
ejpam-6834	354	36	and	and	CCONJ
ejpam-6834	354	37	fluency	fluency	NOUN
ejpam-6834	354	38	(	(	PUNCT
ejpam-6834	354	39	f	f	NOUN
ejpam-6834	354	40	)	)	PUNCT
ejpam-6834	354	41	.	.	PUNCT
ejpam-6834	355	1	for	for	ADP
ejpam-6834	355	2	example	example	NOUN
ejpam-6834	355	3	:	:	PUNCT
ejpam-6834	355	4	pdf	pdf	NOUN
ejpam-6834	355	5	(	(	PUNCT
ejpam-6834	355	6	hiroko	hiroko	NOUN
ejpam-6834	355	7	,	,	PUNCT
ejpam-6834	355	8	beginner	beginner	NOUN
ejpam-6834	355	9	)	)	PUNCT
ejpam-6834	355	10	=	=	PUNCT
ejpam-6834	355	11	(	(	PUNCT
ejpam-6834	355	12	0.10	0.10	NUM
ejpam-6834	355	13	,	,	PUNCT
ejpam-6834	355	14	0.20	0.20	NUM
ejpam-6834	355	15	,	,	PUNCT
ejpam-6834	355	16	0.10	0.10	NUM
ejpam-6834	355	17	)	)	PUNCT
ejpam-6834	355	18	,	,	PUNCT
ejpam-6834	355	19	pdf	pdf	NOUN
ejpam-6834	355	20	(	(	PUNCT
ejpam-6834	355	21	hiroko	hiroko	NOUN
ejpam-6834	355	22	,	,	PUNCT
ejpam-6834	355	23	intermediate	intermediate	ADJ
ejpam-6834	355	24	)	)	PUNCT
ejpam-6834	355	25	=	=	SYM
ejpam-6834	355	26	(	(	PUNCT
ejpam-6834	355	27	0.60	0.60	NUM
ejpam-6834	355	28	,	,	PUNCT
ejpam-6834	355	29	0.70	0.70	NUM
ejpam-6834	355	30	,	,	PUNCT
ejpam-6834	355	31	0.50	0.50	NUM
ejpam-6834	355	32	)	)	PUNCT
ejpam-6834	355	33	,	,	PUNCT
ejpam-6834	355	34	pdf	pdf	NOUN
ejpam-6834	355	35	(	(	PUNCT
ejpam-6834	355	36	hiroko	hiroko	NOUN
ejpam-6834	355	37	,	,	PUNCT
ejpam-6834	355	38	advanced	advanced	ADJ
ejpam-6834	355	39	)	)	PUNCT
ejpam-6834	355	40	=	=	SYM
ejpam-6834	355	41	(	(	PUNCT
ejpam-6834	355	42	0.80	0.80	NUM
ejpam-6834	355	43	,	,	PUNCT
ejpam-6834	355	44	0.90	0.90	NUM
ejpam-6834	355	45	,	,	PUNCT
ejpam-6834	355	46	0.70	0.70	NUM
ejpam-6834	355	47	)	)	PUNCT
ejpam-6834	355	48	.	.	PUNCT
ejpam-6834	356	1	•	•	NUM
ejpam-6834	356	2	the	the	DET
ejpam-6834	356	3	degree	degree	NOUN
ejpam-6834	356	4	of	of	ADP
ejpam-6834	356	5	contradiction	contradiction	NOUN
ejpam-6834	356	6	function	function	NOUN
ejpam-6834	356	7	pcf	pcf	PROPN
ejpam-6834	356	8	:	:	PUNCT
ejpam-6834	356	9	pv	pv	INTJ
ejpam-6834	356	10	×	×	NOUN
ejpam-6834	356	11	pv	pv	INTJ
ejpam-6834	357	1	→	→	PUNCT
ejpam-6834	357	2	[	[	X
ejpam-6834	357	3	0	0	NUM
ejpam-6834	357	4	,	,	PUNCT
ejpam-6834	357	5	1	1	NUM
ejpam-6834	357	6	]	]	PUNCT
ejpam-6834	357	7	measures	measure	VERB
ejpam-6834	357	8	the	the	DET
ejpam-6834	357	9	contradiction	contradiction	NOUN
ejpam-6834	357	10	between	between	ADP
ejpam-6834	357	11	two	two	NUM
ejpam-6834	357	12	proficiency	proficiency	NOUN
ejpam-6834	357	13	levels	level	NOUN
ejpam-6834	357	14	.	.	PUNCT
ejpam-6834	358	1	it	it	PRON
ejpam-6834	358	2	satisfies	satisfy	VERB
ejpam-6834	358	3	:	:	PUNCT
ejpam-6834	358	4	pcf	pcf	PROPN
ejpam-6834	358	5	(	(	PUNCT
ejpam-6834	358	6	a	a	PRON
ejpam-6834	358	7	,	,	PUNCT
ejpam-6834	358	8	a	a	NOUN
ejpam-6834	358	9	)	)	PUNCT
ejpam-6834	358	10	=	=	SYM
ejpam-6834	358	11	0	0	NUM
ejpam-6834	358	12	,	,	PUNCT
ejpam-6834	358	13	pcf	pcf	PROPN
ejpam-6834	358	14	(	(	PUNCT
ejpam-6834	358	15	beginner	beginner	NOUN
ejpam-6834	358	16	,	,	PUNCT
ejpam-6834	358	17	advanced	advanced	ADJ
ejpam-6834	358	18	)	)	PUNCT
ejpam-6834	358	19	=	=	SYM
ejpam-6834	358	20	1	1	NUM
ejpam-6834	358	21	,	,	PUNCT
ejpam-6834	358	22	pcf	pcf	PROPN
ejpam-6834	358	23	(	(	PUNCT
ejpam-6834	358	24	beginner	beginner	NOUN
ejpam-6834	358	25	,	,	PUNCT
ejpam-6834	358	26	intermediate	intermediate	ADJ
ejpam-6834	358	27	)	)	PUNCT
ejpam-6834	358	28	=	=	SYM
ejpam-6834	358	29	0.5	0.5	NUM
ejpam-6834	358	30	,	,	PUNCT
ejpam-6834	358	31	and	and	CCONJ
ejpam-6834	358	32	by	by	ADP
ejpam-6834	358	33	symmetry	symmetry	PROPN
ejpam-6834	358	34	pcf	pcf	PROPN
ejpam-6834	358	35	(	(	PUNCT
ejpam-6834	358	36	b	b	PROPN
ejpam-6834	358	37	,	,	PUNCT
ejpam-6834	358	38	a	a	PRON
ejpam-6834	358	39	)	)	PUNCT
ejpam-6834	358	40	=	=	SYM
ejpam-6834	358	41	pcf	pcf	PROPN
ejpam-6834	358	42	(	(	PUNCT
ejpam-6834	358	43	a	a	PRON
ejpam-6834	358	44	,	,	PUNCT
ejpam-6834	358	45	b	b	NOUN
ejpam-6834	358	46	)	)	PUNCT
ejpam-6834	358	47	.	.	PUNCT
ejpam-6834	359	1	this	this	DET
ejpam-6834	359	2	plithogenic	plithogenic	ADJ
ejpam-6834	359	3	set	set	VERB
ejpam-6834	359	4	captures	capture	NOUN
ejpam-6834	359	5	for	for	ADP
ejpam-6834	359	6	each	each	DET
ejpam-6834	359	7	candidate	candidate	NOUN
ejpam-6834	359	8	not	not	PART
ejpam-6834	359	9	only	only	ADV
ejpam-6834	359	10	a	a	DET
ejpam-6834	359	11	single	single	ADJ
ejpam-6834	359	12	“	"	PUNCT
ejpam-6834	359	13	level	level	NOUN
ejpam-6834	359	14	”	"	PUNCT
ejpam-6834	359	15	but	but	CCONJ
ejpam-6834	359	16	a	a	DET
ejpam-6834	359	17	vector	vector	NOUN
ejpam-6834	359	18	of	of	ADP
ejpam-6834	359	19	sub	sub	NOUN
ejpam-6834	359	20	-	-	NOUN
ejpam-6834	359	21	scores	score	NOUN
ejpam-6834	359	22	(	(	PUNCT
ejpam-6834	359	23	g	g	NOUN
ejpam-6834	359	24	,	,	PUNCT
ejpam-6834	359	25	w	w	PROPN
ejpam-6834	359	26	,	,	PUNCT
ejpam-6834	359	27	f	f	PROPN
ejpam-6834	359	28	)	)	PUNCT
ejpam-6834	359	29	,	,	PUNCT
ejpam-6834	359	30	while	while	SCONJ
ejpam-6834	359	31	the	the	DET
ejpam-6834	359	32	contradiction	contradiction	NOUN
ejpam-6834	359	33	function	function	VERB
ejpam-6834	359	34	quantifies	quantifie	NOUN
ejpam-6834	359	35	how	how	SCONJ
ejpam-6834	359	36	mutually	mutually	ADV
ejpam-6834	359	37	incompatible	incompatible	ADJ
ejpam-6834	359	38	two	two	NUM
ejpam-6834	359	39	levels	level	NOUN
ejpam-6834	359	40	are	be	AUX
ejpam-6834	359	41	.	.	PUNCT
ejpam-6834	360	1	t.	t.	PROPN
ejpam-6834	360	2	fujita	fujita	PROPN
ejpam-6834	360	3	,	,	PUNCT
ejpam-6834	360	4	f.smarandache	f.smarandache	NOUN
ejpam-6834	360	5	/	/	SYM
ejpam-6834	360	6	eur	eur	PROPN
ejpam-6834	360	7	.	.	PUNCT
ejpam-6834	361	1	j.	j.	PROPN
ejpam-6834	361	2	pure	pure	PROPN
ejpam-6834	361	3	appl	appl	PROPN
ejpam-6834	361	4	.	.	PROPN
ejpam-6834	361	5	math	math	PROPN
ejpam-6834	361	6	,	,	PUNCT
ejpam-6834	361	7	18	18	NUM
ejpam-6834	361	8	(	(	PUNCT
ejpam-6834	361	9	4	4	NUM
ejpam-6834	361	10	)	)	PUNCT
ejpam-6834	361	11	(	(	PUNCT
ejpam-6834	361	12	2025	2025	NUM
ejpam-6834	361	13	)	)	PUNCT
ejpam-6834	361	14	,	,	PUNCT
ejpam-6834	361	15	6834	6834	NUM
ejpam-6834	361	16	18	18	NUM
ejpam-6834	361	17	of	of	ADP
ejpam-6834	361	18	69	69	NUM
ejpam-6834	361	19	these	these	DET
ejpam-6834	361	20	definitions	definition	NOUN
ejpam-6834	361	21	establish	establish	VERB
ejpam-6834	361	22	the	the	DET
ejpam-6834	361	23	foundational	foundational	ADJ
ejpam-6834	361	24	framework	framework	NOUN
ejpam-6834	361	25	necessary	necessary	ADJ
ejpam-6834	361	26	for	for	ADP
ejpam-6834	361	27	exploring	explore	VERB
ejpam-6834	361	28	the	the	DET
ejpam-6834	361	29	hyperplithogenic	hyperplithogenic	ADJ
ejpam-6834	361	30	set	set	NOUN
ejpam-6834	361	31	and	and	CCONJ
ejpam-6834	361	32	the	the	DET
ejpam-6834	361	33	superhyperplithogenic	superhyperplithogenic	ADJ
ejpam-6834	361	34	set	set	NOUN
ejpam-6834	361	35	.	.	PUNCT
ejpam-6834	362	1	the	the	DET
ejpam-6834	362	2	definitions	definition	NOUN
ejpam-6834	362	3	of	of	ADP
ejpam-6834	362	4	the	the	DET
ejpam-6834	362	5	hyperplithogenic	hyperplithogenic	ADJ
ejpam-6834	362	6	set	set	NOUN
ejpam-6834	362	7	and	and	CCONJ
ejpam-6834	362	8	the	the	DET
ejpam-6834	362	9	superhyperplithogenic	superhyperplithogenic	ADJ
ejpam-6834	362	10	set	set	NOUN
ejpam-6834	362	11	are	be	AUX
ejpam-6834	362	12	presented	present	VERB
ejpam-6834	362	13	below[46	below[46	PROPN
ejpam-6834	362	14	,	,	PUNCT
ejpam-6834	362	15	67	67	NUM
ejpam-6834	362	16	]	]	PUNCT
ejpam-6834	362	17	.	.	PUNCT
ejpam-6834	363	1	definition	definition	NOUN
ejpam-6834	363	2	17	17	NUM
ejpam-6834	363	3	(	(	PUNCT
ejpam-6834	363	4	hyperplithogenic	hyperplithogenic	ADJ
ejpam-6834	363	5	set	set	NOUN
ejpam-6834	363	6	)	)	PUNCT
ejpam-6834	363	7	.	.	PUNCT
ejpam-6834	364	1	[	[	X
ejpam-6834	364	2	1	1	NUM
ejpam-6834	364	3	,	,	PUNCT
ejpam-6834	364	4	46	46	NUM
ejpam-6834	364	5	]	]	PUNCT
ejpam-6834	364	6	let	let	VERB
ejpam-6834	364	7	x	x	PRON
ejpam-6834	364	8	be	be	AUX
ejpam-6834	364	9	a	a	DET
ejpam-6834	364	10	non	non	ADJ
ejpam-6834	364	11	-	-	ADJ
ejpam-6834	364	12	empty	empty	ADJ
ejpam-6834	364	13	set	set	NOUN
ejpam-6834	364	14	,	,	PUNCT
ejpam-6834	364	15	and	and	CCONJ
ejpam-6834	364	16	let	let	VERB
ejpam-6834	364	17	a	a	PRON
ejpam-6834	364	18	be	be	AUX
ejpam-6834	364	19	a	a	DET
ejpam-6834	364	20	set	set	NOUN
ejpam-6834	364	21	of	of	ADP
ejpam-6834	364	22	attributes	attribute	NOUN
ejpam-6834	364	23	.	.	PUNCT
ejpam-6834	365	1	for	for	ADP
ejpam-6834	365	2	each	each	DET
ejpam-6834	365	3	attribute	attribute	NOUN
ejpam-6834	365	4	v	v	ADP
ejpam-6834	365	5	∈	∈	PROPN
ejpam-6834	365	6	a	a	PRON
ejpam-6834	365	7	,	,	PUNCT
ejpam-6834	365	8	let	let	VERB
ejpam-6834	365	9	pv	pv	INTJ
ejpam-6834	365	10	be	be	AUX
ejpam-6834	365	11	the	the	DET
ejpam-6834	365	12	set	set	NOUN
ejpam-6834	365	13	of	of	ADP
ejpam-6834	365	14	possible	possible	ADJ
ejpam-6834	365	15	values	value	NOUN
ejpam-6834	365	16	of	of	ADP
ejpam-6834	365	17	v.	v.	ADP
ejpam-6834	365	18	a	a	DET
ejpam-6834	365	19	hyperplithogenic	hyperplithogenic	ADJ
ejpam-6834	365	20	set	set	VERB
ejpam-6834	365	21	hps	hps	NOUN
ejpam-6834	365	22	over	over	ADP
ejpam-6834	365	23	x	x	PUNCT
ejpam-6834	365	24	is	be	AUX
ejpam-6834	365	25	defined	define	VERB
ejpam-6834	365	26	as	as	ADP
ejpam-6834	365	27	:	:	PUNCT
ejpam-6834	365	28	hps	hps	NOUN
ejpam-6834	365	29	=	=	SYM
ejpam-6834	365	30	(	(	PUNCT
ejpam-6834	365	31	p	p	X
ejpam-6834	365	32	,	,	PUNCT
ejpam-6834	365	33	{	{	PUNCT
ejpam-6834	365	34	vi}ni=1	vi}ni=1	PROPN
ejpam-6834	365	35	,	,	PUNCT
ejpam-6834	365	36	{	{	PUNCT
ejpam-6834	365	37	pvi}ni=1	pvi}ni=1	PROPN
ejpam-6834	365	38	,	,	PUNCT
ejpam-6834	365	39	{	{	PUNCT
ejpam-6834	365	40	˜pdf	˜pdf	NOUN
ejpam-6834	365	41	i}ni=1	i}ni=1	NUM
ejpam-6834	365	42	,	,	PUNCT
ejpam-6834	365	43	pcf	pcf	PROPN
ejpam-6834	365	44	)	)	PUNCT
ejpam-6834	366	1	where	where	SCONJ
ejpam-6834	366	2	:	:	PUNCT
ejpam-6834	366	3	•	•	ADP
ejpam-6834	366	4	p	p	NOUN
ejpam-6834	366	5	⊆	⊆	NUM
ejpam-6834	366	6	x	x	X
ejpam-6834	366	7	is	be	AUX
ejpam-6834	366	8	a	a	DET
ejpam-6834	366	9	subset	subset	NOUN
ejpam-6834	366	10	of	of	ADP
ejpam-6834	366	11	the	the	DET
ejpam-6834	366	12	universe	universe	NOUN
ejpam-6834	366	13	.	.	PUNCT
ejpam-6834	367	1	•	•	NUM
ejpam-6834	367	2	for	for	ADP
ejpam-6834	367	3	each	each	DET
ejpam-6834	367	4	attribute	attribute	NOUN
ejpam-6834	367	5	vi	vi	PROPN
ejpam-6834	367	6	,	,	PUNCT
ejpam-6834	367	7	pvi	pvi	PROPN
ejpam-6834	367	8	is	be	AUX
ejpam-6834	367	9	the	the	DET
ejpam-6834	367	10	set	set	NOUN
ejpam-6834	367	11	of	of	ADP
ejpam-6834	367	12	possible	possible	ADJ
ejpam-6834	367	13	values	value	NOUN
ejpam-6834	367	14	.	.	PUNCT
ejpam-6834	368	1	•	•	NUM
ejpam-6834	368	2	for	for	ADP
ejpam-6834	368	3	each	each	DET
ejpam-6834	368	4	attribute	attribute	NOUN
ejpam-6834	368	5	vi	vi	PROPN
ejpam-6834	368	6	,	,	PUNCT
ejpam-6834	368	7	˜pdf	˜pdf	NOUN
ejpam-6834	369	1	i	i	NOUN
ejpam-6834	369	2	:	:	PUNCT
ejpam-6834	369	3	p×pvi	p×pvi	ADV
ejpam-6834	369	4	→	→	SYM
ejpam-6834	369	5	p̃	p̃	PROPN
ejpam-6834	369	6	(	(	PUNCT
ejpam-6834	369	7	[	[	X
ejpam-6834	369	8	0	0	NUM
ejpam-6834	369	9	,	,	PUNCT
ejpam-6834	369	10	1]s	1]s	NUM
ejpam-6834	369	11	)	)	PUNCT
ejpam-6834	369	12	is	be	AUX
ejpam-6834	369	13	the	the	DET
ejpam-6834	369	14	hyper	hyper	ADJ
ejpam-6834	369	15	degree	degree	NOUN
ejpam-6834	369	16	of	of	ADP
ejpam-6834	369	17	appurtenance	appurtenance	NOUN
ejpam-6834	369	18	function	function	NOUN
ejpam-6834	369	19	(	(	PUNCT
ejpam-6834	369	20	hdaf	hdaf	NOUN
ejpam-6834	369	21	)	)	PUNCT
ejpam-6834	369	22	,	,	PUNCT
ejpam-6834	369	23	assigning	assign	VERB
ejpam-6834	369	24	to	to	ADP
ejpam-6834	369	25	each	each	DET
ejpam-6834	369	26	element	element	NOUN
ejpam-6834	369	27	x	x	SYM
ejpam-6834	369	28	∈	∈	PROPN
ejpam-6834	369	29	p	p	NOUN
ejpam-6834	369	30	and	and	CCONJ
ejpam-6834	369	31	attribute	attribute	NOUN
ejpam-6834	369	32	value	value	NOUN
ejpam-6834	369	33	ai	ai	PROPN
ejpam-6834	369	34	∈	∈	NOUN
ejpam-6834	369	35	pvi	pvi	NOUN
ejpam-6834	369	36	a	a	DET
ejpam-6834	369	37	set	set	NOUN
ejpam-6834	369	38	of	of	ADP
ejpam-6834	369	39	membership	membership	NOUN
ejpam-6834	369	40	degrees	degree	NOUN
ejpam-6834	369	41	.	.	PUNCT
ejpam-6834	370	1	•	•	NUM
ejpam-6834	370	2	pcf	pcf	PROPN
ejpam-6834	370	3	:	:	PUNCT
ejpam-6834	370	4	(	(	PUNCT
ejpam-6834	370	5	⋃n	⋃n	NOUN
ejpam-6834	370	6	i=1	i=1	PROPN
ejpam-6834	370	7	pvi	pvi	NOUN
ejpam-6834	370	8	)	)	PUNCT
ejpam-6834	370	9	×	×	NOUN
ejpam-6834	370	10	(	(	PUNCT
ejpam-6834	370	11	⋃n	⋃n	NOUN
ejpam-6834	370	12	i=1	i=1	PROPN
ejpam-6834	370	13	pvi	pvi	NOUN
ejpam-6834	370	14	)	)	PUNCT
ejpam-6834	370	15	→	→	PUNCT
ejpam-6834	371	1	[	[	X
ejpam-6834	371	2	0	0	NUM
ejpam-6834	371	3	,	,	PUNCT
ejpam-6834	371	4	1]t	1]t	NUM
ejpam-6834	371	5	is	be	AUX
ejpam-6834	371	6	the	the	DET
ejpam-6834	371	7	degree	degree	NOUN
ejpam-6834	371	8	of	of	ADP
ejpam-6834	371	9	contradiction	contradiction	NOUN
ejpam-6834	371	10	function	function	NOUN
ejpam-6834	371	11	(	(	PUNCT
ejpam-6834	371	12	dcf	dcf	PROPN
ejpam-6834	371	13	)	)	PUNCT
ejpam-6834	371	14	.	.	PUNCT
ejpam-6834	372	1	example	example	NOUN
ejpam-6834	372	2	12	12	NUM
ejpam-6834	372	3	(	(	PUNCT
ejpam-6834	372	4	hyperplithogenic	hyperplithogenic	ADJ
ejpam-6834	372	5	set	set	NOUN
ejpam-6834	372	6	in	in	ADP
ejpam-6834	372	7	a	a	DET
ejpam-6834	372	8	smartphone	smartphone	NOUN
ejpam-6834	372	9	purchase	purchase	NOUN
ejpam-6834	372	10	decision	decision	NOUN
ejpam-6834	372	11	)	)	PUNCT
ejpam-6834	372	12	.	.	PUNCT
ejpam-6834	373	1	let	let	VERB
ejpam-6834	373	2	x	x	PUNCT
ejpam-6834	373	3	=	=	PRON
ejpam-6834	373	4	{	{	PUNCT
ejpam-6834	373	5	a	a	PRON
ejpam-6834	373	6	,	,	PUNCT
ejpam-6834	373	7	b	b	NOUN
ejpam-6834	373	8	,	,	PUNCT
ejpam-6834	373	9	c	c	AUX
ejpam-6834	373	10	}	}	PUNCT
ejpam-6834	373	11	be	be	AUX
ejpam-6834	373	12	a	a	DET
ejpam-6834	373	13	set	set	NOUN
ejpam-6834	373	14	of	of	ADP
ejpam-6834	373	15	smartphone	smartphone	NOUN
ejpam-6834	373	16	models	model	NOUN
ejpam-6834	373	17	under	under	ADP
ejpam-6834	373	18	consideration	consideration	NOUN
ejpam-6834	373	19	,	,	PUNCT
ejpam-6834	373	20	and	and	CCONJ
ejpam-6834	373	21	set	set	VERB
ejpam-6834	373	22	p	p	NOUN
ejpam-6834	373	23	=	=	PUNCT
ejpam-6834	373	24	x.	x.	NOUN
ejpam-6834	373	25	we	we	PRON
ejpam-6834	373	26	evaluate	evaluate	VERB
ejpam-6834	373	27	each	each	DET
ejpam-6834	373	28	model	model	NOUN
ejpam-6834	373	29	with	with	ADP
ejpam-6834	373	30	two	two	NUM
ejpam-6834	373	31	attributes	attribute	NOUN
ejpam-6834	373	32	:	:	PUNCT
ejpam-6834	373	33	v1	v1	NOUN
ejpam-6834	373	34	=	=	SYM
ejpam-6834	373	35	battery	battery	NOUN
ejpam-6834	373	36	life	life	NOUN
ejpam-6834	373	37	,	,	PUNCT
ejpam-6834	373	38	pv1	pv1	NOUN
ejpam-6834	373	39	=	=	PUNCT
ejpam-6834	373	40	{	{	PUNCT
ejpam-6834	373	41	short	short	ADJ
ejpam-6834	373	42	,	,	PUNCT
ejpam-6834	373	43	moderate	moderate	ADJ
ejpam-6834	373	44	,	,	PUNCT
ejpam-6834	373	45	long	long	ADJ
ejpam-6834	373	46	}	}	PUNCT
ejpam-6834	373	47	,	,	PUNCT
ejpam-6834	373	48	v2	v2	PROPN
ejpam-6834	373	49	=	=	SYM
ejpam-6834	373	50	camera	camera	NOUN
ejpam-6834	373	51	quality	quality	NOUN
ejpam-6834	373	52	,	,	PUNCT
ejpam-6834	373	53	pv2	pv2	NOUN
ejpam-6834	373	54	=	=	PRON
ejpam-6834	373	55	{	{	PUNCT
ejpam-6834	373	56	low	low	ADJ
ejpam-6834	373	57	,	,	PUNCT
ejpam-6834	373	58	medium	medium	ADJ
ejpam-6834	373	59	,	,	PUNCT
ejpam-6834	373	60	high	high	ADJ
ejpam-6834	373	61	}	}	PUNCT
ejpam-6834	373	62	.	.	PUNCT
ejpam-6834	374	1	for	for	ADP
ejpam-6834	374	2	simplicity	simplicity	NOUN
ejpam-6834	374	3	,	,	PUNCT
ejpam-6834	374	4	take	take	VERB
ejpam-6834	374	5	s	s	NOUN
ejpam-6834	374	6	=	=	NOUN
ejpam-6834	374	7	1	1	NUM
ejpam-6834	374	8	so	so	SCONJ
ejpam-6834	374	9	that	that	PRON
ejpam-6834	374	10	p̃([0	p̃([0	NUM
ejpam-6834	374	11	,	,	PUNCT
ejpam-6834	374	12	1]s	1]s	NUM
ejpam-6834	374	13	)	)	PUNCT
ejpam-6834	374	14	=	=	PUNCT
ejpam-6834	375	1	p̃([0	p̃([0	VERB
ejpam-6834	375	2	,	,	PUNCT
ejpam-6834	375	3	1	1	NUM
ejpam-6834	375	4	]	]	NUM
ejpam-6834	375	5	)	)	PUNCT
ejpam-6834	375	6	.	.	PUNCT
ejpam-6834	376	1	the	the	DET
ejpam-6834	376	2	hyper	hyper	ADJ
ejpam-6834	376	3	degree	degree	NOUN
ejpam-6834	376	4	of	of	ADP
ejpam-6834	376	5	appurtenance	appurtenance	NOUN
ejpam-6834	376	6	functions	function	NOUN
ejpam-6834	376	7	are	be	AUX
ejpam-6834	376	8	defined	define	VERB
ejpam-6834	376	9	as	as	SCONJ
ejpam-6834	376	10	follows	follow	VERB
ejpam-6834	376	11	:	:	PUNCT
ejpam-6834	376	12	˜pdf1(a	˜pdf1(a	ADV
ejpam-6834	376	13	,	,	PUNCT
ejpam-6834	376	14	short	short	ADJ
ejpam-6834	376	15	)	)	PUNCT
ejpam-6834	376	16	=	=	PUNCT
ejpam-6834	376	17	{	{	PUNCT
ejpam-6834	376	18	0.2	0.2	NUM
ejpam-6834	376	19	,	,	PUNCT
ejpam-6834	376	20	0.3	0.3	NUM
ejpam-6834	376	21	}	}	PUNCT
ejpam-6834	376	22	,	,	PUNCT
ejpam-6834	376	23	˜pdf1(a	˜pdf1(a	ADV
ejpam-6834	376	24	,	,	PUNCT
ejpam-6834	376	25	moderate	moderate	ADJ
ejpam-6834	376	26	)	)	PUNCT
ejpam-6834	376	27	=	=	SYM
ejpam-6834	376	28	{	{	PUNCT
ejpam-6834	376	29	0.6	0.6	NUM
ejpam-6834	376	30	,	,	PUNCT
ejpam-6834	376	31	0.7	0.7	NUM
ejpam-6834	376	32	}	}	PUNCT
ejpam-6834	376	33	,	,	PUNCT
ejpam-6834	376	34	˜pdf1(a	˜pdf1(a	ADV
ejpam-6834	376	35	,	,	PUNCT
ejpam-6834	376	36	long	long	ADJ
ejpam-6834	376	37	)	)	PUNCT
ejpam-6834	377	1	=	=	PUNCT
ejpam-6834	377	2	{	{	PUNCT
ejpam-6834	377	3	0.4	0.4	NUM
ejpam-6834	377	4	,	,	PUNCT
ejpam-6834	377	5	0.5	0.5	NUM
ejpam-6834	377	6	}	}	PUNCT
ejpam-6834	377	7	,	,	PUNCT
ejpam-6834	377	8	˜pdf1(b	˜pdf1(b	NOUN
ejpam-6834	377	9	,	,	PUNCT
ejpam-6834	377	10	short	short	ADJ
ejpam-6834	377	11	)	)	PUNCT
ejpam-6834	377	12	=	=	PUNCT
ejpam-6834	377	13	{	{	PUNCT
ejpam-6834	377	14	0.3	0.3	NUM
ejpam-6834	377	15	,	,	PUNCT
ejpam-6834	377	16	0.4	0.4	NUM
ejpam-6834	377	17	}	}	PUNCT
ejpam-6834	377	18	,	,	PUNCT
ejpam-6834	377	19	˜pdf1(b	˜pdf1(b	NOUN
ejpam-6834	377	20	,	,	PUNCT
ejpam-6834	377	21	moderate	moderate	ADJ
ejpam-6834	377	22	)	)	PUNCT
ejpam-6834	377	23	=	=	SYM
ejpam-6834	377	24	{	{	PUNCT
ejpam-6834	377	25	0.5	0.5	NUM
ejpam-6834	377	26	,	,	PUNCT
ejpam-6834	377	27	0.6	0.6	NUM
ejpam-6834	377	28	}	}	PUNCT
ejpam-6834	377	29	,	,	PUNCT
ejpam-6834	377	30	˜pdf1(b	˜pdf1(b	NOUN
ejpam-6834	377	31	,	,	PUNCT
ejpam-6834	377	32	long	long	ADJ
ejpam-6834	377	33	)	)	PUNCT
ejpam-6834	377	34	=	=	PUNCT
ejpam-6834	377	35	{	{	PUNCT
ejpam-6834	377	36	0.7	0.7	NUM
ejpam-6834	377	37	,	,	PUNCT
ejpam-6834	377	38	0.8	0.8	NUM
ejpam-6834	377	39	}	}	PUNCT
ejpam-6834	377	40	,	,	PUNCT
ejpam-6834	377	41	˜pdf1(c	˜pdf1(c	NOUN
ejpam-6834	377	42	,	,	PUNCT
ejpam-6834	377	43	short	short	ADJ
ejpam-6834	377	44	)	)	PUNCT
ejpam-6834	377	45	=	=	PUNCT
ejpam-6834	377	46	{	{	PUNCT
ejpam-6834	377	47	0.1	0.1	NUM
ejpam-6834	377	48	,	,	PUNCT
ejpam-6834	377	49	0.2	0.2	NUM
ejpam-6834	377	50	}	}	PUNCT
ejpam-6834	377	51	,	,	PUNCT
ejpam-6834	377	52	˜pdf1(c	˜pdf1(c	NOUN
ejpam-6834	377	53	,	,	PUNCT
ejpam-6834	377	54	moderate	moderate	ADJ
ejpam-6834	377	55	)	)	PUNCT
ejpam-6834	377	56	=	=	SYM
ejpam-6834	377	57	{	{	PUNCT
ejpam-6834	377	58	0.4	0.4	NUM
ejpam-6834	377	59	,	,	PUNCT
ejpam-6834	377	60	0.5	0.5	NUM
ejpam-6834	377	61	}	}	PUNCT
ejpam-6834	377	62	,	,	PUNCT
ejpam-6834	377	63	˜pdf1(c	˜pdf1(c	NOUN
ejpam-6834	377	64	,	,	PUNCT
ejpam-6834	377	65	long	long	ADJ
ejpam-6834	377	66	)	)	PUNCT
ejpam-6834	377	67	=	=	PUNCT
ejpam-6834	377	68	{	{	PUNCT
ejpam-6834	377	69	0.6	0.6	NUM
ejpam-6834	377	70	,	,	PUNCT
ejpam-6834	377	71	0.7	0.7	NUM
ejpam-6834	377	72	}	}	PUNCT
ejpam-6834	377	73	,	,	PUNCT
ejpam-6834	377	74	˜pdf2(a	˜pdf2(a	NOUN
ejpam-6834	377	75	,	,	PUNCT
ejpam-6834	377	76	low	low	ADJ
ejpam-6834	377	77	)	)	PUNCT
ejpam-6834	377	78	=	=	PUNCT
ejpam-6834	377	79	{	{	PUNCT
ejpam-6834	377	80	0.1	0.1	NUM
ejpam-6834	377	81	,	,	PUNCT
ejpam-6834	377	82	0.2	0.2	NUM
ejpam-6834	377	83	}	}	PUNCT
ejpam-6834	377	84	,	,	PUNCT
ejpam-6834	377	85	˜pdf2(a	˜pdf2(a	NOUN
ejpam-6834	377	86	,	,	PUNCT
ejpam-6834	377	87	medium	medium	NOUN
ejpam-6834	377	88	)	)	PUNCT
ejpam-6834	377	89	=	=	SYM
ejpam-6834	377	90	{	{	PUNCT
ejpam-6834	377	91	0.5	0.5	NUM
ejpam-6834	377	92	,	,	PUNCT
ejpam-6834	377	93	0.6	0.6	NUM
ejpam-6834	377	94	}	}	PUNCT
ejpam-6834	377	95	,	,	PUNCT
ejpam-6834	377	96	˜pdf2(a	˜pdf2(a	NOUN
ejpam-6834	377	97	,	,	PUNCT
ejpam-6834	377	98	high	high	ADJ
ejpam-6834	377	99	)	)	PUNCT
ejpam-6834	377	100	=	=	PUNCT
ejpam-6834	377	101	{	{	PUNCT
ejpam-6834	377	102	0.7	0.7	NUM
ejpam-6834	377	103	,	,	PUNCT
ejpam-6834	377	104	0.8	0.8	NUM
ejpam-6834	377	105	}	}	PUNCT
ejpam-6834	377	106	,	,	PUNCT
ejpam-6834	377	107	˜pdf2(b	˜pdf2(b	ADJ
ejpam-6834	377	108	,	,	PUNCT
ejpam-6834	377	109	low	low	ADJ
ejpam-6834	377	110	)	)	PUNCT
ejpam-6834	377	111	=	=	PUNCT
ejpam-6834	377	112	{	{	PUNCT
ejpam-6834	377	113	0.2	0.2	NUM
ejpam-6834	377	114	,	,	PUNCT
ejpam-6834	377	115	0.3	0.3	NUM
ejpam-6834	377	116	}	}	PUNCT
ejpam-6834	377	117	,	,	PUNCT
ejpam-6834	377	118	˜pdf2(b	˜pdf2(b	ADJ
ejpam-6834	377	119	,	,	PUNCT
ejpam-6834	377	120	medium	medium	NOUN
ejpam-6834	377	121	)	)	PUNCT
ejpam-6834	377	122	=	=	SYM
ejpam-6834	377	123	{	{	PUNCT
ejpam-6834	377	124	0.6	0.6	NUM
ejpam-6834	377	125	,	,	PUNCT
ejpam-6834	377	126	0.7	0.7	NUM
ejpam-6834	377	127	}	}	PUNCT
ejpam-6834	377	128	,	,	PUNCT
ejpam-6834	377	129	˜pdf2(b	˜pdf2(b	ADJ
ejpam-6834	377	130	,	,	PUNCT
ejpam-6834	377	131	high	high	ADJ
ejpam-6834	377	132	)	)	PUNCT
ejpam-6834	377	133	=	=	PUNCT
ejpam-6834	377	134	{	{	PUNCT
ejpam-6834	377	135	0.8	0.8	NUM
ejpam-6834	377	136	,	,	PUNCT
ejpam-6834	377	137	0.9	0.9	NUM
ejpam-6834	377	138	}	}	PUNCT
ejpam-6834	377	139	,	,	PUNCT
ejpam-6834	377	140	˜pdf2(c	˜pdf2(c	NOUN
ejpam-6834	377	141	,	,	PUNCT
ejpam-6834	377	142	low	low	ADJ
ejpam-6834	377	143	)	)	PUNCT
ejpam-6834	377	144	=	=	PUNCT
ejpam-6834	377	145	{	{	PUNCT
ejpam-6834	377	146	0.3	0.3	NUM
ejpam-6834	377	147	,	,	PUNCT
ejpam-6834	377	148	0.4	0.4	NUM
ejpam-6834	377	149	}	}	PUNCT
ejpam-6834	377	150	,	,	PUNCT
ejpam-6834	377	151	˜pdf2(c	˜pdf2(c	NOUN
ejpam-6834	377	152	,	,	PUNCT
ejpam-6834	377	153	medium	medium	NOUN
ejpam-6834	377	154	)	)	PUNCT
ejpam-6834	377	155	=	=	PUNCT
ejpam-6834	377	156	{	{	PUNCT
ejpam-6834	377	157	0.4	0.4	NUM
ejpam-6834	377	158	,	,	PUNCT
ejpam-6834	377	159	0.5	0.5	NUM
ejpam-6834	377	160	}	}	PUNCT
ejpam-6834	377	161	,	,	PUNCT
ejpam-6834	377	162	˜pdf2(c	˜pdf2(c	NOUN
ejpam-6834	377	163	,	,	PUNCT
ejpam-6834	377	164	high	high	ADJ
ejpam-6834	377	165	)	)	PUNCT
ejpam-6834	377	166	=	=	PUNCT
ejpam-6834	377	167	{	{	PUNCT
ejpam-6834	377	168	0.6	0.6	NUM
ejpam-6834	377	169	,	,	PUNCT
ejpam-6834	377	170	0.7	0.7	NUM
ejpam-6834	377	171	}	}	PUNCT
ejpam-6834	377	172	.	.	PUNCT
ejpam-6834	378	1	the	the	DET
ejpam-6834	378	2	degree	degree	NOUN
ejpam-6834	378	3	of	of	ADP
ejpam-6834	378	4	contradiction	contradiction	NOUN
ejpam-6834	378	5	function	function	NOUN
ejpam-6834	378	6	pcf	pcf	PROPN
ejpam-6834	378	7	:	:	PUNCT
ejpam-6834	378	8	(	(	PUNCT
ejpam-6834	378	9	pv1	pv1	NOUN
ejpam-6834	378	10	∪pv2)×	∪pv2)×	X
ejpam-6834	378	11	(	(	PUNCT
ejpam-6834	378	12	pv1	pv1	VERB
ejpam-6834	378	13	∪pv2	∪pv2	PROPN
ejpam-6834	378	14	)	)	PUNCT
ejpam-6834	378	15	→	→	PUNCT
ejpam-6834	379	1	[	[	X
ejpam-6834	379	2	0	0	NUM
ejpam-6834	379	3	,	,	PUNCT
ejpam-6834	379	4	1	1	NUM
ejpam-6834	379	5	]	]	PUNCT
ejpam-6834	379	6	is	be	AUX
ejpam-6834	379	7	given	give	VERB
ejpam-6834	379	8	by	by	ADP
ejpam-6834	379	9	pcf	pcf	PROPN
ejpam-6834	379	10	(	(	PUNCT
ejpam-6834	379	11	short	short	ADJ
ejpam-6834	379	12	,	,	PUNCT
ejpam-6834	379	13	long	long	ADJ
ejpam-6834	379	14	)	)	PUNCT
ejpam-6834	379	15	=	=	SYM
ejpam-6834	379	16	0.9	0.9	NUM
ejpam-6834	379	17	,	,	PUNCT
ejpam-6834	379	18	pcf	pcf	PROPN
ejpam-6834	379	19	(	(	PUNCT
ejpam-6834	379	20	low	low	ADJ
ejpam-6834	379	21	,	,	PUNCT
ejpam-6834	379	22	high	high	ADJ
ejpam-6834	379	23	)	)	PUNCT
ejpam-6834	379	24	=	=	SYM
ejpam-6834	379	25	0.8	0.8	NUM
ejpam-6834	379	26	,	,	PUNCT
ejpam-6834	379	27	t.	t.	PROPN
ejpam-6834	379	28	fujita	fujita	PROPN
ejpam-6834	379	29	,	,	PUNCT
ejpam-6834	379	30	f.smarandache	f.smarandache	NOUN
ejpam-6834	379	31	/	/	SYM
ejpam-6834	379	32	eur	eur	PROPN
ejpam-6834	379	33	.	.	PUNCT
ejpam-6834	380	1	j.	j.	PROPN
ejpam-6834	380	2	pure	pure	PROPN
ejpam-6834	380	3	appl	appl	PROPN
ejpam-6834	380	4	.	.	PROPN
ejpam-6834	380	5	math	math	PROPN
ejpam-6834	380	6	,	,	PUNCT
ejpam-6834	380	7	18	18	NUM
ejpam-6834	380	8	(	(	PUNCT
ejpam-6834	380	9	4	4	NUM
ejpam-6834	380	10	)	)	PUNCT
ejpam-6834	380	11	(	(	PUNCT
ejpam-6834	380	12	2025	2025	NUM
ejpam-6834	380	13	)	)	PUNCT
ejpam-6834	380	14	,	,	PUNCT
ejpam-6834	380	15	6834	6834	NUM
ejpam-6834	380	16	19	19	NUM
ejpam-6834	380	17	of	of	ADP
ejpam-6834	380	18	69	69	NUM
ejpam-6834	380	19	with	with	ADP
ejpam-6834	380	20	pcf	pcf	PROPN
ejpam-6834	380	21	(	(	PUNCT
ejpam-6834	380	22	a	a	PRON
ejpam-6834	380	23	,	,	PUNCT
ejpam-6834	380	24	a	a	NOUN
ejpam-6834	380	25	)	)	PUNCT
ejpam-6834	380	26	=	=	SYM
ejpam-6834	380	27	0	0	NUM
ejpam-6834	380	28	and	and	CCONJ
ejpam-6834	380	29	symmetry	symmetry	PROPN
ejpam-6834	380	30	pcf	pcf	PROPN
ejpam-6834	380	31	(	(	PUNCT
ejpam-6834	380	32	a	a	DET
ejpam-6834	380	33	,	,	PUNCT
ejpam-6834	380	34	b	b	NOUN
ejpam-6834	380	35	)	)	PUNCT
ejpam-6834	380	36	=	=	SYM
ejpam-6834	380	37	pcf	pcf	PROPN
ejpam-6834	380	38	(	(	PUNCT
ejpam-6834	380	39	b	b	PROPN
ejpam-6834	380	40	,	,	PUNCT
ejpam-6834	380	41	a	a	PRON
ejpam-6834	380	42	)	)	PUNCT
ejpam-6834	380	43	.	.	PUNCT
ejpam-6834	381	1	hence	hence	ADV
ejpam-6834	381	2	the	the	DET
ejpam-6834	381	3	hyperplithogenic	hyperplithogenic	ADJ
ejpam-6834	381	4	set	set	NOUN
ejpam-6834	381	5	is	be	AUX
ejpam-6834	381	6	hps	hps	NOUN
ejpam-6834	381	7	=	=	PUNCT
ejpam-6834	381	8	(	(	PUNCT
ejpam-6834	381	9	p	p	X
ejpam-6834	381	10	,	,	PUNCT
ejpam-6834	381	11	{	{	PUNCT
ejpam-6834	381	12	v1	v1	NOUN
ejpam-6834	381	13	,	,	PUNCT
ejpam-6834	381	14	v2	v2	PROPN
ejpam-6834	381	15	}	}	PUNCT
ejpam-6834	381	16	,	,	PUNCT
ejpam-6834	381	17	{	{	PUNCT
ejpam-6834	381	18	pv1	pv1	NOUN
ejpam-6834	381	19	,	,	PUNCT
ejpam-6834	381	20	pv2	pv2	NOUN
ejpam-6834	381	21	}	}	PUNCT
ejpam-6834	381	22	,	,	PUNCT
ejpam-6834	381	23	{	{	PUNCT
ejpam-6834	381	24	˜pdf1	˜pdf1	NOUN
ejpam-6834	381	25	,	,	PUNCT
ejpam-6834	381	26	˜pdf2	˜pdf2	NUM
ejpam-6834	381	27	}	}	PUNCT
ejpam-6834	381	28	,	,	PUNCT
ejpam-6834	381	29	pcf	pcf	PROPN
ejpam-6834	381	30	)	)	PUNCT
ejpam-6834	381	31	,	,	PUNCT
ejpam-6834	381	32	which	which	PRON
ejpam-6834	381	33	captures	capture	VERB
ejpam-6834	381	34	for	for	ADP
ejpam-6834	381	35	each	each	DET
ejpam-6834	381	36	phone	phone	NOUN
ejpam-6834	381	37	model	model	NOUN
ejpam-6834	381	38	both	both	CCONJ
ejpam-6834	381	39	the	the	DET
ejpam-6834	381	40	hyper	hyper	ADV
ejpam-6834	381	41	-	-	PUNCT
ejpam-6834	381	42	valued	value	VERB
ejpam-6834	381	43	membership	membership	NOUN
ejpam-6834	381	44	degrees	degree	NOUN
ejpam-6834	381	45	and	and	CCONJ
ejpam-6834	381	46	the	the	DET
ejpam-6834	381	47	contradictions	contradiction	NOUN
ejpam-6834	381	48	among	among	ADP
ejpam-6834	381	49	attribute	attribute	NOUN
ejpam-6834	381	50	levels	level	NOUN
ejpam-6834	381	51	.	.	PUNCT
ejpam-6834	382	1	definition	definition	NOUN
ejpam-6834	382	2	18	18	NUM
ejpam-6834	382	3	(	(	PUNCT
ejpam-6834	382	4	n	n	CCONJ
ejpam-6834	382	5	-	-	PUNCT
ejpam-6834	382	6	superhyperplithogenic	superhyperplithogenic	ADJ
ejpam-6834	382	7	set	set	NOUN
ejpam-6834	382	8	)	)	PUNCT
ejpam-6834	382	9	.	.	PUNCT
ejpam-6834	383	1	[	[	X
ejpam-6834	383	2	1	1	NUM
ejpam-6834	383	3	,	,	PUNCT
ejpam-6834	383	4	68	68	NUM
ejpam-6834	383	5	]	]	PUNCT
ejpam-6834	383	6	let	let	VERB
ejpam-6834	383	7	x	x	PRON
ejpam-6834	383	8	be	be	AUX
ejpam-6834	383	9	a	a	DET
ejpam-6834	383	10	non	non	ADJ
ejpam-6834	383	11	-	-	ADJ
ejpam-6834	383	12	empty	empty	ADJ
ejpam-6834	383	13	set	set	NOUN
ejpam-6834	383	14	,	,	PUNCT
ejpam-6834	383	15	and	and	CCONJ
ejpam-6834	383	16	let	let	VERB
ejpam-6834	383	17	v	v	VERB
ejpam-6834	383	18	=	=	SYM
ejpam-6834	383	19	{	{	PUNCT
ejpam-6834	383	20	v1	v1	PROPN
ejpam-6834	383	21	,	,	PUNCT
ejpam-6834	383	22	v2	v2	PROPN
ejpam-6834	383	23	,	,	PUNCT
ejpam-6834	383	24	.	.	PUNCT
ejpam-6834	383	25	.	.	PUNCT
ejpam-6834	383	26	.	.	PUNCT
ejpam-6834	384	1	,	,	PUNCT
ejpam-6834	384	2	vn	vn	AUX
ejpam-6834	384	3	}	}	PUNCT
ejpam-6834	384	4	be	be	AUX
ejpam-6834	384	5	a	a	DET
ejpam-6834	384	6	set	set	NOUN
ejpam-6834	384	7	of	of	ADP
ejpam-6834	384	8	attributes	attribute	NOUN
ejpam-6834	384	9	,	,	PUNCT
ejpam-6834	384	10	each	each	PRON
ejpam-6834	384	11	associated	associate	VERB
ejpam-6834	384	12	with	with	ADP
ejpam-6834	384	13	a	a	DET
ejpam-6834	384	14	set	set	NOUN
ejpam-6834	384	15	of	of	ADP
ejpam-6834	384	16	possible	possible	ADJ
ejpam-6834	384	17	values	value	NOUN
ejpam-6834	384	18	pvi	pvi	NOUN
ejpam-6834	384	19	.	.	PUNCT
ejpam-6834	385	1	an	an	DET
ejpam-6834	385	2	n	n	CCONJ
ejpam-6834	385	3	-	-	PUNCT
ejpam-6834	385	4	superhyperplithogenic	superhyperplithogenic	ADJ
ejpam-6834	385	5	set	set	NOUN
ejpam-6834	385	6	(	(	PUNCT
ejpam-6834	385	7	shpsn	shpsn	X
ejpam-6834	385	8	)	)	PUNCT
ejpam-6834	385	9	is	be	AUX
ejpam-6834	385	10	defined	define	VERB
ejpam-6834	385	11	recursively	recursively	ADV
ejpam-6834	385	12	as	as	ADP
ejpam-6834	385	13	:	:	PUNCT
ejpam-6834	385	14	shpsn	shpsn	PROPN
ejpam-6834	385	15	=	=	SYM
ejpam-6834	385	16	(	(	PUNCT
ejpam-6834	385	17	pn	pn	PROPN
ejpam-6834	385	18	,	,	PUNCT
ejpam-6834	385	19	v	v	NOUN
ejpam-6834	385	20	,	,	PUNCT
ejpam-6834	385	21	{	{	PUNCT
ejpam-6834	385	22	pvi}ni=1	pvi}ni=1	PROPN
ejpam-6834	385	23	,	,	PUNCT
ejpam-6834	385	24	{	{	PUNCT
ejpam-6834	385	25	˜pdf	˜pdf	NOUN
ejpam-6834	385	26	(	(	PUNCT
ejpam-6834	385	27	n	n	CCONJ
ejpam-6834	385	28	)	)	PUNCT
ejpam-6834	386	1	i	i	NOUN
ejpam-6834	386	2	}	}	PUNCT
ejpam-6834	386	3	ni=1	ni=1	PROPN
ejpam-6834	386	4	,	,	PUNCT
ejpam-6834	386	5	pcf	pcf	PROPN
ejpam-6834	386	6	(	(	PUNCT
ejpam-6834	386	7	n	n	CCONJ
ejpam-6834	386	8	)	)	PUNCT
ejpam-6834	386	9	)	)	PUNCT
ejpam-6834	386	10	,	,	PUNCT
ejpam-6834	386	11	where	where	SCONJ
ejpam-6834	386	12	:	:	PUNCT
ejpam-6834	386	13	•	•	NUM
ejpam-6834	386	14	p1	p1	NOUN
ejpam-6834	386	15	⊆	⊆	NUM
ejpam-6834	386	16	x	x	NOUN
ejpam-6834	386	17	,	,	PUNCT
ejpam-6834	386	18	and	and	CCONJ
ejpam-6834	386	19	for	for	ADP
ejpam-6834	386	20	k	k	PROPN
ejpam-6834	386	21	≥	≥	NUM
ejpam-6834	386	22	2	2	NUM
ejpam-6834	386	23	,	,	PUNCT
ejpam-6834	386	24	pk	pk	NOUN
ejpam-6834	386	25	=	=	SYM
ejpam-6834	386	26	p̃(pk−1	p̃(pk−1	PROPN
ejpam-6834	386	27	)	)	PUNCT
ejpam-6834	386	28	,	,	PUNCT
ejpam-6834	386	29	represents	represent	VERB
ejpam-6834	386	30	the	the	DET
ejpam-6834	386	31	k	k	NOUN
ejpam-6834	386	32	-	-	PUNCT
ejpam-6834	386	33	th	th	X
ejpam-6834	386	34	nested	nested	ADJ
ejpam-6834	386	35	family	family	NOUN
ejpam-6834	386	36	of	of	ADP
ejpam-6834	386	37	non	non	ADJ
ejpam-6834	386	38	-	-	ADJ
ejpam-6834	386	39	empty	empty	ADJ
ejpam-6834	386	40	subsets	subset	NOUN
ejpam-6834	386	41	of	of	ADP
ejpam-6834	386	42	p1	p1	PROPN
ejpam-6834	386	43	.	.	PROPN
ejpam-6834	386	44	•	•	NUM
ejpam-6834	386	45	for	for	ADP
ejpam-6834	386	46	each	each	DET
ejpam-6834	386	47	attribute	attribute	NOUN
ejpam-6834	386	48	vi	vi	PROPN
ejpam-6834	386	49	∈	∈	PROPN
ejpam-6834	386	50	v	v	NOUN
ejpam-6834	386	51	,	,	PUNCT
ejpam-6834	386	52	pvi	pvi	PROPN
ejpam-6834	386	53	is	be	AUX
ejpam-6834	386	54	the	the	DET
ejpam-6834	386	55	set	set	NOUN
ejpam-6834	386	56	of	of	ADP
ejpam-6834	386	57	possible	possible	ADJ
ejpam-6834	386	58	values	value	NOUN
ejpam-6834	386	59	of	of	ADP
ejpam-6834	386	60	the	the	DET
ejpam-6834	386	61	attribute	attribute	NOUN
ejpam-6834	386	62	vi	vi	PROPN
ejpam-6834	386	63	.	.	NOUN
ejpam-6834	386	64	•	•	NUM
ejpam-6834	386	65	for	for	ADP
ejpam-6834	386	66	each	each	DET
ejpam-6834	386	67	k	k	NOUN
ejpam-6834	386	68	-	-	PUNCT
ejpam-6834	386	69	th	th	VERB
ejpam-6834	386	70	level	level	NOUN
ejpam-6834	386	71	subset	subset	NOUN
ejpam-6834	386	72	pk	pk	NOUN
ejpam-6834	386	73	,	,	PUNCT
ejpam-6834	386	74	˜pdf	˜pdf	NOUN
ejpam-6834	386	75	(	(	PUNCT
ejpam-6834	386	76	n	n	CCONJ
ejpam-6834	386	77	)	)	PUNCT
ejpam-6834	386	78	i	i	PRON
ejpam-6834	386	79	:	:	PUNCT
ejpam-6834	386	80	pn	pn	VERB
ejpam-6834	386	81	×	×	PROPN
ejpam-6834	386	82	pvi	pvi	NOUN
ejpam-6834	386	83	→	→	SYM
ejpam-6834	386	84	p̃([0	p̃([0	NUM
ejpam-6834	386	85	,	,	PUNCT
ejpam-6834	386	86	1]s	1]s	NUM
ejpam-6834	386	87	)	)	PUNCT
ejpam-6834	386	88	is	be	AUX
ejpam-6834	386	89	the	the	DET
ejpam-6834	386	90	hyper	hyper	ADJ
ejpam-6834	386	91	degree	degree	NOUN
ejpam-6834	386	92	of	of	ADP
ejpam-6834	386	93	appurtenance	appurtenance	NOUN
ejpam-6834	386	94	function	function	NOUN
ejpam-6834	386	95	(	(	PUNCT
ejpam-6834	386	96	hdaf	hdaf	NOUN
ejpam-6834	386	97	)	)	PUNCT
ejpam-6834	386	98	,	,	PUNCT
ejpam-6834	386	99	assigning	assign	VERB
ejpam-6834	386	100	to	to	ADP
ejpam-6834	386	101	each	each	DET
ejpam-6834	386	102	element	element	NOUN
ejpam-6834	386	103	x	x	SYM
ejpam-6834	386	104	∈	∈	PROPN
ejpam-6834	386	105	pn	pn	PROPN
ejpam-6834	386	106	and	and	CCONJ
ejpam-6834	386	107	attribute	attribute	NOUN
ejpam-6834	386	108	value	value	NOUN
ejpam-6834	386	109	ai	ai	PROPN
ejpam-6834	386	110	∈	∈	NOUN
ejpam-6834	386	111	pvi	pvi	NOUN
ejpam-6834	386	112	a	a	DET
ejpam-6834	386	113	subset	subset	NOUN
ejpam-6834	386	114	of	of	ADP
ejpam-6834	386	115	[	[	X
ejpam-6834	386	116	0	0	NUM
ejpam-6834	386	117	,	,	PUNCT
ejpam-6834	386	118	1]s	1]s	NOUN
ejpam-6834	386	119	.	.	PUNCT
ejpam-6834	386	120	•	•	NUM
ejpam-6834	386	121	pcf	pcf	PROPN
ejpam-6834	386	122	(	(	PUNCT
ejpam-6834	386	123	n	n	CCONJ
ejpam-6834	386	124	)	)	PUNCT
ejpam-6834	386	125	:	:	PUNCT
ejpam-6834	386	126	⋃n	⋃n	VERB
ejpam-6834	386	127	i=1	i=1	ADP
ejpam-6834	386	128	pvi	pvi	PROPN
ejpam-6834	386	129	×	×	PROPN
ejpam-6834	386	130	⋃n	⋃n	NOUN
ejpam-6834	386	131	i=1	i=1	ADP
ejpam-6834	386	132	pvi	pvi	NOUN
ejpam-6834	386	133	→	→	SYM
ejpam-6834	386	134	[	[	X
ejpam-6834	386	135	0	0	NUM
ejpam-6834	386	136	,	,	PUNCT
ejpam-6834	386	137	1]t	1]t	NUM
ejpam-6834	386	138	is	be	AUX
ejpam-6834	386	139	the	the	DET
ejpam-6834	386	140	degree	degree	NOUN
ejpam-6834	386	141	of	of	ADP
ejpam-6834	386	142	contradiction	contradiction	NOUN
ejpam-6834	386	143	function	function	NOUN
ejpam-6834	386	144	(	(	PUNCT
ejpam-6834	386	145	dcf	dcf	PROPN
ejpam-6834	386	146	)	)	PUNCT
ejpam-6834	386	147	,	,	PUNCT
ejpam-6834	386	148	satisfying	satisfy	VERB
ejpam-6834	386	149	:	:	PUNCT
ejpam-6834	386	150	(	(	PUNCT
ejpam-6834	386	151	i	i	NOUN
ejpam-6834	386	152	)	)	PUNCT
ejpam-6834	386	153	reflexivity	reflexivity	NOUN
ejpam-6834	386	154	:	:	PUNCT
ejpam-6834	386	155	pcf	pcf	PROPN
ejpam-6834	386	156	(	(	PUNCT
ejpam-6834	386	157	n)(a	n)(a	PROPN
ejpam-6834	386	158	,	,	PUNCT
ejpam-6834	386	159	a	a	PRON
ejpam-6834	386	160	)	)	PUNCT
ejpam-6834	386	161	=	=	SYM
ejpam-6834	386	162	0	0	NUM
ejpam-6834	386	163	for	for	SCONJ
ejpam-6834	386	164	all	all	DET
ejpam-6834	386	165	a	a	DET
ejpam-6834	386	166	∈	∈	PROPN
ejpam-6834	386	167	⋃n	⋃n	NOUN
ejpam-6834	386	168	i=1	i=1	ADP
ejpam-6834	386	169	pvi	pvi	NOUN
ejpam-6834	386	170	,	,	PUNCT
ejpam-6834	386	171	(	(	PUNCT
ejpam-6834	386	172	ii	ii	NOUN
ejpam-6834	386	173	)	)	PUNCT
ejpam-6834	386	174	symmetry	symmetry	NOUN
ejpam-6834	386	175	:	:	PUNCT
ejpam-6834	386	176	pcf	pcf	PROPN
ejpam-6834	386	177	(	(	PUNCT
ejpam-6834	386	178	n)(a	n)(a	PROPN
ejpam-6834	386	179	,	,	PUNCT
ejpam-6834	386	180	b	b	NOUN
ejpam-6834	386	181	)	)	PUNCT
ejpam-6834	386	182	=	=	SYM
ejpam-6834	386	183	pcf	pcf	PROPN
ejpam-6834	386	184	(	(	PUNCT
ejpam-6834	386	185	n)(b	n)(b	ADJ
ejpam-6834	386	186	,	,	PUNCT
ejpam-6834	386	187	a	a	PRON
ejpam-6834	386	188	)	)	PUNCT
ejpam-6834	386	189	for	for	ADP
ejpam-6834	386	190	all	all	DET
ejpam-6834	386	191	a	a	DET
ejpam-6834	386	192	,	,	PUNCT
ejpam-6834	386	193	b	b	PROPN
ejpam-6834	386	194	∈	∈	PROPN
ejpam-6834	386	195	⋃n	⋃n	PROPN
ejpam-6834	386	196	i=1	i=1	PROPN
ejpam-6834	386	197	pvi	pvi	NOUN
ejpam-6834	386	198	.	.	PUNCT
ejpam-6834	386	199	•	•	NUM
ejpam-6834	386	200	s	s	NOUN
ejpam-6834	386	201	and	and	CCONJ
ejpam-6834	386	202	t	t	PROPN
ejpam-6834	386	203	are	be	AUX
ejpam-6834	386	204	positive	positive	ADJ
ejpam-6834	386	205	integers	integer	NOUN
ejpam-6834	386	206	representing	represent	VERB
ejpam-6834	386	207	the	the	DET
ejpam-6834	386	208	dimensions	dimension	NOUN
ejpam-6834	386	209	of	of	ADP
ejpam-6834	386	210	the	the	DET
ejpam-6834	386	211	membership	membership	NOUN
ejpam-6834	386	212	degrees	degree	NOUN
ejpam-6834	386	213	and	and	CCONJ
ejpam-6834	386	214	contradiction	contradiction	NOUN
ejpam-6834	386	215	degrees	degree	NOUN
ejpam-6834	386	216	,	,	PUNCT
ejpam-6834	386	217	respectively	respectively	ADV
ejpam-6834	386	218	.	.	PUNCT
ejpam-6834	386	219	example	example	NOUN
ejpam-6834	386	220	13	13	NUM
ejpam-6834	386	221	(	(	PUNCT
ejpam-6834	386	222	nested	nest	VERB
ejpam-6834	386	223	project	project	NOUN
ejpam-6834	386	224	evaluation	evaluation	NOUN
ejpam-6834	386	225	under	under	ADP
ejpam-6834	386	226	uncertainty	uncertainty	NOUN
ejpam-6834	386	227	)	)	PUNCT
ejpam-6834	386	228	.	.	PUNCT
ejpam-6834	387	1	let	let	VERB
ejpam-6834	387	2	x	x	PUNCT
ejpam-6834	387	3	=	=	PRON
ejpam-6834	387	4	{	{	PUNCT
ejpam-6834	387	5	proj1	proj1	NOUN
ejpam-6834	387	6	,	,	PUNCT
ejpam-6834	387	7	proj2	proj2	NOUN
ejpam-6834	387	8	}	}	PUNCT
ejpam-6834	387	9	,	,	PUNCT
ejpam-6834	387	10	and	and	CCONJ
ejpam-6834	387	11	take	take	VERB
ejpam-6834	387	12	n	n	NOUN
ejpam-6834	387	13	=	=	SYM
ejpam-6834	387	14	2	2	NUM
ejpam-6834	387	15	.	.	PUNCT
ejpam-6834	387	16	then	then	ADV
ejpam-6834	387	17	p1	p1	PROPN
ejpam-6834	387	18	=	=	SYM
ejpam-6834	387	19	x	x	PROPN
ejpam-6834	387	20	,	,	PUNCT
ejpam-6834	387	21	p2	p2	PROPN
ejpam-6834	387	22	=	=	SYM
ejpam-6834	387	23	p̃(p1	p̃(p1	PROPN
ejpam-6834	387	24	)	)	PUNCT
ejpam-6834	388	1	=	=	PRON
ejpam-6834	388	2	{	{	PUNCT
ejpam-6834	388	3	{	{	PUNCT
ejpam-6834	388	4	proj1	proj1	NOUN
ejpam-6834	388	5	}	}	PUNCT
ejpam-6834	388	6	,	,	PUNCT
ejpam-6834	388	7	{	{	PUNCT
ejpam-6834	388	8	proj2	proj2	NOUN
ejpam-6834	388	9	}	}	PUNCT
ejpam-6834	388	10	,	,	PUNCT
ejpam-6834	388	11	{	{	PUNCT
ejpam-6834	388	12	proj1,proj2	proj1,proj2	ADJ
ejpam-6834	388	13	}	}	PUNCT
ejpam-6834	388	14	}	}	PUNCT
ejpam-6834	388	15	.	.	PUNCT
ejpam-6834	389	1	choose	choose	VERB
ejpam-6834	389	2	two	two	NUM
ejpam-6834	389	3	attributes	attribute	NOUN
ejpam-6834	389	4	:	:	PUNCT
ejpam-6834	389	5	v1	v1	NOUN
ejpam-6834	389	6	=	=	SYM
ejpam-6834	389	7	risk	risk	NOUN
ejpam-6834	389	8	level	level	NOUN
ejpam-6834	389	9	,	,	PUNCT
ejpam-6834	389	10	pv1	pv1	NOUN
ejpam-6834	389	11	=	=	PUNCT
ejpam-6834	389	12	{	{	PUNCT
ejpam-6834	389	13	low	low	ADJ
ejpam-6834	389	14	,	,	PUNCT
ejpam-6834	389	15	high	high	ADJ
ejpam-6834	389	16	}	}	PUNCT
ejpam-6834	389	17	,	,	PUNCT
ejpam-6834	389	18	t.	t.	PROPN
ejpam-6834	389	19	fujita	fujita	PROPN
ejpam-6834	389	20	,	,	PUNCT
ejpam-6834	389	21	f.smarandache	f.smarandache	NOUN
ejpam-6834	389	22	/	/	SYM
ejpam-6834	389	23	eur	eur	PROPN
ejpam-6834	389	24	.	.	PUNCT
ejpam-6834	390	1	j.	j.	PROPN
ejpam-6834	390	2	pure	pure	PROPN
ejpam-6834	390	3	appl	appl	PROPN
ejpam-6834	390	4	.	.	PROPN
ejpam-6834	390	5	math	math	PROPN
ejpam-6834	390	6	,	,	PUNCT
ejpam-6834	390	7	18	18	NUM
ejpam-6834	390	8	(	(	PUNCT
ejpam-6834	390	9	4	4	NUM
ejpam-6834	390	10	)	)	PUNCT
ejpam-6834	390	11	(	(	PUNCT
ejpam-6834	390	12	2025	2025	NUM
ejpam-6834	390	13	)	)	PUNCT
ejpam-6834	390	14	,	,	PUNCT
ejpam-6834	390	15	6834	6834	NUM
ejpam-6834	390	16	20	20	NUM
ejpam-6834	390	17	of	of	ADP
ejpam-6834	390	18	69	69	NUM
ejpam-6834	390	19	v2	v2	NOUN
ejpam-6834	390	20	=	=	NOUN
ejpam-6834	390	21	cost	cost	NOUN
ejpam-6834	390	22	,	,	PUNCT
ejpam-6834	390	23	pv2	pv2	NOUN
ejpam-6834	390	24	=	=	PRON
ejpam-6834	390	25	{	{	PUNCT
ejpam-6834	390	26	cheap	cheap	ADJ
ejpam-6834	390	27	,	,	PUNCT
ejpam-6834	390	28	expensive	expensive	ADJ
ejpam-6834	390	29	}	}	PUNCT
ejpam-6834	390	30	.	.	PUNCT
ejpam-6834	391	1	let	let	VERB
ejpam-6834	391	2	s	s	NOUN
ejpam-6834	391	3	=	=	SYM
ejpam-6834	391	4	1	1	NUM
ejpam-6834	391	5	,	,	PUNCT
ejpam-6834	391	6	so	so	SCONJ
ejpam-6834	391	7	that	that	PRON
ejpam-6834	391	8	p̃([0	p̃([0	NUM
ejpam-6834	391	9	,	,	PUNCT
ejpam-6834	391	10	1]s	1]s	NUM
ejpam-6834	391	11	)	)	PUNCT
ejpam-6834	391	12	=	=	PUNCT
ejpam-6834	391	13	p̃([0	p̃([0	VERB
ejpam-6834	391	14	,	,	PUNCT
ejpam-6834	391	15	1	1	NUM
ejpam-6834	391	16	]	]	NUM
ejpam-6834	391	17	)	)	PUNCT
ejpam-6834	391	18	.	.	PUNCT
ejpam-6834	392	1	define	define	VERB
ejpam-6834	392	2	the	the	DET
ejpam-6834	392	3	hyper	hyper	ADJ
ejpam-6834	392	4	degree	degree	NOUN
ejpam-6834	392	5	of	of	ADP
ejpam-6834	392	6	appurtenance	appurtenance	NOUN
ejpam-6834	392	7	functions	function	NOUN
ejpam-6834	392	8	˜pdf	˜pdf	NOUN
ejpam-6834	392	9	(	(	PUNCT
ejpam-6834	392	10	2	2	X
ejpam-6834	392	11	)	)	PUNCT
ejpam-6834	392	12	i	i	PRON
ejpam-6834	392	13	:	:	PUNCT
ejpam-6834	392	14	p2	p2	PROPN
ejpam-6834	392	15	×	×	NOUN
ejpam-6834	392	16	pvi	pvi	NOUN
ejpam-6834	392	17	→	→	SYM
ejpam-6834	392	18	p̃([0	p̃([0	NUM
ejpam-6834	392	19	,	,	PUNCT
ejpam-6834	392	20	1	1	NUM
ejpam-6834	392	21	]	]	PUNCT
ejpam-6834	392	22	)	)	PUNCT
ejpam-6834	392	23	by	by	ADP
ejpam-6834	392	24	:	:	PUNCT
ejpam-6834	392	25	˜pdf	˜pdf	NOUN
ejpam-6834	392	26	(	(	PUNCT
ejpam-6834	392	27	2	2	NUM
ejpam-6834	392	28	)	)	PUNCT
ejpam-6834	392	29	1	1	NUM
ejpam-6834	392	30	(	(	PUNCT
ejpam-6834	392	31	{	{	PUNCT
ejpam-6834	392	32	proj1},low	proj1},low	NUM
ejpam-6834	392	33	)	)	PUNCT
ejpam-6834	392	34	=	=	PUNCT
ejpam-6834	392	35	{	{	PUNCT
ejpam-6834	392	36	0.2	0.2	NUM
ejpam-6834	392	37	,	,	PUNCT
ejpam-6834	392	38	0.3	0.3	NUM
ejpam-6834	392	39	}	}	PUNCT
ejpam-6834	392	40	,	,	PUNCT
ejpam-6834	392	41	˜pdf	˜pdf	NOUN
ejpam-6834	392	42	(	(	PUNCT
ejpam-6834	392	43	2	2	NUM
ejpam-6834	392	44	)	)	SYM
ejpam-6834	392	45	1	1	NUM
ejpam-6834	392	46	(	(	PUNCT
ejpam-6834	392	47	{	{	PUNCT
ejpam-6834	392	48	proj1},high	proj1},high	NOUN
ejpam-6834	392	49	)	)	PUNCT
ejpam-6834	392	50	=	=	PUNCT
ejpam-6834	392	51	{	{	PUNCT
ejpam-6834	392	52	0.7	0.7	NUM
ejpam-6834	392	53	,	,	PUNCT
ejpam-6834	392	54	0.8	0.8	NUM
ejpam-6834	392	55	}	}	PUNCT
ejpam-6834	392	56	,	,	PUNCT
ejpam-6834	392	57	˜pdf	˜pdf	NOUN
ejpam-6834	392	58	(	(	PUNCT
ejpam-6834	392	59	2	2	NUM
ejpam-6834	392	60	)	)	PUNCT
ejpam-6834	392	61	1	1	NUM
ejpam-6834	392	62	(	(	PUNCT
ejpam-6834	392	63	{	{	PUNCT
ejpam-6834	392	64	proj2},low	proj2},low	INTJ
ejpam-6834	392	65	)	)	PUNCT
ejpam-6834	392	66	=	=	PUNCT
ejpam-6834	392	67	{	{	PUNCT
ejpam-6834	392	68	0.3	0.3	NUM
ejpam-6834	392	69	,	,	PUNCT
ejpam-6834	392	70	0.4	0.4	NUM
ejpam-6834	392	71	}	}	PUNCT
ejpam-6834	392	72	,	,	PUNCT
ejpam-6834	392	73	˜pdf	˜pdf	NOUN
ejpam-6834	392	74	(	(	PUNCT
ejpam-6834	392	75	2	2	NUM
ejpam-6834	392	76	)	)	SYM
ejpam-6834	392	77	1	1	NUM
ejpam-6834	392	78	(	(	PUNCT
ejpam-6834	392	79	{	{	PUNCT
ejpam-6834	392	80	proj2},high	proj2},high	NOUN
ejpam-6834	392	81	)	)	PUNCT
ejpam-6834	392	82	=	=	PUNCT
ejpam-6834	392	83	{	{	PUNCT
ejpam-6834	392	84	0.6	0.6	NUM
ejpam-6834	392	85	,	,	PUNCT
ejpam-6834	392	86	0.7	0.7	NUM
ejpam-6834	392	87	}	}	PUNCT
ejpam-6834	392	88	,	,	PUNCT
ejpam-6834	392	89	˜pdf	˜pdf	NOUN
ejpam-6834	392	90	(	(	PUNCT
ejpam-6834	392	91	2	2	NUM
ejpam-6834	392	92	)	)	SYM
ejpam-6834	392	93	1	1	NUM
ejpam-6834	392	94	(	(	PUNCT
ejpam-6834	392	95	{	{	PUNCT
ejpam-6834	392	96	proj1,proj2},low	proj1,proj2},low	NOUN
ejpam-6834	392	97	)	)	PUNCT
ejpam-6834	392	98	=	=	PUNCT
ejpam-6834	392	99	{	{	PUNCT
ejpam-6834	392	100	0.4	0.4	NUM
ejpam-6834	392	101	,	,	PUNCT
ejpam-6834	392	102	0.5	0.5	NUM
ejpam-6834	392	103	}	}	PUNCT
ejpam-6834	392	104	,	,	PUNCT
ejpam-6834	392	105	˜pdf	˜pdf	NOUN
ejpam-6834	392	106	(	(	PUNCT
ejpam-6834	392	107	2	2	NUM
ejpam-6834	392	108	)	)	PUNCT
ejpam-6834	392	109	1	1	NUM
ejpam-6834	392	110	(	(	PUNCT
ejpam-6834	392	111	{	{	PUNCT
ejpam-6834	392	112	proj1,proj2},high	proj1,proj2},high	NOUN
ejpam-6834	392	113	)	)	PUNCT
ejpam-6834	392	114	=	=	PUNCT
ejpam-6834	392	115	{	{	PUNCT
ejpam-6834	392	116	0.8	0.8	NUM
ejpam-6834	392	117	,	,	PUNCT
ejpam-6834	392	118	0.9	0.9	NUM
ejpam-6834	392	119	}	}	PUNCT
ejpam-6834	392	120	,	,	PUNCT
ejpam-6834	392	121	˜pdf	˜pdf	NOUN
ejpam-6834	392	122	(	(	PUNCT
ejpam-6834	392	123	2	2	NUM
ejpam-6834	392	124	)	)	SYM
ejpam-6834	392	125	2	2	NUM
ejpam-6834	392	126	(	(	PUNCT
ejpam-6834	392	127	{	{	PUNCT
ejpam-6834	392	128	proj1},cheap	proj1},cheap	NOUN
ejpam-6834	392	129	)	)	PUNCT
ejpam-6834	393	1	=	=	PUNCT
ejpam-6834	393	2	{	{	PUNCT
ejpam-6834	393	3	0.5	0.5	NUM
ejpam-6834	393	4	,	,	PUNCT
ejpam-6834	393	5	0.6	0.6	NUM
ejpam-6834	393	6	}	}	PUNCT
ejpam-6834	393	7	,	,	PUNCT
ejpam-6834	393	8	˜pdf	˜pdf	NOUN
ejpam-6834	393	9	(	(	PUNCT
ejpam-6834	393	10	2	2	NUM
ejpam-6834	393	11	)	)	SYM
ejpam-6834	393	12	2	2	NUM
ejpam-6834	393	13	(	(	PUNCT
ejpam-6834	393	14	{	{	PUNCT
ejpam-6834	393	15	proj1},expensive	proj1},expensive	NOUN
ejpam-6834	393	16	)	)	PUNCT
ejpam-6834	393	17	=	=	PUNCT
ejpam-6834	393	18	{	{	PUNCT
ejpam-6834	393	19	0.7	0.7	NUM
ejpam-6834	393	20	,	,	PUNCT
ejpam-6834	393	21	0.8	0.8	NUM
ejpam-6834	393	22	}	}	PUNCT
ejpam-6834	393	23	,	,	PUNCT
ejpam-6834	393	24	˜pdf	˜pdf	NOUN
ejpam-6834	393	25	(	(	PUNCT
ejpam-6834	393	26	2	2	NUM
ejpam-6834	393	27	)	)	SYM
ejpam-6834	393	28	2	2	NUM
ejpam-6834	393	29	(	(	PUNCT
ejpam-6834	393	30	{	{	PUNCT
ejpam-6834	393	31	proj2},cheap	proj2},cheap	ADJ
ejpam-6834	393	32	)	)	PUNCT
ejpam-6834	393	33	=	=	PUNCT
ejpam-6834	393	34	{	{	PUNCT
ejpam-6834	393	35	0.4	0.4	NUM
ejpam-6834	393	36	,	,	PUNCT
ejpam-6834	393	37	0.5	0.5	NUM
ejpam-6834	393	38	}	}	PUNCT
ejpam-6834	393	39	,	,	PUNCT
ejpam-6834	393	40	˜pdf	˜pdf	NOUN
ejpam-6834	393	41	(	(	PUNCT
ejpam-6834	393	42	2	2	NUM
ejpam-6834	393	43	)	)	SYM
ejpam-6834	393	44	2	2	NUM
ejpam-6834	393	45	(	(	PUNCT
ejpam-6834	393	46	{	{	PUNCT
ejpam-6834	393	47	proj2},expensive	proj2},expensive	ADJ
ejpam-6834	393	48	)	)	PUNCT
ejpam-6834	393	49	=	=	PUNCT
ejpam-6834	393	50	{	{	PUNCT
ejpam-6834	393	51	0.6	0.6	NUM
ejpam-6834	393	52	,	,	PUNCT
ejpam-6834	393	53	0.7	0.7	NUM
ejpam-6834	393	54	}	}	PUNCT
ejpam-6834	393	55	,	,	PUNCT
ejpam-6834	393	56	˜pdf	˜pdf	NOUN
ejpam-6834	393	57	(	(	PUNCT
ejpam-6834	393	58	2	2	NUM
ejpam-6834	393	59	)	)	SYM
ejpam-6834	393	60	2	2	NUM
ejpam-6834	393	61	(	(	PUNCT
ejpam-6834	393	62	{	{	PUNCT
ejpam-6834	393	63	proj1,proj2},cheap	proj1,proj2},cheap	NOUN
ejpam-6834	393	64	)	)	PUNCT
ejpam-6834	393	65	=	=	PRON
ejpam-6834	393	66	{	{	PUNCT
ejpam-6834	393	67	0.6	0.6	NUM
ejpam-6834	393	68	,	,	PUNCT
ejpam-6834	393	69	0.7	0.7	NUM
ejpam-6834	393	70	}	}	PUNCT
ejpam-6834	393	71	,	,	PUNCT
ejpam-6834	393	72	˜pdf	˜pdf	NOUN
ejpam-6834	393	73	(	(	PUNCT
ejpam-6834	393	74	2	2	NUM
ejpam-6834	393	75	)	)	SYM
ejpam-6834	393	76	2	2	NUM
ejpam-6834	393	77	(	(	PUNCT
ejpam-6834	393	78	{	{	PUNCT
ejpam-6834	393	79	proj1,proj2},expensive	proj1,proj2},expensive	PROPN
ejpam-6834	393	80	)	)	PUNCT
ejpam-6834	393	81	=	=	PUNCT
ejpam-6834	393	82	{	{	PUNCT
ejpam-6834	393	83	0.8	0.8	NUM
ejpam-6834	393	84	,	,	PUNCT
ejpam-6834	393	85	0.9	0.9	NUM
ejpam-6834	393	86	}	}	PUNCT
ejpam-6834	393	87	.	.	PUNCT
ejpam-6834	394	1	define	define	VERB
ejpam-6834	394	2	the	the	DET
ejpam-6834	394	3	degree	degree	NOUN
ejpam-6834	394	4	of	of	ADP
ejpam-6834	394	5	contradiction	contradiction	NOUN
ejpam-6834	394	6	pcf	pcf	PROPN
ejpam-6834	394	7	(	(	PUNCT
ejpam-6834	394	8	2	2	NUM
ejpam-6834	394	9	)	)	PUNCT
ejpam-6834	394	10	:	:	PUNCT
ejpam-6834	394	11	(	(	PUNCT
ejpam-6834	394	12	pv1	pv1	VERB
ejpam-6834	394	13	∪	∪	X
ejpam-6834	394	14	pv2)2	pv2)2	NOUN
ejpam-6834	394	15	→	→	SYM
ejpam-6834	394	16	[	[	X
ejpam-6834	394	17	0	0	NUM
ejpam-6834	394	18	,	,	PUNCT
ejpam-6834	394	19	1	1	NUM
ejpam-6834	394	20	]	]	PUNCT
ejpam-6834	394	21	by	by	ADP
ejpam-6834	394	22	:	:	PUNCT
ejpam-6834	394	23	pcf	pcf	PROPN
ejpam-6834	394	24	(	(	PUNCT
ejpam-6834	394	25	2)(low	2)(low	NOUN
ejpam-6834	394	26	,	,	PUNCT
ejpam-6834	394	27	high	high	ADJ
ejpam-6834	394	28	)	)	PUNCT
ejpam-6834	394	29	=	=	SYM
ejpam-6834	394	30	0.9	0.9	NUM
ejpam-6834	394	31	,	,	PUNCT
ejpam-6834	394	32	pcf	pcf	PROPN
ejpam-6834	394	33	(	(	PUNCT
ejpam-6834	394	34	2)(cheap	2)(cheap	NOUN
ejpam-6834	394	35	,	,	PUNCT
ejpam-6834	394	36	expensive	expensive	ADJ
ejpam-6834	394	37	)	)	PUNCT
ejpam-6834	394	38	=	=	SYM
ejpam-6834	394	39	0.8	0.8	NUM
ejpam-6834	394	40	,	,	PUNCT
ejpam-6834	394	41	with	with	ADP
ejpam-6834	394	42	reflexivity	reflexivity	PROPN
ejpam-6834	394	43	pcf	pcf	PROPN
ejpam-6834	394	44	(	(	PUNCT
ejpam-6834	394	45	2)(a	2)(a	NUM
ejpam-6834	394	46	,	,	PUNCT
ejpam-6834	394	47	a	a	PRON
ejpam-6834	394	48	)	)	PUNCT
ejpam-6834	394	49	=	=	SYM
ejpam-6834	394	50	0	0	NUM
ejpam-6834	394	51	and	and	CCONJ
ejpam-6834	394	52	symmetry	symmetry	PROPN
ejpam-6834	394	53	pcf	pcf	PROPN
ejpam-6834	394	54	(	(	PUNCT
ejpam-6834	394	55	2)(a	2)(a	NUM
ejpam-6834	394	56	,	,	PUNCT
ejpam-6834	394	57	b	b	NOUN
ejpam-6834	394	58	)	)	PUNCT
ejpam-6834	394	59	=	=	SYM
ejpam-6834	394	60	pcf	pcf	PROPN
ejpam-6834	394	61	(	(	PUNCT
ejpam-6834	394	62	2)(b	2)(b	NUM
ejpam-6834	394	63	,	,	PUNCT
ejpam-6834	394	64	a	a	PRON
ejpam-6834	394	65	)	)	PUNCT
ejpam-6834	394	66	.	.	PUNCT
ejpam-6834	395	1	thus	thus	ADV
ejpam-6834	395	2	the	the	DET
ejpam-6834	395	3	2	2	NUM
ejpam-6834	395	4	-	-	PUNCT
ejpam-6834	395	5	superhyperplithogenic	superhyperplithogenic	ADJ
ejpam-6834	395	6	set	set	NOUN
ejpam-6834	395	7	is	be	AUX
ejpam-6834	395	8	shps2	shps2	X
ejpam-6834	396	1	=	=	SYM
ejpam-6834	396	2	(	(	PUNCT
ejpam-6834	396	3	p2	p2	X
ejpam-6834	396	4	,	,	PUNCT
ejpam-6834	396	5	{	{	PUNCT
ejpam-6834	396	6	v1	v1	NOUN
ejpam-6834	396	7	,	,	PUNCT
ejpam-6834	396	8	v2	v2	PROPN
ejpam-6834	396	9	}	}	PUNCT
ejpam-6834	396	10	,	,	PUNCT
ejpam-6834	396	11	{	{	PUNCT
ejpam-6834	396	12	pv1	pv1	NOUN
ejpam-6834	396	13	,	,	PUNCT
ejpam-6834	396	14	pv2	pv2	NOUN
ejpam-6834	396	15	}	}	PUNCT
ejpam-6834	396	16	,	,	PUNCT
ejpam-6834	396	17	{	{	PUNCT
ejpam-6834	396	18	˜pdf	˜pdf	NOUN
ejpam-6834	396	19	(	(	PUNCT
ejpam-6834	396	20	2	2	NUM
ejpam-6834	396	21	)	)	PUNCT
ejpam-6834	396	22	1	1	NUM
ejpam-6834	396	23	,	,	PUNCT
ejpam-6834	396	24	˜pdf	˜pdf	NOUN
ejpam-6834	396	25	(	(	PUNCT
ejpam-6834	396	26	2	2	NUM
ejpam-6834	396	27	)	)	PUNCT
ejpam-6834	396	28	2	2	NUM
ejpam-6834	396	29	}	}	PUNCT
ejpam-6834	396	30	,	,	PUNCT
ejpam-6834	396	31	pcf	pcf	PROPN
ejpam-6834	396	32	(	(	PUNCT
ejpam-6834	396	33	2	2	NUM
ejpam-6834	396	34	)	)	PUNCT
ejpam-6834	396	35	)	)	PUNCT
ejpam-6834	396	36	,	,	PUNCT
ejpam-6834	396	37	which	which	PRON
ejpam-6834	396	38	captures	capture	VERB
ejpam-6834	396	39	nested	nest	VERB
ejpam-6834	396	40	,	,	PUNCT
ejpam-6834	396	41	hyper	hyper	NOUN
ejpam-6834	396	42	-	-	ADJ
ejpam-6834	396	43	valued	value	VERB
ejpam-6834	396	44	appurtenance	appurtenance	NOUN
ejpam-6834	396	45	degrees	degree	NOUN
ejpam-6834	396	46	and	and	CCONJ
ejpam-6834	396	47	contradictions	contradiction	NOUN
ejpam-6834	396	48	for	for	ADP
ejpam-6834	396	49	multicriteria	multicriteria	PROPN
ejpam-6834	396	50	project	project	NOUN
ejpam-6834	396	51	evaluation	evaluation	NOUN
ejpam-6834	396	52	.	.	PUNCT
ejpam-6834	397	1	3	3	X
ejpam-6834	397	2	.	.	X
ejpam-6834	397	3	main	main	ADJ
ejpam-6834	397	4	results	result	NOUN
ejpam-6834	397	5	of	of	ADP
ejpam-6834	397	6	this	this	DET
ejpam-6834	397	7	paper	paper	NOUN
ejpam-6834	397	8	this	this	DET
ejpam-6834	397	9	section	section	NOUN
ejpam-6834	397	10	presents	present	VERB
ejpam-6834	397	11	the	the	DET
ejpam-6834	397	12	main	main	ADJ
ejpam-6834	397	13	results	result	NOUN
ejpam-6834	397	14	of	of	ADP
ejpam-6834	397	15	this	this	DET
ejpam-6834	397	16	paper	paper	NOUN
ejpam-6834	397	17	.	.	PUNCT
ejpam-6834	398	1	3.1	3.1	NUM
ejpam-6834	398	2	.	.	PUNCT
ejpam-6834	398	3	(	(	PUNCT
ejpam-6834	398	4	m	m	PROPN
ejpam-6834	398	5	,	,	PUNCT
ejpam-6834	398	6	n)-superhyperuncertain	n)-superhyperuncertain	ADV
ejpam-6834	398	7	set	set	VERB
ejpam-6834	398	8	we	we	PRON
ejpam-6834	398	9	provide	provide	VERB
ejpam-6834	398	10	the	the	DET
ejpam-6834	398	11	definition	definition	NOUN
ejpam-6834	398	12	of	of	ADP
ejpam-6834	398	13	the	the	DET
ejpam-6834	398	14	(	(	PUNCT
ejpam-6834	398	15	m	m	PROPN
ejpam-6834	398	16	,	,	PUNCT
ejpam-6834	398	17	n)-superhyperuncertain	n)-superhyperuncertain	ADV
ejpam-6834	398	18	set	set	VERB
ejpam-6834	398	19	.	.	PUNCT
ejpam-6834	399	1	3.1.1	3.1.1	X
ejpam-6834	399	2	.	.	PUNCT
ejpam-6834	400	1	(	(	PUNCT
ejpam-6834	400	2	m	m	X
ejpam-6834	400	3	,	,	PUNCT
ejpam-6834	400	4	n)-superhyperfuzzy	n)-superhyperfuzzy	PUNCT
ejpam-6834	400	5	set	set	VERB
ejpam-6834	400	6	a	a	DET
ejpam-6834	400	7	(	(	PUNCT
ejpam-6834	400	8	m	m	NOUN
ejpam-6834	400	9	,	,	PUNCT
ejpam-6834	400	10	n)-superhyperfuzzy	n)-superhyperfuzzy	PUNCT
ejpam-6834	400	11	set	set	VERB
ejpam-6834	400	12	maps	map	NOUN
ejpam-6834	400	13	m	m	NOUN
ejpam-6834	400	14	-	-	PUNCT
ejpam-6834	400	15	level	level	NOUN
ejpam-6834	400	16	nested	nest	VERB
ejpam-6834	400	17	subsets	subset	NOUN
ejpam-6834	400	18	of	of	ADP
ejpam-6834	400	19	x	x	NUM
ejpam-6834	400	20	to	to	ADP
ejpam-6834	400	21	n	n	CCONJ
ejpam-6834	400	22	-	-	PUNCT
ejpam-6834	400	23	level	level	NOUN
ejpam-6834	400	24	nested	nest	VERB
ejpam-6834	400	25	fuzzy	fuzzy	ADJ
ejpam-6834	400	26	membership	membership	NOUN
ejpam-6834	400	27	-	-	PUNCT
ejpam-6834	400	28	value	value	NOUN
ejpam-6834	400	29	subsets	subset	NOUN
ejpam-6834	400	30	in	in	ADP
ejpam-6834	400	31	[	[	X
ejpam-6834	400	32	0	0	NUM
ejpam-6834	400	33	,	,	PUNCT
ejpam-6834	400	34	1	1	NUM
ejpam-6834	400	35	]	]	PUNCT
ejpam-6834	400	36	,	,	PUNCT
ejpam-6834	400	37	capturing	capture	VERB
ejpam-6834	400	38	distinct	distinct	ADJ
ejpam-6834	400	39	hierarchical	hierarchical	ADJ
ejpam-6834	400	40	fuzzy	fuzzy	ADJ
ejpam-6834	400	41	uncertainty	uncertainty	NOUN
ejpam-6834	400	42	patterns	pattern	NOUN
ejpam-6834	400	43	.	.	PUNCT
ejpam-6834	401	1	the	the	DET
ejpam-6834	401	2	definition	definition	NOUN
ejpam-6834	401	3	of	of	ADP
ejpam-6834	401	4	the	the	DET
ejpam-6834	401	5	(	(	PUNCT
ejpam-6834	401	6	m	m	PROPN
ejpam-6834	401	7	,	,	PUNCT
ejpam-6834	401	8	n)-superhyperfuzzy	n)-superhyperfuzzy	PUNCT
ejpam-6834	401	9	set	set	NOUN
ejpam-6834	401	10	is	be	AUX
ejpam-6834	401	11	presented	present	VERB
ejpam-6834	401	12	below	below	ADV
ejpam-6834	401	13	.	.	PUNCT
ejpam-6834	402	1	definition	definition	NOUN
ejpam-6834	402	2	19	19	NUM
ejpam-6834	402	3	(	(	PUNCT
ejpam-6834	402	4	(	(	PUNCT
ejpam-6834	402	5	m	m	NOUN
ejpam-6834	402	6	,	,	PUNCT
ejpam-6834	402	7	n)-superhyperfuzzy	n)-superhyperfuzzy	PUNCT
ejpam-6834	402	8	set	set	NOUN
ejpam-6834	402	9	)	)	PUNCT
ejpam-6834	402	10	.	.	PUNCT
ejpam-6834	403	1	let	let	VERB
ejpam-6834	403	2	u	u	PRON
ejpam-6834	403	3	be	be	AUX
ejpam-6834	403	4	a	a	DET
ejpam-6834	403	5	universe	universe	NOUN
ejpam-6834	403	6	of	of	ADP
ejpam-6834	403	7	discourse	discourse	NOUN
ejpam-6834	403	8	and	and	CCONJ
ejpam-6834	403	9	let	let	VERB
ejpam-6834	403	10	a	a	DET
ejpam-6834	403	11	⊆	⊆	NUM
ejpam-6834	403	12	u	u	NOUN
ejpam-6834	403	13	be	be	AUX
ejpam-6834	403	14	nonempty	nonempty	ADJ
ejpam-6834	403	15	.	.	PUNCT
ejpam-6834	404	1	fix	fix	VERB
ejpam-6834	404	2	integers	integer	NOUN
ejpam-6834	404	3	m	m	PRON
ejpam-6834	404	4	,	,	PUNCT
ejpam-6834	404	5	n	n	PRON
ejpam-6834	404	6	≥	≥	NOUN
ejpam-6834	404	7	0	0	NUM
ejpam-6834	404	8	.	.	PUNCT
ejpam-6834	405	1	define	define	VERB
ejpam-6834	405	2	the	the	DET
ejpam-6834	405	3	m	m	PROPN
ejpam-6834	405	4	-	-	PUNCT
ejpam-6834	405	5	th	th	X
ejpam-6834	405	6	nested	nest	VERB
ejpam-6834	405	7	power	power	NOUN
ejpam-6834	405	8	-	-	PUNCT
ejpam-6834	405	9	set	set	NOUN
ejpam-6834	405	10	of	of	ADP
ejpam-6834	405	11	a	a	PRON
ejpam-6834	405	12	by	by	ADP
ejpam-6834	405	13	p0(a	p0(a	PROPN
ejpam-6834	405	14	)	)	PUNCT
ejpam-6834	405	15	=	=	SYM
ejpam-6834	405	16	a	a	PRON
ejpam-6834	405	17	,	,	PUNCT
ejpam-6834	405	18	pk(a	pk(a	X
ejpam-6834	405	19	)	)	PUNCT
ejpam-6834	406	1	=	=	SYM
ejpam-6834	406	2	p	p	X
ejpam-6834	406	3	(	(	PUNCT
ejpam-6834	406	4	pk−1(a	pk−1(a	NOUN
ejpam-6834	406	5	)	)	PUNCT
ejpam-6834	406	6	)	)	PUNCT
ejpam-6834	407	1	(	(	PUNCT
ejpam-6834	407	2	k	k	X
ejpam-6834	407	3	≥	≥	NUM
ejpam-6834	407	4	1	1	NUM
ejpam-6834	407	5	)	)	PUNCT
ejpam-6834	407	6	,	,	PUNCT
ejpam-6834	407	7	t.	t.	PROPN
ejpam-6834	407	8	fujita	fujita	PROPN
ejpam-6834	407	9	,	,	PUNCT
ejpam-6834	407	10	f.smarandache	f.smarandache	NOUN
ejpam-6834	407	11	/	/	SYM
ejpam-6834	407	12	eur	eur	PROPN
ejpam-6834	407	13	.	.	PUNCT
ejpam-6834	408	1	j.	j.	PROPN
ejpam-6834	408	2	pure	pure	PROPN
ejpam-6834	408	3	appl	appl	PROPN
ejpam-6834	408	4	.	.	PROPN
ejpam-6834	408	5	math	math	PROPN
ejpam-6834	408	6	,	,	PUNCT
ejpam-6834	408	7	18	18	NUM
ejpam-6834	408	8	(	(	PUNCT
ejpam-6834	408	9	4	4	NUM
ejpam-6834	408	10	)	)	PUNCT
ejpam-6834	408	11	(	(	PUNCT
ejpam-6834	408	12	2025	2025	NUM
ejpam-6834	408	13	)	)	PUNCT
ejpam-6834	408	14	,	,	PUNCT
ejpam-6834	408	15	6834	6834	NUM
ejpam-6834	408	16	21	21	NUM
ejpam-6834	408	17	of	of	ADP
ejpam-6834	408	18	69	69	NUM
ejpam-6834	408	19	and	and	CCONJ
ejpam-6834	408	20	similarly	similarly	ADV
ejpam-6834	408	21	define	define	VERB
ejpam-6834	408	22	pn([0	pn([0	NOUN
ejpam-6834	408	23	,	,	PUNCT
ejpam-6834	408	24	1	1	NUM
ejpam-6834	408	25	]	]	PUNCT
ejpam-6834	408	26	)	)	PUNCT
ejpam-6834	408	27	for	for	ADP
ejpam-6834	408	28	the	the	DET
ejpam-6834	408	29	unit	unit	NOUN
ejpam-6834	408	30	interval	interval	NOUN
ejpam-6834	408	31	.	.	PUNCT
ejpam-6834	409	1	an	an	PRON
ejpam-6834	409	2	(	(	PUNCT
ejpam-6834	409	3	m	m	NOUN
ejpam-6834	409	4	,	,	PUNCT
ejpam-6834	409	5	n)-superhyperfuzzy	n)-superhyperfuzzy	PUNCT
ejpam-6834	409	6	set	set	VERB
ejpam-6834	409	7	on	on	ADP
ejpam-6834	409	8	a	a	PRON
ejpam-6834	409	9	is	be	AUX
ejpam-6834	409	10	a	a	DET
ejpam-6834	409	11	function	function	NOUN
ejpam-6834	409	12	τ	τ	X
ejpam-6834	409	13	:	:	PUNCT
ejpam-6834	409	14	pm(a	pm(a	NOUN
ejpam-6834	409	15	)	)	PUNCT
ejpam-6834	409	16	−→	−→	NOUN
ejpam-6834	409	17	pn([0	pn([0	NOUN
ejpam-6834	409	18	,	,	PUNCT
ejpam-6834	409	19	1	1	NUM
ejpam-6834	409	20	]	]	PUNCT
ejpam-6834	409	21	)	)	PUNCT
ejpam-6834	409	22	such	such	ADJ
ejpam-6834	409	23	that	that	PRON
ejpam-6834	409	24	for	for	ADP
ejpam-6834	409	25	each	each	DET
ejpam-6834	409	26	x	x	SYM
ejpam-6834	409	27	∈	∈	PROPN
ejpam-6834	409	28	pm(a	pm(a	NOUN
ejpam-6834	409	29	)	)	PUNCT
ejpam-6834	409	30	,	,	PUNCT
ejpam-6834	409	31	the	the	DET
ejpam-6834	409	32	image	image	NOUN
ejpam-6834	409	33	τ(x	τ(x	NOUN
ejpam-6834	409	34	)	)	PUNCT
ejpam-6834	410	1	⊆	⊆	NUM
ejpam-6834	410	2	[	[	X
ejpam-6834	410	3	0	0	NUM
ejpam-6834	410	4	,	,	PUNCT
ejpam-6834	410	5	1	1	NUM
ejpam-6834	410	6	]	]	PUNCT
ejpam-6834	410	7	is	be	AUX
ejpam-6834	410	8	nonempty	nonempty	ADJ
ejpam-6834	410	9	.	.	PUNCT
ejpam-6834	411	1	in	in	ADP
ejpam-6834	411	2	other	other	ADJ
ejpam-6834	411	3	words	word	NOUN
ejpam-6834	411	4	,	,	PUNCT
ejpam-6834	411	5	the	the	DET
ejpam-6834	411	6	“	"	PUNCT
ejpam-6834	411	7	membership	membership	NOUN
ejpam-6834	411	8	grade	grade	NOUN
ejpam-6834	411	9	”	"	PUNCT
ejpam-6834	411	10	of	of	ADP
ejpam-6834	411	11	the	the	DET
ejpam-6834	411	12	(	(	PUNCT
ejpam-6834	411	13	possibly	possibly	ADV
ejpam-6834	411	14	nested	nested	ADJ
ejpam-6834	411	15	)	)	PUNCT
ejpam-6834	411	16	element	element	NOUN
ejpam-6834	411	17	x	x	PUNCT
ejpam-6834	411	18	is	be	AUX
ejpam-6834	411	19	not	not	PART
ejpam-6834	411	20	a	a	DET
ejpam-6834	411	21	single	single	ADJ
ejpam-6834	411	22	number	number	NOUN
ejpam-6834	411	23	but	but	CCONJ
ejpam-6834	411	24	a	a	DET
ejpam-6834	411	25	set	set	NOUN
ejpam-6834	411	26	of	of	ADP
ejpam-6834	411	27	values	value	NOUN
ejpam-6834	411	28	—	—	PUNCT
ejpam-6834	411	29	intervals	interval	NOUN
ejpam-6834	411	30	and/or	and/or	CCONJ
ejpam-6834	411	31	discrete	discrete	ADJ
ejpam-6834	411	32	points	point	NOUN
ejpam-6834	411	33	—	—	PUNCT
ejpam-6834	411	34	drawn	draw	VERB
ejpam-6834	411	35	from	from	ADP
ejpam-6834	411	36	[	[	X
ejpam-6834	411	37	0	0	NUM
ejpam-6834	411	38	,	,	PUNCT
ejpam-6834	411	39	1	1	NUM
ejpam-6834	411	40	]	]	PUNCT
ejpam-6834	411	41	.	.	PUNCT
ejpam-6834	412	1	example	example	NOUN
ejpam-6834	412	2	14	14	NUM
ejpam-6834	412	3	(	(	PUNCT
ejpam-6834	412	4	student	student	NOUN
ejpam-6834	412	5	group	group	NOUN
ejpam-6834	412	6	assignment	assignment	NOUN
ejpam-6834	412	7	)	)	PUNCT
ejpam-6834	412	8	.	.	PUNCT
ejpam-6834	413	1	let	let	VERB
ejpam-6834	413	2	u	u	PRON
ejpam-6834	413	3	=	=	X
ejpam-6834	413	4	{	{	PUNCT
ejpam-6834	413	5	hiroko	hiroko	PROPN
ejpam-6834	413	6	,	,	PUNCT
ejpam-6834	413	7	masahiro	masahiro	PROPN
ejpam-6834	413	8	,	,	PUNCT
ejpam-6834	413	9	shinya	shinya	PROPN
ejpam-6834	413	10	}	}	PUNCT
ejpam-6834	413	11	be	be	AUX
ejpam-6834	413	12	a	a	DET
ejpam-6834	413	13	class	class	NOUN
ejpam-6834	413	14	roster	roster	NOUN
ejpam-6834	413	15	,	,	PUNCT
ejpam-6834	413	16	and	and	CCONJ
ejpam-6834	413	17	set	set	VERB
ejpam-6834	413	18	a	a	DET
ejpam-6834	413	19	=	=	X
ejpam-6834	413	20	u	u	PROPN
ejpam-6834	413	21	.	.	PUNCT
ejpam-6834	414	1	choose	choose	VERB
ejpam-6834	414	2	m	m	NOUN
ejpam-6834	414	3	=	=	SYM
ejpam-6834	414	4	1	1	NUM
ejpam-6834	414	5	and	and	CCONJ
ejpam-6834	414	6	n	n	CCONJ
ejpam-6834	414	7	=	=	SYM
ejpam-6834	414	8	1	1	NUM
ejpam-6834	414	9	.	.	PUNCT
ejpam-6834	415	1	then	then	ADV
ejpam-6834	415	2	p1(a	p1(a	NUM
ejpam-6834	415	3	)	)	PUNCT
ejpam-6834	415	4	=	=	SYM
ejpam-6834	415	5	p(a	p(a	NOUN
ejpam-6834	415	6	)	)	PUNCT
ejpam-6834	415	7	=	=	NOUN
ejpam-6834	415	8	{	{	PUNCT
ejpam-6834	415	9	∅	∅	NOUN
ejpam-6834	415	10	,	,	PUNCT
ejpam-6834	415	11	{	{	PUNCT
ejpam-6834	415	12	hiroko	hiroko	NOUN
ejpam-6834	415	13	}	}	PUNCT
ejpam-6834	415	14	,	,	PUNCT
ejpam-6834	415	15	.	.	PUNCT
ejpam-6834	415	16	.	.	PUNCT
ejpam-6834	415	17	.	.	PUNCT
ejpam-6834	416	1	,	,	PUNCT
ejpam-6834	416	2	{	{	PUNCT
ejpam-6834	416	3	hiroko	hiroko	PROPN
ejpam-6834	416	4	,	,	PUNCT
ejpam-6834	416	5	masahiro	masahiro	PROPN
ejpam-6834	416	6	,	,	PUNCT
ejpam-6834	416	7	shinya	shinya	PROPN
ejpam-6834	416	8	}	}	PUNCT
ejpam-6834	416	9	}	}	PUNCT
ejpam-6834	416	10	,	,	PUNCT
ejpam-6834	416	11	p1([0	p1([0	NOUN
ejpam-6834	416	12	,	,	PUNCT
ejpam-6834	416	13	1	1	NUM
ejpam-6834	416	14	]	]	PUNCT
ejpam-6834	416	15	)	)	PUNCT
ejpam-6834	416	16	=	=	SYM
ejpam-6834	416	17	p([0	p([0	PROPN
ejpam-6834	416	18	,	,	PUNCT
ejpam-6834	416	19	1	1	NUM
ejpam-6834	416	20	]	]	NUM
ejpam-6834	416	21	)	)	PUNCT
ejpam-6834	416	22	.	.	PUNCT
ejpam-6834	417	1	define	define	PROPN
ejpam-6834	417	2	τ({hiroko	τ({hiroko	PROPN
ejpam-6834	417	3	,	,	PUNCT
ejpam-6834	417	4	masahiro	masahiro	PROPN
ejpam-6834	417	5	}	}	PUNCT
ejpam-6834	417	6	)	)	PUNCT
ejpam-6834	418	1	=	=	PUNCT
ejpam-6834	419	1	[	[	X
ejpam-6834	419	2	0.75	0.75	NUM
ejpam-6834	419	3	,	,	PUNCT
ejpam-6834	419	4	0.85	0.85	NUM
ejpam-6834	419	5	]	]	PUNCT
ejpam-6834	419	6	,	,	PUNCT
ejpam-6834	419	7	τ({shinya	τ({shinya	ADJ
ejpam-6834	419	8	}	}	PUNCT
ejpam-6834	419	9	)	)	PUNCT
ejpam-6834	419	10	=	=	PUNCT
ejpam-6834	419	11	{	{	PUNCT
ejpam-6834	419	12	0.60	0.60	NUM
ejpam-6834	419	13	,	,	PUNCT
ejpam-6834	419	14	0.65	0.65	NUM
ejpam-6834	419	15	}	}	PUNCT
ejpam-6834	419	16	,	,	PUNCT
ejpam-6834	419	17	τ(∅	τ(∅	ADP
ejpam-6834	419	18	)	)	PUNCT
ejpam-6834	419	19	=	=	PRON
ejpam-6834	419	20	{	{	PUNCT
ejpam-6834	419	21	0	0	NUM
ejpam-6834	419	22	}	}	PUNCT
ejpam-6834	419	23	,	,	PUNCT
ejpam-6834	419	24	and	and	CCONJ
ejpam-6834	419	25	similarly	similarly	ADV
ejpam-6834	419	26	for	for	ADP
ejpam-6834	419	27	the	the	DET
ejpam-6834	419	28	remaining	remain	VERB
ejpam-6834	419	29	subsets	subset	NOUN
ejpam-6834	419	30	.	.	PUNCT
ejpam-6834	420	1	here	here	ADV
ejpam-6834	420	2	τ	τ	PROPN
ejpam-6834	420	3	assigns	assign	VERB
ejpam-6834	420	4	each	each	DET
ejpam-6834	420	5	student	student	NOUN
ejpam-6834	420	6	group	group	NOUN
ejpam-6834	420	7	a	a	DET
ejpam-6834	420	8	range	range	NOUN
ejpam-6834	420	9	or	or	CCONJ
ejpam-6834	420	10	set	set	NOUN
ejpam-6834	420	11	of	of	ADP
ejpam-6834	420	12	possible	possible	ADJ
ejpam-6834	420	13	average	average	ADJ
ejpam-6834	420	14	grades	grade	NOUN
ejpam-6834	420	15	(	(	PUNCT
ejpam-6834	420	16	e.g.	e.g.	ADV
ejpam-6834	420	17	from	from	ADP
ejpam-6834	420	18	different	different	ADJ
ejpam-6834	420	19	project	project	NOUN
ejpam-6834	420	20	evaluations	evaluation	NOUN
ejpam-6834	420	21	)	)	PUNCT
ejpam-6834	420	22	,	,	PUNCT
ejpam-6834	420	23	rather	rather	ADV
ejpam-6834	420	24	than	than	ADP
ejpam-6834	420	25	a	a	DET
ejpam-6834	420	26	single	single	ADJ
ejpam-6834	420	27	score	score	NOUN
ejpam-6834	420	28	.	.	PUNCT
ejpam-6834	421	1	example	example	NOUN
ejpam-6834	421	2	15	15	NUM
ejpam-6834	421	3	(	(	PUNCT
ejpam-6834	421	4	grocery	grocery	NOUN
ejpam-6834	421	5	–	–	PUNCT
ejpam-6834	421	6	delivery	delivery	NOUN
ejpam-6834	421	7	freshness	freshness	NOUN
ejpam-6834	421	8	(	(	PUNCT
ejpam-6834	421	9	simple	simple	ADJ
ejpam-6834	421	10	(	(	PUNCT
ejpam-6834	421	11	1	1	NUM
ejpam-6834	421	12	,	,	PUNCT
ejpam-6834	421	13	1)-superhyperfuzzy	1)-superhyperfuzzy	NUM
ejpam-6834	421	14	set	set	NOUN
ejpam-6834	421	15	)	)	PUNCT
ejpam-6834	421	16	)	)	PUNCT
ejpam-6834	421	17	.	.	PUNCT
ejpam-6834	422	1	let	let	VERB
ejpam-6834	422	2	the	the	DET
ejpam-6834	422	3	universe	universe	NOUN
ejpam-6834	422	4	be	be	AUX
ejpam-6834	422	5	the	the	DET
ejpam-6834	422	6	set	set	NOUN
ejpam-6834	422	7	of	of	ADP
ejpam-6834	422	8	items	item	NOUN
ejpam-6834	422	9	in	in	ADP
ejpam-6834	422	10	a	a	DET
ejpam-6834	422	11	small	small	ADJ
ejpam-6834	422	12	grocery	grocery	NOUN
ejpam-6834	422	13	order	order	NOUN
ejpam-6834	422	14	,	,	PUNCT
ejpam-6834	422	15	u	u	NOUN
ejpam-6834	422	16	=	=	NOUN
ejpam-6834	422	17	{	{	PUNCT
ejpam-6834	422	18	milk	milk	NOUN
ejpam-6834	422	19	,	,	PUNCT
ejpam-6834	422	20	lettuce	lettuce	NOUN
ejpam-6834	422	21	,	,	PUNCT
ejpam-6834	422	22	fish	fish	NOUN
ejpam-6834	422	23	}	}	PUNCT
ejpam-6834	422	24	,	,	PUNCT
ejpam-6834	422	25	and	and	CCONJ
ejpam-6834	422	26	take	take	VERB
ejpam-6834	422	27	a	a	DET
ejpam-6834	422	28	=	=	X
ejpam-6834	422	29	u	u	NOUN
ejpam-6834	422	30	.	.	PUNCT
ejpam-6834	423	1	fix	fix	VERB
ejpam-6834	423	2	m	m	NOUN
ejpam-6834	423	3	=	=	SYM
ejpam-6834	423	4	n	n	PROPN
ejpam-6834	423	5	=	=	SYM
ejpam-6834	423	6	1	1	X
ejpam-6834	423	7	.	.	PUNCT
ejpam-6834	424	1	we	we	PRON
ejpam-6834	424	2	interpret	interpret	VERB
ejpam-6834	424	3	τ	τ	PROPN
ejpam-6834	424	4	:	:	PUNCT
ejpam-6834	424	5	p1(a	p1(a	NOUN
ejpam-6834	424	6	)	)	PUNCT
ejpam-6834	424	7	=	=	SYM
ejpam-6834	424	8	p(a	p(a	NOUN
ejpam-6834	424	9	)	)	PUNCT
ejpam-6834	424	10	−→	−→	NOUN
ejpam-6834	424	11	p1([0	p1([0	NOUN
ejpam-6834	424	12	,	,	PUNCT
ejpam-6834	424	13	1	1	NUM
ejpam-6834	424	14	]	]	PUNCT
ejpam-6834	424	15	)	)	PUNCT
ejpam-6834	424	16	=	=	SYM
ejpam-6834	424	17	p([0	p([0	PROPN
ejpam-6834	424	18	,	,	PUNCT
ejpam-6834	424	19	1	1	NUM
ejpam-6834	424	20	]	]	PUNCT
ejpam-6834	424	21	)	)	PUNCT
ejpam-6834	424	22	so	so	SCONJ
ejpam-6834	424	23	that	that	SCONJ
ejpam-6834	424	24	,	,	PUNCT
ejpam-6834	424	25	for	for	ADP
ejpam-6834	424	26	each	each	DET
ejpam-6834	424	27	subset	subset	NOUN
ejpam-6834	424	28	x	x	PUNCT
ejpam-6834	424	29	⊆	⊆	NUM
ejpam-6834	424	30	a	a	PRON
ejpam-6834	424	31	,	,	PUNCT
ejpam-6834	424	32	the	the	DET
ejpam-6834	424	33	value	value	NOUN
ejpam-6834	424	34	τ(x	τ(x	NOUN
ejpam-6834	424	35	)	)	PUNCT
ejpam-6834	424	36	⊆	⊆	NUM
ejpam-6834	425	1	[	[	X
ejpam-6834	425	2	0	0	NUM
ejpam-6834	425	3	,	,	PUNCT
ejpam-6834	425	4	1	1	NUM
ejpam-6834	425	5	]	]	PUNCT
ejpam-6834	425	6	is	be	AUX
ejpam-6834	425	7	a	a	DET
ejpam-6834	425	8	set	set	NOUN
ejpam-6834	425	9	of	of	ADP
ejpam-6834	425	10	plausible	plausible	ADJ
ejpam-6834	425	11	freshness	freshness	NOUN
ejpam-6834	425	12	degrees	degree	NOUN
ejpam-6834	425	13	for	for	ADP
ejpam-6834	425	14	the	the	DET
ejpam-6834	425	15	delivery	delivery	NOUN
ejpam-6834	425	16	(	(	PUNCT
ejpam-6834	425	17	aggregating	aggregate	VERB
ejpam-6834	425	18	uncertainty	uncertainty	NOUN
ejpam-6834	425	19	from	from	ADP
ejpam-6834	425	20	traffic	traffic	NOUN
ejpam-6834	425	21	,	,	PUNCT
ejpam-6834	425	22	temperature	temperature	NOUN
ejpam-6834	425	23	,	,	PUNCT
ejpam-6834	425	24	and	and	CCONJ
ejpam-6834	425	25	handling	handling	NOUN
ejpam-6834	425	26	)	)	PUNCT
ejpam-6834	425	27	.	.	PUNCT
ejpam-6834	426	1	concretely	concretely	ADV
ejpam-6834	426	2	,	,	PUNCT
ejpam-6834	426	3	define	define	VERB
ejpam-6834	426	4	τ(∅	τ(∅	NOUN
ejpam-6834	426	5	)	)	PUNCT
ejpam-6834	426	6	=	=	PRON
ejpam-6834	426	7	{	{	PUNCT
ejpam-6834	426	8	0	0	NUM
ejpam-6834	426	9	}	}	PUNCT
ejpam-6834	426	10	,	,	PUNCT
ejpam-6834	426	11	τ({milk	τ({milk	NOUN
ejpam-6834	426	12	}	}	PUNCT
ejpam-6834	426	13	)	)	PUNCT
ejpam-6834	427	1	=	=	PUNCT
ejpam-6834	428	1	[	[	X
ejpam-6834	428	2	0.60	0.60	NUM
ejpam-6834	428	3	,	,	PUNCT
ejpam-6834	428	4	0.80	0.80	NUM
ejpam-6834	428	5	]	]	PUNCT
ejpam-6834	428	6	,	,	PUNCT
ejpam-6834	428	7	τ({lettuce	τ({lettuce	X
ejpam-6834	428	8	}	}	PUNCT
ejpam-6834	428	9	)	)	PUNCT
ejpam-6834	429	1	=	=	PUNCT
ejpam-6834	430	1	[	[	X
ejpam-6834	430	2	0.50	0.50	NUM
ejpam-6834	430	3	,	,	PUNCT
ejpam-6834	430	4	0.70	0.70	NUM
ejpam-6834	430	5	]	]	PUNCT
ejpam-6834	430	6	,	,	PUNCT
ejpam-6834	430	7	τ({fish	τ({fish	ADJ
ejpam-6834	430	8	}	}	PUNCT
ejpam-6834	430	9	)	)	PUNCT
ejpam-6834	431	1	=	=	PUNCT
ejpam-6834	432	1	[	[	X
ejpam-6834	432	2	0.40	0.40	NUM
ejpam-6834	432	3	,	,	PUNCT
ejpam-6834	432	4	0.60	0.60	NUM
ejpam-6834	432	5	]	]	PUNCT
ejpam-6834	432	6	,	,	PUNCT
ejpam-6834	432	7	τ({milk	τ({milk	NOUN
ejpam-6834	432	8	,	,	PUNCT
ejpam-6834	432	9	lettuce	lettuce	NOUN
ejpam-6834	432	10	}	}	PUNCT
ejpam-6834	432	11	)	)	PUNCT
ejpam-6834	433	1	=	=	PUNCT
ejpam-6834	434	1	[	[	X
ejpam-6834	434	2	0.55	0.55	NUM
ejpam-6834	434	3	,	,	PUNCT
ejpam-6834	434	4	0.75	0.75	NUM
ejpam-6834	434	5	]	]	PUNCT
ejpam-6834	434	6	,	,	PUNCT
ejpam-6834	434	7	τ({milk	τ({milk	NOUN
ejpam-6834	434	8	,	,	PUNCT
ejpam-6834	434	9	fish	fish	NOUN
ejpam-6834	434	10	}	}	PUNCT
ejpam-6834	434	11	)	)	PUNCT
ejpam-6834	435	1	=	=	PUNCT
ejpam-6834	436	1	[	[	X
ejpam-6834	436	2	0.45	0.45	NUM
ejpam-6834	436	3	,	,	PUNCT
ejpam-6834	436	4	0.65	0.65	NUM
ejpam-6834	436	5	]	]	PUNCT
ejpam-6834	436	6	,	,	PUNCT
ejpam-6834	436	7	τ({lettuce	τ({lettuce	NOUN
ejpam-6834	436	8	,	,	PUNCT
ejpam-6834	436	9	fish	fish	NOUN
ejpam-6834	436	10	}	}	PUNCT
ejpam-6834	436	11	)	)	PUNCT
ejpam-6834	437	1	=	=	PUNCT
ejpam-6834	438	1	[	[	X
ejpam-6834	438	2	0.40	0.40	NUM
ejpam-6834	438	3	,	,	PUNCT
ejpam-6834	438	4	0.60	0.60	NUM
ejpam-6834	438	5	]	]	PUNCT
ejpam-6834	438	6	,	,	PUNCT
ejpam-6834	438	7	τ({milk	τ({milk	NOUN
ejpam-6834	438	8	,	,	PUNCT
ejpam-6834	438	9	lettuce	lettuce	NOUN
ejpam-6834	438	10	,	,	PUNCT
ejpam-6834	438	11	fish	fish	NOUN
ejpam-6834	438	12	}	}	PUNCT
ejpam-6834	438	13	)	)	PUNCT
ejpam-6834	439	1	=	=	PUNCT
ejpam-6834	440	1	[	[	X
ejpam-6834	440	2	0.35	0.35	NUM
ejpam-6834	440	3	,	,	PUNCT
ejpam-6834	440	4	0.55	0.55	NUM
ejpam-6834	440	5	]	]	PUNCT
ejpam-6834	440	6	.	.	PUNCT
ejpam-6834	441	1	each	each	DET
ejpam-6834	441	2	image	image	NOUN
ejpam-6834	441	3	is	be	AUX
ejpam-6834	441	4	a	a	DET
ejpam-6834	441	5	nonempty	nonempty	ADJ
ejpam-6834	441	6	subset	subset	NOUN
ejpam-6834	441	7	of	of	ADP
ejpam-6834	441	8	[	[	X
ejpam-6834	441	9	0	0	NUM
ejpam-6834	441	10	,	,	PUNCT
ejpam-6834	441	11	1	1	NUM
ejpam-6834	441	12	]	]	PUNCT
ejpam-6834	441	13	,	,	PUNCT
ejpam-6834	441	14	so	so	ADV
ejpam-6834	441	15	τ	τ	PROPN
ejpam-6834	441	16	is	be	AUX
ejpam-6834	441	17	an	an	DET
ejpam-6834	441	18	(	(	PUNCT
ejpam-6834	441	19	1	1	NUM
ejpam-6834	441	20	,	,	PUNCT
ejpam-6834	441	21	1)-superhyperfuzzy	1)-superhyperfuzzy	NUM
ejpam-6834	441	22	set	set	NOUN
ejpam-6834	441	23	.	.	PUNCT
ejpam-6834	442	1	intervals	interval	NOUN
ejpam-6834	442	2	narrow	narrow	VERB
ejpam-6834	442	3	or	or	CCONJ
ejpam-6834	442	4	widen	widen	VERB
ejpam-6834	442	5	to	to	PART
ejpam-6834	442	6	encode	encode	VERB
ejpam-6834	442	7	uncertainty	uncertainty	NOUN
ejpam-6834	442	8	(	(	PUNCT
ejpam-6834	442	9	e.g.	e.g.	ADV
ejpam-6834	442	10	,	,	PUNCT
ejpam-6834	442	11	fish	fish	NOUN
ejpam-6834	442	12	is	be	AUX
ejpam-6834	442	13	more	more	ADJ
ejpam-6834	442	14	temperature	temperature	NOUN
ejpam-6834	442	15	–	–	PUNCT
ejpam-6834	442	16	sensitive	sensitive	ADJ
ejpam-6834	442	17	,	,	PUNCT
ejpam-6834	442	18	hence	hence	ADV
ejpam-6834	442	19	a	a	DET
ejpam-6834	442	20	lower	low	ADJ
ejpam-6834	442	21	range	range	NOUN
ejpam-6834	442	22	;	;	PUNCT
ejpam-6834	442	23	mixing	mix	VERB
ejpam-6834	442	24	sensitive	sensitive	ADJ
ejpam-6834	442	25	items	item	NOUN
ejpam-6834	442	26	widens	widen	VERB
ejpam-6834	442	27	risk	risk	NOUN
ejpam-6834	442	28	and	and	CCONJ
ejpam-6834	442	29	lowers	lower	VERB
ejpam-6834	442	30	the	the	DET
ejpam-6834	442	31	aggregated	aggregated	ADJ
ejpam-6834	442	32	plausibility	plausibility	NOUN
ejpam-6834	442	33	of	of	ADP
ejpam-6834	442	34	“	"	PUNCT
ejpam-6834	442	35	fresh	fresh	ADJ
ejpam-6834	442	36	on	on	ADP
ejpam-6834	442	37	arrival	arrival	NOUN
ejpam-6834	442	38	”	"	PUNCT
ejpam-6834	442	39	)	)	PUNCT
ejpam-6834	442	40	.	.	PUNCT
ejpam-6834	443	1	notation	notation	NOUN
ejpam-6834	443	2	1	1	NUM
ejpam-6834	443	3	(	(	PUNCT
ejpam-6834	443	4	iterated	iterate	VERB
ejpam-6834	443	5	embeddings	embedding	NOUN
ejpam-6834	443	6	and	and	CCONJ
ejpam-6834	443	7	flattenings	flattening	NOUN
ejpam-6834	443	8	)	)	PUNCT
ejpam-6834	443	9	.	.	PUNCT
ejpam-6834	444	1	for	for	ADP
ejpam-6834	444	2	a	a	DET
ejpam-6834	444	3	set	set	NOUN
ejpam-6834	444	4	s	s	PART
ejpam-6834	444	5	and	and	CCONJ
ejpam-6834	444	6	integers	integer	NOUN
ejpam-6834	444	7	r	r	NOUN
ejpam-6834	444	8	≤	≤	NUM
ejpam-6834	444	9	s	s	VERB
ejpam-6834	444	10	with	with	ADP
ejpam-6834	444	11	r	r	NOUN
ejpam-6834	444	12	≥	≥	NUM
ejpam-6834	444	13	1	1	NUM
ejpam-6834	444	14	,	,	PUNCT
ejpam-6834	444	15	define	define	VERB
ejpam-6834	444	16	the	the	DET
ejpam-6834	444	17	canonical	canonical	NOUN
ejpam-6834	444	18	embedding	embed	VERB
ejpam-6834	444	19	ιr→s	ιr→s	NOUN
ejpam-6834	444	20	:	:	PUNCT
ejpam-6834	444	21	p	p	X
ejpam-6834	444	22	r(s	r(s	NOUN
ejpam-6834	444	23	)	)	PUNCT
ejpam-6834	444	24	−→	−→	NOUN
ejpam-6834	444	25	p	p	PROPN
ejpam-6834	444	26	s(s	s(s	PROPN
ejpam-6834	444	27	)	)	PUNCT
ejpam-6834	444	28	t.	t.	PROPN
ejpam-6834	444	29	fujita	fujita	PROPN
ejpam-6834	444	30	,	,	PUNCT
ejpam-6834	444	31	f.smarandache	f.smarandache	NOUN
ejpam-6834	444	32	/	/	SYM
ejpam-6834	444	33	eur	eur	PROPN
ejpam-6834	444	34	.	.	PUNCT
ejpam-6834	445	1	j.	j.	PROPN
ejpam-6834	445	2	pure	pure	PROPN
ejpam-6834	445	3	appl	appl	PROPN
ejpam-6834	445	4	.	.	PROPN
ejpam-6834	445	5	math	math	PROPN
ejpam-6834	445	6	,	,	PUNCT
ejpam-6834	445	7	18	18	NUM
ejpam-6834	445	8	(	(	PUNCT
ejpam-6834	445	9	4	4	NUM
ejpam-6834	445	10	)	)	PUNCT
ejpam-6834	445	11	(	(	PUNCT
ejpam-6834	445	12	2025	2025	NUM
ejpam-6834	445	13	)	)	PUNCT
ejpam-6834	445	14	,	,	PUNCT
ejpam-6834	445	15	6834	6834	NUM
ejpam-6834	445	16	22	22	NUM
ejpam-6834	445	17	of	of	ADP
ejpam-6834	445	18	69	69	NUM
ejpam-6834	445	19	recursively	recursively	ADV
ejpam-6834	445	20	by	by	ADP
ejpam-6834	445	21	ιr→r	ιr→r	PUNCT
ejpam-6834	446	1	=	=	PUNCT
ejpam-6834	446	2	i	i	PROPN
ejpam-6834	446	3	d	d	PROPN
ejpam-6834	446	4	and	and	CCONJ
ejpam-6834	446	5	ιr→(t+1)(x	ιr→(t+1)(x	PROPN
ejpam-6834	446	6	)	)	PUNCT
ejpam-6834	447	1	=	=	PRON
ejpam-6834	447	2	{	{	PUNCT
ejpam-6834	447	3	ιr→t(x	ιr→t(x	NOUN
ejpam-6834	447	4	)	)	PUNCT
ejpam-6834	447	5	}	}	PUNCT
ejpam-6834	447	6	(	(	PUNCT
ejpam-6834	447	7	t	t	PROPN
ejpam-6834	447	8	≥	≥	PROPN
ejpam-6834	447	9	r	r	NOUN
ejpam-6834	447	10	)	)	PUNCT
ejpam-6834	447	11	.	.	PUNCT
ejpam-6834	448	1	thus	thus	ADV
ejpam-6834	448	2	ιr→s	ιr→s	ADP
ejpam-6834	448	3	nests	nest	NOUN
ejpam-6834	448	4	x	x	PUNCT
ejpam-6834	448	5	inside	inside	ADP
ejpam-6834	448	6	s−	s−	PROPN
ejpam-6834	448	7	r	r	VERB
ejpam-6834	448	8	successive	successive	ADJ
ejpam-6834	448	9	singletons	singleton	NOUN
ejpam-6834	448	10	.	.	PUNCT
ejpam-6834	449	1	for	for	ADP
ejpam-6834	449	2	a	a	DET
ejpam-6834	449	3	set	set	NOUN
ejpam-6834	449	4	s	s	PART
ejpam-6834	449	5	and	and	CCONJ
ejpam-6834	449	6	integers	integer	NOUN
ejpam-6834	449	7	s	s	PART
ejpam-6834	449	8	>	>	X
ejpam-6834	449	9	r	r	NOUN
ejpam-6834	449	10	≥	≥	NOUN
ejpam-6834	449	11	0	0	NUM
ejpam-6834	449	12	,	,	PUNCT
ejpam-6834	449	13	define	define	VERB
ejpam-6834	449	14	the	the	DET
ejpam-6834	449	15	level	level	NOUN
ejpam-6834	449	16	-	-	PUNCT
ejpam-6834	449	17	flattening	flattening	NOUN
ejpam-6834	449	18	(	(	PUNCT
ejpam-6834	449	19	union	union	NOUN
ejpam-6834	449	20	)	)	PUNCT
ejpam-6834	449	21	map	map	NOUN
ejpam-6834	449	22	us→r	us→r	NOUN
ejpam-6834	450	1	:	:	PUNCT
ejpam-6834	450	2	p	p	PROPN
ejpam-6834	450	3	s(s	s(s	PROPN
ejpam-6834	450	4	)	)	PUNCT
ejpam-6834	451	1	−→	−→	NOUN
ejpam-6834	451	2	p	p	PROPN
ejpam-6834	451	3	r(s	r(s	PROPN
ejpam-6834	451	4	)	)	PUNCT
ejpam-6834	451	5	by	by	ADP
ejpam-6834	451	6	us→(s−1)(y	us→(s−1)(y	PROPN
ejpam-6834	451	7	)	)	PUNCT
ejpam-6834	452	1	=	=	PUNCT
ejpam-6834	453	1	⋃	⋃	PUNCT
ejpam-6834	453	2	y	y	NOUN
ejpam-6834	453	3	and	and	CCONJ
ejpam-6834	453	4	,	,	PUNCT
ejpam-6834	453	5	for	for	ADP
ejpam-6834	453	6	r	r	NOUN
ejpam-6834	453	7	<	<	X
ejpam-6834	453	8	s	s	X
ejpam-6834	453	9	−	−	PROPN
ejpam-6834	453	10	1	1	NUM
ejpam-6834	453	11	,	,	PUNCT
ejpam-6834	453	12	by	by	ADP
ejpam-6834	453	13	us→r	us→r	NOUN
ejpam-6834	453	14	=	=	NOUN
ejpam-6834	453	15	u(r+1)→r	u(r+1)→r	NOUN
ejpam-6834	453	16	◦	◦	NOUN
ejpam-6834	453	17	·	·	PUNCT
ejpam-6834	453	18	·	·	PUNCT
ejpam-6834	453	19	·	·	PUNCT
ejpam-6834	453	20	◦	◦	NOUN
ejpam-6834	453	21	us→(s−1	us→(s−1	NOUN
ejpam-6834	453	22	)	)	PUNCT
ejpam-6834	453	23	.	.	PUNCT
ejpam-6834	454	1	when	when	SCONJ
ejpam-6834	454	2	s	s	VERB
ejpam-6834	454	3	=	=	PUNCT
ejpam-6834	455	1	[	[	X
ejpam-6834	455	2	0	0	NUM
ejpam-6834	455	3	,	,	PUNCT
ejpam-6834	455	4	1	1	NUM
ejpam-6834	455	5	]	]	PUNCT
ejpam-6834	455	6	,	,	PUNCT
ejpam-6834	455	7	nonemptiness	nonemptiness	PROPN
ejpam-6834	455	8	is	be	AUX
ejpam-6834	455	9	preserved	preserve	VERB
ejpam-6834	455	10	because	because	SCONJ
ejpam-6834	455	11	the	the	DET
ejpam-6834	455	12	families	family	NOUN
ejpam-6834	455	13	we	we	PRON
ejpam-6834	455	14	consider	consider	VERB
ejpam-6834	455	15	consist	consist	VERB
ejpam-6834	455	16	of	of	ADP
ejpam-6834	455	17	nonempty	nonempty	ADJ
ejpam-6834	455	18	members	member	NOUN
ejpam-6834	455	19	at	at	ADP
ejpam-6834	455	20	every	every	DET
ejpam-6834	455	21	level	level	NOUN
ejpam-6834	455	22	(	(	PUNCT
ejpam-6834	455	23	see	see	VERB
ejpam-6834	455	24	the	the	DET
ejpam-6834	455	25	definitions	definition	NOUN
ejpam-6834	455	26	of	of	ADP
ejpam-6834	455	27	superhyperfuzzy	superhyperfuzzy	ADJ
ejpam-6834	455	28	codomains	codomain	NOUN
ejpam-6834	455	29	used	use	VERB
ejpam-6834	455	30	in	in	ADP
ejpam-6834	455	31	this	this	DET
ejpam-6834	455	32	paper	paper	NOUN
ejpam-6834	455	33	)	)	PUNCT
ejpam-6834	455	34	.	.	PUNCT
ejpam-6834	456	1	theorem	theorem	NOUN
ejpam-6834	456	2	1	1	NUM
ejpam-6834	456	3	.	.	PUNCT
ejpam-6834	457	1	if	if	SCONJ
ejpam-6834	457	2	µ̃n	µ̃n	INTJ
ejpam-6834	457	3	:	:	PUNCT
ejpam-6834	457	4	p	p	X
ejpam-6834	457	5	n(x	n(x	PROPN
ejpam-6834	457	6	)	)	PUNCT
ejpam-6834	457	7	→	→	SYM
ejpam-6834	458	1	p	p	X
ejpam-6834	458	2	n([0	n([0	NOUN
ejpam-6834	458	3	,	,	PUNCT
ejpam-6834	458	4	1	1	NUM
ejpam-6834	458	5	]	]	PUNCT
ejpam-6834	458	6	)	)	PUNCT
ejpam-6834	458	7	is	be	AUX
ejpam-6834	458	8	an	an	DET
ejpam-6834	458	9	n	n	CCONJ
ejpam-6834	458	10	-	-	PUNCT
ejpam-6834	458	11	superhyperfuzzy	superhyperfuzzy	NOUN
ejpam-6834	458	12	set	set	NOUN
ejpam-6834	458	13	,	,	PUNCT
ejpam-6834	458	14	then	then	ADV
ejpam-6834	458	15	τ	τ	X
ejpam-6834	458	16	:	:	PUNCT
ejpam-6834	458	17	=	=	SYM
ejpam-6834	458	18	µ̃n	µ̃n	ADP
ejpam-6834	458	19	◦	◦	NOUN
ejpam-6834	458	20	ι1→n	ι1→n	INTJ
ejpam-6834	458	21	:	:	PUNCT
ejpam-6834	458	22	p	p	NOUN
ejpam-6834	458	23	1(x	1(x	NUM
ejpam-6834	458	24	)	)	PUNCT
ejpam-6834	458	25	−→	−→	NOUN
ejpam-6834	458	26	p	p	NOUN
ejpam-6834	458	27	n([0	n([0	NOUN
ejpam-6834	458	28	,	,	PUNCT
ejpam-6834	458	29	1	1	NUM
ejpam-6834	458	30	]	]	PUNCT
ejpam-6834	458	31	)	)	PUNCT
ejpam-6834	458	32	is	be	AUX
ejpam-6834	458	33	an	an	DET
ejpam-6834	458	34	(	(	PUNCT
ejpam-6834	458	35	1	1	NUM
ejpam-6834	458	36	,	,	PUNCT
ejpam-6834	458	37	n)-superhyperfuzzy	n)-superhyperfuzzy	PUNCT
ejpam-6834	458	38	set	set	NOUN
ejpam-6834	458	39	.	.	PUNCT
ejpam-6834	459	1	moreover	moreover	ADV
ejpam-6834	459	2	,	,	PUNCT
ejpam-6834	459	3	for	for	ADP
ejpam-6834	459	4	every	every	DET
ejpam-6834	459	5	z	z	NOUN
ejpam-6834	459	6	in	in	ADP
ejpam-6834	459	7	the	the	DET
ejpam-6834	459	8	image	image	NOUN
ejpam-6834	459	9	of	of	ADP
ejpam-6834	459	10	ι1→n	ι1→n	PROPN
ejpam-6834	459	11	,	,	PUNCT
ejpam-6834	459	12	writing	write	VERB
ejpam-6834	459	13	z	z	PROPN
ejpam-6834	459	14	=	=	SYM
ejpam-6834	459	15	ι1→n(a	ι1→n(a	PROPN
ejpam-6834	459	16	)	)	PUNCT
ejpam-6834	459	17	with	with	ADP
ejpam-6834	459	18	a	a	DET
ejpam-6834	459	19	∈	∈	PROPN
ejpam-6834	459	20	p(x	p(x	NOUN
ejpam-6834	459	21	)	)	PUNCT
ejpam-6834	459	22	,	,	PUNCT
ejpam-6834	459	23	one	one	PRON
ejpam-6834	459	24	has	have	VERB
ejpam-6834	459	25	τ(a	τ(a	NOUN
ejpam-6834	459	26	)	)	PUNCT
ejpam-6834	459	27	=	=	PUNCT
ejpam-6834	459	28	µ̃n(z	µ̃n(z	X
ejpam-6834	459	29	)	)	PUNCT
ejpam-6834	459	30	,	,	PUNCT
ejpam-6834	459	31	i.e.	i.e.	X
ejpam-6834	459	32	τ	τ	X
ejpam-6834	459	33	agrees	agree	VERB
ejpam-6834	459	34	with	with	ADP
ejpam-6834	459	35	µ̃n	µ̃n	NOUN
ejpam-6834	459	36	on	on	ADP
ejpam-6834	459	37	all	all	DET
ejpam-6834	459	38	level	level	NOUN
ejpam-6834	459	39	-	-	PUNCT
ejpam-6834	459	40	n	n	NOUN
ejpam-6834	459	41	inputs	input	NOUN
ejpam-6834	459	42	obtained	obtain	VERB
ejpam-6834	459	43	by	by	ADP
ejpam-6834	459	44	the	the	DET
ejpam-6834	459	45	canonical	canonical	NOUN
ejpam-6834	459	46	embedding	embed	VERB
ejpam-6834	459	47	from	from	ADP
ejpam-6834	459	48	level	level	NOUN
ejpam-6834	459	49	1	1	NUM
ejpam-6834	459	50	.	.	PUNCT
ejpam-6834	460	1	proof	proof	NOUN
ejpam-6834	460	2	.	.	PUNCT
ejpam-6834	461	1	by	by	ADP
ejpam-6834	461	2	hypothesis	hypothesis	NOUN
ejpam-6834	461	3	µ̃n	µ̃n	INTJ
ejpam-6834	461	4	has	have	AUX
ejpam-6834	461	5	codomain	codomain	NOUN
ejpam-6834	461	6	p	p	NOUN
ejpam-6834	461	7	n([0	n([0	NOUN
ejpam-6834	461	8	,	,	PUNCT
ejpam-6834	461	9	1	1	NUM
ejpam-6834	461	10	]	]	NUM
ejpam-6834	461	11	)	)	PUNCT
ejpam-6834	461	12	.	.	PUNCT
ejpam-6834	462	1	the	the	DET
ejpam-6834	462	2	canonical	canonical	NOUN
ejpam-6834	462	3	embedding	embed	VERB
ejpam-6834	462	4	ι1→n	ι1→n	X
ejpam-6834	462	5	:	:	PUNCT
ejpam-6834	462	6	p(x	p(x	PROPN
ejpam-6834	462	7	)	)	PUNCT
ejpam-6834	462	8	→	→	SYM
ejpam-6834	462	9	p	p	X
ejpam-6834	462	10	n(x	n(x	PROPN
ejpam-6834	462	11	)	)	PUNCT
ejpam-6834	462	12	is	be	AUX
ejpam-6834	462	13	well	well	ADV
ejpam-6834	462	14	-	-	PUNCT
ejpam-6834	462	15	defined	define	VERB
ejpam-6834	462	16	by	by	ADP
ejpam-6834	462	17	the	the	DET
ejpam-6834	462	18	recursion	recursion	NOUN
ejpam-6834	462	19	in	in	ADP
ejpam-6834	462	20	the	the	DET
ejpam-6834	462	21	notation	notation	NOUN
ejpam-6834	462	22	:	:	PUNCT
ejpam-6834	463	1	ι1→1	ι1→1	NOUN
ejpam-6834	463	2	=	=	PUNCT
ejpam-6834	463	3	i	i	PROPN
ejpam-6834	463	4	d	d	PROPN
ejpam-6834	463	5	and	and	CCONJ
ejpam-6834	463	6	ι1→(t+1)(a	ι1→(t+1)(a	NOUN
ejpam-6834	463	7	)	)	PUNCT
ejpam-6834	463	8	=	=	PRON
ejpam-6834	463	9	{	{	PUNCT
ejpam-6834	463	10	ι1→t(a	ι1→t(a	NOUN
ejpam-6834	463	11	)	)	PUNCT
ejpam-6834	463	12	}	}	PUNCT
ejpam-6834	463	13	for	for	ADP
ejpam-6834	463	14	t	t	PROPN
ejpam-6834	463	15	≥	≥	NUM
ejpam-6834	463	16	1	1	NUM
ejpam-6834	463	17	.	.	PUNCT
ejpam-6834	464	1	therefore	therefore	ADV
ejpam-6834	464	2	the	the	DET
ejpam-6834	464	3	composition	composition	NOUN
ejpam-6834	464	4	τ	τ	X
ejpam-6834	464	5	=	=	PUNCT
ejpam-6834	464	6	µ̃n	µ̃n	ADP
ejpam-6834	464	7	◦	◦	NOUN
ejpam-6834	464	8	ι1→n	ι1→n	INTJ
ejpam-6834	464	9	is	be	AUX
ejpam-6834	464	10	a	a	DET
ejpam-6834	464	11	map	map	NOUN
ejpam-6834	464	12	p(x	p(x	NOUN
ejpam-6834	464	13	)	)	PUNCT
ejpam-6834	464	14	→	→	SYM
ejpam-6834	464	15	p	p	X
ejpam-6834	464	16	n([0	n([0	NOUN
ejpam-6834	464	17	,	,	PUNCT
ejpam-6834	464	18	1	1	NUM
ejpam-6834	464	19	]	]	NUM
ejpam-6834	464	20	)	)	PUNCT
ejpam-6834	464	21	,	,	PUNCT
ejpam-6834	464	22	which	which	PRON
ejpam-6834	464	23	is	be	AUX
ejpam-6834	464	24	precisely	precisely	ADV
ejpam-6834	464	25	an	an	PRON
ejpam-6834	464	26	(	(	PUNCT
ejpam-6834	464	27	1	1	NUM
ejpam-6834	464	28	,	,	PUNCT
ejpam-6834	464	29	n)-superhyperfuzzy	n)-superhyperfuzzy	PUNCT
ejpam-6834	464	30	set	set	VERB
ejpam-6834	464	31	by	by	ADP
ejpam-6834	464	32	definition	definition	NOUN
ejpam-6834	464	33	.	.	PUNCT
ejpam-6834	465	1	for	for	ADP
ejpam-6834	465	2	the	the	DET
ejpam-6834	465	3	agreement	agreement	NOUN
ejpam-6834	465	4	statement	statement	NOUN
ejpam-6834	465	5	,	,	PUNCT
ejpam-6834	465	6	take	take	VERB
ejpam-6834	465	7	any	any	DET
ejpam-6834	465	8	z	z	NOUN
ejpam-6834	465	9	in	in	ADP
ejpam-6834	465	10	the	the	DET
ejpam-6834	465	11	image	image	NOUN
ejpam-6834	465	12	of	of	ADP
ejpam-6834	465	13	ι1→n	ι1→n	SYM
ejpam-6834	465	14	,	,	PUNCT
ejpam-6834	465	15	so	so	SCONJ
ejpam-6834	465	16	z	z	NOUN
ejpam-6834	465	17	=	=	SYM
ejpam-6834	465	18	ι1→n(a	ι1→n(a	NOUN
ejpam-6834	465	19	)	)	PUNCT
ejpam-6834	465	20	for	for	ADP
ejpam-6834	465	21	some	some	PRON
ejpam-6834	465	22	a	a	DET
ejpam-6834	465	23	∈	∈	PROPN
ejpam-6834	465	24	p(x	p(x	NOUN
ejpam-6834	465	25	)	)	PUNCT
ejpam-6834	465	26	.	.	PUNCT
ejpam-6834	466	1	then	then	ADV
ejpam-6834	466	2	by	by	ADP
ejpam-6834	466	3	construction	construction	NOUN
ejpam-6834	466	4	τ(a	τ(a	NOUN
ejpam-6834	466	5	)	)	PUNCT
ejpam-6834	466	6	=	=	PUNCT
ejpam-6834	466	7	µ̃n	µ̃n	INTJ
ejpam-6834	466	8	(	(	PUNCT
ejpam-6834	466	9	ι1→n(a	ι1→n(a	NOUN
ejpam-6834	466	10	)	)	PUNCT
ejpam-6834	466	11	)	)	PUNCT
ejpam-6834	467	1	=	=	SYM
ejpam-6834	467	2	µ̃n(z	µ̃n(z	X
ejpam-6834	467	3	)	)	PUNCT
ejpam-6834	467	4	,	,	PUNCT
ejpam-6834	467	5	which	which	PRON
ejpam-6834	467	6	establishes	establish	VERB
ejpam-6834	467	7	that	that	SCONJ
ejpam-6834	467	8	τ	τ	PROPN
ejpam-6834	467	9	reproduces	reproduce	VERB
ejpam-6834	467	10	µ̃n	µ̃n	VERB
ejpam-6834	467	11	on	on	ADP
ejpam-6834	467	12	those	those	DET
ejpam-6834	467	13	level	level	NOUN
ejpam-6834	467	14	-	-	PUNCT
ejpam-6834	467	15	n	n	NOUN
ejpam-6834	467	16	elements	element	NOUN
ejpam-6834	467	17	canonically	canonically	ADV
ejpam-6834	467	18	obtained	obtain	VERB
ejpam-6834	467	19	from	from	ADP
ejpam-6834	467	20	level	level	NOUN
ejpam-6834	467	21	1	1	NUM
ejpam-6834	467	22	.	.	PUNCT
ejpam-6834	467	23	theorem	theorem	NOUN
ejpam-6834	467	24	2	2	NUM
ejpam-6834	467	25	(	(	PUNCT
ejpam-6834	467	26	restriction	restriction	NOUN
ejpam-6834	467	27	to	to	PART
ejpam-6834	467	28	lower	low	ADJ
ejpam-6834	467	29	m	m	NOUN
ejpam-6834	467	30	)	)	PUNCT
ejpam-6834	467	31	.	.	PUNCT
ejpam-6834	468	1	let	let	VERB
ejpam-6834	469	1	τ	τ	PROPN
ejpam-6834	469	2	:	:	PUNCT
ejpam-6834	469	3	p	p	PROPN
ejpam-6834	469	4	m(a	m(a	PROPN
ejpam-6834	469	5	)	)	PUNCT
ejpam-6834	469	6	→	→	SYM
ejpam-6834	469	7	p	p	X
ejpam-6834	469	8	n([0	n([0	NOUN
ejpam-6834	469	9	,	,	PUNCT
ejpam-6834	469	10	1	1	NUM
ejpam-6834	469	11	]	]	PUNCT
ejpam-6834	469	12	)	)	PUNCT
ejpam-6834	469	13	be	be	AUX
ejpam-6834	469	14	an	an	DET
ejpam-6834	469	15	(	(	PUNCT
ejpam-6834	469	16	m	m	PROPN
ejpam-6834	469	17	,	,	PUNCT
ejpam-6834	469	18	n)superhyperfuzzy	n)superhyperfuzzy	ADV
ejpam-6834	469	19	set	set	VERB
ejpam-6834	469	20	and	and	CCONJ
ejpam-6834	469	21	let	let	VERB
ejpam-6834	469	22	m′	m′	NOUN
ejpam-6834	469	23	satisfy	satisfy	VERB
ejpam-6834	469	24	0	0	NUM
ejpam-6834	469	25	≤	≤	NUM
ejpam-6834	469	26	m′	m′	NOUN
ejpam-6834	469	27	<	<	X
ejpam-6834	469	28	m.	m.	NOUN
ejpam-6834	469	29	define	define	VERB
ejpam-6834	469	30	the	the	DET
ejpam-6834	469	31	inclusion	inclusion	NOUN
ejpam-6834	469	32	ιm′→m	ιm′→m	NOUN
ejpam-6834	469	33	:	:	PUNCT
ejpam-6834	469	34	p	p	X
ejpam-6834	469	35	m′	m′	NOUN
ejpam-6834	469	36	(	(	PUNCT
ejpam-6834	469	37	a	a	NOUN
ejpam-6834	469	38	)	)	PUNCT
ejpam-6834	469	39	↪	↪	PROPN
ejpam-6834	469	40	→	→	SYM
ejpam-6834	469	41	p	p	NOUN
ejpam-6834	469	42	m(a	m(a	PROPN
ejpam-6834	469	43	)	)	PUNCT
ejpam-6834	469	44	,	,	PUNCT
ejpam-6834	469	45	ιm′→m	ιm′→m	PUNCT
ejpam-6834	469	46	=	=	PUNCT
ejpam-6834	469	47	ι(m−1)→m	ι(m−1)→m	PROPN
ejpam-6834	469	48	◦	◦	NOUN
ejpam-6834	469	49	·	·	PUNCT
ejpam-6834	469	50	·	·	PUNCT
ejpam-6834	469	51	·	·	PUNCT
ejpam-6834	470	1	◦	◦	NOUN
ejpam-6834	470	2	ιm′→(m′+1	ιm′→(m′+1	NOUN
ejpam-6834	470	3	)	)	PUNCT
ejpam-6834	470	4	,	,	PUNCT
ejpam-6834	470	5	where	where	SCONJ
ejpam-6834	470	6	each	each	DET
ejpam-6834	470	7	step	step	NOUN
ejpam-6834	470	8	ιt→(t+1)(x	ιt→(t+1)(x	NOUN
ejpam-6834	470	9	)	)	PUNCT
ejpam-6834	470	10	=	=	PRON
ejpam-6834	470	11	{	{	PUNCT
ejpam-6834	470	12	x	x	NOUN
ejpam-6834	470	13	}	}	PUNCT
ejpam-6834	470	14	.	.	PUNCT
ejpam-6834	471	1	then	then	ADV
ejpam-6834	471	2	τ	τ	X
ejpam-6834	471	3	′	′	NUM
ejpam-6834	471	4	=	=	PUNCT
ejpam-6834	471	5	τ	τ	PROPN
ejpam-6834	471	6	◦	◦	NOUN
ejpam-6834	471	7	ιm′→m	ιm′→m	NOUN
ejpam-6834	471	8	:	:	PUNCT
ejpam-6834	471	9	p	p	X
ejpam-6834	471	10	m′	m′	NOUN
ejpam-6834	471	11	(	(	PUNCT
ejpam-6834	471	12	a	a	X
ejpam-6834	471	13	)	)	PUNCT
ejpam-6834	471	14	−→	−→	NOUN
ejpam-6834	471	15	p	p	X
ejpam-6834	471	16	n([0	n([0	NOUN
ejpam-6834	471	17	,	,	PUNCT
ejpam-6834	471	18	1	1	NUM
ejpam-6834	471	19	]	]	PUNCT
ejpam-6834	471	20	)	)	PUNCT
ejpam-6834	471	21	is	be	AUX
ejpam-6834	471	22	an	an	DET
ejpam-6834	471	23	(	(	PUNCT
ejpam-6834	471	24	m′	m′	NUM
ejpam-6834	471	25	,	,	PUNCT
ejpam-6834	471	26	n)-superhyperfuzzy	n)-superhyperfuzzy	PUNCT
ejpam-6834	471	27	set	set	NOUN
ejpam-6834	471	28	.	.	PUNCT
ejpam-6834	472	1	t.	t.	PROPN
ejpam-6834	472	2	fujita	fujita	PROPN
ejpam-6834	472	3	,	,	PUNCT
ejpam-6834	472	4	f.smarandache	f.smarandache	NOUN
ejpam-6834	472	5	/	/	SYM
ejpam-6834	472	6	eur	eur	PROPN
ejpam-6834	472	7	.	.	PUNCT
ejpam-6834	473	1	j.	j.	PROPN
ejpam-6834	473	2	pure	pure	PROPN
ejpam-6834	473	3	appl	appl	PROPN
ejpam-6834	473	4	.	.	PROPN
ejpam-6834	473	5	math	math	PROPN
ejpam-6834	473	6	,	,	PUNCT
ejpam-6834	473	7	18	18	NUM
ejpam-6834	473	8	(	(	PUNCT
ejpam-6834	473	9	4	4	NUM
ejpam-6834	473	10	)	)	PUNCT
ejpam-6834	473	11	(	(	PUNCT
ejpam-6834	473	12	2025	2025	NUM
ejpam-6834	473	13	)	)	PUNCT
ejpam-6834	473	14	,	,	PUNCT
ejpam-6834	473	15	6834	6834	NUM
ejpam-6834	473	16	23	23	NUM
ejpam-6834	473	17	of	of	ADP
ejpam-6834	473	18	69	69	NUM
ejpam-6834	473	19	proof	proof	NOUN
ejpam-6834	473	20	.	.	PUNCT
ejpam-6834	474	1	fix	fix	VERB
ejpam-6834	474	2	x	x	X
ejpam-6834	474	3	∈	∈	PROPN
ejpam-6834	474	4	p	p	NOUN
ejpam-6834	474	5	m′	m′	NOUN
ejpam-6834	474	6	(	(	PUNCT
ejpam-6834	474	7	a	a	NOUN
ejpam-6834	474	8	)	)	PUNCT
ejpam-6834	474	9	.	.	PUNCT
ejpam-6834	475	1	by	by	ADP
ejpam-6834	475	2	construction	construction	NOUN
ejpam-6834	475	3	ιm′→m(x	ιm′→m(x	PROPN
ejpam-6834	475	4	)	)	PUNCT
ejpam-6834	475	5	∈	∈	PROPN
ejpam-6834	475	6	p	p	PROPN
ejpam-6834	475	7	m(a	m(a	PROPN
ejpam-6834	475	8	)	)	PUNCT
ejpam-6834	475	9	,	,	PUNCT
ejpam-6834	475	10	so	so	ADV
ejpam-6834	475	11	τ	τ	PROPN
ejpam-6834	475	12	(	(	PUNCT
ejpam-6834	475	13	ιm′→m(x	ιm′→m(x	PROPN
ejpam-6834	475	14	)	)	PUNCT
ejpam-6834	475	15	)	)	PUNCT
ejpam-6834	476	1	∈	∈	PROPN
ejpam-6834	476	2	p	p	NOUN
ejpam-6834	476	3	n([0	n([0	PROPN
ejpam-6834	476	4	,	,	PUNCT
ejpam-6834	476	5	1	1	NUM
ejpam-6834	476	6	]	]	NUM
ejpam-6834	476	7	)	)	PUNCT
ejpam-6834	476	8	.	.	PUNCT
ejpam-6834	477	1	hence	hence	ADV
ejpam-6834	477	2	τ	τ	PROPN
ejpam-6834	477	3	′	′	NOUN
ejpam-6834	477	4	is	be	AUX
ejpam-6834	477	5	well	well	ADV
ejpam-6834	477	6	-	-	PUNCT
ejpam-6834	477	7	defined	define	VERB
ejpam-6834	477	8	with	with	ADP
ejpam-6834	477	9	the	the	DET
ejpam-6834	477	10	required	require	VERB
ejpam-6834	477	11	codomain	codomain	NOUN
ejpam-6834	477	12	.	.	PUNCT
ejpam-6834	478	1	no	no	DET
ejpam-6834	478	2	additional	additional	ADJ
ejpam-6834	478	3	axioms	axiom	NOUN
ejpam-6834	478	4	are	be	AUX
ejpam-6834	478	5	needed	need	VERB
ejpam-6834	478	6	,	,	PUNCT
ejpam-6834	478	7	so	so	ADV
ejpam-6834	478	8	τ	τ	PROPN
ejpam-6834	478	9	′	′	NOUN
ejpam-6834	478	10	is	be	AUX
ejpam-6834	478	11	an	an	DET
ejpam-6834	478	12	(	(	PUNCT
ejpam-6834	478	13	m′	m′	NUM
ejpam-6834	478	14	,	,	PUNCT
ejpam-6834	478	15	n)-superhyperfuzzy	n)-superhyperfuzzy	PUNCT
ejpam-6834	478	16	set	set	NOUN
ejpam-6834	478	17	.	.	PUNCT
ejpam-6834	479	1	theorem	theorem	ADJ
ejpam-6834	479	2	3	3	NUM
ejpam-6834	479	3	(	(	PUNCT
ejpam-6834	479	4	projection	projection	NOUN
ejpam-6834	479	5	to	to	PART
ejpam-6834	479	6	lower	low	ADJ
ejpam-6834	479	7	n	n	CCONJ
ejpam-6834	479	8	)	)	PUNCT
ejpam-6834	479	9	.	.	PUNCT
ejpam-6834	480	1	let	let	VERB
ejpam-6834	481	1	τ	τ	PROPN
ejpam-6834	481	2	:	:	PUNCT
ejpam-6834	481	3	p	p	PROPN
ejpam-6834	481	4	m(a	m(a	PROPN
ejpam-6834	481	5	)	)	PUNCT
ejpam-6834	481	6	→	→	SYM
ejpam-6834	481	7	p	p	X
ejpam-6834	481	8	n([0	n([0	NOUN
ejpam-6834	481	9	,	,	PUNCT
ejpam-6834	481	10	1	1	NUM
ejpam-6834	481	11	]	]	PUNCT
ejpam-6834	481	12	)	)	PUNCT
ejpam-6834	481	13	be	be	AUX
ejpam-6834	481	14	an	an	DET
ejpam-6834	481	15	(	(	PUNCT
ejpam-6834	481	16	m	m	NOUN
ejpam-6834	481	17	,	,	PUNCT
ejpam-6834	481	18	n)-superhyperfuzzy	n)-superhyperfuzzy	PUNCT
ejpam-6834	481	19	set	set	VERB
ejpam-6834	481	20	and	and	CCONJ
ejpam-6834	481	21	let	let	VERB
ejpam-6834	481	22	n′	n′	NOUN
ejpam-6834	481	23	satisfy	satisfy	VERB
ejpam-6834	481	24	0	0	NUM
ejpam-6834	481	25	≤	≤	NOUN
ejpam-6834	481	26	n′	n′	NOUN
ejpam-6834	481	27	<	<	X
ejpam-6834	481	28	n.	n.	NOUN
ejpam-6834	481	29	define	define	VERB
ejpam-6834	481	30	the	the	DET
ejpam-6834	481	31	level	level	NOUN
ejpam-6834	481	32	-	-	PUNCT
ejpam-6834	481	33	flattening	flattening	NOUN
ejpam-6834	481	34	map	map	NOUN
ejpam-6834	481	35	πn→n′	πn→n′	X
ejpam-6834	481	36	:	:	PUNCT
ejpam-6834	482	1	=	=	PUNCT
ejpam-6834	482	2	un→n′	un→n′	NOUN
ejpam-6834	482	3	:	:	PUNCT
ejpam-6834	482	4	p	p	NOUN
ejpam-6834	482	5	n([0	n([0	NOUN
ejpam-6834	482	6	,	,	PUNCT
ejpam-6834	482	7	1	1	NUM
ejpam-6834	482	8	]	]	PUNCT
ejpam-6834	482	9	)	)	PUNCT
ejpam-6834	483	1	−→	−→	NOUN
ejpam-6834	483	2	p	p	NOUN
ejpam-6834	483	3	n′	n′	PROPN
ejpam-6834	483	4	(	(	PUNCT
ejpam-6834	483	5	[	[	X
ejpam-6834	483	6	0	0	NUM
ejpam-6834	483	7	,	,	PUNCT
ejpam-6834	483	8	1	1	NUM
ejpam-6834	483	9	]	]	NUM
ejpam-6834	483	10	)	)	PUNCT
ejpam-6834	484	1	,	,	PUNCT
ejpam-6834	484	2	i.e.	i.e.	X
ejpam-6834	484	3	iterated	iterated	ADJ
ejpam-6834	484	4	unions	union	NOUN
ejpam-6834	484	5	taken	take	VERB
ejpam-6834	484	6	(	(	PUNCT
ejpam-6834	484	7	n−	n−	NOUN
ejpam-6834	484	8	n′	n′	ADJ
ejpam-6834	484	9	)	)	PUNCT
ejpam-6834	484	10	times	time	NOUN
ejpam-6834	484	11	.	.	PUNCT
ejpam-6834	485	1	then	then	ADV
ejpam-6834	485	2	τ	τ	X
ejpam-6834	485	3	′′	′′	PROPN
ejpam-6834	485	4	=	=	PRON
ejpam-6834	486	1	πn→n′	πn→n′	PUNCT
ejpam-6834	487	1	◦	◦	NOUN
ejpam-6834	487	2	τ	τ	X
ejpam-6834	487	3	:	:	PUNCT
ejpam-6834	487	4	p	p	PROPN
ejpam-6834	487	5	m(a	m(a	PROPN
ejpam-6834	487	6	)	)	PUNCT
ejpam-6834	487	7	−→	−→	NOUN
ejpam-6834	487	8	p	p	NOUN
ejpam-6834	487	9	n′	n′	PROPN
ejpam-6834	487	10	(	(	PUNCT
ejpam-6834	487	11	[	[	X
ejpam-6834	487	12	0	0	NUM
ejpam-6834	487	13	,	,	PUNCT
ejpam-6834	487	14	1	1	NUM
ejpam-6834	487	15	]	]	PUNCT
ejpam-6834	487	16	)	)	PUNCT
ejpam-6834	487	17	is	be	AUX
ejpam-6834	487	18	an	an	DET
ejpam-6834	487	19	(	(	PUNCT
ejpam-6834	487	20	m	m	PROPN
ejpam-6834	487	21	,	,	PUNCT
ejpam-6834	487	22	n′)-superhyperfuzzy	n′)-superhyperfuzzy	ADV
ejpam-6834	487	23	set	set	NOUN
ejpam-6834	487	24	.	.	PUNCT
ejpam-6834	488	1	proof	proof	NOUN
ejpam-6834	488	2	.	.	PUNCT
ejpam-6834	489	1	fix	fix	VERB
ejpam-6834	489	2	x	x	X
ejpam-6834	489	3	∈	∈	PROPN
ejpam-6834	489	4	p	p	PROPN
ejpam-6834	489	5	m(a	m(a	PROPN
ejpam-6834	489	6	)	)	PUNCT
ejpam-6834	489	7	.	.	PUNCT
ejpam-6834	490	1	since	since	SCONJ
ejpam-6834	490	2	τ(x	τ(x	NOUN
ejpam-6834	490	3	)	)	PUNCT
ejpam-6834	490	4	∈	∈	PROPN
ejpam-6834	490	5	p	p	NOUN
ejpam-6834	490	6	n([0	n([0	PROPN
ejpam-6834	490	7	,	,	PUNCT
ejpam-6834	490	8	1	1	NUM
ejpam-6834	490	9	]	]	NUM
ejpam-6834	490	10	)	)	PUNCT
ejpam-6834	490	11	,	,	PUNCT
ejpam-6834	490	12	applying	apply	VERB
ejpam-6834	490	13	un→(n−1	un→(n−1	ADJ
ejpam-6834	490	14	)	)	PUNCT
ejpam-6834	490	15	produces⋃	produces⋃	PROPN
ejpam-6834	490	16	τ(x	τ(x	NOUN
ejpam-6834	490	17	)	)	PUNCT
ejpam-6834	490	18	∈	∈	PROPN
ejpam-6834	490	19	p	p	NOUN
ejpam-6834	490	20	n−1([0	n−1([0	PROPN
ejpam-6834	490	21	,	,	PUNCT
ejpam-6834	490	22	1	1	NUM
ejpam-6834	490	23	]	]	NUM
ejpam-6834	490	24	)	)	PUNCT
ejpam-6834	490	25	.	.	PUNCT
ejpam-6834	491	1	by	by	ADP
ejpam-6834	491	2	the	the	DET
ejpam-6834	491	3	convention	convention	NOUN
ejpam-6834	491	4	of	of	ADP
ejpam-6834	491	5	this	this	DET
ejpam-6834	491	6	paper	paper	NOUN
ejpam-6834	491	7	,	,	PUNCT
ejpam-6834	491	8	members	member	NOUN
ejpam-6834	491	9	at	at	ADP
ejpam-6834	491	10	each	each	DET
ejpam-6834	491	11	level	level	NOUN
ejpam-6834	491	12	are	be	AUX
ejpam-6834	491	13	nonempty	nonempty	ADJ
ejpam-6834	491	14	,	,	PUNCT
ejpam-6834	491	15	so	so	SCONJ
ejpam-6834	491	16	the	the	DET
ejpam-6834	491	17	union	union	NOUN
ejpam-6834	491	18	is	be	AUX
ejpam-6834	491	19	nonempty	nonempty	ADJ
ejpam-6834	491	20	.	.	PUNCT
ejpam-6834	492	1	iterating	iterate	VERB
ejpam-6834	492	2	this	this	PRON
ejpam-6834	492	3	(	(	PUNCT
ejpam-6834	492	4	n−	n−	NOUN
ejpam-6834	492	5	n′	n′	ADJ
ejpam-6834	492	6	)	)	PUNCT
ejpam-6834	493	1	times	times	PROPN
ejpam-6834	493	2	yields	yield	VERB
ejpam-6834	493	3	πn→n′	πn→n′	X
ejpam-6834	493	4	(	(	PUNCT
ejpam-6834	493	5	τ(x	τ(x	NOUN
ejpam-6834	493	6	)	)	PUNCT
ejpam-6834	493	7	)	)	PUNCT
ejpam-6834	494	1	∈	∈	PROPN
ejpam-6834	495	1	p	p	NOUN
ejpam-6834	495	2	n′	n′	PROPN
ejpam-6834	495	3	(	(	PUNCT
ejpam-6834	495	4	[	[	X
ejpam-6834	495	5	0	0	NUM
ejpam-6834	495	6	,	,	PUNCT
ejpam-6834	495	7	1	1	NUM
ejpam-6834	495	8	]	]	NUM
ejpam-6834	495	9	)	)	PUNCT
ejpam-6834	495	10	.	.	PUNCT
ejpam-6834	496	1	therefore	therefore	ADV
ejpam-6834	496	2	τ	τ	X
ejpam-6834	496	3	′′	′′	PROPN
ejpam-6834	496	4	is	be	AUX
ejpam-6834	496	5	well	well	ADV
ejpam-6834	496	6	-	-	PUNCT
ejpam-6834	496	7	defined	define	VERB
ejpam-6834	496	8	with	with	ADP
ejpam-6834	496	9	codomain	codomain	NOUN
ejpam-6834	496	10	p	p	NOUN
ejpam-6834	496	11	n′	n′	NOUN
ejpam-6834	496	12	(	(	PUNCT
ejpam-6834	496	13	[	[	X
ejpam-6834	496	14	0	0	NUM
ejpam-6834	496	15	,	,	PUNCT
ejpam-6834	496	16	1	1	NUM
ejpam-6834	496	17	]	]	NUM
ejpam-6834	496	18	)	)	PUNCT
ejpam-6834	496	19	,	,	PUNCT
ejpam-6834	496	20	and	and	CCONJ
ejpam-6834	496	21	hence	hence	ADV
ejpam-6834	496	22	is	be	AUX
ejpam-6834	496	23	an	an	DET
ejpam-6834	496	24	(	(	PUNCT
ejpam-6834	496	25	m	m	PROPN
ejpam-6834	496	26	,	,	PUNCT
ejpam-6834	496	27	n′)-superhyperfuzzy	n′)-superhyperfuzzy	ADV
ejpam-6834	496	28	set	set	NOUN
ejpam-6834	496	29	.	.	PUNCT
ejpam-6834	497	1	theorem	theorem	VERB
ejpam-6834	497	2	4	4	NUM
ejpam-6834	497	3	(	(	PUNCT
ejpam-6834	497	4	closure	closure	NOUN
ejpam-6834	497	5	under	under	ADP
ejpam-6834	497	6	pointwise	pointwise	PROPN
ejpam-6834	497	7	union	union	NOUN
ejpam-6834	497	8	)	)	PUNCT
ejpam-6834	497	9	.	.	PUNCT
ejpam-6834	498	1	if	if	SCONJ
ejpam-6834	498	2	τ1	τ1	NOUN
ejpam-6834	498	3	,	,	PUNCT
ejpam-6834	498	4	τ2	τ2	NOUN
ejpam-6834	498	5	:	:	PUNCT
ejpam-6834	498	6	p	p	PROPN
ejpam-6834	498	7	m(a	m(a	PROPN
ejpam-6834	498	8	)	)	PUNCT
ejpam-6834	498	9	→	→	SYM
ejpam-6834	499	1	p	p	X
ejpam-6834	499	2	n([0	n([0	NOUN
ejpam-6834	499	3	,	,	PUNCT
ejpam-6834	499	4	1	1	NUM
ejpam-6834	499	5	]	]	PUNCT
ejpam-6834	499	6	)	)	PUNCT
ejpam-6834	499	7	are	be	AUX
ejpam-6834	499	8	(	(	PUNCT
ejpam-6834	499	9	m	m	NOUN
ejpam-6834	499	10	,	,	PUNCT
ejpam-6834	499	11	n)superhyperfuzzy	n)superhyperfuzzy	PRON
ejpam-6834	499	12	sets	set	VERB
ejpam-6834	499	13	,	,	PUNCT
ejpam-6834	499	14	then	then	ADV
ejpam-6834	499	15	the	the	DET
ejpam-6834	499	16	map	map	NOUN
ejpam-6834	499	17	(	(	PUNCT
ejpam-6834	499	18	τ1	τ1	NOUN
ejpam-6834	499	19	∪	∪	ADJ
ejpam-6834	499	20	τ2)(x	τ2)(x	PROPN
ejpam-6834	499	21	)	)	PUNCT
ejpam-6834	499	22	:	:	PUNCT
ejpam-6834	500	1	=	=	PUNCT
ejpam-6834	500	2	τ1(x	τ1(x	NOUN
ejpam-6834	500	3	)	)	PUNCT
ejpam-6834	500	4	∪	∪	ADP
ejpam-6834	500	5	τ2(x	τ2(x	PUNCT
ejpam-6834	500	6	)	)	PUNCT
ejpam-6834	500	7	(	(	PUNCT
ejpam-6834	500	8	x	x	SYM
ejpam-6834	500	9	∈	∈	PROPN
ejpam-6834	500	10	p	p	PROPN
ejpam-6834	500	11	m(a	m(a	PROPN
ejpam-6834	500	12	)	)	PUNCT
ejpam-6834	500	13	)	)	PUNCT
ejpam-6834	500	14	is	be	AUX
ejpam-6834	500	15	also	also	ADV
ejpam-6834	500	16	an	an	DET
ejpam-6834	500	17	(	(	PUNCT
ejpam-6834	500	18	m	m	NOUN
ejpam-6834	500	19	,	,	PUNCT
ejpam-6834	500	20	n)-superhyperfuzzy	n)-superhyperfuzzy	PUNCT
ejpam-6834	500	21	set	set	NOUN
ejpam-6834	500	22	.	.	PUNCT
ejpam-6834	501	1	proof	proof	NOUN
ejpam-6834	501	2	.	.	PUNCT
ejpam-6834	502	1	for	for	ADP
ejpam-6834	502	2	each	each	DET
ejpam-6834	502	3	x	x	NOUN
ejpam-6834	502	4	,	,	PUNCT
ejpam-6834	502	5	both	both	PRON
ejpam-6834	502	6	τ1(x	τ1(x	NUM
ejpam-6834	502	7	)	)	PUNCT
ejpam-6834	502	8	and	and	CCONJ
ejpam-6834	502	9	τ2(x	τ2(x	X
ejpam-6834	502	10	)	)	PUNCT
ejpam-6834	502	11	are	be	AUX
ejpam-6834	502	12	elements	element	NOUN
ejpam-6834	502	13	of	of	ADP
ejpam-6834	502	14	p	p	NOUN
ejpam-6834	502	15	n([0	n([0	NOUN
ejpam-6834	502	16	,	,	PUNCT
ejpam-6834	502	17	1	1	NUM
ejpam-6834	502	18	]	]	NUM
ejpam-6834	502	19	)	)	PUNCT
ejpam-6834	502	20	,	,	PUNCT
ejpam-6834	502	21	i.e.	i.e.	X
ejpam-6834	502	22	subsets	subset	NOUN
ejpam-6834	502	23	of	of	ADP
ejpam-6834	502	24	p	p	NOUN
ejpam-6834	502	25	n−1([0	n−1([0	NOUN
ejpam-6834	502	26	,	,	PUNCT
ejpam-6834	502	27	1	1	NUM
ejpam-6834	502	28	]	]	NUM
ejpam-6834	502	29	)	)	PUNCT
ejpam-6834	502	30	.	.	PUNCT
ejpam-6834	503	1	their	their	PRON
ejpam-6834	503	2	union	union	NOUN
ejpam-6834	503	3	is	be	AUX
ejpam-6834	503	4	again	again	ADV
ejpam-6834	503	5	a	a	DET
ejpam-6834	503	6	subset	subset	NOUN
ejpam-6834	503	7	of	of	ADP
ejpam-6834	503	8	p	p	PROPN
ejpam-6834	503	9	n−1([0	n−1([0	NOUN
ejpam-6834	503	10	,	,	PUNCT
ejpam-6834	503	11	1	1	NUM
ejpam-6834	503	12	]	]	PUNCT
ejpam-6834	503	13	)	)	PUNCT
ejpam-6834	503	14	and	and	CCONJ
ejpam-6834	503	15	is	be	AUX
ejpam-6834	503	16	nonempty	nonempty	ADJ
ejpam-6834	503	17	because	because	SCONJ
ejpam-6834	503	18	each	each	DET
ejpam-6834	503	19	term	term	NOUN
ejpam-6834	503	20	is	be	AUX
ejpam-6834	503	21	nonempty	nonempty	ADJ
ejpam-6834	503	22	.	.	PUNCT
ejpam-6834	504	1	thus	thus	ADV
ejpam-6834	504	2	(	(	PUNCT
ejpam-6834	504	3	τ1	τ1	ADP
ejpam-6834	504	4	∪	∪	ADJ
ejpam-6834	504	5	τ2)(x	τ2)(x	PROPN
ejpam-6834	504	6	)	)	PUNCT
ejpam-6834	504	7	∈	∈	PROPN
ejpam-6834	504	8	p	p	NOUN
ejpam-6834	504	9	n([0	n([0	PROPN
ejpam-6834	504	10	,	,	PUNCT
ejpam-6834	504	11	1	1	NUM
ejpam-6834	504	12	]	]	PUNCT
ejpam-6834	504	13	)	)	PUNCT
ejpam-6834	504	14	for	for	ADP
ejpam-6834	504	15	all	all	DET
ejpam-6834	504	16	x	x	NOUN
ejpam-6834	504	17	,	,	PUNCT
ejpam-6834	504	18	which	which	PRON
ejpam-6834	504	19	proves	prove	VERB
ejpam-6834	504	20	the	the	DET
ejpam-6834	504	21	claim	claim	NOUN
ejpam-6834	504	22	.	.	PUNCT
ejpam-6834	505	1	theorem	theorem	ADJ
ejpam-6834	505	2	5	5	NUM
ejpam-6834	505	3	(	(	PUNCT
ejpam-6834	505	4	closure	closure	NOUN
ejpam-6834	505	5	under	under	ADP
ejpam-6834	505	6	pointwise	pointwise	NOUN
ejpam-6834	505	7	intersection	intersection	NOUN
ejpam-6834	505	8	)	)	PUNCT
ejpam-6834	505	9	.	.	PUNCT
ejpam-6834	506	1	let	let	VERB
ejpam-6834	506	2	τ1	τ1	NOUN
ejpam-6834	506	3	,	,	PUNCT
ejpam-6834	506	4	τ2	τ2	NOUN
ejpam-6834	506	5	:	:	PUNCT
ejpam-6834	506	6	p	p	PROPN
ejpam-6834	506	7	m(a	m(a	PROPN
ejpam-6834	506	8	)	)	PUNCT
ejpam-6834	506	9	→	→	SYM
ejpam-6834	507	1	p	p	X
ejpam-6834	507	2	n([0	n([0	NOUN
ejpam-6834	507	3	,	,	PUNCT
ejpam-6834	507	4	1	1	NUM
ejpam-6834	507	5	]	]	PUNCT
ejpam-6834	507	6	)	)	PUNCT
ejpam-6834	507	7	be	be	AUX
ejpam-6834	507	8	(	(	PUNCT
ejpam-6834	507	9	m	m	NOUN
ejpam-6834	507	10	,	,	PUNCT
ejpam-6834	507	11	n)-superhyperfuzzy	n)-superhyperfuzzy	NOUN
ejpam-6834	507	12	sets	set	NOUN
ejpam-6834	507	13	.	.	PUNCT
ejpam-6834	508	1	define	define	NOUN
ejpam-6834	508	2	(	(	PUNCT
ejpam-6834	508	3	τ1	τ1	NOUN
ejpam-6834	508	4	∩	∩	NOUN
ejpam-6834	508	5	τ2)(x	τ2)(x	PROPN
ejpam-6834	508	6	)	)	PUNCT
ejpam-6834	508	7	:	:	PUNCT
ejpam-6834	509	1	=	=	PUNCT
ejpam-6834	509	2	τ1(x	τ1(x	NOUN
ejpam-6834	509	3	)	)	PUNCT
ejpam-6834	509	4	∩	∩	NOUN
ejpam-6834	509	5	τ2(x	τ2(x	X
ejpam-6834	509	6	)	)	PUNCT
ejpam-6834	509	7	(	(	PUNCT
ejpam-6834	509	8	x	x	SYM
ejpam-6834	509	9	∈	∈	PROPN
ejpam-6834	509	10	p	p	PROPN
ejpam-6834	509	11	m(a	m(a	PROPN
ejpam-6834	509	12	)	)	PUNCT
ejpam-6834	509	13	)	)	PUNCT
ejpam-6834	509	14	.	.	PUNCT
ejpam-6834	510	1	then	then	ADV
ejpam-6834	510	2	(	(	PUNCT
ejpam-6834	510	3	τ1	τ1	ADP
ejpam-6834	510	4	∩	∩	ADJ
ejpam-6834	510	5	τ2	τ2	NOUN
ejpam-6834	510	6	)	)	PUNCT
ejpam-6834	510	7	is	be	AUX
ejpam-6834	510	8	an	an	DET
ejpam-6834	510	9	(	(	PUNCT
ejpam-6834	510	10	m	m	NOUN
ejpam-6834	510	11	,	,	PUNCT
ejpam-6834	510	12	n)-superhyperfuzzy	n)-superhyperfuzzy	PUNCT
ejpam-6834	510	13	set	set	VERB
ejpam-6834	510	14	provided	provide	VERB
ejpam-6834	510	15	each	each	DET
ejpam-6834	510	16	intersection	intersection	NOUN
ejpam-6834	510	17	is	be	AUX
ejpam-6834	510	18	nonempty	nonempty	ADJ
ejpam-6834	510	19	.	.	PUNCT
ejpam-6834	511	1	if	if	SCONJ
ejpam-6834	511	2	some	some	DET
ejpam-6834	511	3	intersections	intersection	NOUN
ejpam-6834	511	4	are	be	AUX
ejpam-6834	511	5	empty	empty	ADJ
ejpam-6834	511	6	,	,	PUNCT
ejpam-6834	511	7	one	one	PRON
ejpam-6834	511	8	may	may	AUX
ejpam-6834	511	9	either	either	CCONJ
ejpam-6834	511	10	restrict	restrict	VERB
ejpam-6834	511	11	the	the	DET
ejpam-6834	511	12	effective	effective	ADJ
ejpam-6834	511	13	domain	domain	NOUN
ejpam-6834	511	14	to	to	ADP
ejpam-6834	511	15	those	those	PRON
ejpam-6834	511	16	x	x	PUNCT
ejpam-6834	511	17	with	with	ADP
ejpam-6834	511	18	nonempty	nonempty	ADJ
ejpam-6834	511	19	intersection	intersection	NOUN
ejpam-6834	511	20	,	,	PUNCT
ejpam-6834	511	21	or	or	CCONJ
ejpam-6834	511	22	define	define	VERB
ejpam-6834	511	23	the	the	DET
ejpam-6834	511	24	modified	modify	VERB
ejpam-6834	511	25	map	map	NOUN
ejpam-6834	511	26	(	(	PUNCT
ejpam-6834	511	27	τ1	τ1	NOUN
ejpam-6834	511	28	⊓	⊓	PROPN
ejpam-6834	511	29	τ2)(x	τ2)(x	PROPN
ejpam-6834	511	30	)	)	PUNCT
ejpam-6834	511	31	:	:	PUNCT
ejpam-6834	512	1	=	=	PRON
ejpam-6834	512	2	{	{	PUNCT
ejpam-6834	512	3	τ1(x	τ1(x	NOUN
ejpam-6834	512	4	)	)	PUNCT
ejpam-6834	512	5	∩	∩	NOUN
ejpam-6834	512	6	τ2(x	τ2(x	PROPN
ejpam-6834	512	7	)	)	PUNCT
ejpam-6834	512	8	,	,	PUNCT
ejpam-6834	512	9	if	if	SCONJ
ejpam-6834	512	10	τ1(x	τ1(x	NOUN
ejpam-6834	512	11	)	)	PUNCT
ejpam-6834	512	12	∩	∩	NOUN
ejpam-6834	512	13	τ2(x	τ2(x	SYM
ejpam-6834	512	14	)	)	PUNCT
ejpam-6834	512	15	̸=	̸=	PROPN
ejpam-6834	512	16	∅	∅	NOUN
ejpam-6834	512	17	,	,	PUNCT
ejpam-6834	512	18	{	{	PUNCT
ejpam-6834	512	19	0	0	NUM
ejpam-6834	512	20	}	}	PUNCT
ejpam-6834	512	21	,	,	PUNCT
ejpam-6834	512	22	otherwise	otherwise	ADV
ejpam-6834	512	23	,	,	PUNCT
ejpam-6834	512	24	which	which	PRON
ejpam-6834	512	25	is	be	AUX
ejpam-6834	512	26	again	again	ADV
ejpam-6834	512	27	(	(	PUNCT
ejpam-6834	512	28	m	m	NOUN
ejpam-6834	512	29	,	,	PUNCT
ejpam-6834	512	30	n)-superhyperfuzzy	n)-superhyperfuzzy	X
ejpam-6834	512	31	.	.	PUNCT
ejpam-6834	513	1	t.	t.	PROPN
ejpam-6834	513	2	fujita	fujita	PROPN
ejpam-6834	513	3	,	,	PUNCT
ejpam-6834	513	4	f.smarandache	f.smarandache	NOUN
ejpam-6834	513	5	/	/	SYM
ejpam-6834	513	6	eur	eur	PROPN
ejpam-6834	513	7	.	.	PUNCT
ejpam-6834	514	1	j.	j.	PROPN
ejpam-6834	514	2	pure	pure	PROPN
ejpam-6834	514	3	appl	appl	PROPN
ejpam-6834	514	4	.	.	PROPN
ejpam-6834	514	5	math	math	PROPN
ejpam-6834	514	6	,	,	PUNCT
ejpam-6834	514	7	18	18	NUM
ejpam-6834	514	8	(	(	PUNCT
ejpam-6834	514	9	4	4	NUM
ejpam-6834	514	10	)	)	PUNCT
ejpam-6834	514	11	(	(	PUNCT
ejpam-6834	514	12	2025	2025	NUM
ejpam-6834	514	13	)	)	PUNCT
ejpam-6834	514	14	,	,	PUNCT
ejpam-6834	514	15	6834	6834	NUM
ejpam-6834	514	16	24	24	NUM
ejpam-6834	514	17	of	of	ADP
ejpam-6834	514	18	69	69	NUM
ejpam-6834	514	19	proof	proof	NOUN
ejpam-6834	514	20	.	.	PUNCT
ejpam-6834	515	1	fix	fix	NOUN
ejpam-6834	515	2	x.	x.	NOUN
ejpam-6834	515	3	since	since	SCONJ
ejpam-6834	515	4	τi(x	τi(x	NUM
ejpam-6834	515	5	)	)	PUNCT
ejpam-6834	515	6	∈	∈	PROPN
ejpam-6834	515	7	p	p	NOUN
ejpam-6834	515	8	n([0	n([0	PROPN
ejpam-6834	515	9	,	,	PUNCT
ejpam-6834	515	10	1	1	NUM
ejpam-6834	515	11	]	]	NUM
ejpam-6834	515	12	)	)	PUNCT
ejpam-6834	516	1	(	(	PUNCT
ejpam-6834	516	2	i	i	NOUN
ejpam-6834	516	3	=	=	NOUN
ejpam-6834	516	4	1	1	NUM
ejpam-6834	516	5	,	,	PUNCT
ejpam-6834	516	6	2	2	NUM
ejpam-6834	516	7	)	)	PUNCT
ejpam-6834	516	8	,	,	PUNCT
ejpam-6834	516	9	the	the	DET
ejpam-6834	516	10	intersection	intersection	NOUN
ejpam-6834	516	11	τ1(x	τ1(x	NOUN
ejpam-6834	516	12	)	)	PUNCT
ejpam-6834	516	13	∩	∩	NOUN
ejpam-6834	516	14	τ2(x	τ2(x	X
ejpam-6834	516	15	)	)	PUNCT
ejpam-6834	516	16	is	be	AUX
ejpam-6834	516	17	a	a	DET
ejpam-6834	516	18	subset	subset	NOUN
ejpam-6834	516	19	of	of	ADP
ejpam-6834	516	20	p	p	PROPN
ejpam-6834	516	21	n−1([0	n−1([0	NOUN
ejpam-6834	516	22	,	,	PUNCT
ejpam-6834	516	23	1	1	NUM
ejpam-6834	516	24	]	]	NUM
ejpam-6834	516	25	)	)	PUNCT
ejpam-6834	516	26	.	.	PUNCT
ejpam-6834	517	1	if	if	SCONJ
ejpam-6834	517	2	it	it	PRON
ejpam-6834	517	3	is	be	AUX
ejpam-6834	517	4	nonempty	nonempty	ADJ
ejpam-6834	517	5	,	,	PUNCT
ejpam-6834	517	6	then	then	ADV
ejpam-6834	517	7	it	it	PRON
ejpam-6834	517	8	lies	lie	VERB
ejpam-6834	517	9	in	in	ADP
ejpam-6834	517	10	p	p	NOUN
ejpam-6834	517	11	n([0	n([0	NOUN
ejpam-6834	517	12	,	,	PUNCT
ejpam-6834	517	13	1	1	NUM
ejpam-6834	517	14	]	]	PUNCT
ejpam-6834	517	15	)	)	PUNCT
ejpam-6834	517	16	and	and	CCONJ
ejpam-6834	517	17	we	we	PRON
ejpam-6834	517	18	are	be	AUX
ejpam-6834	517	19	done	do	VERB
ejpam-6834	517	20	.	.	PUNCT
ejpam-6834	518	1	if	if	SCONJ
ejpam-6834	518	2	it	it	PRON
ejpam-6834	518	3	happens	happen	VERB
ejpam-6834	518	4	to	to	PART
ejpam-6834	518	5	be	be	AUX
ejpam-6834	518	6	empty	empty	ADJ
ejpam-6834	518	7	for	for	ADP
ejpam-6834	518	8	some	some	DET
ejpam-6834	518	9	x	x	NOUN
ejpam-6834	518	10	,	,	PUNCT
ejpam-6834	518	11	the	the	DET
ejpam-6834	518	12	two	two	NUM
ejpam-6834	518	13	remedies	remedy	NOUN
ejpam-6834	518	14	stated	state	VERB
ejpam-6834	518	15	in	in	ADP
ejpam-6834	518	16	the	the	DET
ejpam-6834	518	17	theorem	theorem	NOUN
ejpam-6834	518	18	ensure	ensure	VERB
ejpam-6834	518	19	the	the	DET
ejpam-6834	518	20	resulting	result	VERB
ejpam-6834	518	21	value	value	NOUN
ejpam-6834	518	22	remains	remain	VERB
ejpam-6834	518	23	a	a	DET
ejpam-6834	518	24	(	(	PUNCT
ejpam-6834	518	25	nonempty	nonempty	NOUN
ejpam-6834	518	26	)	)	PUNCT
ejpam-6834	518	27	element	element	NOUN
ejpam-6834	518	28	of	of	ADP
ejpam-6834	518	29	p	p	PROPN
ejpam-6834	518	30	n([0	n([0	NOUN
ejpam-6834	518	31	,	,	PUNCT
ejpam-6834	518	32	1	1	NUM
ejpam-6834	518	33	]	]	NUM
ejpam-6834	518	34	)	)	PUNCT
ejpam-6834	518	35	.	.	PUNCT
ejpam-6834	519	1	theorem	theorem	NOUN
ejpam-6834	519	2	6	6	NUM
ejpam-6834	519	3	(	(	PUNCT
ejpam-6834	519	4	nested	nest	VERB
ejpam-6834	519	5	α	α	NOUN
ejpam-6834	519	6	-	-	NOUN
ejpam-6834	519	7	cuts	cut	NOUN
ejpam-6834	519	8	)	)	PUNCT
ejpam-6834	519	9	.	.	PUNCT
ejpam-6834	520	1	let	let	VERB
ejpam-6834	521	1	τ	τ	PROPN
ejpam-6834	521	2	:	:	PUNCT
ejpam-6834	521	3	p	p	PROPN
ejpam-6834	521	4	m(a	m(a	PROPN
ejpam-6834	521	5	)	)	PUNCT
ejpam-6834	521	6	→	→	SYM
ejpam-6834	521	7	p	p	X
ejpam-6834	521	8	n([0	n([0	NOUN
ejpam-6834	521	9	,	,	PUNCT
ejpam-6834	521	10	1	1	NUM
ejpam-6834	521	11	]	]	PUNCT
ejpam-6834	521	12	)	)	PUNCT
ejpam-6834	521	13	be	be	AUX
ejpam-6834	521	14	an	an	DET
ejpam-6834	521	15	(	(	PUNCT
ejpam-6834	521	16	m	m	NOUN
ejpam-6834	521	17	,	,	PUNCT
ejpam-6834	521	18	n)-superhyperfuzzy	n)-superhyperfuzzy	PUNCT
ejpam-6834	521	19	set	set	VERB
ejpam-6834	521	20	with	with	ADP
ejpam-6834	521	21	n	n	PRON
ejpam-6834	521	22	≥	≥	NUM
ejpam-6834	521	23	1	1	NUM
ejpam-6834	521	24	.	.	PUNCT
ejpam-6834	522	1	for	for	ADP
ejpam-6834	522	2	α	α	PRON
ejpam-6834	522	3	∈	∈	PROPN
ejpam-6834	523	1	[	[	X
ejpam-6834	523	2	0	0	NUM
ejpam-6834	523	3	,	,	PUNCT
ejpam-6834	523	4	1	1	NUM
ejpam-6834	523	5	]	]	PUNCT
ejpam-6834	523	6	,	,	PUNCT
ejpam-6834	523	7	define	define	VERB
ejpam-6834	523	8	cα	cα	ADP
ejpam-6834	523	9	=	=	PUNCT
ejpam-6834	523	10	{	{	PUNCT
ejpam-6834	523	11	x	x	PUNCT
ejpam-6834	523	12	∈	∈	PROPN
ejpam-6834	523	13	p	p	PROPN
ejpam-6834	523	14	m(a	m(a	PROPN
ejpam-6834	523	15	)	)	PUNCT
ejpam-6834	523	16	∣∣	∣∣	NUM
ejpam-6834	523	17	∃t	∃t	NOUN
ejpam-6834	523	18	∈	∈	PROPN
ejpam-6834	523	19	un→1	un→1	PROPN
ejpam-6834	523	20	(	(	PUNCT
ejpam-6834	523	21	τ(x	τ(x	NOUN
ejpam-6834	523	22	)	)	PUNCT
ejpam-6834	523	23	)	)	PUNCT
ejpam-6834	524	1	with	with	ADP
ejpam-6834	524	2	t	t	PROPN
ejpam-6834	524	3	≥	≥	PROPN
ejpam-6834	524	4	α	α	NOUN
ejpam-6834	524	5	}	}	PUNCT
ejpam-6834	524	6	.	.	PUNCT
ejpam-6834	525	1	then	then	ADV
ejpam-6834	525	2	for	for	ADP
ejpam-6834	525	3	α1	α1	PROPN
ejpam-6834	525	4	<	<	X
ejpam-6834	525	5	α2	α2	ADJ
ejpam-6834	525	6	one	one	NUM
ejpam-6834	525	7	has	have	VERB
ejpam-6834	525	8	cα2	cα2	VERB
ejpam-6834	525	9	⊆	⊆	NUM
ejpam-6834	525	10	cα1	cα1	NOUN
ejpam-6834	525	11	.	.	PUNCT
ejpam-6834	526	1	proof	proof	NOUN
ejpam-6834	526	2	.	.	PUNCT
ejpam-6834	527	1	suppose	suppose	VERB
ejpam-6834	527	2	x	x	SYM
ejpam-6834	527	3	∈	∈	NOUN
ejpam-6834	527	4	cα2	cα2	NOUN
ejpam-6834	527	5	.	.	PUNCT
ejpam-6834	528	1	by	by	ADP
ejpam-6834	528	2	definition	definition	NOUN
ejpam-6834	528	3	there	there	PRON
ejpam-6834	528	4	exists	exist	VERB
ejpam-6834	528	5	t	t	PROPN
ejpam-6834	528	6	∈	∈	PROPN
ejpam-6834	528	7	un→1(τ(x	un→1(τ(x	NOUN
ejpam-6834	528	8	)	)	PUNCT
ejpam-6834	528	9	)	)	PUNCT
ejpam-6834	529	1	⊆	⊆	NUM
ejpam-6834	529	2	[	[	X
ejpam-6834	529	3	0	0	NUM
ejpam-6834	529	4	,	,	PUNCT
ejpam-6834	529	5	1	1	NUM
ejpam-6834	529	6	]	]	PUNCT
ejpam-6834	529	7	with	with	ADP
ejpam-6834	529	8	t	t	PROPN
ejpam-6834	529	9	≥	≥	PROPN
ejpam-6834	529	10	α2	α2	PROPN
ejpam-6834	529	11	.	.	PUNCT
ejpam-6834	530	1	since	since	SCONJ
ejpam-6834	530	2	α2	α2	PROPN
ejpam-6834	530	3	>	>	SYM
ejpam-6834	530	4	α1	α1	PROPN
ejpam-6834	530	5	,	,	PUNCT
ejpam-6834	530	6	the	the	DET
ejpam-6834	530	7	same	same	ADJ
ejpam-6834	530	8	t	t	NOUN
ejpam-6834	530	9	satisfies	satisfie	NOUN
ejpam-6834	530	10	t	t	PROPN
ejpam-6834	530	11	≥	≥	PROPN
ejpam-6834	530	12	α1	α1	PROPN
ejpam-6834	530	13	,	,	PUNCT
ejpam-6834	530	14	hence	hence	ADV
ejpam-6834	530	15	x	x	PART
ejpam-6834	530	16	∈	∈	PROPN
ejpam-6834	530	17	cα1	cα1	NOUN
ejpam-6834	530	18	.	.	PUNCT
ejpam-6834	531	1	therefore	therefore	ADV
ejpam-6834	531	2	cα2	cα2	PROPN
ejpam-6834	531	3	⊆	⊆	NUM
ejpam-6834	531	4	cα1	cα1	NOUN
ejpam-6834	531	5	.	.	PUNCT
ejpam-6834	532	1	theorem	theorem	ADJ
ejpam-6834	532	2	7	7	NUM
ejpam-6834	532	3	(	(	PUNCT
ejpam-6834	532	4	functoriality	functoriality	NOUN
ejpam-6834	532	5	under	under	ADP
ejpam-6834	532	6	surjections	surjection	NOUN
ejpam-6834	532	7	)	)	PUNCT
ejpam-6834	532	8	.	.	PUNCT
ejpam-6834	533	1	let	let	VERB
ejpam-6834	533	2	f	f	NOUN
ejpam-6834	533	3	:	:	PUNCT
ejpam-6834	533	4	u	u	PROPN
ejpam-6834	533	5	→	→	SYM
ejpam-6834	533	6	v	v	NUM
ejpam-6834	533	7	be	be	AUX
ejpam-6834	533	8	a	a	DET
ejpam-6834	533	9	surjection	surjection	NOUN
ejpam-6834	533	10	and	and	CCONJ
ejpam-6834	533	11	let	let	VERB
ejpam-6834	533	12	τ	τ	PROPN
ejpam-6834	533	13	:	:	PUNCT
ejpam-6834	533	14	p	p	X
ejpam-6834	533	15	m(u	m(u	PROPN
ejpam-6834	533	16	)	)	PUNCT
ejpam-6834	533	17	→	→	SYM
ejpam-6834	534	1	p	p	X
ejpam-6834	534	2	n([0	n([0	NOUN
ejpam-6834	534	3	,	,	PUNCT
ejpam-6834	534	4	1	1	NUM
ejpam-6834	534	5	]	]	PUNCT
ejpam-6834	534	6	)	)	PUNCT
ejpam-6834	534	7	be	be	AUX
ejpam-6834	534	8	an	an	DET
ejpam-6834	534	9	(	(	PUNCT
ejpam-6834	534	10	m	m	NOUN
ejpam-6834	534	11	,	,	PUNCT
ejpam-6834	534	12	n)-superhyperfuzzy	n)-superhyperfuzzy	PUNCT
ejpam-6834	534	13	set	set	NOUN
ejpam-6834	534	14	.	.	PUNCT
ejpam-6834	535	1	define	define	VERB
ejpam-6834	535	2	the	the	DET
ejpam-6834	535	3	lifted	lift	VERB
ejpam-6834	535	4	preimage	preimage	NOUN
ejpam-6834	535	5	(	(	PUNCT
ejpam-6834	535	6	by	by	ADP
ejpam-6834	535	7	recursion	recursion	NOUN
ejpam-6834	535	8	on	on	ADP
ejpam-6834	535	9	m	m	NOUN
ejpam-6834	535	10	)	)	PUNCT
ejpam-6834	535	11	f−1	f−1	PROPN
ejpam-6834	535	12	(	(	PUNCT
ejpam-6834	535	13	1	1	NUM
ejpam-6834	535	14	)	)	PUNCT
ejpam-6834	535	15	:	:	PUNCT
ejpam-6834	535	16	p(v	p(v	NOUN
ejpam-6834	535	17	)	)	PUNCT
ejpam-6834	535	18	→	→	SYM
ejpam-6834	535	19	p(u	p(u	NUM
ejpam-6834	535	20	)	)	PUNCT
ejpam-6834	535	21	,	,	PUNCT
ejpam-6834	535	22	f−1	f−1	PROPN
ejpam-6834	535	23	(	(	PUNCT
ejpam-6834	535	24	1	1	NUM
ejpam-6834	535	25	)	)	PUNCT
ejpam-6834	535	26	(	(	PUNCT
ejpam-6834	535	27	y	y	NOUN
ejpam-6834	535	28	)	)	PUNCT
ejpam-6834	535	29	=	=	PUNCT
ejpam-6834	536	1	{	{	PUNCT
ejpam-6834	536	2	u	u	NOUN
ejpam-6834	536	3	∈	∈	PROPN
ejpam-6834	536	4	u	u	NOUN
ejpam-6834	536	5	|	|	ADV
ejpam-6834	536	6	f(u	f(u	PROPN
ejpam-6834	536	7	)	)	PUNCT
ejpam-6834	536	8	∈	∈	PROPN
ejpam-6834	536	9	y	y	PROPN
ejpam-6834	536	10	}	}	PUNCT
ejpam-6834	536	11	,	,	PUNCT
ejpam-6834	536	12	and	and	CCONJ
ejpam-6834	536	13	for	for	ADP
ejpam-6834	536	14	t	t	PROPN
ejpam-6834	536	15	≥	≥	NUM
ejpam-6834	536	16	1	1	NUM
ejpam-6834	536	17	,	,	PUNCT
ejpam-6834	536	18	f−1	f−1	PROPN
ejpam-6834	536	19	(	(	PUNCT
ejpam-6834	536	20	t+1	t+1	PROPN
ejpam-6834	536	21	)	)	PUNCT
ejpam-6834	536	22	:	:	PUNCT
ejpam-6834	536	23	p	p	PROPN
ejpam-6834	536	24	t+1(v	t+1(v	PROPN
ejpam-6834	536	25	)	)	PUNCT
ejpam-6834	536	26	→	→	PUNCT
ejpam-6834	536	27	p	p	X
ejpam-6834	536	28	t+1(u	t+1(u	NOUN
ejpam-6834	536	29	)	)	PUNCT
ejpam-6834	536	30	,	,	PUNCT
ejpam-6834	536	31	f−1	f−1	PROPN
ejpam-6834	536	32	(	(	PUNCT
ejpam-6834	536	33	t+1)(y	t+1)(y	PROPN
ejpam-6834	536	34	)	)	PUNCT
ejpam-6834	536	35	=	=	PRON
ejpam-6834	536	36	{	{	PUNCT
ejpam-6834	536	37	f−1	f−1	PROPN
ejpam-6834	536	38	(	(	PUNCT
ejpam-6834	536	39	t	t	PROPN
ejpam-6834	536	40	)	)	PUNCT
ejpam-6834	536	41	(	(	PUNCT
ejpam-6834	536	42	y	y	X
ejpam-6834	536	43	)	)	PUNCT
ejpam-6834	537	1	|	|	ADV
ejpam-6834	537	2	y	y	PROPN
ejpam-6834	537	3	∈	∈	PROPN
ejpam-6834	537	4	y	y	PROPN
ejpam-6834	537	5	}	}	PUNCT
ejpam-6834	537	6	.	.	PUNCT
ejpam-6834	538	1	then	then	ADV
ejpam-6834	538	2	the	the	DET
ejpam-6834	538	3	pushforward	pushforward	ADJ
ejpam-6834	538	4	f∗(τ	f∗(τ	PROPN
ejpam-6834	538	5	)	)	PUNCT
ejpam-6834	538	6	:	:	PUNCT
ejpam-6834	539	1	p	p	X
ejpam-6834	539	2	m(v	m(v	PROPN
ejpam-6834	539	3	)	)	PUNCT
ejpam-6834	540	1	−→	−→	NOUN
ejpam-6834	540	2	p	p	X
ejpam-6834	540	3	n([0	n([0	NOUN
ejpam-6834	540	4	,	,	PUNCT
ejpam-6834	540	5	1	1	NUM
ejpam-6834	540	6	]	]	NUM
ejpam-6834	540	7	)	)	PUNCT
ejpam-6834	540	8	,	,	PUNCT
ejpam-6834	540	9	f∗(τ)(y	f∗(τ)(y	NOUN
ejpam-6834	540	10	)	)	PUNCT
ejpam-6834	540	11	=	=	SYM
ejpam-6834	540	12	τ	τ	PROPN
ejpam-6834	540	13	(	(	PUNCT
ejpam-6834	540	14	f−1	f−1	PROPN
ejpam-6834	540	15	(	(	PUNCT
ejpam-6834	540	16	m)(y	m)(y	NOUN
ejpam-6834	540	17	)	)	PUNCT
ejpam-6834	540	18	)	)	PUNCT
ejpam-6834	540	19	is	be	AUX
ejpam-6834	540	20	an	an	DET
ejpam-6834	540	21	(	(	PUNCT
ejpam-6834	540	22	m	m	NOUN
ejpam-6834	540	23	,	,	PUNCT
ejpam-6834	540	24	n)-superhyperfuzzy	n)-superhyperfuzzy	PUNCT
ejpam-6834	540	25	set	set	VERB
ejpam-6834	540	26	on	on	ADP
ejpam-6834	540	27	v	v	NOUN
ejpam-6834	540	28	.	.	PUNCT
ejpam-6834	541	1	proof	proof	NOUN
ejpam-6834	541	2	.	.	PUNCT
ejpam-6834	542	1	let	let	VERB
ejpam-6834	542	2	y	y	PROPN
ejpam-6834	542	3	∈	∈	PROPN
ejpam-6834	542	4	p	p	PROPN
ejpam-6834	542	5	m(v	m(v	PROPN
ejpam-6834	542	6	)	)	PUNCT
ejpam-6834	542	7	.	.	PUNCT
ejpam-6834	543	1	by	by	ADP
ejpam-6834	543	2	the	the	DET
ejpam-6834	543	3	recursive	recursive	ADJ
ejpam-6834	543	4	definition	definition	NOUN
ejpam-6834	543	5	of	of	ADP
ejpam-6834	543	6	f−1	f−1	PROPN
ejpam-6834	543	7	(	(	PUNCT
ejpam-6834	543	8	m	m	PROPN
ejpam-6834	543	9	)	)	PUNCT
ejpam-6834	543	10	,	,	PUNCT
ejpam-6834	543	11	we	we	PRON
ejpam-6834	543	12	have	have	VERB
ejpam-6834	543	13	f−1	f−1	PROPN
ejpam-6834	543	14	(	(	PUNCT
ejpam-6834	543	15	m)(y	m)(y	PROPN
ejpam-6834	543	16	)	)	PUNCT
ejpam-6834	543	17	∈	∈	PROPN
ejpam-6834	543	18	p	p	NOUN
ejpam-6834	543	19	m(u	m(u	PROPN
ejpam-6834	543	20	)	)	PUNCT
ejpam-6834	543	21	.	.	PUNCT
ejpam-6834	544	1	therefore	therefore	ADV
ejpam-6834	544	2	τ	τ	PROPN
ejpam-6834	544	3	(	(	PUNCT
ejpam-6834	544	4	f−1	f−1	PROPN
ejpam-6834	544	5	(	(	PUNCT
ejpam-6834	544	6	m)(y	m)(y	NOUN
ejpam-6834	544	7	)	)	PUNCT
ejpam-6834	544	8	)	)	PUNCT
ejpam-6834	545	1	∈	∈	PROPN
ejpam-6834	545	2	p	p	NOUN
ejpam-6834	545	3	n([0	n([0	PROPN
ejpam-6834	545	4	,	,	PUNCT
ejpam-6834	545	5	1	1	NUM
ejpam-6834	545	6	]	]	NUM
ejpam-6834	545	7	)	)	PUNCT
ejpam-6834	545	8	,	,	PUNCT
ejpam-6834	545	9	showing	show	VERB
ejpam-6834	545	10	f∗(τ	f∗(τ	NOUN
ejpam-6834	545	11	)	)	PUNCT
ejpam-6834	545	12	is	be	AUX
ejpam-6834	545	13	well	well	ADV
ejpam-6834	545	14	-	-	PUNCT
ejpam-6834	545	15	defined	define	VERB
ejpam-6834	545	16	with	with	ADP
ejpam-6834	545	17	the	the	DET
ejpam-6834	545	18	required	require	VERB
ejpam-6834	545	19	codomain	codomain	NOUN
ejpam-6834	545	20	.	.	PUNCT
ejpam-6834	546	1	no	no	DET
ejpam-6834	546	2	additional	additional	ADJ
ejpam-6834	546	3	properties	property	NOUN
ejpam-6834	546	4	are	be	AUX
ejpam-6834	546	5	needed	need	VERB
ejpam-6834	546	6	to	to	PART
ejpam-6834	546	7	conclude	conclude	VERB
ejpam-6834	546	8	that	that	DET
ejpam-6834	546	9	f∗(τ	f∗(τ	NOUN
ejpam-6834	546	10	)	)	PUNCT
ejpam-6834	546	11	is	be	AUX
ejpam-6834	546	12	an	an	DET
ejpam-6834	546	13	(	(	PUNCT
ejpam-6834	546	14	m	m	PROPN
ejpam-6834	546	15	,	,	PUNCT
ejpam-6834	546	16	n)superhyperfuzzy	n)superhyperfuzzy	ADV
ejpam-6834	546	17	set	set	VERB
ejpam-6834	546	18	.	.	PUNCT
ejpam-6834	547	1	3.1.2	3.1.2	X
ejpam-6834	547	2	.	.	PUNCT
ejpam-6834	547	3	(	(	PUNCT
ejpam-6834	547	4	m	m	PROPN
ejpam-6834	547	5	,	,	PUNCT
ejpam-6834	547	6	n)-superhyperneutrosophic	n)-superhyperneutrosophic	PUNCT
ejpam-6834	547	7	set	set	VERB
ejpam-6834	547	8	an	an	DET
ejpam-6834	547	9	(	(	PUNCT
ejpam-6834	547	10	m	m	PROPN
ejpam-6834	547	11	,	,	PUNCT
ejpam-6834	547	12	n)-superhyperneutrosophic	n)-superhyperneutrosophic	ADJ
ejpam-6834	547	13	set	set	VERB
ejpam-6834	547	14	maps	map	NOUN
ejpam-6834	547	15	m	m	NOUN
ejpam-6834	547	16	-	-	PUNCT
ejpam-6834	547	17	level	level	NOUN
ejpam-6834	547	18	nested	nest	VERB
ejpam-6834	547	19	subsets	subset	NOUN
ejpam-6834	547	20	to	to	ADP
ejpam-6834	547	21	nonempty	nonempty	VERB
ejpam-6834	547	22	families	family	NOUN
ejpam-6834	547	23	of	of	ADP
ejpam-6834	547	24	n	n	CCONJ
ejpam-6834	547	25	-	-	PUNCT
ejpam-6834	547	26	level	level	NOUN
ejpam-6834	547	27	neutrosophic	neutrosophic	ADJ
ejpam-6834	547	28	triples	triple	NOUN
ejpam-6834	547	29	(	(	PUNCT
ejpam-6834	547	30	t	t	PROPN
ejpam-6834	547	31	,	,	PUNCT
ejpam-6834	547	32	i	i	PRON
ejpam-6834	547	33	,	,	PUNCT
ejpam-6834	547	34	f	f	PROPN
ejpam-6834	547	35	)	)	PUNCT
ejpam-6834	547	36	∈	∈	PROPN
ejpam-6834	548	1	[	[	X
ejpam-6834	548	2	0	0	NUM
ejpam-6834	548	3	,	,	PUNCT
ejpam-6834	548	4	1]3	1]3	NUM
ejpam-6834	548	5	,	,	PUNCT
ejpam-6834	548	6	thereby	thereby	ADV
ejpam-6834	548	7	modeling	model	VERB
ejpam-6834	548	8	hierarchical	hierarchical	ADJ
ejpam-6834	548	9	uncertainty	uncertainty	NOUN
ejpam-6834	548	10	across	across	ADP
ejpam-6834	548	11	levels	level	NOUN
ejpam-6834	548	12	.	.	PUNCT
ejpam-6834	549	1	t.	t.	PROPN
ejpam-6834	549	2	fujita	fujita	PROPN
ejpam-6834	549	3	,	,	PUNCT
ejpam-6834	549	4	f.smarandache	f.smarandache	NOUN
ejpam-6834	549	5	/	/	SYM
ejpam-6834	549	6	eur	eur	PROPN
ejpam-6834	549	7	.	.	PUNCT
ejpam-6834	550	1	j.	j.	PROPN
ejpam-6834	550	2	pure	pure	PROPN
ejpam-6834	550	3	appl	appl	PROPN
ejpam-6834	550	4	.	.	PROPN
ejpam-6834	550	5	math	math	PROPN
ejpam-6834	550	6	,	,	PUNCT
ejpam-6834	550	7	18	18	NUM
ejpam-6834	550	8	(	(	PUNCT
ejpam-6834	550	9	4	4	NUM
ejpam-6834	550	10	)	)	PUNCT
ejpam-6834	550	11	(	(	PUNCT
ejpam-6834	550	12	2025	2025	NUM
ejpam-6834	550	13	)	)	PUNCT
ejpam-6834	550	14	,	,	PUNCT
ejpam-6834	550	15	6834	6834	NUM
ejpam-6834	550	16	25	25	NUM
ejpam-6834	550	17	of	of	ADP
ejpam-6834	550	18	69	69	NUM
ejpam-6834	550	19	definition	definition	NOUN
ejpam-6834	550	20	20	20	NUM
ejpam-6834	550	21	(	(	PUNCT
ejpam-6834	550	22	(	(	PUNCT
ejpam-6834	550	23	m	m	PROPN
ejpam-6834	550	24	,	,	PUNCT
ejpam-6834	550	25	n)-superhyperneutrosophic	n)-superhyperneutrosophic	ADJ
ejpam-6834	550	26	set	set	NOUN
ejpam-6834	550	27	)	)	PUNCT
ejpam-6834	550	28	.	.	PUNCT
ejpam-6834	551	1	let	let	VERB
ejpam-6834	551	2	u	u	PRON
ejpam-6834	551	3	be	be	AUX
ejpam-6834	551	4	a	a	DET
ejpam-6834	551	5	universe	universe	NOUN
ejpam-6834	551	6	of	of	ADP
ejpam-6834	551	7	discourse	discourse	NOUN
ejpam-6834	551	8	and	and	CCONJ
ejpam-6834	551	9	let	let	VERB
ejpam-6834	551	10	a	a	DET
ejpam-6834	551	11	⊆	⊆	NUM
ejpam-6834	551	12	u	u	NOUN
ejpam-6834	551	13	be	be	AUX
ejpam-6834	551	14	nonempty	nonempty	ADJ
ejpam-6834	551	15	.	.	PUNCT
ejpam-6834	552	1	fix	fix	NOUN
ejpam-6834	552	2	m	m	PRON
ejpam-6834	552	3	,	,	PUNCT
ejpam-6834	552	4	n	n	PRON
ejpam-6834	552	5	∈	∈	PROPN
ejpam-6834	552	6	n	n	NOUN
ejpam-6834	552	7	∪	∪	X
ejpam-6834	552	8	{	{	PUNCT
ejpam-6834	552	9	0	0	NUM
ejpam-6834	552	10	}	}	PUNCT
ejpam-6834	552	11	.	.	PUNCT
ejpam-6834	553	1	define	define	VERB
ejpam-6834	553	2	recursively	recursively	ADV
ejpam-6834	553	3	p	p	NOUN
ejpam-6834	553	4	0(a	0(a	NOUN
ejpam-6834	553	5	)	)	PUNCT
ejpam-6834	553	6	=	=	SYM
ejpam-6834	554	1	a	a	PRON
ejpam-6834	554	2	,	,	PUNCT
ejpam-6834	554	3	p	p	NOUN
ejpam-6834	554	4	k(a	k(a	NOUN
ejpam-6834	554	5	)	)	PUNCT
ejpam-6834	554	6	=	=	SYM
ejpam-6834	555	1	p	p	X
ejpam-6834	555	2	(	(	PUNCT
ejpam-6834	555	3	p	p	PROPN
ejpam-6834	555	4	k−1(a	k−1(a	PROPN
ejpam-6834	555	5	)	)	PUNCT
ejpam-6834	555	6	)	)	PUNCT
ejpam-6834	556	1	(	(	PUNCT
ejpam-6834	556	2	k	k	X
ejpam-6834	556	3	≥	≥	NUM
ejpam-6834	556	4	1	1	NUM
ejpam-6834	556	5	)	)	PUNCT
ejpam-6834	556	6	,	,	PUNCT
ejpam-6834	556	7	and	and	CCONJ
ejpam-6834	556	8	analogously	analogously	ADV
ejpam-6834	556	9	for	for	ADP
ejpam-6834	556	10	p	p	PRON
ejpam-6834	556	11	n([0	n([0	NOUN
ejpam-6834	556	12	,	,	PUNCT
ejpam-6834	556	13	1]3	1]3	NUM
ejpam-6834	556	14	)	)	PUNCT
ejpam-6834	556	15	.	.	PUNCT
ejpam-6834	557	1	an	an	PRON
ejpam-6834	557	2	(	(	PUNCT
ejpam-6834	557	3	m	m	PROPN
ejpam-6834	557	4	,	,	PUNCT
ejpam-6834	557	5	n)-superhyperneutrosophic	n)-superhyperneutrosophic	PUNCT
ejpam-6834	557	6	set	set	VERB
ejpam-6834	557	7	on	on	ADP
ejpam-6834	557	8	a	a	PRON
ejpam-6834	557	9	is	be	AUX
ejpam-6834	557	10	a	a	DET
ejpam-6834	557	11	mapping	mapping	NOUN
ejpam-6834	557	12	µ	µ	NOUN
ejpam-6834	557	13	:	:	PUNCT
ejpam-6834	557	14	p	p	PROPN
ejpam-6834	557	15	m(a	m(a	PROPN
ejpam-6834	557	16	)	)	PUNCT
ejpam-6834	557	17	−→	−→	NOUN
ejpam-6834	557	18	p	p	NOUN
ejpam-6834	557	19	n	n	NOUN
ejpam-6834	557	20	(	(	PUNCT
ejpam-6834	557	21	[	[	X
ejpam-6834	557	22	0	0	NUM
ejpam-6834	557	23	,	,	PUNCT
ejpam-6834	557	24	1]3	1]3	NUM
ejpam-6834	557	25	)	)	PUNCT
ejpam-6834	557	26	such	such	ADJ
ejpam-6834	557	27	that	that	PRON
ejpam-6834	557	28	for	for	ADP
ejpam-6834	557	29	each	each	DET
ejpam-6834	557	30	x	x	SYM
ejpam-6834	557	31	∈	∈	PROPN
ejpam-6834	557	32	p	p	PROPN
ejpam-6834	557	33	m(a	m(a	PROPN
ejpam-6834	557	34	)	)	PUNCT
ejpam-6834	557	35	the	the	DET
ejpam-6834	557	36	value	value	NOUN
ejpam-6834	557	37	µ(x	µ(x	X
ejpam-6834	557	38	)	)	PUNCT
ejpam-6834	557	39	is	be	AUX
ejpam-6834	557	40	nonempty	nonempty	ADJ
ejpam-6834	557	41	and	and	CCONJ
ejpam-6834	557	42	every	every	DET
ejpam-6834	557	43	triple	triple	ADJ
ejpam-6834	557	44	(	(	PUNCT
ejpam-6834	557	45	t	t	PROPN
ejpam-6834	557	46	,	,	PUNCT
ejpam-6834	557	47	i	i	PRON
ejpam-6834	557	48	,	,	PUNCT
ejpam-6834	557	49	f	f	PROPN
ejpam-6834	557	50	)	)	PUNCT
ejpam-6834	557	51	occurring	occur	VERB
ejpam-6834	557	52	at	at	ADP
ejpam-6834	557	53	level	level	NOUN
ejpam-6834	557	54	1	1	NUM
ejpam-6834	557	55	inside	inside	ADP
ejpam-6834	557	56	µ(x	µ(x	NOUN
ejpam-6834	557	57	)	)	PUNCT
ejpam-6834	557	58	satisfies	satisfie	NOUN
ejpam-6834	557	59	0	0	NUM
ejpam-6834	557	60	≤	≤	NUM
ejpam-6834	557	61	t	t	NOUN
ejpam-6834	558	1	+	+	CCONJ
ejpam-6834	558	2	i	i	PRON
ejpam-6834	558	3	+	+	NUM
ejpam-6834	558	4	f	f	PROPN
ejpam-6834	558	5	≤	≤	ADV
ejpam-6834	558	6	3	3	NUM
ejpam-6834	558	7	.	.	PUNCT
ejpam-6834	559	1	equivalently	equivalently	ADV
ejpam-6834	559	2	,	,	PUNCT
ejpam-6834	559	3	un→1	un→1	PROPN
ejpam-6834	559	4	(	(	PUNCT
ejpam-6834	559	5	µ(x	µ(x	PROPN
ejpam-6834	559	6	)	)	PUNCT
ejpam-6834	559	7	)	)	PUNCT
ejpam-6834	560	1	⊆	⊆	NUM
ejpam-6834	560	2	[	[	X
ejpam-6834	560	3	0	0	NUM
ejpam-6834	560	4	,	,	PUNCT
ejpam-6834	560	5	1]3	1]3	NUM
ejpam-6834	560	6	is	be	AUX
ejpam-6834	560	7	nonempty	nonempty	ADJ
ejpam-6834	560	8	and	and	CCONJ
ejpam-6834	560	9	consists	consist	VERB
ejpam-6834	560	10	of	of	ADP
ejpam-6834	560	11	triples	triple	NOUN
ejpam-6834	560	12	obeying	obey	VERB
ejpam-6834	560	13	t	t	NOUN
ejpam-6834	560	14	+	+	PROPN
ejpam-6834	560	15	i+f	i+f	PROPN
ejpam-6834	560	16	≤	≤	NUM
ejpam-6834	560	17	3	3	NUM
ejpam-6834	560	18	,	,	PUNCT
ejpam-6834	560	19	where	where	SCONJ
ejpam-6834	560	20	un→1	un→1	PROPN
ejpam-6834	560	21	denotes	denote	NOUN
ejpam-6834	560	22	iterated	iterate	VERB
ejpam-6834	560	23	union	union	NOUN
ejpam-6834	560	24	(	(	PUNCT
ejpam-6834	560	25	flattening	flattening	NOUN
ejpam-6834	560	26	)	)	PUNCT
ejpam-6834	560	27	from	from	ADP
ejpam-6834	560	28	level	level	NOUN
ejpam-6834	560	29	n	n	ADP
ejpam-6834	560	30	to	to	PART
ejpam-6834	560	31	level	level	VERB
ejpam-6834	560	32	1	1	NUM
ejpam-6834	560	33	.	.	PUNCT
ejpam-6834	560	34	notation	notation	NOUN
ejpam-6834	560	35	2	2	NUM
ejpam-6834	560	36	(	(	PUNCT
ejpam-6834	560	37	canonical	canonical	ADJ
ejpam-6834	560	38	embedding	embed	VERB
ejpam-6834	560	39	and	and	CCONJ
ejpam-6834	560	40	flattening	flattening	NOUN
ejpam-6834	560	41	)	)	PUNCT
ejpam-6834	560	42	.	.	PUNCT
ejpam-6834	561	1	for	for	ADP
ejpam-6834	561	2	r	r	NOUN
ejpam-6834	561	3	≤	≤	NUM
ejpam-6834	561	4	s	s	VERB
ejpam-6834	561	5	with	with	ADP
ejpam-6834	561	6	r	r	NOUN
ejpam-6834	561	7	≥	≥	NUM
ejpam-6834	561	8	1	1	NUM
ejpam-6834	561	9	,	,	PUNCT
ejpam-6834	561	10	the	the	DET
ejpam-6834	561	11	canonical	canonical	NOUN
ejpam-6834	561	12	embedding	embed	VERB
ejpam-6834	561	13	ιr→s	ιr→s	NOUN
ejpam-6834	561	14	:	:	PUNCT
ejpam-6834	561	15	p	p	X
ejpam-6834	561	16	r(s	r(s	PROPN
ejpam-6834	561	17	)	)	PUNCT
ejpam-6834	561	18	→	→	SYM
ejpam-6834	561	19	p	p	PROPN
ejpam-6834	561	20	s(s	s(s	PROPN
ejpam-6834	561	21	)	)	PUNCT
ejpam-6834	561	22	is	be	AUX
ejpam-6834	561	23	defined	define	VERB
ejpam-6834	561	24	by	by	ADP
ejpam-6834	561	25	ιr→r	ιr→r	PUNCT
ejpam-6834	562	1	=	=	PUNCT
ejpam-6834	562	2	i	i	PROPN
ejpam-6834	562	3	d	d	PROPN
ejpam-6834	562	4	and	and	CCONJ
ejpam-6834	562	5	ιr→(t+1)(x	ιr→(t+1)(x	PROPN
ejpam-6834	562	6	)	)	PUNCT
ejpam-6834	563	1	=	=	PRON
ejpam-6834	563	2	{	{	PUNCT
ejpam-6834	563	3	ιr→t(x	ιr→t(x	NOUN
ejpam-6834	563	4	)	)	PUNCT
ejpam-6834	563	5	}	}	PUNCT
ejpam-6834	563	6	for	for	ADP
ejpam-6834	563	7	t	t	PROPN
ejpam-6834	563	8	≥	≥	NOUN
ejpam-6834	563	9	r	r	NOUN
ejpam-6834	563	10	;	;	PUNCT
ejpam-6834	563	11	hence	hence	ADV
ejpam-6834	563	12	it	it	PRON
ejpam-6834	563	13	nests	nest	VERB
ejpam-6834	563	14	x	x	PUNCT
ejpam-6834	563	15	by	by	ADP
ejpam-6834	563	16	s−	s−	PROPN
ejpam-6834	563	17	r	r	NOUN
ejpam-6834	563	18	singletons	singleton	NOUN
ejpam-6834	563	19	.	.	PUNCT
ejpam-6834	564	1	for	for	ADP
ejpam-6834	564	2	s	s	PRON
ejpam-6834	564	3	>	>	X
ejpam-6834	564	4	r	r	NOUN
ejpam-6834	564	5	≥	≥	NOUN
ejpam-6834	564	6	0	0	NUM
ejpam-6834	564	7	,	,	PUNCT
ejpam-6834	564	8	the	the	DET
ejpam-6834	564	9	level	level	NOUN
ejpam-6834	564	10	-	-	PUNCT
ejpam-6834	564	11	flattening	flattening	NOUN
ejpam-6834	564	12	map	map	NOUN
ejpam-6834	564	13	us→r	us→r	NOUN
ejpam-6834	564	14	:	:	PUNCT
ejpam-6834	564	15	p	p	PROPN
ejpam-6834	564	16	s(s	s(s	PROPN
ejpam-6834	564	17	)	)	PUNCT
ejpam-6834	564	18	→	→	PUNCT
ejpam-6834	564	19	p	p	PRON
ejpam-6834	564	20	r(s	r(s	PROPN
ejpam-6834	564	21	)	)	PUNCT
ejpam-6834	564	22	is	be	AUX
ejpam-6834	564	23	given	give	VERB
ejpam-6834	564	24	by	by	ADP
ejpam-6834	564	25	us→(s−1)(y	us→(s−1)(y	PROPN
ejpam-6834	564	26	)	)	PUNCT
ejpam-6834	565	1	=	=	PUNCT
ejpam-6834	566	1	⋃	⋃	PUNCT
ejpam-6834	566	2	y	y	NOUN
ejpam-6834	566	3	and	and	CCONJ
ejpam-6834	566	4	us→r	us→r	NOUN
ejpam-6834	566	5	=	=	NOUN
ejpam-6834	566	6	u(r+1)→r	u(r+1)→r	NOUN
ejpam-6834	566	7	◦	◦	NOUN
ejpam-6834	566	8	·	·	PUNCT
ejpam-6834	566	9	·	·	PUNCT
ejpam-6834	566	10	·	·	PUNCT
ejpam-6834	566	11	◦	◦	NOUN
ejpam-6834	566	12	us→(s−1	us→(s−1	NOUN
ejpam-6834	566	13	)	)	PUNCT
ejpam-6834	566	14	.	.	PUNCT
ejpam-6834	567	1	example	example	NOUN
ejpam-6834	567	2	16	16	NUM
ejpam-6834	567	3	(	(	PUNCT
ejpam-6834	567	4	multi	multi	ADJ
ejpam-6834	567	5	-	-	ADJ
ejpam-6834	567	6	expert	expert	ADJ
ejpam-6834	567	7	risk	risk	NOUN
ejpam-6834	567	8	assessment	assessment	NOUN
ejpam-6834	567	9	)	)	PUNCT
ejpam-6834	567	10	.	.	PUNCT
ejpam-6834	568	1	let	let	VERB
ejpam-6834	568	2	a	a	DET
ejpam-6834	568	3	=	=	PUNCT
ejpam-6834	568	4	{	{	PUNCT
ejpam-6834	568	5	a1	a1	PROPN
ejpam-6834	568	6	,	,	PUNCT
ejpam-6834	568	7	a2	a2	PROPN
ejpam-6834	568	8	}	}	PUNCT
ejpam-6834	568	9	and	and	CCONJ
ejpam-6834	568	10	m	m	PROPN
ejpam-6834	568	11	=	=	SYM
ejpam-6834	568	12	n	n	PROPN
ejpam-6834	568	13	=	=	SYM
ejpam-6834	568	14	1	1	NUM
ejpam-6834	568	15	,	,	PUNCT
ejpam-6834	568	16	so	so	ADV
ejpam-6834	568	17	p	p	NOUN
ejpam-6834	568	18	1(a	1(a	NUM
ejpam-6834	568	19	)	)	PUNCT
ejpam-6834	569	1	=	=	SYM
ejpam-6834	569	2	p(a	p(a	PROPN
ejpam-6834	569	3	)	)	PUNCT
ejpam-6834	569	4	and	and	CCONJ
ejpam-6834	569	5	p	p	NOUN
ejpam-6834	569	6	1([0	1([0	NUM
ejpam-6834	569	7	,	,	PUNCT
ejpam-6834	569	8	1]3	1]3	NUM
ejpam-6834	569	9	)	)	PUNCT
ejpam-6834	569	10	=	=	SYM
ejpam-6834	569	11	p([0	p([0	ADJ
ejpam-6834	569	12	,	,	PUNCT
ejpam-6834	569	13	1]3	1]3	NUM
ejpam-6834	569	14	)	)	PUNCT
ejpam-6834	569	15	.	.	PUNCT
ejpam-6834	570	1	suppose	suppose	VERB
ejpam-6834	570	2	two	two	NUM
ejpam-6834	570	3	experts	expert	NOUN
ejpam-6834	570	4	assess	assess	VERB
ejpam-6834	570	5	{	{	PUNCT
ejpam-6834	570	6	a1	a1	NOUN
ejpam-6834	570	7	,	,	PUNCT
ejpam-6834	570	8	a2	a2	PROPN
ejpam-6834	570	9	}	}	PUNCT
ejpam-6834	570	10	.	.	PUNCT
ejpam-6834	571	1	define	define	VERB
ejpam-6834	571	2	µ({a1	µ({a1	NOUN
ejpam-6834	571	3	,	,	PUNCT
ejpam-6834	571	4	a2	a2	NOUN
ejpam-6834	571	5	}	}	PUNCT
ejpam-6834	571	6	)	)	PUNCT
ejpam-6834	572	1	=	=	PRON
ejpam-6834	572	2	{	{	PUNCT
ejpam-6834	572	3	(	(	PUNCT
ejpam-6834	572	4	0.80	0.80	NUM
ejpam-6834	572	5	,	,	PUNCT
ejpam-6834	572	6	0.15	0.15	NUM
ejpam-6834	572	7	,	,	PUNCT
ejpam-6834	572	8	0.05	0.05	NUM
ejpam-6834	572	9	)	)	PUNCT
ejpam-6834	572	10	,	,	PUNCT
ejpam-6834	572	11	(	(	PUNCT
ejpam-6834	572	12	0.75	0.75	NUM
ejpam-6834	572	13	,	,	PUNCT
ejpam-6834	572	14	0.20	0.20	NUM
ejpam-6834	572	15	,	,	PUNCT
ejpam-6834	572	16	0.05	0.05	NUM
ejpam-6834	572	17	)	)	PUNCT
ejpam-6834	572	18	}	}	PUNCT
ejpam-6834	572	19	,	,	PUNCT
ejpam-6834	572	20	µ({a1	µ({a1	NOUN
ejpam-6834	572	21	}	}	PUNCT
ejpam-6834	572	22	)	)	PUNCT
ejpam-6834	572	23	=	=	PRON
ejpam-6834	572	24	{	{	PUNCT
ejpam-6834	572	25	(	(	PUNCT
ejpam-6834	572	26	0.60	0.60	NUM
ejpam-6834	572	27	,	,	PUNCT
ejpam-6834	572	28	0.25	0.25	NUM
ejpam-6834	572	29	,	,	PUNCT
ejpam-6834	572	30	0.15	0.15	NUM
ejpam-6834	572	31	)	)	PUNCT
ejpam-6834	572	32	}	}	PUNCT
ejpam-6834	572	33	,	,	PUNCT
ejpam-6834	572	34	µ({a2	µ({a2	PROPN
ejpam-6834	572	35	}	}	PUNCT
ejpam-6834	572	36	)	)	PUNCT
ejpam-6834	572	37	=	=	PRON
ejpam-6834	572	38	{	{	PUNCT
ejpam-6834	572	39	(	(	PUNCT
ejpam-6834	572	40	0.50	0.50	NUM
ejpam-6834	572	41	,	,	PUNCT
ejpam-6834	572	42	0.30	0.30	NUM
ejpam-6834	572	43	,	,	PUNCT
ejpam-6834	572	44	0.20	0.20	NUM
ejpam-6834	572	45	)	)	PUNCT
ejpam-6834	572	46	}	}	PUNCT
ejpam-6834	572	47	,	,	PUNCT
ejpam-6834	572	48	µ(∅	µ(∅	NOUN
ejpam-6834	572	49	)	)	PUNCT
ejpam-6834	572	50	=	=	PRON
ejpam-6834	572	51	{	{	PUNCT
ejpam-6834	572	52	(	(	PUNCT
ejpam-6834	572	53	0	0	NUM
ejpam-6834	572	54	,	,	PUNCT
ejpam-6834	572	55	0	0	NUM
ejpam-6834	572	56	,	,	PUNCT
ejpam-6834	572	57	0	0	NUM
ejpam-6834	572	58	)	)	PUNCT
ejpam-6834	572	59	}	}	PUNCT
ejpam-6834	572	60	.	.	PUNCT
ejpam-6834	573	1	each	each	DET
ejpam-6834	573	2	triple	triple	ADJ
ejpam-6834	573	3	satisfies	satisfie	NOUN
ejpam-6834	573	4	0	0	NUM
ejpam-6834	573	5	≤	≤	NUM
ejpam-6834	573	6	t	t	NOUN
ejpam-6834	574	1	+	+	CCONJ
ejpam-6834	574	2	i	i	PRON
ejpam-6834	574	3	+	+	NUM
ejpam-6834	574	4	f	f	PROPN
ejpam-6834	574	5	≤	≤	ADV
ejpam-6834	574	6	3	3	NUM
ejpam-6834	574	7	,	,	PUNCT
ejpam-6834	574	8	so	so	ADV
ejpam-6834	574	9	µ	µ	NOUN
ejpam-6834	574	10	is	be	AUX
ejpam-6834	574	11	(	(	PUNCT
ejpam-6834	574	12	1	1	NUM
ejpam-6834	574	13	,	,	PUNCT
ejpam-6834	574	14	1)-superhyperneutrosophic	1)-superhyperneutrosophic	NUM
ejpam-6834	574	15	.	.	PUNCT
ejpam-6834	574	16	example	example	NOUN
ejpam-6834	575	1	17	17	NUM
ejpam-6834	575	2	(	(	PUNCT
ejpam-6834	575	3	hierarchical	hierarchical	ADJ
ejpam-6834	575	4	fault	fault	NOUN
ejpam-6834	575	5	diagnosis	diagnosis	NOUN
ejpam-6834	575	6	in	in	ADP
ejpam-6834	575	7	an	an	DET
ejpam-6834	575	8	industrial	industrial	ADJ
ejpam-6834	575	9	iot	iot	NOUN
ejpam-6834	575	10	network	network	NOUN
ejpam-6834	575	11	)	)	PUNCT
ejpam-6834	575	12	.	.	PUNCT
ejpam-6834	576	1	let	let	VERB
ejpam-6834	576	2	a	a	DET
ejpam-6834	576	3	=	=	PUNCT
ejpam-6834	576	4	{	{	PUNCT
ejpam-6834	576	5	tempsensor	tempsensor	PROPN
ejpam-6834	576	6	,	,	PUNCT
ejpam-6834	576	7	vibsensor	vibsensor	NOUN
ejpam-6834	576	8	}	}	PUNCT
ejpam-6834	576	9	,	,	PUNCT
ejpam-6834	576	10	m	m	VERB
ejpam-6834	576	11	=	=	NOUN
ejpam-6834	576	12	1	1	NUM
ejpam-6834	576	13	,	,	PUNCT
ejpam-6834	576	14	n	n	NOUN
ejpam-6834	576	15	=	=	SYM
ejpam-6834	576	16	2	2	X
ejpam-6834	576	17	.	.	PUNCT
ejpam-6834	576	18	define	define	VERB
ejpam-6834	576	19	µ	µ	X
ejpam-6834	576	20	:	:	PUNCT
ejpam-6834	576	21	p(a	p(a	PROPN
ejpam-6834	576	22	)	)	PUNCT
ejpam-6834	576	23	−→	−→	NOUN
ejpam-6834	576	24	p	p	X
ejpam-6834	576	25	(	(	PUNCT
ejpam-6834	576	26	p([0	p([0	ADJ
ejpam-6834	576	27	,	,	PUNCT
ejpam-6834	576	28	1]3	1]3	NUM
ejpam-6834	576	29	)	)	PUNCT
ejpam-6834	576	30	)	)	PUNCT
ejpam-6834	576	31	by	by	ADP
ejpam-6834	576	32	,	,	PUNCT
ejpam-6834	576	33	for	for	ADP
ejpam-6834	576	34	x	x	SYM
ejpam-6834	576	35	=	=	PRON
ejpam-6834	576	36	{	{	PUNCT
ejpam-6834	576	37	tempsensor	tempsensor	PROPN
ejpam-6834	576	38	,	,	PUNCT
ejpam-6834	576	39	vibsensor	vibsensor	NOUN
ejpam-6834	576	40	}	}	PUNCT
ejpam-6834	576	41	,	,	PUNCT
ejpam-6834	576	42	µ(x	µ(x	X
ejpam-6834	576	43	)	)	PUNCT
ejpam-6834	576	44	=	=	PRON
ejpam-6834	576	45	{	{	PUNCT
ejpam-6834	576	46	{	{	PUNCT
ejpam-6834	576	47	(	(	PUNCT
ejpam-6834	576	48	0.85	0.85	NUM
ejpam-6834	576	49	,	,	PUNCT
ejpam-6834	576	50	0.10	0.10	NUM
ejpam-6834	576	51	,	,	PUNCT
ejpam-6834	576	52	0.05	0.05	NUM
ejpam-6834	576	53	)	)	PUNCT
ejpam-6834	576	54	,	,	PUNCT
ejpam-6834	576	55	(	(	PUNCT
ejpam-6834	576	56	0.80	0.80	NUM
ejpam-6834	576	57	,	,	PUNCT
ejpam-6834	576	58	0.15	0.15	NUM
ejpam-6834	576	59	,	,	PUNCT
ejpam-6834	576	60	0.05	0.05	NUM
ejpam-6834	576	61	)	)	PUNCT
ejpam-6834	576	62	}	}	PUNCT
ejpam-6834	576	63	,	,	PUNCT
ejpam-6834	576	64	{	{	PUNCT
ejpam-6834	576	65	(	(	PUNCT
ejpam-6834	576	66	0.60	0.60	NUM
ejpam-6834	576	67	,	,	PUNCT
ejpam-6834	576	68	0.25	0.25	NUM
ejpam-6834	576	69	,	,	PUNCT
ejpam-6834	576	70	0.15	0.15	NUM
ejpam-6834	576	71	)	)	PUNCT
ejpam-6834	576	72	}	}	PUNCT
ejpam-6834	576	73	}	}	PUNCT
ejpam-6834	576	74	.	.	PUNCT
ejpam-6834	577	1	flattening	flattening	NOUN
ejpam-6834	577	2	gives	give	VERB
ejpam-6834	577	3	u2→1(µ(x	u2→1(µ(x	NOUN
ejpam-6834	577	4	)	)	PUNCT
ejpam-6834	577	5	)	)	PUNCT
ejpam-6834	578	1	=	=	PRON
ejpam-6834	578	2	{	{	PUNCT
ejpam-6834	578	3	(	(	PUNCT
ejpam-6834	578	4	0.85	0.85	NUM
ejpam-6834	578	5	,	,	PUNCT
ejpam-6834	578	6	0.10	0.10	NUM
ejpam-6834	578	7	,	,	PUNCT
ejpam-6834	578	8	0.05	0.05	NUM
ejpam-6834	578	9	)	)	PUNCT
ejpam-6834	578	10	,	,	PUNCT
ejpam-6834	578	11	(	(	PUNCT
ejpam-6834	578	12	0.80	0.80	NUM
ejpam-6834	578	13	,	,	PUNCT
ejpam-6834	578	14	0.15	0.15	NUM
ejpam-6834	578	15	,	,	PUNCT
ejpam-6834	578	16	0.05	0.05	NUM
ejpam-6834	578	17	)	)	PUNCT
ejpam-6834	578	18	,	,	PUNCT
ejpam-6834	578	19	(	(	PUNCT
ejpam-6834	578	20	0.60	0.60	NUM
ejpam-6834	578	21	,	,	PUNCT
ejpam-6834	578	22	0.25	0.25	NUM
ejpam-6834	578	23	,	,	PUNCT
ejpam-6834	578	24	0.15	0.15	NUM
ejpam-6834	578	25	)	)	PUNCT
ejpam-6834	578	26	}	}	PUNCT
ejpam-6834	578	27	,	,	PUNCT
ejpam-6834	578	28	all	all	DET
ejpam-6834	578	29	obeying	obey	VERB
ejpam-6834	578	30	t	t	NOUN
ejpam-6834	579	1	+	+	CCONJ
ejpam-6834	579	2	i	i	PRON
ejpam-6834	579	3	+	+	NUM
ejpam-6834	579	4	f	f	PROPN
ejpam-6834	579	5	≤	≤	ADV
ejpam-6834	579	6	3	3	NUM
ejpam-6834	579	7	.	.	PUNCT
ejpam-6834	579	8	t.	t.	PROPN
ejpam-6834	579	9	fujita	fujita	PROPN
ejpam-6834	579	10	,	,	PUNCT
ejpam-6834	579	11	f.smarandache	f.smarandache	NOUN
ejpam-6834	579	12	/	/	SYM
ejpam-6834	579	13	eur	eur	PROPN
ejpam-6834	579	14	.	.	PUNCT
ejpam-6834	580	1	j.	j.	PROPN
ejpam-6834	580	2	pure	pure	PROPN
ejpam-6834	580	3	appl	appl	PROPN
ejpam-6834	580	4	.	.	PROPN
ejpam-6834	580	5	math	math	PROPN
ejpam-6834	580	6	,	,	PUNCT
ejpam-6834	580	7	18	18	NUM
ejpam-6834	580	8	(	(	PUNCT
ejpam-6834	580	9	4	4	NUM
ejpam-6834	580	10	)	)	PUNCT
ejpam-6834	580	11	(	(	PUNCT
ejpam-6834	580	12	2025	2025	NUM
ejpam-6834	580	13	)	)	PUNCT
ejpam-6834	580	14	,	,	PUNCT
ejpam-6834	580	15	6834	6834	NUM
ejpam-6834	580	16	26	26	NUM
ejpam-6834	580	17	of	of	ADP
ejpam-6834	580	18	69	69	NUM
ejpam-6834	580	19	theorem	theorem	NOUN
ejpam-6834	580	20	8	8	NUM
ejpam-6834	580	21	.	.	PUNCT
ejpam-6834	581	1	every	every	DET
ejpam-6834	581	2	n	n	ADV
ejpam-6834	581	3	-	-	PUNCT
ejpam-6834	581	4	superhyperneutrosophic	superhyperneutrosophic	ADJ
ejpam-6834	581	5	set	set	NOUN
ejpam-6834	581	6	ãn	ãn	NOUN
ejpam-6834	581	7	:	:	PUNCT
ejpam-6834	581	8	p	p	X
ejpam-6834	581	9	n(x	n(x	PROPN
ejpam-6834	581	10	)	)	PUNCT
ejpam-6834	581	11	→	→	SYM
ejpam-6834	581	12	p	p	X
ejpam-6834	581	13	n([0	n([0	NOUN
ejpam-6834	581	14	,	,	PUNCT
ejpam-6834	581	15	1]3	1]3	NUM
ejpam-6834	581	16	)	)	PUNCT
ejpam-6834	581	17	is	be	AUX
ejpam-6834	581	18	obtained	obtain	VERB
ejpam-6834	581	19	as	as	ADP
ejpam-6834	581	20	the	the	DET
ejpam-6834	581	21	special	special	ADJ
ejpam-6834	581	22	case	case	NOUN
ejpam-6834	581	23	m	m	NOUN
ejpam-6834	581	24	=	=	NOUN
ejpam-6834	581	25	1	1	NUM
ejpam-6834	581	26	of	of	ADP
ejpam-6834	581	27	an	an	DET
ejpam-6834	581	28	(	(	PUNCT
ejpam-6834	581	29	m	m	PROPN
ejpam-6834	581	30	,	,	PUNCT
ejpam-6834	581	31	n)-superhyperneutrosophic	n)-superhyperneutrosophic	PUNCT
ejpam-6834	581	32	set	set	VERB
ejpam-6834	581	33	on	on	ADP
ejpam-6834	581	34	x.	x.	NOUN
ejpam-6834	581	35	proof	proof	NOUN
ejpam-6834	581	36	.	.	PUNCT
ejpam-6834	582	1	define	define	VERB
ejpam-6834	582	2	µ	µ	X
ejpam-6834	582	3	:	:	PUNCT
ejpam-6834	582	4	=	=	SYM
ejpam-6834	582	5	ãn	ãn	ADP
ejpam-6834	582	6	◦	◦	VERB
ejpam-6834	582	7	ι1→n	ι1→n	INTJ
ejpam-6834	582	8	:	:	PUNCT
ejpam-6834	582	9	p	p	NOUN
ejpam-6834	582	10	1(x	1(x	NUM
ejpam-6834	582	11	)	)	PUNCT
ejpam-6834	582	12	→	→	SYM
ejpam-6834	583	1	p	p	X
ejpam-6834	583	2	n([0	n([0	NOUN
ejpam-6834	583	3	,	,	PUNCT
ejpam-6834	583	4	1]3	1]3	NUM
ejpam-6834	583	5	)	)	PUNCT
ejpam-6834	583	6	.	.	PUNCT
ejpam-6834	584	1	this	this	DET
ejpam-6834	584	2	composition	composition	NOUN
ejpam-6834	584	3	is	be	AUX
ejpam-6834	584	4	well	well	ADV
ejpam-6834	584	5	-	-	PUNCT
ejpam-6834	584	6	defined	define	VERB
ejpam-6834	584	7	since	since	SCONJ
ejpam-6834	584	8	ι1→n	ι1→n	PROPN
ejpam-6834	584	9	maps	maps	PROPN
ejpam-6834	584	10	p(x	p(x	PROPN
ejpam-6834	584	11	)	)	PUNCT
ejpam-6834	584	12	into	into	ADP
ejpam-6834	584	13	p	p	NOUN
ejpam-6834	584	14	n(x	n(x	PROPN
ejpam-6834	584	15	)	)	PUNCT
ejpam-6834	584	16	.	.	PUNCT
ejpam-6834	585	1	for	for	ADP
ejpam-6834	585	2	any	any	DET
ejpam-6834	585	3	a	a	DET
ejpam-6834	585	4	∈	∈	PROPN
ejpam-6834	585	5	p(x	p(x	NOUN
ejpam-6834	585	6	)	)	PUNCT
ejpam-6834	585	7	we	we	PRON
ejpam-6834	585	8	have	have	VERB
ejpam-6834	585	9	µ(a	µ(a	PROPN
ejpam-6834	585	10	)	)	PUNCT
ejpam-6834	586	1	=	=	SYM
ejpam-6834	586	2	ãn	ãn	X
ejpam-6834	586	3	(	(	PUNCT
ejpam-6834	586	4	ι1→n(a	ι1→n(a	NOUN
ejpam-6834	586	5	)	)	PUNCT
ejpam-6834	586	6	)	)	PUNCT
ejpam-6834	586	7	,	,	PUNCT
ejpam-6834	586	8	hence	hence	ADV
ejpam-6834	586	9	µ	µ	ADV
ejpam-6834	586	10	agrees	agree	VERB
ejpam-6834	586	11	with	with	ADP
ejpam-6834	586	12	ãn	ãn	NOUN
ejpam-6834	586	13	on	on	ADP
ejpam-6834	586	14	the	the	DET
ejpam-6834	586	15	level	level	NOUN
ejpam-6834	586	16	-	-	PUNCT
ejpam-6834	586	17	n	n	NOUN
ejpam-6834	586	18	images	image	NOUN
ejpam-6834	586	19	of	of	ADP
ejpam-6834	586	20	level-1	level-1	NUM
ejpam-6834	586	21	inputs	input	NOUN
ejpam-6834	586	22	.	.	PUNCT
ejpam-6834	587	1	because	because	SCONJ
ejpam-6834	587	2	ãn(a′	ãn(a′	NUM
ejpam-6834	587	3	)	)	PUNCT
ejpam-6834	587	4	is	be	AUX
ejpam-6834	587	5	nonempty	nonempty	ADJ
ejpam-6834	587	6	for	for	ADP
ejpam-6834	587	7	each	each	DET
ejpam-6834	587	8	a′	a′	NOUN
ejpam-6834	587	9	∈	∈	PROPN
ejpam-6834	587	10	p	p	PROPN
ejpam-6834	587	11	n(x	n(x	PROPN
ejpam-6834	587	12	)	)	PUNCT
ejpam-6834	587	13	and	and	CCONJ
ejpam-6834	587	14	its	its	PRON
ejpam-6834	587	15	level-1	level-1	NUM
ejpam-6834	587	16	elements	element	NOUN
ejpam-6834	587	17	satisfy	satisfy	VERB
ejpam-6834	587	18	t	t	PROPN
ejpam-6834	588	1	+	+	CCONJ
ejpam-6834	588	2	i	i	PRON
ejpam-6834	588	3	+	+	NUM
ejpam-6834	588	4	f	f	PROPN
ejpam-6834	588	5	≤	≤	ADV
ejpam-6834	588	6	3	3	NUM
ejpam-6834	588	7	,	,	PUNCT
ejpam-6834	588	8	the	the	DET
ejpam-6834	588	9	same	same	ADJ
ejpam-6834	588	10	properties	property	NOUN
ejpam-6834	588	11	hold	hold	VERB
ejpam-6834	588	12	for	for	ADP
ejpam-6834	588	13	µ(a	µ(a	PROPN
ejpam-6834	588	14	)	)	PUNCT
ejpam-6834	588	15	.	.	PUNCT
ejpam-6834	589	1	thus	thus	ADV
ejpam-6834	589	2	µ	µ	X
ejpam-6834	589	3	is	be	AUX
ejpam-6834	589	4	(	(	PUNCT
ejpam-6834	589	5	1	1	NUM
ejpam-6834	589	6	,	,	PUNCT
ejpam-6834	589	7	n)-superhyperneutrosophic	n)-superhyperneutrosophic	ADJ
ejpam-6834	589	8	,	,	PUNCT
ejpam-6834	589	9	realizing	realize	VERB
ejpam-6834	589	10	ãn	ãn	NOUN
ejpam-6834	589	11	as	as	ADP
ejpam-6834	589	12	the	the	DET
ejpam-6834	589	13	m	m	NOUN
ejpam-6834	589	14	=	=	SYM
ejpam-6834	589	15	1	1	NUM
ejpam-6834	589	16	case	case	NOUN
ejpam-6834	589	17	.	.	PUNCT
ejpam-6834	590	1	theorem	theorem	NOUN
ejpam-6834	590	2	9	9	NUM
ejpam-6834	590	3	(	(	PUNCT
ejpam-6834	590	4	restriction	restriction	NOUN
ejpam-6834	590	5	to	to	PART
ejpam-6834	590	6	lower	low	ADJ
ejpam-6834	590	7	m	m	NOUN
ejpam-6834	590	8	)	)	PUNCT
ejpam-6834	590	9	.	.	PUNCT
ejpam-6834	591	1	let	let	VERB
ejpam-6834	591	2	µ	µ	PRON
ejpam-6834	591	3	:	:	PUNCT
ejpam-6834	591	4	p	p	PROPN
ejpam-6834	591	5	m(a	m(a	PROPN
ejpam-6834	591	6	)	)	PUNCT
ejpam-6834	591	7	→	→	SYM
ejpam-6834	592	1	p	p	X
ejpam-6834	592	2	n([0	n([0	NOUN
ejpam-6834	592	3	,	,	PUNCT
ejpam-6834	592	4	1]3	1]3	NUM
ejpam-6834	592	5	)	)	PUNCT
ejpam-6834	593	1	be	be	AUX
ejpam-6834	593	2	(	(	PUNCT
ejpam-6834	593	3	m	m	NOUN
ejpam-6834	593	4	,	,	PUNCT
ejpam-6834	593	5	n)-superhyperneutrosophic	n)-superhyperneutrosophic	PUNCT
ejpam-6834	593	6	and	and	CCONJ
ejpam-6834	593	7	let	let	VERB
ejpam-6834	593	8	0	0	NUM
ejpam-6834	593	9	≤	≤	NUM
ejpam-6834	593	10	m′	m′	NOUN
ejpam-6834	593	11	<	<	X
ejpam-6834	593	12	m.	m.	NOUN
ejpam-6834	593	13	let	let	VERB
ejpam-6834	593	14	ιm′→m	ιm′→m	VERB
ejpam-6834	593	15	be	be	AUX
ejpam-6834	593	16	the	the	DET
ejpam-6834	593	17	canonical	canonical	ADJ
ejpam-6834	593	18	embedding	embed	VERB
ejpam-6834	593	19	.	.	PUNCT
ejpam-6834	594	1	then	then	ADV
ejpam-6834	594	2	µ′	µ′	PUNCT
ejpam-6834	594	3	=	=	SYM
ejpam-6834	594	4	µ	µ	X
ejpam-6834	594	5	◦	◦	NOUN
ejpam-6834	594	6	ιm′→m	ιm′→m	PUNCT
ejpam-6834	594	7	:	:	PUNCT
ejpam-6834	594	8	p	p	X
ejpam-6834	594	9	m′	m′	NOUN
ejpam-6834	594	10	(	(	PUNCT
ejpam-6834	594	11	a	a	X
ejpam-6834	594	12	)	)	PUNCT
ejpam-6834	594	13	−→	−→	NOUN
ejpam-6834	594	14	p	p	X
ejpam-6834	594	15	n([0	n([0	NOUN
ejpam-6834	594	16	,	,	PUNCT
ejpam-6834	594	17	1]3	1]3	NUM
ejpam-6834	594	18	)	)	PUNCT
ejpam-6834	594	19	is	be	AUX
ejpam-6834	594	20	(	(	PUNCT
ejpam-6834	594	21	m′	m′	PRON
ejpam-6834	594	22	,	,	PUNCT
ejpam-6834	594	23	n)-superhyperneutrosophic	n)-superhyperneutrosophic	NUM
ejpam-6834	594	24	.	.	PUNCT
ejpam-6834	595	1	proof	proof	NOUN
ejpam-6834	595	2	.	.	PUNCT
ejpam-6834	596	1	fix	fix	VERB
ejpam-6834	596	2	x	x	X
ejpam-6834	596	3	∈	∈	PROPN
ejpam-6834	596	4	p	p	NOUN
ejpam-6834	596	5	m′	m′	NOUN
ejpam-6834	596	6	(	(	PUNCT
ejpam-6834	596	7	a	a	NOUN
ejpam-6834	596	8	)	)	PUNCT
ejpam-6834	596	9	.	.	PUNCT
ejpam-6834	597	1	then	then	ADV
ejpam-6834	597	2	ιm′→m(x	ιm′→m(x	NOUN
ejpam-6834	597	3	)	)	PUNCT
ejpam-6834	597	4	∈	∈	PROPN
ejpam-6834	597	5	p	p	PROPN
ejpam-6834	597	6	m(a	m(a	PROPN
ejpam-6834	597	7	)	)	PUNCT
ejpam-6834	597	8	and	and	CCONJ
ejpam-6834	597	9	µ	µ	PROPN
ejpam-6834	597	10	(	(	PUNCT
ejpam-6834	597	11	ιm′→m(x	ιm′→m(x	PROPN
ejpam-6834	597	12	)	)	PUNCT
ejpam-6834	597	13	)	)	PUNCT
ejpam-6834	598	1	∈	∈	PROPN
ejpam-6834	598	2	p	p	NOUN
ejpam-6834	598	3	n([0	n([0	PROPN
ejpam-6834	598	4	,	,	PUNCT
ejpam-6834	598	5	1]3	1]3	NUM
ejpam-6834	598	6	)	)	PUNCT
ejpam-6834	598	7	is	be	AUX
ejpam-6834	598	8	nonempty	nonempty	ADJ
ejpam-6834	598	9	with	with	ADP
ejpam-6834	598	10	all	all	PRON
ejpam-6834	598	11	(	(	PUNCT
ejpam-6834	598	12	t	t	PROPN
ejpam-6834	598	13	,	,	PUNCT
ejpam-6834	598	14	i	i	PRON
ejpam-6834	598	15	,	,	PUNCT
ejpam-6834	598	16	f	f	PROPN
ejpam-6834	598	17	)	)	PUNCT
ejpam-6834	598	18	at	at	ADP
ejpam-6834	598	19	level	level	NOUN
ejpam-6834	598	20	1	1	NUM
ejpam-6834	598	21	obeying	obeying	NOUN
ejpam-6834	598	22	t	t	NOUN
ejpam-6834	599	1	+	+	CCONJ
ejpam-6834	599	2	i	i	PRON
ejpam-6834	599	3	+	+	NUM
ejpam-6834	599	4	f	f	PROPN
ejpam-6834	599	5	≤	≤	ADV
ejpam-6834	599	6	3	3	NUM
ejpam-6834	599	7	.	.	PUNCT
ejpam-6834	600	1	hence	hence	ADV
ejpam-6834	600	2	µ′(x	µ′(x	NUM
ejpam-6834	600	3	)	)	PUNCT
ejpam-6834	600	4	has	have	VERB
ejpam-6834	600	5	the	the	DET
ejpam-6834	600	6	required	require	VERB
ejpam-6834	600	7	codomain	codomain	NOUN
ejpam-6834	600	8	and	and	CCONJ
ejpam-6834	600	9	constraints	constraint	NOUN
ejpam-6834	600	10	.	.	PUNCT
ejpam-6834	601	1	theorem	theorem	VERB
ejpam-6834	601	2	10	10	NUM
ejpam-6834	601	3	(	(	PUNCT
ejpam-6834	601	4	projection	projection	NOUN
ejpam-6834	601	5	onto	onto	ADP
ejpam-6834	601	6	truth	truth	NOUN
ejpam-6834	601	7	component	component	NOUN
ejpam-6834	601	8	)	)	PUNCT
ejpam-6834	601	9	.	.	PUNCT
ejpam-6834	602	1	let	let	VERB
ejpam-6834	602	2	µ	µ	PRON
ejpam-6834	602	3	:	:	PUNCT
ejpam-6834	602	4	p	p	PROPN
ejpam-6834	602	5	m(a	m(a	PROPN
ejpam-6834	602	6	)	)	PUNCT
ejpam-6834	602	7	→	→	SYM
ejpam-6834	603	1	p	p	X
ejpam-6834	603	2	n([0	n([0	NOUN
ejpam-6834	603	3	,	,	PUNCT
ejpam-6834	603	4	1]3	1]3	NUM
ejpam-6834	603	5	)	)	PUNCT
ejpam-6834	604	1	be	be	AUX
ejpam-6834	604	2	(	(	PUNCT
ejpam-6834	604	3	m	m	NOUN
ejpam-6834	604	4	,	,	PUNCT
ejpam-6834	604	5	n)-superhyperneutrosophic	n)-superhyperneutrosophic	PROPN
ejpam-6834	604	6	.	.	PUNCT
ejpam-6834	605	1	define	define	VERB
ejpam-6834	605	2	πt	πt	X
ejpam-6834	605	3	:	:	PUNCT
ejpam-6834	606	1	[	[	X
ejpam-6834	606	2	0	0	NUM
ejpam-6834	606	3	,	,	PUNCT
ejpam-6834	606	4	1]3	1]3	NUM
ejpam-6834	606	5	→	→	SYM
ejpam-6834	606	6	[	[	X
ejpam-6834	606	7	0	0	NUM
ejpam-6834	606	8	,	,	PUNCT
ejpam-6834	606	9	1	1	NUM
ejpam-6834	606	10	]	]	PUNCT
ejpam-6834	606	11	,	,	PUNCT
ejpam-6834	606	12	πt	πt	X
ejpam-6834	606	13	(	(	PUNCT
ejpam-6834	606	14	t	t	PROPN
ejpam-6834	606	15	,	,	PUNCT
ejpam-6834	606	16	i	i	PRON
ejpam-6834	606	17	,	,	PUNCT
ejpam-6834	606	18	f	f	PROPN
ejpam-6834	606	19	)	)	PUNCT
ejpam-6834	606	20	=	=	SYM
ejpam-6834	606	21	t	t	PROPN
ejpam-6834	606	22	,	,	PUNCT
ejpam-6834	606	23	and	and	CCONJ
ejpam-6834	606	24	lift	lift	VERB
ejpam-6834	606	25	it	it	PRON
ejpam-6834	606	26	levelwise	levelwise	NOUN
ejpam-6834	606	27	to	to	ADP
ejpam-6834	606	28	πt	πt	PROPN
ejpam-6834	606	29	:	:	PUNCT
ejpam-6834	606	30	p	p	NOUN
ejpam-6834	606	31	n([0	n([0	NOUN
ejpam-6834	606	32	,	,	PUNCT
ejpam-6834	606	33	1]3	1]3	NUM
ejpam-6834	606	34	)	)	PUNCT
ejpam-6834	606	35	−→	−→	NOUN
ejpam-6834	606	36	p	p	NOUN
ejpam-6834	606	37	n([0	n([0	NOUN
ejpam-6834	606	38	,	,	PUNCT
ejpam-6834	606	39	1	1	NUM
ejpam-6834	606	40	]	]	NUM
ejpam-6834	606	41	)	)	PUNCT
ejpam-6834	606	42	,	,	PUNCT
ejpam-6834	606	43	πt	πt	ADP
ejpam-6834	606	44	=	=	SYM
ejpam-6834	606	45	p	p	PRON
ejpam-6834	606	46	n(πt	n(πt	PROPN
ejpam-6834	606	47	)	)	PUNCT
ejpam-6834	606	48	.	.	PUNCT
ejpam-6834	607	1	then	then	ADV
ejpam-6834	607	2	τ	τ	X
ejpam-6834	607	3	:	:	PUNCT
ejpam-6834	607	4	=	=	SYM
ejpam-6834	607	5	πt	πt	AUX
ejpam-6834	607	6	◦	◦	VERB
ejpam-6834	607	7	µ	µ	X
ejpam-6834	607	8	:	:	PUNCT
ejpam-6834	607	9	p	p	PROPN
ejpam-6834	607	10	m(a	m(a	PROPN
ejpam-6834	607	11	)	)	PUNCT
ejpam-6834	607	12	→	→	SYM
ejpam-6834	608	1	p	p	X
ejpam-6834	608	2	n([0	n([0	NOUN
ejpam-6834	608	3	,	,	PUNCT
ejpam-6834	608	4	1	1	NUM
ejpam-6834	608	5	]	]	PUNCT
ejpam-6834	608	6	)	)	PUNCT
ejpam-6834	608	7	is	be	AUX
ejpam-6834	608	8	an	an	DET
ejpam-6834	608	9	(	(	PUNCT
ejpam-6834	608	10	m	m	NOUN
ejpam-6834	608	11	,	,	PUNCT
ejpam-6834	608	12	n)-superhyperfuzzy	n)-superhyperfuzzy	PUNCT
ejpam-6834	608	13	set	set	NOUN
ejpam-6834	608	14	.	.	PUNCT
ejpam-6834	609	1	proof	proof	NOUN
ejpam-6834	609	2	.	.	PUNCT
ejpam-6834	610	1	for	for	ADP
ejpam-6834	610	2	any	any	DET
ejpam-6834	610	3	x	x	SYM
ejpam-6834	610	4	∈	∈	PROPN
ejpam-6834	610	5	p	p	PROPN
ejpam-6834	610	6	m(a	m(a	PROPN
ejpam-6834	610	7	)	)	PUNCT
ejpam-6834	610	8	,	,	PUNCT
ejpam-6834	610	9	the	the	DET
ejpam-6834	610	10	inner	inner	ADV
ejpam-6834	610	11	-	-	PUNCT
ejpam-6834	610	12	most	most	ADJ
ejpam-6834	610	13	(	(	PUNCT
ejpam-6834	610	14	level	level	NOUN
ejpam-6834	610	15	1	1	NUM
ejpam-6834	610	16	)	)	PUNCT
ejpam-6834	610	17	set	set	NOUN
ejpam-6834	610	18	un→1(µ(x	un→1(µ(x	NOUN
ejpam-6834	610	19	)	)	PUNCT
ejpam-6834	610	20	)	)	PUNCT
ejpam-6834	611	1	⊆	⊆	NUM
ejpam-6834	611	2	[	[	X
ejpam-6834	611	3	0	0	NUM
ejpam-6834	611	4	,	,	PUNCT
ejpam-6834	611	5	1]3	1]3	NUM
ejpam-6834	611	6	is	be	AUX
ejpam-6834	611	7	nonempty	nonempty	ADJ
ejpam-6834	611	8	.	.	PUNCT
ejpam-6834	612	1	applying	apply	VERB
ejpam-6834	612	2	πt	πt	ADP
ejpam-6834	612	3	pointwise	pointwise	NOUN
ejpam-6834	612	4	yields	yield	NOUN
ejpam-6834	612	5	the	the	DET
ejpam-6834	612	6	nonempty	nonempty	ADV
ejpam-6834	612	7	set	set	VERB
ejpam-6834	612	8	πt	πt	ADV
ejpam-6834	612	9	(	(	PUNCT
ejpam-6834	612	10	un→1(µ(x	un→1(µ(x	NOUN
ejpam-6834	612	11	)	)	PUNCT
ejpam-6834	612	12	)	)	PUNCT
ejpam-6834	612	13	)	)	PUNCT
ejpam-6834	613	1	⊆	⊆	NUM
ejpam-6834	613	2	[	[	X
ejpam-6834	613	3	0	0	NUM
ejpam-6834	613	4	,	,	PUNCT
ejpam-6834	613	5	1	1	NUM
ejpam-6834	613	6	]	]	PUNCT
ejpam-6834	613	7	.	.	PUNCT
ejpam-6834	614	1	lifting	lift	VERB
ejpam-6834	614	2	this	this	DET
ejpam-6834	614	3	operation	operation	NOUN
ejpam-6834	614	4	consistently	consistently	ADV
ejpam-6834	614	5	to	to	ADP
ejpam-6834	614	6	higher	high	ADJ
ejpam-6834	614	7	levels	level	NOUN
ejpam-6834	614	8	defines	define	VERB
ejpam-6834	614	9	πt	πt	ADP
ejpam-6834	614	10	,	,	PUNCT
ejpam-6834	614	11	so	so	ADV
ejpam-6834	614	12	τ(x	τ(x	PUNCT
ejpam-6834	614	13	)	)	PUNCT
ejpam-6834	615	1	=	=	SYM
ejpam-6834	615	2	πt	πt	X
ejpam-6834	615	3	(	(	PUNCT
ejpam-6834	615	4	µ(x	µ(x	NOUN
ejpam-6834	615	5	)	)	PUNCT
ejpam-6834	615	6	)	)	PUNCT
ejpam-6834	616	1	∈	∈	PROPN
ejpam-6834	616	2	p	p	NOUN
ejpam-6834	616	3	n([0	n([0	PROPN
ejpam-6834	616	4	,	,	PUNCT
ejpam-6834	616	5	1	1	NUM
ejpam-6834	616	6	]	]	NUM
ejpam-6834	616	7	)	)	PUNCT
ejpam-6834	616	8	.	.	PUNCT
ejpam-6834	617	1	thus	thus	ADV
ejpam-6834	617	2	τ	τ	X
ejpam-6834	617	3	is	be	AUX
ejpam-6834	617	4	(	(	PUNCT
ejpam-6834	617	5	m	m	X
ejpam-6834	617	6	,	,	PUNCT
ejpam-6834	617	7	n)-superhyperfuzzy	n)-superhyperfuzzy	X
ejpam-6834	617	8	.	.	PUNCT
ejpam-6834	618	1	theorem	theorem	VERB
ejpam-6834	618	2	11	11	NUM
ejpam-6834	618	3	(	(	PUNCT
ejpam-6834	618	4	pointwise	pointwise	NOUN
ejpam-6834	618	5	union	union	NOUN
ejpam-6834	618	6	)	)	PUNCT
ejpam-6834	618	7	.	.	PUNCT
ejpam-6834	619	1	if	if	SCONJ
ejpam-6834	619	2	µ1	µ1	PROPN
ejpam-6834	619	3	,	,	PUNCT
ejpam-6834	619	4	µ2	µ2	PROPN
ejpam-6834	619	5	:	:	PUNCT
ejpam-6834	619	6	p	p	PROPN
ejpam-6834	619	7	m(a	m(a	PROPN
ejpam-6834	619	8	)	)	PUNCT
ejpam-6834	619	9	→	→	SYM
ejpam-6834	620	1	p	p	X
ejpam-6834	620	2	n([0	n([0	NOUN
ejpam-6834	620	3	,	,	PUNCT
ejpam-6834	620	4	1]3	1]3	NUM
ejpam-6834	620	5	)	)	PUNCT
ejpam-6834	620	6	are	be	AUX
ejpam-6834	620	7	(	(	PUNCT
ejpam-6834	620	8	m	m	X
ejpam-6834	620	9	,	,	PUNCT
ejpam-6834	620	10	n)-superhyperneutrosophic	n)-superhyperneutrosophic	NUM
ejpam-6834	620	11	,	,	PUNCT
ejpam-6834	620	12	then	then	ADV
ejpam-6834	620	13	(	(	PUNCT
ejpam-6834	620	14	µ1	µ1	NOUN
ejpam-6834	620	15	∪	∪	ADJ
ejpam-6834	620	16	µ2)(x	µ2)(x	PROPN
ejpam-6834	620	17	)	)	PUNCT
ejpam-6834	620	18	:	:	PUNCT
ejpam-6834	621	1	=	=	PUNCT
ejpam-6834	621	2	µ1(x	µ1(x	NOUN
ejpam-6834	621	3	)	)	PUNCT
ejpam-6834	621	4	∪	∪	ADP
ejpam-6834	621	5	µ2(x	µ2(x	NOUN
ejpam-6834	621	6	)	)	PUNCT
ejpam-6834	621	7	defines	define	VERB
ejpam-6834	621	8	another	another	PRON
ejpam-6834	621	9	(	(	PUNCT
ejpam-6834	621	10	m	m	PROPN
ejpam-6834	621	11	,	,	PUNCT
ejpam-6834	621	12	n)-superhyperneutrosophic	n)-superhyperneutrosophic	ADJ
ejpam-6834	621	13	set	set	NOUN
ejpam-6834	621	14	.	.	PUNCT
ejpam-6834	622	1	t.	t.	PROPN
ejpam-6834	622	2	fujita	fujita	PROPN
ejpam-6834	622	3	,	,	PUNCT
ejpam-6834	622	4	f.smarandache	f.smarandache	NOUN
ejpam-6834	622	5	/	/	SYM
ejpam-6834	622	6	eur	eur	PROPN
ejpam-6834	622	7	.	.	PUNCT
ejpam-6834	623	1	j.	j.	PROPN
ejpam-6834	623	2	pure	pure	PROPN
ejpam-6834	623	3	appl	appl	PROPN
ejpam-6834	623	4	.	.	PROPN
ejpam-6834	623	5	math	math	PROPN
ejpam-6834	623	6	,	,	PUNCT
ejpam-6834	623	7	18	18	NUM
ejpam-6834	623	8	(	(	PUNCT
ejpam-6834	623	9	4	4	NUM
ejpam-6834	623	10	)	)	PUNCT
ejpam-6834	623	11	(	(	PUNCT
ejpam-6834	623	12	2025	2025	NUM
ejpam-6834	623	13	)	)	PUNCT
ejpam-6834	623	14	,	,	PUNCT
ejpam-6834	623	15	6834	6834	NUM
ejpam-6834	623	16	27	27	NUM
ejpam-6834	623	17	of	of	ADP
ejpam-6834	623	18	69	69	NUM
ejpam-6834	623	19	proof	proof	NOUN
ejpam-6834	623	20	.	.	PUNCT
ejpam-6834	624	1	for	for	ADP
ejpam-6834	624	2	each	each	DET
ejpam-6834	624	3	x	x	NOUN
ejpam-6834	624	4	,	,	PUNCT
ejpam-6834	624	5	both	both	PRON
ejpam-6834	624	6	µ1(x	µ1(x	NOUN
ejpam-6834	624	7	)	)	PUNCT
ejpam-6834	624	8	and	and	CCONJ
ejpam-6834	624	9	µ2(x	µ2(x	PROPN
ejpam-6834	624	10	)	)	PUNCT
ejpam-6834	624	11	lie	lie	NOUN
ejpam-6834	624	12	in	in	ADP
ejpam-6834	624	13	p	p	PROPN
ejpam-6834	624	14	n([0	n([0	NOUN
ejpam-6834	624	15	,	,	PUNCT
ejpam-6834	624	16	1]3	1]3	NUM
ejpam-6834	624	17	)	)	PUNCT
ejpam-6834	624	18	and	and	CCONJ
ejpam-6834	624	19	are	be	AUX
ejpam-6834	624	20	nonempty	nonempty	ADJ
ejpam-6834	624	21	.	.	PUNCT
ejpam-6834	625	1	their	their	PRON
ejpam-6834	625	2	union	union	NOUN
ejpam-6834	625	3	is	be	AUX
ejpam-6834	625	4	again	again	ADV
ejpam-6834	625	5	a	a	DET
ejpam-6834	625	6	nonempty	nonempty	ADJ
ejpam-6834	625	7	element	element	NOUN
ejpam-6834	625	8	of	of	ADP
ejpam-6834	625	9	p	p	NOUN
ejpam-6834	625	10	n([0	n([0	NOUN
ejpam-6834	625	11	,	,	PUNCT
ejpam-6834	625	12	1]3	1]3	NUM
ejpam-6834	625	13	)	)	PUNCT
ejpam-6834	625	14	.	.	PUNCT
ejpam-6834	626	1	every	every	DET
ejpam-6834	626	2	triple	triple	NOUN
ejpam-6834	626	3	in	in	ADP
ejpam-6834	626	4	the	the	DET
ejpam-6834	626	5	union	union	NOUN
ejpam-6834	626	6	comes	come	VERB
ejpam-6834	626	7	from	from	ADP
ejpam-6834	626	8	either	either	PRON
ejpam-6834	626	9	µ1(x	µ1(x	PROPN
ejpam-6834	626	10	)	)	PUNCT
ejpam-6834	626	11	or	or	CCONJ
ejpam-6834	626	12	µ2(x	µ2(x	NUM
ejpam-6834	626	13	)	)	PUNCT
ejpam-6834	626	14	and	and	CCONJ
ejpam-6834	626	15	thus	thus	ADV
ejpam-6834	626	16	satisfies	satisfy	VERB
ejpam-6834	626	17	t	t	PROPN
ejpam-6834	627	1	+	+	CCONJ
ejpam-6834	627	2	i	i	PRON
ejpam-6834	627	3	+	+	NUM
ejpam-6834	628	1	f	f	PROPN
ejpam-6834	628	2	≤	≤	ADV
ejpam-6834	628	3	3	3	NUM
ejpam-6834	628	4	.	.	PUNCT
ejpam-6834	628	5	theorem	theorem	NOUN
ejpam-6834	628	6	12	12	NUM
ejpam-6834	628	7	(	(	PUNCT
ejpam-6834	628	8	pointwise	pointwise	NOUN
ejpam-6834	628	9	intersection	intersection	NOUN
ejpam-6834	628	10	)	)	PUNCT
ejpam-6834	628	11	.	.	PUNCT
ejpam-6834	629	1	under	under	ADP
ejpam-6834	629	2	the	the	DET
ejpam-6834	629	3	same	same	ADJ
ejpam-6834	629	4	hypotheses	hypothesis	NOUN
ejpam-6834	629	5	as	as	ADP
ejpam-6834	629	6	theorem	theorem	ADJ
ejpam-6834	629	7	11	11	NUM
ejpam-6834	629	8	,	,	PUNCT
ejpam-6834	629	9	let	let	VERB
ejpam-6834	629	10	(	(	PUNCT
ejpam-6834	629	11	µ1	µ1	PROPN
ejpam-6834	629	12	∩	∩	ADJ
ejpam-6834	629	13	µ2)(x	µ2)(x	PROPN
ejpam-6834	629	14	)	)	PUNCT
ejpam-6834	629	15	:	:	PUNCT
ejpam-6834	630	1	=	=	SYM
ejpam-6834	630	2	µ1(x	µ1(x	NOUN
ejpam-6834	630	3	)	)	PUNCT
ejpam-6834	630	4	∩	∩	NOUN
ejpam-6834	630	5	µ2(x	µ2(x	ADJ
ejpam-6834	630	6	)	)	PUNCT
ejpam-6834	630	7	.	.	PUNCT
ejpam-6834	631	1	if	if	SCONJ
ejpam-6834	631	2	µ1(x	µ1(x	NOUN
ejpam-6834	631	3	)	)	PUNCT
ejpam-6834	631	4	∩	∩	NOUN
ejpam-6834	631	5	µ2(x	µ2(x	ADJ
ejpam-6834	631	6	)	)	PUNCT
ejpam-6834	631	7	̸=	̸=	PROPN
ejpam-6834	631	8	∅	∅	NOUN
ejpam-6834	631	9	for	for	ADP
ejpam-6834	631	10	all	all	DET
ejpam-6834	631	11	x	x	NOUN
ejpam-6834	631	12	,	,	PUNCT
ejpam-6834	631	13	then	then	ADV
ejpam-6834	631	14	(	(	PUNCT
ejpam-6834	631	15	µ1	µ1	PROPN
ejpam-6834	631	16	∩	∩	ADJ
ejpam-6834	631	17	µ2	µ2	NOUN
ejpam-6834	631	18	)	)	PUNCT
ejpam-6834	631	19	is	be	AUX
ejpam-6834	631	20	(	(	PUNCT
ejpam-6834	631	21	m	m	X
ejpam-6834	631	22	,	,	PUNCT
ejpam-6834	631	23	n)-superhyperneutrosophic	n)-superhyperneutrosophic	ADJ
ejpam-6834	631	24	.	.	PUNCT
ejpam-6834	632	1	proof	proof	NOUN
ejpam-6834	632	2	.	.	PUNCT
ejpam-6834	633	1	for	for	ADP
ejpam-6834	633	2	each	each	DET
ejpam-6834	633	3	x	x	NOUN
ejpam-6834	633	4	,	,	PUNCT
ejpam-6834	633	5	the	the	DET
ejpam-6834	633	6	intersection	intersection	NOUN
ejpam-6834	633	7	is	be	AUX
ejpam-6834	633	8	a	a	DET
ejpam-6834	633	9	(	(	PUNCT
ejpam-6834	633	10	by	by	ADP
ejpam-6834	633	11	assumption	assumption	NOUN
ejpam-6834	633	12	nonempty	nonempty	NOUN
ejpam-6834	633	13	)	)	PUNCT
ejpam-6834	633	14	subset	subset	NOUN
ejpam-6834	633	15	of	of	ADP
ejpam-6834	633	16	p	p	PROPN
ejpam-6834	633	17	n−1([0	n−1([0	NOUN
ejpam-6834	633	18	,	,	PUNCT
ejpam-6834	633	19	1]3	1]3	NUM
ejpam-6834	633	20	)	)	PUNCT
ejpam-6834	633	21	,	,	PUNCT
ejpam-6834	633	22	hence	hence	ADV
ejpam-6834	633	23	an	an	DET
ejpam-6834	633	24	element	element	NOUN
ejpam-6834	633	25	of	of	ADP
ejpam-6834	633	26	p	p	NOUN
ejpam-6834	633	27	n([0	n([0	NOUN
ejpam-6834	633	28	,	,	PUNCT
ejpam-6834	633	29	1]3	1]3	NUM
ejpam-6834	633	30	)	)	PUNCT
ejpam-6834	633	31	.	.	PUNCT
ejpam-6834	634	1	any	any	DET
ejpam-6834	634	2	triple	triple	ADJ
ejpam-6834	634	3	in	in	ADP
ejpam-6834	634	4	the	the	DET
ejpam-6834	634	5	intersection	intersection	NOUN
ejpam-6834	634	6	already	already	ADV
ejpam-6834	634	7	satisfies	satisfy	VERB
ejpam-6834	634	8	t+i+f	t+i+f	NOUN
ejpam-6834	634	9	≤	≤	NOUN
ejpam-6834	634	10	3	3	NUM
ejpam-6834	634	11	because	because	SCONJ
ejpam-6834	634	12	it	it	PRON
ejpam-6834	634	13	belongs	belong	VERB
ejpam-6834	634	14	to	to	ADP
ejpam-6834	634	15	both	both	DET
ejpam-6834	634	16	µ1(x	µ1(x	NOUN
ejpam-6834	634	17	)	)	PUNCT
ejpam-6834	634	18	and	and	CCONJ
ejpam-6834	634	19	µ2(x	µ2(x	PROPN
ejpam-6834	634	20	)	)	PUNCT
ejpam-6834	634	21	.	.	PUNCT
ejpam-6834	635	1	theorem	theorem	ADJ
ejpam-6834	635	2	13	13	NUM
ejpam-6834	635	3	(	(	PUNCT
ejpam-6834	635	4	nested	nest	VERB
ejpam-6834	635	5	λ	λ	NOUN
ejpam-6834	635	6	-	-	NOUN
ejpam-6834	635	7	cuts	cut	NOUN
ejpam-6834	635	8	)	)	PUNCT
ejpam-6834	635	9	.	.	PUNCT
ejpam-6834	636	1	let	let	VERB
ejpam-6834	636	2	µ	µ	X
ejpam-6834	636	3	:	:	PUNCT
ejpam-6834	636	4	p	p	PROPN
ejpam-6834	636	5	m(a	m(a	PROPN
ejpam-6834	636	6	)	)	PUNCT
ejpam-6834	636	7	→	→	SYM
ejpam-6834	637	1	p	p	X
ejpam-6834	637	2	n([0	n([0	NOUN
ejpam-6834	637	3	,	,	PUNCT
ejpam-6834	637	4	1]3	1]3	NUM
ejpam-6834	637	5	)	)	PUNCT
ejpam-6834	638	1	be	be	AUX
ejpam-6834	638	2	(	(	PUNCT
ejpam-6834	638	3	m	m	NOUN
ejpam-6834	638	4	,	,	PUNCT
ejpam-6834	638	5	n)-superhyperneutrosophic	n)-superhyperneutrosophic	PUNCT
ejpam-6834	638	6	.	.	PUNCT
ejpam-6834	639	1	for	for	ADP
ejpam-6834	639	2	λ	λ	PROPN
ejpam-6834	639	3	=	=	SYM
ejpam-6834	639	4	(	(	PUNCT
ejpam-6834	639	5	α	α	X
ejpam-6834	639	6	,	,	PUNCT
ejpam-6834	639	7	β	β	X
ejpam-6834	639	8	,	,	PUNCT
ejpam-6834	639	9	γ	γ	NOUN
ejpam-6834	639	10	)	)	PUNCT
ejpam-6834	639	11	∈	∈	NOUN
ejpam-6834	640	1	[	[	X
ejpam-6834	640	2	0	0	NUM
ejpam-6834	640	3	,	,	PUNCT
ejpam-6834	640	4	1]3	1]3	NUM
ejpam-6834	640	5	define	define	VERB
ejpam-6834	640	6	cλ	cλ	PROPN
ejpam-6834	640	7	=	=	PUNCT
ejpam-6834	640	8	{	{	PUNCT
ejpam-6834	640	9	x	x	PUNCT
ejpam-6834	640	10	∈	∈	PROPN
ejpam-6834	640	11	p	p	PROPN
ejpam-6834	640	12	m(a	m(a	PROPN
ejpam-6834	640	13	)	)	PUNCT
ejpam-6834	640	14	∣∣∣	∣∣∣	ADP
ejpam-6834	641	1	∃(t	∃(t	PROPN
ejpam-6834	641	2	,	,	PUNCT
ejpam-6834	641	3	i	i	PRON
ejpam-6834	641	4	,	,	PUNCT
ejpam-6834	641	5	f	f	PROPN
ejpam-6834	641	6	)	)	PUNCT
ejpam-6834	641	7	∈	∈	PROPN
ejpam-6834	641	8	un→1(µ(x	un→1(µ(x	NOUN
ejpam-6834	641	9	)	)	PUNCT
ejpam-6834	641	10	)	)	PUNCT
ejpam-6834	642	1	with	with	ADP
ejpam-6834	642	2	t	t	PROPN
ejpam-6834	642	3	≥	≥	PROPN
ejpam-6834	642	4	α	α	NOUN
ejpam-6834	642	5	,	,	PUNCT
ejpam-6834	642	6	i	i	NOUN
ejpam-6834	642	7	≤	≤	NOUN
ejpam-6834	642	8	β	β	X
ejpam-6834	642	9	,	,	PUNCT
ejpam-6834	642	10	f	f	PROPN
ejpam-6834	642	11	≤	≤	NUM
ejpam-6834	642	12	γ	γ	X
ejpam-6834	642	13	}	}	PUNCT
ejpam-6834	642	14	.	.	PUNCT
ejpam-6834	643	1	if	if	SCONJ
ejpam-6834	643	2	λ′	λ′	X
ejpam-6834	643	3	=	=	SYM
ejpam-6834	643	4	(	(	PUNCT
ejpam-6834	643	5	α′	α′	NUM
ejpam-6834	643	6	,	,	PUNCT
ejpam-6834	643	7	β′	β′	NUM
ejpam-6834	643	8	,	,	PUNCT
ejpam-6834	643	9	γ′	γ′	NOUN
ejpam-6834	643	10	)	)	PUNCT
ejpam-6834	643	11	satisfies	satisfy	VERB
ejpam-6834	643	12	α′	α′	NUM
ejpam-6834	643	13	≥	≥	NOUN
ejpam-6834	643	14	α	α	NOUN
ejpam-6834	643	15	,	,	PUNCT
ejpam-6834	643	16	β′	β′	NUM
ejpam-6834	643	17	≤	≤	ADV
ejpam-6834	643	18	β	β	NOUN
ejpam-6834	643	19	,	,	PUNCT
ejpam-6834	643	20	γ′	γ′	PROPN
ejpam-6834	643	21	≤	≤	NUM
ejpam-6834	643	22	γ	γ	X
ejpam-6834	643	23	,	,	PUNCT
ejpam-6834	643	24	then	then	ADV
ejpam-6834	643	25	cλ′	cλ′	PROPN
ejpam-6834	643	26	⊆	⊆	NUM
ejpam-6834	643	27	cλ	cλ	PROPN
ejpam-6834	643	28	.	.	PUNCT
ejpam-6834	644	1	proof	proof	NOUN
ejpam-6834	644	2	.	.	PUNCT
ejpam-6834	645	1	take	take	VERB
ejpam-6834	645	2	x	x	PUNCT
ejpam-6834	645	3	∈	∈	PROPN
ejpam-6834	645	4	cλ′	cλ′	NOUN
ejpam-6834	645	5	.	.	PUNCT
ejpam-6834	646	1	then	then	ADV
ejpam-6834	646	2	some	some	PRON
ejpam-6834	646	3	(	(	PUNCT
ejpam-6834	646	4	t	t	PROPN
ejpam-6834	646	5	,	,	PUNCT
ejpam-6834	646	6	i	i	PRON
ejpam-6834	646	7	,	,	PUNCT
ejpam-6834	646	8	f	f	PROPN
ejpam-6834	646	9	)	)	PUNCT
ejpam-6834	646	10	∈	∈	PROPN
ejpam-6834	646	11	un→1(µ(x	un→1(µ(x	NOUN
ejpam-6834	646	12	)	)	PUNCT
ejpam-6834	646	13	)	)	PUNCT
ejpam-6834	646	14	obeys	obey	VERB
ejpam-6834	646	15	t	t	PROPN
ejpam-6834	646	16	≥	≥	PROPN
ejpam-6834	646	17	α′	α′	NUM
ejpam-6834	646	18	,	,	PUNCT
ejpam-6834	646	19	i	i	PRON
ejpam-6834	646	20	≤	≤	NOUN
ejpam-6834	646	21	β′	β′	PUNCT
ejpam-6834	646	22	,	,	PUNCT
ejpam-6834	646	23	f	f	PROPN
ejpam-6834	646	24	≤	≤	PROPN
ejpam-6834	646	25	γ′.	γ′.	VERB
ejpam-6834	646	26	since	since	SCONJ
ejpam-6834	646	27	α′	α′	NUM
ejpam-6834	646	28	≥	≥	NOUN
ejpam-6834	646	29	α	α	NOUN
ejpam-6834	646	30	,	,	PUNCT
ejpam-6834	646	31	β′	β′	NUM
ejpam-6834	646	32	≤	≤	NOUN
ejpam-6834	646	33	β	β	NOUN
ejpam-6834	646	34	,	,	PUNCT
ejpam-6834	646	35	and	and	CCONJ
ejpam-6834	646	36	γ′	γ′	PROPN
ejpam-6834	646	37	≤	≤	NOUN
ejpam-6834	646	38	γ	γ	X
ejpam-6834	646	39	,	,	PUNCT
ejpam-6834	646	40	the	the	DET
ejpam-6834	646	41	same	same	ADJ
ejpam-6834	646	42	triple	triple	ADJ
ejpam-6834	646	43	witnesses	witness	NOUN
ejpam-6834	646	44	x	x	X
ejpam-6834	646	45	∈	∈	PROPN
ejpam-6834	646	46	cλ	cλ	PROPN
ejpam-6834	646	47	.	.	PUNCT
ejpam-6834	647	1	hence	hence	ADV
ejpam-6834	647	2	cλ′	cλ′	PROPN
ejpam-6834	647	3	⊆	⊆	NUM
ejpam-6834	647	4	cλ	cλ	PROPN
ejpam-6834	647	5	.	.	PUNCT
ejpam-6834	648	1	theorem	theorem	VERB
ejpam-6834	648	2	14	14	NUM
ejpam-6834	648	3	(	(	PUNCT
ejpam-6834	648	4	functoriality	functoriality	NOUN
ejpam-6834	648	5	under	under	ADP
ejpam-6834	648	6	surjections	surjection	NOUN
ejpam-6834	648	7	)	)	PUNCT
ejpam-6834	648	8	.	.	PUNCT
ejpam-6834	649	1	let	let	VERB
ejpam-6834	649	2	f	f	NOUN
ejpam-6834	649	3	:	:	PUNCT
ejpam-6834	649	4	a	a	DET
ejpam-6834	649	5	→	→	SYM
ejpam-6834	649	6	b	b	X
ejpam-6834	649	7	be	be	AUX
ejpam-6834	649	8	surjective	surjective	ADJ
ejpam-6834	649	9	and	and	CCONJ
ejpam-6834	649	10	let	let	VERB
ejpam-6834	649	11	µ	µ	X
ejpam-6834	649	12	:	:	PUNCT
ejpam-6834	649	13	p	p	PROPN
ejpam-6834	649	14	m(a	m(a	PROPN
ejpam-6834	649	15	)	)	PUNCT
ejpam-6834	650	1	−→	−→	NOUN
ejpam-6834	650	2	p	p	NOUN
ejpam-6834	650	3	n	n	NOUN
ejpam-6834	650	4	(	(	PUNCT
ejpam-6834	650	5	[	[	X
ejpam-6834	650	6	0	0	NUM
ejpam-6834	650	7	,	,	PUNCT
ejpam-6834	650	8	1]3	1]3	NUM
ejpam-6834	650	9	)	)	PUNCT
ejpam-6834	650	10	be	be	AUX
ejpam-6834	650	11	an	an	DET
ejpam-6834	650	12	(	(	PUNCT
ejpam-6834	650	13	m	m	PROPN
ejpam-6834	650	14	,	,	PUNCT
ejpam-6834	650	15	n)-superhyperneutrosophic	n)-superhyperneutrosophic	ADJ
ejpam-6834	650	16	map	map	NOUN
ejpam-6834	650	17	.	.	PUNCT
ejpam-6834	651	1	define	define	VERB
ejpam-6834	651	2	the	the	DET
ejpam-6834	651	3	lifted	lift	VERB
ejpam-6834	651	4	preimage	preimage	NOUN
ejpam-6834	651	5	at	at	ADP
ejpam-6834	651	6	level	level	NOUN
ejpam-6834	651	7	1	1	NUM
ejpam-6834	651	8	by	by	ADP
ejpam-6834	651	9	f−1	f−1	PROPN
ejpam-6834	651	10	(	(	PUNCT
ejpam-6834	651	11	1	1	NUM
ejpam-6834	651	12	)	)	PUNCT
ejpam-6834	651	13	:	:	PUNCT
ejpam-6834	651	14	p(b	p(b	NUM
ejpam-6834	651	15	)	)	PUNCT
ejpam-6834	651	16	−→	−→	NOUN
ejpam-6834	651	17	p(a	p(a	PROPN
ejpam-6834	651	18	)	)	PUNCT
ejpam-6834	651	19	,	,	PUNCT
ejpam-6834	651	20	f−1	f−1	PROPN
ejpam-6834	651	21	(	(	PUNCT
ejpam-6834	651	22	1	1	NUM
ejpam-6834	651	23	)	)	PUNCT
ejpam-6834	651	24	(	(	PUNCT
ejpam-6834	651	25	y	y	PROPN
ejpam-6834	651	26	)	)	PUNCT
ejpam-6834	651	27	:	:	PUNCT
ejpam-6834	652	1	=	=	X
ejpam-6834	652	2	{	{	PUNCT
ejpam-6834	652	3	a	a	DET
ejpam-6834	652	4	∈	∈	PROPN
ejpam-6834	652	5	a	a	DET
ejpam-6834	652	6	:	:	PUNCT
ejpam-6834	652	7	f(a	f(a	NOUN
ejpam-6834	652	8	)	)	PUNCT
ejpam-6834	652	9	∈	∈	PROPN
ejpam-6834	652	10	y	y	PROPN
ejpam-6834	652	11	}	}	PUNCT
ejpam-6834	652	12	.	.	PUNCT
ejpam-6834	653	1	inductively	inductively	ADV
ejpam-6834	653	2	f−1	f−1	PROPN
ejpam-6834	653	3	(	(	PUNCT
ejpam-6834	653	4	t+1)(y	t+1)(y	PROPN
ejpam-6834	653	5	)	)	PUNCT
ejpam-6834	653	6	=	=	PRON
ejpam-6834	653	7	{	{	PUNCT
ejpam-6834	653	8	f−1	f−1	PROPN
ejpam-6834	653	9	(	(	PUNCT
ejpam-6834	653	10	t	t	PROPN
ejpam-6834	653	11	)	)	PUNCT
ejpam-6834	653	12	(	(	PUNCT
ejpam-6834	653	13	y	y	PROPN
ejpam-6834	653	14	)	)	PUNCT
ejpam-6834	653	15	:	:	PUNCT
ejpam-6834	653	16	y	y	PROPN
ejpam-6834	653	17	∈	∈	PROPN
ejpam-6834	653	18	y	y	PROPN
ejpam-6834	653	19	}	}	PUNCT
ejpam-6834	653	20	(	(	PUNCT
ejpam-6834	653	21	t	t	PROPN
ejpam-6834	653	22	≥	≥	PROPN
ejpam-6834	653	23	1	1	NUM
ejpam-6834	653	24	)	)	PUNCT
ejpam-6834	653	25	.	.	PUNCT
ejpam-6834	654	1	then	then	ADV
ejpam-6834	654	2	f∗µ	f∗µ	NUM
ejpam-6834	654	3	:	:	PUNCT
ejpam-6834	654	4	p	p	PRON
ejpam-6834	654	5	m(b	m(b	NOUN
ejpam-6834	654	6	)	)	PUNCT
ejpam-6834	654	7	−→	−→	NOUN
ejpam-6834	654	8	p	p	X
ejpam-6834	654	9	n([0	n([0	NOUN
ejpam-6834	654	10	,	,	PUNCT
ejpam-6834	654	11	1]3	1]3	NUM
ejpam-6834	654	12	)	)	PUNCT
ejpam-6834	654	13	,	,	PUNCT
ejpam-6834	654	14	f∗µ(y	f∗µ(y	PROPN
ejpam-6834	654	15	)	)	PUNCT
ejpam-6834	654	16	=	=	SYM
ejpam-6834	654	17	µ	µ	X
ejpam-6834	654	18	(	(	PUNCT
ejpam-6834	654	19	f−1	f−1	PROPN
ejpam-6834	654	20	(	(	PUNCT
ejpam-6834	654	21	m)(y	m)(y	NOUN
ejpam-6834	654	22	)	)	PUNCT
ejpam-6834	654	23	)	)	PUNCT
ejpam-6834	654	24	is	be	AUX
ejpam-6834	654	25	(	(	PUNCT
ejpam-6834	654	26	m	m	PROPN
ejpam-6834	654	27	,	,	PUNCT
ejpam-6834	654	28	n)-superhyperneutrosophic	n)-superhyperneutrosophic	PUNCT
ejpam-6834	654	29	on	on	ADP
ejpam-6834	654	30	b.	b.	PROPN
ejpam-6834	654	31	proof	proof	NOUN
ejpam-6834	654	32	.	.	PUNCT
ejpam-6834	655	1	let	let	VERB
ejpam-6834	655	2	y	y	PROPN
ejpam-6834	655	3	∈	∈	PROPN
ejpam-6834	655	4	p	p	PROPN
ejpam-6834	655	5	m(b	m(b	NOUN
ejpam-6834	655	6	)	)	PUNCT
ejpam-6834	655	7	.	.	PUNCT
ejpam-6834	656	1	by	by	ADP
ejpam-6834	656	2	construction	construction	NOUN
ejpam-6834	656	3	f−1	f−1	PROPN
ejpam-6834	656	4	(	(	PUNCT
ejpam-6834	656	5	m)(y	m)(y	PROPN
ejpam-6834	656	6	)	)	PUNCT
ejpam-6834	656	7	∈	∈	PROPN
ejpam-6834	656	8	p	p	PROPN
ejpam-6834	656	9	m(a	m(a	PROPN
ejpam-6834	656	10	)	)	PUNCT
ejpam-6834	656	11	;	;	PUNCT
ejpam-6834	656	12	surjectivity	surjectivity	NOUN
ejpam-6834	656	13	of	of	ADP
ejpam-6834	656	14	f	f	PROPN
ejpam-6834	656	15	ensures	ensure	VERB
ejpam-6834	656	16	this	this	DET
ejpam-6834	656	17	recursion	recursion	NOUN
ejpam-6834	656	18	does	do	AUX
ejpam-6834	656	19	not	not	PART
ejpam-6834	656	20	collapse	collapse	VERB
ejpam-6834	656	21	to	to	ADP
ejpam-6834	656	22	the	the	DET
ejpam-6834	656	23	empty	empty	ADJ
ejpam-6834	656	24	family	family	NOUN
ejpam-6834	657	1	when	when	SCONJ
ejpam-6834	657	2	y	y	PROPN
ejpam-6834	657	3	̸=	̸=	PROPN
ejpam-6834	657	4	∅.	∅.	PRON
ejpam-6834	657	5	hence	hence	ADV
ejpam-6834	657	6	µ	µ	X
ejpam-6834	657	7	(	(	PUNCT
ejpam-6834	657	8	f−1	f−1	PROPN
ejpam-6834	657	9	(	(	PUNCT
ejpam-6834	657	10	m)(y	m)(y	NOUN
ejpam-6834	657	11	)	)	PUNCT
ejpam-6834	657	12	)	)	PUNCT
ejpam-6834	657	13	∈	∈	PROPN
ejpam-6834	657	14	p	p	NOUN
ejpam-6834	657	15	n([0	n([0	PROPN
ejpam-6834	657	16	,	,	PUNCT
ejpam-6834	657	17	1]3	1]3	NUM
ejpam-6834	657	18	)	)	PUNCT
ejpam-6834	657	19	is	be	AUX
ejpam-6834	657	20	nonempty	nonempty	ADJ
ejpam-6834	657	21	,	,	PUNCT
ejpam-6834	657	22	and	and	CCONJ
ejpam-6834	657	23	all	all	PRON
ejpam-6834	657	24	its	its	PRON
ejpam-6834	657	25	level-1	level-1	NUM
ejpam-6834	657	26	elements	element	NOUN
ejpam-6834	657	27	satisfy	satisfy	VERB
ejpam-6834	657	28	t	t	PROPN
ejpam-6834	658	1	+	+	CCONJ
ejpam-6834	658	2	i	i	PRON
ejpam-6834	658	3	+	+	NUM
ejpam-6834	658	4	f	f	PROPN
ejpam-6834	658	5	≤	≤	ADV
ejpam-6834	658	6	3	3	NUM
ejpam-6834	658	7	.	.	PUNCT
ejpam-6834	659	1	therefore	therefore	ADV
ejpam-6834	659	2	f∗µ	f∗µ	X
ejpam-6834	659	3	has	have	VERB
ejpam-6834	659	4	the	the	DET
ejpam-6834	659	5	required	require	VERB
ejpam-6834	659	6	codomain	codomain	NOUN
ejpam-6834	659	7	and	and	CCONJ
ejpam-6834	659	8	constraints	constraint	NOUN
ejpam-6834	659	9	,	,	PUNCT
ejpam-6834	659	10	completing	complete	VERB
ejpam-6834	659	11	the	the	DET
ejpam-6834	659	12	proof	proof	NOUN
ejpam-6834	659	13	.	.	PUNCT
ejpam-6834	660	1	t.	t.	PROPN
ejpam-6834	660	2	fujita	fujita	PROPN
ejpam-6834	660	3	,	,	PUNCT
ejpam-6834	660	4	f.smarandache	f.smarandache	NOUN
ejpam-6834	660	5	/	/	SYM
ejpam-6834	660	6	eur	eur	PROPN
ejpam-6834	660	7	.	.	PUNCT
ejpam-6834	661	1	j.	j.	PROPN
ejpam-6834	661	2	pure	pure	PROPN
ejpam-6834	661	3	appl	appl	PROPN
ejpam-6834	661	4	.	.	PROPN
ejpam-6834	661	5	math	math	PROPN
ejpam-6834	661	6	,	,	PUNCT
ejpam-6834	661	7	18	18	NUM
ejpam-6834	661	8	(	(	PUNCT
ejpam-6834	661	9	4	4	NUM
ejpam-6834	661	10	)	)	PUNCT
ejpam-6834	661	11	(	(	PUNCT
ejpam-6834	661	12	2025	2025	NUM
ejpam-6834	661	13	)	)	PUNCT
ejpam-6834	661	14	,	,	PUNCT
ejpam-6834	661	15	6834	6834	NUM
ejpam-6834	661	16	28	28	NUM
ejpam-6834	661	17	of	of	ADP
ejpam-6834	661	18	69	69	NUM
ejpam-6834	661	19	3.1.3	3.1.3	NUM
ejpam-6834	661	20	.	.	PUNCT
ejpam-6834	662	1	(	(	PUNCT
ejpam-6834	662	2	m	m	PROPN
ejpam-6834	662	3	,	,	PUNCT
ejpam-6834	662	4	n)-superhyperplithogenic	n)-superhyperplithogenic	PUNCT
ejpam-6834	662	5	set	set	VERB
ejpam-6834	662	6	a	a	DET
ejpam-6834	662	7	(	(	PUNCT
ejpam-6834	662	8	m	m	PROPN
ejpam-6834	662	9	,	,	PUNCT
ejpam-6834	662	10	n)-superhyperplithogenic	n)-superhyperplithogenic	PUNCT
ejpam-6834	662	11	set	set	VERB
ejpam-6834	662	12	assigns	assign	NOUN
ejpam-6834	662	13	m	m	NOUN
ejpam-6834	662	14	-	-	PUNCT
ejpam-6834	662	15	level	level	NOUN
ejpam-6834	662	16	parameter	parameter	NOUN
ejpam-6834	662	17	-	-	PUNCT
ejpam-6834	662	18	subsets	subset	NOUN
ejpam-6834	662	19	and	and	CCONJ
ejpam-6834	662	20	their	their	PRON
ejpam-6834	662	21	attribute	attribute	NOUN
ejpam-6834	662	22	values	value	NOUN
ejpam-6834	662	23	to	to	ADP
ejpam-6834	662	24	n	n	CCONJ
ejpam-6834	662	25	-	-	PUNCT
ejpam-6834	662	26	level	level	NOUN
ejpam-6834	662	27	fuzzy	fuzzy	ADJ
ejpam-6834	662	28	-	-	PUNCT
ejpam-6834	662	29	contradiction	contradiction	NOUN
ejpam-6834	662	30	degree	degree	NOUN
ejpam-6834	662	31	-	-	PUNCT
ejpam-6834	662	32	sets	set	NOUN
ejpam-6834	662	33	,	,	PUNCT
ejpam-6834	662	34	capturing	capture	VERB
ejpam-6834	662	35	multi	multi	ADJ
ejpam-6834	662	36	-	-	ADJ
ejpam-6834	662	37	faceted	faceted	ADJ
ejpam-6834	662	38	membership	membership	NOUN
ejpam-6834	662	39	and	and	CCONJ
ejpam-6834	662	40	inter	inter	ADJ
ejpam-6834	662	41	-	-	NOUN
ejpam-6834	662	42	attribute	attribute	NOUN
ejpam-6834	662	43	conflicts	conflict	NOUN
ejpam-6834	662	44	and	and	CCONJ
ejpam-6834	662	45	uncertainty	uncertainty	NOUN
ejpam-6834	662	46	patterns	pattern	NOUN
ejpam-6834	662	47	.	.	PUNCT
ejpam-6834	663	1	the	the	DET
ejpam-6834	663	2	definition	definition	NOUN
ejpam-6834	663	3	of	of	ADP
ejpam-6834	663	4	the	the	DET
ejpam-6834	663	5	(	(	PUNCT
ejpam-6834	663	6	m	m	PROPN
ejpam-6834	663	7	,	,	PUNCT
ejpam-6834	663	8	n)-superhyperplithogenic	n)-superhyperplithogenic	PUNCT
ejpam-6834	663	9	set	set	NOUN
ejpam-6834	663	10	is	be	AUX
ejpam-6834	663	11	presented	present	VERB
ejpam-6834	663	12	below	below	ADV
ejpam-6834	663	13	.	.	PUNCT
ejpam-6834	664	1	definition	definition	NOUN
ejpam-6834	664	2	21	21	NUM
ejpam-6834	664	3	(	(	PUNCT
ejpam-6834	664	4	(	(	PUNCT
ejpam-6834	664	5	m	m	X
ejpam-6834	664	6	,	,	PUNCT
ejpam-6834	664	7	n)-superhyperplithogenic	n)-superhyperplithogenic	PUNCT
ejpam-6834	664	8	set	set	NOUN
ejpam-6834	664	9	)	)	PUNCT
ejpam-6834	664	10	.	.	PUNCT
ejpam-6834	665	1	let	let	VERB
ejpam-6834	665	2	x	x	PRON
ejpam-6834	665	3	be	be	AUX
ejpam-6834	665	4	a	a	DET
ejpam-6834	665	5	nonempty	nonempty	ADV
ejpam-6834	665	6	set	set	VERB
ejpam-6834	665	7	and	and	CCONJ
ejpam-6834	665	8	let	let	VERB
ejpam-6834	665	9	v	v	VERB
ejpam-6834	665	10	=	=	SYM
ejpam-6834	665	11	{	{	PUNCT
ejpam-6834	665	12	v1	v1	NOUN
ejpam-6834	665	13	,	,	PUNCT
ejpam-6834	665	14	.	.	PUNCT
ejpam-6834	665	15	.	.	PUNCT
ejpam-6834	666	1	.	.	PUNCT
ejpam-6834	667	1	,	,	PUNCT
ejpam-6834	667	2	vk	vk	PART
ejpam-6834	667	3	}	}	PUNCT
ejpam-6834	667	4	be	be	AUX
ejpam-6834	667	5	a	a	DET
ejpam-6834	667	6	finite	finite	ADJ
ejpam-6834	667	7	set	set	NOUN
ejpam-6834	667	8	of	of	ADP
ejpam-6834	667	9	attributes	attribute	NOUN
ejpam-6834	667	10	.	.	PUNCT
ejpam-6834	668	1	for	for	ADP
ejpam-6834	668	2	each	each	DET
ejpam-6834	668	3	v	v	NUM
ejpam-6834	668	4	∈	∈	PROPN
ejpam-6834	668	5	v	v	NOUN
ejpam-6834	668	6	,	,	PUNCT
ejpam-6834	668	7	let	let	VERB
ejpam-6834	668	8	pv	pv	INTJ
ejpam-6834	668	9	be	be	AUX
ejpam-6834	668	10	the	the	DET
ejpam-6834	668	11	set	set	NOUN
ejpam-6834	668	12	of	of	ADP
ejpam-6834	668	13	its	its	PRON
ejpam-6834	668	14	possible	possible	ADJ
ejpam-6834	668	15	values	value	NOUN
ejpam-6834	668	16	.	.	PUNCT
ejpam-6834	669	1	fix	fix	VERB
ejpam-6834	669	2	positive	positive	ADJ
ejpam-6834	669	3	integers	integer	NOUN
ejpam-6834	669	4	m	m	PRON
ejpam-6834	669	5	,	,	PUNCT
ejpam-6834	669	6	n	n	PROPN
ejpam-6834	669	7	and	and	CCONJ
ejpam-6834	669	8	positive	positive	ADJ
ejpam-6834	669	9	dimensions	dimension	NOUN
ejpam-6834	669	10	s	s	PART
ejpam-6834	669	11	,	,	PUNCT
ejpam-6834	669	12	t.	t.	NOUN
ejpam-6834	669	13	define	define	VERB
ejpam-6834	669	14	the	the	DET
ejpam-6834	669	15	m	m	PROPN
ejpam-6834	669	16	-	-	PUNCT
ejpam-6834	669	17	th	th	VERB
ejpam-6834	669	18	nested	nested	ADJ
ejpam-6834	669	19	powerset	powerset	NOUN
ejpam-6834	669	20	of	of	ADP
ejpam-6834	669	21	x	x	PUNCT
ejpam-6834	669	22	by	by	ADP
ejpam-6834	669	23	p0(x	p0(x	PRON
ejpam-6834	669	24	)	)	PUNCT
ejpam-6834	670	1	=	=	SYM
ejpam-6834	670	2	x	x	NOUN
ejpam-6834	670	3	,	,	PUNCT
ejpam-6834	670	4	pr(x	pr(x	NOUN
ejpam-6834	670	5	)	)	PUNCT
ejpam-6834	671	1	=	=	SYM
ejpam-6834	671	2	p	p	X
ejpam-6834	671	3	(	(	PUNCT
ejpam-6834	671	4	pr−1(x	pr−1(x	NOUN
ejpam-6834	671	5	)	)	PUNCT
ejpam-6834	671	6	)	)	PUNCT
ejpam-6834	672	1	(	(	PUNCT
ejpam-6834	672	2	r	r	NOUN
ejpam-6834	672	3	≥	≥	NOUN
ejpam-6834	672	4	1	1	NUM
ejpam-6834	672	5	)	)	PUNCT
ejpam-6834	672	6	,	,	PUNCT
ejpam-6834	672	7	and	and	CCONJ
ejpam-6834	672	8	similarly	similarly	ADV
ejpam-6834	672	9	pn	pn	X
ejpam-6834	672	10	(	(	PUNCT
ejpam-6834	672	11	[	[	X
ejpam-6834	672	12	0	0	NUM
ejpam-6834	672	13	,	,	PUNCT
ejpam-6834	672	14	1]s	1]s	NUM
ejpam-6834	672	15	)	)	PUNCT
ejpam-6834	672	16	for	for	ADP
ejpam-6834	672	17	the	the	DET
ejpam-6834	672	18	s	s	ADJ
ejpam-6834	672	19	-	-	ADJ
ejpam-6834	672	20	dimensional	dimensional	ADJ
ejpam-6834	672	21	unit	unit	NOUN
ejpam-6834	672	22	cube	cube	NOUN
ejpam-6834	672	23	.	.	PUNCT
ejpam-6834	673	1	an	an	DET
ejpam-6834	673	2	(	(	PUNCT
ejpam-6834	673	3	m	m	PROPN
ejpam-6834	673	4	,	,	PUNCT
ejpam-6834	673	5	n)-superhyperplithogenic	n)-superhyperplithogenic	PUNCT
ejpam-6834	673	6	set	set	VERB
ejpam-6834	673	7	over	over	ADP
ejpam-6834	673	8	x	x	SYM
ejpam-6834	673	9	is	be	AUX
ejpam-6834	673	10	the	the	DET
ejpam-6834	673	11	quintuple	quintuple	NOUN
ejpam-6834	673	12	shp	shp	NOUN
ejpam-6834	673	13	(	(	PUNCT
ejpam-6834	673	14	m	m	PROPN
ejpam-6834	673	15	,	,	PUNCT
ejpam-6834	673	16	n	n	CCONJ
ejpam-6834	673	17	)	)	PUNCT
ejpam-6834	673	18	=	=	SYM
ejpam-6834	673	19	(	(	PUNCT
ejpam-6834	673	20	pm(x	pm(x	X
ejpam-6834	673	21	)	)	PUNCT
ejpam-6834	673	22	,	,	PUNCT
ejpam-6834	674	1	v	v	NOUN
ejpam-6834	674	2	,	,	PUNCT
ejpam-6834	674	3	{	{	PUNCT
ejpam-6834	674	4	pv}v∈v	pv}v∈v	ADJ
ejpam-6834	674	5	,	,	PUNCT
ejpam-6834	674	6	{	{	PUNCT
ejpam-6834	674	7	˜pdf	˜pdf	NOUN
ejpam-6834	674	8	(	(	PUNCT
ejpam-6834	674	9	m	m	NOUN
ejpam-6834	674	10	,	,	PUNCT
ejpam-6834	674	11	n	n	CCONJ
ejpam-6834	674	12	)	)	PUNCT
ejpam-6834	674	13	v	v	NOUN
ejpam-6834	674	14	}	}	PUNCT
ejpam-6834	674	15	v∈v	v∈v	NOUN
ejpam-6834	674	16	,	,	PUNCT
ejpam-6834	674	17	pcf	pcf	PROPN
ejpam-6834	674	18	(	(	PUNCT
ejpam-6834	674	19	m	m	PROPN
ejpam-6834	674	20	,	,	PUNCT
ejpam-6834	674	21	n	n	CCONJ
ejpam-6834	674	22	)	)	PUNCT
ejpam-6834	674	23	)	)	PUNCT
ejpam-6834	674	24	,	,	PUNCT
ejpam-6834	674	25	where	where	SCONJ
ejpam-6834	674	26	(	(	PUNCT
ejpam-6834	674	27	i	i	NOUN
ejpam-6834	674	28	)	)	PUNCT
ejpam-6834	674	29	pm(x	pm(x	PUNCT
ejpam-6834	674	30	)	)	PUNCT
ejpam-6834	674	31	is	be	AUX
ejpam-6834	674	32	the	the	DET
ejpam-6834	674	33	domain	domain	NOUN
ejpam-6834	674	34	of	of	ADP
ejpam-6834	674	35	“	"	PUNCT
ejpam-6834	674	36	super	super	NOUN
ejpam-6834	674	37	-	-	NOUN
ejpam-6834	674	38	elements	element	NOUN
ejpam-6834	674	39	”	"	PUNCT
ejpam-6834	674	40	of	of	ADP
ejpam-6834	674	41	level	level	NOUN
ejpam-6834	674	42	m.	m.	NOUN
ejpam-6834	674	43	(	(	PUNCT
ejpam-6834	674	44	ii	ii	NOUN
ejpam-6834	674	45	)	)	PUNCT
ejpam-6834	674	46	for	for	ADP
ejpam-6834	674	47	each	each	DET
ejpam-6834	674	48	v	v	NUM
ejpam-6834	674	49	∈	∈	PROPN
ejpam-6834	674	50	v	v	NOUN
ejpam-6834	674	51	,	,	PUNCT
ejpam-6834	674	52	pv	pv	X
ejpam-6834	674	53	is	be	AUX
ejpam-6834	674	54	the	the	DET
ejpam-6834	674	55	finite	finite	ADJ
ejpam-6834	674	56	set	set	NOUN
ejpam-6834	674	57	of	of	ADP
ejpam-6834	674	58	its	its	PRON
ejpam-6834	674	59	values	value	NOUN
ejpam-6834	674	60	.	.	PUNCT
ejpam-6834	675	1	(	(	PUNCT
ejpam-6834	675	2	iii	iii	X
ejpam-6834	675	3	)	)	PUNCT
ejpam-6834	675	4	the	the	DET
ejpam-6834	675	5	hyper	hyper	ADJ
ejpam-6834	675	6	degree	degree	NOUN
ejpam-6834	675	7	of	of	ADP
ejpam-6834	675	8	appurtenance	appurtenance	NOUN
ejpam-6834	675	9	function	function	NOUN
ejpam-6834	675	10	˜pdf	˜pdf	NOUN
ejpam-6834	675	11	(	(	PUNCT
ejpam-6834	675	12	m	m	NOUN
ejpam-6834	675	13	,	,	PUNCT
ejpam-6834	675	14	n	n	CCONJ
ejpam-6834	675	15	)	)	PUNCT
ejpam-6834	675	16	v	v	NOUN
ejpam-6834	675	17	:	:	PUNCT
ejpam-6834	675	18	pm(x	pm(x	X
ejpam-6834	675	19	)	)	PUNCT
ejpam-6834	675	20	×	×	NOUN
ejpam-6834	675	21	pv	pv	INTJ
ejpam-6834	675	22	−→	−→	NOUN
ejpam-6834	676	1	pn	pn	PROPN
ejpam-6834	676	2	(	(	PUNCT
ejpam-6834	676	3	[	[	X
ejpam-6834	676	4	0	0	NUM
ejpam-6834	676	5	,	,	PUNCT
ejpam-6834	676	6	1]s	1]s	NUM
ejpam-6834	676	7	)	)	PUNCT
ejpam-6834	676	8	assigns	assign	NOUN
ejpam-6834	676	9	to	to	ADP
ejpam-6834	676	10	each	each	PRON
ejpam-6834	676	11	(	(	PUNCT
ejpam-6834	676	12	a	a	DET
ejpam-6834	676	13	,	,	PUNCT
ejpam-6834	676	14	a	a	NOUN
ejpam-6834	676	15	)	)	PUNCT
ejpam-6834	676	16	with	with	ADP
ejpam-6834	676	17	a	a	DET
ejpam-6834	676	18	∈	∈	NOUN
ejpam-6834	676	19	pm(x	pm(x	X
ejpam-6834	676	20	)	)	PUNCT
ejpam-6834	676	21	and	and	CCONJ
ejpam-6834	676	22	a	a	DET
ejpam-6834	676	23	∈	∈	NOUN
ejpam-6834	676	24	pv	pv	VERB
ejpam-6834	676	25	a	a	DET
ejpam-6834	676	26	nonempty	nonempty	NOUN
ejpam-6834	676	27	subset	subset	VERB
ejpam-6834	676	28	˜pdf	˜pdf	NOUN
ejpam-6834	676	29	(	(	PUNCT
ejpam-6834	676	30	m	m	NOUN
ejpam-6834	676	31	,	,	PUNCT
ejpam-6834	676	32	n	n	CCONJ
ejpam-6834	676	33	)	)	PUNCT
ejpam-6834	676	34	v	v	NOUN
ejpam-6834	676	35	(	(	PUNCT
ejpam-6834	676	36	a	a	PRON
ejpam-6834	676	37	,	,	PUNCT
ejpam-6834	676	38	a	a	NOUN
ejpam-6834	676	39	)	)	PUNCT
ejpam-6834	676	40	⊆	⊆	NUM
ejpam-6834	676	41	[	[	X
ejpam-6834	676	42	0	0	NUM
ejpam-6834	676	43	,	,	PUNCT
ejpam-6834	676	44	1]s	1]s	NOUN
ejpam-6834	676	45	representing	represent	VERB
ejpam-6834	676	46	all	all	DET
ejpam-6834	676	47	possible	possible	ADJ
ejpam-6834	676	48	membership	membership	NOUN
ejpam-6834	676	49	-	-	PUNCT
ejpam-6834	676	50	degree	degree	NOUN
ejpam-6834	676	51	vectors	vector	NOUN
ejpam-6834	676	52	of	of	ADP
ejpam-6834	676	53	dimension	dimension	NOUN
ejpam-6834	676	54	s.	s.	PROPN
ejpam-6834	676	55	(	(	PUNCT
ejpam-6834	676	56	iv	iv	X
ejpam-6834	676	57	)	)	PUNCT
ejpam-6834	676	58	the	the	DET
ejpam-6834	676	59	degree	degree	NOUN
ejpam-6834	676	60	of	of	ADP
ejpam-6834	676	61	contradiction	contradiction	NOUN
ejpam-6834	676	62	function	function	NOUN
ejpam-6834	676	63	pcf	pcf	PROPN
ejpam-6834	676	64	(	(	PUNCT
ejpam-6834	676	65	m	m	PROPN
ejpam-6834	676	66	,	,	PUNCT
ejpam-6834	676	67	n	n	CCONJ
ejpam-6834	676	68	)	)	PUNCT
ejpam-6834	676	69	:	:	PUNCT
ejpam-6834	676	70	(	(	PUNCT
ejpam-6834	676	71	⋃	⋃	NOUN
ejpam-6834	676	72	v∈v	v∈v	NOUN
ejpam-6834	676	73	pv	pv	NOUN
ejpam-6834	676	74	)	)	PUNCT
ejpam-6834	676	75	×	×	NOUN
ejpam-6834	676	76	(	(	PUNCT
ejpam-6834	676	77	⋃	⋃	NOUN
ejpam-6834	676	78	v∈v	v∈v	NOUN
ejpam-6834	676	79	pv	pv	NOUN
ejpam-6834	676	80	)	)	PUNCT
ejpam-6834	677	1	−→	−→	NOUN
ejpam-6834	678	1	[	[	X
ejpam-6834	678	2	0	0	NUM
ejpam-6834	678	3	,	,	PUNCT
ejpam-6834	678	4	1]t	1]t	NUM
ejpam-6834	678	5	satisfies	satisfie	NOUN
ejpam-6834	678	6	for	for	ADP
ejpam-6834	678	7	all	all	DET
ejpam-6834	678	8	a	a	DET
ejpam-6834	678	9	,	,	PUNCT
ejpam-6834	678	10	b	b	NOUN
ejpam-6834	678	11	:	:	PUNCT
ejpam-6834	678	12	(	(	PUNCT
ejpam-6834	678	13	a	a	X
ejpam-6834	678	14	)	)	PUNCT
ejpam-6834	678	15	pcf	pcf	PROPN
ejpam-6834	678	16	(	(	PUNCT
ejpam-6834	678	17	m	m	PROPN
ejpam-6834	678	18	,	,	PUNCT
ejpam-6834	678	19	n)(a	n)(a	NUM
ejpam-6834	678	20	,	,	PUNCT
ejpam-6834	678	21	a	a	PRON
ejpam-6834	678	22	)	)	PUNCT
ejpam-6834	678	23	=	=	SYM
ejpam-6834	678	24	0	0	NUM
ejpam-6834	679	1	(	(	PUNCT
ejpam-6834	679	2	reflexivity	reflexivity	NOUN
ejpam-6834	679	3	)	)	PUNCT
ejpam-6834	679	4	,	,	PUNCT
ejpam-6834	679	5	(	(	PUNCT
ejpam-6834	679	6	b	b	X
ejpam-6834	679	7	)	)	PUNCT
ejpam-6834	679	8	pcf	pcf	PROPN
ejpam-6834	679	9	(	(	PUNCT
ejpam-6834	679	10	m	m	PROPN
ejpam-6834	679	11	,	,	PUNCT
ejpam-6834	679	12	n)(a	n)(a	NUM
ejpam-6834	679	13	,	,	PUNCT
ejpam-6834	679	14	b	b	X
ejpam-6834	679	15	)	)	PUNCT
ejpam-6834	679	16	=	=	SYM
ejpam-6834	679	17	pcf	pcf	PROPN
ejpam-6834	679	18	(	(	PUNCT
ejpam-6834	679	19	m	m	PROPN
ejpam-6834	679	20	,	,	PUNCT
ejpam-6834	679	21	n)(b	n)(b	ADJ
ejpam-6834	679	22	,	,	PUNCT
ejpam-6834	679	23	a	a	PRON
ejpam-6834	679	24	)	)	PUNCT
ejpam-6834	679	25	(	(	PUNCT
ejpam-6834	679	26	symmetry	symmetry	NOUN
ejpam-6834	679	27	)	)	PUNCT
ejpam-6834	679	28	.	.	PUNCT
ejpam-6834	680	1	example	example	NOUN
ejpam-6834	680	2	18	18	NUM
ejpam-6834	680	3	(	(	PUNCT
ejpam-6834	680	4	simple	simple	ADJ
ejpam-6834	680	5	(	(	PUNCT
ejpam-6834	680	6	1	1	NUM
ejpam-6834	680	7	,	,	PUNCT
ejpam-6834	680	8	1)-superhyperplithogenic	1)-superhyperplithogenic	NUM
ejpam-6834	680	9	set	set	NOUN
ejpam-6834	680	10	)	)	PUNCT
ejpam-6834	680	11	.	.	PUNCT
ejpam-6834	681	1	let	let	VERB
ejpam-6834	681	2	x	x	PUNCT
ejpam-6834	681	3	=	=	PRON
ejpam-6834	681	4	{	{	PUNCT
ejpam-6834	681	5	a1	a1	PROPN
ejpam-6834	681	6	,	,	PUNCT
ejpam-6834	681	7	a2	a2	PROPN
ejpam-6834	681	8	}	}	PUNCT
ejpam-6834	681	9	and	and	CCONJ
ejpam-6834	681	10	v	v	NOUN
ejpam-6834	681	11	=	=	SYM
ejpam-6834	681	12	{	{	PUNCT
ejpam-6834	681	13	v	v	NOUN
ejpam-6834	681	14	}	}	PUNCT
ejpam-6834	681	15	with	with	ADP
ejpam-6834	681	16	pv	pv	NOUN
ejpam-6834	681	17	=	=	SYM
ejpam-6834	681	18	{	{	PUNCT
ejpam-6834	681	19	p1	p1	NOUN
ejpam-6834	681	20	,	,	PUNCT
ejpam-6834	681	21	p2	p2	PROPN
ejpam-6834	681	22	}	}	PUNCT
ejpam-6834	681	23	.	.	PUNCT
ejpam-6834	682	1	take	take	VERB
ejpam-6834	682	2	m	m	NOUN
ejpam-6834	682	3	=	=	SYM
ejpam-6834	682	4	n	n	PROPN
ejpam-6834	682	5	=	=	SYM
ejpam-6834	682	6	1	1	NUM
ejpam-6834	682	7	and	and	CCONJ
ejpam-6834	682	8	s	s	NOUN
ejpam-6834	683	1	=	=	X
ejpam-6834	683	2	t	t	X
ejpam-6834	683	3	=	=	SYM
ejpam-6834	683	4	1	1	X
ejpam-6834	683	5	.	.	PUNCT
ejpam-6834	683	6	then	then	ADV
ejpam-6834	683	7	p1(x	p1(x	NOUN
ejpam-6834	683	8	)	)	PUNCT
ejpam-6834	683	9	=	=	SYM
ejpam-6834	683	10	p(x	p(x	PROPN
ejpam-6834	683	11	)	)	PUNCT
ejpam-6834	683	12	,	,	PUNCT
ejpam-6834	683	13	p1([0	p1([0	PROPN
ejpam-6834	683	14	,	,	PUNCT
ejpam-6834	683	15	1	1	NUM
ejpam-6834	683	16	]	]	PUNCT
ejpam-6834	683	17	)	)	PUNCT
ejpam-6834	684	1	=	=	SYM
ejpam-6834	684	2	p([0	p([0	PROPN
ejpam-6834	684	3	,	,	PUNCT
ejpam-6834	684	4	1	1	NUM
ejpam-6834	684	5	]	]	NUM
ejpam-6834	684	6	)	)	PUNCT
ejpam-6834	684	7	.	.	PUNCT
ejpam-6834	685	1	t.	t.	PROPN
ejpam-6834	685	2	fujita	fujita	PROPN
ejpam-6834	685	3	,	,	PUNCT
ejpam-6834	685	4	f.smarandache	f.smarandache	NOUN
ejpam-6834	685	5	/	/	SYM
ejpam-6834	685	6	eur	eur	PROPN
ejpam-6834	685	7	.	.	PUNCT
ejpam-6834	686	1	j.	j.	PROPN
ejpam-6834	686	2	pure	pure	PROPN
ejpam-6834	686	3	appl	appl	PROPN
ejpam-6834	686	4	.	.	PROPN
ejpam-6834	686	5	math	math	PROPN
ejpam-6834	686	6	,	,	PUNCT
ejpam-6834	686	7	18	18	NUM
ejpam-6834	686	8	(	(	PUNCT
ejpam-6834	686	9	4	4	NUM
ejpam-6834	686	10	)	)	PUNCT
ejpam-6834	686	11	(	(	PUNCT
ejpam-6834	686	12	2025	2025	NUM
ejpam-6834	686	13	)	)	PUNCT
ejpam-6834	686	14	,	,	PUNCT
ejpam-6834	686	15	6834	6834	NUM
ejpam-6834	686	16	29	29	NUM
ejpam-6834	686	17	of	of	ADP
ejpam-6834	686	18	69	69	NUM
ejpam-6834	686	19	define	define	ADJ
ejpam-6834	686	20	˜pdf	˜pdf	NOUN
ejpam-6834	686	21	(	(	PUNCT
ejpam-6834	686	22	1,1	1,1	NUM
ejpam-6834	686	23	)	)	PUNCT
ejpam-6834	686	24	v	v	NOUN
ejpam-6834	686	25	:	:	PUNCT
ejpam-6834	686	26	p(x	p(x	PROPN
ejpam-6834	686	27	)	)	PUNCT
ejpam-6834	686	28	×	×	NOUN
ejpam-6834	686	29	pv	pv	NOUN
ejpam-6834	686	30	→	→	SYM
ejpam-6834	686	31	p([0	p([0	ADJ
ejpam-6834	686	32	,	,	PUNCT
ejpam-6834	686	33	1	1	NUM
ejpam-6834	686	34	]	]	PUNCT
ejpam-6834	686	35	)	)	PUNCT
ejpam-6834	686	36	by	by	ADP
ejpam-6834	686	37	˜pdf	˜pdf	NOUN
ejpam-6834	686	38	(	(	PUNCT
ejpam-6834	686	39	1,1	1,1	NUM
ejpam-6834	686	40	)	)	PUNCT
ejpam-6834	686	41	v	v	NOUN
ejpam-6834	686	42	(	(	PUNCT
ejpam-6834	686	43	{	{	PUNCT
ejpam-6834	686	44	a1	a1	NOUN
ejpam-6834	686	45	,	,	PUNCT
ejpam-6834	686	46	a2	a2	PROPN
ejpam-6834	686	47	}	}	PUNCT
ejpam-6834	686	48	,	,	PUNCT
ejpam-6834	686	49	p1	p1	PROPN
ejpam-6834	686	50	)	)	PUNCT
ejpam-6834	686	51	=	=	PUNCT
ejpam-6834	687	1	[	[	X
ejpam-6834	687	2	0.7	0.7	NUM
ejpam-6834	687	3	,	,	PUNCT
ejpam-6834	687	4	0.8	0.8	NUM
ejpam-6834	687	5	]	]	PUNCT
ejpam-6834	687	6	,	,	PUNCT
ejpam-6834	687	7	˜pdf	˜pdf	NOUN
ejpam-6834	687	8	(	(	PUNCT
ejpam-6834	687	9	1,1	1,1	NUM
ejpam-6834	687	10	)	)	PUNCT
ejpam-6834	687	11	v	v	NOUN
ejpam-6834	687	12	(	(	PUNCT
ejpam-6834	687	13	{	{	PUNCT
ejpam-6834	687	14	a1	a1	NOUN
ejpam-6834	687	15	}	}	PUNCT
ejpam-6834	687	16	,	,	PUNCT
ejpam-6834	687	17	p1	p1	PROPN
ejpam-6834	687	18	)	)	PUNCT
ejpam-6834	687	19	=	=	PUNCT
ejpam-6834	687	20	{	{	PUNCT
ejpam-6834	687	21	0.5	0.5	NUM
ejpam-6834	687	22	,	,	PUNCT
ejpam-6834	687	23	0.6	0.6	NUM
ejpam-6834	687	24	}	}	PUNCT
ejpam-6834	687	25	,	,	PUNCT
ejpam-6834	687	26	˜pdf	˜pdf	NOUN
ejpam-6834	687	27	(	(	PUNCT
ejpam-6834	687	28	1,1	1,1	NUM
ejpam-6834	687	29	)	)	PUNCT
ejpam-6834	687	30	v	v	NOUN
ejpam-6834	687	31	(	(	PUNCT
ejpam-6834	687	32	{	{	PUNCT
ejpam-6834	687	33	a2	a2	NOUN
ejpam-6834	687	34	}	}	PUNCT
ejpam-6834	687	35	,	,	PUNCT
ejpam-6834	687	36	p1	p1	PROPN
ejpam-6834	687	37	)	)	PUNCT
ejpam-6834	687	38	=	=	PUNCT
ejpam-6834	688	1	[	[	X
ejpam-6834	688	2	0.3	0.3	NUM
ejpam-6834	688	3	,	,	PUNCT
ejpam-6834	688	4	0.4	0.4	NUM
ejpam-6834	688	5	]	]	PUNCT
ejpam-6834	688	6	,	,	PUNCT
ejpam-6834	688	7	˜pdf	˜pdf	NOUN
ejpam-6834	688	8	(	(	PUNCT
ejpam-6834	688	9	1,1	1,1	NUM
ejpam-6834	688	10	)	)	PUNCT
ejpam-6834	688	11	v	v	NOUN
ejpam-6834	688	12	(	(	PUNCT
ejpam-6834	688	13	∅	∅	NOUN
ejpam-6834	688	14	,	,	PUNCT
ejpam-6834	688	15	p1	p1	NOUN
ejpam-6834	688	16	)	)	PUNCT
ejpam-6834	688	17	=	=	PRON
ejpam-6834	688	18	{	{	PUNCT
ejpam-6834	688	19	0	0	NUM
ejpam-6834	688	20	}	}	PUNCT
ejpam-6834	688	21	,	,	PUNCT
ejpam-6834	688	22	and	and	CCONJ
ejpam-6834	688	23	similarly	similarly	ADV
ejpam-6834	688	24	for	for	ADP
ejpam-6834	688	25	p2	p2	NOUN
ejpam-6834	688	26	.	.	PUNCT
ejpam-6834	689	1	for	for	ADP
ejpam-6834	689	2	the	the	DET
ejpam-6834	689	3	contradiction	contradiction	NOUN
ejpam-6834	689	4	,	,	PUNCT
ejpam-6834	689	5	pcf	pcf	PROPN
ejpam-6834	689	6	(	(	PUNCT
ejpam-6834	689	7	1,1	1,1	NUM
ejpam-6834	689	8	)	)	PUNCT
ejpam-6834	689	9	:	:	PUNCT
ejpam-6834	689	10	pv	pv	INTJ
ejpam-6834	689	11	×	×	NOUN
ejpam-6834	689	12	pv	pv	INTJ
ejpam-6834	689	13	→	→	PUNCT
ejpam-6834	690	1	[	[	X
ejpam-6834	690	2	0	0	NUM
ejpam-6834	690	3	,	,	PUNCT
ejpam-6834	690	4	1	1	NUM
ejpam-6834	690	5	]	]	PUNCT
ejpam-6834	690	6	,	,	PUNCT
ejpam-6834	690	7	set	set	VERB
ejpam-6834	690	8	pcf	pcf	PROPN
ejpam-6834	690	9	(	(	PUNCT
ejpam-6834	690	10	1,1)(p1	1,1)(p1	NUM
ejpam-6834	690	11	,	,	PUNCT
ejpam-6834	690	12	p1	p1	PROPN
ejpam-6834	690	13	)	)	PUNCT
ejpam-6834	690	14	=	=	SYM
ejpam-6834	690	15	0	0	NUM
ejpam-6834	690	16	,	,	PUNCT
ejpam-6834	690	17	pcf	pcf	PROPN
ejpam-6834	690	18	(	(	PUNCT
ejpam-6834	690	19	1,1)(p1	1,1)(p1	NUM
ejpam-6834	690	20	,	,	PUNCT
ejpam-6834	690	21	p2	p2	X
ejpam-6834	690	22	)	)	PUNCT
ejpam-6834	690	23	=	=	SYM
ejpam-6834	690	24	0.2	0.2	NUM
ejpam-6834	690	25	,	,	PUNCT
ejpam-6834	690	26	pcf	pcf	PROPN
ejpam-6834	690	27	(	(	PUNCT
ejpam-6834	690	28	1,1)(p2	1,1)(p2	NUM
ejpam-6834	690	29	,	,	PUNCT
ejpam-6834	690	30	p2	p2	X
ejpam-6834	690	31	)	)	PUNCT
ejpam-6834	690	32	=	=	SYM
ejpam-6834	690	33	0	0	NUM
ejpam-6834	690	34	,	,	PUNCT
ejpam-6834	690	35	with	with	ADP
ejpam-6834	690	36	symmetry	symmetry	PROPN
ejpam-6834	690	37	pcf	pcf	PROPN
ejpam-6834	690	38	(	(	PUNCT
ejpam-6834	690	39	p2	p2	PROPN
ejpam-6834	690	40	,	,	PUNCT
ejpam-6834	690	41	p1	p1	NOUN
ejpam-6834	690	42	)	)	PUNCT
ejpam-6834	690	43	=	=	SYM
ejpam-6834	690	44	0.2	0.2	NUM
ejpam-6834	690	45	.	.	PUNCT
ejpam-6834	691	1	then	then	ADV
ejpam-6834	691	2	shp	shp	NOUN
ejpam-6834	691	3	(	(	PUNCT
ejpam-6834	691	4	1,1	1,1	NUM
ejpam-6834	691	5	)	)	PUNCT
ejpam-6834	691	6	=	=	SYM
ejpam-6834	691	7	(	(	PUNCT
ejpam-6834	691	8	p(x	p(x	PROPN
ejpam-6834	691	9	)	)	PUNCT
ejpam-6834	691	10	,	,	PUNCT
ejpam-6834	691	11	{	{	PUNCT
ejpam-6834	691	12	v	v	NOUN
ejpam-6834	691	13	}	}	PUNCT
ejpam-6834	691	14	,	,	PUNCT
ejpam-6834	691	15	{	{	PUNCT
ejpam-6834	691	16	pv	pv	NOUN
ejpam-6834	691	17	}	}	PUNCT
ejpam-6834	691	18	,	,	PUNCT
ejpam-6834	691	19	{	{	PUNCT
ejpam-6834	691	20	˜pdf	˜pdf	NOUN
ejpam-6834	691	21	(	(	PUNCT
ejpam-6834	691	22	1,1	1,1	NUM
ejpam-6834	691	23	)	)	PUNCT
ejpam-6834	691	24	v	v	NOUN
ejpam-6834	691	25	}	}	PUNCT
ejpam-6834	691	26	,	,	PUNCT
ejpam-6834	691	27	pcf	pcf	PROPN
ejpam-6834	691	28	(	(	PUNCT
ejpam-6834	691	29	1,1	1,1	NUM
ejpam-6834	691	30	)	)	PUNCT
ejpam-6834	691	31	)	)	PUNCT
ejpam-6834	691	32	is	be	AUX
ejpam-6834	691	33	a	a	DET
ejpam-6834	691	34	valid	valid	ADJ
ejpam-6834	691	35	(	(	PUNCT
ejpam-6834	691	36	1	1	NUM
ejpam-6834	691	37	,	,	PUNCT
ejpam-6834	691	38	1)-superhyperplithogenic	1)-superhyperplithogenic	NUM
ejpam-6834	691	39	set	set	NOUN
ejpam-6834	691	40	.	.	PUNCT
ejpam-6834	692	1	example	example	NOUN
ejpam-6834	692	2	19	19	NUM
ejpam-6834	692	3	(	(	PUNCT
ejpam-6834	692	4	hackathon	hackathon	PROPN
ejpam-6834	692	5	team	team	NOUN
ejpam-6834	692	6	evaluation	evaluation	NOUN
ejpam-6834	692	7	)	)	PUNCT
ejpam-6834	692	8	.	.	PUNCT
ejpam-6834	693	1	let	let	VERB
ejpam-6834	693	2	x	x	PUNCT
ejpam-6834	693	3	=	=	PRON
ejpam-6834	693	4	{	{	PUNCT
ejpam-6834	693	5	hiroko	hiroko	PROPN
ejpam-6834	693	6	,	,	PUNCT
ejpam-6834	693	7	masahiro	masahiro	PROPN
ejpam-6834	693	8	,	,	PUNCT
ejpam-6834	693	9	shinya	shinya	PROPN
ejpam-6834	693	10	,	,	PUNCT
ejpam-6834	693	11	dave	dave	PROPN
ejpam-6834	693	12	}	}	PUNCT
ejpam-6834	693	13	,	,	PUNCT
ejpam-6834	693	14	and	and	CCONJ
ejpam-6834	693	15	take	take	VERB
ejpam-6834	693	16	m	m	NOUN
ejpam-6834	693	17	=	=	SYM
ejpam-6834	693	18	n	n	PROPN
ejpam-6834	693	19	=	=	SYM
ejpam-6834	693	20	1	1	NUM
ejpam-6834	693	21	,	,	PUNCT
ejpam-6834	693	22	so	so	SCONJ
ejpam-6834	693	23	that	that	DET
ejpam-6834	693	24	p1(x	p1(x	NOUN
ejpam-6834	693	25	)	)	PUNCT
ejpam-6834	693	26	=	=	SYM
ejpam-6834	693	27	p(x	p(x	PROPN
ejpam-6834	693	28	)	)	PUNCT
ejpam-6834	693	29	.	.	PUNCT
ejpam-6834	694	1	we	we	PRON
ejpam-6834	694	2	consider	consider	VERB
ejpam-6834	694	3	two	two	NUM
ejpam-6834	694	4	evaluation	evaluation	NOUN
ejpam-6834	694	5	attributes	attribute	NOUN
ejpam-6834	694	6	:	:	PUNCT
ejpam-6834	694	7	v1	v1	NOUN
ejpam-6834	694	8	=	=	SYM
ejpam-6834	694	9	innovation	innovation	NOUN
ejpam-6834	694	10	,	,	PUNCT
ejpam-6834	694	11	pv1	pv1	NOUN
ejpam-6834	694	12	=	=	PUNCT
ejpam-6834	694	13	{	{	PUNCT
ejpam-6834	694	14	low	low	ADJ
ejpam-6834	694	15	,	,	PUNCT
ejpam-6834	694	16	medium	medium	ADJ
ejpam-6834	694	17	,	,	PUNCT
ejpam-6834	694	18	high	high	ADJ
ejpam-6834	694	19	}	}	PUNCT
ejpam-6834	694	20	,	,	PUNCT
ejpam-6834	694	21	v2	v2	PROPN
ejpam-6834	694	22	=	=	SYM
ejpam-6834	694	23	feasibility	feasibility	NOUN
ejpam-6834	694	24	,	,	PUNCT
ejpam-6834	694	25	pv2	pv2	NOUN
ejpam-6834	694	26	=	=	PRON
ejpam-6834	694	27	{	{	PUNCT
ejpam-6834	694	28	low	low	ADJ
ejpam-6834	694	29	,	,	PUNCT
ejpam-6834	694	30	medium	medium	ADJ
ejpam-6834	694	31	,	,	PUNCT
ejpam-6834	694	32	high	high	ADJ
ejpam-6834	694	33	}	}	PUNCT
ejpam-6834	694	34	.	.	PUNCT
ejpam-6834	695	1	for	for	ADP
ejpam-6834	695	2	richness	richness	NOUN
ejpam-6834	695	3	,	,	PUNCT
ejpam-6834	695	4	let	let	VERB
ejpam-6834	695	5	the	the	DET
ejpam-6834	695	6	membership	membership	NOUN
ejpam-6834	695	7	–	–	PUNCT
ejpam-6834	695	8	degree	degree	NOUN
ejpam-6834	695	9	vectors	vector	NOUN
ejpam-6834	695	10	be	be	AUX
ejpam-6834	695	11	two	two	NUM
ejpam-6834	695	12	–	–	PUNCT
ejpam-6834	695	13	dimensional	dimensional	ADJ
ejpam-6834	695	14	(	(	PUNCT
ejpam-6834	695	15	peer	peer	NOUN
ejpam-6834	695	16	score	score	NOUN
ejpam-6834	695	17	,	,	PUNCT
ejpam-6834	695	18	judge	judge	NOUN
ejpam-6834	695	19	score	score	NOUN
ejpam-6834	695	20	)	)	PUNCT
ejpam-6834	695	21	,	,	PUNCT
ejpam-6834	695	22	so	so	SCONJ
ejpam-6834	695	23	s	s	VERB
ejpam-6834	695	24	=	=	SYM
ejpam-6834	695	25	2	2	NUM
ejpam-6834	695	26	,	,	PUNCT
ejpam-6834	695	27	and	and	CCONJ
ejpam-6834	695	28	let	let	VERB
ejpam-6834	695	29	the	the	DET
ejpam-6834	695	30	contradiction	contradiction	NOUN
ejpam-6834	695	31	measure	measure	NOUN
ejpam-6834	695	32	be	be	AUX
ejpam-6834	695	33	scalar	scalar	ADJ
ejpam-6834	695	34	,	,	PUNCT
ejpam-6834	695	35	so	so	SCONJ
ejpam-6834	695	36	t	t	NOUN
ejpam-6834	695	37	=	=	SYM
ejpam-6834	695	38	1	1	X
ejpam-6834	695	39	.	.	PUNCT
ejpam-6834	695	40	then	then	ADV
ejpam-6834	695	41	˜pdf	˜pdf	NOUN
ejpam-6834	695	42	(	(	PUNCT
ejpam-6834	695	43	1,1	1,1	NUM
ejpam-6834	695	44	)	)	PUNCT
ejpam-6834	695	45	vi	vi	NOUN
ejpam-6834	695	46	:	:	PUNCT
ejpam-6834	695	47	p(x	p(x	PROPN
ejpam-6834	695	48	)	)	PUNCT
ejpam-6834	695	49	×	×	NOUN
ejpam-6834	695	50	pvi	pvi	NOUN
ejpam-6834	695	51	−→	−→	NOUN
ejpam-6834	695	52	p	p	X
ejpam-6834	695	53	(	(	PUNCT
ejpam-6834	695	54	[	[	X
ejpam-6834	695	55	0	0	NUM
ejpam-6834	695	56	,	,	PUNCT
ejpam-6834	695	57	1]2	1]2	NUM
ejpam-6834	695	58	)	)	PUNCT
ejpam-6834	695	59	assigns	assign	NOUN
ejpam-6834	695	60	to	to	ADP
ejpam-6834	695	61	each	each	DET
ejpam-6834	695	62	team	team	NOUN
ejpam-6834	695	63	a	a	DET
ejpam-6834	695	64	⊆	⊆	NUM
ejpam-6834	695	65	x	x	PUNCT
ejpam-6834	695	66	and	and	CCONJ
ejpam-6834	695	67	level	level	VERB
ejpam-6834	695	68	a	a	DET
ejpam-6834	695	69	∈	∈	NOUN
ejpam-6834	695	70	pvi	pvi	NOUN
ejpam-6834	695	71	a	a	DET
ejpam-6834	695	72	nonempty	nonempty	ADJ
ejpam-6834	695	73	set	set	NOUN
ejpam-6834	695	74	of	of	ADP
ejpam-6834	695	75	vectors	vector	NOUN
ejpam-6834	695	76	in	in	ADP
ejpam-6834	695	77	[	[	X
ejpam-6834	695	78	0	0	NUM
ejpam-6834	695	79	,	,	PUNCT
ejpam-6834	695	80	1]2	1]2	NUM
ejpam-6834	695	81	.	.	PUNCT
ejpam-6834	696	1	for	for	ADP
ejpam-6834	696	2	example	example	NOUN
ejpam-6834	696	3	,	,	PUNCT
ejpam-6834	696	4	for	for	ADP
ejpam-6834	696	5	the	the	DET
ejpam-6834	696	6	team	team	NOUN
ejpam-6834	696	7	a	a	DET
ejpam-6834	696	8	=	=	X
ejpam-6834	696	9	{	{	PUNCT
ejpam-6834	696	10	hiroko	hiroko	PROPN
ejpam-6834	696	11	,	,	PUNCT
ejpam-6834	696	12	masahiro	masahiro	PROPN
ejpam-6834	696	13	}	}	PUNCT
ejpam-6834	696	14	:	:	PUNCT
ejpam-6834	696	15	˜pdf	˜pdf	NOUN
ejpam-6834	696	16	(	(	PUNCT
ejpam-6834	696	17	1,1	1,1	NUM
ejpam-6834	696	18	)	)	PUNCT
ejpam-6834	696	19	innovation(a	innovation(a	PROPN
ejpam-6834	696	20	,	,	PUNCT
ejpam-6834	696	21	high	high	ADJ
ejpam-6834	696	22	)	)	PUNCT
ejpam-6834	696	23	=	=	PRON
ejpam-6834	696	24	{	{	PUNCT
ejpam-6834	696	25	(	(	PUNCT
ejpam-6834	696	26	0.90	0.90	NUM
ejpam-6834	696	27	,	,	PUNCT
ejpam-6834	696	28	0.85	0.85	NUM
ejpam-6834	696	29	)	)	PUNCT
ejpam-6834	696	30	,	,	PUNCT
ejpam-6834	696	31	(	(	PUNCT
ejpam-6834	696	32	0.88	0.88	NUM
ejpam-6834	696	33	,	,	PUNCT
ejpam-6834	696	34	0.82	0.82	NUM
ejpam-6834	696	35	)	)	PUNCT
ejpam-6834	696	36	}	}	PUNCT
ejpam-6834	696	37	,	,	PUNCT
ejpam-6834	696	38	˜pdf	˜pdf	NOUN
ejpam-6834	696	39	(	(	PUNCT
ejpam-6834	696	40	1,1	1,1	NUM
ejpam-6834	696	41	)	)	PUNCT
ejpam-6834	696	42	innovation(a	innovation(a	NOUN
ejpam-6834	696	43	,	,	PUNCT
ejpam-6834	696	44	medium	medium	NOUN
ejpam-6834	696	45	)	)	PUNCT
ejpam-6834	696	46	=	=	SYM
ejpam-6834	696	47	{	{	PUNCT
ejpam-6834	696	48	(	(	PUNCT
ejpam-6834	696	49	0.70	0.70	NUM
ejpam-6834	696	50	,	,	PUNCT
ejpam-6834	696	51	0.75	0.75	NUM
ejpam-6834	696	52	)	)	PUNCT
ejpam-6834	696	53	}	}	PUNCT
ejpam-6834	696	54	,	,	PUNCT
ejpam-6834	696	55	˜pdf	˜pdf	NOUN
ejpam-6834	696	56	(	(	PUNCT
ejpam-6834	696	57	1,1	1,1	NUM
ejpam-6834	696	58	)	)	PUNCT
ejpam-6834	696	59	feasibility(a	feasibility(a	NOUN
ejpam-6834	696	60	,	,	PUNCT
ejpam-6834	696	61	high	high	ADJ
ejpam-6834	696	62	)	)	PUNCT
ejpam-6834	696	63	=	=	PRON
ejpam-6834	696	64	{	{	PUNCT
ejpam-6834	696	65	(	(	PUNCT
ejpam-6834	696	66	0.80	0.80	NUM
ejpam-6834	696	67	,	,	PUNCT
ejpam-6834	696	68	0.78	0.78	NUM
ejpam-6834	696	69	)	)	PUNCT
ejpam-6834	696	70	,	,	PUNCT
ejpam-6834	696	71	(	(	PUNCT
ejpam-6834	696	72	0.82	0.82	NUM
ejpam-6834	696	73	,	,	PUNCT
ejpam-6834	696	74	0.80	0.80	NUM
ejpam-6834	696	75	)	)	PUNCT
ejpam-6834	696	76	}	}	PUNCT
ejpam-6834	696	77	,	,	PUNCT
ejpam-6834	696	78	˜pdf	˜pdf	NOUN
ejpam-6834	696	79	(	(	PUNCT
ejpam-6834	696	80	1,1	1,1	NUM
ejpam-6834	696	81	)	)	PUNCT
ejpam-6834	696	82	feasibility(a	feasibility(a	NOUN
ejpam-6834	696	83	,	,	PUNCT
ejpam-6834	696	84	low	low	ADJ
ejpam-6834	696	85	)	)	PUNCT
ejpam-6834	696	86	=	=	SYM
ejpam-6834	696	87	{	{	PUNCT
ejpam-6834	696	88	(	(	PUNCT
ejpam-6834	696	89	0.50	0.50	NUM
ejpam-6834	696	90	,	,	PUNCT
ejpam-6834	696	91	0.55	0.55	NUM
ejpam-6834	696	92	)	)	PUNCT
ejpam-6834	696	93	}	}	PUNCT
ejpam-6834	696	94	.	.	PUNCT
ejpam-6834	697	1	t.	t.	PROPN
ejpam-6834	697	2	fujita	fujita	PROPN
ejpam-6834	697	3	,	,	PUNCT
ejpam-6834	697	4	f.smarandache	f.smarandache	NOUN
ejpam-6834	697	5	/	/	SYM
ejpam-6834	697	6	eur	eur	PROPN
ejpam-6834	697	7	.	.	PUNCT
ejpam-6834	698	1	j.	j.	PROPN
ejpam-6834	698	2	pure	pure	PROPN
ejpam-6834	698	3	appl	appl	PROPN
ejpam-6834	698	4	.	.	PROPN
ejpam-6834	698	5	math	math	PROPN
ejpam-6834	698	6	,	,	PUNCT
ejpam-6834	698	7	18	18	NUM
ejpam-6834	698	8	(	(	PUNCT
ejpam-6834	698	9	4	4	NUM
ejpam-6834	698	10	)	)	PUNCT
ejpam-6834	698	11	(	(	PUNCT
ejpam-6834	698	12	2025	2025	NUM
ejpam-6834	698	13	)	)	PUNCT
ejpam-6834	698	14	,	,	PUNCT
ejpam-6834	698	15	6834	6834	NUM
ejpam-6834	698	16	30	30	NUM
ejpam-6834	698	17	of	of	ADP
ejpam-6834	698	18	69	69	NUM
ejpam-6834	698	19	the	the	DET
ejpam-6834	698	20	degree	degree	NOUN
ejpam-6834	698	21	of	of	ADP
ejpam-6834	698	22	contradiction	contradiction	NOUN
ejpam-6834	698	23	function	function	NOUN
ejpam-6834	698	24	pcf	pcf	PROPN
ejpam-6834	698	25	(	(	PUNCT
ejpam-6834	698	26	1,1	1,1	NUM
ejpam-6834	698	27	)	)	PUNCT
ejpam-6834	698	28	:	:	PUNCT
ejpam-6834	698	29	(	(	PUNCT
ejpam-6834	698	30	pv1	pv1	VERB
ejpam-6834	698	31	∪	∪	ADP
ejpam-6834	698	32	pv2	pv2	NOUN
ejpam-6834	698	33	)	)	PUNCT
ejpam-6834	698	34	×	×	NOUN
ejpam-6834	698	35	(	(	PUNCT
ejpam-6834	698	36	pv1	pv1	VERB
ejpam-6834	698	37	∪	∪	ADP
ejpam-6834	698	38	pv2	pv2	NOUN
ejpam-6834	698	39	)	)	PUNCT
ejpam-6834	699	1	−→	−→	NOUN
ejpam-6834	700	1	[	[	X
ejpam-6834	700	2	0	0	NUM
ejpam-6834	700	3	,	,	PUNCT
ejpam-6834	700	4	1	1	NUM
ejpam-6834	700	5	]	]	PUNCT
ejpam-6834	700	6	is	be	AUX
ejpam-6834	700	7	defined	define	VERB
ejpam-6834	700	8	by	by	ADP
ejpam-6834	700	9	pcf	pcf	PROPN
ejpam-6834	700	10	(	(	PUNCT
ejpam-6834	700	11	1,1)(high	1,1)(high	NOUN
ejpam-6834	700	12	,	,	PUNCT
ejpam-6834	700	13	low	low	ADJ
ejpam-6834	700	14	)	)	PUNCT
ejpam-6834	700	15	=	=	SYM
ejpam-6834	700	16	1.0	1.0	NUM
ejpam-6834	700	17	,	,	PUNCT
ejpam-6834	700	18	pcf	pcf	PROPN
ejpam-6834	700	19	(	(	PUNCT
ejpam-6834	700	20	1,1)(high	1,1)(high	NOUN
ejpam-6834	700	21	,	,	PUNCT
ejpam-6834	700	22	medium	medium	NOUN
ejpam-6834	700	23	)	)	PUNCT
ejpam-6834	700	24	=	=	SYM
ejpam-6834	700	25	0.5	0.5	NUM
ejpam-6834	700	26	,	,	PUNCT
ejpam-6834	700	27	pcf	pcf	PROPN
ejpam-6834	700	28	(	(	PUNCT
ejpam-6834	700	29	1,1)(a	1,1)(a	NUM
ejpam-6834	700	30	,	,	PUNCT
ejpam-6834	700	31	a	a	PRON
ejpam-6834	700	32	)	)	PUNCT
ejpam-6834	700	33	=	=	SYM
ejpam-6834	700	34	0	0	NUM
ejpam-6834	700	35	,	,	PUNCT
ejpam-6834	700	36	with	with	ADP
ejpam-6834	700	37	symmetry	symmetry	PROPN
ejpam-6834	700	38	pcf	pcf	PROPN
ejpam-6834	700	39	(	(	PUNCT
ejpam-6834	700	40	b	b	PROPN
ejpam-6834	700	41	,	,	PUNCT
ejpam-6834	700	42	a	a	PRON
ejpam-6834	700	43	)	)	PUNCT
ejpam-6834	700	44	=	=	SYM
ejpam-6834	700	45	pcf	pcf	PROPN
ejpam-6834	700	46	(	(	PUNCT
ejpam-6834	700	47	a	a	DET
ejpam-6834	700	48	,	,	PUNCT
ejpam-6834	700	49	b	b	NOUN
ejpam-6834	700	50	)	)	PUNCT
ejpam-6834	700	51	.	.	PUNCT
ejpam-6834	701	1	hence	hence	ADV
ejpam-6834	701	2	shp	shp	NOUN
ejpam-6834	701	3	(	(	PUNCT
ejpam-6834	701	4	1,1	1,1	NUM
ejpam-6834	701	5	)	)	PUNCT
ejpam-6834	701	6	=	=	SYM
ejpam-6834	701	7	(	(	PUNCT
ejpam-6834	701	8	p(x	p(x	PROPN
ejpam-6834	701	9	)	)	PUNCT
ejpam-6834	701	10	,	,	PUNCT
ejpam-6834	701	11	{	{	PUNCT
ejpam-6834	701	12	v1	v1	NOUN
ejpam-6834	701	13	,	,	PUNCT
ejpam-6834	701	14	v2	v2	PROPN
ejpam-6834	701	15	}	}	PUNCT
ejpam-6834	701	16	,	,	PUNCT
ejpam-6834	701	17	{	{	PUNCT
ejpam-6834	701	18	pv1	pv1	NOUN
ejpam-6834	701	19	,	,	PUNCT
ejpam-6834	701	20	pv2	pv2	NOUN
ejpam-6834	701	21	}	}	PUNCT
ejpam-6834	701	22	,	,	PUNCT
ejpam-6834	701	23	{	{	PUNCT
ejpam-6834	701	24	˜pdf	˜pdf	NOUN
ejpam-6834	701	25	(	(	PUNCT
ejpam-6834	701	26	1,1	1,1	NUM
ejpam-6834	701	27	)	)	PUNCT
ejpam-6834	701	28	v1	v1	NOUN
ejpam-6834	701	29	,	,	PUNCT
ejpam-6834	701	30	˜pdf	˜pdf	NOUN
ejpam-6834	701	31	(	(	PUNCT
ejpam-6834	701	32	1,1	1,1	NUM
ejpam-6834	701	33	)	)	PUNCT
ejpam-6834	701	34	v2	v2	PROPN
ejpam-6834	701	35	}	}	PUNCT
ejpam-6834	701	36	,	,	PUNCT
ejpam-6834	701	37	pcf	pcf	PROPN
ejpam-6834	701	38	(	(	PUNCT
ejpam-6834	701	39	1,1	1,1	NUM
ejpam-6834	701	40	)	)	PUNCT
ejpam-6834	701	41	)	)	PUNCT
ejpam-6834	701	42	is	be	AUX
ejpam-6834	701	43	a	a	DET
ejpam-6834	701	44	concrete	concrete	ADJ
ejpam-6834	701	45	(	(	PUNCT
ejpam-6834	701	46	1	1	NUM
ejpam-6834	701	47	,	,	PUNCT
ejpam-6834	701	48	1)-superhyperplithogenic	1)-superhyperplithogenic	NUM
ejpam-6834	701	49	set	set	VERB
ejpam-6834	701	50	modeling	model	VERB
ejpam-6834	701	51	multi	multi	ADJ
ejpam-6834	701	52	-	-	ADJ
ejpam-6834	701	53	dimensional	dimensional	ADJ
ejpam-6834	701	54	team	team	NOUN
ejpam-6834	701	55	evaluations	evaluation	NOUN
ejpam-6834	701	56	in	in	ADP
ejpam-6834	701	57	a	a	DET
ejpam-6834	701	58	hackathon	hackathon	PROPN
ejpam-6834	701	59	.	.	PUNCT
ejpam-6834	701	60	example	example	NOUN
ejpam-6834	701	61	20	20	NUM
ejpam-6834	701	62	(	(	PUNCT
ejpam-6834	701	63	supply	supply	NOUN
ejpam-6834	701	64	chain	chain	NOUN
ejpam-6834	701	65	resilience	resilience	NOUN
ejpam-6834	701	66	evaluation	evaluation	NOUN
ejpam-6834	701	67	with	with	ADP
ejpam-6834	701	68	(	(	PUNCT
ejpam-6834	701	69	2	2	NUM
ejpam-6834	701	70	,	,	PUNCT
ejpam-6834	701	71	2)-superhyperplithogenic	2)-superhyperplithogenic	NUM
ejpam-6834	701	72	set	set	NOUN
ejpam-6834	701	73	)	)	PUNCT
ejpam-6834	701	74	.	.	PUNCT
ejpam-6834	702	1	let	let	VERB
ejpam-6834	702	2	x	x	PUNCT
ejpam-6834	702	3	=	=	PRON
ejpam-6834	702	4	{	{	PUNCT
ejpam-6834	702	5	factorya	factorya	NOUN
ejpam-6834	702	6	,	,	PUNCT
ejpam-6834	702	7	factoryb	factoryb	ADV
ejpam-6834	702	8	}	}	PUNCT
ejpam-6834	702	9	,	,	PUNCT
ejpam-6834	702	10	and	and	CCONJ
ejpam-6834	702	11	take	take	VERB
ejpam-6834	702	12	m	m	NOUN
ejpam-6834	702	13	=	=	SYM
ejpam-6834	702	14	n	n	NOUN
ejpam-6834	702	15	=	=	SYM
ejpam-6834	702	16	2	2	NUM
ejpam-6834	702	17	.	.	PUNCT
ejpam-6834	702	18	then	then	ADV
ejpam-6834	702	19	p1(x	p1(x	NOUN
ejpam-6834	702	20	)	)	PUNCT
ejpam-6834	702	21	=	=	SYM
ejpam-6834	702	22	p(x	p(x	PROPN
ejpam-6834	702	23	)	)	PUNCT
ejpam-6834	702	24	=	=	SYM
ejpam-6834	702	25	{	{	PUNCT
ejpam-6834	702	26	∅	∅	NOUN
ejpam-6834	702	27	,	,	PUNCT
ejpam-6834	702	28	{	{	PUNCT
ejpam-6834	702	29	factorya	factorya	NOUN
ejpam-6834	702	30	}	}	PUNCT
ejpam-6834	702	31	,	,	PUNCT
ejpam-6834	702	32	{	{	PUNCT
ejpam-6834	702	33	factoryb	factoryb	ADV
ejpam-6834	702	34	}	}	PUNCT
ejpam-6834	702	35	,	,	PUNCT
ejpam-6834	702	36	{	{	PUNCT
ejpam-6834	702	37	factorya	factorya	NOUN
ejpam-6834	702	38	,	,	PUNCT
ejpam-6834	702	39	factoryb	factoryb	ADV
ejpam-6834	702	40	}	}	PUNCT
ejpam-6834	702	41	}	}	PUNCT
ejpam-6834	702	42	,	,	PUNCT
ejpam-6834	702	43	p2(x	p2(x	X
ejpam-6834	702	44	)	)	PUNCT
ejpam-6834	702	45	=	=	SYM
ejpam-6834	702	46	p	p	X
ejpam-6834	702	47	(	(	PUNCT
ejpam-6834	702	48	p1(x	p1(x	NOUN
ejpam-6834	702	49	)	)	PUNCT
ejpam-6834	702	50	)	)	PUNCT
ejpam-6834	702	51	,	,	PUNCT
ejpam-6834	702	52	the	the	DET
ejpam-6834	702	53	set	set	NOUN
ejpam-6834	702	54	of	of	ADP
ejpam-6834	702	55	all	all	DET
ejpam-6834	702	56	subsets	subset	NOUN
ejpam-6834	702	57	of	of	ADP
ejpam-6834	702	58	p1(x	p1(x	NOUN
ejpam-6834	702	59	)	)	PUNCT
ejpam-6834	702	60	.	.	PUNCT
ejpam-6834	703	1	for	for	ADP
ejpam-6834	703	2	concreteness	concreteness	NOUN
ejpam-6834	703	3	,	,	PUNCT
ejpam-6834	703	4	choose	choose	VERB
ejpam-6834	703	5	the	the	DET
ejpam-6834	703	6	level-2	level-2	PROPN
ejpam-6834	703	7	element	element	NOUN
ejpam-6834	703	8	a	a	DET
ejpam-6834	703	9	=	=	X
ejpam-6834	703	10	{	{	PUNCT
ejpam-6834	703	11	{	{	PUNCT
ejpam-6834	703	12	factorya	factorya	NOUN
ejpam-6834	703	13	}	}	PUNCT
ejpam-6834	703	14	,	,	PUNCT
ejpam-6834	703	15	{	{	PUNCT
ejpam-6834	703	16	factorya	factorya	NOUN
ejpam-6834	703	17	,	,	PUNCT
ejpam-6834	703	18	factoryb	factoryb	ADV
ejpam-6834	703	19	}	}	PUNCT
ejpam-6834	703	20	}	}	PUNCT
ejpam-6834	703	21	∈	∈	PROPN
ejpam-6834	703	22	p2(x	p2(x	NOUN
ejpam-6834	703	23	)	)	PUNCT
ejpam-6834	703	24	.	.	PUNCT
ejpam-6834	704	1	we	we	PRON
ejpam-6834	704	2	evaluate	evaluate	VERB
ejpam-6834	704	3	two	two	NUM
ejpam-6834	704	4	attributes	attribute	NOUN
ejpam-6834	704	5	:	:	PUNCT
ejpam-6834	704	6	v1	v1	NOUN
ejpam-6834	704	7	=	=	SYM
ejpam-6834	704	8	cost	cost	NOUN
ejpam-6834	704	9	efficiency	efficiency	NOUN
ejpam-6834	704	10	,	,	PUNCT
ejpam-6834	704	11	pv1	pv1	NOUN
ejpam-6834	704	12	=	=	PUNCT
ejpam-6834	704	13	{	{	PUNCT
ejpam-6834	704	14	low	low	ADJ
ejpam-6834	704	15	,	,	PUNCT
ejpam-6834	704	16	medium	medium	ADJ
ejpam-6834	704	17	,	,	PUNCT
ejpam-6834	704	18	high	high	ADJ
ejpam-6834	704	19	}	}	PUNCT
ejpam-6834	704	20	,	,	PUNCT
ejpam-6834	704	21	v2	v2	NOUN
ejpam-6834	704	22	=	=	SYM
ejpam-6834	704	23	delivery	delivery	NOUN
ejpam-6834	704	24	reliability	reliability	NOUN
ejpam-6834	704	25	,	,	PUNCT
ejpam-6834	704	26	pv2	pv2	NOUN
ejpam-6834	704	27	=	=	PRON
ejpam-6834	704	28	{	{	PUNCT
ejpam-6834	704	29	slow	slow	ADJ
ejpam-6834	704	30	,	,	PUNCT
ejpam-6834	704	31	moderate	moderate	ADJ
ejpam-6834	704	32	,	,	PUNCT
ejpam-6834	704	33	fast	fast	ADJ
ejpam-6834	704	34	}	}	PUNCT
ejpam-6834	704	35	.	.	PUNCT
ejpam-6834	705	1	let	let	VERB
ejpam-6834	705	2	the	the	DET
ejpam-6834	705	3	membership	membership	NOUN
ejpam-6834	705	4	–	–	PUNCT
ejpam-6834	705	5	degree	degree	NOUN
ejpam-6834	705	6	vectors	vector	NOUN
ejpam-6834	705	7	be	be	AUX
ejpam-6834	705	8	one	one	NUM
ejpam-6834	705	9	-	-	PUNCT
ejpam-6834	705	10	dimensional	dimensional	ADJ
ejpam-6834	705	11	(	(	PUNCT
ejpam-6834	705	12	s	s	NOUN
ejpam-6834	705	13	=	=	NOUN
ejpam-6834	705	14	1	1	NUM
ejpam-6834	705	15	)	)	PUNCT
ejpam-6834	705	16	and	and	CCONJ
ejpam-6834	705	17	the	the	DET
ejpam-6834	705	18	contradiction	contradiction	NOUN
ejpam-6834	705	19	measure	measure	NOUN
ejpam-6834	705	20	scalar	scalar	ADJ
ejpam-6834	705	21	(	(	PUNCT
ejpam-6834	705	22	t	t	NOUN
ejpam-6834	705	23	=	=	SYM
ejpam-6834	705	24	1	1	NUM
ejpam-6834	705	25	)	)	PUNCT
ejpam-6834	705	26	.	.	PUNCT
ejpam-6834	706	1	define	define	VERB
ejpam-6834	706	2	the	the	DET
ejpam-6834	706	3	hyper	hyper	ADJ
ejpam-6834	706	4	–	–	PUNCT
ejpam-6834	706	5	degree	degree	NOUN
ejpam-6834	706	6	functions	function	NOUN
ejpam-6834	706	7	˜pdf	˜pdf	NOUN
ejpam-6834	706	8	(	(	PUNCT
ejpam-6834	706	9	2,2	2,2	NUM
ejpam-6834	706	10	)	)	PUNCT
ejpam-6834	706	11	vi	vi	NOUN
ejpam-6834	706	12	:	:	PUNCT
ejpam-6834	706	13	p2(x	p2(x	X
ejpam-6834	706	14	)	)	PUNCT
ejpam-6834	706	15	×	×	NOUN
ejpam-6834	706	16	pvi	pvi	NOUN
ejpam-6834	706	17	−→	−→	NOUN
ejpam-6834	706	18	p2([0	p2([0	PROPN
ejpam-6834	706	19	,	,	PUNCT
ejpam-6834	706	20	1	1	NUM
ejpam-6834	706	21	]	]	PUNCT
ejpam-6834	706	22	)	)	PUNCT
ejpam-6834	706	23	by	by	ADP
ejpam-6834	706	24	giving	give	VERB
ejpam-6834	706	25	their	their	PRON
ejpam-6834	706	26	values	value	NOUN
ejpam-6834	706	27	on	on	ADP
ejpam-6834	706	28	a	a	DET
ejpam-6834	706	29	:	:	PUNCT
ejpam-6834	706	30	˜pdf	˜pdf	NOUN
ejpam-6834	706	31	(	(	PUNCT
ejpam-6834	706	32	2,2	2,2	NOUN
ejpam-6834	706	33	)	)	PUNCT
ejpam-6834	706	34	v1	v1	NOUN
ejpam-6834	706	35	(	(	PUNCT
ejpam-6834	706	36	a	a	DET
ejpam-6834	706	37	,	,	PUNCT
ejpam-6834	706	38	low	low	ADJ
ejpam-6834	706	39	)	)	PUNCT
ejpam-6834	706	40	=	=	PRON
ejpam-6834	706	41	{	{	PUNCT
ejpam-6834	706	42	{	{	PUNCT
ejpam-6834	706	43	0.40	0.40	NUM
ejpam-6834	706	44	,	,	PUNCT
ejpam-6834	706	45	0.50	0.50	NUM
ejpam-6834	706	46	}	}	PUNCT
ejpam-6834	706	47	,	,	PUNCT
ejpam-6834	706	48	{	{	PUNCT
ejpam-6834	706	49	0.45	0.45	NUM
ejpam-6834	706	50	,	,	PUNCT
ejpam-6834	706	51	0.55	0.55	NUM
ejpam-6834	706	52	}	}	PUNCT
ejpam-6834	706	53	}	}	PUNCT
ejpam-6834	706	54	,	,	PUNCT
ejpam-6834	706	55	˜pdf	˜pdf	NOUN
ejpam-6834	706	56	(	(	PUNCT
ejpam-6834	706	57	2,2	2,2	NOUN
ejpam-6834	706	58	)	)	PUNCT
ejpam-6834	706	59	v1	v1	NOUN
ejpam-6834	706	60	(	(	PUNCT
ejpam-6834	706	61	a	a	DET
ejpam-6834	706	62	,	,	PUNCT
ejpam-6834	706	63	medium	medium	NOUN
ejpam-6834	706	64	)	)	PUNCT
ejpam-6834	706	65	=	=	SYM
ejpam-6834	706	66	{	{	PUNCT
ejpam-6834	707	1	[	[	X
ejpam-6834	707	2	0.55	0.55	NUM
ejpam-6834	707	3	,	,	PUNCT
ejpam-6834	707	4	0.65	0.65	NUM
ejpam-6834	707	5	]	]	PUNCT
ejpam-6834	707	6	}	}	PUNCT
ejpam-6834	707	7	,	,	PUNCT
ejpam-6834	707	8	˜pdf	˜pdf	NOUN
ejpam-6834	707	9	(	(	PUNCT
ejpam-6834	707	10	2,2	2,2	NOUN
ejpam-6834	707	11	)	)	PUNCT
ejpam-6834	707	12	v1	v1	NOUN
ejpam-6834	707	13	(	(	PUNCT
ejpam-6834	707	14	a	a	DET
ejpam-6834	707	15	,	,	PUNCT
ejpam-6834	707	16	high	high	ADJ
ejpam-6834	707	17	)	)	PUNCT
ejpam-6834	707	18	=	=	SYM
ejpam-6834	708	1	{	{	PUNCT
ejpam-6834	709	1	[	[	X
ejpam-6834	709	2	0.70	0.70	NUM
ejpam-6834	709	3	,	,	PUNCT
ejpam-6834	709	4	0.80	0.80	NUM
ejpam-6834	709	5	]	]	PUNCT
ejpam-6834	709	6	,	,	PUNCT
ejpam-6834	709	7	{	{	PUNCT
ejpam-6834	709	8	0.75	0.75	NUM
ejpam-6834	709	9	}	}	PUNCT
ejpam-6834	709	10	}	}	PUNCT
ejpam-6834	709	11	,	,	PUNCT
ejpam-6834	709	12	t.	t.	PROPN
ejpam-6834	709	13	fujita	fujita	PROPN
ejpam-6834	709	14	,	,	PUNCT
ejpam-6834	709	15	f.smarandache	f.smarandache	NOUN
ejpam-6834	709	16	/	/	SYM
ejpam-6834	709	17	eur	eur	PROPN
ejpam-6834	709	18	.	.	PUNCT
ejpam-6834	710	1	j.	j.	PROPN
ejpam-6834	710	2	pure	pure	PROPN
ejpam-6834	710	3	appl	appl	PROPN
ejpam-6834	710	4	.	.	PROPN
ejpam-6834	710	5	math	math	PROPN
ejpam-6834	710	6	,	,	PUNCT
ejpam-6834	710	7	18	18	NUM
ejpam-6834	710	8	(	(	PUNCT
ejpam-6834	710	9	4	4	NUM
ejpam-6834	710	10	)	)	PUNCT
ejpam-6834	710	11	(	(	PUNCT
ejpam-6834	710	12	2025	2025	NUM
ejpam-6834	710	13	)	)	PUNCT
ejpam-6834	710	14	,	,	PUNCT
ejpam-6834	710	15	6834	6834	NUM
ejpam-6834	710	16	31	31	NUM
ejpam-6834	710	17	of	of	ADP
ejpam-6834	710	18	69	69	NUM
ejpam-6834	710	19	˜pdf	˜pdf	NOUN
ejpam-6834	710	20	(	(	PUNCT
ejpam-6834	710	21	2,2	2,2	NUM
ejpam-6834	710	22	)	)	PUNCT
ejpam-6834	710	23	v2	v2	NOUN
ejpam-6834	710	24	(	(	PUNCT
ejpam-6834	710	25	a	a	DET
ejpam-6834	710	26	,	,	PUNCT
ejpam-6834	710	27	slow	slow	ADJ
ejpam-6834	710	28	)	)	PUNCT
ejpam-6834	710	29	=	=	PRON
ejpam-6834	710	30	{	{	PUNCT
ejpam-6834	710	31	{	{	PUNCT
ejpam-6834	710	32	0.30	0.30	NUM
ejpam-6834	710	33	,	,	PUNCT
ejpam-6834	710	34	0.40	0.40	NUM
ejpam-6834	710	35	}	}	PUNCT
ejpam-6834	710	36	}	}	PUNCT
ejpam-6834	710	37	,	,	PUNCT
ejpam-6834	710	38	˜pdf	˜pdf	NOUN
ejpam-6834	710	39	(	(	PUNCT
ejpam-6834	710	40	2,2	2,2	NOUN
ejpam-6834	710	41	)	)	PUNCT
ejpam-6834	710	42	v2	v2	NOUN
ejpam-6834	710	43	(	(	PUNCT
ejpam-6834	710	44	a	a	DET
ejpam-6834	710	45	,	,	PUNCT
ejpam-6834	710	46	moderate	moderate	ADJ
ejpam-6834	710	47	)	)	PUNCT
ejpam-6834	710	48	=	=	PRON
ejpam-6834	710	49	{	{	PUNCT
ejpam-6834	710	50	{	{	PUNCT
ejpam-6834	710	51	0.60	0.60	NUM
ejpam-6834	710	52	}	}	PUNCT
ejpam-6834	710	53	,	,	PUNCT
ejpam-6834	711	1	[	[	X
ejpam-6834	711	2	0.60	0.60	NUM
ejpam-6834	711	3	,	,	PUNCT
ejpam-6834	711	4	0.70	0.70	NUM
ejpam-6834	711	5	]	]	PUNCT
ejpam-6834	711	6	}	}	PUNCT
ejpam-6834	711	7	,	,	PUNCT
ejpam-6834	711	8	˜pdf	˜pdf	NOUN
ejpam-6834	711	9	(	(	PUNCT
ejpam-6834	711	10	2,2	2,2	NOUN
ejpam-6834	711	11	)	)	PUNCT
ejpam-6834	711	12	v2	v2	NOUN
ejpam-6834	711	13	(	(	PUNCT
ejpam-6834	711	14	a	a	DET
ejpam-6834	711	15	,	,	PUNCT
ejpam-6834	711	16	fast	fast	ADJ
ejpam-6834	711	17	)	)	PUNCT
ejpam-6834	711	18	=	=	SYM
ejpam-6834	711	19	{	{	PUNCT
ejpam-6834	712	1	[	[	X
ejpam-6834	712	2	0.80	0.80	NUM
ejpam-6834	712	3	,	,	PUNCT
ejpam-6834	712	4	0.90	0.90	NUM
ejpam-6834	712	5	]	]	PUNCT
ejpam-6834	712	6	,	,	PUNCT
ejpam-6834	712	7	{	{	PUNCT
ejpam-6834	712	8	0.85	0.85	NUM
ejpam-6834	712	9	}	}	PUNCT
ejpam-6834	712	10	}	}	PUNCT
ejpam-6834	712	11	.	.	PUNCT
ejpam-6834	713	1	the	the	DET
ejpam-6834	713	2	degree	degree	NOUN
ejpam-6834	713	3	of	of	ADP
ejpam-6834	713	4	contradiction	contradiction	NOUN
ejpam-6834	713	5	function	function	NOUN
ejpam-6834	713	6	pcf	pcf	PROPN
ejpam-6834	713	7	(	(	PUNCT
ejpam-6834	713	8	2,2	2,2	NUM
ejpam-6834	713	9	)	)	PUNCT
ejpam-6834	713	10	:	:	PUNCT
ejpam-6834	713	11	(	(	PUNCT
ejpam-6834	713	12	pv1	pv1	VERB
ejpam-6834	713	13	∪	∪	ADP
ejpam-6834	713	14	pv2	pv2	NOUN
ejpam-6834	713	15	)	)	PUNCT
ejpam-6834	713	16	×	×	NOUN
ejpam-6834	713	17	(	(	PUNCT
ejpam-6834	713	18	pv1	pv1	VERB
ejpam-6834	713	19	∪	∪	ADP
ejpam-6834	713	20	pv2	pv2	NOUN
ejpam-6834	713	21	)	)	PUNCT
ejpam-6834	713	22	−→	−→	NOUN
ejpam-6834	714	1	[	[	X
ejpam-6834	714	2	0	0	NUM
ejpam-6834	714	3	,	,	PUNCT
ejpam-6834	714	4	1	1	NUM
ejpam-6834	714	5	]	]	PUNCT
ejpam-6834	714	6	is	be	AUX
ejpam-6834	714	7	specified	specify	VERB
ejpam-6834	714	8	by	by	ADP
ejpam-6834	714	9	:	:	PUNCT
ejpam-6834	714	10	pcf	pcf	PROPN
ejpam-6834	714	11	(	(	PUNCT
ejpam-6834	714	12	2,2)(low	2,2)(low	NUM
ejpam-6834	714	13	,	,	PUNCT
ejpam-6834	714	14	high	high	ADJ
ejpam-6834	714	15	)	)	PUNCT
ejpam-6834	714	16	=	=	SYM
ejpam-6834	714	17	1.0	1.0	NUM
ejpam-6834	714	18	,	,	PUNCT
ejpam-6834	714	19	pcf	pcf	PROPN
ejpam-6834	714	20	(	(	PUNCT
ejpam-6834	714	21	2,2)(low	2,2)(low	ADJ
ejpam-6834	714	22	,	,	PUNCT
ejpam-6834	714	23	medium	medium	NOUN
ejpam-6834	714	24	)	)	PUNCT
ejpam-6834	714	25	=	=	SYM
ejpam-6834	714	26	0.3	0.3	NUM
ejpam-6834	714	27	,	,	PUNCT
ejpam-6834	714	28	pcf	pcf	PROPN
ejpam-6834	714	29	(	(	PUNCT
ejpam-6834	714	30	2,2)(medium	2,2)(medium	NOUN
ejpam-6834	714	31	,	,	PUNCT
ejpam-6834	714	32	high	high	ADJ
ejpam-6834	714	33	)	)	PUNCT
ejpam-6834	714	34	=	=	SYM
ejpam-6834	714	35	0.5	0.5	NUM
ejpam-6834	714	36	,	,	PUNCT
ejpam-6834	714	37	pcf	pcf	PROPN
ejpam-6834	714	38	(	(	PUNCT
ejpam-6834	714	39	2,2)(slow	2,2)(slow	ADJ
ejpam-6834	714	40	,	,	PUNCT
ejpam-6834	714	41	fast	fast	ADJ
ejpam-6834	714	42	)	)	PUNCT
ejpam-6834	714	43	=	=	SYM
ejpam-6834	714	44	0.8	0.8	NUM
ejpam-6834	714	45	,	,	PUNCT
ejpam-6834	714	46	pcf	pcf	PROPN
ejpam-6834	714	47	(	(	PUNCT
ejpam-6834	714	48	2,2)(a	2,2)(a	NUM
ejpam-6834	714	49	,	,	PUNCT
ejpam-6834	714	50	a	a	PRON
ejpam-6834	714	51	)	)	PUNCT
ejpam-6834	714	52	=	=	SYM
ejpam-6834	714	53	0	0	NUM
ejpam-6834	714	54	,	,	PUNCT
ejpam-6834	714	55	pcf	pcf	PROPN
ejpam-6834	714	56	(	(	PUNCT
ejpam-6834	714	57	2,2)(a	2,2)(a	NUM
ejpam-6834	714	58	,	,	PUNCT
ejpam-6834	714	59	b	b	NOUN
ejpam-6834	714	60	)	)	PUNCT
ejpam-6834	714	61	=	=	SYM
ejpam-6834	714	62	pcf	pcf	PROPN
ejpam-6834	714	63	(	(	PUNCT
ejpam-6834	714	64	2,2)(b	2,2)(b	PROPN
ejpam-6834	714	65	,	,	PUNCT
ejpam-6834	714	66	a	a	PRON
ejpam-6834	714	67	)	)	PUNCT
ejpam-6834	714	68	.	.	PUNCT
ejpam-6834	715	1	thus	thus	ADV
ejpam-6834	715	2	the	the	DET
ejpam-6834	715	3	structure	structure	NOUN
ejpam-6834	715	4	shp	shp	NOUN
ejpam-6834	715	5	(	(	PUNCT
ejpam-6834	715	6	2,2	2,2	NUM
ejpam-6834	715	7	)	)	PUNCT
ejpam-6834	715	8	=	=	SYM
ejpam-6834	715	9	(	(	PUNCT
ejpam-6834	715	10	p2(x	p2(x	NOUN
ejpam-6834	715	11	)	)	PUNCT
ejpam-6834	715	12	,	,	PUNCT
ejpam-6834	715	13	{	{	PUNCT
ejpam-6834	715	14	v1	v1	NOUN
ejpam-6834	715	15	,	,	PUNCT
ejpam-6834	715	16	v2	v2	PROPN
ejpam-6834	715	17	}	}	PUNCT
ejpam-6834	715	18	,	,	PUNCT
ejpam-6834	715	19	{	{	PUNCT
ejpam-6834	715	20	pv1	pv1	NOUN
ejpam-6834	715	21	,	,	PUNCT
ejpam-6834	715	22	pv2	pv2	NOUN
ejpam-6834	715	23	}	}	PUNCT
ejpam-6834	715	24	,	,	PUNCT
ejpam-6834	715	25	{	{	PUNCT
ejpam-6834	715	26	˜pdf	˜pdf	NOUN
ejpam-6834	715	27	(	(	PUNCT
ejpam-6834	715	28	2,2	2,2	NOUN
ejpam-6834	715	29	)	)	PUNCT
ejpam-6834	715	30	v1	v1	NOUN
ejpam-6834	715	31	,	,	PUNCT
ejpam-6834	715	32	˜pdf	˜pdf	NOUN
ejpam-6834	715	33	(	(	PUNCT
ejpam-6834	715	34	2,2	2,2	NOUN
ejpam-6834	715	35	)	)	PUNCT
ejpam-6834	715	36	v2	v2	NOUN
ejpam-6834	715	37	}	}	PUNCT
ejpam-6834	715	38	,	,	PUNCT
ejpam-6834	715	39	pcf	pcf	PROPN
ejpam-6834	715	40	(	(	PUNCT
ejpam-6834	715	41	2,2	2,2	NUM
ejpam-6834	715	42	)	)	PUNCT
ejpam-6834	715	43	)	)	PUNCT
ejpam-6834	715	44	models	model	NOUN
ejpam-6834	715	45	,	,	PUNCT
ejpam-6834	715	46	at	at	ADP
ejpam-6834	715	47	two	two	NUM
ejpam-6834	715	48	hierarchical	hierarchical	ADJ
ejpam-6834	715	49	levels	level	NOUN
ejpam-6834	715	50	,	,	PUNCT
ejpam-6834	715	51	the	the	DET
ejpam-6834	715	52	cost	cost	NOUN
ejpam-6834	715	53	-	-	PUNCT
ejpam-6834	715	54	efficiency	efficiency	NOUN
ejpam-6834	715	55	and	and	CCONJ
ejpam-6834	715	56	delivery	delivery	NOUN
ejpam-6834	715	57	-	-	PUNCT
ejpam-6834	715	58	reliability	reliability	NOUN
ejpam-6834	715	59	uncertainties	uncertainty	NOUN
ejpam-6834	715	60	of	of	ADP
ejpam-6834	715	61	the	the	DET
ejpam-6834	715	62	supply	supply	NOUN
ejpam-6834	715	63	chain	chain	NOUN
ejpam-6834	715	64	with	with	ADP
ejpam-6834	715	65	hyper	hyper	ADV
ejpam-6834	715	66	-	-	ADJ
ejpam-6834	715	67	valued	value	VERB
ejpam-6834	715	68	degrees	degree	NOUN
ejpam-6834	715	69	and	and	CCONJ
ejpam-6834	715	70	quantified	quantified	ADJ
ejpam-6834	715	71	contradictions	contradiction	NOUN
ejpam-6834	715	72	.	.	PUNCT
ejpam-6834	715	73	theorem	theorem	VERB
ejpam-6834	715	74	15	15	NUM
ejpam-6834	715	75	.	.	PUNCT
ejpam-6834	716	1	every	every	DET
ejpam-6834	716	2	n	n	CCONJ
ejpam-6834	716	3	-	-	PUNCT
ejpam-6834	716	4	superhyperplithogenic	superhyperplithogenic	ADJ
ejpam-6834	716	5	set	set	NOUN
ejpam-6834	716	6	(	(	PUNCT
ejpam-6834	716	7	p1(x	p1(x	NOUN
ejpam-6834	716	8	)	)	PUNCT
ejpam-6834	716	9	,	,	PUNCT
ejpam-6834	716	10	v	v	NOUN
ejpam-6834	716	11	,	,	PUNCT
ejpam-6834	716	12	{	{	PUNCT
ejpam-6834	716	13	pv	pv	NOUN
ejpam-6834	716	14	}	}	PUNCT
ejpam-6834	716	15	,	,	PUNCT
ejpam-6834	716	16	{	{	PUNCT
ejpam-6834	716	17	˜pdf	˜pdf	NOUN
ejpam-6834	716	18	(	(	PUNCT
ejpam-6834	716	19	1,n	1,n	NUM
ejpam-6834	716	20	)	)	PUNCT
ejpam-6834	716	21	v	v	NOUN
ejpam-6834	716	22	}	}	PUNCT
ejpam-6834	716	23	,	,	PUNCT
ejpam-6834	716	24	pcf	pcf	PROPN
ejpam-6834	716	25	(	(	PUNCT
ejpam-6834	716	26	1,n	1,n	NUM
ejpam-6834	716	27	)	)	PUNCT
ejpam-6834	716	28	)	)	PUNCT
ejpam-6834	716	29	arises	arise	VERB
ejpam-6834	716	30	as	as	SCONJ
ejpam-6834	716	31	the	the	DET
ejpam-6834	716	32	special	special	ADJ
ejpam-6834	716	33	case	case	NOUN
ejpam-6834	716	34	m	m	NOUN
ejpam-6834	716	35	=	=	NOUN
ejpam-6834	716	36	1	1	NUM
ejpam-6834	716	37	of	of	ADP
ejpam-6834	716	38	an	an	DET
ejpam-6834	716	39	(	(	PUNCT
ejpam-6834	716	40	m	m	PROPN
ejpam-6834	716	41	,	,	PUNCT
ejpam-6834	716	42	n)-superhyperplithogenic	n)-superhyperplithogenic	PUNCT
ejpam-6834	716	43	set	set	NOUN
ejpam-6834	716	44	.	.	PUNCT
ejpam-6834	717	1	proof	proof	NOUN
ejpam-6834	717	2	.	.	PUNCT
ejpam-6834	718	1	by	by	ADP
ejpam-6834	718	2	definition	definition	NOUN
ejpam-6834	718	3	,	,	PUNCT
ejpam-6834	718	4	an	an	DET
ejpam-6834	718	5	n	n	CCONJ
ejpam-6834	718	6	-	-	PUNCT
ejpam-6834	718	7	superhyperplithogenic	superhyperplithogenic	ADJ
ejpam-6834	718	8	set	set	NOUN
ejpam-6834	718	9	has	have	VERB
ejpam-6834	718	10	domain	domain	NOUN
ejpam-6834	718	11	p1(x	p1(x	NOUN
ejpam-6834	718	12	)	)	PUNCT
ejpam-6834	718	13	=	=	SYM
ejpam-6834	718	14	p(x	p(x	PROPN
ejpam-6834	718	15	)	)	PUNCT
ejpam-6834	718	16	.	.	PUNCT
ejpam-6834	719	1	in	in	ADP
ejpam-6834	719	2	the	the	DET
ejpam-6834	719	3	general	general	ADJ
ejpam-6834	719	4	(	(	PUNCT
ejpam-6834	719	5	m	m	PROPN
ejpam-6834	719	6	,	,	PUNCT
ejpam-6834	719	7	n	n	CCONJ
ejpam-6834	719	8	)	)	PUNCT
ejpam-6834	719	9	framework	framework	NOUN
ejpam-6834	719	10	,	,	PUNCT
ejpam-6834	719	11	setting	set	VERB
ejpam-6834	719	12	m	m	NOUN
ejpam-6834	719	13	=	=	SYM
ejpam-6834	719	14	1	1	NUM
ejpam-6834	719	15	replaces	replace	VERB
ejpam-6834	719	16	pm(x	pm(x	NOUN
ejpam-6834	719	17	)	)	PUNCT
ejpam-6834	719	18	by	by	ADP
ejpam-6834	719	19	p1(x	p1(x	NOUN
ejpam-6834	719	20	)	)	PUNCT
ejpam-6834	719	21	and	and	CCONJ
ejpam-6834	719	22	leaves	leave	VERB
ejpam-6834	719	23	all	all	DET
ejpam-6834	719	24	other	other	ADJ
ejpam-6834	719	25	components	component	NOUN
ejpam-6834	719	26	identical	identical	ADJ
ejpam-6834	719	27	.	.	PUNCT
ejpam-6834	720	1	hence	hence	ADV
ejpam-6834	720	2	the	the	DET
ejpam-6834	720	3	two	two	NUM
ejpam-6834	720	4	structures	structure	NOUN
ejpam-6834	720	5	coincide	coincide	VERB
ejpam-6834	720	6	exactly	exactly	ADV
ejpam-6834	720	7	when	when	SCONJ
ejpam-6834	720	8	m	m	VERB
ejpam-6834	720	9	=	=	SYM
ejpam-6834	720	10	1	1	X
ejpam-6834	720	11	.	.	PUNCT
ejpam-6834	720	12	theorem	theorem	VERB
ejpam-6834	720	13	16	16	NUM
ejpam-6834	720	14	(	(	PUNCT
ejpam-6834	720	15	restriction	restriction	NOUN
ejpam-6834	720	16	to	to	PART
ejpam-6834	720	17	lower	low	ADJ
ejpam-6834	720	18	m	m	NOUN
ejpam-6834	720	19	)	)	PUNCT
ejpam-6834	720	20	.	.	PUNCT
ejpam-6834	721	1	let	let	VERB
ejpam-6834	721	2	shp	shp	NOUN
ejpam-6834	721	3	(	(	PUNCT
ejpam-6834	721	4	m	m	PROPN
ejpam-6834	721	5	,	,	PUNCT
ejpam-6834	721	6	n	n	CCONJ
ejpam-6834	721	7	)	)	PUNCT
ejpam-6834	721	8	=	=	SYM
ejpam-6834	721	9	(	(	PUNCT
ejpam-6834	721	10	p	p	PROPN
ejpam-6834	721	11	m(x	m(x	PROPN
ejpam-6834	721	12	)	)	PUNCT
ejpam-6834	721	13	,	,	PUNCT
ejpam-6834	721	14	v	v	NOUN
ejpam-6834	721	15	,	,	PUNCT
ejpam-6834	721	16	{	{	PUNCT
ejpam-6834	721	17	pv	pv	NOUN
ejpam-6834	721	18	}	}	PUNCT
ejpam-6834	721	19	,	,	PUNCT
ejpam-6834	721	20	{	{	PUNCT
ejpam-6834	721	21	˜pdf	˜pdf	NOUN
ejpam-6834	721	22	(	(	PUNCT
ejpam-6834	721	23	m	m	NOUN
ejpam-6834	721	24	,	,	PUNCT
ejpam-6834	721	25	n	n	CCONJ
ejpam-6834	721	26	)	)	PUNCT
ejpam-6834	721	27	v	v	NOUN
ejpam-6834	721	28	}	}	PUNCT
ejpam-6834	721	29	,	,	PUNCT
ejpam-6834	721	30	pcf	pcf	PROPN
ejpam-6834	721	31	(	(	PUNCT
ejpam-6834	721	32	m	m	PROPN
ejpam-6834	721	33	,	,	PUNCT
ejpam-6834	721	34	n	n	CCONJ
ejpam-6834	721	35	)	)	PUNCT
ejpam-6834	721	36	)	)	PUNCT
ejpam-6834	721	37	be	be	AUX
ejpam-6834	721	38	an	an	DET
ejpam-6834	721	39	(	(	PUNCT
ejpam-6834	721	40	m	m	NOUN
ejpam-6834	721	41	,	,	PUNCT
ejpam-6834	721	42	n)-superhyperplithogenic	n)-superhyperplithogenic	PUNCT
ejpam-6834	721	43	set	set	VERB
ejpam-6834	721	44	and	and	CCONJ
ejpam-6834	721	45	let	let	VERB
ejpam-6834	721	46	m′	m′	NOUN
ejpam-6834	721	47	satisfy	satisfy	VERB
ejpam-6834	721	48	0	0	NUM
ejpam-6834	721	49	≤	≤	NUM
ejpam-6834	721	50	m′	m′	NOUN
ejpam-6834	721	51	<	<	X
ejpam-6834	721	52	m.	m.	NOUN
ejpam-6834	721	53	define	define	NOUN
ejpam-6834	721	54	,	,	PUNCT
ejpam-6834	721	55	for	for	ADP
ejpam-6834	721	56	each	each	DET
ejpam-6834	721	57	v	v	NUM
ejpam-6834	721	58	∈	∈	PROPN
ejpam-6834	721	59	v	v	NOUN
ejpam-6834	721	60	and	and	CCONJ
ejpam-6834	721	61	a	a	DET
ejpam-6834	721	62	∈	∈	ADJ
ejpam-6834	721	63	pv	pv	NOUN
ejpam-6834	721	64	,	,	PUNCT
ejpam-6834	721	65	˜pdf	˜pdf	NOUN
ejpam-6834	721	66	(	(	PUNCT
ejpam-6834	721	67	m′,n	m′,n	PROPN
ejpam-6834	721	68	)	)	PUNCT
ejpam-6834	721	69	v,↓m	v,↓m	NOUN
ejpam-6834	721	70	(	(	PUNCT
ejpam-6834	721	71	a	a	DET
ejpam-6834	721	72	,	,	PUNCT
ejpam-6834	721	73	a	a	NOUN
ejpam-6834	721	74	)	)	PUNCT
ejpam-6834	721	75	:	:	PUNCT
ejpam-6834	722	1	=	=	SYM
ejpam-6834	722	2	˜pdf	˜pdf	X
ejpam-6834	722	3	(	(	PUNCT
ejpam-6834	722	4	m	m	NOUN
ejpam-6834	722	5	,	,	PUNCT
ejpam-6834	722	6	n	n	CCONJ
ejpam-6834	722	7	)	)	PUNCT
ejpam-6834	722	8	v	v	NOUN
ejpam-6834	722	9	(	(	PUNCT
ejpam-6834	722	10	ιm′→m(a	ιm′→m(a	PROPN
ejpam-6834	722	11	)	)	PUNCT
ejpam-6834	722	12	,	,	PUNCT
ejpam-6834	722	13	a	a	X
ejpam-6834	722	14	)	)	PUNCT
ejpam-6834	722	15	for	for	ADP
ejpam-6834	722	16	a	a	DET
ejpam-6834	722	17	∈	∈	PROPN
ejpam-6834	722	18	p	p	NOUN
ejpam-6834	722	19	m′	m′	NOUN
ejpam-6834	722	20	(	(	PUNCT
ejpam-6834	722	21	x	x	NOUN
ejpam-6834	722	22	)	)	PUNCT
ejpam-6834	722	23	,	,	PUNCT
ejpam-6834	722	24	and	and	CCONJ
ejpam-6834	722	25	keep	keep	VERB
ejpam-6834	722	26	pcf	pcf	PROPN
ejpam-6834	722	27	(	(	PUNCT
ejpam-6834	722	28	m	m	PROPN
ejpam-6834	722	29	,	,	PUNCT
ejpam-6834	722	30	n	n	CCONJ
ejpam-6834	722	31	)	)	PUNCT
ejpam-6834	722	32	unchanged	unchanged	ADJ
ejpam-6834	722	33	.	.	PUNCT
ejpam-6834	723	1	then	then	ADV
ejpam-6834	723	2	shp	shp	PROPN
ejpam-6834	723	3	(	(	PUNCT
ejpam-6834	723	4	m′,n	m′,n	PROPN
ejpam-6834	723	5	)	)	PUNCT
ejpam-6834	723	6	↓	↓	NOUN
ejpam-6834	724	1	=	=	PUNCT
ejpam-6834	724	2	(	(	PUNCT
ejpam-6834	724	3	p	p	NOUN
ejpam-6834	724	4	m′	m′	NOUN
ejpam-6834	724	5	(	(	PUNCT
ejpam-6834	724	6	x	x	NOUN
ejpam-6834	724	7	)	)	PUNCT
ejpam-6834	724	8	,	,	PUNCT
ejpam-6834	724	9	v	v	NOUN
ejpam-6834	724	10	,	,	PUNCT
ejpam-6834	724	11	{	{	PUNCT
ejpam-6834	724	12	pv	pv	NOUN
ejpam-6834	724	13	}	}	PUNCT
ejpam-6834	724	14	,	,	PUNCT
ejpam-6834	724	15	{	{	PUNCT
ejpam-6834	724	16	˜pdf	˜pdf	NOUN
ejpam-6834	724	17	(	(	PUNCT
ejpam-6834	724	18	m′,n	m′,n	PROPN
ejpam-6834	724	19	)	)	PUNCT
ejpam-6834	724	20	v,↓m	v,↓m	NOUN
ejpam-6834	724	21	}	}	PUNCT
ejpam-6834	724	22	,	,	PUNCT
ejpam-6834	724	23	pcf	pcf	PROPN
ejpam-6834	724	24	(	(	PUNCT
ejpam-6834	724	25	m	m	PROPN
ejpam-6834	724	26	,	,	PUNCT
ejpam-6834	724	27	n	n	CCONJ
ejpam-6834	724	28	)	)	PUNCT
ejpam-6834	724	29	)	)	PUNCT
ejpam-6834	724	30	is	be	AUX
ejpam-6834	724	31	an	an	DET
ejpam-6834	724	32	(	(	PUNCT
ejpam-6834	724	33	m′	m′	NUM
ejpam-6834	724	34	,	,	PUNCT
ejpam-6834	724	35	n)-superhyperplithogenic	n)-superhyperplithogenic	PUNCT
ejpam-6834	724	36	set	set	NOUN
ejpam-6834	724	37	.	.	PUNCT
ejpam-6834	725	1	t.	t.	PROPN
ejpam-6834	725	2	fujita	fujita	PROPN
ejpam-6834	725	3	,	,	PUNCT
ejpam-6834	725	4	f.smarandache	f.smarandache	NOUN
ejpam-6834	725	5	/	/	SYM
ejpam-6834	725	6	eur	eur	PROPN
ejpam-6834	725	7	.	.	PUNCT
ejpam-6834	726	1	j.	j.	PROPN
ejpam-6834	726	2	pure	pure	PROPN
ejpam-6834	726	3	appl	appl	PROPN
ejpam-6834	726	4	.	.	PROPN
ejpam-6834	726	5	math	math	PROPN
ejpam-6834	726	6	,	,	PUNCT
ejpam-6834	726	7	18	18	NUM
ejpam-6834	726	8	(	(	PUNCT
ejpam-6834	726	9	4	4	NUM
ejpam-6834	726	10	)	)	PUNCT
ejpam-6834	726	11	(	(	PUNCT
ejpam-6834	726	12	2025	2025	NUM
ejpam-6834	726	13	)	)	PUNCT
ejpam-6834	726	14	,	,	PUNCT
ejpam-6834	726	15	6834	6834	NUM
ejpam-6834	726	16	32	32	NUM
ejpam-6834	726	17	of	of	ADP
ejpam-6834	726	18	69	69	NUM
ejpam-6834	726	19	proof	proof	NOUN
ejpam-6834	726	20	.	.	PUNCT
ejpam-6834	727	1	fix	fix	VERB
ejpam-6834	727	2	a	a	DET
ejpam-6834	727	3	∈	∈	NOUN
ejpam-6834	727	4	p	p	NOUN
ejpam-6834	727	5	m′	m′	NOUN
ejpam-6834	727	6	(	(	PUNCT
ejpam-6834	727	7	x	x	NOUN
ejpam-6834	727	8	)	)	PUNCT
ejpam-6834	727	9	,	,	PUNCT
ejpam-6834	727	10	v	v	X
ejpam-6834	727	11	∈	∈	PROPN
ejpam-6834	727	12	v	v	NOUN
ejpam-6834	727	13	,	,	PUNCT
ejpam-6834	727	14	a	a	DET
ejpam-6834	727	15	∈	∈	NOUN
ejpam-6834	727	16	pv	pv	NOUN
ejpam-6834	727	17	.	.	PUNCT
ejpam-6834	728	1	since	since	SCONJ
ejpam-6834	728	2	ιm′→m(a	ιm′→m(a	PROPN
ejpam-6834	728	3	)	)	PUNCT
ejpam-6834	728	4	∈	∈	PROPN
ejpam-6834	728	5	p	p	PROPN
ejpam-6834	728	6	m(x	m(x	PROPN
ejpam-6834	728	7	)	)	PUNCT
ejpam-6834	728	8	,	,	PUNCT
ejpam-6834	728	9	the	the	DET
ejpam-6834	728	10	value	value	NOUN
ejpam-6834	728	11	˜pdf	˜pdf	NOUN
ejpam-6834	728	12	(	(	PUNCT
ejpam-6834	728	13	m	m	NOUN
ejpam-6834	728	14	,	,	PUNCT
ejpam-6834	728	15	n	n	CCONJ
ejpam-6834	728	16	)	)	PUNCT
ejpam-6834	728	17	v	v	NOUN
ejpam-6834	728	18	(	(	PUNCT
ejpam-6834	728	19	ιm′→m(a	ιm′→m(a	PROPN
ejpam-6834	728	20	)	)	PUNCT
ejpam-6834	728	21	,	,	PUNCT
ejpam-6834	728	22	a	a	PRON
ejpam-6834	728	23	)	)	PUNCT
ejpam-6834	728	24	∈	∈	PROPN
ejpam-6834	728	25	p	p	NOUN
ejpam-6834	728	26	n([0	n([0	PROPN
ejpam-6834	728	27	,	,	PUNCT
ejpam-6834	728	28	1]s	1]s	NUM
ejpam-6834	728	29	)	)	PUNCT
ejpam-6834	728	30	is	be	AUX
ejpam-6834	728	31	well	well	ADV
ejpam-6834	728	32	-	-	PUNCT
ejpam-6834	728	33	defined	define	VERB
ejpam-6834	728	34	and	and	CCONJ
ejpam-6834	728	35	nonempty	nonempty	ADJ
ejpam-6834	728	36	by	by	ADP
ejpam-6834	728	37	the	the	DET
ejpam-6834	728	38	(	(	PUNCT
ejpam-6834	728	39	m	m	PROPN
ejpam-6834	728	40	,	,	PUNCT
ejpam-6834	728	41	n)-definition	n)-definition	NOUN
ejpam-6834	728	42	.	.	PUNCT
ejpam-6834	729	1	hence	hence	ADV
ejpam-6834	729	2	˜pdf	˜pdf	NOUN
ejpam-6834	729	3	(	(	PUNCT
ejpam-6834	729	4	m′,n	m′,n	PROPN
ejpam-6834	729	5	)	)	PUNCT
ejpam-6834	729	6	v,↓m	v,↓m	NOUN
ejpam-6834	729	7	(	(	PUNCT
ejpam-6834	729	8	a	a	DET
ejpam-6834	729	9	,	,	PUNCT
ejpam-6834	729	10	a	a	PRON
ejpam-6834	729	11	)	)	PUNCT
ejpam-6834	729	12	has	have	VERB
ejpam-6834	729	13	the	the	DET
ejpam-6834	729	14	required	require	VERB
ejpam-6834	729	15	codomain	codomain	NOUN
ejpam-6834	729	16	.	.	PUNCT
ejpam-6834	730	1	the	the	DET
ejpam-6834	730	2	contradiction	contradiction	NOUN
ejpam-6834	730	3	map	map	NOUN
ejpam-6834	730	4	pcf	pcf	PROPN
ejpam-6834	730	5	(	(	PUNCT
ejpam-6834	730	6	m	m	PROPN
ejpam-6834	730	7	,	,	PUNCT
ejpam-6834	730	8	n	n	CCONJ
ejpam-6834	730	9	)	)	PUNCT
ejpam-6834	730	10	is	be	AUX
ejpam-6834	730	11	unchanged	unchanged	ADJ
ejpam-6834	730	12	,	,	PUNCT
ejpam-6834	730	13	so	so	SCONJ
ejpam-6834	730	14	all	all	DET
ejpam-6834	730	15	axioms	axiom	NOUN
ejpam-6834	730	16	are	be	AUX
ejpam-6834	730	17	preserved	preserve	VERB
ejpam-6834	730	18	.	.	PUNCT
ejpam-6834	731	1	theorem	theorem	VERB
ejpam-6834	731	2	17	17	NUM
ejpam-6834	731	3	(	(	PUNCT
ejpam-6834	731	4	projection	projection	NOUN
ejpam-6834	731	5	to	to	PART
ejpam-6834	731	6	lower	low	ADJ
ejpam-6834	731	7	n	n	CCONJ
ejpam-6834	731	8	)	)	PUNCT
ejpam-6834	731	9	.	.	PUNCT
ejpam-6834	732	1	let	let	VERB
ejpam-6834	732	2	shp	shp	NOUN
ejpam-6834	732	3	(	(	PUNCT
ejpam-6834	732	4	m	m	PROPN
ejpam-6834	732	5	,	,	PUNCT
ejpam-6834	732	6	n	n	CCONJ
ejpam-6834	732	7	)	)	PUNCT
ejpam-6834	732	8	be	be	AUX
ejpam-6834	732	9	as	as	ADV
ejpam-6834	732	10	above	above	ADV
ejpam-6834	732	11	and	and	CCONJ
ejpam-6834	732	12	let	let	VERB
ejpam-6834	732	13	n′	n′	NOUN
ejpam-6834	732	14	satisfy	satisfy	VERB
ejpam-6834	732	15	0	0	NUM
ejpam-6834	732	16	≤	≤	NOUN
ejpam-6834	732	17	n′	n′	NOUN
ejpam-6834	732	18	<	<	X
ejpam-6834	732	19	n.	n.	NOUN
ejpam-6834	732	20	for	for	ADP
ejpam-6834	732	21	each	each	DET
ejpam-6834	732	22	v	v	NUM
ejpam-6834	732	23	∈	∈	PROPN
ejpam-6834	732	24	v	v	NOUN
ejpam-6834	732	25	,	,	PUNCT
ejpam-6834	732	26	a	a	DET
ejpam-6834	732	27	∈	∈	PROPN
ejpam-6834	732	28	pv	pv	NOUN
ejpam-6834	732	29	,	,	PUNCT
ejpam-6834	732	30	define	define	VERB
ejpam-6834	732	31	˜pdf	˜pdf	NOUN
ejpam-6834	732	32	(	(	PUNCT
ejpam-6834	732	33	m	m	PROPN
ejpam-6834	732	34	,	,	PUNCT
ejpam-6834	732	35	n′	n′	PROPN
ejpam-6834	732	36	)	)	PUNCT
ejpam-6834	732	37	v,↓n	v,↓n	ADJ
ejpam-6834	732	38	(	(	PUNCT
ejpam-6834	732	39	a	a	PRON
ejpam-6834	732	40	,	,	PUNCT
ejpam-6834	732	41	a	a	NOUN
ejpam-6834	732	42	)	)	PUNCT
ejpam-6834	732	43	:	:	PUNCT
ejpam-6834	733	1	=	=	PUNCT
ejpam-6834	733	2	un→n′	un→n′	INTJ
ejpam-6834	733	3	(	(	PUNCT
ejpam-6834	733	4	˜pdf	˜pdf	NOUN
ejpam-6834	733	5	(	(	PUNCT
ejpam-6834	733	6	m	m	NOUN
ejpam-6834	733	7	,	,	PUNCT
ejpam-6834	733	8	n	n	CCONJ
ejpam-6834	733	9	)	)	PUNCT
ejpam-6834	733	10	v	v	NOUN
ejpam-6834	733	11	(	(	PUNCT
ejpam-6834	733	12	a	a	PRON
ejpam-6834	733	13	,	,	PUNCT
ejpam-6834	733	14	a	a	NOUN
ejpam-6834	733	15	)	)	PUNCT
ejpam-6834	733	16	)	)	PUNCT
ejpam-6834	733	17	∈	∈	PROPN
ejpam-6834	733	18	p	p	NOUN
ejpam-6834	733	19	n′	n′	PROPN
ejpam-6834	733	20	(	(	PUNCT
ejpam-6834	733	21	[	[	X
ejpam-6834	733	22	0	0	NUM
ejpam-6834	733	23	,	,	PUNCT
ejpam-6834	733	24	1]s	1]s	NUM
ejpam-6834	733	25	)	)	PUNCT
ejpam-6834	733	26	,	,	PUNCT
ejpam-6834	733	27	and	and	CCONJ
ejpam-6834	733	28	keep	keep	VERB
ejpam-6834	733	29	pcf	pcf	PROPN
ejpam-6834	733	30	(	(	PUNCT
ejpam-6834	733	31	m	m	PROPN
ejpam-6834	733	32	,	,	PUNCT
ejpam-6834	733	33	n	n	CCONJ
ejpam-6834	733	34	)	)	PUNCT
ejpam-6834	733	35	unchanged	unchanged	ADJ
ejpam-6834	733	36	.	.	PUNCT
ejpam-6834	734	1	then	then	ADV
ejpam-6834	734	2	shp	shp	PROPN
ejpam-6834	734	3	(	(	PUNCT
ejpam-6834	734	4	m	m	PROPN
ejpam-6834	734	5	,	,	PUNCT
ejpam-6834	734	6	n′	n′	PROPN
ejpam-6834	734	7	)	)	PUNCT
ejpam-6834	734	8	↓	↓	NOUN
ejpam-6834	735	1	=	=	PUNCT
ejpam-6834	735	2	(	(	PUNCT
ejpam-6834	735	3	p	p	PROPN
ejpam-6834	735	4	m(x	m(x	PROPN
ejpam-6834	735	5	)	)	PUNCT
ejpam-6834	735	6	,	,	PUNCT
ejpam-6834	735	7	v	v	NOUN
ejpam-6834	735	8	,	,	PUNCT
ejpam-6834	735	9	{	{	PUNCT
ejpam-6834	735	10	pv	pv	NOUN
ejpam-6834	735	11	}	}	PUNCT
ejpam-6834	735	12	,	,	PUNCT
ejpam-6834	735	13	{	{	PUNCT
ejpam-6834	735	14	˜pdf	˜pdf	NOUN
ejpam-6834	735	15	(	(	PUNCT
ejpam-6834	735	16	m	m	PROPN
ejpam-6834	735	17	,	,	PUNCT
ejpam-6834	735	18	n′	n′	PROPN
ejpam-6834	735	19	)	)	PUNCT
ejpam-6834	735	20	v,↓n	v,↓n	CCONJ
ejpam-6834	735	21	}	}	PUNCT
ejpam-6834	735	22	,	,	PUNCT
ejpam-6834	735	23	pcf	pcf	PROPN
ejpam-6834	735	24	(	(	PUNCT
ejpam-6834	735	25	m	m	PROPN
ejpam-6834	735	26	,	,	PUNCT
ejpam-6834	735	27	n	n	CCONJ
ejpam-6834	735	28	)	)	PUNCT
ejpam-6834	735	29	)	)	PUNCT
ejpam-6834	735	30	is	be	AUX
ejpam-6834	735	31	an	an	DET
ejpam-6834	735	32	(	(	PUNCT
ejpam-6834	735	33	m	m	PROPN
ejpam-6834	735	34	,	,	PUNCT
ejpam-6834	735	35	n′)-superhyperplithogenic	n′)-superhyperplithogenic	ADJ
ejpam-6834	735	36	set	set	NOUN
ejpam-6834	735	37	.	.	PUNCT
ejpam-6834	736	1	proof	proof	NOUN
ejpam-6834	736	2	.	.	PUNCT
ejpam-6834	737	1	fix	fix	VERB
ejpam-6834	737	2	a	a	DET
ejpam-6834	737	3	∈	∈	NOUN
ejpam-6834	737	4	p	p	ADJ
ejpam-6834	737	5	m(x	m(x	PROPN
ejpam-6834	737	6	)	)	PUNCT
ejpam-6834	737	7	,	,	PUNCT
ejpam-6834	737	8	v	v	NOUN
ejpam-6834	737	9	,	,	PUNCT
ejpam-6834	737	10	a.	a.	NOUN
ejpam-6834	737	11	since	since	SCONJ
ejpam-6834	737	12	˜pdf	˜pdf	NOUN
ejpam-6834	737	13	(	(	PUNCT
ejpam-6834	737	14	m	m	NOUN
ejpam-6834	737	15	,	,	PUNCT
ejpam-6834	737	16	n	n	CCONJ
ejpam-6834	737	17	)	)	PUNCT
ejpam-6834	737	18	v	v	NOUN
ejpam-6834	737	19	(	(	PUNCT
ejpam-6834	737	20	a	a	PRON
ejpam-6834	737	21	,	,	PUNCT
ejpam-6834	737	22	a	a	PRON
ejpam-6834	737	23	)	)	PUNCT
ejpam-6834	737	24	∈	∈	PROPN
ejpam-6834	737	25	p	p	NOUN
ejpam-6834	737	26	n([0	n([0	PROPN
ejpam-6834	737	27	,	,	PUNCT
ejpam-6834	737	28	1]s	1]s	NUM
ejpam-6834	737	29	)	)	PUNCT
ejpam-6834	737	30	is	be	AUX
ejpam-6834	737	31	nonempty	nonempty	ADJ
ejpam-6834	737	32	and	and	CCONJ
ejpam-6834	737	33	every	every	DET
ejpam-6834	737	34	level	level	NOUN
ejpam-6834	737	35	is	be	AUX
ejpam-6834	737	36	nonempty	nonempty	ADJ
ejpam-6834	737	37	by	by	ADP
ejpam-6834	737	38	definition	definition	NOUN
ejpam-6834	737	39	,	,	PUNCT
ejpam-6834	737	40	applying	apply	VERB
ejpam-6834	737	41	un→(n−1	un→(n−1	VERB
ejpam-6834	737	42	)	)	PUNCT
ejpam-6834	737	43	gives	give	VERB
ejpam-6834	737	44	a	a	DET
ejpam-6834	737	45	nonempty	nonempty	ADJ
ejpam-6834	737	46	element	element	NOUN
ejpam-6834	737	47	of	of	ADP
ejpam-6834	737	48	p	p	ADJ
ejpam-6834	737	49	n−1([0	n−1([0	NOUN
ejpam-6834	737	50	,	,	PUNCT
ejpam-6834	737	51	1]s	1]s	NUM
ejpam-6834	737	52	)	)	PUNCT
ejpam-6834	737	53	.	.	PUNCT
ejpam-6834	738	1	iterating	iterate	VERB
ejpam-6834	738	2	(	(	PUNCT
ejpam-6834	738	3	n	n	CCONJ
ejpam-6834	738	4	−	−	PROPN
ejpam-6834	738	5	n′	n′	PROPN
ejpam-6834	738	6	)	)	PUNCT
ejpam-6834	738	7	times	times	PROPN
ejpam-6834	738	8	yields	yield	VERB
ejpam-6834	738	9	a	a	DET
ejpam-6834	738	10	nonempty	nonempty	ADJ
ejpam-6834	738	11	element	element	NOUN
ejpam-6834	738	12	of	of	ADP
ejpam-6834	738	13	p	p	NOUN
ejpam-6834	738	14	n′	n′	PROPN
ejpam-6834	738	15	(	(	PUNCT
ejpam-6834	738	16	[	[	X
ejpam-6834	738	17	0	0	NUM
ejpam-6834	738	18	,	,	PUNCT
ejpam-6834	738	19	1]s	1]s	NUM
ejpam-6834	738	20	)	)	PUNCT
ejpam-6834	738	21	.	.	PUNCT
ejpam-6834	739	1	the	the	DET
ejpam-6834	739	2	contradiction	contradiction	NOUN
ejpam-6834	739	3	map	map	NOUN
ejpam-6834	739	4	is	be	AUX
ejpam-6834	739	5	unaffected	unaffected	ADJ
ejpam-6834	739	6	,	,	PUNCT
ejpam-6834	739	7	so	so	CCONJ
ejpam-6834	739	8	the	the	DET
ejpam-6834	739	9	structure	structure	NOUN
ejpam-6834	739	10	satisfies	satisfy	VERB
ejpam-6834	739	11	the	the	DET
ejpam-6834	739	12	definition	definition	NOUN
ejpam-6834	739	13	at	at	ADP
ejpam-6834	739	14	level	level	NOUN
ejpam-6834	739	15	n′.	n′.	PROPN
ejpam-6834	739	16	theorem	theorem	VERB
ejpam-6834	739	17	18	18	NUM
ejpam-6834	739	18	(	(	PUNCT
ejpam-6834	739	19	closure	closure	NOUN
ejpam-6834	739	20	under	under	ADP
ejpam-6834	739	21	pointwise	pointwise	PROPN
ejpam-6834	739	22	union	union	NOUN
ejpam-6834	739	23	)	)	PUNCT
ejpam-6834	739	24	.	.	PUNCT
ejpam-6834	740	1	let	let	VERB
ejpam-6834	740	2	shp	shp	NOUN
ejpam-6834	740	3	(	(	PUNCT
ejpam-6834	740	4	m	m	PROPN
ejpam-6834	740	5	,	,	PUNCT
ejpam-6834	740	6	n	n	CCONJ
ejpam-6834	740	7	)	)	PUNCT
ejpam-6834	740	8	1	1	NUM
ejpam-6834	740	9	and	and	CCONJ
ejpam-6834	740	10	shp	shp	NOUN
ejpam-6834	740	11	(	(	PUNCT
ejpam-6834	740	12	m	m	PROPN
ejpam-6834	740	13	,	,	PUNCT
ejpam-6834	740	14	n	n	CCONJ
ejpam-6834	740	15	)	)	PUNCT
ejpam-6834	740	16	2	2	NUM
ejpam-6834	740	17	be	be	AUX
ejpam-6834	740	18	(	(	PUNCT
ejpam-6834	740	19	m	m	NOUN
ejpam-6834	740	20	,	,	PUNCT
ejpam-6834	740	21	n)superhyperplithogenic	n)superhyperplithogenic	ADJ
ejpam-6834	740	22	sets	set	NOUN
ejpam-6834	740	23	on	on	ADP
ejpam-6834	740	24	the	the	DET
ejpam-6834	740	25	same	same	ADJ
ejpam-6834	740	26	(	(	PUNCT
ejpam-6834	740	27	x	x	NOUN
ejpam-6834	740	28	,	,	PUNCT
ejpam-6834	740	29	v	v	NOUN
ejpam-6834	740	30	,	,	PUNCT
ejpam-6834	740	31	{	{	PUNCT
ejpam-6834	740	32	pv	pv	NOUN
ejpam-6834	740	33	}	}	PUNCT
ejpam-6834	740	34	)	)	PUNCT
ejpam-6834	740	35	and	and	CCONJ
ejpam-6834	740	36	with	with	ADP
ejpam-6834	740	37	the	the	DET
ejpam-6834	740	38	same	same	ADJ
ejpam-6834	740	39	pcf	pcf	PROPN
ejpam-6834	740	40	(	(	PUNCT
ejpam-6834	740	41	m	m	PROPN
ejpam-6834	740	42	,	,	PUNCT
ejpam-6834	740	43	n	n	CCONJ
ejpam-6834	740	44	)	)	PUNCT
ejpam-6834	740	45	.	.	PUNCT
ejpam-6834	741	1	define	define	VERB
ejpam-6834	741	2	,	,	PUNCT
ejpam-6834	741	3	for	for	ADP
ejpam-6834	741	4	each	each	DET
ejpam-6834	741	5	v	v	NUM
ejpam-6834	741	6	∈	∈	PROPN
ejpam-6834	741	7	v	v	NOUN
ejpam-6834	741	8	,	,	PUNCT
ejpam-6834	741	9	a	a	DET
ejpam-6834	741	10	∈	∈	PROPN
ejpam-6834	741	11	pv	pv	NOUN
ejpam-6834	741	12	,	,	PUNCT
ejpam-6834	741	13	(	(	PUNCT
ejpam-6834	741	14	˜pdf	˜pdf	X
ejpam-6834	741	15	(	(	PUNCT
ejpam-6834	741	16	m	m	NOUN
ejpam-6834	741	17	,	,	PUNCT
ejpam-6834	741	18	n	n	CCONJ
ejpam-6834	741	19	)	)	PUNCT
ejpam-6834	741	20	v	v	NOUN
ejpam-6834	741	21	)	)	PUNCT
ejpam-6834	741	22	∪	∪	X
ejpam-6834	741	23	(	(	PUNCT
ejpam-6834	741	24	a	a	DET
ejpam-6834	741	25	,	,	PUNCT
ejpam-6834	741	26	a	a	NOUN
ejpam-6834	741	27	)	)	PUNCT
ejpam-6834	741	28	:	:	PUNCT
ejpam-6834	741	29	=	=	SYM
ejpam-6834	741	30	˜pdf	˜pdf	X
ejpam-6834	741	31	(	(	PUNCT
ejpam-6834	741	32	m	m	NOUN
ejpam-6834	741	33	,	,	PUNCT
ejpam-6834	741	34	n	n	CCONJ
ejpam-6834	741	35	)	)	PUNCT
ejpam-6834	741	36	v,1	v,1	NOUN
ejpam-6834	741	37	(	(	PUNCT
ejpam-6834	741	38	a	a	PRON
ejpam-6834	741	39	,	,	PUNCT
ejpam-6834	741	40	a	a	PRON
ejpam-6834	741	41	)	)	PUNCT
ejpam-6834	741	42	∪	∪	X
ejpam-6834	741	43	˜pdf	˜pdf	X
ejpam-6834	741	44	(	(	PUNCT
ejpam-6834	741	45	m	m	NOUN
ejpam-6834	741	46	,	,	PUNCT
ejpam-6834	741	47	n	n	CCONJ
ejpam-6834	741	48	)	)	PUNCT
ejpam-6834	741	49	v,2	v,2	X
ejpam-6834	741	50	(	(	PUNCT
ejpam-6834	741	51	a	a	DET
ejpam-6834	741	52	,	,	PUNCT
ejpam-6834	741	53	a	a	NOUN
ejpam-6834	741	54	)	)	PUNCT
ejpam-6834	741	55	for	for	ADP
ejpam-6834	741	56	a	a	DET
ejpam-6834	741	57	∈	∈	PROPN
ejpam-6834	741	58	p	p	ADJ
ejpam-6834	741	59	m(x	m(x	PROPN
ejpam-6834	741	60	)	)	PUNCT
ejpam-6834	741	61	.	.	PUNCT
ejpam-6834	742	1	then	then	ADV
ejpam-6834	742	2	shp	shp	PROPN
ejpam-6834	742	3	(	(	PUNCT
ejpam-6834	742	4	m	m	PROPN
ejpam-6834	742	5	,	,	PUNCT
ejpam-6834	742	6	n	n	CCONJ
ejpam-6834	742	7	)	)	PUNCT
ejpam-6834	742	8	∪	∪	ADV
ejpam-6834	742	9	=	=	SYM
ejpam-6834	742	10	(	(	PUNCT
ejpam-6834	742	11	p	p	PROPN
ejpam-6834	742	12	m(x	m(x	PROPN
ejpam-6834	742	13	)	)	PUNCT
ejpam-6834	742	14	,	,	PUNCT
ejpam-6834	742	15	v	v	NOUN
ejpam-6834	742	16	,	,	PUNCT
ejpam-6834	742	17	{	{	PUNCT
ejpam-6834	742	18	pv	pv	NOUN
ejpam-6834	742	19	}	}	PUNCT
ejpam-6834	742	20	,	,	PUNCT
ejpam-6834	742	21	{	{	PUNCT
ejpam-6834	742	22	(	(	PUNCT
ejpam-6834	742	23	˜pdf	˜pdf	X
ejpam-6834	742	24	(	(	PUNCT
ejpam-6834	742	25	m	m	NOUN
ejpam-6834	742	26	,	,	PUNCT
ejpam-6834	742	27	n	n	CCONJ
ejpam-6834	742	28	)	)	PUNCT
ejpam-6834	742	29	v	v	NOUN
ejpam-6834	742	30	)	)	PUNCT
ejpam-6834	742	31	∪	∪	ADP
ejpam-6834	742	32	}	}	PUNCT
ejpam-6834	742	33	,	,	PUNCT
ejpam-6834	742	34	pcf	pcf	PROPN
ejpam-6834	742	35	(	(	PUNCT
ejpam-6834	742	36	m	m	PROPN
ejpam-6834	742	37	,	,	PUNCT
ejpam-6834	742	38	n	n	CCONJ
ejpam-6834	742	39	)	)	PUNCT
ejpam-6834	742	40	)	)	PUNCT
ejpam-6834	742	41	is	be	AUX
ejpam-6834	742	42	an	an	DET
ejpam-6834	742	43	(	(	PUNCT
ejpam-6834	742	44	m	m	NOUN
ejpam-6834	742	45	,	,	PUNCT
ejpam-6834	742	46	n)-superhyperplithogenic	n)-superhyperplithogenic	PUNCT
ejpam-6834	742	47	set	set	NOUN
ejpam-6834	742	48	.	.	PUNCT
ejpam-6834	743	1	proof	proof	NOUN
ejpam-6834	743	2	.	.	PUNCT
ejpam-6834	744	1	for	for	ADP
ejpam-6834	744	2	each	each	PRON
ejpam-6834	744	3	(	(	PUNCT
ejpam-6834	744	4	a	a	PRON
ejpam-6834	744	5	,	,	PUNCT
ejpam-6834	744	6	a	a	NOUN
ejpam-6834	744	7	)	)	PUNCT
ejpam-6834	744	8	,	,	PUNCT
ejpam-6834	744	9	both	both	PRON
ejpam-6834	744	10	˜pdf	˜pdf	X
ejpam-6834	744	11	(	(	PUNCT
ejpam-6834	744	12	m	m	NOUN
ejpam-6834	744	13	,	,	PUNCT
ejpam-6834	744	14	n	n	CCONJ
ejpam-6834	744	15	)	)	PUNCT
ejpam-6834	744	16	v,1	v,1	NOUN
ejpam-6834	744	17	(	(	PUNCT
ejpam-6834	744	18	a	a	PRON
ejpam-6834	744	19	,	,	PUNCT
ejpam-6834	744	20	a	a	NOUN
ejpam-6834	744	21	)	)	PUNCT
ejpam-6834	744	22	and	and	CCONJ
ejpam-6834	744	23	˜pdf	˜pdf	NOUN
ejpam-6834	744	24	(	(	PUNCT
ejpam-6834	744	25	m	m	NOUN
ejpam-6834	744	26	,	,	PUNCT
ejpam-6834	744	27	n	n	CCONJ
ejpam-6834	744	28	)	)	PUNCT
ejpam-6834	744	29	v,2	v,2	X
ejpam-6834	744	30	(	(	PUNCT
ejpam-6834	744	31	a	a	DET
ejpam-6834	744	32	,	,	PUNCT
ejpam-6834	744	33	a	a	PRON
ejpam-6834	744	34	)	)	PUNCT
ejpam-6834	744	35	lie	lie	NOUN
ejpam-6834	744	36	in	in	ADP
ejpam-6834	744	37	p	p	NOUN
ejpam-6834	744	38	n([0	n([0	ADJ
ejpam-6834	744	39	,	,	PUNCT
ejpam-6834	744	40	1]s	1]s	NUM
ejpam-6834	744	41	)	)	PUNCT
ejpam-6834	744	42	and	and	CCONJ
ejpam-6834	744	43	are	be	AUX
ejpam-6834	744	44	nonempty	nonempty	ADJ
ejpam-6834	744	45	.	.	PUNCT
ejpam-6834	745	1	their	their	PRON
ejpam-6834	745	2	union	union	NOUN
ejpam-6834	745	3	is	be	AUX
ejpam-6834	745	4	a	a	DET
ejpam-6834	745	5	nonempty	nonempty	ADJ
ejpam-6834	745	6	subset	subset	NOUN
ejpam-6834	745	7	of	of	ADP
ejpam-6834	745	8	p	p	PROPN
ejpam-6834	745	9	n−1([0	n−1([0	NOUN
ejpam-6834	745	10	,	,	PUNCT
ejpam-6834	745	11	1]s	1]s	NOUN
ejpam-6834	745	12	)	)	PUNCT
ejpam-6834	745	13	,	,	PUNCT
ejpam-6834	745	14	hence	hence	ADV
ejpam-6834	745	15	an	an	DET
ejpam-6834	745	16	element	element	NOUN
ejpam-6834	745	17	of	of	ADP
ejpam-6834	745	18	p	p	NOUN
ejpam-6834	745	19	n([0	n([0	ADJ
ejpam-6834	745	20	,	,	PUNCT
ejpam-6834	745	21	1]s	1]s	NUM
ejpam-6834	745	22	)	)	PUNCT
ejpam-6834	745	23	.	.	PUNCT
ejpam-6834	746	1	the	the	DET
ejpam-6834	746	2	shared	share	VERB
ejpam-6834	746	3	pcf	pcf	PROPN
ejpam-6834	746	4	(	(	PUNCT
ejpam-6834	746	5	m	m	PROPN
ejpam-6834	746	6	,	,	PUNCT
ejpam-6834	746	7	n	n	CCONJ
ejpam-6834	746	8	)	)	PUNCT
ejpam-6834	746	9	remains	remain	VERB
ejpam-6834	746	10	valid	valid	ADJ
ejpam-6834	746	11	.	.	PUNCT
ejpam-6834	747	1	theorem	theorem	ADJ
ejpam-6834	747	2	19	19	NUM
ejpam-6834	747	3	(	(	PUNCT
ejpam-6834	747	4	attribute	attribute	NOUN
ejpam-6834	747	5	–	–	PUNCT
ejpam-6834	747	6	value	value	NOUN
ejpam-6834	747	7	α	α	NOUN
ejpam-6834	747	8	-	-	PUNCT
ejpam-6834	747	9	cuts	cut	NOUN
ejpam-6834	747	10	are	be	AUX
ejpam-6834	747	11	nested	nest	VERB
ejpam-6834	747	12	)	)	PUNCT
ejpam-6834	747	13	.	.	PUNCT
ejpam-6834	748	1	fix	fix	VERB
ejpam-6834	748	2	v	v	NUM
ejpam-6834	748	3	∈	∈	NOUN
ejpam-6834	748	4	v	v	NOUN
ejpam-6834	748	5	and	and	CCONJ
ejpam-6834	748	6	a	a	DET
ejpam-6834	748	7	∈	∈	NOUN
ejpam-6834	748	8	pv	pv	NOUN
ejpam-6834	748	9	.	.	PUNCT
ejpam-6834	749	1	for	for	ADP
ejpam-6834	749	2	a	a	DET
ejpam-6834	749	3	threshold	threshold	NOUN
ejpam-6834	749	4	vector	vector	NOUN
ejpam-6834	749	5	α	α	NOUN
ejpam-6834	749	6	=	=	SYM
ejpam-6834	749	7	(	(	PUNCT
ejpam-6834	749	8	α1	α1	PROPN
ejpam-6834	749	9	,	,	PUNCT
ejpam-6834	749	10	.	.	PUNCT
ejpam-6834	749	11	.	.	PUNCT
ejpam-6834	749	12	.	.	PUNCT
ejpam-6834	750	1	,	,	PUNCT
ejpam-6834	750	2	αs	αs	X
ejpam-6834	750	3	)	)	PUNCT
ejpam-6834	750	4	∈	∈	PROPN
ejpam-6834	751	1	[	[	X
ejpam-6834	751	2	0	0	NUM
ejpam-6834	751	3	,	,	PUNCT
ejpam-6834	751	4	1]s	1]s	NOUN
ejpam-6834	751	5	,	,	PUNCT
ejpam-6834	751	6	define	define	VERB
ejpam-6834	751	7	cv	cv	PROPN
ejpam-6834	751	8	,	,	PUNCT
ejpam-6834	751	9	a(α	a(α	ADV
ejpam-6834	751	10	)	)	PUNCT
ejpam-6834	751	11	=	=	SYM
ejpam-6834	751	12	{	{	PUNCT
ejpam-6834	751	13	a	a	DET
ejpam-6834	751	14	∈	∈	PROPN
ejpam-6834	751	15	p	p	PROPN
ejpam-6834	751	16	m(x	m(x	PROPN
ejpam-6834	751	17	)	)	PUNCT
ejpam-6834	751	18	∣∣∣	∣∣∣	NOUN
ejpam-6834	751	19	∃d	∃d	PROPN
ejpam-6834	751	20	∈	∈	PROPN
ejpam-6834	751	21	un→1	un→1	PROPN
ejpam-6834	751	22	(	(	PUNCT
ejpam-6834	751	23	˜pdf	˜pdf	NOUN
ejpam-6834	751	24	(	(	PUNCT
ejpam-6834	751	25	m	m	NOUN
ejpam-6834	751	26	,	,	PUNCT
ejpam-6834	751	27	n	n	CCONJ
ejpam-6834	751	28	)	)	PUNCT
ejpam-6834	751	29	v	v	NOUN
ejpam-6834	751	30	(	(	PUNCT
ejpam-6834	751	31	a	a	DET
ejpam-6834	751	32	,	,	PUNCT
ejpam-6834	751	33	a	a	NOUN
ejpam-6834	751	34	)	)	PUNCT
ejpam-6834	751	35	)	)	PUNCT
ejpam-6834	751	36	with	with	ADP
ejpam-6834	751	37	d	d	PROPN
ejpam-6834	751	38	≥	≥	PROPN
ejpam-6834	751	39	α	α	PROPN
ejpam-6834	751	40	(	(	PUNCT
ejpam-6834	751	41	componentwise	componentwise	NOUN
ejpam-6834	751	42	)	)	PUNCT
ejpam-6834	751	43	}	}	PUNCT
ejpam-6834	751	44	.	.	PUNCT
ejpam-6834	752	1	if	if	SCONJ
ejpam-6834	752	2	α′,α	α′,α	NUM
ejpam-6834	752	3	∈	∈	PROPN
ejpam-6834	752	4	[	[	X
ejpam-6834	752	5	0	0	NUM
ejpam-6834	752	6	,	,	PUNCT
ejpam-6834	752	7	1]s	1]s	NOUN
ejpam-6834	752	8	satisfy	satisfy	VERB
ejpam-6834	752	9	α′	α′	NUM
ejpam-6834	752	10	≥	≥	NOUN
ejpam-6834	752	11	α	α	DET
ejpam-6834	752	12	componentwise	componentwise	NOUN
ejpam-6834	752	13	,	,	PUNCT
ejpam-6834	752	14	then	then	ADV
ejpam-6834	752	15	cv	cv	PROPN
ejpam-6834	752	16	,	,	PUNCT
ejpam-6834	752	17	a(α′	a(α′	PROPN
ejpam-6834	752	18	)	)	PUNCT
ejpam-6834	752	19	⊆	⊆	NUM
ejpam-6834	752	20	cv	cv	PROPN
ejpam-6834	752	21	,	,	PUNCT
ejpam-6834	752	22	a(α	a(α	NOUN
ejpam-6834	752	23	)	)	PUNCT
ejpam-6834	752	24	.	.	PUNCT
ejpam-6834	753	1	t.	t.	PROPN
ejpam-6834	753	2	fujita	fujita	PROPN
ejpam-6834	753	3	,	,	PUNCT
ejpam-6834	753	4	f.smarandache	f.smarandache	NOUN
ejpam-6834	753	5	/	/	SYM
ejpam-6834	753	6	eur	eur	PROPN
ejpam-6834	753	7	.	.	PUNCT
ejpam-6834	754	1	j.	j.	PROPN
ejpam-6834	754	2	pure	pure	PROPN
ejpam-6834	754	3	appl	appl	PROPN
ejpam-6834	754	4	.	.	PROPN
ejpam-6834	754	5	math	math	PROPN
ejpam-6834	754	6	,	,	PUNCT
ejpam-6834	754	7	18	18	NUM
ejpam-6834	754	8	(	(	PUNCT
ejpam-6834	754	9	4	4	NUM
ejpam-6834	754	10	)	)	PUNCT
ejpam-6834	754	11	(	(	PUNCT
ejpam-6834	754	12	2025	2025	NUM
ejpam-6834	754	13	)	)	PUNCT
ejpam-6834	754	14	,	,	PUNCT
ejpam-6834	754	15	6834	6834	NUM
ejpam-6834	754	16	33	33	NUM
ejpam-6834	754	17	of	of	ADP
ejpam-6834	754	18	69	69	NUM
ejpam-6834	754	19	proof	proof	NOUN
ejpam-6834	754	20	.	.	PUNCT
ejpam-6834	755	1	let	let	VERB
ejpam-6834	755	2	a	a	DET
ejpam-6834	755	3	∈	∈	PROPN
ejpam-6834	755	4	cv	cv	PROPN
ejpam-6834	755	5	,	,	PUNCT
ejpam-6834	755	6	a(α′	a(α′	PROPN
ejpam-6834	755	7	)	)	PUNCT
ejpam-6834	755	8	.	.	PUNCT
ejpam-6834	756	1	then	then	ADV
ejpam-6834	756	2	there	there	PRON
ejpam-6834	756	3	exists	exist	VERB
ejpam-6834	756	4	d	d	X
ejpam-6834	756	5	=	=	PUNCT
ejpam-6834	756	6	(	(	PUNCT
ejpam-6834	756	7	d1	d1	PROPN
ejpam-6834	756	8	,	,	PUNCT
ejpam-6834	756	9	.	.	PUNCT
ejpam-6834	756	10	.	.	PUNCT
ejpam-6834	757	1	.	.	PUNCT
ejpam-6834	758	1	,	,	PUNCT
ejpam-6834	758	2	ds	ds	ADJ
ejpam-6834	758	3	)	)	PUNCT
ejpam-6834	758	4	∈	∈	NOUN
ejpam-6834	758	5	un→1	un→1	PROPN
ejpam-6834	758	6	(	(	PUNCT
ejpam-6834	758	7	˜pdf	˜pdf	NOUN
ejpam-6834	758	8	(	(	PUNCT
ejpam-6834	758	9	m	m	NOUN
ejpam-6834	758	10	,	,	PUNCT
ejpam-6834	758	11	n	n	CCONJ
ejpam-6834	758	12	)	)	PUNCT
ejpam-6834	758	13	v	v	NOUN
ejpam-6834	758	14	(	(	PUNCT
ejpam-6834	758	15	a	a	DET
ejpam-6834	758	16	,	,	PUNCT
ejpam-6834	758	17	a	a	NOUN
ejpam-6834	758	18	)	)	PUNCT
ejpam-6834	758	19	)	)	PUNCT
ejpam-6834	758	20	with	with	ADP
ejpam-6834	758	21	di	di	X
ejpam-6834	758	22	≥	≥	X
ejpam-6834	758	23	α′	α′	NUM
ejpam-6834	758	24	i	i	PRON
ejpam-6834	758	25	for	for	ADP
ejpam-6834	758	26	all	all	DET
ejpam-6834	758	27	i.	i.	NOUN
ejpam-6834	758	28	since	since	SCONJ
ejpam-6834	758	29	α′	α′	NUM
ejpam-6834	758	30	i	i	PRON
ejpam-6834	758	31	≥	≥	VERB
ejpam-6834	758	32	αi	αi	VERB
ejpam-6834	758	33	for	for	ADP
ejpam-6834	758	34	each	each	DET
ejpam-6834	758	35	i	i	PRON
ejpam-6834	758	36	,	,	PUNCT
ejpam-6834	758	37	we	we	PRON
ejpam-6834	758	38	also	also	ADV
ejpam-6834	758	39	have	have	VERB
ejpam-6834	758	40	di	di	X
ejpam-6834	758	41	≥	≥	NOUN
ejpam-6834	758	42	αi	αi	NOUN
ejpam-6834	758	43	;	;	PUNCT
ejpam-6834	758	44	hence	hence	ADV
ejpam-6834	758	45	the	the	DET
ejpam-6834	758	46	same	same	ADJ
ejpam-6834	758	47	d	d	NOUN
ejpam-6834	758	48	witnesses	witness	VERB
ejpam-6834	758	49	a	a	DET
ejpam-6834	758	50	∈	∈	PROPN
ejpam-6834	758	51	cv	cv	PROPN
ejpam-6834	758	52	,	,	PUNCT
ejpam-6834	758	53	a(α	a(α	ADV
ejpam-6834	758	54	)	)	PUNCT
ejpam-6834	758	55	.	.	PUNCT
ejpam-6834	759	1	theorem	theorem	NOUN
ejpam-6834	759	2	20	20	NUM
ejpam-6834	759	3	(	(	PUNCT
ejpam-6834	759	4	functoriality	functoriality	NOUN
ejpam-6834	759	5	under	under	ADP
ejpam-6834	759	6	surjections	surjection	NOUN
ejpam-6834	759	7	on	on	ADP
ejpam-6834	759	8	the	the	DET
ejpam-6834	759	9	base	base	NOUN
ejpam-6834	759	10	)	)	PUNCT
ejpam-6834	759	11	.	.	PUNCT
ejpam-6834	760	1	let	let	VERB
ejpam-6834	760	2	f	f	NOUN
ejpam-6834	760	3	:	:	PUNCT
ejpam-6834	760	4	x	x	X
ejpam-6834	760	5	→	→	SYM
ejpam-6834	760	6	y	y	PROPN
ejpam-6834	760	7	be	be	AUX
ejpam-6834	760	8	surjective	surjective	ADJ
ejpam-6834	760	9	and	and	CCONJ
ejpam-6834	760	10	let	let	VERB
ejpam-6834	760	11	shp	shp	NOUN
ejpam-6834	760	12	(	(	PUNCT
ejpam-6834	760	13	m	m	PROPN
ejpam-6834	760	14	,	,	PUNCT
ejpam-6834	760	15	n	n	CCONJ
ejpam-6834	760	16	)	)	PUNCT
ejpam-6834	760	17	x	x	X
ejpam-6834	761	1	=	=	PUNCT
ejpam-6834	762	1	(	(	PUNCT
ejpam-6834	762	2	p	p	PROPN
ejpam-6834	762	3	m(x	m(x	PROPN
ejpam-6834	762	4	)	)	PUNCT
ejpam-6834	762	5	,	,	PUNCT
ejpam-6834	762	6	v	v	NOUN
ejpam-6834	762	7	,	,	PUNCT
ejpam-6834	762	8	{	{	PUNCT
ejpam-6834	762	9	pv	pv	NOUN
ejpam-6834	762	10	}	}	PUNCT
ejpam-6834	762	11	,	,	PUNCT
ejpam-6834	762	12	{	{	PUNCT
ejpam-6834	762	13	˜pdf	˜pdf	NOUN
ejpam-6834	762	14	(	(	PUNCT
ejpam-6834	762	15	m	m	NOUN
ejpam-6834	762	16	,	,	PUNCT
ejpam-6834	762	17	n	n	CCONJ
ejpam-6834	762	18	)	)	PUNCT
ejpam-6834	762	19	v	v	NOUN
ejpam-6834	762	20	}	}	PUNCT
ejpam-6834	762	21	,	,	PUNCT
ejpam-6834	762	22	pcf	pcf	PROPN
ejpam-6834	762	23	(	(	PUNCT
ejpam-6834	762	24	m	m	PROPN
ejpam-6834	762	25	,	,	PUNCT
ejpam-6834	762	26	n	n	CCONJ
ejpam-6834	762	27	)	)	PUNCT
ejpam-6834	762	28	)	)	PUNCT
ejpam-6834	762	29	be	be	AUX
ejpam-6834	762	30	an	an	DET
ejpam-6834	762	31	(	(	PUNCT
ejpam-6834	762	32	m	m	PROPN
ejpam-6834	762	33	,	,	PUNCT
ejpam-6834	762	34	n)-superhyperplithogenic	n)-superhyperplithogenic	PUNCT
ejpam-6834	762	35	set	set	VERB
ejpam-6834	762	36	on	on	ADP
ejpam-6834	762	37	x.	x.	NOUN
ejpam-6834	762	38	define	define	PROPN
ejpam-6834	762	39	lifted	lift	VERB
ejpam-6834	762	40	preimages	preimage	NOUN
ejpam-6834	762	41	recursively	recursively	ADV
ejpam-6834	762	42	:	:	PUNCT
ejpam-6834	762	43	f−1	f−1	PROPN
ejpam-6834	762	44	(	(	PUNCT
ejpam-6834	762	45	1	1	NUM
ejpam-6834	762	46	)	)	PUNCT
ejpam-6834	762	47	:	:	PUNCT
ejpam-6834	763	1	p(y	p(y	PROPN
ejpam-6834	763	2	)	)	PUNCT
ejpam-6834	763	3	→	→	SYM
ejpam-6834	763	4	p(x	p(x	PROPN
ejpam-6834	763	5	)	)	PUNCT
ejpam-6834	763	6	,	,	PUNCT
ejpam-6834	763	7	f−1	f−1	PROPN
ejpam-6834	763	8	(	(	PUNCT
ejpam-6834	763	9	1	1	NUM
ejpam-6834	763	10	)	)	PUNCT
ejpam-6834	763	11	(	(	PUNCT
ejpam-6834	763	12	b	b	X
ejpam-6834	763	13	)	)	PUNCT
ejpam-6834	763	14	=	=	SYM
ejpam-6834	763	15	{	{	PUNCT
ejpam-6834	763	16	x	x	PUNCT
ejpam-6834	763	17	∈	∈	NOUN
ejpam-6834	763	18	x	x	X
ejpam-6834	763	19	:	:	PUNCT
ejpam-6834	763	20	f(x	f(x	PROPN
ejpam-6834	763	21	)	)	PUNCT
ejpam-6834	763	22	∈	∈	PROPN
ejpam-6834	763	23	b	b	X
ejpam-6834	763	24	}	}	PUNCT
ejpam-6834	763	25	,	,	PUNCT
ejpam-6834	763	26	f−1	f−1	PROPN
ejpam-6834	763	27	(	(	PUNCT
ejpam-6834	763	28	t+1)(b	t+1)(b	PROPN
ejpam-6834	763	29	)	)	PUNCT
ejpam-6834	763	30	=	=	PRON
ejpam-6834	763	31	{	{	PUNCT
ejpam-6834	763	32	f−1	f−1	PROPN
ejpam-6834	763	33	(	(	PUNCT
ejpam-6834	763	34	t	t	PROPN
ejpam-6834	763	35	)	)	PUNCT
ejpam-6834	763	36	(	(	PUNCT
ejpam-6834	763	37	b	b	X
ejpam-6834	763	38	)	)	PUNCT
ejpam-6834	763	39	|	|	ADV
ejpam-6834	763	40	b	b	X
ejpam-6834	763	41	∈	∈	PROPN
ejpam-6834	763	42	b	b	PROPN
ejpam-6834	763	43	}	}	PUNCT
ejpam-6834	763	44	(	(	PUNCT
ejpam-6834	763	45	t	t	PROPN
ejpam-6834	763	46	≥	≥	PROPN
ejpam-6834	763	47	1	1	NUM
ejpam-6834	763	48	)	)	PUNCT
ejpam-6834	763	49	.	.	PUNCT
ejpam-6834	764	1	define	define	VERB
ejpam-6834	764	2	,	,	PUNCT
ejpam-6834	764	3	for	for	ADP
ejpam-6834	764	4	a′	a′	PROPN
ejpam-6834	764	5	∈	∈	PROPN
ejpam-6834	764	6	p	p	PROPN
ejpam-6834	764	7	m(y	m(y	PROPN
ejpam-6834	764	8	)	)	PUNCT
ejpam-6834	764	9	,	,	PUNCT
ejpam-6834	764	10	v	v	X
ejpam-6834	764	11	∈	∈	PROPN
ejpam-6834	764	12	v	v	NOUN
ejpam-6834	764	13	,	,	PUNCT
ejpam-6834	764	14	a	a	DET
ejpam-6834	764	15	∈	∈	PROPN
ejpam-6834	764	16	pv	pv	NOUN
ejpam-6834	764	17	,	,	PUNCT
ejpam-6834	764	18	˜pdf	˜pdf	NOUN
ejpam-6834	764	19	(	(	PUNCT
ejpam-6834	764	20	m	m	NOUN
ejpam-6834	764	21	,	,	PUNCT
ejpam-6834	764	22	n	n	CCONJ
ejpam-6834	764	23	)	)	PUNCT
ejpam-6834	764	24	v	v	NOUN
ejpam-6834	764	25	,	,	PUNCT
ejpam-6834	764	26	f	f	PROPN
ejpam-6834	764	27	(	(	PUNCT
ejpam-6834	764	28	a′	a′	PROPN
ejpam-6834	764	29	,	,	PUNCT
ejpam-6834	764	30	a	a	PRON
ejpam-6834	764	31	)	)	PUNCT
ejpam-6834	764	32	:	:	PUNCT
ejpam-6834	764	33	=	=	SYM
ejpam-6834	764	34	˜pdf	˜pdf	X
ejpam-6834	764	35	(	(	PUNCT
ejpam-6834	764	36	m	m	NOUN
ejpam-6834	764	37	,	,	PUNCT
ejpam-6834	764	38	n	n	CCONJ
ejpam-6834	764	39	)	)	PUNCT
ejpam-6834	764	40	v	v	NOUN
ejpam-6834	764	41	(	(	PUNCT
ejpam-6834	764	42	f−1	f−1	PROPN
ejpam-6834	764	43	(	(	PUNCT
ejpam-6834	764	44	m)(a	m)(a	PROPN
ejpam-6834	764	45	′	′	NUM
ejpam-6834	764	46	)	)	PUNCT
ejpam-6834	764	47	,	,	PUNCT
ejpam-6834	764	48	a	a	PRON
ejpam-6834	764	49	)	)	PUNCT
ejpam-6834	764	50	,	,	PUNCT
ejpam-6834	764	51	and	and	CCONJ
ejpam-6834	764	52	keep	keep	VERB
ejpam-6834	764	53	pcf	pcf	PROPN
ejpam-6834	764	54	(	(	PUNCT
ejpam-6834	764	55	m	m	PROPN
ejpam-6834	764	56	,	,	PUNCT
ejpam-6834	764	57	n	n	CCONJ
ejpam-6834	764	58	)	)	PUNCT
ejpam-6834	764	59	unchanged	unchanged	ADJ
ejpam-6834	764	60	.	.	PUNCT
ejpam-6834	765	1	then	then	ADV
ejpam-6834	765	2	shp	shp	PROPN
ejpam-6834	765	3	(	(	PUNCT
ejpam-6834	765	4	m	m	PROPN
ejpam-6834	765	5	,	,	PUNCT
ejpam-6834	765	6	n	n	CCONJ
ejpam-6834	765	7	)	)	PUNCT
ejpam-6834	765	8	y	y	NOUN
ejpam-6834	765	9	=	=	PUNCT
ejpam-6834	765	10	(	(	PUNCT
ejpam-6834	765	11	p	p	PROPN
ejpam-6834	765	12	m(y	m(y	NOUN
ejpam-6834	765	13	)	)	PUNCT
ejpam-6834	765	14	,	,	PUNCT
ejpam-6834	765	15	v	v	NOUN
ejpam-6834	765	16	,	,	PUNCT
ejpam-6834	765	17	{	{	PUNCT
ejpam-6834	765	18	pv	pv	NOUN
ejpam-6834	765	19	}	}	PUNCT
ejpam-6834	765	20	,	,	PUNCT
ejpam-6834	765	21	{	{	PUNCT
ejpam-6834	765	22	˜pdf	˜pdf	NOUN
ejpam-6834	765	23	(	(	PUNCT
ejpam-6834	765	24	m	m	NOUN
ejpam-6834	765	25	,	,	PUNCT
ejpam-6834	765	26	n	n	CCONJ
ejpam-6834	765	27	)	)	PUNCT
ejpam-6834	765	28	v	v	NOUN
ejpam-6834	765	29	,	,	PUNCT
ejpam-6834	765	30	f	f	PROPN
ejpam-6834	765	31	}	}	PUNCT
ejpam-6834	765	32	,	,	PUNCT
ejpam-6834	765	33	pcf	pcf	PROPN
ejpam-6834	765	34	(	(	PUNCT
ejpam-6834	765	35	m	m	PROPN
ejpam-6834	765	36	,	,	PUNCT
ejpam-6834	765	37	n	n	CCONJ
ejpam-6834	765	38	)	)	PUNCT
ejpam-6834	765	39	)	)	PUNCT
ejpam-6834	765	40	is	be	AUX
ejpam-6834	765	41	an	an	DET
ejpam-6834	765	42	(	(	PUNCT
ejpam-6834	765	43	m	m	PROPN
ejpam-6834	765	44	,	,	PUNCT
ejpam-6834	765	45	n)-superhyperplithogenic	n)-superhyperplithogenic	PUNCT
ejpam-6834	765	46	set	set	VERB
ejpam-6834	765	47	on	on	ADP
ejpam-6834	765	48	y	y	PROPN
ejpam-6834	765	49	.	.	PUNCT
ejpam-6834	766	1	proof	proof	NOUN
ejpam-6834	766	2	.	.	PUNCT
ejpam-6834	767	1	for	for	ADP
ejpam-6834	767	2	each	each	DET
ejpam-6834	767	3	a′	a′	NOUN
ejpam-6834	767	4	∈	∈	PROPN
ejpam-6834	767	5	p	p	PROPN
ejpam-6834	767	6	m(y	m(y	PROPN
ejpam-6834	767	7	)	)	PUNCT
ejpam-6834	767	8	,	,	PUNCT
ejpam-6834	767	9	the	the	DET
ejpam-6834	767	10	recursive	recursive	ADJ
ejpam-6834	767	11	construction	construction	NOUN
ejpam-6834	767	12	yields	yield	NOUN
ejpam-6834	767	13	f−1	f−1	PROPN
ejpam-6834	767	14	(	(	PUNCT
ejpam-6834	767	15	m)(a	m)(a	PROPN
ejpam-6834	767	16	′	′	NUM
ejpam-6834	767	17	)	)	PUNCT
ejpam-6834	767	18	∈	∈	PROPN
ejpam-6834	767	19	p	p	PROPN
ejpam-6834	767	20	m(x	m(x	PROPN
ejpam-6834	767	21	)	)	PUNCT
ejpam-6834	767	22	.	.	PUNCT
ejpam-6834	768	1	hence	hence	ADV
ejpam-6834	768	2	˜pdf	˜pdf	NOUN
ejpam-6834	768	3	(	(	PUNCT
ejpam-6834	768	4	m	m	NOUN
ejpam-6834	768	5	,	,	PUNCT
ejpam-6834	768	6	n	n	CCONJ
ejpam-6834	768	7	)	)	PUNCT
ejpam-6834	768	8	v	v	NOUN
ejpam-6834	768	9	(	(	PUNCT
ejpam-6834	768	10	f−1	f−1	PROPN
ejpam-6834	768	11	(	(	PUNCT
ejpam-6834	768	12	m)(a	m)(a	PROPN
ejpam-6834	768	13	′	′	NUM
ejpam-6834	768	14	)	)	PUNCT
ejpam-6834	768	15	,	,	PUNCT
ejpam-6834	768	16	a	a	PRON
ejpam-6834	768	17	)	)	PUNCT
ejpam-6834	768	18	∈	∈	PROPN
ejpam-6834	768	19	p	p	NOUN
ejpam-6834	768	20	n([0	n([0	PROPN
ejpam-6834	768	21	,	,	PUNCT
ejpam-6834	768	22	1]s	1]s	NUM
ejpam-6834	768	23	)	)	PUNCT
ejpam-6834	768	24	is	be	AUX
ejpam-6834	768	25	nonempty	nonempty	ADJ
ejpam-6834	768	26	,	,	PUNCT
ejpam-6834	768	27	so	so	ADV
ejpam-6834	768	28	˜pdf	˜pdf	NOUN
ejpam-6834	768	29	(	(	PUNCT
ejpam-6834	768	30	m	m	NOUN
ejpam-6834	768	31	,	,	PUNCT
ejpam-6834	768	32	n	n	CCONJ
ejpam-6834	768	33	)	)	PUNCT
ejpam-6834	768	34	v	v	NOUN
ejpam-6834	768	35	,	,	PUNCT
ejpam-6834	768	36	f	f	PROPN
ejpam-6834	768	37	(	(	PUNCT
ejpam-6834	768	38	a′	a′	PROPN
ejpam-6834	768	39	,	,	PUNCT
ejpam-6834	768	40	a	a	PRON
ejpam-6834	768	41	)	)	PUNCT
ejpam-6834	768	42	is	be	AUX
ejpam-6834	768	43	well	well	ADV
ejpam-6834	768	44	-	-	PUNCT
ejpam-6834	768	45	defined	define	VERB
ejpam-6834	768	46	with	with	ADP
ejpam-6834	768	47	the	the	DET
ejpam-6834	768	48	required	require	VERB
ejpam-6834	768	49	codomain	codomain	NOUN
ejpam-6834	768	50	.	.	PUNCT
ejpam-6834	769	1	the	the	DET
ejpam-6834	769	2	contradiction	contradiction	NOUN
ejpam-6834	769	3	map	map	NOUN
ejpam-6834	769	4	is	be	AUX
ejpam-6834	769	5	copied	copy	VERB
ejpam-6834	769	6	verbatim	verbatim	ADJ
ejpam-6834	769	7	,	,	PUNCT
ejpam-6834	769	8	preserving	preserve	VERB
ejpam-6834	769	9	its	its	PRON
ejpam-6834	769	10	axioms	axiom	NOUN
ejpam-6834	769	11	.	.	PUNCT
ejpam-6834	770	1	theorem	theorem	NOUN
ejpam-6834	770	2	21	21	NUM
ejpam-6834	770	3	(	(	PUNCT
ejpam-6834	770	4	monotone	monotone	ADJ
ejpam-6834	770	5	scalarization	scalarization	NOUN
ejpam-6834	770	6	to	to	PART
ejpam-6834	770	7	superhyperfuzzy	superhyperfuzzy	VERB
ejpam-6834	770	8	)	)	PUNCT
ejpam-6834	770	9	.	.	PUNCT
ejpam-6834	771	1	let	let	VERB
ejpam-6834	771	2	ϕ	ϕ	NOUN
ejpam-6834	771	3	:	:	PUNCT
ejpam-6834	772	1	[	[	X
ejpam-6834	772	2	0	0	NUM
ejpam-6834	772	3	,	,	PUNCT
ejpam-6834	772	4	1]s	1]s	NUM
ejpam-6834	772	5	→	→	SYM
ejpam-6834	772	6	[	[	X
ejpam-6834	772	7	0	0	NUM
ejpam-6834	772	8	,	,	PUNCT
ejpam-6834	772	9	1	1	NUM
ejpam-6834	772	10	]	]	PUNCT
ejpam-6834	772	11	be	be	AUX
ejpam-6834	772	12	componentwise	componentwise	NOUN
ejpam-6834	772	13	nondecreasing	nondecrease	VERB
ejpam-6834	772	14	.	.	PUNCT
ejpam-6834	773	1	lift	lift	VERB
ejpam-6834	773	2	ϕ	ϕ	PROPN
ejpam-6834	773	3	levelwise	levelwise	NOUN
ejpam-6834	773	4	to	to	ADP
ejpam-6834	773	5	φ	φ	NOUN
ejpam-6834	773	6	:	:	PUNCT
ejpam-6834	773	7	p	p	X
ejpam-6834	773	8	n([0	n([0	ADJ
ejpam-6834	773	9	,	,	PUNCT
ejpam-6834	773	10	1]s	1]s	NUM
ejpam-6834	773	11	)	)	PUNCT
ejpam-6834	773	12	−→	−→	NOUN
ejpam-6834	773	13	p	p	NOUN
ejpam-6834	773	14	n([0	n([0	NOUN
ejpam-6834	773	15	,	,	PUNCT
ejpam-6834	773	16	1	1	NUM
ejpam-6834	773	17	]	]	NUM
ejpam-6834	773	18	)	)	PUNCT
ejpam-6834	773	19	,	,	PUNCT
ejpam-6834	773	20	φ	φ	PROPN
ejpam-6834	773	21	=	=	PUNCT
ejpam-6834	773	22	p	p	NOUN
ejpam-6834	773	23	n(ϕ	n(ϕ	NOUN
ejpam-6834	773	24	)	)	PUNCT
ejpam-6834	773	25	.	.	PUNCT
ejpam-6834	774	1	for	for	ADP
ejpam-6834	774	2	fixed	fix	VERB
ejpam-6834	774	3	v	v	NUM
ejpam-6834	774	4	∈	∈	PROPN
ejpam-6834	774	5	v	v	NOUN
ejpam-6834	774	6	,	,	PUNCT
ejpam-6834	774	7	a	a	DET
ejpam-6834	774	8	∈	∈	PROPN
ejpam-6834	774	9	pv	pv	NOUN
ejpam-6834	774	10	,	,	PUNCT
ejpam-6834	774	11	define	define	VERB
ejpam-6834	774	12	τv	τv	PROPN
ejpam-6834	774	13	,	,	PUNCT
ejpam-6834	774	14	a(a	a(a	PROPN
ejpam-6834	774	15	)	)	PUNCT
ejpam-6834	774	16	:	:	PUNCT
ejpam-6834	775	1	=	=	SYM
ejpam-6834	775	2	φ	φ	PROPN
ejpam-6834	775	3	(	(	PUNCT
ejpam-6834	775	4	˜pdf	˜pdf	NOUN
ejpam-6834	775	5	(	(	PUNCT
ejpam-6834	775	6	m	m	NOUN
ejpam-6834	775	7	,	,	PUNCT
ejpam-6834	775	8	n	n	CCONJ
ejpam-6834	775	9	)	)	PUNCT
ejpam-6834	775	10	v	v	NOUN
ejpam-6834	775	11	(	(	PUNCT
ejpam-6834	775	12	a	a	DET
ejpam-6834	775	13	,	,	PUNCT
ejpam-6834	775	14	a	a	NOUN
ejpam-6834	775	15	)	)	PUNCT
ejpam-6834	775	16	)	)	PUNCT
ejpam-6834	775	17	for	for	ADP
ejpam-6834	775	18	a	a	DET
ejpam-6834	775	19	∈	∈	PROPN
ejpam-6834	775	20	p	p	ADJ
ejpam-6834	775	21	m(x	m(x	PROPN
ejpam-6834	775	22	)	)	PUNCT
ejpam-6834	775	23	.	.	PUNCT
ejpam-6834	776	1	then	then	ADV
ejpam-6834	776	2	τv	τv	PROPN
ejpam-6834	776	3	,	,	PUNCT
ejpam-6834	776	4	a	a	PRON
ejpam-6834	776	5	:	:	PUNCT
ejpam-6834	776	6	p	p	PROPN
ejpam-6834	776	7	m(x	m(x	PROPN
ejpam-6834	776	8	)	)	PUNCT
ejpam-6834	776	9	→	→	SYM
ejpam-6834	777	1	p	p	X
ejpam-6834	777	2	n([0	n([0	NOUN
ejpam-6834	777	3	,	,	PUNCT
ejpam-6834	777	4	1	1	NUM
ejpam-6834	777	5	]	]	PUNCT
ejpam-6834	777	6	)	)	PUNCT
ejpam-6834	777	7	is	be	AUX
ejpam-6834	777	8	an	an	DET
ejpam-6834	777	9	(	(	PUNCT
ejpam-6834	777	10	m	m	NOUN
ejpam-6834	777	11	,	,	PUNCT
ejpam-6834	777	12	n)-superhyperfuzzy	n)-superhyperfuzzy	PUNCT
ejpam-6834	777	13	set	set	NOUN
ejpam-6834	777	14	(	(	PUNCT
ejpam-6834	777	15	parametrized	parametrize	VERB
ejpam-6834	777	16	by	by	ADP
ejpam-6834	777	17	(	(	PUNCT
ejpam-6834	777	18	v	v	NOUN
ejpam-6834	777	19	,	,	PUNCT
ejpam-6834	777	20	a	a	PRON
ejpam-6834	777	21	)	)	PUNCT
ejpam-6834	777	22	)	)	PUNCT
ejpam-6834	777	23	.	.	PUNCT
ejpam-6834	778	1	proof	proof	NOUN
ejpam-6834	778	2	.	.	PUNCT
ejpam-6834	779	1	fix	fix	VERB
ejpam-6834	779	2	a.	a.	NOUN
ejpam-6834	779	3	since	since	SCONJ
ejpam-6834	779	4	˜pdf	˜pdf	NOUN
ejpam-6834	779	5	(	(	PUNCT
ejpam-6834	779	6	m	m	NOUN
ejpam-6834	779	7	,	,	PUNCT
ejpam-6834	779	8	n	n	CCONJ
ejpam-6834	779	9	)	)	PUNCT
ejpam-6834	779	10	v	v	NOUN
ejpam-6834	779	11	(	(	PUNCT
ejpam-6834	779	12	a	a	PRON
ejpam-6834	779	13	,	,	PUNCT
ejpam-6834	779	14	a	a	PRON
ejpam-6834	779	15	)	)	PUNCT
ejpam-6834	779	16	∈	∈	PROPN
ejpam-6834	779	17	p	p	NOUN
ejpam-6834	779	18	n([0	n([0	PROPN
ejpam-6834	779	19	,	,	PUNCT
ejpam-6834	779	20	1]s	1]s	NUM
ejpam-6834	779	21	)	)	PUNCT
ejpam-6834	779	22	is	be	AUX
ejpam-6834	779	23	nonempty	nonempty	ADJ
ejpam-6834	779	24	,	,	PUNCT
ejpam-6834	779	25	applying	apply	VERB
ejpam-6834	779	26	ϕ	ϕ	DET
ejpam-6834	779	27	pointwise	pointwise	NOUN
ejpam-6834	779	28	at	at	ADP
ejpam-6834	779	29	level	level	NOUN
ejpam-6834	779	30	1	1	NUM
ejpam-6834	779	31	yields	yield	NOUN
ejpam-6834	779	32	a	a	DET
ejpam-6834	779	33	nonempty	nonempty	NOUN
ejpam-6834	779	34	subset	subset	NOUN
ejpam-6834	779	35	of	of	ADP
ejpam-6834	779	36	[	[	X
ejpam-6834	779	37	0	0	NUM
ejpam-6834	779	38	,	,	PUNCT
ejpam-6834	779	39	1	1	NUM
ejpam-6834	779	40	]	]	PUNCT
ejpam-6834	779	41	.	.	PUNCT
ejpam-6834	780	1	lifting	lift	VERB
ejpam-6834	780	2	to	to	ADP
ejpam-6834	780	3	higher	high	ADJ
ejpam-6834	780	4	levels	level	NOUN
ejpam-6834	780	5	preserves	preserve	VERB
ejpam-6834	780	6	nonemptiness	nonemptiness	NOUN
ejpam-6834	780	7	and	and	CCONJ
ejpam-6834	780	8	nesting	nesting	ADJ
ejpam-6834	780	9	,	,	PUNCT
ejpam-6834	780	10	so	so	ADV
ejpam-6834	780	11	τv	τv	PROPN
ejpam-6834	780	12	,	,	PUNCT
ejpam-6834	780	13	a(a	a(a	PROPN
ejpam-6834	780	14	)	)	PUNCT
ejpam-6834	781	1	∈	∈	PROPN
ejpam-6834	781	2	p	p	NOUN
ejpam-6834	781	3	n([0	n([0	PROPN
ejpam-6834	781	4	,	,	PUNCT
ejpam-6834	781	5	1	1	NUM
ejpam-6834	781	6	]	]	NUM
ejpam-6834	781	7	)	)	PUNCT
ejpam-6834	781	8	.	.	PUNCT
ejpam-6834	782	1	no	no	DET
ejpam-6834	782	2	further	further	ADJ
ejpam-6834	782	3	axioms	axiom	NOUN
ejpam-6834	782	4	are	be	AUX
ejpam-6834	782	5	needed	need	VERB
ejpam-6834	782	6	for	for	ADP
ejpam-6834	782	7	the	the	DET
ejpam-6834	782	8	fuzzy	fuzzy	ADJ
ejpam-6834	782	9	case	case	NOUN
ejpam-6834	782	10	;	;	PUNCT
ejpam-6834	782	11	hence	hence	ADV
ejpam-6834	782	12	τv	τv	PROPN
ejpam-6834	782	13	,	,	PUNCT
ejpam-6834	782	14	a	a	PRON
ejpam-6834	782	15	is	be	AUX
ejpam-6834	782	16	(	(	PUNCT
ejpam-6834	782	17	m	m	NOUN
ejpam-6834	782	18	,	,	PUNCT
ejpam-6834	782	19	n)-superhyperfuzzy	n)-superhyperfuzzy	X
ejpam-6834	782	20	.	.	PUNCT
ejpam-6834	783	1	t.	t.	PROPN
ejpam-6834	783	2	fujita	fujita	PROPN
ejpam-6834	783	3	,	,	PUNCT
ejpam-6834	783	4	f.smarandache	f.smarandache	NOUN
ejpam-6834	783	5	/	/	SYM
ejpam-6834	783	6	eur	eur	PROPN
ejpam-6834	783	7	.	.	PUNCT
ejpam-6834	784	1	j.	j.	PROPN
ejpam-6834	784	2	pure	pure	PROPN
ejpam-6834	784	3	appl	appl	PROPN
ejpam-6834	784	4	.	.	PROPN
ejpam-6834	784	5	math	math	PROPN
ejpam-6834	784	6	,	,	PUNCT
ejpam-6834	784	7	18	18	NUM
ejpam-6834	784	8	(	(	PUNCT
ejpam-6834	784	9	4	4	NUM
ejpam-6834	784	10	)	)	PUNCT
ejpam-6834	784	11	(	(	PUNCT
ejpam-6834	784	12	2025	2025	NUM
ejpam-6834	784	13	)	)	PUNCT
ejpam-6834	784	14	,	,	PUNCT
ejpam-6834	784	15	6834	6834	NUM
ejpam-6834	784	16	34	34	NUM
ejpam-6834	784	17	of	of	ADP
ejpam-6834	784	18	69	69	NUM
ejpam-6834	784	19	theorem	theorem	NOUN
ejpam-6834	784	20	22	22	NUM
ejpam-6834	784	21	(	(	PUNCT
ejpam-6834	784	22	contradiction	contradiction	NOUN
ejpam-6834	784	23	-	-	PUNCT
ejpam-6834	784	24	bounded	bound	VERB
ejpam-6834	784	25	selections	selection	NOUN
ejpam-6834	784	26	are	be	AUX
ejpam-6834	784	27	stable	stable	ADJ
ejpam-6834	784	28	)	)	PUNCT
ejpam-6834	784	29	.	.	PUNCT
ejpam-6834	785	1	fix	fix	VERB
ejpam-6834	785	2	v	v	NUM
ejpam-6834	785	3	∈	∈	NOUN
ejpam-6834	785	4	v	v	NOUN
ejpam-6834	785	5	and	and	CCONJ
ejpam-6834	785	6	a	a	DET
ejpam-6834	785	7	bound	bind	VERB
ejpam-6834	785	8	δ	δ	NOUN
ejpam-6834	785	9	∈	∈	PROPN
ejpam-6834	786	1	[	[	X
ejpam-6834	786	2	0	0	NUM
ejpam-6834	786	3	,	,	PUNCT
ejpam-6834	786	4	1]t	1]t	NUM
ejpam-6834	786	5	.	.	PUNCT
ejpam-6834	786	6	for	for	ADP
ejpam-6834	786	7	a	a	DET
ejpam-6834	786	8	∈	∈	PROPN
ejpam-6834	786	9	p	p	PROPN
ejpam-6834	786	10	m(x	m(x	PROPN
ejpam-6834	786	11	)	)	PUNCT
ejpam-6834	786	12	define	define	VERB
ejpam-6834	786	13	the	the	DET
ejpam-6834	786	14	δ	δ	NOUN
ejpam-6834	786	15	-	-	PUNCT
ejpam-6834	786	16	admissible	admissible	ADJ
ejpam-6834	786	17	value	value	NOUN
ejpam-6834	786	18	set	set	VERB
ejpam-6834	786	19	av	av	PROPN
ejpam-6834	786	20	,	,	PUNCT
ejpam-6834	786	21	δ(a	δ(a	PROPN
ejpam-6834	786	22	)	)	PUNCT
ejpam-6834	787	1	=	=	PRON
ejpam-6834	787	2	{	{	PUNCT
ejpam-6834	787	3	a	a	DET
ejpam-6834	787	4	∈	∈	NOUN
ejpam-6834	787	5	pv	pv	CCONJ
ejpam-6834	787	6	∣∣∣	∣∣∣	NOUN
ejpam-6834	787	7	∀b	∀b	NOUN
ejpam-6834	787	8	∈	∈	PROPN
ejpam-6834	787	9	pv	pv	NOUN
ejpam-6834	787	10	,	,	PUNCT
ejpam-6834	787	11	∥pcf	∥pcf	PROPN
ejpam-6834	787	12	(	(	PUNCT
ejpam-6834	787	13	m	m	PROPN
ejpam-6834	787	14	,	,	PUNCT
ejpam-6834	787	15	n)(a	n)(a	NUM
ejpam-6834	787	16	,	,	PUNCT
ejpam-6834	787	17	b)∥∞	b)∥∞	NUM
ejpam-6834	787	18	≤	≤	NOUN
ejpam-6834	787	19	∥δ∥∞	∥δ∥∞	NUM
ejpam-6834	787	20	}	}	PUNCT
ejpam-6834	787	21	.	.	PUNCT
ejpam-6834	788	1	then	then	ADV
ejpam-6834	788	2	for	for	ADP
ejpam-6834	788	3	any	any	PRON
ejpam-6834	788	4	δ′	δ′	NOUN
ejpam-6834	788	5	≤	≤	NUM
ejpam-6834	788	6	δ	δ	PROPN
ejpam-6834	788	7	(	(	PUNCT
ejpam-6834	788	8	componentwise	componentwise	NOUN
ejpam-6834	788	9	)	)	PUNCT
ejpam-6834	788	10	one	one	NOUN
ejpam-6834	788	11	has	have	VERB
ejpam-6834	788	12	av	av	PROPN
ejpam-6834	788	13	,	,	PUNCT
ejpam-6834	788	14	δ′(a	δ′(a	NOUN
ejpam-6834	788	15	)	)	PUNCT
ejpam-6834	788	16	⊆	⊆	NUM
ejpam-6834	788	17	av	av	PROPN
ejpam-6834	788	18	,	,	PUNCT
ejpam-6834	788	19	δ(a	δ(a	PROPN
ejpam-6834	788	20	)	)	PUNCT
ejpam-6834	788	21	.	.	PUNCT
ejpam-6834	789	1	proof	proof	NOUN
ejpam-6834	789	2	.	.	PUNCT
ejpam-6834	790	1	if	if	SCONJ
ejpam-6834	790	2	a	a	DET
ejpam-6834	790	3	∈	∈	PROPN
ejpam-6834	790	4	av	av	NOUN
ejpam-6834	790	5	,	,	PUNCT
ejpam-6834	790	6	δ′(a	δ′(a	PROPN
ejpam-6834	790	7	)	)	PUNCT
ejpam-6834	790	8	,	,	PUNCT
ejpam-6834	790	9	then	then	ADV
ejpam-6834	790	10	∥pcf	∥pcf	PROPN
ejpam-6834	790	11	(	(	PUNCT
ejpam-6834	790	12	m	m	PROPN
ejpam-6834	790	13	,	,	PUNCT
ejpam-6834	790	14	n)(a	n)(a	NUM
ejpam-6834	790	15	,	,	PUNCT
ejpam-6834	790	16	b)∥∞	b)∥∞	NOUN
ejpam-6834	790	17	≤	≤	X
ejpam-6834	790	18	∥δ′∥∞	∥δ′∥∞	ADV
ejpam-6834	790	19	for	for	ADP
ejpam-6834	790	20	all	all	DET
ejpam-6834	790	21	b	b	PROPN
ejpam-6834	790	22	∈	∈	NOUN
ejpam-6834	790	23	pv	pv	NOUN
ejpam-6834	790	24	.	.	PUNCT
ejpam-6834	791	1	since	since	SCONJ
ejpam-6834	791	2	∥δ′∥∞	∥δ′∥∞	PROPN
ejpam-6834	791	3	≤	≤	NOUN
ejpam-6834	791	4	∥δ∥∞	∥δ∥∞	NUM
ejpam-6834	791	5	,	,	PUNCT
ejpam-6834	791	6	the	the	DET
ejpam-6834	791	7	same	same	ADJ
ejpam-6834	791	8	a	a	DET
ejpam-6834	791	9	satisfies	satisfie	NOUN
ejpam-6834	791	10	the	the	DET
ejpam-6834	791	11	bound	bind	VERB
ejpam-6834	791	12	for	for	ADP
ejpam-6834	791	13	δ	δ	PROPN
ejpam-6834	791	14	,	,	PUNCT
ejpam-6834	791	15	hence	hence	ADV
ejpam-6834	791	16	a	a	DET
ejpam-6834	791	17	∈	∈	PROPN
ejpam-6834	791	18	av	av	NOUN
ejpam-6834	791	19	,	,	PUNCT
ejpam-6834	791	20	δ(a	δ(a	PROPN
ejpam-6834	791	21	)	)	PUNCT
ejpam-6834	791	22	.	.	PUNCT
ejpam-6834	792	1	3.2	3.2	NUM
ejpam-6834	792	2	.	.	PUNCT
ejpam-6834	793	1	(	(	PUNCT
ejpam-6834	793	2	h	h	NOUN
ejpam-6834	793	3	,	,	PUNCT
ejpam-6834	793	4	k)-ary	k)-ary	X
ejpam-6834	793	5	(	(	PUNCT
ejpam-6834	793	6	m	m	PROPN
ejpam-6834	793	7	,	,	PUNCT
ejpam-6834	793	8	n)-superhyperuncertain	n)-superhyperuncertain	ADV
ejpam-6834	793	9	set	set	VERB
ejpam-6834	793	10	we	we	PRON
ejpam-6834	793	11	provide	provide	VERB
ejpam-6834	793	12	an	an	DET
ejpam-6834	793	13	explanation	explanation	NOUN
ejpam-6834	793	14	of	of	ADP
ejpam-6834	793	15	the	the	DET
ejpam-6834	793	16	(	(	PUNCT
ejpam-6834	793	17	h	h	NOUN
ejpam-6834	793	18	,	,	PUNCT
ejpam-6834	793	19	k)-ary	k)-ary	X
ejpam-6834	793	20	(	(	PUNCT
ejpam-6834	793	21	m	m	PROPN
ejpam-6834	793	22	,	,	PUNCT
ejpam-6834	793	23	n)-superhyperuncertain	n)-superhyperuncertain	ADV
ejpam-6834	793	24	set	set	VERB
ejpam-6834	793	25	below	below	ADV
ejpam-6834	793	26	.	.	PUNCT
ejpam-6834	794	1	3.2.1	3.2.1	NUM
ejpam-6834	794	2	.	.	PUNCT
ejpam-6834	795	1	(	(	PUNCT
ejpam-6834	795	2	h	h	NOUN
ejpam-6834	795	3	,	,	PUNCT
ejpam-6834	795	4	k)-ary	k)-ary	X
ejpam-6834	795	5	(	(	PUNCT
ejpam-6834	795	6	m	m	PROPN
ejpam-6834	795	7	,	,	PUNCT
ejpam-6834	795	8	n)-superhyperfuzzy	n)-superhyperfuzzy	PUNCT
ejpam-6834	795	9	set	set	VERB
ejpam-6834	795	10	a	a	DET
ejpam-6834	795	11	(	(	PUNCT
ejpam-6834	795	12	h	h	NOUN
ejpam-6834	795	13	,	,	PUNCT
ejpam-6834	795	14	k)-ary	k)-ary	X
ejpam-6834	795	15	(	(	PUNCT
ejpam-6834	795	16	m	m	PROPN
ejpam-6834	795	17	,	,	PUNCT
ejpam-6834	795	18	n)-superhyperfuzzy	n)-superhyperfuzzy	PUNCT
ejpam-6834	795	19	set	set	NOUN
ejpam-6834	795	20	generalizes	generalize	VERB
ejpam-6834	795	21	the	the	DET
ejpam-6834	795	22	(	(	PUNCT
ejpam-6834	795	23	m	m	NOUN
ejpam-6834	795	24	,	,	PUNCT
ejpam-6834	795	25	n)-superhyperfuzzy	n)-superhyperfuzzy	PUNCT
ejpam-6834	795	26	notion	notion	NOUN
ejpam-6834	795	27	by	by	ADP
ejpam-6834	795	28	accepting	accept	VERB
ejpam-6834	795	29	h	h	NOUN
ejpam-6834	795	30	inputs	input	NOUN
ejpam-6834	795	31	and	and	CCONJ
ejpam-6834	795	32	producing	produce	VERB
ejpam-6834	795	33	k	k	PROPN
ejpam-6834	795	34	outputs	output	NOUN
ejpam-6834	795	35	,	,	PUNCT
ejpam-6834	795	36	where	where	SCONJ
ejpam-6834	795	37	the	the	DET
ejpam-6834	795	38	inputs	input	NOUN
ejpam-6834	795	39	are	be	AUX
ejpam-6834	795	40	m	m	NOUN
ejpam-6834	795	41	-	-	PUNCT
ejpam-6834	795	42	level	level	NOUN
ejpam-6834	795	43	nested	nest	VERB
ejpam-6834	795	44	subsets	subset	NOUN
ejpam-6834	795	45	of	of	ADP
ejpam-6834	795	46	a	a	DET
ejpam-6834	795	47	base	base	NOUN
ejpam-6834	795	48	set	set	NOUN
ejpam-6834	795	49	and	and	CCONJ
ejpam-6834	795	50	the	the	DET
ejpam-6834	795	51	outputs	output	NOUN
ejpam-6834	795	52	are	be	AUX
ejpam-6834	795	53	n	n	CCONJ
ejpam-6834	795	54	-	-	PUNCT
ejpam-6834	795	55	level	level	NOUN
ejpam-6834	795	56	nested	nest	VERB
ejpam-6834	795	57	fuzzy	fuzzy	ADJ
ejpam-6834	795	58	–	–	PUNCT
ejpam-6834	795	59	degree	degree	NOUN
ejpam-6834	795	60	sets	set	NOUN
ejpam-6834	795	61	.	.	PUNCT
ejpam-6834	796	1	definition	definition	NOUN
ejpam-6834	796	2	22	22	NUM
ejpam-6834	796	3	(	(	PUNCT
ejpam-6834	796	4	(	(	PUNCT
ejpam-6834	796	5	h	h	NOUN
ejpam-6834	796	6	,	,	PUNCT
ejpam-6834	796	7	k)-ary	k)-ary	X
ejpam-6834	796	8	(	(	PUNCT
ejpam-6834	796	9	m	m	NOUN
ejpam-6834	796	10	,	,	PUNCT
ejpam-6834	796	11	n)-superhyperfuzzy	n)-superhyperfuzzy	X
ejpam-6834	796	12	set	set	NOUN
ejpam-6834	796	13	)	)	PUNCT
ejpam-6834	796	14	.	.	PUNCT
ejpam-6834	797	1	let	let	VERB
ejpam-6834	797	2	x	x	PRON
ejpam-6834	797	3	be	be	AUX
ejpam-6834	797	4	a	a	DET
ejpam-6834	797	5	nonempty	nonempty	ADV
ejpam-6834	797	6	set	set	VERB
ejpam-6834	797	7	and	and	CCONJ
ejpam-6834	797	8	let	let	VERB
ejpam-6834	797	9	m	m	PRON
ejpam-6834	797	10	,	,	PUNCT
ejpam-6834	797	11	n	n	CCONJ
ejpam-6834	797	12	,	,	PUNCT
ejpam-6834	797	13	h	h	NOUN
ejpam-6834	797	14	,	,	PUNCT
ejpam-6834	797	15	k	k	PROPN
ejpam-6834	797	16	∈	∈	PROPN
ejpam-6834	797	17	n	n	X
ejpam-6834	797	18	with	with	ADP
ejpam-6834	797	19	m	m	PROPN
ejpam-6834	797	20	,	,	PUNCT
ejpam-6834	797	21	n	n	CCONJ
ejpam-6834	797	22	,	,	PUNCT
ejpam-6834	797	23	h	h	NOUN
ejpam-6834	797	24	,	,	PUNCT
ejpam-6834	797	25	k	k	PROPN
ejpam-6834	797	26	≥	≥	NUM
ejpam-6834	797	27	1	1	X
ejpam-6834	797	28	.	.	PUNCT
ejpam-6834	797	29	define	define	VERB
ejpam-6834	797	30	p0(x	p0(x	NOUN
ejpam-6834	797	31	)	)	PUNCT
ejpam-6834	797	32	=	=	SYM
ejpam-6834	797	33	x	x	NOUN
ejpam-6834	797	34	,	,	PUNCT
ejpam-6834	797	35	pr(x	pr(x	NOUN
ejpam-6834	797	36	)	)	PUNCT
ejpam-6834	798	1	=	=	SYM
ejpam-6834	798	2	p	p	X
ejpam-6834	798	3	(	(	PUNCT
ejpam-6834	798	4	pr−1(x	pr−1(x	NOUN
ejpam-6834	798	5	)	)	PUNCT
ejpam-6834	798	6	)	)	PUNCT
ejpam-6834	799	1	(	(	PUNCT
ejpam-6834	799	2	r	r	NOUN
ejpam-6834	799	3	≥	≥	NOUN
ejpam-6834	799	4	1	1	NUM
ejpam-6834	799	5	)	)	PUNCT
ejpam-6834	799	6	,	,	PUNCT
ejpam-6834	799	7	and	and	CCONJ
ejpam-6834	799	8	analogously	analogously	ADV
ejpam-6834	799	9	pr([0	pr([0	VERB
ejpam-6834	799	10	,	,	PUNCT
ejpam-6834	799	11	1	1	NUM
ejpam-6834	799	12	]	]	PUNCT
ejpam-6834	799	13	)	)	PUNCT
ejpam-6834	799	14	for	for	ADP
ejpam-6834	799	15	the	the	DET
ejpam-6834	799	16	unit	unit	NOUN
ejpam-6834	799	17	interval	interval	NOUN
ejpam-6834	799	18	.	.	PUNCT
ejpam-6834	800	1	an	an	DET
ejpam-6834	800	2	(	(	PUNCT
ejpam-6834	800	3	h	h	NOUN
ejpam-6834	800	4	,	,	PUNCT
ejpam-6834	800	5	k)-ary	k)-ary	X
ejpam-6834	800	6	(	(	PUNCT
ejpam-6834	800	7	m	m	PROPN
ejpam-6834	800	8	,	,	PUNCT
ejpam-6834	800	9	n)-superhyperfuzzy	n)-superhyperfuzzy	PUNCT
ejpam-6834	800	10	set	set	VERB
ejpam-6834	800	11	on	on	ADP
ejpam-6834	800	12	x	x	SYM
ejpam-6834	800	13	is	be	AUX
ejpam-6834	800	14	a	a	DET
ejpam-6834	800	15	mapping	mapping	NOUN
ejpam-6834	800	16	µ	µ	X
ejpam-6834	800	17	(	(	PUNCT
ejpam-6834	800	18	m	m	PROPN
ejpam-6834	800	19	,	,	PUNCT
ejpam-6834	800	20	n	n	CCONJ
ejpam-6834	800	21	)	)	PUNCT
ejpam-6834	800	22	(	(	PUNCT
ejpam-6834	800	23	h	h	NOUN
ejpam-6834	800	24	,	,	PUNCT
ejpam-6834	800	25	k	k	NOUN
ejpam-6834	800	26	)	)	PUNCT
ejpam-6834	800	27	:	:	PUNCT
ejpam-6834	800	28	(	(	PUNCT
ejpam-6834	800	29	pm(x	pm(x	X
ejpam-6834	800	30	)	)	PUNCT
ejpam-6834	800	31	)	)	PUNCT
ejpam-6834	801	1	h	h	NOUN
ejpam-6834	801	2	−→	−→	NOUN
ejpam-6834	801	3	(	(	PUNCT
ejpam-6834	801	4	pn([0	pn([0	NOUN
ejpam-6834	801	5	,	,	PUNCT
ejpam-6834	801	6	1	1	NUM
ejpam-6834	801	7	]	]	NUM
ejpam-6834	801	8	)	)	PUNCT
ejpam-6834	801	9	)	)	PUNCT
ejpam-6834	802	1	k	k	NOUN
ejpam-6834	802	2	,	,	PUNCT
ejpam-6834	802	3	which	which	PRON
ejpam-6834	802	4	to	to	ADP
ejpam-6834	802	5	each	each	DET
ejpam-6834	802	6	input	input	NOUN
ejpam-6834	802	7	tuple	tuple	NOUN
ejpam-6834	802	8	a	a	PRON
ejpam-6834	802	9	=	=	X
ejpam-6834	802	10	(	(	PUNCT
ejpam-6834	802	11	a1	a1	PROPN
ejpam-6834	802	12	,	,	PUNCT
ejpam-6834	802	13	.	.	PUNCT
ejpam-6834	802	14	.	.	PUNCT
ejpam-6834	802	15	.	.	PUNCT
ejpam-6834	803	1	,	,	PUNCT
ejpam-6834	803	2	ah	ah	INTJ
ejpam-6834	803	3	)	)	PUNCT
ejpam-6834	803	4	∈	∈	PROPN
ejpam-6834	803	5	(	(	PUNCT
ejpam-6834	803	6	pm(x))h	pm(x))h	PRON
ejpam-6834	803	7	assigns	assign	VERB
ejpam-6834	803	8	an	an	DET
ejpam-6834	803	9	output	output	NOUN
ejpam-6834	803	10	tuple	tuple	NOUN
ejpam-6834	803	11	µ	µ	X
ejpam-6834	803	12	(	(	PUNCT
ejpam-6834	803	13	m	m	PROPN
ejpam-6834	803	14	,	,	PUNCT
ejpam-6834	803	15	n	n	CCONJ
ejpam-6834	803	16	)	)	PUNCT
ejpam-6834	803	17	(	(	PUNCT
ejpam-6834	803	18	h	h	NOUN
ejpam-6834	803	19	,	,	PUNCT
ejpam-6834	803	20	k	k	NOUN
ejpam-6834	803	21	)	)	PUNCT
ejpam-6834	803	22	(	(	PUNCT
ejpam-6834	803	23	a	a	X
ejpam-6834	803	24	)	)	PUNCT
ejpam-6834	803	25	=	=	SYM
ejpam-6834	803	26	(	(	PUNCT
ejpam-6834	803	27	b1	b1	NOUN
ejpam-6834	803	28	,	,	PUNCT
ejpam-6834	803	29	.	.	PUNCT
ejpam-6834	803	30	.	.	PUNCT
ejpam-6834	803	31	.	.	PUNCT
ejpam-6834	804	1	,	,	PUNCT
ejpam-6834	804	2	bk	bk	VERB
ejpam-6834	804	3	)	)	PUNCT
ejpam-6834	804	4	with	with	ADP
ejpam-6834	804	5	bj	bj	ADP
ejpam-6834	804	6	∈	∈	NOUN
ejpam-6834	804	7	pn([0	pn([0	NOUN
ejpam-6834	804	8	,	,	PUNCT
ejpam-6834	804	9	1	1	NUM
ejpam-6834	804	10	]	]	PUNCT
ejpam-6834	804	11	)	)	PUNCT
ejpam-6834	804	12	for	for	ADP
ejpam-6834	804	13	every	every	DET
ejpam-6834	804	14	1	1	NUM
ejpam-6834	804	15	≤	≤	NUM
ejpam-6834	804	16	j	j	PROPN
ejpam-6834	804	17	≤	≤	PROPN
ejpam-6834	804	18	k.	k.	PROPN
ejpam-6834	805	1	we	we	PRON
ejpam-6834	805	2	additionally	additionally	ADV
ejpam-6834	805	3	require	require	VERB
ejpam-6834	805	4	nonemptiness	nonemptiness	NOUN
ejpam-6834	805	5	at	at	ADP
ejpam-6834	805	6	the	the	DET
ejpam-6834	805	7	outer	outer	ADJ
ejpam-6834	805	8	level	level	NOUN
ejpam-6834	805	9	:	:	PUNCT
ejpam-6834	805	10	for	for	ADP
ejpam-6834	805	11	each	each	DET
ejpam-6834	805	12	a	a	PRON
ejpam-6834	805	13	and	and	CCONJ
ejpam-6834	805	14	each	each	DET
ejpam-6834	805	15	j	j	NOUN
ejpam-6834	805	16	,	,	PUNCT
ejpam-6834	805	17	bj	bj	ADP
ejpam-6834	805	18	̸=	̸=	PROPN
ejpam-6834	805	19	∅.	∅.	ADP
ejpam-6834	805	20	equivalently	equivalently	ADV
ejpam-6834	805	21	,	,	PUNCT
ejpam-6834	805	22	writing	write	VERB
ejpam-6834	805	23	the	the	DET
ejpam-6834	805	24	coordinate	coordinate	NOUN
ejpam-6834	805	25	maps	map	NOUN
ejpam-6834	805	26	as	as	ADP
ejpam-6834	805	27	µ	µ	X
ejpam-6834	805	28	(	(	PUNCT
ejpam-6834	805	29	m	m	PROPN
ejpam-6834	805	30	,	,	PUNCT
ejpam-6834	805	31	n	n	CCONJ
ejpam-6834	805	32	)	)	PUNCT
ejpam-6834	805	33	j	j	NOUN
ejpam-6834	805	34	:	:	PUNCT
ejpam-6834	805	35	(	(	PUNCT
ejpam-6834	805	36	pm(x))h	pm(x))h	X
ejpam-6834	805	37	→	→	SYM
ejpam-6834	805	38	pn([0	pn([0	NOUN
ejpam-6834	805	39	,	,	PUNCT
ejpam-6834	805	40	1	1	NUM
ejpam-6834	805	41	]	]	NUM
ejpam-6834	805	42	)	)	PUNCT
ejpam-6834	805	43	,	,	PUNCT
ejpam-6834	805	44	we	we	PRON
ejpam-6834	805	45	demand	demand	VERB
ejpam-6834	805	46	µ	µ	PRON
ejpam-6834	805	47	(	(	PUNCT
ejpam-6834	805	48	m	m	PROPN
ejpam-6834	805	49	,	,	PUNCT
ejpam-6834	805	50	n	n	CCONJ
ejpam-6834	805	51	)	)	PUNCT
ejpam-6834	805	52	j	j	PROPN
ejpam-6834	805	53	(	(	PUNCT
ejpam-6834	805	54	a	a	NOUN
ejpam-6834	805	55	)	)	PUNCT
ejpam-6834	805	56	∈	∈	NOUN
ejpam-6834	805	57	pn([0	pn([0	NOUN
ejpam-6834	805	58	,	,	PUNCT
ejpam-6834	805	59	1	1	NUM
ejpam-6834	805	60	]	]	PUNCT
ejpam-6834	805	61	)	)	PUNCT
ejpam-6834	805	62	\	\	NOUN
ejpam-6834	805	63	{	{	PUNCT
ejpam-6834	805	64	∅	∅	NOUN
ejpam-6834	805	65	}	}	PUNCT
ejpam-6834	805	66	for	for	ADP
ejpam-6834	805	67	all	all	DET
ejpam-6834	805	68	a	a	PRON
ejpam-6834	805	69	and	and	CCONJ
ejpam-6834	805	70	all	all	DET
ejpam-6834	805	71	j.	j.	PROPN
ejpam-6834	805	72	example	example	PROPN
ejpam-6834	805	73	21	21	NUM
ejpam-6834	805	74	(	(	PUNCT
ejpam-6834	805	75	smart	smart	ADJ
ejpam-6834	805	76	building	building	NOUN
ejpam-6834	805	77	comfort	comfort	NOUN
ejpam-6834	805	78	control	control	NOUN
ejpam-6834	805	79	as	as	ADP
ejpam-6834	805	80	a	a	DET
ejpam-6834	805	81	(	(	PUNCT
ejpam-6834	805	82	2	2	NUM
ejpam-6834	805	83	,	,	PUNCT
ejpam-6834	805	84	2)-ary	2)-ary	NUM
ejpam-6834	805	85	(	(	PUNCT
ejpam-6834	805	86	1	1	NUM
ejpam-6834	805	87	,	,	PUNCT
ejpam-6834	805	88	1)-superhyperfuzzy	1)-superhyperfuzzy	NUM
ejpam-6834	805	89	set	set	NOUN
ejpam-6834	805	90	)	)	PUNCT
ejpam-6834	805	91	.	.	PUNCT
ejpam-6834	806	1	let	let	VERB
ejpam-6834	806	2	x	x	PUNCT
ejpam-6834	806	3	=	=	PRON
ejpam-6834	806	4	{	{	PUNCT
ejpam-6834	806	5	room1,room2,room3	room1,room2,room3	NOUN
ejpam-6834	806	6	}	}	PUNCT
ejpam-6834	806	7	and	and	CCONJ
ejpam-6834	806	8	fix	fix	VERB
ejpam-6834	806	9	m	m	NOUN
ejpam-6834	806	10	=	=	SYM
ejpam-6834	806	11	n	n	PROPN
ejpam-6834	806	12	=	=	SYM
ejpam-6834	806	13	1	1	NUM
ejpam-6834	806	14	,	,	PUNCT
ejpam-6834	806	15	h	h	NOUN
ejpam-6834	807	1	=	=	SYM
ejpam-6834	807	2	k	k	NOUN
ejpam-6834	807	3	=	=	SYM
ejpam-6834	807	4	2	2	X
ejpam-6834	807	5	.	.	PUNCT
ejpam-6834	807	6	thus	thus	ADV
ejpam-6834	807	7	p1(x	p1(x	NOUN
ejpam-6834	807	8	)	)	PUNCT
ejpam-6834	807	9	=	=	SYM
ejpam-6834	807	10	p(x	p(x	PROPN
ejpam-6834	807	11	)	)	PUNCT
ejpam-6834	807	12	and	and	CCONJ
ejpam-6834	807	13	p1([0	p1([0	NOUN
ejpam-6834	807	14	,	,	PUNCT
ejpam-6834	807	15	1	1	NUM
ejpam-6834	807	16	]	]	PUNCT
ejpam-6834	807	17	)	)	PUNCT
ejpam-6834	808	1	=	=	SYM
ejpam-6834	808	2	p([0	p([0	PROPN
ejpam-6834	808	3	,	,	PUNCT
ejpam-6834	808	4	1	1	NUM
ejpam-6834	808	5	]	]	NUM
ejpam-6834	808	6	)	)	PUNCT
ejpam-6834	808	7	,	,	PUNCT
ejpam-6834	808	8	so	so	CCONJ
ejpam-6834	808	9	the	the	DET
ejpam-6834	808	10	domain	domain	NOUN
ejpam-6834	808	11	is	be	AUX
ejpam-6834	808	12	d	d	NOUN
ejpam-6834	808	13	=	=	SYM
ejpam-6834	808	14	p(x	p(x	PROPN
ejpam-6834	808	15	)	)	PUNCT
ejpam-6834	808	16	×	×	NOUN
ejpam-6834	808	17	p(x	p(x	PROPN
ejpam-6834	808	18	)	)	PUNCT
ejpam-6834	808	19	and	and	CCONJ
ejpam-6834	808	20	the	the	DET
ejpam-6834	808	21	codomain	codomain	NOUN
ejpam-6834	808	22	is	be	AUX
ejpam-6834	808	23	c	c	NOUN
ejpam-6834	808	24	=	=	SYM
ejpam-6834	808	25	p([0	p([0	PROPN
ejpam-6834	808	26	,	,	PUNCT
ejpam-6834	808	27	1	1	NUM
ejpam-6834	808	28	]	]	PUNCT
ejpam-6834	808	29	)	)	PUNCT
ejpam-6834	808	30	×	×	NOUN
ejpam-6834	808	31	p([0	p([0	NOUN
ejpam-6834	808	32	,	,	PUNCT
ejpam-6834	808	33	1	1	NUM
ejpam-6834	808	34	]	]	NUM
ejpam-6834	808	35	)	)	PUNCT
ejpam-6834	808	36	.	.	PUNCT
ejpam-6834	809	1	interpret	interpret	VERB
ejpam-6834	809	2	an	an	DET
ejpam-6834	809	3	input	input	NOUN
ejpam-6834	809	4	(	(	PUNCT
ejpam-6834	809	5	a1	a1	NOUN
ejpam-6834	809	6	,	,	PUNCT
ejpam-6834	809	7	a2	a2	NOUN
ejpam-6834	809	8	)	)	PUNCT
ejpam-6834	809	9	∈	∈	PROPN
ejpam-6834	810	1	d	d	NOUN
ejpam-6834	810	2	as	as	SCONJ
ejpam-6834	810	3	:	:	PUNCT
ejpam-6834	810	4	a1	a1	NOUN
ejpam-6834	810	5	is	be	AUX
ejpam-6834	810	6	the	the	DET
ejpam-6834	810	7	set	set	NOUN
ejpam-6834	810	8	of	of	ADP
ejpam-6834	810	9	occupied	occupied	ADJ
ejpam-6834	810	10	rooms	room	NOUN
ejpam-6834	810	11	,	,	PUNCT
ejpam-6834	810	12	and	and	CCONJ
ejpam-6834	810	13	a2	a2	VERB
ejpam-6834	810	14	the	the	DET
ejpam-6834	810	15	set	set	NOUN
ejpam-6834	810	16	of	of	ADP
ejpam-6834	810	17	rooms	room	NOUN
ejpam-6834	810	18	with	with	ADP
ejpam-6834	810	19	windows	window	NOUN
ejpam-6834	810	20	open	open	ADJ
ejpam-6834	810	21	.	.	PUNCT
ejpam-6834	811	1	define	define	VERB
ejpam-6834	811	2	the	the	DET
ejpam-6834	811	3	following	follow	VERB
ejpam-6834	811	4	concrete	concrete	ADJ
ejpam-6834	811	5	mapping	mapping	NOUN
ejpam-6834	811	6	:	:	PUNCT
ejpam-6834	811	7	µ	µ	X
ejpam-6834	811	8	(	(	PUNCT
ejpam-6834	811	9	1,1	1,1	NUM
ejpam-6834	811	10	)	)	PUNCT
ejpam-6834	811	11	(	(	PUNCT
ejpam-6834	811	12	2,2)(a1	2,2)(a1	NUM
ejpam-6834	811	13	,	,	PUNCT
ejpam-6834	811	14	a2	a2	NOUN
ejpam-6834	811	15	)	)	PUNCT
ejpam-6834	811	16	=	=	SYM
ejpam-6834	811	17	(	(	PUNCT
ejpam-6834	811	18	bcomfort(a1	bcomfort(a1	X
ejpam-6834	811	19	,	,	PUNCT
ejpam-6834	811	20	a2	a2	PROPN
ejpam-6834	811	21	)	)	PUNCT
ejpam-6834	811	22	,	,	PUNCT
ejpam-6834	811	23	benergy(a1	benergy(a1	NOUN
ejpam-6834	811	24	,	,	PUNCT
ejpam-6834	811	25	a2	a2	PROPN
ejpam-6834	811	26	)	)	PUNCT
ejpam-6834	811	27	)	)	PUNCT
ejpam-6834	811	28	,	,	PUNCT
ejpam-6834	811	29	t.	t.	PROPN
ejpam-6834	811	30	fujita	fujita	PROPN
ejpam-6834	811	31	,	,	PUNCT
ejpam-6834	811	32	f.smarandache	f.smarandache	NOUN
ejpam-6834	811	33	/	/	SYM
ejpam-6834	811	34	eur	eur	PROPN
ejpam-6834	811	35	.	.	PUNCT
ejpam-6834	812	1	j.	j.	PROPN
ejpam-6834	812	2	pure	pure	PROPN
ejpam-6834	812	3	appl	appl	PROPN
ejpam-6834	812	4	.	.	PROPN
ejpam-6834	812	5	math	math	PROPN
ejpam-6834	812	6	,	,	PUNCT
ejpam-6834	812	7	18	18	NUM
ejpam-6834	812	8	(	(	PUNCT
ejpam-6834	812	9	4	4	NUM
ejpam-6834	812	10	)	)	PUNCT
ejpam-6834	812	11	(	(	PUNCT
ejpam-6834	812	12	2025	2025	NUM
ejpam-6834	812	13	)	)	PUNCT
ejpam-6834	812	14	,	,	PUNCT
ejpam-6834	812	15	6834	6834	NUM
ejpam-6834	812	16	35	35	NUM
ejpam-6834	812	17	of	of	ADP
ejpam-6834	812	18	69	69	NUM
ejpam-6834	812	19	where	where	SCONJ
ejpam-6834	812	20	,	,	PUNCT
ejpam-6834	812	21	with	with	ADP
ejpam-6834	812	22	the	the	DET
ejpam-6834	812	23	shorthand	shorthand	NOUN
ejpam-6834	812	24	θ(a1	θ(a1	NOUN
ejpam-6834	812	25	,	,	PUNCT
ejpam-6834	812	26	a2	a2	PROPN
ejpam-6834	812	27	)	)	PUNCT
ejpam-6834	812	28	:	:	PUNCT
ejpam-6834	812	29	=	=	PUNCT
ejpam-6834	812	30	|a1	|a1	NOUN
ejpam-6834	812	31	∩a2|	∩a2|	PROPN
ejpam-6834	812	32	max{1	max{1	PROPN
ejpam-6834	812	33	,	,	PUNCT
ejpam-6834	812	34	|a1|	|a1|	X
ejpam-6834	812	35	}	}	PUNCT
ejpam-6834	812	36	,	,	PUNCT
ejpam-6834	812	37	ω(a2	ω(a2	ADJ
ejpam-6834	812	38	)	)	PUNCT
ejpam-6834	812	39	:	:	PUNCT
ejpam-6834	812	40	=	=	PUNCT
ejpam-6834	812	41	|a2|	|a2|	NOUN
ejpam-6834	812	42	|x|	|x|	PROPN
ejpam-6834	812	43	,	,	PUNCT
ejpam-6834	812	44	we	we	PRON
ejpam-6834	812	45	set	set	VERB
ejpam-6834	812	46	bcomfort(a1	bcomfort(a1	PROPN
ejpam-6834	812	47	,	,	PUNCT
ejpam-6834	812	48	a2	a2	PROPN
ejpam-6834	812	49	)	)	PUNCT
ejpam-6834	812	50	=	=	PUNCT
ejpam-6834	813	1	[	[	PUNCT
ejpam-6834	813	2	0.60	0.60	NUM
ejpam-6834	813	3	+	+	NUM
ejpam-6834	813	4	0.30	0.30	NUM
ejpam-6834	813	5	θ(a1	θ(a1	NOUN
ejpam-6834	813	6	,	,	PUNCT
ejpam-6834	813	7	a2	a2	PROPN
ejpam-6834	813	8	)	)	PUNCT
ejpam-6834	813	9	,	,	PUNCT
ejpam-6834	813	10	0.70	0.70	NUM
ejpam-6834	813	11	+	+	CCONJ
ejpam-6834	813	12	0.25	0.25	NUM
ejpam-6834	813	13	θ(a1	θ(a1	NOUN
ejpam-6834	813	14	,	,	PUNCT
ejpam-6834	813	15	a2	a2	PROPN
ejpam-6834	813	16	)	)	PUNCT
ejpam-6834	813	17	]	]	PUNCT
ejpam-6834	814	1	⊂	⊂	PROPN
ejpam-6834	815	1	[	[	X
ejpam-6834	815	2	0	0	NUM
ejpam-6834	815	3	,	,	PUNCT
ejpam-6834	815	4	1	1	NUM
ejpam-6834	815	5	]	]	PUNCT
ejpam-6834	815	6	,	,	PUNCT
ejpam-6834	815	7	benergy(a1	benergy(a1	NOUN
ejpam-6834	815	8	,	,	PUNCT
ejpam-6834	815	9	a2	a2	PROPN
ejpam-6834	815	10	)	)	PUNCT
ejpam-6834	815	11	=	=	PUNCT
ejpam-6834	816	1	[	[	PUNCT
ejpam-6834	816	2	0.20	0.20	NUM
ejpam-6834	816	3	+	+	CCONJ
ejpam-6834	816	4	0.40ω(a2	0.40ω(a2	NOUN
ejpam-6834	816	5	)	)	PUNCT
ejpam-6834	816	6	,	,	PUNCT
ejpam-6834	816	7	0.30	0.30	NUM
ejpam-6834	816	8	+	+	NOUN
ejpam-6834	816	9	0.45ω(a2	0.45ω(a2	NUM
ejpam-6834	816	10	)	)	PUNCT
ejpam-6834	816	11	]	]	PUNCT
ejpam-6834	817	1	⊂	⊂	X
ejpam-6834	818	1	[	[	X
ejpam-6834	818	2	0	0	NUM
ejpam-6834	818	3	,	,	PUNCT
ejpam-6834	818	4	1	1	NUM
ejpam-6834	818	5	]	]	PUNCT
ejpam-6834	818	6	.	.	PUNCT
ejpam-6834	819	1	thus	thus	ADV
ejpam-6834	819	2	,	,	PUNCT
ejpam-6834	819	3	if	if	SCONJ
ejpam-6834	819	4	a1	a1	NOUN
ejpam-6834	819	5	=	=	SYM
ejpam-6834	819	6	{	{	PUNCT
ejpam-6834	819	7	room1,room2	room1,room2	NOUN
ejpam-6834	819	8	}	}	PUNCT
ejpam-6834	819	9	and	and	CCONJ
ejpam-6834	819	10	a2	a2	PROPN
ejpam-6834	819	11	=	=	SYM
ejpam-6834	819	12	{	{	PUNCT
ejpam-6834	819	13	room2	room2	PROPN
ejpam-6834	819	14	}	}	PUNCT
ejpam-6834	819	15	,	,	PUNCT
ejpam-6834	819	16	then	then	ADV
ejpam-6834	819	17	θ	θ	PROPN
ejpam-6834	819	18	=	=	SYM
ejpam-6834	819	19	1/2	1/2	NUM
ejpam-6834	819	20	and	and	CCONJ
ejpam-6834	819	21	ω	ω	NUM
ejpam-6834	819	22	=	=	SYM
ejpam-6834	819	23	1/3	1/3	NUM
ejpam-6834	819	24	,	,	PUNCT
ejpam-6834	819	25	hence	hence	ADV
ejpam-6834	819	26	bcomfort	bcomfort	NOUN
ejpam-6834	819	27	=	=	PUNCT
ejpam-6834	820	1	[	[	X
ejpam-6834	820	2	0.60	0.60	NUM
ejpam-6834	821	1	+	+	CCONJ
ejpam-6834	821	2	0.15	0.15	NUM
ejpam-6834	821	3	,	,	PUNCT
ejpam-6834	821	4	0.70	0.70	NUM
ejpam-6834	822	1	+	+	NOUN
ejpam-6834	822	2	0.125	0.125	NUM
ejpam-6834	822	3	]	]	X
ejpam-6834	823	1	=	=	PUNCT
ejpam-6834	824	1	[	[	X
ejpam-6834	824	2	0.75	0.75	NUM
ejpam-6834	824	3	,	,	PUNCT
ejpam-6834	824	4	0.825	0.825	NUM
ejpam-6834	824	5	]	]	PUNCT
ejpam-6834	824	6	,	,	PUNCT
ejpam-6834	824	7	benergy	benergy	NOUN
ejpam-6834	824	8	=	=	PUNCT
ejpam-6834	825	1	[	[	X
ejpam-6834	825	2	0.20	0.20	NUM
ejpam-6834	825	3	+	+	NOUN
ejpam-6834	825	4	0.1333	0.1333	NUM
ejpam-6834	825	5	,	,	PUNCT
ejpam-6834	825	6	0.30	0.30	NUM
ejpam-6834	826	1	+	+	NOUN
ejpam-6834	826	2	0.15	0.15	NUM
ejpam-6834	826	3	]	]	X
ejpam-6834	827	1	=	=	PUNCT
ejpam-6834	828	1	[	[	X
ejpam-6834	828	2	0.3333	0.3333	NUM
ejpam-6834	828	3	,	,	PUNCT
ejpam-6834	828	4	0.45	0.45	NUM
ejpam-6834	828	5	]	]	PUNCT
ejpam-6834	828	6	,	,	PUNCT
ejpam-6834	828	7	so	so	SCONJ
ejpam-6834	828	8	one	one	PRON
ejpam-6834	828	9	may	may	AUX
ejpam-6834	828	10	choose	choose	VERB
ejpam-6834	828	11	,	,	PUNCT
ejpam-6834	828	12	for	for	ADP
ejpam-6834	828	13	instance	instance	NOUN
ejpam-6834	828	14	,	,	PUNCT
ejpam-6834	828	15	µ	µ	X
ejpam-6834	828	16	(	(	PUNCT
ejpam-6834	828	17	1,1	1,1	NUM
ejpam-6834	828	18	)	)	PUNCT
ejpam-6834	828	19	(	(	PUNCT
ejpam-6834	828	20	2,2)(a1	2,2)(a1	NUM
ejpam-6834	828	21	,	,	PUNCT
ejpam-6834	828	22	a2	a2	NOUN
ejpam-6834	828	23	)	)	PUNCT
ejpam-6834	828	24	=	=	PUNCT
ejpam-6834	829	1	(	(	PUNCT
ejpam-6834	829	2	[	[	X
ejpam-6834	829	3	0.75	0.75	NUM
ejpam-6834	829	4	,	,	PUNCT
ejpam-6834	829	5	0.825	0.825	NUM
ejpam-6834	829	6	]	]	PUNCT
ejpam-6834	829	7	,	,	PUNCT
ejpam-6834	829	8	[	[	X
ejpam-6834	829	9	0.3333	0.3333	NUM
ejpam-6834	829	10	,	,	PUNCT
ejpam-6834	829	11	0.45	0.45	NUM
ejpam-6834	829	12	]	]	PUNCT
ejpam-6834	829	13	)	)	PUNCT
ejpam-6834	829	14	∈	∈	PROPN
ejpam-6834	829	15	c.	c.	NOUN
ejpam-6834	830	1	this	this	PRON
ejpam-6834	830	2	implements	implement	VERB
ejpam-6834	830	3	a	a	DET
ejpam-6834	830	4	concrete	concrete	NOUN
ejpam-6834	830	5	(	(	PUNCT
ejpam-6834	830	6	2	2	NUM
ejpam-6834	830	7	,	,	PUNCT
ejpam-6834	830	8	2)-ary	2)-ary	NUM
ejpam-6834	830	9	(	(	PUNCT
ejpam-6834	830	10	1	1	NUM
ejpam-6834	830	11	,	,	PUNCT
ejpam-6834	830	12	1)-superhyperfuzzy	1)-superhyperfuzzy	NUM
ejpam-6834	830	13	set	set	VERB
ejpam-6834	830	14	with	with	ADP
ejpam-6834	830	15	explicitly	explicitly	ADV
ejpam-6834	830	16	computed	compute	VERB
ejpam-6834	830	17	fuzzy	fuzzy	ADJ
ejpam-6834	830	18	outputs	output	NOUN
ejpam-6834	830	19	.	.	PUNCT
ejpam-6834	831	1	example	example	NOUN
ejpam-6834	831	2	22	22	NUM
ejpam-6834	831	3	(	(	PUNCT
ejpam-6834	831	4	two	two	NUM
ejpam-6834	831	5	–	–	PUNCT
ejpam-6834	831	6	symptom	symptom	NOUN
ejpam-6834	831	7	,	,	PUNCT
ejpam-6834	831	8	two	two	NUM
ejpam-6834	831	9	–	–	PUNCT
ejpam-6834	831	10	disease	disease	NOUN
ejpam-6834	831	11	risk	risk	NOUN
ejpam-6834	831	12	assessment	assessment	NOUN
ejpam-6834	831	13	)	)	PUNCT
ejpam-6834	831	14	.	.	PUNCT
ejpam-6834	832	1	let	let	VERB
ejpam-6834	832	2	x	x	PUNCT
ejpam-6834	832	3	=	=	PRON
ejpam-6834	832	4	{	{	PUNCT
ejpam-6834	832	5	fever	fever	NOUN
ejpam-6834	832	6	,	,	PUNCT
ejpam-6834	832	7	cough	cough	NOUN
ejpam-6834	832	8	,	,	PUNCT
ejpam-6834	832	9	fatigue	fatigue	NOUN
ejpam-6834	832	10	}	}	PUNCT
ejpam-6834	832	11	,	,	PUNCT
ejpam-6834	832	12	again	again	ADV
ejpam-6834	832	13	with	with	ADP
ejpam-6834	832	14	m	m	PROPN
ejpam-6834	832	15	=	=	SYM
ejpam-6834	832	16	n	n	NOUN
ejpam-6834	832	17	=	=	SYM
ejpam-6834	832	18	1	1	NUM
ejpam-6834	832	19	and	and	CCONJ
ejpam-6834	832	20	h	h	NOUN
ejpam-6834	832	21	=	=	SYM
ejpam-6834	832	22	k	k	NOUN
ejpam-6834	832	23	=	=	SYM
ejpam-6834	832	24	2	2	X
ejpam-6834	832	25	.	.	PUNCT
ejpam-6834	832	26	given	give	VERB
ejpam-6834	832	27	two	two	NUM
ejpam-6834	832	28	symptom	symptom	NOUN
ejpam-6834	832	29	–	–	PUNCT
ejpam-6834	832	30	subsets	subset	NOUN
ejpam-6834	832	31	(	(	PUNCT
ejpam-6834	832	32	a1	a1	NOUN
ejpam-6834	832	33	,	,	PUNCT
ejpam-6834	832	34	a2	a2	PROPN
ejpam-6834	832	35	)	)	PUNCT
ejpam-6834	832	36	∈	∈	PROPN
ejpam-6834	832	37	p(x	p(x	PROPN
ejpam-6834	832	38	)	)	PUNCT
ejpam-6834	832	39	×	×	NOUN
ejpam-6834	832	40	p(x	p(x	PROPN
ejpam-6834	832	41	)	)	PUNCT
ejpam-6834	832	42	,	,	PUNCT
ejpam-6834	832	43	define	define	VERB
ejpam-6834	832	44	µ	µ	X
ejpam-6834	832	45	(	(	PUNCT
ejpam-6834	832	46	1,1	1,1	NUM
ejpam-6834	832	47	)	)	PUNCT
ejpam-6834	832	48	(	(	PUNCT
ejpam-6834	832	49	2,2)(a1	2,2)(a1	NUM
ejpam-6834	832	50	,	,	PUNCT
ejpam-6834	832	51	a2	a2	NOUN
ejpam-6834	832	52	)	)	PUNCT
ejpam-6834	832	53	=	=	SYM
ejpam-6834	832	54	(	(	PUNCT
ejpam-6834	832	55	bdisa(a1	bdisa(a1	NOUN
ejpam-6834	832	56	)	)	PUNCT
ejpam-6834	832	57	,	,	PUNCT
ejpam-6834	832	58	bdisb(a2	bdisb(a2	NOUN
ejpam-6834	832	59	)	)	PUNCT
ejpam-6834	832	60	)	)	PUNCT
ejpam-6834	832	61	,	,	PUNCT
ejpam-6834	832	62	where	where	SCONJ
ejpam-6834	832	63	bdisa(a1	bdisa(a1	NOUN
ejpam-6834	832	64	)	)	PUNCT
ejpam-6834	832	65	=	=	PUNCT
ejpam-6834	833	1	[	[	PUNCT
ejpam-6834	833	2	0.30	0.30	NUM
ejpam-6834	833	3	+	+	NUM
ejpam-6834	833	4	0.20	0.20	NUM
ejpam-6834	833	5	|a1|	|a1|	NOUN
ejpam-6834	833	6	3	3	NUM
ejpam-6834	833	7	,	,	PUNCT
ejpam-6834	833	8	0.50	0.50	NUM
ejpam-6834	833	9	+	+	NUM
ejpam-6834	833	10	0.30	0.30	NUM
ejpam-6834	833	11	|a1|	|a1|	NOUN
ejpam-6834	833	12	3	3	NUM
ejpam-6834	833	13	]	]	PUNCT
ejpam-6834	833	14	,	,	PUNCT
ejpam-6834	833	15	bdisb(a2	bdisb(a2	NOUN
ejpam-6834	833	16	)	)	PUNCT
ejpam-6834	833	17	=	=	PRON
ejpam-6834	833	18	{	{	PUNCT
ejpam-6834	833	19	0.25	0.25	NUM
ejpam-6834	834	1	+	+	NUM
ejpam-6834	834	2	0.15	0.15	NUM
ejpam-6834	834	3	|a2|	|a2|	NOUN
ejpam-6834	834	4	3	3	NUM
ejpam-6834	834	5	,	,	PUNCT
ejpam-6834	834	6	0.35	0.35	NUM
ejpam-6834	834	7	+	+	NOUN
ejpam-6834	834	8	0.20	0.20	NUM
ejpam-6834	834	9	|a2|	|a2|	NOUN
ejpam-6834	834	10	3	3	NUM
ejpam-6834	834	11	}	}	PUNCT
ejpam-6834	834	12	.	.	PUNCT
ejpam-6834	835	1	for	for	ADP
ejpam-6834	835	2	instance	instance	NOUN
ejpam-6834	835	3	,	,	PUNCT
ejpam-6834	835	4	µ	µ	X
ejpam-6834	835	5	(	(	PUNCT
ejpam-6834	835	6	1,1	1,1	NUM
ejpam-6834	835	7	)	)	PUNCT
ejpam-6834	835	8	(	(	PUNCT
ejpam-6834	835	9	2,2	2,2	NUM
ejpam-6834	835	10	)	)	PUNCT
ejpam-6834	835	11	(	(	PUNCT
ejpam-6834	835	12	{	{	PUNCT
ejpam-6834	835	13	fever	fever	NOUN
ejpam-6834	835	14	,	,	PUNCT
ejpam-6834	835	15	cough	cough	NOUN
ejpam-6834	835	16	}	}	PUNCT
ejpam-6834	835	17	,	,	PUNCT
ejpam-6834	835	18	{	{	PUNCT
ejpam-6834	835	19	fatigue	fatigue	NOUN
ejpam-6834	835	20	}	}	PUNCT
ejpam-6834	835	21	)	)	PUNCT
ejpam-6834	836	1	=	=	PUNCT
ejpam-6834	837	1	(	(	PUNCT
ejpam-6834	837	2	[	[	X
ejpam-6834	837	3	0.30	0.30	NUM
ejpam-6834	837	4	+	+	NOUN
ejpam-6834	837	5	0.20	0.20	NUM
ejpam-6834	837	6	·	·	SYM
ejpam-6834	837	7	23	23	NUM
ejpam-6834	837	8	,	,	PUNCT
ejpam-6834	837	9	0.50	0.50	NUM
ejpam-6834	837	10	+	+	NOUN
ejpam-6834	837	11	0.30	0.30	NUM
ejpam-6834	837	12	·	·	SYM
ejpam-6834	837	13	23	23	NUM
ejpam-6834	837	14	]	]	PUNCT
ejpam-6834	837	15	,	,	PUNCT
ejpam-6834	837	16	{	{	PUNCT
ejpam-6834	837	17	0.25	0.25	NUM
ejpam-6834	837	18	+	+	NUM
ejpam-6834	837	19	0.15	0.15	NUM
ejpam-6834	837	20	·	·	SYM
ejpam-6834	837	21	1	1	NUM
ejpam-6834	837	22	3	3	NUM
ejpam-6834	837	23	,	,	PUNCT
ejpam-6834	837	24	0.35	0.35	NUM
ejpam-6834	837	25	+	+	CCONJ
ejpam-6834	837	26	0.20	0.20	NUM
ejpam-6834	837	27	·	·	SYM
ejpam-6834	837	28	1	1	NUM
ejpam-6834	837	29	3	3	NUM
ejpam-6834	837	30	}	}	PUNCT
ejpam-6834	837	31	)	)	PUNCT
ejpam-6834	837	32	=	=	PUNCT
ejpam-6834	838	1	(	(	PUNCT
ejpam-6834	838	2	[	[	X
ejpam-6834	838	3	0.4333	0.4333	NUM
ejpam-6834	838	4	,	,	PUNCT
ejpam-6834	838	5	0.70	0.70	NUM
ejpam-6834	838	6	]	]	X
ejpam-6834	838	7	,	,	PUNCT
ejpam-6834	838	8	{	{	PUNCT
ejpam-6834	838	9	0.30	0.30	NUM
ejpam-6834	838	10	,	,	PUNCT
ejpam-6834	838	11	0.4166	0.4166	NUM
ejpam-6834	838	12	}	}	PUNCT
ejpam-6834	838	13	)	)	PUNCT
ejpam-6834	838	14	.	.	PUNCT
ejpam-6834	839	1	theorem	theorem	VERB
ejpam-6834	839	2	23	23	NUM
ejpam-6834	839	3	.	.	PUNCT
ejpam-6834	840	1	if	if	SCONJ
ejpam-6834	840	2	h	h	NOUN
ejpam-6834	840	3	=	=	SYM
ejpam-6834	840	4	k	k	NOUN
ejpam-6834	840	5	=	=	SYM
ejpam-6834	840	6	1	1	NUM
ejpam-6834	840	7	,	,	PUNCT
ejpam-6834	840	8	then	then	ADV
ejpam-6834	840	9	any	any	DET
ejpam-6834	840	10	(	(	PUNCT
ejpam-6834	840	11	h	h	NOUN
ejpam-6834	840	12	,	,	PUNCT
ejpam-6834	840	13	k)-ary	k)-ary	X
ejpam-6834	840	14	(	(	PUNCT
ejpam-6834	840	15	m	m	PROPN
ejpam-6834	840	16	,	,	PUNCT
ejpam-6834	840	17	n)-superhyperfuzzy	n)-superhyperfuzzy	PUNCT
ejpam-6834	840	18	set	set	NOUN
ejpam-6834	840	19	reduces	reduce	VERB
ejpam-6834	840	20	to	to	ADP
ejpam-6834	840	21	an	an	DET
ejpam-6834	840	22	ordinary	ordinary	ADJ
ejpam-6834	840	23	(	(	PUNCT
ejpam-6834	840	24	m	m	NOUN
ejpam-6834	840	25	,	,	PUNCT
ejpam-6834	840	26	n)-superhyperfuzzy	n)-superhyperfuzzy	PUNCT
ejpam-6834	840	27	set	set	NOUN
ejpam-6834	840	28	.	.	PUNCT
ejpam-6834	841	1	proof	proof	NOUN
ejpam-6834	841	2	.	.	PUNCT
ejpam-6834	842	1	let	let	VERB
ejpam-6834	842	2	µ	µ	X
ejpam-6834	842	3	(	(	PUNCT
ejpam-6834	842	4	m	m	PROPN
ejpam-6834	842	5	,	,	PUNCT
ejpam-6834	842	6	n	n	CCONJ
ejpam-6834	842	7	)	)	PUNCT
ejpam-6834	842	8	(	(	PUNCT
ejpam-6834	842	9	1,1	1,1	NUM
ejpam-6834	842	10	)	)	PUNCT
ejpam-6834	842	11	:	:	PUNCT
ejpam-6834	842	12	(	(	PUNCT
ejpam-6834	842	13	pm(x))1	pm(x))1	PROPN
ejpam-6834	842	14	→	→	SYM
ejpam-6834	842	15	(	(	PUNCT
ejpam-6834	842	16	pn([0	pn([0	NOUN
ejpam-6834	842	17	,	,	PUNCT
ejpam-6834	842	18	1]))1	1]))1	NUM
ejpam-6834	842	19	be	be	AUX
ejpam-6834	842	20	given	give	VERB
ejpam-6834	842	21	.	.	PUNCT
ejpam-6834	843	1	define	define	VERB
ejpam-6834	843	2	the	the	DET
ejpam-6834	843	3	canonical	canonical	ADJ
ejpam-6834	843	4	bijections	bijection	NOUN
ejpam-6834	843	5	ϕh	ϕh	NOUN
ejpam-6834	843	6	:	:	PUNCT
ejpam-6834	843	7	(	(	PUNCT
ejpam-6834	843	8	pm(x))1	pm(x))1	NOUN
ejpam-6834	843	9	−→	−→	NOUN
ejpam-6834	843	10	pm(x	pm(x	PUNCT
ejpam-6834	843	11	)	)	PUNCT
ejpam-6834	843	12	,	,	PUNCT
ejpam-6834	843	13	ϕh((a	ϕh((a	PROPN
ejpam-6834	843	14	)	)	PUNCT
ejpam-6834	843	15	)	)	PUNCT
ejpam-6834	844	1	=	=	PUNCT
ejpam-6834	844	2	a	a	X
ejpam-6834	844	3	,	,	PUNCT
ejpam-6834	844	4	ϕk	ϕk	INTJ
ejpam-6834	844	5	:	:	PUNCT
ejpam-6834	844	6	(	(	PUNCT
ejpam-6834	844	7	pn([0	pn([0	NOUN
ejpam-6834	844	8	,	,	PUNCT
ejpam-6834	844	9	1]))1	1]))1	NUM
ejpam-6834	844	10	−→	−→	NOUN
ejpam-6834	844	11	pn([0	pn([0	NOUN
ejpam-6834	844	12	,	,	PUNCT
ejpam-6834	844	13	1	1	NUM
ejpam-6834	844	14	]	]	NUM
ejpam-6834	844	15	)	)	PUNCT
ejpam-6834	844	16	,	,	PUNCT
ejpam-6834	844	17	ϕk((b	ϕk((b	NOUN
ejpam-6834	844	18	)	)	PUNCT
ejpam-6834	844	19	)	)	PUNCT
ejpam-6834	844	20	=	=	PUNCT
ejpam-6834	845	1	b.	b.	PROPN
ejpam-6834	845	2	both	both	CCONJ
ejpam-6834	845	3	ϕh	ϕh	PROPN
ejpam-6834	846	1	and	and	CCONJ
ejpam-6834	846	2	ϕk	ϕk	ADV
ejpam-6834	846	3	are	be	AUX
ejpam-6834	846	4	bijective	bijective	ADJ
ejpam-6834	846	5	with	with	ADP
ejpam-6834	846	6	inverses	inverses	PROPN
ejpam-6834	846	7	a	a	DET
ejpam-6834	846	8	7→	7→	PROPN
ejpam-6834	846	9	(	(	PUNCT
ejpam-6834	846	10	a	a	NOUN
ejpam-6834	846	11	)	)	PUNCT
ejpam-6834	846	12	and	and	CCONJ
ejpam-6834	846	13	b	b	X
ejpam-6834	846	14	7→	7→	NUM
ejpam-6834	846	15	(	(	PUNCT
ejpam-6834	846	16	b	b	NOUN
ejpam-6834	846	17	)	)	PUNCT
ejpam-6834	846	18	,	,	PUNCT
ejpam-6834	846	19	respectively	respectively	ADV
ejpam-6834	846	20	.	.	PUNCT
ejpam-6834	847	1	define	define	VERB
ejpam-6834	847	2	µ̃	µ̃	PROPN
ejpam-6834	847	3	:	:	PUNCT
ejpam-6834	847	4	=	=	SYM
ejpam-6834	847	5	ϕk	ϕk	ADP
ejpam-6834	847	6	◦	◦	NOUN
ejpam-6834	847	7	µ	µ	X
ejpam-6834	847	8	(	(	PUNCT
ejpam-6834	847	9	m	m	PROPN
ejpam-6834	847	10	,	,	PUNCT
ejpam-6834	847	11	n	n	CCONJ
ejpam-6834	847	12	)	)	PUNCT
ejpam-6834	847	13	(	(	PUNCT
ejpam-6834	847	14	1,1	1,1	X
ejpam-6834	847	15	)	)	PUNCT
ejpam-6834	847	16	◦	◦	NOUN
ejpam-6834	847	17	ϕ−1	ϕ−1	NOUN
ejpam-6834	847	18	h	h	NOUN
ejpam-6834	847	19	:	:	PUNCT
ejpam-6834	847	20	pm(x	pm(x	X
ejpam-6834	847	21	)	)	PUNCT
ejpam-6834	847	22	−→	−→	NOUN
ejpam-6834	847	23	pn([0	pn([0	NOUN
ejpam-6834	847	24	,	,	PUNCT
ejpam-6834	847	25	1	1	NUM
ejpam-6834	847	26	]	]	PUNCT
ejpam-6834	847	27	)	)	PUNCT
ejpam-6834	847	28	.	.	PUNCT
ejpam-6834	848	1	t.	t.	PROPN
ejpam-6834	848	2	fujita	fujita	PROPN
ejpam-6834	848	3	,	,	PUNCT
ejpam-6834	848	4	f.smarandache	f.smarandache	NOUN
ejpam-6834	848	5	/	/	SYM
ejpam-6834	848	6	eur	eur	PROPN
ejpam-6834	848	7	.	.	PUNCT
ejpam-6834	849	1	j.	j.	PROPN
ejpam-6834	849	2	pure	pure	PROPN
ejpam-6834	849	3	appl	appl	PROPN
ejpam-6834	849	4	.	.	PROPN
ejpam-6834	849	5	math	math	PROPN
ejpam-6834	849	6	,	,	PUNCT
ejpam-6834	849	7	18	18	NUM
ejpam-6834	849	8	(	(	PUNCT
ejpam-6834	849	9	4	4	NUM
ejpam-6834	849	10	)	)	PUNCT
ejpam-6834	849	11	(	(	PUNCT
ejpam-6834	849	12	2025	2025	NUM
ejpam-6834	849	13	)	)	PUNCT
ejpam-6834	849	14	,	,	PUNCT
ejpam-6834	849	15	6834	6834	NUM
ejpam-6834	849	16	36	36	NUM
ejpam-6834	849	17	of	of	ADP
ejpam-6834	849	18	69	69	NUM
ejpam-6834	849	19	for	for	ADP
ejpam-6834	849	20	any	any	DET
ejpam-6834	849	21	a	a	DET
ejpam-6834	849	22	∈	∈	NOUN
ejpam-6834	849	23	pm(x	pm(x	PUNCT
ejpam-6834	849	24	)	)	PUNCT
ejpam-6834	850	1	we	we	PRON
ejpam-6834	850	2	have	have	VERB
ejpam-6834	850	3	ϕ−1	ϕ−1	PROPN
ejpam-6834	850	4	h	h	NOUN
ejpam-6834	850	5	(	(	PUNCT
ejpam-6834	850	6	a	a	NOUN
ejpam-6834	850	7	)	)	PUNCT
ejpam-6834	850	8	=	=	SYM
ejpam-6834	850	9	(	(	PUNCT
ejpam-6834	850	10	a	a	NOUN
ejpam-6834	850	11	)	)	PUNCT
ejpam-6834	850	12	and	and	CCONJ
ejpam-6834	850	13	thus	thus	ADV
ejpam-6834	850	14	µ̃(a	µ̃(a	VERB
ejpam-6834	850	15	)	)	PUNCT
ejpam-6834	850	16	=	=	SYM
ejpam-6834	851	1	ϕk	ϕk	PROPN
ejpam-6834	851	2	(	(	PUNCT
ejpam-6834	851	3	µ	µ	X
ejpam-6834	851	4	(	(	PUNCT
ejpam-6834	851	5	m	m	PROPN
ejpam-6834	851	6	,	,	PUNCT
ejpam-6834	851	7	n	n	CCONJ
ejpam-6834	851	8	)	)	PUNCT
ejpam-6834	851	9	(	(	PUNCT
ejpam-6834	851	10	1,1	1,1	NUM
ejpam-6834	851	11	)	)	PUNCT
ejpam-6834	851	12	(	(	PUNCT
ejpam-6834	851	13	(	(	PUNCT
ejpam-6834	851	14	a	a	NOUN
ejpam-6834	851	15	)	)	PUNCT
ejpam-6834	851	16	)	)	PUNCT
ejpam-6834	851	17	)	)	PUNCT
ejpam-6834	852	1	=	=	SYM
ejpam-6834	852	2	b	b	NOUN
ejpam-6834	852	3	,	,	PUNCT
ejpam-6834	852	4	where	where	SCONJ
ejpam-6834	852	5	µ	µ	X
ejpam-6834	852	6	(	(	PUNCT
ejpam-6834	852	7	m	m	PROPN
ejpam-6834	852	8	,	,	PUNCT
ejpam-6834	852	9	n	n	CCONJ
ejpam-6834	852	10	)	)	PUNCT
ejpam-6834	852	11	(	(	PUNCT
ejpam-6834	852	12	1,1	1,1	NUM
ejpam-6834	852	13	)	)	PUNCT
ejpam-6834	852	14	(	(	PUNCT
ejpam-6834	852	15	(	(	PUNCT
ejpam-6834	852	16	a	a	NOUN
ejpam-6834	852	17	)	)	PUNCT
ejpam-6834	852	18	)	)	PUNCT
ejpam-6834	852	19	=	=	PUNCT
ejpam-6834	853	1	(	(	PUNCT
ejpam-6834	853	2	b	b	NOUN
ejpam-6834	853	3	)	)	PUNCT
ejpam-6834	853	4	with	with	ADP
ejpam-6834	853	5	b	b	PROPN
ejpam-6834	853	6	∈	∈	PROPN
ejpam-6834	853	7	pn([0	pn([0	NOUN
ejpam-6834	853	8	,	,	PUNCT
ejpam-6834	853	9	1	1	NUM
ejpam-6834	853	10	]	]	PUNCT
ejpam-6834	853	11	)	)	PUNCT
ejpam-6834	853	12	nonempty	nonempty	ADV
ejpam-6834	853	13	by	by	ADP
ejpam-6834	853	14	definition	definition	NOUN
ejpam-6834	853	15	of	of	ADP
ejpam-6834	853	16	an	an	DET
ejpam-6834	853	17	(	(	PUNCT
ejpam-6834	853	18	h	h	NOUN
ejpam-6834	853	19	,	,	PUNCT
ejpam-6834	853	20	k)-ary	k)-ary	X
ejpam-6834	853	21	(	(	PUNCT
ejpam-6834	853	22	m	m	NOUN
ejpam-6834	853	23	,	,	PUNCT
ejpam-6834	853	24	n)-superhyperfuzzy	n)-superhyperfuzzy	PUNCT
ejpam-6834	853	25	set	set	NOUN
ejpam-6834	853	26	.	.	PUNCT
ejpam-6834	854	1	hence	hence	ADV
ejpam-6834	854	2	µ̃	µ̃	PROPN
ejpam-6834	854	3	is	be	AUX
ejpam-6834	854	4	a	a	DET
ejpam-6834	854	5	well	well	ADV
ejpam-6834	854	6	-	-	PUNCT
ejpam-6834	854	7	defined	define	VERB
ejpam-6834	854	8	map	map	NOUN
ejpam-6834	854	9	pm(x	pm(x	PUNCT
ejpam-6834	854	10	)	)	PUNCT
ejpam-6834	854	11	→	→	SYM
ejpam-6834	854	12	pn([0	pn([0	NOUN
ejpam-6834	854	13	,	,	PUNCT
ejpam-6834	854	14	1	1	NUM
ejpam-6834	854	15	]	]	PUNCT
ejpam-6834	854	16	)	)	PUNCT
ejpam-6834	854	17	with	with	ADP
ejpam-6834	854	18	nonempty	nonempty	ADJ
ejpam-6834	854	19	outer	outer	ADJ
ejpam-6834	854	20	values	value	NOUN
ejpam-6834	854	21	;	;	PUNCT
ejpam-6834	854	22	that	that	PRON
ejpam-6834	854	23	is	is	ADV
ejpam-6834	854	24	,	,	PUNCT
ejpam-6834	854	25	an	an	DET
ejpam-6834	854	26	ordinary	ordinary	ADJ
ejpam-6834	854	27	(	(	PUNCT
ejpam-6834	854	28	m	m	NOUN
ejpam-6834	854	29	,	,	PUNCT
ejpam-6834	854	30	n)-superhyperfuzzy	n)-superhyperfuzzy	PUNCT
ejpam-6834	854	31	set	set	NOUN
ejpam-6834	854	32	.	.	PUNCT
ejpam-6834	855	1	theorem	theorem	VERB
ejpam-6834	855	2	24	24	NUM
ejpam-6834	855	3	(	(	PUNCT
ejpam-6834	855	4	fixing	fix	VERB
ejpam-6834	855	5	inputs	input	NOUN
ejpam-6834	855	6	)	)	PUNCT
ejpam-6834	855	7	.	.	PUNCT
ejpam-6834	856	1	fix	fix	NOUN
ejpam-6834	856	2	indices	indice	VERB
ejpam-6834	856	3	1	1	NUM
ejpam-6834	856	4	≤	≤	NUM
ejpam-6834	856	5	i1	i1	X
ejpam-6834	856	6	<	<	X
ejpam-6834	856	7	·	·	PUNCT
ejpam-6834	856	8	·	·	PUNCT
ejpam-6834	856	9	·	·	PUNCT
ejpam-6834	857	1	<	<	X
ejpam-6834	857	2	ir	ir	PROPN
ejpam-6834	857	3	≤	≤	NUM
ejpam-6834	857	4	h	h	NOUN
ejpam-6834	857	5	and	and	CCONJ
ejpam-6834	857	6	elements	element	NOUN
ejpam-6834	857	7	aij	aij	PROPN
ejpam-6834	857	8	∈	∈	PROPN
ejpam-6834	857	9	pm(x	pm(x	PUNCT
ejpam-6834	857	10	)	)	PUNCT
ejpam-6834	857	11	.	.	PUNCT
ejpam-6834	858	1	define	define	VERB
ejpam-6834	858	2	µfix	µfix	NOUN
ejpam-6834	858	3	:	:	PUNCT
ejpam-6834	858	4	(	(	PUNCT
ejpam-6834	858	5	pm(x))h−r	pm(x))h−r	X
ejpam-6834	858	6	→	→	SYM
ejpam-6834	858	7	(	(	PUNCT
ejpam-6834	858	8	pn([0	pn([0	NOUN
ejpam-6834	858	9	,	,	PUNCT
ejpam-6834	858	10	1]))k	1]))k	NUM
ejpam-6834	858	11	by	by	ADP
ejpam-6834	858	12	inserting	insert	VERB
ejpam-6834	858	13	the	the	DET
ejpam-6834	858	14	fixed	fix	VERB
ejpam-6834	858	15	aij	aij	NOUN
ejpam-6834	858	16	in	in	ADP
ejpam-6834	858	17	the	the	DET
ejpam-6834	858	18	corresponding	corresponding	ADJ
ejpam-6834	858	19	coordinates	coordinate	NOUN
ejpam-6834	858	20	and	and	CCONJ
ejpam-6834	858	21	applying	apply	VERB
ejpam-6834	858	22	µ	µ	PROPN
ejpam-6834	858	23	(	(	PUNCT
ejpam-6834	858	24	m	m	PROPN
ejpam-6834	858	25	,	,	PUNCT
ejpam-6834	858	26	n	n	CCONJ
ejpam-6834	858	27	)	)	PUNCT
ejpam-6834	858	28	(	(	PUNCT
ejpam-6834	858	29	h	h	NOUN
ejpam-6834	858	30	,	,	PUNCT
ejpam-6834	858	31	k	k	NOUN
ejpam-6834	858	32	)	)	PUNCT
ejpam-6834	858	33	.	.	PUNCT
ejpam-6834	859	1	then	then	ADV
ejpam-6834	859	2	µfix	µfix	NOUN
ejpam-6834	859	3	is	be	AUX
ejpam-6834	859	4	an	an	DET
ejpam-6834	859	5	(	(	PUNCT
ejpam-6834	859	6	h	h	NOUN
ejpam-6834	859	7	−	−	NOUN
ejpam-6834	859	8	r	r	NOUN
ejpam-6834	859	9	,	,	PUNCT
ejpam-6834	859	10	k)-ary	k)-ary	X
ejpam-6834	859	11	(	(	PUNCT
ejpam-6834	859	12	m	m	PROPN
ejpam-6834	859	13	,	,	PUNCT
ejpam-6834	859	14	n)superhyperfuzzy	n)superhyperfuzzy	ADV
ejpam-6834	859	15	set	set	VERB
ejpam-6834	859	16	.	.	PUNCT
ejpam-6834	860	1	proof	proof	NOUN
ejpam-6834	860	2	.	.	PUNCT
ejpam-6834	861	1	write	write	VERB
ejpam-6834	861	2	afree	afree	ADJ
ejpam-6834	861	3	=	=	SYM
ejpam-6834	861	4	(	(	PUNCT
ejpam-6834	861	5	aℓ)ℓ∈ifree	aℓ)ℓ∈ifree	NUM
ejpam-6834	861	6	∈	∈	PROPN
ejpam-6834	861	7	(	(	PUNCT
ejpam-6834	861	8	pm(x))h−r	pm(x))h−r	PROPN
ejpam-6834	861	9	,	,	PUNCT
ejpam-6834	861	10	where	where	SCONJ
ejpam-6834	861	11	i	i	PRON
ejpam-6834	861	12	free	free	VERB
ejpam-6834	861	13	=	=	PUNCT
ejpam-6834	861	14	{	{	PUNCT
ejpam-6834	861	15	1	1	NUM
ejpam-6834	861	16	,	,	PUNCT
ejpam-6834	861	17	.	.	PUNCT
ejpam-6834	861	18	.	.	PUNCT
ejpam-6834	861	19	.	.	PUNCT
ejpam-6834	862	1	,	,	PUNCT
ejpam-6834	862	2	h	h	NOUN
ejpam-6834	862	3	}	}	PUNCT
ejpam-6834	862	4	\	\	NOUN
ejpam-6834	862	5	{	{	PUNCT
ejpam-6834	862	6	i1	i1	PROPN
ejpam-6834	862	7	,	,	PUNCT
ejpam-6834	862	8	.	.	PUNCT
ejpam-6834	862	9	.	.	PUNCT
ejpam-6834	863	1	.	.	PUNCT
ejpam-6834	864	1	,	,	PUNCT
ejpam-6834	864	2	ir	ir	AUX
ejpam-6834	864	3	}	}	PUNCT
ejpam-6834	864	4	(	(	PUNCT
ejpam-6834	864	5	ordered	order	VERB
ejpam-6834	864	6	increasingly	increasingly	ADV
ejpam-6834	864	7	)	)	PUNCT
ejpam-6834	864	8	.	.	PUNCT
ejpam-6834	865	1	define	define	VERB
ejpam-6834	865	2	the	the	DET
ejpam-6834	865	3	insertion	insertion	NOUN
ejpam-6834	865	4	operator	operator	NOUN
ejpam-6834	865	5	ι	ι	X
ejpam-6834	865	6	:	:	PUNCT
ejpam-6834	865	7	(	(	PUNCT
ejpam-6834	865	8	pm(x))h−r	pm(x))h−r	X
ejpam-6834	865	9	−→	−→	NOUN
ejpam-6834	865	10	(	(	PUNCT
ejpam-6834	865	11	pm(x))h	pm(x))h	ADJ
ejpam-6834	865	12	,	,	PUNCT
ejpam-6834	865	13	ι(afree	ι(afree	NOUN
ejpam-6834	865	14	)	)	PUNCT
ejpam-6834	866	1	=	=	SYM
ejpam-6834	866	2	b	b	X
ejpam-6834	866	3	=	=	SYM
ejpam-6834	866	4	(	(	PUNCT
ejpam-6834	866	5	b1	b1	PROPN
ejpam-6834	866	6	,	,	PUNCT
ejpam-6834	866	7	.	.	PUNCT
ejpam-6834	866	8	.	.	PUNCT
ejpam-6834	866	9	.	.	PUNCT
ejpam-6834	867	1	,	,	PUNCT
ejpam-6834	867	2	bh	bh	PROPN
ejpam-6834	867	3	)	)	PUNCT
ejpam-6834	867	4	,	,	PUNCT
ejpam-6834	867	5	by	by	ADP
ejpam-6834	867	6	bu	bu	PROPN
ejpam-6834	868	1	=	=	X
ejpam-6834	868	2	{	{	PUNCT
ejpam-6834	868	3	aij	aij	PROPN
ejpam-6834	868	4	if	if	SCONJ
ejpam-6834	868	5	u	u	NOUN
ejpam-6834	868	6	=	=	X
ejpam-6834	868	7	ij	ij	NOUN
ejpam-6834	868	8	for	for	ADP
ejpam-6834	868	9	some	some	DET
ejpam-6834	868	10	j	j	NOUN
ejpam-6834	868	11	,	,	PUNCT
ejpam-6834	868	12	aℓ	aℓ	VERB
ejpam-6834	868	13	if	if	SCONJ
ejpam-6834	868	14	u	u	NOUN
ejpam-6834	868	15	=	=	NOUN
ejpam-6834	868	16	ℓ	ℓ	PROPN
ejpam-6834	868	17	∈	∈	PROPN
ejpam-6834	868	18	i	i	PRON
ejpam-6834	868	19	free	free	ADJ
ejpam-6834	868	20	.	.	PUNCT
ejpam-6834	869	1	then	then	ADV
ejpam-6834	869	2	set	set	VERB
ejpam-6834	869	3	µfix	µfix	NOUN
ejpam-6834	869	4	:	:	PUNCT
ejpam-6834	869	5	=	=	SYM
ejpam-6834	869	6	µ	µ	X
ejpam-6834	869	7	(	(	PUNCT
ejpam-6834	869	8	m	m	PROPN
ejpam-6834	869	9	,	,	PUNCT
ejpam-6834	869	10	n	n	CCONJ
ejpam-6834	869	11	)	)	PUNCT
ejpam-6834	869	12	(	(	PUNCT
ejpam-6834	869	13	h	h	NOUN
ejpam-6834	869	14	,	,	PUNCT
ejpam-6834	869	15	k	k	NOUN
ejpam-6834	869	16	)	)	PUNCT
ejpam-6834	869	17	◦	◦	NOUN
ejpam-6834	869	18	ι	ι	PRON
ejpam-6834	869	19	.	.	PUNCT
ejpam-6834	870	1	for	for	ADP
ejpam-6834	870	2	any	any	DET
ejpam-6834	870	3	afree	afree	ADJ
ejpam-6834	870	4	,	,	PUNCT
ejpam-6834	870	5	ι(afree	ι(afree	NOUN
ejpam-6834	870	6	)	)	PUNCT
ejpam-6834	870	7	∈	∈	PROPN
ejpam-6834	870	8	(	(	PUNCT
ejpam-6834	870	9	pm(x))h	pm(x))h	X
ejpam-6834	870	10	;	;	PUNCT
ejpam-6834	870	11	hence	hence	ADV
ejpam-6834	870	12	µ	µ	X
ejpam-6834	870	13	(	(	PUNCT
ejpam-6834	870	14	m	m	PROPN
ejpam-6834	870	15	,	,	PUNCT
ejpam-6834	870	16	n	n	CCONJ
ejpam-6834	870	17	)	)	PUNCT
ejpam-6834	870	18	(	(	PUNCT
ejpam-6834	870	19	h	h	NOUN
ejpam-6834	870	20	,	,	PUNCT
ejpam-6834	870	21	k	k	NOUN
ejpam-6834	870	22	)	)	PUNCT
ejpam-6834	870	23	yields	yield	VERB
ejpam-6834	870	24	a	a	DET
ejpam-6834	870	25	k	k	NOUN
ejpam-6834	870	26	-	-	NOUN
ejpam-6834	870	27	tuple	tuple	ADJ
ejpam-6834	870	28	(	(	PUNCT
ejpam-6834	870	29	µ	µ	X
ejpam-6834	870	30	(	(	PUNCT
ejpam-6834	870	31	m	m	PROPN
ejpam-6834	870	32	,	,	PUNCT
ejpam-6834	870	33	n	n	CCONJ
ejpam-6834	870	34	)	)	PUNCT
ejpam-6834	870	35	1	1	NUM
ejpam-6834	870	36	(	(	PUNCT
ejpam-6834	870	37	ι(afree	ι(afree	NOUN
ejpam-6834	870	38	)	)	PUNCT
ejpam-6834	870	39	)	)	PUNCT
ejpam-6834	870	40	,	,	PUNCT
ejpam-6834	870	41	.	.	PUNCT
ejpam-6834	870	42	.	.	PUNCT
ejpam-6834	871	1	.	.	PUNCT
ejpam-6834	872	1	,	,	PUNCT
ejpam-6834	872	2	µ	µ	X
ejpam-6834	872	3	(	(	PUNCT
ejpam-6834	872	4	m	m	PROPN
ejpam-6834	872	5	,	,	PUNCT
ejpam-6834	872	6	n	n	CCONJ
ejpam-6834	872	7	)	)	PUNCT
ejpam-6834	872	8	k	k	PROPN
ejpam-6834	872	9	(	(	PUNCT
ejpam-6834	872	10	ι(afree	ι(afree	NOUN
ejpam-6834	872	11	)	)	PUNCT
ejpam-6834	872	12	)	)	PUNCT
ejpam-6834	872	13	)	)	PUNCT
ejpam-6834	872	14	with	with	ADP
ejpam-6834	872	15	each	each	DET
ejpam-6834	872	16	coordinate	coordinate	NOUN
ejpam-6834	872	17	in	in	ADP
ejpam-6834	872	18	pn([0	pn([0	NOUN
ejpam-6834	872	19	,	,	PUNCT
ejpam-6834	872	20	1	1	NUM
ejpam-6834	872	21	]	]	PUNCT
ejpam-6834	872	22	)	)	PUNCT
ejpam-6834	872	23	and	and	CCONJ
ejpam-6834	872	24	nonempty	nonempty	NOUN
ejpam-6834	872	25	.	.	PUNCT
ejpam-6834	873	1	therefore	therefore	ADV
ejpam-6834	873	2	µfix	µfix	NOUN
ejpam-6834	873	3	is	be	AUX
ejpam-6834	873	4	a	a	DET
ejpam-6834	873	5	well	well	ADV
ejpam-6834	873	6	-	-	PUNCT
ejpam-6834	873	7	defined	define	VERB
ejpam-6834	873	8	(	(	PUNCT
ejpam-6834	873	9	h−	h−	NOUN
ejpam-6834	873	10	r	r	NOUN
ejpam-6834	873	11	,	,	PUNCT
ejpam-6834	873	12	k)-ary	k)-ary	X
ejpam-6834	873	13	(	(	PUNCT
ejpam-6834	873	14	m	m	NOUN
ejpam-6834	873	15	,	,	PUNCT
ejpam-6834	873	16	n)-superhyperfuzzy	n)-superhyperfuzzy	PUNCT
ejpam-6834	873	17	set	set	NOUN
ejpam-6834	873	18	.	.	PUNCT
ejpam-6834	874	1	theorem	theorem	VERB
ejpam-6834	874	2	25	25	NUM
ejpam-6834	874	3	(	(	PUNCT
ejpam-6834	874	4	projection	projection	NOUN
ejpam-6834	874	5	to	to	ADP
ejpam-6834	874	6	a	a	DET
ejpam-6834	874	7	subset	subset	NOUN
ejpam-6834	874	8	of	of	ADP
ejpam-6834	874	9	outputs	output	NOUN
ejpam-6834	874	10	)	)	PUNCT
ejpam-6834	874	11	.	.	PUNCT
ejpam-6834	875	1	let	let	VERB
ejpam-6834	875	2	1	1	NUM
ejpam-6834	875	3	≤	≤	NOUN
ejpam-6834	875	4	j1	j1	X
ejpam-6834	875	5	<	<	X
ejpam-6834	875	6	·	·	PUNCT
ejpam-6834	875	7	·	·	PUNCT
ejpam-6834	875	8	·	·	PUNCT
ejpam-6834	876	1	<	<	X
ejpam-6834	876	2	js	js	PROPN
ejpam-6834	876	3	≤	≤	PROPN
ejpam-6834	876	4	k.	k.	PROPN
ejpam-6834	877	1	the	the	DET
ejpam-6834	877	2	coordinate	coordinate	NOUN
ejpam-6834	877	3	projection	projection	NOUN
ejpam-6834	877	4	µproj	µproj	NOUN
ejpam-6834	877	5	:	:	PUNCT
ejpam-6834	877	6	(	(	PUNCT
ejpam-6834	877	7	pm(x))h	pm(x))h	X
ejpam-6834	877	8	−→	−→	NOUN
ejpam-6834	877	9	(	(	PUNCT
ejpam-6834	877	10	pn([0	pn([0	NOUN
ejpam-6834	877	11	,	,	PUNCT
ejpam-6834	877	12	1]))s	1]))s	NUM
ejpam-6834	877	13	,	,	PUNCT
ejpam-6834	877	14	µproj(a	µproj(a	PROPN
ejpam-6834	877	15	)	)	PUNCT
ejpam-6834	877	16	=	=	SYM
ejpam-6834	877	17	(	(	PUNCT
ejpam-6834	877	18	µ	µ	X
ejpam-6834	877	19	(	(	PUNCT
ejpam-6834	877	20	m	m	PROPN
ejpam-6834	877	21	,	,	PUNCT
ejpam-6834	877	22	n	n	CCONJ
ejpam-6834	877	23	)	)	PUNCT
ejpam-6834	877	24	j1	j1	PROPN
ejpam-6834	877	25	(	(	PUNCT
ejpam-6834	877	26	a	a	NOUN
ejpam-6834	877	27	)	)	PUNCT
ejpam-6834	877	28	,	,	PUNCT
ejpam-6834	877	29	.	.	PUNCT
ejpam-6834	877	30	.	.	PUNCT
ejpam-6834	878	1	.	.	PUNCT
ejpam-6834	879	1	,	,	PUNCT
ejpam-6834	879	2	µ	µ	X
ejpam-6834	879	3	(	(	PUNCT
ejpam-6834	879	4	m	m	PROPN
ejpam-6834	879	5	,	,	PUNCT
ejpam-6834	879	6	n	n	CCONJ
ejpam-6834	879	7	)	)	PUNCT
ejpam-6834	879	8	js	js	NOUN
ejpam-6834	879	9	(	(	PUNCT
ejpam-6834	879	10	a	a	NOUN
ejpam-6834	879	11	)	)	PUNCT
ejpam-6834	879	12	)	)	PUNCT
ejpam-6834	879	13	,	,	PUNCT
ejpam-6834	879	14	is	be	AUX
ejpam-6834	879	15	an	an	DET
ejpam-6834	879	16	(	(	PUNCT
ejpam-6834	879	17	h	h	NOUN
ejpam-6834	879	18	,	,	PUNCT
ejpam-6834	879	19	s)-ary	s)-ary	NOUN
ejpam-6834	879	20	(	(	PUNCT
ejpam-6834	879	21	m	m	NOUN
ejpam-6834	879	22	,	,	PUNCT
ejpam-6834	879	23	n)-superhyperfuzzy	n)-superhyperfuzzy	PUNCT
ejpam-6834	879	24	set	set	NOUN
ejpam-6834	879	25	.	.	PUNCT
ejpam-6834	880	1	proof	proof	NOUN
ejpam-6834	880	2	.	.	PUNCT
ejpam-6834	881	1	let	let	VERB
ejpam-6834	881	2	prj	prj	VERB
ejpam-6834	881	3	:	:	PUNCT
ejpam-6834	881	4	(	(	PUNCT
ejpam-6834	881	5	pn([0	pn([0	NOUN
ejpam-6834	881	6	,	,	PUNCT
ejpam-6834	881	7	1]))k	1]))k	NUM
ejpam-6834	881	8	→	→	SYM
ejpam-6834	881	9	(	(	PUNCT
ejpam-6834	881	10	pn([0	pn([0	NOUN
ejpam-6834	881	11	,	,	PUNCT
ejpam-6834	881	12	1]))s	1]))s	NUM
ejpam-6834	881	13	be	be	AUX
ejpam-6834	881	14	the	the	DET
ejpam-6834	881	15	coordinate	coordinate	NOUN
ejpam-6834	881	16	projection	projection	NOUN
ejpam-6834	881	17	to	to	ADP
ejpam-6834	881	18	j	j	PROPN
ejpam-6834	881	19	=	=	PUNCT
ejpam-6834	881	20	{	{	PUNCT
ejpam-6834	881	21	j1	j1	PROPN
ejpam-6834	881	22	,	,	PUNCT
ejpam-6834	881	23	.	.	PUNCT
ejpam-6834	881	24	.	.	PUNCT
ejpam-6834	881	25	.	.	PUNCT
ejpam-6834	882	1	,	,	PUNCT
ejpam-6834	882	2	js	js	ADP
ejpam-6834	882	3	}	}	PUNCT
ejpam-6834	882	4	.	.	PUNCT
ejpam-6834	883	1	then	then	ADV
ejpam-6834	883	2	µproj	µproj	VERB
ejpam-6834	883	3	=	=	PUNCT
ejpam-6834	883	4	prj	prj	VERB
ejpam-6834	883	5	◦	◦	PROPN
ejpam-6834	883	6	µ	µ	X
ejpam-6834	883	7	(	(	PUNCT
ejpam-6834	883	8	m	m	PROPN
ejpam-6834	883	9	,	,	PUNCT
ejpam-6834	883	10	n	n	CCONJ
ejpam-6834	883	11	)	)	PUNCT
ejpam-6834	883	12	(	(	PUNCT
ejpam-6834	883	13	h	h	NOUN
ejpam-6834	883	14	,	,	PUNCT
ejpam-6834	883	15	k	k	NOUN
ejpam-6834	883	16	)	)	PUNCT
ejpam-6834	883	17	.	.	PUNCT
ejpam-6834	884	1	since	since	SCONJ
ejpam-6834	884	2	each	each	DET
ejpam-6834	884	3	output	output	NOUN
ejpam-6834	884	4	coordinate	coordinate	NOUN
ejpam-6834	884	5	µ	µ	PROPN
ejpam-6834	884	6	(	(	PUNCT
ejpam-6834	884	7	m	m	PROPN
ejpam-6834	884	8	,	,	PUNCT
ejpam-6834	884	9	n	n	CCONJ
ejpam-6834	884	10	)	)	PUNCT
ejpam-6834	884	11	j	j	PROPN
ejpam-6834	884	12	(	(	PUNCT
ejpam-6834	884	13	a	a	NOUN
ejpam-6834	884	14	)	)	PUNCT
ejpam-6834	884	15	is	be	AUX
ejpam-6834	884	16	a	a	DET
ejpam-6834	884	17	nonempty	nonempty	ADJ
ejpam-6834	884	18	element	element	NOUN
ejpam-6834	884	19	of	of	ADP
ejpam-6834	884	20	pn([0	pn([0	NOUN
ejpam-6834	884	21	,	,	PUNCT
ejpam-6834	884	22	1	1	NUM
ejpam-6834	884	23	]	]	NUM
ejpam-6834	884	24	)	)	PUNCT
ejpam-6834	884	25	,	,	PUNCT
ejpam-6834	884	26	their	their	PRON
ejpam-6834	884	27	s	s	NOUN
ejpam-6834	884	28	-	-	NOUN
ejpam-6834	884	29	tuple	tuple	NOUN
ejpam-6834	884	30	lies	lie	VERB
ejpam-6834	884	31	in	in	ADP
ejpam-6834	884	32	(	(	PUNCT
ejpam-6834	884	33	pn([0	pn([0	NOUN
ejpam-6834	884	34	,	,	PUNCT
ejpam-6834	884	35	1]))s	1]))s	NUM
ejpam-6834	884	36	with	with	ADP
ejpam-6834	884	37	nonempty	nonempty	ADJ
ejpam-6834	884	38	coordinates	coordinate	NOUN
ejpam-6834	884	39	.	.	PUNCT
ejpam-6834	885	1	hence	hence	ADV
ejpam-6834	885	2	µproj	µproj	VERB
ejpam-6834	885	3	has	have	VERB
ejpam-6834	885	4	the	the	DET
ejpam-6834	885	5	required	required	ADJ
ejpam-6834	885	6	type	type	NOUN
ejpam-6834	885	7	.	.	PUNCT
ejpam-6834	886	1	theorem	theorem	VERB
ejpam-6834	886	2	26	26	NUM
ejpam-6834	886	3	(	(	PUNCT
ejpam-6834	886	4	pointwise	pointwise	NOUN
ejpam-6834	886	5	union	union	NOUN
ejpam-6834	886	6	)	)	PUNCT
ejpam-6834	886	7	.	.	PUNCT
ejpam-6834	887	1	if	if	SCONJ
ejpam-6834	887	2	µ	µ	NUM
ejpam-6834	887	3	,	,	PUNCT
ejpam-6834	887	4	ν	ν	X
ejpam-6834	887	5	:	:	PUNCT
ejpam-6834	887	6	(	(	PUNCT
ejpam-6834	887	7	pm(x))h	pm(x))h	X
ejpam-6834	887	8	→	→	PUNCT
ejpam-6834	887	9	(	(	PUNCT
ejpam-6834	887	10	pn([0	pn([0	NOUN
ejpam-6834	887	11	,	,	PUNCT
ejpam-6834	887	12	1]))k	1]))k	NUM
ejpam-6834	887	13	are	be	AUX
ejpam-6834	887	14	(	(	PUNCT
ejpam-6834	887	15	h	h	NOUN
ejpam-6834	887	16	,	,	PUNCT
ejpam-6834	887	17	k)-ary	k)-ary	X
ejpam-6834	887	18	(	(	PUNCT
ejpam-6834	887	19	m	m	PROPN
ejpam-6834	887	20	,	,	PUNCT
ejpam-6834	887	21	n)superhyperfuzzy	n)superhyperfuzzy	PRON
ejpam-6834	887	22	sets	set	VERB
ejpam-6834	887	23	,	,	PUNCT
ejpam-6834	887	24	then	then	ADV
ejpam-6834	887	25	the	the	DET
ejpam-6834	887	26	map	map	NOUN
ejpam-6834	887	27	(	(	PUNCT
ejpam-6834	887	28	µ	µ	X
ejpam-6834	887	29	∪	∪	ADP
ejpam-6834	887	30	ν)(a	ν)(a	NOUN
ejpam-6834	887	31	)	)	PUNCT
ejpam-6834	887	32	=	=	PUNCT
ejpam-6834	887	33	(	(	PUNCT
ejpam-6834	887	34	µ1(a	µ1(a	NOUN
ejpam-6834	887	35	)	)	PUNCT
ejpam-6834	887	36	∪	∪	ADP
ejpam-6834	887	37	ν1(a	ν1(a	NOUN
ejpam-6834	887	38	)	)	PUNCT
ejpam-6834	887	39	,	,	PUNCT
ejpam-6834	887	40	.	.	PUNCT
ejpam-6834	887	41	.	.	PUNCT
ejpam-6834	887	42	.	.	PUNCT
ejpam-6834	888	1	,	,	PUNCT
ejpam-6834	888	2	µk(a	µk(a	PUNCT
ejpam-6834	888	3	)	)	PUNCT
ejpam-6834	888	4	∪	∪	ADP
ejpam-6834	888	5	νk(a	νk(a	NOUN
ejpam-6834	888	6	)	)	PUNCT
ejpam-6834	888	7	)	)	PUNCT
ejpam-6834	888	8	is	be	AUX
ejpam-6834	888	9	again	again	ADV
ejpam-6834	888	10	an	an	DET
ejpam-6834	888	11	(	(	PUNCT
ejpam-6834	888	12	h	h	NOUN
ejpam-6834	888	13	,	,	PUNCT
ejpam-6834	888	14	k)-ary	k)-ary	X
ejpam-6834	888	15	(	(	PUNCT
ejpam-6834	888	16	m	m	NOUN
ejpam-6834	888	17	,	,	PUNCT
ejpam-6834	888	18	n)-superhyperfuzzy	n)-superhyperfuzzy	PUNCT
ejpam-6834	888	19	set	set	NOUN
ejpam-6834	888	20	.	.	PUNCT
ejpam-6834	889	1	t.	t.	PROPN
ejpam-6834	889	2	fujita	fujita	PROPN
ejpam-6834	889	3	,	,	PUNCT
ejpam-6834	889	4	f.smarandache	f.smarandache	NOUN
ejpam-6834	889	5	/	/	SYM
ejpam-6834	889	6	eur	eur	PROPN
ejpam-6834	889	7	.	.	PUNCT
ejpam-6834	890	1	j.	j.	PROPN
ejpam-6834	890	2	pure	pure	PROPN
ejpam-6834	890	3	appl	appl	PROPN
ejpam-6834	890	4	.	.	PROPN
ejpam-6834	890	5	math	math	PROPN
ejpam-6834	890	6	,	,	PUNCT
ejpam-6834	890	7	18	18	NUM
ejpam-6834	890	8	(	(	PUNCT
ejpam-6834	890	9	4	4	NUM
ejpam-6834	890	10	)	)	PUNCT
ejpam-6834	890	11	(	(	PUNCT
ejpam-6834	890	12	2025	2025	NUM
ejpam-6834	890	13	)	)	PUNCT
ejpam-6834	890	14	,	,	PUNCT
ejpam-6834	890	15	6834	6834	NUM
ejpam-6834	890	16	37	37	NUM
ejpam-6834	890	17	of	of	ADP
ejpam-6834	890	18	69	69	NUM
ejpam-6834	890	19	proof	proof	NOUN
ejpam-6834	890	20	.	.	PUNCT
ejpam-6834	891	1	fix	fix	VERB
ejpam-6834	891	2	a	a	DET
ejpam-6834	891	3	∈	∈	NOUN
ejpam-6834	891	4	(	(	PUNCT
ejpam-6834	891	5	pm(x))h	pm(x))h	X
ejpam-6834	891	6	and	and	CCONJ
ejpam-6834	891	7	a	a	DET
ejpam-6834	891	8	coordinate	coordinate	NOUN
ejpam-6834	891	9	1	1	NUM
ejpam-6834	891	10	≤	≤	NUM
ejpam-6834	891	11	j	j	PROPN
ejpam-6834	891	12	≤	≤	PROPN
ejpam-6834	891	13	k.	k.	PROPN
ejpam-6834	891	14	by	by	ADP
ejpam-6834	891	15	hypothesis	hypothesis	NOUN
ejpam-6834	891	16	,	,	PUNCT
ejpam-6834	891	17	µj(a	µj(a	NOUN
ejpam-6834	891	18	)	)	PUNCT
ejpam-6834	891	19	,	,	PUNCT
ejpam-6834	891	20	νj(a	νj(a	NUM
ejpam-6834	891	21	)	)	PUNCT
ejpam-6834	891	22	∈	∈	NOUN
ejpam-6834	891	23	pn([0	pn([0	NOUN
ejpam-6834	891	24	,	,	PUNCT
ejpam-6834	891	25	1	1	NUM
ejpam-6834	891	26	]	]	PUNCT
ejpam-6834	891	27	)	)	PUNCT
ejpam-6834	891	28	and	and	CCONJ
ejpam-6834	891	29	are	be	AUX
ejpam-6834	891	30	nonempty	nonempty	X
ejpam-6834	891	31	.	.	PUNCT
ejpam-6834	892	1	recall	recall	VERB
ejpam-6834	892	2	that	that	SCONJ
ejpam-6834	892	3	pn([0	pn([0	NOUN
ejpam-6834	892	4	,	,	PUNCT
ejpam-6834	892	5	1	1	NUM
ejpam-6834	892	6	]	]	PUNCT
ejpam-6834	892	7	)	)	PUNCT
ejpam-6834	892	8	consists	consist	VERB
ejpam-6834	892	9	of	of	ADP
ejpam-6834	892	10	sets	set	NOUN
ejpam-6834	892	11	of	of	ADP
ejpam-6834	892	12	level	level	NOUN
ejpam-6834	892	13	n−	n−	NOUN
ejpam-6834	892	14	1	1	NUM
ejpam-6834	892	15	objects	object	NOUN
ejpam-6834	892	16	;	;	PUNCT
ejpam-6834	892	17	the	the	DET
ejpam-6834	892	18	union	union	NOUN
ejpam-6834	892	19	of	of	ADP
ejpam-6834	892	20	two	two	NUM
ejpam-6834	892	21	sets	set	NOUN
ejpam-6834	892	22	at	at	ADP
ejpam-6834	892	23	the	the	DET
ejpam-6834	892	24	same	same	ADJ
ejpam-6834	892	25	level	level	NOUN
ejpam-6834	892	26	is	be	AUX
ejpam-6834	892	27	again	again	ADV
ejpam-6834	892	28	a	a	DET
ejpam-6834	892	29	set	set	NOUN
ejpam-6834	892	30	at	at	ADP
ejpam-6834	892	31	that	that	DET
ejpam-6834	892	32	level	level	NOUN
ejpam-6834	892	33	.	.	PUNCT
ejpam-6834	893	1	hence	hence	ADV
ejpam-6834	893	2	µj(a)∪	µj(a)∪	VERB
ejpam-6834	893	3	νj(a	νj(a	NOUN
ejpam-6834	893	4	)	)	PUNCT
ejpam-6834	893	5	∈	∈	NOUN
ejpam-6834	893	6	pn([0	pn([0	NOUN
ejpam-6834	893	7	,	,	PUNCT
ejpam-6834	893	8	1	1	NUM
ejpam-6834	893	9	]	]	NUM
ejpam-6834	893	10	)	)	PUNCT
ejpam-6834	893	11	,	,	PUNCT
ejpam-6834	893	12	and	and	CCONJ
ejpam-6834	893	13	it	it	PRON
ejpam-6834	893	14	is	be	AUX
ejpam-6834	893	15	nonempty	nonempty	ADJ
ejpam-6834	893	16	because	because	SCONJ
ejpam-6834	893	17	the	the	DET
ejpam-6834	893	18	union	union	NOUN
ejpam-6834	893	19	of	of	ADP
ejpam-6834	893	20	two	two	NUM
ejpam-6834	893	21	nonempty	nonempty	ADJ
ejpam-6834	893	22	sets	set	NOUN
ejpam-6834	893	23	is	be	AUX
ejpam-6834	893	24	nonempty	nonempty	ADJ
ejpam-6834	893	25	.	.	PUNCT
ejpam-6834	894	1	doing	do	VERB
ejpam-6834	894	2	this	this	PRON
ejpam-6834	894	3	for	for	SCONJ
ejpam-6834	894	4	each	each	DET
ejpam-6834	894	5	j	j	PROPN
ejpam-6834	894	6	produces	produce	VERB
ejpam-6834	894	7	a	a	DET
ejpam-6834	894	8	k	k	NOUN
ejpam-6834	894	9	-	-	NOUN
ejpam-6834	894	10	tuple	tuple	NOUN
ejpam-6834	894	11	in	in	ADP
ejpam-6834	894	12	(	(	PUNCT
ejpam-6834	894	13	pn([0	pn([0	NOUN
ejpam-6834	894	14	,	,	PUNCT
ejpam-6834	894	15	1]))k	1]))k	NUM
ejpam-6834	894	16	with	with	ADP
ejpam-6834	894	17	all	all	DET
ejpam-6834	894	18	coordinates	coordinate	NOUN
ejpam-6834	894	19	nonempty	nonempty	VERB
ejpam-6834	894	20	,	,	PUNCT
ejpam-6834	894	21	as	as	SCONJ
ejpam-6834	894	22	required	require	VERB
ejpam-6834	894	23	.	.	PUNCT
ejpam-6834	895	1	theorem	theorem	VERB
ejpam-6834	895	2	27	27	NUM
ejpam-6834	895	3	(	(	PUNCT
ejpam-6834	895	4	nested	nest	VERB
ejpam-6834	895	5	α	α	NOUN
ejpam-6834	895	6	-	-	NOUN
ejpam-6834	895	7	cuts	cut	NOUN
ejpam-6834	895	8	)	)	PUNCT
ejpam-6834	895	9	.	.	PUNCT
ejpam-6834	896	1	for	for	ADP
ejpam-6834	896	2	α	α	PRON
ejpam-6834	896	3	∈	∈	PROPN
ejpam-6834	897	1	[	[	X
ejpam-6834	897	2	0	0	NUM
ejpam-6834	897	3	,	,	PUNCT
ejpam-6834	897	4	1	1	NUM
ejpam-6834	897	5	]	]	PUNCT
ejpam-6834	897	6	,	,	PUNCT
ejpam-6834	897	7	define	define	VERB
ejpam-6834	897	8	cα	cα	ADP
ejpam-6834	897	9	=	=	PUNCT
ejpam-6834	897	10	{	{	PUNCT
ejpam-6834	897	11	a	a	DET
ejpam-6834	897	12	∈	∈	PROPN
ejpam-6834	897	13	(	(	PUNCT
ejpam-6834	897	14	pm(x))h	pm(x))h	X
ejpam-6834	897	15	∣∣∣	∣∣∣	PROPN
ejpam-6834	897	16	∃j	∃j	PROPN
ejpam-6834	897	17	∃t	∃t	PROPN
ejpam-6834	897	18	∈	∈	PROPN
ejpam-6834	897	19	µ	µ	X
ejpam-6834	897	20	(	(	PUNCT
ejpam-6834	897	21	m	m	PROPN
ejpam-6834	897	22	,	,	PUNCT
ejpam-6834	897	23	n	n	CCONJ
ejpam-6834	897	24	)	)	PUNCT
ejpam-6834	897	25	j	j	PROPN
ejpam-6834	897	26	(	(	PUNCT
ejpam-6834	897	27	a	a	NOUN
ejpam-6834	897	28	)	)	PUNCT
ejpam-6834	897	29	with	with	ADP
ejpam-6834	897	30	t	t	PROPN
ejpam-6834	897	31	≥	≥	PROPN
ejpam-6834	897	32	α	α	NOUN
ejpam-6834	897	33	}	}	PUNCT
ejpam-6834	897	34	.	.	PUNCT
ejpam-6834	898	1	if	if	SCONJ
ejpam-6834	898	2	0	0	NUM
ejpam-6834	898	3	≤	≤	NUM
ejpam-6834	898	4	α1	α1	PROPN
ejpam-6834	898	5	<	<	X
ejpam-6834	898	6	α2	α2	PROPN
ejpam-6834	898	7	≤	≤	ADV
ejpam-6834	898	8	1	1	NUM
ejpam-6834	898	9	,	,	PUNCT
ejpam-6834	898	10	then	then	ADV
ejpam-6834	898	11	cα2	cα2	VERB
ejpam-6834	898	12	⊆	⊆	NUM
ejpam-6834	898	13	cα1	cα1	NOUN
ejpam-6834	898	14	.	.	PUNCT
ejpam-6834	899	1	proof	proof	NOUN
ejpam-6834	899	2	.	.	PUNCT
ejpam-6834	900	1	let	let	VERB
ejpam-6834	900	2	a	a	DET
ejpam-6834	900	3	∈	∈	ADJ
ejpam-6834	900	4	cα2	cα2	NOUN
ejpam-6834	900	5	.	.	PUNCT
ejpam-6834	901	1	by	by	ADP
ejpam-6834	901	2	definition	definition	NOUN
ejpam-6834	901	3	,	,	PUNCT
ejpam-6834	901	4	there	there	PRON
ejpam-6834	901	5	exists	exist	VERB
ejpam-6834	901	6	an	an	DET
ejpam-6834	901	7	index	index	NOUN
ejpam-6834	901	8	j	j	PROPN
ejpam-6834	901	9	and	and	CCONJ
ejpam-6834	901	10	a	a	DET
ejpam-6834	901	11	value	value	NOUN
ejpam-6834	901	12	t	t	PROPN
ejpam-6834	901	13	∈	∈	PROPN
ejpam-6834	901	14	µ	µ	X
ejpam-6834	901	15	(	(	PUNCT
ejpam-6834	901	16	m	m	PROPN
ejpam-6834	901	17	,	,	PUNCT
ejpam-6834	901	18	n	n	CCONJ
ejpam-6834	901	19	)	)	PUNCT
ejpam-6834	901	20	j	j	PROPN
ejpam-6834	901	21	(	(	PUNCT
ejpam-6834	901	22	a	a	NOUN
ejpam-6834	901	23	)	)	PUNCT
ejpam-6834	901	24	such	such	ADJ
ejpam-6834	901	25	that	that	SCONJ
ejpam-6834	901	26	t	t	PROPN
ejpam-6834	901	27	≥	≥	PROPN
ejpam-6834	901	28	α2	α2	PROPN
ejpam-6834	901	29	.	.	PUNCT
ejpam-6834	902	1	since	since	SCONJ
ejpam-6834	902	2	α2	α2	PROPN
ejpam-6834	902	3	>	>	SYM
ejpam-6834	902	4	α1	α1	PROPN
ejpam-6834	902	5	,	,	PUNCT
ejpam-6834	902	6	we	we	PRON
ejpam-6834	902	7	have	have	VERB
ejpam-6834	902	8	t	t	PROPN
ejpam-6834	902	9	≥	≥	NOUN
ejpam-6834	902	10	α2	α2	PROPN
ejpam-6834	902	11	>	>	X
ejpam-6834	902	12	α1	α1	PROPN
ejpam-6834	902	13	,	,	PUNCT
ejpam-6834	902	14	hence	hence	ADV
ejpam-6834	902	15	the	the	DET
ejpam-6834	902	16	same	same	ADJ
ejpam-6834	902	17	j	j	NOUN
ejpam-6834	902	18	and	and	CCONJ
ejpam-6834	902	19	t	t	PROPN
ejpam-6834	902	20	witness	witness	NOUN
ejpam-6834	902	21	that	that	SCONJ
ejpam-6834	902	22	a	a	DET
ejpam-6834	902	23	∈	∈	PROPN
ejpam-6834	902	24	cα1	cα1	NOUN
ejpam-6834	902	25	.	.	PUNCT
ejpam-6834	903	1	therefore	therefore	ADV
ejpam-6834	903	2	cα2	cα2	PROPN
ejpam-6834	903	3	⊆	⊆	NUM
ejpam-6834	903	4	cα1	cα1	NOUN
ejpam-6834	903	5	.	.	PUNCT
ejpam-6834	904	1	theorem	theorem	ADJ
ejpam-6834	904	2	28	28	NUM
ejpam-6834	904	3	(	(	PUNCT
ejpam-6834	904	4	compatibility	compatibility	NOUN
ejpam-6834	904	5	with	with	ADP
ejpam-6834	904	6	surjections	surjection	NOUN
ejpam-6834	904	7	)	)	PUNCT
ejpam-6834	904	8	.	.	PUNCT
ejpam-6834	905	1	let	let	VERB
ejpam-6834	905	2	f	f	NOUN
ejpam-6834	905	3	:	:	PUNCT
ejpam-6834	905	4	x	x	X
ejpam-6834	905	5	→	→	SYM
ejpam-6834	905	6	y	y	PROPN
ejpam-6834	905	7	be	be	AUX
ejpam-6834	905	8	surjective	surjective	ADJ
ejpam-6834	905	9	.	.	PUNCT
ejpam-6834	906	1	define	define	VERB
ejpam-6834	906	2	f−1	f−1	PROPN
ejpam-6834	906	3	(	(	PUNCT
ejpam-6834	906	4	1	1	NUM
ejpam-6834	906	5	)	)	PUNCT
ejpam-6834	906	6	:	:	PUNCT
ejpam-6834	907	1	p(y	p(y	PROPN
ejpam-6834	907	2	)	)	PUNCT
ejpam-6834	907	3	→	→	SYM
ejpam-6834	907	4	p(x	p(x	PROPN
ejpam-6834	907	5	)	)	PUNCT
ejpam-6834	907	6	by	by	ADP
ejpam-6834	907	7	f−1	f−1	PROPN
ejpam-6834	907	8	(	(	PUNCT
ejpam-6834	907	9	1	1	NUM
ejpam-6834	907	10	)	)	PUNCT
ejpam-6834	907	11	(	(	PUNCT
ejpam-6834	907	12	b	b	X
ejpam-6834	907	13	)	)	PUNCT
ejpam-6834	907	14	=	=	SYM
ejpam-6834	907	15	{	{	PUNCT
ejpam-6834	907	16	x	x	PUNCT
ejpam-6834	907	17	∈	∈	NOUN
ejpam-6834	907	18	x	x	X
ejpam-6834	907	19	:	:	PUNCT
ejpam-6834	907	20	f(x	f(x	PROPN
ejpam-6834	907	21	)	)	PUNCT
ejpam-6834	907	22	∈	∈	PROPN
ejpam-6834	907	23	b	b	X
ejpam-6834	907	24	}	}	PUNCT
ejpam-6834	907	25	and	and	CCONJ
ejpam-6834	907	26	recursively	recursively	ADV
ejpam-6834	907	27	f−1	f−1	PROPN
ejpam-6834	907	28	(	(	PUNCT
ejpam-6834	907	29	r+1)(b	r+1)(b	PROPN
ejpam-6834	907	30	)	)	PUNCT
ejpam-6834	907	31	=	=	PRON
ejpam-6834	907	32	{	{	PUNCT
ejpam-6834	907	33	f−1	f−1	PROPN
ejpam-6834	907	34	(	(	PUNCT
ejpam-6834	907	35	r	r	NOUN
ejpam-6834	907	36	)	)	PUNCT
ejpam-6834	907	37	(	(	PUNCT
ejpam-6834	907	38	b	b	X
ejpam-6834	907	39	)	)	PUNCT
ejpam-6834	907	40	∣∣	∣∣	NUM
ejpam-6834	907	41	b	b	X
ejpam-6834	907	42	∈	∈	PROPN
ejpam-6834	907	43	b	b	PROPN
ejpam-6834	907	44	}	}	PUNCT
ejpam-6834	907	45	(	(	PUNCT
ejpam-6834	907	46	r	r	NOUN
ejpam-6834	907	47	≥	≥	NOUN
ejpam-6834	907	48	1	1	NUM
ejpam-6834	907	49	)	)	PUNCT
ejpam-6834	907	50	.	.	PUNCT
ejpam-6834	908	1	given	give	VERB
ejpam-6834	908	2	µ	µ	PROPN
ejpam-6834	908	3	(	(	PUNCT
ejpam-6834	908	4	m	m	PROPN
ejpam-6834	908	5	,	,	PUNCT
ejpam-6834	908	6	n	n	CCONJ
ejpam-6834	908	7	)	)	PUNCT
ejpam-6834	908	8	(	(	PUNCT
ejpam-6834	908	9	h	h	NOUN
ejpam-6834	908	10	,	,	PUNCT
ejpam-6834	908	11	k	k	NOUN
ejpam-6834	908	12	)	)	PUNCT
ejpam-6834	908	13	on	on	ADP
ejpam-6834	908	14	x	x	SYM
ejpam-6834	908	15	,	,	PUNCT
ejpam-6834	908	16	the	the	DET
ejpam-6834	908	17	pushforward	pushforward	NOUN
ejpam-6834	908	18	(	(	PUNCT
ejpam-6834	908	19	f∗µ	f∗µ	NUM
ejpam-6834	908	20	)	)	PUNCT
ejpam-6834	908	21	(	(	PUNCT
ejpam-6834	908	22	m	m	PROPN
ejpam-6834	908	23	,	,	PUNCT
ejpam-6834	908	24	n	n	CCONJ
ejpam-6834	908	25	)	)	PUNCT
ejpam-6834	908	26	(	(	PUNCT
ejpam-6834	908	27	h	h	NOUN
ejpam-6834	908	28	,	,	PUNCT
ejpam-6834	908	29	k	k	NOUN
ejpam-6834	908	30	)	)	PUNCT
ejpam-6834	908	31	:	:	PUNCT
ejpam-6834	908	32	(	(	PUNCT
ejpam-6834	908	33	pm(y	pm(y	X
ejpam-6834	908	34	)	)	PUNCT
ejpam-6834	908	35	)	)	PUNCT
ejpam-6834	908	36	h	h	NOUN
ejpam-6834	908	37	−→	−→	NOUN
ejpam-6834	908	38	(	(	PUNCT
ejpam-6834	908	39	pn([0	pn([0	NOUN
ejpam-6834	908	40	,	,	PUNCT
ejpam-6834	908	41	1]))k	1]))k	NUM
ejpam-6834	908	42	,	,	PUNCT
ejpam-6834	908	43	(	(	PUNCT
ejpam-6834	908	44	f∗µ	f∗µ	NUM
ejpam-6834	908	45	)	)	PUNCT
ejpam-6834	908	46	(	(	PUNCT
ejpam-6834	908	47	m	m	PROPN
ejpam-6834	908	48	,	,	PUNCT
ejpam-6834	908	49	n	n	CCONJ
ejpam-6834	908	50	)	)	PUNCT
ejpam-6834	908	51	(	(	PUNCT
ejpam-6834	908	52	h	h	NOUN
ejpam-6834	908	53	,	,	PUNCT
ejpam-6834	908	54	k	k	NOUN
ejpam-6834	908	55	)	)	PUNCT
ejpam-6834	908	56	(	(	PUNCT
ejpam-6834	908	57	a′	a′	PROPN
ejpam-6834	908	58	1	1	NUM
ejpam-6834	908	59	,	,	PUNCT
ejpam-6834	908	60	.	.	PUNCT
ejpam-6834	908	61	.	.	PUNCT
ejpam-6834	909	1	.	.	PUNCT
ejpam-6834	910	1	,	,	PUNCT
ejpam-6834	910	2	a	a	DET
ejpam-6834	910	3	′	′	NOUN
ejpam-6834	910	4	h	h	NOUN
ejpam-6834	910	5	)	)	PUNCT
ejpam-6834	911	1	=	=	SYM
ejpam-6834	911	2	µ	µ	X
ejpam-6834	911	3	(	(	PUNCT
ejpam-6834	911	4	m	m	PROPN
ejpam-6834	911	5	,	,	PUNCT
ejpam-6834	911	6	n	n	CCONJ
ejpam-6834	911	7	)	)	PUNCT
ejpam-6834	911	8	(	(	PUNCT
ejpam-6834	911	9	h	h	NOUN
ejpam-6834	911	10	,	,	PUNCT
ejpam-6834	911	11	k	k	NOUN
ejpam-6834	911	12	)	)	PUNCT
ejpam-6834	911	13	(	(	PUNCT
ejpam-6834	911	14	f−1	f−1	PROPN
ejpam-6834	911	15	(	(	PUNCT
ejpam-6834	911	16	m)(a	m)(a	PROPN
ejpam-6834	911	17	′	′	NOUN
ejpam-6834	911	18	1	1	NUM
ejpam-6834	911	19	)	)	PUNCT
ejpam-6834	911	20	,	,	PUNCT
ejpam-6834	911	21	.	.	PUNCT
ejpam-6834	911	22	.	.	PUNCT
ejpam-6834	911	23	.	.	PUNCT
ejpam-6834	912	1	,	,	PUNCT
ejpam-6834	912	2	f	f	PROPN
ejpam-6834	912	3	−1	−1	NOUN
ejpam-6834	912	4	(	(	PUNCT
ejpam-6834	912	5	m)(a	m)(a	PROPN
ejpam-6834	912	6	′	′	NUM
ejpam-6834	912	7	h	h	NOUN
ejpam-6834	912	8	)	)	PUNCT
ejpam-6834	912	9	)	)	PUNCT
ejpam-6834	912	10	,	,	PUNCT
ejpam-6834	912	11	is	be	AUX
ejpam-6834	912	12	an	an	DET
ejpam-6834	912	13	(	(	PUNCT
ejpam-6834	912	14	h	h	NOUN
ejpam-6834	912	15	,	,	PUNCT
ejpam-6834	912	16	k)-ary	k)-ary	X
ejpam-6834	912	17	(	(	PUNCT
ejpam-6834	912	18	m	m	PROPN
ejpam-6834	912	19	,	,	PUNCT
ejpam-6834	912	20	n)-superhyperfuzzy	n)-superhyperfuzzy	PUNCT
ejpam-6834	912	21	set	set	VERB
ejpam-6834	912	22	on	on	ADP
ejpam-6834	912	23	y	y	PROPN
ejpam-6834	912	24	.	.	PUNCT
ejpam-6834	913	1	proof	proof	NOUN
ejpam-6834	913	2	.	.	PUNCT
ejpam-6834	914	1	we	we	PRON
ejpam-6834	914	2	first	first	ADV
ejpam-6834	914	3	show	show	VERB
ejpam-6834	914	4	by	by	ADP
ejpam-6834	914	5	induction	induction	NOUN
ejpam-6834	914	6	on	on	ADP
ejpam-6834	914	7	r	r	PROPN
ejpam-6834	914	8	≥	≥	NUM
ejpam-6834	914	9	1	1	NUM
ejpam-6834	914	10	that	that	PRON
ejpam-6834	914	11	f−1	f−1	PROPN
ejpam-6834	914	12	(	(	PUNCT
ejpam-6834	914	13	r	r	NOUN
ejpam-6834	914	14	)	)	PUNCT
ejpam-6834	914	15	:	:	PUNCT
ejpam-6834	914	16	pr(y	pr(y	ADJ
ejpam-6834	914	17	)	)	PUNCT
ejpam-6834	914	18	→	→	SYM
ejpam-6834	914	19	pr(x	pr(x	X
ejpam-6834	914	20	)	)	PUNCT
ejpam-6834	914	21	is	be	AUX
ejpam-6834	914	22	well	well	ADV
ejpam-6834	914	23	defined	define	VERB
ejpam-6834	914	24	.	.	PUNCT
ejpam-6834	915	1	for	for	ADP
ejpam-6834	915	2	r	r	NOUN
ejpam-6834	915	3	=	=	SYM
ejpam-6834	915	4	1	1	NUM
ejpam-6834	915	5	,	,	PUNCT
ejpam-6834	915	6	this	this	PRON
ejpam-6834	915	7	is	be	AUX
ejpam-6834	915	8	the	the	DET
ejpam-6834	915	9	usual	usual	ADJ
ejpam-6834	915	10	preimage	preimage	NOUN
ejpam-6834	915	11	map	map	NOUN
ejpam-6834	915	12	on	on	ADP
ejpam-6834	915	13	subsets	subset	NOUN
ejpam-6834	915	14	:	:	PUNCT
ejpam-6834	915	15	if	if	SCONJ
ejpam-6834	915	16	b	b	PROPN
ejpam-6834	915	17	⊆	⊆	NUM
ejpam-6834	915	18	y	y	PROPN
ejpam-6834	915	19	,	,	PUNCT
ejpam-6834	915	20	then	then	ADV
ejpam-6834	915	21	f−1	f−1	PROPN
ejpam-6834	915	22	(	(	PUNCT
ejpam-6834	915	23	1	1	NUM
ejpam-6834	915	24	)	)	PUNCT
ejpam-6834	915	25	(	(	PUNCT
ejpam-6834	915	26	b	b	X
ejpam-6834	915	27	)	)	PUNCT
ejpam-6834	915	28	⊆	⊆	NUM
ejpam-6834	915	29	x	x	SYM
ejpam-6834	915	30	,	,	PUNCT
ejpam-6834	915	31	so	so	ADV
ejpam-6834	915	32	f−1	f−1	PROPN
ejpam-6834	915	33	(	(	PUNCT
ejpam-6834	915	34	1	1	NUM
ejpam-6834	915	35	)	)	PUNCT
ejpam-6834	915	36	(	(	PUNCT
ejpam-6834	915	37	b	b	X
ejpam-6834	915	38	)	)	PUNCT
ejpam-6834	915	39	∈	∈	PROPN
ejpam-6834	915	40	p(x	p(x	PROPN
ejpam-6834	915	41	)	)	PUNCT
ejpam-6834	915	42	=	=	SYM
ejpam-6834	915	43	p1(x	p1(x	NOUN
ejpam-6834	915	44	)	)	PUNCT
ejpam-6834	915	45	.	.	PUNCT
ejpam-6834	916	1	assume	assume	VERB
ejpam-6834	916	2	f−1	f−1	PROPN
ejpam-6834	916	3	(	(	PUNCT
ejpam-6834	916	4	r	r	NOUN
ejpam-6834	916	5	)	)	PUNCT
ejpam-6834	916	6	is	be	AUX
ejpam-6834	916	7	defined	define	VERB
ejpam-6834	916	8	on	on	ADP
ejpam-6834	916	9	pr(y	pr(y	ADJ
ejpam-6834	916	10	)	)	PUNCT
ejpam-6834	916	11	with	with	ADP
ejpam-6834	916	12	values	value	NOUN
ejpam-6834	916	13	in	in	ADP
ejpam-6834	916	14	pr(x	pr(x	PROPN
ejpam-6834	916	15	)	)	PUNCT
ejpam-6834	916	16	.	.	PUNCT
ejpam-6834	917	1	if	if	SCONJ
ejpam-6834	917	2	b	b	X
ejpam-6834	917	3	∈	∈	PROPN
ejpam-6834	917	4	pr+1(y	pr+1(y	PROPN
ejpam-6834	917	5	)	)	PUNCT
ejpam-6834	917	6	,	,	PUNCT
ejpam-6834	917	7	then	then	ADV
ejpam-6834	917	8	b	b	PROPN
ejpam-6834	917	9	is	be	AUX
ejpam-6834	917	10	a	a	DET
ejpam-6834	917	11	set	set	NOUN
ejpam-6834	917	12	of	of	ADP
ejpam-6834	917	13	elements	element	NOUN
ejpam-6834	917	14	b	b	PROPN
ejpam-6834	917	15	∈	∈	PROPN
ejpam-6834	917	16	pr(y	pr(y	VERB
ejpam-6834	917	17	)	)	PUNCT
ejpam-6834	917	18	,	,	PUNCT
ejpam-6834	917	19	and	and	CCONJ
ejpam-6834	917	20	by	by	ADP
ejpam-6834	917	21	induction	induction	NOUN
ejpam-6834	917	22	f−1	f−1	PROPN
ejpam-6834	917	23	(	(	PUNCT
ejpam-6834	917	24	r	r	NOUN
ejpam-6834	917	25	)	)	PUNCT
ejpam-6834	917	26	(	(	PUNCT
ejpam-6834	917	27	b	b	X
ejpam-6834	917	28	)	)	PUNCT
ejpam-6834	917	29	∈	∈	PROPN
ejpam-6834	917	30	pr(x	pr(x	NOUN
ejpam-6834	917	31	)	)	PUNCT
ejpam-6834	917	32	for	for	ADP
ejpam-6834	917	33	each	each	DET
ejpam-6834	917	34	such	such	ADJ
ejpam-6834	917	35	b.	b.	PROPN
ejpam-6834	917	36	therefore	therefore	ADV
ejpam-6834	917	37	the	the	DET
ejpam-6834	917	38	set	set	NOUN
ejpam-6834	917	39	{	{	PUNCT
ejpam-6834	917	40	f−1	f−1	PROPN
ejpam-6834	917	41	(	(	PUNCT
ejpam-6834	917	42	r	r	NOUN
ejpam-6834	917	43	)	)	PUNCT
ejpam-6834	917	44	(	(	PUNCT
ejpam-6834	917	45	b	b	X
ejpam-6834	917	46	)	)	PUNCT
ejpam-6834	917	47	|	|	ADV
ejpam-6834	917	48	b	b	X
ejpam-6834	917	49	∈	∈	PROPN
ejpam-6834	917	50	b	b	PROPN
ejpam-6834	917	51	}	}	PUNCT
ejpam-6834	917	52	belongs	belong	VERB
ejpam-6834	917	53	to	to	ADP
ejpam-6834	917	54	p(pr(x	p(pr(x	PROPN
ejpam-6834	917	55	)	)	PUNCT
ejpam-6834	917	56	)	)	PUNCT
ejpam-6834	918	1	=	=	SYM
ejpam-6834	918	2	pr+1(x	pr+1(x	PROPN
ejpam-6834	918	3	)	)	PUNCT
ejpam-6834	918	4	,	,	PUNCT
ejpam-6834	918	5	which	which	PRON
ejpam-6834	918	6	establishes	establish	VERB
ejpam-6834	918	7	the	the	DET
ejpam-6834	918	8	inductive	inductive	ADJ
ejpam-6834	918	9	step	step	NOUN
ejpam-6834	918	10	.	.	PUNCT
ejpam-6834	919	1	now	now	ADV
ejpam-6834	919	2	fix	fix	VERB
ejpam-6834	919	3	(	(	PUNCT
ejpam-6834	919	4	a′	a′	PROPN
ejpam-6834	919	5	1	1	NUM
ejpam-6834	919	6	,	,	PUNCT
ejpam-6834	919	7	.	.	PUNCT
ejpam-6834	919	8	.	.	PUNCT
ejpam-6834	920	1	.	.	PUNCT
ejpam-6834	921	1	,	,	PUNCT
ejpam-6834	921	2	a	a	DET
ejpam-6834	921	3	′	′	NOUN
ejpam-6834	921	4	h	h	NOUN
ejpam-6834	921	5	)	)	PUNCT
ejpam-6834	921	6	∈	∈	PROPN
ejpam-6834	921	7	(	(	PUNCT
ejpam-6834	921	8	pm(y	pm(y	ADJ
ejpam-6834	921	9	)	)	PUNCT
ejpam-6834	921	10	)	)	PUNCT
ejpam-6834	922	1	h.	h.	NOUN
ejpam-6834	922	2	by	by	ADP
ejpam-6834	922	3	the	the	DET
ejpam-6834	922	4	previous	previous	ADJ
ejpam-6834	922	5	paragraph	paragraph	NOUN
ejpam-6834	922	6	,	,	PUNCT
ejpam-6834	922	7	f−1	f−1	PROPN
ejpam-6834	922	8	(	(	PUNCT
ejpam-6834	922	9	m)(a	m)(a	PROPN
ejpam-6834	922	10	′	′	NUM
ejpam-6834	922	11	i	i	NOUN
ejpam-6834	922	12	)	)	PUNCT
ejpam-6834	922	13	∈	∈	PROPN
ejpam-6834	922	14	pm(x	pm(x	PUNCT
ejpam-6834	922	15	)	)	PUNCT
ejpam-6834	922	16	for	for	ADP
ejpam-6834	922	17	each	each	DET
ejpam-6834	922	18	i	i	PRON
ejpam-6834	922	19	,	,	PUNCT
ejpam-6834	922	20	so	so	ADV
ejpam-6834	922	21	the	the	DET
ejpam-6834	922	22	h	h	NOUN
ejpam-6834	922	23	-	-	PUNCT
ejpam-6834	922	24	tuple	tuple	NOUN
ejpam-6834	922	25	(	(	PUNCT
ejpam-6834	922	26	f−1	f−1	PROPN
ejpam-6834	922	27	(	(	PUNCT
ejpam-6834	922	28	m)(a	m)(a	PROPN
ejpam-6834	922	29	′	′	NOUN
ejpam-6834	922	30	1	1	NUM
ejpam-6834	922	31	)	)	PUNCT
ejpam-6834	922	32	,	,	PUNCT
ejpam-6834	922	33	.	.	PUNCT
ejpam-6834	922	34	.	.	PUNCT
ejpam-6834	922	35	.	.	PUNCT
ejpam-6834	923	1	,	,	PUNCT
ejpam-6834	923	2	f	f	PROPN
ejpam-6834	923	3	−1	−1	NOUN
ejpam-6834	923	4	(	(	PUNCT
ejpam-6834	923	5	m)(a	m)(a	PROPN
ejpam-6834	923	6	′	′	NUM
ejpam-6834	923	7	h	h	NOUN
ejpam-6834	923	8	)	)	PUNCT
ejpam-6834	923	9	)	)	PUNCT
ejpam-6834	923	10	lies	lie	VERB
ejpam-6834	923	11	in	in	ADP
ejpam-6834	923	12	(	(	PUNCT
ejpam-6834	923	13	pm(x))h	pm(x))h	X
ejpam-6834	923	14	.	.	PUNCT
ejpam-6834	923	15	applying	apply	VERB
ejpam-6834	923	16	µ	µ	PROPN
ejpam-6834	923	17	(	(	PUNCT
ejpam-6834	923	18	m	m	PROPN
ejpam-6834	923	19	,	,	PUNCT
ejpam-6834	923	20	n	n	CCONJ
ejpam-6834	923	21	)	)	PUNCT
ejpam-6834	923	22	(	(	PUNCT
ejpam-6834	923	23	h	h	NOUN
ejpam-6834	923	24	,	,	PUNCT
ejpam-6834	923	25	k	k	NOUN
ejpam-6834	923	26	)	)	PUNCT
ejpam-6834	923	27	yields	yield	VERB
ejpam-6834	923	28	a	a	DET
ejpam-6834	923	29	k	k	NOUN
ejpam-6834	923	30	-	-	NOUN
ejpam-6834	923	31	tuple	tuple	NOUN
ejpam-6834	923	32	in	in	ADP
ejpam-6834	923	33	(	(	PUNCT
ejpam-6834	923	34	pn([0	pn([0	NOUN
ejpam-6834	923	35	,	,	PUNCT
ejpam-6834	923	36	1]))k	1]))k	NUM
ejpam-6834	923	37	with	with	ADP
ejpam-6834	923	38	nonempty	nonempty	ADJ
ejpam-6834	923	39	coordinates	coordinate	NOUN
ejpam-6834	923	40	(	(	PUNCT
ejpam-6834	923	41	by	by	ADP
ejpam-6834	923	42	the	the	DET
ejpam-6834	923	43	defining	define	VERB
ejpam-6834	923	44	nonemptiness	nonemptiness	NOUN
ejpam-6834	923	45	property	property	NOUN
ejpam-6834	923	46	of	of	ADP
ejpam-6834	923	47	µ	µ	X
ejpam-6834	923	48	(	(	PUNCT
ejpam-6834	923	49	m	m	PROPN
ejpam-6834	923	50	,	,	PUNCT
ejpam-6834	923	51	n	n	CCONJ
ejpam-6834	923	52	)	)	PUNCT
ejpam-6834	923	53	(	(	PUNCT
ejpam-6834	923	54	h	h	NOUN
ejpam-6834	923	55	,	,	PUNCT
ejpam-6834	923	56	k	k	NOUN
ejpam-6834	923	57	)	)	PUNCT
ejpam-6834	923	58	)	)	PUNCT
ejpam-6834	923	59	.	.	PUNCT
ejpam-6834	924	1	therefore	therefore	ADV
ejpam-6834	924	2	(	(	PUNCT
ejpam-6834	924	3	f∗µ	f∗µ	NUM
ejpam-6834	924	4	)	)	PUNCT
ejpam-6834	924	5	(	(	PUNCT
ejpam-6834	924	6	m	m	PROPN
ejpam-6834	924	7	,	,	PUNCT
ejpam-6834	924	8	n	n	CCONJ
ejpam-6834	924	9	)	)	PUNCT
ejpam-6834	924	10	(	(	PUNCT
ejpam-6834	924	11	h	h	NOUN
ejpam-6834	924	12	,	,	PUNCT
ejpam-6834	924	13	k	k	NOUN
ejpam-6834	924	14	)	)	PUNCT
ejpam-6834	924	15	is	be	AUX
ejpam-6834	924	16	a	a	DET
ejpam-6834	924	17	well	well	ADV
ejpam-6834	924	18	-	-	PUNCT
ejpam-6834	924	19	defined	define	VERB
ejpam-6834	924	20	(	(	PUNCT
ejpam-6834	924	21	h	h	NOUN
ejpam-6834	924	22	,	,	PUNCT
ejpam-6834	924	23	k)-ary	k)-ary	X
ejpam-6834	924	24	(	(	PUNCT
ejpam-6834	924	25	m	m	PROPN
ejpam-6834	924	26	,	,	PUNCT
ejpam-6834	924	27	n)-superhyperfuzzy	n)-superhyperfuzzy	PUNCT
ejpam-6834	924	28	set	set	VERB
ejpam-6834	924	29	on	on	ADP
ejpam-6834	924	30	y	y	PROPN
ejpam-6834	924	31	.	.	PUNCT
ejpam-6834	925	1	t.	t.	PROPN
ejpam-6834	925	2	fujita	fujita	PROPN
ejpam-6834	925	3	,	,	PUNCT
ejpam-6834	925	4	f.smarandache	f.smarandache	NOUN
ejpam-6834	925	5	/	/	SYM
ejpam-6834	925	6	eur	eur	PROPN
ejpam-6834	925	7	.	.	PUNCT
ejpam-6834	926	1	j.	j.	PROPN
ejpam-6834	926	2	pure	pure	PROPN
ejpam-6834	926	3	appl	appl	PROPN
ejpam-6834	926	4	.	.	PROPN
ejpam-6834	926	5	math	math	PROPN
ejpam-6834	926	6	,	,	PUNCT
ejpam-6834	926	7	18	18	NUM
ejpam-6834	926	8	(	(	PUNCT
ejpam-6834	926	9	4	4	NUM
ejpam-6834	926	10	)	)	PUNCT
ejpam-6834	926	11	(	(	PUNCT
ejpam-6834	926	12	2025	2025	NUM
ejpam-6834	926	13	)	)	PUNCT
ejpam-6834	926	14	,	,	PUNCT
ejpam-6834	926	15	6834	6834	NUM
ejpam-6834	926	16	38	38	NUM
ejpam-6834	926	17	of	of	ADP
ejpam-6834	926	18	69	69	NUM
ejpam-6834	926	19	3.2.2	3.2.2	NUM
ejpam-6834	926	20	.	.	PUNCT
ejpam-6834	927	1	(	(	PUNCT
ejpam-6834	927	2	h	h	NOUN
ejpam-6834	927	3	,	,	PUNCT
ejpam-6834	927	4	k)-ary	k)-ary	X
ejpam-6834	927	5	(	(	PUNCT
ejpam-6834	927	6	m	m	PROPN
ejpam-6834	927	7	,	,	PUNCT
ejpam-6834	927	8	n)-superhyperneutrosophic	n)-superhyperneutrosophic	PUNCT
ejpam-6834	927	9	set	set	VERB
ejpam-6834	927	10	an	an	DET
ejpam-6834	927	11	(	(	PUNCT
ejpam-6834	927	12	h	h	NOUN
ejpam-6834	927	13	,	,	PUNCT
ejpam-6834	927	14	k)-ary	k)-ary	X
ejpam-6834	927	15	(	(	PUNCT
ejpam-6834	927	16	m	m	PROPN
ejpam-6834	927	17	,	,	PUNCT
ejpam-6834	927	18	n)-superhyperneutrosophic	n)-superhyperneutrosophic	PUNCT
ejpam-6834	927	19	set	set	NOUN
ejpam-6834	927	20	accepts	accept	VERB
ejpam-6834	927	21	h	h	NOUN
ejpam-6834	927	22	inputs	input	NOUN
ejpam-6834	927	23	taken	take	VERB
ejpam-6834	927	24	from	from	ADP
ejpam-6834	927	25	the	the	DET
ejpam-6834	927	26	m	m	PROPN
ejpam-6834	927	27	-	-	PUNCT
ejpam-6834	927	28	th	th	VERB
ejpam-6834	927	29	nonempty	nonempty	ADV
ejpam-6834	927	30	iterated	iterate	VERB
ejpam-6834	927	31	powerset	powerset	NOUN
ejpam-6834	927	32	of	of	ADP
ejpam-6834	927	33	a	a	DET
ejpam-6834	927	34	base	base	NOUN
ejpam-6834	927	35	set	set	NOUN
ejpam-6834	927	36	and	and	CCONJ
ejpam-6834	927	37	returns	return	VERB
ejpam-6834	927	38	k	k	PROPN
ejpam-6834	927	39	outputs	output	NOUN
ejpam-6834	927	40	that	that	PRON
ejpam-6834	927	41	are	be	AUX
ejpam-6834	927	42	elements	element	NOUN
ejpam-6834	927	43	of	of	ADP
ejpam-6834	927	44	the	the	DET
ejpam-6834	927	45	n	n	ADV
ejpam-6834	927	46	-	-	PUNCT
ejpam-6834	927	47	th	th	X
ejpam-6834	927	48	nonempty	nonempty	ADV
ejpam-6834	927	49	iterated	iterate	VERB
ejpam-6834	927	50	powerset	powerset	NOUN
ejpam-6834	927	51	of	of	ADP
ejpam-6834	927	52	the	the	DET
ejpam-6834	927	53	unit	unit	NOUN
ejpam-6834	927	54	cube	cube	NOUN
ejpam-6834	928	1	[	[	X
ejpam-6834	928	2	0	0	NUM
ejpam-6834	928	3	,	,	PUNCT
ejpam-6834	928	4	1]3	1]3	NUM
ejpam-6834	928	5	of	of	ADP
ejpam-6834	928	6	neutrosophic	neutrosophic	ADJ
ejpam-6834	928	7	triples	triple	NOUN
ejpam-6834	928	8	.	.	PUNCT
ejpam-6834	929	1	in	in	ADP
ejpam-6834	929	2	this	this	DET
ejpam-6834	929	3	way	way	NOUN
ejpam-6834	929	4	,	,	PUNCT
ejpam-6834	929	5	it	it	PRON
ejpam-6834	929	6	models	model	VERB
ejpam-6834	929	7	multi	multi	ADJ
ejpam-6834	929	8	-	-	ADJ
ejpam-6834	929	9	ary	ary	ADJ
ejpam-6834	929	10	interactions	interaction	NOUN
ejpam-6834	929	11	between	between	ADP
ejpam-6834	929	12	hierarchical	hierarchical	ADJ
ejpam-6834	929	13	(	(	PUNCT
ejpam-6834	929	14	nested	nested	ADJ
ejpam-6834	929	15	)	)	PUNCT
ejpam-6834	929	16	collections	collection	NOUN
ejpam-6834	929	17	of	of	ADP
ejpam-6834	929	18	objects	object	NOUN
ejpam-6834	929	19	and	and	CCONJ
ejpam-6834	929	20	produces	produce	VERB
ejpam-6834	929	21	hierarchical	hierarchical	ADJ
ejpam-6834	929	22	collections	collection	NOUN
ejpam-6834	929	23	of	of	ADP
ejpam-6834	929	24	neutrosophic	neutrosophic	ADJ
ejpam-6834	929	25	assessments	assessment	NOUN
ejpam-6834	929	26	—	—	PUNCT
ejpam-6834	929	27	each	each	DET
ejpam-6834	929	28	assessment	assessment	NOUN
ejpam-6834	929	29	being	be	AUX
ejpam-6834	929	30	a	a	DET
ejpam-6834	929	31	triple	triple	ADJ
ejpam-6834	929	32	(	(	PUNCT
ejpam-6834	929	33	t	t	PROPN
ejpam-6834	929	34	,	,	PUNCT
ejpam-6834	929	35	i	i	PRON
ejpam-6834	929	36	,	,	PUNCT
ejpam-6834	929	37	f	f	PROPN
ejpam-6834	929	38	)	)	PUNCT
ejpam-6834	929	39	∈	∈	PROPN
ejpam-6834	930	1	[	[	X
ejpam-6834	930	2	0	0	NUM
ejpam-6834	930	3	,	,	PUNCT
ejpam-6834	930	4	1]3	1]3	NUM
ejpam-6834	930	5	of	of	ADP
ejpam-6834	930	6	truth	truth	NOUN
ejpam-6834	930	7	,	,	PUNCT
ejpam-6834	930	8	indeterminacy	indeterminacy	NOUN
ejpam-6834	930	9	,	,	PUNCT
ejpam-6834	930	10	and	and	CCONJ
ejpam-6834	930	11	falsity	falsity	NOUN
ejpam-6834	930	12	degrees	degree	NOUN
ejpam-6834	930	13	satisfying	satisfy	VERB
ejpam-6834	930	14	0	0	NUM
ejpam-6834	930	15	≤	≤	NUM
ejpam-6834	930	16	t	t	NOUN
ejpam-6834	931	1	+	+	CCONJ
ejpam-6834	931	2	i	i	PRON
ejpam-6834	931	3	+	+	NUM
ejpam-6834	932	1	f	f	PROPN
ejpam-6834	932	2	≤	≤	ADV
ejpam-6834	932	3	3	3	NUM
ejpam-6834	932	4	.	.	PUNCT
ejpam-6834	932	5	definition	definition	NOUN
ejpam-6834	932	6	23	23	NUM
ejpam-6834	932	7	(	(	PUNCT
ejpam-6834	932	8	(	(	PUNCT
ejpam-6834	932	9	h	h	NOUN
ejpam-6834	932	10	,	,	PUNCT
ejpam-6834	932	11	k)-ary	k)-ary	X
ejpam-6834	932	12	(	(	PUNCT
ejpam-6834	932	13	m	m	PROPN
ejpam-6834	932	14	,	,	PUNCT
ejpam-6834	932	15	n)-superhyperneutrosophic	n)-superhyperneutrosophic	ADJ
ejpam-6834	932	16	set	set	NOUN
ejpam-6834	932	17	)	)	PUNCT
ejpam-6834	932	18	.	.	PUNCT
ejpam-6834	933	1	let	let	VERB
ejpam-6834	933	2	x	x	PRON
ejpam-6834	933	3	be	be	AUX
ejpam-6834	933	4	a	a	DET
ejpam-6834	933	5	nonempty	nonempty	ADJ
ejpam-6834	933	6	set	set	NOUN
ejpam-6834	933	7	,	,	PUNCT
ejpam-6834	933	8	and	and	CCONJ
ejpam-6834	933	9	let	let	VERB
ejpam-6834	933	10	m	m	PRON
ejpam-6834	933	11	,	,	PUNCT
ejpam-6834	933	12	n	n	CCONJ
ejpam-6834	933	13	,	,	PUNCT
ejpam-6834	933	14	h	h	NOUN
ejpam-6834	933	15	,	,	PUNCT
ejpam-6834	933	16	k	k	PROPN
ejpam-6834	933	17	∈	∈	PROPN
ejpam-6834	933	18	n	n	X
ejpam-6834	933	19	with	with	ADP
ejpam-6834	933	20	m	m	PROPN
ejpam-6834	933	21	,	,	PUNCT
ejpam-6834	933	22	n	n	CCONJ
ejpam-6834	933	23	,	,	PUNCT
ejpam-6834	933	24	h	h	NOUN
ejpam-6834	933	25	,	,	PUNCT
ejpam-6834	933	26	k	k	PROPN
ejpam-6834	933	27	≥	≥	NUM
ejpam-6834	933	28	1	1	NUM
ejpam-6834	933	29	.	.	PUNCT
ejpam-6834	934	1	an	an	DET
ejpam-6834	934	2	(	(	PUNCT
ejpam-6834	934	3	h	h	NOUN
ejpam-6834	934	4	,	,	PUNCT
ejpam-6834	934	5	k)-ary	k)-ary	X
ejpam-6834	934	6	(	(	PUNCT
ejpam-6834	934	7	m	m	PROPN
ejpam-6834	934	8	,	,	PUNCT
ejpam-6834	934	9	n)-superhyperneutrosophic	n)-superhyperneutrosophic	PUNCT
ejpam-6834	934	10	set	set	VERB
ejpam-6834	934	11	on	on	ADP
ejpam-6834	934	12	x	x	SYM
ejpam-6834	934	13	is	be	AUX
ejpam-6834	934	14	a	a	DET
ejpam-6834	934	15	mapping	mapping	NOUN
ejpam-6834	934	16	ã	ã	PROPN
ejpam-6834	934	17	(	(	PUNCT
ejpam-6834	934	18	m	m	PROPN
ejpam-6834	934	19	,	,	PUNCT
ejpam-6834	934	20	n	n	CCONJ
ejpam-6834	934	21	)	)	PUNCT
ejpam-6834	934	22	(	(	PUNCT
ejpam-6834	934	23	h	h	NOUN
ejpam-6834	934	24	,	,	PUNCT
ejpam-6834	934	25	k	k	NOUN
ejpam-6834	934	26	)	)	PUNCT
ejpam-6834	934	27	:	:	PUNCT
ejpam-6834	934	28	(	(	PUNCT
ejpam-6834	934	29	p̃m(x	p̃m(x	X
ejpam-6834	934	30	)	)	PUNCT
ejpam-6834	934	31	)	)	PUNCT
ejpam-6834	935	1	h	h	NOUN
ejpam-6834	935	2	−→	−→	NOUN
ejpam-6834	935	3	(	(	PUNCT
ejpam-6834	935	4	p̃n([0	p̃n([0	PROPN
ejpam-6834	935	5	,	,	PUNCT
ejpam-6834	935	6	1]3	1]3	NUM
ejpam-6834	935	7	)	)	PUNCT
ejpam-6834	935	8	)	)	PUNCT
ejpam-6834	936	1	k	k	NOUN
ejpam-6834	936	2	with	with	ADP
ejpam-6834	936	3	the	the	DET
ejpam-6834	936	4	following	follow	VERB
ejpam-6834	936	5	property	property	NOUN
ejpam-6834	936	6	:	:	PUNCT
ejpam-6834	936	7	for	for	ADP
ejpam-6834	936	8	every	every	DET
ejpam-6834	936	9	input	input	NOUN
ejpam-6834	936	10	h	h	NOUN
ejpam-6834	936	11	-	-	PUNCT
ejpam-6834	936	12	tuple	tuple	NOUN
ejpam-6834	936	13	(	(	PUNCT
ejpam-6834	936	14	a1	a1	PROPN
ejpam-6834	936	15	,	,	PUNCT
ejpam-6834	936	16	.	.	PUNCT
ejpam-6834	936	17	.	.	PUNCT
ejpam-6834	936	18	.	.	PUNCT
ejpam-6834	937	1	,	,	PUNCT
ejpam-6834	937	2	ah	ah	INTJ
ejpam-6834	937	3	)	)	PUNCT
ejpam-6834	937	4	∈	∈	PROPN
ejpam-6834	937	5	(	(	PUNCT
ejpam-6834	937	6	p̃m(x))h	p̃m(x))h	NOUN
ejpam-6834	937	7	the	the	DET
ejpam-6834	937	8	image	image	NOUN
ejpam-6834	937	9	is	be	AUX
ejpam-6834	937	10	a	a	DET
ejpam-6834	937	11	k	k	NOUN
ejpam-6834	937	12	-	-	NOUN
ejpam-6834	937	13	tuple	tuple	NOUN
ejpam-6834	937	14	(	(	PUNCT
ejpam-6834	937	15	c1	c1	PROPN
ejpam-6834	937	16	,	,	PUNCT
ejpam-6834	937	17	.	.	PUNCT
ejpam-6834	937	18	.	.	PUNCT
ejpam-6834	938	1	.	.	PUNCT
ejpam-6834	939	1	,	,	PUNCT
ejpam-6834	939	2	ck	ck	X
ejpam-6834	939	3	)	)	PUNCT
ejpam-6834	939	4	with	with	ADP
ejpam-6834	939	5	each	each	DET
ejpam-6834	939	6	cj	cj	NOUN
ejpam-6834	939	7	∈	∈	PROPN
ejpam-6834	939	8	p̃n([0	p̃n([0	PROPN
ejpam-6834	939	9	,	,	PUNCT
ejpam-6834	939	10	1]3	1]3	NUM
ejpam-6834	939	11	)	)	PUNCT
ejpam-6834	939	12	;	;	PUNCT
ejpam-6834	939	13	in	in	ADP
ejpam-6834	939	14	particular	particular	ADJ
ejpam-6834	939	15	,	,	PUNCT
ejpam-6834	939	16	every	every	DET
ejpam-6834	939	17	base	base	NOUN
ejpam-6834	939	18	-	-	PUNCT
ejpam-6834	939	19	level	level	NOUN
ejpam-6834	939	20	element	element	NOUN
ejpam-6834	939	21	of	of	ADP
ejpam-6834	939	22	each	each	DET
ejpam-6834	939	23	cj	cj	NOUN
ejpam-6834	939	24	is	be	AUX
ejpam-6834	939	25	a	a	DET
ejpam-6834	939	26	triple	triple	ADJ
ejpam-6834	939	27	(	(	PUNCT
ejpam-6834	939	28	t	t	PROPN
ejpam-6834	939	29	,	,	PUNCT
ejpam-6834	939	30	i	i	PRON
ejpam-6834	939	31	,	,	PUNCT
ejpam-6834	939	32	f	f	PROPN
ejpam-6834	939	33	)	)	PUNCT
ejpam-6834	939	34	∈	∈	PROPN
ejpam-6834	940	1	[	[	X
ejpam-6834	940	2	0	0	NUM
ejpam-6834	940	3	,	,	PUNCT
ejpam-6834	940	4	1]3	1]3	NUM
ejpam-6834	940	5	satisfying	satisfy	VERB
ejpam-6834	940	6	0	0	NUM
ejpam-6834	940	7	≤	≤	NUM
ejpam-6834	940	8	t	t	NOUN
ejpam-6834	941	1	+	+	CCONJ
ejpam-6834	941	2	i	i	PRON
ejpam-6834	941	3	+	+	NUM
ejpam-6834	942	1	f	f	PROPN
ejpam-6834	942	2	≤	≤	ADV
ejpam-6834	942	3	3	3	NUM
ejpam-6834	942	4	.	.	X
ejpam-6834	943	1	nonemptiness	nonemptiness	PROPN
ejpam-6834	943	2	is	be	AUX
ejpam-6834	943	3	enforced	enforce	VERB
ejpam-6834	943	4	at	at	ADP
ejpam-6834	943	5	every	every	DET
ejpam-6834	943	6	nested	nested	ADJ
ejpam-6834	943	7	level	level	NOUN
ejpam-6834	943	8	by	by	ADP
ejpam-6834	943	9	the	the	DET
ejpam-6834	943	10	use	use	NOUN
ejpam-6834	943	11	of	of	ADP
ejpam-6834	943	12	p̃•.	p̃•.	PROPN
ejpam-6834	943	13	example	example	NOUN
ejpam-6834	943	14	23	23	NUM
ejpam-6834	943	15	(	(	PUNCT
ejpam-6834	943	16	unary	unary	ADJ
ejpam-6834	943	17	case	case	NOUN
ejpam-6834	943	18	(	(	PUNCT
ejpam-6834	943	19	h	h	NOUN
ejpam-6834	943	20	,	,	PUNCT
ejpam-6834	943	21	k	k	NOUN
ejpam-6834	943	22	)	)	PUNCT
ejpam-6834	943	23	=	=	SYM
ejpam-6834	943	24	(	(	PUNCT
ejpam-6834	943	25	1	1	NUM
ejpam-6834	943	26	,	,	PUNCT
ejpam-6834	943	27	1	1	NUM
ejpam-6834	943	28	)	)	PUNCT
ejpam-6834	943	29	)	)	PUNCT
ejpam-6834	943	30	.	.	PUNCT
ejpam-6834	944	1	let	let	VERB
ejpam-6834	944	2	x	x	PUNCT
ejpam-6834	944	3	=	=	PRON
ejpam-6834	944	4	{	{	PUNCT
ejpam-6834	944	5	a	a	DET
ejpam-6834	944	6	,	,	PUNCT
ejpam-6834	944	7	b	b	NOUN
ejpam-6834	944	8	}	}	PUNCT
ejpam-6834	944	9	and	and	CCONJ
ejpam-6834	944	10	take	take	VERB
ejpam-6834	944	11	m	m	NOUN
ejpam-6834	944	12	=	=	SYM
ejpam-6834	944	13	n	n	NOUN
ejpam-6834	944	14	=	=	SYM
ejpam-6834	944	15	1	1	X
ejpam-6834	944	16	.	.	PUNCT
ejpam-6834	944	17	then	then	ADV
ejpam-6834	944	18	p̃1(x	p̃1(x	NOUN
ejpam-6834	944	19	)	)	PUNCT
ejpam-6834	944	20	=	=	PUNCT
ejpam-6834	944	21	p̃(x	p̃(x	PROPN
ejpam-6834	944	22	)	)	PUNCT
ejpam-6834	944	23	=	=	PRON
ejpam-6834	944	24	{	{	PUNCT
ejpam-6834	944	25	{	{	PUNCT
ejpam-6834	944	26	a	a	NOUN
ejpam-6834	944	27	}	}	PUNCT
ejpam-6834	944	28	,	,	PUNCT
ejpam-6834	944	29	{	{	PUNCT
ejpam-6834	944	30	b	b	NOUN
ejpam-6834	944	31	}	}	PUNCT
ejpam-6834	944	32	,	,	PUNCT
ejpam-6834	944	33	{	{	PUNCT
ejpam-6834	944	34	a	a	DET
ejpam-6834	944	35	,	,	PUNCT
ejpam-6834	944	36	b	b	NOUN
ejpam-6834	944	37	}	}	PUNCT
ejpam-6834	944	38	}	}	PUNCT
ejpam-6834	944	39	and	and	CCONJ
ejpam-6834	944	40	p̃1([0	p̃1([0	NOUN
ejpam-6834	944	41	,	,	PUNCT
ejpam-6834	944	42	1]3	1]3	NUM
ejpam-6834	944	43	)	)	PUNCT
ejpam-6834	944	44	=	=	PUNCT
ejpam-6834	945	1	p̃([0	p̃([0	VERB
ejpam-6834	945	2	,	,	PUNCT
ejpam-6834	945	3	1]3	1]3	NUM
ejpam-6834	945	4	)	)	PUNCT
ejpam-6834	945	5	.	.	PUNCT
ejpam-6834	946	1	a	a	DET
ejpam-6834	946	2	map	map	NOUN
ejpam-6834	946	3	ã	ã	PROPN
ejpam-6834	946	4	(	(	PUNCT
ejpam-6834	946	5	1,1	1,1	NUM
ejpam-6834	946	6	)	)	PUNCT
ejpam-6834	946	7	(	(	PUNCT
ejpam-6834	946	8	1,1	1,1	NUM
ejpam-6834	946	9	)	)	PUNCT
ejpam-6834	946	10	:	:	PUNCT
ejpam-6834	946	11	p̃(x	p̃(x	NOUN
ejpam-6834	946	12	)	)	PUNCT
ejpam-6834	946	13	−→	−→	NOUN
ejpam-6834	946	14	p̃([0	p̃([0	NUM
ejpam-6834	946	15	,	,	PUNCT
ejpam-6834	946	16	1]3	1]3	NUM
ejpam-6834	946	17	)	)	PUNCT
ejpam-6834	946	18	is	be	AUX
ejpam-6834	946	19	given	give	VERB
ejpam-6834	946	20	,	,	PUNCT
ejpam-6834	946	21	for	for	ADP
ejpam-6834	946	22	instance	instance	NOUN
ejpam-6834	946	23	,	,	PUNCT
ejpam-6834	946	24	by	by	ADP
ejpam-6834	946	25	ã	ã	PROPN
ejpam-6834	946	26	(	(	PUNCT
ejpam-6834	946	27	1,1	1,1	NUM
ejpam-6834	946	28	)	)	PUNCT
ejpam-6834	946	29	(	(	PUNCT
ejpam-6834	946	30	1,1)({a	1,1)({a	NUM
ejpam-6834	946	31	}	}	PUNCT
ejpam-6834	946	32	)	)	PUNCT
ejpam-6834	946	33	=	=	PRON
ejpam-6834	946	34	{	{	PUNCT
ejpam-6834	946	35	(	(	PUNCT
ejpam-6834	946	36	0.6	0.6	NUM
ejpam-6834	946	37	,	,	PUNCT
ejpam-6834	946	38	0.2	0.2	NUM
ejpam-6834	946	39	,	,	PUNCT
ejpam-6834	946	40	0.1	0.1	NUM
ejpam-6834	946	41	)	)	PUNCT
ejpam-6834	946	42	}	}	PUNCT
ejpam-6834	946	43	,	,	PUNCT
ejpam-6834	946	44	ã	ã	PROPN
ejpam-6834	946	45	(	(	PUNCT
ejpam-6834	946	46	1,1	1,1	NUM
ejpam-6834	946	47	)	)	PUNCT
ejpam-6834	946	48	(	(	PUNCT
ejpam-6834	946	49	1,1)({b	1,1)({b	NUM
ejpam-6834	946	50	}	}	PUNCT
ejpam-6834	946	51	)	)	PUNCT
ejpam-6834	946	52	=	=	PRON
ejpam-6834	946	53	{	{	PUNCT
ejpam-6834	946	54	(	(	PUNCT
ejpam-6834	946	55	0.4	0.4	NUM
ejpam-6834	946	56	,	,	PUNCT
ejpam-6834	946	57	0.3	0.3	NUM
ejpam-6834	946	58	,	,	PUNCT
ejpam-6834	946	59	0.2	0.2	NUM
ejpam-6834	946	60	)	)	PUNCT
ejpam-6834	946	61	}	}	PUNCT
ejpam-6834	946	62	,	,	PUNCT
ejpam-6834	946	63	ã	ã	PROPN
ejpam-6834	946	64	(	(	PUNCT
ejpam-6834	946	65	1,1	1,1	NUM
ejpam-6834	946	66	)	)	PUNCT
ejpam-6834	946	67	(	(	PUNCT
ejpam-6834	946	68	1,1)({a	1,1)({a	NUM
ejpam-6834	946	69	,	,	PUNCT
ejpam-6834	946	70	b	b	NOUN
ejpam-6834	946	71	}	}	PUNCT
ejpam-6834	946	72	)	)	PUNCT
ejpam-6834	946	73	=	=	PRON
ejpam-6834	946	74	{	{	PUNCT
ejpam-6834	946	75	(	(	PUNCT
ejpam-6834	946	76	0.7	0.7	NUM
ejpam-6834	946	77	,	,	PUNCT
ejpam-6834	946	78	0.1	0.1	NUM
ejpam-6834	946	79	,	,	PUNCT
ejpam-6834	946	80	0.1	0.1	NUM
ejpam-6834	946	81	)	)	PUNCT
ejpam-6834	946	82	,	,	PUNCT
ejpam-6834	946	83	(	(	PUNCT
ejpam-6834	946	84	0.8	0.8	NUM
ejpam-6834	946	85	,	,	PUNCT
ejpam-6834	946	86	0.0	0.0	NUM
ejpam-6834	946	87	,	,	PUNCT
ejpam-6834	946	88	0.1	0.1	NUM
ejpam-6834	946	89	)	)	PUNCT
ejpam-6834	946	90	}	}	PUNCT
ejpam-6834	946	91	.	.	PUNCT
ejpam-6834	947	1	each	each	DET
ejpam-6834	947	2	triple	triple	ADJ
ejpam-6834	947	3	lies	lie	VERB
ejpam-6834	947	4	in	in	ADP
ejpam-6834	947	5	[	[	X
ejpam-6834	947	6	0	0	NUM
ejpam-6834	947	7	,	,	PUNCT
ejpam-6834	947	8	1]3	1]3	NUM
ejpam-6834	947	9	and	and	CCONJ
ejpam-6834	947	10	satisfies	satisfie	NOUN
ejpam-6834	947	11	t	t	PROPN
ejpam-6834	948	1	+	+	CCONJ
ejpam-6834	948	2	i	i	PRON
ejpam-6834	948	3	+	+	NUM
ejpam-6834	948	4	f	f	PROPN
ejpam-6834	948	5	≤	≤	ADV
ejpam-6834	948	6	3	3	NUM
ejpam-6834	948	7	,	,	PUNCT
ejpam-6834	948	8	as	as	SCONJ
ejpam-6834	948	9	required	require	VERB
ejpam-6834	948	10	.	.	PUNCT
ejpam-6834	949	1	example	example	NOUN
ejpam-6834	949	2	24	24	NUM
ejpam-6834	949	3	(	(	PUNCT
ejpam-6834	949	4	credit	credit	NOUN
ejpam-6834	949	5	&	&	CCONJ
ejpam-6834	949	6	liquidity	liquidity	NOUN
ejpam-6834	949	7	risk	risk	NOUN
ejpam-6834	949	8	as	as	ADP
ejpam-6834	949	9	a	a	DET
ejpam-6834	949	10	(	(	PUNCT
ejpam-6834	949	11	2	2	NUM
ejpam-6834	949	12	,	,	PUNCT
ejpam-6834	949	13	2)-ary	2)-ary	NUM
ejpam-6834	949	14	(	(	PUNCT
ejpam-6834	949	15	1	1	NUM
ejpam-6834	949	16	,	,	PUNCT
ejpam-6834	949	17	1)-system	1)-system	NUM
ejpam-6834	949	18	)	)	PUNCT
ejpam-6834	949	19	.	.	PUNCT
ejpam-6834	950	1	consider	consider	VERB
ejpam-6834	950	2	banking	banking	NOUN
ejpam-6834	950	3	indicators	indicator	NOUN
ejpam-6834	950	4	x	x	PUNCT
ejpam-6834	950	5	=	=	PRON
ejpam-6834	950	6	{	{	PUNCT
ejpam-6834	950	7	debttoincome	debttoincome	PROPN
ejpam-6834	950	8	,	,	PUNCT
ejpam-6834	950	9	creditscore	creditscore	NOUN
ejpam-6834	950	10	,	,	PUNCT
ejpam-6834	950	11	marketvolatility	marketvolatility	NOUN
ejpam-6834	950	12	,	,	PUNCT
ejpam-6834	950	13	interestrate	interestrate	NOUN
ejpam-6834	950	14	}	}	PUNCT
ejpam-6834	950	15	,	,	PUNCT
ejpam-6834	950	16	and	and	CCONJ
ejpam-6834	950	17	set	set	VERB
ejpam-6834	950	18	m	m	PROPN
ejpam-6834	950	19	=	=	SYM
ejpam-6834	950	20	n	n	PROPN
ejpam-6834	950	21	=	=	SYM
ejpam-6834	950	22	1	1	NUM
ejpam-6834	950	23	,	,	PUNCT
ejpam-6834	950	24	h	h	NOUN
ejpam-6834	951	1	=	=	SYM
ejpam-6834	951	2	k	k	NOUN
ejpam-6834	951	3	=	=	SYM
ejpam-6834	951	4	2	2	X
ejpam-6834	951	5	.	.	PUNCT
ejpam-6834	952	1	the	the	DET
ejpam-6834	952	2	domain	domain	NOUN
ejpam-6834	952	3	and	and	CCONJ
ejpam-6834	952	4	codomain	codomain	NOUN
ejpam-6834	952	5	are	be	AUX
ejpam-6834	952	6	d	d	NOUN
ejpam-6834	952	7	=	=	SYM
ejpam-6834	952	8	p̃(x	p̃(x	PROPN
ejpam-6834	952	9	)	)	PUNCT
ejpam-6834	952	10	×	×	PROPN
ejpam-6834	952	11	p̃(x	p̃(x	PROPN
ejpam-6834	952	12	)	)	PUNCT
ejpam-6834	952	13	,	,	PUNCT
ejpam-6834	952	14	c	c	NOUN
ejpam-6834	952	15	=	=	SYM
ejpam-6834	952	16	p̃([0	p̃([0	NUM
ejpam-6834	952	17	,	,	PUNCT
ejpam-6834	952	18	1]3	1]3	NUM
ejpam-6834	952	19	)	)	PUNCT
ejpam-6834	952	20	×	×	NOUN
ejpam-6834	952	21	p̃([0	p̃([0	NUM
ejpam-6834	952	22	,	,	PUNCT
ejpam-6834	952	23	1]3	1]3	NUM
ejpam-6834	952	24	)	)	PUNCT
ejpam-6834	952	25	.	.	PUNCT
ejpam-6834	953	1	t.	t.	PROPN
ejpam-6834	953	2	fujita	fujita	PROPN
ejpam-6834	953	3	,	,	PUNCT
ejpam-6834	953	4	f.smarandache	f.smarandache	NOUN
ejpam-6834	953	5	/	/	SYM
ejpam-6834	953	6	eur	eur	PROPN
ejpam-6834	953	7	.	.	PUNCT
ejpam-6834	954	1	j.	j.	PROPN
ejpam-6834	954	2	pure	pure	PROPN
ejpam-6834	954	3	appl	appl	PROPN
ejpam-6834	954	4	.	.	PROPN
ejpam-6834	954	5	math	math	PROPN
ejpam-6834	954	6	,	,	PUNCT
ejpam-6834	954	7	18	18	NUM
ejpam-6834	954	8	(	(	PUNCT
ejpam-6834	954	9	4	4	NUM
ejpam-6834	954	10	)	)	PUNCT
ejpam-6834	954	11	(	(	PUNCT
ejpam-6834	954	12	2025	2025	NUM
ejpam-6834	954	13	)	)	PUNCT
ejpam-6834	954	14	,	,	PUNCT
ejpam-6834	954	15	6834	6834	NUM
ejpam-6834	954	16	39	39	NUM
ejpam-6834	954	17	of	of	ADP
ejpam-6834	954	18	69	69	NUM
ejpam-6834	954	19	given	give	VERB
ejpam-6834	954	20	(	(	PUNCT
ejpam-6834	954	21	a1	a1	PROPN
ejpam-6834	954	22	,	,	PUNCT
ejpam-6834	954	23	a2	a2	NOUN
ejpam-6834	954	24	)	)	PUNCT
ejpam-6834	954	25	∈	∈	PROPN
ejpam-6834	955	1	d	d	X
ejpam-6834	955	2	—	—	PUNCT
ejpam-6834	955	3	say	say	VERB
ejpam-6834	955	4	a1	a1	NOUN
ejpam-6834	955	5	=	=	SYM
ejpam-6834	955	6	{	{	PUNCT
ejpam-6834	955	7	debttoincome	debttoincome	PROPN
ejpam-6834	955	8	,	,	PUNCT
ejpam-6834	955	9	creditscore	creditscore	NOUN
ejpam-6834	955	10	}	}	PUNCT
ejpam-6834	955	11	and	and	CCONJ
ejpam-6834	955	12	a2	a2	PROPN
ejpam-6834	955	13	=	=	SYM
ejpam-6834	955	14	{	{	PUNCT
ejpam-6834	955	15	marketvolatility	marketvolatility	NOUN
ejpam-6834	955	16	,	,	PUNCT
ejpam-6834	955	17	interestrate	interestrate	NOUN
ejpam-6834	955	18	}	}	PUNCT
ejpam-6834	955	19	—	—	PUNCT
ejpam-6834	955	20	define	define	VERB
ejpam-6834	955	21	ã	ã	PROPN
ejpam-6834	955	22	(	(	PUNCT
ejpam-6834	955	23	1,1	1,1	NUM
ejpam-6834	955	24	)	)	PUNCT
ejpam-6834	955	25	(	(	PUNCT
ejpam-6834	955	26	2,2)(a1	2,2)(a1	NUM
ejpam-6834	955	27	,	,	PUNCT
ejpam-6834	955	28	a2	a2	NOUN
ejpam-6834	955	29	)	)	PUNCT
ejpam-6834	955	30	=	=	PRON
ejpam-6834	955	31	(	(	PUNCT
ejpam-6834	955	32	cdefault	cdefault	NOUN
ejpam-6834	955	33	,	,	PUNCT
ejpam-6834	955	34	cliquidity	cliquidity	NOUN
ejpam-6834	955	35	)	)	PUNCT
ejpam-6834	955	36	,	,	PUNCT
ejpam-6834	955	37	with	with	ADP
ejpam-6834	955	38	cdefault	cdefault	NOUN
ejpam-6834	955	39	=	=	SYM
ejpam-6834	955	40	{	{	PUNCT
ejpam-6834	955	41	(	(	PUNCT
ejpam-6834	955	42	0.70	0.70	NUM
ejpam-6834	955	43	,	,	PUNCT
ejpam-6834	955	44	0.20	0.20	NUM
ejpam-6834	955	45	,	,	PUNCT
ejpam-6834	955	46	0.10	0.10	NUM
ejpam-6834	955	47	)	)	PUNCT
ejpam-6834	955	48	,	,	PUNCT
ejpam-6834	955	49	(	(	PUNCT
ejpam-6834	955	50	0.65	0.65	NUM
ejpam-6834	955	51	,	,	PUNCT
ejpam-6834	955	52	0.25	0.25	NUM
ejpam-6834	955	53	,	,	PUNCT
ejpam-6834	955	54	0.10	0.10	NUM
ejpam-6834	955	55	)	)	PUNCT
ejpam-6834	955	56	}	}	PUNCT
ejpam-6834	955	57	,	,	PUNCT
ejpam-6834	955	58	cliquidity	cliquidity	NOUN
ejpam-6834	955	59	=	=	SYM
ejpam-6834	955	60	{	{	PUNCT
ejpam-6834	955	61	(	(	PUNCT
ejpam-6834	955	62	0.40	0.40	NUM
ejpam-6834	955	63	,	,	PUNCT
ejpam-6834	955	64	0.40	0.40	NUM
ejpam-6834	955	65	,	,	PUNCT
ejpam-6834	955	66	0.20	0.20	NUM
ejpam-6834	955	67	)	)	PUNCT
ejpam-6834	955	68	}	}	PUNCT
ejpam-6834	955	69	.	.	PUNCT
ejpam-6834	956	1	all	all	DET
ejpam-6834	956	2	triples	triple	NOUN
ejpam-6834	956	3	satisfy	satisfy	VERB
ejpam-6834	956	4	0	0	NUM
ejpam-6834	956	5	≤	≤	NOUN
ejpam-6834	956	6	t	t	NOUN
ejpam-6834	957	1	+	+	CCONJ
ejpam-6834	957	2	i	i	PRON
ejpam-6834	957	3	+	+	NUM
ejpam-6834	957	4	f	f	PROPN
ejpam-6834	957	5	≤	≤	ADV
ejpam-6834	957	6	3	3	NUM
ejpam-6834	957	7	.	.	PUNCT
ejpam-6834	958	1	thus	thus	ADV
ejpam-6834	958	2	ã	ã	PROPN
ejpam-6834	958	3	(	(	PUNCT
ejpam-6834	958	4	1,1	1,1	NUM
ejpam-6834	958	5	)	)	PUNCT
ejpam-6834	958	6	(	(	PUNCT
ejpam-6834	958	7	2,2	2,2	NUM
ejpam-6834	958	8	)	)	PUNCT
ejpam-6834	958	9	is	be	AUX
ejpam-6834	958	10	a	a	DET
ejpam-6834	958	11	concrete	concrete	ADJ
ejpam-6834	958	12	(	(	PUNCT
ejpam-6834	958	13	2	2	NUM
ejpam-6834	958	14	,	,	PUNCT
ejpam-6834	958	15	2)-ary	2)-ary	NUM
ejpam-6834	958	16	(	(	PUNCT
ejpam-6834	958	17	1	1	NUM
ejpam-6834	958	18	,	,	PUNCT
ejpam-6834	958	19	1)superhyperneutrosophic	1)superhyperneutrosophic	NUM
ejpam-6834	958	20	set	set	NOUN
ejpam-6834	958	21	.	.	PUNCT
ejpam-6834	959	1	theorem	theorem	VERB
ejpam-6834	959	2	29	29	NUM
ejpam-6834	959	3	(	(	PUNCT
ejpam-6834	959	4	relation	relation	NOUN
ejpam-6834	959	5	to	to	ADP
ejpam-6834	959	6	classical	classical	ADJ
ejpam-6834	959	7	and	and	CCONJ
ejpam-6834	959	8	fuzzy	fuzzy	ADJ
ejpam-6834	959	9	cases	case	NOUN
ejpam-6834	959	10	)	)	PUNCT
ejpam-6834	959	11	.	.	PUNCT
ejpam-6834	960	1	every	every	DET
ejpam-6834	960	2	(	(	PUNCT
ejpam-6834	960	3	h	h	NOUN
ejpam-6834	960	4	,	,	PUNCT
ejpam-6834	960	5	k)-ary	k)-ary	X
ejpam-6834	960	6	(	(	PUNCT
ejpam-6834	960	7	m	m	PROPN
ejpam-6834	960	8	,	,	PUNCT
ejpam-6834	960	9	n)-superhyperneutrosophic	n)-superhyperneutrosophic	ADJ
ejpam-6834	960	10	set	set	NOUN
ejpam-6834	960	11	generalizes	generalize	VERB
ejpam-6834	960	12	both	both	DET
ejpam-6834	960	13	(	(	PUNCT
ejpam-6834	960	14	i	i	NOUN
ejpam-6834	960	15	)	)	PUNCT
ejpam-6834	960	16	the	the	DET
ejpam-6834	960	17	classical	classical	ADJ
ejpam-6834	960	18	(	(	PUNCT
ejpam-6834	960	19	m	m	PROPN
ejpam-6834	960	20	,	,	PUNCT
ejpam-6834	960	21	n)-superhyperneutrosophic	n)-superhyperneutrosophic	ADJ
ejpam-6834	960	22	set	set	NOUN
ejpam-6834	960	23	(	(	PUNCT
ejpam-6834	960	24	when	when	SCONJ
ejpam-6834	960	25	h	h	NOUN
ejpam-6834	960	26	=	=	SYM
ejpam-6834	960	27	k	k	NOUN
ejpam-6834	960	28	=	=	SYM
ejpam-6834	960	29	1	1	X
ejpam-6834	960	30	)	)	PUNCT
ejpam-6834	960	31	and	and	CCONJ
ejpam-6834	960	32	(	(	PUNCT
ejpam-6834	960	33	ii	ii	NOUN
ejpam-6834	960	34	)	)	PUNCT
ejpam-6834	960	35	the	the	DET
ejpam-6834	960	36	(	(	PUNCT
ejpam-6834	960	37	h	h	NOUN
ejpam-6834	960	38	,	,	PUNCT
ejpam-6834	960	39	k)-ary	k)-ary	X
ejpam-6834	960	40	(	(	PUNCT
ejpam-6834	960	41	m	m	PROPN
ejpam-6834	960	42	,	,	PUNCT
ejpam-6834	960	43	n)-superhyperfuzzy	n)-superhyperfuzzy	PUNCT
ejpam-6834	960	44	set	set	NOUN
ejpam-6834	960	45	(	(	PUNCT
ejpam-6834	960	46	by	by	ADP
ejpam-6834	960	47	projecting	project	VERB
ejpam-6834	960	48	triples	triple	NOUN
ejpam-6834	960	49	to	to	ADP
ejpam-6834	960	50	their	their	PRON
ejpam-6834	960	51	truth	truth	NOUN
ejpam-6834	960	52	components	component	NOUN
ejpam-6834	960	53	)	)	PUNCT
ejpam-6834	960	54	.	.	PUNCT
ejpam-6834	961	1	proof	proof	NOUN
ejpam-6834	961	2	.	.	PUNCT
ejpam-6834	962	1	let	let	VERB
ejpam-6834	962	2	ã	ã	PROPN
ejpam-6834	962	3	=	=	PUNCT
ejpam-6834	962	4	ã	ã	PROPN
ejpam-6834	962	5	(	(	PUNCT
ejpam-6834	962	6	m	m	PROPN
ejpam-6834	962	7	,	,	PUNCT
ejpam-6834	962	8	n	n	CCONJ
ejpam-6834	962	9	)	)	PUNCT
ejpam-6834	962	10	(	(	PUNCT
ejpam-6834	962	11	h	h	NOUN
ejpam-6834	962	12	,	,	PUNCT
ejpam-6834	962	13	k	k	NOUN
ejpam-6834	962	14	)	)	PUNCT
ejpam-6834	962	15	:	:	PUNCT
ejpam-6834	962	16	(	(	PUNCT
ejpam-6834	962	17	p̃m(x))h	p̃m(x))h	X
ejpam-6834	962	18	→	→	SYM
ejpam-6834	962	19	(	(	PUNCT
ejpam-6834	962	20	p̃n([0	p̃n([0	PROPN
ejpam-6834	962	21	,	,	PUNCT
ejpam-6834	962	22	1]3))k	1]3))k	PROPN
ejpam-6834	962	23	.	.	PUNCT
ejpam-6834	963	1	(	(	PUNCT
ejpam-6834	963	2	i	i	NOUN
ejpam-6834	963	3	)	)	PUNCT
ejpam-6834	963	4	classical	classical	ADJ
ejpam-6834	963	5	case	case	NOUN
ejpam-6834	963	6	.	.	PUNCT
ejpam-6834	964	1	assume	assume	VERB
ejpam-6834	964	2	h	h	NOUN
ejpam-6834	965	1	=	=	SYM
ejpam-6834	965	2	k	k	PROPN
ejpam-6834	965	3	=	=	SYM
ejpam-6834	965	4	1	1	X
ejpam-6834	965	5	.	.	PUNCT
ejpam-6834	966	1	then	then	ADV
ejpam-6834	966	2	the	the	DET
ejpam-6834	966	3	cartesian	cartesian	ADJ
ejpam-6834	966	4	powers	power	NOUN
ejpam-6834	966	5	collapse	collapse	VERB
ejpam-6834	966	6	via	via	ADP
ejpam-6834	966	7	the	the	DET
ejpam-6834	966	8	canonical	canonical	ADJ
ejpam-6834	966	9	bijections	bijection	NOUN
ejpam-6834	966	10	ιh	ιh	X
ejpam-6834	966	11	:	:	PUNCT
ejpam-6834	966	12	(	(	PUNCT
ejpam-6834	966	13	p̃m(x))1	p̃m(x))1	NOUN
ejpam-6834	966	14	∼=−−→	∼=−−→	PROPN
ejpam-6834	966	15	p̃m(x	p̃m(x	NOUN
ejpam-6834	966	16	)	)	PUNCT
ejpam-6834	966	17	,	,	PUNCT
ejpam-6834	966	18	ιk	ιk	X
ejpam-6834	966	19	:	:	PUNCT
ejpam-6834	966	20	(	(	PUNCT
ejpam-6834	966	21	p̃n([0	p̃n([0	PROPN
ejpam-6834	966	22	,	,	PUNCT
ejpam-6834	966	23	1]3))1	1]3))1	NUM
ejpam-6834	966	24	∼=−−→	∼=−−→	PROPN
ejpam-6834	966	25	p̃n([0	p̃n([0	PROPN
ejpam-6834	966	26	,	,	PUNCT
ejpam-6834	966	27	1]3	1]3	NUM
ejpam-6834	966	28	)	)	PUNCT
ejpam-6834	966	29	,	,	PUNCT
ejpam-6834	966	30	given	give	VERB
ejpam-6834	966	31	by	by	ADP
ejpam-6834	966	32	ιh(a	ιh(a	ADP
ejpam-6834	966	33	)	)	PUNCT
ejpam-6834	966	34	=	=	SYM
ejpam-6834	966	35	a	a	PRON
ejpam-6834	966	36	and	and	CCONJ
ejpam-6834	966	37	ιk(c	ιk(c	NUM
ejpam-6834	966	38	)	)	PUNCT
ejpam-6834	967	1	=	=	SYM
ejpam-6834	967	2	c.	c.	NOUN
ejpam-6834	967	3	under	under	ADP
ejpam-6834	967	4	these	these	DET
ejpam-6834	967	5	identifications	identification	NOUN
ejpam-6834	967	6	,	,	PUNCT
ejpam-6834	967	7	ã	ã	PROPN
ejpam-6834	967	8	is	be	AUX
ejpam-6834	967	9	precisely	precisely	ADV
ejpam-6834	967	10	a	a	DET
ejpam-6834	967	11	map	map	NOUN
ejpam-6834	967	12	ã	ã	PROPN
ejpam-6834	967	13	:	:	PUNCT
ejpam-6834	967	14	p̃m(x	p̃m(x	X
ejpam-6834	967	15	)	)	PUNCT
ejpam-6834	967	16	−→	−→	NOUN
ejpam-6834	967	17	p̃n([0	p̃n([0	PROPN
ejpam-6834	967	18	,	,	PUNCT
ejpam-6834	967	19	1]3	1]3	NUM
ejpam-6834	967	20	)	)	PUNCT
ejpam-6834	967	21	,	,	PUNCT
ejpam-6834	967	22	whose	whose	DET
ejpam-6834	967	23	values	value	NOUN
ejpam-6834	967	24	are	be	AUX
ejpam-6834	967	25	nonempty	nonempty	ADJ
ejpam-6834	967	26	n	n	CCONJ
ejpam-6834	967	27	-	-	PUNCT
ejpam-6834	967	28	level	level	NOUN
ejpam-6834	967	29	neutrosophic	neutrosophic	ADJ
ejpam-6834	967	30	sets	set	NOUN
ejpam-6834	967	31	.	.	PUNCT
ejpam-6834	968	1	this	this	PRON
ejpam-6834	968	2	is	be	AUX
ejpam-6834	968	3	exactly	exactly	ADV
ejpam-6834	968	4	the	the	DET
ejpam-6834	968	5	classical	classical	ADJ
ejpam-6834	968	6	(	(	PUNCT
ejpam-6834	968	7	m	m	PROPN
ejpam-6834	968	8	,	,	PUNCT
ejpam-6834	968	9	n)superhyperneutrosophic	n)superhyperneutrosophic	ADJ
ejpam-6834	968	10	definition	definition	NOUN
ejpam-6834	968	11	.	.	PUNCT
ejpam-6834	969	1	(	(	PUNCT
ejpam-6834	969	2	ii	ii	NOUN
ejpam-6834	969	3	)	)	PUNCT
ejpam-6834	969	4	fuzzy	fuzzy	ADJ
ejpam-6834	969	5	case	case	NOUN
ejpam-6834	969	6	via	via	ADP
ejpam-6834	969	7	truth	truth	NOUN
ejpam-6834	969	8	–	–	PUNCT
ejpam-6834	969	9	projection	projection	NOUN
ejpam-6834	969	10	.	.	PUNCT
ejpam-6834	970	1	define	define	VERB
ejpam-6834	970	2	πt	πt	ADV
ejpam-6834	970	3	:	:	PUNCT
ejpam-6834	971	1	[	[	X
ejpam-6834	971	2	0	0	NUM
ejpam-6834	971	3	,	,	PUNCT
ejpam-6834	971	4	1]3	1]3	NUM
ejpam-6834	971	5	→	→	SYM
ejpam-6834	971	6	[	[	X
ejpam-6834	971	7	0	0	NUM
ejpam-6834	971	8	,	,	PUNCT
ejpam-6834	971	9	1	1	NUM
ejpam-6834	971	10	]	]	PUNCT
ejpam-6834	971	11	by	by	ADP
ejpam-6834	971	12	πt	πt	PROPN
ejpam-6834	971	13	(	(	PUNCT
ejpam-6834	971	14	t	t	PROPN
ejpam-6834	971	15	,	,	PUNCT
ejpam-6834	971	16	i	i	PRON
ejpam-6834	971	17	,	,	PUNCT
ejpam-6834	971	18	f	f	PROPN
ejpam-6834	971	19	)	)	PUNCT
ejpam-6834	971	20	=	=	SYM
ejpam-6834	971	21	t	t	PROPN
ejpam-6834	971	22	.	.	PUNCT
ejpam-6834	972	1	we	we	PRON
ejpam-6834	972	2	extend	extend	VERB
ejpam-6834	972	3	πt	πt	ADP
ejpam-6834	972	4	to	to	ADP
ejpam-6834	972	5	all	all	DET
ejpam-6834	972	6	nesting	nesting	ADJ
ejpam-6834	972	7	levels	level	NOUN
ejpam-6834	972	8	by	by	ADP
ejpam-6834	972	9	recursion	recursion	NOUN
ejpam-6834	972	10	on	on	ADP
ejpam-6834	972	11	r	r	NOUN
ejpam-6834	972	12	≥	≥	NUM
ejpam-6834	972	13	1	1	NUM
ejpam-6834	972	14	:	:	PUNCT
ejpam-6834	972	15	π	π	X
ejpam-6834	972	16	(	(	PUNCT
ejpam-6834	972	17	1	1	NUM
ejpam-6834	972	18	)	)	PUNCT
ejpam-6834	972	19	t	t	NOUN
ejpam-6834	972	20	:	:	PUNCT
ejpam-6834	972	21	p̃1([0	p̃1([0	NOUN
ejpam-6834	972	22	,	,	PUNCT
ejpam-6834	972	23	1]3	1]3	NUM
ejpam-6834	972	24	)	)	PUNCT
ejpam-6834	972	25	→	→	SYM
ejpam-6834	972	26	p̃1([0	p̃1([0	NOUN
ejpam-6834	972	27	,	,	PUNCT
ejpam-6834	972	28	1	1	NUM
ejpam-6834	972	29	]	]	NUM
ejpam-6834	972	30	)	)	PUNCT
ejpam-6834	972	31	,	,	PUNCT
ejpam-6834	972	32	π	π	X
ejpam-6834	972	33	(	(	PUNCT
ejpam-6834	972	34	1	1	NUM
ejpam-6834	972	35	)	)	PUNCT
ejpam-6834	972	36	t	t	NOUN
ejpam-6834	972	37	(	(	PUNCT
ejpam-6834	972	38	s	s	NOUN
ejpam-6834	972	39	)	)	PUNCT
ejpam-6834	972	40	:	:	PUNCT
ejpam-6834	972	41	=	=	X
ejpam-6834	972	42	{	{	PUNCT
ejpam-6834	972	43	πt	πt	INTJ
ejpam-6834	972	44	(	(	PUNCT
ejpam-6834	972	45	t	t	NOUN
ejpam-6834	972	46	)	)	PUNCT
ejpam-6834	973	1	|	|	ADV
ejpam-6834	973	2	t	t	X
ejpam-6834	973	3	∈	∈	NOUN
ejpam-6834	973	4	s	s	PART
ejpam-6834	973	5	}	}	PUNCT
ejpam-6834	973	6	,	,	PUNCT
ejpam-6834	973	7	and	and	CCONJ
ejpam-6834	973	8	,	,	PUNCT
ejpam-6834	973	9	for	for	ADP
ejpam-6834	973	10	r	r	NOUN
ejpam-6834	973	11	≥	≥	NUM
ejpam-6834	973	12	1	1	NUM
ejpam-6834	973	13	,	,	PUNCT
ejpam-6834	973	14	π	π	PROPN
ejpam-6834	973	15	(	(	PUNCT
ejpam-6834	973	16	r+1	r+1	PROPN
ejpam-6834	973	17	)	)	PUNCT
ejpam-6834	973	18	t	t	NOUN
ejpam-6834	973	19	:	:	PUNCT
ejpam-6834	973	20	p̃r+1([0	p̃r+1([0	NOUN
ejpam-6834	973	21	,	,	PUNCT
ejpam-6834	973	22	1]3	1]3	NUM
ejpam-6834	973	23	)	)	PUNCT
ejpam-6834	973	24	→	→	SYM
ejpam-6834	973	25	p̃r+1([0	p̃r+1([0	NOUN
ejpam-6834	973	26	,	,	PUNCT
ejpam-6834	973	27	1	1	NUM
ejpam-6834	973	28	]	]	NUM
ejpam-6834	973	29	)	)	PUNCT
ejpam-6834	973	30	,	,	PUNCT
ejpam-6834	973	31	π	π	PROPN
ejpam-6834	973	32	(	(	PUNCT
ejpam-6834	973	33	r+1	r+1	PROPN
ejpam-6834	973	34	)	)	PUNCT
ejpam-6834	973	35	t	t	PROPN
ejpam-6834	973	36	(	(	PUNCT
ejpam-6834	973	37	s	s	NOUN
ejpam-6834	973	38	)	)	PUNCT
ejpam-6834	973	39	:	:	PUNCT
ejpam-6834	973	40	=	=	SYM
ejpam-6834	973	41	{	{	PUNCT
ejpam-6834	973	42	π	π	X
ejpam-6834	973	43	(	(	PUNCT
ejpam-6834	973	44	r	r	NOUN
ejpam-6834	973	45	)	)	PUNCT
ejpam-6834	973	46	t	t	NOUN
ejpam-6834	973	47	(	(	PUNCT
ejpam-6834	973	48	s	s	X
ejpam-6834	973	49	)	)	PUNCT
ejpam-6834	974	1	|	|	ADV
ejpam-6834	974	2	s	s	VERB
ejpam-6834	974	3	∈	∈	PROPN
ejpam-6834	974	4	s	s	PART
ejpam-6834	974	5	}	}	PUNCT
ejpam-6834	974	6	.	.	PUNCT
ejpam-6834	975	1	t.	t.	PROPN
ejpam-6834	975	2	fujita	fujita	PROPN
ejpam-6834	975	3	,	,	PUNCT
ejpam-6834	975	4	f.smarandache	f.smarandache	NOUN
ejpam-6834	975	5	/	/	SYM
ejpam-6834	975	6	eur	eur	PROPN
ejpam-6834	975	7	.	.	PUNCT
ejpam-6834	976	1	j.	j.	PROPN
ejpam-6834	976	2	pure	pure	PROPN
ejpam-6834	976	3	appl	appl	PROPN
ejpam-6834	976	4	.	.	PROPN
ejpam-6834	976	5	math	math	PROPN
ejpam-6834	976	6	,	,	PUNCT
ejpam-6834	976	7	18	18	NUM
ejpam-6834	976	8	(	(	PUNCT
ejpam-6834	976	9	4	4	NUM
ejpam-6834	976	10	)	)	PUNCT
ejpam-6834	976	11	(	(	PUNCT
ejpam-6834	976	12	2025	2025	NUM
ejpam-6834	976	13	)	)	PUNCT
ejpam-6834	976	14	,	,	PUNCT
ejpam-6834	976	15	6834	6834	NUM
ejpam-6834	976	16	40	40	NUM
ejpam-6834	976	17	of	of	ADP
ejpam-6834	976	18	69	69	NUM
ejpam-6834	976	19	nonemptiness	nonemptiness	NOUN
ejpam-6834	976	20	is	be	AUX
ejpam-6834	976	21	preserved	preserve	VERB
ejpam-6834	976	22	at	at	ADP
ejpam-6834	976	23	each	each	DET
ejpam-6834	976	24	step	step	NOUN
ejpam-6834	976	25	:	:	PUNCT
ejpam-6834	976	26	if	if	SCONJ
ejpam-6834	976	27	s	s	VERB
ejpam-6834	976	28	̸=	̸=	PROPN
ejpam-6834	976	29	∅	∅	NOUN
ejpam-6834	976	30	,	,	PUNCT
ejpam-6834	976	31	then	then	ADV
ejpam-6834	976	32	π	π	X
ejpam-6834	976	33	(	(	PUNCT
ejpam-6834	976	34	1	1	NUM
ejpam-6834	976	35	)	)	PUNCT
ejpam-6834	976	36	t	t	NOUN
ejpam-6834	976	37	(	(	PUNCT
ejpam-6834	976	38	s	s	X
ejpam-6834	976	39	)	)	PUNCT
ejpam-6834	976	40	̸=	̸=	NOUN
ejpam-6834	976	41	∅	∅	NOUN
ejpam-6834	976	42	;	;	PUNCT
ejpam-6834	976	43	if	if	SCONJ
ejpam-6834	976	44	s	s	VERB
ejpam-6834	976	45	̸=	̸=	PROPN
ejpam-6834	976	46	∅	∅	NOUN
ejpam-6834	976	47	,	,	PUNCT
ejpam-6834	976	48	then	then	ADV
ejpam-6834	976	49	π	π	X
ejpam-6834	976	50	(	(	PUNCT
ejpam-6834	976	51	r+1	r+1	PROPN
ejpam-6834	976	52	)	)	PUNCT
ejpam-6834	976	53	t	t	PROPN
ejpam-6834	976	54	(	(	PUNCT
ejpam-6834	976	55	s	s	X
ejpam-6834	976	56	)	)	PUNCT
ejpam-6834	976	57	̸=	̸=	NOUN
ejpam-6834	976	58	∅	∅	NOUN
ejpam-6834	976	59	because	because	SCONJ
ejpam-6834	976	60	it	it	PRON
ejpam-6834	976	61	collects	collect	VERB
ejpam-6834	976	62	the	the	DET
ejpam-6834	976	63	nonempty	nonempty	ADJ
ejpam-6834	976	64	images	image	NOUN
ejpam-6834	976	65	of	of	ADP
ejpam-6834	976	66	members	member	NOUN
ejpam-6834	976	67	of	of	ADP
ejpam-6834	976	68	s.	s.	PROPN
ejpam-6834	976	69	put	put	VERB
ejpam-6834	976	70	πt	πt	ADP
ejpam-6834	976	71	:	:	PUNCT
ejpam-6834	976	72	=	=	SYM
ejpam-6834	976	73	π	π	X
ejpam-6834	976	74	(	(	PUNCT
ejpam-6834	976	75	n	n	CCONJ
ejpam-6834	976	76	)	)	PUNCT
ejpam-6834	976	77	t	t	NOUN
ejpam-6834	976	78	and	and	CCONJ
ejpam-6834	976	79	define	define	VERB
ejpam-6834	976	80	π̂t	π̂t	NOUN
ejpam-6834	976	81	:	:	PUNCT
ejpam-6834	976	82	(	(	PUNCT
ejpam-6834	976	83	p̃n([0	p̃n([0	PROPN
ejpam-6834	976	84	,	,	PUNCT
ejpam-6834	976	85	1]3))k	1]3))k	PROPN
ejpam-6834	976	86	→	→	SYM
ejpam-6834	976	87	(	(	PUNCT
ejpam-6834	976	88	p̃n([0	p̃n([0	PROPN
ejpam-6834	976	89	,	,	PUNCT
ejpam-6834	976	90	1]))k	1]))k	NUM
ejpam-6834	976	91	,	,	PUNCT
ejpam-6834	976	92	π̂t	π̂t	X
ejpam-6834	976	93	(	(	PUNCT
ejpam-6834	976	94	c1	c1	NOUN
ejpam-6834	976	95	,	,	PUNCT
ejpam-6834	976	96	.	.	PUNCT
ejpam-6834	976	97	.	.	PUNCT
ejpam-6834	977	1	.	.	PUNCT
ejpam-6834	978	1	,	,	PUNCT
ejpam-6834	978	2	ck	ck	X
ejpam-6834	978	3	)	)	PUNCT
ejpam-6834	978	4	:	:	PUNCT
ejpam-6834	979	1	=	=	SYM
ejpam-6834	979	2	(	(	PUNCT
ejpam-6834	979	3	πt	πt	INTJ
ejpam-6834	979	4	(	(	PUNCT
ejpam-6834	979	5	c1	c1	PROPN
ejpam-6834	979	6	)	)	PUNCT
ejpam-6834	979	7	,	,	PUNCT
ejpam-6834	979	8	.	.	PUNCT
ejpam-6834	979	9	.	.	PUNCT
ejpam-6834	979	10	.	.	PUNCT
ejpam-6834	980	1	,	,	PUNCT
ejpam-6834	980	2	πt	πt	INTJ
ejpam-6834	980	3	(	(	PUNCT
ejpam-6834	980	4	ck	ck	NOUN
ejpam-6834	980	5	)	)	PUNCT
ejpam-6834	980	6	)	)	PUNCT
ejpam-6834	980	7	.	.	PUNCT
ejpam-6834	981	1	then	then	ADV
ejpam-6834	981	2	π̂t	π̂t	X
ejpam-6834	981	3	◦	◦	NOUN
ejpam-6834	981	4	ã	ã	PROPN
ejpam-6834	981	5	maps	map	VERB
ejpam-6834	981	6	any	any	DET
ejpam-6834	981	7	a	a	DET
ejpam-6834	981	8	∈	∈	NOUN
ejpam-6834	981	9	(	(	PUNCT
ejpam-6834	981	10	p̃m(x))h	p̃m(x))h	NOUN
ejpam-6834	981	11	to	to	ADP
ejpam-6834	981	12	a	a	DET
ejpam-6834	981	13	k	k	NOUN
ejpam-6834	981	14	-	-	NOUN
ejpam-6834	981	15	tuple	tuple	NOUN
ejpam-6834	981	16	of	of	ADP
ejpam-6834	981	17	nonempty	nonempty	ADJ
ejpam-6834	981	18	n	n	CCONJ
ejpam-6834	981	19	-	-	PUNCT
ejpam-6834	981	20	level	level	NOUN
ejpam-6834	981	21	subsets	subset	NOUN
ejpam-6834	981	22	of	of	ADP
ejpam-6834	981	23	[	[	X
ejpam-6834	981	24	0	0	NUM
ejpam-6834	981	25	,	,	PUNCT
ejpam-6834	981	26	1	1	NUM
ejpam-6834	981	27	]	]	PUNCT
ejpam-6834	981	28	,	,	PUNCT
ejpam-6834	981	29	i.e.	i.e.	X
ejpam-6834	981	30	an	an	DET
ejpam-6834	981	31	(	(	PUNCT
ejpam-6834	981	32	h	h	NOUN
ejpam-6834	981	33	,	,	PUNCT
ejpam-6834	981	34	k)-ary	k)-ary	X
ejpam-6834	981	35	(	(	PUNCT
ejpam-6834	981	36	m	m	NOUN
ejpam-6834	981	37	,	,	PUNCT
ejpam-6834	981	38	n)-superhyperfuzzy	n)-superhyperfuzzy	PUNCT
ejpam-6834	981	39	set	set	NOUN
ejpam-6834	981	40	.	.	PUNCT
ejpam-6834	982	1	theorem	theorem	VERB
ejpam-6834	982	2	30	30	NUM
ejpam-6834	982	3	(	(	PUNCT
ejpam-6834	982	4	fixing	fix	VERB
ejpam-6834	982	5	some	some	DET
ejpam-6834	982	6	inputs	input	NOUN
ejpam-6834	982	7	)	)	PUNCT
ejpam-6834	982	8	.	.	PUNCT
ejpam-6834	983	1	fix	fix	NOUN
ejpam-6834	983	2	indices	indice	VERB
ejpam-6834	983	3	1	1	NUM
ejpam-6834	983	4	≤	≤	NUM
ejpam-6834	983	5	i1	i1	X
ejpam-6834	983	6	<	<	X
ejpam-6834	983	7	·	·	PUNCT
ejpam-6834	983	8	·	·	PUNCT
ejpam-6834	983	9	·	·	PUNCT
ejpam-6834	984	1	<	<	X
ejpam-6834	984	2	ir	ir	PROPN
ejpam-6834	984	3	≤	≤	NUM
ejpam-6834	984	4	h	h	NOUN
ejpam-6834	984	5	and	and	CCONJ
ejpam-6834	984	6	super	super	ADJ
ejpam-6834	984	7	-	-	ADJ
ejpam-6834	984	8	elements	element	NOUN
ejpam-6834	984	9	aij	aij	PROPN
ejpam-6834	984	10	∈	∈	PROPN
ejpam-6834	984	11	p̃m(x	p̃m(x	NOUN
ejpam-6834	984	12	)	)	PUNCT
ejpam-6834	984	13	.	.	PUNCT
ejpam-6834	985	1	the	the	DET
ejpam-6834	985	2	map	map	NOUN
ejpam-6834	985	3	ãfix	ãfix	NOUN
ejpam-6834	985	4	:	:	PUNCT
ejpam-6834	985	5	(	(	PUNCT
ejpam-6834	985	6	p̃m(x	p̃m(x	X
ejpam-6834	985	7	)	)	PUNCT
ejpam-6834	985	8	)	)	PUNCT
ejpam-6834	985	9	h−r	h−r	VERB
ejpam-6834	985	10	−→	−→	NOUN
ejpam-6834	985	11	(	(	PUNCT
ejpam-6834	985	12	p̃n([0	p̃n([0	PROPN
ejpam-6834	985	13	,	,	PUNCT
ejpam-6834	985	14	1]3	1]3	NUM
ejpam-6834	985	15	)	)	PUNCT
ejpam-6834	985	16	)	)	PUNCT
ejpam-6834	986	1	k	k	NOUN
ejpam-6834	986	2	,	,	PUNCT
ejpam-6834	986	3	defined	define	VERB
ejpam-6834	986	4	by	by	ADP
ejpam-6834	986	5	inserting	insert	VERB
ejpam-6834	986	6	the	the	DET
ejpam-6834	986	7	fixed	fix	VERB
ejpam-6834	986	8	aij	aij	PROPN
ejpam-6834	986	9	into	into	ADP
ejpam-6834	986	10	the	the	DET
ejpam-6834	986	11	corresponding	corresponding	ADJ
ejpam-6834	986	12	coordinates	coordinate	NOUN
ejpam-6834	986	13	of	of	ADP
ejpam-6834	986	14	an	an	DET
ejpam-6834	986	15	(	(	PUNCT
ejpam-6834	986	16	h	h	NOUN
ejpam-6834	986	17	−	−	PROPN
ejpam-6834	986	18	r)-tuple	r)-tuple	NOUN
ejpam-6834	986	19	and	and	CCONJ
ejpam-6834	986	20	then	then	ADV
ejpam-6834	986	21	applying	apply	VERB
ejpam-6834	986	22	ã	ã	PROPN
ejpam-6834	986	23	,	,	PUNCT
ejpam-6834	986	24	is	be	AUX
ejpam-6834	986	25	an	an	DET
ejpam-6834	986	26	(	(	PUNCT
ejpam-6834	986	27	h−	h−	NOUN
ejpam-6834	986	28	r	r	NOUN
ejpam-6834	986	29	,	,	PUNCT
ejpam-6834	986	30	k)-ary	k)-ary	X
ejpam-6834	986	31	(	(	PUNCT
ejpam-6834	986	32	m	m	PROPN
ejpam-6834	986	33	,	,	PUNCT
ejpam-6834	986	34	n)-superhyperneutrosophic	n)-superhyperneutrosophic	ADJ
ejpam-6834	986	35	set	set	NOUN
ejpam-6834	986	36	.	.	PUNCT
ejpam-6834	987	1	proof	proof	NOUN
ejpam-6834	987	2	.	.	PUNCT
ejpam-6834	988	1	let	let	VERB
ejpam-6834	988	2	i	i	PRON
ejpam-6834	988	3	=	=	PUNCT
ejpam-6834	988	4	{	{	PUNCT
ejpam-6834	988	5	1	1	NUM
ejpam-6834	988	6	,	,	PUNCT
ejpam-6834	988	7	.	.	PUNCT
ejpam-6834	988	8	.	.	PUNCT
ejpam-6834	989	1	.	.	PUNCT
ejpam-6834	990	1	,	,	PUNCT
ejpam-6834	990	2	h	h	NOUN
ejpam-6834	990	3	}	}	PUNCT
ejpam-6834	990	4	and	and	CCONJ
ejpam-6834	990	5	j	j	PROPN
ejpam-6834	990	6	=	=	SYM
ejpam-6834	990	7	{	{	PUNCT
ejpam-6834	990	8	i1	i1	PROPN
ejpam-6834	990	9	,	,	PUNCT
ejpam-6834	990	10	.	.	PUNCT
ejpam-6834	990	11	.	.	PUNCT
ejpam-6834	991	1	.	.	PUNCT
ejpam-6834	992	1	,	,	PUNCT
ejpam-6834	992	2	ir	ir	PROPN
ejpam-6834	992	3	}	}	PUNCT
ejpam-6834	992	4	.	.	PUNCT
ejpam-6834	993	1	for	for	ADP
ejpam-6834	993	2	a	a	DET
ejpam-6834	993	3	free	free	ADJ
ejpam-6834	993	4	-	-	PUNCT
ejpam-6834	993	5	input	input	NOUN
ejpam-6834	993	6	tuple	tuple	NOUN
ejpam-6834	993	7	b	b	PROPN
ejpam-6834	993	8	=	=	PUNCT
ejpam-6834	993	9	(	(	PUNCT
ejpam-6834	993	10	bℓ)ℓ∈i\j	bℓ)ℓ∈i\j	NOUN
ejpam-6834	993	11	∈	∈	PROPN
ejpam-6834	993	12	(	(	PUNCT
ejpam-6834	993	13	p̃m(x))h−r	p̃m(x))h−r	PROPN
ejpam-6834	993	14	,	,	PUNCT
ejpam-6834	993	15	define	define	VERB
ejpam-6834	993	16	the	the	DET
ejpam-6834	993	17	insertion	insertion	NOUN
ejpam-6834	993	18	map	map	NOUN
ejpam-6834	993	19	ι(b	ι(b	NOUN
ejpam-6834	993	20	)	)	PUNCT
ejpam-6834	993	21	=	=	SYM
ejpam-6834	993	22	a	a	PRON
ejpam-6834	993	23	=	=	PUNCT
ejpam-6834	993	24	(	(	PUNCT
ejpam-6834	993	25	a1	a1	PROPN
ejpam-6834	993	26	,	,	PUNCT
ejpam-6834	993	27	.	.	PUNCT
ejpam-6834	993	28	.	.	PUNCT
ejpam-6834	993	29	.	.	PUNCT
ejpam-6834	994	1	,	,	PUNCT
ejpam-6834	994	2	ah	ah	INTJ
ejpam-6834	994	3	)	)	PUNCT
ejpam-6834	994	4	∈	∈	PROPN
ejpam-6834	994	5	(	(	PUNCT
ejpam-6834	994	6	p̃m(x))h	p̃m(x))h	NOUN
ejpam-6834	994	7	,	,	PUNCT
ejpam-6834	994	8	au	au	X
ejpam-6834	994	9	=	=	PUNCT
ejpam-6834	994	10	{	{	PUNCT
ejpam-6834	994	11	aij	aij	PROPN
ejpam-6834	994	12	,	,	PUNCT
ejpam-6834	994	13	u	u	PROPN
ejpam-6834	994	14	∈	∈	PROPN
ejpam-6834	994	15	j	j	PROPN
ejpam-6834	994	16	with	with	ADP
ejpam-6834	994	17	u	u	NOUN
ejpam-6834	994	18	=	=	X
ejpam-6834	994	19	ij	ij	INTJ
ejpam-6834	994	20	,	,	PUNCT
ejpam-6834	994	21	bu	bu	PROPN
ejpam-6834	994	22	,	,	PUNCT
ejpam-6834	994	23	u	u	NOUN
ejpam-6834	994	24	∈	∈	PROPN
ejpam-6834	995	1	i	i	PRON
ejpam-6834	995	2	\	\	PROPN
ejpam-6834	996	1	j.	j.	PROPN
ejpam-6834	996	2	then	then	ADV
ejpam-6834	996	3	ι	ι	PROPN
ejpam-6834	996	4	is	be	AUX
ejpam-6834	996	5	well	well	ADV
ejpam-6834	996	6	-	-	PUNCT
ejpam-6834	996	7	defined	define	VERB
ejpam-6834	996	8	and	and	CCONJ
ejpam-6834	996	9	ι(b	ι(b	NUM
ejpam-6834	996	10	)	)	PUNCT
ejpam-6834	997	1	has	have	VERB
ejpam-6834	997	2	every	every	DET
ejpam-6834	997	3	coordinate	coordinate	NOUN
ejpam-6834	997	4	in	in	ADP
ejpam-6834	997	5	p̃m(x	p̃m(x	NOUN
ejpam-6834	997	6	)	)	PUNCT
ejpam-6834	997	7	.	.	PUNCT
ejpam-6834	998	1	set	set	VERB
ejpam-6834	998	2	ãfix	ãfix	NOUN
ejpam-6834	998	3	:	:	PUNCT
ejpam-6834	998	4	=	=	PUNCT
ejpam-6834	999	1	ã	ã	PROPN
ejpam-6834	999	2	◦	◦	VERB
ejpam-6834	999	3	ι	ι	X
ejpam-6834	999	4	.	.	PUNCT
ejpam-6834	1000	1	for	for	ADP
ejpam-6834	1000	2	any	any	DET
ejpam-6834	1000	3	b	b	NOUN
ejpam-6834	1000	4	,	,	PUNCT
ejpam-6834	1000	5	ãfix(b	ãfix(b	NOUN
ejpam-6834	1000	6	)	)	PUNCT
ejpam-6834	1000	7	=	=	SYM
ejpam-6834	1000	8	ã(ι(b	ã(ι(b	NOUN
ejpam-6834	1000	9	)	)	PUNCT
ejpam-6834	1000	10	)	)	PUNCT
ejpam-6834	1000	11	is	be	AUX
ejpam-6834	1000	12	a	a	DET
ejpam-6834	1000	13	k	k	NOUN
ejpam-6834	1000	14	-	-	NOUN
ejpam-6834	1000	15	tuple	tuple	NOUN
ejpam-6834	1000	16	whose	whose	DET
ejpam-6834	1000	17	jth	jth	PROPN
ejpam-6834	1000	18	coordinate	coordinate	NOUN
ejpam-6834	1000	19	lies	lie	VERB
ejpam-6834	1000	20	in	in	ADP
ejpam-6834	1000	21	p̃n([0	p̃n([0	ADJ
ejpam-6834	1000	22	,	,	PUNCT
ejpam-6834	1000	23	1]3	1]3	NUM
ejpam-6834	1000	24	)	)	PUNCT
ejpam-6834	1000	25	by	by	ADP
ejpam-6834	1000	26	definition	definition	NOUN
ejpam-6834	1000	27	of	of	ADP
ejpam-6834	1000	28	ã.	ã.	NOUN
ejpam-6834	1000	29	thus	thus	ADV
ejpam-6834	1000	30	ãfix	ãfix	NOUN
ejpam-6834	1000	31	is	be	AUX
ejpam-6834	1000	32	an	an	DET
ejpam-6834	1000	33	(	(	PUNCT
ejpam-6834	1000	34	h−	h−	NOUN
ejpam-6834	1000	35	r	r	NOUN
ejpam-6834	1000	36	,	,	PUNCT
ejpam-6834	1000	37	k)-ary	k)-ary	X
ejpam-6834	1000	38	(	(	PUNCT
ejpam-6834	1000	39	m	m	PROPN
ejpam-6834	1000	40	,	,	PUNCT
ejpam-6834	1000	41	n)-superhyperneutrosophic	n)-superhyperneutrosophic	ADJ
ejpam-6834	1000	42	set	set	NOUN
ejpam-6834	1000	43	.	.	PUNCT
ejpam-6834	1001	1	theorem	theorem	VERB
ejpam-6834	1001	2	31	31	NUM
ejpam-6834	1001	3	(	(	PUNCT
ejpam-6834	1001	4	projection	projection	NOUN
ejpam-6834	1001	5	to	to	ADP
ejpam-6834	1001	6	selected	select	VERB
ejpam-6834	1001	7	outputs	output	NOUN
ejpam-6834	1001	8	)	)	PUNCT
ejpam-6834	1001	9	.	.	PUNCT
ejpam-6834	1002	1	let	let	VERB
ejpam-6834	1002	2	1	1	NUM
ejpam-6834	1002	3	≤	≤	NOUN
ejpam-6834	1002	4	j1	j1	X
ejpam-6834	1002	5	<	<	X
ejpam-6834	1002	6	·	·	PUNCT
ejpam-6834	1002	7	·	·	PUNCT
ejpam-6834	1002	8	·	·	PUNCT
ejpam-6834	1003	1	<	<	X
ejpam-6834	1003	2	js	js	PROPN
ejpam-6834	1003	3	≤	≤	PROPN
ejpam-6834	1003	4	k.	k.	PROPN
ejpam-6834	1004	1	the	the	DET
ejpam-6834	1004	2	coordinate	coordinate	NOUN
ejpam-6834	1004	3	projection	projection	NOUN
ejpam-6834	1004	4	ãproj(a	ãproj(a	NOUN
ejpam-6834	1004	5	)	)	PUNCT
ejpam-6834	1005	1	=	=	PRON
ejpam-6834	1005	2	(	(	PUNCT
ejpam-6834	1005	3	cj1	cj1	NOUN
ejpam-6834	1005	4	,	,	PUNCT
ejpam-6834	1005	5	.	.	PUNCT
ejpam-6834	1005	6	.	.	PUNCT
ejpam-6834	1006	1	.	.	PUNCT
ejpam-6834	1007	1	,	,	PUNCT
ejpam-6834	1007	2	cjs	cjs	PROPN
ejpam-6834	1007	3	)	)	PUNCT
ejpam-6834	1007	4	,	,	PUNCT
ejpam-6834	1007	5	where	where	SCONJ
ejpam-6834	1007	6	ã(a	ã(a	ADV
ejpam-6834	1007	7	)	)	PUNCT
ejpam-6834	1008	1	=	=	SYM
ejpam-6834	1008	2	(	(	PUNCT
ejpam-6834	1008	3	c1	c1	PROPN
ejpam-6834	1008	4	,	,	PUNCT
ejpam-6834	1008	5	.	.	PUNCT
ejpam-6834	1008	6	.	.	PUNCT
ejpam-6834	1009	1	.	.	PUNCT
ejpam-6834	1010	1	,	,	PUNCT
ejpam-6834	1010	2	ck	ck	PROPN
ejpam-6834	1010	3	)	)	PUNCT
ejpam-6834	1010	4	,	,	PUNCT
ejpam-6834	1010	5	defines	define	VERB
ejpam-6834	1010	6	an	an	DET
ejpam-6834	1010	7	(	(	PUNCT
ejpam-6834	1010	8	h	h	NOUN
ejpam-6834	1010	9	,	,	PUNCT
ejpam-6834	1010	10	s)-ary	s)-ary	NOUN
ejpam-6834	1010	11	(	(	PUNCT
ejpam-6834	1010	12	m	m	PROPN
ejpam-6834	1010	13	,	,	PUNCT
ejpam-6834	1010	14	n)-superhyperneutrosophic	n)-superhyperneutrosophic	PUNCT
ejpam-6834	1010	15	set	set	NOUN
ejpam-6834	1010	16	ãproj	ãproj	NOUN
ejpam-6834	1010	17	:	:	PUNCT
ejpam-6834	1010	18	(	(	PUNCT
ejpam-6834	1010	19	p̃m(x))h	p̃m(x))h	X
ejpam-6834	1010	20	→	→	SYM
ejpam-6834	1010	21	(	(	PUNCT
ejpam-6834	1010	22	p̃n([0	p̃n([0	PROPN
ejpam-6834	1010	23	,	,	PUNCT
ejpam-6834	1010	24	1]3))s	1]3))s	NUM
ejpam-6834	1010	25	.	.	PUNCT
ejpam-6834	1011	1	proof	proof	NOUN
ejpam-6834	1011	2	.	.	PUNCT
ejpam-6834	1012	1	define	define	VERB
ejpam-6834	1012	2	pj	pj	PROPN
ejpam-6834	1012	3	:	:	PUNCT
ejpam-6834	1012	4	(	(	PUNCT
ejpam-6834	1012	5	p̃n([0	p̃n([0	PROPN
ejpam-6834	1012	6	,	,	PUNCT
ejpam-6834	1012	7	1]3))k	1]3))k	PROPN
ejpam-6834	1012	8	→	→	SYM
ejpam-6834	1012	9	(	(	PUNCT
ejpam-6834	1012	10	p̃n([0	p̃n([0	PROPN
ejpam-6834	1012	11	,	,	PUNCT
ejpam-6834	1012	12	1]3))s	1]3))s	NUM
ejpam-6834	1012	13	by	by	ADP
ejpam-6834	1012	14	pj(c1	pj(c1	NOUN
ejpam-6834	1012	15	,	,	PUNCT
ejpam-6834	1012	16	.	.	PUNCT
ejpam-6834	1012	17	.	.	PUNCT
ejpam-6834	1013	1	.	.	PUNCT
ejpam-6834	1014	1	,	,	PUNCT
ejpam-6834	1014	2	ck	ck	X
ejpam-6834	1014	3	)	)	PUNCT
ejpam-6834	1014	4	=	=	SYM
ejpam-6834	1015	1	(	(	PUNCT
ejpam-6834	1015	2	cj1	cj1	NOUN
ejpam-6834	1015	3	,	,	PUNCT
ejpam-6834	1015	4	.	.	PUNCT
ejpam-6834	1015	5	.	.	PUNCT
ejpam-6834	1016	1	.	.	PUNCT
ejpam-6834	1017	1	,	,	PUNCT
ejpam-6834	1017	2	cjs	cjs	PROPN
ejpam-6834	1017	3	)	)	PUNCT
ejpam-6834	1017	4	.	.	PUNCT
ejpam-6834	1018	1	each	each	DET
ejpam-6834	1018	2	cjr	cjr	PROPN
ejpam-6834	1018	3	∈	∈	PROPN
ejpam-6834	1018	4	p̃n([0	p̃n([0	PROPN
ejpam-6834	1018	5	,	,	PUNCT
ejpam-6834	1018	6	1]3	1]3	NUM
ejpam-6834	1018	7	)	)	PUNCT
ejpam-6834	1018	8	and	and	CCONJ
ejpam-6834	1018	9	is	be	AUX
ejpam-6834	1018	10	nonempty	nonempty	ADJ
ejpam-6834	1018	11	,	,	PUNCT
ejpam-6834	1018	12	so	so	SCONJ
ejpam-6834	1018	13	pj	pj	PROPN
ejpam-6834	1018	14	is	be	AUX
ejpam-6834	1018	15	well	well	ADV
ejpam-6834	1018	16	-	-	PUNCT
ejpam-6834	1018	17	defined	define	VERB
ejpam-6834	1018	18	.	.	PUNCT
ejpam-6834	1019	1	put	put	VERB
ejpam-6834	1019	2	ãproj	ãproj	ADJ
ejpam-6834	1019	3	:	:	PUNCT
ejpam-6834	1019	4	=	=	SYM
ejpam-6834	1019	5	pj	pj	PROPN
ejpam-6834	1019	6	◦	◦	NOUN
ejpam-6834	1019	7	ã	ã	PROPN
ejpam-6834	1019	8	to	to	PART
ejpam-6834	1019	9	obtain	obtain	VERB
ejpam-6834	1019	10	a	a	DET
ejpam-6834	1019	11	map	map	NOUN
ejpam-6834	1019	12	with	with	ADP
ejpam-6834	1019	13	domain	domain	NOUN
ejpam-6834	1019	14	(	(	PUNCT
ejpam-6834	1019	15	p̃m(x))h	p̃m(x))h	NOUN
ejpam-6834	1019	16	and	and	CCONJ
ejpam-6834	1019	17	codomain	codomain	NOUN
ejpam-6834	1019	18	(	(	PUNCT
ejpam-6834	1019	19	p̃n([0	p̃n([0	PROPN
ejpam-6834	1019	20	,	,	PUNCT
ejpam-6834	1019	21	1]3))s	1]3))s	NUM
ejpam-6834	1019	22	,	,	PUNCT
ejpam-6834	1019	23	as	as	SCONJ
ejpam-6834	1019	24	required	require	VERB
ejpam-6834	1019	25	.	.	PUNCT
ejpam-6834	1020	1	theorem	theorem	VERB
ejpam-6834	1020	2	32	32	NUM
ejpam-6834	1020	3	(	(	PUNCT
ejpam-6834	1020	4	pointwise	pointwise	PROPN
ejpam-6834	1020	5	union	union	NOUN
ejpam-6834	1020	6	)	)	PUNCT
ejpam-6834	1020	7	.	.	PUNCT
ejpam-6834	1021	1	if	if	SCONJ
ejpam-6834	1021	2	ã1	ã1	PROPN
ejpam-6834	1021	3	,	,	PUNCT
ejpam-6834	1021	4	ã2	ã2	PROPN
ejpam-6834	1021	5	:	:	PUNCT
ejpam-6834	1021	6	(	(	PUNCT
ejpam-6834	1021	7	p̃m(x))h	p̃m(x))h	X
ejpam-6834	1021	8	→	→	SYM
ejpam-6834	1021	9	(	(	PUNCT
ejpam-6834	1021	10	p̃n([0	p̃n([0	PROPN
ejpam-6834	1021	11	,	,	PUNCT
ejpam-6834	1021	12	1]3))k	1]3))k	PROPN
ejpam-6834	1021	13	are	be	AUX
ejpam-6834	1021	14	(	(	PUNCT
ejpam-6834	1021	15	h	h	NOUN
ejpam-6834	1021	16	,	,	PUNCT
ejpam-6834	1021	17	k)-ary	k)-ary	X
ejpam-6834	1021	18	(	(	PUNCT
ejpam-6834	1021	19	m	m	PROPN
ejpam-6834	1021	20	,	,	PUNCT
ejpam-6834	1021	21	n)-superhyperneutrosophic	n)-superhyperneutrosophic	ADJ
ejpam-6834	1021	22	sets	set	NOUN
ejpam-6834	1021	23	,	,	PUNCT
ejpam-6834	1021	24	then	then	ADV
ejpam-6834	1021	25	(	(	PUNCT
ejpam-6834	1021	26	ã1	ã1	PROPN
ejpam-6834	1021	27	∪	∪	ADP
ejpam-6834	1021	28	ã2)(a	ã2)(a	NOUN
ejpam-6834	1021	29	)	)	PUNCT
ejpam-6834	1022	1	:	:	PUNCT
ejpam-6834	1022	2	=	=	SYM
ejpam-6834	1022	3	(	(	PUNCT
ejpam-6834	1022	4	ã1(a)j	ã1(a)j	PROPN
ejpam-6834	1022	5	∪	∪	ADJ
ejpam-6834	1022	6	ã2(a)j	ã2(a)j	NOUN
ejpam-6834	1022	7	)	)	PUNCT
ejpam-6834	1023	1	k	k	PROPN
ejpam-6834	1023	2	j=1	j=1	PROPN
ejpam-6834	1023	3	is	be	AUX
ejpam-6834	1023	4	again	again	ADV
ejpam-6834	1023	5	an	an	DET
ejpam-6834	1023	6	(	(	PUNCT
ejpam-6834	1023	7	h	h	NOUN
ejpam-6834	1023	8	,	,	PUNCT
ejpam-6834	1023	9	k)-ary	k)-ary	X
ejpam-6834	1023	10	(	(	PUNCT
ejpam-6834	1023	11	m	m	PROPN
ejpam-6834	1023	12	,	,	PUNCT
ejpam-6834	1023	13	n)-superhyperneutrosophic	n)-superhyperneutrosophic	ADJ
ejpam-6834	1023	14	set	set	NOUN
ejpam-6834	1023	15	.	.	PUNCT
ejpam-6834	1024	1	t.	t.	PROPN
ejpam-6834	1024	2	fujita	fujita	PROPN
ejpam-6834	1024	3	,	,	PUNCT
ejpam-6834	1024	4	f.smarandache	f.smarandache	NOUN
ejpam-6834	1024	5	/	/	SYM
ejpam-6834	1024	6	eur	eur	PROPN
ejpam-6834	1024	7	.	.	PUNCT
ejpam-6834	1025	1	j.	j.	PROPN
ejpam-6834	1025	2	pure	pure	PROPN
ejpam-6834	1025	3	appl	appl	PROPN
ejpam-6834	1025	4	.	.	PROPN
ejpam-6834	1025	5	math	math	PROPN
ejpam-6834	1025	6	,	,	PUNCT
ejpam-6834	1025	7	18	18	NUM
ejpam-6834	1025	8	(	(	PUNCT
ejpam-6834	1025	9	4	4	NUM
ejpam-6834	1025	10	)	)	PUNCT
ejpam-6834	1025	11	(	(	PUNCT
ejpam-6834	1025	12	2025	2025	NUM
ejpam-6834	1025	13	)	)	PUNCT
ejpam-6834	1025	14	,	,	PUNCT
ejpam-6834	1025	15	6834	6834	NUM
ejpam-6834	1025	16	41	41	NUM
ejpam-6834	1025	17	of	of	ADP
ejpam-6834	1025	18	69	69	NUM
ejpam-6834	1025	19	proof	proof	NOUN
ejpam-6834	1025	20	.	.	PUNCT
ejpam-6834	1026	1	we	we	PRON
ejpam-6834	1026	2	prove	prove	VERB
ejpam-6834	1026	3	a	a	DET
ejpam-6834	1026	4	general	general	ADJ
ejpam-6834	1026	5	lemma	lemma	NOUN
ejpam-6834	1026	6	by	by	ADP
ejpam-6834	1026	7	induction	induction	NOUN
ejpam-6834	1026	8	on	on	ADP
ejpam-6834	1026	9	r	r	PROPN
ejpam-6834	1026	10	≥	≥	NUM
ejpam-6834	1026	11	1	1	NUM
ejpam-6834	1026	12	:	:	PUNCT
ejpam-6834	1026	13	lemma	lemma	PROPN
ejpam-6834	1026	14	.	.	PUNCT
ejpam-6834	1027	1	if	if	SCONJ
ejpam-6834	1027	2	u	u	PROPN
ejpam-6834	1027	3	,	,	PUNCT
ejpam-6834	1027	4	v	v	NOUN
ejpam-6834	1027	5	∈	∈	PROPN
ejpam-6834	1027	6	p̃r(s	p̃r(s	NOUN
ejpam-6834	1027	7	)	)	PUNCT
ejpam-6834	1027	8	,	,	PUNCT
ejpam-6834	1027	9	then	then	ADV
ejpam-6834	1027	10	u	u	NOUN
ejpam-6834	1027	11	∪	∪	VERB
ejpam-6834	1027	12	v	v	NUM
ejpam-6834	1027	13	∈	∈	PROPN
ejpam-6834	1027	14	p̃r(s	p̃r(s	NOUN
ejpam-6834	1027	15	)	)	PUNCT
ejpam-6834	1027	16	.	.	PUNCT
ejpam-6834	1028	1	r	r	NOUN
ejpam-6834	1028	2	=	=	SYM
ejpam-6834	1028	3	1	1	NUM
ejpam-6834	1028	4	:	:	PUNCT
ejpam-6834	1028	5	u	u	NOUN
ejpam-6834	1028	6	,	,	PUNCT
ejpam-6834	1028	7	v	v	NUM
ejpam-6834	1028	8	are	be	AUX
ejpam-6834	1028	9	nonempty	nonempty	ADJ
ejpam-6834	1028	10	subsets	subset	NOUN
ejpam-6834	1028	11	of	of	ADP
ejpam-6834	1028	12	s	s	NOUN
ejpam-6834	1028	13	,	,	PUNCT
ejpam-6834	1028	14	hence	hence	ADV
ejpam-6834	1028	15	u	u	NOUN
ejpam-6834	1028	16	∪	∪	ADJ
ejpam-6834	1028	17	v	v	NOUN
ejpam-6834	1028	18	is	be	AUX
ejpam-6834	1028	19	a	a	DET
ejpam-6834	1028	20	nonempty	nonempty	ADJ
ejpam-6834	1028	21	subset	subset	NOUN
ejpam-6834	1028	22	of	of	ADP
ejpam-6834	1028	23	s	s	NOUN
ejpam-6834	1028	24	,	,	PUNCT
ejpam-6834	1028	25	i.e.	i.e.	X
ejpam-6834	1028	26	in	in	ADP
ejpam-6834	1028	27	p̃1(s	p̃1(	NOUN
ejpam-6834	1028	28	)	)	PUNCT
ejpam-6834	1028	29	.	.	PUNCT
ejpam-6834	1029	1	r	r	NOUN
ejpam-6834	1029	2	→	→	SYM
ejpam-6834	1029	3	r	r	NOUN
ejpam-6834	1029	4	+	+	NOUN
ejpam-6834	1029	5	1	1	NUM
ejpam-6834	1029	6	:	:	PUNCT
ejpam-6834	1029	7	u	u	NOUN
ejpam-6834	1029	8	,	,	PUNCT
ejpam-6834	1029	9	v	v	NUM
ejpam-6834	1029	10	are	be	AUX
ejpam-6834	1029	11	nonempty	nonempty	ADJ
ejpam-6834	1029	12	families	family	NOUN
ejpam-6834	1029	13	of	of	ADP
ejpam-6834	1029	14	r	r	NOUN
ejpam-6834	1029	15	-	-	PUNCT
ejpam-6834	1029	16	level	level	NOUN
ejpam-6834	1029	17	elements	element	NOUN
ejpam-6834	1029	18	.	.	PUNCT
ejpam-6834	1030	1	thus	thus	ADV
ejpam-6834	1030	2	u	u	NOUN
ejpam-6834	1030	3	∪	∪	ADJ
ejpam-6834	1030	4	v	v	NOUN
ejpam-6834	1030	5	is	be	AUX
ejpam-6834	1030	6	a	a	DET
ejpam-6834	1030	7	nonempty	nonempty	ADJ
ejpam-6834	1030	8	family	family	NOUN
ejpam-6834	1030	9	whose	whose	DET
ejpam-6834	1030	10	members	member	NOUN
ejpam-6834	1030	11	all	all	PRON
ejpam-6834	1030	12	lie	lie	VERB
ejpam-6834	1030	13	in	in	ADP
ejpam-6834	1030	14	p̃r(s	p̃r(s	NOUN
ejpam-6834	1030	15	)	)	PUNCT
ejpam-6834	1030	16	;	;	PUNCT
ejpam-6834	1030	17	hence	hence	ADV
ejpam-6834	1030	18	u	u	PROPN
ejpam-6834	1030	19	∪	∪	ADJ
ejpam-6834	1030	20	v	v	ADP
ejpam-6834	1030	21	∈	∈	PROPN
ejpam-6834	1030	22	p̃r+1(s	p̃r+1(s	NOUN
ejpam-6834	1030	23	)	)	PUNCT
ejpam-6834	1030	24	.	.	PUNCT
ejpam-6834	1031	1	apply	apply	VERB
ejpam-6834	1031	2	the	the	DET
ejpam-6834	1031	3	lemma	lemma	PROPN
ejpam-6834	1031	4	with	with	ADP
ejpam-6834	1031	5	s	s	NOUN
ejpam-6834	1031	6	=	=	PUNCT
ejpam-6834	1032	1	[	[	X
ejpam-6834	1032	2	0	0	NUM
ejpam-6834	1032	3	,	,	PUNCT
ejpam-6834	1032	4	1]3	1]3	NUM
ejpam-6834	1032	5	and	and	CCONJ
ejpam-6834	1032	6	r	r	NOUN
ejpam-6834	1032	7	=	=	SYM
ejpam-6834	1032	8	n.	n.	NOUN
ejpam-6834	1032	9	for	for	ADP
ejpam-6834	1032	10	each	each	DET
ejpam-6834	1032	11	input	input	NOUN
ejpam-6834	1032	12	a	a	DET
ejpam-6834	1032	13	and	and	CCONJ
ejpam-6834	1032	14	coordinate	coordinate	NOUN
ejpam-6834	1032	15	j	j	PROPN
ejpam-6834	1032	16	,	,	PUNCT
ejpam-6834	1032	17	both	both	CCONJ
ejpam-6834	1032	18	ã1(a)j	ã1(a)j	ADJ
ejpam-6834	1032	19	and	and	CCONJ
ejpam-6834	1032	20	ã2(a)j	ã2(a)j	ADJ
ejpam-6834	1032	21	lie	lie	NOUN
ejpam-6834	1032	22	in	in	ADP
ejpam-6834	1032	23	p̃n([0	p̃n([0	ADJ
ejpam-6834	1032	24	,	,	PUNCT
ejpam-6834	1032	25	1]3	1]3	NUM
ejpam-6834	1032	26	)	)	PUNCT
ejpam-6834	1032	27	and	and	CCONJ
ejpam-6834	1032	28	are	be	AUX
ejpam-6834	1032	29	nonempty	nonempty	ADJ
ejpam-6834	1032	30	,	,	PUNCT
ejpam-6834	1032	31	so	so	SCONJ
ejpam-6834	1032	32	their	their	PRON
ejpam-6834	1032	33	union	union	NOUN
ejpam-6834	1032	34	does	do	VERB
ejpam-6834	1032	35	as	as	ADV
ejpam-6834	1032	36	well	well	ADV
ejpam-6834	1032	37	.	.	PUNCT
ejpam-6834	1033	1	moreover	moreover	ADV
ejpam-6834	1033	2	,	,	PUNCT
ejpam-6834	1033	3	every	every	DET
ejpam-6834	1033	4	base	base	NOUN
ejpam-6834	1033	5	-	-	PUNCT
ejpam-6834	1033	6	level	level	NOUN
ejpam-6834	1033	7	element	element	NOUN
ejpam-6834	1033	8	of	of	ADP
ejpam-6834	1033	9	the	the	DET
ejpam-6834	1033	10	union	union	NOUN
ejpam-6834	1033	11	is	be	AUX
ejpam-6834	1033	12	still	still	ADV
ejpam-6834	1033	13	a	a	DET
ejpam-6834	1033	14	triple	triple	ADJ
ejpam-6834	1033	15	(	(	PUNCT
ejpam-6834	1033	16	t	t	PROPN
ejpam-6834	1033	17	,	,	PUNCT
ejpam-6834	1033	18	i	i	PRON
ejpam-6834	1033	19	,	,	PUNCT
ejpam-6834	1033	20	f	f	PROPN
ejpam-6834	1033	21	)	)	PUNCT
ejpam-6834	1033	22	with	with	ADP
ejpam-6834	1033	23	0	0	NUM
ejpam-6834	1033	24	≤	≤	NUM
ejpam-6834	1033	25	t+i+f	t+i+f	NOUN
ejpam-6834	1033	26	≤	≤	ADJ
ejpam-6834	1033	27	3	3	NUM
ejpam-6834	1033	28	(	(	PUNCT
ejpam-6834	1033	29	the	the	DET
ejpam-6834	1033	30	constraint	constraint	NOUN
ejpam-6834	1033	31	is	be	AUX
ejpam-6834	1033	32	preserved	preserve	VERB
ejpam-6834	1033	33	under	under	ADP
ejpam-6834	1033	34	set	set	ADJ
ejpam-6834	1033	35	union	union	NOUN
ejpam-6834	1033	36	)	)	PUNCT
ejpam-6834	1033	37	.	.	PUNCT
ejpam-6834	1034	1	therefore	therefore	ADV
ejpam-6834	1034	2	(	(	PUNCT
ejpam-6834	1034	3	ã1	ã1	ADP
ejpam-6834	1034	4	∪	∪	ADP
ejpam-6834	1034	5	ã2)(a	ã2)(a	NOUN
ejpam-6834	1034	6	)	)	PUNCT
ejpam-6834	1034	7	∈	∈	PROPN
ejpam-6834	1034	8	(	(	PUNCT
ejpam-6834	1034	9	p̃n([0	p̃n([0	PROPN
ejpam-6834	1034	10	,	,	PUNCT
ejpam-6834	1034	11	1]3))k	1]3))k	PROPN
ejpam-6834	1034	12	for	for	ADP
ejpam-6834	1034	13	all	all	DET
ejpam-6834	1034	14	a.	a.	NOUN
ejpam-6834	1034	15	theorem	theorem	NOUN
ejpam-6834	1034	16	33	33	NUM
ejpam-6834	1034	17	(	(	PUNCT
ejpam-6834	1034	18	pointwise	pointwise	NOUN
ejpam-6834	1034	19	intersection	intersection	NOUN
ejpam-6834	1034	20	)	)	PUNCT
ejpam-6834	1034	21	.	.	PUNCT
ejpam-6834	1035	1	with	with	ADP
ejpam-6834	1035	2	the	the	DET
ejpam-6834	1035	3	same	same	ADJ
ejpam-6834	1035	4	hypotheses	hypothesis	NOUN
ejpam-6834	1035	5	,	,	PUNCT
ejpam-6834	1035	6	define	define	VERB
ejpam-6834	1035	7	(	(	PUNCT
ejpam-6834	1035	8	ã1	ã1	PROPN
ejpam-6834	1035	9	∩	∩	ADJ
ejpam-6834	1035	10	ã2)(a	ã2)(a	NOUN
ejpam-6834	1035	11	)	)	PUNCT
ejpam-6834	1036	1	:	:	PUNCT
ejpam-6834	1036	2	=	=	SYM
ejpam-6834	1036	3	(	(	PUNCT
ejpam-6834	1036	4	ã1(a)j	ã1(a)j	PROPN
ejpam-6834	1036	5	∩	∩	ADJ
ejpam-6834	1036	6	ã2(a)j	ã2(a)j	NOUN
ejpam-6834	1036	7	)	)	PUNCT
ejpam-6834	1037	1	k	k	PROPN
ejpam-6834	1037	2	j=1	j=1	NOUN
ejpam-6834	1037	3	.	.	PUNCT
ejpam-6834	1038	1	if	if	SCONJ
ejpam-6834	1038	2	every	every	DET
ejpam-6834	1038	3	coordinate	coordinate	NOUN
ejpam-6834	1038	4	-	-	PUNCT
ejpam-6834	1038	5	wise	wise	ADJ
ejpam-6834	1038	6	intersection	intersection	NOUN
ejpam-6834	1038	7	is	be	AUX
ejpam-6834	1038	8	nonempty	nonempty	ADJ
ejpam-6834	1038	9	,	,	PUNCT
ejpam-6834	1038	10	then	then	ADV
ejpam-6834	1038	11	(	(	PUNCT
ejpam-6834	1038	12	ã1	ã1	PROPN
ejpam-6834	1038	13	∩	∩	NOUN
ejpam-6834	1038	14	ã2	ã2	NOUN
ejpam-6834	1038	15	)	)	PUNCT
ejpam-6834	1038	16	is	be	AUX
ejpam-6834	1038	17	an	an	DET
ejpam-6834	1038	18	(	(	PUNCT
ejpam-6834	1038	19	h	h	NOUN
ejpam-6834	1038	20	,	,	PUNCT
ejpam-6834	1038	21	k)-ary	k)-ary	X
ejpam-6834	1038	22	(	(	PUNCT
ejpam-6834	1038	23	m	m	PROPN
ejpam-6834	1038	24	,	,	PUNCT
ejpam-6834	1038	25	n)superhyperneutrosophic	n)superhyperneutrosophic	ADJ
ejpam-6834	1038	26	set	set	NOUN
ejpam-6834	1038	27	.	.	PUNCT
ejpam-6834	1039	1	proof	proof	NOUN
ejpam-6834	1039	2	.	.	PUNCT
ejpam-6834	1040	1	we	we	PRON
ejpam-6834	1040	2	use	use	VERB
ejpam-6834	1040	3	the	the	DET
ejpam-6834	1040	4	companion	companion	NOUN
ejpam-6834	1040	5	lemma	lemma	PROPN
ejpam-6834	1040	6	(	(	PUNCT
ejpam-6834	1040	7	proved	prove	VERB
ejpam-6834	1040	8	by	by	ADP
ejpam-6834	1040	9	induction	induction	NOUN
ejpam-6834	1040	10	on	on	ADP
ejpam-6834	1040	11	r	r	PROPN
ejpam-6834	1040	12	≥	≥	NUM
ejpam-6834	1040	13	1	1	NUM
ejpam-6834	1040	14	):	):	PUNCT
ejpam-6834	1040	15	lemma	lemma	PROPN
ejpam-6834	1040	16	.	.	PUNCT
ejpam-6834	1041	1	if	if	SCONJ
ejpam-6834	1041	2	u	u	PROPN
ejpam-6834	1041	3	,	,	PUNCT
ejpam-6834	1041	4	v	v	NOUN
ejpam-6834	1041	5	∈	∈	PROPN
ejpam-6834	1041	6	p̃r(s	p̃r(s	NOUN
ejpam-6834	1041	7	)	)	PUNCT
ejpam-6834	1041	8	and	and	CCONJ
ejpam-6834	1041	9	u	u	NOUN
ejpam-6834	1041	10	∩	∩	NOUN
ejpam-6834	1041	11	v	v	ADP
ejpam-6834	1041	12	̸=	̸=	PROPN
ejpam-6834	1041	13	∅	∅	NOUN
ejpam-6834	1041	14	,	,	PUNCT
ejpam-6834	1041	15	then	then	ADV
ejpam-6834	1041	16	u	u	NOUN
ejpam-6834	1041	17	∩	∩	NOUN
ejpam-6834	1041	18	v	v	ADP
ejpam-6834	1041	19	∈	∈	PROPN
ejpam-6834	1041	20	p̃r(s	p̃r(s	NOUN
ejpam-6834	1041	21	)	)	PUNCT
ejpam-6834	1041	22	.	.	PUNCT
ejpam-6834	1042	1	r	r	NOUN
ejpam-6834	1042	2	=	=	SYM
ejpam-6834	1042	3	1	1	NUM
ejpam-6834	1042	4	:	:	PUNCT
ejpam-6834	1042	5	u	u	NOUN
ejpam-6834	1042	6	,	,	PUNCT
ejpam-6834	1042	7	v	v	NUM
ejpam-6834	1042	8	are	be	AUX
ejpam-6834	1042	9	nonempty	nonempty	ADJ
ejpam-6834	1042	10	subsets	subset	NOUN
ejpam-6834	1042	11	of	of	ADP
ejpam-6834	1042	12	s.	s.	PROPN
ejpam-6834	1042	13	if	if	SCONJ
ejpam-6834	1042	14	u	u	PROPN
ejpam-6834	1042	15	∩v	∩v	NOUN
ejpam-6834	1042	16	̸=	̸=	PROPN
ejpam-6834	1042	17	∅	∅	NOUN
ejpam-6834	1042	18	,	,	PUNCT
ejpam-6834	1042	19	then	then	ADV
ejpam-6834	1042	20	u	u	NOUN
ejpam-6834	1042	21	∩v	∩v	NOUN
ejpam-6834	1042	22	is	be	AUX
ejpam-6834	1042	23	a	a	DET
ejpam-6834	1042	24	nonempty	nonempty	ADJ
ejpam-6834	1042	25	subset	subset	NOUN
ejpam-6834	1042	26	of	of	ADP
ejpam-6834	1042	27	s	s	NOUN
ejpam-6834	1042	28	,	,	PUNCT
ejpam-6834	1042	29	i.e.	i.e.	X
ejpam-6834	1042	30	in	in	ADP
ejpam-6834	1042	31	p̃1(s	p̃1(	NOUN
ejpam-6834	1042	32	)	)	PUNCT
ejpam-6834	1042	33	.	.	PUNCT
ejpam-6834	1043	1	r	r	NOUN
ejpam-6834	1043	2	→	→	PUNCT
ejpam-6834	1043	3	r+	r+	NOUN
ejpam-6834	1043	4	1	1	NUM
ejpam-6834	1043	5	:	:	PUNCT
ejpam-6834	1043	6	u	u	NOUN
ejpam-6834	1043	7	,	,	PUNCT
ejpam-6834	1043	8	v	v	NUM
ejpam-6834	1043	9	are	be	AUX
ejpam-6834	1043	10	nonempty	nonempty	ADJ
ejpam-6834	1043	11	families	family	NOUN
ejpam-6834	1043	12	of	of	ADP
ejpam-6834	1043	13	r	r	NOUN
ejpam-6834	1043	14	-	-	PUNCT
ejpam-6834	1043	15	level	level	NOUN
ejpam-6834	1043	16	elements	element	NOUN
ejpam-6834	1043	17	.	.	PUNCT
ejpam-6834	1044	1	if	if	SCONJ
ejpam-6834	1044	2	u	u	PRON
ejpam-6834	1044	3	∩v	∩v	NOUN
ejpam-6834	1044	4	̸=	̸=	PROPN
ejpam-6834	1044	5	∅	∅	NOUN
ejpam-6834	1044	6	,	,	PUNCT
ejpam-6834	1044	7	every	every	DET
ejpam-6834	1044	8	element	element	NOUN
ejpam-6834	1044	9	of	of	ADP
ejpam-6834	1044	10	u	u	PROPN
ejpam-6834	1044	11	∩	∩	ADJ
ejpam-6834	1044	12	v	v	NOUN
ejpam-6834	1044	13	is	be	AUX
ejpam-6834	1044	14	itself	itself	PRON
ejpam-6834	1044	15	in	in	ADP
ejpam-6834	1044	16	p̃r(s	p̃r(s	NOUN
ejpam-6834	1044	17	)	)	PUNCT
ejpam-6834	1044	18	,	,	PUNCT
ejpam-6834	1044	19	and	and	CCONJ
ejpam-6834	1044	20	u	u	NOUN
ejpam-6834	1044	21	∩	∩	NOUN
ejpam-6834	1044	22	v	v	NOUN
ejpam-6834	1044	23	is	be	AUX
ejpam-6834	1044	24	nonempty	nonempty	ADJ
ejpam-6834	1044	25	;	;	PUNCT
ejpam-6834	1044	26	hence	hence	ADV
ejpam-6834	1044	27	u	u	NOUN
ejpam-6834	1044	28	∩	∩	NOUN
ejpam-6834	1044	29	v	v	ADP
ejpam-6834	1044	30	∈	∈	PROPN
ejpam-6834	1044	31	p̃r+1(s	p̃r+1(s	NOUN
ejpam-6834	1044	32	)	)	PUNCT
ejpam-6834	1044	33	.	.	PUNCT
ejpam-6834	1045	1	apply	apply	VERB
ejpam-6834	1045	2	the	the	DET
ejpam-6834	1045	3	lemma	lemma	PROPN
ejpam-6834	1045	4	with	with	ADP
ejpam-6834	1045	5	s	s	NOUN
ejpam-6834	1045	6	=	=	PUNCT
ejpam-6834	1046	1	[	[	X
ejpam-6834	1046	2	0	0	NUM
ejpam-6834	1046	3	,	,	PUNCT
ejpam-6834	1046	4	1]3	1]3	NUM
ejpam-6834	1046	5	and	and	CCONJ
ejpam-6834	1046	6	r	r	NOUN
ejpam-6834	1046	7	=	=	SYM
ejpam-6834	1046	8	n.	n.	NOUN
ejpam-6834	1046	9	the	the	DET
ejpam-6834	1046	10	nonemptiness	nonemptiness	PROPN
ejpam-6834	1046	11	hypothesis	hypothesis	NOUN
ejpam-6834	1046	12	ensures	ensure	VERB
ejpam-6834	1046	13	each	each	DET
ejpam-6834	1046	14	coordinate	coordinate	NOUN
ejpam-6834	1046	15	-	-	PUNCT
ejpam-6834	1046	16	wise	wise	ADJ
ejpam-6834	1046	17	intersection	intersection	NOUN
ejpam-6834	1046	18	lies	lie	VERB
ejpam-6834	1046	19	in	in	ADP
ejpam-6834	1046	20	p̃n([0	p̃n([0	ADJ
ejpam-6834	1046	21	,	,	PUNCT
ejpam-6834	1046	22	1]3	1]3	NUM
ejpam-6834	1046	23	)	)	PUNCT
ejpam-6834	1046	24	.	.	PUNCT
ejpam-6834	1047	1	neutrosophic	neutrosophic	ADJ
ejpam-6834	1047	2	constraints	constraint	NOUN
ejpam-6834	1047	3	are	be	AUX
ejpam-6834	1047	4	pointwise	pointwise	ADJ
ejpam-6834	1047	5	and	and	CCONJ
ejpam-6834	1047	6	are	be	AUX
ejpam-6834	1047	7	preserved	preserve	VERB
ejpam-6834	1047	8	by	by	ADP
ejpam-6834	1047	9	set	set	NOUN
ejpam-6834	1047	10	-	-	PUNCT
ejpam-6834	1047	11	theoretic	theoretic	NOUN
ejpam-6834	1047	12	intersection	intersection	NOUN
ejpam-6834	1047	13	.	.	PUNCT
ejpam-6834	1048	1	therefore	therefore	ADV
ejpam-6834	1048	2	(	(	PUNCT
ejpam-6834	1048	3	ã1	ã1	PROPN
ejpam-6834	1048	4	∩	∩	NOUN
ejpam-6834	1048	5	ã2	ã2	NOUN
ejpam-6834	1048	6	)	)	PUNCT
ejpam-6834	1048	7	has	have	VERB
ejpam-6834	1048	8	the	the	DET
ejpam-6834	1048	9	desired	desire	VERB
ejpam-6834	1048	10	codomain	codomain	NOUN
ejpam-6834	1048	11	.	.	PUNCT
ejpam-6834	1049	1	theorem	theorem	NOUN
ejpam-6834	1049	2	34	34	NUM
ejpam-6834	1049	3	(	(	PUNCT
ejpam-6834	1049	4	neutrosophic	neutrosophic	PROPN
ejpam-6834	1049	5	λ	λ	NOUN
ejpam-6834	1049	6	-	-	NOUN
ejpam-6834	1049	7	cuts	cut	NOUN
ejpam-6834	1049	8	)	)	PUNCT
ejpam-6834	1049	9	.	.	PUNCT
ejpam-6834	1050	1	for	for	ADP
ejpam-6834	1050	2	λ	λ	PROPN
ejpam-6834	1050	3	=	=	SYM
ejpam-6834	1050	4	(	(	PUNCT
ejpam-6834	1050	5	α	α	X
ejpam-6834	1050	6	,	,	PUNCT
ejpam-6834	1050	7	β	β	X
ejpam-6834	1050	8	,	,	PUNCT
ejpam-6834	1050	9	γ	γ	NOUN
ejpam-6834	1050	10	)	)	PUNCT
ejpam-6834	1050	11	∈	∈	NOUN
ejpam-6834	1051	1	[	[	X
ejpam-6834	1051	2	0	0	NUM
ejpam-6834	1051	3	,	,	PUNCT
ejpam-6834	1051	4	1]3	1]3	NUM
ejpam-6834	1051	5	,	,	PUNCT
ejpam-6834	1051	6	define	define	VERB
ejpam-6834	1051	7	the	the	DET
ejpam-6834	1051	8	cut	cut	NOUN
ejpam-6834	1051	9	cλ	cλ	INTJ
ejpam-6834	1051	10	=	=	PUNCT
ejpam-6834	1051	11	{	{	PUNCT
ejpam-6834	1051	12	a	a	DET
ejpam-6834	1051	13	∈	∈	PROPN
ejpam-6834	1051	14	(	(	PUNCT
ejpam-6834	1051	15	p̃m(x))h	p̃m(x))h	NOUN
ejpam-6834	1051	16	∣∣∣	∣∣∣	NOUN
ejpam-6834	1051	17	∃j	∃j	PROPN
ejpam-6834	1051	18	,	,	PUNCT
ejpam-6834	1051	19	∃(t	∃(t	PROPN
ejpam-6834	1051	20	,	,	PUNCT
ejpam-6834	1051	21	i	i	PRON
ejpam-6834	1051	22	,	,	PUNCT
ejpam-6834	1051	23	f	f	PROPN
ejpam-6834	1051	24	)	)	PUNCT
ejpam-6834	1051	25	∈	∈	PROPN
ejpam-6834	1051	26	ã(a)j	ã(a)j	ADJ
ejpam-6834	1051	27	with	with	ADP
ejpam-6834	1051	28	t	t	PROPN
ejpam-6834	1051	29	≥	≥	PROPN
ejpam-6834	1051	30	α	α	NOUN
ejpam-6834	1051	31	,	,	PUNCT
ejpam-6834	1051	32	i	i	NOUN
ejpam-6834	1051	33	≤	≤	NOUN
ejpam-6834	1051	34	β	β	X
ejpam-6834	1051	35	,	,	PUNCT
ejpam-6834	1051	36	f	f	PROPN
ejpam-6834	1051	37	≤	≤	NUM
ejpam-6834	1051	38	γ	γ	X
ejpam-6834	1051	39	}	}	PUNCT
ejpam-6834	1051	40	.	.	PUNCT
ejpam-6834	1052	1	if	if	SCONJ
ejpam-6834	1052	2	λ′	λ′	X
ejpam-6834	1052	3	=	=	SYM
ejpam-6834	1052	4	(	(	PUNCT
ejpam-6834	1052	5	α′	α′	NUM
ejpam-6834	1052	6	,	,	PUNCT
ejpam-6834	1052	7	β′	β′	NUM
ejpam-6834	1052	8	,	,	PUNCT
ejpam-6834	1052	9	γ′	γ′	NOUN
ejpam-6834	1052	10	)	)	PUNCT
ejpam-6834	1052	11	satisfies	satisfy	VERB
ejpam-6834	1052	12	α′	α′	NUM
ejpam-6834	1052	13	≥	≥	NOUN
ejpam-6834	1052	14	α	α	NOUN
ejpam-6834	1052	15	,	,	PUNCT
ejpam-6834	1052	16	β′	β′	NUM
ejpam-6834	1052	17	≤	≤	NOUN
ejpam-6834	1052	18	β	β	NOUN
ejpam-6834	1052	19	,	,	PUNCT
ejpam-6834	1052	20	and	and	CCONJ
ejpam-6834	1052	21	γ′	γ′	NOUN
ejpam-6834	1052	22	≤	≤	NOUN
ejpam-6834	1052	23	γ	γ	X
ejpam-6834	1052	24	,	,	PUNCT
ejpam-6834	1052	25	then	then	ADV
ejpam-6834	1052	26	cλ′	cλ′	PROPN
ejpam-6834	1052	27	⊆	⊆	NUM
ejpam-6834	1052	28	cλ	cλ	PROPN
ejpam-6834	1052	29	.	.	PUNCT
ejpam-6834	1052	30	proof	proof	NOUN
ejpam-6834	1052	31	.	.	PUNCT
ejpam-6834	1053	1	take	take	VERB
ejpam-6834	1053	2	any	any	DET
ejpam-6834	1053	3	a	a	DET
ejpam-6834	1053	4	∈	∈	NOUN
ejpam-6834	1053	5	cλ′	cλ′	NOUN
ejpam-6834	1053	6	.	.	PUNCT
ejpam-6834	1054	1	by	by	ADP
ejpam-6834	1054	2	definition	definition	NOUN
ejpam-6834	1054	3	,	,	PUNCT
ejpam-6834	1054	4	there	there	PRON
ejpam-6834	1054	5	exist	exist	VERB
ejpam-6834	1054	6	an	an	DET
ejpam-6834	1054	7	index	index	NOUN
ejpam-6834	1054	8	j	j	PROPN
ejpam-6834	1054	9	and	and	CCONJ
ejpam-6834	1054	10	a	a	DET
ejpam-6834	1054	11	triple	triple	ADJ
ejpam-6834	1054	12	(	(	PUNCT
ejpam-6834	1054	13	t	t	PROPN
ejpam-6834	1054	14	,	,	PUNCT
ejpam-6834	1054	15	i	i	PRON
ejpam-6834	1054	16	,	,	PUNCT
ejpam-6834	1054	17	f	f	PROPN
ejpam-6834	1054	18	)	)	PUNCT
ejpam-6834	1054	19	∈	∈	PROPN
ejpam-6834	1054	20	ã(a)j	ã(a)j	ADJ
ejpam-6834	1054	21	with	with	ADP
ejpam-6834	1054	22	t	t	PROPN
ejpam-6834	1054	23	≥	≥	X
ejpam-6834	1054	24	α′	α′	NUM
ejpam-6834	1054	25	,	,	PUNCT
ejpam-6834	1054	26	i	i	PRON
ejpam-6834	1054	27	≤	≤	NOUN
ejpam-6834	1054	28	β′	β′	PUNCT
ejpam-6834	1054	29	,	,	PUNCT
ejpam-6834	1054	30	f	f	PROPN
ejpam-6834	1054	31	≤	≤	PROPN
ejpam-6834	1054	32	γ′.	γ′.	VERB
ejpam-6834	1054	33	since	since	SCONJ
ejpam-6834	1054	34	α′	α′	NUM
ejpam-6834	1054	35	≥	≥	NOUN
ejpam-6834	1054	36	α	α	NOUN
ejpam-6834	1054	37	,	,	PUNCT
ejpam-6834	1054	38	β′	β′	NUM
ejpam-6834	1054	39	≤	≤	NOUN
ejpam-6834	1054	40	β	β	NOUN
ejpam-6834	1054	41	,	,	PUNCT
ejpam-6834	1054	42	and	and	CCONJ
ejpam-6834	1054	43	γ′	γ′	PROPN
ejpam-6834	1054	44	≤	≤	NOUN
ejpam-6834	1054	45	γ	γ	X
ejpam-6834	1054	46	,	,	PUNCT
ejpam-6834	1054	47	the	the	DET
ejpam-6834	1054	48	same	same	ADJ
ejpam-6834	1054	49	triple	triple	ADJ
ejpam-6834	1054	50	satisfies	satisfie	NOUN
ejpam-6834	1054	51	t	t	PROPN
ejpam-6834	1054	52	≥	≥	PROPN
ejpam-6834	1054	53	α	α	NOUN
ejpam-6834	1054	54	,	,	PUNCT
ejpam-6834	1054	55	i	i	NOUN
ejpam-6834	1054	56	≤	≤	NOUN
ejpam-6834	1054	57	β	β	X
ejpam-6834	1054	58	,	,	PUNCT
ejpam-6834	1054	59	f	f	PROPN
ejpam-6834	1054	60	≤	≤	PROPN
ejpam-6834	1054	61	γ	γ	PROPN
ejpam-6834	1054	62	,	,	PUNCT
ejpam-6834	1054	63	so	so	SCONJ
ejpam-6834	1054	64	a	a	DET
ejpam-6834	1054	65	∈	∈	PROPN
ejpam-6834	1054	66	cλ	cλ	PROPN
ejpam-6834	1054	67	.	.	PUNCT
ejpam-6834	1055	1	thus	thus	ADV
ejpam-6834	1055	2	cλ′	cλ′	X
ejpam-6834	1055	3	⊆	⊆	NUM
ejpam-6834	1055	4	cλ	cλ	PROPN
ejpam-6834	1055	5	.	.	PUNCT
ejpam-6834	1056	1	theorem	theorem	VERB
ejpam-6834	1056	2	35	35	NUM
ejpam-6834	1056	3	(	(	PUNCT
ejpam-6834	1056	4	truth	truth	NOUN
ejpam-6834	1056	5	-	-	PUNCT
ejpam-6834	1056	6	projection	projection	NOUN
ejpam-6834	1056	7	yields	yield	NOUN
ejpam-6834	1056	8	fuzzy	fuzzy	ADJ
ejpam-6834	1056	9	structure	structure	NOUN
ejpam-6834	1056	10	)	)	PUNCT
ejpam-6834	1056	11	.	.	PUNCT
ejpam-6834	1057	1	let	let	VERB
ejpam-6834	1057	2	πt	πt	VERB
ejpam-6834	1057	3	:	:	PUNCT
ejpam-6834	1058	1	[	[	X
ejpam-6834	1058	2	0	0	NUM
ejpam-6834	1058	3	,	,	PUNCT
ejpam-6834	1058	4	1]3	1]3	NUM
ejpam-6834	1058	5	→	→	SYM
ejpam-6834	1058	6	[	[	X
ejpam-6834	1058	7	0	0	NUM
ejpam-6834	1058	8	,	,	PUNCT
ejpam-6834	1058	9	1	1	NUM
ejpam-6834	1058	10	]	]	PUNCT
ejpam-6834	1058	11	be	be	AUX
ejpam-6834	1058	12	πt	πt	ADP
ejpam-6834	1058	13	(	(	PUNCT
ejpam-6834	1058	14	t	t	PROPN
ejpam-6834	1058	15	,	,	PUNCT
ejpam-6834	1058	16	i	i	PRON
ejpam-6834	1058	17	,	,	PUNCT
ejpam-6834	1058	18	f	f	PROPN
ejpam-6834	1058	19	)	)	PUNCT
ejpam-6834	1059	1	=	=	SYM
ejpam-6834	1059	2	t	t	NOUN
ejpam-6834	1059	3	and	and	CCONJ
ejpam-6834	1059	4	extend	extend	VERB
ejpam-6834	1059	5	it	it	PRON
ejpam-6834	1059	6	levelwise	levelwise	NOUN
ejpam-6834	1059	7	to	to	ADP
ejpam-6834	1059	8	πt	πt	PROPN
ejpam-6834	1059	9	:	:	PUNCT
ejpam-6834	1059	10	(	(	PUNCT
ejpam-6834	1059	11	p̃n([0	p̃n([0	PROPN
ejpam-6834	1059	12	,	,	PUNCT
ejpam-6834	1059	13	1]3))k	1]3))k	PROPN
ejpam-6834	1059	14	→	→	SYM
ejpam-6834	1059	15	(	(	PUNCT
ejpam-6834	1059	16	p̃n([0	p̃n([0	PROPN
ejpam-6834	1059	17	,	,	PUNCT
ejpam-6834	1059	18	1]))k	1]))k	NUM
ejpam-6834	1059	19	.	.	PUNCT
ejpam-6834	1060	1	then	then	ADV
ejpam-6834	1060	2	πt	πt	ADP
ejpam-6834	1060	3	◦	◦	NOUN
ejpam-6834	1060	4	ã	ã	PROPN
ejpam-6834	1060	5	is	be	AUX
ejpam-6834	1060	6	an	an	DET
ejpam-6834	1060	7	(	(	PUNCT
ejpam-6834	1060	8	h	h	NOUN
ejpam-6834	1060	9	,	,	PUNCT
ejpam-6834	1060	10	k)ary	k)ary	PROPN
ejpam-6834	1060	11	(	(	PUNCT
ejpam-6834	1060	12	m	m	NOUN
ejpam-6834	1060	13	,	,	PUNCT
ejpam-6834	1060	14	n)-superhyperfuzzy	n)-superhyperfuzzy	PUNCT
ejpam-6834	1060	15	set	set	NOUN
ejpam-6834	1060	16	.	.	PUNCT
ejpam-6834	1061	1	t.	t.	PROPN
ejpam-6834	1061	2	fujita	fujita	PROPN
ejpam-6834	1061	3	,	,	PUNCT
ejpam-6834	1061	4	f.smarandache	f.smarandache	NOUN
ejpam-6834	1061	5	/	/	SYM
ejpam-6834	1061	6	eur	eur	PROPN
ejpam-6834	1061	7	.	.	PUNCT
ejpam-6834	1062	1	j.	j.	PROPN
ejpam-6834	1062	2	pure	pure	PROPN
ejpam-6834	1062	3	appl	appl	PROPN
ejpam-6834	1062	4	.	.	PROPN
ejpam-6834	1062	5	math	math	PROPN
ejpam-6834	1062	6	,	,	PUNCT
ejpam-6834	1062	7	18	18	NUM
ejpam-6834	1062	8	(	(	PUNCT
ejpam-6834	1062	9	4	4	NUM
ejpam-6834	1062	10	)	)	PUNCT
ejpam-6834	1062	11	(	(	PUNCT
ejpam-6834	1062	12	2025	2025	NUM
ejpam-6834	1062	13	)	)	PUNCT
ejpam-6834	1062	14	,	,	PUNCT
ejpam-6834	1062	15	6834	6834	NUM
ejpam-6834	1062	16	42	42	NUM
ejpam-6834	1062	17	of	of	ADP
ejpam-6834	1062	18	69	69	NUM
ejpam-6834	1062	19	proof	proof	NOUN
ejpam-6834	1062	20	.	.	PUNCT
ejpam-6834	1063	1	define	define	VERB
ejpam-6834	1063	2	πt	πt	ADP
ejpam-6834	1063	3	recursively	recursively	ADV
ejpam-6834	1063	4	as	as	ADP
ejpam-6834	1063	5	in	in	ADP
ejpam-6834	1063	6	the	the	DET
ejpam-6834	1063	7	proof	proof	NOUN
ejpam-6834	1063	8	of	of	ADP
ejpam-6834	1063	9	the	the	DET
ejpam-6834	1063	10	relation	relation	NOUN
ejpam-6834	1063	11	theorem	theorem	NOUN
ejpam-6834	1063	12	:	:	PUNCT
ejpam-6834	1063	13	base	base	ADJ
ejpam-6834	1063	14	level	level	NOUN
ejpam-6834	1063	15	n	n	NOUN
ejpam-6834	1063	16	=	=	SYM
ejpam-6834	1063	17	1	1	NUM
ejpam-6834	1063	18	by	by	ADP
ejpam-6834	1063	19	taking	take	VERB
ejpam-6834	1063	20	elementwise	elementwise	ADJ
ejpam-6834	1063	21	truth	truth	NOUN
ejpam-6834	1063	22	components	component	NOUN
ejpam-6834	1063	23	,	,	PUNCT
ejpam-6834	1063	24	and	and	CCONJ
ejpam-6834	1063	25	for	for	ADP
ejpam-6834	1063	26	n	n	X
ejpam-6834	1063	27	>	>	X
ejpam-6834	1063	28	1	1	NUM
ejpam-6834	1063	29	by	by	ADP
ejpam-6834	1063	30	applying	apply	VERB
ejpam-6834	1063	31	the	the	DET
ejpam-6834	1063	32	previous	previous	ADJ
ejpam-6834	1063	33	level	level	NOUN
ejpam-6834	1063	34	to	to	ADP
ejpam-6834	1063	35	each	each	DET
ejpam-6834	1063	36	member	member	NOUN
ejpam-6834	1063	37	of	of	ADP
ejpam-6834	1063	38	a	a	DET
ejpam-6834	1063	39	nonempty	nonempty	ADJ
ejpam-6834	1063	40	family	family	NOUN
ejpam-6834	1063	41	.	.	PUNCT
ejpam-6834	1064	1	nonemptiness	nonemptiness	PROPN
ejpam-6834	1064	2	and	and	CCONJ
ejpam-6834	1064	3	the	the	DET
ejpam-6834	1064	4	nesting	nesting	ADJ
ejpam-6834	1064	5	level	level	NOUN
ejpam-6834	1064	6	are	be	AUX
ejpam-6834	1064	7	preserved	preserve	VERB
ejpam-6834	1064	8	at	at	ADP
ejpam-6834	1064	9	each	each	DET
ejpam-6834	1064	10	step	step	NOUN
ejpam-6834	1064	11	.	.	PUNCT
ejpam-6834	1065	1	hence	hence	ADV
ejpam-6834	1065	2	for	for	ADP
ejpam-6834	1065	3	every	every	DET
ejpam-6834	1065	4	input	input	NOUN
ejpam-6834	1065	5	a	a	PRON
ejpam-6834	1065	6	,	,	PUNCT
ejpam-6834	1065	7	(	(	PUNCT
ejpam-6834	1065	8	πt	πt	ADP
ejpam-6834	1065	9	◦	◦	NOUN
ejpam-6834	1065	10	ã)(a	ã)(a	NOUN
ejpam-6834	1065	11	)	)	PUNCT
ejpam-6834	1065	12	is	be	AUX
ejpam-6834	1065	13	a	a	DET
ejpam-6834	1065	14	k	k	NOUN
ejpam-6834	1065	15	-	-	NOUN
ejpam-6834	1065	16	tuple	tuple	NOUN
ejpam-6834	1065	17	of	of	ADP
ejpam-6834	1065	18	nonempty	nonempty	ADJ
ejpam-6834	1065	19	n	n	CCONJ
ejpam-6834	1065	20	-	-	PUNCT
ejpam-6834	1065	21	level	level	NOUN
ejpam-6834	1065	22	subsets	subset	NOUN
ejpam-6834	1065	23	of	of	ADP
ejpam-6834	1065	24	[	[	X
ejpam-6834	1065	25	0	0	NUM
ejpam-6834	1065	26	,	,	PUNCT
ejpam-6834	1065	27	1	1	NUM
ejpam-6834	1065	28	]	]	PUNCT
ejpam-6834	1065	29	,	,	PUNCT
ejpam-6834	1065	30	i.e.	i.e.	X
ejpam-6834	1065	31	an	an	DET
ejpam-6834	1065	32	element	element	NOUN
ejpam-6834	1065	33	of	of	ADP
ejpam-6834	1065	34	(	(	PUNCT
ejpam-6834	1065	35	p̃n([0	p̃n([0	PROPN
ejpam-6834	1065	36	,	,	PUNCT
ejpam-6834	1065	37	1]))k	1]))k	NUM
ejpam-6834	1065	38	.	.	PUNCT
ejpam-6834	1066	1	therefore	therefore	ADV
ejpam-6834	1066	2	πt	πt	AUX
ejpam-6834	1066	3	◦	◦	VERB
ejpam-6834	1066	4	ã	ã	PROPN
ejpam-6834	1066	5	satisfies	satisfy	VERB
ejpam-6834	1066	6	the	the	DET
ejpam-6834	1066	7	definition	definition	NOUN
ejpam-6834	1066	8	of	of	ADP
ejpam-6834	1066	9	an	an	DET
ejpam-6834	1066	10	(	(	PUNCT
ejpam-6834	1066	11	h	h	NOUN
ejpam-6834	1066	12	,	,	PUNCT
ejpam-6834	1066	13	k)-ary	k)-ary	X
ejpam-6834	1066	14	(	(	PUNCT
ejpam-6834	1066	15	m	m	NOUN
ejpam-6834	1066	16	,	,	PUNCT
ejpam-6834	1066	17	n)-superhyperfuzzy	n)-superhyperfuzzy	PUNCT
ejpam-6834	1066	18	set	set	NOUN
ejpam-6834	1066	19	.	.	PUNCT
ejpam-6834	1067	1	theorem	theorem	VERB
ejpam-6834	1067	2	36	36	NUM
ejpam-6834	1067	3	(	(	PUNCT
ejpam-6834	1067	4	functoriality	functoriality	NOUN
ejpam-6834	1067	5	under	under	ADP
ejpam-6834	1067	6	surjections	surjection	NOUN
ejpam-6834	1067	7	)	)	PUNCT
ejpam-6834	1067	8	.	.	PUNCT
ejpam-6834	1068	1	let	let	VERB
ejpam-6834	1068	2	f	f	NOUN
ejpam-6834	1068	3	:	:	PUNCT
ejpam-6834	1068	4	x	x	X
ejpam-6834	1068	5	→	→	SYM
ejpam-6834	1068	6	y	y	PROPN
ejpam-6834	1068	7	be	be	AUX
ejpam-6834	1068	8	surjective	surjective	ADJ
ejpam-6834	1068	9	.	.	PUNCT
ejpam-6834	1069	1	define	define	VERB
ejpam-6834	1069	2	recursively	recursively	ADV
ejpam-6834	1069	3	the	the	DET
ejpam-6834	1069	4	nonempty	nonempty	ADJ
ejpam-6834	1069	5	preimage	preimage	NOUN
ejpam-6834	1069	6	maps	map	NOUN
ejpam-6834	1069	7	f−1	f−1	PROPN
ejpam-6834	1069	8	(	(	PUNCT
ejpam-6834	1069	9	r	r	NOUN
ejpam-6834	1069	10	)	)	PUNCT
ejpam-6834	1069	11	:	:	PUNCT
ejpam-6834	1069	12	p̃r(y	p̃r(y	VERB
ejpam-6834	1069	13	)	)	PUNCT
ejpam-6834	1069	14	→	→	SYM
ejpam-6834	1069	15	p̃r(x	p̃r(x	NUM
ejpam-6834	1069	16	)	)	PUNCT
ejpam-6834	1069	17	by	by	ADP
ejpam-6834	1069	18	f−1	f−1	PROPN
ejpam-6834	1069	19	(	(	PUNCT
ejpam-6834	1069	20	1	1	NUM
ejpam-6834	1069	21	)	)	PUNCT
ejpam-6834	1069	22	(	(	PUNCT
ejpam-6834	1069	23	b	b	NOUN
ejpam-6834	1069	24	)	)	PUNCT
ejpam-6834	1069	25	:	:	PUNCT
ejpam-6834	1069	26	=	=	SYM
ejpam-6834	1069	27	{	{	PUNCT
ejpam-6834	1069	28	x	x	PUNCT
ejpam-6834	1069	29	∈	∈	PROPN
ejpam-6834	1069	30	x	x	X
ejpam-6834	1069	31	:	:	PUNCT
ejpam-6834	1069	32	f(x	f(x	PROPN
ejpam-6834	1069	33	)	)	PUNCT
ejpam-6834	1069	34	∈	∈	PROPN
ejpam-6834	1069	35	b	b	X
ejpam-6834	1069	36	}	}	PUNCT
ejpam-6834	1069	37	(	(	PUNCT
ejpam-6834	1069	38	b	b	X
ejpam-6834	1069	39	∈	∈	PROPN
ejpam-6834	1069	40	p̃(y	p̃(y	PROPN
ejpam-6834	1069	41	)	)	PUNCT
ejpam-6834	1069	42	)	)	PUNCT
ejpam-6834	1069	43	,	,	PUNCT
ejpam-6834	1069	44	f−1	f−1	PROPN
ejpam-6834	1069	45	(	(	PUNCT
ejpam-6834	1069	46	r+1)(b	r+1)(b	PROPN
ejpam-6834	1069	47	)	)	PUNCT
ejpam-6834	1069	48	:	:	PUNCT
ejpam-6834	1070	1	=	=	SYM
ejpam-6834	1070	2	{	{	PUNCT
ejpam-6834	1070	3	f−1	f−1	PROPN
ejpam-6834	1070	4	(	(	PUNCT
ejpam-6834	1070	5	r	r	NOUN
ejpam-6834	1070	6	)	)	PUNCT
ejpam-6834	1070	7	(	(	PUNCT
ejpam-6834	1070	8	b	b	X
ejpam-6834	1070	9	)	)	PUNCT
ejpam-6834	1070	10	∣∣	∣∣	NUM
ejpam-6834	1070	11	b	b	X
ejpam-6834	1070	12	∈	∈	PROPN
ejpam-6834	1070	13	b	b	PROPN
ejpam-6834	1070	14	}	}	PUNCT
ejpam-6834	1070	15	.	.	PUNCT
ejpam-6834	1071	1	then	then	ADV
ejpam-6834	1071	2	the	the	DET
ejpam-6834	1071	3	pushforward	pushforward	NOUN
ejpam-6834	1071	4	(	(	PUNCT
ejpam-6834	1071	5	f∗ã)(b1	f∗ã)(b1	PROPN
ejpam-6834	1071	6	,	,	PUNCT
ejpam-6834	1071	7	.	.	PUNCT
ejpam-6834	1071	8	.	.	PUNCT
ejpam-6834	1071	9	.	.	PUNCT
ejpam-6834	1072	1	,	,	PUNCT
ejpam-6834	1072	2	bh	bh	NOUN
ejpam-6834	1072	3	)	)	PUNCT
ejpam-6834	1072	4	:	:	PUNCT
ejpam-6834	1073	1	=	=	PUNCT
ejpam-6834	1073	2	ã	ã	PROPN
ejpam-6834	1073	3	(	(	PUNCT
ejpam-6834	1073	4	f−1	f−1	PROPN
ejpam-6834	1073	5	(	(	PUNCT
ejpam-6834	1073	6	m)(b1	m)(b1	PROPN
ejpam-6834	1073	7	)	)	PUNCT
ejpam-6834	1073	8	,	,	PUNCT
ejpam-6834	1073	9	.	.	PUNCT
ejpam-6834	1073	10	.	.	PUNCT
ejpam-6834	1073	11	.	.	PUNCT
ejpam-6834	1074	1	,	,	PUNCT
ejpam-6834	1074	2	f	f	PROPN
ejpam-6834	1074	3	−1	−1	NOUN
ejpam-6834	1074	4	(	(	PUNCT
ejpam-6834	1074	5	m)(bh	m)(bh	NOUN
ejpam-6834	1074	6	)	)	PUNCT
ejpam-6834	1074	7	)	)	PUNCT
ejpam-6834	1074	8	,	,	PUNCT
ejpam-6834	1074	9	(	(	PUNCT
ejpam-6834	1074	10	bi	bi	NOUN
ejpam-6834	1074	11	∈	∈	PROPN
ejpam-6834	1074	12	p̃m(y	p̃m(y	ADV
ejpam-6834	1074	13	)	)	PUNCT
ejpam-6834	1074	14	)	)	PUNCT
ejpam-6834	1074	15	,	,	PUNCT
ejpam-6834	1074	16	defines	define	VERB
ejpam-6834	1074	17	an	an	DET
ejpam-6834	1074	18	(	(	PUNCT
ejpam-6834	1074	19	h	h	NOUN
ejpam-6834	1074	20	,	,	PUNCT
ejpam-6834	1074	21	k)-ary	k)-ary	X
ejpam-6834	1074	22	(	(	PUNCT
ejpam-6834	1074	23	m	m	PROPN
ejpam-6834	1074	24	,	,	PUNCT
ejpam-6834	1074	25	n)-superhyperneutrosophic	n)-superhyperneutrosophic	PUNCT
ejpam-6834	1074	26	set	set	VERB
ejpam-6834	1074	27	on	on	ADP
ejpam-6834	1074	28	y	y	PROPN
ejpam-6834	1074	29	.	.	PUNCT
ejpam-6834	1075	1	proof	proof	NOUN
ejpam-6834	1075	2	.	.	PUNCT
ejpam-6834	1076	1	we	we	PRON
ejpam-6834	1076	2	show	show	VERB
ejpam-6834	1076	3	by	by	ADP
ejpam-6834	1076	4	induction	induction	NOUN
ejpam-6834	1076	5	on	on	ADP
ejpam-6834	1076	6	r	r	PROPN
ejpam-6834	1076	7	≥	≥	NUM
ejpam-6834	1076	8	1	1	NUM
ejpam-6834	1076	9	that	that	PRON
ejpam-6834	1076	10	f−1	f−1	PROPN
ejpam-6834	1076	11	(	(	PUNCT
ejpam-6834	1076	12	r	r	NOUN
ejpam-6834	1076	13	)	)	PUNCT
ejpam-6834	1076	14	maps	map	NOUN
ejpam-6834	1076	15	p̃r(y	p̃r(y	VERB
ejpam-6834	1076	16	)	)	PUNCT
ejpam-6834	1076	17	into	into	ADP
ejpam-6834	1076	18	p̃r(x	p̃r(x	NUM
ejpam-6834	1076	19	)	)	PUNCT
ejpam-6834	1076	20	and	and	CCONJ
ejpam-6834	1076	21	preserves	preserve	VERB
ejpam-6834	1076	22	nonemptiness	nonemptiness	NOUN
ejpam-6834	1076	23	.	.	PUNCT
ejpam-6834	1077	1	r	r	NOUN
ejpam-6834	1077	2	=	=	NOUN
ejpam-6834	1077	3	1	1	NUM
ejpam-6834	1077	4	:	:	PUNCT
ejpam-6834	1077	5	let	let	VERB
ejpam-6834	1077	6	b	b	X
ejpam-6834	1077	7	∈	∈	PROPN
ejpam-6834	1077	8	p̃(y	p̃(y	PROPN
ejpam-6834	1077	9	)	)	PUNCT
ejpam-6834	1077	10	be	be	AUX
ejpam-6834	1077	11	nonempty	nonempty	X
ejpam-6834	1077	12	.	.	PUNCT
ejpam-6834	1078	1	pick	pick	VERB
ejpam-6834	1078	2	y	y	PROPN
ejpam-6834	1078	3	∈	∈	PROPN
ejpam-6834	1078	4	b	b	PROPN
ejpam-6834	1078	5	;	;	PUNCT
ejpam-6834	1078	6	surjectivity	surjectivity	NOUN
ejpam-6834	1078	7	gives	give	VERB
ejpam-6834	1078	8	x	x	PUNCT
ejpam-6834	1078	9	∈	∈	PROPN
ejpam-6834	1078	10	x	x	PUNCT
ejpam-6834	1078	11	with	with	ADP
ejpam-6834	1078	12	f(x	f(x	PROPN
ejpam-6834	1078	13	)	)	PUNCT
ejpam-6834	1079	1	=	=	SYM
ejpam-6834	1079	2	y	y	PROPN
ejpam-6834	1079	3	,	,	PUNCT
ejpam-6834	1079	4	hence	hence	ADV
ejpam-6834	1079	5	x	x	PART
ejpam-6834	1079	6	∈	∈	PROPN
ejpam-6834	1079	7	f−1	f−1	PROPN
ejpam-6834	1079	8	(	(	PUNCT
ejpam-6834	1079	9	1	1	NUM
ejpam-6834	1079	10	)	)	PUNCT
ejpam-6834	1079	11	(	(	PUNCT
ejpam-6834	1079	12	b	b	X
ejpam-6834	1079	13	)	)	PUNCT
ejpam-6834	1079	14	and	and	CCONJ
ejpam-6834	1079	15	f−1	f−1	PROPN
ejpam-6834	1079	16	(	(	PUNCT
ejpam-6834	1079	17	1	1	NUM
ejpam-6834	1079	18	)	)	PUNCT
ejpam-6834	1079	19	(	(	PUNCT
ejpam-6834	1079	20	b	b	X
ejpam-6834	1079	21	)	)	PUNCT
ejpam-6834	1079	22	∈	∈	PROPN
ejpam-6834	1079	23	p̃(x	p̃(x	PROPN
ejpam-6834	1079	24	)	)	PUNCT
ejpam-6834	1079	25	.	.	PUNCT
ejpam-6834	1080	1	r	r	NOUN
ejpam-6834	1080	2	→	→	SYM
ejpam-6834	1080	3	r	r	NOUN
ejpam-6834	1080	4	+	+	NOUN
ejpam-6834	1080	5	1	1	NUM
ejpam-6834	1080	6	:	:	PUNCT
ejpam-6834	1080	7	let	let	VERB
ejpam-6834	1080	8	b	b	X
ejpam-6834	1080	9	∈	∈	PROPN
ejpam-6834	1080	10	p̃r+1(y	p̃r+1(y	ADV
ejpam-6834	1080	11	)	)	PUNCT
ejpam-6834	1080	12	be	be	AUX
ejpam-6834	1080	13	nonempty	nonempty	VERB
ejpam-6834	1080	14	.	.	PUNCT
ejpam-6834	1081	1	for	for	ADP
ejpam-6834	1081	2	each	each	DET
ejpam-6834	1081	3	b	b	PROPN
ejpam-6834	1081	4	∈	∈	PROPN
ejpam-6834	1081	5	b	b	PROPN
ejpam-6834	1081	6	,	,	PUNCT
ejpam-6834	1081	7	the	the	DET
ejpam-6834	1081	8	inductive	inductive	ADJ
ejpam-6834	1081	9	hypothesis	hypothesis	NOUN
ejpam-6834	1081	10	yields	yield	NOUN
ejpam-6834	1081	11	f−1	f−1	PROPN
ejpam-6834	1081	12	(	(	PUNCT
ejpam-6834	1081	13	r	r	NOUN
ejpam-6834	1081	14	)	)	PUNCT
ejpam-6834	1081	15	(	(	PUNCT
ejpam-6834	1081	16	b	b	X
ejpam-6834	1081	17	)	)	PUNCT
ejpam-6834	1081	18	∈	∈	PROPN
ejpam-6834	1081	19	p̃r(x	p̃r(x	NUM
ejpam-6834	1081	20	)	)	PUNCT
ejpam-6834	1081	21	.	.	PUNCT
ejpam-6834	1082	1	since	since	SCONJ
ejpam-6834	1082	2	b	b	PROPN
ejpam-6834	1082	3	̸=	̸=	PROPN
ejpam-6834	1082	4	∅	∅	NOUN
ejpam-6834	1082	5	,	,	PUNCT
ejpam-6834	1082	6	the	the	DET
ejpam-6834	1082	7	collection	collection	NOUN
ejpam-6834	1082	8	{	{	PUNCT
ejpam-6834	1082	9	f−1	f−1	PROPN
ejpam-6834	1082	10	(	(	PUNCT
ejpam-6834	1082	11	r	r	NOUN
ejpam-6834	1082	12	)	)	PUNCT
ejpam-6834	1082	13	(	(	PUNCT
ejpam-6834	1082	14	b	b	X
ejpam-6834	1082	15	)	)	PUNCT
ejpam-6834	1083	1	|	|	ADV
ejpam-6834	1083	2	b	b	X
ejpam-6834	1083	3	∈	∈	PROPN
ejpam-6834	1083	4	b	b	AUX
ejpam-6834	1083	5	}	}	PUNCT
ejpam-6834	1083	6	is	be	AUX
ejpam-6834	1083	7	a	a	DET
ejpam-6834	1083	8	nonempty	nonempty	ADJ
ejpam-6834	1083	9	family	family	NOUN
ejpam-6834	1083	10	in	in	ADP
ejpam-6834	1083	11	p̃r(x	p̃r(x	PROPN
ejpam-6834	1083	12	)	)	PUNCT
ejpam-6834	1083	13	,	,	PUNCT
ejpam-6834	1083	14	i.e.	i.e.	X
ejpam-6834	1083	15	an	an	DET
ejpam-6834	1083	16	element	element	NOUN
ejpam-6834	1083	17	of	of	ADP
ejpam-6834	1083	18	p̃r+1(x	p̃r+1(x	NOUN
ejpam-6834	1083	19	)	)	PUNCT
ejpam-6834	1083	20	.	.	PUNCT
ejpam-6834	1084	1	now	now	ADV
ejpam-6834	1084	2	let	let	VERB
ejpam-6834	1084	3	(	(	PUNCT
ejpam-6834	1084	4	b1	b1	NOUN
ejpam-6834	1084	5	,	,	PUNCT
ejpam-6834	1084	6	.	.	PUNCT
ejpam-6834	1084	7	.	.	PUNCT
ejpam-6834	1084	8	.	.	PUNCT
ejpam-6834	1085	1	,	,	PUNCT
ejpam-6834	1085	2	bh	bh	NOUN
ejpam-6834	1085	3	)	)	PUNCT
ejpam-6834	1085	4	∈	∈	PROPN
ejpam-6834	1085	5	(	(	PUNCT
ejpam-6834	1085	6	p̃m(y	p̃m(y	NOUN
ejpam-6834	1085	7	)	)	PUNCT
ejpam-6834	1085	8	)	)	PUNCT
ejpam-6834	1086	1	h.	h.	PROPN
ejpam-6834	1086	2	then	then	ADV
ejpam-6834	1086	3	f−1	f−1	PROPN
ejpam-6834	1086	4	(	(	PUNCT
ejpam-6834	1086	5	m)(bi	m)(bi	NOUN
ejpam-6834	1086	6	)	)	PUNCT
ejpam-6834	1086	7	∈	∈	PROPN
ejpam-6834	1086	8	p̃m(x	p̃m(x	NOUN
ejpam-6834	1086	9	)	)	PUNCT
ejpam-6834	1086	10	for	for	ADP
ejpam-6834	1086	11	each	each	DET
ejpam-6834	1086	12	i	i	PRON
ejpam-6834	1086	13	,	,	PUNCT
ejpam-6834	1086	14	so	so	ADV
ejpam-6834	1086	15	ã	ã	PROPN
ejpam-6834	1086	16	applies	apply	VERB
ejpam-6834	1086	17	to	to	PART
ejpam-6834	1086	18	yield	yield	VERB
ejpam-6834	1086	19	a	a	DET
ejpam-6834	1086	20	k	k	NOUN
ejpam-6834	1086	21	-	-	NOUN
ejpam-6834	1086	22	tuple	tuple	NOUN
ejpam-6834	1086	23	in	in	ADP
ejpam-6834	1086	24	(	(	PUNCT
ejpam-6834	1086	25	p̃n([0	p̃n([0	PROPN
ejpam-6834	1086	26	,	,	PUNCT
ejpam-6834	1086	27	1]3))k	1]3))k	PROPN
ejpam-6834	1086	28	with	with	ADP
ejpam-6834	1086	29	nonempty	nonempty	ADJ
ejpam-6834	1086	30	coordinates	coordinate	NOUN
ejpam-6834	1086	31	.	.	PUNCT
ejpam-6834	1087	1	hence	hence	ADV
ejpam-6834	1087	2	f∗ã	f∗ã	PROPN
ejpam-6834	1087	3	is	be	AUX
ejpam-6834	1087	4	well	well	ADV
ejpam-6834	1087	5	-	-	PUNCT
ejpam-6834	1087	6	defined	define	VERB
ejpam-6834	1087	7	and	and	CCONJ
ejpam-6834	1087	8	has	have	VERB
ejpam-6834	1087	9	the	the	DET
ejpam-6834	1087	10	required	require	VERB
ejpam-6834	1087	11	domain	domain	NOUN
ejpam-6834	1087	12	and	and	CCONJ
ejpam-6834	1087	13	codomain	codomain	NOUN
ejpam-6834	1087	14	.	.	PUNCT
ejpam-6834	1088	1	theorem	theorem	VERB
ejpam-6834	1088	2	37	37	NUM
ejpam-6834	1088	3	(	(	PUNCT
ejpam-6834	1088	4	reduction	reduction	NOUN
ejpam-6834	1088	5	to	to	ADP
ejpam-6834	1088	6	the	the	DET
ejpam-6834	1088	7	classical	classical	ADJ
ejpam-6834	1088	8	unary	unary	ADJ
ejpam-6834	1088	9	case	case	NOUN
ejpam-6834	1088	10	)	)	PUNCT
ejpam-6834	1088	11	.	.	PUNCT
ejpam-6834	1089	1	if	if	SCONJ
ejpam-6834	1089	2	h	h	NOUN
ejpam-6834	1089	3	=	=	SYM
ejpam-6834	1089	4	k	k	NOUN
ejpam-6834	1089	5	=	=	SYM
ejpam-6834	1089	6	1	1	NUM
ejpam-6834	1089	7	,	,	PUNCT
ejpam-6834	1089	8	then	then	ADV
ejpam-6834	1089	9	an	an	DET
ejpam-6834	1089	10	(	(	PUNCT
ejpam-6834	1089	11	h	h	NOUN
ejpam-6834	1089	12	,	,	PUNCT
ejpam-6834	1089	13	k)-ary	k)-ary	X
ejpam-6834	1089	14	(	(	PUNCT
ejpam-6834	1089	15	m	m	PROPN
ejpam-6834	1089	16	,	,	PUNCT
ejpam-6834	1089	17	n)-superhyperneutrosophic	n)-superhyperneutrosophic	PUNCT
ejpam-6834	1089	18	set	set	VERB
ejpam-6834	1089	19	ã	ã	PROPN
ejpam-6834	1089	20	reduces	reduce	VERB
ejpam-6834	1089	21	to	to	ADP
ejpam-6834	1089	22	the	the	DET
ejpam-6834	1089	23	classical	classical	ADJ
ejpam-6834	1089	24	(	(	PUNCT
ejpam-6834	1089	25	m	m	PROPN
ejpam-6834	1089	26	,	,	PUNCT
ejpam-6834	1089	27	n)-superhyperneutrosophic	n)-superhyperneutrosophic	PUNCT
ejpam-6834	1089	28	mapping	mapping	NOUN
ejpam-6834	1089	29	ã	ã	PROPN
ejpam-6834	1089	30	:	:	PUNCT
ejpam-6834	1089	31	p̃m(x	p̃m(x	X
ejpam-6834	1089	32	)	)	PUNCT
ejpam-6834	1089	33	→	→	SYM
ejpam-6834	1089	34	p̃n([0	p̃n([0	PROPN
ejpam-6834	1089	35	,	,	PUNCT
ejpam-6834	1089	36	1]3	1]3	NUM
ejpam-6834	1089	37	)	)	PUNCT
ejpam-6834	1089	38	.	.	PUNCT
ejpam-6834	1090	1	proof	proof	NOUN
ejpam-6834	1090	2	.	.	PUNCT
ejpam-6834	1091	1	the	the	DET
ejpam-6834	1091	2	canonical	canonical	ADJ
ejpam-6834	1091	3	bijections	bijection	NOUN
ejpam-6834	1091	4	(	(	PUNCT
ejpam-6834	1091	5	p̃m(x))1	p̃m(x))1	NOUN
ejpam-6834	1091	6	∼=	∼=	PART
ejpam-6834	1091	7	p̃m(x	p̃m(x	NOUN
ejpam-6834	1091	8	)	)	PUNCT
ejpam-6834	1091	9	and	and	CCONJ
ejpam-6834	1091	10	(	(	PUNCT
ejpam-6834	1091	11	p̃n([0	p̃n([0	PROPN
ejpam-6834	1091	12	,	,	PUNCT
ejpam-6834	1091	13	1]3))1	1]3))1	NUM
ejpam-6834	1091	14	∼=	∼=	VERB
ejpam-6834	1091	15	p̃n([0	p̃n([0	ADJ
ejpam-6834	1091	16	,	,	PUNCT
ejpam-6834	1091	17	1]3	1]3	NUM
ejpam-6834	1091	18	)	)	PUNCT
ejpam-6834	1091	19	identify	identify	VERB
ejpam-6834	1091	20	the	the	DET
ejpam-6834	1091	21	(	(	PUNCT
ejpam-6834	1091	22	h	h	NOUN
ejpam-6834	1091	23	,	,	PUNCT
ejpam-6834	1091	24	k)-ary	k)-ary	ADJ
ejpam-6834	1091	25	map	map	NOUN
ejpam-6834	1091	26	with	with	ADP
ejpam-6834	1091	27	a	a	DET
ejpam-6834	1091	28	unary	unary	ADJ
ejpam-6834	1091	29	map	map	NOUN
ejpam-6834	1091	30	of	of	ADP
ejpam-6834	1091	31	the	the	DET
ejpam-6834	1091	32	stated	state	VERB
ejpam-6834	1091	33	type	type	NOUN
ejpam-6834	1091	34	.	.	PUNCT
ejpam-6834	1092	1	no	no	DET
ejpam-6834	1092	2	additional	additional	ADJ
ejpam-6834	1092	3	properties	property	NOUN
ejpam-6834	1092	4	are	be	AUX
ejpam-6834	1092	5	needed	need	VERB
ejpam-6834	1092	6	,	,	PUNCT
ejpam-6834	1092	7	since	since	SCONJ
ejpam-6834	1092	8	nonemptiness	nonemptiness	NOUN
ejpam-6834	1092	9	and	and	CCONJ
ejpam-6834	1092	10	neutrosophic	neutrosophic	ADJ
ejpam-6834	1092	11	constraints	constraint	NOUN
ejpam-6834	1092	12	are	be	AUX
ejpam-6834	1092	13	part	part	NOUN
ejpam-6834	1092	14	of	of	ADP
ejpam-6834	1092	15	ã	ã	PROPN
ejpam-6834	1092	16	’s	’s	PART
ejpam-6834	1092	17	codomain	codomain	NOUN
ejpam-6834	1092	18	by	by	ADP
ejpam-6834	1092	19	definition	definition	NOUN
ejpam-6834	1092	20	.	.	PUNCT
ejpam-6834	1093	1	3.2.3	3.2.3	X
ejpam-6834	1093	2	.	.	PUNCT
ejpam-6834	1093	3	(	(	PUNCT
ejpam-6834	1093	4	h	h	NOUN
ejpam-6834	1093	5	,	,	PUNCT
ejpam-6834	1093	6	k)-ary	k)-ary	X
ejpam-6834	1093	7	(	(	PUNCT
ejpam-6834	1093	8	m	m	PROPN
ejpam-6834	1093	9	,	,	PUNCT
ejpam-6834	1093	10	n)-superhyperplithogenic	n)-superhyperplithogenic	PUNCT
ejpam-6834	1093	11	set	set	VERB
ejpam-6834	1093	12	an	an	DET
ejpam-6834	1093	13	(	(	PUNCT
ejpam-6834	1093	14	h	h	NOUN
ejpam-6834	1093	15	,	,	PUNCT
ejpam-6834	1093	16	k)-ary	k)-ary	X
ejpam-6834	1093	17	(	(	PUNCT
ejpam-6834	1093	18	m	m	PROPN
ejpam-6834	1093	19	,	,	PUNCT
ejpam-6834	1093	20	n)-superhyperplithogenic	n)-superhyperplithogenic	PUNCT
ejpam-6834	1093	21	set	set	VERB
ejpam-6834	1093	22	assigns	assign	NOUN
ejpam-6834	1093	23	to	to	ADP
ejpam-6834	1093	24	each	each	DET
ejpam-6834	1093	25	h	h	NOUN
ejpam-6834	1093	26	–	–	PUNCT
ejpam-6834	1093	27	tuple	tuple	NOUN
ejpam-6834	1093	28	of	of	ADP
ejpam-6834	1093	29	m	m	PROPN
ejpam-6834	1093	30	–	–	PUNCT
ejpam-6834	1093	31	level	level	NOUN
ejpam-6834	1093	32	(	(	PUNCT
ejpam-6834	1093	33	nested	nested	ADJ
ejpam-6834	1093	34	)	)	PUNCT
ejpam-6834	1093	35	parameter	parameter	NOUN
ejpam-6834	1093	36	–	–	PUNCT
ejpam-6834	1093	37	subsets	subset	VERB
ejpam-6834	1093	38	a	a	DET
ejpam-6834	1093	39	k	k	NOUN
ejpam-6834	1093	40	–	–	PUNCT
ejpam-6834	1093	41	tuple	tuple	NOUN
ejpam-6834	1093	42	of	of	ADP
ejpam-6834	1093	43	n	n	CCONJ
ejpam-6834	1093	44	–	–	PUNCT
ejpam-6834	1093	45	level	level	NOUN
ejpam-6834	1093	46	sets	set	NOUN
ejpam-6834	1093	47	of	of	ADP
ejpam-6834	1093	48	attribute	attribute	NOUN
ejpam-6834	1093	49	–	–	PUNCT
ejpam-6834	1093	50	based	base	VERB
ejpam-6834	1093	51	membership	membership	NOUN
ejpam-6834	1093	52	vectors	vector	NOUN
ejpam-6834	1093	53	in	in	ADP
ejpam-6834	1093	54	[	[	X
ejpam-6834	1093	55	0	0	NUM
ejpam-6834	1093	56	,	,	PUNCT
ejpam-6834	1093	57	1]s	1]s	NUM
ejpam-6834	1093	58	,	,	PUNCT
ejpam-6834	1093	59	together	together	ADV
ejpam-6834	1093	60	with	with	ADP
ejpam-6834	1093	61	a	a	DET
ejpam-6834	1093	62	quantified	quantified	ADJ
ejpam-6834	1093	63	,	,	PUNCT
ejpam-6834	1093	64	symmetric	symmetric	ADJ
ejpam-6834	1093	65	degree	degree	NOUN
ejpam-6834	1093	66	of	of	ADP
ejpam-6834	1093	67	contradiction	contradiction	NOUN
ejpam-6834	1093	68	on	on	ADP
ejpam-6834	1093	69	attribute	attribute	NOUN
ejpam-6834	1093	70	values	value	NOUN
ejpam-6834	1093	71	.	.	PUNCT
ejpam-6834	1094	1	t.	t.	PROPN
ejpam-6834	1094	2	fujita	fujita	PROPN
ejpam-6834	1094	3	,	,	PUNCT
ejpam-6834	1094	4	f.smarandache	f.smarandache	NOUN
ejpam-6834	1094	5	/	/	SYM
ejpam-6834	1094	6	eur	eur	PROPN
ejpam-6834	1094	7	.	.	PUNCT
ejpam-6834	1095	1	j.	j.	PROPN
ejpam-6834	1095	2	pure	pure	PROPN
ejpam-6834	1095	3	appl	appl	PROPN
ejpam-6834	1095	4	.	.	PROPN
ejpam-6834	1095	5	math	math	PROPN
ejpam-6834	1095	6	,	,	PUNCT
ejpam-6834	1095	7	18	18	NUM
ejpam-6834	1095	8	(	(	PUNCT
ejpam-6834	1095	9	4	4	NUM
ejpam-6834	1095	10	)	)	PUNCT
ejpam-6834	1095	11	(	(	PUNCT
ejpam-6834	1095	12	2025	2025	NUM
ejpam-6834	1095	13	)	)	PUNCT
ejpam-6834	1095	14	,	,	PUNCT
ejpam-6834	1095	15	6834	6834	NUM
ejpam-6834	1095	16	43	43	NUM
ejpam-6834	1095	17	of	of	ADP
ejpam-6834	1095	18	69	69	NUM
ejpam-6834	1095	19	for	for	ADP
ejpam-6834	1095	20	a	a	DET
ejpam-6834	1095	21	nonempty	nonempty	ADJ
ejpam-6834	1095	22	set	set	VERB
ejpam-6834	1095	23	s	s	PROPN
ejpam-6834	1095	24	,	,	PUNCT
ejpam-6834	1095	25	write	write	VERB
ejpam-6834	1095	26	p0	p0	NOUN
ejpam-6834	1095	27	+	+	PROPN
ejpam-6834	1095	28	(	(	PUNCT
ejpam-6834	1095	29	s	s	NOUN
ejpam-6834	1095	30	)	)	PUNCT
ejpam-6834	1095	31	:	:	PUNCT
ejpam-6834	1096	1	=	=	SYM
ejpam-6834	1096	2	s	s	X
ejpam-6834	1096	3	,	,	PUNCT
ejpam-6834	1096	4	pr+1	pr+1	PROPN
ejpam-6834	1096	5	+	+	CCONJ
ejpam-6834	1096	6	(	(	PUNCT
ejpam-6834	1096	7	s	s	X
ejpam-6834	1096	8	)	)	PUNCT
ejpam-6834	1096	9	:	:	PUNCT
ejpam-6834	1096	10	=	=	SYM
ejpam-6834	1096	11	{	{	PUNCT
ejpam-6834	1096	12	t	t	NOUN
ejpam-6834	1096	13	⊆	⊆	NUM
ejpam-6834	1096	14	pr	pr	NOUN
ejpam-6834	1096	15	+	+	NOUN
ejpam-6834	1096	16	(	(	PUNCT
ejpam-6834	1096	17	s	s	X
ejpam-6834	1096	18	)	)	PUNCT
ejpam-6834	1096	19	|	|	ADV
ejpam-6834	1096	20	t	t	NOUN
ejpam-6834	1096	21	̸=	̸=	PROPN
ejpam-6834	1096	22	∅	∅	NOUN
ejpam-6834	1096	23	}	}	PUNCT
ejpam-6834	1096	24	(	(	PUNCT
ejpam-6834	1096	25	r	r	NOUN
ejpam-6834	1096	26	≥	≥	NOUN
ejpam-6834	1096	27	0	0	NUM
ejpam-6834	1096	28	)	)	PUNCT
ejpam-6834	1096	29	,	,	PUNCT
ejpam-6834	1096	30	so	so	ADV
ejpam-6834	1096	31	p1	p1	PROPN
ejpam-6834	1096	32	+	+	PROPN
ejpam-6834	1096	33	(	(	PUNCT
ejpam-6834	1096	34	s	s	X
ejpam-6834	1096	35	)	)	PUNCT
ejpam-6834	1096	36	is	be	AUX
ejpam-6834	1096	37	the	the	DET
ejpam-6834	1096	38	collection	collection	NOUN
ejpam-6834	1096	39	of	of	ADP
ejpam-6834	1096	40	all	all	DET
ejpam-6834	1096	41	nonempty	nonempty	ADJ
ejpam-6834	1096	42	subsets	subset	NOUN
ejpam-6834	1096	43	of	of	ADP
ejpam-6834	1096	44	s	s	PROPN
ejpam-6834	1096	45	,	,	PUNCT
ejpam-6834	1096	46	p2	p2	X
ejpam-6834	1096	47	+	+	PROPN
ejpam-6834	1096	48	(	(	PUNCT
ejpam-6834	1096	49	s	s	X
ejpam-6834	1096	50	)	)	PUNCT
ejpam-6834	1096	51	is	be	AUX
ejpam-6834	1096	52	the	the	DET
ejpam-6834	1096	53	collection	collection	NOUN
ejpam-6834	1096	54	of	of	ADP
ejpam-6834	1096	55	all	all	DET
ejpam-6834	1096	56	nonempty	nonempty	ADJ
ejpam-6834	1096	57	families	family	NOUN
ejpam-6834	1096	58	of	of	ADP
ejpam-6834	1096	59	nonempty	nonempty	ADJ
ejpam-6834	1096	60	subsets	subset	NOUN
ejpam-6834	1096	61	of	of	ADP
ejpam-6834	1096	62	s	s	PROPN
ejpam-6834	1096	63	,	,	PUNCT
ejpam-6834	1096	64	and	and	CCONJ
ejpam-6834	1096	65	so	so	ADV
ejpam-6834	1096	66	on	on	ADV
ejpam-6834	1096	67	.	.	PUNCT
ejpam-6834	1097	1	on	on	ADP
ejpam-6834	1097	2	[	[	X
ejpam-6834	1097	3	0	0	NUM
ejpam-6834	1097	4	,	,	PUNCT
ejpam-6834	1097	5	1]s	1]s	NOUN
ejpam-6834	1097	6	we	we	PRON
ejpam-6834	1097	7	use	use	VERB
ejpam-6834	1097	8	the	the	DET
ejpam-6834	1097	9	componentwise	componentwise	NOUN
ejpam-6834	1097	10	order	order	NOUN
ejpam-6834	1097	11	:	:	PUNCT
ejpam-6834	1097	12	for	for	ADP
ejpam-6834	1097	13	x	x	X
ejpam-6834	1097	14	,	,	PUNCT
ejpam-6834	1097	15	y	y	PROPN
ejpam-6834	1097	16	∈	∈	PROPN
ejpam-6834	1098	1	[	[	X
ejpam-6834	1098	2	0	0	NUM
ejpam-6834	1098	3	,	,	PUNCT
ejpam-6834	1098	4	1]s	1]s	NUM
ejpam-6834	1098	5	,	,	PUNCT
ejpam-6834	1098	6	x	x	X
ejpam-6834	1098	7	⪯	⪯	PROPN
ejpam-6834	1098	8	y	y	PROPN
ejpam-6834	1098	9	⇐	⇐	ADJ
ejpam-6834	1098	10	⇒	⇒	NOUN
ejpam-6834	1098	11	xi	xi	ADP
ejpam-6834	1098	12	≤	≤	ADJ
ejpam-6834	1098	13	yi	yi	NOUN
ejpam-6834	1098	14	for	for	ADP
ejpam-6834	1098	15	all	all	DET
ejpam-6834	1098	16	i	i	PRON
ejpam-6834	1098	17	=	=	NOUN
ejpam-6834	1098	18	1	1	NUM
ejpam-6834	1098	19	,	,	PUNCT
ejpam-6834	1098	20	.	.	PUNCT
ejpam-6834	1098	21	.	.	PUNCT
ejpam-6834	1098	22	.	.	PUNCT
ejpam-6834	1099	1	,	,	PUNCT
ejpam-6834	1099	2	s.	s.	PROPN
ejpam-6834	1099	3	definition	definition	NOUN
ejpam-6834	1099	4	24	24	NUM
ejpam-6834	1099	5	(	(	PUNCT
ejpam-6834	1099	6	(	(	PUNCT
ejpam-6834	1099	7	h	h	NOUN
ejpam-6834	1099	8	,	,	PUNCT
ejpam-6834	1099	9	k)-ary	k)-ary	X
ejpam-6834	1099	10	(	(	PUNCT
ejpam-6834	1099	11	m	m	PROPN
ejpam-6834	1099	12	,	,	PUNCT
ejpam-6834	1099	13	n)-superhyperplithogenic	n)-superhyperplithogenic	PUNCT
ejpam-6834	1099	14	set	set	NOUN
ejpam-6834	1099	15	)	)	PUNCT
ejpam-6834	1099	16	.	.	PUNCT
ejpam-6834	1100	1	let	let	VERB
ejpam-6834	1100	2	p	p	PRON
ejpam-6834	1100	3	be	be	AUX
ejpam-6834	1100	4	a	a	DET
ejpam-6834	1100	5	nonempty	nonempty	ADJ
ejpam-6834	1100	6	base	base	NOUN
ejpam-6834	1100	7	set	set	NOUN
ejpam-6834	1100	8	of	of	ADP
ejpam-6834	1100	9	parameters	parameter	NOUN
ejpam-6834	1100	10	,	,	PUNCT
ejpam-6834	1100	11	fix	fix	VERB
ejpam-6834	1100	12	integers	integer	NOUN
ejpam-6834	1100	13	m	m	PRON
ejpam-6834	1100	14	,	,	PUNCT
ejpam-6834	1100	15	n	n	CCONJ
ejpam-6834	1100	16	,	,	PUNCT
ejpam-6834	1100	17	h	h	NOUN
ejpam-6834	1100	18	,	,	PUNCT
ejpam-6834	1100	19	k	k	PROPN
ejpam-6834	1100	20	∈	∈	PROPN
ejpam-6834	1100	21	n	n	X
ejpam-6834	1100	22	with	with	ADP
ejpam-6834	1100	23	m	m	PROPN
ejpam-6834	1100	24	,	,	PUNCT
ejpam-6834	1100	25	n	n	CCONJ
ejpam-6834	1100	26	,	,	PUNCT
ejpam-6834	1100	27	h	h	NOUN
ejpam-6834	1100	28	,	,	PUNCT
ejpam-6834	1100	29	k	k	PROPN
ejpam-6834	1100	30	≥	≥	NUM
ejpam-6834	1100	31	1	1	NUM
ejpam-6834	1100	32	,	,	PUNCT
ejpam-6834	1100	33	and	and	CCONJ
ejpam-6834	1100	34	fix	fix	VERB
ejpam-6834	1100	35	dimensions	dimension	NOUN
ejpam-6834	1100	36	s	s	PART
ejpam-6834	1100	37	,	,	PUNCT
ejpam-6834	1100	38	t	t	PROPN
ejpam-6834	1100	39	∈	∈	PROPN
ejpam-6834	1100	40	n	n	INTJ
ejpam-6834	1100	41	with	with	ADP
ejpam-6834	1100	42	s	s	PROPN
ejpam-6834	1100	43	,	,	PUNCT
ejpam-6834	1100	44	t	t	PROPN
ejpam-6834	1100	45	≥	≥	NUM
ejpam-6834	1100	46	1	1	NUM
ejpam-6834	1100	47	.	.	PUNCT
ejpam-6834	1101	1	let	let	VERB
ejpam-6834	1101	2	v	v	PART
ejpam-6834	1101	3	be	be	AUX
ejpam-6834	1101	4	an	an	DET
ejpam-6834	1101	5	attribute	attribute	NOUN
ejpam-6834	1101	6	with	with	ADP
ejpam-6834	1101	7	value	value	NOUN
ejpam-6834	1101	8	set	set	VERB
ejpam-6834	1101	9	pv	pv	NOUN
ejpam-6834	1101	10	(	(	PUNCT
ejpam-6834	1101	11	nonempty	nonempty	NOUN
ejpam-6834	1101	12	)	)	PUNCT
ejpam-6834	1101	13	.	.	PUNCT
ejpam-6834	1102	1	define	define	VERB
ejpam-6834	1102	2	d	d	NOUN
ejpam-6834	1102	3	:	:	PUNCT
ejpam-6834	1102	4	=	=	SYM
ejpam-6834	1102	5	(	(	PUNCT
ejpam-6834	1102	6	pm	pm	NOUN
ejpam-6834	1102	7	+	+	CCONJ
ejpam-6834	1102	8	(	(	PUNCT
ejpam-6834	1102	9	p	p	NOUN
ejpam-6834	1102	10	)	)	PUNCT
ejpam-6834	1102	11	)	)	PUNCT
ejpam-6834	1103	1	h	h	NOUN
ejpam-6834	1103	2	,	,	PUNCT
ejpam-6834	1103	3	c	c	NOUN
ejpam-6834	1103	4	:	:	PUNCT
ejpam-6834	1103	5	=	=	SYM
ejpam-6834	1103	6	(	(	PUNCT
ejpam-6834	1103	7	pn	pn	INTJ
ejpam-6834	1103	8	+	+	PROPN
ejpam-6834	1103	9	(	(	PUNCT
ejpam-6834	1103	10	[	[	NOUN
ejpam-6834	1103	11	0	0	NUM
ejpam-6834	1103	12	,	,	PUNCT
ejpam-6834	1103	13	1]s	1]s	NUM
ejpam-6834	1103	14	)	)	PUNCT
ejpam-6834	1103	15	)	)	PUNCT
ejpam-6834	1104	1	k	k	PROPN
ejpam-6834	1104	2	.	.	PUNCT
ejpam-6834	1105	1	an	an	DET
ejpam-6834	1105	2	(	(	PUNCT
ejpam-6834	1105	3	h	h	NOUN
ejpam-6834	1105	4	,	,	PUNCT
ejpam-6834	1105	5	k)-ary	k)-ary	X
ejpam-6834	1105	6	(	(	PUNCT
ejpam-6834	1105	7	m	m	PROPN
ejpam-6834	1105	8	,	,	PUNCT
ejpam-6834	1105	9	n)-superhyperplithogenic	n)-superhyperplithogenic	PUNCT
ejpam-6834	1105	10	set	set	NOUN
ejpam-6834	1105	11	(	(	PUNCT
ejpam-6834	1105	12	with	with	ADP
ejpam-6834	1105	13	respect	respect	NOUN
ejpam-6834	1105	14	to	to	ADP
ejpam-6834	1105	15	v	v	NOUN
ejpam-6834	1105	16	)	)	PUNCT
ejpam-6834	1105	17	is	be	AUX
ejpam-6834	1105	18	a	a	DET
ejpam-6834	1105	19	quintuple	quintuple	NOUN
ejpam-6834	1105	20	shp	shp	NOUN
ejpam-6834	1105	21	(	(	PUNCT
ejpam-6834	1105	22	h	h	NOUN
ejpam-6834	1105	23	,	,	PUNCT
ejpam-6834	1105	24	k	k	NOUN
ejpam-6834	1105	25	)	)	PUNCT
ejpam-6834	1105	26	pl	pl	PROPN
ejpam-6834	1105	27	(	(	PUNCT
ejpam-6834	1105	28	m	m	PROPN
ejpam-6834	1105	29	,	,	PUNCT
ejpam-6834	1105	30	n	n	CCONJ
ejpam-6834	1105	31	)	)	PUNCT
ejpam-6834	1105	32	=	=	SYM
ejpam-6834	1106	1	(	(	PUNCT
ejpam-6834	1106	2	d	d	PROPN
ejpam-6834	1106	3	,	,	PUNCT
ejpam-6834	1106	4	v	v	NOUN
ejpam-6834	1106	5	,	,	PUNCT
ejpam-6834	1106	6	pv	pv	INTJ
ejpam-6834	1106	7	,	,	PUNCT
ejpam-6834	1106	8	˜pdf	˜pdf	NOUN
ejpam-6834	1106	9	(	(	PUNCT
ejpam-6834	1106	10	m	m	NOUN
ejpam-6834	1106	11	,	,	PUNCT
ejpam-6834	1106	12	n	n	CCONJ
ejpam-6834	1106	13	)	)	PUNCT
ejpam-6834	1106	14	v	v	NOUN
ejpam-6834	1106	15	,	,	PUNCT
ejpam-6834	1106	16	pcf	pcf	PROPN
ejpam-6834	1106	17	)	)	PUNCT
ejpam-6834	1106	18	,	,	PUNCT
ejpam-6834	1107	1	where	where	SCONJ
ejpam-6834	1107	2	:	:	PUNCT
ejpam-6834	1107	3	(	(	PUNCT
ejpam-6834	1107	4	i	i	NOUN
ejpam-6834	1107	5	)	)	PUNCT
ejpam-6834	1107	6	˜pdf	˜pdf	NOUN
ejpam-6834	1107	7	(	(	PUNCT
ejpam-6834	1107	8	m	m	NOUN
ejpam-6834	1107	9	,	,	PUNCT
ejpam-6834	1107	10	n	n	CCONJ
ejpam-6834	1107	11	)	)	PUNCT
ejpam-6834	1107	12	v	v	NOUN
ejpam-6834	1107	13	:	:	PUNCT
ejpam-6834	1107	14	d	d	X
ejpam-6834	1107	15	×	×	NOUN
ejpam-6834	1107	16	pv	pv	NOUN
ejpam-6834	1107	17	→	→	SYM
ejpam-6834	1107	18	c	c	X
ejpam-6834	1107	19	(	(	PUNCT
ejpam-6834	1107	20	the	the	DET
ejpam-6834	1107	21	hyper	hyper	ADJ
ejpam-6834	1107	22	degree	degree	NOUN
ejpam-6834	1107	23	of	of	ADP
ejpam-6834	1107	24	appurtenance	appurtenance	NOUN
ejpam-6834	1107	25	)	)	PUNCT
ejpam-6834	1107	26	assigns	assign	NOUN
ejpam-6834	1107	27	,	,	PUNCT
ejpam-6834	1107	28	to	to	ADP
ejpam-6834	1107	29	each	each	DET
ejpam-6834	1107	30	(	(	PUNCT
ejpam-6834	1107	31	a	a	PRON
ejpam-6834	1107	32	,	,	PUNCT
ejpam-6834	1107	33	a	a	NOUN
ejpam-6834	1107	34	)	)	PUNCT
ejpam-6834	1107	35	with	with	ADP
ejpam-6834	1107	36	a	a	DET
ejpam-6834	1107	37	=	=	SYM
ejpam-6834	1107	38	(	(	PUNCT
ejpam-6834	1107	39	a1	a1	PROPN
ejpam-6834	1107	40	,	,	PUNCT
ejpam-6834	1107	41	.	.	PUNCT
ejpam-6834	1107	42	.	.	PUNCT
ejpam-6834	1107	43	.	.	PUNCT
ejpam-6834	1108	1	,	,	PUNCT
ejpam-6834	1108	2	ah	ah	INTJ
ejpam-6834	1108	3	)	)	PUNCT
ejpam-6834	1108	4	∈	∈	PROPN
ejpam-6834	1108	5	d	d	NOUN
ejpam-6834	1108	6	and	and	CCONJ
ejpam-6834	1108	7	a	a	DET
ejpam-6834	1108	8	∈	∈	PROPN
ejpam-6834	1108	9	pv	pv	NOUN
ejpam-6834	1108	10	,	,	PUNCT
ejpam-6834	1108	11	a	a	DET
ejpam-6834	1108	12	k	k	ADJ
ejpam-6834	1108	13	–	–	PUNCT
ejpam-6834	1108	14	tuple	tuple	ADJ
ejpam-6834	1108	15	˜pdf	˜pdf	NOUN
ejpam-6834	1108	16	(	(	PUNCT
ejpam-6834	1108	17	m	m	NOUN
ejpam-6834	1108	18	,	,	PUNCT
ejpam-6834	1108	19	n	n	CCONJ
ejpam-6834	1108	20	)	)	PUNCT
ejpam-6834	1108	21	v	v	NOUN
ejpam-6834	1108	22	(	(	PUNCT
ejpam-6834	1108	23	a	a	PRON
ejpam-6834	1108	24	,	,	PUNCT
ejpam-6834	1108	25	a	a	NOUN
ejpam-6834	1108	26	)	)	PUNCT
ejpam-6834	1108	27	=	=	SYM
ejpam-6834	1108	28	(	(	PUNCT
ejpam-6834	1108	29	b1	b1	NOUN
ejpam-6834	1108	30	,	,	PUNCT
ejpam-6834	1108	31	.	.	PUNCT
ejpam-6834	1108	32	.	.	PUNCT
ejpam-6834	1109	1	.	.	PUNCT
ejpam-6834	1110	1	,	,	PUNCT
ejpam-6834	1110	2	bk	bk	VERB
ejpam-6834	1110	3	)	)	PUNCT
ejpam-6834	1110	4	∈	∈	PROPN
ejpam-6834	1110	5	c	c	NOUN
ejpam-6834	1110	6	,	,	PUNCT
ejpam-6834	1110	7	where	where	SCONJ
ejpam-6834	1110	8	each	each	PRON
ejpam-6834	1110	9	bj	bj	VERB
ejpam-6834	1110	10	∈	∈	PROPN
ejpam-6834	1110	11	pn	pn	NOUN
ejpam-6834	1110	12	+	+	PROPN
ejpam-6834	1110	13	(	(	PUNCT
ejpam-6834	1110	14	[	[	NOUN
ejpam-6834	1110	15	0	0	NUM
ejpam-6834	1110	16	,	,	PUNCT
ejpam-6834	1110	17	1]s	1]s	NUM
ejpam-6834	1110	18	)	)	PUNCT
ejpam-6834	1110	19	is	be	AUX
ejpam-6834	1110	20	a	a	DET
ejpam-6834	1110	21	nonempty	nonempty	ADJ
ejpam-6834	1110	22	,	,	PUNCT
ejpam-6834	1110	23	level	level	NOUN
ejpam-6834	1110	24	–	–	PUNCT
ejpam-6834	1110	25	n	n	PRON
ejpam-6834	1110	26	collection	collection	NOUN
ejpam-6834	1110	27	of	of	ADP
ejpam-6834	1110	28	membership	membership	NOUN
ejpam-6834	1110	29	vectors	vector	NOUN
ejpam-6834	1110	30	x	x	SYM
ejpam-6834	1110	31	∈	∈	PROPN
ejpam-6834	1111	1	[	[	X
ejpam-6834	1111	2	0	0	NUM
ejpam-6834	1111	3	,	,	PUNCT
ejpam-6834	1111	4	1]s	1]s	NUM
ejpam-6834	1111	5	;	;	PUNCT
ejpam-6834	1111	6	(	(	PUNCT
ejpam-6834	1111	7	ii	ii	NOUN
ejpam-6834	1111	8	)	)	PUNCT
ejpam-6834	1111	9	pcf	pcf	PROPN
ejpam-6834	1111	10	:	:	PUNCT
ejpam-6834	1112	1	pv	pv	INTJ
ejpam-6834	1112	2	×	×	NOUN
ejpam-6834	1112	3	pv	pv	INTJ
ejpam-6834	1112	4	→	→	PUNCT
ejpam-6834	1112	5	[	[	X
ejpam-6834	1112	6	0	0	NUM
ejpam-6834	1112	7	,	,	PUNCT
ejpam-6834	1112	8	1]t	1]t	NUM
ejpam-6834	1112	9	(	(	PUNCT
ejpam-6834	1112	10	the	the	DET
ejpam-6834	1112	11	degree	degree	NOUN
ejpam-6834	1112	12	of	of	ADP
ejpam-6834	1112	13	contradiction	contradiction	NOUN
ejpam-6834	1112	14	)	)	PUNCT
ejpam-6834	1112	15	is	be	AUX
ejpam-6834	1112	16	reflexive	reflexive	ADJ
ejpam-6834	1112	17	and	and	CCONJ
ejpam-6834	1112	18	symmetric	symmetric	ADJ
ejpam-6834	1112	19	:	:	PUNCT
ejpam-6834	1112	20	pcf	pcf	PROPN
ejpam-6834	1112	21	(	(	PUNCT
ejpam-6834	1112	22	a	a	PRON
ejpam-6834	1112	23	,	,	PUNCT
ejpam-6834	1112	24	a	a	NOUN
ejpam-6834	1112	25	)	)	PUNCT
ejpam-6834	1112	26	=	=	SYM
ejpam-6834	1112	27	0	0	NUM
ejpam-6834	1113	1	∈	∈	PROPN
ejpam-6834	1114	1	[	[	X
ejpam-6834	1114	2	0	0	NUM
ejpam-6834	1114	3	,	,	PUNCT
ejpam-6834	1114	4	1]t	1]t	NUM
ejpam-6834	1114	5	,	,	PUNCT
ejpam-6834	1114	6	pcf	pcf	PROPN
ejpam-6834	1114	7	(	(	PUNCT
ejpam-6834	1114	8	a	a	DET
ejpam-6834	1114	9	,	,	PUNCT
ejpam-6834	1114	10	b	b	NOUN
ejpam-6834	1114	11	)	)	PUNCT
ejpam-6834	1114	12	=	=	SYM
ejpam-6834	1114	13	pcf	pcf	PROPN
ejpam-6834	1114	14	(	(	PUNCT
ejpam-6834	1114	15	b	b	PROPN
ejpam-6834	1114	16	,	,	PUNCT
ejpam-6834	1114	17	a	a	PRON
ejpam-6834	1114	18	)	)	PUNCT
ejpam-6834	1114	19	for	for	ADP
ejpam-6834	1114	20	all	all	DET
ejpam-6834	1114	21	a	a	PRON
ejpam-6834	1114	22	,	,	PUNCT
ejpam-6834	1114	23	b	b	X
ejpam-6834	1114	24	∈	∈	PROPN
ejpam-6834	1114	25	pv	pv	NOUN
ejpam-6834	1114	26	.	.	PUNCT
ejpam-6834	1114	27	example	example	NOUN
ejpam-6834	1115	1	25	25	NUM
ejpam-6834	1115	2	(	(	PUNCT
ejpam-6834	1115	3	smartphone	smartphone	NOUN
ejpam-6834	1115	4	selection	selection	NOUN
ejpam-6834	1115	5	:	:	PUNCT
ejpam-6834	1115	6	(	(	PUNCT
ejpam-6834	1115	7	2	2	NUM
ejpam-6834	1115	8	,	,	PUNCT
ejpam-6834	1115	9	2)-ary	2)-ary	NUM
ejpam-6834	1115	10	(	(	PUNCT
ejpam-6834	1115	11	1	1	NUM
ejpam-6834	1115	12	,	,	PUNCT
ejpam-6834	1115	13	1	1	X
ejpam-6834	1115	14	)	)	PUNCT
ejpam-6834	1115	15	case	case	NOUN
ejpam-6834	1115	16	)	)	PUNCT
ejpam-6834	1115	17	.	.	PUNCT
ejpam-6834	1116	1	let	let	VERB
ejpam-6834	1116	2	p	p	NOUN
ejpam-6834	1116	3	=	=	X
ejpam-6834	1116	4	{	{	PUNCT
ejpam-6834	1116	5	iphone	iphone	NOUN
ejpam-6834	1116	6	,	,	PUNCT
ejpam-6834	1116	7	galaxy	galaxy	NOUN
ejpam-6834	1116	8	,	,	PUNCT
ejpam-6834	1116	9	pixel	pixel	PROPN
ejpam-6834	1116	10	}	}	PUNCT
ejpam-6834	1116	11	and	and	CCONJ
ejpam-6834	1116	12	the	the	DET
ejpam-6834	1116	13	attribute	attribute	NOUN
ejpam-6834	1116	14	v	v	ADP
ejpam-6834	1116	15	=	=	NOUN
ejpam-6834	1116	16	batterylifecategory	batterylifecategory	NOUN
ejpam-6834	1116	17	,	,	PUNCT
ejpam-6834	1116	18	pv	pv	NOUN
ejpam-6834	1117	1	=	=	PUNCT
ejpam-6834	1117	2	{	{	PUNCT
ejpam-6834	1117	3	low	low	ADJ
ejpam-6834	1117	4	,	,	PUNCT
ejpam-6834	1117	5	medium	medium	ADJ
ejpam-6834	1117	6	,	,	PUNCT
ejpam-6834	1117	7	high	high	ADJ
ejpam-6834	1117	8	}	}	PUNCT
ejpam-6834	1117	9	.	.	PUNCT
ejpam-6834	1118	1	fix	fix	VERB
ejpam-6834	1118	2	m	m	NOUN
ejpam-6834	1118	3	=	=	SYM
ejpam-6834	1118	4	n	n	PROPN
ejpam-6834	1118	5	=	=	SYM
ejpam-6834	1118	6	1	1	NUM
ejpam-6834	1118	7	,	,	PUNCT
ejpam-6834	1119	1	h	h	NOUN
ejpam-6834	1120	1	=	=	SYM
ejpam-6834	1120	2	k	k	NOUN
ejpam-6834	1120	3	=	=	SYM
ejpam-6834	1120	4	2	2	NUM
ejpam-6834	1120	5	,	,	PUNCT
ejpam-6834	1120	6	s	s	PART
ejpam-6834	1120	7	=	=	SYM
ejpam-6834	1120	8	1	1	NUM
ejpam-6834	1120	9	,	,	PUNCT
ejpam-6834	1120	10	so	so	ADV
ejpam-6834	1120	11	d	d	NOUN
ejpam-6834	1120	12	=	=	SYM
ejpam-6834	1120	13	p1	p1	PROPN
ejpam-6834	1121	1	+	+	PROPN
ejpam-6834	1121	2	(	(	PUNCT
ejpam-6834	1121	3	p	p	ADJ
ejpam-6834	1121	4	)	)	PUNCT
ejpam-6834	1121	5	×	×	PROPN
ejpam-6834	1121	6	p1	p1	PROPN
ejpam-6834	1121	7	+	+	PROPN
ejpam-6834	1121	8	(	(	PUNCT
ejpam-6834	1121	9	p	p	NOUN
ejpam-6834	1121	10	)	)	PUNCT
ejpam-6834	1121	11	=	=	PUNCT
ejpam-6834	1122	1	p(p	p(p	NOUN
ejpam-6834	1122	2	)	)	PUNCT
ejpam-6834	1122	3	×	×	NOUN
ejpam-6834	1122	4	p(p	p(p	ADV
ejpam-6834	1122	5	)	)	PUNCT
ejpam-6834	1122	6	and	and	CCONJ
ejpam-6834	1122	7	c	c	NOUN
ejpam-6834	1122	8	=	=	SYM
ejpam-6834	1122	9	p([0	p([0	PROPN
ejpam-6834	1122	10	,	,	PUNCT
ejpam-6834	1122	11	1	1	NUM
ejpam-6834	1122	12	]	]	PUNCT
ejpam-6834	1122	13	)	)	PUNCT
ejpam-6834	1122	14	×	×	NOUN
ejpam-6834	1122	15	p([0	p([0	NOUN
ejpam-6834	1122	16	,	,	PUNCT
ejpam-6834	1122	17	1	1	NUM
ejpam-6834	1122	18	]	]	PUNCT
ejpam-6834	1122	19	)	)	PUNCT
ejpam-6834	1122	20	t.	t.	PROPN
ejpam-6834	1122	21	fujita	fujita	PROPN
ejpam-6834	1122	22	,	,	PUNCT
ejpam-6834	1122	23	f.smarandache	f.smarandache	NOUN
ejpam-6834	1122	24	/	/	SYM
ejpam-6834	1122	25	eur	eur	PROPN
ejpam-6834	1122	26	.	.	PUNCT
ejpam-6834	1123	1	j.	j.	PROPN
ejpam-6834	1123	2	pure	pure	PROPN
ejpam-6834	1123	3	appl	appl	PROPN
ejpam-6834	1123	4	.	.	PROPN
ejpam-6834	1123	5	math	math	PROPN
ejpam-6834	1123	6	,	,	PUNCT
ejpam-6834	1123	7	18	18	NUM
ejpam-6834	1123	8	(	(	PUNCT
ejpam-6834	1123	9	4	4	NUM
ejpam-6834	1123	10	)	)	PUNCT
ejpam-6834	1123	11	(	(	PUNCT
ejpam-6834	1123	12	2025	2025	NUM
ejpam-6834	1123	13	)	)	PUNCT
ejpam-6834	1123	14	,	,	PUNCT
ejpam-6834	1123	15	6834	6834	NUM
ejpam-6834	1123	16	44	44	NUM
ejpam-6834	1123	17	of	of	ADP
ejpam-6834	1123	18	69	69	NUM
ejpam-6834	1123	19	.	.	PUNCT
ejpam-6834	1124	1	interpret	interpret	VERB
ejpam-6834	1124	2	an	an	DET
ejpam-6834	1124	3	input	input	NOUN
ejpam-6834	1124	4	a	a	PRON
ejpam-6834	1124	5	=	=	SYM
ejpam-6834	1124	6	(	(	PUNCT
ejpam-6834	1124	7	a1	a1	PROPN
ejpam-6834	1124	8	,	,	PUNCT
ejpam-6834	1124	9	a2	a2	NOUN
ejpam-6834	1124	10	)	)	PUNCT
ejpam-6834	1124	11	∈	∈	PROPN
ejpam-6834	1125	1	d	d	NOUN
ejpam-6834	1125	2	as	as	ADP
ejpam-6834	1125	3	:	:	PUNCT
ejpam-6834	1125	4	a1	a1	NOUN
ejpam-6834	1125	5	=	=	PUNCT
ejpam-6834	1125	6	phones	phone	NOUN
ejpam-6834	1125	7	within	within	ADP
ejpam-6834	1125	8	the	the	DET
ejpam-6834	1125	9	preferred	preferred	ADJ
ejpam-6834	1125	10	price	price	NOUN
ejpam-6834	1125	11	range	range	NOUN
ejpam-6834	1125	12	;	;	PUNCT
ejpam-6834	1125	13	a2	a2	PROPN
ejpam-6834	1125	14	=	=	PUNCT
ejpam-6834	1125	15	phones	phone	NOUN
ejpam-6834	1125	16	from	from	ADP
ejpam-6834	1125	17	preferred	preferred	ADJ
ejpam-6834	1125	18	brands	brand	NOUN
ejpam-6834	1125	19	.	.	PUNCT
ejpam-6834	1126	1	define	define	NOUN
ejpam-6834	1126	2	,	,	PUNCT
ejpam-6834	1126	3	for	for	ADP
ejpam-6834	1126	4	the	the	DET
ejpam-6834	1126	5	value	value	NOUN
ejpam-6834	1126	6	a	a	DET
ejpam-6834	1126	7	=	=	PUNCT
ejpam-6834	1126	8	high	high	ADJ
ejpam-6834	1126	9	,	,	PUNCT
ejpam-6834	1126	10	˜pdf	˜pdf	NOUN
ejpam-6834	1126	11	(	(	PUNCT
ejpam-6834	1126	12	1,1	1,1	NUM
ejpam-6834	1126	13	)	)	PUNCT
ejpam-6834	1126	14	v	v	NOUN
ejpam-6834	1126	15	(	(	PUNCT
ejpam-6834	1126	16	(	(	PUNCT
ejpam-6834	1126	17	{	{	PUNCT
ejpam-6834	1126	18	iphone	iphone	NOUN
ejpam-6834	1126	19	,	,	PUNCT
ejpam-6834	1126	20	galaxy	galaxy	NOUN
ejpam-6834	1126	21	}	}	PUNCT
ejpam-6834	1126	22	,	,	PUNCT
ejpam-6834	1126	23	{	{	PUNCT
ejpam-6834	1126	24	iphone	iphone	NOUN
ejpam-6834	1126	25	,	,	PUNCT
ejpam-6834	1126	26	pixel	pixel	PROPN
ejpam-6834	1126	27	}	}	PUNCT
ejpam-6834	1126	28	)	)	PUNCT
ejpam-6834	1126	29	,	,	PUNCT
ejpam-6834	1126	30	a	a	X
ejpam-6834	1126	31	)	)	PUNCT
ejpam-6834	1126	32	=	=	SYM
ejpam-6834	1127	1	(	(	PUNCT
ejpam-6834	1127	2	[	[	X
ejpam-6834	1127	3	0.7	0.7	NUM
ejpam-6834	1127	4	,	,	PUNCT
ejpam-6834	1127	5	0.9	0.9	NUM
ejpam-6834	1127	6	]	]	PUNCT
ejpam-6834	1127	7	,	,	PUNCT
ejpam-6834	1127	8	{	{	PUNCT
ejpam-6834	1127	9	0.8	0.8	NUM
ejpam-6834	1127	10	}	}	PUNCT
ejpam-6834	1127	11	)	)	PUNCT
ejpam-6834	1127	12	,	,	PUNCT
ejpam-6834	1127	13	and	and	CCONJ
ejpam-6834	1127	14	for	for	ADP
ejpam-6834	1127	15	a	a	DET
ejpam-6834	1127	16	=	=	PUNCT
ejpam-6834	1127	17	medium	medium	ADJ
ejpam-6834	1127	18	,	,	PUNCT
ejpam-6834	1127	19	˜pdf	˜pdf	NOUN
ejpam-6834	1127	20	(	(	PUNCT
ejpam-6834	1127	21	1,1	1,1	NUM
ejpam-6834	1127	22	)	)	PUNCT
ejpam-6834	1127	23	v	v	NOUN
ejpam-6834	1127	24	(	(	PUNCT
ejpam-6834	1127	25	(	(	PUNCT
ejpam-6834	1127	26	{	{	PUNCT
ejpam-6834	1127	27	iphone	iphone	NOUN
ejpam-6834	1127	28	,	,	PUNCT
ejpam-6834	1127	29	galaxy	galaxy	NOUN
ejpam-6834	1127	30	}	}	PUNCT
ejpam-6834	1127	31	,	,	PUNCT
ejpam-6834	1127	32	{	{	PUNCT
ejpam-6834	1127	33	iphone	iphone	NOUN
ejpam-6834	1127	34	,	,	PUNCT
ejpam-6834	1127	35	pixel	pixel	PROPN
ejpam-6834	1127	36	}	}	PUNCT
ejpam-6834	1127	37	)	)	PUNCT
ejpam-6834	1127	38	,	,	PUNCT
ejpam-6834	1127	39	a	a	X
ejpam-6834	1127	40	)	)	PUNCT
ejpam-6834	1127	41	=	=	SYM
ejpam-6834	1127	42	(	(	PUNCT
ejpam-6834	1127	43	{	{	PUNCT
ejpam-6834	1127	44	0.5	0.5	NUM
ejpam-6834	1127	45	,	,	PUNCT
ejpam-6834	1127	46	0.6	0.6	NUM
ejpam-6834	1127	47	}	}	PUNCT
ejpam-6834	1127	48	,	,	PUNCT
ejpam-6834	1128	1	[	[	X
ejpam-6834	1128	2	0.4	0.4	NUM
ejpam-6834	1128	3	,	,	PUNCT
ejpam-6834	1128	4	0.6	0.6	NUM
ejpam-6834	1128	5	]	]	PUNCT
ejpam-6834	1128	6	)	)	PUNCT
ejpam-6834	1128	7	.	.	PUNCT
ejpam-6834	1129	1	here	here	ADV
ejpam-6834	1129	2	the	the	DET
ejpam-6834	1129	3	first	first	ADJ
ejpam-6834	1129	4	coordinate	coordinate	NOUN
ejpam-6834	1129	5	encodes	encode	VERB
ejpam-6834	1129	6	the	the	DET
ejpam-6834	1129	7	fuzzy	fuzzy	ADJ
ejpam-6834	1129	8	membership	membership	NOUN
ejpam-6834	1129	9	to	to	ADP
ejpam-6834	1129	10	“	"	PUNCT
ejpam-6834	1129	11	high	high	ADJ
ejpam-6834	1129	12	battery	battery	NOUN
ejpam-6834	1129	13	life	life	NOUN
ejpam-6834	1129	14	”	"	PUNCT
ejpam-6834	1129	15	,	,	PUNCT
ejpam-6834	1129	16	while	while	SCONJ
ejpam-6834	1129	17	the	the	DET
ejpam-6834	1129	18	second	second	ADJ
ejpam-6834	1129	19	aggregates	aggregate	VERB
ejpam-6834	1129	20	a	a	DET
ejpam-6834	1129	21	secondary	secondary	ADJ
ejpam-6834	1129	22	satisfaction	satisfaction	NOUN
ejpam-6834	1129	23	score	score	NOUN
ejpam-6834	1129	24	.	.	PUNCT
ejpam-6834	1130	1	set	set	PROPN
ejpam-6834	1130	2	pcf	pcf	PROPN
ejpam-6834	1130	3	(	(	PUNCT
ejpam-6834	1130	4	low	low	ADJ
ejpam-6834	1130	5	,	,	PUNCT
ejpam-6834	1130	6	high	high	ADJ
ejpam-6834	1130	7	)	)	PUNCT
ejpam-6834	1130	8	=	=	SYM
ejpam-6834	1130	9	1	1	NUM
ejpam-6834	1130	10	,	,	PUNCT
ejpam-6834	1130	11	pcf	pcf	PROPN
ejpam-6834	1130	12	(	(	PUNCT
ejpam-6834	1130	13	medium	medium	ADJ
ejpam-6834	1130	14	,	,	PUNCT
ejpam-6834	1130	15	low	low	ADJ
ejpam-6834	1130	16	)	)	PUNCT
ejpam-6834	1130	17	=	=	SYM
ejpam-6834	1130	18	0.5	0.5	NUM
ejpam-6834	1130	19	,	,	PUNCT
ejpam-6834	1130	20	pcf	pcf	PROPN
ejpam-6834	1130	21	(	(	PUNCT
ejpam-6834	1130	22	a	a	PRON
ejpam-6834	1130	23	,	,	PUNCT
ejpam-6834	1130	24	a	a	NOUN
ejpam-6834	1130	25	)	)	PUNCT
ejpam-6834	1130	26	=	=	SYM
ejpam-6834	1130	27	0	0	NUM
ejpam-6834	1130	28	,	,	PUNCT
ejpam-6834	1130	29	and	and	CCONJ
ejpam-6834	1130	30	extend	extend	VERB
ejpam-6834	1130	31	by	by	ADP
ejpam-6834	1130	32	symmetry	symmetry	NOUN
ejpam-6834	1130	33	.	.	PUNCT
ejpam-6834	1131	1	then	then	ADV
ejpam-6834	1131	2	shp	shp	NOUN
ejpam-6834	1131	3	(	(	PUNCT
ejpam-6834	1131	4	2,2	2,2	NUM
ejpam-6834	1131	5	)	)	PUNCT
ejpam-6834	1131	6	pl	pl	NOUN
ejpam-6834	1131	7	(	(	PUNCT
ejpam-6834	1131	8	1	1	NUM
ejpam-6834	1131	9	,	,	PUNCT
ejpam-6834	1131	10	1	1	X
ejpam-6834	1131	11	)	)	PUNCT
ejpam-6834	1131	12	models	model	NOUN
ejpam-6834	1131	13	two	two	NUM
ejpam-6834	1131	14	–	–	PUNCT
ejpam-6834	1131	15	stage	stage	NOUN
ejpam-6834	1131	16	,	,	PUNCT
ejpam-6834	1131	17	attribute	attribute	NOUN
ejpam-6834	1131	18	–	–	PUNCT
ejpam-6834	1131	19	based	base	VERB
ejpam-6834	1131	20	assessments	assessment	NOUN
ejpam-6834	1131	21	with	with	ADP
ejpam-6834	1131	22	quantified	quantified	ADJ
ejpam-6834	1131	23	contradictions	contradiction	NOUN
ejpam-6834	1131	24	.	.	PUNCT
ejpam-6834	1132	1	example	example	NOUN
ejpam-6834	1132	2	26	26	NUM
ejpam-6834	1132	3	(	(	PUNCT
ejpam-6834	1132	4	customer	customer	NOUN
ejpam-6834	1132	5	pricing	pricing	NOUN
ejpam-6834	1132	6	preference	preference	NOUN
ejpam-6834	1132	7	:	:	PUNCT
ejpam-6834	1132	8	(	(	PUNCT
ejpam-6834	1132	9	1	1	NUM
ejpam-6834	1132	10	,	,	PUNCT
ejpam-6834	1132	11	1)-ary	1)-ary	ADJ
ejpam-6834	1132	12	(	(	PUNCT
ejpam-6834	1132	13	1	1	NUM
ejpam-6834	1132	14	,	,	PUNCT
ejpam-6834	1132	15	1	1	NUM
ejpam-6834	1132	16	)	)	PUNCT
ejpam-6834	1132	17	case	case	NOUN
ejpam-6834	1132	18	)	)	PUNCT
ejpam-6834	1132	19	.	.	PUNCT
ejpam-6834	1133	1	let	let	VERB
ejpam-6834	1133	2	p	p	NOUN
ejpam-6834	1133	3	=	=	X
ejpam-6834	1133	4	{	{	PUNCT
ejpam-6834	1133	5	laptop	laptop	NOUN
ejpam-6834	1133	6	,	,	PUNCT
ejpam-6834	1133	7	smartphone	smartphone	NOUN
ejpam-6834	1133	8	}	}	PUNCT
ejpam-6834	1133	9	and	and	CCONJ
ejpam-6834	1133	10	v	v	NOUN
ejpam-6834	1133	11	=	=	NOUN
ejpam-6834	1133	12	pricingtier	pricingtier	NOUN
ejpam-6834	1133	13	with	with	ADP
ejpam-6834	1133	14	pv	pv	NOUN
ejpam-6834	1133	15	=	=	PUNCT
ejpam-6834	1133	16	{	{	PUNCT
ejpam-6834	1133	17	budget	budget	NOUN
ejpam-6834	1133	18	,	,	PUNCT
ejpam-6834	1133	19	premium	premium	NOUN
ejpam-6834	1133	20	}	}	PUNCT
ejpam-6834	1133	21	.	.	PUNCT
ejpam-6834	1134	1	fix	fix	VERB
ejpam-6834	1134	2	m	m	NOUN
ejpam-6834	1134	3	=	=	SYM
ejpam-6834	1134	4	n	n	PROPN
ejpam-6834	1134	5	=	=	NOUN
ejpam-6834	1134	6	h	h	NOUN
ejpam-6834	1135	1	=	=	SYM
ejpam-6834	1135	2	k	k	PROPN
ejpam-6834	1135	3	=	=	PUNCT
ejpam-6834	1135	4	s	s	PART
ejpam-6834	1135	5	=	=	X
ejpam-6834	1135	6	t	t	X
ejpam-6834	1135	7	=	=	SYM
ejpam-6834	1135	8	1	1	X
ejpam-6834	1135	9	.	.	PUNCT
ejpam-6834	1136	1	then	then	ADV
ejpam-6834	1136	2	d	d	NOUN
ejpam-6834	1136	3	=	=	SYM
ejpam-6834	1136	4	p(p	p(p	NOUN
ejpam-6834	1136	5	)	)	PUNCT
ejpam-6834	1136	6	and	and	CCONJ
ejpam-6834	1136	7	c	c	NOUN
ejpam-6834	1136	8	=	=	SYM
ejpam-6834	1136	9	p([0	p([0	PROPN
ejpam-6834	1136	10	,	,	PUNCT
ejpam-6834	1136	11	1	1	NUM
ejpam-6834	1136	12	]	]	NUM
ejpam-6834	1136	13	)	)	PUNCT
ejpam-6834	1136	14	.	.	PUNCT
ejpam-6834	1137	1	define	define	VERB
ejpam-6834	1137	2	˜pdf	˜pdf	NOUN
ejpam-6834	1137	3	(	(	PUNCT
ejpam-6834	1137	4	1,1	1,1	NUM
ejpam-6834	1137	5	)	)	PUNCT
ejpam-6834	1137	6	v	v	NOUN
ejpam-6834	1137	7	(	(	PUNCT
ejpam-6834	1137	8	{	{	PUNCT
ejpam-6834	1137	9	laptop},premium	laptop},premium	NOUN
ejpam-6834	1137	10	)	)	PUNCT
ejpam-6834	1137	11	=	=	PUNCT
ejpam-6834	1138	1	[	[	X
ejpam-6834	1138	2	0.70	0.70	NUM
ejpam-6834	1138	3	,	,	PUNCT
ejpam-6834	1138	4	0.90	0.90	NUM
ejpam-6834	1138	5	]	]	PUNCT
ejpam-6834	1138	6	,	,	PUNCT
ejpam-6834	1138	7	˜pdf	˜pdf	NOUN
ejpam-6834	1138	8	(	(	PUNCT
ejpam-6834	1138	9	1,1	1,1	NUM
ejpam-6834	1138	10	)	)	PUNCT
ejpam-6834	1138	11	v	v	NOUN
ejpam-6834	1138	12	(	(	PUNCT
ejpam-6834	1138	13	{	{	PUNCT
ejpam-6834	1138	14	laptop},budget	laptop},budget	NOUN
ejpam-6834	1138	15	)	)	PUNCT
ejpam-6834	1138	16	=	=	PUNCT
ejpam-6834	1138	17	{	{	PUNCT
ejpam-6834	1138	18	0.40	0.40	NUM
ejpam-6834	1138	19	,	,	PUNCT
ejpam-6834	1138	20	0.50	0.50	NUM
ejpam-6834	1138	21	}	}	PUNCT
ejpam-6834	1138	22	,	,	PUNCT
ejpam-6834	1138	23	˜pdf	˜pdf	NOUN
ejpam-6834	1138	24	(	(	PUNCT
ejpam-6834	1138	25	1,1	1,1	NUM
ejpam-6834	1138	26	)	)	PUNCT
ejpam-6834	1138	27	v	v	NOUN
ejpam-6834	1138	28	(	(	PUNCT
ejpam-6834	1138	29	{	{	PUNCT
ejpam-6834	1138	30	smartphone},premium	smartphone},premium	NOUN
ejpam-6834	1138	31	)	)	PUNCT
ejpam-6834	1138	32	=	=	PUNCT
ejpam-6834	1138	33	{	{	PUNCT
ejpam-6834	1138	34	0.80	0.80	NUM
ejpam-6834	1138	35	}	}	PUNCT
ejpam-6834	1138	36	,	,	PUNCT
ejpam-6834	1138	37	˜pdf	˜pdf	NOUN
ejpam-6834	1138	38	(	(	PUNCT
ejpam-6834	1138	39	1,1	1,1	NUM
ejpam-6834	1138	40	)	)	PUNCT
ejpam-6834	1138	41	v	v	NOUN
ejpam-6834	1138	42	(	(	PUNCT
ejpam-6834	1138	43	{	{	PUNCT
ejpam-6834	1138	44	smartphone},budget	smartphone},budget	NOUN
ejpam-6834	1138	45	)	)	PUNCT
ejpam-6834	1138	46	=	=	PUNCT
ejpam-6834	1139	1	[	[	X
ejpam-6834	1139	2	0.30	0.30	NUM
ejpam-6834	1139	3	,	,	PUNCT
ejpam-6834	1139	4	0.45	0.45	NUM
ejpam-6834	1139	5	]	]	PUNCT
ejpam-6834	1139	6	,	,	PUNCT
ejpam-6834	1139	7	˜pdf	˜pdf	NOUN
ejpam-6834	1139	8	(	(	PUNCT
ejpam-6834	1139	9	1,1	1,1	NUM
ejpam-6834	1139	10	)	)	PUNCT
ejpam-6834	1139	11	v	v	NOUN
ejpam-6834	1139	12	(	(	PUNCT
ejpam-6834	1139	13	{	{	PUNCT
ejpam-6834	1139	14	laptop	laptop	NOUN
ejpam-6834	1139	15	,	,	PUNCT
ejpam-6834	1139	16	smartphone},premium	smartphone},premium	NOUN
ejpam-6834	1139	17	)	)	PUNCT
ejpam-6834	1139	18	=	=	PUNCT
ejpam-6834	1140	1	[	[	X
ejpam-6834	1140	2	0.65	0.65	NUM
ejpam-6834	1140	3	,	,	PUNCT
ejpam-6834	1140	4	0.85	0.85	NUM
ejpam-6834	1140	5	]	]	PUNCT
ejpam-6834	1140	6	,	,	PUNCT
ejpam-6834	1140	7	˜pdf	˜pdf	NOUN
ejpam-6834	1140	8	(	(	PUNCT
ejpam-6834	1140	9	1,1	1,1	NUM
ejpam-6834	1140	10	)	)	PUNCT
ejpam-6834	1140	11	v	v	NOUN
ejpam-6834	1140	12	(	(	PUNCT
ejpam-6834	1140	13	{	{	PUNCT
ejpam-6834	1140	14	laptop	laptop	NOUN
ejpam-6834	1140	15	,	,	PUNCT
ejpam-6834	1140	16	smartphone},budget	smartphone},budget	NOUN
ejpam-6834	1140	17	)	)	PUNCT
ejpam-6834	1140	18	=	=	PUNCT
ejpam-6834	1140	19	{	{	PUNCT
ejpam-6834	1140	20	0.35	0.35	NUM
ejpam-6834	1140	21	,	,	PUNCT
ejpam-6834	1140	22	0.55	0.55	NUM
ejpam-6834	1140	23	}	}	PUNCT
ejpam-6834	1140	24	.	.	PUNCT
ejpam-6834	1141	1	with	with	ADP
ejpam-6834	1141	2	pcf	pcf	PROPN
ejpam-6834	1141	3	(	(	PUNCT
ejpam-6834	1141	4	budget	budget	NOUN
ejpam-6834	1141	5	,	,	PUNCT
ejpam-6834	1141	6	premium	premium	NOUN
ejpam-6834	1141	7	)	)	PUNCT
ejpam-6834	1141	8	=	=	SYM
ejpam-6834	1141	9	pcf	pcf	PROPN
ejpam-6834	1141	10	(	(	PUNCT
ejpam-6834	1141	11	premium	premium	NOUN
ejpam-6834	1141	12	,	,	PUNCT
ejpam-6834	1141	13	budget	budget	NOUN
ejpam-6834	1141	14	)	)	PUNCT
ejpam-6834	1141	15	=	=	SYM
ejpam-6834	1141	16	0.8	0.8	NUM
ejpam-6834	1141	17	and	and	CCONJ
ejpam-6834	1141	18	pcf	pcf	PROPN
ejpam-6834	1141	19	(	(	PUNCT
ejpam-6834	1141	20	a	a	PRON
ejpam-6834	1141	21	,	,	PUNCT
ejpam-6834	1141	22	a	a	NOUN
ejpam-6834	1141	23	)	)	PUNCT
ejpam-6834	1141	24	=	=	SYM
ejpam-6834	1141	25	0	0	NUM
ejpam-6834	1141	26	,	,	PUNCT
ejpam-6834	1141	27	the	the	DET
ejpam-6834	1141	28	structure	structure	NOUN
ejpam-6834	1141	29	records	record	VERB
ejpam-6834	1141	30	fuzzy	fuzzy	ADJ
ejpam-6834	1141	31	membership	membership	NOUN
ejpam-6834	1141	32	to	to	ADP
ejpam-6834	1141	33	pricing	pricing	NOUN
ejpam-6834	1141	34	tiers	tier	NOUN
ejpam-6834	1141	35	and	and	CCONJ
ejpam-6834	1141	36	their	their	PRON
ejpam-6834	1141	37	quantified	quantified	ADJ
ejpam-6834	1141	38	contradiction	contradiction	NOUN
ejpam-6834	1141	39	.	.	PUNCT
ejpam-6834	1142	1	example	example	NOUN
ejpam-6834	1142	2	27	27	NUM
ejpam-6834	1142	3	(	(	PUNCT
ejpam-6834	1142	4	filtered	filter	VERB
ejpam-6834	1142	5	product	product	NOUN
ejpam-6834	1142	6	satisfaction	satisfaction	NOUN
ejpam-6834	1142	7	:	:	PUNCT
ejpam-6834	1142	8	(	(	PUNCT
ejpam-6834	1142	9	2	2	NUM
ejpam-6834	1142	10	,	,	PUNCT
ejpam-6834	1142	11	2)-ary	2)-ary	NUM
ejpam-6834	1142	12	(	(	PUNCT
ejpam-6834	1142	13	1	1	NUM
ejpam-6834	1142	14	,	,	PUNCT
ejpam-6834	1142	15	1	1	NUM
ejpam-6834	1142	16	)	)	PUNCT
ejpam-6834	1142	17	with	with	ADP
ejpam-6834	1142	18	vector	vector	NOUN
ejpam-6834	1142	19	degrees	degree	NOUN
ejpam-6834	1142	20	)	)	PUNCT
ejpam-6834	1142	21	.	.	PUNCT
ejpam-6834	1143	1	let	let	VERB
ejpam-6834	1143	2	p	p	NOUN
ejpam-6834	1143	3	=	=	NOUN
ejpam-6834	1143	4	{	{	PUNCT
ejpam-6834	1143	5	laptop	laptop	NOUN
ejpam-6834	1143	6	,	,	PUNCT
ejpam-6834	1143	7	tablet	tablet	NOUN
ejpam-6834	1143	8	,	,	PUNCT
ejpam-6834	1143	9	smartphone	smartphone	NOUN
ejpam-6834	1143	10	}	}	PUNCT
ejpam-6834	1143	11	,	,	PUNCT
ejpam-6834	1143	12	and	and	CCONJ
ejpam-6834	1143	13	fix	fix	NOUN
ejpam-6834	1143	14	m	m	NOUN
ejpam-6834	1143	15	=	=	SYM
ejpam-6834	1143	16	n	n	PROPN
ejpam-6834	1143	17	=	=	SYM
ejpam-6834	1143	18	1	1	NUM
ejpam-6834	1143	19	,	,	PUNCT
ejpam-6834	1143	20	h	h	NOUN
ejpam-6834	1144	1	=	=	SYM
ejpam-6834	1144	2	k	k	NOUN
ejpam-6834	1144	3	=	=	SYM
ejpam-6834	1144	4	2	2	NUM
ejpam-6834	1144	5	,	,	PUNCT
ejpam-6834	1144	6	s	s	PART
ejpam-6834	1144	7	=	=	SYM
ejpam-6834	1144	8	2	2	NUM
ejpam-6834	1144	9	,	,	PUNCT
ejpam-6834	1144	10	t	t	NOUN
ejpam-6834	1145	1	=	=	SYM
ejpam-6834	1145	2	1	1	X
ejpam-6834	1145	3	.	.	PUNCT
ejpam-6834	1146	1	let	let	VERB
ejpam-6834	1146	2	v	v	NOUN
ejpam-6834	1146	3	=	=	NOUN
ejpam-6834	1146	4	satisfaction	satisfaction	NOUN
ejpam-6834	1146	5	with	with	ADP
ejpam-6834	1146	6	pv	pv	NOUN
ejpam-6834	1146	7	=	=	PUNCT
ejpam-6834	1146	8	{	{	PUNCT
ejpam-6834	1146	9	low	low	ADJ
ejpam-6834	1146	10	,	,	PUNCT
ejpam-6834	1146	11	medium	medium	ADJ
ejpam-6834	1146	12	,	,	PUNCT
ejpam-6834	1146	13	high	high	ADJ
ejpam-6834	1146	14	}	}	PUNCT
ejpam-6834	1146	15	.	.	PUNCT
ejpam-6834	1147	1	for	for	ADP
ejpam-6834	1147	2	the	the	DET
ejpam-6834	1147	3	input	input	NOUN
ejpam-6834	1147	4	(	(	PUNCT
ejpam-6834	1147	5	{	{	PUNCT
ejpam-6834	1147	6	laptop	laptop	NOUN
ejpam-6834	1147	7	,	,	PUNCT
ejpam-6834	1147	8	tablet	tablet	NOUN
ejpam-6834	1147	9	}	}	PUNCT
ejpam-6834	1147	10	,	,	PUNCT
ejpam-6834	1147	11	{	{	PUNCT
ejpam-6834	1147	12	premium	premium	NOUN
ejpam-6834	1147	13	}	}	PUNCT
ejpam-6834	1147	14	)	)	PUNCT
ejpam-6834	1147	15	at	at	ADP
ejpam-6834	1147	16	a	a	DET
ejpam-6834	1147	17	=	=	PUNCT
ejpam-6834	1147	18	high	high	ADJ
ejpam-6834	1147	19	,	,	PUNCT
ejpam-6834	1147	20	set	set	VERB
ejpam-6834	1147	21	˜pdf	˜pdf	NOUN
ejpam-6834	1147	22	(	(	PUNCT
ejpam-6834	1147	23	1,1	1,1	NUM
ejpam-6834	1147	24	)	)	PUNCT
ejpam-6834	1147	25	v	v	NOUN
ejpam-6834	1147	26	(	(	PUNCT
ejpam-6834	1147	27	(	(	PUNCT
ejpam-6834	1147	28	{	{	PUNCT
ejpam-6834	1147	29	laptop	laptop	NOUN
ejpam-6834	1147	30	,	,	PUNCT
ejpam-6834	1147	31	tablet	tablet	NOUN
ejpam-6834	1147	32	}	}	PUNCT
ejpam-6834	1147	33	,	,	PUNCT
ejpam-6834	1147	34	{	{	PUNCT
ejpam-6834	1147	35	premium	premium	NOUN
ejpam-6834	1147	36	}	}	PUNCT
ejpam-6834	1147	37	)	)	PUNCT
ejpam-6834	1147	38	,	,	PUNCT
ejpam-6834	1147	39	high	high	ADJ
ejpam-6834	1147	40	)	)	PUNCT
ejpam-6834	1148	1	=	=	SYM
ejpam-6834	1148	2	(	(	PUNCT
ejpam-6834	1148	3	{	{	PUNCT
ejpam-6834	1148	4	(	(	PUNCT
ejpam-6834	1148	5	0.85	0.85	NUM
ejpam-6834	1148	6	,	,	PUNCT
ejpam-6834	1148	7	0.80	0.80	NUM
ejpam-6834	1148	8	)	)	PUNCT
ejpam-6834	1148	9	,	,	PUNCT
ejpam-6834	1148	10	(	(	PUNCT
ejpam-6834	1148	11	0.88	0.88	NUM
ejpam-6834	1148	12	,	,	PUNCT
ejpam-6834	1148	13	0.82	0.82	NUM
ejpam-6834	1148	14	)	)	PUNCT
ejpam-6834	1148	15	}	}	PUNCT
ejpam-6834	1148	16	,	,	PUNCT
ejpam-6834	1148	17	{	{	PUNCT
ejpam-6834	1148	18	(	(	PUNCT
ejpam-6834	1148	19	0.90	0.90	NUM
ejpam-6834	1148	20	,	,	PUNCT
ejpam-6834	1148	21	0.85	0.85	NUM
ejpam-6834	1148	22	)	)	PUNCT
ejpam-6834	1148	23	}	}	PUNCT
ejpam-6834	1148	24	)	)	PUNCT
ejpam-6834	1148	25	,	,	PUNCT
ejpam-6834	1148	26	where	where	SCONJ
ejpam-6834	1148	27	each	each	PRON
ejpam-6834	1148	28	(	(	PUNCT
ejpam-6834	1148	29	x	x	NOUN
ejpam-6834	1148	30	,	,	PUNCT
ejpam-6834	1148	31	y	y	NOUN
ejpam-6834	1148	32	)	)	PUNCT
ejpam-6834	1148	33	∈	∈	PROPN
ejpam-6834	1149	1	[	[	X
ejpam-6834	1149	2	0	0	NUM
ejpam-6834	1149	3	,	,	PUNCT
ejpam-6834	1149	4	1]2	1]2	NUM
ejpam-6834	1149	5	denotes	denote	NOUN
ejpam-6834	1149	6	(	(	PUNCT
ejpam-6834	1149	7	reviewscore	reviewscore	ADJ
ejpam-6834	1149	8	,	,	PUNCT
ejpam-6834	1149	9	returnratescore	returnratescore	ADV
ejpam-6834	1149	10	)	)	PUNCT
ejpam-6834	1149	11	.	.	PUNCT
ejpam-6834	1150	1	let	let	VERB
ejpam-6834	1150	2	pcf	pcf	PROPN
ejpam-6834	1150	3	(	(	PUNCT
ejpam-6834	1150	4	high	high	ADJ
ejpam-6834	1150	5	,	,	PUNCT
ejpam-6834	1150	6	low	low	ADJ
ejpam-6834	1150	7	)	)	PUNCT
ejpam-6834	1150	8	=	=	SYM
ejpam-6834	1150	9	1	1	NUM
ejpam-6834	1150	10	,	,	PUNCT
ejpam-6834	1150	11	pcf	pcf	PROPN
ejpam-6834	1150	12	(	(	PUNCT
ejpam-6834	1150	13	high	high	ADJ
ejpam-6834	1150	14	,	,	PUNCT
ejpam-6834	1150	15	medium	medium	NOUN
ejpam-6834	1150	16	)	)	PUNCT
ejpam-6834	1150	17	=	=	SYM
ejpam-6834	1150	18	0.6	0.6	NUM
ejpam-6834	1150	19	,	,	PUNCT
ejpam-6834	1150	20	pcf	pcf	PROPN
ejpam-6834	1150	21	(	(	PUNCT
ejpam-6834	1150	22	medium	medium	ADJ
ejpam-6834	1150	23	,	,	PUNCT
ejpam-6834	1150	24	low	low	ADJ
ejpam-6834	1150	25	)	)	PUNCT
ejpam-6834	1150	26	=	=	SYM
ejpam-6834	1150	27	0.4	0.4	NUM
ejpam-6834	1150	28	,	,	PUNCT
ejpam-6834	1150	29	pcf	pcf	PROPN
ejpam-6834	1150	30	(	(	PUNCT
ejpam-6834	1150	31	a	a	PRON
ejpam-6834	1150	32	,	,	PUNCT
ejpam-6834	1150	33	a	a	NOUN
ejpam-6834	1150	34	)	)	PUNCT
ejpam-6834	1150	35	=	=	SYM
ejpam-6834	1150	36	0	0	NUM
ejpam-6834	1150	37	,	,	PUNCT
ejpam-6834	1150	38	with	with	ADP
ejpam-6834	1150	39	symmetry	symmetry	NOUN
ejpam-6834	1150	40	.	.	PUNCT
ejpam-6834	1151	1	t.	t.	PROPN
ejpam-6834	1151	2	fujita	fujita	PROPN
ejpam-6834	1151	3	,	,	PUNCT
ejpam-6834	1151	4	f.smarandache	f.smarandache	NOUN
ejpam-6834	1151	5	/	/	SYM
ejpam-6834	1151	6	eur	eur	PROPN
ejpam-6834	1151	7	.	.	PUNCT
ejpam-6834	1152	1	j.	j.	PROPN
ejpam-6834	1152	2	pure	pure	PROPN
ejpam-6834	1152	3	appl	appl	PROPN
ejpam-6834	1152	4	.	.	PROPN
ejpam-6834	1152	5	math	math	PROPN
ejpam-6834	1152	6	,	,	PUNCT
ejpam-6834	1152	7	18	18	NUM
ejpam-6834	1152	8	(	(	PUNCT
ejpam-6834	1152	9	4	4	NUM
ejpam-6834	1152	10	)	)	PUNCT
ejpam-6834	1152	11	(	(	PUNCT
ejpam-6834	1152	12	2025	2025	NUM
ejpam-6834	1152	13	)	)	PUNCT
ejpam-6834	1152	14	,	,	PUNCT
ejpam-6834	1152	15	6834	6834	NUM
ejpam-6834	1152	16	45	45	NUM
ejpam-6834	1152	17	of	of	ADP
ejpam-6834	1152	18	69	69	NUM
ejpam-6834	1152	19	example	example	NOUN
ejpam-6834	1152	20	28	28	NUM
ejpam-6834	1152	21	(	(	PUNCT
ejpam-6834	1152	22	hierarchical	hierarchical	ADJ
ejpam-6834	1152	23	sensor	sensor	NOUN
ejpam-6834	1152	24	–	–	PUNCT
ejpam-6834	1152	25	analytics	analytic	NOUN
ejpam-6834	1152	26	confidence	confidence	NOUN
ejpam-6834	1152	27	:	:	PUNCT
ejpam-6834	1152	28	(	(	PUNCT
ejpam-6834	1152	29	2	2	NUM
ejpam-6834	1152	30	,	,	PUNCT
ejpam-6834	1152	31	2)-ary	2)-ary	NUM
ejpam-6834	1152	32	(	(	PUNCT
ejpam-6834	1152	33	3	3	NUM
ejpam-6834	1152	34	,	,	PUNCT
ejpam-6834	1152	35	3	3	NUM
ejpam-6834	1152	36	)	)	PUNCT
ejpam-6834	1152	37	)	)	PUNCT
ejpam-6834	1152	38	.	.	PUNCT
ejpam-6834	1153	1	let	let	VERB
ejpam-6834	1153	2	p	p	NOUN
ejpam-6834	1153	3	=	=	NOUN
ejpam-6834	1153	4	{	{	PUNCT
ejpam-6834	1153	5	temp	temp	NOUN
ejpam-6834	1153	6	,	,	PUNCT
ejpam-6834	1153	7	pressure	pressure	NOUN
ejpam-6834	1153	8	}	}	PUNCT
ejpam-6834	1153	9	,	,	PUNCT
ejpam-6834	1153	10	m	m	VERB
ejpam-6834	1153	11	=	=	SYM
ejpam-6834	1153	12	n	n	PROPN
ejpam-6834	1153	13	=	=	SYM
ejpam-6834	1153	14	3	3	NUM
ejpam-6834	1153	15	,	,	PUNCT
ejpam-6834	1153	16	h	h	NOUN
ejpam-6834	1154	1	=	=	SYM
ejpam-6834	1154	2	k	k	NOUN
ejpam-6834	1154	3	=	=	SYM
ejpam-6834	1154	4	2	2	NUM
ejpam-6834	1154	5	,	,	PUNCT
ejpam-6834	1154	6	s	s	PART
ejpam-6834	1154	7	=	=	SYM
ejpam-6834	1154	8	2	2	NUM
ejpam-6834	1154	9	,	,	PUNCT
ejpam-6834	1154	10	t	t	NOUN
ejpam-6834	1154	11	=	=	SYM
ejpam-6834	1154	12	1	1	NUM
ejpam-6834	1154	13	,	,	PUNCT
ejpam-6834	1154	14	and	and	CCONJ
ejpam-6834	1154	15	v	v	X
ejpam-6834	1154	16	=	=	X
ejpam-6834	1154	17	confidencetype	confidencetype	NOUN
ejpam-6834	1154	18	with	with	ADP
ejpam-6834	1154	19	pv	pv	NOUN
ejpam-6834	1154	20	=	=	PUNCT
ejpam-6834	1154	21	{	{	PUNCT
ejpam-6834	1154	22	low	low	ADJ
ejpam-6834	1154	23	,	,	PUNCT
ejpam-6834	1154	24	medium	medium	ADJ
ejpam-6834	1154	25	,	,	PUNCT
ejpam-6834	1154	26	high	high	ADJ
ejpam-6834	1154	27	}	}	PUNCT
ejpam-6834	1154	28	.	.	PUNCT
ejpam-6834	1155	1	then	then	ADV
ejpam-6834	1155	2	d	d	X
ejpam-6834	1155	3	=	=	SYM
ejpam-6834	1155	4	p3	p3	PROPN
ejpam-6834	1155	5	+	+	PROPN
ejpam-6834	1155	6	(	(	PUNCT
ejpam-6834	1155	7	p	p	NOUN
ejpam-6834	1155	8	)	)	PUNCT
ejpam-6834	1155	9	×	×	PROPN
ejpam-6834	1155	10	p3	p3	PROPN
ejpam-6834	1155	11	+	+	PROPN
ejpam-6834	1155	12	(	(	PUNCT
ejpam-6834	1155	13	p	p	NOUN
ejpam-6834	1155	14	)	)	PUNCT
ejpam-6834	1155	15	and	and	CCONJ
ejpam-6834	1155	16	c	c	X
ejpam-6834	1155	17	=	=	SYM
ejpam-6834	1155	18	(	(	PUNCT
ejpam-6834	1155	19	p3	p3	PROPN
ejpam-6834	1155	20	+	+	PROPN
ejpam-6834	1155	21	(	(	PUNCT
ejpam-6834	1155	22	[	[	NOUN
ejpam-6834	1155	23	0	0	NUM
ejpam-6834	1155	24	,	,	PUNCT
ejpam-6834	1155	25	1]2))2	1]2))2	NUM
ejpam-6834	1155	26	.	.	PUNCT
ejpam-6834	1156	1	pick	pick	VERB
ejpam-6834	1156	2	a	a	DET
ejpam-6834	1156	3	=	=	X
ejpam-6834	1156	4	{	{	PUNCT
ejpam-6834	1156	5	{	{	PUNCT
ejpam-6834	1156	6	{	{	PUNCT
ejpam-6834	1156	7	temp	temp	NOUN
ejpam-6834	1156	8	}	}	PUNCT
ejpam-6834	1156	9	,	,	PUNCT
ejpam-6834	1156	10	{	{	PUNCT
ejpam-6834	1156	11	temp	temp	NOUN
ejpam-6834	1156	12	,	,	PUNCT
ejpam-6834	1156	13	pressure	pressure	NOUN
ejpam-6834	1156	14	}	}	PUNCT
ejpam-6834	1156	15	}	}	PUNCT
ejpam-6834	1156	16	,	,	PUNCT
ejpam-6834	1156	17	{	{	PUNCT
ejpam-6834	1156	18	{	{	PUNCT
ejpam-6834	1156	19	pressure	pressure	NOUN
ejpam-6834	1156	20	}	}	PUNCT
ejpam-6834	1156	21	}	}	PUNCT
ejpam-6834	1156	22	}	}	PUNCT
ejpam-6834	1156	23	,	,	PUNCT
ejpam-6834	1156	24	b	b	X
ejpam-6834	1156	25	=	=	PRON
ejpam-6834	1156	26	{	{	PUNCT
ejpam-6834	1156	27	{	{	PUNCT
ejpam-6834	1156	28	{	{	PUNCT
ejpam-6834	1156	29	pressure	pressure	NOUN
ejpam-6834	1156	30	}	}	PUNCT
ejpam-6834	1156	31	,	,	PUNCT
ejpam-6834	1156	32	{	{	PUNCT
ejpam-6834	1156	33	temp	temp	NOUN
ejpam-6834	1156	34	,	,	PUNCT
ejpam-6834	1156	35	pressure	pressure	NOUN
ejpam-6834	1156	36	}	}	PUNCT
ejpam-6834	1156	37	}	}	PUNCT
ejpam-6834	1156	38	}	}	PUNCT
ejpam-6834	1156	39	,	,	PUNCT
ejpam-6834	1156	40	and	and	CCONJ
ejpam-6834	1156	41	define	define	VERB
ejpam-6834	1156	42	,	,	PUNCT
ejpam-6834	1156	43	at	at	ADP
ejpam-6834	1156	44	a	a	DET
ejpam-6834	1156	45	=	=	X
ejpam-6834	1156	46	(	(	PUNCT
ejpam-6834	1156	47	a	a	DET
ejpam-6834	1156	48	,	,	PUNCT
ejpam-6834	1156	49	b	b	NOUN
ejpam-6834	1156	50	)	)	PUNCT
ejpam-6834	1156	51	and	and	CCONJ
ejpam-6834	1156	52	a	a	DET
ejpam-6834	1156	53	=	=	PUNCT
ejpam-6834	1156	54	high	high	ADJ
ejpam-6834	1156	55	,	,	PUNCT
ejpam-6834	1156	56	˜pdf	˜pdf	NOUN
ejpam-6834	1156	57	(	(	PUNCT
ejpam-6834	1156	58	3,3	3,3	NOUN
ejpam-6834	1156	59	)	)	PUNCT
ejpam-6834	1156	60	v	v	NOUN
ejpam-6834	1156	61	(	(	PUNCT
ejpam-6834	1156	62	a	a	PRON
ejpam-6834	1156	63	,	,	PUNCT
ejpam-6834	1156	64	a	a	NOUN
ejpam-6834	1156	65	)	)	PUNCT
ejpam-6834	1156	66	=	=	SYM
ejpam-6834	1156	67	(	(	PUNCT
ejpam-6834	1156	68	e1	e1	PROPN
ejpam-6834	1156	69	,	,	PUNCT
ejpam-6834	1156	70	e2	e2	PROPN
ejpam-6834	1156	71	)	)	PUNCT
ejpam-6834	1156	72	,	,	PUNCT
ejpam-6834	1156	73	where	where	SCONJ
ejpam-6834	1156	74	e1	e1	NOUN
ejpam-6834	1156	75	=	=	SYM
ejpam-6834	1156	76	{	{	PUNCT
ejpam-6834	1156	77	{	{	PUNCT
ejpam-6834	1156	78	(	(	PUNCT
ejpam-6834	1156	79	0.90	0.90	NUM
ejpam-6834	1156	80	,	,	PUNCT
ejpam-6834	1156	81	0.85	0.85	NUM
ejpam-6834	1156	82	)	)	PUNCT
ejpam-6834	1156	83	,	,	PUNCT
ejpam-6834	1156	84	(	(	PUNCT
ejpam-6834	1156	85	0.92	0.92	NUM
ejpam-6834	1156	86	,	,	PUNCT
ejpam-6834	1156	87	0.88	0.88	NUM
ejpam-6834	1156	88	)	)	PUNCT
ejpam-6834	1156	89	}	}	PUNCT
ejpam-6834	1156	90	,	,	PUNCT
ejpam-6834	1156	91	{	{	PUNCT
ejpam-6834	1156	92	(	(	PUNCT
ejpam-6834	1156	93	0.88	0.88	NUM
ejpam-6834	1156	94	,	,	PUNCT
ejpam-6834	1156	95	0.80	0.80	NUM
ejpam-6834	1156	96	)	)	PUNCT
ejpam-6834	1156	97	}	}	PUNCT
ejpam-6834	1156	98	}	}	PUNCT
ejpam-6834	1156	99	,	,	PUNCT
ejpam-6834	1156	100	e2	e2	PROPN
ejpam-6834	1156	101	=	=	PUNCT
ejpam-6834	1156	102	{	{	PUNCT
ejpam-6834	1156	103	{	{	PUNCT
ejpam-6834	1156	104	(	(	PUNCT
ejpam-6834	1156	105	0.75	0.75	NUM
ejpam-6834	1156	106	,	,	PUNCT
ejpam-6834	1156	107	0.70	0.70	NUM
ejpam-6834	1156	108	)	)	PUNCT
ejpam-6834	1156	109	}	}	PUNCT
ejpam-6834	1156	110	,	,	PUNCT
ejpam-6834	1156	111	{	{	PUNCT
ejpam-6834	1156	112	(	(	PUNCT
ejpam-6834	1156	113	0.78	0.78	NUM
ejpam-6834	1156	114	,	,	PUNCT
ejpam-6834	1156	115	0.73	0.73	NUM
ejpam-6834	1156	116	)	)	PUNCT
ejpam-6834	1156	117	,	,	PUNCT
ejpam-6834	1156	118	(	(	PUNCT
ejpam-6834	1156	119	0.80	0.80	NUM
ejpam-6834	1156	120	,	,	PUNCT
ejpam-6834	1156	121	0.75	0.75	NUM
ejpam-6834	1156	122	)	)	PUNCT
ejpam-6834	1156	123	}	}	PUNCT
ejpam-6834	1156	124	}	}	PUNCT
ejpam-6834	1156	125	.	.	PUNCT
ejpam-6834	1157	1	set	set	PROPN
ejpam-6834	1157	2	pcf	pcf	PROPN
ejpam-6834	1157	3	(	(	PUNCT
ejpam-6834	1157	4	low	low	ADJ
ejpam-6834	1157	5	,	,	PUNCT
ejpam-6834	1157	6	high	high	ADJ
ejpam-6834	1157	7	)	)	PUNCT
ejpam-6834	1157	8	=	=	SYM
ejpam-6834	1157	9	0.9	0.9	NUM
ejpam-6834	1157	10	,	,	PUNCT
ejpam-6834	1157	11	pcf	pcf	PROPN
ejpam-6834	1157	12	(	(	PUNCT
ejpam-6834	1157	13	low	low	ADJ
ejpam-6834	1157	14	,	,	PUNCT
ejpam-6834	1157	15	medium	medium	NOUN
ejpam-6834	1157	16	)	)	PUNCT
ejpam-6834	1157	17	=	=	SYM
ejpam-6834	1157	18	0.5	0.5	NUM
ejpam-6834	1157	19	,	,	PUNCT
ejpam-6834	1157	20	pcf	pcf	PROPN
ejpam-6834	1157	21	(	(	PUNCT
ejpam-6834	1157	22	medium	medium	ADJ
ejpam-6834	1157	23	,	,	PUNCT
ejpam-6834	1157	24	high	high	ADJ
ejpam-6834	1157	25	)	)	PUNCT
ejpam-6834	1157	26	=	=	SYM
ejpam-6834	1157	27	0.6	0.6	NUM
ejpam-6834	1157	28	,	,	PUNCT
ejpam-6834	1157	29	pcf	pcf	PROPN
ejpam-6834	1157	30	(	(	PUNCT
ejpam-6834	1157	31	a	a	PRON
ejpam-6834	1157	32	,	,	PUNCT
ejpam-6834	1157	33	a	a	NOUN
ejpam-6834	1157	34	)	)	PUNCT
ejpam-6834	1157	35	=	=	SYM
ejpam-6834	1157	36	0	0	NUM
ejpam-6834	1157	37	,	,	PUNCT
ejpam-6834	1157	38	with	with	ADP
ejpam-6834	1157	39	symmetry	symmetry	NOUN
ejpam-6834	1157	40	.	.	PUNCT
ejpam-6834	1158	1	example	example	NOUN
ejpam-6834	1158	2	29	29	NUM
ejpam-6834	1158	3	(	(	PUNCT
ejpam-6834	1158	4	urban	urban	ADJ
ejpam-6834	1158	5	route	route	NOUN
ejpam-6834	1158	6	planning	planning	NOUN
ejpam-6834	1158	7	as	as	ADP
ejpam-6834	1158	8	a	a	DET
ejpam-6834	1158	9	(	(	PUNCT
ejpam-6834	1158	10	2	2	NUM
ejpam-6834	1158	11	,	,	PUNCT
ejpam-6834	1158	12	2)-ary	2)-ary	NUM
ejpam-6834	1158	13	(	(	PUNCT
ejpam-6834	1158	14	2	2	NUM
ejpam-6834	1158	15	,	,	PUNCT
ejpam-6834	1158	16	2)-superhyperplithogenic	2)-superhyperplithogenic	NUM
ejpam-6834	1158	17	set	set	NOUN
ejpam-6834	1158	18	)	)	PUNCT
ejpam-6834	1158	19	.	.	PUNCT
ejpam-6834	1159	1	setting	set	VERB
ejpam-6834	1159	2	.	.	PUNCT
ejpam-6834	1160	1	consider	consider	VERB
ejpam-6834	1160	2	an	an	DET
ejpam-6834	1160	3	urban	urban	ADJ
ejpam-6834	1160	4	mobility	mobility	NOUN
ejpam-6834	1160	5	platform	platform	NOUN
ejpam-6834	1160	6	that	that	PRON
ejpam-6834	1160	7	recommends	recommend	VERB
ejpam-6834	1160	8	public	public	ADJ
ejpam-6834	1160	9	–	–	PUNCT
ejpam-6834	1160	10	transport	transport	NOUN
ejpam-6834	1160	11	routes	route	NOUN
ejpam-6834	1160	12	.	.	PUNCT
ejpam-6834	1161	1	let	let	VERB
ejpam-6834	1161	2	the	the	DET
ejpam-6834	1161	3	base	base	NOUN
ejpam-6834	1161	4	parameter	parameter	NOUN
ejpam-6834	1161	5	set	set	NOUN
ejpam-6834	1161	6	be	be	AUX
ejpam-6834	1161	7	p	p	NOUN
ejpam-6834	1161	8	=	=	X
ejpam-6834	1161	9	{	{	PUNCT
ejpam-6834	1161	10	costcap	costcap	NOUN
ejpam-6834	1161	11	,	,	PUNCT
ejpam-6834	1161	12	timewindow	timewindow	NOUN
ejpam-6834	1161	13	,	,	PUNCT
ejpam-6834	1161	14	maxtransfers	maxtransfer	NOUN
ejpam-6834	1161	15	,	,	PUNCT
ejpam-6834	1161	16	emissioncap	emissioncap	NOUN
ejpam-6834	1161	17	}	}	PUNCT
ejpam-6834	1161	18	.	.	PUNCT
ejpam-6834	1162	1	fix	fix	NOUN
ejpam-6834	1162	2	(	(	PUNCT
ejpam-6834	1162	3	m	m	PROPN
ejpam-6834	1162	4	,	,	PUNCT
ejpam-6834	1162	5	n	n	CCONJ
ejpam-6834	1162	6	,	,	PUNCT
ejpam-6834	1162	7	h	h	NOUN
ejpam-6834	1162	8	,	,	PUNCT
ejpam-6834	1162	9	k	k	NOUN
ejpam-6834	1162	10	)	)	PUNCT
ejpam-6834	1162	11	=	=	SYM
ejpam-6834	1162	12	(	(	PUNCT
ejpam-6834	1162	13	2	2	NUM
ejpam-6834	1162	14	,	,	PUNCT
ejpam-6834	1162	15	2	2	NUM
ejpam-6834	1162	16	,	,	PUNCT
ejpam-6834	1162	17	2	2	NUM
ejpam-6834	1162	18	,	,	PUNCT
ejpam-6834	1162	19	2	2	NUM
ejpam-6834	1162	20	)	)	PUNCT
ejpam-6834	1162	21	and	and	CCONJ
ejpam-6834	1162	22	dimensions	dimension	NOUN
ejpam-6834	1162	23	s	s	PART
ejpam-6834	1162	24	=	=	SYM
ejpam-6834	1162	25	2	2	NUM
ejpam-6834	1162	26	,	,	PUNCT
ejpam-6834	1162	27	t	t	NOUN
ejpam-6834	1162	28	=	=	SYM
ejpam-6834	1162	29	1	1	X
ejpam-6834	1162	30	.	.	PUNCT
ejpam-6834	1163	1	we	we	PRON
ejpam-6834	1163	2	interpret	interpret	VERB
ejpam-6834	1163	3	the	the	DET
ejpam-6834	1163	4	two	two	NUM
ejpam-6834	1163	5	membership	membership	NOUN
ejpam-6834	1163	6	coordinates	coordinate	NOUN
ejpam-6834	1163	7	x	x	PUNCT
ejpam-6834	1163	8	=	=	SYM
ejpam-6834	1163	9	(	(	PUNCT
ejpam-6834	1163	10	x1	x1	PROPN
ejpam-6834	1163	11	,	,	PUNCT
ejpam-6834	1163	12	x2	x2	PROPN
ejpam-6834	1163	13	)	)	PUNCT
ejpam-6834	1163	14	∈	∈	PROPN
ejpam-6834	1164	1	[	[	X
ejpam-6834	1164	2	0	0	NUM
ejpam-6834	1164	3	,	,	PUNCT
ejpam-6834	1164	4	1]2	1]2	NUM
ejpam-6834	1164	5	as	as	ADP
ejpam-6834	1164	6	x1	x1	PROPN
ejpam-6834	1164	7	=	=	SYM
ejpam-6834	1164	8	(	(	PUNCT
ejpam-6834	1164	9	commuter	commuter	NOUN
ejpam-6834	1164	10	satisfaction	satisfaction	NOUN
ejpam-6834	1164	11	)	)	PUNCT
ejpam-6834	1164	12	,	,	PUNCT
ejpam-6834	1164	13	x2	x2	NOUN
ejpam-6834	1164	14	=	=	PRON
ejpam-6834	1164	15	(	(	PUNCT
ejpam-6834	1164	16	operational	operational	ADJ
ejpam-6834	1164	17	reliability	reliability	NOUN
ejpam-6834	1164	18	)	)	PUNCT
ejpam-6834	1164	19	.	.	PUNCT
ejpam-6834	1165	1	the	the	DET
ejpam-6834	1165	2	two	two	NUM
ejpam-6834	1165	3	output	output	NOUN
ejpam-6834	1165	4	coordinates	coordinate	NOUN
ejpam-6834	1165	5	(	(	PUNCT
ejpam-6834	1165	6	k	k	NOUN
ejpam-6834	1165	7	=	=	SYM
ejpam-6834	1165	8	2	2	X
ejpam-6834	1165	9	)	)	PUNCT
ejpam-6834	1165	10	will	will	AUX
ejpam-6834	1165	11	represent	represent	VERB
ejpam-6834	1165	12	two	two	NUM
ejpam-6834	1165	13	stakeholder	stakeholder	NOUN
ejpam-6834	1165	14	views	view	NOUN
ejpam-6834	1165	15	:	:	PUNCT
ejpam-6834	1165	16	output	output	NOUN
ejpam-6834	1165	17	1	1	NUM
ejpam-6834	1165	18	=	=	NOUN
ejpam-6834	1165	19	commuter	commuter	NOUN
ejpam-6834	1165	20	view	view	NOUN
ejpam-6834	1165	21	,	,	PUNCT
ejpam-6834	1165	22	output	output	NOUN
ejpam-6834	1165	23	2	2	NUM
ejpam-6834	1165	24	=	=	NOUN
ejpam-6834	1165	25	operator	operator	NOUN
ejpam-6834	1165	26	view	view	NOUN
ejpam-6834	1165	27	.	.	PUNCT
ejpam-6834	1166	1	domain	domain	NOUN
ejpam-6834	1166	2	and	and	CCONJ
ejpam-6834	1166	3	codomain	codomain	NOUN
ejpam-6834	1166	4	.	.	PUNCT
ejpam-6834	1167	1	the	the	DET
ejpam-6834	1167	2	input	input	NOUN
ejpam-6834	1167	3	space	space	NOUN
ejpam-6834	1167	4	is	be	AUX
ejpam-6834	1167	5	d	d	NOUN
ejpam-6834	1167	6	=	=	PUNCT
ejpam-6834	1167	7	(	(	PUNCT
ejpam-6834	1167	8	p2	p2	X
ejpam-6834	1167	9	+	+	PROPN
ejpam-6834	1167	10	(	(	PUNCT
ejpam-6834	1167	11	p	p	NOUN
ejpam-6834	1167	12	)	)	PUNCT
ejpam-6834	1167	13	)	)	PUNCT
ejpam-6834	1167	14	2	2	NUM
ejpam-6834	1167	15	,	,	PUNCT
ejpam-6834	1167	16	so	so	ADV
ejpam-6834	1167	17	each	each	DET
ejpam-6834	1167	18	input	input	NOUN
ejpam-6834	1167	19	is	be	AUX
ejpam-6834	1167	20	a	a	DET
ejpam-6834	1167	21	pair	pair	NOUN
ejpam-6834	1167	22	a	a	DET
ejpam-6834	1167	23	=	=	SYM
ejpam-6834	1167	24	(	(	PUNCT
ejpam-6834	1167	25	a1	a1	PROPN
ejpam-6834	1167	26	,	,	PUNCT
ejpam-6834	1167	27	a2	a2	PROPN
ejpam-6834	1167	28	)	)	PUNCT
ejpam-6834	1167	29	of	of	ADP
ejpam-6834	1167	30	level–2	level–2	PROPN
ejpam-6834	1167	31	hyper	hyper	PROPN
ejpam-6834	1167	32	–	–	PUNCT
ejpam-6834	1167	33	parameters	parameter	NOUN
ejpam-6834	1167	34	,	,	PUNCT
ejpam-6834	1167	35	with	with	ADP
ejpam-6834	1167	36	ai	ai	INTJ
ejpam-6834	1167	37	∈	∈	PROPN
ejpam-6834	1167	38	p2	p2	X
ejpam-6834	1168	1	+	+	PROPN
ejpam-6834	1168	2	(	(	PUNCT
ejpam-6834	1168	3	p	p	NOUN
ejpam-6834	1168	4	)	)	PUNCT
ejpam-6834	1168	5	=	=	SYM
ejpam-6834	1168	6	{	{	PUNCT
ejpam-6834	1168	7	γ	γ	PROPN
ejpam-6834	1168	8	⊆	⊆	NUM
ejpam-6834	1168	9	p1	p1	PROPN
ejpam-6834	1168	10	+	+	PROPN
ejpam-6834	1168	11	(	(	PUNCT
ejpam-6834	1168	12	p	p	NOUN
ejpam-6834	1168	13	)	)	PUNCT
ejpam-6834	1169	1	|	|	ADV
ejpam-6834	1169	2	γ	γ	X
ejpam-6834	1169	3	̸=	̸=	PROPN
ejpam-6834	1169	4	∅	∅	NOUN
ejpam-6834	1169	5	}	}	PUNCT
ejpam-6834	1169	6	.	.	PUNCT
ejpam-6834	1170	1	the	the	DET
ejpam-6834	1170	2	output	output	NOUN
ejpam-6834	1170	3	space	space	NOUN
ejpam-6834	1170	4	is	be	AUX
ejpam-6834	1170	5	c	c	NOUN
ejpam-6834	1170	6	=	=	PUNCT
ejpam-6834	1170	7	(	(	PUNCT
ejpam-6834	1170	8	p2	p2	X
ejpam-6834	1170	9	+	+	PROPN
ejpam-6834	1170	10	(	(	PUNCT
ejpam-6834	1170	11	[	[	NOUN
ejpam-6834	1170	12	0	0	NUM
ejpam-6834	1170	13	,	,	PUNCT
ejpam-6834	1170	14	1]2	1]2	NUM
ejpam-6834	1170	15	)	)	PUNCT
ejpam-6834	1170	16	)	)	PUNCT
ejpam-6834	1170	17	2	2	NUM
ejpam-6834	1170	18	,	,	PUNCT
ejpam-6834	1170	19	so	so	ADV
ejpam-6834	1170	20	each	each	DET
ejpam-6834	1170	21	output	output	NOUN
ejpam-6834	1170	22	coordinate	coordinate	NOUN
ejpam-6834	1170	23	is	be	AUX
ejpam-6834	1170	24	a	a	DET
ejpam-6834	1170	25	nonempty	nonempty	ADJ
ejpam-6834	1170	26	family	family	NOUN
ejpam-6834	1170	27	(	(	PUNCT
ejpam-6834	1170	28	level–2	level–2	PROPN
ejpam-6834	1170	29	)	)	PUNCT
ejpam-6834	1170	30	of	of	ADP
ejpam-6834	1170	31	nonempty	nonempty	ADJ
ejpam-6834	1170	32	subsets	subset	NOUN
ejpam-6834	1170	33	(	(	PUNCT
ejpam-6834	1170	34	level–1	level–1	PROPN
ejpam-6834	1170	35	)	)	PUNCT
ejpam-6834	1170	36	of	of	ADP
ejpam-6834	1170	37	[	[	X
ejpam-6834	1170	38	0	0	NUM
ejpam-6834	1170	39	,	,	PUNCT
ejpam-6834	1170	40	1]2	1]2	NUM
ejpam-6834	1170	41	.	.	PUNCT
ejpam-6834	1171	1	t.	t.	PROPN
ejpam-6834	1171	2	fujita	fujita	PROPN
ejpam-6834	1171	3	,	,	PUNCT
ejpam-6834	1171	4	f.smarandache	f.smarandache	NOUN
ejpam-6834	1171	5	/	/	SYM
ejpam-6834	1171	6	eur	eur	PROPN
ejpam-6834	1171	7	.	.	PUNCT
ejpam-6834	1172	1	j.	j.	PROPN
ejpam-6834	1172	2	pure	pure	PROPN
ejpam-6834	1172	3	appl	appl	PROPN
ejpam-6834	1172	4	.	.	PROPN
ejpam-6834	1172	5	math	math	PROPN
ejpam-6834	1172	6	,	,	PUNCT
ejpam-6834	1172	7	18	18	NUM
ejpam-6834	1172	8	(	(	PUNCT
ejpam-6834	1172	9	4	4	NUM
ejpam-6834	1172	10	)	)	PUNCT
ejpam-6834	1172	11	(	(	PUNCT
ejpam-6834	1172	12	2025	2025	NUM
ejpam-6834	1172	13	)	)	PUNCT
ejpam-6834	1172	14	,	,	PUNCT
ejpam-6834	1172	15	6834	6834	NUM
ejpam-6834	1172	16	46	46	NUM
ejpam-6834	1172	17	of	of	ADP
ejpam-6834	1172	18	69	69	NUM
ejpam-6834	1172	19	attribute	attribute	NOUN
ejpam-6834	1172	20	and	and	CCONJ
ejpam-6834	1172	21	its	its	PRON
ejpam-6834	1172	22	values	value	NOUN
ejpam-6834	1172	23	.	.	PUNCT
ejpam-6834	1173	1	let	let	VERB
ejpam-6834	1173	2	the	the	DET
ejpam-6834	1173	3	plithogenic	plithogenic	ADJ
ejpam-6834	1173	4	attribute	attribute	NOUN
ejpam-6834	1173	5	be	be	AUX
ejpam-6834	1173	6	v	v	NOUN
ejpam-6834	1173	7	=	=	SYM
ejpam-6834	1173	8	routequality	routequality	NOUN
ejpam-6834	1173	9	,	,	PUNCT
ejpam-6834	1173	10	pv	pv	NOUN
ejpam-6834	1173	11	=	=	PRON
ejpam-6834	1173	12	{	{	PUNCT
ejpam-6834	1173	13	eco	eco	PROPN
ejpam-6834	1173	14	,	,	PUNCT
ejpam-6834	1173	15	fast	fast	ADJ
ejpam-6834	1173	16	,	,	PUNCT
ejpam-6834	1173	17	cheap	cheap	ADJ
ejpam-6834	1173	18	}	}	PUNCT
ejpam-6834	1173	19	.	.	PUNCT
ejpam-6834	1174	1	we	we	PRON
ejpam-6834	1174	2	quantify	quantify	VERB
ejpam-6834	1174	3	incompatibility	incompatibility	NOUN
ejpam-6834	1174	4	between	between	ADP
ejpam-6834	1174	5	attribute	attribute	NOUN
ejpam-6834	1174	6	values	value	NOUN
ejpam-6834	1174	7	via	via	ADP
ejpam-6834	1174	8	the	the	DET
ejpam-6834	1174	9	degree	degree	NOUN
ejpam-6834	1174	10	–	–	PUNCT
ejpam-6834	1174	11	of	of	ADP
ejpam-6834	1174	12	–	–	PUNCT
ejpam-6834	1174	13	contradiction	contradiction	NOUN
ejpam-6834	1174	14	pcf	pcf	PROPN
ejpam-6834	1174	15	:	:	PUNCT
ejpam-6834	1175	1	pv	pv	INTJ
ejpam-6834	1175	2	×	×	NOUN
ejpam-6834	1175	3	pv	pv	INTJ
ejpam-6834	1175	4	→	→	PUNCT
ejpam-6834	1175	5	[	[	X
ejpam-6834	1175	6	0	0	NUM
ejpam-6834	1175	7	,	,	PUNCT
ejpam-6834	1175	8	1	1	NUM
ejpam-6834	1175	9	]	]	PUNCT
ejpam-6834	1175	10	,	,	PUNCT
ejpam-6834	1175	11	pcf	pcf	PROPN
ejpam-6834	1175	12	(	(	PUNCT
ejpam-6834	1175	13	a	a	PRON
ejpam-6834	1175	14	,	,	PUNCT
ejpam-6834	1175	15	a	a	NOUN
ejpam-6834	1175	16	)	)	PUNCT
ejpam-6834	1175	17	=	=	SYM
ejpam-6834	1175	18	0	0	NUM
ejpam-6834	1175	19	,	,	PUNCT
ejpam-6834	1175	20	pcf	pcf	PROPN
ejpam-6834	1175	21	(	(	PUNCT
ejpam-6834	1175	22	a	a	DET
ejpam-6834	1175	23	,	,	PUNCT
ejpam-6834	1175	24	b	b	NOUN
ejpam-6834	1175	25	)	)	PUNCT
ejpam-6834	1175	26	=	=	SYM
ejpam-6834	1175	27	pcf	pcf	PROPN
ejpam-6834	1175	28	(	(	PUNCT
ejpam-6834	1175	29	b	b	PROPN
ejpam-6834	1175	30	,	,	PUNCT
ejpam-6834	1175	31	a	a	PRON
ejpam-6834	1175	32	)	)	PUNCT
ejpam-6834	1175	33	,	,	PUNCT
ejpam-6834	1175	34	specified	specify	VERB
ejpam-6834	1175	35	by	by	ADP
ejpam-6834	1175	36	pcf	pcf	PROPN
ejpam-6834	1175	37	(	(	PUNCT
ejpam-6834	1175	38	eco	eco	PROPN
ejpam-6834	1175	39	,	,	PUNCT
ejpam-6834	1175	40	fast	fast	ADJ
ejpam-6834	1175	41	)	)	PUNCT
ejpam-6834	1175	42	=	=	SYM
ejpam-6834	1175	43	0.6	0.6	NUM
ejpam-6834	1175	44	,	,	PUNCT
ejpam-6834	1175	45	pcf	pcf	PROPN
ejpam-6834	1175	46	(	(	PUNCT
ejpam-6834	1175	47	eco	eco	PROPN
ejpam-6834	1175	48	,	,	PUNCT
ejpam-6834	1175	49	cheap	cheap	ADJ
ejpam-6834	1175	50	)	)	PUNCT
ejpam-6834	1175	51	=	=	SYM
ejpam-6834	1175	52	0.4	0.4	NUM
ejpam-6834	1175	53	,	,	PUNCT
ejpam-6834	1175	54	pcf	pcf	PROPN
ejpam-6834	1175	55	(	(	PUNCT
ejpam-6834	1175	56	fast	fast	ADJ
ejpam-6834	1175	57	,	,	PUNCT
ejpam-6834	1175	58	cheap	cheap	ADJ
ejpam-6834	1175	59	)	)	PUNCT
ejpam-6834	1175	60	=	=	SYM
ejpam-6834	1175	61	0.5	0.5	NUM
ejpam-6834	1175	62	.	.	PUNCT
ejpam-6834	1176	1	a	a	DET
ejpam-6834	1176	2	concrete	concrete	ADJ
ejpam-6834	1176	3	input	input	NOUN
ejpam-6834	1176	4	.	.	PUNCT
ejpam-6834	1177	1	interpret	interpret	VERB
ejpam-6834	1177	2	a1	a1	NOUN
ejpam-6834	1177	3	as	as	ADP
ejpam-6834	1177	4	a	a	DET
ejpam-6834	1177	5	policy	policy	NOUN
ejpam-6834	1177	6	/	/	SYM
ejpam-6834	1177	7	constraint	constraint	NOUN
ejpam-6834	1177	8	cluster	cluster	NOUN
ejpam-6834	1177	9	and	and	CCONJ
ejpam-6834	1177	10	a2	a2	PROPN
ejpam-6834	1177	11	as	as	ADP
ejpam-6834	1177	12	a	a	DET
ejpam-6834	1177	13	user	user	NOUN
ejpam-6834	1177	14	–	–	PUNCT
ejpam-6834	1177	15	preference	preference	NOUN
ejpam-6834	1177	16	cluster	cluster	NOUN
ejpam-6834	1177	17	.	.	PUNCT
ejpam-6834	1178	1	choose	choose	VERB
ejpam-6834	1178	2	a1	a1	NOUN
ejpam-6834	1178	3	=	=	PUNCT
ejpam-6834	1178	4	{	{	PUNCT
ejpam-6834	1178	5	{	{	PUNCT
ejpam-6834	1178	6	costcap	costcap	NOUN
ejpam-6834	1178	7	,	,	PUNCT
ejpam-6834	1178	8	emissioncap	emissioncap	NOUN
ejpam-6834	1178	9	}	}	PUNCT
ejpam-6834	1178	10	,	,	PUNCT
ejpam-6834	1178	11	{	{	PUNCT
ejpam-6834	1178	12	timewindow	timewindow	NOUN
ejpam-6834	1178	13	}	}	PUNCT
ejpam-6834	1178	14	}	}	PUNCT
ejpam-6834	1178	15	,	,	PUNCT
ejpam-6834	1178	16	a2	a2	PROPN
ejpam-6834	1178	17	=	=	PRON
ejpam-6834	1178	18	{	{	PUNCT
ejpam-6834	1178	19	{	{	PUNCT
ejpam-6834	1178	20	maxtransfers	maxtransfer	NOUN
ejpam-6834	1178	21	}	}	PUNCT
ejpam-6834	1178	22	,	,	PUNCT
ejpam-6834	1178	23	{	{	PUNCT
ejpam-6834	1178	24	timewindow	timewindow	NOUN
ejpam-6834	1178	25	,	,	PUNCT
ejpam-6834	1178	26	emissioncap	emissioncap	NOUN
ejpam-6834	1178	27	}	}	PUNCT
ejpam-6834	1178	28	}	}	PUNCT
ejpam-6834	1178	29	,	,	PUNCT
ejpam-6834	1179	1	so	so	ADV
ejpam-6834	1179	2	a	a	DET
ejpam-6834	1179	3	=	=	SYM
ejpam-6834	1179	4	(	(	PUNCT
ejpam-6834	1179	5	a1	a1	PROPN
ejpam-6834	1179	6	,	,	PUNCT
ejpam-6834	1179	7	a2	a2	PROPN
ejpam-6834	1179	8	)	)	PUNCT
ejpam-6834	1179	9	∈	∈	PROPN
ejpam-6834	1179	10	d.	d.	PROPN
ejpam-6834	1179	11	hyper	hyper	PROPN
ejpam-6834	1179	12	degree	degree	NOUN
ejpam-6834	1179	13	of	of	ADP
ejpam-6834	1179	14	appurtenance	appurtenance	NOUN
ejpam-6834	1179	15	(	(	PUNCT
ejpam-6834	1179	16	hdaf	hdaf	NOUN
ejpam-6834	1179	17	)	)	PUNCT
ejpam-6834	1179	18	.	.	PUNCT
ejpam-6834	1180	1	for	for	SCONJ
ejpam-6834	1180	2	each	each	DET
ejpam-6834	1180	3	attribute	attribute	NOUN
ejpam-6834	1180	4	value	value	VERB
ejpam-6834	1180	5	a	a	DET
ejpam-6834	1180	6	∈	∈	NOUN
ejpam-6834	1180	7	pv	pv	NOUN
ejpam-6834	1180	8	,	,	PUNCT
ejpam-6834	1180	9	the	the	DET
ejpam-6834	1180	10	map	map	NOUN
ejpam-6834	1180	11	˜pdf	˜pdf	NOUN
ejpam-6834	1180	12	(	(	PUNCT
ejpam-6834	1180	13	2,2	2,2	NOUN
ejpam-6834	1180	14	)	)	PUNCT
ejpam-6834	1180	15	v	v	NOUN
ejpam-6834	1180	16	:	:	PUNCT
ejpam-6834	1180	17	d	d	X
ejpam-6834	1180	18	×	×	NOUN
ejpam-6834	1180	19	pv	pv	INTJ
ejpam-6834	1180	20	−→	−→	NOUN
ejpam-6834	1180	21	c	c	NOUN
ejpam-6834	1180	22	returns	return	VERB
ejpam-6834	1180	23	a	a	DET
ejpam-6834	1180	24	pair	pair	NOUN
ejpam-6834	1180	25	(	(	PUNCT
ejpam-6834	1180	26	b	b	X
ejpam-6834	1180	27	(	(	PUNCT
ejpam-6834	1180	28	a	a	NOUN
ejpam-6834	1180	29	)	)	PUNCT
ejpam-6834	1180	30	1	1	NUM
ejpam-6834	1180	31	,	,	PUNCT
ejpam-6834	1180	32	b	b	X
ejpam-6834	1180	33	(	(	PUNCT
ejpam-6834	1180	34	a	a	NOUN
ejpam-6834	1180	35	)	)	PUNCT
ejpam-6834	1180	36	2	2	NUM
ejpam-6834	1180	37	)	)	PUNCT
ejpam-6834	1180	38	with	with	ADP
ejpam-6834	1180	39	b	b	PROPN
ejpam-6834	1180	40	(	(	PUNCT
ejpam-6834	1180	41	a	a	NOUN
ejpam-6834	1180	42	)	)	PUNCT
ejpam-6834	1180	43	j	j	PROPN
ejpam-6834	1180	44	∈	∈	PROPN
ejpam-6834	1180	45	p2	p2	X
ejpam-6834	1181	1	+	+	NOUN
ejpam-6834	1181	2	(	(	PUNCT
ejpam-6834	1181	3	[	[	NOUN
ejpam-6834	1181	4	0	0	NUM
ejpam-6834	1181	5	,	,	PUNCT
ejpam-6834	1181	6	1]2	1]2	NUM
ejpam-6834	1181	7	)	)	PUNCT
ejpam-6834	1181	8	.	.	PUNCT
ejpam-6834	1182	1	at	at	ADP
ejpam-6834	1182	2	the	the	DET
ejpam-6834	1182	3	input	input	NOUN
ejpam-6834	1182	4	a	a	PRON
ejpam-6834	1182	5	above	above	ADJ
ejpam-6834	1182	6	,	,	PUNCT
ejpam-6834	1182	7	define	define	NOUN
ejpam-6834	1182	8	:	:	PUNCT
ejpam-6834	1182	9	eco	eco	NOUN
ejpam-6834	1182	10	:	:	PUNCT
ejpam-6834	1183	1	b	b	X
ejpam-6834	1183	2	(	(	PUNCT
ejpam-6834	1183	3	eco	eco	PROPN
ejpam-6834	1183	4	)	)	PUNCT
ejpam-6834	1183	5	1	1	NUM
ejpam-6834	1183	6	=	=	NOUN
ejpam-6834	1183	7	{	{	PUNCT
ejpam-6834	1183	8	{	{	PUNCT
ejpam-6834	1183	9	(	(	PUNCT
ejpam-6834	1183	10	0.88	0.88	NUM
ejpam-6834	1183	11	,	,	PUNCT
ejpam-6834	1183	12	0.84	0.84	NUM
ejpam-6834	1183	13	)	)	PUNCT
ejpam-6834	1183	14	,	,	PUNCT
ejpam-6834	1183	15	(	(	PUNCT
ejpam-6834	1183	16	0.86	0.86	NUM
ejpam-6834	1183	17	,	,	PUNCT
ejpam-6834	1183	18	0.83	0.83	NUM
ejpam-6834	1183	19	)	)	PUNCT
ejpam-6834	1183	20	}	}	PUNCT
ejpam-6834	1183	21	,	,	PUNCT
ejpam-6834	1183	22	{	{	PUNCT
ejpam-6834	1183	23	(	(	PUNCT
ejpam-6834	1183	24	0.82	0.82	NUM
ejpam-6834	1183	25	,	,	PUNCT
ejpam-6834	1183	26	0.80	0.80	NUM
ejpam-6834	1183	27	)	)	PUNCT
ejpam-6834	1183	28	}	}	PUNCT
ejpam-6834	1183	29	}	}	PUNCT
ejpam-6834	1183	30	,	,	PUNCT
ejpam-6834	1183	31	b	b	X
ejpam-6834	1183	32	(	(	PUNCT
ejpam-6834	1183	33	eco	eco	PROPN
ejpam-6834	1183	34	)	)	PUNCT
ejpam-6834	1183	35	2	2	NUM
ejpam-6834	1183	36	=	=	SYM
ejpam-6834	1183	37	{	{	PUNCT
ejpam-6834	1183	38	{	{	PUNCT
ejpam-6834	1183	39	(	(	PUNCT
ejpam-6834	1183	40	0.78	0.78	NUM
ejpam-6834	1183	41	,	,	PUNCT
ejpam-6834	1183	42	0.75	0.75	NUM
ejpam-6834	1183	43	)	)	PUNCT
ejpam-6834	1183	44	}	}	PUNCT
ejpam-6834	1183	45	,	,	PUNCT
ejpam-6834	1183	46	{	{	PUNCT
ejpam-6834	1183	47	(	(	PUNCT
ejpam-6834	1183	48	0.81	0.81	NUM
ejpam-6834	1183	49	,	,	PUNCT
ejpam-6834	1183	50	0.79	0.79	NUM
ejpam-6834	1183	51	)	)	PUNCT
ejpam-6834	1183	52	}	}	PUNCT
ejpam-6834	1183	53	}	}	PUNCT
ejpam-6834	1183	54	.	.	PUNCT
ejpam-6834	1184	1	fast	fast	ADV
ejpam-6834	1184	2	:	:	PUNCT
ejpam-6834	1184	3	b	b	X
ejpam-6834	1184	4	(	(	PUNCT
ejpam-6834	1184	5	fast	fast	ADJ
ejpam-6834	1184	6	)	)	PUNCT
ejpam-6834	1184	7	1	1	NUM
ejpam-6834	1184	8	=	=	NOUN
ejpam-6834	1184	9	{	{	PUNCT
ejpam-6834	1184	10	{	{	PUNCT
ejpam-6834	1184	11	(	(	PUNCT
ejpam-6834	1184	12	0.90	0.90	NUM
ejpam-6834	1184	13	,	,	PUNCT
ejpam-6834	1184	14	0.72	0.72	NUM
ejpam-6834	1184	15	)	)	PUNCT
ejpam-6834	1184	16	}	}	PUNCT
ejpam-6834	1184	17	,	,	PUNCT
ejpam-6834	1184	18	{	{	PUNCT
ejpam-6834	1184	19	(	(	PUNCT
ejpam-6834	1184	20	0.85	0.85	NUM
ejpam-6834	1184	21	,	,	PUNCT
ejpam-6834	1184	22	0.70	0.70	NUM
ejpam-6834	1184	23	)	)	PUNCT
ejpam-6834	1184	24	,	,	PUNCT
ejpam-6834	1184	25	(	(	PUNCT
ejpam-6834	1184	26	0.83	0.83	NUM
ejpam-6834	1184	27	,	,	PUNCT
ejpam-6834	1184	28	0.69	0.69	NUM
ejpam-6834	1184	29	)	)	PUNCT
ejpam-6834	1184	30	}	}	PUNCT
ejpam-6834	1184	31	}	}	PUNCT
ejpam-6834	1184	32	,	,	PUNCT
ejpam-6834	1184	33	b	b	X
ejpam-6834	1184	34	(	(	PUNCT
ejpam-6834	1184	35	fast	fast	ADJ
ejpam-6834	1184	36	)	)	PUNCT
ejpam-6834	1184	37	2	2	NUM
ejpam-6834	1184	38	=	=	SYM
ejpam-6834	1184	39	{	{	PUNCT
ejpam-6834	1184	40	{	{	PUNCT
ejpam-6834	1184	41	(	(	PUNCT
ejpam-6834	1184	42	0.76	0.76	NUM
ejpam-6834	1184	43	,	,	PUNCT
ejpam-6834	1184	44	0.68	0.68	NUM
ejpam-6834	1184	45	)	)	PUNCT
ejpam-6834	1184	46	}	}	PUNCT
ejpam-6834	1184	47	}	}	PUNCT
ejpam-6834	1184	48	.	.	PUNCT
ejpam-6834	1185	1	cheap	cheap	ADJ
ejpam-6834	1185	2	:	:	PUNCT
ejpam-6834	1185	3	b	b	X
ejpam-6834	1185	4	(	(	PUNCT
ejpam-6834	1185	5	cheap	cheap	ADJ
ejpam-6834	1185	6	)	)	PUNCT
ejpam-6834	1185	7	1	1	NUM
ejpam-6834	1185	8	=	=	NOUN
ejpam-6834	1185	9	{	{	PUNCT
ejpam-6834	1185	10	{	{	PUNCT
ejpam-6834	1185	11	(	(	PUNCT
ejpam-6834	1185	12	0.80	0.80	NUM
ejpam-6834	1185	13	,	,	PUNCT
ejpam-6834	1185	14	0.77	0.77	NUM
ejpam-6834	1185	15	)	)	PUNCT
ejpam-6834	1185	16	}	}	PUNCT
ejpam-6834	1185	17	,	,	PUNCT
ejpam-6834	1185	18	{	{	PUNCT
ejpam-6834	1185	19	(	(	PUNCT
ejpam-6834	1185	20	0.74	0.74	NUM
ejpam-6834	1185	21	,	,	PUNCT
ejpam-6834	1185	22	0.73	0.73	NUM
ejpam-6834	1185	23	)	)	PUNCT
ejpam-6834	1185	24	}	}	PUNCT
ejpam-6834	1185	25	}	}	PUNCT
ejpam-6834	1185	26	,	,	PUNCT
ejpam-6834	1185	27	b	b	X
ejpam-6834	1185	28	(	(	PUNCT
ejpam-6834	1185	29	cheap	cheap	ADJ
ejpam-6834	1185	30	)	)	PUNCT
ejpam-6834	1185	31	2	2	NUM
ejpam-6834	1185	32	=	=	SYM
ejpam-6834	1185	33	{	{	PUNCT
ejpam-6834	1185	34	{	{	PUNCT
ejpam-6834	1185	35	(	(	PUNCT
ejpam-6834	1185	36	0.88	0.88	NUM
ejpam-6834	1185	37	,	,	PUNCT
ejpam-6834	1185	38	0.65	0.65	NUM
ejpam-6834	1185	39	)	)	PUNCT
ejpam-6834	1185	40	}	}	PUNCT
ejpam-6834	1185	41	}	}	PUNCT
ejpam-6834	1185	42	.	.	PUNCT
ejpam-6834	1186	1	each	each	DET
ejpam-6834	1186	2	b	b	X
ejpam-6834	1186	3	(	(	PUNCT
ejpam-6834	1186	4	a	a	NOUN
ejpam-6834	1186	5	)	)	PUNCT
ejpam-6834	1186	6	j	j	PROPN
ejpam-6834	1186	7	is	be	AUX
ejpam-6834	1186	8	a	a	DET
ejpam-6834	1186	9	level–2	level–2	PROPN
ejpam-6834	1186	10	object	object	NOUN
ejpam-6834	1186	11	:	:	PUNCT
ejpam-6834	1186	12	a	a	DET
ejpam-6834	1186	13	nonempty	nonempty	ADJ
ejpam-6834	1186	14	family	family	NOUN
ejpam-6834	1186	15	of	of	ADP
ejpam-6834	1186	16	nonempty	nonempty	ADJ
ejpam-6834	1186	17	sets	set	NOUN
ejpam-6834	1186	18	of	of	ADP
ejpam-6834	1186	19	two	two	NUM
ejpam-6834	1186	20	–	–	PUNCT
ejpam-6834	1186	21	dimensional	dimensional	ADJ
ejpam-6834	1186	22	membership	membership	NOUN
ejpam-6834	1186	23	vectors	vector	NOUN
ejpam-6834	1186	24	(	(	PUNCT
ejpam-6834	1186	25	satisfaction	satisfaction	NOUN
ejpam-6834	1186	26	,	,	PUNCT
ejpam-6834	1186	27	reliability	reliability	NOUN
ejpam-6834	1186	28	)	)	PUNCT
ejpam-6834	1186	29	∈	∈	PROPN
ejpam-6834	1187	1	[	[	X
ejpam-6834	1187	2	0	0	NUM
ejpam-6834	1187	3	,	,	PUNCT
ejpam-6834	1187	4	1]2	1]2	NUM
ejpam-6834	1187	5	.	.	PUNCT
ejpam-6834	1188	1	the	the	DET
ejpam-6834	1188	2	first	first	ADJ
ejpam-6834	1188	3	coordinate	coordinate	NOUN
ejpam-6834	1188	4	(	(	PUNCT
ejpam-6834	1188	5	j=1	j=1	NOUN
ejpam-6834	1188	6	)	)	PUNCT
ejpam-6834	1188	7	aggregates	aggregate	VERB
ejpam-6834	1188	8	commuter	commuter	NOUN
ejpam-6834	1188	9	–	–	PUNCT
ejpam-6834	1188	10	side	side	NOUN
ejpam-6834	1188	11	appraisals	appraisal	NOUN
ejpam-6834	1188	12	;	;	PUNCT
ejpam-6834	1188	13	the	the	DET
ejpam-6834	1188	14	second	second	ADJ
ejpam-6834	1188	15	(	(	PUNCT
ejpam-6834	1188	16	j=2	j=2	NOUN
ejpam-6834	1188	17	)	)	PUNCT
ejpam-6834	1188	18	aggregates	aggregate	VERB
ejpam-6834	1188	19	operator	operator	NOUN
ejpam-6834	1188	20	–	–	PUNCT
ejpam-6834	1188	21	side	side	NOUN
ejpam-6834	1188	22	appraisals	appraisal	NOUN
ejpam-6834	1188	23	.	.	PUNCT
ejpam-6834	1189	1	the	the	DET
ejpam-6834	1189	2	plithogenic	plithogenic	ADJ
ejpam-6834	1189	3	nature	nature	NOUN
ejpam-6834	1189	4	appears	appear	VERB
ejpam-6834	1189	5	in	in	ADP
ejpam-6834	1189	6	the	the	DET
ejpam-6834	1189	7	simultaneous	simultaneous	ADJ
ejpam-6834	1189	8	presence	presence	NOUN
ejpam-6834	1189	9	of	of	ADP
ejpam-6834	1189	10	multiple	multiple	ADJ
ejpam-6834	1189	11	attribute	attribute	NOUN
ejpam-6834	1189	12	values	value	VERB
ejpam-6834	1189	13	a	a	DET
ejpam-6834	1189	14	together	together	NOUN
ejpam-6834	1189	15	with	with	ADP
ejpam-6834	1189	16	the	the	DET
ejpam-6834	1189	17	quantified	quantified	ADJ
ejpam-6834	1189	18	contradictions	contradiction	NOUN
ejpam-6834	1189	19	pcf	pcf	PROPN
ejpam-6834	1189	20	between	between	ADP
ejpam-6834	1189	21	them	they	PRON
ejpam-6834	1189	22	.	.	PUNCT
ejpam-6834	1190	1	the	the	DET
ejpam-6834	1190	2	choice	choice	NOUN
ejpam-6834	1190	3	(	(	PUNCT
ejpam-6834	1190	4	a1	a1	NOUN
ejpam-6834	1190	5	,	,	PUNCT
ejpam-6834	1190	6	a2	a2	PROPN
ejpam-6834	1190	7	)	)	PUNCT
ejpam-6834	1190	8	prioritizes	prioritize	VERB
ejpam-6834	1190	9	emission	emission	NOUN
ejpam-6834	1190	10	limits	limit	NOUN
ejpam-6834	1190	11	,	,	PUNCT
ejpam-6834	1190	12	moderate	moderate	ADJ
ejpam-6834	1190	13	cost	cost	NOUN
ejpam-6834	1190	14	caps	cap	NOUN
ejpam-6834	1190	15	,	,	PUNCT
ejpam-6834	1190	16	and	and	CCONJ
ejpam-6834	1190	17	few	few	ADJ
ejpam-6834	1190	18	transfers	transfer	NOUN
ejpam-6834	1190	19	within	within	ADP
ejpam-6834	1190	20	a	a	DET
ejpam-6834	1190	21	usable	usable	ADJ
ejpam-6834	1190	22	time	time	NOUN
ejpam-6834	1190	23	window	window	NOUN
ejpam-6834	1190	24	.	.	PUNCT
ejpam-6834	1191	1	consequently	consequently	ADV
ejpam-6834	1191	2	,	,	PUNCT
ejpam-6834	1191	3	eco	eco	PROPN
ejpam-6834	1191	4	achieves	achieve	VERB
ejpam-6834	1191	5	high	high	ADJ
ejpam-6834	1191	6	(	(	PUNCT
ejpam-6834	1191	7	x1	x1	PROPN
ejpam-6834	1191	8	,	,	PUNCT
ejpam-6834	1191	9	x2	x2	PROPN
ejpam-6834	1191	10	)	)	PUNCT
ejpam-6834	1191	11	on	on	ADP
ejpam-6834	1191	12	both	both	DET
ejpam-6834	1191	13	outputs	output	NOUN
ejpam-6834	1191	14	t.	t.	PROPN
ejpam-6834	1191	15	fujita	fujita	PROPN
ejpam-6834	1191	16	,	,	PUNCT
ejpam-6834	1191	17	f.smarandache	f.smarandache	NOUN
ejpam-6834	1191	18	/	/	SYM
ejpam-6834	1191	19	eur	eur	PROPN
ejpam-6834	1191	20	.	.	PUNCT
ejpam-6834	1192	1	j.	j.	PROPN
ejpam-6834	1192	2	pure	pure	PROPN
ejpam-6834	1192	3	appl	appl	PROPN
ejpam-6834	1192	4	.	.	PROPN
ejpam-6834	1192	5	math	math	PROPN
ejpam-6834	1192	6	,	,	PUNCT
ejpam-6834	1192	7	18	18	NUM
ejpam-6834	1192	8	(	(	PUNCT
ejpam-6834	1192	9	4	4	NUM
ejpam-6834	1192	10	)	)	PUNCT
ejpam-6834	1192	11	(	(	PUNCT
ejpam-6834	1192	12	2025	2025	NUM
ejpam-6834	1192	13	)	)	PUNCT
ejpam-6834	1192	14	,	,	PUNCT
ejpam-6834	1192	15	6834	6834	NUM
ejpam-6834	1192	16	47	47	NUM
ejpam-6834	1192	17	of	of	ADP
ejpam-6834	1192	18	69	69	NUM
ejpam-6834	1192	19	(	(	PUNCT
ejpam-6834	1192	20	good	good	ADJ
ejpam-6834	1192	21	satisfaction	satisfaction	NOUN
ejpam-6834	1192	22	without	without	ADP
ejpam-6834	1192	23	sacrificing	sacrifice	VERB
ejpam-6834	1192	24	reliability	reliability	NOUN
ejpam-6834	1192	25	)	)	PUNCT
ejpam-6834	1192	26	,	,	PUNCT
ejpam-6834	1192	27	whereas	whereas	SCONJ
ejpam-6834	1192	28	fast	fast	ADJ
ejpam-6834	1192	29	increases	increase	NOUN
ejpam-6834	1192	30	satisfaction	satisfaction	NOUN
ejpam-6834	1192	31	but	but	CCONJ
ejpam-6834	1192	32	lowers	lower	VERB
ejpam-6834	1192	33	reliability	reliability	NOUN
ejpam-6834	1192	34	for	for	ADP
ejpam-6834	1192	35	the	the	DET
ejpam-6834	1192	36	operator	operator	NOUN
ejpam-6834	1192	37	;	;	PUNCT
ejpam-6834	1192	38	cheap	cheap	ADJ
ejpam-6834	1192	39	is	be	AUX
ejpam-6834	1192	40	relatively	relatively	ADV
ejpam-6834	1192	41	reliable	reliable	ADJ
ejpam-6834	1192	42	for	for	ADP
ejpam-6834	1192	43	the	the	DET
ejpam-6834	1192	44	operator	operator	NOUN
ejpam-6834	1192	45	yet	yet	ADV
ejpam-6834	1192	46	yields	yield	VERB
ejpam-6834	1192	47	only	only	ADV
ejpam-6834	1192	48	moderate	moderate	ADJ
ejpam-6834	1192	49	commuter	commuter	NOUN
ejpam-6834	1192	50	satisfaction	satisfaction	NOUN
ejpam-6834	1192	51	.	.	PUNCT
ejpam-6834	1193	1	the	the	DET
ejpam-6834	1193	2	contradiction	contradiction	NOUN
ejpam-6834	1193	3	matrix	matrix	NOUN
ejpam-6834	1193	4	pcf	pcf	PROPN
ejpam-6834	1193	5	quantifies	quantifie	NOUN
ejpam-6834	1193	6	these	these	DET
ejpam-6834	1193	7	trade	trade	NOUN
ejpam-6834	1193	8	–	–	PUNCT
ejpam-6834	1193	9	offs	off	NOUN
ejpam-6834	1193	10	(	(	PUNCT
ejpam-6834	1193	11	e.g.	e.g.	ADV
ejpam-6834	1193	12	,	,	PUNCT
ejpam-6834	1193	13	eco	eco	PROPN
ejpam-6834	1193	14	vs.	vs.	X
ejpam-6834	1193	15	fast	fast	ADV
ejpam-6834	1193	16	at	at	ADP
ejpam-6834	1193	17	0.6	0.6	NUM
ejpam-6834	1193	18	)	)	PUNCT
ejpam-6834	1193	19	,	,	PUNCT
ejpam-6834	1193	20	enabling	enable	VERB
ejpam-6834	1193	21	plithogenic	plithogenic	ADJ
ejpam-6834	1193	22	decision	decision	NOUN
ejpam-6834	1193	23	aggregation	aggregation	NOUN
ejpam-6834	1193	24	across	across	ADP
ejpam-6834	1193	25	attribute	attribute	NOUN
ejpam-6834	1193	26	values	value	NOUN
ejpam-6834	1193	27	.	.	PUNCT
ejpam-6834	1194	1	thus	thus	ADV
ejpam-6834	1194	2	,	,	PUNCT
ejpam-6834	1194	3	all	all	DET
ejpam-6834	1194	4	components	component	NOUN
ejpam-6834	1194	5	(	(	PUNCT
ejpam-6834	1194	6	d	d	NOUN
ejpam-6834	1194	7	,	,	PUNCT
ejpam-6834	1194	8	v	v	NOUN
ejpam-6834	1194	9	,	,	PUNCT
ejpam-6834	1194	10	pv	pv	INTJ
ejpam-6834	1194	11	,	,	PUNCT
ejpam-6834	1194	12	˜pdf	˜pdf	NOUN
ejpam-6834	1194	13	(	(	PUNCT
ejpam-6834	1194	14	2,2	2,2	NOUN
ejpam-6834	1194	15	)	)	PUNCT
ejpam-6834	1194	16	v	v	NOUN
ejpam-6834	1194	17	,	,	PUNCT
ejpam-6834	1194	18	pcf	pcf	PROPN
ejpam-6834	1194	19	)	)	PUNCT
ejpam-6834	1194	20	instantiate	instantiate	VERB
ejpam-6834	1194	21	a	a	DET
ejpam-6834	1194	22	concrete	concrete	NOUN
ejpam-6834	1194	23	(	(	PUNCT
ejpam-6834	1194	24	2	2	NUM
ejpam-6834	1194	25	,	,	PUNCT
ejpam-6834	1194	26	2)-ary	2)-ary	NUM
ejpam-6834	1194	27	(	(	PUNCT
ejpam-6834	1194	28	2	2	NUM
ejpam-6834	1194	29	,	,	PUNCT
ejpam-6834	1194	30	2)-superhyperplithogenic	2)-superhyperplithogenic	NUM
ejpam-6834	1194	31	set	set	NOUN
ejpam-6834	1194	32	for	for	ADP
ejpam-6834	1194	33	multi	multi	ADJ
ejpam-6834	1194	34	–	–	PUNCT
ejpam-6834	1194	35	criteria	criterion	NOUN
ejpam-6834	1194	36	route	route	NOUN
ejpam-6834	1194	37	planning	planning	NOUN
ejpam-6834	1194	38	.	.	PUNCT
ejpam-6834	1195	1	theorem	theorem	VERB
ejpam-6834	1195	2	38	38	NUM
ejpam-6834	1195	3	(	(	PUNCT
ejpam-6834	1195	4	unary	unary	ADJ
ejpam-6834	1195	5	reduction	reduction	NOUN
ejpam-6834	1195	6	)	)	PUNCT
ejpam-6834	1195	7	.	.	PUNCT
ejpam-6834	1196	1	every	every	PRON
ejpam-6834	1196	2	(	(	PUNCT
ejpam-6834	1196	3	m	m	PROPN
ejpam-6834	1196	4	,	,	PUNCT
ejpam-6834	1196	5	n)-superhyperplithogenic	n)-superhyperplithogenic	PUNCT
ejpam-6834	1196	6	set	set	NOUN
ejpam-6834	1196	7	is	be	AUX
ejpam-6834	1196	8	the	the	DET
ejpam-6834	1196	9	special	special	ADJ
ejpam-6834	1196	10	case	case	NOUN
ejpam-6834	1196	11	h	h	NOUN
ejpam-6834	1197	1	=	=	SYM
ejpam-6834	1197	2	k	k	PROPN
ejpam-6834	1197	3	=	=	SYM
ejpam-6834	1197	4	1	1	NUM
ejpam-6834	1197	5	of	of	ADP
ejpam-6834	1197	6	definition	definition	NOUN
ejpam-6834	1197	7	24	24	NUM
ejpam-6834	1197	8	.	.	PUNCT
ejpam-6834	1198	1	proof	proof	NOUN
ejpam-6834	1198	2	.	.	PUNCT
ejpam-6834	1199	1	by	by	ADP
ejpam-6834	1199	2	definition	definition	NOUN
ejpam-6834	1199	3	24	24	NUM
ejpam-6834	1199	4	,	,	PUNCT
ejpam-6834	1199	5	the	the	DET
ejpam-6834	1199	6	multi	multi	ADJ
ejpam-6834	1199	7	–	–	PUNCT
ejpam-6834	1199	8	ary	ary	ADJ
ejpam-6834	1199	9	structure	structure	NOUN
ejpam-6834	1199	10	is	be	AUX
ejpam-6834	1199	11	shp	shp	NOUN
ejpam-6834	1199	12	(	(	PUNCT
ejpam-6834	1199	13	h	h	NOUN
ejpam-6834	1199	14	,	,	PUNCT
ejpam-6834	1199	15	k	k	NOUN
ejpam-6834	1199	16	)	)	PUNCT
ejpam-6834	1199	17	pl	pl	PROPN
ejpam-6834	1199	18	(	(	PUNCT
ejpam-6834	1199	19	m	m	PROPN
ejpam-6834	1199	20	,	,	PUNCT
ejpam-6834	1199	21	n	n	CCONJ
ejpam-6834	1199	22	)	)	PUNCT
ejpam-6834	1199	23	=	=	SYM
ejpam-6834	1200	1	(	(	PUNCT
ejpam-6834	1200	2	d	d	PROPN
ejpam-6834	1200	3	,	,	PUNCT
ejpam-6834	1200	4	v	v	NOUN
ejpam-6834	1200	5	,	,	PUNCT
ejpam-6834	1200	6	pv	pv	INTJ
ejpam-6834	1200	7	,	,	PUNCT
ejpam-6834	1200	8	˜pdf	˜pdf	NOUN
ejpam-6834	1200	9	(	(	PUNCT
ejpam-6834	1200	10	m	m	NOUN
ejpam-6834	1200	11	,	,	PUNCT
ejpam-6834	1200	12	n	n	CCONJ
ejpam-6834	1200	13	)	)	PUNCT
ejpam-6834	1200	14	v	v	NOUN
ejpam-6834	1200	15	,	,	PUNCT
ejpam-6834	1200	16	pcf	pcf	PROPN
ejpam-6834	1200	17	)	)	PUNCT
ejpam-6834	1200	18	,	,	PUNCT
ejpam-6834	1201	1	d	d	NOUN
ejpam-6834	1201	2	=	=	PRON
ejpam-6834	1201	3	(	(	PUNCT
ejpam-6834	1201	4	pm	pm	NOUN
ejpam-6834	1201	5	+	+	CCONJ
ejpam-6834	1201	6	(	(	PUNCT
ejpam-6834	1201	7	p	p	NOUN
ejpam-6834	1201	8	)	)	PUNCT
ejpam-6834	1201	9	)	)	PUNCT
ejpam-6834	1201	10	h	h	NOUN
ejpam-6834	1201	11	,	,	PUNCT
ejpam-6834	1201	12	c	c	NOUN
ejpam-6834	1201	13	=	=	PUNCT
ejpam-6834	1201	14	(	(	PUNCT
ejpam-6834	1201	15	pn	pn	PROPN
ejpam-6834	1201	16	+	+	PROPN
ejpam-6834	1201	17	(	(	PUNCT
ejpam-6834	1201	18	[	[	NOUN
ejpam-6834	1201	19	0	0	NUM
ejpam-6834	1201	20	,	,	PUNCT
ejpam-6834	1201	21	1]s))k	1]s))k	PROPN
ejpam-6834	1201	22	.	.	PUNCT
ejpam-6834	1202	1	set	set	VERB
ejpam-6834	1202	2	h	h	NOUN
ejpam-6834	1203	1	=	=	SYM
ejpam-6834	1203	2	k	k	NOUN
ejpam-6834	1203	3	=	=	SYM
ejpam-6834	1203	4	1	1	X
ejpam-6834	1203	5	.	.	X
ejpam-6834	1203	6	there	there	PRON
ejpam-6834	1203	7	are	be	VERB
ejpam-6834	1203	8	canonical	canonical	ADJ
ejpam-6834	1203	9	bijections	bijection	NOUN
ejpam-6834	1203	10	φ	φ	PROPN
ejpam-6834	1203	11	:	:	PUNCT
ejpam-6834	1203	12	(	(	PUNCT
ejpam-6834	1203	13	pm	pm	NOUN
ejpam-6834	1203	14	+	+	CCONJ
ejpam-6834	1203	15	(	(	PUNCT
ejpam-6834	1203	16	p	p	NOUN
ejpam-6834	1203	17	)	)	PUNCT
ejpam-6834	1203	18	)	)	PUNCT
ejpam-6834	1203	19	1	1	NUM
ejpam-6834	1203	20	→	→	SYM
ejpam-6834	1203	21	pm	pm	NOUN
ejpam-6834	1203	22	+	+	CCONJ
ejpam-6834	1203	23	(	(	PUNCT
ejpam-6834	1203	24	p	p	NOUN
ejpam-6834	1203	25	)	)	PUNCT
ejpam-6834	1203	26	,	,	PUNCT
ejpam-6834	1203	27	ψ	ψ	X
ejpam-6834	1203	28	:	:	PUNCT
ejpam-6834	1203	29	(	(	PUNCT
ejpam-6834	1203	30	pn	pn	NOUN
ejpam-6834	1203	31	+	+	PROPN
ejpam-6834	1203	32	(	(	PUNCT
ejpam-6834	1203	33	[	[	NOUN
ejpam-6834	1203	34	0	0	NUM
ejpam-6834	1203	35	,	,	PUNCT
ejpam-6834	1203	36	1]s	1]s	NUM
ejpam-6834	1203	37	)	)	PUNCT
ejpam-6834	1203	38	)	)	PUNCT
ejpam-6834	1203	39	1	1	X
ejpam-6834	1203	40	→	→	SYM
ejpam-6834	1203	41	pn	pn	NOUN
ejpam-6834	1203	42	+	+	PROPN
ejpam-6834	1203	43	(	(	PUNCT
ejpam-6834	1203	44	[	[	NOUN
ejpam-6834	1203	45	0	0	NUM
ejpam-6834	1203	46	,	,	PUNCT
ejpam-6834	1203	47	1]s	1]s	NUM
ejpam-6834	1203	48	)	)	PUNCT
ejpam-6834	1203	49	,	,	PUNCT
ejpam-6834	1203	50	given	give	VERB
ejpam-6834	1203	51	by	by	ADP
ejpam-6834	1203	52	φ(a	φ(a	ADJ
ejpam-6834	1203	53	)	)	PUNCT
ejpam-6834	1203	54	=	=	PUNCT
ejpam-6834	1203	55	a	a	PRON
ejpam-6834	1203	56	and	and	CCONJ
ejpam-6834	1203	57	ψ(b	ψ(b	NOUN
ejpam-6834	1203	58	)	)	PUNCT
ejpam-6834	1203	59	=	=	SYM
ejpam-6834	1204	1	b.	b.	PROPN
ejpam-6834	1204	2	under	under	ADP
ejpam-6834	1204	3	φ	φ	PROPN
ejpam-6834	1204	4	and	and	CCONJ
ejpam-6834	1204	5	ψ	ψ	NOUN
ejpam-6834	1204	6	,	,	PUNCT
ejpam-6834	1204	7	the	the	DET
ejpam-6834	1204	8	map	map	NOUN
ejpam-6834	1204	9	˜pdf	˜pdf	NOUN
ejpam-6834	1204	10	(	(	PUNCT
ejpam-6834	1204	11	m	m	NOUN
ejpam-6834	1204	12	,	,	PUNCT
ejpam-6834	1204	13	n	n	CCONJ
ejpam-6834	1204	14	)	)	PUNCT
ejpam-6834	1204	15	v	v	NOUN
ejpam-6834	1204	16	:	:	PUNCT
ejpam-6834	1204	17	(	(	PUNCT
ejpam-6834	1204	18	pm	pm	NOUN
ejpam-6834	1204	19	+	+	CCONJ
ejpam-6834	1204	20	(	(	PUNCT
ejpam-6834	1204	21	p	p	NOUN
ejpam-6834	1204	22	)	)	PUNCT
ejpam-6834	1204	23	)	)	PUNCT
ejpam-6834	1204	24	1	1	NUM
ejpam-6834	1204	25	×	×	NOUN
ejpam-6834	1204	26	pv	pv	INTJ
ejpam-6834	1204	27	−→	−→	NOUN
ejpam-6834	1204	28	(	(	PUNCT
ejpam-6834	1204	29	pn	pn	NOUN
ejpam-6834	1204	30	+	+	PROPN
ejpam-6834	1204	31	(	(	PUNCT
ejpam-6834	1204	32	[	[	NOUN
ejpam-6834	1204	33	0	0	NUM
ejpam-6834	1204	34	,	,	PUNCT
ejpam-6834	1204	35	1]s	1]s	NUM
ejpam-6834	1204	36	)	)	PUNCT
ejpam-6834	1204	37	)	)	PUNCT
ejpam-6834	1204	38	1	1	NUM
ejpam-6834	1204	39	is	be	AUX
ejpam-6834	1204	40	identified	identify	VERB
ejpam-6834	1204	41	with	with	ADP
ejpam-6834	1204	42	˜pdf	˜pdf	NOUN
ejpam-6834	1204	43	(	(	PUNCT
ejpam-6834	1204	44	m	m	NOUN
ejpam-6834	1204	45	,	,	PUNCT
ejpam-6834	1204	46	n	n	CCONJ
ejpam-6834	1204	47	)	)	PUNCT
ejpam-6834	1204	48	v	v	NOUN
ejpam-6834	1204	49	:	:	PUNCT
ejpam-6834	1204	50	pm	pm	NOUN
ejpam-6834	1204	51	+	+	CCONJ
ejpam-6834	1204	52	(	(	PUNCT
ejpam-6834	1204	53	p	p	NOUN
ejpam-6834	1204	54	)	)	PUNCT
ejpam-6834	1204	55	×	×	NOUN
ejpam-6834	1204	56	pv	pv	INTJ
ejpam-6834	1204	57	−→	−→	NOUN
ejpam-6834	1205	1	pn	pn	PROPN
ejpam-6834	1205	2	+	+	PROPN
ejpam-6834	1205	3	(	(	PUNCT
ejpam-6834	1205	4	[	[	X
ejpam-6834	1205	5	0	0	NUM
ejpam-6834	1205	6	,	,	PUNCT
ejpam-6834	1205	7	1]s	1]s	NUM
ejpam-6834	1205	8	)	)	PUNCT
ejpam-6834	1205	9	,	,	PUNCT
ejpam-6834	1205	10	which	which	PRON
ejpam-6834	1205	11	is	be	AUX
ejpam-6834	1205	12	precisely	precisely	ADV
ejpam-6834	1205	13	the	the	DET
ejpam-6834	1205	14	classical	classical	ADJ
ejpam-6834	1205	15	(	(	PUNCT
ejpam-6834	1205	16	m	m	NOUN
ejpam-6834	1205	17	,	,	PUNCT
ejpam-6834	1205	18	n)-superhyperplithogenic	n)-superhyperplithogenic	PUNCT
ejpam-6834	1205	19	mapping	mapping	NOUN
ejpam-6834	1205	20	(	(	PUNCT
ejpam-6834	1205	21	with	with	ADP
ejpam-6834	1205	22	the	the	DET
ejpam-6834	1205	23	same	same	ADJ
ejpam-6834	1205	24	attribute	attribute	NOUN
ejpam-6834	1205	25	v	v	NOUN
ejpam-6834	1205	26	,	,	PUNCT
ejpam-6834	1205	27	value	value	NOUN
ejpam-6834	1205	28	set	set	VERB
ejpam-6834	1205	29	pv	pv	NOUN
ejpam-6834	1205	30	,	,	PUNCT
ejpam-6834	1205	31	and	and	CCONJ
ejpam-6834	1205	32	contradiction	contradiction	NOUN
ejpam-6834	1205	33	function	function	NOUN
ejpam-6834	1205	34	pcf	pcf	PROPN
ejpam-6834	1205	35	)	)	PUNCT
ejpam-6834	1205	36	.	.	PUNCT
ejpam-6834	1206	1	reflexivity	reflexivity	PROPN
ejpam-6834	1206	2	pcf	pcf	PROPN
ejpam-6834	1206	3	(	(	PUNCT
ejpam-6834	1206	4	a	a	DET
ejpam-6834	1206	5	,	,	PUNCT
ejpam-6834	1206	6	a	a	NOUN
ejpam-6834	1206	7	)	)	PUNCT
ejpam-6834	1206	8	=	=	SYM
ejpam-6834	1206	9	0	0	NUM
ejpam-6834	1206	10	and	and	CCONJ
ejpam-6834	1206	11	symmetry	symmetry	PROPN
ejpam-6834	1206	12	pcf	pcf	PROPN
ejpam-6834	1206	13	(	(	PUNCT
ejpam-6834	1206	14	a	a	DET
ejpam-6834	1206	15	,	,	PUNCT
ejpam-6834	1206	16	b	b	NOUN
ejpam-6834	1206	17	)	)	PUNCT
ejpam-6834	1206	18	=	=	SYM
ejpam-6834	1206	19	pcf	pcf	PROPN
ejpam-6834	1206	20	(	(	PUNCT
ejpam-6834	1206	21	b	b	PROPN
ejpam-6834	1206	22	,	,	PUNCT
ejpam-6834	1206	23	a	a	PRON
ejpam-6834	1206	24	)	)	PUNCT
ejpam-6834	1206	25	are	be	AUX
ejpam-6834	1206	26	unaffected	unaffected	ADJ
ejpam-6834	1206	27	by	by	ADP
ejpam-6834	1206	28	the	the	DET
ejpam-6834	1206	29	identifications	identification	NOUN
ejpam-6834	1206	30	.	.	PUNCT
ejpam-6834	1207	1	hence	hence	ADV
ejpam-6834	1207	2	the	the	DET
ejpam-6834	1207	3	unary	unary	ADJ
ejpam-6834	1207	4	case	case	NOUN
ejpam-6834	1207	5	is	be	AUX
ejpam-6834	1207	6	exactly	exactly	ADV
ejpam-6834	1207	7	the	the	DET
ejpam-6834	1207	8	classical	classical	ADJ
ejpam-6834	1207	9	one	one	NUM
ejpam-6834	1207	10	.	.	PUNCT
ejpam-6834	1208	1	theorem	theorem	VERB
ejpam-6834	1208	2	39	39	NUM
ejpam-6834	1208	3	(	(	PUNCT
ejpam-6834	1208	4	fuzzy	fuzzy	ADJ
ejpam-6834	1208	5	and	and	CCONJ
ejpam-6834	1208	6	neutrosophic	neutrosophic	ADJ
ejpam-6834	1208	7	specializations	specialization	NOUN
ejpam-6834	1208	8	)	)	PUNCT
ejpam-6834	1208	9	.	.	PUNCT
ejpam-6834	1209	1	an	an	DET
ejpam-6834	1209	2	(	(	PUNCT
ejpam-6834	1209	3	h	h	NOUN
ejpam-6834	1209	4	,	,	PUNCT
ejpam-6834	1209	5	k)-ary	k)-ary	X
ejpam-6834	1209	6	(	(	PUNCT
ejpam-6834	1209	7	m	m	PROPN
ejpam-6834	1209	8	,	,	PUNCT
ejpam-6834	1209	9	n)-superhyperplithogenic	n)-superhyperplithogenic	PUNCT
ejpam-6834	1209	10	set	set	NOUN
ejpam-6834	1209	11	specializes	specialize	VERB
ejpam-6834	1209	12	to	to	ADP
ejpam-6834	1209	13	(	(	PUNCT
ejpam-6834	1209	14	i	i	NOUN
ejpam-6834	1209	15	)	)	PUNCT
ejpam-6834	1209	16	an	an	DET
ejpam-6834	1209	17	(	(	PUNCT
ejpam-6834	1209	18	h	h	NOUN
ejpam-6834	1209	19	,	,	PUNCT
ejpam-6834	1209	20	k)-ary	k)-ary	X
ejpam-6834	1209	21	(	(	PUNCT
ejpam-6834	1209	22	m	m	PROPN
ejpam-6834	1209	23	,	,	PUNCT
ejpam-6834	1209	24	n)-superhyperfuzzy	n)-superhyperfuzzy	PUNCT
ejpam-6834	1209	25	set	set	VERB
ejpam-6834	1209	26	when	when	SCONJ
ejpam-6834	1209	27	s	s	VERB
ejpam-6834	1209	28	=	=	NOUN
ejpam-6834	1209	29	1	1	NUM
ejpam-6834	1209	30	,	,	PUNCT
ejpam-6834	1209	31	and	and	CCONJ
ejpam-6834	1209	32	(	(	PUNCT
ejpam-6834	1209	33	ii	ii	NOUN
ejpam-6834	1209	34	)	)	PUNCT
ejpam-6834	1209	35	an	an	DET
ejpam-6834	1209	36	(	(	PUNCT
ejpam-6834	1209	37	h	h	NOUN
ejpam-6834	1209	38	,	,	PUNCT
ejpam-6834	1209	39	k)-ary	k)-ary	X
ejpam-6834	1209	40	(	(	PUNCT
ejpam-6834	1209	41	m	m	PROPN
ejpam-6834	1209	42	,	,	PUNCT
ejpam-6834	1209	43	n)-superhyperneutrosophic	n)-superhyperneutrosophic	PUNCT
ejpam-6834	1209	44	set	set	VERB
ejpam-6834	1209	45	when	when	SCONJ
ejpam-6834	1209	46	s	s	VERB
ejpam-6834	1209	47	=	=	SYM
ejpam-6834	1209	48	3	3	NUM
ejpam-6834	1209	49	(	(	PUNCT
ejpam-6834	1209	50	with	with	ADP
ejpam-6834	1209	51	triples	triple	NOUN
ejpam-6834	1209	52	(	(	PUNCT
ejpam-6834	1209	53	t	t	PROPN
ejpam-6834	1209	54	,	,	PUNCT
ejpam-6834	1209	55	i	i	PRON
ejpam-6834	1209	56	,	,	PUNCT
ejpam-6834	1209	57	f	f	PROPN
ejpam-6834	1209	58	)	)	PUNCT
ejpam-6834	1209	59	)	)	PUNCT
ejpam-6834	1209	60	.	.	PUNCT
ejpam-6834	1210	1	proof	proof	NOUN
ejpam-6834	1210	2	.	.	PUNCT
ejpam-6834	1211	1	let	let	VERB
ejpam-6834	1211	2	˜pdf	˜pdf	NOUN
ejpam-6834	1211	3	(	(	PUNCT
ejpam-6834	1211	4	m	m	NOUN
ejpam-6834	1211	5	,	,	PUNCT
ejpam-6834	1211	6	n	n	CCONJ
ejpam-6834	1211	7	)	)	PUNCT
ejpam-6834	1211	8	v	v	NOUN
ejpam-6834	1211	9	:	:	PUNCT
ejpam-6834	1211	10	d	d	X
ejpam-6834	1211	11	×	×	NOUN
ejpam-6834	1212	1	pv	pv	NOUN
ejpam-6834	1212	2	→	→	SYM
ejpam-6834	1212	3	c	c	NOUN
ejpam-6834	1212	4	with	with	ADP
ejpam-6834	1212	5	d	d	PROPN
ejpam-6834	1212	6	=	=	PUNCT
ejpam-6834	1212	7	(	(	PUNCT
ejpam-6834	1212	8	pm	pm	NOUN
ejpam-6834	1212	9	+	+	CCONJ
ejpam-6834	1212	10	(	(	PUNCT
ejpam-6834	1212	11	p	p	NOUN
ejpam-6834	1212	12	)	)	PUNCT
ejpam-6834	1212	13	)	)	PUNCT
ejpam-6834	1212	14	h	h	NOUN
ejpam-6834	1212	15	and	and	CCONJ
ejpam-6834	1212	16	c	c	NOUN
ejpam-6834	1212	17	=	=	SYM
ejpam-6834	1212	18	(	(	PUNCT
ejpam-6834	1212	19	pn	pn	PROPN
ejpam-6834	1212	20	+	+	PROPN
ejpam-6834	1212	21	(	(	PUNCT
ejpam-6834	1212	22	[	[	NOUN
ejpam-6834	1212	23	0	0	NUM
ejpam-6834	1212	24	,	,	PUNCT
ejpam-6834	1212	25	1]s))k	1]s))k	NUM
ejpam-6834	1212	26	.	.	PUNCT
ejpam-6834	1213	1	(	(	PUNCT
ejpam-6834	1213	2	i	i	NOUN
ejpam-6834	1213	3	)	)	PUNCT
ejpam-6834	1213	4	if	if	SCONJ
ejpam-6834	1213	5	s	s	PART
ejpam-6834	1213	6	=	=	NOUN
ejpam-6834	1213	7	1	1	NUM
ejpam-6834	1213	8	,	,	PUNCT
ejpam-6834	1213	9	then	then	ADV
ejpam-6834	1213	10	[	[	X
ejpam-6834	1213	11	0	0	NUM
ejpam-6834	1213	12	,	,	PUNCT
ejpam-6834	1213	13	1]s	1]s	NOUN
ejpam-6834	1213	14	=	=	PUNCT
ejpam-6834	1214	1	[	[	X
ejpam-6834	1214	2	0	0	NUM
ejpam-6834	1214	3	,	,	PUNCT
ejpam-6834	1214	4	1	1	NUM
ejpam-6834	1214	5	]	]	PUNCT
ejpam-6834	1214	6	and	and	CCONJ
ejpam-6834	1214	7	c	c	X
ejpam-6834	1214	8	=	=	SYM
ejpam-6834	1214	9	(	(	PUNCT
ejpam-6834	1214	10	pn	pn	PROPN
ejpam-6834	1214	11	+	+	PROPN
ejpam-6834	1214	12	(	(	PUNCT
ejpam-6834	1214	13	[	[	NOUN
ejpam-6834	1214	14	0	0	NUM
ejpam-6834	1214	15	,	,	PUNCT
ejpam-6834	1214	16	1]))k	1]))k	NUM
ejpam-6834	1214	17	.	.	PUNCT
ejpam-6834	1214	18	thus	thus	ADV
ejpam-6834	1214	19	˜pdf	˜pdf	NOUN
ejpam-6834	1214	20	(	(	PUNCT
ejpam-6834	1214	21	m	m	NOUN
ejpam-6834	1214	22	,	,	PUNCT
ejpam-6834	1214	23	n	n	CCONJ
ejpam-6834	1214	24	)	)	PUNCT
ejpam-6834	1214	25	v	v	NOUN
ejpam-6834	1214	26	:	:	PUNCT
ejpam-6834	1214	27	d	d	X
ejpam-6834	1214	28	×	×	NOUN
ejpam-6834	1214	29	pv	pv	INTJ
ejpam-6834	1214	30	−→	−→	NOUN
ejpam-6834	1214	31	(	(	PUNCT
ejpam-6834	1214	32	pn	pn	NOUN
ejpam-6834	1214	33	+	+	PROPN
ejpam-6834	1214	34	(	(	PUNCT
ejpam-6834	1214	35	[	[	X
ejpam-6834	1214	36	0	0	NUM
ejpam-6834	1214	37	,	,	PUNCT
ejpam-6834	1214	38	1	1	NUM
ejpam-6834	1214	39	]	]	NUM
ejpam-6834	1214	40	)	)	PUNCT
ejpam-6834	1214	41	)	)	PUNCT
ejpam-6834	1215	1	k	k	PROPN
ejpam-6834	1215	2	assigns	assign	NOUN
ejpam-6834	1215	3	to	to	ADP
ejpam-6834	1215	4	each	each	DET
ejpam-6834	1215	5	input	input	NOUN
ejpam-6834	1215	6	a	a	DET
ejpam-6834	1215	7	k	k	NOUN
ejpam-6834	1215	8	–	–	PUNCT
ejpam-6834	1215	9	tuple	tuple	NOUN
ejpam-6834	1215	10	of	of	ADP
ejpam-6834	1215	11	nonempty	nonempty	ADJ
ejpam-6834	1215	12	,	,	PUNCT
ejpam-6834	1215	13	level	level	NOUN
ejpam-6834	1215	14	–	–	PUNCT
ejpam-6834	1215	15	n	n	CCONJ
ejpam-6834	1215	16	fuzzy	fuzzy	ADJ
ejpam-6834	1215	17	degree	degree	NOUN
ejpam-6834	1215	18	sets	set	NOUN
ejpam-6834	1215	19	,	,	PUNCT
ejpam-6834	1215	20	which	which	PRON
ejpam-6834	1215	21	is	be	AUX
ejpam-6834	1215	22	exactly	exactly	ADV
ejpam-6834	1215	23	the	the	DET
ejpam-6834	1215	24	codomain	codomain	NOUN
ejpam-6834	1215	25	required	require	VERB
ejpam-6834	1215	26	by	by	ADP
ejpam-6834	1215	27	the	the	DET
ejpam-6834	1215	28	(	(	PUNCT
ejpam-6834	1215	29	h	h	NOUN
ejpam-6834	1215	30	,	,	PUNCT
ejpam-6834	1215	31	k)-ary	k)-ary	X
ejpam-6834	1215	32	(	(	PUNCT
ejpam-6834	1215	33	m	m	NOUN
ejpam-6834	1215	34	,	,	PUNCT
ejpam-6834	1215	35	n)-superhyperfuzzy	n)-superhyperfuzzy	NOUN
ejpam-6834	1215	36	structure	structure	NOUN
ejpam-6834	1215	37	.	.	PUNCT
ejpam-6834	1216	1	the	the	DET
ejpam-6834	1216	2	domain	domain	NOUN
ejpam-6834	1216	3	and	and	CCONJ
ejpam-6834	1216	4	pcf	pcf	PROPN
ejpam-6834	1216	5	are	be	AUX
ejpam-6834	1216	6	unchanged	unchanged	ADJ
ejpam-6834	1216	7	,	,	PUNCT
ejpam-6834	1216	8	so	so	SCONJ
ejpam-6834	1216	9	all	all	DET
ejpam-6834	1216	10	axioms	axiom	NOUN
ejpam-6834	1216	11	remain	remain	VERB
ejpam-6834	1216	12	valid	valid	ADJ
ejpam-6834	1216	13	.	.	PUNCT
ejpam-6834	1217	1	t.	t.	PROPN
ejpam-6834	1217	2	fujita	fujita	PROPN
ejpam-6834	1217	3	,	,	PUNCT
ejpam-6834	1217	4	f.smarandache	f.smarandache	NOUN
ejpam-6834	1217	5	/	/	SYM
ejpam-6834	1217	6	eur	eur	PROPN
ejpam-6834	1217	7	.	.	PUNCT
ejpam-6834	1218	1	j.	j.	PROPN
ejpam-6834	1218	2	pure	pure	PROPN
ejpam-6834	1218	3	appl	appl	PROPN
ejpam-6834	1218	4	.	.	PROPN
ejpam-6834	1218	5	math	math	PROPN
ejpam-6834	1218	6	,	,	PUNCT
ejpam-6834	1218	7	18	18	NUM
ejpam-6834	1218	8	(	(	PUNCT
ejpam-6834	1218	9	4	4	NUM
ejpam-6834	1218	10	)	)	PUNCT
ejpam-6834	1218	11	(	(	PUNCT
ejpam-6834	1218	12	2025	2025	NUM
ejpam-6834	1218	13	)	)	PUNCT
ejpam-6834	1218	14	,	,	PUNCT
ejpam-6834	1218	15	6834	6834	NUM
ejpam-6834	1218	16	48	48	NUM
ejpam-6834	1218	17	of	of	ADP
ejpam-6834	1218	18	69	69	NUM
ejpam-6834	1218	19	(	(	PUNCT
ejpam-6834	1218	20	ii	ii	NOUN
ejpam-6834	1218	21	)	)	PUNCT
ejpam-6834	1218	22	if	if	SCONJ
ejpam-6834	1218	23	s	s	PART
ejpam-6834	1218	24	=	=	SYM
ejpam-6834	1218	25	3	3	NUM
ejpam-6834	1218	26	,	,	PUNCT
ejpam-6834	1218	27	then	then	ADV
ejpam-6834	1218	28	[	[	X
ejpam-6834	1218	29	0	0	NUM
ejpam-6834	1218	30	,	,	PUNCT
ejpam-6834	1218	31	1]s	1]s	NOUN
ejpam-6834	1218	32	=	=	PUNCT
ejpam-6834	1219	1	[	[	X
ejpam-6834	1219	2	0	0	NUM
ejpam-6834	1219	3	,	,	PUNCT
ejpam-6834	1219	4	1]3	1]3	NUM
ejpam-6834	1219	5	and	and	CCONJ
ejpam-6834	1219	6	c	c	X
ejpam-6834	1219	7	=	=	SYM
ejpam-6834	1219	8	(	(	PUNCT
ejpam-6834	1219	9	pn	pn	PROPN
ejpam-6834	1219	10	+	+	PROPN
ejpam-6834	1219	11	(	(	PUNCT
ejpam-6834	1219	12	[	[	NOUN
ejpam-6834	1219	13	0	0	NUM
ejpam-6834	1219	14	,	,	PUNCT
ejpam-6834	1219	15	1]3))k	1]3))k	PROPN
ejpam-6834	1219	16	.	.	PUNCT
ejpam-6834	1220	1	hence	hence	ADV
ejpam-6834	1220	2	˜pdf	˜pdf	NOUN
ejpam-6834	1220	3	(	(	PUNCT
ejpam-6834	1220	4	m	m	NOUN
ejpam-6834	1220	5	,	,	PUNCT
ejpam-6834	1220	6	n	n	CCONJ
ejpam-6834	1220	7	)	)	PUNCT
ejpam-6834	1220	8	v	v	NOUN
ejpam-6834	1220	9	:	:	PUNCT
ejpam-6834	1220	10	d	d	X
ejpam-6834	1220	11	×	×	NOUN
ejpam-6834	1220	12	pv	pv	INTJ
ejpam-6834	1220	13	−→	−→	NOUN
ejpam-6834	1220	14	(	(	PUNCT
ejpam-6834	1220	15	pn	pn	NOUN
ejpam-6834	1220	16	+	+	PROPN
ejpam-6834	1220	17	(	(	PUNCT
ejpam-6834	1220	18	[	[	X
ejpam-6834	1220	19	0	0	NUM
ejpam-6834	1220	20	,	,	PUNCT
ejpam-6834	1220	21	1]3	1]3	NUM
ejpam-6834	1220	22	)	)	PUNCT
ejpam-6834	1220	23	)	)	PUNCT
ejpam-6834	1221	1	k	k	PROPN
ejpam-6834	1221	2	returns	return	VERB
ejpam-6834	1221	3	k	k	INTJ
ejpam-6834	1221	4	level	level	NOUN
ejpam-6834	1221	5	–	–	PUNCT
ejpam-6834	1221	6	n	n	CCONJ
ejpam-6834	1221	7	families	family	NOUN
ejpam-6834	1221	8	of	of	ADP
ejpam-6834	1221	9	neutrosophic	neutrosophic	ADJ
ejpam-6834	1221	10	triples	triple	NOUN
ejpam-6834	1221	11	(	(	PUNCT
ejpam-6834	1221	12	t	t	PROPN
ejpam-6834	1221	13	,	,	PUNCT
ejpam-6834	1221	14	i	i	PRON
ejpam-6834	1221	15	,	,	PUNCT
ejpam-6834	1221	16	f	f	PROPN
ejpam-6834	1221	17	)	)	PUNCT
ejpam-6834	1221	18	∈	∈	PROPN
ejpam-6834	1222	1	[	[	X
ejpam-6834	1222	2	0	0	NUM
ejpam-6834	1222	3	,	,	PUNCT
ejpam-6834	1222	4	1]3	1]3	NUM
ejpam-6834	1222	5	(	(	PUNCT
ejpam-6834	1222	6	with	with	ADP
ejpam-6834	1222	7	any	any	DET
ejpam-6834	1222	8	standard	standard	ADJ
ejpam-6834	1222	9	neutrosophic	neutrosophic	ADJ
ejpam-6834	1222	10	constraint	constraint	NOUN
ejpam-6834	1222	11	,	,	PUNCT
ejpam-6834	1222	12	e.g.	e.g.	ADV
ejpam-6834	1222	13	0	0	NUM
ejpam-6834	1222	14	≤	≤	NUM
ejpam-6834	1222	15	t	t	NOUN
ejpam-6834	1223	1	+	+	CCONJ
ejpam-6834	1223	2	i	i	PRON
ejpam-6834	1223	3	+	+	NUM
ejpam-6834	1223	4	f	f	PROPN
ejpam-6834	1223	5	≤	≤	ADV
ejpam-6834	1223	6	3	3	NUM
ejpam-6834	1223	7	,	,	PUNCT
ejpam-6834	1223	8	enforced	enforce	VERB
ejpam-6834	1223	9	elementwise	elementwise	ADV
ejpam-6834	1223	10	when	when	SCONJ
ejpam-6834	1223	11	imposed	impose	VERB
ejpam-6834	1223	12	)	)	PUNCT
ejpam-6834	1223	13	.	.	PUNCT
ejpam-6834	1224	1	this	this	PRON
ejpam-6834	1224	2	is	be	AUX
ejpam-6834	1224	3	precisely	precisely	ADV
ejpam-6834	1224	4	the	the	DET
ejpam-6834	1224	5	codomain	codomain	NOUN
ejpam-6834	1224	6	of	of	ADP
ejpam-6834	1224	7	the	the	DET
ejpam-6834	1224	8	(	(	PUNCT
ejpam-6834	1224	9	h	h	NOUN
ejpam-6834	1224	10	,	,	PUNCT
ejpam-6834	1224	11	k)-ary	k)-ary	X
ejpam-6834	1224	12	(	(	PUNCT
ejpam-6834	1224	13	m	m	PROPN
ejpam-6834	1224	14	,	,	PUNCT
ejpam-6834	1224	15	n)-superhyperneutrosophic	n)-superhyperneutrosophic	ADJ
ejpam-6834	1224	16	structure	structure	NOUN
ejpam-6834	1224	17	.	.	PUNCT
ejpam-6834	1225	1	theorem	theorem	VERB
ejpam-6834	1225	2	40	40	NUM
ejpam-6834	1225	3	(	(	PUNCT
ejpam-6834	1225	4	fixing	fix	VERB
ejpam-6834	1225	5	some	some	DET
ejpam-6834	1225	6	inputs	input	NOUN
ejpam-6834	1225	7	)	)	PUNCT
ejpam-6834	1225	8	.	.	PUNCT
ejpam-6834	1226	1	fix	fix	NOUN
ejpam-6834	1226	2	indices	indice	VERB
ejpam-6834	1226	3	1	1	NUM
ejpam-6834	1226	4	≤	≤	NUM
ejpam-6834	1226	5	i1	i1	X
ejpam-6834	1226	6	<	<	X
ejpam-6834	1226	7	·	·	PUNCT
ejpam-6834	1226	8	·	·	PUNCT
ejpam-6834	1226	9	·	·	PUNCT
ejpam-6834	1227	1	<	<	X
ejpam-6834	1227	2	ir	ir	PROPN
ejpam-6834	1227	3	≤	≤	NUM
ejpam-6834	1227	4	h	h	NOUN
ejpam-6834	1227	5	and	and	CCONJ
ejpam-6834	1227	6	super	super	ADJ
ejpam-6834	1227	7	–	–	PUNCT
ejpam-6834	1227	8	elements	element	NOUN
ejpam-6834	1227	9	aij	aij	PROPN
ejpam-6834	1227	10	∈	∈	PROPN
ejpam-6834	1227	11	pm	pm	NOUN
ejpam-6834	1227	12	+	+	CCONJ
ejpam-6834	1227	13	(	(	PUNCT
ejpam-6834	1227	14	p	p	NOUN
ejpam-6834	1227	15	)	)	PUNCT
ejpam-6834	1227	16	.	.	PUNCT
ejpam-6834	1228	1	define	define	VERB
ejpam-6834	1228	2	ι	ι	X
ejpam-6834	1228	3	:	:	PUNCT
ejpam-6834	1228	4	(	(	PUNCT
ejpam-6834	1228	5	pm	pm	NOUN
ejpam-6834	1228	6	+	+	CCONJ
ejpam-6834	1228	7	(	(	PUNCT
ejpam-6834	1228	8	p	p	NOUN
ejpam-6834	1228	9	)	)	PUNCT
ejpam-6834	1228	10	)	)	PUNCT
ejpam-6834	1228	11	h−r	h−r	PROPN
ejpam-6834	1228	12	↪	↪	PROPN
ejpam-6834	1228	13	→	→	SYM
ejpam-6834	1228	14	(	(	PUNCT
ejpam-6834	1228	15	pm	pm	NOUN
ejpam-6834	1228	16	+	+	CCONJ
ejpam-6834	1228	17	(	(	PUNCT
ejpam-6834	1228	18	p	p	NOUN
ejpam-6834	1228	19	)	)	PUNCT
ejpam-6834	1228	20	)	)	PUNCT
ejpam-6834	1228	21	h	h	NOUN
ejpam-6834	1228	22	by	by	ADP
ejpam-6834	1228	23	inserting	insert	VERB
ejpam-6834	1228	24	the	the	DET
ejpam-6834	1228	25	fixed	fix	VERB
ejpam-6834	1228	26	aij	aij	NOUN
ejpam-6834	1228	27	in	in	ADP
ejpam-6834	1228	28	the	the	DET
ejpam-6834	1228	29	positions	position	NOUN
ejpam-6834	1228	30	ij	ij	NOUN
ejpam-6834	1228	31	.	.	PUNCT
ejpam-6834	1229	1	then	then	ADV
ejpam-6834	1229	2	˜pdf	˜pdf	NOUN
ejpam-6834	1229	3	(	(	PUNCT
ejpam-6834	1229	4	m	m	NOUN
ejpam-6834	1229	5	,	,	PUNCT
ejpam-6834	1229	6	n	n	CCONJ
ejpam-6834	1229	7	)	)	PUNCT
ejpam-6834	1229	8	fix	fix	NOUN
ejpam-6834	1229	9	(	(	PUNCT
ejpam-6834	1229	10	b	b	NOUN
ejpam-6834	1229	11	,	,	PUNCT
ejpam-6834	1229	12	a	a	NOUN
ejpam-6834	1229	13	)	)	PUNCT
ejpam-6834	1229	14	:	:	PUNCT
ejpam-6834	1229	15	=	=	SYM
ejpam-6834	1229	16	˜pdf	˜pdf	X
ejpam-6834	1229	17	(	(	PUNCT
ejpam-6834	1229	18	m	m	NOUN
ejpam-6834	1229	19	,	,	PUNCT
ejpam-6834	1229	20	n	n	CCONJ
ejpam-6834	1229	21	)	)	PUNCT
ejpam-6834	1229	22	v	v	NOUN
ejpam-6834	1229	23	(	(	PUNCT
ejpam-6834	1229	24	ι(b	ι(b	PROPN
ejpam-6834	1229	25	)	)	PUNCT
ejpam-6834	1229	26	,	,	PUNCT
ejpam-6834	1229	27	a	a	PRON
ejpam-6834	1229	28	)	)	PUNCT
ejpam-6834	1229	29	together	together	ADV
ejpam-6834	1229	30	with	with	ADP
ejpam-6834	1229	31	pcf	pcf	PROPN
ejpam-6834	1229	32	yields	yield	VERB
ejpam-6834	1229	33	an	an	DET
ejpam-6834	1229	34	(	(	PUNCT
ejpam-6834	1229	35	h−	h−	NOUN
ejpam-6834	1229	36	r	r	NOUN
ejpam-6834	1229	37	,	,	PUNCT
ejpam-6834	1229	38	k)-ary	k)-ary	X
ejpam-6834	1229	39	(	(	PUNCT
ejpam-6834	1229	40	m	m	PROPN
ejpam-6834	1229	41	,	,	PUNCT
ejpam-6834	1229	42	n)-superhyperplithogenic	n)-superhyperplithogenic	PUNCT
ejpam-6834	1229	43	set	set	NOUN
ejpam-6834	1229	44	.	.	PUNCT
ejpam-6834	1230	1	proof	proof	NOUN
ejpam-6834	1230	2	.	.	PUNCT
ejpam-6834	1231	1	let	let	VERB
ejpam-6834	1231	2	b	b	NOUN
ejpam-6834	1231	3	=	=	SYM
ejpam-6834	1231	4	(	(	PUNCT
ejpam-6834	1231	5	bℓ)ℓ∈ifree	bℓ)ℓ∈ifree	NUM
ejpam-6834	1231	6	∈	∈	PROPN
ejpam-6834	1231	7	(	(	PUNCT
ejpam-6834	1231	8	pm	pm	NOUN
ejpam-6834	1231	9	+	+	CCONJ
ejpam-6834	1231	10	(	(	PUNCT
ejpam-6834	1231	11	p	p	NOUN
ejpam-6834	1231	12	)	)	PUNCT
ejpam-6834	1231	13	)	)	PUNCT
ejpam-6834	1232	1	h−r	h−r	NOUN
ejpam-6834	1232	2	,	,	PUNCT
ejpam-6834	1232	3	where	where	SCONJ
ejpam-6834	1232	4	i	i	PRON
ejpam-6834	1232	5	free	free	VERB
ejpam-6834	1232	6	=	=	PUNCT
ejpam-6834	1232	7	{	{	PUNCT
ejpam-6834	1232	8	1	1	NUM
ejpam-6834	1232	9	,	,	PUNCT
ejpam-6834	1232	10	.	.	PUNCT
ejpam-6834	1232	11	.	.	PUNCT
ejpam-6834	1232	12	.	.	PUNCT
ejpam-6834	1233	1	,	,	PUNCT
ejpam-6834	1233	2	h}\{i1	h}\{i1	ADV
ejpam-6834	1233	3	,	,	PUNCT
ejpam-6834	1233	4	.	.	PUNCT
ejpam-6834	1233	5	.	.	PUNCT
ejpam-6834	1233	6	.	.	PUNCT
ejpam-6834	1234	1	,	,	PUNCT
ejpam-6834	1234	2	ir	ir	PROPN
ejpam-6834	1234	3	}	}	PUNCT
ejpam-6834	1234	4	.	.	PUNCT
ejpam-6834	1235	1	define	define	VERB
ejpam-6834	1235	2	the	the	DET
ejpam-6834	1235	3	h	h	NOUN
ejpam-6834	1235	4	–	–	PUNCT
ejpam-6834	1235	5	tuple	tuple	NOUN
ejpam-6834	1235	6	ι(b	ι(b	NOUN
ejpam-6834	1235	7	)	)	PUNCT
ejpam-6834	1236	1	=	=	SYM
ejpam-6834	1236	2	(	(	PUNCT
ejpam-6834	1236	3	c1	c1	PROPN
ejpam-6834	1236	4	,	,	PUNCT
ejpam-6834	1236	5	.	.	PUNCT
ejpam-6834	1236	6	.	.	PUNCT
ejpam-6834	1237	1	.	.	PUNCT
ejpam-6834	1238	1	,	,	PUNCT
ejpam-6834	1238	2	ch	ch	NOUN
ejpam-6834	1238	3	)	)	PUNCT
ejpam-6834	1238	4	by	by	ADP
ejpam-6834	1238	5	cu	cu	PROPN
ejpam-6834	1238	6	=	=	PROPN
ejpam-6834	1238	7	{	{	PUNCT
ejpam-6834	1238	8	aij	aij	PROPN
ejpam-6834	1238	9	,	,	PUNCT
ejpam-6834	1238	10	u	u	NOUN
ejpam-6834	1239	1	=	=	NOUN
ejpam-6834	1239	2	ij	ij	NOUN
ejpam-6834	1239	3	for	for	ADP
ejpam-6834	1239	4	some	some	DET
ejpam-6834	1239	5	j	j	PROPN
ejpam-6834	1239	6	,	,	PUNCT
ejpam-6834	1239	7	bℓ	bℓ	PROPN
ejpam-6834	1239	8	,	,	PUNCT
ejpam-6834	1239	9	u	u	NOUN
ejpam-6834	1239	10	=	=	PROPN
ejpam-6834	1239	11	ℓ	ℓ	PROPN
ejpam-6834	1239	12	∈	∈	PROPN
ejpam-6834	1239	13	i	i	PRON
ejpam-6834	1239	14	free	free	ADJ
ejpam-6834	1239	15	.	.	PUNCT
ejpam-6834	1240	1	thus	thus	ADV
ejpam-6834	1240	2	ι(b	ι(b	NUM
ejpam-6834	1240	3	)	)	PUNCT
ejpam-6834	1240	4	∈	∈	PROPN
ejpam-6834	1240	5	(	(	PUNCT
ejpam-6834	1240	6	pm	pm	NOUN
ejpam-6834	1240	7	+	+	CCONJ
ejpam-6834	1240	8	(	(	PUNCT
ejpam-6834	1240	9	p	p	NOUN
ejpam-6834	1240	10	)	)	PUNCT
ejpam-6834	1240	11	)	)	PUNCT
ejpam-6834	1241	1	h.	h.	NOUN
ejpam-6834	1241	2	for	for	ADP
ejpam-6834	1241	3	any	any	DET
ejpam-6834	1241	4	a	a	DET
ejpam-6834	1241	5	∈	∈	ADJ
ejpam-6834	1241	6	pv	pv	NOUN
ejpam-6834	1241	7	,	,	PUNCT
ejpam-6834	1241	8	˜pdf	˜pdf	NOUN
ejpam-6834	1241	9	(	(	PUNCT
ejpam-6834	1241	10	m	m	NOUN
ejpam-6834	1241	11	,	,	PUNCT
ejpam-6834	1241	12	n	n	CCONJ
ejpam-6834	1241	13	)	)	PUNCT
ejpam-6834	1241	14	fix	fix	NOUN
ejpam-6834	1241	15	(	(	PUNCT
ejpam-6834	1241	16	b	b	NOUN
ejpam-6834	1241	17	,	,	PUNCT
ejpam-6834	1241	18	a	a	PRON
ejpam-6834	1241	19	)	)	PUNCT
ejpam-6834	1241	20	=	=	SYM
ejpam-6834	1241	21	˜pdf	˜pdf	NOUN
ejpam-6834	1241	22	(	(	PUNCT
ejpam-6834	1241	23	m	m	NOUN
ejpam-6834	1241	24	,	,	PUNCT
ejpam-6834	1241	25	n	n	CCONJ
ejpam-6834	1241	26	)	)	PUNCT
ejpam-6834	1241	27	v	v	NOUN
ejpam-6834	1241	28	(	(	PUNCT
ejpam-6834	1241	29	ι(b	ι(b	PROPN
ejpam-6834	1241	30	)	)	PUNCT
ejpam-6834	1241	31	,	,	PUNCT
ejpam-6834	1241	32	a	a	X
ejpam-6834	1241	33	)	)	PUNCT
ejpam-6834	1241	34	∈	∈	PROPN
ejpam-6834	1241	35	(	(	PUNCT
ejpam-6834	1241	36	pn	pn	NOUN
ejpam-6834	1241	37	+	+	PROPN
ejpam-6834	1241	38	(	(	PUNCT
ejpam-6834	1241	39	[	[	NOUN
ejpam-6834	1241	40	0	0	NUM
ejpam-6834	1241	41	,	,	PUNCT
ejpam-6834	1241	42	1]s))k	1]s))k	PROPN
ejpam-6834	1241	43	has	have	AUX
ejpam-6834	1241	44	nonempty	nonempty	VERB
ejpam-6834	1241	45	coordinates	coordinate	NOUN
ejpam-6834	1241	46	because	because	SCONJ
ejpam-6834	1241	47	˜pdf	˜pdf	NOUN
ejpam-6834	1241	48	(	(	PUNCT
ejpam-6834	1241	49	m	m	NOUN
ejpam-6834	1241	50	,	,	PUNCT
ejpam-6834	1241	51	n	n	CCONJ
ejpam-6834	1241	52	)	)	PUNCT
ejpam-6834	1241	53	v	v	NOUN
ejpam-6834	1241	54	does	do	VERB
ejpam-6834	1241	55	so	so	ADV
ejpam-6834	1241	56	for	for	ADP
ejpam-6834	1241	57	every	every	DET
ejpam-6834	1241	58	h	h	NOUN
ejpam-6834	1241	59	–	–	PUNCT
ejpam-6834	1241	60	tuple	tuple	NOUN
ejpam-6834	1241	61	.	.	PUNCT
ejpam-6834	1242	1	hence	hence	ADV
ejpam-6834	1242	2	˜pdf	˜pdf	NOUN
ejpam-6834	1242	3	(	(	PUNCT
ejpam-6834	1242	4	m	m	NOUN
ejpam-6834	1242	5	,	,	PUNCT
ejpam-6834	1242	6	n	n	CCONJ
ejpam-6834	1242	7	)	)	PUNCT
ejpam-6834	1242	8	fix	fix	NOUN
ejpam-6834	1242	9	is	be	AUX
ejpam-6834	1242	10	a	a	DET
ejpam-6834	1242	11	valid	valid	ADJ
ejpam-6834	1242	12	hyper	hyper	NOUN
ejpam-6834	1242	13	degree	degree	NOUN
ejpam-6834	1242	14	function	function	NOUN
ejpam-6834	1242	15	on	on	ADP
ejpam-6834	1242	16	the	the	DET
ejpam-6834	1242	17	smaller	small	ADJ
ejpam-6834	1242	18	domain	domain	NOUN
ejpam-6834	1242	19	(	(	PUNCT
ejpam-6834	1242	20	pm	pm	NOUN
ejpam-6834	1242	21	+	+	CCONJ
ejpam-6834	1242	22	(	(	PUNCT
ejpam-6834	1242	23	p	p	NOUN
ejpam-6834	1242	24	)	)	PUNCT
ejpam-6834	1242	25	)	)	PUNCT
ejpam-6834	1243	1	h−r	h−r	ADV
ejpam-6834	1243	2	×	×	NOUN
ejpam-6834	1243	3	pv	pv	INTJ
ejpam-6834	1243	4	.	.	PUNCT
ejpam-6834	1244	1	the	the	DET
ejpam-6834	1244	2	contradiction	contradiction	NOUN
ejpam-6834	1244	3	function	function	NOUN
ejpam-6834	1244	4	pcf	pcf	PROPN
ejpam-6834	1244	5	is	be	AUX
ejpam-6834	1244	6	defined	define	VERB
ejpam-6834	1244	7	only	only	ADV
ejpam-6834	1244	8	on	on	ADP
ejpam-6834	1244	9	pv	pv	INTJ
ejpam-6834	1244	10	×pv	×pv	PROPN
ejpam-6834	1244	11	and	and	CCONJ
ejpam-6834	1244	12	does	do	AUX
ejpam-6834	1244	13	not	not	PART
ejpam-6834	1244	14	depend	depend	VERB
ejpam-6834	1244	15	on	on	ADP
ejpam-6834	1244	16	the	the	DET
ejpam-6834	1244	17	arity	arity	NOUN
ejpam-6834	1244	18	of	of	ADP
ejpam-6834	1244	19	the	the	DET
ejpam-6834	1244	20	domain	domain	NOUN
ejpam-6834	1244	21	;	;	PUNCT
ejpam-6834	1244	22	its	its	PRON
ejpam-6834	1244	23	axioms	axiom	NOUN
ejpam-6834	1244	24	(	(	PUNCT
ejpam-6834	1244	25	reflexivity	reflexivity	NOUN
ejpam-6834	1244	26	,	,	PUNCT
ejpam-6834	1244	27	symmetry	symmetry	NOUN
ejpam-6834	1244	28	)	)	PUNCT
ejpam-6834	1244	29	are	be	AUX
ejpam-6834	1244	30	preserved	preserve	VERB
ejpam-6834	1244	31	.	.	PUNCT
ejpam-6834	1245	1	theorem	theorem	VERB
ejpam-6834	1245	2	41	41	NUM
ejpam-6834	1245	3	(	(	PUNCT
ejpam-6834	1245	4	projection	projection	NOUN
ejpam-6834	1245	5	to	to	ADP
ejpam-6834	1245	6	fewer	few	ADJ
ejpam-6834	1245	7	outputs	output	NOUN
ejpam-6834	1245	8	)	)	PUNCT
ejpam-6834	1245	9	.	.	PUNCT
ejpam-6834	1246	1	let	let	VERB
ejpam-6834	1246	2	1	1	NUM
ejpam-6834	1246	3	≤	≤	NOUN
ejpam-6834	1246	4	j1	j1	X
ejpam-6834	1246	5	<	<	X
ejpam-6834	1246	6	·	·	PUNCT
ejpam-6834	1246	7	·	·	PUNCT
ejpam-6834	1246	8	·	·	PUNCT
ejpam-6834	1247	1	<	<	X
ejpam-6834	1247	2	js	js	PROPN
ejpam-6834	1247	3	≤	≤	PROPN
ejpam-6834	1247	4	k.	k.	PROPN
ejpam-6834	1247	5	define	define	VERB
ejpam-6834	1247	6	πj1,	πj1,	PRON
ejpam-6834	1247	7	...	...	PUNCT
ejpam-6834	1247	8	,js	,js	PUNCT
ejpam-6834	1247	9	:	:	PUNCT
ejpam-6834	1247	10	c	c	X
ejpam-6834	1247	11	→	→	PUNCT
ejpam-6834	1247	12	(	(	PUNCT
ejpam-6834	1247	13	pn	pn	NOUN
ejpam-6834	1247	14	+	+	PROPN
ejpam-6834	1247	15	(	(	PUNCT
ejpam-6834	1247	16	[	[	NOUN
ejpam-6834	1247	17	0	0	NUM
ejpam-6834	1247	18	,	,	PUNCT
ejpam-6834	1247	19	1]s	1]s	NUM
ejpam-6834	1247	20	)	)	PUNCT
ejpam-6834	1247	21	)	)	PUNCT
ejpam-6834	1247	22	s	s	X
ejpam-6834	1247	23	by	by	ADP
ejpam-6834	1247	24	πj1,	πj1,	PRON
ejpam-6834	1247	25	...	...	PUNCT
ejpam-6834	1247	26	,js(b1	,js(b1	PUNCT
ejpam-6834	1247	27	,	,	PUNCT
ejpam-6834	1247	28	.	.	PUNCT
ejpam-6834	1247	29	.	.	PUNCT
ejpam-6834	1248	1	.	.	PUNCT
ejpam-6834	1249	1	,	,	PUNCT
ejpam-6834	1249	2	bk	bk	X
ejpam-6834	1249	3	)	)	PUNCT
ejpam-6834	1249	4	:	:	PUNCT
ejpam-6834	1250	1	=	=	SYM
ejpam-6834	1250	2	(	(	PUNCT
ejpam-6834	1250	3	bj1	bj1	ADJ
ejpam-6834	1250	4	,	,	PUNCT
ejpam-6834	1250	5	.	.	PUNCT
ejpam-6834	1250	6	.	.	PUNCT
ejpam-6834	1250	7	.	.	PUNCT
ejpam-6834	1251	1	,	,	PUNCT
ejpam-6834	1251	2	bjs	bjs	PROPN
ejpam-6834	1251	3	)	)	PUNCT
ejpam-6834	1251	4	.	.	PUNCT
ejpam-6834	1252	1	then	then	ADV
ejpam-6834	1252	2	(	(	PUNCT
ejpam-6834	1252	3	a	a	PRON
ejpam-6834	1252	4	,	,	PUNCT
ejpam-6834	1252	5	a	a	PRON
ejpam-6834	1252	6	)	)	PUNCT
ejpam-6834	1252	7	7→	7→	NUM
ejpam-6834	1252	8	πj1,	πj1,	NOUN
ejpam-6834	1252	9	...	...	PUNCT
ejpam-6834	1252	10	,js	,js	PUNCT
ejpam-6834	1252	11	(	(	PUNCT
ejpam-6834	1252	12	˜pdf	˜pdf	X
ejpam-6834	1252	13	(	(	PUNCT
ejpam-6834	1252	14	m	m	NOUN
ejpam-6834	1252	15	,	,	PUNCT
ejpam-6834	1252	16	n	n	CCONJ
ejpam-6834	1252	17	)	)	PUNCT
ejpam-6834	1252	18	v	v	NOUN
ejpam-6834	1252	19	(	(	PUNCT
ejpam-6834	1252	20	a	a	DET
ejpam-6834	1252	21	,	,	PUNCT
ejpam-6834	1252	22	a	a	NOUN
ejpam-6834	1252	23	)	)	PUNCT
ejpam-6834	1252	24	)	)	PUNCT
ejpam-6834	1252	25	(	(	PUNCT
ejpam-6834	1252	26	with	with	ADP
ejpam-6834	1252	27	d	d	PROPN
ejpam-6834	1252	28	and	and	CCONJ
ejpam-6834	1252	29	the	the	DET
ejpam-6834	1252	30	same	same	ADJ
ejpam-6834	1252	31	pcf	pcf	PROPN
ejpam-6834	1252	32	)	)	PUNCT
ejpam-6834	1252	33	defines	define	VERB
ejpam-6834	1252	34	an	an	DET
ejpam-6834	1252	35	(	(	PUNCT
ejpam-6834	1252	36	h	h	NOUN
ejpam-6834	1252	37	,	,	PUNCT
ejpam-6834	1252	38	s)-ary	s)-ary	NOUN
ejpam-6834	1252	39	(	(	PUNCT
ejpam-6834	1252	40	m	m	PROPN
ejpam-6834	1252	41	,	,	PUNCT
ejpam-6834	1252	42	n)-superhyperplithogenic	n)-superhyperplithogenic	PUNCT
ejpam-6834	1252	43	set	set	NOUN
ejpam-6834	1252	44	.	.	PUNCT
ejpam-6834	1253	1	proof	proof	NOUN
ejpam-6834	1253	2	.	.	PUNCT
ejpam-6834	1254	1	fix	fix	NOUN
ejpam-6834	1254	2	(	(	PUNCT
ejpam-6834	1254	3	a	a	PRON
ejpam-6834	1254	4	,	,	PUNCT
ejpam-6834	1254	5	a	a	PRON
ejpam-6834	1254	6	)	)	PUNCT
ejpam-6834	1254	7	∈	∈	PROPN
ejpam-6834	1255	1	d	d	X
ejpam-6834	1255	2	×	×	NOUN
ejpam-6834	1255	3	pv	pv	INTJ
ejpam-6834	1255	4	.	.	PUNCT
ejpam-6834	1256	1	since	since	SCONJ
ejpam-6834	1256	2	˜pdf	˜pdf	NOUN
ejpam-6834	1256	3	(	(	PUNCT
ejpam-6834	1256	4	m	m	NOUN
ejpam-6834	1256	5	,	,	PUNCT
ejpam-6834	1256	6	n	n	CCONJ
ejpam-6834	1256	7	)	)	PUNCT
ejpam-6834	1256	8	v	v	NOUN
ejpam-6834	1256	9	(	(	PUNCT
ejpam-6834	1256	10	a	a	PRON
ejpam-6834	1256	11	,	,	PUNCT
ejpam-6834	1256	12	a	a	NOUN
ejpam-6834	1256	13	)	)	PUNCT
ejpam-6834	1256	14	=	=	SYM
ejpam-6834	1256	15	(	(	PUNCT
ejpam-6834	1256	16	b1	b1	NOUN
ejpam-6834	1256	17	,	,	PUNCT
ejpam-6834	1256	18	.	.	PUNCT
ejpam-6834	1256	19	.	.	PUNCT
ejpam-6834	1256	20	.	.	PUNCT
ejpam-6834	1257	1	,	,	PUNCT
ejpam-6834	1257	2	bk	bk	VERB
ejpam-6834	1257	3	)	)	PUNCT
ejpam-6834	1257	4	∈	∈	PROPN
ejpam-6834	1257	5	c	c	NOUN
ejpam-6834	1257	6	,	,	PUNCT
ejpam-6834	1257	7	each	each	DET
ejpam-6834	1257	8	bjr	bjr	NOUN
ejpam-6834	1257	9	is	be	AUX
ejpam-6834	1257	10	a	a	DET
ejpam-6834	1257	11	nonempty	nonempty	ADJ
ejpam-6834	1257	12	element	element	NOUN
ejpam-6834	1257	13	of	of	ADP
ejpam-6834	1257	14	pn	pn	PROPN
ejpam-6834	1257	15	+	+	PROPN
ejpam-6834	1257	16	(	(	PUNCT
ejpam-6834	1257	17	[	[	NOUN
ejpam-6834	1257	18	0	0	NUM
ejpam-6834	1257	19	,	,	PUNCT
ejpam-6834	1257	20	1]s	1]s	NUM
ejpam-6834	1257	21	)	)	PUNCT
ejpam-6834	1257	22	.	.	PUNCT
ejpam-6834	1258	1	therefore	therefore	ADV
ejpam-6834	1258	2	πj1,	πj1,	PRON
ejpam-6834	1258	3	...	...	PUNCT
ejpam-6834	1258	4	,js	,js	PUNCT
ejpam-6834	1258	5	(	(	PUNCT
ejpam-6834	1258	6	˜pdf	˜pdf	X
ejpam-6834	1258	7	(	(	PUNCT
ejpam-6834	1258	8	m	m	NOUN
ejpam-6834	1258	9	,	,	PUNCT
ejpam-6834	1258	10	n	n	CCONJ
ejpam-6834	1258	11	)	)	PUNCT
ejpam-6834	1258	12	v	v	NOUN
ejpam-6834	1258	13	(	(	PUNCT
ejpam-6834	1258	14	a	a	PRON
ejpam-6834	1258	15	,	,	PUNCT
ejpam-6834	1258	16	a	a	NOUN
ejpam-6834	1258	17	)	)	PUNCT
ejpam-6834	1258	18	)	)	PUNCT
ejpam-6834	1259	1	=	=	SYM
ejpam-6834	1259	2	(	(	PUNCT
ejpam-6834	1259	3	bj1	bj1	INTJ
ejpam-6834	1259	4	,	,	PUNCT
ejpam-6834	1259	5	.	.	PUNCT
ejpam-6834	1259	6	.	.	PUNCT
ejpam-6834	1259	7	.	.	PUNCT
ejpam-6834	1260	1	,	,	PUNCT
ejpam-6834	1260	2	bjs	bjs	NOUN
ejpam-6834	1260	3	)	)	PUNCT
ejpam-6834	1260	4	∈	∈	PROPN
ejpam-6834	1260	5	(	(	PUNCT
ejpam-6834	1260	6	pn	pn	NOUN
ejpam-6834	1260	7	+	+	PROPN
ejpam-6834	1260	8	(	(	PUNCT
ejpam-6834	1260	9	[	[	NOUN
ejpam-6834	1260	10	0	0	NUM
ejpam-6834	1260	11	,	,	PUNCT
ejpam-6834	1260	12	1]s	1]s	NUM
ejpam-6834	1260	13	)	)	PUNCT
ejpam-6834	1260	14	)	)	PUNCT
ejpam-6834	1261	1	s	s	X
ejpam-6834	1261	2	.	.	PUNCT
ejpam-6834	1262	1	nonemptiness	nonemptiness	NOUN
ejpam-6834	1262	2	and	and	CCONJ
ejpam-6834	1262	3	level	level	NOUN
ejpam-6834	1262	4	–	–	PUNCT
ejpam-6834	1262	5	n	n	CCONJ
ejpam-6834	1262	6	nesting	nesting	NOUN
ejpam-6834	1262	7	are	be	AUX
ejpam-6834	1262	8	preserved	preserve	VERB
ejpam-6834	1262	9	coordinatewise	coordinatewise	NOUN
ejpam-6834	1262	10	.	.	PUNCT
ejpam-6834	1263	1	the	the	DET
ejpam-6834	1263	2	domain	domain	NOUN
ejpam-6834	1263	3	d	d	NOUN
ejpam-6834	1263	4	and	and	CCONJ
ejpam-6834	1263	5	the	the	DET
ejpam-6834	1263	6	contradiction	contradiction	NOUN
ejpam-6834	1263	7	function	function	NOUN
ejpam-6834	1263	8	pcf	pcf	PROPN
ejpam-6834	1263	9	remain	remain	VERB
ejpam-6834	1263	10	unchanged	unchanged	ADJ
ejpam-6834	1263	11	,	,	PUNCT
ejpam-6834	1263	12	so	so	CCONJ
ejpam-6834	1263	13	the	the	DET
ejpam-6834	1263	14	projected	project	VERB
ejpam-6834	1263	15	structure	structure	NOUN
ejpam-6834	1263	16	satisfies	satisfy	VERB
ejpam-6834	1263	17	definition	definition	NOUN
ejpam-6834	1263	18	24	24	NUM
ejpam-6834	1263	19	with	with	ADP
ejpam-6834	1263	20	output	output	NOUN
ejpam-6834	1263	21	arity	arity	NOUN
ejpam-6834	1263	22	s.	s.	PROPN
ejpam-6834	1263	23	t.	t.	PROPN
ejpam-6834	1263	24	fujita	fujita	PROPN
ejpam-6834	1263	25	,	,	PUNCT
ejpam-6834	1263	26	f.smarandache	f.smarandache	NOUN
ejpam-6834	1263	27	/	/	SYM
ejpam-6834	1263	28	eur	eur	PROPN
ejpam-6834	1263	29	.	.	PUNCT
ejpam-6834	1264	1	j.	j.	PROPN
ejpam-6834	1264	2	pure	pure	PROPN
ejpam-6834	1264	3	appl	appl	PROPN
ejpam-6834	1264	4	.	.	PROPN
ejpam-6834	1264	5	math	math	PROPN
ejpam-6834	1264	6	,	,	PUNCT
ejpam-6834	1264	7	18	18	NUM
ejpam-6834	1264	8	(	(	PUNCT
ejpam-6834	1264	9	4	4	NUM
ejpam-6834	1264	10	)	)	PUNCT
ejpam-6834	1264	11	(	(	PUNCT
ejpam-6834	1264	12	2025	2025	NUM
ejpam-6834	1264	13	)	)	PUNCT
ejpam-6834	1264	14	,	,	PUNCT
ejpam-6834	1264	15	6834	6834	NUM
ejpam-6834	1264	16	49	49	NUM
ejpam-6834	1264	17	of	of	ADP
ejpam-6834	1264	18	69	69	NUM
ejpam-6834	1264	19	theorem	theorem	NOUN
ejpam-6834	1264	20	42	42	NUM
ejpam-6834	1264	21	(	(	PUNCT
ejpam-6834	1264	22	closure	closure	NOUN
ejpam-6834	1264	23	under	under	ADP
ejpam-6834	1264	24	pointwise	pointwise	PROPN
ejpam-6834	1264	25	union	union	NOUN
ejpam-6834	1264	26	)	)	PUNCT
ejpam-6834	1264	27	.	.	PUNCT
ejpam-6834	1265	1	if	if	SCONJ
ejpam-6834	1265	2	˜pdf	˜pdf	NOUN
ejpam-6834	1265	3	,	,	PUNCT
ejpam-6834	1265	4	˜pdf	˜pdf	NOUN
ejpam-6834	1265	5	′	′	NUM
ejpam-6834	1265	6	:	:	PUNCT
ejpam-6834	1266	1	d×pv	d×pv	X
ejpam-6834	1266	2	→	→	PUNCT
ejpam-6834	1266	3	c	c	X
ejpam-6834	1266	4	are	be	AUX
ejpam-6834	1266	5	hyper	hyper	NOUN
ejpam-6834	1266	6	degree	degree	NOUN
ejpam-6834	1266	7	functions	function	NOUN
ejpam-6834	1266	8	(	(	PUNCT
ejpam-6834	1266	9	with	with	ADP
ejpam-6834	1266	10	the	the	DET
ejpam-6834	1266	11	same	same	ADJ
ejpam-6834	1266	12	pcf	pcf	PROPN
ejpam-6834	1266	13	)	)	PUNCT
ejpam-6834	1266	14	,	,	PUNCT
ejpam-6834	1266	15	then	then	ADV
ejpam-6834	1266	16	(	(	PUNCT
ejpam-6834	1266	17	˜pdf	˜pdf	NOUN
ejpam-6834	1266	18	∪	∪	X
ejpam-6834	1266	19	˜pdf	˜pdf	NOUN
ejpam-6834	1266	20	′	′	NUM
ejpam-6834	1266	21	)	)	PUNCT
ejpam-6834	1266	22	(	(	PUNCT
ejpam-6834	1266	23	a	a	PRON
ejpam-6834	1266	24	,	,	PUNCT
ejpam-6834	1266	25	a	a	NOUN
ejpam-6834	1266	26	)	)	PUNCT
ejpam-6834	1266	27	:	:	PUNCT
ejpam-6834	1266	28	=	=	PUNCT
ejpam-6834	1266	29	˜pdf(a	˜pdf(a	PROPN
ejpam-6834	1266	30	,	,	PUNCT
ejpam-6834	1266	31	a	a	PRON
ejpam-6834	1266	32	)	)	PUNCT
ejpam-6834	1266	33	∪	∪	X
ejpam-6834	1266	34	˜pdf	˜pdf	NOUN
ejpam-6834	1266	35	′	′	NUM
ejpam-6834	1266	36	(	(	PUNCT
ejpam-6834	1266	37	a	a	PRON
ejpam-6834	1266	38	,	,	PUNCT
ejpam-6834	1266	39	a	a	NOUN
ejpam-6834	1266	40	)	)	PUNCT
ejpam-6834	1266	41	(	(	PUNCT
ejpam-6834	1266	42	where	where	SCONJ
ejpam-6834	1266	43	the	the	DET
ejpam-6834	1266	44	union	union	NOUN
ejpam-6834	1266	45	is	be	AUX
ejpam-6834	1266	46	taken	take	VERB
ejpam-6834	1266	47	coordinatewise	coordinatewise	NOUN
ejpam-6834	1266	48	in	in	ADP
ejpam-6834	1266	49	c	c	NOUN
ejpam-6834	1266	50	)	)	PUNCT
ejpam-6834	1266	51	defines	define	VERB
ejpam-6834	1266	52	another	another	DET
ejpam-6834	1266	53	hyper	hyper	ADJ
ejpam-6834	1266	54	degree	degree	NOUN
ejpam-6834	1266	55	function	function	NOUN
ejpam-6834	1266	56	,	,	PUNCT
ejpam-6834	1266	57	hence	hence	ADV
ejpam-6834	1266	58	an	an	DET
ejpam-6834	1266	59	(	(	PUNCT
ejpam-6834	1266	60	h	h	NOUN
ejpam-6834	1266	61	,	,	PUNCT
ejpam-6834	1266	62	k)-ary	k)-ary	X
ejpam-6834	1266	63	(	(	PUNCT
ejpam-6834	1266	64	m	m	PROPN
ejpam-6834	1266	65	,	,	PUNCT
ejpam-6834	1266	66	n)-superhyperplithogenic	n)-superhyperplithogenic	PUNCT
ejpam-6834	1266	67	set	set	NOUN
ejpam-6834	1266	68	.	.	PUNCT
ejpam-6834	1267	1	proof	proof	NOUN
ejpam-6834	1267	2	.	.	PUNCT
ejpam-6834	1268	1	fix	fix	NOUN
ejpam-6834	1268	2	(	(	PUNCT
ejpam-6834	1268	3	a	a	PRON
ejpam-6834	1268	4	,	,	PUNCT
ejpam-6834	1268	5	a	a	NOUN
ejpam-6834	1268	6	)	)	PUNCT
ejpam-6834	1268	7	.	.	PUNCT
ejpam-6834	1269	1	write	write	VERB
ejpam-6834	1269	2	˜pdf(a	˜pdf(a	PROPN
ejpam-6834	1269	3	,	,	PUNCT
ejpam-6834	1269	4	a	a	PRON
ejpam-6834	1269	5	)	)	PUNCT
ejpam-6834	1269	6	=	=	SYM
ejpam-6834	1269	7	(	(	PUNCT
ejpam-6834	1269	8	b1	b1	NOUN
ejpam-6834	1269	9	,	,	PUNCT
ejpam-6834	1269	10	.	.	PUNCT
ejpam-6834	1269	11	.	.	PUNCT
ejpam-6834	1269	12	.	.	PUNCT
ejpam-6834	1270	1	,	,	PUNCT
ejpam-6834	1270	2	bk	bk	X
ejpam-6834	1270	3	)	)	PUNCT
ejpam-6834	1270	4	and	and	CCONJ
ejpam-6834	1270	5	˜pdf	˜pdf	NOUN
ejpam-6834	1271	1	′	′	NUM
ejpam-6834	1271	2	(	(	PUNCT
ejpam-6834	1271	3	a	a	PRON
ejpam-6834	1271	4	,	,	PUNCT
ejpam-6834	1271	5	a	a	NOUN
ejpam-6834	1271	6	)	)	PUNCT
ejpam-6834	1271	7	=	=	SYM
ejpam-6834	1271	8	(	(	PUNCT
ejpam-6834	1271	9	b′	b′	NOUN
ejpam-6834	1271	10	1	1	NUM
ejpam-6834	1271	11	,	,	PUNCT
ejpam-6834	1271	12	.	.	PUNCT
ejpam-6834	1271	13	.	.	PUNCT
ejpam-6834	1271	14	.	.	PUNCT
ejpam-6834	1272	1	,	,	PUNCT
ejpam-6834	1272	2	b	b	X
ejpam-6834	1272	3	′	′	NUM
ejpam-6834	1273	1	k	k	NOUN
ejpam-6834	1273	2	)	)	PUNCT
ejpam-6834	1273	3	,	,	PUNCT
ejpam-6834	1273	4	with	with	ADP
ejpam-6834	1273	5	bj	bj	NOUN
ejpam-6834	1273	6	,	,	PUNCT
ejpam-6834	1273	7	b	b	NOUN
ejpam-6834	1273	8	′	′	NUM
ejpam-6834	1273	9	j	j	PROPN
ejpam-6834	1273	10	∈	∈	PROPN
ejpam-6834	1273	11	pn	pn	PROPN
ejpam-6834	1274	1	+	+	PROPN
ejpam-6834	1274	2	(	(	PUNCT
ejpam-6834	1274	3	[	[	NOUN
ejpam-6834	1274	4	0	0	NUM
ejpam-6834	1274	5	,	,	PUNCT
ejpam-6834	1274	6	1]s	1]s	NUM
ejpam-6834	1274	7	)	)	PUNCT
ejpam-6834	1274	8	.	.	PUNCT
ejpam-6834	1275	1	we	we	PRON
ejpam-6834	1275	2	show	show	VERB
ejpam-6834	1275	3	by	by	ADP
ejpam-6834	1275	4	induction	induction	NOUN
ejpam-6834	1275	5	on	on	ADP
ejpam-6834	1275	6	n	n	PRON
ejpam-6834	1275	7	≥	≥	NUM
ejpam-6834	1275	8	1	1	NUM
ejpam-6834	1275	9	that	that	PRON
ejpam-6834	1275	10	bj	bj	VERB
ejpam-6834	1275	11	∪b′	∪b′	NOUN
ejpam-6834	1275	12	j	j	PROPN
ejpam-6834	1275	13	∈	∈	PROPN
ejpam-6834	1275	14	pn	pn	PROPN
ejpam-6834	1276	1	+	+	PROPN
ejpam-6834	1276	2	(	(	PUNCT
ejpam-6834	1276	3	[	[	NOUN
ejpam-6834	1276	4	0	0	NUM
ejpam-6834	1276	5	,	,	PUNCT
ejpam-6834	1276	6	1]s	1]s	NUM
ejpam-6834	1276	7	)	)	PUNCT
ejpam-6834	1276	8	.	.	PUNCT
ejpam-6834	1277	1	base	base	NOUN
ejpam-6834	1277	2	n	n	NOUN
ejpam-6834	1277	3	=	=	SYM
ejpam-6834	1277	4	1	1	NUM
ejpam-6834	1277	5	:	:	PUNCT
ejpam-6834	1277	6	bj	bj	NOUN
ejpam-6834	1277	7	and	and	CCONJ
ejpam-6834	1277	8	b′	b′	NUM
ejpam-6834	1277	9	j	j	NOUN
ejpam-6834	1277	10	are	be	AUX
ejpam-6834	1277	11	nonempty	nonempty	ADJ
ejpam-6834	1277	12	subsets	subset	NOUN
ejpam-6834	1277	13	of	of	ADP
ejpam-6834	1277	14	[	[	X
ejpam-6834	1277	15	0	0	NUM
ejpam-6834	1277	16	,	,	PUNCT
ejpam-6834	1277	17	1]s	1]s	NUM
ejpam-6834	1277	18	,	,	PUNCT
ejpam-6834	1277	19	so	so	ADV
ejpam-6834	1277	20	bj	bj	VERB
ejpam-6834	1277	21	∪	∪	ADP
ejpam-6834	1277	22	b′	b′	NUM
ejpam-6834	1277	23	j	j	PROPN
ejpam-6834	1277	24	is	be	AUX
ejpam-6834	1277	25	a	a	DET
ejpam-6834	1277	26	nonempty	nonempty	NOUN
ejpam-6834	1277	27	subset	subset	NOUN
ejpam-6834	1277	28	of	of	ADP
ejpam-6834	1277	29	[	[	X
ejpam-6834	1277	30	0	0	NUM
ejpam-6834	1277	31	,	,	PUNCT
ejpam-6834	1277	32	1]s	1]s	NUM
ejpam-6834	1277	33	,	,	PUNCT
ejpam-6834	1277	34	i.e.	i.e.	X
ejpam-6834	1277	35	an	an	DET
ejpam-6834	1277	36	element	element	NOUN
ejpam-6834	1277	37	of	of	ADP
ejpam-6834	1277	38	p1	p1	PROPN
ejpam-6834	1277	39	+	+	PROPN
ejpam-6834	1277	40	(	(	PUNCT
ejpam-6834	1277	41	[	[	NOUN
ejpam-6834	1277	42	0	0	NUM
ejpam-6834	1277	43	,	,	PUNCT
ejpam-6834	1277	44	1]s	1]s	NUM
ejpam-6834	1277	45	)	)	PUNCT
ejpam-6834	1277	46	.	.	PUNCT
ejpam-6834	1278	1	inductive	inductive	ADJ
ejpam-6834	1278	2	step	step	NOUN
ejpam-6834	1278	3	:	:	PUNCT
ejpam-6834	1278	4	suppose	suppose	VERB
ejpam-6834	1278	5	the	the	DET
ejpam-6834	1278	6	claim	claim	NOUN
ejpam-6834	1278	7	holds	hold	VERB
ejpam-6834	1278	8	for	for	ADP
ejpam-6834	1278	9	level	level	NOUN
ejpam-6834	1278	10	n.	n.	NOUN
ejpam-6834	1278	11	let	let	VERB
ejpam-6834	1278	12	n+1	n+1	X
ejpam-6834	1278	13	.	.	PUNCT
ejpam-6834	1278	14	then	then	ADV
ejpam-6834	1278	15	bj	bj	VERB
ejpam-6834	1278	16	,	,	PUNCT
ejpam-6834	1278	17	b	b	PROPN
ejpam-6834	1278	18	′	′	NUM
ejpam-6834	1278	19	j	j	PROPN
ejpam-6834	1278	20	⊆	⊆	NUM
ejpam-6834	1278	21	pn	pn	PROPN
ejpam-6834	1278	22	+	+	PROPN
ejpam-6834	1278	23	(	(	PUNCT
ejpam-6834	1278	24	[	[	NOUN
ejpam-6834	1278	25	0	0	NUM
ejpam-6834	1278	26	,	,	PUNCT
ejpam-6834	1278	27	1]s	1]s	NUM
ejpam-6834	1278	28	)	)	PUNCT
ejpam-6834	1278	29	are	be	AUX
ejpam-6834	1278	30	nonempty	nonempty	ADJ
ejpam-6834	1278	31	families	family	NOUN
ejpam-6834	1278	32	of	of	ADP
ejpam-6834	1278	33	level	level	NOUN
ejpam-6834	1278	34	–	–	PUNCT
ejpam-6834	1278	35	n	n	PRON
ejpam-6834	1278	36	elements	element	NOUN
ejpam-6834	1278	37	.	.	PUNCT
ejpam-6834	1279	1	their	their	PRON
ejpam-6834	1279	2	union	union	NOUN
ejpam-6834	1279	3	bj	bj	VERB
ejpam-6834	1279	4	∪	∪	ADP
ejpam-6834	1279	5	b′	b′	NUM
ejpam-6834	1279	6	j	j	PROPN
ejpam-6834	1279	7	is	be	AUX
ejpam-6834	1279	8	nonempty	nonempty	X
ejpam-6834	1279	9	(	(	PUNCT
ejpam-6834	1279	10	as	as	ADP
ejpam-6834	1279	11	a	a	DET
ejpam-6834	1279	12	union	union	NOUN
ejpam-6834	1279	13	of	of	ADP
ejpam-6834	1279	14	two	two	NUM
ejpam-6834	1279	15	nonempty	nonempty	ADJ
ejpam-6834	1279	16	sets	set	NOUN
ejpam-6834	1279	17	)	)	PUNCT
ejpam-6834	1279	18	and	and	CCONJ
ejpam-6834	1279	19	every	every	DET
ejpam-6834	1279	20	element	element	NOUN
ejpam-6834	1279	21	of	of	ADP
ejpam-6834	1279	22	it	it	PRON
ejpam-6834	1279	23	still	still	ADV
ejpam-6834	1279	24	lies	lie	VERB
ejpam-6834	1279	25	in	in	ADP
ejpam-6834	1279	26	pn	pn	PROPN
ejpam-6834	1279	27	+	+	PROPN
ejpam-6834	1279	28	(	(	PUNCT
ejpam-6834	1279	29	[	[	X
ejpam-6834	1279	30	0	0	NUM
ejpam-6834	1279	31	,	,	PUNCT
ejpam-6834	1279	32	1]s	1]s	NUM
ejpam-6834	1279	33	)	)	PUNCT
ejpam-6834	1279	34	.	.	PUNCT
ejpam-6834	1280	1	hence	hence	ADV
ejpam-6834	1280	2	bj	bj	VERB
ejpam-6834	1280	3	∪	∪	ADP
ejpam-6834	1280	4	b′	b′	NUM
ejpam-6834	1280	5	j	j	PROPN
ejpam-6834	1280	6	∈	∈	PROPN
ejpam-6834	1280	7	pn+1	pn+1	PROPN
ejpam-6834	1280	8	+	+	CCONJ
ejpam-6834	1280	9	(	(	PUNCT
ejpam-6834	1280	10	[	[	X
ejpam-6834	1280	11	0	0	NUM
ejpam-6834	1280	12	,	,	PUNCT
ejpam-6834	1280	13	1]s	1]s	NUM
ejpam-6834	1280	14	)	)	PUNCT
ejpam-6834	1280	15	.	.	PUNCT
ejpam-6834	1281	1	applying	apply	VERB
ejpam-6834	1281	2	this	this	DET
ejpam-6834	1281	3	coordinatewise	coordinatewise	NOUN
ejpam-6834	1281	4	yields	yield	NOUN
ejpam-6834	1281	5	(	(	PUNCT
ejpam-6834	1281	6	˜pdf	˜pdf	NOUN
ejpam-6834	1281	7	∪	∪	X
ejpam-6834	1281	8	˜pdf	˜pdf	NOUN
ejpam-6834	1281	9	′	′	NUM
ejpam-6834	1281	10	)	)	PUNCT
ejpam-6834	1281	11	(	(	PUNCT
ejpam-6834	1281	12	a	a	PRON
ejpam-6834	1281	13	,	,	PUNCT
ejpam-6834	1281	14	a	a	PRON
ejpam-6834	1281	15	)	)	PUNCT
ejpam-6834	1281	16	∈	∈	PROPN
ejpam-6834	1281	17	c	c	NOUN
ejpam-6834	1281	18	with	with	ADP
ejpam-6834	1281	19	nonempty	nonempty	ADJ
ejpam-6834	1281	20	coordinates	coordinate	NOUN
ejpam-6834	1281	21	.	.	PUNCT
ejpam-6834	1282	1	the	the	DET
ejpam-6834	1282	2	domain	domain	NOUN
ejpam-6834	1282	3	d	d	NOUN
ejpam-6834	1282	4	,	,	PUNCT
ejpam-6834	1282	5	attribute	attribute	NOUN
ejpam-6834	1282	6	data	datum	NOUN
ejpam-6834	1282	7	(	(	PUNCT
ejpam-6834	1282	8	v	v	NOUN
ejpam-6834	1282	9	,	,	PUNCT
ejpam-6834	1282	10	pv	pv	NOUN
ejpam-6834	1282	11	)	)	PUNCT
ejpam-6834	1282	12	,	,	PUNCT
ejpam-6834	1282	13	and	and	CCONJ
ejpam-6834	1282	14	pcf	pcf	PROPN
ejpam-6834	1282	15	are	be	AUX
ejpam-6834	1282	16	unchanged	unchanged	ADJ
ejpam-6834	1282	17	,	,	PUNCT
ejpam-6834	1282	18	so	so	CCONJ
ejpam-6834	1282	19	(	(	PUNCT
ejpam-6834	1282	20	˜pdf	˜pdf	NOUN
ejpam-6834	1282	21	∪	∪	X
ejpam-6834	1282	22	˜pdf	˜pdf	NOUN
ejpam-6834	1282	23	′	′	NUM
ejpam-6834	1282	24	)	)	PUNCT
ejpam-6834	1282	25	is	be	AUX
ejpam-6834	1282	26	a	a	DET
ejpam-6834	1282	27	valid	valid	ADJ
ejpam-6834	1282	28	hyper	hyper	NOUN
ejpam-6834	1282	29	degree	degree	NOUN
ejpam-6834	1282	30	function	function	NOUN
ejpam-6834	1282	31	.	.	PUNCT
ejpam-6834	1283	1	theorem	theorem	VERB
ejpam-6834	1283	2	43	43	NUM
ejpam-6834	1283	3	(	(	PUNCT
ejpam-6834	1283	4	closure	closure	NOUN
ejpam-6834	1283	5	under	under	ADP
ejpam-6834	1283	6	pointwise	pointwise	NOUN
ejpam-6834	1283	7	intersection	intersection	NOUN
ejpam-6834	1283	8	)	)	PUNCT
ejpam-6834	1283	9	.	.	PUNCT
ejpam-6834	1284	1	with	with	ADP
ejpam-6834	1284	2	the	the	DET
ejpam-6834	1284	3	same	same	ADJ
ejpam-6834	1284	4	hypotheses	hypothesis	NOUN
ejpam-6834	1284	5	as	as	ADP
ejpam-6834	1284	6	theorem	theorem	VERB
ejpam-6834	1284	7	42	42	NUM
ejpam-6834	1284	8	,	,	PUNCT
ejpam-6834	1284	9	define	define	VERB
ejpam-6834	1284	10	(	(	PUNCT
ejpam-6834	1284	11	˜pdf	˜pdf	NOUN
ejpam-6834	1284	12	∩	∩	ADJ
ejpam-6834	1284	13	˜pdf	˜pdf	NOUN
ejpam-6834	1284	14	′	′	NUM
ejpam-6834	1284	15	)	)	PUNCT
ejpam-6834	1284	16	(	(	PUNCT
ejpam-6834	1284	17	a	a	PRON
ejpam-6834	1284	18	,	,	PUNCT
ejpam-6834	1284	19	a	a	NOUN
ejpam-6834	1284	20	)	)	PUNCT
ejpam-6834	1284	21	:	:	PUNCT
ejpam-6834	1285	1	=	=	PUNCT
ejpam-6834	1285	2	˜pdf(a	˜pdf(a	PROPN
ejpam-6834	1285	3	,	,	PUNCT
ejpam-6834	1285	4	a	a	PRON
ejpam-6834	1285	5	)	)	PUNCT
ejpam-6834	1285	6	∩	∩	ADJ
ejpam-6834	1285	7	˜pdf	˜pdf	NOUN
ejpam-6834	1285	8	′	′	NUM
ejpam-6834	1285	9	(	(	PUNCT
ejpam-6834	1285	10	a	a	PRON
ejpam-6834	1285	11	,	,	PUNCT
ejpam-6834	1285	12	a	a	NOUN
ejpam-6834	1285	13	)	)	PUNCT
ejpam-6834	1285	14	(	(	PUNCT
ejpam-6834	1285	15	coordinatewise	coordinatewise	NOUN
ejpam-6834	1285	16	)	)	PUNCT
ejpam-6834	1285	17	.	.	PUNCT
ejpam-6834	1286	1	if	if	SCONJ
ejpam-6834	1286	2	every	every	DET
ejpam-6834	1286	3	coordinatewise	coordinatewise	NOUN
ejpam-6834	1286	4	intersection	intersection	NOUN
ejpam-6834	1286	5	is	be	AUX
ejpam-6834	1286	6	nonempty	nonempty	ADJ
ejpam-6834	1286	7	,	,	PUNCT
ejpam-6834	1286	8	this	this	PRON
ejpam-6834	1286	9	again	again	ADV
ejpam-6834	1286	10	defines	define	VERB
ejpam-6834	1286	11	a	a	DET
ejpam-6834	1286	12	valid	valid	ADJ
ejpam-6834	1286	13	hyper	hyper	NOUN
ejpam-6834	1286	14	degree	degree	NOUN
ejpam-6834	1286	15	function	function	NOUN
ejpam-6834	1286	16	.	.	PUNCT
ejpam-6834	1287	1	proof	proof	NOUN
ejpam-6834	1287	2	.	.	PUNCT
ejpam-6834	1288	1	fix	fix	NOUN
ejpam-6834	1288	2	(	(	PUNCT
ejpam-6834	1288	3	a	a	DET
ejpam-6834	1288	4	,	,	PUNCT
ejpam-6834	1288	5	a	a	NOUN
ejpam-6834	1288	6	)	)	PUNCT
ejpam-6834	1288	7	and	and	CCONJ
ejpam-6834	1288	8	j.	j.	PROPN
ejpam-6834	1288	9	assume	assume	VERB
ejpam-6834	1288	10	bj	bj	ADP
ejpam-6834	1288	11	∩	∩	NOUN
ejpam-6834	1288	12	b′	b′	NUM
ejpam-6834	1288	13	j	j	NOUN
ejpam-6834	1288	14	̸=	̸=	PROPN
ejpam-6834	1288	15	∅	∅	NOUN
ejpam-6834	1288	16	,	,	PUNCT
ejpam-6834	1288	17	where	where	SCONJ
ejpam-6834	1288	18	bj	bj	NOUN
ejpam-6834	1288	19	,	,	PUNCT
ejpam-6834	1288	20	b	b	NOUN
ejpam-6834	1288	21	′	′	NUM
ejpam-6834	1289	1	j	j	PROPN
ejpam-6834	1289	2	∈	∈	PROPN
ejpam-6834	1289	3	pn	pn	PROPN
ejpam-6834	1289	4	+	+	PROPN
ejpam-6834	1289	5	(	(	PUNCT
ejpam-6834	1289	6	[	[	NOUN
ejpam-6834	1289	7	0	0	NUM
ejpam-6834	1289	8	,	,	PUNCT
ejpam-6834	1289	9	1]s	1]s	NUM
ejpam-6834	1289	10	)	)	PUNCT
ejpam-6834	1289	11	.	.	PUNCT
ejpam-6834	1290	1	we	we	PRON
ejpam-6834	1290	2	prove	prove	VERB
ejpam-6834	1290	3	by	by	ADP
ejpam-6834	1290	4	induction	induction	NOUN
ejpam-6834	1290	5	on	on	ADP
ejpam-6834	1290	6	n	n	PRON
ejpam-6834	1290	7	≥	≥	NUM
ejpam-6834	1290	8	1	1	NUM
ejpam-6834	1290	9	that	that	PRON
ejpam-6834	1290	10	bj	bj	VERB
ejpam-6834	1290	11	∩b′	∩b′	NOUN
ejpam-6834	1290	12	j	j	PROPN
ejpam-6834	1290	13	∈	∈	PROPN
ejpam-6834	1290	14	pn	pn	PROPN
ejpam-6834	1291	1	+	+	PROPN
ejpam-6834	1291	2	(	(	PUNCT
ejpam-6834	1291	3	[	[	NOUN
ejpam-6834	1291	4	0	0	NUM
ejpam-6834	1291	5	,	,	PUNCT
ejpam-6834	1291	6	1]s	1]s	NUM
ejpam-6834	1291	7	)	)	PUNCT
ejpam-6834	1291	8	.	.	PUNCT
ejpam-6834	1292	1	base	base	NOUN
ejpam-6834	1292	2	n	n	NOUN
ejpam-6834	1292	3	=	=	SYM
ejpam-6834	1292	4	1	1	NUM
ejpam-6834	1292	5	:	:	PUNCT
ejpam-6834	1292	6	bj	bj	VERB
ejpam-6834	1292	7	,	,	PUNCT
ejpam-6834	1292	8	b	b	X
ejpam-6834	1292	9	′	′	NUM
ejpam-6834	1293	1	j	j	NOUN
ejpam-6834	1293	2	⊆	⊆	NUM
ejpam-6834	1293	3	[	[	X
ejpam-6834	1293	4	0	0	NUM
ejpam-6834	1293	5	,	,	PUNCT
ejpam-6834	1293	6	1]s	1]s	NUM
ejpam-6834	1293	7	are	be	AUX
ejpam-6834	1293	8	nonempty	nonempty	ADJ
ejpam-6834	1293	9	and	and	CCONJ
ejpam-6834	1293	10	bj	bj	VERB
ejpam-6834	1293	11	∩	∩	NOUN
ejpam-6834	1293	12	b′	b′	NUM
ejpam-6834	1293	13	j	j	NOUN
ejpam-6834	1293	14	̸=	̸=	PROPN
ejpam-6834	1293	15	∅	∅	NOUN
ejpam-6834	1293	16	by	by	ADP
ejpam-6834	1293	17	hypothesis	hypothesis	NOUN
ejpam-6834	1293	18	,	,	PUNCT
ejpam-6834	1293	19	so	so	ADV
ejpam-6834	1293	20	bj	bj	VERB
ejpam-6834	1293	21	∩b′	∩b′	PUNCT
ejpam-6834	1293	22	j	j	PROPN
ejpam-6834	1293	23	∈	∈	PROPN
ejpam-6834	1293	24	p1	p1	PROPN
ejpam-6834	1293	25	+	+	PROPN
ejpam-6834	1293	26	(	(	PUNCT
ejpam-6834	1293	27	[	[	X
ejpam-6834	1293	28	0	0	NUM
ejpam-6834	1293	29	,	,	PUNCT
ejpam-6834	1293	30	1]s	1]s	NUM
ejpam-6834	1293	31	)	)	PUNCT
ejpam-6834	1293	32	.	.	PUNCT
ejpam-6834	1294	1	inductive	inductive	ADJ
ejpam-6834	1294	2	step	step	NOUN
ejpam-6834	1294	3	:	:	PUNCT
ejpam-6834	1294	4	suppose	suppose	VERB
ejpam-6834	1294	5	the	the	DET
ejpam-6834	1294	6	claim	claim	NOUN
ejpam-6834	1294	7	holds	hold	VERB
ejpam-6834	1294	8	for	for	ADP
ejpam-6834	1294	9	level	level	NOUN
ejpam-6834	1294	10	n.	n.	NOUN
ejpam-6834	1294	11	for	for	ADP
ejpam-6834	1294	12	level	level	NOUN
ejpam-6834	1294	13	n+1	n+1	NOUN
ejpam-6834	1294	14	,	,	PUNCT
ejpam-6834	1294	15	bj	bj	VERB
ejpam-6834	1294	16	,	,	PUNCT
ejpam-6834	1294	17	b	b	NOUN
ejpam-6834	1294	18	′	′	NUM
ejpam-6834	1294	19	j	j	PROPN
ejpam-6834	1294	20	⊆	⊆	NUM
ejpam-6834	1294	21	pn	pn	PROPN
ejpam-6834	1294	22	+	+	PROPN
ejpam-6834	1294	23	(	(	PUNCT
ejpam-6834	1294	24	[	[	NOUN
ejpam-6834	1294	25	0	0	NUM
ejpam-6834	1294	26	,	,	PUNCT
ejpam-6834	1294	27	1]s	1]s	NUM
ejpam-6834	1294	28	)	)	PUNCT
ejpam-6834	1294	29	are	be	AUX
ejpam-6834	1294	30	nonempty	nonempty	ADJ
ejpam-6834	1294	31	families	family	NOUN
ejpam-6834	1294	32	.	.	PUNCT
ejpam-6834	1295	1	the	the	DET
ejpam-6834	1295	2	intersection	intersection	NOUN
ejpam-6834	1295	3	bj	bj	ADP
ejpam-6834	1295	4	∩	∩	NOUN
ejpam-6834	1295	5	b′	b′	NUM
ejpam-6834	1295	6	j	j	NOUN
ejpam-6834	1295	7	is	be	AUX
ejpam-6834	1295	8	a	a	DET
ejpam-6834	1295	9	family	family	NOUN
ejpam-6834	1295	10	of	of	ADP
ejpam-6834	1295	11	level	level	NOUN
ejpam-6834	1295	12	–	–	PUNCT
ejpam-6834	1295	13	n	n	DET
ejpam-6834	1295	14	elements	element	NOUN
ejpam-6834	1295	15	;	;	PUNCT
ejpam-6834	1295	16	by	by	ADP
ejpam-6834	1295	17	the	the	DET
ejpam-6834	1295	18	nonemptiness	nonemptiness	PROPN
ejpam-6834	1295	19	hypothesis	hypothesis	NOUN
ejpam-6834	1295	20	it	it	PRON
ejpam-6834	1295	21	belongs	belong	VERB
ejpam-6834	1295	22	to	to	PART
ejpam-6834	1295	23	pn+1	pn+1	VERB
ejpam-6834	1295	24	+	+	CCONJ
ejpam-6834	1295	25	(	(	PUNCT
ejpam-6834	1295	26	[	[	X
ejpam-6834	1295	27	0	0	NUM
ejpam-6834	1295	28	,	,	PUNCT
ejpam-6834	1295	29	1]s	1]s	NUM
ejpam-6834	1295	30	)	)	PUNCT
ejpam-6834	1295	31	.	.	PUNCT
ejpam-6834	1296	1	thus	thus	ADV
ejpam-6834	1296	2	each	each	DET
ejpam-6834	1296	3	coordinate	coordinate	NOUN
ejpam-6834	1296	4	intersection	intersection	NOUN
ejpam-6834	1296	5	is	be	AUX
ejpam-6834	1296	6	(	(	PUNCT
ejpam-6834	1296	7	by	by	ADP
ejpam-6834	1296	8	assumption	assumption	NOUN
ejpam-6834	1296	9	)	)	PUNCT
ejpam-6834	1296	10	nonempty	nonempty	NOUN
ejpam-6834	1296	11	and	and	CCONJ
ejpam-6834	1296	12	of	of	ADP
ejpam-6834	1296	13	the	the	DET
ejpam-6834	1296	14	correct	correct	ADJ
ejpam-6834	1296	15	level	level	NOUN
ejpam-6834	1296	16	.	.	PUNCT
ejpam-6834	1297	1	collecting	collect	VERB
ejpam-6834	1297	2	the	the	DET
ejpam-6834	1297	3	k	k	PROPN
ejpam-6834	1297	4	coordinates	coordinate	NOUN
ejpam-6834	1297	5	gives	give	VERB
ejpam-6834	1297	6	(	(	PUNCT
ejpam-6834	1297	7	˜pdf	˜pdf	NOUN
ejpam-6834	1297	8	∩	∩	ADJ
ejpam-6834	1297	9	˜pdf	˜pdf	NOUN
ejpam-6834	1297	10	′	′	NUM
ejpam-6834	1297	11	)	)	PUNCT
ejpam-6834	1298	1	(	(	PUNCT
ejpam-6834	1298	2	a	a	DET
ejpam-6834	1298	3	,	,	PUNCT
ejpam-6834	1298	4	a	a	PRON
ejpam-6834	1298	5	)	)	PUNCT
ejpam-6834	1298	6	∈	∈	PROPN
ejpam-6834	1298	7	c	c	NOUN
ejpam-6834	1298	8	,	,	PUNCT
ejpam-6834	1298	9	so	so	ADV
ejpam-6834	1298	10	the	the	DET
ejpam-6834	1298	11	result	result	NOUN
ejpam-6834	1298	12	is	be	AUX
ejpam-6834	1298	13	a	a	DET
ejpam-6834	1298	14	valid	valid	ADJ
ejpam-6834	1298	15	hyper	hyper	NOUN
ejpam-6834	1298	16	degree	degree	NOUN
ejpam-6834	1298	17	function	function	NOUN
ejpam-6834	1298	18	.	.	PUNCT
ejpam-6834	1299	1	theorem	theorem	VERB
ejpam-6834	1299	2	44	44	NUM
ejpam-6834	1299	3	(	(	PUNCT
ejpam-6834	1299	4	nested	nest	VERB
ejpam-6834	1299	5	α	α	NOUN
ejpam-6834	1299	6	-	-	NOUN
ejpam-6834	1299	7	cuts	cut	NOUN
ejpam-6834	1299	8	)	)	PUNCT
ejpam-6834	1299	9	.	.	PUNCT
ejpam-6834	1300	1	fix	fix	VERB
ejpam-6834	1300	2	a	a	DET
ejpam-6834	1300	3	∈	∈	NOUN
ejpam-6834	1300	4	pv	pv	NOUN
ejpam-6834	1300	5	and	and	CCONJ
ejpam-6834	1300	6	α	α	PRON
ejpam-6834	1300	7	∈	∈	PROPN
ejpam-6834	1301	1	[	[	X
ejpam-6834	1301	2	0	0	NUM
ejpam-6834	1301	3	,	,	PUNCT
ejpam-6834	1301	4	1]s	1]s	NOUN
ejpam-6834	1301	5	.	.	PUNCT
ejpam-6834	1302	1	define	define	VERB
ejpam-6834	1302	2	c	c	PROPN
ejpam-6834	1302	3	a	a	DET
ejpam-6834	1302	4	α	α	NOUN
ejpam-6834	1302	5	:	:	PUNCT
ejpam-6834	1302	6	=	=	X
ejpam-6834	1302	7	{	{	PUNCT
ejpam-6834	1302	8	a	a	DET
ejpam-6834	1302	9	∈	∈	PROPN
ejpam-6834	1302	10	d	d	X
ejpam-6834	1302	11	∣∣∣	∣∣∣	NOUN
ejpam-6834	1302	12	∃	∃	PROPN
ejpam-6834	1302	13	j	j	PROPN
ejpam-6834	1302	14	∈	∈	PROPN
ejpam-6834	1302	15	{	{	PUNCT
ejpam-6834	1302	16	1	1	NUM
ejpam-6834	1302	17	,	,	PUNCT
ejpam-6834	1302	18	.	.	PUNCT
ejpam-6834	1302	19	.	.	PUNCT
ejpam-6834	1303	1	.	.	PUNCT
ejpam-6834	1304	1	,	,	PUNCT
ejpam-6834	1304	2	k	k	X
ejpam-6834	1304	3	}	}	PUNCT
ejpam-6834	1304	4	∃x	∃x	PROPN
ejpam-6834	1304	5	∈	∈	NOUN
ejpam-6834	1304	6	[	[	PUNCT
ejpam-6834	1304	7	˜pdf	˜pdf	NOUN
ejpam-6834	1304	8	(	(	PUNCT
ejpam-6834	1304	9	m	m	NOUN
ejpam-6834	1304	10	,	,	PUNCT
ejpam-6834	1304	11	n	n	CCONJ
ejpam-6834	1304	12	)	)	PUNCT
ejpam-6834	1304	13	v	v	NOUN
ejpam-6834	1304	14	(	(	PUNCT
ejpam-6834	1304	15	a	a	PRON
ejpam-6834	1304	16	,	,	PUNCT
ejpam-6834	1304	17	a	a	NOUN
ejpam-6834	1304	18	)	)	PUNCT
ejpam-6834	1304	19	]	]	PUNCT
ejpam-6834	1305	1	j	j	NOUN
ejpam-6834	1305	2	with	with	ADP
ejpam-6834	1305	3	x	x	PUNCT
ejpam-6834	1305	4	⪰	⪰	NOUN
ejpam-6834	1305	5	α	α	NOUN
ejpam-6834	1305	6	}	}	PUNCT
ejpam-6834	1305	7	,	,	PUNCT
ejpam-6834	1305	8	where	where	SCONJ
ejpam-6834	1305	9	⪰	⪰	NOUN
ejpam-6834	1305	10	is	be	AUX
ejpam-6834	1305	11	the	the	DET
ejpam-6834	1305	12	componentwise	componentwise	NOUN
ejpam-6834	1305	13	order	order	NOUN
ejpam-6834	1305	14	on	on	ADP
ejpam-6834	1305	15	[	[	X
ejpam-6834	1305	16	0	0	NUM
ejpam-6834	1305	17	,	,	PUNCT
ejpam-6834	1305	18	1]s	1]s	NOUN
ejpam-6834	1305	19	.	.	PUNCT
ejpam-6834	1306	1	if	if	SCONJ
ejpam-6834	1306	2	α′	α′	NUM
ejpam-6834	1306	3	,	,	PUNCT
ejpam-6834	1306	4	α	α	PROPN
ejpam-6834	1306	5	∈	∈	PROPN
ejpam-6834	1307	1	[	[	X
ejpam-6834	1307	2	0	0	NUM
ejpam-6834	1307	3	,	,	PUNCT
ejpam-6834	1307	4	1]s	1]s	NOUN
ejpam-6834	1307	5	with	with	ADP
ejpam-6834	1307	6	α′	α′	NUM
ejpam-6834	1307	7	⪰	⪰	NOUN
ejpam-6834	1307	8	α	α	NOUN
ejpam-6834	1307	9	,	,	PUNCT
ejpam-6834	1307	10	then	then	ADV
ejpam-6834	1307	11	c	c	X
ejpam-6834	1307	12	a	a	DET
ejpam-6834	1307	13	α′	α′	NUM
ejpam-6834	1307	14	⊆	⊆	NUM
ejpam-6834	1307	15	c	c	NOUN
ejpam-6834	1307	16	a	a	DET
ejpam-6834	1307	17	α	α	NOUN
ejpam-6834	1307	18	.	.	PUNCT
ejpam-6834	1308	1	t.	t.	PROPN
ejpam-6834	1308	2	fujita	fujita	PROPN
ejpam-6834	1308	3	,	,	PUNCT
ejpam-6834	1308	4	f.smarandache	f.smarandache	NOUN
ejpam-6834	1308	5	/	/	SYM
ejpam-6834	1308	6	eur	eur	PROPN
ejpam-6834	1308	7	.	.	PUNCT
ejpam-6834	1309	1	j.	j.	PROPN
ejpam-6834	1309	2	pure	pure	PROPN
ejpam-6834	1309	3	appl	appl	PROPN
ejpam-6834	1309	4	.	.	PROPN
ejpam-6834	1309	5	math	math	PROPN
ejpam-6834	1309	6	,	,	PUNCT
ejpam-6834	1309	7	18	18	NUM
ejpam-6834	1309	8	(	(	PUNCT
ejpam-6834	1309	9	4	4	NUM
ejpam-6834	1309	10	)	)	PUNCT
ejpam-6834	1309	11	(	(	PUNCT
ejpam-6834	1309	12	2025	2025	NUM
ejpam-6834	1309	13	)	)	PUNCT
ejpam-6834	1309	14	,	,	PUNCT
ejpam-6834	1309	15	6834	6834	NUM
ejpam-6834	1309	16	50	50	NUM
ejpam-6834	1309	17	of	of	ADP
ejpam-6834	1309	18	69	69	NUM
ejpam-6834	1309	19	proof	proof	NOUN
ejpam-6834	1309	20	.	.	PUNCT
ejpam-6834	1310	1	let	let	VERB
ejpam-6834	1310	2	a	a	DET
ejpam-6834	1310	3	∈	∈	NOUN
ejpam-6834	1310	4	c	c	NOUN
ejpam-6834	1310	5	a	a	DET
ejpam-6834	1310	6	α′	α′	NUM
ejpam-6834	1310	7	.	.	PUNCT
ejpam-6834	1311	1	then	then	ADV
ejpam-6834	1311	2	there	there	PRON
ejpam-6834	1311	3	exist	exist	VERB
ejpam-6834	1311	4	a	a	DET
ejpam-6834	1311	5	coordinate	coordinate	NOUN
ejpam-6834	1311	6	j	j	NOUN
ejpam-6834	1311	7	and	and	CCONJ
ejpam-6834	1311	8	a	a	DET
ejpam-6834	1311	9	vector	vector	NOUN
ejpam-6834	1311	10	x	x	X
ejpam-6834	1311	11	∈	∈	PROPN
ejpam-6834	1311	12	[	[	PUNCT
ejpam-6834	1311	13	˜pdf	˜pdf	NOUN
ejpam-6834	1311	14	(	(	PUNCT
ejpam-6834	1311	15	m	m	NOUN
ejpam-6834	1311	16	,	,	PUNCT
ejpam-6834	1311	17	n	n	CCONJ
ejpam-6834	1311	18	)	)	PUNCT
ejpam-6834	1311	19	v	v	NOUN
ejpam-6834	1311	20	(	(	PUNCT
ejpam-6834	1311	21	a	a	PRON
ejpam-6834	1311	22	,	,	PUNCT
ejpam-6834	1311	23	a)]j	a)]j	NOUN
ejpam-6834	1311	24	such	such	ADJ
ejpam-6834	1311	25	that	that	SCONJ
ejpam-6834	1311	26	x	x	PUNCT
ejpam-6834	1311	27	⪰	⪰	VERB
ejpam-6834	1311	28	α′.	α′.	NOUN
ejpam-6834	1311	29	since	since	SCONJ
ejpam-6834	1311	30	α′	α′	NUM
ejpam-6834	1311	31	⪰	⪰	NOUN
ejpam-6834	1311	32	α	α	NOUN
ejpam-6834	1311	33	,	,	PUNCT
ejpam-6834	1311	34	transitivity	transitivity	NOUN
ejpam-6834	1311	35	of	of	ADP
ejpam-6834	1311	36	⪰	⪰	NOUN
ejpam-6834	1311	37	implies	imply	VERB
ejpam-6834	1311	38	x	x	PUNCT
ejpam-6834	1311	39	⪰	⪰	VERB
ejpam-6834	1311	40	α	α	X
ejpam-6834	1311	41	.	.	PUNCT
ejpam-6834	1312	1	hence	hence	ADV
ejpam-6834	1312	2	the	the	DET
ejpam-6834	1312	3	same	same	ADJ
ejpam-6834	1312	4	j	j	NOUN
ejpam-6834	1312	5	and	and	CCONJ
ejpam-6834	1312	6	x	x	PART
ejpam-6834	1312	7	witness	witness	VERB
ejpam-6834	1312	8	a	a	DET
ejpam-6834	1312	9	∈	∈	NOUN
ejpam-6834	1312	10	c	c	NOUN
ejpam-6834	1312	11	a	a	DET
ejpam-6834	1312	12	α	α	NOUN
ejpam-6834	1312	13	.	.	PUNCT
ejpam-6834	1313	1	therefore	therefore	ADV
ejpam-6834	1313	2	c	c	VERB
ejpam-6834	1313	3	a	a	DET
ejpam-6834	1313	4	α′	α′	NUM
ejpam-6834	1313	5	⊆	⊆	NUM
ejpam-6834	1313	6	c	c	NOUN
ejpam-6834	1313	7	a	a	DET
ejpam-6834	1313	8	α	α	NOUN
ejpam-6834	1313	9	,	,	PUNCT
ejpam-6834	1313	10	i.e.	i.e.	X
ejpam-6834	1313	11	the	the	DET
ejpam-6834	1313	12	family	family	NOUN
ejpam-6834	1313	13	{	{	PUNCT
ejpam-6834	1313	14	c	c	PROPN
ejpam-6834	1313	15	a	a	DET
ejpam-6834	1313	16	α	α	NOUN
ejpam-6834	1313	17	}	}	PUNCT
ejpam-6834	1313	18	α	α	PROPN
ejpam-6834	1313	19	is	be	AUX
ejpam-6834	1313	20	nested	nest	VERB
ejpam-6834	1313	21	decreasing	decrease	VERB
ejpam-6834	1313	22	in	in	ADP
ejpam-6834	1313	23	the	the	DET
ejpam-6834	1313	24	threshold	threshold	NOUN
ejpam-6834	1313	25	α	α	PROPN
ejpam-6834	1313	26	.	.	PUNCT
ejpam-6834	1314	1	theorem	theorem	VERB
ejpam-6834	1314	2	45	45	NUM
ejpam-6834	1314	3	(	(	PUNCT
ejpam-6834	1314	4	compatibility	compatibility	NOUN
ejpam-6834	1314	5	with	with	ADP
ejpam-6834	1314	6	surjective	surjective	ADJ
ejpam-6834	1314	7	mappings	mapping	NOUN
ejpam-6834	1314	8	)	)	PUNCT
ejpam-6834	1314	9	.	.	PUNCT
ejpam-6834	1315	1	let	let	VERB
ejpam-6834	1315	2	f	f	NOUN
ejpam-6834	1315	3	:	:	PUNCT
ejpam-6834	1315	4	p	p	X
ejpam-6834	1315	5	→	→	PUNCT
ejpam-6834	1315	6	q	q	X
ejpam-6834	1315	7	be	be	AUX
ejpam-6834	1315	8	surjective	surjective	ADJ
ejpam-6834	1315	9	.	.	PUNCT
ejpam-6834	1316	1	for	for	SCONJ
ejpam-6834	1316	2	r	r	PROPN
ejpam-6834	1316	3	≥	≥	NOUN
ejpam-6834	1316	4	1	1	NUM
ejpam-6834	1316	5	define	define	VERB
ejpam-6834	1316	6	recursively	recursively	ADV
ejpam-6834	1316	7	f−1	f−1	PROPN
ejpam-6834	1316	8	(	(	PUNCT
ejpam-6834	1316	9	1	1	NUM
ejpam-6834	1316	10	)	)	PUNCT
ejpam-6834	1316	11	(	(	PUNCT
ejpam-6834	1316	12	b	b	NOUN
ejpam-6834	1316	13	)	)	PUNCT
ejpam-6834	1316	14	:	:	PUNCT
ejpam-6834	1317	1	=	=	SYM
ejpam-6834	1317	2	{	{	PUNCT
ejpam-6834	1317	3	x	x	SYM
ejpam-6834	1317	4	∈	∈	PROPN
ejpam-6834	1317	5	p	p	NOUN
ejpam-6834	1317	6	|	|	NOUN
ejpam-6834	1317	7	f(x	f(x	PROPN
ejpam-6834	1317	8	)	)	PUNCT
ejpam-6834	1318	1	∈	∈	PROPN
ejpam-6834	1318	2	b	b	PROPN
ejpam-6834	1318	3	}	}	PUNCT
ejpam-6834	1318	4	(	(	PUNCT
ejpam-6834	1318	5	b	b	X
ejpam-6834	1318	6	∈	∈	PROPN
ejpam-6834	1318	7	p1	p1	NOUN
ejpam-6834	1318	8	+	+	PROPN
ejpam-6834	1318	9	(	(	PUNCT
ejpam-6834	1318	10	q	q	NOUN
ejpam-6834	1318	11	)	)	PUNCT
ejpam-6834	1318	12	)	)	PUNCT
ejpam-6834	1318	13	,	,	PUNCT
ejpam-6834	1318	14	f−1	f−1	PROPN
ejpam-6834	1318	15	(	(	PUNCT
ejpam-6834	1318	16	r+1)(b	r+1)(b	PROPN
ejpam-6834	1318	17	)	)	PUNCT
ejpam-6834	1318	18	:	:	PUNCT
ejpam-6834	1319	1	=	=	SYM
ejpam-6834	1319	2	{	{	PUNCT
ejpam-6834	1319	3	f−1	f−1	PROPN
ejpam-6834	1319	4	(	(	PUNCT
ejpam-6834	1319	5	r	r	NOUN
ejpam-6834	1319	6	)	)	PUNCT
ejpam-6834	1319	7	(	(	PUNCT
ejpam-6834	1319	8	b	b	X
ejpam-6834	1319	9	)	)	PUNCT
ejpam-6834	1320	1	|	|	ADV
ejpam-6834	1321	1	b	b	X
ejpam-6834	1321	2	∈	∈	PROPN
ejpam-6834	1321	3	b	b	PROPN
ejpam-6834	1321	4	}	}	PUNCT
ejpam-6834	1321	5	.	.	PUNCT
ejpam-6834	1322	1	given	give	VERB
ejpam-6834	1322	2	˜pdf	˜pdf	NOUN
ejpam-6834	1322	3	(	(	PUNCT
ejpam-6834	1322	4	m	m	NOUN
ejpam-6834	1322	5	,	,	PUNCT
ejpam-6834	1322	6	n	n	CCONJ
ejpam-6834	1322	7	)	)	PUNCT
ejpam-6834	1322	8	v	v	NOUN
ejpam-6834	1322	9	:	:	PUNCT
ejpam-6834	1322	10	dp	dp	NOUN
ejpam-6834	1322	11	×	×	NOUN
ejpam-6834	1322	12	pv	pv	NOUN
ejpam-6834	1322	13	→	→	SYM
ejpam-6834	1322	14	c	c	NOUN
ejpam-6834	1322	15	on	on	ADP
ejpam-6834	1322	16	p	p	X
ejpam-6834	1322	17	,	,	PUNCT
ejpam-6834	1322	18	set	set	ADJ
ejpam-6834	1322	19	˜pdf	˜pdf	NOUN
ejpam-6834	1322	20	(	(	PUNCT
ejpam-6834	1322	21	m	m	NOUN
ejpam-6834	1322	22	,	,	PUNCT
ejpam-6834	1322	23	n	n	CCONJ
ejpam-6834	1322	24	)	)	PUNCT
ejpam-6834	1322	25	v;q	v;q	PROPN
ejpam-6834	1322	26	(	(	PUNCT
ejpam-6834	1322	27	b	b	NOUN
ejpam-6834	1322	28	,	,	PUNCT
ejpam-6834	1322	29	a	a	NOUN
ejpam-6834	1322	30	)	)	PUNCT
ejpam-6834	1322	31	:	:	PUNCT
ejpam-6834	1322	32	=	=	SYM
ejpam-6834	1322	33	˜pdf	˜pdf	X
ejpam-6834	1322	34	(	(	PUNCT
ejpam-6834	1322	35	m	m	NOUN
ejpam-6834	1322	36	,	,	PUNCT
ejpam-6834	1322	37	n	n	CCONJ
ejpam-6834	1322	38	)	)	PUNCT
ejpam-6834	1322	39	v	v	NOUN
ejpam-6834	1322	40	(	(	PUNCT
ejpam-6834	1322	41	f−1	f−1	PROPN
ejpam-6834	1322	42	(	(	PUNCT
ejpam-6834	1322	43	m)(b	m)(b	PROPN
ejpam-6834	1322	44	)	)	PUNCT
ejpam-6834	1322	45	,	,	PUNCT
ejpam-6834	1322	46	a	a	PRON
ejpam-6834	1322	47	)	)	PUNCT
ejpam-6834	1322	48	,	,	PUNCT
ejpam-6834	1322	49	b	b	X
ejpam-6834	1322	50	∈	∈	ADJ
ejpam-6834	1322	51	dq	dq	ADP
ejpam-6834	1322	52	:	:	PUNCT
ejpam-6834	1322	53	=	=	SYM
ejpam-6834	1322	54	(	(	PUNCT
ejpam-6834	1322	55	pm	pm	NOUN
ejpam-6834	1322	56	+	+	CCONJ
ejpam-6834	1322	57	(	(	PUNCT
ejpam-6834	1322	58	q))h	q))h	ADJ
ejpam-6834	1322	59	.	.	PUNCT
ejpam-6834	1323	1	then	then	ADV
ejpam-6834	1323	2	(	(	PUNCT
ejpam-6834	1323	3	dq	dq	PROPN
ejpam-6834	1323	4	,	,	PUNCT
ejpam-6834	1323	5	v	v	NOUN
ejpam-6834	1323	6	,	,	PUNCT
ejpam-6834	1323	7	pv	pv	INTJ
ejpam-6834	1323	8	,	,	PUNCT
ejpam-6834	1323	9	˜pdf	˜pdf	NOUN
ejpam-6834	1323	10	(	(	PUNCT
ejpam-6834	1323	11	m	m	NOUN
ejpam-6834	1323	12	,	,	PUNCT
ejpam-6834	1323	13	n	n	CCONJ
ejpam-6834	1323	14	)	)	PUNCT
ejpam-6834	1323	15	v;q	v;q	PROPN
ejpam-6834	1323	16	,	,	PUNCT
ejpam-6834	1323	17	pcf	pcf	PROPN
ejpam-6834	1323	18	)	)	PUNCT
ejpam-6834	1323	19	is	be	AUX
ejpam-6834	1323	20	an	an	DET
ejpam-6834	1323	21	(	(	PUNCT
ejpam-6834	1323	22	h	h	NOUN
ejpam-6834	1323	23	,	,	PUNCT
ejpam-6834	1323	24	k)-ary	k)-ary	X
ejpam-6834	1323	25	(	(	PUNCT
ejpam-6834	1323	26	m	m	PROPN
ejpam-6834	1323	27	,	,	PUNCT
ejpam-6834	1323	28	n)-superhyperplithogenic	n)-superhyperplithogenic	PUNCT
ejpam-6834	1323	29	set	set	VERB
ejpam-6834	1323	30	on	on	ADP
ejpam-6834	1323	31	q.	q.	NOUN
ejpam-6834	1323	32	proof	proof	NOUN
ejpam-6834	1323	33	.	.	PUNCT
ejpam-6834	1324	1	step	step	NOUN
ejpam-6834	1324	2	1	1	NUM
ejpam-6834	1324	3	(	(	PUNCT
ejpam-6834	1324	4	well	well	NOUN
ejpam-6834	1324	5	-	-	PUNCT
ejpam-6834	1324	6	definedness	definedness	NOUN
ejpam-6834	1324	7	and	and	CCONJ
ejpam-6834	1324	8	nonemptiness	nonemptiness	NOUN
ejpam-6834	1324	9	of	of	ADP
ejpam-6834	1324	10	f−1	f−1	PROPN
ejpam-6834	1324	11	(	(	PUNCT
ejpam-6834	1324	12	r	r	NOUN
ejpam-6834	1324	13	)	)	PUNCT
ejpam-6834	1324	14	)	)	PUNCT
ejpam-6834	1324	15	.	.	PUNCT
ejpam-6834	1325	1	we	we	PRON
ejpam-6834	1325	2	prove	prove	VERB
ejpam-6834	1325	3	by	by	ADP
ejpam-6834	1325	4	induction	induction	NOUN
ejpam-6834	1325	5	on	on	ADP
ejpam-6834	1325	6	r	r	PROPN
ejpam-6834	1325	7	≥	≥	NUM
ejpam-6834	1325	8	1	1	NUM
ejpam-6834	1325	9	that	that	PRON
ejpam-6834	1325	10	f−1	f−1	PROPN
ejpam-6834	1325	11	(	(	PUNCT
ejpam-6834	1325	12	r	r	NOUN
ejpam-6834	1325	13	)	)	PUNCT
ejpam-6834	1325	14	:	:	PUNCT
ejpam-6834	1325	15	pr	pr	X
ejpam-6834	1326	1	+	+	ADJ
ejpam-6834	1326	2	(	(	PUNCT
ejpam-6834	1326	3	q	q	NOUN
ejpam-6834	1326	4	)	)	PUNCT
ejpam-6834	1326	5	→	→	SYM
ejpam-6834	1326	6	pr	pr	X
ejpam-6834	1326	7	+	+	ADJ
ejpam-6834	1326	8	(	(	PUNCT
ejpam-6834	1326	9	p	p	NOUN
ejpam-6834	1326	10	)	)	PUNCT
ejpam-6834	1326	11	is	be	AUX
ejpam-6834	1326	12	well	well	ADV
ejpam-6834	1326	13	defined	define	VERB
ejpam-6834	1326	14	and	and	CCONJ
ejpam-6834	1326	15	preserves	preserve	VERB
ejpam-6834	1326	16	nonemptiness	nonemptiness	PROPN
ejpam-6834	1326	17	.	.	PUNCT
ejpam-6834	1327	1	base	base	NOUN
ejpam-6834	1327	2	r	r	NOUN
ejpam-6834	1327	3	=	=	NOUN
ejpam-6834	1327	4	1	1	NUM
ejpam-6834	1327	5	:	:	PUNCT
ejpam-6834	1327	6	if	if	SCONJ
ejpam-6834	1327	7	b	b	PROPN
ejpam-6834	1327	8	∈	∈	PROPN
ejpam-6834	1327	9	p1	p1	NOUN
ejpam-6834	1327	10	+	+	PROPN
ejpam-6834	1327	11	(	(	PUNCT
ejpam-6834	1327	12	q	q	NOUN
ejpam-6834	1327	13	)	)	PUNCT
ejpam-6834	1327	14	,	,	PUNCT
ejpam-6834	1327	15	then	then	ADV
ejpam-6834	1327	16	b	b	X
ejpam-6834	1327	17	̸=	̸=	PROPN
ejpam-6834	1327	18	∅.	∅.	PRON
ejpam-6834	1327	19	surjectivity	surjectivity	NOUN
ejpam-6834	1327	20	of	of	ADP
ejpam-6834	1327	21	f	f	PROPN
ejpam-6834	1327	22	ensures	ensure	VERB
ejpam-6834	1327	23	∃x	∃x	PROPN
ejpam-6834	1327	24	∈	∈	PROPN
ejpam-6834	1327	25	p	p	NOUN
ejpam-6834	1327	26	with	with	ADP
ejpam-6834	1327	27	f(x	f(x	PROPN
ejpam-6834	1327	28	)	)	PUNCT
ejpam-6834	1327	29	∈	∈	PROPN
ejpam-6834	1327	30	b	b	NOUN
ejpam-6834	1327	31	,	,	PUNCT
ejpam-6834	1327	32	hence	hence	ADV
ejpam-6834	1327	33	f−1	f−1	PROPN
ejpam-6834	1327	34	(	(	PUNCT
ejpam-6834	1327	35	1	1	NUM
ejpam-6834	1327	36	)	)	PUNCT
ejpam-6834	1327	37	(	(	PUNCT
ejpam-6834	1327	38	b	b	X
ejpam-6834	1327	39	)	)	PUNCT
ejpam-6834	1327	40	̸=	̸=	PROPN
ejpam-6834	1327	41	∅	∅	NOUN
ejpam-6834	1327	42	and	and	CCONJ
ejpam-6834	1327	43	f−1	f−1	PROPN
ejpam-6834	1327	44	(	(	PUNCT
ejpam-6834	1327	45	1	1	NUM
ejpam-6834	1327	46	)	)	PUNCT
ejpam-6834	1327	47	(	(	PUNCT
ejpam-6834	1327	48	b	b	X
ejpam-6834	1327	49	)	)	PUNCT
ejpam-6834	1327	50	⊆	⊆	NUM
ejpam-6834	1327	51	p	p	NOUN
ejpam-6834	1327	52	,	,	PUNCT
ejpam-6834	1327	53	so	so	ADV
ejpam-6834	1327	54	f−1	f−1	PROPN
ejpam-6834	1327	55	(	(	PUNCT
ejpam-6834	1327	56	1	1	NUM
ejpam-6834	1327	57	)	)	PUNCT
ejpam-6834	1327	58	(	(	PUNCT
ejpam-6834	1327	59	b	b	X
ejpam-6834	1327	60	)	)	PUNCT
ejpam-6834	1327	61	∈	∈	PROPN
ejpam-6834	1327	62	p1	p1	NOUN
ejpam-6834	1327	63	+	+	PROPN
ejpam-6834	1327	64	(	(	PUNCT
ejpam-6834	1327	65	p	p	NOUN
ejpam-6834	1327	66	)	)	PUNCT
ejpam-6834	1327	67	.	.	PUNCT
ejpam-6834	1328	1	inductive	inductive	ADJ
ejpam-6834	1328	2	step	step	NOUN
ejpam-6834	1328	3	:	:	PUNCT
ejpam-6834	1328	4	suppose	suppose	VERB
ejpam-6834	1328	5	f−1	f−1	PROPN
ejpam-6834	1328	6	(	(	PUNCT
ejpam-6834	1328	7	r	r	NOUN
ejpam-6834	1328	8	)	)	PUNCT
ejpam-6834	1328	9	maps	map	NOUN
ejpam-6834	1328	10	pr	pr	X
ejpam-6834	1328	11	+	+	NOUN
ejpam-6834	1328	12	(	(	PUNCT
ejpam-6834	1328	13	q	q	NOUN
ejpam-6834	1328	14	)	)	PUNCT
ejpam-6834	1328	15	into	into	ADP
ejpam-6834	1328	16	pr	pr	NOUN
ejpam-6834	1329	1	+	+	PROPN
ejpam-6834	1329	2	(	(	PUNCT
ejpam-6834	1329	3	p	p	NOUN
ejpam-6834	1329	4	)	)	PUNCT
ejpam-6834	1329	5	and	and	CCONJ
ejpam-6834	1329	6	preserves	preserve	VERB
ejpam-6834	1329	7	nonemptiness	nonemptiness	PROPN
ejpam-6834	1329	8	.	.	PUNCT
ejpam-6834	1330	1	let	let	VERB
ejpam-6834	1330	2	b	b	NOUN
ejpam-6834	1330	3	∈	∈	PROPN
ejpam-6834	1330	4	pr+1	pr+1	NOUN
ejpam-6834	1330	5	+	+	CCONJ
ejpam-6834	1330	6	(	(	PUNCT
ejpam-6834	1330	7	q	q	X
ejpam-6834	1330	8	)	)	PUNCT
ejpam-6834	1330	9	be	be	AUX
ejpam-6834	1330	10	nonempty	nonempty	VERB
ejpam-6834	1330	11	.	.	PUNCT
ejpam-6834	1331	1	for	for	ADP
ejpam-6834	1331	2	each	each	PRON
ejpam-6834	1331	3	b	b	PROPN
ejpam-6834	1331	4	∈	∈	PROPN
ejpam-6834	1331	5	b	b	PROPN
ejpam-6834	1331	6	,	,	PUNCT
ejpam-6834	1331	7	f−1	f−1	PROPN
ejpam-6834	1331	8	(	(	PUNCT
ejpam-6834	1331	9	r	r	NOUN
ejpam-6834	1331	10	)	)	PUNCT
ejpam-6834	1331	11	(	(	PUNCT
ejpam-6834	1331	12	b	b	X
ejpam-6834	1331	13	)	)	PUNCT
ejpam-6834	1331	14	∈	∈	NOUN
ejpam-6834	1331	15	pr	pr	NOUN
ejpam-6834	1332	1	+	+	NOUN
ejpam-6834	1332	2	(	(	PUNCT
ejpam-6834	1332	3	p	p	NOUN
ejpam-6834	1332	4	)	)	PUNCT
ejpam-6834	1332	5	and	and	CCONJ
ejpam-6834	1332	6	the	the	DET
ejpam-6834	1332	7	family	family	NOUN
ejpam-6834	1332	8	{	{	PUNCT
ejpam-6834	1332	9	f−1	f−1	PROPN
ejpam-6834	1332	10	(	(	PUNCT
ejpam-6834	1332	11	r	r	NOUN
ejpam-6834	1332	12	)	)	PUNCT
ejpam-6834	1332	13	(	(	PUNCT
ejpam-6834	1332	14	b	b	X
ejpam-6834	1332	15	)	)	PUNCT
ejpam-6834	1333	1	|	|	ADV
ejpam-6834	1333	2	b	b	X
ejpam-6834	1333	3	∈	∈	PROPN
ejpam-6834	1334	1	b	b	PROPN
ejpam-6834	1334	2	}	}	PUNCT
ejpam-6834	1334	3	is	be	AUX
ejpam-6834	1334	4	nonempty	nonempty	ADJ
ejpam-6834	1334	5	.	.	PUNCT
ejpam-6834	1335	1	hence	hence	ADV
ejpam-6834	1335	2	f−1	f−1	PROPN
ejpam-6834	1335	3	(	(	PUNCT
ejpam-6834	1335	4	r+1)(b	r+1)(b	PROPN
ejpam-6834	1335	5	)	)	PUNCT
ejpam-6834	1335	6	∈	∈	PROPN
ejpam-6834	1336	1	pr+1	pr+1	NOUN
ejpam-6834	1336	2	+	+	CCONJ
ejpam-6834	1336	3	(	(	PUNCT
ejpam-6834	1336	4	p	p	NOUN
ejpam-6834	1336	5	)	)	PUNCT
ejpam-6834	1336	6	.	.	PUNCT
ejpam-6834	1337	1	step	step	NOUN
ejpam-6834	1337	2	2	2	NUM
ejpam-6834	1337	3	(	(	PUNCT
ejpam-6834	1337	4	type	type	NOUN
ejpam-6834	1337	5	checking	checking	NOUN
ejpam-6834	1337	6	for	for	ADP
ejpam-6834	1337	7	the	the	DET
ejpam-6834	1337	8	pushforward	pushforward	NOUN
ejpam-6834	1337	9	)	)	PUNCT
ejpam-6834	1337	10	.	.	PUNCT
ejpam-6834	1338	1	take	take	VERB
ejpam-6834	1338	2	any	any	DET
ejpam-6834	1338	3	b	b	NOUN
ejpam-6834	1338	4	=	=	SYM
ejpam-6834	1338	5	(	(	PUNCT
ejpam-6834	1338	6	b1	b1	PROPN
ejpam-6834	1338	7	,	,	PUNCT
ejpam-6834	1338	8	.	.	PUNCT
ejpam-6834	1338	9	.	.	PUNCT
ejpam-6834	1339	1	.	.	PUNCT
ejpam-6834	1340	1	,	,	PUNCT
ejpam-6834	1340	2	bh	bh	NOUN
ejpam-6834	1340	3	)	)	PUNCT
ejpam-6834	1340	4	∈	∈	PROPN
ejpam-6834	1340	5	dq	dq	NOUN
ejpam-6834	1340	6	=	=	PUNCT
ejpam-6834	1340	7	(	(	PUNCT
ejpam-6834	1340	8	pm	pm	NOUN
ejpam-6834	1340	9	+	+	CCONJ
ejpam-6834	1340	10	(	(	PUNCT
ejpam-6834	1340	11	q))h	q))h	ADJ
ejpam-6834	1340	12	.	.	PUNCT
ejpam-6834	1341	1	by	by	ADP
ejpam-6834	1341	2	step	step	NOUN
ejpam-6834	1341	3	1	1	NUM
ejpam-6834	1341	4	,	,	PUNCT
ejpam-6834	1341	5	f−1	f−1	PROPN
ejpam-6834	1341	6	(	(	PUNCT
ejpam-6834	1341	7	m)(bi	m)(bi	NOUN
ejpam-6834	1341	8	)	)	PUNCT
ejpam-6834	1341	9	∈	∈	NOUN
ejpam-6834	1341	10	pm	pm	NOUN
ejpam-6834	1341	11	+	+	CCONJ
ejpam-6834	1341	12	(	(	PUNCT
ejpam-6834	1341	13	p	p	NOUN
ejpam-6834	1341	14	)	)	PUNCT
ejpam-6834	1341	15	for	for	ADP
ejpam-6834	1341	16	every	every	DET
ejpam-6834	1341	17	i	i	PROPN
ejpam-6834	1341	18	,	,	PUNCT
ejpam-6834	1341	19	so	so	ADV
ejpam-6834	1341	20	f−1	f−1	PROPN
ejpam-6834	1341	21	(	(	PUNCT
ejpam-6834	1341	22	m)(b	m)(b	ADJ
ejpam-6834	1341	23	)	)	PUNCT
ejpam-6834	1341	24	:	:	PUNCT
ejpam-6834	1342	1	=	=	SYM
ejpam-6834	1342	2	(	(	PUNCT
ejpam-6834	1342	3	f−1	f−1	PROPN
ejpam-6834	1342	4	(	(	PUNCT
ejpam-6834	1342	5	m)(b1	m)(b1	PROPN
ejpam-6834	1342	6	)	)	PUNCT
ejpam-6834	1342	7	,	,	PUNCT
ejpam-6834	1342	8	.	.	PUNCT
ejpam-6834	1342	9	.	.	PUNCT
ejpam-6834	1342	10	.	.	PUNCT
ejpam-6834	1343	1	,	,	PUNCT
ejpam-6834	1343	2	f	f	PROPN
ejpam-6834	1343	3	−1	−1	NOUN
ejpam-6834	1343	4	(	(	PUNCT
ejpam-6834	1343	5	m)(bh	m)(bh	NOUN
ejpam-6834	1343	6	)	)	PUNCT
ejpam-6834	1343	7	)	)	PUNCT
ejpam-6834	1344	1	∈	∈	PROPN
ejpam-6834	1344	2	dp	dp	NOUN
ejpam-6834	1344	3	.	.	PUNCT
ejpam-6834	1345	1	therefore	therefore	ADV
ejpam-6834	1345	2	˜pdf	˜pdf	NOUN
ejpam-6834	1345	3	(	(	PUNCT
ejpam-6834	1345	4	m	m	NOUN
ejpam-6834	1345	5	,	,	PUNCT
ejpam-6834	1345	6	n	n	CCONJ
ejpam-6834	1345	7	)	)	PUNCT
ejpam-6834	1345	8	v;q	v;q	PROPN
ejpam-6834	1345	9	(	(	PUNCT
ejpam-6834	1345	10	b	b	NOUN
ejpam-6834	1345	11	,	,	PUNCT
ejpam-6834	1345	12	a	a	PRON
ejpam-6834	1345	13	)	)	PUNCT
ejpam-6834	1345	14	=	=	SYM
ejpam-6834	1345	15	˜pdf	˜pdf	NOUN
ejpam-6834	1345	16	(	(	PUNCT
ejpam-6834	1345	17	m	m	NOUN
ejpam-6834	1345	18	,	,	PUNCT
ejpam-6834	1345	19	n	n	CCONJ
ejpam-6834	1345	20	)	)	PUNCT
ejpam-6834	1345	21	v	v	NOUN
ejpam-6834	1345	22	(	(	PUNCT
ejpam-6834	1345	23	f−1	f−1	PROPN
ejpam-6834	1345	24	(	(	PUNCT
ejpam-6834	1345	25	m)(b	m)(b	PROPN
ejpam-6834	1345	26	)	)	PUNCT
ejpam-6834	1345	27	,	,	PUNCT
ejpam-6834	1345	28	a	a	DET
ejpam-6834	1345	29	)	)	PUNCT
ejpam-6834	1345	30	∈	∈	PROPN
ejpam-6834	1345	31	c	c	NOUN
ejpam-6834	1345	32	=	=	PUNCT
ejpam-6834	1345	33	(	(	PUNCT
ejpam-6834	1345	34	pn	pn	PROPN
ejpam-6834	1345	35	+	+	PROPN
ejpam-6834	1345	36	(	(	PUNCT
ejpam-6834	1345	37	[	[	NOUN
ejpam-6834	1345	38	0	0	NUM
ejpam-6834	1345	39	,	,	PUNCT
ejpam-6834	1345	40	1]s))k	1]s))k	PROPN
ejpam-6834	1345	41	with	with	ADP
ejpam-6834	1345	42	nonempty	nonempty	ADJ
ejpam-6834	1345	43	coordinates	coordinate	NOUN
ejpam-6834	1345	44	.	.	PUNCT
ejpam-6834	1346	1	the	the	DET
ejpam-6834	1346	2	attribute	attribute	NOUN
ejpam-6834	1346	3	v	v	NOUN
ejpam-6834	1346	4	,	,	PUNCT
ejpam-6834	1346	5	its	its	PRON
ejpam-6834	1346	6	value	value	NOUN
ejpam-6834	1346	7	set	set	VERB
ejpam-6834	1346	8	pv	pv	INTJ
ejpam-6834	1346	9	,	,	PUNCT
ejpam-6834	1346	10	and	and	CCONJ
ejpam-6834	1346	11	the	the	DET
ejpam-6834	1346	12	contradiction	contradiction	NOUN
ejpam-6834	1346	13	function	function	NOUN
ejpam-6834	1346	14	pcf	pcf	PROPN
ejpam-6834	1346	15	are	be	AUX
ejpam-6834	1346	16	unchanged	unchanged	ADJ
ejpam-6834	1346	17	.	.	PUNCT
ejpam-6834	1347	1	hence	hence	ADV
ejpam-6834	1347	2	all	all	DET
ejpam-6834	1347	3	clauses	clause	NOUN
ejpam-6834	1347	4	of	of	ADP
ejpam-6834	1347	5	definition	definition	NOUN
ejpam-6834	1347	6	24	24	NUM
ejpam-6834	1347	7	hold	hold	NOUN
ejpam-6834	1347	8	on	on	ADP
ejpam-6834	1347	9	q.	q.	PROPN
ejpam-6834	1347	10	theorem	theorem	VERB
ejpam-6834	1347	11	46	46	NUM
ejpam-6834	1347	12	(	(	PUNCT
ejpam-6834	1347	13	reduction	reduction	NOUN
ejpam-6834	1347	14	to	to	ADP
ejpam-6834	1347	15	the	the	DET
ejpam-6834	1347	16	classical	classical	ADJ
ejpam-6834	1347	17	case	case	NOUN
ejpam-6834	1347	18	)	)	PUNCT
ejpam-6834	1347	19	.	.	PUNCT
ejpam-6834	1348	1	if	if	SCONJ
ejpam-6834	1348	2	h	h	NOUN
ejpam-6834	1348	3	=	=	SYM
ejpam-6834	1348	4	k	k	NOUN
ejpam-6834	1348	5	=	=	SYM
ejpam-6834	1348	6	1	1	NUM
ejpam-6834	1348	7	,	,	PUNCT
ejpam-6834	1348	8	then	then	ADV
ejpam-6834	1348	9	˜pdf	˜pdf	NOUN
ejpam-6834	1348	10	(	(	PUNCT
ejpam-6834	1348	11	m	m	NOUN
ejpam-6834	1348	12	,	,	PUNCT
ejpam-6834	1348	13	n	n	CCONJ
ejpam-6834	1348	14	)	)	PUNCT
ejpam-6834	1348	15	v	v	NOUN
ejpam-6834	1348	16	:	:	PUNCT
ejpam-6834	1348	17	pm	pm	NOUN
ejpam-6834	1348	18	+	+	CCONJ
ejpam-6834	1348	19	(	(	PUNCT
ejpam-6834	1348	20	p	p	NOUN
ejpam-6834	1348	21	)	)	PUNCT
ejpam-6834	1348	22	×	×	NOUN
ejpam-6834	1348	23	pv	pv	NOUN
ejpam-6834	1348	24	→	→	PUNCT
ejpam-6834	1348	25	pn	pn	NOUN
ejpam-6834	1348	26	+	+	PROPN
ejpam-6834	1348	27	(	(	PUNCT
ejpam-6834	1348	28	[	[	NOUN
ejpam-6834	1348	29	0	0	NUM
ejpam-6834	1348	30	,	,	PUNCT
ejpam-6834	1348	31	1]s	1]s	NUM
ejpam-6834	1348	32	)	)	PUNCT
ejpam-6834	1348	33	is	be	AUX
ejpam-6834	1348	34	exactly	exactly	ADV
ejpam-6834	1348	35	the	the	DET
ejpam-6834	1348	36	classical	classical	ADJ
ejpam-6834	1348	37	(	(	PUNCT
ejpam-6834	1348	38	m	m	PROPN
ejpam-6834	1348	39	,	,	PUNCT
ejpam-6834	1348	40	n)-superhyperplithogenic	n)-superhyperplithogenic	PUNCT
ejpam-6834	1348	41	set	set	NOUN
ejpam-6834	1348	42	.	.	PUNCT
ejpam-6834	1349	1	proof	proof	NOUN
ejpam-6834	1349	2	.	.	PUNCT
ejpam-6834	1350	1	as	as	ADP
ejpam-6834	1350	2	in	in	ADP
ejpam-6834	1350	3	the	the	DET
ejpam-6834	1350	4	proof	proof	NOUN
ejpam-6834	1350	5	of	of	ADP
ejpam-6834	1350	6	unary	unary	ADJ
ejpam-6834	1350	7	reduction	reduction	NOUN
ejpam-6834	1350	8	,	,	PUNCT
ejpam-6834	1350	9	apply	apply	VERB
ejpam-6834	1350	10	the	the	DET
ejpam-6834	1350	11	canonical	canonical	ADJ
ejpam-6834	1350	12	identifications	identification	NOUN
ejpam-6834	1350	13	(	(	PUNCT
ejpam-6834	1350	14	pm	pm	NOUN
ejpam-6834	1350	15	+	+	CCONJ
ejpam-6834	1350	16	(	(	PUNCT
ejpam-6834	1350	17	p	p	NOUN
ejpam-6834	1350	18	)	)	PUNCT
ejpam-6834	1350	19	)	)	PUNCT
ejpam-6834	1351	1	1	1	NUM
ejpam-6834	1351	2	∼=	∼=	NOUN
ejpam-6834	1351	3	pm	pm	NOUN
ejpam-6834	1351	4	+	+	CCONJ
ejpam-6834	1351	5	(	(	PUNCT
ejpam-6834	1351	6	p	p	NOUN
ejpam-6834	1351	7	)	)	PUNCT
ejpam-6834	1351	8	,	,	PUNCT
ejpam-6834	1351	9	(	(	PUNCT
ejpam-6834	1351	10	pn	pn	NOUN
ejpam-6834	1351	11	+	+	PROPN
ejpam-6834	1351	12	(	(	PUNCT
ejpam-6834	1351	13	[	[	NOUN
ejpam-6834	1351	14	0	0	NUM
ejpam-6834	1351	15	,	,	PUNCT
ejpam-6834	1351	16	1]s	1]s	NUM
ejpam-6834	1351	17	)	)	PUNCT
ejpam-6834	1351	18	)	)	PUNCT
ejpam-6834	1352	1	1	1	NUM
ejpam-6834	1352	2	∼=	∼=	NOUN
ejpam-6834	1352	3	pn	pn	NOUN
ejpam-6834	1352	4	+	+	NOUN
ejpam-6834	1352	5	(	(	PUNCT
ejpam-6834	1352	6	[	[	X
ejpam-6834	1352	7	0	0	NUM
ejpam-6834	1352	8	,	,	PUNCT
ejpam-6834	1352	9	1]s	1]s	NUM
ejpam-6834	1352	10	)	)	PUNCT
ejpam-6834	1352	11	,	,	PUNCT
ejpam-6834	1352	12	to	to	PART
ejpam-6834	1352	13	rewrite	rewrite	VERB
ejpam-6834	1352	14	the	the	DET
ejpam-6834	1352	15	multi	multi	ADJ
ejpam-6834	1352	16	–	–	PUNCT
ejpam-6834	1352	17	ary	ary	ADJ
ejpam-6834	1352	18	map	map	NOUN
ejpam-6834	1352	19	on	on	ADP
ejpam-6834	1352	20	d	d	X
ejpam-6834	1352	21	×	×	NOUN
ejpam-6834	1352	22	pv	pv	INTJ
ejpam-6834	1352	23	into	into	ADP
ejpam-6834	1352	24	the	the	DET
ejpam-6834	1352	25	unary	unary	ADJ
ejpam-6834	1352	26	map	map	NOUN
ejpam-6834	1352	27	˜pdf	˜pdf	NOUN
ejpam-6834	1352	28	(	(	PUNCT
ejpam-6834	1352	29	m	m	NOUN
ejpam-6834	1352	30	,	,	PUNCT
ejpam-6834	1352	31	n	n	CCONJ
ejpam-6834	1352	32	)	)	PUNCT
ejpam-6834	1352	33	v	v	NOUN
ejpam-6834	1352	34	:	:	PUNCT
ejpam-6834	1352	35	pm	pm	NOUN
ejpam-6834	1352	36	+	+	CCONJ
ejpam-6834	1352	37	(	(	PUNCT
ejpam-6834	1352	38	p	p	NOUN
ejpam-6834	1352	39	)	)	PUNCT
ejpam-6834	1352	40	×	×	NOUN
ejpam-6834	1352	41	pv	pv	INTJ
ejpam-6834	1352	42	−→	−→	NOUN
ejpam-6834	1352	43	pn	pn	PROPN
ejpam-6834	1353	1	+	+	PROPN
ejpam-6834	1353	2	(	(	PUNCT
ejpam-6834	1353	3	[	[	X
ejpam-6834	1353	4	0	0	NUM
ejpam-6834	1353	5	,	,	PUNCT
ejpam-6834	1353	6	1]s	1]s	NUM
ejpam-6834	1353	7	)	)	PUNCT
ejpam-6834	1353	8	.	.	PUNCT
ejpam-6834	1354	1	all	all	DET
ejpam-6834	1354	2	structural	structural	ADJ
ejpam-6834	1354	3	data	datum	NOUN
ejpam-6834	1354	4	(	(	PUNCT
ejpam-6834	1354	5	v	v	NOUN
ejpam-6834	1354	6	,	,	PUNCT
ejpam-6834	1354	7	pv	pv	INTJ
ejpam-6834	1354	8	,	,	PUNCT
ejpam-6834	1354	9	pcf	pcf	PROPN
ejpam-6834	1354	10	)	)	PUNCT
ejpam-6834	1354	11	are	be	AUX
ejpam-6834	1354	12	preserved	preserve	VERB
ejpam-6834	1354	13	verbatim	verbatim	ADJ
ejpam-6834	1354	14	,	,	PUNCT
ejpam-6834	1354	15	and	and	CCONJ
ejpam-6834	1354	16	nonemptiness	nonemptiness	NOUN
ejpam-6834	1354	17	/	/	SYM
ejpam-6834	1354	18	level	level	NOUN
ejpam-6834	1354	19	constraints	constraint	NOUN
ejpam-6834	1354	20	in	in	ADP
ejpam-6834	1354	21	the	the	DET
ejpam-6834	1354	22	codomain	codomain	NOUN
ejpam-6834	1354	23	are	be	AUX
ejpam-6834	1354	24	unchanged	unchanged	ADJ
ejpam-6834	1354	25	.	.	PUNCT
ejpam-6834	1355	1	this	this	PRON
ejpam-6834	1355	2	is	be	AUX
ejpam-6834	1355	3	precisely	precisely	ADV
ejpam-6834	1355	4	the	the	DET
ejpam-6834	1355	5	classical	classical	ADJ
ejpam-6834	1355	6	definition	definition	NOUN
ejpam-6834	1355	7	.	.	PUNCT
ejpam-6834	1356	1	t.	t.	PROPN
ejpam-6834	1356	2	fujita	fujita	PROPN
ejpam-6834	1356	3	,	,	PUNCT
ejpam-6834	1356	4	f.smarandache	f.smarandache	NOUN
ejpam-6834	1356	5	/	/	SYM
ejpam-6834	1356	6	eur	eur	PROPN
ejpam-6834	1356	7	.	.	PUNCT
ejpam-6834	1357	1	j.	j.	PROPN
ejpam-6834	1357	2	pure	pure	PROPN
ejpam-6834	1357	3	appl	appl	PROPN
ejpam-6834	1357	4	.	.	PROPN
ejpam-6834	1357	5	math	math	PROPN
ejpam-6834	1357	6	,	,	PUNCT
ejpam-6834	1357	7	18	18	NUM
ejpam-6834	1357	8	(	(	PUNCT
ejpam-6834	1357	9	4	4	NUM
ejpam-6834	1357	10	)	)	PUNCT
ejpam-6834	1357	11	(	(	PUNCT
ejpam-6834	1357	12	2025	2025	NUM
ejpam-6834	1357	13	)	)	PUNCT
ejpam-6834	1357	14	,	,	PUNCT
ejpam-6834	1357	15	6834	6834	NUM
ejpam-6834	1357	16	51	51	NUM
ejpam-6834	1357	17	of	of	ADP
ejpam-6834	1357	18	69	69	NUM
ejpam-6834	1357	19	4	4	NUM
ejpam-6834	1357	20	.	.	PUNCT
ejpam-6834	1358	1	additional	additional	ADJ
ejpam-6834	1358	2	result	result	NOUN
ejpam-6834	1358	3	:	:	PUNCT
ejpam-6834	1358	4	(	(	PUNCT
ejpam-6834	1358	5	h	h	NOUN
ejpam-6834	1358	6	,	,	PUNCT
ejpam-6834	1358	7	k)-ary	k)-ary	X
ejpam-6834	1358	8	(	(	PUNCT
ejpam-6834	1358	9	m	m	PROPN
ejpam-6834	1358	10	,	,	PUNCT
ejpam-6834	1358	11	n)-superhypersoft	n)-superhypersoft	ADV
ejpam-6834	1358	12	set	set	ADJ
ejpam-6834	1358	13	and	and	CCONJ
ejpam-6834	1358	14	(	(	PUNCT
ejpam-6834	1358	15	h	h	NOUN
ejpam-6834	1358	16	,	,	PUNCT
ejpam-6834	1358	17	k)-ary	k)-ary	X
ejpam-6834	1358	18	(	(	PUNCT
ejpam-6834	1358	19	m	m	PROPN
ejpam-6834	1358	20	,	,	PUNCT
ejpam-6834	1358	21	n)-superhyperrough	n)-superhyperrough	PUNCT
ejpam-6834	1358	22	set	set	VERB
ejpam-6834	1358	23	although	although	SCONJ
ejpam-6834	1358	24	superhypersoft	superhypersoft	PROPN
ejpam-6834	1358	25	sets	set	VERB
ejpam-6834	1358	26	and	and	CCONJ
ejpam-6834	1358	27	superhyperrough	superhyperrough	ADJ
ejpam-6834	1358	28	sets	set	NOUN
ejpam-6834	1358	29	have	have	AUX
ejpam-6834	1358	30	already	already	ADV
ejpam-6834	1358	31	been	be	AUX
ejpam-6834	1358	32	studied	study	VERB
ejpam-6834	1358	33	in	in	ADP
ejpam-6834	1358	34	existing	exist	VERB
ejpam-6834	1358	35	literature	literature	NOUN
ejpam-6834	1358	36	,	,	PUNCT
ejpam-6834	1358	37	their	their	PRON
ejpam-6834	1358	38	formulations	formulation	NOUN
ejpam-6834	1358	39	exhibit	exhibit	VERB
ejpam-6834	1358	40	slight	slight	ADJ
ejpam-6834	1358	41	conceptual	conceptual	ADJ
ejpam-6834	1358	42	differences	difference	NOUN
ejpam-6834	1358	43	from	from	ADP
ejpam-6834	1358	44	the	the	DET
ejpam-6834	1358	45	framework	framework	NOUN
ejpam-6834	1358	46	of	of	ADP
ejpam-6834	1358	47	superhyperuncertain	superhyperuncertain	ADJ
ejpam-6834	1358	48	sets	set	NOUN
ejpam-6834	1358	49	presented	present	VERB
ejpam-6834	1358	50	above	above	ADV
ejpam-6834	1358	51	.	.	PUNCT
ejpam-6834	1359	1	therefore	therefore	ADV
ejpam-6834	1359	2	,	,	PUNCT
ejpam-6834	1359	3	in	in	ADP
ejpam-6834	1359	4	this	this	DET
ejpam-6834	1359	5	paper	paper	NOUN
ejpam-6834	1359	6	,	,	PUNCT
ejpam-6834	1359	7	we	we	PRON
ejpam-6834	1359	8	deliberately	deliberately	ADV
ejpam-6834	1359	9	reconsider	reconsider	VERB
ejpam-6834	1359	10	and	and	CCONJ
ejpam-6834	1359	11	refine	refine	VERB
ejpam-6834	1359	12	their	their	PRON
ejpam-6834	1359	13	definitions	definition	NOUN
ejpam-6834	1359	14	to	to	PART
ejpam-6834	1359	15	better	well	ADJ
ejpam-6834	1359	16	suit	suit	VERB
ejpam-6834	1359	17	the	the	DET
ejpam-6834	1359	18	context	context	NOUN
ejpam-6834	1359	19	and	and	CCONJ
ejpam-6834	1359	20	objectives	objective	NOUN
ejpam-6834	1359	21	of	of	ADP
ejpam-6834	1359	22	the	the	DET
ejpam-6834	1359	23	present	present	ADJ
ejpam-6834	1359	24	study	study	NOUN
ejpam-6834	1359	25	.	.	PUNCT
ejpam-6834	1360	1	it	it	PRON
ejpam-6834	1360	2	is	be	AUX
ejpam-6834	1360	3	important	important	ADJ
ejpam-6834	1360	4	to	to	PART
ejpam-6834	1360	5	note	note	VERB
ejpam-6834	1360	6	that	that	SCONJ
ejpam-6834	1360	7	the	the	DET
ejpam-6834	1360	8	existing	exist	VERB
ejpam-6834	1360	9	definitions	definition	NOUN
ejpam-6834	1360	10	of	of	ADP
ejpam-6834	1360	11	superhypersoft	superhypersoft	NOUN
ejpam-6834	1360	12	sets	set	NOUN
ejpam-6834	1360	13	and	and	CCONJ
ejpam-6834	1360	14	superhyperrough	superhyperrough	ADJ
ejpam-6834	1360	15	sets	set	NOUN
ejpam-6834	1360	16	are	be	AUX
ejpam-6834	1360	17	,	,	PUNCT
ejpam-6834	1360	18	of	of	ADP
ejpam-6834	1360	19	course	course	NOUN
ejpam-6834	1360	20	,	,	PUNCT
ejpam-6834	1360	21	mathematically	mathematically	ADV
ejpam-6834	1360	22	correct	correct	ADJ
ejpam-6834	1360	23	.	.	PUNCT
ejpam-6834	1361	1	note	note	VERB
ejpam-6834	1361	2	that	that	SCONJ
ejpam-6834	1361	3	soft	soft	ADJ
ejpam-6834	1361	4	sets	set	NOUN
ejpam-6834	1361	5	assign	assign	VERB
ejpam-6834	1361	6	parameters	parameter	NOUN
ejpam-6834	1361	7	to	to	ADP
ejpam-6834	1361	8	subsets	subset	NOUN
ejpam-6834	1361	9	of	of	ADP
ejpam-6834	1361	10	a	a	DET
ejpam-6834	1361	11	universe	universe	NOUN
ejpam-6834	1361	12	,	,	PUNCT
ejpam-6834	1361	13	while	while	SCONJ
ejpam-6834	1361	14	k	k	ADJ
ejpam-6834	1361	15	-	-	ADJ
ejpam-6834	1361	16	ary	ary	ADJ
ejpam-6834	1361	17	soft	soft	ADJ
ejpam-6834	1361	18	sets	set	NOUN
ejpam-6834	1361	19	extend	extend	VERB
ejpam-6834	1361	20	this	this	DET
ejpam-6834	1361	21	mapping	mapping	NOUN
ejpam-6834	1361	22	to	to	ADP
ejpam-6834	1361	23	tuples	tuple	NOUN
ejpam-6834	1361	24	.	.	PUNCT
ejpam-6834	1362	1	in	in	ADP
ejpam-6834	1362	2	contrast	contrast	NOUN
ejpam-6834	1362	3	,	,	PUNCT
ejpam-6834	1362	4	(	(	PUNCT
ejpam-6834	1362	5	h	h	NOUN
ejpam-6834	1362	6	,	,	PUNCT
ejpam-6834	1362	7	k)-ary	k)-ary	X
ejpam-6834	1362	8	(	(	PUNCT
ejpam-6834	1362	9	m	m	PROPN
ejpam-6834	1362	10	,	,	PUNCT
ejpam-6834	1362	11	n)-superhypersoft	n)-superhypersoft	ADV
ejpam-6834	1362	12	sets	set	VERB
ejpam-6834	1362	13	embed	embed	VERB
ejpam-6834	1362	14	hierarchical	hierarchical	ADJ
ejpam-6834	1362	15	multi	multi	NOUN
ejpam-6834	1362	16	-	-	ADJ
ejpam-6834	1362	17	uncertainty	uncertainty	NOUN
ejpam-6834	1362	18	using	use	VERB
ejpam-6834	1362	19	iterated	iterated	ADJ
ejpam-6834	1362	20	powersets	powerset	NOUN
ejpam-6834	1362	21	and	and	CCONJ
ejpam-6834	1362	22	superhyperoperations	superhyperoperation	NOUN
ejpam-6834	1362	23	,	,	PUNCT
ejpam-6834	1362	24	capturing	capture	VERB
ejpam-6834	1362	25	complex	complex	ADJ
ejpam-6834	1362	26	interactions	interaction	NOUN
ejpam-6834	1362	27	across	across	ADP
ejpam-6834	1362	28	multiple	multiple	ADJ
ejpam-6834	1362	29	structural	structural	ADJ
ejpam-6834	1362	30	levels	level	NOUN
ejpam-6834	1362	31	.	.	PUNCT
ejpam-6834	1363	1	rough	rough	ADJ
ejpam-6834	1363	2	sets	set	NOUN
ejpam-6834	1363	3	approximate	approximate	ADJ
ejpam-6834	1363	4	subsets	subset	NOUN
ejpam-6834	1363	5	by	by	ADP
ejpam-6834	1363	6	lower	low	ADJ
ejpam-6834	1363	7	and	and	CCONJ
ejpam-6834	1363	8	upper	upper	ADJ
ejpam-6834	1363	9	bounds	bound	NOUN
ejpam-6834	1363	10	under	under	ADP
ejpam-6834	1363	11	an	an	DET
ejpam-6834	1363	12	indiscernibility	indiscernibility	NOUN
ejpam-6834	1363	13	relation	relation	NOUN
ejpam-6834	1363	14	.	.	PUNCT
ejpam-6834	1364	1	(	(	PUNCT
ejpam-6834	1364	2	h	h	NOUN
ejpam-6834	1364	3	,	,	PUNCT
ejpam-6834	1364	4	k)-ary	k)-ary	X
ejpam-6834	1364	5	(	(	PUNCT
ejpam-6834	1364	6	m	m	PROPN
ejpam-6834	1364	7	,	,	PUNCT
ejpam-6834	1364	8	n)superhyperrough	n)superhyperrough	ADJ
ejpam-6834	1364	9	sets	set	NOUN
ejpam-6834	1364	10	extend	extend	VERB
ejpam-6834	1364	11	this	this	PRON
ejpam-6834	1364	12	by	by	ADP
ejpam-6834	1364	13	encoding	encode	VERB
ejpam-6834	1364	14	hierarchical	hierarchical	ADJ
ejpam-6834	1364	15	,	,	PUNCT
ejpam-6834	1364	16	multi	multi	ADJ
ejpam-6834	1364	17	-	-	ADJ
ejpam-6834	1364	18	ary	ary	ADJ
ejpam-6834	1364	19	superhyperstructures	superhyperstructure	NOUN
ejpam-6834	1364	20	,	,	PUNCT
ejpam-6834	1364	21	enabling	enable	VERB
ejpam-6834	1364	22	refined	refined	ADJ
ejpam-6834	1364	23	layered	layered	ADJ
ejpam-6834	1364	24	approximations	approximation	NOUN
ejpam-6834	1364	25	,	,	PUNCT
ejpam-6834	1364	26	multi	multi	ADJ
ejpam-6834	1364	27	-	-	ADJ
ejpam-6834	1364	28	level	level	ADJ
ejpam-6834	1364	29	granularity	granularity	NOUN
ejpam-6834	1364	30	,	,	PUNCT
ejpam-6834	1364	31	and	and	CCONJ
ejpam-6834	1364	32	advanced	advanced	ADJ
ejpam-6834	1364	33	attribute	attribute	NOUN
ejpam-6834	1364	34	interactions	interaction	NOUN
ejpam-6834	1364	35	for	for	ADP
ejpam-6834	1364	36	complex	complex	ADJ
ejpam-6834	1364	37	uncertain	uncertain	ADJ
ejpam-6834	1364	38	domains	domain	NOUN
ejpam-6834	1364	39	.	.	PUNCT
ejpam-6834	1365	1	4.1	4.1	NUM
ejpam-6834	1365	2	.	.	PUNCT
ejpam-6834	1366	1	(	(	PUNCT
ejpam-6834	1366	2	h	h	NOUN
ejpam-6834	1366	3	,	,	PUNCT
ejpam-6834	1366	4	k)-ary	k)-ary	X
ejpam-6834	1366	5	(	(	PUNCT
ejpam-6834	1366	6	m	m	PROPN
ejpam-6834	1366	7	,	,	PUNCT
ejpam-6834	1366	8	n)-superhypersoft	n)-superhypersoft	ADV
ejpam-6834	1366	9	set	set	VERB
ejpam-6834	1366	10	for	for	ADP
ejpam-6834	1366	11	a	a	DET
ejpam-6834	1366	12	nonempty	nonempty	ADJ
ejpam-6834	1366	13	set	set	VERB
ejpam-6834	1366	14	x	x	NOUN
ejpam-6834	1366	15	,	,	PUNCT
ejpam-6834	1366	16	write	write	VERB
ejpam-6834	1366	17	p+(x	p+(x	PROPN
ejpam-6834	1366	18	)	)	PUNCT
ejpam-6834	1367	1	:	:	PUNCT
ejpam-6834	1367	2	=	=	X
ejpam-6834	1367	3	{	{	PUNCT
ejpam-6834	1367	4	a	a	PRON
ejpam-6834	1367	5	⊆	⊆	NUM
ejpam-6834	1367	6	x	x	SYM
ejpam-6834	1367	7	|	|	ADV
ejpam-6834	1367	8	a	a	DET
ejpam-6834	1367	9	̸=	̸=	PROPN
ejpam-6834	1367	10	∅	∅	NOUN
ejpam-6834	1367	11	}	}	PUNCT
ejpam-6834	1367	12	for	for	ADP
ejpam-6834	1367	13	the	the	DET
ejpam-6834	1367	14	nonempty	nonempty	ADJ
ejpam-6834	1367	15	powerset	powerset	NOUN
ejpam-6834	1367	16	.	.	PUNCT
ejpam-6834	1367	17	define	define	VERB
ejpam-6834	1367	18	the	the	DET
ejpam-6834	1367	19	rth	rth	NOUN
ejpam-6834	1367	20	nonempty	nonempty	ADV
ejpam-6834	1367	21	iterated	iterate	VERB
ejpam-6834	1367	22	powerset	powerset	NOUN
ejpam-6834	1367	23	recursively	recursively	ADV
ejpam-6834	1367	24	by	by	ADP
ejpam-6834	1367	25	p̃0(x	p̃0(x	NOUN
ejpam-6834	1367	26	)	)	PUNCT
ejpam-6834	1367	27	:	:	PUNCT
ejpam-6834	1368	1	=	=	SYM
ejpam-6834	1368	2	x	x	NOUN
ejpam-6834	1368	3	,	,	PUNCT
ejpam-6834	1368	4	p̃r+1(x	p̃r+1(x	NOUN
ejpam-6834	1368	5	)	)	PUNCT
ejpam-6834	1368	6	:	:	PUNCT
ejpam-6834	1369	1	=	=	SYM
ejpam-6834	1369	2	p+	p+	X
ejpam-6834	1369	3	(	(	PUNCT
ejpam-6834	1369	4	p̃r(x	p̃r(x	NOUN
ejpam-6834	1369	5	)	)	PUNCT
ejpam-6834	1369	6	)	)	PUNCT
ejpam-6834	1370	1	(	(	PUNCT
ejpam-6834	1370	2	r	r	NOUN
ejpam-6834	1370	3	≥	≥	NOUN
ejpam-6834	1370	4	0	0	NUM
ejpam-6834	1370	5	)	)	PUNCT
ejpam-6834	1370	6	.	.	PUNCT
ejpam-6834	1371	1	we	we	PRON
ejpam-6834	1371	2	use	use	VERB
ejpam-6834	1371	3	the	the	DET
ejpam-6834	1371	4	componentwise	componentwise	NOUN
ejpam-6834	1371	5	inclusion	inclusion	NOUN
ejpam-6834	1371	6	order	order	NOUN
ejpam-6834	1371	7	on	on	ADP
ejpam-6834	1371	8	cartesian	cartesian	ADJ
ejpam-6834	1371	9	powers	power	NOUN
ejpam-6834	1371	10	:	:	PUNCT
ejpam-6834	1371	11	for	for	ADP
ejpam-6834	1371	12	a	a	DET
ejpam-6834	1371	13	=	=	SYM
ejpam-6834	1371	14	(	(	PUNCT
ejpam-6834	1371	15	a1	a1	PROPN
ejpam-6834	1371	16	,	,	PUNCT
ejpam-6834	1371	17	.	.	PUNCT
ejpam-6834	1371	18	.	.	PUNCT
ejpam-6834	1371	19	.	.	PUNCT
ejpam-6834	1372	1	,	,	PUNCT
ejpam-6834	1372	2	ah	ah	INTJ
ejpam-6834	1372	3	)	)	PUNCT
ejpam-6834	1372	4	,	,	PUNCT
ejpam-6834	1372	5	a′	a′	PROPN
ejpam-6834	1372	6	=	=	SYM
ejpam-6834	1372	7	(	(	PUNCT
ejpam-6834	1372	8	a′	a′	PROPN
ejpam-6834	1372	9	1	1	NUM
ejpam-6834	1372	10	,	,	PUNCT
ejpam-6834	1372	11	.	.	PUNCT
ejpam-6834	1372	12	.	.	PUNCT
ejpam-6834	1373	1	.	.	PUNCT
ejpam-6834	1374	1	,	,	PUNCT
ejpam-6834	1374	2	a	a	PRON
ejpam-6834	1374	3	′	′	NOUN
ejpam-6834	1374	4	h	h	NOUN
ejpam-6834	1374	5	)	)	PUNCT
ejpam-6834	1374	6	∈	∈	PROPN
ejpam-6834	1374	7	(	(	PUNCT
ejpam-6834	1374	8	p̃m(s))h	p̃m(s))h	PROPN
ejpam-6834	1374	9	,	,	PUNCT
ejpam-6834	1374	10	write	write	VERB
ejpam-6834	1374	11	a	a	DET
ejpam-6834	1374	12	⊆	⊆	NUM
ejpam-6834	1374	13	a′	a′	NOUN
ejpam-6834	1374	14	if	if	SCONJ
ejpam-6834	1374	15	ai	ai	VERB
ejpam-6834	1374	16	⊆	⊆	NUM
ejpam-6834	1374	17	a′	a′	NOUN
ejpam-6834	1374	18	i	i	PRON
ejpam-6834	1374	19	for	for	ADP
ejpam-6834	1374	20	all	all	DET
ejpam-6834	1374	21	i.	i.	NOUN
ejpam-6834	1374	22	in	in	ADP
ejpam-6834	1374	23	classical	classical	ADJ
ejpam-6834	1374	24	soft	soft	ADJ
ejpam-6834	1374	25	set	set	NOUN
ejpam-6834	1374	26	theory	theory	NOUN
ejpam-6834	1374	27	[	[	X
ejpam-6834	1374	28	8	8	NUM
ejpam-6834	1374	29	,	,	PUNCT
ejpam-6834	1374	30	69	69	NUM
ejpam-6834	1374	31	]	]	PUNCT
ejpam-6834	1374	32	,	,	PUNCT
ejpam-6834	1374	33	one	one	NUM
ejpam-6834	1374	34	fixes	fix	VERB
ejpam-6834	1374	35	a	a	DET
ejpam-6834	1374	36	parameter	parameter	NOUN
ejpam-6834	1374	37	set	set	NOUN
ejpam-6834	1374	38	s	s	PART
ejpam-6834	1374	39	and	and	CCONJ
ejpam-6834	1374	40	uses	use	VERB
ejpam-6834	1374	41	a	a	DET
ejpam-6834	1374	42	mapping	mapping	NOUN
ejpam-6834	1374	43	f	f	NOUN
ejpam-6834	1374	44	:	:	PUNCT
ejpam-6834	1374	45	s	s	X
ejpam-6834	1374	46	→	→	PUNCT
ejpam-6834	1374	47	p(u	p(u	ADJ
ejpam-6834	1374	48	)	)	PUNCT
ejpam-6834	1374	49	.	.	PUNCT
ejpam-6834	1375	1	to	to	PART
ejpam-6834	1375	2	capture	capture	VERB
ejpam-6834	1375	3	hierarchical	hierarchical	ADJ
ejpam-6834	1375	4	parameter	parameter	NOUN
ejpam-6834	1375	5	groupings	grouping	NOUN
ejpam-6834	1375	6	and	and	CCONJ
ejpam-6834	1375	7	multi	multi	ADJ
ejpam-6834	1375	8	-	-	ADJ
ejpam-6834	1375	9	output	output	ADJ
ejpam-6834	1375	10	responses	response	NOUN
ejpam-6834	1375	11	,	,	PUNCT
ejpam-6834	1375	12	we	we	PRON
ejpam-6834	1375	13	lift	lift	VERB
ejpam-6834	1375	14	parameters	parameter	NOUN
ejpam-6834	1375	15	to	to	ADP
ejpam-6834	1375	16	the	the	DET
ejpam-6834	1375	17	mth	mth	NOUN
ejpam-6834	1375	18	iterated	iterate	VERB
ejpam-6834	1375	19	nonempty	nonempty	NOUN
ejpam-6834	1375	20	powerset	powerset	NOUN
ejpam-6834	1375	21	and	and	CCONJ
ejpam-6834	1375	22	allow	allow	VERB
ejpam-6834	1375	23	h	h	NOUN
ejpam-6834	1375	24	inputs	input	NOUN
ejpam-6834	1375	25	(	(	PUNCT
ejpam-6834	1375	26	interacting	interact	VERB
ejpam-6834	1375	27	parameter	parameter	NOUN
ejpam-6834	1375	28	aggregates	aggregate	NOUN
ejpam-6834	1375	29	)	)	PUNCT
ejpam-6834	1375	30	,	,	PUNCT
ejpam-6834	1375	31	while	while	SCONJ
ejpam-6834	1375	32	the	the	DET
ejpam-6834	1375	33	outputs	output	NOUN
ejpam-6834	1375	34	are	be	AUX
ejpam-6834	1375	35	lifted	lift	VERB
ejpam-6834	1375	36	to	to	ADP
ejpam-6834	1375	37	the	the	DET
ejpam-6834	1375	38	nth	nth	NOUN
ejpam-6834	1375	39	iterated	iterate	VERB
ejpam-6834	1375	40	nonempty	nonempty	NOUN
ejpam-6834	1375	41	powerset	powerset	NOUN
ejpam-6834	1375	42	and	and	CCONJ
ejpam-6834	1375	43	replicated	replicate	VERB
ejpam-6834	1375	44	in	in	ADP
ejpam-6834	1375	45	k	k	PROPN
ejpam-6834	1375	46	coordinates	coordinate	NOUN
ejpam-6834	1375	47	.	.	PUNCT
ejpam-6834	1376	1	definition	definition	NOUN
ejpam-6834	1376	2	25	25	NUM
ejpam-6834	1376	3	(	(	PUNCT
ejpam-6834	1376	4	(	(	PUNCT
ejpam-6834	1376	5	h	h	NOUN
ejpam-6834	1376	6	,	,	PUNCT
ejpam-6834	1376	7	k)-ary	k)-ary	X
ejpam-6834	1376	8	(	(	PUNCT
ejpam-6834	1376	9	m	m	PROPN
ejpam-6834	1376	10	,	,	PUNCT
ejpam-6834	1376	11	n)-superhypersoft	n)-superhypersoft	ADV
ejpam-6834	1376	12	set	set	NOUN
ejpam-6834	1376	13	)	)	PUNCT
ejpam-6834	1376	14	.	.	PUNCT
ejpam-6834	1377	1	let	let	VERB
ejpam-6834	1377	2	u	u	PRON
ejpam-6834	1377	3	be	be	AUX
ejpam-6834	1377	4	a	a	DET
ejpam-6834	1377	5	nonempty	nonempty	ADJ
ejpam-6834	1377	6	universe	universe	NOUN
ejpam-6834	1377	7	and	and	CCONJ
ejpam-6834	1377	8	s	s	VERB
ejpam-6834	1377	9	a	a	DET
ejpam-6834	1377	10	nonempty	nonempty	ADJ
ejpam-6834	1377	11	parameter	parameter	NOUN
ejpam-6834	1377	12	set	set	NOUN
ejpam-6834	1377	13	.	.	PUNCT
ejpam-6834	1378	1	fix	fix	VERB
ejpam-6834	1378	2	integers	integer	NOUN
ejpam-6834	1378	3	m	m	PRON
ejpam-6834	1378	4	,	,	PUNCT
ejpam-6834	1378	5	n	n	CCONJ
ejpam-6834	1378	6	,	,	PUNCT
ejpam-6834	1378	7	h	h	NOUN
ejpam-6834	1378	8	,	,	PUNCT
ejpam-6834	1378	9	k	k	PROPN
ejpam-6834	1378	10	≥	≥	NUM
ejpam-6834	1378	11	1	1	NUM
ejpam-6834	1378	12	.	.	PUNCT
ejpam-6834	1379	1	an	an	DET
ejpam-6834	1379	2	(	(	PUNCT
ejpam-6834	1379	3	h	h	NOUN
ejpam-6834	1379	4	,	,	PUNCT
ejpam-6834	1379	5	k)-ary	k)-ary	X
ejpam-6834	1379	6	(	(	PUNCT
ejpam-6834	1379	7	m	m	PROPN
ejpam-6834	1379	8	,	,	PUNCT
ejpam-6834	1379	9	n)superhypersoft	n)superhypersoft	PROPN
ejpam-6834	1379	10	set	set	VERB
ejpam-6834	1379	11	over	over	ADP
ejpam-6834	1379	12	u	u	NOUN
ejpam-6834	1379	13	(	(	PUNCT
ejpam-6834	1379	14	with	with	ADP
ejpam-6834	1379	15	respect	respect	NOUN
ejpam-6834	1379	16	to	to	ADP
ejpam-6834	1379	17	s	s	NOUN
ejpam-6834	1379	18	)	)	PUNCT
ejpam-6834	1379	19	is	be	AUX
ejpam-6834	1379	20	a	a	DET
ejpam-6834	1379	21	mapping	mapping	NOUN
ejpam-6834	1379	22	f	f	NOUN
ejpam-6834	1379	23	:	:	PUNCT
ejpam-6834	1379	24	(	(	PUNCT
ejpam-6834	1379	25	p̃m(s	p̃m(s	NOUN
ejpam-6834	1379	26	)	)	PUNCT
ejpam-6834	1379	27	)	)	PUNCT
ejpam-6834	1380	1	h	h	NOUN
ejpam-6834	1380	2	−→	−→	NOUN
ejpam-6834	1380	3	(	(	PUNCT
ejpam-6834	1380	4	p̃n(u	p̃n(u	NOUN
ejpam-6834	1380	5	)	)	PUNCT
ejpam-6834	1380	6	)	)	PUNCT
ejpam-6834	1381	1	k	k	X
ejpam-6834	1381	2	.	.	PUNCT
ejpam-6834	1382	1	for	for	ADP
ejpam-6834	1382	2	every	every	DET
ejpam-6834	1382	3	input	input	NOUN
ejpam-6834	1382	4	a	a	PRON
ejpam-6834	1382	5	=	=	SYM
ejpam-6834	1382	6	(	(	PUNCT
ejpam-6834	1382	7	a1	a1	PROPN
ejpam-6834	1382	8	,	,	PUNCT
ejpam-6834	1382	9	.	.	PUNCT
ejpam-6834	1382	10	.	.	PUNCT
ejpam-6834	1382	11	.	.	PUNCT
ejpam-6834	1383	1	,	,	PUNCT
ejpam-6834	1383	2	ah	ah	INTJ
ejpam-6834	1383	3	)	)	PUNCT
ejpam-6834	1383	4	∈	∈	PROPN
ejpam-6834	1383	5	(	(	PUNCT
ejpam-6834	1383	6	p̃m(s))h	p̃m(s))h	VERB
ejpam-6834	1383	7	the	the	DET
ejpam-6834	1383	8	value	value	NOUN
ejpam-6834	1383	9	f	f	X
ejpam-6834	1383	10	(	(	PUNCT
ejpam-6834	1383	11	a	a	X
ejpam-6834	1383	12	)	)	PUNCT
ejpam-6834	1383	13	=	=	SYM
ejpam-6834	1383	14	(	(	PUNCT
ejpam-6834	1383	15	b1	b1	PROPN
ejpam-6834	1383	16	,	,	PUNCT
ejpam-6834	1383	17	.	.	PUNCT
ejpam-6834	1383	18	.	.	PUNCT
ejpam-6834	1383	19	.	.	PUNCT
ejpam-6834	1384	1	,	,	PUNCT
ejpam-6834	1384	2	bk	bk	INTJ
ejpam-6834	1384	3	)	)	PUNCT
ejpam-6834	1384	4	t.	t.	PROPN
ejpam-6834	1384	5	fujita	fujita	PROPN
ejpam-6834	1384	6	,	,	PUNCT
ejpam-6834	1384	7	f.smarandache	f.smarandache	NOUN
ejpam-6834	1384	8	/	/	SYM
ejpam-6834	1384	9	eur	eur	PROPN
ejpam-6834	1384	10	.	.	PUNCT
ejpam-6834	1385	1	j.	j.	PROPN
ejpam-6834	1385	2	pure	pure	PROPN
ejpam-6834	1385	3	appl	appl	PROPN
ejpam-6834	1385	4	.	.	PROPN
ejpam-6834	1385	5	math	math	PROPN
ejpam-6834	1385	6	,	,	PUNCT
ejpam-6834	1385	7	18	18	NUM
ejpam-6834	1385	8	(	(	PUNCT
ejpam-6834	1385	9	4	4	NUM
ejpam-6834	1385	10	)	)	PUNCT
ejpam-6834	1385	11	(	(	PUNCT
ejpam-6834	1385	12	2025	2025	NUM
ejpam-6834	1385	13	)	)	PUNCT
ejpam-6834	1385	14	,	,	PUNCT
ejpam-6834	1385	15	6834	6834	NUM
ejpam-6834	1385	16	52	52	NUM
ejpam-6834	1385	17	of	of	ADP
ejpam-6834	1385	18	69	69	NUM
ejpam-6834	1385	19	is	be	AUX
ejpam-6834	1385	20	a	a	DET
ejpam-6834	1385	21	k	k	NOUN
ejpam-6834	1385	22	-	-	NOUN
ejpam-6834	1385	23	tuple	tuple	NOUN
ejpam-6834	1385	24	with	with	ADP
ejpam-6834	1385	25	each	each	PRON
ejpam-6834	1385	26	bj	bj	ADP
ejpam-6834	1385	27	∈	∈	PROPN
ejpam-6834	1385	28	p̃n(u	p̃n(u	NOUN
ejpam-6834	1385	29	)	)	PUNCT
ejpam-6834	1385	30	(	(	PUNCT
ejpam-6834	1385	31	in	in	ADP
ejpam-6834	1385	32	particular	particular	ADJ
ejpam-6834	1385	33	,	,	PUNCT
ejpam-6834	1385	34	each	each	DET
ejpam-6834	1385	35	bj	bj	VERB
ejpam-6834	1385	36	is	be	AUX
ejpam-6834	1385	37	nonempty	nonempty	ADJ
ejpam-6834	1385	38	and	and	CCONJ
ejpam-6834	1385	39	n	n	CCONJ
ejpam-6834	1385	40	-	-	PUNCT
ejpam-6834	1385	41	nested	nest	VERB
ejpam-6834	1385	42	)	)	PUNCT
ejpam-6834	1385	43	.	.	PUNCT
ejpam-6834	1386	1	when	when	SCONJ
ejpam-6834	1386	2	m	m	VERB
ejpam-6834	1386	3	=	=	SYM
ejpam-6834	1386	4	n	n	NOUN
ejpam-6834	1386	5	=	=	NOUN
ejpam-6834	1386	6	h	h	NOUN
ejpam-6834	1387	1	=	=	SYM
ejpam-6834	1387	2	k	k	NOUN
ejpam-6834	1387	3	=	=	PUNCT
ejpam-6834	1387	4	1	1	NUM
ejpam-6834	1387	5	this	this	PRON
ejpam-6834	1387	6	reduces	reduce	VERB
ejpam-6834	1387	7	(	(	PUNCT
ejpam-6834	1387	8	up	up	ADP
ejpam-6834	1387	9	to	to	ADP
ejpam-6834	1387	10	the	the	DET
ejpam-6834	1387	11	conventional	conventional	ADJ
ejpam-6834	1387	12	treatment	treatment	NOUN
ejpam-6834	1387	13	of	of	ADP
ejpam-6834	1387	14	the	the	DET
ejpam-6834	1387	15	empty	empty	ADJ
ejpam-6834	1387	16	set	set	NOUN
ejpam-6834	1387	17	)	)	PUNCT
ejpam-6834	1387	18	to	to	ADP
ejpam-6834	1387	19	the	the	DET
ejpam-6834	1387	20	classical	classical	ADJ
ejpam-6834	1387	21	soft	soft	ADJ
ejpam-6834	1387	22	set	set	NOUN
ejpam-6834	1387	23	.	.	PUNCT
ejpam-6834	1388	1	example	example	NOUN
ejpam-6834	1388	2	30	30	NUM
ejpam-6834	1388	3	(	(	PUNCT
ejpam-6834	1388	4	unary	unary	ADJ
ejpam-6834	1388	5	case	case	NOUN
ejpam-6834	1388	6	)	)	PUNCT
ejpam-6834	1388	7	.	.	PUNCT
ejpam-6834	1389	1	let	let	VERB
ejpam-6834	1389	2	u	u	PRON
ejpam-6834	1389	3	=	=	NOUN
ejpam-6834	1389	4	{	{	PUNCT
ejpam-6834	1389	5	u1	u1	NOUN
ejpam-6834	1389	6	,	,	PUNCT
ejpam-6834	1389	7	u2	u2	NOUN
ejpam-6834	1389	8	,	,	PUNCT
ejpam-6834	1389	9	u3	u3	NOUN
ejpam-6834	1389	10	}	}	PUNCT
ejpam-6834	1389	11	and	and	CCONJ
ejpam-6834	1389	12	s	s	NOUN
ejpam-6834	1389	13	=	=	X
ejpam-6834	1389	14	{	{	PUNCT
ejpam-6834	1389	15	a	a	PRON
ejpam-6834	1389	16	,	,	PUNCT
ejpam-6834	1389	17	b	b	NOUN
ejpam-6834	1389	18	}	}	PUNCT
ejpam-6834	1389	19	.	.	PUNCT
ejpam-6834	1390	1	then	then	ADV
ejpam-6834	1390	2	p̃1(s	p̃1(	VERB
ejpam-6834	1390	3	)	)	PUNCT
ejpam-6834	1390	4	=	=	SYM
ejpam-6834	1390	5	{	{	PUNCT
ejpam-6834	1390	6	{	{	PUNCT
ejpam-6834	1390	7	a	a	NOUN
ejpam-6834	1390	8	}	}	PUNCT
ejpam-6834	1390	9	,	,	PUNCT
ejpam-6834	1390	10	{	{	PUNCT
ejpam-6834	1390	11	b	b	NOUN
ejpam-6834	1390	12	}	}	PUNCT
ejpam-6834	1390	13	,	,	PUNCT
ejpam-6834	1390	14	{	{	PUNCT
ejpam-6834	1390	15	a	a	PRON
ejpam-6834	1390	16	,	,	PUNCT
ejpam-6834	1390	17	b	b	NOUN
ejpam-6834	1390	18	}	}	PUNCT
ejpam-6834	1390	19	}	}	PUNCT
ejpam-6834	1390	20	and	and	CCONJ
ejpam-6834	1390	21	p̃1(u	p̃1(u	PROPN
ejpam-6834	1390	22	)	)	PUNCT
ejpam-6834	1391	1	=	=	PRON
ejpam-6834	1391	2	{	{	PUNCT
ejpam-6834	1391	3	b	b	NOUN
ejpam-6834	1391	4	⊆	⊆	NUM
ejpam-6834	1391	5	u	u	NOUN
ejpam-6834	1391	6	|	|	NOUN
ejpam-6834	1391	7	b	b	NOUN
ejpam-6834	1391	8	̸=	̸=	PROPN
ejpam-6834	1391	9	∅	∅	NOUN
ejpam-6834	1391	10	}	}	PUNCT
ejpam-6834	1391	11	.	.	PUNCT
ejpam-6834	1392	1	for	for	ADP
ejpam-6834	1392	2	m	m	PROPN
ejpam-6834	1392	3	=	=	SYM
ejpam-6834	1392	4	n	n	PROPN
ejpam-6834	1392	5	=	=	NOUN
ejpam-6834	1392	6	h	h	NOUN
ejpam-6834	1392	7	=	=	SYM
ejpam-6834	1392	8	k	k	NOUN
ejpam-6834	1392	9	=	=	SYM
ejpam-6834	1392	10	1	1	NUM
ejpam-6834	1392	11	,	,	PUNCT
ejpam-6834	1392	12	an	an	DET
ejpam-6834	1392	13	(	(	PUNCT
ejpam-6834	1392	14	1	1	NUM
ejpam-6834	1392	15	,	,	PUNCT
ejpam-6834	1392	16	1)-ary	1)-ary	ADJ
ejpam-6834	1392	17	(	(	PUNCT
ejpam-6834	1392	18	1	1	NUM
ejpam-6834	1392	19	,	,	PUNCT
ejpam-6834	1392	20	1)-superhypersoft	1)-superhypersoft	NUM
ejpam-6834	1392	21	set	set	NOUN
ejpam-6834	1392	22	is	be	AUX
ejpam-6834	1392	23	a	a	DET
ejpam-6834	1392	24	map	map	NOUN
ejpam-6834	1392	25	f	f	NOUN
ejpam-6834	1392	26	:	:	PUNCT
ejpam-6834	1392	27	p̃1(s	p̃1(s	PROPN
ejpam-6834	1392	28	)	)	PUNCT
ejpam-6834	1392	29	→	→	SYM
ejpam-6834	1392	30	p̃1(u	p̃1(u	PROPN
ejpam-6834	1392	31	)	)	PUNCT
ejpam-6834	1392	32	,	,	PUNCT
ejpam-6834	1392	33	e.g.	e.g.	ADV
ejpam-6834	1392	34	f	f	X
ejpam-6834	1392	35	(	(	PUNCT
ejpam-6834	1392	36	{	{	PUNCT
ejpam-6834	1392	37	a	a	NOUN
ejpam-6834	1392	38	}	}	PUNCT
ejpam-6834	1392	39	)	)	PUNCT
ejpam-6834	1392	40	=	=	SYM
ejpam-6834	1392	41	{	{	PUNCT
ejpam-6834	1392	42	u1	u1	NOUN
ejpam-6834	1392	43	,	,	PUNCT
ejpam-6834	1392	44	u2	u2	PROPN
ejpam-6834	1392	45	}	}	PUNCT
ejpam-6834	1392	46	,	,	PUNCT
ejpam-6834	1392	47	f	f	X
ejpam-6834	1392	48	(	(	PUNCT
ejpam-6834	1392	49	{	{	PUNCT
ejpam-6834	1392	50	b	b	NOUN
ejpam-6834	1392	51	}	}	PUNCT
ejpam-6834	1392	52	)	)	PUNCT
ejpam-6834	1393	1	=	=	PRON
ejpam-6834	1393	2	{	{	PUNCT
ejpam-6834	1393	3	u2	u2	NOUN
ejpam-6834	1393	4	,	,	PUNCT
ejpam-6834	1393	5	u3	u3	NOUN
ejpam-6834	1393	6	}	}	PUNCT
ejpam-6834	1393	7	,	,	PUNCT
ejpam-6834	1393	8	f	f	PROPN
ejpam-6834	1393	9	(	(	PUNCT
ejpam-6834	1393	10	{	{	PUNCT
ejpam-6834	1393	11	a	a	PRON
ejpam-6834	1393	12	,	,	PUNCT
ejpam-6834	1393	13	b	b	NOUN
ejpam-6834	1393	14	}	}	PUNCT
ejpam-6834	1393	15	)	)	PUNCT
ejpam-6834	1393	16	=	=	PRON
ejpam-6834	1393	17	{	{	PUNCT
ejpam-6834	1393	18	u1	u1	NOUN
ejpam-6834	1393	19	,	,	PUNCT
ejpam-6834	1393	20	u2	u2	NOUN
ejpam-6834	1393	21	,	,	PUNCT
ejpam-6834	1393	22	u3	u3	NOUN
ejpam-6834	1393	23	}	}	PUNCT
ejpam-6834	1393	24	.	.	PUNCT
ejpam-6834	1394	1	if	if	SCONJ
ejpam-6834	1394	2	one	one	PRON
ejpam-6834	1394	3	increases	increase	VERB
ejpam-6834	1394	4	h	h	NOUN
ejpam-6834	1394	5	and	and	CCONJ
ejpam-6834	1394	6	k	k	NOUN
ejpam-6834	1394	7	,	,	PUNCT
ejpam-6834	1394	8	inputs	input	NOUN
ejpam-6834	1394	9	become	become	VERB
ejpam-6834	1394	10	tuples	tuple	NOUN
ejpam-6834	1394	11	of	of	ADP
ejpam-6834	1394	12	parameter	parameter	NOUN
ejpam-6834	1394	13	-	-	PUNCT
ejpam-6834	1394	14	aggregates	aggregate	NOUN
ejpam-6834	1394	15	and	and	CCONJ
ejpam-6834	1394	16	outputs	output	NOUN
ejpam-6834	1394	17	become	become	VERB
ejpam-6834	1394	18	tuples	tuple	NOUN
ejpam-6834	1394	19	of	of	ADP
ejpam-6834	1394	20	nonempty	nonempty	ADJ
ejpam-6834	1394	21	u	u	NOUN
ejpam-6834	1394	22	-subsets	-subset	NOUN
ejpam-6834	1394	23	(	(	PUNCT
ejpam-6834	1394	24	or	or	CCONJ
ejpam-6834	1394	25	,	,	PUNCT
ejpam-6834	1394	26	for	for	ADP
ejpam-6834	1394	27	n	n	PROPN
ejpam-6834	1394	28	>	>	X
ejpam-6834	1394	29	1	1	NUM
ejpam-6834	1394	30	,	,	PUNCT
ejpam-6834	1394	31	of	of	ADP
ejpam-6834	1394	32	nested	nested	ADJ
ejpam-6834	1394	33	nonempty	nonempty	ADJ
ejpam-6834	1394	34	families	family	NOUN
ejpam-6834	1394	35	of	of	ADP
ejpam-6834	1394	36	such	such	ADJ
ejpam-6834	1394	37	)	)	PUNCT
ejpam-6834	1394	38	.	.	PUNCT
ejpam-6834	1395	1	example	example	NOUN
ejpam-6834	1395	2	31	31	NUM
ejpam-6834	1395	3	(	(	PUNCT
ejpam-6834	1395	4	personalized	personalize	VERB
ejpam-6834	1395	5	movie	movie	NOUN
ejpam-6834	1395	6	recommendations	recommendation	NOUN
ejpam-6834	1395	7	)	)	PUNCT
ejpam-6834	1395	8	.	.	PUNCT
ejpam-6834	1396	1	let	let	VERB
ejpam-6834	1396	2	u	u	PRON
ejpam-6834	1396	3	=	=	X
ejpam-6834	1396	4	{	{	PUNCT
ejpam-6834	1396	5	m1	m1	NOUN
ejpam-6834	1396	6	,	,	PUNCT
ejpam-6834	1396	7	.	.	PUNCT
ejpam-6834	1396	8	.	.	PUNCT
ejpam-6834	1397	1	.	.	PUNCT
ejpam-6834	1398	1	,	,	PUNCT
ejpam-6834	1398	2	m6	m6	PROPN
ejpam-6834	1398	3	}	}	PUNCT
ejpam-6834	1398	4	be	be	AUX
ejpam-6834	1398	5	a	a	DET
ejpam-6834	1398	6	catalog	catalog	NOUN
ejpam-6834	1398	7	and	and	CCONJ
ejpam-6834	1398	8	s	s	NOUN
ejpam-6834	1398	9	=	=	NOUN
ejpam-6834	1398	10	{	{	PUNCT
ejpam-6834	1398	11	comedy	comedy	NOUN
ejpam-6834	1398	12	,	,	PUNCT
ejpam-6834	1398	13	action	action	NOUN
ejpam-6834	1398	14	,	,	PUNCT
ejpam-6834	1398	15	drama	drama	NOUN
ejpam-6834	1398	16	}	}	PUNCT
ejpam-6834	1398	17	.	.	PUNCT
ejpam-6834	1399	1	choose	choose	VERB
ejpam-6834	1399	2	m	m	NOUN
ejpam-6834	1399	3	=	=	SYM
ejpam-6834	1399	4	2	2	NUM
ejpam-6834	1399	5	,	,	PUNCT
ejpam-6834	1399	6	n	n	NOUN
ejpam-6834	1399	7	=	=	SYM
ejpam-6834	1399	8	1	1	NUM
ejpam-6834	1399	9	,	,	PUNCT
ejpam-6834	1399	10	h	h	NOUN
ejpam-6834	1399	11	=	=	SYM
ejpam-6834	1399	12	2	2	NUM
ejpam-6834	1399	13	,	,	PUNCT
ejpam-6834	1399	14	k	k	NOUN
ejpam-6834	1399	15	=	=	SYM
ejpam-6834	1399	16	2	2	X
ejpam-6834	1399	17	.	.	PUNCT
ejpam-6834	1399	18	then	then	ADV
ejpam-6834	1399	19	p̃1(s	p̃1(	VERB
ejpam-6834	1399	20	)	)	PUNCT
ejpam-6834	1399	21	=	=	SYM
ejpam-6834	1399	22	p+(s	p+(s	PROPN
ejpam-6834	1399	23	)	)	PUNCT
ejpam-6834	1399	24	,	,	PUNCT
ejpam-6834	1399	25	p̃2(s	p̃2(s	PROPN
ejpam-6834	1399	26	)	)	PUNCT
ejpam-6834	1400	1	=	=	SYM
ejpam-6834	1400	2	p+	p+	X
ejpam-6834	1400	3	(	(	PUNCT
ejpam-6834	1400	4	p+(s	p+(s	NOUN
ejpam-6834	1400	5	)	)	PUNCT
ejpam-6834	1400	6	)	)	PUNCT
ejpam-6834	1400	7	,	,	PUNCT
ejpam-6834	1400	8	so	so	ADV
ejpam-6834	1400	9	each	each	DET
ejpam-6834	1400	10	element	element	NOUN
ejpam-6834	1400	11	of	of	ADP
ejpam-6834	1400	12	p̃2(s	p̃2(s	PROPN
ejpam-6834	1400	13	)	)	PUNCT
ejpam-6834	1400	14	is	be	AUX
ejpam-6834	1400	15	a	a	DET
ejpam-6834	1400	16	nonempty	nonempty	ADJ
ejpam-6834	1400	17	collection	collection	NOUN
ejpam-6834	1400	18	of	of	ADP
ejpam-6834	1400	19	nonempty	nonempty	ADJ
ejpam-6834	1400	20	genre	genre	NOUN
ejpam-6834	1400	21	-	-	PUNCT
ejpam-6834	1400	22	subsets	subset	NOUN
ejpam-6834	1400	23	.	.	PUNCT
ejpam-6834	1401	1	set	set	VERB
ejpam-6834	1401	2	d	d	NOUN
ejpam-6834	1401	3	=	=	PUNCT
ejpam-6834	1401	4	(	(	PUNCT
ejpam-6834	1401	5	p̃2(s	p̃2(s	PROPN
ejpam-6834	1401	6	)	)	PUNCT
ejpam-6834	1401	7	)	)	PUNCT
ejpam-6834	1401	8	2	2	NUM
ejpam-6834	1401	9	,	,	PUNCT
ejpam-6834	1401	10	c	c	NOUN
ejpam-6834	1401	11	=	=	SYM
ejpam-6834	1401	12	(	(	PUNCT
ejpam-6834	1401	13	p̃1(u	p̃1(u	PROPN
ejpam-6834	1401	14	)	)	PUNCT
ejpam-6834	1401	15	)	)	PUNCT
ejpam-6834	1401	16	2	2	X
ejpam-6834	1401	17	.	.	PUNCT
ejpam-6834	1401	18	pick	pick	VERB
ejpam-6834	1401	19	γ(1	γ(1	PROPN
ejpam-6834	1401	20	)	)	PUNCT
ejpam-6834	1402	1	=	=	PRON
ejpam-6834	1402	2	{	{	PUNCT
ejpam-6834	1402	3	{	{	PUNCT
ejpam-6834	1402	4	comedy	comedy	NOUN
ejpam-6834	1402	5	}	}	PUNCT
ejpam-6834	1402	6	,	,	PUNCT
ejpam-6834	1402	7	{	{	PUNCT
ejpam-6834	1402	8	action	action	NOUN
ejpam-6834	1402	9	,	,	PUNCT
ejpam-6834	1402	10	drama	drama	NOUN
ejpam-6834	1402	11	}	}	PUNCT
ejpam-6834	1402	12	}	}	PUNCT
ejpam-6834	1402	13	,	,	PUNCT
ejpam-6834	1402	14	γ(2	γ(2	PROPN
ejpam-6834	1402	15	)	)	PUNCT
ejpam-6834	1402	16	=	=	PRON
ejpam-6834	1402	17	{	{	PUNCT
ejpam-6834	1402	18	{	{	PUNCT
ejpam-6834	1402	19	action	action	NOUN
ejpam-6834	1402	20	}	}	PUNCT
ejpam-6834	1402	21	,	,	PUNCT
ejpam-6834	1402	22	{	{	PUNCT
ejpam-6834	1402	23	drama	drama	NOUN
ejpam-6834	1402	24	,	,	PUNCT
ejpam-6834	1402	25	comedy	comedy	NOUN
ejpam-6834	1402	26	}	}	PUNCT
ejpam-6834	1402	27	}	}	PUNCT
ejpam-6834	1402	28	∈	∈	PROPN
ejpam-6834	1402	29	p̃2(s	p̃2(s	NOUN
ejpam-6834	1402	30	)	)	PUNCT
ejpam-6834	1402	31	.	.	PUNCT
ejpam-6834	1403	1	a	a	PRON
ejpam-6834	1403	2	(	(	PUNCT
ejpam-6834	1403	3	2	2	NUM
ejpam-6834	1403	4	,	,	PUNCT
ejpam-6834	1403	5	2)-ary	2)-ary	NUM
ejpam-6834	1403	6	(	(	PUNCT
ejpam-6834	1403	7	2	2	NUM
ejpam-6834	1403	8	,	,	PUNCT
ejpam-6834	1403	9	1)-superhypersoft	1)-superhypersoft	NUM
ejpam-6834	1403	10	map	map	VERB
ejpam-6834	1403	11	f	f	NOUN
ejpam-6834	1404	1	:	:	PUNCT
ejpam-6834	1404	2	d	d	X
ejpam-6834	1404	3	→	→	SYM
ejpam-6834	1404	4	c	c	NOUN
ejpam-6834	1404	5	may	may	AUX
ejpam-6834	1404	6	assign	assign	VERB
ejpam-6834	1404	7	f	f	PROPN
ejpam-6834	1404	8	(	(	PUNCT
ejpam-6834	1404	9	γ(1	γ(1	PROPN
ejpam-6834	1404	10	)	)	PUNCT
ejpam-6834	1404	11	,	,	PUNCT
ejpam-6834	1404	12	γ(2	γ(2	PROPN
ejpam-6834	1404	13	)	)	PUNCT
ejpam-6834	1404	14	)	)	PUNCT
ejpam-6834	1405	1	=	=	PRON
ejpam-6834	1405	2	(	(	PUNCT
ejpam-6834	1405	3	b1	b1	NOUN
ejpam-6834	1405	4	,	,	PUNCT
ejpam-6834	1405	5	b2	b2	NOUN
ejpam-6834	1405	6	)	)	PUNCT
ejpam-6834	1405	7	,	,	PUNCT
ejpam-6834	1405	8	b1	b1	NOUN
ejpam-6834	1405	9	=	=	SYM
ejpam-6834	1405	10	{	{	PUNCT
ejpam-6834	1405	11	m1,m3,m5	m1,m3,m5	ADJ
ejpam-6834	1405	12	}	}	PUNCT
ejpam-6834	1405	13	,	,	PUNCT
ejpam-6834	1405	14	b2	b2	NOUN
ejpam-6834	1405	15	=	=	SYM
ejpam-6834	1405	16	{	{	PUNCT
ejpam-6834	1405	17	m2,m4	m2,m4	PROPN
ejpam-6834	1405	18	}	}	PUNCT
ejpam-6834	1405	19	,	,	PUNCT
ejpam-6834	1405	20	interpreted	interpret	VERB
ejpam-6834	1405	21	as	as	ADP
ejpam-6834	1405	22	primary	primary	ADJ
ejpam-6834	1405	23	and	and	CCONJ
ejpam-6834	1405	24	secondary	secondary	ADJ
ejpam-6834	1405	25	recommendations	recommendation	NOUN
ejpam-6834	1405	26	driven	drive	VERB
ejpam-6834	1405	27	by	by	ADP
ejpam-6834	1405	28	two	two	NUM
ejpam-6834	1405	29	hierarchical	hierarchical	ADJ
ejpam-6834	1405	30	genre	genre	NOUN
ejpam-6834	1405	31	profiles	profile	NOUN
ejpam-6834	1405	32	.	.	PUNCT
ejpam-6834	1406	1	example	example	NOUN
ejpam-6834	1406	2	32	32	NUM
ejpam-6834	1406	3	(	(	PUNCT
ejpam-6834	1406	4	university	university	NOUN
ejpam-6834	1406	5	course	course	NOUN
ejpam-6834	1406	6	planning	planning	NOUN
ejpam-6834	1406	7	as	as	ADP
ejpam-6834	1406	8	a	a	DET
ejpam-6834	1406	9	(	(	PUNCT
ejpam-6834	1406	10	2	2	NUM
ejpam-6834	1406	11	,	,	PUNCT
ejpam-6834	1406	12	2)-ary	2)-ary	NUM
ejpam-6834	1406	13	(	(	PUNCT
ejpam-6834	1406	14	2	2	NUM
ejpam-6834	1406	15	,	,	PUNCT
ejpam-6834	1406	16	1)-superhypersoft	1)-superhypersoft	NUM
ejpam-6834	1406	17	set	set	NOUN
ejpam-6834	1406	18	)	)	PUNCT
ejpam-6834	1406	19	.	.	PUNCT
ejpam-6834	1407	1	let	let	VERB
ejpam-6834	1407	2	the	the	DET
ejpam-6834	1407	3	universe	universe	NOUN
ejpam-6834	1407	4	of	of	ADP
ejpam-6834	1407	5	objects	object	NOUN
ejpam-6834	1407	6	be	be	AUX
ejpam-6834	1407	7	the	the	DET
ejpam-6834	1407	8	catalog	catalog	NOUN
ejpam-6834	1407	9	of	of	ADP
ejpam-6834	1407	10	next	next	ADJ
ejpam-6834	1407	11	-	-	PUNCT
ejpam-6834	1407	12	term	term	NOUN
ejpam-6834	1407	13	courses	course	NOUN
ejpam-6834	1407	14	u	u	NOUN
ejpam-6834	1407	15	=	=	X
ejpam-6834	1407	16	{	{	PUNCT
ejpam-6834	1407	17	cs101,cs102,math201,stat210,ai310,nlp320,sys220,hci230	cs101,cs102,math201,stat210,ai310,nlp320,sys220,hci230	ADJ
ejpam-6834	1407	18	}	}	PUNCT
ejpam-6834	1407	19	.	.	PUNCT
ejpam-6834	1408	1	let	let	VERB
ejpam-6834	1408	2	the	the	DET
ejpam-6834	1408	3	parameter	parameter	NOUN
ejpam-6834	1408	4	set	set	VERB
ejpam-6834	1408	5	encode	encode	ADJ
ejpam-6834	1408	6	requirement	requirement	NOUN
ejpam-6834	1408	7	tags	tag	NOUN
ejpam-6834	1408	8	and	and	CCONJ
ejpam-6834	1408	9	scheduling	scheduling	NOUN
ejpam-6834	1408	10	constraints	constraint	NOUN
ejpam-6834	1408	11	:	:	PUNCT
ejpam-6834	1408	12	s	s	X
ejpam-6834	1408	13	=	=	PUNCT
ejpam-6834	1408	14	{	{	PUNCT
ejpam-6834	1408	15	req	req	NOUN
ejpam-6834	1408	16	-	-	PUNCT
ejpam-6834	1408	17	core	core	ADJ
ejpam-6834	1408	18	,	,	PUNCT
ejpam-6834	1408	19	req	req	NOUN
ejpam-6834	1408	20	-	-	PUNCT
ejpam-6834	1408	21	math	math	NOUN
ejpam-6834	1408	22	,	,	PUNCT
ejpam-6834	1408	23	req	req	NOUN
ejpam-6834	1408	24	-	-	PUNCT
ejpam-6834	1408	25	ai	ai	VERB
ejpam-6834	1408	26	,	,	PUNCT
ejpam-6834	1408	27	req	req	ADJ
ejpam-6834	1408	28	-	-	PUNCT
ejpam-6834	1408	29	systems	system	NOUN
ejpam-6834	1408	30	,	,	PUNCT
ejpam-6834	1408	31	time	time	NOUN
ejpam-6834	1408	32	-	-	PUNCT
ejpam-6834	1408	33	morning	morning	NOUN
ejpam-6834	1408	34	,	,	PUNCT
ejpam-6834	1408	35	time	time	NOUN
ejpam-6834	1408	36	-	-	PUNCT
ejpam-6834	1408	37	afternoon	afternoon	NOUN
ejpam-6834	1408	38	,	,	PUNCT
ejpam-6834	1408	39	mode	mode	NOUN
ejpam-6834	1408	40	-	-	PUNCT
ejpam-6834	1408	41	inperson	inperson	NOUN
ejpam-6834	1408	42	,	,	PUNCT
ejpam-6834	1408	43	no	no	PRON
ejpam-6834	1408	44	-	-	PUNCT
ejpam-6834	1408	45	friday	friday	PROPN
ejpam-6834	1408	46	}	}	PUNCT
ejpam-6834	1408	47	.	.	PUNCT
ejpam-6834	1409	1	we	we	PRON
ejpam-6834	1409	2	choose	choose	VERB
ejpam-6834	1409	3	m	m	NOUN
ejpam-6834	1409	4	=	=	SYM
ejpam-6834	1409	5	2	2	NUM
ejpam-6834	1409	6	,	,	PUNCT
ejpam-6834	1409	7	n	n	NOUN
ejpam-6834	1409	8	=	=	SYM
ejpam-6834	1409	9	1	1	NUM
ejpam-6834	1409	10	,	,	PUNCT
ejpam-6834	1409	11	h	h	NOUN
ejpam-6834	1409	12	=	=	SYM
ejpam-6834	1409	13	2	2	NUM
ejpam-6834	1409	14	,	,	PUNCT
ejpam-6834	1409	15	k	k	NOUN
ejpam-6834	1409	16	=	=	SYM
ejpam-6834	1409	17	2	2	X
ejpam-6834	1409	18	.	.	PUNCT
ejpam-6834	1410	1	thus	thus	ADV
ejpam-6834	1410	2	the	the	DET
ejpam-6834	1410	3	domain	domain	NOUN
ejpam-6834	1410	4	is	be	AUX
ejpam-6834	1410	5	d	d	NOUN
ejpam-6834	1410	6	=	=	PUNCT
ejpam-6834	1410	7	(	(	PUNCT
ejpam-6834	1410	8	p̃2(s))2	p̃2(s))2	NOUN
ejpam-6834	1410	9	,	,	PUNCT
ejpam-6834	1410	10	where	where	SCONJ
ejpam-6834	1410	11	p̃1(s	p̃1(	VERB
ejpam-6834	1410	12	)	)	PUNCT
ejpam-6834	1410	13	=	=	SYM
ejpam-6834	1410	14	{	{	PUNCT
ejpam-6834	1410	15	a	a	DET
ejpam-6834	1410	16	⊆	⊆	NUM
ejpam-6834	1410	17	s	s	NOUN
ejpam-6834	1410	18	|	|	ADV
ejpam-6834	1410	19	a	a	DET
ejpam-6834	1410	20	̸=	̸=	PROPN
ejpam-6834	1410	21	∅	∅	NOUN
ejpam-6834	1410	22	}	}	PUNCT
ejpam-6834	1410	23	,	,	PUNCT
ejpam-6834	1410	24	p̃2(s	p̃2(s	PROPN
ejpam-6834	1410	25	)	)	PUNCT
ejpam-6834	1411	1	=	=	SYM
ejpam-6834	1411	2	{	{	PUNCT
ejpam-6834	1411	3	γ	γ	X
ejpam-6834	1411	4	⊆	⊆	NUM
ejpam-6834	1411	5	p̃1(s	p̃1(	NOUN
ejpam-6834	1411	6	)	)	PUNCT
ejpam-6834	1411	7	|	|	ADV
ejpam-6834	1411	8	γ	γ	PROPN
ejpam-6834	1411	9	̸=	̸=	PROPN
ejpam-6834	1411	10	∅	∅	NOUN
ejpam-6834	1411	11	}	}	PUNCT
ejpam-6834	1411	12	.	.	PUNCT
ejpam-6834	1412	1	the	the	DET
ejpam-6834	1412	2	codomain	codomain	NOUN
ejpam-6834	1412	3	is	be	AUX
ejpam-6834	1412	4	(	(	PUNCT
ejpam-6834	1412	5	p̃1(u))2	p̃1(u))2	NOUN
ejpam-6834	1412	6	,	,	PUNCT
ejpam-6834	1412	7	i.e.	i.e.	X
ejpam-6834	1412	8	,	,	PUNCT
ejpam-6834	1412	9	ordered	order	VERB
ejpam-6834	1412	10	pairs	pair	NOUN
ejpam-6834	1412	11	of	of	ADP
ejpam-6834	1412	12	nonempty	nonempty	ADJ
ejpam-6834	1412	13	subsets	subset	NOUN
ejpam-6834	1412	14	of	of	ADP
ejpam-6834	1412	15	u	u	PROPN
ejpam-6834	1412	16	.	.	PUNCT
ejpam-6834	1413	1	interpret	interpret	VERB
ejpam-6834	1413	2	the	the	DET
ejpam-6834	1413	3	two	two	NUM
ejpam-6834	1413	4	input	input	NOUN
ejpam-6834	1413	5	coordinates	coordinate	NOUN
ejpam-6834	1413	6	as	as	ADP
ejpam-6834	1413	7	:	:	PUNCT
ejpam-6834	1413	8	t.	t.	PROPN
ejpam-6834	1413	9	fujita	fujita	PROPN
ejpam-6834	1413	10	,	,	PUNCT
ejpam-6834	1413	11	f.smarandache	f.smarandache	NOUN
ejpam-6834	1413	12	/	/	SYM
ejpam-6834	1413	13	eur	eur	PROPN
ejpam-6834	1413	14	.	.	PUNCT
ejpam-6834	1414	1	j.	j.	PROPN
ejpam-6834	1414	2	pure	pure	PROPN
ejpam-6834	1414	3	appl	appl	PROPN
ejpam-6834	1414	4	.	.	PROPN
ejpam-6834	1414	5	math	math	PROPN
ejpam-6834	1414	6	,	,	PUNCT
ejpam-6834	1414	7	18	18	NUM
ejpam-6834	1414	8	(	(	PUNCT
ejpam-6834	1414	9	4	4	NUM
ejpam-6834	1414	10	)	)	PUNCT
ejpam-6834	1414	11	(	(	PUNCT
ejpam-6834	1414	12	2025	2025	NUM
ejpam-6834	1414	13	)	)	PUNCT
ejpam-6834	1414	14	,	,	PUNCT
ejpam-6834	1414	15	6834	6834	NUM
ejpam-6834	1414	16	53	53	NUM
ejpam-6834	1414	17	of	of	ADP
ejpam-6834	1414	18	69	69	NUM
ejpam-6834	1414	19	•	•	NUM
ejpam-6834	1414	20	coordinate	coordinate	NOUN
ejpam-6834	1414	21	1	1	NUM
ejpam-6834	1414	22	:	:	PUNCT
ejpam-6834	1414	23	a	a	DET
ejpam-6834	1414	24	cluster	cluster	NOUN
ejpam-6834	1414	25	of	of	ADP
ejpam-6834	1414	26	degree	degree	NOUN
ejpam-6834	1414	27	requirements	requirement	NOUN
ejpam-6834	1414	28	(	(	PUNCT
ejpam-6834	1414	29	hyper	hyper	ADJ
ejpam-6834	1414	30	–	–	PUNCT
ejpam-6834	1414	31	parameter	parameter	NOUN
ejpam-6834	1414	32	on	on	ADP
ejpam-6834	1414	33	s	s	NOUN
ejpam-6834	1414	34	)	)	PUNCT
ejpam-6834	1414	35	,	,	PUNCT
ejpam-6834	1414	36	•	•	NUM
ejpam-6834	1414	37	coordinate	coordinate	NOUN
ejpam-6834	1414	38	2	2	NUM
ejpam-6834	1414	39	:	:	PUNCT
ejpam-6834	1414	40	a	a	DET
ejpam-6834	1414	41	cluster	cluster	NOUN
ejpam-6834	1414	42	of	of	ADP
ejpam-6834	1414	43	personal	personal	ADJ
ejpam-6834	1414	44	constraints	constraint	NOUN
ejpam-6834	1414	45	/	/	SYM
ejpam-6834	1414	46	preferences	preference	NOUN
ejpam-6834	1414	47	(	(	PUNCT
ejpam-6834	1414	48	hyper	hyper	NOUN
ejpam-6834	1414	49	–	–	PUNCT
ejpam-6834	1414	50	parameter	parameter	NOUN
ejpam-6834	1414	51	on	on	ADP
ejpam-6834	1414	52	s	s	NOUN
ejpam-6834	1414	53	)	)	PUNCT
ejpam-6834	1414	54	.	.	PUNCT
ejpam-6834	1415	1	consider	consider	VERB
ejpam-6834	1415	2	the	the	DET
ejpam-6834	1415	3	concrete	concrete	ADJ
ejpam-6834	1415	4	hyper	hyper	NOUN
ejpam-6834	1415	5	–	–	PUNCT
ejpam-6834	1415	6	parameters	parameter	NOUN
ejpam-6834	1415	7	γreq	γreq	NOUN
ejpam-6834	1415	8	=	=	PUNCT
ejpam-6834	1415	9	{	{	PUNCT
ejpam-6834	1415	10	{	{	PUNCT
ejpam-6834	1415	11	req	req	NOUN
ejpam-6834	1415	12	-	-	PUNCT
ejpam-6834	1415	13	core	core	NOUN
ejpam-6834	1415	14	}	}	PUNCT
ejpam-6834	1415	15	,	,	PUNCT
ejpam-6834	1415	16	{	{	PUNCT
ejpam-6834	1415	17	req	req	NOUN
ejpam-6834	1415	18	-	-	PUNCT
ejpam-6834	1415	19	math	math	NOUN
ejpam-6834	1415	20	,	,	PUNCT
ejpam-6834	1415	21	req	req	NOUN
ejpam-6834	1415	22	-	-	PUNCT
ejpam-6834	1415	23	ai	ai	PROPN
ejpam-6834	1415	24	}	}	PUNCT
ejpam-6834	1415	25	}	}	PUNCT
ejpam-6834	1415	26	∈	∈	PROPN
ejpam-6834	1415	27	p̃2(s	p̃2(s	NOUN
ejpam-6834	1415	28	)	)	PUNCT
ejpam-6834	1415	29	,	,	PUNCT
ejpam-6834	1415	30	γpref	γpref	NOUN
ejpam-6834	1415	31	=	=	PRON
ejpam-6834	1415	32	{	{	PUNCT
ejpam-6834	1415	33	{	{	PUNCT
ejpam-6834	1415	34	time	time	NOUN
ejpam-6834	1415	35	-	-	PUNCT
ejpam-6834	1415	36	afternoon	afternoon	NOUN
ejpam-6834	1415	37	}	}	PUNCT
ejpam-6834	1415	38	,	,	PUNCT
ejpam-6834	1415	39	{	{	PUNCT
ejpam-6834	1415	40	mode	mode	NOUN
ejpam-6834	1415	41	-	-	PUNCT
ejpam-6834	1415	42	inperson	inperson	NOUN
ejpam-6834	1415	43	}	}	PUNCT
ejpam-6834	1415	44	,	,	PUNCT
ejpam-6834	1415	45	{	{	PUNCT
ejpam-6834	1415	46	no	no	DET
ejpam-6834	1415	47	-	-	PUNCT
ejpam-6834	1415	48	friday	friday	NOUN
ejpam-6834	1415	49	}	}	PUNCT
ejpam-6834	1415	50	}	}	PUNCT
ejpam-6834	1415	51	∈	∈	PROPN
ejpam-6834	1415	52	p̃2(s	p̃2(s	NOUN
ejpam-6834	1415	53	)	)	PUNCT
ejpam-6834	1415	54	.	.	PUNCT
ejpam-6834	1416	1	an	an	DET
ejpam-6834	1416	2	(	(	PUNCT
ejpam-6834	1416	3	h	h	NOUN
ejpam-6834	1416	4	,	,	PUNCT
ejpam-6834	1416	5	k)-ary	k)-ary	X
ejpam-6834	1416	6	(	(	PUNCT
ejpam-6834	1416	7	m	m	PROPN
ejpam-6834	1416	8	,	,	PUNCT
ejpam-6834	1416	9	n)-superhypersoft	n)-superhypersoft	ADV
ejpam-6834	1416	10	set	set	VERB
ejpam-6834	1416	11	is	be	AUX
ejpam-6834	1416	12	a	a	DET
ejpam-6834	1416	13	mapping	mapping	NOUN
ejpam-6834	1416	14	f	f	NOUN
ejpam-6834	1417	1	:	:	PUNCT
ejpam-6834	1417	2	d	d	X
ejpam-6834	1417	3	=	=	SYM
ejpam-6834	1417	4	(	(	PUNCT
ejpam-6834	1417	5	p̃2(s))2	p̃2(s))2	X
ejpam-6834	1417	6	−→	−→	NOUN
ejpam-6834	1417	7	(	(	PUNCT
ejpam-6834	1417	8	p̃1(u))2	p̃1(u))2	NUM
ejpam-6834	1417	9	,	,	PUNCT
ejpam-6834	1417	10	(	(	PUNCT
ejpam-6834	1417	11	γreq	γreq	ADJ
ejpam-6834	1417	12	,	,	PUNCT
ejpam-6834	1417	13	γpref	γpref	NOUN
ejpam-6834	1417	14	)	)	PUNCT
ejpam-6834	1417	15	7−→	7−→	PROPN
ejpam-6834	1417	16	(	(	PUNCT
ejpam-6834	1417	17	b1	b1	NOUN
ejpam-6834	1417	18	,	,	PUNCT
ejpam-6834	1417	19	b2	b2	NOUN
ejpam-6834	1417	20	)	)	PUNCT
ejpam-6834	1417	21	,	,	PUNCT
ejpam-6834	1417	22	where	where	SCONJ
ejpam-6834	1417	23	b1	b1	NOUN
ejpam-6834	1417	24	,	,	PUNCT
ejpam-6834	1417	25	b2	b2	NOUN
ejpam-6834	1417	26	⊆	⊆	NUM
ejpam-6834	1417	27	u	u	NOUN
ejpam-6834	1417	28	are	be	AUX
ejpam-6834	1417	29	nonempty	nonempty	X
ejpam-6834	1417	30	.	.	PUNCT
ejpam-6834	1418	1	for	for	ADP
ejpam-6834	1418	2	the	the	DET
ejpam-6834	1418	3	above	above	ADJ
ejpam-6834	1418	4	input	input	NOUN
ejpam-6834	1418	5	,	,	PUNCT
ejpam-6834	1418	6	define	define	VERB
ejpam-6834	1418	7	(	(	PUNCT
ejpam-6834	1418	8	one	one	NUM
ejpam-6834	1418	9	valid	valid	ADJ
ejpam-6834	1418	10	instantiation	instantiation	NOUN
ejpam-6834	1418	11	)	)	PUNCT
ejpam-6834	1418	12	b1	b1	NOUN
ejpam-6834	1418	13	=	=	SYM
ejpam-6834	1418	14	{	{	PUNCT
ejpam-6834	1418	15	cs101,math201,ai310	cs101,math201,ai310	PROPN
ejpam-6834	1418	16	}	}	PUNCT
ejpam-6834	1418	17	(	(	PUNCT
ejpam-6834	1418	18	primary	primary	ADJ
ejpam-6834	1418	19	plan	plan	NOUN
ejpam-6834	1418	20	:	:	PUNCT
ejpam-6834	1418	21	meets	meet	VERB
ejpam-6834	1418	22	core	core	NOUN
ejpam-6834	1418	23	/	/	SYM
ejpam-6834	1418	24	math	math	NOUN
ejpam-6834	1418	25	/	/	SYM
ejpam-6834	1418	26	ai	ai	NOUN
ejpam-6834	1418	27	while	while	SCONJ
ejpam-6834	1418	28	fitting	fitting	ADJ
ejpam-6834	1418	29	afternoon	afternoon	NOUN
ejpam-6834	1418	30	,	,	PUNCT
ejpam-6834	1418	31	in	in	ADP
ejpam-6834	1418	32	–	–	PUNCT
ejpam-6834	1418	33	person	person	NOUN
ejpam-6834	1418	34	,	,	PUNCT
ejpam-6834	1418	35	no	no	PRON
ejpam-6834	1418	36	–	–	PUNCT
ejpam-6834	1418	37	friday	friday	PROPN
ejpam-6834	1418	38	)	)	PUNCT
ejpam-6834	1418	39	,	,	PUNCT
ejpam-6834	1418	40	b2	b2	NOUN
ejpam-6834	1418	41	=	=	SYM
ejpam-6834	1418	42	{	{	PUNCT
ejpam-6834	1418	43	stat210,nlp320,hci230	stat210,nlp320,hci230	INTJ
ejpam-6834	1418	44	}	}	PUNCT
ejpam-6834	1418	45	(	(	PUNCT
ejpam-6834	1418	46	contingency	contingency	NOUN
ejpam-6834	1418	47	plan	plan	NOUN
ejpam-6834	1418	48	under	under	ADP
ejpam-6834	1418	49	the	the	DET
ejpam-6834	1418	50	same	same	ADJ
ejpam-6834	1418	51	preferences	preference	NOUN
ejpam-6834	1418	52	)	)	PUNCT
ejpam-6834	1418	53	.	.	PUNCT
ejpam-6834	1419	1	hence	hence	ADV
ejpam-6834	1419	2	f	f	PROPN
ejpam-6834	1419	3	(	(	PUNCT
ejpam-6834	1419	4	γreq	γreq	PROPN
ejpam-6834	1419	5	,	,	PUNCT
ejpam-6834	1419	6	γpref	γpref	NOUN
ejpam-6834	1419	7	)	)	PUNCT
ejpam-6834	1419	8	=	=	SYM
ejpam-6834	1419	9	(	(	PUNCT
ejpam-6834	1419	10	b1	b1	NOUN
ejpam-6834	1419	11	,	,	PUNCT
ejpam-6834	1419	12	b2	b2	NOUN
ejpam-6834	1419	13	)	)	PUNCT
ejpam-6834	1419	14	∈	∈	PROPN
ejpam-6834	1419	15	(	(	PUNCT
ejpam-6834	1419	16	p̃1(u	p̃1(u	NOUN
ejpam-6834	1419	17	)	)	PUNCT
ejpam-6834	1419	18	)	)	PUNCT
ejpam-6834	1419	19	2	2	X
ejpam-6834	1419	20	.	.	PUNCT
ejpam-6834	1420	1	the	the	DET
ejpam-6834	1420	2	nested	nested	ADJ
ejpam-6834	1420	3	,	,	PUNCT
ejpam-6834	1420	4	set	set	VERB
ejpam-6834	1420	5	–	–	PUNCT
ejpam-6834	1420	6	of	of	ADP
ejpam-6834	1420	7	–	–	PUNCT
ejpam-6834	1420	8	subsets	subset	NOUN
ejpam-6834	1420	9	form	form	NOUN
ejpam-6834	1420	10	of	of	ADP
ejpam-6834	1420	11	γreq	γreq	NOUN
ejpam-6834	1420	12	and	and	CCONJ
ejpam-6834	1420	13	γpref	γpref	NOUN
ejpam-6834	1420	14	lets	let	VERB
ejpam-6834	1420	15	a	a	DET
ejpam-6834	1420	16	program	program	NOUN
ejpam-6834	1420	17	advisor	advisor	NOUN
ejpam-6834	1420	18	encode	encode	ADJ
ejpam-6834	1420	19	hierarchical	hierarchical	ADJ
ejpam-6834	1420	20	requirement	requirement	NOUN
ejpam-6834	1420	21	/	/	SYM
ejpam-6834	1420	22	preference	preference	NOUN
ejpam-6834	1420	23	groupings	grouping	NOUN
ejpam-6834	1420	24	(	(	PUNCT
ejpam-6834	1420	25	e.g.	e.g.	ADV
ejpam-6834	1420	26	,	,	PUNCT
ejpam-6834	1420	27	“	"	PUNCT
ejpam-6834	1420	28	satisfy	satisfy	VERB
ejpam-6834	1420	29	req	req	NOUN
ejpam-6834	1420	30	-	-	PUNCT
ejpam-6834	1420	31	core	core	NOUN
ejpam-6834	1420	32	and	and	CCONJ
ejpam-6834	1420	33	at	at	ADV
ejpam-6834	1420	34	least	least	ADJ
ejpam-6834	1420	35	one	one	NUM
ejpam-6834	1420	36	of	of	ADP
ejpam-6834	1420	37	{	{	PUNCT
ejpam-6834	1420	38	req	req	NOUN
ejpam-6834	1420	39	-	-	PUNCT
ejpam-6834	1420	40	math	math	NOUN
ejpam-6834	1420	41	,	,	PUNCT
ejpam-6834	1420	42	req	req	NOUN
ejpam-6834	1420	43	-	-	PUNCT
ejpam-6834	1420	44	ai	ai	NOUN
ejpam-6834	1420	45	}	}	PUNCT
ejpam-6834	1420	46	”	"	PUNCT
ejpam-6834	1420	47	)	)	PUNCT
ejpam-6834	1420	48	together	together	ADV
ejpam-6834	1420	49	with	with	ADP
ejpam-6834	1420	50	scheduling	scheduling	NOUN
ejpam-6834	1420	51	clusters	cluster	NOUN
ejpam-6834	1420	52	(	(	PUNCT
ejpam-6834	1420	53	e.g.	e.g.	ADV
ejpam-6834	1420	54	,	,	PUNCT
ejpam-6834	1420	55	“	"	PUNCT
ejpam-6834	1420	56	afternoon	afternoon	NOUN
ejpam-6834	1420	57	and	and	CCONJ
ejpam-6834	1420	58	in	in	ADP
ejpam-6834	1420	59	–	–	PUNCT
ejpam-6834	1420	60	person	person	NOUN
ejpam-6834	1420	61	and	and	CCONJ
ejpam-6834	1420	62	no	no	NOUN
ejpam-6834	1420	63	–	–	PUNCT
ejpam-6834	1420	64	friday	friday	PROPN
ejpam-6834	1420	65	”	"	PUNCT
ejpam-6834	1420	66	)	)	PUNCT
ejpam-6834	1420	67	.	.	PUNCT
ejpam-6834	1421	1	the	the	DET
ejpam-6834	1421	2	two	two	NUM
ejpam-6834	1421	3	outputs	output	NOUN
ejpam-6834	1421	4	b1	b1	NOUN
ejpam-6834	1421	5	,	,	PUNCT
ejpam-6834	1421	6	b2	b2	NOUN
ejpam-6834	1421	7	provide	provide	VERB
ejpam-6834	1421	8	a	a	DET
ejpam-6834	1421	9	primary	primary	NOUN
ejpam-6834	1421	10	and	and	CCONJ
ejpam-6834	1421	11	a	a	DET
ejpam-6834	1421	12	backup	backup	ADJ
ejpam-6834	1421	13	recommendation	recommendation	NOUN
ejpam-6834	1421	14	set	set	NOUN
ejpam-6834	1421	15	,	,	PUNCT
ejpam-6834	1421	16	each	each	DET
ejpam-6834	1421	17	a	a	DET
ejpam-6834	1421	18	nonempty	nonempty	ADJ
ejpam-6834	1421	19	element	element	NOUN
ejpam-6834	1421	20	of	of	ADP
ejpam-6834	1421	21	p̃1(u	p̃1(u	PROPN
ejpam-6834	1421	22	)	)	PUNCT
ejpam-6834	1421	23	.	.	PUNCT
ejpam-6834	1422	1	this	this	PRON
ejpam-6834	1422	2	realizes	realize	VERB
ejpam-6834	1422	3	,	,	PUNCT
ejpam-6834	1422	4	in	in	ADP
ejpam-6834	1422	5	a	a	DET
ejpam-6834	1422	6	real	real	ADJ
ejpam-6834	1422	7	advising	advise	VERB
ejpam-6834	1422	8	scenario	scenario	NOUN
ejpam-6834	1422	9	,	,	PUNCT
ejpam-6834	1422	10	a	a	DET
ejpam-6834	1422	11	(	(	PUNCT
ejpam-6834	1422	12	2	2	NUM
ejpam-6834	1422	13	,	,	PUNCT
ejpam-6834	1422	14	2)-ary	2)-ary	NUM
ejpam-6834	1422	15	(	(	PUNCT
ejpam-6834	1422	16	2	2	NUM
ejpam-6834	1422	17	,	,	PUNCT
ejpam-6834	1422	18	1)-superhypersoft	1)-superhypersoft	NUM
ejpam-6834	1422	19	set	set	VERB
ejpam-6834	1422	20	in	in	ADP
ejpam-6834	1422	21	the	the	DET
ejpam-6834	1422	22	sense	sense	NOUN
ejpam-6834	1422	23	of	of	ADP
ejpam-6834	1422	24	the	the	DET
ejpam-6834	1422	25	definition	definition	NOUN
ejpam-6834	1422	26	above	above	ADV
ejpam-6834	1422	27	.	.	PUNCT
ejpam-6834	1423	1	theorem	theorem	VERB
ejpam-6834	1423	2	47	47	NUM
ejpam-6834	1423	3	(	(	PUNCT
ejpam-6834	1423	4	classical	classical	ADJ
ejpam-6834	1423	5	case	case	NOUN
ejpam-6834	1423	6	as	as	ADP
ejpam-6834	1423	7	a	a	DET
ejpam-6834	1423	8	special	special	ADJ
ejpam-6834	1423	9	instance	instance	NOUN
ejpam-6834	1423	10	)	)	PUNCT
ejpam-6834	1423	11	.	.	PUNCT
ejpam-6834	1424	1	every	every	DET
ejpam-6834	1424	2	classical	classical	ADJ
ejpam-6834	1424	3	soft	soft	ADJ
ejpam-6834	1424	4	set	set	ADJ
ejpam-6834	1424	5	fcl	fcl	PROPN
ejpam-6834	1424	6	:	:	PUNCT
ejpam-6834	1424	7	s	s	X
ejpam-6834	1424	8	→	→	PUNCT
ejpam-6834	1424	9	p(u	p(u	ADJ
ejpam-6834	1424	10	)	)	PUNCT
ejpam-6834	1424	11	is	be	AUX
ejpam-6834	1424	12	naturally	naturally	ADV
ejpam-6834	1424	13	represented	represent	VERB
ejpam-6834	1424	14	by	by	ADP
ejpam-6834	1424	15	an	an	DET
ejpam-6834	1424	16	(	(	PUNCT
ejpam-6834	1424	17	h	h	NOUN
ejpam-6834	1424	18	,	,	PUNCT
ejpam-6834	1424	19	k)-ary	k)-ary	X
ejpam-6834	1424	20	(	(	PUNCT
ejpam-6834	1424	21	m	m	PROPN
ejpam-6834	1424	22	,	,	PUNCT
ejpam-6834	1424	23	n)-superhypersoft	n)-superhypersoft	ADV
ejpam-6834	1424	24	set	set	VERB
ejpam-6834	1424	25	with	with	ADP
ejpam-6834	1424	26	m	m	PROPN
ejpam-6834	1424	27	=	=	SYM
ejpam-6834	1424	28	n	n	PROPN
ejpam-6834	1425	1	=	=	NOUN
ejpam-6834	1425	2	h	h	NOUN
ejpam-6834	1426	1	=	=	SYM
ejpam-6834	1426	2	k	k	NOUN
ejpam-6834	1426	3	=	=	SYM
ejpam-6834	1426	4	1	1	X
ejpam-6834	1426	5	.	.	PUNCT
ejpam-6834	1426	6	proof	proof	NOUN
ejpam-6834	1426	7	.	.	PUNCT
ejpam-6834	1427	1	set	set	VERB
ejpam-6834	1427	2	m	m	PROPN
ejpam-6834	1427	3	=	=	SYM
ejpam-6834	1427	4	n	n	PROPN
ejpam-6834	1427	5	=	=	NOUN
ejpam-6834	1427	6	h	h	NOUN
ejpam-6834	1428	1	=	=	SYM
ejpam-6834	1428	2	k	k	NOUN
ejpam-6834	1428	3	=	=	SYM
ejpam-6834	1428	4	1	1	X
ejpam-6834	1428	5	.	.	PUNCT
ejpam-6834	1429	1	the	the	DET
ejpam-6834	1429	2	domain	domain	NOUN
ejpam-6834	1429	3	of	of	ADP
ejpam-6834	1429	4	a	a	PRON
ejpam-6834	1429	5	(	(	PUNCT
ejpam-6834	1429	6	1	1	NUM
ejpam-6834	1429	7	,	,	PUNCT
ejpam-6834	1429	8	1)-ary	1)-ary	ADJ
ejpam-6834	1429	9	(	(	PUNCT
ejpam-6834	1429	10	1	1	NUM
ejpam-6834	1429	11	,	,	PUNCT
ejpam-6834	1429	12	1)-superhypersoft	1)-superhypersoft	NUM
ejpam-6834	1429	13	set	set	NOUN
ejpam-6834	1429	14	is	be	AUX
ejpam-6834	1429	15	p̃1(s	p̃1(	NOUN
ejpam-6834	1429	16	)	)	PUNCT
ejpam-6834	1429	17	=	=	SYM
ejpam-6834	1429	18	p+(s	p+(s	PROPN
ejpam-6834	1429	19	)	)	PUNCT
ejpam-6834	1429	20	(	(	PUNCT
ejpam-6834	1429	21	nonempty	nonempty	VERB
ejpam-6834	1429	22	subsets	subset	NOUN
ejpam-6834	1429	23	of	of	ADP
ejpam-6834	1429	24	s	s	NOUN
ejpam-6834	1429	25	)	)	PUNCT
ejpam-6834	1429	26	and	and	CCONJ
ejpam-6834	1429	27	its	its	PRON
ejpam-6834	1429	28	codomain	codomain	NOUN
ejpam-6834	1429	29	is	be	AUX
ejpam-6834	1429	30	p̃1(u	p̃1(u	PROPN
ejpam-6834	1429	31	)	)	PUNCT
ejpam-6834	1429	32	=	=	SYM
ejpam-6834	1430	1	p+(u	p+(u	PROPN
ejpam-6834	1430	2	)	)	PUNCT
ejpam-6834	1430	3	(	(	PUNCT
ejpam-6834	1430	4	nonempty	nonempty	VERB
ejpam-6834	1430	5	subsets	subset	NOUN
ejpam-6834	1430	6	of	of	ADP
ejpam-6834	1430	7	u	u	NOUN
ejpam-6834	1430	8	)	)	PUNCT
ejpam-6834	1430	9	.	.	PUNCT
ejpam-6834	1431	1	step	step	NOUN
ejpam-6834	1431	2	1	1	NUM
ejpam-6834	1431	3	(	(	PUNCT
ejpam-6834	1431	4	embedding	embed	VERB
ejpam-6834	1431	5	singletons	singleton	NOUN
ejpam-6834	1431	6	)	)	PUNCT
ejpam-6834	1431	7	.	.	PUNCT
ejpam-6834	1432	1	define	define	VERB
ejpam-6834	1432	2	the	the	DET
ejpam-6834	1432	3	canonical	canonical	ADJ
ejpam-6834	1432	4	injection	injection	NOUN
ejpam-6834	1432	5	ιs	ιs	NOUN
ejpam-6834	1432	6	:	:	PUNCT
ejpam-6834	1432	7	s	s	VERB
ejpam-6834	1432	8	−→	−→	NOUN
ejpam-6834	1432	9	p+(s	p+(	NOUN
ejpam-6834	1432	10	)	)	PUNCT
ejpam-6834	1432	11	,	,	PUNCT
ejpam-6834	1432	12	ιs(s	ιs(s	PUNCT
ejpam-6834	1432	13	)	)	PUNCT
ejpam-6834	1432	14	:	:	PUNCT
ejpam-6834	1433	1	=	=	PUNCT
ejpam-6834	1433	2	{	{	PUNCT
ejpam-6834	1433	3	s	s	NOUN
ejpam-6834	1433	4	}	}	PUNCT
ejpam-6834	1433	5	.	.	PUNCT
ejpam-6834	1434	1	although	although	SCONJ
ejpam-6834	1434	2	ιs	ιs	PRON
ejpam-6834	1434	3	is	be	AUX
ejpam-6834	1434	4	not	not	PART
ejpam-6834	1434	5	surjective	surjective	ADJ
ejpam-6834	1434	6	(	(	PUNCT
ejpam-6834	1434	7	multielement	multielement	NOUN
ejpam-6834	1434	8	parameter	parameter	NOUN
ejpam-6834	1434	9	blocks	block	NOUN
ejpam-6834	1434	10	are	be	AUX
ejpam-6834	1434	11	not	not	PART
ejpam-6834	1434	12	hit	hit	VERB
ejpam-6834	1434	13	)	)	PUNCT
ejpam-6834	1434	14	,	,	PUNCT
ejpam-6834	1434	15	it	it	PRON
ejpam-6834	1434	16	embeds	embed	VERB
ejpam-6834	1434	17	the	the	DET
ejpam-6834	1434	18	classical	classical	ADJ
ejpam-6834	1434	19	parameter	parameter	NOUN
ejpam-6834	1434	20	space	space	NOUN
ejpam-6834	1434	21	into	into	ADP
ejpam-6834	1434	22	the	the	DET
ejpam-6834	1434	23	level–1	level–1	PROPN
ejpam-6834	1434	24	parameter	parameter	NOUN
ejpam-6834	1434	25	space	space	NOUN
ejpam-6834	1434	26	on	on	ADP
ejpam-6834	1434	27	which	which	PRON
ejpam-6834	1434	28	superhypersoft	superhypersoft	PROPN
ejpam-6834	1434	29	sets	set	VERB
ejpam-6834	1434	30	act	act	PROPN
ejpam-6834	1434	31	.	.	PUNCT
ejpam-6834	1435	1	step	step	NOUN
ejpam-6834	1435	2	2	2	NUM
ejpam-6834	1435	3	(	(	PUNCT
ejpam-6834	1435	4	lifting	lift	VERB
ejpam-6834	1435	5	the	the	DET
ejpam-6834	1435	6	codomain	codomain	NOUN
ejpam-6834	1435	7	to	to	AUX
ejpam-6834	1435	8	nonempty	nonempty	VERB
ejpam-6834	1435	9	subsets	subset	NOUN
ejpam-6834	1435	10	)	)	PUNCT
ejpam-6834	1435	11	.	.	PUNCT
ejpam-6834	1436	1	if	if	SCONJ
ejpam-6834	1436	2	fcl(s	fcl(s	PROPN
ejpam-6834	1436	3	)	)	PUNCT
ejpam-6834	1436	4	̸=	̸=	PROPN
ejpam-6834	1436	5	∅	∅	NOUN
ejpam-6834	1436	6	for	for	ADP
ejpam-6834	1436	7	all	all	PRON
ejpam-6834	1436	8	s	s	PART
ejpam-6834	1436	9	∈	∈	PROPN
ejpam-6834	1436	10	s	s	NOUN
ejpam-6834	1436	11	,	,	PUNCT
ejpam-6834	1436	12	define	define	VERB
ejpam-6834	1436	13	lu	lu	NOUN
ejpam-6834	1436	14	:	:	PUNCT
ejpam-6834	1436	15	p(u	p(u	X
ejpam-6834	1436	16	)	)	PUNCT
ejpam-6834	1436	17	−→	−→	NOUN
ejpam-6834	1436	18	p+(u	p+(u	NUM
ejpam-6834	1436	19	)	)	PUNCT
ejpam-6834	1436	20	,	,	PUNCT
ejpam-6834	1436	21	lu	lu	PROPN
ejpam-6834	1436	22	(	(	PUNCT
ejpam-6834	1436	23	b	b	NOUN
ejpam-6834	1436	24	)	)	PUNCT
ejpam-6834	1436	25	:	:	PUNCT
ejpam-6834	1437	1	=	=	SYM
ejpam-6834	1437	2	b	b	X
ejpam-6834	1437	3	(	(	PUNCT
ejpam-6834	1437	4	which	which	PRON
ejpam-6834	1437	5	lies	lie	VERB
ejpam-6834	1437	6	in	in	ADP
ejpam-6834	1437	7	p+(u	p+(u	NOUN
ejpam-6834	1437	8	)	)	PUNCT
ejpam-6834	1437	9	)	)	PUNCT
ejpam-6834	1437	10	.	.	PUNCT
ejpam-6834	1438	1	if	if	SCONJ
ejpam-6834	1438	2	some	some	DET
ejpam-6834	1438	3	fcl(s	fcl(s	PROPN
ejpam-6834	1438	4	)	)	PUNCT
ejpam-6834	1438	5	may	may	AUX
ejpam-6834	1438	6	be	be	AUX
ejpam-6834	1438	7	empty	empty	ADJ
ejpam-6834	1438	8	,	,	PUNCT
ejpam-6834	1438	9	one	one	PRON
ejpam-6834	1438	10	may	may	AUX
ejpam-6834	1438	11	either	either	ADV
ejpam-6834	1438	12	:	:	PUNCT
ejpam-6834	1438	13	t.	t.	PROPN
ejpam-6834	1438	14	fujita	fujita	PROPN
ejpam-6834	1438	15	,	,	PUNCT
ejpam-6834	1438	16	f.smarandache	f.smarandache	NOUN
ejpam-6834	1438	17	/	/	SYM
ejpam-6834	1438	18	eur	eur	PROPN
ejpam-6834	1438	19	.	.	PUNCT
ejpam-6834	1439	1	j.	j.	PROPN
ejpam-6834	1439	2	pure	pure	PROPN
ejpam-6834	1439	3	appl	appl	PROPN
ejpam-6834	1439	4	.	.	PROPN
ejpam-6834	1439	5	math	math	PROPN
ejpam-6834	1439	6	,	,	PUNCT
ejpam-6834	1439	7	18	18	NUM
ejpam-6834	1439	8	(	(	PUNCT
ejpam-6834	1439	9	4	4	NUM
ejpam-6834	1439	10	)	)	PUNCT
ejpam-6834	1439	11	(	(	PUNCT
ejpam-6834	1439	12	2025	2025	NUM
ejpam-6834	1439	13	)	)	PUNCT
ejpam-6834	1439	14	,	,	PUNCT
ejpam-6834	1439	15	6834	6834	NUM
ejpam-6834	1439	16	54	54	NUM
ejpam-6834	1439	17	of	of	ADP
ejpam-6834	1439	18	69	69	NUM
ejpam-6834	1439	19	•	•	NOUN
ejpam-6834	1439	20	(	(	PUNCT
ejpam-6834	1439	21	a	a	X
ejpam-6834	1439	22	)	)	PUNCT
ejpam-6834	1439	23	adjoin	adjoin	NOUN
ejpam-6834	1439	24	a	a	DET
ejpam-6834	1439	25	dummy	dummy	ADJ
ejpam-6834	1439	26	element	element	NOUN
ejpam-6834	1439	27	⋆	⋆	NOUN
ejpam-6834	1439	28	/∈	/∈	PUNCT
ejpam-6834	1439	29	u	u	NOUN
ejpam-6834	1439	30	and	and	CCONJ
ejpam-6834	1439	31	lift	lift	VERB
ejpam-6834	1439	32	to	to	ADP
ejpam-6834	1439	33	u⋆	u⋆	ADJ
ejpam-6834	1439	34	:	:	PUNCT
ejpam-6834	1439	35	=	=	SYM
ejpam-6834	1439	36	u	u	SYM
ejpam-6834	1439	37	⊔	⊔	PROPN
ejpam-6834	1439	38	{	{	PUNCT
ejpam-6834	1439	39	⋆	⋆	NOUN
ejpam-6834	1439	40	}	}	PUNCT
ejpam-6834	1439	41	by	by	ADP
ejpam-6834	1439	42	lu⋆(b	lu⋆(b	NOUN
ejpam-6834	1439	43	)	)	PUNCT
ejpam-6834	1439	44	:	:	PUNCT
ejpam-6834	1439	45	=	=	SYM
ejpam-6834	1439	46	b	b	X
ejpam-6834	1439	47	if	if	SCONJ
ejpam-6834	1439	48	b	b	PROPN
ejpam-6834	1439	49	̸=	̸=	PROPN
ejpam-6834	1439	50	∅	∅	NOUN
ejpam-6834	1439	51	,	,	PUNCT
ejpam-6834	1439	52	and	and	CCONJ
ejpam-6834	1439	53	lu⋆(∅	lu⋆(∅	NOUN
ejpam-6834	1439	54	)	)	PUNCT
ejpam-6834	1439	55	:	:	PUNCT
ejpam-6834	1439	56	=	=	PRON
ejpam-6834	1439	57	{	{	PUNCT
ejpam-6834	1439	58	⋆	⋆	NOUN
ejpam-6834	1439	59	}	}	PUNCT
ejpam-6834	1439	60	,	,	PUNCT
ejpam-6834	1439	61	or	or	CCONJ
ejpam-6834	1439	62	•	•	NOUN
ejpam-6834	1439	63	(	(	PUNCT
ejpam-6834	1439	64	b	b	X
ejpam-6834	1439	65	)	)	PUNCT
ejpam-6834	1439	66	relax	relax	VERB
ejpam-6834	1439	67	the	the	DET
ejpam-6834	1439	68	codomain	codomain	NOUN
ejpam-6834	1439	69	to	to	ADP
ejpam-6834	1439	70	p(u	p(u	VERB
ejpam-6834	1439	71	)	)	PUNCT
ejpam-6834	1439	72	(	(	PUNCT
ejpam-6834	1439	73	dropping	drop	VERB
ejpam-6834	1439	74	the	the	DET
ejpam-6834	1439	75	“	"	PUNCT
ejpam-6834	1439	76	nonempty	nonempty	NOUN
ejpam-6834	1439	77	”	"	PUNCT
ejpam-6834	1439	78	requirement	requirement	NOUN
ejpam-6834	1439	79	)	)	PUNCT
ejpam-6834	1439	80	.	.	PUNCT
ejpam-6834	1440	1	to	to	PART
ejpam-6834	1440	2	stay	stay	VERB
ejpam-6834	1440	3	within	within	ADP
ejpam-6834	1440	4	the	the	DET
ejpam-6834	1440	5	present	present	ADJ
ejpam-6834	1440	6	definition	definition	NOUN
ejpam-6834	1440	7	p̃1(u	p̃1(u	PROPN
ejpam-6834	1440	8	)	)	PUNCT
ejpam-6834	1441	1	=	=	SYM
ejpam-6834	1441	2	p+(u	p+(u	PROPN
ejpam-6834	1441	3	)	)	PUNCT
ejpam-6834	1441	4	,	,	PUNCT
ejpam-6834	1441	5	we	we	PRON
ejpam-6834	1441	6	adopt	adopt	VERB
ejpam-6834	1441	7	(	(	PUNCT
ejpam-6834	1441	8	a	a	X
ejpam-6834	1441	9	)	)	PUNCT
ejpam-6834	1441	10	.	.	PUNCT
ejpam-6834	1442	1	step	step	NOUN
ejpam-6834	1442	2	3	3	NUM
ejpam-6834	1442	3	(	(	PUNCT
ejpam-6834	1442	4	a	a	DET
ejpam-6834	1442	5	canonical	canonical	ADJ
ejpam-6834	1442	6	extension	extension	NOUN
ejpam-6834	1442	7	to	to	ADP
ejpam-6834	1442	8	p+(s	p+(s	PROPN
ejpam-6834	1442	9	)	)	PUNCT
ejpam-6834	1442	10	)	)	PUNCT
ejpam-6834	1442	11	.	.	PUNCT
ejpam-6834	1443	1	define	define	VERB
ejpam-6834	1443	2	the	the	DET
ejpam-6834	1443	3	union	union	NOUN
ejpam-6834	1443	4	–	–	PUNCT
ejpam-6834	1443	5	lift	lift	NOUN
ejpam-6834	1443	6	f	f	X
ejpam-6834	1443	7	:	:	PUNCT
ejpam-6834	1443	8	p+(s	p+(s	NUM
ejpam-6834	1443	9	)	)	PUNCT
ejpam-6834	1443	10	→	→	SYM
ejpam-6834	1443	11	p+(u⋆	p+(u⋆	NOUN
ejpam-6834	1443	12	)	)	PUNCT
ejpam-6834	1443	13	by	by	ADP
ejpam-6834	1443	14	f	f	PROPN
ejpam-6834	1443	15	(	(	PUNCT
ejpam-6834	1443	16	a	a	NOUN
ejpam-6834	1443	17	)	)	PUNCT
ejpam-6834	1443	18	:	:	PUNCT
ejpam-6834	1444	1	=	=	SYM
ejpam-6834	1444	2	lu⋆	lu⋆	PROPN
ejpam-6834	1444	3	(	(	PUNCT
ejpam-6834	1444	4	⋃	⋃	PROPN
ejpam-6834	1444	5	s∈a	s∈a	ADJ
ejpam-6834	1444	6	fcl(s	fcl(s	PROPN
ejpam-6834	1444	7	)	)	PUNCT
ejpam-6834	1444	8	)	)	PUNCT
ejpam-6834	1444	9	.	.	PUNCT
ejpam-6834	1445	1	then	then	ADV
ejpam-6834	1445	2	f	f	PROPN
ejpam-6834	1445	3	is	be	AUX
ejpam-6834	1445	4	well	well	ADV
ejpam-6834	1445	5	defined	define	VERB
ejpam-6834	1445	6	and	and	CCONJ
ejpam-6834	1445	7	nonempty	nonempty	NOUN
ejpam-6834	1445	8	-	-	PUNCT
ejpam-6834	1445	9	valued	value	VERB
ejpam-6834	1445	10	:	:	PUNCT
ejpam-6834	1445	11	if	if	SCONJ
ejpam-6834	1445	12	⋃	⋃	PUNCT
ejpam-6834	1445	13	s∈a	s∈a	ADJ
ejpam-6834	1445	14	fcl(s	fcl(s	PROPN
ejpam-6834	1445	15	)	)	PUNCT
ejpam-6834	1445	16	̸=	̸=	PROPN
ejpam-6834	1445	17	∅	∅	NOUN
ejpam-6834	1445	18	,	,	PUNCT
ejpam-6834	1445	19	we	we	PRON
ejpam-6834	1445	20	keep	keep	VERB
ejpam-6834	1445	21	that	that	DET
ejpam-6834	1445	22	set	set	NOUN
ejpam-6834	1445	23	;	;	PUNCT
ejpam-6834	1445	24	otherwise	otherwise	ADV
ejpam-6834	1445	25	lu⋆	lu⋆	VERB
ejpam-6834	1445	26	returns	return	NOUN
ejpam-6834	1445	27	{	{	PUNCT
ejpam-6834	1445	28	⋆	⋆	NOUN
ejpam-6834	1445	29	}	}	PUNCT
ejpam-6834	1445	30	.	.	PUNCT
ejpam-6834	1446	1	step	step	NOUN
ejpam-6834	1446	2	4	4	NUM
ejpam-6834	1446	3	(	(	PUNCT
ejpam-6834	1446	4	agreement	agreement	NOUN
ejpam-6834	1446	5	with	with	ADP
ejpam-6834	1446	6	the	the	DET
ejpam-6834	1446	7	classical	classical	ADJ
ejpam-6834	1446	8	soft	soft	ADJ
ejpam-6834	1446	9	set	set	NOUN
ejpam-6834	1446	10	on	on	ADP
ejpam-6834	1446	11	singletons	singleton	NOUN
ejpam-6834	1446	12	)	)	PUNCT
ejpam-6834	1446	13	.	.	PUNCT
ejpam-6834	1447	1	for	for	ADP
ejpam-6834	1447	2	s	s	PROPN
ejpam-6834	1447	3	∈	∈	PROPN
ejpam-6834	1447	4	s	s	PROPN
ejpam-6834	1447	5	,	,	PUNCT
ejpam-6834	1447	6	f	f	X
ejpam-6834	1447	7	(	(	PUNCT
ejpam-6834	1447	8	{	{	PUNCT
ejpam-6834	1447	9	s	s	NOUN
ejpam-6834	1447	10	}	}	PUNCT
ejpam-6834	1447	11	)	)	PUNCT
ejpam-6834	1447	12	=	=	SYM
ejpam-6834	1447	13	lu⋆	lu⋆	NOUN
ejpam-6834	1447	14	(	(	PUNCT
ejpam-6834	1447	15	fcl(s	fcl(s	PROPN
ejpam-6834	1447	16	)	)	PUNCT
ejpam-6834	1447	17	)	)	PUNCT
ejpam-6834	1448	1	=	=	PRON
ejpam-6834	1448	2	{	{	PUNCT
ejpam-6834	1448	3	fcl(s	fcl(s	PROPN
ejpam-6834	1448	4	)	)	PUNCT
ejpam-6834	1448	5	,	,	PUNCT
ejpam-6834	1448	6	if	if	SCONJ
ejpam-6834	1448	7	fcl(s	fcl(s	PROPN
ejpam-6834	1448	8	)	)	PUNCT
ejpam-6834	1448	9	̸=	̸=	PROPN
ejpam-6834	1448	10	∅	∅	NOUN
ejpam-6834	1448	11	,	,	PUNCT
ejpam-6834	1448	12	{	{	PUNCT
ejpam-6834	1448	13	⋆	⋆	NOUN
ejpam-6834	1448	14	}	}	PUNCT
ejpam-6834	1448	15	,	,	PUNCT
ejpam-6834	1448	16	if	if	SCONJ
ejpam-6834	1448	17	fcl(s	fcl(s	PROPN
ejpam-6834	1448	18	)	)	PUNCT
ejpam-6834	1448	19	=	=	PUNCT
ejpam-6834	1448	20	∅.	∅.	VERB
ejpam-6834	1448	21	hence	hence	ADV
ejpam-6834	1448	22	,	,	PUNCT
ejpam-6834	1448	23	modulo	modulo	VERB
ejpam-6834	1448	24	the	the	DET
ejpam-6834	1448	25	harmless	harmless	ADJ
ejpam-6834	1448	26	convention	convention	NOUN
ejpam-6834	1448	27	of	of	ADP
ejpam-6834	1448	28	representing	represent	VERB
ejpam-6834	1448	29	the	the	DET
ejpam-6834	1448	30	classical	classical	ADJ
ejpam-6834	1448	31	empty	empty	ADJ
ejpam-6834	1448	32	image	image	NOUN
ejpam-6834	1448	33	by	by	ADP
ejpam-6834	1448	34	{	{	PUNCT
ejpam-6834	1448	35	⋆	⋆	NOUN
ejpam-6834	1448	36	}	}	PUNCT
ejpam-6834	1448	37	,	,	PUNCT
ejpam-6834	1448	38	the	the	DET
ejpam-6834	1448	39	mapping	mapping	NOUN
ejpam-6834	1448	40	f	f	PROPN
ejpam-6834	1448	41	reproduces	reproduce	VERB
ejpam-6834	1448	42	fcl	fcl	PROPN
ejpam-6834	1448	43	on	on	ADP
ejpam-6834	1448	44	the	the	DET
ejpam-6834	1448	45	embedded	embed	VERB
ejpam-6834	1448	46	copy	copy	NOUN
ejpam-6834	1448	47	ιs(s	ιs(s	PUNCT
ejpam-6834	1448	48	)	)	PUNCT
ejpam-6834	1448	49	of	of	ADP
ejpam-6834	1448	50	s	s	PROPN
ejpam-6834	1448	51	,	,	PUNCT
ejpam-6834	1448	52	and	and	CCONJ
ejpam-6834	1448	53	extends	extend	VERB
ejpam-6834	1448	54	it	it	PRON
ejpam-6834	1448	55	canonically	canonically	ADV
ejpam-6834	1448	56	to	to	ADP
ejpam-6834	1448	57	all	all	DET
ejpam-6834	1448	58	nonempty	nonempty	ADJ
ejpam-6834	1448	59	parameter	parameter	NOUN
ejpam-6834	1448	60	blocks	block	NOUN
ejpam-6834	1448	61	via	via	ADP
ejpam-6834	1448	62	union	union	NOUN
ejpam-6834	1448	63	.	.	PUNCT
ejpam-6834	1449	1	(	(	PUNCT
ejpam-6834	1449	2	one	one	PRON
ejpam-6834	1449	3	could	could	AUX
ejpam-6834	1449	4	just	just	ADV
ejpam-6834	1449	5	as	as	ADV
ejpam-6834	1449	6	well	well	ADV
ejpam-6834	1449	7	choose	choose	VERB
ejpam-6834	1449	8	the	the	DET
ejpam-6834	1449	9	intersection	intersection	NOUN
ejpam-6834	1449	10	–	–	PUNCT
ejpam-6834	1449	11	lift	lift	VERB
ejpam-6834	1449	12	a	a	DET
ejpam-6834	1449	13	7→	7→	NUM
ejpam-6834	1449	14	⋂	⋂	PROPN
ejpam-6834	1449	15	s∈a	s∈a	ADJ
ejpam-6834	1449	16	fcl(s	fcl(s	PROPN
ejpam-6834	1449	17	)	)	PUNCT
ejpam-6834	1449	18	if	if	SCONJ
ejpam-6834	1449	19	conjunctive	conjunctive	ADJ
ejpam-6834	1449	20	semantics	semantic	NOUN
ejpam-6834	1449	21	are	be	AUX
ejpam-6834	1449	22	desired	desire	VERB
ejpam-6834	1449	23	.	.	PUNCT
ejpam-6834	1449	24	)	)	PUNCT
ejpam-6834	1450	1	therefore	therefore	ADV
ejpam-6834	1450	2	f	f	X
ejpam-6834	1450	3	:	:	PUNCT
ejpam-6834	1450	4	(	(	PUNCT
ejpam-6834	1450	5	p̃1(s))1	p̃1(s))1	X
ejpam-6834	1450	6	→	→	SYM
ejpam-6834	1450	7	(	(	PUNCT
ejpam-6834	1450	8	p̃1(u	p̃1(u	PROPN
ejpam-6834	1450	9	⋆))1	⋆))1	PROPN
ejpam-6834	1450	10	is	be	AUX
ejpam-6834	1450	11	a	a	DET
ejpam-6834	1450	12	(	(	PUNCT
ejpam-6834	1450	13	1	1	NUM
ejpam-6834	1450	14	,	,	PUNCT
ejpam-6834	1450	15	1)-ary	1)-ary	ADJ
ejpam-6834	1450	16	(	(	PUNCT
ejpam-6834	1450	17	1	1	NUM
ejpam-6834	1450	18	,	,	PUNCT
ejpam-6834	1450	19	1)-superhypersoft	1)-superhypersoft	NUM
ejpam-6834	1450	20	set	set	NOUN
ejpam-6834	1450	21	that	that	PRON
ejpam-6834	1450	22	represents	represent	VERB
ejpam-6834	1450	23	the	the	DET
ejpam-6834	1450	24	given	give	VERB
ejpam-6834	1450	25	classical	classical	ADJ
ejpam-6834	1450	26	soft	soft	ADJ
ejpam-6834	1450	27	set	set	NOUN
ejpam-6834	1450	28	.	.	PUNCT
ejpam-6834	1451	1	theorem	theorem	VERB
ejpam-6834	1451	2	48	48	NUM
ejpam-6834	1451	3	(	(	PUNCT
ejpam-6834	1451	4	fixing	fix	VERB
ejpam-6834	1451	5	some	some	DET
ejpam-6834	1451	6	parameters	parameter	NOUN
ejpam-6834	1451	7	)	)	PUNCT
ejpam-6834	1451	8	.	.	PUNCT
ejpam-6834	1452	1	fix	fix	NOUN
ejpam-6834	1452	2	indices	indice	VERB
ejpam-6834	1452	3	1	1	NUM
ejpam-6834	1452	4	≤	≤	NUM
ejpam-6834	1452	5	i1	i1	X
ejpam-6834	1452	6	<	<	X
ejpam-6834	1452	7	·	·	PUNCT
ejpam-6834	1452	8	·	·	PUNCT
ejpam-6834	1452	9	·	·	PUNCT
ejpam-6834	1453	1	<	<	X
ejpam-6834	1453	2	ir	ir	PROPN
ejpam-6834	1453	3	≤	≤	NUM
ejpam-6834	1453	4	h	h	NOUN
ejpam-6834	1453	5	and	and	CCONJ
ejpam-6834	1453	6	elements	element	NOUN
ejpam-6834	1453	7	aij	aij	PROPN
ejpam-6834	1453	8	∈	∈	PROPN
ejpam-6834	1453	9	p̃m(s	p̃m(s	NOUN
ejpam-6834	1453	10	)	)	PUNCT
ejpam-6834	1453	11	.	.	PUNCT
ejpam-6834	1454	1	define	define	VERB
ejpam-6834	1454	2	ffix	ffix	NOUN
ejpam-6834	1454	3	:	:	PUNCT
ejpam-6834	1454	4	(	(	PUNCT
ejpam-6834	1454	5	p̃m(s	p̃m(s	NOUN
ejpam-6834	1454	6	)	)	PUNCT
ejpam-6834	1454	7	)	)	PUNCT
ejpam-6834	1455	1	h−r	h−r	VERB
ejpam-6834	1455	2	−→	−→	NOUN
ejpam-6834	1455	3	(	(	PUNCT
ejpam-6834	1455	4	p̃n(u	p̃n(u	NOUN
ejpam-6834	1455	5	)	)	PUNCT
ejpam-6834	1455	6	)	)	PUNCT
ejpam-6834	1456	1	k	k	X
ejpam-6834	1456	2	by	by	ADP
ejpam-6834	1456	3	inserting	insert	VERB
ejpam-6834	1456	4	the	the	DET
ejpam-6834	1456	5	fixed	fix	VERB
ejpam-6834	1456	6	aij	aij	PROPN
ejpam-6834	1456	7	into	into	ADP
ejpam-6834	1456	8	the	the	DET
ejpam-6834	1456	9	corresponding	corresponding	ADJ
ejpam-6834	1456	10	coordinates	coordinate	NOUN
ejpam-6834	1456	11	of	of	ADP
ejpam-6834	1456	12	each	each	DET
ejpam-6834	1456	13	(	(	PUNCT
ejpam-6834	1456	14	h−	h−	PROPN
ejpam-6834	1456	15	r)-tuple	r)-tuple	NOUN
ejpam-6834	1456	16	and	and	CCONJ
ejpam-6834	1456	17	then	then	ADV
ejpam-6834	1456	18	applying	apply	VERB
ejpam-6834	1456	19	f	f	PROPN
ejpam-6834	1456	20	.	.	PUNCT
ejpam-6834	1457	1	then	then	ADV
ejpam-6834	1457	2	ffix	ffix	PROPN
ejpam-6834	1457	3	is	be	AUX
ejpam-6834	1457	4	an	an	DET
ejpam-6834	1457	5	(	(	PUNCT
ejpam-6834	1457	6	h−	h−	NOUN
ejpam-6834	1457	7	r	r	NOUN
ejpam-6834	1457	8	,	,	PUNCT
ejpam-6834	1457	9	k)-ary	k)-ary	X
ejpam-6834	1457	10	(	(	PUNCT
ejpam-6834	1457	11	m	m	PROPN
ejpam-6834	1457	12	,	,	PUNCT
ejpam-6834	1457	13	n)-superhypersoft	n)-superhypersoft	ADV
ejpam-6834	1457	14	set	set	NOUN
ejpam-6834	1457	15	.	.	PUNCT
ejpam-6834	1458	1	proof	proof	NOUN
ejpam-6834	1458	2	.	.	PUNCT
ejpam-6834	1459	1	let	let	VERB
ejpam-6834	1459	2	i	i	PRON
ejpam-6834	1459	3	=	=	PUNCT
ejpam-6834	1459	4	{	{	PUNCT
ejpam-6834	1459	5	1	1	NUM
ejpam-6834	1459	6	,	,	PUNCT
ejpam-6834	1459	7	.	.	PUNCT
ejpam-6834	1459	8	.	.	PUNCT
ejpam-6834	1460	1	.	.	PUNCT
ejpam-6834	1461	1	,	,	PUNCT
ejpam-6834	1461	2	h	h	X
ejpam-6834	1461	3	}	}	PUNCT
ejpam-6834	1461	4	and	and	CCONJ
ejpam-6834	1461	5	i	i	PRON
ejpam-6834	1461	6	free	free	ADJ
ejpam-6834	1461	7	:	:	PUNCT
ejpam-6834	1461	8	=	=	SYM
ejpam-6834	1461	9	i	i	PRON
ejpam-6834	1461	10	\	\	PROPN
ejpam-6834	1461	11	{	{	PUNCT
ejpam-6834	1461	12	i1	i1	PROPN
ejpam-6834	1461	13	,	,	PUNCT
ejpam-6834	1461	14	.	.	PUNCT
ejpam-6834	1461	15	.	.	PUNCT
ejpam-6834	1462	1	.	.	PUNCT
ejpam-6834	1463	1	,	,	PUNCT
ejpam-6834	1463	2	ir	ir	PROPN
ejpam-6834	1463	3	}	}	PUNCT
ejpam-6834	1463	4	.	.	PUNCT
ejpam-6834	1464	1	define	define	VERB
ejpam-6834	1464	2	the	the	DET
ejpam-6834	1464	3	insertion	insertion	NOUN
ejpam-6834	1464	4	map	map	NOUN
ejpam-6834	1464	5	ιfix	ιfix	NOUN
ejpam-6834	1464	6	:	:	PUNCT
ejpam-6834	1464	7	(	(	PUNCT
ejpam-6834	1464	8	p̃m(s	p̃m(s	NOUN
ejpam-6834	1464	9	)	)	PUNCT
ejpam-6834	1464	10	)	)	PUNCT
ejpam-6834	1465	1	h−r	h−r	VERB
ejpam-6834	1465	2	−→	−→	NOUN
ejpam-6834	1465	3	(	(	PUNCT
ejpam-6834	1465	4	p̃m(s	p̃m(s	NOUN
ejpam-6834	1465	5	)	)	PUNCT
ejpam-6834	1465	6	)	)	PUNCT
ejpam-6834	1466	1	h	h	NOUN
ejpam-6834	1466	2	as	as	SCONJ
ejpam-6834	1466	3	follows	follow	VERB
ejpam-6834	1466	4	:	:	PUNCT
ejpam-6834	1466	5	for	for	ADP
ejpam-6834	1466	6	b	b	NOUN
ejpam-6834	1466	7	=	=	SYM
ejpam-6834	1466	8	(	(	PUNCT
ejpam-6834	1466	9	bℓ)ℓ∈ifree	bℓ)ℓ∈ifree	PROPN
ejpam-6834	1466	10	,	,	PUNCT
ejpam-6834	1466	11	put	put	VERB
ejpam-6834	1466	12	ιfix(b	ιfix(b	NOUN
ejpam-6834	1466	13	)	)	PUNCT
ejpam-6834	1466	14	=	=	PUNCT
ejpam-6834	1467	1	a	a	PRON
ejpam-6834	1467	2	with	with	ADP
ejpam-6834	1467	3	au	au	NOUN
ejpam-6834	1467	4	:	:	PUNCT
ejpam-6834	1467	5	=	=	SYM
ejpam-6834	1467	6	{	{	PUNCT
ejpam-6834	1467	7	aij	aij	PROPN
ejpam-6834	1467	8	,	,	PUNCT
ejpam-6834	1467	9	u	u	NOUN
ejpam-6834	1467	10	=	=	NOUN
ejpam-6834	1467	11	ij	ij	NOUN
ejpam-6834	1467	12	for	for	ADP
ejpam-6834	1467	13	some	some	DET
ejpam-6834	1467	14	j	j	PROPN
ejpam-6834	1467	15	,	,	PUNCT
ejpam-6834	1467	16	bℓ	bℓ	PROPN
ejpam-6834	1467	17	,	,	PUNCT
ejpam-6834	1467	18	u	u	NOUN
ejpam-6834	1467	19	=	=	PROPN
ejpam-6834	1467	20	ℓ	ℓ	PROPN
ejpam-6834	1467	21	∈	∈	PROPN
ejpam-6834	1467	22	i	i	PRON
ejpam-6834	1467	23	free	free	ADJ
ejpam-6834	1467	24	.	.	PUNCT
ejpam-6834	1468	1	this	this	PRON
ejpam-6834	1468	2	is	be	AUX
ejpam-6834	1468	3	well	well	ADV
ejpam-6834	1468	4	defined	define	VERB
ejpam-6834	1468	5	and	and	CCONJ
ejpam-6834	1468	6	injective	injective	ADJ
ejpam-6834	1468	7	.	.	PUNCT
ejpam-6834	1469	1	set	set	VERB
ejpam-6834	1469	2	ffix	ffix	NOUN
ejpam-6834	1469	3	:	:	PUNCT
ejpam-6834	1470	1	=	=	SYM
ejpam-6834	1470	2	f	f	PROPN
ejpam-6834	1470	3	◦	◦	NOUN
ejpam-6834	1470	4	ιfix	ιfix	PROPN
ejpam-6834	1470	5	.	.	PUNCT
ejpam-6834	1471	1	since	since	SCONJ
ejpam-6834	1471	2	f	f	PROPN
ejpam-6834	1471	3	takes	take	VERB
ejpam-6834	1471	4	values	value	NOUN
ejpam-6834	1471	5	in	in	ADP
ejpam-6834	1471	6	(	(	PUNCT
ejpam-6834	1471	7	p̃n(u))k	p̃n(u))k	ADJ
ejpam-6834	1471	8	,	,	PUNCT
ejpam-6834	1471	9	so	so	ADV
ejpam-6834	1471	10	does	do	VERB
ejpam-6834	1471	11	ffix	ffix	NOUN
ejpam-6834	1471	12	.	.	PUNCT
ejpam-6834	1472	1	thus	thus	ADV
ejpam-6834	1472	2	ffix	ffix	PROPN
ejpam-6834	1472	3	is	be	AUX
ejpam-6834	1472	4	a	a	DET
ejpam-6834	1472	5	mapping	mapping	NOUN
ejpam-6834	1472	6	with	with	ADP
ejpam-6834	1472	7	domain	domain	NOUN
ejpam-6834	1472	8	(	(	PUNCT
ejpam-6834	1472	9	p̃m(s))h−r	p̃m(s))h−r	NOUN
ejpam-6834	1472	10	and	and	CCONJ
ejpam-6834	1472	11	codomain	codomain	ADJ
ejpam-6834	1472	12	(	(	PUNCT
ejpam-6834	1472	13	p̃n(u))k	p̃n(u))k	ADJ
ejpam-6834	1472	14	,	,	PUNCT
ejpam-6834	1472	15	i.e.	i.e.	X
ejpam-6834	1472	16	,	,	PUNCT
ejpam-6834	1472	17	an	an	DET
ejpam-6834	1472	18	(	(	PUNCT
ejpam-6834	1472	19	h−	h−	NOUN
ejpam-6834	1472	20	r	r	NOUN
ejpam-6834	1472	21	,	,	PUNCT
ejpam-6834	1472	22	k)-ary	k)-ary	X
ejpam-6834	1472	23	(	(	PUNCT
ejpam-6834	1472	24	m	m	PROPN
ejpam-6834	1472	25	,	,	PUNCT
ejpam-6834	1472	26	n)-superhypersoft	n)-superhypersoft	ADV
ejpam-6834	1472	27	set	set	NOUN
ejpam-6834	1472	28	.	.	PUNCT
ejpam-6834	1473	1	t.	t.	PROPN
ejpam-6834	1473	2	fujita	fujita	PROPN
ejpam-6834	1473	3	,	,	PUNCT
ejpam-6834	1473	4	f.smarandache	f.smarandache	NOUN
ejpam-6834	1473	5	/	/	SYM
ejpam-6834	1473	6	eur	eur	PROPN
ejpam-6834	1473	7	.	.	PUNCT
ejpam-6834	1474	1	j.	j.	PROPN
ejpam-6834	1474	2	pure	pure	PROPN
ejpam-6834	1474	3	appl	appl	PROPN
ejpam-6834	1474	4	.	.	PROPN
ejpam-6834	1474	5	math	math	PROPN
ejpam-6834	1474	6	,	,	PUNCT
ejpam-6834	1474	7	18	18	NUM
ejpam-6834	1474	8	(	(	PUNCT
ejpam-6834	1474	9	4	4	NUM
ejpam-6834	1474	10	)	)	PUNCT
ejpam-6834	1474	11	(	(	PUNCT
ejpam-6834	1474	12	2025	2025	NUM
ejpam-6834	1474	13	)	)	PUNCT
ejpam-6834	1474	14	,	,	PUNCT
ejpam-6834	1474	15	6834	6834	NUM
ejpam-6834	1474	16	55	55	NUM
ejpam-6834	1474	17	of	of	ADP
ejpam-6834	1474	18	69	69	NUM
ejpam-6834	1474	19	theorem	theorem	NOUN
ejpam-6834	1474	20	49	49	NUM
ejpam-6834	1474	21	(	(	PUNCT
ejpam-6834	1474	22	projection	projection	NOUN
ejpam-6834	1474	23	to	to	ADP
ejpam-6834	1474	24	selected	select	VERB
ejpam-6834	1474	25	outputs	output	NOUN
ejpam-6834	1474	26	)	)	PUNCT
ejpam-6834	1474	27	.	.	PUNCT
ejpam-6834	1475	1	let	let	VERB
ejpam-6834	1475	2	1	1	NUM
ejpam-6834	1475	3	≤	≤	NOUN
ejpam-6834	1475	4	j1	j1	X
ejpam-6834	1475	5	<	<	X
ejpam-6834	1475	6	·	·	PUNCT
ejpam-6834	1475	7	·	·	PUNCT
ejpam-6834	1475	8	·	·	PUNCT
ejpam-6834	1476	1	<	<	X
ejpam-6834	1476	2	js	js	PROPN
ejpam-6834	1476	3	≤	≤	PROPN
ejpam-6834	1476	4	k.	k.	PROPN
ejpam-6834	1477	1	the	the	DET
ejpam-6834	1477	2	coordinate	coordinate	NOUN
ejpam-6834	1477	3	projection	projection	NOUN
ejpam-6834	1477	4	πj1,	πj1,	NUM
ejpam-6834	1477	5	...	...	PUNCT
ejpam-6834	1477	6	,js	,js	PUNCT
ejpam-6834	1477	7	:	:	PUNCT
ejpam-6834	1477	8	(	(	PUNCT
ejpam-6834	1477	9	p̃n(u	p̃n(u	NOUN
ejpam-6834	1477	10	)	)	PUNCT
ejpam-6834	1477	11	)	)	PUNCT
ejpam-6834	1478	1	k	k	X
ejpam-6834	1478	2	−→	−→	ADJ
ejpam-6834	1478	3	(	(	PUNCT
ejpam-6834	1478	4	p̃n(u	p̃n(u	NOUN
ejpam-6834	1478	5	)	)	PUNCT
ejpam-6834	1478	6	)	)	PUNCT
ejpam-6834	1479	1	s	s	X
ejpam-6834	1479	2	,	,	PUNCT
ejpam-6834	1479	3	(	(	PUNCT
ejpam-6834	1479	4	b1	b1	NOUN
ejpam-6834	1479	5	,	,	PUNCT
ejpam-6834	1479	6	.	.	PUNCT
ejpam-6834	1479	7	.	.	PUNCT
ejpam-6834	1479	8	.	.	PUNCT
ejpam-6834	1480	1	,	,	PUNCT
ejpam-6834	1480	2	bk	bk	VERB
ejpam-6834	1480	3	)	)	PUNCT
ejpam-6834	1480	4	7→	7→	PROPN
ejpam-6834	1480	5	(	(	PUNCT
ejpam-6834	1480	6	bj1	bj1	ADJ
ejpam-6834	1480	7	,	,	PUNCT
ejpam-6834	1480	8	.	.	PUNCT
ejpam-6834	1480	9	.	.	PUNCT
ejpam-6834	1480	10	.	.	PUNCT
ejpam-6834	1481	1	,	,	PUNCT
ejpam-6834	1481	2	bjs	bjs	PROPN
ejpam-6834	1481	3	)	)	PUNCT
ejpam-6834	1481	4	,	,	PUNCT
ejpam-6834	1481	5	composed	compose	VERB
ejpam-6834	1481	6	with	with	ADP
ejpam-6834	1481	7	f	f	PROPN
ejpam-6834	1481	8	,	,	PUNCT
ejpam-6834	1481	9	yields	yield	VERB
ejpam-6834	1481	10	an	an	DET
ejpam-6834	1481	11	(	(	PUNCT
ejpam-6834	1481	12	h	h	NOUN
ejpam-6834	1481	13	,	,	PUNCT
ejpam-6834	1481	14	s)-ary	s)-ary	NOUN
ejpam-6834	1481	15	(	(	PUNCT
ejpam-6834	1481	16	m	m	PROPN
ejpam-6834	1481	17	,	,	PUNCT
ejpam-6834	1481	18	n)-superhypersoft	n)-superhypersoft	ADV
ejpam-6834	1481	19	set	set	NOUN
ejpam-6834	1481	20	.	.	PUNCT
ejpam-6834	1482	1	proof	proof	NOUN
ejpam-6834	1482	2	.	.	PUNCT
ejpam-6834	1483	1	by	by	ADP
ejpam-6834	1483	2	definition	definition	NOUN
ejpam-6834	1483	3	,	,	PUNCT
ejpam-6834	1483	4	each	each	DET
ejpam-6834	1483	5	bjr	bjr	NOUN
ejpam-6834	1483	6	∈	∈	PROPN
ejpam-6834	1483	7	p̃n(u	p̃n(u	PROPN
ejpam-6834	1483	8	)	)	PUNCT
ejpam-6834	1483	9	is	be	AUX
ejpam-6834	1483	10	nonempty	nonempty	ADJ
ejpam-6834	1483	11	and	and	CCONJ
ejpam-6834	1483	12	level	level	NOUN
ejpam-6834	1483	13	–	–	PUNCT
ejpam-6834	1483	14	n.	n.	NOUN
ejpam-6834	1483	15	hence	hence	ADV
ejpam-6834	1483	16	πj1,	πj1,	PRON
ejpam-6834	1483	17	...	...	PUNCT
ejpam-6834	1483	18	,js	,js	PUNCT
ejpam-6834	1483	19	maps	map	NOUN
ejpam-6834	1483	20	(	(	PUNCT
ejpam-6834	1483	21	p̃n(u))k	p̃n(u))k	ADJ
ejpam-6834	1483	22	into	into	ADP
ejpam-6834	1483	23	(	(	PUNCT
ejpam-6834	1483	24	p̃n(u))s	p̃n(u))s	ADV
ejpam-6834	1483	25	,	,	PUNCT
ejpam-6834	1483	26	preserving	preserve	VERB
ejpam-6834	1483	27	nonemptiness	nonemptiness	NOUN
ejpam-6834	1483	28	coordinatewise	coordinatewise	NOUN
ejpam-6834	1483	29	.	.	PUNCT
ejpam-6834	1484	1	therefore	therefore	ADV
ejpam-6834	1484	2	πj1,	πj1,	PRON
ejpam-6834	1484	3	...	...	PUNCT
ejpam-6834	1484	4	,js	,js	PUNCT
ejpam-6834	1485	1	◦	◦	NOUN
ejpam-6834	1485	2	f	f	X
ejpam-6834	1485	3	:	:	PUNCT
ejpam-6834	1485	4	(	(	PUNCT
ejpam-6834	1485	5	p̃m(s))h	p̃m(s))h	X
ejpam-6834	1485	6	→	→	SYM
ejpam-6834	1485	7	(	(	PUNCT
ejpam-6834	1485	8	p̃n(u))s	p̃n(u))s	X
ejpam-6834	1485	9	is	be	AUX
ejpam-6834	1485	10	an	an	DET
ejpam-6834	1485	11	(	(	PUNCT
ejpam-6834	1485	12	h	h	NOUN
ejpam-6834	1485	13	,	,	PUNCT
ejpam-6834	1485	14	s)-ary	s)-ary	NOUN
ejpam-6834	1485	15	(	(	PUNCT
ejpam-6834	1485	16	m	m	PROPN
ejpam-6834	1485	17	,	,	PUNCT
ejpam-6834	1485	18	n)-superhypersoft	n)-superhypersoft	ADV
ejpam-6834	1485	19	set	set	VERB
ejpam-6834	1485	20	.	.	PUNCT
ejpam-6834	1486	1	theorem	theorem	VERB
ejpam-6834	1486	2	50	50	NUM
ejpam-6834	1486	3	(	(	PUNCT
ejpam-6834	1486	4	pointwise	pointwise	NOUN
ejpam-6834	1486	5	union	union	NOUN
ejpam-6834	1486	6	)	)	PUNCT
ejpam-6834	1486	7	.	.	PUNCT
ejpam-6834	1487	1	if	if	SCONJ
ejpam-6834	1487	2	f1	f1	PROPN
ejpam-6834	1487	3	,	,	PUNCT
ejpam-6834	1487	4	f2	f2	PROPN
ejpam-6834	1487	5	:	:	PUNCT
ejpam-6834	1487	6	(	(	PUNCT
ejpam-6834	1487	7	p̃m(s))h	p̃m(s))h	PROPN
ejpam-6834	1487	8	→	→	SYM
ejpam-6834	1487	9	(	(	PUNCT
ejpam-6834	1487	10	p̃n(u))k	p̃n(u))k	NOUN
ejpam-6834	1487	11	are	be	AUX
ejpam-6834	1487	12	(	(	PUNCT
ejpam-6834	1487	13	h	h	NOUN
ejpam-6834	1487	14	,	,	PUNCT
ejpam-6834	1487	15	k)-ary	k)-ary	X
ejpam-6834	1487	16	(	(	PUNCT
ejpam-6834	1487	17	m	m	PROPN
ejpam-6834	1487	18	,	,	PUNCT
ejpam-6834	1487	19	n)superhypersoft	n)superhypersoft	NOUN
ejpam-6834	1487	20	sets	set	NOUN
ejpam-6834	1487	21	,	,	PUNCT
ejpam-6834	1487	22	then	then	ADV
ejpam-6834	1487	23	(	(	PUNCT
ejpam-6834	1487	24	f1	f1	PROPN
ejpam-6834	1487	25	∪	∪	ADJ
ejpam-6834	1487	26	f2)(a	f2)(a	NOUN
ejpam-6834	1487	27	)	)	PUNCT
ejpam-6834	1487	28	:	:	PUNCT
ejpam-6834	1488	1	=	=	SYM
ejpam-6834	1488	2	(	(	PUNCT
ejpam-6834	1488	3	f1(a)j	f1(a)j	ADJ
ejpam-6834	1488	4	∪	∪	X
ejpam-6834	1488	5	f2(a)j	f2(a)j	NOUN
ejpam-6834	1488	6	)	)	PUNCT
ejpam-6834	1489	1	k	k	X
ejpam-6834	1489	2	j=1	j=1	PROPN
ejpam-6834	1489	3	is	be	AUX
ejpam-6834	1489	4	again	again	ADV
ejpam-6834	1489	5	an	an	DET
ejpam-6834	1489	6	(	(	PUNCT
ejpam-6834	1489	7	h	h	NOUN
ejpam-6834	1489	8	,	,	PUNCT
ejpam-6834	1489	9	k)-ary	k)-ary	X
ejpam-6834	1489	10	(	(	PUNCT
ejpam-6834	1489	11	m	m	PROPN
ejpam-6834	1489	12	,	,	PUNCT
ejpam-6834	1489	13	n)-superhypersoft	n)-superhypersoft	ADV
ejpam-6834	1489	14	set	set	NOUN
ejpam-6834	1489	15	.	.	PUNCT
ejpam-6834	1490	1	proof	proof	NOUN
ejpam-6834	1490	2	.	.	PUNCT
ejpam-6834	1491	1	fix	fix	VERB
ejpam-6834	1491	2	a	a	PRON
ejpam-6834	1491	3	and	and	CCONJ
ejpam-6834	1491	4	a	a	DET
ejpam-6834	1491	5	coordinate	coordinate	NOUN
ejpam-6834	1491	6	j.	j.	PROPN
ejpam-6834	1491	7	we	we	PRON
ejpam-6834	1491	8	prove	prove	VERB
ejpam-6834	1491	9	by	by	ADP
ejpam-6834	1491	10	induction	induction	NOUN
ejpam-6834	1491	11	on	on	ADP
ejpam-6834	1491	12	n	n	PROPN
ejpam-6834	1491	13	that	that	DET
ejpam-6834	1491	14	f1(a)j	f1(a)j	PROPN
ejpam-6834	1491	15	∪f2(a)j	∪f2(a)j	PROPN
ejpam-6834	1491	16	∈	∈	PROPN
ejpam-6834	1491	17	p̃n(u	p̃n(u	PROPN
ejpam-6834	1491	18	)	)	PUNCT
ejpam-6834	1491	19	.	.	PUNCT
ejpam-6834	1492	1	base	base	NOUN
ejpam-6834	1492	2	n	n	NOUN
ejpam-6834	1492	3	=	=	SYM
ejpam-6834	1492	4	1	1	NUM
ejpam-6834	1492	5	.	.	PUNCT
ejpam-6834	1493	1	then	then	ADV
ejpam-6834	1493	2	fi(a)j	fi(a)j	PROPN
ejpam-6834	1493	3	∈	∈	PROPN
ejpam-6834	1493	4	p+(u	p+(u	NOUN
ejpam-6834	1493	5	)	)	PUNCT
ejpam-6834	1493	6	,	,	PUNCT
ejpam-6834	1493	7	so	so	ADV
ejpam-6834	1493	8	each	each	PRON
ejpam-6834	1493	9	is	be	AUX
ejpam-6834	1493	10	a	a	DET
ejpam-6834	1493	11	nonempty	nonempty	ADJ
ejpam-6834	1493	12	subset	subset	NOUN
ejpam-6834	1493	13	of	of	ADP
ejpam-6834	1493	14	u	u	PROPN
ejpam-6834	1493	15	.	.	PUNCT
ejpam-6834	1494	1	the	the	DET
ejpam-6834	1494	2	union	union	NOUN
ejpam-6834	1494	3	of	of	ADP
ejpam-6834	1494	4	two	two	NUM
ejpam-6834	1494	5	nonempty	nonempty	ADJ
ejpam-6834	1494	6	subsets	subset	NOUN
ejpam-6834	1494	7	of	of	ADP
ejpam-6834	1494	8	u	u	NOUN
ejpam-6834	1494	9	is	be	AUX
ejpam-6834	1494	10	nonempty	nonempty	ADJ
ejpam-6834	1494	11	,	,	PUNCT
ejpam-6834	1494	12	hence	hence	ADV
ejpam-6834	1494	13	lies	lie	VERB
ejpam-6834	1494	14	in	in	ADP
ejpam-6834	1494	15	p+(u	p+(u	ADJ
ejpam-6834	1494	16	)	)	PUNCT
ejpam-6834	1494	17	=	=	SYM
ejpam-6834	1494	18	p̃1(u	p̃1(u	PROPN
ejpam-6834	1494	19	)	)	PUNCT
ejpam-6834	1494	20	.	.	PUNCT
ejpam-6834	1495	1	step	step	NOUN
ejpam-6834	1495	2	n	n	PROPN
ejpam-6834	1495	3	⇒	⇒	PROPN
ejpam-6834	1495	4	n+1	n+1	PROPN
ejpam-6834	1495	5	.	.	PUNCT
ejpam-6834	1496	1	now	now	ADV
ejpam-6834	1496	2	fi(a)j	fi(a)j	PROPN
ejpam-6834	1496	3	∈	∈	NOUN
ejpam-6834	1496	4	p̃n+1(u	p̃n+1(u	NOUN
ejpam-6834	1496	5	)	)	PUNCT
ejpam-6834	1496	6	=	=	SYM
ejpam-6834	1496	7	p+(p̃n(u	p+(p̃n(u	NOUN
ejpam-6834	1496	8	)	)	PUNCT
ejpam-6834	1496	9	)	)	PUNCT
ejpam-6834	1496	10	,	,	PUNCT
ejpam-6834	1496	11	i.e.	i.e.	X
ejpam-6834	1496	12	,	,	PUNCT
ejpam-6834	1496	13	each	each	PRON
ejpam-6834	1496	14	is	be	AUX
ejpam-6834	1496	15	a	a	DET
ejpam-6834	1496	16	nonempty	nonempty	ADJ
ejpam-6834	1496	17	family	family	NOUN
ejpam-6834	1496	18	of	of	ADP
ejpam-6834	1496	19	level	level	NOUN
ejpam-6834	1496	20	–	–	PUNCT
ejpam-6834	1496	21	n	n	DET
ejpam-6834	1496	22	elements	element	NOUN
ejpam-6834	1496	23	.	.	PUNCT
ejpam-6834	1497	1	their	their	PRON
ejpam-6834	1497	2	union	union	NOUN
ejpam-6834	1497	3	is	be	AUX
ejpam-6834	1497	4	a	a	DET
ejpam-6834	1497	5	nonempty	nonempty	ADJ
ejpam-6834	1497	6	family	family	NOUN
ejpam-6834	1497	7	of	of	ADP
ejpam-6834	1497	8	level	level	NOUN
ejpam-6834	1497	9	–	–	PUNCT
ejpam-6834	1497	10	n	n	CCONJ
ejpam-6834	1497	11	elements	element	NOUN
ejpam-6834	1497	12	and	and	CCONJ
ejpam-6834	1497	13	therefore	therefore	ADV
ejpam-6834	1497	14	belongs	belong	VERB
ejpam-6834	1497	15	to	to	PART
ejpam-6834	1497	16	p+(p̃n(u	p+(p̃n(u	VERB
ejpam-6834	1497	17	)	)	PUNCT
ejpam-6834	1497	18	)	)	PUNCT
ejpam-6834	1498	1	=	=	SYM
ejpam-6834	1498	2	p̃n+1(u	p̃n+1(u	NOUN
ejpam-6834	1498	3	)	)	PUNCT
ejpam-6834	1498	4	.	.	PUNCT
ejpam-6834	1499	1	doing	do	VERB
ejpam-6834	1499	2	this	this	PRON
ejpam-6834	1499	3	in	in	ADP
ejpam-6834	1499	4	each	each	DET
ejpam-6834	1499	5	coordinate	coordinate	NOUN
ejpam-6834	1499	6	j	j	PROPN
ejpam-6834	1499	7	=	=	SYM
ejpam-6834	1499	8	1	1	NUM
ejpam-6834	1499	9	,	,	PUNCT
ejpam-6834	1499	10	.	.	PUNCT
ejpam-6834	1499	11	.	.	PUNCT
ejpam-6834	1500	1	.	.	PUNCT
ejpam-6834	1501	1	,	,	PUNCT
ejpam-6834	1501	2	k	k	PROPN
ejpam-6834	1501	3	gives	give	VERB
ejpam-6834	1501	4	the	the	DET
ejpam-6834	1501	5	claim	claim	NOUN
ejpam-6834	1501	6	.	.	PUNCT
ejpam-6834	1502	1	theorem	theorem	VERB
ejpam-6834	1502	2	51	51	NUM
ejpam-6834	1502	3	(	(	PUNCT
ejpam-6834	1502	4	pointwise	pointwise	NOUN
ejpam-6834	1502	5	intersection	intersection	NOUN
ejpam-6834	1502	6	)	)	PUNCT
ejpam-6834	1502	7	.	.	PUNCT
ejpam-6834	1503	1	with	with	ADP
ejpam-6834	1503	2	the	the	DET
ejpam-6834	1503	3	same	same	ADJ
ejpam-6834	1503	4	hypotheses	hypothesis	NOUN
ejpam-6834	1503	5	,	,	PUNCT
ejpam-6834	1503	6	define	define	NOUN
ejpam-6834	1503	7	(	(	PUNCT
ejpam-6834	1503	8	f1	f1	NOUN
ejpam-6834	1503	9	∩	∩	NOUN
ejpam-6834	1503	10	f2)(a	f2)(a	PROPN
ejpam-6834	1503	11	)	)	PUNCT
ejpam-6834	1503	12	:	:	PUNCT
ejpam-6834	1504	1	=	=	SYM
ejpam-6834	1504	2	(	(	PUNCT
ejpam-6834	1504	3	f1(a)j	f1(a)j	ADJ
ejpam-6834	1504	4	∩	∩	X
ejpam-6834	1504	5	f2(a)j	f2(a)j	INTJ
ejpam-6834	1504	6	)	)	PUNCT
ejpam-6834	1505	1	k	k	X
ejpam-6834	1505	2	j=1	j=1	NOUN
ejpam-6834	1505	3	.	.	PUNCT
ejpam-6834	1506	1	if	if	SCONJ
ejpam-6834	1506	2	each	each	DET
ejpam-6834	1506	3	intersection	intersection	NOUN
ejpam-6834	1506	4	is	be	AUX
ejpam-6834	1506	5	nonempty	nonempty	ADJ
ejpam-6834	1506	6	,	,	PUNCT
ejpam-6834	1506	7	then	then	ADV
ejpam-6834	1506	8	(	(	PUNCT
ejpam-6834	1506	9	f1∩f2	f1∩f2	PROPN
ejpam-6834	1506	10	)	)	PUNCT
ejpam-6834	1506	11	is	be	AUX
ejpam-6834	1506	12	an	an	DET
ejpam-6834	1506	13	(	(	PUNCT
ejpam-6834	1506	14	h	h	NOUN
ejpam-6834	1506	15	,	,	PUNCT
ejpam-6834	1506	16	k)-ary	k)-ary	X
ejpam-6834	1506	17	(	(	PUNCT
ejpam-6834	1506	18	m	m	PROPN
ejpam-6834	1506	19	,	,	PUNCT
ejpam-6834	1506	20	n)-superhypersoft	n)-superhypersoft	ADV
ejpam-6834	1506	21	set	set	NOUN
ejpam-6834	1506	22	.	.	PUNCT
ejpam-6834	1507	1	proof	proof	NOUN
ejpam-6834	1507	2	.	.	PUNCT
ejpam-6834	1508	1	fix	fix	VERB
ejpam-6834	1508	2	a	a	PRON
ejpam-6834	1508	3	and	and	CCONJ
ejpam-6834	1508	4	j	j	NOUN
ejpam-6834	1508	5	,	,	PUNCT
ejpam-6834	1508	6	and	and	CCONJ
ejpam-6834	1508	7	assume	assume	VERB
ejpam-6834	1508	8	f1(a)j	f1(a)j	ADJ
ejpam-6834	1508	9	∩	∩	ADJ
ejpam-6834	1508	10	f2(a)j	f2(a)j	ADJ
ejpam-6834	1508	11	̸=	̸=	PROPN
ejpam-6834	1508	12	∅.	∅.	NOUN
ejpam-6834	1508	13	induct	induct	PROPN
ejpam-6834	1508	14	on	on	ADP
ejpam-6834	1508	15	n.	n.	PROPN
ejpam-6834	1508	16	base	base	PROPN
ejpam-6834	1508	17	n	n	NOUN
ejpam-6834	1508	18	=	=	SYM
ejpam-6834	1508	19	1	1	NUM
ejpam-6834	1508	20	.	.	X
ejpam-6834	1508	21	two	two	NUM
ejpam-6834	1508	22	nonempty	nonempty	ADJ
ejpam-6834	1508	23	subsets	subset	NOUN
ejpam-6834	1508	24	of	of	ADP
ejpam-6834	1508	25	u	u	PRON
ejpam-6834	1508	26	that	that	PRON
ejpam-6834	1508	27	meet	meet	VERB
ejpam-6834	1508	28	have	have	VERB
ejpam-6834	1508	29	a	a	DET
ejpam-6834	1508	30	nonempty	nonempty	ADJ
ejpam-6834	1508	31	intersection	intersection	NOUN
ejpam-6834	1508	32	,	,	PUNCT
ejpam-6834	1508	33	which	which	PRON
ejpam-6834	1508	34	lies	lie	VERB
ejpam-6834	1508	35	in	in	ADP
ejpam-6834	1508	36	p+(u	p+(u	ADJ
ejpam-6834	1508	37	)	)	PUNCT
ejpam-6834	1508	38	=	=	SYM
ejpam-6834	1508	39	p̃1(u	p̃1(u	PROPN
ejpam-6834	1508	40	)	)	PUNCT
ejpam-6834	1508	41	.	.	PUNCT
ejpam-6834	1509	1	step	step	NOUN
ejpam-6834	1509	2	n	n	PROPN
ejpam-6834	1509	3	⇒	⇒	PROPN
ejpam-6834	1509	4	n+1	n+1	PROPN
ejpam-6834	1509	5	.	.	PUNCT
ejpam-6834	1510	1	here	here	ADV
ejpam-6834	1510	2	fi(a)j	fi(a)j	X
ejpam-6834	1510	3	are	be	AUX
ejpam-6834	1510	4	nonempty	nonempty	ADJ
ejpam-6834	1510	5	families	family	NOUN
ejpam-6834	1510	6	of	of	ADP
ejpam-6834	1510	7	level	level	NOUN
ejpam-6834	1510	8	–	–	PUNCT
ejpam-6834	1510	9	n	n	PRON
ejpam-6834	1510	10	elements	element	NOUN
ejpam-6834	1510	11	.	.	PUNCT
ejpam-6834	1511	1	a	a	DET
ejpam-6834	1511	2	nontrivial	nontrivial	ADJ
ejpam-6834	1511	3	intersection	intersection	NOUN
ejpam-6834	1511	4	of	of	ADP
ejpam-6834	1511	5	such	such	ADJ
ejpam-6834	1511	6	families	family	NOUN
ejpam-6834	1511	7	is	be	AUX
ejpam-6834	1511	8	again	again	ADV
ejpam-6834	1511	9	a	a	DET
ejpam-6834	1511	10	nonempty	nonempty	ADJ
ejpam-6834	1511	11	family	family	NOUN
ejpam-6834	1511	12	of	of	ADP
ejpam-6834	1511	13	level	level	NOUN
ejpam-6834	1511	14	–	–	PUNCT
ejpam-6834	1511	15	n	n	DET
ejpam-6834	1511	16	elements	element	NOUN
ejpam-6834	1511	17	;	;	PUNCT
ejpam-6834	1511	18	hence	hence	ADV
ejpam-6834	1511	19	it	it	PRON
ejpam-6834	1511	20	lies	lie	VERB
ejpam-6834	1511	21	in	in	ADP
ejpam-6834	1511	22	p+(p̃n(u	p+(p̃n(u	NOUN
ejpam-6834	1511	23	)	)	PUNCT
ejpam-6834	1511	24	)	)	PUNCT
ejpam-6834	1512	1	=	=	SYM
ejpam-6834	1512	2	p̃n+1(u	p̃n+1(u	NOUN
ejpam-6834	1512	3	)	)	PUNCT
ejpam-6834	1512	4	.	.	PUNCT
ejpam-6834	1513	1	coordinatewise	coordinatewise	ADJ
ejpam-6834	1513	2	application	application	NOUN
ejpam-6834	1513	3	yields	yield	VERB
ejpam-6834	1513	4	the	the	DET
ejpam-6834	1513	5	result	result	NOUN
ejpam-6834	1513	6	in	in	ADP
ejpam-6834	1513	7	(	(	PUNCT
ejpam-6834	1513	8	p̃n(u))k	p̃n(u))k	NOUN
ejpam-6834	1513	9	.	.	PUNCT
ejpam-6834	1514	1	t.	t.	PROPN
ejpam-6834	1514	2	fujita	fujita	PROPN
ejpam-6834	1514	3	,	,	PUNCT
ejpam-6834	1514	4	f.smarandache	f.smarandache	NOUN
ejpam-6834	1514	5	/	/	SYM
ejpam-6834	1514	6	eur	eur	PROPN
ejpam-6834	1514	7	.	.	PUNCT
ejpam-6834	1515	1	j.	j.	PROPN
ejpam-6834	1515	2	pure	pure	PROPN
ejpam-6834	1515	3	appl	appl	PROPN
ejpam-6834	1515	4	.	.	PROPN
ejpam-6834	1515	5	math	math	PROPN
ejpam-6834	1515	6	,	,	PUNCT
ejpam-6834	1515	7	18	18	NUM
ejpam-6834	1515	8	(	(	PUNCT
ejpam-6834	1515	9	4	4	NUM
ejpam-6834	1515	10	)	)	PUNCT
ejpam-6834	1515	11	(	(	PUNCT
ejpam-6834	1515	12	2025	2025	NUM
ejpam-6834	1515	13	)	)	PUNCT
ejpam-6834	1515	14	,	,	PUNCT
ejpam-6834	1515	15	6834	6834	NUM
ejpam-6834	1515	16	56	56	NUM
ejpam-6834	1515	17	of	of	ADP
ejpam-6834	1515	18	69	69	NUM
ejpam-6834	1515	19	theorem	theorem	NOUN
ejpam-6834	1515	20	52	52	NUM
ejpam-6834	1515	21	(	(	PUNCT
ejpam-6834	1515	22	functoriality	functoriality	NOUN
ejpam-6834	1515	23	under	under	ADP
ejpam-6834	1515	24	surjections	surjection	NOUN
ejpam-6834	1515	25	)	)	PUNCT
ejpam-6834	1515	26	.	.	PUNCT
ejpam-6834	1516	1	let	let	VERB
ejpam-6834	1516	2	f	f	NOUN
ejpam-6834	1516	3	:	:	PUNCT
ejpam-6834	1516	4	u	u	PROPN
ejpam-6834	1516	5	→	→	SYM
ejpam-6834	1516	6	v	v	NUM
ejpam-6834	1516	7	be	be	AUX
ejpam-6834	1516	8	surjective	surjective	ADJ
ejpam-6834	1516	9	.	.	PUNCT
ejpam-6834	1517	1	define	define	VERB
ejpam-6834	1517	2	recursively	recursively	NOUN
ejpam-6834	1517	3	maps	map	NOUN
ejpam-6834	1517	4	f	f	PROPN
ejpam-6834	1517	5	(	(	PUNCT
ejpam-6834	1517	6	1	1	X
ejpam-6834	1517	7	)	)	PUNCT
ejpam-6834	1517	8	∗	∗	NOUN
ejpam-6834	1517	9	:	:	PUNCT
ejpam-6834	1518	1	p̃1(u	p̃1(u	NOUN
ejpam-6834	1518	2	)	)	PUNCT
ejpam-6834	1518	3	→	→	SYM
ejpam-6834	1518	4	p̃1(v	p̃1(v	PROPN
ejpam-6834	1518	5	)	)	PUNCT
ejpam-6834	1518	6	by	by	ADP
ejpam-6834	1518	7	f	f	PROPN
ejpam-6834	1518	8	(	(	PUNCT
ejpam-6834	1518	9	1	1	X
ejpam-6834	1518	10	)	)	PUNCT
ejpam-6834	1518	11	∗	∗	NOUN
ejpam-6834	1518	12	(	(	PUNCT
ejpam-6834	1518	13	b	b	NOUN
ejpam-6834	1518	14	)	)	PUNCT
ejpam-6834	1518	15	:	:	PUNCT
ejpam-6834	1519	1	=	=	PUNCT
ejpam-6834	1519	2	f	f	X
ejpam-6834	1520	1	[	[	X
ejpam-6834	1520	2	b	b	X
ejpam-6834	1520	3	]	]	X
ejpam-6834	1520	4	=	=	SYM
ejpam-6834	1520	5	{	{	PUNCT
ejpam-6834	1520	6	f(u	f(u	PROPN
ejpam-6834	1520	7	)	)	PUNCT
ejpam-6834	1520	8	|	|	CCONJ
ejpam-6834	1520	9	u	u	NOUN
ejpam-6834	1520	10	∈	∈	PROPN
ejpam-6834	1520	11	b	b	PROPN
ejpam-6834	1520	12	}	}	PUNCT
ejpam-6834	1520	13	and	and	CCONJ
ejpam-6834	1520	14	,	,	PUNCT
ejpam-6834	1520	15	for	for	ADP
ejpam-6834	1520	16	r	r	NOUN
ejpam-6834	1520	17	≥	≥	NUM
ejpam-6834	1520	18	1	1	NUM
ejpam-6834	1520	19	,	,	PUNCT
ejpam-6834	1520	20	f	f	PROPN
ejpam-6834	1520	21	(	(	PUNCT
ejpam-6834	1520	22	r+1	r+1	NOUN
ejpam-6834	1520	23	)	)	PUNCT
ejpam-6834	1520	24	∗	∗	NOUN
ejpam-6834	1520	25	:	:	PUNCT
ejpam-6834	1520	26	p̃r+1(u	p̃r+1(u	ADJ
ejpam-6834	1520	27	)	)	PUNCT
ejpam-6834	1520	28	−→	−→	ADJ
ejpam-6834	1520	29	p̃r+1(v	p̃r+1(v	NOUN
ejpam-6834	1520	30	)	)	PUNCT
ejpam-6834	1520	31	,	,	PUNCT
ejpam-6834	1520	32	f	f	PROPN
ejpam-6834	1520	33	(	(	PUNCT
ejpam-6834	1520	34	r+1	r+1	PROPN
ejpam-6834	1520	35	)	)	PUNCT
ejpam-6834	1520	36	∗	∗	NOUN
ejpam-6834	1520	37	(	(	PUNCT
ejpam-6834	1520	38	b	b	NOUN
ejpam-6834	1520	39	)	)	PUNCT
ejpam-6834	1520	40	:	:	PUNCT
ejpam-6834	1521	1	=	=	PRON
ejpam-6834	1521	2	{	{	PUNCT
ejpam-6834	1521	3	f	f	X
ejpam-6834	1521	4	(	(	PUNCT
ejpam-6834	1521	5	r	r	NOUN
ejpam-6834	1521	6	)	)	PUNCT
ejpam-6834	1521	7	∗	∗	NOUN
ejpam-6834	1521	8	(	(	PUNCT
ejpam-6834	1521	9	b	b	NOUN
ejpam-6834	1521	10	)	)	PUNCT
ejpam-6834	1521	11	∣∣	∣∣	NUM
ejpam-6834	1521	12	b	b	X
ejpam-6834	1521	13	∈	∈	PROPN
ejpam-6834	1521	14	b	b	PROPN
ejpam-6834	1521	15	}	}	PUNCT
ejpam-6834	1521	16	.	.	PUNCT
ejpam-6834	1522	1	then	then	ADV
ejpam-6834	1522	2	the	the	DET
ejpam-6834	1522	3	pushforward	pushforward	NOUN
ejpam-6834	1522	4	f∗f	f∗f	VERB
ejpam-6834	1522	5	:	:	PUNCT
ejpam-6834	1522	6	(	(	PUNCT
ejpam-6834	1522	7	p̃m(s))h	p̃m(s))h	ADP
ejpam-6834	1522	8	−→	−→	NOUN
ejpam-6834	1522	9	(	(	PUNCT
ejpam-6834	1522	10	p̃n(v	p̃n(v	NOUN
ejpam-6834	1522	11	)	)	PUNCT
ejpam-6834	1522	12	)	)	PUNCT
ejpam-6834	1523	1	k	k	NOUN
ejpam-6834	1523	2	,	,	PUNCT
ejpam-6834	1523	3	f∗f	f∗f	X
ejpam-6834	1523	4	(	(	PUNCT
ejpam-6834	1523	5	a	a	X
ejpam-6834	1523	6	)	)	PUNCT
ejpam-6834	1523	7	=	=	SYM
ejpam-6834	1523	8	(	(	PUNCT
ejpam-6834	1523	9	f	f	X
ejpam-6834	1523	10	(	(	PUNCT
ejpam-6834	1523	11	n	n	CCONJ
ejpam-6834	1523	12	)	)	PUNCT
ejpam-6834	1523	13	∗	∗	NOUN
ejpam-6834	1523	14	(	(	PUNCT
ejpam-6834	1523	15	f	f	PROPN
ejpam-6834	1523	16	(	(	PUNCT
ejpam-6834	1523	17	a)j	a)j	ADJ
ejpam-6834	1523	18	)	)	PUNCT
ejpam-6834	1523	19	)	)	PUNCT
ejpam-6834	1524	1	k	k	X
ejpam-6834	1524	2	j=1	j=1	NOUN
ejpam-6834	1524	3	,	,	PUNCT
ejpam-6834	1524	4	is	be	AUX
ejpam-6834	1524	5	an	an	DET
ejpam-6834	1524	6	(	(	PUNCT
ejpam-6834	1524	7	h	h	NOUN
ejpam-6834	1524	8	,	,	PUNCT
ejpam-6834	1524	9	k)-ary	k)-ary	X
ejpam-6834	1524	10	(	(	PUNCT
ejpam-6834	1524	11	m	m	PROPN
ejpam-6834	1524	12	,	,	PUNCT
ejpam-6834	1524	13	n)-superhypersoft	n)-superhypersoft	ADV
ejpam-6834	1524	14	set	set	VERB
ejpam-6834	1524	15	over	over	ADP
ejpam-6834	1524	16	v	v	NOUN
ejpam-6834	1524	17	.	.	PUNCT
ejpam-6834	1525	1	proof	proof	NOUN
ejpam-6834	1525	2	.	.	PUNCT
ejpam-6834	1526	1	we	we	PRON
ejpam-6834	1526	2	prove	prove	VERB
ejpam-6834	1526	3	by	by	ADP
ejpam-6834	1526	4	induction	induction	NOUN
ejpam-6834	1526	5	on	on	ADP
ejpam-6834	1526	6	r	r	PROPN
ejpam-6834	1526	7	≥	≥	NUM
ejpam-6834	1526	8	1	1	NUM
ejpam-6834	1526	9	that	that	PRON
ejpam-6834	1526	10	f	f	X
ejpam-6834	1526	11	(	(	PUNCT
ejpam-6834	1526	12	r	r	NOUN
ejpam-6834	1526	13	)	)	PUNCT
ejpam-6834	1526	14	∗	∗	NOUN
ejpam-6834	1526	15	is	be	AUX
ejpam-6834	1526	16	well	well	ADV
ejpam-6834	1526	17	defined	define	VERB
ejpam-6834	1526	18	and	and	CCONJ
ejpam-6834	1526	19	preserves	preserve	VERB
ejpam-6834	1526	20	nonemptiness	nonemptiness	PROPN
ejpam-6834	1526	21	.	.	PUNCT
ejpam-6834	1527	1	base	base	NOUN
ejpam-6834	1527	2	r	r	NOUN
ejpam-6834	1527	3	=	=	SYM
ejpam-6834	1527	4	1	1	X
ejpam-6834	1527	5	.	.	PUNCT
ejpam-6834	1528	1	if	if	SCONJ
ejpam-6834	1528	2	b	b	PROPN
ejpam-6834	1528	3	∈	∈	PROPN
ejpam-6834	1528	4	p̃1(u	p̃1(u	PROPN
ejpam-6834	1528	5	)	)	PUNCT
ejpam-6834	1528	6	then	then	ADV
ejpam-6834	1528	7	b	b	X
ejpam-6834	1528	8	̸=	̸=	PROPN
ejpam-6834	1528	9	∅	∅	NOUN
ejpam-6834	1528	10	;	;	PUNCT
ejpam-6834	1528	11	surjectivity	surjectivity	NOUN
ejpam-6834	1528	12	of	of	ADP
ejpam-6834	1528	13	f	f	PROPN
ejpam-6834	1528	14	implies	imply	VERB
ejpam-6834	1528	15	f	f	PROPN
ejpam-6834	1528	16	[	[	X
ejpam-6834	1528	17	b	b	X
ejpam-6834	1528	18	]	]	X
ejpam-6834	1528	19	̸=	̸=	PROPN
ejpam-6834	1528	20	∅	∅	NOUN
ejpam-6834	1528	21	,	,	PUNCT
ejpam-6834	1528	22	so	so	SCONJ
ejpam-6834	1528	23	f	f	X
ejpam-6834	1528	24	(	(	PUNCT
ejpam-6834	1528	25	1	1	X
ejpam-6834	1528	26	)	)	PUNCT
ejpam-6834	1528	27	∗	∗	NOUN
ejpam-6834	1528	28	(	(	PUNCT
ejpam-6834	1528	29	b	b	X
ejpam-6834	1528	30	)	)	PUNCT
ejpam-6834	1528	31	∈	∈	NOUN
ejpam-6834	1528	32	p̃1(v	p̃1(v	NOUN
ejpam-6834	1528	33	)	)	PUNCT
ejpam-6834	1528	34	.	.	PUNCT
ejpam-6834	1529	1	step	step	NOUN
ejpam-6834	1529	2	r	r	NOUN
ejpam-6834	1529	3	⇒	⇒	NOUN
ejpam-6834	1529	4	r+1	r+1	PROPN
ejpam-6834	1529	5	.	.	PUNCT
ejpam-6834	1530	1	let	let	VERB
ejpam-6834	1530	2	b	b	NOUN
ejpam-6834	1530	3	∈	∈	PROPN
ejpam-6834	1530	4	p̃r+1(u	p̃r+1(u	NOUN
ejpam-6834	1530	5	)	)	PUNCT
ejpam-6834	1530	6	,	,	PUNCT
ejpam-6834	1530	7	so	so	PROPN
ejpam-6834	1530	8	b	b	PROPN
ejpam-6834	1530	9	̸=	̸=	PROPN
ejpam-6834	1530	10	∅	∅	NOUN
ejpam-6834	1530	11	and	and	CCONJ
ejpam-6834	1530	12	each	each	DET
ejpam-6834	1530	13	b	b	PROPN
ejpam-6834	1530	14	∈	∈	PROPN
ejpam-6834	1530	15	b	b	PROPN
ejpam-6834	1530	16	lies	lie	VERB
ejpam-6834	1530	17	in	in	ADP
ejpam-6834	1530	18	p̃r(u	p̃r(u	PROPN
ejpam-6834	1530	19	)	)	PUNCT
ejpam-6834	1530	20	.	.	PUNCT
ejpam-6834	1531	1	by	by	ADP
ejpam-6834	1531	2	induction	induction	NOUN
ejpam-6834	1531	3	,	,	PUNCT
ejpam-6834	1531	4	each	each	DET
ejpam-6834	1531	5	f	f	X
ejpam-6834	1531	6	(	(	PUNCT
ejpam-6834	1531	7	r	r	NOUN
ejpam-6834	1531	8	)	)	PUNCT
ejpam-6834	1531	9	∗	∗	NOUN
ejpam-6834	1531	10	(	(	PUNCT
ejpam-6834	1531	11	b	b	X
ejpam-6834	1531	12	)	)	PUNCT
ejpam-6834	1531	13	∈	∈	PROPN
ejpam-6834	1531	14	p̃r(v	p̃r(v	NOUN
ejpam-6834	1531	15	)	)	PUNCT
ejpam-6834	1531	16	;	;	PUNCT
ejpam-6834	1531	17	since	since	SCONJ
ejpam-6834	1531	18	b	b	PROPN
ejpam-6834	1531	19	̸=	̸=	PROPN
ejpam-6834	1531	20	∅	∅	NOUN
ejpam-6834	1531	21	,	,	PUNCT
ejpam-6834	1531	22	the	the	DET
ejpam-6834	1531	23	set	set	NOUN
ejpam-6834	1531	24	{	{	PUNCT
ejpam-6834	1531	25	f	f	X
ejpam-6834	1531	26	(	(	PUNCT
ejpam-6834	1531	27	r	r	NOUN
ejpam-6834	1531	28	)	)	PUNCT
ejpam-6834	1531	29	∗	∗	NOUN
ejpam-6834	1531	30	(	(	PUNCT
ejpam-6834	1531	31	b	b	NOUN
ejpam-6834	1531	32	)	)	PUNCT
ejpam-6834	1531	33	|	|	ADV
ejpam-6834	1531	34	b	b	X
ejpam-6834	1531	35	∈	∈	PROPN
ejpam-6834	1531	36	b	b	AUX
ejpam-6834	1531	37	}	}	PUNCT
ejpam-6834	1531	38	is	be	AUX
ejpam-6834	1531	39	a	a	DET
ejpam-6834	1531	40	nonempty	nonempty	ADJ
ejpam-6834	1531	41	subset	subset	NOUN
ejpam-6834	1531	42	of	of	ADP
ejpam-6834	1531	43	p̃r(v	p̃r(v	PROPN
ejpam-6834	1531	44	)	)	PUNCT
ejpam-6834	1531	45	,	,	PUNCT
ejpam-6834	1531	46	hence	hence	ADV
ejpam-6834	1531	47	belongs	belong	VERB
ejpam-6834	1531	48	to	to	ADP
ejpam-6834	1531	49	p+(p̃r(v	p+(p̃r(v	PROPN
ejpam-6834	1531	50	)	)	PUNCT
ejpam-6834	1531	51	)	)	PUNCT
ejpam-6834	1532	1	=	=	PUNCT
ejpam-6834	1532	2	p̃r+1(v	p̃r+1(v	NOUN
ejpam-6834	1532	3	)	)	PUNCT
ejpam-6834	1532	4	.	.	PUNCT
ejpam-6834	1533	1	now	now	ADV
ejpam-6834	1533	2	,	,	PUNCT
ejpam-6834	1533	3	for	for	ADP
ejpam-6834	1533	4	any	any	DET
ejpam-6834	1533	5	input	input	NOUN
ejpam-6834	1533	6	a	a	DET
ejpam-6834	1533	7	∈	∈	NOUN
ejpam-6834	1533	8	(	(	PUNCT
ejpam-6834	1533	9	p̃m(s))h	p̃m(s))h	PROPN
ejpam-6834	1533	10	,	,	PUNCT
ejpam-6834	1533	11	f	f	PROPN
ejpam-6834	1533	12	(	(	PUNCT
ejpam-6834	1533	13	a	a	PRON
ejpam-6834	1533	14	)	)	PUNCT
ejpam-6834	1533	15	∈	∈	PROPN
ejpam-6834	1533	16	(	(	PUNCT
ejpam-6834	1533	17	p̃n(u))k	p̃n(u))k	PROPN
ejpam-6834	1533	18	;	;	PUNCT
ejpam-6834	1533	19	applying	apply	VERB
ejpam-6834	1533	20	f	f	PROPN
ejpam-6834	1533	21	(	(	PUNCT
ejpam-6834	1533	22	n	n	CCONJ
ejpam-6834	1533	23	)	)	PUNCT
ejpam-6834	1533	24	∗	∗	NOUN
ejpam-6834	1533	25	to	to	ADP
ejpam-6834	1533	26	each	each	DET
ejpam-6834	1533	27	coordinate	coordinate	NOUN
ejpam-6834	1533	28	yields	yield	VERB
ejpam-6834	1533	29	an	an	DET
ejpam-6834	1533	30	element	element	NOUN
ejpam-6834	1533	31	of	of	ADP
ejpam-6834	1533	32	(	(	PUNCT
ejpam-6834	1533	33	p̃n(v	p̃n(v	PROPN
ejpam-6834	1533	34	)	)	PUNCT
ejpam-6834	1533	35	)	)	PUNCT
ejpam-6834	1534	1	k.	k.	PROPN
ejpam-6834	1534	2	thus	thus	ADV
ejpam-6834	1534	3	f∗f	f∗f	X
ejpam-6834	1534	4	has	have	VERB
ejpam-6834	1534	5	the	the	DET
ejpam-6834	1534	6	required	require	VERB
ejpam-6834	1534	7	domain	domain	NOUN
ejpam-6834	1534	8	and	and	CCONJ
ejpam-6834	1534	9	codomain	codomain	NOUN
ejpam-6834	1534	10	and	and	CCONJ
ejpam-6834	1534	11	is	be	AUX
ejpam-6834	1534	12	an	an	DET
ejpam-6834	1534	13	(	(	PUNCT
ejpam-6834	1534	14	h	h	NOUN
ejpam-6834	1534	15	,	,	PUNCT
ejpam-6834	1534	16	k)-ary	k)-ary	X
ejpam-6834	1534	17	(	(	PUNCT
ejpam-6834	1534	18	m	m	PROPN
ejpam-6834	1534	19	,	,	PUNCT
ejpam-6834	1534	20	n)-superhypersoft	n)-superhypersoft	ADV
ejpam-6834	1534	21	set	set	VERB
ejpam-6834	1534	22	over	over	ADP
ejpam-6834	1534	23	v	v	NOUN
ejpam-6834	1534	24	.	.	PUNCT
ejpam-6834	1535	1	theorem	theorem	VERB
ejpam-6834	1535	2	53	53	NUM
ejpam-6834	1535	3	(	(	PUNCT
ejpam-6834	1535	4	reduction	reduction	NOUN
ejpam-6834	1535	5	to	to	ADP
ejpam-6834	1535	6	the	the	DET
ejpam-6834	1535	7	classical	classical	ADJ
ejpam-6834	1535	8	soft	soft	ADJ
ejpam-6834	1535	9	set	set	NOUN
ejpam-6834	1535	10	)	)	PUNCT
ejpam-6834	1535	11	.	.	PUNCT
ejpam-6834	1536	1	if	if	SCONJ
ejpam-6834	1536	2	m	m	PROPN
ejpam-6834	1536	3	=	=	SYM
ejpam-6834	1537	1	n	n	NOUN
ejpam-6834	1537	2	=	=	NOUN
ejpam-6834	1537	3	h	h	NOUN
ejpam-6834	1537	4	=	=	SYM
ejpam-6834	1537	5	k	k	NOUN
ejpam-6834	1537	6	=	=	SYM
ejpam-6834	1537	7	1	1	NUM
ejpam-6834	1537	8	,	,	PUNCT
ejpam-6834	1537	9	then	then	ADV
ejpam-6834	1537	10	f	f	X
ejpam-6834	1537	11	:	:	PUNCT
ejpam-6834	1537	12	p̃1(s	p̃1(s	PROPN
ejpam-6834	1537	13	)	)	PUNCT
ejpam-6834	1537	14	→	→	SYM
ejpam-6834	1537	15	p̃1(u	p̃1(u	NOUN
ejpam-6834	1537	16	)	)	PUNCT
ejpam-6834	1537	17	corresponds	correspond	VERB
ejpam-6834	1537	18	naturally	naturally	ADV
ejpam-6834	1537	19	to	to	ADP
ejpam-6834	1537	20	a	a	DET
ejpam-6834	1537	21	classical	classical	ADJ
ejpam-6834	1537	22	soft	soft	ADJ
ejpam-6834	1537	23	set	set	ADJ
ejpam-6834	1537	24	fcl	fcl	PROPN
ejpam-6834	1537	25	:	:	PUNCT
ejpam-6834	1537	26	s	s	X
ejpam-6834	1537	27	→	→	PUNCT
ejpam-6834	1537	28	p(u	p(u	ADJ
ejpam-6834	1537	29	)	)	PUNCT
ejpam-6834	1537	30	(	(	PUNCT
ejpam-6834	1537	31	up	up	ADP
ejpam-6834	1537	32	to	to	ADP
ejpam-6834	1537	33	the	the	DET
ejpam-6834	1537	34	treatment	treatment	NOUN
ejpam-6834	1537	35	of	of	ADP
ejpam-6834	1537	36	the	the	DET
ejpam-6834	1537	37	empty	empty	ADJ
ejpam-6834	1537	38	set	set	NOUN
ejpam-6834	1537	39	)	)	PUNCT
ejpam-6834	1537	40	.	.	PUNCT
ejpam-6834	1538	1	proof	proof	NOUN
ejpam-6834	1538	2	.	.	PUNCT
ejpam-6834	1539	1	consider	consider	VERB
ejpam-6834	1539	2	the	the	DET
ejpam-6834	1539	3	restriction	restriction	NOUN
ejpam-6834	1539	4	of	of	ADP
ejpam-6834	1539	5	f	f	PROPN
ejpam-6834	1539	6	to	to	PART
ejpam-6834	1539	7	singleton	singleton	VERB
ejpam-6834	1539	8	parameters	parameter	NOUN
ejpam-6834	1539	9	via	via	ADP
ejpam-6834	1539	10	ιs	ιs	INTJ
ejpam-6834	1539	11	:	:	PUNCT
ejpam-6834	1539	12	s	s	X
ejpam-6834	1539	13	→	→	SYM
ejpam-6834	1539	14	p+(s	p+(s	NUM
ejpam-6834	1539	15	)	)	PUNCT
ejpam-6834	1539	16	,	,	PUNCT
ejpam-6834	1539	17	s	s	VERB
ejpam-6834	1539	18	7→	7→	NUM
ejpam-6834	1539	19	{	{	PUNCT
ejpam-6834	1539	20	s	s	NOUN
ejpam-6834	1539	21	}	}	PUNCT
ejpam-6834	1539	22	.	.	PUNCT
ejpam-6834	1540	1	define	define	VERB
ejpam-6834	1540	2	fcl(s	fcl(s	PROPN
ejpam-6834	1540	3	)	)	PUNCT
ejpam-6834	1540	4	:	:	PUNCT
ejpam-6834	1541	1	=	=	SYM
ejpam-6834	1541	2	f	f	X
ejpam-6834	1541	3	(	(	PUNCT
ejpam-6834	1541	4	{	{	PUNCT
ejpam-6834	1541	5	s	s	NOUN
ejpam-6834	1541	6	}	}	PUNCT
ejpam-6834	1541	7	)	)	PUNCT
ejpam-6834	1541	8	if	if	SCONJ
ejpam-6834	1541	9	f	f	PROPN
ejpam-6834	1541	10	(	(	PUNCT
ejpam-6834	1541	11	{	{	PUNCT
ejpam-6834	1541	12	s	s	NOUN
ejpam-6834	1541	13	}	}	PUNCT
ejpam-6834	1541	14	)	)	PUNCT
ejpam-6834	1541	15	̸=	̸=	PROPN
ejpam-6834	1541	16	∅	∅	NOUN
ejpam-6834	1541	17	and	and	CCONJ
ejpam-6834	1541	18	fcl(s	fcl(s	PROPN
ejpam-6834	1541	19	)	)	PUNCT
ejpam-6834	1541	20	:	:	PUNCT
ejpam-6834	1541	21	=	=	NOUN
ejpam-6834	1541	22	∅	∅	NOUN
ejpam-6834	1541	23	otherwise	otherwise	ADV
ejpam-6834	1541	24	(	(	PUNCT
ejpam-6834	1541	25	if	if	SCONJ
ejpam-6834	1541	26	one	one	PRON
ejpam-6834	1541	27	insists	insist	VERB
ejpam-6834	1541	28	on	on	ADP
ejpam-6834	1541	29	allowing	allow	VERB
ejpam-6834	1541	30	empties	empty	NOUN
ejpam-6834	1541	31	in	in	ADP
ejpam-6834	1541	32	the	the	DET
ejpam-6834	1541	33	classical	classical	ADJ
ejpam-6834	1541	34	codomain	codomain	NOUN
ejpam-6834	1541	35	)	)	PUNCT
ejpam-6834	1541	36	.	.	PUNCT
ejpam-6834	1542	1	this	this	PRON
ejpam-6834	1542	2	recovers	recover	VERB
ejpam-6834	1542	3	a	a	DET
ejpam-6834	1542	4	map	map	NOUN
ejpam-6834	1542	5	fcl	fcl	ADJ
ejpam-6834	1542	6	:	:	PUNCT
ejpam-6834	1542	7	s	s	X
ejpam-6834	1542	8	→	→	PUNCT
ejpam-6834	1542	9	p(u	p(u	ADJ
ejpam-6834	1542	10	)	)	PUNCT
ejpam-6834	1542	11	.	.	PUNCT
ejpam-6834	1543	1	conversely	conversely	ADV
ejpam-6834	1543	2	,	,	PUNCT
ejpam-6834	1543	3	given	give	VERB
ejpam-6834	1543	4	fcl	fcl	PROPN
ejpam-6834	1543	5	,	,	PUNCT
ejpam-6834	1543	6	the	the	DET
ejpam-6834	1543	7	union	union	NOUN
ejpam-6834	1543	8	–	–	PUNCT
ejpam-6834	1543	9	or	or	CCONJ
ejpam-6834	1543	10	intersection	intersection	NOUN
ejpam-6834	1543	11	–	–	PUNCT
ejpam-6834	1543	12	lift	lift	NOUN
ejpam-6834	1543	13	(	(	PUNCT
ejpam-6834	1543	14	as	as	ADP
ejpam-6834	1543	15	in	in	ADP
ejpam-6834	1543	16	the	the	DET
ejpam-6834	1543	17	proof	proof	NOUN
ejpam-6834	1543	18	of	of	ADP
ejpam-6834	1543	19	the	the	DET
ejpam-6834	1543	20	first	first	ADJ
ejpam-6834	1543	21	theorem	theorem	NOUN
ejpam-6834	1543	22	)	)	PUNCT
ejpam-6834	1543	23	produces	produce	VERB
ejpam-6834	1543	24	an	an	DET
ejpam-6834	1543	25	f	f	NOUN
ejpam-6834	1543	26	:	:	PUNCT
ejpam-6834	1543	27	p+(s	p+(s	PROPN
ejpam-6834	1543	28	)	)	PUNCT
ejpam-6834	1543	29	→	→	SYM
ejpam-6834	1543	30	p+(u	p+(u	X
ejpam-6834	1543	31	)	)	PUNCT
ejpam-6834	1543	32	whose	whose	DET
ejpam-6834	1543	33	restriction	restriction	NOUN
ejpam-6834	1543	34	to	to	ADP
ejpam-6834	1543	35	singletons	singleton	NOUN
ejpam-6834	1543	36	coincides	coincide	VERB
ejpam-6834	1543	37	with	with	ADP
ejpam-6834	1543	38	fcl	fcl	PROPN
ejpam-6834	1543	39	(	(	PUNCT
ejpam-6834	1543	40	up	up	ADP
ejpam-6834	1543	41	to	to	ADP
ejpam-6834	1543	42	the	the	DET
ejpam-6834	1543	43	chosen	choose	VERB
ejpam-6834	1543	44	convention	convention	NOUN
ejpam-6834	1543	45	for	for	ADP
ejpam-6834	1543	46	the	the	DET
ejpam-6834	1543	47	empty	empty	ADJ
ejpam-6834	1543	48	set	set	NOUN
ejpam-6834	1543	49	)	)	PUNCT
ejpam-6834	1543	50	.	.	PUNCT
ejpam-6834	1544	1	hence	hence	ADV
ejpam-6834	1544	2	the	the	DET
ejpam-6834	1544	3	two	two	NUM
ejpam-6834	1544	4	notions	notion	NOUN
ejpam-6834	1544	5	correspond	correspond	VERB
ejpam-6834	1544	6	naturally	naturally	ADV
ejpam-6834	1544	7	in	in	ADP
ejpam-6834	1544	8	the	the	DET
ejpam-6834	1544	9	unary	unary	ADJ
ejpam-6834	1544	10	,	,	PUNCT
ejpam-6834	1544	11	level–1	level–1	PROPN
ejpam-6834	1544	12	case	case	NOUN
ejpam-6834	1544	13	.	.	PUNCT
ejpam-6834	1545	1	theorem	theorem	VERB
ejpam-6834	1545	2	54	54	NUM
ejpam-6834	1545	3	(	(	PUNCT
ejpam-6834	1545	4	nested	nest	VERB
ejpam-6834	1545	5	inclusion	inclusion	NOUN
ejpam-6834	1545	6	under	under	ADP
ejpam-6834	1545	7	antitone	antitone	ADJ
ejpam-6834	1545	8	monotonicity	monotonicity	NOUN
ejpam-6834	1545	9	)	)	PUNCT
ejpam-6834	1545	10	.	.	PUNCT
ejpam-6834	1546	1	suppose	suppose	VERB
ejpam-6834	1546	2	f	f	PROPN
ejpam-6834	1546	3	is	be	AUX
ejpam-6834	1546	4	antitone	antitone	ADJ
ejpam-6834	1546	5	in	in	ADP
ejpam-6834	1546	6	each	each	DET
ejpam-6834	1546	7	parameter	parameter	NOUN
ejpam-6834	1546	8	coordinate	coordinate	NOUN
ejpam-6834	1546	9	,	,	PUNCT
ejpam-6834	1546	10	i.e.	i.e.	X
ejpam-6834	1546	11	,	,	PUNCT
ejpam-6834	1546	12	for	for	ADP
ejpam-6834	1546	13	every	every	DET
ejpam-6834	1546	14	i	i	PROPN
ejpam-6834	1546	15	∈	∈	PROPN
ejpam-6834	1546	16	{	{	PUNCT
ejpam-6834	1546	17	1	1	NUM
ejpam-6834	1546	18	,	,	PUNCT
ejpam-6834	1546	19	.	.	PUNCT
ejpam-6834	1546	20	.	.	PUNCT
ejpam-6834	1547	1	.	.	PUNCT
ejpam-6834	1548	1	,	,	PUNCT
ejpam-6834	1548	2	h	h	NOUN
ejpam-6834	1548	3	}	}	PUNCT
ejpam-6834	1548	4	and	and	CCONJ
ejpam-6834	1548	5	tuples	tuple	VERB
ejpam-6834	1548	6	a	a	PRON
ejpam-6834	1548	7	,	,	PUNCT
ejpam-6834	1548	8	a′	a′	PROPN
ejpam-6834	1548	9	that	that	DET
ejpam-6834	1548	10	coincide	coincide	NOUN
ejpam-6834	1548	11	in	in	ADP
ejpam-6834	1548	12	all	all	DET
ejpam-6834	1548	13	coordinates	coordinate	NOUN
ejpam-6834	1548	14	except	except	SCONJ
ejpam-6834	1548	15	possibly	possibly	ADV
ejpam-6834	1548	16	i	i	PRON
ejpam-6834	1548	17	,	,	PUNCT
ejpam-6834	1548	18	ai	ai	VERB
ejpam-6834	1548	19	⊆	⊆	NUM
ejpam-6834	1548	20	a′	a′	NOUN
ejpam-6834	1548	21	i	i	PRON
ejpam-6834	1548	22	=	=	VERB
ejpam-6834	1548	23	⇒	⇒	PROPN
ejpam-6834	1548	24	f	f	PROPN
ejpam-6834	1548	25	(	(	PUNCT
ejpam-6834	1548	26	a)j	a)j	X
ejpam-6834	1548	27	⊇	⊇	PROPN
ejpam-6834	1548	28	f	f	PROPN
ejpam-6834	1548	29	(	(	PUNCT
ejpam-6834	1548	30	a′)j	a′)j	NOUN
ejpam-6834	1548	31	for	for	ADP
ejpam-6834	1548	32	all	all	DET
ejpam-6834	1548	33	j	j	NOUN
ejpam-6834	1549	1	=	=	SYM
ejpam-6834	1549	2	1	1	NUM
ejpam-6834	1549	3	,	,	PUNCT
ejpam-6834	1549	4	.	.	PUNCT
ejpam-6834	1549	5	.	.	PUNCT
ejpam-6834	1550	1	.	.	PUNCT
ejpam-6834	1551	1	,	,	PUNCT
ejpam-6834	1551	2	k.	k.	PROPN
ejpam-6834	1551	3	then	then	ADV
ejpam-6834	1551	4	for	for	ADP
ejpam-6834	1551	5	any	any	DET
ejpam-6834	1551	6	a	a	NOUN
ejpam-6834	1551	7	,	,	PUNCT
ejpam-6834	1551	8	a′	a′	PROPN
ejpam-6834	1551	9	∈	∈	PROPN
ejpam-6834	1551	10	(	(	PUNCT
ejpam-6834	1551	11	p̃m(s))h	p̃m(s))h	PROPN
ejpam-6834	1551	12	with	with	ADP
ejpam-6834	1551	13	a	a	DET
ejpam-6834	1551	14	⊆	⊆	NUM
ejpam-6834	1551	15	a′	a′	NOUN
ejpam-6834	1551	16	coordinatewise	coordinatewise	NOUN
ejpam-6834	1551	17	,	,	PUNCT
ejpam-6834	1551	18	one	one	PRON
ejpam-6834	1551	19	has	have	VERB
ejpam-6834	1551	20	f	f	PROPN
ejpam-6834	1551	21	(	(	PUNCT
ejpam-6834	1551	22	a)j	a)j	X
ejpam-6834	1551	23	⊇	⊇	PROPN
ejpam-6834	1551	24	f	f	PROPN
ejpam-6834	1551	25	(	(	PUNCT
ejpam-6834	1551	26	a′)j	a′)j	NOUN
ejpam-6834	1551	27	(	(	PUNCT
ejpam-6834	1551	28	j	j	NOUN
ejpam-6834	1551	29	=	=	SYM
ejpam-6834	1551	30	1	1	NUM
ejpam-6834	1551	31	,	,	PUNCT
ejpam-6834	1551	32	.	.	PUNCT
ejpam-6834	1551	33	.	.	PUNCT
ejpam-6834	1552	1	.	.	PUNCT
ejpam-6834	1553	1	,	,	PUNCT
ejpam-6834	1553	2	k	k	X
ejpam-6834	1553	3	)	)	PUNCT
ejpam-6834	1553	4	.	.	PUNCT
ejpam-6834	1554	1	t.	t.	PROPN
ejpam-6834	1554	2	fujita	fujita	PROPN
ejpam-6834	1554	3	,	,	PUNCT
ejpam-6834	1554	4	f.smarandache	f.smarandache	NOUN
ejpam-6834	1554	5	/	/	SYM
ejpam-6834	1554	6	eur	eur	PROPN
ejpam-6834	1554	7	.	.	PUNCT
ejpam-6834	1555	1	j.	j.	PROPN
ejpam-6834	1555	2	pure	pure	PROPN
ejpam-6834	1555	3	appl	appl	PROPN
ejpam-6834	1555	4	.	.	PROPN
ejpam-6834	1555	5	math	math	PROPN
ejpam-6834	1555	6	,	,	PUNCT
ejpam-6834	1555	7	18	18	NUM
ejpam-6834	1555	8	(	(	PUNCT
ejpam-6834	1555	9	4	4	NUM
ejpam-6834	1555	10	)	)	PUNCT
ejpam-6834	1555	11	(	(	PUNCT
ejpam-6834	1555	12	2025	2025	NUM
ejpam-6834	1555	13	)	)	PUNCT
ejpam-6834	1555	14	,	,	PUNCT
ejpam-6834	1555	15	6834	6834	NUM
ejpam-6834	1555	16	57	57	NUM
ejpam-6834	1555	17	of	of	ADP
ejpam-6834	1555	18	69	69	NUM
ejpam-6834	1555	19	proof	proof	NOUN
ejpam-6834	1555	20	.	.	PUNCT
ejpam-6834	1556	1	enumerate	enumerate	VERB
ejpam-6834	1556	2	the	the	DET
ejpam-6834	1556	3	coordinates	coordinate	NOUN
ejpam-6834	1556	4	so	so	SCONJ
ejpam-6834	1556	5	that	that	SCONJ
ejpam-6834	1556	6	we	we	PRON
ejpam-6834	1556	7	can	can	AUX
ejpam-6834	1556	8	move	move	VERB
ejpam-6834	1556	9	from	from	ADP
ejpam-6834	1556	10	a	a	PRON
ejpam-6834	1556	11	to	to	ADP
ejpam-6834	1556	12	a′	a′	NOUN
ejpam-6834	1556	13	by	by	ADP
ejpam-6834	1556	14	changing	change	VERB
ejpam-6834	1556	15	one	one	NUM
ejpam-6834	1556	16	coordinate	coordinate	NOUN
ejpam-6834	1556	17	at	at	ADP
ejpam-6834	1556	18	a	a	DET
ejpam-6834	1556	19	time	time	NOUN
ejpam-6834	1556	20	.	.	PUNCT
ejpam-6834	1557	1	define	define	VERB
ejpam-6834	1557	2	a	a	DET
ejpam-6834	1557	3	chain	chain	NOUN
ejpam-6834	1557	4	of	of	ADP
ejpam-6834	1557	5	tuples	tuple	NOUN
ejpam-6834	1557	6	a(0	a(0	VERB
ejpam-6834	1557	7	)	)	PUNCT
ejpam-6834	1558	1	:	:	PUNCT
ejpam-6834	1558	2	=	=	PUNCT
ejpam-6834	1558	3	a	a	PRON
ejpam-6834	1558	4	,	,	PUNCT
ejpam-6834	1558	5	a(t	a(t	NOUN
ejpam-6834	1558	6	)	)	PUNCT
ejpam-6834	1558	7	:	:	PUNCT
ejpam-6834	1559	1	=	=	SYM
ejpam-6834	1559	2	(	(	PUNCT
ejpam-6834	1559	3	a′	a′	PROPN
ejpam-6834	1559	4	1	1	NUM
ejpam-6834	1559	5	,	,	PUNCT
ejpam-6834	1559	6	.	.	PUNCT
ejpam-6834	1559	7	.	.	PUNCT
ejpam-6834	1559	8	.	.	PUNCT
ejpam-6834	1560	1	,	,	PUNCT
ejpam-6834	1560	2	a	a	DET
ejpam-6834	1560	3	′	′	NUM
ejpam-6834	1560	4	t	t	PROPN
ejpam-6834	1560	5	,	,	PUNCT
ejpam-6834	1560	6	at+1	at+1	X
ejpam-6834	1560	7	,	,	PUNCT
ejpam-6834	1560	8	.	.	PUNCT
ejpam-6834	1560	9	.	.	PUNCT
ejpam-6834	1560	10	.	.	PUNCT
ejpam-6834	1561	1	,	,	PUNCT
ejpam-6834	1561	2	ah	ah	INTJ
ejpam-6834	1561	3	)	)	PUNCT
ejpam-6834	1561	4	(	(	PUNCT
ejpam-6834	1561	5	1	1	NUM
ejpam-6834	1561	6	≤	≤	NOUN
ejpam-6834	1561	7	t	t	PROPN
ejpam-6834	1561	8	≤	≤	NUM
ejpam-6834	1561	9	h	h	NOUN
ejpam-6834	1561	10	)	)	PUNCT
ejpam-6834	1561	11	,	,	PUNCT
ejpam-6834	1561	12	so	so	ADV
ejpam-6834	1561	13	a(h	a(h	PROPN
ejpam-6834	1561	14	)	)	PUNCT
ejpam-6834	1561	15	=	=	PUNCT
ejpam-6834	1561	16	a′	a′	PROPN
ejpam-6834	1561	17	and	and	CCONJ
ejpam-6834	1561	18	a(t−1	a(t−1	X
ejpam-6834	1561	19	)	)	PUNCT
ejpam-6834	1561	20	and	and	CCONJ
ejpam-6834	1561	21	a(t	a(t	NOUN
ejpam-6834	1561	22	)	)	PUNCT
ejpam-6834	1561	23	differ	differ	VERB
ejpam-6834	1561	24	only	only	ADV
ejpam-6834	1561	25	in	in	ADP
ejpam-6834	1561	26	coordinate	coordinate	NOUN
ejpam-6834	1561	27	t	t	PROPN
ejpam-6834	1561	28	,	,	PUNCT
ejpam-6834	1561	29	with	with	ADP
ejpam-6834	1561	30	at	at	ADP
ejpam-6834	1561	31	⊆	⊆	NUM
ejpam-6834	1561	32	a′	a′	NOUN
ejpam-6834	1561	33	t.	t.	NOUN
ejpam-6834	1561	34	by	by	ADP
ejpam-6834	1561	35	antitonicity	antitonicity	NOUN
ejpam-6834	1561	36	in	in	ADP
ejpam-6834	1561	37	coordinate	coordinate	NOUN
ejpam-6834	1561	38	t	t	PROPN
ejpam-6834	1561	39	,	,	PUNCT
ejpam-6834	1561	40	f	f	PROPN
ejpam-6834	1561	41	(	(	PUNCT
ejpam-6834	1561	42	a(t−1	a(t−1	X
ejpam-6834	1561	43	)	)	PUNCT
ejpam-6834	1561	44	)	)	PUNCT
ejpam-6834	1562	1	j	j	PROPN
ejpam-6834	1562	2	⊇	⊇	PROPN
ejpam-6834	1562	3	f	f	PROPN
ejpam-6834	1562	4	(	(	PUNCT
ejpam-6834	1562	5	a(t	a(t	PROPN
ejpam-6834	1562	6	)	)	PUNCT
ejpam-6834	1562	7	)	)	PUNCT
ejpam-6834	1563	1	j	j	PROPN
ejpam-6834	1563	2	for	for	ADP
ejpam-6834	1563	3	all	all	DET
ejpam-6834	1563	4	j.	j.	NOUN
ejpam-6834	1563	5	chaining	chain	VERB
ejpam-6834	1563	6	these	these	DET
ejpam-6834	1563	7	inclusions	inclusion	NOUN
ejpam-6834	1563	8	for	for	ADP
ejpam-6834	1563	9	t	t	NOUN
ejpam-6834	1563	10	=	=	SYM
ejpam-6834	1563	11	1	1	NUM
ejpam-6834	1563	12	,	,	PUNCT
ejpam-6834	1563	13	.	.	PUNCT
ejpam-6834	1563	14	.	.	PUNCT
ejpam-6834	1563	15	.	.	PUNCT
ejpam-6834	1564	1	,	,	PUNCT
ejpam-6834	1564	2	h	h	PROPN
ejpam-6834	1564	3	yields	yield	NOUN
ejpam-6834	1564	4	f	f	PROPN
ejpam-6834	1564	5	(	(	PUNCT
ejpam-6834	1564	6	a)j	a)j	PROPN
ejpam-6834	1564	7	=	=	SYM
ejpam-6834	1564	8	f	f	PROPN
ejpam-6834	1564	9	(	(	PUNCT
ejpam-6834	1564	10	a(0))j	a(0))j	X
ejpam-6834	1564	11	⊇	⊇	PROPN
ejpam-6834	1564	12	f	f	PROPN
ejpam-6834	1564	13	(	(	PUNCT
ejpam-6834	1564	14	a(h))j	a(h))j	PROPN
ejpam-6834	1564	15	=	=	SYM
ejpam-6834	1564	16	f	f	X
ejpam-6834	1564	17	(	(	PUNCT
ejpam-6834	1564	18	a′)j	a′)j	NOUN
ejpam-6834	1564	19	for	for	ADP
ejpam-6834	1564	20	all	all	DET
ejpam-6834	1564	21	j	j	NOUN
ejpam-6834	1564	22	,	,	PUNCT
ejpam-6834	1564	23	as	as	SCONJ
ejpam-6834	1564	24	required	require	VERB
ejpam-6834	1564	25	.	.	PUNCT
ejpam-6834	1565	1	4.2	4.2	NUM
ejpam-6834	1565	2	.	.	PUNCT
ejpam-6834	1566	1	(	(	PUNCT
ejpam-6834	1566	2	h	h	NOUN
ejpam-6834	1566	3	,	,	PUNCT
ejpam-6834	1566	4	k)-ary	k)-ary	X
ejpam-6834	1566	5	(	(	PUNCT
ejpam-6834	1566	6	m	m	PROPN
ejpam-6834	1566	7	,	,	PUNCT
ejpam-6834	1566	8	n)-superhyperrough	n)-superhyperrough	PUNCT
ejpam-6834	1566	9	set	set	VERB
ejpam-6834	1566	10	an	an	DET
ejpam-6834	1566	11	(	(	PUNCT
ejpam-6834	1566	12	h	h	NOUN
ejpam-6834	1566	13	,	,	PUNCT
ejpam-6834	1566	14	k)-ary	k)-ary	X
ejpam-6834	1566	15	(	(	PUNCT
ejpam-6834	1566	16	m	m	PROPN
ejpam-6834	1566	17	,	,	PUNCT
ejpam-6834	1566	18	n)-superhyperrough	n)-superhyperrough	PUNCT
ejpam-6834	1566	19	set	set	VERB
ejpam-6834	1566	20	extends	extend	VERB
ejpam-6834	1566	21	classical	classical	ADJ
ejpam-6834	1566	22	rough	rough	ADJ
ejpam-6834	1566	23	sets	set	NOUN
ejpam-6834	1566	24	by	by	ADP
ejpam-6834	1566	25	allowing	allow	VERB
ejpam-6834	1566	26	multiblock	multiblock	NOUN
ejpam-6834	1566	27	,	,	PUNCT
ejpam-6834	1566	28	higher	high	ADJ
ejpam-6834	1566	29	–	–	PUNCT
ejpam-6834	1566	30	order	order	NOUN
ejpam-6834	1566	31	parameterization	parameterization	NOUN
ejpam-6834	1566	32	and	and	CCONJ
ejpam-6834	1566	33	nested	nested	ADJ
ejpam-6834	1566	34	outputs	output	NOUN
ejpam-6834	1566	35	.	.	PUNCT
ejpam-6834	1567	1	concretely	concretely	ADV
ejpam-6834	1567	2	,	,	PUNCT
ejpam-6834	1567	3	we	we	PRON
ejpam-6834	1567	4	collect	collect	VERB
ejpam-6834	1567	5	k	k	PROPN
ejpam-6834	1567	6	input	input	NOUN
ejpam-6834	1567	7	blocks	block	NOUN
ejpam-6834	1567	8	,	,	PUNCT
ejpam-6834	1567	9	each	each	DET
ejpam-6834	1567	10	block	block	NOUN
ejpam-6834	1567	11	being	be	AUX
ejpam-6834	1567	12	an	an	DET
ejpam-6834	1567	13	h	h	NOUN
ejpam-6834	1567	14	-	-	PUNCT
ejpam-6834	1567	15	tuple	tuple	NOUN
ejpam-6834	1567	16	of	of	ADP
ejpam-6834	1567	17	m	m	NOUN
ejpam-6834	1567	18	-	-	PUNCT
ejpam-6834	1567	19	level	level	NOUN
ejpam-6834	1567	20	(	(	PUNCT
ejpam-6834	1567	21	nonempty	nonempty	NOUN
ejpam-6834	1567	22	)	)	PUNCT
ejpam-6834	1567	23	parameter	parameter	NOUN
ejpam-6834	1567	24	subsets	subset	NOUN
ejpam-6834	1567	25	,	,	PUNCT
ejpam-6834	1567	26	and	and	CCONJ
ejpam-6834	1567	27	we	we	PRON
ejpam-6834	1567	28	output	output	VERB
ejpam-6834	1567	29	an	an	DET
ejpam-6834	1567	30	n	n	NOUN
ejpam-6834	1567	31	-	-	PUNCT
ejpam-6834	1567	32	level	level	NOUN
ejpam-6834	1567	33	(	(	PUNCT
ejpam-6834	1567	34	nonempty	nonempty	NOUN
ejpam-6834	1567	35	)	)	PUNCT
ejpam-6834	1567	36	subset	subset	NOUN
ejpam-6834	1567	37	of	of	ADP
ejpam-6834	1567	38	the	the	DET
ejpam-6834	1567	39	universe	universe	NOUN
ejpam-6834	1567	40	.	.	PUNCT
ejpam-6834	1568	1	lower	low	ADJ
ejpam-6834	1568	2	and	and	CCONJ
ejpam-6834	1568	3	upper	upper	ADJ
ejpam-6834	1568	4	approximations	approximation	NOUN
ejpam-6834	1568	5	are	be	AUX
ejpam-6834	1568	6	then	then	ADV
ejpam-6834	1568	7	taken	take	VERB
ejpam-6834	1568	8	on	on	ADP
ejpam-6834	1568	9	the	the	DET
ejpam-6834	1568	10	ground	ground	NOUN
ejpam-6834	1568	11	subset	subset	NOUN
ejpam-6834	1568	12	of	of	ADP
ejpam-6834	1568	13	the	the	DET
ejpam-6834	1568	14	universe	universe	NOUN
ejpam-6834	1568	15	obtained	obtain	VERB
ejpam-6834	1568	16	by	by	ADP
ejpam-6834	1568	17	flattening	flatten	VERB
ejpam-6834	1568	18	the	the	DET
ejpam-6834	1568	19	nested	nested	ADJ
ejpam-6834	1568	20	output	output	NOUN
ejpam-6834	1568	21	.	.	PUNCT
ejpam-6834	1569	1	notation	notation	NOUN
ejpam-6834	1569	2	(	(	PUNCT
ejpam-6834	1569	3	nonempty	nonempty	X
ejpam-6834	1569	4	nested	nested	ADJ
ejpam-6834	1569	5	powerset	powerset	NOUN
ejpam-6834	1569	6	and	and	CCONJ
ejpam-6834	1569	7	flattening	flattening	NOUN
ejpam-6834	1569	8	)	)	PUNCT
ejpam-6834	1569	9	.	.	PUNCT
ejpam-6834	1570	1	for	for	ADP
ejpam-6834	1570	2	a	a	DET
ejpam-6834	1570	3	nonempty	nonempty	ADV
ejpam-6834	1570	4	set	set	VERB
ejpam-6834	1570	5	y	y	PROPN
ejpam-6834	1570	6	and	and	CCONJ
ejpam-6834	1570	7	r	r	PROPN
ejpam-6834	1570	8	∈	∈	PROPN
ejpam-6834	1570	9	n≥1	n≥1	NOUN
ejpam-6834	1570	10	,	,	PUNCT
ejpam-6834	1570	11	define	define	VERB
ejpam-6834	1570	12	recursively	recursively	ADJ
ejpam-6834	1570	13	p̃1(y	p̃1(y	PROPN
ejpam-6834	1570	14	)	)	PUNCT
ejpam-6834	1571	1	:	:	PUNCT
ejpam-6834	1571	2	=	=	X
ejpam-6834	1571	3	{	{	PUNCT
ejpam-6834	1571	4	a	a	PRON
ejpam-6834	1571	5	⊆	⊆	NUM
ejpam-6834	1571	6	y	y	NOUN
ejpam-6834	1571	7	|	|	ADV
ejpam-6834	1571	8	a	a	DET
ejpam-6834	1571	9	̸=	̸=	PROPN
ejpam-6834	1571	10	∅	∅	NOUN
ejpam-6834	1571	11	}	}	PUNCT
ejpam-6834	1571	12	,	,	PUNCT
ejpam-6834	1571	13	p̃r+1(y	p̃r+1(y	ADV
ejpam-6834	1571	14	)	)	PUNCT
ejpam-6834	1571	15	:	:	PUNCT
ejpam-6834	1571	16	=	=	SYM
ejpam-6834	1571	17	{	{	PUNCT
ejpam-6834	1571	18	a	a	PRON
ejpam-6834	1571	19	⊆	⊆	NUM
ejpam-6834	1571	20	p̃r(y	p̃r(y	VERB
ejpam-6834	1571	21	)	)	PUNCT
ejpam-6834	1571	22	|	|	ADV
ejpam-6834	1571	23	a	a	DET
ejpam-6834	1571	24	̸=	̸=	PROPN
ejpam-6834	1571	25	∅	∅	NOUN
ejpam-6834	1571	26	}	}	PUNCT
ejpam-6834	1571	27	.	.	PUNCT
ejpam-6834	1572	1	the	the	DET
ejpam-6834	1572	2	level	level	NOUN
ejpam-6834	1572	3	–	–	PUNCT
ejpam-6834	1572	4	r	r	NOUN
ejpam-6834	1572	5	flattening	flattening	NOUN
ejpam-6834	1572	6	flatr	flatr	NOUN
ejpam-6834	1572	7	:	:	PUNCT
ejpam-6834	1572	8	p̃r(y	p̃r(y	VERB
ejpam-6834	1572	9	)	)	PUNCT
ejpam-6834	1572	10	→	→	SYM
ejpam-6834	1572	11	p(y	p(y	PROPN
ejpam-6834	1572	12	)	)	PUNCT
ejpam-6834	1572	13	is	be	AUX
ejpam-6834	1572	14	defined	define	VERB
ejpam-6834	1572	15	by	by	ADP
ejpam-6834	1572	16	flat1(w	flat1(w	ADP
ejpam-6834	1572	17	)	)	PUNCT
ejpam-6834	1572	18	:	:	PUNCT
ejpam-6834	1573	1	=	=	SYM
ejpam-6834	1573	2	w	w	NOUN
ejpam-6834	1573	3	,	,	PUNCT
ejpam-6834	1573	4	flatr+1(w	flatr+1(w	NOUN
ejpam-6834	1573	5	)	)	PUNCT
ejpam-6834	1573	6	:	:	PUNCT
ejpam-6834	1573	7	=	=	SYM
ejpam-6834	1573	8	⋃	⋃	NOUN
ejpam-6834	1573	9	w∈w	w∈w	VERB
ejpam-6834	1573	10	flatr(w	flatr(w	NOUN
ejpam-6834	1573	11	)	)	PUNCT
ejpam-6834	1573	12	.	.	PUNCT
ejpam-6834	1574	1	thus	thus	ADV
ejpam-6834	1574	2	flatr(w	flatr(w	VERB
ejpam-6834	1574	3	)	)	PUNCT
ejpam-6834	1574	4	⊆	⊆	NUM
ejpam-6834	1574	5	y	y	NOUN
ejpam-6834	1574	6	for	for	ADP
ejpam-6834	1574	7	every	every	DET
ejpam-6834	1574	8	w	w	PROPN
ejpam-6834	1574	9	∈	∈	PROPN
ejpam-6834	1574	10	p̃r(y	p̃r(y	VERB
ejpam-6834	1574	11	)	)	PUNCT
ejpam-6834	1574	12	,	,	PUNCT
ejpam-6834	1574	13	and	and	CCONJ
ejpam-6834	1574	14	flatr(w1	flatr(w1	NOUN
ejpam-6834	1574	15	∪w2	∪w2	NOUN
ejpam-6834	1574	16	)	)	PUNCT
ejpam-6834	1574	17	=	=	SYM
ejpam-6834	1574	18	flatr(w1)∪flatr(w2	flatr(w1)∪flatr(w2	PROPN
ejpam-6834	1574	19	)	)	PUNCT
ejpam-6834	1574	20	.	.	PUNCT
ejpam-6834	1575	1	moreover	moreover	ADV
ejpam-6834	1575	2	,	,	PUNCT
ejpam-6834	1575	3	flatr(w1	flatr(w1	NOUN
ejpam-6834	1575	4	∩w2	∩w2	ADP
ejpam-6834	1575	5	)	)	PUNCT
ejpam-6834	1575	6	⊆	⊆	NUM
ejpam-6834	1575	7	flatr(w1	flatr(w1	NOUN
ejpam-6834	1575	8	)	)	PUNCT
ejpam-6834	1575	9	∩	∩	NOUN
ejpam-6834	1575	10	flatr(w2	flatr(w2	NOUN
ejpam-6834	1575	11	)	)	PUNCT
ejpam-6834	1575	12	.	.	PUNCT
ejpam-6834	1576	1	definition	definition	NOUN
ejpam-6834	1576	2	26	26	NUM
ejpam-6834	1576	3	(	(	PUNCT
ejpam-6834	1576	4	(	(	PUNCT
ejpam-6834	1576	5	h	h	NOUN
ejpam-6834	1576	6	,	,	PUNCT
ejpam-6834	1576	7	k)-ary	k)-ary	X
ejpam-6834	1576	8	(	(	PUNCT
ejpam-6834	1576	9	m	m	PROPN
ejpam-6834	1576	10	,	,	PUNCT
ejpam-6834	1576	11	n)-superhyperrough	n)-superhyperrough	ADV
ejpam-6834	1576	12	set	set	NOUN
ejpam-6834	1576	13	)	)	PUNCT
ejpam-6834	1576	14	.	.	PUNCT
ejpam-6834	1577	1	let	let	VERB
ejpam-6834	1577	2	x	x	PRON
ejpam-6834	1577	3	be	be	AUX
ejpam-6834	1577	4	a	a	DET
ejpam-6834	1577	5	nonempty	nonempty	ADJ
ejpam-6834	1577	6	finite	finite	ADJ
ejpam-6834	1577	7	universe	universe	NOUN
ejpam-6834	1577	8	and	and	CCONJ
ejpam-6834	1577	9	let	let	VERB
ejpam-6834	1577	10	r	r	NOUN
ejpam-6834	1577	11	⊆	⊆	NUM
ejpam-6834	1577	12	x	x	SYM
ejpam-6834	1577	13	×	×	NOUN
ejpam-6834	1577	14	x	x	VERB
ejpam-6834	1577	15	be	be	AUX
ejpam-6834	1577	16	an	an	DET
ejpam-6834	1577	17	equivalence	equivalence	NOUN
ejpam-6834	1577	18	relation	relation	NOUN
ejpam-6834	1577	19	;	;	PUNCT
ejpam-6834	1577	20	write	write	VERB
ejpam-6834	1577	21	[	[	X
ejpam-6834	1577	22	x]r	x]r	NOUN
ejpam-6834	1577	23	for	for	ADP
ejpam-6834	1577	24	the	the	DET
ejpam-6834	1577	25	r	r	NOUN
ejpam-6834	1577	26	-	-	PUNCT
ejpam-6834	1577	27	class	class	NOUN
ejpam-6834	1577	28	of	of	ADP
ejpam-6834	1577	29	x.	x.	NOUN
ejpam-6834	1577	30	let	let	VERB
ejpam-6834	1577	31	j	j	PROPN
ejpam-6834	1577	32	be	be	AUX
ejpam-6834	1577	33	a	a	DET
ejpam-6834	1577	34	nonempty	nonempty	ADJ
ejpam-6834	1577	35	parameter	parameter	NOUN
ejpam-6834	1577	36	space	space	NOUN
ejpam-6834	1577	37	(	(	PUNCT
ejpam-6834	1577	38	e.g.	e.g.	ADV
ejpam-6834	1577	39	a	a	DET
ejpam-6834	1577	40	cartesian	cartesian	ADJ
ejpam-6834	1577	41	product	product	NOUN
ejpam-6834	1577	42	of	of	ADP
ejpam-6834	1577	43	attribute	attribute	NOUN
ejpam-6834	1577	44	sets	set	NOUN
ejpam-6834	1577	45	)	)	PUNCT
ejpam-6834	1577	46	.	.	PUNCT
ejpam-6834	1578	1	fix	fix	VERB
ejpam-6834	1578	2	integers	integer	NOUN
ejpam-6834	1578	3	m	m	PRON
ejpam-6834	1578	4	,	,	PUNCT
ejpam-6834	1578	5	n	n	CCONJ
ejpam-6834	1578	6	,	,	PUNCT
ejpam-6834	1578	7	h	h	NOUN
ejpam-6834	1578	8	,	,	PUNCT
ejpam-6834	1578	9	k	k	PROPN
ejpam-6834	1578	10	≥	≥	NUM
ejpam-6834	1578	11	1	1	NUM
ejpam-6834	1578	12	.	.	PUNCT
ejpam-6834	1578	13	input	input	NOUN
ejpam-6834	1578	14	space	space	NOUN
ejpam-6834	1578	15	.	.	PUNCT
ejpam-6834	1579	1	put	put	VERB
ejpam-6834	1579	2	d	d	NOUN
ejpam-6834	1579	3	:	:	PUNCT
ejpam-6834	1579	4	=	=	SYM
ejpam-6834	1579	5	(	(	PUNCT
ejpam-6834	1579	6	p̃m(j	p̃m(j	NOUN
ejpam-6834	1579	7	)	)	PUNCT
ejpam-6834	1579	8	)	)	PUNCT
ejpam-6834	1580	1	h	h	NOUN
ejpam-6834	1580	2	and	and	CCONJ
ejpam-6834	1580	3	d	d	NOUN
ejpam-6834	1580	4	k	k	NOUN
ejpam-6834	1581	1	:	:	PUNCT
ejpam-6834	1581	2	=	=	SYM
ejpam-6834	1581	3	d	d	SYM
ejpam-6834	1581	4	×	×	PROPN
ejpam-6834	1581	5	·	·	PUNCT
ejpam-6834	1581	6	·	·	PUNCT
ejpam-6834	1581	7	·	·	PUNCT
ejpam-6834	1581	8	×d︸	×d︸	VERB
ejpam-6834	1581	9	︷︷	︷︷	PROPN
ejpam-6834	1581	10	︸	︸	X
ejpam-6834	1582	1	k	k	PROPN
ejpam-6834	1582	2	factors	factor	NOUN
ejpam-6834	1582	3	,	,	PUNCT
ejpam-6834	1582	4	so	so	CCONJ
ejpam-6834	1582	5	an	an	DET
ejpam-6834	1582	6	input	input	NOUN
ejpam-6834	1582	7	to	to	ADP
ejpam-6834	1582	8	our	our	PRON
ejpam-6834	1582	9	map	map	NOUN
ejpam-6834	1582	10	is	be	AUX
ejpam-6834	1582	11	a	a	DET
ejpam-6834	1582	12	k	k	NOUN
ejpam-6834	1582	13	-	-	ADJ
ejpam-6834	1582	14	tuple	tuple	ADJ
ejpam-6834	1582	15	γ	γ	X
ejpam-6834	1582	16	=	=	SYM
ejpam-6834	1582	17	(	(	PUNCT
ejpam-6834	1582	18	γ1	γ1	PROPN
ejpam-6834	1582	19	,	,	PUNCT
ejpam-6834	1582	20	.	.	PUNCT
ejpam-6834	1582	21	.	.	PUNCT
ejpam-6834	1583	1	.	.	PUNCT
ejpam-6834	1584	1	,	,	PUNCT
ejpam-6834	1584	2	γk	γk	PROPN
ejpam-6834	1584	3	)	)	PUNCT
ejpam-6834	1584	4	,	,	PUNCT
ejpam-6834	1584	5	each	each	DET
ejpam-6834	1584	6	γℓ	γℓ	NOUN
ejpam-6834	1584	7	=	=	SYM
ejpam-6834	1584	8	(	(	PUNCT
ejpam-6834	1584	9	aℓ,1	aℓ,1	PROPN
ejpam-6834	1584	10	,	,	PUNCT
ejpam-6834	1584	11	.	.	PUNCT
ejpam-6834	1584	12	.	.	PUNCT
ejpam-6834	1584	13	.	.	PUNCT
ejpam-6834	1585	1	,	,	PUNCT
ejpam-6834	1585	2	aℓ,h	aℓ,h	NOUN
ejpam-6834	1585	3	)	)	PUNCT
ejpam-6834	1585	4	∈	∈	PROPN
ejpam-6834	1585	5	d	d	X
ejpam-6834	1585	6	t.	t.	PROPN
ejpam-6834	1585	7	fujita	fujita	PROPN
ejpam-6834	1585	8	,	,	PUNCT
ejpam-6834	1585	9	f.smarandache	f.smarandache	NOUN
ejpam-6834	1585	10	/	/	SYM
ejpam-6834	1585	11	eur	eur	PROPN
ejpam-6834	1585	12	.	.	PUNCT
ejpam-6834	1586	1	j.	j.	PROPN
ejpam-6834	1586	2	pure	pure	PROPN
ejpam-6834	1586	3	appl	appl	PROPN
ejpam-6834	1586	4	.	.	PROPN
ejpam-6834	1586	5	math	math	PROPN
ejpam-6834	1586	6	,	,	PUNCT
ejpam-6834	1586	7	18	18	NUM
ejpam-6834	1586	8	(	(	PUNCT
ejpam-6834	1586	9	4	4	NUM
ejpam-6834	1586	10	)	)	PUNCT
ejpam-6834	1586	11	(	(	PUNCT
ejpam-6834	1586	12	2025	2025	NUM
ejpam-6834	1586	13	)	)	PUNCT
ejpam-6834	1586	14	,	,	PUNCT
ejpam-6834	1586	15	6834	6834	NUM
ejpam-6834	1586	16	58	58	NUM
ejpam-6834	1586	17	of	of	ADP
ejpam-6834	1586	18	69	69	NUM
ejpam-6834	1586	19	with	with	ADP
ejpam-6834	1586	20	aℓ,i	aℓ,i	PUNCT
ejpam-6834	1586	21	∈	∈	PROPN
ejpam-6834	1586	22	p̃m(j	p̃m(j	NUM
ejpam-6834	1586	23	)	)	PUNCT
ejpam-6834	1586	24	.	.	PUNCT
ejpam-6834	1587	1	output	output	NOUN
ejpam-6834	1587	2	space	space	NOUN
ejpam-6834	1587	3	.	.	PUNCT
ejpam-6834	1588	1	put	put	VERB
ejpam-6834	1588	2	c	c	NOUN
ejpam-6834	1589	1	:	:	PUNCT
ejpam-6834	1589	2	=	=	SYM
ejpam-6834	1589	3	p̃n(x	p̃n(x	X
ejpam-6834	1589	4	)	)	PUNCT
ejpam-6834	1589	5	.	.	PUNCT
ejpam-6834	1590	1	its	its	PRON
ejpam-6834	1590	2	elements	element	NOUN
ejpam-6834	1590	3	are	be	AUX
ejpam-6834	1590	4	nonempty	nonempty	ADJ
ejpam-6834	1590	5	level	level	NOUN
ejpam-6834	1590	6	–	–	PUNCT
ejpam-6834	1590	7	n	n	CCONJ
ejpam-6834	1590	8	families	family	NOUN
ejpam-6834	1590	9	of	of	ADP
ejpam-6834	1590	10	subsets	subset	NOUN
ejpam-6834	1590	11	of	of	ADP
ejpam-6834	1590	12	x.	x.	PROPN
ejpam-6834	1590	13	an	an	DET
ejpam-6834	1590	14	(	(	PUNCT
ejpam-6834	1590	15	h	h	NOUN
ejpam-6834	1590	16	,	,	PUNCT
ejpam-6834	1590	17	k)-ary	k)-ary	X
ejpam-6834	1590	18	(	(	PUNCT
ejpam-6834	1590	19	m	m	PROPN
ejpam-6834	1590	20	,	,	PUNCT
ejpam-6834	1590	21	n)-superhyperrough	n)-superhyperrough	PUNCT
ejpam-6834	1590	22	set	set	VERB
ejpam-6834	1590	23	is	be	AUX
ejpam-6834	1590	24	a	a	DET
ejpam-6834	1590	25	function	function	NOUN
ejpam-6834	1591	1	f	f	NOUN
ejpam-6834	1591	2	:	:	PUNCT
ejpam-6834	1592	1	d	d	X
ejpam-6834	1592	2	k	k	X
ejpam-6834	1592	3	−→	−→	PROPN
ejpam-6834	1592	4	c	c	X
ejpam-6834	1592	5	,	,	PUNCT
ejpam-6834	1592	6	γ	γ	PROPN
ejpam-6834	1592	7	7−→	7−→	PROPN
ejpam-6834	1592	8	w	w	ADP
ejpam-6834	1592	9	:	:	PUNCT
ejpam-6834	1592	10	=	=	SYM
ejpam-6834	1592	11	f	f	X
ejpam-6834	1592	12	(	(	PUNCT
ejpam-6834	1592	13	γ	γ	PROPN
ejpam-6834	1592	14	)	)	PUNCT
ejpam-6834	1592	15	.	.	PUNCT
ejpam-6834	1593	1	the	the	DET
ejpam-6834	1593	2	rough	rough	ADJ
ejpam-6834	1593	3	lower	low	ADJ
ejpam-6834	1593	4	and	and	CCONJ
ejpam-6834	1593	5	upper	upper	ADJ
ejpam-6834	1593	6	approximations	approximation	NOUN
ejpam-6834	1593	7	of	of	ADP
ejpam-6834	1593	8	w	w	PROPN
ejpam-6834	1593	9	(	(	PUNCT
ejpam-6834	1593	10	relative	relative	ADJ
ejpam-6834	1593	11	to	to	ADP
ejpam-6834	1593	12	r	r	NOUN
ejpam-6834	1593	13	)	)	PUNCT
ejpam-6834	1593	14	are	be	AUX
ejpam-6834	1593	15	defined	define	VERB
ejpam-6834	1593	16	on	on	ADP
ejpam-6834	1593	17	the	the	DET
ejpam-6834	1593	18	ground	ground	NOUN
ejpam-6834	1593	19	subset	subset	VERB
ejpam-6834	1593	20	flatn(w	flatn(w	ADV
ejpam-6834	1593	21	)	)	PUNCT
ejpam-6834	1594	1	⊆	⊆	NUM
ejpam-6834	1594	2	x	x	SYM
ejpam-6834	1594	3	by	by	ADP
ejpam-6834	1594	4	w	w	NOUN
ejpam-6834	1594	5	:	:	PUNCT
ejpam-6834	1594	6	=	=	SYM
ejpam-6834	1594	7	{	{	PUNCT
ejpam-6834	1594	8	x	x	SYM
ejpam-6834	1594	9	∈	∈	PROPN
ejpam-6834	1594	10	x	x	PUNCT
ejpam-6834	1595	1	|	|	NOUN
ejpam-6834	1595	2	[	[	X
ejpam-6834	1595	3	x]r	x]r	X
ejpam-6834	1595	4	⊆	⊆	NUM
ejpam-6834	1595	5	flatn(w	flatn(w	NOUN
ejpam-6834	1595	6	)	)	PUNCT
ejpam-6834	1595	7	}	}	PUNCT
ejpam-6834	1595	8	,	,	PUNCT
ejpam-6834	1595	9	w	w	X
ejpam-6834	1595	10	:	:	PUNCT
ejpam-6834	1595	11	=	=	SYM
ejpam-6834	1595	12	{	{	PUNCT
ejpam-6834	1595	13	x	x	SYM
ejpam-6834	1595	14	∈	∈	PROPN
ejpam-6834	1595	15	x	x	PUNCT
ejpam-6834	1596	1	|	|	NOUN
ejpam-6834	1597	1	[	[	X
ejpam-6834	1597	2	x]r	x]r	NOUN
ejpam-6834	1597	3	∩	∩	ADJ
ejpam-6834	1597	4	flatn(w	flatn(w	NOUN
ejpam-6834	1597	5	)	)	PUNCT
ejpam-6834	1597	6	̸=	̸=	PROPN
ejpam-6834	1597	7	∅	∅	NOUN
ejpam-6834	1597	8	}	}	PUNCT
ejpam-6834	1597	9	.	.	PUNCT
ejpam-6834	1598	1	when	when	SCONJ
ejpam-6834	1598	2	n	n	X
ejpam-6834	1598	3	=	=	SYM
ejpam-6834	1598	4	1	1	NUM
ejpam-6834	1598	5	,	,	PUNCT
ejpam-6834	1598	6	flat1(w	flat1(w	PUNCT
ejpam-6834	1598	7	)	)	PUNCT
ejpam-6834	1599	1	=	=	SYM
ejpam-6834	1599	2	w	w	NOUN
ejpam-6834	1599	3	and	and	CCONJ
ejpam-6834	1599	4	these	these	PRON
ejpam-6834	1599	5	are	be	AUX
ejpam-6834	1599	6	the	the	DET
ejpam-6834	1599	7	classical	classical	ADJ
ejpam-6834	1599	8	rough	rough	ADJ
ejpam-6834	1599	9	approximations	approximation	NOUN
ejpam-6834	1599	10	of	of	ADP
ejpam-6834	1599	11	w	w	PROPN
ejpam-6834	1599	12	⊆	⊆	PROPN
ejpam-6834	1599	13	x.	x.	NOUN
ejpam-6834	1599	14	example	example	NOUN
ejpam-6834	1599	15	33	33	NUM
ejpam-6834	1599	16	(	(	PUNCT
ejpam-6834	1599	17	2	2	NUM
ejpam-6834	1599	18	-	-	NUM
ejpam-6834	1599	19	ary	ary	NOUN
ejpam-6834	1599	20	(	(	PUNCT
ejpam-6834	1599	21	1	1	NUM
ejpam-6834	1599	22	,	,	PUNCT
ejpam-6834	1599	23	1	1	NUM
ejpam-6834	1599	24	)	)	PUNCT
ejpam-6834	1599	25	superhyperrough	superhyperrough	NOUN
ejpam-6834	1599	26	set	set	NOUN
ejpam-6834	1599	27	)	)	PUNCT
ejpam-6834	1599	28	.	.	PUNCT
ejpam-6834	1600	1	let	let	VERB
ejpam-6834	1600	2	x	x	PUNCT
ejpam-6834	1600	3	=	=	PRON
ejpam-6834	1600	4	{	{	PUNCT
ejpam-6834	1600	5	u1	u1	NOUN
ejpam-6834	1600	6	,	,	PUNCT
ejpam-6834	1600	7	u2	u2	NOUN
ejpam-6834	1600	8	,	,	PUNCT
ejpam-6834	1600	9	u3	u3	NOUN
ejpam-6834	1600	10	,	,	PUNCT
ejpam-6834	1600	11	u4	u4	PROPN
ejpam-6834	1600	12	}	}	PUNCT
ejpam-6834	1600	13	with	with	ADP
ejpam-6834	1600	14	r	r	NOUN
ejpam-6834	1600	15	-	-	PUNCT
ejpam-6834	1600	16	classes	class	NOUN
ejpam-6834	1601	1	[	[	X
ejpam-6834	1601	2	u1]r	u1]r	X
ejpam-6834	1601	3	=	=	PUNCT
ejpam-6834	1602	1	[	[	X
ejpam-6834	1602	2	u2]r	u2]r	X
ejpam-6834	1602	3	=	=	PUNCT
ejpam-6834	1602	4	{	{	PUNCT
ejpam-6834	1602	5	u1	u1	NOUN
ejpam-6834	1602	6	,	,	PUNCT
ejpam-6834	1602	7	u2	u2	NOUN
ejpam-6834	1602	8	}	}	PUNCT
ejpam-6834	1602	9	and	and	CCONJ
ejpam-6834	1602	10	[	[	X
ejpam-6834	1602	11	u3]r	u3]r	X
ejpam-6834	1602	12	=	=	SYM
ejpam-6834	1603	1	[	[	X
ejpam-6834	1603	2	u4]r	u4]r	X
ejpam-6834	1603	3	=	=	SYM
ejpam-6834	1603	4	{	{	PUNCT
ejpam-6834	1603	5	u3	u3	PROPN
ejpam-6834	1603	6	,	,	PUNCT
ejpam-6834	1603	7	u4	u4	PROPN
ejpam-6834	1603	8	}	}	PUNCT
ejpam-6834	1603	9	.	.	PUNCT
ejpam-6834	1604	1	choose	choose	VERB
ejpam-6834	1604	2	m	m	PROPN
ejpam-6834	1604	3	=	=	SYM
ejpam-6834	1604	4	n	n	PROPN
ejpam-6834	1604	5	=	=	NOUN
ejpam-6834	1604	6	h	h	NOUN
ejpam-6834	1604	7	=	=	SYM
ejpam-6834	1604	8	1	1	NUM
ejpam-6834	1604	9	and	and	CCONJ
ejpam-6834	1604	10	k	k	NOUN
ejpam-6834	1604	11	=	=	NOUN
ejpam-6834	1604	12	2	2	X
ejpam-6834	1604	13	.	.	X
ejpam-6834	1604	14	take	take	VERB
ejpam-6834	1604	15	any	any	DET
ejpam-6834	1604	16	nonempty	nonempty	ADJ
ejpam-6834	1604	17	parameter	parameter	NOUN
ejpam-6834	1604	18	set	set	VERB
ejpam-6834	1604	19	j	j	PROPN
ejpam-6834	1604	20	(	(	PUNCT
ejpam-6834	1604	21	its	its	PRON
ejpam-6834	1604	22	internal	internal	ADJ
ejpam-6834	1604	23	structure	structure	NOUN
ejpam-6834	1604	24	is	be	AUX
ejpam-6834	1604	25	irrelevant	irrelevant	ADJ
ejpam-6834	1604	26	here	here	ADV
ejpam-6834	1604	27	)	)	PUNCT
ejpam-6834	1604	28	,	,	PUNCT
ejpam-6834	1604	29	so	so	CCONJ
ejpam-6834	1604	30	d	d	NOUN
ejpam-6834	1604	31	=	=	PUNCT
ejpam-6834	1604	32	p̃1(j	p̃1(j	NOUN
ejpam-6834	1604	33	)	)	PUNCT
ejpam-6834	1605	1	∼=	∼=	PROPN
ejpam-6834	1605	2	j	j	NOUN
ejpam-6834	1605	3	,	,	PUNCT
ejpam-6834	1605	4	hence	hence	ADV
ejpam-6834	1605	5	d2	d2	VERB
ejpam-6834	1605	6	∼=	∼=	PROPN
ejpam-6834	1605	7	j	j	PROPN
ejpam-6834	1605	8	×	×	PROPN
ejpam-6834	1605	9	j	j	PROPN
ejpam-6834	1605	10	,	,	PUNCT
ejpam-6834	1605	11	and	and	CCONJ
ejpam-6834	1605	12	c	c	NOUN
ejpam-6834	1605	13	=	=	SYM
ejpam-6834	1605	14	p̃1(x	p̃1(x	NOUN
ejpam-6834	1605	15	)	)	PUNCT
ejpam-6834	1605	16	=	=	SYM
ejpam-6834	1605	17	p+(x	p+(x	PROPN
ejpam-6834	1605	18	)	)	PUNCT
ejpam-6834	1605	19	.	.	PUNCT
ejpam-6834	1606	1	define	define	VERB
ejpam-6834	1606	2	f	f	X
ejpam-6834	1606	3	:	:	PUNCT
ejpam-6834	1606	4	j	j	PROPN
ejpam-6834	1606	5	×	×	PROPN
ejpam-6834	1606	6	j	j	PROPN
ejpam-6834	1606	7	→	→	SYM
ejpam-6834	1606	8	p+(x	p+(x	PROPN
ejpam-6834	1606	9	)	)	PUNCT
ejpam-6834	1606	10	by	by	ADP
ejpam-6834	1606	11	f	f	PROPN
ejpam-6834	1606	12	(	(	PUNCT
ejpam-6834	1606	13	a	a	DET
ejpam-6834	1606	14	,	,	PUNCT
ejpam-6834	1606	15	b	b	NOUN
ejpam-6834	1606	16	)	)	PUNCT
ejpam-6834	1606	17	:	:	PUNCT
ejpam-6834	1607	1	=	=	SYM
ejpam-6834	1607	2	{	{	PUNCT
ejpam-6834	1607	3	u1	u1	NOUN
ejpam-6834	1607	4	,	,	PUNCT
ejpam-6834	1607	5	u2	u2	NOUN
ejpam-6834	1607	6	,	,	PUNCT
ejpam-6834	1607	7	u3	u3	NOUN
ejpam-6834	1607	8	}	}	PUNCT
ejpam-6834	1607	9	(	(	PUNCT
ejpam-6834	1607	10	for	for	ADP
ejpam-6834	1607	11	all	all	PRON
ejpam-6834	1607	12	(	(	PUNCT
ejpam-6834	1607	13	a	a	DET
ejpam-6834	1607	14	,	,	PUNCT
ejpam-6834	1607	15	b	b	NOUN
ejpam-6834	1607	16	)	)	PUNCT
ejpam-6834	1607	17	)	)	PUNCT
ejpam-6834	1607	18	.	.	PUNCT
ejpam-6834	1608	1	then	then	ADV
ejpam-6834	1608	2	w	w	X
ejpam-6834	1608	3	=	=	SYM
ejpam-6834	1608	4	f	f	PROPN
ejpam-6834	1608	5	(	(	PUNCT
ejpam-6834	1608	6	a	a	DET
ejpam-6834	1608	7	,	,	PUNCT
ejpam-6834	1608	8	b	b	NOUN
ejpam-6834	1608	9	)	)	PUNCT
ejpam-6834	1608	10	has	have	VERB
ejpam-6834	1608	11	approximations	approximation	NOUN
ejpam-6834	1608	12	w	w	NOUN
ejpam-6834	1608	13	=	=	SYM
ejpam-6834	1608	14	{	{	PUNCT
ejpam-6834	1608	15	u1	u1	NOUN
ejpam-6834	1608	16	,	,	PUNCT
ejpam-6834	1608	17	u2	u2	PROPN
ejpam-6834	1608	18	}	}	PUNCT
ejpam-6834	1608	19	,	,	PUNCT
ejpam-6834	1608	20	w	w	NOUN
ejpam-6834	1608	21	=	=	SYM
ejpam-6834	1608	22	{	{	PUNCT
ejpam-6834	1608	23	u1	u1	NOUN
ejpam-6834	1608	24	,	,	PUNCT
ejpam-6834	1608	25	u2	u2	NOUN
ejpam-6834	1608	26	,	,	PUNCT
ejpam-6834	1608	27	u3	u3	NOUN
ejpam-6834	1608	28	,	,	PUNCT
ejpam-6834	1608	29	u4	u4	PROPN
ejpam-6834	1608	30	}	}	PUNCT
ejpam-6834	1608	31	.	.	PUNCT
ejpam-6834	1609	1	thus	thus	ADV
ejpam-6834	1609	2	f	f	PROPN
ejpam-6834	1609	3	is	be	AUX
ejpam-6834	1609	4	a	a	DET
ejpam-6834	1609	5	concrete	concrete	ADJ
ejpam-6834	1609	6	2	2	NUM
ejpam-6834	1609	7	-	-	NUM
ejpam-6834	1609	8	ary	ary	NOUN
ejpam-6834	1609	9	(	(	PUNCT
ejpam-6834	1609	10	1	1	NUM
ejpam-6834	1609	11	,	,	PUNCT
ejpam-6834	1609	12	1)-superhyperrough	1)-superhyperrough	NUM
ejpam-6834	1609	13	set	set	NOUN
ejpam-6834	1609	14	.	.	PUNCT
ejpam-6834	1610	1	example	example	NOUN
ejpam-6834	1610	2	34	34	NUM
ejpam-6834	1610	3	(	(	PUNCT
ejpam-6834	1610	4	medical	medical	ADJ
ejpam-6834	1610	5	diagnosis	diagnosis	NOUN
ejpam-6834	1610	6	as	as	ADP
ejpam-6834	1610	7	a	a	DET
ejpam-6834	1610	8	2	2	NUM
ejpam-6834	1610	9	-	-	PUNCT
ejpam-6834	1610	10	ary	ary	NOUN
ejpam-6834	1610	11	(	(	PUNCT
ejpam-6834	1610	12	2	2	NUM
ejpam-6834	1610	13	,	,	PUNCT
ejpam-6834	1610	14	2)-superhyperrough	2)-superhyperrough	NOUN
ejpam-6834	1610	15	set	set	NOUN
ejpam-6834	1610	16	)	)	PUNCT
ejpam-6834	1610	17	.	.	PUNCT
ejpam-6834	1611	1	let	let	VERB
ejpam-6834	1611	2	x	x	PUNCT
ejpam-6834	1611	3	=	=	PRON
ejpam-6834	1611	4	{	{	PUNCT
ejpam-6834	1611	5	p1,p2,p3,p4	p1,p2,p3,p4	NOUN
ejpam-6834	1611	6	}	}	PUNCT
ejpam-6834	1611	7	and	and	CCONJ
ejpam-6834	1611	8	let	let	VERB
ejpam-6834	1611	9	r	r	NOUN
ejpam-6834	1611	10	group	group	NOUN
ejpam-6834	1611	11	patients	patient	NOUN
ejpam-6834	1611	12	by	by	ADP
ejpam-6834	1611	13	age	age	NOUN
ejpam-6834	1611	14	:	:	PUNCT
ejpam-6834	1612	1	[	[	X
ejpam-6834	1612	2	p1]r	p1]r	X
ejpam-6834	1612	3	=	=	SYM
ejpam-6834	1613	1	[	[	X
ejpam-6834	1613	2	p2]r	p2]r	X
ejpam-6834	1613	3	,	,	PUNCT
ejpam-6834	1613	4	[	[	X
ejpam-6834	1613	5	p3]r	p3]r	X
ejpam-6834	1613	6	=	=	SYM
ejpam-6834	1613	7	[	[	X
ejpam-6834	1613	8	p4]r	p4]r	X
ejpam-6834	1613	9	.	.	PUNCT
ejpam-6834	1614	1	let	let	VERB
ejpam-6834	1614	2	j	j	PROPN
ejpam-6834	1614	3	=	=	PUNCT
ejpam-6834	1614	4	{	{	PUNCT
ejpam-6834	1614	5	fever	fever	NOUN
ejpam-6834	1614	6	,	,	PUNCT
ejpam-6834	1614	7	cough	cough	NOUN
ejpam-6834	1614	8	}	}	PUNCT
ejpam-6834	1614	9	×	×	NOUN
ejpam-6834	1614	10	{	{	PUNCT
ejpam-6834	1614	11	pain	pain	NOUN
ejpam-6834	1614	12	,	,	PUNCT
ejpam-6834	1614	13	nausea	nausea	NOUN
ejpam-6834	1614	14	}	}	PUNCT
ejpam-6834	1614	15	t.	t.	PROPN
ejpam-6834	1614	16	fujita	fujita	PROPN
ejpam-6834	1614	17	,	,	PUNCT
ejpam-6834	1614	18	f.smarandache	f.smarandache	NOUN
ejpam-6834	1614	19	/	/	SYM
ejpam-6834	1614	20	eur	eur	PROPN
ejpam-6834	1614	21	.	.	PUNCT
ejpam-6834	1615	1	j.	j.	PROPN
ejpam-6834	1615	2	pure	pure	PROPN
ejpam-6834	1615	3	appl	appl	PROPN
ejpam-6834	1615	4	.	.	PROPN
ejpam-6834	1615	5	math	math	PROPN
ejpam-6834	1615	6	,	,	PUNCT
ejpam-6834	1615	7	18	18	NUM
ejpam-6834	1615	8	(	(	PUNCT
ejpam-6834	1615	9	4	4	NUM
ejpam-6834	1615	10	)	)	PUNCT
ejpam-6834	1615	11	(	(	PUNCT
ejpam-6834	1615	12	2025	2025	NUM
ejpam-6834	1615	13	)	)	PUNCT
ejpam-6834	1615	14	,	,	PUNCT
ejpam-6834	1615	15	6834	6834	NUM
ejpam-6834	1615	16	59	59	NUM
ejpam-6834	1615	17	of	of	ADP
ejpam-6834	1615	18	69	69	NUM
ejpam-6834	1615	19	.	.	PUNCT
ejpam-6834	1616	1	take	take	VERB
ejpam-6834	1616	2	m	m	NOUN
ejpam-6834	1616	3	=	=	SYM
ejpam-6834	1616	4	2	2	NUM
ejpam-6834	1616	5	,	,	PUNCT
ejpam-6834	1616	6	n	n	NOUN
ejpam-6834	1616	7	=	=	SYM
ejpam-6834	1616	8	1	1	NUM
ejpam-6834	1616	9	,	,	PUNCT
ejpam-6834	1616	10	h	h	NOUN
ejpam-6834	1616	11	=	=	SYM
ejpam-6834	1616	12	2	2	NUM
ejpam-6834	1616	13	,	,	PUNCT
ejpam-6834	1616	14	k	k	NOUN
ejpam-6834	1617	1	=	=	SYM
ejpam-6834	1617	2	2	2	X
ejpam-6834	1617	3	.	.	PUNCT
ejpam-6834	1618	1	then	then	ADV
ejpam-6834	1618	2	d	d	PROPN
ejpam-6834	1618	3	=	=	SYM
ejpam-6834	1618	4	(	(	PUNCT
ejpam-6834	1618	5	p̃2(j	p̃2(j	PROPN
ejpam-6834	1618	6	)	)	PUNCT
ejpam-6834	1618	7	)	)	PUNCT
ejpam-6834	1618	8	2	2	NUM
ejpam-6834	1618	9	,	,	PUNCT
ejpam-6834	1618	10	c	c	NOUN
ejpam-6834	1618	11	=	=	SYM
ejpam-6834	1618	12	p̃1(x	p̃1(x	NOUN
ejpam-6834	1618	13	)	)	PUNCT
ejpam-6834	1618	14	=	=	SYM
ejpam-6834	1618	15	p+(x	p+(x	PROPN
ejpam-6834	1618	16	)	)	PUNCT
ejpam-6834	1618	17	.	.	PUNCT
ejpam-6834	1619	1	choose	choose	VERB
ejpam-6834	1619	2	γ1	γ1	PROPN
ejpam-6834	1619	3	=	=	PRON
ejpam-6834	1619	4	{	{	PUNCT
ejpam-6834	1619	5	{	{	PUNCT
ejpam-6834	1619	6	(	(	PUNCT
ejpam-6834	1619	7	fever	fever	NOUN
ejpam-6834	1619	8	,	,	PUNCT
ejpam-6834	1619	9	pain	pain	NOUN
ejpam-6834	1619	10	)	)	PUNCT
ejpam-6834	1619	11	}	}	PUNCT
ejpam-6834	1619	12	,	,	PUNCT
ejpam-6834	1619	13	{	{	PUNCT
ejpam-6834	1619	14	(	(	PUNCT
ejpam-6834	1619	15	cough	cough	NOUN
ejpam-6834	1619	16	,	,	PUNCT
ejpam-6834	1619	17	nausea	nausea	NOUN
ejpam-6834	1619	18	)	)	PUNCT
ejpam-6834	1619	19	}	}	PUNCT
ejpam-6834	1619	20	}	}	PUNCT
ejpam-6834	1619	21	,	,	PUNCT
ejpam-6834	1619	22	γ2	γ2	PROPN
ejpam-6834	1619	23	=	=	SYM
ejpam-6834	1619	24	{	{	PUNCT
ejpam-6834	1619	25	{	{	PUNCT
ejpam-6834	1619	26	(	(	PUNCT
ejpam-6834	1619	27	fever	fever	NOUN
ejpam-6834	1619	28	,	,	PUNCT
ejpam-6834	1619	29	nausea	nausea	NOUN
ejpam-6834	1619	30	)	)	PUNCT
ejpam-6834	1619	31	}	}	PUNCT
ejpam-6834	1619	32	}	}	PUNCT
ejpam-6834	1619	33	.	.	PUNCT
ejpam-6834	1620	1	define	define	VERB
ejpam-6834	1620	2	f	f	PROPN
ejpam-6834	1620	3	(	(	PUNCT
ejpam-6834	1620	4	γ1	γ1	PROPN
ejpam-6834	1620	5	,	,	PUNCT
ejpam-6834	1620	6	γ2	γ2	PROPN
ejpam-6834	1620	7	)	)	PUNCT
ejpam-6834	1620	8	:	:	PUNCT
ejpam-6834	1621	1	=	=	SYM
ejpam-6834	1621	2	{	{	PUNCT
ejpam-6834	1621	3	p1,p2,p3	p1,p2,p3	PROPN
ejpam-6834	1621	4	}	}	PUNCT
ejpam-6834	1621	5	.	.	PUNCT
ejpam-6834	1622	1	then	then	ADV
ejpam-6834	1622	2	(	(	PUNCT
ejpam-6834	1622	3	with	with	ADP
ejpam-6834	1622	4	n	n	NOUN
ejpam-6834	1622	5	=	=	SYM
ejpam-6834	1622	6	1	1	NUM
ejpam-6834	1622	7	)	)	PUNCT
ejpam-6834	1622	8	the	the	DET
ejpam-6834	1622	9	approximations	approximation	NOUN
ejpam-6834	1622	10	are	be	AUX
ejpam-6834	1622	11	w	w	NOUN
ejpam-6834	1622	12	=	=	X
ejpam-6834	1622	13	{	{	PUNCT
ejpam-6834	1622	14	p1,p2	p1,p2	PROPN
ejpam-6834	1622	15	}	}	PUNCT
ejpam-6834	1622	16	,	,	PUNCT
ejpam-6834	1622	17	w	w	X
ejpam-6834	1622	18	=	=	SYM
ejpam-6834	1622	19	{	{	PUNCT
ejpam-6834	1622	20	p1,p2,p3,p4	p1,p2,p3,p4	PROPN
ejpam-6834	1622	21	}	}	PUNCT
ejpam-6834	1622	22	.	.	PUNCT
ejpam-6834	1623	1	hence	hence	ADV
ejpam-6834	1623	2	f	f	PROPN
ejpam-6834	1623	3	models	model	VERB
ejpam-6834	1623	4	a	a	DET
ejpam-6834	1623	5	two	two	NUM
ejpam-6834	1623	6	–	–	PUNCT
ejpam-6834	1623	7	block	block	NOUN
ejpam-6834	1623	8	,	,	PUNCT
ejpam-6834	1623	9	hierarchical	hierarchical	ADJ
ejpam-6834	1623	10	symptom	symptom	NOUN
ejpam-6834	1623	11	selection	selection	NOUN
ejpam-6834	1623	12	yielding	yield	VERB
ejpam-6834	1623	13	a	a	DET
ejpam-6834	1623	14	rough	rough	ADJ
ejpam-6834	1623	15	decision	decision	NOUN
ejpam-6834	1623	16	set	set	NOUN
ejpam-6834	1623	17	.	.	PUNCT
ejpam-6834	1624	1	example	example	NOUN
ejpam-6834	1624	2	35	35	NUM
ejpam-6834	1624	3	(	(	PUNCT
ejpam-6834	1624	4	household	household	NOUN
ejpam-6834	1624	5	contact	contact	NOUN
ejpam-6834	1624	6	tracing	trace	VERB
ejpam-6834	1624	7	as	as	ADP
ejpam-6834	1624	8	a	a	DET
ejpam-6834	1624	9	(	(	PUNCT
ejpam-6834	1624	10	2	2	NUM
ejpam-6834	1624	11	,	,	PUNCT
ejpam-6834	1624	12	2)-ary	2)-ary	NUM
ejpam-6834	1624	13	(	(	PUNCT
ejpam-6834	1624	14	2	2	NUM
ejpam-6834	1624	15	,	,	PUNCT
ejpam-6834	1624	16	1)-superhyperrough	1)-superhyperrough	NUM
ejpam-6834	1624	17	set	set	NOUN
ejpam-6834	1624	18	)	)	PUNCT
ejpam-6834	1624	19	.	.	PUNCT
ejpam-6834	1625	1	universe	universe	NOUN
ejpam-6834	1625	2	and	and	CCONJ
ejpam-6834	1625	3	indiscernibility	indiscernibility	NOUN
ejpam-6834	1625	4	.	.	PUNCT
ejpam-6834	1626	1	let	let	VERB
ejpam-6834	1626	2	the	the	DET
ejpam-6834	1626	3	finite	finite	ADJ
ejpam-6834	1626	4	universe	universe	NOUN
ejpam-6834	1626	5	x	x	VERB
ejpam-6834	1626	6	be	be	VERB
ejpam-6834	1626	7	six	six	NUM
ejpam-6834	1626	8	residents	resident	NOUN
ejpam-6834	1626	9	labeled	label	VERB
ejpam-6834	1626	10	x	x	X
ejpam-6834	1626	11	=	=	X
ejpam-6834	1626	12	{	{	PUNCT
ejpam-6834	1626	13	a	a	DET
ejpam-6834	1626	14	,	,	PUNCT
ejpam-6834	1626	15	b	b	NOUN
ejpam-6834	1626	16	,	,	PUNCT
ejpam-6834	1626	17	c	c	NOUN
ejpam-6834	1626	18	,	,	PUNCT
ejpam-6834	1626	19	d	d	NOUN
ejpam-6834	1626	20	,	,	PUNCT
ejpam-6834	1626	21	e	e	NOUN
ejpam-6834	1626	22	,	,	PUNCT
ejpam-6834	1626	23	f	f	NOUN
ejpam-6834	1626	24	}	}	PUNCT
ejpam-6834	1626	25	.	.	PUNCT
ejpam-6834	1627	1	let	let	VERB
ejpam-6834	1627	2	r	r	NOUN
ejpam-6834	1627	3	⊆	⊆	NUM
ejpam-6834	1627	4	x	x	X
ejpam-6834	1627	5	×x	×x	X
ejpam-6834	1627	6	encode	encode	VERB
ejpam-6834	1627	7	the	the	DET
ejpam-6834	1627	8	household	household	NOUN
ejpam-6834	1627	9	equivalence	equivalence	NOUN
ejpam-6834	1627	10	:	:	PUNCT
ejpam-6834	1628	1	[	[	X
ejpam-6834	1628	2	a]r	a]r	NOUN
ejpam-6834	1628	3	=	=	PUNCT
ejpam-6834	1629	1	[	[	X
ejpam-6834	1629	2	b]r	b]r	NOUN
ejpam-6834	1629	3	=	=	SYM
ejpam-6834	1629	4	{	{	PUNCT
ejpam-6834	1629	5	a	a	DET
ejpam-6834	1629	6	,	,	PUNCT
ejpam-6834	1629	7	b	b	NOUN
ejpam-6834	1629	8	}	}	PUNCT
ejpam-6834	1629	9	,	,	PUNCT
ejpam-6834	1630	1	[	[	X
ejpam-6834	1630	2	c]r	c]r	NOUN
ejpam-6834	1630	3	=	=	PUNCT
ejpam-6834	1631	1	[	[	X
ejpam-6834	1631	2	d]r	d]r	X
ejpam-6834	1631	3	=	=	X
ejpam-6834	1631	4	{	{	PUNCT
ejpam-6834	1631	5	c	c	NOUN
ejpam-6834	1631	6	,	,	PUNCT
ejpam-6834	1631	7	d	d	NOUN
ejpam-6834	1631	8	}	}	PUNCT
ejpam-6834	1631	9	,	,	PUNCT
ejpam-6834	1631	10	[	[	X
ejpam-6834	1631	11	e]r	e]r	NOUN
ejpam-6834	1631	12	=	=	PUNCT
ejpam-6834	1632	1	[	[	X
ejpam-6834	1632	2	f	f	X
ejpam-6834	1632	3	]	]	X
ejpam-6834	1632	4	r	r	NOUN
ejpam-6834	1632	5	=	=	SYM
ejpam-6834	1632	6	{	{	PUNCT
ejpam-6834	1632	7	e	e	NOUN
ejpam-6834	1632	8	,	,	PUNCT
ejpam-6834	1632	9	f	f	NOUN
ejpam-6834	1632	10	}	}	PUNCT
ejpam-6834	1632	11	.	.	PUNCT
ejpam-6834	1633	1	parameter	parameter	NOUN
ejpam-6834	1633	2	space	space	NOUN
ejpam-6834	1633	3	and	and	CCONJ
ejpam-6834	1633	4	hyperparameters	hyperparameter	NOUN
ejpam-6834	1633	5	.	.	PUNCT
ejpam-6834	1634	1	consider	consider	VERB
ejpam-6834	1634	2	the	the	DET
ejpam-6834	1634	3	attribute	attribute	NOUN
ejpam-6834	1634	4	space	space	NOUN
ejpam-6834	1634	5	j	j	PROPN
ejpam-6834	1634	6	=	=	SYM
ejpam-6834	1634	7	ssymp×sexpo	ssymp×sexpo	PROPN
ejpam-6834	1634	8	,	,	PUNCT
ejpam-6834	1634	9	ssymp	ssymp	NOUN
ejpam-6834	1634	10	=	=	SYM
ejpam-6834	1634	11	{	{	PUNCT
ejpam-6834	1634	12	fever	fever	NOUN
ejpam-6834	1634	13	,	,	PUNCT
ejpam-6834	1634	14	cough	cough	NOUN
ejpam-6834	1634	15	,	,	PUNCT
ejpam-6834	1634	16	asympt	asympt	NOUN
ejpam-6834	1634	17	.	.	PUNCT
ejpam-6834	1634	18	}	}	PUNCT
ejpam-6834	1634	19	,	,	PUNCT
ejpam-6834	1634	20	sexpo	sexpo	NOUN
ejpam-6834	1634	21	=	=	PUNCT
ejpam-6834	1634	22	{	{	PUNCT
ejpam-6834	1634	23	close	close	ADJ
ejpam-6834	1634	24	,	,	PUNCT
ejpam-6834	1634	25	casual	casual	ADJ
ejpam-6834	1634	26	,	,	PUNCT
ejpam-6834	1634	27	travel	travel	NOUN
ejpam-6834	1634	28	}	}	PUNCT
ejpam-6834	1634	29	.	.	PUNCT
ejpam-6834	1635	1	fix	fix	NOUN
ejpam-6834	1635	2	(	(	PUNCT
ejpam-6834	1635	3	m	m	PROPN
ejpam-6834	1635	4	,	,	PUNCT
ejpam-6834	1635	5	n	n	CCONJ
ejpam-6834	1635	6	,	,	PUNCT
ejpam-6834	1635	7	h	h	NOUN
ejpam-6834	1635	8	,	,	PUNCT
ejpam-6834	1635	9	k	k	NOUN
ejpam-6834	1635	10	)	)	PUNCT
ejpam-6834	1635	11	=	=	SYM
ejpam-6834	1635	12	(	(	PUNCT
ejpam-6834	1635	13	2	2	NUM
ejpam-6834	1635	14	,	,	PUNCT
ejpam-6834	1635	15	1	1	NUM
ejpam-6834	1635	16	,	,	PUNCT
ejpam-6834	1635	17	2	2	NUM
ejpam-6834	1635	18	,	,	PUNCT
ejpam-6834	1635	19	2	2	NUM
ejpam-6834	1635	20	)	)	PUNCT
ejpam-6834	1635	21	.	.	PUNCT
ejpam-6834	1636	1	then	then	ADV
ejpam-6834	1636	2	p̃1(j	p̃1(j	NOUN
ejpam-6834	1636	3	)	)	PUNCT
ejpam-6834	1636	4	=	=	PRON
ejpam-6834	1636	5	{	{	PUNCT
ejpam-6834	1636	6	u	u	NOUN
ejpam-6834	1636	7	⊆	⊆	NUM
ejpam-6834	1636	8	j	j	PROPN
ejpam-6834	1636	9	|	|	CCONJ
ejpam-6834	1636	10	u	u	NOUN
ejpam-6834	1636	11	̸=	̸=	PROPN
ejpam-6834	1636	12	∅	∅	NOUN
ejpam-6834	1636	13	}	}	PUNCT
ejpam-6834	1636	14	,	,	PUNCT
ejpam-6834	1636	15	p̃2(j	p̃2(j	PROPN
ejpam-6834	1636	16	)	)	PUNCT
ejpam-6834	1636	17	=	=	SYM
ejpam-6834	1636	18	{	{	PUNCT
ejpam-6834	1636	19	γ	γ	PROPN
ejpam-6834	1636	20	⊆	⊆	NUM
ejpam-6834	1636	21	p̃1(j	p̃1(j	NOUN
ejpam-6834	1636	22	)	)	PUNCT
ejpam-6834	1636	23	|	|	ADV
ejpam-6834	1636	24	γ	γ	PROPN
ejpam-6834	1636	25	̸=	̸=	PROPN
ejpam-6834	1636	26	∅	∅	NOUN
ejpam-6834	1636	27	}	}	PUNCT
ejpam-6834	1636	28	.	.	PUNCT
ejpam-6834	1637	1	the	the	DET
ejpam-6834	1637	2	input	input	NOUN
ejpam-6834	1637	3	space	space	NOUN
ejpam-6834	1637	4	is	be	AUX
ejpam-6834	1637	5	d	d	NOUN
ejpam-6834	1637	6	=	=	PUNCT
ejpam-6834	1637	7	(	(	PUNCT
ejpam-6834	1637	8	p̃2(j))2	p̃2(j))2	NOUN
ejpam-6834	1637	9	(	(	PUNCT
ejpam-6834	1637	10	two	two	NUM
ejpam-6834	1637	11	coordinates	coordinate	NOUN
ejpam-6834	1637	12	)	)	PUNCT
ejpam-6834	1637	13	,	,	PUNCT
ejpam-6834	1637	14	and	and	CCONJ
ejpam-6834	1637	15	an	an	DET
ejpam-6834	1637	16	input	input	NOUN
ejpam-6834	1637	17	to	to	ADP
ejpam-6834	1637	18	f	f	PROPN
ejpam-6834	1637	19	is	be	AUX
ejpam-6834	1637	20	a	a	DET
ejpam-6834	1637	21	pair	pair	NOUN
ejpam-6834	1637	22	γ	γ	X
ejpam-6834	1637	23	=	=	SYM
ejpam-6834	1637	24	(	(	PUNCT
ejpam-6834	1637	25	γ1	γ1	PROPN
ejpam-6834	1637	26	,	,	PUNCT
ejpam-6834	1637	27	γ2	γ2	ADJ
ejpam-6834	1637	28	)	)	PUNCT
ejpam-6834	1637	29	∈	∈	PROPN
ejpam-6834	1637	30	d2	d2	PROPN
ejpam-6834	1637	31	with	with	ADP
ejpam-6834	1637	32	γℓ	γℓ	PROPN
ejpam-6834	1637	33	=	=	SYM
ejpam-6834	1637	34	(	(	PUNCT
ejpam-6834	1637	35	aℓ,1	aℓ,1	PROPN
ejpam-6834	1637	36	,	,	PUNCT
ejpam-6834	1637	37	aℓ,2	aℓ,2	PROPN
ejpam-6834	1637	38	)	)	PUNCT
ejpam-6834	1637	39	,	,	PUNCT
ejpam-6834	1637	40	aℓ,i	aℓ,i	PUNCT
ejpam-6834	1637	41	∈	∈	PROPN
ejpam-6834	1637	42	p̃2(j	p̃2(j	PROPN
ejpam-6834	1637	43	)	)	PUNCT
ejpam-6834	1637	44	.	.	PUNCT
ejpam-6834	1638	1	the	the	DET
ejpam-6834	1638	2	output	output	NOUN
ejpam-6834	1638	3	space	space	NOUN
ejpam-6834	1638	4	is	be	AUX
ejpam-6834	1638	5	c	c	NOUN
ejpam-6834	1638	6	=	=	SYM
ejpam-6834	1638	7	p̃1(x	p̃1(x	NOUN
ejpam-6834	1638	8	)	)	PUNCT
ejpam-6834	1639	1	=	=	PRON
ejpam-6834	1639	2	{	{	PUNCT
ejpam-6834	1639	3	w	w	NOUN
ejpam-6834	1639	4	⊆	⊆	NUM
ejpam-6834	1639	5	x	x	SYM
ejpam-6834	1639	6	|	|	ADV
ejpam-6834	1639	7	w	w	PROPN
ejpam-6834	1639	8	̸=	̸=	PROPN
ejpam-6834	1639	9	∅	∅	NOUN
ejpam-6834	1639	10	}	}	PUNCT
ejpam-6834	1639	11	.	.	PUNCT
ejpam-6834	1640	1	interpret	interpret	VERB
ejpam-6834	1640	2	the	the	DET
ejpam-6834	1640	3	two	two	NUM
ejpam-6834	1640	4	coordinates	coordinate	NOUN
ejpam-6834	1640	5	in	in	ADP
ejpam-6834	1640	6	each	each	DET
ejpam-6834	1640	7	γℓ	γℓ	NOUN
ejpam-6834	1640	8	as	as	ADP
ejpam-6834	1640	9	:	:	PUNCT
ejpam-6834	1640	10	•	•	NUM
ejpam-6834	1640	11	coordinate	coordinate	NOUN
ejpam-6834	1640	12	1	1	NUM
ejpam-6834	1640	13	:	:	PUNCT
ejpam-6834	1640	14	a	a	DET
ejpam-6834	1640	15	cluster	cluster	NOUN
ejpam-6834	1640	16	of	of	ADP
ejpam-6834	1640	17	symptom	symptom	NOUN
ejpam-6834	1640	18	patterns	pattern	NOUN
ejpam-6834	1640	19	,	,	PUNCT
ejpam-6834	1640	20	•	•	NUM
ejpam-6834	1640	21	coordinate	coordinate	NOUN
ejpam-6834	1640	22	2	2	NUM
ejpam-6834	1640	23	:	:	PUNCT
ejpam-6834	1640	24	a	a	DET
ejpam-6834	1640	25	cluster	cluster	NOUN
ejpam-6834	1640	26	of	of	ADP
ejpam-6834	1640	27	exposure	exposure	NOUN
ejpam-6834	1640	28	contexts	contexts	NOUN
ejpam-6834	1640	29	.	.	PUNCT
ejpam-6834	1641	1	choose	choose	VERB
ejpam-6834	1641	2	the	the	DET
ejpam-6834	1641	3	concrete	concrete	ADJ
ejpam-6834	1641	4	hyperparameters	hyperparameter	NOUN
ejpam-6834	1641	5	a1,1	a1,1	NOUN
ejpam-6834	1642	1	=	=	SYM
ejpam-6834	1642	2	{	{	PUNCT
ejpam-6834	1642	3	{	{	PUNCT
ejpam-6834	1642	4	(	(	PUNCT
ejpam-6834	1642	5	fever	fever	NOUN
ejpam-6834	1642	6	,	,	PUNCT
ejpam-6834	1642	7	close	close	ADJ
ejpam-6834	1642	8	)	)	PUNCT
ejpam-6834	1642	9	}	}	PUNCT
ejpam-6834	1642	10	,	,	PUNCT
ejpam-6834	1642	11	{	{	PUNCT
ejpam-6834	1642	12	(	(	PUNCT
ejpam-6834	1642	13	cough	cough	NOUN
ejpam-6834	1642	14	,	,	PUNCT
ejpam-6834	1642	15	close	close	ADJ
ejpam-6834	1642	16	)	)	PUNCT
ejpam-6834	1642	17	}	}	PUNCT
ejpam-6834	1642	18	}	}	PUNCT
ejpam-6834	1642	19	,	,	PUNCT
ejpam-6834	1643	1	a1,2	a1,2	PROPN
ejpam-6834	1643	2	=	=	PRON
ejpam-6834	1643	3	{	{	PUNCT
ejpam-6834	1643	4	{	{	PUNCT
ejpam-6834	1643	5	(	(	PUNCT
ejpam-6834	1643	6	asympt	asympt	NOUN
ejpam-6834	1643	7	.	.	PUNCT
ejpam-6834	1643	8	,close	,close	PUNCT
ejpam-6834	1643	9	)	)	PUNCT
ejpam-6834	1643	10	}	}	PUNCT
ejpam-6834	1643	11	}	}	PUNCT
ejpam-6834	1643	12	,	,	PUNCT
ejpam-6834	1643	13	a2,1	a2,1	PROPN
ejpam-6834	1643	14	=	=	PUNCT
ejpam-6834	1643	15	{	{	PUNCT
ejpam-6834	1643	16	{	{	PUNCT
ejpam-6834	1643	17	(	(	PUNCT
ejpam-6834	1643	18	fever	fever	NOUN
ejpam-6834	1643	19	,	,	PUNCT
ejpam-6834	1643	20	travel	travel	NOUN
ejpam-6834	1643	21	)	)	PUNCT
ejpam-6834	1643	22	}	}	PUNCT
ejpam-6834	1643	23	}	}	PUNCT
ejpam-6834	1643	24	,	,	PUNCT
ejpam-6834	1643	25	a2,2	a2,2	PROPN
ejpam-6834	1643	26	=	=	PUNCT
ejpam-6834	1643	27	{	{	PUNCT
ejpam-6834	1643	28	{	{	PUNCT
ejpam-6834	1643	29	(	(	PUNCT
ejpam-6834	1643	30	cough	cough	NOUN
ejpam-6834	1643	31	,	,	PUNCT
ejpam-6834	1643	32	casual	casual	NOUN
ejpam-6834	1643	33	)	)	PUNCT
ejpam-6834	1643	34	}	}	PUNCT
ejpam-6834	1643	35	,	,	PUNCT
ejpam-6834	1643	36	{	{	PUNCT
ejpam-6834	1643	37	(	(	PUNCT
ejpam-6834	1643	38	asympt	asympt	NOUN
ejpam-6834	1643	39	.	.	PUNCT
ejpam-6834	1643	40	,travel	,travel	PUNCT
ejpam-6834	1643	41	)	)	PUNCT
ejpam-6834	1643	42	}	}	PUNCT
ejpam-6834	1643	43	}	}	PUNCT
ejpam-6834	1643	44	.	.	PUNCT
ejpam-6834	1644	1	thus	thus	ADV
ejpam-6834	1644	2	γ1	γ1	PROPN
ejpam-6834	1644	3	=	=	SYM
ejpam-6834	1644	4	(	(	PUNCT
ejpam-6834	1644	5	a1,1	a1,1	NOUN
ejpam-6834	1644	6	,	,	PUNCT
ejpam-6834	1644	7	a1,2	a1,2	NOUN
ejpam-6834	1644	8	)	)	PUNCT
ejpam-6834	1644	9	captures	capture	VERB
ejpam-6834	1644	10	high	high	ADJ
ejpam-6834	1644	11	-	-	PUNCT
ejpam-6834	1644	12	risk	risk	NOUN
ejpam-6834	1644	13	local	local	ADJ
ejpam-6834	1644	14	symptoms	symptom	NOUN
ejpam-6834	1644	15	/	/	SYM
ejpam-6834	1644	16	close	close	ADJ
ejpam-6834	1644	17	contacts	contact	NOUN
ejpam-6834	1644	18	,	,	PUNCT
ejpam-6834	1644	19	while	while	SCONJ
ejpam-6834	1644	20	γ2	γ2	ADJ
ejpam-6834	1644	21	=	=	SYM
ejpam-6834	1644	22	(	(	PUNCT
ejpam-6834	1644	23	a2,1	a2,1	NOUN
ejpam-6834	1644	24	,	,	PUNCT
ejpam-6834	1644	25	a2,2	a2,2	PROPN
ejpam-6834	1644	26	)	)	PUNCT
ejpam-6834	1644	27	captures	capture	VERB
ejpam-6834	1644	28	travel	travel	VERB
ejpam-6834	1644	29	–	–	PUNCT
ejpam-6834	1644	30	related	related	ADJ
ejpam-6834	1644	31	or	or	CCONJ
ejpam-6834	1644	32	casual	casual	ADJ
ejpam-6834	1644	33	exposures	exposure	NOUN
ejpam-6834	1644	34	.	.	PUNCT
ejpam-6834	1645	1	t.	t.	PROPN
ejpam-6834	1645	2	fujita	fujita	PROPN
ejpam-6834	1645	3	,	,	PUNCT
ejpam-6834	1645	4	f.smarandache	f.smarandache	NOUN
ejpam-6834	1645	5	/	/	SYM
ejpam-6834	1645	6	eur	eur	PROPN
ejpam-6834	1645	7	.	.	PUNCT
ejpam-6834	1646	1	j.	j.	PROPN
ejpam-6834	1646	2	pure	pure	PROPN
ejpam-6834	1646	3	appl	appl	PROPN
ejpam-6834	1646	4	.	.	PROPN
ejpam-6834	1646	5	math	math	PROPN
ejpam-6834	1646	6	,	,	PUNCT
ejpam-6834	1646	7	18	18	NUM
ejpam-6834	1646	8	(	(	PUNCT
ejpam-6834	1646	9	4	4	NUM
ejpam-6834	1646	10	)	)	PUNCT
ejpam-6834	1646	11	(	(	PUNCT
ejpam-6834	1646	12	2025	2025	NUM
ejpam-6834	1646	13	)	)	PUNCT
ejpam-6834	1646	14	,	,	PUNCT
ejpam-6834	1646	15	6834	6834	NUM
ejpam-6834	1646	16	60	60	NUM
ejpam-6834	1646	17	of	of	ADP
ejpam-6834	1646	18	69	69	NUM
ejpam-6834	1646	19	superhyperrough	superhyperrough	ADJ
ejpam-6834	1646	20	mapping	mapping	NOUN
ejpam-6834	1646	21	.	.	PUNCT
ejpam-6834	1647	1	define	define	VERB
ejpam-6834	1647	2	f	f	PROPN
ejpam-6834	1647	3	:	:	PUNCT
ejpam-6834	1647	4	d2	d2	VERB
ejpam-6834	1647	5	−→	−→	NOUN
ejpam-6834	1647	6	c	c	NOUN
ejpam-6834	1647	7	=	=	SYM
ejpam-6834	1647	8	p̃1(x	p̃1(x	NOUN
ejpam-6834	1647	9	)	)	PUNCT
ejpam-6834	1647	10	,	,	PUNCT
ejpam-6834	1647	11	(	(	PUNCT
ejpam-6834	1647	12	γ1	γ1	NOUN
ejpam-6834	1647	13	,	,	PUNCT
ejpam-6834	1647	14	γ2	γ2	ADJ
ejpam-6834	1647	15	)	)	PUNCT
ejpam-6834	1647	16	7−→	7−→	PROPN
ejpam-6834	1647	17	w	w	NOUN
ejpam-6834	1647	18	,	,	PUNCT
ejpam-6834	1647	19	and	and	CCONJ
ejpam-6834	1647	20	,	,	PUNCT
ejpam-6834	1647	21	for	for	ADP
ejpam-6834	1647	22	the	the	DET
ejpam-6834	1647	23	above	above	ADJ
ejpam-6834	1647	24	input	input	NOUN
ejpam-6834	1647	25	,	,	PUNCT
ejpam-6834	1647	26	set	set	VERB
ejpam-6834	1647	27	(	(	PUNCT
ejpam-6834	1647	28	one	one	NUM
ejpam-6834	1647	29	valid	valid	ADJ
ejpam-6834	1647	30	epidemiological	epidemiological	ADJ
ejpam-6834	1647	31	decision	decision	NOUN
ejpam-6834	1647	32	rule	rule	NOUN
ejpam-6834	1647	33	)	)	PUNCT
ejpam-6834	1647	34	w	w	NOUN
ejpam-6834	1648	1	=	=	PUNCT
ejpam-6834	1648	2	{	{	PUNCT
ejpam-6834	1648	3	a	a	PRON
ejpam-6834	1648	4	,	,	PUNCT
ejpam-6834	1648	5	b	b	NOUN
ejpam-6834	1648	6	,	,	PUNCT
ejpam-6834	1648	7	d	d	NOUN
ejpam-6834	1648	8	}	}	PUNCT
ejpam-6834	1648	9	.	.	PUNCT
ejpam-6834	1649	1	intuitively	intuitively	ADV
ejpam-6834	1649	2	,	,	PUNCT
ejpam-6834	1649	3	{	{	PUNCT
ejpam-6834	1649	4	a	a	DET
ejpam-6834	1649	5	,	,	PUNCT
ejpam-6834	1649	6	b	b	NOUN
ejpam-6834	1649	7	}	}	PUNCT
ejpam-6834	1649	8	are	be	AUX
ejpam-6834	1649	9	flagged	flag	VERB
ejpam-6834	1649	10	due	due	ADP
ejpam-6834	1649	11	to	to	PART
ejpam-6834	1649	12	close	close	VERB
ejpam-6834	1649	13	symptomatic	symptomatic	ADJ
ejpam-6834	1649	14	contact	contact	NOUN
ejpam-6834	1649	15	(	(	PUNCT
ejpam-6834	1649	16	household	household	NOUN
ejpam-6834	1649	17	cluster	cluster	NOUN
ejpam-6834	1649	18	)	)	PUNCT
ejpam-6834	1649	19	,	,	PUNCT
ejpam-6834	1649	20	and	and	CCONJ
ejpam-6834	1649	21	d	d	NOUN
ejpam-6834	1649	22	is	be	AUX
ejpam-6834	1649	23	flagged	flag	VERB
ejpam-6834	1649	24	due	due	ADP
ejpam-6834	1649	25	to	to	ADP
ejpam-6834	1649	26	a	a	DET
ejpam-6834	1649	27	travel	travel	NOUN
ejpam-6834	1649	28	–	–	PUNCT
ejpam-6834	1649	29	symptom	symptom	NOUN
ejpam-6834	1649	30	combination	combination	NOUN
ejpam-6834	1649	31	matching	match	VERB
ejpam-6834	1649	32	a2,1	a2,1	NOUN
ejpam-6834	1649	33	.	.	PUNCT
ejpam-6834	1650	1	rough	rough	ADJ
ejpam-6834	1650	2	approximations	approximation	NOUN
ejpam-6834	1650	3	(	(	PUNCT
ejpam-6834	1650	4	with	with	ADP
ejpam-6834	1650	5	n	n	NOUN
ejpam-6834	1650	6	=	=	SYM
ejpam-6834	1650	7	1	1	NUM
ejpam-6834	1650	8	)	)	PUNCT
ejpam-6834	1650	9	.	.	PUNCT
ejpam-6834	1651	1	since	since	SCONJ
ejpam-6834	1651	2	n	n	NOUN
ejpam-6834	1651	3	=	=	SYM
ejpam-6834	1651	4	1	1	NUM
ejpam-6834	1651	5	,	,	PUNCT
ejpam-6834	1651	6	flat1(w	flat1(w	PUNCT
ejpam-6834	1651	7	)	)	PUNCT
ejpam-6834	1651	8	=	=	PUNCT
ejpam-6834	1652	1	w	w	X
ejpam-6834	1652	2	.	.	PUNCT
ejpam-6834	1653	1	the	the	DET
ejpam-6834	1653	2	lower	low	ADJ
ejpam-6834	1653	3	and	and	CCONJ
ejpam-6834	1653	4	upper	upper	ADJ
ejpam-6834	1653	5	rough	rough	ADJ
ejpam-6834	1653	6	approximations	approximation	NOUN
ejpam-6834	1653	7	of	of	ADP
ejpam-6834	1653	8	w	w	PROPN
ejpam-6834	1653	9	(	(	PUNCT
ejpam-6834	1653	10	relative	relative	ADJ
ejpam-6834	1653	11	to	to	ADP
ejpam-6834	1653	12	r	r	NOUN
ejpam-6834	1653	13	)	)	PUNCT
ejpam-6834	1653	14	are	be	AUX
ejpam-6834	1653	15	w	w	NOUN
ejpam-6834	1653	16	=	=	PRON
ejpam-6834	1653	17	{	{	PUNCT
ejpam-6834	1653	18	x	x	PUNCT
ejpam-6834	1653	19	∈	∈	PROPN
ejpam-6834	1653	20	x	x	PUNCT
ejpam-6834	1654	1	|	|	NOUN
ejpam-6834	1655	1	[	[	X
ejpam-6834	1655	2	x]r	x]r	X
ejpam-6834	1655	3	⊆	⊆	NUM
ejpam-6834	1655	4	w	w	NOUN
ejpam-6834	1655	5	}	}	PUNCT
ejpam-6834	1655	6	,	,	PUNCT
ejpam-6834	1655	7	w	w	X
ejpam-6834	1655	8	=	=	PRON
ejpam-6834	1655	9	{	{	PUNCT
ejpam-6834	1655	10	x	x	PUNCT
ejpam-6834	1655	11	∈	∈	PROPN
ejpam-6834	1655	12	x	x	PUNCT
ejpam-6834	1655	13	|	|	NOUN
ejpam-6834	1656	1	[	[	X
ejpam-6834	1656	2	x]r	x]r	NOUN
ejpam-6834	1656	3	∩w	∩w	ADJ
ejpam-6834	1656	4	̸=	̸=	NOUN
ejpam-6834	1656	5	∅	∅	NOUN
ejpam-6834	1656	6	}	}	PUNCT
ejpam-6834	1656	7	.	.	PUNCT
ejpam-6834	1657	1	compute	compute	NOUN
ejpam-6834	1657	2	using	use	VERB
ejpam-6834	1657	3	the	the	DET
ejpam-6834	1657	4	three	three	NUM
ejpam-6834	1657	5	households	household	NOUN
ejpam-6834	1657	6	:	:	PUNCT
ejpam-6834	1658	1	[	[	X
ejpam-6834	1658	2	a]r	a]r	NOUN
ejpam-6834	1658	3	=	=	PUNCT
ejpam-6834	1659	1	[	[	X
ejpam-6834	1659	2	b]r	b]r	NOUN
ejpam-6834	1659	3	=	=	SYM
ejpam-6834	1659	4	{	{	PUNCT
ejpam-6834	1659	5	a	a	PRON
ejpam-6834	1659	6	,	,	PUNCT
ejpam-6834	1659	7	b	b	NOUN
ejpam-6834	1659	8	}	}	PUNCT
ejpam-6834	1659	9	⊆	⊆	NUM
ejpam-6834	1659	10	w	w	NOUN
ejpam-6834	1659	11	=	=	VERB
ejpam-6834	1659	12	⇒	⇒	NOUN
ejpam-6834	1659	13	{	{	PUNCT
ejpam-6834	1659	14	a	a	PRON
ejpam-6834	1659	15	,	,	PUNCT
ejpam-6834	1659	16	b	b	NOUN
ejpam-6834	1659	17	}	}	PUNCT
ejpam-6834	1659	18	⊆	⊆	NUM
ejpam-6834	1659	19	w	w	NOUN
ejpam-6834	1659	20	,	,	PUNCT
ejpam-6834	1659	21	[	[	X
ejpam-6834	1659	22	c]r	c]r	NOUN
ejpam-6834	1659	23	=	=	PUNCT
ejpam-6834	1660	1	[	[	X
ejpam-6834	1660	2	d]r	d]r	X
ejpam-6834	1660	3	=	=	X
ejpam-6834	1660	4	{	{	PUNCT
ejpam-6834	1660	5	c	c	NOUN
ejpam-6834	1660	6	,	,	PUNCT
ejpam-6834	1660	7	d	d	NOUN
ejpam-6834	1660	8	}	}	PUNCT
ejpam-6834	1660	9	̸⊆	̸⊆	NOUN
ejpam-6834	1660	10	w	w	NOUN
ejpam-6834	1660	11	but	but	CCONJ
ejpam-6834	1660	12	{	{	PUNCT
ejpam-6834	1660	13	c	c	X
ejpam-6834	1660	14	,	,	PUNCT
ejpam-6834	1660	15	d	d	NOUN
ejpam-6834	1660	16	}	}	PUNCT
ejpam-6834	1660	17	∩w	∩w	NOUN
ejpam-6834	1660	18	=	=	PUNCT
ejpam-6834	1660	19	{	{	PUNCT
ejpam-6834	1660	20	d	d	NOUN
ejpam-6834	1660	21	}	}	PUNCT
ejpam-6834	1660	22	̸=	̸=	PROPN
ejpam-6834	1660	23	∅	∅	NOUN
ejpam-6834	1660	24	,	,	PUNCT
ejpam-6834	1661	1	[	[	X
ejpam-6834	1661	2	e]r	e]r	NOUN
ejpam-6834	1661	3	=	=	PUNCT
ejpam-6834	1662	1	[	[	X
ejpam-6834	1662	2	f	f	X
ejpam-6834	1662	3	]	]	X
ejpam-6834	1662	4	r	r	NOUN
ejpam-6834	1662	5	=	=	SYM
ejpam-6834	1662	6	{	{	PUNCT
ejpam-6834	1662	7	e	e	NOUN
ejpam-6834	1662	8	,	,	PUNCT
ejpam-6834	1662	9	f	f	NOUN
ejpam-6834	1662	10	}	}	PUNCT
ejpam-6834	1662	11	̸⊆	̸⊆	PROPN
ejpam-6834	1662	12	w	w	PROPN
ejpam-6834	1662	13	and	and	CCONJ
ejpam-6834	1662	14	{	{	PUNCT
ejpam-6834	1662	15	e	e	NOUN
ejpam-6834	1662	16	,	,	PUNCT
ejpam-6834	1662	17	f	f	NOUN
ejpam-6834	1662	18	}	}	PUNCT
ejpam-6834	1662	19	∩w	∩w	NOUN
ejpam-6834	1662	20	=	=	PUNCT
ejpam-6834	1662	21	∅.	∅.	VERB
ejpam-6834	1662	22	hence	hence	ADV
ejpam-6834	1662	23	w	w	NOUN
ejpam-6834	1662	24	=	=	X
ejpam-6834	1662	25	{	{	PUNCT
ejpam-6834	1662	26	a	a	DET
ejpam-6834	1662	27	,	,	PUNCT
ejpam-6834	1662	28	b	b	NOUN
ejpam-6834	1662	29	}	}	PUNCT
ejpam-6834	1662	30	,	,	PUNCT
ejpam-6834	1662	31	w	w	NOUN
ejpam-6834	1662	32	=	=	X
ejpam-6834	1662	33	{	{	PUNCT
ejpam-6834	1662	34	a	a	PRON
ejpam-6834	1662	35	,	,	PUNCT
ejpam-6834	1662	36	b	b	NOUN
ejpam-6834	1662	37	,	,	PUNCT
ejpam-6834	1662	38	c	c	X
ejpam-6834	1662	39	,	,	PUNCT
ejpam-6834	1662	40	d	d	NOUN
ejpam-6834	1662	41	}	}	PUNCT
ejpam-6834	1662	42	.	.	PUNCT
ejpam-6834	1663	1	interpretation	interpretation	NOUN
ejpam-6834	1663	2	.	.	PUNCT
ejpam-6834	1664	1	the	the	DET
ejpam-6834	1664	2	lower	low	ADJ
ejpam-6834	1664	3	approximation	approximation	NOUN
ejpam-6834	1664	4	w	w	NOUN
ejpam-6834	1664	5	contains	contain	VERB
ejpam-6834	1664	6	residents	resident	NOUN
ejpam-6834	1664	7	whose	whose	DET
ejpam-6834	1664	8	entire	entire	ADJ
ejpam-6834	1664	9	household	household	NOUN
ejpam-6834	1664	10	is	be	AUX
ejpam-6834	1664	11	flagged	flag	VERB
ejpam-6834	1664	12	(	(	PUNCT
ejpam-6834	1664	13	{	{	PUNCT
ejpam-6834	1664	14	a	a	DET
ejpam-6834	1664	15	,	,	PUNCT
ejpam-6834	1664	16	b	b	NOUN
ejpam-6834	1664	17	}	}	PUNCT
ejpam-6834	1664	18	)	)	PUNCT
ejpam-6834	1664	19	;	;	PUNCT
ejpam-6834	1664	20	they	they	PRON
ejpam-6834	1664	21	are	be	AUX
ejpam-6834	1664	22	quarantined	quarantine	VERB
ejpam-6834	1664	23	with	with	ADP
ejpam-6834	1664	24	certainty	certainty	NOUN
ejpam-6834	1664	25	under	under	ADP
ejpam-6834	1664	26	the	the	DET
ejpam-6834	1664	27	household	household	NOUN
ejpam-6834	1664	28	–	–	PUNCT
ejpam-6834	1664	29	indiscernibility	indiscernibility	NOUN
ejpam-6834	1664	30	r.	r.	VERB
ejpam-6834	1664	31	the	the	DET
ejpam-6834	1664	32	upper	upper	ADJ
ejpam-6834	1664	33	approximation	approximation	NOUN
ejpam-6834	1664	34	w	w	NOUN
ejpam-6834	1664	35	additionally	additionally	ADV
ejpam-6834	1664	36	includes	include	VERB
ejpam-6834	1664	37	residents	resident	NOUN
ejpam-6834	1664	38	whose	whose	DET
ejpam-6834	1664	39	household	household	NOUN
ejpam-6834	1664	40	has	have	VERB
ejpam-6834	1664	41	some	some	DET
ejpam-6834	1664	42	flagged	flag	VERB
ejpam-6834	1664	43	member	member	NOUN
ejpam-6834	1664	44	(	(	PUNCT
ejpam-6834	1664	45	c	c	PROPN
ejpam-6834	1664	46	is	be	AUX
ejpam-6834	1664	47	included	include	VERB
ejpam-6834	1664	48	because	because	SCONJ
ejpam-6834	1664	49	d	d	NOUN
ejpam-6834	1664	50	is	be	AUX
ejpam-6834	1664	51	in	in	ADP
ejpam-6834	1664	52	w	w	PROPN
ejpam-6834	1664	53	)	)	PUNCT
ejpam-6834	1664	54	.	.	PUNCT
ejpam-6834	1665	1	this	this	DET
ejpam-6834	1665	2	example	example	NOUN
ejpam-6834	1665	3	realizes	realize	VERB
ejpam-6834	1665	4	a	a	DET
ejpam-6834	1665	5	real	real	ADJ
ejpam-6834	1665	6	–	–	PUNCT
ejpam-6834	1665	7	world	world	NOUN
ejpam-6834	1665	8	(	(	PUNCT
ejpam-6834	1665	9	2	2	NUM
ejpam-6834	1665	10	,	,	PUNCT
ejpam-6834	1665	11	2)-ary	2)-ary	NUM
ejpam-6834	1665	12	(	(	PUNCT
ejpam-6834	1665	13	2	2	NUM
ejpam-6834	1665	14	,	,	PUNCT
ejpam-6834	1665	15	1)-superhyperrough	1)-superhyperrough	NUM
ejpam-6834	1665	16	set	set	NOUN
ejpam-6834	1665	17	:	:	PUNCT
ejpam-6834	1665	18	multi	multi	ADJ
ejpam-6834	1665	19	–	–	PUNCT
ejpam-6834	1665	20	level	level	ADJ
ejpam-6834	1665	21	,	,	PUNCT
ejpam-6834	1665	22	clustered	clustered	ADJ
ejpam-6834	1665	23	parameters	parameter	NOUN
ejpam-6834	1665	24	(	(	PUNCT
ejpam-6834	1665	25	m=2	m=2	PROPN
ejpam-6834	1665	26	,	,	PUNCT
ejpam-6834	1665	27	h=2	h=2	PART
ejpam-6834	1665	28	)	)	PUNCT
ejpam-6834	1665	29	,	,	PUNCT
ejpam-6834	1665	30	two	two	NUM
ejpam-6834	1665	31	input	input	NOUN
ejpam-6834	1665	32	tuples	tuple	NOUN
ejpam-6834	1665	33	(	(	PUNCT
ejpam-6834	1665	34	k=2	k=2	PROPN
ejpam-6834	1665	35	)	)	PUNCT
ejpam-6834	1665	36	,	,	PUNCT
ejpam-6834	1665	37	and	and	CCONJ
ejpam-6834	1665	38	rough	rough	ADJ
ejpam-6834	1665	39	reasoning	reasoning	NOUN
ejpam-6834	1665	40	on	on	ADP
ejpam-6834	1665	41	the	the	DET
ejpam-6834	1665	42	ground	ground	NOUN
ejpam-6834	1665	43	set	set	NOUN
ejpam-6834	1665	44	x	x	PUNCT
ejpam-6834	1665	45	with	with	ADP
ejpam-6834	1665	46	n=1	n=1	PROPN
ejpam-6834	1665	47	.	.	PUNCT
ejpam-6834	1665	48	theorem	theorem	VERB
ejpam-6834	1665	49	55	55	NUM
ejpam-6834	1665	50	(	(	PUNCT
ejpam-6834	1665	51	classical	classical	ADJ
ejpam-6834	1665	52	rough	rough	ADJ
ejpam-6834	1665	53	sets	set	NOUN
ejpam-6834	1665	54	as	as	ADP
ejpam-6834	1665	55	a	a	DET
ejpam-6834	1665	56	special	special	ADJ
ejpam-6834	1665	57	case	case	NOUN
ejpam-6834	1665	58	)	)	PUNCT
ejpam-6834	1665	59	.	.	PUNCT
ejpam-6834	1666	1	if	if	SCONJ
ejpam-6834	1666	2	m	m	VERB
ejpam-6834	1666	3	=	=	NOUN
ejpam-6834	1667	1	h	h	NOUN
ejpam-6834	1667	2	=	=	SYM
ejpam-6834	1667	3	k	k	NOUN
ejpam-6834	1667	4	=	=	SYM
ejpam-6834	1667	5	1	1	NUM
ejpam-6834	1667	6	and	and	CCONJ
ejpam-6834	1667	7	n	n	CCONJ
ejpam-6834	1667	8	=	=	SYM
ejpam-6834	1667	9	1	1	NUM
ejpam-6834	1667	10	,	,	PUNCT
ejpam-6834	1667	11	then	then	ADV
ejpam-6834	1667	12	any	any	DET
ejpam-6834	1667	13	classical	classical	ADJ
ejpam-6834	1667	14	rough	rough	ADJ
ejpam-6834	1667	15	set	set	NOUN
ejpam-6834	1667	16	mapping	map	VERB
ejpam-6834	1667	17	fcl	fcl	PROPN
ejpam-6834	1667	18	:	:	PUNCT
ejpam-6834	1667	19	j	j	PROPN
ejpam-6834	1667	20	→	→	SYM
ejpam-6834	1667	21	p(x	p(x	PROPN
ejpam-6834	1667	22	)	)	PUNCT
ejpam-6834	1667	23	is	be	AUX
ejpam-6834	1667	24	exactly	exactly	ADV
ejpam-6834	1667	25	a	a	DET
ejpam-6834	1667	26	(	(	PUNCT
ejpam-6834	1667	27	1	1	NUM
ejpam-6834	1667	28	,	,	PUNCT
ejpam-6834	1667	29	1)-ary	1)-ary	ADJ
ejpam-6834	1667	30	(	(	PUNCT
ejpam-6834	1667	31	1	1	NUM
ejpam-6834	1667	32	,	,	PUNCT
ejpam-6834	1667	33	1)superhyperrough	1)superhyperrough	NUM
ejpam-6834	1667	34	set	set	NOUN
ejpam-6834	1667	35	.	.	PUNCT
ejpam-6834	1668	1	more	more	ADV
ejpam-6834	1668	2	generally	generally	ADV
ejpam-6834	1668	3	,	,	PUNCT
ejpam-6834	1668	4	for	for	ADP
ejpam-6834	1668	5	arbitrary	arbitrary	ADJ
ejpam-6834	1668	6	n	n	PRON
ejpam-6834	1668	7	≥	≥	NOUN
ejpam-6834	1668	8	1	1	NUM
ejpam-6834	1668	9	,	,	PUNCT
ejpam-6834	1668	10	the	the	DET
ejpam-6834	1668	11	composition	composition	NOUN
ejpam-6834	1668	12	flatn	flatn	NOUN
ejpam-6834	1668	13	◦	◦	NOUN
ejpam-6834	1668	14	f	f	PROPN
ejpam-6834	1668	15	recovers	recover	VERB
ejpam-6834	1668	16	the	the	DET
ejpam-6834	1668	17	classical	classical	ADJ
ejpam-6834	1668	18	setting	setting	NOUN
ejpam-6834	1668	19	on	on	ADP
ejpam-6834	1668	20	x.	x.	NOUN
ejpam-6834	1668	21	proof	proof	NOUN
ejpam-6834	1668	22	.	.	PUNCT
ejpam-6834	1669	1	when	when	SCONJ
ejpam-6834	1669	2	m	m	VERB
ejpam-6834	1669	3	=	=	ADJ
ejpam-6834	1669	4	h	h	NOUN
ejpam-6834	1669	5	=	=	SYM
ejpam-6834	1669	6	k	k	PROPN
ejpam-6834	1669	7	=	=	PUNCT
ejpam-6834	1669	8	n	n	PROPN
ejpam-6834	1669	9	=	=	SYM
ejpam-6834	1669	10	1	1	NUM
ejpam-6834	1669	11	we	we	PRON
ejpam-6834	1669	12	have	have	VERB
ejpam-6834	1669	13	d1	d1	NOUN
ejpam-6834	1669	14	=	=	SYM
ejpam-6834	1669	15	p̃1(j	p̃1(j	NOUN
ejpam-6834	1669	16	)	)	PUNCT
ejpam-6834	1669	17	∼=	∼=	PROPN
ejpam-6834	1669	18	j	j	NOUN
ejpam-6834	1669	19	and	and	CCONJ
ejpam-6834	1669	20	c	c	NOUN
ejpam-6834	1669	21	=	=	SYM
ejpam-6834	1669	22	p̃1(x	p̃1(x	NOUN
ejpam-6834	1669	23	)	)	PUNCT
ejpam-6834	1669	24	=	=	SYM
ejpam-6834	1669	25	p+(x	p+(x	PROPN
ejpam-6834	1669	26	)	)	PUNCT
ejpam-6834	1669	27	.	.	PUNCT
ejpam-6834	1670	1	thus	thus	ADV
ejpam-6834	1670	2	every	every	DET
ejpam-6834	1670	3	fcl	fcl	ADJ
ejpam-6834	1670	4	:	:	PUNCT
ejpam-6834	1670	5	j	j	PROPN
ejpam-6834	1670	6	→	→	SYM
ejpam-6834	1670	7	p+(x	p+(x	PROPN
ejpam-6834	1670	8	)	)	PUNCT
ejpam-6834	1670	9	is	be	AUX
ejpam-6834	1670	10	a	a	DET
ejpam-6834	1670	11	(	(	PUNCT
ejpam-6834	1670	12	1	1	NUM
ejpam-6834	1670	13	,	,	PUNCT
ejpam-6834	1670	14	1)-ary	1)-ary	ADJ
ejpam-6834	1670	15	(	(	PUNCT
ejpam-6834	1670	16	1	1	NUM
ejpam-6834	1670	17	,	,	PUNCT
ejpam-6834	1670	18	1)-superhyperrough	1)-superhyperrough	NUM
ejpam-6834	1670	19	set	set	NOUN
ejpam-6834	1670	20	.	.	PUNCT
ejpam-6834	1671	1	if	if	SCONJ
ejpam-6834	1671	2	n	n	PROPN
ejpam-6834	1671	3	>	>	X
ejpam-6834	1671	4	1	1	NUM
ejpam-6834	1671	5	,	,	PUNCT
ejpam-6834	1671	6	then	then	ADV
ejpam-6834	1671	7	f	f	X
ejpam-6834	1671	8	:	:	PUNCT
ejpam-6834	1671	9	d1	d1	PROPN
ejpam-6834	1671	10	→	→	SYM
ejpam-6834	1671	11	p̃n(x	p̃n(x	NUM
ejpam-6834	1671	12	)	)	PUNCT
ejpam-6834	1671	13	and	and	CCONJ
ejpam-6834	1671	14	flatn	flatn	VERB
ejpam-6834	1672	1	◦	◦	NOUN
ejpam-6834	1672	2	f	f	X
ejpam-6834	1672	3	:	:	PUNCT
ejpam-6834	1672	4	d1	d1	PROPN
ejpam-6834	1672	5	→	→	SYM
ejpam-6834	1672	6	p(x	p(x	PROPN
ejpam-6834	1672	7	)	)	PUNCT
ejpam-6834	1672	8	produces	produce	VERB
ejpam-6834	1672	9	ground	ground	NOUN
ejpam-6834	1672	10	subsets	subset	NOUN
ejpam-6834	1672	11	on	on	ADP
ejpam-6834	1672	12	which	which	PRON
ejpam-6834	1672	13	the	the	DET
ejpam-6834	1672	14	classical	classical	ADJ
ejpam-6834	1672	15	lower	low	ADJ
ejpam-6834	1672	16	/	/	SYM
ejpam-6834	1672	17	upper	upper	ADJ
ejpam-6834	1672	18	approximations	approximation	NOUN
ejpam-6834	1672	19	are	be	AUX
ejpam-6834	1672	20	taken	take	VERB
ejpam-6834	1672	21	.	.	PUNCT
ejpam-6834	1673	1	hence	hence	ADV
ejpam-6834	1673	2	the	the	DET
ejpam-6834	1673	3	generalized	generalized	ADJ
ejpam-6834	1673	4	model	model	NOUN
ejpam-6834	1673	5	subsumes	subsume	VERB
ejpam-6834	1673	6	the	the	DET
ejpam-6834	1673	7	classical	classical	ADJ
ejpam-6834	1673	8	one	one	NUM
ejpam-6834	1673	9	.	.	PUNCT
ejpam-6834	1674	1	theorem	theorem	VERB
ejpam-6834	1674	2	56	56	NUM
ejpam-6834	1674	3	(	(	PUNCT
ejpam-6834	1674	4	reduction	reduction	NOUN
ejpam-6834	1674	5	of	of	ADP
ejpam-6834	1674	6	input	input	NOUN
ejpam-6834	1674	7	arity	arity	NOUN
ejpam-6834	1674	8	)	)	PUNCT
ejpam-6834	1674	9	.	.	PUNCT
ejpam-6834	1675	1	fix	fix	NOUN
ejpam-6834	1675	2	indices	indice	VERB
ejpam-6834	1675	3	1	1	NUM
ejpam-6834	1675	4	≤	≤	NUM
ejpam-6834	1675	5	i1	i1	X
ejpam-6834	1675	6	<	<	X
ejpam-6834	1675	7	·	·	PUNCT
ejpam-6834	1675	8	·	·	PUNCT
ejpam-6834	1675	9	·	·	PUNCT
ejpam-6834	1676	1	<	<	X
ejpam-6834	1676	2	ir	ir	PROPN
ejpam-6834	1676	3	≤	≤	PUNCT
ejpam-6834	1676	4	k	k	X
ejpam-6834	1676	5	and	and	CCONJ
ejpam-6834	1676	6	blocks	block	VERB
ejpam-6834	1676	7	γ∗ij	γ∗ij	PROPN
ejpam-6834	1676	8	∈	∈	PROPN
ejpam-6834	1676	9	d.	d.	NOUN
ejpam-6834	1676	10	define	define	VERB
ejpam-6834	1676	11	ι	ι	X
ejpam-6834	1676	12	:	:	PUNCT
ejpam-6834	1676	13	d	d	X
ejpam-6834	1676	14	k−r	k−r	PROPN
ejpam-6834	1676	15	−→	−→	NOUN
ejpam-6834	1676	16	d	d	PROPN
ejpam-6834	1676	17	k	k	PROPN
ejpam-6834	1676	18	,	,	PUNCT
ejpam-6834	1676	19	ι(δ1	ι(δ1	NOUN
ejpam-6834	1676	20	,	,	PUNCT
ejpam-6834	1676	21	.	.	PUNCT
ejpam-6834	1676	22	.	.	PUNCT
ejpam-6834	1676	23	.	.	PUNCT
ejpam-6834	1677	1	,	,	PUNCT
ejpam-6834	1677	2	δk−r	δk−r	NOUN
ejpam-6834	1677	3	)	)	PUNCT
ejpam-6834	1678	1	=	=	PUNCT
ejpam-6834	1678	2	γ	γ	X
ejpam-6834	1678	3	by	by	ADP
ejpam-6834	1678	4	inserting	insert	VERB
ejpam-6834	1678	5	the	the	DET
ejpam-6834	1678	6	fixed	fix	VERB
ejpam-6834	1678	7	blocks	block	NOUN
ejpam-6834	1678	8	at	at	ADP
ejpam-6834	1678	9	slots	slot	NOUN
ejpam-6834	1678	10	i1	i1	PROPN
ejpam-6834	1678	11	,	,	PUNCT
ejpam-6834	1678	12	.	.	PUNCT
ejpam-6834	1678	13	.	.	PUNCT
ejpam-6834	1678	14	.	.	PUNCT
ejpam-6834	1679	1	,	,	PUNCT
ejpam-6834	1679	2	ir	ir	PROPN
ejpam-6834	1679	3	and	and	CCONJ
ejpam-6834	1679	4	the	the	DET
ejpam-6834	1679	5	free	free	ADJ
ejpam-6834	1679	6	blocks	block	NOUN
ejpam-6834	1679	7	elsewhere	elsewhere	ADV
ejpam-6834	1679	8	,	,	PUNCT
ejpam-6834	1679	9	and	and	CCONJ
ejpam-6834	1679	10	put	put	VERB
ejpam-6834	1679	11	ffix	ffix	NOUN
ejpam-6834	1679	12	:	:	PUNCT
ejpam-6834	1679	13	=	=	SYM
ejpam-6834	1679	14	f	f	AUX
ejpam-6834	1679	15	◦	◦	NOUN
ejpam-6834	1679	16	ι	ι	X
ejpam-6834	1679	17	.	.	PUNCT
ejpam-6834	1680	1	then	then	ADV
ejpam-6834	1680	2	ffix	ffix	NOUN
ejpam-6834	1680	3	:	:	PUNCT
ejpam-6834	1681	1	d	d	X
ejpam-6834	1681	2	k−r	k−r	X
ejpam-6834	1681	3	→	→	SYM
ejpam-6834	1681	4	p̃n(x	p̃n(x	X
ejpam-6834	1681	5	)	)	PUNCT
ejpam-6834	1681	6	is	be	AUX
ejpam-6834	1681	7	an	an	DET
ejpam-6834	1681	8	(	(	PUNCT
ejpam-6834	1681	9	h	h	NOUN
ejpam-6834	1681	10	,	,	PUNCT
ejpam-6834	1681	11	k	k	PROPN
ejpam-6834	1681	12	−	−	PROPN
ejpam-6834	1681	13	r)-ary	r)-ary	ADJ
ejpam-6834	1681	14	(	(	PUNCT
ejpam-6834	1681	15	m	m	PROPN
ejpam-6834	1681	16	,	,	PUNCT
ejpam-6834	1681	17	n)-superhyperrough	n)-superhyperrough	PUNCT
ejpam-6834	1681	18	set	set	NOUN
ejpam-6834	1681	19	.	.	PUNCT
ejpam-6834	1682	1	t.	t.	PROPN
ejpam-6834	1682	2	fujita	fujita	PROPN
ejpam-6834	1682	3	,	,	PUNCT
ejpam-6834	1682	4	f.smarandache	f.smarandache	NOUN
ejpam-6834	1682	5	/	/	SYM
ejpam-6834	1682	6	eur	eur	PROPN
ejpam-6834	1682	7	.	.	PUNCT
ejpam-6834	1683	1	j.	j.	PROPN
ejpam-6834	1683	2	pure	pure	PROPN
ejpam-6834	1683	3	appl	appl	PROPN
ejpam-6834	1683	4	.	.	PROPN
ejpam-6834	1683	5	math	math	PROPN
ejpam-6834	1683	6	,	,	PUNCT
ejpam-6834	1683	7	18	18	NUM
ejpam-6834	1683	8	(	(	PUNCT
ejpam-6834	1683	9	4	4	NUM
ejpam-6834	1683	10	)	)	PUNCT
ejpam-6834	1683	11	(	(	PUNCT
ejpam-6834	1683	12	2025	2025	NUM
ejpam-6834	1683	13	)	)	PUNCT
ejpam-6834	1683	14	,	,	PUNCT
ejpam-6834	1683	15	6834	6834	NUM
ejpam-6834	1683	16	61	61	NUM
ejpam-6834	1683	17	of	of	ADP
ejpam-6834	1683	18	69	69	NUM
ejpam-6834	1683	19	proof	proof	NOUN
ejpam-6834	1683	20	.	.	PUNCT
ejpam-6834	1684	1	the	the	DET
ejpam-6834	1684	2	insertion	insertion	NOUN
ejpam-6834	1684	3	map	map	NOUN
ejpam-6834	1684	4	ι	ι	PROPN
ejpam-6834	1684	5	is	be	AUX
ejpam-6834	1684	6	well	well	ADV
ejpam-6834	1684	7	defined	define	VERB
ejpam-6834	1684	8	;	;	PUNCT
ejpam-6834	1684	9	composing	compose	VERB
ejpam-6834	1684	10	with	with	ADP
ejpam-6834	1684	11	f	f	PROPN
ejpam-6834	1684	12	yields	yield	VERB
ejpam-6834	1684	13	a	a	DET
ejpam-6834	1684	14	map	map	NOUN
ejpam-6834	1684	15	into	into	ADP
ejpam-6834	1684	16	c.	c.	PROPN
ejpam-6834	1684	17	nonemptiness	nonemptiness	PROPN
ejpam-6834	1684	18	and	and	CCONJ
ejpam-6834	1684	19	the	the	DET
ejpam-6834	1684	20	definition	definition	NOUN
ejpam-6834	1684	21	of	of	ADP
ejpam-6834	1684	22	·	·	PUNCT
ejpam-6834	1684	23	,	,	PUNCT
ejpam-6834	1684	24	·	·	PUNCT
ejpam-6834	1684	25	depend	depend	VERB
ejpam-6834	1684	26	only	only	ADV
ejpam-6834	1684	27	on	on	ADP
ejpam-6834	1684	28	the	the	DET
ejpam-6834	1684	29	image	image	NOUN
ejpam-6834	1684	30	w	w	PROPN
ejpam-6834	1684	31	=	=	SYM
ejpam-6834	1684	32	f	f	X
ejpam-6834	1684	33	(	(	PUNCT
ejpam-6834	1684	34	γ	γ	PROPN
ejpam-6834	1684	35	)	)	PUNCT
ejpam-6834	1684	36	,	,	PUNCT
ejpam-6834	1684	37	which	which	PRON
ejpam-6834	1684	38	is	be	AUX
ejpam-6834	1684	39	unaffected	unaffected	ADJ
ejpam-6834	1684	40	by	by	ADP
ejpam-6834	1684	41	viewing	view	VERB
ejpam-6834	1684	42	the	the	DET
ejpam-6834	1684	43	fixed	fix	VERB
ejpam-6834	1684	44	coordinates	coordinate	NOUN
ejpam-6834	1684	45	as	as	ADP
ejpam-6834	1684	46	parameters	parameter	NOUN
ejpam-6834	1684	47	of	of	ADP
ejpam-6834	1684	48	the	the	DET
ejpam-6834	1684	49	new	new	ADJ
ejpam-6834	1684	50	map	map	NOUN
ejpam-6834	1684	51	.	.	PUNCT
ejpam-6834	1685	1	thus	thus	ADV
ejpam-6834	1685	2	the	the	DET
ejpam-6834	1685	3	structure	structure	NOUN
ejpam-6834	1685	4	and	and	CCONJ
ejpam-6834	1685	5	approximations	approximation	NOUN
ejpam-6834	1685	6	remain	remain	VERB
ejpam-6834	1685	7	valid	valid	ADJ
ejpam-6834	1685	8	with	with	ADP
ejpam-6834	1685	9	arity	arity	NOUN
ejpam-6834	1685	10	k	k	PROPN
ejpam-6834	1685	11	−	−	PROPN
ejpam-6834	1685	12	r.	r.	PROPN
ejpam-6834	1685	13	theorem	theorem	VERB
ejpam-6834	1685	14	57	57	NUM
ejpam-6834	1685	15	(	(	PUNCT
ejpam-6834	1685	16	union	union	NOUN
ejpam-6834	1685	17	)	)	PUNCT
ejpam-6834	1685	18	.	.	PUNCT
ejpam-6834	1686	1	if	if	SCONJ
ejpam-6834	1686	2	f1	f1	PROPN
ejpam-6834	1686	3	,	,	PUNCT
ejpam-6834	1686	4	f2	f2	PROPN
ejpam-6834	1686	5	:	:	PUNCT
ejpam-6834	1686	6	d	d	X
ejpam-6834	1686	7	k	k	X
ejpam-6834	1686	8	→	→	SYM
ejpam-6834	1686	9	p̃n(x	p̃n(x	X
ejpam-6834	1686	10	)	)	PUNCT
ejpam-6834	1686	11	are	be	AUX
ejpam-6834	1686	12	(	(	PUNCT
ejpam-6834	1686	13	h	h	NOUN
ejpam-6834	1686	14	,	,	PUNCT
ejpam-6834	1686	15	k)-ary	k)-ary	X
ejpam-6834	1686	16	(	(	PUNCT
ejpam-6834	1686	17	m	m	PROPN
ejpam-6834	1686	18	,	,	PUNCT
ejpam-6834	1686	19	n)-superhyperrough	n)-superhyperrough	PUNCT
ejpam-6834	1686	20	sets	set	NOUN
ejpam-6834	1686	21	,	,	PUNCT
ejpam-6834	1686	22	then	then	ADV
ejpam-6834	1686	23	(	(	PUNCT
ejpam-6834	1686	24	f1	f1	PROPN
ejpam-6834	1686	25	∪	∪	X
ejpam-6834	1686	26	f2)(γ	f2)(γ	PROPN
ejpam-6834	1686	27	)	)	PUNCT
ejpam-6834	1686	28	:	:	PUNCT
ejpam-6834	1687	1	=	=	SYM
ejpam-6834	1687	2	f1(γ	f1(γ	PROPN
ejpam-6834	1687	3	)	)	PUNCT
ejpam-6834	1687	4	∪	∪	ADP
ejpam-6834	1687	5	f2(γ	f2(γ	NOUN
ejpam-6834	1687	6	)	)	PUNCT
ejpam-6834	1687	7	is	be	AUX
ejpam-6834	1687	8	again	again	ADV
ejpam-6834	1687	9	an	an	DET
ejpam-6834	1687	10	(	(	PUNCT
ejpam-6834	1687	11	h	h	NOUN
ejpam-6834	1687	12	,	,	PUNCT
ejpam-6834	1687	13	k)-ary	k)-ary	X
ejpam-6834	1687	14	(	(	PUNCT
ejpam-6834	1687	15	m	m	PROPN
ejpam-6834	1687	16	,	,	PUNCT
ejpam-6834	1687	17	n)-superhyperrough	n)-superhyperrough	PUNCT
ejpam-6834	1687	18	set	set	NOUN
ejpam-6834	1687	19	.	.	PUNCT
ejpam-6834	1688	1	moreover	moreover	ADV
ejpam-6834	1688	2	,	,	PUNCT
ejpam-6834	1688	3	flatn	flatn	ADJ
ejpam-6834	1688	4	(	(	PUNCT
ejpam-6834	1688	5	(	(	PUNCT
ejpam-6834	1688	6	f1	f1	PROPN
ejpam-6834	1688	7	∪	∪	X
ejpam-6834	1688	8	f2)(γ	f2)(γ	PROPN
ejpam-6834	1688	9	)	)	PUNCT
ejpam-6834	1688	10	)	)	PUNCT
ejpam-6834	1689	1	=	=	PUNCT
ejpam-6834	1689	2	flatn	flatn	ADJ
ejpam-6834	1689	3	(	(	PUNCT
ejpam-6834	1689	4	f1(γ	f1(γ	PROPN
ejpam-6834	1689	5	)	)	PUNCT
ejpam-6834	1689	6	)	)	PUNCT
ejpam-6834	1689	7	∪	∪	ADP
ejpam-6834	1689	8	flatn	flatn	NOUN
ejpam-6834	1689	9	(	(	PUNCT
ejpam-6834	1689	10	f2(γ	f2(γ	NOUN
ejpam-6834	1689	11	)	)	PUNCT
ejpam-6834	1689	12	)	)	PUNCT
ejpam-6834	1689	13	,	,	PUNCT
ejpam-6834	1689	14	hence	hence	ADV
ejpam-6834	1689	15	f1	f1	NOUN
ejpam-6834	1689	16	∪	∪	VERB
ejpam-6834	1689	17	f2	f2	ADJ
ejpam-6834	1689	18	=	=	SYM
ejpam-6834	1689	19	f1	f1	PROPN
ejpam-6834	1689	20	∪	∪	ADP
ejpam-6834	1689	21	f2	f2	PROPN
ejpam-6834	1689	22	and	and	CCONJ
ejpam-6834	1689	23	f1	f1	PROPN
ejpam-6834	1689	24	∪	∪	VERB
ejpam-6834	1689	25	f2	f2	ADJ
ejpam-6834	1689	26	=	=	SYM
ejpam-6834	1689	27	f1	f1	PROPN
ejpam-6834	1689	28	∪	∪	X
ejpam-6834	1689	29	f2	f2	PROPN
ejpam-6834	1689	30	.	.	PUNCT
ejpam-6834	1690	1	proof	proof	NOUN
ejpam-6834	1690	2	.	.	PUNCT
ejpam-6834	1691	1	by	by	ADP
ejpam-6834	1691	2	induction	induction	NOUN
ejpam-6834	1691	3	on	on	ADP
ejpam-6834	1691	4	n	n	CCONJ
ejpam-6834	1691	5	,	,	PUNCT
ejpam-6834	1691	6	the	the	DET
ejpam-6834	1691	7	union	union	NOUN
ejpam-6834	1691	8	of	of	ADP
ejpam-6834	1691	9	two	two	NUM
ejpam-6834	1691	10	nonempty	nonempty	ADJ
ejpam-6834	1691	11	level	level	NOUN
ejpam-6834	1691	12	–	–	PUNCT
ejpam-6834	1691	13	n	n	CCONJ
ejpam-6834	1691	14	families	family	NOUN
ejpam-6834	1691	15	is	be	AUX
ejpam-6834	1691	16	nonempty	nonempty	ADJ
ejpam-6834	1691	17	level	level	NOUN
ejpam-6834	1691	18	–	–	PUNCT
ejpam-6834	1691	19	n.	n.	NOUN
ejpam-6834	1691	20	thus	thus	ADV
ejpam-6834	1691	21	(	(	PUNCT
ejpam-6834	1691	22	f1∪f2)(γ	f1∪f2)(γ	NOUN
ejpam-6834	1691	23	)	)	PUNCT
ejpam-6834	1691	24	∈	∈	PROPN
ejpam-6834	1691	25	p̃n(x	p̃n(x	NOUN
ejpam-6834	1691	26	)	)	PUNCT
ejpam-6834	1691	27	.	.	PUNCT
ejpam-6834	1692	1	the	the	DET
ejpam-6834	1692	2	displayed	display	VERB
ejpam-6834	1692	3	equality	equality	NOUN
ejpam-6834	1692	4	follows	follow	VERB
ejpam-6834	1692	5	from	from	ADP
ejpam-6834	1692	6	the	the	DET
ejpam-6834	1692	7	definition	definition	NOUN
ejpam-6834	1692	8	of	of	ADP
ejpam-6834	1692	9	flatn	flatn	NOUN
ejpam-6834	1692	10	and	and	CCONJ
ejpam-6834	1692	11	distributivity	distributivity	NOUN
ejpam-6834	1692	12	of	of	ADP
ejpam-6834	1692	13	ordinary	ordinary	ADJ
ejpam-6834	1692	14	unions	union	NOUN
ejpam-6834	1692	15	.	.	PUNCT
ejpam-6834	1693	1	the	the	DET
ejpam-6834	1693	2	identities	identity	NOUN
ejpam-6834	1693	3	for	for	ADP
ejpam-6834	1693	4	lower	low	ADJ
ejpam-6834	1693	5	/	/	SYM
ejpam-6834	1693	6	upper	upper	ADJ
ejpam-6834	1693	7	approximations	approximation	NOUN
ejpam-6834	1693	8	are	be	AUX
ejpam-6834	1693	9	the	the	DET
ejpam-6834	1693	10	classical	classical	ADJ
ejpam-6834	1693	11	rough	rough	ADJ
ejpam-6834	1693	12	equalities	equality	NOUN
ejpam-6834	1693	13	applied	apply	VERB
ejpam-6834	1693	14	to	to	ADP
ejpam-6834	1693	15	the	the	DET
ejpam-6834	1693	16	ground	ground	NOUN
ejpam-6834	1693	17	sets	set	VERB
ejpam-6834	1693	18	flatn	flatn	ADJ
ejpam-6834	1693	19	(	(	PUNCT
ejpam-6834	1693	20	·	·	PUNCT
ejpam-6834	1693	21	)	)	PUNCT
ejpam-6834	1693	22	.	.	PUNCT
ejpam-6834	1694	1	theorem	theorem	VERB
ejpam-6834	1694	2	58	58	NUM
ejpam-6834	1694	3	(	(	PUNCT
ejpam-6834	1694	4	intersection	intersection	NOUN
ejpam-6834	1694	5	)	)	PUNCT
ejpam-6834	1694	6	.	.	PUNCT
ejpam-6834	1695	1	with	with	ADP
ejpam-6834	1695	2	the	the	DET
ejpam-6834	1695	3	same	same	ADJ
ejpam-6834	1695	4	hypotheses	hypothesis	NOUN
ejpam-6834	1695	5	,	,	PUNCT
ejpam-6834	1695	6	define	define	NOUN
ejpam-6834	1695	7	(	(	PUNCT
ejpam-6834	1695	8	f1	f1	NOUN
ejpam-6834	1695	9	∩	∩	NOUN
ejpam-6834	1695	10	f2)(γ	f2)(γ	PROPN
ejpam-6834	1695	11	)	)	PUNCT
ejpam-6834	1695	12	:	:	PUNCT
ejpam-6834	1695	13	=	=	SYM
ejpam-6834	1695	14	f1(γ	f1(γ	PROPN
ejpam-6834	1695	15	)	)	PUNCT
ejpam-6834	1695	16	∩	∩	NOUN
ejpam-6834	1695	17	f2(γ	f2(γ	NUM
ejpam-6834	1695	18	)	)	PUNCT
ejpam-6834	1695	19	.	.	PUNCT
ejpam-6834	1696	1	if	if	SCONJ
ejpam-6834	1696	2	this	this	DET
ejpam-6834	1696	3	intersection	intersection	NOUN
ejpam-6834	1696	4	is	be	AUX
ejpam-6834	1696	5	nonempty	nonempty	ADJ
ejpam-6834	1696	6	for	for	ADP
ejpam-6834	1696	7	all	all	DET
ejpam-6834	1696	8	γ	γ	NOUN
ejpam-6834	1696	9	,	,	PUNCT
ejpam-6834	1696	10	then	then	ADV
ejpam-6834	1696	11	f1∩f2	f1∩f2	PROPN
ejpam-6834	1696	12	is	be	AUX
ejpam-6834	1696	13	an	an	DET
ejpam-6834	1696	14	(	(	PUNCT
ejpam-6834	1696	15	h	h	NOUN
ejpam-6834	1696	16	,	,	PUNCT
ejpam-6834	1696	17	k)-ary	k)-ary	X
ejpam-6834	1696	18	(	(	PUNCT
ejpam-6834	1696	19	m	m	PROPN
ejpam-6834	1696	20	,	,	PUNCT
ejpam-6834	1696	21	n)-superhyperrough	n)-superhyperrough	PUNCT
ejpam-6834	1696	22	set	set	NOUN
ejpam-6834	1696	23	.	.	PUNCT
ejpam-6834	1697	1	furthermore	furthermore	ADV
ejpam-6834	1697	2	,	,	PUNCT
ejpam-6834	1697	3	flatn	flatn	ADJ
ejpam-6834	1697	4	(	(	PUNCT
ejpam-6834	1697	5	(	(	PUNCT
ejpam-6834	1697	6	f1	f1	PROPN
ejpam-6834	1697	7	∩	∩	NOUN
ejpam-6834	1697	8	f2)(γ	f2)(γ	NOUN
ejpam-6834	1697	9	)	)	PUNCT
ejpam-6834	1697	10	)	)	PUNCT
ejpam-6834	1698	1	⊆	⊆	NUM
ejpam-6834	1698	2	flatn	flatn	NOUN
ejpam-6834	1698	3	(	(	PUNCT
ejpam-6834	1698	4	f1(γ	f1(γ	PROPN
ejpam-6834	1698	5	)	)	PUNCT
ejpam-6834	1698	6	)	)	PUNCT
ejpam-6834	1698	7	∩	∩	NOUN
ejpam-6834	1698	8	flatn	flatn	NOUN
ejpam-6834	1698	9	(	(	PUNCT
ejpam-6834	1698	10	f2(γ	f2(γ	NOUN
ejpam-6834	1698	11	)	)	PUNCT
ejpam-6834	1698	12	)	)	PUNCT
ejpam-6834	1698	13	,	,	PUNCT
ejpam-6834	1698	14	whence	whence	ADP
ejpam-6834	1698	15	f1	f1	PROPN
ejpam-6834	1698	16	∩	∩	NOUN
ejpam-6834	1698	17	f2	f2	ADJ
ejpam-6834	1698	18	⊆	⊆	NUM
ejpam-6834	1698	19	f1	f1	NOUN
ejpam-6834	1698	20	∩	∩	NOUN
ejpam-6834	1698	21	f2	f2	PROPN
ejpam-6834	1698	22	and	and	CCONJ
ejpam-6834	1698	23	f1	f1	PROPN
ejpam-6834	1698	24	∩	∩	NOUN
ejpam-6834	1698	25	f2	f2	ADJ
ejpam-6834	1698	26	⊆	⊆	NUM
ejpam-6834	1698	27	f1	f1	NOUN
ejpam-6834	1698	28	∩	∩	NOUN
ejpam-6834	1698	29	f2	f2	PROPN
ejpam-6834	1698	30	.	.	PUNCT
ejpam-6834	1699	1	equality	equality	NOUN
ejpam-6834	1699	2	holds	hold	VERB
ejpam-6834	1699	3	in	in	ADP
ejpam-6834	1699	4	all	all	DET
ejpam-6834	1699	5	three	three	NUM
ejpam-6834	1699	6	inclusions	inclusion	NOUN
ejpam-6834	1699	7	when	when	SCONJ
ejpam-6834	1699	8	n	n	X
ejpam-6834	1699	9	=	=	SYM
ejpam-6834	1699	10	1	1	X
ejpam-6834	1699	11	.	.	PUNCT
ejpam-6834	1700	1	proof	proof	NOUN
ejpam-6834	1700	2	.	.	PUNCT
ejpam-6834	1701	1	as	as	ADP
ejpam-6834	1701	2	for	for	ADP
ejpam-6834	1701	3	union	union	NOUN
ejpam-6834	1701	4	,	,	PUNCT
ejpam-6834	1701	5	the	the	DET
ejpam-6834	1701	6	intersection	intersection	NOUN
ejpam-6834	1701	7	of	of	ADP
ejpam-6834	1701	8	two	two	NUM
ejpam-6834	1701	9	level	level	NOUN
ejpam-6834	1701	10	–	–	PUNCT
ejpam-6834	1701	11	n	n	NUM
ejpam-6834	1701	12	families	family	NOUN
ejpam-6834	1701	13	that	that	PRON
ejpam-6834	1701	14	meets	meet	VERB
ejpam-6834	1701	15	nontrivially	nontrivially	ADV
ejpam-6834	1701	16	is	be	AUX
ejpam-6834	1701	17	again	again	ADV
ejpam-6834	1701	18	a	a	DET
ejpam-6834	1701	19	nonempty	nonempty	ADJ
ejpam-6834	1701	20	level	level	NOUN
ejpam-6834	1701	21	–	–	PUNCT
ejpam-6834	1701	22	n	n	NUM
ejpam-6834	1701	23	family	family	NOUN
ejpam-6834	1701	24	,	,	PUNCT
ejpam-6834	1701	25	by	by	ADP
ejpam-6834	1701	26	induction	induction	NOUN
ejpam-6834	1701	27	on	on	ADP
ejpam-6834	1701	28	n.	n.	NOUN
ejpam-6834	1701	29	the	the	DET
ejpam-6834	1701	30	inclusion	inclusion	NOUN
ejpam-6834	1701	31	for	for	ADP
ejpam-6834	1701	32	flatn	flatn	NOUN
ejpam-6834	1701	33	is	be	AUX
ejpam-6834	1701	34	immediate	immediate	ADJ
ejpam-6834	1701	35	from	from	ADP
ejpam-6834	1701	36	the	the	DET
ejpam-6834	1701	37	definition	definition	NOUN
ejpam-6834	1701	38	(	(	PUNCT
ejpam-6834	1701	39	the	the	DET
ejpam-6834	1701	40	base	base	NOUN
ejpam-6834	1701	41	elements	element	NOUN
ejpam-6834	1701	42	surviving	survive	VERB
ejpam-6834	1701	43	the	the	DET
ejpam-6834	1701	44	intersection	intersection	NOUN
ejpam-6834	1701	45	are	be	AUX
ejpam-6834	1701	46	a	a	DET
ejpam-6834	1701	47	subfamily	subfamily	NOUN
ejpam-6834	1701	48	of	of	ADP
ejpam-6834	1701	49	those	those	PRON
ejpam-6834	1701	50	present	present	ADJ
ejpam-6834	1701	51	in	in	ADP
ejpam-6834	1701	52	each	each	DET
ejpam-6834	1701	53	factor	factor	NOUN
ejpam-6834	1701	54	)	)	PUNCT
ejpam-6834	1701	55	.	.	PUNCT
ejpam-6834	1702	1	the	the	DET
ejpam-6834	1702	2	inclusions	inclusion	NOUN
ejpam-6834	1702	3	for	for	ADP
ejpam-6834	1702	4	rough	rough	ADJ
ejpam-6834	1702	5	approximations	approximation	NOUN
ejpam-6834	1702	6	follow	follow	VERB
ejpam-6834	1702	7	from	from	ADP
ejpam-6834	1702	8	the	the	DET
ejpam-6834	1702	9	monotonicity	monotonicity	NOUN
ejpam-6834	1702	10	of	of	ADP
ejpam-6834	1702	11	·	·	PUNCT
ejpam-6834	1702	12	,	,	PUNCT
ejpam-6834	1702	13	·	·	PUNCT
ejpam-6834	1702	14	with	with	ADP
ejpam-6834	1702	15	respect	respect	NOUN
ejpam-6834	1702	16	to	to	PART
ejpam-6834	1702	17	set	set	VERB
ejpam-6834	1702	18	inclusion	inclusion	NOUN
ejpam-6834	1702	19	on	on	ADP
ejpam-6834	1702	20	ground	ground	NOUN
ejpam-6834	1702	21	subsets	subset	NOUN
ejpam-6834	1702	22	.	.	PUNCT
ejpam-6834	1703	1	when	when	SCONJ
ejpam-6834	1703	2	n	n	X
ejpam-6834	1703	3	=	=	SYM
ejpam-6834	1703	4	1	1	NUM
ejpam-6834	1703	5	,	,	PUNCT
ejpam-6834	1703	6	flat1	flat1	NOUN
ejpam-6834	1703	7	is	be	AUX
ejpam-6834	1703	8	the	the	DET
ejpam-6834	1703	9	identity	identity	NOUN
ejpam-6834	1703	10	and	and	CCONJ
ejpam-6834	1703	11	all	all	DET
ejpam-6834	1703	12	inclusions	inclusion	NOUN
ejpam-6834	1703	13	become	become	VERB
ejpam-6834	1703	14	equalities	equality	NOUN
ejpam-6834	1703	15	.	.	PUNCT
ejpam-6834	1704	1	theorem	theorem	VERB
ejpam-6834	1704	2	59	59	NUM
ejpam-6834	1704	3	(	(	PUNCT
ejpam-6834	1704	4	monotonicity	monotonicity	NOUN
ejpam-6834	1704	5	of	of	ADP
ejpam-6834	1704	6	approximations	approximation	NOUN
ejpam-6834	1704	7	)	)	PUNCT
ejpam-6834	1704	8	.	.	PUNCT
ejpam-6834	1705	1	if	if	SCONJ
ejpam-6834	1705	2	γ	γ	X
ejpam-6834	1705	3	,	,	PUNCT
ejpam-6834	1705	4	γ	γ	X
ejpam-6834	1705	5	′	′	NOUN
ejpam-6834	1705	6	∈	∈	PROPN
ejpam-6834	1706	1	d	d	X
ejpam-6834	1706	2	k	k	PROPN
ejpam-6834	1706	3	satisfy	satisfy	PROPN
ejpam-6834	1706	4	f	f	PROPN
ejpam-6834	1706	5	(	(	PUNCT
ejpam-6834	1706	6	γ	γ	NOUN
ejpam-6834	1706	7	′	′	NOUN
ejpam-6834	1706	8	)	)	PUNCT
ejpam-6834	1706	9	⊆	⊆	NUM
ejpam-6834	1706	10	f	f	X
ejpam-6834	1706	11	(	(	PUNCT
ejpam-6834	1706	12	γ	γ	X
ejpam-6834	1706	13	)	)	PUNCT
ejpam-6834	1706	14	(	(	PUNCT
ejpam-6834	1706	15	in	in	ADP
ejpam-6834	1706	16	p̃n(x	p̃n(x	NUM
ejpam-6834	1706	17	)	)	PUNCT
ejpam-6834	1706	18	)	)	PUNCT
ejpam-6834	1706	19	,	,	PUNCT
ejpam-6834	1706	20	then	then	ADV
ejpam-6834	1706	21	f	f	X
ejpam-6834	1706	22	(	(	PUNCT
ejpam-6834	1706	23	γ	γ	NOUN
ejpam-6834	1706	24	′	′	NOUN
ejpam-6834	1706	25	)	)	PUNCT
ejpam-6834	1706	26	⊆	⊆	NUM
ejpam-6834	1706	27	f	f	X
ejpam-6834	1706	28	(	(	PUNCT
ejpam-6834	1706	29	γ	γ	PROPN
ejpam-6834	1706	30	)	)	PUNCT
ejpam-6834	1706	31	,	,	PUNCT
ejpam-6834	1706	32	f	f	PROPN
ejpam-6834	1706	33	(	(	PUNCT
ejpam-6834	1706	34	γ	γ	NOUN
ejpam-6834	1706	35	′	′	NOUN
ejpam-6834	1706	36	)	)	PUNCT
ejpam-6834	1706	37	⊆	⊆	NUM
ejpam-6834	1706	38	f	f	X
ejpam-6834	1706	39	(	(	PUNCT
ejpam-6834	1706	40	γ	γ	NOUN
ejpam-6834	1706	41	)	)	PUNCT
ejpam-6834	1706	42	.	.	PUNCT
ejpam-6834	1707	1	proof	proof	NOUN
ejpam-6834	1707	2	.	.	PUNCT
ejpam-6834	1708	1	from	from	ADP
ejpam-6834	1708	2	f	f	PROPN
ejpam-6834	1708	3	(	(	PUNCT
ejpam-6834	1708	4	γ	γ	NOUN
ejpam-6834	1708	5	′	′	NOUN
ejpam-6834	1708	6	)	)	PUNCT
ejpam-6834	1708	7	⊆	⊆	NUM
ejpam-6834	1708	8	f	f	X
ejpam-6834	1708	9	(	(	PUNCT
ejpam-6834	1708	10	γ	γ	X
ejpam-6834	1708	11	)	)	PUNCT
ejpam-6834	1708	12	we	we	PRON
ejpam-6834	1708	13	get	get	VERB
ejpam-6834	1708	14	flatn(f	flatn(f	INTJ
ejpam-6834	1708	15	(	(	PUNCT
ejpam-6834	1708	16	γ	γ	NOUN
ejpam-6834	1708	17	′	′	NUM
ejpam-6834	1708	18	)	)	PUNCT
ejpam-6834	1708	19	)	)	PUNCT
ejpam-6834	1709	1	⊆	⊆	NUM
ejpam-6834	1709	2	flatn(f	flatn(f	INTJ
ejpam-6834	1709	3	(	(	PUNCT
ejpam-6834	1709	4	γ	γ	NOUN
ejpam-6834	1709	5	)	)	PUNCT
ejpam-6834	1709	6	)	)	PUNCT
ejpam-6834	1709	7	.	.	PUNCT
ejpam-6834	1710	1	if	if	SCONJ
ejpam-6834	1710	2	[	[	X
ejpam-6834	1710	3	x]r	x]r	NOUN
ejpam-6834	1710	4	⊆	⊆	NUM
ejpam-6834	1710	5	flatn(f	flatn(f	INTJ
ejpam-6834	1710	6	(	(	PUNCT
ejpam-6834	1710	7	γ	γ	NOUN
ejpam-6834	1710	8	′	′	NUM
ejpam-6834	1710	9	)	)	PUNCT
ejpam-6834	1710	10	)	)	PUNCT
ejpam-6834	1710	11	,	,	PUNCT
ejpam-6834	1710	12	then	then	ADV
ejpam-6834	1710	13	[	[	X
ejpam-6834	1710	14	x]r	x]r	X
ejpam-6834	1710	15	⊆	⊆	NUM
ejpam-6834	1710	16	flatn(f	flatn(f	INTJ
ejpam-6834	1710	17	(	(	PUNCT
ejpam-6834	1710	18	γ	γ	NOUN
ejpam-6834	1710	19	)	)	PUNCT
ejpam-6834	1710	20	)	)	PUNCT
ejpam-6834	1710	21	,	,	PUNCT
ejpam-6834	1710	22	hence	hence	ADV
ejpam-6834	1710	23	x	x	SYM
ejpam-6834	1710	24	∈	∈	PROPN
ejpam-6834	1710	25	f	f	X
ejpam-6834	1710	26	(	(	PUNCT
ejpam-6834	1710	27	γ	γ	PROPN
ejpam-6834	1710	28	)	)	PUNCT
ejpam-6834	1710	29	.	.	PUNCT
ejpam-6834	1711	1	similarly	similarly	ADV
ejpam-6834	1711	2	,	,	PUNCT
ejpam-6834	1711	3	if	if	SCONJ
ejpam-6834	1711	4	[	[	X
ejpam-6834	1711	5	x]r	x]r	NOUN
ejpam-6834	1711	6	∩	∩	ADJ
ejpam-6834	1711	7	flatn(f	flatn(f	INTJ
ejpam-6834	1711	8	(	(	PUNCT
ejpam-6834	1711	9	γ	γ	NOUN
ejpam-6834	1711	10	′	′	NUM
ejpam-6834	1711	11	)	)	PUNCT
ejpam-6834	1711	12	)	)	PUNCT
ejpam-6834	1712	1	̸=	̸=	NOUN
ejpam-6834	1712	2	∅	∅	NOUN
ejpam-6834	1712	3	,	,	PUNCT
ejpam-6834	1712	4	then	then	ADV
ejpam-6834	1712	5	[	[	X
ejpam-6834	1712	6	x]r	x]r	NOUN
ejpam-6834	1712	7	∩	∩	ADJ
ejpam-6834	1712	8	flatn(f	flatn(f	INTJ
ejpam-6834	1712	9	(	(	PUNCT
ejpam-6834	1712	10	γ	γ	NOUN
ejpam-6834	1712	11	)	)	PUNCT
ejpam-6834	1712	12	)	)	PUNCT
ejpam-6834	1713	1	̸=	̸=	NOUN
ejpam-6834	1713	2	∅	∅	NOUN
ejpam-6834	1713	3	,	,	PUNCT
ejpam-6834	1713	4	whence	whence	ADP
ejpam-6834	1713	5	the	the	DET
ejpam-6834	1713	6	upper	upper	ADJ
ejpam-6834	1713	7	inclusion	inclusion	NOUN
ejpam-6834	1713	8	.	.	PUNCT
ejpam-6834	1714	1	t.	t.	PROPN
ejpam-6834	1714	2	fujita	fujita	PROPN
ejpam-6834	1714	3	,	,	PUNCT
ejpam-6834	1714	4	f.smarandache	f.smarandache	NOUN
ejpam-6834	1714	5	/	/	SYM
ejpam-6834	1714	6	eur	eur	PROPN
ejpam-6834	1714	7	.	.	PUNCT
ejpam-6834	1715	1	j.	j.	PROPN
ejpam-6834	1715	2	pure	pure	PROPN
ejpam-6834	1715	3	appl	appl	PROPN
ejpam-6834	1715	4	.	.	PROPN
ejpam-6834	1715	5	math	math	PROPN
ejpam-6834	1715	6	,	,	PUNCT
ejpam-6834	1715	7	18	18	NUM
ejpam-6834	1715	8	(	(	PUNCT
ejpam-6834	1715	9	4	4	NUM
ejpam-6834	1715	10	)	)	PUNCT
ejpam-6834	1715	11	(	(	PUNCT
ejpam-6834	1715	12	2025	2025	NUM
ejpam-6834	1715	13	)	)	PUNCT
ejpam-6834	1715	14	,	,	PUNCT
ejpam-6834	1715	15	6834	6834	NUM
ejpam-6834	1715	16	62	62	NUM
ejpam-6834	1715	17	of	of	ADP
ejpam-6834	1715	18	69	69	NUM
ejpam-6834	1715	19	theorem	theorem	NOUN
ejpam-6834	1715	20	60	60	NUM
ejpam-6834	1715	21	(	(	PUNCT
ejpam-6834	1715	22	functoriality	functoriality	NOUN
ejpam-6834	1715	23	under	under	ADP
ejpam-6834	1715	24	quotients	quotient	NOUN
ejpam-6834	1715	25	)	)	PUNCT
ejpam-6834	1715	26	.	.	PUNCT
ejpam-6834	1716	1	let	let	VERB
ejpam-6834	1716	2	f	f	NOUN
ejpam-6834	1716	3	:	:	PUNCT
ejpam-6834	1716	4	x	x	X
ejpam-6834	1716	5	→	→	SYM
ejpam-6834	1716	6	y	y	X
ejpam-6834	1716	7	be	be	AUX
ejpam-6834	1716	8	a	a	DET
ejpam-6834	1716	9	surjection	surjection	NOUN
ejpam-6834	1716	10	that	that	PRON
ejpam-6834	1716	11	is	be	AUX
ejpam-6834	1716	12	constant	constant	ADJ
ejpam-6834	1716	13	on	on	ADP
ejpam-6834	1716	14	r	r	NOUN
ejpam-6834	1716	15	-	-	PUNCT
ejpam-6834	1716	16	classes	class	NOUN
ejpam-6834	1716	17	(	(	PUNCT
ejpam-6834	1716	18	i.e.	i.e.	X
ejpam-6834	1716	19	,	,	PUNCT
ejpam-6834	1716	20	xrx′	xrx′	ADJ
ejpam-6834	1716	21	⇒	⇒	VERB
ejpam-6834	1716	22	f(x	f(x	PROPN
ejpam-6834	1716	23	)	)	PUNCT
ejpam-6834	1716	24	=	=	SYM
ejpam-6834	1716	25	f(x′	f(x′	PROPN
ejpam-6834	1716	26	)	)	PUNCT
ejpam-6834	1716	27	)	)	PUNCT
ejpam-6834	1716	28	.	.	PUNCT
ejpam-6834	1717	1	let	let	VERB
ejpam-6834	1717	2	s	s	PRON
ejpam-6834	1717	3	be	be	AUX
ejpam-6834	1717	4	the	the	DET
ejpam-6834	1717	5	induced	induced	ADJ
ejpam-6834	1717	6	equivalence	equivalence	NOUN
ejpam-6834	1717	7	on	on	ADP
ejpam-6834	1717	8	y	y	PROPN
ejpam-6834	1717	9	whose	whose	DET
ejpam-6834	1717	10	classes	class	NOUN
ejpam-6834	1717	11	are	be	AUX
ejpam-6834	1717	12	the	the	DET
ejpam-6834	1717	13	images	image	NOUN
ejpam-6834	1717	14	f([x]r	f([x]r	NOUN
ejpam-6834	1717	15	)	)	PUNCT
ejpam-6834	1718	1	(	(	PUNCT
ejpam-6834	1718	2	x	x	PUNCT
ejpam-6834	1718	3	∈	∈	NOUN
ejpam-6834	1718	4	x	x	NOUN
ejpam-6834	1718	5	)	)	PUNCT
ejpam-6834	1718	6	.	.	PUNCT
ejpam-6834	1719	1	define	define	VERB
ejpam-6834	1719	2	the	the	DET
ejpam-6834	1719	3	level	level	NOUN
ejpam-6834	1719	4	–	–	PUNCT
ejpam-6834	1719	5	n	n	CCONJ
ejpam-6834	1719	6	direct	direct	ADJ
ejpam-6834	1719	7	image	image	NOUN
ejpam-6834	1719	8	f	f	PROPN
ejpam-6834	1719	9	(	(	PUNCT
ejpam-6834	1719	10	1	1	X
ejpam-6834	1719	11	)	)	PUNCT
ejpam-6834	1719	12	∗	∗	NOUN
ejpam-6834	1719	13	:	:	PUNCT
ejpam-6834	1719	14	p̃1(x	p̃1(x	NOUN
ejpam-6834	1719	15	)	)	PUNCT
ejpam-6834	1719	16	→	→	PUNCT
ejpam-6834	1719	17	p̃1(y	p̃1(y	PROPN
ejpam-6834	1719	18	)	)	PUNCT
ejpam-6834	1719	19	,	,	PUNCT
ejpam-6834	1719	20	b	b	X
ejpam-6834	1719	21	7→	7→	NUM
ejpam-6834	1720	1	f	f	NOUN
ejpam-6834	1721	1	[	[	X
ejpam-6834	1721	2	b	b	X
ejpam-6834	1721	3	]	]	X
ejpam-6834	1721	4	,	,	PUNCT
ejpam-6834	1721	5	f	f	PROPN
ejpam-6834	1721	6	(	(	PUNCT
ejpam-6834	1721	7	r+1	r+1	PROPN
ejpam-6834	1721	8	)	)	PUNCT
ejpam-6834	1721	9	∗	∗	NOUN
ejpam-6834	1721	10	(	(	PUNCT
ejpam-6834	1721	11	b	b	NOUN
ejpam-6834	1721	12	)	)	PUNCT
ejpam-6834	1721	13	:	:	PUNCT
ejpam-6834	1722	1	=	=	PRON
ejpam-6834	1722	2	{	{	PUNCT
ejpam-6834	1722	3	f	f	X
ejpam-6834	1722	4	(	(	PUNCT
ejpam-6834	1722	5	r	r	NOUN
ejpam-6834	1722	6	)	)	PUNCT
ejpam-6834	1722	7	∗	∗	NOUN
ejpam-6834	1722	8	(	(	PUNCT
ejpam-6834	1722	9	b	b	NOUN
ejpam-6834	1722	10	)	)	PUNCT
ejpam-6834	1723	1	|	|	ADV
ejpam-6834	1724	1	b	b	X
ejpam-6834	1724	2	∈	∈	PROPN
ejpam-6834	1724	3	b	b	PROPN
ejpam-6834	1724	4	}	}	PUNCT
ejpam-6834	1724	5	.	.	PUNCT
ejpam-6834	1725	1	then	then	ADV
ejpam-6834	1725	2	(	(	PUNCT
ejpam-6834	1725	3	f∗f	f∗f	X
ejpam-6834	1725	4	)	)	PUNCT
ejpam-6834	1725	5	(	(	PUNCT
ejpam-6834	1725	6	γ	γ	X
ejpam-6834	1725	7	)	)	PUNCT
ejpam-6834	1725	8	:	:	PUNCT
ejpam-6834	1725	9	=	=	SYM
ejpam-6834	1725	10	f	f	X
ejpam-6834	1725	11	(	(	PUNCT
ejpam-6834	1725	12	n	n	CCONJ
ejpam-6834	1725	13	)	)	PUNCT
ejpam-6834	1725	14	∗	∗	NOUN
ejpam-6834	1725	15	(	(	PUNCT
ejpam-6834	1725	16	f	f	X
ejpam-6834	1725	17	(	(	PUNCT
ejpam-6834	1725	18	γ	γ	NOUN
ejpam-6834	1725	19	)	)	PUNCT
ejpam-6834	1725	20	)	)	PUNCT
ejpam-6834	1726	1	∈	∈	PROPN
ejpam-6834	1726	2	p̃n(y	p̃n(y	PROPN
ejpam-6834	1726	3	)	)	PUNCT
ejpam-6834	1726	4	defines	define	VERB
ejpam-6834	1726	5	an	an	DET
ejpam-6834	1726	6	(	(	PUNCT
ejpam-6834	1726	7	h	h	NOUN
ejpam-6834	1726	8	,	,	PUNCT
ejpam-6834	1726	9	k)-ary	k)-ary	X
ejpam-6834	1726	10	(	(	PUNCT
ejpam-6834	1726	11	m	m	PROPN
ejpam-6834	1726	12	,	,	PUNCT
ejpam-6834	1726	13	n)-superhyperrough	n)-superhyperrough	PUNCT
ejpam-6834	1726	14	set	set	VERB
ejpam-6834	1726	15	on	on	ADP
ejpam-6834	1726	16	y	y	PROPN
ejpam-6834	1726	17	.	.	PUNCT
ejpam-6834	1727	1	moreover	moreover	ADV
ejpam-6834	1727	2	,	,	PUNCT
ejpam-6834	1727	3	flatn	flatn	ADJ
ejpam-6834	1727	4	(	(	PUNCT
ejpam-6834	1727	5	(	(	PUNCT
ejpam-6834	1727	6	f∗f	f∗f	X
ejpam-6834	1727	7	)	)	PUNCT
ejpam-6834	1727	8	(	(	PUNCT
ejpam-6834	1727	9	γ	γ	NOUN
ejpam-6834	1727	10	)	)	PUNCT
ejpam-6834	1727	11	)	)	PUNCT
ejpam-6834	1728	1	=	=	PUNCT
ejpam-6834	1728	2	f(flatn(f	f(flatn(f	INTJ
ejpam-6834	1728	3	(	(	PUNCT
ejpam-6834	1728	4	γ	γ	NOUN
ejpam-6834	1728	5	)	)	PUNCT
ejpam-6834	1728	6	)	)	PUNCT
ejpam-6834	1728	7	)	)	PUNCT
ejpam-6834	1728	8	,	,	PUNCT
ejpam-6834	1728	9	and	and	CCONJ
ejpam-6834	1728	10	for	for	ADP
ejpam-6834	1728	11	rough	rough	ADJ
ejpam-6834	1728	12	approximations	approximation	NOUN
ejpam-6834	1728	13	with	with	ADP
ejpam-6834	1728	14	respect	respect	NOUN
ejpam-6834	1728	15	to	to	ADP
ejpam-6834	1728	16	s	s	PRON
ejpam-6834	1728	17	one	one	NUM
ejpam-6834	1728	18	has	have	VERB
ejpam-6834	1728	19	f	f	PROPN
ejpam-6834	1728	20	(	(	PUNCT
ejpam-6834	1728	21	f	f	X
ejpam-6834	1728	22	(	(	PUNCT
ejpam-6834	1728	23	γ	γ	NOUN
ejpam-6834	1728	24	)	)	PUNCT
ejpam-6834	1728	25	)	)	PUNCT
ejpam-6834	1729	1	⊆	⊆	NUM
ejpam-6834	1729	2	(	(	PUNCT
ejpam-6834	1729	3	f∗f	f∗f	X
ejpam-6834	1729	4	)	)	PUNCT
ejpam-6834	1729	5	(	(	PUNCT
ejpam-6834	1729	6	γ	γ	NOUN
ejpam-6834	1729	7	)	)	PUNCT
ejpam-6834	1729	8	,	,	PUNCT
ejpam-6834	1729	9	f	f	PROPN
ejpam-6834	1729	10	(	(	PUNCT
ejpam-6834	1729	11	f	f	X
ejpam-6834	1729	12	(	(	PUNCT
ejpam-6834	1729	13	γ	γ	NOUN
ejpam-6834	1729	14	)	)	PUNCT
ejpam-6834	1729	15	)	)	PUNCT
ejpam-6834	1730	1	⊆	⊆	NUM
ejpam-6834	1730	2	(	(	PUNCT
ejpam-6834	1730	3	f∗f	f∗f	X
ejpam-6834	1730	4	)	)	PUNCT
ejpam-6834	1730	5	(	(	PUNCT
ejpam-6834	1730	6	γ	γ	NOUN
ejpam-6834	1730	7	)	)	PUNCT
ejpam-6834	1730	8	,	,	PUNCT
ejpam-6834	1730	9	with	with	ADP
ejpam-6834	1730	10	equality	equality	NOUN
ejpam-6834	1730	11	whenever	whenever	SCONJ
ejpam-6834	1730	12	f	f	PROPN
ejpam-6834	1730	13	is	be	AUX
ejpam-6834	1730	14	the	the	DET
ejpam-6834	1730	15	quotient	quotient	NOUN
ejpam-6834	1730	16	map	map	NOUN
ejpam-6834	1730	17	x	x	PUNCT
ejpam-6834	1730	18	→	→	SYM
ejpam-6834	1730	19	x	x	X
ejpam-6834	1730	20	/	/	SYM
ejpam-6834	1730	21	r	r	NOUN
ejpam-6834	1730	22	followed	follow	VERB
ejpam-6834	1730	23	by	by	ADP
ejpam-6834	1730	24	a	a	DET
ejpam-6834	1730	25	bijection	bijection	NOUN
ejpam-6834	1730	26	onto	onto	ADP
ejpam-6834	1730	27	y	y	PROPN
ejpam-6834	1730	28	.	.	PUNCT
ejpam-6834	1731	1	proof	proof	NOUN
ejpam-6834	1731	2	.	.	PUNCT
ejpam-6834	1732	1	the	the	DET
ejpam-6834	1732	2	construction	construction	NOUN
ejpam-6834	1732	3	of	of	ADP
ejpam-6834	1732	4	f	f	PROPN
ejpam-6834	1732	5	(	(	PUNCT
ejpam-6834	1732	6	n	n	CCONJ
ejpam-6834	1732	7	)	)	PUNCT
ejpam-6834	1732	8	∗	∗	NOUN
ejpam-6834	1732	9	preserves	preserve	VERB
ejpam-6834	1732	10	nonemptiness	nonemptiness	NOUN
ejpam-6834	1732	11	by	by	ADP
ejpam-6834	1732	12	induction	induction	NOUN
ejpam-6834	1732	13	on	on	ADP
ejpam-6834	1732	14	n	n	PROPN
ejpam-6834	1732	15	(	(	PUNCT
ejpam-6834	1732	16	surjectivity	surjectivity	NOUN
ejpam-6834	1732	17	gives	give	VERB
ejpam-6834	1732	18	f	f	PROPN
ejpam-6834	1733	1	[	[	X
ejpam-6834	1733	2	b	b	X
ejpam-6834	1733	3	]	]	X
ejpam-6834	1733	4	̸=	̸=	PROPN
ejpam-6834	1733	5	∅	∅	NOUN
ejpam-6834	1733	6	when	when	SCONJ
ejpam-6834	1733	7	b	b	PROPN
ejpam-6834	1733	8	̸=	̸=	PROPN
ejpam-6834	1733	9	∅	∅	NOUN
ejpam-6834	1733	10	;	;	PUNCT
ejpam-6834	1733	11	passing	pass	VERB
ejpam-6834	1733	12	from	from	ADP
ejpam-6834	1733	13	n	n	ADP
ejpam-6834	1733	14	to	to	PART
ejpam-6834	1733	15	n+1	n+1	PROPN
ejpam-6834	1733	16	takes	take	VERB
ejpam-6834	1733	17	nonempty	nonempty	ADJ
ejpam-6834	1733	18	families	family	NOUN
ejpam-6834	1733	19	to	to	ADP
ejpam-6834	1733	20	nonempty	nonempty	ADJ
ejpam-6834	1733	21	families	family	NOUN
ejpam-6834	1733	22	)	)	PUNCT
ejpam-6834	1733	23	.	.	PUNCT
ejpam-6834	1734	1	the	the	DET
ejpam-6834	1734	2	identity	identity	NOUN
ejpam-6834	1734	3	flatn(f	flatn(f	X
ejpam-6834	1734	4	(	(	PUNCT
ejpam-6834	1734	5	n	n	CCONJ
ejpam-6834	1734	6	)	)	PUNCT
ejpam-6834	1734	7	∗	∗	NOUN
ejpam-6834	1734	8	(	(	PUNCT
ejpam-6834	1734	9	w	w	NOUN
ejpam-6834	1734	10	)	)	PUNCT
ejpam-6834	1734	11	)	)	PUNCT
ejpam-6834	1735	1	=	=	SYM
ejpam-6834	1735	2	f(flatn(w	f(flatn(w	NOUN
ejpam-6834	1735	3	)	)	PUNCT
ejpam-6834	1735	4	)	)	PUNCT
ejpam-6834	1735	5	follows	follow	VERB
ejpam-6834	1735	6	directly	directly	ADV
ejpam-6834	1735	7	from	from	ADP
ejpam-6834	1735	8	the	the	DET
ejpam-6834	1735	9	recursive	recursive	ADJ
ejpam-6834	1735	10	definitions	definition	NOUN
ejpam-6834	1735	11	.	.	PUNCT
ejpam-6834	1736	1	let	let	VERB
ejpam-6834	1736	2	wx	wx	NOUN
ejpam-6834	1736	3	:	:	PUNCT
ejpam-6834	1736	4	=	=	SYM
ejpam-6834	1736	5	flatn(f	flatn(f	INTJ
ejpam-6834	1736	6	(	(	PUNCT
ejpam-6834	1736	7	γ	γ	NOUN
ejpam-6834	1736	8	)	)	PUNCT
ejpam-6834	1736	9	)	)	PUNCT
ejpam-6834	1737	1	⊆	⊆	NUM
ejpam-6834	1737	2	x	x	PUNCT
ejpam-6834	1737	3	and	and	CCONJ
ejpam-6834	1737	4	wy	wy	PROPN
ejpam-6834	1737	5	:	:	PUNCT
ejpam-6834	1737	6	=	=	SYM
ejpam-6834	1737	7	f(wx	f(wx	NOUN
ejpam-6834	1737	8	)	)	PUNCT
ejpam-6834	1737	9	=	=	PRON
ejpam-6834	1737	10	flatn((f∗f	flatn((f∗f	NOUN
ejpam-6834	1737	11	)	)	PUNCT
ejpam-6834	1737	12	(	(	PUNCT
ejpam-6834	1737	13	γ	γ	NOUN
ejpam-6834	1737	14	)	)	PUNCT
ejpam-6834	1737	15	)	)	PUNCT
ejpam-6834	1737	16	.	.	PUNCT
ejpam-6834	1738	1	if	if	SCONJ
ejpam-6834	1738	2	x	x	SYM
ejpam-6834	1738	3	∈	∈	PROPN
ejpam-6834	1738	4	f	f	X
ejpam-6834	1738	5	(	(	PUNCT
ejpam-6834	1738	6	γ	γ	PROPN
ejpam-6834	1738	7	)	)	PUNCT
ejpam-6834	1738	8	then	then	ADV
ejpam-6834	1738	9	[	[	X
ejpam-6834	1738	10	x]r	x]r	X
ejpam-6834	1738	11	⊆	⊆	NUM
ejpam-6834	1738	12	wx	wx	NOUN
ejpam-6834	1738	13	.	.	PUNCT
ejpam-6834	1739	1	by	by	ADP
ejpam-6834	1739	2	construction	construction	NOUN
ejpam-6834	1739	3	of	of	ADP
ejpam-6834	1739	4	s	s	NOUN
ejpam-6834	1739	5	,	,	PUNCT
ejpam-6834	1739	6	f([x]r	f([x]r	NOUN
ejpam-6834	1739	7	)	)	PUNCT
ejpam-6834	1740	1	=	=	PUNCT
ejpam-6834	1741	1	[	[	X
ejpam-6834	1741	2	f(x)]s	f(x)]s	INTJ
ejpam-6834	1741	3	⊆	⊆	NUM
ejpam-6834	1741	4	f(wx	f(wx	NOUN
ejpam-6834	1741	5	)	)	PUNCT
ejpam-6834	1741	6	=	=	SYM
ejpam-6834	1741	7	wy	wy	PROPN
ejpam-6834	1741	8	,	,	PUNCT
ejpam-6834	1741	9	so	so	ADV
ejpam-6834	1741	10	f(x	f(x	PROPN
ejpam-6834	1741	11	)	)	PUNCT
ejpam-6834	1741	12	∈	∈	PROPN
ejpam-6834	1741	13	(	(	PUNCT
ejpam-6834	1741	14	f∗f	f∗f	X
ejpam-6834	1741	15	)	)	PUNCT
ejpam-6834	1741	16	(	(	PUNCT
ejpam-6834	1741	17	γ	γ	NOUN
ejpam-6834	1741	18	)	)	PUNCT
ejpam-6834	1741	19	,	,	PUNCT
ejpam-6834	1741	20	proving	prove	VERB
ejpam-6834	1741	21	the	the	DET
ejpam-6834	1741	22	first	first	ADJ
ejpam-6834	1741	23	inclusion	inclusion	NOUN
ejpam-6834	1741	24	.	.	PUNCT
ejpam-6834	1742	1	if	if	SCONJ
ejpam-6834	1742	2	x	x	SYM
ejpam-6834	1742	3	∈	∈	PROPN
ejpam-6834	1742	4	f	f	X
ejpam-6834	1742	5	(	(	PUNCT
ejpam-6834	1742	6	γ	γ	PROPN
ejpam-6834	1742	7	)	)	PUNCT
ejpam-6834	1742	8	then	then	ADV
ejpam-6834	1742	9	[	[	X
ejpam-6834	1742	10	x]r∩wx	x]r∩wx	X
ejpam-6834	1742	11	̸=	̸=	NOUN
ejpam-6834	1742	12	∅	∅	NOUN
ejpam-6834	1742	13	,	,	PUNCT
ejpam-6834	1742	14	hence	hence	ADV
ejpam-6834	1742	15	[	[	X
ejpam-6834	1742	16	f(x)]s	f(x)]s	X
ejpam-6834	1742	17	=	=	NOUN
ejpam-6834	1742	18	f([x]r	f([x]r	NOUN
ejpam-6834	1742	19	)	)	PUNCT
ejpam-6834	1742	20	meets	meet	VERB
ejpam-6834	1742	21	wy	wy	PROPN
ejpam-6834	1742	22	=	=	SYM
ejpam-6834	1742	23	f(wx	f(wx	NUM
ejpam-6834	1742	24	)	)	PUNCT
ejpam-6834	1742	25	,	,	PUNCT
ejpam-6834	1742	26	and	and	CCONJ
ejpam-6834	1742	27	f(x	f(x	PROPN
ejpam-6834	1742	28	)	)	PUNCT
ejpam-6834	1742	29	∈	∈	PROPN
ejpam-6834	1742	30	(	(	PUNCT
ejpam-6834	1742	31	f∗f	f∗f	X
ejpam-6834	1742	32	)	)	PUNCT
ejpam-6834	1742	33	(	(	PUNCT
ejpam-6834	1742	34	γ	γ	NOUN
ejpam-6834	1742	35	)	)	PUNCT
ejpam-6834	1742	36	.	.	PUNCT
ejpam-6834	1743	1	if	if	SCONJ
ejpam-6834	1743	2	,	,	PUNCT
ejpam-6834	1743	3	moreover	moreover	ADV
ejpam-6834	1743	4	,	,	PUNCT
ejpam-6834	1743	5	f	f	PROPN
ejpam-6834	1743	6	is	be	AUX
ejpam-6834	1743	7	the	the	DET
ejpam-6834	1743	8	canonical	canonical	ADJ
ejpam-6834	1743	9	quotient	quotient	NOUN
ejpam-6834	1743	10	collapsing	collapse	VERB
ejpam-6834	1743	11	r	r	NOUN
ejpam-6834	1743	12	-	-	PUNCT
ejpam-6834	1743	13	classes	class	NOUN
ejpam-6834	1743	14	(	(	PUNCT
ejpam-6834	1743	15	up	up	ADP
ejpam-6834	1743	16	to	to	ADP
ejpam-6834	1743	17	bijection	bijection	NOUN
ejpam-6834	1743	18	)	)	PUNCT
ejpam-6834	1743	19	,	,	PUNCT
ejpam-6834	1743	20	these	these	DET
ejpam-6834	1743	21	inclusions	inclusion	NOUN
ejpam-6834	1743	22	are	be	AUX
ejpam-6834	1743	23	equalities	equality	NOUN
ejpam-6834	1743	24	by	by	ADP
ejpam-6834	1743	25	standard	standard	ADJ
ejpam-6834	1743	26	properties	property	NOUN
ejpam-6834	1743	27	of	of	ADP
ejpam-6834	1743	28	rough	rough	ADJ
ejpam-6834	1743	29	sets	set	NOUN
ejpam-6834	1743	30	on	on	ADP
ejpam-6834	1743	31	quotient	quotient	NOUN
ejpam-6834	1743	32	spaces	space	NOUN
ejpam-6834	1743	33	.	.	PUNCT
ejpam-6834	1744	1	5	5	X
ejpam-6834	1744	2	.	.	X
ejpam-6834	1744	3	conclusion	conclusion	NOUN
ejpam-6834	1744	4	in	in	ADP
ejpam-6834	1744	5	this	this	DET
ejpam-6834	1744	6	paper	paper	NOUN
ejpam-6834	1744	7	,	,	PUNCT
ejpam-6834	1744	8	we	we	PRON
ejpam-6834	1744	9	introduced	introduce	VERB
ejpam-6834	1744	10	two	two	NUM
ejpam-6834	1744	11	new	new	ADJ
ejpam-6834	1744	12	and	and	CCONJ
ejpam-6834	1744	13	more	more	ADV
ejpam-6834	1744	14	general	general	ADJ
ejpam-6834	1744	15	frameworks	framework	NOUN
ejpam-6834	1744	16	:	:	PUNCT
ejpam-6834	1744	17	the	the	PRON
ejpam-6834	1744	18	(	(	PUNCT
ejpam-6834	1744	19	m	m	PROPN
ejpam-6834	1744	20	,	,	PUNCT
ejpam-6834	1744	21	n)–superhyperuncertain	n)–superhyperuncertain	AUX
ejpam-6834	1744	22	set	set	VERB
ejpam-6834	1744	23	and	and	CCONJ
ejpam-6834	1744	24	the	the	DET
ejpam-6834	1744	25	(	(	PUNCT
ejpam-6834	1744	26	h	h	NOUN
ejpam-6834	1744	27	,	,	PUNCT
ejpam-6834	1744	28	k)–ary	k)–ary	PROPN
ejpam-6834	1744	29	(	(	PUNCT
ejpam-6834	1744	30	m	m	PROPN
ejpam-6834	1744	31	,	,	PUNCT
ejpam-6834	1744	32	n)–superhyperuncertain	n)–superhyperuncertain	PRON
ejpam-6834	1744	33	set	set	VERB
ejpam-6834	1744	34	.	.	PUNCT
ejpam-6834	1745	1	in	in	ADP
ejpam-6834	1745	2	particular	particular	ADJ
ejpam-6834	1745	3	,	,	PUNCT
ejpam-6834	1745	4	we	we	PRON
ejpam-6834	1745	5	formally	formally	ADV
ejpam-6834	1745	6	defined	define	VERB
ejpam-6834	1745	7	the	the	DET
ejpam-6834	1745	8	concepts	concept	NOUN
ejpam-6834	1745	9	summarized	summarize	VERB
ejpam-6834	1745	10	in	in	ADP
ejpam-6834	1745	11	table	table	NOUN
ejpam-6834	1745	12	6	6	NUM
ejpam-6834	1745	13	.	.	PUNCT
ejpam-6834	1746	1	these	these	DET
ejpam-6834	1746	2	frameworks	framework	NOUN
ejpam-6834	1746	3	are	be	AUX
ejpam-6834	1746	4	expected	expect	VERB
ejpam-6834	1746	5	to	to	PART
ejpam-6834	1746	6	provide	provide	VERB
ejpam-6834	1746	7	a	a	DET
ejpam-6834	1746	8	refined	refined	ADJ
ejpam-6834	1746	9	means	mean	NOUN
ejpam-6834	1746	10	of	of	ADP
ejpam-6834	1746	11	representing	represent	VERB
ejpam-6834	1746	12	real	real	ADJ
ejpam-6834	1746	13	–	–	PUNCT
ejpam-6834	1746	14	world	world	NOUN
ejpam-6834	1746	15	notions	notion	NOUN
ejpam-6834	1746	16	involving	involve	VERB
ejpam-6834	1746	17	hierarchical	hierarchical	ADJ
ejpam-6834	1746	18	uncertainty	uncertainty	NOUN
ejpam-6834	1746	19	.	.	PUNCT
ejpam-6834	1747	1	modern	modern	ADJ
ejpam-6834	1747	2	datasets	dataset	NOUN
ejpam-6834	1747	3	often	often	ADV
ejpam-6834	1747	4	exhibit	exhibit	VERB
ejpam-6834	1747	5	hierarchical	hierarchical	ADJ
ejpam-6834	1747	6	,	,	PUNCT
ejpam-6834	1747	7	multi	multi	ADJ
ejpam-6834	1747	8	–	–	PUNCT
ejpam-6834	1747	9	source	source	NOUN
ejpam-6834	1747	10	uncertainty	uncertainty	NOUN
ejpam-6834	1747	11	with	with	ADP
ejpam-6834	1747	12	interacting	interact	VERB
ejpam-6834	1747	13	attributes	attribute	NOUN
ejpam-6834	1747	14	.	.	PUNCT
ejpam-6834	1748	1	the	the	DET
ejpam-6834	1748	2	(	(	PUNCT
ejpam-6834	1748	3	m	m	PROPN
ejpam-6834	1748	4	,	,	PUNCT
ejpam-6834	1748	5	n	n	CCONJ
ejpam-6834	1748	6	)	)	PUNCT
ejpam-6834	1748	7	and	and	CCONJ
ejpam-6834	1748	8	(	(	PUNCT
ejpam-6834	1748	9	h	h	NOUN
ejpam-6834	1748	10	,	,	PUNCT
ejpam-6834	1748	11	k)–ary	k)–ary	PROPN
ejpam-6834	1748	12	superhyperuncertain	superhyperuncertain	ADJ
ejpam-6834	1748	13	sets	set	NOUN
ejpam-6834	1748	14	unify	unify	VERB
ejpam-6834	1748	15	classical	classical	ADJ
ejpam-6834	1748	16	models	model	NOUN
ejpam-6834	1748	17	,	,	PUNCT
ejpam-6834	1748	18	support	support	VERB
ejpam-6834	1748	19	multi	multi	ADJ
ejpam-6834	1748	20	–	–	NOUN
ejpam-6834	1748	21	ary	ary	ADJ
ejpam-6834	1748	22	composition	composition	NOUN
ejpam-6834	1748	23	,	,	PUNCT
ejpam-6834	1748	24	and	and	CCONJ
ejpam-6834	1748	25	enable	enable	VERB
ejpam-6834	1748	26	provably	provably	ADV
ejpam-6834	1748	27	consistent	consistent	ADJ
ejpam-6834	1748	28	and	and	CCONJ
ejpam-6834	1748	29	scalable	scalable	ADJ
ejpam-6834	1748	30	reasoning	reasoning	NOUN
ejpam-6834	1748	31	across	across	ADP
ejpam-6834	1748	32	multiple	multiple	ADJ
ejpam-6834	1748	33	levels	level	NOUN
ejpam-6834	1748	34	and	and	CCONJ
ejpam-6834	1748	35	modalities	modality	NOUN
ejpam-6834	1748	36	.	.	PUNCT
ejpam-6834	1749	1	future	future	ADJ
ejpam-6834	1749	2	work	work	NOUN
ejpam-6834	1749	3	on	on	ADP
ejpam-6834	1749	4	the	the	DET
ejpam-6834	1749	5	(	(	PUNCT
ejpam-6834	1749	6	m	m	PROPN
ejpam-6834	1749	7	,	,	PUNCT
ejpam-6834	1749	8	n)-superhyperuncertain	n)-superhyperuncertain	ADV
ejpam-6834	1749	9	set	set	VERB
ejpam-6834	1749	10	and	and	CCONJ
ejpam-6834	1749	11	the	the	DET
ejpam-6834	1749	12	(	(	PUNCT
ejpam-6834	1749	13	h	h	NOUN
ejpam-6834	1749	14	,	,	PUNCT
ejpam-6834	1749	15	k)-ary	k)-ary	X
ejpam-6834	1749	16	(	(	PUNCT
ejpam-6834	1749	17	m	m	PROPN
ejpam-6834	1749	18	,	,	PUNCT
ejpam-6834	1749	19	n)-superhyperuncertain	n)-superhyperuncertain	ADV
ejpam-6834	1749	20	set	set	VERB
ejpam-6834	1749	21	includes	include	VERB
ejpam-6834	1749	22	:	:	PUNCT
ejpam-6834	1749	23	t.	t.	PROPN
ejpam-6834	1749	24	fujita	fujita	PROPN
ejpam-6834	1749	25	,	,	PUNCT
ejpam-6834	1749	26	f.smarandache	f.smarandache	NOUN
ejpam-6834	1749	27	/	/	SYM
ejpam-6834	1749	28	eur	eur	PROPN
ejpam-6834	1749	29	.	.	PUNCT
ejpam-6834	1750	1	j.	j.	PROPN
ejpam-6834	1750	2	pure	pure	PROPN
ejpam-6834	1750	3	appl	appl	PROPN
ejpam-6834	1750	4	.	.	PROPN
ejpam-6834	1750	5	math	math	PROPN
ejpam-6834	1750	6	,	,	PUNCT
ejpam-6834	1750	7	18	18	NUM
ejpam-6834	1750	8	(	(	PUNCT
ejpam-6834	1750	9	4	4	NUM
ejpam-6834	1750	10	)	)	PUNCT
ejpam-6834	1750	11	(	(	PUNCT
ejpam-6834	1750	12	2025	2025	NUM
ejpam-6834	1750	13	)	)	PUNCT
ejpam-6834	1750	14	,	,	PUNCT
ejpam-6834	1750	15	6834	6834	NUM
ejpam-6834	1750	16	63	63	NUM
ejpam-6834	1750	17	of	of	ADP
ejpam-6834	1750	18	69	69	NUM
ejpam-6834	1750	19	table	table	NOUN
ejpam-6834	1750	20	6	6	NUM
ejpam-6834	1750	21	:	:	PUNCT
ejpam-6834	1750	22	concise	concise	ADJ
ejpam-6834	1750	23	overview	overview	NOUN
ejpam-6834	1750	24	of	of	ADP
ejpam-6834	1750	25	(	(	PUNCT
ejpam-6834	1750	26	h	h	NOUN
ejpam-6834	1750	27	,	,	PUNCT
ejpam-6834	1750	28	k)-ary	k)-ary	X
ejpam-6834	1750	29	(	(	PUNCT
ejpam-6834	1750	30	m	m	PROPN
ejpam-6834	1750	31	,	,	PUNCT
ejpam-6834	1750	32	n)-superhyperset	n)-superhyperset	NOUN
ejpam-6834	1750	33	families	family	NOUN
ejpam-6834	1750	34	family	family	NOUN
ejpam-6834	1750	35	essence	essence	NOUN
ejpam-6834	1750	36	(	(	PUNCT
ejpam-6834	1750	37	h	h	NOUN
ejpam-6834	1750	38	,	,	PUNCT
ejpam-6834	1750	39	k)-ary	k)-ary	X
ejpam-6834	1750	40	(	(	PUNCT
ejpam-6834	1750	41	m	m	PROPN
ejpam-6834	1750	42	,	,	PUNCT
ejpam-6834	1750	43	n)-superhyperfuzzy	n)-superhyperfuzzy	PUNCT
ejpam-6834	1750	44	set	set	VERB
ejpam-6834	1750	45	maps	map	VERB
ejpam-6834	1750	46	hyper	hyper	NOUN
ejpam-6834	1750	47	-	-	NOUN
ejpam-6834	1750	48	parameters	parameter	NOUN
ejpam-6834	1750	49	to	to	ADP
ejpam-6834	1750	50	fuzzy	fuzzy	ADJ
ejpam-6834	1750	51	degrees	degree	NOUN
ejpam-6834	1750	52	[	[	X
ejpam-6834	1750	53	0	0	NUM
ejpam-6834	1750	54	,	,	PUNCT
ejpam-6834	1750	55	1	1	NUM
ejpam-6834	1750	56	]	]	PUNCT
ejpam-6834	1750	57	.	.	PUNCT
ejpam-6834	1751	1	(	(	PUNCT
ejpam-6834	1751	2	h	h	NOUN
ejpam-6834	1751	3	,	,	PUNCT
ejpam-6834	1751	4	k)-ary	k)-ary	X
ejpam-6834	1751	5	(	(	PUNCT
ejpam-6834	1751	6	m	m	PROPN
ejpam-6834	1751	7	,	,	PUNCT
ejpam-6834	1751	8	n)-superhyperneutrosophic	n)-superhyperneutrosophic	ADJ
ejpam-6834	1751	9	set	set	VERB
ejpam-6834	1751	10	encodes	encodes	PROPN
ejpam-6834	1751	11	triples	triple	NOUN
ejpam-6834	1751	12	(	(	PUNCT
ejpam-6834	1751	13	t	t	PROPN
ejpam-6834	1751	14	,	,	PUNCT
ejpam-6834	1751	15	i	i	PRON
ejpam-6834	1751	16	,	,	PUNCT
ejpam-6834	1751	17	f	f	PROPN
ejpam-6834	1751	18	)	)	PUNCT
ejpam-6834	1751	19	for	for	ADP
ejpam-6834	1751	20	truth	truth	NOUN
ejpam-6834	1751	21	,	,	PUNCT
ejpam-6834	1751	22	indeterminacy	indeterminacy	NOUN
ejpam-6834	1751	23	,	,	PUNCT
ejpam-6834	1751	24	falsity	falsity	NOUN
ejpam-6834	1751	25	.	.	PUNCT
ejpam-6834	1752	1	(	(	PUNCT
ejpam-6834	1752	2	h	h	NOUN
ejpam-6834	1752	3	,	,	PUNCT
ejpam-6834	1752	4	k)-ary	k)-ary	X
ejpam-6834	1752	5	(	(	PUNCT
ejpam-6834	1752	6	m	m	PROPN
ejpam-6834	1752	7	,	,	PUNCT
ejpam-6834	1752	8	n)-superhyperplithogenic	n)-superhyperplithogenic	PUNCT
ejpam-6834	1752	9	set	set	NOUN
ejpam-6834	1752	10	adds	add	VERB
ejpam-6834	1752	11	contradiction	contradiction	NOUN
ejpam-6834	1752	12	function	function	NOUN
ejpam-6834	1752	13	pcf	pcf	PROPN
ejpam-6834	1752	14	to	to	PART
ejpam-6834	1752	15	capture	capture	VERB
ejpam-6834	1752	16	attribute	attribute	NOUN
ejpam-6834	1752	17	conflicts	conflict	NOUN
ejpam-6834	1752	18	.	.	PUNCT
ejpam-6834	1753	1	(	(	PUNCT
ejpam-6834	1753	2	h	h	NOUN
ejpam-6834	1753	3	,	,	PUNCT
ejpam-6834	1753	4	k)-ary	k)-ary	X
ejpam-6834	1753	5	(	(	PUNCT
ejpam-6834	1753	6	m	m	PROPN
ejpam-6834	1753	7	,	,	PUNCT
ejpam-6834	1753	8	n)-superhypersoft	n)-superhypersoft	ADV
ejpam-6834	1753	9	set	set	VERB
ejpam-6834	1753	10	extends	extend	VERB
ejpam-6834	1753	11	soft	soft	ADJ
ejpam-6834	1753	12	sets	set	NOUN
ejpam-6834	1753	13	with	with	ADP
ejpam-6834	1753	14	higher	high	ADJ
ejpam-6834	1753	15	-	-	PUNCT
ejpam-6834	1753	16	order	order	NOUN
ejpam-6834	1753	17	parameters	parameter	NOUN
ejpam-6834	1753	18	and	and	CCONJ
ejpam-6834	1753	19	multioutputs	multioutput	NOUN
ejpam-6834	1753	20	.	.	PUNCT
ejpam-6834	1754	1	(	(	PUNCT
ejpam-6834	1754	2	h	h	NOUN
ejpam-6834	1754	3	,	,	PUNCT
ejpam-6834	1754	4	k)-ary	k)-ary	X
ejpam-6834	1754	5	(	(	PUNCT
ejpam-6834	1754	6	m	m	PROPN
ejpam-6834	1754	7	,	,	PUNCT
ejpam-6834	1754	8	n)-superhyperrough	n)-superhyperrough	PUNCT
ejpam-6834	1754	9	set	set	VERB
ejpam-6834	1754	10	provides	provide	VERB
ejpam-6834	1754	11	hierarchical	hierarchical	ADJ
ejpam-6834	1754	12	lower	low	ADJ
ejpam-6834	1754	13	and	and	CCONJ
ejpam-6834	1754	14	upper	upper	ADJ
ejpam-6834	1754	15	approximations	approximation	NOUN
ejpam-6834	1754	16	.	.	PUNCT
ejpam-6834	1755	1	•	•	NUM
ejpam-6834	1755	2	designing	design	VERB
ejpam-6834	1755	3	efficient	efficient	ADJ
ejpam-6834	1755	4	algorithms	algorithm	NOUN
ejpam-6834	1755	5	for	for	ADP
ejpam-6834	1755	6	constructing	construct	VERB
ejpam-6834	1755	7	and	and	CCONJ
ejpam-6834	1755	8	manipulating	manipulate	VERB
ejpam-6834	1755	9	these	these	DET
ejpam-6834	1755	10	superhyperuncertain	superhyperuncertain	ADJ
ejpam-6834	1755	11	sets	set	NOUN
ejpam-6834	1755	12	;	;	PUNCT
ejpam-6834	1755	13	•	•	ADP
ejpam-6834	1755	14	investigating	investigate	VERB
ejpam-6834	1755	15	in	in	ADP
ejpam-6834	1755	16	detail	detail	NOUN
ejpam-6834	1755	17	the	the	DET
ejpam-6834	1755	18	mathematical	mathematical	ADJ
ejpam-6834	1755	19	properties	property	NOUN
ejpam-6834	1755	20	and	and	CCONJ
ejpam-6834	1755	21	structural	structural	ADJ
ejpam-6834	1755	22	features	feature	NOUN
ejpam-6834	1755	23	of	of	ADP
ejpam-6834	1755	24	the	the	DET
ejpam-6834	1755	25	proposed	propose	VERB
ejpam-6834	1755	26	frameworks	framework	NOUN
ejpam-6834	1755	27	;	;	PUNCT
ejpam-6834	1755	28	•	•	ADP
ejpam-6834	1755	29	exploring	explore	VERB
ejpam-6834	1755	30	potential	potential	ADJ
ejpam-6834	1755	31	applications	application	NOUN
ejpam-6834	1755	32	for	for	ADP
ejpam-6834	1755	33	modeling	model	VERB
ejpam-6834	1755	34	hierarchical	hierarchical	ADJ
ejpam-6834	1755	35	uncertainty	uncertainty	NOUN
ejpam-6834	1755	36	in	in	ADP
ejpam-6834	1755	37	practical	practical	ADJ
ejpam-6834	1755	38	systems	system	NOUN
ejpam-6834	1755	39	.	.	PUNCT
ejpam-6834	1756	1	furthermore	furthermore	ADV
ejpam-6834	1756	2	,	,	PUNCT
ejpam-6834	1756	3	it	it	PRON
ejpam-6834	1756	4	is	be	AUX
ejpam-6834	1756	5	our	our	PRON
ejpam-6834	1756	6	hope	hope	NOUN
ejpam-6834	1756	7	that	that	SCONJ
ejpam-6834	1756	8	the	the	DET
ejpam-6834	1756	9	concepts	concept	NOUN
ejpam-6834	1756	10	presented	present	VERB
ejpam-6834	1756	11	in	in	ADP
ejpam-6834	1756	12	this	this	DET
ejpam-6834	1756	13	work	work	NOUN
ejpam-6834	1756	14	will	will	AUX
ejpam-6834	1756	15	stimulate	stimulate	VERB
ejpam-6834	1756	16	further	further	ADJ
ejpam-6834	1756	17	research	research	NOUN
ejpam-6834	1756	18	into	into	ADP
ejpam-6834	1756	19	their	their	PRON
ejpam-6834	1756	20	applications	application	NOUN
ejpam-6834	1756	21	in	in	ADP
ejpam-6834	1756	22	areas	area	NOUN
ejpam-6834	1756	23	such	such	ADJ
ejpam-6834	1756	24	as	as	ADP
ejpam-6834	1756	25	graphs	graph	NOUN
ejpam-6834	1756	26	,	,	PUNCT
ejpam-6834	1756	27	hyperfunctions	hyperfunction	NOUN
ejpam-6834	1756	28	[	[	X
ejpam-6834	1756	29	70	70	NUM
ejpam-6834	1756	30	,	,	PUNCT
ejpam-6834	1756	31	71	71	NUM
ejpam-6834	1756	32	]	]	PUNCT
ejpam-6834	1756	33	,	,	PUNCT
ejpam-6834	1756	34	hypergraphs	hypergraph	NOUN
ejpam-6834	1756	35	[	[	X
ejpam-6834	1756	36	30	30	NUM
ejpam-6834	1756	37	,	,	PUNCT
ejpam-6834	1756	38	72	72	NUM
ejpam-6834	1756	39	,	,	PUNCT
ejpam-6834	1756	40	73	73	NUM
ejpam-6834	1756	41	]	]	PUNCT
ejpam-6834	1756	42	,	,	PUNCT
ejpam-6834	1756	43	and	and	CCONJ
ejpam-6834	1756	44	superhypergraphs	superhypergraph	VERB
ejpam-6834	1756	45	[	[	X
ejpam-6834	1756	46	32	32	NUM
ejpam-6834	1756	47	,	,	PUNCT
ejpam-6834	1756	48	74	74	NUM
ejpam-6834	1756	49	]	]	PUNCT
ejpam-6834	1756	50	.	.	PUNCT
ejpam-6834	1757	1	acknowledgmeents	acknowledgmeent	NOUN
ejpam-6834	1757	2	we	we	PRON
ejpam-6834	1757	3	wish	wish	VERB
ejpam-6834	1757	4	to	to	PART
ejpam-6834	1757	5	thank	thank	VERB
ejpam-6834	1757	6	everyone	everyone	PRON
ejpam-6834	1757	7	whose	whose	DET
ejpam-6834	1757	8	guidance	guidance	NOUN
ejpam-6834	1757	9	,	,	PUNCT
ejpam-6834	1757	10	ideas	idea	NOUN
ejpam-6834	1757	11	,	,	PUNCT
ejpam-6834	1757	12	and	and	CCONJ
ejpam-6834	1757	13	assistance	assistance	NOUN
ejpam-6834	1757	14	contributed	contribute	VERB
ejpam-6834	1757	15	to	to	ADP
ejpam-6834	1757	16	this	this	DET
ejpam-6834	1757	17	research	research	NOUN
ejpam-6834	1757	18	.	.	PUNCT
ejpam-6834	1758	1	our	our	PRON
ejpam-6834	1758	2	appreciation	appreciation	NOUN
ejpam-6834	1758	3	goes	go	VERB
ejpam-6834	1758	4	to	to	ADP
ejpam-6834	1758	5	the	the	DET
ejpam-6834	1758	6	readers	reader	NOUN
ejpam-6834	1758	7	for	for	ADP
ejpam-6834	1758	8	their	their	PRON
ejpam-6834	1758	9	interest	interest	NOUN
ejpam-6834	1758	10	and	and	CCONJ
ejpam-6834	1758	11	to	to	ADP
ejpam-6834	1758	12	the	the	DET
ejpam-6834	1758	13	scholars	scholar	NOUN
ejpam-6834	1758	14	whose	whose	DET
ejpam-6834	1758	15	publications	publication	NOUN
ejpam-6834	1758	16	provided	provide	VERB
ejpam-6834	1758	17	the	the	DET
ejpam-6834	1758	18	groundwork	groundwork	NOUN
ejpam-6834	1758	19	for	for	ADP
ejpam-6834	1758	20	this	this	DET
ejpam-6834	1758	21	study	study	NOUN
ejpam-6834	1758	22	.	.	PUNCT
ejpam-6834	1759	1	we	we	PRON
ejpam-6834	1759	2	are	be	AUX
ejpam-6834	1759	3	also	also	ADV
ejpam-6834	1759	4	indebted	indebted	ADJ
ejpam-6834	1759	5	to	to	ADP
ejpam-6834	1759	6	the	the	DET
ejpam-6834	1759	7	individuals	individual	NOUN
ejpam-6834	1759	8	and	and	CCONJ
ejpam-6834	1759	9	institutions	institution	NOUN
ejpam-6834	1759	10	that	that	PRON
ejpam-6834	1759	11	supplied	supply	VERB
ejpam-6834	1759	12	the	the	DET
ejpam-6834	1759	13	resources	resource	NOUN
ejpam-6834	1759	14	and	and	CCONJ
ejpam-6834	1759	15	infrastructure	infrastructure	NOUN
ejpam-6834	1759	16	necessary	necessary	ADJ
ejpam-6834	1759	17	for	for	ADP
ejpam-6834	1759	18	completing	complete	VERB
ejpam-6834	1759	19	and	and	CCONJ
ejpam-6834	1759	20	disseminating	disseminate	VERB
ejpam-6834	1759	21	this	this	DET
ejpam-6834	1759	22	paper	paper	NOUN
ejpam-6834	1759	23	.	.	PUNCT
ejpam-6834	1760	1	lastly	lastly	ADV
ejpam-6834	1760	2	,	,	PUNCT
ejpam-6834	1760	3	we	we	PRON
ejpam-6834	1760	4	extend	extend	VERB
ejpam-6834	1760	5	our	our	PRON
ejpam-6834	1760	6	gratitude	gratitude	NOUN
ejpam-6834	1760	7	to	to	ADP
ejpam-6834	1760	8	all	all	PRON
ejpam-6834	1760	9	who	who	PRON
ejpam-6834	1760	10	offered	offer	VERB
ejpam-6834	1760	11	their	their	PRON
ejpam-6834	1760	12	support	support	NOUN
ejpam-6834	1760	13	in	in	ADP
ejpam-6834	1760	14	various	various	ADJ
ejpam-6834	1760	15	capacities	capacity	NOUN
ejpam-6834	1760	16	.	.	PUNCT
ejpam-6834	1761	1	data	datum	NOUN
ejpam-6834	1761	2	availability	availability	NOUN
ejpam-6834	1761	3	this	this	DET
ejpam-6834	1761	4	paper	paper	NOUN
ejpam-6834	1761	5	is	be	AUX
ejpam-6834	1761	6	purely	purely	ADV
ejpam-6834	1761	7	theoretical	theoretical	ADJ
ejpam-6834	1761	8	and	and	CCONJ
ejpam-6834	1761	9	does	do	AUX
ejpam-6834	1761	10	not	not	PART
ejpam-6834	1761	11	involve	involve	VERB
ejpam-6834	1761	12	any	any	DET
ejpam-6834	1761	13	empirical	empirical	ADJ
ejpam-6834	1761	14	data	datum	NOUN
ejpam-6834	1761	15	.	.	PUNCT
ejpam-6834	1762	1	we	we	PRON
ejpam-6834	1762	2	welcome	welcome	VERB
ejpam-6834	1762	3	future	future	ADJ
ejpam-6834	1762	4	empirical	empirical	ADJ
ejpam-6834	1762	5	studies	study	NOUN
ejpam-6834	1762	6	that	that	PRON
ejpam-6834	1762	7	build	build	VERB
ejpam-6834	1762	8	upon	upon	SCONJ
ejpam-6834	1762	9	and	and	CCONJ
ejpam-6834	1762	10	test	test	VERB
ejpam-6834	1762	11	the	the	DET
ejpam-6834	1762	12	concepts	concept	NOUN
ejpam-6834	1762	13	presented	present	VERB
ejpam-6834	1762	14	here	here	ADV
ejpam-6834	1762	15	.	.	PUNCT
ejpam-6834	1763	1	ethical	ethical	ADJ
ejpam-6834	1763	2	approval	approval	NOUN
ejpam-6834	1763	3	as	as	SCONJ
ejpam-6834	1763	4	this	this	DET
ejpam-6834	1763	5	work	work	NOUN
ejpam-6834	1763	6	is	be	AUX
ejpam-6834	1763	7	entirely	entirely	ADV
ejpam-6834	1763	8	conceptual	conceptual	ADJ
ejpam-6834	1763	9	and	and	CCONJ
ejpam-6834	1763	10	involves	involve	VERB
ejpam-6834	1763	11	no	no	DET
ejpam-6834	1763	12	human	human	ADJ
ejpam-6834	1763	13	or	or	CCONJ
ejpam-6834	1763	14	animal	animal	NOUN
ejpam-6834	1763	15	subjects	subject	NOUN
ejpam-6834	1763	16	,	,	PUNCT
ejpam-6834	1763	17	ethical	ethical	ADJ
ejpam-6834	1763	18	approval	approval	NOUN
ejpam-6834	1763	19	was	be	AUX
ejpam-6834	1763	20	not	not	PART
ejpam-6834	1763	21	required	require	VERB
ejpam-6834	1763	22	.	.	PUNCT
ejpam-6834	1764	1	t.	t.	PROPN
ejpam-6834	1764	2	fujita	fujita	PROPN
ejpam-6834	1764	3	,	,	PUNCT
ejpam-6834	1764	4	f.smarandache	f.smarandache	NOUN
ejpam-6834	1764	5	/	/	SYM
ejpam-6834	1764	6	eur	eur	PROPN
ejpam-6834	1764	7	.	.	PUNCT
ejpam-6834	1765	1	j.	j.	PROPN
ejpam-6834	1765	2	pure	pure	PROPN
ejpam-6834	1765	3	appl	appl	PROPN
ejpam-6834	1765	4	.	.	PROPN
ejpam-6834	1765	5	math	math	PROPN
ejpam-6834	1765	6	,	,	PUNCT
ejpam-6834	1765	7	18	18	NUM
ejpam-6834	1765	8	(	(	PUNCT
ejpam-6834	1765	9	4	4	NUM
ejpam-6834	1765	10	)	)	PUNCT
ejpam-6834	1765	11	(	(	PUNCT
ejpam-6834	1765	12	2025	2025	NUM
ejpam-6834	1765	13	)	)	PUNCT
ejpam-6834	1765	14	,	,	PUNCT
ejpam-6834	1765	15	6834	6834	NUM
ejpam-6834	1765	16	64	64	NUM
ejpam-6834	1765	17	of	of	ADP
ejpam-6834	1765	18	69	69	NUM
ejpam-6834	1765	19	conflicts	conflict	NOUN
ejpam-6834	1765	20	of	of	ADP
ejpam-6834	1765	21	interest	interest	NOUN
ejpam-6834	1765	22	the	the	DET
ejpam-6834	1765	23	authors	author	NOUN
ejpam-6834	1765	24	declare	declare	VERB
ejpam-6834	1765	25	no	no	DET
ejpam-6834	1765	26	conflicts	conflict	NOUN
ejpam-6834	1765	27	of	of	ADP
ejpam-6834	1765	28	interest	interest	NOUN
ejpam-6834	1765	29	in	in	ADP
ejpam-6834	1765	30	connection	connection	NOUN
ejpam-6834	1765	31	with	with	ADP
ejpam-6834	1765	32	this	this	DET
ejpam-6834	1765	33	study	study	NOUN
ejpam-6834	1765	34	or	or	CCONJ
ejpam-6834	1765	35	its	its	PRON
ejpam-6834	1765	36	publication	publication	NOUN
ejpam-6834	1765	37	.	.	PUNCT
ejpam-6834	1766	1	funding	fund	VERB
ejpam-6834	1766	2	no	no	DET
ejpam-6834	1766	3	external	external	ADJ
ejpam-6834	1766	4	or	or	CCONJ
ejpam-6834	1766	5	organizational	organizational	ADJ
ejpam-6834	1766	6	funding	funding	NOUN
ejpam-6834	1766	7	supported	support	VERB
ejpam-6834	1766	8	this	this	DET
ejpam-6834	1766	9	work	work	NOUN
ejpam-6834	1766	10	.	.	PUNCT
ejpam-6834	1767	1	research	research	NOUN
ejpam-6834	1767	2	integrity	integrity	NOUN
ejpam-6834	1767	3	the	the	DET
ejpam-6834	1767	4	authors	author	NOUN
ejpam-6834	1767	5	affirm	affirm	VERB
ejpam-6834	1767	6	that	that	SCONJ
ejpam-6834	1767	7	,	,	PUNCT
ejpam-6834	1767	8	to	to	ADP
ejpam-6834	1767	9	the	the	DET
ejpam-6834	1767	10	best	good	ADJ
ejpam-6834	1767	11	of	of	ADP
ejpam-6834	1767	12	their	their	PRON
ejpam-6834	1767	13	knowledge	knowledge	NOUN
ejpam-6834	1767	14	,	,	PUNCT
ejpam-6834	1767	15	this	this	DET
ejpam-6834	1767	16	manuscript	manuscript	NOUN
ejpam-6834	1767	17	represents	represent	VERB
ejpam-6834	1767	18	their	their	PRON
ejpam-6834	1767	19	original	original	ADJ
ejpam-6834	1767	20	research	research	NOUN
ejpam-6834	1767	21	.	.	PUNCT
ejpam-6834	1768	1	it	it	PRON
ejpam-6834	1768	2	has	have	AUX
ejpam-6834	1768	3	not	not	PART
ejpam-6834	1768	4	been	be	AUX
ejpam-6834	1768	5	previously	previously	ADV
ejpam-6834	1768	6	published	publish	VERB
ejpam-6834	1768	7	in	in	ADP
ejpam-6834	1768	8	any	any	DET
ejpam-6834	1768	9	journal	journal	NOUN
ejpam-6834	1768	10	,	,	PUNCT
ejpam-6834	1768	11	nor	nor	CCONJ
ejpam-6834	1768	12	is	be	AUX
ejpam-6834	1768	13	it	it	PRON
ejpam-6834	1768	14	currently	currently	ADV
ejpam-6834	1768	15	being	be	AUX
ejpam-6834	1768	16	considered	consider	VERB
ejpam-6834	1768	17	for	for	ADP
ejpam-6834	1768	18	publication	publication	NOUN
ejpam-6834	1768	19	elsewhere	elsewhere	ADV
ejpam-6834	1768	20	.	.	PUNCT
ejpam-6834	1769	1	disclaimer	disclaimer	NOUN
ejpam-6834	1769	2	on	on	ADP
ejpam-6834	1769	3	computational	computational	ADJ
ejpam-6834	1769	4	tools	tool	NOUN
ejpam-6834	1769	5	no	no	DET
ejpam-6834	1769	6	computer	computer	NOUN
ejpam-6834	1769	7	-	-	PUNCT
ejpam-6834	1769	8	based	base	VERB
ejpam-6834	1769	9	tools	tool	NOUN
ejpam-6834	1769	10	—	—	PUNCT
ejpam-6834	1769	11	such	such	ADJ
ejpam-6834	1769	12	as	as	ADP
ejpam-6834	1769	13	symbolic	symbolic	ADJ
ejpam-6834	1769	14	computation	computation	NOUN
ejpam-6834	1769	15	systems	system	NOUN
ejpam-6834	1769	16	,	,	PUNCT
ejpam-6834	1769	17	automated	automate	VERB
ejpam-6834	1769	18	theorem	theorem	ADJ
ejpam-6834	1769	19	provers	prover	NOUN
ejpam-6834	1769	20	,	,	PUNCT
ejpam-6834	1769	21	or	or	CCONJ
ejpam-6834	1769	22	proof	proof	ADJ
ejpam-6834	1769	23	assistants	assistant	NOUN
ejpam-6834	1769	24	(	(	PUNCT
ejpam-6834	1769	25	e.g.	e.g.	ADV
ejpam-6834	1769	26	,	,	PUNCT
ejpam-6834	1769	27	mathematica	mathematica	PROPN
ejpam-6834	1769	28	,	,	PUNCT
ejpam-6834	1769	29	sagemath	sagemath	NOUN
ejpam-6834	1769	30	,	,	PUNCT
ejpam-6834	1769	31	coq)—were	coq)—were	X
ejpam-6834	1769	32	employed	employ	VERB
ejpam-6834	1769	33	in	in	ADP
ejpam-6834	1769	34	the	the	DET
ejpam-6834	1769	35	development	development	NOUN
ejpam-6834	1769	36	,	,	PUNCT
ejpam-6834	1769	37	analysis	analysis	NOUN
ejpam-6834	1769	38	,	,	PUNCT
ejpam-6834	1769	39	or	or	CCONJ
ejpam-6834	1769	40	verification	verification	NOUN
ejpam-6834	1769	41	of	of	ADP
ejpam-6834	1769	42	the	the	DET
ejpam-6834	1769	43	results	result	NOUN
ejpam-6834	1769	44	contained	contain	VERB
ejpam-6834	1769	45	in	in	ADP
ejpam-6834	1769	46	this	this	DET
ejpam-6834	1769	47	paper	paper	NOUN
ejpam-6834	1769	48	.	.	PUNCT
ejpam-6834	1770	1	all	all	DET
ejpam-6834	1770	2	derivations	derivation	NOUN
ejpam-6834	1770	3	and	and	CCONJ
ejpam-6834	1770	4	proofs	proof	NOUN
ejpam-6834	1770	5	were	be	AUX
ejpam-6834	1770	6	conducted	conduct	VERB
ejpam-6834	1770	7	manually	manually	ADV
ejpam-6834	1770	8	through	through	ADP
ejpam-6834	1770	9	analytical	analytical	ADJ
ejpam-6834	1770	10	methods	method	NOUN
ejpam-6834	1770	11	by	by	ADP
ejpam-6834	1770	12	the	the	DET
ejpam-6834	1770	13	authors	author	NOUN
ejpam-6834	1770	14	.	.	PUNCT
ejpam-6834	1771	1	code	code	NOUN
ejpam-6834	1771	2	availability	availability	NOUN
ejpam-6834	1771	3	no	no	DET
ejpam-6834	1771	4	code	code	NOUN
ejpam-6834	1771	5	or	or	CCONJ
ejpam-6834	1771	6	software	software	NOUN
ejpam-6834	1771	7	was	be	AUX
ejpam-6834	1771	8	developed	develop	VERB
ejpam-6834	1771	9	for	for	ADP
ejpam-6834	1771	10	this	this	DET
ejpam-6834	1771	11	study	study	NOUN
ejpam-6834	1771	12	.	.	PUNCT
ejpam-6834	1772	1	clinical	clinical	ADJ
ejpam-6834	1772	2	trial	trial	NOUN
ejpam-6834	1772	3	this	this	DET
ejpam-6834	1772	4	study	study	NOUN
ejpam-6834	1772	5	did	do	AUX
ejpam-6834	1772	6	not	not	PART
ejpam-6834	1772	7	involve	involve	VERB
ejpam-6834	1772	8	any	any	DET
ejpam-6834	1772	9	clinical	clinical	ADJ
ejpam-6834	1772	10	trials	trial	NOUN
ejpam-6834	1772	11	.	.	PUNCT
ejpam-6834	1773	1	consent	consent	NOUN
ejpam-6834	1773	2	to	to	PART
ejpam-6834	1773	3	participate	participate	VERB
ejpam-6834	1773	4	not	not	PART
ejpam-6834	1773	5	applicable	applicable	ADJ
ejpam-6834	1773	6	.	.	PUNCT
ejpam-6834	1774	1	disclaimer	disclaimer	NOUN
ejpam-6834	1774	2	on	on	ADP
ejpam-6834	1774	3	scope	scope	NOUN
ejpam-6834	1774	4	and	and	CCONJ
ejpam-6834	1774	5	accuracy	accuracy	NOUN
ejpam-6834	1774	6	the	the	DET
ejpam-6834	1774	7	theoretical	theoretical	ADJ
ejpam-6834	1774	8	models	model	NOUN
ejpam-6834	1774	9	and	and	CCONJ
ejpam-6834	1774	10	concepts	concept	NOUN
ejpam-6834	1774	11	proposed	propose	VERB
ejpam-6834	1774	12	in	in	ADP
ejpam-6834	1774	13	this	this	DET
ejpam-6834	1774	14	manuscript	manuscript	NOUN
ejpam-6834	1774	15	have	have	AUX
ejpam-6834	1774	16	not	not	PART
ejpam-6834	1774	17	yet	yet	ADV
ejpam-6834	1774	18	undergone	undergo	VERB
ejpam-6834	1774	19	empirical	empirical	ADJ
ejpam-6834	1774	20	testing	testing	NOUN
ejpam-6834	1774	21	or	or	CCONJ
ejpam-6834	1774	22	practical	practical	ADJ
ejpam-6834	1774	23	deployment	deployment	NOUN
ejpam-6834	1774	24	.	.	PUNCT
ejpam-6834	1775	1	future	future	ADJ
ejpam-6834	1775	2	work	work	NOUN
ejpam-6834	1775	3	may	may	AUX
ejpam-6834	1775	4	investigate	investigate	VERB
ejpam-6834	1775	5	their	their	PRON
ejpam-6834	1775	6	utility	utility	NOUN
ejpam-6834	1775	7	in	in	ADP
ejpam-6834	1775	8	applied	applied	ADJ
ejpam-6834	1775	9	or	or	CCONJ
ejpam-6834	1775	10	experimental	experimental	ADJ
ejpam-6834	1775	11	contexts	context	NOUN
ejpam-6834	1775	12	.	.	PUNCT
ejpam-6834	1776	1	while	while	SCONJ
ejpam-6834	1776	2	the	the	DET
ejpam-6834	1776	3	authors	author	NOUN
ejpam-6834	1776	4	have	have	AUX
ejpam-6834	1776	5	taken	take	VERB
ejpam-6834	1776	6	care	care	NOUN
ejpam-6834	1776	7	to	to	PART
ejpam-6834	1776	8	maintain	maintain	VERB
ejpam-6834	1776	9	accuracy	accuracy	NOUN
ejpam-6834	1776	10	and	and	CCONJ
ejpam-6834	1776	11	provide	provide	VERB
ejpam-6834	1776	12	appropriate	appropriate	ADJ
ejpam-6834	1776	13	citations	citation	NOUN
ejpam-6834	1776	14	,	,	PUNCT
ejpam-6834	1776	15	inadvertent	inadvertent	ADJ
ejpam-6834	1776	16	errors	error	NOUN
ejpam-6834	1776	17	or	or	CCONJ
ejpam-6834	1776	18	omissions	omission	NOUN
ejpam-6834	1776	19	may	may	AUX
ejpam-6834	1776	20	remain	remain	VERB
ejpam-6834	1776	21	.	.	PUNCT
ejpam-6834	1777	1	readers	reader	NOUN
ejpam-6834	1777	2	are	be	AUX
ejpam-6834	1777	3	encouraged	encourage	VERB
ejpam-6834	1777	4	to	to	PART
ejpam-6834	1777	5	consult	consult	VERB
ejpam-6834	1777	6	original	original	ADJ
ejpam-6834	1777	7	references	reference	NOUN
ejpam-6834	1777	8	for	for	ADP
ejpam-6834	1777	9	confirmation	confirmation	NOUN
ejpam-6834	1777	10	and	and	CCONJ
ejpam-6834	1777	11	further	further	ADJ
ejpam-6834	1777	12	study	study	NOUN
ejpam-6834	1777	13	.	.	PUNCT
ejpam-6834	1778	1	the	the	DET
ejpam-6834	1778	2	authors	author	NOUN
ejpam-6834	1778	3	assert	assert	VERB
ejpam-6834	1778	4	that	that	SCONJ
ejpam-6834	1778	5	all	all	DET
ejpam-6834	1778	6	mathematical	mathematical	ADJ
ejpam-6834	1778	7	results	result	NOUN
ejpam-6834	1778	8	and	and	CCONJ
ejpam-6834	1778	9	justifications	justification	NOUN
ejpam-6834	1778	10	included	include	VERB
ejpam-6834	1778	11	in	in	ADP
ejpam-6834	1778	12	this	this	DET
ejpam-6834	1778	13	work	work	NOUN
ejpam-6834	1778	14	have	have	AUX
ejpam-6834	1778	15	been	be	AUX
ejpam-6834	1778	16	carefully	carefully	ADV
ejpam-6834	1778	17	reviewed	review	VERB
ejpam-6834	1778	18	and	and	CCONJ
ejpam-6834	1778	19	are	be	AUX
ejpam-6834	1778	20	believed	believe	VERB
ejpam-6834	1778	21	to	to	PART
ejpam-6834	1778	22	be	be	AUX
ejpam-6834	1778	23	correct	correct	ADJ
ejpam-6834	1778	24	.	.	PUNCT
ejpam-6834	1779	1	should	should	AUX
ejpam-6834	1779	2	any	any	DET
ejpam-6834	1779	3	inaccuracies	inaccuracy	NOUN
ejpam-6834	1779	4	t.	t.	PROPN
ejpam-6834	1779	5	fujita	fujita	PROPN
ejpam-6834	1779	6	,	,	PUNCT
ejpam-6834	1779	7	f.smarandache	f.smarandache	NOUN
ejpam-6834	1779	8	/	/	SYM
ejpam-6834	1779	9	eur	eur	PROPN
ejpam-6834	1779	10	.	.	PUNCT
ejpam-6834	1780	1	j.	j.	PROPN
ejpam-6834	1780	2	pure	pure	PROPN
ejpam-6834	1780	3	appl	appl	PROPN
ejpam-6834	1780	4	.	.	PROPN
ejpam-6834	1780	5	math	math	PROPN
ejpam-6834	1780	6	,	,	PUNCT
ejpam-6834	1780	7	18	18	NUM
ejpam-6834	1780	8	(	(	PUNCT
ejpam-6834	1780	9	4	4	NUM
ejpam-6834	1780	10	)	)	PUNCT
ejpam-6834	1780	11	(	(	PUNCT
ejpam-6834	1780	12	2025	2025	NUM
ejpam-6834	1780	13	)	)	PUNCT
ejpam-6834	1780	14	,	,	PUNCT
ejpam-6834	1780	15	6834	6834	NUM
ejpam-6834	1780	16	65	65	NUM
ejpam-6834	1780	17	of	of	ADP
ejpam-6834	1780	18	69	69	NUM
ejpam-6834	1780	19	or	or	CCONJ
ejpam-6834	1780	20	ambiguities	ambiguity	NOUN
ejpam-6834	1780	21	be	be	AUX
ejpam-6834	1780	22	discovered	discover	VERB
ejpam-6834	1780	23	,	,	PUNCT
ejpam-6834	1780	24	the	the	DET
ejpam-6834	1780	25	authors	author	NOUN
ejpam-6834	1780	26	welcome	welcome	VERB
ejpam-6834	1780	27	constructive	constructive	ADJ
ejpam-6834	1780	28	feedback	feedback	NOUN
ejpam-6834	1780	29	and	and	CCONJ
ejpam-6834	1780	30	will	will	AUX
ejpam-6834	1780	31	provide	provide	VERB
ejpam-6834	1780	32	clarification	clarification	NOUN
ejpam-6834	1780	33	upon	upon	SCONJ
ejpam-6834	1780	34	request	request	NOUN
ejpam-6834	1780	35	.	.	PUNCT
ejpam-6834	1781	1	the	the	DET
ejpam-6834	1781	2	conclusions	conclusion	NOUN
ejpam-6834	1781	3	presented	present	VERB
ejpam-6834	1781	4	are	be	AUX
ejpam-6834	1781	5	valid	valid	ADJ
ejpam-6834	1781	6	only	only	ADV
ejpam-6834	1781	7	within	within	ADP
ejpam-6834	1781	8	the	the	DET
ejpam-6834	1781	9	specific	specific	ADJ
ejpam-6834	1781	10	theoretical	theoretical	ADJ
ejpam-6834	1781	11	framework	framework	NOUN
ejpam-6834	1781	12	and	and	CCONJ
ejpam-6834	1781	13	assumptions	assumption	NOUN
ejpam-6834	1781	14	described	describe	VERB
ejpam-6834	1781	15	in	in	ADP
ejpam-6834	1781	16	the	the	DET
ejpam-6834	1781	17	text	text	NOUN
ejpam-6834	1781	18	.	.	PUNCT
ejpam-6834	1782	1	generalizing	generalize	VERB
ejpam-6834	1782	2	these	these	DET
ejpam-6834	1782	3	results	result	NOUN
ejpam-6834	1782	4	to	to	ADP
ejpam-6834	1782	5	other	other	ADJ
ejpam-6834	1782	6	mathematical	mathematical	ADJ
ejpam-6834	1782	7	contexts	contexts	NOUN
ejpam-6834	1782	8	may	may	AUX
ejpam-6834	1782	9	require	require	VERB
ejpam-6834	1782	10	further	further	ADJ
ejpam-6834	1782	11	investigation	investigation	NOUN
ejpam-6834	1782	12	.	.	PUNCT
ejpam-6834	1783	1	all	all	DET
ejpam-6834	1783	2	opinions	opinion	NOUN
ejpam-6834	1783	3	and	and	CCONJ
ejpam-6834	1783	4	interpretations	interpretation	NOUN
ejpam-6834	1783	5	expressed	express	VERB
ejpam-6834	1783	6	herein	herein	NOUN
ejpam-6834	1783	7	are	be	AUX
ejpam-6834	1783	8	solely	solely	ADV
ejpam-6834	1783	9	those	those	PRON
ejpam-6834	1783	10	of	of	ADP
ejpam-6834	1783	11	the	the	DET
ejpam-6834	1783	12	authors	author	NOUN
ejpam-6834	1783	13	and	and	CCONJ
ejpam-6834	1783	14	do	do	AUX
ejpam-6834	1783	15	not	not	PART
ejpam-6834	1783	16	necessarily	necessarily	ADV
ejpam-6834	1783	17	reflect	reflect	VERB
ejpam-6834	1783	18	the	the	DET
ejpam-6834	1783	19	views	view	NOUN
ejpam-6834	1783	20	of	of	ADP
ejpam-6834	1783	21	their	their	PRON
ejpam-6834	1783	22	respective	respective	ADJ
ejpam-6834	1783	23	institutions	institution	NOUN
ejpam-6834	1783	24	.	.	PUNCT
ejpam-6834	1784	1	use	use	NOUN
ejpam-6834	1784	2	of	of	ADP
ejpam-6834	1784	3	generative	generative	ADJ
ejpam-6834	1784	4	ai	ai	NOUN
ejpam-6834	1784	5	and	and	CCONJ
ejpam-6834	1784	6	ai	ai	ADJ
ejpam-6834	1784	7	-	-	PUNCT
ejpam-6834	1784	8	assisted	assist	VERB
ejpam-6834	1784	9	tools	tool	NOUN
ejpam-6834	1784	10	i	i	PRON
ejpam-6834	1784	11	use	use	VERB
ejpam-6834	1784	12	generative	generative	ADJ
ejpam-6834	1784	13	ai	ai	NOUN
ejpam-6834	1784	14	and	and	CCONJ
ejpam-6834	1784	15	ai	ai	ADJ
ejpam-6834	1784	16	-	-	PUNCT
ejpam-6834	1784	17	assisted	assist	VERB
ejpam-6834	1784	18	tools	tool	NOUN
ejpam-6834	1784	19	for	for	ADP
ejpam-6834	1784	20	tasks	task	NOUN
ejpam-6834	1784	21	such	such	ADJ
ejpam-6834	1784	22	as	as	ADP
ejpam-6834	1784	23	english	english	ADJ
ejpam-6834	1784	24	grammar	grammar	NOUN
ejpam-6834	1784	25	checking	checking	NOUN
ejpam-6834	1784	26	,	,	PUNCT
ejpam-6834	1784	27	and	and	CCONJ
ejpam-6834	1784	28	i	i	PRON
ejpam-6834	1784	29	do	do	AUX
ejpam-6834	1784	30	not	not	PART
ejpam-6834	1784	31	employ	employ	VERB
ejpam-6834	1784	32	them	they	PRON
ejpam-6834	1784	33	in	in	ADP
ejpam-6834	1784	34	any	any	DET
ejpam-6834	1784	35	way	way	NOUN
ejpam-6834	1784	36	that	that	PRON
ejpam-6834	1784	37	violates	violate	VERB
ejpam-6834	1784	38	ethical	ethical	ADJ
ejpam-6834	1784	39	standards	standard	NOUN
ejpam-6834	1784	40	.	.	PUNCT
ejpam-6834	1785	1	consent	consent	NOUN
ejpam-6834	1785	2	to	to	PART
ejpam-6834	1785	3	publish	publish	VERB
ejpam-6834	1785	4	all	all	DET
ejpam-6834	1785	5	authors	author	NOUN
ejpam-6834	1785	6	have	have	AUX
ejpam-6834	1785	7	given	give	VERB
ejpam-6834	1785	8	their	their	PRON
ejpam-6834	1785	9	consent	consent	NOUN
ejpam-6834	1785	10	for	for	ADP
ejpam-6834	1785	11	submission	submission	NOUN
ejpam-6834	1785	12	of	of	ADP
ejpam-6834	1785	13	this	this	DET
ejpam-6834	1785	14	manuscript	manuscript	NOUN
ejpam-6834	1785	15	to	to	ADP
ejpam-6834	1785	16	the	the	DET
ejpam-6834	1785	17	journal	journal	NOUN
ejpam-6834	1785	18	.	.	PUNCT
ejpam-6834	1786	1	references	reference	NOUN
ejpam-6834	1786	2	[	[	X
ejpam-6834	1786	3	1	1	NUM
ejpam-6834	1786	4	]	]	PUNCT
ejpam-6834	1786	5	takaaki	takaaki	NOUN
ejpam-6834	1786	6	fujita	fujita	NOUN
ejpam-6834	1786	7	.	.	PUNCT
ejpam-6834	1787	1	advancing	advance	VERB
ejpam-6834	1787	2	uncertain	uncertain	ADJ
ejpam-6834	1787	3	combinatorics	combinatoric	NOUN
ejpam-6834	1787	4	through	through	ADP
ejpam-6834	1787	5	graphization	graphization	NOUN
ejpam-6834	1787	6	,	,	PUNCT
ejpam-6834	1787	7	hyperization	hyperization	NOUN
ejpam-6834	1787	8	,	,	PUNCT
ejpam-6834	1787	9	and	and	CCONJ
ejpam-6834	1787	10	uncertainization	uncertainization	NOUN
ejpam-6834	1787	11	:	:	PUNCT
ejpam-6834	1787	12	fuzzy	fuzzy	ADJ
ejpam-6834	1787	13	,	,	PUNCT
ejpam-6834	1787	14	neutrosophic	neutrosophic	ADJ
ejpam-6834	1787	15	,	,	PUNCT
ejpam-6834	1787	16	soft	soft	ADJ
ejpam-6834	1787	17	,	,	PUNCT
ejpam-6834	1787	18	rough	rough	ADJ
ejpam-6834	1787	19	,	,	PUNCT
ejpam-6834	1787	20	and	and	CCONJ
ejpam-6834	1787	21	beyond	beyond	ADP
ejpam-6834	1787	22	.	.	PUNCT
ejpam-6834	1788	1	biblio	biblio	PROPN
ejpam-6834	1788	2	publishing	publishing	PROPN
ejpam-6834	1788	3	,	,	PUNCT
ejpam-6834	1788	4	2025	2025	NUM
ejpam-6834	1788	5	.	.	PUNCT
ejpam-6834	1789	1	[	[	X
ejpam-6834	1789	2	2	2	NUM
ejpam-6834	1789	3	]	]	PUNCT
ejpam-6834	1789	4	florentin	florentin	PROPN
ejpam-6834	1789	5	smarandache	smarandache	PROPN
ejpam-6834	1789	6	.	.	PUNCT
ejpam-6834	1790	1	hyperuncertain	hyperuncertain	PROPN
ejpam-6834	1790	2	,	,	PUNCT
ejpam-6834	1790	3	superuncertain	superuncertain	VERB
ejpam-6834	1790	4	,	,	PUNCT
ejpam-6834	1790	5	and	and	CCONJ
ejpam-6834	1790	6	superhyperuncertain	superhyperuncertain	ADJ
ejpam-6834	1790	7	sets	set	NOUN
ejpam-6834	1790	8	/	/	SYM
ejpam-6834	1790	9	logics	logic	NOUN
ejpam-6834	1790	10	/	/	SYM
ejpam-6834	1790	11	probabilities	probability	NOUN
ejpam-6834	1790	12	/	/	SYM
ejpam-6834	1790	13	statistics	statistic	NOUN
ejpam-6834	1790	14	.	.	PUNCT
ejpam-6834	1791	1	critical	critical	ADJ
ejpam-6834	1791	2	review	review	PROPN
ejpam-6834	1791	3	,	,	PUNCT
ejpam-6834	1791	4	xiv	xiv	PROPN
ejpam-6834	1791	5	,	,	PUNCT
ejpam-6834	1791	6	2017	2017	NUM
ejpam-6834	1791	7	.	.	PUNCT
ejpam-6834	1792	1	[	[	X
ejpam-6834	1792	2	3	3	X
ejpam-6834	1792	3	]	]	PUNCT
ejpam-6834	1792	4	thomas	thomas	PROPN
ejpam-6834	1792	5	jech	jech	PROPN
ejpam-6834	1792	6	.	.	PUNCT
ejpam-6834	1793	1	set	set	PROPN
ejpam-6834	1793	2	theory	theory	NOUN
ejpam-6834	1793	3	:	:	PUNCT
ejpam-6834	1793	4	the	the	DET
ejpam-6834	1793	5	third	third	ADJ
ejpam-6834	1793	6	millennium	millennium	PROPN
ejpam-6834	1793	7	edition	edition	NOUN
ejpam-6834	1793	8	,	,	PUNCT
ejpam-6834	1793	9	revised	revise	VERB
ejpam-6834	1793	10	and	and	CCONJ
ejpam-6834	1793	11	expanded	expand	VERB
ejpam-6834	1793	12	.	.	PUNCT
ejpam-6834	1794	1	springer	springer	NOUN
ejpam-6834	1794	2	,	,	PUNCT
ejpam-6834	1794	3	2003	2003	NUM
ejpam-6834	1794	4	.	.	PUNCT
ejpam-6834	1795	1	[	[	X
ejpam-6834	1795	2	4	4	NUM
ejpam-6834	1795	3	]	]	X
ejpam-6834	1795	4	takaaki	takaaki	NOUN
ejpam-6834	1795	5	fujita	fujita	NOUN
ejpam-6834	1795	6	and	and	CCONJ
ejpam-6834	1795	7	florentin	florentin	PROPN
ejpam-6834	1795	8	smarandache	smarandache	PROPN
ejpam-6834	1795	9	.	.	PUNCT
ejpam-6834	1796	1	a	a	DET
ejpam-6834	1796	2	unified	unify	VERB
ejpam-6834	1796	3	framework	framework	NOUN
ejpam-6834	1796	4	for	for	ADP
ejpam-6834	1796	5	u	u	NOUN
ejpam-6834	1796	6	-	-	NOUN
ejpam-6834	1796	7	structures	structure	NOUN
ejpam-6834	1796	8	and	and	CCONJ
ejpam-6834	1796	9	functorial	functorial	NOUN
ejpam-6834	1796	10	structure	structure	NOUN
ejpam-6834	1796	11	:	:	PUNCT
ejpam-6834	1796	12	managing	manage	VERB
ejpam-6834	1796	13	super	super	ADJ
ejpam-6834	1796	14	,	,	PUNCT
ejpam-6834	1796	15	hyper	hyper	ADJ
ejpam-6834	1796	16	,	,	PUNCT
ejpam-6834	1796	17	superhyper	superhyper	NOUN
ejpam-6834	1796	18	,	,	PUNCT
ejpam-6834	1796	19	tree	tree	NOUN
ejpam-6834	1796	20	,	,	PUNCT
ejpam-6834	1796	21	and	and	CCONJ
ejpam-6834	1796	22	forest	forest	NOUN
ejpam-6834	1796	23	uncertain	uncertain	ADJ
ejpam-6834	1796	24	over	over	ADP
ejpam-6834	1796	25	/	/	SYM
ejpam-6834	1796	26	under	under	ADP
ejpam-6834	1796	27	/	/	PUNCT
ejpam-6834	1796	28	off	off	ADP
ejpam-6834	1796	29	models	model	NOUN
ejpam-6834	1796	30	.	.	PUNCT
ejpam-6834	1797	1	neutrosophic	neutrosophic	ADJ
ejpam-6834	1797	2	sets	set	NOUN
ejpam-6834	1797	3	and	and	CCONJ
ejpam-6834	1797	4	systems	system	NOUN
ejpam-6834	1797	5	,	,	PUNCT
ejpam-6834	1797	6	91:337–380	91:337–380	PROPN
ejpam-6834	1797	7	,	,	PUNCT
ejpam-6834	1797	8	2025	2025	NUM
ejpam-6834	1797	9	.	.	PUNCT
ejpam-6834	1798	1	[	[	X
ejpam-6834	1798	2	5	5	NUM
ejpam-6834	1798	3	]	]	PUNCT
ejpam-6834	1798	4	lotfi	lotfi	X
ejpam-6834	1798	5	a	a	DET
ejpam-6834	1798	6	zadeh	zadeh	PROPN
ejpam-6834	1798	7	.	.	PUNCT
ejpam-6834	1798	8	fuzzy	fuzzy	ADJ
ejpam-6834	1798	9	sets	set	NOUN
ejpam-6834	1798	10	.	.	PUNCT
ejpam-6834	1799	1	information	information	NOUN
ejpam-6834	1799	2	and	and	CCONJ
ejpam-6834	1799	3	control	control	NOUN
ejpam-6834	1799	4	,	,	PUNCT
ejpam-6834	1799	5	8(3):338–353	8(3):338–353	NUM
ejpam-6834	1799	6	,	,	PUNCT
ejpam-6834	1799	7	1965	1965	NUM
ejpam-6834	1799	8	.	.	PUNCT
ejpam-6834	1800	1	[	[	X
ejpam-6834	1800	2	6	6	NUM
ejpam-6834	1800	3	]	]	PUNCT
ejpam-6834	1800	4	krassimir	krassimir	PROPN
ejpam-6834	1800	5	t	t	PROPN
ejpam-6834	1800	6	atanassov	atanassov	NOUN
ejpam-6834	1800	7	.	.	PUNCT
ejpam-6834	1801	1	on	on	ADP
ejpam-6834	1801	2	intuitionistic	intuitionistic	ADJ
ejpam-6834	1801	3	fuzzy	fuzzy	ADJ
ejpam-6834	1801	4	sets	set	NOUN
ejpam-6834	1801	5	theory	theory	NOUN
ejpam-6834	1801	6	,	,	PUNCT
ejpam-6834	1801	7	volume	volume	NOUN
ejpam-6834	1801	8	283	283	NUM
ejpam-6834	1801	9	.	.	PUNCT
ejpam-6834	1802	1	springer	springer	NOUN
ejpam-6834	1802	2	,	,	PUNCT
ejpam-6834	1802	3	2012	2012	NUM
ejpam-6834	1802	4	.	.	PUNCT
ejpam-6834	1803	1	[	[	X
ejpam-6834	1803	2	7	7	NUM
ejpam-6834	1803	3	]	]	SYM
ejpam-6834	1803	4	w	w	NOUN
ejpam-6834	1803	5	-	-	PUNCT
ejpam-6834	1803	6	l	l	NOUN
ejpam-6834	1803	7	gau	gau	NOUN
ejpam-6834	1803	8	and	and	CCONJ
ejpam-6834	1803	9	daniel	daniel	PROPN
ejpam-6834	1803	10	j	j	PROPN
ejpam-6834	1803	11	buehrer	buehrer	PROPN
ejpam-6834	1803	12	.	.	PUNCT
ejpam-6834	1804	1	vague	vague	ADJ
ejpam-6834	1804	2	sets	set	NOUN
ejpam-6834	1804	3	.	.	PUNCT
ejpam-6834	1805	1	ieee	ieee	NOUN
ejpam-6834	1805	2	transactions	transaction	NOUN
ejpam-6834	1805	3	on	on	ADP
ejpam-6834	1805	4	systems	system	NOUN
ejpam-6834	1805	5	,	,	PUNCT
ejpam-6834	1805	6	man	man	NOUN
ejpam-6834	1805	7	,	,	PUNCT
ejpam-6834	1805	8	and	and	CCONJ
ejpam-6834	1805	9	cybernetics	cybernetic	NOUN
ejpam-6834	1805	10	,	,	PUNCT
ejpam-6834	1805	11	23(2):610–614	23(2):610–614	NUM
ejpam-6834	1805	12	,	,	PUNCT
ejpam-6834	1805	13	1993	1993	NUM
ejpam-6834	1805	14	.	.	PUNCT
ejpam-6834	1806	1	[	[	X
ejpam-6834	1806	2	8	8	NUM
ejpam-6834	1806	3	]	]	PUNCT
ejpam-6834	1806	4	pradip	pradip	NOUN
ejpam-6834	1806	5	kumar	kumar	PROPN
ejpam-6834	1806	6	maji	maji	PROPN
ejpam-6834	1806	7	,	,	PUNCT
ejpam-6834	1806	8	ranjit	ranjit	PROPN
ejpam-6834	1806	9	biswas	biswas	PROPN
ejpam-6834	1806	10	,	,	PUNCT
ejpam-6834	1806	11	and	and	CCONJ
ejpam-6834	1806	12	a	a	DET
ejpam-6834	1806	13	ranjan	ranjan	PROPN
ejpam-6834	1806	14	roy	roy	PROPN
ejpam-6834	1806	15	.	.	PROPN
ejpam-6834	1806	16	soft	soft	ADJ
ejpam-6834	1806	17	set	set	NOUN
ejpam-6834	1806	18	theory	theory	NOUN
ejpam-6834	1806	19	.	.	PUNCT
ejpam-6834	1807	1	computers	computer	NOUN
ejpam-6834	1807	2	&	&	CCONJ
ejpam-6834	1807	3	mathematics	mathematics	PROPN
ejpam-6834	1807	4	with	with	ADP
ejpam-6834	1807	5	applications	application	NOUN
ejpam-6834	1807	6	,	,	PUNCT
ejpam-6834	1807	7	45(4	45(4	NOUN
ejpam-6834	1807	8	-	-	PUNCT
ejpam-6834	1807	9	5):555–562	5):555–562	NUM
ejpam-6834	1807	10	,	,	PUNCT
ejpam-6834	1807	11	2003	2003	NUM
ejpam-6834	1807	12	.	.	PUNCT
ejpam-6834	1808	1	[	[	X
ejpam-6834	1808	2	9	9	NUM
ejpam-6834	1808	3	]	]	SYM
ejpam-6834	1808	4	zdzis	zdzis	NOUN
ejpam-6834	1808	5	law	law	NOUN
ejpam-6834	1808	6	pawlak	pawlak	NOUN
ejpam-6834	1808	7	.	.	PUNCT
ejpam-6834	1809	1	rough	rough	ADJ
ejpam-6834	1809	2	sets	set	NOUN
ejpam-6834	1809	3	.	.	PUNCT
ejpam-6834	1810	1	international	international	ADJ
ejpam-6834	1810	2	journal	journal	PROPN
ejpam-6834	1810	3	of	of	ADP
ejpam-6834	1810	4	computer	computer	PROPN
ejpam-6834	1810	5	&	&	CCONJ
ejpam-6834	1810	6	information	information	NOUN
ejpam-6834	1810	7	sciences	sciences	PROPN
ejpam-6834	1810	8	,	,	PUNCT
ejpam-6834	1810	9	11:341–356	11:341–356	NUM
ejpam-6834	1810	10	,	,	PUNCT
ejpam-6834	1810	11	1982	1982	NUM
ejpam-6834	1810	12	.	.	PUNCT
ejpam-6834	1811	1	[	[	X
ejpam-6834	1811	2	10	10	NUM
ejpam-6834	1811	3	]	]	PUNCT
ejpam-6834	1811	4	florentin	florentin	PROPN
ejpam-6834	1811	5	smarandache	smarandache	NOUN
ejpam-6834	1811	6	.	.	PUNCT
ejpam-6834	1812	1	a	a	DET
ejpam-6834	1812	2	unifying	unifying	ADJ
ejpam-6834	1812	3	field	field	NOUN
ejpam-6834	1812	4	in	in	ADP
ejpam-6834	1812	5	logics	logic	NOUN
ejpam-6834	1812	6	:	:	PUNCT
ejpam-6834	1812	7	neutrosophic	neutrosophic	ADJ
ejpam-6834	1812	8	logic	logic	NOUN
ejpam-6834	1812	9	.	.	PUNCT
ejpam-6834	1813	1	in	in	ADP
ejpam-6834	1813	2	philosophy	philosophy	NOUN
ejpam-6834	1813	3	,	,	PUNCT
ejpam-6834	1813	4	pages	page	NOUN
ejpam-6834	1813	5	1–141	1–141	NUM
ejpam-6834	1813	6	.	.	PUNCT
ejpam-6834	1814	1	american	american	ADJ
ejpam-6834	1814	2	research	research	PROPN
ejpam-6834	1814	3	press	press	PROPN
ejpam-6834	1814	4	,	,	PUNCT
ejpam-6834	1814	5	1999	1999	NUM
ejpam-6834	1814	6	.	.	PUNCT
ejpam-6834	1815	1	[	[	X
ejpam-6834	1815	2	11	11	NUM
ejpam-6834	1815	3	]	]	X
ejpam-6834	1815	4	g	g	PROPN
ejpam-6834	1815	5	muhiuddin	muhiuddin	PROPN
ejpam-6834	1815	6	,	,	PUNCT
ejpam-6834	1815	7	mohamed	mohamed	PROPN
ejpam-6834	1815	8	e	e	PROPN
ejpam-6834	1815	9	elnair	elnair	NOUN
ejpam-6834	1815	10	,	,	PUNCT
ejpam-6834	1815	11	satham	satham	VERB
ejpam-6834	1815	12	hussain	hussain	PROPN
ejpam-6834	1815	13	,	,	PUNCT
ejpam-6834	1815	14	and	and	CCONJ
ejpam-6834	1815	15	durga	durga	PROPN
ejpam-6834	1815	16	nagarajan	nagarajan	PROPN
ejpam-6834	1815	17	.	.	PROPN
ejpam-6834	1816	1	topsis	topsis	PROPN
ejpam-6834	1816	2	method	method	NOUN
ejpam-6834	1816	3	-	-	PUNCT
ejpam-6834	1816	4	based	base	VERB
ejpam-6834	1816	5	decision	decision	NOUN
ejpam-6834	1816	6	-	-	PUNCT
ejpam-6834	1816	7	making	make	VERB
ejpam-6834	1816	8	model	model	NOUN
ejpam-6834	1816	9	for	for	ADP
ejpam-6834	1816	10	bipolar	bipolar	ADJ
ejpam-6834	1816	11	quadripartitioned	quadripartitione	VERB
ejpam-6834	1816	12	neutrosophic	neutrosophic	ADJ
ejpam-6834	1816	13	environment	environment	NOUN
ejpam-6834	1816	14	.	.	PUNCT
ejpam-6834	1817	1	neutrosophic	neutrosophic	ADJ
ejpam-6834	1817	2	sets	set	NOUN
ejpam-6834	1817	3	and	and	CCONJ
ejpam-6834	1817	4	systems	system	NOUN
ejpam-6834	1817	5	,	,	PUNCT
ejpam-6834	1817	6	85:899–918	85:899–918	NUM
ejpam-6834	1817	7	,	,	PUNCT
ejpam-6834	1817	8	2025	2025	NUM
ejpam-6834	1817	9	.	.	PUNCT
ejpam-6834	1818	1	t.	t.	PROPN
ejpam-6834	1818	2	fujita	fujita	PROPN
ejpam-6834	1818	3	,	,	PUNCT
ejpam-6834	1818	4	f.smarandache	f.smarandache	NOUN
ejpam-6834	1818	5	/	/	SYM
ejpam-6834	1818	6	eur	eur	PROPN
ejpam-6834	1818	7	.	.	PUNCT
ejpam-6834	1819	1	j.	j.	PROPN
ejpam-6834	1819	2	pure	pure	PROPN
ejpam-6834	1819	3	appl	appl	PROPN
ejpam-6834	1819	4	.	.	PROPN
ejpam-6834	1819	5	math	math	PROPN
ejpam-6834	1819	6	,	,	PUNCT
ejpam-6834	1819	7	18	18	NUM
ejpam-6834	1819	8	(	(	PUNCT
ejpam-6834	1819	9	4	4	NUM
ejpam-6834	1819	10	)	)	PUNCT
ejpam-6834	1819	11	(	(	PUNCT
ejpam-6834	1819	12	2025	2025	NUM
ejpam-6834	1819	13	)	)	PUNCT
ejpam-6834	1819	14	,	,	PUNCT
ejpam-6834	1819	15	6834	6834	NUM
ejpam-6834	1819	16	66	66	NUM
ejpam-6834	1819	17	of	of	ADP
ejpam-6834	1819	18	69	69	NUM
ejpam-6834	1820	1	[	[	X
ejpam-6834	1820	2	12	12	NUM
ejpam-6834	1820	3	]	]	PUNCT
ejpam-6834	1820	4	maha	maha	PROPN
ejpam-6834	1820	5	mohammed	mohammed	PROPN
ejpam-6834	1820	6	saeed	saeed	PROPN
ejpam-6834	1820	7	,	,	PUNCT
ejpam-6834	1820	8	raed	raed	PROPN
ejpam-6834	1820	9	hatamleh	hatamleh	PROPN
ejpam-6834	1820	10	,	,	PUNCT
ejpam-6834	1820	11	alaa	alaa	PROPN
ejpam-6834	1820	12	m	m	PROPN
ejpam-6834	1820	13	abdel	abdel	PROPN
ejpam-6834	1820	14	-	-	PUNCT
ejpam-6834	1820	15	latif	latif	PROPN
ejpam-6834	1820	16	,	,	PUNCT
ejpam-6834	1820	17	abdallah	abdallah	PROPN
ejpam-6834	1820	18	al	al	PROPN
ejpam-6834	1820	19	-	-	PROPN
ejpam-6834	1820	20	husban	husban	PROPN
ejpam-6834	1820	21	al	al	PROPN
ejpam-6834	1820	22	-	-	PUNCT
ejpam-6834	1820	23	husban	husban	PROPN
ejpam-6834	1820	24	,	,	PUNCT
ejpam-6834	1820	25	husham	husham	PROPN
ejpam-6834	1820	26	m	m	PROPN
ejpam-6834	1820	27	attaalfadeel	attaalfadeel	NOUN
ejpam-6834	1820	28	,	,	PUNCT
ejpam-6834	1820	29	takaaki	takaaki	NOUN
ejpam-6834	1820	30	fujita	fujita	PROPN
ejpam-6834	1820	31	,	,	PUNCT
ejpam-6834	1820	32	khaled	khale	VERB
ejpam-6834	1820	33	a	a	DET
ejpam-6834	1820	34	aldwoah	aldwoah	NOUN
ejpam-6834	1820	35	,	,	PUNCT
ejpam-6834	1820	36	and	and	CCONJ
ejpam-6834	1820	37	arif	arif	PROPN
ejpam-6834	1820	38	mehmood	mehmood	PROPN
ejpam-6834	1820	39	khattak	khattak	PROPN
ejpam-6834	1820	40	.	.	PUNCT
ejpam-6834	1821	1	a	a	DET
ejpam-6834	1821	2	breakthrough	breakthrough	ADJ
ejpam-6834	1821	3	approach	approach	NOUN
ejpam-6834	1821	4	to	to	ADP
ejpam-6834	1821	5	quadri	quadri	NOUN
ejpam-6834	1821	6	-	-	PUNCT
ejpam-6834	1821	7	partitioned	partition	VERB
ejpam-6834	1821	8	neutrosophic	neutrosophic	ADJ
ejpam-6834	1821	9	soft	soft	ADJ
ejpam-6834	1821	10	topological	topological	ADJ
ejpam-6834	1821	11	spaces	space	NOUN
ejpam-6834	1821	12	.	.	PUNCT
ejpam-6834	1822	1	european	european	ADJ
ejpam-6834	1822	2	journal	journal	PROPN
ejpam-6834	1822	3	of	of	ADP
ejpam-6834	1822	4	pure	pure	ADJ
ejpam-6834	1822	5	and	and	CCONJ
ejpam-6834	1822	6	applied	applied	ADJ
ejpam-6834	1822	7	mathematics	mathematic	NOUN
ejpam-6834	1822	8	,	,	PUNCT
ejpam-6834	1822	9	18(2):5845–5845	18(2):5845–5845	NUM
ejpam-6834	1822	10	,	,	PUNCT
ejpam-6834	1822	11	2025	2025	NUM
ejpam-6834	1822	12	.	.	PUNCT
ejpam-6834	1823	1	[	[	X
ejpam-6834	1823	2	13	13	NUM
ejpam-6834	1823	3	]	]	PUNCT
ejpam-6834	1823	4	maha	maha	PROPN
ejpam-6834	1823	5	mohammed	mohammed	PROPN
ejpam-6834	1823	6	saeed	saeed	PROPN
ejpam-6834	1823	7	,	,	PUNCT
ejpam-6834	1823	8	raed	raed	PROPN
ejpam-6834	1823	9	hatamleh	hatamleh	PROPN
ejpam-6834	1823	10	,	,	PUNCT
ejpam-6834	1823	11	hamza	hamza	PROPN
ejpam-6834	1823	12	ali	ali	PROPN
ejpam-6834	1823	13	abujabal	abujabal	PROPN
ejpam-6834	1823	14	,	,	PUNCT
ejpam-6834	1823	15	yahya	yahya	PROPN
ejpam-6834	1823	16	khan	khan	PROPN
ejpam-6834	1823	17	,	,	PUNCT
ejpam-6834	1823	18	abdallah	abdallah	PROPN
ejpam-6834	1823	19	al	al	PROPN
ejpam-6834	1823	20	-	-	PUNCT
ejpam-6834	1823	21	husban	husban	PROPN
ejpam-6834	1823	22	,	,	PUNCT
ejpam-6834	1823	23	amy	amy	PROPN
ejpam-6834	1823	24	a	a	DET
ejpam-6834	1823	25	laja	laja	NOUN
ejpam-6834	1823	26	,	,	PUNCT
ejpam-6834	1823	27	sulfaisa	sulfaisa	NOUN
ejpam-6834	1823	28	mm	mm	PROPN
ejpam-6834	1823	29	pangilan	pangilan	NOUN
ejpam-6834	1823	30	,	,	PUNCT
ejpam-6834	1823	31	cris	cris	PROPN
ejpam-6834	1823	32	l	l	PROPN
ejpam-6834	1823	33	armada	armada	PROPN
ejpam-6834	1823	34	,	,	PUNCT
ejpam-6834	1823	35	jamil	jamil	PROPN
ejpam-6834	1823	36	j	j	PROPN
ejpam-6834	1823	37	hamja	hamja	PROPN
ejpam-6834	1823	38	,	,	PUNCT
ejpam-6834	1823	39	and	and	CCONJ
ejpam-6834	1823	40	arif	arif	PROPN
ejpam-6834	1823	41	mehmood	mehmood	PROPN
ejpam-6834	1823	42	khattak	khattak	PROPN
ejpam-6834	1823	43	.	.	PUNCT
ejpam-6834	1824	1	heptapartitioned	heptapartitione	VERB
ejpam-6834	1824	2	neutrosophic	neutrosophic	ADJ
ejpam-6834	1824	3	soft	soft	ADJ
ejpam-6834	1824	4	topologies	topology	NOUN
ejpam-6834	1824	5	and	and	CCONJ
ejpam-6834	1824	6	machine	machine	NOUN
ejpam-6834	1824	7	learning	learn	VERB
ejpam-6834	1824	8	techniques	technique	NOUN
ejpam-6834	1824	9	for	for	ADP
ejpam-6834	1824	10	exploring	explore	VERB
ejpam-6834	1824	11	romantic	romantic	ADJ
ejpam-6834	1824	12	feelings	feeling	NOUN
ejpam-6834	1824	13	.	.	PUNCT
ejpam-6834	1825	1	european	european	ADJ
ejpam-6834	1825	2	journal	journal	PROPN
ejpam-6834	1825	3	of	of	ADP
ejpam-6834	1825	4	pure	pure	ADJ
ejpam-6834	1825	5	and	and	CCONJ
ejpam-6834	1825	6	applied	applied	ADJ
ejpam-6834	1825	7	mathematics	mathematic	NOUN
ejpam-6834	1825	8	,	,	PUNCT
ejpam-6834	1825	9	18(3):6221–6221	18(3):6221–6221	NUM
ejpam-6834	1825	10	,	,	PUNCT
ejpam-6834	1825	11	2025	2025	NUM
ejpam-6834	1825	12	.	.	PUNCT
ejpam-6834	1826	1	[	[	X
ejpam-6834	1826	2	14	14	NUM
ejpam-6834	1826	3	]	]	X
ejpam-6834	1826	4	maha	maha	PROPN
ejpam-6834	1826	5	mohammed	mohammed	PROPN
ejpam-6834	1826	6	saeed	saeed	PROPN
ejpam-6834	1826	7	,	,	PUNCT
ejpam-6834	1826	8	haitham	haitham	PROPN
ejpam-6834	1826	9	alqawaqneh	alqawaqneh	PROPN
ejpam-6834	1826	10	,	,	PUNCT
ejpam-6834	1826	11	ghaziyah	ghaziyah	PROPN
ejpam-6834	1826	12	alsahli	alsahli	NOUN
ejpam-6834	1826	13	,	,	PUNCT
ejpam-6834	1826	14	alaa	alaa	PROPN
ejpam-6834	1826	15	m	m	PROPN
ejpam-6834	1826	16	abd	abd	PROPN
ejpam-6834	1826	17	ellatif	ellatif	PROPN
ejpam-6834	1826	18	,	,	PUNCT
ejpam-6834	1826	19	yahya	yahya	PROPN
ejpam-6834	1826	20	khan	khan	PROPN
ejpam-6834	1826	21	,	,	PUNCT
ejpam-6834	1826	22	jamil	jamil	PROPN
ejpam-6834	1826	23	j	j	PROPN
ejpam-6834	1826	24	hamja	hamja	PROPN
ejpam-6834	1826	25	,	,	PUNCT
ejpam-6834	1826	26	cris	cris	PROPN
ejpam-6834	1826	27	l	l	PROPN
ejpam-6834	1826	28	armada	armada	PROPN
ejpam-6834	1826	29	,	,	PUNCT
ejpam-6834	1826	30	and	and	CCONJ
ejpam-6834	1826	31	arif	arif	PROPN
ejpam-6834	1826	32	mehmood	mehmood	PROPN
ejpam-6834	1826	33	khattak	khattak	PROPN
ejpam-6834	1826	34	.	.	PUNCT
ejpam-6834	1827	1	heptapartitioned	heptapartitione	VERB
ejpam-6834	1827	2	neutrosophic	neutrosophic	ADJ
ejpam-6834	1827	3	soft	soft	ADJ
ejpam-6834	1827	4	topological	topological	ADJ
ejpam-6834	1827	5	spaces	space	NOUN
ejpam-6834	1827	6	and	and	CCONJ
ejpam-6834	1827	7	some	some	DET
ejpam-6834	1827	8	graphical	graphical	ADJ
ejpam-6834	1827	9	representation	representation	NOUN
ejpam-6834	1827	10	of	of	ADP
ejpam-6834	1827	11	sternberg	sternberg	PROPN
ejpam-6834	1827	12	’s	’s	PART
ejpam-6834	1827	13	triangular	triangular	PROPN
ejpam-6834	1827	14	theory	theory	NOUN
ejpam-6834	1827	15	of	of	ADP
ejpam-6834	1827	16	love	love	NOUN
ejpam-6834	1827	17	in	in	ADP
ejpam-6834	1827	18	terms	term	NOUN
ejpam-6834	1827	19	of	of	ADP
ejpam-6834	1827	20	heptapartitioned	heptapartitioned	ADJ
ejpam-6834	1827	21	neutrosophic	neutrosophic	ADJ
ejpam-6834	1827	22	soft	soft	ADJ
ejpam-6834	1827	23	sets	set	NOUN
ejpam-6834	1827	24	with	with	ADP
ejpam-6834	1827	25	the	the	DET
ejpam-6834	1827	26	applications	application	NOUN
ejpam-6834	1827	27	of	of	ADP
ejpam-6834	1827	28	some	some	DET
ejpam-6834	1827	29	advanced	advanced	ADJ
ejpam-6834	1827	30	machine	machine	NOUN
ejpam-6834	1827	31	learning	learn	VERB
ejpam-6834	1827	32	techniques	technique	NOUN
ejpam-6834	1827	33	.	.	PUNCT
ejpam-6834	1828	1	european	european	ADJ
ejpam-6834	1828	2	journal	journal	PROPN
ejpam-6834	1828	3	of	of	ADP
ejpam-6834	1828	4	pure	pure	ADJ
ejpam-6834	1828	5	and	and	CCONJ
ejpam-6834	1828	6	applied	applied	ADJ
ejpam-6834	1828	7	mathematics	mathematic	NOUN
ejpam-6834	1828	8	,	,	PUNCT
ejpam-6834	1828	9	18(3):6207–6207	18(3):6207–6207	NUM
ejpam-6834	1828	10	,	,	PUNCT
ejpam-6834	1828	11	2025	2025	NUM
ejpam-6834	1828	12	.	.	PUNCT
ejpam-6834	1829	1	[	[	X
ejpam-6834	1829	2	15	15	NUM
ejpam-6834	1829	3	]	]	X
ejpam-6834	1829	4	florentin	florentin	PROPN
ejpam-6834	1829	5	smarandache	smarandache	PROPN
ejpam-6834	1829	6	.	.	PUNCT
ejpam-6834	1830	1	plithogeny	plithogeny	PROPN
ejpam-6834	1830	2	,	,	PUNCT
ejpam-6834	1830	3	plithogenic	plithogenic	ADJ
ejpam-6834	1830	4	set	set	NOUN
ejpam-6834	1830	5	,	,	PUNCT
ejpam-6834	1830	6	logic	logic	NOUN
ejpam-6834	1830	7	,	,	PUNCT
ejpam-6834	1830	8	probability	probability	NOUN
ejpam-6834	1830	9	,	,	PUNCT
ejpam-6834	1830	10	and	and	CCONJ
ejpam-6834	1830	11	statistics	statistic	NOUN
ejpam-6834	1830	12	.	.	PUNCT
ejpam-6834	1831	1	arxiv	arxiv	PROPN
ejpam-6834	1831	2	preprint	preprint	VERB
ejpam-6834	1831	3	arxiv:1808.03948	arxiv:1808.03948	NOUN
ejpam-6834	1831	4	,	,	PUNCT
ejpam-6834	1831	5	2018	2018	NUM
ejpam-6834	1831	6	.	.	PUNCT
ejpam-6834	1832	1	[	[	X
ejpam-6834	1832	2	16	16	NUM
ejpam-6834	1832	3	]	]	X
ejpam-6834	1832	4	vicenç	vicenç	PROPN
ejpam-6834	1832	5	torra	torra	VERB
ejpam-6834	1832	6	and	and	CCONJ
ejpam-6834	1832	7	yasuo	yasuo	NOUN
ejpam-6834	1832	8	narukawa	narukawa	NOUN
ejpam-6834	1832	9	.	.	PUNCT
ejpam-6834	1833	1	on	on	ADP
ejpam-6834	1833	2	hesitant	hesitant	ADJ
ejpam-6834	1833	3	fuzzy	fuzzy	ADJ
ejpam-6834	1833	4	sets	set	NOUN
ejpam-6834	1833	5	and	and	CCONJ
ejpam-6834	1833	6	decision	decision	NOUN
ejpam-6834	1833	7	.	.	PUNCT
ejpam-6834	1834	1	in	in	ADP
ejpam-6834	1834	2	2009	2009	NUM
ejpam-6834	1834	3	ieee	ieee	NOUN
ejpam-6834	1834	4	international	international	ADJ
ejpam-6834	1834	5	conference	conference	NOUN
ejpam-6834	1834	6	on	on	ADP
ejpam-6834	1834	7	fuzzy	fuzzy	ADJ
ejpam-6834	1834	8	systems	system	NOUN
ejpam-6834	1834	9	,	,	PUNCT
ejpam-6834	1834	10	pages	page	NOUN
ejpam-6834	1834	11	1378–1382	1378–1382	NUM
ejpam-6834	1834	12	.	.	PUNCT
ejpam-6834	1835	1	ieee	ieee	PROPN
ejpam-6834	1835	2	,	,	PUNCT
ejpam-6834	1835	3	2009	2009	NUM
ejpam-6834	1835	4	.	.	PUNCT
ejpam-6834	1836	1	[	[	X
ejpam-6834	1836	2	17	17	NUM
ejpam-6834	1836	3	]	]	X
ejpam-6834	1836	4	muhammad	muhammad	PROPN
ejpam-6834	1836	5	akram	akram	PROPN
ejpam-6834	1836	6	,	,	PUNCT
ejpam-6834	1836	7	danish	danish	NOUN
ejpam-6834	1836	8	saleem	saleem	PROPN
ejpam-6834	1836	9	,	,	PUNCT
ejpam-6834	1836	10	and	and	CCONJ
ejpam-6834	1836	11	talal	talal	PROPN
ejpam-6834	1836	12	al	al	PROPN
ejpam-6834	1836	13	-	-	PUNCT
ejpam-6834	1836	14	hawary	hawary	PROPN
ejpam-6834	1836	15	.	.	PUNCT
ejpam-6834	1837	1	spherical	spherical	ADJ
ejpam-6834	1837	2	fuzzy	fuzzy	ADJ
ejpam-6834	1837	3	graphs	graph	NOUN
ejpam-6834	1837	4	with	with	ADP
ejpam-6834	1837	5	application	application	NOUN
ejpam-6834	1837	6	to	to	ADP
ejpam-6834	1837	7	decision	decision	NOUN
ejpam-6834	1837	8	-	-	PUNCT
ejpam-6834	1837	9	making	making	NOUN
ejpam-6834	1837	10	.	.	PUNCT
ejpam-6834	1838	1	mathematical	mathematical	ADJ
ejpam-6834	1838	2	and	and	CCONJ
ejpam-6834	1838	3	computational	computational	ADJ
ejpam-6834	1838	4	applications	application	NOUN
ejpam-6834	1838	5	,	,	PUNCT
ejpam-6834	1838	6	25(1):8	25(1):8	NUM
ejpam-6834	1838	7	,	,	PUNCT
ejpam-6834	1838	8	2020	2020	NUM
ejpam-6834	1838	9	.	.	PUNCT
ejpam-6834	1839	1	[	[	X
ejpam-6834	1839	2	18	18	NUM
ejpam-6834	1839	3	]	]	PUNCT
ejpam-6834	1839	4	krassimir	krassimir	PROPN
ejpam-6834	1839	5	t	t	PROPN
ejpam-6834	1839	6	atanassov	atanassov	NOUN
ejpam-6834	1839	7	.	.	PUNCT
ejpam-6834	1840	1	circular	circular	ADJ
ejpam-6834	1840	2	intuitionistic	intuitionistic	ADJ
ejpam-6834	1840	3	fuzzy	fuzzy	ADJ
ejpam-6834	1840	4	sets	set	NOUN
ejpam-6834	1840	5	.	.	PUNCT
ejpam-6834	1841	1	journal	journal	NOUN
ejpam-6834	1841	2	of	of	ADP
ejpam-6834	1841	3	intelligent	intelligent	ADJ
ejpam-6834	1841	4	&	&	CCONJ
ejpam-6834	1841	5	fuzzy	fuzzy	ADJ
ejpam-6834	1841	6	systems	system	NOUN
ejpam-6834	1841	7	,	,	PUNCT
ejpam-6834	1841	8	39(5):5981–5986	39(5):5981–5986	NUM
ejpam-6834	1841	9	,	,	PUNCT
ejpam-6834	1841	10	2020	2020	NUM
ejpam-6834	1841	11	.	.	PUNCT
ejpam-6834	1842	1	[	[	X
ejpam-6834	1842	2	19	19	NUM
ejpam-6834	1842	3	]	]	PUNCT
ejpam-6834	1842	4	yiyu	yiyu	NOUN
ejpam-6834	1842	5	yao	yao	PROPN
ejpam-6834	1842	6	and	and	CCONJ
ejpam-6834	1842	7	jilin	jilin	PROPN
ejpam-6834	1842	8	yang	yang	PROPN
ejpam-6834	1842	9	.	.	PUNCT
ejpam-6834	1843	1	granular	granular	ADJ
ejpam-6834	1843	2	rough	rough	ADJ
ejpam-6834	1843	3	sets	set	NOUN
ejpam-6834	1843	4	and	and	CCONJ
ejpam-6834	1843	5	granular	granular	ADJ
ejpam-6834	1843	6	shadowed	shadow	VERB
ejpam-6834	1843	7	sets	set	NOUN
ejpam-6834	1843	8	:	:	PUNCT
ejpam-6834	1843	9	three	three	NUM
ejpam-6834	1843	10	-	-	PUNCT
ejpam-6834	1843	11	way	way	NOUN
ejpam-6834	1843	12	approximations	approximation	NOUN
ejpam-6834	1843	13	in	in	ADP
ejpam-6834	1843	14	pawlak	pawlak	ADJ
ejpam-6834	1843	15	approximation	approximation	NOUN
ejpam-6834	1843	16	spaces	space	NOUN
ejpam-6834	1843	17	.	.	PUNCT
ejpam-6834	1844	1	int	int	NOUN
ejpam-6834	1844	2	.	.	PUNCT
ejpam-6834	1845	1	j.	j.	PROPN
ejpam-6834	1845	2	approx	approx	PROPN
ejpam-6834	1845	3	.	.	PUNCT
ejpam-6834	1846	1	reason	reason	NOUN
ejpam-6834	1846	2	.	.	PUNCT
ejpam-6834	1846	3	,	,	PUNCT
ejpam-6834	1846	4	142:231	142:231	NUM
ejpam-6834	1846	5	–	–	PUNCT
ejpam-6834	1846	6	247	247	NUM
ejpam-6834	1846	7	,	,	PUNCT
ejpam-6834	1846	8	2022	2022	NUM
ejpam-6834	1846	9	.	.	PUNCT
ejpam-6834	1847	1	[	[	X
ejpam-6834	1847	2	20	20	NUM
ejpam-6834	1847	3	]	]	PUNCT
ejpam-6834	1847	4	yiyu	yiyu	NOUN
ejpam-6834	1847	5	yao	yao	PROPN
ejpam-6834	1847	6	,	,	PUNCT
ejpam-6834	1847	7	salvatore	salvatore	PROPN
ejpam-6834	1847	8	greco	greco	PROPN
ejpam-6834	1847	9	,	,	PUNCT
ejpam-6834	1847	10	and	and	CCONJ
ejpam-6834	1847	11	roman	roman	PROPN
ejpam-6834	1847	12	s	s	PART
ejpam-6834	1847	13	lowiński	lowiński	PROPN
ejpam-6834	1847	14	.	.	PUNCT
ejpam-6834	1847	15	probabilistic	probabilistic	ADJ
ejpam-6834	1847	16	rough	rough	ADJ
ejpam-6834	1847	17	sets	set	NOUN
ejpam-6834	1847	18	.	.	PUNCT
ejpam-6834	1848	1	springer	springer	NOUN
ejpam-6834	1848	2	handbook	handbook	NOUN
ejpam-6834	1848	3	of	of	ADP
ejpam-6834	1848	4	computational	computational	ADJ
ejpam-6834	1848	5	intelligence	intelligence	NOUN
ejpam-6834	1848	6	,	,	PUNCT
ejpam-6834	1848	7	pages	page	NOUN
ejpam-6834	1848	8	387–411	387–411	NUM
ejpam-6834	1848	9	,	,	PUNCT
ejpam-6834	1848	10	2015	2015	NUM
ejpam-6834	1848	11	.	.	PUNCT
ejpam-6834	1849	1	[	[	X
ejpam-6834	1849	2	21	21	NUM
ejpam-6834	1849	3	]	]	X
ejpam-6834	1849	4	mohamed	mohamed	PROPN
ejpam-6834	1849	5	abdel	abdel	PROPN
ejpam-6834	1849	6	-	-	PUNCT
ejpam-6834	1849	7	basset	basset	PROPN
ejpam-6834	1849	8	,	,	PUNCT
ejpam-6834	1849	9	mai	mai	PROPN
ejpam-6834	1849	10	mohamed	mohamed	PROPN
ejpam-6834	1849	11	,	,	PUNCT
ejpam-6834	1849	12	mohamed	mohamed	PROPN
ejpam-6834	1849	13	elhoseny	elhoseny	PROPN
ejpam-6834	1849	14	,	,	PUNCT
ejpam-6834	1849	15	le	le	PROPN
ejpam-6834	1849	16	hoang	hoang	PROPN
ejpam-6834	1849	17	son	son	PROPN
ejpam-6834	1849	18	,	,	PUNCT
ejpam-6834	1849	19	francisco	francisco	PROPN
ejpam-6834	1849	20	chiclana	chiclana	PROPN
ejpam-6834	1849	21	,	,	PUNCT
ejpam-6834	1849	22	and	and	CCONJ
ejpam-6834	1849	23	abdel	abdel	PROPN
ejpam-6834	1849	24	nasser	nasser	PROPN
ejpam-6834	1849	25	h.	h.	PROPN
ejpam-6834	1849	26	zaied	zaie	VERB
ejpam-6834	1849	27	.	.	PUNCT
ejpam-6834	1850	1	cosine	cosine	NOUN
ejpam-6834	1850	2	similarity	similarity	NOUN
ejpam-6834	1850	3	measures	measure	NOUN
ejpam-6834	1850	4	of	of	ADP
ejpam-6834	1850	5	bipolar	bipolar	ADJ
ejpam-6834	1850	6	neutrosophic	neutrosophic	ADJ
ejpam-6834	1850	7	set	set	NOUN
ejpam-6834	1850	8	for	for	ADP
ejpam-6834	1850	9	diagnosis	diagnosis	NOUN
ejpam-6834	1850	10	of	of	ADP
ejpam-6834	1850	11	bipolar	bipolar	ADJ
ejpam-6834	1850	12	disorder	disorder	NOUN
ejpam-6834	1850	13	diseases	disease	NOUN
ejpam-6834	1850	14	.	.	PUNCT
ejpam-6834	1851	1	artificial	artificial	ADJ
ejpam-6834	1851	2	intelligence	intelligence	NOUN
ejpam-6834	1851	3	in	in	ADP
ejpam-6834	1851	4	medicine	medicine	NOUN
ejpam-6834	1851	5	,	,	PUNCT
ejpam-6834	1851	6	101:101735	101:101735	NUM
ejpam-6834	1851	7	,	,	PUNCT
ejpam-6834	1851	8	2019	2019	NUM
ejpam-6834	1851	9	.	.	PUNCT
ejpam-6834	1852	1	[	[	X
ejpam-6834	1852	2	22	22	NUM
ejpam-6834	1852	3	]	]	PUNCT
ejpam-6834	1852	4	hongyu	hongyu	PROPN
ejpam-6834	1852	5	zhang	zhang	PROPN
ejpam-6834	1852	6	,	,	PUNCT
ejpam-6834	1852	7	jianqiang	jianqiang	PROPN
ejpam-6834	1852	8	wang	wang	PROPN
ejpam-6834	1852	9	,	,	PUNCT
ejpam-6834	1852	10	and	and	CCONJ
ejpam-6834	1852	11	xiaohong	xiaohong	PROPN
ejpam-6834	1852	12	chen	chen	PROPN
ejpam-6834	1852	13	.	.	PUNCT
ejpam-6834	1853	1	an	an	DET
ejpam-6834	1853	2	outranking	outrank	VERB
ejpam-6834	1853	3	approach	approach	NOUN
ejpam-6834	1853	4	for	for	ADP
ejpam-6834	1853	5	multi	multi	ADJ
ejpam-6834	1853	6	-	-	ADJ
ejpam-6834	1853	7	criteria	criterion	NOUN
ejpam-6834	1853	8	decision	decision	NOUN
ejpam-6834	1853	9	-	-	PUNCT
ejpam-6834	1853	10	making	make	VERB
ejpam-6834	1853	11	problems	problem	NOUN
ejpam-6834	1853	12	with	with	ADP
ejpam-6834	1853	13	interval	interval	NOUN
ejpam-6834	1853	14	-	-	PUNCT
ejpam-6834	1853	15	valued	value	VERB
ejpam-6834	1853	16	neutrosophic	neutrosophic	ADJ
ejpam-6834	1853	17	sets	set	NOUN
ejpam-6834	1853	18	.	.	PUNCT
ejpam-6834	1854	1	neural	neural	ADJ
ejpam-6834	1854	2	computing	computing	NOUN
ejpam-6834	1854	3	and	and	CCONJ
ejpam-6834	1854	4	applications	application	NOUN
ejpam-6834	1854	5	,	,	PUNCT
ejpam-6834	1854	6	27:615–627	27:615–627	PROPN
ejpam-6834	1854	7	,	,	PUNCT
ejpam-6834	1854	8	2016	2016	NUM
ejpam-6834	1854	9	.	.	PUNCT
ejpam-6834	1855	1	[	[	X
ejpam-6834	1855	2	23	23	NUM
ejpam-6834	1855	3	]	]	PUNCT
ejpam-6834	1855	4	takaaki	takaaki	NOUN
ejpam-6834	1855	5	fujita	fujita	PROPN
ejpam-6834	1855	6	,	,	PUNCT
ejpam-6834	1855	7	arif	arif	PROPN
ejpam-6834	1855	8	mehmood	mehmood	PROPN
ejpam-6834	1855	9	,	,	PUNCT
ejpam-6834	1855	10	and	and	CCONJ
ejpam-6834	1855	11	arkan	arkan	VERB
ejpam-6834	1855	12	a	a	DET
ejpam-6834	1855	13	ghaib	ghaib	NOUN
ejpam-6834	1855	14	.	.	PUNCT
ejpam-6834	1856	1	a	a	DET
ejpam-6834	1856	2	reconsideration	reconsideration	NOUN
ejpam-6834	1856	3	note	note	NOUN
ejpam-6834	1856	4	of	of	ADP
ejpam-6834	1856	5	the	the	DET
ejpam-6834	1856	6	mathematical	mathematical	ADJ
ejpam-6834	1856	7	frameworks	framework	NOUN
ejpam-6834	1856	8	for	for	ADP
ejpam-6834	1856	9	fuzzy	fuzzy	ADJ
ejpam-6834	1856	10	and	and	CCONJ
ejpam-6834	1856	11	neutrosophic	neutrosophic	ADJ
ejpam-6834	1856	12	risk	risk	NOUN
ejpam-6834	1856	13	management	management	NOUN
ejpam-6834	1856	14	.	.	PUNCT
ejpam-6834	1857	1	management	management	NOUN
ejpam-6834	1857	2	science	science	NOUN
ejpam-6834	1857	3	advances	advance	NOUN
ejpam-6834	1857	4	,	,	PUNCT
ejpam-6834	1857	5	2(1):223–238	2(1):223–238	NUM
ejpam-6834	1857	6	,	,	PUNCT
ejpam-6834	1857	7	2025	2025	NUM
ejpam-6834	1857	8	.	.	PUNCT
ejpam-6834	1858	1	[	[	X
ejpam-6834	1858	2	24	24	NUM
ejpam-6834	1858	3	]	]	X
ejpam-6834	1858	4	tripti	tripti	PROPN
ejpam-6834	1858	5	basuri	basuri	PROPN
ejpam-6834	1858	6	,	,	PUNCT
ejpam-6834	1858	7	kamal	kamal	PROPN
ejpam-6834	1858	8	hossain	hossain	PROPN
ejpam-6834	1858	9	gazi	gazi	PROPN
ejpam-6834	1858	10	,	,	PUNCT
ejpam-6834	1858	11	prodip	prodip	ADJ
ejpam-6834	1858	12	bhaduri	bhaduri	PROPN
ejpam-6834	1858	13	,	,	PUNCT
ejpam-6834	1858	14	srabani	srabani	PROPN
ejpam-6834	1858	15	guria	guria	PROPN
ejpam-6834	1858	16	das	das	PROPN
ejpam-6834	1858	17	,	,	PUNCT
ejpam-6834	1858	18	and	and	CCONJ
ejpam-6834	1858	19	sankar	sankar	PROPN
ejpam-6834	1858	20	prasad	prasad	PROPN
ejpam-6834	1858	21	mondal	mondal	PROPN
ejpam-6834	1858	22	.	.	PUNCT
ejpam-6834	1859	1	decision	decision	NOUN
ejpam-6834	1859	2	-	-	PUNCT
ejpam-6834	1859	3	analytics	analytic	NOUN
ejpam-6834	1859	4	-	-	PUNCT
ejpam-6834	1859	5	based	base	VERB
ejpam-6834	1859	6	sustainable	sustainable	ADJ
ejpam-6834	1859	7	location	location	NOUN
ejpam-6834	1859	8	problemneutrosophic	problemneutrosophic	ADJ
ejpam-6834	1859	9	critic	critic	NOUN
ejpam-6834	1859	10	-	-	PUNCT
ejpam-6834	1859	11	copras	copras	PROPN
ejpam-6834	1859	12	assessment	assessment	NOUN
ejpam-6834	1859	13	model	model	NOUN
ejpam-6834	1859	14	.	.	PUNCT
ejpam-6834	1860	1	management	management	NOUN
ejpam-6834	1860	2	science	science	NOUN
ejpam-6834	1860	3	advances	advance	NOUN
ejpam-6834	1860	4	,	,	PUNCT
ejpam-6834	1860	5	2(1):19	2(1):19	NUM
ejpam-6834	1860	6	–	–	PUNCT
ejpam-6834	1860	7	t.	t.	NOUN
ejpam-6834	1860	8	fujita	fujita	PROPN
ejpam-6834	1860	9	,	,	PUNCT
ejpam-6834	1860	10	f.smarandache	f.smarandache	NOUN
ejpam-6834	1860	11	/	/	SYM
ejpam-6834	1860	12	eur	eur	PROPN
ejpam-6834	1860	13	.	.	PUNCT
ejpam-6834	1861	1	j.	j.	PROPN
ejpam-6834	1861	2	pure	pure	PROPN
ejpam-6834	1861	3	appl	appl	PROPN
ejpam-6834	1861	4	.	.	PROPN
ejpam-6834	1861	5	math	math	PROPN
ejpam-6834	1861	6	,	,	PUNCT
ejpam-6834	1861	7	18	18	NUM
ejpam-6834	1861	8	(	(	PUNCT
ejpam-6834	1861	9	4	4	NUM
ejpam-6834	1861	10	)	)	PUNCT
ejpam-6834	1861	11	(	(	PUNCT
ejpam-6834	1861	12	2025	2025	NUM
ejpam-6834	1861	13	)	)	PUNCT
ejpam-6834	1861	14	,	,	PUNCT
ejpam-6834	1861	15	6834	6834	NUM
ejpam-6834	1861	16	67	67	NUM
ejpam-6834	1861	17	of	of	ADP
ejpam-6834	1861	18	69	69	NUM
ejpam-6834	1861	19	58	58	NUM
ejpam-6834	1861	20	,	,	PUNCT
ejpam-6834	1861	21	2025	2025	NUM
ejpam-6834	1861	22	.	.	PUNCT
ejpam-6834	1862	1	[	[	X
ejpam-6834	1862	2	25	25	NUM
ejpam-6834	1862	3	]	]	X
ejpam-6834	1862	4	sajida	sajida	PROPN
ejpam-6834	1862	5	kousar	kousar	VERB
ejpam-6834	1862	6	and	and	CCONJ
ejpam-6834	1862	7	nasreen	nasreen	VERB
ejpam-6834	1862	8	kausar	kausar	PROPN
ejpam-6834	1862	9	.	.	PUNCT
ejpam-6834	1863	1	multi	multi	ADJ
ejpam-6834	1863	2	-	-	ADJ
ejpam-6834	1863	3	criteria	criterion	NOUN
ejpam-6834	1863	4	decision	decision	NOUN
ejpam-6834	1863	5	-	-	PUNCT
ejpam-6834	1863	6	making	making	NOUN
ejpam-6834	1863	7	for	for	ADP
ejpam-6834	1863	8	sustainable	sustainable	ADJ
ejpam-6834	1863	9	agritourism	agritourism	NOUN
ejpam-6834	1863	10	:	:	PUNCT
ejpam-6834	1863	11	an	an	DET
ejpam-6834	1863	12	integrated	integrate	VERB
ejpam-6834	1863	13	fuzzy	fuzzy	ADJ
ejpam-6834	1863	14	-	-	PUNCT
ejpam-6834	1863	15	rough	rough	ADJ
ejpam-6834	1863	16	approach	approach	NOUN
ejpam-6834	1863	17	.	.	PUNCT
ejpam-6834	1864	1	spectrum	spectrum	NOUN
ejpam-6834	1864	2	of	of	ADP
ejpam-6834	1864	3	operational	operational	ADJ
ejpam-6834	1864	4	research	research	NOUN
ejpam-6834	1864	5	,	,	PUNCT
ejpam-6834	1864	6	2(1):134–150	2(1):134–150	NOUN
ejpam-6834	1864	7	,	,	PUNCT
ejpam-6834	1864	8	2025	2025	NUM
ejpam-6834	1864	9	.	.	PUNCT
ejpam-6834	1865	1	[	[	X
ejpam-6834	1865	2	26	26	NUM
ejpam-6834	1865	3	]	]	X
ejpam-6834	1865	4	m	m	VERB
ejpam-6834	1865	5	al	al	PROPN
ejpam-6834	1865	6	tahan	tahan	PROPN
ejpam-6834	1865	7	and	and	CCONJ
ejpam-6834	1865	8	bijan	bijan	PROPN
ejpam-6834	1865	9	davvaz	davvaz	PROPN
ejpam-6834	1865	10	.	.	PUNCT
ejpam-6834	1866	1	weak	weak	ADJ
ejpam-6834	1866	2	chemical	chemical	ADJ
ejpam-6834	1866	3	hyperstructures	hyperstructure	NOUN
ejpam-6834	1866	4	associated	associate	VERB
ejpam-6834	1866	5	to	to	ADP
ejpam-6834	1866	6	electrochemical	electrochemical	ADJ
ejpam-6834	1866	7	cells	cell	NOUN
ejpam-6834	1866	8	.	.	PUNCT
ejpam-6834	1867	1	iranian	iranian	ADJ
ejpam-6834	1867	2	journal	journal	PROPN
ejpam-6834	1867	3	of	of	ADP
ejpam-6834	1867	4	mathematical	mathematical	ADJ
ejpam-6834	1867	5	chemistry	chemistry	NOUN
ejpam-6834	1867	6	,	,	PUNCT
ejpam-6834	1867	7	9(1):65–75	9(1):65–75	NUM
ejpam-6834	1867	8	,	,	PUNCT
ejpam-6834	1867	9	2018	2018	NUM
ejpam-6834	1867	10	.	.	PUNCT
ejpam-6834	1868	1	[	[	X
ejpam-6834	1868	2	27	27	NUM
ejpam-6834	1868	3	]	]	X
ejpam-6834	1868	4	madeleine	madeleine	PROPN
ejpam-6834	1868	5	al	al	PROPN
ejpam-6834	1868	6	-	-	PUNCT
ejpam-6834	1868	7	tahan	tahan	PROPN
ejpam-6834	1868	8	,	,	PUNCT
ejpam-6834	1868	9	bijan	bijan	PROPN
ejpam-6834	1868	10	davvaz	davvaz	PROPN
ejpam-6834	1868	11	,	,	PUNCT
ejpam-6834	1868	12	florentin	florentin	NOUN
ejpam-6834	1868	13	smarandache	smarandache	NOUN
ejpam-6834	1868	14	,	,	PUNCT
ejpam-6834	1868	15	and	and	CCONJ
ejpam-6834	1868	16	osman	osman	PROPN
ejpam-6834	1868	17	anis	anis	PROPN
ejpam-6834	1868	18	.	.	PUNCT
ejpam-6834	1869	1	on	on	ADP
ejpam-6834	1869	2	some	some	DET
ejpam-6834	1869	3	neutrohyperstructures	neutrohyperstructure	NOUN
ejpam-6834	1869	4	.	.	PUNCT
ejpam-6834	1870	1	symmetry	symmetry	PROPN
ejpam-6834	1870	2	,	,	PUNCT
ejpam-6834	1870	3	13(4):535	13(4):535	NUM
ejpam-6834	1870	4	,	,	PUNCT
ejpam-6834	1870	5	2021	2021	NUM
ejpam-6834	1870	6	.	.	PUNCT
ejpam-6834	1871	1	[	[	X
ejpam-6834	1871	2	28	28	NUM
ejpam-6834	1871	3	]	]	X
ejpam-6834	1871	4	florentin	florentin	PROPN
ejpam-6834	1871	5	smarandache	smarandache	PROPN
ejpam-6834	1871	6	.	.	PUNCT
ejpam-6834	1872	1	foundation	foundation	NOUN
ejpam-6834	1872	2	of	of	ADP
ejpam-6834	1872	3	superhyperstructure	superhyperstructure	PROPN
ejpam-6834	1872	4	&	&	CCONJ
ejpam-6834	1872	5	neutrosophic	neutrosophic	ADJ
ejpam-6834	1872	6	superhyperstructure	superhyperstructure	NOUN
ejpam-6834	1872	7	.	.	PUNCT
ejpam-6834	1873	1	neutrosophic	neutrosophic	ADJ
ejpam-6834	1873	2	sets	set	NOUN
ejpam-6834	1873	3	and	and	CCONJ
ejpam-6834	1873	4	systems	system	NOUN
ejpam-6834	1873	5	,	,	PUNCT
ejpam-6834	1873	6	63(1):21	63(1):21	NUM
ejpam-6834	1873	7	,	,	PUNCT
ejpam-6834	1873	8	2024	2024	NUM
ejpam-6834	1873	9	.	.	PUNCT
ejpam-6834	1874	1	[	[	X
ejpam-6834	1874	2	29	29	NUM
ejpam-6834	1874	3	]	]	X
ejpam-6834	1874	4	ajoy	ajoy	PROPN
ejpam-6834	1874	5	kanti	kanti	PROPN
ejpam-6834	1874	6	das	das	PROPN
ejpam-6834	1874	7	,	,	PUNCT
ejpam-6834	1874	8	rajat	rajat	PROPN
ejpam-6834	1874	9	das	das	PROPN
ejpam-6834	1874	10	,	,	PUNCT
ejpam-6834	1874	11	suman	suman	PROPN
ejpam-6834	1874	12	das	das	PROPN
ejpam-6834	1874	13	,	,	PUNCT
ejpam-6834	1874	14	bijoy	bijoy	PROPN
ejpam-6834	1874	15	krishna	krishna	PROPN
ejpam-6834	1874	16	debnath	debnath	PROPN
ejpam-6834	1874	17	,	,	PUNCT
ejpam-6834	1874	18	carlos	carlos	PROPN
ejpam-6834	1874	19	granados	granados	PROPN
ejpam-6834	1874	20	,	,	PUNCT
ejpam-6834	1874	21	bimal	bimal	ADJ
ejpam-6834	1874	22	shil	shil	NOUN
ejpam-6834	1874	23	,	,	PUNCT
ejpam-6834	1874	24	and	and	CCONJ
ejpam-6834	1874	25	rakhal	rakhal	VERB
ejpam-6834	1874	26	das	das	PROPN
ejpam-6834	1874	27	.	.	PUNCT
ejpam-6834	1875	1	a	a	DET
ejpam-6834	1875	2	comprehensive	comprehensive	ADJ
ejpam-6834	1875	3	study	study	NOUN
ejpam-6834	1875	4	of	of	ADP
ejpam-6834	1875	5	neutrosophic	neutrosophic	ADJ
ejpam-6834	1875	6	superhyper	superhyper	NOUN
ejpam-6834	1875	7	bcisemigroups	bcisemigroup	NOUN
ejpam-6834	1875	8	and	and	CCONJ
ejpam-6834	1875	9	their	their	PRON
ejpam-6834	1875	10	algebraic	algebraic	ADJ
ejpam-6834	1875	11	significance	significance	NOUN
ejpam-6834	1875	12	.	.	PUNCT
ejpam-6834	1876	1	transactions	transaction	NOUN
ejpam-6834	1876	2	on	on	ADP
ejpam-6834	1876	3	fuzzy	fuzzy	ADJ
ejpam-6834	1876	4	sets	set	NOUN
ejpam-6834	1876	5	and	and	CCONJ
ejpam-6834	1876	6	systems	system	NOUN
ejpam-6834	1876	7	,	,	PUNCT
ejpam-6834	1876	8	8(2):80	8(2):80	NUM
ejpam-6834	1876	9	,	,	PUNCT
ejpam-6834	1876	10	2025	2025	NUM
ejpam-6834	1876	11	.	.	PUNCT
ejpam-6834	1877	1	[	[	X
ejpam-6834	1877	2	30	30	NUM
ejpam-6834	1877	3	]	]	X
ejpam-6834	1877	4	claude	claude	PROPN
ejpam-6834	1877	5	berge	berge	PROPN
ejpam-6834	1877	6	.	.	PUNCT
ejpam-6834	1878	1	hypergraphs	hypergraph	NOUN
ejpam-6834	1878	2	:	:	PUNCT
ejpam-6834	1878	3	combinatorics	combinatoric	NOUN
ejpam-6834	1878	4	of	of	ADP
ejpam-6834	1878	5	finite	finite	PROPN
ejpam-6834	1878	6	sets	set	NOUN
ejpam-6834	1878	7	,	,	PUNCT
ejpam-6834	1878	8	volume	volume	NOUN
ejpam-6834	1878	9	45	45	NUM
ejpam-6834	1878	10	.	.	PUNCT
ejpam-6834	1879	1	elsevier	elsevier	NOUN
ejpam-6834	1879	2	,	,	PUNCT
ejpam-6834	1879	3	1984	1984	NUM
ejpam-6834	1879	4	.	.	PUNCT
ejpam-6834	1880	1	[	[	X
ejpam-6834	1880	2	31	31	NUM
ejpam-6834	1880	3	]	]	PUNCT
ejpam-6834	1880	4	alain	alain	PROPN
ejpam-6834	1880	5	bretto	bretto	PROPN
ejpam-6834	1880	6	.	.	PUNCT
ejpam-6834	1881	1	hypergraph	hypergraph	PROPN
ejpam-6834	1881	2	theory	theory	NOUN
ejpam-6834	1881	3	.	.	PUNCT
ejpam-6834	1882	1	an	an	DET
ejpam-6834	1882	2	introduction	introduction	NOUN
ejpam-6834	1882	3	.	.	PUNCT
ejpam-6834	1883	1	mathematical	mathematical	ADJ
ejpam-6834	1883	2	engineering	engineering	NOUN
ejpam-6834	1883	3	.	.	PUNCT
ejpam-6834	1884	1	cham	cham	PROPN
ejpam-6834	1884	2	:	:	PUNCT
ejpam-6834	1884	3	springer	springer	NOUN
ejpam-6834	1884	4	,	,	PUNCT
ejpam-6834	1884	5	1	1	NUM
ejpam-6834	1884	6	,	,	PUNCT
ejpam-6834	1884	7	2013	2013	NUM
ejpam-6834	1884	8	.	.	PUNCT
ejpam-6834	1885	1	[	[	X
ejpam-6834	1885	2	32	32	NUM
ejpam-6834	1885	3	]	]	PUNCT
ejpam-6834	1885	4	florentin	florentin	PROPN
ejpam-6834	1885	5	smarandache	smarandache	NOUN
ejpam-6834	1885	6	.	.	PUNCT
ejpam-6834	1886	1	introduction	introduction	NOUN
ejpam-6834	1886	2	to	to	ADP
ejpam-6834	1886	3	the	the	DET
ejpam-6834	1886	4	n	n	CCONJ
ejpam-6834	1886	5	-	-	PUNCT
ejpam-6834	1886	6	superhypergraph	superhypergraph	NOUN
ejpam-6834	1886	7	-	-	PUNCT
ejpam-6834	1886	8	the	the	DET
ejpam-6834	1886	9	most	most	ADV
ejpam-6834	1886	10	general	general	ADJ
ejpam-6834	1886	11	form	form	NOUN
ejpam-6834	1886	12	of	of	ADP
ejpam-6834	1886	13	graph	graph	NOUN
ejpam-6834	1886	14	today	today	NOUN
ejpam-6834	1886	15	.	.	PUNCT
ejpam-6834	1887	1	infinite	infinite	ADJ
ejpam-6834	1887	2	study	study	NOUN
ejpam-6834	1887	3	,	,	PUNCT
ejpam-6834	1887	4	2022	2022	NUM
ejpam-6834	1887	5	.	.	PUNCT
ejpam-6834	1888	1	[	[	X
ejpam-6834	1888	2	33	33	NUM
ejpam-6834	1888	3	]	]	PUNCT
ejpam-6834	1888	4	mohammed	mohammed	PROPN
ejpam-6834	1888	5	alqahtani	alqahtani	PROPN
ejpam-6834	1888	6	.	.	PUNCT
ejpam-6834	1889	1	intuitionistic	intuitionistic	ADJ
ejpam-6834	1889	2	fuzzy	fuzzy	ADJ
ejpam-6834	1889	3	quasi	quasi	ADJ
ejpam-6834	1889	4	-	-	ADJ
ejpam-6834	1889	5	supergraph	supergraph	ADJ
ejpam-6834	1889	6	integration	integration	NOUN
ejpam-6834	1889	7	for	for	ADP
ejpam-6834	1889	8	social	social	ADJ
ejpam-6834	1889	9	network	network	NOUN
ejpam-6834	1889	10	decision	decision	NOUN
ejpam-6834	1889	11	making	making	NOUN
ejpam-6834	1889	12	.	.	PUNCT
ejpam-6834	1890	1	international	international	ADJ
ejpam-6834	1890	2	journal	journal	NOUN
ejpam-6834	1890	3	of	of	ADP
ejpam-6834	1890	4	analysis	analysis	NOUN
ejpam-6834	1890	5	and	and	CCONJ
ejpam-6834	1890	6	applications	application	NOUN
ejpam-6834	1890	7	,	,	PUNCT
ejpam-6834	1890	8	23:137	23:137	NUM
ejpam-6834	1890	9	–	–	PUNCT
ejpam-6834	1890	10	137	137	NUM
ejpam-6834	1890	11	,	,	PUNCT
ejpam-6834	1890	12	2025	2025	NUM
ejpam-6834	1890	13	.	.	PUNCT
ejpam-6834	1891	1	[	[	X
ejpam-6834	1891	2	34	34	NUM
ejpam-6834	1891	3	]	]	X
ejpam-6834	1891	4	abdullah	abdullah	PROPN
ejpam-6834	1891	5	kargın	kargın	PROPN
ejpam-6834	1891	6	and	and	CCONJ
ejpam-6834	1891	7	memet	memet	ADJ
ejpam-6834	1891	8	şahin	şahin	PROPN
ejpam-6834	1891	9	.	.	PUNCT
ejpam-6834	1892	1	superhyper	superhyper	NOUN
ejpam-6834	1892	2	groups	group	NOUN
ejpam-6834	1892	3	and	and	CCONJ
ejpam-6834	1892	4	neutro	neutro	NOUN
ejpam-6834	1892	5	–	–	PUNCT
ejpam-6834	1892	6	superhyper	superhyper	NOUN
ejpam-6834	1892	7	groups	group	NOUN
ejpam-6834	1892	8	.	.	PUNCT
ejpam-6834	1893	1	2023	2023	NUM
ejpam-6834	1893	2	neutrosophic	neutrosophic	ADJ
ejpam-6834	1893	3	superhyperalgebra	superhyperalgebra	NOUN
ejpam-6834	1893	4	and	and	CCONJ
ejpam-6834	1893	5	new	new	ADJ
ejpam-6834	1893	6	types	type	NOUN
ejpam-6834	1893	7	of	of	ADP
ejpam-6834	1893	8	topologies	topology	NOUN
ejpam-6834	1893	9	,	,	PUNCT
ejpam-6834	1893	10	page	page	NOUN
ejpam-6834	1893	11	25	25	NUM
ejpam-6834	1893	12	,	,	PUNCT
ejpam-6834	1893	13	2023	2023	NUM
ejpam-6834	1893	14	.	.	PUNCT
ejpam-6834	1894	1	[	[	X
ejpam-6834	1894	2	35	35	NUM
ejpam-6834	1894	3	]	]	PUNCT
ejpam-6834	1894	4	florentin	florentin	PROPN
ejpam-6834	1894	5	smarandache	smarandache	NOUN
ejpam-6834	1894	6	.	.	PUNCT
ejpam-6834	1895	1	introduction	introduction	NOUN
ejpam-6834	1895	2	to	to	ADP
ejpam-6834	1895	3	superhyperalgebra	superhyperalgebra	NOUN
ejpam-6834	1895	4	and	and	CCONJ
ejpam-6834	1895	5	neutrosophic	neutrosophic	ADJ
ejpam-6834	1895	6	superhyperalgebra	superhyperalgebra	NOUN
ejpam-6834	1895	7	.	.	PUNCT
ejpam-6834	1896	1	infinite	infinite	ADJ
ejpam-6834	1896	2	study	study	NOUN
ejpam-6834	1896	3	,	,	PUNCT
ejpam-6834	1896	4	2022	2022	NUM
ejpam-6834	1896	5	.	.	PUNCT
ejpam-6834	1897	1	[	[	X
ejpam-6834	1897	2	36	36	NUM
ejpam-6834	1897	3	]	]	PUNCT
ejpam-6834	1897	4	takaaki	takaaki	NOUN
ejpam-6834	1897	5	fujita	fujita	PROPN
ejpam-6834	1897	6	.	.	PUNCT
ejpam-6834	1898	1	chemical	chemical	NOUN
ejpam-6834	1898	2	hyperstructures	hyperstructure	NOUN
ejpam-6834	1898	3	,	,	PUNCT
ejpam-6834	1898	4	superhyperstructures	superhyperstructure	NOUN
ejpam-6834	1898	5	,	,	PUNCT
ejpam-6834	1898	6	and	and	CCONJ
ejpam-6834	1898	7	shv	shv	NOUN
ejpam-6834	1898	8	-	-	PUNCT
ejpam-6834	1898	9	structures	structure	NOUN
ejpam-6834	1898	10	:	:	PUNCT
ejpam-6834	1898	11	toward	toward	ADP
ejpam-6834	1898	12	a	a	DET
ejpam-6834	1898	13	generalized	generalize	VERB
ejpam-6834	1898	14	framework	framework	NOUN
ejpam-6834	1898	15	for	for	ADP
ejpam-6834	1898	16	hierarchical	hierarchical	ADJ
ejpam-6834	1898	17	chemical	chemical	NOUN
ejpam-6834	1898	18	modeling	modeling	NOUN
ejpam-6834	1898	19	.	.	PUNCT
ejpam-6834	1899	1	2025	2025	NUM
ejpam-6834	1899	2	.	.	PUNCT
ejpam-6834	1900	1	[	[	X
ejpam-6834	1900	2	37	37	NUM
ejpam-6834	1900	3	]	]	PUNCT
ejpam-6834	1900	4	takaaki	takaaki	NOUN
ejpam-6834	1900	5	fujita	fujita	PROPN
ejpam-6834	1900	6	.	.	PUNCT
ejpam-6834	1901	1	analysis	analysis	NOUN
ejpam-6834	1901	2	and	and	CCONJ
ejpam-6834	1901	3	proposal	proposal	NOUN
ejpam-6834	1901	4	of	of	ADP
ejpam-6834	1901	5	chemical	chemical	ADJ
ejpam-6834	1901	6	hyperstructures	hyperstructure	NOUN
ejpam-6834	1901	7	and	and	CCONJ
ejpam-6834	1901	8	superhyperstructures	superhyperstructure	NOUN
ejpam-6834	1901	9	:	:	PUNCT
ejpam-6834	1901	10	extending	extend	VERB
ejpam-6834	1901	11	chemical	chemical	NOUN
ejpam-6834	1901	12	topology	topology	NOUN
ejpam-6834	1901	13	,	,	PUNCT
ejpam-6834	1901	14	molecular	molecular	ADJ
ejpam-6834	1901	15	knots	knot	NOUN
ejpam-6834	1901	16	,	,	PUNCT
ejpam-6834	1901	17	molecular	molecular	ADJ
ejpam-6834	1901	18	geometry	geometry	NOUN
ejpam-6834	1901	19	,	,	PUNCT
ejpam-6834	1901	20	and	and	CCONJ
ejpam-6834	1901	21	circuit	circuit	NOUN
ejpam-6834	1901	22	topology	topology	NOUN
ejpam-6834	1901	23	.	.	PUNCT
ejpam-6834	1902	1	2025	2025	NUM
ejpam-6834	1902	2	.	.	PUNCT
ejpam-6834	1903	1	[	[	X
ejpam-6834	1903	2	38	38	NUM
ejpam-6834	1903	3	]	]	PUNCT
ejpam-6834	1903	4	m	m	PROPN
ejpam-6834	1903	5	maharin	maharin	NOUN
ejpam-6834	1903	6	.	.	PUNCT
ejpam-6834	1904	1	hyper	hyper	ADJ
ejpam-6834	1904	2	fuzzy	fuzzy	ADJ
ejpam-6834	1904	3	cosets	coset	NOUN
ejpam-6834	1904	4	.	.	PUNCT
ejpam-6834	1905	1	scholar	scholar	NOUN
ejpam-6834	1905	2	:	:	PUNCT
ejpam-6834	1905	3	national	national	ADJ
ejpam-6834	1905	4	school	school	NOUN
ejpam-6834	1905	5	of	of	ADP
ejpam-6834	1905	6	leadership	leadership	NOUN
ejpam-6834	1905	7	,	,	PUNCT
ejpam-6834	1905	8	9(1.2	9(1.2	NUM
ejpam-6834	1905	9	)	)	PUNCT
ejpam-6834	1905	10	,	,	PUNCT
ejpam-6834	1905	11	2020	2020	NUM
ejpam-6834	1905	12	.	.	PUNCT
ejpam-6834	1906	1	[	[	X
ejpam-6834	1906	2	39	39	NUM
ejpam-6834	1906	3	]	]	PUNCT
ejpam-6834	1906	4	m	m	PROPN
ejpam-6834	1906	5	maharin	maharin	NOUN
ejpam-6834	1906	6	.	.	PUNCT
ejpam-6834	1907	1	an	an	DET
ejpam-6834	1907	2	over	over	ADP
ejpam-6834	1907	3	view	view	NOUN
ejpam-6834	1907	4	on	on	ADP
ejpam-6834	1907	5	hyper	hyper	ADJ
ejpam-6834	1907	6	fuzzy	fuzzy	ADJ
ejpam-6834	1907	7	subgroups	subgroup	NOUN
ejpam-6834	1907	8	.	.	PUNCT
ejpam-6834	1908	1	scholar	scholar	NOUN
ejpam-6834	1908	2	:	:	PUNCT
ejpam-6834	1908	3	national	national	ADJ
ejpam-6834	1908	4	school	school	NOUN
ejpam-6834	1908	5	of	of	ADP
ejpam-6834	1908	6	leadership	leadership	NOUN
ejpam-6834	1908	7	,	,	PUNCT
ejpam-6834	1908	8	9(1.2	9(1.2	NUM
ejpam-6834	1908	9	)	)	PUNCT
ejpam-6834	1908	10	,	,	PUNCT
ejpam-6834	1908	11	2020	2020	NUM
ejpam-6834	1908	12	.	.	PUNCT
ejpam-6834	1909	1	[	[	X
ejpam-6834	1909	2	40	40	NUM
ejpam-6834	1909	3	]	]	PUNCT
ejpam-6834	1909	4	florentin	florentin	PROPN
ejpam-6834	1909	5	smarandache	smarandache	NOUN
ejpam-6834	1909	6	.	.	PUNCT
ejpam-6834	1910	1	extension	extension	NOUN
ejpam-6834	1910	2	of	of	ADP
ejpam-6834	1910	3	soft	soft	ADJ
ejpam-6834	1910	4	set	set	NOUN
ejpam-6834	1910	5	to	to	ADP
ejpam-6834	1910	6	hypersoft	hypersoft	PROPN
ejpam-6834	1910	7	set	set	PROPN
ejpam-6834	1910	8	,	,	PUNCT
ejpam-6834	1910	9	and	and	CCONJ
ejpam-6834	1910	10	then	then	ADV
ejpam-6834	1910	11	to	to	ADP
ejpam-6834	1910	12	plithogenic	plithogenic	ADJ
ejpam-6834	1910	13	hypersoft	hypersoft	PROPN
ejpam-6834	1910	14	set	set	PROPN
ejpam-6834	1910	15	.	.	PUNCT
ejpam-6834	1911	1	neutrosophic	neutrosophic	ADJ
ejpam-6834	1911	2	sets	set	NOUN
ejpam-6834	1911	3	and	and	CCONJ
ejpam-6834	1911	4	systems	system	NOUN
ejpam-6834	1911	5	,	,	PUNCT
ejpam-6834	1911	6	22(1):168–170	22(1):168–170	PROPN
ejpam-6834	1911	7	,	,	PUNCT
ejpam-6834	1911	8	2018	2018	NUM
ejpam-6834	1911	9	.	.	PUNCT
ejpam-6834	1912	1	[	[	X
ejpam-6834	1912	2	41	41	NUM
ejpam-6834	1912	3	]	]	X
ejpam-6834	1912	4	takaaki	takaaki	NOUN
ejpam-6834	1912	5	fujita	fujita	NOUN
ejpam-6834	1912	6	and	and	CCONJ
ejpam-6834	1912	7	florentin	florentin	PROPN
ejpam-6834	1912	8	smarandache	smarandache	PROPN
ejpam-6834	1912	9	.	.	PUNCT
ejpam-6834	1913	1	an	an	DET
ejpam-6834	1913	2	introduction	introduction	NOUN
ejpam-6834	1913	3	to	to	ADP
ejpam-6834	1913	4	advanced	advanced	ADJ
ejpam-6834	1913	5	soft	soft	ADJ
ejpam-6834	1913	6	set	set	ADJ
ejpam-6834	1913	7	variants	variant	NOUN
ejpam-6834	1913	8	:	:	PUNCT
ejpam-6834	1913	9	superhypersoft	superhypersoft	PROPN
ejpam-6834	1913	10	sets	set	VERB
ejpam-6834	1913	11	,	,	PUNCT
ejpam-6834	1913	12	indetermsuperhypersoft	indetermsuperhypersoft	NOUN
ejpam-6834	1913	13	sets	set	NOUN
ejpam-6834	1913	14	,	,	PUNCT
ejpam-6834	1913	15	indetermtreesoft	indetermtreesoft	ADJ
ejpam-6834	1913	16	sets	set	NOUN
ejpam-6834	1913	17	,	,	PUNCT
ejpam-6834	1913	18	bihypersoft	bihypersoft	NOUN
ejpam-6834	1913	19	sets	set	NOUN
ejpam-6834	1913	20	,	,	PUNCT
ejpam-6834	1913	21	graphicsoft	graphicsoft	PROPN
ejpam-6834	1913	22	sets	set	NOUN
ejpam-6834	1913	23	,	,	PUNCT
ejpam-6834	1913	24	and	and	CCONJ
ejpam-6834	1913	25	beyond	beyond	ADP
ejpam-6834	1913	26	.	.	PUNCT
ejpam-6834	1913	27	neutrosophic	neutrosophic	ADJ
ejpam-6834	1913	28	sets	set	NOUN
ejpam-6834	1913	29	and	and	CCONJ
ejpam-6834	1913	30	systems	system	NOUN
ejpam-6834	1913	31	,	,	PUNCT
ejpam-6834	1913	32	82:817	82:817	NUM
ejpam-6834	1913	33	–	–	PUNCT
ejpam-6834	1913	34	843	843	NUM
ejpam-6834	1913	35	,	,	PUNCT
ejpam-6834	1913	36	2025	2025	NUM
ejpam-6834	1913	37	.	.	PUNCT
ejpam-6834	1914	1	[	[	X
ejpam-6834	1914	2	42	42	NUM
ejpam-6834	1914	3	]	]	PUNCT
ejpam-6834	1914	4	takaaki	takaaki	NOUN
ejpam-6834	1914	5	fujita	fujita	NOUN
ejpam-6834	1914	6	and	and	CCONJ
ejpam-6834	1914	7	florentin	florentin	PROPN
ejpam-6834	1914	8	smarandache	smarandache	NOUN
ejpam-6834	1914	9	.	.	PUNCT
ejpam-6834	1915	1	harnessing	harness	VERB
ejpam-6834	1915	2	quantum	quantum	ADJ
ejpam-6834	1915	3	superposition	superposition	NOUN
ejpam-6834	1915	4	in	in	ADP
ejpam-6834	1915	5	soft	soft	ADJ
ejpam-6834	1915	6	set	set	NOUN
ejpam-6834	1915	7	theory	theory	NOUN
ejpam-6834	1915	8	:	:	PUNCT
ejpam-6834	1915	9	introducing	introduce	VERB
ejpam-6834	1915	10	quantum	quantum	ADJ
ejpam-6834	1915	11	hypersoft	hypersoft	NOUN
ejpam-6834	1915	12	and	and	CCONJ
ejpam-6834	1915	13	superhypersoft	superhypersoft	PROPN
ejpam-6834	1915	14	sets	set	VERB
ejpam-6834	1915	15	.	.	PUNCT
ejpam-6834	1916	1	european	european	PROPN
ejpam-6834	1916	2	t.	t.	PROPN
ejpam-6834	1916	3	fujita	fujita	PROPN
ejpam-6834	1916	4	,	,	PUNCT
ejpam-6834	1916	5	f.smarandache	f.smarandache	NOUN
ejpam-6834	1916	6	/	/	SYM
ejpam-6834	1916	7	eur	eur	PROPN
ejpam-6834	1916	8	.	.	PUNCT
ejpam-6834	1917	1	j.	j.	PROPN
ejpam-6834	1917	2	pure	pure	PROPN
ejpam-6834	1917	3	appl	appl	PROPN
ejpam-6834	1917	4	.	.	PROPN
ejpam-6834	1917	5	math	math	PROPN
ejpam-6834	1917	6	,	,	PUNCT
ejpam-6834	1917	7	18	18	NUM
ejpam-6834	1917	8	(	(	PUNCT
ejpam-6834	1917	9	4	4	NUM
ejpam-6834	1917	10	)	)	PUNCT
ejpam-6834	1917	11	(	(	PUNCT
ejpam-6834	1917	12	2025	2025	NUM
ejpam-6834	1917	13	)	)	PUNCT
ejpam-6834	1917	14	,	,	PUNCT
ejpam-6834	1917	15	6834	6834	NUM
ejpam-6834	1917	16	68	68	NUM
ejpam-6834	1917	17	of	of	ADP
ejpam-6834	1917	18	69	69	NUM
ejpam-6834	1917	19	journal	journal	NOUN
ejpam-6834	1917	20	of	of	ADP
ejpam-6834	1917	21	pure	pure	ADJ
ejpam-6834	1917	22	and	and	CCONJ
ejpam-6834	1917	23	applied	applied	ADJ
ejpam-6834	1917	24	mathematics	mathematic	NOUN
ejpam-6834	1917	25	,	,	PUNCT
ejpam-6834	1917	26	18(3):6607–6607	18(3):6607–6607	NUM
ejpam-6834	1917	27	,	,	PUNCT
ejpam-6834	1917	28	2025	2025	NUM
ejpam-6834	1917	29	.	.	PUNCT
ejpam-6834	1918	1	[	[	X
ejpam-6834	1918	2	43	43	NUM
ejpam-6834	1918	3	]	]	PUNCT
ejpam-6834	1918	4	takaaki	takaaki	NOUN
ejpam-6834	1918	5	fujita	fujita	PROPN
ejpam-6834	1918	6	.	.	PUNCT
ejpam-6834	1919	1	a	a	DET
ejpam-6834	1919	2	study	study	NOUN
ejpam-6834	1919	3	on	on	ADP
ejpam-6834	1919	4	hyperfuzzy	hyperfuzzy	PROPN
ejpam-6834	1919	5	hyperrough	hyperrough	NOUN
ejpam-6834	1919	6	sets	set	NOUN
ejpam-6834	1919	7	,	,	PUNCT
ejpam-6834	1919	8	hyperneutrosophic	hyperneutrosophic	ADJ
ejpam-6834	1919	9	hyperrough	hyperrough	NOUN
ejpam-6834	1919	10	sets	set	NOUN
ejpam-6834	1919	11	,	,	PUNCT
ejpam-6834	1919	12	and	and	CCONJ
ejpam-6834	1919	13	hypersoft	hypersoft	NOUN
ejpam-6834	1919	14	hyperrough	hyperrough	NOUN
ejpam-6834	1919	15	sets	set	VERB
ejpam-6834	1919	16	with	with	ADP
ejpam-6834	1919	17	applications	application	NOUN
ejpam-6834	1919	18	in	in	ADP
ejpam-6834	1919	19	cybersecurity	cybersecurity	NOUN
ejpam-6834	1919	20	.	.	PUNCT
ejpam-6834	1920	1	artificial	artificial	ADJ
ejpam-6834	1920	2	intelligence	intelligence	NOUN
ejpam-6834	1920	3	in	in	ADP
ejpam-6834	1920	4	cybersecurity	cybersecurity	NOUN
ejpam-6834	1920	5	,	,	PUNCT
ejpam-6834	1920	6	2:14–36	2:14–36	NUM
ejpam-6834	1920	7	,	,	PUNCT
ejpam-6834	1920	8	2025	2025	NUM
ejpam-6834	1920	9	.	.	PUNCT
ejpam-6834	1921	1	[	[	X
ejpam-6834	1921	2	44	44	NUM
ejpam-6834	1921	3	]	]	PUNCT
ejpam-6834	1921	4	takaaki	takaaki	NOUN
ejpam-6834	1921	5	fujita	fujita	NOUN
ejpam-6834	1921	6	and	and	CCONJ
ejpam-6834	1921	7	florentin	florentin	PROPN
ejpam-6834	1921	8	smarandache	smarandache	PROPN
ejpam-6834	1921	9	.	.	PUNCT
ejpam-6834	1922	1	a	a	DET
ejpam-6834	1922	2	concise	concise	ADJ
ejpam-6834	1922	3	introduction	introduction	NOUN
ejpam-6834	1922	4	to	to	ADP
ejpam-6834	1922	5	hyperfuzzy	hyperfuzzy	PROPN
ejpam-6834	1922	6	,	,	PUNCT
ejpam-6834	1922	7	hyperneutrosophic	hyperneutrosophic	ADJ
ejpam-6834	1922	8	,	,	PUNCT
ejpam-6834	1922	9	hyperplithogenic	hyperplithogenic	ADJ
ejpam-6834	1922	10	,	,	PUNCT
ejpam-6834	1922	11	hypersoft	hypersoft	NOUN
ejpam-6834	1922	12	,	,	PUNCT
ejpam-6834	1922	13	and	and	CCONJ
ejpam-6834	1922	14	hyperrough	hyperrough	NOUN
ejpam-6834	1922	15	sets	set	VERB
ejpam-6834	1922	16	with	with	ADP
ejpam-6834	1922	17	practical	practical	ADJ
ejpam-6834	1922	18	examples	example	NOUN
ejpam-6834	1922	19	.	.	PUNCT
ejpam-6834	1923	1	neutrosophic	neutrosophic	ADJ
ejpam-6834	1923	2	sets	set	NOUN
ejpam-6834	1923	3	and	and	CCONJ
ejpam-6834	1923	4	systems	system	NOUN
ejpam-6834	1923	5	,	,	PUNCT
ejpam-6834	1923	6	80:609–631	80:609–631	NUM
ejpam-6834	1923	7	,	,	PUNCT
ejpam-6834	1923	8	2025	2025	NUM
ejpam-6834	1923	9	.	.	PUNCT
ejpam-6834	1924	1	[	[	X
ejpam-6834	1924	2	45	45	NUM
ejpam-6834	1924	3	]	]	PUNCT
ejpam-6834	1924	4	takaaki	takaaki	NOUN
ejpam-6834	1924	5	fujita	fujita	NOUN
ejpam-6834	1924	6	and	and	CCONJ
ejpam-6834	1924	7	florentin	florentin	PROPN
ejpam-6834	1924	8	smarandache	smarandache	NOUN
ejpam-6834	1924	9	.	.	PUNCT
ejpam-6834	1925	1	some	some	DET
ejpam-6834	1925	2	types	type	NOUN
ejpam-6834	1925	3	of	of	ADP
ejpam-6834	1925	4	hyperneutrosophic	hyperneutrosophic	ADJ
ejpam-6834	1925	5	set	set	NOUN
ejpam-6834	1925	6	(	(	PUNCT
ejpam-6834	1925	7	7	7	NUM
ejpam-6834	1925	8	):	):	PUNCT
ejpam-6834	1925	9	type	type	NOUN
ejpam-6834	1925	10	-	-	PUNCT
ejpam-6834	1925	11	m	m	NOUN
ejpam-6834	1925	12	,	,	PUNCT
ejpam-6834	1925	13	nonstationary	nonstationary	ADJ
ejpam-6834	1925	14	,	,	PUNCT
ejpam-6834	1925	15	subset	subset	NOUN
ejpam-6834	1925	16	-	-	PUNCT
ejpam-6834	1925	17	valued	value	VERB
ejpam-6834	1925	18	,	,	PUNCT
ejpam-6834	1925	19	and	and	CCONJ
ejpam-6834	1925	20	complex	complex	ADJ
ejpam-6834	1925	21	refined	refine	VERB
ejpam-6834	1925	22	.	.	PUNCT
ejpam-6834	1926	1	infinite	infinite	ADJ
ejpam-6834	1926	2	study	study	NOUN
ejpam-6834	1926	3	,	,	PUNCT
ejpam-6834	1926	4	2025	2025	NUM
ejpam-6834	1926	5	.	.	PUNCT
ejpam-6834	1927	1	[	[	X
ejpam-6834	1927	2	46	46	NUM
ejpam-6834	1927	3	]	]	PUNCT
ejpam-6834	1927	4	takaaki	takaaki	NOUN
ejpam-6834	1927	5	fujita	fujita	PROPN
ejpam-6834	1927	6	.	.	PUNCT
ejpam-6834	1928	1	hyperplithogenic	hyperplithogenic	ADJ
ejpam-6834	1928	2	cubic	cubic	ADJ
ejpam-6834	1928	3	set	set	VERB
ejpam-6834	1928	4	and	and	CCONJ
ejpam-6834	1928	5	superhyperplithogenic	superhyperplithogenic	ADJ
ejpam-6834	1928	6	cubic	cubic	ADJ
ejpam-6834	1928	7	set	set	NOUN
ejpam-6834	1928	8	.	.	PUNCT
ejpam-6834	1929	1	advancing	advance	VERB
ejpam-6834	1929	2	uncertain	uncertain	ADJ
ejpam-6834	1929	3	combinatorics	combinatoric	NOUN
ejpam-6834	1929	4	through	through	ADP
ejpam-6834	1929	5	graphization	graphization	NOUN
ejpam-6834	1929	6	,	,	PUNCT
ejpam-6834	1929	7	hyperization	hyperization	NOUN
ejpam-6834	1929	8	,	,	PUNCT
ejpam-6834	1929	9	and	and	CCONJ
ejpam-6834	1929	10	uncertainization	uncertainization	NOUN
ejpam-6834	1929	11	:	:	PUNCT
ejpam-6834	1929	12	fuzzy	fuzzy	ADJ
ejpam-6834	1929	13	,	,	PUNCT
ejpam-6834	1929	14	neutrosophic	neutrosophic	ADJ
ejpam-6834	1929	15	,	,	PUNCT
ejpam-6834	1929	16	soft	soft	ADJ
ejpam-6834	1929	17	,	,	PUNCT
ejpam-6834	1929	18	rough	rough	ADJ
ejpam-6834	1929	19	,	,	PUNCT
ejpam-6834	1929	20	and	and	CCONJ
ejpam-6834	1929	21	beyond	beyond	ADP
ejpam-6834	1929	22	,	,	PUNCT
ejpam-6834	1929	23	page	page	NOUN
ejpam-6834	1929	24	79	79	NUM
ejpam-6834	1929	25	,	,	PUNCT
ejpam-6834	1929	26	2025	2025	NUM
ejpam-6834	1929	27	.	.	PUNCT
ejpam-6834	1930	1	[	[	X
ejpam-6834	1930	2	47	47	NUM
ejpam-6834	1930	3	]	]	PUNCT
ejpam-6834	1930	4	takaaki	takaaki	NOUN
ejpam-6834	1930	5	fujitar	fujitar	NOUN
ejpam-6834	1930	6	.	.	PUNCT
ejpam-6834	1931	1	hyperfuzzy	hyperfuzzy	ADJ
ejpam-6834	1931	2	and	and	CCONJ
ejpam-6834	1931	3	superhyperfuzzy	superhyperfuzzy	ADJ
ejpam-6834	1931	4	extensions	extension	NOUN
ejpam-6834	1931	5	of	of	ADP
ejpam-6834	1931	6	linear	linear	PROPN
ejpam-6834	1931	7	programming	programming	NOUN
ejpam-6834	1931	8	:	:	PUNCT
ejpam-6834	1931	9	modelsand	modelsand	PROPN
ejpam-6834	1931	10	mathematical	mathematical	ADJ
ejpam-6834	1931	11	foundations	foundation	NOUN
ejpam-6834	1931	12	.	.	PUNCT
ejpam-6834	1932	1	optimality	optimality	NOUN
ejpam-6834	1932	2	,	,	PUNCT
ejpam-6834	1932	3	2(3):127–140	2(3):127–140	NUM
ejpam-6834	1932	4	,	,	PUNCT
ejpam-6834	1932	5	2025	2025	NUM
ejpam-6834	1932	6	.	.	PUNCT
ejpam-6834	1933	1	[	[	X
ejpam-6834	1933	2	48	48	NUM
ejpam-6834	1933	3	]	]	X
ejpam-6834	1933	4	john	john	PROPN
ejpam-6834	1933	5	t	t	PROPN
ejpam-6834	1933	6	rickard	rickard	PROPN
ejpam-6834	1933	7	,	,	PUNCT
ejpam-6834	1933	8	janet	janet	PROPN
ejpam-6834	1933	9	aisbett	aisbett	PROPN
ejpam-6834	1933	10	,	,	PUNCT
ejpam-6834	1933	11	and	and	CCONJ
ejpam-6834	1933	12	j	j	PROPN
ejpam-6834	1933	13	tyler	tyler	PROPN
ejpam-6834	1933	14	rickard	rickard	PROPN
ejpam-6834	1933	15	.	.	PUNCT
ejpam-6834	1934	1	on	on	ADP
ejpam-6834	1934	2	a	a	DET
ejpam-6834	1934	3	class	class	NOUN
ejpam-6834	1934	4	of	of	ADP
ejpam-6834	1934	5	general	general	ADJ
ejpam-6834	1934	6	type	type	NOUN
ejpam-6834	1934	7	-	-	PUNCT
ejpam-6834	1934	8	n	n	CCONJ
ejpam-6834	1934	9	normal	normal	ADJ
ejpam-6834	1934	10	fuzzy	fuzzy	ADJ
ejpam-6834	1934	11	sets	set	NOUN
ejpam-6834	1934	12	synthesized	synthesize	VERB
ejpam-6834	1934	13	from	from	ADP
ejpam-6834	1934	14	subject	subject	ADJ
ejpam-6834	1934	15	matter	matter	NOUN
ejpam-6834	1934	16	expert	expert	NOUN
ejpam-6834	1934	17	inputs	input	NOUN
ejpam-6834	1934	18	.	.	PUNCT
ejpam-6834	1935	1	ieee	ieee	NOUN
ejpam-6834	1935	2	transactions	transaction	NOUN
ejpam-6834	1935	3	on	on	ADP
ejpam-6834	1935	4	fuzzy	fuzzy	ADJ
ejpam-6834	1935	5	systems	system	NOUN
ejpam-6834	1935	6	,	,	PUNCT
ejpam-6834	1935	7	2024	2024	NUM
ejpam-6834	1935	8	.	.	PUNCT
ejpam-6834	1936	1	[	[	X
ejpam-6834	1936	2	49	49	NUM
ejpam-6834	1936	3	]	]	PUNCT
ejpam-6834	1936	4	f.	f.	PROPN
ejpam-6834	1936	5	smarandache	smarandache	PROPN
ejpam-6834	1936	6	.	.	PUNCT
ejpam-6834	1937	1	introduction	introduction	NOUN
ejpam-6834	1937	2	to	to	ADP
ejpam-6834	1937	3	superhyperalgebra	superhyperalgebra	NOUN
ejpam-6834	1937	4	and	and	CCONJ
ejpam-6834	1937	5	neutrosophic	neutrosophic	ADJ
ejpam-6834	1937	6	superhyperalgebra	superhyperalgebra	NOUN
ejpam-6834	1937	7	.	.	PUNCT
ejpam-6834	1938	1	journal	journal	NOUN
ejpam-6834	1938	2	of	of	ADP
ejpam-6834	1938	3	algebraic	algebraic	PROPN
ejpam-6834	1938	4	hyperstructures	hyperstructure	NOUN
ejpam-6834	1938	5	and	and	CCONJ
ejpam-6834	1938	6	logical	logical	ADJ
ejpam-6834	1938	7	algebras	algebra	NOUN
ejpam-6834	1938	8	,	,	PUNCT
ejpam-6834	1938	9	2022	2022	NUM
ejpam-6834	1938	10	.	.	PUNCT
ejpam-6834	1939	1	[	[	X
ejpam-6834	1939	2	50	50	NUM
ejpam-6834	1939	3	]	]	X
ejpam-6834	1939	4	souzana	souzana	PROPN
ejpam-6834	1939	5	vougioukli	vougioukli	ADJ
ejpam-6834	1939	6	.	.	PUNCT
ejpam-6834	1940	1	helix	helix	ADJ
ejpam-6834	1940	2	hyperoperation	hyperoperation	NOUN
ejpam-6834	1940	3	in	in	ADP
ejpam-6834	1940	4	teaching	teach	VERB
ejpam-6834	1940	5	research	research	NOUN
ejpam-6834	1940	6	.	.	PUNCT
ejpam-6834	1941	1	science	science	NOUN
ejpam-6834	1941	2	&	&	CCONJ
ejpam-6834	1941	3	philosophy	philosophy	PROPN
ejpam-6834	1941	4	,	,	PUNCT
ejpam-6834	1941	5	8(2):157–163	8(2):157–163	NUM
ejpam-6834	1941	6	,	,	PUNCT
ejpam-6834	1941	7	2020	2020	NUM
ejpam-6834	1941	8	.	.	PUNCT
ejpam-6834	1942	1	[	[	X
ejpam-6834	1942	2	51	51	NUM
ejpam-6834	1942	3	]	]	X
ejpam-6834	1942	4	souzana	souzana	PROPN
ejpam-6834	1942	5	vougioukli	vougioukli	NOUN
ejpam-6834	1942	6	.	.	PUNCT
ejpam-6834	1943	1	hyperoperations	hyperoperation	NOUN
ejpam-6834	1943	2	defined	define	VERB
ejpam-6834	1943	3	on	on	ADP
ejpam-6834	1943	4	sets	set	NOUN
ejpam-6834	1943	5	of	of	ADP
ejpam-6834	1943	6	s	s	NOUN
ejpam-6834	1943	7	-helix	-helix	ADJ
ejpam-6834	1943	8	matrices	matrix	NOUN
ejpam-6834	1943	9	.	.	PUNCT
ejpam-6834	1944	1	2020	2020	NUM
ejpam-6834	1944	2	.	.	PUNCT
ejpam-6834	1945	1	[	[	X
ejpam-6834	1945	2	52	52	NUM
ejpam-6834	1945	3	]	]	SYM
ejpam-6834	1945	4	bijan	bijan	PROPN
ejpam-6834	1945	5	davvaz	davvaz	PROPN
ejpam-6834	1945	6	and	and	CCONJ
ejpam-6834	1945	7	thomas	thomas	PROPN
ejpam-6834	1945	8	vougiouklis	vougiouklis	PROPN
ejpam-6834	1945	9	.	.	PUNCT
ejpam-6834	1946	1	walk	walk	VERB
ejpam-6834	1946	2	through	through	ADP
ejpam-6834	1946	3	weak	weak	ADJ
ejpam-6834	1946	4	hyperstructures	hyperstructure	NOUN
ejpam-6834	1946	5	,	,	PUNCT
ejpam-6834	1946	6	a	a	DET
ejpam-6834	1946	7	:	:	PUNCT
ejpam-6834	1946	8	hv	hv	NOUN
ejpam-6834	1946	9	-	-	PUNCT
ejpam-6834	1946	10	structures	structure	NOUN
ejpam-6834	1946	11	.	.	PUNCT
ejpam-6834	1947	1	world	world	NOUN
ejpam-6834	1947	2	scientific	scientific	ADJ
ejpam-6834	1947	3	,	,	PUNCT
ejpam-6834	1947	4	2018	2018	NUM
ejpam-6834	1947	5	.	.	PUNCT
ejpam-6834	1948	1	[	[	X
ejpam-6834	1948	2	53	53	NUM
ejpam-6834	1948	3	]	]	PUNCT
ejpam-6834	1948	4	takaaki	takaaki	NOUN
ejpam-6834	1948	5	fujita	fujita	NOUN
ejpam-6834	1948	6	.	.	PUNCT
ejpam-6834	1949	1	expanding	expand	VERB
ejpam-6834	1949	2	horizons	horizon	NOUN
ejpam-6834	1949	3	of	of	ADP
ejpam-6834	1949	4	plithogenic	plithogenic	ADJ
ejpam-6834	1949	5	superhyperstructures	superhyperstructure	NOUN
ejpam-6834	1949	6	:	:	PUNCT
ejpam-6834	1949	7	applications	application	NOUN
ejpam-6834	1949	8	in	in	ADP
ejpam-6834	1949	9	decision	decision	NOUN
ejpam-6834	1949	10	-	-	PUNCT
ejpam-6834	1949	11	making	making	NOUN
ejpam-6834	1949	12	,	,	PUNCT
ejpam-6834	1949	13	control	control	NOUN
ejpam-6834	1949	14	,	,	PUNCT
ejpam-6834	1949	15	and	and	CCONJ
ejpam-6834	1949	16	neuro	neuro	PROPN
ejpam-6834	1949	17	systems	system	NOUN
ejpam-6834	1949	18	.	.	PUNCT
ejpam-6834	1950	1	advancing	advance	VERB
ejpam-6834	1950	2	uncertain	uncertain	ADJ
ejpam-6834	1950	3	combinatorics	combinatoric	NOUN
ejpam-6834	1950	4	through	through	ADP
ejpam-6834	1950	5	graphization	graphization	NOUN
ejpam-6834	1950	6	,	,	PUNCT
ejpam-6834	1950	7	hyperization	hyperization	NOUN
ejpam-6834	1950	8	,	,	PUNCT
ejpam-6834	1950	9	and	and	CCONJ
ejpam-6834	1950	10	uncertainization	uncertainization	NOUN
ejpam-6834	1950	11	:	:	PUNCT
ejpam-6834	1950	12	fuzzy	fuzzy	ADJ
ejpam-6834	1950	13	,	,	PUNCT
ejpam-6834	1950	14	neutrosophic	neutrosophic	ADJ
ejpam-6834	1950	15	,	,	PUNCT
ejpam-6834	1950	16	soft	soft	ADJ
ejpam-6834	1950	17	,	,	PUNCT
ejpam-6834	1950	18	rough	rough	ADJ
ejpam-6834	1950	19	,	,	PUNCT
ejpam-6834	1950	20	and	and	CCONJ
ejpam-6834	1950	21	beyond	beyond	ADP
ejpam-6834	1950	22	,	,	PUNCT
ejpam-6834	1950	23	page	page	NOUN
ejpam-6834	1950	24	416	416	NUM
ejpam-6834	1950	25	,	,	PUNCT
ejpam-6834	1950	26	2025	2025	NUM
ejpam-6834	1950	27	.	.	PUNCT
ejpam-6834	1951	1	[	[	X
ejpam-6834	1951	2	54	54	NUM
ejpam-6834	1951	3	]	]	PUNCT
ejpam-6834	1951	4	tm	tm	PROPN
ejpam-6834	1951	5	nishad	nishad	PROPN
ejpam-6834	1951	6	,	,	PUNCT
ejpam-6834	1951	7	talal	talal	PROPN
ejpam-6834	1951	8	ali	ali	PROPN
ejpam-6834	1951	9	al	al	PROPN
ejpam-6834	1951	10	-	-	PUNCT
ejpam-6834	1951	11	hawary	hawary	PROPN
ejpam-6834	1951	12	,	,	PUNCT
ejpam-6834	1951	13	and	and	CCONJ
ejpam-6834	1951	14	b	b	PROPN
ejpam-6834	1951	15	mohamed	mohamed	PROPN
ejpam-6834	1951	16	harif	harif	PROPN
ejpam-6834	1951	17	.	.	PUNCT
ejpam-6834	1952	1	general	general	ADJ
ejpam-6834	1952	2	fuzzy	fuzzy	ADJ
ejpam-6834	1952	3	graphs	graph	NOUN
ejpam-6834	1952	4	.	.	PUNCT
ejpam-6834	1953	1	ratio	ratio	PROPN
ejpam-6834	1953	2	mathematica	mathematica	PROPN
ejpam-6834	1953	3	,	,	PUNCT
ejpam-6834	1953	4	47	47	NUM
ejpam-6834	1953	5	,	,	PUNCT
ejpam-6834	1953	6	2023	2023	NUM
ejpam-6834	1953	7	.	.	PUNCT
ejpam-6834	1954	1	[	[	X
ejpam-6834	1954	2	55	55	NUM
ejpam-6834	1954	3	]	]	X
ejpam-6834	1954	4	talal	talal	PROPN
ejpam-6834	1954	5	al	al	PROPN
ejpam-6834	1954	6	-	-	PUNCT
ejpam-6834	1954	7	hawary	hawary	PROPN
ejpam-6834	1954	8	.	.	PUNCT
ejpam-6834	1955	1	complete	complete	ADJ
ejpam-6834	1955	2	fuzzy	fuzzy	ADJ
ejpam-6834	1955	3	graphs	graph	NOUN
ejpam-6834	1955	4	.	.	PUNCT
ejpam-6834	1956	1	international	international	ADJ
ejpam-6834	1956	2	journal	journal	PROPN
ejpam-6834	1956	3	of	of	ADP
ejpam-6834	1956	4	mathematical	mathematical	ADJ
ejpam-6834	1956	5	combinatorics	combinatoric	NOUN
ejpam-6834	1956	6	,	,	PUNCT
ejpam-6834	1956	7	4:26	4:26	NUM
ejpam-6834	1956	8	,	,	PUNCT
ejpam-6834	1956	9	2011	2011	NUM
ejpam-6834	1956	10	.	.	PUNCT
ejpam-6834	1957	1	[	[	X
ejpam-6834	1957	2	56	56	NUM
ejpam-6834	1957	3	]	]	SYM
ejpam-6834	1957	4	z	z	NOUN
ejpam-6834	1957	5	nazari	nazari	NOUN
ejpam-6834	1957	6	and	and	CCONJ
ejpam-6834	1957	7	b	b	NOUN
ejpam-6834	1957	8	mosapour	mosapour	NOUN
ejpam-6834	1957	9	.	.	PUNCT
ejpam-6834	1958	1	the	the	DET
ejpam-6834	1958	2	entropy	entropy	NOUN
ejpam-6834	1958	3	of	of	ADP
ejpam-6834	1958	4	hyperfuzzy	hyperfuzzy	NOUN
ejpam-6834	1958	5	sets	set	NOUN
ejpam-6834	1958	6	.	.	PUNCT
ejpam-6834	1959	1	journal	journal	NOUN
ejpam-6834	1959	2	of	of	ADP
ejpam-6834	1959	3	dynamical	dynamical	ADJ
ejpam-6834	1959	4	systems	system	NOUN
ejpam-6834	1959	5	and	and	CCONJ
ejpam-6834	1959	6	geometric	geometric	ADJ
ejpam-6834	1959	7	theories	theory	NOUN
ejpam-6834	1959	8	,	,	PUNCT
ejpam-6834	1959	9	16(2):173–185	16(2):173–185	NUM
ejpam-6834	1959	10	,	,	PUNCT
ejpam-6834	1959	11	2018	2018	NUM
ejpam-6834	1959	12	.	.	PUNCT
ejpam-6834	1960	1	[	[	X
ejpam-6834	1960	2	57	57	NUM
ejpam-6834	1960	3	]	]	X
ejpam-6834	1960	4	yong	yong	PROPN
ejpam-6834	1960	5	lin	lin	PROPN
ejpam-6834	1960	6	liu	liu	PROPN
ejpam-6834	1960	7	,	,	PUNCT
ejpam-6834	1960	8	hee	hee	PROPN
ejpam-6834	1960	9	sik	sik	CCONJ
ejpam-6834	1960	10	kim	kim	PROPN
ejpam-6834	1960	11	,	,	PUNCT
ejpam-6834	1960	12	and	and	CCONJ
ejpam-6834	1960	13	j.	j.	PROPN
ejpam-6834	1960	14	neggers	neggers	PROPN
ejpam-6834	1960	15	.	.	PUNCT
ejpam-6834	1961	1	hyperfuzzy	hyperfuzzy	ADJ
ejpam-6834	1961	2	subsets	subset	NOUN
ejpam-6834	1961	3	and	and	CCONJ
ejpam-6834	1961	4	subgroupoids	subgroupoid	NOUN
ejpam-6834	1961	5	.	.	PUNCT
ejpam-6834	1962	1	j.	j.	PROPN
ejpam-6834	1962	2	intell	intell	PROPN
ejpam-6834	1962	3	.	.	PUNCT
ejpam-6834	1963	1	fuzzy	fuzzy	ADJ
ejpam-6834	1963	2	syst	syst	PROPN
ejpam-6834	1963	3	.	.	PUNCT
ejpam-6834	1963	4	,	,	PUNCT
ejpam-6834	1963	5	33:1553–1562	33:1553–1562	NUM
ejpam-6834	1963	6	,	,	PUNCT
ejpam-6834	1963	7	2017	2017	NUM
ejpam-6834	1963	8	.	.	PUNCT
ejpam-6834	1964	1	[	[	X
ejpam-6834	1964	2	58	58	NUM
ejpam-6834	1964	3	]	]	PUNCT
ejpam-6834	1964	4	takaaki	takaaki	NOUN
ejpam-6834	1964	5	fujita	fujita	NOUN
ejpam-6834	1964	6	and	and	CCONJ
ejpam-6834	1964	7	florentin	florentin	PROPN
ejpam-6834	1964	8	smarandache	smarandache	PROPN
ejpam-6834	1964	9	.	.	PUNCT
ejpam-6834	1965	1	examples	example	NOUN
ejpam-6834	1965	2	of	of	ADP
ejpam-6834	1965	3	fuzzy	fuzzy	ADJ
ejpam-6834	1965	4	sets	set	NOUN
ejpam-6834	1965	5	,	,	PUNCT
ejpam-6834	1965	6	hyperfuzzy	hyperfuzzy	NOUN
ejpam-6834	1965	7	sets	set	NOUN
ejpam-6834	1965	8	,	,	PUNCT
ejpam-6834	1965	9	and	and	CCONJ
ejpam-6834	1965	10	superhyperfuzzy	superhyperfuzzy	ADJ
ejpam-6834	1965	11	sets	set	NOUN
ejpam-6834	1965	12	in	in	ADP
ejpam-6834	1965	13	climate	climate	NOUN
ejpam-6834	1965	14	change	change	NOUN
ejpam-6834	1965	15	and	and	CCONJ
ejpam-6834	1965	16	the	the	DET
ejpam-6834	1965	17	proposal	proposal	NOUN
ejpam-6834	1965	18	of	of	ADP
ejpam-6834	1965	19	several	several	ADJ
ejpam-6834	1965	20	new	new	ADJ
ejpam-6834	1965	21	concepts	concept	NOUN
ejpam-6834	1965	22	.	.	PUNCT
ejpam-6834	1966	1	climate	climate	NOUN
ejpam-6834	1966	2	change	change	NOUN
ejpam-6834	1966	3	reports	report	NOUN
ejpam-6834	1966	4	,	,	PUNCT
ejpam-6834	1966	5	2:1–18	2:1–18	NUM
ejpam-6834	1966	6	,	,	PUNCT
ejpam-6834	1966	7	2025	2025	NUM
ejpam-6834	1966	8	.	.	PUNCT
ejpam-6834	1967	1	[	[	X
ejpam-6834	1967	2	59	59	NUM
ejpam-6834	1967	3	]	]	PUNCT
ejpam-6834	1967	4	young	young	ADJ
ejpam-6834	1967	5	bae	bae	PROPN
ejpam-6834	1967	6	jun	jun	PROPN
ejpam-6834	1967	7	,	,	PUNCT
ejpam-6834	1967	8	kul	kul	PROPN
ejpam-6834	1967	9	hur	hur	PROPN
ejpam-6834	1967	10	,	,	PUNCT
ejpam-6834	1967	11	and	and	CCONJ
ejpam-6834	1967	12	kyoung	kyoung	PROPN
ejpam-6834	1967	13	ja	ja	PROPN
ejpam-6834	1967	14	lee	lee	PROPN
ejpam-6834	1967	15	.	.	PROPN
ejpam-6834	1967	16	hyperfuzzy	hyperfuzzy	PROPN
ejpam-6834	1967	17	subalgebras	subalgebras	PROPN
ejpam-6834	1967	18	of	of	ADP
ejpam-6834	1967	19	bck	bck	PROPN
ejpam-6834	1967	20	/	/	SYM
ejpam-6834	1967	21	bcialgebras	bcialgebra	NOUN
ejpam-6834	1967	22	.	.	PUNCT
ejpam-6834	1968	1	annals	annal	NOUN
ejpam-6834	1968	2	of	of	ADP
ejpam-6834	1968	3	fuzzy	fuzzy	ADJ
ejpam-6834	1968	4	mathematics	mathematic	NOUN
ejpam-6834	1968	5	and	and	CCONJ
ejpam-6834	1968	6	informatics	informatic	NOUN
ejpam-6834	1968	7	,	,	PUNCT
ejpam-6834	1968	8	2017	2017	NUM
ejpam-6834	1968	9	.	.	PUNCT
ejpam-6834	1969	1	[	[	X
ejpam-6834	1969	2	60	60	NUM
ejpam-6834	1969	3	]	]	X
ejpam-6834	1969	4	jayanta	jayanta	PROPN
ejpam-6834	1969	5	ghosh	ghosh	PROPN
ejpam-6834	1969	6	and	and	CCONJ
ejpam-6834	1969	7	tapas	tapas	PROPN
ejpam-6834	1969	8	kumar	kumar	PROPN
ejpam-6834	1969	9	samanta	samanta	PROPN
ejpam-6834	1969	10	.	.	PUNCT
ejpam-6834	1970	1	hyperfuzzy	hyperfuzzy	PROPN
ejpam-6834	1970	2	sets	set	NOUN
ejpam-6834	1970	3	and	and	CCONJ
ejpam-6834	1970	4	hyperfuzzy	hyperfuzzy	NOUN
ejpam-6834	1970	5	group	group	NOUN
ejpam-6834	1970	6	.	.	PUNCT
ejpam-6834	1971	1	t.	t.	PROPN
ejpam-6834	1971	2	fujita	fujita	PROPN
ejpam-6834	1971	3	,	,	PUNCT
ejpam-6834	1971	4	f.smarandache	f.smarandache	NOUN
ejpam-6834	1971	5	/	/	SYM
ejpam-6834	1971	6	eur	eur	PROPN
ejpam-6834	1971	7	.	.	PUNCT
ejpam-6834	1972	1	j.	j.	PROPN
ejpam-6834	1972	2	pure	pure	PROPN
ejpam-6834	1972	3	appl	appl	PROPN
ejpam-6834	1972	4	.	.	PROPN
ejpam-6834	1972	5	math	math	PROPN
ejpam-6834	1972	6	,	,	PUNCT
ejpam-6834	1972	7	18	18	NUM
ejpam-6834	1972	8	(	(	PUNCT
ejpam-6834	1972	9	4	4	NUM
ejpam-6834	1972	10	)	)	PUNCT
ejpam-6834	1972	11	(	(	PUNCT
ejpam-6834	1972	12	2025	2025	NUM
ejpam-6834	1972	13	)	)	PUNCT
ejpam-6834	1972	14	,	,	PUNCT
ejpam-6834	1972	15	6834	6834	NUM
ejpam-6834	1972	16	69	69	NUM
ejpam-6834	1972	17	of	of	ADP
ejpam-6834	1972	18	69	69	NUM
ejpam-6834	1972	19	int	int	NOUN
ejpam-6834	1972	20	.	.	PUNCT
ejpam-6834	1973	1	j.	j.	PROPN
ejpam-6834	1973	2	adv	adv	PROPN
ejpam-6834	1973	3	.	.	PUNCT
ejpam-6834	1974	1	sci	sci	PROPN
ejpam-6834	1974	2	.	.	PROPN
ejpam-6834	1974	3	technol	technol	PROPN
ejpam-6834	1974	4	,	,	PUNCT
ejpam-6834	1974	5	41:27–37	41:27–37	PROPN
ejpam-6834	1974	6	,	,	PUNCT
ejpam-6834	1974	7	2012	2012	NUM
ejpam-6834	1974	8	.	.	PUNCT
ejpam-6834	1975	1	[	[	X
ejpam-6834	1975	2	61	61	NUM
ejpam-6834	1975	3	]	]	X
ejpam-6834	1975	4	seok	seok	PROPN
ejpam-6834	1975	5	-	-	PUNCT
ejpam-6834	1975	6	zun	zun	NOUN
ejpam-6834	1975	7	song	song	NOUN
ejpam-6834	1975	8	,	,	PUNCT
ejpam-6834	1975	9	seon	seon	PROPN
ejpam-6834	1975	10	jeong	jeong	PROPN
ejpam-6834	1975	11	kim	kim	PROPN
ejpam-6834	1975	12	,	,	PUNCT
ejpam-6834	1975	13	and	and	CCONJ
ejpam-6834	1975	14	young	young	ADJ
ejpam-6834	1975	15	bae	bae	PROPN
ejpam-6834	1975	16	jun	jun	PROPN
ejpam-6834	1975	17	.	.	PROPN
ejpam-6834	1975	18	hyperfuzzy	hyperfuzzy	PROPN
ejpam-6834	1975	19	ideals	ideal	NOUN
ejpam-6834	1975	20	in	in	ADP
ejpam-6834	1975	21	bck	bck	PROPN
ejpam-6834	1975	22	/	/	SYM
ejpam-6834	1975	23	bcialgebras	bcialgebra	NOUN
ejpam-6834	1975	24	.	.	PUNCT
ejpam-6834	1976	1	mathematics	mathematic	NOUN
ejpam-6834	1976	2	,	,	PUNCT
ejpam-6834	1976	3	5(4):81	5(4):81	NUM
ejpam-6834	1976	4	,	,	PUNCT
ejpam-6834	1976	5	2017	2017	NUM
ejpam-6834	1976	6	.	.	PUNCT
ejpam-6834	1977	1	[	[	X
ejpam-6834	1977	2	62	62	NUM
ejpam-6834	1977	3	]	]	PUNCT
ejpam-6834	1977	4	florentin	florentin	PROPN
ejpam-6834	1977	5	smarandache	smarandache	NOUN
ejpam-6834	1977	6	.	.	PUNCT
ejpam-6834	1978	1	neutrosophy	neutrosophy	NOUN
ejpam-6834	1978	2	:	:	PUNCT
ejpam-6834	1978	3	neutrosophic	neutrosophic	ADJ
ejpam-6834	1978	4	probability	probability	NOUN
ejpam-6834	1978	5	,	,	PUNCT
ejpam-6834	1978	6	set	set	NOUN
ejpam-6834	1978	7	,	,	PUNCT
ejpam-6834	1978	8	and	and	CCONJ
ejpam-6834	1978	9	logic	logic	NOUN
ejpam-6834	1978	10	:	:	PUNCT
ejpam-6834	1978	11	analytic	analytic	ADJ
ejpam-6834	1978	12	synthesis	synthesis	NOUN
ejpam-6834	1978	13	&	&	CCONJ
ejpam-6834	1978	14	synthetic	synthetic	ADJ
ejpam-6834	1978	15	analysis	analysis	NOUN
ejpam-6834	1978	16	.	.	PUNCT
ejpam-6834	1979	1	1998	1998	NUM
ejpam-6834	1979	2	.	.	PUNCT
ejpam-6834	1980	1	[	[	X
ejpam-6834	1980	2	63	63	NUM
ejpam-6834	1980	3	]	]	X
ejpam-6834	1980	4	haibin	haibin	PROPN
ejpam-6834	1980	5	wang	wang	PROPN
ejpam-6834	1980	6	,	,	PUNCT
ejpam-6834	1980	7	florentin	florentin	PROPN
ejpam-6834	1980	8	smarandache	smarandache	PROPN
ejpam-6834	1980	9	,	,	PUNCT
ejpam-6834	1980	10	yanqing	yanqe	VERB
ejpam-6834	1980	11	zhang	zhang	PROPN
ejpam-6834	1980	12	,	,	PUNCT
ejpam-6834	1980	13	and	and	CCONJ
ejpam-6834	1980	14	rajshekhar	rajshekhar	PROPN
ejpam-6834	1980	15	sunderraman	sunderraman	NOUN
ejpam-6834	1980	16	.	.	PUNCT
ejpam-6834	1981	1	single	single	ADJ
ejpam-6834	1981	2	valued	value	VERB
ejpam-6834	1981	3	neutrosophic	neutrosophic	ADJ
ejpam-6834	1981	4	sets	set	NOUN
ejpam-6834	1981	5	.	.	PUNCT
ejpam-6834	1982	1	infinite	infinite	ADJ
ejpam-6834	1982	2	study	study	NOUN
ejpam-6834	1982	3	,	,	PUNCT
ejpam-6834	1982	4	2010	2010	NUM
ejpam-6834	1982	5	.	.	PUNCT
ejpam-6834	1983	1	[	[	X
ejpam-6834	1983	2	64	64	NUM
ejpam-6834	1983	3	]	]	PUNCT
ejpam-6834	1983	4	takaaki	takaaki	NOUN
ejpam-6834	1983	5	fujita	fujita	NOUN
ejpam-6834	1983	6	and	and	CCONJ
ejpam-6834	1983	7	florentin	florentin	PROPN
ejpam-6834	1983	8	smarandache	smarandache	PROPN
ejpam-6834	1983	9	.	.	PUNCT
ejpam-6834	1984	1	considerations	consideration	NOUN
ejpam-6834	1984	2	of	of	ADP
ejpam-6834	1984	3	hyperneutrosophic	hyperneutrosophic	ADJ
ejpam-6834	1984	4	set	set	VERB
ejpam-6834	1984	5	and	and	CCONJ
ejpam-6834	1984	6	forestneutrosophic	forestneutrosophic	ADJ
ejpam-6834	1984	7	set	set	VERB
ejpam-6834	1984	8	in	in	ADP
ejpam-6834	1984	9	livestock	livestock	NOUN
ejpam-6834	1984	10	applications	application	NOUN
ejpam-6834	1984	11	and	and	CCONJ
ejpam-6834	1984	12	proposal	proposal	NOUN
ejpam-6834	1984	13	of	of	ADP
ejpam-6834	1984	14	new	new	ADJ
ejpam-6834	1984	15	neutrosophic	neutrosophic	ADJ
ejpam-6834	1984	16	sets	set	NOUN
ejpam-6834	1984	17	.	.	PUNCT
ejpam-6834	1985	1	precision	precision	NOUN
ejpam-6834	1985	2	livestock	livestock	NOUN
ejpam-6834	1985	3	,	,	PUNCT
ejpam-6834	1985	4	2:11–22	2:11–22	NUM
ejpam-6834	1985	5	,	,	PUNCT
ejpam-6834	1985	6	2025	2025	NUM
ejpam-6834	1985	7	.	.	PUNCT
ejpam-6834	1986	1	[	[	X
ejpam-6834	1986	2	65	65	NUM
ejpam-6834	1986	3	]	]	X
ejpam-6834	1986	4	florentin	florentin	PROPN
ejpam-6834	1986	5	smarandache	smarandache	NOUN
ejpam-6834	1986	6	.	.	PUNCT
ejpam-6834	1987	1	plithogenic	plithogenic	PROPN
ejpam-6834	1987	2	set	set	PROPN
ejpam-6834	1987	3	,	,	PUNCT
ejpam-6834	1987	4	an	an	DET
ejpam-6834	1987	5	extension	extension	NOUN
ejpam-6834	1987	6	of	of	ADP
ejpam-6834	1987	7	crisp	crisp	ADJ
ejpam-6834	1987	8	,	,	PUNCT
ejpam-6834	1987	9	fuzzy	fuzzy	ADJ
ejpam-6834	1987	10	,	,	PUNCT
ejpam-6834	1987	11	intuitionistic	intuitionistic	ADJ
ejpam-6834	1987	12	fuzzy	fuzzy	ADJ
ejpam-6834	1987	13	,	,	PUNCT
ejpam-6834	1987	14	and	and	CCONJ
ejpam-6834	1987	15	neutrosophic	neutrosophic	ADJ
ejpam-6834	1987	16	sets	set	NOUN
ejpam-6834	1987	17	-	-	PUNCT
ejpam-6834	1987	18	revisited	revisit	VERB
ejpam-6834	1987	19	.	.	PUNCT
ejpam-6834	1988	1	infinite	infinite	ADJ
ejpam-6834	1988	2	study	study	NOUN
ejpam-6834	1988	3	,	,	PUNCT
ejpam-6834	1988	4	2018	2018	NUM
ejpam-6834	1988	5	.	.	PUNCT
ejpam-6834	1989	1	[	[	X
ejpam-6834	1989	2	66	66	NUM
ejpam-6834	1989	3	]	]	PUNCT
ejpam-6834	1989	4	nehmat	nehmat	PROPN
ejpam-6834	1989	5	ahmed	ahme	VERB
ejpam-6834	1989	6	and	and	CCONJ
ejpam-6834	1989	7	osama	osama	PROPN
ejpam-6834	1989	8	t.	t.	PROPN
ejpam-6834	1989	9	pirbal	pirbal	PROPN
ejpam-6834	1989	10	.	.	PUNCT
ejpam-6834	1990	1	plithogenic	plithogenic	ADJ
ejpam-6834	1990	2	crisp	crisp	ADJ
ejpam-6834	1990	3	hypersoft	hypersoft	NOUN
ejpam-6834	1990	4	topology	topology	NOUN
ejpam-6834	1990	5	.	.	PUNCT
ejpam-6834	1991	1	european	european	PROPN
ejpam-6834	1991	2	journal	journal	PROPN
ejpam-6834	1991	3	of	of	ADP
ejpam-6834	1991	4	pure	pure	ADJ
ejpam-6834	1991	5	and	and	CCONJ
ejpam-6834	1991	6	applied	applied	ADJ
ejpam-6834	1991	7	mathematics	mathematic	NOUN
ejpam-6834	1991	8	,	,	PUNCT
ejpam-6834	1991	9	2024	2024	NUM
ejpam-6834	1991	10	.	.	PUNCT
ejpam-6834	1992	1	[	[	X
ejpam-6834	1992	2	67	67	NUM
ejpam-6834	1992	3	]	]	PUNCT
ejpam-6834	1992	4	takaaki	takaaki	NOUN
ejpam-6834	1992	5	fujita	fujita	PROPN
ejpam-6834	1992	6	.	.	PUNCT
ejpam-6834	1993	1	forest	forest	PROPN
ejpam-6834	1993	2	hyperplithogenic	hyperplithogenic	PROPN
ejpam-6834	1993	3	set	set	NOUN
ejpam-6834	1993	4	and	and	CCONJ
ejpam-6834	1993	5	forest	forest	NOUN
ejpam-6834	1993	6	hyperrough	hyperrough	PROPN
ejpam-6834	1993	7	set	set	VERB
ejpam-6834	1993	8	.	.	PUNCT
ejpam-6834	1994	1	advancing	advance	VERB
ejpam-6834	1994	2	uncertain	uncertain	ADJ
ejpam-6834	1994	3	combinatorics	combinatoric	NOUN
ejpam-6834	1994	4	through	through	ADP
ejpam-6834	1994	5	graphization	graphization	NOUN
ejpam-6834	1994	6	,	,	PUNCT
ejpam-6834	1994	7	hyperization	hyperization	NOUN
ejpam-6834	1994	8	,	,	PUNCT
ejpam-6834	1994	9	and	and	CCONJ
ejpam-6834	1994	10	uncertainization	uncertainization	NOUN
ejpam-6834	1994	11	:	:	PUNCT
ejpam-6834	1994	12	fuzzy	fuzzy	ADJ
ejpam-6834	1994	13	,	,	PUNCT
ejpam-6834	1994	14	neutrosophic	neutrosophic	ADJ
ejpam-6834	1994	15	,	,	PUNCT
ejpam-6834	1994	16	soft	soft	ADJ
ejpam-6834	1994	17	,	,	PUNCT
ejpam-6834	1994	18	rough	rough	ADJ
ejpam-6834	1994	19	,	,	PUNCT
ejpam-6834	1994	20	and	and	CCONJ
ejpam-6834	1994	21	beyond	beyond	ADP
ejpam-6834	1994	22	,	,	PUNCT
ejpam-6834	1994	23	2025	2025	NUM
ejpam-6834	1994	24	.	.	PUNCT
ejpam-6834	1995	1	[	[	X
ejpam-6834	1995	2	68	68	NUM
ejpam-6834	1995	3	]	]	PUNCT
ejpam-6834	1995	4	takaaki	takaaki	NOUN
ejpam-6834	1995	5	fujita	fujita	NOUN
ejpam-6834	1995	6	and	and	CCONJ
ejpam-6834	1995	7	florentin	florentin	PROPN
ejpam-6834	1995	8	smarandache	smarandache	PROPN
ejpam-6834	1995	9	.	.	PUNCT
ejpam-6834	1996	1	exploring	explore	VERB
ejpam-6834	1996	2	concepts	concept	NOUN
ejpam-6834	1996	3	of	of	ADP
ejpam-6834	1996	4	hyperfuzzy	hyperfuzzy	NOUN
ejpam-6834	1996	5	,	,	PUNCT
ejpam-6834	1996	6	hyperneutrosophic	hyperneutrosophic	ADJ
ejpam-6834	1996	7	,	,	PUNCT
ejpam-6834	1996	8	and	and	CCONJ
ejpam-6834	1996	9	hyperplithogenic	hyperplithogenic	ADJ
ejpam-6834	1996	10	sets	set	NOUN
ejpam-6834	1996	11	ii	ii	PROPN
ejpam-6834	1996	12	.	.	PUNCT
ejpam-6834	1996	13	advancing	advance	VERB
ejpam-6834	1996	14	uncertain	uncertain	ADJ
ejpam-6834	1996	15	combinatorics	combinatoric	NOUN
ejpam-6834	1996	16	through	through	ADP
ejpam-6834	1996	17	graphization	graphization	NOUN
ejpam-6834	1996	18	,	,	PUNCT
ejpam-6834	1996	19	hyperization	hyperization	NOUN
ejpam-6834	1996	20	,	,	PUNCT
ejpam-6834	1996	21	and	and	CCONJ
ejpam-6834	1996	22	uncertainization	uncertainization	NOUN
ejpam-6834	1996	23	:	:	PUNCT
ejpam-6834	1996	24	fuzzy	fuzzy	ADJ
ejpam-6834	1996	25	,	,	PUNCT
ejpam-6834	1996	26	neutrosophic	neutrosophic	ADJ
ejpam-6834	1996	27	,	,	PUNCT
ejpam-6834	1996	28	soft	soft	ADJ
ejpam-6834	1996	29	,	,	PUNCT
ejpam-6834	1996	30	rough	rough	ADJ
ejpam-6834	1996	31	,	,	PUNCT
ejpam-6834	1996	32	and	and	CCONJ
ejpam-6834	1996	33	beyond	beyond	ADP
ejpam-6834	1996	34	,	,	PUNCT
ejpam-6834	1996	35	2025	2025	NUM
ejpam-6834	1996	36	.	.	PUNCT
ejpam-6834	1997	1	[	[	X
ejpam-6834	1997	2	69	69	NUM
ejpam-6834	1997	3	]	]	X
ejpam-6834	1997	4	dmitriy	dmitriy	PROPN
ejpam-6834	1997	5	molodtsov	molodtsov	PROPN
ejpam-6834	1997	6	.	.	PUNCT
ejpam-6834	1998	1	soft	soft	ADJ
ejpam-6834	1998	2	set	set	NOUN
ejpam-6834	1998	3	theory	theory	NOUN
ejpam-6834	1998	4	-	-	PUNCT
ejpam-6834	1998	5	first	first	ADJ
ejpam-6834	1998	6	results	result	NOUN
ejpam-6834	1998	7	.	.	PUNCT
ejpam-6834	1999	1	computers	computer	NOUN
ejpam-6834	1999	2	&	&	CCONJ
ejpam-6834	1999	3	mathematics	mathematics	PROPN
ejpam-6834	1999	4	with	with	ADP
ejpam-6834	1999	5	applications	application	NOUN
ejpam-6834	1999	6	,	,	PUNCT
ejpam-6834	1999	7	37(4	37(4	PROPN
ejpam-6834	1999	8	-	-	PUNCT
ejpam-6834	1999	9	5):19–31	5):19–31	NUM
ejpam-6834	1999	10	,	,	PUNCT
ejpam-6834	1999	11	1999	1999	NUM
ejpam-6834	1999	12	.	.	PUNCT
ejpam-6834	2000	1	[	[	X
ejpam-6834	2000	2	70	70	NUM
ejpam-6834	2000	3	]	]	PUNCT
ejpam-6834	2000	4	florentin	florentin	PROPN
ejpam-6834	2000	5	smarandache	smarandache	PROPN
ejpam-6834	2000	6	.	.	PUNCT
ejpam-6834	2001	1	superhyperfunction	superhyperfunction	NOUN
ejpam-6834	2001	2	,	,	PUNCT
ejpam-6834	2001	3	superhyperstructure	superhyperstructure	ADJ
ejpam-6834	2001	4	,	,	PUNCT
ejpam-6834	2001	5	neutrosophic	neutrosophic	ADJ
ejpam-6834	2001	6	superhyperfunction	superhyperfunction	NOUN
ejpam-6834	2001	7	and	and	CCONJ
ejpam-6834	2001	8	neutrosophic	neutrosophic	ADJ
ejpam-6834	2001	9	superhyperstructure	superhyperstructure	NOUN
ejpam-6834	2001	10	:	:	PUNCT
ejpam-6834	2001	11	current	current	ADJ
ejpam-6834	2001	12	understanding	understanding	NOUN
ejpam-6834	2001	13	and	and	CCONJ
ejpam-6834	2001	14	future	future	ADJ
ejpam-6834	2001	15	directions	direction	NOUN
ejpam-6834	2001	16	.	.	PUNCT
ejpam-6834	2002	1	infinite	infinite	ADJ
ejpam-6834	2002	2	study	study	NOUN
ejpam-6834	2002	3	,	,	PUNCT
ejpam-6834	2002	4	2023	2023	NUM
ejpam-6834	2002	5	.	.	PUNCT
ejpam-6834	2003	1	[	[	X
ejpam-6834	2003	2	71	71	NUM
ejpam-6834	2003	3	]	]	X
ejpam-6834	2003	4	maissam	maissam	PROPN
ejpam-6834	2003	5	jdid	jdid	PROPN
ejpam-6834	2003	6	,	,	PUNCT
ejpam-6834	2003	7	florentin	florentin	NOUN
ejpam-6834	2003	8	smarandache	smarandache	NOUN
ejpam-6834	2003	9	,	,	PUNCT
ejpam-6834	2003	10	and	and	CCONJ
ejpam-6834	2003	11	takaaki	takaaki	NOUN
ejpam-6834	2003	12	fujita	fujita	PROPN
ejpam-6834	2003	13	.	.	PUNCT
ejpam-6834	2004	1	a	a	DET
ejpam-6834	2004	2	linear	linear	ADJ
ejpam-6834	2004	3	mathematical	mathematical	ADJ
ejpam-6834	2004	4	model	model	NOUN
ejpam-6834	2004	5	of	of	ADP
ejpam-6834	2004	6	the	the	DET
ejpam-6834	2004	7	vocational	vocational	ADJ
ejpam-6834	2004	8	training	training	NOUN
ejpam-6834	2004	9	problem	problem	NOUN
ejpam-6834	2004	10	in	in	ADP
ejpam-6834	2004	11	a	a	DET
ejpam-6834	2004	12	company	company	NOUN
ejpam-6834	2004	13	using	use	VERB
ejpam-6834	2004	14	neutrosophic	neutrosophic	ADJ
ejpam-6834	2004	15	logic	logic	NOUN
ejpam-6834	2004	16	,	,	PUNCT
ejpam-6834	2004	17	hyperfunctions	hyperfunction	NOUN
ejpam-6834	2004	18	,	,	PUNCT
ejpam-6834	2004	19	and	and	CCONJ
ejpam-6834	2004	20	superhyperfunction	superhyperfunction	NOUN
ejpam-6834	2004	21	.	.	PUNCT
ejpam-6834	2005	1	neutrosophic	neutrosophic	ADJ
ejpam-6834	2005	2	sets	set	NOUN
ejpam-6834	2005	3	and	and	CCONJ
ejpam-6834	2005	4	systems	system	NOUN
ejpam-6834	2005	5	,	,	PUNCT
ejpam-6834	2005	6	87:1–11	87:1–11	NUM
ejpam-6834	2005	7	,	,	PUNCT
ejpam-6834	2005	8	2025	2025	NUM
ejpam-6834	2005	9	.	.	PUNCT
ejpam-6834	2006	1	[	[	X
ejpam-6834	2006	2	72	72	NUM
ejpam-6834	2006	3	]	]	X
ejpam-6834	2006	4	muhammad	muhammad	PROPN
ejpam-6834	2006	5	akram	akram	PROPN
ejpam-6834	2006	6	and	and	CCONJ
ejpam-6834	2006	7	gulfam	gulfam	PROPN
ejpam-6834	2006	8	shahzadi	shahzadi	PROPN
ejpam-6834	2006	9	.	.	PUNCT
ejpam-6834	2007	1	hypergraphs	hypergraph	NOUN
ejpam-6834	2007	2	in	in	ADP
ejpam-6834	2007	3	m	m	ADJ
ejpam-6834	2007	4	-	-	ADJ
ejpam-6834	2007	5	polar	polar	ADJ
ejpam-6834	2007	6	fuzzy	fuzzy	ADJ
ejpam-6834	2007	7	environment	environment	NOUN
ejpam-6834	2007	8	.	.	PUNCT
ejpam-6834	2008	1	mathematics	mathematic	NOUN
ejpam-6834	2008	2	,	,	PUNCT
ejpam-6834	2008	3	6(2):28	6(2):28	NOUN
ejpam-6834	2008	4	,	,	PUNCT
ejpam-6834	2008	5	2018	2018	NUM
ejpam-6834	2008	6	.	.	PUNCT
ejpam-6834	2009	1	[	[	X
ejpam-6834	2009	2	73	73	NUM
ejpam-6834	2009	3	]	]	PUNCT
ejpam-6834	2009	4	yifan	yifan	PROPN
ejpam-6834	2009	5	feng	feng	PROPN
ejpam-6834	2009	6	,	,	PUNCT
ejpam-6834	2009	7	haoxuan	haoxuan	PROPN
ejpam-6834	2009	8	you	you	PRON
ejpam-6834	2009	9	,	,	PUNCT
ejpam-6834	2009	10	zizhao	zizhao	PROPN
ejpam-6834	2009	11	zhang	zhang	PROPN
ejpam-6834	2009	12	,	,	PUNCT
ejpam-6834	2009	13	rongrong	rongrong	PROPN
ejpam-6834	2009	14	ji	ji	PROPN
ejpam-6834	2009	15	,	,	PUNCT
ejpam-6834	2009	16	and	and	CCONJ
ejpam-6834	2009	17	yue	yue	PROPN
ejpam-6834	2009	18	gao	gao	PROPN
ejpam-6834	2009	19	.	.	PUNCT
ejpam-6834	2010	1	hypergraph	hypergraph	VERB
ejpam-6834	2010	2	neural	neural	ADJ
ejpam-6834	2010	3	networks	network	NOUN
ejpam-6834	2010	4	.	.	PUNCT
ejpam-6834	2011	1	in	in	ADP
ejpam-6834	2011	2	proceedings	proceeding	NOUN
ejpam-6834	2011	3	of	of	ADP
ejpam-6834	2011	4	the	the	DET
ejpam-6834	2011	5	aaai	aaai	PROPN
ejpam-6834	2011	6	conference	conference	NOUN
ejpam-6834	2011	7	on	on	ADP
ejpam-6834	2011	8	artificial	artificial	ADJ
ejpam-6834	2011	9	intelligence	intelligence	NOUN
ejpam-6834	2011	10	,	,	PUNCT
ejpam-6834	2011	11	volume	volume	NOUN
ejpam-6834	2011	12	33	33	NUM
ejpam-6834	2011	13	,	,	PUNCT
ejpam-6834	2011	14	pages	page	NOUN
ejpam-6834	2011	15	3558–3565	3558–3565	NUM
ejpam-6834	2011	16	,	,	PUNCT
ejpam-6834	2011	17	2019	2019	NUM
ejpam-6834	2011	18	.	.	PUNCT
ejpam-6834	2012	1	[	[	X
ejpam-6834	2012	2	74	74	NUM
ejpam-6834	2012	3	]	]	PUNCT
ejpam-6834	2012	4	takaaki	takaaki	NOUN
ejpam-6834	2012	5	fujita	fujita	NOUN
ejpam-6834	2012	6	and	and	CCONJ
ejpam-6834	2012	7	florentin	florentin	PROPN
ejpam-6834	2012	8	smarandache	smarandache	PROPN
ejpam-6834	2012	9	.	.	PUNCT
ejpam-6834	2013	1	a	a	DET
ejpam-6834	2013	2	concise	concise	ADJ
ejpam-6834	2013	3	study	study	NOUN
ejpam-6834	2013	4	of	of	ADP
ejpam-6834	2013	5	some	some	DET
ejpam-6834	2013	6	superhypergraph	superhypergraph	NOUN
ejpam-6834	2013	7	classes	class	NOUN
ejpam-6834	2013	8	.	.	PUNCT
ejpam-6834	2014	1	neutrosophic	neutrosophic	ADJ
ejpam-6834	2014	2	sets	set	NOUN
ejpam-6834	2014	3	and	and	CCONJ
ejpam-6834	2014	4	systems	system	NOUN
ejpam-6834	2014	5	,	,	PUNCT
ejpam-6834	2014	6	77:548–593	77:548–593	PROPN
ejpam-6834	2014	7	,	,	PUNCT
ejpam-6834	2014	8	2024	2024	NUM
ejpam-6834	2014	9	.	.	PUNCT