id	sid	tid	token	lemma	pos
ejpam-3575	1	1	european	european	PROPN
ejpam-3575	1	2	journal	journal	PROPN
ejpam-3575	1	3	of	of	ADP
ejpam-3575	1	4	pure	pure	ADJ
ejpam-3575	1	5	and	and	CCONJ
ejpam-3575	1	6	applied	apply	VERB
ejpam-3575	1	7	mathematics	mathematic	NOUN
ejpam-3575	1	8	vol	vol	NOUN
ejpam-3575	1	9	.	.	PROPN
ejpam-3575	2	1	13	13	NUM
ejpam-3575	2	2	,	,	PUNCT
ejpam-3575	2	3	no	no	INTJ
ejpam-3575	2	4	.	.	NOUN
ejpam-3575	2	5	1	1	NUM
ejpam-3575	2	6	,	,	PUNCT
ejpam-3575	2	7	2020	2020	NUM
ejpam-3575	2	8	,	,	PUNCT
ejpam-3575	2	9	9	9	NUM
ejpam-3575	2	10	-	-	SYM
ejpam-3575	2	11	18	18	NUM
ejpam-3575	2	12	issn	issn	PROPN
ejpam-3575	2	13	1307	1307	NUM
ejpam-3575	2	14	-	-	SYM
ejpam-3575	2	15	5543	5543	NUM
ejpam-3575	2	16	–	–	PUNCT
ejpam-3575	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3575	2	18	published	publish	VERB
ejpam-3575	2	19	by	by	ADP
ejpam-3575	2	20	new	new	PROPN
ejpam-3575	2	21	york	york	PROPN
ejpam-3575	2	22	business	business	PROPN
ejpam-3575	2	23	global	global	PROPN
ejpam-3575	2	24	inf	inf	ADJ
ejpam-3575	2	25	-	-	PUNCT
ejpam-3575	2	26	hesitant	hesitant	ADJ
ejpam-3575	2	27	fuzzy	fuzzy	ADJ
ejpam-3575	2	28	subalgebras	subalgebra	NOUN
ejpam-3575	2	29	and	and	CCONJ
ejpam-3575	2	30	ideals	ideal	NOUN
ejpam-3575	2	31	in	in	ADP
ejpam-3575	2	32	bck	bck	PROPN
ejpam-3575	2	33	/	/	SYM
ejpam-3575	2	34	bci	bci	NOUN
ejpam-3575	2	35	-	-	PUNCT
ejpam-3575	2	36	algebras	algebras	PROPN
ejpam-3575	2	37	g.	g.	PROPN
ejpam-3575	2	38	muhiuddin1,∗	muhiuddin1,∗	PROPN
ejpam-3575	2	39	,	,	PUNCT
ejpam-3575	2	40	abdulaziz	abdulaziz	PROPN
ejpam-3575	2	41	m.	m.	PROPN
ejpam-3575	2	42	alanazi1	alanazi1	PROPN
ejpam-3575	2	43	,	,	PUNCT
ejpam-3575	3	1	mohamed	mohamed	PROPN
ejpam-3575	3	2	e.	e.	PROPN
ejpam-3575	3	3	a.	a.	PROPN
ejpam-3575	3	4	elnair1	elnair1	PROPN
ejpam-3575	3	5	,	,	PUNCT
ejpam-3575	3	6	k.	k.	PROPN
ejpam-3575	4	1	p.	p.	PROPN
ejpam-3575	4	2	shum2	shum2	NOUN
ejpam-3575	5	1	1	1	NUM
ejpam-3575	5	2	department	department	NOUN
ejpam-3575	5	3	of	of	ADP
ejpam-3575	5	4	mathematics	mathematic	NOUN
ejpam-3575	5	5	,	,	PUNCT
ejpam-3575	5	6	university	university	PROPN
ejpam-3575	5	7	of	of	ADP
ejpam-3575	5	8	tabuk	tabuk	PROPN
ejpam-3575	5	9	,	,	PUNCT
ejpam-3575	5	10	tabuk	tabuk	NOUN
ejpam-3575	5	11	71491	71491	NUM
ejpam-3575	5	12	,	,	PUNCT
ejpam-3575	5	13	saudi	saudi	PROPN
ejpam-3575	5	14	arabia	arabia	PROPN
ejpam-3575	5	15	2	2	NUM
ejpam-3575	5	16	institute	institute	NOUN
ejpam-3575	5	17	of	of	ADP
ejpam-3575	5	18	mathematics	mathematics	PROPN
ejpam-3575	5	19	,	,	PUNCT
ejpam-3575	5	20	yunnan	yunnan	PROPN
ejpam-3575	5	21	university	university	PROPN
ejpam-3575	5	22	,	,	PUNCT
ejpam-3575	5	23	kunming	kunme	VERB
ejpam-3575	5	24	650091	650091	NUM
ejpam-3575	5	25	,	,	PUNCT
ejpam-3575	5	26	people	people	NOUN
ejpam-3575	5	27	’s	’s	PART
ejpam-3575	5	28	republic	republic	PROPN
ejpam-3575	5	29	of	of	ADP
ejpam-3575	5	30	china	china	PROPN
ejpam-3575	5	31	abstract	abstract	PROPN
ejpam-3575	5	32	.	.	PUNCT
ejpam-3575	6	1	in	in	ADP
ejpam-3575	6	2	the	the	DET
ejpam-3575	6	3	present	present	ADJ
ejpam-3575	6	4	paper	paper	NOUN
ejpam-3575	6	5	,	,	PUNCT
ejpam-3575	6	6	we	we	PRON
ejpam-3575	6	7	introduce	introduce	VERB
ejpam-3575	6	8	the	the	DET
ejpam-3575	6	9	notions	notion	NOUN
ejpam-3575	6	10	of	of	ADP
ejpam-3575	6	11	inf	inf	ADJ
ejpam-3575	6	12	-	-	PUNCT
ejpam-3575	6	13	hesitant	hesitant	ADJ
ejpam-3575	6	14	fuzzy	fuzzy	ADJ
ejpam-3575	6	15	subalgebras	subalgebra	NOUN
ejpam-3575	6	16	and	and	CCONJ
ejpam-3575	6	17	inf	inf	ADJ
ejpam-3575	6	18	-	-	PUNCT
ejpam-3575	6	19	hesitant	hesitant	ADJ
ejpam-3575	6	20	fuzzy	fuzzy	ADJ
ejpam-3575	6	21	ideals	ideal	NOUN
ejpam-3575	6	22	in	in	ADP
ejpam-3575	6	23	bck	bck	PROPN
ejpam-3575	6	24	/	/	SYM
ejpam-3575	6	25	bci	bci	NOUN
ejpam-3575	6	26	-	-	PUNCT
ejpam-3575	6	27	algebras	algebras	PROPN
ejpam-3575	6	28	and	and	CCONJ
ejpam-3575	6	29	investigate	investigate	VERB
ejpam-3575	6	30	their	their	PRON
ejpam-3575	6	31	relations	relation	NOUN
ejpam-3575	6	32	and	and	CCONJ
ejpam-3575	6	33	properties	property	NOUN
ejpam-3575	6	34	.	.	PUNCT
ejpam-3575	7	1	in	in	ADP
ejpam-3575	7	2	addition	addition	NOUN
ejpam-3575	7	3	,	,	PUNCT
ejpam-3575	7	4	we	we	PRON
ejpam-3575	7	5	discuss	discuss	VERB
ejpam-3575	7	6	the	the	DET
ejpam-3575	7	7	characterizations	characterization	NOUN
ejpam-3575	7	8	of	of	ADP
ejpam-3575	7	9	inf	inf	ADJ
ejpam-3575	7	10	-	-	PUNCT
ejpam-3575	7	11	hesitant	hesitant	ADJ
ejpam-3575	7	12	fuzzy	fuzzy	ADJ
ejpam-3575	7	13	subalgebras	subalgebra	NOUN
ejpam-3575	7	14	and	and	CCONJ
ejpam-3575	7	15	inf	inf	ADJ
ejpam-3575	7	16	-	-	PUNCT
ejpam-3575	7	17	hesitant	hesitant	ADJ
ejpam-3575	7	18	fuzzy	fuzzy	ADJ
ejpam-3575	7	19	ideals	ideal	NOUN
ejpam-3575	7	20	in	in	ADP
ejpam-3575	7	21	bck	bck	PROPN
ejpam-3575	7	22	/	/	SYM
ejpam-3575	7	23	bci	bci	NOUN
ejpam-3575	7	24	-	-	PUNCT
ejpam-3575	7	25	algebras	algebra	NOUN
ejpam-3575	7	26	.	.	PUNCT
ejpam-3575	8	1	2020	2020	NUM
ejpam-3575	8	2	mathematics	mathematics	PROPN
ejpam-3575	8	3	subject	subject	NOUN
ejpam-3575	8	4	classifications	classification	NOUN
ejpam-3575	8	5	:	:	PUNCT
ejpam-3575	8	6	06f35	06f35	NUM
ejpam-3575	8	7	,	,	PUNCT
ejpam-3575	8	8	03g25	03g25	NUM
ejpam-3575	8	9	,	,	PUNCT
ejpam-3575	8	10	08a72	08a72	NOUN
ejpam-3575	8	11	key	key	ADJ
ejpam-3575	8	12	words	word	NOUN
ejpam-3575	8	13	and	and	CCONJ
ejpam-3575	8	14	phrases	phrase	NOUN
ejpam-3575	8	15	:	:	PUNCT
ejpam-3575	8	16	p	p	X
ejpam-3575	8	17	-	-	PUNCT
ejpam-3575	8	18	semisimple	semisimple	NOUN
ejpam-3575	8	19	bci	bci	NOUN
ejpam-3575	8	20	-	-	NOUN
ejpam-3575	8	21	algebra	algebra	NOUN
ejpam-3575	8	22	;	;	PUNCT
ejpam-3575	8	23	inf	inf	ADJ
ejpam-3575	8	24	-	-	PUNCT
ejpam-3575	8	25	hesitant	hesitant	ADJ
ejpam-3575	8	26	fuzzy	fuzzy	ADJ
ejpam-3575	8	27	subalgebras	subalgebra	NOUN
ejpam-3575	8	28	;	;	PUNCT
ejpam-3575	8	29	infhesitant	infhesitant	VERB
ejpam-3575	8	30	fuzzy	fuzzy	ADJ
ejpam-3575	8	31	ideals	ideal	NOUN
ejpam-3575	8	32	.	.	PUNCT
ejpam-3575	9	1	1	1	X
ejpam-3575	9	2	.	.	X
ejpam-3575	9	3	introduction	introduction	NOUN
ejpam-3575	9	4	the	the	DET
ejpam-3575	9	5	motivation	motivation	NOUN
ejpam-3575	9	6	for	for	ADP
ejpam-3575	9	7	introducing	introduce	VERB
ejpam-3575	9	8	hesitant	hesitant	ADJ
ejpam-3575	9	9	fuzzy	fuzzy	ADJ
ejpam-3575	9	10	sets	set	NOUN
ejpam-3575	9	11	is	be	AUX
ejpam-3575	9	12	that	that	SCONJ
ejpam-3575	9	13	it	it	PRON
ejpam-3575	9	14	is	be	AUX
ejpam-3575	9	15	sometimes	sometimes	ADV
ejpam-3575	9	16	difficult	difficult	ADJ
ejpam-3575	9	17	to	to	PART
ejpam-3575	9	18	determine	determine	VERB
ejpam-3575	9	19	the	the	DET
ejpam-3575	9	20	membership	membership	NOUN
ejpam-3575	9	21	of	of	ADP
ejpam-3575	9	22	an	an	DET
ejpam-3575	9	23	element	element	NOUN
ejpam-3575	9	24	into	into	ADP
ejpam-3575	9	25	a	a	DET
ejpam-3575	9	26	set	set	NOUN
ejpam-3575	9	27	and	and	CCONJ
ejpam-3575	9	28	in	in	ADP
ejpam-3575	9	29	some	some	DET
ejpam-3575	9	30	circumstances	circumstance	NOUN
ejpam-3575	9	31	this	this	DET
ejpam-3575	9	32	difficulty	difficulty	NOUN
ejpam-3575	9	33	is	be	AUX
ejpam-3575	9	34	caused	cause	VERB
ejpam-3575	9	35	by	by	ADP
ejpam-3575	9	36	a	a	DET
ejpam-3575	9	37	doubt	doubt	NOUN
ejpam-3575	9	38	between	between	ADP
ejpam-3575	9	39	a	a	DET
ejpam-3575	9	40	few	few	ADJ
ejpam-3575	9	41	different	different	ADJ
ejpam-3575	9	42	values	value	NOUN
ejpam-3575	9	43	.	.	PUNCT
ejpam-3575	10	1	for	for	ADP
ejpam-3575	10	2	example	example	NOUN
ejpam-3575	10	3	,	,	PUNCT
ejpam-3575	10	4	two	two	NUM
ejpam-3575	10	5	experts	expert	NOUN
ejpam-3575	10	6	discuss	discuss	VERB
ejpam-3575	10	7	the	the	DET
ejpam-3575	10	8	membership	membership	NOUN
ejpam-3575	10	9	of	of	ADP
ejpam-3575	10	10	x	x	PUNCT
ejpam-3575	10	11	into	into	ADP
ejpam-3575	10	12	a	a	PRON
ejpam-3575	10	13	,	,	PUNCT
ejpam-3575	10	14	and	and	CCONJ
ejpam-3575	10	15	one	one	PRON
ejpam-3575	10	16	wants	want	VERB
ejpam-3575	10	17	to	to	PART
ejpam-3575	10	18	assign	assign	VERB
ejpam-3575	10	19	0.3	0.3	NUM
ejpam-3575	10	20	and	and	CCONJ
ejpam-3575	10	21	the	the	DET
ejpam-3575	10	22	other	other	ADJ
ejpam-3575	10	23	0.4	0.4	NUM
ejpam-3575	10	24	.	.	PUNCT
ejpam-3575	11	1	so	so	ADV
ejpam-3575	11	2	,	,	PUNCT
ejpam-3575	11	3	the	the	DET
ejpam-3575	11	4	uncertainty	uncertainty	NOUN
ejpam-3575	11	5	on	on	ADP
ejpam-3575	11	6	the	the	DET
ejpam-3575	11	7	possible	possible	ADJ
ejpam-3575	11	8	values	value	NOUN
ejpam-3575	11	9	is	be	AUX
ejpam-3575	11	10	somehow	somehow	ADV
ejpam-3575	11	11	limited	limited	ADJ
ejpam-3575	11	12	.	.	PUNCT
ejpam-3575	12	1	torra	torra	VERB
ejpam-3575	13	1	[	[	X
ejpam-3575	13	2	25	25	NUM
ejpam-3575	13	3	]	]	PUNCT
ejpam-3575	13	4	proposed	propose	VERB
ejpam-3575	13	5	the	the	DET
ejpam-3575	13	6	concept	concept	NOUN
ejpam-3575	13	7	of	of	ADP
ejpam-3575	13	8	hesitant	hesitant	ADJ
ejpam-3575	13	9	fuzzy	fuzzy	ADJ
ejpam-3575	13	10	sets	set	NOUN
ejpam-3575	13	11	as	as	ADP
ejpam-3575	13	12	a	a	DET
ejpam-3575	13	13	new	new	ADJ
ejpam-3575	13	14	generalization	generalization	NOUN
ejpam-3575	13	15	of	of	ADP
ejpam-3575	13	16	fuzzy	fuzzy	ADJ
ejpam-3575	13	17	sets	set	NOUN
ejpam-3575	13	18	[	[	X
ejpam-3575	13	19	33	33	NUM
ejpam-3575	13	20	]	]	PUNCT
ejpam-3575	13	21	,	,	PUNCT
ejpam-3575	13	22	which	which	PRON
ejpam-3575	13	23	allows	allow	VERB
ejpam-3575	13	24	the	the	DET
ejpam-3575	13	25	membership	membership	NOUN
ejpam-3575	13	26	of	of	ADP
ejpam-3575	13	27	an	an	DET
ejpam-3575	13	28	element	element	NOUN
ejpam-3575	13	29	of	of	ADP
ejpam-3575	13	30	a	a	DET
ejpam-3575	13	31	set	set	NOUN
ejpam-3575	13	32	to	to	PART
ejpam-3575	13	33	be	be	AUX
ejpam-3575	13	34	represented	represent	VERB
ejpam-3575	13	35	by	by	ADP
ejpam-3575	13	36	several	several	ADJ
ejpam-3575	13	37	possible	possible	ADJ
ejpam-3575	13	38	values	value	NOUN
ejpam-3575	13	39	.	.	PUNCT
ejpam-3575	14	1	they	they	PRON
ejpam-3575	14	2	also	also	ADV
ejpam-3575	14	3	discussed	discuss	VERB
ejpam-3575	14	4	relationships	relationship	NOUN
ejpam-3575	14	5	among	among	ADP
ejpam-3575	14	6	hesitant	hesitant	ADJ
ejpam-3575	14	7	fuzzy	fuzzy	ADJ
ejpam-3575	14	8	sets	set	NOUN
ejpam-3575	14	9	and	and	CCONJ
ejpam-3575	14	10	other	other	ADJ
ejpam-3575	14	11	generalizations	generalization	NOUN
ejpam-3575	14	12	of	of	ADP
ejpam-3575	14	13	fuzzy	fuzzy	ADJ
ejpam-3575	14	14	sets	set	NOUN
ejpam-3575	14	15	such	such	ADJ
ejpam-3575	14	16	as	as	ADP
ejpam-3575	14	17	intuitionistic	intuitionistic	ADJ
ejpam-3575	14	18	fuzzy	fuzzy	ADJ
ejpam-3575	14	19	sets	set	NOUN
ejpam-3575	14	20	,	,	PUNCT
ejpam-3575	14	21	type-2	type-2	NUM
ejpam-3575	14	22	fuzzy	fuzzy	ADJ
ejpam-3575	14	23	sets	set	NOUN
ejpam-3575	14	24	,	,	PUNCT
ejpam-3575	14	25	and	and	CCONJ
ejpam-3575	14	26	fuzzy	fuzzy	ADJ
ejpam-3575	14	27	multisets	multiset	NOUN
ejpam-3575	14	28	.	.	PUNCT
ejpam-3575	15	1	some	some	DET
ejpam-3575	15	2	set	set	VERB
ejpam-3575	15	3	theoretic	theoretic	ADJ
ejpam-3575	15	4	operations	operation	NOUN
ejpam-3575	15	5	such	such	ADJ
ejpam-3575	15	6	as	as	ADP
ejpam-3575	15	7	union	union	NOUN
ejpam-3575	15	8	,	,	PUNCT
ejpam-3575	15	9	intersection	intersection	NOUN
ejpam-3575	15	10	and	and	CCONJ
ejpam-3575	15	11	complement	complement	NOUN
ejpam-3575	15	12	on	on	ADP
ejpam-3575	15	13	hesitant	hesitant	ADJ
ejpam-3575	15	14	fuzzy	fuzzy	ADJ
ejpam-3575	15	15	sets	set	NOUN
ejpam-3575	15	16	have	have	AUX
ejpam-3575	15	17	also	also	ADV
ejpam-3575	15	18	been	be	AUX
ejpam-3575	15	19	proposed	propose	VERB
ejpam-3575	15	20	by	by	ADP
ejpam-3575	15	21	torra	torra	NOUN
ejpam-3575	15	22	[	[	X
ejpam-3575	15	23	25	25	NUM
ejpam-3575	15	24	]	]	PUNCT
ejpam-3575	15	25	.	.	PUNCT
ejpam-3575	16	1	hesitant	hesitant	ADJ
ejpam-3575	16	2	fuzzy	fuzzy	ADJ
ejpam-3575	16	3	sets	set	NOUN
ejpam-3575	16	4	can	can	AUX
ejpam-3575	16	5	be	be	AUX
ejpam-3575	16	6	used	use	VERB
ejpam-3575	16	7	as	as	ADP
ejpam-3575	16	8	an	an	DET
ejpam-3575	16	9	efficient	efficient	ADJ
ejpam-3575	16	10	mathematical	mathematical	ADJ
ejpam-3575	16	11	tool	tool	NOUN
ejpam-3575	16	12	for	for	ADP
ejpam-3575	16	13	modeling	model	VERB
ejpam-3575	16	14	peoples	people	NOUN
ejpam-3575	16	15	hesitancy	hesitancy	NOUN
ejpam-3575	16	16	in	in	ADP
ejpam-3575	16	17	daily	daily	ADJ
ejpam-3575	16	18	life	life	NOUN
ejpam-3575	16	19	than	than	ADP
ejpam-3575	16	20	the	the	DET
ejpam-3575	16	21	other	other	ADJ
ejpam-3575	16	22	classical	classical	ADJ
ejpam-3575	16	23	extensions	extension	NOUN
ejpam-3575	16	24	of	of	ADP
ejpam-3575	16	25	fuzzy	fuzzy	ADJ
ejpam-3575	16	26	sets	set	NOUN
ejpam-3575	16	27	.	.	PUNCT
ejpam-3575	17	1	hesitant	hesitant	ADJ
ejpam-3575	17	2	fuzzy	fuzzy	ADJ
ejpam-3575	17	3	sets	set	NOUN
ejpam-3575	17	4	are	be	AUX
ejpam-3575	17	5	a	a	DET
ejpam-3575	17	6	very	very	ADV
ejpam-3575	17	7	useful	useful	ADJ
ejpam-3575	17	8	to	to	PART
ejpam-3575	17	9	express	express	VERB
ejpam-3575	17	10	peoples	people	NOUN
ejpam-3575	17	11	hesitancy	hesitancy	NOUN
ejpam-3575	17	12	in	in	ADP
ejpam-3575	17	13	daily	daily	ADJ
ejpam-3575	17	14	life	life	NOUN
ejpam-3575	17	15	and	and	CCONJ
ejpam-3575	17	16	a	a	DET
ejpam-3575	17	17	very	very	ADV
ejpam-3575	17	18	useful	useful	ADJ
ejpam-3575	17	19	tool	tool	NOUN
ejpam-3575	17	20	to	to	PART
ejpam-3575	17	21	deal	deal	VERB
ejpam-3575	17	22	with	with	ADP
ejpam-3575	17	23	uncertainty	uncertainty	NOUN
ejpam-3575	17	24	,	,	PUNCT
ejpam-3575	17	25	which	which	PRON
ejpam-3575	17	26	can	can	AUX
ejpam-3575	17	27	be	be	AUX
ejpam-3575	17	28	accurately	accurately	ADV
ejpam-3575	17	29	and	and	CCONJ
ejpam-3575	17	30	perfectly	perfectly	ADV
ejpam-3575	17	31	described	describe	VERB
ejpam-3575	17	32	in	in	ADP
ejpam-3575	17	33	∗corresponding	∗corresponde	VERB
ejpam-3575	17	34	author	author	NOUN
ejpam-3575	17	35	.	.	PUNCT
ejpam-3575	18	1	doi	doi	NOUN
ejpam-3575	18	2	:	:	PUNCT
ejpam-3575	18	3	https://doi.org/10.29020/nybg.ejpam.v13i1.3575	https://doi.org/10.29020/nybg.ejpam.v13i1.3575	DET
ejpam-3575	18	4	email	email	NOUN
ejpam-3575	18	5	addresses	address	VERB
ejpam-3575	18	6	:	:	PUNCT
ejpam-3575	19	1	chishtygm@gmail.com	chishtygm@gmail.com	X
ejpam-3575	19	2	(	(	PUNCT
ejpam-3575	19	3	g.	g.	PROPN
ejpam-3575	19	4	muhiuddin	muhiuddin	PROPN
ejpam-3575	19	5	)	)	PUNCT
ejpam-3575	19	6	,	,	PUNCT
ejpam-3575	19	7	am.alenezi@ut.edu.sa	am.alenezi@ut.edu.sa	PROPN
ejpam-3575	19	8	(	(	PUNCT
ejpam-3575	19	9	a.	a.	NOUN
ejpam-3575	19	10	m.	m.	PROPN
ejpam-3575	19	11	alanazi	alanazi	PROPN
ejpam-3575	19	12	)	)	PUNCT
ejpam-3575	19	13	,	,	PUNCT
ejpam-3575	19	14	abomunzir124@gmail.com	abomunzir124@gmail.com	X
ejpam-3575	19	15	(	(	PUNCT
ejpam-3575	19	16	m.	m.	PROPN
ejpam-3575	19	17	e.	e.	PROPN
ejpam-3575	19	18	a.	a.	PROPN
ejpam-3575	19	19	elnair	elnair	PROPN
ejpam-3575	19	20	)	)	PUNCT
ejpam-3575	19	21	,	,	PUNCT
ejpam-3575	19	22	kpshum@ynu.edu.cn	kpshum@ynu.edu.cn	PROPN
ejpam-3575	19	23	(	(	PUNCT
ejpam-3575	19	24	k.	k.	PROPN
ejpam-3575	19	25	p.	p.	PROPN
ejpam-3575	19	26	shum	shum	PROPN
ejpam-3575	19	27	)	)	PUNCT
ejpam-3575	19	28	,	,	PUNCT
ejpam-3575	19	29	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3575	19	30	9	9	NUM
ejpam-3575	19	31	c	c	X
ejpam-3575	19	32	©	©	NOUN
ejpam-3575	19	33	2020	2020	NUM
ejpam-3575	19	34	ejpam	ejpam	VERB
ejpam-3575	19	35	all	all	DET
ejpam-3575	19	36	rights	right	NOUN
ejpam-3575	19	37	reserved	reserve	VERB
ejpam-3575	19	38	.	.	PUNCT
ejpam-3575	20	1	g.	g.	PROPN
ejpam-3575	20	2	muhiuddin	muhiuddin	PROPN
ejpam-3575	20	3	et	et	PROPN
ejpam-3575	20	4	al	al	PROPN
ejpam-3575	20	5	.	.	PUNCT
ejpam-3575	20	6	/	/	SYM
ejpam-3575	20	7	eur	eur	PROPN
ejpam-3575	20	8	.	.	PUNCT
ejpam-3575	21	1	j.	j.	PROPN
ejpam-3575	21	2	pure	pure	PROPN
ejpam-3575	21	3	appl	appl	PROPN
ejpam-3575	21	4	.	.	PROPN
ejpam-3575	21	5	math	math	PROPN
ejpam-3575	21	6	,	,	PUNCT
ejpam-3575	21	7	13	13	NUM
ejpam-3575	21	8	(	(	PUNCT
ejpam-3575	21	9	1	1	NUM
ejpam-3575	21	10	)	)	PUNCT
ejpam-3575	21	11	(	(	PUNCT
ejpam-3575	21	12	2020	2020	NUM
ejpam-3575	21	13	)	)	PUNCT
ejpam-3575	21	14	,	,	PUNCT
ejpam-3575	21	15	9	9	NUM
ejpam-3575	21	16	-	-	SYM
ejpam-3575	21	17	18	18	NUM
ejpam-3575	21	18	10	10	NUM
ejpam-3575	21	19	terms	term	NOUN
ejpam-3575	21	20	of	of	ADP
ejpam-3575	21	21	the	the	DET
ejpam-3575	21	22	opinions	opinion	NOUN
ejpam-3575	21	23	of	of	ADP
ejpam-3575	21	24	decision	decision	NOUN
ejpam-3575	21	25	makers	maker	NOUN
ejpam-3575	21	26	.	.	PUNCT
ejpam-3575	22	1	after	after	ADP
ejpam-3575	22	2	the	the	DET
ejpam-3575	22	3	pioneering	pioneering	ADJ
ejpam-3575	22	4	work	work	NOUN
ejpam-3575	22	5	of	of	ADP
ejpam-3575	22	6	torra	torra	NOUN
ejpam-3575	22	7	,	,	PUNCT
ejpam-3575	22	8	the	the	DET
ejpam-3575	22	9	hesitant	hesitant	ADJ
ejpam-3575	22	10	fuzzy	fuzzy	NOUN
ejpam-3575	22	11	has	have	AUX
ejpam-3575	22	12	received	receive	VERB
ejpam-3575	22	13	much	much	ADJ
ejpam-3575	22	14	attention	attention	NOUN
ejpam-3575	22	15	from	from	ADP
ejpam-3575	22	16	many	many	ADJ
ejpam-3575	22	17	authors	author	NOUN
ejpam-3575	22	18	in	in	ADP
ejpam-3575	22	19	many	many	ADJ
ejpam-3575	22	20	fields	field	NOUN
ejpam-3575	22	21	for	for	ADP
ejpam-3575	22	22	eg	eg	NOUN
ejpam-3575	22	23	.	.	PUNCT
ejpam-3575	23	1	xu	xu	PROPN
ejpam-3575	23	2	and	and	CCONJ
ejpam-3575	23	3	xia	xia	PROPN
ejpam-3575	24	1	[	[	X
ejpam-3575	24	2	30	30	NUM
ejpam-3575	24	3	]	]	PUNCT
ejpam-3575	24	4	proposed	propose	VERB
ejpam-3575	24	5	a	a	DET
ejpam-3575	24	6	variety	variety	NOUN
ejpam-3575	24	7	of	of	ADP
ejpam-3575	24	8	distance	distance	NOUN
ejpam-3575	24	9	measures	measure	NOUN
ejpam-3575	24	10	for	for	ADP
ejpam-3575	24	11	hesitant	hesitant	ADJ
ejpam-3575	24	12	fuzzy	fuzzy	ADJ
ejpam-3575	24	13	sets	set	NOUN
ejpam-3575	24	14	,	,	PUNCT
ejpam-3575	24	15	based	base	VERB
ejpam-3575	24	16	on	on	ADP
ejpam-3575	24	17	which	which	PRON
ejpam-3575	24	18	the	the	DET
ejpam-3575	24	19	corresponding	correspond	VERB
ejpam-3575	24	20	similarity	similarity	NOUN
ejpam-3575	24	21	measures	measure	NOUN
ejpam-3575	24	22	can	can	AUX
ejpam-3575	24	23	be	be	AUX
ejpam-3575	24	24	obtained	obtain	VERB
ejpam-3575	24	25	.	.	PUNCT
ejpam-3575	25	1	they	they	PRON
ejpam-3575	25	2	investigated	investigate	VERB
ejpam-3575	25	3	the	the	DET
ejpam-3575	25	4	connections	connection	NOUN
ejpam-3575	25	5	of	of	ADP
ejpam-3575	25	6	the	the	DET
ejpam-3575	25	7	aforementioned	aforementioned	ADJ
ejpam-3575	25	8	distance	distance	NOUN
ejpam-3575	25	9	measures	measure	NOUN
ejpam-3575	25	10	and	and	CCONJ
ejpam-3575	25	11	further	far	ADV
ejpam-3575	25	12	develop	develop	VERB
ejpam-3575	25	13	a	a	DET
ejpam-3575	25	14	number	number	NOUN
ejpam-3575	25	15	of	of	ADP
ejpam-3575	25	16	hesitant	hesitant	ADJ
ejpam-3575	25	17	ordered	order	VERB
ejpam-3575	25	18	weighted	weight	VERB
ejpam-3575	25	19	distance	distance	NOUN
ejpam-3575	25	20	measures	measure	NOUN
ejpam-3575	25	21	and	and	CCONJ
ejpam-3575	25	22	hesitant	hesitant	ADJ
ejpam-3575	25	23	ordered	order	VERB
ejpam-3575	25	24	weighted	weight	VERB
ejpam-3575	25	25	similarity	similarity	NOUN
ejpam-3575	25	26	measures	measure	NOUN
ejpam-3575	25	27	.	.	PUNCT
ejpam-3575	26	1	a	a	DET
ejpam-3575	26	2	number	number	NOUN
ejpam-3575	26	3	of	of	ADP
ejpam-3575	26	4	research	research	NOUN
ejpam-3575	26	5	papers	paper	NOUN
ejpam-3575	26	6	have	have	AUX
ejpam-3575	26	7	been	be	AUX
ejpam-3575	26	8	appeared	appear	VERB
ejpam-3575	26	9	on	on	ADP
ejpam-3575	26	10	hesitant	hesitant	ADJ
ejpam-3575	26	11	fuzzy	fuzzy	ADJ
ejpam-3575	26	12	set	set	NOUN
ejpam-3575	26	13	theory	theory	NOUN
ejpam-3575	26	14	in	in	ADP
ejpam-3575	26	15	decision	decision	NOUN
ejpam-3575	26	16	making	make	VERB
ejpam-3575	26	17	problem	problem	NOUN
ejpam-3575	26	18	etc	etc	X
ejpam-3575	26	19	.	.	X
ejpam-3575	27	1	(	(	PUNCT
ejpam-3575	27	2	see	see	VERB
ejpam-3575	27	3	[	[	X
ejpam-3575	27	4	23	23	NUM
ejpam-3575	27	5	,	,	PUNCT
ejpam-3575	27	6	27–29	27–29	NUM
ejpam-3575	27	7	,	,	PUNCT
ejpam-3575	27	8	31	31	NUM
ejpam-3575	27	9	]	]	PUNCT
ejpam-3575	27	10	)	)	PUNCT
ejpam-3575	27	11	.	.	PUNCT
ejpam-3575	28	1	fuzzy	fuzzy	ADJ
ejpam-3575	28	2	set	set	PROPN
ejpam-3575	28	3	theory	theory	NOUN
ejpam-3575	28	4	plays	play	VERB
ejpam-3575	28	5	an	an	DET
ejpam-3575	28	6	important	important	ADJ
ejpam-3575	28	7	role	role	NOUN
ejpam-3575	28	8	in	in	ADP
ejpam-3575	28	9	the	the	DET
ejpam-3575	28	10	development	development	NOUN
ejpam-3575	28	11	of	of	ADP
ejpam-3575	28	12	hesitant	hesitant	ADJ
ejpam-3575	28	13	fuzzy	fuzzy	ADJ
ejpam-3575	28	14	sets	set	NOUN
ejpam-3575	28	15	theory	theory	NOUN
ejpam-3575	28	16	.	.	PUNCT
ejpam-3575	29	1	muhiuddin	muhiuddin	AUX
ejpam-3575	29	2	et	et	PROPN
ejpam-3575	29	3	al	al	PROPN
ejpam-3575	29	4	.	.	PROPN
ejpam-3575	29	5	have	have	AUX
ejpam-3575	29	6	applied	apply	VERB
ejpam-3575	29	7	the	the	DET
ejpam-3575	29	8	fuzzy	fuzzy	ADJ
ejpam-3575	29	9	set	set	NOUN
ejpam-3575	29	10	theory	theory	NOUN
ejpam-3575	29	11	and	and	CCONJ
ejpam-3575	29	12	related	related	ADJ
ejpam-3575	29	13	notions	notion	NOUN
ejpam-3575	29	14	to	to	ADP
ejpam-3575	29	15	different	different	ADJ
ejpam-3575	29	16	algebraic	algebraic	ADJ
ejpam-3575	29	17	structures	structure	NOUN
ejpam-3575	29	18	(	(	PUNCT
ejpam-3575	29	19	see	see	VERB
ejpam-3575	29	20	for	for	ADP
ejpam-3575	29	21	e.g.	e.g.	ADV
ejpam-3575	29	22	,	,	PUNCT
ejpam-3575	29	23	[	[	X
ejpam-3575	29	24	15–18	15–18	NUM
ejpam-3575	29	25	,	,	PUNCT
ejpam-3575	29	26	18	18	NUM
ejpam-3575	29	27	,	,	PUNCT
ejpam-3575	29	28	19	19	NUM
ejpam-3575	29	29	,	,	PUNCT
ejpam-3575	29	30	19–22	19–22	NUM
ejpam-3575	29	31	]	]	PUNCT
ejpam-3575	29	32	)	)	PUNCT
ejpam-3575	29	33	.	.	PUNCT
ejpam-3575	30	1	in	in	ADP
ejpam-3575	30	2	recent	recent	ADJ
ejpam-3575	30	3	years	year	NOUN
ejpam-3575	30	4	,	,	PUNCT
ejpam-3575	30	5	a	a	DET
ejpam-3575	30	6	number	number	NOUN
ejpam-3575	30	7	of	of	ADP
ejpam-3575	30	8	research	research	NOUN
ejpam-3575	30	9	papers	paper	NOUN
ejpam-3575	30	10	have	have	AUX
ejpam-3575	30	11	been	be	AUX
ejpam-3575	30	12	devoted	devote	VERB
ejpam-3575	30	13	to	to	ADP
ejpam-3575	30	14	the	the	DET
ejpam-3575	30	15	study	study	NOUN
ejpam-3575	30	16	of	of	ADP
ejpam-3575	30	17	fuzzy	fuzzy	ADJ
ejpam-3575	30	18	sets	set	NOUN
ejpam-3575	30	19	theory	theory	NOUN
ejpam-3575	30	20	and	and	CCONJ
ejpam-3575	30	21	related	related	ADJ
ejpam-3575	30	22	concepts	concept	NOUN
ejpam-3575	30	23	on	on	ADP
ejpam-3575	30	24	different	different	ADJ
ejpam-3575	30	25	algebraic	algebraic	ADJ
ejpam-3575	30	26	structures	structure	NOUN
ejpam-3575	30	27	(	(	PUNCT
ejpam-3575	30	28	see	see	VERB
ejpam-3575	30	29	e.g.	e.g.	ADV
ejpam-3575	30	30	,	,	PUNCT
ejpam-3575	30	31	[	[	X
ejpam-3575	30	32	5–8	5–8	NUM
ejpam-3575	30	33	,	,	PUNCT
ejpam-3575	30	34	24	24	NUM
ejpam-3575	30	35	]	]	PUNCT
ejpam-3575	30	36	)	)	PUNCT
ejpam-3575	30	37	.	.	PUNCT
ejpam-3575	31	1	recently	recently	ADV
ejpam-3575	31	2	,	,	PUNCT
ejpam-3575	31	3	hesitant	hesitant	ADJ
ejpam-3575	31	4	fuzzy	fuzzy	ADJ
ejpam-3575	31	5	sets	set	NOUN
ejpam-3575	31	6	theory	theory	NOUN
ejpam-3575	31	7	have	have	AUX
ejpam-3575	31	8	been	be	AUX
ejpam-3575	31	9	applied	apply	VERB
ejpam-3575	31	10	to	to	ADP
ejpam-3575	31	11	different	different	ADJ
ejpam-3575	31	12	algebraic	algebraic	ADJ
ejpam-3575	31	13	structures	structure	NOUN
ejpam-3575	31	14	on	on	ADP
ejpam-3575	31	15	various	various	ADJ
ejpam-3575	31	16	aspects	aspect	NOUN
ejpam-3575	31	17	viz	viz	PROPN
ejpam-3575	31	18	.	.	PROPN
ejpam-3575	31	19	,	,	PUNCT
ejpam-3575	31	20	jun	jun	PROPN
ejpam-3575	31	21	et	et	PROPN
ejpam-3575	31	22	al	al	PROPN
ejpam-3575	31	23	.	.	PROPN
ejpam-3575	31	24	have	have	AUX
ejpam-3575	31	25	applied	apply	VERB
ejpam-3575	31	26	the	the	DET
ejpam-3575	31	27	hesitant	hesitant	ADJ
ejpam-3575	31	28	fuzzy	fuzzy	ADJ
ejpam-3575	31	29	sets	set	NOUN
ejpam-3575	31	30	theory	theory	NOUN
ejpam-3575	31	31	to	to	PART
ejpam-3575	31	32	bck	bck	VERB
ejpam-3575	31	33	/	/	SYM
ejpam-3575	31	34	bci	bci	NOUN
ejpam-3575	31	35	-	-	PUNCT
ejpam-3575	31	36	algebras	algebra	NOUN
ejpam-3575	31	37	and	and	CCONJ
ejpam-3575	31	38	semigroups	semigroup	NOUN
ejpam-3575	31	39	(	(	PUNCT
ejpam-3575	31	40	see	see	VERB
ejpam-3575	31	41	[	[	X
ejpam-3575	31	42	2–4	2–4	NUM
ejpam-3575	31	43	]	]	PUNCT
ejpam-3575	31	44	)	)	PUNCT
ejpam-3575	31	45	.	.	PUNCT
ejpam-3575	32	1	also	also	ADV
ejpam-3575	32	2	,	,	PUNCT
ejpam-3575	32	3	muhiuddin	muhiuddin	VERB
ejpam-3575	32	4	et	et	PROPN
ejpam-3575	32	5	al	al	PROPN
ejpam-3575	32	6	.	.	PROPN
ejpam-3575	32	7	have	have	AUX
ejpam-3575	32	8	applied	apply	VERB
ejpam-3575	32	9	the	the	DET
ejpam-3575	32	10	hesitant	hesitant	ADJ
ejpam-3575	32	11	fuzzy	fuzzy	ADJ
ejpam-3575	32	12	sets	set	NOUN
ejpam-3575	32	13	theory	theory	NOUN
ejpam-3575	32	14	to	to	ADP
ejpam-3575	32	15	residuated	residuate	VERB
ejpam-3575	32	16	lattices	lattice	NOUN
ejpam-3575	32	17	,	,	PUNCT
ejpam-3575	32	18	lattice	lattice	ADJ
ejpam-3575	32	19	implication	implication	NOUN
ejpam-3575	32	20	algebras	algebra	NOUN
ejpam-3575	32	21	and	and	CCONJ
ejpam-3575	32	22	bck	bck	PROPN
ejpam-3575	32	23	/	/	SYM
ejpam-3575	32	24	bci	bci	NOUN
ejpam-3575	32	25	-	-	PUNCT
ejpam-3575	32	26	algebras	algebras	X
ejpam-3575	32	27	(	(	PUNCT
ejpam-3575	32	28	see	see	VERB
ejpam-3575	32	29	[	[	X
ejpam-3575	32	30	10	10	NUM
ejpam-3575	32	31	–	–	PUNCT
ejpam-3575	32	32	14	14	NUM
ejpam-3575	32	33	]	]	PUNCT
ejpam-3575	32	34	)	)	PUNCT
ejpam-3575	32	35	.	.	PUNCT
ejpam-3575	33	1	in	in	ADP
ejpam-3575	33	2	this	this	DET
ejpam-3575	33	3	paper	paper	NOUN
ejpam-3575	33	4	,	,	PUNCT
ejpam-3575	33	5	we	we	PRON
ejpam-3575	33	6	introduce	introduce	VERB
ejpam-3575	33	7	some	some	DET
ejpam-3575	33	8	new	new	ADJ
ejpam-3575	33	9	types	type	NOUN
ejpam-3575	33	10	of	of	ADP
ejpam-3575	33	11	hesitant	hesitant	ADJ
ejpam-3575	33	12	fuzzy	fuzzy	ADJ
ejpam-3575	33	13	subalgebras	subalgebra	NOUN
ejpam-3575	33	14	and	and	CCONJ
ejpam-3575	33	15	ideals	ideal	NOUN
ejpam-3575	33	16	in	in	ADP
ejpam-3575	33	17	bck	bck	PROPN
ejpam-3575	33	18	/	/	SYM
ejpam-3575	33	19	bci	bci	NOUN
ejpam-3575	33	20	-	-	PUNCT
ejpam-3575	33	21	algebras	algebras	X
ejpam-3575	33	22	,	,	PUNCT
ejpam-3575	33	23	and	and	CCONJ
ejpam-3575	33	24	investigate	investigate	VERB
ejpam-3575	33	25	their	their	PRON
ejpam-3575	33	26	relations	relation	NOUN
ejpam-3575	33	27	and	and	CCONJ
ejpam-3575	33	28	properties	property	NOUN
ejpam-3575	33	29	.	.	PUNCT
ejpam-3575	34	1	finally	finally	ADV
ejpam-3575	34	2	,	,	PUNCT
ejpam-3575	34	3	we	we	PRON
ejpam-3575	34	4	discuss	discuss	VERB
ejpam-3575	34	5	the	the	DET
ejpam-3575	34	6	characterizations	characterization	NOUN
ejpam-3575	34	7	of	of	ADP
ejpam-3575	34	8	these	these	DET
ejpam-3575	34	9	new	new	ADJ
ejpam-3575	34	10	types	type	NOUN
ejpam-3575	34	11	of	of	ADP
ejpam-3575	34	12	hesitant	hesitant	ADJ
ejpam-3575	34	13	fuzzy	fuzzy	ADJ
ejpam-3575	34	14	subalgebras	subalgebra	NOUN
ejpam-3575	34	15	and	and	CCONJ
ejpam-3575	34	16	hesitant	hesitant	ADJ
ejpam-3575	34	17	fuzzy	fuzzy	ADJ
ejpam-3575	34	18	ideals	ideal	NOUN
ejpam-3575	34	19	in	in	ADP
ejpam-3575	34	20	bck	bck	PROPN
ejpam-3575	34	21	/	/	SYM
ejpam-3575	34	22	bci	bci	NOUN
ejpam-3575	34	23	-	-	PUNCT
ejpam-3575	34	24	algebras	algebra	NOUN
ejpam-3575	34	25	.	.	PUNCT
ejpam-3575	35	1	2	2	X
ejpam-3575	35	2	.	.	NUM
ejpam-3575	35	3	preliminaries	preliminary	NOUN
ejpam-3575	35	4	a	a	DET
ejpam-3575	35	5	bck	bck	PROPN
ejpam-3575	35	6	/	/	SYM
ejpam-3575	35	7	bci	bci	NOUN
ejpam-3575	35	8	-	-	NOUN
ejpam-3575	35	9	algebra	algebra	NOUN
ejpam-3575	35	10	is	be	AUX
ejpam-3575	35	11	an	an	DET
ejpam-3575	35	12	important	important	ADJ
ejpam-3575	35	13	class	class	NOUN
ejpam-3575	35	14	of	of	ADP
ejpam-3575	35	15	logical	logical	ADJ
ejpam-3575	35	16	algebras	algebra	NOUN
ejpam-3575	35	17	introduced	introduce	VERB
ejpam-3575	35	18	by	by	ADP
ejpam-3575	35	19	k.	k.	PROPN
ejpam-3575	35	20	iséki	iséki	PROPN
ejpam-3575	35	21	and	and	CCONJ
ejpam-3575	35	22	was	be	AUX
ejpam-3575	35	23	extensively	extensively	ADV
ejpam-3575	35	24	investigated	investigate	VERB
ejpam-3575	35	25	by	by	ADP
ejpam-3575	35	26	several	several	ADJ
ejpam-3575	35	27	researchers	researcher	NOUN
ejpam-3575	35	28	.	.	PUNCT
ejpam-3575	36	1	an	an	DET
ejpam-3575	36	2	algebra	algebra	NOUN
ejpam-3575	36	3	(	(	PUNCT
ejpam-3575	36	4	x	x	NOUN
ejpam-3575	36	5	;	;	PUNCT
ejpam-3575	36	6	∗	∗	NOUN
ejpam-3575	36	7	,	,	PUNCT
ejpam-3575	36	8	0	0	NUM
ejpam-3575	36	9	)	)	PUNCT
ejpam-3575	36	10	of	of	ADP
ejpam-3575	36	11	type	type	NOUN
ejpam-3575	36	12	(	(	PUNCT
ejpam-3575	36	13	2	2	NUM
ejpam-3575	36	14	,	,	PUNCT
ejpam-3575	36	15	0	0	NUM
ejpam-3575	36	16	)	)	PUNCT
ejpam-3575	36	17	is	be	AUX
ejpam-3575	36	18	called	call	VERB
ejpam-3575	36	19	a	a	DET
ejpam-3575	36	20	bci	bci	NOUN
ejpam-3575	36	21	-	-	NOUN
ejpam-3575	36	22	algebra	algebra	NOUN
ejpam-3575	36	23	if	if	SCONJ
ejpam-3575	36	24	it	it	PRON
ejpam-3575	36	25	satisfies	satisfy	VERB
ejpam-3575	36	26	the	the	DET
ejpam-3575	36	27	following	follow	VERB
ejpam-3575	36	28	conditions	condition	NOUN
ejpam-3575	36	29	:	:	PUNCT
ejpam-3575	36	30	(	(	PUNCT
ejpam-3575	36	31	i	i	NOUN
ejpam-3575	36	32	)	)	PUNCT
ejpam-3575	36	33	(	(	PUNCT
ejpam-3575	36	34	∀x	∀x	X
ejpam-3575	36	35	,	,	PUNCT
ejpam-3575	36	36	y	y	PROPN
ejpam-3575	36	37	,	,	PUNCT
ejpam-3575	36	38	z	z	NOUN
ejpam-3575	36	39	∈	∈	PROPN
ejpam-3575	36	40	x	x	X
ejpam-3575	36	41	)	)	PUNCT
ejpam-3575	36	42	(	(	PUNCT
ejpam-3575	36	43	(	(	PUNCT
ejpam-3575	36	44	(	(	PUNCT
ejpam-3575	36	45	x	x	SYM
ejpam-3575	36	46	∗	∗	PROPN
ejpam-3575	36	47	y	y	NOUN
ejpam-3575	36	48	)	)	PUNCT
ejpam-3575	36	49	∗	∗	NOUN
ejpam-3575	36	50	(	(	PUNCT
ejpam-3575	36	51	x	x	X
ejpam-3575	36	52	∗	∗	PROPN
ejpam-3575	36	53	z	z	NOUN
ejpam-3575	36	54	)	)	PUNCT
ejpam-3575	36	55	)	)	PUNCT
ejpam-3575	36	56	∗	∗	NOUN
ejpam-3575	36	57	(	(	PUNCT
ejpam-3575	36	58	z	z	NOUN
ejpam-3575	36	59	∗	∗	NOUN
ejpam-3575	36	60	y	y	NOUN
ejpam-3575	36	61	)	)	PUNCT
ejpam-3575	36	62	=	=	SYM
ejpam-3575	36	63	0	0	NUM
ejpam-3575	36	64	)	)	PUNCT
ejpam-3575	36	65	,	,	PUNCT
ejpam-3575	36	66	(	(	PUNCT
ejpam-3575	36	67	ii	ii	NOUN
ejpam-3575	36	68	)	)	PUNCT
ejpam-3575	36	69	(	(	PUNCT
ejpam-3575	36	70	∀x	∀x	X
ejpam-3575	36	71	,	,	PUNCT
ejpam-3575	36	72	y	y	PROPN
ejpam-3575	36	73	∈	∈	PROPN
ejpam-3575	36	74	x	x	X
ejpam-3575	36	75	)	)	PUNCT
ejpam-3575	36	76	(	(	PUNCT
ejpam-3575	36	77	(	(	PUNCT
ejpam-3575	36	78	x	x	SYM
ejpam-3575	36	79	∗	∗	NOUN
ejpam-3575	36	80	(	(	PUNCT
ejpam-3575	36	81	x	x	X
ejpam-3575	36	82	∗	∗	PROPN
ejpam-3575	36	83	y	y	NOUN
ejpam-3575	36	84	)	)	PUNCT
ejpam-3575	36	85	)	)	PUNCT
ejpam-3575	37	1	∗	∗	NOUN
ejpam-3575	37	2	y	y	NOUN
ejpam-3575	38	1	=	=	SYM
ejpam-3575	39	1	0	0	NUM
ejpam-3575	39	2	)	)	PUNCT
ejpam-3575	40	1	,	,	PUNCT
ejpam-3575	40	2	(	(	PUNCT
ejpam-3575	40	3	iii	iii	X
ejpam-3575	40	4	)	)	PUNCT
ejpam-3575	40	5	(	(	PUNCT
ejpam-3575	40	6	∀x	∀x	X
ejpam-3575	40	7	∈	∈	PROPN
ejpam-3575	40	8	x	x	NOUN
ejpam-3575	40	9	)	)	PUNCT
ejpam-3575	40	10	(	(	PUNCT
ejpam-3575	40	11	x	x	X
ejpam-3575	40	12	∗	∗	NOUN
ejpam-3575	40	13	x	x	SYM
ejpam-3575	40	14	=	=	NOUN
ejpam-3575	40	15	0	0	NUM
ejpam-3575	40	16	)	)	PUNCT
ejpam-3575	40	17	,	,	PUNCT
ejpam-3575	40	18	(	(	PUNCT
ejpam-3575	40	19	iv	iv	X
ejpam-3575	40	20	)	)	PUNCT
ejpam-3575	40	21	(	(	PUNCT
ejpam-3575	40	22	∀x	∀x	X
ejpam-3575	40	23	,	,	PUNCT
ejpam-3575	40	24	y	y	PROPN
ejpam-3575	40	25	∈	∈	PROPN
ejpam-3575	40	26	x	x	X
ejpam-3575	40	27	)	)	PUNCT
ejpam-3575	40	28	(	(	PUNCT
ejpam-3575	40	29	x	x	SYM
ejpam-3575	40	30	∗	∗	NOUN
ejpam-3575	40	31	y	y	NOUN
ejpam-3575	40	32	=	=	SYM
ejpam-3575	40	33	0	0	PROPN
ejpam-3575	40	34	,	,	PUNCT
ejpam-3575	40	35	y	y	PROPN
ejpam-3575	40	36	∗	∗	NOUN
ejpam-3575	40	37	x	x	PUNCT
ejpam-3575	40	38	=	=	SYM
ejpam-3575	40	39	0	0	NUM
ejpam-3575	40	40	⇒	⇒	NOUN
ejpam-3575	40	41	x	x	PUNCT
ejpam-3575	41	1	=	=	SYM
ejpam-3575	41	2	y	y	PROPN
ejpam-3575	41	3	)	)	PUNCT
ejpam-3575	41	4	.	.	PUNCT
ejpam-3575	42	1	if	if	SCONJ
ejpam-3575	42	2	a	a	DET
ejpam-3575	42	3	bci	bci	NOUN
ejpam-3575	42	4	-	-	NOUN
ejpam-3575	42	5	algebra	algebra	NOUN
ejpam-3575	42	6	x	x	PRON
ejpam-3575	42	7	satisfies	satisfy	VERB
ejpam-3575	42	8	the	the	DET
ejpam-3575	42	9	following	follow	VERB
ejpam-3575	42	10	identity	identity	NOUN
ejpam-3575	42	11	:	:	PUNCT
ejpam-3575	42	12	(	(	PUNCT
ejpam-3575	42	13	v	v	NOUN
ejpam-3575	42	14	)	)	PUNCT
ejpam-3575	42	15	(	(	PUNCT
ejpam-3575	42	16	∀x	∀x	X
ejpam-3575	42	17	∈	∈	PROPN
ejpam-3575	42	18	x	x	X
ejpam-3575	42	19	)	)	PUNCT
ejpam-3575	42	20	(	(	PUNCT
ejpam-3575	42	21	0	0	NUM
ejpam-3575	42	22	∗	∗	NOUN
ejpam-3575	42	23	x	x	SYM
ejpam-3575	42	24	=	=	NOUN
ejpam-3575	42	25	0	0	NUM
ejpam-3575	42	26	)	)	PUNCT
ejpam-3575	42	27	,	,	PUNCT
ejpam-3575	42	28	then	then	ADV
ejpam-3575	42	29	x	x	PUNCT
ejpam-3575	42	30	is	be	AUX
ejpam-3575	42	31	called	call	VERB
ejpam-3575	42	32	a	a	DET
ejpam-3575	42	33	bck	bck	NOUN
ejpam-3575	42	34	-	-	PUNCT
ejpam-3575	42	35	algebra	algebra	NOUN
ejpam-3575	42	36	.	.	PUNCT
ejpam-3575	43	1	a	a	DET
ejpam-3575	43	2	bck	bck	NOUN
ejpam-3575	43	3	-	-	PUNCT
ejpam-3575	43	4	algebra	algebra	NOUN
ejpam-3575	43	5	x	x	PUNCT
ejpam-3575	43	6	is	be	AUX
ejpam-3575	43	7	said	say	VERB
ejpam-3575	43	8	to	to	PART
ejpam-3575	43	9	be	be	AUX
ejpam-3575	43	10	positive	positive	ADJ
ejpam-3575	43	11	implicative	implicative	NOUN
ejpam-3575	43	12	if	if	SCONJ
ejpam-3575	43	13	it	it	PRON
ejpam-3575	43	14	satisfies	satisfy	VERB
ejpam-3575	43	15	:	:	PUNCT
ejpam-3575	43	16	(	(	PUNCT
ejpam-3575	43	17	∀x	∀x	X
ejpam-3575	43	18	,	,	PUNCT
ejpam-3575	43	19	y	y	PROPN
ejpam-3575	43	20	,	,	PUNCT
ejpam-3575	43	21	z	z	NOUN
ejpam-3575	43	22	∈	∈	PROPN
ejpam-3575	43	23	x	x	X
ejpam-3575	43	24	)	)	PUNCT
ejpam-3575	43	25	(	(	PUNCT
ejpam-3575	43	26	(	(	PUNCT
ejpam-3575	43	27	x	x	SYM
ejpam-3575	43	28	∗	∗	PROPN
ejpam-3575	43	29	y	y	NOUN
ejpam-3575	43	30	)	)	PUNCT
ejpam-3575	43	31	∗	∗	NOUN
ejpam-3575	43	32	z	z	NOUN
ejpam-3575	44	1	=	=	SYM
ejpam-3575	44	2	(	(	PUNCT
ejpam-3575	44	3	x	x	X
ejpam-3575	44	4	∗	∗	PROPN
ejpam-3575	44	5	z	z	NOUN
ejpam-3575	44	6	)	)	PUNCT
ejpam-3575	44	7	∗	∗	NOUN
ejpam-3575	44	8	(	(	PUNCT
ejpam-3575	44	9	y	y	PROPN
ejpam-3575	44	10	∗	∗	PROPN
ejpam-3575	44	11	z	z	PROPN
ejpam-3575	44	12	)	)	PUNCT
ejpam-3575	44	13	)	)	PUNCT
ejpam-3575	44	14	.	.	PUNCT
ejpam-3575	45	1	(	(	PUNCT
ejpam-3575	45	2	1	1	X
ejpam-3575	45	3	)	)	PUNCT
ejpam-3575	45	4	g.	g.	PROPN
ejpam-3575	45	5	muhiuddin	muhiuddin	PROPN
ejpam-3575	45	6	et	et	PROPN
ejpam-3575	45	7	al	al	PROPN
ejpam-3575	45	8	.	.	PUNCT
ejpam-3575	45	9	/	/	SYM
ejpam-3575	45	10	eur	eur	PROPN
ejpam-3575	45	11	.	.	PUNCT
ejpam-3575	46	1	j.	j.	PROPN
ejpam-3575	46	2	pure	pure	PROPN
ejpam-3575	46	3	appl	appl	PROPN
ejpam-3575	46	4	.	.	PROPN
ejpam-3575	46	5	math	math	PROPN
ejpam-3575	46	6	,	,	PUNCT
ejpam-3575	46	7	13	13	NUM
ejpam-3575	46	8	(	(	PUNCT
ejpam-3575	46	9	1	1	NUM
ejpam-3575	46	10	)	)	PUNCT
ejpam-3575	46	11	(	(	PUNCT
ejpam-3575	46	12	2020	2020	NUM
ejpam-3575	46	13	)	)	PUNCT
ejpam-3575	46	14	,	,	PUNCT
ejpam-3575	46	15	9	9	NUM
ejpam-3575	46	16	-	-	SYM
ejpam-3575	46	17	18	18	NUM
ejpam-3575	46	18	11	11	NUM
ejpam-3575	46	19	a	a	DET
ejpam-3575	46	20	bck	bck	NOUN
ejpam-3575	46	21	-	-	PUNCT
ejpam-3575	46	22	algebra	algebra	NOUN
ejpam-3575	46	23	x	x	PUNCT
ejpam-3575	46	24	is	be	AUX
ejpam-3575	46	25	said	say	VERB
ejpam-3575	46	26	to	to	PART
ejpam-3575	46	27	be	be	AUX
ejpam-3575	46	28	implicative	implicative	ADJ
ejpam-3575	46	29	if	if	SCONJ
ejpam-3575	46	30	it	it	PRON
ejpam-3575	46	31	satisfies	satisfy	VERB
ejpam-3575	46	32	:	:	PUNCT
ejpam-3575	46	33	(	(	PUNCT
ejpam-3575	46	34	∀x	∀x	X
ejpam-3575	46	35	,	,	PUNCT
ejpam-3575	46	36	y	y	PROPN
ejpam-3575	46	37	∈	∈	PROPN
ejpam-3575	46	38	x	x	X
ejpam-3575	46	39	)	)	PUNCT
ejpam-3575	46	40	(	(	PUNCT
ejpam-3575	46	41	x	x	X
ejpam-3575	46	42	=	=	SYM
ejpam-3575	47	1	x	x	SYM
ejpam-3575	47	2	∗	∗	NOUN
ejpam-3575	47	3	(	(	PUNCT
ejpam-3575	47	4	y	y	PROPN
ejpam-3575	47	5	∗	∗	NOUN
ejpam-3575	47	6	x	x	NOUN
ejpam-3575	47	7	)	)	PUNCT
ejpam-3575	47	8	)	)	PUNCT
ejpam-3575	47	9	.	.	PUNCT
ejpam-3575	48	1	(	(	PUNCT
ejpam-3575	48	2	2	2	X
ejpam-3575	48	3	)	)	PUNCT
ejpam-3575	48	4	any	any	DET
ejpam-3575	48	5	bck	bck	PROPN
ejpam-3575	48	6	/	/	SYM
ejpam-3575	48	7	bci	bci	NOUN
ejpam-3575	48	8	-	-	NOUN
ejpam-3575	48	9	algebra	algebra	NOUN
ejpam-3575	48	10	x	x	PRON
ejpam-3575	48	11	satisfies	satisfy	VERB
ejpam-3575	48	12	the	the	DET
ejpam-3575	48	13	following	follow	VERB
ejpam-3575	48	14	conditions	condition	NOUN
ejpam-3575	48	15	:	:	PUNCT
ejpam-3575	48	16	(	(	PUNCT
ejpam-3575	48	17	∀x	∀x	X
ejpam-3575	48	18	∈	∈	PROPN
ejpam-3575	48	19	x	x	NOUN
ejpam-3575	48	20	)	)	PUNCT
ejpam-3575	48	21	(	(	PUNCT
ejpam-3575	48	22	x	x	NOUN
ejpam-3575	48	23	∗	∗	NOUN
ejpam-3575	48	24	0	0	NUM
ejpam-3575	49	1	=	=	SYM
ejpam-3575	49	2	x	x	NOUN
ejpam-3575	49	3	)	)	PUNCT
ejpam-3575	49	4	,	,	PUNCT
ejpam-3575	49	5	(	(	PUNCT
ejpam-3575	49	6	3	3	X
ejpam-3575	49	7	)	)	PUNCT
ejpam-3575	49	8	(	(	PUNCT
ejpam-3575	49	9	∀x	∀x	X
ejpam-3575	49	10	,	,	PUNCT
ejpam-3575	49	11	y	y	PROPN
ejpam-3575	49	12	,	,	PUNCT
ejpam-3575	49	13	z	z	NOUN
ejpam-3575	49	14	∈	∈	PROPN
ejpam-3575	49	15	x	x	X
ejpam-3575	49	16	)	)	PUNCT
ejpam-3575	49	17	(	(	PUNCT
ejpam-3575	49	18	x	x	X
ejpam-3575	49	19	≤	≤	NOUN
ejpam-3575	49	20	y	y	PROPN
ejpam-3575	49	21	⇒	⇒	NOUN
ejpam-3575	49	22	x	x	PUNCT
ejpam-3575	50	1	∗	∗	NOUN
ejpam-3575	50	2	z	z	NOUN
ejpam-3575	50	3	≤	≤	NOUN
ejpam-3575	50	4	y	y	PROPN
ejpam-3575	50	5	∗	∗	PROPN
ejpam-3575	50	6	z	z	PROPN
ejpam-3575	50	7	,	,	PUNCT
ejpam-3575	50	8	z	z	PROPN
ejpam-3575	50	9	∗	∗	NOUN
ejpam-3575	50	10	y	y	PROPN
ejpam-3575	50	11	≤	≤	PROPN
ejpam-3575	50	12	z	z	NOUN
ejpam-3575	50	13	∗	∗	NOUN
ejpam-3575	50	14	x	x	NOUN
ejpam-3575	50	15	)	)	PUNCT
ejpam-3575	50	16	,	,	PUNCT
ejpam-3575	50	17	(	(	PUNCT
ejpam-3575	50	18	4	4	X
ejpam-3575	50	19	)	)	PUNCT
ejpam-3575	50	20	(	(	PUNCT
ejpam-3575	50	21	∀x	∀x	X
ejpam-3575	50	22	,	,	PUNCT
ejpam-3575	50	23	y	y	PROPN
ejpam-3575	50	24	,	,	PUNCT
ejpam-3575	50	25	z	z	NOUN
ejpam-3575	50	26	∈	∈	PROPN
ejpam-3575	50	27	x	x	X
ejpam-3575	50	28	)	)	PUNCT
ejpam-3575	50	29	(	(	PUNCT
ejpam-3575	50	30	(	(	PUNCT
ejpam-3575	50	31	x	x	SYM
ejpam-3575	50	32	∗	∗	PROPN
ejpam-3575	50	33	y	y	NOUN
ejpam-3575	50	34	)	)	PUNCT
ejpam-3575	50	35	∗	∗	NOUN
ejpam-3575	50	36	z	z	NOUN
ejpam-3575	50	37	=	=	SYM
ejpam-3575	50	38	(	(	PUNCT
ejpam-3575	50	39	x	x	X
ejpam-3575	50	40	∗	∗	PROPN
ejpam-3575	50	41	z	z	NOUN
ejpam-3575	50	42	)	)	PUNCT
ejpam-3575	50	43	∗	∗	PROPN
ejpam-3575	50	44	y	y	PROPN
ejpam-3575	50	45	)	)	PUNCT
ejpam-3575	50	46	,	,	PUNCT
ejpam-3575	50	47	(	(	PUNCT
ejpam-3575	50	48	5	5	X
ejpam-3575	50	49	)	)	PUNCT
ejpam-3575	50	50	(	(	PUNCT
ejpam-3575	50	51	∀x	∀x	X
ejpam-3575	50	52	,	,	PUNCT
ejpam-3575	50	53	y	y	PROPN
ejpam-3575	50	54	,	,	PUNCT
ejpam-3575	50	55	z	z	NOUN
ejpam-3575	50	56	∈	∈	PROPN
ejpam-3575	50	57	x	x	X
ejpam-3575	50	58	)	)	PUNCT
ejpam-3575	50	59	(	(	PUNCT
ejpam-3575	50	60	(	(	PUNCT
ejpam-3575	50	61	x	x	SYM
ejpam-3575	50	62	∗	∗	PROPN
ejpam-3575	50	63	z	z	NOUN
ejpam-3575	50	64	)	)	PUNCT
ejpam-3575	50	65	∗	∗	NOUN
ejpam-3575	50	66	(	(	PUNCT
ejpam-3575	50	67	y	y	PROPN
ejpam-3575	50	68	∗	∗	PROPN
ejpam-3575	50	69	z	z	NOUN
ejpam-3575	50	70	)	)	PUNCT
ejpam-3575	50	71	≤	≤	NUM
ejpam-3575	50	72	x	x	PUNCT
ejpam-3575	50	73	∗	∗	PROPN
ejpam-3575	50	74	y	y	PROPN
ejpam-3575	50	75	)	)	PUNCT
ejpam-3575	50	76	(	(	PUNCT
ejpam-3575	50	77	6	6	NUM
ejpam-3575	50	78	)	)	PUNCT
ejpam-3575	50	79	where	where	SCONJ
ejpam-3575	50	80	x	x	PUNCT
ejpam-3575	50	81	≤	≤	ADJ
ejpam-3575	50	82	y	y	NOUN
ejpam-3575	51	1	if	if	SCONJ
ejpam-3575	52	1	and	and	CCONJ
ejpam-3575	52	2	only	only	ADV
ejpam-3575	52	3	if	if	SCONJ
ejpam-3575	52	4	x	x	X
ejpam-3575	52	5	∗	∗	VERB
ejpam-3575	52	6	y	y	NOUN
ejpam-3575	52	7	=	=	SYM
ejpam-3575	52	8	0	0	PROPN
ejpam-3575	52	9	.	.	PUNCT
ejpam-3575	53	1	any	any	DET
ejpam-3575	53	2	bci	bci	NOUN
ejpam-3575	53	3	-	-	NOUN
ejpam-3575	53	4	algebra	algebra	NOUN
ejpam-3575	53	5	x	x	PRON
ejpam-3575	53	6	satisfies	satisfy	VERB
ejpam-3575	53	7	the	the	DET
ejpam-3575	53	8	following	follow	VERB
ejpam-3575	53	9	conditions	condition	NOUN
ejpam-3575	53	10	:	:	PUNCT
ejpam-3575	53	11	(	(	PUNCT
ejpam-3575	53	12	∀x	∀x	X
ejpam-3575	53	13	,	,	PUNCT
ejpam-3575	53	14	y	y	PROPN
ejpam-3575	53	15	,	,	PUNCT
ejpam-3575	53	16	z	z	NOUN
ejpam-3575	53	17	∈	∈	PROPN
ejpam-3575	53	18	x	x	X
ejpam-3575	53	19	)	)	PUNCT
ejpam-3575	53	20	(	(	PUNCT
ejpam-3575	53	21	0	0	NUM
ejpam-3575	53	22	∗	∗	NOUN
ejpam-3575	53	23	(	(	PUNCT
ejpam-3575	53	24	0	0	NUM
ejpam-3575	53	25	∗	∗	NOUN
ejpam-3575	53	26	(	(	PUNCT
ejpam-3575	53	27	(	(	PUNCT
ejpam-3575	53	28	x	x	SYM
ejpam-3575	53	29	∗	∗	PROPN
ejpam-3575	53	30	z	z	NOUN
ejpam-3575	53	31	)	)	PUNCT
ejpam-3575	53	32	∗	∗	NOUN
ejpam-3575	53	33	(	(	PUNCT
ejpam-3575	53	34	y	y	PROPN
ejpam-3575	53	35	∗	∗	PROPN
ejpam-3575	53	36	z	z	PROPN
ejpam-3575	53	37	)	)	PUNCT
ejpam-3575	53	38	)	)	PUNCT
ejpam-3575	53	39	)	)	PUNCT
ejpam-3575	54	1	=	=	PUNCT
ejpam-3575	54	2	(	(	PUNCT
ejpam-3575	54	3	0	0	NUM
ejpam-3575	54	4	∗	∗	PROPN
ejpam-3575	54	5	y	y	NOUN
ejpam-3575	54	6	)	)	PUNCT
ejpam-3575	54	7	∗	∗	NOUN
ejpam-3575	54	8	(	(	PUNCT
ejpam-3575	54	9	0	0	NUM
ejpam-3575	54	10	∗	∗	NOUN
ejpam-3575	54	11	x	x	NOUN
ejpam-3575	54	12	)	)	PUNCT
ejpam-3575	54	13	)	)	PUNCT
ejpam-3575	54	14	,	,	PUNCT
ejpam-3575	54	15	(	(	PUNCT
ejpam-3575	54	16	7	7	X
ejpam-3575	54	17	)	)	PUNCT
ejpam-3575	54	18	(	(	PUNCT
ejpam-3575	54	19	∀x	∀x	X
ejpam-3575	54	20	,	,	PUNCT
ejpam-3575	54	21	y	y	PROPN
ejpam-3575	54	22	∈	∈	PROPN
ejpam-3575	54	23	x	x	X
ejpam-3575	54	24	)	)	PUNCT
ejpam-3575	54	25	(	(	PUNCT
ejpam-3575	54	26	0	0	NUM
ejpam-3575	54	27	∗	∗	NOUN
ejpam-3575	54	28	(	(	PUNCT
ejpam-3575	54	29	0	0	NUM
ejpam-3575	54	30	∗	∗	NOUN
ejpam-3575	54	31	(	(	PUNCT
ejpam-3575	54	32	x	x	X
ejpam-3575	54	33	∗	∗	PROPN
ejpam-3575	54	34	y	y	NOUN
ejpam-3575	54	35	)	)	PUNCT
ejpam-3575	54	36	)	)	PUNCT
ejpam-3575	55	1	=	=	PUNCT
ejpam-3575	55	2	(	(	PUNCT
ejpam-3575	55	3	0	0	NUM
ejpam-3575	55	4	∗	∗	PROPN
ejpam-3575	55	5	y	y	NOUN
ejpam-3575	55	6	)	)	PUNCT
ejpam-3575	55	7	∗	∗	NOUN
ejpam-3575	55	8	(	(	PUNCT
ejpam-3575	55	9	0	0	NUM
ejpam-3575	55	10	∗	∗	NOUN
ejpam-3575	55	11	x	x	NOUN
ejpam-3575	55	12	)	)	PUNCT
ejpam-3575	55	13	)	)	PUNCT
ejpam-3575	55	14	,	,	PUNCT
ejpam-3575	55	15	(	(	PUNCT
ejpam-3575	55	16	8)	8)	NUM
ejpam-3575	55	17	(	(	PUNCT
ejpam-3575	55	18	∀x	∀x	X
ejpam-3575	55	19	∈	∈	PROPN
ejpam-3575	55	20	x	x	X
ejpam-3575	55	21	)	)	PUNCT
ejpam-3575	55	22	(	(	PUNCT
ejpam-3575	55	23	0	0	NUM
ejpam-3575	55	24	∗	∗	NOUN
ejpam-3575	55	25	(	(	PUNCT
ejpam-3575	55	26	0	0	NUM
ejpam-3575	55	27	∗	∗	NOUN
ejpam-3575	55	28	(	(	PUNCT
ejpam-3575	55	29	0	0	NUM
ejpam-3575	55	30	∗	∗	NOUN
ejpam-3575	55	31	x	x	NOUN
ejpam-3575	55	32	)	)	PUNCT
ejpam-3575	55	33	)	)	PUNCT
ejpam-3575	55	34	=	=	SYM
ejpam-3575	56	1	0	0	NUM
ejpam-3575	56	2	∗	∗	NOUN
ejpam-3575	56	3	x	x	NOUN
ejpam-3575	56	4	)	)	PUNCT
ejpam-3575	56	5	.	.	PUNCT
ejpam-3575	57	1	(	(	PUNCT
ejpam-3575	57	2	9	9	X
ejpam-3575	57	3	)	)	PUNCT
ejpam-3575	57	4	a	a	DET
ejpam-3575	57	5	bci	bci	NOUN
ejpam-3575	57	6	-	-	NOUN
ejpam-3575	57	7	algebra	algebra	NOUN
ejpam-3575	57	8	x	x	PUNCT
ejpam-3575	57	9	is	be	AUX
ejpam-3575	57	10	said	say	VERB
ejpam-3575	57	11	to	to	PART
ejpam-3575	57	12	be	be	AUX
ejpam-3575	57	13	p	p	NOUN
ejpam-3575	57	14	-	-	PUNCT
ejpam-3575	57	15	semisimple	semisimple	NOUN
ejpam-3575	57	16	(	(	PUNCT
ejpam-3575	57	17	see	see	VERB
ejpam-3575	57	18	[	[	X
ejpam-3575	57	19	1	1	NUM
ejpam-3575	57	20	]	]	SYM
ejpam-3575	57	21	)	)	PUNCT
ejpam-3575	57	22	if	if	SCONJ
ejpam-3575	57	23	0	0	NUM
ejpam-3575	57	24	∗	∗	NOUN
ejpam-3575	57	25	(	(	PUNCT
ejpam-3575	57	26	0	0	NUM
ejpam-3575	57	27	∗	∗	NOUN
ejpam-3575	57	28	x	x	NOUN
ejpam-3575	57	29	)	)	PUNCT
ejpam-3575	57	30	=	=	PUNCT
ejpam-3575	58	1	x	x	PUNCT
ejpam-3575	58	2	for	for	ADP
ejpam-3575	58	3	all	all	DET
ejpam-3575	58	4	x	x	SYM
ejpam-3575	58	5	∈	∈	NOUN
ejpam-3575	58	6	x.	x.	NOUN
ejpam-3575	59	1	every	every	DET
ejpam-3575	59	2	p	p	ADJ
ejpam-3575	59	3	-	-	PUNCT
ejpam-3575	59	4	semisimple	semisimple	NOUN
ejpam-3575	59	5	bci	bci	NOUN
ejpam-3575	59	6	-	-	NOUN
ejpam-3575	59	7	algebra	algebra	NOUN
ejpam-3575	59	8	x	x	SYM
ejpam-3575	59	9	satisfies	satisfie	NOUN
ejpam-3575	59	10	:	:	PUNCT
ejpam-3575	59	11	(	(	PUNCT
ejpam-3575	59	12	∀x	∀x	X
ejpam-3575	59	13	,	,	PUNCT
ejpam-3575	59	14	y	y	PROPN
ejpam-3575	59	15	,	,	PUNCT
ejpam-3575	59	16	z	z	NOUN
ejpam-3575	59	17	∈	∈	PROPN
ejpam-3575	59	18	x	x	X
ejpam-3575	59	19	)	)	PUNCT
ejpam-3575	59	20	(	(	PUNCT
ejpam-3575	59	21	(	(	PUNCT
ejpam-3575	59	22	x	x	SYM
ejpam-3575	59	23	∗	∗	PROPN
ejpam-3575	59	24	z	z	NOUN
ejpam-3575	59	25	)	)	PUNCT
ejpam-3575	59	26	∗	∗	NOUN
ejpam-3575	59	27	(	(	PUNCT
ejpam-3575	59	28	y	y	PROPN
ejpam-3575	59	29	∗	∗	PROPN
ejpam-3575	59	30	z	z	NOUN
ejpam-3575	59	31	)	)	PUNCT
ejpam-3575	59	32	=	=	PUNCT
ejpam-3575	59	33	x	x	PROPN
ejpam-3575	59	34	∗	∗	NOUN
ejpam-3575	59	35	y	y	PROPN
ejpam-3575	59	36	)	)	PUNCT
ejpam-3575	59	37	.	.	PUNCT
ejpam-3575	60	1	(	(	PUNCT
ejpam-3575	60	2	10	10	NUM
ejpam-3575	60	3	)	)	PUNCT
ejpam-3575	60	4	a	a	DET
ejpam-3575	60	5	nonempty	nonempty	NOUN
ejpam-3575	60	6	subset	subset	VERB
ejpam-3575	60	7	s	s	NOUN
ejpam-3575	60	8	of	of	ADP
ejpam-3575	60	9	a	a	DET
ejpam-3575	60	10	bck	bck	PROPN
ejpam-3575	60	11	/	/	SYM
ejpam-3575	60	12	bci	bci	NOUN
ejpam-3575	60	13	-	-	NOUN
ejpam-3575	60	14	algebra	algebra	NOUN
ejpam-3575	60	15	x	x	PUNCT
ejpam-3575	60	16	is	be	AUX
ejpam-3575	60	17	called	call	VERB
ejpam-3575	60	18	a	a	DET
ejpam-3575	60	19	subalgebra	subalgebra	NOUN
ejpam-3575	60	20	of	of	ADP
ejpam-3575	60	21	x	x	PRON
ejpam-3575	60	22	if	if	SCONJ
ejpam-3575	60	23	x∗y	x∗y	X
ejpam-3575	60	24	∈	∈	PROPN
ejpam-3575	60	25	s	s	VERB
ejpam-3575	60	26	for	for	ADP
ejpam-3575	60	27	all	all	DET
ejpam-3575	60	28	x	x	NOUN
ejpam-3575	60	29	,	,	PUNCT
ejpam-3575	60	30	y	y	PROPN
ejpam-3575	60	31	∈	∈	PROPN
ejpam-3575	60	32	s.	s.	PROPN
ejpam-3575	60	33	a	a	PRON
ejpam-3575	60	34	subset	subset	VERB
ejpam-3575	60	35	a	a	PRON
ejpam-3575	60	36	of	of	ADP
ejpam-3575	60	37	a	a	DET
ejpam-3575	60	38	bck	bck	PROPN
ejpam-3575	60	39	/	/	SYM
ejpam-3575	60	40	bci	bci	NOUN
ejpam-3575	60	41	-	-	NOUN
ejpam-3575	60	42	algebra	algebra	NOUN
ejpam-3575	60	43	x	x	PUNCT
ejpam-3575	60	44	is	be	AUX
ejpam-3575	60	45	called	call	VERB
ejpam-3575	60	46	an	an	DET
ejpam-3575	60	47	ideal	ideal	NOUN
ejpam-3575	60	48	of	of	ADP
ejpam-3575	60	49	x	x	PRON
ejpam-3575	60	50	if	if	SCONJ
ejpam-3575	60	51	it	it	PRON
ejpam-3575	60	52	satisfies	satisfy	VERB
ejpam-3575	60	53	:	:	PUNCT
ejpam-3575	60	54	0	0	NUM
ejpam-3575	60	55	∈	∈	PROPN
ejpam-3575	60	56	a	a	DET
ejpam-3575	60	57	,	,	PUNCT
ejpam-3575	60	58	(	(	PUNCT
ejpam-3575	60	59	11	11	NUM
ejpam-3575	60	60	)	)	PUNCT
ejpam-3575	60	61	(	(	PUNCT
ejpam-3575	60	62	∀x	∀x	X
ejpam-3575	60	63	∈	∈	PROPN
ejpam-3575	60	64	x	x	NOUN
ejpam-3575	60	65	)	)	PUNCT
ejpam-3575	60	66	(	(	PUNCT
ejpam-3575	60	67	x	x	SYM
ejpam-3575	60	68	∗	∗	VERB
ejpam-3575	60	69	y	y	PROPN
ejpam-3575	60	70	∈	∈	PROPN
ejpam-3575	60	71	a	a	PRON
ejpam-3575	60	72	,	,	PUNCT
ejpam-3575	60	73	y	y	PROPN
ejpam-3575	60	74	∈	∈	PROPN
ejpam-3575	60	75	a	a	DET
ejpam-3575	60	76	⇒	⇒	NOUN
ejpam-3575	60	77	x	x	PUNCT
ejpam-3575	60	78	∈	∈	PROPN
ejpam-3575	60	79	a	a	PRON
ejpam-3575	60	80	)	)	PUNCT
ejpam-3575	60	81	.	.	PUNCT
ejpam-3575	61	1	(	(	PUNCT
ejpam-3575	61	2	12	12	NUM
ejpam-3575	61	3	)	)	PUNCT
ejpam-3575	61	4	a	a	DET
ejpam-3575	61	5	subset	subset	NOUN
ejpam-3575	61	6	a	a	PRON
ejpam-3575	61	7	of	of	ADP
ejpam-3575	61	8	a	a	DET
ejpam-3575	61	9	bci	bci	NOUN
ejpam-3575	61	10	-	-	NOUN
ejpam-3575	61	11	algebra	algebra	NOUN
ejpam-3575	61	12	x	x	PUNCT
ejpam-3575	61	13	is	be	AUX
ejpam-3575	61	14	called	call	VERB
ejpam-3575	61	15	a	a	DET
ejpam-3575	61	16	p	p	NOUN
ejpam-3575	61	17	-	-	PUNCT
ejpam-3575	61	18	ideal	ideal	NOUN
ejpam-3575	61	19	of	of	ADP
ejpam-3575	61	20	x	x	PUNCT
ejpam-3575	61	21	(	(	PUNCT
ejpam-3575	61	22	see	see	VERB
ejpam-3575	61	23	[	[	X
ejpam-3575	61	24	32	32	NUM
ejpam-3575	61	25	]	]	SYM
ejpam-3575	61	26	)	)	PUNCT
ejpam-3575	61	27	if	if	SCONJ
ejpam-3575	61	28	it	it	PRON
ejpam-3575	61	29	satisfies	satisfy	VERB
ejpam-3575	61	30	(	(	PUNCT
ejpam-3575	61	31	11	11	NUM
ejpam-3575	61	32	)	)	PUNCT
ejpam-3575	61	33	and	and	CCONJ
ejpam-3575	61	34	(	(	PUNCT
ejpam-3575	61	35	∀x	∀x	NUM
ejpam-3575	61	36	,	,	PUNCT
ejpam-3575	61	37	y	y	PROPN
ejpam-3575	61	38	,	,	PUNCT
ejpam-3575	61	39	z	z	NOUN
ejpam-3575	61	40	∈	∈	PROPN
ejpam-3575	61	41	x	x	X
ejpam-3575	61	42	)	)	PUNCT
ejpam-3575	61	43	(	(	PUNCT
ejpam-3575	61	44	(	(	PUNCT
ejpam-3575	61	45	x	x	SYM
ejpam-3575	61	46	∗	∗	PROPN
ejpam-3575	61	47	z	z	NOUN
ejpam-3575	61	48	)	)	PUNCT
ejpam-3575	61	49	∗	∗	NOUN
ejpam-3575	61	50	(	(	PUNCT
ejpam-3575	61	51	y	y	PROPN
ejpam-3575	61	52	∗	∗	PROPN
ejpam-3575	61	53	z	z	PROPN
ejpam-3575	61	54	)	)	PUNCT
ejpam-3575	61	55	∈	∈	PROPN
ejpam-3575	62	1	a	a	PRON
ejpam-3575	62	2	,	,	PUNCT
ejpam-3575	62	3	y	y	PROPN
ejpam-3575	62	4	∈	∈	PROPN
ejpam-3575	62	5	a	a	DET
ejpam-3575	62	6	⇒	⇒	NOUN
ejpam-3575	62	7	x	x	PUNCT
ejpam-3575	62	8	∈	∈	PROPN
ejpam-3575	62	9	a	a	PRON
ejpam-3575	62	10	)	)	PUNCT
ejpam-3575	62	11	.	.	PUNCT
ejpam-3575	63	1	(	(	PUNCT
ejpam-3575	63	2	13	13	X
ejpam-3575	63	3	)	)	PUNCT
ejpam-3575	63	4	note	note	VERB
ejpam-3575	63	5	that	that	SCONJ
ejpam-3575	63	6	every	every	DET
ejpam-3575	63	7	p	p	NOUN
ejpam-3575	63	8	-	-	PUNCT
ejpam-3575	63	9	ideal	ideal	NOUN
ejpam-3575	63	10	is	be	AUX
ejpam-3575	63	11	an	an	DET
ejpam-3575	63	12	ideal	ideal	NOUN
ejpam-3575	63	13	,	,	PUNCT
ejpam-3575	63	14	but	but	CCONJ
ejpam-3575	63	15	the	the	DET
ejpam-3575	63	16	converse	converse	NOUN
ejpam-3575	63	17	is	be	AUX
ejpam-3575	63	18	not	not	PART
ejpam-3575	63	19	true	true	ADJ
ejpam-3575	63	20	in	in	ADP
ejpam-3575	63	21	general	general	ADJ
ejpam-3575	63	22	(	(	PUNCT
ejpam-3575	63	23	see	see	VERB
ejpam-3575	63	24	[	[	X
ejpam-3575	63	25	32	32	NUM
ejpam-3575	63	26	]	]	NUM
ejpam-3575	63	27	)	)	PUNCT
ejpam-3575	63	28	.	.	PUNCT
ejpam-3575	64	1	note	note	VERB
ejpam-3575	64	2	that	that	SCONJ
ejpam-3575	64	3	an	an	DET
ejpam-3575	64	4	ideal	ideal	NOUN
ejpam-3575	64	5	a	a	PRON
ejpam-3575	64	6	of	of	ADP
ejpam-3575	64	7	a	a	DET
ejpam-3575	64	8	bci	bci	NOUN
ejpam-3575	64	9	-	-	NOUN
ejpam-3575	64	10	algebra	algebra	NOUN
ejpam-3575	64	11	x	x	PUNCT
ejpam-3575	64	12	is	be	AUX
ejpam-3575	64	13	a	a	DET
ejpam-3575	64	14	p	p	NOUN
ejpam-3575	64	15	-	-	PUNCT
ejpam-3575	64	16	ideal	ideal	NOUN
ejpam-3575	64	17	of	of	ADP
ejpam-3575	64	18	x	x	SYM
ejpam-3575	64	19	if	if	SCONJ
ejpam-3575	64	20	and	and	CCONJ
ejpam-3575	64	21	only	only	ADV
ejpam-3575	64	22	if	if	SCONJ
ejpam-3575	64	23	the	the	DET
ejpam-3575	64	24	following	follow	VERB
ejpam-3575	64	25	assertion	assertion	NOUN
ejpam-3575	64	26	is	be	AUX
ejpam-3575	64	27	valid	valid	ADJ
ejpam-3575	64	28	:	:	PUNCT
ejpam-3575	64	29	(	(	PUNCT
ejpam-3575	64	30	∀x	∀x	X
ejpam-3575	64	31	,	,	PUNCT
ejpam-3575	64	32	y	y	PROPN
ejpam-3575	64	33	,	,	PUNCT
ejpam-3575	64	34	z	z	NOUN
ejpam-3575	64	35	∈	∈	PROPN
ejpam-3575	64	36	x	x	X
ejpam-3575	64	37	)	)	PUNCT
ejpam-3575	64	38	(	(	PUNCT
ejpam-3575	64	39	(	(	PUNCT
ejpam-3575	64	40	x	x	SYM
ejpam-3575	64	41	∗	∗	PROPN
ejpam-3575	64	42	z	z	NOUN
ejpam-3575	64	43	)	)	PUNCT
ejpam-3575	64	44	∗	∗	NOUN
ejpam-3575	64	45	(	(	PUNCT
ejpam-3575	64	46	y	y	PROPN
ejpam-3575	64	47	∗	∗	PROPN
ejpam-3575	64	48	z	z	PROPN
ejpam-3575	64	49	)	)	PUNCT
ejpam-3575	64	50	∈	∈	PROPN
ejpam-3575	64	51	a	a	DET
ejpam-3575	64	52	⇒	⇒	NOUN
ejpam-3575	64	53	x	x	PUNCT
ejpam-3575	64	54	∗	∗	NOUN
ejpam-3575	64	55	y	y	PROPN
ejpam-3575	64	56	∈	∈	PROPN
ejpam-3575	64	57	a	a	PRON
ejpam-3575	64	58	)	)	PUNCT
ejpam-3575	64	59	.	.	PUNCT
ejpam-3575	65	1	(	(	PUNCT
ejpam-3575	65	2	14	14	NUM
ejpam-3575	65	3	)	)	PUNCT
ejpam-3575	65	4	we	we	PRON
ejpam-3575	65	5	refer	refer	VERB
ejpam-3575	65	6	the	the	DET
ejpam-3575	65	7	reader	reader	NOUN
ejpam-3575	65	8	to	to	ADP
ejpam-3575	65	9	the	the	DET
ejpam-3575	65	10	books	book	NOUN
ejpam-3575	65	11	[	[	X
ejpam-3575	65	12	1	1	NUM
ejpam-3575	65	13	,	,	PUNCT
ejpam-3575	65	14	9	9	NUM
ejpam-3575	65	15	]	]	PUNCT
ejpam-3575	65	16	for	for	ADP
ejpam-3575	65	17	further	further	ADJ
ejpam-3575	65	18	information	information	NOUN
ejpam-3575	65	19	regarding	regard	VERB
ejpam-3575	65	20	bck	bck	PROPN
ejpam-3575	65	21	/	/	SYM
ejpam-3575	65	22	bcialgebras	bcialgebras	NOUN
ejpam-3575	65	23	.	.	PUNCT
ejpam-3575	66	1	g.	g.	PROPN
ejpam-3575	66	2	muhiuddin	muhiuddin	PROPN
ejpam-3575	66	3	et	et	PROPN
ejpam-3575	66	4	al	al	PROPN
ejpam-3575	66	5	.	.	PUNCT
ejpam-3575	66	6	/	/	SYM
ejpam-3575	66	7	eur	eur	PROPN
ejpam-3575	66	8	.	.	PUNCT
ejpam-3575	67	1	j.	j.	PROPN
ejpam-3575	67	2	pure	pure	PROPN
ejpam-3575	67	3	appl	appl	PROPN
ejpam-3575	67	4	.	.	PROPN
ejpam-3575	67	5	math	math	PROPN
ejpam-3575	67	6	,	,	PUNCT
ejpam-3575	67	7	13	13	NUM
ejpam-3575	67	8	(	(	PUNCT
ejpam-3575	67	9	1	1	NUM
ejpam-3575	67	10	)	)	PUNCT
ejpam-3575	67	11	(	(	PUNCT
ejpam-3575	67	12	2020	2020	NUM
ejpam-3575	67	13	)	)	PUNCT
ejpam-3575	67	14	,	,	PUNCT
ejpam-3575	67	15	9	9	NUM
ejpam-3575	67	16	-	-	SYM
ejpam-3575	67	17	18	18	NUM
ejpam-3575	67	18	12	12	NUM
ejpam-3575	67	19	3	3	NUM
ejpam-3575	67	20	.	.	PUNCT
ejpam-3575	67	21	inf	inf	ADJ
ejpam-3575	67	22	-	-	PUNCT
ejpam-3575	67	23	hesitant	hesitant	ADJ
ejpam-3575	67	24	fuzzy	fuzzy	ADJ
ejpam-3575	67	25	subalgebras	subalgebra	NOUN
ejpam-3575	67	26	and	and	CCONJ
ejpam-3575	67	27	ideals	ideal	NOUN
ejpam-3575	67	28	torra	torra	VERB
ejpam-3575	67	29	[	[	X
ejpam-3575	67	30	25	25	NUM
ejpam-3575	67	31	]	]	PUNCT
ejpam-3575	67	32	introduced	introduce	VERB
ejpam-3575	67	33	a	a	DET
ejpam-3575	67	34	new	new	ADJ
ejpam-3575	67	35	extension	extension	NOUN
ejpam-3575	67	36	for	for	ADP
ejpam-3575	67	37	fuzzy	fuzzy	ADJ
ejpam-3575	67	38	sets	set	NOUN
ejpam-3575	67	39	to	to	PART
ejpam-3575	67	40	manage	manage	VERB
ejpam-3575	67	41	those	those	DET
ejpam-3575	67	42	situations	situation	NOUN
ejpam-3575	67	43	in	in	ADP
ejpam-3575	67	44	which	which	PRON
ejpam-3575	67	45	several	several	ADJ
ejpam-3575	67	46	values	value	NOUN
ejpam-3575	67	47	are	be	AUX
ejpam-3575	67	48	possible	possible	ADJ
ejpam-3575	67	49	for	for	ADP
ejpam-3575	67	50	the	the	DET
ejpam-3575	67	51	definition	definition	NOUN
ejpam-3575	67	52	of	of	ADP
ejpam-3575	67	53	a	a	DET
ejpam-3575	67	54	membership	membership	NOUN
ejpam-3575	67	55	function	function	NOUN
ejpam-3575	67	56	of	of	ADP
ejpam-3575	67	57	a	a	DET
ejpam-3575	67	58	fuzzy	fuzzy	ADJ
ejpam-3575	67	59	set	set	NOUN
ejpam-3575	67	60	.	.	PUNCT
ejpam-3575	68	1	definition	definition	NOUN
ejpam-3575	68	2	1	1	NUM
ejpam-3575	68	3	(	(	PUNCT
ejpam-3575	68	4	[	[	X
ejpam-3575	68	5	25	25	NUM
ejpam-3575	68	6	,	,	PUNCT
ejpam-3575	68	7	26	26	NUM
ejpam-3575	68	8	]	]	PUNCT
ejpam-3575	68	9	)	)	PUNCT
ejpam-3575	68	10	.	.	PUNCT
ejpam-3575	69	1	let	let	VERB
ejpam-3575	69	2	x	x	PRON
ejpam-3575	69	3	be	be	AUX
ejpam-3575	69	4	a	a	DET
ejpam-3575	69	5	reference	reference	NOUN
ejpam-3575	69	6	set	set	VERB
ejpam-3575	69	7	.	.	PUNCT
ejpam-3575	70	1	a	a	DET
ejpam-3575	70	2	hesitant	hesitant	ADJ
ejpam-3575	70	3	fuzzy	fuzzy	ADJ
ejpam-3575	70	4	set	set	NOUN
ejpam-3575	70	5	on	on	ADP
ejpam-3575	70	6	x	x	PUNCT
ejpam-3575	70	7	is	be	AUX
ejpam-3575	70	8	defined	define	VERB
ejpam-3575	70	9	in	in	ADP
ejpam-3575	70	10	terms	term	NOUN
ejpam-3575	70	11	of	of	ADP
ejpam-3575	70	12	a	a	DET
ejpam-3575	70	13	function	function	NOUN
ejpam-3575	70	14	that	that	SCONJ
ejpam-3575	70	15	when	when	SCONJ
ejpam-3575	70	16	applied	apply	VERB
ejpam-3575	70	17	to	to	ADP
ejpam-3575	70	18	x	x	PROPN
ejpam-3575	70	19	returns	return	NOUN
ejpam-3575	70	20	a	a	DET
ejpam-3575	70	21	subset	subset	NOUN
ejpam-3575	70	22	of	of	ADP
ejpam-3575	70	23	[	[	X
ejpam-3575	70	24	0	0	NUM
ejpam-3575	70	25	,	,	PUNCT
ejpam-3575	70	26	1	1	NUM
ejpam-3575	70	27	]	]	PUNCT
ejpam-3575	70	28	,	,	PUNCT
ejpam-3575	70	29	which	which	PRON
ejpam-3575	70	30	can	can	AUX
ejpam-3575	70	31	be	be	AUX
ejpam-3575	70	32	viewed	view	VERB
ejpam-3575	70	33	as	as	ADP
ejpam-3575	70	34	the	the	DET
ejpam-3575	70	35	following	following	ADJ
ejpam-3575	70	36	mathematical	mathematical	ADJ
ejpam-3575	70	37	representation	representation	NOUN
ejpam-3575	70	38	:	:	PUNCT
ejpam-3575	70	39	h	h	NOUN
ejpam-3575	70	40	:	:	PUNCT
ejpam-3575	70	41	=	=	SYM
ejpam-3575	70	42	{	{	PUNCT
ejpam-3575	70	43	(	(	PUNCT
ejpam-3575	70	44	x	x	NOUN
ejpam-3575	70	45	,	,	PUNCT
ejpam-3575	70	46	h(x	h(x	PROPN
ejpam-3575	70	47	)	)	PUNCT
ejpam-3575	70	48	)	)	PUNCT
ejpam-3575	71	1	|	|	ADV
ejpam-3575	71	2	x	x	SYM
ejpam-3575	71	3	∈	∈	NOUN
ejpam-3575	71	4	x	x	X
ejpam-3575	71	5	}	}	PUNCT
ejpam-3575	71	6	where	where	SCONJ
ejpam-3575	71	7	h	h	NOUN
ejpam-3575	71	8	:	:	PUNCT
ejpam-3575	71	9	x	x	X
ejpam-3575	71	10	→	→	X
ejpam-3575	71	11	p	p	X
ejpam-3575	71	12	(	(	PUNCT
ejpam-3575	71	13	[	[	X
ejpam-3575	71	14	0	0	NUM
ejpam-3575	71	15	,	,	PUNCT
ejpam-3575	71	16	1	1	NUM
ejpam-3575	71	17	]	]	PUNCT
ejpam-3575	71	18	)	)	PUNCT
ejpam-3575	71	19	.	.	PUNCT
ejpam-3575	72	1	in	in	ADP
ejpam-3575	72	2	what	what	PRON
ejpam-3575	72	3	follows	follow	VERB
ejpam-3575	72	4	,	,	PUNCT
ejpam-3575	72	5	the	the	DET
ejpam-3575	72	6	power	power	NOUN
ejpam-3575	72	7	set	set	NOUN
ejpam-3575	72	8	of	of	ADP
ejpam-3575	72	9	[	[	X
ejpam-3575	72	10	0	0	NUM
ejpam-3575	72	11	,	,	PUNCT
ejpam-3575	72	12	1	1	NUM
ejpam-3575	72	13	]	]	PUNCT
ejpam-3575	72	14	is	be	AUX
ejpam-3575	72	15	denoted	denote	VERB
ejpam-3575	72	16	by	by	ADP
ejpam-3575	72	17	p	p	X
ejpam-3575	72	18	(	(	PUNCT
ejpam-3575	72	19	[	[	X
ejpam-3575	72	20	0	0	NUM
ejpam-3575	72	21	,	,	PUNCT
ejpam-3575	72	22	1	1	NUM
ejpam-3575	72	23	]	]	PUNCT
ejpam-3575	72	24	)	)	PUNCT
ejpam-3575	72	25	and	and	CCONJ
ejpam-3575	72	26	p	p	NOUN
ejpam-3575	72	27	∗([0	∗([0	NOUN
ejpam-3575	72	28	,	,	PUNCT
ejpam-3575	72	29	1	1	NUM
ejpam-3575	72	30	]	]	PUNCT
ejpam-3575	72	31	)	)	PUNCT
ejpam-3575	73	1	=	=	SYM
ejpam-3575	73	2	p	p	X
ejpam-3575	73	3	(	(	PUNCT
ejpam-3575	73	4	[	[	X
ejpam-3575	73	5	0	0	NUM
ejpam-3575	73	6	,	,	PUNCT
ejpam-3575	73	7	1	1	NUM
ejpam-3575	73	8	]	]	PUNCT
ejpam-3575	73	9	)	)	PUNCT
ejpam-3575	73	10	\	\	NOUN
ejpam-3575	73	11	{	{	PUNCT
ejpam-3575	73	12	∅	∅	NOUN
ejpam-3575	73	13	}	}	PUNCT
ejpam-3575	73	14	.	.	PUNCT
ejpam-3575	74	1	for	for	ADP
ejpam-3575	74	2	any	any	DET
ejpam-3575	74	3	element	element	NOUN
ejpam-3575	74	4	d	d	PROPN
ejpam-3575	74	5	∈	∈	PROPN
ejpam-3575	74	6	p	p	NOUN
ejpam-3575	74	7	∗([0	∗([0	NOUN
ejpam-3575	74	8	,	,	PUNCT
ejpam-3575	74	9	1	1	NUM
ejpam-3575	74	10	]	]	NUM
ejpam-3575	74	11	)	)	PUNCT
ejpam-3575	74	12	,	,	PUNCT
ejpam-3575	74	13	the	the	DET
ejpam-3575	74	14	infimum	infimum	NOUN
ejpam-3575	74	15	of	of	ADP
ejpam-3575	74	16	d	d	PROPN
ejpam-3575	74	17	is	be	AUX
ejpam-3575	74	18	denoted	denote	VERB
ejpam-3575	74	19	by	by	ADP
ejpam-3575	74	20	inf	inf	PROPN
ejpam-3575	74	21	d.	d.	PROPN
ejpam-3575	74	22	for	for	ADP
ejpam-3575	74	23	any	any	DET
ejpam-3575	74	24	hesitant	hesitant	ADJ
ejpam-3575	74	25	fuzzy	fuzzy	ADJ
ejpam-3575	74	26	set	set	NOUN
ejpam-3575	74	27	h	h	NOUN
ejpam-3575	74	28	:	:	PUNCT
ejpam-3575	74	29	=	=	SYM
ejpam-3575	74	30	{	{	PUNCT
ejpam-3575	74	31	(	(	PUNCT
ejpam-3575	74	32	x	x	NOUN
ejpam-3575	74	33	,	,	PUNCT
ejpam-3575	74	34	h(x	h(x	PROPN
ejpam-3575	74	35	)	)	PUNCT
ejpam-3575	74	36	)	)	PUNCT
ejpam-3575	75	1	|	|	ADV
ejpam-3575	75	2	x	x	SYM
ejpam-3575	75	3	∈	∈	NOUN
ejpam-3575	75	4	x	x	NOUN
ejpam-3575	75	5	}	}	PUNCT
ejpam-3575	75	6	and	and	CCONJ
ejpam-3575	75	7	d	d	PROPN
ejpam-3575	75	8	∈	∈	PROPN
ejpam-3575	75	9	p	p	NOUN
ejpam-3575	75	10	∗([0	∗([0	NOUN
ejpam-3575	75	11	,	,	PUNCT
ejpam-3575	75	12	1	1	NUM
ejpam-3575	75	13	]	]	NUM
ejpam-3575	75	14	)	)	PUNCT
ejpam-3575	75	15	,	,	PUNCT
ejpam-3575	75	16	consider	consider	VERB
ejpam-3575	75	17	the	the	DET
ejpam-3575	75	18	set	set	NOUN
ejpam-3575	75	19	inf[h;d	inf[h;d	NOUN
ejpam-3575	75	20	]	]	PUNCT
ejpam-3575	75	21	:	:	PUNCT
ejpam-3575	75	22	=	=	SYM
ejpam-3575	75	23	{	{	PUNCT
ejpam-3575	75	24	x	x	PUNCT
ejpam-3575	75	25	∈	∈	PROPN
ejpam-3575	75	26	x	x	X
ejpam-3575	75	27	|	|	ADV
ejpam-3575	75	28	inf	inf	ADJ
ejpam-3575	75	29	h(x	h(x	PROPN
ejpam-3575	75	30	)	)	PUNCT
ejpam-3575	75	31	≥	≥	NOUN
ejpam-3575	75	32	inf	inf	NOUN
ejpam-3575	75	33	d	d	NOUN
ejpam-3575	75	34	}	}	PUNCT
ejpam-3575	75	35	.	.	PUNCT
ejpam-3575	76	1	definition	definition	NOUN
ejpam-3575	76	2	2	2	NUM
ejpam-3575	76	3	.	.	PUNCT
ejpam-3575	77	1	let	let	VERB
ejpam-3575	77	2	x	x	PRON
ejpam-3575	77	3	be	be	AUX
ejpam-3575	77	4	a	a	DET
ejpam-3575	77	5	bck	bck	VERB
ejpam-3575	77	6	/	/	SYM
ejpam-3575	77	7	bci	bci	NOUN
ejpam-3575	77	8	-	-	NOUN
ejpam-3575	77	9	algebra	algebra	NOUN
ejpam-3575	77	10	.	.	PUNCT
ejpam-3575	78	1	given	give	VERB
ejpam-3575	78	2	an	an	DET
ejpam-3575	78	3	element	element	NOUN
ejpam-3575	78	4	d	d	PROPN
ejpam-3575	78	5	∈	∈	PROPN
ejpam-3575	78	6	p	p	NOUN
ejpam-3575	78	7	∗([0	∗([0	NOUN
ejpam-3575	78	8	,	,	PUNCT
ejpam-3575	78	9	1	1	NUM
ejpam-3575	78	10	]	]	NUM
ejpam-3575	78	11	)	)	PUNCT
ejpam-3575	78	12	,	,	PUNCT
ejpam-3575	78	13	a	a	DET
ejpam-3575	78	14	hesitant	hesitant	ADJ
ejpam-3575	78	15	fuzzy	fuzzy	ADJ
ejpam-3575	78	16	set	set	NOUN
ejpam-3575	78	17	h	h	NOUN
ejpam-3575	78	18	:	:	PUNCT
ejpam-3575	78	19	=	=	SYM
ejpam-3575	78	20	{	{	PUNCT
ejpam-3575	78	21	(	(	PUNCT
ejpam-3575	78	22	x	x	NOUN
ejpam-3575	78	23	,	,	PUNCT
ejpam-3575	78	24	h(x	h(x	PROPN
ejpam-3575	78	25	)	)	PUNCT
ejpam-3575	78	26	)	)	PUNCT
ejpam-3575	79	1	|	|	ADV
ejpam-3575	79	2	x	x	SYM
ejpam-3575	79	3	∈	∈	NOUN
ejpam-3575	79	4	x	x	VERB
ejpam-3575	79	5	}	}	PUNCT
ejpam-3575	79	6	is	be	AUX
ejpam-3575	79	7	called	call	VERB
ejpam-3575	79	8	an	an	DET
ejpam-3575	79	9	inf	inf	ADJ
ejpam-3575	79	10	-	-	PUNCT
ejpam-3575	79	11	hesitant	hesitant	ADJ
ejpam-3575	79	12	fuzzy	fuzzy	ADJ
ejpam-3575	79	13	subalgebra	subalgebra	NOUN
ejpam-3575	79	14	of	of	ADP
ejpam-3575	79	15	x	x	PUNCT
ejpam-3575	79	16	related	relate	VERB
ejpam-3575	79	17	to	to	ADP
ejpam-3575	79	18	d	d	PROPN
ejpam-3575	79	19	(	(	PUNCT
ejpam-3575	79	20	briefly	briefly	ADV
ejpam-3575	79	21	,	,	PUNCT
ejpam-3575	79	22	d	d	X
ejpam-3575	79	23	-	-	PUNCT
ejpam-3575	79	24	inf	inf	ADJ
ejpam-3575	79	25	-	-	PUNCT
ejpam-3575	79	26	hesitant	hesitant	ADJ
ejpam-3575	79	27	fuzzy	fuzzy	ADJ
ejpam-3575	79	28	subalgebra	subalgebra	NOUN
ejpam-3575	79	29	of	of	ADP
ejpam-3575	79	30	x	x	PRON
ejpam-3575	79	31	if	if	SCONJ
ejpam-3575	79	32	the	the	DET
ejpam-3575	79	33	set	set	NOUN
ejpam-3575	79	34	inf[h;d	inf[h;d	NOUN
ejpam-3575	79	35	]	]	PUNCT
ejpam-3575	79	36	is	be	AUX
ejpam-3575	79	37	a	a	DET
ejpam-3575	79	38	subalgebra	subalgebra	NOUN
ejpam-3575	79	39	of	of	ADP
ejpam-3575	79	40	x	x	SYM
ejpam-3575	79	41	whenever	whenever	SCONJ
ejpam-3575	79	42	it	it	PRON
ejpam-3575	79	43	is	be	AUX
ejpam-3575	79	44	non	non	ADJ
ejpam-3575	79	45	-	-	ADJ
ejpam-3575	79	46	empty	empty	ADJ
ejpam-3575	79	47	.	.	PUNCT
ejpam-3575	80	1	if	if	SCONJ
ejpam-3575	80	2	h	h	NOUN
ejpam-3575	80	3	:	:	PUNCT
ejpam-3575	80	4	=	=	SYM
ejpam-3575	80	5	{	{	PUNCT
ejpam-3575	80	6	(	(	PUNCT
ejpam-3575	80	7	x	x	NOUN
ejpam-3575	80	8	,	,	PUNCT
ejpam-3575	80	9	h(x	h(x	PROPN
ejpam-3575	80	10	)	)	PUNCT
ejpam-3575	80	11	)	)	PUNCT
ejpam-3575	81	1	|	|	ADV
ejpam-3575	81	2	x	x	SYM
ejpam-3575	81	3	∈	∈	NOUN
ejpam-3575	81	4	x	x	X
ejpam-3575	81	5	}	}	PUNCT
ejpam-3575	81	6	is	be	AUX
ejpam-3575	81	7	a	a	DET
ejpam-3575	81	8	d	d	PROPN
ejpam-3575	81	9	-	-	PUNCT
ejpam-3575	81	10	inf	inf	ADJ
ejpam-3575	81	11	-	-	PUNCT
ejpam-3575	81	12	hesitant	hesitant	ADJ
ejpam-3575	81	13	fuzzy	fuzzy	ADJ
ejpam-3575	81	14	subalgebra	subalgebra	NOUN
ejpam-3575	81	15	of	of	ADP
ejpam-3575	81	16	x	x	PUNCT
ejpam-3575	81	17	for	for	ADP
ejpam-3575	81	18	all	all	DET
ejpam-3575	81	19	d	d	PROPN
ejpam-3575	81	20	∈	∈	PROPN
ejpam-3575	81	21	p	p	NOUN
ejpam-3575	81	22	∗([0	∗([0	NOUN
ejpam-3575	81	23	,	,	PUNCT
ejpam-3575	81	24	1	1	NUM
ejpam-3575	81	25	]	]	PUNCT
ejpam-3575	81	26	)	)	PUNCT
ejpam-3575	81	27	with	with	ADP
ejpam-3575	81	28	inf[h;d	inf[h;d	PROPN
ejpam-3575	81	29	]	]	PUNCT
ejpam-3575	81	30	6=	6=	NUM
ejpam-3575	81	31	∅	∅	NOUN
ejpam-3575	81	32	,	,	PUNCT
ejpam-3575	81	33	then	then	ADV
ejpam-3575	81	34	we	we	PRON
ejpam-3575	81	35	say	say	VERB
ejpam-3575	81	36	that	that	SCONJ
ejpam-3575	81	37	h	h	NOUN
ejpam-3575	81	38	:	:	PUNCT
ejpam-3575	81	39	=	=	SYM
ejpam-3575	81	40	{	{	PUNCT
ejpam-3575	81	41	(	(	PUNCT
ejpam-3575	81	42	x	x	NOUN
ejpam-3575	81	43	,	,	PUNCT
ejpam-3575	81	44	h(x	h(x	PROPN
ejpam-3575	81	45	)	)	PUNCT
ejpam-3575	81	46	)	)	PUNCT
ejpam-3575	82	1	|	|	ADV
ejpam-3575	82	2	x	x	SYM
ejpam-3575	82	3	∈	∈	NOUN
ejpam-3575	82	4	x	x	X
ejpam-3575	82	5	}	}	PUNCT
ejpam-3575	82	6	is	be	AUX
ejpam-3575	82	7	an	an	DET
ejpam-3575	82	8	inf	inf	ADJ
ejpam-3575	82	9	-	-	PUNCT
ejpam-3575	82	10	hesitant	hesitant	ADJ
ejpam-3575	82	11	fuzzy	fuzzy	ADJ
ejpam-3575	82	12	subalgebra	subalgebra	NOUN
ejpam-3575	82	13	of	of	ADP
ejpam-3575	82	14	x.	x.	PROPN
ejpam-3575	82	15	example	example	NOUN
ejpam-3575	83	1	1	1	NUM
ejpam-3575	83	2	.	.	PUNCT
ejpam-3575	84	1	(	(	PUNCT
ejpam-3575	84	2	1	1	X
ejpam-3575	84	3	)	)	PUNCT
ejpam-3575	84	4	let	let	VERB
ejpam-3575	84	5	x	x	PUNCT
ejpam-3575	84	6	=	=	PUNCT
ejpam-3575	84	7	{	{	PUNCT
ejpam-3575	84	8	0	0	NUM
ejpam-3575	84	9	,	,	PUNCT
ejpam-3575	84	10	a	a	DET
ejpam-3575	84	11	,	,	PUNCT
ejpam-3575	84	12	b	b	NOUN
ejpam-3575	84	13	,	,	PUNCT
ejpam-3575	84	14	c	c	AUX
ejpam-3575	84	15	}	}	PUNCT
ejpam-3575	84	16	be	be	AUX
ejpam-3575	84	17	a	a	DET
ejpam-3575	84	18	bck	bck	NOUN
ejpam-3575	84	19	-	-	PUNCT
ejpam-3575	84	20	algebra	algebra	NOUN
ejpam-3575	84	21	with	with	ADP
ejpam-3575	84	22	the	the	DET
ejpam-3575	84	23	following	follow	VERB
ejpam-3575	84	24	cayley	cayley	ADJ
ejpam-3575	84	25	table	table	NOUN
ejpam-3575	84	26	:	:	PUNCT
ejpam-3575	84	27	∗	∗	NOUN
ejpam-3575	84	28	0	0	PUNCT
ejpam-3575	85	1	a	a	DET
ejpam-3575	85	2	b	b	NOUN
ejpam-3575	85	3	c	c	NOUN
ejpam-3575	85	4	0	0	NUM
ejpam-3575	85	5	0	0	NUM
ejpam-3575	85	6	0	0	NUM
ejpam-3575	85	7	0	0	NUM
ejpam-3575	85	8	0	0	NUM
ejpam-3575	85	9	a	a	DET
ejpam-3575	85	10	a	a	DET
ejpam-3575	85	11	0	0	NUM
ejpam-3575	85	12	a	a	DET
ejpam-3575	85	13	0	0	NUM
ejpam-3575	85	14	b	b	PROPN
ejpam-3575	85	15	b	b	PROPN
ejpam-3575	85	16	b	b	PROPN
ejpam-3575	85	17	0	0	NUM
ejpam-3575	85	18	0	0	NUM
ejpam-3575	85	19	c	c	NOUN
ejpam-3575	85	20	c	c	PROPN
ejpam-3575	85	21	b	b	PROPN
ejpam-3575	85	22	a	a	DET
ejpam-3575	85	23	0	0	NUM
ejpam-3575	85	24	let	let	VERB
ejpam-3575	85	25	h	h	NOUN
ejpam-3575	85	26	:	:	PUNCT
ejpam-3575	85	27	=	=	SYM
ejpam-3575	85	28	{	{	PUNCT
ejpam-3575	85	29	(	(	PUNCT
ejpam-3575	85	30	x	x	NOUN
ejpam-3575	85	31	,	,	PUNCT
ejpam-3575	85	32	h(x	h(x	PROPN
ejpam-3575	85	33	)	)	PUNCT
ejpam-3575	85	34	)	)	PUNCT
ejpam-3575	86	1	|	|	ADV
ejpam-3575	86	2	x	x	SYM
ejpam-3575	86	3	∈	∈	NOUN
ejpam-3575	86	4	x	x	VERB
ejpam-3575	86	5	}	}	PUNCT
ejpam-3575	86	6	be	be	AUX
ejpam-3575	86	7	a	a	DET
ejpam-3575	86	8	hesitant	hesitant	ADJ
ejpam-3575	86	9	fuzzy	fuzzy	ADJ
ejpam-3575	86	10	set	set	NOUN
ejpam-3575	86	11	on	on	ADP
ejpam-3575	86	12	x	x	PUNCT
ejpam-3575	86	13	defined	define	VERB
ejpam-3575	86	14	by	by	ADP
ejpam-3575	86	15	h	h	NOUN
ejpam-3575	86	16	=	=	SYM
ejpam-3575	86	17	{	{	PUNCT
ejpam-3575	86	18	(	(	PUNCT
ejpam-3575	86	19	0	0	NUM
ejpam-3575	86	20	,	,	PUNCT
ejpam-3575	86	21	(	(	PUNCT
ejpam-3575	86	22	0.8	0.8	NUM
ejpam-3575	86	23	,	,	PUNCT
ejpam-3575	86	24	1	1	NUM
ejpam-3575	86	25	]	]	NUM
ejpam-3575	86	26	)	)	PUNCT
ejpam-3575	86	27	,	,	PUNCT
ejpam-3575	86	28	(	(	PUNCT
ejpam-3575	86	29	a	a	X
ejpam-3575	86	30	,	,	PUNCT
ejpam-3575	86	31	(	(	PUNCT
ejpam-3575	86	32	0.3	0.3	NUM
ejpam-3575	86	33	,	,	PUNCT
ejpam-3575	86	34	0.5	0.5	NUM
ejpam-3575	86	35	)	)	PUNCT
ejpam-3575	86	36	∪	∪	NOUN
ejpam-3575	86	37	{	{	PUNCT
ejpam-3575	86	38	0.9	0.9	NUM
ejpam-3575	86	39	}	}	PUNCT
ejpam-3575	86	40	)	)	PUNCT
ejpam-3575	86	41	,	,	PUNCT
ejpam-3575	86	42	(	(	PUNCT
ejpam-3575	86	43	b	b	X
ejpam-3575	86	44	,	,	PUNCT
ejpam-3575	86	45	[	[	X
ejpam-3575	86	46	0.5	0.5	NUM
ejpam-3575	86	47	,	,	PUNCT
ejpam-3575	86	48	0.7	0.7	NUM
ejpam-3575	86	49	]	]	PUNCT
ejpam-3575	86	50	)	)	PUNCT
ejpam-3575	86	51	,	,	PUNCT
ejpam-3575	86	52	(	(	PUNCT
ejpam-3575	86	53	c	c	X
ejpam-3575	86	54	,	,	PUNCT
ejpam-3575	86	55	(	(	PUNCT
ejpam-3575	86	56	0.3	0.3	NUM
ejpam-3575	86	57	,	,	PUNCT
ejpam-3575	86	58	0.5	0.5	NUM
ejpam-3575	86	59	)	)	PUNCT
ejpam-3575	86	60	∪	∪	NOUN
ejpam-3575	86	61	{	{	PUNCT
ejpam-3575	86	62	0.7	0.7	NUM
ejpam-3575	86	63	}	}	PUNCT
ejpam-3575	86	64	)	)	PUNCT
ejpam-3575	86	65	}	}	PUNCT
ejpam-3575	86	66	.	.	PUNCT
ejpam-3575	87	1	since	since	SCONJ
ejpam-3575	87	2	inf	inf	NOUN
ejpam-3575	87	3	h(0	h(0	PROPN
ejpam-3575	87	4	)	)	PUNCT
ejpam-3575	87	5	=	=	SYM
ejpam-3575	87	6	0.8	0.8	NUM
ejpam-3575	87	7	,	,	PUNCT
ejpam-3575	87	8	inf	inf	PROPN
ejpam-3575	87	9	h(a	h(a	PROPN
ejpam-3575	87	10	)	)	PUNCT
ejpam-3575	87	11	=	=	SYM
ejpam-3575	87	12	0.3	0.3	NUM
ejpam-3575	87	13	=	=	SYM
ejpam-3575	87	14	inf	inf	NOUN
ejpam-3575	87	15	h(c	h(c	PROPN
ejpam-3575	87	16	)	)	PUNCT
ejpam-3575	87	17	and	and	CCONJ
ejpam-3575	87	18	inf	inf	PROPN
ejpam-3575	87	19	h(b	h(b	PROPN
ejpam-3575	87	20	)	)	PUNCT
ejpam-3575	88	1	=	=	SYM
ejpam-3575	88	2	0.5	0.5	NUM
ejpam-3575	88	3	,	,	PUNCT
ejpam-3575	88	4	it	it	PRON
ejpam-3575	88	5	is	be	AUX
ejpam-3575	88	6	routine	routine	ADJ
ejpam-3575	88	7	to	to	PART
ejpam-3575	88	8	verify	verify	VERB
ejpam-3575	88	9	that	that	DET
ejpam-3575	88	10	h	h	NOUN
ejpam-3575	88	11	:	:	PUNCT
ejpam-3575	88	12	=	=	SYM
ejpam-3575	88	13	{	{	PUNCT
ejpam-3575	88	14	(	(	PUNCT
ejpam-3575	88	15	x	x	NOUN
ejpam-3575	88	16	,	,	PUNCT
ejpam-3575	88	17	h(x	h(x	PROPN
ejpam-3575	88	18	)	)	PUNCT
ejpam-3575	88	19	)	)	PUNCT
ejpam-3575	89	1	|	|	ADV
ejpam-3575	89	2	x	x	SYM
ejpam-3575	89	3	∈	∈	NOUN
ejpam-3575	89	4	x	x	X
ejpam-3575	89	5	}	}	PUNCT
ejpam-3575	89	6	is	be	AUX
ejpam-3575	89	7	an	an	DET
ejpam-3575	89	8	inf	inf	ADJ
ejpam-3575	89	9	-	-	PUNCT
ejpam-3575	89	10	hesitant	hesitant	ADJ
ejpam-3575	89	11	fuzzy	fuzzy	ADJ
ejpam-3575	89	12	subalgebra	subalgebra	NOUN
ejpam-3575	89	13	of	of	ADP
ejpam-3575	89	14	x.	x.	PROPN
ejpam-3575	89	15	g.	g.	PROPN
ejpam-3575	89	16	muhiuddin	muhiuddin	PROPN
ejpam-3575	89	17	et	et	PROPN
ejpam-3575	89	18	al	al	PROPN
ejpam-3575	89	19	.	.	PUNCT
ejpam-3575	89	20	/	/	SYM
ejpam-3575	89	21	eur	eur	PROPN
ejpam-3575	89	22	.	.	PUNCT
ejpam-3575	90	1	j.	j.	PROPN
ejpam-3575	90	2	pure	pure	PROPN
ejpam-3575	90	3	appl	appl	PROPN
ejpam-3575	90	4	.	.	PROPN
ejpam-3575	90	5	math	math	PROPN
ejpam-3575	90	6	,	,	PUNCT
ejpam-3575	90	7	13	13	NUM
ejpam-3575	90	8	(	(	PUNCT
ejpam-3575	90	9	1	1	NUM
ejpam-3575	90	10	)	)	PUNCT
ejpam-3575	90	11	(	(	PUNCT
ejpam-3575	90	12	2020	2020	NUM
ejpam-3575	90	13	)	)	PUNCT
ejpam-3575	90	14	,	,	PUNCT
ejpam-3575	90	15	9	9	NUM
ejpam-3575	90	16	-	-	SYM
ejpam-3575	90	17	18	18	NUM
ejpam-3575	90	18	13	13	NUM
ejpam-3575	90	19	(	(	PUNCT
ejpam-3575	90	20	2	2	NUM
ejpam-3575	90	21	)	)	PUNCT
ejpam-3575	90	22	let	let	VERB
ejpam-3575	90	23	x	x	PUNCT
ejpam-3575	90	24	=	=	PUNCT
ejpam-3575	90	25	{	{	PUNCT
ejpam-3575	90	26	0	0	NUM
ejpam-3575	90	27	,	,	PUNCT
ejpam-3575	90	28	a	a	DET
ejpam-3575	90	29	,	,	PUNCT
ejpam-3575	90	30	b	b	NOUN
ejpam-3575	90	31	,	,	PUNCT
ejpam-3575	90	32	c	c	NOUN
ejpam-3575	90	33	,	,	PUNCT
ejpam-3575	90	34	d	d	AUX
ejpam-3575	90	35	}	}	PUNCT
ejpam-3575	90	36	be	be	AUX
ejpam-3575	90	37	a	a	DET
ejpam-3575	90	38	bck	bck	NOUN
ejpam-3575	90	39	-	-	PUNCT
ejpam-3575	90	40	algebra	algebra	NOUN
ejpam-3575	90	41	with	with	ADP
ejpam-3575	90	42	the	the	DET
ejpam-3575	90	43	following	follow	VERB
ejpam-3575	90	44	cayley	cayley	ADJ
ejpam-3575	90	45	table	table	NOUN
ejpam-3575	90	46	:	:	PUNCT
ejpam-3575	91	1	∗	∗	NOUN
ejpam-3575	91	2	0	0	PUNCT
ejpam-3575	92	1	a	a	DET
ejpam-3575	92	2	b	b	NOUN
ejpam-3575	92	3	c	c	NOUN
ejpam-3575	92	4	d	d	NOUN
ejpam-3575	92	5	0	0	NUM
ejpam-3575	92	6	0	0	NUM
ejpam-3575	92	7	0	0	NUM
ejpam-3575	92	8	0	0	NUM
ejpam-3575	92	9	0	0	NUM
ejpam-3575	92	10	0	0	NUM
ejpam-3575	92	11	a	a	DET
ejpam-3575	92	12	a	a	DET
ejpam-3575	92	13	0	0	NUM
ejpam-3575	92	14	0	0	NUM
ejpam-3575	92	15	0	0	NUM
ejpam-3575	92	16	0	0	NUM
ejpam-3575	92	17	b	b	X
ejpam-3575	92	18	b	b	NOUN
ejpam-3575	92	19	a	a	PRON
ejpam-3575	92	20	0	0	NUM
ejpam-3575	92	21	0	0	NUM
ejpam-3575	92	22	0	0	NUM
ejpam-3575	93	1	c	c	NOUN
ejpam-3575	93	2	c	c	NOUN
ejpam-3575	93	3	c	c	NOUN
ejpam-3575	93	4	c	c	NOUN
ejpam-3575	93	5	0	0	NUM
ejpam-3575	93	6	0	0	NUM
ejpam-3575	94	1	d	d	NOUN
ejpam-3575	94	2	d	d	NOUN
ejpam-3575	94	3	c	c	NOUN
ejpam-3575	94	4	c	c	PROPN
ejpam-3575	94	5	a	a	DET
ejpam-3575	94	6	0	0	NUM
ejpam-3575	94	7	let	let	VERB
ejpam-3575	94	8	h	h	NOUN
ejpam-3575	94	9	:	:	PUNCT
ejpam-3575	94	10	=	=	SYM
ejpam-3575	94	11	{	{	PUNCT
ejpam-3575	94	12	(	(	PUNCT
ejpam-3575	94	13	x	x	NOUN
ejpam-3575	94	14	,	,	PUNCT
ejpam-3575	94	15	h(x	h(x	PROPN
ejpam-3575	94	16	)	)	PUNCT
ejpam-3575	94	17	)	)	PUNCT
ejpam-3575	95	1	|	|	ADV
ejpam-3575	95	2	x	x	SYM
ejpam-3575	95	3	∈	∈	NOUN
ejpam-3575	95	4	x	x	VERB
ejpam-3575	95	5	}	}	PUNCT
ejpam-3575	95	6	be	be	AUX
ejpam-3575	95	7	a	a	DET
ejpam-3575	95	8	hesitant	hesitant	ADJ
ejpam-3575	95	9	fuzzy	fuzzy	ADJ
ejpam-3575	95	10	set	set	NOUN
ejpam-3575	95	11	on	on	ADP
ejpam-3575	95	12	x	x	PUNCT
ejpam-3575	95	13	defined	define	VERB
ejpam-3575	95	14	by	by	ADP
ejpam-3575	95	15	h	h	NOUN
ejpam-3575	95	16	=	=	SYM
ejpam-3575	95	17	{	{	PUNCT
ejpam-3575	95	18	(	(	PUNCT
ejpam-3575	95	19	0	0	NUM
ejpam-3575	95	20	,	,	PUNCT
ejpam-3575	95	21	{	{	PUNCT
ejpam-3575	95	22	0.8	0.8	NUM
ejpam-3575	95	23	,	,	PUNCT
ejpam-3575	95	24	0.9	0.9	NUM
ejpam-3575	95	25	}	}	PUNCT
ejpam-3575	95	26	)	)	PUNCT
ejpam-3575	95	27	,	,	PUNCT
ejpam-3575	95	28	(	(	PUNCT
ejpam-3575	95	29	a	a	X
ejpam-3575	95	30	,	,	PUNCT
ejpam-3575	95	31	[	[	X
ejpam-3575	95	32	0.2	0.2	NUM
ejpam-3575	95	33	,	,	PUNCT
ejpam-3575	95	34	0.9	0.9	NUM
ejpam-3575	95	35	)	)	PUNCT
ejpam-3575	95	36	)	)	PUNCT
ejpam-3575	95	37	,	,	PUNCT
ejpam-3575	95	38	(	(	PUNCT
ejpam-3575	95	39	b	b	X
ejpam-3575	95	40	,	,	PUNCT
ejpam-3575	95	41	(	(	PUNCT
ejpam-3575	95	42	0.7	0.7	NUM
ejpam-3575	95	43	,	,	PUNCT
ejpam-3575	95	44	0.8	0.8	NUM
ejpam-3575	95	45	]	]	PUNCT
ejpam-3575	95	46	)	)	PUNCT
ejpam-3575	95	47	,	,	PUNCT
ejpam-3575	95	48	(	(	PUNCT
ejpam-3575	95	49	c	c	X
ejpam-3575	95	50	,	,	PUNCT
ejpam-3575	95	51	{	{	PUNCT
ejpam-3575	95	52	0.5	0.5	NUM
ejpam-3575	95	53	}	}	PUNCT
ejpam-3575	95	54	∪	∪	NOUN
ejpam-3575	95	55	(	(	PUNCT
ejpam-3575	95	56	0.7	0.7	NUM
ejpam-3575	95	57	,	,	PUNCT
ejpam-3575	95	58	0.9	0.9	NUM
ejpam-3575	95	59	)	)	PUNCT
ejpam-3575	95	60	)	)	PUNCT
ejpam-3575	95	61	,	,	PUNCT
ejpam-3575	95	62	(	(	PUNCT
ejpam-3575	95	63	d	d	X
ejpam-3575	95	64	,	,	PUNCT
ejpam-3575	95	65	[	[	X
ejpam-3575	95	66	0.1	0.1	NUM
ejpam-3575	95	67	,	,	PUNCT
ejpam-3575	95	68	0.5	0.5	NUM
ejpam-3575	95	69	]	]	PUNCT
ejpam-3575	95	70	)	)	PUNCT
ejpam-3575	95	71	}	}	PUNCT
ejpam-3575	95	72	.	.	PUNCT
ejpam-3575	96	1	note	note	VERB
ejpam-3575	96	2	that	that	SCONJ
ejpam-3575	96	3	inf	inf	NOUN
ejpam-3575	96	4	h(0	h(0	PROPN
ejpam-3575	96	5	)	)	PUNCT
ejpam-3575	96	6	=	=	SYM
ejpam-3575	96	7	0.8	0.8	NUM
ejpam-3575	96	8	,	,	PUNCT
ejpam-3575	96	9	inf	inf	PROPN
ejpam-3575	96	10	h(a	h(a	PROPN
ejpam-3575	96	11	)	)	PUNCT
ejpam-3575	97	1	=	=	NOUN
ejpam-3575	97	2	0.2	0.2	NUM
ejpam-3575	97	3	,	,	PUNCT
ejpam-3575	97	4	inf	inf	NOUN
ejpam-3575	97	5	h(b	h(b	PROPN
ejpam-3575	97	6	)	)	PUNCT
ejpam-3575	97	7	=	=	SYM
ejpam-3575	97	8	0.7	0.7	NUM
ejpam-3575	97	9	,	,	PUNCT
ejpam-3575	97	10	inf	inf	NOUN
ejpam-3575	97	11	h(c	h(c	PROPN
ejpam-3575	97	12	)	)	PUNCT
ejpam-3575	97	13	=	=	SYM
ejpam-3575	97	14	0.5	0.5	NUM
ejpam-3575	97	15	and	and	CCONJ
ejpam-3575	97	16	inf	inf	PROPN
ejpam-3575	97	17	h(d	h(d	PROPN
ejpam-3575	97	18	)	)	PUNCT
ejpam-3575	97	19	=	=	PUNCT
ejpam-3575	97	20	0.1	0.1	NUM
ejpam-3575	97	21	.	.	PUNCT
ejpam-3575	98	1	it	it	PRON
ejpam-3575	98	2	is	be	AUX
ejpam-3575	98	3	easy	easy	ADJ
ejpam-3575	98	4	to	to	PART
ejpam-3575	98	5	check	check	VERB
ejpam-3575	98	6	that	that	DET
ejpam-3575	98	7	h	h	NOUN
ejpam-3575	98	8	:	:	PUNCT
ejpam-3575	98	9	=	=	SYM
ejpam-3575	98	10	{	{	PUNCT
ejpam-3575	98	11	(	(	PUNCT
ejpam-3575	98	12	x	x	NOUN
ejpam-3575	98	13	,	,	PUNCT
ejpam-3575	98	14	h(x	h(x	PROPN
ejpam-3575	98	15	)	)	PUNCT
ejpam-3575	98	16	)	)	PUNCT
ejpam-3575	99	1	|	|	ADV
ejpam-3575	99	2	x	x	SYM
ejpam-3575	99	3	∈	∈	NOUN
ejpam-3575	99	4	x	x	X
ejpam-3575	99	5	}	}	PUNCT
ejpam-3575	99	6	is	be	AUX
ejpam-3575	99	7	an	an	DET
ejpam-3575	99	8	inf	inf	ADJ
ejpam-3575	99	9	-	-	PUNCT
ejpam-3575	99	10	hesitant	hesitant	ADJ
ejpam-3575	99	11	fuzzy	fuzzy	ADJ
ejpam-3575	99	12	subalgebra	subalgebra	NOUN
ejpam-3575	99	13	of	of	ADP
ejpam-3575	99	14	x.	x.	NOUN
ejpam-3575	99	15	(	(	PUNCT
ejpam-3575	99	16	3	3	X
ejpam-3575	99	17	)	)	PUNCT
ejpam-3575	99	18	consider	consider	VERB
ejpam-3575	99	19	a	a	DET
ejpam-3575	99	20	bci	bci	NOUN
ejpam-3575	99	21	-	-	NOUN
ejpam-3575	99	22	algebra	algebra	NOUN
ejpam-3575	99	23	x	x	PUNCT
ejpam-3575	99	24	=	=	SYM
ejpam-3575	99	25	{	{	PUNCT
ejpam-3575	99	26	0	0	NUM
ejpam-3575	99	27	,	,	PUNCT
ejpam-3575	99	28	1	1	NUM
ejpam-3575	99	29	,	,	PUNCT
ejpam-3575	99	30	a	a	DET
ejpam-3575	99	31	,	,	PUNCT
ejpam-3575	99	32	b	b	NOUN
ejpam-3575	99	33	,	,	PUNCT
ejpam-3575	99	34	c	c	NOUN
ejpam-3575	99	35	}	}	PUNCT
ejpam-3575	99	36	with	with	ADP
ejpam-3575	99	37	the	the	DET
ejpam-3575	99	38	following	follow	VERB
ejpam-3575	99	39	cayley	cayley	ADJ
ejpam-3575	99	40	table	table	NOUN
ejpam-3575	99	41	.	.	PUNCT
ejpam-3575	100	1	∗	∗	NOUN
ejpam-3575	100	2	0	0	NUM
ejpam-3575	100	3	1	1	NUM
ejpam-3575	100	4	a	a	DET
ejpam-3575	100	5	b	b	NOUN
ejpam-3575	100	6	c	c	NOUN
ejpam-3575	100	7	0	0	NUM
ejpam-3575	100	8	0	0	NUM
ejpam-3575	100	9	0	0	NUM
ejpam-3575	101	1	c	c	NOUN
ejpam-3575	101	2	c	c	NOUN
ejpam-3575	101	3	a	a	DET
ejpam-3575	101	4	1	1	NUM
ejpam-3575	101	5	1	1	NUM
ejpam-3575	101	6	0	0	NUM
ejpam-3575	101	7	c	c	NOUN
ejpam-3575	101	8	c	c	NOUN
ejpam-3575	101	9	a	a	DET
ejpam-3575	101	10	a	a	PRON
ejpam-3575	101	11	a	a	PRON
ejpam-3575	101	12	a	a	PRON
ejpam-3575	101	13	0	0	NUM
ejpam-3575	101	14	0	0	NUM
ejpam-3575	102	1	c	c	PROPN
ejpam-3575	102	2	b	b	PROPN
ejpam-3575	102	3	b	b	PROPN
ejpam-3575	102	4	a	a	DET
ejpam-3575	102	5	1	1	NUM
ejpam-3575	102	6	0	0	NUM
ejpam-3575	102	7	c	c	NOUN
ejpam-3575	102	8	c	c	NOUN
ejpam-3575	102	9	c	c	NOUN
ejpam-3575	102	10	c	c	PROPN
ejpam-3575	102	11	a	a	DET
ejpam-3575	102	12	a	a	DET
ejpam-3575	102	13	0	0	NUM
ejpam-3575	102	14	let	let	NOUN
ejpam-3575	102	15	h	h	NOUN
ejpam-3575	102	16	:	:	PUNCT
ejpam-3575	102	17	=	=	SYM
ejpam-3575	102	18	{	{	PUNCT
ejpam-3575	102	19	(	(	PUNCT
ejpam-3575	102	20	x	x	NOUN
ejpam-3575	102	21	,	,	PUNCT
ejpam-3575	102	22	h(x	h(x	PROPN
ejpam-3575	102	23	)	)	PUNCT
ejpam-3575	102	24	)	)	PUNCT
ejpam-3575	103	1	|	|	ADV
ejpam-3575	103	2	x	x	SYM
ejpam-3575	103	3	∈	∈	NOUN
ejpam-3575	103	4	x	x	VERB
ejpam-3575	103	5	}	}	PUNCT
ejpam-3575	103	6	be	be	AUX
ejpam-3575	103	7	a	a	DET
ejpam-3575	103	8	hesitant	hesitant	ADJ
ejpam-3575	103	9	fuzzy	fuzzy	ADJ
ejpam-3575	103	10	set	set	NOUN
ejpam-3575	103	11	on	on	ADP
ejpam-3575	103	12	x	x	PUNCT
ejpam-3575	103	13	defined	define	VERB
ejpam-3575	103	14	by	by	ADP
ejpam-3575	103	15	h	h	NOUN
ejpam-3575	103	16	=	=	SYM
ejpam-3575	103	17	{	{	PUNCT
ejpam-3575	103	18	(	(	PUNCT
ejpam-3575	103	19	0	0	NUM
ejpam-3575	103	20	,	,	PUNCT
ejpam-3575	103	21	[	[	X
ejpam-3575	103	22	0.8	0.8	NUM
ejpam-3575	103	23	,	,	PUNCT
ejpam-3575	103	24	0.9	0.9	NUM
ejpam-3575	103	25	]	]	PUNCT
ejpam-3575	103	26	)	)	PUNCT
ejpam-3575	103	27	,	,	PUNCT
ejpam-3575	103	28	(	(	PUNCT
ejpam-3575	103	29	1	1	NUM
ejpam-3575	103	30	,	,	PUNCT
ejpam-3575	103	31	(	(	PUNCT
ejpam-3575	103	32	0.6	0.6	NUM
ejpam-3575	103	33	,	,	PUNCT
ejpam-3575	103	34	0.7	0.7	NUM
ejpam-3575	103	35	]	]	PUNCT
ejpam-3575	103	36	)	)	PUNCT
ejpam-3575	103	37	,	,	PUNCT
ejpam-3575	103	38	(	(	PUNCT
ejpam-3575	103	39	a	a	X
ejpam-3575	103	40	,	,	PUNCT
ejpam-3575	103	41	[	[	X
ejpam-3575	103	42	0.5	0.5	NUM
ejpam-3575	103	43	,	,	PUNCT
ejpam-3575	103	44	0.6	0.6	NUM
ejpam-3575	103	45	]	]	PUNCT
ejpam-3575	103	46	)	)	PUNCT
ejpam-3575	103	47	,	,	PUNCT
ejpam-3575	103	48	(	(	PUNCT
ejpam-3575	103	49	b	b	X
ejpam-3575	103	50	,	,	PUNCT
ejpam-3575	103	51	[	[	X
ejpam-3575	103	52	0.5	0.5	NUM
ejpam-3575	103	53	,	,	PUNCT
ejpam-3575	103	54	0.6	0.6	NUM
ejpam-3575	103	55	]	]	PUNCT
ejpam-3575	103	56	)	)	PUNCT
ejpam-3575	103	57	,	,	PUNCT
ejpam-3575	103	58	(	(	PUNCT
ejpam-3575	103	59	c	c	X
ejpam-3575	103	60	,	,	PUNCT
ejpam-3575	103	61	[	[	X
ejpam-3575	103	62	0.3	0.3	NUM
ejpam-3575	103	63	,	,	PUNCT
ejpam-3575	103	64	0.7	0.7	NUM
ejpam-3575	103	65	]	]	PUNCT
ejpam-3575	103	66	)	)	PUNCT
ejpam-3575	103	67	}	}	PUNCT
ejpam-3575	103	68	.	.	PUNCT
ejpam-3575	104	1	then	then	ADV
ejpam-3575	104	2	h	h	NOUN
ejpam-3575	104	3	:	:	PUNCT
ejpam-3575	104	4	=	=	SYM
ejpam-3575	104	5	{	{	PUNCT
ejpam-3575	104	6	(	(	PUNCT
ejpam-3575	104	7	x	x	NOUN
ejpam-3575	104	8	,	,	PUNCT
ejpam-3575	104	9	h(x	h(x	PROPN
ejpam-3575	104	10	)	)	PUNCT
ejpam-3575	104	11	)	)	PUNCT
ejpam-3575	105	1	|	|	ADV
ejpam-3575	105	2	x	x	SYM
ejpam-3575	105	3	∈	∈	NOUN
ejpam-3575	105	4	x	x	X
ejpam-3575	105	5	}	}	PUNCT
ejpam-3575	105	6	is	be	AUX
ejpam-3575	105	7	a	a	DET
ejpam-3575	105	8	d1	d1	NOUN
ejpam-3575	105	9	-	-	PUNCT
ejpam-3575	105	10	inf	inf	ADJ
ejpam-3575	105	11	-	-	PUNCT
ejpam-3575	105	12	hesitant	hesitant	ADJ
ejpam-3575	105	13	fuzzy	fuzzy	ADJ
ejpam-3575	105	14	subalgebra	subalgebra	NOUN
ejpam-3575	105	15	of	of	ADP
ejpam-3575	105	16	x	x	PUNCT
ejpam-3575	105	17	with	with	ADP
ejpam-3575	105	18	d1	d1	NOUN
ejpam-3575	105	19	:	:	PUNCT
ejpam-3575	105	20	=	=	PUNCT
ejpam-3575	106	1	[	[	X
ejpam-3575	106	2	0.55	0.55	NUM
ejpam-3575	106	3	,	,	PUNCT
ejpam-3575	106	4	0.65	0.65	NUM
ejpam-3575	106	5	]	]	PUNCT
ejpam-3575	106	6	.	.	PUNCT
ejpam-3575	107	1	but	but	CCONJ
ejpam-3575	107	2	it	it	PRON
ejpam-3575	107	3	is	be	AUX
ejpam-3575	107	4	not	not	PART
ejpam-3575	107	5	a	a	DET
ejpam-3575	107	6	d2	d2	NOUN
ejpam-3575	107	7	-	-	PUNCT
ejpam-3575	107	8	inf	inf	ADJ
ejpam-3575	107	9	-	-	PUNCT
ejpam-3575	107	10	hesitant	hesitant	ADJ
ejpam-3575	107	11	fuzzy	fuzzy	ADJ
ejpam-3575	107	12	subalgebra	subalgebra	NOUN
ejpam-3575	107	13	of	of	ADP
ejpam-3575	107	14	x	x	PUNCT
ejpam-3575	107	15	with	with	ADP
ejpam-3575	107	16	d2	d2	PROPN
ejpam-3575	107	17	:	:	PUNCT
ejpam-3575	107	18	=	=	PUNCT
ejpam-3575	108	1	[	[	X
ejpam-3575	108	2	0.4	0.4	NUM
ejpam-3575	108	3	,	,	PUNCT
ejpam-3575	108	4	0.6	0.6	NUM
ejpam-3575	108	5	]	]	PUNCT
ejpam-3575	108	6	since	since	SCONJ
ejpam-3575	108	7	inf[h;d2	inf[h;d2	VERB
ejpam-3575	108	8	]	]	X
ejpam-3575	108	9	=	=	SYM
ejpam-3575	108	10	{	{	PUNCT
ejpam-3575	108	11	0	0	NUM
ejpam-3575	108	12	,	,	PUNCT
ejpam-3575	108	13	1	1	NUM
ejpam-3575	108	14	,	,	PUNCT
ejpam-3575	108	15	a	a	DET
ejpam-3575	108	16	,	,	PUNCT
ejpam-3575	108	17	b	b	NOUN
ejpam-3575	108	18	}	}	PUNCT
ejpam-3575	108	19	is	be	AUX
ejpam-3575	108	20	not	not	PART
ejpam-3575	108	21	a	a	DET
ejpam-3575	108	22	subalgebra	subalgebra	NOUN
ejpam-3575	108	23	of	of	ADP
ejpam-3575	108	24	x.	x.	NOUN
ejpam-3575	108	25	(	(	PUNCT
ejpam-3575	108	26	4	4	X
ejpam-3575	108	27	)	)	PUNCT
ejpam-3575	108	28	consider	consider	VERB
ejpam-3575	108	29	a	a	DET
ejpam-3575	108	30	bck	bck	NOUN
ejpam-3575	108	31	-	-	PUNCT
ejpam-3575	108	32	algebra	algebra	NOUN
ejpam-3575	108	33	x	x	PUNCT
ejpam-3575	108	34	=	=	SYM
ejpam-3575	108	35	{	{	PUNCT
ejpam-3575	108	36	0	0	NUM
ejpam-3575	108	37	,	,	PUNCT
ejpam-3575	108	38	a	a	DET
ejpam-3575	108	39	,	,	PUNCT
ejpam-3575	108	40	b	b	NOUN
ejpam-3575	108	41	,	,	PUNCT
ejpam-3575	108	42	c	c	NOUN
ejpam-3575	108	43	,	,	PUNCT
ejpam-3575	108	44	d	d	NOUN
ejpam-3575	108	45	}	}	PUNCT
ejpam-3575	108	46	with	with	ADP
ejpam-3575	108	47	the	the	DET
ejpam-3575	108	48	following	follow	VERB
ejpam-3575	108	49	cayley	cayley	ADJ
ejpam-3575	108	50	table	table	NOUN
ejpam-3575	108	51	.	.	PUNCT
ejpam-3575	109	1	∗	∗	NOUN
ejpam-3575	109	2	0	0	NUM
ejpam-3575	110	1	a	a	DET
ejpam-3575	110	2	b	b	NOUN
ejpam-3575	110	3	c	c	NOUN
ejpam-3575	110	4	d	d	NOUN
ejpam-3575	110	5	0	0	NUM
ejpam-3575	110	6	0	0	NUM
ejpam-3575	110	7	0	0	NUM
ejpam-3575	110	8	0	0	NUM
ejpam-3575	110	9	0	0	NUM
ejpam-3575	110	10	0	0	NUM
ejpam-3575	110	11	a	a	DET
ejpam-3575	110	12	a	a	DET
ejpam-3575	110	13	0	0	NUM
ejpam-3575	110	14	0	0	NUM
ejpam-3575	110	15	0	0	NUM
ejpam-3575	111	1	a	a	DET
ejpam-3575	111	2	b	b	PROPN
ejpam-3575	111	3	b	b	PROPN
ejpam-3575	111	4	a	a	PRON
ejpam-3575	111	5	0	0	NUM
ejpam-3575	111	6	0	0	NUM
ejpam-3575	111	7	b	b	NOUN
ejpam-3575	111	8	c	c	NOUN
ejpam-3575	111	9	c	c	PROPN
ejpam-3575	111	10	b	b	PROPN
ejpam-3575	111	11	a	a	DET
ejpam-3575	111	12	0	0	NUM
ejpam-3575	111	13	c	c	NOUN
ejpam-3575	112	1	d	d	PROPN
ejpam-3575	112	2	d	d	PROPN
ejpam-3575	112	3	d	d	PROPN
ejpam-3575	112	4	d	d	PROPN
ejpam-3575	112	5	d	d	PROPN
ejpam-3575	112	6	0	0	PUNCT
ejpam-3575	112	7	let	let	VERB
ejpam-3575	112	8	h	h	NOUN
ejpam-3575	112	9	:	:	PUNCT
ejpam-3575	112	10	=	=	SYM
ejpam-3575	112	11	{	{	PUNCT
ejpam-3575	112	12	(	(	PUNCT
ejpam-3575	112	13	x	x	NOUN
ejpam-3575	112	14	,	,	PUNCT
ejpam-3575	112	15	h(x	h(x	PROPN
ejpam-3575	112	16	)	)	PUNCT
ejpam-3575	112	17	)	)	PUNCT
ejpam-3575	113	1	|	|	ADV
ejpam-3575	113	2	x	x	SYM
ejpam-3575	113	3	∈	∈	NOUN
ejpam-3575	113	4	x	x	VERB
ejpam-3575	113	5	}	}	PUNCT
ejpam-3575	113	6	be	be	AUX
ejpam-3575	113	7	a	a	DET
ejpam-3575	113	8	hesitant	hesitant	ADJ
ejpam-3575	113	9	fuzzy	fuzzy	ADJ
ejpam-3575	113	10	set	set	NOUN
ejpam-3575	113	11	on	on	ADP
ejpam-3575	113	12	x	x	PUNCT
ejpam-3575	113	13	defined	define	VERB
ejpam-3575	113	14	by	by	ADP
ejpam-3575	113	15	h	h	NOUN
ejpam-3575	113	16	=	=	SYM
ejpam-3575	113	17	{	{	PUNCT
ejpam-3575	113	18	(	(	PUNCT
ejpam-3575	113	19	0	0	NUM
ejpam-3575	113	20	,	,	PUNCT
ejpam-3575	113	21	[	[	X
ejpam-3575	113	22	0.7	0.7	NUM
ejpam-3575	113	23	,	,	PUNCT
ejpam-3575	113	24	0.8	0.8	NUM
ejpam-3575	113	25	]	]	PUNCT
ejpam-3575	113	26	)	)	PUNCT
ejpam-3575	113	27	,	,	PUNCT
ejpam-3575	113	28	(	(	PUNCT
ejpam-3575	113	29	a	a	X
ejpam-3575	113	30	,	,	PUNCT
ejpam-3575	113	31	(	(	PUNCT
ejpam-3575	113	32	0.6	0.6	NUM
ejpam-3575	113	33	,	,	PUNCT
ejpam-3575	113	34	0.7	0.7	NUM
ejpam-3575	113	35	]	]	PUNCT
ejpam-3575	113	36	)	)	PUNCT
ejpam-3575	113	37	,	,	PUNCT
ejpam-3575	113	38	(	(	PUNCT
ejpam-3575	113	39	b	b	X
ejpam-3575	113	40	,	,	PUNCT
ejpam-3575	113	41	[	[	X
ejpam-3575	113	42	0.3	0.3	NUM
ejpam-3575	113	43	,	,	PUNCT
ejpam-3575	113	44	0.6	0.6	NUM
ejpam-3575	113	45	]	]	PUNCT
ejpam-3575	113	46	)	)	PUNCT
ejpam-3575	113	47	,	,	PUNCT
ejpam-3575	113	48	(	(	PUNCT
ejpam-3575	113	49	c	c	X
ejpam-3575	113	50	,	,	PUNCT
ejpam-3575	113	51	[	[	X
ejpam-3575	113	52	0.5	0.5	NUM
ejpam-3575	113	53	,	,	PUNCT
ejpam-3575	113	54	0.7	0.7	NUM
ejpam-3575	113	55	]	]	PUNCT
ejpam-3575	113	56	)	)	PUNCT
ejpam-3575	113	57	,	,	PUNCT
ejpam-3575	113	58	(	(	PUNCT
ejpam-3575	113	59	d	d	X
ejpam-3575	113	60	,	,	PUNCT
ejpam-3575	113	61	[	[	X
ejpam-3575	113	62	0.2	0.2	NUM
ejpam-3575	113	63	,	,	PUNCT
ejpam-3575	113	64	0.4	0.4	NUM
ejpam-3575	113	65	]	]	PUNCT
ejpam-3575	113	66	)	)	PUNCT
ejpam-3575	113	67	}	}	PUNCT
ejpam-3575	113	68	.	.	PUNCT
ejpam-3575	114	1	then	then	ADV
ejpam-3575	114	2	h	h	NOUN
ejpam-3575	114	3	:	:	PUNCT
ejpam-3575	114	4	=	=	SYM
ejpam-3575	114	5	{	{	PUNCT
ejpam-3575	114	6	(	(	PUNCT
ejpam-3575	114	7	x	x	NOUN
ejpam-3575	114	8	,	,	PUNCT
ejpam-3575	114	9	h(x	h(x	PROPN
ejpam-3575	114	10	)	)	PUNCT
ejpam-3575	114	11	)	)	PUNCT
ejpam-3575	115	1	|	|	ADV
ejpam-3575	115	2	x	x	SYM
ejpam-3575	115	3	∈	∈	NOUN
ejpam-3575	115	4	x	x	X
ejpam-3575	115	5	}	}	PUNCT
ejpam-3575	115	6	is	be	AUX
ejpam-3575	115	7	a	a	DET
ejpam-3575	115	8	d1	d1	NOUN
ejpam-3575	115	9	-	-	PUNCT
ejpam-3575	115	10	inf	inf	ADJ
ejpam-3575	115	11	-	-	PUNCT
ejpam-3575	115	12	hesitant	hesitant	ADJ
ejpam-3575	115	13	fuzzy	fuzzy	ADJ
ejpam-3575	115	14	subalgebra	subalgebra	NOUN
ejpam-3575	115	15	of	of	ADP
ejpam-3575	115	16	x	x	PUNCT
ejpam-3575	115	17	with	with	ADP
ejpam-3575	115	18	d1	d1	NOUN
ejpam-3575	115	19	:	:	PUNCT
ejpam-3575	115	20	=	=	PUNCT
ejpam-3575	116	1	[	[	X
ejpam-3575	116	2	0.2	0.2	NUM
ejpam-3575	116	3	,	,	PUNCT
ejpam-3575	116	4	0.4	0.4	NUM
ejpam-3575	116	5	]	]	PUNCT
ejpam-3575	116	6	.	.	PUNCT
ejpam-3575	117	1	if	if	SCONJ
ejpam-3575	117	2	we	we	PRON
ejpam-3575	117	3	take	take	VERB
ejpam-3575	117	4	d2	d2	NOUN
ejpam-3575	117	5	:	:	PUNCT
ejpam-3575	117	6	=	=	SYM
ejpam-3575	117	7	(	(	PUNCT
ejpam-3575	117	8	0.4	0.4	NUM
ejpam-3575	117	9	,	,	PUNCT
ejpam-3575	117	10	0.6	0.6	NUM
ejpam-3575	117	11	]	]	PUNCT
ejpam-3575	117	12	,	,	PUNCT
ejpam-3575	117	13	then	then	ADV
ejpam-3575	117	14	inf[h;d2	inf[h;d2	ADV
ejpam-3575	117	15	]	]	X
ejpam-3575	117	16	=	=	SYM
ejpam-3575	117	17	{	{	PUNCT
ejpam-3575	117	18	0	0	NUM
ejpam-3575	117	19	,	,	PUNCT
ejpam-3575	117	20	a	a	DET
ejpam-3575	117	21	,	,	PUNCT
ejpam-3575	117	22	c	c	NOUN
ejpam-3575	117	23	}	}	PUNCT
ejpam-3575	117	24	which	which	PRON
ejpam-3575	117	25	is	be	AUX
ejpam-3575	117	26	not	not	PART
ejpam-3575	117	27	a	a	DET
ejpam-3575	117	28	subalgebra	subalgebra	NOUN
ejpam-3575	117	29	of	of	ADP
ejpam-3575	117	30	x.	x.	NOUN
ejpam-3575	117	31	hence	hence	NOUN
ejpam-3575	117	32	h	h	NOUN
ejpam-3575	117	33	:	:	PUNCT
ejpam-3575	117	34	=	=	SYM
ejpam-3575	117	35	{	{	PUNCT
ejpam-3575	117	36	(	(	PUNCT
ejpam-3575	117	37	x	x	NOUN
ejpam-3575	117	38	,	,	PUNCT
ejpam-3575	117	39	h(x	h(x	PROPN
ejpam-3575	117	40	)	)	PUNCT
ejpam-3575	117	41	)	)	PUNCT
ejpam-3575	118	1	|	|	ADV
ejpam-3575	118	2	x	x	SYM
ejpam-3575	118	3	∈	∈	NOUN
ejpam-3575	118	4	x	x	X
ejpam-3575	118	5	}	}	PUNCT
ejpam-3575	118	6	is	be	AUX
ejpam-3575	118	7	not	not	PART
ejpam-3575	118	8	a	a	DET
ejpam-3575	118	9	d2	d2	NOUN
ejpam-3575	118	10	-	-	PUNCT
ejpam-3575	118	11	inf	inf	ADJ
ejpam-3575	118	12	-	-	PUNCT
ejpam-3575	118	13	hesitant	hesitant	ADJ
ejpam-3575	118	14	fuzzy	fuzzy	ADJ
ejpam-3575	118	15	subalgebra	subalgebra	NOUN
ejpam-3575	118	16	of	of	ADP
ejpam-3575	118	17	x.	x.	PROPN
ejpam-3575	118	18	g.	g.	PROPN
ejpam-3575	118	19	muhiuddin	muhiuddin	PROPN
ejpam-3575	118	20	et	et	PROPN
ejpam-3575	118	21	al	al	PROPN
ejpam-3575	118	22	.	.	PUNCT
ejpam-3575	118	23	/	/	SYM
ejpam-3575	118	24	eur	eur	PROPN
ejpam-3575	118	25	.	.	PUNCT
ejpam-3575	119	1	j.	j.	PROPN
ejpam-3575	119	2	pure	pure	PROPN
ejpam-3575	119	3	appl	appl	PROPN
ejpam-3575	119	4	.	.	PROPN
ejpam-3575	119	5	math	math	PROPN
ejpam-3575	119	6	,	,	PUNCT
ejpam-3575	119	7	13	13	NUM
ejpam-3575	119	8	(	(	PUNCT
ejpam-3575	119	9	1	1	NUM
ejpam-3575	119	10	)	)	PUNCT
ejpam-3575	119	11	(	(	PUNCT
ejpam-3575	119	12	2020	2020	NUM
ejpam-3575	119	13	)	)	PUNCT
ejpam-3575	119	14	,	,	PUNCT
ejpam-3575	119	15	9	9	NUM
ejpam-3575	119	16	-	-	SYM
ejpam-3575	119	17	18	18	NUM
ejpam-3575	119	18	14	14	NUM
ejpam-3575	119	19	theorem	theorem	NOUN
ejpam-3575	119	20	1	1	NUM
ejpam-3575	119	21	.	.	PUNCT
ejpam-3575	120	1	a	a	DET
ejpam-3575	120	2	hesitant	hesitant	ADJ
ejpam-3575	120	3	fuzzy	fuzzy	ADJ
ejpam-3575	120	4	set	set	NOUN
ejpam-3575	120	5	h	h	NOUN
ejpam-3575	120	6	:	:	PUNCT
ejpam-3575	120	7	=	=	SYM
ejpam-3575	120	8	{	{	PUNCT
ejpam-3575	120	9	(	(	PUNCT
ejpam-3575	120	10	x	x	NOUN
ejpam-3575	120	11	,	,	PUNCT
ejpam-3575	120	12	h(x	h(x	PROPN
ejpam-3575	120	13	)	)	PUNCT
ejpam-3575	120	14	)	)	PUNCT
ejpam-3575	121	1	|	|	ADV
ejpam-3575	121	2	x	x	SYM
ejpam-3575	121	3	∈	∈	NOUN
ejpam-3575	121	4	x	x	X
ejpam-3575	121	5	}	}	PUNCT
ejpam-3575	121	6	on	on	ADP
ejpam-3575	121	7	a	a	DET
ejpam-3575	121	8	bck	bck	VERB
ejpam-3575	121	9	/	/	SYM
ejpam-3575	121	10	bci	bci	NOUN
ejpam-3575	121	11	-	-	NOUN
ejpam-3575	121	12	algebra	algebra	NOUN
ejpam-3575	121	13	x	x	PUNCT
ejpam-3575	121	14	is	be	AUX
ejpam-3575	121	15	an	an	DET
ejpam-3575	121	16	inf	inf	ADJ
ejpam-3575	121	17	-	-	PUNCT
ejpam-3575	121	18	hesitant	hesitant	ADJ
ejpam-3575	121	19	fuzzy	fuzzy	ADJ
ejpam-3575	121	20	subalgebra	subalgebra	NOUN
ejpam-3575	121	21	of	of	ADP
ejpam-3575	121	22	x	x	PUNCT
ejpam-3575	121	23	if	if	SCONJ
ejpam-3575	121	24	and	and	CCONJ
ejpam-3575	121	25	only	only	ADV
ejpam-3575	121	26	if	if	SCONJ
ejpam-3575	121	27	the	the	DET
ejpam-3575	121	28	following	follow	VERB
ejpam-3575	121	29	assertion	assertion	NOUN
ejpam-3575	121	30	is	be	AUX
ejpam-3575	121	31	valid	valid	ADJ
ejpam-3575	121	32	:	:	PUNCT
ejpam-3575	121	33	(	(	PUNCT
ejpam-3575	121	34	∀x	∀x	X
ejpam-3575	121	35	,	,	PUNCT
ejpam-3575	121	36	y	y	PROPN
ejpam-3575	121	37	∈	∈	PROPN
ejpam-3575	121	38	x	x	X
ejpam-3575	121	39	)	)	PUNCT
ejpam-3575	121	40	(	(	PUNCT
ejpam-3575	121	41	inf	inf	PROPN
ejpam-3575	121	42	h(x	h(x	PROPN
ejpam-3575	121	43	∗	∗	PROPN
ejpam-3575	121	44	y	y	PROPN
ejpam-3575	121	45	)	)	PUNCT
ejpam-3575	121	46	≥	≥	NOUN
ejpam-3575	121	47	min{inf	min{inf	PROPN
ejpam-3575	121	48	h(x	h(x	PROPN
ejpam-3575	121	49	)	)	PUNCT
ejpam-3575	121	50	,	,	PUNCT
ejpam-3575	121	51	inf	inf	PROPN
ejpam-3575	121	52	h(y	h(y	ADV
ejpam-3575	121	53	)	)	PUNCT
ejpam-3575	121	54	}	}	PUNCT
ejpam-3575	121	55	)	)	PUNCT
ejpam-3575	121	56	.	.	PUNCT
ejpam-3575	122	1	(	(	PUNCT
ejpam-3575	122	2	15	15	X
ejpam-3575	122	3	)	)	PUNCT
ejpam-3575	122	4	proof	proof	NOUN
ejpam-3575	122	5	.	.	PUNCT
ejpam-3575	123	1	assume	assume	VERB
ejpam-3575	123	2	that	that	SCONJ
ejpam-3575	123	3	h	h	NOUN
ejpam-3575	123	4	:	:	PUNCT
ejpam-3575	123	5	=	=	SYM
ejpam-3575	123	6	{	{	PUNCT
ejpam-3575	123	7	(	(	PUNCT
ejpam-3575	123	8	x	x	NOUN
ejpam-3575	123	9	,	,	PUNCT
ejpam-3575	123	10	h(x	h(x	PROPN
ejpam-3575	123	11	)	)	PUNCT
ejpam-3575	123	12	)	)	PUNCT
ejpam-3575	124	1	|	|	ADV
ejpam-3575	124	2	x	x	SYM
ejpam-3575	124	3	∈	∈	NOUN
ejpam-3575	124	4	x	x	X
ejpam-3575	124	5	}	}	PUNCT
ejpam-3575	124	6	is	be	AUX
ejpam-3575	124	7	an	an	DET
ejpam-3575	124	8	inf	inf	ADJ
ejpam-3575	124	9	-	-	PUNCT
ejpam-3575	124	10	hesitant	hesitant	ADJ
ejpam-3575	124	11	fuzzy	fuzzy	ADJ
ejpam-3575	124	12	subalgebra	subalgebra	NOUN
ejpam-3575	124	13	of	of	ADP
ejpam-3575	124	14	x.	x.	NOUN
ejpam-3575	124	15	assume	assume	VERB
ejpam-3575	124	16	that	that	SCONJ
ejpam-3575	124	17	there	there	PRON
ejpam-3575	124	18	exists	exist	VERB
ejpam-3575	124	19	q	q	PROPN
ejpam-3575	124	20	∈	∈	PROPN
ejpam-3575	124	21	p	p	NOUN
ejpam-3575	124	22	∗([0	∗([0	NOUN
ejpam-3575	124	23	,	,	PUNCT
ejpam-3575	124	24	1	1	NUM
ejpam-3575	124	25	]	]	PUNCT
ejpam-3575	124	26	)	)	PUNCT
ejpam-3575	124	27	such	such	ADJ
ejpam-3575	124	28	that	that	DET
ejpam-3575	124	29	inf	inf	PROPN
ejpam-3575	124	30	h(x	h(x	PROPN
ejpam-3575	124	31	∗	∗	PROPN
ejpam-3575	124	32	y	y	PROPN
ejpam-3575	124	33	)	)	PUNCT
ejpam-3575	124	34	<	<	X
ejpam-3575	124	35	inf	inf	PROPN
ejpam-3575	124	36	q	q	PROPN
ejpam-3575	124	37	≤	≤	PROPN
ejpam-3575	124	38	min{inf	min{inf	PROPN
ejpam-3575	124	39	h(x	h(x	PROPN
ejpam-3575	124	40	)	)	PUNCT
ejpam-3575	124	41	,	,	PUNCT
ejpam-3575	124	42	inf	inf	PROPN
ejpam-3575	124	43	h(y	h(y	ADV
ejpam-3575	124	44	)	)	PUNCT
ejpam-3575	124	45	}	}	PUNCT
ejpam-3575	124	46	.	.	PUNCT
ejpam-3575	125	1	then	then	ADV
ejpam-3575	125	2	x	x	X
ejpam-3575	125	3	,	,	PUNCT
ejpam-3575	125	4	y	y	PROPN
ejpam-3575	125	5	∈	∈	PROPN
ejpam-3575	125	6	inf[h;d	inf[h;d	NOUN
ejpam-3575	125	7	]	]	PUNCT
ejpam-3575	125	8	and	and	CCONJ
ejpam-3575	125	9	x	x	AUX
ejpam-3575	125	10	∗	∗	PROPN
ejpam-3575	125	11	y	y	PROPN
ejpam-3575	125	12	/∈	/∈	PUNCT
ejpam-3575	125	13	inf[h;d	inf[h;d	PROPN
ejpam-3575	125	14	]	]	PUNCT
ejpam-3575	125	15	.	.	PUNCT
ejpam-3575	126	1	this	this	PRON
ejpam-3575	126	2	is	be	AUX
ejpam-3575	126	3	a	a	DET
ejpam-3575	126	4	contradiction	contradiction	NOUN
ejpam-3575	126	5	,	,	PUNCT
ejpam-3575	126	6	and	and	CCONJ
ejpam-3575	126	7	so	so	ADV
ejpam-3575	126	8	inf	inf	PROPN
ejpam-3575	126	9	h(x	h(x	PROPN
ejpam-3575	126	10	∗	∗	PROPN
ejpam-3575	126	11	y	y	PROPN
ejpam-3575	126	12	)	)	PUNCT
ejpam-3575	126	13	≥	≥	NOUN
ejpam-3575	126	14	min{inf	min{inf	PROPN
ejpam-3575	126	15	h(x	h(x	PROPN
ejpam-3575	126	16	)	)	PUNCT
ejpam-3575	126	17	,	,	PUNCT
ejpam-3575	126	18	inf	inf	PROPN
ejpam-3575	126	19	h(y	h(y	ADV
ejpam-3575	126	20	)	)	PUNCT
ejpam-3575	126	21	}	}	PUNCT
ejpam-3575	126	22	for	for	ADP
ejpam-3575	126	23	all	all	DET
ejpam-3575	126	24	x	x	NOUN
ejpam-3575	126	25	,	,	PUNCT
ejpam-3575	126	26	y	y	PROPN
ejpam-3575	126	27	∈	∈	PROPN
ejpam-3575	126	28	x.	x.	NOUN
ejpam-3575	126	29	conversely	conversely	ADV
ejpam-3575	126	30	,	,	PUNCT
ejpam-3575	126	31	suppose	suppose	VERB
ejpam-3575	126	32	that	that	SCONJ
ejpam-3575	126	33	(	(	PUNCT
ejpam-3575	126	34	15	15	NUM
ejpam-3575	126	35	)	)	PUNCT
ejpam-3575	126	36	is	be	AUX
ejpam-3575	126	37	valid	valid	ADJ
ejpam-3575	126	38	.	.	PUNCT
ejpam-3575	127	1	let	let	VERB
ejpam-3575	127	2	d	d	X
ejpam-3575	127	3	∈	∈	PROPN
ejpam-3575	127	4	p	p	PROPN
ejpam-3575	127	5	∗([0	∗([0	NOUN
ejpam-3575	127	6	,	,	PUNCT
ejpam-3575	127	7	1	1	NUM
ejpam-3575	127	8	]	]	PUNCT
ejpam-3575	127	9	)	)	PUNCT
ejpam-3575	127	10	and	and	CCONJ
ejpam-3575	127	11	x	x	X
ejpam-3575	127	12	,	,	PUNCT
ejpam-3575	127	13	y	y	PROPN
ejpam-3575	127	14	∈	∈	PROPN
ejpam-3575	127	15	inf[h;d	inf[h;d	NOUN
ejpam-3575	127	16	]	]	PUNCT
ejpam-3575	127	17	.	.	PUNCT
ejpam-3575	128	1	then	then	ADV
ejpam-3575	128	2	inf	inf	PROPN
ejpam-3575	128	3	h(x	h(x	PROPN
ejpam-3575	128	4	)	)	PUNCT
ejpam-3575	128	5	≥	≥	NOUN
ejpam-3575	128	6	inf	inf	PROPN
ejpam-3575	128	7	d	d	NOUN
ejpam-3575	128	8	and	and	CCONJ
ejpam-3575	128	9	inf	inf	PROPN
ejpam-3575	128	10	h(y	h(y	ADV
ejpam-3575	128	11	)	)	PUNCT
ejpam-3575	128	12	≥	≥	PROPN
ejpam-3575	128	13	inf	inf	PROPN
ejpam-3575	128	14	d.	d.	PROPN
ejpam-3575	128	15	it	it	PRON
ejpam-3575	128	16	follows	follow	VERB
ejpam-3575	128	17	from	from	ADP
ejpam-3575	128	18	(	(	PUNCT
ejpam-3575	128	19	15	15	NUM
ejpam-3575	128	20	)	)	PUNCT
ejpam-3575	128	21	that	that	PRON
ejpam-3575	128	22	inf	inf	NOUN
ejpam-3575	128	23	h(x	h(x	PROPN
ejpam-3575	128	24	∗	∗	PROPN
ejpam-3575	128	25	y	y	PROPN
ejpam-3575	128	26	)	)	PUNCT
ejpam-3575	128	27	≥	≥	NOUN
ejpam-3575	128	28	min{inf	min{inf	PROPN
ejpam-3575	128	29	h(x	h(x	PROPN
ejpam-3575	128	30	)	)	PUNCT
ejpam-3575	128	31	,	,	PUNCT
ejpam-3575	128	32	inf	inf	PROPN
ejpam-3575	128	33	h(y	h(y	ADV
ejpam-3575	128	34	)	)	PUNCT
ejpam-3575	128	35	}	}	PUNCT
ejpam-3575	128	36	≥	≥	NOUN
ejpam-3575	128	37	inf	inf	PROPN
ejpam-3575	128	38	d	d	NOUN
ejpam-3575	128	39	and	and	CCONJ
ejpam-3575	128	40	that	that	SCONJ
ejpam-3575	128	41	x	x	PUNCT
ejpam-3575	128	42	∗	∗	NOUN
ejpam-3575	128	43	y	y	PROPN
ejpam-3575	128	44	∈	∈	PROPN
ejpam-3575	128	45	inf[h;d	inf[h;d	NOUN
ejpam-3575	128	46	]	]	PUNCT
ejpam-3575	128	47	.	.	PUNCT
ejpam-3575	129	1	hence	hence	ADV
ejpam-3575	129	2	the	the	DET
ejpam-3575	129	3	set	set	ADJ
ejpam-3575	129	4	inf[h;d	inf[h;d	NOUN
ejpam-3575	129	5	]	]	PUNCT
ejpam-3575	129	6	is	be	AUX
ejpam-3575	129	7	a	a	DET
ejpam-3575	129	8	subalgebra	subalgebra	NOUN
ejpam-3575	129	9	of	of	ADP
ejpam-3575	129	10	x	x	PRON
ejpam-3575	129	11	,	,	PUNCT
ejpam-3575	129	12	and	and	CCONJ
ejpam-3575	129	13	so	so	ADV
ejpam-3575	129	14	h	h	NOUN
ejpam-3575	129	15	:	:	PUNCT
ejpam-3575	129	16	=	=	SYM
ejpam-3575	129	17	{	{	PUNCT
ejpam-3575	129	18	(	(	PUNCT
ejpam-3575	129	19	x	x	NOUN
ejpam-3575	129	20	,	,	PUNCT
ejpam-3575	129	21	h(x	h(x	PROPN
ejpam-3575	129	22	)	)	PUNCT
ejpam-3575	129	23	)	)	PUNCT
ejpam-3575	130	1	|	|	ADV
ejpam-3575	130	2	x	x	SYM
ejpam-3575	130	3	∈	∈	NOUN
ejpam-3575	130	4	x	x	X
ejpam-3575	130	5	}	}	PUNCT
ejpam-3575	130	6	is	be	AUX
ejpam-3575	130	7	an	an	DET
ejpam-3575	130	8	inf	inf	ADJ
ejpam-3575	130	9	-	-	PUNCT
ejpam-3575	130	10	hesitant	hesitant	ADJ
ejpam-3575	130	11	fuzzy	fuzzy	ADJ
ejpam-3575	130	12	subalgebra	subalgebra	NOUN
ejpam-3575	130	13	of	of	ADP
ejpam-3575	130	14	x.	x.	PROPN
ejpam-3575	130	15	lemma	lemma	PROPN
ejpam-3575	131	1	1	1	X
ejpam-3575	131	2	.	.	PUNCT
ejpam-3575	132	1	if	if	SCONJ
ejpam-3575	132	2	h	h	NOUN
ejpam-3575	132	3	:	:	PUNCT
ejpam-3575	132	4	=	=	SYM
ejpam-3575	132	5	{	{	PUNCT
ejpam-3575	132	6	(	(	PUNCT
ejpam-3575	132	7	x	x	NOUN
ejpam-3575	132	8	,	,	PUNCT
ejpam-3575	132	9	h(x	h(x	PROPN
ejpam-3575	132	10	)	)	PUNCT
ejpam-3575	132	11	)	)	PUNCT
ejpam-3575	133	1	|	|	ADV
ejpam-3575	133	2	x	x	SYM
ejpam-3575	133	3	∈	∈	NOUN
ejpam-3575	133	4	x	x	X
ejpam-3575	133	5	}	}	PUNCT
ejpam-3575	133	6	is	be	AUX
ejpam-3575	133	7	an	an	DET
ejpam-3575	133	8	inf	inf	ADJ
ejpam-3575	133	9	-	-	PUNCT
ejpam-3575	133	10	hesitant	hesitant	ADJ
ejpam-3575	133	11	fuzzy	fuzzy	ADJ
ejpam-3575	133	12	subalgebra	subalgebra	NOUN
ejpam-3575	133	13	of	of	ADP
ejpam-3575	133	14	a	a	DET
ejpam-3575	133	15	bck	bck	NOUN
ejpam-3575	133	16	/	/	SYM
ejpam-3575	133	17	bcialgebra	bcialgebra	NOUN
ejpam-3575	133	18	x	x	X
ejpam-3575	133	19	,	,	PUNCT
ejpam-3575	133	20	then	then	ADV
ejpam-3575	133	21	(	(	PUNCT
ejpam-3575	133	22	∀x	∀x	X
ejpam-3575	133	23	∈	∈	PROPN
ejpam-3575	133	24	x	x	NOUN
ejpam-3575	133	25	)	)	PUNCT
ejpam-3575	133	26	(	(	PUNCT
ejpam-3575	133	27	inf	inf	PROPN
ejpam-3575	133	28	h(0	h(0	PROPN
ejpam-3575	133	29	)	)	PUNCT
ejpam-3575	133	30	≥	≥	NOUN
ejpam-3575	133	31	inf	inf	NOUN
ejpam-3575	133	32	h(x	h(x	PROPN
ejpam-3575	133	33	)	)	PUNCT
ejpam-3575	133	34	)	)	PUNCT
ejpam-3575	133	35	.	.	PUNCT
ejpam-3575	134	1	(	(	PUNCT
ejpam-3575	134	2	16	16	X
ejpam-3575	134	3	)	)	PUNCT
ejpam-3575	134	4	proof	proof	NOUN
ejpam-3575	134	5	.	.	PUNCT
ejpam-3575	135	1	using	use	VERB
ejpam-3575	135	2	(	(	PUNCT
ejpam-3575	135	3	iii	iii	NOUN
ejpam-3575	135	4	)	)	PUNCT
ejpam-3575	135	5	and	and	CCONJ
ejpam-3575	135	6	(	(	PUNCT
ejpam-3575	135	7	15	15	NUM
ejpam-3575	135	8	)	)	PUNCT
ejpam-3575	135	9	,	,	PUNCT
ejpam-3575	135	10	we	we	PRON
ejpam-3575	135	11	have	have	VERB
ejpam-3575	135	12	inf	inf	VERB
ejpam-3575	135	13	h(0	h(0	PROPN
ejpam-3575	135	14	)	)	PUNCT
ejpam-3575	136	1	=	=	PROPN
ejpam-3575	136	2	inf	inf	PROPN
ejpam-3575	136	3	h(x	h(x	PROPN
ejpam-3575	136	4	∗	∗	PROPN
ejpam-3575	136	5	x	x	PROPN
ejpam-3575	136	6	)	)	PUNCT
ejpam-3575	136	7	≥	≥	PROPN
ejpam-3575	136	8	min	min	PROPN
ejpam-3575	136	9	{	{	PUNCT
ejpam-3575	136	10	inf	inf	NOUN
ejpam-3575	136	11	h(x	h(x	PROPN
ejpam-3575	136	12	)	)	PUNCT
ejpam-3575	136	13	,	,	PUNCT
ejpam-3575	136	14	inf	inf	PROPN
ejpam-3575	136	15	h(x	h(x	PROPN
ejpam-3575	136	16	)	)	PUNCT
ejpam-3575	136	17	}	}	PUNCT
ejpam-3575	137	1	=	=	SYM
ejpam-3575	137	2	inf	inf	PROPN
ejpam-3575	137	3	h(x	h(x	PROPN
ejpam-3575	137	4	)	)	PUNCT
ejpam-3575	137	5	for	for	ADP
ejpam-3575	137	6	all	all	DET
ejpam-3575	137	7	x	x	SYM
ejpam-3575	137	8	∈	∈	NOUN
ejpam-3575	137	9	x.	x.	NOUN
ejpam-3575	137	10	proposition	proposition	NOUN
ejpam-3575	137	11	1	1	NUM
ejpam-3575	137	12	.	.	PUNCT
ejpam-3575	138	1	let	let	VERB
ejpam-3575	138	2	h	h	NOUN
ejpam-3575	138	3	:	:	PUNCT
ejpam-3575	138	4	=	=	SYM
ejpam-3575	138	5	{	{	PUNCT
ejpam-3575	138	6	(	(	PUNCT
ejpam-3575	138	7	x	x	NOUN
ejpam-3575	138	8	,	,	PUNCT
ejpam-3575	138	9	h(x	h(x	PROPN
ejpam-3575	138	10	)	)	PUNCT
ejpam-3575	138	11	)	)	PUNCT
ejpam-3575	139	1	|	|	ADV
ejpam-3575	139	2	x	x	SYM
ejpam-3575	139	3	∈	∈	NOUN
ejpam-3575	139	4	x	x	AUX
ejpam-3575	139	5	}	}	PUNCT
ejpam-3575	139	6	be	be	VERB
ejpam-3575	139	7	an	an	DET
ejpam-3575	139	8	inf	inf	ADJ
ejpam-3575	139	9	-	-	PUNCT
ejpam-3575	139	10	hesitant	hesitant	ADJ
ejpam-3575	139	11	fuzzy	fuzzy	ADJ
ejpam-3575	139	12	subalgebra	subalgebra	NOUN
ejpam-3575	139	13	of	of	ADP
ejpam-3575	139	14	a	a	DET
ejpam-3575	139	15	bck	bck	NOUN
ejpam-3575	139	16	-	-	PUNCT
ejpam-3575	139	17	algebra	algebra	NOUN
ejpam-3575	139	18	x.	x.	NOUN
ejpam-3575	139	19	for	for	ADP
ejpam-3575	139	20	any	any	DET
ejpam-3575	139	21	elements	element	NOUN
ejpam-3575	139	22	a1	a1	NOUN
ejpam-3575	139	23	,	,	PUNCT
ejpam-3575	139	24	a2	a2	PROPN
ejpam-3575	139	25	,	,	PUNCT
ejpam-3575	139	26	·	·	PUNCT
ejpam-3575	139	27	·	·	PUNCT
ejpam-3575	139	28	·	·	PUNCT
ejpam-3575	139	29	,	,	PUNCT
ejpam-3575	139	30	an	an	DET
ejpam-3575	139	31	∈	∈	PROPN
ejpam-3575	139	32	x	x	PART
ejpam-3575	139	33	,	,	PUNCT
ejpam-3575	139	34	if	if	SCONJ
ejpam-3575	139	35	there	there	PRON
ejpam-3575	139	36	exists	exist	VERB
ejpam-3575	139	37	ak	ak	PROPN
ejpam-3575	139	38	∈	∈	PROPN
ejpam-3575	139	39	{	{	PUNCT
ejpam-3575	139	40	a1	a1	PROPN
ejpam-3575	139	41	,	,	PUNCT
ejpam-3575	139	42	a2	a2	PROPN
ejpam-3575	139	43	,	,	PUNCT
ejpam-3575	139	44	·	·	PUNCT
ejpam-3575	139	45	·	·	PUNCT
ejpam-3575	139	46	·	·	PUNCT
ejpam-3575	139	47	,	,	PUNCT
ejpam-3575	139	48	an	an	X
ejpam-3575	139	49	}	}	PUNCT
ejpam-3575	139	50	such	such	ADJ
ejpam-3575	139	51	that	that	DET
ejpam-3575	139	52	a1	a1	NOUN
ejpam-3575	139	53	=	=	SYM
ejpam-3575	139	54	ak	ak	PROPN
ejpam-3575	139	55	,	,	PUNCT
ejpam-3575	139	56	then	then	ADV
ejpam-3575	139	57	(	(	PUNCT
ejpam-3575	139	58	∀x	∀x	X
ejpam-3575	139	59	∈	∈	PROPN
ejpam-3575	139	60	x	x	NOUN
ejpam-3575	139	61	)	)	PUNCT
ejpam-3575	139	62	(	(	PUNCT
ejpam-3575	139	63	inf	inf	PROPN
ejpam-3575	139	64	h	h	NOUN
ejpam-3575	139	65	(	(	PUNCT
ejpam-3575	139	66	(	(	PUNCT
ejpam-3575	139	67	·	·	PUNCT
ejpam-3575	139	68	·	·	PUNCT
ejpam-3575	139	69	·	·	PUNCT
ejpam-3575	139	70	(	(	PUNCT
ejpam-3575	139	71	(	(	PUNCT
ejpam-3575	139	72	a1	a1	NOUN
ejpam-3575	139	73	∗	∗	NOUN
ejpam-3575	139	74	a2	a2	PROPN
ejpam-3575	139	75	)	)	PUNCT
ejpam-3575	139	76	∗	∗	NOUN
ejpam-3575	139	77	a3	a3	NOUN
ejpam-3575	139	78	)	)	PUNCT
ejpam-3575	139	79	∗	∗	NOUN
ejpam-3575	139	80	·	·	PUNCT
ejpam-3575	139	81	·	·	PUNCT
ejpam-3575	139	82	·	·	PUNCT
ejpam-3575	139	83	)	)	PUNCT
ejpam-3575	140	1	∗	∗	NOUN
ejpam-3575	140	2	an	an	PRON
ejpam-3575	140	3	)	)	PUNCT
ejpam-3575	140	4	≥	≥	NOUN
ejpam-3575	140	5	inf	inf	NOUN
ejpam-3575	140	6	h(x	h(x	PROPN
ejpam-3575	140	7	)	)	PUNCT
ejpam-3575	140	8	)	)	PUNCT
ejpam-3575	140	9	.	.	PUNCT
ejpam-3575	141	1	proof	proof	NOUN
ejpam-3575	141	2	.	.	PUNCT
ejpam-3575	142	1	using	use	VERB
ejpam-3575	142	2	(	(	PUNCT
ejpam-3575	142	3	5	5	NUM
ejpam-3575	142	4	)	)	PUNCT
ejpam-3575	142	5	,	,	PUNCT
ejpam-3575	142	6	(	(	PUNCT
ejpam-3575	142	7	iii	iii	NOUN
ejpam-3575	142	8	)	)	PUNCT
ejpam-3575	142	9	and	and	CCONJ
ejpam-3575	142	10	(	(	PUNCT
ejpam-3575	142	11	iv	iv	X
ejpam-3575	142	12	)	)	PUNCT
ejpam-3575	142	13	,	,	PUNCT
ejpam-3575	142	14	we	we	PRON
ejpam-3575	142	15	have	have	VERB
ejpam-3575	142	16	(	(	PUNCT
ejpam-3575	142	17	·	·	PUNCT
ejpam-3575	142	18	·	·	PUNCT
ejpam-3575	142	19	·	·	PUNCT
ejpam-3575	142	20	(	(	PUNCT
ejpam-3575	142	21	(	(	PUNCT
ejpam-3575	142	22	a1	a1	NOUN
ejpam-3575	142	23	∗	∗	NOUN
ejpam-3575	142	24	a2	a2	PROPN
ejpam-3575	142	25	)	)	PUNCT
ejpam-3575	142	26	∗	∗	NOUN
ejpam-3575	142	27	a3	a3	NOUN
ejpam-3575	142	28	)	)	PUNCT
ejpam-3575	142	29	∗	∗	NOUN
ejpam-3575	142	30	·	·	PUNCT
ejpam-3575	142	31	·	·	PUNCT
ejpam-3575	142	32	·	·	PUNCT
ejpam-3575	142	33	)	)	PUNCT
ejpam-3575	143	1	∗	∗	VERB
ejpam-3575	143	2	an	an	DET
ejpam-3575	143	3	=	=	NOUN
ejpam-3575	143	4	0	0	NUM
ejpam-3575	143	5	.	.	PUNCT
ejpam-3575	144	1	thus	thus	ADV
ejpam-3575	144	2	the	the	DET
ejpam-3575	144	3	desired	desire	VERB
ejpam-3575	144	4	result	result	NOUN
ejpam-3575	144	5	follows	follow	VERB
ejpam-3575	144	6	from	from	ADP
ejpam-3575	144	7	lemma	lemma	PROPN
ejpam-3575	144	8	1	1	NUM
ejpam-3575	144	9	.	.	PUNCT
ejpam-3575	144	10	definition	definition	NOUN
ejpam-3575	144	11	3	3	X
ejpam-3575	144	12	.	.	PUNCT
ejpam-3575	145	1	let	let	VERB
ejpam-3575	145	2	x	x	PRON
ejpam-3575	145	3	be	be	AUX
ejpam-3575	145	4	a	a	DET
ejpam-3575	145	5	bck	bck	VERB
ejpam-3575	145	6	/	/	SYM
ejpam-3575	145	7	bci	bci	NOUN
ejpam-3575	145	8	-	-	NOUN
ejpam-3575	145	9	algebra	algebra	NOUN
ejpam-3575	145	10	.	.	PUNCT
ejpam-3575	146	1	given	give	VERB
ejpam-3575	146	2	an	an	DET
ejpam-3575	146	3	element	element	NOUN
ejpam-3575	146	4	d	d	PROPN
ejpam-3575	146	5	∈	∈	PROPN
ejpam-3575	146	6	p	p	NOUN
ejpam-3575	146	7	∗([0	∗([0	NOUN
ejpam-3575	146	8	,	,	PUNCT
ejpam-3575	146	9	1	1	NUM
ejpam-3575	146	10	]	]	NUM
ejpam-3575	146	11	)	)	PUNCT
ejpam-3575	146	12	,	,	PUNCT
ejpam-3575	146	13	a	a	DET
ejpam-3575	146	14	hesitant	hesitant	ADJ
ejpam-3575	146	15	fuzzy	fuzzy	ADJ
ejpam-3575	146	16	set	set	NOUN
ejpam-3575	146	17	h	h	NOUN
ejpam-3575	146	18	:	:	PUNCT
ejpam-3575	146	19	=	=	SYM
ejpam-3575	146	20	{	{	PUNCT
ejpam-3575	146	21	(	(	PUNCT
ejpam-3575	146	22	x	x	NOUN
ejpam-3575	146	23	,	,	PUNCT
ejpam-3575	146	24	h(x	h(x	PROPN
ejpam-3575	146	25	)	)	PUNCT
ejpam-3575	146	26	)	)	PUNCT
ejpam-3575	147	1	|	|	ADV
ejpam-3575	147	2	x	x	SYM
ejpam-3575	147	3	∈	∈	NOUN
ejpam-3575	147	4	x	x	VERB
ejpam-3575	147	5	}	}	PUNCT
ejpam-3575	147	6	is	be	AUX
ejpam-3575	147	7	called	call	VERB
ejpam-3575	147	8	an	an	DET
ejpam-3575	147	9	inf	inf	ADJ
ejpam-3575	147	10	-	-	PUNCT
ejpam-3575	147	11	hesitant	hesitant	ADJ
ejpam-3575	147	12	fuzzy	fuzzy	ADJ
ejpam-3575	147	13	ideal	ideal	NOUN
ejpam-3575	147	14	of	of	ADP
ejpam-3575	147	15	x	x	SYM
ejpam-3575	147	16	related	relate	VERB
ejpam-3575	147	17	to	to	ADP
ejpam-3575	147	18	d	d	PROPN
ejpam-3575	147	19	(	(	PUNCT
ejpam-3575	147	20	briefly	briefly	ADV
ejpam-3575	147	21	,	,	PUNCT
ejpam-3575	147	22	d	d	X
ejpam-3575	147	23	-	-	PUNCT
ejpam-3575	147	24	inf	inf	ADJ
ejpam-3575	147	25	-	-	PUNCT
ejpam-3575	147	26	hesitant	hesitant	ADJ
ejpam-3575	147	27	fuzzy	fuzzy	ADJ
ejpam-3575	147	28	ideal	ideal	NOUN
ejpam-3575	147	29	of	of	ADP
ejpam-3575	147	30	x	x	SYM
ejpam-3575	147	31	)	)	PUNCT
ejpam-3575	147	32	if	if	SCONJ
ejpam-3575	147	33	the	the	DET
ejpam-3575	147	34	set	set	NOUN
ejpam-3575	147	35	inf[h;d	inf[h;d	NOUN
ejpam-3575	147	36	]	]	PUNCT
ejpam-3575	147	37	is	be	AUX
ejpam-3575	147	38	an	an	DET
ejpam-3575	147	39	ideal	ideal	NOUN
ejpam-3575	147	40	of	of	ADP
ejpam-3575	147	41	x	x	SYM
ejpam-3575	147	42	whenever	whenever	SCONJ
ejpam-3575	147	43	it	it	PRON
ejpam-3575	147	44	is	be	AUX
ejpam-3575	147	45	non	non	ADJ
ejpam-3575	147	46	-	-	ADJ
ejpam-3575	147	47	empty	empty	ADJ
ejpam-3575	147	48	.	.	PUNCT
ejpam-3575	148	1	if	if	SCONJ
ejpam-3575	148	2	h	h	NOUN
ejpam-3575	148	3	:	:	PUNCT
ejpam-3575	148	4	=	=	SYM
ejpam-3575	148	5	{	{	PUNCT
ejpam-3575	148	6	(	(	PUNCT
ejpam-3575	148	7	x	x	NOUN
ejpam-3575	148	8	,	,	PUNCT
ejpam-3575	148	9	h(x	h(x	PROPN
ejpam-3575	148	10	)	)	PUNCT
ejpam-3575	148	11	)	)	PUNCT
ejpam-3575	149	1	|	|	ADV
ejpam-3575	149	2	x	x	SYM
ejpam-3575	149	3	∈	∈	NOUN
ejpam-3575	149	4	x	x	X
ejpam-3575	149	5	}	}	PUNCT
ejpam-3575	149	6	is	be	AUX
ejpam-3575	149	7	a	a	DET
ejpam-3575	149	8	d	d	PROPN
ejpam-3575	149	9	-	-	PUNCT
ejpam-3575	149	10	inf	inf	ADJ
ejpam-3575	149	11	-	-	PUNCT
ejpam-3575	149	12	hesitant	hesitant	ADJ
ejpam-3575	149	13	fuzzy	fuzzy	ADJ
ejpam-3575	149	14	ideal	ideal	NOUN
ejpam-3575	149	15	of	of	ADP
ejpam-3575	149	16	x	x	PUNCT
ejpam-3575	149	17	for	for	ADP
ejpam-3575	149	18	all	all	DET
ejpam-3575	149	19	d	d	PROPN
ejpam-3575	149	20	∈	∈	PROPN
ejpam-3575	149	21	p	p	NOUN
ejpam-3575	149	22	∗([0	∗([0	NOUN
ejpam-3575	149	23	,	,	PUNCT
ejpam-3575	149	24	1	1	NUM
ejpam-3575	149	25	]	]	PUNCT
ejpam-3575	149	26	)	)	PUNCT
ejpam-3575	149	27	with	with	ADP
ejpam-3575	149	28	inf[h;d	inf[h;d	PROPN
ejpam-3575	149	29	]	]	PUNCT
ejpam-3575	149	30	6=	6=	NUM
ejpam-3575	149	31	∅	∅	NOUN
ejpam-3575	149	32	,	,	PUNCT
ejpam-3575	149	33	then	then	ADV
ejpam-3575	149	34	we	we	PRON
ejpam-3575	149	35	say	say	VERB
ejpam-3575	149	36	that	that	SCONJ
ejpam-3575	149	37	h	h	NOUN
ejpam-3575	149	38	:	:	PUNCT
ejpam-3575	149	39	=	=	SYM
ejpam-3575	149	40	{	{	PUNCT
ejpam-3575	149	41	(	(	PUNCT
ejpam-3575	149	42	x	x	NOUN
ejpam-3575	149	43	,	,	PUNCT
ejpam-3575	149	44	h(x	h(x	PROPN
ejpam-3575	149	45	)	)	PUNCT
ejpam-3575	149	46	)	)	PUNCT
ejpam-3575	150	1	|	|	ADV
ejpam-3575	150	2	x	x	SYM
ejpam-3575	150	3	∈	∈	NOUN
ejpam-3575	150	4	x	x	X
ejpam-3575	150	5	}	}	PUNCT
ejpam-3575	150	6	is	be	AUX
ejpam-3575	150	7	an	an	DET
ejpam-3575	150	8	inf	inf	ADJ
ejpam-3575	150	9	-	-	PUNCT
ejpam-3575	150	10	hesitant	hesitant	ADJ
ejpam-3575	150	11	fuzzy	fuzzy	ADJ
ejpam-3575	150	12	ideal	ideal	NOUN
ejpam-3575	150	13	of	of	ADP
ejpam-3575	150	14	x.	x.	PROPN
ejpam-3575	150	15	g.	g.	PROPN
ejpam-3575	150	16	muhiuddin	muhiuddin	PROPN
ejpam-3575	150	17	et	et	PROPN
ejpam-3575	150	18	al	al	PROPN
ejpam-3575	150	19	.	.	PUNCT
ejpam-3575	150	20	/	/	SYM
ejpam-3575	150	21	eur	eur	PROPN
ejpam-3575	150	22	.	.	PUNCT
ejpam-3575	151	1	j.	j.	PROPN
ejpam-3575	151	2	pure	pure	PROPN
ejpam-3575	151	3	appl	appl	PROPN
ejpam-3575	151	4	.	.	PROPN
ejpam-3575	151	5	math	math	PROPN
ejpam-3575	151	6	,	,	PUNCT
ejpam-3575	151	7	13	13	NUM
ejpam-3575	151	8	(	(	PUNCT
ejpam-3575	151	9	1	1	NUM
ejpam-3575	151	10	)	)	PUNCT
ejpam-3575	151	11	(	(	PUNCT
ejpam-3575	151	12	2020	2020	NUM
ejpam-3575	151	13	)	)	PUNCT
ejpam-3575	151	14	,	,	PUNCT
ejpam-3575	151	15	9	9	NUM
ejpam-3575	151	16	-	-	SYM
ejpam-3575	151	17	18	18	NUM
ejpam-3575	151	18	15	15	NUM
ejpam-3575	151	19	example	example	NOUN
ejpam-3575	151	20	2	2	NUM
ejpam-3575	151	21	.	.	PUNCT
ejpam-3575	151	22	(	(	PUNCT
ejpam-3575	151	23	1	1	X
ejpam-3575	151	24	)	)	PUNCT
ejpam-3575	151	25	the	the	DET
ejpam-3575	151	26	hesitant	hesitant	ADJ
ejpam-3575	151	27	fuzzy	fuzzy	ADJ
ejpam-3575	151	28	set	set	NOUN
ejpam-3575	151	29	h	h	NOUN
ejpam-3575	151	30	:	:	PUNCT
ejpam-3575	151	31	=	=	SYM
ejpam-3575	151	32	{	{	PUNCT
ejpam-3575	151	33	(	(	PUNCT
ejpam-3575	151	34	x	x	NOUN
ejpam-3575	151	35	,	,	PUNCT
ejpam-3575	151	36	h(x	h(x	PROPN
ejpam-3575	151	37	)	)	PUNCT
ejpam-3575	151	38	)	)	PUNCT
ejpam-3575	152	1	|	|	ADV
ejpam-3575	152	2	x	x	SYM
ejpam-3575	152	3	∈	∈	NOUN
ejpam-3575	152	4	x	x	X
ejpam-3575	152	5	}	}	PUNCT
ejpam-3575	152	6	in	in	ADP
ejpam-3575	152	7	example	example	NOUN
ejpam-3575	152	8	1(1	1(1	NUM
ejpam-3575	152	9	)	)	PUNCT
ejpam-3575	152	10	is	be	AUX
ejpam-3575	152	11	an	an	DET
ejpam-3575	152	12	inf	inf	ADJ
ejpam-3575	152	13	-	-	PUNCT
ejpam-3575	152	14	hesitant	hesitant	ADJ
ejpam-3575	152	15	fuzzy	fuzzy	ADJ
ejpam-3575	152	16	ideal	ideal	NOUN
ejpam-3575	152	17	of	of	ADP
ejpam-3575	152	18	x.	x.	NOUN
ejpam-3575	152	19	(	(	PUNCT
ejpam-3575	152	20	2	2	X
ejpam-3575	152	21	)	)	PUNCT
ejpam-3575	152	22	let	let	VERB
ejpam-3575	152	23	(	(	PUNCT
ejpam-3575	152	24	y	y	PROPN
ejpam-3575	152	25	,	,	PUNCT
ejpam-3575	152	26	∗	∗	NOUN
ejpam-3575	152	27	,	,	PUNCT
ejpam-3575	152	28	0	0	NUM
ejpam-3575	152	29	)	)	PUNCT
ejpam-3575	152	30	be	be	AUX
ejpam-3575	152	31	a	a	DET
ejpam-3575	152	32	bci	bci	NOUN
ejpam-3575	152	33	-	-	NOUN
ejpam-3575	152	34	algebra	algebra	NOUN
ejpam-3575	152	35	and	and	CCONJ
ejpam-3575	152	36	(	(	PUNCT
ejpam-3575	152	37	z,+	z,+	NUM
ejpam-3575	152	38	,	,	PUNCT
ejpam-3575	152	39	0	0	NUM
ejpam-3575	152	40	)	)	PUNCT
ejpam-3575	152	41	an	an	DET
ejpam-3575	152	42	additive	additive	ADJ
ejpam-3575	152	43	group	group	NOUN
ejpam-3575	152	44	of	of	ADP
ejpam-3575	152	45	integers	integer	NOUN
ejpam-3575	152	46	.	.	PUNCT
ejpam-3575	153	1	let	let	VERB
ejpam-3575	153	2	(	(	PUNCT
ejpam-3575	153	3	z,−	z,−	PROPN
ejpam-3575	153	4	,	,	PUNCT
ejpam-3575	153	5	0	0	NUM
ejpam-3575	153	6	)	)	PUNCT
ejpam-3575	153	7	be	be	VERB
ejpam-3575	153	8	the	the	DET
ejpam-3575	153	9	adjoint	adjoint	NOUN
ejpam-3575	153	10	bci	bci	NOUN
ejpam-3575	153	11	-	-	NOUN
ejpam-3575	153	12	algebra	algebra	NOUN
ejpam-3575	153	13	of	of	ADP
ejpam-3575	153	14	(	(	PUNCT
ejpam-3575	153	15	z,+	z,+	NUM
ejpam-3575	153	16	,	,	PUNCT
ejpam-3575	153	17	0	0	NUM
ejpam-3575	153	18	)	)	PUNCT
ejpam-3575	153	19	and	and	CCONJ
ejpam-3575	153	20	let	let	VERB
ejpam-3575	153	21	x	x	PRON
ejpam-3575	153	22	:	:	PUNCT
ejpam-3575	153	23	=	=	SYM
ejpam-3575	153	24	y	y	NUM
ejpam-3575	153	25	×	×	PROPN
ejpam-3575	153	26	z.	z.	PROPN
ejpam-3575	153	27	then	then	ADV
ejpam-3575	153	28	(	(	PUNCT
ejpam-3575	153	29	x,⊗	x,⊗	NOUN
ejpam-3575	153	30	,	,	PUNCT
ejpam-3575	153	31	(	(	PUNCT
ejpam-3575	153	32	0	0	NUM
ejpam-3575	153	33	,	,	PUNCT
ejpam-3575	153	34	0	0	NUM
ejpam-3575	153	35	)	)	PUNCT
ejpam-3575	153	36	)	)	PUNCT
ejpam-3575	153	37	is	be	AUX
ejpam-3575	153	38	a	a	DET
ejpam-3575	153	39	bci	bci	NOUN
ejpam-3575	153	40	-	-	NOUN
ejpam-3575	153	41	algebra	algebra	NOUN
ejpam-3575	153	42	where	where	SCONJ
ejpam-3575	153	43	the	the	DET
ejpam-3575	153	44	operation	operation	NOUN
ejpam-3575	153	45	⊗	⊗	PROPN
ejpam-3575	153	46	is	be	AUX
ejpam-3575	153	47	given	give	VERB
ejpam-3575	153	48	by	by	ADP
ejpam-3575	153	49	(	(	PUNCT
ejpam-3575	153	50	∀(x	∀(x	INTJ
ejpam-3575	153	51	,	,	PUNCT
ejpam-3575	153	52	m	m	NOUN
ejpam-3575	153	53	)	)	PUNCT
ejpam-3575	153	54	,	,	PUNCT
ejpam-3575	153	55	(	(	PUNCT
ejpam-3575	153	56	y	y	NOUN
ejpam-3575	153	57	,	,	PUNCT
ejpam-3575	153	58	n	n	CCONJ
ejpam-3575	153	59	)	)	PUNCT
ejpam-3575	153	60	∈	∈	PROPN
ejpam-3575	153	61	x	x	X
ejpam-3575	153	62	)	)	PUNCT
ejpam-3575	153	63	(	(	PUNCT
ejpam-3575	153	64	(	(	PUNCT
ejpam-3575	153	65	x	x	X
ejpam-3575	153	66	,	,	PUNCT
ejpam-3575	153	67	m)⊗	m)⊗	PROPN
ejpam-3575	153	68	(	(	PUNCT
ejpam-3575	153	69	y	y	NOUN
ejpam-3575	153	70	,	,	PUNCT
ejpam-3575	153	71	n	n	CCONJ
ejpam-3575	153	72	)	)	PUNCT
ejpam-3575	154	1	=	=	SYM
ejpam-3575	154	2	(	(	PUNCT
ejpam-3575	154	3	x	x	X
ejpam-3575	154	4	∗	∗	PROPN
ejpam-3575	154	5	y	y	PROPN
ejpam-3575	154	6	,	,	PUNCT
ejpam-3575	154	7	m−	m−	PROPN
ejpam-3575	154	8	n	n	CCONJ
ejpam-3575	154	9	)	)	PUNCT
ejpam-3575	154	10	)	)	PUNCT
ejpam-3575	154	11	.	.	PUNCT
ejpam-3575	155	1	for	for	ADP
ejpam-3575	155	2	a	a	DET
ejpam-3575	155	3	subset	subset	NOUN
ejpam-3575	155	4	a	a	DET
ejpam-3575	155	5	:	:	PUNCT
ejpam-3575	155	6	=	=	SYM
ejpam-3575	155	7	y	y	PROPN
ejpam-3575	155	8	×	×	PROPN
ejpam-3575	155	9	n0	n0	PROPN
ejpam-3575	155	10	of	of	ADP
ejpam-3575	155	11	x	x	SYM
ejpam-3575	155	12	where	where	SCONJ
ejpam-3575	155	13	n0	n0	PROPN
ejpam-3575	155	14	is	be	AUX
ejpam-3575	155	15	the	the	DET
ejpam-3575	155	16	set	set	NOUN
ejpam-3575	155	17	of	of	ADP
ejpam-3575	155	18	nonnegative	nonnegative	ADJ
ejpam-3575	155	19	integers	integer	NOUN
ejpam-3575	155	20	,	,	PUNCT
ejpam-3575	155	21	let	let	VERB
ejpam-3575	155	22	h	h	NOUN
ejpam-3575	155	23	:	:	PUNCT
ejpam-3575	155	24	=	=	SYM
ejpam-3575	155	25	{	{	PUNCT
ejpam-3575	155	26	(	(	PUNCT
ejpam-3575	155	27	x	x	NOUN
ejpam-3575	155	28	,	,	PUNCT
ejpam-3575	155	29	h(x	h(x	PROPN
ejpam-3575	155	30	)	)	PUNCT
ejpam-3575	155	31	)	)	PUNCT
ejpam-3575	156	1	|	|	ADV
ejpam-3575	156	2	x	x	SYM
ejpam-3575	156	3	∈	∈	NOUN
ejpam-3575	156	4	x	x	VERB
ejpam-3575	156	5	}	}	PUNCT
ejpam-3575	156	6	be	be	AUX
ejpam-3575	156	7	a	a	DET
ejpam-3575	156	8	hesitant	hesitant	ADJ
ejpam-3575	156	9	fuzzy	fuzzy	ADJ
ejpam-3575	156	10	set	set	NOUN
ejpam-3575	156	11	on	on	ADP
ejpam-3575	156	12	x	x	PUNCT
ejpam-3575	156	13	defined	define	VERB
ejpam-3575	156	14	by	by	ADP
ejpam-3575	156	15	h	h	NOUN
ejpam-3575	156	16	=	=	SYM
ejpam-3575	156	17	{	{	PUNCT
ejpam-3575	156	18	(	(	PUNCT
ejpam-3575	156	19	x	x	X
ejpam-3575	156	20	,	,	PUNCT
ejpam-3575	156	21	(	(	PUNCT
ejpam-3575	156	22	0.5	0.5	NUM
ejpam-3575	156	23	,	,	PUNCT
ejpam-3575	156	24	1	1	NUM
ejpam-3575	156	25	]	]	NUM
ejpam-3575	156	26	)	)	PUNCT
ejpam-3575	156	27	,	,	PUNCT
ejpam-3575	156	28	(	(	PUNCT
ejpam-3575	156	29	y	y	NOUN
ejpam-3575	156	30	,	,	PUNCT
ejpam-3575	156	31	[	[	X
ejpam-3575	156	32	0.4	0.4	NUM
ejpam-3575	156	33	,	,	PUNCT
ejpam-3575	156	34	0.9	0.9	NUM
ejpam-3575	156	35	]	]	PUNCT
ejpam-3575	156	36	)	)	PUNCT
ejpam-3575	157	1	|	|	ADV
ejpam-3575	157	2	x	x	SYM
ejpam-3575	157	3	∈	∈	PROPN
ejpam-3575	157	4	a	a	X
ejpam-3575	157	5	,	,	PUNCT
ejpam-3575	157	6	y	y	PROPN
ejpam-3575	157	7	∈	∈	PROPN
ejpam-3575	157	8	x	x	PUNCT
ejpam-3575	157	9	\a	\a	ADJ
ejpam-3575	157	10	}	}	PUNCT
ejpam-3575	157	11	.	.	PUNCT
ejpam-3575	158	1	then	then	ADV
ejpam-3575	158	2	h	h	NOUN
ejpam-3575	158	3	:	:	PUNCT
ejpam-3575	158	4	=	=	SYM
ejpam-3575	158	5	{	{	PUNCT
ejpam-3575	158	6	(	(	PUNCT
ejpam-3575	158	7	x	x	NOUN
ejpam-3575	158	8	,	,	PUNCT
ejpam-3575	158	9	h(x	h(x	PROPN
ejpam-3575	158	10	)	)	PUNCT
ejpam-3575	158	11	)	)	PUNCT
ejpam-3575	159	1	|	|	ADV
ejpam-3575	159	2	x	x	SYM
ejpam-3575	159	3	∈	∈	NOUN
ejpam-3575	159	4	x	x	X
ejpam-3575	159	5	}	}	PUNCT
ejpam-3575	159	6	is	be	AUX
ejpam-3575	159	7	an	an	DET
ejpam-3575	159	8	inf	inf	ADJ
ejpam-3575	159	9	-	-	PUNCT
ejpam-3575	159	10	hesitant	hesitant	ADJ
ejpam-3575	159	11	fuzzy	fuzzy	ADJ
ejpam-3575	159	12	ideal	ideal	NOUN
ejpam-3575	159	13	of	of	ADP
ejpam-3575	159	14	x.	x.	NOUN
ejpam-3575	159	15	(	(	PUNCT
ejpam-3575	159	16	3	3	X
ejpam-3575	159	17	)	)	PUNCT
ejpam-3575	159	18	let	let	VERB
ejpam-3575	159	19	x	x	PUNCT
ejpam-3575	159	20	=	=	PUNCT
ejpam-3575	159	21	{	{	PUNCT
ejpam-3575	159	22	0	0	NUM
ejpam-3575	159	23	,	,	PUNCT
ejpam-3575	159	24	a	a	DET
ejpam-3575	159	25	,	,	PUNCT
ejpam-3575	159	26	b	b	NOUN
ejpam-3575	159	27	,	,	PUNCT
ejpam-3575	159	28	c	c	NOUN
ejpam-3575	159	29	,	,	PUNCT
ejpam-3575	159	30	d	d	AUX
ejpam-3575	159	31	}	}	PUNCT
ejpam-3575	159	32	be	be	AUX
ejpam-3575	159	33	a	a	DET
ejpam-3575	159	34	bck	bck	NOUN
ejpam-3575	159	35	-	-	PUNCT
ejpam-3575	159	36	algebra	algebra	NOUN
ejpam-3575	159	37	with	with	ADP
ejpam-3575	159	38	the	the	DET
ejpam-3575	159	39	following	follow	VERB
ejpam-3575	159	40	cayley	cayley	ADJ
ejpam-3575	159	41	table	table	NOUN
ejpam-3575	159	42	:	:	PUNCT
ejpam-3575	159	43	∗	∗	NOUN
ejpam-3575	159	44	0	0	PUNCT
ejpam-3575	160	1	a	a	DET
ejpam-3575	160	2	b	b	NOUN
ejpam-3575	160	3	c	c	NOUN
ejpam-3575	160	4	d	d	NOUN
ejpam-3575	160	5	0	0	NUM
ejpam-3575	160	6	0	0	NUM
ejpam-3575	160	7	0	0	NUM
ejpam-3575	160	8	0	0	NUM
ejpam-3575	160	9	0	0	NUM
ejpam-3575	160	10	0	0	NUM
ejpam-3575	160	11	a	a	DET
ejpam-3575	160	12	a	a	DET
ejpam-3575	160	13	0	0	NUM
ejpam-3575	160	14	a	a	DET
ejpam-3575	160	15	0	0	NUM
ejpam-3575	160	16	0	0	NUM
ejpam-3575	160	17	b	b	PROPN
ejpam-3575	160	18	b	b	PROPN
ejpam-3575	160	19	b	b	PROPN
ejpam-3575	160	20	0	0	NUM
ejpam-3575	160	21	0	0	NUM
ejpam-3575	160	22	0	0	NUM
ejpam-3575	161	1	c	c	NOUN
ejpam-3575	161	2	c	c	PROPN
ejpam-3575	161	3	b	b	PROPN
ejpam-3575	161	4	a	a	DET
ejpam-3575	161	5	0	0	NUM
ejpam-3575	161	6	0	0	NUM
ejpam-3575	162	1	d	d	NOUN
ejpam-3575	162	2	d	d	PROPN
ejpam-3575	162	3	d	d	PROPN
ejpam-3575	162	4	d	d	PROPN
ejpam-3575	162	5	d	d	PROPN
ejpam-3575	162	6	0	0	PUNCT
ejpam-3575	162	7	let	let	VERB
ejpam-3575	162	8	h	h	NOUN
ejpam-3575	162	9	:	:	PUNCT
ejpam-3575	162	10	=	=	SYM
ejpam-3575	162	11	{	{	PUNCT
ejpam-3575	162	12	(	(	PUNCT
ejpam-3575	162	13	x	x	NOUN
ejpam-3575	162	14	,	,	PUNCT
ejpam-3575	162	15	h(x	h(x	PROPN
ejpam-3575	162	16	)	)	PUNCT
ejpam-3575	162	17	)	)	PUNCT
ejpam-3575	163	1	|	|	ADV
ejpam-3575	163	2	x	x	SYM
ejpam-3575	163	3	∈	∈	NOUN
ejpam-3575	163	4	x	x	VERB
ejpam-3575	163	5	}	}	PUNCT
ejpam-3575	163	6	be	be	AUX
ejpam-3575	163	7	a	a	DET
ejpam-3575	163	8	hesitant	hesitant	ADJ
ejpam-3575	163	9	fuzzy	fuzzy	ADJ
ejpam-3575	163	10	set	set	NOUN
ejpam-3575	163	11	on	on	ADP
ejpam-3575	163	12	x	x	PUNCT
ejpam-3575	163	13	defined	define	VERB
ejpam-3575	163	14	by	by	ADP
ejpam-3575	163	15	h	h	NOUN
ejpam-3575	163	16	=	=	SYM
ejpam-3575	163	17	{	{	PUNCT
ejpam-3575	163	18	(	(	PUNCT
ejpam-3575	163	19	0	0	NUM
ejpam-3575	163	20	,	,	PUNCT
ejpam-3575	163	21	[	[	X
ejpam-3575	163	22	0.8	0.8	NUM
ejpam-3575	163	23	,	,	PUNCT
ejpam-3575	163	24	1	1	NUM
ejpam-3575	163	25	)	)	PUNCT
ejpam-3575	163	26	)	)	PUNCT
ejpam-3575	163	27	,	,	PUNCT
ejpam-3575	163	28	(	(	PUNCT
ejpam-3575	163	29	a	a	X
ejpam-3575	163	30	,	,	PUNCT
ejpam-3575	163	31	[	[	X
ejpam-3575	163	32	0.4	0.4	NUM
ejpam-3575	163	33	,	,	PUNCT
ejpam-3575	163	34	0.7	0.7	NUM
ejpam-3575	163	35	]	]	PUNCT
ejpam-3575	163	36	)	)	PUNCT
ejpam-3575	163	37	,	,	PUNCT
ejpam-3575	163	38	(	(	PUNCT
ejpam-3575	163	39	b	b	X
ejpam-3575	163	40	,	,	PUNCT
ejpam-3575	163	41	{	{	PUNCT
ejpam-3575	163	42	0.3	0.3	NUM
ejpam-3575	163	43	}	}	PUNCT
ejpam-3575	163	44	∪	∪	ADJ
ejpam-3575	163	45	(	(	PUNCT
ejpam-3575	163	46	0.4	0.4	NUM
ejpam-3575	163	47	,	,	PUNCT
ejpam-3575	163	48	0.6	0.6	NUM
ejpam-3575	163	49	]	]	PUNCT
ejpam-3575	163	50	)	)	PUNCT
ejpam-3575	163	51	,	,	PUNCT
ejpam-3575	163	52	(	(	PUNCT
ejpam-3575	163	53	c	c	X
ejpam-3575	163	54	,	,	PUNCT
ejpam-3575	163	55	[	[	X
ejpam-3575	163	56	0.6	0.6	NUM
ejpam-3575	163	57	,	,	PUNCT
ejpam-3575	163	58	0.9	0.9	NUM
ejpam-3575	163	59	]	]	PUNCT
ejpam-3575	163	60	)	)	PUNCT
ejpam-3575	163	61	,	,	PUNCT
ejpam-3575	163	62	(	(	PUNCT
ejpam-3575	163	63	d	d	X
ejpam-3575	163	64	,	,	PUNCT
ejpam-3575	163	65	[	[	X
ejpam-3575	163	66	0.1	0.1	NUM
ejpam-3575	163	67	,	,	PUNCT
ejpam-3575	163	68	0.5	0.5	NUM
ejpam-3575	163	69	]	]	PUNCT
ejpam-3575	163	70	)	)	PUNCT
ejpam-3575	163	71	}	}	PUNCT
ejpam-3575	163	72	.	.	PUNCT
ejpam-3575	164	1	if	if	SCONJ
ejpam-3575	164	2	d1	d1	PROPN
ejpam-3575	164	3	:	:	PUNCT
ejpam-3575	164	4	=	=	PUNCT
ejpam-3575	165	1	[	[	X
ejpam-3575	165	2	0.5	0.5	NUM
ejpam-3575	165	3	,	,	PUNCT
ejpam-3575	165	4	0.8	0.8	NUM
ejpam-3575	165	5	)	)	PUNCT
ejpam-3575	165	6	,	,	PUNCT
ejpam-3575	165	7	then	then	ADV
ejpam-3575	165	8	inf[h;d1	inf[h;d1	X
ejpam-3575	165	9	]	]	X
ejpam-3575	165	10	=	=	PUNCT
ejpam-3575	165	11	{	{	PUNCT
ejpam-3575	165	12	0	0	NUM
ejpam-3575	165	13	,	,	PUNCT
ejpam-3575	165	14	c	c	NOUN
ejpam-3575	165	15	}	}	PUNCT
ejpam-3575	165	16	which	which	PRON
ejpam-3575	165	17	is	be	AUX
ejpam-3575	165	18	not	not	PART
ejpam-3575	165	19	an	an	DET
ejpam-3575	165	20	ideal	ideal	NOUN
ejpam-3575	165	21	of	of	ADP
ejpam-3575	165	22	x	x	PRON
ejpam-3575	165	23	since	since	SCONJ
ejpam-3575	165	24	b	b	NOUN
ejpam-3575	165	25	∗	∗	NOUN
ejpam-3575	165	26	c	c	NOUN
ejpam-3575	165	27	=	=	SYM
ejpam-3575	165	28	0	0	NUM
ejpam-3575	165	29	∈	∈	NOUN
ejpam-3575	165	30	inf[h;d1	inf[h;d1	NOUN
ejpam-3575	165	31	]	]	X
ejpam-3575	165	32	but	but	CCONJ
ejpam-3575	165	33	b	b	X
ejpam-3575	165	34	/∈	/∈	NOUN
ejpam-3575	165	35	inf[h;d1	inf[h;d1	NOUN
ejpam-3575	165	36	]	]	PUNCT
ejpam-3575	165	37	.	.	PUNCT
ejpam-3575	166	1	thus	thus	ADV
ejpam-3575	166	2	h	h	NOUN
ejpam-3575	166	3	:	:	PUNCT
ejpam-3575	166	4	=	=	SYM
ejpam-3575	166	5	{	{	PUNCT
ejpam-3575	166	6	(	(	PUNCT
ejpam-3575	166	7	x	x	NOUN
ejpam-3575	166	8	,	,	PUNCT
ejpam-3575	166	9	h(x	h(x	PROPN
ejpam-3575	166	10	)	)	PUNCT
ejpam-3575	166	11	)	)	PUNCT
ejpam-3575	167	1	|	|	ADV
ejpam-3575	167	2	x	x	SYM
ejpam-3575	167	3	∈	∈	NOUN
ejpam-3575	167	4	x	x	X
ejpam-3575	167	5	}	}	PUNCT
ejpam-3575	167	6	is	be	AUX
ejpam-3575	167	7	not	not	PART
ejpam-3575	167	8	a	a	DET
ejpam-3575	167	9	d1	d1	NOUN
ejpam-3575	167	10	-	-	PUNCT
ejpam-3575	167	11	inf	inf	ADJ
ejpam-3575	167	12	-	-	PUNCT
ejpam-3575	167	13	hesitant	hesitant	ADJ
ejpam-3575	167	14	fuzzy	fuzzy	ADJ
ejpam-3575	167	15	ideal	ideal	NOUN
ejpam-3575	167	16	of	of	ADP
ejpam-3575	167	17	x.	x.	NOUN
ejpam-3575	167	18	we	we	PRON
ejpam-3575	167	19	can	can	AUX
ejpam-3575	167	20	easily	easily	ADV
ejpam-3575	167	21	verify	verify	VERB
ejpam-3575	167	22	that	that	DET
ejpam-3575	167	23	h	h	NOUN
ejpam-3575	167	24	:	:	PUNCT
ejpam-3575	167	25	=	=	SYM
ejpam-3575	167	26	{	{	PUNCT
ejpam-3575	167	27	(	(	PUNCT
ejpam-3575	167	28	x	x	NOUN
ejpam-3575	167	29	,	,	PUNCT
ejpam-3575	167	30	h(x	h(x	PROPN
ejpam-3575	167	31	)	)	PUNCT
ejpam-3575	167	32	)	)	PUNCT
ejpam-3575	168	1	|	|	ADV
ejpam-3575	168	2	x	x	SYM
ejpam-3575	168	3	∈	∈	NOUN
ejpam-3575	168	4	x	x	X
ejpam-3575	168	5	}	}	PUNCT
ejpam-3575	168	6	is	be	AUX
ejpam-3575	168	7	a	a	DET
ejpam-3575	168	8	d2	d2	NOUN
ejpam-3575	168	9	-	-	PUNCT
ejpam-3575	168	10	inf	inf	ADJ
ejpam-3575	168	11	-	-	PUNCT
ejpam-3575	168	12	hesitant	hesitant	ADJ
ejpam-3575	168	13	fuzzy	fuzzy	ADJ
ejpam-3575	168	14	ideal	ideal	NOUN
ejpam-3575	168	15	of	of	ADP
ejpam-3575	168	16	x	x	PUNCT
ejpam-3575	168	17	with	with	ADP
ejpam-3575	168	18	d2	d2	PROPN
ejpam-3575	168	19	=	=	PUNCT
ejpam-3575	169	1	[	[	X
ejpam-3575	169	2	0.25	0.25	NUM
ejpam-3575	169	3	,	,	PUNCT
ejpam-3575	169	4	0.5	0.5	NUM
ejpam-3575	169	5	]	]	PUNCT
ejpam-3575	169	6	.	.	PUNCT
ejpam-3575	170	1	theorem	theorem	NOUN
ejpam-3575	170	2	2	2	NUM
ejpam-3575	170	3	.	.	PUNCT
ejpam-3575	170	4	a	a	DET
ejpam-3575	170	5	hesitant	hesitant	ADJ
ejpam-3575	170	6	fuzzy	fuzzy	ADJ
ejpam-3575	170	7	set	set	NOUN
ejpam-3575	170	8	h	h	NOUN
ejpam-3575	170	9	:	:	PUNCT
ejpam-3575	170	10	=	=	SYM
ejpam-3575	170	11	{	{	PUNCT
ejpam-3575	170	12	(	(	PUNCT
ejpam-3575	170	13	x	x	NOUN
ejpam-3575	170	14	,	,	PUNCT
ejpam-3575	170	15	h(x	h(x	PROPN
ejpam-3575	170	16	)	)	PUNCT
ejpam-3575	170	17	)	)	PUNCT
ejpam-3575	171	1	|	|	ADV
ejpam-3575	171	2	x	x	SYM
ejpam-3575	171	3	∈	∈	NOUN
ejpam-3575	171	4	x	x	X
ejpam-3575	171	5	}	}	PUNCT
ejpam-3575	171	6	on	on	ADP
ejpam-3575	171	7	a	a	DET
ejpam-3575	171	8	bck	bck	VERB
ejpam-3575	171	9	/	/	SYM
ejpam-3575	171	10	bci	bci	NOUN
ejpam-3575	171	11	-	-	NOUN
ejpam-3575	171	12	algebra	algebra	NOUN
ejpam-3575	171	13	x	x	PUNCT
ejpam-3575	171	14	is	be	AUX
ejpam-3575	171	15	an	an	DET
ejpam-3575	171	16	inf	inf	ADJ
ejpam-3575	171	17	-	-	PUNCT
ejpam-3575	171	18	hesitant	hesitant	ADJ
ejpam-3575	171	19	fuzzy	fuzzy	ADJ
ejpam-3575	171	20	ideal	ideal	NOUN
ejpam-3575	171	21	of	of	ADP
ejpam-3575	171	22	x	x	SYM
ejpam-3575	171	23	if	if	SCONJ
ejpam-3575	171	24	and	and	CCONJ
ejpam-3575	171	25	only	only	ADV
ejpam-3575	171	26	if	if	SCONJ
ejpam-3575	171	27	it	it	PRON
ejpam-3575	171	28	satisfies	satisfy	VERB
ejpam-3575	171	29	(	(	PUNCT
ejpam-3575	171	30	16	16	NUM
ejpam-3575	171	31	)	)	PUNCT
ejpam-3575	171	32	and	and	CCONJ
ejpam-3575	171	33	(	(	PUNCT
ejpam-3575	171	34	∀x	∀x	X
ejpam-3575	171	35	,	,	PUNCT
ejpam-3575	171	36	y	y	PROPN
ejpam-3575	171	37	∈	∈	PROPN
ejpam-3575	171	38	x	x	X
ejpam-3575	171	39	)	)	PUNCT
ejpam-3575	171	40	(	(	PUNCT
ejpam-3575	171	41	inf	inf	PROPN
ejpam-3575	171	42	h(x	h(x	PROPN
ejpam-3575	171	43	)	)	PUNCT
ejpam-3575	171	44	≥	≥	NOUN
ejpam-3575	171	45	min{inf	min{inf	VERB
ejpam-3575	171	46	h(x	h(x	PROPN
ejpam-3575	171	47	∗	∗	PROPN
ejpam-3575	171	48	y	y	PROPN
ejpam-3575	171	49	)	)	PUNCT
ejpam-3575	171	50	,	,	PUNCT
ejpam-3575	171	51	inf	inf	PROPN
ejpam-3575	171	52	h(y	h(y	ADV
ejpam-3575	171	53	)	)	PUNCT
ejpam-3575	171	54	}	}	PUNCT
ejpam-3575	171	55	)	)	PUNCT
ejpam-3575	171	56	.	.	PUNCT
ejpam-3575	172	1	(	(	PUNCT
ejpam-3575	172	2	17	17	NUM
ejpam-3575	172	3	)	)	PUNCT
ejpam-3575	172	4	proof	proof	NOUN
ejpam-3575	172	5	.	.	PUNCT
ejpam-3575	173	1	let	let	VERB
ejpam-3575	173	2	h	h	NOUN
ejpam-3575	173	3	:	:	PUNCT
ejpam-3575	173	4	=	=	SYM
ejpam-3575	173	5	{	{	PUNCT
ejpam-3575	173	6	(	(	PUNCT
ejpam-3575	173	7	x	x	NOUN
ejpam-3575	173	8	,	,	PUNCT
ejpam-3575	173	9	h(x	h(x	PROPN
ejpam-3575	173	10	)	)	PUNCT
ejpam-3575	173	11	)	)	PUNCT
ejpam-3575	174	1	|	|	ADV
ejpam-3575	174	2	x	x	SYM
ejpam-3575	174	3	∈	∈	NOUN
ejpam-3575	174	4	x	x	AUX
ejpam-3575	174	5	}	}	PUNCT
ejpam-3575	174	6	be	be	VERB
ejpam-3575	174	7	an	an	DET
ejpam-3575	174	8	inf	inf	ADJ
ejpam-3575	174	9	-	-	PUNCT
ejpam-3575	174	10	hesitant	hesitant	ADJ
ejpam-3575	174	11	fuzzy	fuzzy	ADJ
ejpam-3575	174	12	ideal	ideal	NOUN
ejpam-3575	174	13	of	of	ADP
ejpam-3575	174	14	x.	x.	NOUN
ejpam-3575	174	15	if	if	SCONJ
ejpam-3575	174	16	(	(	PUNCT
ejpam-3575	174	17	16	16	NUM
ejpam-3575	174	18	)	)	PUNCT
ejpam-3575	174	19	is	be	AUX
ejpam-3575	174	20	not	not	PART
ejpam-3575	174	21	valid	valid	ADJ
ejpam-3575	174	22	,	,	PUNCT
ejpam-3575	174	23	then	then	ADV
ejpam-3575	174	24	there	there	PRON
ejpam-3575	174	25	exists	exist	VERB
ejpam-3575	174	26	d	d	PROPN
ejpam-3575	174	27	∈	∈	PROPN
ejpam-3575	174	28	p	p	NOUN
ejpam-3575	174	29	∗([0	∗([0	NOUN
ejpam-3575	174	30	,	,	PUNCT
ejpam-3575	174	31	1	1	NUM
ejpam-3575	174	32	]	]	PUNCT
ejpam-3575	174	33	)	)	PUNCT
ejpam-3575	174	34	and	and	CCONJ
ejpam-3575	174	35	a	a	DET
ejpam-3575	174	36	∈	∈	NOUN
ejpam-3575	174	37	x	x	PUNCT
ejpam-3575	174	38	such	such	ADJ
ejpam-3575	174	39	that	that	DET
ejpam-3575	174	40	inf	inf	NOUN
ejpam-3575	174	41	h(0	h(0	PROPN
ejpam-3575	174	42	)	)	PUNCT
ejpam-3575	174	43	<	<	X
ejpam-3575	174	44	inf	inf	PROPN
ejpam-3575	174	45	d	d	PROPN
ejpam-3575	174	46	≤	≤	PROPN
ejpam-3575	174	47	inf	inf	PROPN
ejpam-3575	174	48	h(a	h(a	PROPN
ejpam-3575	174	49	)	)	PUNCT
ejpam-3575	174	50	.	.	PUNCT
ejpam-3575	175	1	it	it	PRON
ejpam-3575	175	2	follows	follow	VERB
ejpam-3575	175	3	that	that	SCONJ
ejpam-3575	175	4	a	a	DET
ejpam-3575	175	5	∈	∈	PROPN
ejpam-3575	175	6	inf[h;d	inf[h;d	NOUN
ejpam-3575	175	7	]	]	PUNCT
ejpam-3575	175	8	and	and	CCONJ
ejpam-3575	175	9	0	0	NUM
ejpam-3575	175	10	/∈	/∈	NOUN
ejpam-3575	176	1	inf[h;d	inf[h;d	PROPN
ejpam-3575	176	2	]	]	PUNCT
ejpam-3575	176	3	.	.	PUNCT
ejpam-3575	177	1	this	this	PRON
ejpam-3575	177	2	is	be	AUX
ejpam-3575	177	3	a	a	DET
ejpam-3575	177	4	contradiction	contradiction	NOUN
ejpam-3575	177	5	,	,	PUNCT
ejpam-3575	177	6	and	and	CCONJ
ejpam-3575	177	7	so	so	ADV
ejpam-3575	177	8	(	(	PUNCT
ejpam-3575	177	9	16	16	NUM
ejpam-3575	177	10	)	)	PUNCT
ejpam-3575	177	11	is	be	AUX
ejpam-3575	177	12	valid	valid	ADJ
ejpam-3575	177	13	.	.	PUNCT
ejpam-3575	178	1	now	now	ADV
ejpam-3575	178	2	assume	assume	VERB
ejpam-3575	178	3	that	that	SCONJ
ejpam-3575	178	4	there	there	PRON
ejpam-3575	178	5	exist	exist	VERB
ejpam-3575	178	6	a	a	DET
ejpam-3575	178	7	,	,	PUNCT
ejpam-3575	178	8	b	b	X
ejpam-3575	178	9	∈	∈	PROPN
ejpam-3575	178	10	x	x	PUNCT
ejpam-3575	178	11	such	such	ADJ
ejpam-3575	178	12	that	that	DET
ejpam-3575	178	13	inf	inf	PROPN
ejpam-3575	178	14	h(a	h(a	PROPN
ejpam-3575	178	15	)	)	PUNCT
ejpam-3575	179	1	<	<	X
ejpam-3575	179	2	min{inf	min{inf	PROPN
ejpam-3575	179	3	h(a∗b	h(a∗b	PROPN
ejpam-3575	179	4	)	)	PUNCT
ejpam-3575	179	5	,	,	PUNCT
ejpam-3575	179	6	inf	inf	PROPN
ejpam-3575	179	7	h(b	h(b	PROPN
ejpam-3575	179	8	)	)	PUNCT
ejpam-3575	179	9	}	}	PUNCT
ejpam-3575	179	10	.	.	PUNCT
ejpam-3575	180	1	then	then	ADV
ejpam-3575	180	2	there	there	PRON
ejpam-3575	180	3	exists	exist	VERB
ejpam-3575	180	4	k	k	PROPN
ejpam-3575	180	5	∈	∈	PROPN
ejpam-3575	180	6	p	p	PROPN
ejpam-3575	180	7	∗([0	∗([0	NOUN
ejpam-3575	180	8	,	,	PUNCT
ejpam-3575	180	9	1	1	NUM
ejpam-3575	180	10	]	]	PUNCT
ejpam-3575	180	11	)	)	PUNCT
ejpam-3575	180	12	such	such	ADJ
ejpam-3575	180	13	that	that	DET
ejpam-3575	180	14	inf	inf	PROPN
ejpam-3575	180	15	h(a	h(a	PROPN
ejpam-3575	180	16	)	)	PUNCT
ejpam-3575	180	17	<	<	X
ejpam-3575	180	18	inf	inf	PROPN
ejpam-3575	180	19	k	k	PROPN
ejpam-3575	180	20	≤	≤	PROPN
ejpam-3575	180	21	min{inf	min{inf	VERB
ejpam-3575	180	22	h(a	h(a	PROPN
ejpam-3575	180	23	∗	∗	PROPN
ejpam-3575	180	24	b	b	NOUN
ejpam-3575	180	25	)	)	PUNCT
ejpam-3575	180	26	,	,	PUNCT
ejpam-3575	180	27	inf	inf	PROPN
ejpam-3575	180	28	h(b	h(b	PROPN
ejpam-3575	180	29	)	)	PUNCT
ejpam-3575	180	30	}	}	PUNCT
ejpam-3575	180	31	,	,	PUNCT
ejpam-3575	180	32	which	which	PRON
ejpam-3575	180	33	implies	imply	VERB
ejpam-3575	180	34	that	that	SCONJ
ejpam-3575	180	35	a	a	DET
ejpam-3575	180	36	∗	∗	NOUN
ejpam-3575	180	37	b	b	NOUN
ejpam-3575	180	38	∈	∈	PROPN
ejpam-3575	180	39	inf[h;k	inf[h;k	NOUN
ejpam-3575	180	40	]	]	PUNCT
ejpam-3575	180	41	,	,	PUNCT
ejpam-3575	180	42	b	b	X
ejpam-3575	180	43	∈	∈	PROPN
ejpam-3575	180	44	inf[h;k	inf[h;k	NOUN
ejpam-3575	180	45	]	]	PUNCT
ejpam-3575	180	46	but	but	CCONJ
ejpam-3575	180	47	a	a	DET
ejpam-3575	180	48	/∈	/∈	NOUN
ejpam-3575	180	49	inf[h;k	inf[h;k	NOUN
ejpam-3575	180	50	]	]	PUNCT
ejpam-3575	180	51	.	.	PUNCT
ejpam-3575	181	1	this	this	PRON
ejpam-3575	181	2	is	be	AUX
ejpam-3575	181	3	a	a	DET
ejpam-3575	181	4	contradiction	contradiction	NOUN
ejpam-3575	181	5	,	,	PUNCT
ejpam-3575	181	6	and	and	CCONJ
ejpam-3575	181	7	thus	thus	ADV
ejpam-3575	181	8	(	(	PUNCT
ejpam-3575	181	9	17	17	NUM
ejpam-3575	181	10	)	)	PUNCT
ejpam-3575	181	11	holds	hold	VERB
ejpam-3575	181	12	.	.	PUNCT
ejpam-3575	182	1	references	reference	NOUN
ejpam-3575	182	2	16	16	NUM
ejpam-3575	182	3	conversely	conversely	ADV
ejpam-3575	182	4	,	,	PUNCT
ejpam-3575	182	5	suppose	suppose	VERB
ejpam-3575	182	6	that	that	SCONJ
ejpam-3575	182	7	h	h	NOUN
ejpam-3575	182	8	:	:	PUNCT
ejpam-3575	182	9	=	=	SYM
ejpam-3575	182	10	{	{	PUNCT
ejpam-3575	182	11	(	(	PUNCT
ejpam-3575	182	12	x	x	NOUN
ejpam-3575	182	13	,	,	PUNCT
ejpam-3575	182	14	h(x	h(x	PROPN
ejpam-3575	182	15	)	)	PUNCT
ejpam-3575	182	16	)	)	PUNCT
ejpam-3575	183	1	|	|	ADV
ejpam-3575	183	2	x	x	SYM
ejpam-3575	183	3	∈	∈	NOUN
ejpam-3575	183	4	x	x	PRON
ejpam-3575	183	5	}	}	PUNCT
ejpam-3575	183	6	satisfies	satisfy	VERB
ejpam-3575	183	7	two	two	NUM
ejpam-3575	183	8	conditions	condition	NOUN
ejpam-3575	183	9	(	(	PUNCT
ejpam-3575	183	10	16	16	NUM
ejpam-3575	183	11	)	)	PUNCT
ejpam-3575	183	12	and	and	CCONJ
ejpam-3575	183	13	(	(	PUNCT
ejpam-3575	183	14	17	17	NUM
ejpam-3575	183	15	)	)	PUNCT
ejpam-3575	183	16	.	.	PUNCT
ejpam-3575	184	1	let	let	VERB
ejpam-3575	184	2	k	k	PROPN
ejpam-3575	184	3	∈	∈	PROPN
ejpam-3575	184	4	p	p	PROPN
ejpam-3575	184	5	∗([0	∗([0	NOUN
ejpam-3575	184	6	,	,	PUNCT
ejpam-3575	184	7	1	1	NUM
ejpam-3575	184	8	]	]	PUNCT
ejpam-3575	184	9	)	)	PUNCT
ejpam-3575	184	10	be	be	AUX
ejpam-3575	184	11	such	such	ADJ
ejpam-3575	184	12	that	that	DET
ejpam-3575	184	13	inf[h;k	inf[h;k	NOUN
ejpam-3575	184	14	]	]	PUNCT
ejpam-3575	184	15	6=	6=	ADP
ejpam-3575	184	16	∅.	∅.	ADP
ejpam-3575	184	17	obviously	obviously	ADV
ejpam-3575	184	18	,	,	PUNCT
ejpam-3575	184	19	0	0	NUM
ejpam-3575	184	20	∈	∈	NOUN
ejpam-3575	184	21	inf[h;k	inf[h;k	NOUN
ejpam-3575	184	22	]	]	PUNCT
ejpam-3575	184	23	.	.	PUNCT
ejpam-3575	185	1	let	let	VERB
ejpam-3575	185	2	x	x	PRON
ejpam-3575	185	3	,	,	PUNCT
ejpam-3575	185	4	y	y	PROPN
ejpam-3575	185	5	∈	∈	PROPN
ejpam-3575	185	6	x	x	AUX
ejpam-3575	185	7	be	be	AUX
ejpam-3575	185	8	such	such	ADJ
ejpam-3575	185	9	that	that	SCONJ
ejpam-3575	185	10	x	x	PUNCT
ejpam-3575	185	11	∗	∗	NOUN
ejpam-3575	185	12	y	y	PROPN
ejpam-3575	185	13	∈	∈	PROPN
ejpam-3575	185	14	inf[h;k	inf[h;k	NOUN
ejpam-3575	185	15	]	]	PUNCT
ejpam-3575	185	16	and	and	CCONJ
ejpam-3575	185	17	y	y	PROPN
ejpam-3575	185	18	∈	∈	PROPN
ejpam-3575	185	19	inf[h;k	inf[h;k	NOUN
ejpam-3575	185	20	]	]	PUNCT
ejpam-3575	185	21	.	.	PUNCT
ejpam-3575	186	1	then	then	ADV
ejpam-3575	186	2	inf	inf	PROPN
ejpam-3575	186	3	h(x	h(x	PROPN
ejpam-3575	186	4	∗	∗	PROPN
ejpam-3575	186	5	y	y	PROPN
ejpam-3575	186	6	)	)	PUNCT
ejpam-3575	186	7	≥	≥	PROPN
ejpam-3575	186	8	inf	inf	PROPN
ejpam-3575	186	9	k	k	PROPN
ejpam-3575	186	10	and	and	CCONJ
ejpam-3575	186	11	inf	inf	PROPN
ejpam-3575	186	12	h(y	h(y	ADV
ejpam-3575	186	13	)	)	PUNCT
ejpam-3575	186	14	≥	≥	PROPN
ejpam-3575	186	15	inf	inf	PROPN
ejpam-3575	186	16	k.	k.	PROPN
ejpam-3575	187	1	it	it	PRON
ejpam-3575	187	2	follows	follow	VERB
ejpam-3575	187	3	from	from	ADP
ejpam-3575	187	4	(	(	PUNCT
ejpam-3575	187	5	17	17	NUM
ejpam-3575	187	6	)	)	PUNCT
ejpam-3575	187	7	that	that	PRON
ejpam-3575	187	8	inf	inf	PROPN
ejpam-3575	187	9	h(x	h(x	PROPN
ejpam-3575	187	10	)	)	PUNCT
ejpam-3575	187	11	≥	≥	NOUN
ejpam-3575	187	12	min{inf	min{inf	VERB
ejpam-3575	187	13	h(x	h(x	PROPN
ejpam-3575	187	14	∗	∗	PROPN
ejpam-3575	187	15	y	y	PROPN
ejpam-3575	187	16	)	)	PUNCT
ejpam-3575	187	17	,	,	PUNCT
ejpam-3575	187	18	inf	inf	PROPN
ejpam-3575	187	19	h(y	h(y	ADV
ejpam-3575	187	20	)	)	PUNCT
ejpam-3575	187	21	}	}	PUNCT
ejpam-3575	188	1	≥	≥	NOUN
ejpam-3575	188	2	inf	inf	PROPN
ejpam-3575	188	3	k	k	PROPN
ejpam-3575	188	4	and	and	CCONJ
ejpam-3575	188	5	that	that	SCONJ
ejpam-3575	188	6	x	x	PUNCT
ejpam-3575	188	7	∈	∈	PROPN
ejpam-3575	188	8	inf[h;k	inf[h;k	NOUN
ejpam-3575	188	9	]	]	PUNCT
ejpam-3575	188	10	.	.	PUNCT
ejpam-3575	189	1	hence	hence	ADV
ejpam-3575	189	2	inf[h;k	inf[h;k	PROPN
ejpam-3575	189	3	]	]	PUNCT
ejpam-3575	189	4	is	be	AUX
ejpam-3575	189	5	an	an	DET
ejpam-3575	189	6	ideal	ideal	NOUN
ejpam-3575	189	7	of	of	ADP
ejpam-3575	189	8	x	x	PUNCT
ejpam-3575	189	9	for	for	ADP
ejpam-3575	189	10	all	all	DET
ejpam-3575	189	11	k	k	PROPN
ejpam-3575	189	12	∈	∈	PROPN
ejpam-3575	189	13	p	p	PROPN
ejpam-3575	189	14	∗([0	∗([0	NOUN
ejpam-3575	189	15	,	,	PUNCT
ejpam-3575	189	16	1	1	NUM
ejpam-3575	189	17	]	]	NUM
ejpam-3575	189	18	)	)	PUNCT
ejpam-3575	189	19	,	,	PUNCT
ejpam-3575	189	20	and	and	CCONJ
ejpam-3575	189	21	therefore	therefore	ADV
ejpam-3575	189	22	h	h	NOUN
ejpam-3575	189	23	:	:	PUNCT
ejpam-3575	189	24	=	=	SYM
ejpam-3575	189	25	{	{	PUNCT
ejpam-3575	189	26	(	(	PUNCT
ejpam-3575	189	27	x	x	NOUN
ejpam-3575	189	28	,	,	PUNCT
ejpam-3575	189	29	h(x	h(x	PROPN
ejpam-3575	189	30	)	)	PUNCT
ejpam-3575	189	31	)	)	PUNCT
ejpam-3575	190	1	|	|	ADV
ejpam-3575	190	2	x	x	SYM
ejpam-3575	190	3	∈	∈	NOUN
ejpam-3575	190	4	x	x	X
ejpam-3575	190	5	}	}	PUNCT
ejpam-3575	190	6	is	be	AUX
ejpam-3575	190	7	an	an	DET
ejpam-3575	190	8	inf	inf	ADJ
ejpam-3575	190	9	-	-	PUNCT
ejpam-3575	190	10	hesitant	hesitant	ADJ
ejpam-3575	190	11	fuzzy	fuzzy	ADJ
ejpam-3575	190	12	ideal	ideal	NOUN
ejpam-3575	190	13	of	of	ADP
ejpam-3575	190	14	x.	x.	PROPN
ejpam-3575	190	15	theorem	theorem	NOUN
ejpam-3575	190	16	3	3	X
ejpam-3575	190	17	.	.	PUNCT
ejpam-3575	191	1	let	let	VERB
ejpam-3575	191	2	h	h	NOUN
ejpam-3575	191	3	:	:	PUNCT
ejpam-3575	191	4	=	=	SYM
ejpam-3575	191	5	{	{	PUNCT
ejpam-3575	191	6	(	(	PUNCT
ejpam-3575	191	7	x	x	NOUN
ejpam-3575	191	8	,	,	PUNCT
ejpam-3575	191	9	h(x	h(x	PROPN
ejpam-3575	191	10	)	)	PUNCT
ejpam-3575	191	11	)	)	PUNCT
ejpam-3575	192	1	|	|	ADV
ejpam-3575	192	2	x	x	SYM
ejpam-3575	192	3	∈	∈	NOUN
ejpam-3575	192	4	x	x	VERB
ejpam-3575	192	5	}	}	PUNCT
ejpam-3575	192	6	be	be	AUX
ejpam-3575	192	7	a	a	DET
ejpam-3575	192	8	hesitant	hesitant	ADJ
ejpam-3575	192	9	fuzzy	fuzzy	ADJ
ejpam-3575	192	10	set	set	NOUN
ejpam-3575	192	11	on	on	ADP
ejpam-3575	192	12	a	a	DET
ejpam-3575	192	13	bci	bci	NOUN
ejpam-3575	192	14	-	-	NOUN
ejpam-3575	192	15	algebra	algebra	NOUN
ejpam-3575	192	16	x	x	PUNCT
ejpam-3575	192	17	defined	define	VERB
ejpam-3575	192	18	by	by	ADP
ejpam-3575	192	19	h	h	NOUN
ejpam-3575	192	20	=	=	SYM
ejpam-3575	192	21	{	{	PUNCT
ejpam-3575	192	22	(	(	PUNCT
ejpam-3575	192	23	x	x	X
ejpam-3575	192	24	,	,	PUNCT
ejpam-3575	192	25	d	d	NOUN
ejpam-3575	192	26	)	)	PUNCT
ejpam-3575	192	27	,	,	PUNCT
ejpam-3575	192	28	(	(	PUNCT
ejpam-3575	192	29	y	y	NOUN
ejpam-3575	192	30	,	,	PUNCT
ejpam-3575	192	31	e	e	NOUN
ejpam-3575	192	32	)	)	PUNCT
ejpam-3575	193	1	|	|	ADV
ejpam-3575	193	2	x	x	SYM
ejpam-3575	193	3	∈	∈	PROPN
ejpam-3575	193	4	b	b	PROPN
ejpam-3575	193	5	,	,	PUNCT
ejpam-3575	193	6	y	y	PROPN
ejpam-3575	193	7	∈	∈	PROPN
ejpam-3575	193	8	x	x	X
ejpam-3575	193	9	\b	\b	X
ejpam-3575	193	10	,	,	PUNCT
ejpam-3575	193	11	inf	inf	PROPN
ejpam-3575	193	12	d	d	X
ejpam-3575	193	13	≥	≥	X
ejpam-3575	193	14	inf	inf	PROPN
ejpam-3575	193	15	e	e	NOUN
ejpam-3575	193	16	}	}	PUNCT
ejpam-3575	193	17	where	where	SCONJ
ejpam-3575	193	18	d	d	NOUN
ejpam-3575	193	19	,	,	PUNCT
ejpam-3575	193	20	e	e	PROPN
ejpam-3575	193	21	∈	∈	PROPN
ejpam-3575	193	22	p	p	NOUN
ejpam-3575	193	23	∗([0	∗([0	NOUN
ejpam-3575	193	24	,	,	PUNCT
ejpam-3575	193	25	1	1	NUM
ejpam-3575	193	26	]	]	PUNCT
ejpam-3575	193	27	)	)	PUNCT
ejpam-3575	193	28	and	and	CCONJ
ejpam-3575	193	29	b	b	X
ejpam-3575	193	30	is	be	AUX
ejpam-3575	193	31	the	the	DET
ejpam-3575	193	32	bck	bck	NOUN
ejpam-3575	193	33	-	-	PUNCT
ejpam-3575	193	34	part	part	NOUN
ejpam-3575	193	35	of	of	ADP
ejpam-3575	193	36	x.	x.	NOUN
ejpam-3575	193	37	then	then	ADV
ejpam-3575	193	38	h	h	VERB
ejpam-3575	193	39	:	:	PUNCT
ejpam-3575	193	40	=	=	SYM
ejpam-3575	193	41	{	{	PUNCT
ejpam-3575	193	42	(	(	PUNCT
ejpam-3575	193	43	x	x	NOUN
ejpam-3575	193	44	,	,	PUNCT
ejpam-3575	193	45	h(x	h(x	PROPN
ejpam-3575	193	46	)	)	PUNCT
ejpam-3575	193	47	)	)	PUNCT
ejpam-3575	194	1	|	|	ADV
ejpam-3575	194	2	x	x	SYM
ejpam-3575	194	3	∈	∈	NOUN
ejpam-3575	194	4	x	x	X
ejpam-3575	194	5	}	}	PUNCT
ejpam-3575	194	6	is	be	AUX
ejpam-3575	194	7	an	an	DET
ejpam-3575	194	8	inf	inf	ADJ
ejpam-3575	194	9	-	-	PUNCT
ejpam-3575	194	10	hesitant	hesitant	ADJ
ejpam-3575	194	11	fuzzy	fuzzy	ADJ
ejpam-3575	194	12	ideal	ideal	NOUN
ejpam-3575	194	13	of	of	ADP
ejpam-3575	194	14	x.	x.	NOUN
ejpam-3575	194	15	proof	proof	NOUN
ejpam-3575	194	16	.	.	PUNCT
ejpam-3575	195	1	since	since	SCONJ
ejpam-3575	195	2	0	0	NUM
ejpam-3575	195	3	∈	∈	PROPN
ejpam-3575	195	4	b	b	NOUN
ejpam-3575	195	5	,	,	PUNCT
ejpam-3575	195	6	we	we	PRON
ejpam-3575	195	7	have	have	VERB
ejpam-3575	195	8	inf	inf	VERB
ejpam-3575	195	9	h(0	h(0	PROPN
ejpam-3575	195	10	)	)	PUNCT
ejpam-3575	195	11	=	=	SYM
ejpam-3575	195	12	inf	inf	PROPN
ejpam-3575	195	13	d	d	PROPN
ejpam-3575	195	14	≥	≥	PROPN
ejpam-3575	195	15	inf	inf	PROPN
ejpam-3575	195	16	h(x	h(x	PROPN
ejpam-3575	195	17	)	)	PUNCT
ejpam-3575	195	18	for	for	ADP
ejpam-3575	195	19	all	all	PRON
ejpam-3575	195	20	x	x	SYM
ejpam-3575	195	21	∈	∈	NOUN
ejpam-3575	195	22	x.	x.	NOUN
ejpam-3575	195	23	let	let	VERB
ejpam-3575	195	24	x	x	PRON
ejpam-3575	195	25	,	,	PUNCT
ejpam-3575	195	26	y	y	PROPN
ejpam-3575	195	27	∈	∈	PROPN
ejpam-3575	195	28	x.	x.	NOUN
ejpam-3575	196	1	if	if	SCONJ
ejpam-3575	196	2	x	x	PROPN
ejpam-3575	196	3	∈	∈	PROPN
ejpam-3575	196	4	b	b	PROPN
ejpam-3575	196	5	,	,	PUNCT
ejpam-3575	196	6	then	then	ADV
ejpam-3575	196	7	it	it	PRON
ejpam-3575	196	8	is	be	AUX
ejpam-3575	196	9	clear	clear	ADJ
ejpam-3575	196	10	that	that	SCONJ
ejpam-3575	196	11	inf	inf	PROPN
ejpam-3575	196	12	h(x	h(x	PROPN
ejpam-3575	196	13	)	)	PUNCT
ejpam-3575	196	14	≥	≥	NOUN
ejpam-3575	196	15	min{inf	min{inf	VERB
ejpam-3575	196	16	h(x	h(x	PROPN
ejpam-3575	196	17	∗	∗	PROPN
ejpam-3575	196	18	y	y	PROPN
ejpam-3575	196	19	)	)	PUNCT
ejpam-3575	196	20	,	,	PUNCT
ejpam-3575	196	21	inf	inf	PROPN
ejpam-3575	196	22	h(y	h(y	ADV
ejpam-3575	196	23	)	)	PUNCT
ejpam-3575	196	24	}	}	PUNCT
ejpam-3575	196	25	.	.	PUNCT
ejpam-3575	197	1	assume	assume	VERB
ejpam-3575	197	2	that	that	SCONJ
ejpam-3575	197	3	x	x	PUNCT
ejpam-3575	197	4	∈	∈	PROPN
ejpam-3575	197	5	x	x	PUNCT
ejpam-3575	197	6	\b	\b	NOUN
ejpam-3575	197	7	.	.	PUNCT
ejpam-3575	198	1	since	since	SCONJ
ejpam-3575	198	2	b	b	PROPN
ejpam-3575	198	3	is	be	AUX
ejpam-3575	198	4	an	an	DET
ejpam-3575	198	5	ideal	ideal	NOUN
ejpam-3575	198	6	of	of	ADP
ejpam-3575	198	7	x	x	PRON
ejpam-3575	198	8	,	,	PUNCT
ejpam-3575	198	9	it	it	PRON
ejpam-3575	198	10	follows	follow	VERB
ejpam-3575	198	11	that	that	SCONJ
ejpam-3575	198	12	x∗y	x∗y	PUNCT
ejpam-3575	198	13	∈	∈	PROPN
ejpam-3575	198	14	x	x	SYM
ejpam-3575	198	15	\b	\b	NOUN
ejpam-3575	198	16	or	or	CCONJ
ejpam-3575	198	17	y	y	PROPN
ejpam-3575	198	18	∈	∈	PROPN
ejpam-3575	198	19	x	x	X
ejpam-3575	198	20	\b	\b	NOUN
ejpam-3575	198	21	and	and	CCONJ
ejpam-3575	198	22	that	that	DET
ejpam-3575	198	23	inf	inf	NOUN
ejpam-3575	198	24	h(x	h(x	PROPN
ejpam-3575	198	25	)	)	PUNCT
ejpam-3575	199	1	=	=	VERB
ejpam-3575	199	2	min{inf	min{inf	VERB
ejpam-3575	199	3	h(x	h(x	PROPN
ejpam-3575	199	4	∗	∗	PROPN
ejpam-3575	199	5	y	y	PROPN
ejpam-3575	199	6	)	)	PUNCT
ejpam-3575	199	7	,	,	PUNCT
ejpam-3575	199	8	inf	inf	PROPN
ejpam-3575	199	9	h(y	h(y	ADV
ejpam-3575	199	10	)	)	PUNCT
ejpam-3575	199	11	}	}	PUNCT
ejpam-3575	199	12	.	.	PUNCT
ejpam-3575	200	1	therefore	therefore	ADV
ejpam-3575	200	2	h	h	NOUN
ejpam-3575	200	3	:	:	PUNCT
ejpam-3575	200	4	=	=	SYM
ejpam-3575	200	5	{	{	PUNCT
ejpam-3575	200	6	(	(	PUNCT
ejpam-3575	200	7	x	x	NOUN
ejpam-3575	200	8	,	,	PUNCT
ejpam-3575	200	9	h(x	h(x	PROPN
ejpam-3575	200	10	)	)	PUNCT
ejpam-3575	200	11	)	)	PUNCT
ejpam-3575	201	1	|	|	ADV
ejpam-3575	201	2	x	x	SYM
ejpam-3575	201	3	∈	∈	NOUN
ejpam-3575	201	4	x	x	X
ejpam-3575	201	5	}	}	PUNCT
ejpam-3575	201	6	is	be	AUX
ejpam-3575	201	7	an	an	DET
ejpam-3575	201	8	int	int	NOUN
ejpam-3575	201	9	-	-	PUNCT
ejpam-3575	201	10	hesitant	hesitant	ADJ
ejpam-3575	201	11	fuzzy	fuzzy	ADJ
ejpam-3575	201	12	ideal	ideal	NOUN
ejpam-3575	201	13	of	of	ADP
ejpam-3575	201	14	x	x	PUNCT
ejpam-3575	201	15	by	by	ADP
ejpam-3575	201	16	theorem	theorem	NOUN
ejpam-3575	201	17	2	2	NUM
ejpam-3575	201	18	.	.	PUNCT
ejpam-3575	201	19	acknowledgements	acknowledgement	NOUN
ejpam-3575	201	20	the	the	DET
ejpam-3575	201	21	authors	author	NOUN
ejpam-3575	201	22	would	would	AUX
ejpam-3575	201	23	like	like	VERB
ejpam-3575	201	24	to	to	PART
ejpam-3575	201	25	express	express	VERB
ejpam-3575	201	26	their	their	PRON
ejpam-3575	201	27	sincere	sincere	ADJ
ejpam-3575	201	28	thanks	thank	NOUN
ejpam-3575	201	29	to	to	ADP
ejpam-3575	201	30	the	the	DET
ejpam-3575	201	31	learned	learn	VERB
ejpam-3575	201	32	reviewers	reviewer	NOUN
ejpam-3575	201	33	for	for	ADP
ejpam-3575	201	34	valuable	valuable	ADJ
ejpam-3575	201	35	comments	comment	NOUN
ejpam-3575	201	36	and	and	CCONJ
ejpam-3575	201	37	several	several	ADJ
ejpam-3575	201	38	useful	useful	ADJ
ejpam-3575	201	39	suggestions	suggestion	NOUN
ejpam-3575	201	40	.	.	PUNCT
ejpam-3575	202	1	this	this	DET
ejpam-3575	202	2	research	research	NOUN
ejpam-3575	202	3	was	be	AUX
ejpam-3575	202	4	partially	partially	ADV
ejpam-3575	202	5	supported	support	VERB
ejpam-3575	202	6	by	by	ADP
ejpam-3575	202	7	the	the	DET
ejpam-3575	202	8	research	research	NOUN
ejpam-3575	202	9	grant	grant	NOUN
ejpam-3575	202	10	s-0198	s-0198	NOUN
ejpam-3575	202	11	-	-	PUNCT
ejpam-3575	202	12	1440	1440	NUM
ejpam-3575	202	13	,	,	PUNCT
ejpam-3575	202	14	deanship	deanship	NOUN
ejpam-3575	202	15	of	of	ADP
ejpam-3575	202	16	scientific	scientific	ADJ
ejpam-3575	202	17	research	research	NOUN
ejpam-3575	202	18	,	,	PUNCT
ejpam-3575	202	19	university	university	NOUN
ejpam-3575	202	20	of	of	ADP
ejpam-3575	202	21	tabuk	tabuk	PROPN
ejpam-3575	202	22	,	,	PUNCT
ejpam-3575	202	23	tabuk-71491	tabuk-71491	NOUN
ejpam-3575	202	24	,	,	PUNCT
ejpam-3575	202	25	saudi	saudi	PROPN
ejpam-3575	202	26	arabia	arabia	PROPN
ejpam-3575	202	27	.	.	PUNCT
ejpam-3575	203	1	references	reference	NOUN
ejpam-3575	203	2	[	[	X
ejpam-3575	203	3	1	1	NUM
ejpam-3575	203	4	]	]	X
ejpam-3575	203	5	y.	y.	PROPN
ejpam-3575	203	6	huang	huang	PROPN
ejpam-3575	203	7	,	,	PUNCT
ejpam-3575	203	8	bci	bci	PROPN
ejpam-3575	203	9	-	-	NOUN
ejpam-3575	203	10	algebra	algebra	NOUN
ejpam-3575	203	11	,	,	PUNCT
ejpam-3575	203	12	science	science	NOUN
ejpam-3575	203	13	press	press	NOUN
ejpam-3575	203	14	,	,	PUNCT
ejpam-3575	203	15	beijing	beijing	PROPN
ejpam-3575	203	16	2006	2006	NUM
ejpam-3575	203	17	.	.	PUNCT
ejpam-3575	204	1	[	[	X
ejpam-3575	204	2	2	2	NUM
ejpam-3575	204	3	]	]	X
ejpam-3575	204	4	y.b	y.b	PROPN
ejpam-3575	204	5	.	.	PROPN
ejpam-3575	204	6	jun	jun	PROPN
ejpam-3575	204	7	and	and	CCONJ
ejpam-3575	204	8	s.s	s.s	PROPN
ejpam-3575	204	9	.	.	PROPN
ejpam-3575	204	10	ahn	ahn	PROPN
ejpam-3575	204	11	,	,	PUNCT
ejpam-3575	204	12	hesitant	hesitant	ADJ
ejpam-3575	204	13	fuzzy	fuzzy	ADJ
ejpam-3575	204	14	set	set	NOUN
ejpam-3575	204	15	theory	theory	NOUN
ejpam-3575	204	16	applied	apply	VERB
ejpam-3575	204	17	to	to	PART
ejpam-3575	204	18	bck	bck	VERB
ejpam-3575	204	19	/	/	SYM
ejpam-3575	204	20	bci	bci	NOUN
ejpam-3575	204	21	-	-	PUNCT
ejpam-3575	204	22	algerbas	algerbas	ADJ
ejpam-3575	204	23	,	,	PUNCT
ejpam-3575	204	24	j.	j.	PROPN
ejpam-3575	204	25	comput	comput	PROPN
ejpam-3575	204	26	.	.	PUNCT
ejpam-3575	205	1	anal	anal	PROPN
ejpam-3575	205	2	.	.	PUNCT
ejpam-3575	205	3	appl	appl	PROPN
ejpam-3575	205	4	.	.	PROPN
ejpam-3575	206	1	2016	2016	NUM
ejpam-3575	206	2	,	,	PUNCT
ejpam-3575	206	3	20(4	20(4	NOUN
ejpam-3575	206	4	)	)	PUNCT
ejpam-3575	206	5	,	,	PUNCT
ejpam-3575	206	6	635–646	635–646	NUM
ejpam-3575	206	7	.	.	PUNCT
ejpam-3575	207	1	[	[	X
ejpam-3575	207	2	3	3	NUM
ejpam-3575	207	3	]	]	X
ejpam-3575	207	4	y.	y.	PROPN
ejpam-3575	207	5	b.	b.	PROPN
ejpam-3575	207	6	jun	jun	PROPN
ejpam-3575	207	7	,	,	PUNCT
ejpam-3575	207	8	sun	sun	PROPN
ejpam-3575	207	9	shin	shin	PROPN
ejpam-3575	207	10	ahn	ahn	PROPN
ejpam-3575	207	11	and	and	CCONJ
ejpam-3575	207	12	g.	g.	PROPN
ejpam-3575	207	13	muhiuddin	muhiuddin	PROPN
ejpam-3575	207	14	,	,	PUNCT
ejpam-3575	207	15	hesitant	hesitant	ADJ
ejpam-3575	207	16	fuzzy	fuzzy	ADJ
ejpam-3575	207	17	soft	soft	ADJ
ejpam-3575	207	18	subalgebras	subalgebra	NOUN
ejpam-3575	207	19	and	and	CCONJ
ejpam-3575	207	20	ideals	ideal	NOUN
ejpam-3575	207	21	in	in	ADP
ejpam-3575	207	22	bck	bck	PROPN
ejpam-3575	207	23	/	/	SYM
ejpam-3575	207	24	bci	bci	NOUN
ejpam-3575	207	25	-	-	PUNCT
ejpam-3575	207	26	algebras	algebra	NOUN
ejpam-3575	207	27	,	,	PUNCT
ejpam-3575	207	28	the	the	DET
ejpam-3575	207	29	scientific	scientific	ADJ
ejpam-3575	207	30	world	world	NOUN
ejpam-3575	207	31	journal	journal	NOUN
ejpam-3575	207	32	,	,	PUNCT
ejpam-3575	207	33	volume	volume	NOUN
ejpam-3575	207	34	2014	2014	NUM
ejpam-3575	207	35	,	,	PUNCT
ejpam-3575	207	36	article	article	NOUN
ejpam-3575	207	37	i	i	PROPN
ejpam-3575	207	38	d	d	PROPN
ejpam-3575	207	39	763929	763929	NUM
ejpam-3575	207	40	,	,	PUNCT
ejpam-3575	207	41	7	7	NUM
ejpam-3575	207	42	pages	page	NOUN
ejpam-3575	207	43	(	(	PUNCT
ejpam-3575	207	44	2014	2014	NUM
ejpam-3575	207	45	)	)	PUNCT
ejpam-3575	207	46	.	.	PUNCT
ejpam-3575	208	1	references	reference	NOUN
ejpam-3575	208	2	17	17	NUM
ejpam-3575	209	1	[	[	X
ejpam-3575	209	2	4	4	NUM
ejpam-3575	209	3	]	]	X
ejpam-3575	209	4	y.	y.	PROPN
ejpam-3575	209	5	b.	b.	PROPN
ejpam-3575	209	6	jun	jun	PROPN
ejpam-3575	209	7	and	and	CCONJ
ejpam-3575	209	8	s.	s.	PROPN
ejpam-3575	209	9	z.	z.	PROPN
ejpam-3575	209	10	song	song	PROPN
ejpam-3575	209	11	and	and	CCONJ
ejpam-3575	209	12	g.	g.	PROPN
ejpam-3575	209	13	muhiuddin	muhiuddin	PROPN
ejpam-3575	209	14	,	,	PUNCT
ejpam-3575	209	15	hesitant	hesitant	ADJ
ejpam-3575	209	16	fuzzy	fuzzy	ADJ
ejpam-3575	209	17	semigroups	semigroup	NOUN
ejpam-3575	209	18	with	with	ADP
ejpam-3575	209	19	a	a	DET
ejpam-3575	209	20	frontier	frontier	NOUN
ejpam-3575	209	21	,	,	PUNCT
ejpam-3575	209	22	journal	journal	NOUN
ejpam-3575	209	23	of	of	ADP
ejpam-3575	209	24	intelligent	intelligent	ADJ
ejpam-3575	209	25	and	and	CCONJ
ejpam-3575	209	26	fuzzy	fuzzy	ADJ
ejpam-3575	209	27	systems	system	NOUN
ejpam-3575	209	28	,	,	PUNCT
ejpam-3575	209	29	vol	vol	NOUN
ejpam-3575	209	30	.	.	PROPN
ejpam-3575	209	31	30	30	NUM
ejpam-3575	209	32	,	,	PUNCT
ejpam-3575	209	33	no	no	INTJ
ejpam-3575	209	34	.	.	NOUN
ejpam-3575	209	35	3	3	NUM
ejpam-3575	209	36	,	,	PUNCT
ejpam-3575	209	37	pp	pp	ADJ
ejpam-3575	209	38	.	.	PUNCT
ejpam-3575	210	1	1613	1613	NUM
ejpam-3575	210	2	-	-	SYM
ejpam-3575	210	3	1618	1618	NUM
ejpam-3575	210	4	(	(	PUNCT
ejpam-3575	210	5	2016	2016	NUM
ejpam-3575	210	6	)	)	PUNCT
ejpam-3575	210	7	.	.	PUNCT
ejpam-3575	211	1	[	[	X
ejpam-3575	211	2	5	5	X
ejpam-3575	211	3	]	]	X
ejpam-3575	211	4	y.	y.	PROPN
ejpam-3575	211	5	b.	b.	PROPN
ejpam-3575	211	6	jun	jun	PROPN
ejpam-3575	211	7	,	,	PUNCT
ejpam-3575	211	8	m.	m.	NOUN
ejpam-3575	211	9	a.	a.	NOUN
ejpam-3575	211	10	ozturk	ozturk	PROPN
ejpam-3575	211	11	and	and	CCONJ
ejpam-3575	211	12	g.	g.	PROPN
ejpam-3575	211	13	muhiuddin	muhiuddin	PROPN
ejpam-3575	211	14	,	,	PUNCT
ejpam-3575	211	15	a	a	DET
ejpam-3575	211	16	novel	novel	ADJ
ejpam-3575	211	17	generalization	generalization	NOUN
ejpam-3575	211	18	of	of	ADP
ejpam-3575	211	19	fuzzy	fuzzy	ADJ
ejpam-3575	211	20	subsemigroups	subsemigroup	NOUN
ejpam-3575	211	21	,	,	PUNCT
ejpam-3575	211	22	annals	annal	NOUN
ejpam-3575	211	23	of	of	ADP
ejpam-3575	211	24	fuzzy	fuzzy	ADJ
ejpam-3575	211	25	mathematics	mathematic	NOUN
ejpam-3575	211	26	and	and	CCONJ
ejpam-3575	211	27	informatics	informatic	NOUN
ejpam-3575	211	28	,	,	PUNCT
ejpam-3575	211	29	(	(	PUNCT
ejpam-3575	211	30	2017	2017	NUM
ejpam-3575	211	31	)	)	PUNCT
ejpam-3575	211	32	volume	volume	NOUN
ejpam-3575	211	33	14	14	NUM
ejpam-3575	211	34	,	,	PUNCT
ejpam-3575	211	35	no	no	INTJ
ejpam-3575	211	36	.	.	NOUN
ejpam-3575	211	37	4	4	NUM
ejpam-3575	211	38	,	,	PUNCT
ejpam-3575	211	39	(	(	PUNCT
ejpam-3575	211	40	october	october	PROPN
ejpam-3575	211	41	2017	2017	NUM
ejpam-3575	211	42	)	)	PUNCT
ejpam-3575	211	43	,	,	PUNCT
ejpam-3575	211	44	pp	pp	ADP
ejpam-3575	211	45	.	.	PUNCT
ejpam-3575	212	1	359370	359370	NUM
ejpam-3575	212	2	.	.	PUNCT
ejpam-3575	213	1	[	[	X
ejpam-3575	213	2	6	6	NUM
ejpam-3575	213	3	]	]	X
ejpam-3575	213	4	y.	y.	PROPN
ejpam-3575	213	5	b.	b.	PROPN
ejpam-3575	213	6	jun	jun	PROPN
ejpam-3575	213	7	and	and	CCONJ
ejpam-3575	213	8	s.	s.	PROPN
ejpam-3575	213	9	z.	z.	PROPN
ejpam-3575	213	10	song	song	PROPN
ejpam-3575	213	11	and	and	CCONJ
ejpam-3575	213	12	g.	g.	PROPN
ejpam-3575	213	13	muhiuddin	muhiuddin	PROPN
ejpam-3575	213	14	,	,	PUNCT
ejpam-3575	213	15	hesitant	hesitant	ADJ
ejpam-3575	213	16	fuzzy	fuzzy	ADJ
ejpam-3575	213	17	semigroups	semigroup	NOUN
ejpam-3575	213	18	with	with	ADP
ejpam-3575	213	19	a	a	DET
ejpam-3575	213	20	frontier	frontier	NOUN
ejpam-3575	213	21	,	,	PUNCT
ejpam-3575	213	22	journal	journal	NOUN
ejpam-3575	213	23	of	of	ADP
ejpam-3575	213	24	intelligent	intelligent	ADJ
ejpam-3575	213	25	and	and	CCONJ
ejpam-3575	213	26	fuzzy	fuzzy	ADJ
ejpam-3575	213	27	systems	system	NOUN
ejpam-3575	213	28	,	,	PUNCT
ejpam-3575	213	29	vol	vol	NOUN
ejpam-3575	213	30	.	.	PROPN
ejpam-3575	213	31	30	30	NUM
ejpam-3575	213	32	,	,	PUNCT
ejpam-3575	213	33	no	no	INTJ
ejpam-3575	213	34	.	.	NOUN
ejpam-3575	213	35	3	3	NUM
ejpam-3575	213	36	,	,	PUNCT
ejpam-3575	213	37	pp	pp	ADJ
ejpam-3575	213	38	.	.	PUNCT
ejpam-3575	213	39	1613	1613	NUM
ejpam-3575	213	40	-	-	SYM
ejpam-3575	213	41	1618	1618	NUM
ejpam-3575	213	42	(	(	PUNCT
ejpam-3575	213	43	2016	2016	NUM
ejpam-3575	213	44	)	)	PUNCT
ejpam-3575	213	45	.	.	PUNCT
ejpam-3575	214	1	[	[	X
ejpam-3575	214	2	7	7	NUM
ejpam-3575	214	3	]	]	X
ejpam-3575	214	4	young	young	ADJ
ejpam-3575	214	5	bae	bae	PROPN
ejpam-3575	214	6	jun	jun	PROPN
ejpam-3575	214	7	,	,	PUNCT
ejpam-3575	214	8	seok	seok	PROPN
ejpam-3575	214	9	zun	zun	PROPN
ejpam-3575	214	10	song	song	NOUN
ejpam-3575	214	11	and	and	CCONJ
ejpam-3575	214	12	g.	g.	PROPN
ejpam-3575	214	13	muhiuddin	muhiuddin	PROPN
ejpam-3575	214	14	,	,	PUNCT
ejpam-3575	214	15	concave	concave	VERB
ejpam-3575	214	16	soft	soft	ADJ
ejpam-3575	214	17	sets	set	NOUN
ejpam-3575	214	18	,	,	PUNCT
ejpam-3575	214	19	critical	critical	ADJ
ejpam-3575	214	20	soft	soft	ADJ
ejpam-3575	214	21	points	point	NOUN
ejpam-3575	214	22	,	,	PUNCT
ejpam-3575	214	23	and	and	CCONJ
ejpam-3575	214	24	union	union	NOUN
ejpam-3575	214	25	-	-	PUNCT
ejpam-3575	214	26	soft	soft	ADJ
ejpam-3575	214	27	ideals	ideal	NOUN
ejpam-3575	214	28	of	of	ADP
ejpam-3575	214	29	ordered	order	VERB
ejpam-3575	214	30	semigroups	semigroup	NOUN
ejpam-3575	214	31	,	,	PUNCT
ejpam-3575	214	32	the	the	DET
ejpam-3575	214	33	scientific	scientific	ADJ
ejpam-3575	214	34	world	world	NOUN
ejpam-3575	214	35	journal	journal	NOUN
ejpam-3575	214	36	,	,	PUNCT
ejpam-3575	214	37	volume	volume	NOUN
ejpam-3575	214	38	2014	2014	NUM
ejpam-3575	214	39	,	,	PUNCT
ejpam-3575	214	40	article	article	NOUN
ejpam-3575	214	41	i	i	PROPN
ejpam-3575	214	42	d	d	PROPN
ejpam-3575	214	43	467968	467968	NUM
ejpam-3575	214	44	,	,	PUNCT
ejpam-3575	214	45	11	11	NUM
ejpam-3575	214	46	pages	page	NOUN
ejpam-3575	214	47	(	(	PUNCT
ejpam-3575	214	48	2014	2014	NUM
ejpam-3575	214	49	)	)	PUNCT
ejpam-3575	214	50	.	.	PUNCT
ejpam-3575	215	1	[	[	X
ejpam-3575	215	2	8	8	NUM
ejpam-3575	215	3	]	]	X
ejpam-3575	215	4	young	young	ADJ
ejpam-3575	215	5	bae	bae	PROPN
ejpam-3575	215	6	jun	jun	PROPN
ejpam-3575	215	7	,	,	PUNCT
ejpam-3575	215	8	seok	seok	PROPN
ejpam-3575	215	9	zun	zun	PROPN
ejpam-3575	215	10	song	song	NOUN
ejpam-3575	215	11	and	and	CCONJ
ejpam-3575	215	12	g.	g.	PROPN
ejpam-3575	215	13	muhiuddin	muhiuddin	PROPN
ejpam-3575	215	14	,	,	PUNCT
ejpam-3575	215	15	concave	concave	VERB
ejpam-3575	215	16	soft	soft	ADJ
ejpam-3575	215	17	sets	set	NOUN
ejpam-3575	215	18	,	,	PUNCT
ejpam-3575	215	19	critical	critical	ADJ
ejpam-3575	215	20	soft	soft	ADJ
ejpam-3575	215	21	points	point	NOUN
ejpam-3575	215	22	,	,	PUNCT
ejpam-3575	215	23	and	and	CCONJ
ejpam-3575	215	24	union	union	NOUN
ejpam-3575	215	25	-	-	PUNCT
ejpam-3575	215	26	soft	soft	ADJ
ejpam-3575	215	27	ideals	ideal	NOUN
ejpam-3575	215	28	of	of	ADP
ejpam-3575	215	29	ordered	order	VERB
ejpam-3575	215	30	semigroups	semigroup	NOUN
ejpam-3575	215	31	,	,	PUNCT
ejpam-3575	215	32	the	the	DET
ejpam-3575	215	33	scientific	scientific	ADJ
ejpam-3575	215	34	world	world	NOUN
ejpam-3575	215	35	journal	journal	NOUN
ejpam-3575	215	36	,	,	PUNCT
ejpam-3575	215	37	volume	volume	NOUN
ejpam-3575	215	38	2014	2014	NUM
ejpam-3575	215	39	,	,	PUNCT
ejpam-3575	215	40	article	article	NOUN
ejpam-3575	215	41	i	i	PROPN
ejpam-3575	215	42	d	d	PROPN
ejpam-3575	215	43	467968	467968	NUM
ejpam-3575	215	44	,	,	PUNCT
ejpam-3575	215	45	11	11	NUM
ejpam-3575	215	46	pages	page	NOUN
ejpam-3575	215	47	(	(	PUNCT
ejpam-3575	215	48	2014	2014	NUM
ejpam-3575	215	49	)	)	PUNCT
ejpam-3575	215	50	.	.	PUNCT
ejpam-3575	216	1	[	[	X
ejpam-3575	216	2	9	9	X
ejpam-3575	216	3	]	]	PUNCT
ejpam-3575	216	4	j.	j.	PROPN
ejpam-3575	216	5	meng	meng	PROPN
ejpam-3575	216	6	and	and	CCONJ
ejpam-3575	216	7	y.	y.	PROPN
ejpam-3575	216	8	b.	b.	PROPN
ejpam-3575	216	9	jun	jun	PROPN
ejpam-3575	216	10	,	,	PUNCT
ejpam-3575	216	11	bck	bck	PROPN
ejpam-3575	216	12	-	-	PUNCT
ejpam-3575	216	13	algebras	algebras	PROPN
ejpam-3575	216	14	,	,	PUNCT
ejpam-3575	216	15	kyungmoon	kyungmoon	PROPN
ejpam-3575	216	16	sa	sa	PROPN
ejpam-3575	216	17	co.	co.	PROPN
ejpam-3575	216	18	seoul	seoul	PROPN
ejpam-3575	216	19	1994	1994	NUM
ejpam-3575	216	20	.	.	PUNCT
ejpam-3575	217	1	[	[	X
ejpam-3575	217	2	10	10	NUM
ejpam-3575	217	3	]	]	X
ejpam-3575	217	4	g.	g.	PROPN
ejpam-3575	217	5	muhiuddin	muhiuddin	PROPN
ejpam-3575	217	6	,	,	PUNCT
ejpam-3575	217	7	hesitant	hesitant	ADJ
ejpam-3575	217	8	fuzzy	fuzzy	ADJ
ejpam-3575	217	9	filters	filter	NOUN
ejpam-3575	217	10	and	and	CCONJ
ejpam-3575	217	11	hesitant	hesitant	ADJ
ejpam-3575	217	12	fuzzy	fuzzy	ADJ
ejpam-3575	217	13	g	g	NOUN
ejpam-3575	217	14	-	-	PUNCT
ejpam-3575	217	15	filters	filter	NOUN
ejpam-3575	217	16	in	in	ADP
ejpam-3575	217	17	residuated	residuate	VERB
ejpam-3575	217	18	lattices	lattice	NOUN
ejpam-3575	217	19	,	,	PUNCT
ejpam-3575	217	20	j.	j.	PROPN
ejpam-3575	217	21	comput	comput	PROPN
ejpam-3575	217	22	.	.	PUNCT
ejpam-3575	218	1	anal	anal	PROPN
ejpam-3575	218	2	.	.	PUNCT
ejpam-3575	218	3	appl	appl	PROPN
ejpam-3575	218	4	.	.	PROPN
ejpam-3575	218	5	,	,	PUNCT
ejpam-3575	218	6	20(2	20(2	NUM
ejpam-3575	218	7	)	)	PUNCT
ejpam-3575	218	8	(	(	PUNCT
ejpam-3575	218	9	2016	2016	NUM
ejpam-3575	218	10	)	)	PUNCT
ejpam-3575	218	11	,	,	PUNCT
ejpam-3575	218	12	394–404	394–404	NUM
ejpam-3575	218	13	.	.	PUNCT
ejpam-3575	219	1	[	[	X
ejpam-3575	219	2	11	11	NUM
ejpam-3575	219	3	]	]	X
ejpam-3575	219	4	g.	g.	PROPN
ejpam-3575	219	5	muhiuddin	muhiuddin	PROPN
ejpam-3575	219	6	and	and	CCONJ
ejpam-3575	219	7	abdullah	abdullah	PROPN
ejpam-3575	219	8	m.	m.	PROPN
ejpam-3575	219	9	al	al	PROPN
ejpam-3575	219	10	-	-	PUNCT
ejpam-3575	219	11	roqi	roqi	ADJ
ejpam-3575	219	12	,	,	PUNCT
ejpam-3575	219	13	regular	regular	ADJ
ejpam-3575	219	14	hesitant	hesitant	ADJ
ejpam-3575	219	15	fuzzy	fuzzy	ADJ
ejpam-3575	219	16	filters	filter	NOUN
ejpam-3575	219	17	and	and	CCONJ
ejpam-3575	219	18	mv	mv	PROPN
ejpam-3575	219	19	hesitant	hesitant	ADJ
ejpam-3575	219	20	fuzzy	fuzzy	ADJ
ejpam-3575	219	21	filters	filter	NOUN
ejpam-3575	219	22	of	of	ADP
ejpam-3575	219	23	residuated	residuate	VERB
ejpam-3575	219	24	lattices	lattice	NOUN
ejpam-3575	219	25	,	,	PUNCT
ejpam-3575	219	26	journal	journal	NOUN
ejpam-3575	219	27	of	of	ADP
ejpam-3575	219	28	computational	computational	ADJ
ejpam-3575	219	29	analysis	analysis	NOUN
ejpam-3575	219	30	and	and	CCONJ
ejpam-3575	219	31	applications	application	NOUN
ejpam-3575	219	32	,	,	PUNCT
ejpam-3575	219	33	vol	vol	NOUN
ejpam-3575	219	34	.	.	PROPN
ejpam-3575	219	35	24	24	NUM
ejpam-3575	219	36	,	,	PUNCT
ejpam-3575	219	37	no.6	no.6	PROPN
ejpam-3575	219	38	(	(	PUNCT
ejpam-3575	219	39	2018	2018	NUM
ejpam-3575	219	40	)	)	PUNCT
ejpam-3575	219	41	,	,	PUNCT
ejpam-3575	219	42	1133–1144	1133–1144	NUM
ejpam-3575	219	43	.	.	PUNCT
ejpam-3575	220	1	[	[	X
ejpam-3575	220	2	12	12	NUM
ejpam-3575	220	3	]	]	X
ejpam-3575	220	4	g.	g.	PROPN
ejpam-3575	220	5	muhiuddin	muhiuddin	PROPN
ejpam-3575	220	6	,	,	PUNCT
ejpam-3575	220	7	e.	e.	PROPN
ejpam-3575	220	8	h.	h.	PROPN
ejpam-3575	220	9	roh	roh	PROPN
ejpam-3575	220	10	,	,	PUNCT
ejpam-3575	220	11	sun	sun	PROPN
ejpam-3575	220	12	shin	shin	PROPN
ejpam-3575	220	13	ahn	ahn	PROPN
ejpam-3575	220	14	and	and	CCONJ
ejpam-3575	220	15	y.	y.	PROPN
ejpam-3575	220	16	b.	b.	PROPN
ejpam-3575	220	17	jun	jun	PROPN
ejpam-3575	220	18	,	,	PUNCT
ejpam-3575	220	19	hesitant	hesitant	ADJ
ejpam-3575	220	20	fuzzy	fuzzy	ADJ
ejpam-3575	220	21	filters	filter	NOUN
ejpam-3575	220	22	in	in	ADP
ejpam-3575	220	23	lattice	lattice	PROPN
ejpam-3575	220	24	implication	implication	NOUN
ejpam-3575	220	25	algebras	algebra	NOUN
ejpam-3575	220	26	,	,	PUNCT
ejpam-3575	220	27	journal	journal	NOUN
ejpam-3575	220	28	of	of	ADP
ejpam-3575	220	29	computational	computational	ADJ
ejpam-3575	220	30	analysis	analysis	NOUN
ejpam-3575	220	31	and	and	CCONJ
ejpam-3575	220	32	applications	application	NOUN
ejpam-3575	220	33	,	,	PUNCT
ejpam-3575	220	34	vol	vol	NOUN
ejpam-3575	220	35	.	.	PROPN
ejpam-3575	220	36	22	22	NUM
ejpam-3575	220	37	,	,	PUNCT
ejpam-3575	220	38	no.6	no.6	PROPN
ejpam-3575	220	39	,	,	PUNCT
ejpam-3575	220	40	(	(	PUNCT
ejpam-3575	220	41	2017	2017	NUM
ejpam-3575	220	42	)	)	PUNCT
ejpam-3575	220	43	,	,	PUNCT
ejpam-3575	220	44	1105	1105	NUM
ejpam-3575	220	45	-	-	SYM
ejpam-3575	220	46	1113	1113	NUM
ejpam-3575	220	47	.	.	PUNCT
ejpam-3575	221	1	[	[	X
ejpam-3575	221	2	13	13	NUM
ejpam-3575	221	3	]	]	X
ejpam-3575	221	4	g.	g.	PROPN
ejpam-3575	221	5	muhiuddin	muhiuddin	PROPN
ejpam-3575	221	6	,	,	PUNCT
ejpam-3575	221	7	and	and	CCONJ
ejpam-3575	221	8	s.	s.	PROPN
ejpam-3575	221	9	aldhafeeri	aldhafeeri	PROPN
ejpam-3575	221	10	,	,	PUNCT
ejpam-3575	221	11	subalgebras	subalgebras	PROPN
ejpam-3575	221	12	and	and	CCONJ
ejpam-3575	221	13	ideals	ideal	NOUN
ejpam-3575	221	14	in	in	ADP
ejpam-3575	221	15	bck	bck	PROPN
ejpam-3575	221	16	/	/	SYM
ejpam-3575	221	17	bci	bci	NOUN
ejpam-3575	221	18	-	-	PUNCT
ejpam-3575	221	19	algebras	algebras	PROPN
ejpam-3575	221	20	based	base	VERB
ejpam-3575	221	21	on	on	ADP
ejpam-3575	221	22	uni	uni	ADJ
ejpam-3575	221	23	-	-	ADJ
ejpam-3575	221	24	hesitant	hesitant	ADJ
ejpam-3575	221	25	fuzzy	fuzzy	ADJ
ejpam-3575	221	26	set	set	NOUN
ejpam-3575	221	27	theory	theory	NOUN
ejpam-3575	221	28	.	.	PUNCT
ejpam-3575	222	1	eur	eur	PROPN
ejpam-3575	222	2	.	.	PUNCT
ejpam-3575	223	1	j.	j.	PROPN
ejpam-3575	223	2	pure	pure	PROPN
ejpam-3575	223	3	appl	appl	PROPN
ejpam-3575	223	4	.	.	PUNCT
ejpam-3575	223	5	math	math	PROPN
ejpam-3575	223	6	.	.	PUNCT
ejpam-3575	223	7	,	,	PUNCT
ejpam-3575	223	8	11(2	11(2	X
ejpam-3575	223	9	)	)	PUNCT
ejpam-3575	223	10	(	(	PUNCT
ejpam-3575	223	11	2018	2018	NUM
ejpam-3575	223	12	)	)	PUNCT
ejpam-3575	223	13	,	,	PUNCT
ejpam-3575	223	14	417–430	417–430	NUM
ejpam-3575	223	15	.	.	PUNCT
ejpam-3575	224	1	[	[	X
ejpam-3575	224	2	14	14	NUM
ejpam-3575	224	3	]	]	X
ejpam-3575	224	4	g.	g.	PROPN
ejpam-3575	224	5	muhiuddin	muhiuddin	PROPN
ejpam-3575	224	6	,	,	PUNCT
ejpam-3575	224	7	h.	h.	PROPN
ejpam-3575	224	8	s.	s.	PROPN
ejpam-3575	224	9	kim	kim	PROPN
ejpam-3575	224	10	,	,	PUNCT
ejpam-3575	224	11	s.	s.	PROPN
ejpam-3575	224	12	z.	z.	PROPN
ejpam-3575	224	13	song	song	PROPN
ejpam-3575	224	14	and	and	CCONJ
ejpam-3575	224	15	y.	y.	PROPN
ejpam-3575	224	16	b.	b.	PROPN
ejpam-3575	224	17	jun	jun	PROPN
ejpam-3575	224	18	,	,	PUNCT
ejpam-3575	224	19	hesitant	hesitant	ADJ
ejpam-3575	224	20	fuzzy	fuzzy	ADJ
ejpam-3575	224	21	translations	translation	NOUN
ejpam-3575	224	22	and	and	CCONJ
ejpam-3575	224	23	extensions	extension	NOUN
ejpam-3575	224	24	of	of	ADP
ejpam-3575	224	25	subalgebras	subalgebra	NOUN
ejpam-3575	224	26	and	and	CCONJ
ejpam-3575	224	27	ideals	ideal	NOUN
ejpam-3575	224	28	in	in	ADP
ejpam-3575	224	29	bck	bck	PROPN
ejpam-3575	224	30	/	/	SYM
ejpam-3575	224	31	bci	bci	NOUN
ejpam-3575	224	32	-	-	PUNCT
ejpam-3575	224	33	algebras	algebra	NOUN
ejpam-3575	224	34	,	,	PUNCT
ejpam-3575	224	35	journal	journal	NOUN
ejpam-3575	224	36	of	of	ADP
ejpam-3575	224	37	intelligent	intelligent	ADJ
ejpam-3575	224	38	and	and	CCONJ
ejpam-3575	224	39	fuzzy	fuzzy	ADJ
ejpam-3575	224	40	systems	system	NOUN
ejpam-3575	224	41	,	,	PUNCT
ejpam-3575	224	42	vol	vol	NOUN
ejpam-3575	224	43	.	.	PROPN
ejpam-3575	225	1	32	32	NUM
ejpam-3575	225	2	,	,	PUNCT
ejpam-3575	225	3	no	no	INTJ
ejpam-3575	225	4	.	.	NOUN
ejpam-3575	225	5	1	1	NUM
ejpam-3575	225	6	(	(	PUNCT
ejpam-3575	225	7	2017	2017	NUM
ejpam-3575	225	8	)	)	PUNCT
ejpam-3575	225	9	,	,	PUNCT
ejpam-3575	225	10	43–48	43–48	NUM
ejpam-3575	225	11	.	.	PUNCT
ejpam-3575	226	1	[	[	X
ejpam-3575	226	2	15	15	NUM
ejpam-3575	226	3	]	]	X
ejpam-3575	226	4	g.	g.	PROPN
ejpam-3575	226	5	muhiuddin	muhiuddin	PROPN
ejpam-3575	226	6	,	,	PUNCT
ejpam-3575	226	7	abdullah	abdullah	PROPN
ejpam-3575	226	8	m.	m.	PROPN
ejpam-3575	226	9	al	al	PROPN
ejpam-3575	226	10	-	-	PUNCT
ejpam-3575	226	11	roqi	roqi	PROPN
ejpam-3575	226	12	and	and	CCONJ
ejpam-3575	226	13	shuaa	shuaa	ADV
ejpam-3575	226	14	aldhafeeri	aldhafeeri	PROPN
ejpam-3575	226	15	,	,	PUNCT
ejpam-3575	226	16	filter	filter	NOUN
ejpam-3575	226	17	theory	theory	NOUN
ejpam-3575	226	18	in	in	ADP
ejpam-3575	226	19	mtlalgebras	mtlalgebras	PROPN
ejpam-3575	226	20	based	base	VERB
ejpam-3575	226	21	on	on	ADP
ejpam-3575	226	22	uni	uni	ADJ
ejpam-3575	226	23	-	-	ADJ
ejpam-3575	226	24	soft	soft	ADJ
ejpam-3575	226	25	property	property	NOUN
ejpam-3575	226	26	,	,	PUNCT
ejpam-3575	226	27	bulletin	bulletin	NOUN
ejpam-3575	226	28	of	of	ADP
ejpam-3575	226	29	the	the	DET
ejpam-3575	226	30	iranian	iranian	PROPN
ejpam-3575	226	31	mathematical	mathematical	ADJ
ejpam-3575	226	32	society	society	NOUN
ejpam-3575	226	33	,	,	PUNCT
ejpam-3575	226	34	vol	vol	NOUN
ejpam-3575	226	35	.	.	PROPN
ejpam-3575	226	36	43	43	NUM
ejpam-3575	226	37	,	,	PUNCT
ejpam-3575	226	38	no.7	no.7	PROPN
ejpam-3575	226	39	(	(	PUNCT
ejpam-3575	226	40	2017	2017	NUM
ejpam-3575	226	41	)	)	PUNCT
ejpam-3575	226	42	2293–2306	2293–2306	NUM
ejpam-3575	226	43	.	.	PUNCT
ejpam-3575	227	1	[	[	X
ejpam-3575	227	2	16	16	NUM
ejpam-3575	227	3	]	]	PUNCT
ejpam-3575	227	4	a.	a.	PROPN
ejpam-3575	227	5	al	al	PROPN
ejpam-3575	227	6	-	-	PUNCT
ejpam-3575	227	7	roqi	roqi	ADV
ejpam-3575	227	8	,	,	PUNCT
ejpam-3575	227	9	g.	g.	PROPN
ejpam-3575	227	10	muhiuddin	muhiuddin	PROPN
ejpam-3575	227	11	and	and	CCONJ
ejpam-3575	227	12	s.	s.	PROPN
ejpam-3575	227	13	aldhafeeri	aldhafeeri	PROPN
ejpam-3575	227	14	,	,	PUNCT
ejpam-3575	227	15	normal	normal	ADJ
ejpam-3575	227	16	unisoft	unisoft	ADJ
ejpam-3575	227	17	filters	filter	NOUN
ejpam-3575	227	18	in	in	ADP
ejpam-3575	227	19	r0	r0	NOUN
ejpam-3575	227	20	-	-	PUNCT
ejpam-3575	227	21	algebras	algebras	PROPN
ejpam-3575	227	22	,	,	PUNCT
ejpam-3575	227	23	cogent	cogent	NOUN
ejpam-3575	227	24	mathematics	mathematic	NOUN
ejpam-3575	227	25	,	,	PUNCT
ejpam-3575	227	26	vol	vol	NOUN
ejpam-3575	227	27	.	.	PROPN
ejpam-3575	227	28	1	1	NUM
ejpam-3575	227	29	,	,	PUNCT
ejpam-3575	227	30	no.4	no.4	PROPN
ejpam-3575	227	31	(	(	PUNCT
ejpam-3575	227	32	2017	2017	NUM
ejpam-3575	227	33	)	)	PUNCT
ejpam-3575	227	34	1–9	1–9	NOUN
ejpam-3575	227	35	.	.	PUNCT
ejpam-3575	228	1	[	[	X
ejpam-3575	228	2	17	17	NUM
ejpam-3575	228	3	]	]	X
ejpam-3575	228	4	g.	g.	PROPN
ejpam-3575	228	5	muhiuddin	muhiuddin	PROPN
ejpam-3575	228	6	and	and	CCONJ
ejpam-3575	228	7	abdullah	abdullah	PROPN
ejpam-3575	228	8	m.	m.	PROPN
ejpam-3575	228	9	al	al	PROPN
ejpam-3575	228	10	-	-	PUNCT
ejpam-3575	228	11	roqi	roqi	PROPN
ejpam-3575	228	12	,	,	PUNCT
ejpam-3575	228	13	unisoft	unisoft	ADJ
ejpam-3575	228	14	filters	filter	NOUN
ejpam-3575	228	15	in	in	ADP
ejpam-3575	228	16	r0	r0	NOUN
ejpam-3575	228	17	-	-	PUNCT
ejpam-3575	228	18	algebras	algebras	PROPN
ejpam-3575	228	19	,	,	PUNCT
ejpam-3575	228	20	journal	journal	NOUN
ejpam-3575	228	21	of	of	ADP
ejpam-3575	228	22	computational	computational	ADJ
ejpam-3575	228	23	analysis	analysis	NOUN
ejpam-3575	228	24	and	and	CCONJ
ejpam-3575	228	25	applications	application	NOUN
ejpam-3575	228	26	,	,	PUNCT
ejpam-3575	228	27	19	19	NUM
ejpam-3575	228	28	,	,	PUNCT
ejpam-3575	228	29	no	no	INTJ
ejpam-3575	228	30	.	.	NOUN
ejpam-3575	228	31	1	1	NUM
ejpam-3575	228	32	,	,	PUNCT
ejpam-3575	228	33	(	(	PUNCT
ejpam-3575	228	34	2015	2015	NUM
ejpam-3575	228	35	)	)	PUNCT
ejpam-3575	228	36	133–143	133–143	NUM
ejpam-3575	228	37	.	.	PUNCT
ejpam-3575	229	1	references	reference	NOUN
ejpam-3575	229	2	18	18	NUM
ejpam-3575	229	3	[	[	SYM
ejpam-3575	229	4	18	18	NUM
ejpam-3575	229	5	]	]	X
ejpam-3575	229	6	g.	g.	PROPN
ejpam-3575	229	7	muhiuddin	muhiuddin	PROPN
ejpam-3575	229	8	,	,	PUNCT
ejpam-3575	229	9	feng	feng	PROPN
ejpam-3575	229	10	feng	feng	PROPN
ejpam-3575	229	11	and	and	CCONJ
ejpam-3575	229	12	young	young	PROPN
ejpam-3575	229	13	bae	bae	PROPN
ejpam-3575	229	14	jun	jun	PROPN
ejpam-3575	229	15	,	,	PUNCT
ejpam-3575	229	16	subalgebras	subalgebras	PROPN
ejpam-3575	229	17	of	of	ADP
ejpam-3575	229	18	bck	bck	PROPN
ejpam-3575	229	19	/	/	SYM
ejpam-3575	229	20	bci	bci	NOUN
ejpam-3575	229	21	-	-	PUNCT
ejpam-3575	229	22	algebras	algebras	PROPN
ejpam-3575	229	23	based	base	VERB
ejpam-3575	229	24	on	on	ADP
ejpam-3575	229	25	cubic	cubic	ADJ
ejpam-3575	229	26	soft	soft	ADJ
ejpam-3575	229	27	sets	set	NOUN
ejpam-3575	229	28	,	,	PUNCT
ejpam-3575	229	29	the	the	DET
ejpam-3575	229	30	scientific	scientific	ADJ
ejpam-3575	229	31	world	world	NOUN
ejpam-3575	229	32	journal	journal	NOUN
ejpam-3575	229	33	,	,	PUNCT
ejpam-3575	229	34	volume	volume	NOUN
ejpam-3575	229	35	2014	2014	NUM
ejpam-3575	229	36	,	,	PUNCT
ejpam-3575	229	37	article	article	NOUN
ejpam-3575	229	38	i	i	PROPN
ejpam-3575	229	39	d	d	PROPN
ejpam-3575	229	40	458638	458638	NUM
ejpam-3575	229	41	,	,	PUNCT
ejpam-3575	229	42	(	(	PUNCT
ejpam-3575	229	43	2014	2014	NUM
ejpam-3575	229	44	)	)	PUNCT
ejpam-3575	229	45	9	9	NUM
ejpam-3575	229	46	pages	page	NOUN
ejpam-3575	229	47	.	.	PUNCT
ejpam-3575	230	1	[	[	X
ejpam-3575	230	2	19	19	NUM
ejpam-3575	230	3	]	]	X
ejpam-3575	230	4	g.	g.	PROPN
ejpam-3575	230	5	muhiuddin	muhiuddin	PROPN
ejpam-3575	230	6	and	and	CCONJ
ejpam-3575	230	7	abdullah	abdullah	PROPN
ejpam-3575	230	8	m.	m.	PROPN
ejpam-3575	230	9	al	al	PROPN
ejpam-3575	230	10	-	-	PUNCT
ejpam-3575	230	11	roqi	roqi	ADJ
ejpam-3575	230	12	,	,	PUNCT
ejpam-3575	230	13	cubic	cubic	ADJ
ejpam-3575	230	14	soft	soft	ADJ
ejpam-3575	230	15	sets	set	NOUN
ejpam-3575	230	16	with	with	ADP
ejpam-3575	230	17	applications	application	NOUN
ejpam-3575	230	18	in	in	ADP
ejpam-3575	230	19	bck	bck	PROPN
ejpam-3575	230	20	/	/	SYM
ejpam-3575	230	21	bci	bci	PROPN
ejpam-3575	230	22	-	-	PUNCT
ejpam-3575	230	23	algebras	algebra	NOUN
ejpam-3575	230	24	,	,	PUNCT
ejpam-3575	230	25	annals	annal	NOUN
ejpam-3575	230	26	of	of	ADP
ejpam-3575	230	27	fuzzy	fuzzy	ADJ
ejpam-3575	230	28	mathematics	mathematic	NOUN
ejpam-3575	230	29	and	and	CCONJ
ejpam-3575	230	30	informatics	informatic	NOUN
ejpam-3575	230	31	,	,	PUNCT
ejpam-3575	230	32	volume	volume	NOUN
ejpam-3575	230	33	8	8	NUM
ejpam-3575	230	34	,	,	PUNCT
ejpam-3575	230	35	no	no	INTJ
ejpam-3575	230	36	.	.	NOUN
ejpam-3575	230	37	2	2	NUM
ejpam-3575	230	38	,	,	PUNCT
ejpam-3575	230	39	(	(	PUNCT
ejpam-3575	230	40	2014	2014	NUM
ejpam-3575	230	41	)	)	PUNCT
ejpam-3575	230	42	291–304	291–304	NUM
ejpam-3575	230	43	.	.	PUNCT
ejpam-3575	231	1	[	[	X
ejpam-3575	231	2	20	20	NUM
ejpam-3575	231	3	]	]	X
ejpam-3575	231	4	g.	g.	PROPN
ejpam-3575	231	5	muhiuddin	muhiuddin	PROPN
ejpam-3575	231	6	,	,	PUNCT
ejpam-3575	231	7	neutrosophic	neutrosophic	ADJ
ejpam-3575	231	8	subsemigroups	subsemigroup	NOUN
ejpam-3575	231	9	,	,	PUNCT
ejpam-3575	231	10	annals	annal	NOUN
ejpam-3575	231	11	of	of	ADP
ejpam-3575	231	12	communications	communication	NOUN
ejpam-3575	231	13	in	in	ADP
ejpam-3575	231	14	mathematics	mathematic	NOUN
ejpam-3575	231	15	,	,	PUNCT
ejpam-3575	231	16	vol	vol	NOUN
ejpam-3575	231	17	.	.	PROPN
ejpam-3575	231	18	1	1	NUM
ejpam-3575	231	19	,	,	PUNCT
ejpam-3575	231	20	no.1	no.1	NUM
ejpam-3575	231	21	,	,	PUNCT
ejpam-3575	231	22	1	1	NUM
ejpam-3575	231	23	-	-	SYM
ejpam-3575	231	24	10	10	NUM
ejpam-3575	231	25	(	(	PUNCT
ejpam-3575	231	26	2018	2018	NUM
ejpam-3575	231	27	)	)	PUNCT
ejpam-3575	231	28	.	.	PUNCT
ejpam-3575	232	1	[	[	X
ejpam-3575	232	2	21	21	NUM
ejpam-3575	232	3	]	]	X
ejpam-3575	232	4	g.	g.	PROPN
ejpam-3575	232	5	muhiuddin	muhiuddin	PROPN
ejpam-3575	232	6	,	,	PUNCT
ejpam-3575	232	7	cubic	cubic	ADJ
ejpam-3575	232	8	interior	interior	ADJ
ejpam-3575	232	9	ideals	ideal	NOUN
ejpam-3575	232	10	in	in	ADP
ejpam-3575	232	11	semigroups	semigroup	NOUN
ejpam-3575	232	12	,	,	PUNCT
ejpam-3575	232	13	applications	application	NOUN
ejpam-3575	232	14	and	and	CCONJ
ejpam-3575	232	15	applied	apply	VERB
ejpam-3575	232	16	mathematics	mathematic	NOUN
ejpam-3575	232	17	,	,	PUNCT
ejpam-3575	232	18	vol	vol	NOUN
ejpam-3575	232	19	.	.	PROPN
ejpam-3575	232	20	14	14	NUM
ejpam-3575	232	21	,	,	PUNCT
ejpam-3575	232	22	issue	issue	NOUN
ejpam-3575	232	23	1	1	NUM
ejpam-3575	232	24	(	(	PUNCT
ejpam-3575	232	25	june	june	PROPN
ejpam-3575	232	26	2019	2019	NUM
ejpam-3575	232	27	)	)	PUNCT
ejpam-3575	232	28	,	,	PUNCT
ejpam-3575	232	29	463	463	NUM
ejpam-3575	232	30	474	474	NUM
ejpam-3575	232	31	(	(	PUNCT
ejpam-3575	232	32	2019	2019	NUM
ejpam-3575	232	33	)	)	PUNCT
ejpam-3575	232	34	(	(	PUNCT
ejpam-3575	232	35	usa	usa	PROPN
ejpam-3575	232	36	)	)	PUNCT
ejpam-3575	232	37	.	.	PUNCT
ejpam-3575	233	1	[	[	X
ejpam-3575	233	2	22	22	NUM
ejpam-3575	233	3	]	]	X
ejpam-3575	233	4	g.	g.	PROPN
ejpam-3575	233	5	muhiuddin	muhiuddin	PROPN
ejpam-3575	233	6	,	,	PUNCT
ejpam-3575	233	7	ahsan	ahsan	PROPN
ejpam-3575	233	8	mahboob	mahboob	PROPN
ejpam-3575	233	9	and	and	CCONJ
ejpam-3575	233	10	noor	noor	PROPN
ejpam-3575	233	11	mohammad	mohammad	PROPN
ejpam-3575	233	12	khan	khan	PROPN
ejpam-3575	233	13	,	,	PUNCT
ejpam-3575	233	14	a	a	DET
ejpam-3575	233	15	new	new	ADJ
ejpam-3575	233	16	type	type	NOUN
ejpam-3575	233	17	of	of	ADP
ejpam-3575	233	18	fuzzy	fuzzy	ADJ
ejpam-3575	233	19	semiprime	semiprime	NOUN
ejpam-3575	233	20	subsets	subset	NOUN
ejpam-3575	233	21	in	in	ADP
ejpam-3575	233	22	ordered	order	VERB
ejpam-3575	233	23	semigroups	semigroup	NOUN
ejpam-3575	233	24	,	,	PUNCT
ejpam-3575	233	25	journal	journal	NOUN
ejpam-3575	233	26	of	of	ADP
ejpam-3575	233	27	intelligent	intelligent	ADJ
ejpam-3575	233	28	and	and	CCONJ
ejpam-3575	233	29	fuzzy	fuzzy	ADJ
ejpam-3575	233	30	systems	system	NOUN
ejpam-3575	233	31	,	,	PUNCT
ejpam-3575	233	32	vol	vol	NOUN
ejpam-3575	233	33	.	.	PROPN
ejpam-3575	234	1	37	37	NUM
ejpam-3575	234	2	,	,	PUNCT
ejpam-3575	234	3	no	no	INTJ
ejpam-3575	234	4	.	.	NOUN
ejpam-3575	234	5	3	3	NUM
ejpam-3575	234	6	,	,	PUNCT
ejpam-3575	234	7	pp	pp	ADJ
ejpam-3575	234	8	.	.	PUNCT
ejpam-3575	235	1	4195–4204	4195–4204	NUM
ejpam-3575	235	2	(	(	PUNCT
ejpam-3575	235	3	2019	2019	NUM
ejpam-3575	235	4	)	)	PUNCT
ejpam-3575	236	1	[	[	X
ejpam-3575	236	2	23	23	NUM
ejpam-3575	236	3	]	]	X
ejpam-3575	236	4	rosa	rosa	PROPN
ejpam-3575	236	5	m.	m.	PROPN
ejpam-3575	236	6	rodriguez	rodriguez	PROPN
ejpam-3575	236	7	,	,	PUNCT
ejpam-3575	236	8	luis	luis	PROPN
ejpam-3575	236	9	martinez	martinez	PROPN
ejpam-3575	236	10	and	and	CCONJ
ejpam-3575	236	11	francisco	francisco	PROPN
ejpam-3575	236	12	herrera	herrera	PROPN
ejpam-3575	236	13	,	,	PUNCT
ejpam-3575	236	14	hesitant	hesitant	ADJ
ejpam-3575	236	15	fuzzy	fuzzy	ADJ
ejpam-3575	236	16	linguistic	linguistic	ADJ
ejpam-3575	236	17	term	term	NOUN
ejpam-3575	236	18	sets	set	NOUN
ejpam-3575	236	19	for	for	ADP
ejpam-3575	236	20	decision	decision	NOUN
ejpam-3575	236	21	making	making	NOUN
ejpam-3575	236	22	,	,	PUNCT
ejpam-3575	236	23	ieee	ieee	NOUN
ejpam-3575	236	24	trans	tran	NOUN
ejpam-3575	236	25	.	.	PUNCT
ejpam-3575	237	1	fuzzy	fuzzy	ADJ
ejpam-3575	237	2	syst	syst	PROPN
ejpam-3575	237	3	.	.	PUNCT
ejpam-3575	238	1	20(1	20(1	NUM
ejpam-3575	238	2	)	)	PUNCT
ejpam-3575	238	3	(	(	PUNCT
ejpam-3575	238	4	2012	2012	NUM
ejpam-3575	238	5	)	)	PUNCT
ejpam-3575	238	6	,	,	PUNCT
ejpam-3575	238	7	109–119	109–119	NUM
ejpam-3575	238	8	.	.	PUNCT
ejpam-3575	239	1	[	[	X
ejpam-3575	239	2	24	24	NUM
ejpam-3575	239	3	]	]	PUNCT
ejpam-3575	239	4	tapan	tapan	NOUN
ejpam-3575	239	5	senapati	senapati	PROPN
ejpam-3575	239	6	,	,	PUNCT
ejpam-3575	239	7	y.b	y.b	PROPN
ejpam-3575	239	8	.	.	PROPN
ejpam-3575	239	9	jun	jun	PROPN
ejpam-3575	239	10	,	,	PUNCT
ejpam-3575	239	11	g.	g.	PROPN
ejpam-3575	239	12	muhiuddin	muhiuddin	PROPN
ejpam-3575	239	13	and	and	CCONJ
ejpam-3575	239	14	k.	k.	PROPN
ejpam-3575	239	15	p.	p.	PROPN
ejpam-3575	239	16	shum	shum	PROPN
ejpam-3575	239	17	,	,	PUNCT
ejpam-3575	239	18	cubic	cubic	ADJ
ejpam-3575	239	19	intuitionistic	intuitionistic	ADJ
ejpam-3575	239	20	structures	structure	NOUN
ejpam-3575	239	21	applied	apply	VERB
ejpam-3575	239	22	to	to	ADP
ejpam-3575	239	23	ideals	ideal	NOUN
ejpam-3575	239	24	of	of	ADP
ejpam-3575	239	25	bci	bci	NOUN
ejpam-3575	239	26	-	-	PUNCT
ejpam-3575	239	27	algebras	algebra	NOUN
ejpam-3575	239	28	,	,	PUNCT
ejpam-3575	239	29	analele	analele	ADP
ejpam-3575	239	30	stiintifice	stiintifice	NOUN
ejpam-3575	239	31	ale	ale	PROPN
ejpam-3575	239	32	universitatii	universitatii	PROPN
ejpam-3575	239	33	ovidius	ovidius	PROPN
ejpam-3575	239	34	constanta	constanta	PROPN
ejpam-3575	239	35	-	-	PUNCT
ejpam-3575	239	36	seria	seria	PROPN
ejpam-3575	239	37	matematica	matematica	PROPN
ejpam-3575	239	38	,	,	PUNCT
ejpam-3575	239	39	vol	vol	NOUN
ejpam-3575	239	40	.	.	PROPN
ejpam-3575	239	41	27	27	NUM
ejpam-3575	239	42	(	(	PUNCT
ejpam-3575	239	43	2	2	NUM
ejpam-3575	239	44	)	)	PUNCT
ejpam-3575	239	45	,	,	PUNCT
ejpam-3575	239	46	213–232	213–232	NUM
ejpam-3575	239	47	(	(	PUNCT
ejpam-3575	239	48	2019	2019	NUM
ejpam-3575	239	49	)	)	PUNCT
ejpam-3575	239	50	.	.	PUNCT
ejpam-3575	240	1	[	[	X
ejpam-3575	240	2	25	25	NUM
ejpam-3575	240	3	]	]	X
ejpam-3575	240	4	v.	v.	CCONJ
ejpam-3575	240	5	torra	torra	ADJ
ejpam-3575	240	6	,	,	PUNCT
ejpam-3575	240	7	hesitant	hesitant	ADJ
ejpam-3575	240	8	fuzzy	fuzzy	ADJ
ejpam-3575	240	9	sets	set	NOUN
ejpam-3575	240	10	,	,	PUNCT
ejpam-3575	240	11	int	int	NOUN
ejpam-3575	240	12	.	.	PUNCT
ejpam-3575	241	1	j.	j.	PROPN
ejpam-3575	241	2	intell	intell	PROPN
ejpam-3575	241	3	.	.	PUNCT
ejpam-3575	242	1	syst	syst	PROPN
ejpam-3575	242	2	.	.	PUNCT
ejpam-3575	243	1	25	25	NUM
ejpam-3575	243	2	(	(	PUNCT
ejpam-3575	243	3	2010	2010	NUM
ejpam-3575	243	4	)	)	PUNCT
ejpam-3575	243	5	,	,	PUNCT
ejpam-3575	243	6	529–539	529–539	NUM
ejpam-3575	243	7	.	.	PUNCT
ejpam-3575	244	1	[	[	X
ejpam-3575	244	2	26	26	NUM
ejpam-3575	244	3	]	]	PUNCT
ejpam-3575	244	4	v.	v.	CCONJ
ejpam-3575	244	5	torra	torra	NOUN
ejpam-3575	244	6	and	and	CCONJ
ejpam-3575	244	7	y.	y.	PROPN
ejpam-3575	244	8	narukawa	narukawa	PROPN
ejpam-3575	244	9	,	,	PUNCT
ejpam-3575	244	10	on	on	ADP
ejpam-3575	244	11	hesitant	hesitant	ADJ
ejpam-3575	244	12	fuzzy	fuzzy	ADJ
ejpam-3575	244	13	sets	set	NOUN
ejpam-3575	244	14	and	and	CCONJ
ejpam-3575	244	15	decision	decision	NOUN
ejpam-3575	244	16	,	,	PUNCT
ejpam-3575	244	17	in	in	ADP
ejpam-3575	244	18	:	:	PUNCT
ejpam-3575	244	19	the	the	DET
ejpam-3575	244	20	18th	18th	ADJ
ejpam-3575	244	21	ieee	ieee	NOUN
ejpam-3575	244	22	international	international	ADJ
ejpam-3575	244	23	conference	conference	NOUN
ejpam-3575	244	24	on	on	ADP
ejpam-3575	244	25	fuzzy	fuzzy	ADJ
ejpam-3575	244	26	systems	system	NOUN
ejpam-3575	244	27	,	,	PUNCT
ejpam-3575	244	28	jeju	jeju	PROPN
ejpam-3575	244	29	island	island	PROPN
ejpam-3575	244	30	,	,	PUNCT
ejpam-3575	244	31	korea	korea	PROPN
ejpam-3575	244	32	,	,	PUNCT
ejpam-3575	244	33	2009	2009	NUM
ejpam-3575	244	34	,	,	PUNCT
ejpam-3575	244	35	pp	pp	ADJ
ejpam-3575	244	36	.	.	PUNCT
ejpam-3575	245	1	1378–1382	1378–1382	NUM
ejpam-3575	245	2	.	.	PUNCT
ejpam-3575	246	1	[	[	X
ejpam-3575	246	2	27	27	NUM
ejpam-3575	246	3	]	]	X
ejpam-3575	246	4	f.	f.	PROPN
ejpam-3575	246	5	q.	q.	PROPN
ejpam-3575	246	6	wang	wang	PROPN
ejpam-3575	246	7	,	,	PUNCT
ejpam-3575	246	8	x.	x.	PROPN
ejpam-3575	246	9	li	li	PROPN
ejpam-3575	246	10	and	and	CCONJ
ejpam-3575	246	11	x.	x.	PROPN
ejpam-3575	246	12	h.	h.	PROPN
ejpam-3575	246	13	chen	chen	PROPN
ejpam-3575	246	14	,	,	PUNCT
ejpam-3575	246	15	hesitant	hesitant	ADJ
ejpam-3575	246	16	fuzzy	fuzzy	ADJ
ejpam-3575	246	17	soft	soft	ADJ
ejpam-3575	246	18	set	set	NOUN
ejpam-3575	246	19	and	and	CCONJ
ejpam-3575	246	20	its	its	PRON
ejpam-3575	246	21	applications	application	NOUN
ejpam-3575	246	22	in	in	ADP
ejpam-3575	246	23	multicriteria	multicriteria	PROPN
ejpam-3575	246	24	decision	decision	NOUN
ejpam-3575	246	25	making	making	NOUN
ejpam-3575	246	26	,	,	PUNCT
ejpam-3575	246	27	j.	j.	PROPN
ejpam-3575	246	28	appl	appl	PROPN
ejpam-3575	246	29	.	.	PROPN
ejpam-3575	246	30	math	math	PROPN
ejpam-3575	246	31	.	.	PUNCT
ejpam-3575	247	1	volume	volume	NOUN
ejpam-3575	247	2	2014	2014	NUM
ejpam-3575	247	3	,	,	PUNCT
ejpam-3575	247	4	article	article	NOUN
ejpam-3575	247	5	i	i	PROPN
ejpam-3575	247	6	d	d	PROPN
ejpam-3575	247	7	643785	643785	NUM
ejpam-3575	247	8	,	,	PUNCT
ejpam-3575	247	9	10	10	NUM
ejpam-3575	247	10	pages	page	NOUN
ejpam-3575	247	11	.	.	PUNCT
ejpam-3575	248	1	[	[	X
ejpam-3575	248	2	28	28	NUM
ejpam-3575	248	3	]	]	X
ejpam-3575	248	4	g.	g.	PROPN
ejpam-3575	248	5	wei	wei	PROPN
ejpam-3575	248	6	,	,	PUNCT
ejpam-3575	248	7	hesitant	hesitant	ADJ
ejpam-3575	248	8	fuzzy	fuzzy	ADJ
ejpam-3575	248	9	prioritized	prioritize	VERB
ejpam-3575	248	10	operators	operator	NOUN
ejpam-3575	248	11	and	and	CCONJ
ejpam-3575	248	12	their	their	PRON
ejpam-3575	248	13	application	application	NOUN
ejpam-3575	248	14	to	to	ADP
ejpam-3575	248	15	multiple	multiple	ADJ
ejpam-3575	248	16	attribute	attribute	NOUN
ejpam-3575	248	17	decision	decision	NOUN
ejpam-3575	248	18	making	making	NOUN
ejpam-3575	248	19	,	,	PUNCT
ejpam-3575	248	20	knowledge	knowledge	NOUN
ejpam-3575	248	21	-	-	PUNCT
ejpam-3575	248	22	based	base	VERB
ejpam-3575	248	23	systems	system	NOUN
ejpam-3575	248	24	31	31	NUM
ejpam-3575	248	25	(	(	PUNCT
ejpam-3575	248	26	2012	2012	NUM
ejpam-3575	248	27	)	)	PUNCT
ejpam-3575	248	28	,	,	PUNCT
ejpam-3575	248	29	176–182	176–182	NUM
ejpam-3575	248	30	.	.	PUNCT
ejpam-3575	249	1	[	[	X
ejpam-3575	249	2	29	29	NUM
ejpam-3575	249	3	]	]	PUNCT
ejpam-3575	249	4	m.	m.	NOUN
ejpam-3575	249	5	xia	xia	PROPN
ejpam-3575	249	6	and	and	CCONJ
ejpam-3575	249	7	z.	z.	PROPN
ejpam-3575	249	8	s.	s.	PROPN
ejpam-3575	249	9	xu	xu	PROPN
ejpam-3575	249	10	,	,	PUNCT
ejpam-3575	249	11	hesitant	hesitant	ADJ
ejpam-3575	249	12	fuzzy	fuzzy	ADJ
ejpam-3575	249	13	information	information	NOUN
ejpam-3575	249	14	aggregation	aggregation	NOUN
ejpam-3575	249	15	in	in	ADP
ejpam-3575	249	16	decision	decision	NOUN
ejpam-3575	249	17	making	making	NOUN
ejpam-3575	249	18	,	,	PUNCT
ejpam-3575	249	19	internat	internat	PROPN
ejpam-3575	249	20	.	.	PUNCT
ejpam-3575	250	1	j.	j.	PROPN
ejpam-3575	250	2	approx	approx	PROPN
ejpam-3575	250	3	.	.	PUNCT
ejpam-3575	251	1	reason	reason	NOUN
ejpam-3575	251	2	.	.	PUNCT
ejpam-3575	252	1	52(3	52(3	X
ejpam-3575	252	2	)	)	PUNCT
ejpam-3575	252	3	(	(	PUNCT
ejpam-3575	252	4	2011	2011	NUM
ejpam-3575	252	5	)	)	PUNCT
ejpam-3575	252	6	,	,	PUNCT
ejpam-3575	252	7	395–407	395–407	NUM
ejpam-3575	252	8	.	.	PUNCT
ejpam-3575	253	1	[	[	X
ejpam-3575	253	2	30	30	NUM
ejpam-3575	253	3	]	]	PUNCT
ejpam-3575	253	4	z.	z.	PROPN
ejpam-3575	253	5	s.	s.	PROPN
ejpam-3575	253	6	xu	xu	PROPN
ejpam-3575	253	7	and	and	CCONJ
ejpam-3575	253	8	m.	m.	PROPN
ejpam-3575	253	9	xia	xia	PROPN
ejpam-3575	253	10	,	,	PUNCT
ejpam-3575	253	11	distance	distance	NOUN
ejpam-3575	253	12	and	and	CCONJ
ejpam-3575	253	13	similarity	similarity	NOUN
ejpam-3575	253	14	measures	measure	NOUN
ejpam-3575	253	15	for	for	ADP
ejpam-3575	253	16	hesitant	hesitant	ADJ
ejpam-3575	253	17	fuzzy	fuzzy	ADJ
ejpam-3575	253	18	sets	set	NOUN
ejpam-3575	253	19	,	,	PUNCT
ejpam-3575	253	20	inform	inform	NOUN
ejpam-3575	253	21	.	.	PUNCT
ejpam-3575	254	1	sci	sci	PROPN
ejpam-3575	254	2	.	.	PROPN
ejpam-3575	254	3	181(11	181(11	NUM
ejpam-3575	254	4	)	)	PUNCT
ejpam-3575	254	5	(	(	PUNCT
ejpam-3575	254	6	2011	2011	NUM
ejpam-3575	254	7	)	)	PUNCT
ejpam-3575	254	8	,	,	PUNCT
ejpam-3575	254	9	2128–2138	2128–2138	NUM
ejpam-3575	254	10	.	.	PUNCT
ejpam-3575	255	1	[	[	X
ejpam-3575	255	2	31	31	NUM
ejpam-3575	255	3	]	]	PUNCT
ejpam-3575	255	4	z.	z.	PROPN
ejpam-3575	255	5	s.	s.	PROPN
ejpam-3575	255	6	xu	xu	PROPN
ejpam-3575	255	7	and	and	CCONJ
ejpam-3575	255	8	m.	m.	PROPN
ejpam-3575	255	9	xia	xia	PROPN
ejpam-3575	255	10	,	,	PUNCT
ejpam-3575	255	11	on	on	ADP
ejpam-3575	255	12	distance	distance	NOUN
ejpam-3575	255	13	and	and	CCONJ
ejpam-3575	255	14	correlation	correlation	NOUN
ejpam-3575	255	15	measures	measure	NOUN
ejpam-3575	255	16	of	of	ADP
ejpam-3575	255	17	hesitant	hesitant	ADJ
ejpam-3575	255	18	fuzzy	fuzzy	ADJ
ejpam-3575	255	19	information	information	NOUN
ejpam-3575	255	20	,	,	PUNCT
ejpam-3575	255	21	int	int	PROPN
ejpam-3575	255	22	.	.	PUNCT
ejpam-3575	256	1	j.	j.	PROPN
ejpam-3575	256	2	intell	intell	PROPN
ejpam-3575	256	3	.	.	PUNCT
ejpam-3575	257	1	syst	syst	PROPN
ejpam-3575	257	2	.	.	PUNCT
ejpam-3575	258	1	26(5	26(5	PROPN
ejpam-3575	258	2	)	)	PUNCT
ejpam-3575	259	1	(	(	PUNCT
ejpam-3575	259	2	2011	2011	NUM
ejpam-3575	259	3	)	)	PUNCT
ejpam-3575	259	4	,	,	PUNCT
ejpam-3575	259	5	410–425	410–425	NUM
ejpam-3575	259	6	.	.	PUNCT
ejpam-3575	260	1	[	[	X
ejpam-3575	260	2	32	32	NUM
ejpam-3575	260	3	]	]	PUNCT
ejpam-3575	260	4	x.	x.	PROPN
ejpam-3575	260	5	h.	h.	PROPN
ejpam-3575	260	6	zhang	zhang	PROPN
ejpam-3575	260	7	,	,	PUNCT
ejpam-3575	260	8	h.	h.	PROPN
ejpam-3575	260	9	jiang	jiang	PROPN
ejpam-3575	260	10	and	and	CCONJ
ejpam-3575	260	11	s.	s.	PROPN
ejpam-3575	260	12	a.	a.	PROPN
ejpam-3575	260	13	bhatti	bhatti	PROPN
ejpam-3575	260	14	,	,	PUNCT
ejpam-3575	260	15	on	on	ADP
ejpam-3575	260	16	p	p	NOUN
ejpam-3575	260	17	-	-	PUNCT
ejpam-3575	260	18	ideals	ideal	NOUN
ejpam-3575	260	19	of	of	ADP
ejpam-3575	260	20	a	a	DET
ejpam-3575	260	21	bci	bci	NOUN
ejpam-3575	260	22	-	-	NOUN
ejpam-3575	260	23	algebra	algebra	NOUN
ejpam-3575	260	24	,	,	PUNCT
ejpam-3575	260	25	punjab	punjab	PROPN
ejpam-3575	260	26	univ	univ	PROPN
ejpam-3575	260	27	.	.	PUNCT
ejpam-3575	261	1	j.	j.	PROPN
ejpam-3575	261	2	math	math	PROPN
ejpam-3575	261	3	.	.	PUNCT
ejpam-3575	262	1	(	(	PUNCT
ejpam-3575	262	2	lahore	lahore	NOUN
ejpam-3575	262	3	)	)	PUNCT
ejpam-3575	262	4	27	27	NUM
ejpam-3575	262	5	(	(	PUNCT
ejpam-3575	262	6	1994	1994	NUM
ejpam-3575	262	7	)	)	PUNCT
ejpam-3575	262	8	,	,	PUNCT
ejpam-3575	262	9	121–128	121–128	NUM
ejpam-3575	262	10	.	.	PUNCT
ejpam-3575	263	1	[	[	X
ejpam-3575	263	2	33	33	NUM
ejpam-3575	263	3	]	]	PUNCT
ejpam-3575	263	4	l.	l.	PROPN
ejpam-3575	263	5	a.	a.	PROPN
ejpam-3575	263	6	zadeh	zadeh	PROPN
ejpam-3575	263	7	,	,	PUNCT
ejpam-3575	263	8	fuzzy	fuzzy	ADJ
ejpam-3575	263	9	sets	set	NOUN
ejpam-3575	263	10	,	,	PUNCT
ejpam-3575	263	11	inform	inform	NOUN
ejpam-3575	263	12	.	.	PUNCT
ejpam-3575	264	1	control	control	NOUN
ejpam-3575	264	2	8	8	NUM
ejpam-3575	264	3	(	(	PUNCT
ejpam-3575	264	4	1965	1965	NUM
ejpam-3575	264	5	)	)	PUNCT
ejpam-3575	264	6	338–353	338–353	NUM
ejpam-3575	264	7	.	.	PUNCT