id	sid	tid	token	lemma	pos
ejpam-6189	1	1	european	european	PROPN
ejpam-6189	1	2	journal	journal	PROPN
ejpam-6189	1	3	of	of	ADP
ejpam-6189	1	4	pure	pure	ADJ
ejpam-6189	1	5	and	and	CCONJ
ejpam-6189	1	6	applied	applied	ADJ
ejpam-6189	1	7	mathematics	mathematic	NOUN
ejpam-6189	1	8	2025	2025	NUM
ejpam-6189	1	9	,	,	PUNCT
ejpam-6189	1	10	vol	vol	NOUN
ejpam-6189	1	11	.	.	PROPN
ejpam-6189	1	12	18	18	NUM
ejpam-6189	1	13	,	,	PUNCT
ejpam-6189	1	14	issue	issue	NOUN
ejpam-6189	1	15	3	3	NUM
ejpam-6189	1	16	,	,	PUNCT
ejpam-6189	1	17	article	article	NOUN
ejpam-6189	1	18	number	number	NOUN
ejpam-6189	1	19	6189	6189	NUM
ejpam-6189	1	20	issn	issn	VERB
ejpam-6189	1	21	1307	1307	NUM
ejpam-6189	1	22	-	-	SYM
ejpam-6189	1	23	5543	5543	NUM
ejpam-6189	1	24	–	–	PUNCT
ejpam-6189	1	25	ejpam.com	ejpam.com	X
ejpam-6189	1	26	published	publish	VERB
ejpam-6189	1	27	by	by	ADP
ejpam-6189	1	28	new	new	PROPN
ejpam-6189	1	29	york	york	PROPN
ejpam-6189	1	30	business	business	PROPN
ejpam-6189	1	31	global	global	ADJ
ejpam-6189	1	32	applications	application	NOUN
ejpam-6189	1	33	of	of	ADP
ejpam-6189	1	34	strongest	strong	ADJ
ejpam-6189	1	35	fuzzy	fuzzy	ADJ
ejpam-6189	1	36	dot	dot	NOUN
ejpam-6189	1	37	bd	bd	NOUN
ejpam-6189	1	38	-	-	PUNCT
ejpam-6189	1	39	subalgebras	subalgebras	PROPN
ejpam-6189	1	40	in	in	ADP
ejpam-6189	1	41	bd	bd	PROPN
ejpam-6189	1	42	-	-	PUNCT
ejpam-6189	1	43	algebras	algebras	PROPN
ejpam-6189	1	44	warud	warud	PROPN
ejpam-6189	1	45	nakkhasen1,∗	nakkhasen1,∗	PROPN
ejpam-6189	1	46	,	,	PUNCT
ejpam-6189	1	47	narinthon	narinthon	ADJ
ejpam-6189	1	48	jaroenwan1	jaroenwan1	NOUN
ejpam-6189	1	49	,	,	PUNCT
ejpam-6189	1	50	panida	panida	PROPN
ejpam-6189	1	51	huekkhunthod1	huekkhunthod1	NOUN
ejpam-6189	1	52	,	,	PUNCT
ejpam-6189	1	53	atthchai	atthchai	ADJ
ejpam-6189	1	54	chada2	chada2	NOUN
ejpam-6189	1	55	1	1	NUM
ejpam-6189	1	56	department	department	NOUN
ejpam-6189	1	57	of	of	ADP
ejpam-6189	1	58	mathematics	mathematic	NOUN
ejpam-6189	1	59	,	,	PUNCT
ejpam-6189	1	60	faculty	faculty	NOUN
ejpam-6189	1	61	of	of	ADP
ejpam-6189	1	62	science	science	NOUN
ejpam-6189	1	63	,	,	PUNCT
ejpam-6189	1	64	mahasarakham	mahasarakham	PROPN
ejpam-6189	1	65	university	university	PROPN
ejpam-6189	1	66	,	,	PUNCT
ejpam-6189	1	67	maha	maha	PROPN
ejpam-6189	1	68	sarakham	sarakham	PROPN
ejpam-6189	1	69	44150	44150	NUM
ejpam-6189	1	70	,	,	PUNCT
ejpam-6189	1	71	thailand	thailand	PROPN
ejpam-6189	1	72	2	2	NUM
ejpam-6189	1	73	department	department	NOUN
ejpam-6189	1	74	of	of	ADP
ejpam-6189	1	75	mathematics	mathematic	NOUN
ejpam-6189	1	76	,	,	PUNCT
ejpam-6189	1	77	faculty	faculty	NOUN
ejpam-6189	1	78	of	of	ADP
ejpam-6189	1	79	science	science	NOUN
ejpam-6189	1	80	and	and	CCONJ
ejpam-6189	1	81	technology	technology	NOUN
ejpam-6189	1	82	,	,	PUNCT
ejpam-6189	1	83	rajabhat	rajabhat	PRON
ejpam-6189	1	84	mahasarakham	mahasarakham	PROPN
ejpam-6189	1	85	university	university	PROPN
ejpam-6189	1	86	,	,	PUNCT
ejpam-6189	1	87	maha	maha	PROPN
ejpam-6189	1	88	sarakham	sarakham	PROPN
ejpam-6189	1	89	44000	44000	NUM
ejpam-6189	1	90	,	,	PUNCT
ejpam-6189	1	91	thailand	thailand	PROPN
ejpam-6189	1	92	abstract	abstract	NOUN
ejpam-6189	1	93	.	.	PUNCT
ejpam-6189	2	1	in	in	ADP
ejpam-6189	2	2	2024	2024	NUM
ejpam-6189	2	3	,	,	PUNCT
ejpam-6189	2	4	nakkhasen	nakkhasen	PROPN
ejpam-6189	2	5	et	et	PROPN
ejpam-6189	2	6	al	al	PROPN
ejpam-6189	2	7	.	.	PROPN
ejpam-6189	2	8	introduced	introduce	VERB
ejpam-6189	2	9	the	the	DET
ejpam-6189	2	10	concept	concept	NOUN
ejpam-6189	2	11	of	of	ADP
ejpam-6189	2	12	fuzzy	fuzzy	ADJ
ejpam-6189	2	13	bd	bd	NOUN
ejpam-6189	2	14	-	-	PUNCT
ejpam-6189	2	15	subalgebras	subalgebras	PROPN
ejpam-6189	2	16	of	of	ADP
ejpam-6189	2	17	bdalgebras	bdalgebras	PROPN
ejpam-6189	2	18	.	.	PUNCT
ejpam-6189	3	1	this	this	DET
ejpam-6189	3	2	paper	paper	NOUN
ejpam-6189	3	3	will	will	AUX
ejpam-6189	3	4	present	present	VERB
ejpam-6189	3	5	the	the	DET
ejpam-6189	3	6	concept	concept	NOUN
ejpam-6189	3	7	of	of	ADP
ejpam-6189	3	8	fuzzy	fuzzy	ADJ
ejpam-6189	3	9	dot	dot	NOUN
ejpam-6189	3	10	bd	bd	NOUN
ejpam-6189	3	11	-	-	PUNCT
ejpam-6189	3	12	subalgebras	subalgebras	PROPN
ejpam-6189	3	13	in	in	ADP
ejpam-6189	3	14	bd	bd	PROPN
ejpam-6189	3	15	-	-	PUNCT
ejpam-6189	3	16	algebras	algebras	PROPN
ejpam-6189	3	17	as	as	ADP
ejpam-6189	3	18	a	a	DET
ejpam-6189	3	19	generalization	generalization	NOUN
ejpam-6189	3	20	of	of	ADP
ejpam-6189	3	21	fuzzy	fuzzy	ADJ
ejpam-6189	3	22	bd	bd	PROPN
ejpam-6189	3	23	-	-	PUNCT
ejpam-6189	3	24	subalgebras	subalgebras	PROPN
ejpam-6189	3	25	.	.	PUNCT
ejpam-6189	4	1	subsequently	subsequently	ADV
ejpam-6189	4	2	,	,	PUNCT
ejpam-6189	4	3	we	we	PRON
ejpam-6189	4	4	evaluate	evaluate	VERB
ejpam-6189	4	5	the	the	DET
ejpam-6189	4	6	connections	connection	NOUN
ejpam-6189	4	7	of	of	ADP
ejpam-6189	4	8	fuzzy	fuzzy	ADJ
ejpam-6189	4	9	dot	dot	NOUN
ejpam-6189	4	10	bd	bd	NOUN
ejpam-6189	4	11	-	-	PUNCT
ejpam-6189	4	12	subalgebras	subalgebras	PROPN
ejpam-6189	4	13	in	in	ADP
ejpam-6189	4	14	the	the	DET
ejpam-6189	4	15	framework	framework	NOUN
ejpam-6189	4	16	of	of	ADP
ejpam-6189	4	17	a	a	DET
ejpam-6189	4	18	homomorphism	homomorphism	NOUN
ejpam-6189	4	19	of	of	ADP
ejpam-6189	4	20	bd	bd	PROPN
ejpam-6189	4	21	-	-	PUNCT
ejpam-6189	4	22	algebras	algebras	PROPN
ejpam-6189	4	23	.	.	PUNCT
ejpam-6189	5	1	finally	finally	ADV
ejpam-6189	5	2	,	,	PUNCT
ejpam-6189	5	3	we	we	PRON
ejpam-6189	5	4	propose	propose	VERB
ejpam-6189	5	5	the	the	DET
ejpam-6189	5	6	concept	concept	NOUN
ejpam-6189	5	7	of	of	ADP
ejpam-6189	5	8	strongest	strong	ADJ
ejpam-6189	5	9	fuzzy	fuzzy	ADJ
ejpam-6189	5	10	dot	dot	NOUN
ejpam-6189	5	11	bd	bd	NOUN
ejpam-6189	5	12	-	-	PUNCT
ejpam-6189	5	13	subalgebras	subalgebras	PROPN
ejpam-6189	5	14	and	and	CCONJ
ejpam-6189	5	15	explain	explain	VERB
ejpam-6189	5	16	their	their	PRON
ejpam-6189	5	17	characteristics	characteristic	NOUN
ejpam-6189	5	18	in	in	ADP
ejpam-6189	5	19	relation	relation	NOUN
ejpam-6189	5	20	to	to	ADP
ejpam-6189	5	21	bdsubalgebras	bdsubalgebra	NOUN
ejpam-6189	5	22	.	.	PUNCT
ejpam-6189	6	1	2020	2020	NUM
ejpam-6189	6	2	mathematics	mathematic	NOUN
ejpam-6189	6	3	subject	subject	NOUN
ejpam-6189	6	4	classifications	classification	NOUN
ejpam-6189	6	5	:	:	PUNCT
ejpam-6189	6	6	08a30	08a30	NOUN
ejpam-6189	6	7	,	,	PUNCT
ejpam-6189	6	8	08a72	08a72	NOUN
ejpam-6189	6	9	key	key	ADJ
ejpam-6189	6	10	words	word	NOUN
ejpam-6189	6	11	and	and	CCONJ
ejpam-6189	6	12	phrases	phrase	NOUN
ejpam-6189	6	13	:	:	PUNCT
ejpam-6189	6	14	bd	bd	NOUN
ejpam-6189	6	15	-	-	NOUN
ejpam-6189	6	16	algebra	algebra	PROPN
ejpam-6189	6	17	,	,	PUNCT
ejpam-6189	6	18	bd	bd	NOUN
ejpam-6189	6	19	-	-	PUNCT
ejpam-6189	6	20	subalgebra	subalgebra	NOUN
ejpam-6189	6	21	,	,	PUNCT
ejpam-6189	6	22	fuzzy	fuzzy	ADJ
ejpam-6189	6	23	bd	bd	NOUN
ejpam-6189	6	24	-	-	PUNCT
ejpam-6189	6	25	subalgebra	subalgebra	ADJ
ejpam-6189	6	26	,	,	PUNCT
ejpam-6189	6	27	fuzzy	fuzzy	ADJ
ejpam-6189	6	28	dot	dot	NOUN
ejpam-6189	6	29	bdsubalgebra	bdsubalgebra	NOUN
ejpam-6189	6	30	1	1	NUM
ejpam-6189	6	31	.	.	PUNCT
ejpam-6189	6	32	introduction	introduction	NOUN
ejpam-6189	6	33	the	the	DET
ejpam-6189	6	34	subalgebras	subalgebra	NOUN
ejpam-6189	6	35	,	,	PUNCT
ejpam-6189	6	36	such	such	ADJ
ejpam-6189	6	37	as	as	ADP
ejpam-6189	6	38	bck	bck	PROPN
ejpam-6189	6	39	/	/	SYM
ejpam-6189	6	40	bci	bci	NOUN
ejpam-6189	6	41	-	-	ADJ
ejpam-6189	6	42	subalgebras	subalgebras	X
ejpam-6189	7	1	[	[	X
ejpam-6189	7	2	1	1	NUM
ejpam-6189	7	3	]	]	PUNCT
ejpam-6189	7	4	,	,	PUNCT
ejpam-6189	7	5	be	be	AUX
ejpam-6189	7	6	-	-	PUNCT
ejpam-6189	7	7	subalgebras	subalgebras	X
ejpam-6189	7	8	[	[	X
ejpam-6189	7	9	2	2	NUM
ejpam-6189	7	10	]	]	PUNCT
ejpam-6189	7	11	,	,	PUNCT
ejpam-6189	7	12	and	and	CCONJ
ejpam-6189	7	13	bgsubalgebras	bgsubalgebra	NOUN
ejpam-6189	8	1	[	[	X
ejpam-6189	8	2	3	3	NUM
ejpam-6189	8	3	]	]	PUNCT
ejpam-6189	8	4	,	,	PUNCT
ejpam-6189	8	5	are	be	AUX
ejpam-6189	8	6	the	the	DET
ejpam-6189	8	7	most	most	ADV
ejpam-6189	8	8	frequently	frequently	ADV
ejpam-6189	8	9	examined	examine	VERB
ejpam-6189	8	10	concepts	concept	NOUN
ejpam-6189	8	11	when	when	SCONJ
ejpam-6189	8	12	examining	examine	VERB
ejpam-6189	8	13	the	the	DET
ejpam-6189	8	14	characteristics	characteristic	NOUN
ejpam-6189	8	15	of	of	ADP
ejpam-6189	8	16	different	different	ADJ
ejpam-6189	8	17	ideas	idea	NOUN
ejpam-6189	8	18	in	in	ADP
ejpam-6189	8	19	each	each	DET
ejpam-6189	8	20	algebraic	algebraic	ADJ
ejpam-6189	8	21	structure	structure	NOUN
ejpam-6189	8	22	.	.	PUNCT
ejpam-6189	9	1	exploring	explore	VERB
ejpam-6189	9	2	the	the	DET
ejpam-6189	9	3	characteristics	characteristic	NOUN
ejpam-6189	9	4	of	of	ADP
ejpam-6189	9	5	non	non	ADJ
ejpam-6189	9	6	-	-	ADJ
ejpam-6189	9	7	empty	empty	ADJ
ejpam-6189	9	8	subsets	subset	NOUN
ejpam-6189	9	9	of	of	ADP
ejpam-6189	9	10	an	an	DET
ejpam-6189	9	11	algebra	algebra	NOUN
ejpam-6189	9	12	and	and	CCONJ
ejpam-6189	9	13	applying	apply	VERB
ejpam-6189	9	14	the	the	DET
ejpam-6189	9	15	same	same	ADJ
ejpam-6189	9	16	operations	operation	NOUN
ejpam-6189	9	17	as	as	ADP
ejpam-6189	9	18	that	that	DET
ejpam-6189	9	19	algebra	algebra	NOUN
ejpam-6189	9	20	while	while	SCONJ
ejpam-6189	9	21	preserving	preserve	VERB
ejpam-6189	9	22	the	the	DET
ejpam-6189	9	23	structure	structure	NOUN
ejpam-6189	9	24	of	of	ADP
ejpam-6189	9	25	the	the	DET
ejpam-6189	9	26	original	original	ADJ
ejpam-6189	9	27	algebra	algebra	NOUN
ejpam-6189	9	28	are	be	AUX
ejpam-6189	9	29	key	key	ADJ
ejpam-6189	9	30	components	component	NOUN
ejpam-6189	9	31	of	of	ADP
ejpam-6189	9	32	the	the	DET
ejpam-6189	9	33	subalgebra	subalgebra	NOUN
ejpam-6189	9	34	notion	notion	NOUN
ejpam-6189	9	35	.	.	PUNCT
ejpam-6189	10	1	in	in	ADP
ejpam-6189	10	2	b	b	NOUN
ejpam-6189	10	3	-	-	PUNCT
ejpam-6189	10	4	algebras	algebras	X
ejpam-6189	10	5	,	,	PUNCT
ejpam-6189	10	6	walendziak	walendziak	ADJ
ejpam-6189	11	1	[	[	X
ejpam-6189	11	2	4	4	NUM
ejpam-6189	11	3	]	]	PUNCT
ejpam-6189	11	4	investigated	investigate	VERB
ejpam-6189	11	5	the	the	DET
ejpam-6189	11	6	concept	concept	NOUN
ejpam-6189	11	7	of	of	ADP
ejpam-6189	11	8	normal	normal	ADJ
ejpam-6189	11	9	subalgebras	subalgebra	NOUN
ejpam-6189	11	10	by	by	ADP
ejpam-6189	11	11	showing	show	VERB
ejpam-6189	11	12	that	that	SCONJ
ejpam-6189	11	13	the	the	DET
ejpam-6189	11	14	notion	notion	NOUN
ejpam-6189	11	15	of	of	ADP
ejpam-6189	11	16	a	a	DET
ejpam-6189	11	17	normal	normal	ADJ
ejpam-6189	11	18	subalgebra	subalgebra	NOUN
ejpam-6189	11	19	is	be	AUX
ejpam-6189	11	20	equivalent	equivalent	ADJ
ejpam-6189	11	21	to	to	ADP
ejpam-6189	11	22	the	the	DET
ejpam-6189	11	23	normal	normal	ADJ
ejpam-6189	11	24	subgroup	subgroup	NOUN
ejpam-6189	11	25	of	of	ADP
ejpam-6189	11	26	the	the	DET
ejpam-6189	11	27	derived	derive	VERB
ejpam-6189	11	28	group.jun	group.jun	PROPN
ejpam-6189	11	29	et	et	NOUN
ejpam-6189	11	30	al	al	PROPN
ejpam-6189	11	31	.	.	PUNCT
ejpam-6189	12	1	[	[	X
ejpam-6189	12	2	5	5	NUM
ejpam-6189	12	3	]	]	PUNCT
ejpam-6189	12	4	researched	research	VERB
ejpam-6189	12	5	d	d	NOUN
ejpam-6189	12	6	-	-	PUNCT
ejpam-6189	12	7	algebras	algebras	ADJ
ejpam-6189	12	8	using	use	VERB
ejpam-6189	12	9	the	the	DET
ejpam-6189	12	10	theory	theory	NOUN
ejpam-6189	12	11	of	of	ADP
ejpam-6189	12	12	a	a	DET
ejpam-6189	12	13	falling	fall	VERB
ejpam-6189	12	14	shadow	shadow	NOUN
ejpam-6189	12	15	.	.	PUNCT
ejpam-6189	13	1	to	to	PART
ejpam-6189	13	2	accomplish	accomplish	VERB
ejpam-6189	13	3	this	this	PRON
ejpam-6189	13	4	,	,	PUNCT
ejpam-6189	13	5	they	they	PRON
ejpam-6189	13	6	developed	develop	VERB
ejpam-6189	13	7	the	the	DET
ejpam-6189	13	8	concept	concept	NOUN
ejpam-6189	13	9	of	of	ADP
ejpam-6189	13	10	falling	fall	VERB
ejpam-6189	13	11	d	d	NOUN
ejpam-6189	13	12	-	-	PUNCT
ejpam-6189	13	13	subalgebras	subalgebras	PROPN
ejpam-6189	13	14	and	and	CCONJ
ejpam-6189	13	15	examined	examine	VERB
ejpam-6189	13	16	their	their	PRON
ejpam-6189	13	17	various	various	ADJ
ejpam-6189	13	18	characteristics	characteristic	NOUN
ejpam-6189	13	19	,	,	PUNCT
ejpam-6189	13	20	including	include	VERB
ejpam-6189	13	21	how	how	SCONJ
ejpam-6189	13	22	to	to	PART
ejpam-6189	13	23	classify	classify	VERB
ejpam-6189	13	24	the	the	DET
ejpam-6189	13	25	properties	property	NOUN
ejpam-6189	13	26	of	of	ADP
ejpam-6189	13	27	falling	fall	VERB
ejpam-6189	13	28	d	d	NOUN
ejpam-6189	13	29	-	-	PUNCT
ejpam-6189	13	30	subalgebras	subalgebras	PROPN
ejpam-6189	13	31	in	in	ADP
ejpam-6189	13	32	d-algebras.in	d-algebras.in	PROPN
ejpam-6189	13	33	bck	bck	PROPN
ejpam-6189	13	34	/	/	SYM
ejpam-6189	13	35	bci	bci	NOUN
ejpam-6189	13	36	-	-	PUNCT
ejpam-6189	13	37	algebras	algebra	NOUN
ejpam-6189	13	38	,	,	PUNCT
ejpam-6189	13	39	balami	balami	PROPN
ejpam-6189	13	40	et	et	PROPN
ejpam-6189	13	41	al	al	PROPN
ejpam-6189	13	42	.	.	PUNCT
ejpam-6189	14	1	[	[	X
ejpam-6189	14	2	6	6	NUM
ejpam-6189	14	3	]	]	PUNCT
ejpam-6189	14	4	presented	present	VERB
ejpam-6189	14	5	the	the	DET
ejpam-6189	14	6	concepts	concept	NOUN
ejpam-6189	14	7	of	of	ADP
ejpam-6189	14	8	soft	soft	ADJ
ejpam-6189	14	9	∗corresponding	∗corresponding	NOUN
ejpam-6189	14	10	author	author	NOUN
ejpam-6189	14	11	.	.	PUNCT
ejpam-6189	15	1	doi	doi	NOUN
ejpam-6189	15	2	:	:	PUNCT
ejpam-6189	15	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6189	https://doi.org/10.29020/nybg.ejpam.v18i3.6189	ADJ
ejpam-6189	15	4	email	email	NOUN
ejpam-6189	15	5	addresses	address	VERB
ejpam-6189	15	6	:	:	PUNCT
ejpam-6189	15	7	warud.n@msu.ac.th	warud.n@msu.ac.th	PRON
ejpam-6189	15	8	(	(	PUNCT
ejpam-6189	15	9	w.	w.	PROPN
ejpam-6189	15	10	nakkhasen	nakkhasen	PROPN
ejpam-6189	15	11	)	)	PUNCT
ejpam-6189	15	12	,	,	PUNCT
ejpam-6189	15	13	64010213033@msu.ac.th	64010213033@msu.ac.th	NOUN
ejpam-6189	15	14	(	(	PUNCT
ejpam-6189	15	15	n.	n.	NOUN
ejpam-6189	15	16	jaroenwan	jaroenwan	PROPN
ejpam-6189	15	17	)	)	PUNCT
ejpam-6189	15	18	,	,	PUNCT
ejpam-6189	15	19	64010213041@msu.ac.th	64010213041@msu.ac.th	INTJ
ejpam-6189	15	20	(	(	PUNCT
ejpam-6189	15	21	p.	p.	NOUN
ejpam-6189	15	22	huekkhunthod	huekkhunthod	NOUN
ejpam-6189	15	23	)	)	PUNCT
ejpam-6189	15	24	,	,	PUNCT
ejpam-6189	15	25	atthchaichada@gmail.com	atthchaichada@gmail.com	X
ejpam-6189	15	26	(	(	PUNCT
ejpam-6189	15	27	a.	a.	PROPN
ejpam-6189	15	28	chada	chada	PROPN
ejpam-6189	15	29	)	)	PUNCT
ejpam-6189	15	30	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6189	16	1	1	1	NUM
ejpam-6189	16	2	copyright	copyright	NOUN
ejpam-6189	16	3	:	:	PUNCT
ejpam-6189	16	4	©	©	PROPN
ejpam-6189	16	5	2025	2025	NUM
ejpam-6189	16	6	the	the	DET
ejpam-6189	16	7	author(s	author(s	NOUN
ejpam-6189	16	8	)	)	PUNCT
ejpam-6189	16	9	.	.	PUNCT
ejpam-6189	17	1	(	(	PUNCT
ejpam-6189	17	2	cc	cc	NOUN
ejpam-6189	17	3	by	by	ADP
ejpam-6189	17	4	-	-	PUNCT
ejpam-6189	17	5	nc	nc	PROPN
ejpam-6189	17	6	4.0	4.0	NUM
ejpam-6189	17	7	)	)	PUNCT
ejpam-6189	17	8	w.	w.	PROPN
ejpam-6189	17	9	nakkhasen	nakkhasen	PROPN
ejpam-6189	17	10	et	et	PROPN
ejpam-6189	17	11	al	al	PROPN
ejpam-6189	17	12	.	.	PUNCT
ejpam-6189	17	13	/	/	SYM
ejpam-6189	17	14	eur	eur	PROPN
ejpam-6189	17	15	.	.	PUNCT
ejpam-6189	18	1	j.	j.	PROPN
ejpam-6189	18	2	pure	pure	PROPN
ejpam-6189	18	3	appl	appl	PROPN
ejpam-6189	18	4	.	.	PROPN
ejpam-6189	18	5	math	math	PROPN
ejpam-6189	18	6	,	,	PUNCT
ejpam-6189	18	7	18	18	NUM
ejpam-6189	18	8	(	(	PUNCT
ejpam-6189	18	9	3	3	NUM
ejpam-6189	18	10	)	)	PUNCT
ejpam-6189	18	11	(	(	PUNCT
ejpam-6189	18	12	2025	2025	NUM
ejpam-6189	18	13	)	)	PUNCT
ejpam-6189	18	14	,	,	PUNCT
ejpam-6189	18	15	6189	6189	NUM
ejpam-6189	18	16	2	2	NUM
ejpam-6189	18	17	of	of	ADP
ejpam-6189	18	18	13	13	NUM
ejpam-6189	18	19	bck	bck	NOUN
ejpam-6189	18	20	/	/	SYM
ejpam-6189	18	21	bci	bci	NOUN
ejpam-6189	18	22	-	-	PUNCT
ejpam-6189	18	23	algebras	algebras	ADJ
ejpam-6189	18	24	and	and	CCONJ
ejpam-6189	18	25	soft	soft	ADJ
ejpam-6189	18	26	bck	bck	NOUN
ejpam-6189	18	27	/	/	SYM
ejpam-6189	18	28	bci	bci	NOUN
ejpam-6189	18	29	-	-	PUNCT
ejpam-6189	18	30	subalgebras	subalgebras	X
ejpam-6189	18	31	and	and	CCONJ
ejpam-6189	18	32	discussed	discuss	VERB
ejpam-6189	18	33	some	some	PRON
ejpam-6189	18	34	of	of	ADP
ejpam-6189	18	35	their	their	PRON
ejpam-6189	18	36	characteristics	characteristic	NOUN
ejpam-6189	18	37	.	.	PUNCT
ejpam-6189	19	1	mathematicians	mathematician	NOUN
ejpam-6189	19	2	also	also	ADV
ejpam-6189	19	3	study	study	VERB
ejpam-6189	19	4	the	the	DET
ejpam-6189	19	5	features	feature	NOUN
ejpam-6189	19	6	of	of	ADP
ejpam-6189	19	7	subalgebras	subalgebras	PROPN
ejpam-6189	19	8	in	in	ADP
ejpam-6189	19	9	additional	additional	ADJ
ejpam-6189	19	10	intriguing	intriguing	ADJ
ejpam-6189	19	11	algebraic	algebraic	ADJ
ejpam-6189	19	12	structures	structure	NOUN
ejpam-6189	19	13	,	,	PUNCT
ejpam-6189	19	14	such	such	ADJ
ejpam-6189	19	15	as	as	ADP
ejpam-6189	19	16	[	[	X
ejpam-6189	19	17	7	7	NUM
ejpam-6189	19	18	]	]	PUNCT
ejpam-6189	19	19	,	,	PUNCT
ejpam-6189	19	20	[	[	X
ejpam-6189	19	21	8	8	NUM
ejpam-6189	19	22	]	]	PUNCT
ejpam-6189	19	23	,	,	PUNCT
ejpam-6189	19	24	[	[	X
ejpam-6189	19	25	9	9	NUM
ejpam-6189	19	26	]	]	PUNCT
ejpam-6189	19	27	,	,	PUNCT
ejpam-6189	19	28	and	and	CCONJ
ejpam-6189	19	29	[	[	X
ejpam-6189	19	30	10	10	NUM
ejpam-6189	19	31	]	]	PUNCT
ejpam-6189	19	32	.	.	PUNCT
ejpam-6189	20	1	those	those	PRON
ejpam-6189	20	2	who	who	PRON
ejpam-6189	20	3	are	be	AUX
ejpam-6189	20	4	interested	interested	ADJ
ejpam-6189	20	5	can	can	AUX
ejpam-6189	20	6	learn	learn	VERB
ejpam-6189	20	7	more	more	ADJ
ejpam-6189	20	8	about	about	ADP
ejpam-6189	20	9	these	these	DET
ejpam-6189	20	10	structures	structure	NOUN
ejpam-6189	20	11	.	.	PUNCT
ejpam-6189	21	1	the	the	DET
ejpam-6189	21	2	concept	concept	NOUN
ejpam-6189	21	3	of	of	ADP
ejpam-6189	21	4	the	the	DET
ejpam-6189	21	5	fuzzy	fuzzy	ADJ
ejpam-6189	21	6	set	set	NOUN
ejpam-6189	21	7	of	of	ADP
ejpam-6189	21	8	δ	δ	PROPN
ejpam-6189	21	9	in	in	ADP
ejpam-6189	21	10	a	a	DET
ejpam-6189	21	11	non	non	ADJ
ejpam-6189	21	12	-	-	ADJ
ejpam-6189	21	13	empty	empty	ADJ
ejpam-6189	21	14	set	set	NOUN
ejpam-6189	21	15	x	x	PUNCT
ejpam-6189	21	16	is	be	AUX
ejpam-6189	21	17	a	a	DET
ejpam-6189	21	18	function	function	NOUN
ejpam-6189	21	19	δ	δ	NOUN
ejpam-6189	21	20	from	from	ADP
ejpam-6189	21	21	x	x	PRON
ejpam-6189	21	22	to	to	ADP
ejpam-6189	21	23	the	the	DET
ejpam-6189	21	24	closed	closed	ADJ
ejpam-6189	21	25	interval	interval	NOUN
ejpam-6189	21	26	[	[	X
ejpam-6189	21	27	0	0	NUM
ejpam-6189	21	28	,	,	PUNCT
ejpam-6189	21	29	1	1	NUM
ejpam-6189	21	30	]	]	PUNCT
ejpam-6189	21	31	in	in	ADP
ejpam-6189	21	32	the	the	DET
ejpam-6189	21	33	real	real	ADJ
ejpam-6189	21	34	numbers	number	NOUN
ejpam-6189	21	35	.	.	PUNCT
ejpam-6189	22	1	this	this	DET
ejpam-6189	22	2	concept	concept	NOUN
ejpam-6189	22	3	was	be	AUX
ejpam-6189	22	4	introduced	introduce	VERB
ejpam-6189	22	5	by	by	ADP
ejpam-6189	22	6	zadeh	zadeh	PROPN
ejpam-6189	23	1	[	[	X
ejpam-6189	23	2	11	11	NUM
ejpam-6189	23	3	]	]	PUNCT
ejpam-6189	23	4	,	,	PUNCT
ejpam-6189	23	5	and	and	CCONJ
ejpam-6189	23	6	it	it	PRON
ejpam-6189	23	7	has	have	AUX
ejpam-6189	23	8	since	since	SCONJ
ejpam-6189	23	9	become	become	VERB
ejpam-6189	23	10	a	a	DET
ejpam-6189	23	11	fundamental	fundamental	ADJ
ejpam-6189	23	12	tool	tool	NOUN
ejpam-6189	23	13	in	in	ADP
ejpam-6189	23	14	various	various	ADJ
ejpam-6189	23	15	fields	field	NOUN
ejpam-6189	23	16	,	,	PUNCT
ejpam-6189	23	17	such	such	ADJ
ejpam-6189	23	18	as	as	ADP
ejpam-6189	23	19	artificial	artificial	ADJ
ejpam-6189	23	20	intelligence	intelligence	NOUN
ejpam-6189	23	21	,	,	PUNCT
ejpam-6189	23	22	control	control	NOUN
ejpam-6189	23	23	systems	system	NOUN
ejpam-6189	23	24	,	,	PUNCT
ejpam-6189	23	25	and	and	CCONJ
ejpam-6189	23	26	decision	decision	NOUN
ejpam-6189	23	27	-	-	PUNCT
ejpam-6189	23	28	making	make	VERB
ejpam-6189	23	29	processes	process	NOUN
ejpam-6189	23	30	.	.	PUNCT
ejpam-6189	24	1	fuzzy	fuzzy	ADJ
ejpam-6189	24	2	sets	set	NOUN
ejpam-6189	24	3	allow	allow	VERB
ejpam-6189	24	4	for	for	ADP
ejpam-6189	24	5	the	the	DET
ejpam-6189	24	6	representation	representation	NOUN
ejpam-6189	24	7	of	of	ADP
ejpam-6189	24	8	uncertain	uncertain	ADJ
ejpam-6189	24	9	and	and	CCONJ
ejpam-6189	24	10	imprecise	imprecise	ADJ
ejpam-6189	24	11	information	information	NOUN
ejpam-6189	24	12	,	,	PUNCT
ejpam-6189	24	13	enabling	enable	VERB
ejpam-6189	24	14	more	more	ADV
ejpam-6189	24	15	flexible	flexible	ADJ
ejpam-6189	24	16	and	and	CCONJ
ejpam-6189	24	17	realistic	realistic	ADJ
ejpam-6189	24	18	modelling	modelling	NOUN
ejpam-6189	24	19	than	than	ADP
ejpam-6189	24	20	traditional	traditional	ADJ
ejpam-6189	24	21	binary	binary	ADJ
ejpam-6189	24	22	sets	set	NOUN
ejpam-6189	24	23	.	.	PUNCT
ejpam-6189	25	1	rosenfeld	rosenfeld	PROPN
ejpam-6189	26	1	[	[	X
ejpam-6189	26	2	12	12	NUM
ejpam-6189	26	3	]	]	PUNCT
ejpam-6189	26	4	applied	apply	VERB
ejpam-6189	26	5	fuzzy	fuzzy	ADJ
ejpam-6189	26	6	sets	set	NOUN
ejpam-6189	26	7	to	to	PART
ejpam-6189	26	8	establish	establish	VERB
ejpam-6189	26	9	the	the	DET
ejpam-6189	26	10	concepts	concept	NOUN
ejpam-6189	26	11	of	of	ADP
ejpam-6189	26	12	fuzzy	fuzzy	ADJ
ejpam-6189	26	13	subgroups	subgroup	NOUN
ejpam-6189	26	14	and	and	CCONJ
ejpam-6189	26	15	fuzzy	fuzzy	ADJ
ejpam-6189	26	16	ideals	ideal	NOUN
ejpam-6189	26	17	in	in	ADP
ejpam-6189	26	18	groups	group	NOUN
ejpam-6189	26	19	.	.	PUNCT
ejpam-6189	27	1	subsequently	subsequently	ADV
ejpam-6189	27	2	,	,	PUNCT
ejpam-6189	27	3	kuroki	kuroki	PROPN
ejpam-6189	27	4	[	[	X
ejpam-6189	27	5	13	13	NUM
ejpam-6189	27	6	]	]	PUNCT
ejpam-6189	27	7	examined	examine	VERB
ejpam-6189	27	8	the	the	DET
ejpam-6189	27	9	classifications	classification	NOUN
ejpam-6189	27	10	of	of	ADP
ejpam-6189	27	11	fuzzy	fuzzy	ADJ
ejpam-6189	27	12	subsemigroups	subsemigroup	NOUN
ejpam-6189	27	13	,	,	PUNCT
ejpam-6189	27	14	investigating	investigate	VERB
ejpam-6189	27	15	the	the	DET
ejpam-6189	27	16	features	feature	NOUN
ejpam-6189	27	17	and	and	CCONJ
ejpam-6189	27	18	uses	use	VERB
ejpam-6189	27	19	in	in	ADP
ejpam-6189	27	20	semigroups	semigroup	NOUN
ejpam-6189	27	21	.	.	PUNCT
ejpam-6189	28	1	next	next	ADJ
ejpam-6189	28	2	,	,	PUNCT
ejpam-6189	28	3	rezaei	rezaei	NOUN
ejpam-6189	28	4	and	and	CCONJ
ejpam-6189	28	5	saeid	saeid	PROPN
ejpam-6189	29	1	[	[	X
ejpam-6189	29	2	14	14	NUM
ejpam-6189	29	3	]	]	PUNCT
ejpam-6189	29	4	developed	develop	VERB
ejpam-6189	29	5	the	the	DET
ejpam-6189	29	6	concept	concept	NOUN
ejpam-6189	29	7	of	of	ADP
ejpam-6189	29	8	fuzzy	fuzzy	ADJ
ejpam-6189	29	9	subalgebras	subalgebra	NOUN
ejpam-6189	29	10	into	into	ADP
ejpam-6189	29	11	be	be	AUX
ejpam-6189	29	12	-	-	PUNCT
ejpam-6189	29	13	algebras	algebra	VERB
ejpam-6189	29	14	and	and	CCONJ
ejpam-6189	29	15	studied	study	VERB
ejpam-6189	29	16	various	various	ADJ
ejpam-6189	29	17	characterizations	characterization	NOUN
ejpam-6189	29	18	of	of	ADP
ejpam-6189	29	19	these	these	DET
ejpam-6189	29	20	fuzzy	fuzzy	ADJ
ejpam-6189	29	21	subalgebras	subalgebra	NOUN
ejpam-6189	29	22	.	.	PUNCT
ejpam-6189	30	1	afterwards	afterwards	ADV
ejpam-6189	30	2	,	,	PUNCT
ejpam-6189	30	3	muhiuddin	muhiuddin	VERB
ejpam-6189	30	4	[	[	X
ejpam-6189	30	5	15	15	NUM
ejpam-6189	30	6	]	]	PUNCT
ejpam-6189	30	7	defined	define	VERB
ejpam-6189	30	8	the	the	DET
ejpam-6189	30	9	concept	concept	NOUN
ejpam-6189	30	10	of	of	ADP
ejpam-6189	30	11	(	(	PUNCT
ejpam-6189	30	12	∈,∈	∈,∈	X
ejpam-6189	30	13	∨qδ0)-fuzzy	∨qδ0)-fuzzy	PROPN
ejpam-6189	30	14	subalgebras	subalgebra	NOUN
ejpam-6189	30	15	of	of	ADP
ejpam-6189	30	16	bck	bck	PROPN
ejpam-6189	30	17	/	/	SYM
ejpam-6189	30	18	bci	bci	NOUN
ejpam-6189	30	19	-	-	PUNCT
ejpam-6189	30	20	algebras	algebra	NOUN
ejpam-6189	30	21	as	as	ADP
ejpam-6189	30	22	a	a	DET
ejpam-6189	30	23	more	more	ADV
ejpam-6189	30	24	general	general	ADJ
ejpam-6189	30	25	type	type	NOUN
ejpam-6189	30	26	of	of	ADP
ejpam-6189	30	27	(	(	PUNCT
ejpam-6189	30	28	∈,∈	∈,∈	X
ejpam-6189	30	29	∨q)-fuzzy	∨q)-fuzzy	ADJ
ejpam-6189	30	30	subalgebras	subalgebra	NOUN
ejpam-6189	30	31	.	.	PUNCT
ejpam-6189	31	1	following	follow	VERB
ejpam-6189	31	2	that	that	PRON
ejpam-6189	31	3	,	,	PUNCT
ejpam-6189	31	4	tacha	tacha	PROPN
ejpam-6189	31	5	et	et	PROPN
ejpam-6189	31	6	al	al	PROPN
ejpam-6189	31	7	.	.	PUNCT
ejpam-6189	32	1	[	[	X
ejpam-6189	32	2	16	16	NUM
ejpam-6189	32	3	]	]	PUNCT
ejpam-6189	32	4	introduced	introduce	VERB
ejpam-6189	32	5	the	the	DET
ejpam-6189	32	6	concepts	concept	NOUN
ejpam-6189	32	7	of	of	ADP
ejpam-6189	32	8	length	length	NOUN
ejpam-6189	32	9	fuzzy	fuzzy	ADJ
ejpam-6189	32	10	up	up	ADP
ejpam-6189	32	11	-subalgebras	-subalgebra	NOUN
ejpam-6189	32	12	and	and	CCONJ
ejpam-6189	32	13	mean	mean	VERB
ejpam-6189	32	14	fuzzy	fuzzy	ADJ
ejpam-6189	32	15	up	up	ADP
ejpam-6189	32	16	-subalgebras	-subalgebra	NOUN
ejpam-6189	32	17	of	of	ADP
ejpam-6189	32	18	up	up	NOUN
ejpam-6189	32	19	-algebras	-algebra	NOUN
ejpam-6189	32	20	.	.	PUNCT
ejpam-6189	33	1	the	the	DET
ejpam-6189	33	2	researchers	researcher	NOUN
ejpam-6189	33	3	also	also	ADV
ejpam-6189	33	4	investigated	investigate	VERB
ejpam-6189	33	5	the	the	DET
ejpam-6189	33	6	relationships	relationship	NOUN
ejpam-6189	33	7	between	between	ADP
ejpam-6189	33	8	length	length	NOUN
ejpam-6189	33	9	fuzzy	fuzzy	ADJ
ejpam-6189	33	10	up	up	ADP
ejpam-6189	33	11	-subalgebras	-subalgebra	NOUN
ejpam-6189	33	12	(	(	PUNCT
ejpam-6189	33	13	mean	mean	ADV
ejpam-6189	33	14	fuzzy	fuzzy	ADJ
ejpam-6189	33	15	up	up	ADP
ejpam-6189	33	16	-subalgebras	-subalgebra	NOUN
ejpam-6189	33	17	)	)	PUNCT
ejpam-6189	33	18	and	and	CCONJ
ejpam-6189	33	19	hyper	hyper	ADJ
ejpam-6189	33	20	fuzzy	fuzzy	ADJ
ejpam-6189	33	21	up	up	ADP
ejpam-6189	33	22	-subalgebras	-subalgebra	NOUN
ejpam-6189	33	23	of	of	ADP
ejpam-6189	33	24	up	up	ADV
ejpam-6189	33	25	-subalgebras	-subalgebra	NOUN
ejpam-6189	33	26	.	.	PUNCT
ejpam-6189	34	1	for	for	ADP
ejpam-6189	34	2	research	research	NOUN
ejpam-6189	34	3	related	relate	VERB
ejpam-6189	34	4	to	to	ADP
ejpam-6189	34	5	fuzzy	fuzzy	ADJ
ejpam-6189	34	6	subalgebras	subalgebra	NOUN
ejpam-6189	34	7	,	,	PUNCT
ejpam-6189	34	8	further	further	ADJ
ejpam-6189	34	9	studies	study	NOUN
ejpam-6189	34	10	can	can	AUX
ejpam-6189	34	11	be	be	AUX
ejpam-6189	34	12	found	find	VERB
ejpam-6189	34	13	in	in	ADP
ejpam-6189	34	14	[	[	X
ejpam-6189	34	15	17	17	NUM
ejpam-6189	34	16	]	]	PUNCT
ejpam-6189	34	17	,	,	PUNCT
ejpam-6189	34	18	[	[	X
ejpam-6189	34	19	18	18	NUM
ejpam-6189	34	20	]	]	PUNCT
ejpam-6189	34	21	,	,	PUNCT
ejpam-6189	34	22	[	[	X
ejpam-6189	34	23	19	19	NUM
ejpam-6189	34	24	]	]	PUNCT
ejpam-6189	34	25	,	,	PUNCT
ejpam-6189	34	26	and	and	CCONJ
ejpam-6189	34	27	[	[	X
ejpam-6189	34	28	20	20	NUM
ejpam-6189	34	29	]	]	PUNCT
ejpam-6189	34	30	.	.	PUNCT
ejpam-6189	35	1	for	for	ADP
ejpam-6189	35	2	the	the	DET
ejpam-6189	35	3	general	general	ADJ
ejpam-6189	35	4	concept	concept	NOUN
ejpam-6189	35	5	of	of	ADP
ejpam-6189	35	6	fuzzy	fuzzy	ADJ
ejpam-6189	35	7	subalgebras	subalgebra	NOUN
ejpam-6189	35	8	,	,	PUNCT
ejpam-6189	35	9	another	another	DET
ejpam-6189	35	10	concept	concept	NOUN
ejpam-6189	35	11	that	that	PRON
ejpam-6189	35	12	has	have	AUX
ejpam-6189	35	13	been	be	AUX
ejpam-6189	35	14	continuously	continuously	ADV
ejpam-6189	35	15	studied	study	VERB
ejpam-6189	35	16	is	be	AUX
ejpam-6189	35	17	the	the	DET
ejpam-6189	35	18	fuzzy	fuzzy	ADJ
ejpam-6189	35	19	dot	dot	NOUN
ejpam-6189	35	20	.	.	PUNCT
ejpam-6189	36	1	saeid	saeid	PROPN
ejpam-6189	36	2	[	[	X
ejpam-6189	36	3	21	21	NUM
ejpam-6189	36	4	]	]	PUNCT
ejpam-6189	36	5	presented	present	VERB
ejpam-6189	36	6	the	the	DET
ejpam-6189	36	7	notion	notion	NOUN
ejpam-6189	36	8	of	of	ADP
ejpam-6189	36	9	fuzzy	fuzzy	ADJ
ejpam-6189	36	10	dot	dot	NOUN
ejpam-6189	36	11	bcksubalgebras	bcksubalgebra	NOUN
ejpam-6189	36	12	and	and	CCONJ
ejpam-6189	36	13	fuzzy	fuzzy	ADJ
ejpam-6189	36	14	dot	dot	NOUN
ejpam-6189	36	15	topological	topological	NOUN
ejpam-6189	36	16	bck	bck	NOUN
ejpam-6189	36	17	-	-	PUNCT
ejpam-6189	36	18	algebras	algebras	PROPN
ejpam-6189	36	19	within	within	ADP
ejpam-6189	36	20	the	the	DET
ejpam-6189	36	21	framework	framework	NOUN
ejpam-6189	36	22	of	of	ADP
ejpam-6189	36	23	bckalgebras	bckalgebras	PROPN
ejpam-6189	36	24	.	.	PUNCT
ejpam-6189	37	1	following	follow	VERB
ejpam-6189	37	2	this	this	PRON
ejpam-6189	37	3	,	,	PUNCT
ejpam-6189	37	4	senapati	senapati	PROPN
ejpam-6189	37	5	et	et	PROPN
ejpam-6189	37	6	al	al	PROPN
ejpam-6189	37	7	.	.	PUNCT
ejpam-6189	38	1	[	[	X
ejpam-6189	38	2	22	22	NUM
ejpam-6189	38	3	]	]	PUNCT
ejpam-6189	38	4	provided	provide	VERB
ejpam-6189	38	5	definitions	definition	NOUN
ejpam-6189	38	6	and	and	CCONJ
ejpam-6189	38	7	examined	examine	VERB
ejpam-6189	38	8	related	related	ADJ
ejpam-6189	38	9	features	feature	NOUN
ejpam-6189	38	10	of	of	ADP
ejpam-6189	38	11	fuzzy	fuzzy	ADJ
ejpam-6189	38	12	dot	dot	NOUN
ejpam-6189	38	13	subalgebras	subalgebras	X
ejpam-6189	38	14	,	,	PUNCT
ejpam-6189	38	15	fuzzy	fuzzy	ADJ
ejpam-6189	38	16	normal	normal	ADJ
ejpam-6189	38	17	dot	dot	NOUN
ejpam-6189	38	18	subalgebras	subalgebras	X
ejpam-6189	38	19	,	,	PUNCT
ejpam-6189	38	20	and	and	CCONJ
ejpam-6189	38	21	fuzzy	fuzzy	ADJ
ejpam-6189	38	22	dot	dot	NOUN
ejpam-6189	38	23	ideals	ideal	NOUN
ejpam-6189	38	24	of	of	ADP
ejpam-6189	38	25	bg	bg	PROPN
ejpam-6189	38	26	-	-	PUNCT
ejpam-6189	38	27	algebras	algebras	PROPN
ejpam-6189	38	28	.	.	PUNCT
ejpam-6189	39	1	in	in	ADP
ejpam-6189	39	2	the	the	DET
ejpam-6189	39	3	same	same	ADJ
ejpam-6189	39	4	year	year	NOUN
ejpam-6189	39	5	,	,	PUNCT
ejpam-6189	39	6	senapati	senapati	PROPN
ejpam-6189	39	7	et	et	PROPN
ejpam-6189	39	8	al	al	PROPN
ejpam-6189	39	9	.	.	PUNCT
ejpam-6189	40	1	[	[	X
ejpam-6189	40	2	23	23	NUM
ejpam-6189	40	3	]	]	PUNCT
ejpam-6189	40	4	introduced	introduce	VERB
ejpam-6189	40	5	fuzzy	fuzzy	ADJ
ejpam-6189	40	6	dot	dot	NOUN
ejpam-6189	40	7	subalgebras	subalgebras	X
ejpam-6189	40	8	,	,	PUNCT
ejpam-6189	40	9	fuzzy	fuzzy	ADJ
ejpam-6189	40	10	normal	normal	ADJ
ejpam-6189	40	11	dot	dot	NOUN
ejpam-6189	40	12	subalgebras	subalgebras	X
ejpam-6189	40	13	,	,	PUNCT
ejpam-6189	40	14	and	and	CCONJ
ejpam-6189	40	15	fuzzy	fuzzy	ADJ
ejpam-6189	40	16	dot	dot	NOUN
ejpam-6189	40	17	ideals	ideal	NOUN
ejpam-6189	40	18	to	to	ADP
ejpam-6189	40	19	the	the	DET
ejpam-6189	40	20	investigation	investigation	NOUN
ejpam-6189	40	21	in	in	ADP
ejpam-6189	40	22	b	b	NOUN
ejpam-6189	40	23	-	-	PUNCT
ejpam-6189	40	24	algebras	algebras	PROPN
ejpam-6189	40	25	.	.	PUNCT
ejpam-6189	41	1	later	later	ADV
ejpam-6189	41	2	,	,	PUNCT
ejpam-6189	41	3	dejen	dejen	PROPN
ejpam-6189	42	1	[	[	X
ejpam-6189	42	2	24	24	NUM
ejpam-6189	42	3	]	]	PUNCT
ejpam-6189	42	4	gave	give	VERB
ejpam-6189	42	5	the	the	DET
ejpam-6189	42	6	idea	idea	NOUN
ejpam-6189	42	7	of	of	ADP
ejpam-6189	42	8	fuzzy	fuzzy	ADJ
ejpam-6189	42	9	dot	dot	NOUN
ejpam-6189	42	10	subalgebras	subalgebra	NOUN
ejpam-6189	42	11	in	in	ADP
ejpam-6189	42	12	the	the	DET
ejpam-6189	42	13	structure	structure	NOUN
ejpam-6189	42	14	of	of	ADP
ejpam-6189	42	15	fuzzy	fuzzy	ADJ
ejpam-6189	42	16	dot	dot	NOUN
ejpam-6189	42	17	d	d	NOUN
ejpam-6189	42	18	-	-	PUNCT
ejpam-6189	42	19	subalgebras	subalgebras	PROPN
ejpam-6189	42	20	and	and	CCONJ
ejpam-6189	42	21	studied	study	VERB
ejpam-6189	42	22	several	several	ADJ
ejpam-6189	42	23	of	of	ADP
ejpam-6189	42	24	its	its	PRON
ejpam-6189	42	25	characteristics	characteristic	NOUN
ejpam-6189	42	26	.	.	PUNCT
ejpam-6189	43	1	in	in	ADP
ejpam-6189	43	2	addition	addition	NOUN
ejpam-6189	43	3	,	,	PUNCT
ejpam-6189	43	4	jiang	jiang	PROPN
ejpam-6189	44	1	[	[	X
ejpam-6189	44	2	25	25	NUM
ejpam-6189	44	3	]	]	PUNCT
ejpam-6189	44	4	established	establish	VERB
ejpam-6189	44	5	the	the	DET
ejpam-6189	44	6	notions	notion	NOUN
ejpam-6189	44	7	of	of	ADP
ejpam-6189	44	8	hesitant	hesitant	ADJ
ejpam-6189	44	9	fuzzy	fuzzy	ADJ
ejpam-6189	44	10	dot	dot	NOUN
ejpam-6189	44	11	subalgebras	subalgebras	X
ejpam-6189	44	12	,	,	PUNCT
ejpam-6189	44	13	hesitant	hesitant	ADJ
ejpam-6189	44	14	fuzzy	fuzzy	ADJ
ejpam-6189	44	15	normal	normal	ADJ
ejpam-6189	44	16	dot	dot	NOUN
ejpam-6189	44	17	subalgebras	subalgebras	X
ejpam-6189	44	18	,	,	PUNCT
ejpam-6189	44	19	and	and	CCONJ
ejpam-6189	44	20	hesitant	hesitant	ADJ
ejpam-6189	44	21	fuzzy	fuzzy	ADJ
ejpam-6189	44	22	dot	dot	NOUN
ejpam-6189	44	23	ideals	ideal	NOUN
ejpam-6189	44	24	of	of	ADP
ejpam-6189	44	25	b	b	NOUN
ejpam-6189	44	26	-	-	PUNCT
ejpam-6189	44	27	algebras	algebras	PROPN
ejpam-6189	44	28	and	and	CCONJ
ejpam-6189	44	29	explored	explore	VERB
ejpam-6189	44	30	properties	property	NOUN
ejpam-6189	44	31	related	relate	VERB
ejpam-6189	44	32	to	to	ADP
ejpam-6189	44	33	these	these	DET
ejpam-6189	44	34	concepts	concept	NOUN
ejpam-6189	44	35	of	of	ADP
ejpam-6189	44	36	b	b	NOUN
ejpam-6189	44	37	-	-	PUNCT
ejpam-6189	44	38	algebras	algebras	PROPN
ejpam-6189	44	39	.	.	PUNCT
ejpam-6189	45	1	in	in	ADP
ejpam-6189	45	2	2022	2022	NUM
ejpam-6189	45	3	,	,	PUNCT
ejpam-6189	45	4	the	the	DET
ejpam-6189	45	5	concept	concept	NOUN
ejpam-6189	45	6	of	of	ADP
ejpam-6189	45	7	bd	bd	PROPN
ejpam-6189	45	8	-	-	PUNCT
ejpam-6189	45	9	algebras	algebras	PROPN
ejpam-6189	45	10	is	be	AUX
ejpam-6189	45	11	derived	derive	VERB
ejpam-6189	45	12	from	from	ADP
ejpam-6189	45	13	certain	certain	ADJ
ejpam-6189	45	14	properties	property	NOUN
ejpam-6189	45	15	of	of	ADP
ejpam-6189	45	16	d	d	NOUN
ejpam-6189	45	17	-	-	PUNCT
ejpam-6189	45	18	algebras	algebras	PROPN
ejpam-6189	45	19	and	and	CCONJ
ejpam-6189	45	20	b	b	NOUN
ejpam-6189	45	21	-	-	PUNCT
ejpam-6189	45	22	algebras	algebras	X
ejpam-6189	45	23	,	,	PUNCT
ejpam-6189	45	24	introduced	introduce	VERB
ejpam-6189	45	25	by	by	ADP
ejpam-6189	45	26	bantaojai	bantaojai	NOUN
ejpam-6189	45	27	et	et	PROPN
ejpam-6189	45	28	al	al	PROPN
ejpam-6189	45	29	.	.	PUNCT
ejpam-6189	46	1	[	[	X
ejpam-6189	46	2	26	26	NUM
ejpam-6189	46	3	]	]	X
ejpam-6189	46	4	,	,	PUNCT
ejpam-6189	46	5	who	who	PRON
ejpam-6189	46	6	defined	define	VERB
ejpam-6189	46	7	various	various	ADJ
ejpam-6189	46	8	concepts	concept	NOUN
ejpam-6189	46	9	,	,	PUNCT
ejpam-6189	46	10	one	one	NUM
ejpam-6189	46	11	of	of	ADP
ejpam-6189	46	12	which	which	PRON
ejpam-6189	46	13	is	be	AUX
ejpam-6189	46	14	bd	bd	PROPN
ejpam-6189	46	15	-	-	PUNCT
ejpam-6189	46	16	subalgebras	subalgebras	PROPN
ejpam-6189	46	17	.	.	PUNCT
ejpam-6189	47	1	thereafter	thereafter	ADV
ejpam-6189	47	2	,	,	PUNCT
ejpam-6189	47	3	the	the	DET
ejpam-6189	47	4	notion	notion	NOUN
ejpam-6189	47	5	of	of	ADP
ejpam-6189	47	6	fuzzy	fuzzy	ADJ
ejpam-6189	47	7	bd	bd	PROPN
ejpam-6189	47	8	-	-	PUNCT
ejpam-6189	47	9	subalgebras	subalgebras	PROPN
ejpam-6189	47	10	of	of	ADP
ejpam-6189	47	11	bd	bd	PROPN
ejpam-6189	47	12	-	-	PUNCT
ejpam-6189	47	13	algebras	algebras	PROPN
ejpam-6189	47	14	was	be	AUX
ejpam-6189	47	15	recently	recently	ADV
ejpam-6189	47	16	defined	define	VERB
ejpam-6189	47	17	by	by	ADP
ejpam-6189	47	18	nakkhasen	nakkhasen	PROPN
ejpam-6189	47	19	et	et	PROPN
ejpam-6189	47	20	al	al	PROPN
ejpam-6189	47	21	.	.	PUNCT
ejpam-6189	48	1	[	[	X
ejpam-6189	48	2	27	27	NUM
ejpam-6189	48	3	]	]	PUNCT
ejpam-6189	48	4	.	.	PUNCT
ejpam-6189	49	1	in	in	ADP
ejpam-6189	49	2	their	their	PRON
ejpam-6189	49	3	presentation	presentation	NOUN
ejpam-6189	49	4	,	,	PUNCT
ejpam-6189	49	5	they	they	PRON
ejpam-6189	49	6	discussed	discuss	VERB
ejpam-6189	49	7	an	an	DET
ejpam-6189	49	8	opportunity	opportunity	NOUN
ejpam-6189	49	9	of	of	ADP
ejpam-6189	49	10	fuzzy	fuzzy	ADJ
ejpam-6189	49	11	multiplications	multiplication	NOUN
ejpam-6189	49	12	,	,	PUNCT
ejpam-6189	49	13	fuzzy	fuzzy	ADJ
ejpam-6189	49	14	magnified	magnify	VERB
ejpam-6189	49	15	translations	translation	NOUN
ejpam-6189	49	16	,	,	PUNCT
ejpam-6189	49	17	and	and	CCONJ
ejpam-6189	49	18	fuzzy	fuzzy	ADJ
ejpam-6189	49	19	translations	translation	NOUN
ejpam-6189	49	20	to	to	PART
ejpam-6189	49	21	characterize	characterize	VERB
ejpam-6189	49	22	fuzzy	fuzzy	ADJ
ejpam-6189	49	23	bd	bd	NOUN
ejpam-6189	49	24	-	-	NOUN
ejpam-6189	49	25	subalgebras	subalgebras	PROPN
ejpam-6189	49	26	in	in	ADP
ejpam-6189	49	27	bd	bd	PROPN
ejpam-6189	49	28	-	-	PUNCT
ejpam-6189	49	29	algebras	algebras	PROPN
ejpam-6189	49	30	.	.	PUNCT
ejpam-6189	50	1	to	to	PART
ejpam-6189	50	2	further	far	ADV
ejpam-6189	50	3	investigate	investigate	VERB
ejpam-6189	50	4	the	the	DET
ejpam-6189	50	5	general	general	ADJ
ejpam-6189	50	6	idea	idea	NOUN
ejpam-6189	50	7	of	of	ADP
ejpam-6189	50	8	fuzzy	fuzzy	ADJ
ejpam-6189	50	9	bd	bd	PROPN
ejpam-6189	50	10	-	-	PUNCT
ejpam-6189	50	11	subalgebras	subalgebras	PROPN
ejpam-6189	50	12	,	,	PUNCT
ejpam-6189	50	13	this	this	DET
ejpam-6189	50	14	article	article	NOUN
ejpam-6189	50	15	will	will	AUX
ejpam-6189	50	16	introduce	introduce	VERB
ejpam-6189	50	17	the	the	DET
ejpam-6189	50	18	notion	notion	NOUN
ejpam-6189	50	19	of	of	ADP
ejpam-6189	50	20	fuzzy	fuzzy	ADJ
ejpam-6189	50	21	dot	dot	NOUN
ejpam-6189	50	22	bd	bd	PROPN
ejpam-6189	50	23	-	-	PUNCT
ejpam-6189	50	24	subalgebras	subalgebras	PROPN
ejpam-6189	50	25	,	,	PUNCT
ejpam-6189	50	26	which	which	PRON
ejpam-6189	50	27	serves	serve	VERB
ejpam-6189	50	28	as	as	ADP
ejpam-6189	50	29	a	a	DET
ejpam-6189	50	30	generalization	generalization	NOUN
ejpam-6189	50	31	of	of	ADP
ejpam-6189	50	32	fuzzy	fuzzy	ADJ
ejpam-6189	50	33	bd	bd	NOUN
ejpam-6189	50	34	-	-	PUNCT
ejpam-6189	50	35	subalgebras	subalgebras	PROPN
ejpam-6189	50	36	in	in	ADP
ejpam-6189	50	37	bd	bd	PROPN
ejpam-6189	50	38	-	-	PUNCT
ejpam-6189	50	39	algebras	algebras	PROPN
ejpam-6189	50	40	.	.	PUNCT
ejpam-6189	51	1	in	in	ADP
ejpam-6189	51	2	section	section	NOUN
ejpam-6189	51	3	3	3	NUM
ejpam-6189	51	4	,	,	PUNCT
ejpam-6189	51	5	we	we	PRON
ejpam-6189	51	6	explore	explore	VERB
ejpam-6189	51	7	certain	certain	ADJ
ejpam-6189	51	8	features	feature	NOUN
ejpam-6189	51	9	of	of	ADP
ejpam-6189	51	10	fuzzy	fuzzy	ADJ
ejpam-6189	51	11	dot	dot	NOUN
ejpam-6189	51	12	bd	bd	NOUN
ejpam-6189	51	13	-	-	PUNCT
ejpam-6189	51	14	subalgebras	subalgebras	PROPN
ejpam-6189	51	15	in	in	ADP
ejpam-6189	51	16	bd	bd	PROPN
ejpam-6189	51	17	-	-	PUNCT
ejpam-6189	51	18	algebras	algebras	PROPN
ejpam-6189	51	19	.	.	PUNCT
ejpam-6189	52	1	moreover	moreover	ADV
ejpam-6189	52	2	,	,	PUNCT
ejpam-6189	52	3	we	we	PRON
ejpam-6189	52	4	further	far	ADV
ejpam-6189	52	5	examine	examine	VERB
ejpam-6189	52	6	the	the	DET
ejpam-6189	52	7	relationships	relationship	NOUN
ejpam-6189	52	8	of	of	ADP
ejpam-6189	52	9	fuzzy	fuzzy	ADJ
ejpam-6189	52	10	dot	dot	NOUN
ejpam-6189	52	11	bd	bd	NOUN
ejpam-6189	52	12	-	-	PUNCT
ejpam-6189	52	13	subalgebras	subalgebras	PROPN
ejpam-6189	52	14	under	under	ADP
ejpam-6189	52	15	a	a	DET
ejpam-6189	52	16	homomorphism	homomorphism	NOUN
ejpam-6189	52	17	of	of	ADP
ejpam-6189	52	18	bdw	bdw	PROPN
ejpam-6189	52	19	.	.	PROPN
ejpam-6189	52	20	nakkhasen	nakkhasen	PROPN
ejpam-6189	52	21	et	et	PROPN
ejpam-6189	52	22	al	al	PROPN
ejpam-6189	52	23	.	.	PUNCT
ejpam-6189	52	24	/	/	SYM
ejpam-6189	52	25	eur	eur	PROPN
ejpam-6189	52	26	.	.	PUNCT
ejpam-6189	53	1	j.	j.	PROPN
ejpam-6189	53	2	pure	pure	PROPN
ejpam-6189	53	3	appl	appl	PROPN
ejpam-6189	53	4	.	.	PROPN
ejpam-6189	53	5	math	math	PROPN
ejpam-6189	53	6	,	,	PUNCT
ejpam-6189	53	7	18	18	NUM
ejpam-6189	53	8	(	(	PUNCT
ejpam-6189	53	9	3	3	NUM
ejpam-6189	53	10	)	)	PUNCT
ejpam-6189	53	11	(	(	PUNCT
ejpam-6189	53	12	2025	2025	NUM
ejpam-6189	53	13	)	)	PUNCT
ejpam-6189	53	14	,	,	PUNCT
ejpam-6189	53	15	6189	6189	NUM
ejpam-6189	53	16	3	3	NUM
ejpam-6189	53	17	of	of	ADP
ejpam-6189	53	18	13	13	NUM
ejpam-6189	53	19	algebras	algebra	NOUN
ejpam-6189	53	20	.	.	PUNCT
ejpam-6189	54	1	finally	finally	ADV
ejpam-6189	54	2	,	,	PUNCT
ejpam-6189	54	3	section	section	NOUN
ejpam-6189	54	4	4	4	NUM
ejpam-6189	54	5	presents	present	VERB
ejpam-6189	54	6	the	the	DET
ejpam-6189	54	7	concept	concept	NOUN
ejpam-6189	54	8	of	of	ADP
ejpam-6189	54	9	strongest	strong	ADJ
ejpam-6189	54	10	fuzzy	fuzzy	ADJ
ejpam-6189	54	11	dot	dot	NOUN
ejpam-6189	54	12	bd	bd	NOUN
ejpam-6189	54	13	-	-	PUNCT
ejpam-6189	54	14	subalgebras	subalgebras	PROPN
ejpam-6189	54	15	in	in	ADP
ejpam-6189	54	16	bd	bd	PROPN
ejpam-6189	54	17	-	-	PUNCT
ejpam-6189	54	18	algebras	algebras	PROPN
ejpam-6189	54	19	and	and	CCONJ
ejpam-6189	54	20	studies	study	NOUN
ejpam-6189	54	21	the	the	DET
ejpam-6189	54	22	connections	connection	NOUN
ejpam-6189	54	23	between	between	ADP
ejpam-6189	54	24	strongest	strong	ADJ
ejpam-6189	54	25	fuzzy	fuzzy	ADJ
ejpam-6189	54	26	dot	dot	NOUN
ejpam-6189	54	27	bd	bd	NOUN
ejpam-6189	54	28	-	-	PUNCT
ejpam-6189	54	29	subalgebras	subalgebras	PROPN
ejpam-6189	54	30	and	and	CCONJ
ejpam-6189	54	31	fuzzy	fuzzy	ADJ
ejpam-6189	54	32	dot	dot	NOUN
ejpam-6189	54	33	bd	bd	NOUN
ejpam-6189	54	34	-	-	PUNCT
ejpam-6189	54	35	subalgebras	subalgebras	PROPN
ejpam-6189	54	36	in	in	ADP
ejpam-6189	54	37	bd	bd	PROPN
ejpam-6189	54	38	-	-	PUNCT
ejpam-6189	54	39	algebras	algebras	X
ejpam-6189	54	40	,	,	PUNCT
ejpam-6189	54	41	while	while	SCONJ
ejpam-6189	54	42	characterizing	characterize	VERB
ejpam-6189	54	43	the	the	DET
ejpam-6189	54	44	strongest	strong	ADJ
ejpam-6189	54	45	fuzzy	fuzzy	ADJ
ejpam-6189	54	46	dot	dot	NOUN
ejpam-6189	54	47	bd	bd	NOUN
ejpam-6189	54	48	-	-	PUNCT
ejpam-6189	54	49	subalgebras	subalgebras	PROPN
ejpam-6189	54	50	via	via	ADP
ejpam-6189	54	51	bd	bd	PROPN
ejpam-6189	54	52	-	-	PUNCT
ejpam-6189	54	53	subalgebras	subalgebras	PROPN
ejpam-6189	54	54	of	of	ADP
ejpam-6189	54	55	bd	bd	PROPN
ejpam-6189	54	56	-	-	NOUN
ejpam-6189	54	57	algebra	algebra	NOUN
ejpam-6189	54	58	.	.	PUNCT
ejpam-6189	55	1	2	2	X
ejpam-6189	55	2	.	.	NUM
ejpam-6189	55	3	preliminaries	preliminary	NOUN
ejpam-6189	55	4	in	in	ADP
ejpam-6189	55	5	this	this	DET
ejpam-6189	55	6	section	section	NOUN
ejpam-6189	55	7	,	,	PUNCT
ejpam-6189	55	8	we	we	PRON
ejpam-6189	55	9	will	will	AUX
ejpam-6189	55	10	review	review	VERB
ejpam-6189	55	11	the	the	DET
ejpam-6189	55	12	fundamental	fundamental	ADJ
ejpam-6189	55	13	concepts	concept	NOUN
ejpam-6189	55	14	necessary	necessary	ADJ
ejpam-6189	55	15	for	for	ADP
ejpam-6189	55	16	use	use	NOUN
ejpam-6189	55	17	in	in	ADP
ejpam-6189	55	18	the	the	DET
ejpam-6189	55	19	following	follow	VERB
ejpam-6189	55	20	sections	section	NOUN
ejpam-6189	55	21	.	.	PUNCT
ejpam-6189	56	1	let	let	VERB
ejpam-6189	56	2	x	x	PRON
ejpam-6189	56	3	be	be	AUX
ejpam-6189	56	4	a	a	DET
ejpam-6189	56	5	nonempty	nonempty	ADV
ejpam-6189	56	6	set	set	VERB
ejpam-6189	56	7	.	.	PUNCT
ejpam-6189	57	1	a	a	DET
ejpam-6189	57	2	fuzzy	fuzzy	ADJ
ejpam-6189	57	3	set	set	NOUN
ejpam-6189	57	4	[	[	X
ejpam-6189	57	5	11	11	NUM
ejpam-6189	57	6	]	]	X
ejpam-6189	57	7	ζ	ζ	NOUN
ejpam-6189	57	8	of	of	ADP
ejpam-6189	57	9	x	x	NOUN
ejpam-6189	57	10	is	be	AUX
ejpam-6189	57	11	a	a	DET
ejpam-6189	57	12	function	function	NOUN
ejpam-6189	57	13	from	from	ADP
ejpam-6189	57	14	x	x	NOUN
ejpam-6189	57	15	into	into	ADP
ejpam-6189	57	16	the	the	DET
ejpam-6189	57	17	interval	interval	NOUN
ejpam-6189	57	18	[	[	X
ejpam-6189	57	19	0	0	NUM
ejpam-6189	57	20	,	,	PUNCT
ejpam-6189	57	21	1	1	NUM
ejpam-6189	57	22	]	]	PUNCT
ejpam-6189	57	23	.	.	PUNCT
ejpam-6189	58	1	let	let	VERB
ejpam-6189	58	2	ζ	ζ	NOUN
ejpam-6189	58	3	and	and	CCONJ
ejpam-6189	58	4	ξ	ξ	PROPN
ejpam-6189	58	5	be	be	VERB
ejpam-6189	58	6	any	any	DET
ejpam-6189	58	7	two	two	NUM
ejpam-6189	58	8	fuzzy	fuzzy	ADJ
ejpam-6189	58	9	sets	set	NOUN
ejpam-6189	58	10	of	of	ADP
ejpam-6189	58	11	a	a	DET
ejpam-6189	58	12	nonempty	nonempty	ADV
ejpam-6189	58	13	set	set	VERB
ejpam-6189	58	14	x.	x.	NOUN
ejpam-6189	58	15	then	then	ADV
ejpam-6189	58	16	we	we	PRON
ejpam-6189	58	17	denote	denote	VERB
ejpam-6189	58	18	:	:	PUNCT
ejpam-6189	58	19	(	(	PUNCT
ejpam-6189	58	20	i	i	NOUN
ejpam-6189	58	21	)	)	PUNCT
ejpam-6189	58	22	(	(	PUNCT
ejpam-6189	58	23	ζ	ζ	NOUN
ejpam-6189	58	24	∩	∩	ADJ
ejpam-6189	58	25	ξ)(x	ξ)(x	PROPN
ejpam-6189	58	26	)	)	PUNCT
ejpam-6189	58	27	:	:	PUNCT
ejpam-6189	59	1	=	=	PUNCT
ejpam-6189	59	2	min{ζ(x	min{ζ(x	PROPN
ejpam-6189	59	3	)	)	PUNCT
ejpam-6189	59	4	,	,	PUNCT
ejpam-6189	59	5	ξ(x	ξ(x	NOUN
ejpam-6189	59	6	)	)	PUNCT
ejpam-6189	59	7	}	}	PUNCT
ejpam-6189	59	8	for	for	ADP
ejpam-6189	59	9	all	all	DET
ejpam-6189	59	10	x	x	SYM
ejpam-6189	59	11	∈	∈	PROPN
ejpam-6189	59	12	x	x	X
ejpam-6189	59	13	;	;	PUNCT
ejpam-6189	59	14	(	(	PUNCT
ejpam-6189	59	15	ii	ii	NOUN
ejpam-6189	59	16	)	)	PUNCT
ejpam-6189	59	17	(	(	PUNCT
ejpam-6189	59	18	ζ	ζ	PROPN
ejpam-6189	59	19	∪	∪	VERB
ejpam-6189	59	20	ξ)(x	ξ)(x	PROPN
ejpam-6189	59	21	)	)	PUNCT
ejpam-6189	59	22	:	:	PUNCT
ejpam-6189	60	1	=	=	PUNCT
ejpam-6189	60	2	max{ζ(x	max{ζ(x	PROPN
ejpam-6189	60	3	)	)	PUNCT
ejpam-6189	60	4	,	,	PUNCT
ejpam-6189	60	5	ξ(x	ξ(x	NOUN
ejpam-6189	60	6	)	)	PUNCT
ejpam-6189	60	7	}	}	PUNCT
ejpam-6189	60	8	for	for	ADP
ejpam-6189	60	9	all	all	PRON
ejpam-6189	60	10	x	x	SYM
ejpam-6189	60	11	∈	∈	NOUN
ejpam-6189	60	12	x.	x.	NOUN
ejpam-6189	60	13	let	let	VERB
ejpam-6189	60	14	{	{	PUNCT
ejpam-6189	60	15	ri	ri	VERB
ejpam-6189	61	1	|	|	ADV
ejpam-6189	61	2	i	i	PRON
ejpam-6189	61	3	∈	∈	PROPN
ejpam-6189	61	4	λ	λ	NOUN
ejpam-6189	61	5	}	}	PUNCT
ejpam-6189	61	6	be	be	VERB
ejpam-6189	61	7	a	a	DET
ejpam-6189	61	8	family	family	NOUN
ejpam-6189	61	9	of	of	ADP
ejpam-6189	61	10	real	real	ADJ
ejpam-6189	61	11	numbers	number	NOUN
ejpam-6189	61	12	.	.	PUNCT
ejpam-6189	62	1	then	then	ADV
ejpam-6189	62	2	we	we	PRON
ejpam-6189	62	3	denote	denote	VERB
ejpam-6189	62	4	⋂	⋂	PROPN
ejpam-6189	62	5	i∈λ	i∈λ	NOUN
ejpam-6189	62	6	ri	ri	PROPN
ejpam-6189	63	1	=	=	PUNCT
ejpam-6189	63	2	min	min	PROPN
ejpam-6189	63	3	i∈λ	i∈λ	PROPN
ejpam-6189	63	4	ri	ri	PROPN
ejpam-6189	63	5	if	if	SCONJ
ejpam-6189	63	6	λ	λ	PROPN
ejpam-6189	63	7	is	be	AUX
ejpam-6189	63	8	finite	finite	ADJ
ejpam-6189	63	9	,	,	PUNCT
ejpam-6189	63	10	inf	inf	ADJ
ejpam-6189	63	11	i∈λ	i∈λ	NOUN
ejpam-6189	63	12	ri	ri	PROPN
ejpam-6189	63	13	otherwise	otherwise	ADV
ejpam-6189	63	14	.	.	PUNCT
ejpam-6189	64	1	let	let	VERB
ejpam-6189	64	2	x	x	PRON
ejpam-6189	64	3	be	be	AUX
ejpam-6189	64	4	a	a	DET
ejpam-6189	64	5	nonempty	nonempty	ADV
ejpam-6189	64	6	set	set	VERB
ejpam-6189	64	7	and	and	CCONJ
ejpam-6189	64	8	ζ	ζ	NOUN
ejpam-6189	64	9	be	be	AUX
ejpam-6189	64	10	a	a	DET
ejpam-6189	64	11	fuzzy	fuzzy	ADJ
ejpam-6189	64	12	set	set	NOUN
ejpam-6189	64	13	of	of	ADP
ejpam-6189	64	14	x.	x.	NOUN
ejpam-6189	64	15	the	the	DET
ejpam-6189	64	16	set	set	NOUN
ejpam-6189	64	17	ζt	ζt	X
ejpam-6189	64	18	:	:	PUNCT
ejpam-6189	64	19	=	=	SYM
ejpam-6189	64	20	{	{	PUNCT
ejpam-6189	64	21	x	x	PUNCT
ejpam-6189	64	22	∈	∈	PROPN
ejpam-6189	64	23	x	x	X
ejpam-6189	64	24	|	|	ADV
ejpam-6189	64	25	ζ(x	ζ(x	NOUN
ejpam-6189	64	26	)	)	PUNCT
ejpam-6189	64	27	≥	≥	NOUN
ejpam-6189	64	28	t	t	PROPN
ejpam-6189	64	29	}	}	PUNCT
ejpam-6189	64	30	,	,	PUNCT
ejpam-6189	64	31	where	where	SCONJ
ejpam-6189	64	32	t	t	PROPN
ejpam-6189	64	33	∈	∈	PROPN
ejpam-6189	65	1	[	[	X
ejpam-6189	65	2	0	0	NUM
ejpam-6189	65	3	,	,	PUNCT
ejpam-6189	65	4	1	1	NUM
ejpam-6189	65	5	]	]	PUNCT
ejpam-6189	65	6	is	be	AUX
ejpam-6189	65	7	celled	celle	VERB
ejpam-6189	65	8	a	a	DET
ejpam-6189	65	9	level	level	NOUN
ejpam-6189	65	10	subset	subset	NOUN
ejpam-6189	65	11	of	of	ADP
ejpam-6189	65	12	ζ	ζ	NOUN
ejpam-6189	65	13	(	(	PUNCT
ejpam-6189	65	14	see	see	VERB
ejpam-6189	65	15	,	,	PUNCT
ejpam-6189	65	16	[	[	X
ejpam-6189	65	17	27	27	NUM
ejpam-6189	65	18	]	]	PUNCT
ejpam-6189	65	19	)	)	PUNCT
ejpam-6189	65	20	.	.	PUNCT
ejpam-6189	66	1	let	let	VERB
ejpam-6189	66	2	a	a	DET
ejpam-6189	66	3	be	be	AUX
ejpam-6189	66	4	a	a	DET
ejpam-6189	66	5	subset	subset	NOUN
ejpam-6189	66	6	of	of	ADP
ejpam-6189	66	7	a	a	DET
ejpam-6189	66	8	nonempty	nonempty	ADV
ejpam-6189	66	9	set	set	VERB
ejpam-6189	66	10	x.	x.	NOUN
ejpam-6189	66	11	the	the	DET
ejpam-6189	66	12	characteristic	characteristic	ADJ
ejpam-6189	66	13	function	function	NOUN
ejpam-6189	66	14	(	(	PUNCT
ejpam-6189	66	15	see	see	VERB
ejpam-6189	66	16	,	,	PUNCT
ejpam-6189	66	17	[	[	X
ejpam-6189	66	18	27	27	NUM
ejpam-6189	66	19	]	]	SYM
ejpam-6189	66	20	)	)	PUNCT
ejpam-6189	66	21	ca	ca	NOUN
ejpam-6189	66	22	of	of	ADP
ejpam-6189	66	23	a	a	PRON
ejpam-6189	66	24	is	be	AUX
ejpam-6189	66	25	a	a	DET
ejpam-6189	66	26	fuzzy	fuzzy	ADJ
ejpam-6189	66	27	set	set	NOUN
ejpam-6189	66	28	of	of	ADP
ejpam-6189	66	29	x	x	PRON
ejpam-6189	66	30	,	,	PUNCT
ejpam-6189	66	31	defined	define	VERB
ejpam-6189	66	32	by	by	ADP
ejpam-6189	66	33	for	for	ADP
ejpam-6189	66	34	every	every	DET
ejpam-6189	66	35	x	x	SYM
ejpam-6189	66	36	∈	∈	PROPN
ejpam-6189	66	37	x	x	NOUN
ejpam-6189	66	38	,	,	PUNCT
ejpam-6189	66	39	ca(x	ca(x	NOUN
ejpam-6189	66	40	)	)	PUNCT
ejpam-6189	66	41	=	=	PRON
ejpam-6189	66	42	{	{	PUNCT
ejpam-6189	66	43	1	1	NUM
ejpam-6189	66	44	if	if	SCONJ
ejpam-6189	66	45	x	x	PROPN
ejpam-6189	66	46	∈	∈	PROPN
ejpam-6189	66	47	a	a	PRON
ejpam-6189	66	48	,	,	PUNCT
ejpam-6189	66	49	0	0	NUM
ejpam-6189	66	50	otherwise	otherwise	ADV
ejpam-6189	66	51	.	.	PUNCT
ejpam-6189	67	1	lemma	lemma	PROPN
ejpam-6189	67	2	1	1	NUM
ejpam-6189	67	3	.	.	PUNCT
ejpam-6189	68	1	if	if	SCONJ
ejpam-6189	68	2	a	a	DET
ejpam-6189	68	3	,	,	PUNCT
ejpam-6189	68	4	b	b	NOUN
ejpam-6189	68	5	,	,	PUNCT
ejpam-6189	68	6	c	c	NOUN
ejpam-6189	68	7	,	,	PUNCT
ejpam-6189	68	8	d	d	X
ejpam-6189	68	9	are	be	AUX
ejpam-6189	68	10	elements	element	NOUN
ejpam-6189	68	11	in	in	ADP
ejpam-6189	68	12	real	real	ADJ
ejpam-6189	68	13	numbers	number	NOUN
ejpam-6189	68	14	,	,	PUNCT
ejpam-6189	68	15	then	then	ADV
ejpam-6189	68	16	min{ab	min{ab	X
ejpam-6189	68	17	,	,	PUNCT
ejpam-6189	68	18	cd	cd	PROPN
ejpam-6189	68	19	}	}	PUNCT
ejpam-6189	68	20	≥	≥	NOUN
ejpam-6189	68	21	min{a	min{a	NOUN
ejpam-6189	68	22	,	,	PUNCT
ejpam-6189	68	23	c}min{b	c}min{b	NOUN
ejpam-6189	68	24	,	,	PUNCT
ejpam-6189	68	25	d	d	NOUN
ejpam-6189	68	26	}	}	PUNCT
ejpam-6189	68	27	.	.	PUNCT
ejpam-6189	69	1	proof	proof	NOUN
ejpam-6189	69	2	.	.	PUNCT
ejpam-6189	70	1	without	without	ADP
ejpam-6189	70	2	loss	loss	NOUN
ejpam-6189	70	3	of	of	ADP
ejpam-6189	70	4	generality	generality	NOUN
ejpam-6189	70	5	,	,	PUNCT
ejpam-6189	70	6	assume	assume	VERB
ejpam-6189	70	7	that	that	SCONJ
ejpam-6189	70	8	a	a	DET
ejpam-6189	70	9	≤	≤	ADJ
ejpam-6189	70	10	c.	c.	NOUN
ejpam-6189	70	11	then	then	ADV
ejpam-6189	70	12	min{a	min{a	PROPN
ejpam-6189	70	13	,	,	PUNCT
ejpam-6189	70	14	c	c	NOUN
ejpam-6189	70	15	}	}	PUNCT
ejpam-6189	70	16	=	=	PUNCT
ejpam-6189	70	17	a.	a.	NOUN
ejpam-6189	70	18	if	if	SCONJ
ejpam-6189	70	19	b	b	PROPN
ejpam-6189	70	20	≤	≤	X
ejpam-6189	70	21	d	d	PROPN
ejpam-6189	70	22	,	,	PUNCT
ejpam-6189	70	23	then	then	ADV
ejpam-6189	70	24	min{b	min{b	NOUN
ejpam-6189	70	25	,	,	PUNCT
ejpam-6189	70	26	d	d	NOUN
ejpam-6189	70	27	}	}	PUNCT
ejpam-6189	70	28	=	=	SYM
ejpam-6189	70	29	b.	b.	PROPN
ejpam-6189	70	30	thus	thus	ADV
ejpam-6189	70	31	,	,	PUNCT
ejpam-6189	70	32	ab	ab	PROPN
ejpam-6189	70	33	≤	≤	PROPN
ejpam-6189	70	34	cb	cb	PROPN
ejpam-6189	70	35	≤	≤	PROPN
ejpam-6189	70	36	cd	cd	PROPN
ejpam-6189	70	37	.	.	PUNCT
ejpam-6189	71	1	it	it	PRON
ejpam-6189	71	2	turns	turn	VERB
ejpam-6189	71	3	out	out	ADP
ejpam-6189	71	4	that	that	SCONJ
ejpam-6189	71	5	min{ab	min{ab	X
ejpam-6189	71	6	,	,	PUNCT
ejpam-6189	71	7	cd	cd	NOUN
ejpam-6189	71	8	}	}	PUNCT
ejpam-6189	71	9	=	=	SYM
ejpam-6189	71	10	ab	ab	PROPN
ejpam-6189	71	11	=	=	SYM
ejpam-6189	71	12	min{a	min{a	PROPN
ejpam-6189	71	13	,	,	PUNCT
ejpam-6189	71	14	c}min{b	c}min{b	NOUN
ejpam-6189	71	15	,	,	PUNCT
ejpam-6189	71	16	d	d	NOUN
ejpam-6189	71	17	}	}	PUNCT
ejpam-6189	71	18	.	.	PUNCT
ejpam-6189	72	1	on	on	ADP
ejpam-6189	72	2	the	the	DET
ejpam-6189	72	3	other	other	ADJ
ejpam-6189	72	4	case	case	NOUN
ejpam-6189	72	5	,	,	PUNCT
ejpam-6189	72	6	if	if	SCONJ
ejpam-6189	72	7	d	d	PROPN
ejpam-6189	72	8	<	<	X
ejpam-6189	72	9	b	b	PROPN
ejpam-6189	72	10	,	,	PUNCT
ejpam-6189	72	11	then	then	ADV
ejpam-6189	72	12	min{b	min{b	NOUN
ejpam-6189	72	13	,	,	PUNCT
ejpam-6189	72	14	d	d	NOUN
ejpam-6189	72	15	}	}	PUNCT
ejpam-6189	72	16	=	=	SYM
ejpam-6189	72	17	d.	d.	NOUN
ejpam-6189	72	18	since	since	SCONJ
ejpam-6189	72	19	a	a	DET
ejpam-6189	72	20	≤	≤	NUM
ejpam-6189	72	21	c	c	NOUN
ejpam-6189	72	22	and	and	CCONJ
ejpam-6189	72	23	d	d	X
ejpam-6189	72	24	<	<	X
ejpam-6189	72	25	b	b	X
ejpam-6189	72	26	,	,	PUNCT
ejpam-6189	72	27	we	we	PRON
ejpam-6189	72	28	have	have	VERB
ejpam-6189	72	29	ad	ad	NOUN
ejpam-6189	72	30	≤	≤	NUM
ejpam-6189	72	31	cd	cd	NOUN
ejpam-6189	72	32	and	and	CCONJ
ejpam-6189	72	33	ad	ad	NOUN
ejpam-6189	72	34	<	<	X
ejpam-6189	72	35	ab	ab	PROPN
ejpam-6189	72	36	.	.	PUNCT
ejpam-6189	73	1	this	this	PRON
ejpam-6189	73	2	implies	imply	VERB
ejpam-6189	73	3	that	that	SCONJ
ejpam-6189	73	4	min{ab	min{ab	X
ejpam-6189	73	5	,	,	PUNCT
ejpam-6189	73	6	cd	cd	PROPN
ejpam-6189	73	7	}	}	PUNCT
ejpam-6189	73	8	≥	≥	NOUN
ejpam-6189	73	9	ad	ad	NOUN
ejpam-6189	73	10	=	=	SYM
ejpam-6189	73	11	min{a	min{a	NOUN
ejpam-6189	73	12	,	,	PUNCT
ejpam-6189	73	13	c}min{b	c}min{b	NOUN
ejpam-6189	73	14	,	,	PUNCT
ejpam-6189	73	15	d	d	NOUN
ejpam-6189	73	16	}	}	PUNCT
ejpam-6189	73	17	.	.	PUNCT
ejpam-6189	74	1	therefore	therefore	ADV
ejpam-6189	74	2	,	,	PUNCT
ejpam-6189	74	3	min{ab	min{ab	X
ejpam-6189	74	4	,	,	PUNCT
ejpam-6189	74	5	cd	cd	PROPN
ejpam-6189	74	6	}	}	PUNCT
ejpam-6189	74	7	≥	≥	NOUN
ejpam-6189	74	8	min{a	min{a	NOUN
ejpam-6189	74	9	,	,	PUNCT
ejpam-6189	74	10	c}min{b	c}min{b	NOUN
ejpam-6189	74	11	,	,	PUNCT
ejpam-6189	74	12	d	d	NOUN
ejpam-6189	74	13	}	}	PUNCT
ejpam-6189	74	14	.	.	PUNCT
ejpam-6189	75	1	definition	definition	NOUN
ejpam-6189	75	2	1	1	NUM
ejpam-6189	75	3	.	.	PUNCT
ejpam-6189	76	1	[	[	X
ejpam-6189	76	2	26	26	NUM
ejpam-6189	76	3	]	]	PUNCT
ejpam-6189	76	4	let	let	VERB
ejpam-6189	76	5	x	x	PRON
ejpam-6189	76	6	be	be	AUX
ejpam-6189	76	7	a	a	DET
ejpam-6189	76	8	nonempty	nonempty	ADV
ejpam-6189	76	9	set	set	VERB
ejpam-6189	76	10	and	and	CCONJ
ejpam-6189	76	11	∗	∗	NOUN
ejpam-6189	76	12	be	be	VERB
ejpam-6189	76	13	a	a	DET
ejpam-6189	76	14	binary	binary	ADJ
ejpam-6189	76	15	operation	operation	NOUN
ejpam-6189	76	16	on	on	ADP
ejpam-6189	76	17	x.	x.	PROPN
ejpam-6189	76	18	an	an	DET
ejpam-6189	76	19	algebraic	algebraic	ADJ
ejpam-6189	76	20	structure	structure	NOUN
ejpam-6189	76	21	(	(	PUNCT
ejpam-6189	76	22	x	x	X
ejpam-6189	76	23	,	,	PUNCT
ejpam-6189	76	24	∗	∗	NOUN
ejpam-6189	76	25	,	,	PUNCT
ejpam-6189	76	26	0	0	NUM
ejpam-6189	76	27	)	)	PUNCT
ejpam-6189	76	28	is	be	AUX
ejpam-6189	76	29	called	call	VERB
ejpam-6189	76	30	a	a	DET
ejpam-6189	76	31	bd	bd	NOUN
ejpam-6189	76	32	-	-	NOUN
ejpam-6189	76	33	algebra	algebra	NOUN
ejpam-6189	76	34	if	if	SCONJ
ejpam-6189	76	35	it	it	PRON
ejpam-6189	76	36	satisfies	satisfy	VERB
ejpam-6189	76	37	the	the	DET
ejpam-6189	76	38	following	follow	VERB
ejpam-6189	76	39	conditions	condition	NOUN
ejpam-6189	76	40	:	:	PUNCT
ejpam-6189	76	41	for	for	ADP
ejpam-6189	76	42	each	each	DET
ejpam-6189	76	43	x	x	NOUN
ejpam-6189	76	44	,	,	PUNCT
ejpam-6189	76	45	y	y	PROPN
ejpam-6189	76	46	∈	∈	PROPN
ejpam-6189	76	47	x	x	X
ejpam-6189	76	48	,	,	PUNCT
ejpam-6189	76	49	(	(	PUNCT
ejpam-6189	76	50	i	i	NOUN
ejpam-6189	76	51	)	)	PUNCT
ejpam-6189	76	52	x	x	SYM
ejpam-6189	76	53	∗	∗	NOUN
ejpam-6189	76	54	0	0	NUM
ejpam-6189	77	1	=	=	SYM
ejpam-6189	77	2	x	x	X
ejpam-6189	77	3	;	;	PUNCT
ejpam-6189	77	4	(	(	PUNCT
ejpam-6189	77	5	ii	ii	NOUN
ejpam-6189	77	6	)	)	PUNCT
ejpam-6189	77	7	if	if	SCONJ
ejpam-6189	77	8	x	x	PROPN
ejpam-6189	77	9	∗	∗	VERB
ejpam-6189	77	10	y	y	NOUN
ejpam-6189	77	11	=	=	SYM
ejpam-6189	77	12	0	0	PROPN
ejpam-6189	78	1	and	and	CCONJ
ejpam-6189	78	2	y	y	PROPN
ejpam-6189	78	3	∗	∗	NOUN
ejpam-6189	78	4	x	x	PUNCT
ejpam-6189	79	1	=	=	SYM
ejpam-6189	79	2	0	0	NUM
ejpam-6189	79	3	,	,	PUNCT
ejpam-6189	79	4	then	then	ADV
ejpam-6189	79	5	x	x	X
ejpam-6189	79	6	=	=	PUNCT
ejpam-6189	79	7	y.	y.	PROPN
ejpam-6189	79	8	throughout	throughout	ADP
ejpam-6189	79	9	this	this	DET
ejpam-6189	79	10	study	study	NOUN
ejpam-6189	79	11	,	,	PUNCT
ejpam-6189	79	12	we	we	PRON
ejpam-6189	79	13	denote	denote	VERB
ejpam-6189	79	14	a	a	DET
ejpam-6189	79	15	bd	bd	NOUN
ejpam-6189	79	16	-	-	NOUN
ejpam-6189	79	17	algebra	algebra	PROPN
ejpam-6189	79	18	(	(	PUNCT
ejpam-6189	79	19	x	x	X
ejpam-6189	79	20	,	,	PUNCT
ejpam-6189	79	21	∗	∗	NOUN
ejpam-6189	79	22	,	,	PUNCT
ejpam-6189	79	23	0	0	NUM
ejpam-6189	79	24	)	)	PUNCT
ejpam-6189	79	25	by	by	ADP
ejpam-6189	79	26	x	x	SYM
ejpam-6189	79	27	the	the	DET
ejpam-6189	79	28	bold	bold	ADJ
ejpam-6189	79	29	letter	letter	NOUN
ejpam-6189	79	30	of	of	ADP
ejpam-6189	79	31	its	its	PRON
ejpam-6189	79	32	universe	universe	NOUN
ejpam-6189	79	33	set	set	NOUN
ejpam-6189	79	34	.	.	PUNCT
ejpam-6189	80	1	w.	w.	PROPN
ejpam-6189	80	2	nakkhasen	nakkhasen	PROPN
ejpam-6189	80	3	et	et	PROPN
ejpam-6189	80	4	al	al	PROPN
ejpam-6189	80	5	.	.	PUNCT
ejpam-6189	80	6	/	/	SYM
ejpam-6189	80	7	eur	eur	PROPN
ejpam-6189	80	8	.	.	PUNCT
ejpam-6189	81	1	j.	j.	PROPN
ejpam-6189	81	2	pure	pure	PROPN
ejpam-6189	81	3	appl	appl	PROPN
ejpam-6189	81	4	.	.	PROPN
ejpam-6189	81	5	math	math	PROPN
ejpam-6189	81	6	,	,	PUNCT
ejpam-6189	81	7	18	18	NUM
ejpam-6189	81	8	(	(	PUNCT
ejpam-6189	81	9	3	3	NUM
ejpam-6189	81	10	)	)	PUNCT
ejpam-6189	81	11	(	(	PUNCT
ejpam-6189	81	12	2025	2025	NUM
ejpam-6189	81	13	)	)	PUNCT
ejpam-6189	81	14	,	,	PUNCT
ejpam-6189	81	15	6189	6189	NUM
ejpam-6189	81	16	4	4	NUM
ejpam-6189	81	17	of	of	ADP
ejpam-6189	81	18	13	13	NUM
ejpam-6189	81	19	definition	definition	NOUN
ejpam-6189	81	20	2	2	NUM
ejpam-6189	81	21	.	.	PUNCT
ejpam-6189	82	1	[	[	X
ejpam-6189	82	2	26	26	NUM
ejpam-6189	82	3	]	]	PUNCT
ejpam-6189	82	4	let	let	VERB
ejpam-6189	82	5	x	x	PRON
ejpam-6189	82	6	be	be	AUX
ejpam-6189	82	7	a	a	DET
ejpam-6189	82	8	bd	bd	NOUN
ejpam-6189	82	9	-	-	NOUN
ejpam-6189	82	10	algebra	algebra	NOUN
ejpam-6189	82	11	.	.	PUNCT
ejpam-6189	83	1	a	a	DET
ejpam-6189	83	2	nonempty	nonempty	NOUN
ejpam-6189	83	3	subset	subset	VERB
ejpam-6189	83	4	a	a	PRON
ejpam-6189	83	5	of	of	ADP
ejpam-6189	83	6	x	x	SYM
ejpam-6189	83	7	is	be	AUX
ejpam-6189	83	8	said	say	VERB
ejpam-6189	83	9	to	to	PART
ejpam-6189	83	10	be	be	AUX
ejpam-6189	83	11	a	a	DET
ejpam-6189	83	12	bd	bd	NOUN
ejpam-6189	83	13	-	-	PUNCT
ejpam-6189	83	14	subalgebra	subalgebra	NOUN
ejpam-6189	83	15	of	of	ADP
ejpam-6189	83	16	x	x	PRON
ejpam-6189	83	17	if	if	SCONJ
ejpam-6189	83	18	0	0	NUM
ejpam-6189	83	19	∈	∈	PROPN
ejpam-6189	83	20	a	a	PRON
ejpam-6189	83	21	and	and	CCONJ
ejpam-6189	83	22	x	x	SYM
ejpam-6189	83	23	∗	∗	NOUN
ejpam-6189	83	24	y	y	PROPN
ejpam-6189	83	25	∈	∈	PROPN
ejpam-6189	83	26	a	a	PRON
ejpam-6189	83	27	for	for	ADP
ejpam-6189	83	28	all	all	DET
ejpam-6189	83	29	x	x	NOUN
ejpam-6189	83	30	,	,	PUNCT
ejpam-6189	83	31	y	y	PROPN
ejpam-6189	83	32	∈	∈	PROPN
ejpam-6189	83	33	a.	a.	NOUN
ejpam-6189	83	34	definition	definition	NOUN
ejpam-6189	83	35	3	3	NUM
ejpam-6189	83	36	.	.	PUNCT
ejpam-6189	84	1	[	[	X
ejpam-6189	84	2	27	27	NUM
ejpam-6189	84	3	]	]	PUNCT
ejpam-6189	84	4	let	let	VERB
ejpam-6189	84	5	x	x	PRON
ejpam-6189	84	6	be	be	AUX
ejpam-6189	84	7	a	a	DET
ejpam-6189	84	8	bd	bd	NOUN
ejpam-6189	84	9	-	-	NOUN
ejpam-6189	84	10	algebra	algebra	NOUN
ejpam-6189	84	11	.	.	PUNCT
ejpam-6189	85	1	a	a	DET
ejpam-6189	85	2	fuzzy	fuzzy	ADJ
ejpam-6189	85	3	set	set	VERB
ejpam-6189	85	4	ζ	ζ	NOUN
ejpam-6189	85	5	of	of	ADP
ejpam-6189	85	6	x	x	PROPN
ejpam-6189	85	7	is	be	AUX
ejpam-6189	85	8	called	call	VERB
ejpam-6189	85	9	a	a	DET
ejpam-6189	85	10	fuzzy	fuzzy	ADJ
ejpam-6189	85	11	bdsubalgebra	bdsubalgebra	NOUN
ejpam-6189	85	12	of	of	ADP
ejpam-6189	85	13	x	x	PRON
ejpam-6189	85	14	if	if	SCONJ
ejpam-6189	85	15	it	it	PRON
ejpam-6189	85	16	satisfies	satisfy	VERB
ejpam-6189	85	17	the	the	DET
ejpam-6189	85	18	following	follow	VERB
ejpam-6189	85	19	inequality	inequality	NOUN
ejpam-6189	85	20	:	:	PUNCT
ejpam-6189	85	21	for	for	ADP
ejpam-6189	85	22	any	any	DET
ejpam-6189	85	23	x	x	NOUN
ejpam-6189	85	24	,	,	PUNCT
ejpam-6189	85	25	y	y	PROPN
ejpam-6189	85	26	∈	∈	PROPN
ejpam-6189	85	27	x	x	X
ejpam-6189	85	28	,	,	PUNCT
ejpam-6189	85	29	(	(	PUNCT
ejpam-6189	85	30	i	i	NOUN
ejpam-6189	85	31	)	)	PUNCT
ejpam-6189	85	32	ζ(0	ζ(0	PROPN
ejpam-6189	85	33	)	)	PUNCT
ejpam-6189	85	34	≥	≥	NOUN
ejpam-6189	85	35	ζ(x	ζ(x	NOUN
ejpam-6189	85	36	)	)	PUNCT
ejpam-6189	85	37	;	;	PUNCT
ejpam-6189	85	38	(	(	PUNCT
ejpam-6189	85	39	ii	ii	X
ejpam-6189	85	40	)	)	PUNCT
ejpam-6189	85	41	ζ(x	ζ(x	PROPN
ejpam-6189	85	42	∗	∗	NOUN
ejpam-6189	85	43	y	y	NOUN
ejpam-6189	85	44	)	)	PUNCT
ejpam-6189	85	45	≥	≥	NOUN
ejpam-6189	85	46	min{ζ(x	min{ζ(x	PROPN
ejpam-6189	85	47	)	)	PUNCT
ejpam-6189	85	48	,	,	PUNCT
ejpam-6189	85	49	ζ(y	ζ(y	PROPN
ejpam-6189	85	50	)	)	PUNCT
ejpam-6189	85	51	}	}	PUNCT
ejpam-6189	85	52	.	.	PUNCT
ejpam-6189	86	1	3	3	X
ejpam-6189	86	2	.	.	X
ejpam-6189	86	3	fuzzy	fuzzy	ADJ
ejpam-6189	86	4	dot	dot	NOUN
ejpam-6189	86	5	bd	bd	PROPN
ejpam-6189	86	6	-	-	PUNCT
ejpam-6189	86	7	subalgebras	subalgebras	PROPN
ejpam-6189	86	8	of	of	ADP
ejpam-6189	86	9	bd	bd	PROPN
ejpam-6189	86	10	-	-	PUNCT
ejpam-6189	86	11	algebras	algebras	PROPN
ejpam-6189	86	12	in	in	ADP
ejpam-6189	86	13	this	this	DET
ejpam-6189	86	14	section	section	NOUN
ejpam-6189	86	15	,	,	PUNCT
ejpam-6189	86	16	we	we	PRON
ejpam-6189	86	17	apply	apply	VERB
ejpam-6189	86	18	the	the	DET
ejpam-6189	86	19	usual	usual	ADJ
ejpam-6189	86	20	multiplication	multiplication	NOUN
ejpam-6189	86	21	in	in	ADP
ejpam-6189	86	22	real	real	ADJ
ejpam-6189	86	23	numbers	number	NOUN
ejpam-6189	86	24	to	to	ADP
ejpam-6189	86	25	the	the	DET
ejpam-6189	86	26	fuzzy	fuzzy	ADJ
ejpam-6189	86	27	sets	set	NOUN
ejpam-6189	86	28	by	by	ADP
ejpam-6189	86	29	introducing	introduce	VERB
ejpam-6189	86	30	the	the	DET
ejpam-6189	86	31	notion	notion	NOUN
ejpam-6189	86	32	of	of	ADP
ejpam-6189	86	33	fuzzy	fuzzy	ADJ
ejpam-6189	86	34	dot	dot	NOUN
ejpam-6189	86	35	bd	bd	PROPN
ejpam-6189	86	36	-	-	PUNCT
ejpam-6189	86	37	subalgebras	subalgebras	PROPN
ejpam-6189	86	38	,	,	PUNCT
ejpam-6189	86	39	which	which	PRON
ejpam-6189	86	40	is	be	AUX
ejpam-6189	86	41	useful	useful	ADJ
ejpam-6189	86	42	as	as	ADP
ejpam-6189	86	43	a	a	DET
ejpam-6189	86	44	generalization	generalization	NOUN
ejpam-6189	86	45	of	of	ADP
ejpam-6189	86	46	fuzzy	fuzzy	ADJ
ejpam-6189	86	47	bd	bd	NOUN
ejpam-6189	86	48	-	-	NOUN
ejpam-6189	86	49	subalgebras	subalgebras	PROPN
ejpam-6189	86	50	in	in	ADP
ejpam-6189	86	51	the	the	DET
ejpam-6189	86	52	bd	bd	PROPN
ejpam-6189	86	53	-	-	PUNCT
ejpam-6189	86	54	algebras	algebras	PROPN
ejpam-6189	86	55	.	.	PUNCT
ejpam-6189	87	1	then	then	ADV
ejpam-6189	87	2	we	we	PRON
ejpam-6189	87	3	examine	examine	VERB
ejpam-6189	87	4	certain	certain	ADJ
ejpam-6189	87	5	characteristics	characteristic	NOUN
ejpam-6189	87	6	of	of	ADP
ejpam-6189	87	7	fuzzy	fuzzy	ADJ
ejpam-6189	87	8	dot	dot	NOUN
ejpam-6189	87	9	bd	bd	NOUN
ejpam-6189	87	10	-	-	PUNCT
ejpam-6189	87	11	subalgebras	subalgebras	PROPN
ejpam-6189	87	12	within	within	ADP
ejpam-6189	87	13	the	the	DET
ejpam-6189	87	14	bd	bd	PROPN
ejpam-6189	87	15	-	-	PUNCT
ejpam-6189	87	16	algebras	algebras	PROPN
ejpam-6189	87	17	.	.	PUNCT
ejpam-6189	88	1	subsequently	subsequently	ADV
ejpam-6189	88	2	,	,	PUNCT
ejpam-6189	88	3	we	we	PRON
ejpam-6189	88	4	investigate	investigate	VERB
ejpam-6189	88	5	the	the	DET
ejpam-6189	88	6	connections	connection	NOUN
ejpam-6189	88	7	of	of	ADP
ejpam-6189	88	8	fuzzy	fuzzy	ADJ
ejpam-6189	88	9	dot	dot	NOUN
ejpam-6189	88	10	bd	bd	NOUN
ejpam-6189	88	11	-	-	PUNCT
ejpam-6189	88	12	subalgebras	subalgebras	PROPN
ejpam-6189	88	13	under	under	ADP
ejpam-6189	88	14	a	a	DET
ejpam-6189	88	15	homomorphism	homomorphism	NOUN
ejpam-6189	88	16	of	of	ADP
ejpam-6189	88	17	bd	bd	PROPN
ejpam-6189	88	18	-	-	PUNCT
ejpam-6189	88	19	algebras	algebras	PROPN
ejpam-6189	88	20	.	.	PUNCT
ejpam-6189	89	1	definition	definition	NOUN
ejpam-6189	89	2	4	4	NUM
ejpam-6189	89	3	.	.	PUNCT
ejpam-6189	90	1	let	let	VERB
ejpam-6189	90	2	x	x	PRON
ejpam-6189	90	3	be	be	AUX
ejpam-6189	90	4	a	a	DET
ejpam-6189	90	5	bd	bd	NOUN
ejpam-6189	90	6	-	-	NOUN
ejpam-6189	90	7	algebra	algebra	NOUN
ejpam-6189	90	8	,	,	PUNCT
ejpam-6189	90	9	and	and	CCONJ
ejpam-6189	90	10	let	let	VERB
ejpam-6189	90	11	ζ	ζ	NOUN
ejpam-6189	90	12	be	be	AUX
ejpam-6189	90	13	a	a	DET
ejpam-6189	90	14	fuzzy	fuzzy	ADJ
ejpam-6189	90	15	sets	set	NOUN
ejpam-6189	90	16	of	of	ADP
ejpam-6189	90	17	x.	x.	NOUN
ejpam-6189	90	18	then	then	ADV
ejpam-6189	90	19	ζ	ζ	NOUN
ejpam-6189	90	20	is	be	AUX
ejpam-6189	90	21	called	call	VERB
ejpam-6189	90	22	a	a	DET
ejpam-6189	90	23	fuzzy	fuzzy	ADJ
ejpam-6189	90	24	dot	dot	NOUN
ejpam-6189	90	25	bd	bd	NOUN
ejpam-6189	90	26	-	-	PUNCT
ejpam-6189	90	27	subalgebra	subalgebra	NOUN
ejpam-6189	90	28	of	of	ADP
ejpam-6189	90	29	x	x	PRON
ejpam-6189	90	30	if	if	SCONJ
ejpam-6189	90	31	for	for	ADP
ejpam-6189	90	32	every	every	DET
ejpam-6189	90	33	x	x	NOUN
ejpam-6189	90	34	,	,	PUNCT
ejpam-6189	90	35	y	y	PROPN
ejpam-6189	90	36	∈	∈	PROPN
ejpam-6189	91	1	x	x	X
ejpam-6189	91	2	:	:	PUNCT
ejpam-6189	91	3	(	(	PUNCT
ejpam-6189	91	4	i	i	NOUN
ejpam-6189	91	5	)	)	PUNCT
ejpam-6189	91	6	ζ(0	ζ(0	PROPN
ejpam-6189	91	7	)	)	PUNCT
ejpam-6189	91	8	≥	≥	NOUN
ejpam-6189	91	9	ζ(x	ζ(x	NOUN
ejpam-6189	91	10	)	)	PUNCT
ejpam-6189	91	11	;	;	PUNCT
ejpam-6189	91	12	(	(	PUNCT
ejpam-6189	91	13	ii	ii	X
ejpam-6189	91	14	)	)	PUNCT
ejpam-6189	91	15	ζ(x	ζ(x	PROPN
ejpam-6189	91	16	∗	∗	NOUN
ejpam-6189	91	17	y	y	NOUN
ejpam-6189	91	18	)	)	PUNCT
ejpam-6189	91	19	≥	≥	NOUN
ejpam-6189	91	20	ζ(x	ζ(x	NOUN
ejpam-6189	91	21	)	)	PUNCT
ejpam-6189	91	22	·	·	PUNCT
ejpam-6189	91	23	ζ(y	ζ(y	PROPN
ejpam-6189	91	24	)	)	PUNCT
ejpam-6189	91	25	,	,	PUNCT
ejpam-6189	91	26	where	where	SCONJ
ejpam-6189	91	27	“	"	PUNCT
ejpam-6189	91	28	·	·	PUNCT
ejpam-6189	91	29	”	"	PUNCT
ejpam-6189	91	30	denotes	denote	VERB
ejpam-6189	91	31	ordinary	ordinary	ADJ
ejpam-6189	91	32	multiplication	multiplication	NOUN
ejpam-6189	91	33	in	in	ADP
ejpam-6189	91	34	real	real	ADJ
ejpam-6189	91	35	numbers	number	NOUN
ejpam-6189	91	36	.	.	PUNCT
ejpam-6189	92	1	example	example	NOUN
ejpam-6189	93	1	1	1	NUM
ejpam-6189	93	2	.	.	PUNCT
ejpam-6189	93	3	let	let	VERB
ejpam-6189	93	4	x	x	PUNCT
ejpam-6189	93	5	=	=	PUNCT
ejpam-6189	93	6	{	{	PUNCT
ejpam-6189	93	7	0	0	NUM
ejpam-6189	93	8	,	,	PUNCT
ejpam-6189	93	9	a	a	DET
ejpam-6189	93	10	,	,	PUNCT
ejpam-6189	93	11	b	b	NOUN
ejpam-6189	93	12	,	,	PUNCT
ejpam-6189	93	13	c	c	NOUN
ejpam-6189	93	14	}	}	PUNCT
ejpam-6189	93	15	and	and	CCONJ
ejpam-6189	93	16	∗	∗	NOUN
ejpam-6189	93	17	be	be	VERB
ejpam-6189	93	18	a	a	DET
ejpam-6189	93	19	binary	binary	ADJ
ejpam-6189	93	20	operation	operation	NOUN
ejpam-6189	93	21	on	on	ADP
ejpam-6189	93	22	x	x	PUNCT
ejpam-6189	93	23	as	as	SCONJ
ejpam-6189	93	24	defined	define	VERB
ejpam-6189	93	25	in	in	ADP
ejpam-6189	93	26	the	the	DET
ejpam-6189	93	27	following	follow	VERB
ejpam-6189	93	28	table	table	NOUN
ejpam-6189	93	29	:	:	PUNCT
ejpam-6189	93	30	∗	∗	NOUN
ejpam-6189	93	31	0	0	PUNCT
ejpam-6189	94	1	a	a	DET
ejpam-6189	94	2	b	b	NOUN
ejpam-6189	94	3	c	c	NOUN
ejpam-6189	94	4	0	0	NUM
ejpam-6189	94	5	0	0	NUM
ejpam-6189	94	6	0	0	NUM
ejpam-6189	94	7	a	a	DET
ejpam-6189	94	8	0	0	NUM
ejpam-6189	94	9	a	a	DET
ejpam-6189	94	10	a	a	DET
ejpam-6189	94	11	b	b	NOUN
ejpam-6189	94	12	a	a	DET
ejpam-6189	94	13	a	a	DET
ejpam-6189	94	14	b	b	PROPN
ejpam-6189	94	15	b	b	PROPN
ejpam-6189	94	16	b	b	PROPN
ejpam-6189	94	17	b	b	PROPN
ejpam-6189	94	18	c	c	NOUN
ejpam-6189	94	19	c	c	NOUN
ejpam-6189	94	20	c	c	NOUN
ejpam-6189	94	21	a	a	DET
ejpam-6189	94	22	a	a	DET
ejpam-6189	94	23	c	c	NOUN
ejpam-6189	94	24	table	table	NOUN
ejpam-6189	94	25	1	1	NUM
ejpam-6189	94	26	:	:	PUNCT
ejpam-6189	94	27	the	the	DET
ejpam-6189	94	28	binary	binary	PROPN
ejpam-6189	94	29	operation	operation	NOUN
ejpam-6189	94	30	∗	∗	NOUN
ejpam-6189	94	31	on	on	ADP
ejpam-6189	94	32	x.	x.	NOUN
ejpam-6189	94	33	then	then	ADV
ejpam-6189	94	34	x	x	X
ejpam-6189	94	35	:	:	PUNCT
ejpam-6189	94	36	=	=	SYM
ejpam-6189	94	37	(	(	PUNCT
ejpam-6189	94	38	x	x	X
ejpam-6189	94	39	,	,	PUNCT
ejpam-6189	94	40	∗	∗	NOUN
ejpam-6189	94	41	,	,	PUNCT
ejpam-6189	94	42	0	0	NUM
ejpam-6189	94	43	)	)	PUNCT
ejpam-6189	94	44	is	be	AUX
ejpam-6189	94	45	a	a	DET
ejpam-6189	94	46	bd	bd	NOUN
ejpam-6189	94	47	-	-	NOUN
ejpam-6189	94	48	algebra	algebra	NOUN
ejpam-6189	94	49	.	.	PUNCT
ejpam-6189	95	1	define	define	VERB
ejpam-6189	95	2	a	a	DET
ejpam-6189	95	3	fuzzy	fuzzy	ADJ
ejpam-6189	95	4	set	set	VERB
ejpam-6189	95	5	ζ	ζ	NOUN
ejpam-6189	95	6	of	of	ADP
ejpam-6189	95	7	x	x	PUNCT
ejpam-6189	95	8	by	by	ADP
ejpam-6189	95	9	ζ(0	ζ(0	NOUN
ejpam-6189	95	10	)	)	PUNCT
ejpam-6189	95	11	=	=	PUNCT
ejpam-6189	95	12	0.80	0.80	NUM
ejpam-6189	95	13	,	,	PUNCT
ejpam-6189	95	14	ζ(a	ζ(a	PRON
ejpam-6189	95	15	)	)	PUNCT
ejpam-6189	95	16	=	=	SYM
ejpam-6189	95	17	0.60	0.60	NUM
ejpam-6189	95	18	,	,	PUNCT
ejpam-6189	95	19	ζ(b	ζ(b	PROPN
ejpam-6189	95	20	)	)	PUNCT
ejpam-6189	95	21	=	=	NOUN
ejpam-6189	95	22	0.70	0.70	NUM
ejpam-6189	95	23	,	,	PUNCT
ejpam-6189	95	24	and	and	CCONJ
ejpam-6189	95	25	ζ(c	ζ(c	ADJ
ejpam-6189	95	26	)	)	PUNCT
ejpam-6189	95	27	=	=	SYM
ejpam-6189	95	28	0.70	0.70	NUM
ejpam-6189	95	29	.	.	PUNCT
ejpam-6189	96	1	by	by	ADP
ejpam-6189	96	2	calculate	calculate	NOUN
ejpam-6189	96	3	routine	routine	NOUN
ejpam-6189	96	4	,	,	PUNCT
ejpam-6189	96	5	we	we	PRON
ejpam-6189	96	6	have	have	VERB
ejpam-6189	96	7	ζ	ζ	NOUN
ejpam-6189	96	8	is	be	AUX
ejpam-6189	96	9	a	a	DET
ejpam-6189	96	10	fuzzy	fuzzy	ADJ
ejpam-6189	96	11	dot	dot	NOUN
ejpam-6189	96	12	bd	bd	NOUN
ejpam-6189	96	13	-	-	PUNCT
ejpam-6189	96	14	subalgebra	subalgebra	NOUN
ejpam-6189	96	15	of	of	ADP
ejpam-6189	96	16	x.	x.	NOUN
ejpam-6189	96	17	proposition	proposition	NOUN
ejpam-6189	96	18	1	1	NUM
ejpam-6189	96	19	.	.	PUNCT
ejpam-6189	97	1	every	every	DET
ejpam-6189	97	2	fuzzy	fuzzy	ADJ
ejpam-6189	97	3	bd	bd	NOUN
ejpam-6189	97	4	-	-	NOUN
ejpam-6189	97	5	subalgebra	subalgebra	NOUN
ejpam-6189	97	6	of	of	ADP
ejpam-6189	97	7	a	a	DET
ejpam-6189	97	8	bd	bd	NOUN
ejpam-6189	97	9	-	-	NOUN
ejpam-6189	97	10	algebra	algebra	NOUN
ejpam-6189	97	11	x	x	PUNCT
ejpam-6189	97	12	is	be	AUX
ejpam-6189	97	13	also	also	ADV
ejpam-6189	97	14	a	a	DET
ejpam-6189	97	15	fuzzy	fuzzy	ADJ
ejpam-6189	97	16	dot	dot	NOUN
ejpam-6189	97	17	bdsubalgebra	bdsubalgebra	NOUN
ejpam-6189	97	18	.	.	PUNCT
ejpam-6189	98	1	proof	proof	NOUN
ejpam-6189	98	2	.	.	PUNCT
ejpam-6189	99	1	let	let	VERB
ejpam-6189	99	2	ζ	ζ	NOUN
ejpam-6189	99	3	is	be	AUX
ejpam-6189	99	4	a	a	DET
ejpam-6189	99	5	fuzzy	fuzzy	ADJ
ejpam-6189	99	6	bd	bd	NOUN
ejpam-6189	99	7	-	-	NOUN
ejpam-6189	99	8	subalgebra	subalgebra	NOUN
ejpam-6189	99	9	of	of	ADP
ejpam-6189	99	10	a	a	DET
ejpam-6189	99	11	bd	bd	PROPN
ejpam-6189	99	12	-	-	NOUN
ejpam-6189	99	13	algebra	algebra	PROPN
ejpam-6189	99	14	x.	x.	NOUN
ejpam-6189	99	15	then	then	ADV
ejpam-6189	99	16	ζ(0	ζ(0	PROPN
ejpam-6189	99	17	)	)	PUNCT
ejpam-6189	99	18	≥	≥	NOUN
ejpam-6189	99	19	ζ(a	ζ(a	NOUN
ejpam-6189	99	20	)	)	PUNCT
ejpam-6189	99	21	for	for	ADP
ejpam-6189	99	22	all	all	DET
ejpam-6189	99	23	a	a	DET
ejpam-6189	99	24	∈	∈	NOUN
ejpam-6189	99	25	x.	x.	NOUN
ejpam-6189	99	26	now	now	ADV
ejpam-6189	99	27	,	,	PUNCT
ejpam-6189	99	28	let	let	VERB
ejpam-6189	99	29	x	x	PRON
ejpam-6189	99	30	,	,	PUNCT
ejpam-6189	99	31	y	y	PROPN
ejpam-6189	99	32	∈	∈	PROPN
ejpam-6189	99	33	x.	x.	NOUN
ejpam-6189	100	1	if	if	SCONJ
ejpam-6189	100	2	ζ(x	ζ(x	NOUN
ejpam-6189	100	3	)	)	PUNCT
ejpam-6189	100	4	≤	≤	NOUN
ejpam-6189	100	5	ζ(y	ζ(y	PROPN
ejpam-6189	100	6	)	)	PUNCT
ejpam-6189	100	7	,	,	PUNCT
ejpam-6189	100	8	then	then	ADV
ejpam-6189	100	9	min{ζ(x	min{ζ(x	PROPN
ejpam-6189	100	10	)	)	PUNCT
ejpam-6189	100	11	,	,	PUNCT
ejpam-6189	100	12	ζ(y	ζ(y	PROPN
ejpam-6189	100	13	)	)	PUNCT
ejpam-6189	100	14	}	}	PUNCT
ejpam-6189	100	15	=	=	SYM
ejpam-6189	100	16	ζ(x	ζ(x	NOUN
ejpam-6189	100	17	)	)	PUNCT
ejpam-6189	100	18	.	.	PUNCT
ejpam-6189	101	1	so	so	ADV
ejpam-6189	101	2	,	,	PUNCT
ejpam-6189	101	3	ζ(x	ζ(x	PROPN
ejpam-6189	101	4	∗	∗	NOUN
ejpam-6189	101	5	y	y	NOUN
ejpam-6189	101	6	)	)	PUNCT
ejpam-6189	101	7	≥	≥	NOUN
ejpam-6189	101	8	min{ζ(x	min{ζ(x	PROPN
ejpam-6189	101	9	)	)	PUNCT
ejpam-6189	101	10	,	,	PUNCT
ejpam-6189	101	11	ζ(y	ζ(y	PROPN
ejpam-6189	101	12	)	)	PUNCT
ejpam-6189	101	13	}	}	PUNCT
ejpam-6189	102	1	=	=	SYM
ejpam-6189	102	2	ζ(x	ζ(x	NOUN
ejpam-6189	102	3	)	)	PUNCT
ejpam-6189	102	4	≥	≥	NOUN
ejpam-6189	102	5	ζ(x	ζ(x	NOUN
ejpam-6189	102	6	)	)	PUNCT
ejpam-6189	102	7	·	·	PUNCT
ejpam-6189	102	8	ζ(y	ζ(y	X
ejpam-6189	102	9	)	)	PUNCT
ejpam-6189	102	10	.	.	PUNCT
ejpam-6189	103	1	on	on	ADP
ejpam-6189	103	2	the	the	DET
ejpam-6189	103	3	other	other	ADJ
ejpam-6189	103	4	hand	hand	NOUN
ejpam-6189	103	5	,	,	PUNCT
ejpam-6189	103	6	if	if	SCONJ
ejpam-6189	103	7	ζ(x	ζ(x	NOUN
ejpam-6189	103	8	)	)	PUNCT
ejpam-6189	103	9	>	>	X
ejpam-6189	103	10	ζ(y	ζ(y	PROPN
ejpam-6189	103	11	)	)	PUNCT
ejpam-6189	103	12	,	,	PUNCT
ejpam-6189	103	13	then	then	ADV
ejpam-6189	103	14	w.	w.	PROPN
ejpam-6189	103	15	nakkhasen	nakkhasen	PROPN
ejpam-6189	103	16	et	et	PROPN
ejpam-6189	103	17	al	al	PROPN
ejpam-6189	103	18	.	.	PUNCT
ejpam-6189	103	19	/	/	SYM
ejpam-6189	103	20	eur	eur	PROPN
ejpam-6189	103	21	.	.	PUNCT
ejpam-6189	104	1	j.	j.	PROPN
ejpam-6189	104	2	pure	pure	PROPN
ejpam-6189	104	3	appl	appl	PROPN
ejpam-6189	104	4	.	.	PROPN
ejpam-6189	104	5	math	math	PROPN
ejpam-6189	104	6	,	,	PUNCT
ejpam-6189	104	7	18	18	NUM
ejpam-6189	104	8	(	(	PUNCT
ejpam-6189	104	9	3	3	NUM
ejpam-6189	104	10	)	)	PUNCT
ejpam-6189	104	11	(	(	PUNCT
ejpam-6189	104	12	2025	2025	NUM
ejpam-6189	104	13	)	)	PUNCT
ejpam-6189	104	14	,	,	PUNCT
ejpam-6189	104	15	6189	6189	NUM
ejpam-6189	104	16	5	5	NUM
ejpam-6189	104	17	of	of	ADP
ejpam-6189	104	18	13	13	NUM
ejpam-6189	104	19	min{ζ(x	min{ζ(x	NUM
ejpam-6189	104	20	)	)	PUNCT
ejpam-6189	104	21	,	,	PUNCT
ejpam-6189	104	22	ζ(y	ζ(y	PROPN
ejpam-6189	104	23	)	)	PUNCT
ejpam-6189	104	24	}	}	PUNCT
ejpam-6189	104	25	=	=	SYM
ejpam-6189	104	26	ζ(y	ζ(y	PROPN
ejpam-6189	104	27	)	)	PUNCT
ejpam-6189	104	28	.	.	PUNCT
ejpam-6189	105	1	thus	thus	ADV
ejpam-6189	105	2	,	,	PUNCT
ejpam-6189	105	3	ζ(x	ζ(x	PROPN
ejpam-6189	105	4	∗	∗	NOUN
ejpam-6189	105	5	y	y	NOUN
ejpam-6189	105	6	)	)	PUNCT
ejpam-6189	105	7	≥	≥	NOUN
ejpam-6189	105	8	min{ζ(x	min{ζ(x	PROPN
ejpam-6189	105	9	)	)	PUNCT
ejpam-6189	105	10	,	,	PUNCT
ejpam-6189	105	11	ζ(y	ζ(y	PROPN
ejpam-6189	105	12	)	)	PUNCT
ejpam-6189	105	13	}	}	PUNCT
ejpam-6189	105	14	=	=	SYM
ejpam-6189	105	15	ζ(y	ζ(y	PROPN
ejpam-6189	105	16	)	)	PUNCT
ejpam-6189	105	17	≥	≥	NOUN
ejpam-6189	105	18	ζ(x	ζ(x	NOUN
ejpam-6189	105	19	)	)	PUNCT
ejpam-6189	105	20	·	·	PUNCT
ejpam-6189	105	21	ζ(y	ζ(y	X
ejpam-6189	105	22	)	)	PUNCT
ejpam-6189	105	23	.	.	PUNCT
ejpam-6189	106	1	hence	hence	ADV
ejpam-6189	106	2	,	,	PUNCT
ejpam-6189	106	3	ζ	ζ	PROPN
ejpam-6189	106	4	is	be	AUX
ejpam-6189	106	5	a	a	DET
ejpam-6189	106	6	fuzzy	fuzzy	ADJ
ejpam-6189	106	7	dot	dot	NOUN
ejpam-6189	106	8	bd	bd	NOUN
ejpam-6189	106	9	-	-	PUNCT
ejpam-6189	106	10	subalgebra	subalgebra	NOUN
ejpam-6189	106	11	of	of	ADP
ejpam-6189	106	12	x.	x.	NOUN
ejpam-6189	106	13	generally	generally	ADV
ejpam-6189	106	14	,	,	PUNCT
ejpam-6189	106	15	the	the	DET
ejpam-6189	106	16	fuzzy	fuzzy	ADJ
ejpam-6189	106	17	dot	dot	NOUN
ejpam-6189	106	18	bd	bd	NOUN
ejpam-6189	106	19	-	-	PUNCT
ejpam-6189	106	20	subalgebras	subalgebras	PROPN
ejpam-6189	106	21	need	need	AUX
ejpam-6189	106	22	not	not	PART
ejpam-6189	106	23	be	be	AUX
ejpam-6189	106	24	a	a	DET
ejpam-6189	106	25	fuzzy	fuzzy	ADJ
ejpam-6189	106	26	bd	bd	NOUN
ejpam-6189	106	27	-	-	PUNCT
ejpam-6189	106	28	subalgebras	subalgebras	PROPN
ejpam-6189	106	29	in	in	ADP
ejpam-6189	106	30	bdalgebras	bdalgebras	PROPN
ejpam-6189	106	31	,	,	PUNCT
ejpam-6189	106	32	as	as	SCONJ
ejpam-6189	106	33	shown	show	VERB
ejpam-6189	106	34	in	in	ADP
ejpam-6189	106	35	the	the	DET
ejpam-6189	106	36	following	follow	VERB
ejpam-6189	106	37	example	example	NOUN
ejpam-6189	106	38	.	.	PUNCT
ejpam-6189	107	1	example	example	NOUN
ejpam-6189	108	1	2	2	NUM
ejpam-6189	108	2	.	.	X
ejpam-6189	108	3	in	in	ADP
ejpam-6189	108	4	example	example	NOUN
ejpam-6189	108	5	1	1	NUM
ejpam-6189	108	6	,	,	PUNCT
ejpam-6189	108	7	we	we	PRON
ejpam-6189	108	8	have	have	VERB
ejpam-6189	108	9	the	the	DET
ejpam-6189	108	10	fuzzy	fuzzy	ADJ
ejpam-6189	108	11	set	set	NOUN
ejpam-6189	108	12	ζ	ζ	NOUN
ejpam-6189	108	13	is	be	AUX
ejpam-6189	108	14	a	a	DET
ejpam-6189	108	15	fuzzy	fuzzy	ADJ
ejpam-6189	108	16	dot	dot	NOUN
ejpam-6189	108	17	bd	bd	NOUN
ejpam-6189	108	18	-	-	PUNCT
ejpam-6189	108	19	subalgebra	subalgebra	NOUN
ejpam-6189	108	20	of	of	ADP
ejpam-6189	108	21	a	a	DET
ejpam-6189	108	22	bd	bd	PROPN
ejpam-6189	108	23	-	-	NOUN
ejpam-6189	108	24	algebra	algebra	PROPN
ejpam-6189	108	25	x.	x.	NOUN
ejpam-6189	108	26	however	however	ADV
ejpam-6189	108	27	,	,	PUNCT
ejpam-6189	108	28	ζ	ζ	NOUN
ejpam-6189	108	29	is	be	AUX
ejpam-6189	108	30	not	not	PART
ejpam-6189	108	31	a	a	DET
ejpam-6189	108	32	fuzzy	fuzzy	ADJ
ejpam-6189	108	33	bd	bd	NOUN
ejpam-6189	108	34	-	-	NOUN
ejpam-6189	108	35	subalgebra	subalgebra	NOUN
ejpam-6189	108	36	of	of	ADP
ejpam-6189	108	37	x	x	PRON
ejpam-6189	108	38	,	,	PUNCT
ejpam-6189	108	39	because	because	SCONJ
ejpam-6189	108	40	ζ(0	ζ(0	NOUN
ejpam-6189	108	41	∗	∗	NOUN
ejpam-6189	108	42	b	b	NOUN
ejpam-6189	108	43	)	)	PUNCT
ejpam-6189	108	44	=	=	SYM
ejpam-6189	108	45	0.60	0.60	NUM
ejpam-6189	108	46	≱	≱	PROPN
ejpam-6189	108	47	0.70	0.70	NUM
ejpam-6189	108	48	=	=	SYM
ejpam-6189	108	49	min{ζ(0	min{ζ(0	NOUN
ejpam-6189	108	50	)	)	PUNCT
ejpam-6189	108	51	,	,	PUNCT
ejpam-6189	108	52	ζ(b	ζ(b	PROPN
ejpam-6189	108	53	)	)	PUNCT
ejpam-6189	108	54	}	}	PUNCT
ejpam-6189	108	55	.	.	PUNCT
ejpam-6189	109	1	proposition	proposition	NOUN
ejpam-6189	109	2	2	2	NUM
ejpam-6189	109	3	.	.	PUNCT
ejpam-6189	109	4	let	let	VERB
ejpam-6189	109	5	ζ	ζ	NOUN
ejpam-6189	109	6	be	be	AUX
ejpam-6189	109	7	a	a	DET
ejpam-6189	109	8	fuzzy	fuzzy	ADJ
ejpam-6189	109	9	dot	dot	NOUN
ejpam-6189	109	10	bd	bd	NOUN
ejpam-6189	109	11	-	-	PUNCT
ejpam-6189	109	12	subalgebra	subalgebra	NOUN
ejpam-6189	109	13	of	of	ADP
ejpam-6189	109	14	a	a	DET
ejpam-6189	109	15	bd	bd	PROPN
ejpam-6189	109	16	-	-	NOUN
ejpam-6189	109	17	algebra	algebra	NOUN
ejpam-6189	109	18	x.	x.	NOUN
ejpam-6189	110	1	if	if	SCONJ
ejpam-6189	110	2	there	there	PRON
ejpam-6189	110	3	exists	exist	VERB
ejpam-6189	110	4	a	a	DET
ejpam-6189	110	5	nonempty	nonempty	NOUN
ejpam-6189	110	6	subset	subset	VERB
ejpam-6189	110	7	a	a	PRON
ejpam-6189	110	8	of	of	ADP
ejpam-6189	110	9	x	x	SYM
ejpam-6189	110	10	such	such	ADJ
ejpam-6189	110	11	that	that	SCONJ
ejpam-6189	110	12	supa∈a	supa∈a	PROPN
ejpam-6189	110	13	ζ(a	ζ(a	PROPN
ejpam-6189	110	14	)	)	PUNCT
ejpam-6189	110	15	=	=	SYM
ejpam-6189	110	16	1	1	NUM
ejpam-6189	110	17	,	,	PUNCT
ejpam-6189	110	18	then	then	ADV
ejpam-6189	110	19	ζ(0	ζ(0	NOUN
ejpam-6189	110	20	)	)	PUNCT
ejpam-6189	110	21	=	=	SYM
ejpam-6189	110	22	1	1	X
ejpam-6189	110	23	.	.	PUNCT
ejpam-6189	110	24	proof	proof	NOUN
ejpam-6189	110	25	.	.	PUNCT
ejpam-6189	111	1	assume	assume	VERB
ejpam-6189	111	2	that	that	SCONJ
ejpam-6189	111	3	x	x	PRON
ejpam-6189	111	4	contains	contain	VERB
ejpam-6189	111	5	a	a	DET
ejpam-6189	111	6	nonempty	nonempty	NOUN
ejpam-6189	111	7	subset	subset	VERB
ejpam-6189	111	8	a	a	PRON
ejpam-6189	111	9	of	of	ADP
ejpam-6189	111	10	x	x	SYM
ejpam-6189	111	11	such	such	ADJ
ejpam-6189	111	12	that	that	SCONJ
ejpam-6189	111	13	supa∈a	supa∈a	PROPN
ejpam-6189	111	14	ζ(a	ζ(a	PROPN
ejpam-6189	111	15	)	)	PUNCT
ejpam-6189	111	16	=	=	SYM
ejpam-6189	112	1	1	1	X
ejpam-6189	112	2	.	.	PUNCT
ejpam-6189	112	3	since	since	SCONJ
ejpam-6189	112	4	ζ	ζ	NOUN
ejpam-6189	112	5	is	be	AUX
ejpam-6189	112	6	a	a	DET
ejpam-6189	112	7	fuzzy	fuzzy	ADJ
ejpam-6189	112	8	dot	dot	NOUN
ejpam-6189	112	9	bd	bd	NOUN
ejpam-6189	112	10	-	-	PUNCT
ejpam-6189	112	11	subalgebra	subalgebra	NOUN
ejpam-6189	112	12	of	of	ADP
ejpam-6189	112	13	x	x	PRON
ejpam-6189	112	14	,	,	PUNCT
ejpam-6189	112	15	we	we	PRON
ejpam-6189	112	16	have	have	VERB
ejpam-6189	112	17	ζ(0	ζ(0	NOUN
ejpam-6189	112	18	)	)	PUNCT
ejpam-6189	112	19	≥	≥	NOUN
ejpam-6189	112	20	ζ(x	ζ(x	NOUN
ejpam-6189	112	21	)	)	PUNCT
ejpam-6189	112	22	for	for	ADP
ejpam-6189	112	23	all	all	PRON
ejpam-6189	112	24	x	x	SYM
ejpam-6189	112	25	∈	∈	ADJ
ejpam-6189	112	26	x.	x.	NOUN
ejpam-6189	112	27	then	then	ADV
ejpam-6189	112	28	1	1	NUM
ejpam-6189	112	29	≥	≥	NOUN
ejpam-6189	112	30	ζ(0	ζ(0	PROPN
ejpam-6189	112	31	)	)	PUNCT
ejpam-6189	112	32	≥	≥	NOUN
ejpam-6189	113	1	supa∈a	supa∈a	PROPN
ejpam-6189	113	2	ζ(a	ζ(a	PROPN
ejpam-6189	113	3	)	)	PUNCT
ejpam-6189	114	1	=	=	SYM
ejpam-6189	115	1	1	1	X
ejpam-6189	115	2	.	.	PUNCT
ejpam-6189	115	3	this	this	PRON
ejpam-6189	115	4	implies	imply	VERB
ejpam-6189	115	5	that	that	SCONJ
ejpam-6189	115	6	ζ(0	ζ(0	NOUN
ejpam-6189	115	7	)	)	PUNCT
ejpam-6189	115	8	=	=	SYM
ejpam-6189	116	1	1	1	X
ejpam-6189	116	2	.	.	PUNCT
ejpam-6189	116	3	let	let	VERB
ejpam-6189	116	4	ζ	ζ	NOUN
ejpam-6189	116	5	be	be	AUX
ejpam-6189	116	6	any	any	DET
ejpam-6189	116	7	fuzzy	fuzzy	ADJ
ejpam-6189	116	8	set	set	NOUN
ejpam-6189	116	9	of	of	ADP
ejpam-6189	116	10	a	a	DET
ejpam-6189	116	11	nonempty	nonempty	ADV
ejpam-6189	116	12	set	set	VERB
ejpam-6189	116	13	x	x	NOUN
ejpam-6189	116	14	,	,	PUNCT
ejpam-6189	116	15	and	and	CCONJ
ejpam-6189	116	16	m	m	AUX
ejpam-6189	116	17	be	be	AUX
ejpam-6189	116	18	a	a	DET
ejpam-6189	116	19	positive	positive	ADJ
ejpam-6189	116	20	integer	integer	NOUN
ejpam-6189	116	21	.	.	PUNCT
ejpam-6189	117	1	define	define	VERB
ejpam-6189	117	2	a	a	DET
ejpam-6189	117	3	fuzzy	fuzzy	ADJ
ejpam-6189	117	4	set	set	NOUN
ejpam-6189	117	5	ζm	ζm	ADP
ejpam-6189	117	6	of	of	ADP
ejpam-6189	117	7	x	x	PUNCT
ejpam-6189	117	8	by	by	ADP
ejpam-6189	117	9	ζm(x	ζm(x	NOUN
ejpam-6189	117	10	)	)	PUNCT
ejpam-6189	118	1	=	=	SYM
ejpam-6189	119	1	(	(	PUNCT
ejpam-6189	119	2	ζ(x))m	ζ(x))m	PROPN
ejpam-6189	119	3	for	for	ADP
ejpam-6189	119	4	all	all	DET
ejpam-6189	119	5	x	x	SYM
ejpam-6189	119	6	∈	∈	NOUN
ejpam-6189	119	7	x.	x.	NOUN
ejpam-6189	119	8	proposition	proposition	NOUN
ejpam-6189	119	9	3	3	NUM
ejpam-6189	119	10	.	.	PUNCT
ejpam-6189	120	1	let	let	VERB
ejpam-6189	120	2	x	x	PRON
ejpam-6189	120	3	be	be	AUX
ejpam-6189	120	4	a	a	DET
ejpam-6189	120	5	bd	bd	NOUN
ejpam-6189	120	6	-	-	NOUN
ejpam-6189	120	7	algebra	algebra	NOUN
ejpam-6189	120	8	.	.	PUNCT
ejpam-6189	121	1	if	if	SCONJ
ejpam-6189	121	2	ζ	ζ	NOUN
ejpam-6189	121	3	is	be	AUX
ejpam-6189	121	4	a	a	DET
ejpam-6189	121	5	fuzzy	fuzzy	ADJ
ejpam-6189	121	6	dot	dot	NOUN
ejpam-6189	121	7	bd	bd	NOUN
ejpam-6189	121	8	-	-	PUNCT
ejpam-6189	121	9	subalgebra	subalgebra	NOUN
ejpam-6189	121	10	of	of	ADP
ejpam-6189	121	11	x	x	PRON
ejpam-6189	121	12	,	,	PUNCT
ejpam-6189	121	13	then	then	ADV
ejpam-6189	121	14	ζm	ζm	VERB
ejpam-6189	121	15	is	be	AUX
ejpam-6189	121	16	also	also	ADV
ejpam-6189	121	17	a	a	DET
ejpam-6189	121	18	fuzzy	fuzzy	ADJ
ejpam-6189	121	19	dot	dot	NOUN
ejpam-6189	121	20	bd	bd	NOUN
ejpam-6189	121	21	-	-	PUNCT
ejpam-6189	121	22	subalgebra	subalgebra	NOUN
ejpam-6189	121	23	of	of	ADP
ejpam-6189	121	24	x	x	SYM
ejpam-6189	121	25	whenever	whenever	SCONJ
ejpam-6189	121	26	m	m	VERB
ejpam-6189	121	27	is	be	AUX
ejpam-6189	121	28	a	a	DET
ejpam-6189	121	29	positive	positive	ADJ
ejpam-6189	121	30	integer	integer	NOUN
ejpam-6189	121	31	.	.	PUNCT
ejpam-6189	122	1	proof	proof	NOUN
ejpam-6189	122	2	.	.	PUNCT
ejpam-6189	123	1	let	let	VERB
ejpam-6189	123	2	ζ	ζ	NOUN
ejpam-6189	123	3	be	be	AUX
ejpam-6189	123	4	a	a	DET
ejpam-6189	123	5	fuzzy	fuzzy	ADJ
ejpam-6189	123	6	dot	dot	NOUN
ejpam-6189	123	7	bd	bd	NOUN
ejpam-6189	123	8	-	-	PUNCT
ejpam-6189	123	9	subalgebra	subalgebra	NOUN
ejpam-6189	123	10	of	of	ADP
ejpam-6189	123	11	x	x	X
ejpam-6189	123	12	and	and	CCONJ
ejpam-6189	123	13	m	m	AUX
ejpam-6189	123	14	be	be	VERB
ejpam-6189	123	15	a	a	DET
ejpam-6189	123	16	positive	positive	ADJ
ejpam-6189	123	17	integer	integer	NOUN
ejpam-6189	123	18	.	.	PUNCT
ejpam-6189	124	1	for	for	ADP
ejpam-6189	124	2	every	every	DET
ejpam-6189	124	3	x	x	NOUN
ejpam-6189	124	4	,	,	PUNCT
ejpam-6189	124	5	y	y	PROPN
ejpam-6189	124	6	∈	∈	PROPN
ejpam-6189	124	7	x	x	X
ejpam-6189	124	8	,	,	PUNCT
ejpam-6189	124	9	we	we	PRON
ejpam-6189	124	10	have	have	VERB
ejpam-6189	124	11	ζm(0	ζm(0	NOUN
ejpam-6189	124	12	)	)	PUNCT
ejpam-6189	124	13	=	=	SYM
ejpam-6189	124	14	(	(	PUNCT
ejpam-6189	124	15	ζ(0))m	ζ(0))m	X
ejpam-6189	124	16	≥	≥	NUM
ejpam-6189	124	17	(	(	PUNCT
ejpam-6189	124	18	ζ(x))m	ζ(x))m	PROPN
ejpam-6189	124	19	=	=	PRON
ejpam-6189	124	20	ζm(x	ζm(x	X
ejpam-6189	124	21	)	)	PUNCT
ejpam-6189	124	22	and	and	CCONJ
ejpam-6189	124	23	ζm(x	ζm(x	X
ejpam-6189	124	24	∗	∗	X
ejpam-6189	124	25	y	y	NOUN
ejpam-6189	124	26	)	)	PUNCT
ejpam-6189	124	27	=	=	NOUN
ejpam-6189	124	28	(	(	PUNCT
ejpam-6189	124	29	ζ(x	ζ(x	PROPN
ejpam-6189	124	30	∗	∗	NOUN
ejpam-6189	124	31	y))m	y))m	PROPN
ejpam-6189	124	32	≥	≥	X
ejpam-6189	124	33	(	(	PUNCT
ejpam-6189	124	34	ζ(x	ζ(x	NOUN
ejpam-6189	124	35	)	)	PUNCT
ejpam-6189	124	36	·	·	PUNCT
ejpam-6189	124	37	ζ(y))m	ζ(y))m	X
ejpam-6189	124	38	=	=	PRON
ejpam-6189	124	39	(	(	PUNCT
ejpam-6189	124	40	ζ(x))m	ζ(x))m	PROPN
ejpam-6189	124	41	·	·	PUNCT
ejpam-6189	124	42	(	(	PUNCT
ejpam-6189	124	43	ζ(y))m	ζ(y))m	X
ejpam-6189	124	44	=	=	PUNCT
ejpam-6189	124	45	ζm(x	ζm(x	X
ejpam-6189	124	46	)	)	PUNCT
ejpam-6189	124	47	·	·	PUNCT
ejpam-6189	124	48	ζm(y	ζm(y	NUM
ejpam-6189	124	49	)	)	PUNCT
ejpam-6189	124	50	.	.	PUNCT
ejpam-6189	125	1	consequently	consequently	ADV
ejpam-6189	125	2	,	,	PUNCT
ejpam-6189	125	3	ζm	ζm	VERB
ejpam-6189	125	4	is	be	AUX
ejpam-6189	125	5	a	a	DET
ejpam-6189	125	6	fuzzy	fuzzy	ADJ
ejpam-6189	125	7	dot	dot	NOUN
ejpam-6189	125	8	bd	bd	NOUN
ejpam-6189	125	9	-	-	PUNCT
ejpam-6189	125	10	subalgebra	subalgebra	NOUN
ejpam-6189	125	11	of	of	ADP
ejpam-6189	125	12	x.	x.	NOUN
ejpam-6189	125	13	theorem	theorem	NOUN
ejpam-6189	125	14	1	1	X
ejpam-6189	125	15	.	.	PUNCT
ejpam-6189	126	1	let	let	VERB
ejpam-6189	126	2	x	x	PRON
ejpam-6189	126	3	be	be	AUX
ejpam-6189	126	4	a	a	DET
ejpam-6189	126	5	bd	bd	NOUN
ejpam-6189	126	6	-	-	NOUN
ejpam-6189	126	7	algebra	algebra	NOUN
ejpam-6189	126	8	.	.	PUNCT
ejpam-6189	127	1	if	if	SCONJ
ejpam-6189	127	2	ζ	ζ	PROPN
ejpam-6189	127	3	and	and	CCONJ
ejpam-6189	127	4	ξ	ξ	PROPN
ejpam-6189	127	5	are	be	AUX
ejpam-6189	127	6	fuzzy	fuzzy	ADJ
ejpam-6189	127	7	dot	dot	NOUN
ejpam-6189	127	8	bd	bd	NOUN
ejpam-6189	127	9	-	-	PUNCT
ejpam-6189	127	10	subalgebras	subalgebras	PROPN
ejpam-6189	127	11	of	of	ADP
ejpam-6189	127	12	x	x	PRON
ejpam-6189	127	13	,	,	PUNCT
ejpam-6189	127	14	then	then	ADV
ejpam-6189	127	15	ζ	ζ	NOUN
ejpam-6189	127	16	∩	∩	NOUN
ejpam-6189	127	17	ξ	ξ	PROPN
ejpam-6189	127	18	is	be	AUX
ejpam-6189	127	19	a	a	DET
ejpam-6189	127	20	fuzzy	fuzzy	ADJ
ejpam-6189	127	21	dot	dot	NOUN
ejpam-6189	127	22	bd	bd	NOUN
ejpam-6189	127	23	-	-	PUNCT
ejpam-6189	127	24	subalgebra	subalgebra	NOUN
ejpam-6189	127	25	of	of	ADP
ejpam-6189	127	26	x.	x.	NOUN
ejpam-6189	127	27	proof	proof	PROPN
ejpam-6189	127	28	.	.	PUNCT
ejpam-6189	128	1	assume	assume	VERB
ejpam-6189	128	2	that	that	SCONJ
ejpam-6189	128	3	ζ	ζ	NOUN
ejpam-6189	128	4	and	and	CCONJ
ejpam-6189	128	5	ξ	ξ	PROPN
ejpam-6189	128	6	are	be	AUX
ejpam-6189	128	7	fuzzy	fuzzy	ADJ
ejpam-6189	128	8	dot	dot	NOUN
ejpam-6189	128	9	bd	bd	NOUN
ejpam-6189	128	10	-	-	PUNCT
ejpam-6189	128	11	subalgebras	subalgebras	PROPN
ejpam-6189	128	12	of	of	ADP
ejpam-6189	128	13	x.	x.	PROPN
ejpam-6189	128	14	let	let	VERB
ejpam-6189	128	15	x	x	PRON
ejpam-6189	128	16	,	,	PUNCT
ejpam-6189	128	17	y	y	PROPN
ejpam-6189	128	18	∈	∈	PROPN
ejpam-6189	128	19	x.	x.	NOUN
ejpam-6189	128	20	by	by	ADP
ejpam-6189	128	21	lemma	lemma	PROPN
ejpam-6189	128	22	1	1	NUM
ejpam-6189	128	23	and	and	CCONJ
ejpam-6189	128	24	assumption	assumption	NOUN
ejpam-6189	128	25	,	,	PUNCT
ejpam-6189	128	26	we	we	PRON
ejpam-6189	128	27	have	have	VERB
ejpam-6189	128	28	(	(	PUNCT
ejpam-6189	128	29	ζ	ζ	NOUN
ejpam-6189	128	30	∩	∩	NOUN
ejpam-6189	128	31	ξ)(0	ξ)(0	NUM
ejpam-6189	128	32	)	)	PUNCT
ejpam-6189	128	33	=	=	SYM
ejpam-6189	128	34	min{ζ(0	min{ζ(0	NOUN
ejpam-6189	128	35	)	)	PUNCT
ejpam-6189	128	36	,	,	PUNCT
ejpam-6189	128	37	ξ(0	ξ(0	NOUN
ejpam-6189	128	38	)	)	PUNCT
ejpam-6189	128	39	}	}	PUNCT
ejpam-6189	128	40	≥	≥	NOUN
ejpam-6189	128	41	min{ζ(x	min{ζ(x	NOUN
ejpam-6189	128	42	)	)	PUNCT
ejpam-6189	128	43	,	,	PUNCT
ejpam-6189	128	44	ξ(x	ξ(x	NOUN
ejpam-6189	128	45	)	)	PUNCT
ejpam-6189	128	46	}	}	PUNCT
ejpam-6189	128	47	=	=	SYM
ejpam-6189	128	48	(	(	PUNCT
ejpam-6189	128	49	ζ	ζ	NOUN
ejpam-6189	128	50	∩	∩	ADJ
ejpam-6189	128	51	ξ)(x	ξ)(x	PROPN
ejpam-6189	128	52	)	)	PUNCT
ejpam-6189	128	53	and	and	CCONJ
ejpam-6189	128	54	(	(	PUNCT
ejpam-6189	128	55	ζ	ζ	NOUN
ejpam-6189	128	56	∩	∩	NOUN
ejpam-6189	128	57	ξ)(x	ξ)(x	PROPN
ejpam-6189	128	58	∗	∗	NOUN
ejpam-6189	128	59	y	y	PROPN
ejpam-6189	128	60	)	)	PUNCT
ejpam-6189	129	1	=	=	PUNCT
ejpam-6189	129	2	min{ζ(x	min{ζ(x	PROPN
ejpam-6189	129	3	∗	∗	X
ejpam-6189	129	4	y	y	NOUN
ejpam-6189	129	5	)	)	PUNCT
ejpam-6189	129	6	,	,	PUNCT
ejpam-6189	129	7	ξ(x	ξ(x	PROPN
ejpam-6189	129	8	∗	∗	NOUN
ejpam-6189	129	9	y	y	NOUN
ejpam-6189	129	10	)	)	PUNCT
ejpam-6189	129	11	}	}	PUNCT
ejpam-6189	129	12	≥	≥	NUM
ejpam-6189	129	13	min{ζ(x	min{ζ(x	NUM
ejpam-6189	129	14	)	)	PUNCT
ejpam-6189	129	15	·	·	PUNCT
ejpam-6189	129	16	ζ(y	ζ(y	PROPN
ejpam-6189	129	17	)	)	PUNCT
ejpam-6189	129	18	,	,	PUNCT
ejpam-6189	129	19	ξ(x	ξ(x	NOUN
ejpam-6189	129	20	)	)	PUNCT
ejpam-6189	129	21	·	·	PUNCT
ejpam-6189	130	1	ξ(y	ξ(y	PROPN
ejpam-6189	130	2	)	)	PUNCT
ejpam-6189	130	3	}	}	PUNCT
ejpam-6189	130	4	≥	≥	NUM
ejpam-6189	130	5	min{ζ(x	min{ζ(x	NOUN
ejpam-6189	130	6	)	)	PUNCT
ejpam-6189	130	7	,	,	PUNCT
ejpam-6189	130	8	ξ(x	ξ(x	NOUN
ejpam-6189	130	9	)	)	PUNCT
ejpam-6189	130	10	}	}	PUNCT
ejpam-6189	130	11	·	·	PUNCT
ejpam-6189	130	12	min{ζ(y	min{ζ(y	PROPN
ejpam-6189	130	13	)	)	PUNCT
ejpam-6189	130	14	,	,	PUNCT
ejpam-6189	130	15	ξ(y	ξ(y	PROPN
ejpam-6189	130	16	)	)	PUNCT
ejpam-6189	130	17	}	}	PUNCT
ejpam-6189	130	18	=	=	SYM
ejpam-6189	130	19	(	(	PUNCT
ejpam-6189	130	20	ζ	ζ	NOUN
ejpam-6189	130	21	∩	∩	ADJ
ejpam-6189	130	22	ξ)(x	ξ)(x	PROPN
ejpam-6189	130	23	)	)	PUNCT
ejpam-6189	130	24	·	·	PUNCT
ejpam-6189	130	25	(	(	PUNCT
ejpam-6189	130	26	ζ	ζ	NOUN
ejpam-6189	130	27	∩	∩	X
ejpam-6189	130	28	ξ)(y	ξ)(y	PROPN
ejpam-6189	130	29	)	)	PUNCT
ejpam-6189	130	30	.	.	PUNCT
ejpam-6189	131	1	therefore	therefore	ADV
ejpam-6189	131	2	,	,	PUNCT
ejpam-6189	131	3	ζ	ζ	NOUN
ejpam-6189	131	4	∩	∩	NOUN
ejpam-6189	131	5	ξ	ξ	PROPN
ejpam-6189	131	6	is	be	AUX
ejpam-6189	131	7	a	a	DET
ejpam-6189	131	8	fuzzy	fuzzy	ADJ
ejpam-6189	131	9	dot	dot	NOUN
ejpam-6189	131	10	bd	bd	NOUN
ejpam-6189	131	11	-	-	PUNCT
ejpam-6189	131	12	subalgebra	subalgebra	NOUN
ejpam-6189	131	13	of	of	ADP
ejpam-6189	131	14	x.	x.	PROPN
ejpam-6189	131	15	w.	w.	PROPN
ejpam-6189	131	16	nakkhasen	nakkhasen	PROPN
ejpam-6189	131	17	et	et	PROPN
ejpam-6189	131	18	al	al	PROPN
ejpam-6189	131	19	.	.	PUNCT
ejpam-6189	131	20	/	/	SYM
ejpam-6189	131	21	eur	eur	PROPN
ejpam-6189	131	22	.	.	PUNCT
ejpam-6189	132	1	j.	j.	PROPN
ejpam-6189	132	2	pure	pure	PROPN
ejpam-6189	132	3	appl	appl	PROPN
ejpam-6189	132	4	.	.	PROPN
ejpam-6189	132	5	math	math	PROPN
ejpam-6189	132	6	,	,	PUNCT
ejpam-6189	132	7	18	18	NUM
ejpam-6189	132	8	(	(	PUNCT
ejpam-6189	132	9	3	3	NUM
ejpam-6189	132	10	)	)	PUNCT
ejpam-6189	132	11	(	(	PUNCT
ejpam-6189	132	12	2025	2025	NUM
ejpam-6189	132	13	)	)	PUNCT
ejpam-6189	132	14	,	,	PUNCT
ejpam-6189	132	15	6189	6189	NUM
ejpam-6189	132	16	6	6	NUM
ejpam-6189	132	17	of	of	ADP
ejpam-6189	132	18	13	13	NUM
ejpam-6189	132	19	corollary	corollary	ADJ
ejpam-6189	132	20	1	1	NUM
ejpam-6189	132	21	.	.	PUNCT
ejpam-6189	133	1	let	let	VERB
ejpam-6189	133	2	{	{	PUNCT
ejpam-6189	133	3	ζi	ζi	VERB
ejpam-6189	134	1	|	|	ADV
ejpam-6189	135	1	i	i	PRON
ejpam-6189	135	2	∈	∈	PROPN
ejpam-6189	135	3	λ	λ	NOUN
ejpam-6189	135	4	}	}	PUNCT
ejpam-6189	135	5	be	be	VERB
ejpam-6189	135	6	a	a	DET
ejpam-6189	135	7	family	family	NOUN
ejpam-6189	135	8	of	of	ADP
ejpam-6189	135	9	fuzzy	fuzzy	ADJ
ejpam-6189	135	10	dot	dot	NOUN
ejpam-6189	135	11	bd	bd	NOUN
ejpam-6189	135	12	-	-	PUNCT
ejpam-6189	135	13	subalgebras	subalgebras	PROPN
ejpam-6189	135	14	of	of	ADP
ejpam-6189	135	15	a	a	DET
ejpam-6189	135	16	bd	bd	PROPN
ejpam-6189	135	17	-	-	NOUN
ejpam-6189	135	18	algebra	algebra	PROPN
ejpam-6189	135	19	x.	x.	NOUN
ejpam-6189	136	1	then	then	ADV
ejpam-6189	136	2	⋂	⋂	PROPN
ejpam-6189	136	3	i∈λ	i∈λ	VERB
ejpam-6189	136	4	ζi	ζi	PROPN
ejpam-6189	136	5	is	be	AUX
ejpam-6189	136	6	also	also	ADV
ejpam-6189	136	7	a	a	DET
ejpam-6189	136	8	fuzzy	fuzzy	ADJ
ejpam-6189	136	9	dot	dot	NOUN
ejpam-6189	136	10	bd	bd	NOUN
ejpam-6189	136	11	-	-	PUNCT
ejpam-6189	136	12	subalgebra	subalgebra	NOUN
ejpam-6189	136	13	of	of	ADP
ejpam-6189	136	14	x	x	NOUN
ejpam-6189	136	15	,	,	PUNCT
ejpam-6189	136	16	where	where	SCONJ
ejpam-6189	136	17	λ	λ	PROPN
ejpam-6189	136	18	is	be	AUX
ejpam-6189	136	19	any	any	DET
ejpam-6189	136	20	index	index	NOUN
ejpam-6189	136	21	set	set	NOUN
ejpam-6189	136	22	.	.	PUNCT
ejpam-6189	137	1	proof	proof	NOUN
ejpam-6189	137	2	.	.	PUNCT
ejpam-6189	138	1	let	let	VERB
ejpam-6189	138	2	ζ	ζ	NOUN
ejpam-6189	138	3	:	:	PUNCT
ejpam-6189	138	4	=	=	SYM
ejpam-6189	138	5	⋂	⋂	PROPN
ejpam-6189	138	6	i∈λ	i∈λ	NOUN
ejpam-6189	138	7	ζi	ζi	NOUN
ejpam-6189	138	8	.	.	PUNCT
ejpam-6189	139	1	we	we	PRON
ejpam-6189	139	2	recall	recall	VERB
ejpam-6189	139	3	that	that	SCONJ
ejpam-6189	139	4	ζ(x	ζ(x	NOUN
ejpam-6189	139	5	)	)	PUNCT
ejpam-6189	139	6	=	=	SYM
ejpam-6189	139	7	⋂	⋂	PROPN
ejpam-6189	139	8	i∈λ	i∈λ	NOUN
ejpam-6189	139	9	ζi(x	ζi(x	NUM
ejpam-6189	139	10	)	)	PUNCT
ejpam-6189	139	11	=	=	SYM
ejpam-6189	139	12	infi∈λ	infi∈λ	PROPN
ejpam-6189	139	13	ζi(x	ζi(x	CCONJ
ejpam-6189	139	14	)	)	PUNCT
ejpam-6189	139	15	for	for	ADP
ejpam-6189	139	16	all	all	PRON
ejpam-6189	139	17	x	x	SYM
ejpam-6189	139	18	∈	∈	ADJ
ejpam-6189	139	19	x.	x.	NOUN
ejpam-6189	139	20	for	for	ADP
ejpam-6189	139	21	every	every	DET
ejpam-6189	139	22	x	x	PROPN
ejpam-6189	139	23	,	,	PUNCT
ejpam-6189	139	24	y	y	PROPN
ejpam-6189	139	25	∈	∈	PROPN
ejpam-6189	139	26	x	x	X
ejpam-6189	139	27	,	,	PUNCT
ejpam-6189	139	28	we	we	PRON
ejpam-6189	139	29	have	have	VERB
ejpam-6189	139	30	ζ(0	ζ(0	NOUN
ejpam-6189	139	31	)	)	PUNCT
ejpam-6189	139	32	=	=	PUNCT
ejpam-6189	140	1	infi∈λ	infi∈λ	PROPN
ejpam-6189	140	2	ζi(0	ζi(0	PROPN
ejpam-6189	140	3	)	)	PUNCT
ejpam-6189	140	4	≥	≥	PROPN
ejpam-6189	140	5	infi∈λ	infi∈λ	PROPN
ejpam-6189	140	6	ζi(x	ζi(x	NUM
ejpam-6189	140	7	)	)	PUNCT
ejpam-6189	141	1	=	=	SYM
ejpam-6189	141	2	ζ(x	ζ(x	NOUN
ejpam-6189	141	3	)	)	PUNCT
ejpam-6189	141	4	and	and	CCONJ
ejpam-6189	141	5	ζ(x	ζ(x	PROPN
ejpam-6189	141	6	∗	∗	NOUN
ejpam-6189	141	7	y	y	NOUN
ejpam-6189	141	8	)	)	PUNCT
ejpam-6189	142	1	=	=	SYM
ejpam-6189	142	2	infi∈λ	infi∈λ	PROPN
ejpam-6189	142	3	ζi(x	ζi(x	NOUN
ejpam-6189	142	4	∗	∗	PROPN
ejpam-6189	142	5	y	y	PROPN
ejpam-6189	142	6	)	)	PUNCT
ejpam-6189	142	7	≥	≥	PROPN
ejpam-6189	142	8	infi∈λ	infi∈λ	PROPN
ejpam-6189	142	9	ζi(x	ζi(x	NUM
ejpam-6189	142	10	)	)	PUNCT
ejpam-6189	142	11	·	·	PUNCT
ejpam-6189	142	12	ζi(y	ζi(y	NOUN
ejpam-6189	142	13	)	)	PUNCT
ejpam-6189	142	14	=	=	SYM
ejpam-6189	142	15	infi∈λ	infi∈λ	PROPN
ejpam-6189	142	16	ζi(x	ζi(x	NUM
ejpam-6189	142	17	)	)	PUNCT
ejpam-6189	142	18	·	·	PUNCT
ejpam-6189	143	1	infi∈λ	infi∈λ	NOUN
ejpam-6189	143	2	ζi(y	ζi(y	PUNCT
ejpam-6189	143	3	)	)	PUNCT
ejpam-6189	143	4	=	=	SYM
ejpam-6189	143	5	ζ(x	ζ(x	NOUN
ejpam-6189	143	6	)	)	PUNCT
ejpam-6189	143	7	·	·	PUNCT
ejpam-6189	143	8	ζ(y	ζ(y	X
ejpam-6189	143	9	)	)	PUNCT
ejpam-6189	143	10	.	.	PUNCT
ejpam-6189	144	1	hence	hence	ADV
ejpam-6189	144	2	,	,	PUNCT
ejpam-6189	144	3	⋂	⋂	PROPN
ejpam-6189	144	4	i∈λ	i∈λ	VERB
ejpam-6189	144	5	ζi	ζi	PROPN
ejpam-6189	144	6	is	be	AUX
ejpam-6189	144	7	a	a	DET
ejpam-6189	144	8	fuzzy	fuzzy	ADJ
ejpam-6189	144	9	dot	dot	NOUN
ejpam-6189	144	10	bd	bd	NOUN
ejpam-6189	144	11	-	-	PUNCT
ejpam-6189	144	12	subalgebra	subalgebra	NOUN
ejpam-6189	144	13	of	of	ADP
ejpam-6189	144	14	x.	x.	NOUN
ejpam-6189	144	15	example	example	NOUN
ejpam-6189	145	1	3	3	X
ejpam-6189	145	2	.	.	PUNCT
ejpam-6189	145	3	by	by	ADP
ejpam-6189	145	4	example	example	NOUN
ejpam-6189	145	5	1	1	NUM
ejpam-6189	145	6	,	,	PUNCT
ejpam-6189	145	7	we	we	PRON
ejpam-6189	145	8	have	have	VERB
ejpam-6189	145	9	the	the	DET
ejpam-6189	145	10	ζ	ζ	NOUN
ejpam-6189	145	11	is	be	AUX
ejpam-6189	145	12	a	a	DET
ejpam-6189	145	13	fuzzy	fuzzy	ADJ
ejpam-6189	145	14	dot	dot	NOUN
ejpam-6189	145	15	bd	bd	NOUN
ejpam-6189	145	16	-	-	PUNCT
ejpam-6189	145	17	subalgebra	subalgebra	NOUN
ejpam-6189	145	18	of	of	ADP
ejpam-6189	145	19	a	a	DET
ejpam-6189	145	20	bd	bd	NOUN
ejpam-6189	145	21	-	-	NOUN
ejpam-6189	145	22	algebra	algebra	NOUN
ejpam-6189	145	23	x	x	PUNCT
ejpam-6189	145	24	where	where	SCONJ
ejpam-6189	145	25	ζ(0	ζ(0	NOUN
ejpam-6189	145	26	)	)	PUNCT
ejpam-6189	145	27	=	=	PUNCT
ejpam-6189	145	28	0.80	0.80	NUM
ejpam-6189	145	29	,	,	PUNCT
ejpam-6189	145	30	ζ(a	ζ(a	PRON
ejpam-6189	145	31	)	)	PUNCT
ejpam-6189	145	32	=	=	SYM
ejpam-6189	145	33	0.60	0.60	NUM
ejpam-6189	145	34	,	,	PUNCT
ejpam-6189	145	35	ζ(b	ζ(b	PROPN
ejpam-6189	145	36	)	)	PUNCT
ejpam-6189	145	37	=	=	NOUN
ejpam-6189	145	38	0.70	0.70	NUM
ejpam-6189	145	39	,	,	PUNCT
ejpam-6189	145	40	and	and	CCONJ
ejpam-6189	145	41	ζ(c	ζ(c	ADJ
ejpam-6189	145	42	)	)	PUNCT
ejpam-6189	145	43	=	=	SYM
ejpam-6189	145	44	0.70	0.70	NUM
ejpam-6189	145	45	.	.	PUNCT
ejpam-6189	146	1	additionally	additionally	ADV
ejpam-6189	146	2	,	,	PUNCT
ejpam-6189	146	3	we	we	PRON
ejpam-6189	146	4	define	define	VERB
ejpam-6189	146	5	a	a	DET
ejpam-6189	146	6	fuzzy	fuzzy	ADJ
ejpam-6189	146	7	dot	dot	NOUN
ejpam-6189	146	8	bd	bd	NOUN
ejpam-6189	146	9	-	-	PUNCT
ejpam-6189	146	10	subalgebra	subalgebra	ADJ
ejpam-6189	146	11	ξ	ξ	PROPN
ejpam-6189	146	12	of	of	ADP
ejpam-6189	146	13	x	x	PUNCT
ejpam-6189	146	14	by	by	ADP
ejpam-6189	146	15	ξ(0	ξ(0	NOUN
ejpam-6189	146	16	)	)	PUNCT
ejpam-6189	146	17	=	=	SYM
ejpam-6189	146	18	0.90	0.90	NUM
ejpam-6189	146	19	,	,	PUNCT
ejpam-6189	146	20	ξ(a	ξ(a	NUM
ejpam-6189	146	21	)	)	PUNCT
ejpam-6189	146	22	=	=	SYM
ejpam-6189	146	23	0.60	0.60	NUM
ejpam-6189	146	24	,	,	PUNCT
ejpam-6189	146	25	ξ(b	ξ(b	NOUN
ejpam-6189	146	26	)	)	PUNCT
ejpam-6189	146	27	=	=	SYM
ejpam-6189	146	28	0.60	0.60	NUM
ejpam-6189	146	29	,	,	PUNCT
ejpam-6189	146	30	and	and	CCONJ
ejpam-6189	146	31	ξ(c	ξ(c	NUM
ejpam-6189	146	32	)	)	PUNCT
ejpam-6189	146	33	=	=	SYM
ejpam-6189	147	1	0.50	0.50	NUM
ejpam-6189	147	2	.	.	PUNCT
ejpam-6189	148	1	we	we	PRON
ejpam-6189	148	2	obtain	obtain	VERB
ejpam-6189	148	3	that	that	SCONJ
ejpam-6189	148	4	(	(	PUNCT
ejpam-6189	148	5	ζ	ζ	NOUN
ejpam-6189	148	6	∪	∪	X
ejpam-6189	148	7	ξ)(0	ξ)(0	PROPN
ejpam-6189	148	8	∗	∗	X
ejpam-6189	148	9	b	b	NOUN
ejpam-6189	148	10	)	)	PUNCT
ejpam-6189	148	11	=	=	SYM
ejpam-6189	148	12	0.60	0.60	NUM
ejpam-6189	148	13	≱	≱	PROPN
ejpam-6189	148	14	0.63	0.63	NUM
ejpam-6189	148	15	=	=	SYM
ejpam-6189	148	16	(	(	PUNCT
ejpam-6189	148	17	ζ	ζ	PROPN
ejpam-6189	148	18	∪	∪	X
ejpam-6189	148	19	ξ)(0	ξ)(0	PROPN
ejpam-6189	148	20	)	)	PUNCT
ejpam-6189	148	21	·	·	PUNCT
ejpam-6189	148	22	(	(	PUNCT
ejpam-6189	148	23	ζ	ζ	NOUN
ejpam-6189	148	24	∪	∪	ADP
ejpam-6189	148	25	ξ)(b	ξ)(b	ADJ
ejpam-6189	148	26	)	)	PUNCT
ejpam-6189	148	27	.	.	PUNCT
ejpam-6189	149	1	this	this	PRON
ejpam-6189	149	2	show	show	VERB
ejpam-6189	149	3	that	that	SCONJ
ejpam-6189	149	4	ζ	ζ	NOUN
ejpam-6189	149	5	∪	∪	X
ejpam-6189	149	6	ξ	ξ	PROPN
ejpam-6189	149	7	is	be	AUX
ejpam-6189	149	8	not	not	PART
ejpam-6189	149	9	a	a	DET
ejpam-6189	149	10	fuzzy	fuzzy	ADJ
ejpam-6189	149	11	dot	dot	NOUN
ejpam-6189	149	12	bd	bd	NOUN
ejpam-6189	149	13	-	-	PUNCT
ejpam-6189	149	14	subalgebra	subalgebra	NOUN
ejpam-6189	149	15	of	of	ADP
ejpam-6189	149	16	x.	x.	NOUN
ejpam-6189	149	17	from	from	ADP
ejpam-6189	149	18	example	example	NOUN
ejpam-6189	149	19	3	3	NUM
ejpam-6189	149	20	,	,	PUNCT
ejpam-6189	149	21	we	we	PRON
ejpam-6189	149	22	conclude	conclude	VERB
ejpam-6189	149	23	that	that	SCONJ
ejpam-6189	149	24	the	the	DET
ejpam-6189	149	25	union	union	NOUN
ejpam-6189	149	26	of	of	ADP
ejpam-6189	149	27	fuzzy	fuzzy	ADJ
ejpam-6189	149	28	dot	dot	NOUN
ejpam-6189	149	29	bd	bd	NOUN
ejpam-6189	149	30	-	-	PUNCT
ejpam-6189	149	31	subalgebras	subalgebras	PROPN
ejpam-6189	149	32	of	of	ADP
ejpam-6189	149	33	bdalgebras	bdalgebras	PROPN
ejpam-6189	149	34	does	do	AUX
ejpam-6189	149	35	n’t	not	PART
ejpam-6189	149	36	necessarily	necessarily	ADV
ejpam-6189	149	37	have	have	VERB
ejpam-6189	149	38	to	to	PART
ejpam-6189	149	39	be	be	AUX
ejpam-6189	149	40	a	a	DET
ejpam-6189	149	41	fuzzy	fuzzy	ADJ
ejpam-6189	149	42	dotbd	dotbd	NOUN
ejpam-6189	149	43	-	-	PUNCT
ejpam-6189	149	44	subalgebra	subalgebra	NOUN
ejpam-6189	149	45	ofbd	ofbd	ADV
ejpam-6189	149	46	-	-	PUNCT
ejpam-6189	149	47	algebras	algebras	PROPN
ejpam-6189	149	48	in	in	ADP
ejpam-6189	149	49	general	general	ADJ
ejpam-6189	149	50	.	.	PUNCT
ejpam-6189	150	1	theorem	theorem	NOUN
ejpam-6189	150	2	2	2	NUM
ejpam-6189	150	3	.	.	PUNCT
ejpam-6189	151	1	let	let	VERB
ejpam-6189	151	2	x	x	PRON
ejpam-6189	151	3	be	be	AUX
ejpam-6189	151	4	a	a	DET
ejpam-6189	151	5	bd	bd	NOUN
ejpam-6189	151	6	-	-	NOUN
ejpam-6189	151	7	algebra	algebra	NOUN
ejpam-6189	151	8	,	,	PUNCT
ejpam-6189	151	9	and	and	CCONJ
ejpam-6189	151	10	a	a	PRON
ejpam-6189	151	11	be	be	AUX
ejpam-6189	151	12	a	a	DET
ejpam-6189	151	13	nonempty	nonempty	ADJ
ejpam-6189	151	14	subset	subset	NOUN
ejpam-6189	151	15	of	of	ADP
ejpam-6189	151	16	x.	x.	NOUN
ejpam-6189	151	17	then	then	ADV
ejpam-6189	151	18	a	a	PRON
ejpam-6189	151	19	is	be	AUX
ejpam-6189	151	20	a	a	DET
ejpam-6189	151	21	bd	bd	NOUN
ejpam-6189	151	22	-	-	PUNCT
ejpam-6189	151	23	subalgebra	subalgebra	NOUN
ejpam-6189	151	24	of	of	ADP
ejpam-6189	151	25	x	x	PRON
ejpam-6189	151	26	if	if	SCONJ
ejpam-6189	151	27	and	and	CCONJ
ejpam-6189	151	28	only	only	ADV
ejpam-6189	151	29	if	if	SCONJ
ejpam-6189	151	30	ca	ca	NOUN
ejpam-6189	151	31	is	be	AUX
ejpam-6189	151	32	a	a	DET
ejpam-6189	151	33	fuzzy	fuzzy	ADJ
ejpam-6189	151	34	dot	dot	NOUN
ejpam-6189	151	35	bd	bd	NOUN
ejpam-6189	151	36	-	-	PUNCT
ejpam-6189	151	37	subalgebra	subalgebra	NOUN
ejpam-6189	151	38	of	of	ADP
ejpam-6189	151	39	x.	x.	NOUN
ejpam-6189	151	40	proof	proof	PROPN
ejpam-6189	151	41	.	.	PUNCT
ejpam-6189	152	1	assume	assume	VERB
ejpam-6189	152	2	that	that	SCONJ
ejpam-6189	152	3	a	a	PRON
ejpam-6189	152	4	is	be	AUX
ejpam-6189	152	5	a	a	DET
ejpam-6189	152	6	bd	bd	NOUN
ejpam-6189	152	7	-	-	PUNCT
ejpam-6189	152	8	subalgebra	subalgebra	NOUN
ejpam-6189	152	9	of	of	ADP
ejpam-6189	152	10	x.	x.	NOUN
ejpam-6189	152	11	then	then	ADV
ejpam-6189	152	12	0	0	NUM
ejpam-6189	152	13	∈	∈	NOUN
ejpam-6189	152	14	a.	a.	NOUN
ejpam-6189	152	15	so	so	ADV
ejpam-6189	152	16	,	,	PUNCT
ejpam-6189	152	17	ca(0	ca(0	PROPN
ejpam-6189	152	18	)	)	PUNCT
ejpam-6189	152	19	=	=	SYM
ejpam-6189	152	20	1	1	NUM
ejpam-6189	152	21	≥	≥	NOUN
ejpam-6189	152	22	ca(x	ca(x	NOUN
ejpam-6189	152	23	)	)	PUNCT
ejpam-6189	152	24	for	for	ADP
ejpam-6189	152	25	all	all	PRON
ejpam-6189	152	26	x	x	SYM
ejpam-6189	152	27	∈	∈	PROPN
ejpam-6189	152	28	x.	x.	NOUN
ejpam-6189	152	29	suppose	suppose	VERB
ejpam-6189	152	30	that	that	SCONJ
ejpam-6189	152	31	there	there	PRON
ejpam-6189	152	32	exist	exist	VERB
ejpam-6189	152	33	a	a	DET
ejpam-6189	152	34	,	,	PUNCT
ejpam-6189	152	35	b	b	X
ejpam-6189	152	36	∈	∈	PROPN
ejpam-6189	152	37	x	x	PUNCT
ejpam-6189	152	38	such	such	ADJ
ejpam-6189	152	39	that	that	SCONJ
ejpam-6189	152	40	ca(a	ca(a	PROPN
ejpam-6189	152	41	∗	∗	NOUN
ejpam-6189	152	42	b	b	NOUN
ejpam-6189	152	43	)	)	PUNCT
ejpam-6189	152	44	<	<	X
ejpam-6189	152	45	ca(a	ca(a	PROPN
ejpam-6189	152	46	)	)	PUNCT
ejpam-6189	152	47	·	·	PUNCT
ejpam-6189	153	1	ca(b	ca(b	PUNCT
ejpam-6189	153	2	)	)	PUNCT
ejpam-6189	153	3	.	.	PUNCT
ejpam-6189	154	1	thus	thus	ADV
ejpam-6189	154	2	,	,	PUNCT
ejpam-6189	154	3	ca(a	ca(a	PROPN
ejpam-6189	154	4	∗	∗	NOUN
ejpam-6189	154	5	b	b	NOUN
ejpam-6189	154	6	)	)	PUNCT
ejpam-6189	154	7	=	=	SYM
ejpam-6189	154	8	0	0	NUM
ejpam-6189	154	9	and	and	CCONJ
ejpam-6189	154	10	ca(a	ca(a	NUM
ejpam-6189	154	11	)	)	PUNCT
ejpam-6189	154	12	·	·	PUNCT
ejpam-6189	154	13	ca(b	ca(b	PUNCT
ejpam-6189	154	14	)	)	PUNCT
ejpam-6189	154	15	=	=	SYM
ejpam-6189	155	1	1	1	NUM
ejpam-6189	155	2	;	;	PUNCT
ejpam-6189	155	3	that	that	PRON
ejpam-6189	155	4	is	is	ADV
ejpam-6189	155	5	,	,	PUNCT
ejpam-6189	155	6	ca(a	ca(a	PUNCT
ejpam-6189	155	7	)	)	PUNCT
ejpam-6189	155	8	=	=	SYM
ejpam-6189	155	9	1	1	NUM
ejpam-6189	155	10	and	and	CCONJ
ejpam-6189	155	11	ca(b	ca(b	NUM
ejpam-6189	155	12	)	)	PUNCT
ejpam-6189	155	13	=	=	SYM
ejpam-6189	156	1	1	1	X
ejpam-6189	156	2	.	.	PUNCT
ejpam-6189	156	3	it	it	PRON
ejpam-6189	156	4	follows	follow	VERB
ejpam-6189	156	5	that	that	SCONJ
ejpam-6189	156	6	a∗	a∗	PROPN
ejpam-6189	156	7	b	b	PROPN
ejpam-6189	156	8	̸∈	̸∈	PROPN
ejpam-6189	156	9	a	a	PROPN
ejpam-6189	156	10	and	and	CCONJ
ejpam-6189	156	11	a	a	PRON
ejpam-6189	156	12	,	,	PUNCT
ejpam-6189	156	13	b	b	X
ejpam-6189	156	14	∈	∈	PROPN
ejpam-6189	156	15	a.	a.	NOUN
ejpam-6189	156	16	by	by	ADP
ejpam-6189	156	17	assumption	assumption	NOUN
ejpam-6189	156	18	,	,	PUNCT
ejpam-6189	156	19	we	we	PRON
ejpam-6189	156	20	have	have	VERB
ejpam-6189	156	21	a∗	a∗	PROPN
ejpam-6189	156	22	b	b	PROPN
ejpam-6189	156	23	∈	∈	PROPN
ejpam-6189	156	24	a	a	PRON
ejpam-6189	156	25	,	,	PUNCT
ejpam-6189	156	26	which	which	PRON
ejpam-6189	156	27	is	be	AUX
ejpam-6189	156	28	a	a	DET
ejpam-6189	156	29	contradiction	contradiction	NOUN
ejpam-6189	156	30	.	.	PUNCT
ejpam-6189	157	1	hence	hence	ADV
ejpam-6189	157	2	,	,	PUNCT
ejpam-6189	157	3	ca(x	ca(x	NOUN
ejpam-6189	157	4	∗	∗	NOUN
ejpam-6189	157	5	y	y	NOUN
ejpam-6189	157	6	)	)	PUNCT
ejpam-6189	157	7	≥	≥	NOUN
ejpam-6189	157	8	ca(x	ca(x	NOUN
ejpam-6189	157	9	)	)	PUNCT
ejpam-6189	157	10	·	·	PUNCT
ejpam-6189	157	11	ca(y	ca(y	PROPN
ejpam-6189	157	12	)	)	PUNCT
ejpam-6189	157	13	for	for	ADP
ejpam-6189	157	14	all	all	DET
ejpam-6189	157	15	x	x	NOUN
ejpam-6189	157	16	,	,	PUNCT
ejpam-6189	157	17	y	y	PROPN
ejpam-6189	157	18	∈	∈	PROPN
ejpam-6189	157	19	x.	x.	NOUN
ejpam-6189	157	20	therefore	therefore	ADV
ejpam-6189	157	21	,	,	PUNCT
ejpam-6189	157	22	ca	can	AUX
ejpam-6189	157	23	is	be	AUX
ejpam-6189	157	24	a	a	DET
ejpam-6189	157	25	fuzzy	fuzzy	ADJ
ejpam-6189	157	26	dot	dot	NOUN
ejpam-6189	157	27	bd	bd	NOUN
ejpam-6189	157	28	-	-	PUNCT
ejpam-6189	157	29	subalgebra	subalgebra	NOUN
ejpam-6189	157	30	of	of	ADP
ejpam-6189	157	31	x.	x.	NOUN
ejpam-6189	157	32	conversely	conversely	ADV
ejpam-6189	157	33	,	,	PUNCT
ejpam-6189	157	34	assume	assume	VERB
ejpam-6189	157	35	that	that	SCONJ
ejpam-6189	157	36	ca	can	AUX
ejpam-6189	157	37	is	be	AUX
ejpam-6189	157	38	a	a	DET
ejpam-6189	157	39	fuzzy	fuzzy	ADJ
ejpam-6189	157	40	dot	dot	NOUN
ejpam-6189	157	41	bd	bd	NOUN
ejpam-6189	157	42	-	-	PUNCT
ejpam-6189	157	43	subalgebra	subalgebra	NOUN
ejpam-6189	157	44	of	of	ADP
ejpam-6189	157	45	x.	x.	NOUN
ejpam-6189	157	46	if	if	SCONJ
ejpam-6189	157	47	0	0	NUM
ejpam-6189	157	48	̸∈	̸∈	PROPN
ejpam-6189	157	49	a	a	PROPN
ejpam-6189	157	50	,	,	PUNCT
ejpam-6189	157	51	then	then	ADV
ejpam-6189	157	52	0	0	X
ejpam-6189	157	53	=	=	SYM
ejpam-6189	157	54	ca(0	ca(0	PROPN
ejpam-6189	157	55	)	)	PUNCT
ejpam-6189	157	56	≥	≥	NOUN
ejpam-6189	157	57	ca(x	ca(x	NOUN
ejpam-6189	157	58	)	)	PUNCT
ejpam-6189	157	59	for	for	ADP
ejpam-6189	157	60	all	all	PRON
ejpam-6189	157	61	x	x	SYM
ejpam-6189	157	62	∈	∈	NOUN
ejpam-6189	157	63	x.	x.	NOUN
ejpam-6189	157	64	also	also	ADV
ejpam-6189	157	65	,	,	PUNCT
ejpam-6189	157	66	ca(x	ca(x	NOUN
ejpam-6189	157	67	)	)	PUNCT
ejpam-6189	157	68	=	=	SYM
ejpam-6189	157	69	0	0	NUM
ejpam-6189	157	70	for	for	ADP
ejpam-6189	157	71	all	all	DET
ejpam-6189	157	72	x	x	SYM
ejpam-6189	157	73	∈	∈	PROPN
ejpam-6189	157	74	x	x	NOUN
ejpam-6189	157	75	,	,	PUNCT
ejpam-6189	157	76	implies	imply	VERB
ejpam-6189	157	77	that	that	SCONJ
ejpam-6189	157	78	a	a	DET
ejpam-6189	157	79	=	=	PUNCT
ejpam-6189	157	80	∅.	∅.	NOUN
ejpam-6189	157	81	this	this	PRON
ejpam-6189	157	82	is	be	AUX
ejpam-6189	157	83	a	a	DET
ejpam-6189	157	84	contradiction	contradiction	NOUN
ejpam-6189	157	85	.	.	PUNCT
ejpam-6189	158	1	so	so	ADV
ejpam-6189	158	2	,	,	PUNCT
ejpam-6189	158	3	0	0	NUM
ejpam-6189	158	4	∈	∈	NOUN
ejpam-6189	158	5	a.	a.	NOUN
ejpam-6189	158	6	next	next	ADV
ejpam-6189	158	7	,	,	PUNCT
ejpam-6189	158	8	let	let	VERB
ejpam-6189	158	9	x	x	PRON
ejpam-6189	158	10	,	,	PUNCT
ejpam-6189	158	11	y	y	PROPN
ejpam-6189	158	12	∈	∈	PROPN
ejpam-6189	158	13	a.	a.	NOUN
ejpam-6189	158	14	then	then	ADV
ejpam-6189	158	15	,	,	PUNCT
ejpam-6189	159	1	ca(x	ca(x	NOUN
ejpam-6189	159	2	∗	∗	NOUN
ejpam-6189	159	3	y	y	NOUN
ejpam-6189	159	4	)	)	PUNCT
ejpam-6189	159	5	≥	≥	NOUN
ejpam-6189	159	6	ca(x	ca(x	NOUN
ejpam-6189	159	7	)	)	PUNCT
ejpam-6189	159	8	·	·	PUNCT
ejpam-6189	159	9	ca(y	ca(y	PROPN
ejpam-6189	159	10	)	)	PUNCT
ejpam-6189	159	11	=	=	SYM
ejpam-6189	160	1	1	1	X
ejpam-6189	160	2	.	.	X
ejpam-6189	160	3	we	we	PRON
ejpam-6189	160	4	obtain	obtain	VERB
ejpam-6189	160	5	that	that	PRON
ejpam-6189	160	6	ca(x	ca(x	NOUN
ejpam-6189	160	7	∗	∗	NOUN
ejpam-6189	160	8	y	y	NOUN
ejpam-6189	160	9	)	)	PUNCT
ejpam-6189	160	10	=	=	SYM
ejpam-6189	161	1	1	1	NUM
ejpam-6189	161	2	;	;	PUNCT
ejpam-6189	161	3	that	that	PRON
ejpam-6189	161	4	is	is	ADV
ejpam-6189	161	5	,	,	PUNCT
ejpam-6189	161	6	x	x	SYM
ejpam-6189	161	7	∗	∗	NOUN
ejpam-6189	161	8	y	y	PROPN
ejpam-6189	161	9	∈	∈	PROPN
ejpam-6189	161	10	a.	a.	NOUN
ejpam-6189	161	11	consequently	consequently	ADV
ejpam-6189	161	12	,	,	PUNCT
ejpam-6189	161	13	a	a	PRON
ejpam-6189	161	14	is	be	AUX
ejpam-6189	161	15	a	a	DET
ejpam-6189	161	16	bd	bd	NOUN
ejpam-6189	161	17	-	-	PUNCT
ejpam-6189	161	18	subalgebra	subalgebra	NOUN
ejpam-6189	161	19	of	of	ADP
ejpam-6189	161	20	x.	x.	NOUN
ejpam-6189	161	21	theorem	theorem	NOUN
ejpam-6189	161	22	3	3	X
ejpam-6189	161	23	.	.	PUNCT
ejpam-6189	162	1	let	let	VERB
ejpam-6189	162	2	x	x	PRON
ejpam-6189	162	3	be	be	AUX
ejpam-6189	162	4	a	a	DET
ejpam-6189	162	5	bd	bd	NOUN
ejpam-6189	162	6	-	-	NOUN
ejpam-6189	162	7	algebra	algebra	NOUN
ejpam-6189	162	8	,	,	PUNCT
ejpam-6189	162	9	and	and	CCONJ
ejpam-6189	162	10	ζ	ζ	NOUN
ejpam-6189	162	11	be	be	AUX
ejpam-6189	162	12	a	a	DET
ejpam-6189	162	13	fuzzy	fuzzy	ADJ
ejpam-6189	162	14	set	set	NOUN
ejpam-6189	162	15	of	of	ADP
ejpam-6189	162	16	x.	x.	NOUN
ejpam-6189	162	17	if	if	SCONJ
ejpam-6189	162	18	a	a	DET
ejpam-6189	162	19	nonempty	nonempty	ADJ
ejpam-6189	162	20	level	level	NOUN
ejpam-6189	162	21	subset	subset	NOUN
ejpam-6189	162	22	ζt	ζt	NOUN
ejpam-6189	162	23	is	be	AUX
ejpam-6189	162	24	a	a	DET
ejpam-6189	162	25	bd	bd	NOUN
ejpam-6189	162	26	-	-	PUNCT
ejpam-6189	162	27	subalgebra	subalgebra	NOUN
ejpam-6189	162	28	of	of	ADP
ejpam-6189	162	29	x	x	PUNCT
ejpam-6189	162	30	for	for	ADP
ejpam-6189	162	31	all	all	DET
ejpam-6189	162	32	t	t	NOUN
ejpam-6189	162	33	∈	∈	PROPN
ejpam-6189	163	1	[	[	X
ejpam-6189	163	2	0	0	NUM
ejpam-6189	163	3	,	,	PUNCT
ejpam-6189	163	4	1	1	NUM
ejpam-6189	163	5	]	]	PUNCT
ejpam-6189	163	6	,	,	PUNCT
ejpam-6189	163	7	then	then	ADV
ejpam-6189	163	8	ζ	ζ	NOUN
ejpam-6189	163	9	is	be	AUX
ejpam-6189	163	10	a	a	DET
ejpam-6189	163	11	fuzzy	fuzzy	ADJ
ejpam-6189	163	12	dot	dot	NOUN
ejpam-6189	163	13	bd	bd	NOUN
ejpam-6189	163	14	-	-	PUNCT
ejpam-6189	163	15	subalgebra	subalgebra	NOUN
ejpam-6189	163	16	of	of	ADP
ejpam-6189	163	17	x.	x.	NOUN
ejpam-6189	163	18	proof	proof	NOUN
ejpam-6189	163	19	.	.	PUNCT
ejpam-6189	164	1	let	let	VERB
ejpam-6189	164	2	x	x	PRON
ejpam-6189	164	3	,	,	PUNCT
ejpam-6189	164	4	y	y	PROPN
ejpam-6189	164	5	∈	∈	PROPN
ejpam-6189	164	6	x.	x.	NOUN
ejpam-6189	164	7	take	take	VERB
ejpam-6189	164	8	ζ(x	ζ(x	NOUN
ejpam-6189	164	9	)	)	PUNCT
ejpam-6189	164	10	=	=	SYM
ejpam-6189	164	11	t′	t′	NUM
ejpam-6189	164	12	for	for	ADP
ejpam-6189	164	13	some	some	DET
ejpam-6189	164	14	t′	t′	NUM
ejpam-6189	164	15	∈	∈	NOUN
ejpam-6189	165	1	[	[	X
ejpam-6189	165	2	0	0	NUM
ejpam-6189	165	3	,	,	PUNCT
ejpam-6189	165	4	1	1	NUM
ejpam-6189	165	5	]	]	PUNCT
ejpam-6189	165	6	.	.	PUNCT
ejpam-6189	166	1	then	then	ADV
ejpam-6189	166	2	x	x	SYM
ejpam-6189	166	3	∈	∈	NOUN
ejpam-6189	166	4	ζt′	ζt′	ADV
ejpam-6189	166	5	,	,	PUNCT
ejpam-6189	166	6	and	and	CCONJ
ejpam-6189	166	7	so	so	ADV
ejpam-6189	166	8	ζt′	ζt′	ADJ
ejpam-6189	166	9	̸=	̸=	PROPN
ejpam-6189	166	10	∅.	∅.	NOUN
ejpam-6189	166	11	by	by	ADP
ejpam-6189	166	12	assumption	assumption	NOUN
ejpam-6189	166	13	,	,	PUNCT
ejpam-6189	166	14	we	we	PRON
ejpam-6189	166	15	have	have	AUX
ejpam-6189	166	16	ζt′	ζt′	ADV
ejpam-6189	166	17	is	be	AUX
ejpam-6189	166	18	a	a	DET
ejpam-6189	166	19	bd	bd	NOUN
ejpam-6189	166	20	-	-	NOUN
ejpam-6189	166	21	algebra	algebra	NOUN
ejpam-6189	166	22	of	of	ADP
ejpam-6189	166	23	x.	x.	NOUN
ejpam-6189	166	24	that	that	PRON
ejpam-6189	166	25	is	be	AUX
ejpam-6189	166	26	,	,	PUNCT
ejpam-6189	166	27	0	0	X
ejpam-6189	166	28	∈	∈	NOUN
ejpam-6189	166	29	ζt′	ζt′	X
ejpam-6189	166	30	.	.	PUNCT
ejpam-6189	167	1	it	it	PRON
ejpam-6189	167	2	follows	follow	VERB
ejpam-6189	167	3	that	that	PRON
ejpam-6189	167	4	ζ(0	ζ(0	NOUN
ejpam-6189	167	5	)	)	PUNCT
ejpam-6189	167	6	≥	≥	NOUN
ejpam-6189	167	7	t′	t′	NUM
ejpam-6189	167	8	=	=	SYM
ejpam-6189	167	9	ζ(x	ζ(x	NOUN
ejpam-6189	167	10	)	)	PUNCT
ejpam-6189	167	11	.	.	PUNCT
ejpam-6189	168	1	next	next	ADV
ejpam-6189	168	2	,	,	PUNCT
ejpam-6189	168	3	letting	let	VERB
ejpam-6189	168	4	ζ(x	ζ(x	NOUN
ejpam-6189	168	5	)	)	PUNCT
ejpam-6189	168	6	·	·	PUNCT
ejpam-6189	168	7	ζ(y	ζ(y	X
ejpam-6189	168	8	)	)	PUNCT
ejpam-6189	169	1	=	=	PUNCT
ejpam-6189	169	2	s′	s′	PROPN
ejpam-6189	169	3	for	for	ADP
ejpam-6189	169	4	some	some	DET
ejpam-6189	169	5	s′	s′	ADJ
ejpam-6189	169	6	∈	∈	PROPN
ejpam-6189	170	1	[	[	X
ejpam-6189	170	2	0	0	NUM
ejpam-6189	170	3	,	,	PUNCT
ejpam-6189	170	4	1	1	NUM
ejpam-6189	170	5	]	]	PUNCT
ejpam-6189	170	6	.	.	PUNCT
ejpam-6189	171	1	since	since	SCONJ
ejpam-6189	171	2	ζ(x	ζ(x	NOUN
ejpam-6189	171	3	)	)	PUNCT
ejpam-6189	171	4	,	,	PUNCT
ejpam-6189	171	5	ζ(y	ζ(y	PROPN
ejpam-6189	171	6	)	)	PUNCT
ejpam-6189	171	7	∈	∈	PROPN
ejpam-6189	172	1	[	[	X
ejpam-6189	172	2	0	0	NUM
ejpam-6189	172	3	,	,	PUNCT
ejpam-6189	172	4	1	1	NUM
ejpam-6189	172	5	]	]	PUNCT
ejpam-6189	172	6	,	,	PUNCT
ejpam-6189	172	7	we	we	PRON
ejpam-6189	172	8	get	get	VERB
ejpam-6189	172	9	ζ(x	ζ(x	NOUN
ejpam-6189	172	10	)	)	PUNCT
ejpam-6189	172	11	≥	≥	NOUN
ejpam-6189	172	12	ζ(x	ζ(x	NOUN
ejpam-6189	172	13	)	)	PUNCT
ejpam-6189	172	14	·	·	PUNCT
ejpam-6189	172	15	ζ(y	ζ(y	X
ejpam-6189	172	16	)	)	PUNCT
ejpam-6189	173	1	=	=	SYM
ejpam-6189	173	2	s′	s′	PROPN
ejpam-6189	173	3	and	and	CCONJ
ejpam-6189	173	4	ζ(y	ζ(y	PROPN
ejpam-6189	173	5	)	)	PUNCT
ejpam-6189	173	6	≥	≥	NOUN
ejpam-6189	173	7	ζ(x	ζ(x	NOUN
ejpam-6189	173	8	)	)	PUNCT
ejpam-6189	173	9	·	·	PUNCT
ejpam-6189	173	10	ζ(y	ζ(y	X
ejpam-6189	173	11	)	)	PUNCT
ejpam-6189	174	1	=	=	SYM
ejpam-6189	174	2	s′.	s′.	PROPN
ejpam-6189	175	1	thus	thus	ADV
ejpam-6189	175	2	,	,	PUNCT
ejpam-6189	175	3	x	x	PRON
ejpam-6189	175	4	,	,	PUNCT
ejpam-6189	175	5	y	y	PROPN
ejpam-6189	175	6	∈	∈	PROPN
ejpam-6189	175	7	ζs′	ζs′	NOUN
ejpam-6189	175	8	.	.	PUNCT
ejpam-6189	176	1	by	by	ADP
ejpam-6189	176	2	the	the	DET
ejpam-6189	176	3	given	give	VERB
ejpam-6189	176	4	assumption	assumption	NOUN
ejpam-6189	176	5	,	,	PUNCT
ejpam-6189	176	6	we	we	PRON
ejpam-6189	176	7	have	have	VERB
ejpam-6189	176	8	x	x	NOUN
ejpam-6189	176	9	∗	∗	NOUN
ejpam-6189	176	10	y	y	PROPN
ejpam-6189	176	11	∈	∈	PROPN
ejpam-6189	176	12	ζs′	ζs′	NOUN
ejpam-6189	176	13	.	.	PUNCT
ejpam-6189	177	1	this	this	PRON
ejpam-6189	177	2	implies	imply	VERB
ejpam-6189	177	3	that	that	SCONJ
ejpam-6189	177	4	ζ(x	ζ(x	PROPN
ejpam-6189	177	5	∗	∗	NOUN
ejpam-6189	177	6	y	y	NOUN
ejpam-6189	177	7	)	)	PUNCT
ejpam-6189	177	8	≥	≥	NOUN
ejpam-6189	177	9	s′	s′	VERB
ejpam-6189	177	10	=	=	PUNCT
ejpam-6189	177	11	ζ(x	ζ(x	NOUN
ejpam-6189	177	12	)	)	PUNCT
ejpam-6189	177	13	·	·	PUNCT
ejpam-6189	177	14	ζ(y	ζ(y	X
ejpam-6189	177	15	)	)	PUNCT
ejpam-6189	177	16	.	.	PUNCT
ejpam-6189	178	1	therefore	therefore	ADV
ejpam-6189	178	2	,	,	PUNCT
ejpam-6189	178	3	ζ	ζ	NOUN
ejpam-6189	178	4	is	be	AUX
ejpam-6189	178	5	a	a	DET
ejpam-6189	178	6	fuzzy	fuzzy	ADJ
ejpam-6189	178	7	dot	dot	NOUN
ejpam-6189	178	8	bd	bd	NOUN
ejpam-6189	178	9	-	-	PUNCT
ejpam-6189	178	10	subalgebra	subalgebra	NOUN
ejpam-6189	178	11	of	of	ADP
ejpam-6189	178	12	x.	x.	NOUN
ejpam-6189	178	13	the	the	DET
ejpam-6189	178	14	converse	converse	NOUN
ejpam-6189	178	15	of	of	ADP
ejpam-6189	178	16	theorem	theorem	NOUN
ejpam-6189	178	17	3	3	NUM
ejpam-6189	178	18	is	be	AUX
ejpam-6189	178	19	not	not	PART
ejpam-6189	178	20	always	always	ADV
ejpam-6189	178	21	true	true	ADJ
ejpam-6189	178	22	,	,	PUNCT
ejpam-6189	178	23	as	as	SCONJ
ejpam-6189	178	24	shown	show	VERB
ejpam-6189	178	25	in	in	ADP
ejpam-6189	178	26	the	the	DET
ejpam-6189	178	27	following	follow	VERB
ejpam-6189	178	28	example	example	NOUN
ejpam-6189	178	29	.	.	PUNCT
ejpam-6189	179	1	w.	w.	PROPN
ejpam-6189	179	2	nakkhasen	nakkhasen	PROPN
ejpam-6189	179	3	et	et	PROPN
ejpam-6189	179	4	al	al	PROPN
ejpam-6189	179	5	.	.	PUNCT
ejpam-6189	179	6	/	/	SYM
ejpam-6189	179	7	eur	eur	PROPN
ejpam-6189	179	8	.	.	PUNCT
ejpam-6189	180	1	j.	j.	PROPN
ejpam-6189	180	2	pure	pure	PROPN
ejpam-6189	180	3	appl	appl	PROPN
ejpam-6189	180	4	.	.	PROPN
ejpam-6189	180	5	math	math	PROPN
ejpam-6189	180	6	,	,	PUNCT
ejpam-6189	180	7	18	18	NUM
ejpam-6189	180	8	(	(	PUNCT
ejpam-6189	180	9	3	3	NUM
ejpam-6189	180	10	)	)	PUNCT
ejpam-6189	180	11	(	(	PUNCT
ejpam-6189	180	12	2025	2025	NUM
ejpam-6189	180	13	)	)	PUNCT
ejpam-6189	180	14	,	,	PUNCT
ejpam-6189	180	15	6189	6189	NUM
ejpam-6189	180	16	7	7	NUM
ejpam-6189	180	17	of	of	ADP
ejpam-6189	180	18	13	13	NUM
ejpam-6189	180	19	example	example	NOUN
ejpam-6189	180	20	4	4	NUM
ejpam-6189	180	21	.	.	PUNCT
ejpam-6189	181	1	in	in	ADP
ejpam-6189	181	2	example	example	NOUN
ejpam-6189	181	3	1	1	NUM
ejpam-6189	181	4	,	,	PUNCT
ejpam-6189	181	5	we	we	PRON
ejpam-6189	181	6	have	have	VERB
ejpam-6189	181	7	the	the	DET
ejpam-6189	181	8	fuzzy	fuzzy	ADJ
ejpam-6189	181	9	set	set	NOUN
ejpam-6189	181	10	ζ	ζ	NOUN
ejpam-6189	181	11	is	be	AUX
ejpam-6189	181	12	a	a	DET
ejpam-6189	181	13	fuzzy	fuzzy	ADJ
ejpam-6189	181	14	dot	dot	NOUN
ejpam-6189	181	15	bd	bd	NOUN
ejpam-6189	181	16	-	-	PUNCT
ejpam-6189	181	17	subalgebra	subalgebra	NOUN
ejpam-6189	181	18	of	of	ADP
ejpam-6189	181	19	x	x	PRON
ejpam-6189	181	20	,	,	PUNCT
ejpam-6189	181	21	but	but	CCONJ
ejpam-6189	181	22	the	the	DET
ejpam-6189	181	23	level	level	NOUN
ejpam-6189	181	24	subset	subset	VERB
ejpam-6189	181	25	ζ0.70	ζ0.70	PROPN
ejpam-6189	181	26	=	=	PUNCT
ejpam-6189	181	27	{	{	PUNCT
ejpam-6189	181	28	0	0	NUM
ejpam-6189	181	29	,	,	PUNCT
ejpam-6189	181	30	b	b	NOUN
ejpam-6189	181	31	,	,	PUNCT
ejpam-6189	181	32	c	c	NOUN
ejpam-6189	181	33	}	}	PUNCT
ejpam-6189	181	34	of	of	ADP
ejpam-6189	181	35	ζ	ζ	NOUN
ejpam-6189	181	36	is	be	AUX
ejpam-6189	181	37	not	not	PART
ejpam-6189	181	38	a	a	DET
ejpam-6189	181	39	bd	bd	NOUN
ejpam-6189	181	40	-	-	PUNCT
ejpam-6189	181	41	subalgebra	subalgebra	NOUN
ejpam-6189	181	42	of	of	ADP
ejpam-6189	181	43	x	x	PRON
ejpam-6189	181	44	,	,	PUNCT
ejpam-6189	181	45	since	since	SCONJ
ejpam-6189	181	46	0	0	NUM
ejpam-6189	181	47	∗	∗	NOUN
ejpam-6189	181	48	b	b	NOUN
ejpam-6189	181	49	=	=	SYM
ejpam-6189	181	50	a	a	DET
ejpam-6189	181	51	̸∈	̸∈	PROPN
ejpam-6189	181	52	ζ0.70	ζ0.70	PROPN
ejpam-6189	181	53	.	.	PUNCT
ejpam-6189	182	1	let	let	VERB
ejpam-6189	182	2	x	x	PRON
ejpam-6189	182	3	:	:	PUNCT
ejpam-6189	182	4	=	=	SYM
ejpam-6189	182	5	(	(	PUNCT
ejpam-6189	182	6	x	x	X
ejpam-6189	182	7	,	,	PUNCT
ejpam-6189	182	8	∗	∗	NOUN
ejpam-6189	182	9	,	,	PUNCT
ejpam-6189	182	10	0x	0x	NOUN
ejpam-6189	182	11	)	)	PUNCT
ejpam-6189	182	12	and	and	CCONJ
ejpam-6189	182	13	y	y	NOUN
ejpam-6189	182	14	:	:	PUNCT
ejpam-6189	183	1	=	=	SYM
ejpam-6189	183	2	(	(	PUNCT
ejpam-6189	183	3	y	y	PROPN
ejpam-6189	183	4	,	,	PUNCT
ejpam-6189	183	5	◦	◦	NOUN
ejpam-6189	183	6	,	,	PUNCT
ejpam-6189	183	7	0y	0y	NUM
ejpam-6189	183	8	)	)	PUNCT
ejpam-6189	183	9	be	be	AUX
ejpam-6189	183	10	bd	bd	PROPN
ejpam-6189	183	11	-	-	PUNCT
ejpam-6189	183	12	algebras	algebras	X
ejpam-6189	183	13	.	.	PUNCT
ejpam-6189	184	1	let	let	VERB
ejpam-6189	184	2	ω	ω	NOUN
ejpam-6189	184	3	:	:	PUNCT
ejpam-6189	184	4	x	x	SYM
ejpam-6189	184	5	→	→	SYM
ejpam-6189	184	6	y	y	X
ejpam-6189	184	7	be	be	AUX
ejpam-6189	184	8	a	a	DET
ejpam-6189	184	9	mapping	mapping	NOUN
ejpam-6189	184	10	of	of	ADP
ejpam-6189	184	11	bd	bd	PROPN
ejpam-6189	184	12	-	-	PUNCT
ejpam-6189	184	13	algebras	algebras	ADJ
ejpam-6189	184	14	x	x	X
ejpam-6189	184	15	and	and	CCONJ
ejpam-6189	184	16	y	y	PROPN
ejpam-6189	184	17	,	,	PUNCT
ejpam-6189	184	18	and	and	CCONJ
ejpam-6189	184	19	let	let	VERB
ejpam-6189	184	20	ζ	ζ	NOUN
ejpam-6189	184	21	be	be	AUX
ejpam-6189	184	22	a	a	DET
ejpam-6189	184	23	fuzzy	fuzzy	ADJ
ejpam-6189	184	24	set	set	NOUN
ejpam-6189	184	25	of	of	ADP
ejpam-6189	184	26	y.	y.	NOUN
ejpam-6189	184	27	the	the	DET
ejpam-6189	184	28	fuzzy	fuzzy	ADJ
ejpam-6189	184	29	set	set	VERB
ejpam-6189	184	30	ζω	ζω	NOUN
ejpam-6189	184	31	of	of	ADP
ejpam-6189	184	32	x	x	PUNCT
ejpam-6189	184	33	is	be	AUX
ejpam-6189	184	34	defined	define	VERB
ejpam-6189	184	35	by	by	ADP
ejpam-6189	184	36	ζω(x	ζω(x	NOUN
ejpam-6189	184	37	)	)	PUNCT
ejpam-6189	184	38	=	=	SYM
ejpam-6189	184	39	ζ(ω(x	ζ(ω(x	NOUN
ejpam-6189	184	40	)	)	PUNCT
ejpam-6189	184	41	)	)	PUNCT
ejpam-6189	184	42	for	for	ADP
ejpam-6189	184	43	all	all	DET
ejpam-6189	184	44	x	x	SYM
ejpam-6189	184	45	∈	∈	ADJ
ejpam-6189	184	46	x.	x.	NOUN
ejpam-6189	184	47	a	a	DET
ejpam-6189	184	48	function	function	NOUN
ejpam-6189	184	49	ω	ω	NOUN
ejpam-6189	184	50	:	:	PUNCT
ejpam-6189	184	51	x	x	X
ejpam-6189	184	52	→	→	SYM
ejpam-6189	184	53	y	y	PROPN
ejpam-6189	184	54	is	be	AUX
ejpam-6189	184	55	called	call	VERB
ejpam-6189	184	56	a	a	DET
ejpam-6189	184	57	homomorphism	homomorphism	NOUN
ejpam-6189	184	58	if	if	SCONJ
ejpam-6189	184	59	ω(0x	ω(0x	NOUN
ejpam-6189	184	60	)	)	PUNCT
ejpam-6189	184	61	=	=	SYM
ejpam-6189	184	62	0y	0y	NOUN
ejpam-6189	184	63	and	and	CCONJ
ejpam-6189	184	64	ω(x	ω(x	X
ejpam-6189	184	65	∗	∗	NOUN
ejpam-6189	184	66	y	y	NOUN
ejpam-6189	184	67	)	)	PUNCT
ejpam-6189	184	68	=	=	PUNCT
ejpam-6189	184	69	ω(x	ω(x	NOUN
ejpam-6189	184	70	)	)	PUNCT
ejpam-6189	184	71	◦	◦	NOUN
ejpam-6189	184	72	ω(y	ω(y	NUM
ejpam-6189	184	73	)	)	PUNCT
ejpam-6189	184	74	for	for	ADP
ejpam-6189	184	75	all	all	DET
ejpam-6189	184	76	x	x	NOUN
ejpam-6189	184	77	,	,	PUNCT
ejpam-6189	184	78	y	y	PROPN
ejpam-6189	184	79	∈	∈	PROPN
ejpam-6189	184	80	x	x	X
ejpam-6189	184	81	,	,	PUNCT
ejpam-6189	184	82	and	and	CCONJ
ejpam-6189	184	83	a	a	DET
ejpam-6189	184	84	homomorphism	homomorphism	PROPN
ejpam-6189	184	85	ω	ω	PROPN
ejpam-6189	184	86	is	be	AUX
ejpam-6189	184	87	called	call	VERB
ejpam-6189	184	88	an	an	DET
ejpam-6189	184	89	epimorphism	epimorphism	NOUN
ejpam-6189	184	90	if	if	SCONJ
ejpam-6189	184	91	ω	ω	PROPN
ejpam-6189	184	92	is	be	AUX
ejpam-6189	184	93	onto	onto	ADP
ejpam-6189	184	94	.	.	PUNCT
ejpam-6189	185	1	theorem	theorem	ADJ
ejpam-6189	185	2	4	4	NUM
ejpam-6189	185	3	.	.	PUNCT
ejpam-6189	186	1	let	let	VERB
ejpam-6189	186	2	ω	ω	NOUN
ejpam-6189	186	3	:	:	PUNCT
ejpam-6189	186	4	x	x	SYM
ejpam-6189	186	5	→	→	SYM
ejpam-6189	186	6	y	y	X
ejpam-6189	186	7	be	be	AUX
ejpam-6189	186	8	a	a	DET
ejpam-6189	186	9	homomorphism	homomorphism	NOUN
ejpam-6189	186	10	of	of	ADP
ejpam-6189	186	11	bd	bd	PROPN
ejpam-6189	186	12	-	-	PUNCT
ejpam-6189	186	13	algebras	algebras	ADV
ejpam-6189	186	14	x	x	X
ejpam-6189	186	15	:	:	PUNCT
ejpam-6189	186	16	=	=	SYM
ejpam-6189	186	17	(	(	PUNCT
ejpam-6189	186	18	x	x	X
ejpam-6189	186	19	,	,	PUNCT
ejpam-6189	186	20	∗	∗	NOUN
ejpam-6189	186	21	,	,	PUNCT
ejpam-6189	186	22	0x	0x	NOUN
ejpam-6189	186	23	)	)	PUNCT
ejpam-6189	186	24	and	and	CCONJ
ejpam-6189	186	25	y	y	NOUN
ejpam-6189	186	26	:	:	PUNCT
ejpam-6189	186	27	=	=	SYM
ejpam-6189	186	28	(	(	PUNCT
ejpam-6189	186	29	y	y	PROPN
ejpam-6189	186	30	,	,	PUNCT
ejpam-6189	186	31	◦	◦	NOUN
ejpam-6189	186	32	,	,	PUNCT
ejpam-6189	186	33	0y	0y	NUM
ejpam-6189	186	34	)	)	PUNCT
ejpam-6189	186	35	.	.	PUNCT
ejpam-6189	187	1	if	if	SCONJ
ejpam-6189	187	2	ζ	ζ	NOUN
ejpam-6189	187	3	is	be	AUX
ejpam-6189	187	4	a	a	DET
ejpam-6189	187	5	fuzzy	fuzzy	ADJ
ejpam-6189	187	6	dot	dot	NOUN
ejpam-6189	187	7	bd	bd	NOUN
ejpam-6189	187	8	-	-	PUNCT
ejpam-6189	187	9	subalgebra	subalgebra	NOUN
ejpam-6189	187	10	of	of	ADP
ejpam-6189	187	11	y	y	PROPN
ejpam-6189	187	12	,	,	PUNCT
ejpam-6189	187	13	then	then	ADV
ejpam-6189	187	14	ζω	ζω	NOUN
ejpam-6189	187	15	is	be	AUX
ejpam-6189	187	16	a	a	DET
ejpam-6189	187	17	fuzzy	fuzzy	ADJ
ejpam-6189	187	18	dot	dot	NOUN
ejpam-6189	187	19	bd	bd	NOUN
ejpam-6189	187	20	-	-	PUNCT
ejpam-6189	187	21	subalgebra	subalgebra	NOUN
ejpam-6189	187	22	of	of	ADP
ejpam-6189	187	23	x.	x.	NOUN
ejpam-6189	187	24	proof	proof	PROPN
ejpam-6189	187	25	.	.	PUNCT
ejpam-6189	188	1	assume	assume	VERB
ejpam-6189	188	2	that	that	SCONJ
ejpam-6189	188	3	ζ	ζ	NOUN
ejpam-6189	188	4	is	be	AUX
ejpam-6189	188	5	a	a	DET
ejpam-6189	188	6	fuzzy	fuzzy	ADJ
ejpam-6189	188	7	dot	dot	NOUN
ejpam-6189	188	8	bd	bd	NOUN
ejpam-6189	188	9	-	-	PUNCT
ejpam-6189	188	10	subalgebra	subalgebra	NOUN
ejpam-6189	188	11	of	of	ADP
ejpam-6189	188	12	y.	y.	PROPN
ejpam-6189	188	13	let	let	VERB
ejpam-6189	188	14	x	x	PRON
ejpam-6189	188	15	,	,	PUNCT
ejpam-6189	188	16	y	y	PROPN
ejpam-6189	188	17	∈	∈	PROPN
ejpam-6189	188	18	x.	x.	NOUN
ejpam-6189	189	1	then	then	ADV
ejpam-6189	189	2	we	we	PRON
ejpam-6189	189	3	have	have	VERB
ejpam-6189	189	4	ζω(0x	ζω(0x	NUM
ejpam-6189	189	5	)	)	PUNCT
ejpam-6189	189	6	=	=	SYM
ejpam-6189	189	7	ζ(ω(0x	ζ(ω(0x	NUM
ejpam-6189	189	8	)	)	PUNCT
ejpam-6189	189	9	)	)	PUNCT
ejpam-6189	190	1	=	=	SYM
ejpam-6189	190	2	ζ(0y	ζ(0y	NUM
ejpam-6189	190	3	)	)	PUNCT
ejpam-6189	190	4	≥	≥	NOUN
ejpam-6189	190	5	ζ(ω(x	ζ(ω(x	NOUN
ejpam-6189	190	6	)	)	PUNCT
ejpam-6189	190	7	)	)	PUNCT
ejpam-6189	191	1	=	=	PRON
ejpam-6189	191	2	ζω(x	ζω(x	X
ejpam-6189	191	3	)	)	PUNCT
ejpam-6189	191	4	and	and	CCONJ
ejpam-6189	191	5	ζω(x	ζω(x	X
ejpam-6189	191	6	∗	∗	X
ejpam-6189	191	7	y	y	NOUN
ejpam-6189	191	8	)	)	PUNCT
ejpam-6189	191	9	=	=	SYM
ejpam-6189	192	1	ζ(ω(x	ζ(ω(x	PROPN
ejpam-6189	192	2	∗	∗	PROPN
ejpam-6189	192	3	y	y	NOUN
ejpam-6189	192	4	)	)	PUNCT
ejpam-6189	192	5	)	)	PUNCT
ejpam-6189	193	1	=	=	SYM
ejpam-6189	193	2	ζ(ω(x	ζ(ω(x	NOUN
ejpam-6189	193	3	)	)	PUNCT
ejpam-6189	193	4	◦	◦	NOUN
ejpam-6189	193	5	ω(y	ω(y	PROPN
ejpam-6189	193	6	)	)	PUNCT
ejpam-6189	193	7	)	)	PUNCT
ejpam-6189	193	8	≥	≥	NOUN
ejpam-6189	193	9	ζ(ω(x	ζ(ω(x	NOUN
ejpam-6189	193	10	)	)	PUNCT
ejpam-6189	193	11	)	)	PUNCT
ejpam-6189	193	12	·	·	PUNCT
ejpam-6189	194	1	ζ(ω(y	ζ(ω(y	PROPN
ejpam-6189	194	2	)	)	PUNCT
ejpam-6189	194	3	)	)	PUNCT
ejpam-6189	195	1	=	=	SYM
ejpam-6189	195	2	ζω(x	ζω(x	X
ejpam-6189	195	3	)	)	PUNCT
ejpam-6189	195	4	·	·	PUNCT
ejpam-6189	195	5	ζω(y	ζω(y	NUM
ejpam-6189	195	6	)	)	PUNCT
ejpam-6189	195	7	.	.	PUNCT
ejpam-6189	196	1	thus	thus	ADV
ejpam-6189	196	2	,	,	PUNCT
ejpam-6189	196	3	ζω	ζω	NOUN
ejpam-6189	196	4	is	be	AUX
ejpam-6189	196	5	a	a	DET
ejpam-6189	196	6	fuzzy	fuzzy	ADJ
ejpam-6189	196	7	dot	dot	NOUN
ejpam-6189	196	8	bd	bd	NOUN
ejpam-6189	196	9	-	-	PUNCT
ejpam-6189	196	10	subalgebra	subalgebra	NOUN
ejpam-6189	196	11	of	of	ADP
ejpam-6189	196	12	x.	x.	NOUN
ejpam-6189	196	13	by	by	ADP
ejpam-6189	196	14	adding	add	VERB
ejpam-6189	196	15	specific	specific	ADJ
ejpam-6189	196	16	properties	property	NOUN
ejpam-6189	196	17	into	into	ADP
ejpam-6189	196	18	theorem	theorem	ADJ
ejpam-6189	196	19	4	4	NUM
ejpam-6189	196	20	,	,	PUNCT
ejpam-6189	196	21	the	the	DET
ejpam-6189	196	22	converse	converse	NOUN
ejpam-6189	196	23	of	of	ADP
ejpam-6189	196	24	this	this	DET
ejpam-6189	196	25	theorem	theorem	NOUN
ejpam-6189	196	26	will	will	AUX
ejpam-6189	196	27	ultimately	ultimately	ADV
ejpam-6189	196	28	hold	hold	VERB
ejpam-6189	196	29	true	true	ADJ
ejpam-6189	196	30	as	as	ADV
ejpam-6189	196	31	delineated	delineated	ADJ
ejpam-6189	196	32	below	below	ADV
ejpam-6189	196	33	.	.	PUNCT
ejpam-6189	197	1	theorem	theorem	NOUN
ejpam-6189	197	2	5	5	NUM
ejpam-6189	197	3	.	.	PUNCT
ejpam-6189	198	1	let	let	VERB
ejpam-6189	198	2	ω	ω	NOUN
ejpam-6189	198	3	:	:	PUNCT
ejpam-6189	198	4	x	x	SYM
ejpam-6189	198	5	→	→	SYM
ejpam-6189	198	6	y	y	X
ejpam-6189	198	7	be	be	AUX
ejpam-6189	198	8	an	an	DET
ejpam-6189	198	9	epimorphism	epimorphism	NOUN
ejpam-6189	198	10	of	of	ADP
ejpam-6189	198	11	bd	bd	PROPN
ejpam-6189	198	12	-	-	PUNCT
ejpam-6189	198	13	algebras	algebras	ADV
ejpam-6189	198	14	x	x	X
ejpam-6189	198	15	:	:	PUNCT
ejpam-6189	198	16	=	=	SYM
ejpam-6189	198	17	(	(	PUNCT
ejpam-6189	198	18	x	x	X
ejpam-6189	198	19	,	,	PUNCT
ejpam-6189	198	20	∗	∗	NOUN
ejpam-6189	198	21	,	,	PUNCT
ejpam-6189	198	22	0x	0x	NOUN
ejpam-6189	198	23	)	)	PUNCT
ejpam-6189	198	24	and	and	CCONJ
ejpam-6189	198	25	y	y	NOUN
ejpam-6189	198	26	:	:	PUNCT
ejpam-6189	198	27	=	=	SYM
ejpam-6189	198	28	(	(	PUNCT
ejpam-6189	198	29	y	y	PROPN
ejpam-6189	198	30	,	,	PUNCT
ejpam-6189	198	31	◦	◦	NOUN
ejpam-6189	198	32	,	,	PUNCT
ejpam-6189	198	33	0y	0y	NUM
ejpam-6189	198	34	)	)	PUNCT
ejpam-6189	198	35	.	.	PUNCT
ejpam-6189	199	1	if	if	SCONJ
ejpam-6189	199	2	ζω	ζω	NOUN
ejpam-6189	199	3	is	be	AUX
ejpam-6189	199	4	a	a	DET
ejpam-6189	199	5	fuzzy	fuzzy	ADJ
ejpam-6189	199	6	dot	dot	NOUN
ejpam-6189	199	7	bd	bd	NOUN
ejpam-6189	199	8	-	-	PUNCT
ejpam-6189	199	9	subalgebra	subalgebra	NOUN
ejpam-6189	199	10	of	of	ADP
ejpam-6189	199	11	x	x	PRON
ejpam-6189	199	12	,	,	PUNCT
ejpam-6189	199	13	then	then	ADV
ejpam-6189	199	14	ζ	ζ	NOUN
ejpam-6189	199	15	is	be	AUX
ejpam-6189	199	16	a	a	DET
ejpam-6189	199	17	fuzzy	fuzzy	ADJ
ejpam-6189	199	18	dot	dot	NOUN
ejpam-6189	199	19	bdsubalgebra	bdsubalgebra	NOUN
ejpam-6189	199	20	of	of	ADP
ejpam-6189	199	21	y.	y.	PROPN
ejpam-6189	199	22	proof	proof	PROPN
ejpam-6189	199	23	.	.	PUNCT
ejpam-6189	200	1	assume	assume	VERB
ejpam-6189	200	2	that	that	SCONJ
ejpam-6189	200	3	ζω	ζω	NOUN
ejpam-6189	200	4	is	be	AUX
ejpam-6189	200	5	a	a	DET
ejpam-6189	200	6	fuzzy	fuzzy	ADJ
ejpam-6189	200	7	dot	dot	NOUN
ejpam-6189	200	8	bd	bd	NOUN
ejpam-6189	200	9	-	-	PUNCT
ejpam-6189	200	10	subalgebra	subalgebra	NOUN
ejpam-6189	200	11	of	of	ADP
ejpam-6189	200	12	x.	x.	NOUN
ejpam-6189	200	13	let	let	VERB
ejpam-6189	200	14	a	a	DET
ejpam-6189	200	15	,	,	PUNCT
ejpam-6189	200	16	b	b	PROPN
ejpam-6189	200	17	∈	∈	PROPN
ejpam-6189	200	18	y	y	PROPN
ejpam-6189	200	19	.	.	PUNCT
ejpam-6189	201	1	then	then	ADV
ejpam-6189	201	2	there	there	PRON
ejpam-6189	201	3	exist	exist	VERB
ejpam-6189	201	4	x	x	NOUN
ejpam-6189	201	5	,	,	PUNCT
ejpam-6189	201	6	y	y	PROPN
ejpam-6189	201	7	∈	∈	PROPN
ejpam-6189	201	8	x	x	PUNCT
ejpam-6189	201	9	such	such	ADJ
ejpam-6189	201	10	that	that	SCONJ
ejpam-6189	201	11	ω(x	ω(x	NOUN
ejpam-6189	201	12	)	)	PUNCT
ejpam-6189	201	13	=	=	SYM
ejpam-6189	201	14	a	a	PRON
ejpam-6189	201	15	and	and	CCONJ
ejpam-6189	201	16	ω(y	ω(y	NUM
ejpam-6189	201	17	)	)	PUNCT
ejpam-6189	201	18	=	=	SYM
ejpam-6189	201	19	b.	b.	PROPN
ejpam-6189	202	1	thus	thus	ADV
ejpam-6189	202	2	,	,	PUNCT
ejpam-6189	202	3	we	we	PRON
ejpam-6189	202	4	have	have	VERB
ejpam-6189	202	5	ζ(0y	ζ(0y	NUM
ejpam-6189	202	6	)	)	PUNCT
ejpam-6189	202	7	=	=	SYM
ejpam-6189	202	8	ζ(ω(0x	ζ(ω(0x	NUM
ejpam-6189	202	9	)	)	PUNCT
ejpam-6189	202	10	)	)	PUNCT
ejpam-6189	203	1	=	=	SYM
ejpam-6189	203	2	ζω(0x	ζω(0x	X
ejpam-6189	203	3	)	)	PUNCT
ejpam-6189	203	4	≥	≥	NOUN
ejpam-6189	203	5	ζω(x	ζω(x	X
ejpam-6189	203	6	)	)	PUNCT
ejpam-6189	203	7	=	=	SYM
ejpam-6189	203	8	ζ(ω(x	ζ(ω(x	NOUN
ejpam-6189	203	9	)	)	PUNCT
ejpam-6189	203	10	)	)	PUNCT
ejpam-6189	204	1	=	=	SYM
ejpam-6189	204	2	ζ(a	ζ(a	X
ejpam-6189	204	3	)	)	PUNCT
ejpam-6189	204	4	and	and	CCONJ
ejpam-6189	204	5	ζ(a	ζ(a	PROPN
ejpam-6189	204	6	◦	◦	NOUN
ejpam-6189	204	7	b	b	NOUN
ejpam-6189	204	8	)	)	PUNCT
ejpam-6189	204	9	=	=	SYM
ejpam-6189	204	10	ζ(ω(x)	ζ(ω(x)	NUM
ejpam-6189	204	11	◦	◦	NOUN
ejpam-6189	204	12	ω(y	ω(y	NOUN
ejpam-6189	204	13	)	)	PUNCT
ejpam-6189	204	14	)	)	PUNCT
ejpam-6189	204	15	)	)	PUNCT
ejpam-6189	205	1	=	=	SYM
ejpam-6189	205	2	ζ(ω(x∗y	ζ(ω(x∗y	X
ejpam-6189	205	3	)	)	PUNCT
ejpam-6189	205	4	)	)	PUNCT
ejpam-6189	205	5	=	=	SYM
ejpam-6189	205	6	ζω(x∗y	ζω(x∗y	X
ejpam-6189	205	7	)	)	PUNCT
ejpam-6189	205	8	≥	≥	NOUN
ejpam-6189	205	9	ζω(x)·ζω(y	ζω(x)·ζω(y	PROPN
ejpam-6189	205	10	)	)	PUNCT
ejpam-6189	205	11	=	=	SYM
ejpam-6189	205	12	ζ(ω(x))·ζ(ω(y	ζ(ω(x))·ζ(ω(y	ADJ
ejpam-6189	205	13	)	)	PUNCT
ejpam-6189	205	14	)	)	PUNCT
ejpam-6189	206	1	=	=	SYM
ejpam-6189	206	2	ζ(a)·ζ(b	ζ(a)·ζ(b	PROPN
ejpam-6189	206	3	)	)	PUNCT
ejpam-6189	206	4	.	.	PUNCT
ejpam-6189	207	1	therefore	therefore	ADV
ejpam-6189	207	2	,	,	PUNCT
ejpam-6189	207	3	ζ	ζ	NOUN
ejpam-6189	207	4	is	be	AUX
ejpam-6189	207	5	a	a	DET
ejpam-6189	207	6	fuzzy	fuzzy	ADJ
ejpam-6189	207	7	dot	dot	NOUN
ejpam-6189	207	8	bd	bd	NOUN
ejpam-6189	207	9	-	-	PUNCT
ejpam-6189	207	10	subalgebra	subalgebra	NOUN
ejpam-6189	207	11	of	of	ADP
ejpam-6189	207	12	y.	y.	PROPN
ejpam-6189	207	13	4	4	NUM
ejpam-6189	207	14	.	.	PUNCT
ejpam-6189	207	15	strongest	strong	ADJ
ejpam-6189	207	16	fuzzy	fuzzy	ADJ
ejpam-6189	207	17	dot	dot	NOUN
ejpam-6189	207	18	bd	bd	NOUN
ejpam-6189	207	19	-	-	PUNCT
ejpam-6189	207	20	subalgebras	subalgebras	PROPN
ejpam-6189	207	21	on	on	ADP
ejpam-6189	207	22	bd	bd	PROPN
ejpam-6189	207	23	-	-	PUNCT
ejpam-6189	207	24	algebras	algebras	PROPN
ejpam-6189	207	25	in	in	ADP
ejpam-6189	207	26	this	this	DET
ejpam-6189	207	27	section	section	NOUN
ejpam-6189	207	28	,	,	PUNCT
ejpam-6189	207	29	we	we	PRON
ejpam-6189	207	30	present	present	VERB
ejpam-6189	207	31	some	some	DET
ejpam-6189	207	32	properties	property	NOUN
ejpam-6189	207	33	of	of	ADP
ejpam-6189	207	34	the	the	DET
ejpam-6189	207	35	cartesian	cartesian	ADJ
ejpam-6189	207	36	product	product	NOUN
ejpam-6189	207	37	of	of	ADP
ejpam-6189	207	38	fuzzy	fuzzy	ADJ
ejpam-6189	207	39	dot	dot	NOUN
ejpam-6189	207	40	bdsubalgebras	bdsubalgebra	NOUN
ejpam-6189	207	41	of	of	ADP
ejpam-6189	207	42	bd	bd	PROPN
ejpam-6189	207	43	-	-	PUNCT
ejpam-6189	207	44	algebras	algebras	PROPN
ejpam-6189	207	45	.	.	PUNCT
ejpam-6189	208	1	after	after	ADP
ejpam-6189	208	2	that	that	PRON
ejpam-6189	208	3	,	,	PUNCT
ejpam-6189	208	4	we	we	PRON
ejpam-6189	208	5	introduce	introduce	VERB
ejpam-6189	208	6	the	the	DET
ejpam-6189	208	7	concept	concept	NOUN
ejpam-6189	208	8	of	of	ADP
ejpam-6189	208	9	strongest	strong	ADJ
ejpam-6189	208	10	fuzzy	fuzzy	ADJ
ejpam-6189	208	11	dot	dot	NOUN
ejpam-6189	208	12	bd	bd	NOUN
ejpam-6189	208	13	-	-	PUNCT
ejpam-6189	208	14	subalgebras	subalgebras	PROPN
ejpam-6189	208	15	on	on	ADP
ejpam-6189	208	16	bd	bd	PROPN
ejpam-6189	208	17	-	-	PUNCT
ejpam-6189	208	18	algebras	algebras	PROPN
ejpam-6189	208	19	and	and	CCONJ
ejpam-6189	208	20	investigate	investigate	VERB
ejpam-6189	208	21	some	some	PRON
ejpam-6189	208	22	of	of	ADP
ejpam-6189	208	23	its	its	PRON
ejpam-6189	208	24	properties	property	NOUN
ejpam-6189	208	25	and	and	CCONJ
ejpam-6189	208	26	the	the	DET
ejpam-6189	208	27	relationships	relationship	NOUN
ejpam-6189	208	28	between	between	ADP
ejpam-6189	208	29	strongest	strong	ADJ
ejpam-6189	208	30	fuzzy	fuzzy	ADJ
ejpam-6189	208	31	dot	dot	NOUN
ejpam-6189	208	32	bd	bd	NOUN
ejpam-6189	208	33	-	-	PUNCT
ejpam-6189	208	34	subalgebras	subalgebras	PROPN
ejpam-6189	208	35	and	and	CCONJ
ejpam-6189	208	36	fuzzy	fuzzy	ADJ
ejpam-6189	208	37	dot	dot	NOUN
ejpam-6189	208	38	bd	bd	NOUN
ejpam-6189	208	39	-	-	PUNCT
ejpam-6189	208	40	subalgebras	subalgebras	PROPN
ejpam-6189	208	41	in	in	ADP
ejpam-6189	208	42	bd	bd	PROPN
ejpam-6189	208	43	-	-	PUNCT
ejpam-6189	208	44	algebras	algebras	PROPN
ejpam-6189	208	45	.	.	PUNCT
ejpam-6189	209	1	w.	w.	PROPN
ejpam-6189	209	2	nakkhasen	nakkhasen	PROPN
ejpam-6189	209	3	et	et	PROPN
ejpam-6189	209	4	al	al	PROPN
ejpam-6189	209	5	.	.	PUNCT
ejpam-6189	209	6	/	/	SYM
ejpam-6189	209	7	eur	eur	PROPN
ejpam-6189	209	8	.	.	PUNCT
ejpam-6189	210	1	j.	j.	PROPN
ejpam-6189	210	2	pure	pure	PROPN
ejpam-6189	210	3	appl	appl	PROPN
ejpam-6189	210	4	.	.	PROPN
ejpam-6189	210	5	math	math	PROPN
ejpam-6189	210	6	,	,	PUNCT
ejpam-6189	210	7	18	18	NUM
ejpam-6189	210	8	(	(	PUNCT
ejpam-6189	210	9	3	3	NUM
ejpam-6189	210	10	)	)	PUNCT
ejpam-6189	210	11	(	(	PUNCT
ejpam-6189	210	12	2025	2025	NUM
ejpam-6189	210	13	)	)	PUNCT
ejpam-6189	210	14	,	,	PUNCT
ejpam-6189	210	15	6189	6189	NUM
ejpam-6189	210	16	8	8	NUM
ejpam-6189	210	17	of	of	ADP
ejpam-6189	210	18	13	13	NUM
ejpam-6189	210	19	finally	finally	ADV
ejpam-6189	211	1	,	,	PUNCT
ejpam-6189	211	2	we	we	PRON
ejpam-6189	211	3	characterize	characterize	VERB
ejpam-6189	211	4	the	the	DET
ejpam-6189	211	5	strongest	strong	ADJ
ejpam-6189	211	6	fuzzy	fuzzy	ADJ
ejpam-6189	211	7	dot	dot	NOUN
ejpam-6189	211	8	bd	bd	NOUN
ejpam-6189	211	9	-	-	PUNCT
ejpam-6189	211	10	subalgebras	subalgebras	PROPN
ejpam-6189	211	11	by	by	ADP
ejpam-6189	211	12	bd	bd	PROPN
ejpam-6189	211	13	-	-	PUNCT
ejpam-6189	211	14	subalgebras	subalgebras	PROPN
ejpam-6189	211	15	of	of	ADP
ejpam-6189	211	16	bdalgebras	bdalgebras	PROPN
ejpam-6189	211	17	.	.	PUNCT
ejpam-6189	212	1	let	let	VERB
ejpam-6189	212	2	x	x	PRON
ejpam-6189	212	3	:	:	PUNCT
ejpam-6189	212	4	=	=	SYM
ejpam-6189	212	5	(	(	PUNCT
ejpam-6189	212	6	x	x	X
ejpam-6189	212	7	,	,	PUNCT
ejpam-6189	212	8	∗	∗	NOUN
ejpam-6189	212	9	,	,	PUNCT
ejpam-6189	212	10	0x	0x	NOUN
ejpam-6189	212	11	)	)	PUNCT
ejpam-6189	212	12	and	and	CCONJ
ejpam-6189	212	13	y	y	NOUN
ejpam-6189	212	14	:	:	PUNCT
ejpam-6189	213	1	=	=	SYM
ejpam-6189	213	2	(	(	PUNCT
ejpam-6189	213	3	y	y	PROPN
ejpam-6189	213	4	,	,	PUNCT
ejpam-6189	213	5	◦	◦	NOUN
ejpam-6189	213	6	,	,	PUNCT
ejpam-6189	213	7	0y	0y	NUM
ejpam-6189	213	8	)	)	PUNCT
ejpam-6189	213	9	be	be	AUX
ejpam-6189	213	10	bd	bd	PROPN
ejpam-6189	213	11	-	-	PUNCT
ejpam-6189	213	12	algebras	algebras	X
ejpam-6189	213	13	.	.	PUNCT
ejpam-6189	214	1	the	the	DET
ejpam-6189	214	2	mapping	mapping	NOUN
ejpam-6189	214	3	⊛	⊛	NUM
ejpam-6189	214	4	:	:	PUNCT
ejpam-6189	214	5	(	(	PUNCT
ejpam-6189	214	6	x	x	SYM
ejpam-6189	214	7	×	×	PROPN
ejpam-6189	214	8	y	y	PROPN
ejpam-6189	214	9	)	)	PUNCT
ejpam-6189	214	10	×	×	NOUN
ejpam-6189	214	11	(	(	PUNCT
ejpam-6189	214	12	x	x	SYM
ejpam-6189	214	13	×	×	PROPN
ejpam-6189	214	14	y	y	PROPN
ejpam-6189	214	15	)	)	PUNCT
ejpam-6189	214	16	→	→	PUNCT
ejpam-6189	214	17	x	x	SYM
ejpam-6189	214	18	×	×	NOUN
ejpam-6189	214	19	y	y	PROPN
ejpam-6189	214	20	is	be	AUX
ejpam-6189	214	21	defined	define	VERB
ejpam-6189	214	22	by	by	ADP
ejpam-6189	214	23	(	(	PUNCT
ejpam-6189	214	24	x1	x1	PROPN
ejpam-6189	214	25	,	,	PUNCT
ejpam-6189	214	26	y1)⊛	y1)⊛	PROPN
ejpam-6189	215	1	(	(	PUNCT
ejpam-6189	215	2	x2	x2	PROPN
ejpam-6189	215	3	,	,	PUNCT
ejpam-6189	215	4	y2	y2	NOUN
ejpam-6189	215	5	)	)	PUNCT
ejpam-6189	215	6	=	=	PRON
ejpam-6189	215	7	(	(	PUNCT
ejpam-6189	215	8	x1	x1	PROPN
ejpam-6189	215	9	∗	∗	NOUN
ejpam-6189	215	10	x2	x2	PROPN
ejpam-6189	215	11	,	,	PUNCT
ejpam-6189	215	12	y1	y1	NOUN
ejpam-6189	215	13	◦	◦	NOUN
ejpam-6189	215	14	y2	y2	NOUN
ejpam-6189	215	15	)	)	PUNCT
ejpam-6189	215	16	for	for	ADP
ejpam-6189	215	17	all	all	PRON
ejpam-6189	215	18	(	(	PUNCT
ejpam-6189	215	19	x1	x1	PROPN
ejpam-6189	215	20	,	,	PUNCT
ejpam-6189	215	21	y1	y1	PROPN
ejpam-6189	215	22	)	)	PUNCT
ejpam-6189	215	23	,	,	PUNCT
ejpam-6189	215	24	(	(	PUNCT
ejpam-6189	215	25	x2	x2	PROPN
ejpam-6189	215	26	,	,	PUNCT
ejpam-6189	215	27	y2	y2	NOUN
ejpam-6189	215	28	)	)	PUNCT
ejpam-6189	215	29	∈	∈	PROPN
ejpam-6189	216	1	x	x	PUNCT
ejpam-6189	216	2	×	×	NOUN
ejpam-6189	216	3	y	y	PROPN
ejpam-6189	216	4	.	.	PUNCT
ejpam-6189	217	1	we	we	PRON
ejpam-6189	217	2	have	have	VERB
ejpam-6189	217	3	that	that	PRON
ejpam-6189	217	4	x	x	SYM
ejpam-6189	217	5	×	×	NOUN
ejpam-6189	217	6	y	y	NOUN
ejpam-6189	217	7	:	:	PUNCT
ejpam-6189	217	8	=	=	SYM
ejpam-6189	217	9	(	(	PUNCT
ejpam-6189	217	10	x	x	SYM
ejpam-6189	217	11	×	×	NOUN
ejpam-6189	217	12	y,⊛	y,⊛	PROPN
ejpam-6189	217	13	,	,	PUNCT
ejpam-6189	217	14	(	(	PUNCT
ejpam-6189	217	15	0x	0x	X
ejpam-6189	217	16	,	,	PUNCT
ejpam-6189	217	17	0y	0y	NUM
ejpam-6189	217	18	)	)	PUNCT
ejpam-6189	217	19	)	)	PUNCT
ejpam-6189	217	20	is	be	AUX
ejpam-6189	217	21	a	a	DET
ejpam-6189	217	22	bdalgebra	bdalgebra	NOUN
ejpam-6189	217	23	.	.	PUNCT
ejpam-6189	218	1	in	in	ADP
ejpam-6189	218	2	particular	particular	ADJ
ejpam-6189	218	3	,	,	PUNCT
ejpam-6189	218	4	if	if	SCONJ
ejpam-6189	218	5	y	y	PROPN
ejpam-6189	218	6	=	=	SYM
ejpam-6189	218	7	x	x	X
ejpam-6189	218	8	,	,	PUNCT
ejpam-6189	218	9	we	we	PRON
ejpam-6189	218	10	have	have	VERB
ejpam-6189	218	11	x×x	x×x	PROPN
ejpam-6189	218	12	:	:	PUNCT
ejpam-6189	218	13	=	=	SYM
ejpam-6189	218	14	(	(	PUNCT
ejpam-6189	218	15	x	x	SYM
ejpam-6189	218	16	×x,⊛	×x,⊛	PROPN
ejpam-6189	218	17	,	,	PUNCT
ejpam-6189	218	18	(	(	PUNCT
ejpam-6189	218	19	0x	0x	NOUN
ejpam-6189	218	20	,	,	PUNCT
ejpam-6189	218	21	0x	0x	NOUN
ejpam-6189	218	22	)	)	PUNCT
ejpam-6189	218	23	)	)	PUNCT
ejpam-6189	218	24	is	be	AUX
ejpam-6189	218	25	a	a	DET
ejpam-6189	218	26	bd	bd	NOUN
ejpam-6189	218	27	-	-	NOUN
ejpam-6189	218	28	algebra	algebra	NOUN
ejpam-6189	218	29	where	where	SCONJ
ejpam-6189	218	30	the	the	DET
ejpam-6189	218	31	binary	binary	PROPN
ejpam-6189	218	32	operation	operation	PROPN
ejpam-6189	218	33	⊛	⊛	NUM
ejpam-6189	218	34	onx×x	onx×x	PUNCT
ejpam-6189	218	35	is	be	AUX
ejpam-6189	218	36	defined	define	VERB
ejpam-6189	218	37	by	by	ADP
ejpam-6189	218	38	(	(	PUNCT
ejpam-6189	218	39	x1	x1	PROPN
ejpam-6189	218	40	,	,	PUNCT
ejpam-6189	218	41	y1)⊛(x2	y1)⊛(x2	NOUN
ejpam-6189	218	42	,	,	PUNCT
ejpam-6189	218	43	y2	y2	PROPN
ejpam-6189	218	44	)	)	PUNCT
ejpam-6189	219	1	=	=	PRON
ejpam-6189	219	2	(	(	PUNCT
ejpam-6189	219	3	x1∗x2	x1∗x2	NUM
ejpam-6189	219	4	,	,	PUNCT
ejpam-6189	219	5	y1∗y2	y1∗y2	PROPN
ejpam-6189	219	6	)	)	PUNCT
ejpam-6189	219	7	for	for	ADP
ejpam-6189	219	8	all	all	DET
ejpam-6189	219	9	(	(	PUNCT
ejpam-6189	219	10	x1	x1	PROPN
ejpam-6189	219	11	,	,	PUNCT
ejpam-6189	219	12	y1	y1	PROPN
ejpam-6189	219	13	)	)	PUNCT
ejpam-6189	219	14	,	,	PUNCT
ejpam-6189	219	15	(	(	PUNCT
ejpam-6189	219	16	x2	x2	PROPN
ejpam-6189	219	17	,	,	PUNCT
ejpam-6189	219	18	y2	y2	PROPN
ejpam-6189	219	19	)	)	PUNCT
ejpam-6189	219	20	∈	∈	PROPN
ejpam-6189	219	21	x×x	x×x	PROPN
ejpam-6189	219	22	.	.	PUNCT
ejpam-6189	220	1	throughout	throughout	ADP
ejpam-6189	220	2	this	this	DET
ejpam-6189	220	3	section	section	NOUN
ejpam-6189	220	4	,	,	PUNCT
ejpam-6189	220	5	the	the	DET
ejpam-6189	220	6	bd	bd	PROPN
ejpam-6189	220	7	-	-	PROPN
ejpam-6189	220	8	algebra	algebra	PROPN
ejpam-6189	220	9	(	(	PUNCT
ejpam-6189	220	10	x×x,⊛	x×x,⊛	PROPN
ejpam-6189	220	11	,	,	PUNCT
ejpam-6189	220	12	(	(	PUNCT
ejpam-6189	220	13	0x	0x	NOUN
ejpam-6189	220	14	,	,	PUNCT
ejpam-6189	220	15	0x	0x	NOUN
ejpam-6189	220	16	)	)	PUNCT
ejpam-6189	220	17	)	)	PUNCT
ejpam-6189	220	18	will	will	AUX
ejpam-6189	220	19	be	be	AUX
ejpam-6189	220	20	replaced	replace	VERB
ejpam-6189	220	21	by	by	ADP
ejpam-6189	220	22	the	the	DET
ejpam-6189	220	23	symbol	symbol	NOUN
ejpam-6189	220	24	x×x	x×x	PROPN
ejpam-6189	220	25	.	.	PUNCT
ejpam-6189	221	1	let	let	VERB
ejpam-6189	221	2	ζ	ζ	NOUN
ejpam-6189	221	3	and	and	CCONJ
ejpam-6189	221	4	ξ	ξ	PROPN
ejpam-6189	221	5	be	be	VERB
ejpam-6189	221	6	a	a	DET
ejpam-6189	221	7	fuzzy	fuzzy	ADJ
ejpam-6189	221	8	sets	set	NOUN
ejpam-6189	221	9	of	of	ADP
ejpam-6189	221	10	a	a	DET
ejpam-6189	221	11	nonempty	nonempty	ADV
ejpam-6189	221	12	set	set	VERB
ejpam-6189	221	13	x.	x.	NOUN
ejpam-6189	221	14	the	the	DET
ejpam-6189	221	15	cartesian	cartesian	ADJ
ejpam-6189	221	16	product	product	NOUN
ejpam-6189	221	17	[	[	X
ejpam-6189	221	18	28	28	NUM
ejpam-6189	221	19	]	]	X
ejpam-6189	221	20	ζ	ζ	X
ejpam-6189	221	21	×	×	NOUN
ejpam-6189	221	22	ξ	ξ	X
ejpam-6189	221	23	:	:	PUNCT
ejpam-6189	221	24	x	x	PROPN
ejpam-6189	221	25	×x	×x	X
ejpam-6189	221	26	→	→	SYM
ejpam-6189	221	27	[	[	X
ejpam-6189	221	28	0	0	NUM
ejpam-6189	221	29	,	,	PUNCT
ejpam-6189	221	30	1	1	NUM
ejpam-6189	221	31	]	]	PUNCT
ejpam-6189	221	32	is	be	AUX
ejpam-6189	221	33	defined	define	VERB
ejpam-6189	221	34	by	by	ADP
ejpam-6189	221	35	(	(	PUNCT
ejpam-6189	221	36	ζ	ζ	NOUN
ejpam-6189	221	37	×	×	PROPN
ejpam-6189	221	38	ξ)(x	ξ)(x	PROPN
ejpam-6189	221	39	,	,	PUNCT
ejpam-6189	221	40	y	y	NOUN
ejpam-6189	221	41	)	)	PUNCT
ejpam-6189	221	42	=	=	SYM
ejpam-6189	222	1	ζ(x	ζ(x	NOUN
ejpam-6189	222	2	)	)	PUNCT
ejpam-6189	222	3	·	·	PUNCT
ejpam-6189	223	1	ξ(y	ξ(y	PROPN
ejpam-6189	223	2	)	)	PUNCT
ejpam-6189	223	3	for	for	ADP
ejpam-6189	223	4	all	all	DET
ejpam-6189	223	5	x	x	NOUN
ejpam-6189	223	6	,	,	PUNCT
ejpam-6189	223	7	y	y	PROPN
ejpam-6189	223	8	∈	∈	PROPN
ejpam-6189	223	9	x.	x.	NOUN
ejpam-6189	223	10	theorem	theorem	VERB
ejpam-6189	223	11	6	6	NUM
ejpam-6189	223	12	.	.	PUNCT
ejpam-6189	224	1	let	let	VERB
ejpam-6189	224	2	x	x	PRON
ejpam-6189	224	3	be	be	AUX
ejpam-6189	224	4	a	a	DET
ejpam-6189	224	5	bd	bd	NOUN
ejpam-6189	224	6	-	-	NOUN
ejpam-6189	224	7	algebra	algebra	NOUN
ejpam-6189	224	8	.	.	PUNCT
ejpam-6189	225	1	if	if	SCONJ
ejpam-6189	225	2	ζ	ζ	PROPN
ejpam-6189	225	3	and	and	CCONJ
ejpam-6189	225	4	ξ	ξ	PROPN
ejpam-6189	225	5	are	be	AUX
ejpam-6189	225	6	fuzzy	fuzzy	ADJ
ejpam-6189	225	7	dot	dot	NOUN
ejpam-6189	225	8	bd	bd	NOUN
ejpam-6189	225	9	-	-	PUNCT
ejpam-6189	225	10	subalgebras	subalgebras	PROPN
ejpam-6189	225	11	of	of	ADP
ejpam-6189	225	12	x	x	PRON
ejpam-6189	225	13	,	,	PUNCT
ejpam-6189	225	14	then	then	ADV
ejpam-6189	225	15	ζ	ζ	PRON
ejpam-6189	225	16	×	×	NOUN
ejpam-6189	225	17	ξ	ξ	PROPN
ejpam-6189	225	18	is	be	AUX
ejpam-6189	225	19	a	a	DET
ejpam-6189	225	20	fuzzy	fuzzy	ADJ
ejpam-6189	225	21	dot	dot	NOUN
ejpam-6189	225	22	bd	bd	NOUN
ejpam-6189	225	23	-	-	PUNCT
ejpam-6189	225	24	subalgebra	subalgebra	NOUN
ejpam-6189	225	25	of	of	ADP
ejpam-6189	225	26	x×x	x×x	PROPN
ejpam-6189	225	27	.	.	PUNCT
ejpam-6189	226	1	proof	proof	NOUN
ejpam-6189	226	2	.	.	PUNCT
ejpam-6189	227	1	assume	assume	VERB
ejpam-6189	227	2	that	that	SCONJ
ejpam-6189	227	3	ζ	ζ	NOUN
ejpam-6189	227	4	and	and	CCONJ
ejpam-6189	227	5	ξ	ξ	PROPN
ejpam-6189	227	6	are	be	AUX
ejpam-6189	227	7	fuzzy	fuzzy	ADJ
ejpam-6189	227	8	dot	dot	NOUN
ejpam-6189	227	9	bd	bd	NOUN
ejpam-6189	227	10	-	-	PUNCT
ejpam-6189	227	11	subalgebras	subalgebras	PROPN
ejpam-6189	227	12	of	of	ADP
ejpam-6189	227	13	x.	x.	PROPN
ejpam-6189	227	14	let	let	VERB
ejpam-6189	227	15	(	(	PUNCT
ejpam-6189	227	16	x1	x1	PROPN
ejpam-6189	227	17	,	,	PUNCT
ejpam-6189	227	18	y1	y1	PROPN
ejpam-6189	227	19	)	)	PUNCT
ejpam-6189	227	20	,	,	PUNCT
ejpam-6189	228	1	(	(	PUNCT
ejpam-6189	228	2	x2	x2	PROPN
ejpam-6189	228	3	,	,	PUNCT
ejpam-6189	228	4	y2	y2	NOUN
ejpam-6189	228	5	)	)	PUNCT
ejpam-6189	228	6	∈	∈	PROPN
ejpam-6189	228	7	x	x	SYM
ejpam-6189	228	8	×x	×x	PROPN
ejpam-6189	228	9	.	.	PUNCT
ejpam-6189	229	1	then	then	ADV
ejpam-6189	229	2	we	we	PRON
ejpam-6189	229	3	have	have	VERB
ejpam-6189	229	4	(	(	PUNCT
ejpam-6189	229	5	ζ	ζ	X
ejpam-6189	229	6	×	×	NOUN
ejpam-6189	229	7	ξ)(0	ξ)(0	PROPN
ejpam-6189	229	8	,	,	PUNCT
ejpam-6189	229	9	0	0	NUM
ejpam-6189	229	10	)	)	PUNCT
ejpam-6189	229	11	=	=	SYM
ejpam-6189	229	12	ζ(0	ζ(0	NOUN
ejpam-6189	229	13	)	)	PUNCT
ejpam-6189	229	14	·	·	PUNCT
ejpam-6189	229	15	ξ(0	ξ(0	NUM
ejpam-6189	229	16	)	)	PUNCT
ejpam-6189	229	17	≥	≥	NOUN
ejpam-6189	229	18	ζ(x1	ζ(x1	NOUN
ejpam-6189	229	19	)	)	PUNCT
ejpam-6189	229	20	·	·	PUNCT
ejpam-6189	229	21	ξ(y1	ξ(y1	NOUN
ejpam-6189	229	22	)	)	PUNCT
ejpam-6189	229	23	=	=	SYM
ejpam-6189	230	1	(	(	PUNCT
ejpam-6189	230	2	ζ	ζ	PROPN
ejpam-6189	230	3	×	×	PROPN
ejpam-6189	230	4	ξ)(x1	ξ)(x1	PROPN
ejpam-6189	230	5	,	,	PUNCT
ejpam-6189	230	6	y1	y1	NOUN
ejpam-6189	230	7	)	)	PUNCT
ejpam-6189	230	8	and	and	CCONJ
ejpam-6189	230	9	(	(	PUNCT
ejpam-6189	230	10	ζ	ζ	NOUN
ejpam-6189	230	11	×	×	PROPN
ejpam-6189	230	12	ξ)((x1	ξ)((x1	PROPN
ejpam-6189	230	13	,	,	PUNCT
ejpam-6189	230	14	y1)⊛	y1)⊛	PROPN
ejpam-6189	230	15	(	(	PUNCT
ejpam-6189	230	16	x2	x2	PROPN
ejpam-6189	230	17	,	,	PUNCT
ejpam-6189	230	18	y2	y2	PROPN
ejpam-6189	230	19	)	)	PUNCT
ejpam-6189	230	20	)	)	PUNCT
ejpam-6189	231	1	=	=	PRON
ejpam-6189	231	2	(	(	PUNCT
ejpam-6189	231	3	ζ	ζ	NOUN
ejpam-6189	231	4	×	×	NOUN
ejpam-6189	231	5	ξ)(x1	ξ)(x1	PROPN
ejpam-6189	231	6	∗	∗	NOUN
ejpam-6189	231	7	x2	x2	PROPN
ejpam-6189	231	8	,	,	PUNCT
ejpam-6189	231	9	y1	y1	NOUN
ejpam-6189	231	10	∗	∗	NOUN
ejpam-6189	231	11	y2	y2	NOUN
ejpam-6189	231	12	)	)	PUNCT
ejpam-6189	231	13	=	=	SYM
ejpam-6189	231	14	ζ(x1	ζ(x1	X
ejpam-6189	231	15	∗	∗	X
ejpam-6189	231	16	x2	x2	PROPN
ejpam-6189	231	17	)	)	PUNCT
ejpam-6189	231	18	·	·	PUNCT
ejpam-6189	231	19	ξ(y1	ξ(y1	NOUN
ejpam-6189	231	20	∗	∗	NUM
ejpam-6189	231	21	y2	y2	NOUN
ejpam-6189	231	22	)	)	PUNCT
ejpam-6189	231	23	≥	≥	NOUN
ejpam-6189	232	1	[	[	X
ejpam-6189	232	2	ζ(x1	ζ(x1	NOUN
ejpam-6189	232	3	)	)	PUNCT
ejpam-6189	232	4	·	·	PUNCT
ejpam-6189	232	5	ζ(x2	ζ(x2	NOUN
ejpam-6189	232	6	)	)	PUNCT
ejpam-6189	232	7	]	]	PUNCT
ejpam-6189	232	8	·	·	PUNCT
ejpam-6189	233	1	[	[	X
ejpam-6189	233	2	ξ(y1	ξ(y1	NOUN
ejpam-6189	233	3	)	)	PUNCT
ejpam-6189	233	4	·	·	PUNCT
ejpam-6189	233	5	ξ(y2	ξ(y2	NOUN
ejpam-6189	233	6	)	)	PUNCT
ejpam-6189	233	7	]	]	PUNCT
ejpam-6189	234	1	=	=	PUNCT
ejpam-6189	234	2	[	[	X
ejpam-6189	234	3	ζ(x1	ζ(x1	NOUN
ejpam-6189	234	4	)	)	PUNCT
ejpam-6189	234	5	·	·	PUNCT
ejpam-6189	234	6	ξ(y1	ξ(y1	NOUN
ejpam-6189	234	7	)	)	PUNCT
ejpam-6189	234	8	]	]	PUNCT
ejpam-6189	234	9	·	·	PUNCT
ejpam-6189	235	1	[	[	X
ejpam-6189	235	2	ζ(x2	ζ(x2	NOUN
ejpam-6189	235	3	)	)	PUNCT
ejpam-6189	235	4	·	·	PUNCT
ejpam-6189	235	5	ξ(y2	ξ(y2	NOUN
ejpam-6189	235	6	)	)	PUNCT
ejpam-6189	235	7	]	]	PUNCT
ejpam-6189	236	1	=	=	PUNCT
ejpam-6189	236	2	(	(	PUNCT
ejpam-6189	236	3	ζ	ζ	PROPN
ejpam-6189	236	4	×	×	PROPN
ejpam-6189	236	5	ξ)(x1	ξ)(x1	PROPN
ejpam-6189	236	6	,	,	PUNCT
ejpam-6189	236	7	y1	y1	NOUN
ejpam-6189	236	8	)	)	PUNCT
ejpam-6189	236	9	·	·	PUNCT
ejpam-6189	236	10	(	(	PUNCT
ejpam-6189	236	11	ζ	ζ	NOUN
ejpam-6189	236	12	×	×	NOUN
ejpam-6189	236	13	ξ)(x2	ξ)(x2	NOUN
ejpam-6189	236	14	,	,	PUNCT
ejpam-6189	236	15	y2	y2	PROPN
ejpam-6189	236	16	)	)	PUNCT
ejpam-6189	236	17	.	.	PUNCT
ejpam-6189	237	1	consequently	consequently	ADV
ejpam-6189	237	2	,	,	PUNCT
ejpam-6189	237	3	ζ	ζ	PROPN
ejpam-6189	237	4	×	×	NOUN
ejpam-6189	237	5	ξ	ξ	PROPN
ejpam-6189	237	6	is	be	AUX
ejpam-6189	237	7	a	a	DET
ejpam-6189	237	8	fuzzy	fuzzy	ADJ
ejpam-6189	237	9	dot	dot	NOUN
ejpam-6189	237	10	bd	bd	NOUN
ejpam-6189	237	11	-	-	PUNCT
ejpam-6189	237	12	subalgebra	subalgebra	NOUN
ejpam-6189	237	13	of	of	ADP
ejpam-6189	237	14	x×x	x×x	PROPN
ejpam-6189	237	15	.	.	PUNCT
ejpam-6189	238	1	the	the	DET
ejpam-6189	238	2	converse	converse	NOUN
ejpam-6189	238	3	of	of	ADP
ejpam-6189	238	4	theorem	theorem	NOUN
ejpam-6189	238	5	6	6	NUM
ejpam-6189	238	6	is	be	AUX
ejpam-6189	238	7	not	not	PART
ejpam-6189	238	8	true	true	ADJ
ejpam-6189	238	9	,	,	PUNCT
ejpam-6189	238	10	as	as	SCONJ
ejpam-6189	238	11	proved	prove	VERB
ejpam-6189	238	12	by	by	ADP
ejpam-6189	238	13	the	the	DET
ejpam-6189	238	14	following	follow	VERB
ejpam-6189	238	15	example	example	NOUN
ejpam-6189	238	16	.	.	PUNCT
ejpam-6189	239	1	example	example	NOUN
ejpam-6189	240	1	5	5	NUM
ejpam-6189	240	2	.	.	PUNCT
ejpam-6189	240	3	let	let	VERB
ejpam-6189	240	4	x	x	PUNCT
ejpam-6189	240	5	=	=	PUNCT
ejpam-6189	240	6	{	{	PUNCT
ejpam-6189	240	7	0	0	NUM
ejpam-6189	240	8	,	,	PUNCT
ejpam-6189	240	9	1	1	NUM
ejpam-6189	240	10	,	,	PUNCT
ejpam-6189	240	11	2	2	NUM
ejpam-6189	240	12	}	}	PUNCT
ejpam-6189	240	13	be	be	AUX
ejpam-6189	240	14	a	a	DET
ejpam-6189	240	15	set	set	NOUN
ejpam-6189	240	16	with	with	ADP
ejpam-6189	240	17	the	the	DET
ejpam-6189	240	18	binary	binary	PROPN
ejpam-6189	240	19	operation	operation	NOUN
ejpam-6189	240	20	∗	∗	NOUN
ejpam-6189	240	21	on	on	ADP
ejpam-6189	240	22	x	x	PUNCT
ejpam-6189	240	23	define	define	VERB
ejpam-6189	240	24	in	in	ADP
ejpam-6189	240	25	the	the	DET
ejpam-6189	240	26	following	follow	VERB
ejpam-6189	240	27	table	table	NOUN
ejpam-6189	240	28	:	:	PUNCT
ejpam-6189	240	29	∗	∗	NOUN
ejpam-6189	240	30	0	0	NUM
ejpam-6189	240	31	1	1	NUM
ejpam-6189	240	32	2	2	NUM
ejpam-6189	240	33	0	0	NUM
ejpam-6189	240	34	0	0	NUM
ejpam-6189	240	35	2	2	NUM
ejpam-6189	240	36	2	2	NUM
ejpam-6189	240	37	1	1	NUM
ejpam-6189	240	38	1	1	NUM
ejpam-6189	240	39	0	0	NUM
ejpam-6189	240	40	2	2	NUM
ejpam-6189	240	41	2	2	NUM
ejpam-6189	240	42	2	2	NUM
ejpam-6189	240	43	1	1	NUM
ejpam-6189	240	44	1	1	NUM
ejpam-6189	240	45	table	table	NOUN
ejpam-6189	240	46	2	2	NUM
ejpam-6189	240	47	:	:	PUNCT
ejpam-6189	240	48	the	the	DET
ejpam-6189	240	49	binary	binary	PROPN
ejpam-6189	240	50	operation	operation	NOUN
ejpam-6189	240	51	∗	∗	NOUN
ejpam-6189	240	52	on	on	ADP
ejpam-6189	240	53	x.	x.	NOUN
ejpam-6189	240	54	then	then	ADV
ejpam-6189	240	55	x	x	X
ejpam-6189	240	56	:	:	PUNCT
ejpam-6189	240	57	=	=	SYM
ejpam-6189	240	58	(	(	PUNCT
ejpam-6189	240	59	x	x	X
ejpam-6189	240	60	,	,	PUNCT
ejpam-6189	240	61	∗	∗	NOUN
ejpam-6189	240	62	,	,	PUNCT
ejpam-6189	240	63	0	0	NUM
ejpam-6189	240	64	)	)	PUNCT
ejpam-6189	240	65	is	be	AUX
ejpam-6189	240	66	a	a	DET
ejpam-6189	240	67	bd	bd	NOUN
ejpam-6189	240	68	-	-	NOUN
ejpam-6189	240	69	algebra	algebra	NOUN
ejpam-6189	240	70	.	.	PUNCT
ejpam-6189	241	1	define	define	VERB
ejpam-6189	241	2	two	two	NUM
ejpam-6189	241	3	fuzzy	fuzzy	ADJ
ejpam-6189	241	4	sets	set	NOUN
ejpam-6189	241	5	ζ	ζ	NOUN
ejpam-6189	241	6	and	and	CCONJ
ejpam-6189	241	7	ξ	ξ	X
ejpam-6189	241	8	of	of	ADP
ejpam-6189	241	9	x	x	PUNCT
ejpam-6189	241	10	by	by	ADP
ejpam-6189	241	11	w.	w.	PROPN
ejpam-6189	241	12	nakkhasen	nakkhasen	PROPN
ejpam-6189	241	13	et	et	PROPN
ejpam-6189	241	14	al	al	PROPN
ejpam-6189	241	15	.	.	PUNCT
ejpam-6189	241	16	/	/	SYM
ejpam-6189	241	17	eur	eur	PROPN
ejpam-6189	241	18	.	.	PUNCT
ejpam-6189	242	1	j.	j.	PROPN
ejpam-6189	242	2	pure	pure	PROPN
ejpam-6189	242	3	appl	appl	PROPN
ejpam-6189	242	4	.	.	PROPN
ejpam-6189	242	5	math	math	PROPN
ejpam-6189	242	6	,	,	PUNCT
ejpam-6189	242	7	18	18	NUM
ejpam-6189	242	8	(	(	PUNCT
ejpam-6189	242	9	3	3	NUM
ejpam-6189	242	10	)	)	PUNCT
ejpam-6189	242	11	(	(	PUNCT
ejpam-6189	242	12	2025	2025	NUM
ejpam-6189	242	13	)	)	PUNCT
ejpam-6189	242	14	,	,	PUNCT
ejpam-6189	242	15	6189	6189	NUM
ejpam-6189	242	16	9	9	NUM
ejpam-6189	242	17	of	of	ADP
ejpam-6189	242	18	13	13	NUM
ejpam-6189	242	19	ζ(0	ζ(0	NOUN
ejpam-6189	242	20	)	)	PUNCT
ejpam-6189	242	21	=	=	NOUN
ejpam-6189	242	22	0.70	0.70	NUM
ejpam-6189	242	23	,	,	PUNCT
ejpam-6189	242	24	ζ(1	ζ(1	PROPN
ejpam-6189	242	25	)	)	PUNCT
ejpam-6189	242	26	=	=	NOUN
ejpam-6189	242	27	0.70	0.70	NUM
ejpam-6189	242	28	,	,	PUNCT
ejpam-6189	242	29	ζ(2	ζ(2	NOUN
ejpam-6189	242	30	)	)	PUNCT
ejpam-6189	242	31	=	=	NOUN
ejpam-6189	242	32	0.40	0.40	NUM
ejpam-6189	242	33	and	and	CCONJ
ejpam-6189	242	34	ξ(0	ξ(0	PROPN
ejpam-6189	242	35	)	)	PUNCT
ejpam-6189	242	36	=	=	SYM
ejpam-6189	242	37	0.60	0.60	NUM
ejpam-6189	242	38	,	,	PUNCT
ejpam-6189	242	39	ξ(1	ξ(1	PROPN
ejpam-6189	242	40	)	)	PUNCT
ejpam-6189	242	41	=	=	NOUN
ejpam-6189	242	42	0.50	0.50	NUM
ejpam-6189	242	43	,	,	PUNCT
ejpam-6189	242	44	ξ(2	ξ(2	PROPN
ejpam-6189	242	45	)	)	PUNCT
ejpam-6189	242	46	=	=	PUNCT
ejpam-6189	243	1	0.60	0.60	NUM
ejpam-6189	243	2	.	.	PUNCT
ejpam-6189	244	1	it	it	PRON
ejpam-6189	244	2	is	be	AUX
ejpam-6189	244	3	not	not	PART
ejpam-6189	244	4	difficult	difficult	ADJ
ejpam-6189	244	5	to	to	PART
ejpam-6189	244	6	verify	verify	VERB
ejpam-6189	244	7	that	that	SCONJ
ejpam-6189	244	8	ξ	ξ	PROPN
ejpam-6189	244	9	is	be	AUX
ejpam-6189	244	10	a	a	DET
ejpam-6189	244	11	fuzzy	fuzzy	ADJ
ejpam-6189	244	12	dot	dot	NOUN
ejpam-6189	244	13	bd	bd	NOUN
ejpam-6189	244	14	-	-	PUNCT
ejpam-6189	244	15	subalgebra	subalgebra	NOUN
ejpam-6189	244	16	of	of	ADP
ejpam-6189	244	17	x	x	PRON
ejpam-6189	244	18	,	,	PUNCT
ejpam-6189	244	19	but	but	CCONJ
ejpam-6189	244	20	ζ	ζ	NOUN
ejpam-6189	244	21	is	be	AUX
ejpam-6189	244	22	not	not	PART
ejpam-6189	244	23	a	a	DET
ejpam-6189	244	24	fuzzy	fuzzy	ADJ
ejpam-6189	244	25	dot	dot	NOUN
ejpam-6189	244	26	bd	bd	NOUN
ejpam-6189	244	27	-	-	PUNCT
ejpam-6189	244	28	subalgebra	subalgebra	NOUN
ejpam-6189	244	29	of	of	ADP
ejpam-6189	244	30	x.	x.	NOUN
ejpam-6189	244	31	at	at	ADP
ejpam-6189	244	32	the	the	DET
ejpam-6189	244	33	same	same	ADJ
ejpam-6189	244	34	time	time	NOUN
ejpam-6189	244	35	,	,	PUNCT
ejpam-6189	244	36	ζ	ζ	NOUN
ejpam-6189	244	37	×	×	NOUN
ejpam-6189	244	38	ξ	ξ	PROPN
ejpam-6189	244	39	is	be	AUX
ejpam-6189	244	40	also	also	ADV
ejpam-6189	244	41	a	a	DET
ejpam-6189	244	42	fuzzy	fuzzy	ADJ
ejpam-6189	244	43	dot	dot	NOUN
ejpam-6189	244	44	bd	bd	NOUN
ejpam-6189	244	45	-	-	PUNCT
ejpam-6189	244	46	subalgebra	subalgebra	NOUN
ejpam-6189	244	47	of	of	ADP
ejpam-6189	244	48	x×x	x×x	PROPN
ejpam-6189	244	49	as	as	SCONJ
ejpam-6189	244	50	shown	show	VERB
ejpam-6189	244	51	below	below	ADV
ejpam-6189	244	52	.	.	PUNCT
ejpam-6189	245	1	now	now	ADV
ejpam-6189	245	2	,	,	PUNCT
ejpam-6189	245	3	we	we	PRON
ejpam-6189	245	4	consider	consider	VERB
ejpam-6189	245	5	the	the	DET
ejpam-6189	245	6	results	result	NOUN
ejpam-6189	245	7	of	of	ADP
ejpam-6189	245	8	the	the	DET
ejpam-6189	245	9	cartesian	cartesian	ADJ
ejpam-6189	245	10	product	product	NOUN
ejpam-6189	245	11	ζ	ζ	NOUN
ejpam-6189	245	12	×	×	NOUN
ejpam-6189	245	13	ξ	ξ	PROPN
ejpam-6189	245	14	as	as	SCONJ
ejpam-6189	245	15	follows	follow	VERB
ejpam-6189	245	16	.	.	PUNCT
ejpam-6189	246	1	(	(	PUNCT
ejpam-6189	246	2	ζ	ζ	NOUN
ejpam-6189	246	3	×	×	NOUN
ejpam-6189	246	4	ξ)(0	ξ)(0	PROPN
ejpam-6189	246	5	,	,	PUNCT
ejpam-6189	246	6	0	0	NUM
ejpam-6189	246	7	)	)	PUNCT
ejpam-6189	246	8	=	=	SYM
ejpam-6189	247	1	0.42,(ζ	0.42,(ζ	PROPN
ejpam-6189	247	2	×	×	PROPN
ejpam-6189	247	3	ξ)(0	ξ)(0	PROPN
ejpam-6189	247	4	,	,	PUNCT
ejpam-6189	247	5	1	1	X
ejpam-6189	247	6	)	)	PUNCT
ejpam-6189	247	7	=	=	SYM
ejpam-6189	247	8	0.35	0.35	NUM
ejpam-6189	247	9	,	,	PUNCT
ejpam-6189	247	10	(	(	PUNCT
ejpam-6189	247	11	ζ	ζ	NOUN
ejpam-6189	247	12	×	×	NOUN
ejpam-6189	247	13	ξ)(0	ξ)(0	PROPN
ejpam-6189	247	14	,	,	PUNCT
ejpam-6189	247	15	2	2	X
ejpam-6189	247	16	)	)	PUNCT
ejpam-6189	247	17	=	=	NOUN
ejpam-6189	247	18	0.42	0.42	NUM
ejpam-6189	247	19	,	,	PUNCT
ejpam-6189	247	20	(	(	PUNCT
ejpam-6189	247	21	ζ	ζ	NOUN
ejpam-6189	247	22	×	×	NOUN
ejpam-6189	247	23	ξ)(1	ξ)(1	ADP
ejpam-6189	247	24	,	,	PUNCT
ejpam-6189	247	25	0	0	NUM
ejpam-6189	247	26	)	)	PUNCT
ejpam-6189	247	27	=	=	SYM
ejpam-6189	248	1	0.42,(ζ	0.42,(ζ	NUM
ejpam-6189	248	2	×	×	NOUN
ejpam-6189	248	3	ξ)(1	ξ)(1	NOUN
ejpam-6189	248	4	,	,	PUNCT
ejpam-6189	248	5	1	1	NUM
ejpam-6189	248	6	)	)	PUNCT
ejpam-6189	248	7	=	=	SYM
ejpam-6189	248	8	0.35	0.35	NUM
ejpam-6189	248	9	,	,	PUNCT
ejpam-6189	248	10	(	(	PUNCT
ejpam-6189	248	11	ζ	ζ	NOUN
ejpam-6189	248	12	×	×	NOUN
ejpam-6189	248	13	ξ)(1	ξ)(1	ADP
ejpam-6189	248	14	,	,	PUNCT
ejpam-6189	248	15	2	2	NUM
ejpam-6189	248	16	)	)	PUNCT
ejpam-6189	248	17	=	=	NOUN
ejpam-6189	248	18	0.42	0.42	NUM
ejpam-6189	248	19	,	,	PUNCT
ejpam-6189	248	20	(	(	PUNCT
ejpam-6189	248	21	ζ	ζ	NOUN
ejpam-6189	248	22	×	×	NOUN
ejpam-6189	248	23	ξ)(2	ξ)(2	NOUN
ejpam-6189	248	24	,	,	PUNCT
ejpam-6189	248	25	0	0	NUM
ejpam-6189	248	26	)	)	PUNCT
ejpam-6189	248	27	=	=	SYM
ejpam-6189	248	28	0.24,(ζ	0.24,(ζ	NUM
ejpam-6189	248	29	×	×	NOUN
ejpam-6189	248	30	ξ)(2	ξ)(2	NOUN
ejpam-6189	248	31	,	,	PUNCT
ejpam-6189	248	32	1	1	NUM
ejpam-6189	248	33	)	)	PUNCT
ejpam-6189	248	34	=	=	SYM
ejpam-6189	248	35	0.20	0.20	NUM
ejpam-6189	248	36	,	,	PUNCT
ejpam-6189	248	37	(	(	PUNCT
ejpam-6189	248	38	ζ	ζ	NOUN
ejpam-6189	248	39	×	×	NOUN
ejpam-6189	248	40	ξ)(2	ξ)(2	NOUN
ejpam-6189	248	41	,	,	PUNCT
ejpam-6189	248	42	2	2	NUM
ejpam-6189	248	43	)	)	PUNCT
ejpam-6189	248	44	=	=	NOUN
ejpam-6189	248	45	0.24	0.24	NUM
ejpam-6189	248	46	.	.	PUNCT
ejpam-6189	249	1	we	we	PRON
ejpam-6189	249	2	see	see	VERB
ejpam-6189	249	3	that	that	SCONJ
ejpam-6189	249	4	(	(	PUNCT
ejpam-6189	249	5	ζ	ζ	NOUN
ejpam-6189	249	6	×	×	NOUN
ejpam-6189	249	7	ξ)(0	ξ)(0	PROPN
ejpam-6189	249	8	,	,	PUNCT
ejpam-6189	249	9	0	0	NUM
ejpam-6189	249	10	)	)	PUNCT
ejpam-6189	249	11	≥	≥	NOUN
ejpam-6189	249	12	(	(	PUNCT
ejpam-6189	249	13	ζ	ζ	NOUN
ejpam-6189	249	14	×	×	PROPN
ejpam-6189	249	15	ξ)(x	ξ)(x	PROPN
ejpam-6189	249	16	,	,	PUNCT
ejpam-6189	249	17	y	y	NOUN
ejpam-6189	249	18	)	)	PUNCT
ejpam-6189	249	19	for	for	ADP
ejpam-6189	249	20	all	all	DET
ejpam-6189	249	21	(	(	PUNCT
ejpam-6189	249	22	x	x	NOUN
ejpam-6189	249	23	,	,	PUNCT
ejpam-6189	249	24	y	y	NOUN
ejpam-6189	249	25	)	)	PUNCT
ejpam-6189	249	26	∈	∈	PROPN
ejpam-6189	249	27	x	x	SYM
ejpam-6189	249	28	×x	×x	PROPN
ejpam-6189	249	29	.	.	NOUN
ejpam-6189	249	30	subsequently	subsequently	ADV
ejpam-6189	249	31	,	,	PUNCT
ejpam-6189	249	32	below	below	ADV
ejpam-6189	249	33	are	be	AUX
ejpam-6189	249	34	some	some	DET
ejpam-6189	249	35	computed	compute	VERB
ejpam-6189	249	36	results	result	NOUN
ejpam-6189	249	37	.	.	PUNCT
ejpam-6189	250	1	(	(	PUNCT
ejpam-6189	250	2	ζ	ζ	NOUN
ejpam-6189	250	3	×	×	PROPN
ejpam-6189	250	4	ξ)((0	ξ)((0	PROPN
ejpam-6189	250	5	,	,	PUNCT
ejpam-6189	250	6	2)⊛	2)⊛	NUM
ejpam-6189	250	7	(	(	PUNCT
ejpam-6189	250	8	2	2	NUM
ejpam-6189	250	9	,	,	PUNCT
ejpam-6189	250	10	1	1	NUM
ejpam-6189	250	11	)	)	PUNCT
ejpam-6189	250	12	)	)	PUNCT
ejpam-6189	251	1	=	=	PRON
ejpam-6189	251	2	(	(	PUNCT
ejpam-6189	251	3	ζ	ζ	NOUN
ejpam-6189	251	4	×	×	NOUN
ejpam-6189	251	5	ξ)(2	ξ)(2	NOUN
ejpam-6189	251	6	,	,	PUNCT
ejpam-6189	251	7	1	1	NUM
ejpam-6189	251	8	)	)	PUNCT
ejpam-6189	251	9	=	=	SYM
ejpam-6189	252	1	0.20	0.20	NUM
ejpam-6189	252	2	>	>	SYM
ejpam-6189	252	3	0.08	0.08	NUM
ejpam-6189	252	4	=	=	SYM
ejpam-6189	252	5	(	(	PUNCT
ejpam-6189	252	6	ζ	ζ	X
ejpam-6189	252	7	×	×	PROPN
ejpam-6189	252	8	ξ)(0	ξ)(0	PROPN
ejpam-6189	252	9	,	,	PUNCT
ejpam-6189	252	10	2	2	NUM
ejpam-6189	252	11	)	)	PUNCT
ejpam-6189	252	12	·	·	PUNCT
ejpam-6189	253	1	(	(	PUNCT
ejpam-6189	253	2	ζ	ζ	NOUN
ejpam-6189	253	3	×	×	NOUN
ejpam-6189	253	4	ξ)(2	ξ)(2	NOUN
ejpam-6189	253	5	,	,	PUNCT
ejpam-6189	253	6	1	1	NUM
ejpam-6189	253	7	)	)	PUNCT
ejpam-6189	253	8	,	,	PUNCT
ejpam-6189	253	9	(	(	PUNCT
ejpam-6189	253	10	ζ	ζ	NOUN
ejpam-6189	253	11	×	×	PROPN
ejpam-6189	253	12	ξ)((1	ξ)((1	PROPN
ejpam-6189	253	13	,	,	PUNCT
ejpam-6189	253	14	1)⊛	1)⊛	NUM
ejpam-6189	253	15	(	(	PUNCT
ejpam-6189	253	16	0	0	NUM
ejpam-6189	253	17	,	,	PUNCT
ejpam-6189	253	18	1	1	NUM
ejpam-6189	253	19	)	)	PUNCT
ejpam-6189	253	20	)	)	PUNCT
ejpam-6189	253	21	=	=	PRON
ejpam-6189	254	1	(	(	PUNCT
ejpam-6189	254	2	ζ	ζ	X
ejpam-6189	254	3	×	×	NOUN
ejpam-6189	254	4	ξ)(1	ξ)(1	ADP
ejpam-6189	254	5	,	,	PUNCT
ejpam-6189	254	6	0	0	NUM
ejpam-6189	254	7	)	)	PUNCT
ejpam-6189	254	8	=	=	PUNCT
ejpam-6189	254	9	0.42	0.42	NUM
ejpam-6189	254	10	>	>	PUNCT
ejpam-6189	254	11	0.12	0.12	NUM
ejpam-6189	254	12	=	=	SYM
ejpam-6189	254	13	(	(	PUNCT
ejpam-6189	254	14	ζ	ζ	PROPN
ejpam-6189	254	15	×	×	NOUN
ejpam-6189	254	16	ξ)(1	ξ)(1	ADP
ejpam-6189	254	17	,	,	PUNCT
ejpam-6189	254	18	1	1	NUM
ejpam-6189	254	19	)	)	PUNCT
ejpam-6189	254	20	·	·	PUNCT
ejpam-6189	255	1	(	(	PUNCT
ejpam-6189	255	2	ζ	ζ	NOUN
ejpam-6189	255	3	×	×	PROPN
ejpam-6189	255	4	ξ)(0	ξ)(0	PROPN
ejpam-6189	255	5	,	,	PUNCT
ejpam-6189	255	6	1	1	NUM
ejpam-6189	255	7	)	)	PUNCT
ejpam-6189	255	8	,	,	PUNCT
ejpam-6189	255	9	(	(	PUNCT
ejpam-6189	255	10	ζ	ζ	NOUN
ejpam-6189	255	11	×	×	PROPN
ejpam-6189	255	12	ξ)((2	ξ)((2	PROPN
ejpam-6189	255	13	,	,	PUNCT
ejpam-6189	255	14	0)⊛	0)⊛	PROPN
ejpam-6189	255	15	(	(	PUNCT
ejpam-6189	255	16	1	1	NUM
ejpam-6189	255	17	,	,	PUNCT
ejpam-6189	255	18	2	2	NUM
ejpam-6189	255	19	)	)	PUNCT
ejpam-6189	255	20	)	)	PUNCT
ejpam-6189	256	1	=	=	PRON
ejpam-6189	256	2	(	(	PUNCT
ejpam-6189	256	3	ζ	ζ	X
ejpam-6189	256	4	×	×	NOUN
ejpam-6189	256	5	ξ)(1	ξ)(1	ADP
ejpam-6189	256	6	,	,	PUNCT
ejpam-6189	256	7	2	2	NUM
ejpam-6189	256	8	)	)	PUNCT
ejpam-6189	256	9	=	=	NOUN
ejpam-6189	257	1	0.42	0.42	NUM
ejpam-6189	257	2	>	>	PUNCT
ejpam-6189	257	3	0.10	0.10	NUM
ejpam-6189	257	4	=	=	SYM
ejpam-6189	257	5	(	(	PUNCT
ejpam-6189	257	6	ζ	ζ	NOUN
ejpam-6189	257	7	×	×	NOUN
ejpam-6189	257	8	ξ)(2	ξ)(2	NOUN
ejpam-6189	257	9	,	,	PUNCT
ejpam-6189	257	10	0	0	NUM
ejpam-6189	257	11	)	)	PUNCT
ejpam-6189	257	12	·	·	PUNCT
ejpam-6189	258	1	(	(	PUNCT
ejpam-6189	258	2	ζ	ζ	NOUN
ejpam-6189	258	3	×	×	NOUN
ejpam-6189	258	4	ξ)(1	ξ)(1	ADP
ejpam-6189	258	5	,	,	PUNCT
ejpam-6189	258	6	2	2	NUM
ejpam-6189	258	7	)	)	PUNCT
ejpam-6189	258	8	,	,	PUNCT
ejpam-6189	258	9	(	(	PUNCT
ejpam-6189	258	10	ζ	ζ	NOUN
ejpam-6189	258	11	×	×	PROPN
ejpam-6189	258	12	ξ)((2	ξ)((2	PROPN
ejpam-6189	258	13	,	,	PUNCT
ejpam-6189	258	14	2)⊛	2)⊛	NUM
ejpam-6189	258	15	(	(	PUNCT
ejpam-6189	258	16	2	2	NUM
ejpam-6189	258	17	,	,	PUNCT
ejpam-6189	258	18	1	1	NUM
ejpam-6189	258	19	)	)	PUNCT
ejpam-6189	258	20	)	)	PUNCT
ejpam-6189	259	1	=	=	PRON
ejpam-6189	259	2	(	(	PUNCT
ejpam-6189	259	3	ζ	ζ	X
ejpam-6189	259	4	×	×	NOUN
ejpam-6189	259	5	ξ)(1	ξ)(1	ADP
ejpam-6189	259	6	,	,	PUNCT
ejpam-6189	259	7	0	0	NUM
ejpam-6189	259	8	)	)	PUNCT
ejpam-6189	259	9	=	=	PUNCT
ejpam-6189	260	1	0.42	0.42	NUM
ejpam-6189	260	2	>	>	SYM
ejpam-6189	260	3	0.08	0.08	NUM
ejpam-6189	260	4	=	=	SYM
ejpam-6189	260	5	(	(	PUNCT
ejpam-6189	260	6	ζ	ζ	NOUN
ejpam-6189	260	7	×	×	NOUN
ejpam-6189	260	8	ξ)(2	ξ)(2	NOUN
ejpam-6189	260	9	,	,	PUNCT
ejpam-6189	260	10	2	2	NUM
ejpam-6189	260	11	)	)	PUNCT
ejpam-6189	260	12	·	·	PUNCT
ejpam-6189	260	13	(	(	PUNCT
ejpam-6189	260	14	ζ	ζ	NOUN
ejpam-6189	260	15	×	×	NOUN
ejpam-6189	260	16	ξ)(1	ξ)(1	ADP
ejpam-6189	260	17	,	,	PUNCT
ejpam-6189	260	18	1	1	NUM
ejpam-6189	260	19	)	)	PUNCT
ejpam-6189	260	20	.	.	PUNCT
ejpam-6189	261	1	by	by	ADP
ejpam-6189	261	2	meticulous	meticulous	ADJ
ejpam-6189	261	3	computations	computation	NOUN
ejpam-6189	261	4	,	,	PUNCT
ejpam-6189	261	5	we	we	PRON
ejpam-6189	261	6	have	have	VERB
ejpam-6189	261	7	(	(	PUNCT
ejpam-6189	261	8	ζ	ζ	NOUN
ejpam-6189	261	9	×	×	PROPN
ejpam-6189	261	10	ξ)((x1	ξ)((x1	NUM
ejpam-6189	261	11	,	,	PUNCT
ejpam-6189	261	12	y1	y1	NOUN
ejpam-6189	261	13	)	)	PUNCT
ejpam-6189	261	14	⊛	⊛	NUM
ejpam-6189	261	15	(	(	PUNCT
ejpam-6189	261	16	x2	x2	PROPN
ejpam-6189	261	17	,	,	PUNCT
ejpam-6189	261	18	y2	y2	PROPN
ejpam-6189	261	19	)	)	PUNCT
ejpam-6189	261	20	)	)	PUNCT
ejpam-6189	261	21	≥	≥	NOUN
ejpam-6189	262	1	(	(	PUNCT
ejpam-6189	262	2	ζ	ζ	NOUN
ejpam-6189	262	3	×	×	PROPN
ejpam-6189	262	4	ξ)(x1	ξ)(x1	PROPN
ejpam-6189	262	5	,	,	PUNCT
ejpam-6189	262	6	y1	y1	NOUN
ejpam-6189	262	7	)	)	PUNCT
ejpam-6189	262	8	·	·	PUNCT
ejpam-6189	262	9	(	(	PUNCT
ejpam-6189	262	10	ζ	ζ	NOUN
ejpam-6189	262	11	×	×	NOUN
ejpam-6189	262	12	ξ)(x2	ξ)(x2	NOUN
ejpam-6189	262	13	,	,	PUNCT
ejpam-6189	262	14	y2	y2	PROPN
ejpam-6189	262	15	)	)	PUNCT
ejpam-6189	262	16	for	for	ADP
ejpam-6189	262	17	all	all	PRON
ejpam-6189	262	18	(	(	PUNCT
ejpam-6189	262	19	x1	x1	PROPN
ejpam-6189	262	20	,	,	PUNCT
ejpam-6189	262	21	y1	y1	PROPN
ejpam-6189	262	22	)	)	PUNCT
ejpam-6189	262	23	,	,	PUNCT
ejpam-6189	262	24	(	(	PUNCT
ejpam-6189	262	25	x2	x2	PROPN
ejpam-6189	262	26	,	,	PUNCT
ejpam-6189	262	27	y2	y2	PROPN
ejpam-6189	262	28	)	)	PUNCT
ejpam-6189	262	29	∈	∈	PROPN
ejpam-6189	262	30	x×x	x×x	PROPN
ejpam-6189	262	31	.	.	PUNCT
ejpam-6189	262	32	consequently	consequently	ADV
ejpam-6189	262	33	,	,	PUNCT
ejpam-6189	262	34	ζ×ξ	ζ×ξ	PROPN
ejpam-6189	262	35	is	be	AUX
ejpam-6189	262	36	a	a	DET
ejpam-6189	262	37	fuzzy	fuzzy	ADJ
ejpam-6189	262	38	dot	dot	NOUN
ejpam-6189	262	39	bd	bd	NOUN
ejpam-6189	262	40	-	-	PUNCT
ejpam-6189	262	41	subalgebra	subalgebra	NOUN
ejpam-6189	262	42	of	of	ADP
ejpam-6189	262	43	x×x	x×x	PROPN
ejpam-6189	262	44	.	.	PUNCT
ejpam-6189	263	1	let	let	VERB
ejpam-6189	263	2	x	x	PRON
ejpam-6189	263	3	be	be	AUX
ejpam-6189	263	4	a	a	DET
ejpam-6189	263	5	nonempty	nonempty	ADV
ejpam-6189	263	6	set	set	VERB
ejpam-6189	263	7	and	and	CCONJ
ejpam-6189	263	8	ζ	ζ	NOUN
ejpam-6189	263	9	be	be	AUX
ejpam-6189	263	10	any	any	DET
ejpam-6189	263	11	fuzzy	fuzzy	ADJ
ejpam-6189	263	12	set	set	NOUN
ejpam-6189	263	13	of	of	ADP
ejpam-6189	263	14	x.	x.	NOUN
ejpam-6189	263	15	a	a	DET
ejpam-6189	263	16	fuzzy	fuzzy	ADJ
ejpam-6189	263	17	relation	relation	NOUN
ejpam-6189	263	18	s	s	PART
ejpam-6189	263	19	on	on	ADP
ejpam-6189	263	20	x	x	PUNCT
ejpam-6189	264	1	[	[	X
ejpam-6189	264	2	28	28	NUM
ejpam-6189	264	3	]	]	PUNCT
ejpam-6189	264	4	is	be	AUX
ejpam-6189	264	5	a	a	DET
ejpam-6189	264	6	fuzzy	fuzzy	ADJ
ejpam-6189	264	7	set	set	NOUN
ejpam-6189	264	8	of	of	ADP
ejpam-6189	264	9	x	x	PROPN
ejpam-6189	264	10	×x	×x	PROPN
ejpam-6189	264	11	.	.	PUNCT
ejpam-6189	265	1	then	then	ADV
ejpam-6189	265	2	the	the	DET
ejpam-6189	265	3	fuzzy	fuzzy	ADJ
ejpam-6189	265	4	relation	relation	NOUN
ejpam-6189	265	5	sζ	sζ	VERB
ejpam-6189	265	6	on	on	ADP
ejpam-6189	265	7	x	x	PUNCT
ejpam-6189	265	8	is	be	AUX
ejpam-6189	265	9	called	call	VERB
ejpam-6189	265	10	a	a	DET
ejpam-6189	265	11	fuzzy	fuzzy	ADJ
ejpam-6189	265	12	ζ	ζ	NOUN
ejpam-6189	265	13	-	-	PUNCT
ejpam-6189	265	14	product	product	NOUN
ejpam-6189	265	15	relation	relation	NOUN
ejpam-6189	265	16	on	on	ADP
ejpam-6189	265	17	x	x	PUNCT
ejpam-6189	266	1	[	[	X
ejpam-6189	266	2	22	22	NUM
ejpam-6189	266	3	]	]	PUNCT
ejpam-6189	266	4	if	if	SCONJ
ejpam-6189	266	5	sζ(x	sζ(x	NUM
ejpam-6189	266	6	,	,	PUNCT
ejpam-6189	266	7	y	y	PROPN
ejpam-6189	266	8	)	)	PUNCT
ejpam-6189	266	9	≥	≥	NOUN
ejpam-6189	266	10	ζ(x	ζ(x	NOUN
ejpam-6189	266	11	)	)	PUNCT
ejpam-6189	266	12	·	·	PUNCT
ejpam-6189	266	13	ζ(y	ζ(y	X
ejpam-6189	266	14	)	)	PUNCT
ejpam-6189	266	15	for	for	ADP
ejpam-6189	266	16	all	all	DET
ejpam-6189	266	17	x	x	NOUN
ejpam-6189	266	18	,	,	PUNCT
ejpam-6189	266	19	y	y	PROPN
ejpam-6189	266	20	∈	∈	PROPN
ejpam-6189	266	21	x.	x.	NOUN
ejpam-6189	267	1	moreover	moreover	ADV
ejpam-6189	267	2	,	,	PUNCT
ejpam-6189	267	3	the	the	DET
ejpam-6189	267	4	strongest	strong	ADJ
ejpam-6189	267	5	fuzzy	fuzzy	ADJ
ejpam-6189	267	6	ζ	ζ	NOUN
ejpam-6189	267	7	-	-	PUNCT
ejpam-6189	267	8	relation	relation	NOUN
ejpam-6189	267	9	sζ	sζ	NOUN
ejpam-6189	267	10	on	on	ADP
ejpam-6189	267	11	x	x	PUNCT
ejpam-6189	268	1	[	[	X
ejpam-6189	268	2	22	22	NUM
ejpam-6189	268	3	]	]	PUNCT
ejpam-6189	268	4	given	give	VERB
ejpam-6189	268	5	by	by	ADP
ejpam-6189	268	6	sζ(x	sζ(x	NUM
ejpam-6189	268	7	,	,	PUNCT
ejpam-6189	268	8	y	y	NOUN
ejpam-6189	268	9	)	)	PUNCT
ejpam-6189	268	10	=	=	SYM
ejpam-6189	268	11	ζ(x	ζ(x	NOUN
ejpam-6189	268	12	)	)	PUNCT
ejpam-6189	268	13	·	·	PUNCT
ejpam-6189	268	14	ζ(y	ζ(y	X
ejpam-6189	268	15	)	)	PUNCT
ejpam-6189	268	16	for	for	ADP
ejpam-6189	268	17	all	all	DET
ejpam-6189	268	18	x	x	NOUN
ejpam-6189	268	19	,	,	PUNCT
ejpam-6189	268	20	y	y	PROPN
ejpam-6189	268	21	∈	∈	PROPN
ejpam-6189	268	22	x.	x.	NOUN
ejpam-6189	268	23	for	for	ADP
ejpam-6189	268	24	any	any	DET
ejpam-6189	268	25	t	t	NOUN
ejpam-6189	268	26	∈	∈	PROPN
ejpam-6189	269	1	[	[	X
ejpam-6189	269	2	0	0	NUM
ejpam-6189	269	3	,	,	PUNCT
ejpam-6189	269	4	1	1	NUM
ejpam-6189	269	5	]	]	PUNCT
ejpam-6189	269	6	,	,	PUNCT
ejpam-6189	269	7	the	the	DET
ejpam-6189	269	8	set	set	NOUN
ejpam-6189	269	9	(	(	PUNCT
ejpam-6189	269	10	sζ)t	sζ)t	X
ejpam-6189	269	11	:	:	PUNCT
ejpam-6189	269	12	=	=	SYM
ejpam-6189	269	13	{	{	PUNCT
ejpam-6189	269	14	(	(	PUNCT
ejpam-6189	269	15	x	x	NOUN
ejpam-6189	269	16	,	,	PUNCT
ejpam-6189	269	17	y	y	NOUN
ejpam-6189	269	18	)	)	PUNCT
ejpam-6189	269	19	|	|	ADV
ejpam-6189	269	20	sζ(x	sζ(x	ADV
ejpam-6189	269	21	,	,	PUNCT
ejpam-6189	269	22	y	y	PROPN
ejpam-6189	269	23	)	)	PUNCT
ejpam-6189	269	24	≥	≥	NOUN
ejpam-6189	269	25	t	t	PROPN
ejpam-6189	269	26	}	}	PUNCT
ejpam-6189	269	27	is	be	AUX
ejpam-6189	269	28	called	call	VERB
ejpam-6189	269	29	a	a	DET
ejpam-6189	269	30	level	level	NOUN
ejpam-6189	269	31	subset	subset	NOUN
ejpam-6189	269	32	of	of	ADP
ejpam-6189	269	33	sζ	sζ	PROPN
ejpam-6189	269	34	,	,	PUNCT
ejpam-6189	269	35	see	see	VERB
ejpam-6189	269	36	[	[	X
ejpam-6189	269	37	28	28	NUM
ejpam-6189	269	38	]	]	PUNCT
ejpam-6189	269	39	.	.	PUNCT
ejpam-6189	270	1	let	let	VERB
ejpam-6189	270	2	a	a	DET
ejpam-6189	270	3	be	be	AUX
ejpam-6189	270	4	any	any	DET
ejpam-6189	270	5	subset	subset	NOUN
ejpam-6189	270	6	of	of	ADP
ejpam-6189	270	7	a	a	DET
ejpam-6189	270	8	nonempty	nonempty	ADV
ejpam-6189	270	9	set	set	VERB
ejpam-6189	270	10	x	x	PUNCT
ejpam-6189	270	11	and	and	CCONJ
ejpam-6189	270	12	ζ	ζ	NOUN
ejpam-6189	270	13	be	be	AUX
ejpam-6189	270	14	a	a	DET
ejpam-6189	270	15	fuzzy	fuzzy	ADJ
ejpam-6189	270	16	set	set	NOUN
ejpam-6189	270	17	of	of	ADP
ejpam-6189	270	18	x.	x.	NOUN
ejpam-6189	270	19	the	the	DET
ejpam-6189	270	20	characteristic	characteristic	ADJ
ejpam-6189	270	21	function	function	NOUN
ejpam-6189	270	22	ca	can	AUX
ejpam-6189	270	23	ζ	ζ	NOUN
ejpam-6189	270	24	of	of	ADP
ejpam-6189	270	25	a×a	a×a	PROPN
ejpam-6189	270	26	is	be	AUX
ejpam-6189	270	27	defined	define	VERB
ejpam-6189	270	28	by	by	ADP
ejpam-6189	270	29	for	for	ADP
ejpam-6189	270	30	every	every	DET
ejpam-6189	270	31	x	x	NOUN
ejpam-6189	270	32	,	,	PUNCT
ejpam-6189	270	33	y	y	PROPN
ejpam-6189	270	34	∈	∈	PROPN
ejpam-6189	271	1	x	x	X
ejpam-6189	271	2	,	,	PUNCT
ejpam-6189	271	3	ca	can	AUX
ejpam-6189	271	4	ζ	ζ	NOUN
ejpam-6189	271	5	(	(	PUNCT
ejpam-6189	271	6	x	x	NOUN
ejpam-6189	271	7	,	,	PUNCT
ejpam-6189	271	8	y	y	PROPN
ejpam-6189	271	9	)	)	PUNCT
ejpam-6189	271	10	:	:	PUNCT
ejpam-6189	271	11	=	=	SYM
ejpam-6189	271	12	{	{	PUNCT
ejpam-6189	271	13	1	1	NUM
ejpam-6189	271	14	if	if	SCONJ
ejpam-6189	271	15	(	(	PUNCT
ejpam-6189	271	16	x	x	NOUN
ejpam-6189	271	17	,	,	PUNCT
ejpam-6189	271	18	y	y	NOUN
ejpam-6189	271	19	)	)	PUNCT
ejpam-6189	271	20	∈	∈	PROPN
ejpam-6189	271	21	a×a	a×a	PROPN
ejpam-6189	271	22	,	,	PUNCT
ejpam-6189	271	23	0	0	NUM
ejpam-6189	271	24	otherwise	otherwise	ADV
ejpam-6189	271	25	.	.	PUNCT
ejpam-6189	272	1	next	next	ADV
ejpam-6189	272	2	,	,	PUNCT
ejpam-6189	272	3	the	the	DET
ejpam-6189	272	4	notion	notion	NOUN
ejpam-6189	272	5	of	of	ADP
ejpam-6189	272	6	strongest	strong	ADJ
ejpam-6189	272	7	fuzzy	fuzzy	ADJ
ejpam-6189	272	8	dot	dot	NOUN
ejpam-6189	272	9	bd	bd	NOUN
ejpam-6189	272	10	-	-	PUNCT
ejpam-6189	272	11	subalgebras	subalgebras	PROPN
ejpam-6189	272	12	on	on	ADP
ejpam-6189	272	13	bd	bd	PROPN
ejpam-6189	272	14	-	-	PUNCT
ejpam-6189	272	15	algebras	algebras	PROPN
ejpam-6189	272	16	is	be	AUX
ejpam-6189	272	17	further	far	ADV
ejpam-6189	272	18	introduced	introduce	VERB
ejpam-6189	272	19	as	as	SCONJ
ejpam-6189	272	20	follows	follow	VERB
ejpam-6189	272	21	.	.	PUNCT
ejpam-6189	273	1	definition	definition	NOUN
ejpam-6189	273	2	5	5	NUM
ejpam-6189	273	3	.	.	PUNCT
ejpam-6189	274	1	let	let	VERB
ejpam-6189	274	2	x	x	PRON
ejpam-6189	274	3	be	be	AUX
ejpam-6189	274	4	a	a	DET
ejpam-6189	274	5	bd	bd	NOUN
ejpam-6189	274	6	-	-	NOUN
ejpam-6189	274	7	algebra	algebra	NOUN
ejpam-6189	274	8	,	,	PUNCT
ejpam-6189	274	9	ζ	ζ	NOUN
ejpam-6189	274	10	be	be	VERB
ejpam-6189	274	11	a	a	DET
ejpam-6189	274	12	fuzzy	fuzzy	ADJ
ejpam-6189	274	13	set	set	NOUN
ejpam-6189	274	14	of	of	ADP
ejpam-6189	274	15	x	x	PRON
ejpam-6189	274	16	,	,	PUNCT
ejpam-6189	274	17	and	and	CCONJ
ejpam-6189	274	18	sζ	sζ	PROPN
ejpam-6189	274	19	be	be	AUX
ejpam-6189	274	20	a	a	DET
ejpam-6189	274	21	strongest	strong	ADJ
ejpam-6189	274	22	fuzzy	fuzzy	ADJ
ejpam-6189	274	23	ζ	ζ	NOUN
ejpam-6189	274	24	-	-	PUNCT
ejpam-6189	274	25	relation	relation	NOUN
ejpam-6189	274	26	on	on	ADP
ejpam-6189	274	27	x.	x.	NOUN
ejpam-6189	274	28	then	then	ADV
ejpam-6189	274	29	sζ	sζ	PROPN
ejpam-6189	274	30	is	be	AUX
ejpam-6189	274	31	called	call	VERB
ejpam-6189	274	32	a	a	DET
ejpam-6189	274	33	strongest	strong	ADJ
ejpam-6189	274	34	fuzzy	fuzzy	ADJ
ejpam-6189	274	35	dot	dot	NOUN
ejpam-6189	274	36	bd	bd	NOUN
ejpam-6189	274	37	-	-	NOUN
ejpam-6189	274	38	subalgebra	subalgebra	NOUN
ejpam-6189	274	39	on	on	ADP
ejpam-6189	274	40	x	x	SYM
ejpam-6189	274	41	if	if	SCONJ
ejpam-6189	274	42	for	for	ADP
ejpam-6189	274	43	every	every	DET
ejpam-6189	274	44	x1	x1	PROPN
ejpam-6189	274	45	,	,	PUNCT
ejpam-6189	274	46	x2	x2	PROPN
ejpam-6189	274	47	,	,	PUNCT
ejpam-6189	274	48	y1	y1	NOUN
ejpam-6189	274	49	,	,	PUNCT
ejpam-6189	274	50	y2	y2	NOUN
ejpam-6189	274	51	∈	∈	PROPN
ejpam-6189	275	1	x	x	X
ejpam-6189	275	2	:	:	PUNCT
ejpam-6189	275	3	(	(	PUNCT
ejpam-6189	275	4	i	i	NOUN
ejpam-6189	275	5	)	)	PUNCT
ejpam-6189	275	6	sζ(0	sζ(0	PROPN
ejpam-6189	275	7	,	,	PUNCT
ejpam-6189	275	8	0	0	NUM
ejpam-6189	275	9	)	)	PUNCT
ejpam-6189	275	10	≥	≥	NOUN
ejpam-6189	275	11	sζ(x1	sζ(x1	PROPN
ejpam-6189	275	12	,	,	PUNCT
ejpam-6189	275	13	y1	y1	PROPN
ejpam-6189	275	14	)	)	PUNCT
ejpam-6189	275	15	;	;	PUNCT
ejpam-6189	275	16	(	(	PUNCT
ejpam-6189	275	17	ii	ii	NOUN
ejpam-6189	275	18	)	)	PUNCT
ejpam-6189	275	19	sζ(x1	sζ(x1	ADJ
ejpam-6189	275	20	∗	∗	NOUN
ejpam-6189	275	21	x2	x2	PROPN
ejpam-6189	275	22	,	,	PUNCT
ejpam-6189	275	23	y1	y1	NOUN
ejpam-6189	275	24	∗	∗	NOUN
ejpam-6189	275	25	y2	y2	NOUN
ejpam-6189	275	26	)	)	PUNCT
ejpam-6189	275	27	≥	≥	NOUN
ejpam-6189	275	28	sζ(x1	sζ(x1	PROPN
ejpam-6189	275	29	,	,	PUNCT
ejpam-6189	275	30	y1	y1	PROPN
ejpam-6189	275	31	)	)	PUNCT
ejpam-6189	275	32	·	·	PUNCT
ejpam-6189	275	33	sζ(x2	sζ(x2	NOUN
ejpam-6189	275	34	,	,	PUNCT
ejpam-6189	275	35	y2	y2	PROPN
ejpam-6189	275	36	)	)	PUNCT
ejpam-6189	275	37	.	.	PUNCT
ejpam-6189	276	1	w.	w.	PROPN
ejpam-6189	276	2	nakkhasen	nakkhasen	PROPN
ejpam-6189	276	3	et	et	PROPN
ejpam-6189	276	4	al	al	PROPN
ejpam-6189	276	5	.	.	PUNCT
ejpam-6189	276	6	/	/	SYM
ejpam-6189	276	7	eur	eur	PROPN
ejpam-6189	276	8	.	.	PUNCT
ejpam-6189	277	1	j.	j.	PROPN
ejpam-6189	277	2	pure	pure	PROPN
ejpam-6189	277	3	appl	appl	PROPN
ejpam-6189	277	4	.	.	PROPN
ejpam-6189	277	5	math	math	PROPN
ejpam-6189	277	6	,	,	PUNCT
ejpam-6189	277	7	18	18	NUM
ejpam-6189	277	8	(	(	PUNCT
ejpam-6189	277	9	3	3	NUM
ejpam-6189	277	10	)	)	PUNCT
ejpam-6189	277	11	(	(	PUNCT
ejpam-6189	277	12	2025	2025	NUM
ejpam-6189	277	13	)	)	PUNCT
ejpam-6189	277	14	,	,	PUNCT
ejpam-6189	277	15	6189	6189	NUM
ejpam-6189	277	16	10	10	NUM
ejpam-6189	277	17	of	of	ADP
ejpam-6189	277	18	13	13	NUM
ejpam-6189	277	19	example	example	NOUN
ejpam-6189	277	20	6	6	NUM
ejpam-6189	277	21	.	.	PUNCT
ejpam-6189	277	22	consider	consider	VERB
ejpam-6189	277	23	the	the	DET
ejpam-6189	277	24	bd	bd	NOUN
ejpam-6189	277	25	-	-	NOUN
ejpam-6189	277	26	algebra	algebra	NOUN
ejpam-6189	277	27	x	x	X
ejpam-6189	277	28	:	:	PUNCT
ejpam-6189	277	29	=	=	SYM
ejpam-6189	277	30	(	(	PUNCT
ejpam-6189	277	31	x	x	X
ejpam-6189	277	32	,	,	PUNCT
ejpam-6189	277	33	∗	∗	NOUN
ejpam-6189	277	34	,	,	PUNCT
ejpam-6189	277	35	0	0	NUM
ejpam-6189	277	36	)	)	PUNCT
ejpam-6189	277	37	as	as	SCONJ
ejpam-6189	277	38	defined	define	VERB
ejpam-6189	277	39	in	in	ADP
ejpam-6189	277	40	example	example	NOUN
ejpam-6189	278	1	1	1	X
ejpam-6189	278	2	.	.	PUNCT
ejpam-6189	279	1	afterward	afterward	ADV
ejpam-6189	279	2	,	,	PUNCT
ejpam-6189	279	3	we	we	PRON
ejpam-6189	279	4	define	define	VERB
ejpam-6189	279	5	a	a	DET
ejpam-6189	279	6	fuzzy	fuzzy	ADJ
ejpam-6189	279	7	set	set	VERB
ejpam-6189	279	8	ζ	ζ	NOUN
ejpam-6189	279	9	of	of	ADP
ejpam-6189	279	10	x	x	PUNCT
ejpam-6189	279	11	by	by	ADP
ejpam-6189	279	12	ζ(0	ζ(0	NOUN
ejpam-6189	279	13	)	)	PUNCT
ejpam-6189	279	14	=	=	NOUN
ejpam-6189	279	15	0.90	0.90	NUM
ejpam-6189	279	16	,	,	PUNCT
ejpam-6189	279	17	ζ(a	ζ(a	PRON
ejpam-6189	279	18	)	)	PUNCT
ejpam-6189	279	19	=	=	SYM
ejpam-6189	280	1	0.70	0.70	NUM
ejpam-6189	280	2	,	,	PUNCT
ejpam-6189	280	3	ζ(b	ζ(b	PROPN
ejpam-6189	280	4	)	)	PUNCT
ejpam-6189	280	5	=	=	SYM
ejpam-6189	280	6	0.80	0.80	NUM
ejpam-6189	280	7	,	,	PUNCT
ejpam-6189	280	8	ζ(c	ζ(c	NOUN
ejpam-6189	280	9	)	)	PUNCT
ejpam-6189	280	10	=	=	SYM
ejpam-6189	280	11	0.80	0.80	NUM
ejpam-6189	280	12	.	.	PUNCT
ejpam-6189	281	1	then	then	ADV
ejpam-6189	281	2	the	the	DET
ejpam-6189	281	3	strongest	strong	ADJ
ejpam-6189	281	4	fuzzy	fuzzy	ADJ
ejpam-6189	281	5	ζ	ζ	NOUN
ejpam-6189	281	6	-	-	PUNCT
ejpam-6189	281	7	relation	relation	NOUN
ejpam-6189	281	8	sζ	sζ	NOUN
ejpam-6189	281	9	on	on	ADP
ejpam-6189	281	10	x	x	SYM
ejpam-6189	281	11	is	be	AUX
ejpam-6189	281	12	as	as	SCONJ
ejpam-6189	281	13	follows	follow	VERB
ejpam-6189	281	14	.	.	PUNCT
ejpam-6189	282	1	sζ(0	sζ(0	NOUN
ejpam-6189	282	2	,	,	PUNCT
ejpam-6189	282	3	0	0	NUM
ejpam-6189	282	4	)	)	PUNCT
ejpam-6189	282	5	=	=	SYM
ejpam-6189	283	1	0.81,sζ(0	0.81,sζ(0	NUM
ejpam-6189	283	2	,	,	PUNCT
ejpam-6189	283	3	a	a	PRON
ejpam-6189	283	4	)	)	PUNCT
ejpam-6189	283	5	=	=	SYM
ejpam-6189	283	6	0.63,sζ(0	0.63,sζ(0	NUM
ejpam-6189	283	7	,	,	PUNCT
ejpam-6189	283	8	b	b	NOUN
ejpam-6189	283	9	)	)	PUNCT
ejpam-6189	283	10	=	=	SYM
ejpam-6189	283	11	0.72,sζ(0	0.72,sζ(0	NOUN
ejpam-6189	283	12	,	,	PUNCT
ejpam-6189	283	13	c	c	NOUN
ejpam-6189	283	14	)	)	PUNCT
ejpam-6189	283	15	=	=	SYM
ejpam-6189	283	16	0.72	0.72	NUM
ejpam-6189	283	17	,	,	PUNCT
ejpam-6189	283	18	sζ(a	sζ(a	NOUN
ejpam-6189	283	19	,	,	PUNCT
ejpam-6189	283	20	0	0	NUM
ejpam-6189	283	21	)	)	PUNCT
ejpam-6189	283	22	=	=	SYM
ejpam-6189	283	23	0.63,sζ(a	0.63,sζ(a	NOUN
ejpam-6189	283	24	,	,	PUNCT
ejpam-6189	283	25	a	a	PRON
ejpam-6189	283	26	)	)	PUNCT
ejpam-6189	283	27	=	=	SYM
ejpam-6189	283	28	0.49,sζ(a	0.49,sζ(a	NOUN
ejpam-6189	283	29	,	,	PUNCT
ejpam-6189	283	30	b	b	NOUN
ejpam-6189	283	31	)	)	PUNCT
ejpam-6189	283	32	=	=	SYM
ejpam-6189	284	1	0.56,sζ(a	0.56,sζ(a	NOUN
ejpam-6189	284	2	,	,	PUNCT
ejpam-6189	284	3	c	c	NOUN
ejpam-6189	284	4	)	)	PUNCT
ejpam-6189	284	5	=	=	SYM
ejpam-6189	284	6	0.56	0.56	NUM
ejpam-6189	284	7	,	,	PUNCT
ejpam-6189	284	8	sζ(b	sζ(b	NOUN
ejpam-6189	284	9	,	,	PUNCT
ejpam-6189	284	10	0	0	NUM
ejpam-6189	284	11	)	)	PUNCT
ejpam-6189	284	12	=	=	SYM
ejpam-6189	284	13	0.72,sζ(b	0.72,sζ(b	PROPN
ejpam-6189	284	14	,	,	PUNCT
ejpam-6189	284	15	a	a	PRON
ejpam-6189	284	16	)	)	PUNCT
ejpam-6189	285	1	=	=	SYM
ejpam-6189	285	2	0.56,sζ(b	0.56,sζ(b	NUM
ejpam-6189	285	3	,	,	PUNCT
ejpam-6189	285	4	b	b	NOUN
ejpam-6189	285	5	)	)	PUNCT
ejpam-6189	285	6	=	=	SYM
ejpam-6189	285	7	0.64,sζ(b	0.64,sζ(b	NOUN
ejpam-6189	285	8	,	,	PUNCT
ejpam-6189	285	9	c	c	NOUN
ejpam-6189	285	10	)	)	PUNCT
ejpam-6189	285	11	=	=	SYM
ejpam-6189	285	12	0.64	0.64	NUM
ejpam-6189	285	13	,	,	PUNCT
ejpam-6189	285	14	sζ(c	sζ(c	PUNCT
ejpam-6189	285	15	,	,	PUNCT
ejpam-6189	285	16	0	0	NUM
ejpam-6189	285	17	)	)	PUNCT
ejpam-6189	285	18	=	=	SYM
ejpam-6189	285	19	0.72,sζ(c	0.72,sζ(c	PROPN
ejpam-6189	285	20	,	,	PUNCT
ejpam-6189	285	21	a	a	PRON
ejpam-6189	285	22	)	)	PUNCT
ejpam-6189	285	23	=	=	SYM
ejpam-6189	285	24	0.56,sζ(c	0.56,sζ(c	NUM
ejpam-6189	285	25	,	,	PUNCT
ejpam-6189	285	26	b	b	NOUN
ejpam-6189	285	27	)	)	PUNCT
ejpam-6189	285	28	=	=	SYM
ejpam-6189	286	1	0.56,sζ(c	0.56,sζ(c	NUM
ejpam-6189	286	2	,	,	PUNCT
ejpam-6189	286	3	c	c	NOUN
ejpam-6189	286	4	)	)	PUNCT
ejpam-6189	286	5	=	=	NOUN
ejpam-6189	287	1	0.64	0.64	NUM
ejpam-6189	287	2	.	.	PUNCT
ejpam-6189	288	1	it	it	PRON
ejpam-6189	288	2	turns	turn	VERB
ejpam-6189	288	3	out	out	ADP
ejpam-6189	288	4	that	that	DET
ejpam-6189	288	5	sζ(0	sζ(0	NOUN
ejpam-6189	288	6	,	,	PUNCT
ejpam-6189	288	7	0	0	NUM
ejpam-6189	288	8	)	)	PUNCT
ejpam-6189	288	9	≥	≥	NOUN
ejpam-6189	288	10	sζ(x	sζ(x	NOUN
ejpam-6189	288	11	,	,	PUNCT
ejpam-6189	288	12	y	y	NOUN
ejpam-6189	288	13	)	)	PUNCT
ejpam-6189	288	14	for	for	ADP
ejpam-6189	288	15	all	all	DET
ejpam-6189	288	16	x	x	NOUN
ejpam-6189	288	17	,	,	PUNCT
ejpam-6189	288	18	y	y	PROPN
ejpam-6189	288	19	∈	∈	PROPN
ejpam-6189	288	20	x.	x.	NOUN
ejpam-6189	288	21	a	a	DET
ejpam-6189	288	22	select	select	ADJ
ejpam-6189	288	23	few	few	ADJ
ejpam-6189	288	24	of	of	ADP
ejpam-6189	288	25	results	result	NOUN
ejpam-6189	288	26	are	be	AUX
ejpam-6189	288	27	calculated	calculate	VERB
ejpam-6189	288	28	below	below	ADV
ejpam-6189	288	29	.	.	PUNCT
ejpam-6189	289	1	sζ(a	sζ(a	NOUN
ejpam-6189	289	2	∗	∗	PROPN
ejpam-6189	289	3	0	0	NUM
ejpam-6189	289	4	,	,	PUNCT
ejpam-6189	289	5	b	b	PROPN
ejpam-6189	289	6	∗	∗	X
ejpam-6189	289	7	a	a	NOUN
ejpam-6189	289	8	)	)	PUNCT
ejpam-6189	289	9	=	=	SYM
ejpam-6189	289	10	sζ(a	sζ(a	NOUN
ejpam-6189	289	11	,	,	PUNCT
ejpam-6189	289	12	b	b	NOUN
ejpam-6189	289	13	)	)	PUNCT
ejpam-6189	289	14	=	=	SYM
ejpam-6189	289	15	0.56	0.56	NUM
ejpam-6189	289	16	>	>	SYM
ejpam-6189	289	17	0.35	0.35	NUM
ejpam-6189	289	18	=	=	SYM
ejpam-6189	289	19	sζ(a	sζ(a	NOUN
ejpam-6189	289	20	,	,	PUNCT
ejpam-6189	289	21	b	b	NOUN
ejpam-6189	289	22	)	)	PUNCT
ejpam-6189	289	23	·	·	PUNCT
ejpam-6189	289	24	sζ(0	sζ(0	NOUN
ejpam-6189	289	25	,	,	PUNCT
ejpam-6189	289	26	a	a	PRON
ejpam-6189	289	27	)	)	PUNCT
ejpam-6189	289	28	,	,	PUNCT
ejpam-6189	289	29	sζ(c	sζ(c	PUNCT
ejpam-6189	289	30	∗	∗	X
ejpam-6189	289	31	a	a	PROPN
ejpam-6189	289	32	,	,	PUNCT
ejpam-6189	289	33	0	0	NUM
ejpam-6189	289	34	∗	∗	NOUN
ejpam-6189	289	35	b	b	NOUN
ejpam-6189	289	36	)	)	PUNCT
ejpam-6189	289	37	=	=	SYM
ejpam-6189	289	38	sζ(a	sζ(a	NOUN
ejpam-6189	289	39	,	,	PUNCT
ejpam-6189	289	40	a	a	PRON
ejpam-6189	289	41	)	)	PUNCT
ejpam-6189	289	42	=	=	SYM
ejpam-6189	290	1	0.49	0.49	NUM
ejpam-6189	290	2	>	>	SYM
ejpam-6189	290	3	0.40	0.40	NUM
ejpam-6189	290	4	=	=	SYM
ejpam-6189	290	5	sζ(c	sζ(c	X
ejpam-6189	290	6	,	,	PUNCT
ejpam-6189	290	7	0	0	NUM
ejpam-6189	290	8	)	)	PUNCT
ejpam-6189	290	9	·	·	PUNCT
ejpam-6189	290	10	sζ(a	sζ(a	NOUN
ejpam-6189	290	11	,	,	PUNCT
ejpam-6189	290	12	b	b	NOUN
ejpam-6189	290	13	)	)	PUNCT
ejpam-6189	290	14	,	,	PUNCT
ejpam-6189	290	15	sζ(b	sζ(b	PUNCT
ejpam-6189	290	16	∗	∗	NOUN
ejpam-6189	290	17	c	c	PROPN
ejpam-6189	290	18	,	,	PUNCT
ejpam-6189	290	19	0	0	NUM
ejpam-6189	290	20	∗	∗	NOUN
ejpam-6189	290	21	c	c	NOUN
ejpam-6189	290	22	)	)	PUNCT
ejpam-6189	290	23	=	=	SYM
ejpam-6189	290	24	sζ(c	sζ(c	X
ejpam-6189	290	25	,	,	PUNCT
ejpam-6189	290	26	0	0	NUM
ejpam-6189	290	27	)	)	PUNCT
ejpam-6189	290	28	=	=	SYM
ejpam-6189	291	1	0.72	0.72	NUM
ejpam-6189	291	2	>	>	SYM
ejpam-6189	291	3	0.46	0.46	NUM
ejpam-6189	291	4	=	=	SYM
ejpam-6189	291	5	sζ(b	sζ(b	NOUN
ejpam-6189	291	6	,	,	PUNCT
ejpam-6189	291	7	0	0	NUM
ejpam-6189	291	8	)	)	PUNCT
ejpam-6189	291	9	·	·	PUNCT
ejpam-6189	291	10	sζ(c	sζ(c	PUNCT
ejpam-6189	291	11	,	,	PUNCT
ejpam-6189	291	12	c	c	NOUN
ejpam-6189	291	13	)	)	PUNCT
ejpam-6189	291	14	.	.	PUNCT
ejpam-6189	292	1	by	by	ADP
ejpam-6189	292	2	routine	routine	ADJ
ejpam-6189	292	3	calculations	calculation	NOUN
ejpam-6189	292	4	,	,	PUNCT
ejpam-6189	292	5	we	we	PRON
ejpam-6189	292	6	obtain	obtain	VERB
ejpam-6189	292	7	sζ(x1	sζ(x1	ADJ
ejpam-6189	292	8	∗	∗	NOUN
ejpam-6189	292	9	x2	x2	PROPN
ejpam-6189	292	10	,	,	PUNCT
ejpam-6189	292	11	y1	y1	NOUN
ejpam-6189	292	12	∗	∗	NOUN
ejpam-6189	292	13	y2	y2	NOUN
ejpam-6189	292	14	)	)	PUNCT
ejpam-6189	292	15	≥	≥	NOUN
ejpam-6189	292	16	sζ(x1	sζ(x1	PROPN
ejpam-6189	292	17	,	,	PUNCT
ejpam-6189	292	18	y1	y1	PROPN
ejpam-6189	292	19	)	)	PUNCT
ejpam-6189	292	20	·	·	PUNCT
ejpam-6189	292	21	sζ(x2	sζ(x2	NOUN
ejpam-6189	292	22	,	,	PUNCT
ejpam-6189	292	23	y2	y2	PROPN
ejpam-6189	292	24	)	)	PUNCT
ejpam-6189	292	25	for	for	ADP
ejpam-6189	292	26	all	all	PRON
ejpam-6189	292	27	x1	x1	PROPN
ejpam-6189	292	28	,	,	PUNCT
ejpam-6189	292	29	x2	x2	PROPN
ejpam-6189	292	30	,	,	PUNCT
ejpam-6189	292	31	y1	y1	NOUN
ejpam-6189	292	32	,	,	PUNCT
ejpam-6189	292	33	y2	y2	PROPN
ejpam-6189	292	34	∈	∈	PROPN
ejpam-6189	292	35	x.	x.	NOUN
ejpam-6189	292	36	therefore	therefore	ADV
ejpam-6189	292	37	,	,	PUNCT
ejpam-6189	292	38	sζ	sζ	PROPN
ejpam-6189	292	39	is	be	AUX
ejpam-6189	292	40	a	a	DET
ejpam-6189	292	41	strongest	strong	ADJ
ejpam-6189	292	42	fuzzy	fuzzy	ADJ
ejpam-6189	292	43	dot	dot	NOUN
ejpam-6189	292	44	bd	bd	NOUN
ejpam-6189	292	45	-	-	PUNCT
ejpam-6189	292	46	subalgebra	subalgebra	NOUN
ejpam-6189	292	47	on	on	ADP
ejpam-6189	292	48	x.	x.	NOUN
ejpam-6189	292	49	theorem	theorem	VERB
ejpam-6189	292	50	7	7	NUM
ejpam-6189	292	51	.	.	PUNCT
ejpam-6189	293	1	let	let	VERB
ejpam-6189	293	2	x	x	PRON
ejpam-6189	293	3	be	be	AUX
ejpam-6189	293	4	a	a	DET
ejpam-6189	293	5	bd	bd	NOUN
ejpam-6189	293	6	-	-	NOUN
ejpam-6189	293	7	algebra	algebra	NOUN
ejpam-6189	293	8	,	,	PUNCT
ejpam-6189	293	9	ζ	ζ	NOUN
ejpam-6189	293	10	be	be	VERB
ejpam-6189	293	11	a	a	DET
ejpam-6189	293	12	fuzzy	fuzzy	ADJ
ejpam-6189	293	13	set	set	NOUN
ejpam-6189	293	14	of	of	ADP
ejpam-6189	293	15	x	x	PRON
ejpam-6189	293	16	,	,	PUNCT
ejpam-6189	293	17	and	and	CCONJ
ejpam-6189	293	18	sζ	sζ	PROPN
ejpam-6189	293	19	be	be	AUX
ejpam-6189	293	20	a	a	DET
ejpam-6189	293	21	strongest	strong	ADJ
ejpam-6189	293	22	fuzzy	fuzzy	ADJ
ejpam-6189	293	23	ζ	ζ	NOUN
ejpam-6189	293	24	-	-	PUNCT
ejpam-6189	293	25	relation	relation	NOUN
ejpam-6189	293	26	on	on	ADP
ejpam-6189	293	27	x.	x.	NOUN
ejpam-6189	293	28	then	then	ADV
ejpam-6189	293	29	ζ	ζ	NOUN
ejpam-6189	293	30	is	be	AUX
ejpam-6189	293	31	a	a	DET
ejpam-6189	293	32	fuzzy	fuzzy	ADJ
ejpam-6189	293	33	dot	dot	NOUN
ejpam-6189	293	34	bd	bd	NOUN
ejpam-6189	293	35	-	-	PUNCT
ejpam-6189	293	36	subalgebra	subalgebra	NOUN
ejpam-6189	293	37	of	of	ADP
ejpam-6189	293	38	x	x	PRON
ejpam-6189	293	39	if	if	SCONJ
ejpam-6189	293	40	and	and	CCONJ
ejpam-6189	293	41	only	only	ADV
ejpam-6189	293	42	if	if	SCONJ
ejpam-6189	293	43	sζ	sζ	PROPN
ejpam-6189	293	44	is	be	AUX
ejpam-6189	293	45	a	a	DET
ejpam-6189	293	46	strongest	strong	ADJ
ejpam-6189	293	47	fuzzy	fuzzy	ADJ
ejpam-6189	293	48	dot	dot	NOUN
ejpam-6189	293	49	bd	bd	NOUN
ejpam-6189	293	50	-	-	PUNCT
ejpam-6189	293	51	subalgebra	subalgebra	NOUN
ejpam-6189	293	52	on	on	ADP
ejpam-6189	293	53	x.	x.	NOUN
ejpam-6189	293	54	proof	proof	PROPN
ejpam-6189	293	55	.	.	PUNCT
ejpam-6189	294	1	assume	assume	VERB
ejpam-6189	294	2	that	that	SCONJ
ejpam-6189	294	3	ζ	ζ	NOUN
ejpam-6189	294	4	is	be	AUX
ejpam-6189	294	5	a	a	DET
ejpam-6189	294	6	fuzzy	fuzzy	ADJ
ejpam-6189	294	7	dot	dot	NOUN
ejpam-6189	294	8	bd	bd	NOUN
ejpam-6189	294	9	-	-	PUNCT
ejpam-6189	294	10	subalgebra	subalgebra	NOUN
ejpam-6189	294	11	of	of	ADP
ejpam-6189	294	12	x.	x.	NOUN
ejpam-6189	294	13	let	let	VERB
ejpam-6189	294	14	x1	x1	NUM
ejpam-6189	294	15	,	,	PUNCT
ejpam-6189	294	16	x2	x2	PROPN
ejpam-6189	294	17	,	,	PUNCT
ejpam-6189	294	18	y1	y1	NOUN
ejpam-6189	294	19	,	,	PUNCT
ejpam-6189	294	20	y2	y2	PROPN
ejpam-6189	294	21	∈	∈	PROPN
ejpam-6189	295	1	x.	x.	NOUN
ejpam-6189	295	2	then	then	ADV
ejpam-6189	295	3	we	we	PRON
ejpam-6189	295	4	have	have	VERB
ejpam-6189	295	5	sζ(0	sζ(0	NOUN
ejpam-6189	295	6	,	,	PUNCT
ejpam-6189	295	7	0	0	NUM
ejpam-6189	295	8	)	)	PUNCT
ejpam-6189	295	9	=	=	SYM
ejpam-6189	295	10	ζ(0	ζ(0	NOUN
ejpam-6189	295	11	)	)	PUNCT
ejpam-6189	295	12	·	·	PUNCT
ejpam-6189	295	13	ζ(0	ζ(0	NOUN
ejpam-6189	295	14	)	)	PUNCT
ejpam-6189	295	15	≥	≥	NOUN
ejpam-6189	295	16	ζ(x1	ζ(x1	NOUN
ejpam-6189	295	17	)	)	PUNCT
ejpam-6189	295	18	·	·	PUNCT
ejpam-6189	295	19	ζ(y1	ζ(y1	ADJ
ejpam-6189	295	20	)	)	PUNCT
ejpam-6189	295	21	=	=	SYM
ejpam-6189	295	22	sζ(x1	sζ(x1	ADJ
ejpam-6189	295	23	,	,	PUNCT
ejpam-6189	295	24	y1	y1	NOUN
ejpam-6189	295	25	)	)	PUNCT
ejpam-6189	295	26	and	and	CCONJ
ejpam-6189	295	27	sζ(x1	sζ(x1	NUM
ejpam-6189	295	28	∗	∗	NOUN
ejpam-6189	295	29	x2	x2	PROPN
ejpam-6189	295	30	,	,	PUNCT
ejpam-6189	295	31	y1	y1	NOUN
ejpam-6189	295	32	∗	∗	NOUN
ejpam-6189	295	33	y2	y2	NOUN
ejpam-6189	295	34	)	)	PUNCT
ejpam-6189	295	35	=	=	SYM
ejpam-6189	295	36	ζ(x1	ζ(x1	X
ejpam-6189	295	37	∗	∗	X
ejpam-6189	295	38	x2	x2	PROPN
ejpam-6189	295	39	)	)	PUNCT
ejpam-6189	295	40	·	·	PUNCT
ejpam-6189	295	41	ζ(y1	ζ(y1	NOUN
ejpam-6189	295	42	∗	∗	NOUN
ejpam-6189	295	43	y2	y2	NOUN
ejpam-6189	295	44	)	)	PUNCT
ejpam-6189	295	45	≥	≥	NOUN
ejpam-6189	296	1	[	[	X
ejpam-6189	296	2	ζ(x1	ζ(x1	NOUN
ejpam-6189	296	3	)	)	PUNCT
ejpam-6189	296	4	·	·	PUNCT
ejpam-6189	296	5	ζ(x2	ζ(x2	NOUN
ejpam-6189	296	6	)	)	PUNCT
ejpam-6189	296	7	]	]	PUNCT
ejpam-6189	296	8	·	·	PUNCT
ejpam-6189	297	1	[	[	X
ejpam-6189	297	2	ζ(y1	ζ(y1	NOUN
ejpam-6189	297	3	)	)	PUNCT
ejpam-6189	297	4	·	·	PUNCT
ejpam-6189	297	5	ζ(y2	ζ(y2	NOUN
ejpam-6189	297	6	)	)	PUNCT
ejpam-6189	297	7	]	]	PUNCT
ejpam-6189	298	1	=	=	PUNCT
ejpam-6189	299	1	[	[	X
ejpam-6189	299	2	ζ(x1	ζ(x1	NOUN
ejpam-6189	299	3	)	)	PUNCT
ejpam-6189	299	4	·	·	PUNCT
ejpam-6189	299	5	ζ(y1	ζ(y1	NOUN
ejpam-6189	299	6	)	)	PUNCT
ejpam-6189	299	7	]	]	PUNCT
ejpam-6189	299	8	·	·	PUNCT
ejpam-6189	300	1	[	[	X
ejpam-6189	300	2	ζ(x2	ζ(x2	NOUN
ejpam-6189	300	3	)	)	PUNCT
ejpam-6189	300	4	·	·	PUNCT
ejpam-6189	300	5	ζ(y2	ζ(y2	NOUN
ejpam-6189	300	6	)	)	PUNCT
ejpam-6189	300	7	]	]	PUNCT
ejpam-6189	301	1	=	=	SYM
ejpam-6189	301	2	sζ(x1	sζ(x1	PROPN
ejpam-6189	301	3	,	,	PUNCT
ejpam-6189	301	4	y1	y1	PROPN
ejpam-6189	301	5	)	)	PUNCT
ejpam-6189	301	6	·	·	PUNCT
ejpam-6189	301	7	sζ(y1	sζ(y1	X
ejpam-6189	301	8	,	,	PUNCT
ejpam-6189	301	9	y2	y2	PROPN
ejpam-6189	301	10	)	)	PUNCT
ejpam-6189	301	11	.	.	PUNCT
ejpam-6189	302	1	therefore	therefore	ADV
ejpam-6189	302	2	,	,	PUNCT
ejpam-6189	302	3	sζ	sζ	PROPN
ejpam-6189	302	4	is	be	AUX
ejpam-6189	302	5	a	a	DET
ejpam-6189	302	6	strongest	strong	ADJ
ejpam-6189	302	7	fuzzy	fuzzy	ADJ
ejpam-6189	302	8	dot	dot	NOUN
ejpam-6189	302	9	bd	bd	NOUN
ejpam-6189	302	10	-	-	PUNCT
ejpam-6189	302	11	subalgebra	subalgebra	NOUN
ejpam-6189	302	12	on	on	ADP
ejpam-6189	302	13	x.	x.	NOUN
ejpam-6189	302	14	conversely	conversely	ADV
ejpam-6189	302	15	,	,	PUNCT
ejpam-6189	302	16	assume	assume	VERB
ejpam-6189	302	17	that	that	SCONJ
ejpam-6189	302	18	sζ	sζ	PROPN
ejpam-6189	302	19	is	be	AUX
ejpam-6189	302	20	a	a	DET
ejpam-6189	302	21	strongest	strong	ADJ
ejpam-6189	302	22	fuzzy	fuzzy	ADJ
ejpam-6189	302	23	dot	dot	NOUN
ejpam-6189	302	24	bd	bd	NOUN
ejpam-6189	302	25	-	-	PUNCT
ejpam-6189	302	26	subalgebra	subalgebra	NOUN
ejpam-6189	302	27	on	on	ADP
ejpam-6189	302	28	x.	x.	NOUN
ejpam-6189	302	29	let	let	VERB
ejpam-6189	302	30	x	x	PRON
ejpam-6189	302	31	,	,	PUNCT
ejpam-6189	302	32	y	y	PROPN
ejpam-6189	302	33	∈	∈	PROPN
ejpam-6189	302	34	x.	x.	NOUN
ejpam-6189	303	1	we	we	PRON
ejpam-6189	303	2	consider	consider	VERB
ejpam-6189	303	3	(	(	PUNCT
ejpam-6189	303	4	ζ(0))2	ζ(0))2	X
ejpam-6189	303	5	=	=	SYM
ejpam-6189	303	6	ζ(0	ζ(0	NOUN
ejpam-6189	303	7	)	)	PUNCT
ejpam-6189	303	8	·	·	PUNCT
ejpam-6189	304	1	ζ(0	ζ(0	NOUN
ejpam-6189	304	2	)	)	PUNCT
ejpam-6189	304	3	=	=	SYM
ejpam-6189	304	4	sζ(0	sζ(0	NOUN
ejpam-6189	304	5	,	,	PUNCT
ejpam-6189	304	6	0	0	NUM
ejpam-6189	304	7	)	)	PUNCT
ejpam-6189	304	8	≥	≥	NOUN
ejpam-6189	304	9	sζ(x	sζ(x	SYM
ejpam-6189	304	10	,	,	PUNCT
ejpam-6189	304	11	x	x	X
ejpam-6189	304	12	)	)	PUNCT
ejpam-6189	304	13	=	=	SYM
ejpam-6189	304	14	ζ(x	ζ(x	NOUN
ejpam-6189	304	15	)	)	PUNCT
ejpam-6189	304	16	·	·	PUNCT
ejpam-6189	304	17	ζ(x	ζ(x	NOUN
ejpam-6189	304	18	)	)	PUNCT
ejpam-6189	304	19	=	=	SYM
ejpam-6189	304	20	(	(	PUNCT
ejpam-6189	304	21	ζ(x))2	ζ(x))2	PROPN
ejpam-6189	304	22	and	and	CCONJ
ejpam-6189	304	23	(	(	PUNCT
ejpam-6189	304	24	ζ(x	ζ(x	NOUN
ejpam-6189	304	25	∗	∗	VERB
ejpam-6189	304	26	y))2	y))2	NOUN
ejpam-6189	304	27	=	=	SYM
ejpam-6189	304	28	ζ(x	ζ(x	PROPN
ejpam-6189	304	29	∗	∗	NOUN
ejpam-6189	304	30	y	y	NOUN
ejpam-6189	304	31	)	)	PUNCT
ejpam-6189	304	32	·	·	PUNCT
ejpam-6189	305	1	ζ(x	ζ(x	NOUN
ejpam-6189	305	2	∗	∗	NOUN
ejpam-6189	305	3	y	y	NOUN
ejpam-6189	305	4	)	)	PUNCT
ejpam-6189	305	5	w.	w.	PROPN
ejpam-6189	305	6	nakkhasen	nakkhasen	PROPN
ejpam-6189	305	7	et	et	PROPN
ejpam-6189	305	8	al	al	PROPN
ejpam-6189	305	9	.	.	PUNCT
ejpam-6189	305	10	/	/	SYM
ejpam-6189	305	11	eur	eur	PROPN
ejpam-6189	305	12	.	.	PUNCT
ejpam-6189	306	1	j.	j.	PROPN
ejpam-6189	306	2	pure	pure	PROPN
ejpam-6189	306	3	appl	appl	PROPN
ejpam-6189	306	4	.	.	PROPN
ejpam-6189	306	5	math	math	PROPN
ejpam-6189	306	6	,	,	PUNCT
ejpam-6189	306	7	18	18	NUM
ejpam-6189	306	8	(	(	PUNCT
ejpam-6189	306	9	3	3	NUM
ejpam-6189	306	10	)	)	PUNCT
ejpam-6189	306	11	(	(	PUNCT
ejpam-6189	306	12	2025	2025	NUM
ejpam-6189	306	13	)	)	PUNCT
ejpam-6189	306	14	,	,	PUNCT
ejpam-6189	306	15	6189	6189	NUM
ejpam-6189	306	16	11	11	NUM
ejpam-6189	306	17	of	of	ADP
ejpam-6189	306	18	13	13	NUM
ejpam-6189	306	19	=	=	SYM
ejpam-6189	306	20	sζ(x	sζ(x	ADP
ejpam-6189	306	21	∗	∗	NOUN
ejpam-6189	306	22	y	y	PROPN
ejpam-6189	306	23	,	,	PUNCT
ejpam-6189	306	24	x	x	PROPN
ejpam-6189	306	25	∗	∗	PROPN
ejpam-6189	306	26	y	y	PROPN
ejpam-6189	306	27	)	)	PUNCT
ejpam-6189	306	28	≥	≥	NOUN
ejpam-6189	306	29	sζ(x	sζ(x	SYM
ejpam-6189	306	30	,	,	PUNCT
ejpam-6189	306	31	x	x	X
ejpam-6189	306	32	)	)	PUNCT
ejpam-6189	306	33	·	·	PUNCT
ejpam-6189	307	1	sζ(y	sζ(y	X
ejpam-6189	307	2	,	,	PUNCT
ejpam-6189	307	3	y	y	NOUN
ejpam-6189	307	4	)	)	PUNCT
ejpam-6189	308	1	=	=	PUNCT
ejpam-6189	309	1	[	[	X
ejpam-6189	309	2	ζ(x	ζ(x	NOUN
ejpam-6189	309	3	)	)	PUNCT
ejpam-6189	309	4	·	·	PUNCT
ejpam-6189	309	5	ζ(x	ζ(x	NOUN
ejpam-6189	309	6	)	)	PUNCT
ejpam-6189	309	7	]	]	PUNCT
ejpam-6189	309	8	·	·	PUNCT
ejpam-6189	310	1	[	[	X
ejpam-6189	310	2	ζ(y	ζ(y	X
ejpam-6189	310	3	)	)	PUNCT
ejpam-6189	310	4	·	·	PUNCT
ejpam-6189	310	5	ζ(y	ζ(y	X
ejpam-6189	310	6	)	)	PUNCT
ejpam-6189	310	7	]	]	PUNCT
ejpam-6189	311	1	=	=	PUNCT
ejpam-6189	312	1	[	[	X
ejpam-6189	312	2	ζ(x	ζ(x	NOUN
ejpam-6189	312	3	)	)	PUNCT
ejpam-6189	312	4	·	·	PUNCT
ejpam-6189	312	5	ζ(y	ζ(y	X
ejpam-6189	312	6	)	)	PUNCT
ejpam-6189	312	7	]	]	PUNCT
ejpam-6189	312	8	·	·	PUNCT
ejpam-6189	313	1	[	[	X
ejpam-6189	313	2	ζ(x	ζ(x	NOUN
ejpam-6189	313	3	)	)	PUNCT
ejpam-6189	313	4	·	·	PUNCT
ejpam-6189	313	5	ζ(y	ζ(y	X
ejpam-6189	313	6	)	)	PUNCT
ejpam-6189	313	7	]	]	PUNCT
ejpam-6189	313	8	=	=	PUNCT
ejpam-6189	313	9	(	(	PUNCT
ejpam-6189	313	10	ζ(x	ζ(x	NOUN
ejpam-6189	313	11	)	)	PUNCT
ejpam-6189	313	12	·	·	PUNCT
ejpam-6189	314	1	ζ(y))2	ζ(y))2	PROPN
ejpam-6189	314	2	.	.	PUNCT
ejpam-6189	314	3	since	since	SCONJ
ejpam-6189	314	4	ζ(0	ζ(0	NOUN
ejpam-6189	314	5	)	)	PUNCT
ejpam-6189	314	6	,	,	PUNCT
ejpam-6189	314	7	ζ(x	ζ(x	NOUN
ejpam-6189	314	8	)	)	PUNCT
ejpam-6189	314	9	,	,	PUNCT
ejpam-6189	314	10	ζ(x	ζ(x	PROPN
ejpam-6189	314	11	∗	∗	NOUN
ejpam-6189	314	12	y	y	NOUN
ejpam-6189	314	13	)	)	PUNCT
ejpam-6189	314	14	,	,	PUNCT
ejpam-6189	314	15	ζ(x	ζ(x	NOUN
ejpam-6189	314	16	)	)	PUNCT
ejpam-6189	314	17	·	·	PUNCT
ejpam-6189	314	18	ζ(y	ζ(y	PROPN
ejpam-6189	314	19	)	)	PUNCT
ejpam-6189	314	20	≥	≥	NOUN
ejpam-6189	314	21	0	0	NUM
ejpam-6189	314	22	,	,	PUNCT
ejpam-6189	314	23	we	we	PRON
ejpam-6189	314	24	have	have	VERB
ejpam-6189	314	25	ζ(0	ζ(0	NOUN
ejpam-6189	314	26	)	)	PUNCT
ejpam-6189	314	27	≥	≥	NOUN
ejpam-6189	314	28	ζ(x	ζ(x	NOUN
ejpam-6189	314	29	)	)	PUNCT
ejpam-6189	314	30	and	and	CCONJ
ejpam-6189	314	31	ζ(x	ζ(x	PROPN
ejpam-6189	314	32	∗	∗	NOUN
ejpam-6189	314	33	y	y	NOUN
ejpam-6189	314	34	)	)	PUNCT
ejpam-6189	314	35	≥	≥	NOUN
ejpam-6189	314	36	ζ(x	ζ(x	NOUN
ejpam-6189	314	37	)	)	PUNCT
ejpam-6189	314	38	·	·	PUNCT
ejpam-6189	314	39	ζ(y	ζ(y	X
ejpam-6189	314	40	)	)	PUNCT
ejpam-6189	314	41	.	.	PUNCT
ejpam-6189	315	1	consequently	consequently	ADV
ejpam-6189	315	2	,	,	PUNCT
ejpam-6189	315	3	ζ	ζ	PROPN
ejpam-6189	315	4	is	be	AUX
ejpam-6189	315	5	a	a	DET
ejpam-6189	315	6	fuzzy	fuzzy	ADJ
ejpam-6189	315	7	dot	dot	NOUN
ejpam-6189	315	8	bd	bd	NOUN
ejpam-6189	315	9	-	-	PUNCT
ejpam-6189	315	10	subalgebra	subalgebra	NOUN
ejpam-6189	315	11	of	of	ADP
ejpam-6189	315	12	x.	x.	NOUN
ejpam-6189	315	13	theorem	theorem	VERB
ejpam-6189	315	14	8	8	NUM
ejpam-6189	315	15	.	.	PUNCT
ejpam-6189	316	1	let	let	VERB
ejpam-6189	316	2	x	x	PRON
ejpam-6189	316	3	be	be	AUX
ejpam-6189	316	4	a	a	DET
ejpam-6189	316	5	bd	bd	NOUN
ejpam-6189	316	6	-	-	NOUN
ejpam-6189	316	7	algebra	algebra	PROPN
ejpam-6189	316	8	and	and	CCONJ
ejpam-6189	316	9	sζ	sζ	PROPN
ejpam-6189	316	10	be	be	AUX
ejpam-6189	316	11	a	a	DET
ejpam-6189	316	12	strongest	strong	ADJ
ejpam-6189	316	13	fuzzy	fuzzy	ADJ
ejpam-6189	316	14	ζ	ζ	NOUN
ejpam-6189	316	15	-	-	PUNCT
ejpam-6189	316	16	relation	relation	NOUN
ejpam-6189	316	17	on	on	ADP
ejpam-6189	316	18	x	x	NOUN
ejpam-6189	316	19	,	,	PUNCT
ejpam-6189	316	20	where	where	SCONJ
ejpam-6189	316	21	ζ	ζ	NOUN
ejpam-6189	316	22	is	be	AUX
ejpam-6189	316	23	a	a	DET
ejpam-6189	316	24	fuzzy	fuzzy	ADJ
ejpam-6189	316	25	set	set	NOUN
ejpam-6189	316	26	of	of	ADP
ejpam-6189	316	27	x.	x.	NOUN
ejpam-6189	316	28	if	if	SCONJ
ejpam-6189	316	29	a	a	DET
ejpam-6189	316	30	nonempty	nonempty	ADJ
ejpam-6189	316	31	level	level	NOUN
ejpam-6189	316	32	subset	subset	NOUN
ejpam-6189	316	33	(	(	PUNCT
ejpam-6189	316	34	sζ)t	sζ)t	PROPN
ejpam-6189	316	35	is	be	AUX
ejpam-6189	316	36	a	a	DET
ejpam-6189	316	37	bd	bd	NOUN
ejpam-6189	316	38	-	-	PUNCT
ejpam-6189	316	39	subalgebra	subalgebra	NOUN
ejpam-6189	316	40	of	of	ADP
ejpam-6189	316	41	x	x	X
ejpam-6189	316	42	×x	×x	VERB
ejpam-6189	316	43	for	for	ADP
ejpam-6189	316	44	all	all	DET
ejpam-6189	316	45	t	t	NOUN
ejpam-6189	316	46	∈	∈	PROPN
ejpam-6189	317	1	[	[	X
ejpam-6189	317	2	0	0	NUM
ejpam-6189	317	3	,	,	PUNCT
ejpam-6189	317	4	1	1	NUM
ejpam-6189	317	5	]	]	PUNCT
ejpam-6189	317	6	,	,	PUNCT
ejpam-6189	317	7	then	then	ADV
ejpam-6189	317	8	sζ	sζ	PROPN
ejpam-6189	317	9	is	be	AUX
ejpam-6189	317	10	a	a	DET
ejpam-6189	317	11	strongest	strong	ADJ
ejpam-6189	317	12	fuzzy	fuzzy	ADJ
ejpam-6189	317	13	dot	dot	NOUN
ejpam-6189	317	14	bd	bd	NOUN
ejpam-6189	317	15	-	-	PUNCT
ejpam-6189	317	16	subalgebra	subalgebra	NOUN
ejpam-6189	317	17	on	on	ADP
ejpam-6189	317	18	x.	x.	NOUN
ejpam-6189	317	19	proof	proof	NOUN
ejpam-6189	317	20	.	.	PUNCT
ejpam-6189	318	1	let	let	VERB
ejpam-6189	318	2	x1	x1	NUM
ejpam-6189	318	3	,	,	PUNCT
ejpam-6189	318	4	x2	x2	PROPN
ejpam-6189	318	5	,	,	PUNCT
ejpam-6189	318	6	y1	y1	NOUN
ejpam-6189	318	7	,	,	PUNCT
ejpam-6189	318	8	y2	y2	PROPN
ejpam-6189	318	9	∈	∈	PROPN
ejpam-6189	318	10	x.	x.	NOUN
ejpam-6189	318	11	choose	choose	VERB
ejpam-6189	318	12	t′	t′	X
ejpam-6189	318	13	=	=	SYM
ejpam-6189	318	14	sζ(x1	sζ(x1	PROPN
ejpam-6189	318	15	,	,	PUNCT
ejpam-6189	318	16	y1	y1	NOUN
ejpam-6189	318	17	)	)	PUNCT
ejpam-6189	318	18	for	for	ADP
ejpam-6189	318	19	some	some	DET
ejpam-6189	318	20	t′	t′	NUM
ejpam-6189	318	21	∈	∈	PROPN
ejpam-6189	319	1	[	[	X
ejpam-6189	319	2	0	0	NUM
ejpam-6189	319	3	,	,	PUNCT
ejpam-6189	319	4	1	1	NUM
ejpam-6189	319	5	]	]	PUNCT
ejpam-6189	319	6	.	.	PUNCT
ejpam-6189	320	1	then	then	ADV
ejpam-6189	320	2	(	(	PUNCT
ejpam-6189	320	3	x1	x1	PROPN
ejpam-6189	320	4	,	,	PUNCT
ejpam-6189	320	5	y1	y1	ADJ
ejpam-6189	320	6	)	)	PUNCT
ejpam-6189	320	7	∈	∈	PROPN
ejpam-6189	320	8	(	(	PUNCT
ejpam-6189	320	9	sζ)t′	sζ)t′	NUM
ejpam-6189	320	10	;	;	PUNCT
ejpam-6189	320	11	that	that	PRON
ejpam-6189	320	12	is	is	ADV
ejpam-6189	320	13	,	,	PUNCT
ejpam-6189	320	14	(	(	PUNCT
ejpam-6189	320	15	sζ)t′	sζ)t′	ADP
ejpam-6189	320	16	̸=	̸=	PROPN
ejpam-6189	320	17	∅.	∅.	NOUN
ejpam-6189	320	18	by	by	ADP
ejpam-6189	320	19	assumption	assumption	NOUN
ejpam-6189	320	20	,	,	PUNCT
ejpam-6189	320	21	we	we	PRON
ejpam-6189	320	22	have	have	AUX
ejpam-6189	320	23	(	(	PUNCT
ejpam-6189	320	24	sζ)t′	sζ)t′	X
ejpam-6189	320	25	is	be	AUX
ejpam-6189	320	26	a	a	DET
ejpam-6189	320	27	bd	bd	NOUN
ejpam-6189	320	28	-	-	PUNCT
ejpam-6189	320	29	subalgebra	subalgebra	NOUN
ejpam-6189	320	30	of	of	ADP
ejpam-6189	320	31	x×x	x×x	PROPN
ejpam-6189	320	32	.	.	PUNCT
ejpam-6189	321	1	this	this	PRON
ejpam-6189	321	2	implies	imply	VERB
ejpam-6189	321	3	that	that	SCONJ
ejpam-6189	321	4	(	(	PUNCT
ejpam-6189	321	5	0	0	NUM
ejpam-6189	321	6	,	,	PUNCT
ejpam-6189	321	7	0	0	NUM
ejpam-6189	321	8	)	)	PUNCT
ejpam-6189	321	9	∈	∈	NOUN
ejpam-6189	321	10	(	(	PUNCT
ejpam-6189	321	11	sζ)t′	sζ)t′	NOUN
ejpam-6189	321	12	,	,	PUNCT
ejpam-6189	321	13	and	and	CCONJ
ejpam-6189	321	14	then	then	ADV
ejpam-6189	321	15	sζ(0	sζ(0	PROPN
ejpam-6189	321	16	,	,	PUNCT
ejpam-6189	321	17	0	0	NUM
ejpam-6189	321	18	)	)	PUNCT
ejpam-6189	321	19	≥	≥	NOUN
ejpam-6189	321	20	t′	t′	NUM
ejpam-6189	321	21	=	=	SYM
ejpam-6189	321	22	sζ(x1	sζ(x1	PROPN
ejpam-6189	321	23	,	,	PUNCT
ejpam-6189	321	24	y1	y1	NOUN
ejpam-6189	321	25	)	)	PUNCT
ejpam-6189	321	26	.	.	PUNCT
ejpam-6189	322	1	next	next	ADV
ejpam-6189	322	2	,	,	PUNCT
ejpam-6189	322	3	take	take	VERB
ejpam-6189	322	4	s	s	PRON
ejpam-6189	322	5	′	′	NOUN
ejpam-6189	322	6	=	=	SYM
ejpam-6189	322	7	sζ(x1	sζ(x1	PROPN
ejpam-6189	322	8	,	,	PUNCT
ejpam-6189	322	9	y1)·sζ(x2	y1)·sζ(x2	PROPN
ejpam-6189	322	10	,	,	PUNCT
ejpam-6189	322	11	y2	y2	PROPN
ejpam-6189	322	12	)	)	PUNCT
ejpam-6189	322	13	for	for	ADP
ejpam-6189	322	14	some	some	DET
ejpam-6189	322	15	s′	s′	ADJ
ejpam-6189	322	16	∈	∈	PROPN
ejpam-6189	323	1	[	[	X
ejpam-6189	323	2	0	0	NUM
ejpam-6189	323	3	,	,	PUNCT
ejpam-6189	323	4	1	1	NUM
ejpam-6189	323	5	]	]	PUNCT
ejpam-6189	323	6	.	.	PUNCT
ejpam-6189	324	1	so	so	ADV
ejpam-6189	324	2	,	,	PUNCT
ejpam-6189	324	3	we	we	PRON
ejpam-6189	324	4	have	have	VERB
ejpam-6189	324	5	sζ(x1	sζ(x1	ADJ
ejpam-6189	324	6	,	,	PUNCT
ejpam-6189	324	7	y1	y1	PROPN
ejpam-6189	324	8	)	)	PUNCT
ejpam-6189	324	9	≥	≥	NOUN
ejpam-6189	324	10	sζ(x1	sζ(x1	PROPN
ejpam-6189	324	11	,	,	PUNCT
ejpam-6189	324	12	y1)·sζ(x2	y1)·sζ(x2	PROPN
ejpam-6189	324	13	,	,	PUNCT
ejpam-6189	324	14	y2	y2	NOUN
ejpam-6189	324	15	)	)	PUNCT
ejpam-6189	324	16	=	=	NOUN
ejpam-6189	325	1	s′	s′	PROPN
ejpam-6189	325	2	and	and	CCONJ
ejpam-6189	325	3	sζ(x2	sζ(x2	NOUN
ejpam-6189	325	4	,	,	PUNCT
ejpam-6189	325	5	y2	y2	PROPN
ejpam-6189	325	6	)	)	PUNCT
ejpam-6189	325	7	≥	≥	NOUN
ejpam-6189	325	8	sζ(x1	sζ(x1	PROPN
ejpam-6189	325	9	,	,	PUNCT
ejpam-6189	325	10	y1	y1	PROPN
ejpam-6189	325	11	)	)	PUNCT
ejpam-6189	325	12	·	·	PUNCT
ejpam-6189	325	13	sζ(x2	sζ(x2	NOUN
ejpam-6189	325	14	,	,	PUNCT
ejpam-6189	325	15	y2	y2	NOUN
ejpam-6189	325	16	)	)	PUNCT
ejpam-6189	326	1	=	=	PUNCT
ejpam-6189	327	1	s′.	s′.	X
ejpam-6189	327	2	it	it	PRON
ejpam-6189	327	3	turns	turn	VERB
ejpam-6189	327	4	out	out	ADP
ejpam-6189	327	5	that	that	SCONJ
ejpam-6189	327	6	(	(	PUNCT
ejpam-6189	327	7	x1	x1	PROPN
ejpam-6189	327	8	,	,	PUNCT
ejpam-6189	327	9	y1	y1	PROPN
ejpam-6189	327	10	)	)	PUNCT
ejpam-6189	327	11	,	,	PUNCT
ejpam-6189	327	12	(	(	PUNCT
ejpam-6189	327	13	x2	x2	PROPN
ejpam-6189	327	14	,	,	PUNCT
ejpam-6189	327	15	y2	y2	NOUN
ejpam-6189	327	16	)	)	PUNCT
ejpam-6189	327	17	∈	∈	PROPN
ejpam-6189	327	18	(	(	PUNCT
ejpam-6189	327	19	sζ)s′	sζ)s′	NOUN
ejpam-6189	327	20	.	.	PUNCT
ejpam-6189	328	1	by	by	ADP
ejpam-6189	328	2	the	the	DET
ejpam-6189	328	3	hypothesis	hypothesis	NOUN
ejpam-6189	328	4	,	,	PUNCT
ejpam-6189	328	5	we	we	PRON
ejpam-6189	328	6	get	get	VERB
ejpam-6189	328	7	(	(	PUNCT
ejpam-6189	328	8	x1	x1	PROPN
ejpam-6189	328	9	∗x2	∗x2	PROPN
ejpam-6189	328	10	,	,	PUNCT
ejpam-6189	328	11	y1	y1	NOUN
ejpam-6189	328	12	∗	∗	NOUN
ejpam-6189	328	13	y2	y2	NOUN
ejpam-6189	328	14	)	)	PUNCT
ejpam-6189	329	1	=	=	PRON
ejpam-6189	329	2	(	(	PUNCT
ejpam-6189	329	3	x1	x1	PROPN
ejpam-6189	329	4	,	,	PUNCT
ejpam-6189	329	5	y1)⊛	y1)⊛	PROPN
ejpam-6189	329	6	(	(	PUNCT
ejpam-6189	329	7	x2	x2	PROPN
ejpam-6189	329	8	,	,	PUNCT
ejpam-6189	329	9	y2	y2	PROPN
ejpam-6189	329	10	)	)	PUNCT
ejpam-6189	329	11	∈	∈	PROPN
ejpam-6189	329	12	(	(	PUNCT
ejpam-6189	329	13	sζ)s′	sζ)s′	NOUN
ejpam-6189	329	14	.	.	PUNCT
ejpam-6189	330	1	thus	thus	ADV
ejpam-6189	330	2	,	,	PUNCT
ejpam-6189	330	3	sζ(x1	sζ(x1	PROPN
ejpam-6189	330	4	∗x2	∗x2	PROPN
ejpam-6189	330	5	,	,	PUNCT
ejpam-6189	330	6	y1	y1	NOUN
ejpam-6189	330	7	∗	∗	NOUN
ejpam-6189	330	8	y2	y2	NOUN
ejpam-6189	330	9	)	)	PUNCT
ejpam-6189	330	10	≥	≥	NOUN
ejpam-6189	330	11	s′	s′	VERB
ejpam-6189	330	12	=	=	SYM
ejpam-6189	330	13	sζ(x1	sζ(x1	ADJ
ejpam-6189	330	14	,	,	PUNCT
ejpam-6189	330	15	y1	y1	NOUN
ejpam-6189	330	16	)	)	PUNCT
ejpam-6189	330	17	·	·	PUNCT
ejpam-6189	330	18	sζ(x2	sζ(x2	NOUN
ejpam-6189	330	19	,	,	PUNCT
ejpam-6189	330	20	y2	y2	PROPN
ejpam-6189	330	21	)	)	PUNCT
ejpam-6189	330	22	.	.	PUNCT
ejpam-6189	331	1	therefore	therefore	ADV
ejpam-6189	331	2	,	,	PUNCT
ejpam-6189	331	3	sζ	sζ	PROPN
ejpam-6189	331	4	is	be	AUX
ejpam-6189	331	5	a	a	DET
ejpam-6189	331	6	strongest	strong	ADJ
ejpam-6189	331	7	fuzzy	fuzzy	ADJ
ejpam-6189	331	8	dot	dot	NOUN
ejpam-6189	331	9	bd	bd	NOUN
ejpam-6189	331	10	-	-	PUNCT
ejpam-6189	331	11	subalgebra	subalgebra	NOUN
ejpam-6189	331	12	on	on	ADP
ejpam-6189	331	13	x.	x.	NOUN
ejpam-6189	331	14	the	the	DET
ejpam-6189	331	15	converse	converse	NOUN
ejpam-6189	331	16	of	of	ADP
ejpam-6189	331	17	theorem	theorem	NOUN
ejpam-6189	331	18	8	8	NUM
ejpam-6189	331	19	is	be	AUX
ejpam-6189	331	20	generally	generally	ADV
ejpam-6189	331	21	not	not	PART
ejpam-6189	331	22	valid	valid	ADJ
ejpam-6189	331	23	,	,	PUNCT
ejpam-6189	331	24	as	as	SCONJ
ejpam-6189	331	25	seen	see	VERB
ejpam-6189	331	26	by	by	ADP
ejpam-6189	331	27	the	the	DET
ejpam-6189	331	28	following	follow	VERB
ejpam-6189	331	29	example	example	NOUN
ejpam-6189	331	30	.	.	PUNCT
ejpam-6189	332	1	example	example	NOUN
ejpam-6189	333	1	7	7	NUM
ejpam-6189	333	2	.	.	PUNCT
ejpam-6189	333	3	by	by	ADP
ejpam-6189	333	4	example	example	NOUN
ejpam-6189	333	5	6	6	NUM
ejpam-6189	333	6	,	,	PUNCT
ejpam-6189	333	7	we	we	PRON
ejpam-6189	333	8	have	have	AUX
ejpam-6189	333	9	sζ	sζ	PROPN
ejpam-6189	333	10	is	be	AUX
ejpam-6189	333	11	a	a	DET
ejpam-6189	333	12	strongest	strong	ADJ
ejpam-6189	333	13	fuzzy	fuzzy	ADJ
ejpam-6189	333	14	dot	dot	NOUN
ejpam-6189	333	15	bd	bd	NOUN
ejpam-6189	333	16	-	-	NOUN
ejpam-6189	333	17	subalgebra	subalgebra	NOUN
ejpam-6189	333	18	on	on	ADP
ejpam-6189	333	19	x	x	SYM
ejpam-6189	333	20	:	:	PUNCT
ejpam-6189	333	21	=	=	SYM
ejpam-6189	333	22	(	(	PUNCT
ejpam-6189	333	23	x	x	X
ejpam-6189	333	24	,	,	PUNCT
ejpam-6189	333	25	∗	∗	NOUN
ejpam-6189	333	26	,	,	PUNCT
ejpam-6189	333	27	0	0	NUM
ejpam-6189	333	28	)	)	PUNCT
ejpam-6189	333	29	.	.	PUNCT
ejpam-6189	334	1	then	then	ADV
ejpam-6189	334	2	the	the	DET
ejpam-6189	334	3	level	level	NOUN
ejpam-6189	334	4	subset	subset	NOUN
ejpam-6189	334	5	(	(	PUNCT
ejpam-6189	334	6	sζ)0.72	sζ)0.72	NOUN
ejpam-6189	334	7	=	=	SYM
ejpam-6189	334	8	{	{	PUNCT
ejpam-6189	334	9	(	(	PUNCT
ejpam-6189	334	10	0	0	NUM
ejpam-6189	334	11	,	,	PUNCT
ejpam-6189	334	12	b	b	NOUN
ejpam-6189	334	13	)	)	PUNCT
ejpam-6189	334	14	,	,	PUNCT
ejpam-6189	334	15	(	(	PUNCT
ejpam-6189	334	16	0	0	NUM
ejpam-6189	334	17	,	,	PUNCT
ejpam-6189	334	18	c	c	NOUN
ejpam-6189	334	19	)	)	PUNCT
ejpam-6189	334	20	,	,	PUNCT
ejpam-6189	334	21	(	(	PUNCT
ejpam-6189	334	22	b	b	NOUN
ejpam-6189	334	23	,	,	PUNCT
ejpam-6189	334	24	0	0	NUM
ejpam-6189	334	25	)	)	PUNCT
ejpam-6189	334	26	,	,	PUNCT
ejpam-6189	334	27	(	(	PUNCT
ejpam-6189	334	28	c	c	X
ejpam-6189	334	29	,	,	PUNCT
ejpam-6189	334	30	0	0	NUM
ejpam-6189	334	31	)	)	PUNCT
ejpam-6189	334	32	}	}	PUNCT
ejpam-6189	334	33	.	.	PUNCT
ejpam-6189	335	1	we	we	PRON
ejpam-6189	335	2	observe	observe	VERB
ejpam-6189	335	3	that	that	SCONJ
ejpam-6189	335	4	(	(	PUNCT
ejpam-6189	335	5	sζ)0.72	sζ)0.72	PROPN
ejpam-6189	335	6	is	be	AUX
ejpam-6189	335	7	not	not	PART
ejpam-6189	335	8	a	a	DET
ejpam-6189	335	9	bd	bd	NOUN
ejpam-6189	335	10	-	-	PUNCT
ejpam-6189	335	11	subalgebra	subalgebra	NOUN
ejpam-6189	335	12	of	of	ADP
ejpam-6189	335	13	x×x	x×x	PROPN
ejpam-6189	335	14	,	,	PUNCT
ejpam-6189	335	15	since	since	SCONJ
ejpam-6189	335	16	(	(	PUNCT
ejpam-6189	335	17	0	0	NUM
ejpam-6189	335	18	,	,	PUNCT
ejpam-6189	335	19	b)⊛	b)⊛	X
ejpam-6189	335	20	(	(	PUNCT
ejpam-6189	335	21	b	b	NOUN
ejpam-6189	335	22	,	,	PUNCT
ejpam-6189	335	23	0	0	NUM
ejpam-6189	335	24	)	)	PUNCT
ejpam-6189	335	25	=	=	NOUN
ejpam-6189	335	26	(	(	PUNCT
ejpam-6189	335	27	a	a	PRON
ejpam-6189	335	28	,	,	PUNCT
ejpam-6189	335	29	b	b	NOUN
ejpam-6189	335	30	)	)	PUNCT
ejpam-6189	335	31	̸∈	̸∈	PROPN
ejpam-6189	335	32	(	(	PUNCT
ejpam-6189	335	33	sζ)0.72	sζ)0.72	PROPN
ejpam-6189	335	34	.	.	PUNCT
ejpam-6189	335	35	theorem	theorem	VERB
ejpam-6189	335	36	9	9	NUM
ejpam-6189	335	37	.	.	PUNCT
ejpam-6189	336	1	let	let	VERB
ejpam-6189	336	2	x	x	PRON
ejpam-6189	336	3	be	be	AUX
ejpam-6189	336	4	a	a	DET
ejpam-6189	336	5	bd	bd	NOUN
ejpam-6189	336	6	-	-	NOUN
ejpam-6189	336	7	algebra	algebra	PROPN
ejpam-6189	336	8	,	,	PUNCT
ejpam-6189	336	9	a	a	PRON
ejpam-6189	336	10	be	be	AUX
ejpam-6189	336	11	a	a	DET
ejpam-6189	336	12	nonempty	nonempty	ADJ
ejpam-6189	336	13	subset	subset	NOUN
ejpam-6189	336	14	of	of	ADP
ejpam-6189	336	15	x	x	PRON
ejpam-6189	336	16	,	,	PUNCT
ejpam-6189	336	17	and	and	CCONJ
ejpam-6189	336	18	ζ	ζ	NOUN
ejpam-6189	336	19	be	be	AUX
ejpam-6189	336	20	a	a	DET
ejpam-6189	336	21	fuzzy	fuzzy	ADJ
ejpam-6189	336	22	set	set	NOUN
ejpam-6189	336	23	of	of	ADP
ejpam-6189	336	24	x.	x.	NOUN
ejpam-6189	336	25	then	then	ADV
ejpam-6189	336	26	a×a	a×a	PROPN
ejpam-6189	336	27	is	be	AUX
ejpam-6189	336	28	a	a	DET
ejpam-6189	336	29	bd	bd	NOUN
ejpam-6189	336	30	-	-	PUNCT
ejpam-6189	336	31	subalgebra	subalgebra	NOUN
ejpam-6189	336	32	of	of	ADP
ejpam-6189	336	33	x×x	x×x	PROPN
ejpam-6189	336	34	if	if	SCONJ
ejpam-6189	336	35	and	and	CCONJ
ejpam-6189	336	36	only	only	ADV
ejpam-6189	336	37	if	if	SCONJ
ejpam-6189	336	38	ca	can	AUX
ejpam-6189	336	39	ζ	ζ	NOUN
ejpam-6189	336	40	is	be	AUX
ejpam-6189	336	41	a	a	DET
ejpam-6189	336	42	strongest	strong	ADJ
ejpam-6189	336	43	fuzzy	fuzzy	ADJ
ejpam-6189	336	44	dot	dot	NOUN
ejpam-6189	336	45	bd	bd	NOUN
ejpam-6189	336	46	-	-	PUNCT
ejpam-6189	336	47	subalgebra	subalgebra	NOUN
ejpam-6189	336	48	on	on	ADP
ejpam-6189	336	49	x.	x.	NOUN
ejpam-6189	336	50	proof	proof	PROPN
ejpam-6189	336	51	.	.	PUNCT
ejpam-6189	337	1	assume	assume	VERB
ejpam-6189	337	2	that	that	SCONJ
ejpam-6189	337	3	a×a	a×a	PROPN
ejpam-6189	337	4	is	be	AUX
ejpam-6189	337	5	a	a	DET
ejpam-6189	337	6	bd	bd	NOUN
ejpam-6189	337	7	-	-	PUNCT
ejpam-6189	337	8	subalgebra	subalgebra	NOUN
ejpam-6189	337	9	of	of	ADP
ejpam-6189	337	10	x×x	x×x	PROPN
ejpam-6189	337	11	.	.	PUNCT
ejpam-6189	338	1	then	then	ADV
ejpam-6189	338	2	(	(	PUNCT
ejpam-6189	338	3	0	0	NUM
ejpam-6189	338	4	,	,	PUNCT
ejpam-6189	338	5	0	0	NUM
ejpam-6189	338	6	)	)	PUNCT
ejpam-6189	338	7	∈	∈	PROPN
ejpam-6189	338	8	a×a	a×a	PROPN
ejpam-6189	338	9	,	,	PUNCT
ejpam-6189	338	10	implies	imply	VERB
ejpam-6189	338	11	that	that	SCONJ
ejpam-6189	338	12	ca	can	AUX
ejpam-6189	338	13	ζ	ζ	X
ejpam-6189	338	14	(	(	PUNCT
ejpam-6189	338	15	0	0	NUM
ejpam-6189	338	16	,	,	PUNCT
ejpam-6189	338	17	0	0	NUM
ejpam-6189	338	18	)	)	PUNCT
ejpam-6189	338	19	=	=	SYM
ejpam-6189	338	20	1	1	NUM
ejpam-6189	338	21	≥	≥	NOUN
ejpam-6189	338	22	ca	ca	NOUN
ejpam-6189	338	23	ζ	ζ	NOUN
ejpam-6189	338	24	(	(	PUNCT
ejpam-6189	338	25	x	x	NOUN
ejpam-6189	338	26	,	,	PUNCT
ejpam-6189	338	27	y	y	NOUN
ejpam-6189	338	28	)	)	PUNCT
ejpam-6189	338	29	for	for	ADP
ejpam-6189	338	30	all	all	DET
ejpam-6189	338	31	(	(	PUNCT
ejpam-6189	338	32	x	x	NOUN
ejpam-6189	338	33	,	,	PUNCT
ejpam-6189	338	34	y	y	NOUN
ejpam-6189	338	35	)	)	PUNCT
ejpam-6189	338	36	∈	∈	PROPN
ejpam-6189	338	37	x	x	X
ejpam-6189	338	38	×	×	NOUN
ejpam-6189	338	39	x.	x.	NOUN
ejpam-6189	338	40	now	now	ADV
ejpam-6189	338	41	,	,	PUNCT
ejpam-6189	338	42	suppose	suppose	VERB
ejpam-6189	338	43	that	that	SCONJ
ejpam-6189	338	44	there	there	PRON
ejpam-6189	338	45	exist	exist	VERB
ejpam-6189	338	46	(	(	PUNCT
ejpam-6189	338	47	a1	a1	NOUN
ejpam-6189	338	48	,	,	PUNCT
ejpam-6189	338	49	b1	b1	NOUN
ejpam-6189	338	50	)	)	PUNCT
ejpam-6189	338	51	,	,	PUNCT
ejpam-6189	338	52	(	(	PUNCT
ejpam-6189	338	53	a2	a2	PROPN
ejpam-6189	338	54	,	,	PUNCT
ejpam-6189	338	55	b2	b2	NOUN
ejpam-6189	338	56	)	)	PUNCT
ejpam-6189	338	57	∈	∈	PROPN
ejpam-6189	338	58	x	x	X
ejpam-6189	338	59	×x	×x	VERB
ejpam-6189	338	60	such	such	ADJ
ejpam-6189	338	61	that	that	SCONJ
ejpam-6189	338	62	ca	can	AUX
ejpam-6189	338	63	ζ	ζ	NOUN
ejpam-6189	338	64	(	(	PUNCT
ejpam-6189	338	65	a1	a1	NOUN
ejpam-6189	338	66	∗	∗	NOUN
ejpam-6189	338	67	a2	a2	PROPN
ejpam-6189	338	68	,	,	PUNCT
ejpam-6189	338	69	b1	b1	NOUN
ejpam-6189	338	70	∗	∗	NOUN
ejpam-6189	338	71	b2	b2	NOUN
ejpam-6189	338	72	)	)	PUNCT
ejpam-6189	338	73	<	<	X
ejpam-6189	338	74	ca	can	AUX
ejpam-6189	338	75	ζ	ζ	NOUN
ejpam-6189	338	76	(	(	PUNCT
ejpam-6189	338	77	a1	a1	NOUN
ejpam-6189	338	78	,	,	PUNCT
ejpam-6189	338	79	b1	b1	NOUN
ejpam-6189	338	80	)	)	PUNCT
ejpam-6189	338	81	·	·	PUNCT
ejpam-6189	338	82	ca	can	AUX
ejpam-6189	338	83	ζ	ζ	NOUN
ejpam-6189	338	84	(	(	PUNCT
ejpam-6189	338	85	a2	a2	PROPN
ejpam-6189	338	86	,	,	PUNCT
ejpam-6189	338	87	b2	b2	NOUN
ejpam-6189	338	88	)	)	PUNCT
ejpam-6189	338	89	.	.	PUNCT
ejpam-6189	339	1	we	we	PRON
ejpam-6189	339	2	obtain	obtain	VERB
ejpam-6189	339	3	that	that	DET
ejpam-6189	339	4	ca	can	AUX
ejpam-6189	339	5	ζ	ζ	NOUN
ejpam-6189	339	6	(	(	PUNCT
ejpam-6189	339	7	a1	a1	NOUN
ejpam-6189	339	8	∗a2	∗a2	NOUN
ejpam-6189	339	9	,	,	PUNCT
ejpam-6189	339	10	b1	b1	NOUN
ejpam-6189	339	11	∗b2	∗b2	NOUN
ejpam-6189	339	12	)	)	PUNCT
ejpam-6189	339	13	=	=	SYM
ejpam-6189	339	14	0	0	PUNCT
ejpam-6189	340	1	and	and	CCONJ
ejpam-6189	340	2	ca	can	AUX
ejpam-6189	340	3	ζ	ζ	PROPN
ejpam-6189	340	4	(	(	PUNCT
ejpam-6189	340	5	a1	a1	NOUN
ejpam-6189	340	6	,	,	PUNCT
ejpam-6189	340	7	b1	b1	NOUN
ejpam-6189	340	8	)	)	PUNCT
ejpam-6189	340	9	·	·	PUNCT
ejpam-6189	340	10	ca	can	AUX
ejpam-6189	340	11	ζ	ζ	PROPN
ejpam-6189	340	12	(	(	PUNCT
ejpam-6189	340	13	a2	a2	PROPN
ejpam-6189	340	14	,	,	PUNCT
ejpam-6189	340	15	b2	b2	NOUN
ejpam-6189	340	16	)	)	PUNCT
ejpam-6189	340	17	=	=	SYM
ejpam-6189	341	1	1	1	X
ejpam-6189	341	2	.	.	PUNCT
ejpam-6189	342	1	since	since	SCONJ
ejpam-6189	342	2	ca	ca	NOUN
ejpam-6189	342	3	ζ	ζ	PROPN
ejpam-6189	342	4	(	(	PUNCT
ejpam-6189	342	5	a1	a1	NOUN
ejpam-6189	342	6	,	,	PUNCT
ejpam-6189	342	7	b1	b1	NOUN
ejpam-6189	342	8	)	)	PUNCT
ejpam-6189	342	9	·	·	PUNCT
ejpam-6189	342	10	ca	can	AUX
ejpam-6189	342	11	ζ	ζ	PROPN
ejpam-6189	342	12	(	(	PUNCT
ejpam-6189	342	13	a2	a2	PROPN
ejpam-6189	342	14	,	,	PUNCT
ejpam-6189	342	15	b2	b2	NOUN
ejpam-6189	342	16	)	)	PUNCT
ejpam-6189	342	17	=	=	SYM
ejpam-6189	342	18	1	1	NUM
ejpam-6189	342	19	,	,	PUNCT
ejpam-6189	342	20	we	we	PRON
ejpam-6189	342	21	have	have	VERB
ejpam-6189	342	22	ca	can	AUX
ejpam-6189	342	23	ζ	ζ	X
ejpam-6189	342	24	(	(	PUNCT
ejpam-6189	342	25	a1	a1	NOUN
ejpam-6189	342	26	,	,	PUNCT
ejpam-6189	342	27	b1	b1	NOUN
ejpam-6189	342	28	)	)	PUNCT
ejpam-6189	342	29	=	=	SYM
ejpam-6189	342	30	1	1	NUM
ejpam-6189	342	31	and	and	CCONJ
ejpam-6189	342	32	ca	can	AUX
ejpam-6189	342	33	ζ	ζ	PROPN
ejpam-6189	342	34	(	(	PUNCT
ejpam-6189	342	35	a2	a2	PROPN
ejpam-6189	342	36	,	,	PUNCT
ejpam-6189	342	37	b2	b2	NOUN
ejpam-6189	342	38	)	)	PUNCT
ejpam-6189	342	39	=	=	SYM
ejpam-6189	343	1	1	1	X
ejpam-6189	343	2	.	.	PUNCT
ejpam-6189	344	1	it	it	PRON
ejpam-6189	344	2	follows	follow	VERB
ejpam-6189	344	3	that	that	SCONJ
ejpam-6189	344	4	(	(	PUNCT
ejpam-6189	344	5	a1	a1	NOUN
ejpam-6189	344	6	∗	∗	NOUN
ejpam-6189	344	7	a2	a2	PROPN
ejpam-6189	344	8	,	,	PUNCT
ejpam-6189	344	9	b1	b1	NOUN
ejpam-6189	344	10	∗	∗	NOUN
ejpam-6189	344	11	b2	b2	NOUN
ejpam-6189	344	12	)	)	PUNCT
ejpam-6189	344	13	̸∈	̸∈	PROPN
ejpam-6189	344	14	a	a	DET
ejpam-6189	344	15	×	×	NOUN
ejpam-6189	344	16	a	a	DET
ejpam-6189	344	17	and	and	CCONJ
ejpam-6189	344	18	(	(	PUNCT
ejpam-6189	344	19	a1	a1	NOUN
ejpam-6189	344	20	,	,	PUNCT
ejpam-6189	344	21	b1	b1	NOUN
ejpam-6189	344	22	)	)	PUNCT
ejpam-6189	344	23	,	,	PUNCT
ejpam-6189	344	24	(	(	PUNCT
ejpam-6189	344	25	a2	a2	PROPN
ejpam-6189	344	26	,	,	PUNCT
ejpam-6189	344	27	b2	b2	NOUN
ejpam-6189	344	28	)	)	PUNCT
ejpam-6189	344	29	∈	∈	PROPN
ejpam-6189	344	30	a×a	a×a	PROPN
ejpam-6189	344	31	.	.	PUNCT
ejpam-6189	345	1	by	by	ADP
ejpam-6189	345	2	the	the	DET
ejpam-6189	345	3	hypothesis	hypothesis	NOUN
ejpam-6189	345	4	,	,	PUNCT
ejpam-6189	345	5	we	we	PRON
ejpam-6189	345	6	have	have	VERB
ejpam-6189	345	7	(	(	PUNCT
ejpam-6189	345	8	a1	a1	NOUN
ejpam-6189	345	9	∗a2	∗a2	NOUN
ejpam-6189	345	10	,	,	PUNCT
ejpam-6189	345	11	b1	b1	NOUN
ejpam-6189	345	12	∗	∗	NOUN
ejpam-6189	345	13	b2	b2	NOUN
ejpam-6189	345	14	)	)	PUNCT
ejpam-6189	345	15	=	=	SYM
ejpam-6189	345	16	(	(	PUNCT
ejpam-6189	345	17	a1	a1	PROPN
ejpam-6189	345	18	,	,	PUNCT
ejpam-6189	345	19	b1)⊛	b1)⊛	X
ejpam-6189	345	20	(	(	PUNCT
ejpam-6189	345	21	a2	a2	PROPN
ejpam-6189	345	22	,	,	PUNCT
ejpam-6189	345	23	b2	b2	NOUN
ejpam-6189	345	24	)	)	PUNCT
ejpam-6189	345	25	∈	∈	PROPN
ejpam-6189	345	26	a×a	a×a	PROPN
ejpam-6189	345	27	.	.	PUNCT
ejpam-6189	346	1	this	this	PRON
ejpam-6189	346	2	is	be	AUX
ejpam-6189	346	3	a	a	DET
ejpam-6189	346	4	contradiction	contradiction	NOUN
ejpam-6189	346	5	.	.	PUNCT
ejpam-6189	347	1	hence	hence	ADV
ejpam-6189	347	2	,	,	PUNCT
ejpam-6189	347	3	ca	can	AUX
ejpam-6189	347	4	ζ	ζ	NOUN
ejpam-6189	347	5	(	(	PUNCT
ejpam-6189	347	6	x1	x1	PROPN
ejpam-6189	347	7	∗	∗	NOUN
ejpam-6189	347	8	x2	x2	PROPN
ejpam-6189	347	9	,	,	PUNCT
ejpam-6189	347	10	y1	y1	NOUN
ejpam-6189	347	11	∗	∗	NOUN
ejpam-6189	347	12	y2	y2	NOUN
ejpam-6189	347	13	)	)	PUNCT
ejpam-6189	347	14	≥	≥	PROPN
ejpam-6189	347	15	ca	ca	NOUN
ejpam-6189	347	16	ζ	ζ	NOUN
ejpam-6189	347	17	(	(	PUNCT
ejpam-6189	347	18	x1	x1	PROPN
ejpam-6189	347	19	,	,	PUNCT
ejpam-6189	347	20	y1	y1	PROPN
ejpam-6189	347	21	)	)	PUNCT
ejpam-6189	347	22	·	·	PUNCT
ejpam-6189	347	23	ca	can	AUX
ejpam-6189	347	24	ζ	ζ	NOUN
ejpam-6189	347	25	(	(	PUNCT
ejpam-6189	347	26	x2	x2	PROPN
ejpam-6189	347	27	,	,	PUNCT
ejpam-6189	347	28	y2	y2	PROPN
ejpam-6189	347	29	)	)	PUNCT
ejpam-6189	347	30	for	for	ADP
ejpam-6189	347	31	all	all	PRON
ejpam-6189	347	32	(	(	PUNCT
ejpam-6189	347	33	x1	x1	PROPN
ejpam-6189	347	34	,	,	PUNCT
ejpam-6189	347	35	y1	y1	PROPN
ejpam-6189	347	36	)	)	PUNCT
ejpam-6189	347	37	,	,	PUNCT
ejpam-6189	347	38	(	(	PUNCT
ejpam-6189	347	39	x2	x2	PROPN
ejpam-6189	347	40	,	,	PUNCT
ejpam-6189	347	41	y2	y2	NOUN
ejpam-6189	347	42	)	)	PUNCT
ejpam-6189	347	43	∈	∈	PROPN
ejpam-6189	347	44	x	x	SYM
ejpam-6189	347	45	×x	×x	PROPN
ejpam-6189	347	46	.	.	PUNCT
ejpam-6189	348	1	therefore	therefore	ADV
ejpam-6189	348	2	,	,	PUNCT
ejpam-6189	348	3	ca	can	AUX
ejpam-6189	348	4	ζ	ζ	PROPN
ejpam-6189	348	5	is	be	AUX
ejpam-6189	348	6	a	a	DET
ejpam-6189	348	7	strongest	strong	ADJ
ejpam-6189	348	8	fuzzy	fuzzy	ADJ
ejpam-6189	348	9	dot	dot	NOUN
ejpam-6189	348	10	bd	bd	NOUN
ejpam-6189	348	11	-	-	PUNCT
ejpam-6189	348	12	subalgebra	subalgebra	NOUN
ejpam-6189	348	13	on	on	ADP
ejpam-6189	348	14	x.	x.	NOUN
ejpam-6189	348	15	conversely	conversely	ADV
ejpam-6189	348	16	,	,	PUNCT
ejpam-6189	348	17	assume	assume	VERB
ejpam-6189	348	18	that	that	SCONJ
ejpam-6189	348	19	ca	can	AUX
ejpam-6189	348	20	ζ	ζ	NOUN
ejpam-6189	348	21	is	be	AUX
ejpam-6189	348	22	a	a	DET
ejpam-6189	348	23	strongest	strong	ADJ
ejpam-6189	348	24	fuzzy	fuzzy	ADJ
ejpam-6189	348	25	dot	dot	NOUN
ejpam-6189	348	26	bd	bd	NOUN
ejpam-6189	348	27	-	-	PUNCT
ejpam-6189	348	28	subalgebra	subalgebra	NOUN
ejpam-6189	348	29	on	on	ADP
ejpam-6189	348	30	x.	x.	NOUN
ejpam-6189	348	31	if	if	SCONJ
ejpam-6189	348	32	(	(	PUNCT
ejpam-6189	348	33	0	0	NUM
ejpam-6189	348	34	,	,	PUNCT
ejpam-6189	348	35	0	0	NUM
ejpam-6189	348	36	)	)	PUNCT
ejpam-6189	348	37	̸∈	̸∈	PROPN
ejpam-6189	348	38	a	a	DET
ejpam-6189	348	39	×	×	NOUN
ejpam-6189	348	40	a	a	X
ejpam-6189	348	41	,	,	PUNCT
ejpam-6189	348	42	then	then	ADV
ejpam-6189	348	43	0	0	X
ejpam-6189	349	1	=	=	SYM
ejpam-6189	349	2	ca	can	AUX
ejpam-6189	349	3	ζ	ζ	X
ejpam-6189	349	4	(	(	PUNCT
ejpam-6189	349	5	0	0	NUM
ejpam-6189	349	6	,	,	PUNCT
ejpam-6189	349	7	0	0	NUM
ejpam-6189	349	8	)	)	PUNCT
ejpam-6189	349	9	≥	≥	NOUN
ejpam-6189	349	10	ca	ca	NOUN
ejpam-6189	349	11	ζ	ζ	NOUN
ejpam-6189	349	12	(	(	PUNCT
ejpam-6189	349	13	x	x	NOUN
ejpam-6189	349	14	,	,	PUNCT
ejpam-6189	349	15	y	y	NOUN
ejpam-6189	349	16	)	)	PUNCT
ejpam-6189	349	17	for	for	ADP
ejpam-6189	349	18	all	all	DET
ejpam-6189	349	19	(	(	PUNCT
ejpam-6189	349	20	x	x	NOUN
ejpam-6189	349	21	,	,	PUNCT
ejpam-6189	349	22	y	y	NOUN
ejpam-6189	349	23	)	)	PUNCT
ejpam-6189	349	24	∈	∈	PROPN
ejpam-6189	349	25	x	x	X
ejpam-6189	349	26	×	×	NOUN
ejpam-6189	349	27	x.	x.	NOUN
ejpam-6189	349	28	thus	thus	ADV
ejpam-6189	349	29	,	,	PUNCT
ejpam-6189	349	30	ca	can	AUX
ejpam-6189	349	31	ζ	ζ	NOUN
ejpam-6189	349	32	(	(	PUNCT
ejpam-6189	349	33	x	x	NOUN
ejpam-6189	349	34	,	,	PUNCT
ejpam-6189	349	35	y	y	NOUN
ejpam-6189	349	36	)	)	PUNCT
ejpam-6189	349	37	=	=	SYM
ejpam-6189	349	38	0	0	NUM
ejpam-6189	349	39	for	for	ADP
ejpam-6189	349	40	all	all	PRON
ejpam-6189	349	41	(	(	PUNCT
ejpam-6189	349	42	x	x	NOUN
ejpam-6189	349	43	,	,	PUNCT
ejpam-6189	349	44	y	y	NOUN
ejpam-6189	349	45	)	)	PUNCT
ejpam-6189	349	46	∈	∈	PROPN
ejpam-6189	349	47	x	x	X
ejpam-6189	349	48	×	×	NOUN
ejpam-6189	349	49	x.	x.	NOUN
ejpam-6189	350	1	this	this	PRON
ejpam-6189	350	2	means	mean	VERB
ejpam-6189	350	3	that	that	SCONJ
ejpam-6189	350	4	a	a	DET
ejpam-6189	350	5	×	×	NOUN
ejpam-6189	350	6	a	a	DET
ejpam-6189	350	7	=	=	PUNCT
ejpam-6189	350	8	∅.	∅.	NOUN
ejpam-6189	350	9	this	this	PRON
ejpam-6189	350	10	is	be	AUX
ejpam-6189	350	11	a	a	DET
ejpam-6189	350	12	contradiction	contradiction	NOUN
ejpam-6189	350	13	,	,	PUNCT
ejpam-6189	350	14	because	because	SCONJ
ejpam-6189	350	15	a	a	PRON
ejpam-6189	350	16	is	be	AUX
ejpam-6189	350	17	a	a	DET
ejpam-6189	350	18	nonempty	nonempty	ADJ
ejpam-6189	350	19	subset	subset	NOUN
ejpam-6189	350	20	of	of	ADP
ejpam-6189	350	21	x.	x.	NOUN
ejpam-6189	350	22	hence	hence	ADV
ejpam-6189	350	23	,	,	PUNCT
ejpam-6189	350	24	(	(	PUNCT
ejpam-6189	350	25	0	0	NUM
ejpam-6189	350	26	,	,	PUNCT
ejpam-6189	350	27	0	0	NUM
ejpam-6189	350	28	)	)	PUNCT
ejpam-6189	350	29	∈	∈	NOUN
ejpam-6189	350	30	a×	a×	NOUN
ejpam-6189	350	31	a.	a.	NOUN
ejpam-6189	350	32	now	now	ADV
ejpam-6189	350	33	,	,	PUNCT
ejpam-6189	350	34	let	let	VERB
ejpam-6189	350	35	(	(	PUNCT
ejpam-6189	350	36	x1	x1	ADJ
ejpam-6189	350	37	,	,	PUNCT
ejpam-6189	350	38	y1	y1	PROPN
ejpam-6189	350	39	)	)	PUNCT
ejpam-6189	350	40	,	,	PUNCT
ejpam-6189	350	41	(	(	PUNCT
ejpam-6189	350	42	x2	x2	PROPN
ejpam-6189	350	43	,	,	PUNCT
ejpam-6189	350	44	y2	y2	NOUN
ejpam-6189	350	45	)	)	PUNCT
ejpam-6189	351	1	∈	∈	PROPN
ejpam-6189	351	2	a×	a×	NOUN
ejpam-6189	351	3	a.	a.	NOUN
ejpam-6189	351	4	then	then	ADV
ejpam-6189	351	5	,	,	PUNCT
ejpam-6189	351	6	w.	w.	PROPN
ejpam-6189	351	7	nakkhasen	nakkhasen	PROPN
ejpam-6189	351	8	et	et	PROPN
ejpam-6189	351	9	al	al	PROPN
ejpam-6189	351	10	.	.	PUNCT
ejpam-6189	351	11	/	/	SYM
ejpam-6189	351	12	eur	eur	PROPN
ejpam-6189	351	13	.	.	PUNCT
ejpam-6189	352	1	j.	j.	PROPN
ejpam-6189	352	2	pure	pure	PROPN
ejpam-6189	352	3	appl	appl	PROPN
ejpam-6189	352	4	.	.	PROPN
ejpam-6189	352	5	math	math	PROPN
ejpam-6189	352	6	,	,	PUNCT
ejpam-6189	352	7	18	18	NUM
ejpam-6189	352	8	(	(	PUNCT
ejpam-6189	352	9	3	3	NUM
ejpam-6189	352	10	)	)	PUNCT
ejpam-6189	352	11	(	(	PUNCT
ejpam-6189	352	12	2025	2025	NUM
ejpam-6189	352	13	)	)	PUNCT
ejpam-6189	352	14	,	,	PUNCT
ejpam-6189	352	15	6189	6189	NUM
ejpam-6189	352	16	12	12	NUM
ejpam-6189	352	17	of	of	ADP
ejpam-6189	352	18	13	13	NUM
ejpam-6189	352	19	ca	ca	NOUN
ejpam-6189	352	20	ζ	ζ	NOUN
ejpam-6189	352	21	(	(	PUNCT
ejpam-6189	352	22	x1	x1	PROPN
ejpam-6189	352	23	∗	∗	NOUN
ejpam-6189	352	24	x2	x2	PROPN
ejpam-6189	352	25	,	,	PUNCT
ejpam-6189	352	26	y1	y1	NOUN
ejpam-6189	352	27	∗	∗	NOUN
ejpam-6189	352	28	y2	y2	NOUN
ejpam-6189	352	29	)	)	PUNCT
ejpam-6189	352	30	≥	≥	PROPN
ejpam-6189	352	31	ca	ca	NOUN
ejpam-6189	352	32	ζ	ζ	NOUN
ejpam-6189	352	33	(	(	PUNCT
ejpam-6189	352	34	x1	x1	PROPN
ejpam-6189	352	35	,	,	PUNCT
ejpam-6189	352	36	y1	y1	PROPN
ejpam-6189	352	37	)	)	PUNCT
ejpam-6189	352	38	·	·	PUNCT
ejpam-6189	352	39	ca	can	AUX
ejpam-6189	352	40	ζ	ζ	NOUN
ejpam-6189	352	41	(	(	PUNCT
ejpam-6189	352	42	x2	x2	PROPN
ejpam-6189	352	43	,	,	PUNCT
ejpam-6189	352	44	y2	y2	PROPN
ejpam-6189	352	45	)	)	PUNCT
ejpam-6189	352	46	=	=	SYM
ejpam-6189	352	47	1	1	NUM
ejpam-6189	352	48	,	,	PUNCT
ejpam-6189	352	49	and	and	CCONJ
ejpam-6189	352	50	so	so	ADV
ejpam-6189	352	51	ca	can	AUX
ejpam-6189	352	52	ζ	ζ	PROPN
ejpam-6189	352	53	(	(	PUNCT
ejpam-6189	352	54	x1	x1	PROPN
ejpam-6189	352	55	∗	∗	NOUN
ejpam-6189	352	56	x2	x2	PROPN
ejpam-6189	352	57	,	,	PUNCT
ejpam-6189	352	58	y1	y1	NOUN
ejpam-6189	352	59	∗	∗	NOUN
ejpam-6189	352	60	y2	y2	NOUN
ejpam-6189	352	61	)	)	PUNCT
ejpam-6189	353	1	=	=	SYM
ejpam-6189	353	2	1	1	X
ejpam-6189	353	3	.	.	PUNCT
ejpam-6189	354	1	this	this	PRON
ejpam-6189	354	2	implies	imply	VERB
ejpam-6189	354	3	that	that	SCONJ
ejpam-6189	354	4	(	(	PUNCT
ejpam-6189	354	5	x1	x1	ADJ
ejpam-6189	354	6	,	,	PUNCT
ejpam-6189	354	7	y1	y1	PROPN
ejpam-6189	354	8	)	)	PUNCT
ejpam-6189	354	9	⊛	⊛	NUM
ejpam-6189	354	10	(	(	PUNCT
ejpam-6189	354	11	x2	x2	PROPN
ejpam-6189	354	12	,	,	PUNCT
ejpam-6189	354	13	y2	y2	NOUN
ejpam-6189	354	14	)	)	PUNCT
ejpam-6189	354	15	=	=	PRON
ejpam-6189	355	1	(	(	PUNCT
ejpam-6189	355	2	x1	x1	PROPN
ejpam-6189	355	3	∗	∗	PROPN
ejpam-6189	355	4	x2	x2	PROPN
ejpam-6189	355	5	,	,	PUNCT
ejpam-6189	355	6	y1	y1	NOUN
ejpam-6189	355	7	∗	∗	NOUN
ejpam-6189	355	8	y2	y2	NOUN
ejpam-6189	355	9	)	)	PUNCT
ejpam-6189	355	10	∈	∈	PROPN
ejpam-6189	355	11	a	a	DET
ejpam-6189	355	12	×	×	NOUN
ejpam-6189	355	13	a.	a.	NOUN
ejpam-6189	355	14	consequently	consequently	ADV
ejpam-6189	355	15	,	,	PUNCT
ejpam-6189	355	16	a	a	DET
ejpam-6189	355	17	×	×	NOUN
ejpam-6189	355	18	a	a	PRON
ejpam-6189	355	19	is	be	AUX
ejpam-6189	355	20	a	a	DET
ejpam-6189	355	21	bd	bd	NOUN
ejpam-6189	355	22	-	-	PUNCT
ejpam-6189	355	23	subalgebra	subalgebra	NOUN
ejpam-6189	355	24	of	of	ADP
ejpam-6189	355	25	x×x	x×x	PROPN
ejpam-6189	355	26	.	.	PROPN
ejpam-6189	356	1	5	5	NUM
ejpam-6189	356	2	.	.	PUNCT
ejpam-6189	356	3	conclusions	conclusion	NOUN
ejpam-6189	356	4	in	in	ADP
ejpam-6189	356	5	2024	2024	NUM
ejpam-6189	356	6	,	,	PUNCT
ejpam-6189	356	7	nakkhasen	nakkhasen	PROPN
ejpam-6189	356	8	et	et	PROPN
ejpam-6189	356	9	al	al	PROPN
ejpam-6189	356	10	.	.	PUNCT
ejpam-6189	357	1	[	[	X
ejpam-6189	357	2	27	27	NUM
ejpam-6189	357	3	]	]	PUNCT
ejpam-6189	357	4	applied	apply	VERB
ejpam-6189	357	5	the	the	DET
ejpam-6189	357	6	concept	concept	NOUN
ejpam-6189	357	7	of	of	ADP
ejpam-6189	357	8	fuzzy	fuzzy	ADJ
ejpam-6189	357	9	sets	set	NOUN
ejpam-6189	357	10	to	to	ADP
ejpam-6189	357	11	bd	bd	PROPN
ejpam-6189	357	12	-	-	PUNCT
ejpam-6189	357	13	algebras	algebras	X
ejpam-6189	357	14	,	,	PUNCT
ejpam-6189	357	15	defining	define	VERB
ejpam-6189	357	16	the	the	DET
ejpam-6189	357	17	concept	concept	NOUN
ejpam-6189	357	18	of	of	ADP
ejpam-6189	357	19	fuzzy	fuzzy	ADJ
ejpam-6189	357	20	bd	bd	PROPN
ejpam-6189	357	21	-	-	PUNCT
ejpam-6189	357	22	subalgebras	subalgebras	PROPN
ejpam-6189	357	23	.	.	PUNCT
ejpam-6189	358	1	this	this	DET
ejpam-6189	358	2	article	article	NOUN
ejpam-6189	358	3	presents	present	VERB
ejpam-6189	358	4	the	the	DET
ejpam-6189	358	5	notion	notion	NOUN
ejpam-6189	358	6	of	of	ADP
ejpam-6189	358	7	fuzzy	fuzzy	ADJ
ejpam-6189	358	8	dot	dot	NOUN
ejpam-6189	358	9	bdsubalgebras	bdsubalgebra	NOUN
ejpam-6189	358	10	,	,	PUNCT
ejpam-6189	358	11	which	which	PRON
ejpam-6189	358	12	provide	provide	VERB
ejpam-6189	358	13	as	as	ADP
ejpam-6189	358	14	a	a	DET
ejpam-6189	358	15	generalization	generalization	NOUN
ejpam-6189	358	16	of	of	ADP
ejpam-6189	358	17	fuzzy	fuzzy	ADJ
ejpam-6189	358	18	bd	bd	PROPN
ejpam-6189	358	19	-	-	PUNCT
ejpam-6189	358	20	subalgebras	subalgebras	PROPN
ejpam-6189	358	21	.	.	PUNCT
ejpam-6189	359	1	that	that	PRON
ejpam-6189	359	2	means	mean	VERB
ejpam-6189	359	3	that	that	SCONJ
ejpam-6189	359	4	some	some	PRON
ejpam-6189	359	5	of	of	ADP
ejpam-6189	359	6	the	the	DET
ejpam-6189	359	7	results	result	NOUN
ejpam-6189	359	8	obtained	obtain	VERB
ejpam-6189	359	9	from	from	ADP
ejpam-6189	359	10	this	this	DET
ejpam-6189	359	11	work	work	NOUN
ejpam-6189	359	12	will	will	AUX
ejpam-6189	359	13	generalize	generalize	VERB
ejpam-6189	359	14	those	those	PRON
ejpam-6189	359	15	from	from	ADP
ejpam-6189	359	16	[	[	X
ejpam-6189	359	17	27	27	NUM
ejpam-6189	359	18	]	]	PUNCT
ejpam-6189	359	19	.	.	PUNCT
ejpam-6189	360	1	for	for	ADP
ejpam-6189	360	2	example	example	NOUN
ejpam-6189	360	3	,	,	PUNCT
ejpam-6189	360	4	theorem	theorem	VERB
ejpam-6189	360	5	1	1	NUM
ejpam-6189	360	6	will	will	AUX
ejpam-6189	360	7	be	be	AUX
ejpam-6189	360	8	a	a	DET
ejpam-6189	360	9	general	general	ADJ
ejpam-6189	360	10	implication	implication	NOUN
ejpam-6189	360	11	of	of	ADP
ejpam-6189	360	12	proposition	proposition	NOUN
ejpam-6189	360	13	3.1	3.1	NUM
ejpam-6189	360	14	in	in	ADP
ejpam-6189	360	15	[	[	X
ejpam-6189	360	16	27	27	NUM
ejpam-6189	360	17	]	]	PUNCT
ejpam-6189	360	18	.	.	PUNCT
ejpam-6189	361	1	in	in	ADP
ejpam-6189	361	2	section	section	NOUN
ejpam-6189	361	3	3	3	NUM
ejpam-6189	361	4	,	,	PUNCT
ejpam-6189	361	5	we	we	PRON
ejpam-6189	361	6	studied	study	VERB
ejpam-6189	361	7	certain	certain	ADJ
ejpam-6189	361	8	properties	property	NOUN
ejpam-6189	361	9	of	of	ADP
ejpam-6189	361	10	fuzzy	fuzzy	ADJ
ejpam-6189	361	11	dot	dot	NOUN
ejpam-6189	361	12	bd	bd	NOUN
ejpam-6189	361	13	-	-	PUNCT
ejpam-6189	361	14	subalgebras	subalgebras	PROPN
ejpam-6189	361	15	of	of	ADP
ejpam-6189	361	16	the	the	DET
ejpam-6189	361	17	bd	bd	PROPN
ejpam-6189	361	18	-	-	PUNCT
ejpam-6189	361	19	algebras	algebras	PROPN
ejpam-6189	361	20	.	.	PUNCT
ejpam-6189	362	1	also	also	ADV
ejpam-6189	362	2	,	,	PUNCT
ejpam-6189	362	3	the	the	DET
ejpam-6189	362	4	relationships	relationship	NOUN
ejpam-6189	362	5	between	between	ADP
ejpam-6189	362	6	fuzzy	fuzzy	ADJ
ejpam-6189	362	7	dot	dot	NOUN
ejpam-6189	362	8	bd	bd	NOUN
ejpam-6189	362	9	-	-	PUNCT
ejpam-6189	362	10	subalgebras	subalgebras	PROPN
ejpam-6189	362	11	under	under	ADP
ejpam-6189	362	12	a	a	DET
ejpam-6189	362	13	homomorphism	homomorphism	NOUN
ejpam-6189	362	14	of	of	ADP
ejpam-6189	362	15	bd	bd	PROPN
ejpam-6189	362	16	-	-	PUNCT
ejpam-6189	362	17	algebras	algebras	PROPN
ejpam-6189	362	18	were	be	AUX
ejpam-6189	362	19	then	then	ADV
ejpam-6189	362	20	considered	consider	VERB
ejpam-6189	362	21	.	.	PUNCT
ejpam-6189	363	1	subsequently	subsequently	ADV
ejpam-6189	363	2	,	,	PUNCT
ejpam-6189	363	3	the	the	DET
ejpam-6189	363	4	notion	notion	NOUN
ejpam-6189	363	5	of	of	ADP
ejpam-6189	363	6	strongest	strong	ADJ
ejpam-6189	363	7	fuzzy	fuzzy	ADJ
ejpam-6189	363	8	dot	dot	NOUN
ejpam-6189	363	9	bd	bd	NOUN
ejpam-6189	363	10	-	-	PUNCT
ejpam-6189	363	11	subalgebras	subalgebras	PROPN
ejpam-6189	363	12	on	on	ADP
ejpam-6189	363	13	bd	bd	PROPN
ejpam-6189	363	14	-	-	PUNCT
ejpam-6189	363	15	algebras	algebras	PROPN
ejpam-6189	363	16	introduced	introduce	VERB
ejpam-6189	363	17	in	in	ADP
ejpam-6189	363	18	section	section	NOUN
ejpam-6189	363	19	4	4	NUM
ejpam-6189	363	20	and	and	CCONJ
ejpam-6189	363	21	some	some	PRON
ejpam-6189	363	22	of	of	ADP
ejpam-6189	363	23	its	its	PRON
ejpam-6189	363	24	characteristics	characteristic	NOUN
ejpam-6189	363	25	are	be	AUX
ejpam-6189	363	26	examined	examine	VERB
ejpam-6189	363	27	along	along	ADP
ejpam-6189	363	28	with	with	ADP
ejpam-6189	363	29	the	the	DET
ejpam-6189	363	30	relationships	relationship	NOUN
ejpam-6189	363	31	with	with	ADP
ejpam-6189	363	32	fuzzy	fuzzy	ADJ
ejpam-6189	363	33	dot	dot	NOUN
ejpam-6189	363	34	bd	bd	NOUN
ejpam-6189	363	35	-	-	PUNCT
ejpam-6189	363	36	subalgebras	subalgebras	PROPN
ejpam-6189	363	37	in	in	ADP
ejpam-6189	363	38	bd	bd	PROPN
ejpam-6189	363	39	-	-	PUNCT
ejpam-6189	363	40	algebras	algebras	PROPN
ejpam-6189	363	41	.	.	PUNCT
ejpam-6189	364	1	for	for	ADP
ejpam-6189	364	2	future	future	ADJ
ejpam-6189	364	3	work	work	NOUN
ejpam-6189	364	4	that	that	PRON
ejpam-6189	364	5	will	will	AUX
ejpam-6189	364	6	extend	extend	VERB
ejpam-6189	364	7	the	the	DET
ejpam-6189	364	8	knowledge	knowledge	NOUN
ejpam-6189	364	9	from	from	ADP
ejpam-6189	364	10	this	this	DET
ejpam-6189	364	11	article	article	NOUN
ejpam-6189	364	12	,	,	PUNCT
ejpam-6189	364	13	we	we	PRON
ejpam-6189	364	14	will	will	AUX
ejpam-6189	364	15	study	study	VERB
ejpam-6189	364	16	the	the	DET
ejpam-6189	364	17	properties	property	NOUN
ejpam-6189	364	18	of	of	ADP
ejpam-6189	364	19	the	the	DET
ejpam-6189	364	20	concept	concept	NOUN
ejpam-6189	364	21	of	of	ADP
ejpam-6189	364	22	fuzzy	fuzzy	ADJ
ejpam-6189	364	23	dot	dot	NOUN
ejpam-6189	364	24	bd	bd	NOUN
ejpam-6189	364	25	-	-	NOUN
ejpam-6189	364	26	ideals	ideal	NOUN
ejpam-6189	364	27	on	on	ADP
ejpam-6189	364	28	bd	bd	PROPN
ejpam-6189	364	29	-	-	PUNCT
ejpam-6189	364	30	algebras	algebras	PROPN
ejpam-6189	364	31	or	or	CCONJ
ejpam-6189	364	32	may	may	AUX
ejpam-6189	364	33	study	study	VERB
ejpam-6189	364	34	the	the	DET
ejpam-6189	364	35	properties	property	NOUN
ejpam-6189	364	36	of	of	ADP
ejpam-6189	364	37	fuzzy	fuzzy	ADJ
ejpam-6189	364	38	dot	dot	NOUN
ejpam-6189	364	39	subalgebras	subalgebra	NOUN
ejpam-6189	364	40	on	on	ADP
ejpam-6189	364	41	other	other	ADJ
ejpam-6189	364	42	algebraic	algebraic	ADJ
ejpam-6189	364	43	structures	structure	NOUN
ejpam-6189	364	44	.	.	PUNCT
ejpam-6189	365	1	acknowledgements	acknowledgement	NOUN
ejpam-6189	365	2	this	this	DET
ejpam-6189	365	3	research	research	NOUN
ejpam-6189	365	4	project	project	NOUN
ejpam-6189	365	5	was	be	AUX
ejpam-6189	365	6	financially	financially	ADV
ejpam-6189	365	7	supported	support	VERB
ejpam-6189	365	8	by	by	ADP
ejpam-6189	365	9	mahasarakham	mahasarakham	PROPN
ejpam-6189	365	10	university	university	PROPN
ejpam-6189	365	11	.	.	PUNCT
ejpam-6189	366	1	references	reference	NOUN
ejpam-6189	366	2	[	[	X
ejpam-6189	366	3	1	1	NUM
ejpam-6189	366	4	]	]	X
ejpam-6189	366	5	y.	y.	PROPN
ejpam-6189	366	6	b.	b.	PROPN
ejpam-6189	366	7	jun	jun	PROPN
ejpam-6189	366	8	and	and	CCONJ
ejpam-6189	366	9	s.	s.	PROPN
ejpam-6189	366	10	z.	z.	PROPN
ejpam-6189	366	11	song	song	PROPN
ejpam-6189	366	12	.	.	PUNCT
ejpam-6189	367	1	soft	soft	ADJ
ejpam-6189	367	2	subalgebras	subalgebra	NOUN
ejpam-6189	367	3	and	and	CCONJ
ejpam-6189	367	4	soft	soft	ADJ
ejpam-6189	367	5	ideals	ideal	NOUN
ejpam-6189	367	6	of	of	ADP
ejpam-6189	367	7	bck	bck	PROPN
ejpam-6189	367	8	/	/	SYM
ejpam-6189	367	9	bci	bci	NOUN
ejpam-6189	367	10	-	-	PUNCT
ejpam-6189	367	11	algebras	algebras	PROPN
ejpam-6189	367	12	related	relate	VERB
ejpam-6189	367	13	to	to	ADP
ejpam-6189	367	14	fuzzy	fuzzy	ADJ
ejpam-6189	367	15	set	set	NOUN
ejpam-6189	367	16	theory	theory	NOUN
ejpam-6189	367	17	.	.	PUNCT
ejpam-6189	368	1	mathemaical	mathemaical	ADJ
ejpam-6189	368	2	communications	communication	NOUN
ejpam-6189	368	3	,	,	PUNCT
ejpam-6189	368	4	14(2):271–282	14(2):271–282	PROPN
ejpam-6189	368	5	,	,	PUNCT
ejpam-6189	368	6	2009	2009	NUM
ejpam-6189	368	7	.	.	PUNCT
ejpam-6189	369	1	[	[	X
ejpam-6189	369	2	2	2	X
ejpam-6189	369	3	]	]	X
ejpam-6189	369	4	y.	y.	PROPN
ejpam-6189	369	5	b.	b.	PROPN
ejpam-6189	369	6	jun	jun	PROPN
ejpam-6189	369	7	,	,	PUNCT
ejpam-6189	369	8	s.	s.	PROPN
ejpam-6189	369	9	s.	s.	PROPN
ejpam-6189	369	10	ahn	ahn	PROPN
ejpam-6189	369	11	,	,	PUNCT
ejpam-6189	369	12	and	and	CCONJ
ejpam-6189	369	13	e.	e.	PROPN
ejpam-6189	369	14	h.	h.	PROPN
ejpam-6189	369	15	roh	roh	PROPN
ejpam-6189	369	16	.	.	PUNCT
ejpam-6189	370	1	dokdo	dokdo	PROPN
ejpam-6189	370	2	be	be	AUX
ejpam-6189	370	3	-	-	PUNCT
ejpam-6189	370	4	subalgebras	subalgebra	NOUN
ejpam-6189	370	5	and	and	CCONJ
ejpam-6189	370	6	be	be	AUX
ejpam-6189	370	7	-	-	PUNCT
ejpam-6189	370	8	filters	filter	NOUN
ejpam-6189	370	9	of	of	ADP
ejpam-6189	370	10	be	be	NOUN
ejpam-6189	370	11	-	-	PUNCT
ejpam-6189	370	12	algebras	algebras	ADJ
ejpam-6189	370	13	.	.	PUNCT
ejpam-6189	371	1	european	european	PROPN
ejpam-6189	371	2	journal	journal	PROPN
ejpam-6189	371	3	of	of	ADP
ejpam-6189	371	4	pure	pure	ADJ
ejpam-6189	371	5	and	and	CCONJ
ejpam-6189	371	6	applied	applied	ADJ
ejpam-6189	371	7	mathematics	mathematic	NOUN
ejpam-6189	371	8	,	,	PUNCT
ejpam-6189	371	9	15(4):1521–1535	15(4):1521–1535	NUM
ejpam-6189	371	10	,	,	PUNCT
ejpam-6189	371	11	2022	2022	NUM
ejpam-6189	371	12	.	.	PUNCT
ejpam-6189	372	1	[	[	X
ejpam-6189	372	2	3	3	X
ejpam-6189	372	3	]	]	PUNCT
ejpam-6189	372	4	t.	t.	NOUN
ejpam-6189	372	5	senapati	senapati	PROPN
ejpam-6189	372	6	.	.	PUNCT
ejpam-6189	373	1	cubic	cubic	ADJ
ejpam-6189	373	2	structure	structure	NOUN
ejpam-6189	373	3	of	of	ADP
ejpam-6189	373	4	bg	bg	PROPN
ejpam-6189	373	5	-	-	PUNCT
ejpam-6189	373	6	subalgebras	subalgebras	PROPN
ejpam-6189	373	7	of	of	ADP
ejpam-6189	373	8	bg	bg	PROPN
ejpam-6189	373	9	-	-	PUNCT
ejpam-6189	373	10	algebras	algebras	PROPN
ejpam-6189	373	11	.	.	PUNCT
ejpam-6189	374	1	the	the	DET
ejpam-6189	374	2	journal	journal	NOUN
ejpam-6189	374	3	of	of	ADP
ejpam-6189	374	4	fuzzy	fuzzy	ADJ
ejpam-6189	374	5	mathematics	mathematic	NOUN
ejpam-6189	374	6	,	,	PUNCT
ejpam-6189	374	7	24(1):151–162	24(1):151–162	NUM
ejpam-6189	374	8	,	,	PUNCT
ejpam-6189	374	9	2016	2016	NUM
ejpam-6189	374	10	.	.	PUNCT
ejpam-6189	375	1	[	[	X
ejpam-6189	375	2	4	4	NUM
ejpam-6189	375	3	]	]	PUNCT
ejpam-6189	375	4	a.	a.	NOUN
ejpam-6189	375	5	walendziak	walendziak	PROPN
ejpam-6189	375	6	.	.	PUNCT
ejpam-6189	376	1	a	a	DET
ejpam-6189	376	2	note	note	NOUN
ejpam-6189	376	3	on	on	ADP
ejpam-6189	376	4	normal	normal	ADJ
ejpam-6189	376	5	subalgebras	subalgebra	NOUN
ejpam-6189	376	6	in	in	ADP
ejpam-6189	376	7	b	b	NOUN
ejpam-6189	376	8	-	-	PUNCT
ejpam-6189	376	9	algebras	algebras	PROPN
ejpam-6189	376	10	.	.	PUNCT
ejpam-6189	377	1	scientiae	scientiae	PROPN
ejpam-6189	377	2	mathematicae	mathematicae	VERB
ejpam-6189	377	3	japonicae	japonicae	PROPN
ejpam-6189	377	4	online	online	NOUN
ejpam-6189	377	5	,	,	PUNCT
ejpam-6189	377	6	e-2005:49–53	e-2005:49–53	PROPN
ejpam-6189	377	7	,	,	PUNCT
ejpam-6189	377	8	2005	2005	NUM
ejpam-6189	377	9	.	.	PUNCT
ejpam-6189	378	1	[	[	X
ejpam-6189	378	2	5	5	X
ejpam-6189	378	3	]	]	X
ejpam-6189	378	4	y.	y.	PROPN
ejpam-6189	378	5	b.	b.	PROPN
ejpam-6189	378	6	jun	jun	PROPN
ejpam-6189	378	7	,	,	PUNCT
ejpam-6189	378	8	s.	s.	PROPN
ejpam-6189	378	9	s.	s.	PROPN
ejpam-6189	378	10	ahn	ahn	PROPN
ejpam-6189	378	11	,	,	PUNCT
ejpam-6189	378	12	and	and	CCONJ
ejpam-6189	378	13	k.	k.	PROPN
ejpam-6189	378	14	j.	j.	PROPN
ejpam-6189	378	15	lee	lee	PROPN
ejpam-6189	378	16	.	.	PUNCT
ejpam-6189	378	17	falling	fall	VERB
ejpam-6189	378	18	d	d	X
ejpam-6189	378	19	-	-	PUNCT
ejpam-6189	378	20	ideals	ideal	NOUN
ejpam-6189	378	21	in	in	ADP
ejpam-6189	378	22	d	d	NOUN
ejpam-6189	378	23	-	-	PUNCT
ejpam-6189	378	24	algebras	algebra	VERB
ejpam-6189	378	25	.	.	PUNCT
ejpam-6189	379	1	discrete	discrete	ADJ
ejpam-6189	379	2	dynamics	dynamic	NOUN
ejpam-6189	379	3	in	in	ADP
ejpam-6189	379	4	nature	nature	NOUN
ejpam-6189	379	5	and	and	CCONJ
ejpam-6189	379	6	society	society	NOUN
ejpam-6189	379	7	,	,	PUNCT
ejpam-6189	379	8	2011(article	2011(article	NUM
ejpam-6189	380	1	i	i	PROPN
ejpam-6189	380	2	d	d	PROPN
ejpam-6189	380	3	516418):14	516418):14	NUM
ejpam-6189	380	4	pages	page	NOUN
ejpam-6189	380	5	,	,	PUNCT
ejpam-6189	380	6	2011	2011	NUM
ejpam-6189	380	7	.	.	PUNCT
ejpam-6189	381	1	[	[	X
ejpam-6189	381	2	6	6	NUM
ejpam-6189	381	3	]	]	X
ejpam-6189	381	4	h.	h.	PROPN
ejpam-6189	381	5	m.	m.	PROPN
ejpam-6189	381	6	balami	balami	PROPN
ejpam-6189	381	7	,	,	PUNCT
ejpam-6189	381	8	a.	a.	PROPN
ejpam-6189	381	9	o.	o.	PROPN
ejpam-6189	381	10	yusuf	yusuf	PROPN
ejpam-6189	381	11	,	,	PUNCT
ejpam-6189	381	12	and	and	CCONJ
ejpam-6189	381	13	m.	m.	PROPN
ejpam-6189	381	14	hamza	hamza	PROPN
ejpam-6189	381	15	.	.	PUNCT
ejpam-6189	382	1	some	some	DET
ejpam-6189	382	2	results	result	NOUN
ejpam-6189	382	3	on	on	ADP
ejpam-6189	382	4	soft	soft	ADJ
ejpam-6189	382	5	bck	bck	NOUN
ejpam-6189	382	6	/	/	SYM
ejpam-6189	382	7	bci	bci	NOUN
ejpam-6189	382	8	-	-	PUNCT
ejpam-6189	382	9	algebras	algebra	NOUN
ejpam-6189	382	10	.	.	PUNCT
ejpam-6189	383	1	international	international	ADJ
ejpam-6189	383	2	journal	journal	PROPN
ejpam-6189	383	3	of	of	ADP
ejpam-6189	383	4	applied	apply	VERB
ejpam-6189	383	5	science	science	NOUN
ejpam-6189	383	6	and	and	CCONJ
ejpam-6189	383	7	mathematics	mathematic	NOUN
ejpam-6189	383	8	,	,	PUNCT
ejpam-6189	383	9	6(3):69–83	6(3):69–83	NUM
ejpam-6189	383	10	,	,	PUNCT
ejpam-6189	383	11	2019	2019	NUM
ejpam-6189	383	12	.	.	PUNCT
ejpam-6189	384	1	[	[	X
ejpam-6189	384	2	7	7	X
ejpam-6189	384	3	]	]	X
ejpam-6189	384	4	g.	g.	PROPN
ejpam-6189	384	5	dymek	dymek	PROPN
ejpam-6189	384	6	.	.	PUNCT
ejpam-6189	385	1	on	on	ADP
ejpam-6189	385	2	strong	strong	ADJ
ejpam-6189	385	3	subalgebras	subalgebra	NOUN
ejpam-6189	385	4	of	of	ADP
ejpam-6189	385	5	rm	rm	PROPN
ejpam-6189	385	6	algebras	algebras	PROPN
ejpam-6189	385	7	.	.	PUNCT
ejpam-6189	386	1	afrika	afrika	PROPN
ejpam-6189	386	2	matematika	matematika	PROPN
ejpam-6189	386	3	,	,	PUNCT
ejpam-6189	386	4	36:38	36:38	NUM
ejpam-6189	386	5	,	,	PUNCT
ejpam-6189	386	6	2025	2025	NUM
ejpam-6189	386	7	.	.	PUNCT
ejpam-6189	387	1	[	[	X
ejpam-6189	387	2	8	8	NUM
ejpam-6189	387	3	]	]	X
ejpam-6189	387	4	c.	c.	PROPN
ejpam-6189	387	5	janaa	janaa	PROPN
ejpam-6189	387	6	and	and	CCONJ
ejpam-6189	387	7	t.	t.	PROPN
ejpam-6189	387	8	senapati	senapati	PROPN
ejpam-6189	387	9	.	.	PUNCT
ejpam-6189	388	1	cubic	cubic	ADJ
ejpam-6189	388	2	g	g	PROPN
ejpam-6189	388	3	-	-	PUNCT
ejpam-6189	388	4	subalgebras	subalgebras	NOUN
ejpam-6189	388	5	of	of	ADP
ejpam-6189	388	6	g	g	NOUN
ejpam-6189	388	7	-	-	PUNCT
ejpam-6189	388	8	algebras	algebras	NOUN
ejpam-6189	388	9	.	.	PUNCT
ejpam-6189	389	1	annals	annal	NOUN
ejpam-6189	389	2	of	of	ADP
ejpam-6189	389	3	pure	pure	ADJ
ejpam-6189	389	4	and	and	CCONJ
ejpam-6189	389	5	applied	applied	ADJ
ejpam-6189	389	6	mathematics	mathematic	NOUN
ejpam-6189	389	7	,	,	PUNCT
ejpam-6189	389	8	10(1):105–115	10(1):105–115	PROPN
ejpam-6189	389	9	,	,	PUNCT
ejpam-6189	389	10	2015	2015	NUM
ejpam-6189	389	11	.	.	PUNCT
ejpam-6189	390	1	w.	w.	PROPN
ejpam-6189	390	2	nakkhasen	nakkhasen	PROPN
ejpam-6189	390	3	et	et	PROPN
ejpam-6189	390	4	al	al	PROPN
ejpam-6189	390	5	.	.	PUNCT
ejpam-6189	390	6	/	/	SYM
ejpam-6189	390	7	eur	eur	PROPN
ejpam-6189	390	8	.	.	PUNCT
ejpam-6189	391	1	j.	j.	PROPN
ejpam-6189	391	2	pure	pure	PROPN
ejpam-6189	391	3	appl	appl	PROPN
ejpam-6189	391	4	.	.	PROPN
ejpam-6189	391	5	math	math	PROPN
ejpam-6189	391	6	,	,	PUNCT
ejpam-6189	391	7	18	18	NUM
ejpam-6189	391	8	(	(	PUNCT
ejpam-6189	391	9	3	3	NUM
ejpam-6189	391	10	)	)	PUNCT
ejpam-6189	391	11	(	(	PUNCT
ejpam-6189	391	12	2025	2025	NUM
ejpam-6189	391	13	)	)	PUNCT
ejpam-6189	391	14	,	,	PUNCT
ejpam-6189	391	15	6189	6189	NUM
ejpam-6189	391	16	13	13	NUM
ejpam-6189	391	17	of	of	ADP
ejpam-6189	391	18	13	13	NUM
ejpam-6189	392	1	[	[	X
ejpam-6189	392	2	9	9	NUM
ejpam-6189	392	3	]	]	PUNCT
ejpam-6189	392	4	x.	x.	NOUN
ejpam-6189	392	5	li	li	PROPN
ejpam-6189	392	6	.	.	PUNCT
ejpam-6189	393	1	every	every	DET
ejpam-6189	393	2	classifiable	classifiable	ADJ
ejpam-6189	393	3	simple	simple	ADJ
ejpam-6189	393	4	c∗-algebra	c∗-algebra	PROPN
ejpam-6189	393	5	has	have	VERB
ejpam-6189	393	6	a	a	DET
ejpam-6189	393	7	cartan	cartan	ADJ
ejpam-6189	393	8	subalgebr	subalgebr	NOUN
ejpam-6189	393	9	.	.	PUNCT
ejpam-6189	394	1	inventiones	inventione	NOUN
ejpam-6189	394	2	mathematicae	mathematicae	PROPN
ejpam-6189	394	3	,	,	PUNCT
ejpam-6189	394	4	219:653–699	219:653–699	NUM
ejpam-6189	394	5	,	,	PUNCT
ejpam-6189	394	6	2020	2020	NUM
ejpam-6189	394	7	.	.	PUNCT
ejpam-6189	395	1	[	[	X
ejpam-6189	395	2	10	10	NUM
ejpam-6189	395	3	]	]	X
ejpam-6189	395	4	d.	d.	PROPN
ejpam-6189	395	5	a.	a.	PROPN
ejpam-6189	395	6	romano	romano	PROPN
ejpam-6189	395	7	.	.	PUNCT
ejpam-6189	396	1	on	on	ADP
ejpam-6189	396	2	a	a	DET
ejpam-6189	396	3	generalization	generalization	NOUN
ejpam-6189	396	4	of	of	ADP
ejpam-6189	396	5	ku	ku	PROPN
ejpam-6189	396	6	-algebras	-algebras	PROPN
ejpam-6189	396	7	pseudo	pseudo	NOUN
ejpam-6189	396	8	-	-	NOUN
ejpam-6189	396	9	ku	ku	NOUN
ejpam-6189	396	10	algebras	algebras	PROPN
ejpam-6189	396	11	.	.	PUNCT
ejpam-6189	397	1	open	open	ADJ
ejpam-6189	397	2	journal	journal	PROPN
ejpam-6189	397	3	of	of	ADP
ejpam-6189	397	4	mathematical	mathematical	ADJ
ejpam-6189	397	5	sciences	sciences	PROPN
ejpam-6189	397	6	,	,	PUNCT
ejpam-6189	397	7	4:200–210	4:200–210	PROPN
ejpam-6189	397	8	,	,	PUNCT
ejpam-6189	397	9	2020	2020	NUM
ejpam-6189	397	10	.	.	PUNCT
ejpam-6189	398	1	[	[	X
ejpam-6189	398	2	11	11	NUM
ejpam-6189	398	3	]	]	PUNCT
ejpam-6189	398	4	l.	l.	PROPN
ejpam-6189	398	5	a.	a.	PROPN
ejpam-6189	398	6	zadeh	zadeh	PROPN
ejpam-6189	398	7	.	.	PUNCT
ejpam-6189	398	8	fuzzy	fuzzy	ADJ
ejpam-6189	398	9	sets	set	NOUN
ejpam-6189	398	10	.	.	PUNCT
ejpam-6189	399	1	information	information	NOUN
ejpam-6189	399	2	and	and	CCONJ
ejpam-6189	399	3	control	control	NOUN
ejpam-6189	399	4	,	,	PUNCT
ejpam-6189	399	5	8(3):338–353	8(3):338–353	NUM
ejpam-6189	399	6	,	,	PUNCT
ejpam-6189	399	7	1965	1965	NUM
ejpam-6189	399	8	.	.	PUNCT
ejpam-6189	400	1	[	[	X
ejpam-6189	400	2	12	12	NUM
ejpam-6189	400	3	]	]	PUNCT
ejpam-6189	400	4	a.	a.	NOUN
ejpam-6189	400	5	rosenfeld	rosenfeld	PROPN
ejpam-6189	400	6	.	.	PUNCT
ejpam-6189	401	1	fuzzy	fuzzy	ADJ
ejpam-6189	401	2	groups	group	NOUN
ejpam-6189	401	3	.	.	PUNCT
ejpam-6189	402	1	journal	journal	PROPN
ejpam-6189	402	2	of	of	ADP
ejpam-6189	402	3	mathematical	mathematical	ADJ
ejpam-6189	402	4	analysis	analysis	NOUN
ejpam-6189	402	5	and	and	CCONJ
ejpam-6189	402	6	applications	application	NOUN
ejpam-6189	402	7	,	,	PUNCT
ejpam-6189	402	8	35:512–517	35:512–517	PROPN
ejpam-6189	402	9	,	,	PUNCT
ejpam-6189	402	10	1971	1971	NUM
ejpam-6189	402	11	.	.	PUNCT
ejpam-6189	403	1	[	[	X
ejpam-6189	403	2	13	13	NUM
ejpam-6189	403	3	]	]	X
ejpam-6189	403	4	n.	n.	PROPN
ejpam-6189	403	5	kuroki	kuroki	PROPN
ejpam-6189	403	6	.	.	PUNCT
ejpam-6189	404	1	on	on	ADP
ejpam-6189	404	2	fuzzy	fuzzy	ADJ
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ejpam-6189	404	4	and	and	CCONJ
ejpam-6189	404	5	fuzzy	fuzzy	ADJ
ejpam-6189	404	6	bi	bi	NOUN
ejpam-6189	404	7	-	-	NOUN
ejpam-6189	404	8	ideals	ideal	NOUN
ejpam-6189	404	9	in	in	ADP
ejpam-6189	404	10	semigroups	semigroup	NOUN
ejpam-6189	404	11	.	.	PUNCT
ejpam-6189	405	1	fuzzy	fuzzy	ADJ
ejpam-6189	405	2	sets	set	NOUN
ejpam-6189	405	3	and	and	CCONJ
ejpam-6189	405	4	systems	system	NOUN
ejpam-6189	405	5	,	,	PUNCT
ejpam-6189	405	6	5:203–215	5:203–215	NUM
ejpam-6189	405	7	,	,	PUNCT
ejpam-6189	405	8	1981	1981	NUM
ejpam-6189	405	9	.	.	PUNCT
ejpam-6189	406	1	[	[	X
ejpam-6189	406	2	14	14	NUM
ejpam-6189	406	3	]	]	PUNCT
ejpam-6189	406	4	a.	a.	NOUN
ejpam-6189	406	5	rezaei	rezaei	PROPN
ejpam-6189	406	6	and	and	CCONJ
ejpam-6189	406	7	a.	a.	PROPN
ejpam-6189	406	8	b.	b.	PROPN
ejpam-6189	406	9	saeid	saeid	PROPN
ejpam-6189	406	10	.	.	PUNCT
ejpam-6189	407	1	on	on	ADP
ejpam-6189	407	2	fuzzy	fuzzy	ADJ
ejpam-6189	407	3	subalgebras	subalgebra	NOUN
ejpam-6189	407	4	of	of	ADP
ejpam-6189	407	5	be	be	NOUN
ejpam-6189	407	6	-	-	PUNCT
ejpam-6189	407	7	algebras	algebra	NOUN
ejpam-6189	407	8	.	.	PUNCT
ejpam-6189	408	1	afrika	afrika	PROPN
ejpam-6189	408	2	matematika	matematika	PROPN
ejpam-6189	408	3	,	,	PUNCT
ejpam-6189	408	4	22:115–127	22:115–127	PROPN
ejpam-6189	408	5	,	,	PUNCT
ejpam-6189	408	6	2011	2011	NUM
ejpam-6189	408	7	.	.	PUNCT
ejpam-6189	409	1	[	[	X
ejpam-6189	409	2	15	15	NUM
ejpam-6189	409	3	]	]	X
ejpam-6189	409	4	g.	g.	PROPN
ejpam-6189	409	5	muhiuddin	muhiuddin	PROPN
ejpam-6189	409	6	.	.	PUNCT
ejpam-6189	410	1	characterizations	characterization	NOUN
ejpam-6189	410	2	of	of	ADP
ejpam-6189	410	3	fuzzy	fuzzy	ADJ
ejpam-6189	410	4	subalgebras	subalgebras	PROPN
ejpam-6189	410	5	in	in	ADP
ejpam-6189	410	6	bck	bck	PROPN
ejpam-6189	410	7	/	/	SYM
ejpam-6189	410	8	bci	bci	NOUN
ejpam-6189	410	9	-	-	PUNCT
ejpam-6189	410	10	algebras	algebra	NOUN
ejpam-6189	410	11	.	.	PUNCT
ejpam-6189	411	1	applied	apply	VERB
ejpam-6189	411	2	mathematical	mathematical	ADJ
ejpam-6189	411	3	sciences	science	NOUN
ejpam-6189	411	4	,	,	PUNCT
ejpam-6189	411	5	9(144):7187–7196	9(144):7187–7196	NUM
ejpam-6189	411	6	,	,	PUNCT
ejpam-6189	411	7	2015	2015	NUM
ejpam-6189	411	8	.	.	PUNCT
ejpam-6189	412	1	[	[	X
ejpam-6189	412	2	16	16	NUM
ejpam-6189	412	3	]	]	X
ejpam-6189	412	4	n.	n.	PROPN
ejpam-6189	412	5	tacha	tacha	PROPN
ejpam-6189	412	6	,	,	PUNCT
ejpam-6189	412	7	p.	p.	PROPN
ejpam-6189	412	8	phayapsiang	phayapsiang	PROPN
ejpam-6189	412	9	,	,	PUNCT
ejpam-6189	412	10	and	and	CCONJ
ejpam-6189	412	11	a.	a.	NOUN
ejpam-6189	412	12	iampan	iampan	PROPN
ejpam-6189	412	13	.	.	PUNCT
ejpam-6189	413	1	length	length	NOUN
ejpam-6189	413	2	and	and	CCONJ
ejpam-6189	413	3	mean	mean	VERB
ejpam-6189	413	4	fuzzy	fuzzy	ADJ
ejpam-6189	413	5	up	up	ADP
ejpam-6189	413	6	-subalgebras	-subalgebra	NOUN
ejpam-6189	413	7	of	of	ADP
ejpam-6189	413	8	up	up	NOUN
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ejpam-6189	413	10	.	.	PUNCT
ejpam-6189	414	1	caspian	caspian	PROPN
ejpam-6189	414	2	journal	journal	PROPN
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ejpam-6189	414	4	mathematical	mathematical	ADJ
ejpam-6189	414	5	sciences	sciences	PROPN
ejpam-6189	414	6	,	,	PUNCT
ejpam-6189	414	7	11(1):264–303	11(1):264–303	NUM
ejpam-6189	414	8	,	,	PUNCT
ejpam-6189	414	9	2022	2022	NUM
ejpam-6189	414	10	.	.	PUNCT
ejpam-6189	415	1	[	[	X
ejpam-6189	415	2	17	17	NUM
ejpam-6189	415	3	]	]	X
ejpam-6189	415	4	g.	g.	PROPN
ejpam-6189	415	5	n.	n.	PROPN
ejpam-6189	415	6	devi	devi	PROPN
ejpam-6189	415	7	,	,	PUNCT
ejpam-6189	415	8	p.	p.	NOUN
ejpam-6189	415	9	hemavathi	hemavathi	NOUN
ejpam-6189	415	10	,	,	PUNCT
ejpam-6189	415	11	and	and	CCONJ
ejpam-6189	415	12	p.	p.	NOUN
ejpam-6189	415	13	muralikrishna	muralikrishna	NOUN
ejpam-6189	415	14	.	.	PUNCT
ejpam-6189	416	1	comprehensive	comprehensive	ADJ
ejpam-6189	416	2	work	work	NOUN
ejpam-6189	416	3	on	on	ADP
ejpam-6189	416	4	intervalvalued	intervalvalue	VERB
ejpam-6189	416	5	fuzzy	fuzzy	ADJ
ejpam-6189	416	6	translation	translation	NOUN
ejpam-6189	416	7	and	and	CCONJ
ejpam-6189	416	8	multiplication	multiplication	NOUN
ejpam-6189	416	9	in	in	ADP
ejpam-6189	416	10	z	z	NOUN
ejpam-6189	416	11	-	-	PUNCT
ejpam-6189	416	12	subalgebra	subalgebra	NOUN
ejpam-6189	416	13	of	of	ADP
ejpam-6189	416	14	z	z	NOUN
ejpam-6189	416	15	-	-	PUNCT
ejpam-6189	416	16	algebra	algebra	NOUN
ejpam-6189	416	17	.	.	PUNCT
ejpam-6189	417	1	philippine	philippine	ADJ
ejpam-6189	417	2	journal	journal	PROPN
ejpam-6189	417	3	of	of	ADP
ejpam-6189	417	4	science	science	NOUN
ejpam-6189	417	5	,	,	PUNCT
ejpam-6189	417	6	153(1):147–156	153(1):147–156	PROPN
ejpam-6189	417	7	,	,	PUNCT
ejpam-6189	417	8	2024	2024	NUM
ejpam-6189	417	9	.	.	PUNCT
ejpam-6189	418	1	[	[	X
ejpam-6189	418	2	18	18	NUM
ejpam-6189	418	3	]	]	PUNCT
ejpam-6189	418	4	t.	t.	NOUN
ejpam-6189	418	5	kuraoka	kuraoka	NOUN
ejpam-6189	418	6	and	and	CCONJ
ejpam-6189	418	7	n.	n.	PROPN
ejpam-6189	418	8	y.	y.	PROPN
ejpam-6189	418	9	suzuki	suzuki	PROPN
ejpam-6189	418	10	.	.	PUNCT
ejpam-6189	419	1	lattice	lattice	PROPN
ejpam-6189	419	2	of	of	ADP
ejpam-6189	419	3	fuzzy	fuzzy	ADJ
ejpam-6189	419	4	subalgebras	subalgebras	PROPN
ejpam-6189	419	5	in	in	ADP
ejpam-6189	419	6	universal	universal	ADJ
ejpam-6189	419	7	algebra	algebra	PROPN
ejpam-6189	419	8	.	.	PUNCT
ejpam-6189	420	1	algebra	algebra	NOUN
ejpam-6189	420	2	universalis	universali	VERB
ejpam-6189	420	3	,	,	PUNCT
ejpam-6189	420	4	47:223–237	47:223–237	NUM
ejpam-6189	420	5	,	,	PUNCT
ejpam-6189	420	6	2002	2002	NUM
ejpam-6189	420	7	.	.	PUNCT
ejpam-6189	421	1	[	[	X
ejpam-6189	421	2	19	19	NUM
ejpam-6189	421	3	]	]	PUNCT
ejpam-6189	421	4	w.	w.	PROPN
ejpam-6189	421	5	nakkhasen	nakkhasen	PROPN
ejpam-6189	421	6	.	.	PUNCT
ejpam-6189	422	1	on	on	ADP
ejpam-6189	422	2	picture	picture	NOUN
ejpam-6189	422	3	fuzzy	fuzzy	ADJ
ejpam-6189	422	4	(	(	PUNCT
ejpam-6189	422	5	m	m	PROPN
ejpam-6189	422	6	,	,	PUNCT
ejpam-6189	422	7	n)-ideals	n)-ideal	NOUN
ejpam-6189	422	8	of	of	ADP
ejpam-6189	422	9	semigroups	semigroup	NOUN
ejpam-6189	422	10	.	.	PUNCT
ejpam-6189	423	1	iaeng	iaeng	PROPN
ejpam-6189	423	2	international	international	PROPN
ejpam-6189	423	3	journal	journal	PROPN
ejpam-6189	423	4	of	of	ADP
ejpam-6189	423	5	applied	apply	VERB
ejpam-6189	423	6	mathematics	mathematic	NOUN
ejpam-6189	423	7	,	,	PUNCT
ejpam-6189	423	8	52(4):1040–1051	52(4):1040–1051	NUM
ejpam-6189	423	9	,	,	PUNCT
ejpam-6189	423	10	2022	2022	NUM
ejpam-6189	423	11	.	.	PUNCT
ejpam-6189	424	1	[	[	X
ejpam-6189	424	2	20	20	NUM
ejpam-6189	424	3	]	]	X
ejpam-6189	424	4	g.	g.	PROPN
ejpam-6189	424	5	vasantha	vasantha	PROPN
ejpam-6189	424	6	and	and	CCONJ
ejpam-6189	424	7	t.	t.	PROPN
ejpam-6189	424	8	sri	sri	PROPN
ejpam-6189	424	9	lakshmi	lakshmi	PROPN
ejpam-6189	424	10	.	.	PUNCT
ejpam-6189	425	1	impact	impact	NOUN
ejpam-6189	425	2	fuzzy	fuzzy	ADJ
ejpam-6189	425	3	ideal	ideal	ADJ
ejpam-6189	425	4	extension	extension	NOUN
ejpam-6189	425	5	in	in	ADP
ejpam-6189	425	6	terms	term	NOUN
ejpam-6189	425	7	of	of	ADP
ejpam-6189	425	8	gamma	gamma	PROPN
ejpam-6189	425	9	semigroup	semigroup	PROPN
ejpam-6189	425	10	.	.	PUNCT
ejpam-6189	426	1	communications	communication	NOUN
ejpam-6189	426	2	on	on	ADP
ejpam-6189	426	3	applied	apply	VERB
ejpam-6189	426	4	nonlinear	nonlinear	ADJ
ejpam-6189	426	5	analysis	analysis	NOUN
ejpam-6189	426	6	,	,	PUNCT
ejpam-6189	426	7	32(9):635–649	32(9):635–649	NUM
ejpam-6189	426	8	,	,	PUNCT
ejpam-6189	426	9	2025	2025	NUM
ejpam-6189	426	10	.	.	PUNCT
ejpam-6189	427	1	[	[	X
ejpam-6189	427	2	21	21	NUM
ejpam-6189	427	3	]	]	PUNCT
ejpam-6189	427	4	a.	a.	PROPN
ejpam-6189	427	5	b.	b.	PROPN
ejpam-6189	427	6	saeid	saeid	PROPN
ejpam-6189	427	7	.	.	PUNCT
ejpam-6189	428	1	fuzzy	fuzzy	ADJ
ejpam-6189	428	2	dot	dot	NOUN
ejpam-6189	428	3	bck	bck	NOUN
ejpam-6189	428	4	/	/	SYM
ejpam-6189	428	5	bci	bci	NOUN
ejpam-6189	428	6	-	-	PUNCT
ejpam-6189	428	7	algebras	algebra	NOUN
ejpam-6189	428	8	.	.	PUNCT
ejpam-6189	429	1	international	international	ADJ
ejpam-6189	429	2	journal	journal	PROPN
ejpam-6189	429	3	of	of	ADP
ejpam-6189	429	4	algebra	algebra	PROPN
ejpam-6189	429	5	,	,	PUNCT
ejpam-6189	429	6	4(7):341–352	4(7):341–352	NUM
ejpam-6189	429	7	,	,	PUNCT
ejpam-6189	429	8	2010	2010	NUM
ejpam-6189	429	9	.	.	PUNCT
ejpam-6189	430	1	[	[	X
ejpam-6189	430	2	22	22	NUM
ejpam-6189	430	3	]	]	PUNCT
ejpam-6189	430	4	t.	t.	NOUN
ejpam-6189	430	5	senapati	senapati	PROPN
ejpam-6189	430	6	,	,	PUNCT
ejpam-6189	430	7	m.	m.	NOUN
ejpam-6189	430	8	bhowmik	bhowmik	ADJ
ejpam-6189	430	9	,	,	PUNCT
ejpam-6189	430	10	and	and	CCONJ
ejpam-6189	430	11	m.	m.	NOUN
ejpam-6189	430	12	pal	pal	NOUN
ejpam-6189	430	13	.	.	PUNCT
ejpam-6189	431	1	fuzzy	fuzzy	ADJ
ejpam-6189	431	2	dot	dot	NOUN
ejpam-6189	431	3	structure	structure	NOUN
ejpam-6189	431	4	of	of	ADP
ejpam-6189	431	5	bg	bg	PROPN
ejpam-6189	431	6	-	-	PUNCT
ejpam-6189	431	7	algebras	algebras	PROPN
ejpam-6189	431	8	.	.	PUNCT
ejpam-6189	432	1	fuzzy	fuzzy	ADJ
ejpam-6189	432	2	information	information	NOUN
ejpam-6189	432	3	and	and	CCONJ
ejpam-6189	432	4	engineering	engineering	NOUN
ejpam-6189	432	5	,	,	PUNCT
ejpam-6189	432	6	6(3):315–329	6(3):315–329	PROPN
ejpam-6189	432	7	,	,	PUNCT
ejpam-6189	432	8	2014	2014	NUM
ejpam-6189	432	9	.	.	PUNCT
ejpam-6189	433	1	[	[	X
ejpam-6189	433	2	23	23	NUM
ejpam-6189	433	3	]	]	PUNCT
ejpam-6189	433	4	t.	t.	NOUN
ejpam-6189	433	5	senapati	senapati	PROPN
ejpam-6189	433	6	,	,	PUNCT
ejpam-6189	433	7	m.	m.	NOUN
ejpam-6189	433	8	bhowmik	bhowmik	ADJ
ejpam-6189	433	9	,	,	PUNCT
ejpam-6189	433	10	and	and	CCONJ
ejpam-6189	433	11	m.	m.	NOUN
ejpam-6189	433	12	pal	pal	NOUN
ejpam-6189	433	13	.	.	PUNCT
ejpam-6189	434	1	fuzzy	fuzzy	ADJ
ejpam-6189	434	2	dot	dot	NOUN
ejpam-6189	434	3	subalgebras	subalgebra	NOUN
ejpam-6189	434	4	and	and	CCONJ
ejpam-6189	434	5	fuzzy	fuzzy	ADJ
ejpam-6189	434	6	dot	dot	NOUN
ejpam-6189	434	7	ideals	ideal	NOUN
ejpam-6189	434	8	of	of	ADP
ejpam-6189	434	9	b	b	NOUN
ejpam-6189	434	10	-	-	PUNCT
ejpam-6189	434	11	algebras	algebras	PROPN
ejpam-6189	434	12	.	.	PUNCT
ejpam-6189	434	13	journal	journal	PROPN
ejpam-6189	434	14	of	of	ADP
ejpam-6189	434	15	uncertain	uncertain	ADJ
ejpam-6189	434	16	systems	system	NOUN
ejpam-6189	434	17	,	,	PUNCT
ejpam-6189	434	18	8(1):22–30	8(1):22–30	NUM
ejpam-6189	434	19	,	,	PUNCT
ejpam-6189	434	20	2014	2014	NUM
ejpam-6189	434	21	.	.	PUNCT
ejpam-6189	435	1	[	[	X
ejpam-6189	435	2	24	24	NUM
ejpam-6189	435	3	]	]	X
ejpam-6189	435	4	g.	g.	PROPN
ejpam-6189	435	5	t.	t.	PROPN
ejpam-6189	435	6	dejen	dejen	PROPN
ejpam-6189	435	7	.	.	PUNCT
ejpam-6189	436	1	structure	structure	NOUN
ejpam-6189	436	2	of	of	ADP
ejpam-6189	436	3	fuzzy	fuzzy	ADJ
ejpam-6189	436	4	dot	dot	NOUN
ejpam-6189	436	5	d	d	NOUN
ejpam-6189	436	6	-	-	PUNCT
ejpam-6189	436	7	subalgebras	subalgebras	PROPN
ejpam-6189	436	8	.	.	PUNCT
ejpam-6189	437	1	journal	journal	PROPN
ejpam-6189	437	2	of	of	ADP
ejpam-6189	437	3	applied	apply	VERB
ejpam-6189	437	4	mathematics	mathematic	NOUN
ejpam-6189	437	5	and	and	CCONJ
ejpam-6189	437	6	computation	computation	NOUN
ejpam-6189	437	7	,	,	PUNCT
ejpam-6189	437	8	4(4):130–136	4(4):130–136	NUM
ejpam-6189	437	9	,	,	PUNCT
ejpam-6189	437	10	2020	2020	NUM
ejpam-6189	437	11	.	.	PUNCT
ejpam-6189	438	1	[	[	X
ejpam-6189	438	2	25	25	NUM
ejpam-6189	438	3	]	]	PUNCT
ejpam-6189	438	4	m.	m.	PROPN
ejpam-6189	438	5	jiang	jiang	PROPN
ejpam-6189	438	6	.	.	PUNCT
ejpam-6189	439	1	hesitant	hesitant	ADJ
ejpam-6189	439	2	fuzzy	fuzzy	ADJ
ejpam-6189	439	3	dot	dot	NOUN
ejpam-6189	439	4	subalgebra	subalgebra	NOUN
ejpam-6189	439	5	and	and	CCONJ
ejpam-6189	439	6	dot	dot	NOUN
ejpam-6189	439	7	ideals	ideal	NOUN
ejpam-6189	439	8	of	of	ADP
ejpam-6189	439	9	b	b	NOUN
ejpam-6189	439	10	-	-	PUNCT
ejpam-6189	439	11	algebra	algebra	NOUN
ejpam-6189	439	12	.	.	PUNCT
ejpam-6189	440	1	journal	journal	NOUN
ejpam-6189	440	2	of	of	ADP
ejpam-6189	440	3	intelligent	intelligent	ADJ
ejpam-6189	440	4	&	&	CCONJ
ejpam-6189	440	5	fuzzy	fuzzy	ADJ
ejpam-6189	440	6	systems	system	NOUN
ejpam-6189	440	7	,	,	PUNCT
ejpam-6189	440	8	43(5):6203–6212	43(5):6203–6212	NUM
ejpam-6189	440	9	,	,	PUNCT
ejpam-6189	440	10	2022	2022	NUM
ejpam-6189	440	11	.	.	PUNCT
ejpam-6189	441	1	[	[	X
ejpam-6189	441	2	26	26	NUM
ejpam-6189	441	3	]	]	PUNCT
ejpam-6189	441	4	t.	t.	NOUN
ejpam-6189	441	5	bantaojai	bantaojai	PROPN
ejpam-6189	441	6	,	,	PUNCT
ejpam-6189	441	7	c.	c.	PROPN
ejpam-6189	441	8	suanoom	suanoom	PROPN
ejpam-6189	441	9	,	,	PUNCT
ejpam-6189	441	10	j.	j.	PROPN
ejpam-6189	441	11	phuto	phuto	PROPN
ejpam-6189	441	12	,	,	PUNCT
ejpam-6189	441	13	and	and	CCONJ
ejpam-6189	441	14	a.	a.	NOUN
ejpam-6189	441	15	iampan	iampan	PROPN
ejpam-6189	441	16	.	.	PUNCT
ejpam-6189	442	1	on	on	ADP
ejpam-6189	442	2	bd	bd	PROPN
ejpam-6189	442	3	-	-	PUNCT
ejpam-6189	442	4	algebras	algebras	PROPN
ejpam-6189	442	5	.	.	PUNCT
ejpam-6189	443	1	international	international	ADJ
ejpam-6189	443	2	journal	journal	PROPN
ejpam-6189	443	3	of	of	ADP
ejpam-6189	443	4	mathematics	mathematic	NOUN
ejpam-6189	443	5	and	and	CCONJ
ejpam-6189	443	6	computer	computer	NOUN
ejpam-6189	443	7	science	science	NOUN
ejpam-6189	443	8	,	,	PUNCT
ejpam-6189	443	9	17(2):731–737	17(2):731–737	PROPN
ejpam-6189	443	10	,	,	PUNCT
ejpam-6189	443	11	2022	2022	NUM
ejpam-6189	443	12	.	.	PUNCT
ejpam-6189	444	1	[	[	X
ejpam-6189	444	2	27	27	NUM
ejpam-6189	444	3	]	]	X
ejpam-6189	444	4	w.	w.	PROPN
ejpam-6189	444	5	nakkhasen	nakkhasen	PROPN
ejpam-6189	444	6	,	,	PUNCT
ejpam-6189	444	7	p.	p.	PROPN
ejpam-6189	444	8	srisarakham	srisarakham	PROPN
ejpam-6189	444	9	,	,	PUNCT
ejpam-6189	444	10	andw	andw	NOUN
ejpam-6189	444	11	.	.	PUNCT
ejpam-6189	445	1	sakuntanat	sakuntanat	PROPN
ejpam-6189	445	2	.	.	PUNCT
ejpam-6189	446	1	a	a	DET
ejpam-6189	446	2	study	study	NOUN
ejpam-6189	446	3	on	on	ADP
ejpam-6189	446	4	fuzzybd	fuzzybd	NOUN
ejpam-6189	446	5	-	-	PUNCT
ejpam-6189	446	6	subalgebras	subalgebras	PROPN
ejpam-6189	446	7	of	of	ADP
ejpam-6189	446	8	bd	bd	PROPN
ejpam-6189	446	9	-	-	PUNCT
ejpam-6189	446	10	algebras	algebras	PROPN
ejpam-6189	446	11	.	.	PUNCT
ejpam-6189	447	1	icic	icic	PROPN
ejpam-6189	447	2	express	express	PROPN
ejpam-6189	447	3	letters	letter	NOUN
ejpam-6189	447	4	,	,	PUNCT
ejpam-6189	447	5	18(8):777–783	18(8):777–783	PROPN
ejpam-6189	447	6	,	,	PUNCT
ejpam-6189	447	7	2024	2024	NUM
ejpam-6189	447	8	.	.	PUNCT
ejpam-6189	448	1	[	[	X
ejpam-6189	448	2	28	28	NUM
ejpam-6189	448	3	]	]	X
ejpam-6189	448	4	p.	p.	NOUN
ejpam-6189	448	5	bhattacharya	bhattacharya	PROPN
ejpam-6189	448	6	and	and	CCONJ
ejpam-6189	448	7	n.	n.	PROPN
ejpam-6189	448	8	p.	p.	PROPN
ejpam-6189	448	9	mukherjee	mukherjee	PROPN
ejpam-6189	448	10	.	.	PUNCT
ejpam-6189	449	1	fuzzy	fuzzy	ADJ
ejpam-6189	449	2	relations	relation	NOUN
ejpam-6189	449	3	and	and	CCONJ
ejpam-6189	449	4	fuzzy	fuzzy	ADJ
ejpam-6189	449	5	groups	group	NOUN
ejpam-6189	449	6	.	.	PUNCT
ejpam-6189	450	1	information	information	NOUN
ejpam-6189	450	2	sciences	sciences	PROPN
ejpam-6189	450	3	,	,	PUNCT
ejpam-6189	450	4	36(3):267–282	36(3):267–282	PROPN
ejpam-6189	450	5	,	,	PUNCT
ejpam-6189	450	6	1985	1985	NUM
ejpam-6189	450	7	.	.	PUNCT