id	sid	tid	token	lemma	pos
ejpam-5473	1	1	european	european	PROPN
ejpam-5473	1	2	journal	journal	PROPN
ejpam-5473	1	3	of	of	ADP
ejpam-5473	1	4	pure	pure	ADJ
ejpam-5473	1	5	and	and	CCONJ
ejpam-5473	1	6	applied	apply	VERB
ejpam-5473	1	7	mathematics	mathematic	NOUN
ejpam-5473	1	8	vol	vol	NOUN
ejpam-5473	1	9	.	.	PROPN
ejpam-5473	2	1	17	17	NUM
ejpam-5473	2	2	,	,	PUNCT
ejpam-5473	2	3	no	no	INTJ
ejpam-5473	2	4	.	.	NOUN
ejpam-5473	2	5	4	4	NUM
ejpam-5473	2	6	,	,	PUNCT
ejpam-5473	2	7	2024	2024	NUM
ejpam-5473	2	8	,	,	PUNCT
ejpam-5473	2	9	2898	2898	NUM
ejpam-5473	2	10	-	-	SYM
ejpam-5473	2	11	2914	2914	NUM
ejpam-5473	2	12	issn	issn	VERB
ejpam-5473	2	13	1307	1307	NUM
ejpam-5473	2	14	-	-	SYM
ejpam-5473	2	15	5543	5543	NUM
ejpam-5473	2	16	–	–	PUNCT
ejpam-5473	2	17	ejpam.com	ejpam.com	X
ejpam-5473	2	18	published	publish	VERB
ejpam-5473	2	19	by	by	ADP
ejpam-5473	2	20	new	new	PROPN
ejpam-5473	2	21	york	york	PROPN
ejpam-5473	2	22	business	business	PROPN
ejpam-5473	2	23	global	global	PROPN
ejpam-5473	2	24	a	a	DET
ejpam-5473	2	25	novel	novel	ADJ
ejpam-5473	2	26	bipolar	bipolar	NOUN
ejpam-5473	2	27	valued	value	VERB
ejpam-5473	2	28	fuzzy	fuzzy	ADJ
ejpam-5473	2	29	group	group	NOUN
ejpam-5473	2	30	based	base	VERB
ejpam-5473	2	31	on	on	ADP
ejpam-5473	2	32	dib	dib	PROPN
ejpam-5473	2	33	’s	’s	PART
ejpam-5473	2	34	approach	approach	NOUN
ejpam-5473	2	35	fadi	fadi	PROPN
ejpam-5473	2	36	al	al	PROPN
ejpam-5473	2	37	-	-	PROPN
ejpam-5473	2	38	zu’bi1,2,∗	zu’bi1,2,∗	PROPN
ejpam-5473	2	39	,	,	PUNCT
ejpam-5473	2	40	abdul	abdul	PROPN
ejpam-5473	2	41	ghaffur	ghaffur	PROPN
ejpam-5473	2	42	ahmad1	ahmad1	PROPN
ejpam-5473	2	43	,	,	PUNCT
ejpam-5473	2	44	abd	abd	PROPN
ejpam-5473	2	45	ulazeez	ulazeez	PROPN
ejpam-5473	2	46	alkouri3	alkouri3	PROPN
ejpam-5473	2	47	,	,	PUNCT
ejpam-5473	2	48	maslina	maslina	PROPN
ejpam-5473	2	49	darus1	darus1	PROPN
ejpam-5473	2	50	1	1	NUM
ejpam-5473	2	51	department	department	NOUN
ejpam-5473	2	52	of	of	ADP
ejpam-5473	2	53	mathematical	mathematical	ADJ
ejpam-5473	2	54	sciences	science	NOUN
ejpam-5473	2	55	,	,	PUNCT
ejpam-5473	2	56	faculty	faculty	NOUN
ejpam-5473	2	57	of	of	ADP
ejpam-5473	2	58	science	science	PROPN
ejpam-5473	2	59	&	&	CCONJ
ejpam-5473	2	60	technology	technology	PROPN
ejpam-5473	2	61	,	,	PUNCT
ejpam-5473	2	62	universiti	universiti	PROPN
ejpam-5473	2	63	kebangsaan	kebangsaan	PROPN
ejpam-5473	2	64	malaysia	malaysia	PROPN
ejpam-5473	2	65	,	,	PUNCT
ejpam-5473	2	66	43600	43600	NUM
ejpam-5473	2	67	ukm	ukm	PROPN
ejpam-5473	2	68	bangi	bangi	PROPN
ejpam-5473	2	69	,	,	PUNCT
ejpam-5473	2	70	selangor	selangor	PROPN
ejpam-5473	2	71	,	,	PUNCT
ejpam-5473	2	72	malaysia	malaysia	PROPN
ejpam-5473	2	73	2	2	NUM
ejpam-5473	2	74	college	college	NOUN
ejpam-5473	2	75	of	of	ADP
ejpam-5473	2	76	natural	natural	ADJ
ejpam-5473	2	77	and	and	CCONJ
ejpam-5473	2	78	health	health	NOUN
ejpam-5473	2	79	sciences	science	NOUN
ejpam-5473	2	80	,	,	PUNCT
ejpam-5473	2	81	zayed	zayed	PROPN
ejpam-5473	2	82	university	university	PROPN
ejpam-5473	2	83	,	,	PUNCT
ejpam-5473	2	84	abu	abu	PROPN
ejpam-5473	2	85	dhabi	dhabi	PROPN
ejpam-5473	2	86	,	,	PUNCT
ejpam-5473	2	87	united	united	PROPN
ejpam-5473	2	88	arab	arab	PROPN
ejpam-5473	2	89	emirates	emirates	PROPN
ejpam-5473	2	90	3	3	NUM
ejpam-5473	2	91	department	department	NOUN
ejpam-5473	2	92	of	of	ADP
ejpam-5473	2	93	mathematics	mathematic	NOUN
ejpam-5473	2	94	,	,	PUNCT
ejpam-5473	2	95	faculty	faculty	NOUN
ejpam-5473	2	96	of	of	ADP
ejpam-5473	2	97	science	science	NOUN
ejpam-5473	2	98	,	,	PUNCT
ejpam-5473	2	99	ajloun	ajloun	ADJ
ejpam-5473	2	100	national	national	ADJ
ejpam-5473	2	101	university	university	PROPN
ejpam-5473	2	102	,	,	PUNCT
ejpam-5473	2	103	p.o	p.o	PROPN
ejpam-5473	2	104	.	.	PROPN
ejpam-5473	2	105	43	43	NUM
ejpam-5473	2	106	,	,	PUNCT
ejpam-5473	2	107	ajloun26810	ajloun26810	PROPN
ejpam-5473	2	108	,	,	PUNCT
ejpam-5473	2	109	jordan	jordan	PROPN
ejpam-5473	2	110	abstract	abstract	PROPN
ejpam-5473	2	111	.	.	PUNCT
ejpam-5473	3	1	the	the	DET
ejpam-5473	3	2	numerous	numerous	ADJ
ejpam-5473	3	3	extensions	extension	NOUN
ejpam-5473	3	4	of	of	ADP
ejpam-5473	3	5	fuzzy	fuzzy	ADJ
ejpam-5473	3	6	groups	group	NOUN
ejpam-5473	3	7	(	(	PUNCT
ejpam-5473	3	8	fg	fg	NOUN
ejpam-5473	3	9	)	)	PUNCT
ejpam-5473	3	10	and	and	CCONJ
ejpam-5473	3	11	fuzzy	fuzzy	ADJ
ejpam-5473	3	12	subgroups	subgroup	NOUN
ejpam-5473	3	13	are	be	AUX
ejpam-5473	3	14	complicated	complicated	ADJ
ejpam-5473	3	15	.	.	PUNCT
ejpam-5473	4	1	several	several	ADJ
ejpam-5473	4	2	results	result	NOUN
ejpam-5473	4	3	depending	depend	VERB
ejpam-5473	4	4	on	on	ADP
ejpam-5473	4	5	different	different	ADJ
ejpam-5473	4	6	approaches	approach	NOUN
ejpam-5473	4	7	of	of	ADP
ejpam-5473	4	8	fg	fg	PROPN
ejpam-5473	4	9	theory	theory	NOUN
ejpam-5473	4	10	were	be	AUX
ejpam-5473	4	11	introduced	introduce	VERB
ejpam-5473	4	12	.	.	PUNCT
ejpam-5473	5	1	this	this	DET
ejpam-5473	5	2	study	study	NOUN
ejpam-5473	5	3	introduces	introduce	VERB
ejpam-5473	5	4	a	a	DET
ejpam-5473	5	5	novel	novel	ADJ
ejpam-5473	5	6	extension	extension	NOUN
ejpam-5473	5	7	,	,	PUNCT
ejpam-5473	5	8	named	name	VERB
ejpam-5473	5	9	bipolar	bipolar	ADV
ejpam-5473	5	10	-	-	PUNCT
ejpam-5473	5	11	valued	value	VERB
ejpam-5473	5	12	fuzzy	fuzzy	ADJ
ejpam-5473	5	13	groups	group	NOUN
ejpam-5473	5	14	(	(	PUNCT
ejpam-5473	5	15	bvf	bvf	NOUN
ejpam-5473	5	16	-	-	PUNCT
ejpam-5473	5	17	groups	group	NOUN
ejpam-5473	5	18	)	)	PUNCT
ejpam-5473	5	19	,	,	PUNCT
ejpam-5473	5	20	which	which	PRON
ejpam-5473	5	21	are	be	AUX
ejpam-5473	5	22	based	base	VERB
ejpam-5473	5	23	on	on	ADP
ejpam-5473	5	24	bipolar	bipolar	ADV
ejpam-5473	5	25	-	-	PUNCT
ejpam-5473	5	26	valued	value	VERB
ejpam-5473	5	27	fuzzy	fuzzy	ADJ
ejpam-5473	5	28	space	space	NOUN
ejpam-5473	5	29	(	(	PUNCT
ejpam-5473	5	30	bvf	bvf	NOUN
ejpam-5473	5	31	-	-	PUNCT
ejpam-5473	5	32	space	space	NOUN
ejpam-5473	5	33	)	)	PUNCT
ejpam-5473	5	34	and	and	CCONJ
ejpam-5473	5	35	are	be	AUX
ejpam-5473	5	36	created	create	VERB
ejpam-5473	5	37	using	use	VERB
ejpam-5473	5	38	dib	dib	PROPN
ejpam-5473	5	39	’s	’s	PART
ejpam-5473	5	40	methodology	methodology	NOUN
ejpam-5473	5	41	.	.	PUNCT
ejpam-5473	6	1	the	the	DET
ejpam-5473	6	2	bvfspace	bvfspace	NOUN
ejpam-5473	6	3	replaces	replace	VERB
ejpam-5473	6	4	the	the	DET
ejpam-5473	6	5	universal	universal	ADJ
ejpam-5473	6	6	set	set	NOUN
ejpam-5473	6	7	in	in	ADP
ejpam-5473	6	8	conventional	conventional	ADJ
ejpam-5473	6	9	set	set	NOUN
ejpam-5473	6	10	theory	theory	NOUN
ejpam-5473	6	11	.	.	PUNCT
ejpam-5473	7	1	the	the	DET
ejpam-5473	7	2	bvf	bvf	NOUN
ejpam-5473	7	3	-	-	PUNCT
ejpam-5473	7	4	space	space	NOUN
ejpam-5473	7	5	generalizes	generalize	VERB
ejpam-5473	7	6	the	the	DET
ejpam-5473	7	7	notion	notion	NOUN
ejpam-5473	7	8	of	of	ADP
ejpam-5473	7	9	fuzzy	fuzzy	ADJ
ejpam-5473	7	10	space	space	NOUN
ejpam-5473	7	11	(	(	PUNCT
ejpam-5473	7	12	f	f	NOUN
ejpam-5473	7	13	-	-	PUNCT
ejpam-5473	7	14	space	space	NOUN
ejpam-5473	7	15	)	)	PUNCT
ejpam-5473	7	16	from	from	ADP
ejpam-5473	7	17	[	[	X
ejpam-5473	7	18	0	0	NUM
ejpam-5473	7	19	,	,	PUNCT
ejpam-5473	7	20	1	1	NUM
ejpam-5473	7	21	]	]	PUNCT
ejpam-5473	7	22	to	to	ADP
ejpam-5473	7	23	[	[	X
ejpam-5473	7	24	−1	−1	NOUN
ejpam-5473	7	25	,	,	PUNCT
ejpam-5473	7	26	0]×	0]×	PROPN
ejpam-5473	8	1	[	[	X
ejpam-5473	8	2	0	0	NUM
ejpam-5473	8	3	,	,	PUNCT
ejpam-5473	8	4	1	1	NUM
ejpam-5473	8	5	]	]	PUNCT
ejpam-5473	8	6	for	for	ADP
ejpam-5473	8	7	the	the	DET
ejpam-5473	8	8	range	range	NOUN
ejpam-5473	8	9	of	of	ADP
ejpam-5473	8	10	membership	membership	NOUN
ejpam-5473	8	11	function	function	NOUN
ejpam-5473	8	12	.	.	PUNCT
ejpam-5473	9	1	the	the	DET
ejpam-5473	9	2	novel	novel	ADJ
ejpam-5473	9	3	theory	theory	NOUN
ejpam-5473	9	4	of	of	ADP
ejpam-5473	9	5	bvf	bvf	NOUN
ejpam-5473	9	6	-	-	PUNCT
ejpam-5473	9	7	group	group	NOUN
ejpam-5473	9	8	is	be	AUX
ejpam-5473	9	9	achieved	achieve	VERB
ejpam-5473	9	10	through	through	ADP
ejpam-5473	9	11	the	the	DET
ejpam-5473	9	12	bvf	bvf	NOUN
ejpam-5473	9	13	-	-	PUNCT
ejpam-5473	9	14	space	space	NOUN
ejpam-5473	9	15	and	and	CCONJ
ejpam-5473	9	16	bipolar	bipolar	ADJ
ejpam-5473	9	17	valued	value	VERB
ejpam-5473	9	18	binary	binary	ADJ
ejpam-5473	9	19	operation	operation	NOUN
ejpam-5473	9	20	(	(	PUNCT
ejpam-5473	9	21	bvfbo	bvfbo	X
ejpam-5473	9	22	)	)	PUNCT
ejpam-5473	9	23	to	to	PART
ejpam-5473	9	24	build	build	VERB
ejpam-5473	9	25	a	a	DET
ejpam-5473	9	26	new	new	ADJ
ejpam-5473	9	27	algebraic	algebraic	ADJ
ejpam-5473	9	28	structure	structure	NOUN
ejpam-5473	9	29	in	in	ADP
ejpam-5473	9	30	a	a	DET
ejpam-5473	9	31	natural	natural	ADJ
ejpam-5473	9	32	way	way	NOUN
ejpam-5473	9	33	,	,	PUNCT
ejpam-5473	9	34	which	which	PRON
ejpam-5473	9	35	satisfies	satisfy	VERB
ejpam-5473	9	36	four	four	NUM
ejpam-5473	9	37	axioms	axiom	NOUN
ejpam-5473	9	38	as	as	ADP
ejpam-5473	9	39	in	in	ADP
ejpam-5473	9	40	classical	classical	ADJ
ejpam-5473	9	41	group	group	NOUN
ejpam-5473	9	42	and	and	CCONJ
ejpam-5473	9	43	fg	fg	PROPN
ejpam-5473	9	44	theory	theory	NOUN
ejpam-5473	9	45	.	.	PUNCT
ejpam-5473	10	1	the	the	DET
ejpam-5473	10	2	challenges	challenge	NOUN
ejpam-5473	10	3	associated	associate	VERB
ejpam-5473	10	4	with	with	ADP
ejpam-5473	10	5	the	the	DET
ejpam-5473	10	6	lack	lack	NOUN
ejpam-5473	10	7	of	of	ADP
ejpam-5473	10	8	a	a	DET
ejpam-5473	10	9	bipolar	bipolar	ADJ
ejpam-5473	10	10	valued	value	VERB
ejpam-5473	10	11	fuzzy	fuzzy	ADJ
ejpam-5473	10	12	universal	universal	ADJ
ejpam-5473	10	13	set	set	NOUN
ejpam-5473	10	14	may	may	AUX
ejpam-5473	10	15	also	also	ADV
ejpam-5473	10	16	be	be	AUX
ejpam-5473	10	17	resolved	resolve	VERB
ejpam-5473	10	18	using	use	VERB
ejpam-5473	10	19	this	this	DET
ejpam-5473	10	20	approach	approach	NOUN
ejpam-5473	10	21	.	.	PUNCT
ejpam-5473	11	1	this	this	DET
ejpam-5473	11	2	generalization	generalization	NOUN
ejpam-5473	11	3	highlights	highlight	VERB
ejpam-5473	11	4	how	how	SCONJ
ejpam-5473	11	5	to	to	PART
ejpam-5473	11	6	present	present	VERB
ejpam-5473	11	7	and	and	CCONJ
ejpam-5473	11	8	explore	explore	VERB
ejpam-5473	11	9	the	the	DET
ejpam-5473	11	10	bvf	bvf	NOUN
ejpam-5473	11	11	-	-	PUNCT
ejpam-5473	11	12	groupoid	groupoid	NOUN
ejpam-5473	11	13	,	,	PUNCT
ejpam-5473	11	14	bvf	bvf	NOUN
ejpam-5473	11	15	-	-	PUNCT
ejpam-5473	11	16	monoid	monoid	NOUN
ejpam-5473	11	17	,	,	PUNCT
ejpam-5473	11	18	and	and	CCONJ
ejpam-5473	11	19	bvf	bvf	NOUN
ejpam-5473	11	20	-	-	PUNCT
ejpam-5473	11	21	group	group	NOUN
ejpam-5473	11	22	based	base	VERB
ejpam-5473	11	23	on	on	ADP
ejpam-5473	11	24	bvf	bvf	NOUN
ejpam-5473	11	25	-	-	PUNCT
ejpam-5473	11	26	space	space	NOUN
ejpam-5473	11	27	.	.	PUNCT
ejpam-5473	12	1	also	also	ADV
ejpam-5473	12	2	,	,	PUNCT
ejpam-5473	12	3	as	as	ADP
ejpam-5473	12	4	a	a	DET
ejpam-5473	12	5	connection	connection	NOUN
ejpam-5473	12	6	result	result	NOUN
ejpam-5473	12	7	,	,	PUNCT
ejpam-5473	12	8	we	we	PRON
ejpam-5473	12	9	proved	prove	VERB
ejpam-5473	12	10	that	that	SCONJ
ejpam-5473	12	11	every	every	DET
ejpam-5473	12	12	intuitionistic	intuitionistic	ADJ
ejpam-5473	12	13	fuzzy	fuzzy	ADJ
ejpam-5473	12	14	groupoid	groupoid	NOUN
ejpam-5473	12	15	(	(	PUNCT
ejpam-5473	12	16	group	group	NOUN
ejpam-5473	12	17	)	)	PUNCT
ejpam-5473	12	18	is	be	AUX
ejpam-5473	12	19	a	a	DET
ejpam-5473	12	20	bipolar	bipolar	ADJ
ejpam-5473	12	21	valued	value	VERB
ejpam-5473	12	22	fuzzy	fuzzy	ADJ
ejpam-5473	12	23	groupoid	groupoid	NOUN
ejpam-5473	12	24	(	(	PUNCT
ejpam-5473	12	25	group	group	NOUN
ejpam-5473	12	26	)	)	PUNCT
ejpam-5473	12	27	,	,	PUNCT
ejpam-5473	12	28	but	but	CCONJ
ejpam-5473	12	29	the	the	DET
ejpam-5473	12	30	inverse	inverse	NOUN
ejpam-5473	12	31	is	be	AUX
ejpam-5473	12	32	not	not	PART
ejpam-5473	12	33	true	true	ADJ
ejpam-5473	12	34	.	.	PUNCT
ejpam-5473	13	1	some	some	DET
ejpam-5473	13	2	theorems	theorem	NOUN
ejpam-5473	13	3	support	support	VERB
ejpam-5473	13	4	the	the	DET
ejpam-5473	13	5	relations	relation	NOUN
ejpam-5473	13	6	between	between	ADP
ejpam-5473	13	7	bvf	bvf	NOUN
ejpam-5473	13	8	-	-	PUNCT
ejpam-5473	13	9	group	group	NOUN
ejpam-5473	13	10	as	as	ADP
ejpam-5473	13	11	a	a	DET
ejpam-5473	13	12	generalization	generalization	NOUN
ejpam-5473	13	13	of	of	ADP
ejpam-5473	13	14	the	the	DET
ejpam-5473	13	15	classical	classical	ADJ
ejpam-5473	13	16	(	(	PUNCT
ejpam-5473	13	17	fuzzy	fuzzy	ADJ
ejpam-5473	13	18	)	)	PUNCT
ejpam-5473	13	19	group	group	NOUN
ejpam-5473	13	20	are	be	AUX
ejpam-5473	13	21	illustrated	illustrate	VERB
ejpam-5473	13	22	in	in	ADP
ejpam-5473	13	23	detail	detail	NOUN
ejpam-5473	13	24	.	.	PUNCT
ejpam-5473	14	1	2020	2020	NUM
ejpam-5473	14	2	mathematics	mathematic	NOUN
ejpam-5473	14	3	subject	subject	NOUN
ejpam-5473	14	4	classifications	classification	NOUN
ejpam-5473	14	5	:	:	PUNCT
ejpam-5473	14	6	08a72	08a72	NUM
ejpam-5473	14	7	,	,	PUNCT
ejpam-5473	14	8	06d72	06d72	VERB
ejpam-5473	14	9	key	key	ADJ
ejpam-5473	14	10	words	word	NOUN
ejpam-5473	14	11	and	and	CCONJ
ejpam-5473	14	12	phrases	phrase	NOUN
ejpam-5473	14	13	:	:	PUNCT
ejpam-5473	14	14	fuzzy	fuzzy	ADJ
ejpam-5473	14	15	space	space	NOUN
ejpam-5473	14	16	,	,	PUNCT
ejpam-5473	14	17	bipolar	bipolar	ADJ
ejpam-5473	14	18	valued	value	VERB
ejpam-5473	14	19	fuzzy	fuzzy	ADJ
ejpam-5473	14	20	space	space	NOUN
ejpam-5473	14	21	,	,	PUNCT
ejpam-5473	14	22	fuzzy	fuzzy	ADJ
ejpam-5473	14	23	binary	binary	ADJ
ejpam-5473	14	24	operation	operation	NOUN
ejpam-5473	14	25	,	,	PUNCT
ejpam-5473	14	26	bipolar	bipolar	PROPN
ejpam-5473	14	27	valued	value	VERB
ejpam-5473	14	28	fuzzy	fuzzy	ADJ
ejpam-5473	14	29	binary	binary	ADJ
ejpam-5473	14	30	operation	operation	NOUN
ejpam-5473	14	31	,	,	PUNCT
ejpam-5473	14	32	fuzzy	fuzzy	ADJ
ejpam-5473	14	33	function	function	NOUN
ejpam-5473	14	34	,	,	PUNCT
ejpam-5473	14	35	bipolar	bipolar	ADJ
ejpam-5473	14	36	valued	value	VERB
ejpam-5473	14	37	fuzzy	fuzzy	ADJ
ejpam-5473	14	38	function	function	NOUN
ejpam-5473	14	39	,	,	PUNCT
ejpam-5473	14	40	fuzzy	fuzzy	ADJ
ejpam-5473	14	41	group	group	NOUN
ejpam-5473	14	42	,	,	PUNCT
ejpam-5473	14	43	and	and	CCONJ
ejpam-5473	14	44	bipolar	bipolar	ADJ
ejpam-5473	14	45	valued	value	VERB
ejpam-5473	14	46	fuzzy	fuzzy	ADJ
ejpam-5473	14	47	group	group	NOUN
ejpam-5473	14	48	subgroup	subgroup	PROPN
ejpam-5473	14	49	∗corresponding	∗corresponde	VERB
ejpam-5473	14	50	author	author	NOUN
ejpam-5473	14	51	.	.	PUNCT
ejpam-5473	15	1	doi	doi	NOUN
ejpam-5473	15	2	:	:	PUNCT
ejpam-5473	15	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5473	https://doi.org/10.29020/nybg.ejpam.v17i4.5473	NOUN
ejpam-5473	15	4	email	email	NOUN
ejpam-5473	15	5	addresses	address	NOUN
ejpam-5473	15	6	:	:	PUNCT
ejpam-5473	15	7	p115916@siswa.ukm.edu.my	p115916@siswa.ukm.edu.my	PROPN
ejpam-5473	15	8	(	(	PUNCT
ejpam-5473	15	9	f.	f.	PROPN
ejpam-5473	15	10	al	al	PROPN
ejpam-5473	15	11	-	-	PROPN
ejpam-5473	15	12	zu’bi	zu’bi	PROPN
ejpam-5473	15	13	)	)	PUNCT
ejpam-5473	15	14	,	,	PUNCT
ejpam-5473	15	15	ghafur@ukm.edu.my	ghafur@ukm.edu.my	X
ejpam-5473	15	16	(	(	PUNCT
ejpam-5473	15	17	a.	a.	NOUN
ejpam-5473	15	18	g.	g.	PROPN
ejpam-5473	15	19	ahmad	ahmad	PROPN
ejpam-5473	15	20	)	)	PUNCT
ejpam-5473	15	21	,	,	PUNCT
ejpam-5473	15	22	alkouriabdulazeez@anu.edu.jo	alkouriabdulazeez@anu.edu.jo	NOUN
ejpam-5473	15	23	(	(	PUNCT
ejpam-5473	15	24	a.	a.	NOUN
ejpam-5473	15	25	u.	u.	PROPN
ejpam-5473	15	26	alkouri	alkouri	PROPN
ejpam-5473	15	27	)	)	PUNCT
ejpam-5473	15	28	,	,	PUNCT
ejpam-5473	15	29	maslina@ukm.edu.my	maslina@ukm.edu.my	X
ejpam-5473	15	30	(	(	PUNCT
ejpam-5473	15	31	m.	m.	NOUN
ejpam-5473	15	32	darus	darus	PROPN
ejpam-5473	15	33	)	)	PUNCT
ejpam-5473	15	34	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5473	15	35	2898	2898	NUM
ejpam-5473	15	36	copyright	copyright	NOUN
ejpam-5473	15	37	:	:	PUNCT
ejpam-5473	15	38	©	©	PROPN
ejpam-5473	15	39	2024	2024	NUM
ejpam-5473	15	40	the	the	DET
ejpam-5473	15	41	author(s	author(s	NOUN
ejpam-5473	15	42	)	)	PUNCT
ejpam-5473	15	43	.	.	PUNCT
ejpam-5473	16	1	(	(	PUNCT
ejpam-5473	16	2	cc	cc	NOUN
ejpam-5473	16	3	by	by	ADP
ejpam-5473	16	4	-	-	PUNCT
ejpam-5473	16	5	nc	nc	PROPN
ejpam-5473	16	6	4.0	4.0	NUM
ejpam-5473	16	7	)	)	PUNCT
ejpam-5473	16	8	f.	f.	PROPN
ejpam-5473	16	9	al	al	PROPN
ejpam-5473	16	10	-	-	PROPN
ejpam-5473	16	11	zu’bi	zu’bi	PROPN
ejpam-5473	16	12	et	et	NOUN
ejpam-5473	16	13	al	al	PROPN
ejpam-5473	16	14	.	.	PUNCT
ejpam-5473	16	15	/	/	SYM
ejpam-5473	16	16	eur	eur	PROPN
ejpam-5473	16	17	.	.	PUNCT
ejpam-5473	17	1	j.	j.	PROPN
ejpam-5473	17	2	pure	pure	PROPN
ejpam-5473	17	3	appl	appl	PROPN
ejpam-5473	17	4	.	.	PROPN
ejpam-5473	17	5	math	math	PROPN
ejpam-5473	17	6	,	,	PUNCT
ejpam-5473	17	7	17	17	NUM
ejpam-5473	17	8	(	(	PUNCT
ejpam-5473	17	9	4	4	NUM
ejpam-5473	17	10	)	)	PUNCT
ejpam-5473	17	11	(	(	PUNCT
ejpam-5473	17	12	2024	2024	NUM
ejpam-5473	17	13	)	)	PUNCT
ejpam-5473	17	14	,	,	PUNCT
ejpam-5473	17	15	2898	2898	NUM
ejpam-5473	17	16	-	-	SYM
ejpam-5473	17	17	2914	2914	NUM
ejpam-5473	17	18	2899	2899	NUM
ejpam-5473	17	19	1	1	NUM
ejpam-5473	17	20	.	.	PUNCT
ejpam-5473	18	1	introduction	introduction	NOUN
ejpam-5473	18	2	the	the	DET
ejpam-5473	18	3	fuzzy	fuzzy	ADJ
ejpam-5473	18	4	sets	set	NOUN
ejpam-5473	18	5	(	(	PUNCT
ejpam-5473	18	6	fss	fss	NOUN
ejpam-5473	18	7	)	)	PUNCT
ejpam-5473	18	8	were	be	AUX
ejpam-5473	18	9	created	create	VERB
ejpam-5473	18	10	by	by	ADP
ejpam-5473	18	11	zadeh	zadeh	PROPN
ejpam-5473	19	1	[	[	X
ejpam-5473	19	2	37	37	NUM
ejpam-5473	19	3	]	]	PUNCT
ejpam-5473	19	4	.	.	PUNCT
ejpam-5473	20	1	fuzzy	fuzzy	ADJ
ejpam-5473	20	2	mathematics	mathematic	NOUN
ejpam-5473	20	3	has	have	AUX
ejpam-5473	20	4	been	be	AUX
ejpam-5473	20	5	applied	apply	VERB
ejpam-5473	20	6	and	and	CCONJ
ejpam-5473	20	7	manipulated	manipulate	VERB
ejpam-5473	20	8	in	in	ADP
ejpam-5473	20	9	lots	lot	NOUN
ejpam-5473	20	10	of	of	ADP
ejpam-5473	20	11	fields	field	NOUN
ejpam-5473	20	12	and	and	CCONJ
ejpam-5473	20	13	discovered	discover	VERB
ejpam-5473	20	14	applications	application	NOUN
ejpam-5473	20	15	in	in	ADP
ejpam-5473	20	16	an	an	DET
ejpam-5473	20	17	expansive	expansive	ADJ
ejpam-5473	20	18	diversity	diversity	NOUN
ejpam-5473	20	19	of	of	ADP
ejpam-5473	20	20	disciplines	discipline	NOUN
ejpam-5473	20	21	[	[	X
ejpam-5473	20	22	8	8	NUM
ejpam-5473	20	23	,	,	PUNCT
ejpam-5473	20	24	11	11	NUM
ejpam-5473	20	25	,	,	PUNCT
ejpam-5473	20	26	14	14	NUM
ejpam-5473	20	27	,	,	PUNCT
ejpam-5473	20	28	32	32	NUM
ejpam-5473	20	29	,	,	PUNCT
ejpam-5473	20	30	34	34	NUM
ejpam-5473	20	31	,	,	PUNCT
ejpam-5473	20	32	35	35	NUM
ejpam-5473	20	33	]	]	PUNCT
ejpam-5473	20	34	.	.	PUNCT
ejpam-5473	21	1	the	the	DET
ejpam-5473	21	2	primary	primary	ADJ
ejpam-5473	21	3	challenge	challenge	NOUN
ejpam-5473	21	4	in	in	ADP
ejpam-5473	21	5	fuzzy	fuzzy	ADJ
ejpam-5473	21	6	mathematics	mathematic	NOUN
ejpam-5473	21	7	is	be	AUX
ejpam-5473	21	8	translating	translate	VERB
ejpam-5473	21	9	conventional	conventional	ADJ
ejpam-5473	21	10	notions	notion	NOUN
ejpam-5473	21	11	into	into	ADP
ejpam-5473	21	12	a	a	DET
ejpam-5473	21	13	fuzzy	fuzzy	ADJ
ejpam-5473	21	14	form	form	NOUN
ejpam-5473	21	15	.	.	PUNCT
ejpam-5473	22	1	the	the	DET
ejpam-5473	22	2	obstacle	obstacle	NOUN
ejpam-5473	22	3	lies	lie	VERB
ejpam-5473	22	4	in	in	ADP
ejpam-5473	22	5	choosing	choose	VERB
ejpam-5473	22	6	a	a	DET
ejpam-5473	22	7	reasonable	reasonable	ADJ
ejpam-5473	22	8	generalization	generalization	NOUN
ejpam-5473	22	9	from	from	ADP
ejpam-5473	22	10	many	many	ADJ
ejpam-5473	22	11	available	available	ADJ
ejpam-5473	22	12	approaches	approach	NOUN
ejpam-5473	22	13	.	.	PUNCT
ejpam-5473	23	1	in	in	ADP
ejpam-5473	23	2	the	the	DET
ejpam-5473	23	3	literature	literature	NOUN
ejpam-5473	23	4	,	,	PUNCT
ejpam-5473	23	5	we	we	PRON
ejpam-5473	23	6	found	find	VERB
ejpam-5473	23	7	several	several	ADJ
ejpam-5473	23	8	generalizations	generalization	NOUN
ejpam-5473	23	9	of	of	ADP
ejpam-5473	23	10	fss	fss	NOUN
ejpam-5473	23	11	.	.	PUNCT
ejpam-5473	24	1	the	the	DET
ejpam-5473	24	2	notion	notion	NOUN
ejpam-5473	24	3	of	of	ADP
ejpam-5473	24	4	the	the	DET
ejpam-5473	24	5	bipolar	bipolar	ADV
ejpam-5473	24	6	-	-	PUNCT
ejpam-5473	24	7	valued	value	VERB
ejpam-5473	24	8	fuzzy	fuzzy	ADJ
ejpam-5473	24	9	set	set	NOUN
ejpam-5473	24	10	(	(	PUNCT
ejpam-5473	24	11	bvfs	bvfs	ADJ
ejpam-5473	24	12	)	)	PUNCT
ejpam-5473	25	1	[	[	X
ejpam-5473	25	2	23	23	NUM
ejpam-5473	25	3	,	,	PUNCT
ejpam-5473	25	4	24	24	NUM
ejpam-5473	25	5	]	]	PUNCT
ejpam-5473	25	6	is	be	AUX
ejpam-5473	25	7	picked	pick	VERB
ejpam-5473	25	8	to	to	PART
ejpam-5473	25	9	be	be	AUX
ejpam-5473	25	10	studied	study	VERB
ejpam-5473	25	11	in	in	ADP
ejpam-5473	25	12	algebra	algebra	NOUN
ejpam-5473	25	13	.	.	PUNCT
ejpam-5473	26	1	also	also	ADV
ejpam-5473	26	2	,	,	PUNCT
ejpam-5473	26	3	bvfs	bvfs	PROPN
ejpam-5473	26	4	has	have	AUX
ejpam-5473	26	5	been	be	AUX
ejpam-5473	26	6	applied	apply	VERB
ejpam-5473	26	7	in	in	ADP
ejpam-5473	26	8	several	several	ADJ
ejpam-5473	26	9	fields	field	NOUN
ejpam-5473	26	10	such	such	ADJ
ejpam-5473	26	11	as	as	ADP
ejpam-5473	26	12	[	[	X
ejpam-5473	26	13	19	19	NUM
ejpam-5473	26	14	,	,	PUNCT
ejpam-5473	26	15	21	21	NUM
ejpam-5473	26	16	,	,	PUNCT
ejpam-5473	26	17	36	36	NUM
ejpam-5473	26	18	]	]	PUNCT
ejpam-5473	26	19	.	.	PUNCT
ejpam-5473	27	1	the	the	DET
ejpam-5473	27	2	pioneers	pioneer	NOUN
ejpam-5473	27	3	of	of	ADP
ejpam-5473	27	4	fuzzy	fuzzy	ADJ
ejpam-5473	27	5	mathematics	mathematic	NOUN
ejpam-5473	27	6	,	,	PUNCT
ejpam-5473	27	7	rosenfeld	rosenfeld	PROPN
ejpam-5473	28	1	[	[	X
ejpam-5473	28	2	29	29	NUM
ejpam-5473	28	3	]	]	PUNCT
ejpam-5473	28	4	in	in	ADP
ejpam-5473	28	5	algebra	algebra	NOUN
ejpam-5473	28	6	,	,	PUNCT
ejpam-5473	28	7	made	make	VERB
ejpam-5473	28	8	a	a	DET
ejpam-5473	28	9	great	great	ADJ
ejpam-5473	28	10	effort	effort	NOUN
ejpam-5473	28	11	to	to	PART
ejpam-5473	28	12	overcome	overcome	VERB
ejpam-5473	28	13	the	the	DET
ejpam-5473	28	14	difficulties	difficulty	NOUN
ejpam-5473	28	15	arising	arise	VERB
ejpam-5473	28	16	caused	cause	VERB
ejpam-5473	28	17	by	by	ADP
ejpam-5473	28	18	the	the	DET
ejpam-5473	28	19	lack	lack	NOUN
ejpam-5473	28	20	of	of	ADP
ejpam-5473	28	21	a	a	DET
ejpam-5473	28	22	fuzzy	fuzzy	ADJ
ejpam-5473	28	23	universal	universal	ADJ
ejpam-5473	28	24	set	set	NOUN
ejpam-5473	28	25	.	.	PUNCT
ejpam-5473	29	1	rosenfeld	rosenfeld	PROPN
ejpam-5473	29	2	discovered	discover	VERB
ejpam-5473	29	3	a	a	DET
ejpam-5473	29	4	suitable	suitable	ADJ
ejpam-5473	29	5	outlet	outlet	NOUN
ejpam-5473	29	6	to	to	PART
ejpam-5473	29	7	partially	partially	ADV
ejpam-5473	29	8	defeat	defeat	VERB
ejpam-5473	29	9	this	this	DET
ejpam-5473	29	10	obstacle	obstacle	NOUN
ejpam-5473	29	11	on	on	ADP
ejpam-5473	29	12	fuzzy	fuzzy	ADJ
ejpam-5473	29	13	groupoid	groupoid	PROPN
ejpam-5473	29	14	.	.	PUNCT
ejpam-5473	30	1	he	he	PRON
ejpam-5473	30	2	defined	define	VERB
ejpam-5473	30	3	fuzzy	fuzzy	ADJ
ejpam-5473	30	4	subgroupoids	subgroupoid	NOUN
ejpam-5473	30	5	of	of	ADP
ejpam-5473	30	6	℧	℧	PROPN
ejpam-5473	30	7	,	,	PUNCT
ejpam-5473	30	8	by	by	ADP
ejpam-5473	30	9	using	use	VERB
ejpam-5473	30	10	the	the	DET
ejpam-5473	30	11	ordinary	ordinary	ADJ
ejpam-5473	30	12	binary	binary	ADJ
ejpam-5473	30	13	operation	operation	NOUN
ejpam-5473	30	14	of	of	ADP
ejpam-5473	30	15	the	the	DET
ejpam-5473	30	16	assumed	assume	VERB
ejpam-5473	30	17	(	(	PUNCT
ejpam-5473	30	18	ordinary	ordinary	ADJ
ejpam-5473	30	19	)	)	PUNCT
ejpam-5473	30	20	groupoid	groupoid	NOUN
ejpam-5473	30	21	structure	structure	NOUN
ejpam-5473	30	22	on	on	ADP
ejpam-5473	30	23	the	the	DET
ejpam-5473	30	24	classical	classical	ADJ
ejpam-5473	30	25	set	set	NOUN
ejpam-5473	30	26	℧	℧	PROPN
ejpam-5473	30	27	.	.	PROPN
ejpam-5473	31	1	in	in	ADP
ejpam-5473	31	2	the	the	DET
ejpam-5473	31	3	generalization	generalization	NOUN
ejpam-5473	31	4	case	case	NOUN
ejpam-5473	31	5	,	,	PUNCT
ejpam-5473	31	6	dib	dib	PROPN
ejpam-5473	31	7	[	[	X
ejpam-5473	31	8	16	16	NUM
ejpam-5473	31	9	]	]	PUNCT
ejpam-5473	31	10	developed	develop	VERB
ejpam-5473	31	11	the	the	DET
ejpam-5473	31	12	concept	concept	NOUN
ejpam-5473	31	13	of	of	ADP
ejpam-5473	31	14	f	f	NOUN
ejpam-5473	31	15	-	-	PUNCT
ejpam-5473	31	16	space	space	NOUN
ejpam-5473	31	17	to	to	PART
ejpam-5473	31	18	replace	replace	VERB
ejpam-5473	31	19	the	the	DET
ejpam-5473	31	20	concept	concept	NOUN
ejpam-5473	31	21	of	of	ADP
ejpam-5473	31	22	a	a	DET
ejpam-5473	31	23	universal	universal	ADJ
ejpam-5473	31	24	set	set	NOUN
ejpam-5473	31	25	.	.	PUNCT
ejpam-5473	32	1	using	use	VERB
ejpam-5473	32	2	this	this	DET
ejpam-5473	32	3	concept	concept	NOUN
ejpam-5473	32	4	,	,	PUNCT
ejpam-5473	32	5	the	the	DET
ejpam-5473	32	6	fuzzy	fuzzy	ADJ
ejpam-5473	32	7	group	group	NOUN
ejpam-5473	32	8	(	(	PUNCT
ejpam-5473	32	9	fg	fg	PROPN
ejpam-5473	32	10	)	)	PUNCT
ejpam-5473	32	11	is	be	AUX
ejpam-5473	32	12	constructed	construct	VERB
ejpam-5473	32	13	naturally	naturally	ADV
ejpam-5473	32	14	.	.	PUNCT
ejpam-5473	33	1	the	the	DET
ejpam-5473	33	2	fuzzy	fuzzy	ADJ
ejpam-5473	33	3	group	group	NOUN
ejpam-5473	33	4	[	[	X
ejpam-5473	33	5	16	16	NUM
ejpam-5473	33	6	,	,	PUNCT
ejpam-5473	33	7	17	17	NUM
ejpam-5473	33	8	]	]	PUNCT
ejpam-5473	33	9	is	be	AUX
ejpam-5473	33	10	defined	define	VERB
ejpam-5473	33	11	as	as	ADP
ejpam-5473	33	12	a	a	DET
ejpam-5473	33	13	fuzzy	fuzzy	ADJ
ejpam-5473	33	14	binary	binary	ADJ
ejpam-5473	33	15	operation	operation	NOUN
ejpam-5473	33	16	on	on	ADP
ejpam-5473	33	17	a	a	DET
ejpam-5473	33	18	f	f	NOUN
ejpam-5473	33	19	-	-	PUNCT
ejpam-5473	33	20	space	space	NOUN
ejpam-5473	33	21	,	,	PUNCT
ejpam-5473	33	22	satisfying	satisfy	VERB
ejpam-5473	33	23	the	the	DET
ejpam-5473	33	24	usual	usual	ADJ
ejpam-5473	33	25	conditions	condition	NOUN
ejpam-5473	33	26	of	of	ADP
ejpam-5473	33	27	the	the	DET
ejpam-5473	33	28	group	group	NOUN
ejpam-5473	33	29	.	.	PUNCT
ejpam-5473	34	1	having	having	AUX
ejpam-5473	34	2	defined	define	VERB
ejpam-5473	34	3	the	the	DET
ejpam-5473	34	4	fg	fg	PROPN
ejpam-5473	34	5	on	on	ADP
ejpam-5473	34	6	the	the	DET
ejpam-5473	34	7	f	f	NOUN
ejpam-5473	34	8	-	-	PUNCT
ejpam-5473	34	9	space	space	NOUN
ejpam-5473	34	10	(	(	PUNCT
ejpam-5473	34	11	℧	℧	PROPN
ejpam-5473	34	12	,	,	PUNCT
ejpam-5473	34	13	[	[	X
ejpam-5473	34	14	0	0	NUM
ejpam-5473	34	15	,	,	PUNCT
ejpam-5473	34	16	1	1	NUM
ejpam-5473	34	17	]	]	NUM
ejpam-5473	34	18	)	)	PUNCT
ejpam-5473	34	19	,	,	PUNCT
ejpam-5473	34	20	the	the	DET
ejpam-5473	34	21	conditions	condition	NOUN
ejpam-5473	34	22	on	on	ADP
ejpam-5473	34	23	fuzzy	fuzzy	ADJ
ejpam-5473	34	24	subset	subset	VERB
ejpam-5473	34	25	a	a	PRON
ejpam-5473	34	26	of	of	ADP
ejpam-5473	34	27	℧	℧	PROPN
ejpam-5473	34	28	to	to	PART
ejpam-5473	34	29	be	be	AUX
ejpam-5473	34	30	a	a	DET
ejpam-5473	34	31	fuzzy	fuzzy	ADJ
ejpam-5473	34	32	subgroup	subgroup	NOUN
ejpam-5473	34	33	were	be	AUX
ejpam-5473	34	34	naturally	naturally	ADV
ejpam-5473	34	35	deduced	deduce	VERB
ejpam-5473	34	36	.	.	PUNCT
ejpam-5473	35	1	our	our	PRON
ejpam-5473	35	2	objectives	objective	NOUN
ejpam-5473	35	3	can	can	AUX
ejpam-5473	35	4	be	be	AUX
ejpam-5473	35	5	summarized	summarize	VERB
ejpam-5473	35	6	by	by	ADP
ejpam-5473	35	7	introducing	introduce	VERB
ejpam-5473	35	8	and	and	CCONJ
ejpam-5473	35	9	studying	study	VERB
ejpam-5473	35	10	properties	property	NOUN
ejpam-5473	35	11	and	and	CCONJ
ejpam-5473	35	12	algebraic	algebraic	ADJ
ejpam-5473	35	13	structure	structure	NOUN
ejpam-5473	35	14	on	on	ADP
ejpam-5473	35	15	the	the	DET
ejpam-5473	35	16	concept	concept	NOUN
ejpam-5473	35	17	of	of	ADP
ejpam-5473	35	18	bvf	bvf	NOUN
ejpam-5473	35	19	-	-	PUNCT
ejpam-5473	35	20	space	space	NOUN
ejpam-5473	35	21	and	and	CCONJ
ejpam-5473	35	22	bvfbo	bvfbo	NOUN
ejpam-5473	35	23	to	to	PART
ejpam-5473	35	24	present	present	VERB
ejpam-5473	35	25	a	a	DET
ejpam-5473	35	26	novel	novel	ADJ
ejpam-5473	35	27	approach	approach	NOUN
ejpam-5473	35	28	to	to	PART
ejpam-5473	35	29	study	study	VERB
ejpam-5473	35	30	bvf	bvf	NOUN
ejpam-5473	35	31	-	-	PUNCT
ejpam-5473	35	32	group	group	NOUN
ejpam-5473	35	33	theory	theory	NOUN
ejpam-5473	35	34	comparability	comparability	NOUN
ejpam-5473	35	35	and	and	CCONJ
ejpam-5473	35	36	parallel	parallel	NOUN
ejpam-5473	35	37	to	to	ADP
ejpam-5473	35	38	the	the	DET
ejpam-5473	35	39	dip	dip	NOUN
ejpam-5473	35	40	approach	approach	NOUN
ejpam-5473	35	41	.	.	PUNCT
ejpam-5473	36	1	the	the	DET
ejpam-5473	36	2	method	method	NOUN
ejpam-5473	36	3	used	use	VERB
ejpam-5473	36	4	in	in	ADP
ejpam-5473	36	5	this	this	DET
ejpam-5473	36	6	research	research	NOUN
ejpam-5473	36	7	is	be	AUX
ejpam-5473	36	8	to	to	PART
ejpam-5473	36	9	incorporate	incorporate	VERB
ejpam-5473	36	10	bvfs	bvfs	ADV
ejpam-5473	36	11	and	and	CCONJ
ejpam-5473	36	12	fg	fg	X
ejpam-5473	36	13	by	by	ADP
ejpam-5473	36	14	using	use	VERB
ejpam-5473	36	15	the	the	DET
ejpam-5473	36	16	dip	dip	NOUN
ejpam-5473	36	17	approach	approach	NOUN
ejpam-5473	36	18	.	.	PUNCT
ejpam-5473	37	1	our	our	PRON
ejpam-5473	37	2	methodology	methodology	NOUN
ejpam-5473	37	3	started	start	VERB
ejpam-5473	37	4	by	by	ADP
ejpam-5473	37	5	collecting	collect	VERB
ejpam-5473	37	6	data	datum	NOUN
ejpam-5473	37	7	and	and	CCONJ
ejpam-5473	37	8	related	related	ADJ
ejpam-5473	37	9	works	work	NOUN
ejpam-5473	37	10	of	of	ADP
ejpam-5473	37	11	bvfs	bvfs	NOUN
ejpam-5473	38	1	[	[	X
ejpam-5473	38	2	23	23	NUM
ejpam-5473	38	3	,	,	PUNCT
ejpam-5473	38	4	24	24	NUM
ejpam-5473	38	5	]	]	PUNCT
ejpam-5473	38	6	and	and	CCONJ
ejpam-5473	38	7	dip	dip	NOUN
ejpam-5473	38	8	’s	’s	PART
ejpam-5473	38	9	works	work	NOUN
ejpam-5473	39	1	[	[	X
ejpam-5473	39	2	16	16	NUM
ejpam-5473	39	3	,	,	PUNCT
ejpam-5473	39	4	17	17	NUM
ejpam-5473	39	5	]	]	PUNCT
ejpam-5473	39	6	.	.	PUNCT
ejpam-5473	40	1	then	then	ADV
ejpam-5473	40	2	,	,	PUNCT
ejpam-5473	40	3	we	we	PRON
ejpam-5473	40	4	analyze	analyze	VERB
ejpam-5473	40	5	these	these	DET
ejpam-5473	40	6	data	datum	NOUN
ejpam-5473	40	7	by	by	ADP
ejpam-5473	40	8	applying	apply	VERB
ejpam-5473	40	9	the	the	DET
ejpam-5473	40	10	concept	concept	NOUN
ejpam-5473	40	11	of	of	ADP
ejpam-5473	40	12	bvfs	bvfs	NOUN
ejpam-5473	40	13	to	to	ADP
ejpam-5473	40	14	the	the	DET
ejpam-5473	40	15	structure	structure	NOUN
ejpam-5473	40	16	of	of	ADP
ejpam-5473	40	17	fg	fg	PROPN
ejpam-5473	40	18	.	.	PUNCT
ejpam-5473	41	1	lastly	lastly	ADV
ejpam-5473	41	2	,	,	PUNCT
ejpam-5473	41	3	our	our	PRON
ejpam-5473	41	4	expected	expect	VERB
ejpam-5473	41	5	results	result	NOUN
ejpam-5473	41	6	are	be	AUX
ejpam-5473	41	7	comprehensively	comprehensively	ADV
ejpam-5473	41	8	compared	compare	VERB
ejpam-5473	41	9	with	with	ADP
ejpam-5473	41	10	ordinary	ordinary	ADJ
ejpam-5473	41	11	group	group	NOUN
ejpam-5473	41	12	and	and	CCONJ
ejpam-5473	41	13	fg	fg	PROPN
ejpam-5473	41	14	works	work	NOUN
ejpam-5473	41	15	.	.	PUNCT
ejpam-5473	42	1	the	the	DET
ejpam-5473	42	2	bvfs	bvfs	ADJ
ejpam-5473	42	3	is	be	AUX
ejpam-5473	42	4	considered	consider	VERB
ejpam-5473	42	5	as	as	ADP
ejpam-5473	42	6	a	a	DET
ejpam-5473	42	7	generalization	generalization	NOUN
ejpam-5473	42	8	of	of	ADP
ejpam-5473	42	9	fs	fs	PROPN
ejpam-5473	42	10	.	.	PROPN
ejpam-5473	42	11	in	in	ADP
ejpam-5473	42	12	2000	2000	NUM
ejpam-5473	42	13	,	,	PUNCT
ejpam-5473	42	14	lee	lee	PROPN
ejpam-5473	43	1	[	[	X
ejpam-5473	43	2	23	23	NUM
ejpam-5473	43	3	,	,	PUNCT
ejpam-5473	43	4	24	24	NUM
ejpam-5473	43	5	]	]	PUNCT
ejpam-5473	43	6	created	create	VERB
ejpam-5473	43	7	the	the	DET
ejpam-5473	43	8	concept	concept	NOUN
ejpam-5473	43	9	of	of	ADP
ejpam-5473	43	10	bipolar	bipolar	ADJ
ejpam-5473	43	11	valued	value	VERB
ejpam-5473	43	12	fuzzy	fuzzy	ADJ
ejpam-5473	43	13	sets	set	NOUN
ejpam-5473	43	14	.	.	PUNCT
ejpam-5473	44	1	bvfss	bvfss	PROPN
ejpam-5473	44	2	are	be	AUX
ejpam-5473	44	3	an	an	DET
ejpam-5473	44	4	expansion	expansion	NOUN
ejpam-5473	44	5	of	of	ADP
ejpam-5473	44	6	fss	fss	NOUN
ejpam-5473	44	7	whose	whose	DET
ejpam-5473	44	8	membership	membership	NOUN
ejpam-5473	44	9	degree	degree	NOUN
ejpam-5473	44	10	range	range	NOUN
ejpam-5473	44	11	is	be	AUX
ejpam-5473	44	12	expanded	expand	VERB
ejpam-5473	44	13	from	from	ADP
ejpam-5473	44	14	the	the	DET
ejpam-5473	44	15	[	[	X
ejpam-5473	44	16	0	0	NUM
ejpam-5473	44	17	,	,	PUNCT
ejpam-5473	44	18	1	1	NUM
ejpam-5473	44	19	]	]	PUNCT
ejpam-5473	44	20	to	to	ADP
ejpam-5473	44	21	[	[	X
ejpam-5473	44	22	−1	−1	NOUN
ejpam-5473	44	23	,	,	PUNCT
ejpam-5473	44	24	0	0	NUM
ejpam-5473	44	25	]	]	X
ejpam-5473	44	26	×	×	NOUN
ejpam-5473	45	1	[	[	X
ejpam-5473	45	2	0	0	NUM
ejpam-5473	45	3	,	,	PUNCT
ejpam-5473	45	4	1	1	NUM
ejpam-5473	45	5	]	]	PUNCT
ejpam-5473	45	6	.	.	PUNCT
ejpam-5473	46	1	after	after	ADP
ejpam-5473	46	2	that	that	PRON
ejpam-5473	46	3	,	,	PUNCT
ejpam-5473	46	4	anitha	anitha	NOUN
ejpam-5473	46	5	et.al	et.al	PROPN
ejpam-5473	47	1	[	[	X
ejpam-5473	47	2	12	12	NUM
ejpam-5473	47	3	]	]	PUNCT
ejpam-5473	47	4	created	create	VERB
ejpam-5473	47	5	the	the	DET
ejpam-5473	47	6	bipolar	bipolar	ADJ
ejpam-5473	47	7	valued	value	VERB
ejpam-5473	47	8	fuzzy	fuzzy	ADJ
ejpam-5473	47	9	subgroups	subgroup	NOUN
ejpam-5473	47	10	of	of	ADP
ejpam-5473	47	11	a	a	DET
ejpam-5473	47	12	known	know	VERB
ejpam-5473	47	13	group	group	NOUN
ejpam-5473	47	14	.	.	PUNCT
ejpam-5473	48	1	bipolar	bipolar	PROPN
ejpam-5473	48	2	valued	value	VERB
ejpam-5473	48	3	fuzzy	fuzzy	ADJ
ejpam-5473	48	4	bck	bck	PROPN
ejpam-5473	48	5	/	/	SYM
ejpam-5473	48	6	bci	bci	NOUN
ejpam-5473	48	7	-	-	PUNCT
ejpam-5473	48	8	algebras	algebras	PROPN
ejpam-5473	48	9	was	be	AUX
ejpam-5473	48	10	presented	present	VERB
ejpam-5473	48	11	by	by	ADP
ejpam-5473	48	12	arsham	arsham	PROPN
ejpam-5473	49	1	[	[	X
ejpam-5473	49	2	30	30	NUM
ejpam-5473	49	3	]	]	PUNCT
ejpam-5473	49	4	.	.	PUNCT
ejpam-5473	50	1	also	also	ADV
ejpam-5473	50	2	,	,	PUNCT
ejpam-5473	50	3	bipolar	bipolar	ADJ
ejpam-5473	50	4	interval	interval	NOUN
ejpam-5473	50	5	-	-	PUNCT
ejpam-5473	50	6	valued	value	VERB
ejpam-5473	50	7	fuzzy	fuzzy	ADJ
ejpam-5473	50	8	subgroups	subgroup	NOUN
ejpam-5473	50	9	of	of	ADP
ejpam-5473	50	10	a	a	DET
ejpam-5473	50	11	group	group	NOUN
ejpam-5473	50	12	were	be	AUX
ejpam-5473	50	13	defined	define	VERB
ejpam-5473	50	14	by	by	ADP
ejpam-5473	50	15	balasubramanian	balasubramanian	ADJ
ejpam-5473	50	16	et.al	et.al	PROPN
ejpam-5473	51	1	[	[	X
ejpam-5473	51	2	15	15	NUM
ejpam-5473	51	3	]	]	PUNCT
ejpam-5473	51	4	.	.	PUNCT
ejpam-5473	52	1	in	in	ADP
ejpam-5473	52	2	2009	2009	NUM
ejpam-5473	52	3	,	,	PUNCT
ejpam-5473	52	4	lee	lee	PROPN
ejpam-5473	53	1	[	[	X
ejpam-5473	53	2	25	25	NUM
ejpam-5473	53	3	]	]	PUNCT
ejpam-5473	53	4	proposed	propose	VERB
ejpam-5473	53	5	and	and	CCONJ
ejpam-5473	53	6	identified	identify	VERB
ejpam-5473	53	7	the	the	DET
ejpam-5473	53	8	bipolar	bipolar	ADV
ejpam-5473	53	9	-	-	PUNCT
ejpam-5473	53	10	valued	value	VERB
ejpam-5473	53	11	fuzzy	fuzzy	ADJ
ejpam-5473	53	12	subalgebras	subalgebra	NOUN
ejpam-5473	53	13	and	and	CCONJ
ejpam-5473	53	14	bipolar	bipolar	ADV
ejpam-5473	53	15	-	-	PUNCT
ejpam-5473	53	16	valued	value	VERB
ejpam-5473	53	17	fuzzy	fuzzy	ADJ
ejpam-5473	53	18	ideals	ideal	NOUN
ejpam-5473	53	19	of	of	ADP
ejpam-5473	53	20	bck	bck	PROPN
ejpam-5473	53	21	/	/	SYM
ejpam-5473	53	22	bci	bci	NOUN
ejpam-5473	53	23	-	-	PUNCT
ejpam-5473	53	24	algebras	algebras	X
ejpam-5473	53	25	.	.	PUNCT
ejpam-5473	54	1	some	some	DET
ejpam-5473	54	2	properties	property	NOUN
ejpam-5473	54	3	of	of	ADP
ejpam-5473	54	4	fuzzy	fuzzy	ADJ
ejpam-5473	54	5	groups	group	NOUN
ejpam-5473	54	6	were	be	AUX
ejpam-5473	54	7	given	give	VERB
ejpam-5473	54	8	by	by	ADP
ejpam-5473	54	9	mustafa	mustafa	PROPN
ejpam-5473	54	10	[	[	X
ejpam-5473	54	11	2	2	NUM
ejpam-5473	54	12	]	]	PUNCT
ejpam-5473	54	13	.	.	PUNCT
ejpam-5473	55	1	sahaya	sahaya	VERB
ejpam-5473	55	2	et.al	et.al	PROPN
ejpam-5473	55	3	.	.	PUNCT
ejpam-5473	56	1	,	,	PUNCT
ejpam-5473	57	1	[	[	X
ejpam-5473	57	2	31	31	NUM
ejpam-5473	57	3	]	]	PUNCT
ejpam-5473	57	4	initiated	initiate	VERB
ejpam-5473	57	5	the	the	DET
ejpam-5473	57	6	bipolar	bipolar	NOUN
ejpam-5473	57	7	valued	value	VERB
ejpam-5473	57	8	q	q	ADJ
ejpam-5473	57	9	-	-	PUNCT
ejpam-5473	57	10	fuzzy	fuzzy	ADJ
ejpam-5473	57	11	subgroups	subgroup	NOUN
ejpam-5473	57	12	of	of	ADP
ejpam-5473	57	13	a	a	DET
ejpam-5473	57	14	group	group	NOUN
ejpam-5473	57	15	.	.	PUNCT
ejpam-5473	58	1	shanmugapriya	shanmugapriya	PROPN
ejpam-5473	58	2	&	&	CCONJ
ejpam-5473	58	3	arjunan	arjunan	PROPN
ejpam-5473	59	1	[	[	X
ejpam-5473	59	2	33	33	NUM
ejpam-5473	59	3	]	]	PUNCT
ejpam-5473	59	4	introduced	introduce	VERB
ejpam-5473	59	5	some	some	DET
ejpam-5473	59	6	converters	converter	NOUN
ejpam-5473	59	7	in	in	ADP
ejpam-5473	59	8	bipolar	bipolar	ADJ
ejpam-5473	59	9	valued	value	VERB
ejpam-5473	59	10	fuzzy	fuzzy	ADJ
ejpam-5473	59	11	subsemirings	subsemiring	NOUN
ejpam-5473	59	12	of	of	ADP
ejpam-5473	59	13	a	a	DET
ejpam-5473	59	14	semiring	semiring	NOUN
ejpam-5473	59	15	.	.	PUNCT
ejpam-5473	60	1	young	young	ADJ
ejpam-5473	60	2	and	and	CCONJ
ejpam-5473	60	3	song	song	NOUN
ejpam-5473	61	1	[	[	X
ejpam-5473	61	2	22	22	NUM
ejpam-5473	61	3	]	]	PUNCT
ejpam-5473	61	4	presented	present	VERB
ejpam-5473	61	5	ideas	idea	NOUN
ejpam-5473	61	6	stuck	stick	VERB
ejpam-5473	61	7	on	on	ADP
ejpam-5473	61	8	bipolar	bipolar	ADV
ejpam-5473	61	9	-	-	PUNCT
ejpam-5473	61	10	valued	value	VERB
ejpam-5473	61	11	fuzzy	fuzzy	ADJ
ejpam-5473	61	12	sets	set	NOUN
ejpam-5473	61	13	concerning	concern	VERB
ejpam-5473	61	14	the	the	DET
ejpam-5473	61	15	subalgebras	subalgebra	NOUN
ejpam-5473	61	16	and	and	CCONJ
ejpam-5473	61	17	closed	closed	ADJ
ejpam-5473	61	18	ideals	ideal	NOUN
ejpam-5473	61	19	of	of	ADP
ejpam-5473	61	20	bch	bch	PROPN
ejpam-5473	61	21	-	-	PUNCT
ejpam-5473	61	22	algebras	algebras	PROPN
ejpam-5473	61	23	.	.	PUNCT
ejpam-5473	62	1	recently	recently	ADV
ejpam-5473	62	2	,	,	PUNCT
ejpam-5473	62	3	some	some	DET
ejpam-5473	62	4	researchers	researcher	NOUN
ejpam-5473	62	5	followed	follow	VERB
ejpam-5473	62	6	rosenfeld	rosenfeld	PROPN
ejpam-5473	62	7	’s	’s	PART
ejpam-5473	62	8	approach	approach	NOUN
ejpam-5473	62	9	to	to	PART
ejpam-5473	62	10	introduce	introduce	VERB
ejpam-5473	62	11	bipolar	bipolar	ADV
ejpam-5473	62	12	-	-	PUNCT
ejpam-5473	62	13	valued	value	VERB
ejpam-5473	62	14	fuzzy	fuzzy	ADJ
ejpam-5473	62	15	subgroups	subgroup	NOUN
ejpam-5473	62	16	[	[	X
ejpam-5473	62	17	12	12	NUM
ejpam-5473	62	18	,	,	PUNCT
ejpam-5473	62	19	13	13	NUM
ejpam-5473	62	20	]	]	PUNCT
ejpam-5473	62	21	.	.	PUNCT
ejpam-5473	63	1	also	also	ADV
ejpam-5473	63	2	,	,	PUNCT
ejpam-5473	63	3	al	al	PROPN
ejpam-5473	63	4	-	-	PUNCT
ejpam-5473	63	5	sharo	sharo	NOUN
ejpam-5473	63	6	[	[	X
ejpam-5473	63	7	8	8	NUM
ejpam-5473	63	8	]	]	PUNCT
ejpam-5473	63	9	introduced	introduce	VERB
ejpam-5473	63	10	(	(	PUNCT
ejpam-5473	63	11	α1,2	α1,2	ADJ
ejpam-5473	63	12	,	,	PUNCT
ejpam-5473	63	13	β1,2)-complex	β1,2)-complex	ADJ
ejpam-5473	63	14	intuitionistic	intuitionistic	ADJ
ejpam-5473	63	15	fuzzy	fuzzy	ADJ
ejpam-5473	63	16	subgroups	subgroup	NOUN
ejpam-5473	63	17	and	and	CCONJ
ejpam-5473	63	18	their	their	PRON
ejpam-5473	63	19	algebraic	algebraic	ADJ
ejpam-5473	63	20	structure	structure	NOUN
ejpam-5473	63	21	.	.	PUNCT
ejpam-5473	64	1	manivannan	manivannan	NOUN
ejpam-5473	64	2	et	et	PROPN
ejpam-5473	64	3	al	al	PROPN
ejpam-5473	64	4	.	.	PUNCT
ejpam-5473	65	1	[	[	X
ejpam-5473	65	2	14	14	NUM
ejpam-5473	65	3	]	]	PUNCT
ejpam-5473	65	4	introduced	introduce	VERB
ejpam-5473	65	5	a	a	DET
ejpam-5473	65	6	new	new	ADJ
ejpam-5473	65	7	approach	approach	NOUN
ejpam-5473	65	8	to	to	ADP
ejpam-5473	65	9	complex	complex	ADJ
ejpam-5473	65	10	fuzzy	fuzzy	ADJ
ejpam-5473	65	11	ideals	ideal	NOUN
ejpam-5473	65	12	in	in	ADP
ejpam-5473	65	13	bck	bck	PROPN
ejpam-5473	65	14	/	/	SYM
ejpam-5473	65	15	bci	bci	NOUN
ejpam-5473	65	16	-	-	PUNCT
ejpam-5473	65	17	algebras	algebra	NOUN
ejpam-5473	65	18	.	.	PUNCT
ejpam-5473	66	1	in	in	ADP
ejpam-5473	66	2	2021	2021	NUM
ejpam-5473	66	3	,	,	PUNCT
ejpam-5473	66	4	abu	abu	PROPN
ejpam-5473	66	5	-	-	PUNCT
ejpam-5473	66	6	hijleh	hijleh	PROPN
ejpam-5473	66	7	et	et	PROPN
ejpam-5473	66	8	al	al	PROPN
ejpam-5473	66	9	.	.	PUNCT
ejpam-5473	67	1	[	[	X
ejpam-5473	67	2	1	1	X
ejpam-5473	67	3	]	]	PUNCT
ejpam-5473	67	4	introduced	introduce	VERB
ejpam-5473	67	5	complex	complex	ADJ
ejpam-5473	67	6	fuzzy	fuzzy	ADJ
ejpam-5473	67	7	groups	group	NOUN
ejpam-5473	67	8	based	base	VERB
ejpam-5473	67	9	on	on	ADP
ejpam-5473	67	10	rosenfeld	rosenfeld	PROPN
ejpam-5473	67	11	’s	’s	PART
ejpam-5473	67	12	approach	approach	NOUN
ejpam-5473	67	13	.	.	PUNCT
ejpam-5473	68	1	f.	f.	PROPN
ejpam-5473	68	2	al	al	PROPN
ejpam-5473	68	3	-	-	PROPN
ejpam-5473	68	4	zu’bi	zu’bi	PROPN
ejpam-5473	68	5	et	et	NOUN
ejpam-5473	68	6	al	al	PROPN
ejpam-5473	68	7	.	.	PUNCT
ejpam-5473	68	8	/	/	SYM
ejpam-5473	68	9	eur	eur	PROPN
ejpam-5473	68	10	.	.	PUNCT
ejpam-5473	69	1	j.	j.	PROPN
ejpam-5473	69	2	pure	pure	PROPN
ejpam-5473	69	3	appl	appl	PROPN
ejpam-5473	69	4	.	.	PROPN
ejpam-5473	69	5	math	math	PROPN
ejpam-5473	69	6	,	,	PUNCT
ejpam-5473	69	7	17	17	NUM
ejpam-5473	69	8	(	(	PUNCT
ejpam-5473	69	9	4	4	NUM
ejpam-5473	69	10	)	)	PUNCT
ejpam-5473	69	11	(	(	PUNCT
ejpam-5473	69	12	2024	2024	NUM
ejpam-5473	69	13	)	)	PUNCT
ejpam-5473	69	14	,	,	PUNCT
ejpam-5473	69	15	2898	2898	NUM
ejpam-5473	69	16	-	-	SYM
ejpam-5473	69	17	2914	2914	NUM
ejpam-5473	69	18	2900	2900	NUM
ejpam-5473	69	19	nevertheless	nevertheless	ADV
ejpam-5473	69	20	,	,	PUNCT
ejpam-5473	69	21	all	all	DET
ejpam-5473	69	22	mentioned	mention	VERB
ejpam-5473	69	23	scholars	scholar	NOUN
ejpam-5473	69	24	did	do	AUX
ejpam-5473	69	25	not	not	PART
ejpam-5473	69	26	identify	identify	VERB
ejpam-5473	69	27	the	the	DET
ejpam-5473	69	28	notion	notion	NOUN
ejpam-5473	69	29	of	of	ADP
ejpam-5473	69	30	bipolar	bipolar	ADV
ejpam-5473	69	31	-	-	PUNCT
ejpam-5473	69	32	valued	value	VERB
ejpam-5473	69	33	fuzzy	fuzzy	ADJ
ejpam-5473	69	34	groupoid	groupoid	NOUN
ejpam-5473	69	35	as	as	ADP
ejpam-5473	69	36	dib	dib	PROPN
ejpam-5473	69	37	’s	’s	PART
ejpam-5473	69	38	approach	approach	NOUN
ejpam-5473	69	39	,	,	PUNCT
ejpam-5473	69	40	which	which	PRON
ejpam-5473	69	41	is	be	AUX
ejpam-5473	69	42	passed	pass	VERB
ejpam-5473	69	43	on	on	ADP
ejpam-5473	69	44	bvf	bvf	NOUN
ejpam-5473	69	45	-	-	PUNCT
ejpam-5473	69	46	space	space	NOUN
ejpam-5473	69	47	.	.	PUNCT
ejpam-5473	70	1	recently	recently	ADV
ejpam-5473	70	2	,	,	PUNCT
ejpam-5473	70	3	the	the	DET
ejpam-5473	70	4	bipolar	bipolar	ADV
ejpam-5473	70	5	-	-	PUNCT
ejpam-5473	70	6	valued	value	VERB
ejpam-5473	70	7	fuzzy	fuzzy	ADJ
ejpam-5473	70	8	function	function	NOUN
ejpam-5473	70	9	[	[	X
ejpam-5473	70	10	9	9	NUM
ejpam-5473	70	11	]	]	PUNCT
ejpam-5473	70	12	was	be	AUX
ejpam-5473	70	13	prepared	prepare	VERB
ejpam-5473	70	14	in	in	ADP
ejpam-5473	70	15	terms	term	NOUN
ejpam-5473	70	16	of	of	ADP
ejpam-5473	70	17	two	two	NUM
ejpam-5473	70	18	special	special	ADJ
ejpam-5473	70	19	concepts	concept	NOUN
ejpam-5473	70	20	,	,	PUNCT
ejpam-5473	70	21	bipolar	bipolar	ADV
ejpam-5473	70	22	-	-	PUNCT
ejpam-5473	70	23	valued	value	VERB
ejpam-5473	70	24	fuzzy	fuzzy	ADJ
ejpam-5473	70	25	cartesian	cartesian	ADJ
ejpam-5473	70	26	product	product	NOUN
ejpam-5473	70	27	,	,	PUNCT
ejpam-5473	70	28	and	and	CCONJ
ejpam-5473	70	29	bipolar	bipolar	ADV
ejpam-5473	70	30	-	-	PUNCT
ejpam-5473	70	31	valued	value	VERB
ejpam-5473	70	32	fuzzy	fuzzy	ADJ
ejpam-5473	70	33	relation	relation	NOUN
ejpam-5473	70	34	which	which	PRON
ejpam-5473	70	35	were	be	AUX
ejpam-5473	70	36	established	establish	VERB
ejpam-5473	70	37	depending	depend	VERB
ejpam-5473	70	38	on	on	ADP
ejpam-5473	70	39	dib	dib	PROPN
ejpam-5473	70	40	’s	’s	PART
ejpam-5473	70	41	approach	approach	NOUN
ejpam-5473	70	42	[	[	X
ejpam-5473	70	43	17	17	NUM
ejpam-5473	70	44	]	]	PUNCT
ejpam-5473	70	45	.	.	PUNCT
ejpam-5473	71	1	these	these	DET
ejpam-5473	71	2	results	result	VERB
ejpam-5473	71	3	[	[	X
ejpam-5473	71	4	9	9	NUM
ejpam-5473	71	5	]	]	PUNCT
ejpam-5473	71	6	build	build	VERB
ejpam-5473	71	7	the	the	DET
ejpam-5473	71	8	basic	basic	ADJ
ejpam-5473	71	9	structure	structure	NOUN
ejpam-5473	71	10	to	to	PART
ejpam-5473	71	11	start	start	VERB
ejpam-5473	71	12	our	our	PRON
ejpam-5473	71	13	results	result	NOUN
ejpam-5473	71	14	and	and	CCONJ
ejpam-5473	71	15	create	create	VERB
ejpam-5473	71	16	the	the	DET
ejpam-5473	71	17	bvf	bvf	NOUN
ejpam-5473	71	18	-	-	PUNCT
ejpam-5473	71	19	group	group	NOUN
ejpam-5473	71	20	theory	theory	NOUN
ejpam-5473	71	21	.	.	PUNCT
ejpam-5473	72	1	also	also	ADV
ejpam-5473	72	2	,	,	PUNCT
ejpam-5473	72	3	some	some	DET
ejpam-5473	72	4	researchers	researcher	NOUN
ejpam-5473	72	5	followed	follow	VERB
ejpam-5473	72	6	the	the	DET
ejpam-5473	72	7	dib	dib	NOUN
ejpam-5473	72	8	approach	approach	NOUN
ejpam-5473	72	9	and	and	CCONJ
ejpam-5473	72	10	published	publish	VERB
ejpam-5473	72	11	several	several	ADJ
ejpam-5473	72	12	results	result	NOUN
ejpam-5473	72	13	in	in	ADP
ejpam-5473	72	14	algebra	algebra	NOUN
ejpam-5473	72	15	.	.	PUNCT
ejpam-5473	73	1	in	in	ADP
ejpam-5473	73	2	2009	2009	NUM
ejpam-5473	73	3	,	,	PUNCT
ejpam-5473	73	4	fathi	fathi	PROPN
ejpam-5473	73	5	and	and	CCONJ
ejpam-5473	73	6	salleh	salleh	PROPN
ejpam-5473	74	1	[	[	X
ejpam-5473	74	2	18	18	NUM
ejpam-5473	74	3	]	]	PUNCT
ejpam-5473	74	4	introduced	introduce	VERB
ejpam-5473	74	5	an	an	DET
ejpam-5473	74	6	intuitionistic	intuitionistic	ADJ
ejpam-5473	74	7	fuzzy	fuzzy	ADJ
ejpam-5473	74	8	group	group	NOUN
ejpam-5473	74	9	(	(	PUNCT
ejpam-5473	74	10	if	if	SCONJ
ejpam-5473	74	11	-	-	PUNCT
ejpam-5473	74	12	group	group	NOUN
ejpam-5473	74	13	)	)	PUNCT
ejpam-5473	74	14	based	base	VERB
ejpam-5473	74	15	on	on	ADP
ejpam-5473	74	16	intuitionistic	intuitionistic	ADJ
ejpam-5473	74	17	fuzzy	fuzzy	ADJ
ejpam-5473	74	18	space	space	NOUN
ejpam-5473	74	19	.	.	PUNCT
ejpam-5473	75	1	the	the	DET
ejpam-5473	75	2	difference	difference	NOUN
ejpam-5473	75	3	between	between	ADP
ejpam-5473	75	4	the	the	DET
ejpam-5473	75	5	presented	present	VERB
ejpam-5473	75	6	work	work	NOUN
ejpam-5473	75	7	and	and	CCONJ
ejpam-5473	75	8	fathi	fathi	PROPN
ejpam-5473	75	9	and	and	CCONJ
ejpam-5473	75	10	salleh	salleh	PROPN
ejpam-5473	75	11	’s	’s	PART
ejpam-5473	75	12	approach	approach	NOUN
ejpam-5473	75	13	lies	lie	VERB
ejpam-5473	75	14	in	in	ADP
ejpam-5473	75	15	the	the	DET
ejpam-5473	75	16	negative	negative	ADJ
ejpam-5473	75	17	membership	membership	NOUN
ejpam-5473	75	18	component	component	NOUN
ejpam-5473	75	19	.	.	PUNCT
ejpam-5473	76	1	bvf	bvf	NOUN
ejpam-5473	76	2	-	-	PUNCT
ejpam-5473	76	3	space	space	NOUN
ejpam-5473	76	4	has	have	VERB
ejpam-5473	76	5	two	two	NUM
ejpam-5473	76	6	components	component	NOUN
ejpam-5473	76	7	for	for	ADP
ejpam-5473	76	8	each	each	DET
ejpam-5473	76	9	element	element	NOUN
ejpam-5473	76	10	,	,	PUNCT
ejpam-5473	76	11	negative	negative	ADJ
ejpam-5473	76	12	and	and	CCONJ
ejpam-5473	76	13	positive	positive	ADJ
ejpam-5473	76	14	membership	membership	NOUN
ejpam-5473	76	15	values	value	NOUN
ejpam-5473	76	16	with	with	ADP
ejpam-5473	76	17	range	range	NOUN
ejpam-5473	76	18	lies	lie	VERB
ejpam-5473	76	19	in	in	ADP
ejpam-5473	76	20	the	the	DET
ejpam-5473	76	21	interval	interval	NOUN
ejpam-5473	76	22	[	[	X
ejpam-5473	76	23	-1	-1	X
ejpam-5473	76	24	,	,	PUNCT
ejpam-5473	76	25	0	0	NUM
ejpam-5473	76	26	]	]	PUNCT
ejpam-5473	76	27	and	and	CCONJ
ejpam-5473	76	28	[	[	X
ejpam-5473	76	29	0	0	NUM
ejpam-5473	76	30	,	,	PUNCT
ejpam-5473	76	31	1	1	NUM
ejpam-5473	76	32	]	]	PUNCT
ejpam-5473	76	33	,	,	PUNCT
ejpam-5473	76	34	respectively	respectively	ADV
ejpam-5473	76	35	.	.	PUNCT
ejpam-5473	77	1	the	the	DET
ejpam-5473	77	2	if	if	NOUN
ejpam-5473	77	3	-	-	PUNCT
ejpam-5473	77	4	space	space	NOUN
ejpam-5473	77	5	has	have	VERB
ejpam-5473	77	6	two	two	NUM
ejpam-5473	77	7	components	component	NOUN
ejpam-5473	77	8	for	for	ADP
ejpam-5473	77	9	each	each	DET
ejpam-5473	77	10	element	element	NOUN
ejpam-5473	77	11	,	,	PUNCT
ejpam-5473	77	12	both	both	CCONJ
ejpam-5473	77	13	membership	membership	NOUN
ejpam-5473	77	14	and	and	CCONJ
ejpam-5473	77	15	non	non	ADJ
ejpam-5473	77	16	-	-	ADJ
ejpam-5473	77	17	membership	membership	ADJ
ejpam-5473	77	18	values	value	NOUN
ejpam-5473	77	19	with	with	ADP
ejpam-5473	77	20	range	range	NOUN
ejpam-5473	77	21	lie	lie	NOUN
ejpam-5473	77	22	in	in	ADP
ejpam-5473	77	23	the	the	DET
ejpam-5473	77	24	unit	unit	NOUN
ejpam-5473	77	25	interval	interval	NOUN
ejpam-5473	77	26	[	[	X
ejpam-5473	77	27	0	0	NUM
ejpam-5473	77	28	,	,	PUNCT
ejpam-5473	77	29	1	1	NUM
ejpam-5473	77	30	]	]	PUNCT
ejpam-5473	77	31	with	with	ADP
ejpam-5473	77	32	intuitionistic	intuitionistic	ADJ
ejpam-5473	77	33	fuzzy	fuzzy	ADJ
ejpam-5473	77	34	restriction	restriction	NOUN
ejpam-5473	77	35	.	.	PUNCT
ejpam-5473	78	1	in	in	ADP
ejpam-5473	78	2	2016	2016	NUM
ejpam-5473	78	3	,	,	PUNCT
ejpam-5473	78	4	alhusban	alhusban	NOUN
ejpam-5473	78	5	and	and	CCONJ
ejpam-5473	78	6	salleh	salleh	NOUN
ejpam-5473	78	7	and	and	CCONJ
ejpam-5473	78	8	alhusban	alhusban	NOUN
ejpam-5473	78	9	et	et	PROPN
ejpam-5473	78	10	al	al	PROPN
ejpam-5473	79	1	[	[	X
ejpam-5473	79	2	3	3	NUM
ejpam-5473	79	3	]	]	PUNCT
ejpam-5473	79	4	generalized	generalize	VERB
ejpam-5473	79	5	the	the	DET
ejpam-5473	79	6	fuzzy	fuzzy	ADJ
ejpam-5473	79	7	group	group	NOUN
ejpam-5473	79	8	to	to	PART
ejpam-5473	79	9	be	be	AUX
ejpam-5473	79	10	under	under	ADP
ejpam-5473	79	11	the	the	DET
ejpam-5473	79	12	complex	complex	ADJ
ejpam-5473	79	13	numbers	number	NOUN
ejpam-5473	79	14	realm	realm	VERB
ejpam-5473	79	15	.	.	PUNCT
ejpam-5473	80	1	they	they	PRON
ejpam-5473	80	2	[	[	X
ejpam-5473	80	3	3	3	NUM
ejpam-5473	80	4	,	,	PUNCT
ejpam-5473	80	5	20	20	NUM
ejpam-5473	80	6	]	]	PUNCT
ejpam-5473	80	7	introduced	introduce	VERB
ejpam-5473	80	8	the	the	DET
ejpam-5473	80	9	notion	notion	NOUN
ejpam-5473	80	10	of	of	ADP
ejpam-5473	80	11	complex	complex	ADJ
ejpam-5473	80	12	fuzzy	fuzzy	ADJ
ejpam-5473	80	13	group	group	NOUN
ejpam-5473	80	14	and	and	CCONJ
ejpam-5473	80	15	complex	complex	ADJ
ejpam-5473	80	16	intuitionistic	intuitionistic	ADJ
ejpam-5473	80	17	fuzzy	fuzzy	ADJ
ejpam-5473	80	18	group	group	NOUN
ejpam-5473	80	19	based	base	VERB
ejpam-5473	80	20	on	on	ADP
ejpam-5473	80	21	complex	complex	ADJ
ejpam-5473	80	22	fuzzy	fuzzy	ADJ
ejpam-5473	80	23	space	space	NOUN
ejpam-5473	80	24	and	and	CCONJ
ejpam-5473	80	25	complex	complex	ADJ
ejpam-5473	80	26	intuitionistic	intuitionistic	ADJ
ejpam-5473	80	27	fuzzy	fuzzy	ADJ
ejpam-5473	80	28	space	space	NOUN
ejpam-5473	80	29	,	,	PUNCT
ejpam-5473	80	30	respectively	respectively	ADV
ejpam-5473	80	31	.	.	PUNCT
ejpam-5473	81	1	see	see	VERB
ejpam-5473	81	2	[	[	X
ejpam-5473	81	3	4	4	NUM
ejpam-5473	81	4	,	,	PUNCT
ejpam-5473	81	5	5	5	NUM
ejpam-5473	81	6	]	]	PUNCT
ejpam-5473	81	7	.	.	PUNCT
ejpam-5473	82	1	mahmood	mahmood	PROPN
ejpam-5473	82	2	et	et	PROPN
ejpam-5473	82	3	.	.	PUNCT
ejpam-5473	83	1	al	al	PROPN
ejpam-5473	83	2	.	.	PUNCT
ejpam-5473	84	1	[	[	X
ejpam-5473	84	2	26	26	NUM
ejpam-5473	84	3	]	]	PUNCT
ejpam-5473	84	4	have	have	AUX
ejpam-5473	84	5	collaborated	collaborate	VERB
ejpam-5473	84	6	on	on	ADP
ejpam-5473	84	7	numerous	numerous	ADJ
ejpam-5473	84	8	publications	publication	NOUN
ejpam-5473	84	9	regarding	regard	VERB
ejpam-5473	84	10	advanced	advanced	ADJ
ejpam-5473	84	11	fuzzy	fuzzy	ADJ
ejpam-5473	84	12	systems	system	NOUN
ejpam-5473	84	13	.	.	PUNCT
ejpam-5473	85	1	a	a	DET
ejpam-5473	85	2	study	study	NOUN
ejpam-5473	85	3	from	from	ADP
ejpam-5473	85	4	2023	2023	NUM
ejpam-5473	85	5	on	on	ADP
ejpam-5473	85	6	bipolar	bipolar	ADJ
ejpam-5473	85	7	complex	complex	ADJ
ejpam-5473	85	8	fuzzy	fuzzy	ADJ
ejpam-5473	85	9	soft	soft	ADJ
ejpam-5473	85	10	sets	set	NOUN
ejpam-5473	85	11	,	,	PUNCT
ejpam-5473	85	12	which	which	PRON
ejpam-5473	85	13	was	be	AUX
ejpam-5473	85	14	applied	apply	VERB
ejpam-5473	85	15	to	to	ADP
ejpam-5473	85	16	pattern	pattern	NOUN
ejpam-5473	85	17	recognition	recognition	NOUN
ejpam-5473	85	18	and	and	CCONJ
ejpam-5473	85	19	medical	medical	ADJ
ejpam-5473	85	20	diagnosis	diagnosis	NOUN
ejpam-5473	85	21	,	,	PUNCT
ejpam-5473	85	22	was	be	AUX
ejpam-5473	85	23	a	a	DET
ejpam-5473	85	24	prominent	prominent	ADJ
ejpam-5473	85	25	work	work	NOUN
ejpam-5473	85	26	.	.	PUNCT
ejpam-5473	86	1	this	this	DET
ejpam-5473	86	2	article	article	NOUN
ejpam-5473	86	3	explored	explore	VERB
ejpam-5473	86	4	how	how	SCONJ
ejpam-5473	86	5	trigonometric	trigonometric	ADJ
ejpam-5473	86	6	similarity	similarity	NOUN
ejpam-5473	86	7	measures	measure	NOUN
ejpam-5473	86	8	can	can	AUX
ejpam-5473	86	9	be	be	AUX
ejpam-5473	86	10	utilized	utilize	VERB
ejpam-5473	86	11	in	in	ADP
ejpam-5473	86	12	practical	practical	ADJ
ejpam-5473	86	13	situations	situation	NOUN
ejpam-5473	86	14	with	with	ADP
ejpam-5473	86	15	fuzzy	fuzzy	ADJ
ejpam-5473	86	16	systems	system	NOUN
ejpam-5473	86	17	,	,	PUNCT
ejpam-5473	86	18	which	which	PRON
ejpam-5473	86	19	corresponds	correspond	VERB
ejpam-5473	86	20	to	to	ADP
ejpam-5473	86	21	the	the	DET
ejpam-5473	86	22	decision	decision	NOUN
ejpam-5473	86	23	-	-	PUNCT
ejpam-5473	86	24	making	make	VERB
ejpam-5473	86	25	components	component	NOUN
ejpam-5473	86	26	of	of	ADP
ejpam-5473	86	27	our	our	PRON
ejpam-5473	86	28	study	study	NOUN
ejpam-5473	86	29	.	.	PUNCT
ejpam-5473	87	1	furthermore	furthermore	ADV
ejpam-5473	87	2	,	,	PUNCT
ejpam-5473	87	3	the	the	DET
ejpam-5473	87	4	scope	scope	NOUN
ejpam-5473	87	5	of	of	ADP
ejpam-5473	87	6	fuzzy	fuzzy	ADJ
ejpam-5473	87	7	algebra	algebra	NOUN
ejpam-5473	87	8	has	have	AUX
ejpam-5473	87	9	been	be	AUX
ejpam-5473	87	10	further	far	ADV
ejpam-5473	87	11	broadened	broaden	VERB
ejpam-5473	87	12	by	by	ADP
ejpam-5473	87	13	studies	study	NOUN
ejpam-5473	87	14	like	like	ADP
ejpam-5473	87	15	the	the	DET
ejpam-5473	87	16	analysis	analysis	NOUN
ejpam-5473	87	17	of	of	ADP
ejpam-5473	87	18	γ	γ	NOUN
ejpam-5473	87	19	-	-	PUNCT
ejpam-5473	87	20	semigroups	semigroup	NOUN
ejpam-5473	87	21	based	base	VERB
ejpam-5473	87	22	on	on	ADP
ejpam-5473	87	23	bipolar	bipolar	ADJ
ejpam-5473	87	24	complex	complex	ADJ
ejpam-5473	87	25	fuzzy	fuzzy	ADJ
ejpam-5473	87	26	sets	set	NOUN
ejpam-5473	87	27	[	[	X
ejpam-5473	87	28	27	27	NUM
ejpam-5473	87	29	]	]	PUNCT
ejpam-5473	87	30	.	.	PUNCT
ejpam-5473	88	1	γ	γ	NOUN
ejpam-5473	88	2	-	-	PUNCT
ejpam-5473	88	3	semigroups	semigroup	NOUN
ejpam-5473	88	4	,	,	PUNCT
ejpam-5473	88	5	which	which	PRON
ejpam-5473	88	6	extended	extend	VERB
ejpam-5473	88	7	semigroups	semigroup	NOUN
ejpam-5473	88	8	by	by	ADP
ejpam-5473	88	9	permitting	permit	VERB
ejpam-5473	88	10	the	the	DET
ejpam-5473	88	11	binary	binary	ADJ
ejpam-5473	88	12	operation	operation	NOUN
ejpam-5473	88	13	to	to	PART
ejpam-5473	88	14	be	be	AUX
ejpam-5473	88	15	defined	define	VERB
ejpam-5473	88	16	on	on	ADP
ejpam-5473	88	17	a	a	DET
ejpam-5473	88	18	broader	broad	ADJ
ejpam-5473	88	19	domain	domain	NOUN
ejpam-5473	88	20	,	,	PUNCT
ejpam-5473	88	21	have	have	AUX
ejpam-5473	88	22	been	be	AUX
ejpam-5473	88	23	examined	examine	VERB
ejpam-5473	88	24	within	within	ADP
ejpam-5473	88	25	the	the	DET
ejpam-5473	88	26	framework	framework	NOUN
ejpam-5473	88	27	of	of	ADP
ejpam-5473	88	28	bipolar	bipolar	ADJ
ejpam-5473	88	29	complex	complex	ADJ
ejpam-5473	88	30	fuzzy	fuzzy	ADJ
ejpam-5473	88	31	sets	set	NOUN
ejpam-5473	88	32	,	,	PUNCT
ejpam-5473	88	33	offering	offer	VERB
ejpam-5473	88	34	fresh	fresh	ADJ
ejpam-5473	88	35	perspectives	perspective	NOUN
ejpam-5473	88	36	on	on	ADP
ejpam-5473	88	37	algebraic	algebraic	ADJ
ejpam-5473	88	38	structures	structure	NOUN
ejpam-5473	88	39	that	that	PRON
ejpam-5473	88	40	involve	involve	VERB
ejpam-5473	88	41	both	both	DET
ejpam-5473	88	42	positive	positive	ADJ
ejpam-5473	88	43	and	and	CCONJ
ejpam-5473	88	44	negative	negative	ADJ
ejpam-5473	88	45	interactions	interaction	NOUN
ejpam-5473	88	46	concurrently	concurrently	ADV
ejpam-5473	88	47	.	.	PUNCT
ejpam-5473	89	1	this	this	DET
ejpam-5473	89	2	research	research	NOUN
ejpam-5473	89	3	and	and	CCONJ
ejpam-5473	89	4	other	other	ADJ
ejpam-5473	89	5	studies	study	NOUN
ejpam-5473	89	6	are	be	AUX
ejpam-5473	89	7	crucial	crucial	ADJ
ejpam-5473	89	8	for	for	ADP
ejpam-5473	89	9	examining	examine	VERB
ejpam-5473	89	10	algebraic	algebraic	ADJ
ejpam-5473	89	11	systems	system	NOUN
ejpam-5473	89	12	in	in	ADP
ejpam-5473	89	13	complicated	complicated	ADJ
ejpam-5473	89	14	decision	decision	NOUN
ejpam-5473	89	15	-	-	PUNCT
ejpam-5473	89	16	making	make	VERB
ejpam-5473	89	17	settings	setting	NOUN
ejpam-5473	89	18	[	[	X
ejpam-5473	89	19	6	6	NUM
ejpam-5473	89	20	,	,	PUNCT
ejpam-5473	89	21	7	7	NUM
ejpam-5473	89	22	,	,	PUNCT
ejpam-5473	89	23	10	10	NUM
ejpam-5473	89	24	,	,	PUNCT
ejpam-5473	89	25	26–28	26–28	NUM
ejpam-5473	89	26	]	]	PUNCT
ejpam-5473	89	27	.	.	PUNCT
ejpam-5473	90	1	the	the	DET
ejpam-5473	90	2	bvf	bvf	NOUN
ejpam-5473	90	3	-	-	PUNCT
ejpam-5473	90	4	groups	group	NOUN
ejpam-5473	90	5	introduction	introduction	NOUN
ejpam-5473	90	6	holds	hold	VERB
ejpam-5473	90	7	wide	wide	ADV
ejpam-5473	90	8	-	-	PUNCT
ejpam-5473	90	9	reaching	reach	VERB
ejpam-5473	90	10	consequences	consequence	NOUN
ejpam-5473	90	11	for	for	ADP
ejpam-5473	90	12	multiple	multiple	ADJ
ejpam-5473	90	13	practical	practical	ADJ
ejpam-5473	90	14	areas	area	NOUN
ejpam-5473	90	15	.	.	PUNCT
ejpam-5473	91	1	when	when	SCONJ
ejpam-5473	91	2	making	make	VERB
ejpam-5473	91	3	decisions	decision	NOUN
ejpam-5473	91	4	,	,	PUNCT
ejpam-5473	91	5	systems	system	NOUN
ejpam-5473	91	6	frequently	frequently	ADV
ejpam-5473	91	7	need	need	VERB
ejpam-5473	91	8	to	to	PART
ejpam-5473	91	9	consider	consider	VERB
ejpam-5473	91	10	both	both	CCONJ
ejpam-5473	91	11	favorable	favorable	ADJ
ejpam-5473	91	12	and	and	CCONJ
ejpam-5473	91	13	unfavorable	unfavorable	ADJ
ejpam-5473	91	14	assessments	assessment	NOUN
ejpam-5473	91	15	,	,	PUNCT
ejpam-5473	91	16	like	like	ADP
ejpam-5473	91	17	trust	trust	NOUN
ejpam-5473	91	18	as	as	SCONJ
ejpam-5473	91	19	opposed	oppose	VERB
ejpam-5473	91	20	to	to	ADP
ejpam-5473	91	21	distrust	distrust	NOUN
ejpam-5473	91	22	,	,	PUNCT
ejpam-5473	91	23	or	or	CCONJ
ejpam-5473	91	24	approval	approval	NOUN
ejpam-5473	91	25	as	as	SCONJ
ejpam-5473	91	26	opposed	oppose	VERB
ejpam-5473	91	27	to	to	ADP
ejpam-5473	91	28	disapproval	disapproval	NOUN
ejpam-5473	91	29	.	.	PUNCT
ejpam-5473	92	1	bvf	bvf	NOUN
ejpam-5473	92	2	-	-	PUNCT
ejpam-5473	92	3	groups	group	NOUN
ejpam-5473	92	4	offer	offer	VERB
ejpam-5473	92	5	a	a	DET
ejpam-5473	92	6	straightforward	straightforward	ADJ
ejpam-5473	92	7	method	method	NOUN
ejpam-5473	92	8	to	to	PART
ejpam-5473	92	9	represent	represent	VERB
ejpam-5473	92	10	those	those	DET
ejpam-5473	92	11	situations	situation	NOUN
ejpam-5473	92	12	by	by	ADP
ejpam-5473	92	13	incorporating	incorporate	VERB
ejpam-5473	92	14	dual	dual	ADJ
ejpam-5473	92	15	membership	membership	NOUN
ejpam-5473	92	16	values	value	NOUN
ejpam-5473	92	17	in	in	ADP
ejpam-5473	92	18	algebraic	algebraic	PROPN
ejpam-5473	92	19	computations	computation	NOUN
ejpam-5473	92	20	.	.	PUNCT
ejpam-5473	93	1	moreover	moreover	ADV
ejpam-5473	93	2	,	,	PUNCT
ejpam-5473	93	3	in	in	ADP
ejpam-5473	93	4	areas	area	NOUN
ejpam-5473	93	5	like	like	ADP
ejpam-5473	93	6	control	control	NOUN
ejpam-5473	93	7	systems	system	NOUN
ejpam-5473	93	8	and	and	CCONJ
ejpam-5473	93	9	robotics	robotic	NOUN
ejpam-5473	93	10	,	,	PUNCT
ejpam-5473	93	11	where	where	SCONJ
ejpam-5473	93	12	uncertainties	uncertainty	NOUN
ejpam-5473	93	13	can	can	AUX
ejpam-5473	93	14	have	have	VERB
ejpam-5473	93	15	both	both	CCONJ
ejpam-5473	93	16	positive	positive	ADJ
ejpam-5473	93	17	and	and	CCONJ
ejpam-5473	93	18	negative	negative	ADJ
ejpam-5473	93	19	effects	effect	NOUN
ejpam-5473	93	20	on	on	ADP
ejpam-5473	93	21	system	system	NOUN
ejpam-5473	93	22	stability	stability	NOUN
ejpam-5473	93	23	,	,	PUNCT
ejpam-5473	93	24	bvf	bvf	NOUN
ejpam-5473	93	25	-	-	PUNCT
ejpam-5473	93	26	groups	group	NOUN
ejpam-5473	93	27	can	can	AUX
ejpam-5473	93	28	provide	provide	VERB
ejpam-5473	93	29	a	a	DET
ejpam-5473	93	30	more	more	ADV
ejpam-5473	93	31	advanced	advanced	ADJ
ejpam-5473	93	32	approach	approach	NOUN
ejpam-5473	93	33	to	to	ADP
ejpam-5473	93	34	analysis	analysis	NOUN
ejpam-5473	93	35	and	and	CCONJ
ejpam-5473	93	36	design	design	NOUN
ejpam-5473	93	37	.	.	PUNCT
ejpam-5473	94	1	moreover	moreover	ADV
ejpam-5473	94	2	,	,	PUNCT
ejpam-5473	94	3	in	in	ADP
ejpam-5473	94	4	medical	medical	ADJ
ejpam-5473	94	5	diagnosis	diagnosis	NOUN
ejpam-5473	94	6	,	,	PUNCT
ejpam-5473	94	7	patient	patient	ADJ
ejpam-5473	94	8	symptoms	symptom	NOUN
ejpam-5473	94	9	can	can	AUX
ejpam-5473	94	10	positively	positively	ADV
ejpam-5473	94	11	or	or	CCONJ
ejpam-5473	94	12	negatively	negatively	ADV
ejpam-5473	94	13	impact	impact	VERB
ejpam-5473	94	14	health	health	NOUN
ejpam-5473	94	15	outcomes	outcome	NOUN
ejpam-5473	94	16	,	,	PUNCT
ejpam-5473	94	17	and	and	CCONJ
ejpam-5473	94	18	bvf	bvf	NOUN
ejpam-5473	94	19	-	-	PUNCT
ejpam-5473	94	20	algebraic	algebraic	ADJ
ejpam-5473	94	21	structures	structure	NOUN
ejpam-5473	94	22	provide	provide	VERB
ejpam-5473	94	23	a	a	DET
ejpam-5473	94	24	more	more	ADV
ejpam-5473	94	25	precise	precise	ADJ
ejpam-5473	94	26	portrayal	portrayal	NOUN
ejpam-5473	94	27	of	of	ADP
ejpam-5473	94	28	diagnostic	diagnostic	ADJ
ejpam-5473	94	29	procedures	procedure	NOUN
ejpam-5473	94	30	.	.	PUNCT
ejpam-5473	95	1	the	the	DET
ejpam-5473	95	2	bvf	bvf	NOUN
ejpam-5473	95	3	-	-	PUNCT
ejpam-5473	95	4	group	group	NOUN
ejpam-5473	95	5	framework	framework	NOUN
ejpam-5473	95	6	improves	improve	VERB
ejpam-5473	95	7	the	the	DET
ejpam-5473	95	8	theoretical	theoretical	ADJ
ejpam-5473	95	9	understanding	understanding	NOUN
ejpam-5473	95	10	of	of	ADP
ejpam-5473	95	11	fuzzy	fuzzy	ADJ
ejpam-5473	95	12	algebraic	algebraic	ADJ
ejpam-5473	95	13	structures	structure	NOUN
ejpam-5473	95	14	.	.	PUNCT
ejpam-5473	96	1	also	also	ADV
ejpam-5473	96	2	,	,	PUNCT
ejpam-5473	96	3	bvf	bvf	NOUN
ejpam-5473	96	4	-	-	PUNCT
ejpam-5473	96	5	group	group	NOUN
ejpam-5473	96	6	enhances	enhance	VERB
ejpam-5473	96	7	their	their	PRON
ejpam-5473	96	8	practical	practical	ADJ
ejpam-5473	96	9	use	use	NOUN
ejpam-5473	96	10	in	in	ADP
ejpam-5473	96	11	solving	solve	VERB
ejpam-5473	96	12	complex	complex	ADJ
ejpam-5473	96	13	,	,	PUNCT
ejpam-5473	96	14	real	real	ADJ
ejpam-5473	96	15	-	-	PUNCT
ejpam-5473	96	16	world	world	NOUN
ejpam-5473	96	17	problems	problem	NOUN
ejpam-5473	96	18	.	.	PUNCT
ejpam-5473	97	1	the	the	DET
ejpam-5473	97	2	problem	problem	NOUN
ejpam-5473	97	3	in	in	ADP
ejpam-5473	97	4	bipolar	bipolar	ADV
ejpam-5473	97	5	-	-	PUNCT
ejpam-5473	97	6	valued	value	VERB
ejpam-5473	97	7	fuzzy	fuzzy	ADJ
ejpam-5473	97	8	algebra	algebra	NOUN
ejpam-5473	97	9	is	be	AUX
ejpam-5473	97	10	essentially	essentially	ADV
ejpam-5473	97	11	different	different	ADJ
ejpam-5473	97	12	.	.	PUNCT
ejpam-5473	98	1	on	on	ADP
ejpam-5473	98	2	the	the	DET
ejpam-5473	98	3	base	base	NOUN
ejpam-5473	98	4	set	set	VERB
ejpam-5473	98	5	℧	℧	PROPN
ejpam-5473	98	6	,	,	PUNCT
ejpam-5473	98	7	one	one	PRON
ejpam-5473	98	8	should	should	AUX
ejpam-5473	98	9	suppose	suppose	VERB
ejpam-5473	98	10	a	a	DET
ejpam-5473	98	11	priori	priori	NOUN
ejpam-5473	98	12	that	that	SCONJ
ejpam-5473	98	13	the	the	DET
ejpam-5473	98	14	structure	structure	NOUN
ejpam-5473	98	15	is	be	AUX
ejpam-5473	98	16	an	an	DET
ejpam-5473	98	17	ordinary	ordinary	ADJ
ejpam-5473	98	18	groupoid	groupoid	NOUN
ejpam-5473	98	19	.	.	PUNCT
ejpam-5473	99	1	there	there	PRON
ejpam-5473	99	2	is	be	VERB
ejpam-5473	99	3	no	no	DET
ejpam-5473	99	4	f.	f.	PROPN
ejpam-5473	99	5	al	al	PROPN
ejpam-5473	99	6	-	-	PROPN
ejpam-5473	99	7	zu’bi	zu’bi	PROPN
ejpam-5473	99	8	et	et	NOUN
ejpam-5473	99	9	al	al	PROPN
ejpam-5473	99	10	.	.	PUNCT
ejpam-5473	99	11	/	/	SYM
ejpam-5473	99	12	eur	eur	PROPN
ejpam-5473	99	13	.	.	PUNCT
ejpam-5473	100	1	j.	j.	PROPN
ejpam-5473	100	2	pure	pure	PROPN
ejpam-5473	100	3	appl	appl	PROPN
ejpam-5473	100	4	.	.	PROPN
ejpam-5473	100	5	math	math	PROPN
ejpam-5473	100	6	,	,	PUNCT
ejpam-5473	100	7	17	17	NUM
ejpam-5473	100	8	(	(	PUNCT
ejpam-5473	100	9	4	4	NUM
ejpam-5473	100	10	)	)	PUNCT
ejpam-5473	100	11	(	(	PUNCT
ejpam-5473	100	12	2024	2024	NUM
ejpam-5473	100	13	)	)	PUNCT
ejpam-5473	100	14	,	,	PUNCT
ejpam-5473	100	15	2898	2898	NUM
ejpam-5473	100	16	-	-	SYM
ejpam-5473	100	17	2914	2914	NUM
ejpam-5473	100	18	2901	2901	NUM
ejpam-5473	100	19	notion	notion	NOUN
ejpam-5473	100	20	of	of	ADP
ejpam-5473	100	21	a	a	DET
ejpam-5473	100	22	bipolar	bipolar	ADV
ejpam-5473	100	23	-	-	PUNCT
ejpam-5473	100	24	valued	value	VERB
ejpam-5473	100	25	fuzzy	fuzzy	ADJ
ejpam-5473	100	26	subgroupoid	subgroupoid	NOUN
ejpam-5473	100	27	of	of	ADP
ejpam-5473	100	28	℧	℧	PROPN
ejpam-5473	100	29	rather	rather	ADV
ejpam-5473	100	30	than	than	ADP
ejpam-5473	100	31	a	a	DET
ejpam-5473	100	32	concept	concept	NOUN
ejpam-5473	100	33	of	of	ADP
ejpam-5473	100	34	a	a	DET
ejpam-5473	100	35	bipolar	bipolar	ADV
ejpam-5473	100	36	-	-	PUNCT
ejpam-5473	100	37	valued	value	VERB
ejpam-5473	100	38	fuzzy	fuzzy	ADJ
ejpam-5473	100	39	groupoid	groupoid	NOUN
ejpam-5473	100	40	on	on	ADP
ejpam-5473	100	41	℧	℧	PROPN
ejpam-5473	100	42	.	.	PROPN
ejpam-5473	101	1	while	while	SCONJ
ejpam-5473	101	2	the	the	DET
ejpam-5473	101	3	structure	structure	NOUN
ejpam-5473	101	4	of	of	ADP
ejpam-5473	101	5	the	the	DET
ejpam-5473	101	6	notion	notion	NOUN
ejpam-5473	101	7	bipolar	bipolar	ADV
ejpam-5473	101	8	-	-	PUNCT
ejpam-5473	101	9	valued	value	VERB
ejpam-5473	101	10	fuzzy	fuzzy	ADJ
ejpam-5473	101	11	subgroupoid	subgroupoid	NOUN
ejpam-5473	101	12	decreases	decrease	NOUN
ejpam-5473	101	13	to	to	ADP
ejpam-5473	101	14	the	the	DET
ejpam-5473	101	15	ordinary	ordinary	ADJ
ejpam-5473	101	16	structure	structure	NOUN
ejpam-5473	101	17	in	in	ADP
ejpam-5473	101	18	the	the	DET
ejpam-5473	101	19	classical	classical	ADJ
ejpam-5473	101	20	case	case	NOUN
ejpam-5473	101	21	,	,	PUNCT
ejpam-5473	101	22	the	the	DET
ejpam-5473	101	23	progress	progress	NOUN
ejpam-5473	101	24	of	of	ADP
ejpam-5473	101	25	bipolar	bipolar	ADJ
ejpam-5473	101	26	valued	value	VERB
ejpam-5473	101	27	fuzzy	fuzzy	ADJ
ejpam-5473	101	28	algebra	algebra	NOUN
ejpam-5473	101	29	is	be	AUX
ejpam-5473	101	30	effectively	effectively	ADV
ejpam-5473	101	31	slower	slow	ADJ
ejpam-5473	101	32	than	than	ADP
ejpam-5473	101	33	that	that	PRON
ejpam-5473	101	34	of	of	ADP
ejpam-5473	101	35	bipolar	bipolar	ADJ
ejpam-5473	101	36	valued	value	VERB
ejpam-5473	101	37	fuzzy	fuzzy	ADJ
ejpam-5473	101	38	topology	topology	NOUN
ejpam-5473	101	39	due	due	ADP
ejpam-5473	101	40	to	to	ADP
ejpam-5473	101	41	the	the	DET
ejpam-5473	101	42	lack	lack	NOUN
ejpam-5473	101	43	of	of	ADP
ejpam-5473	101	44	an	an	DET
ejpam-5473	101	45	inherent	inherent	ADJ
ejpam-5473	101	46	definition	definition	NOUN
ejpam-5473	101	47	of	of	ADP
ejpam-5473	101	48	bipolar	bipolar	ADV
ejpam-5473	101	49	-	-	PUNCT
ejpam-5473	101	50	valued	value	VERB
ejpam-5473	101	51	fuzzy	fuzzy	ADJ
ejpam-5473	101	52	groupoid	groupoid	NOUN
ejpam-5473	101	53	.	.	PUNCT
ejpam-5473	102	1	not	not	PART
ejpam-5473	102	2	because	because	SCONJ
ejpam-5473	102	3	bipolar	bipolar	ADV
ejpam-5473	102	4	-	-	PUNCT
ejpam-5473	102	5	valued	value	VERB
ejpam-5473	102	6	fuzzy	fuzzy	ADJ
ejpam-5473	102	7	algebra	algebra	NOUN
ejpam-5473	102	8	is	be	AUX
ejpam-5473	102	9	an	an	DET
ejpam-5473	102	10	impossible	impossible	ADJ
ejpam-5473	102	11	or	or	CCONJ
ejpam-5473	102	12	difficult	difficult	ADJ
ejpam-5473	102	13	undertaking	undertaking	NOUN
ejpam-5473	102	14	,	,	PUNCT
ejpam-5473	102	15	but	but	CCONJ
ejpam-5473	102	16	rather	rather	ADV
ejpam-5473	102	17	due	due	ADP
ejpam-5473	102	18	to	to	ADP
ejpam-5473	102	19	the	the	DET
ejpam-5473	102	20	lack	lack	NOUN
ejpam-5473	102	21	of	of	ADP
ejpam-5473	102	22	sufficient	sufficient	ADJ
ejpam-5473	102	23	bipolar	bipolar	ADV
ejpam-5473	102	24	-	-	PUNCT
ejpam-5473	102	25	valued	value	VERB
ejpam-5473	102	26	fuzzy	fuzzy	ADJ
ejpam-5473	102	27	algebraic	algebraic	ADJ
ejpam-5473	102	28	tools	tool	NOUN
ejpam-5473	102	29	,	,	PUNCT
ejpam-5473	102	30	many	many	ADJ
ejpam-5473	102	31	significant	significant	ADJ
ejpam-5473	102	32	discoveries	discovery	NOUN
ejpam-5473	102	33	in	in	ADP
ejpam-5473	102	34	(	(	PUNCT
ejpam-5473	102	35	ordinary	ordinary	ADJ
ejpam-5473	102	36	)	)	PUNCT
ejpam-5473	102	37	algebra	algebra	NOUN
ejpam-5473	102	38	are	be	AUX
ejpam-5473	102	39	not	not	PART
ejpam-5473	102	40	yet	yet	ADV
ejpam-5473	102	41	adapted	adapt	VERB
ejpam-5473	102	42	to	to	ADP
ejpam-5473	102	43	bipolar	bipolar	ADV
ejpam-5473	102	44	-	-	PUNCT
ejpam-5473	102	45	valued	value	VERB
ejpam-5473	102	46	fuzzy	fuzzy	ADJ
ejpam-5473	102	47	algebra	algebra	NOUN
ejpam-5473	102	48	.	.	PUNCT
ejpam-5473	103	1	therefore	therefore	ADV
ejpam-5473	103	2	,	,	PUNCT
ejpam-5473	103	3	defining	define	VERB
ejpam-5473	103	4	the	the	DET
ejpam-5473	103	5	bipolar	bipolar	ADV
ejpam-5473	103	6	-	-	PUNCT
ejpam-5473	103	7	valued	value	VERB
ejpam-5473	103	8	fuzzy	fuzzy	ADJ
ejpam-5473	103	9	group	group	NOUN
ejpam-5473	103	10	is	be	AUX
ejpam-5473	103	11	not	not	PART
ejpam-5473	103	12	intuitive	intuitive	ADJ
ejpam-5473	103	13	and	and	CCONJ
ejpam-5473	103	14	not	not	PART
ejpam-5473	103	15	clear	clear	ADJ
ejpam-5473	103	16	in	in	ADP
ejpam-5473	103	17	the	the	DET
ejpam-5473	103	18	lack	lack	NOUN
ejpam-5473	103	19	of	of	ADP
ejpam-5473	103	20	a	a	DET
ejpam-5473	103	21	notion	notion	NOUN
ejpam-5473	103	22	of	of	ADP
ejpam-5473	103	23	a	a	DET
ejpam-5473	103	24	bipolar	bipolar	ADV
ejpam-5473	103	25	-	-	PUNCT
ejpam-5473	103	26	valued	value	VERB
ejpam-5473	103	27	fuzzy	fuzzy	ADJ
ejpam-5473	103	28	binary	binary	ADJ
ejpam-5473	103	29	operation	operation	NOUN
ejpam-5473	103	30	.	.	PUNCT
ejpam-5473	104	1	in	in	ADP
ejpam-5473	104	2	this	this	DET
ejpam-5473	104	3	study	study	NOUN
ejpam-5473	104	4	,	,	PUNCT
ejpam-5473	104	5	dib	dib	PROPN
ejpam-5473	104	6	’s	’s	PART
ejpam-5473	104	7	technique	technique	NOUN
ejpam-5473	104	8	[	[	X
ejpam-5473	104	9	16	16	NUM
ejpam-5473	104	10	,	,	PUNCT
ejpam-5473	104	11	17	17	NUM
ejpam-5473	104	12	]	]	PUNCT
ejpam-5473	104	13	is	be	AUX
ejpam-5473	104	14	utilized	utilize	VERB
ejpam-5473	104	15	to	to	PART
ejpam-5473	104	16	verify	verify	VERB
ejpam-5473	104	17	a	a	DET
ejpam-5473	104	18	fundamental	fundamental	ADJ
ejpam-5473	104	19	approach	approach	NOUN
ejpam-5473	104	20	that	that	PRON
ejpam-5473	104	21	does	do	AUX
ejpam-5473	104	22	not	not	PART
ejpam-5473	104	23	consider	consider	VERB
ejpam-5473	104	24	any	any	DET
ejpam-5473	104	25	groupoid	groupoid	NOUN
ejpam-5473	104	26	form	form	NOUN
ejpam-5473	104	27	on	on	ADP
ejpam-5473	104	28	the	the	DET
ejpam-5473	104	29	basis	basis	NOUN
ejpam-5473	104	30	set	set	VERB
ejpam-5473	104	31	℧	℧	PROPN
ejpam-5473	104	32	.	.	PUNCT
ejpam-5473	104	33	dib	dib	PROPN
ejpam-5473	104	34	’s	’s	PART
ejpam-5473	104	35	solution	solution	NOUN
ejpam-5473	104	36	hinges	hinge	VERB
ejpam-5473	104	37	on	on	ADP
ejpam-5473	104	38	the	the	DET
ejpam-5473	104	39	notion	notion	NOUN
ejpam-5473	104	40	of	of	ADP
ejpam-5473	104	41	fuzzy	fuzzy	ADJ
ejpam-5473	104	42	binary	binary	ADJ
ejpam-5473	104	43	operations	operation	NOUN
ejpam-5473	104	44	,	,	PUNCT
ejpam-5473	104	45	which	which	PRON
ejpam-5473	104	46	we	we	PRON
ejpam-5473	104	47	utilize	utilize	VERB
ejpam-5473	104	48	here	here	ADV
ejpam-5473	104	49	.	.	PUNCT
ejpam-5473	105	1	the	the	DET
ejpam-5473	105	2	motivations	motivation	NOUN
ejpam-5473	105	3	of	of	ADP
ejpam-5473	105	4	the	the	DET
ejpam-5473	105	5	presented	present	VERB
ejpam-5473	105	6	approach	approach	NOUN
ejpam-5473	105	7	are	be	AUX
ejpam-5473	105	8	:	:	PUNCT
ejpam-5473	105	9	(	(	PUNCT
ejpam-5473	105	10	1	1	X
ejpam-5473	105	11	)	)	PUNCT
ejpam-5473	105	12	a	a	DET
ejpam-5473	105	13	more	more	ADV
ejpam-5473	105	14	thorough	thorough	ADJ
ejpam-5473	105	15	examination	examination	NOUN
ejpam-5473	105	16	of	of	ADP
ejpam-5473	105	17	the	the	DET
ejpam-5473	105	18	characteristics	characteristic	NOUN
ejpam-5473	105	19	and	and	CCONJ
ejpam-5473	105	20	behaviors	behavior	NOUN
ejpam-5473	105	21	of	of	ADP
ejpam-5473	105	22	classical	classical	ADJ
ejpam-5473	105	23	(	(	PUNCT
ejpam-5473	105	24	fuzzy	fuzzy	ADJ
ejpam-5473	105	25	)	)	PUNCT
ejpam-5473	105	26	groups	group	NOUN
ejpam-5473	105	27	is	be	AUX
ejpam-5473	105	28	made	make	VERB
ejpam-5473	105	29	possible	possible	ADJ
ejpam-5473	105	30	by	by	ADP
ejpam-5473	105	31	the	the	DET
ejpam-5473	105	32	bvf	bvf	NOUN
ejpam-5473	105	33	-	-	PUNCT
ejpam-5473	105	34	group	group	NOUN
ejpam-5473	105	35	,	,	PUNCT
ejpam-5473	105	36	which	which	PRON
ejpam-5473	105	37	offers	offer	VERB
ejpam-5473	105	38	a	a	DET
ejpam-5473	105	39	natural	natural	ADJ
ejpam-5473	105	40	generalization	generalization	NOUN
ejpam-5473	105	41	of	of	ADP
ejpam-5473	105	42	them	they	PRON
ejpam-5473	105	43	,	,	PUNCT
ejpam-5473	105	44	(	(	PUNCT
ejpam-5473	105	45	2	2	X
ejpam-5473	105	46	)	)	PUNCT
ejpam-5473	105	47	it	it	PRON
ejpam-5473	105	48	offers	offer	VERB
ejpam-5473	105	49	a	a	DET
ejpam-5473	105	50	way	way	NOUN
ejpam-5473	105	51	to	to	PART
ejpam-5473	105	52	measure	measure	VERB
ejpam-5473	105	53	this	this	DET
ejpam-5473	105	54	uncertainty	uncertainty	NOUN
ejpam-5473	105	55	(	(	PUNCT
ejpam-5473	105	56	bvfs	bvfs	ADJ
ejpam-5473	105	57	)	)	PUNCT
ejpam-5473	105	58	in	in	ADP
ejpam-5473	105	59	the	the	DET
ejpam-5473	105	60	wider	wide	ADJ
ejpam-5473	105	61	context	context	NOUN
ejpam-5473	105	62	of	of	ADP
ejpam-5473	105	63	the	the	DET
ejpam-5473	105	64	bvf	bvf	NOUN
ejpam-5473	105	65	group	group	NOUN
ejpam-5473	105	66	,	,	PUNCT
ejpam-5473	105	67	(	(	PUNCT
ejpam-5473	105	68	3	3	NUM
ejpam-5473	105	69	)	)	PUNCT
ejpam-5473	105	70	because	because	SCONJ
ejpam-5473	105	71	they	they	PRON
ejpam-5473	105	72	offer	offer	VERB
ejpam-5473	105	73	a	a	DET
ejpam-5473	105	74	formalism	formalism	NOUN
ejpam-5473	105	75	for	for	ADP
ejpam-5473	105	76	fs	fs	ADP
ejpam-5473	105	77	reasoning	reasoning	NOUN
ejpam-5473	105	78	,	,	PUNCT
ejpam-5473	105	79	approximation	approximation	NOUN
ejpam-5473	105	80	reasoning	reasoning	NOUN
ejpam-5473	105	81	,	,	PUNCT
ejpam-5473	105	82	and	and	CCONJ
ejpam-5473	105	83	uncertainty	uncertainty	NOUN
ejpam-5473	105	84	management	management	NOUN
ejpam-5473	105	85	inside	inside	ADP
ejpam-5473	105	86	the	the	DET
ejpam-5473	105	87	bvfs	bvfs	ADJ
ejpam-5473	105	88	framework	framework	NOUN
ejpam-5473	105	89	,	,	PUNCT
ejpam-5473	105	90	bvf	bvf	NOUN
ejpam-5473	105	91	-	-	PUNCT
ejpam-5473	105	92	groups	group	NOUN
ejpam-5473	105	93	are	be	AUX
ejpam-5473	105	94	essential	essential	ADJ
ejpam-5473	105	95	to	to	ADP
ejpam-5473	105	96	these	these	DET
ejpam-5473	105	97	applications	application	NOUN
ejpam-5473	105	98	.	.	PUNCT
ejpam-5473	106	1	therefore	therefore	ADV
ejpam-5473	106	2	,	,	PUNCT
ejpam-5473	106	3	upon	upon	SCONJ
ejpam-5473	106	4	establishing	establish	VERB
ejpam-5473	106	5	a	a	DET
ejpam-5473	106	6	bipolar	bipolar	ADV
ejpam-5473	106	7	-	-	PUNCT
ejpam-5473	106	8	valued	value	VERB
ejpam-5473	106	9	fuzzy	fuzzy	ADJ
ejpam-5473	106	10	binary	binary	ADJ
ejpam-5473	106	11	operation	operation	NOUN
ejpam-5473	106	12	on	on	ADP
ejpam-5473	106	13	℧	℧	PROPN
ejpam-5473	106	14	,	,	PUNCT
ejpam-5473	106	15	the	the	DET
ejpam-5473	106	16	notations	notation	NOUN
ejpam-5473	106	17	of	of	ADP
ejpam-5473	106	18	bipolar	bipolar	ADV
ejpam-5473	106	19	-	-	PUNCT
ejpam-5473	106	20	valued	value	VERB
ejpam-5473	106	21	fuzzy	fuzzy	ADJ
ejpam-5473	106	22	groupoid	groupoid	NOUN
ejpam-5473	106	23	,	,	PUNCT
ejpam-5473	106	24	subgroupoid	subgroupoid	NOUN
ejpam-5473	106	25	,	,	PUNCT
ejpam-5473	106	26	monoid	monoid	NOUN
ejpam-5473	106	27	,	,	PUNCT
ejpam-5473	106	28	and	and	CCONJ
ejpam-5473	106	29	other	other	ADJ
ejpam-5473	106	30	findings	finding	NOUN
ejpam-5473	106	31	arise	arise	VERB
ejpam-5473	106	32	naturally	naturally	ADV
ejpam-5473	106	33	and	and	CCONJ
ejpam-5473	106	34	logically	logically	ADV
ejpam-5473	106	35	.	.	PUNCT
ejpam-5473	107	1	also	also	ADV
ejpam-5473	107	2	,	,	PUNCT
ejpam-5473	107	3	the	the	DET
ejpam-5473	107	4	definition	definition	NOUN
ejpam-5473	107	5	of	of	ADP
ejpam-5473	107	6	bipolar	bipolar	ADV
ejpam-5473	107	7	-	-	PUNCT
ejpam-5473	107	8	valued	value	VERB
ejpam-5473	107	9	fuzzy	fuzzy	ADJ
ejpam-5473	107	10	group	group	NOUN
ejpam-5473	107	11	is	be	AUX
ejpam-5473	107	12	constructed	construct	VERB
ejpam-5473	107	13	and	and	CCONJ
ejpam-5473	107	14	formalized	formalize	VERB
ejpam-5473	107	15	.	.	PUNCT
ejpam-5473	108	1	some	some	DET
ejpam-5473	108	2	relations	relation	NOUN
ejpam-5473	108	3	and	and	CCONJ
ejpam-5473	108	4	results	result	NOUN
ejpam-5473	108	5	are	be	AUX
ejpam-5473	108	6	explored	explore	VERB
ejpam-5473	108	7	and	and	CCONJ
ejpam-5473	108	8	proved	prove	VERB
ejpam-5473	108	9	about	about	ADP
ejpam-5473	108	10	bvf	bvf	NOUN
ejpam-5473	108	11	-	-	PUNCT
ejpam-5473	108	12	group	group	NOUN
ejpam-5473	108	13	and	and	CCONJ
ejpam-5473	108	14	intuitionistic	intuitionistic	ADJ
ejpam-5473	108	15	fuzzy	fuzzy	ADJ
ejpam-5473	108	16	groups	group	NOUN
ejpam-5473	108	17	.	.	PUNCT
ejpam-5473	109	1	some	some	DET
ejpam-5473	109	2	theorems	theorem	NOUN
ejpam-5473	109	3	are	be	AUX
ejpam-5473	109	4	introduced	introduce	VERB
ejpam-5473	109	5	to	to	PART
ejpam-5473	109	6	support	support	VERB
ejpam-5473	109	7	and	and	CCONJ
ejpam-5473	109	8	prove	prove	VERB
ejpam-5473	109	9	that	that	SCONJ
ejpam-5473	109	10	our	our	PRON
ejpam-5473	109	11	results	result	NOUN
ejpam-5473	109	12	of	of	ADP
ejpam-5473	109	13	bvf	bvf	NOUN
ejpam-5473	109	14	-	-	PUNCT
ejpam-5473	109	15	groups	group	NOUN
ejpam-5473	109	16	are	be	AUX
ejpam-5473	109	17	a	a	DET
ejpam-5473	109	18	generalization	generalization	NOUN
ejpam-5473	109	19	of	of	ADP
ejpam-5473	109	20	classical	classical	ADJ
ejpam-5473	109	21	(	(	PUNCT
ejpam-5473	109	22	fuzzy	fuzzy	ADJ
ejpam-5473	109	23	)	)	PUNCT
ejpam-5473	109	24	groups	group	NOUN
ejpam-5473	109	25	.	.	PUNCT
ejpam-5473	110	1	2	2	X
ejpam-5473	110	2	.	.	X
ejpam-5473	110	3	preliminaries	preliminary	NOUN
ejpam-5473	110	4	in	in	ADP
ejpam-5473	110	5	this	this	DET
ejpam-5473	110	6	part	part	NOUN
ejpam-5473	110	7	,	,	PUNCT
ejpam-5473	110	8	we	we	PRON
ejpam-5473	110	9	review	review	VERB
ejpam-5473	110	10	key	key	ADJ
ejpam-5473	110	11	theorems	theorem	NOUN
ejpam-5473	110	12	and	and	CCONJ
ejpam-5473	110	13	concepts	concept	NOUN
ejpam-5473	110	14	connected	connect	VERB
ejpam-5473	110	15	to	to	ADP
ejpam-5473	110	16	the	the	DET
ejpam-5473	110	17	current	current	ADJ
ejpam-5473	110	18	findings	finding	NOUN
ejpam-5473	110	19	.	.	PUNCT
ejpam-5473	111	1	definition	definition	NOUN
ejpam-5473	111	2	1	1	NUM
ejpam-5473	111	3	.	.	PUNCT
ejpam-5473	112	1	[	[	X
ejpam-5473	112	2	37	37	NUM
ejpam-5473	112	3	]	]	X
ejpam-5473	112	4	a	a	DET
ejpam-5473	112	5	fuzzy	fuzzy	ADJ
ejpam-5473	112	6	set	set	VERB
ejpam-5473	112	7	a	a	DET
ejpam-5473	112	8	in	in	ADP
ejpam-5473	112	9	universe	universe	NOUN
ejpam-5473	112	10	℧	℧	NUM
ejpam-5473	112	11	is	be	AUX
ejpam-5473	112	12	defined	define	VERB
ejpam-5473	112	13	by	by	ADP
ejpam-5473	112	14	a	a	DET
ejpam-5473	112	15	membership	membership	NOUN
ejpam-5473	112	16	function	function	NOUN
ejpam-5473	112	17	µa:	µa:	VERB
ejpam-5473	112	18	℧	℧	PROPN
ejpam-5473	112	19	→	→	SYM
ejpam-5473	112	20	[	[	X
ejpam-5473	112	21	0	0	NUM
ejpam-5473	112	22	,	,	PUNCT
ejpam-5473	112	23	1	1	NUM
ejpam-5473	112	24	]	]	PUNCT
ejpam-5473	112	25	,	,	PUNCT
ejpam-5473	112	26	indicating	indicate	VERB
ejpam-5473	112	27	the	the	DET
ejpam-5473	112	28	degree	degree	NOUN
ejpam-5473	112	29	of	of	ADP
ejpam-5473	112	30	membership	membership	NOUN
ejpam-5473	112	31	of	of	ADP
ejpam-5473	112	32	x	x	PUNCT
ejpam-5473	112	33	in	in	ADP
ejpam-5473	112	34	a.	a.	NOUN
ejpam-5473	112	35	definition	definition	NOUN
ejpam-5473	112	36	2	2	NUM
ejpam-5473	112	37	.	.	PUNCT
ejpam-5473	113	1	[	[	X
ejpam-5473	113	2	24	24	NUM
ejpam-5473	113	3	]	]	X
ejpam-5473	113	4	an	an	DET
ejpam-5473	113	5	intuitionistic	intuitionistic	ADJ
ejpam-5473	113	6	fuzzy	fuzzy	ADJ
ejpam-5473	113	7	set	set	VERB
ejpam-5473	113	8	a	a	PRON
ejpam-5473	113	9	in	in	ADP
ejpam-5473	113	10	℧	℧	PROPN
ejpam-5473	113	11	is	be	AUX
ejpam-5473	113	12	defined	define	VERB
ejpam-5473	113	13	by	by	ADP
ejpam-5473	113	14	a	a	DET
ejpam-5473	113	15	membership	membership	NOUN
ejpam-5473	113	16	function	function	NOUN
ejpam-5473	113	17	µa	µa	NOUN
ejpam-5473	113	18	:	:	PUNCT
ejpam-5473	113	19	℧	℧	PROPN
ejpam-5473	113	20	→	→	SYM
ejpam-5473	113	21	[	[	X
ejpam-5473	113	22	0	0	NUM
ejpam-5473	113	23	,	,	PUNCT
ejpam-5473	113	24	1	1	NUM
ejpam-5473	113	25	]	]	PUNCT
ejpam-5473	113	26	and	and	CCONJ
ejpam-5473	113	27	a	a	DET
ejpam-5473	113	28	non	non	ADJ
ejpam-5473	113	29	-	-	ADJ
ejpam-5473	113	30	membership	membership	ADJ
ejpam-5473	113	31	function	function	NOUN
ejpam-5473	113	32	νa:	νa:	NOUN
ejpam-5473	113	33	℧	℧	PROPN
ejpam-5473	113	34	→	→	SYM
ejpam-5473	113	35	[	[	X
ejpam-5473	113	36	0	0	NUM
ejpam-5473	113	37	,	,	PUNCT
ejpam-5473	113	38	1	1	NUM
ejpam-5473	113	39	]	]	PUNCT
ejpam-5473	113	40	such	such	ADJ
ejpam-5473	113	41	that	that	DET
ejpam-5473	113	42	0≤	0≤	ADJ
ejpam-5473	113	43	µa	µa	NOUN
ejpam-5473	113	44	(	(	PUNCT
ejpam-5473	113	45	℧	℧	NOUN
ejpam-5473	113	46	)	)	PUNCT
ejpam-5473	113	47	+	+	NOUN
ejpam-5473	113	48	νa	νa	NOUN
ejpam-5473	113	49	(	(	PUNCT
ejpam-5473	113	50	℧	℧	NOUN
ejpam-5473	113	51	)	)	PUNCT
ejpam-5473	113	52	≤1	≤1	PROPN
ejpam-5473	113	53	for	for	ADP
ejpam-5473	113	54	all	all	DET
ejpam-5473	113	55	x∈	x∈	NOUN
ejpam-5473	113	56	℧	℧	NOUN
ejpam-5473	113	57	.	.	PUNCT
ejpam-5473	113	58	definition	definition	NOUN
ejpam-5473	113	59	3	3	NUM
ejpam-5473	113	60	.	.	PUNCT
ejpam-5473	114	1	[	[	X
ejpam-5473	114	2	23	23	NUM
ejpam-5473	114	3	]	]	PUNCT
ejpam-5473	114	4	a	a	DET
ejpam-5473	114	5	bipolar	bipolar	ADV
ejpam-5473	114	6	-	-	PUNCT
ejpam-5473	114	7	valued	value	VERB
ejpam-5473	114	8	fuzzy	fuzzy	NOUN
ejpam-5473	114	9	set	set	VERB
ejpam-5473	114	10	a	a	PRON
ejpam-5473	114	11	in	in	ADP
ejpam-5473	114	12	℧	℧	PROPN
ejpam-5473	114	13	is	be	AUX
ejpam-5473	114	14	defined	define	VERB
ejpam-5473	114	15	by	by	ADP
ejpam-5473	114	16	a	a	DET
ejpam-5473	114	17	membership	membership	NOUN
ejpam-5473	114	18	function	function	NOUN
ejpam-5473	114	19	µa:	µa:	VERB
ejpam-5473	114	20	℧	℧	PROPN
ejpam-5473	114	21	→	→	SYM
ejpam-5473	114	22	[	[	X
ejpam-5473	114	23	−1	−1	NOUN
ejpam-5473	114	24	,	,	PUNCT
ejpam-5473	114	25	1	1	NUM
ejpam-5473	114	26	]	]	PUNCT
ejpam-5473	114	27	,	,	PUNCT
ejpam-5473	114	28	which	which	PRON
ejpam-5473	114	29	can	can	AUX
ejpam-5473	114	30	represent	represent	VERB
ejpam-5473	114	31	positive	positive	ADJ
ejpam-5473	114	32	and	and	CCONJ
ejpam-5473	114	33	negative	negative	ADJ
ejpam-5473	114	34	membership	membership	NOUN
ejpam-5473	114	35	degrees	degree	NOUN
ejpam-5473	114	36	:	:	PUNCT
ejpam-5473	114	37	(	(	PUNCT
ejpam-5473	114	38	i	i	NOUN
ejpam-5473	114	39	)	)	PUNCT
ejpam-5473	114	40	µa	µa	PROPN
ejpam-5473	114	41	(	(	PUNCT
ejpam-5473	114	42	x	x	X
ejpam-5473	114	43	)	)	PUNCT
ejpam-5473	114	44	>	>	X
ejpam-5473	115	1	0	0	NUM
ejpam-5473	115	2	:	:	PUNCT
ejpam-5473	115	3	the	the	DET
ejpam-5473	115	4	extent	extent	NOUN
ejpam-5473	115	5	to	to	PART
ejpam-5473	115	6	which	which	PRON
ejpam-5473	115	7	x	x	PUNCT
ejpam-5473	115	8	is	be	AUX
ejpam-5473	115	9	positively	positively	ADV
ejpam-5473	115	10	part	part	NOUN
ejpam-5473	115	11	of	of	ADP
ejpam-5473	115	12	a.	a.	NOUN
ejpam-5473	115	13	(	(	PUNCT
ejpam-5473	115	14	ii	ii	PROPN
ejpam-5473	115	15	)	)	PUNCT
ejpam-5473	115	16	µa	µa	NOUN
ejpam-5473	115	17	(	(	PUNCT
ejpam-5473	115	18	x	x	X
ejpam-5473	115	19	)	)	PUNCT
ejpam-5473	115	20	<	<	X
ejpam-5473	115	21	0	0	NUM
ejpam-5473	115	22	:	:	PUNCT
ejpam-5473	115	23	the	the	DET
ejpam-5473	115	24	extent	extent	NOUN
ejpam-5473	115	25	to	to	PART
ejpam-5473	115	26	which	which	PRON
ejpam-5473	115	27	x	x	PUNCT
ejpam-5473	115	28	is	be	AUX
ejpam-5473	115	29	negatively	negatively	ADV
ejpam-5473	115	30	part	part	NOUN
ejpam-5473	115	31	to	to	ADP
ejpam-5473	115	32	a.	a.	PROPN
ejpam-5473	115	33	f.	f.	PROPN
ejpam-5473	115	34	al	al	PROPN
ejpam-5473	115	35	-	-	PROPN
ejpam-5473	115	36	zu’bi	zu’bi	PROPN
ejpam-5473	115	37	et	et	NOUN
ejpam-5473	115	38	al	al	PROPN
ejpam-5473	115	39	.	.	PUNCT
ejpam-5473	115	40	/	/	SYM
ejpam-5473	115	41	eur	eur	PROPN
ejpam-5473	115	42	.	.	PUNCT
ejpam-5473	116	1	j.	j.	PROPN
ejpam-5473	116	2	pure	pure	PROPN
ejpam-5473	116	3	appl	appl	PROPN
ejpam-5473	116	4	.	.	PROPN
ejpam-5473	116	5	math	math	PROPN
ejpam-5473	116	6	,	,	PUNCT
ejpam-5473	116	7	17	17	NUM
ejpam-5473	116	8	(	(	PUNCT
ejpam-5473	116	9	4	4	NUM
ejpam-5473	116	10	)	)	PUNCT
ejpam-5473	116	11	(	(	PUNCT
ejpam-5473	116	12	2024	2024	NUM
ejpam-5473	116	13	)	)	PUNCT
ejpam-5473	116	14	,	,	PUNCT
ejpam-5473	116	15	2898	2898	NUM
ejpam-5473	116	16	-	-	SYM
ejpam-5473	116	17	2914	2914	NUM
ejpam-5473	116	18	2902	2902	NUM
ejpam-5473	116	19	definition	definition	NOUN
ejpam-5473	116	20	4	4	NUM
ejpam-5473	116	21	.	.	PUNCT
ejpam-5473	117	1	[	[	X
ejpam-5473	117	2	33	33	NUM
ejpam-5473	117	3	]	]	PUNCT
ejpam-5473	117	4	a	a	DET
ejpam-5473	117	5	bipolar	bipolar	ADV
ejpam-5473	117	6	-	-	PUNCT
ejpam-5473	117	7	valued	value	VERB
ejpam-5473	117	8	fuzzy	fuzzy	NOUN
ejpam-5473	117	9	set	set	VERB
ejpam-5473	117	10	a	a	PRON
ejpam-5473	117	11	is	be	AUX
ejpam-5473	117	12	deemed	deem	VERB
ejpam-5473	117	13	a	a	DET
ejpam-5473	117	14	bipolar	bipolar	ADV
ejpam-5473	117	15	-	-	PUNCT
ejpam-5473	117	16	valued	value	VERB
ejpam-5473	117	17	fuzzy	fuzzy	ADJ
ejpam-5473	117	18	subsemigroup	subsemigroup	ADV
ejpam-5473	117	19	in	in	ADP
ejpam-5473	117	20	a	a	DET
ejpam-5473	117	21	semigroup	semigroup	NOUN
ejpam-5473	117	22	s	s	X
ejpam-5473	117	23	if	if	SCONJ
ejpam-5473	117	24	µa	µa	ADJ
ejpam-5473	117	25	(	(	PUNCT
ejpam-5473	117	26	x·y)≥min	x·y)≥min	PROPN
ejpam-5473	117	27	(	(	PUNCT
ejpam-5473	117	28	µa	µa	PROPN
ejpam-5473	117	29	(	(	PUNCT
ejpam-5473	117	30	x	x	NOUN
ejpam-5473	117	31	)	)	PUNCT
ejpam-5473	117	32	,	,	PUNCT
ejpam-5473	117	33	µa	µa	ADP
ejpam-5473	117	34	(	(	PUNCT
ejpam-5473	117	35	y	y	NOUN
ejpam-5473	117	36	)	)	PUNCT
ejpam-5473	117	37	)	)	PUNCT
ejpam-5473	117	38	for	for	ADP
ejpam-5473	117	39	all	all	DET
ejpam-5473	117	40	x	x	NOUN
ejpam-5473	117	41	,	,	PUNCT
ejpam-5473	117	42	y∈s	y∈s	NOUN
ejpam-5473	117	43	.	.	PUNCT
ejpam-5473	118	1	this	this	PRON
ejpam-5473	118	2	guarantees	guarantee	VERB
ejpam-5473	118	3	that	that	SCONJ
ejpam-5473	118	4	the	the	DET
ejpam-5473	118	5	characteristics	characteristic	NOUN
ejpam-5473	118	6	of	of	ADP
ejpam-5473	118	7	the	the	DET
ejpam-5473	118	8	subsemigroup	subsemigroup	NOUN
ejpam-5473	118	9	are	be	AUX
ejpam-5473	118	10	maintained	maintain	VERB
ejpam-5473	118	11	within	within	ADP
ejpam-5473	118	12	the	the	DET
ejpam-5473	118	13	fuzzy	fuzzy	ADJ
ejpam-5473	118	14	framework	framework	NOUN
ejpam-5473	118	15	.	.	PUNCT
ejpam-5473	119	1	definition	definition	NOUN
ejpam-5473	119	2	5	5	NUM
ejpam-5473	119	3	.	.	PUNCT
ejpam-5473	120	1	[	[	X
ejpam-5473	120	2	29	29	NUM
ejpam-5473	120	3	]	]	X
ejpam-5473	120	4	rosenfeld	rosenfeld	PROPN
ejpam-5473	120	5	expanded	expand	VERB
ejpam-5473	120	6	the	the	DET
ejpam-5473	120	7	idea	idea	NOUN
ejpam-5473	120	8	of	of	ADP
ejpam-5473	120	9	fuzzy	fuzzy	ADJ
ejpam-5473	120	10	sets	set	NOUN
ejpam-5473	120	11	to	to	ADP
ejpam-5473	120	12	group	group	NOUN
ejpam-5473	120	13	theory	theory	NOUN
ejpam-5473	120	14	through	through	ADP
ejpam-5473	120	15	the	the	DET
ejpam-5473	120	16	introduction	introduction	NOUN
ejpam-5473	120	17	of	of	ADP
ejpam-5473	120	18	fuzzy	fuzzy	ADJ
ejpam-5473	120	19	subgroups	subgroup	NOUN
ejpam-5473	120	20	.	.	PUNCT
ejpam-5473	121	1	a	a	DET
ejpam-5473	121	2	fuzzy	fuzzy	NOUN
ejpam-5473	121	3	subset	subset	VERB
ejpam-5473	121	4	a	a	PRON
ejpam-5473	121	5	in	in	ADP
ejpam-5473	121	6	group	group	NOUN
ejpam-5473	121	7	g	g	PROPN
ejpam-5473	121	8	is	be	AUX
ejpam-5473	121	9	termed	term	VERB
ejpam-5473	121	10	a	a	DET
ejpam-5473	121	11	fuzzy	fuzzy	ADJ
ejpam-5473	121	12	subgroup	subgroup	NOUN
ejpam-5473	121	13	when	when	SCONJ
ejpam-5473	121	14	:	:	PUNCT
ejpam-5473	121	15	(	(	PUNCT
ejpam-5473	121	16	i	i	NOUN
ejpam-5473	121	17	)	)	PUNCT
ejpam-5473	121	18	µa	µa	PROPN
ejpam-5473	121	19	(	(	PUNCT
ejpam-5473	121	20	x·y)≥min	x·y)≥min	PROPN
ejpam-5473	121	21	(	(	PUNCT
ejpam-5473	121	22	µa	µa	PROPN
ejpam-5473	121	23	(	(	PUNCT
ejpam-5473	121	24	x	x	NOUN
ejpam-5473	121	25	)	)	PUNCT
ejpam-5473	121	26	,	,	PUNCT
ejpam-5473	121	27	µa	µa	ADP
ejpam-5473	121	28	(	(	PUNCT
ejpam-5473	121	29	y	y	NOUN
ejpam-5473	121	30	)	)	PUNCT
ejpam-5473	121	31	)	)	PUNCT
ejpam-5473	121	32	for	for	ADP
ejpam-5473	121	33	all	all	DET
ejpam-5473	121	34	x	x	NOUN
ejpam-5473	121	35	,	,	PUNCT
ejpam-5473	121	36	y∈g	y∈g	PROPN
ejpam-5473	121	37	,	,	PUNCT
ejpam-5473	121	38	(	(	PUNCT
ejpam-5473	121	39	ii	ii	NOUN
ejpam-5473	121	40	)	)	PUNCT
ejpam-5473	121	41	µa	µa	NOUN
ejpam-5473	121	42	(	(	PUNCT
ejpam-5473	121	43	e	e	NOUN
ejpam-5473	121	44	)	)	PUNCT
ejpam-5473	121	45	=	=	SYM
ejpam-5473	121	46	1	1	NUM
ejpam-5473	121	47	where	where	SCONJ
ejpam-5473	121	48	e	e	NOUN
ejpam-5473	121	49	is	be	AUX
ejpam-5473	121	50	the	the	DET
ejpam-5473	121	51	identity	identity	NOUN
ejpam-5473	121	52	element	element	NOUN
ejpam-5473	121	53	of	of	ADP
ejpam-5473	121	54	g	g	PROPN
ejpam-5473	121	55	,	,	PUNCT
ejpam-5473	121	56	(	(	PUNCT
ejpam-5473	121	57	iii	iii	NOUN
ejpam-5473	121	58	)	)	PUNCT
ejpam-5473	121	59	µa(x	µa(x	NOUN
ejpam-5473	121	60	−1	−1	NOUN
ejpam-5473	121	61	)	)	PUNCT
ejpam-5473	121	62	=	=	SYM
ejpam-5473	122	1	µa	µa	INTJ
ejpam-5473	122	2	(	(	PUNCT
ejpam-5473	122	3	x	x	X
ejpam-5473	122	4	)	)	PUNCT
ejpam-5473	122	5	for	for	ADP
ejpam-5473	122	6	all	all	DET
ejpam-5473	122	7	x∈g	x∈g	NOUN
ejpam-5473	122	8	.	.	PUNCT
ejpam-5473	123	1	these	these	DET
ejpam-5473	123	2	conditions	condition	NOUN
ejpam-5473	123	3	ensure	ensure	VERB
ejpam-5473	123	4	that	that	SCONJ
ejpam-5473	123	5	the	the	DET
ejpam-5473	123	6	fuzziness	fuzziness	NOUN
ejpam-5473	123	7	respects	respect	VERB
ejpam-5473	123	8	the	the	DET
ejpam-5473	123	9	group	group	NOUN
ejpam-5473	123	10	structure	structure	NOUN
ejpam-5473	123	11	.	.	PUNCT
ejpam-5473	124	1	definition	definition	NOUN
ejpam-5473	124	2	6	6	NUM
ejpam-5473	124	3	.	.	PUNCT
ejpam-5473	125	1	[	[	X
ejpam-5473	125	2	17	17	NUM
ejpam-5473	125	3	]	]	PUNCT
ejpam-5473	125	4	a	a	DET
ejpam-5473	125	5	fuzzy	fuzzy	ADJ
ejpam-5473	125	6	relation	relation	NOUN
ejpam-5473	125	7	r	r	NOUN
ejpam-5473	125	8	between	between	ADP
ejpam-5473	125	9	sets	set	NOUN
ejpam-5473	125	10	℧	℧	PROPN
ejpam-5473	125	11	and	and	CCONJ
ejpam-5473	125	12	y	y	PROPN
ejpam-5473	125	13	is	be	AUX
ejpam-5473	125	14	a	a	DET
ejpam-5473	125	15	fuzzy	fuzzy	ADJ
ejpam-5473	125	16	set	set	NOUN
ejpam-5473	125	17	in	in	ADP
ejpam-5473	125	18	the	the	DET
ejpam-5473	125	19	cartesian	cartesian	ADJ
ejpam-5473	125	20	product	product	NOUN
ejpam-5473	125	21	x	x	X
ejpam-5473	125	22	×	×	PROPN
ejpam-5473	125	23	y	y	PROPN
ejpam-5473	125	24	with	with	ADP
ejpam-5473	125	25	a	a	DET
ejpam-5473	125	26	membership	membership	NOUN
ejpam-5473	125	27	function	function	NOUN
ejpam-5473	125	28	µr:	µr:	PROPN
ejpam-5473	125	29	℧	℧	NOUN
ejpam-5473	125	30	×	×	NOUN
ejpam-5473	125	31	y→	y→	NOUN
ejpam-5473	126	1	[	[	X
ejpam-5473	126	2	0	0	NUM
ejpam-5473	126	3	,	,	PUNCT
ejpam-5473	126	4	1	1	NUM
ejpam-5473	126	5	]	]	PUNCT
ejpam-5473	126	6	.	.	PUNCT
ejpam-5473	127	1	definition	definition	NOUN
ejpam-5473	127	2	7	7	NUM
ejpam-5473	127	3	.	.	PUNCT
ejpam-5473	128	1	[	[	X
ejpam-5473	128	2	17	17	NUM
ejpam-5473	128	3	]	]	PUNCT
ejpam-5473	128	4	a	a	DET
ejpam-5473	128	5	fuzzy	fuzzy	ADJ
ejpam-5473	128	6	function	function	NOUN
ejpam-5473	128	7	from	from	ADP
ejpam-5473	128	8	a	a	DET
ejpam-5473	128	9	fuzzy	fuzzy	ADJ
ejpam-5473	128	10	set	set	NOUN
ejpam-5473	128	11	a	a	PRON
ejpam-5473	128	12	in	in	ADP
ejpam-5473	128	13	℧	℧	PROPN
ejpam-5473	128	14	to	to	ADP
ejpam-5473	128	15	a	a	DET
ejpam-5473	128	16	fuzzy	fuzzy	ADJ
ejpam-5473	128	17	set	set	NOUN
ejpam-5473	128	18	b	b	PROPN
ejpam-5473	128	19	in	in	ADP
ejpam-5473	128	20	y	y	PROPN
ejpam-5473	128	21	is	be	AUX
ejpam-5473	128	22	a	a	DET
ejpam-5473	128	23	function	function	NOUN
ejpam-5473	128	24	f	f	NOUN
ejpam-5473	128	25	:	:	PUNCT
ejpam-5473	128	26	℧	℧	PROPN
ejpam-5473	128	27	→y	→y	PROPN
ejpam-5473	128	28	such	such	ADJ
ejpam-5473	128	29	that	that	SCONJ
ejpam-5473	128	30	the	the	DET
ejpam-5473	128	31	membership	membership	NOUN
ejpam-5473	128	32	value	value	NOUN
ejpam-5473	128	33	of	of	ADP
ejpam-5473	128	34	f	f	PROPN
ejpam-5473	128	35	(	(	PUNCT
ejpam-5473	128	36	x	x	X
ejpam-5473	128	37	)	)	PUNCT
ejpam-5473	128	38	in	in	ADP
ejpam-5473	128	39	b	b	NOUN
ejpam-5473	128	40	is	be	AUX
ejpam-5473	128	41	related	relate	VERB
ejpam-5473	128	42	to	to	ADP
ejpam-5473	128	43	the	the	DET
ejpam-5473	128	44	membership	membership	NOUN
ejpam-5473	128	45	value	value	NOUN
ejpam-5473	128	46	of	of	ADP
ejpam-5473	128	47	x	x	PUNCT
ejpam-5473	128	48	in	in	ADP
ejpam-5473	128	49	a.	a.	NOUN
ejpam-5473	128	50	definition	definition	NOUN
ejpam-5473	128	51	8	8	NUM
ejpam-5473	128	52	.	.	PUNCT
ejpam-5473	129	1	[	[	X
ejpam-5473	129	2	16	16	NUM
ejpam-5473	129	3	]	]	PUNCT
ejpam-5473	129	4	a	a	DET
ejpam-5473	129	5	f	f	NOUN
ejpam-5473	129	6	-	-	PUNCT
ejpam-5473	129	7	space	space	NOUN
ejpam-5473	129	8	(	(	PUNCT
ejpam-5473	129	9	℧	℧	PROPN
ejpam-5473	129	10	,	,	PUNCT
ejpam-5473	129	11	i	i	PRON
ejpam-5473	129	12	=	=	PUNCT
ejpam-5473	130	1	[	[	X
ejpam-5473	130	2	0	0	NUM
ejpam-5473	130	3	,	,	PUNCT
ejpam-5473	130	4	1	1	NUM
ejpam-5473	130	5	]	]	PUNCT
ejpam-5473	130	6	)	)	PUNCT
ejpam-5473	130	7	is	be	AUX
ejpam-5473	130	8	the	the	DET
ejpam-5473	130	9	set	set	NOUN
ejpam-5473	130	10	of	of	ADP
ejpam-5473	130	11	all	all	DET
ejpam-5473	130	12	ordered	order	VERB
ejpam-5473	130	13	pairs	pair	NOUN
ejpam-5473	130	14	(	(	PUNCT
ejpam-5473	130	15	x	x	X
ejpam-5473	130	16	,	,	PUNCT
ejpam-5473	130	17	i	i	PROPN
ejpam-5473	130	18	)	)	PUNCT
ejpam-5473	130	19	,	,	PUNCT
ejpam-5473	130	20	x∈	x∈	PROPN
ejpam-5473	130	21	℧	℧	PROPN
ejpam-5473	130	22	(	(	PUNCT
ejpam-5473	130	23	℧	℧	PROPN
ejpam-5473	130	24	,	,	PUNCT
ejpam-5473	130	25	i	i	NOUN
ejpam-5473	130	26	)	)	PUNCT
ejpam-5473	130	27	=	=	PRON
ejpam-5473	130	28	{	{	PUNCT
ejpam-5473	130	29	(	(	PUNCT
ejpam-5473	130	30	x	x	NOUN
ejpam-5473	130	31	,	,	PUNCT
ejpam-5473	130	32	i	i	PROPN
ejpam-5473	130	33	)	)	PUNCT
ejpam-5473	130	34	:	:	PUNCT
ejpam-5473	131	1	x∈	x∈	X
ejpam-5473	131	2	℧	℧	NOUN
ejpam-5473	131	3	}	}	PUNCT
ejpam-5473	131	4	where	where	SCONJ
ejpam-5473	131	5	(	(	PUNCT
ejpam-5473	131	6	x	x	X
ejpam-5473	131	7	,	,	PUNCT
ejpam-5473	131	8	i	i	NOUN
ejpam-5473	131	9	)	)	PUNCT
ejpam-5473	131	10	=	=	PRON
ejpam-5473	131	11	{	{	PUNCT
ejpam-5473	131	12	(	(	PUNCT
ejpam-5473	131	13	x	x	NOUN
ejpam-5473	131	14	,	,	PUNCT
ejpam-5473	131	15	r	r	NOUN
ejpam-5473	131	16	)	)	PUNCT
ejpam-5473	131	17	:	:	PUNCT
ejpam-5473	131	18	r∈i	r∈i	NOUN
ejpam-5473	131	19	}	}	PUNCT
ejpam-5473	131	20	.	.	PUNCT
ejpam-5473	132	1	the	the	DET
ejpam-5473	132	2	ordered	order	VERB
ejpam-5473	132	3	pair	pair	NOUN
ejpam-5473	132	4	(	(	PUNCT
ejpam-5473	132	5	x	x	NOUN
ejpam-5473	132	6	,	,	PUNCT
ejpam-5473	132	7	i	i	NOUN
ejpam-5473	132	8	)	)	PUNCT
ejpam-5473	132	9	is	be	AUX
ejpam-5473	132	10	called	call	VERB
ejpam-5473	132	11	a	a	DET
ejpam-5473	132	12	fuzzy	fuzzy	ADJ
ejpam-5473	132	13	element	element	NOUN
ejpam-5473	132	14	in	in	ADP
ejpam-5473	132	15	the	the	DET
ejpam-5473	132	16	f	f	NOUN
ejpam-5473	132	17	-	-	PUNCT
ejpam-5473	132	18	space	space	NOUN
ejpam-5473	132	19	(	(	PUNCT
ejpam-5473	132	20	℧	℧	PROPN
ejpam-5473	132	21	,	,	PUNCT
ejpam-5473	132	22	i	i	PROPN
ejpam-5473	132	23	)	)	PUNCT
ejpam-5473	132	24	.	.	PUNCT
ejpam-5473	133	1	definition	definition	NOUN
ejpam-5473	133	2	9	9	NUM
ejpam-5473	133	3	.	.	PUNCT
ejpam-5473	134	1	[	[	X
ejpam-5473	134	2	16	16	NUM
ejpam-5473	134	3	]	]	PUNCT
ejpam-5473	134	4	a	a	DET
ejpam-5473	134	5	fuzzy	fuzzy	ADJ
ejpam-5473	134	6	group	group	NOUN
ejpam-5473	134	7	(	(	PUNCT
ejpam-5473	134	8	(	(	PUNCT
ejpam-5473	134	9	℧	℧	PROPN
ejpam-5473	134	10	,	,	PUNCT
ejpam-5473	134	11	i	i	PROPN
ejpam-5473	134	12	)	)	PUNCT
ejpam-5473	134	13	,	,	PUNCT
ejpam-5473	134	14	f	f	PROPN
ejpam-5473	134	15	)	)	PUNCT
ejpam-5473	134	16	is	be	AUX
ejpam-5473	134	17	called	call	VERB
ejpam-5473	134	18	a	a	DET
ejpam-5473	134	19	commutative	commutative	ADJ
ejpam-5473	134	20	or	or	CCONJ
ejpam-5473	134	21	abelian	abelian	ADJ
ejpam-5473	134	22	fuzzy	fuzzy	ADJ
ejpam-5473	134	23	group	group	NOUN
ejpam-5473	135	1	if	if	SCONJ
ejpam-5473	135	2	(	(	PUNCT
ejpam-5473	135	3	x	x	X
ejpam-5473	135	4	,	,	PUNCT
ejpam-5473	135	5	i)f	i)f	ADJ
ejpam-5473	135	6	(	(	PUNCT
ejpam-5473	135	7	y	y	NOUN
ejpam-5473	135	8	,	,	PUNCT
ejpam-5473	135	9	i	i	NOUN
ejpam-5473	135	10	)	)	PUNCT
ejpam-5473	135	11	=	=	SYM
ejpam-5473	135	12	(	(	PUNCT
ejpam-5473	135	13	y	y	NOUN
ejpam-5473	135	14	,	,	PUNCT
ejpam-5473	135	15	i)f	i)f	ADJ
ejpam-5473	135	16	(	(	PUNCT
ejpam-5473	135	17	x	x	X
ejpam-5473	135	18	,	,	PUNCT
ejpam-5473	135	19	i	i	PROPN
ejpam-5473	135	20	)	)	PUNCT
ejpam-5473	135	21	,	,	PUNCT
ejpam-5473	135	22	for	for	ADP
ejpam-5473	135	23	all	all	DET
ejpam-5473	135	24	fuzzy	fuzzy	ADJ
ejpam-5473	135	25	elements	element	NOUN
ejpam-5473	135	26	(	(	PUNCT
ejpam-5473	135	27	x	x	X
ejpam-5473	135	28	,	,	PUNCT
ejpam-5473	135	29	i	i	NOUN
ejpam-5473	135	30	)	)	PUNCT
ejpam-5473	135	31	and	and	CCONJ
ejpam-5473	135	32	(	(	PUNCT
ejpam-5473	135	33	y	y	PROPN
ejpam-5473	135	34	,	,	PUNCT
ejpam-5473	135	35	i	i	NOUN
ejpam-5473	135	36	)	)	PUNCT
ejpam-5473	135	37	of	of	ADP
ejpam-5473	135	38	the	the	DET
ejpam-5473	135	39	f	f	NOUN
ejpam-5473	135	40	-	-	PUNCT
ejpam-5473	135	41	space	space	NOUN
ejpam-5473	135	42	(	(	PUNCT
ejpam-5473	135	43	℧	℧	PROPN
ejpam-5473	135	44	,	,	PUNCT
ejpam-5473	135	45	i	i	PROPN
ejpam-5473	135	46	)	)	PUNCT
ejpam-5473	135	47	.	.	PUNCT
ejpam-5473	136	1	it	it	PRON
ejpam-5473	136	2	is	be	AUX
ejpam-5473	136	3	clear	clear	ADJ
ejpam-5473	136	4	that	that	SCONJ
ejpam-5473	136	5	(	(	PUNCT
ejpam-5473	136	6	(	(	PUNCT
ejpam-5473	136	7	℧	℧	PROPN
ejpam-5473	136	8	,	,	PUNCT
ejpam-5473	136	9	i	i	PROPN
ejpam-5473	136	10	)	)	PUNCT
ejpam-5473	136	11	,	,	PUNCT
ejpam-5473	136	12	f	f	PROPN
ejpam-5473	136	13	)	)	PUNCT
ejpam-5473	136	14	is	be	AUX
ejpam-5473	136	15	a	a	DET
ejpam-5473	136	16	commutative	commutative	ADJ
ejpam-5473	136	17	fuzzy	fuzzy	ADJ
ejpam-5473	136	18	group	group	NOUN
ejpam-5473	136	19	iff	iff	PROPN
ejpam-5473	136	20	(	(	PUNCT
ejpam-5473	136	21	℧	℧	PROPN
ejpam-5473	136	22	,	,	PUNCT
ejpam-5473	136	23	f	f	PROPN
ejpam-5473	136	24	)	)	PUNCT
ejpam-5473	136	25	is	be	AUX
ejpam-5473	136	26	an	an	DET
ejpam-5473	136	27	ordinary	ordinary	ADJ
ejpam-5473	136	28	commutative	commutative	ADJ
ejpam-5473	136	29	group	group	NOUN
ejpam-5473	136	30	.	.	PUNCT
ejpam-5473	137	1	definition	definition	NOUN
ejpam-5473	137	2	10	10	NUM
ejpam-5473	137	3	.	.	PUNCT
ejpam-5473	138	1	[	[	X
ejpam-5473	138	2	18	18	NUM
ejpam-5473	138	3	]	]	PUNCT
ejpam-5473	138	4	an	an	DET
ejpam-5473	138	5	intuitionistic	intuitionistic	ADJ
ejpam-5473	138	6	fuzzy	fuzzy	ADJ
ejpam-5473	138	7	binary	binary	ADJ
ejpam-5473	138	8	operation	operation	NOUN
ejpam-5473	138	9	(	(	PUNCT
ejpam-5473	138	10	ifbo	ifbo	PROPN
ejpam-5473	138	11	)	)	PUNCT
ejpam-5473	138	12	f	f	PROPN
ejpam-5473	138	13	on	on	ADP
ejpam-5473	138	14	an	an	DET
ejpam-5473	138	15	intuitionistic	intuitionistic	ADJ
ejpam-5473	138	16	fuzzy	fuzzy	ADJ
ejpam-5473	138	17	space	space	NOUN
ejpam-5473	138	18	(	(	PUNCT
ejpam-5473	138	19	if	if	SCONJ
ejpam-5473	138	20	-	-	PUNCT
ejpam-5473	138	21	space	space	NOUN
ejpam-5473	138	22	)	)	PUNCT
ejpam-5473	138	23	(	(	PUNCT
ejpam-5473	138	24	℧	℧	PROPN
ejpam-5473	138	25	,	,	PUNCT
ejpam-5473	138	26	i	i	PRON
ejpam-5473	138	27	,	,	PUNCT
ejpam-5473	138	28	i	i	PROPN
ejpam-5473	138	29	)	)	PUNCT
ejpam-5473	138	30	is	be	AUX
ejpam-5473	138	31	an	an	DET
ejpam-5473	138	32	intuitionistic	intuitionistic	ADJ
ejpam-5473	138	33	fuzzy	fuzzy	ADJ
ejpam-5473	138	34	function	function	NOUN
ejpam-5473	138	35	f	f	NOUN
ejpam-5473	138	36	:	:	PUNCT
ejpam-5473	138	37	(	(	PUNCT
ejpam-5473	138	38	℧	℧	PROPN
ejpam-5473	138	39	,	,	PUNCT
ejpam-5473	138	40	i	i	PRON
ejpam-5473	138	41	,	,	PUNCT
ejpam-5473	138	42	i	i	PROPN
ejpam-5473	138	43	)	)	PUNCT
ejpam-5473	138	44	×	×	NOUN
ejpam-5473	138	45	(	(	PUNCT
ejpam-5473	138	46	℧	℧	PROPN
ejpam-5473	138	47	,	,	PUNCT
ejpam-5473	138	48	i	i	PRON
ejpam-5473	138	49	,	,	PUNCT
ejpam-5473	138	50	i	i	PROPN
ejpam-5473	138	51	)	)	PUNCT
ejpam-5473	138	52	−→	−→	NOUN
ejpam-5473	138	53	(	(	PUNCT
ejpam-5473	138	54	℧	℧	PROPN
ejpam-5473	138	55	,	,	PUNCT
ejpam-5473	138	56	i	i	PRON
ejpam-5473	138	57	,	,	PUNCT
ejpam-5473	138	58	i	i	PROPN
ejpam-5473	138	59	)	)	PUNCT
ejpam-5473	138	60	with	with	ADP
ejpam-5473	138	61	comembership	comembership	NOUN
ejpam-5473	138	62	functions	function	NOUN
ejpam-5473	138	63	f	f	PROPN
ejpam-5473	138	64	xy	xy	PROPN
ejpam-5473	138	65	and	and	CCONJ
ejpam-5473	138	66	co	co	ADJ
ejpam-5473	138	67	-	-	NOUN
ejpam-5473	138	68	nonmembership	nonmembership	NOUN
ejpam-5473	138	69	functions	function	NOUN
ejpam-5473	138	70	fxy	fxy	NOUN
ejpam-5473	138	71	satisfying	satisfying	NOUN
ejpam-5473	138	72	:	:	PUNCT
ejpam-5473	138	73	(	(	PUNCT
ejpam-5473	138	74	1)f	1)f	NUM
ejpam-5473	138	75	xy	xy	PROPN
ejpam-5473	138	76	(	(	PUNCT
ejpam-5473	138	77	r	r	NOUN
ejpam-5473	138	78	,	,	PUNCT
ejpam-5473	138	79	s	s	PART
ejpam-5473	138	80	)	)	PUNCT
ejpam-5473	138	81	̸=	̸=	PROPN
ejpam-5473	138	82	0	0	NUM
ejpam-5473	138	83	iff	iff	PROPN
ejpam-5473	138	84	r	r	PROPN
ejpam-5473	138	85	̸=	̸=	PROPN
ejpam-5473	138	86	0	0	NUM
ejpam-5473	138	87	,	,	PUNCT
ejpam-5473	138	88	s	s	VERB
ejpam-5473	138	89	̸=	̸=	PROPN
ejpam-5473	138	90	0	0	NUM
ejpam-5473	138	91	and	and	CCONJ
ejpam-5473	138	92	fxy	fxy	X
ejpam-5473	138	93	(	(	PUNCT
ejpam-5473	138	94	w	w	PROPN
ejpam-5473	138	95	,	,	PUNCT
ejpam-5473	138	96	z	z	NOUN
ejpam-5473	138	97	)	)	PUNCT
ejpam-5473	138	98	̸=	̸=	PROPN
ejpam-5473	138	99	1	1	NUM
ejpam-5473	138	100	iff	iff	PROPN
ejpam-5473	138	101	w	w	PROPN
ejpam-5473	138	102	̸=	̸=	PROPN
ejpam-5473	138	103	1	1	NUM
ejpam-5473	138	104	,	,	PUNCT
ejpam-5473	138	105	z	z	NOUN
ejpam-5473	138	106	̸=	̸=	PROPN
ejpam-5473	138	107	1	1	NUM
ejpam-5473	138	108	.	.	PUNCT
ejpam-5473	139	1	(	(	PUNCT
ejpam-5473	139	2	2	2	X
ejpam-5473	139	3	)	)	PUNCT
ejpam-5473	139	4	f	f	NOUN
ejpam-5473	139	5	xy	xy	PROPN
ejpam-5473	139	6	,	,	PUNCT
ejpam-5473	139	7	fxy	fxy	X
ejpam-5473	139	8	are	be	AUX
ejpam-5473	139	9	onto	onto	ADP
ejpam-5473	139	10	.	.	PUNCT
ejpam-5473	140	1	that	that	PRON
ejpam-5473	140	2	is	be	AUX
ejpam-5473	140	3	,	,	PUNCT
ejpam-5473	140	4	f	f	PROPN
ejpam-5473	140	5	xy	xy	INTJ
ejpam-5473	141	1	(	(	PUNCT
ejpam-5473	141	2	i	i	PRON
ejpam-5473	141	3	×	×	VERB
ejpam-5473	141	4	i	i	NOUN
ejpam-5473	141	5	)	)	PUNCT
ejpam-5473	142	1	=	=	SYM
ejpam-5473	142	2	i	i	PROPN
ejpam-5473	142	3	and	and	CCONJ
ejpam-5473	142	4	fxy	fxy	X
ejpam-5473	143	1	(	(	PUNCT
ejpam-5473	143	2	i	i	PRON
ejpam-5473	143	3	×	×	VERB
ejpam-5473	143	4	i	i	NOUN
ejpam-5473	143	5	)	)	PUNCT
ejpam-5473	144	1	=	=	SYM
ejpam-5473	144	2	i	i	PROPN
ejpam-5473	144	3	,	,	PUNCT
ejpam-5473	144	4	where	where	SCONJ
ejpam-5473	144	5	i	i	PRON
ejpam-5473	144	6	=	=	PUNCT
ejpam-5473	145	1	[	[	X
ejpam-5473	145	2	0	0	NUM
ejpam-5473	145	3	,	,	PUNCT
ejpam-5473	145	4	1	1	NUM
ejpam-5473	145	5	]	]	PUNCT
ejpam-5473	145	6	,	,	PUNCT
ejpam-5473	145	7	thus	thus	ADV
ejpam-5473	145	8	,	,	PUNCT
ejpam-5473	145	9	the	the	DET
ejpam-5473	145	10	intuitionistic	intuitionistic	ADJ
ejpam-5473	145	11	fuzzy	fuzzy	ADJ
ejpam-5473	145	12	binary	binary	ADJ
ejpam-5473	145	13	operation	operation	NOUN
ejpam-5473	145	14	f	f	PROPN
ejpam-5473	145	15	=	=	PUNCT
ejpam-5473	145	16	(	(	PUNCT
ejpam-5473	145	17	f	f	X
ejpam-5473	145	18	,	,	PUNCT
ejpam-5473	145	19	f	f	PROPN
ejpam-5473	145	20	xy	xy	PROPN
ejpam-5473	145	21	,	,	PUNCT
ejpam-5473	145	22	fxy	fxy	NOUN
ejpam-5473	145	23	)	)	PUNCT
ejpam-5473	145	24	over	over	ADP
ejpam-5473	145	25	the	the	DET
ejpam-5473	145	26	if	if	NOUN
ejpam-5473	145	27	-	-	PUNCT
ejpam-5473	145	28	space	space	NOUN
ejpam-5473	145	29	x	x	PUNCT
ejpam-5473	145	30	is	be	AUX
ejpam-5473	145	31	defined	define	VERB
ejpam-5473	145	32	by	by	ADP
ejpam-5473	145	33	(	(	PUNCT
ejpam-5473	145	34	3	3	NUM
ejpam-5473	145	35	)	)	PUNCT
ejpam-5473	145	36	(	(	PUNCT
ejpam-5473	145	37	x	x	X
ejpam-5473	145	38	,	,	PUNCT
ejpam-5473	145	39	i	i	PRON
ejpam-5473	145	40	,	,	PUNCT
ejpam-5473	145	41	i)f	i)f	PROPN
ejpam-5473	145	42	(	(	PUNCT
ejpam-5473	145	43	y	y	PROPN
ejpam-5473	145	44	,	,	PUNCT
ejpam-5473	145	45	i	i	PRON
ejpam-5473	145	46	,	,	PUNCT
ejpam-5473	145	47	i	i	PROPN
ejpam-5473	145	48	)	)	PUNCT
ejpam-5473	146	1	=	=	SYM
ejpam-5473	146	2	f	f	PROPN
ejpam-5473	146	3	(	(	PUNCT
ejpam-5473	146	4	(	(	PUNCT
ejpam-5473	146	5	x	x	X
ejpam-5473	146	6	,	,	PUNCT
ejpam-5473	146	7	i	i	PRON
ejpam-5473	146	8	,	,	PUNCT
ejpam-5473	146	9	i	i	PROPN
ejpam-5473	146	10	)	)	PUNCT
ejpam-5473	146	11	,	,	PUNCT
ejpam-5473	146	12	(	(	PUNCT
ejpam-5473	146	13	y	y	X
ejpam-5473	146	14	,	,	PUNCT
ejpam-5473	146	15	i	i	PRON
ejpam-5473	146	16	,	,	PUNCT
ejpam-5473	146	17	i	i	NOUN
ejpam-5473	146	18	)	)	PUNCT
ejpam-5473	146	19	)	)	PUNCT
ejpam-5473	147	1	=	=	PRON
ejpam-5473	147	2	(	(	PUNCT
ejpam-5473	147	3	f	f	X
ejpam-5473	147	4	(	(	PUNCT
ejpam-5473	147	5	x	x	PROPN
ejpam-5473	147	6	,	,	PUNCT
ejpam-5473	147	7	y	y	PROPN
ejpam-5473	147	8	)	)	PUNCT
ejpam-5473	147	9	,	,	PUNCT
ejpam-5473	148	1	f	f	X
ejpam-5473	148	2	xy	xy	INTJ
ejpam-5473	149	1	(	(	PUNCT
ejpam-5473	149	2	i	i	PRON
ejpam-5473	149	3	×	×	VERB
ejpam-5473	149	4	i	i	NOUN
ejpam-5473	149	5	)	)	PUNCT
ejpam-5473	149	6	,	,	PUNCT
ejpam-5473	149	7	fxy	fxy	X
ejpam-5473	149	8	(	(	PUNCT
ejpam-5473	149	9	i	i	PRON
ejpam-5473	149	10	×	×	VERB
ejpam-5473	149	11	i	i	NOUN
ejpam-5473	149	12	)	)	PUNCT
ejpam-5473	149	13	)	)	PUNCT
ejpam-5473	150	1	=	=	PRON
ejpam-5473	150	2	(	(	PUNCT
ejpam-5473	150	3	f	f	X
ejpam-5473	150	4	(	(	PUNCT
ejpam-5473	150	5	x	x	PROPN
ejpam-5473	150	6	,	,	PUNCT
ejpam-5473	150	7	y	y	PROPN
ejpam-5473	150	8	)	)	PUNCT
ejpam-5473	150	9	,	,	PUNCT
ejpam-5473	150	10	i	i	PRON
ejpam-5473	150	11	,	,	PUNCT
ejpam-5473	150	12	i	i	PROPN
ejpam-5473	150	13	)	)	PUNCT
ejpam-5473	150	14	where	where	SCONJ
ejpam-5473	150	15	,	,	PUNCT
ejpam-5473	150	16	(	(	PUNCT
ejpam-5473	150	17	x	x	X
ejpam-5473	150	18	,	,	PUNCT
ejpam-5473	150	19	i	i	PRON
ejpam-5473	150	20	,	,	PUNCT
ejpam-5473	150	21	i	i	PROPN
ejpam-5473	150	22	)	)	PUNCT
ejpam-5473	150	23	,	,	PUNCT
ejpam-5473	150	24	(	(	PUNCT
ejpam-5473	150	25	y	y	X
ejpam-5473	150	26	,	,	PUNCT
ejpam-5473	150	27	i	i	PRON
ejpam-5473	150	28	,	,	PUNCT
ejpam-5473	150	29	i	i	PROPN
ejpam-5473	150	30	)	)	PUNCT
ejpam-5473	150	31	of	of	ADP
ejpam-5473	150	32	the	the	DET
ejpam-5473	150	33	if	if	NOUN
ejpam-5473	150	34	-	-	PUNCT
ejpam-5473	150	35	space	space	NOUN
ejpam-5473	150	36	x	x	NOUN
ejpam-5473	150	37	are	be	AUX
ejpam-5473	150	38	intuitionistic	intuitionistic	ADJ
ejpam-5473	150	39	fuzzy	fuzzy	ADJ
ejpam-5473	150	40	elements	element	NOUN
ejpam-5473	150	41	(	(	PUNCT
ejpam-5473	150	42	if	if	SCONJ
ejpam-5473	150	43	-	-	PUNCT
ejpam-5473	150	44	element	element	NOUN
ejpam-5473	150	45	)	)	PUNCT
ejpam-5473	150	46	,	,	PUNCT
ejpam-5473	150	47	and	and	CCONJ
ejpam-5473	150	48	f	f	X
ejpam-5473	150	49	=	=	SYM
ejpam-5473	150	50	(	(	PUNCT
ejpam-5473	150	51	f	f	X
ejpam-5473	150	52	,	,	PUNCT
ejpam-5473	150	53	f	f	PROPN
ejpam-5473	150	54	xy	xy	PROPN
ejpam-5473	150	55	,	,	PUNCT
ejpam-5473	150	56	fxy	fxy	NOUN
ejpam-5473	150	57	)	)	PUNCT
ejpam-5473	150	58	is	be	AUX
ejpam-5473	150	59	any	any	DET
ejpam-5473	150	60	ifbo	ifbo	NOUN
ejpam-5473	150	61	defined	define	VERB
ejpam-5473	150	62	on	on	ADP
ejpam-5473	150	63	an	an	DET
ejpam-5473	150	64	if	if	NOUN
ejpam-5473	150	65	-	-	PUNCT
ejpam-5473	150	66	space	space	NOUN
ejpam-5473	150	67	℧	℧	PROPN
ejpam-5473	150	68	.	.	PUNCT
ejpam-5473	151	1	f.	f.	PROPN
ejpam-5473	151	2	al	al	PROPN
ejpam-5473	151	3	-	-	PROPN
ejpam-5473	151	4	zu’bi	zu’bi	PROPN
ejpam-5473	151	5	et	et	NOUN
ejpam-5473	151	6	al	al	PROPN
ejpam-5473	151	7	.	.	PUNCT
ejpam-5473	151	8	/	/	SYM
ejpam-5473	151	9	eur	eur	PROPN
ejpam-5473	151	10	.	.	PUNCT
ejpam-5473	152	1	j.	j.	PROPN
ejpam-5473	152	2	pure	pure	PROPN
ejpam-5473	152	3	appl	appl	PROPN
ejpam-5473	152	4	.	.	PROPN
ejpam-5473	152	5	math	math	PROPN
ejpam-5473	152	6	,	,	PUNCT
ejpam-5473	152	7	17	17	NUM
ejpam-5473	152	8	(	(	PUNCT
ejpam-5473	152	9	4	4	NUM
ejpam-5473	152	10	)	)	PUNCT
ejpam-5473	152	11	(	(	PUNCT
ejpam-5473	152	12	2024	2024	NUM
ejpam-5473	152	13	)	)	PUNCT
ejpam-5473	152	14	,	,	PUNCT
ejpam-5473	152	15	2898	2898	NUM
ejpam-5473	152	16	-	-	SYM
ejpam-5473	152	17	2914	2914	NUM
ejpam-5473	152	18	2903	2903	NUM
ejpam-5473	152	19	an	an	DET
ejpam-5473	152	20	ifbo	ifbo	NOUN
ejpam-5473	152	21	is	be	AUX
ejpam-5473	152	22	identified	identify	VERB
ejpam-5473	152	23	to	to	PART
ejpam-5473	152	24	be	be	AUX
ejpam-5473	152	25	uniform	uniform	ADJ
ejpam-5473	152	26	if	if	SCONJ
ejpam-5473	152	27	both	both	DET
ejpam-5473	152	28	f	f	PROPN
ejpam-5473	152	29	xy	xy	PROPN
ejpam-5473	152	30	and	and	CCONJ
ejpam-5473	152	31	fxy	fxy	NOUN
ejpam-5473	152	32	are	be	AUX
ejpam-5473	152	33	identical	identical	ADJ
ejpam-5473	152	34	.	.	PUNCT
ejpam-5473	153	1	that	that	PRON
ejpam-5473	153	2	is	be	AUX
ejpam-5473	153	3	,	,	PUNCT
ejpam-5473	153	4	f	f	PROPN
ejpam-5473	153	5	xy	xy	NOUN
ejpam-5473	154	1	=	=	SYM
ejpam-5473	154	2	fxy	fxy	X
ejpam-5473	154	3	=	=	SYM
ejpam-5473	154	4	f	f	PROPN
ejpam-5473	154	5	for	for	ADP
ejpam-5473	154	6	all	all	DET
ejpam-5473	154	7	x	x	NOUN
ejpam-5473	154	8	,	,	PUNCT
ejpam-5473	154	9	y	y	PROPN
ejpam-5473	154	10	∈	∈	PROPN
ejpam-5473	154	11	v	v	NOUN
ejpam-5473	154	12	.	.	PUNCT
ejpam-5473	155	1	a	a	DET
ejpam-5473	155	2	left	left	ADJ
ejpam-5473	155	3	uniform	uniform	NOUN
ejpam-5473	155	4	(	(	PUNCT
ejpam-5473	155	5	right	right	ADJ
ejpam-5473	155	6	uniform	uniform	NOUN
ejpam-5473	155	7	)	)	PUNCT
ejpam-5473	155	8	ifbo	ifbo	NOUN
ejpam-5473	155	9	is	be	AUX
ejpam-5473	155	10	ifbo	ifbo	NOUN
ejpam-5473	155	11	having	have	VERB
ejpam-5473	155	12	identical	identical	ADJ
ejpam-5473	155	13	comembership	comembership	NOUN
ejpam-5473	155	14	functions	function	NOUN
ejpam-5473	155	15	(	(	PUNCT
ejpam-5473	155	16	co	co	NOUN
ejpam-5473	155	17	-	-	NOUN
ejpam-5473	155	18	nonmembership	nonmembership	NOUN
ejpam-5473	155	19	functions	function	NOUN
ejpam-5473	155	20	)	)	PUNCT
ejpam-5473	155	21	.	.	PUNCT
ejpam-5473	156	1	definition	definition	NOUN
ejpam-5473	156	2	11	11	NUM
ejpam-5473	156	3	.	.	PUNCT
ejpam-5473	157	1	[	[	X
ejpam-5473	157	2	18	18	NUM
ejpam-5473	157	3	]	]	PUNCT
ejpam-5473	157	4	the	the	DET
ejpam-5473	157	5	structure	structure	NOUN
ejpam-5473	157	6	of	of	ADP
ejpam-5473	157	7	(	(	PUNCT
ejpam-5473	157	8	(	(	PUNCT
ejpam-5473	157	9	g	g	NOUN
ejpam-5473	157	10	,	,	PUNCT
ejpam-5473	157	11	i	i	PRON
ejpam-5473	157	12	,	,	PUNCT
ejpam-5473	157	13	i	i	PROPN
ejpam-5473	157	14	)	)	PUNCT
ejpam-5473	157	15	,	,	PUNCT
ejpam-5473	157	16	f	f	PROPN
ejpam-5473	157	17	)	)	PUNCT
ejpam-5473	157	18	,	,	PUNCT
ejpam-5473	157	19	where	where	SCONJ
ejpam-5473	157	20	if	if	SCONJ
ejpam-5473	157	21	-	-	PUNCT
ejpam-5473	157	22	space	space	NOUN
ejpam-5473	157	23	g	g	NOUN
ejpam-5473	157	24	and	and	CCONJ
ejpam-5473	157	25	i	i	PRON
ejpam-5473	157	26	=	=	PUNCT
ejpam-5473	158	1	[	[	X
ejpam-5473	158	2	0	0	NUM
ejpam-5473	158	3	,	,	PUNCT
ejpam-5473	158	4	1	1	NUM
ejpam-5473	158	5	]	]	PUNCT
ejpam-5473	158	6	,	,	PUNCT
ejpam-5473	158	7	with	with	ADP
ejpam-5473	158	8	ifbo	ifbo	NOUN
ejpam-5473	158	9	f	f	PROPN
ejpam-5473	158	10	defined	define	VERB
ejpam-5473	158	11	on	on	ADP
ejpam-5473	158	12	if	if	SCONJ
ejpam-5473	158	13	-	-	PUNCT
ejpam-5473	158	14	space	space	NOUN
ejpam-5473	158	15	g	g	NOUN
ejpam-5473	158	16	,	,	PUNCT
ejpam-5473	158	17	is	be	AUX
ejpam-5473	158	18	called	call	VERB
ejpam-5473	158	19	an	an	DET
ejpam-5473	158	20	intuitionistic	intuitionistic	ADJ
ejpam-5473	158	21	fuzzy	fuzzy	ADJ
ejpam-5473	158	22	group	group	NOUN
ejpam-5473	158	23	(	(	PUNCT
ejpam-5473	158	24	ifg	ifg	PROPN
ejpam-5473	158	25	)	)	PUNCT
ejpam-5473	158	26	if	if	SCONJ
ejpam-5473	158	27	the	the	DET
ejpam-5473	158	28	following	follow	VERB
ejpam-5473	158	29	conditions	condition	NOUN
ejpam-5473	158	30	are	be	AUX
ejpam-5473	158	31	fulfilled	fulfil	VERB
ejpam-5473	158	32	:	:	PUNCT
ejpam-5473	158	33	(	(	PUNCT
ejpam-5473	158	34	1	1	X
ejpam-5473	158	35	)	)	PUNCT
ejpam-5473	158	36	for	for	ADP
ejpam-5473	158	37	any	any	DET
ejpam-5473	158	38	if	if	NOUN
ejpam-5473	158	39	-	-	PUNCT
ejpam-5473	158	40	element	element	NOUN
ejpam-5473	158	41	of	of	ADP
ejpam-5473	158	42	(	(	PUNCT
ejpam-5473	158	43	x	x	X
ejpam-5473	158	44	,	,	PUNCT
ejpam-5473	158	45	i	i	PRON
ejpam-5473	158	46	,	,	PUNCT
ejpam-5473	158	47	i	i	PROPN
ejpam-5473	158	48	)	)	PUNCT
ejpam-5473	158	49	,	,	PUNCT
ejpam-5473	158	50	(	(	PUNCT
ejpam-5473	158	51	y	y	X
ejpam-5473	158	52	,	,	PUNCT
ejpam-5473	158	53	i	i	PRON
ejpam-5473	158	54	,	,	PUNCT
ejpam-5473	158	55	i	i	PROPN
ejpam-5473	158	56	)	)	PUNCT
ejpam-5473	158	57	,	,	PUNCT
ejpam-5473	158	58	(	(	PUNCT
ejpam-5473	158	59	z	z	X
ejpam-5473	158	60	,	,	PUNCT
ejpam-5473	158	61	i	i	PRON
ejpam-5473	158	62	,	,	PUNCT
ejpam-5473	158	63	i	i	PROPN
ejpam-5473	158	64	)	)	PUNCT
ejpam-5473	158	65	∈	∈	PROPN
ejpam-5473	158	66	(	(	PUNCT
ejpam-5473	158	67	(	(	PUNCT
ejpam-5473	158	68	g	g	NOUN
ejpam-5473	158	69	,	,	PUNCT
ejpam-5473	158	70	i	i	PRON
ejpam-5473	158	71	,	,	PUNCT
ejpam-5473	158	72	i	i	PROPN
ejpam-5473	158	73	)	)	PUNCT
ejpam-5473	158	74	,	,	PUNCT
ejpam-5473	158	75	f	f	PROPN
ejpam-5473	158	76	)	)	PUNCT
ejpam-5473	158	77	(	(	PUNCT
ejpam-5473	158	78	(	(	PUNCT
ejpam-5473	158	79	x	x	X
ejpam-5473	158	80	,	,	PUNCT
ejpam-5473	158	81	i	i	PRON
ejpam-5473	158	82	,	,	PUNCT
ejpam-5473	158	83	i)f	i)f	PROPN
ejpam-5473	158	84	(	(	PUNCT
ejpam-5473	158	85	y	y	PROPN
ejpam-5473	158	86	,	,	PUNCT
ejpam-5473	158	87	i	i	PRON
ejpam-5473	158	88	,	,	PUNCT
ejpam-5473	158	89	i))f	i))f	PROPN
ejpam-5473	158	90	(	(	PUNCT
ejpam-5473	158	91	z	z	X
ejpam-5473	158	92	,	,	PUNCT
ejpam-5473	158	93	i	i	PRON
ejpam-5473	158	94	,	,	PUNCT
ejpam-5473	158	95	i	i	PROPN
ejpam-5473	158	96	)	)	PUNCT
ejpam-5473	158	97	=	=	SYM
ejpam-5473	158	98	(	(	PUNCT
ejpam-5473	158	99	x	x	X
ejpam-5473	158	100	,	,	PUNCT
ejpam-5473	158	101	i	i	PRON
ejpam-5473	158	102	,	,	PUNCT
ejpam-5473	158	103	i)f	i)f	ADJ
ejpam-5473	158	104	(	(	PUNCT
ejpam-5473	158	105	(	(	PUNCT
ejpam-5473	158	106	y	y	PROPN
ejpam-5473	158	107	,	,	PUNCT
ejpam-5473	158	108	i	i	PRON
ejpam-5473	158	109	,	,	PUNCT
ejpam-5473	158	110	i)f	i)f	ADJ
ejpam-5473	158	111	(	(	PUNCT
ejpam-5473	158	112	z	z	X
ejpam-5473	158	113	,	,	PUNCT
ejpam-5473	158	114	i	i	PRON
ejpam-5473	158	115	,	,	PUNCT
ejpam-5473	158	116	i	i	PROPN
ejpam-5473	158	117	)	)	PUNCT
ejpam-5473	158	118	)	)	PUNCT
ejpam-5473	158	119	.	.	PUNCT
ejpam-5473	159	1	(	(	PUNCT
ejpam-5473	159	2	2	2	X
ejpam-5473	159	3	)	)	PUNCT
ejpam-5473	159	4	there	there	PRON
ejpam-5473	159	5	exists	exist	VERB
ejpam-5473	159	6	an	an	DET
ejpam-5473	159	7	if	if	NOUN
ejpam-5473	159	8	-	-	PUNCT
ejpam-5473	159	9	element	element	NOUN
ejpam-5473	159	10	(	(	PUNCT
ejpam-5473	159	11	e	e	NOUN
ejpam-5473	159	12	,	,	PUNCT
ejpam-5473	159	13	i	i	PRON
ejpam-5473	159	14	,	,	PUNCT
ejpam-5473	159	15	i	i	PROPN
ejpam-5473	159	16	)	)	PUNCT
ejpam-5473	159	17	∈	∈	PROPN
ejpam-5473	159	18	(	(	PUNCT
ejpam-5473	159	19	g	g	NOUN
ejpam-5473	159	20	,	,	PUNCT
ejpam-5473	159	21	i	i	PRON
ejpam-5473	159	22	,	,	PUNCT
ejpam-5473	159	23	i	i	PROPN
ejpam-5473	159	24	)	)	PUNCT
ejpam-5473	159	25	such	such	ADJ
ejpam-5473	159	26	that	that	PRON
ejpam-5473	159	27	for	for	ADP
ejpam-5473	159	28	all	all	PRON
ejpam-5473	159	29	(	(	PUNCT
ejpam-5473	159	30	x	x	X
ejpam-5473	159	31	,	,	PUNCT
ejpam-5473	159	32	i	i	PRON
ejpam-5473	159	33	,	,	PUNCT
ejpam-5473	159	34	i	i	PROPN
ejpam-5473	159	35	)	)	PUNCT
ejpam-5473	159	36	in	in	ADP
ejpam-5473	159	37	(	(	PUNCT
ejpam-5473	159	38	(	(	PUNCT
ejpam-5473	159	39	g	g	NOUN
ejpam-5473	159	40	,	,	PUNCT
ejpam-5473	159	41	i	i	PRON
ejpam-5473	159	42	,	,	PUNCT
ejpam-5473	159	43	i	i	PROPN
ejpam-5473	159	44	)	)	PUNCT
ejpam-5473	159	45	,	,	PUNCT
ejpam-5473	159	46	f	f	PROPN
ejpam-5473	159	47	)	)	PUNCT
ejpam-5473	159	48	:	:	PUNCT
ejpam-5473	159	49	(	(	PUNCT
ejpam-5473	159	50	e	e	X
ejpam-5473	159	51	,	,	PUNCT
ejpam-5473	159	52	i	i	PRON
ejpam-5473	159	53	,	,	PUNCT
ejpam-5473	159	54	i)f	i)f	ADJ
ejpam-5473	159	55	(	(	PUNCT
ejpam-5473	159	56	x	x	X
ejpam-5473	159	57	,	,	PUNCT
ejpam-5473	159	58	i	i	PRON
ejpam-5473	159	59	,	,	PUNCT
ejpam-5473	159	60	i	i	PROPN
ejpam-5473	159	61	)	)	PUNCT
ejpam-5473	159	62	=	=	SYM
ejpam-5473	159	63	(	(	PUNCT
ejpam-5473	159	64	x	x	X
ejpam-5473	159	65	,	,	PUNCT
ejpam-5473	159	66	i	i	PRON
ejpam-5473	159	67	,	,	PUNCT
ejpam-5473	159	68	i)f	i)f	ADJ
ejpam-5473	159	69	(	(	PUNCT
ejpam-5473	159	70	e	e	NOUN
ejpam-5473	159	71	,	,	PUNCT
ejpam-5473	159	72	i	i	PRON
ejpam-5473	159	73	,	,	PUNCT
ejpam-5473	159	74	i	i	PROPN
ejpam-5473	159	75	)	)	PUNCT
ejpam-5473	159	76	=	=	SYM
ejpam-5473	160	1	(	(	PUNCT
ejpam-5473	160	2	x	x	X
ejpam-5473	160	3	,	,	PUNCT
ejpam-5473	160	4	i	i	PRON
ejpam-5473	160	5	,	,	PUNCT
ejpam-5473	160	6	i	i	PROPN
ejpam-5473	160	7	)	)	PUNCT
ejpam-5473	160	8	.	.	PUNCT
ejpam-5473	161	1	(	(	PUNCT
ejpam-5473	161	2	3	3	X
ejpam-5473	161	3	)	)	PUNCT
ejpam-5473	161	4	for	for	ADP
ejpam-5473	161	5	every	every	DET
ejpam-5473	161	6	if	if	NOUN
ejpam-5473	161	7	-	-	PUNCT
ejpam-5473	161	8	element	element	NOUN
ejpam-5473	161	9	(	(	PUNCT
ejpam-5473	161	10	x	x	X
ejpam-5473	161	11	,	,	PUNCT
ejpam-5473	161	12	i	i	PRON
ejpam-5473	161	13	,	,	PUNCT
ejpam-5473	161	14	i	i	PROPN
ejpam-5473	161	15	)	)	PUNCT
ejpam-5473	161	16	in	in	ADP
ejpam-5473	161	17	(	(	PUNCT
ejpam-5473	161	18	(	(	PUNCT
ejpam-5473	161	19	g	g	NOUN
ejpam-5473	161	20	,	,	PUNCT
ejpam-5473	161	21	i	i	PRON
ejpam-5473	161	22	,	,	PUNCT
ejpam-5473	161	23	i	i	PROPN
ejpam-5473	161	24	)	)	PUNCT
ejpam-5473	161	25	,	,	PUNCT
ejpam-5473	161	26	f	f	PROPN
ejpam-5473	161	27	)	)	PUNCT
ejpam-5473	161	28	there	there	PRON
ejpam-5473	161	29	exists	exist	VERB
ejpam-5473	161	30	an	an	DET
ejpam-5473	161	31	if	if	NOUN
ejpam-5473	161	32	-	-	PUNCT
ejpam-5473	161	33	element	element	NOUN
ejpam-5473	161	34	(	(	PUNCT
ejpam-5473	161	35	x−1	x−1	PROPN
ejpam-5473	161	36	,	,	PUNCT
ejpam-5473	161	37	i	i	PRON
ejpam-5473	161	38	,	,	PUNCT
ejpam-5473	161	39	i	i	PROPN
ejpam-5473	161	40	)	)	PUNCT
ejpam-5473	161	41	in	in	ADP
ejpam-5473	161	42	(	(	PUNCT
ejpam-5473	161	43	(	(	PUNCT
ejpam-5473	161	44	g	g	NOUN
ejpam-5473	161	45	,	,	PUNCT
ejpam-5473	161	46	i	i	PRON
ejpam-5473	161	47	,	,	PUNCT
ejpam-5473	161	48	i	i	PROPN
ejpam-5473	161	49	)	)	PUNCT
ejpam-5473	161	50	,	,	PUNCT
ejpam-5473	161	51	f	f	PROPN
ejpam-5473	161	52	)	)	PUNCT
ejpam-5473	161	53	such	such	ADJ
ejpam-5473	161	54	that	that	SCONJ
ejpam-5473	161	55	:	:	PUNCT
ejpam-5473	161	56	(	(	PUNCT
ejpam-5473	161	57	x	x	X
ejpam-5473	161	58	,	,	PUNCT
ejpam-5473	161	59	i	i	PRON
ejpam-5473	161	60	,	,	PUNCT
ejpam-5473	161	61	i)f	i)f	PROPN
ejpam-5473	161	62	(	(	PUNCT
ejpam-5473	161	63	x−1	x−1	PROPN
ejpam-5473	161	64	,	,	PUNCT
ejpam-5473	161	65	i	i	PRON
ejpam-5473	161	66	,	,	PUNCT
ejpam-5473	161	67	i	i	PROPN
ejpam-5473	161	68	)	)	PUNCT
ejpam-5473	161	69	=	=	PUNCT
ejpam-5473	162	1	(	(	PUNCT
ejpam-5473	162	2	x−1	x−1	PROPN
ejpam-5473	162	3	,	,	PUNCT
ejpam-5473	162	4	i	i	PRON
ejpam-5473	162	5	,	,	PUNCT
ejpam-5473	162	6	i	i	PROPN
ejpam-5473	162	7	)	)	PUNCT
ejpam-5473	162	8	f	f	PROPN
ejpam-5473	162	9	(	(	PUNCT
ejpam-5473	162	10	x	x	X
ejpam-5473	162	11	,	,	PUNCT
ejpam-5473	162	12	i	i	PRON
ejpam-5473	162	13	,	,	PUNCT
ejpam-5473	162	14	i	i	PROPN
ejpam-5473	162	15	)	)	PUNCT
ejpam-5473	162	16	=	=	SYM
ejpam-5473	162	17	(	(	PUNCT
ejpam-5473	162	18	e	e	NOUN
ejpam-5473	162	19	,	,	PUNCT
ejpam-5473	162	20	i	i	PRON
ejpam-5473	162	21	,	,	PUNCT
ejpam-5473	162	22	i	i	PROPN
ejpam-5473	162	23	)	)	PUNCT
ejpam-5473	162	24	.	.	PUNCT
ejpam-5473	163	1	an	an	DET
ejpam-5473	163	2	ifg	ifg	NOUN
ejpam-5473	163	3	(	(	PUNCT
ejpam-5473	163	4	(	(	PUNCT
ejpam-5473	163	5	g	g	NOUN
ejpam-5473	163	6	,	,	PUNCT
ejpam-5473	163	7	i	i	PRON
ejpam-5473	163	8	,	,	PUNCT
ejpam-5473	163	9	i	i	PROPN
ejpam-5473	163	10	)	)	PUNCT
ejpam-5473	163	11	,	,	PUNCT
ejpam-5473	163	12	f	f	PROPN
ejpam-5473	163	13	)	)	PUNCT
ejpam-5473	163	14	is	be	AUX
ejpam-5473	163	15	called	call	VERB
ejpam-5473	163	16	an	an	DET
ejpam-5473	163	17	abelian	abelian	PROPN
ejpam-5473	163	18	ifg	ifg	VERB
ejpam-5473	163	19	iff	iff	PROPN
ejpam-5473	163	20	for	for	ADP
ejpam-5473	163	21	all	all	PRON
ejpam-5473	163	22	(	(	PUNCT
ejpam-5473	163	23	x	x	X
ejpam-5473	163	24	,	,	PUNCT
ejpam-5473	163	25	i	i	PRON
ejpam-5473	163	26	,	,	PUNCT
ejpam-5473	163	27	i	i	PROPN
ejpam-5473	163	28	)	)	PUNCT
ejpam-5473	163	29	,	,	PUNCT
ejpam-5473	163	30	(	(	PUNCT
ejpam-5473	163	31	y	y	X
ejpam-5473	163	32	,	,	PUNCT
ejpam-5473	163	33	i	i	PRON
ejpam-5473	163	34	,	,	PUNCT
ejpam-5473	163	35	i	i	PROPN
ejpam-5473	163	36	)	)	PUNCT
ejpam-5473	163	37	∈	∈	PROPN
ejpam-5473	163	38	(	(	PUNCT
ejpam-5473	163	39	(	(	PUNCT
ejpam-5473	163	40	g	g	NOUN
ejpam-5473	163	41	,	,	PUNCT
ejpam-5473	163	42	i	i	PRON
ejpam-5473	163	43	,	,	PUNCT
ejpam-5473	163	44	i	i	PROPN
ejpam-5473	163	45	)	)	PUNCT
ejpam-5473	163	46	,	,	PUNCT
ejpam-5473	163	47	f	f	PROPN
ejpam-5473	163	48	)	)	PUNCT
ejpam-5473	163	49	,	,	PUNCT
ejpam-5473	163	50	and	and	CCONJ
ejpam-5473	163	51	(	(	PUNCT
ejpam-5473	163	52	x	x	X
ejpam-5473	163	53	,	,	PUNCT
ejpam-5473	163	54	i	i	PRON
ejpam-5473	163	55	,	,	PUNCT
ejpam-5473	163	56	i)f	i)f	PROPN
ejpam-5473	163	57	(	(	PUNCT
ejpam-5473	163	58	y	y	PROPN
ejpam-5473	163	59	,	,	PUNCT
ejpam-5473	163	60	i	i	PRON
ejpam-5473	163	61	,	,	PUNCT
ejpam-5473	163	62	i	i	PROPN
ejpam-5473	163	63	)	)	PUNCT
ejpam-5473	163	64	=	=	SYM
ejpam-5473	164	1	(	(	PUNCT
ejpam-5473	164	2	y	y	PROPN
ejpam-5473	164	3	,	,	PUNCT
ejpam-5473	164	4	i	i	PRON
ejpam-5473	164	5	,	,	PUNCT
ejpam-5473	164	6	i)f	i)f	ADJ
ejpam-5473	164	7	(	(	PUNCT
ejpam-5473	164	8	x	x	X
ejpam-5473	164	9	,	,	PUNCT
ejpam-5473	164	10	i	i	PRON
ejpam-5473	164	11	,	,	PUNCT
ejpam-5473	164	12	i	i	PROPN
ejpam-5473	164	13	)	)	PUNCT
ejpam-5473	164	14	is	be	AUX
ejpam-5473	164	15	true	true	ADJ
ejpam-5473	164	16	.	.	PUNCT
ejpam-5473	165	1	definition	definition	NOUN
ejpam-5473	165	2	12	12	NUM
ejpam-5473	165	3	.	.	PUNCT
ejpam-5473	166	1	[	[	X
ejpam-5473	166	2	9	9	NUM
ejpam-5473	166	3	]	]	X
ejpam-5473	166	4	the	the	DET
ejpam-5473	166	5	bvfcp	bvfcp	NOUN
ejpam-5473	166	6	of	of	ADP
ejpam-5473	166	7	two	two	NUM
ejpam-5473	166	8	ordinary	ordinary	ADJ
ejpam-5473	166	9	sets	set	NOUN
ejpam-5473	166	10	u	u	NOUN
ejpam-5473	166	11	and	and	CCONJ
ejpam-5473	166	12	v	v	NOUN
ejpam-5473	166	13	,	,	PUNCT
ejpam-5473	166	14	denoted	denote	VERB
ejpam-5473	166	15	by	by	ADP
ejpam-5473	166	16	u×v	u×v	PROPN
ejpam-5473	166	17	,	,	PUNCT
ejpam-5473	166	18	is	be	AUX
ejpam-5473	166	19	the	the	DET
ejpam-5473	166	20	collection	collection	NOUN
ejpam-5473	166	21	of	of	ADP
ejpam-5473	166	22	all	all	DET
ejpam-5473	166	23	k	k	NOUN
ejpam-5473	166	24	-	-	PUNCT
ejpam-5473	166	25	bvf	bvf	NOUN
ejpam-5473	166	26	subsets	subset	NOUN
ejpam-5473	166	27	of	of	ADP
ejpam-5473	166	28	u×v	u×v	PROPN
ejpam-5473	166	29	that	that	PRON
ejpam-5473	166	30	is	be	AUX
ejpam-5473	166	31	u×v	u×v	PROPN
ejpam-5473	166	32	=	=	SYM
ejpam-5473	166	33	ku×v	ku×v	PROPN
ejpam-5473	166	34	,	,	PUNCT
ejpam-5473	166	35	an	an	DET
ejpam-5473	166	36	element	element	NOUN
ejpam-5473	166	37	of	of	ADP
ejpam-5473	166	38	u×v	u×v	PROPN
ejpam-5473	166	39	is	be	AUX
ejpam-5473	166	40	then	then	ADV
ejpam-5473	166	41	a	a	DET
ejpam-5473	166	42	function	function	NOUN
ejpam-5473	166	43	m	m	VERB
ejpam-5473	166	44	:	:	PUNCT
ejpam-5473	166	45	u×v→k	u×v→k	NOUN
ejpam-5473	166	46	,	,	PUNCT
ejpam-5473	166	47	or	or	CCONJ
ejpam-5473	166	48	m=	m=	X
ejpam-5473	166	49	{	{	PUNCT
ejpam-5473	166	50	(	(	PUNCT
ejpam-5473	166	51	(	(	PUNCT
ejpam-5473	166	52	u	u	NOUN
ejpam-5473	166	53	,	,	PUNCT
ejpam-5473	166	54	v	v	NOUN
ejpam-5473	166	55	)	)	PUNCT
ejpam-5473	166	56	,	,	PUNCT
ejpam-5473	166	57	[	[	PUNCT
ejpam-5473	166	58	(	(	PUNCT
ejpam-5473	166	59	δ−	δ−	ADJ
ejpam-5473	166	60	,	,	PUNCT
ejpam-5473	166	61	δ+	δ+	NOUN
ejpam-5473	166	62	)	)	PUNCT
ejpam-5473	166	63	,	,	PUNCT
ejpam-5473	166	64	(	(	PUNCT
ejpam-5473	166	65	ϑ−	ϑ−	PROPN
ejpam-5473	166	66	,	,	PUNCT
ejpam-5473	166	67	ϑ+	ϑ+	NOUN
ejpam-5473	166	68	)	)	PUNCT
ejpam-5473	166	69	]	]	PUNCT
ejpam-5473	166	70	)	)	PUNCT
ejpam-5473	166	71	:	:	PUNCT
ejpam-5473	166	72	(	(	PUNCT
ejpam-5473	166	73	u	u	NOUN
ejpam-5473	166	74	,	,	PUNCT
ejpam-5473	166	75	v)∈u×v	v)∈u×v	ADV
ejpam-5473	166	76	,	,	PUNCT
ejpam-5473	166	77	[	[	PUNCT
ejpam-5473	166	78	(	(	PUNCT
ejpam-5473	166	79	δ−	δ−	ADJ
ejpam-5473	166	80	,	,	PUNCT
ejpam-5473	166	81	δ+	δ+	NOUN
ejpam-5473	166	82	)	)	PUNCT
ejpam-5473	166	83	,	,	PUNCT
ejpam-5473	166	84	(	(	PUNCT
ejpam-5473	166	85	ϑ−	ϑ−	PROPN
ejpam-5473	166	86	,	,	PUNCT
ejpam-5473	166	87	ϑ+	ϑ+	NOUN
ejpam-5473	166	88	)	)	PUNCT
ejpam-5473	166	89	]	]	PUNCT
ejpam-5473	167	1	=	=	SYM
ejpam-5473	167	2	m(u	m(u	PROPN
ejpam-5473	167	3	,	,	PUNCT
ejpam-5473	167	4	v)→k	v)→k	PROPN
ejpam-5473	167	5	}	}	PUNCT
ejpam-5473	167	6	.	.	PUNCT
ejpam-5473	168	1	the	the	DET
ejpam-5473	168	2	bvfcp	bvfcp	NOUN
ejpam-5473	168	3	of	of	ADP
ejpam-5473	168	4	a	a	DET
ejpam-5473	168	5	bvf	bvf	NOUN
ejpam-5473	168	6	subset	subset	VERB
ejpam-5473	168	7	h={(u	h={(u	PROPN
ejpam-5473	168	8	,	,	PUNCT
ejpam-5473	168	9	(	(	PUNCT
ejpam-5473	168	10	δ−	δ−	ADJ
ejpam-5473	168	11	,	,	PUNCT
ejpam-5473	168	12	δ+	δ+	NOUN
ejpam-5473	168	13	)	)	PUNCT
ejpam-5473	168	14	)	)	PUNCT
ejpam-5473	168	15	}	}	PUNCT
ejpam-5473	168	16	of	of	ADP
ejpam-5473	168	17	u	u	NOUN
ejpam-5473	168	18	and	and	CCONJ
ejpam-5473	168	19	a	a	DET
ejpam-5473	168	20	bvf	bvf	NOUN
ejpam-5473	168	21	subset	subset	VERB
ejpam-5473	168	22	t=	t=	PRON
ejpam-5473	168	23	(	(	PUNCT
ejpam-5473	168	24	(	(	PUNCT
ejpam-5473	168	25	v	v	NOUN
ejpam-5473	168	26	,	,	PUNCT
ejpam-5473	168	27	(	(	PUNCT
ejpam-5473	168	28	ϑ−	ϑ−	PROPN
ejpam-5473	168	29	,	,	PUNCT
ejpam-5473	168	30	ϑ+	ϑ+	NOUN
ejpam-5473	168	31	)	)	PUNCT
ejpam-5473	168	32	)	)	PUNCT
ejpam-5473	168	33	}	}	PUNCT
ejpam-5473	168	34	of	of	ADP
ejpam-5473	168	35	v	v	NUM
ejpam-5473	168	36	is	be	AUX
ejpam-5473	168	37	the	the	DET
ejpam-5473	168	38	k	k	NOUN
ejpam-5473	168	39	-	-	PUNCT
ejpam-5473	168	40	bvf	bvf	NOUN
ejpam-5473	168	41	subset	subset	VERB
ejpam-5473	168	42	h×t	h×t	PROPN
ejpam-5473	168	43	of	of	ADP
ejpam-5473	168	44	u×v	u×v	PROPN
ejpam-5473	168	45	defined	define	VERB
ejpam-5473	168	46	by	by	ADP
ejpam-5473	168	47	:	:	PUNCT
ejpam-5473	168	48	h×t=	h×t=	X
ejpam-5473	168	49	{	{	PUNCT
ejpam-5473	168	50	(	(	PUNCT
ejpam-5473	168	51	(	(	PUNCT
ejpam-5473	168	52	u	u	NOUN
ejpam-5473	168	53	,	,	PUNCT
ejpam-5473	168	54	v	v	NOUN
ejpam-5473	168	55	)	)	PUNCT
ejpam-5473	168	56	,	,	PUNCT
ejpam-5473	168	57	(	(	PUNCT
ejpam-5473	168	58	(	(	PUNCT
ejpam-5473	168	59	h−	h−	X
ejpam-5473	168	60	(	(	PUNCT
ejpam-5473	168	61	u	u	NOUN
ejpam-5473	168	62	)	)	PUNCT
ejpam-5473	168	63	,	,	PUNCT
ejpam-5473	168	64	h+	h+	X
ejpam-5473	168	65	(	(	PUNCT
ejpam-5473	168	66	u	u	NOUN
ejpam-5473	168	67	)	)	PUNCT
ejpam-5473	168	68	)	)	PUNCT
ejpam-5473	168	69	,	,	PUNCT
ejpam-5473	168	70	(	(	PUNCT
ejpam-5473	168	71	t−	t−	PROPN
ejpam-5473	168	72	(	(	PUNCT
ejpam-5473	168	73	v	v	NOUN
ejpam-5473	168	74	)	)	PUNCT
ejpam-5473	168	75	,	,	PUNCT
ejpam-5473	168	76	t+	t+	PUNCT
ejpam-5473	168	77	(	(	PUNCT
ejpam-5473	168	78	v	v	NOUN
ejpam-5473	168	79	)	)	PUNCT
ejpam-5473	168	80	)	)	PUNCT
ejpam-5473	168	81	)	)	PUNCT
ejpam-5473	169	1	:	:	PUNCT
ejpam-5473	169	2	u∈u	u∈u	ADJ
ejpam-5473	169	3	,	,	PUNCT
ejpam-5473	169	4	v∈v	v∈v	ADJ
ejpam-5473	169	5	}	}	PUNCT
ejpam-5473	169	6	≡{((u	≡{((u	PROPN
ejpam-5473	169	7	,	,	PUNCT
ejpam-5473	169	8	v	v	NOUN
ejpam-5473	169	9	)	)	PUNCT
ejpam-5473	169	10	,	,	PUNCT
ejpam-5473	169	11	(	(	PUNCT
ejpam-5473	169	12	(	(	PUNCT
ejpam-5473	169	13	δ−	δ−	ADJ
ejpam-5473	169	14	,	,	PUNCT
ejpam-5473	169	15	δ+	δ+	NOUN
ejpam-5473	169	16	)	)	PUNCT
ejpam-5473	169	17	,	,	PUNCT
ejpam-5473	169	18	(	(	PUNCT
ejpam-5473	169	19	ϑ−	ϑ−	PROPN
ejpam-5473	169	20	,	,	PUNCT
ejpam-5473	169	21	ϑ+	ϑ+	NOUN
ejpam-5473	169	22	)	)	PUNCT
ejpam-5473	169	23	)	)	PUNCT
ejpam-5473	169	24	)	)	PUNCT
ejpam-5473	169	25	}	}	PUNCT
ejpam-5473	169	26	.	.	PUNCT
ejpam-5473	170	1	therefore	therefore	ADV
ejpam-5473	170	2	,	,	PUNCT
ejpam-5473	170	3	h×t	h×t	PROPN
ejpam-5473	170	4	is	be	AUX
ejpam-5473	170	5	an	an	DET
ejpam-5473	170	6	element	element	NOUN
ejpam-5473	170	7	of	of	ADP
ejpam-5473	170	8	u×v	u×v	PROPN
ejpam-5473	170	9	,	,	PUNCT
ejpam-5473	170	10	∀h∈wu	∀h∈wu	PROPN
ejpam-5473	170	11	and	and	CCONJ
ejpam-5473	170	12	∀t∈w	∀t∈w	PROPN
ejpam-5473	170	13	v	v	NOUN
ejpam-5473	170	14	.	.	PUNCT
ejpam-5473	171	1	definition	definition	NOUN
ejpam-5473	171	2	13	13	NUM
ejpam-5473	171	3	.	.	PUNCT
ejpam-5473	172	1	[	[	X
ejpam-5473	172	2	9	9	NUM
ejpam-5473	172	3	]	]	PUNCT
ejpam-5473	172	4	a	a	DET
ejpam-5473	172	5	bvfr	bvfr	NOUN
ejpam-5473	172	6	β	β	X
ejpam-5473	172	7	maps	map	VERB
ejpam-5473	172	8	u	u	NOUN
ejpam-5473	172	9	to	to	ADP
ejpam-5473	172	10	v	v	NOUN
ejpam-5473	172	11	is	be	AUX
ejpam-5473	172	12	a	a	DET
ejpam-5473	172	13	subset	subset	NOUN
ejpam-5473	172	14	of	of	ADP
ejpam-5473	172	15	the	the	DET
ejpam-5473	172	16	bvfcp	bvfcp	PROPN
ejpam-5473	172	17	u×v	u×v	PROPN
ejpam-5473	172	18	.	.	PUNCT
ejpam-5473	173	1	in	in	ADP
ejpam-5473	173	2	other	other	ADJ
ejpam-5473	173	3	words	word	NOUN
ejpam-5473	173	4	,	,	PUNCT
ejpam-5473	173	5	β	β	X
ejpam-5473	173	6	is	be	AUX
ejpam-5473	173	7	a	a	DET
ejpam-5473	173	8	member	member	NOUN
ejpam-5473	173	9	of	of	ADP
ejpam-5473	173	10	k	k	PROPN
ejpam-5473	173	11	-	-	PUNCT
ejpam-5473	173	12	bvf	bvf	PROPN
ejpam-5473	173	13	subsets	subset	NOUN
ejpam-5473	173	14	m	m	VERB
ejpam-5473	173	15	:	:	PUNCT
ejpam-5473	173	16	u×v→	u×v→	PROPN
ejpam-5473	173	17	k.	k.	PROPN
ejpam-5473	174	1	a	a	DET
ejpam-5473	174	2	bvfr	bvfr	NOUN
ejpam-5473	174	3	from	from	ADP
ejpam-5473	174	4	u	u	NOUN
ejpam-5473	174	5	to	to	ADP
ejpam-5473	174	6	u	u	NOUN
ejpam-5473	174	7	is	be	AUX
ejpam-5473	174	8	said	say	VERB
ejpam-5473	174	9	to	to	PART
ejpam-5473	174	10	be	be	AUX
ejpam-5473	174	11	a	a	DET
ejpam-5473	174	12	bvfr	bvfr	NOUN
ejpam-5473	174	13	in	in	ADP
ejpam-5473	174	14	u	u	PROPN
ejpam-5473	174	15	.	.	PUNCT
ejpam-5473	175	1	definition	definition	NOUN
ejpam-5473	175	2	14	14	NUM
ejpam-5473	175	3	.	.	PUNCT
ejpam-5473	176	1	[	[	X
ejpam-5473	176	2	9	9	NUM
ejpam-5473	176	3	]	]	PUNCT
ejpam-5473	176	4	let	let	VERB
ejpam-5473	176	5	β1	β1	PROPN
ejpam-5473	176	6	and	and	CCONJ
ejpam-5473	176	7	β2	β2	NOUN
ejpam-5473	176	8	:	:	PUNCT
ejpam-5473	176	9	u→v	u→v	NUM
ejpam-5473	176	10	to	to	PART
ejpam-5473	176	11	v	v	NUM
ejpam-5473	176	12	be	be	AUX
ejpam-5473	176	13	two	two	NUM
ejpam-5473	176	14	bvfrs	bvfrs	NOUN
ejpam-5473	176	15	.	.	PUNCT
ejpam-5473	177	1	we	we	PRON
ejpam-5473	177	2	call	call	VERB
ejpam-5473	177	3	that	that	SCONJ
ejpam-5473	177	4	β2	β2	PROPN
ejpam-5473	177	5	is	be	AUX
ejpam-5473	177	6	containing	contain	VERB
ejpam-5473	177	7	β1	β1	NOUN
ejpam-5473	177	8	,	,	PUNCT
ejpam-5473	177	9	denoted	denote	VERB
ejpam-5473	177	10	by	by	ADP
ejpam-5473	177	11	β1⊂β2	β1⊂β2	NOUN
ejpam-5473	177	12	if	if	SCONJ
ejpam-5473	177	13	and	and	CCONJ
ejpam-5473	177	14	only	only	ADV
ejpam-5473	177	15	if	if	SCONJ
ejpam-5473	177	16	when	when	SCONJ
ejpam-5473	177	17	(	(	PUNCT
ejpam-5473	177	18	(	(	PUNCT
ejpam-5473	177	19	u	u	NOUN
ejpam-5473	177	20	,	,	PUNCT
ejpam-5473	177	21	v	v	NOUN
ejpam-5473	177	22	)	)	PUNCT
ejpam-5473	177	23	,	,	PUNCT
ejpam-5473	177	24	(	(	PUNCT
ejpam-5473	177	25	(	(	PUNCT
ejpam-5473	177	26	δ−	δ−	ADJ
ejpam-5473	177	27	,	,	PUNCT
ejpam-5473	177	28	δ+	δ+	NOUN
ejpam-5473	177	29	)	)	PUNCT
ejpam-5473	177	30	,	,	PUNCT
ejpam-5473	177	31	(	(	PUNCT
ejpam-5473	177	32	ϑ−	ϑ−	PROPN
ejpam-5473	177	33	,	,	PUNCT
ejpam-5473	177	34	ϑ+	ϑ+	NOUN
ejpam-5473	177	35	)	)	PUNCT
ejpam-5473	177	36	)	)	PUNCT
ejpam-5473	177	37	)	)	PUNCT
ejpam-5473	178	1	∈h∈β1	∈h∈β1	PROPN
ejpam-5473	178	2	,	,	PUNCT
ejpam-5473	178	3	there	there	PRON
ejpam-5473	178	4	exists	exist	VERB
ejpam-5473	178	5	b∈β2	b∈β2	NOUN
ejpam-5473	179	1	such	such	ADJ
ejpam-5473	179	2	that	that	SCONJ
ejpam-5473	179	3	(	(	PUNCT
ejpam-5473	179	4	(	(	PUNCT
ejpam-5473	179	5	u	u	NOUN
ejpam-5473	179	6	,	,	PUNCT
ejpam-5473	179	7	v	v	NOUN
ejpam-5473	179	8	)	)	PUNCT
ejpam-5473	179	9	,	,	PUNCT
ejpam-5473	179	10	(	(	PUNCT
ejpam-5473	179	11	(	(	PUNCT
ejpam-5473	179	12	δ−	δ−	ADJ
ejpam-5473	179	13	,	,	PUNCT
ejpam-5473	179	14	δ+	δ+	NOUN
ejpam-5473	179	15	)	)	PUNCT
ejpam-5473	179	16	,	,	PUNCT
ejpam-5473	179	17	(	(	PUNCT
ejpam-5473	179	18	ϑ−	ϑ−	PROPN
ejpam-5473	179	19	,	,	PUNCT
ejpam-5473	179	20	ϑ+	ϑ+	NOUN
ejpam-5473	179	21	)	)	PUNCT
ejpam-5473	179	22	)	)	PUNCT
ejpam-5473	179	23	)	)	PUNCT
ejpam-5473	179	24	∈t∈β2	∈t∈β2	NOUN
ejpam-5473	179	25	.	.	PUNCT
ejpam-5473	180	1	if	if	SCONJ
ejpam-5473	180	2	β1⊂β2	β1⊂β2	PUNCT
ejpam-5473	180	3	and	and	CCONJ
ejpam-5473	180	4	β2	β2	NOUN
ejpam-5473	180	5	⊂β1	⊂β1	PROPN
ejpam-5473	180	6	,	,	PUNCT
ejpam-5473	180	7	then	then	ADV
ejpam-5473	180	8	β1	β1	PROPN
ejpam-5473	180	9	and	and	CCONJ
ejpam-5473	180	10	β2	β2	NOUN
ejpam-5473	180	11	are	be	AUX
ejpam-5473	180	12	equal	equal	ADJ
ejpam-5473	180	13	,	,	PUNCT
ejpam-5473	180	14	that	that	PRON
ejpam-5473	180	15	is	is	ADV
ejpam-5473	180	16	β1	β1	NOUN
ejpam-5473	180	17	=	=	PUNCT
ejpam-5473	180	18	β2	β2	PROPN
ejpam-5473	180	19	.	.	PUNCT
ejpam-5473	181	1	f.	f.	PROPN
ejpam-5473	181	2	al	al	PROPN
ejpam-5473	181	3	-	-	PROPN
ejpam-5473	181	4	zu’bi	zu’bi	PROPN
ejpam-5473	181	5	et	et	NOUN
ejpam-5473	181	6	al	al	PROPN
ejpam-5473	181	7	.	.	PUNCT
ejpam-5473	181	8	/	/	SYM
ejpam-5473	181	9	eur	eur	PROPN
ejpam-5473	181	10	.	.	PUNCT
ejpam-5473	182	1	j.	j.	PROPN
ejpam-5473	182	2	pure	pure	PROPN
ejpam-5473	182	3	appl	appl	PROPN
ejpam-5473	182	4	.	.	PROPN
ejpam-5473	182	5	math	math	PROPN
ejpam-5473	182	6	,	,	PUNCT
ejpam-5473	182	7	17	17	NUM
ejpam-5473	182	8	(	(	PUNCT
ejpam-5473	182	9	4	4	NUM
ejpam-5473	182	10	)	)	PUNCT
ejpam-5473	182	11	(	(	PUNCT
ejpam-5473	182	12	2024	2024	NUM
ejpam-5473	182	13	)	)	PUNCT
ejpam-5473	182	14	,	,	PUNCT
ejpam-5473	182	15	2898	2898	NUM
ejpam-5473	182	16	-	-	SYM
ejpam-5473	182	17	2914	2914	NUM
ejpam-5473	182	18	2904	2904	NUM
ejpam-5473	182	19	definition	definition	NOUN
ejpam-5473	182	20	15	15	NUM
ejpam-5473	182	21	.	.	PUNCT
ejpam-5473	183	1	[	[	X
ejpam-5473	183	2	9	9	NUM
ejpam-5473	183	3	]	]	PUNCT
ejpam-5473	183	4	let	let	VERB
ejpam-5473	183	5	β	β	X
ejpam-5473	183	6	:	:	PUNCT
ejpam-5473	183	7	u→v	u→v	NUM
ejpam-5473	183	8	be	be	AUX
ejpam-5473	183	9	a	a	DET
ejpam-5473	183	10	bvfr	bvfr	NOUN
ejpam-5473	183	11	.	.	PUNCT
ejpam-5473	184	1	the	the	DET
ejpam-5473	184	2	inverse	inverse	NOUN
ejpam-5473	184	3	of	of	ADP
ejpam-5473	184	4	β	β	X
ejpam-5473	184	5	=	=	SYM
ejpam-5473	184	6	β−1	β−1	NUM
ejpam-5473	184	7	:	:	PUNCT
ejpam-5473	184	8	v→u	v→u	PROPN
ejpam-5473	184	9	is	be	AUX
ejpam-5473	184	10	the	the	DET
ejpam-5473	184	11	bvfr	bvfr	NOUN
ejpam-5473	184	12	defined	define	VERB
ejpam-5473	184	13	by	by	ADP
ejpam-5473	184	14	β−1=	β−1=	NOUN
ejpam-5473	184	15	{	{	PUNCT
ejpam-5473	184	16	m−1	m−1	PROPN
ejpam-5473	184	17	:	:	PUNCT
ejpam-5473	184	18	mϵβ	mϵβ	NOUN
ejpam-5473	184	19	}	}	PUNCT
ejpam-5473	184	20	.	.	PUNCT
ejpam-5473	185	1	definition	definition	NOUN
ejpam-5473	185	2	16	16	NUM
ejpam-5473	185	3	.	.	PUNCT
ejpam-5473	186	1	[	[	X
ejpam-5473	186	2	9	9	NUM
ejpam-5473	186	3	]	]	PUNCT
ejpam-5473	186	4	let	let	VERB
ejpam-5473	186	5	β	β	X
ejpam-5473	186	6	:	:	PUNCT
ejpam-5473	186	7	u→v	u→v	NUM
ejpam-5473	186	8	and	and	CCONJ
ejpam-5473	186	9	γ	γ	NOUN
ejpam-5473	186	10	:	:	PUNCT
ejpam-5473	186	11	v→z	v→z	NUM
ejpam-5473	186	12	be	be	AUX
ejpam-5473	186	13	two	two	NUM
ejpam-5473	186	14	bvfrs	bvfrs	NOUN
ejpam-5473	186	15	.	.	PUNCT
ejpam-5473	187	1	the	the	DET
ejpam-5473	187	2	composition	composition	NOUN
ejpam-5473	187	3	of	of	ADP
ejpam-5473	187	4	β	β	X
ejpam-5473	187	5	and	and	CCONJ
ejpam-5473	187	6	γ	γ	PROPN
ejpam-5473	187	7	,	,	PUNCT
ejpam-5473	187	8	denoted	denote	VERB
ejpam-5473	187	9	γ	γ	X
ejpam-5473	187	10	◦	◦	NOUN
ejpam-5473	187	11	β	β	NOUN
ejpam-5473	187	12	:	:	PUNCT
ejpam-5473	187	13	u→z	u→z	NUM
ejpam-5473	187	14	,	,	PUNCT
ejpam-5473	187	15	is	be	AUX
ejpam-5473	187	16	a	a	DET
ejpam-5473	187	17	bvfr	bvfr	NOUN
ejpam-5473	187	18	defined	define	VERB
ejpam-5473	187	19	by	by	ADP
ejpam-5473	187	20	γ	γ	PROPN
ejpam-5473	187	21	◦	◦	NOUN
ejpam-5473	187	22	β=	β=	NOUN
ejpam-5473	187	23	{	{	PUNCT
ejpam-5473	187	24	(	(	PUNCT
ejpam-5473	187	25	(	(	PUNCT
ejpam-5473	187	26	u	u	NOUN
ejpam-5473	187	27	,	,	PUNCT
ejpam-5473	187	28	z	z	NOUN
ejpam-5473	187	29	)	)	PUNCT
ejpam-5473	187	30	,	,	PUNCT
ejpam-5473	187	31	(	(	PUNCT
ejpam-5473	187	32	(	(	PUNCT
ejpam-5473	187	33	δ−	δ−	ADJ
ejpam-5473	187	34	,	,	PUNCT
ejpam-5473	187	35	δ+	δ+	NOUN
ejpam-5473	187	36	)	)	PUNCT
ejpam-5473	187	37	,	,	PUNCT
ejpam-5473	187	38	(	(	PUNCT
ejpam-5473	187	39	α−	α−	ADP
ejpam-5473	187	40	,	,	PUNCT
ejpam-5473	187	41	α+	α+	NOUN
ejpam-5473	187	42	)	)	PUNCT
ejpam-5473	187	43	)	)	PUNCT
ejpam-5473	187	44	)	)	PUNCT
ejpam-5473	188	1	∈m	∈m	ADP
ejpam-5473	188	2	:	:	PUNCT
ejpam-5473	188	3	m∈u×z	m∈u×z	NOUN
ejpam-5473	188	4	}	}	PUNCT
ejpam-5473	188	5	.	.	PUNCT
ejpam-5473	189	1	where	where	SCONJ
ejpam-5473	189	2	a	a	DET
ejpam-5473	189	3	k	k	NOUN
ejpam-5473	189	4	-	-	PUNCT
ejpam-5473	189	5	bvf	bvf	NOUN
ejpam-5473	189	6	subsets	subset	NOUN
ejpam-5473	189	7	m∈u×z	m∈u×z	PRON
ejpam-5473	189	8	defined	define	VERB
ejpam-5473	189	9	by	by	ADP
ejpam-5473	189	10	:	:	PUNCT
ejpam-5473	189	11	(	(	PUNCT
ejpam-5473	189	12	(	(	PUNCT
ejpam-5473	189	13	u	u	NOUN
ejpam-5473	189	14	,	,	PUNCT
ejpam-5473	189	15	z	z	NOUN
ejpam-5473	189	16	)	)	PUNCT
ejpam-5473	189	17	,	,	PUNCT
ejpam-5473	189	18	(	(	PUNCT
ejpam-5473	189	19	(	(	PUNCT
ejpam-5473	189	20	δ−	δ−	ADJ
ejpam-5473	189	21	,	,	PUNCT
ejpam-5473	189	22	δ+	δ+	NOUN
ejpam-5473	189	23	)	)	PUNCT
ejpam-5473	189	24	,	,	PUNCT
ejpam-5473	189	25	(	(	PUNCT
ejpam-5473	189	26	α−	α−	ADP
ejpam-5473	189	27	,	,	PUNCT
ejpam-5473	189	28	α+	α+	NOUN
ejpam-5473	189	29	)	)	PUNCT
ejpam-5473	189	30	)	)	PUNCT
ejpam-5473	189	31	)	)	PUNCT
ejpam-5473	189	32	∈m	∈m	NOUN
ejpam-5473	189	33	if	if	SCONJ
ejpam-5473	189	34	and	and	CCONJ
ejpam-5473	189	35	only	only	ADV
ejpam-5473	189	36	if	if	SCONJ
ejpam-5473	189	37	∃(v	∃(v	PROPN
ejpam-5473	189	38	,	,	PUNCT
ejpam-5473	189	39	(	(	PUNCT
ejpam-5473	189	40	ϑ−	ϑ−	PROPN
ejpam-5473	189	41	,	,	PUNCT
ejpam-5473	189	42	ϑ+	ϑ+	NOUN
ejpam-5473	189	43	)	)	PUNCT
ejpam-5473	189	44	)	)	PUNCT
ejpam-5473	189	45	∈v×w	∈v×w	NOUN
ejpam-5473	189	46	such	such	ADJ
ejpam-5473	189	47	that	that	PRON
ejpam-5473	189	48	(	(	PUNCT
ejpam-5473	189	49	(	(	PUNCT
ejpam-5473	189	50	u	u	NOUN
ejpam-5473	189	51	,	,	PUNCT
ejpam-5473	189	52	v	v	NOUN
ejpam-5473	189	53	)	)	PUNCT
ejpam-5473	189	54	,	,	PUNCT
ejpam-5473	189	55	(	(	PUNCT
ejpam-5473	189	56	(	(	PUNCT
ejpam-5473	189	57	δ−	δ−	ADJ
ejpam-5473	189	58	,	,	PUNCT
ejpam-5473	189	59	δ+	δ+	NOUN
ejpam-5473	189	60	)	)	PUNCT
ejpam-5473	189	61	,	,	PUNCT
ejpam-5473	189	62	(	(	PUNCT
ejpam-5473	189	63	ϑ−	ϑ−	PROPN
ejpam-5473	189	64	,	,	PUNCT
ejpam-5473	189	65	ϑ+	ϑ+	NOUN
ejpam-5473	189	66	)	)	PUNCT
ejpam-5473	189	67	)	)	PUNCT
ejpam-5473	189	68	)	)	PUNCT
ejpam-5473	189	69	∈a	∈a	NUM
ejpam-5473	189	70	and	and	CCONJ
ejpam-5473	189	71	(	(	PUNCT
ejpam-5473	189	72	(	(	PUNCT
ejpam-5473	189	73	v	v	NOUN
ejpam-5473	189	74	,	,	PUNCT
ejpam-5473	189	75	z	z	NOUN
ejpam-5473	189	76	)	)	PUNCT
ejpam-5473	189	77	,	,	PUNCT
ejpam-5473	189	78	(	(	PUNCT
ejpam-5473	189	79	(	(	PUNCT
ejpam-5473	189	80	ϑ−	ϑ−	PROPN
ejpam-5473	189	81	,	,	PUNCT
ejpam-5473	189	82	ϑ+	ϑ+	NOUN
ejpam-5473	189	83	)	)	PUNCT
ejpam-5473	189	84	,	,	PUNCT
ejpam-5473	189	85	(	(	PUNCT
ejpam-5473	189	86	α−	α−	ADP
ejpam-5473	189	87	,	,	PUNCT
ejpam-5473	189	88	α+	α+	NOUN
ejpam-5473	189	89	)	)	PUNCT
ejpam-5473	189	90	)	)	PUNCT
ejpam-5473	189	91	)	)	PUNCT
ejpam-5473	189	92	∈b	∈b	NOUN
ejpam-5473	189	93	for	for	ADP
ejpam-5473	189	94	some	some	DET
ejpam-5473	189	95	β	β	X
ejpam-5473	189	96	and	and	CCONJ
ejpam-5473	189	97	b∈γ	b∈γ	NOUN
ejpam-5473	189	98	.	.	PUNCT
ejpam-5473	190	1	definition	definition	NOUN
ejpam-5473	190	2	17	17	NUM
ejpam-5473	190	3	.	.	PUNCT
ejpam-5473	191	1	[	[	X
ejpam-5473	191	2	9]let	9]let	NOUN
ejpam-5473	191	3	β	β	X
ejpam-5473	191	4	be	be	AUX
ejpam-5473	191	5	a	a	DET
ejpam-5473	191	6	bvfr	bvfr	NOUN
ejpam-5473	191	7	in	in	ADP
ejpam-5473	191	8	u	u	PROPN
ejpam-5473	191	9	,	,	PUNCT
ejpam-5473	191	10	i.e.	i.e.	X
ejpam-5473	191	11	,	,	PUNCT
ejpam-5473	191	12	β⊂u×u	β⊂u×u	PRON
ejpam-5473	191	13	.	.	PUNCT
ejpam-5473	192	1	then	then	ADV
ejpam-5473	192	2	1	1	X
ejpam-5473	192	3	.	.	PUNCT
ejpam-5473	192	4	β	β	PROPN
ejpam-5473	192	5	is	be	AUX
ejpam-5473	192	6	called	call	VERB
ejpam-5473	192	7	reflexive	reflexive	ADJ
ejpam-5473	192	8	in	in	ADP
ejpam-5473	192	9	u	u	NOUN
ejpam-5473	192	10	if	if	SCONJ
ejpam-5473	192	11	and	and	CCONJ
ejpam-5473	192	12	only	only	ADV
ejpam-5473	192	13	if	if	SCONJ
ejpam-5473	192	14	∀u∈u	∀u∈u	PROPN
ejpam-5473	192	15	and	and	CCONJ
ejpam-5473	192	16	∀	∀	X
ejpam-5473	192	17	(	(	PUNCT
ejpam-5473	192	18	δ−	δ−	ADJ
ejpam-5473	192	19	,	,	PUNCT
ejpam-5473	192	20	δ+)∈w	δ+)∈w	NOUN
ejpam-5473	192	21	,	,	PUNCT
ejpam-5473	192	22	∃h∈β	∃h∈β	ADP
ejpam-5473	192	23	such	such	ADJ
ejpam-5473	192	24	that	that	SCONJ
ejpam-5473	192	25	(	(	PUNCT
ejpam-5473	192	26	(	(	PUNCT
ejpam-5473	192	27	u	u	NOUN
ejpam-5473	192	28	,	,	PUNCT
ejpam-5473	192	29	u	u	NOUN
ejpam-5473	192	30	)	)	PUNCT
ejpam-5473	192	31	,	,	PUNCT
ejpam-5473	192	32	(	(	PUNCT
ejpam-5473	192	33	(	(	PUNCT
ejpam-5473	192	34	δ−	δ−	ADJ
ejpam-5473	192	35	,	,	PUNCT
ejpam-5473	192	36	δ+	δ+	NOUN
ejpam-5473	192	37	)	)	PUNCT
ejpam-5473	192	38	,	,	PUNCT
ejpam-5473	192	39	(	(	PUNCT
ejpam-5473	192	40	δ−	δ−	ADJ
ejpam-5473	192	41	,	,	PUNCT
ejpam-5473	192	42	δ+	δ+	NOUN
ejpam-5473	192	43	)	)	PUNCT
ejpam-5473	192	44	)	)	PUNCT
ejpam-5473	192	45	)	)	PUNCT
ejpam-5473	192	46	∈h∈β	∈h∈β	NOUN
ejpam-5473	192	47	,	,	PUNCT
ejpam-5473	192	48	that	that	PRON
ejpam-5473	192	49	is	be	AUX
ejpam-5473	192	50	if	if	SCONJ
ejpam-5473	192	51	and	and	CCONJ
ejpam-5473	192	52	only	only	ADV
ejpam-5473	192	53	if	if	SCONJ
ejpam-5473	192	54	∆u⊂β	∆u⊂β	NOUN
ejpam-5473	192	55	.	.	PUNCT
ejpam-5473	193	1	2	2	X
ejpam-5473	193	2	.	.	X
ejpam-5473	193	3	β	β	X
ejpam-5473	193	4	is	be	AUX
ejpam-5473	193	5	called	call	VERB
ejpam-5473	193	6	symmetric	symmetric	ADJ
ejpam-5473	193	7	if	if	SCONJ
ejpam-5473	193	8	and	and	CCONJ
ejpam-5473	193	9	only	only	ADV
ejpam-5473	193	10	if	if	SCONJ
ejpam-5473	193	11	whenever	whenever	SCONJ
ejpam-5473	193	12	(	(	PUNCT
ejpam-5473	193	13	(	(	PUNCT
ejpam-5473	193	14	u	u	NOUN
ejpam-5473	193	15	,	,	PUNCT
ejpam-5473	193	16	v	v	NOUN
ejpam-5473	193	17	)	)	PUNCT
ejpam-5473	193	18	,	,	PUNCT
ejpam-5473	193	19	(	(	PUNCT
ejpam-5473	193	20	(	(	PUNCT
ejpam-5473	193	21	δ−	δ−	ADJ
ejpam-5473	193	22	,	,	PUNCT
ejpam-5473	193	23	δ+	δ+	NOUN
ejpam-5473	193	24	)	)	PUNCT
ejpam-5473	193	25	,	,	PUNCT
ejpam-5473	193	26	(	(	PUNCT
ejpam-5473	193	27	n−	n−	NOUN
ejpam-5473	193	28	,	,	PUNCT
ejpam-5473	193	29	n+	n+	NUM
ejpam-5473	193	30	)	)	PUNCT
ejpam-5473	193	31	)	)	PUNCT
ejpam-5473	193	32	)	)	PUNCT
ejpam-5473	194	1	∈h∈β	∈h∈β	NOUN
ejpam-5473	194	2	,	,	PUNCT
ejpam-5473	194	3	∃h∈ρ	∃h∈ρ	VERB
ejpam-5473	194	4	such	such	ADJ
ejpam-5473	194	5	that	that	SCONJ
ejpam-5473	194	6	(	(	PUNCT
ejpam-5473	194	7	(	(	PUNCT
ejpam-5473	194	8	v	v	NOUN
ejpam-5473	194	9	,	,	PUNCT
ejpam-5473	194	10	u	u	NOUN
ejpam-5473	194	11	)	)	PUNCT
ejpam-5473	194	12	,	,	PUNCT
ejpam-5473	194	13	(	(	PUNCT
ejpam-5473	194	14	(	(	PUNCT
ejpam-5473	194	15	n−	n−	NOUN
ejpam-5473	194	16	,	,	PUNCT
ejpam-5473	194	17	n+	n+	NUM
ejpam-5473	194	18	)	)	PUNCT
ejpam-5473	194	19	,	,	PUNCT
ejpam-5473	194	20	(	(	PUNCT
ejpam-5473	194	21	δ−	δ−	ADJ
ejpam-5473	194	22	,	,	PUNCT
ejpam-5473	194	23	δ+	δ+	NOUN
ejpam-5473	194	24	)	)	PUNCT
ejpam-5473	194	25	)	)	PUNCT
ejpam-5473	194	26	)	)	PUNCT
ejpam-5473	195	1	∈t∈β	∈t∈β	PROPN
ejpam-5473	195	2	,	,	PUNCT
ejpam-5473	195	3	that	that	PRON
ejpam-5473	195	4	is	be	AUX
ejpam-5473	195	5	if	if	SCONJ
ejpam-5473	195	6	and	and	CCONJ
ejpam-5473	195	7	only	only	ADV
ejpam-5473	195	8	if	if	SCONJ
ejpam-5473	195	9	β−1	β−1	NOUN
ejpam-5473	195	10	=	=	SYM
ejpam-5473	195	11	β	β	NOUN
ejpam-5473	195	12	.	.	NOUN
ejpam-5473	195	13	3	3	X
ejpam-5473	195	14	.	.	X
ejpam-5473	195	15	β	β	PROPN
ejpam-5473	195	16	is	be	AUX
ejpam-5473	195	17	called	call	VERB
ejpam-5473	195	18	transitive	transitive	ADJ
ejpam-5473	195	19	if	if	SCONJ
ejpam-5473	195	20	and	and	CCONJ
ejpam-5473	195	21	only	only	ADV
ejpam-5473	195	22	if	if	SCONJ
ejpam-5473	195	23	whenever	whenever	SCONJ
ejpam-5473	195	24	(	(	PUNCT
ejpam-5473	195	25	(	(	PUNCT
ejpam-5473	195	26	u	u	NOUN
ejpam-5473	195	27	,	,	PUNCT
ejpam-5473	195	28	v	v	NOUN
ejpam-5473	195	29	)	)	PUNCT
ejpam-5473	195	30	,	,	PUNCT
ejpam-5473	195	31	(	(	PUNCT
ejpam-5473	195	32	(	(	PUNCT
ejpam-5473	195	33	δ−	δ−	ADJ
ejpam-5473	195	34	,	,	PUNCT
ejpam-5473	195	35	δ+	δ+	NOUN
ejpam-5473	195	36	)	)	PUNCT
ejpam-5473	195	37	,	,	PUNCT
ejpam-5473	195	38	(	(	PUNCT
ejpam-5473	195	39	ϑ−	ϑ−	PROPN
ejpam-5473	195	40	,	,	PUNCT
ejpam-5473	195	41	ϑ+	ϑ+	NOUN
ejpam-5473	195	42	)	)	PUNCT
ejpam-5473	195	43	)	)	PUNCT
ejpam-5473	195	44	)	)	PUNCT
ejpam-5473	196	1	∈h∈β	∈h∈β	NOUN
ejpam-5473	196	2	and	and	CCONJ
ejpam-5473	196	3	(	(	PUNCT
ejpam-5473	196	4	(	(	PUNCT
ejpam-5473	196	5	v	v	NOUN
ejpam-5473	196	6	,	,	PUNCT
ejpam-5473	196	7	z	z	NOUN
ejpam-5473	196	8	)	)	PUNCT
ejpam-5473	196	9	,	,	PUNCT
ejpam-5473	196	10	(	(	PUNCT
ejpam-5473	196	11	(	(	PUNCT
ejpam-5473	196	12	ϑ−	ϑ−	PROPN
ejpam-5473	196	13	,	,	PUNCT
ejpam-5473	196	14	ϑ+	ϑ+	NOUN
ejpam-5473	196	15	)	)	PUNCT
ejpam-5473	196	16	,	,	PUNCT
ejpam-5473	196	17	(	(	PUNCT
ejpam-5473	196	18	α−	α−	ADP
ejpam-5473	196	19	,	,	PUNCT
ejpam-5473	196	20	α+)))∈t∈β	α+)))∈t∈β	NUM
ejpam-5473	196	21	,	,	PUNCT
ejpam-5473	196	22	∃c∈β	∃c∈β	VERB
ejpam-5473	196	23	such	such	ADJ
ejpam-5473	196	24	that	that	SCONJ
ejpam-5473	196	25	(	(	PUNCT
ejpam-5473	196	26	(	(	PUNCT
ejpam-5473	196	27	u	u	NOUN
ejpam-5473	196	28	,	,	PUNCT
ejpam-5473	196	29	z	z	NOUN
ejpam-5473	196	30	)	)	PUNCT
ejpam-5473	196	31	,	,	PUNCT
ejpam-5473	196	32	(	(	PUNCT
ejpam-5473	196	33	(	(	PUNCT
ejpam-5473	196	34	δ−	δ−	ADJ
ejpam-5473	196	35	,	,	PUNCT
ejpam-5473	196	36	δ+	δ+	NOUN
ejpam-5473	196	37	)	)	PUNCT
ejpam-5473	196	38	,	,	PUNCT
ejpam-5473	196	39	(	(	PUNCT
ejpam-5473	196	40	α−	α−	ADP
ejpam-5473	196	41	,	,	PUNCT
ejpam-5473	196	42	α+	α+	NOUN
ejpam-5473	196	43	)	)	PUNCT
ejpam-5473	196	44	)	)	PUNCT
ejpam-5473	196	45	)	)	PUNCT
ejpam-5473	197	1	∈c∈β	∈c∈β	PROPN
ejpam-5473	197	2	,	,	PUNCT
ejpam-5473	197	3	that	that	PRON
ejpam-5473	197	4	is	be	AUX
ejpam-5473	197	5	if	if	SCONJ
ejpam-5473	197	6	and	and	CCONJ
ejpam-5473	197	7	only	only	ADV
ejpam-5473	197	8	if	if	SCONJ
ejpam-5473	197	9	β	β	NOUN
ejpam-5473	197	10	◦	◦	NOUN
ejpam-5473	197	11	β⊂β	β⊂β	X
ejpam-5473	197	12	.	.	PUNCT
ejpam-5473	198	1	a	a	DET
ejpam-5473	198	2	bvfr	bvfr	NOUN
ejpam-5473	198	3	in	in	ADP
ejpam-5473	198	4	u	u	NOUN
ejpam-5473	198	5	is	be	AUX
ejpam-5473	198	6	called	call	VERB
ejpam-5473	198	7	a	a	DET
ejpam-5473	198	8	bvfer	bvfer	NOUN
ejpam-5473	198	9	in	in	ADP
ejpam-5473	198	10	u	u	NOUN
ejpam-5473	198	11	if	if	SCONJ
ejpam-5473	198	12	and	and	CCONJ
ejpam-5473	198	13	only	only	ADV
ejpam-5473	198	14	if	if	SCONJ
ejpam-5473	198	15	it	it	PRON
ejpam-5473	198	16	satisfies	satisfy	VERB
ejpam-5473	198	17	all	all	DET
ejpam-5473	198	18	three	three	NUM
ejpam-5473	198	19	axioms	axiom	NOUN
ejpam-5473	198	20	above	above	ADV
ejpam-5473	198	21	.	.	PUNCT
ejpam-5473	199	1	definition	definition	NOUN
ejpam-5473	199	2	18	18	NUM
ejpam-5473	199	3	.	.	PUNCT
ejpam-5473	200	1	[	[	X
ejpam-5473	200	2	9	9	NUM
ejpam-5473	200	3	]	]	PUNCT
ejpam-5473	200	4	let	let	VERB
ejpam-5473	200	5	u	u	PRON
ejpam-5473	200	6	and	and	CCONJ
ejpam-5473	200	7	v	v	NOUN
ejpam-5473	200	8	be	be	VERB
ejpam-5473	200	9	nonempty	nonempty	ADJ
ejpam-5473	200	10	sets	set	NOUN
ejpam-5473	200	11	.	.	PUNCT
ejpam-5473	201	1	a	a	DET
ejpam-5473	201	2	bvf	bvf	NOUN
ejpam-5473	201	3	function	function	VERB
ejpam-5473	201	4	from	from	ADP
ejpam-5473	201	5	u	u	NOUN
ejpam-5473	201	6	to	to	ADP
ejpam-5473	201	7	v	v	NOUN
ejpam-5473	201	8	can	can	AUX
ejpam-5473	201	9	be	be	AUX
ejpam-5473	201	10	described	describe	VERB
ejpam-5473	201	11	as	as	ADP
ejpam-5473	201	12	a	a	DET
ejpam-5473	201	13	function	function	NOUN
ejpam-5473	201	14	f	f	NOUN
ejpam-5473	201	15	from	from	ADP
ejpam-5473	201	16	wu	wu	PROPN
ejpam-5473	201	17	to	to	ADP
ejpam-5473	201	18	w	w	PROPN
ejpam-5473	201	19	v	v	NOUN
ejpam-5473	201	20	characterized	characterize	VERB
ejpam-5473	201	21	by	by	ADP
ejpam-5473	201	22	the	the	DET
ejpam-5473	201	23	ordered	order	VERB
ejpam-5473	201	24	pair	pair	NOUN
ejpam-5473	201	25	(	(	PUNCT
ejpam-5473	201	26	f	f	X
ejpam-5473	201	27	,	,	PUNCT
ejpam-5473	201	28	{	{	PUNCT
ejpam-5473	201	29	(	(	PUNCT
ejpam-5473	201	30	fu(δ	fu(δ	NOUN
ejpam-5473	201	31	−	−	NOUN
ejpam-5473	201	32	)	)	PUNCT
ejpam-5473	201	33	,	,	PUNCT
ejpam-5473	201	34	fu(δ	fu(δ	X
ejpam-5473	202	1	+	+	X
ejpam-5473	202	2	)	)	PUNCT
ejpam-5473	202	3	)	)	PUNCT
ejpam-5473	202	4	}	}	PUNCT
ejpam-5473	202	5	u∈u	u∈u	ADJ
ejpam-5473	202	6	)	)	PUNCT
ejpam-5473	202	7	,	,	PUNCT
ejpam-5473	202	8	where	where	SCONJ
ejpam-5473	202	9	f	f	X
ejpam-5473	202	10	:	:	PUNCT
ejpam-5473	202	11	u→v	u→v	NUM
ejpam-5473	202	12	is	be	AUX
ejpam-5473	202	13	a	a	DET
ejpam-5473	202	14	function	function	NOUN
ejpam-5473	202	15	from	from	ADP
ejpam-5473	202	16	u	u	NOUN
ejpam-5473	202	17	to	to	ADP
ejpam-5473	202	18	v	v	NOUN
ejpam-5473	202	19	and	and	CCONJ
ejpam-5473	202	20	{	{	PUNCT
ejpam-5473	202	21	(	(	PUNCT
ejpam-5473	202	22	fu(δ	fu(δ	NOUN
ejpam-5473	202	23	−	−	NOUN
ejpam-5473	202	24	)	)	PUNCT
ejpam-5473	202	25	,	,	PUNCT
ejpam-5473	202	26	fu(δ	fu(δ	X
ejpam-5473	202	27	+	+	X
ejpam-5473	202	28	)	)	PUNCT
ejpam-5473	202	29	)	)	PUNCT
ejpam-5473	202	30	}	}	PUNCT
ejpam-5473	202	31	u∈u	u∈u	ADJ
ejpam-5473	202	32	is	be	AUX
ejpam-5473	202	33	a	a	DET
ejpam-5473	202	34	family	family	NOUN
ejpam-5473	202	35	of	of	ADP
ejpam-5473	202	36	functions	function	NOUN
ejpam-5473	202	37	(	(	PUNCT
ejpam-5473	202	38	fu(δ	fu(δ	NOUN
ejpam-5473	202	39	−	−	NOUN
ejpam-5473	202	40	)	)	PUNCT
ejpam-5473	202	41	,	,	PUNCT
ejpam-5473	202	42	fu(δ	fu(δ	X
ejpam-5473	202	43	+	+	X
ejpam-5473	202	44	)	)	PUNCT
ejpam-5473	202	45	)	)	PUNCT
ejpam-5473	203	1	:	:	PUNCT
ejpam-5473	203	2	w→w	w→w	NOUN
ejpam-5473	203	3	that	that	PRON
ejpam-5473	203	4	satisfy	satisfy	VERB
ejpam-5473	203	5	the	the	DET
ejpam-5473	203	6	following	following	ADJ
ejpam-5473	203	7	conditions	condition	NOUN
ejpam-5473	203	8	:	:	PUNCT
ejpam-5473	203	9	(	(	PUNCT
ejpam-5473	203	10	i	i	NOUN
ejpam-5473	203	11	)	)	PUNCT
ejpam-5473	203	12	fu(δ	fu(δ	NOUN
ejpam-5473	203	13	−	−	NOUN
ejpam-5473	203	14	)	)	PUNCT
ejpam-5473	203	15	,	,	PUNCT
ejpam-5473	203	16	fu(δ	fu(δ	X
ejpam-5473	203	17	+	+	X
ejpam-5473	203	18	)	)	PUNCT
ejpam-5473	203	19	are	be	AUX
ejpam-5473	203	20	nondecreasing	nondecrease	VERB
ejpam-5473	203	21	on	on	ADP
ejpam-5473	203	22	w	w	PROPN
ejpam-5473	203	23	,	,	PUNCT
ejpam-5473	203	24	and	and	CCONJ
ejpam-5473	203	25	(	(	PUNCT
ejpam-5473	203	26	ii	ii	NOUN
ejpam-5473	203	27	)	)	PUNCT
ejpam-5473	203	28	fu	fu	NOUN
ejpam-5473	203	29	(	(	PUNCT
ejpam-5473	203	30	δ	δ	PROPN
ejpam-5473	203	31	−=	−=	X
ejpam-5473	203	32	0)=	0)=	NUM
ejpam-5473	203	33	0	0	NUM
ejpam-5473	203	34	=	=	NOUN
ejpam-5473	203	35	fu	fu	NOUN
ejpam-5473	203	36	(	(	PUNCT
ejpam-5473	203	37	δ	δ	PROPN
ejpam-5473	204	1	+	+	PROPN
ejpam-5473	204	2	=	=	NOUN
ejpam-5473	204	3	0	0	NUM
ejpam-5473	204	4	)	)	PUNCT
ejpam-5473	204	5	,	,	PUNCT
ejpam-5473	204	6	fu	fu	NOUN
ejpam-5473	204	7	(	(	PUNCT
ejpam-5473	204	8	δ	δ	PROPN
ejpam-5473	204	9	−=	−=	VERB
ejpam-5473	204	10	−1)=	−1)=	ADP
ejpam-5473	204	11	−1	−1	NOUN
ejpam-5473	204	12	,	,	PUNCT
ejpam-5473	204	13	and	and	CCONJ
ejpam-5473	204	14	fu(δ	fu(δ	X
ejpam-5473	205	1	+	+	NOUN
ejpam-5473	205	2	=	=	SYM
ejpam-5473	205	3	1	1	NUM
ejpam-5473	205	4	)	)	PUNCT
ejpam-5473	205	5	=	=	SYM
ejpam-5473	205	6	1	1	NUM
ejpam-5473	205	7	.	.	NOUN
ejpam-5473	205	8	3	3	X
ejpam-5473	205	9	.	.	X
ejpam-5473	205	10	bipolar	bipolar	ADJ
ejpam-5473	205	11	valued	value	VERB
ejpam-5473	205	12	fuzzy	fuzzy	ADJ
ejpam-5473	205	13	space	space	NOUN
ejpam-5473	205	14	the	the	DET
ejpam-5473	205	15	central	central	ADJ
ejpam-5473	205	16	result	result	NOUN
ejpam-5473	205	17	of	of	ADP
ejpam-5473	205	18	this	this	DET
ejpam-5473	205	19	part	part	NOUN
ejpam-5473	205	20	is	be	AUX
ejpam-5473	205	21	to	to	PART
ejpam-5473	205	22	generalize	generalize	VERB
ejpam-5473	205	23	f	f	NOUN
ejpam-5473	205	24	-	-	PUNCT
ejpam-5473	205	25	space	space	NOUN
ejpam-5473	205	26	to	to	ADP
ejpam-5473	205	27	the	the	DET
ejpam-5473	205	28	bvf	bvf	NOUN
ejpam-5473	205	29	-	-	PUNCT
ejpam-5473	205	30	space	space	NOUN
ejpam-5473	205	31	.	.	PUNCT
ejpam-5473	206	1	this	this	DET
ejpam-5473	206	2	generalization	generalization	NOUN
ejpam-5473	206	3	can	can	AUX
ejpam-5473	206	4	be	be	AUX
ejpam-5473	206	5	done	do	VERB
ejpam-5473	206	6	by	by	ADP
ejpam-5473	206	7	enlarge	enlarge	VERB
ejpam-5473	206	8	the	the	DET
ejpam-5473	206	9	codomain	codomain	NOUN
ejpam-5473	206	10	of	of	ADP
ejpam-5473	206	11	the	the	DET
ejpam-5473	206	12	membership	membership	NOUN
ejpam-5473	206	13	for	for	ADP
ejpam-5473	206	14	each	each	DET
ejpam-5473	206	15	element	element	NOUN
ejpam-5473	206	16	in	in	ADP
ejpam-5473	206	17	the	the	DET
ejpam-5473	206	18	f	f	NOUN
ejpam-5473	206	19	-	-	PUNCT
ejpam-5473	206	20	space	space	NOUN
ejpam-5473	206	21	from	from	ADP
ejpam-5473	206	22	[	[	X
ejpam-5473	206	23	0	0	NUM
ejpam-5473	206	24	,	,	PUNCT
ejpam-5473	206	25	1	1	NUM
ejpam-5473	206	26	]	]	PUNCT
ejpam-5473	206	27	to	to	ADP
ejpam-5473	206	28	[	[	X
ejpam-5473	206	29	-1	-1	INTJ
ejpam-5473	206	30	,	,	PUNCT
ejpam-5473	206	31	0]×[0	0]×[0	NUM
ejpam-5473	206	32	,	,	PUNCT
ejpam-5473	206	33	1	1	NUM
ejpam-5473	206	34	]	]	PUNCT
ejpam-5473	206	35	in	in	ADP
ejpam-5473	206	36	bvf	bvf	NOUN
ejpam-5473	206	37	-	-	PUNCT
ejpam-5473	206	38	space	space	NOUN
ejpam-5473	206	39	.	.	PUNCT
ejpam-5473	207	1	the	the	DET
ejpam-5473	207	2	concept	concept	NOUN
ejpam-5473	207	3	of	of	ADP
ejpam-5473	207	4	bvf	bvf	NOUN
ejpam-5473	207	5	-	-	PUNCT
ejpam-5473	207	6	space	space	NOUN
ejpam-5473	207	7	is	be	AUX
ejpam-5473	207	8	a	a	DET
ejpam-5473	207	9	replacement	replacement	NOUN
ejpam-5473	207	10	of	of	ADP
ejpam-5473	207	11	universal	universal	ADJ
ejpam-5473	207	12	set	set	NOUN
ejpam-5473	207	13	(	(	PUNCT
ejpam-5473	207	14	f	f	NOUN
ejpam-5473	207	15	-	-	PUNCT
ejpam-5473	207	16	space	space	NOUN
ejpam-5473	207	17	)	)	PUNCT
ejpam-5473	207	18	in	in	ADP
ejpam-5473	207	19	classical	classical	ADJ
ejpam-5473	207	20	mathematics	mathematic	NOUN
ejpam-5473	207	21	(	(	PUNCT
ejpam-5473	207	22	fuzzy	fuzzy	ADJ
ejpam-5473	207	23	mathematics	mathematic	NOUN
ejpam-5473	207	24	)	)	PUNCT
ejpam-5473	207	25	.	.	PUNCT
ejpam-5473	208	1	moreover	moreover	ADV
ejpam-5473	208	2	,	,	PUNCT
ejpam-5473	208	3	bvf	bvf	NOUN
ejpam-5473	208	4	-	-	PUNCT
ejpam-5473	208	5	space	space	NOUN
ejpam-5473	208	6	is	be	AUX
ejpam-5473	208	7	considered	consider	VERB
ejpam-5473	208	8	a	a	DET
ejpam-5473	208	9	cornerstone	cornerstone	NOUN
ejpam-5473	208	10	for	for	ADP
ejpam-5473	208	11	the	the	DET
ejpam-5473	208	12	theory	theory	NOUN
ejpam-5473	208	13	of	of	ADP
ejpam-5473	208	14	bipolar	bipolar	ADJ
ejpam-5473	208	15	valued	value	VERB
ejpam-5473	208	16	fuzzy	fuzzy	ADJ
ejpam-5473	208	17	algebra	algebra	NOUN
ejpam-5473	208	18	.	.	PUNCT
ejpam-5473	209	1	definition	definition	NOUN
ejpam-5473	209	2	19	19	NUM
ejpam-5473	209	3	.	.	PUNCT
ejpam-5473	210	1	let	let	VERB
ejpam-5473	210	2	℧	℧	PRON
ejpam-5473	210	3	be	be	AUX
ejpam-5473	210	4	a	a	DET
ejpam-5473	210	5	nonempty	nonempty	ADV
ejpam-5473	210	6	set	set	VERB
ejpam-5473	210	7	.	.	PUNCT
ejpam-5473	211	1	a	a	DET
ejpam-5473	211	2	bvf	bvf	NOUN
ejpam-5473	211	3	-	-	PUNCT
ejpam-5473	211	4	space	space	NOUN
ejpam-5473	211	5	denoted	denote	VERB
ejpam-5473	211	6	by	by	ADP
ejpam-5473	211	7	(	(	PUNCT
ejpam-5473	211	8	℧	℧	PROPN
ejpam-5473	211	9	,	,	PUNCT
ejpam-5473	211	10	[	[	X
ejpam-5473	211	11	−1	−1	NOUN
ejpam-5473	211	12	,	,	PUNCT
ejpam-5473	211	13	0	0	NUM
ejpam-5473	211	14	]	]	PUNCT
ejpam-5473	211	15	,	,	PUNCT
ejpam-5473	211	16	[	[	X
ejpam-5473	211	17	0	0	NUM
ejpam-5473	211	18	,	,	PUNCT
ejpam-5473	211	19	1	1	NUM
ejpam-5473	211	20	]	]	PUNCT
ejpam-5473	211	21	)	)	PUNCT
ejpam-5473	211	22	is	be	AUX
ejpam-5473	211	23	a	a	DET
ejpam-5473	211	24	set	set	NOUN
ejpam-5473	211	25	of	of	ADP
ejpam-5473	211	26	all	all	DET
ejpam-5473	211	27	triple	triple	ADJ
ejpam-5473	211	28	elements	element	NOUN
ejpam-5473	211	29	on	on	ADP
ejpam-5473	211	30	the	the	DET
ejpam-5473	211	31	form	form	NOUN
ejpam-5473	211	32	(	(	PUNCT
ejpam-5473	211	33	x	x	X
ejpam-5473	211	34	,	,	PUNCT
ejpam-5473	211	35	[	[	X
ejpam-5473	211	36	−1	−1	NOUN
ejpam-5473	211	37	,	,	PUNCT
ejpam-5473	211	38	0	0	NUM
ejpam-5473	211	39	]	]	PUNCT
ejpam-5473	211	40	,	,	PUNCT
ejpam-5473	211	41	[	[	X
ejpam-5473	211	42	0	0	NUM
ejpam-5473	211	43	,	,	PUNCT
ejpam-5473	211	44	1	1	NUM
ejpam-5473	211	45	]	]	NUM
ejpam-5473	211	46	)	)	PUNCT
ejpam-5473	211	47	,	,	PUNCT
ejpam-5473	211	48	where	where	SCONJ
ejpam-5473	211	49	(	(	PUNCT
ejpam-5473	211	50	x	x	X
ejpam-5473	211	51	,	,	PUNCT
ejpam-5473	211	52	[	[	X
ejpam-5473	211	53	−1	−1	NOUN
ejpam-5473	211	54	,	,	PUNCT
ejpam-5473	211	55	0	0	NUM
ejpam-5473	211	56	]	]	PUNCT
ejpam-5473	211	57	,	,	PUNCT
ejpam-5473	211	58	[	[	X
ejpam-5473	211	59	0	0	NUM
ejpam-5473	211	60	,	,	PUNCT
ejpam-5473	211	61	1	1	NUM
ejpam-5473	211	62	]	]	PUNCT
ejpam-5473	211	63	)	)	PUNCT
ejpam-5473	211	64	=	=	SYM
ejpam-5473	211	65	{	{	PUNCT
ejpam-5473	211	66	(	(	PUNCT
ejpam-5473	211	67	x	x	NOUN
ejpam-5473	211	68	,	,	PUNCT
ejpam-5473	211	69	n	n	CCONJ
ejpam-5473	211	70	,	,	PUNCT
ejpam-5473	211	71	m	m	PROPN
ejpam-5473	211	72	)	)	PUNCT
ejpam-5473	211	73	:	:	PUNCT
ejpam-5473	212	1	n	n	X
ejpam-5473	212	2	∈	∈	NOUN
ejpam-5473	213	1	[	[	X
ejpam-5473	213	2	−1	−1	NOUN
ejpam-5473	213	3	,	,	PUNCT
ejpam-5473	213	4	0	0	NUM
ejpam-5473	213	5	]	]	PUNCT
ejpam-5473	213	6	,	,	PUNCT
ejpam-5473	213	7	m	m	VERB
ejpam-5473	213	8	∈	∈	PROPN
ejpam-5473	214	1	[	[	X
ejpam-5473	214	2	0	0	NUM
ejpam-5473	214	3	,	,	PUNCT
ejpam-5473	214	4	1	1	NUM
ejpam-5473	214	5	]	]	PUNCT
ejpam-5473	214	6	,	,	PUNCT
ejpam-5473	214	7	and	and	CCONJ
ejpam-5473	214	8	x	x	X
ejpam-5473	214	9	∈	∈	PROPN
ejpam-5473	214	10	℧	℧	PROPN
ejpam-5473	214	11	}	}	PUNCT
ejpam-5473	214	12	.	.	PUNCT
ejpam-5473	215	1	the	the	DET
ejpam-5473	215	2	element	element	NOUN
ejpam-5473	215	3	(	(	PUNCT
ejpam-5473	215	4	x	x	X
ejpam-5473	215	5	,	,	PUNCT
ejpam-5473	215	6	−i	−i	PROPN
ejpam-5473	215	7	,	,	PUNCT
ejpam-5473	215	8	i	i	PRON
ejpam-5473	215	9	)	)	PUNCT
ejpam-5473	215	10	is	be	AUX
ejpam-5473	215	11	called	call	VERB
ejpam-5473	215	12	a	a	DET
ejpam-5473	215	13	bipolar	bipolar	ADJ
ejpam-5473	215	14	valued	value	VERB
ejpam-5473	215	15	fuzzy	fuzzy	ADJ
ejpam-5473	215	16	element	element	NOUN
ejpam-5473	215	17	(	(	PUNCT
ejpam-5473	215	18	bvf	bvf	NOUN
ejpam-5473	215	19	-	-	PUNCT
ejpam-5473	215	20	element	element	NOUN
ejpam-5473	215	21	)	)	PUNCT
ejpam-5473	215	22	of	of	ADP
ejpam-5473	215	23	the	the	DET
ejpam-5473	215	24	bvf	bvf	NOUN
ejpam-5473	215	25	-	-	PUNCT
ejpam-5473	215	26	space	space	NOUN
ejpam-5473	215	27	(	(	PUNCT
ejpam-5473	215	28	℧	℧	PROPN
ejpam-5473	215	29	,	,	PUNCT
ejpam-5473	215	30	[	[	X
ejpam-5473	215	31	−1	−1	NOUN
ejpam-5473	215	32	,	,	PUNCT
ejpam-5473	215	33	0	0	NUM
ejpam-5473	215	34	]	]	PUNCT
ejpam-5473	215	35	,	,	PUNCT
ejpam-5473	215	36	[	[	X
ejpam-5473	215	37	0	0	NUM
ejpam-5473	215	38	,	,	PUNCT
ejpam-5473	215	39	1	1	NUM
ejpam-5473	215	40	]	]	NUM
ejpam-5473	215	41	)	)	PUNCT
ejpam-5473	215	42	.	.	PUNCT
ejpam-5473	216	1	f.	f.	PROPN
ejpam-5473	216	2	al	al	PROPN
ejpam-5473	216	3	-	-	PROPN
ejpam-5473	216	4	zu’bi	zu’bi	PROPN
ejpam-5473	216	5	et	et	NOUN
ejpam-5473	216	6	al	al	PROPN
ejpam-5473	216	7	.	.	PUNCT
ejpam-5473	216	8	/	/	SYM
ejpam-5473	216	9	eur	eur	PROPN
ejpam-5473	216	10	.	.	PUNCT
ejpam-5473	217	1	j.	j.	PROPN
ejpam-5473	217	2	pure	pure	PROPN
ejpam-5473	217	3	appl	appl	PROPN
ejpam-5473	217	4	.	.	PROPN
ejpam-5473	217	5	math	math	PROPN
ejpam-5473	217	6	,	,	PUNCT
ejpam-5473	217	7	17	17	NUM
ejpam-5473	217	8	(	(	PUNCT
ejpam-5473	217	9	4	4	NUM
ejpam-5473	217	10	)	)	PUNCT
ejpam-5473	217	11	(	(	PUNCT
ejpam-5473	217	12	2024	2024	NUM
ejpam-5473	217	13	)	)	PUNCT
ejpam-5473	217	14	,	,	PUNCT
ejpam-5473	217	15	2898	2898	NUM
ejpam-5473	217	16	-	-	SYM
ejpam-5473	217	17	2914	2914	NUM
ejpam-5473	217	18	2905	2905	NUM
ejpam-5473	217	19	for	for	ADP
ejpam-5473	217	20	elements	element	NOUN
ejpam-5473	217	21	,	,	PUNCT
ejpam-5473	217	22	the	the	DET
ejpam-5473	217	23	first	first	ADJ
ejpam-5473	217	24	component	component	NOUN
ejpam-5473	217	25	represents	represent	VERB
ejpam-5473	217	26	the	the	DET
ejpam-5473	217	27	conventional	conventional	ADJ
ejpam-5473	217	28	element	element	NOUN
ejpam-5473	217	29	,	,	PUNCT
ejpam-5473	217	30	the	the	DET
ejpam-5473	217	31	second	second	ADJ
ejpam-5473	217	32	component	component	NOUN
ejpam-5473	217	33	represents	represent	VERB
ejpam-5473	217	34	the	the	DET
ejpam-5473	217	35	negative	negative	ADJ
ejpam-5473	217	36	and	and	CCONJ
ejpam-5473	217	37	the	the	DET
ejpam-5473	217	38	third	third	ADJ
ejpam-5473	217	39	component	component	NOUN
ejpam-5473	217	40	represents	represent	VERB
ejpam-5473	217	41	the	the	DET
ejpam-5473	217	42	positive	positive	ADJ
ejpam-5473	217	43	membership	membership	NOUN
ejpam-5473	217	44	values	value	NOUN
ejpam-5473	217	45	.	.	PUNCT
ejpam-5473	218	1	support	support	NOUN
ejpam-5473	218	2	of	of	ADP
ejpam-5473	218	3	bvfs	bvfs	PROPN
ejpam-5473	218	4	b	b	PROPN
ejpam-5473	218	5	is	be	AUX
ejpam-5473	218	6	a	a	DET
ejpam-5473	218	7	crisp	crisp	ADJ
ejpam-5473	218	8	set	set	NOUN
ejpam-5473	218	9	b0	b0	NOUN
ejpam-5473	218	10	having	have	VERB
ejpam-5473	218	11	elements	element	NOUN
ejpam-5473	218	12	with	with	ADP
ejpam-5473	218	13	negative	negative	ADJ
ejpam-5473	218	14	and	and	CCONJ
ejpam-5473	218	15	positive	positive	ADJ
ejpam-5473	218	16	values	value	NOUN
ejpam-5473	218	17	less	less	ADJ
ejpam-5473	218	18	than	than	ADP
ejpam-5473	218	19	zero	zero	NUM
ejpam-5473	218	20	and	and	CCONJ
ejpam-5473	218	21	greater	great	ADJ
ejpam-5473	218	22	than	than	ADP
ejpam-5473	218	23	zero	zero	NUM
ejpam-5473	218	24	,	,	PUNCT
ejpam-5473	218	25	respectively	respectively	ADV
ejpam-5473	218	26	.	.	PUNCT
ejpam-5473	219	1	that	that	PRON
ejpam-5473	219	2	is	be	AUX
ejpam-5473	219	3	b0	b0	NOUN
ejpam-5473	219	4	=	=	SYM
ejpam-5473	219	5	{	{	PUNCT
ejpam-5473	219	6	x	x	X
ejpam-5473	219	7	:	:	PUNCT
ejpam-5473	219	8	µ+	µ+	X
ejpam-5473	219	9	(	(	PUNCT
ejpam-5473	219	10	x	x	X
ejpam-5473	219	11	)	)	PUNCT
ejpam-5473	219	12	>	>	X
ejpam-5473	219	13	0	0	PUNCT
ejpam-5473	219	14	and	and	CCONJ
ejpam-5473	219	15	µ−	µ−	PROPN
ejpam-5473	219	16	(	(	PUNCT
ejpam-5473	219	17	x	x	X
ejpam-5473	219	18	)	)	PUNCT
ejpam-5473	219	19	<	<	X
ejpam-5473	219	20	0	0	NUM
ejpam-5473	219	21	}	}	PUNCT
ejpam-5473	219	22	.	.	PUNCT
ejpam-5473	220	1	definition	definition	NOUN
ejpam-5473	220	2	20	20	NUM
ejpam-5473	220	3	.	.	PUNCT
ejpam-5473	221	1	suppose	suppose	VERB
ejpam-5473	221	2	b0	b0	NOUN
ejpam-5473	221	3	is	be	AUX
ejpam-5473	221	4	the	the	DET
ejpam-5473	221	5	support	support	NOUN
ejpam-5473	221	6	of	of	ADP
ejpam-5473	221	7	a	a	DET
ejpam-5473	221	8	specify	specify	ADJ
ejpam-5473	221	9	bipolar	bipolar	ADJ
ejpam-5473	221	10	valued	value	VERB
ejpam-5473	221	11	fuzzy	fuzzy	ADJ
ejpam-5473	221	12	subset	subset	NOUN
ejpam-5473	221	13	(	(	PUNCT
ejpam-5473	221	14	bvfsubset	bvfsubset	NOUN
ejpam-5473	221	15	)	)	PUNCT
ejpam-5473	221	16	b	b	PROPN
ejpam-5473	221	17	of	of	ADP
ejpam-5473	221	18	℧	℧	PROPN
ejpam-5473	221	19	.	.	PUNCT
ejpam-5473	222	1	a	a	DET
ejpam-5473	222	2	bipolar	bipolar	ADJ
ejpam-5473	222	3	valued	value	VERB
ejpam-5473	222	4	fuzzy	fuzzy	ADJ
ejpam-5473	222	5	subspace	subspace	NOUN
ejpam-5473	222	6	(	(	PUNCT
ejpam-5473	222	7	bvf	bvf	NOUN
ejpam-5473	222	8	-	-	PUNCT
ejpam-5473	222	9	subspace	subspace	NOUN
ejpam-5473	222	10	)	)	PUNCT
ejpam-5473	222	11	b	b	NOUN
ejpam-5473	222	12	of	of	ADP
ejpam-5473	222	13	the	the	DET
ejpam-5473	222	14	bvf	bvf	NOUN
ejpam-5473	222	15	-	-	PUNCT
ejpam-5473	222	16	space	space	NOUN
ejpam-5473	222	17	(	(	PUNCT
ejpam-5473	222	18	℧	℧	PROPN
ejpam-5473	222	19	,	,	PUNCT
ejpam-5473	222	20	[	[	X
ejpam-5473	222	21	−1	−1	NOUN
ejpam-5473	222	22	,	,	PUNCT
ejpam-5473	222	23	0	0	NUM
ejpam-5473	222	24	]	]	PUNCT
ejpam-5473	222	25	,	,	PUNCT
ejpam-5473	223	1	[	[	X
ejpam-5473	223	2	0	0	NUM
ejpam-5473	223	3	,	,	PUNCT
ejpam-5473	223	4	1	1	NUM
ejpam-5473	223	5	]	]	PUNCT
ejpam-5473	223	6	)	)	PUNCT
ejpam-5473	223	7	is	be	AUX
ejpam-5473	223	8	the	the	DET
ejpam-5473	223	9	collection	collection	NOUN
ejpam-5473	223	10	of	of	ADP
ejpam-5473	223	11	all	all	DET
ejpam-5473	223	12	elements	element	NOUN
ejpam-5473	223	13	(	(	PUNCT
ejpam-5473	223	14	x	x	X
ejpam-5473	223	15	,	,	PUNCT
ejpam-5473	223	16	b−x	b−x	NOUN
ejpam-5473	223	17	,	,	PUNCT
ejpam-5473	223	18	b+x	b+x	NUM
ejpam-5473	223	19	)	)	PUNCT
ejpam-5473	223	20	,	,	PUNCT
ejpam-5473	223	21	where	where	SCONJ
ejpam-5473	223	22	x	x	PUNCT
ejpam-5473	223	23	∈	∈	PROPN
ejpam-5473	223	24	b0	b0	NOUN
ejpam-5473	223	25	and	and	CCONJ
ejpam-5473	223	26	b−x	b−x	NOUN
ejpam-5473	223	27	,	,	PUNCT
ejpam-5473	223	28	b+x	b+x	NUM
ejpam-5473	223	29	are	be	AUX
ejpam-5473	223	30	subset	subset	VERB
ejpam-5473	223	31	of	of	ADP
ejpam-5473	223	32	[	[	X
ejpam-5473	223	33	−1	−1	NOUN
ejpam-5473	223	34	,	,	PUNCT
ejpam-5473	223	35	0	0	NUM
ejpam-5473	223	36	]	]	PUNCT
ejpam-5473	223	37	and	and	CCONJ
ejpam-5473	223	38	[	[	X
ejpam-5473	223	39	0	0	NUM
ejpam-5473	223	40	,	,	PUNCT
ejpam-5473	223	41	1	1	NUM
ejpam-5473	223	42	]	]	PUNCT
ejpam-5473	223	43	respectively	respectively	ADV
ejpam-5473	223	44	,	,	PUNCT
ejpam-5473	223	45	such	such	ADJ
ejpam-5473	223	46	that	that	SCONJ
ejpam-5473	223	47	b−x	b−x	NOUN
ejpam-5473	223	48	and	and	CCONJ
ejpam-5473	223	49	b+x	b+x	NUM
ejpam-5473	223	50	include	include	VERB
ejpam-5473	223	51	the	the	DET
ejpam-5473	223	52	zero	zero	NUM
ejpam-5473	223	53	element	element	NOUN
ejpam-5473	223	54	with	with	ADP
ejpam-5473	223	55	at	at	ADV
ejpam-5473	223	56	least	least	ADV
ejpam-5473	223	57	one	one	NUM
ejpam-5473	223	58	more	more	ADJ
ejpam-5473	223	59	element	element	NOUN
ejpam-5473	223	60	.	.	PUNCT
ejpam-5473	224	1	if	if	SCONJ
ejpam-5473	224	2	x	x	PROPN
ejpam-5473	224	3	/∈	/∈	PUNCT
ejpam-5473	224	4	b0	b0	NOUN
ejpam-5473	224	5	,	,	PUNCT
ejpam-5473	224	6	then	then	ADV
ejpam-5473	224	7	b−x	b−x	PUNCT
ejpam-5473	224	8	=	=	SYM
ejpam-5473	224	9	0	0	NUM
ejpam-5473	224	10	,	,	PUNCT
ejpam-5473	224	11	b+x	b+x	NUM
ejpam-5473	224	12	=	=	SYM
ejpam-5473	224	13	0	0	X
ejpam-5473	224	14	.	.	PUNCT
ejpam-5473	225	1	the	the	DET
ejpam-5473	225	2	element	element	NOUN
ejpam-5473	225	3	(	(	PUNCT
ejpam-5473	225	4	x	x	X
ejpam-5473	225	5	,	,	PUNCT
ejpam-5473	225	6	b−x	b−x	NOUN
ejpam-5473	225	7	,	,	PUNCT
ejpam-5473	225	8	b+x	b+x	NUM
ejpam-5473	225	9	)	)	PUNCT
ejpam-5473	225	10	is	be	AUX
ejpam-5473	225	11	named	name	VERB
ejpam-5473	225	12	a	a	DET
ejpam-5473	225	13	bvf	bvf	NOUN
ejpam-5473	225	14	-	-	PUNCT
ejpam-5473	225	15	element	element	NOUN
ejpam-5473	225	16	of	of	ADP
ejpam-5473	225	17	the	the	DET
ejpam-5473	225	18	bvf	bvf	NOUN
ejpam-5473	225	19	-	-	PUNCT
ejpam-5473	225	20	subspace	subspace	NOUN
ejpam-5473	225	21	b.	b.	PROPN
ejpam-5473	225	22	also	also	ADV
ejpam-5473	225	23	,	,	PUNCT
ejpam-5473	225	24	the	the	DET
ejpam-5473	225	25	empty	empty	ADJ
ejpam-5473	225	26	bvf	bvf	NOUN
ejpam-5473	225	27	-	-	PUNCT
ejpam-5473	225	28	subspace	subspace	NOUN
ejpam-5473	225	29	indicated	indicate	VERB
ejpam-5473	225	30	by	by	ADP
ejpam-5473	225	31	ϕ	ϕ	NOUN
ejpam-5473	225	32	is	be	AUX
ejpam-5473	225	33	expressed	express	VERB
ejpam-5473	225	34	as	as	ADP
ejpam-5473	225	35	ϕ	ϕ	NOUN
ejpam-5473	225	36	=	=	SYM
ejpam-5473	225	37	{	{	PUNCT
ejpam-5473	225	38	(	(	PUNCT
ejpam-5473	225	39	x	x	X
ejpam-5473	225	40	,	,	PUNCT
ejpam-5473	225	41	ϕ−	ϕ−	PROPN
ejpam-5473	225	42	x	x	X
ejpam-5473	225	43	,	,	PUNCT
ejpam-5473	225	44	ϕ+	ϕ+	NOUN
ejpam-5473	225	45	x	x	X
ejpam-5473	225	46	)	)	PUNCT
ejpam-5473	225	47	:	:	PUNCT
ejpam-5473	225	48	x/∈b0	x/∈b0	PROPN
ejpam-5473	225	49	}	}	PUNCT
ejpam-5473	225	50	.	.	PUNCT
ejpam-5473	226	1	example	example	NOUN
ejpam-5473	226	2	1	1	NUM
ejpam-5473	226	3	.	.	X
ejpam-5473	226	4	consider	consider	VERB
ejpam-5473	226	5	℧	℧	PROPN
ejpam-5473	226	6	is	be	AUX
ejpam-5473	226	7	a	a	DET
ejpam-5473	226	8	bvf	bvf	NOUN
ejpam-5473	226	9	-	-	PUNCT
ejpam-5473	226	10	space	space	NOUN
ejpam-5473	226	11	and	and	CCONJ
ejpam-5473	226	12	suppose	suppose	VERB
ejpam-5473	226	13	b	b	X
ejpam-5473	226	14	=	=	SYM
ejpam-5473	226	15	(	(	PUNCT
ejpam-5473	226	16	b−	b−	PROPN
ejpam-5473	226	17	(	(	PUNCT
ejpam-5473	226	18	x	x	NOUN
ejpam-5473	226	19	)	)	PUNCT
ejpam-5473	226	20	,	,	PUNCT
ejpam-5473	226	21	b+	b+	X
ejpam-5473	226	22	(	(	PUNCT
ejpam-5473	226	23	x	x	NOUN
ejpam-5473	226	24	)	)	PUNCT
ejpam-5473	226	25	)	)	PUNCT
ejpam-5473	226	26	is	be	AUX
ejpam-5473	226	27	a	a	DET
ejpam-5473	226	28	bvfsubset	bvfsubset	NOUN
ejpam-5473	226	29	of	of	ADP
ejpam-5473	226	30	℧	℧	PROPN
ejpam-5473	226	31	.	.	PUNCT
ejpam-5473	227	1	the	the	DET
ejpam-5473	227	2	bvf	bvf	NOUN
ejpam-5473	227	3	-	-	PUNCT
ejpam-5473	227	4	subset	subset	VERB
ejpam-5473	227	5	b	b	NOUN
ejpam-5473	227	6	induces	induce	VERB
ejpam-5473	227	7	some	some	DET
ejpam-5473	227	8	bvf	bvf	NOUN
ejpam-5473	227	9	-	-	PUNCT
ejpam-5473	227	10	subspaces	subspace	NOUN
ejpam-5473	227	11	as	as	SCONJ
ejpam-5473	227	12	follows	follow	VERB
ejpam-5473	227	13	:	:	PUNCT
ejpam-5473	227	14	(	(	PUNCT
ejpam-5473	227	15	i	i	NOUN
ejpam-5473	227	16	)	)	PUNCT
ejpam-5473	227	17	bvf	bvf	NOUN
ejpam-5473	227	18	-	-	PUNCT
ejpam-5473	227	19	subspace	subspace	NOUN
ejpam-5473	227	20	induced	induce	VERB
ejpam-5473	227	21	by	by	ADP
ejpam-5473	227	22	b	b	PROPN
ejpam-5473	227	23	(	(	PUNCT
ejpam-5473	227	24	lower	low	ADJ
ejpam-5473	227	25	form	form	NOUN
ejpam-5473	227	26	):	):	PUNCT
ejpam-5473	227	27	sl	sl	INTJ
ejpam-5473	227	28	(	(	PUNCT
ejpam-5473	227	29	b	b	NOUN
ejpam-5473	227	30	)	)	PUNCT
ejpam-5473	227	31	=	=	NOUN
ejpam-5473	227	32	{	{	PUNCT
ejpam-5473	227	33	(	(	PUNCT
ejpam-5473	227	34	x	x	NOUN
ejpam-5473	227	35	,	,	PUNCT
ejpam-5473	227	36	[	[	PUNCT
ejpam-5473	227	37	b−	b−	NOUN
ejpam-5473	227	38	(	(	PUNCT
ejpam-5473	227	39	x	x	NOUN
ejpam-5473	227	40	)	)	PUNCT
ejpam-5473	227	41	,	,	PUNCT
ejpam-5473	227	42	0	0	NUM
ejpam-5473	227	43	]	]	PUNCT
ejpam-5473	227	44	,	,	PUNCT
ejpam-5473	227	45	[	[	PUNCT
ejpam-5473	227	46	0	0	NUM
ejpam-5473	227	47	,	,	PUNCT
ejpam-5473	227	48	b+	b+	X
ejpam-5473	227	49	(	(	PUNCT
ejpam-5473	227	50	x	x	X
ejpam-5473	227	51	)	)	PUNCT
ejpam-5473	227	52	]	]	PUNCT
ejpam-5473	227	53	)	)	PUNCT
ejpam-5473	227	54	:	:	PUNCT
ejpam-5473	227	55	x	x	X
ejpam-5473	227	56	∈	∈	PROPN
ejpam-5473	227	57	b0	b0	NOUN
ejpam-5473	227	58	}	}	PUNCT
ejpam-5473	227	59	(	(	PUNCT
ejpam-5473	227	60	ii	ii	NOUN
ejpam-5473	227	61	)	)	PUNCT
ejpam-5473	227	62	bvf	bvf	NOUN
ejpam-5473	227	63	-	-	PUNCT
ejpam-5473	227	64	subspace	subspace	NOUN
ejpam-5473	227	65	induced	induce	VERB
ejpam-5473	227	66	by	by	ADP
ejpam-5473	227	67	b	b	PROPN
ejpam-5473	227	68	(	(	PUNCT
ejpam-5473	227	69	upper	upper	ADJ
ejpam-5473	227	70	form	form	NOUN
ejpam-5473	227	71	)	)	PUNCT
ejpam-5473	227	72	su	su	PROPN
ejpam-5473	228	1	(	(	PUNCT
ejpam-5473	228	2	b	b	X
ejpam-5473	228	3	)	)	PUNCT
ejpam-5473	228	4	=	=	NOUN
ejpam-5473	228	5	{	{	PUNCT
ejpam-5473	228	6	(	(	PUNCT
ejpam-5473	228	7	x	x	X
ejpam-5473	228	8	,	,	PUNCT
ejpam-5473	228	9	[	[	X
ejpam-5473	228	10	−1	−1	NOUN
ejpam-5473	228	11	,	,	PUNCT
ejpam-5473	228	12	b−	b−	PROPN
ejpam-5473	228	13	(	(	PUNCT
ejpam-5473	228	14	x	x	NOUN
ejpam-5473	228	15	)	)	PUNCT
ejpam-5473	228	16	]	]	PUNCT
ejpam-5473	228	17	∪	∪	X
ejpam-5473	228	18	{	{	PUNCT
ejpam-5473	228	19	0	0	NUM
ejpam-5473	228	20	}	}	PUNCT
ejpam-5473	228	21	,	,	PUNCT
ejpam-5473	228	22	{	{	PUNCT
ejpam-5473	228	23	0	0	NUM
ejpam-5473	228	24	}	}	PUNCT
ejpam-5473	228	25	∪	∪	X
ejpam-5473	228	26	[	[	PUNCT
ejpam-5473	228	27	b+	b+	X
ejpam-5473	228	28	(	(	PUNCT
ejpam-5473	228	29	x	x	X
ejpam-5473	228	30	)	)	PUNCT
ejpam-5473	228	31	,	,	PUNCT
ejpam-5473	228	32	1	1	NUM
ejpam-5473	228	33	]	]	PUNCT
ejpam-5473	228	34	)	)	PUNCT
ejpam-5473	228	35	:	:	PUNCT
ejpam-5473	229	1	x	x	X
ejpam-5473	229	2	∈	∈	PROPN
ejpam-5473	229	3	b0	b0	NOUN
ejpam-5473	229	4	}	}	PUNCT
ejpam-5473	229	5	(	(	PUNCT
ejpam-5473	229	6	iii	iii	X
ejpam-5473	229	7	)	)	PUNCT
ejpam-5473	229	8	bvf	bvf	NOUN
ejpam-5473	229	9	-	-	PUNCT
ejpam-5473	229	10	subspace	subspace	NOUN
ejpam-5473	229	11	induced	induce	VERB
ejpam-5473	229	12	by	by	ADP
ejpam-5473	229	13	b	b	PROPN
ejpam-5473	229	14	(	(	PUNCT
ejpam-5473	229	15	finite	finite	PROPN
ejpam-5473	229	16	form	form	NOUN
ejpam-5473	229	17	):	):	PUNCT
ejpam-5473	229	18	s0	s0	PROPN
ejpam-5473	229	19	(	(	PUNCT
ejpam-5473	229	20	b	b	NOUN
ejpam-5473	229	21	)	)	PUNCT
ejpam-5473	229	22	=	=	NOUN
ejpam-5473	229	23	{	{	PUNCT
ejpam-5473	229	24	(	(	PUNCT
ejpam-5473	229	25	x	x	X
ejpam-5473	229	26	,	,	PUNCT
ejpam-5473	229	27	{	{	PUNCT
ejpam-5473	229	28	b−	b−	NOUN
ejpam-5473	229	29	(	(	PUNCT
ejpam-5473	229	30	x	x	NOUN
ejpam-5473	229	31	)	)	PUNCT
ejpam-5473	229	32	,	,	PUNCT
ejpam-5473	229	33	0	0	NUM
ejpam-5473	229	34	}	}	PUNCT
ejpam-5473	229	35	,	,	PUNCT
ejpam-5473	229	36	{	{	PUNCT
ejpam-5473	229	37	0	0	NUM
ejpam-5473	229	38	,	,	PUNCT
ejpam-5473	229	39	b+	b+	X
ejpam-5473	229	40	(	(	PUNCT
ejpam-5473	229	41	x	x	X
ejpam-5473	229	42	)	)	PUNCT
ejpam-5473	229	43	}	}	PUNCT
ejpam-5473	229	44	)	)	PUNCT
ejpam-5473	229	45	:	:	PUNCT
ejpam-5473	229	46	x	x	X
ejpam-5473	229	47	∈	∈	PROPN
ejpam-5473	229	48	b0	b0	NOUN
ejpam-5473	229	49	}	}	PUNCT
ejpam-5473	229	50	.	.	PUNCT
ejpam-5473	230	1	definition	definition	NOUN
ejpam-5473	230	2	21	21	NUM
ejpam-5473	230	3	.	.	PUNCT
ejpam-5473	231	1	let	let	VERB
ejpam-5473	231	2	b	b	NOUN
ejpam-5473	231	3	=	=	PRON
ejpam-5473	231	4	{	{	PUNCT
ejpam-5473	231	5	(	(	PUNCT
ejpam-5473	231	6	x	x	X
ejpam-5473	231	7	,	,	PUNCT
ejpam-5473	231	8	b−x	b−x	NOUN
ejpam-5473	231	9	,	,	PUNCT
ejpam-5473	231	10	b+x	b+x	NUM
ejpam-5473	231	11	)	)	PUNCT
ejpam-5473	231	12	:	:	PUNCT
ejpam-5473	232	1	x	x	X
ejpam-5473	232	2	∈	∈	X
ejpam-5473	232	3	b0	b0	NOUN
ejpam-5473	232	4	}	}	PUNCT
ejpam-5473	232	5	,	,	PUNCT
ejpam-5473	232	6	and	and	CCONJ
ejpam-5473	232	7	c	c	X
ejpam-5473	232	8	=	=	SYM
ejpam-5473	232	9	{	{	PUNCT
ejpam-5473	232	10	(	(	PUNCT
ejpam-5473	232	11	x	x	NOUN
ejpam-5473	232	12	,	,	PUNCT
ejpam-5473	232	13	c−x	c−x	NOUN
ejpam-5473	232	14	,	,	PUNCT
ejpam-5473	232	15	c+x	c+x	PROPN
ejpam-5473	232	16	)	)	PUNCT
ejpam-5473	232	17	:	:	PUNCT
ejpam-5473	232	18	x	x	X
ejpam-5473	232	19	∈	∈	NOUN
ejpam-5473	232	20	c0}be	c0}be	NOUN
ejpam-5473	232	21	two	two	NUM
ejpam-5473	232	22	bvf	bvf	NOUN
ejpam-5473	232	23	-	-	PUNCT
ejpam-5473	232	24	subspace	subspace	NOUN
ejpam-5473	232	25	of	of	ADP
ejpam-5473	232	26	a	a	DET
ejpam-5473	232	27	bvf	bvf	NOUN
ejpam-5473	232	28	-	-	PUNCT
ejpam-5473	232	29	space	space	NOUN
ejpam-5473	232	30	℧	℧	NOUN
ejpam-5473	232	31	.	.	PUNCT
ejpam-5473	233	1	the	the	DET
ejpam-5473	233	2	union	union	PROPN
ejpam-5473	233	3	b	b	PROPN
ejpam-5473	233	4	∪c	∪c	PROPN
ejpam-5473	233	5	and	and	CCONJ
ejpam-5473	233	6	the	the	DET
ejpam-5473	233	7	intersection	intersection	NOUN
ejpam-5473	233	8	b	b	NOUN
ejpam-5473	233	9	∩c	∩c	NOUN
ejpam-5473	233	10	are	be	AUX
ejpam-5473	233	11	given	give	VERB
ejpam-5473	233	12	respectively	respectively	ADV
ejpam-5473	233	13	by	by	ADP
ejpam-5473	233	14	:	:	PUNCT
ejpam-5473	233	15	b	b	X
ejpam-5473	233	16	∪	∪	X
ejpam-5473	233	17	c	c	NOUN
ejpam-5473	233	18	=	=	SYM
ejpam-5473	233	19	{	{	PUNCT
ejpam-5473	233	20	(	(	PUNCT
ejpam-5473	233	21	x	x	X
ejpam-5473	233	22	,	,	PUNCT
ejpam-5473	233	23	b−x	b−x	NOUN
ejpam-5473	233	24	∩	∩	X
ejpam-5473	233	25	c−x	c−x	NOUN
ejpam-5473	233	26	,	,	PUNCT
ejpam-5473	233	27	b	b	NOUN
ejpam-5473	233	28	+	+	CCONJ
ejpam-5473	233	29	x	x	SYM
ejpam-5473	233	30	∪	∪	PROPN
ejpam-5473	233	31	c+x	c+x	PROPN
ejpam-5473	233	32	)	)	PUNCT
ejpam-5473	233	33	:	:	PUNCT
ejpam-5473	233	34	x	x	X
ejpam-5473	233	35	∈	∈	PROPN
ejpam-5473	233	36	b0	b0	NOUN
ejpam-5473	233	37	∪	∪	ADJ
ejpam-5473	233	38	c0	c0	NOUN
ejpam-5473	233	39	}	}	PUNCT
ejpam-5473	233	40	,	,	PUNCT
ejpam-5473	233	41	b	b	PROPN
ejpam-5473	233	42	∩	∩	X
ejpam-5473	233	43	c	c	NOUN
ejpam-5473	233	44	=	=	SYM
ejpam-5473	233	45	{	{	PUNCT
ejpam-5473	233	46	(	(	PUNCT
ejpam-5473	233	47	x	x	INTJ
ejpam-5473	233	48	,	,	PUNCT
ejpam-5473	233	49	b−x	b−x	NOUN
ejpam-5473	233	50	∪	∪	ADP
ejpam-5473	233	51	c−x	c−x	NOUN
ejpam-5473	233	52	,	,	PUNCT
ejpam-5473	233	53	b	b	NOUN
ejpam-5473	233	54	+	+	CCONJ
ejpam-5473	233	55	x	x	NOUN
ejpam-5473	233	56	∩	∩	NOUN
ejpam-5473	233	57	c+x	c+x	PROPN
ejpam-5473	233	58	)	)	PUNCT
ejpam-5473	233	59	:	:	PUNCT
ejpam-5473	233	60	x	x	X
ejpam-5473	233	61	∈	∈	PROPN
ejpam-5473	233	62	b0	b0	NOUN
ejpam-5473	233	63	∩	∩	ADJ
ejpam-5473	233	64	c0	c0	NOUN
ejpam-5473	233	65	}	}	PUNCT
ejpam-5473	233	66	.	.	PUNCT
ejpam-5473	234	1	clearly	clearly	ADV
ejpam-5473	234	2	,	,	PUNCT
ejpam-5473	234	3	the	the	DET
ejpam-5473	234	4	union	union	NOUN
ejpam-5473	234	5	and	and	CCONJ
ejpam-5473	234	6	intersection	intersection	NOUN
ejpam-5473	234	7	of	of	ADP
ejpam-5473	234	8	any	any	DET
ejpam-5473	234	9	two	two	NUM
ejpam-5473	234	10	bvf	bvf	NOUN
ejpam-5473	234	11	-	-	PUNCT
ejpam-5473	234	12	subspaces	subspace	NOUN
ejpam-5473	234	13	of	of	ADP
ejpam-5473	234	14	bvf	bvf	NOUN
ejpam-5473	234	15	-	-	PUNCT
ejpam-5473	234	16	space	space	NOUN
ejpam-5473	234	17	℧	℧	NOUN
ejpam-5473	234	18	is	be	AUX
ejpam-5473	234	19	indeed	indeed	ADV
ejpam-5473	234	20	a	a	DET
ejpam-5473	234	21	bvf	bvf	NOUN
ejpam-5473	234	22	-	-	PUNCT
ejpam-5473	234	23	subspace	subspace	NOUN
ejpam-5473	234	24	of	of	ADP
ejpam-5473	234	25	the	the	DET
ejpam-5473	234	26	bvf	bvf	NOUN
ejpam-5473	234	27	-	-	PUNCT
ejpam-5473	234	28	space	space	NOUN
ejpam-5473	234	29	℧	℧	PROPN
ejpam-5473	234	30	.	.	PROPN
ejpam-5473	234	31	example	example	NOUN
ejpam-5473	235	1	2	2	NUM
ejpam-5473	235	2	.	.	PUNCT
ejpam-5473	236	1	let	let	VERB
ejpam-5473	236	2	b	b	NOUN
ejpam-5473	236	3	=	=	PRON
ejpam-5473	236	4	{	{	PUNCT
ejpam-5473	236	5	(	(	PUNCT
ejpam-5473	236	6	x1	x1	PROPN
ejpam-5473	236	7	,	,	PUNCT
ejpam-5473	236	8	−0.3	−0.3	PROPN
ejpam-5473	236	9	,	,	PUNCT
ejpam-5473	236	10	0.6	0.6	NUM
ejpam-5473	236	11	)	)	PUNCT
ejpam-5473	236	12	,	,	PUNCT
ejpam-5473	236	13	(	(	PUNCT
ejpam-5473	236	14	x2	x2	INTJ
ejpam-5473	236	15	,	,	PUNCT
ejpam-5473	236	16	−0.8	−0.8	PROPN
ejpam-5473	236	17	,	,	PUNCT
ejpam-5473	236	18	0.2	0.2	NUM
ejpam-5473	236	19	)	)	PUNCT
ejpam-5473	236	20	:	:	PUNCT
ejpam-5473	237	1	x	x	X
ejpam-5473	237	2	∈	∈	X
ejpam-5473	237	3	b0	b0	NOUN
ejpam-5473	237	4	}	}	PUNCT
ejpam-5473	237	5	,	,	PUNCT
ejpam-5473	237	6	and	and	CCONJ
ejpam-5473	237	7	c	c	X
ejpam-5473	237	8	=	=	SYM
ejpam-5473	237	9	{	{	PUNCT
ejpam-5473	237	10	(	(	PUNCT
ejpam-5473	237	11	x1	x1	PROPN
ejpam-5473	237	12	,	,	PUNCT
ejpam-5473	237	13	−0.5	−0.5	PROPN
ejpam-5473	237	14	,	,	PUNCT
ejpam-5473	237	15	0.9	0.9	NUM
ejpam-5473	237	16	)	)	PUNCT
ejpam-5473	237	17	,	,	PUNCT
ejpam-5473	237	18	(	(	PUNCT
ejpam-5473	237	19	x2	x2	INTJ
ejpam-5473	237	20	,	,	PUNCT
ejpam-5473	237	21	−0.1	−0.1	PROPN
ejpam-5473	237	22	,	,	PUNCT
ejpam-5473	237	23	0.5	0.5	NUM
ejpam-5473	237	24	)	)	PUNCT
ejpam-5473	237	25	:	:	PUNCT
ejpam-5473	237	26	x	x	X
ejpam-5473	237	27	∈	∈	PROPN
ejpam-5473	237	28	c0	c0	NOUN
ejpam-5473	237	29	}	}	PUNCT
ejpam-5473	237	30	be	be	VERB
ejpam-5473	237	31	two	two	NUM
ejpam-5473	237	32	bvf	bvf	NOUN
ejpam-5473	237	33	-	-	PUNCT
ejpam-5473	237	34	subspace	subspace	NOUN
ejpam-5473	237	35	of	of	ADP
ejpam-5473	237	36	a	a	DET
ejpam-5473	237	37	bvf	bvf	NOUN
ejpam-5473	237	38	-	-	PUNCT
ejpam-5473	237	39	space	space	NOUN
ejpam-5473	237	40	℧	℧	NOUN
ejpam-5473	237	41	.	.	PUNCT
ejpam-5473	238	1	the	the	DET
ejpam-5473	238	2	union	union	PROPN
ejpam-5473	238	3	b	b	PROPN
ejpam-5473	238	4	∪	∪	VERB
ejpam-5473	238	5	c	c	NOUN
ejpam-5473	238	6	and	and	CCONJ
ejpam-5473	238	7	the	the	DET
ejpam-5473	238	8	intersection	intersection	NOUN
ejpam-5473	238	9	b	b	PROPN
ejpam-5473	238	10	∩	∩	PROPN
ejpam-5473	238	11	c	c	PROPN
ejpam-5473	238	12	are	be	AUX
ejpam-5473	238	13	calculated	calculate	VERB
ejpam-5473	238	14	,	,	PUNCT
ejpam-5473	238	15	respectively	respectively	ADV
ejpam-5473	238	16	as	as	ADP
ejpam-5473	238	17	:	:	PUNCT
ejpam-5473	238	18	b	b	X
ejpam-5473	238	19	∪	∪	X
ejpam-5473	238	20	c	c	NOUN
ejpam-5473	238	21	=	=	SYM
ejpam-5473	238	22	{	{	PUNCT
ejpam-5473	238	23	(	(	PUNCT
ejpam-5473	238	24	x1	x1	PROPN
ejpam-5473	238	25	,	,	PUNCT
ejpam-5473	238	26	−0.5	−0.5	PROPN
ejpam-5473	238	27	,	,	PUNCT
ejpam-5473	238	28	0.9	0.9	NUM
ejpam-5473	238	29	)	)	PUNCT
ejpam-5473	238	30	,	,	PUNCT
ejpam-5473	238	31	(	(	PUNCT
ejpam-5473	238	32	x2	x2	INTJ
ejpam-5473	238	33	,	,	PUNCT
ejpam-5473	238	34	−0.8	−0.8	PROPN
ejpam-5473	238	35	,	,	PUNCT
ejpam-5473	238	36	0.5	0.5	NUM
ejpam-5473	238	37	)	)	PUNCT
ejpam-5473	238	38	:	:	PUNCT
ejpam-5473	239	1	x	x	X
ejpam-5473	239	2	∈	∈	PROPN
ejpam-5473	239	3	b0	b0	NOUN
ejpam-5473	239	4	∪	∪	ADJ
ejpam-5473	239	5	c0	c0	NOUN
ejpam-5473	239	6	}	}	PUNCT
ejpam-5473	239	7	,	,	PUNCT
ejpam-5473	239	8	b	b	PROPN
ejpam-5473	239	9	∩	∩	X
ejpam-5473	239	10	c	c	NOUN
ejpam-5473	239	11	=	=	SYM
ejpam-5473	239	12	{	{	PUNCT
ejpam-5473	239	13	(	(	PUNCT
ejpam-5473	239	14	x1	x1	PROPN
ejpam-5473	239	15	,	,	PUNCT
ejpam-5473	239	16	−0.3	−0.3	PROPN
ejpam-5473	239	17	,	,	PUNCT
ejpam-5473	239	18	0.6	0.6	NUM
ejpam-5473	239	19	)	)	PUNCT
ejpam-5473	239	20	,	,	PUNCT
ejpam-5473	239	21	(	(	PUNCT
ejpam-5473	239	22	x2	x2	INTJ
ejpam-5473	239	23	,	,	PUNCT
ejpam-5473	239	24	−0.1	−0.1	PROPN
ejpam-5473	239	25	,	,	PUNCT
ejpam-5473	239	26	0.2	0.2	NUM
ejpam-5473	239	27	)	)	PUNCT
ejpam-5473	239	28	:	:	PUNCT
ejpam-5473	239	29	x	x	X
ejpam-5473	239	30	∈	∈	PROPN
ejpam-5473	239	31	b0	b0	NOUN
ejpam-5473	239	32	∩	∩	ADJ
ejpam-5473	239	33	c0	c0	NOUN
ejpam-5473	239	34	}	}	PUNCT
ejpam-5473	239	35	.	.	PUNCT
ejpam-5473	240	1	f.	f.	PROPN
ejpam-5473	240	2	al	al	PROPN
ejpam-5473	240	3	-	-	PROPN
ejpam-5473	240	4	zu’bi	zu’bi	PROPN
ejpam-5473	240	5	et	et	NOUN
ejpam-5473	240	6	al	al	PROPN
ejpam-5473	240	7	.	.	PUNCT
ejpam-5473	240	8	/	/	SYM
ejpam-5473	240	9	eur	eur	PROPN
ejpam-5473	240	10	.	.	PUNCT
ejpam-5473	241	1	j.	j.	PROPN
ejpam-5473	241	2	pure	pure	PROPN
ejpam-5473	241	3	appl	appl	PROPN
ejpam-5473	241	4	.	.	PROPN
ejpam-5473	241	5	math	math	PROPN
ejpam-5473	241	6	,	,	PUNCT
ejpam-5473	241	7	17	17	NUM
ejpam-5473	241	8	(	(	PUNCT
ejpam-5473	241	9	4	4	NUM
ejpam-5473	241	10	)	)	PUNCT
ejpam-5473	241	11	(	(	PUNCT
ejpam-5473	241	12	2024	2024	NUM
ejpam-5473	241	13	)	)	PUNCT
ejpam-5473	241	14	,	,	PUNCT
ejpam-5473	241	15	2898	2898	NUM
ejpam-5473	241	16	-	-	SYM
ejpam-5473	241	17	2914	2914	NUM
ejpam-5473	241	18	2906	2906	NUM
ejpam-5473	241	19	4	4	NUM
ejpam-5473	241	20	.	.	PUNCT
ejpam-5473	241	21	discussion	discussion	NOUN
ejpam-5473	241	22	bipolar	bipolar	PROPN
ejpam-5473	241	23	valued	value	VERB
ejpam-5473	241	24	fuzzy	fuzzy	ADJ
ejpam-5473	241	25	group	group	NOUN
ejpam-5473	241	26	the	the	DET
ejpam-5473	241	27	concept	concept	NOUN
ejpam-5473	241	28	of	of	ADP
ejpam-5473	241	29	bvfbo	bvfbo	NOUN
ejpam-5473	241	30	is	be	AUX
ejpam-5473	241	31	established	establish	VERB
ejpam-5473	241	32	.	.	PUNCT
ejpam-5473	242	1	this	this	DET
ejpam-5473	242	2	definition	definition	NOUN
ejpam-5473	242	3	adds	add	VERB
ejpam-5473	242	4	the	the	DET
ejpam-5473	242	5	negative	negative	ADJ
ejpam-5473	242	6	comembership	comembership	NOUN
ejpam-5473	242	7	function	function	NOUN
ejpam-5473	242	8	to	to	ADP
ejpam-5473	242	9	the	the	DET
ejpam-5473	242	10	structure	structure	NOUN
ejpam-5473	242	11	of	of	ADP
ejpam-5473	242	12	fuzzy	fuzzy	ADJ
ejpam-5473	242	13	function	function	NOUN
ejpam-5473	242	14	in	in	ADP
ejpam-5473	242	15	dib	dib	NOUN
ejpam-5473	242	16	approach	approach	NOUN
ejpam-5473	242	17	.	.	PUNCT
ejpam-5473	243	1	definition	definition	NOUN
ejpam-5473	243	2	22	22	NUM
ejpam-5473	243	3	.	.	PUNCT
ejpam-5473	244	1	an	an	DET
ejpam-5473	244	2	bipolar	bipolar	ADJ
ejpam-5473	244	3	valued	value	VERB
ejpam-5473	244	4	fuzzy	fuzzy	ADJ
ejpam-5473	244	5	binary	binary	NOUN
ejpam-5473	244	6	operation	operation	NOUN
ejpam-5473	244	7	f	f	PROPN
ejpam-5473	244	8	on	on	ADP
ejpam-5473	244	9	an	an	DET
ejpam-5473	244	10	bvf	bvf	NOUN
ejpam-5473	244	11	-	-	PUNCT
ejpam-5473	244	12	space	space	NOUN
ejpam-5473	244	13	(	(	PUNCT
ejpam-5473	244	14	℧	℧	PROPN
ejpam-5473	244	15	,	,	PUNCT
ejpam-5473	244	16	[	[	X
ejpam-5473	244	17	−1	−1	NOUN
ejpam-5473	244	18	,	,	PUNCT
ejpam-5473	244	19	0	0	NUM
ejpam-5473	244	20	]	]	PUNCT
ejpam-5473	244	21	,	,	PUNCT
ejpam-5473	244	22	[	[	X
ejpam-5473	244	23	0	0	NUM
ejpam-5473	244	24	,	,	PUNCT
ejpam-5473	244	25	1	1	NUM
ejpam-5473	244	26	]	]	PUNCT
ejpam-5473	244	27	)	)	PUNCT
ejpam-5473	244	28	is	be	AUX
ejpam-5473	244	29	an	an	DET
ejpam-5473	244	30	bipolar	bipolar	ADJ
ejpam-5473	244	31	valued	value	VERB
ejpam-5473	244	32	fuzzy	fuzzy	ADJ
ejpam-5473	244	33	function	function	NOUN
ejpam-5473	244	34	f	f	NOUN
ejpam-5473	244	35	:	:	PUNCT
ejpam-5473	244	36	(	(	PUNCT
ejpam-5473	244	37	℧	℧	PROPN
ejpam-5473	244	38	,	,	PUNCT
ejpam-5473	244	39	[	[	X
ejpam-5473	244	40	−1	−1	NOUN
ejpam-5473	244	41	,	,	PUNCT
ejpam-5473	244	42	0	0	NUM
ejpam-5473	244	43	]	]	PUNCT
ejpam-5473	244	44	,	,	PUNCT
ejpam-5473	244	45	[	[	X
ejpam-5473	244	46	0	0	NUM
ejpam-5473	244	47	,	,	PUNCT
ejpam-5473	244	48	1	1	NUM
ejpam-5473	244	49	]	]	PUNCT
ejpam-5473	244	50	)	)	PUNCT
ejpam-5473	244	51	×	×	NOUN
ejpam-5473	244	52	(	(	PUNCT
ejpam-5473	244	53	℧	℧	PROPN
ejpam-5473	244	54	,	,	PUNCT
ejpam-5473	244	55	[	[	X
ejpam-5473	244	56	−1	−1	NOUN
ejpam-5473	244	57	,	,	PUNCT
ejpam-5473	244	58	0	0	NUM
ejpam-5473	244	59	]	]	PUNCT
ejpam-5473	244	60	,	,	PUNCT
ejpam-5473	244	61	[	[	X
ejpam-5473	244	62	0	0	NUM
ejpam-5473	244	63	,	,	PUNCT
ejpam-5473	244	64	1	1	NUM
ejpam-5473	244	65	]	]	PUNCT
ejpam-5473	244	66	)	)	PUNCT
ejpam-5473	244	67	−→	−→	NOUN
ejpam-5473	244	68	(	(	PUNCT
ejpam-5473	244	69	℧	℧	PROPN
ejpam-5473	244	70	,	,	PUNCT
ejpam-5473	244	71	[	[	X
ejpam-5473	244	72	−1	−1	NOUN
ejpam-5473	244	73	,	,	PUNCT
ejpam-5473	244	74	0	0	NUM
ejpam-5473	244	75	]	]	PUNCT
ejpam-5473	244	76	,	,	PUNCT
ejpam-5473	244	77	[	[	X
ejpam-5473	244	78	0	0	NUM
ejpam-5473	244	79	,	,	PUNCT
ejpam-5473	244	80	1	1	NUM
ejpam-5473	244	81	]	]	PUNCT
ejpam-5473	244	82	)	)	PUNCT
ejpam-5473	244	83	with	with	ADP
ejpam-5473	244	84	negative	negative	ADJ
ejpam-5473	244	85	comembership	comembership	NOUN
ejpam-5473	244	86	functions	function	NOUN
ejpam-5473	244	87	f−	f−	PROPN
ejpam-5473	244	88	xy	xy	PROPN
ejpam-5473	244	89	and	and	CCONJ
ejpam-5473	244	90	positive	positive	ADJ
ejpam-5473	244	91	comembership	comembership	NOUN
ejpam-5473	244	92	functions	function	NOUN
ejpam-5473	244	93	f+	f+	NOUN
ejpam-5473	244	94	xy	xy	PROPN
ejpam-5473	244	95	satisfying	satisfying	NOUN
ejpam-5473	244	96	:	:	PUNCT
ejpam-5473	244	97	(	(	PUNCT
ejpam-5473	244	98	i	i	NOUN
ejpam-5473	244	99	)	)	PUNCT
ejpam-5473	245	1	f−	f−	PROPN
ejpam-5473	245	2	xy	xy	PROPN
ejpam-5473	245	3	(	(	PUNCT
ejpam-5473	245	4	n−	n−	PROPN
ejpam-5473	245	5	,	,	PUNCT
ejpam-5473	245	6	m−	m−	PROPN
ejpam-5473	245	7	)	)	PUNCT
ejpam-5473	245	8	̸=	̸=	PROPN
ejpam-5473	245	9	0	0	NUM
ejpam-5473	246	1	iff	iff	PROPN
ejpam-5473	246	2	n−	n−	NOUN
ejpam-5473	246	3	̸=	̸=	PROPN
ejpam-5473	246	4	0	0	NUM
ejpam-5473	246	5	,	,	PUNCT
ejpam-5473	246	6	m−	m−	PROPN
ejpam-5473	246	7	̸=	̸=	PROPN
ejpam-5473	246	8	0	0	NUM
ejpam-5473	246	9	,	,	PUNCT
ejpam-5473	246	10	f−	f−	PROPN
ejpam-5473	246	11	xy	xy	PROPN
ejpam-5473	246	12	(	(	PUNCT
ejpam-5473	246	13	w−	w−	PROPN
ejpam-5473	246	14	,	,	PUNCT
ejpam-5473	246	15	z−	z−	PROPN
ejpam-5473	246	16	)	)	PUNCT
ejpam-5473	246	17	̸=	̸=	PROPN
ejpam-5473	246	18	−1	−1	NOUN
ejpam-5473	246	19	iff	iff	PROPN
ejpam-5473	246	20	w−	w−	PROPN
ejpam-5473	246	21	̸=	̸=	PROPN
ejpam-5473	246	22	−1	−1	NOUN
ejpam-5473	246	23	,	,	PUNCT
ejpam-5473	246	24	z−	z−	PROPN
ejpam-5473	246	25	̸=	̸=	PROPN
ejpam-5473	246	26	−1	−1	NOUN
ejpam-5473	246	27	and	and	CCONJ
ejpam-5473	246	28	f+	f+	PROPN
ejpam-5473	246	29	xy	xy	PROPN
ejpam-5473	246	30	(	(	PUNCT
ejpam-5473	246	31	n+	n+	X
ejpam-5473	246	32	,	,	PUNCT
ejpam-5473	246	33	m+	m+	NUM
ejpam-5473	246	34	)	)	PUNCT
ejpam-5473	246	35	̸=	̸=	PROPN
ejpam-5473	246	36	0	0	NUM
ejpam-5473	246	37	iff	iff	PROPN
ejpam-5473	246	38	n+	n+	PUNCT
ejpam-5473	246	39	̸=	̸=	PROPN
ejpam-5473	246	40	0	0	NUM
ejpam-5473	246	41	,	,	PUNCT
ejpam-5473	246	42	m+	m+	NOUN
ejpam-5473	246	43	̸=	̸=	NOUN
ejpam-5473	246	44	0	0	NUM
ejpam-5473	246	45	,	,	PUNCT
ejpam-5473	246	46	and	and	CCONJ
ejpam-5473	246	47	f+	f+	PROPN
ejpam-5473	246	48	xy	xy	PROPN
ejpam-5473	246	49	(	(	PUNCT
ejpam-5473	246	50	w+	w+	X
ejpam-5473	246	51	,	,	PUNCT
ejpam-5473	246	52	z+	z+	NUM
ejpam-5473	246	53	)	)	PUNCT
ejpam-5473	246	54	̸=	̸=	PROPN
ejpam-5473	246	55	1	1	NUM
ejpam-5473	246	56	iff	iff	PROPN
ejpam-5473	246	57	w+	w+	VERB
ejpam-5473	246	58	̸=	̸=	PROPN
ejpam-5473	246	59	1	1	NUM
ejpam-5473	246	60	,	,	PUNCT
ejpam-5473	246	61	z+	z+	NUM
ejpam-5473	246	62	̸=	̸=	PROPN
ejpam-5473	246	63	1	1	NUM
ejpam-5473	246	64	.	.	PUNCT
ejpam-5473	246	65	(	(	PUNCT
ejpam-5473	246	66	ii	ii	NOUN
ejpam-5473	246	67	)	)	PUNCT
ejpam-5473	246	68	f−	f−	PROPN
ejpam-5473	246	69	xy	xy	PROPN
ejpam-5473	246	70	,	,	PUNCT
ejpam-5473	246	71	f	f	PROPN
ejpam-5473	247	1	+	+	CCONJ
ejpam-5473	247	2	xy	xy	PROPN
ejpam-5473	247	3	are	be	AUX
ejpam-5473	247	4	onto	onto	ADP
ejpam-5473	247	5	.	.	PUNCT
ejpam-5473	248	1	that	that	PRON
ejpam-5473	248	2	is	be	AUX
ejpam-5473	248	3	,	,	PUNCT
ejpam-5473	248	4	f−	f−	PROPN
ejpam-5473	248	5	xy	xy	PROPN
ejpam-5473	249	1	(	(	PUNCT
ejpam-5473	249	2	[	[	X
ejpam-5473	249	3	−1	−1	NOUN
ejpam-5473	249	4	,	,	PUNCT
ejpam-5473	249	5	0]×	0]×	NUM
ejpam-5473	250	1	[	[	X
ejpam-5473	250	2	−1	−1	NOUN
ejpam-5473	250	3	,	,	PUNCT
ejpam-5473	250	4	0	0	NUM
ejpam-5473	250	5	]	]	PUNCT
ejpam-5473	250	6	)	)	PUNCT
ejpam-5473	251	1	=	=	PUNCT
ejpam-5473	252	1	[	[	X
ejpam-5473	252	2	−1	−1	NOUN
ejpam-5473	252	3	,	,	PUNCT
ejpam-5473	252	4	0	0	NUM
ejpam-5473	252	5	]	]	PUNCT
ejpam-5473	252	6	and	and	CCONJ
ejpam-5473	252	7	f+	f+	PROPN
ejpam-5473	252	8	xy	xy	PROPN
ejpam-5473	252	9	(	(	PUNCT
ejpam-5473	252	10	[	[	X
ejpam-5473	252	11	0	0	NUM
ejpam-5473	252	12	,	,	PUNCT
ejpam-5473	252	13	1]×	1]×	NUM
ejpam-5473	253	1	[	[	X
ejpam-5473	253	2	0	0	NUM
ejpam-5473	253	3	,	,	PUNCT
ejpam-5473	253	4	1	1	NUM
ejpam-5473	253	5	]	]	PUNCT
ejpam-5473	253	6	)	)	PUNCT
ejpam-5473	254	1	=	=	PUNCT
ejpam-5473	255	1	[	[	X
ejpam-5473	255	2	0	0	NUM
ejpam-5473	255	3	,	,	PUNCT
ejpam-5473	255	4	1	1	NUM
ejpam-5473	255	5	]	]	PUNCT
ejpam-5473	255	6	.	.	PUNCT
ejpam-5473	256	1	thus	thus	ADV
ejpam-5473	256	2	for	for	ADP
ejpam-5473	256	3	any	any	DET
ejpam-5473	256	4	two	two	NUM
ejpam-5473	256	5	bvf	bvf	NOUN
ejpam-5473	256	6	-	-	PUNCT
ejpam-5473	256	7	elements	element	NOUN
ejpam-5473	256	8	(	(	PUNCT
ejpam-5473	256	9	x	x	X
ejpam-5473	256	10	,	,	PUNCT
ejpam-5473	256	11	[	[	X
ejpam-5473	256	12	−1	−1	NOUN
ejpam-5473	256	13	,	,	PUNCT
ejpam-5473	256	14	0	0	NUM
ejpam-5473	256	15	]	]	PUNCT
ejpam-5473	256	16	,	,	PUNCT
ejpam-5473	256	17	[	[	X
ejpam-5473	256	18	0	0	NUM
ejpam-5473	256	19	,	,	PUNCT
ejpam-5473	256	20	1	1	NUM
ejpam-5473	256	21	]	]	NUM
ejpam-5473	256	22	)	)	PUNCT
ejpam-5473	256	23	,	,	PUNCT
ejpam-5473	256	24	(	(	PUNCT
ejpam-5473	256	25	y	y	NOUN
ejpam-5473	256	26	,	,	PUNCT
ejpam-5473	256	27	[	[	X
ejpam-5473	256	28	−1	−1	NOUN
ejpam-5473	256	29	,	,	PUNCT
ejpam-5473	256	30	0	0	NUM
ejpam-5473	256	31	]	]	PUNCT
ejpam-5473	256	32	,	,	PUNCT
ejpam-5473	256	33	[	[	X
ejpam-5473	256	34	0	0	NUM
ejpam-5473	256	35	,	,	PUNCT
ejpam-5473	256	36	1	1	NUM
ejpam-5473	256	37	]	]	PUNCT
ejpam-5473	256	38	)	)	PUNCT
ejpam-5473	256	39	of	of	ADP
ejpam-5473	256	40	the	the	DET
ejpam-5473	256	41	bvf	bvf	NOUN
ejpam-5473	256	42	-	-	PUNCT
ejpam-5473	256	43	space	space	NOUN
ejpam-5473	256	44	℧	℧	PROPN
ejpam-5473	256	45	and	and	CCONJ
ejpam-5473	256	46	any	any	DET
ejpam-5473	256	47	bvfbo	bvfbo	NOUN
ejpam-5473	256	48	f	f	X
ejpam-5473	256	49	=	=	SYM
ejpam-5473	256	50	(	(	PUNCT
ejpam-5473	256	51	f	f	X
ejpam-5473	256	52	,	,	PUNCT
ejpam-5473	256	53	f−	f−	PROPN
ejpam-5473	256	54	xy	xy	PROPN
ejpam-5473	256	55	,	,	PUNCT
ejpam-5473	256	56	f	f	PROPN
ejpam-5473	256	57	+	+	CCONJ
ejpam-5473	256	58	xy	xy	PROPN
ejpam-5473	256	59	)	)	PUNCT
ejpam-5473	256	60	defined	define	VERB
ejpam-5473	256	61	on	on	ADP
ejpam-5473	256	62	a	a	DET
ejpam-5473	256	63	bvf	bvf	NOUN
ejpam-5473	256	64	-	-	PUNCT
ejpam-5473	256	65	space	space	NOUN
ejpam-5473	256	66	℧	℧	NOUN
ejpam-5473	256	67	,	,	PUNCT
ejpam-5473	256	68	the	the	DET
ejpam-5473	256	69	action	action	NOUN
ejpam-5473	256	70	of	of	ADP
ejpam-5473	256	71	the	the	DET
ejpam-5473	256	72	bvfbo	bvfbo	PRON
ejpam-5473	256	73	f	f	PROPN
ejpam-5473	256	74	=	=	SYM
ejpam-5473	256	75	(	(	PUNCT
ejpam-5473	256	76	f	f	X
ejpam-5473	256	77	,	,	PUNCT
ejpam-5473	256	78	f−	f−	PROPN
ejpam-5473	256	79	xy	xy	PROPN
ejpam-5473	256	80	,	,	PUNCT
ejpam-5473	256	81	f	f	PROPN
ejpam-5473	256	82	+	+	CCONJ
ejpam-5473	256	83	xy	xy	PROPN
ejpam-5473	256	84	)	)	PUNCT
ejpam-5473	256	85	over	over	ADP
ejpam-5473	256	86	the	the	DET
ejpam-5473	256	87	bvf	bvf	NOUN
ejpam-5473	256	88	-	-	PUNCT
ejpam-5473	256	89	space	space	NOUN
ejpam-5473	256	90	℧	℧	PROPN
ejpam-5473	256	91	is	be	AUX
ejpam-5473	256	92	given	give	VERB
ejpam-5473	256	93	by	by	ADP
ejpam-5473	256	94	(	(	PUNCT
ejpam-5473	256	95	x	x	INTJ
ejpam-5473	256	96	,	,	PUNCT
ejpam-5473	256	97	−i	−i	ADJ
ejpam-5473	256	98	,	,	PUNCT
ejpam-5473	256	99	i)f	i)f	ADJ
ejpam-5473	256	100	(	(	PUNCT
ejpam-5473	256	101	y,−	y,−	PROPN
ejpam-5473	256	102	i	i	PRON
ejpam-5473	256	103	,	,	PUNCT
ejpam-5473	256	104	i	i	NOUN
ejpam-5473	256	105	)	)	PUNCT
ejpam-5473	257	1	=	=	SYM
ejpam-5473	257	2	f	f	PROPN
ejpam-5473	257	3	(	(	PUNCT
ejpam-5473	257	4	(	(	PUNCT
ejpam-5473	257	5	x	x	X
ejpam-5473	257	6	,	,	PUNCT
ejpam-5473	257	7	[	[	X
ejpam-5473	257	8	−1	−1	NOUN
ejpam-5473	257	9	,	,	PUNCT
ejpam-5473	257	10	0	0	NUM
ejpam-5473	257	11	]	]	PUNCT
ejpam-5473	257	12	,	,	PUNCT
ejpam-5473	257	13	[	[	X
ejpam-5473	257	14	0	0	NUM
ejpam-5473	257	15	,	,	PUNCT
ejpam-5473	257	16	1	1	NUM
ejpam-5473	257	17	]	]	PUNCT
ejpam-5473	257	18	)	)	PUNCT
ejpam-5473	257	19	,	,	PUNCT
ejpam-5473	257	20	(	(	PUNCT
ejpam-5473	257	21	y	y	NOUN
ejpam-5473	257	22	,	,	PUNCT
ejpam-5473	257	23	[	[	X
ejpam-5473	257	24	−1	−1	NOUN
ejpam-5473	257	25	,	,	PUNCT
ejpam-5473	257	26	0	0	NUM
ejpam-5473	257	27	]	]	PUNCT
ejpam-5473	257	28	,	,	PUNCT
ejpam-5473	257	29	[	[	X
ejpam-5473	257	30	0	0	NUM
ejpam-5473	257	31	,	,	PUNCT
ejpam-5473	257	32	1	1	NUM
ejpam-5473	257	33	]	]	NUM
ejpam-5473	257	34	)	)	PUNCT
ejpam-5473	257	35	)	)	PUNCT
ejpam-5473	258	1	=	=	PRON
ejpam-5473	258	2	(	(	PUNCT
ejpam-5473	258	3	f	f	X
ejpam-5473	258	4	(	(	PUNCT
ejpam-5473	258	5	x	x	PROPN
ejpam-5473	258	6	,	,	PUNCT
ejpam-5473	258	7	y	y	PROPN
ejpam-5473	258	8	)	)	PUNCT
ejpam-5473	258	9	,	,	PUNCT
ejpam-5473	258	10	f−	f−	PROPN
ejpam-5473	258	11	xy	xy	PROPN
ejpam-5473	259	1	(	(	PUNCT
ejpam-5473	259	2	[	[	X
ejpam-5473	259	3	−1	−1	NOUN
ejpam-5473	259	4	,	,	PUNCT
ejpam-5473	259	5	0]×	0]×	NUM
ejpam-5473	260	1	[	[	X
ejpam-5473	260	2	−1	−1	NOUN
ejpam-5473	260	3	,	,	PUNCT
ejpam-5473	260	4	0	0	NUM
ejpam-5473	260	5	]	]	PUNCT
ejpam-5473	260	6	)	)	PUNCT
ejpam-5473	260	7	,	,	PUNCT
ejpam-5473	260	8	f+	f+	PROPN
ejpam-5473	260	9	xy	xy	PROPN
ejpam-5473	260	10	(	(	PUNCT
ejpam-5473	260	11	[	[	X
ejpam-5473	260	12	0	0	NUM
ejpam-5473	260	13	,	,	PUNCT
ejpam-5473	260	14	1]×	1]×	NUM
ejpam-5473	261	1	[	[	X
ejpam-5473	261	2	0	0	NUM
ejpam-5473	261	3	,	,	PUNCT
ejpam-5473	261	4	1	1	NUM
ejpam-5473	261	5	]	]	NUM
ejpam-5473	261	6	)	)	PUNCT
ejpam-5473	261	7	)	)	PUNCT
ejpam-5473	262	1	=	=	PRON
ejpam-5473	262	2	(	(	PUNCT
ejpam-5473	262	3	f	f	X
ejpam-5473	262	4	(	(	PUNCT
ejpam-5473	262	5	x	x	PROPN
ejpam-5473	262	6	,	,	PUNCT
ejpam-5473	262	7	y	y	PROPN
ejpam-5473	262	8	)	)	PUNCT
ejpam-5473	262	9	,	,	PUNCT
ejpam-5473	263	1	[	[	X
ejpam-5473	263	2	−1	−1	NOUN
ejpam-5473	263	3	,	,	PUNCT
ejpam-5473	263	4	0	0	NUM
ejpam-5473	263	5	]	]	PUNCT
ejpam-5473	263	6	,	,	PUNCT
ejpam-5473	264	1	[	[	X
ejpam-5473	264	2	0	0	NUM
ejpam-5473	264	3	,	,	PUNCT
ejpam-5473	264	4	1	1	NUM
ejpam-5473	264	5	]	]	PUNCT
ejpam-5473	264	6	)	)	PUNCT
ejpam-5473	264	7	.	.	PUNCT
ejpam-5473	265	1	example	example	NOUN
ejpam-5473	266	1	3	3	X
ejpam-5473	266	2	.	.	X
ejpam-5473	267	1	let	let	AUX
ejpam-5473	267	2	(	(	PUNCT
ejpam-5473	267	3	q+	q+	ADV
ejpam-5473	267	4	,	,	PUNCT
ejpam-5473	267	5	[	[	X
ejpam-5473	267	6	−1	−1	NOUN
ejpam-5473	267	7	,	,	PUNCT
ejpam-5473	267	8	0	0	NUM
ejpam-5473	267	9	]	]	PUNCT
ejpam-5473	267	10	,	,	PUNCT
ejpam-5473	267	11	[	[	X
ejpam-5473	267	12	0	0	NUM
ejpam-5473	267	13	,	,	PUNCT
ejpam-5473	267	14	1	1	NUM
ejpam-5473	267	15	]	]	PUNCT
ejpam-5473	267	16	)	)	PUNCT
ejpam-5473	267	17	be	be	AUX
ejpam-5473	267	18	bvf	bvf	NOUN
ejpam-5473	267	19	-	-	PUNCT
ejpam-5473	267	20	space	space	NOUN
ejpam-5473	267	21	with	with	ADP
ejpam-5473	267	22	bvfbo	bvfbo	PRON
ejpam-5473	267	23	f	f	PROPN
ejpam-5473	267	24	defined	define	VERB
ejpam-5473	267	25	by	by	ADP
ejpam-5473	267	26	f	f	PROPN
ejpam-5473	267	27	(	(	PUNCT
ejpam-5473	267	28	x	x	PROPN
ejpam-5473	267	29	,	,	PUNCT
ejpam-5473	267	30	y	y	NOUN
ejpam-5473	267	31	)	)	PUNCT
ejpam-5473	267	32	=	=	PUNCT
ejpam-5473	268	1	x	x	X
ejpam-5473	268	2	/	/	SYM
ejpam-5473	268	3	y	y	PROPN
ejpam-5473	268	4	,	,	PUNCT
ejpam-5473	268	5	f−	f−	PROPN
ejpam-5473	268	6	xy	xy	PROPN
ejpam-5473	268	7	(	(	PUNCT
ejpam-5473	268	8	n	n	NUM
ejpam-5473	268	9	−	−	PROPN
ejpam-5473	268	10	,	,	PUNCT
ejpam-5473	268	11	m−	m−	PROPN
ejpam-5473	268	12	)	)	PUNCT
ejpam-5473	269	1	=	=	SYM
ejpam-5473	269	2	min{n−,m−	min{n−,m−	ADJ
ejpam-5473	269	3	}	}	PUNCT
ejpam-5473	269	4	,	,	PUNCT
ejpam-5473	269	5	and	and	CCONJ
ejpam-5473	269	6	f+	f+	PROPN
ejpam-5473	269	7	xy	xy	PROPN
ejpam-5473	269	8	(	(	PUNCT
ejpam-5473	269	9	n	n	X
ejpam-5473	269	10	+	+	ADJ
ejpam-5473	269	11	,	,	PUNCT
ejpam-5473	269	12	m+	m+	NUM
ejpam-5473	269	13	)	)	PUNCT
ejpam-5473	269	14	=	=	PUNCT
ejpam-5473	270	1	max{n+,m+	max{n+,m+	NOUN
ejpam-5473	270	2	}	}	PUNCT
ejpam-5473	270	3	.	.	PUNCT
ejpam-5473	271	1	therefore	therefore	ADV
ejpam-5473	271	2	f	f	PROPN
ejpam-5473	271	3	is	be	AUX
ejpam-5473	271	4	a	a	DET
ejpam-5473	271	5	bvfbo	bvfbo	NOUN
ejpam-5473	271	6	on	on	ADP
ejpam-5473	271	7	a	a	DET
ejpam-5473	271	8	bvf	bvf	NOUN
ejpam-5473	271	9	-	-	PUNCT
ejpam-5473	271	10	space	space	NOUN
ejpam-5473	271	11	(	(	PUNCT
ejpam-5473	271	12	q+	q+	ADV
ejpam-5473	271	13	,	,	PUNCT
ejpam-5473	271	14	[	[	X
ejpam-5473	271	15	−1	−1	NOUN
ejpam-5473	271	16	,	,	PUNCT
ejpam-5473	271	17	0	0	NUM
ejpam-5473	271	18	]	]	PUNCT
ejpam-5473	271	19	,	,	PUNCT
ejpam-5473	271	20	[	[	X
ejpam-5473	271	21	0	0	NUM
ejpam-5473	271	22	,	,	PUNCT
ejpam-5473	271	23	1	1	NUM
ejpam-5473	271	24	]	]	NUM
ejpam-5473	271	25	)	)	PUNCT
ejpam-5473	271	26	.	.	PUNCT
ejpam-5473	272	1	example	example	NOUN
ejpam-5473	273	1	4	4	X
ejpam-5473	273	2	.	.	PUNCT
ejpam-5473	274	1	let	let	VERB
ejpam-5473	274	2	(	(	PUNCT
ejpam-5473	274	3	℧	℧	PROPN
ejpam-5473	274	4	=	=	SYM
ejpam-5473	274	5	{	{	PUNCT
ejpam-5473	274	6	h	h	NOUN
ejpam-5473	274	7	,	,	PUNCT
ejpam-5473	274	8	k	k	NOUN
ejpam-5473	274	9	,	,	PUNCT
ejpam-5473	274	10	l	l	NOUN
ejpam-5473	274	11	}	}	PUNCT
ejpam-5473	274	12	,	,	PUNCT
ejpam-5473	275	1	[	[	X
ejpam-5473	275	2	−1	−1	NOUN
ejpam-5473	275	3	,	,	PUNCT
ejpam-5473	275	4	0	0	NUM
ejpam-5473	275	5	]	]	PUNCT
ejpam-5473	275	6	,	,	PUNCT
ejpam-5473	275	7	[	[	X
ejpam-5473	275	8	0	0	NUM
ejpam-5473	275	9	,	,	PUNCT
ejpam-5473	275	10	1	1	NUM
ejpam-5473	275	11	]	]	PUNCT
ejpam-5473	275	12	)	)	PUNCT
ejpam-5473	275	13	be	be	AUX
ejpam-5473	275	14	bvf	bvf	NOUN
ejpam-5473	275	15	-	-	PUNCT
ejpam-5473	275	16	space	space	NOUN
ejpam-5473	275	17	with	with	ADP
ejpam-5473	275	18	bvfbo	bvfbo	PRON
ejpam-5473	275	19	f	f	PROPN
ejpam-5473	275	20	defined	define	VERB
ejpam-5473	275	21	by	by	ADP
ejpam-5473	275	22	table	table	NOUN
ejpam-5473	275	23	1	1	NUM
ejpam-5473	275	24	.	.	PUNCT
ejpam-5473	275	25	table	table	NOUN
ejpam-5473	275	26	1	1	NUM
ejpam-5473	275	27	:	:	PUNCT
ejpam-5473	275	28	bvfbo	bvfbo	PROPN
ejpam-5473	275	29	f	f	PROPN
ejpam-5473	275	30	defined	define	VERB
ejpam-5473	275	31	on	on	ADP
ejpam-5473	275	32	bvf	bvf	NOUN
ejpam-5473	275	33	-	-	PUNCT
ejpam-5473	275	34	space	space	NOUN
ejpam-5473	275	35	(	(	PUNCT
ejpam-5473	275	36	℧	℧	PROPN
ejpam-5473	275	37	=	=	SYM
ejpam-5473	275	38	{	{	PUNCT
ejpam-5473	275	39	h	h	NOUN
ejpam-5473	275	40	,	,	PUNCT
ejpam-5473	275	41	k	k	NOUN
ejpam-5473	275	42	,	,	PUNCT
ejpam-5473	275	43	l	l	NOUN
ejpam-5473	275	44	}	}	PUNCT
ejpam-5473	275	45	,	,	PUNCT
ejpam-5473	276	1	[	[	X
ejpam-5473	276	2	−1	−1	NOUN
ejpam-5473	276	3	,	,	PUNCT
ejpam-5473	276	4	0	0	NUM
ejpam-5473	276	5	]	]	PUNCT
ejpam-5473	276	6	,	,	PUNCT
ejpam-5473	276	7	[	[	X
ejpam-5473	276	8	0	0	NUM
ejpam-5473	276	9	,	,	PUNCT
ejpam-5473	276	10	1	1	NUM
ejpam-5473	276	11	]	]	PUNCT
ejpam-5473	276	12	)	)	PUNCT
ejpam-5473	276	13	.	.	PUNCT
ejpam-5473	277	1	f	f	X
ejpam-5473	277	2	(	(	PUNCT
ejpam-5473	277	3	(	(	PUNCT
ejpam-5473	277	4	x	x	INTJ
ejpam-5473	277	5	,	,	PUNCT
ejpam-5473	277	6	−i	−i	PROPN
ejpam-5473	277	7	,	,	PUNCT
ejpam-5473	277	8	i	i	PROPN
ejpam-5473	277	9	)	)	PUNCT
ejpam-5473	277	10	,	,	PUNCT
ejpam-5473	277	11	(	(	PUNCT
ejpam-5473	277	12	y	y	NOUN
ejpam-5473	277	13	,	,	PUNCT
ejpam-5473	277	14	−i	−i	PROPN
ejpam-5473	277	15	,	,	PUNCT
ejpam-5473	277	16	i	i	NOUN
ejpam-5473	277	17	)	)	PUNCT
ejpam-5473	277	18	)	)	PUNCT
ejpam-5473	278	1	(	(	PUNCT
ejpam-5473	278	2	h	h	NOUN
ejpam-5473	278	3	,	,	PUNCT
ejpam-5473	278	4	−0.3	−0.3	PROPN
ejpam-5473	278	5	,	,	PUNCT
ejpam-5473	278	6	0.5	0.5	NUM
ejpam-5473	278	7	)	)	PUNCT
ejpam-5473	278	8	(	(	PUNCT
ejpam-5473	278	9	k	k	NOUN
ejpam-5473	278	10	,	,	PUNCT
ejpam-5473	278	11	−1	−1	NOUN
ejpam-5473	278	12	,	,	PUNCT
ejpam-5473	278	13	0.2	0.2	NUM
ejpam-5473	278	14	)	)	PUNCT
ejpam-5473	278	15	(	(	PUNCT
ejpam-5473	278	16	l	l	NOUN
ejpam-5473	278	17	,	,	PUNCT
ejpam-5473	278	18	−0.8	−0.8	ADJ
ejpam-5473	278	19	,	,	PUNCT
ejpam-5473	278	20	1	1	NUM
ejpam-5473	278	21	)	)	PUNCT
ejpam-5473	278	22	(	(	PUNCT
ejpam-5473	278	23	h	h	NOUN
ejpam-5473	278	24	,	,	PUNCT
ejpam-5473	278	25	−0.3	−0.3	PROPN
ejpam-5473	278	26	,	,	PUNCT
ejpam-5473	278	27	0.5	0.5	NUM
ejpam-5473	278	28	)	)	PUNCT
ejpam-5473	278	29	(	(	PUNCT
ejpam-5473	278	30	k	k	X
ejpam-5473	278	31	,	,	PUNCT
ejpam-5473	278	32	−0.3	−0.3	PROPN
ejpam-5473	278	33	,	,	PUNCT
ejpam-5473	278	34	0.5	0.5	NUM
ejpam-5473	278	35	)	)	PUNCT
ejpam-5473	278	36	(	(	PUNCT
ejpam-5473	278	37	l	l	NOUN
ejpam-5473	278	38	,	,	PUNCT
ejpam-5473	278	39	−1	−1	NOUN
ejpam-5473	278	40	,	,	PUNCT
ejpam-5473	278	41	0.5	0.5	NUM
ejpam-5473	278	42	)	)	PUNCT
ejpam-5473	278	43	(	(	PUNCT
ejpam-5473	278	44	k	k	NOUN
ejpam-5473	278	45	,	,	PUNCT
ejpam-5473	278	46	−0.8	−0.8	ADJ
ejpam-5473	278	47	,	,	PUNCT
ejpam-5473	278	48	1	1	NUM
ejpam-5473	278	49	)	)	PUNCT
ejpam-5473	278	50	(	(	PUNCT
ejpam-5473	278	51	k	k	NOUN
ejpam-5473	278	52	,	,	PUNCT
ejpam-5473	278	53	−1	−1	NOUN
ejpam-5473	278	54	,	,	PUNCT
ejpam-5473	278	55	0.2	0.2	NUM
ejpam-5473	278	56	)	)	PUNCT
ejpam-5473	278	57	(	(	PUNCT
ejpam-5473	278	58	h	h	NOUN
ejpam-5473	278	59	,	,	PUNCT
ejpam-5473	278	60	−1	−1	NOUN
ejpam-5473	278	61	,	,	PUNCT
ejpam-5473	278	62	0.5	0.5	NUM
ejpam-5473	278	63	)	)	PUNCT
ejpam-5473	278	64	(	(	PUNCT
ejpam-5473	278	65	l	l	NOUN
ejpam-5473	278	66	,	,	PUNCT
ejpam-5473	278	67	−1	−1	NOUN
ejpam-5473	278	68	,	,	PUNCT
ejpam-5473	278	69	0.2	0.2	NUM
ejpam-5473	278	70	)	)	PUNCT
ejpam-5473	278	71	(	(	PUNCT
ejpam-5473	278	72	k	k	NOUN
ejpam-5473	278	73	,	,	PUNCT
ejpam-5473	278	74	−1	−1	NOUN
ejpam-5473	278	75	,	,	PUNCT
ejpam-5473	278	76	1	1	NUM
ejpam-5473	278	77	)	)	PUNCT
ejpam-5473	278	78	(	(	PUNCT
ejpam-5473	278	79	l	l	NOUN
ejpam-5473	278	80	,	,	PUNCT
ejpam-5473	278	81	−0.8	−0.8	ADJ
ejpam-5473	278	82	,	,	PUNCT
ejpam-5473	278	83	1	1	NUM
ejpam-5473	278	84	)	)	PUNCT
ejpam-5473	278	85	(	(	PUNCT
ejpam-5473	278	86	l	l	NOUN
ejpam-5473	278	87	,	,	PUNCT
ejpam-5473	278	88	−0.8	−0.8	ADJ
ejpam-5473	278	89	,	,	PUNCT
ejpam-5473	278	90	1	1	NUM
ejpam-5473	278	91	)	)	PUNCT
ejpam-5473	278	92	(	(	PUNCT
ejpam-5473	278	93	k	k	NOUN
ejpam-5473	278	94	,	,	PUNCT
ejpam-5473	278	95	−1	−1	NOUN
ejpam-5473	278	96	,	,	PUNCT
ejpam-5473	278	97	1	1	NUM
ejpam-5473	278	98	)	)	PUNCT
ejpam-5473	278	99	(	(	PUNCT
ejpam-5473	278	100	h	h	NOUN
ejpam-5473	278	101	,	,	PUNCT
ejpam-5473	278	102	−0.8	−0.8	ADJ
ejpam-5473	278	103	,	,	PUNCT
ejpam-5473	278	104	1	1	X
ejpam-5473	278	105	)	)	PUNCT
ejpam-5473	278	106	a	a	DET
ejpam-5473	278	107	bvfbo	bvfbo	NOUN
ejpam-5473	278	108	is	be	AUX
ejpam-5473	278	109	called	call	VERB
ejpam-5473	278	110	a	a	DET
ejpam-5473	278	111	uniform	uniform	NOUN
ejpam-5473	278	112	if	if	SCONJ
ejpam-5473	278	113	the	the	DET
ejpam-5473	278	114	f−	f−	PROPN
ejpam-5473	278	115	xy	xy	PROPN
ejpam-5473	278	116	,	,	PUNCT
ejpam-5473	278	117	and	and	CCONJ
ejpam-5473	278	118	f+	f+	PROPN
ejpam-5473	278	119	xy	xy	PROPN
ejpam-5473	278	120	are	be	AUX
ejpam-5473	278	121	identical	identical	ADJ
ejpam-5473	278	122	.	.	PUNCT
ejpam-5473	279	1	that	that	PRON
ejpam-5473	279	2	is	be	AUX
ejpam-5473	279	3	,	,	PUNCT
ejpam-5473	279	4	∣∣f−	∣∣f−	PROPN
ejpam-5473	279	5	xy	xy	X
ejpam-5473	279	6	∣∣	∣∣	PUNCT
ejpam-5473	279	7	=	=	SYM
ejpam-5473	279	8	f+	f+	PROPN
ejpam-5473	279	9	xy	xy	NOUN
ejpam-5473	279	10	=	=	SYM
ejpam-5473	279	11	f	f	PROPN
ejpam-5473	279	12	for	for	ADP
ejpam-5473	279	13	all	all	DET
ejpam-5473	279	14	x	x	NOUN
ejpam-5473	279	15	,	,	PUNCT
ejpam-5473	279	16	y	y	PROPN
ejpam-5473	279	17	∈	∈	PROPN
ejpam-5473	279	18	℧	℧	PROPN
ejpam-5473	279	19	.	.	PUNCT
ejpam-5473	280	1	a	a	DET
ejpam-5473	280	2	left	left	ADJ
ejpam-5473	280	3	uniform	uniform	NOUN
ejpam-5473	280	4	(	(	PUNCT
ejpam-5473	280	5	right	right	ADJ
ejpam-5473	280	6	uniform	uniform	NOUN
ejpam-5473	280	7	)	)	PUNCT
ejpam-5473	280	8	bvfbo	bvfbo	NOUN
ejpam-5473	280	9	is	be	AUX
ejpam-5473	280	10	a	a	DET
ejpam-5473	280	11	bvfbo	bvfbo	NOUN
ejpam-5473	280	12	having	have	VERB
ejpam-5473	280	13	identical	identical	ADJ
ejpam-5473	280	14	negative	negative	ADJ
ejpam-5473	280	15	comembership	comembership	NOUN
ejpam-5473	280	16	functions	function	NOUN
ejpam-5473	280	17	(	(	PUNCT
ejpam-5473	280	18	positive	positive	ADJ
ejpam-5473	280	19	comembership	comembership	NOUN
ejpam-5473	280	20	functions	function	NOUN
ejpam-5473	280	21	)	)	PUNCT
ejpam-5473	280	22	.	.	PUNCT
ejpam-5473	281	1	f.	f.	PROPN
ejpam-5473	281	2	al	al	PROPN
ejpam-5473	281	3	-	-	PROPN
ejpam-5473	281	4	zu’bi	zu’bi	PROPN
ejpam-5473	281	5	et	et	NOUN
ejpam-5473	281	6	al	al	PROPN
ejpam-5473	281	7	.	.	PUNCT
ejpam-5473	281	8	/	/	SYM
ejpam-5473	281	9	eur	eur	PROPN
ejpam-5473	281	10	.	.	PUNCT
ejpam-5473	282	1	j.	j.	PROPN
ejpam-5473	282	2	pure	pure	PROPN
ejpam-5473	282	3	appl	appl	PROPN
ejpam-5473	282	4	.	.	PROPN
ejpam-5473	282	5	math	math	PROPN
ejpam-5473	282	6	,	,	PUNCT
ejpam-5473	282	7	17	17	NUM
ejpam-5473	282	8	(	(	PUNCT
ejpam-5473	282	9	4	4	NUM
ejpam-5473	282	10	)	)	PUNCT
ejpam-5473	282	11	(	(	PUNCT
ejpam-5473	282	12	2024	2024	NUM
ejpam-5473	282	13	)	)	PUNCT
ejpam-5473	282	14	,	,	PUNCT
ejpam-5473	282	15	2898	2898	NUM
ejpam-5473	282	16	-	-	SYM
ejpam-5473	282	17	2914	2914	NUM
ejpam-5473	282	18	2907	2907	NUM
ejpam-5473	282	19	definition	definition	NOUN
ejpam-5473	282	20	23	23	NUM
ejpam-5473	282	21	.	.	PUNCT
ejpam-5473	283	1	a	a	DET
ejpam-5473	283	2	bipolar	bipolar	ADJ
ejpam-5473	283	3	valued	value	VERB
ejpam-5473	283	4	fuzzy	fuzzy	ADJ
ejpam-5473	283	5	groupoid	groupoid	NOUN
ejpam-5473	283	6	,	,	PUNCT
ejpam-5473	283	7	denoted	denote	VERB
ejpam-5473	283	8	by	by	ADP
ejpam-5473	283	9	(	(	PUNCT
ejpam-5473	283	10	(	(	PUNCT
ejpam-5473	283	11	℧	℧	PROPN
ejpam-5473	283	12	,	,	PUNCT
ejpam-5473	283	13	[	[	X
ejpam-5473	283	14	−1	−1	NOUN
ejpam-5473	283	15	,	,	PUNCT
ejpam-5473	283	16	0	0	NUM
ejpam-5473	283	17	]	]	PUNCT
ejpam-5473	283	18	,	,	PUNCT
ejpam-5473	283	19	[	[	X
ejpam-5473	283	20	0	0	NUM
ejpam-5473	283	21	,	,	PUNCT
ejpam-5473	283	22	1	1	NUM
ejpam-5473	283	23	]	]	NUM
ejpam-5473	283	24	)	)	PUNCT
ejpam-5473	283	25	,	,	PUNCT
ejpam-5473	283	26	f	f	PROPN
ejpam-5473	283	27	)	)	PUNCT
ejpam-5473	283	28	,	,	PUNCT
ejpam-5473	283	29	is	be	AUX
ejpam-5473	283	30	a	a	DET
ejpam-5473	283	31	bvf	bvf	NOUN
ejpam-5473	283	32	-	-	PUNCT
ejpam-5473	283	33	space	space	NOUN
ejpam-5473	283	34	(	(	PUNCT
ejpam-5473	283	35	℧	℧	PROPN
ejpam-5473	283	36	,	,	PUNCT
ejpam-5473	283	37	[	[	X
ejpam-5473	283	38	−1	−1	NOUN
ejpam-5473	283	39	,	,	PUNCT
ejpam-5473	283	40	0	0	NUM
ejpam-5473	283	41	]	]	PUNCT
ejpam-5473	283	42	,	,	PUNCT
ejpam-5473	283	43	[	[	X
ejpam-5473	283	44	0	0	NUM
ejpam-5473	283	45	,	,	PUNCT
ejpam-5473	283	46	1	1	NUM
ejpam-5473	283	47	]	]	PUNCT
ejpam-5473	283	48	)	)	PUNCT
ejpam-5473	283	49	together	together	ADV
ejpam-5473	283	50	with	with	ADP
ejpam-5473	283	51	a	a	DET
ejpam-5473	283	52	bvfbo	bvfbo	NOUN
ejpam-5473	283	53	f	f	PROPN
ejpam-5473	283	54	defined	define	VERB
ejpam-5473	283	55	over	over	ADP
ejpam-5473	283	56	it	it	PRON
ejpam-5473	283	57	.	.	PUNCT
ejpam-5473	284	1	a	a	DET
ejpam-5473	284	2	uniform	uniform	NOUN
ejpam-5473	284	3	(	(	PUNCT
ejpam-5473	284	4	left	leave	VERB
ejpam-5473	284	5	uniform	uniform	NOUN
ejpam-5473	284	6	,	,	PUNCT
ejpam-5473	284	7	right	right	ADJ
ejpam-5473	284	8	uniform	uniform	NOUN
ejpam-5473	284	9	)	)	PUNCT
ejpam-5473	284	10	bipolar	bipolar	ADJ
ejpam-5473	284	11	valued	value	VERB
ejpam-5473	284	12	fuzzy	fuzzy	ADJ
ejpam-5473	284	13	groupoid	groupoid	PROPN
ejpam-5473	284	14	is	be	AUX
ejpam-5473	284	15	a	a	DET
ejpam-5473	284	16	bipolar	bipolar	ADJ
ejpam-5473	284	17	valued	value	VERB
ejpam-5473	284	18	fuzzy	fuzzy	ADJ
ejpam-5473	284	19	groupoid	groupoid	NOUN
ejpam-5473	284	20	with	with	ADP
ejpam-5473	284	21	uniform	uniform	NOUN
ejpam-5473	284	22	(	(	PUNCT
ejpam-5473	284	23	left	leave	VERB
ejpam-5473	284	24	uniform	uniform	NOUN
ejpam-5473	284	25	,	,	PUNCT
ejpam-5473	284	26	right	right	ADJ
ejpam-5473	284	27	uniform	uniform	NOUN
ejpam-5473	284	28	)	)	PUNCT
ejpam-5473	284	29	bipolar	bipolar	ADJ
ejpam-5473	284	30	valued	value	VERB
ejpam-5473	284	31	fuzzy	fuzzy	ADJ
ejpam-5473	284	32	binary	binary	ADJ
ejpam-5473	284	33	operation	operation	NOUN
ejpam-5473	284	34	.	.	PUNCT
ejpam-5473	285	1	the	the	DET
ejpam-5473	285	2	following	follow	VERB
ejpam-5473	285	3	theorem	theorem	NOUN
ejpam-5473	285	4	establishes	establish	VERB
ejpam-5473	285	5	a	a	DET
ejpam-5473	285	6	relationship	relationship	NOUN
ejpam-5473	285	7	between	between	ADP
ejpam-5473	285	8	bipolar	bipolar	ADJ
ejpam-5473	285	9	valued	value	VERB
ejpam-5473	285	10	fuzzy	fuzzy	ADJ
ejpam-5473	285	11	groupoids	groupoid	NOUN
ejpam-5473	285	12	and	and	CCONJ
ejpam-5473	285	13	ordinary	ordinary	ADJ
ejpam-5473	285	14	(	(	PUNCT
ejpam-5473	285	15	fuzzy	fuzzy	ADJ
ejpam-5473	285	16	)	)	PUNCT
ejpam-5473	285	17	groupoids	groupoid	NOUN
ejpam-5473	285	18	.	.	PUNCT
ejpam-5473	286	1	theorem	theorem	NOUN
ejpam-5473	286	2	1	1	NUM
ejpam-5473	286	3	.	.	PUNCT
ejpam-5473	287	1	(	(	PUNCT
ejpam-5473	287	2	1	1	X
ejpam-5473	287	3	)	)	PUNCT
ejpam-5473	287	4	associated	associate	VERB
ejpam-5473	287	5	to	to	ADP
ejpam-5473	287	6	each	each	DET
ejpam-5473	287	7	bipolar	bipolar	PROPN
ejpam-5473	287	8	valued	value	VERB
ejpam-5473	287	9	fuzzy	fuzzy	ADJ
ejpam-5473	287	10	groupoid	groupoid	NOUN
ejpam-5473	287	11	(	(	PUNCT
ejpam-5473	287	12	℧	℧	PROPN
ejpam-5473	287	13	,	,	PUNCT
ejpam-5473	287	14	[	[	X
ejpam-5473	287	15	−1	−1	NOUN
ejpam-5473	287	16	,	,	PUNCT
ejpam-5473	287	17	0	0	NUM
ejpam-5473	287	18	]	]	PUNCT
ejpam-5473	287	19	,	,	PUNCT
ejpam-5473	288	1	[	[	X
ejpam-5473	288	2	0	0	NUM
ejpam-5473	288	3	,	,	PUNCT
ejpam-5473	288	4	1	1	NUM
ejpam-5473	288	5	]	]	NUM
ejpam-5473	288	6	)	)	PUNCT
ejpam-5473	288	7	,	,	PUNCT
ejpam-5473	288	8	f	f	PROPN
ejpam-5473	288	9	)	)	PUNCT
ejpam-5473	288	10	where	where	SCONJ
ejpam-5473	288	11	f	f	X
ejpam-5473	288	12	=	=	PRON
ejpam-5473	288	13	(	(	PUNCT
ejpam-5473	288	14	f	f	X
ejpam-5473	288	15	,	,	PUNCT
ejpam-5473	288	16	f−	f−	PROPN
ejpam-5473	288	17	xy	xy	PROPN
ejpam-5473	288	18	,	,	PUNCT
ejpam-5473	288	19	f+	f+	PROPN
ejpam-5473	288	20	xy	xy	PROPN
ejpam-5473	288	21	)	)	PUNCT
ejpam-5473	288	22	a	a	DET
ejpam-5473	288	23	fuzzy	fuzzy	ADJ
ejpam-5473	288	24	groupoid	groupoid	NOUN
ejpam-5473	288	25	(	(	PUNCT
ejpam-5473	288	26	(	(	PUNCT
ejpam-5473	288	27	℧	℧	PROPN
ejpam-5473	288	28	,	,	PUNCT
ejpam-5473	288	29	[	[	X
ejpam-5473	288	30	0	0	NUM
ejpam-5473	288	31	,	,	PUNCT
ejpam-5473	288	32	1	1	NUM
ejpam-5473	288	33	]	]	PUNCT
ejpam-5473	288	34	)	)	PUNCT
ejpam-5473	288	35	,	,	PUNCT
ejpam-5473	288	36	f	f	PROPN
ejpam-5473	288	37	)	)	PUNCT
ejpam-5473	288	38	where	where	SCONJ
ejpam-5473	288	39	f	f	X
ejpam-5473	288	40	=	=	PRON
ejpam-5473	288	41	(	(	PUNCT
ejpam-5473	288	42	f	f	X
ejpam-5473	288	43	,	,	PUNCT
ejpam-5473	288	44	f+	f+	PROPN
ejpam-5473	288	45	xy	xy	PROPN
ejpam-5473	288	46	)	)	PUNCT
ejpam-5473	289	1	which	which	PRON
ejpam-5473	289	2	is	be	AUX
ejpam-5473	289	3	isomorphic	isomorphic	ADJ
ejpam-5473	289	4	to	to	ADP
ejpam-5473	289	5	the	the	DET
ejpam-5473	289	6	bipolar	bipolar	ADJ
ejpam-5473	289	7	valued	value	VERB
ejpam-5473	289	8	fuzzy	fuzzy	ADJ
ejpam-5473	289	9	groupoid	groupoid	NOUN
ejpam-5473	289	10	(	(	PUNCT
ejpam-5473	289	11	℧	℧	PROPN
ejpam-5473	289	12	,	,	PUNCT
ejpam-5473	289	13	[	[	X
ejpam-5473	289	14	−1	−1	NOUN
ejpam-5473	289	15	,	,	PUNCT
ejpam-5473	289	16	0	0	NUM
ejpam-5473	289	17	]	]	PUNCT
ejpam-5473	289	18	,	,	PUNCT
ejpam-5473	289	19	[	[	X
ejpam-5473	289	20	0	0	NUM
ejpam-5473	289	21	,	,	PUNCT
ejpam-5473	289	22	1	1	NUM
ejpam-5473	289	23	]	]	NUM
ejpam-5473	289	24	)	)	PUNCT
ejpam-5473	289	25	,	,	PUNCT
ejpam-5473	289	26	f	f	PROPN
ejpam-5473	289	27	)	)	PUNCT
ejpam-5473	289	28	by	by	ADP
ejpam-5473	289	29	the	the	DET
ejpam-5473	289	30	correspondence	correspondence	NOUN
ejpam-5473	289	31	(	(	PUNCT
ejpam-5473	289	32	x,−[−1	x,−[−1	PROPN
ejpam-5473	289	33	,	,	PUNCT
ejpam-5473	289	34	0	0	NUM
ejpam-5473	289	35	]	]	PUNCT
ejpam-5473	289	36	,	,	PUNCT
ejpam-5473	290	1	[	[	X
ejpam-5473	290	2	0	0	NUM
ejpam-5473	290	3	,	,	PUNCT
ejpam-5473	290	4	1	1	NUM
ejpam-5473	290	5	]	]	PUNCT
ejpam-5473	290	6	)	)	PUNCT
ejpam-5473	290	7	↔	↔	PROPN
ejpam-5473	290	8	(	(	PUNCT
ejpam-5473	290	9	x	x	X
ejpam-5473	290	10	,	,	PUNCT
ejpam-5473	290	11	[	[	X
ejpam-5473	290	12	0	0	NUM
ejpam-5473	290	13	,	,	PUNCT
ejpam-5473	290	14	1	1	NUM
ejpam-5473	290	15	]	]	NUM
ejpam-5473	290	16	)	)	PUNCT
ejpam-5473	290	17	.	.	PUNCT
ejpam-5473	291	1	(	(	PUNCT
ejpam-5473	291	2	2	2	X
ejpam-5473	291	3	)	)	PUNCT
ejpam-5473	291	4	there	there	PRON
ejpam-5473	291	5	is	be	VERB
ejpam-5473	291	6	an	an	DET
ejpam-5473	291	7	associated	associate	VERB
ejpam-5473	291	8	(	(	PUNCT
ejpam-5473	291	9	ordinary	ordinary	ADJ
ejpam-5473	291	10	)	)	PUNCT
ejpam-5473	291	11	groupoid	groupoid	NOUN
ejpam-5473	291	12	(	(	PUNCT
ejpam-5473	291	13	℧	℧	PROPN
ejpam-5473	291	14	,	,	PUNCT
ejpam-5473	291	15	f	f	PROPN
ejpam-5473	291	16	)	)	PUNCT
ejpam-5473	291	17	to	to	ADP
ejpam-5473	291	18	any	any	DET
ejpam-5473	291	19	bvf	bvf	NOUN
ejpam-5473	291	20	-	-	PUNCT
ejpam-5473	291	21	groupoid	groupoid	NOUN
ejpam-5473	291	22	(	(	PUNCT
ejpam-5473	291	23	(	(	PUNCT
ejpam-5473	291	24	℧	℧	PROPN
ejpam-5473	291	25	,	,	PUNCT
ejpam-5473	291	26	[	[	X
ejpam-5473	291	27	−1	−1	NOUN
ejpam-5473	291	28	,	,	PUNCT
ejpam-5473	291	29	0	0	NUM
ejpam-5473	291	30	]	]	PUNCT
ejpam-5473	291	31	,	,	PUNCT
ejpam-5473	291	32	[	[	X
ejpam-5473	291	33	0	0	NUM
ejpam-5473	291	34	,	,	PUNCT
ejpam-5473	291	35	1	1	NUM
ejpam-5473	291	36	]	]	NUM
ejpam-5473	291	37	)	)	PUNCT
ejpam-5473	291	38	,	,	PUNCT
ejpam-5473	291	39	f	f	PROPN
ejpam-5473	291	40	)	)	PUNCT
ejpam-5473	291	41	that	that	PRON
ejpam-5473	291	42	is	be	AUX
ejpam-5473	291	43	isomorphic	isomorphic	ADJ
ejpam-5473	291	44	to	to	ADP
ejpam-5473	291	45	the	the	DET
ejpam-5473	291	46	bipolar	bipolar	ADJ
ejpam-5473	291	47	valued	value	VERB
ejpam-5473	291	48	fuzzy	fuzzy	ADJ
ejpam-5473	291	49	groupoid	groupoid	NOUN
ejpam-5473	291	50	via	via	ADP
ejpam-5473	291	51	the	the	DET
ejpam-5473	291	52	corresponding	correspond	VERB
ejpam-5473	291	53	(	(	PUNCT
ejpam-5473	291	54	x	x	X
ejpam-5473	291	55	,	,	PUNCT
ejpam-5473	291	56	[	[	X
ejpam-5473	291	57	−1	−1	NOUN
ejpam-5473	291	58	,	,	PUNCT
ejpam-5473	291	59	0	0	NUM
ejpam-5473	291	60	]	]	PUNCT
ejpam-5473	291	61	,	,	PUNCT
ejpam-5473	291	62	[	[	X
ejpam-5473	291	63	0	0	NUM
ejpam-5473	291	64	,	,	PUNCT
ejpam-5473	291	65	1	1	NUM
ejpam-5473	291	66	]	]	PUNCT
ejpam-5473	291	67	)	)	PUNCT
ejpam-5473	291	68	↔	↔	PROPN
ejpam-5473	291	69	x.	x.	NOUN
ejpam-5473	291	70	proof	proof	NOUN
ejpam-5473	291	71	.	.	PUNCT
ejpam-5473	292	1	(	(	PUNCT
ejpam-5473	292	2	1	1	X
ejpam-5473	292	3	)	)	PUNCT
ejpam-5473	292	4	let	let	VERB
ejpam-5473	292	5	(	(	PUNCT
ejpam-5473	292	6	(	(	PUNCT
ejpam-5473	292	7	℧	℧	PROPN
ejpam-5473	292	8	,	,	PUNCT
ejpam-5473	292	9	[	[	X
ejpam-5473	292	10	−1	−1	NOUN
ejpam-5473	292	11	,	,	PUNCT
ejpam-5473	292	12	0	0	NUM
ejpam-5473	292	13	]	]	PUNCT
ejpam-5473	292	14	,	,	PUNCT
ejpam-5473	293	1	[	[	X
ejpam-5473	293	2	0	0	NUM
ejpam-5473	293	3	,	,	PUNCT
ejpam-5473	293	4	1	1	NUM
ejpam-5473	293	5	]	]	NUM
ejpam-5473	293	6	)	)	PUNCT
ejpam-5473	293	7	,	,	PUNCT
ejpam-5473	293	8	f	f	PROPN
ejpam-5473	293	9	)	)	PUNCT
ejpam-5473	293	10	be	be	AUX
ejpam-5473	293	11	a	a	DET
ejpam-5473	293	12	given	give	VERB
ejpam-5473	293	13	bipolar	bipolar	ADJ
ejpam-5473	293	14	valued	value	VERB
ejpam-5473	293	15	fuzzy	fuzzy	ADJ
ejpam-5473	293	16	groupoid	groupoid	X
ejpam-5473	293	17	.	.	PUNCT
ejpam-5473	294	1	now	now	ADV
ejpam-5473	294	2	redefine	redefine	VERB
ejpam-5473	294	3	f	f	PROPN
ejpam-5473	294	4	=	=	SYM
ejpam-5473	294	5	(	(	PUNCT
ejpam-5473	294	6	f	f	X
ejpam-5473	294	7	,	,	PUNCT
ejpam-5473	294	8	f−	f−	PROPN
ejpam-5473	294	9	xy	xy	PROPN
ejpam-5473	294	10	,	,	PUNCT
ejpam-5473	294	11	f+	f+	PROPN
ejpam-5473	294	12	xy	xy	PROPN
ejpam-5473	294	13	)	)	PUNCT
ejpam-5473	294	14	to	to	PART
ejpam-5473	294	15	be	be	AUX
ejpam-5473	294	16	f	f	PROPN
ejpam-5473	294	17	=	=	SYM
ejpam-5473	294	18	(	(	PUNCT
ejpam-5473	294	19	f	f	PROPN
ejpam-5473	294	20	,	,	PUNCT
ejpam-5473	294	21	f+	f+	PROPN
ejpam-5473	294	22	xy	xy	PROPN
ejpam-5473	294	23	)	)	PUNCT
ejpam-5473	294	24	.	.	PUNCT
ejpam-5473	295	1	since	since	SCONJ
ejpam-5473	295	2	f+	f+	PROPN
ejpam-5473	295	3	xy	xy	PROPN
ejpam-5473	295	4	meets	meet	VERB
ejpam-5473	295	5	the	the	DET
ejpam-5473	295	6	conditions	condition	NOUN
ejpam-5473	295	7	of	of	ADP
ejpam-5473	295	8	fuzzy	fuzzy	ADJ
ejpam-5473	295	9	comembership	comembership	NOUN
ejpam-5473	295	10	function	function	NOUN
ejpam-5473	295	11	,	,	PUNCT
ejpam-5473	295	12	f	f	PROPN
ejpam-5473	295	13	=	=	PRON
ejpam-5473	295	14	(	(	PUNCT
ejpam-5473	295	15	f	f	X
ejpam-5473	295	16	,	,	PUNCT
ejpam-5473	295	17	f+	f+	PROPN
ejpam-5473	295	18	xy	xy	NOUN
ejpam-5473	295	19	)	)	PUNCT
ejpam-5473	295	20	is	be	AUX
ejpam-5473	295	21	a	a	DET
ejpam-5473	295	22	fuzzy	fuzzy	ADJ
ejpam-5473	295	23	binary	binary	ADJ
ejpam-5473	295	24	operation	operation	NOUN
ejpam-5473	295	25	.	.	PUNCT
ejpam-5473	296	1	that	that	PRON
ejpam-5473	296	2	is	is	ADV
ejpam-5473	296	3	(	(	PUNCT
ejpam-5473	296	4	(	(	PUNCT
ejpam-5473	296	5	℧	℧	PROPN
ejpam-5473	296	6	,	,	PUNCT
ejpam-5473	296	7	[	[	X
ejpam-5473	296	8	−1	−1	NOUN
ejpam-5473	296	9	,	,	PUNCT
ejpam-5473	296	10	0	0	NUM
ejpam-5473	296	11	]	]	PUNCT
ejpam-5473	296	12	,	,	PUNCT
ejpam-5473	296	13	[	[	X
ejpam-5473	296	14	0	0	NUM
ejpam-5473	296	15	,	,	PUNCT
ejpam-5473	296	16	1	1	NUM
ejpam-5473	296	17	]	]	NUM
ejpam-5473	296	18	)	)	PUNCT
ejpam-5473	296	19	,	,	PUNCT
ejpam-5473	296	20	f	f	X
ejpam-5473	296	21	=	=	PRON
ejpam-5473	296	22	(	(	PUNCT
ejpam-5473	296	23	f	f	PROPN
ejpam-5473	296	24	,	,	PUNCT
ejpam-5473	296	25	f+	f+	PROPN
ejpam-5473	296	26	xy	xy	PROPN
ejpam-5473	296	27	)	)	PUNCT
ejpam-5473	296	28	)	)	PUNCT
ejpam-5473	296	29	is	be	AUX
ejpam-5473	296	30	a	a	DET
ejpam-5473	296	31	fuzzy	fuzzy	ADJ
ejpam-5473	296	32	groupoid	groupoid	NOUN
ejpam-5473	296	33	.	.	PUNCT
ejpam-5473	297	1	(	(	PUNCT
ejpam-5473	297	2	2	2	X
ejpam-5473	297	3	)	)	PUNCT
ejpam-5473	297	4	again	again	ADV
ejpam-5473	297	5	,	,	PUNCT
ejpam-5473	297	6	consider	consider	VERB
ejpam-5473	297	7	the	the	DET
ejpam-5473	297	8	bipolar	bipolar	ADJ
ejpam-5473	297	9	valued	value	VERB
ejpam-5473	297	10	fuzzy	fuzzy	ADJ
ejpam-5473	297	11	groupoid	groupoid	NOUN
ejpam-5473	297	12	(	(	PUNCT
ejpam-5473	297	13	℧	℧	PROPN
ejpam-5473	297	14	,	,	PUNCT
ejpam-5473	297	15	[	[	X
ejpam-5473	297	16	−1	−1	NOUN
ejpam-5473	297	17	,	,	PUNCT
ejpam-5473	297	18	0	0	NUM
ejpam-5473	297	19	]	]	PUNCT
ejpam-5473	297	20	,	,	PUNCT
ejpam-5473	298	1	[	[	X
ejpam-5473	298	2	0	0	NUM
ejpam-5473	298	3	,	,	PUNCT
ejpam-5473	298	4	1	1	NUM
ejpam-5473	298	5	]	]	NUM
ejpam-5473	298	6	)	)	PUNCT
ejpam-5473	298	7	,	,	PUNCT
ejpam-5473	298	8	f	f	PROPN
ejpam-5473	298	9	)	)	PUNCT
ejpam-5473	298	10	,	,	PUNCT
ejpam-5473	298	11	now	now	ADV
ejpam-5473	298	12	using	use	VERB
ejpam-5473	298	13	the	the	DET
ejpam-5473	298	14	isomorphism	isomorphism	NOUN
ejpam-5473	298	15	(	(	PUNCT
ejpam-5473	298	16	x	x	X
ejpam-5473	298	17	,	,	PUNCT
ejpam-5473	298	18	[	[	X
ejpam-5473	298	19	−1	−1	NOUN
ejpam-5473	298	20	,	,	PUNCT
ejpam-5473	298	21	0	0	NUM
ejpam-5473	298	22	]	]	PUNCT
ejpam-5473	298	23	,	,	PUNCT
ejpam-5473	298	24	[	[	X
ejpam-5473	298	25	0	0	NUM
ejpam-5473	298	26	,	,	PUNCT
ejpam-5473	298	27	1	1	NUM
ejpam-5473	298	28	]	]	PUNCT
ejpam-5473	298	29	)	)	PUNCT
ejpam-5473	299	1	↔	↔	NOUN
ejpam-5473	299	2	x	x	VERB
ejpam-5473	299	3	we	we	PRON
ejpam-5473	299	4	can	can	AUX
ejpam-5473	299	5	redefine	redefine	VERB
ejpam-5473	299	6	the	the	DET
ejpam-5473	299	7	bipolar	bipolar	ADJ
ejpam-5473	299	8	valued	value	VERB
ejpam-5473	299	9	fuzzy	fuzzy	ADJ
ejpam-5473	299	10	function	function	NOUN
ejpam-5473	299	11	f	f	PROPN
ejpam-5473	299	12	=	=	SYM
ejpam-5473	299	13	(	(	PUNCT
ejpam-5473	299	14	f	f	X
ejpam-5473	299	15	,	,	PUNCT
ejpam-5473	299	16	f−	f−	PROPN
ejpam-5473	299	17	xy	xy	PROPN
ejpam-5473	299	18	,	,	PUNCT
ejpam-5473	299	19	f+	f+	PROPN
ejpam-5473	299	20	xy	xy	NOUN
ejpam-5473	299	21	)	)	PUNCT
ejpam-5473	299	22	to	to	PART
ejpam-5473	299	23	be	be	AUX
ejpam-5473	299	24	f	f	X
ejpam-5473	299	25	=	=	SYM
ejpam-5473	299	26	f	f	PROPN
ejpam-5473	299	27	:	:	PUNCT
ejpam-5473	299	28	℧	℧	VERB
ejpam-5473	299	29	×	×	NOUN
ejpam-5473	299	30	℧	℧	PROPN
ejpam-5473	299	31	→	→	SYM
ejpam-5473	299	32	℧	℧	PROPN
ejpam-5473	299	33	.	.	PROPN
ejpam-5473	300	1	that	that	PRON
ejpam-5473	300	2	is	be	AUX
ejpam-5473	300	3	f	f	PROPN
ejpam-5473	300	4	defines	define	VERB
ejpam-5473	300	5	an	an	DET
ejpam-5473	300	6	ordinary	ordinary	ADJ
ejpam-5473	300	7	binary	binary	ADJ
ejpam-5473	300	8	operation	operation	NOUN
ejpam-5473	300	9	over	over	ADP
ejpam-5473	300	10	℧	℧	PROPN
ejpam-5473	300	11	.	.	PUNCT
ejpam-5473	301	1	thus	thus	ADV
ejpam-5473	301	2	,	,	PUNCT
ejpam-5473	301	3	(	(	PUNCT
ejpam-5473	301	4	℧	℧	PROPN
ejpam-5473	301	5	,	,	PUNCT
ejpam-5473	301	6	f	f	PROPN
ejpam-5473	301	7	)	)	PUNCT
ejpam-5473	301	8	is	be	AUX
ejpam-5473	301	9	the	the	DET
ejpam-5473	301	10	associated	associated	ADJ
ejpam-5473	301	11	ordinary	ordinary	ADJ
ejpam-5473	301	12	groupoid	groupoid	PROPN
ejpam-5473	301	13	.	.	PUNCT
ejpam-5473	302	1	theorem	theorem	NOUN
ejpam-5473	302	2	2	2	NUM
ejpam-5473	302	3	.	.	PUNCT
ejpam-5473	303	1	every	every	DET
ejpam-5473	303	2	intuitionistic	intuitionistic	ADJ
ejpam-5473	303	3	fuzzy	fuzzy	ADJ
ejpam-5473	303	4	groupoid	groupoid	NOUN
ejpam-5473	303	5	is	be	AUX
ejpam-5473	303	6	a	a	DET
ejpam-5473	303	7	bipolar	bipolar	ADJ
ejpam-5473	303	8	valued	value	VERB
ejpam-5473	303	9	fuzzy	fuzzy	ADJ
ejpam-5473	303	10	groupoid	groupoid	NOUN
ejpam-5473	303	11	,	,	PUNCT
ejpam-5473	303	12	the	the	DET
ejpam-5473	303	13	inverse	inverse	NOUN
ejpam-5473	303	14	is	be	AUX
ejpam-5473	303	15	not	not	PART
ejpam-5473	303	16	true	true	ADJ
ejpam-5473	303	17	.	.	PUNCT
ejpam-5473	304	1	proof	proof	NOUN
ejpam-5473	304	2	.	.	PUNCT
ejpam-5473	305	1	let	let	VERB
ejpam-5473	305	2	(	(	PUNCT
ejpam-5473	305	3	(	(	PUNCT
ejpam-5473	305	4	℧	℧	PROPN
ejpam-5473	305	5	,	,	PUNCT
ejpam-5473	305	6	[	[	X
ejpam-5473	305	7	0	0	NUM
ejpam-5473	305	8	,	,	PUNCT
ejpam-5473	305	9	1	1	NUM
ejpam-5473	305	10	]	]	PUNCT
ejpam-5473	305	11	,	,	PUNCT
ejpam-5473	305	12	[	[	X
ejpam-5473	305	13	0	0	NUM
ejpam-5473	305	14	,	,	PUNCT
ejpam-5473	305	15	1	1	NUM
ejpam-5473	305	16	]	]	NUM
ejpam-5473	305	17	)	)	PUNCT
ejpam-5473	305	18	,	,	PUNCT
ejpam-5473	305	19	f	f	PROPN
ejpam-5473	305	20	)	)	PUNCT
ejpam-5473	305	21	be	be	AUX
ejpam-5473	305	22	a	a	DET
ejpam-5473	305	23	given	give	VERB
ejpam-5473	305	24	intuitionistic	intuitionistic	ADJ
ejpam-5473	305	25	fuzzy	fuzzy	ADJ
ejpam-5473	305	26	groupoid	groupoid	NOUN
ejpam-5473	305	27	.	.	PUNCT
ejpam-5473	306	1	now	now	ADV
ejpam-5473	306	2	redefine	redefine	VERB
ejpam-5473	306	3	f	f	PROPN
ejpam-5473	306	4	=	=	SYM
ejpam-5473	306	5	(	(	PUNCT
ejpam-5473	306	6	f	f	X
ejpam-5473	306	7	,	,	PUNCT
ejpam-5473	306	8	fxy	fxy	NOUN
ejpam-5473	306	9	,	,	PUNCT
ejpam-5473	306	10	fxy	fxy	NOUN
ejpam-5473	306	11	)	)	PUNCT
ejpam-5473	306	12	to	to	PART
ejpam-5473	306	13	be	be	AUX
ejpam-5473	306	14	f	f	PROPN
ejpam-5473	306	15	=	=	PUNCT
ejpam-5473	306	16	(	(	PUNCT
ejpam-5473	306	17	f	f	X
ejpam-5473	306	18	,	,	PUNCT
ejpam-5473	306	19	f−	f−	PROPN
ejpam-5473	306	20	xy	xy	NOUN
ejpam-5473	306	21	=	=	SYM
ejpam-5473	306	22	−(fxy	−(fxy	NOUN
ejpam-5473	306	23	)	)	PUNCT
ejpam-5473	306	24	,	,	PUNCT
ejpam-5473	306	25	f+	f+	PROPN
ejpam-5473	306	26	xy	xy	PROPN
ejpam-5473	306	27	=	=	SYM
ejpam-5473	306	28	fxy	fxy	NOUN
ejpam-5473	306	29	)	)	PUNCT
ejpam-5473	306	30	.	.	PUNCT
ejpam-5473	307	1	since	since	SCONJ
ejpam-5473	307	2	f−	f−	PROPN
ejpam-5473	307	3	xy	xy	PROPN
ejpam-5473	307	4	,	,	PUNCT
ejpam-5473	307	5	and	and	CCONJ
ejpam-5473	307	6	f+	f+	PROPN
ejpam-5473	307	7	xy	xy	AUX
ejpam-5473	307	8	satisfy	satisfy	VERB
ejpam-5473	307	9	the	the	DET
ejpam-5473	307	10	axioms	axiom	NOUN
ejpam-5473	307	11	of	of	ADP
ejpam-5473	307	12	negative	negative	ADJ
ejpam-5473	307	13	and	and	CCONJ
ejpam-5473	307	14	positive	positive	ADJ
ejpam-5473	307	15	bipolar	bipolar	ADJ
ejpam-5473	307	16	valued	value	VERB
ejpam-5473	307	17	fuzzy	fuzzy	ADJ
ejpam-5473	307	18	comembership	comembership	NOUN
ejpam-5473	307	19	function	function	NOUN
ejpam-5473	307	20	,	,	PUNCT
ejpam-5473	307	21	f	f	PROPN
ejpam-5473	307	22	=(	=(	PROPN
ejpam-5473	308	1	f	f	X
ejpam-5473	308	2	,	,	PUNCT
ejpam-5473	308	3	f−	f−	PROPN
ejpam-5473	308	4	xy	xy	PROPN
ejpam-5473	308	5	,	,	PUNCT
ejpam-5473	308	6	f+	f+	PROPN
ejpam-5473	308	7	xy	xy	PROPN
ejpam-5473	308	8	)	)	PUNCT
ejpam-5473	308	9	will	will	AUX
ejpam-5473	308	10	be	be	AUX
ejpam-5473	308	11	a	a	DET
ejpam-5473	308	12	bvfbo	bvfbo	NOUN
ejpam-5473	308	13	.	.	PUNCT
ejpam-5473	309	1	that	that	PRON
ejpam-5473	309	2	is	is	ADV
ejpam-5473	309	3	(	(	PUNCT
ejpam-5473	309	4	(	(	PUNCT
ejpam-5473	309	5	℧	℧	PROPN
ejpam-5473	309	6	,	,	PUNCT
ejpam-5473	309	7	[	[	X
ejpam-5473	309	8	−1	−1	NOUN
ejpam-5473	309	9	,	,	PUNCT
ejpam-5473	309	10	0	0	NUM
ejpam-5473	309	11	]	]	PUNCT
ejpam-5473	309	12	,	,	PUNCT
ejpam-5473	309	13	[	[	X
ejpam-5473	309	14	0	0	NUM
ejpam-5473	309	15	,	,	PUNCT
ejpam-5473	309	16	1	1	NUM
ejpam-5473	309	17	]	]	NUM
ejpam-5473	309	18	)	)	PUNCT
ejpam-5473	309	19	,	,	PUNCT
ejpam-5473	309	20	f	f	X
ejpam-5473	309	21	=	=	PRON
ejpam-5473	309	22	(	(	PUNCT
ejpam-5473	309	23	f	f	X
ejpam-5473	309	24	,	,	PUNCT
ejpam-5473	309	25	f−	f−	PROPN
ejpam-5473	309	26	xy	xy	PROPN
ejpam-5473	309	27	,	,	PUNCT
ejpam-5473	309	28	f	f	PROPN
ejpam-5473	310	1	+	+	X
ejpam-5473	310	2	xy	xy	PROPN
ejpam-5473	310	3	)	)	PUNCT
ejpam-5473	310	4	)	)	PUNCT
ejpam-5473	311	1	will	will	AUX
ejpam-5473	311	2	define	define	VERB
ejpam-5473	311	3	a	a	DET
ejpam-5473	311	4	bipolar	bipolar	ADJ
ejpam-5473	311	5	valued	value	VERB
ejpam-5473	311	6	fuzzy	fuzzy	ADJ
ejpam-5473	311	7	groupoid	groupoid	PROPN
ejpam-5473	311	8	.	.	PUNCT
ejpam-5473	312	1	the	the	DET
ejpam-5473	312	2	invers	inver	NOUN
ejpam-5473	312	3	is	be	AUX
ejpam-5473	312	4	proved	prove	VERB
ejpam-5473	312	5	by	by	ADP
ejpam-5473	312	6	counter	counter	ADJ
ejpam-5473	312	7	example	example	NOUN
ejpam-5473	312	8	as	as	SCONJ
ejpam-5473	312	9	follows	follow	VERB
ejpam-5473	312	10	:	:	PUNCT
ejpam-5473	312	11	example	example	NOUN
ejpam-5473	312	12	5	5	NUM
ejpam-5473	312	13	(	(	PUNCT
ejpam-5473	312	14	counter	counter	ADJ
ejpam-5473	312	15	example	example	NOUN
ejpam-5473	312	16	)	)	PUNCT
ejpam-5473	312	17	.	.	PUNCT
ejpam-5473	313	1	let	let	VERB
ejpam-5473	313	2	(	(	PUNCT
ejpam-5473	313	3	6	6	NUM
ejpam-5473	313	4	,	,	PUNCT
ejpam-5473	313	5	−0.7	−0.7	PROPN
ejpam-5473	313	6	,	,	PUNCT
ejpam-5473	313	7	0.5	0.5	NUM
ejpam-5473	313	8	)	)	PUNCT
ejpam-5473	313	9	and	and	CCONJ
ejpam-5473	313	10	(	(	PUNCT
ejpam-5473	313	11	2	2	NUM
ejpam-5473	313	12	,	,	PUNCT
ejpam-5473	313	13	−0.8	−0.8	PROPN
ejpam-5473	313	14	,	,	PUNCT
ejpam-5473	313	15	0.9	0.9	NUM
ejpam-5473	313	16	)	)	PUNCT
ejpam-5473	313	17	be	be	VERB
ejpam-5473	313	18	two	two	NUM
ejpam-5473	313	19	bvfelements	bvfelement	NOUN
ejpam-5473	313	20	in	in	ADP
ejpam-5473	313	21	bvf	bvf	NOUN
ejpam-5473	313	22	-	-	PUNCT
ejpam-5473	313	23	space(q+	space(q+	NOUN
ejpam-5473	313	24	,	,	PUNCT
ejpam-5473	313	25	−i	−i	NOUN
ejpam-5473	313	26	,	,	PUNCT
ejpam-5473	313	27	i	i	PROPN
ejpam-5473	313	28	)	)	PUNCT
ejpam-5473	313	29	with	with	ADP
ejpam-5473	313	30	bvfbo	bvfbo	PRON
ejpam-5473	313	31	f	f	PROPN
ejpam-5473	313	32	defined	define	VERB
ejpam-5473	313	33	as	as	ADP
ejpam-5473	313	34	example	example	NOUN
ejpam-5473	314	1	3	3	NUM
ejpam-5473	314	2	.	.	PUNCT
ejpam-5473	315	1	then	then	ADV
ejpam-5473	315	2	(	(	PUNCT
ejpam-5473	315	3	6	6	NUM
ejpam-5473	315	4	,	,	PUNCT
ejpam-5473	315	5	−0.7	−0.7	PROPN
ejpam-5473	315	6	,	,	PUNCT
ejpam-5473	315	7	0.5)f	0.5)f	X
ejpam-5473	315	8	(	(	PUNCT
ejpam-5473	315	9	2	2	NUM
ejpam-5473	315	10	,	,	PUNCT
ejpam-5473	315	11	−0.8	−0.8	PROPN
ejpam-5473	315	12	,	,	PUNCT
ejpam-5473	315	13	0.9	0.9	NUM
ejpam-5473	315	14	)	)	PUNCT
ejpam-5473	315	15	=	=	PUNCT
ejpam-5473	315	16	(	(	PUNCT
ejpam-5473	315	17	4	4	NUM
ejpam-5473	315	18	,	,	PUNCT
ejpam-5473	315	19	−0.8	−0.8	PROPN
ejpam-5473	315	20	,	,	PUNCT
ejpam-5473	315	21	0.9	0.9	NUM
ejpam-5473	315	22	)	)	PUNCT
ejpam-5473	315	23	.	.	PUNCT
ejpam-5473	316	1	now	now	ADV
ejpam-5473	316	2	,	,	PUNCT
ejpam-5473	316	3	if	if	SCONJ
ejpam-5473	316	4	we	we	PRON
ejpam-5473	316	5	redefine	redefine	AUX
ejpam-5473	316	6	now	now	ADV
ejpam-5473	316	7	redefine	redefine	VERB
ejpam-5473	316	8	f	f	PROPN
ejpam-5473	316	9	=	=	SYM
ejpam-5473	316	10	(	(	PUNCT
ejpam-5473	316	11	f	f	X
ejpam-5473	316	12	,	,	PUNCT
ejpam-5473	316	13	f−	f−	PROPN
ejpam-5473	316	14	xy	xy	PROPN
ejpam-5473	316	15	,	,	PUNCT
ejpam-5473	316	16	f	f	PROPN
ejpam-5473	317	1	+	+	X
ejpam-5473	317	2	xy	xy	PROPN
ejpam-5473	317	3	)	)	PUNCT
ejpam-5473	317	4	to	to	PART
ejpam-5473	317	5	be	be	AUX
ejpam-5473	317	6	f	f	PROPN
ejpam-5473	317	7	=	=	PUNCT
ejpam-5473	317	8	(	(	PUNCT
ejpam-5473	317	9	f	f	PROPN
ejpam-5473	317	10	,	,	PUNCT
ejpam-5473	317	11	fxy	fxy	NOUN
ejpam-5473	317	12	=	=	SYM
ejpam-5473	317	13	∣∣f−	∣∣f−	NOUN
ejpam-5473	317	14	xy	xy	ADP
ejpam-5473	317	15	∣∣	∣∣	NUM
ejpam-5473	317	16	,	,	PUNCT
ejpam-5473	317	17	fxy	fxy	X
ejpam-5473	317	18	=	=	SYM
ejpam-5473	317	19	f+	f+	PROPN
ejpam-5473	317	20	xy	xy	PROPN
ejpam-5473	317	21	)	)	PUNCT
ejpam-5473	317	22	,	,	PUNCT
ejpam-5473	317	23	this	this	PRON
ejpam-5473	317	24	implies	imply	VERB
ejpam-5473	317	25	the	the	DET
ejpam-5473	317	26	element	element	NOUN
ejpam-5473	317	27	(	(	PUNCT
ejpam-5473	317	28	6	6	NUM
ejpam-5473	317	29	,	,	PUNCT
ejpam-5473	317	30	0.7	0.7	NUM
ejpam-5473	317	31	,	,	PUNCT
ejpam-5473	317	32	0.5)f	0.5)f	X
ejpam-5473	317	33	(	(	PUNCT
ejpam-5473	317	34	2	2	NUM
ejpam-5473	317	35	,	,	PUNCT
ejpam-5473	317	36	0.8	0.8	NUM
ejpam-5473	317	37	,	,	PUNCT
ejpam-5473	317	38	0.9	0.9	NUM
ejpam-5473	317	39	)	)	PUNCT
ejpam-5473	317	40	=	=	NOUN
ejpam-5473	317	41	(	(	PUNCT
ejpam-5473	317	42	4	4	NUM
ejpam-5473	317	43	,	,	PUNCT
ejpam-5473	317	44	0.8	0.8	NUM
ejpam-5473	317	45	,	,	PUNCT
ejpam-5473	317	46	0.9	0.9	NUM
ejpam-5473	317	47	)	)	PUNCT
ejpam-5473	317	48	which	which	PRON
ejpam-5473	317	49	are	be	AUX
ejpam-5473	317	50	not	not	PART
ejpam-5473	317	51	if	if	SCONJ
ejpam-5473	317	52	-	-	PUNCT
ejpam-5473	317	53	element	element	NOUN
ejpam-5473	317	54	and	and	CCONJ
ejpam-5473	317	55	not	not	PART
ejpam-5473	317	56	defined	define	VERB
ejpam-5473	317	57	on	on	ADP
ejpam-5473	317	58	ifbo	ifbo	NOUN
ejpam-5473	317	59	and	and	CCONJ
ejpam-5473	317	60	its	its	PRON
ejpam-5473	317	61	not	not	PART
ejpam-5473	317	62	in	in	ADP
ejpam-5473	317	63	if	if	SCONJ
ejpam-5473	317	64	-	-	PUNCT
ejpam-5473	317	65	space	space	NOUN
ejpam-5473	317	66	because	because	SCONJ
ejpam-5473	317	67	the	the	DET
ejpam-5473	317	68	sum	sum	NOUN
ejpam-5473	317	69	of	of	ADP
ejpam-5473	317	70	”	"	PUNCT
ejpam-5473	317	71	0.7	0.7	NUM
ejpam-5473	317	72	and	and	CCONJ
ejpam-5473	317	73	0.5	0.5	NUM
ejpam-5473	317	74	”	"	PUNCT
ejpam-5473	317	75	,	,	PUNCT
ejpam-5473	317	76	“	"	PUNCT
ejpam-5473	317	77	0.8	0.8	NUM
ejpam-5473	317	78	and	and	CCONJ
ejpam-5473	317	79	0.9	0.9	NUM
ejpam-5473	317	80	”	"	PUNCT
ejpam-5473	317	81	,	,	PUNCT
ejpam-5473	317	82	and	and	CCONJ
ejpam-5473	317	83	“	"	PUNCT
ejpam-5473	317	84	0.8	0.8	NUM
ejpam-5473	317	85	and	and	CCONJ
ejpam-5473	317	86	0.9	0.9	NUM
ejpam-5473	317	87	”	"	PUNCT
ejpam-5473	317	88	is	be	AUX
ejpam-5473	317	89	not	not	PART
ejpam-5473	317	90	less	less	ADJ
ejpam-5473	317	91	than	than	ADP
ejpam-5473	317	92	1	1	NUM
ejpam-5473	317	93	.	.	PUNCT
ejpam-5473	318	1	f.	f.	PROPN
ejpam-5473	318	2	al	al	PROPN
ejpam-5473	318	3	-	-	PROPN
ejpam-5473	318	4	zu’bi	zu’bi	PROPN
ejpam-5473	318	5	et	et	NOUN
ejpam-5473	318	6	al	al	PROPN
ejpam-5473	318	7	.	.	PUNCT
ejpam-5473	318	8	/	/	SYM
ejpam-5473	318	9	eur	eur	PROPN
ejpam-5473	318	10	.	.	PUNCT
ejpam-5473	319	1	j.	j.	PROPN
ejpam-5473	319	2	pure	pure	PROPN
ejpam-5473	319	3	appl	appl	PROPN
ejpam-5473	319	4	.	.	PROPN
ejpam-5473	319	5	math	math	PROPN
ejpam-5473	319	6	,	,	PUNCT
ejpam-5473	319	7	17	17	NUM
ejpam-5473	319	8	(	(	PUNCT
ejpam-5473	319	9	4	4	NUM
ejpam-5473	319	10	)	)	PUNCT
ejpam-5473	319	11	(	(	PUNCT
ejpam-5473	319	12	2024	2024	NUM
ejpam-5473	319	13	)	)	PUNCT
ejpam-5473	319	14	,	,	PUNCT
ejpam-5473	319	15	2898	2898	NUM
ejpam-5473	319	16	-	-	SYM
ejpam-5473	319	17	2914	2914	NUM
ejpam-5473	319	18	2908	2908	NUM
ejpam-5473	319	19	definition	definition	NOUN
ejpam-5473	319	20	24	24	NUM
ejpam-5473	319	21	.	.	PUNCT
ejpam-5473	320	1	a	a	DET
ejpam-5473	320	2	bipolar	bipolar	ADJ
ejpam-5473	320	3	valued	value	VERB
ejpam-5473	320	4	fuzzy	fuzzy	ADJ
ejpam-5473	320	5	subgroupoid	subgroupoid	NOUN
ejpam-5473	320	6	,	,	PUNCT
ejpam-5473	320	7	(	(	PUNCT
ejpam-5473	320	8	u	u	NOUN
ejpam-5473	320	9	;	;	PUNCT
ejpam-5473	320	10	f	f	PROPN
ejpam-5473	320	11	)	)	PUNCT
ejpam-5473	320	12	,	,	PUNCT
ejpam-5473	320	13	of	of	ADP
ejpam-5473	320	14	the	the	DET
ejpam-5473	320	15	bvf	bvf	NOUN
ejpam-5473	320	16	-	-	PUNCT
ejpam-5473	320	17	groupoid	groupoid	NOUN
ejpam-5473	320	18	(	(	PUNCT
ejpam-5473	320	19	(	(	PUNCT
ejpam-5473	320	20	℧	℧	PROPN
ejpam-5473	320	21	,	,	PUNCT
ejpam-5473	320	22	[	[	X
ejpam-5473	320	23	−1	−1	NOUN
ejpam-5473	320	24	,	,	PUNCT
ejpam-5473	320	25	0	0	NUM
ejpam-5473	320	26	]	]	PUNCT
ejpam-5473	320	27	,	,	PUNCT
ejpam-5473	321	1	[	[	X
ejpam-5473	321	2	0	0	NUM
ejpam-5473	321	3	,	,	PUNCT
ejpam-5473	321	4	1	1	NUM
ejpam-5473	321	5	]	]	NUM
ejpam-5473	321	6	)	)	PUNCT
ejpam-5473	321	7	,	,	PUNCT
ejpam-5473	321	8	f	f	PROPN
ejpam-5473	321	9	)	)	PUNCT
ejpam-5473	321	10	iff	iff	PROPN
ejpam-5473	321	11	u	u	NOUN
ejpam-5473	321	12	is	be	AUX
ejpam-5473	321	13	closed	close	VERB
ejpam-5473	321	14	under	under	ADP
ejpam-5473	321	15	the	the	DET
ejpam-5473	321	16	bvfbo	bvfbo	PROPN
ejpam-5473	321	17	f	f	PROPN
ejpam-5473	321	18	and	and	CCONJ
ejpam-5473	321	19	u	u	PROPN
ejpam-5473	321	20	is	be	AUX
ejpam-5473	321	21	a	a	DET
ejpam-5473	321	22	bvf	bvf	NOUN
ejpam-5473	321	23	-	-	PUNCT
ejpam-5473	321	24	subspace	subspace	NOUN
ejpam-5473	321	25	of	of	ADP
ejpam-5473	321	26	the	the	DET
ejpam-5473	321	27	bvf	bvf	NOUN
ejpam-5473	321	28	-	-	PUNCT
ejpam-5473	321	29	space	space	NOUN
ejpam-5473	321	30	℧	℧	NOUN
ejpam-5473	321	31	.	.	PUNCT
ejpam-5473	322	1	we	we	PRON
ejpam-5473	322	2	may	may	AUX
ejpam-5473	322	3	now	now	ADV
ejpam-5473	322	4	develop	develop	VERB
ejpam-5473	322	5	the	the	DET
ejpam-5473	322	6	concept	concept	NOUN
ejpam-5473	322	7	of	of	ADP
ejpam-5473	322	8	bipolar	bipolar	ADJ
ejpam-5473	322	9	valued	value	VERB
ejpam-5473	322	10	fuzzy	fuzzy	ADJ
ejpam-5473	322	11	groupoid	groupoid	NOUN
ejpam-5473	322	12	to	to	AUX
ejpam-5473	322	13	bipolar	bipolar	ADJ
ejpam-5473	322	14	valued	value	VERB
ejpam-5473	322	15	fuzzy	fuzzy	ADJ
ejpam-5473	322	16	semi	semi	NOUN
ejpam-5473	322	17	-	-	NOUN
ejpam-5473	322	18	groups	group	NOUN
ejpam-5473	322	19	and	and	CCONJ
ejpam-5473	322	20	bipolar	bipolar	ADJ
ejpam-5473	322	21	valued	value	VERB
ejpam-5473	322	22	fuzzy	fuzzy	ADJ
ejpam-5473	322	23	monoids	monoid	NOUN
ejpam-5473	322	24	,	,	PUNCT
ejpam-5473	322	25	just	just	ADV
ejpam-5473	322	26	as	as	SCONJ
ejpam-5473	322	27	we	we	PRON
ejpam-5473	322	28	do	do	VERB
ejpam-5473	322	29	with	with	ADP
ejpam-5473	322	30	ordinary	ordinary	ADJ
ejpam-5473	322	31	(	(	PUNCT
ejpam-5473	322	32	fuzzy	fuzzy	ADJ
ejpam-5473	322	33	)	)	PUNCT
ejpam-5473	322	34	groupoid	groupoid	PROPN
ejpam-5473	322	35	.	.	PUNCT
ejpam-5473	323	1	definition	definition	NOUN
ejpam-5473	323	2	25	25	NUM
ejpam-5473	323	3	.	.	PUNCT
ejpam-5473	324	1	a	a	DET
ejpam-5473	324	2	bipolar	bipolar	ADJ
ejpam-5473	324	3	valued	value	VERB
ejpam-5473	324	4	fuzzy	fuzzy	ADJ
ejpam-5473	324	5	groupoid	groupoid	NOUN
ejpam-5473	324	6	that	that	PRON
ejpam-5473	324	7	is	be	AUX
ejpam-5473	324	8	associative	associative	ADJ
ejpam-5473	324	9	is	be	AUX
ejpam-5473	324	10	called	call	VERB
ejpam-5473	324	11	a	a	DET
ejpam-5473	324	12	bipolar	bipolar	ADV
ejpam-5473	324	13	-	-	PUNCT
ejpam-5473	324	14	valued	value	VERB
ejpam-5473	324	15	fuzzy	fuzzy	ADJ
ejpam-5473	324	16	semi	semi	NOUN
ejpam-5473	324	17	-	-	NOUN
ejpam-5473	324	18	group	group	NOUN
ejpam-5473	324	19	.	.	PUNCT
ejpam-5473	325	1	a	a	DET
ejpam-5473	325	2	bipolar	bipolar	ADJ
ejpam-5473	325	3	valued	value	VERB
ejpam-5473	325	4	fuzzy	fuzzy	ADJ
ejpam-5473	325	5	monoid	monoid	NOUN
ejpam-5473	325	6	is	be	AUX
ejpam-5473	325	7	a	a	DET
ejpam-5473	325	8	bipolar	bipolar	ADJ
ejpam-5473	325	9	valued	value	VERB
ejpam-5473	325	10	fuzzy	fuzzy	ADJ
ejpam-5473	325	11	semi	semi	NOUN
ejpam-5473	325	12	-	-	NOUN
ejpam-5473	325	13	group	group	NOUN
ejpam-5473	325	14	with	with	ADP
ejpam-5473	325	15	existence	existence	NOUN
ejpam-5473	325	16	of	of	ADP
ejpam-5473	325	17	an	an	DET
ejpam-5473	325	18	identity	identity	NOUN
ejpam-5473	325	19	.	.	PUNCT
ejpam-5473	326	1	now	now	ADV
ejpam-5473	326	2	,	,	PUNCT
ejpam-5473	326	3	we	we	PRON
ejpam-5473	326	4	are	be	AUX
ejpam-5473	326	5	able	able	ADJ
ejpam-5473	326	6	to	to	PART
ejpam-5473	326	7	introduce	introduce	VERB
ejpam-5473	326	8	the	the	DET
ejpam-5473	326	9	concept	concept	NOUN
ejpam-5473	326	10	of	of	ADP
ejpam-5473	326	11	bipolar	bipolar	ADV
ejpam-5473	326	12	-	-	PUNCT
ejpam-5473	326	13	valued	value	VERB
ejpam-5473	326	14	fuzzy	fuzzy	ADJ
ejpam-5473	326	15	group	group	NOUN
ejpam-5473	326	16	by	by	ADP
ejpam-5473	326	17	using	use	VERB
ejpam-5473	326	18	the	the	DET
ejpam-5473	326	19	definitions	definition	NOUN
ejpam-5473	326	20	23	23	NUM
ejpam-5473	326	21	,	,	PUNCT
ejpam-5473	326	22	24	24	NUM
ejpam-5473	326	23	,	,	PUNCT
ejpam-5473	326	24	and	and	CCONJ
ejpam-5473	326	25	25	25	NUM
ejpam-5473	326	26	.	.	PUNCT
ejpam-5473	326	27	definition	definition	NOUN
ejpam-5473	326	28	26	26	NUM
ejpam-5473	326	29	.	.	PUNCT
ejpam-5473	327	1	for	for	ADP
ejpam-5473	327	2	all	all	DET
ejpam-5473	327	3	bvf	bvf	NOUN
ejpam-5473	327	4	-	-	PUNCT
ejpam-5473	327	5	elements	element	NOUN
ejpam-5473	327	6	have	have	VERB
ejpam-5473	327	7	an	an	DET
ejpam-5473	327	8	inverse	inverse	NOUN
ejpam-5473	327	9	of	of	ADP
ejpam-5473	327	10	a	a	DET
ejpam-5473	327	11	bipolar	bipolar	ADJ
ejpam-5473	327	12	valued	value	VERB
ejpam-5473	327	13	fuzzy	fuzzy	ADJ
ejpam-5473	327	14	monoid	monoid	NOUN
ejpam-5473	327	15	is	be	AUX
ejpam-5473	327	16	called	call	VERB
ejpam-5473	327	17	a	a	DET
ejpam-5473	327	18	bipolar	bipolar	ADJ
ejpam-5473	327	19	valued	value	VERB
ejpam-5473	327	20	fuzzy	fuzzy	ADJ
ejpam-5473	327	21	group	group	NOUN
ejpam-5473	327	22	.	.	PUNCT
ejpam-5473	328	1	equivalently	equivalently	ADV
ejpam-5473	328	2	,	,	PUNCT
ejpam-5473	328	3	a	a	DET
ejpam-5473	328	4	bipolar	bipolar	ADJ
ejpam-5473	328	5	valued	value	VERB
ejpam-5473	328	6	fuzzy	fuzzy	ADJ
ejpam-5473	328	7	groupoid	groupoid	NOUN
ejpam-5473	328	8	(	(	PUNCT
ejpam-5473	328	9	(	(	PUNCT
ejpam-5473	328	10	g	g	NOUN
ejpam-5473	328	11	,	,	PUNCT
ejpam-5473	328	12	[	[	X
ejpam-5473	328	13	−1	−1	NOUN
ejpam-5473	328	14	,	,	PUNCT
ejpam-5473	328	15	0	0	NUM
ejpam-5473	328	16	]	]	PUNCT
ejpam-5473	328	17	,	,	PUNCT
ejpam-5473	328	18	[	[	X
ejpam-5473	328	19	0	0	NUM
ejpam-5473	328	20	,	,	PUNCT
ejpam-5473	328	21	1	1	NUM
ejpam-5473	328	22	]	]	NUM
ejpam-5473	328	23	)	)	PUNCT
ejpam-5473	328	24	,	,	PUNCT
ejpam-5473	328	25	f	f	PROPN
ejpam-5473	328	26	)	)	PUNCT
ejpam-5473	328	27	is	be	AUX
ejpam-5473	328	28	a	a	DET
ejpam-5473	328	29	bvf	bvf	NOUN
ejpam-5473	328	30	-	-	PUNCT
ejpam-5473	328	31	group	group	NOUN
ejpam-5473	328	32	iff	iff	NOUN
ejpam-5473	328	33	the	the	DET
ejpam-5473	328	34	following	following	ADJ
ejpam-5473	328	35	restrictions	restriction	NOUN
ejpam-5473	328	36	are	be	AUX
ejpam-5473	328	37	hold	hold	ADJ
ejpam-5473	328	38	:	:	PUNCT
ejpam-5473	328	39	(	(	PUNCT
ejpam-5473	328	40	l	l	NOUN
ejpam-5473	328	41	)	)	PUNCT
ejpam-5473	328	42	for	for	ADP
ejpam-5473	328	43	any	any	DET
ejpam-5473	328	44	bvf	bvf	NOUN
ejpam-5473	328	45	-	-	PUNCT
ejpam-5473	328	46	elements	element	NOUN
ejpam-5473	328	47	,	,	PUNCT
ejpam-5473	328	48	(	(	PUNCT
ejpam-5473	328	49	x	x	X
ejpam-5473	328	50	,	,	PUNCT
ejpam-5473	328	51	[	[	X
ejpam-5473	328	52	−1	−1	NOUN
ejpam-5473	328	53	,	,	PUNCT
ejpam-5473	328	54	0	0	NUM
ejpam-5473	328	55	]	]	PUNCT
ejpam-5473	328	56	,	,	PUNCT
ejpam-5473	329	1	[	[	X
ejpam-5473	329	2	0	0	NUM
ejpam-5473	329	3	,	,	PUNCT
ejpam-5473	329	4	1	1	NUM
ejpam-5473	329	5	]	]	NUM
ejpam-5473	329	6	)	)	PUNCT
ejpam-5473	329	7	,	,	PUNCT
ejpam-5473	329	8	(	(	PUNCT
ejpam-5473	329	9	y	y	NOUN
ejpam-5473	329	10	,	,	PUNCT
ejpam-5473	329	11	[	[	X
ejpam-5473	329	12	−1	−1	NOUN
ejpam-5473	329	13	,	,	PUNCT
ejpam-5473	329	14	0	0	NUM
ejpam-5473	329	15	]	]	PUNCT
ejpam-5473	329	16	,	,	PUNCT
ejpam-5473	329	17	[	[	X
ejpam-5473	329	18	0	0	NUM
ejpam-5473	329	19	,	,	PUNCT
ejpam-5473	329	20	1	1	NUM
ejpam-5473	329	21	]	]	NUM
ejpam-5473	329	22	)	)	PUNCT
ejpam-5473	329	23	,	,	PUNCT
ejpam-5473	329	24	(	(	PUNCT
ejpam-5473	329	25	z	z	X
ejpam-5473	329	26	,	,	PUNCT
ejpam-5473	329	27	[	[	X
ejpam-5473	329	28	−1	−1	NOUN
ejpam-5473	329	29	,	,	PUNCT
ejpam-5473	329	30	0	0	NUM
ejpam-5473	329	31	]	]	PUNCT
ejpam-5473	329	32	,	,	PUNCT
ejpam-5473	329	33	[	[	X
ejpam-5473	329	34	0	0	NUM
ejpam-5473	329	35	,	,	PUNCT
ejpam-5473	329	36	1	1	NUM
ejpam-5473	329	37	]	]	PUNCT
ejpam-5473	329	38	)	)	PUNCT
ejpam-5473	329	39	∈	∈	PROPN
ejpam-5473	329	40	(	(	PUNCT
ejpam-5473	329	41	g	g	NOUN
ejpam-5473	329	42	,	,	PUNCT
ejpam-5473	329	43	[	[	X
ejpam-5473	329	44	−1	−1	NOUN
ejpam-5473	329	45	,	,	PUNCT
ejpam-5473	329	46	0	0	NUM
ejpam-5473	329	47	]	]	PUNCT
ejpam-5473	329	48	,	,	PUNCT
ejpam-5473	330	1	[	[	X
ejpam-5473	330	2	0	0	NUM
ejpam-5473	330	3	,	,	PUNCT
ejpam-5473	330	4	1	1	NUM
ejpam-5473	330	5	]	]	NUM
ejpam-5473	330	6	)	)	PUNCT
ejpam-5473	330	7	,	,	PUNCT
ejpam-5473	330	8	f	f	PROPN
ejpam-5473	330	9	):	):	PUNCT
ejpam-5473	330	10	(	(	PUNCT
ejpam-5473	330	11	(	(	PUNCT
ejpam-5473	330	12	x	x	X
ejpam-5473	330	13	,	,	PUNCT
ejpam-5473	330	14	[	[	X
ejpam-5473	330	15	−1	−1	NOUN
ejpam-5473	330	16	,	,	PUNCT
ejpam-5473	330	17	0	0	NUM
ejpam-5473	330	18	]	]	PUNCT
ejpam-5473	330	19	,	,	PUNCT
ejpam-5473	331	1	[	[	X
ejpam-5473	331	2	0	0	NUM
ejpam-5473	331	3	,	,	PUNCT
ejpam-5473	331	4	1])f	1])f	NUM
ejpam-5473	331	5	(	(	PUNCT
ejpam-5473	331	6	y	y	NOUN
ejpam-5473	331	7	,	,	PUNCT
ejpam-5473	331	8	[	[	X
ejpam-5473	331	9	−1	−1	NOUN
ejpam-5473	331	10	,	,	PUNCT
ejpam-5473	331	11	0	0	NUM
ejpam-5473	331	12	]	]	PUNCT
ejpam-5473	331	13	,	,	PUNCT
ejpam-5473	332	1	[	[	X
ejpam-5473	332	2	0	0	NUM
ejpam-5473	332	3	,	,	PUNCT
ejpam-5473	332	4	1]))f	1]))f	NUM
ejpam-5473	332	5	(	(	PUNCT
ejpam-5473	332	6	z	z	NOUN
ejpam-5473	332	7	,	,	PUNCT
ejpam-5473	332	8	[	[	X
ejpam-5473	332	9	−1	−1	NOUN
ejpam-5473	332	10	,	,	PUNCT
ejpam-5473	332	11	0	0	NUM
ejpam-5473	332	12	]	]	PUNCT
ejpam-5473	332	13	,	,	PUNCT
ejpam-5473	332	14	[	[	X
ejpam-5473	332	15	0	0	NUM
ejpam-5473	332	16	,	,	PUNCT
ejpam-5473	332	17	1	1	NUM
ejpam-5473	332	18	]	]	PUNCT
ejpam-5473	332	19	)	)	PUNCT
ejpam-5473	333	1	=	=	SYM
ejpam-5473	333	2	(	(	PUNCT
ejpam-5473	333	3	x	x	X
ejpam-5473	333	4	,	,	PUNCT
ejpam-5473	333	5	[	[	X
ejpam-5473	333	6	−1	−1	NOUN
ejpam-5473	333	7	,	,	PUNCT
ejpam-5473	333	8	0	0	NUM
ejpam-5473	333	9	]	]	PUNCT
ejpam-5473	333	10	,	,	PUNCT
ejpam-5473	334	1	[	[	X
ejpam-5473	334	2	0	0	NUM
ejpam-5473	334	3	,	,	PUNCT
ejpam-5473	334	4	1])f	1])f	NUM
ejpam-5473	334	5	(	(	PUNCT
ejpam-5473	334	6	(	(	PUNCT
ejpam-5473	334	7	y	y	NOUN
ejpam-5473	334	8	,	,	PUNCT
ejpam-5473	334	9	[	[	X
ejpam-5473	334	10	−1	−1	NOUN
ejpam-5473	334	11	,	,	PUNCT
ejpam-5473	334	12	0	0	NUM
ejpam-5473	334	13	]	]	PUNCT
ejpam-5473	334	14	,	,	PUNCT
ejpam-5473	334	15	[	[	X
ejpam-5473	334	16	0	0	NUM
ejpam-5473	334	17	,	,	PUNCT
ejpam-5473	334	18	1])f	1])f	NUM
ejpam-5473	334	19	(	(	PUNCT
ejpam-5473	334	20	z	z	NOUN
ejpam-5473	334	21	,	,	PUNCT
ejpam-5473	334	22	[	[	X
ejpam-5473	334	23	−1	−1	NOUN
ejpam-5473	334	24	,	,	PUNCT
ejpam-5473	334	25	0	0	NUM
ejpam-5473	334	26	]	]	PUNCT
ejpam-5473	334	27	,	,	PUNCT
ejpam-5473	334	28	[	[	X
ejpam-5473	334	29	0	0	NUM
ejpam-5473	334	30	,	,	PUNCT
ejpam-5473	334	31	1	1	NUM
ejpam-5473	334	32	]	]	NUM
ejpam-5473	334	33	)	)	PUNCT
ejpam-5473	334	34	)	)	PUNCT
ejpam-5473	334	35	.	.	PUNCT
ejpam-5473	335	1	(	(	PUNCT
ejpam-5473	335	2	2	2	X
ejpam-5473	335	3	)	)	PUNCT
ejpam-5473	335	4	there	there	PRON
ejpam-5473	335	5	exists	exist	VERB
ejpam-5473	335	6	a	a	DET
ejpam-5473	335	7	bvf	bvf	NOUN
ejpam-5473	335	8	-	-	PUNCT
ejpam-5473	335	9	element	element	NOUN
ejpam-5473	335	10	(	(	PUNCT
ejpam-5473	335	11	e	e	NOUN
ejpam-5473	335	12	,	,	PUNCT
ejpam-5473	335	13	[	[	X
ejpam-5473	335	14	−1	−1	NOUN
ejpam-5473	335	15	,	,	PUNCT
ejpam-5473	335	16	0	0	NUM
ejpam-5473	335	17	]	]	PUNCT
ejpam-5473	335	18	,	,	PUNCT
ejpam-5473	336	1	[	[	X
ejpam-5473	336	2	0	0	NUM
ejpam-5473	336	3	,	,	PUNCT
ejpam-5473	336	4	1	1	NUM
ejpam-5473	336	5	]	]	PUNCT
ejpam-5473	336	6	)	)	PUNCT
ejpam-5473	336	7	∈	∈	PROPN
ejpam-5473	336	8	(	(	PUNCT
ejpam-5473	336	9	g	g	NOUN
ejpam-5473	336	10	,	,	PUNCT
ejpam-5473	336	11	[	[	X
ejpam-5473	336	12	−1	−1	NOUN
ejpam-5473	336	13	,	,	PUNCT
ejpam-5473	336	14	0	0	NUM
ejpam-5473	336	15	]	]	PUNCT
ejpam-5473	336	16	,	,	PUNCT
ejpam-5473	337	1	[	[	X
ejpam-5473	337	2	0	0	NUM
ejpam-5473	337	3	,	,	PUNCT
ejpam-5473	337	4	1	1	NUM
ejpam-5473	337	5	]	]	PUNCT
ejpam-5473	337	6	)	)	PUNCT
ejpam-5473	338	1	such	such	ADJ
ejpam-5473	338	2	that	that	PRON
ejpam-5473	338	3	for	for	ADP
ejpam-5473	338	4	all	all	DET
ejpam-5473	338	5	(	(	PUNCT
ejpam-5473	338	6	x	x	NOUN
ejpam-5473	338	7	,	,	PUNCT
ejpam-5473	338	8	[	[	X
ejpam-5473	338	9	−1	−1	NOUN
ejpam-5473	338	10	,	,	PUNCT
ejpam-5473	338	11	0	0	NUM
ejpam-5473	338	12	]	]	PUNCT
ejpam-5473	338	13	,	,	PUNCT
ejpam-5473	338	14	[	[	X
ejpam-5473	338	15	0	0	NUM
ejpam-5473	338	16	,	,	PUNCT
ejpam-5473	338	17	1	1	NUM
ejpam-5473	338	18	]	]	PUNCT
ejpam-5473	338	19	)	)	PUNCT
ejpam-5473	338	20	in	in	ADP
ejpam-5473	338	21	(	(	PUNCT
ejpam-5473	338	22	(	(	PUNCT
ejpam-5473	338	23	g	g	NOUN
ejpam-5473	338	24	,	,	PUNCT
ejpam-5473	338	25	[	[	X
ejpam-5473	338	26	−1	−1	NOUN
ejpam-5473	338	27	,	,	PUNCT
ejpam-5473	338	28	0	0	NUM
ejpam-5473	338	29	]	]	PUNCT
ejpam-5473	338	30	,	,	PUNCT
ejpam-5473	338	31	[	[	X
ejpam-5473	338	32	0	0	NUM
ejpam-5473	338	33	,	,	PUNCT
ejpam-5473	338	34	1	1	NUM
ejpam-5473	338	35	]	]	NUM
ejpam-5473	338	36	)	)	PUNCT
ejpam-5473	338	37	,	,	PUNCT
ejpam-5473	338	38	f	f	PROPN
ejpam-5473	338	39	)	)	PUNCT
ejpam-5473	338	40	:	:	PUNCT
ejpam-5473	338	41	(	(	PUNCT
ejpam-5473	338	42	e	e	X
ejpam-5473	338	43	,	,	PUNCT
ejpam-5473	338	44	[	[	X
ejpam-5473	338	45	−1	−1	NOUN
ejpam-5473	338	46	,	,	PUNCT
ejpam-5473	338	47	0	0	NUM
ejpam-5473	338	48	]	]	PUNCT
ejpam-5473	338	49	,	,	PUNCT
ejpam-5473	338	50	[	[	X
ejpam-5473	338	51	0	0	NUM
ejpam-5473	338	52	,	,	PUNCT
ejpam-5473	338	53	1])f	1])f	NUM
ejpam-5473	338	54	(	(	PUNCT
ejpam-5473	338	55	x	x	X
ejpam-5473	338	56	,	,	PUNCT
ejpam-5473	338	57	[	[	X
ejpam-5473	338	58	−1	−1	NOUN
ejpam-5473	338	59	,	,	PUNCT
ejpam-5473	338	60	0	0	NUM
ejpam-5473	338	61	]	]	PUNCT
ejpam-5473	338	62	,	,	PUNCT
ejpam-5473	338	63	[	[	X
ejpam-5473	338	64	0	0	NUM
ejpam-5473	338	65	,	,	PUNCT
ejpam-5473	338	66	1	1	NUM
ejpam-5473	338	67	]	]	PUNCT
ejpam-5473	338	68	)	)	PUNCT
ejpam-5473	338	69	=	=	SYM
ejpam-5473	338	70	(	(	PUNCT
ejpam-5473	338	71	x	x	X
ejpam-5473	338	72	,	,	PUNCT
ejpam-5473	338	73	[	[	X
ejpam-5473	338	74	−1	−1	NOUN
ejpam-5473	338	75	,	,	PUNCT
ejpam-5473	338	76	0	0	NUM
ejpam-5473	338	77	]	]	PUNCT
ejpam-5473	338	78	,	,	PUNCT
ejpam-5473	339	1	[	[	X
ejpam-5473	339	2	0	0	NUM
ejpam-5473	339	3	,	,	PUNCT
ejpam-5473	339	4	1])f	1])f	NUM
ejpam-5473	339	5	(	(	PUNCT
ejpam-5473	339	6	e	e	NOUN
ejpam-5473	339	7	,	,	PUNCT
ejpam-5473	339	8	[	[	X
ejpam-5473	339	9	−1	−1	NOUN
ejpam-5473	339	10	,	,	PUNCT
ejpam-5473	339	11	0	0	NUM
ejpam-5473	339	12	]	]	PUNCT
ejpam-5473	339	13	,	,	PUNCT
ejpam-5473	339	14	[	[	X
ejpam-5473	339	15	0	0	NUM
ejpam-5473	339	16	,	,	PUNCT
ejpam-5473	339	17	1	1	NUM
ejpam-5473	339	18	]	]	PUNCT
ejpam-5473	339	19	)	)	PUNCT
ejpam-5473	340	1	=	=	SYM
ejpam-5473	340	2	(	(	PUNCT
ejpam-5473	340	3	x	x	X
ejpam-5473	340	4	,	,	PUNCT
ejpam-5473	340	5	[	[	X
ejpam-5473	340	6	−1	−1	NOUN
ejpam-5473	340	7	,	,	PUNCT
ejpam-5473	340	8	0	0	NUM
ejpam-5473	340	9	]	]	PUNCT
ejpam-5473	340	10	,	,	PUNCT
ejpam-5473	341	1	[	[	X
ejpam-5473	341	2	0	0	NUM
ejpam-5473	341	3	,	,	PUNCT
ejpam-5473	341	4	1	1	NUM
ejpam-5473	341	5	]	]	PUNCT
ejpam-5473	341	6	)	)	PUNCT
ejpam-5473	341	7	.	.	PUNCT
ejpam-5473	342	1	(	(	PUNCT
ejpam-5473	342	2	3	3	X
ejpam-5473	342	3	)	)	PUNCT
ejpam-5473	342	4	for	for	ADP
ejpam-5473	342	5	every	every	DET
ejpam-5473	342	6	bvf	bvf	NOUN
ejpam-5473	342	7	-	-	PUNCT
ejpam-5473	342	8	element	element	NOUN
ejpam-5473	342	9	(	(	PUNCT
ejpam-5473	342	10	x	x	X
ejpam-5473	342	11	,	,	PUNCT
ejpam-5473	342	12	[	[	X
ejpam-5473	342	13	−1	−1	NOUN
ejpam-5473	342	14	,	,	PUNCT
ejpam-5473	342	15	0	0	NUM
ejpam-5473	342	16	]	]	PUNCT
ejpam-5473	342	17	,	,	PUNCT
ejpam-5473	343	1	[	[	X
ejpam-5473	343	2	0	0	NUM
ejpam-5473	343	3	,	,	PUNCT
ejpam-5473	343	4	1	1	NUM
ejpam-5473	343	5	]	]	PUNCT
ejpam-5473	343	6	)	)	PUNCT
ejpam-5473	343	7	in	in	ADP
ejpam-5473	343	8	(	(	PUNCT
ejpam-5473	343	9	(	(	PUNCT
ejpam-5473	343	10	g	g	NOUN
ejpam-5473	343	11	,	,	PUNCT
ejpam-5473	343	12	[	[	X
ejpam-5473	343	13	−1	−1	NOUN
ejpam-5473	343	14	,	,	PUNCT
ejpam-5473	343	15	0	0	NUM
ejpam-5473	343	16	]	]	PUNCT
ejpam-5473	343	17	,	,	PUNCT
ejpam-5473	343	18	[	[	X
ejpam-5473	343	19	0	0	NUM
ejpam-5473	343	20	,	,	PUNCT
ejpam-5473	343	21	1	1	NUM
ejpam-5473	343	22	]	]	NUM
ejpam-5473	343	23	)	)	PUNCT
ejpam-5473	343	24	,	,	PUNCT
ejpam-5473	343	25	f	f	PROPN
ejpam-5473	343	26	)	)	PUNCT
ejpam-5473	343	27	there	there	PRON
ejpam-5473	343	28	exists	exist	VERB
ejpam-5473	343	29	a	a	DET
ejpam-5473	343	30	bvf	bvf	NOUN
ejpam-5473	343	31	-	-	PUNCT
ejpam-5473	343	32	element	element	NOUN
ejpam-5473	343	33	(	(	PUNCT
ejpam-5473	343	34	x−1	x−1	PROPN
ejpam-5473	343	35	,	,	PUNCT
ejpam-5473	343	36	[	[	X
ejpam-5473	343	37	−1	−1	NOUN
ejpam-5473	343	38	,	,	PUNCT
ejpam-5473	343	39	0	0	NUM
ejpam-5473	343	40	]	]	PUNCT
ejpam-5473	343	41	,	,	PUNCT
ejpam-5473	343	42	[	[	X
ejpam-5473	343	43	0	0	NUM
ejpam-5473	343	44	,	,	PUNCT
ejpam-5473	343	45	1	1	NUM
ejpam-5473	343	46	]	]	PUNCT
ejpam-5473	343	47	)	)	PUNCT
ejpam-5473	343	48	in	in	ADP
ejpam-5473	343	49	(	(	PUNCT
ejpam-5473	343	50	g	g	NOUN
ejpam-5473	343	51	,	,	PUNCT
ejpam-5473	343	52	[	[	X
ejpam-5473	343	53	−1	−1	NOUN
ejpam-5473	343	54	,	,	PUNCT
ejpam-5473	343	55	0	0	NUM
ejpam-5473	343	56	]	]	PUNCT
ejpam-5473	343	57	,	,	PUNCT
ejpam-5473	343	58	[	[	X
ejpam-5473	343	59	0	0	NUM
ejpam-5473	343	60	,	,	PUNCT
ejpam-5473	343	61	1	1	NUM
ejpam-5473	343	62	]	]	NUM
ejpam-5473	343	63	)	)	PUNCT
ejpam-5473	343	64	,	,	PUNCT
ejpam-5473	343	65	f	f	PROPN
ejpam-5473	343	66	)	)	PUNCT
ejpam-5473	343	67	such	such	ADJ
ejpam-5473	343	68	that	that	SCONJ
ejpam-5473	343	69	:	:	PUNCT
ejpam-5473	343	70	(	(	PUNCT
ejpam-5473	343	71	x	x	X
ejpam-5473	343	72	,	,	PUNCT
ejpam-5473	343	73	[	[	X
ejpam-5473	343	74	−1	−1	NOUN
ejpam-5473	343	75	,	,	PUNCT
ejpam-5473	343	76	0	0	NUM
ejpam-5473	343	77	]	]	PUNCT
ejpam-5473	343	78	,	,	PUNCT
ejpam-5473	343	79	[	[	X
ejpam-5473	343	80	0	0	NUM
ejpam-5473	343	81	,	,	PUNCT
ejpam-5473	343	82	1])f	1])f	NUM
ejpam-5473	343	83	(	(	PUNCT
ejpam-5473	343	84	x−1	x−1	PROPN
ejpam-5473	343	85	,	,	PUNCT
ejpam-5473	343	86	[	[	X
ejpam-5473	343	87	−1	−1	NOUN
ejpam-5473	343	88	,	,	PUNCT
ejpam-5473	343	89	0	0	NUM
ejpam-5473	343	90	]	]	PUNCT
ejpam-5473	343	91	,	,	PUNCT
ejpam-5473	343	92	[	[	X
ejpam-5473	343	93	0	0	NUM
ejpam-5473	343	94	,	,	PUNCT
ejpam-5473	343	95	1	1	NUM
ejpam-5473	343	96	]	]	PUNCT
ejpam-5473	343	97	)	)	PUNCT
ejpam-5473	344	1	=	=	SYM
ejpam-5473	344	2	(	(	PUNCT
ejpam-5473	344	3	x−1	x−1	PROPN
ejpam-5473	344	4	,	,	PUNCT
ejpam-5473	344	5	[	[	X
ejpam-5473	344	6	−1	−1	NOUN
ejpam-5473	344	7	,	,	PUNCT
ejpam-5473	344	8	0	0	NUM
ejpam-5473	344	9	]	]	PUNCT
ejpam-5473	344	10	,	,	PUNCT
ejpam-5473	345	1	[	[	X
ejpam-5473	345	2	0	0	NUM
ejpam-5473	345	3	,	,	PUNCT
ejpam-5473	345	4	1	1	NUM
ejpam-5473	345	5	]	]	PUNCT
ejpam-5473	345	6	)	)	PUNCT
ejpam-5473	345	7	f	f	PROPN
ejpam-5473	345	8	(	(	PUNCT
ejpam-5473	345	9	x	x	X
ejpam-5473	345	10	,	,	PUNCT
ejpam-5473	345	11	[	[	X
ejpam-5473	345	12	−1	−1	NOUN
ejpam-5473	345	13	,	,	PUNCT
ejpam-5473	345	14	0	0	NUM
ejpam-5473	345	15	]	]	PUNCT
ejpam-5473	345	16	,	,	PUNCT
ejpam-5473	346	1	[	[	X
ejpam-5473	346	2	0	0	NUM
ejpam-5473	346	3	,	,	PUNCT
ejpam-5473	346	4	1	1	NUM
ejpam-5473	346	5	]	]	PUNCT
ejpam-5473	346	6	)	)	PUNCT
ejpam-5473	347	1	=	=	SYM
ejpam-5473	347	2	(	(	PUNCT
ejpam-5473	347	3	e	e	NOUN
ejpam-5473	347	4	,	,	PUNCT
ejpam-5473	347	5	[	[	X
ejpam-5473	347	6	−1	−1	NOUN
ejpam-5473	347	7	,	,	PUNCT
ejpam-5473	347	8	0	0	NUM
ejpam-5473	347	9	]	]	PUNCT
ejpam-5473	347	10	,	,	PUNCT
ejpam-5473	348	1	[	[	X
ejpam-5473	348	2	0	0	NUM
ejpam-5473	348	3	,	,	PUNCT
ejpam-5473	348	4	1	1	NUM
ejpam-5473	348	5	]	]	PUNCT
ejpam-5473	348	6	)	)	PUNCT
ejpam-5473	348	7	.	.	PUNCT
ejpam-5473	349	1	a	a	DET
ejpam-5473	349	2	bvf	bvf	NOUN
ejpam-5473	349	3	-	-	PUNCT
ejpam-5473	349	4	group	group	NOUN
ejpam-5473	349	5	(	(	PUNCT
ejpam-5473	349	6	(	(	PUNCT
ejpam-5473	349	7	g	g	NOUN
ejpam-5473	349	8	,	,	PUNCT
ejpam-5473	349	9	[	[	X
ejpam-5473	349	10	−1	−1	NOUN
ejpam-5473	349	11	,	,	PUNCT
ejpam-5473	349	12	0	0	NUM
ejpam-5473	349	13	]	]	PUNCT
ejpam-5473	349	14	,	,	PUNCT
ejpam-5473	349	15	[	[	X
ejpam-5473	349	16	0	0	NUM
ejpam-5473	349	17	,	,	PUNCT
ejpam-5473	349	18	1	1	NUM
ejpam-5473	349	19	]	]	NUM
ejpam-5473	349	20	)	)	PUNCT
ejpam-5473	349	21	,	,	PUNCT
ejpam-5473	349	22	f	f	PROPN
ejpam-5473	349	23	)	)	PUNCT
ejpam-5473	349	24	is	be	AUX
ejpam-5473	349	25	named	name	VERB
ejpam-5473	349	26	an	an	DET
ejpam-5473	349	27	abelian	abelian	ADJ
ejpam-5473	349	28	bvf	bvf	NOUN
ejpam-5473	349	29	-	-	PUNCT
ejpam-5473	349	30	group	group	NOUN
ejpam-5473	349	31	if	if	SCONJ
ejpam-5473	349	32	and	and	CCONJ
ejpam-5473	349	33	only	only	ADV
ejpam-5473	349	34	if	if	SCONJ
ejpam-5473	349	35	for	for	ADP
ejpam-5473	349	36	all	all	DET
ejpam-5473	349	37	(	(	PUNCT
ejpam-5473	349	38	x	x	NOUN
ejpam-5473	349	39	,	,	PUNCT
ejpam-5473	349	40	[	[	X
ejpam-5473	349	41	−1	−1	NOUN
ejpam-5473	349	42	,	,	PUNCT
ejpam-5473	349	43	0	0	NUM
ejpam-5473	349	44	]	]	PUNCT
ejpam-5473	349	45	,	,	PUNCT
ejpam-5473	349	46	[	[	X
ejpam-5473	349	47	0	0	NUM
ejpam-5473	349	48	,	,	PUNCT
ejpam-5473	349	49	1	1	NUM
ejpam-5473	349	50	]	]	PUNCT
ejpam-5473	349	51	)	)	PUNCT
ejpam-5473	349	52	,	,	PUNCT
ejpam-5473	349	53	(	(	PUNCT
ejpam-5473	349	54	y	y	NOUN
ejpam-5473	349	55	,	,	PUNCT
ejpam-5473	349	56	[	[	X
ejpam-5473	349	57	−1	−1	NOUN
ejpam-5473	349	58	,	,	PUNCT
ejpam-5473	349	59	0	0	NUM
ejpam-5473	349	60	]	]	PUNCT
ejpam-5473	349	61	,	,	PUNCT
ejpam-5473	349	62	[	[	X
ejpam-5473	349	63	0	0	NUM
ejpam-5473	349	64	,	,	PUNCT
ejpam-5473	349	65	1	1	NUM
ejpam-5473	349	66	]	]	PUNCT
ejpam-5473	349	67	)	)	PUNCT
ejpam-5473	349	68	∈	∈	PROPN
ejpam-5473	349	69	(	(	PUNCT
ejpam-5473	349	70	(	(	PUNCT
ejpam-5473	349	71	g	g	NOUN
ejpam-5473	349	72	,	,	PUNCT
ejpam-5473	349	73	[	[	X
ejpam-5473	349	74	−1	−1	NOUN
ejpam-5473	349	75	,	,	PUNCT
ejpam-5473	349	76	0	0	NUM
ejpam-5473	349	77	]	]	PUNCT
ejpam-5473	349	78	,	,	PUNCT
ejpam-5473	350	1	[	[	X
ejpam-5473	350	2	0	0	NUM
ejpam-5473	350	3	,	,	PUNCT
ejpam-5473	350	4	1	1	NUM
ejpam-5473	350	5	]	]	PUNCT
ejpam-5473	350	6	)	)	PUNCT
ejpam-5473	350	7	,	,	PUNCT
ejpam-5473	350	8	f	f	PROPN
ejpam-5473	350	9	)	)	PUNCT
ejpam-5473	350	10	.	.	PUNCT
ejpam-5473	351	1	(	(	PUNCT
ejpam-5473	351	2	x	x	X
ejpam-5473	351	3	,	,	PUNCT
ejpam-5473	351	4	[	[	X
ejpam-5473	351	5	−1	−1	NOUN
ejpam-5473	351	6	,	,	PUNCT
ejpam-5473	351	7	0	0	NUM
ejpam-5473	351	8	]	]	PUNCT
ejpam-5473	351	9	,	,	PUNCT
ejpam-5473	351	10	[	[	X
ejpam-5473	351	11	0	0	NUM
ejpam-5473	351	12	,	,	PUNCT
ejpam-5473	351	13	1])f	1])f	NUM
ejpam-5473	351	14	(	(	PUNCT
ejpam-5473	351	15	y	y	NOUN
ejpam-5473	351	16	,	,	PUNCT
ejpam-5473	351	17	[	[	X
ejpam-5473	351	18	−1	−1	NOUN
ejpam-5473	351	19	,	,	PUNCT
ejpam-5473	351	20	0	0	NUM
ejpam-5473	351	21	]	]	PUNCT
ejpam-5473	351	22	,	,	PUNCT
ejpam-5473	351	23	[	[	X
ejpam-5473	351	24	0	0	NUM
ejpam-5473	351	25	,	,	PUNCT
ejpam-5473	351	26	1	1	NUM
ejpam-5473	351	27	]	]	PUNCT
ejpam-5473	351	28	)	)	PUNCT
ejpam-5473	351	29	=	=	SYM
ejpam-5473	351	30	(	(	PUNCT
ejpam-5473	351	31	y	y	NOUN
ejpam-5473	351	32	,	,	PUNCT
ejpam-5473	351	33	[	[	X
ejpam-5473	351	34	−1	−1	NOUN
ejpam-5473	351	35	,	,	PUNCT
ejpam-5473	351	36	0	0	NUM
ejpam-5473	351	37	]	]	PUNCT
ejpam-5473	351	38	,	,	PUNCT
ejpam-5473	351	39	[	[	X
ejpam-5473	351	40	0	0	NUM
ejpam-5473	351	41	,	,	PUNCT
ejpam-5473	351	42	1])f	1])f	NUM
ejpam-5473	351	43	(	(	PUNCT
ejpam-5473	351	44	x	x	X
ejpam-5473	351	45	,	,	PUNCT
ejpam-5473	351	46	[	[	X
ejpam-5473	351	47	−1	−1	NOUN
ejpam-5473	351	48	,	,	PUNCT
ejpam-5473	351	49	0	0	NUM
ejpam-5473	351	50	]	]	PUNCT
ejpam-5473	351	51	,	,	PUNCT
ejpam-5473	351	52	[	[	X
ejpam-5473	351	53	0	0	NUM
ejpam-5473	351	54	,	,	PUNCT
ejpam-5473	351	55	1	1	NUM
ejpam-5473	351	56	]	]	PUNCT
ejpam-5473	351	57	)	)	PUNCT
ejpam-5473	351	58	.	.	PUNCT
ejpam-5473	352	1	identical	identical	ADJ
ejpam-5473	352	2	to	to	ADP
ejpam-5473	352	3	the	the	DET
ejpam-5473	352	4	bipolar	bipolar	PROPN
ejpam-5473	352	5	valued	value	VERB
ejpam-5473	352	6	fuzzy	fuzzy	ADJ
ejpam-5473	352	7	groupoid	groupoid	NOUN
ejpam-5473	352	8	,	,	PUNCT
ejpam-5473	352	9	the	the	DET
ejpam-5473	352	10	following	follow	VERB
ejpam-5473	352	11	theorem	theorem	NOUN
ejpam-5473	352	12	establishes	establish	VERB
ejpam-5473	352	13	a	a	DET
ejpam-5473	352	14	relationship	relationship	NOUN
ejpam-5473	352	15	between	between	ADP
ejpam-5473	352	16	bvf	bvf	NOUN
ejpam-5473	352	17	-	-	PUNCT
ejpam-5473	352	18	groups	group	NOUN
ejpam-5473	352	19	and	and	CCONJ
ejpam-5473	352	20	both	both	CCONJ
ejpam-5473	352	21	ordinary	ordinary	ADJ
ejpam-5473	352	22	and	and	CCONJ
ejpam-5473	352	23	fuzzy	fuzzy	ADJ
ejpam-5473	352	24	groups	group	NOUN
ejpam-5473	352	25	.	.	PUNCT
ejpam-5473	353	1	f.	f.	PROPN
ejpam-5473	353	2	al	al	PROPN
ejpam-5473	353	3	-	-	PROPN
ejpam-5473	353	4	zu’bi	zu’bi	PROPN
ejpam-5473	353	5	et	et	NOUN
ejpam-5473	353	6	al	al	PROPN
ejpam-5473	353	7	.	.	PUNCT
ejpam-5473	353	8	/	/	SYM
ejpam-5473	353	9	eur	eur	PROPN
ejpam-5473	353	10	.	.	PUNCT
ejpam-5473	354	1	j.	j.	PROPN
ejpam-5473	354	2	pure	pure	PROPN
ejpam-5473	354	3	appl	appl	PROPN
ejpam-5473	354	4	.	.	PROPN
ejpam-5473	354	5	math	math	PROPN
ejpam-5473	354	6	,	,	PUNCT
ejpam-5473	354	7	17	17	NUM
ejpam-5473	354	8	(	(	PUNCT
ejpam-5473	354	9	4	4	NUM
ejpam-5473	354	10	)	)	PUNCT
ejpam-5473	354	11	(	(	PUNCT
ejpam-5473	354	12	2024	2024	NUM
ejpam-5473	354	13	)	)	PUNCT
ejpam-5473	354	14	,	,	PUNCT
ejpam-5473	354	15	2898	2898	NUM
ejpam-5473	354	16	-	-	SYM
ejpam-5473	354	17	2914	2914	NUM
ejpam-5473	354	18	2909	2909	NUM
ejpam-5473	354	19	theorem	theorem	NOUN
ejpam-5473	354	20	3	3	NUM
ejpam-5473	354	21	.	.	PUNCT
ejpam-5473	354	22	(	(	PUNCT
ejpam-5473	354	23	1	1	X
ejpam-5473	354	24	)	)	PUNCT
ejpam-5473	354	25	associated	associate	VERB
ejpam-5473	354	26	to	to	ADP
ejpam-5473	354	27	each	each	DET
ejpam-5473	354	28	bipolar	bipolar	PROPN
ejpam-5473	354	29	valued	value	VERB
ejpam-5473	354	30	fuzzy	fuzzy	ADJ
ejpam-5473	354	31	group	group	NOUN
ejpam-5473	354	32	(	(	PUNCT
ejpam-5473	354	33	(	(	PUNCT
ejpam-5473	354	34	g	g	NOUN
ejpam-5473	354	35	,	,	PUNCT
ejpam-5473	354	36	[	[	X
ejpam-5473	354	37	−1	−1	NOUN
ejpam-5473	354	38	,	,	PUNCT
ejpam-5473	354	39	0	0	NUM
ejpam-5473	354	40	]	]	PUNCT
ejpam-5473	354	41	,	,	PUNCT
ejpam-5473	355	1	[	[	X
ejpam-5473	355	2	0	0	NUM
ejpam-5473	355	3	,	,	PUNCT
ejpam-5473	355	4	1	1	NUM
ejpam-5473	355	5	]	]	NUM
ejpam-5473	355	6	)	)	PUNCT
ejpam-5473	355	7	,	,	PUNCT
ejpam-5473	355	8	f	f	PROPN
ejpam-5473	355	9	)	)	PUNCT
ejpam-5473	355	10	where	where	SCONJ
ejpam-5473	355	11	f	f	X
ejpam-5473	355	12	=	=	PRON
ejpam-5473	355	13	(	(	PUNCT
ejpam-5473	355	14	f	f	X
ejpam-5473	355	15	,	,	PUNCT
ejpam-5473	355	16	f−	f−	PROPN
ejpam-5473	355	17	xy	xy	PROPN
ejpam-5473	355	18	,	,	PUNCT
ejpam-5473	355	19	f+	f+	PROPN
ejpam-5473	355	20	xy	xy	PROPN
ejpam-5473	355	21	)	)	PUNCT
ejpam-5473	355	22	a	a	DET
ejpam-5473	355	23	fuzzy	fuzzy	ADJ
ejpam-5473	355	24	group	group	NOUN
ejpam-5473	355	25	(	(	PUNCT
ejpam-5473	355	26	(	(	PUNCT
ejpam-5473	355	27	g	g	NOUN
ejpam-5473	355	28	,	,	PUNCT
ejpam-5473	355	29	[	[	X
ejpam-5473	355	30	0	0	NUM
ejpam-5473	355	31	,	,	PUNCT
ejpam-5473	355	32	1	1	NUM
ejpam-5473	355	33	]	]	PUNCT
ejpam-5473	355	34	)	)	PUNCT
ejpam-5473	355	35	,	,	PUNCT
ejpam-5473	355	36	f	f	PROPN
ejpam-5473	355	37	)	)	PUNCT
ejpam-5473	355	38	where	where	SCONJ
ejpam-5473	355	39	f	f	X
ejpam-5473	355	40	=	=	PRON
ejpam-5473	355	41	(	(	PUNCT
ejpam-5473	355	42	f	f	X
ejpam-5473	355	43	,	,	PUNCT
ejpam-5473	355	44	f+	f+	PROPN
ejpam-5473	355	45	xy	xy	PROPN
ejpam-5473	355	46	)	)	PUNCT
ejpam-5473	355	47	which	which	PRON
ejpam-5473	355	48	is	be	AUX
ejpam-5473	355	49	isomorphic	isomorphic	ADJ
ejpam-5473	355	50	to	to	ADP
ejpam-5473	355	51	the	the	DET
ejpam-5473	355	52	bipolar	bipolar	ADJ
ejpam-5473	355	53	valued	value	VERB
ejpam-5473	355	54	fuzzy	fuzzy	ADJ
ejpam-5473	355	55	group	group	NOUN
ejpam-5473	355	56	(	(	PUNCT
ejpam-5473	355	57	g	g	NOUN
ejpam-5473	355	58	,	,	PUNCT
ejpam-5473	355	59	[	[	X
ejpam-5473	355	60	−1	−1	NOUN
ejpam-5473	355	61	,	,	PUNCT
ejpam-5473	355	62	0	0	NUM
ejpam-5473	355	63	]	]	PUNCT
ejpam-5473	355	64	,	,	PUNCT
ejpam-5473	355	65	[	[	X
ejpam-5473	355	66	0	0	NUM
ejpam-5473	355	67	,	,	PUNCT
ejpam-5473	355	68	1	1	NUM
ejpam-5473	355	69	]	]	NUM
ejpam-5473	355	70	)	)	PUNCT
ejpam-5473	355	71	,	,	PUNCT
ejpam-5473	355	72	f	f	PROPN
ejpam-5473	355	73	)	)	PUNCT
ejpam-5473	355	74	by	by	ADP
ejpam-5473	355	75	the	the	DET
ejpam-5473	355	76	correspondence	correspondence	NOUN
ejpam-5473	355	77	(	(	PUNCT
ejpam-5473	355	78	x	x	X
ejpam-5473	355	79	,	,	PUNCT
ejpam-5473	355	80	[	[	X
ejpam-5473	355	81	−1	−1	NOUN
ejpam-5473	355	82	,	,	PUNCT
ejpam-5473	355	83	0	0	NUM
ejpam-5473	355	84	]	]	PUNCT
ejpam-5473	355	85	,	,	PUNCT
ejpam-5473	355	86	[	[	X
ejpam-5473	355	87	0	0	NUM
ejpam-5473	355	88	,	,	PUNCT
ejpam-5473	355	89	1	1	NUM
ejpam-5473	355	90	]	]	PUNCT
ejpam-5473	355	91	)	)	PUNCT
ejpam-5473	355	92	↔	↔	PROPN
ejpam-5473	355	93	(	(	PUNCT
ejpam-5473	355	94	x	x	X
ejpam-5473	355	95	,	,	PUNCT
ejpam-5473	355	96	[	[	X
ejpam-5473	355	97	0	0	NUM
ejpam-5473	355	98	,	,	PUNCT
ejpam-5473	355	99	1	1	NUM
ejpam-5473	355	100	]	]	NUM
ejpam-5473	355	101	)	)	PUNCT
ejpam-5473	355	102	.	.	PUNCT
ejpam-5473	356	1	(	(	PUNCT
ejpam-5473	356	2	2	2	X
ejpam-5473	356	3	)	)	PUNCT
ejpam-5473	356	4	there	there	PRON
ejpam-5473	356	5	is	be	VERB
ejpam-5473	356	6	an	an	DET
ejpam-5473	356	7	associated	associate	VERB
ejpam-5473	356	8	(	(	PUNCT
ejpam-5473	356	9	ordinary	ordinary	ADJ
ejpam-5473	356	10	)	)	PUNCT
ejpam-5473	356	11	group	group	NOUN
ejpam-5473	356	12	(	(	PUNCT
ejpam-5473	356	13	g	g	PROPN
ejpam-5473	356	14	,	,	PUNCT
ejpam-5473	356	15	f	f	PROPN
ejpam-5473	356	16	)	)	PUNCT
ejpam-5473	356	17	to	to	ADP
ejpam-5473	356	18	any	any	DET
ejpam-5473	356	19	bipolar	bipolar	ADJ
ejpam-5473	356	20	valued	value	VERB
ejpam-5473	356	21	fuzzy	fuzzy	ADJ
ejpam-5473	356	22	group	group	NOUN
ejpam-5473	356	23	(	(	PUNCT
ejpam-5473	356	24	(	(	PUNCT
ejpam-5473	356	25	g	g	NOUN
ejpam-5473	356	26	,	,	PUNCT
ejpam-5473	356	27	[	[	X
ejpam-5473	356	28	−1	−1	NOUN
ejpam-5473	356	29	,	,	PUNCT
ejpam-5473	356	30	0	0	NUM
ejpam-5473	356	31	]	]	PUNCT
ejpam-5473	356	32	,	,	PUNCT
ejpam-5473	356	33	[	[	X
ejpam-5473	356	34	0	0	NUM
ejpam-5473	356	35	,	,	PUNCT
ejpam-5473	356	36	1]),f	1]),f	NUM
ejpam-5473	356	37	)	)	PUNCT
ejpam-5473	356	38	that	that	PRON
ejpam-5473	356	39	is	be	AUX
ejpam-5473	356	40	isomorphic	isomorphic	ADJ
ejpam-5473	356	41	to	to	ADP
ejpam-5473	356	42	the	the	DET
ejpam-5473	356	43	bipolar	bipolar	ADJ
ejpam-5473	356	44	valued	value	VERB
ejpam-5473	356	45	fuzzy	fuzzy	ADJ
ejpam-5473	356	46	group	group	NOUN
ejpam-5473	356	47	via	via	ADP
ejpam-5473	356	48	the	the	DET
ejpam-5473	356	49	corresponding	correspond	VERB
ejpam-5473	356	50	(	(	PUNCT
ejpam-5473	356	51	x	x	X
ejpam-5473	356	52	,	,	PUNCT
ejpam-5473	356	53	[	[	X
ejpam-5473	356	54	−1	−1	NOUN
ejpam-5473	356	55	,	,	PUNCT
ejpam-5473	356	56	0	0	NUM
ejpam-5473	356	57	]	]	PUNCT
ejpam-5473	356	58	,	,	PUNCT
ejpam-5473	356	59	[	[	X
ejpam-5473	356	60	0	0	NUM
ejpam-5473	356	61	,	,	PUNCT
ejpam-5473	356	62	1	1	NUM
ejpam-5473	356	63	]	]	PUNCT
ejpam-5473	356	64	)	)	PUNCT
ejpam-5473	356	65	↔	↔	PROPN
ejpam-5473	356	66	x.	x.	NOUN
ejpam-5473	356	67	proof	proof	NOUN
ejpam-5473	356	68	.	.	PUNCT
ejpam-5473	357	1	the	the	DET
ejpam-5473	357	2	proof	proof	NOUN
ejpam-5473	357	3	is	be	AUX
ejpam-5473	357	4	like	like	ADP
ejpam-5473	357	5	theorem	theorem	NOUN
ejpam-5473	357	6	1	1	NUM
ejpam-5473	357	7	as	as	ADP
ejpam-5473	357	8	a	a	DET
ejpam-5473	357	9	result	result	NOUN
ejpam-5473	357	10	of	of	ADP
ejpam-5473	357	11	the	the	DET
ejpam-5473	357	12	prior	prior	ADJ
ejpam-5473	357	13	theorems	theorem	NOUN
ejpam-5473	357	14	,	,	PUNCT
ejpam-5473	357	15	the	the	DET
ejpam-5473	357	16	following	follow	VERB
ejpam-5473	357	17	corollary	corollary	ADJ
ejpam-5473	357	18	supplies	supply	NOUN
ejpam-5473	357	19	an	an	DET
ejpam-5473	357	20	adequate	adequate	ADJ
ejpam-5473	357	21	and	and	CCONJ
ejpam-5473	357	22	mandatory	mandatory	ADJ
ejpam-5473	357	23	condition	condition	NOUN
ejpam-5473	357	24	for	for	ADP
ejpam-5473	357	25	a	a	DET
ejpam-5473	357	26	bipolar	bipolar	ADJ
ejpam-5473	357	27	valued	value	VERB
ejpam-5473	357	28	fuzzy	fuzzy	ADJ
ejpam-5473	357	29	group	group	NOUN
ejpam-5473	357	30	.	.	PUNCT
ejpam-5473	358	1	corollary	corollary	ADJ
ejpam-5473	358	2	1	1	NUM
ejpam-5473	358	3	.	.	PUNCT
ejpam-5473	359	1	let	let	VERB
ejpam-5473	359	2	(	(	PUNCT
ejpam-5473	359	3	℧	℧	PROPN
ejpam-5473	359	4	,	,	PUNCT
ejpam-5473	359	5	[	[	X
ejpam-5473	359	6	−1	−1	NOUN
ejpam-5473	359	7	,	,	PUNCT
ejpam-5473	359	8	0	0	NUM
ejpam-5473	359	9	]	]	PUNCT
ejpam-5473	359	10	,	,	PUNCT
ejpam-5473	360	1	[	[	X
ejpam-5473	360	2	0	0	NUM
ejpam-5473	360	3	,	,	PUNCT
ejpam-5473	360	4	1	1	NUM
ejpam-5473	360	5	]	]	PUNCT
ejpam-5473	360	6	)	)	PUNCT
ejpam-5473	360	7	be	be	AUX
ejpam-5473	360	8	an	an	DET
ejpam-5473	360	9	bvf	bvf	NOUN
ejpam-5473	360	10	-	-	PUNCT
ejpam-5473	360	11	space	space	NOUN
ejpam-5473	360	12	and	and	CCONJ
ejpam-5473	360	13	let	let	VERB
ejpam-5473	360	14	f	f	PROPN
ejpam-5473	360	15	=	=	SYM
ejpam-5473	360	16	(	(	PUNCT
ejpam-5473	360	17	f	f	X
ejpam-5473	360	18	,	,	PUNCT
ejpam-5473	360	19	f−	f−	PROPN
ejpam-5473	360	20	xy	xy	PROPN
ejpam-5473	360	21	,	,	PUNCT
ejpam-5473	360	22	f+	f+	PROPN
ejpam-5473	360	23	xy	xy	NOUN
ejpam-5473	360	24	)	)	PUNCT
ejpam-5473	360	25	be	be	AUX
ejpam-5473	360	26	an	an	DET
ejpam-5473	360	27	bipolar	bipolar	ADJ
ejpam-5473	360	28	valued	value	VERB
ejpam-5473	360	29	fuzzy	fuzzy	ADJ
ejpam-5473	360	30	binary	binary	ADJ
ejpam-5473	360	31	operation	operation	NOUN
ejpam-5473	360	32	defined	define	VERB
ejpam-5473	360	33	over	over	ADP
ejpam-5473	360	34	(	(	PUNCT
ejpam-5473	360	35	℧	℧	PROPN
ejpam-5473	360	36	,	,	PUNCT
ejpam-5473	360	37	[	[	X
ejpam-5473	360	38	−1	−1	NOUN
ejpam-5473	360	39	,	,	PUNCT
ejpam-5473	360	40	0	0	NUM
ejpam-5473	360	41	]	]	PUNCT
ejpam-5473	360	42	,	,	PUNCT
ejpam-5473	361	1	[	[	X
ejpam-5473	361	2	0	0	NUM
ejpam-5473	361	3	,	,	PUNCT
ejpam-5473	361	4	1	1	NUM
ejpam-5473	361	5	]	]	PUNCT
ejpam-5473	361	6	)	)	PUNCT
ejpam-5473	361	7	.	.	PUNCT
ejpam-5473	362	1	the	the	DET
ejpam-5473	362	2	algebraic	algebraic	ADJ
ejpam-5473	362	3	structure	structure	NOUN
ejpam-5473	362	4	(	(	PUNCT
ejpam-5473	362	5	(	(	PUNCT
ejpam-5473	362	6	℧	℧	PROPN
ejpam-5473	362	7	,	,	PUNCT
ejpam-5473	362	8	[	[	X
ejpam-5473	362	9	−1	−1	NOUN
ejpam-5473	362	10	,	,	PUNCT
ejpam-5473	362	11	0	0	NUM
ejpam-5473	362	12	]	]	PUNCT
ejpam-5473	362	13	,	,	PUNCT
ejpam-5473	362	14	[	[	X
ejpam-5473	362	15	0	0	NUM
ejpam-5473	362	16	,	,	PUNCT
ejpam-5473	362	17	1	1	NUM
ejpam-5473	362	18	]	]	PUNCT
ejpam-5473	362	19	)	)	PUNCT
ejpam-5473	362	20	,	,	PUNCT
ejpam-5473	362	21	f	f	PROPN
ejpam-5473	362	22	)	)	PUNCT
ejpam-5473	362	23	defines	define	VERB
ejpam-5473	362	24	an	an	DET
ejpam-5473	362	25	bvf	bvf	NOUN
ejpam-5473	362	26	-	-	PUNCT
ejpam-5473	362	27	group	group	NOUN
ejpam-5473	362	28	iff	iff	PROPN
ejpam-5473	362	29	(	(	PUNCT
ejpam-5473	362	30	(	(	PUNCT
ejpam-5473	362	31	℧	℧	PROPN
ejpam-5473	362	32	,	,	PUNCT
ejpam-5473	362	33	[	[	X
ejpam-5473	362	34	0	0	NUM
ejpam-5473	362	35	,	,	PUNCT
ejpam-5473	362	36	1	1	NUM
ejpam-5473	362	37	]	]	PUNCT
ejpam-5473	362	38	)	)	PUNCT
ejpam-5473	362	39	,	,	PUNCT
ejpam-5473	362	40	f	f	PROPN
ejpam-5473	362	41	)	)	PUNCT
ejpam-5473	362	42	and	and	CCONJ
ejpam-5473	362	43	(	(	PUNCT
ejpam-5473	362	44	(	(	PUNCT
ejpam-5473	362	45	℧	℧	PROPN
ejpam-5473	362	46	,	,	PUNCT
ejpam-5473	362	47	[	[	X
ejpam-5473	362	48	0	0	NUM
ejpam-5473	362	49	,	,	PUNCT
ejpam-5473	362	50	1	1	NUM
ejpam-5473	362	51	]	]	PUNCT
ejpam-5473	362	52	)	)	PUNCT
ejpam-5473	362	53	,	,	PUNCT
ejpam-5473	362	54	f	f	PROPN
ejpam-5473	362	55	)	)	PUNCT
ejpam-5473	362	56	are	be	AUX
ejpam-5473	362	57	both	both	PRON
ejpam-5473	362	58	fuzzy	fuzzy	ADJ
ejpam-5473	362	59	groups	group	NOUN
ejpam-5473	362	60	,	,	PUNCT
ejpam-5473	362	61	where	where	SCONJ
ejpam-5473	362	62	f	f	PROPN
ejpam-5473	362	63	=	=	PRON
ejpam-5473	362	64	(	(	PUNCT
ejpam-5473	362	65	f	f	X
ejpam-5473	362	66	,	,	PUNCT
ejpam-5473	362	67	f+	f+	PROPN
ejpam-5473	362	68	xy	xy	PROPN
ejpam-5473	362	69	)	)	PUNCT
ejpam-5473	363	1	and	and	CCONJ
ejpam-5473	363	2	f	f	X
ejpam-5473	363	3	=	=	PRON
ejpam-5473	363	4	(	(	PUNCT
ejpam-5473	363	5	f	f	X
ejpam-5473	363	6	,	,	PUNCT
ejpam-5473	363	7	∣∣f−	∣∣f−	NOUN
ejpam-5473	363	8	xy	xy	PROPN
ejpam-5473	363	9	∣∣	∣∣	PROPN
ejpam-5473	363	10	)	)	PUNCT
ejpam-5473	363	11	.	.	PUNCT
ejpam-5473	364	1	example	example	NOUN
ejpam-5473	365	1	6	6	NUM
ejpam-5473	365	2	.	.	PUNCT
ejpam-5473	366	1	let	let	VERB
ejpam-5473	366	2	g	g	NOUN
ejpam-5473	366	3	=	=	PUNCT
ejpam-5473	366	4	{	{	PUNCT
ejpam-5473	366	5	b	b	AUX
ejpam-5473	366	6	}	}	PUNCT
ejpam-5473	366	7	be	be	AUX
ejpam-5473	366	8	a	a	DET
ejpam-5473	366	9	singleton	singleton	NOUN
ejpam-5473	366	10	set	set	NOUN
ejpam-5473	366	11	.	.	PUNCT
ejpam-5473	367	1	define	define	VERB
ejpam-5473	367	2	the	the	DET
ejpam-5473	367	3	bvfbo	bvfbo	PRON
ejpam-5473	367	4	f	f	PROPN
ejpam-5473	367	5	=	=	SYM
ejpam-5473	367	6	(	(	PUNCT
ejpam-5473	367	7	f	f	X
ejpam-5473	367	8	,	,	PUNCT
ejpam-5473	367	9	f−	f−	PROPN
ejpam-5473	367	10	xy	xy	PROPN
ejpam-5473	367	11	,	,	PUNCT
ejpam-5473	367	12	f+	f+	PROPN
ejpam-5473	367	13	xy	xy	NOUN
ejpam-5473	367	14	)	)	PUNCT
ejpam-5473	367	15	over	over	ADP
ejpam-5473	367	16	the	the	DET
ejpam-5473	367	17	bvf	bvf	NOUN
ejpam-5473	367	18	-	-	PUNCT
ejpam-5473	367	19	space	space	NOUN
ejpam-5473	367	20	(	(	PUNCT
ejpam-5473	367	21	g	g	NOUN
ejpam-5473	367	22	,	,	PUNCT
ejpam-5473	367	23	[	[	X
ejpam-5473	367	24	−1	−1	NOUN
ejpam-5473	367	25	,	,	PUNCT
ejpam-5473	367	26	0	0	NUM
ejpam-5473	367	27	]	]	PUNCT
ejpam-5473	367	28	,	,	PUNCT
ejpam-5473	367	29	[	[	X
ejpam-5473	367	30	0	0	NUM
ejpam-5473	367	31	,	,	PUNCT
ejpam-5473	367	32	1	1	NUM
ejpam-5473	367	33	]	]	PUNCT
ejpam-5473	367	34	)	)	PUNCT
ejpam-5473	367	35	such	such	ADJ
ejpam-5473	367	36	that	that	SCONJ
ejpam-5473	367	37	:	:	PUNCT
ejpam-5473	367	38	f	f	X
ejpam-5473	367	39	(	(	PUNCT
ejpam-5473	367	40	b	b	PROPN
ejpam-5473	367	41	,	,	PUNCT
ejpam-5473	367	42	b	b	NOUN
ejpam-5473	367	43	)	)	PUNCT
ejpam-5473	367	44	=	=	SYM
ejpam-5473	367	45	b	b	PROPN
ejpam-5473	367	46	and	and	CCONJ
ejpam-5473	367	47	f+	f+	NUM
ejpam-5473	367	48	bb	bb	INTJ
ejpam-5473	367	49	(	(	PUNCT
ejpam-5473	367	50	n	n	X
ejpam-5473	367	51	+	+	ADJ
ejpam-5473	367	52	,	,	PUNCT
ejpam-5473	367	53	m+	m+	NUM
ejpam-5473	367	54	)	)	PUNCT
ejpam-5473	367	55	=	=	PRON
ejpam-5473	367	56	n+	n+	PUNCT
ejpam-5473	368	1	∧m+	∧m+	ADJ
ejpam-5473	368	2	,	,	PUNCT
ejpam-5473	368	3	f−	f−	PROPN
ejpam-5473	368	4	bb	bb	PROPN
ejpam-5473	368	5	(	(	PUNCT
ejpam-5473	368	6	n	n	NUM
ejpam-5473	368	7	−	−	PROPN
ejpam-5473	368	8	,	,	PUNCT
ejpam-5473	368	9	m−	m−	PROPN
ejpam-5473	368	10	)	)	PUNCT
ejpam-5473	369	1	=	=	PUNCT
ejpam-5473	370	1	n−	n−	PROPN
ejpam-5473	370	2	∨m−.	∨m−.	ADJ
ejpam-5473	370	3	thus	thus	ADV
ejpam-5473	370	4	,	,	PUNCT
ejpam-5473	370	5	the	the	DET
ejpam-5473	370	6	bvf	bvf	NOUN
ejpam-5473	370	7	-	-	PUNCT
ejpam-5473	370	8	space	space	NOUN
ejpam-5473	370	9	(	(	PUNCT
ejpam-5473	370	10	g	g	NOUN
ejpam-5473	370	11	,	,	PUNCT
ejpam-5473	370	12	[	[	X
ejpam-5473	370	13	−1	−1	NOUN
ejpam-5473	370	14	,	,	PUNCT
ejpam-5473	370	15	0	0	NUM
ejpam-5473	370	16	]	]	PUNCT
ejpam-5473	370	17	,	,	PUNCT
ejpam-5473	370	18	[	[	X
ejpam-5473	370	19	0	0	NUM
ejpam-5473	370	20	,	,	PUNCT
ejpam-5473	370	21	1	1	NUM
ejpam-5473	370	22	]	]	PUNCT
ejpam-5473	370	23	)	)	PUNCT
ejpam-5473	370	24	together	together	ADV
ejpam-5473	370	25	with	with	ADP
ejpam-5473	370	26	f	f	PROPN
ejpam-5473	370	27	identify	identify	VERB
ejpam-5473	370	28	a	a	DET
ejpam-5473	370	29	trivial	trivial	ADJ
ejpam-5473	370	30	bvf	bvf	NOUN
ejpam-5473	370	31	-	-	PUNCT
ejpam-5473	370	32	group	group	NOUN
ejpam-5473	370	33	(	(	PUNCT
ejpam-5473	370	34	g	g	NOUN
ejpam-5473	370	35	,	,	PUNCT
ejpam-5473	370	36	[	[	X
ejpam-5473	370	37	−1	−1	NOUN
ejpam-5473	370	38	,	,	PUNCT
ejpam-5473	370	39	0	0	NUM
ejpam-5473	370	40	]	]	PUNCT
ejpam-5473	370	41	,	,	PUNCT
ejpam-5473	370	42	[	[	X
ejpam-5473	370	43	0	0	NUM
ejpam-5473	370	44	,	,	PUNCT
ejpam-5473	370	45	1	1	NUM
ejpam-5473	370	46	]	]	NUM
ejpam-5473	370	47	)	)	PUNCT
ejpam-5473	370	48	,	,	PUNCT
ejpam-5473	370	49	f	f	PROPN
ejpam-5473	370	50	)	)	PUNCT
ejpam-5473	370	51	.	.	PUNCT
ejpam-5473	371	1	example	example	NOUN
ejpam-5473	372	1	7	7	NUM
ejpam-5473	372	2	.	.	PUNCT
ejpam-5473	372	3	let	let	VERB
ejpam-5473	372	4	z5	z5	PROPN
ejpam-5473	372	5	=	=	SYM
ejpam-5473	372	6	{	{	PUNCT
ejpam-5473	372	7	0	0	NUM
ejpam-5473	372	8	,	,	PUNCT
ejpam-5473	372	9	1	1	NUM
ejpam-5473	372	10	,	,	PUNCT
ejpam-5473	372	11	2	2	NUM
ejpam-5473	372	12	,	,	PUNCT
ejpam-5473	372	13	3	3	NUM
ejpam-5473	372	14	,	,	PUNCT
ejpam-5473	372	15	4	4	NUM
ejpam-5473	372	16	}	}	PUNCT
ejpam-5473	372	17	be	be	AUX
ejpam-5473	372	18	a	a	DET
ejpam-5473	372	19	set	set	NOUN
ejpam-5473	372	20	.	.	PUNCT
ejpam-5473	373	1	define	define	VERB
ejpam-5473	373	2	the	the	DET
ejpam-5473	373	3	bvfbo	bvfbo	PRON
ejpam-5473	373	4	f	f	PROPN
ejpam-5473	373	5	=	=	SYM
ejpam-5473	373	6	(	(	PUNCT
ejpam-5473	373	7	f	f	X
ejpam-5473	373	8	,	,	PUNCT
ejpam-5473	373	9	f−	f−	PROPN
ejpam-5473	373	10	xy	xy	PROPN
ejpam-5473	373	11	,	,	PUNCT
ejpam-5473	373	12	f+	f+	PROPN
ejpam-5473	373	13	xy	xy	NOUN
ejpam-5473	373	14	)	)	PUNCT
ejpam-5473	373	15	over	over	ADP
ejpam-5473	373	16	the	the	DET
ejpam-5473	373	17	bvf	bvf	NOUN
ejpam-5473	373	18	-	-	PUNCT
ejpam-5473	373	19	space	space	NOUN
ejpam-5473	373	20	(	(	PUNCT
ejpam-5473	373	21	z5	z5	X
ejpam-5473	373	22	,	,	PUNCT
ejpam-5473	373	23	[	[	X
ejpam-5473	373	24	−1	−1	NOUN
ejpam-5473	373	25	,	,	PUNCT
ejpam-5473	373	26	0	0	NUM
ejpam-5473	373	27	]	]	PUNCT
ejpam-5473	373	28	,	,	PUNCT
ejpam-5473	373	29	[	[	X
ejpam-5473	373	30	0	0	NUM
ejpam-5473	373	31	,	,	PUNCT
ejpam-5473	373	32	1	1	NUM
ejpam-5473	373	33	]	]	PUNCT
ejpam-5473	373	34	)	)	PUNCT
ejpam-5473	373	35	as	as	SCONJ
ejpam-5473	373	36	follows	follow	VERB
ejpam-5473	373	37	:	:	PUNCT
ejpam-5473	373	38	f	f	PROPN
ejpam-5473	373	39	(	(	PUNCT
ejpam-5473	373	40	x	x	X
ejpam-5473	373	41	,	,	PUNCT
ejpam-5473	373	42	y	y	NOUN
ejpam-5473	373	43	)	)	PUNCT
ejpam-5473	373	44	=	=	PUNCT
ejpam-5473	374	1	x	x	PUNCT
ejpam-5473	374	2	+5	+5	PROPN
ejpam-5473	374	3	y	y	PROPN
ejpam-5473	374	4	,	,	PUNCT
ejpam-5473	374	5	where	where	SCONJ
ejpam-5473	374	6	+5	+5	PROPN
ejpam-5473	374	7	refers	refer	VERB
ejpam-5473	374	8	to	to	ADP
ejpam-5473	374	9	addition	addition	NOUN
ejpam-5473	374	10	modulo	modulo	NOUN
ejpam-5473	374	11	5	5	NUM
ejpam-5473	374	12	,	,	PUNCT
ejpam-5473	374	13	and	and	CCONJ
ejpam-5473	374	14	f+	f+	PROPN
ejpam-5473	374	15	xy	xy	PROPN
ejpam-5473	374	16	(	(	PUNCT
ejpam-5473	374	17	n	n	X
ejpam-5473	374	18	+	+	ADJ
ejpam-5473	374	19	,	,	PUNCT
ejpam-5473	374	20	m+	m+	NUM
ejpam-5473	374	21	)	)	PUNCT
ejpam-5473	374	22	=	=	SYM
ejpam-5473	374	23	n+.m+	n+.m+	NOUN
ejpam-5473	374	24	,	,	PUNCT
ejpam-5473	374	25	f−	f−	PROPN
ejpam-5473	374	26	xy	xy	PROPN
ejpam-5473	375	1	(	(	PUNCT
ejpam-5473	375	2	n	n	NUM
ejpam-5473	375	3	−	−	PROPN
ejpam-5473	375	4	,	,	PUNCT
ejpam-5473	375	5	m−	m−	PROPN
ejpam-5473	375	6	)	)	PUNCT
ejpam-5473	376	1	=	=	SYM
ejpam-5473	376	2	−	−	PROPN
ejpam-5473	376	3	(	(	PUNCT
ejpam-5473	376	4	n−.	n−.	PROPN
ejpam-5473	376	5	m−	m−	PROPN
ejpam-5473	376	6	)	)	PUNCT
ejpam-5473	376	7	.	.	PUNCT
ejpam-5473	377	1	thus	thus	ADV
ejpam-5473	377	2	(	(	PUNCT
ejpam-5473	377	3	(	(	PUNCT
ejpam-5473	377	4	z5	z5	X
ejpam-5473	377	5	,	,	PUNCT
ejpam-5473	377	6	[	[	X
ejpam-5473	377	7	−1	−1	NOUN
ejpam-5473	377	8	,	,	PUNCT
ejpam-5473	377	9	0	0	NUM
ejpam-5473	377	10	]	]	PUNCT
ejpam-5473	377	11	,	,	PUNCT
ejpam-5473	377	12	[	[	X
ejpam-5473	377	13	0	0	NUM
ejpam-5473	377	14	,	,	PUNCT
ejpam-5473	377	15	1	1	NUM
ejpam-5473	377	16	]	]	PUNCT
ejpam-5473	377	17	)	)	PUNCT
ejpam-5473	377	18	,	,	PUNCT
ejpam-5473	377	19	f	f	PROPN
ejpam-5473	377	20	)	)	PUNCT
ejpam-5473	377	21	is	be	AUX
ejpam-5473	377	22	a	a	DET
ejpam-5473	377	23	bvf	bvf	NOUN
ejpam-5473	377	24	-	-	PUNCT
ejpam-5473	377	25	group	group	NOUN
ejpam-5473	377	26	.	.	PUNCT
ejpam-5473	378	1	the	the	DET
ejpam-5473	378	2	following	follow	VERB
ejpam-5473	378	3	theorem	theorem	VERB
ejpam-5473	378	4	derives	derive	NOUN
ejpam-5473	378	5	directly	directly	ADV
ejpam-5473	378	6	from	from	ADP
ejpam-5473	378	7	theorem	theorem	ADJ
ejpam-5473	378	8	1	1	NUM
ejpam-5473	378	9	and	and	CCONJ
ejpam-5473	378	10	the	the	DET
ejpam-5473	378	11	notion	notion	NOUN
ejpam-5473	378	12	of	of	ADP
ejpam-5473	378	13	a	a	DET
ejpam-5473	378	14	bvf	bvf	NOUN
ejpam-5473	378	15	-	-	PUNCT
ejpam-5473	378	16	group	group	NOUN
ejpam-5473	378	17	.	.	PUNCT
ejpam-5473	379	1	theorem	theorem	ADJ
ejpam-5473	379	2	4	4	NUM
ejpam-5473	379	3	.	.	X
ejpam-5473	380	1	for	for	ADP
ejpam-5473	380	2	any	any	DET
ejpam-5473	380	3	bvf	bvf	NOUN
ejpam-5473	380	4	-	-	PUNCT
ejpam-5473	380	5	group	group	NOUN
ejpam-5473	380	6	(	(	PUNCT
ejpam-5473	380	7	(	(	PUNCT
ejpam-5473	380	8	g	g	NOUN
ejpam-5473	380	9	,	,	PUNCT
ejpam-5473	380	10	[	[	X
ejpam-5473	380	11	−1	−1	NOUN
ejpam-5473	380	12	,	,	PUNCT
ejpam-5473	380	13	0	0	NUM
ejpam-5473	380	14	]	]	PUNCT
ejpam-5473	380	15	,	,	PUNCT
ejpam-5473	380	16	[	[	X
ejpam-5473	380	17	0	0	NUM
ejpam-5473	380	18	,	,	PUNCT
ejpam-5473	380	19	1	1	NUM
ejpam-5473	380	20	]	]	NUM
ejpam-5473	380	21	)	)	PUNCT
ejpam-5473	380	22	,	,	PUNCT
ejpam-5473	380	23	f	f	PROPN
ejpam-5473	380	24	)	)	PUNCT
ejpam-5473	380	25	,	,	PUNCT
ejpam-5473	380	26	the	the	DET
ejpam-5473	380	27	next	next	ADJ
ejpam-5473	380	28	statements	statement	NOUN
ejpam-5473	380	29	are	be	AUX
ejpam-5473	380	30	true	true	ADJ
ejpam-5473	380	31	:	:	PUNCT
ejpam-5473	380	32	(	(	PUNCT
ejpam-5473	380	33	i	i	NOUN
ejpam-5473	380	34	)	)	PUNCT
ejpam-5473	380	35	the	the	DET
ejpam-5473	380	36	identity	identity	NOUN
ejpam-5473	380	37	of	of	ADP
ejpam-5473	380	38	element	element	NOUN
ejpam-5473	380	39	of	of	ADP
ejpam-5473	380	40	bvf	bvf	NOUN
ejpam-5473	380	41	-	-	PUNCT
ejpam-5473	380	42	group	group	NOUN
ejpam-5473	380	43	is	be	AUX
ejpam-5473	380	44	unique	unique	ADJ
ejpam-5473	380	45	.	.	PUNCT
ejpam-5473	381	1	(	(	PUNCT
ejpam-5473	381	2	ii	ii	NOUN
ejpam-5473	381	3	)	)	PUNCT
ejpam-5473	381	4	the	the	DET
ejpam-5473	381	5	inverse	inverse	NOUN
ejpam-5473	381	6	of	of	ADP
ejpam-5473	381	7	each	each	DET
ejpam-5473	381	8	bvf	bvf	NOUN
ejpam-5473	381	9	-	-	PUNCT
ejpam-5473	381	10	element	element	NOUN
ejpam-5473	381	11	(	(	PUNCT
ejpam-5473	381	12	x	x	X
ejpam-5473	381	13	,	,	PUNCT
ejpam-5473	381	14	[	[	X
ejpam-5473	381	15	−1	−1	NOUN
ejpam-5473	381	16	,	,	PUNCT
ejpam-5473	381	17	0	0	NUM
ejpam-5473	381	18	]	]	PUNCT
ejpam-5473	381	19	,	,	PUNCT
ejpam-5473	381	20	[	[	X
ejpam-5473	381	21	0	0	NUM
ejpam-5473	381	22	,	,	PUNCT
ejpam-5473	381	23	1	1	NUM
ejpam-5473	381	24	]	]	PUNCT
ejpam-5473	381	25	)	)	PUNCT
ejpam-5473	381	26	∈	∈	PROPN
ejpam-5473	381	27	(	(	PUNCT
ejpam-5473	381	28	(	(	PUNCT
ejpam-5473	381	29	g	g	NOUN
ejpam-5473	381	30	,	,	PUNCT
ejpam-5473	381	31	[	[	X
ejpam-5473	381	32	−1	−1	NOUN
ejpam-5473	381	33	,	,	PUNCT
ejpam-5473	381	34	0	0	NUM
ejpam-5473	381	35	]	]	PUNCT
ejpam-5473	381	36	,	,	PUNCT
ejpam-5473	382	1	[	[	X
ejpam-5473	382	2	0	0	NUM
ejpam-5473	382	3	,	,	PUNCT
ejpam-5473	382	4	1	1	NUM
ejpam-5473	382	5	]	]	NUM
ejpam-5473	382	6	)	)	PUNCT
ejpam-5473	382	7	,	,	PUNCT
ejpam-5473	382	8	f	f	PROPN
ejpam-5473	382	9	)	)	PUNCT
ejpam-5473	382	10	is	be	AUX
ejpam-5473	382	11	unique	unique	ADJ
ejpam-5473	382	12	.	.	PUNCT
ejpam-5473	383	1	(	(	PUNCT
ejpam-5473	383	2	iii	iii	NOUN
ejpam-5473	383	3	)	)	PUNCT
ejpam-5473	383	4	(	(	PUNCT
ejpam-5473	383	5	(	(	PUNCT
ejpam-5473	383	6	x−1)−1	x−1)−1	NOUN
ejpam-5473	383	7	,	,	PUNCT
ejpam-5473	383	8	[	[	X
ejpam-5473	383	9	−1	−1	NOUN
ejpam-5473	383	10	,	,	PUNCT
ejpam-5473	383	11	0	0	NUM
ejpam-5473	383	12	]	]	PUNCT
ejpam-5473	383	13	,	,	PUNCT
ejpam-5473	383	14	[	[	X
ejpam-5473	383	15	0	0	NUM
ejpam-5473	383	16	,	,	PUNCT
ejpam-5473	383	17	1	1	NUM
ejpam-5473	383	18	]	]	PUNCT
ejpam-5473	383	19	)	)	PUNCT
ejpam-5473	383	20	=	=	SYM
ejpam-5473	383	21	(	(	PUNCT
ejpam-5473	383	22	x	x	X
ejpam-5473	383	23	,	,	PUNCT
ejpam-5473	383	24	[	[	X
ejpam-5473	383	25	−1	−1	NOUN
ejpam-5473	383	26	,	,	PUNCT
ejpam-5473	383	27	0	0	NUM
ejpam-5473	383	28	]	]	PUNCT
ejpam-5473	383	29	,	,	PUNCT
ejpam-5473	383	30	[	[	X
ejpam-5473	383	31	0	0	NUM
ejpam-5473	383	32	,	,	PUNCT
ejpam-5473	383	33	1	1	NUM
ejpam-5473	383	34	]	]	NUM
ejpam-5473	383	35	)	)	PUNCT
ejpam-5473	383	36	(	(	PUNCT
ejpam-5473	383	37	iv	iv	X
ejpam-5473	383	38	)	)	PUNCT
ejpam-5473	383	39	for	for	ADP
ejpam-5473	383	40	all	all	DET
ejpam-5473	383	41	(	(	PUNCT
ejpam-5473	383	42	x	x	NOUN
ejpam-5473	383	43	,	,	PUNCT
ejpam-5473	383	44	[	[	X
ejpam-5473	383	45	−1	−1	NOUN
ejpam-5473	383	46	,	,	PUNCT
ejpam-5473	383	47	0	0	NUM
ejpam-5473	383	48	]	]	PUNCT
ejpam-5473	383	49	,	,	PUNCT
ejpam-5473	383	50	[	[	X
ejpam-5473	383	51	0	0	NUM
ejpam-5473	383	52	,	,	PUNCT
ejpam-5473	383	53	1	1	NUM
ejpam-5473	383	54	]	]	PUNCT
ejpam-5473	383	55	)	)	PUNCT
ejpam-5473	383	56	,	,	PUNCT
ejpam-5473	383	57	(	(	PUNCT
ejpam-5473	383	58	y	y	NOUN
ejpam-5473	383	59	,	,	PUNCT
ejpam-5473	383	60	[	[	X
ejpam-5473	383	61	−1	−1	NOUN
ejpam-5473	383	62	,	,	PUNCT
ejpam-5473	383	63	0	0	NUM
ejpam-5473	383	64	]	]	PUNCT
ejpam-5473	383	65	,	,	PUNCT
ejpam-5473	383	66	[	[	X
ejpam-5473	383	67	0	0	NUM
ejpam-5473	383	68	,	,	PUNCT
ejpam-5473	383	69	1	1	NUM
ejpam-5473	383	70	]	]	PUNCT
ejpam-5473	383	71	)	)	PUNCT
ejpam-5473	383	72	∈	∈	PROPN
ejpam-5473	383	73	(	(	PUNCT
ejpam-5473	383	74	(	(	PUNCT
ejpam-5473	383	75	g	g	NOUN
ejpam-5473	383	76	,	,	PUNCT
ejpam-5473	383	77	[	[	X
ejpam-5473	383	78	−1	−1	NOUN
ejpam-5473	383	79	,	,	PUNCT
ejpam-5473	383	80	0	0	NUM
ejpam-5473	383	81	]	]	PUNCT
ejpam-5473	383	82	,	,	PUNCT
ejpam-5473	383	83	[	[	X
ejpam-5473	383	84	0	0	NUM
ejpam-5473	383	85	,	,	PUNCT
ejpam-5473	383	86	1	1	NUM
ejpam-5473	383	87	]	]	PUNCT
ejpam-5473	383	88	)	)	PUNCT
ejpam-5473	383	89	,	,	PUNCT
ejpam-5473	383	90	f	f	PROPN
ejpam-5473	383	91	)	)	PUNCT
ejpam-5473	383	92	:	:	PUNCT
ejpam-5473	383	93	(	(	PUNCT
ejpam-5473	383	94	(	(	PUNCT
ejpam-5473	383	95	x	x	X
ejpam-5473	383	96	,	,	PUNCT
ejpam-5473	383	97	[	[	X
ejpam-5473	383	98	−1	−1	NOUN
ejpam-5473	383	99	,	,	PUNCT
ejpam-5473	383	100	0	0	NUM
ejpam-5473	383	101	]	]	PUNCT
ejpam-5473	383	102	,	,	PUNCT
ejpam-5473	383	103	[	[	X
ejpam-5473	383	104	0	0	NUM
ejpam-5473	383	105	,	,	PUNCT
ejpam-5473	383	106	1])f	1])f	NUM
ejpam-5473	383	107	(	(	PUNCT
ejpam-5473	383	108	y	y	NOUN
ejpam-5473	383	109	,	,	PUNCT
ejpam-5473	383	110	[	[	X
ejpam-5473	383	111	−1	−1	NOUN
ejpam-5473	383	112	,	,	PUNCT
ejpam-5473	383	113	0	0	NUM
ejpam-5473	383	114	]	]	PUNCT
ejpam-5473	383	115	,	,	PUNCT
ejpam-5473	383	116	[	[	X
ejpam-5473	383	117	0	0	NUM
ejpam-5473	383	118	,	,	PUNCT
ejpam-5473	383	119	1]))−1	1]))−1	NOUN
ejpam-5473	383	120	=	=	SYM
ejpam-5473	383	121	(	(	PUNCT
ejpam-5473	383	122	y−1	y−1	PROPN
ejpam-5473	383	123	,	,	PUNCT
ejpam-5473	383	124	[	[	X
ejpam-5473	383	125	−1	−1	NOUN
ejpam-5473	383	126	,	,	PUNCT
ejpam-5473	383	127	0	0	NUM
ejpam-5473	383	128	]	]	PUNCT
ejpam-5473	383	129	,	,	PUNCT
ejpam-5473	383	130	[	[	X
ejpam-5473	383	131	0	0	NUM
ejpam-5473	383	132	,	,	PUNCT
ejpam-5473	383	133	1	1	NUM
ejpam-5473	383	134	]	]	PUNCT
ejpam-5473	383	135	)	)	PUNCT
ejpam-5473	383	136	f	f	PROPN
ejpam-5473	383	137	(	(	PUNCT
ejpam-5473	383	138	x−1	x−1	PROPN
ejpam-5473	383	139	,	,	PUNCT
ejpam-5473	383	140	[	[	X
ejpam-5473	383	141	−1	−1	NOUN
ejpam-5473	383	142	,	,	PUNCT
ejpam-5473	383	143	0	0	NUM
ejpam-5473	383	144	]	]	PUNCT
ejpam-5473	383	145	,	,	PUNCT
ejpam-5473	383	146	[	[	X
ejpam-5473	383	147	0	0	NUM
ejpam-5473	383	148	,	,	PUNCT
ejpam-5473	383	149	1	1	NUM
ejpam-5473	383	150	]	]	PUNCT
ejpam-5473	383	151	)	)	PUNCT
ejpam-5473	383	152	.	.	PUNCT
ejpam-5473	384	1	(	(	PUNCT
ejpam-5473	384	2	v	v	NOUN
ejpam-5473	384	3	)	)	PUNCT
ejpam-5473	384	4	for	for	ADP
ejpam-5473	384	5	all	all	DET
ejpam-5473	384	6	(	(	PUNCT
ejpam-5473	384	7	x	x	NOUN
ejpam-5473	384	8	,	,	PUNCT
ejpam-5473	384	9	[	[	X
ejpam-5473	384	10	−1	−1	NOUN
ejpam-5473	384	11	,	,	PUNCT
ejpam-5473	384	12	0	0	NUM
ejpam-5473	384	13	]	]	PUNCT
ejpam-5473	384	14	,	,	PUNCT
ejpam-5473	385	1	[	[	X
ejpam-5473	385	2	0	0	NUM
ejpam-5473	385	3	,	,	PUNCT
ejpam-5473	385	4	1	1	NUM
ejpam-5473	385	5	]	]	NUM
ejpam-5473	385	6	)	)	PUNCT
ejpam-5473	385	7	,	,	PUNCT
ejpam-5473	385	8	(	(	PUNCT
ejpam-5473	385	9	y	y	NOUN
ejpam-5473	385	10	,	,	PUNCT
ejpam-5473	385	11	[	[	X
ejpam-5473	385	12	−1	−1	NOUN
ejpam-5473	385	13	,	,	PUNCT
ejpam-5473	385	14	0	0	NUM
ejpam-5473	385	15	]	]	PUNCT
ejpam-5473	385	16	,	,	PUNCT
ejpam-5473	385	17	[	[	X
ejpam-5473	385	18	0	0	NUM
ejpam-5473	385	19	,	,	PUNCT
ejpam-5473	385	20	1	1	NUM
ejpam-5473	385	21	]	]	NUM
ejpam-5473	385	22	)	)	PUNCT
ejpam-5473	385	23	,	,	PUNCT
ejpam-5473	385	24	(	(	PUNCT
ejpam-5473	385	25	z	z	X
ejpam-5473	385	26	,	,	PUNCT
ejpam-5473	385	27	[	[	X
ejpam-5473	385	28	−1	−1	NOUN
ejpam-5473	385	29	,	,	PUNCT
ejpam-5473	385	30	0	0	NUM
ejpam-5473	385	31	]	]	PUNCT
ejpam-5473	385	32	,	,	PUNCT
ejpam-5473	385	33	[	[	X
ejpam-5473	385	34	0	0	NUM
ejpam-5473	385	35	,	,	PUNCT
ejpam-5473	385	36	1	1	NUM
ejpam-5473	385	37	]	]	PUNCT
ejpam-5473	385	38	)	)	PUNCT
ejpam-5473	385	39	∈	∈	PROPN
ejpam-5473	385	40	(	(	PUNCT
ejpam-5473	385	41	(	(	PUNCT
ejpam-5473	385	42	g	g	NOUN
ejpam-5473	385	43	,	,	PUNCT
ejpam-5473	385	44	[	[	X
ejpam-5473	385	45	−1	−1	NOUN
ejpam-5473	385	46	,	,	PUNCT
ejpam-5473	385	47	0	0	NUM
ejpam-5473	385	48	]	]	PUNCT
ejpam-5473	385	49	,	,	PUNCT
ejpam-5473	386	1	[	[	X
ejpam-5473	386	2	0	0	NUM
ejpam-5473	386	3	,	,	PUNCT
ejpam-5473	386	4	1	1	NUM
ejpam-5473	386	5	]	]	PUNCT
ejpam-5473	386	6	)	)	PUNCT
ejpam-5473	386	7	,	,	PUNCT
ejpam-5473	386	8	f	f	PROPN
ejpam-5473	386	9	)	)	PUNCT
ejpam-5473	386	10	.	.	PUNCT
ejpam-5473	387	1	if	if	SCONJ
ejpam-5473	387	2	(	(	PUNCT
ejpam-5473	387	3	x	x	X
ejpam-5473	387	4	,	,	PUNCT
ejpam-5473	387	5	[	[	X
ejpam-5473	387	6	−1	−1	NOUN
ejpam-5473	387	7	,	,	PUNCT
ejpam-5473	387	8	0	0	NUM
ejpam-5473	387	9	]	]	PUNCT
ejpam-5473	387	10	,	,	PUNCT
ejpam-5473	387	11	[	[	X
ejpam-5473	387	12	0	0	NUM
ejpam-5473	387	13	,	,	PUNCT
ejpam-5473	387	14	1])f	1])f	NUM
ejpam-5473	387	15	(	(	PUNCT
ejpam-5473	387	16	y	y	NOUN
ejpam-5473	387	17	,	,	PUNCT
ejpam-5473	387	18	[	[	X
ejpam-5473	387	19	−1	−1	NOUN
ejpam-5473	387	20	,	,	PUNCT
ejpam-5473	387	21	0	0	NUM
ejpam-5473	387	22	]	]	PUNCT
ejpam-5473	387	23	,	,	PUNCT
ejpam-5473	387	24	[	[	X
ejpam-5473	387	25	0	0	NUM
ejpam-5473	387	26	,	,	PUNCT
ejpam-5473	387	27	1	1	NUM
ejpam-5473	387	28	]	]	NUM
ejpam-5473	387	29	)	)	PUNCT
ejpam-5473	387	30	,	,	PUNCT
ejpam-5473	387	31	and	and	CCONJ
ejpam-5473	387	32	(	(	PUNCT
ejpam-5473	387	33	z	z	X
ejpam-5473	387	34	,	,	PUNCT
ejpam-5473	387	35	[	[	X
ejpam-5473	387	36	−1	−1	NOUN
ejpam-5473	387	37	,	,	PUNCT
ejpam-5473	387	38	0	0	NUM
ejpam-5473	387	39	]	]	PUNCT
ejpam-5473	387	40	,	,	PUNCT
ejpam-5473	387	41	[	[	X
ejpam-5473	387	42	0	0	NUM
ejpam-5473	387	43	,	,	PUNCT
ejpam-5473	387	44	1])f	1])f	NUM
ejpam-5473	387	45	(	(	PUNCT
ejpam-5473	387	46	y	y	NOUN
ejpam-5473	387	47	,	,	PUNCT
ejpam-5473	387	48	[	[	X
ejpam-5473	387	49	−1	−1	NOUN
ejpam-5473	387	50	,	,	PUNCT
ejpam-5473	387	51	0	0	NUM
ejpam-5473	387	52	]	]	PUNCT
ejpam-5473	387	53	,	,	PUNCT
ejpam-5473	387	54	[	[	X
ejpam-5473	387	55	0	0	NUM
ejpam-5473	387	56	,	,	PUNCT
ejpam-5473	387	57	1	1	NUM
ejpam-5473	387	58	]	]	PUNCT
ejpam-5473	387	59	)	)	PUNCT
ejpam-5473	387	60	,	,	PUNCT
ejpam-5473	387	61	then	then	ADV
ejpam-5473	387	62	(	(	PUNCT
ejpam-5473	387	63	x	x	X
ejpam-5473	387	64	,	,	PUNCT
ejpam-5473	387	65	[	[	X
ejpam-5473	387	66	−1	−1	NOUN
ejpam-5473	387	67	,	,	PUNCT
ejpam-5473	387	68	0	0	NUM
ejpam-5473	387	69	]	]	PUNCT
ejpam-5473	387	70	,	,	PUNCT
ejpam-5473	387	71	[	[	X
ejpam-5473	387	72	0	0	NUM
ejpam-5473	387	73	,	,	PUNCT
ejpam-5473	387	74	1	1	NUM
ejpam-5473	387	75	]	]	PUNCT
ejpam-5473	387	76	)	)	PUNCT
ejpam-5473	387	77	=	=	SYM
ejpam-5473	388	1	(	(	PUNCT
ejpam-5473	388	2	z	z	NOUN
ejpam-5473	388	3	,	,	PUNCT
ejpam-5473	388	4	[	[	X
ejpam-5473	388	5	−1	−1	NOUN
ejpam-5473	388	6	,	,	PUNCT
ejpam-5473	388	7	0	0	NUM
ejpam-5473	388	8	]	]	PUNCT
ejpam-5473	388	9	,	,	PUNCT
ejpam-5473	389	1	[	[	X
ejpam-5473	389	2	0	0	NUM
ejpam-5473	389	3	,	,	PUNCT
ejpam-5473	389	4	1	1	NUM
ejpam-5473	389	5	]	]	NUM
ejpam-5473	389	6	)	)	PUNCT
ejpam-5473	389	7	.	.	PUNCT
ejpam-5473	390	1	f.	f.	PROPN
ejpam-5473	390	2	al	al	PROPN
ejpam-5473	390	3	-	-	PROPN
ejpam-5473	390	4	zu’bi	zu’bi	PROPN
ejpam-5473	390	5	et	et	NOUN
ejpam-5473	390	6	al	al	PROPN
ejpam-5473	390	7	.	.	PUNCT
ejpam-5473	390	8	/	/	SYM
ejpam-5473	390	9	eur	eur	PROPN
ejpam-5473	390	10	.	.	PUNCT
ejpam-5473	391	1	j.	j.	PROPN
ejpam-5473	391	2	pure	pure	PROPN
ejpam-5473	391	3	appl	appl	PROPN
ejpam-5473	391	4	.	.	PROPN
ejpam-5473	391	5	math	math	PROPN
ejpam-5473	391	6	,	,	PUNCT
ejpam-5473	391	7	17	17	NUM
ejpam-5473	391	8	(	(	PUNCT
ejpam-5473	391	9	4	4	NUM
ejpam-5473	391	10	)	)	PUNCT
ejpam-5473	391	11	(	(	PUNCT
ejpam-5473	391	12	2024	2024	NUM
ejpam-5473	391	13	)	)	PUNCT
ejpam-5473	391	14	,	,	PUNCT
ejpam-5473	391	15	2898	2898	NUM
ejpam-5473	391	16	-	-	SYM
ejpam-5473	391	17	2914	2914	NUM
ejpam-5473	391	18	2910	2910	NUM
ejpam-5473	391	19	if	if	SCONJ
ejpam-5473	391	20	(	(	PUNCT
ejpam-5473	391	21	y	y	NOUN
ejpam-5473	391	22	,	,	PUNCT
ejpam-5473	391	23	[	[	X
ejpam-5473	391	24	−1	−1	NOUN
ejpam-5473	391	25	,	,	PUNCT
ejpam-5473	391	26	0	0	NUM
ejpam-5473	391	27	]	]	PUNCT
ejpam-5473	391	28	,	,	PUNCT
ejpam-5473	392	1	[	[	X
ejpam-5473	392	2	0	0	NUM
ejpam-5473	392	3	,	,	PUNCT
ejpam-5473	392	4	1])f	1])f	NUM
ejpam-5473	392	5	(	(	PUNCT
ejpam-5473	392	6	x	x	X
ejpam-5473	392	7	,	,	PUNCT
ejpam-5473	392	8	[	[	X
ejpam-5473	392	9	−1	−1	NOUN
ejpam-5473	392	10	,	,	PUNCT
ejpam-5473	392	11	0	0	NUM
ejpam-5473	392	12	]	]	PUNCT
ejpam-5473	392	13	,	,	PUNCT
ejpam-5473	392	14	[	[	X
ejpam-5473	392	15	0	0	NUM
ejpam-5473	392	16	,	,	PUNCT
ejpam-5473	392	17	1	1	NUM
ejpam-5473	392	18	]	]	PUNCT
ejpam-5473	392	19	)	)	PUNCT
ejpam-5473	393	1	=	=	SYM
ejpam-5473	393	2	(	(	PUNCT
ejpam-5473	393	3	y	y	NOUN
ejpam-5473	393	4	,	,	PUNCT
ejpam-5473	393	5	[	[	X
ejpam-5473	393	6	−1	−1	NOUN
ejpam-5473	393	7	,	,	PUNCT
ejpam-5473	393	8	0	0	NUM
ejpam-5473	393	9	]	]	PUNCT
ejpam-5473	393	10	,	,	PUNCT
ejpam-5473	394	1	[	[	X
ejpam-5473	394	2	0	0	NUM
ejpam-5473	394	3	,	,	PUNCT
ejpam-5473	394	4	1])f	1])f	NUM
ejpam-5473	394	5	(	(	PUNCT
ejpam-5473	394	6	z	z	NOUN
ejpam-5473	394	7	,	,	PUNCT
ejpam-5473	394	8	[	[	X
ejpam-5473	394	9	−1	−1	NOUN
ejpam-5473	394	10	,	,	PUNCT
ejpam-5473	394	11	0	0	NUM
ejpam-5473	394	12	]	]	PUNCT
ejpam-5473	394	13	,	,	PUNCT
ejpam-5473	394	14	[	[	X
ejpam-5473	394	15	0	0	NUM
ejpam-5473	394	16	,	,	PUNCT
ejpam-5473	394	17	1	1	NUM
ejpam-5473	394	18	]	]	PUNCT
ejpam-5473	394	19	)	)	PUNCT
ejpam-5473	394	20	,	,	PUNCT
ejpam-5473	394	21	then	then	ADV
ejpam-5473	394	22	(	(	PUNCT
ejpam-5473	394	23	x	x	X
ejpam-5473	394	24	,	,	PUNCT
ejpam-5473	394	25	[	[	X
ejpam-5473	394	26	−1	−1	NOUN
ejpam-5473	394	27	,	,	PUNCT
ejpam-5473	394	28	0	0	NUM
ejpam-5473	394	29	]	]	PUNCT
ejpam-5473	394	30	,	,	PUNCT
ejpam-5473	394	31	[	[	X
ejpam-5473	394	32	0	0	NUM
ejpam-5473	394	33	,	,	PUNCT
ejpam-5473	394	34	1	1	NUM
ejpam-5473	394	35	]	]	PUNCT
ejpam-5473	394	36	)	)	PUNCT
ejpam-5473	394	37	=	=	SYM
ejpam-5473	395	1	(	(	PUNCT
ejpam-5473	395	2	z	z	NOUN
ejpam-5473	395	3	,	,	PUNCT
ejpam-5473	395	4	[	[	X
ejpam-5473	395	5	−1	−1	NOUN
ejpam-5473	395	6	,	,	PUNCT
ejpam-5473	395	7	0	0	NUM
ejpam-5473	395	8	]	]	PUNCT
ejpam-5473	395	9	,	,	PUNCT
ejpam-5473	396	1	[	[	X
ejpam-5473	396	2	0	0	NUM
ejpam-5473	396	3	,	,	PUNCT
ejpam-5473	396	4	1	1	NUM
ejpam-5473	396	5	]	]	NUM
ejpam-5473	396	6	)	)	PUNCT
ejpam-5473	396	7	.	.	PUNCT
ejpam-5473	397	1	proof	proof	NOUN
ejpam-5473	397	2	.	.	PUNCT
ejpam-5473	398	1	the	the	DET
ejpam-5473	398	2	proof	proof	NOUN
ejpam-5473	398	3	is	be	AUX
ejpam-5473	398	4	straightforward	straightforward	ADJ
ejpam-5473	398	5	.	.	PUNCT
ejpam-5473	399	1	5	5	X
ejpam-5473	399	2	.	.	X
ejpam-5473	399	3	conclusions	conclusion	NOUN
ejpam-5473	399	4	in	in	ADP
ejpam-5473	399	5	this	this	DET
ejpam-5473	399	6	research	research	NOUN
ejpam-5473	399	7	,	,	PUNCT
ejpam-5473	399	8	we	we	PRON
ejpam-5473	399	9	investigated	investigate	VERB
ejpam-5473	399	10	the	the	DET
ejpam-5473	399	11	expansions	expansion	NOUN
ejpam-5473	399	12	of	of	ADP
ejpam-5473	399	13	fuzzy	fuzzy	ADJ
ejpam-5473	399	14	groups	group	NOUN
ejpam-5473	399	15	to	to	ADP
ejpam-5473	399	16	a	a	DET
ejpam-5473	399	17	novel	novel	ADJ
ejpam-5473	399	18	framework	framework	NOUN
ejpam-5473	399	19	for	for	ADP
ejpam-5473	399	20	bvf	bvf	NOUN
ejpam-5473	399	21	-	-	PUNCT
ejpam-5473	399	22	groups	group	NOUN
ejpam-5473	399	23	.	.	PUNCT
ejpam-5473	400	1	we	we	PRON
ejpam-5473	400	2	extended	extend	VERB
ejpam-5473	400	3	traditional	traditional	ADJ
ejpam-5473	400	4	fuzzy	fuzzy	ADJ
ejpam-5473	400	5	set	set	NOUN
ejpam-5473	400	6	theory	theory	NOUN
ejpam-5473	400	7	by	by	ADP
ejpam-5473	400	8	introducing	introduce	VERB
ejpam-5473	400	9	the	the	DET
ejpam-5473	400	10	bvf	bvf	NOUN
ejpam-5473	400	11	-	-	PUNCT
ejpam-5473	400	12	space	space	NOUN
ejpam-5473	400	13	,	,	PUNCT
ejpam-5473	400	14	which	which	PRON
ejpam-5473	400	15	permits	permit	VERB
ejpam-5473	400	16	membership	membership	NOUN
ejpam-5473	400	17	values	value	NOUN
ejpam-5473	400	18	to	to	PART
ejpam-5473	400	19	vary	vary	VERB
ejpam-5473	400	20	between	between	ADP
ejpam-5473	400	21	[	[	X
ejpam-5473	400	22	−1	−1	NOUN
ejpam-5473	400	23	,	,	PUNCT
ejpam-5473	400	24	0	0	NUM
ejpam-5473	400	25	]	]	X
ejpam-5473	400	26	×	×	NOUN
ejpam-5473	401	1	[	[	X
ejpam-5473	401	2	0	0	NUM
ejpam-5473	401	3	,	,	PUNCT
ejpam-5473	401	4	1	1	NUM
ejpam-5473	401	5	]	]	PUNCT
ejpam-5473	401	6	instead	instead	ADV
ejpam-5473	401	7	of	of	ADP
ejpam-5473	401	8	just	just	ADV
ejpam-5473	401	9	[	[	X
ejpam-5473	401	10	0	0	NUM
ejpam-5473	401	11	,	,	PUNCT
ejpam-5473	401	12	1	1	NUM
ejpam-5473	401	13	]	]	PUNCT
ejpam-5473	401	14	.	.	PUNCT
ejpam-5473	402	1	the	the	DET
ejpam-5473	402	2	bvf	bvf	NOUN
ejpam-5473	402	3	-	-	PUNCT
ejpam-5473	402	4	space	space	NOUN
ejpam-5473	402	5	provides	provide	VERB
ejpam-5473	402	6	a	a	DET
ejpam-5473	402	7	more	more	ADV
ejpam-5473	402	8	thorough	thorough	ADJ
ejpam-5473	402	9	depiction	depiction	NOUN
ejpam-5473	402	10	of	of	ADP
ejpam-5473	402	11	bvf	bvf	NOUN
ejpam-5473	402	12	-	-	PUNCT
ejpam-5473	402	13	groups	group	NOUN
ejpam-5473	402	14	,	,	PUNCT
ejpam-5473	402	15	acting	act	VERB
ejpam-5473	402	16	as	as	ADP
ejpam-5473	402	17	a	a	DET
ejpam-5473	402	18	substitute	substitute	NOUN
ejpam-5473	402	19	for	for	ADP
ejpam-5473	402	20	the	the	DET
ejpam-5473	402	21	universal	universal	ADJ
ejpam-5473	402	22	set	set	NOUN
ejpam-5473	402	23	in	in	ADP
ejpam-5473	402	24	classical	classical	ADJ
ejpam-5473	402	25	set	set	NOUN
ejpam-5473	402	26	theory	theory	NOUN
ejpam-5473	402	27	.	.	PUNCT
ejpam-5473	403	1	the	the	DET
ejpam-5473	403	2	incorporation	incorporation	NOUN
ejpam-5473	403	3	of	of	ADP
ejpam-5473	403	4	the	the	DET
ejpam-5473	403	5	bvfbo	bvfbo	NOUN
ejpam-5473	403	6	into	into	ADP
ejpam-5473	403	7	this	this	DET
ejpam-5473	403	8	bvf	bvf	NOUN
ejpam-5473	403	9	-	-	PUNCT
ejpam-5473	403	10	space	space	NOUN
ejpam-5473	403	11	allowed	allow	VERB
ejpam-5473	403	12	for	for	ADP
ejpam-5473	403	13	the	the	DET
ejpam-5473	403	14	creation	creation	NOUN
ejpam-5473	403	15	of	of	ADP
ejpam-5473	403	16	bvf	bvf	NOUN
ejpam-5473	403	17	-	-	PUNCT
ejpam-5473	403	18	groupoids	groupoid	NOUN
ejpam-5473	403	19	,	,	PUNCT
ejpam-5473	403	20	following	follow	VERB
ejpam-5473	403	21	the	the	DET
ejpam-5473	403	22	core	core	ADJ
ejpam-5473	403	23	ideas	idea	NOUN
ejpam-5473	403	24	of	of	ADP
ejpam-5473	403	25	classical	classical	ADJ
ejpam-5473	403	26	groupoid	groupoid	NOUN
ejpam-5473	403	27	and	and	CCONJ
ejpam-5473	403	28	fuzzy	fuzzy	ADJ
ejpam-5473	403	29	groupoid	groupoid	PROPN
ejpam-5473	403	30	theories	theory	NOUN
ejpam-5473	403	31	,	,	PUNCT
ejpam-5473	403	32	as	as	SCONJ
ejpam-5473	403	33	outlined	outline	VERB
ejpam-5473	403	34	in	in	ADP
ejpam-5473	403	35	dib	dib	PROPN
ejpam-5473	403	36	’s	’s	PART
ejpam-5473	403	37	method	method	NOUN
ejpam-5473	403	38	.	.	PUNCT
ejpam-5473	404	1	these	these	DET
ejpam-5473	404	2	principles	principle	NOUN
ejpam-5473	404	3	ensure	ensure	VERB
ejpam-5473	404	4	that	that	SCONJ
ejpam-5473	404	5	the	the	DET
ejpam-5473	404	6	fundamental	fundamental	ADJ
ejpam-5473	404	7	algebraic	algebraic	ADJ
ejpam-5473	404	8	structure	structure	NOUN
ejpam-5473	404	9	of	of	ADP
ejpam-5473	404	10	bvf	bvf	NOUN
ejpam-5473	404	11	-	-	PUNCT
ejpam-5473	404	12	groupoids	groupoid	NOUN
ejpam-5473	404	13	is	be	AUX
ejpam-5473	404	14	preserved	preserve	VERB
ejpam-5473	404	15	,	,	PUNCT
ejpam-5473	404	16	despite	despite	SCONJ
ejpam-5473	404	17	the	the	DET
ejpam-5473	404	18	additional	additional	ADJ
ejpam-5473	404	19	complexity	complexity	NOUN
ejpam-5473	404	20	of	of	ADP
ejpam-5473	404	21	bipolar	bipolar	ADJ
ejpam-5473	404	22	-	-	PUNCT
ejpam-5473	404	23	valued	value	VERB
ejpam-5473	404	24	membership	membership	NOUN
ejpam-5473	404	25	.	.	PUNCT
ejpam-5473	405	1	our	our	PRON
ejpam-5473	405	2	model	model	NOUN
ejpam-5473	405	3	tackles	tackle	VERB
ejpam-5473	405	4	the	the	DET
ejpam-5473	405	5	difficulties	difficulty	NOUN
ejpam-5473	405	6	brought	bring	VERB
ejpam-5473	405	7	about	about	ADP
ejpam-5473	405	8	by	by	ADP
ejpam-5473	405	9	the	the	DET
ejpam-5473	405	10	lack	lack	NOUN
ejpam-5473	405	11	of	of	ADP
ejpam-5473	405	12	a	a	DET
ejpam-5473	405	13	bipolar	bipolar	ADV
ejpam-5473	405	14	-	-	PUNCT
ejpam-5473	405	15	valued	value	VERB
ejpam-5473	405	16	fuzzy	fuzzy	ADJ
ejpam-5473	405	17	universal	universal	ADJ
ejpam-5473	405	18	set	set	NOUN
ejpam-5473	405	19	,	,	PUNCT
ejpam-5473	405	20	providing	provide	VERB
ejpam-5473	405	21	a	a	DET
ejpam-5473	405	22	strong	strong	ADJ
ejpam-5473	405	23	base	base	NOUN
ejpam-5473	405	24	for	for	ADP
ejpam-5473	405	25	additional	additional	ADJ
ejpam-5473	405	26	algebraic	algebraic	ADJ
ejpam-5473	405	27	structures	structure	NOUN
ejpam-5473	405	28	like	like	ADP
ejpam-5473	405	29	bvf	bvf	NOUN
ejpam-5473	405	30	-	-	PUNCT
ejpam-5473	405	31	groupoids	groupoid	NOUN
ejpam-5473	405	32	,	,	PUNCT
ejpam-5473	405	33	bvf	bvf	NOUN
ejpam-5473	405	34	-	-	PUNCT
ejpam-5473	405	35	monoids	monoid	NOUN
ejpam-5473	405	36	,	,	PUNCT
ejpam-5473	405	37	and	and	CCONJ
ejpam-5473	405	38	bvfsubgroups	bvfsubgroup	NOUN
ejpam-5473	405	39	.	.	PUNCT
ejpam-5473	406	1	this	this	DET
ejpam-5473	406	2	generalization	generalization	NOUN
ejpam-5473	406	3	expands	expand	VERB
ejpam-5473	406	4	the	the	DET
ejpam-5473	406	5	theoretical	theoretical	ADJ
ejpam-5473	406	6	scope	scope	NOUN
ejpam-5473	406	7	and	and	CCONJ
ejpam-5473	406	8	improves	improve	VERB
ejpam-5473	406	9	the	the	DET
ejpam-5473	406	10	practical	practical	ADJ
ejpam-5473	406	11	usefulness	usefulness	NOUN
ejpam-5473	406	12	of	of	ADP
ejpam-5473	406	13	fuzzy	fuzzy	ADJ
ejpam-5473	406	14	groups	group	NOUN
ejpam-5473	406	15	by	by	ADP
ejpam-5473	406	16	incorporating	incorporate	VERB
ejpam-5473	406	17	both	both	CCONJ
ejpam-5473	406	18	positive	positive	ADJ
ejpam-5473	406	19	and	and	CCONJ
ejpam-5473	406	20	negative	negative	ADJ
ejpam-5473	406	21	membership	membership	NOUN
ejpam-5473	406	22	values	value	NOUN
ejpam-5473	406	23	in	in	ADP
ejpam-5473	406	24	real	real	ADJ
ejpam-5473	406	25	-	-	PUNCT
ejpam-5473	406	26	world	world	NOUN
ejpam-5473	406	27	problems	problem	NOUN
ejpam-5473	406	28	.	.	PUNCT
ejpam-5473	407	1	the	the	DET
ejpam-5473	407	2	theoretical	theoretical	ADJ
ejpam-5473	407	3	foundation	foundation	NOUN
ejpam-5473	407	4	of	of	ADP
ejpam-5473	407	5	bvf	bvf	NOUN
ejpam-5473	407	6	-	-	PUNCT
ejpam-5473	407	7	groups	group	NOUN
ejpam-5473	407	8	is	be	AUX
ejpam-5473	407	9	well	well	ADV
ejpam-5473	407	10	established	establish	VERB
ejpam-5473	407	11	,	,	PUNCT
ejpam-5473	407	12	yet	yet	CCONJ
ejpam-5473	407	13	its	its	PRON
ejpam-5473	407	14	practical	practical	ADJ
ejpam-5473	407	15	implementation	implementation	NOUN
ejpam-5473	407	16	is	be	AUX
ejpam-5473	407	17	still	still	ADV
ejpam-5473	407	18	in	in	ADP
ejpam-5473	407	19	its	its	PRON
ejpam-5473	407	20	initial	initial	ADJ
ejpam-5473	407	21	phases	phase	NOUN
ejpam-5473	407	22	.	.	PUNCT
ejpam-5473	408	1	additional	additional	ADJ
ejpam-5473	408	2	empirical	empirical	ADJ
ejpam-5473	408	3	research	research	NOUN
ejpam-5473	408	4	is	be	AUX
ejpam-5473	408	5	required	require	VERB
ejpam-5473	408	6	to	to	PART
ejpam-5473	408	7	assess	assess	VERB
ejpam-5473	408	8	the	the	DET
ejpam-5473	408	9	suitability	suitability	NOUN
ejpam-5473	408	10	and	and	CCONJ
ejpam-5473	408	11	efficacy	efficacy	NOUN
ejpam-5473	408	12	of	of	ADP
ejpam-5473	408	13	the	the	DET
ejpam-5473	408	14	method	method	NOUN
ejpam-5473	408	15	in	in	ADP
ejpam-5473	408	16	real	real	ADJ
ejpam-5473	408	17	-	-	PUNCT
ejpam-5473	408	18	world	world	NOUN
ejpam-5473	408	19	scenarios	scenario	NOUN
ejpam-5473	408	20	like	like	ADP
ejpam-5473	408	21	decision	decision	NOUN
ejpam-5473	408	22	-	-	PUNCT
ejpam-5473	408	23	making	making	NOUN
ejpam-5473	408	24	,	,	PUNCT
ejpam-5473	408	25	control	control	NOUN
ejpam-5473	408	26	systems	system	NOUN
ejpam-5473	408	27	,	,	PUNCT
ejpam-5473	408	28	and	and	CCONJ
ejpam-5473	408	29	social	social	ADJ
ejpam-5473	408	30	networks	network	NOUN
ejpam-5473	408	31	.	.	PUNCT
ejpam-5473	409	1	the	the	DET
ejpam-5473	409	2	complete	complete	ADJ
ejpam-5473	409	3	effectiveness	effectiveness	NOUN
ejpam-5473	409	4	of	of	ADP
ejpam-5473	409	5	the	the	DET
ejpam-5473	409	6	method	method	NOUN
ejpam-5473	409	7	will	will	AUX
ejpam-5473	409	8	remain	remain	VERB
ejpam-5473	409	9	theoretical	theoretical	ADJ
ejpam-5473	409	10	until	until	SCONJ
ejpam-5473	409	11	additional	additional	ADJ
ejpam-5473	409	12	real	real	ADJ
ejpam-5473	409	13	-	-	PUNCT
ejpam-5473	409	14	world	world	NOUN
ejpam-5473	409	15	testing	testing	NOUN
ejpam-5473	409	16	is	be	AUX
ejpam-5473	409	17	carried	carry	VERB
ejpam-5473	409	18	out	out	ADP
ejpam-5473	409	19	.	.	PUNCT
ejpam-5473	410	1	as	as	ADP
ejpam-5473	410	2	future	future	ADJ
ejpam-5473	410	3	research	research	NOUN
ejpam-5473	410	4	,	,	PUNCT
ejpam-5473	410	5	the	the	DET
ejpam-5473	410	6	bvf	bvf	NOUN
ejpam-5473	410	7	-	-	PUNCT
ejpam-5473	410	8	space	space	NOUN
ejpam-5473	410	9	and	and	CCONJ
ejpam-5473	410	10	bvfbo	bvfbo	NOUN
ejpam-5473	410	11	offer	offer	VERB
ejpam-5473	410	12	a	a	DET
ejpam-5473	410	13	practical	practical	ADJ
ejpam-5473	410	14	and	and	CCONJ
ejpam-5473	410	15	efficient	efficient	ADJ
ejpam-5473	410	16	approach	approach	NOUN
ejpam-5473	410	17	to	to	ADP
ejpam-5473	410	18	defining	define	VERB
ejpam-5473	410	19	and	and	CCONJ
ejpam-5473	410	20	examining	examine	VERB
ejpam-5473	410	21	bipolar	bipolar	ADJ
ejpam-5473	410	22	valued	value	VERB
ejpam-5473	410	23	fuzzy	fuzzy	ADJ
ejpam-5473	410	24	subgroups	subgroup	NOUN
ejpam-5473	410	25	,	,	PUNCT
ejpam-5473	410	26	bipolar	bipolar	ADJ
ejpam-5473	410	27	valued	value	VERB
ejpam-5473	410	28	fuzzy	fuzzy	ADJ
ejpam-5473	410	29	normal	normal	ADJ
ejpam-5473	410	30	subgroups	subgroup	NOUN
ejpam-5473	410	31	and	and	CCONJ
ejpam-5473	410	32	homeomorphism	homeomorphism	PRON
ejpam-5473	410	33	between	between	ADP
ejpam-5473	410	34	two	two	NUM
ejpam-5473	410	35	bipolar	bipolar	ADJ
ejpam-5473	410	36	valued	value	VERB
ejpam-5473	410	37	fuzzy	fuzzy	ADJ
ejpam-5473	410	38	algebraic	algebraic	ADJ
ejpam-5473	410	39	structures	structure	NOUN
ejpam-5473	410	40	.	.	PUNCT
ejpam-5473	411	1	this	this	DET
ejpam-5473	411	2	development	development	NOUN
ejpam-5473	411	3	in	in	ADP
ejpam-5473	411	4	bvf	bvf	NOUN
ejpam-5473	411	5	-	-	PUNCT
ejpam-5473	411	6	group	group	NOUN
ejpam-5473	411	7	theory	theory	NOUN
ejpam-5473	411	8	provides	provide	VERB
ejpam-5473	411	9	new	new	ADJ
ejpam-5473	411	10	possibilities	possibility	NOUN
ejpam-5473	411	11	for	for	ADP
ejpam-5473	411	12	study	study	NOUN
ejpam-5473	411	13	and	and	CCONJ
ejpam-5473	411	14	application	application	NOUN
ejpam-5473	411	15	in	in	ADP
ejpam-5473	411	16	different	different	ADJ
ejpam-5473	411	17	fields	field	NOUN
ejpam-5473	411	18	that	that	PRON
ejpam-5473	411	19	demand	demand	VERB
ejpam-5473	411	20	a	a	DET
ejpam-5473	411	21	thorough	thorough	ADJ
ejpam-5473	411	22	depiction	depiction	NOUN
ejpam-5473	411	23	of	of	ADP
ejpam-5473	411	24	uncertainty	uncertainty	NOUN
ejpam-5473	411	25	and	and	CCONJ
ejpam-5473	411	26	duality	duality	NOUN
ejpam-5473	411	27	.	.	PUNCT
ejpam-5473	412	1	author	author	NOUN
ejpam-5473	412	2	contributions	contribution	NOUN
ejpam-5473	412	3	fadi	fadi	PROPN
ejpam-5473	412	4	al	al	PROPN
ejpam-5473	412	5	-	-	PROPN
ejpam-5473	412	6	zu’bi	zu’bi	PROPN
ejpam-5473	412	7	validated	validate	VERB
ejpam-5473	412	8	the	the	DET
ejpam-5473	412	9	research	research	NOUN
ejpam-5473	412	10	outputs	output	NOUN
ejpam-5473	412	11	and	and	CCONJ
ejpam-5473	412	12	wrote	write	VERB
ejpam-5473	412	13	the	the	DET
ejpam-5473	412	14	original	original	ADJ
ejpam-5473	412	15	draft	draft	NOUN
ejpam-5473	412	16	of	of	ADP
ejpam-5473	412	17	this	this	DET
ejpam-5473	412	18	research	research	NOUN
ejpam-5473	412	19	;	;	PUNCT
ejpam-5473	412	20	abd	abd	PROPN
ejpam-5473	412	21	ulazeez	ulazeez	PROPN
ejpam-5473	412	22	alkouri	alkouri	PROPN
ejpam-5473	412	23	and	and	CCONJ
ejpam-5473	412	24	fadi	fadi	PROPN
ejpam-5473	412	25	prepared	prepare	VERB
ejpam-5473	412	26	and	and	CCONJ
ejpam-5473	412	27	created	create	VERB
ejpam-5473	412	28	the	the	DET
ejpam-5473	412	29	published	publish	VERB
ejpam-5473	412	30	work	work	NOUN
ejpam-5473	412	31	by	by	ADP
ejpam-5473	412	32	those	those	PRON
ejpam-5473	412	33	from	from	ADP
ejpam-5473	412	34	the	the	DET
ejpam-5473	412	35	original	original	ADJ
ejpam-5473	412	36	research	research	NOUN
ejpam-5473	412	37	group	group	NOUN
ejpam-5473	412	38	and	and	CCONJ
ejpam-5473	412	39	helped	help	VERB
ejpam-5473	412	40	to	to	PART
ejpam-5473	412	41	create	create	VERB
ejpam-5473	412	42	the	the	DET
ejpam-5473	412	43	final	final	ADJ
ejpam-5473	412	44	form	form	NOUN
ejpam-5473	412	45	of	of	ADP
ejpam-5473	412	46	this	this	DET
ejpam-5473	412	47	research	research	NOUN
ejpam-5473	412	48	.	.	PUNCT
ejpam-5473	413	1	abdul	abdul	PROPN
ejpam-5473	413	2	ghaffur	ghaffur	PROPN
ejpam-5473	413	3	ahmad	ahmad	PROPN
ejpam-5473	413	4	:	:	PUNCT
ejpam-5473	413	5	scrutinized	scrutinize	VERB
ejpam-5473	413	6	the	the	DET
ejpam-5473	413	7	formal	formal	ADJ
ejpam-5473	413	8	analysis	analysis	NOUN
ejpam-5473	413	9	,	,	PUNCT
ejpam-5473	413	10	methodology	methodology	NOUN
ejpam-5473	413	11	,	,	PUNCT
ejpam-5473	413	12	ideas	idea	NOUN
ejpam-5473	413	13	and	and	CCONJ
ejpam-5473	413	14	formulated	formulate	VERB
ejpam-5473	413	15	the	the	DET
ejpam-5473	413	16	overarching	overarching	ADJ
ejpam-5473	413	17	research	research	NOUN
ejpam-5473	413	18	goals	goal	NOUN
ejpam-5473	413	19	and	and	CCONJ
ejpam-5473	413	20	aims	aim	VERB
ejpam-5473	413	21	and	and	CCONJ
ejpam-5473	413	22	supervised	supervise	VERB
ejpam-5473	413	23	the	the	DET
ejpam-5473	413	24	presented	present	VERB
ejpam-5473	413	25	research	research	NOUN
ejpam-5473	413	26	.	.	PUNCT
ejpam-5473	414	1	maslina	maslina	PROPN
ejpam-5473	414	2	darua	darua	PROPN
ejpam-5473	414	3	:	:	PUNCT
ejpam-5473	414	4	played	play	VERB
ejpam-5473	414	5	the	the	DET
ejpam-5473	414	6	role	role	NOUN
ejpam-5473	414	7	of	of	ADP
ejpam-5473	414	8	project	project	NOUN
ejpam-5473	414	9	administration	administration	NOUN
ejpam-5473	414	10	and	and	CCONJ
ejpam-5473	414	11	investigation	investigation	NOUN
ejpam-5473	414	12	in	in	ADP
ejpam-5473	414	13	this	this	DET
ejpam-5473	414	14	research	research	NOUN
ejpam-5473	414	15	.	.	PUNCT
ejpam-5473	415	1	references	reference	NOUN
ejpam-5473	415	2	2911	2911	NUM
ejpam-5473	415	3	use	use	NOUN
ejpam-5473	415	4	of	of	ADP
ejpam-5473	415	5	ai	ai	ADJ
ejpam-5473	415	6	tools	tool	NOUN
ejpam-5473	415	7	declaration	declaration	NOUN
ejpam-5473	415	8	the	the	DET
ejpam-5473	415	9	authors	author	NOUN
ejpam-5473	415	10	declare	declare	VERB
ejpam-5473	415	11	they	they	PRON
ejpam-5473	415	12	have	have	AUX
ejpam-5473	415	13	not	not	PART
ejpam-5473	415	14	used	use	VERB
ejpam-5473	415	15	artificial	artificial	ADJ
ejpam-5473	415	16	intelligence	intelligence	NOUN
ejpam-5473	415	17	(	(	PUNCT
ejpam-5473	415	18	ai	ai	NOUN
ejpam-5473	415	19	)	)	PUNCT
ejpam-5473	415	20	tools	tool	NOUN
ejpam-5473	415	21	in	in	ADP
ejpam-5473	415	22	the	the	DET
ejpam-5473	415	23	creation	creation	NOUN
ejpam-5473	415	24	of	of	ADP
ejpam-5473	415	25	this	this	DET
ejpam-5473	415	26	article	article	NOUN
ejpam-5473	415	27	.	.	PUNCT
ejpam-5473	416	1	acknowledgments	acknowledgment	NOUN
ejpam-5473	416	2	we	we	PRON
ejpam-5473	416	3	would	would	AUX
ejpam-5473	416	4	like	like	VERB
ejpam-5473	416	5	to	to	PART
ejpam-5473	416	6	thank	thank	VERB
ejpam-5473	416	7	editor	editor	NOUN
ejpam-5473	416	8	in	in	ADP
ejpam-5473	416	9	chief	chief	NOUN
ejpam-5473	416	10	and	and	CCONJ
ejpam-5473	416	11	reviewers	reviewer	NOUN
ejpam-5473	416	12	for	for	ADP
ejpam-5473	416	13	their	their	PRON
ejpam-5473	416	14	instructions	instruction	NOUN
ejpam-5473	416	15	and	and	CCONJ
ejpam-5473	416	16	comments	comment	NOUN
ejpam-5473	416	17	.	.	PUNCT
ejpam-5473	417	1	conflict	conflict	NOUN
ejpam-5473	417	2	of	of	ADP
ejpam-5473	417	3	interest	interest	NOUN
ejpam-5473	417	4	the	the	DET
ejpam-5473	417	5	authors	author	NOUN
ejpam-5473	417	6	declare	declare	VERB
ejpam-5473	417	7	there	there	PRON
ejpam-5473	417	8	is	be	VERB
ejpam-5473	417	9	no	no	DET
ejpam-5473	417	10	conflict	conflict	NOUN
ejpam-5473	417	11	of	of	ADP
ejpam-5473	417	12	interest	interest	NOUN
ejpam-5473	417	13	.	.	PUNCT
ejpam-5473	418	1	references	reference	NOUN
ejpam-5473	418	2	[	[	X
ejpam-5473	418	3	1	1	NUM
ejpam-5473	418	4	]	]	PUNCT
ejpam-5473	418	5	eman	eman	NOUN
ejpam-5473	418	6	a	a	DET
ejpam-5473	418	7	abuhijleh	abuhijleh	NOUN
ejpam-5473	418	8	,	,	PUNCT
ejpam-5473	418	9	mourad	mourad	PROPN
ejpam-5473	418	10	massa’deh	massa’deh	PROPN
ejpam-5473	418	11	,	,	PUNCT
ejpam-5473	418	12	amani	amani	PROPN
ejpam-5473	418	13	sheimat	sheimat	NOUN
ejpam-5473	418	14	,	,	PUNCT
ejpam-5473	418	15	and	and	CCONJ
ejpam-5473	418	16	abdulazeez	abdulazeez	PROPN
ejpam-5473	418	17	alkouri	alkouri	PROPN
ejpam-5473	418	18	.	.	PUNCT
ejpam-5473	419	1	complex	complex	ADJ
ejpam-5473	419	2	fuzzy	fuzzy	ADJ
ejpam-5473	419	3	groups	group	NOUN
ejpam-5473	419	4	based	base	VERB
ejpam-5473	419	5	on	on	ADP
ejpam-5473	419	6	rosenfeld	rosenfeld	PROPN
ejpam-5473	419	7	’s	’s	PART
ejpam-5473	419	8	approach	approach	NOUN
ejpam-5473	419	9	.	.	PUNCT
ejpam-5473	420	1	wseas	wseas	VERB
ejpam-5473	420	2	transactions	transaction	NOUN
ejpam-5473	420	3	on	on	ADP
ejpam-5473	420	4	mathematics	mathematic	NOUN
ejpam-5473	420	5	,	,	PUNCT
ejpam-5473	420	6	20(1):368–377	20(1):368–377	NOUN
ejpam-5473	420	7	,	,	PUNCT
ejpam-5473	420	8	2021	2021	NUM
ejpam-5473	420	9	.	.	PUNCT
ejpam-5473	421	1	[	[	X
ejpam-5473	421	2	2	2	NUM
ejpam-5473	421	3	]	]	PUNCT
ejpam-5473	421	4	mustafa	mustafa	PROPN
ejpam-5473	421	5	akgül	akgül	PROPN
ejpam-5473	421	6	.	.	PUNCT
ejpam-5473	422	1	some	some	DET
ejpam-5473	422	2	properties	property	NOUN
ejpam-5473	422	3	of	of	ADP
ejpam-5473	422	4	fuzzy	fuzzy	ADJ
ejpam-5473	422	5	groups	group	NOUN
ejpam-5473	422	6	.	.	PUNCT
ejpam-5473	423	1	journal	journal	PROPN
ejpam-5473	423	2	of	of	ADP
ejpam-5473	423	3	mathematical	mathematical	ADJ
ejpam-5473	423	4	analysis	analysis	NOUN
ejpam-5473	423	5	and	and	CCONJ
ejpam-5473	423	6	applications	application	NOUN
ejpam-5473	423	7	,	,	PUNCT
ejpam-5473	423	8	133(1):93–100	133(1):93–100	NUM
ejpam-5473	423	9	,	,	PUNCT
ejpam-5473	423	10	1988	1988	NUM
ejpam-5473	423	11	.	.	PUNCT
ejpam-5473	424	1	[	[	X
ejpam-5473	424	2	3	3	X
ejpam-5473	424	3	]	]	X
ejpam-5473	424	4	abdallah	abdallah	PROPN
ejpam-5473	424	5	al	al	PROPN
ejpam-5473	424	6	-	-	PROPN
ejpam-5473	424	7	husban	husban	PROPN
ejpam-5473	424	8	and	and	CCONJ
ejpam-5473	424	9	abdul	abdul	PROPN
ejpam-5473	424	10	razak	razak	PROPN
ejpam-5473	424	11	salleh	salleh	PROPN
ejpam-5473	424	12	.	.	PUNCT
ejpam-5473	425	1	complex	complex	ADJ
ejpam-5473	425	2	fuzzy	fuzzy	ADJ
ejpam-5473	425	3	group	group	NOUN
ejpam-5473	425	4	based	base	VERB
ejpam-5473	425	5	on	on	ADP
ejpam-5473	425	6	complex	complex	ADJ
ejpam-5473	425	7	fuzzy	fuzzy	ADJ
ejpam-5473	425	8	space	space	NOUN
ejpam-5473	425	9	.	.	PUNCT
ejpam-5473	426	1	global	global	ADJ
ejpam-5473	426	2	journal	journal	PROPN
ejpam-5473	426	3	of	of	ADP
ejpam-5473	426	4	pure	pure	ADJ
ejpam-5473	426	5	and	and	CCONJ
ejpam-5473	426	6	applied	applied	ADJ
ejpam-5473	426	7	mathematics	mathematic	NOUN
ejpam-5473	426	8	,	,	PUNCT
ejpam-5473	426	9	12(2):1433–1450	12(2):1433–1450	NUM
ejpam-5473	426	10	,	,	PUNCT
ejpam-5473	426	11	2016	2016	NUM
ejpam-5473	426	12	.	.	PUNCT
ejpam-5473	427	1	[	[	X
ejpam-5473	427	2	4	4	X
ejpam-5473	427	3	]	]	X
ejpam-5473	427	4	r	r	NOUN
ejpam-5473	427	5	al	al	PROPN
ejpam-5473	427	6	-	-	PUNCT
ejpam-5473	427	7	husban	husban	PROPN
ejpam-5473	427	8	,	,	PUNCT
ejpam-5473	427	9	ar	ar	NOUN
ejpam-5473	427	10	salleh	salleh	PROPN
ejpam-5473	427	11	,	,	PUNCT
ejpam-5473	427	12	and	and	CCONJ
ejpam-5473	427	13	agb	agb	PROPN
ejpam-5473	427	14	ahmad	ahmad	PROPN
ejpam-5473	427	15	.	.	PUNCT
ejpam-5473	428	1	complex	complex	ADJ
ejpam-5473	428	2	intuitionistic	intuitionistic	ADJ
ejpam-5473	428	3	fuzzy	fuzzy	ADJ
ejpam-5473	428	4	normal	normal	ADJ
ejpam-5473	428	5	subgroup	subgroup	NOUN
ejpam-5473	428	6	.	.	PUNCT
ejpam-5473	429	1	int	int	NOUN
ejpam-5473	429	2	.	.	PUNCT
ejpam-5473	430	1	j.	j.	PROPN
ejpam-5473	430	2	pure	pure	PROPN
ejpam-5473	430	3	appl	appl	PROPN
ejpam-5473	430	4	.	.	PUNCT
ejpam-5473	430	5	math	math	PROPN
ejpam-5473	430	6	,	,	PUNCT
ejpam-5473	430	7	115(3):199–210	115(3):199–210	PROPN
ejpam-5473	430	8	,	,	PUNCT
ejpam-5473	430	9	2017	2017	NUM
ejpam-5473	430	10	.	.	PUNCT
ejpam-5473	431	1	[	[	X
ejpam-5473	431	2	5	5	X
ejpam-5473	431	3	]	]	PUNCT
ejpam-5473	431	4	rima	rima	PROPN
ejpam-5473	431	5	al	al	PROPN
ejpam-5473	431	6	-	-	PUNCT
ejpam-5473	431	7	husban	husban	PROPN
ejpam-5473	431	8	,	,	PUNCT
ejpam-5473	431	9	abdul	abdul	PROPN
ejpam-5473	431	10	razak	razak	PROPN
ejpam-5473	431	11	salleh	salleh	PROPN
ejpam-5473	431	12	,	,	PUNCT
ejpam-5473	431	13	and	and	CCONJ
ejpam-5473	431	14	abd	abd	PROPN
ejpam-5473	431	15	ghafur	ghafur	PROPN
ejpam-5473	431	16	bin	bin	PROPN
ejpam-5473	431	17	ahmad	ahmad	PROPN
ejpam-5473	431	18	.	.	PUNCT
ejpam-5473	432	1	complex	complex	ADJ
ejpam-5473	432	2	intuitionistic	intuitionistic	ADJ
ejpam-5473	432	3	fuzzy	fuzzy	ADJ
ejpam-5473	432	4	subrings	subring	NOUN
ejpam-5473	432	5	.	.	PUNCT
ejpam-5473	433	1	in	in	ADP
ejpam-5473	433	2	aip	aip	PROPN
ejpam-5473	433	3	conference	conference	NOUN
ejpam-5473	433	4	proceedings	proceeding	NOUN
ejpam-5473	433	5	,	,	PUNCT
ejpam-5473	433	6	volume	volume	NOUN
ejpam-5473	433	7	1784	1784	NUM
ejpam-5473	433	8	.	.	PUNCT
ejpam-5473	434	1	aip	aip	PROPN
ejpam-5473	434	2	publishing	publishing	PROPN
ejpam-5473	434	3	,	,	PUNCT
ejpam-5473	434	4	2016	2016	NUM
ejpam-5473	434	5	.	.	PUNCT
ejpam-5473	435	1	[	[	X
ejpam-5473	435	2	6	6	NUM
ejpam-5473	435	3	]	]	X
ejpam-5473	435	4	anas	anas	PROPN
ejpam-5473	435	5	al	al	PROPN
ejpam-5473	435	6	-	-	PROPN
ejpam-5473	435	7	masarwah	masarwah	PROPN
ejpam-5473	435	8	,	,	PUNCT
ejpam-5473	435	9	abd	abd	PROPN
ejpam-5473	435	10	ghafur	ghafur	NOUN
ejpam-5473	435	11	ahmad	ahmad	PROPN
ejpam-5473	435	12	,	,	PUNCT
ejpam-5473	435	13	g	g	NOUN
ejpam-5473	435	14	muhiuddin	muhiuddin	NOUN
ejpam-5473	435	15	,	,	PUNCT
ejpam-5473	435	16	and	and	CCONJ
ejpam-5473	435	17	d	d	PROPN
ejpam-5473	435	18	al	al	PROPN
ejpam-5473	435	19	-	-	PUNCT
ejpam-5473	435	20	kadi	kadi	PROPN
ejpam-5473	435	21	.	.	PUNCT
ejpam-5473	436	1	generalized	generalize	VERB
ejpam-5473	436	2	m	m	ADJ
ejpam-5473	436	3	-	-	ADJ
ejpam-5473	436	4	polar	polar	ADJ
ejpam-5473	436	5	fuzzy	fuzzy	ADJ
ejpam-5473	436	6	positive	positive	ADJ
ejpam-5473	436	7	implicative	implicative	ADJ
ejpam-5473	436	8	ideals	ideal	NOUN
ejpam-5473	436	9	of	of	ADP
ejpam-5473	436	10	bck	bck	NOUN
ejpam-5473	436	11	-	-	PUNCT
ejpam-5473	436	12	algebras	algebras	PROPN
ejpam-5473	436	13	.	.	PUNCT
ejpam-5473	437	1	journal	journal	PROPN
ejpam-5473	437	2	of	of	ADP
ejpam-5473	437	3	mathematics	mathematic	NOUN
ejpam-5473	437	4	,	,	PUNCT
ejpam-5473	437	5	2021(1):6610009	2021(1):6610009	NUM
ejpam-5473	437	6	,	,	PUNCT
ejpam-5473	437	7	2021	2021	NUM
ejpam-5473	437	8	.	.	PUNCT
ejpam-5473	438	1	[	[	X
ejpam-5473	438	2	7	7	X
ejpam-5473	438	3	]	]	X
ejpam-5473	438	4	anas	anas	PROPN
ejpam-5473	438	5	al	al	PROPN
ejpam-5473	438	6	-	-	PROPN
ejpam-5473	438	7	masarwah	masarwah	PROPN
ejpam-5473	438	8	and	and	CCONJ
ejpam-5473	438	9	mohammed	mohammed	PROPN
ejpam-5473	438	10	alqahtani	alqahtani	PROPN
ejpam-5473	438	11	.	.	PUNCT
ejpam-5473	439	1	operational	operational	ADJ
ejpam-5473	439	2	algebraic	algebraic	ADJ
ejpam-5473	439	3	properties	property	NOUN
ejpam-5473	439	4	and	and	CCONJ
ejpam-5473	439	5	subsemigroups	subsemigroup	NOUN
ejpam-5473	439	6	of	of	ADP
ejpam-5473	439	7	semigroups	semigroup	NOUN
ejpam-5473	439	8	in	in	ADP
ejpam-5473	439	9	view	view	NOUN
ejpam-5473	439	10	of	of	ADP
ejpam-5473	439	11	k	k	NOUN
ejpam-5473	439	12	-	-	PUNCT
ejpam-5473	439	13	folded	fold	VERB
ejpam-5473	439	14	n	n	CCONJ
ejpam-5473	439	15	-	-	PUNCT
ejpam-5473	439	16	structures	structure	NOUN
ejpam-5473	439	17	.	.	PUNCT
ejpam-5473	440	1	aims	aim	VERB
ejpam-5473	440	2	math	math	NOUN
ejpam-5473	440	3	,	,	PUNCT
ejpam-5473	440	4	8(9):22081–22096	8(9):22081–22096	NUM
ejpam-5473	440	5	,	,	PUNCT
ejpam-5473	440	6	2023	2023	NUM
ejpam-5473	440	7	.	.	PUNCT
ejpam-5473	441	1	[	[	X
ejpam-5473	441	2	8	8	NUM
ejpam-5473	441	3	]	]	PUNCT
ejpam-5473	441	4	doaa	doaa	PROPN
ejpam-5473	441	5	al	al	PROPN
ejpam-5473	441	6	-	-	PUNCT
ejpam-5473	441	7	sharoa	sharoa	NOUN
ejpam-5473	441	8	.	.	PUNCT
ejpam-5473	442	1	(	(	PUNCT
ejpam-5473	442	2	α1	α1	PROPN
ejpam-5473	442	3	,	,	PUNCT
ejpam-5473	442	4	2	2	NUM
ejpam-5473	442	5	,	,	PUNCT
ejpam-5473	442	6	β1	β1	NOUN
ejpam-5473	442	7	,	,	PUNCT
ejpam-5473	442	8	2)-complex	2)-complex	NUM
ejpam-5473	442	9	intuitionistic	intuitionistic	ADJ
ejpam-5473	442	10	fuzzy	fuzzy	ADJ
ejpam-5473	442	11	subgroups	subgroup	NOUN
ejpam-5473	442	12	and	and	CCONJ
ejpam-5473	442	13	its	its	PRON
ejpam-5473	442	14	algebraic	algebraic	ADJ
ejpam-5473	442	15	structure	structure	NOUN
ejpam-5473	442	16	.	.	PUNCT
ejpam-5473	443	1	aims	aim	VERB
ejpam-5473	443	2	mathematics	mathematic	NOUN
ejpam-5473	443	3	,	,	PUNCT
ejpam-5473	443	4	8(4):8082–8116	8(4):8082–8116	PROPN
ejpam-5473	443	5	,	,	PUNCT
ejpam-5473	443	6	2023	2023	NUM
ejpam-5473	443	7	.	.	PUNCT
ejpam-5473	444	1	references	reference	NOUN
ejpam-5473	444	2	2912	2912	NUM
ejpam-5473	444	3	[	[	X
ejpam-5473	444	4	9	9	NUM
ejpam-5473	444	5	]	]	SYM
ejpam-5473	444	6	fadi	fadi	NOUN
ejpam-5473	444	7	ma	ma	PROPN
ejpam-5473	444	8	al	al	PROPN
ejpam-5473	444	9	-	-	PUNCT
ejpam-5473	444	10	zu’bi	zu’bi	PROPN
ejpam-5473	444	11	,	,	PUNCT
ejpam-5473	444	12	abdul	abdul	PROPN
ejpam-5473	444	13	ghafur	ghafur	PROPN
ejpam-5473	444	14	ahmad	ahmad	PROPN
ejpam-5473	444	15	,	,	PUNCT
ejpam-5473	444	16	maslina	maslina	NOUN
ejpam-5473	444	17	darus	darus	PROPN
ejpam-5473	444	18	abd	abd	PROPN
ejpam-5473	444	19	ulazeez	ulazeez	PROPN
ejpam-5473	444	20	alkouri	alkouri	PROPN
ejpam-5473	444	21	,	,	PUNCT
ejpam-5473	444	22	and	and	CCONJ
ejpam-5473	444	23	united	united	PROPN
ejpam-5473	444	24	arab	arab	PROPN
ejpam-5473	444	25	emirates	emirates	PROPN
ejpam-5473	444	26	.	.	PUNCT
ejpam-5473	445	1	a	a	DET
ejpam-5473	445	2	new	new	ADJ
ejpam-5473	445	3	trend	trend	NOUN
ejpam-5473	445	4	of	of	ADP
ejpam-5473	445	5	bipolarvalued	bipolarvalue	VERB
ejpam-5473	445	6	fuzzy	fuzzy	ADJ
ejpam-5473	445	7	cartesian	cartesian	ADJ
ejpam-5473	445	8	products	product	NOUN
ejpam-5473	445	9	,	,	PUNCT
ejpam-5473	445	10	relations	relation	NOUN
ejpam-5473	445	11	,	,	PUNCT
ejpam-5473	445	12	and	and	CCONJ
ejpam-5473	445	13	functions	function	NOUN
ejpam-5473	445	14	.	.	PUNCT
ejpam-5473	446	1	wseas	wseas	VERB
ejpam-5473	446	2	transactions	transaction	NOUN
ejpam-5473	446	3	on	on	ADP
ejpam-5473	446	4	mathematics	mathematic	NOUN
ejpam-5473	446	5	,	,	PUNCT
ejpam-5473	446	6	23:502	23:502	NUM
ejpam-5473	446	7	,	,	PUNCT
ejpam-5473	446	8	2024	2024	NUM
ejpam-5473	446	9	.	.	PUNCT
ejpam-5473	447	1	[	[	X
ejpam-5473	447	2	10	10	NUM
ejpam-5473	447	3	]	]	X
ejpam-5473	447	4	sahar	sahar	PROPN
ejpam-5473	447	5	m	m	PROPN
ejpam-5473	447	6	alqaraleh	alqaraleh	NOUN
ejpam-5473	447	7	,	,	PUNCT
ejpam-5473	447	8	mjs	mjs	NOUN
ejpam-5473	447	9	abd	abd	PROPN
ejpam-5473	447	10	ulazeez	ulazeez	PROPN
ejpam-5473	447	11	,	,	PUNCT
ejpam-5473	447	12	mourad	mourad	PROPN
ejpam-5473	447	13	oqla	oqla	PROPN
ejpam-5473	447	14	massa’deh	massa’deh	PROPN
ejpam-5473	447	15	,	,	PUNCT
ejpam-5473	447	16	adeeb	adeeb	PROPN
ejpam-5473	447	17	g	g	PROPN
ejpam-5473	447	18	talafha	talafha	PROPN
ejpam-5473	447	19	,	,	PUNCT
ejpam-5473	447	20	and	and	CCONJ
ejpam-5473	447	21	anwar	anwar	PROPN
ejpam-5473	447	22	bataihah	bataihah	PROPN
ejpam-5473	447	23	.	.	PUNCT
ejpam-5473	448	1	bipolar	bipolar	ADJ
ejpam-5473	448	2	complex	complex	ADJ
ejpam-5473	448	3	fuzzy	fuzzy	ADJ
ejpam-5473	448	4	soft	soft	ADJ
ejpam-5473	448	5	sets	set	NOUN
ejpam-5473	448	6	and	and	CCONJ
ejpam-5473	448	7	their	their	PRON
ejpam-5473	448	8	application	application	NOUN
ejpam-5473	448	9	.	.	PUNCT
ejpam-5473	449	1	international	international	ADJ
ejpam-5473	449	2	journal	journal	NOUN
ejpam-5473	449	3	of	of	ADP
ejpam-5473	449	4	fuzzy	fuzzy	ADJ
ejpam-5473	449	5	system	system	NOUN
ejpam-5473	449	6	applications	application	NOUN
ejpam-5473	449	7	(	(	PUNCT
ejpam-5473	449	8	ijfsa	ijfsa	NOUN
ejpam-5473	449	9	)	)	PUNCT
ejpam-5473	449	10	,	,	PUNCT
ejpam-5473	449	11	11(1):1–23	11(1):1–23	NUM
ejpam-5473	449	12	,	,	PUNCT
ejpam-5473	449	13	2022	2022	NUM
ejpam-5473	449	14	.	.	PUNCT
ejpam-5473	450	1	[	[	X
ejpam-5473	450	2	11	11	NUM
ejpam-5473	450	3	]	]	AUX
ejpam-5473	450	4	doaa	doaa	VERB
ejpam-5473	450	5	alsharo	alsharo	ADV
ejpam-5473	450	6	,	,	PUNCT
ejpam-5473	450	7	eman	eman	PROPN
ejpam-5473	450	8	abuteen	abuteen	PROPN
ejpam-5473	450	9	,	,	PUNCT
ejpam-5473	450	10	mjs	mjs	NOUN
ejpam-5473	450	11	abd	abd	PROPN
ejpam-5473	450	12	ulazeez	ulazeez	PROPN
ejpam-5473	450	13	,	,	PUNCT
ejpam-5473	450	14	mutasem	mutasem	ADJ
ejpam-5473	450	15	alkhasawneh	alkhasawneh	NOUN
ejpam-5473	450	16	,	,	PUNCT
ejpam-5473	450	17	and	and	CCONJ
ejpam-5473	450	18	fadi	fadi	PROPN
ejpam-5473	450	19	ma	ma	PROPN
ejpam-5473	450	20	al	al	PROPN
ejpam-5473	450	21	-	-	PUNCT
ejpam-5473	450	22	zubi	zubi	PROPN
ejpam-5473	450	23	.	.	PUNCT
ejpam-5473	451	1	complex	complex	ADJ
ejpam-5473	451	2	shadowed	shadow	VERB
ejpam-5473	451	3	set	set	NOUN
ejpam-5473	451	4	theory	theory	NOUN
ejpam-5473	451	5	and	and	CCONJ
ejpam-5473	451	6	its	its	PRON
ejpam-5473	451	7	application	application	NOUN
ejpam-5473	451	8	in	in	ADP
ejpam-5473	451	9	decisionmaking	decisionmake	VERB
ejpam-5473	451	10	problems	problem	NOUN
ejpam-5473	451	11	.	.	PUNCT
ejpam-5473	452	1	aims	aim	VERB
ejpam-5473	452	2	math	math	NOUN
ejpam-5473	452	3	,	,	PUNCT
ejpam-5473	452	4	9:16810–16825	9:16810–16825	NUM
ejpam-5473	452	5	,	,	PUNCT
ejpam-5473	452	6	2024	2024	NUM
ejpam-5473	452	7	.	.	PUNCT
ejpam-5473	453	1	[	[	X
ejpam-5473	453	2	12	12	NUM
ejpam-5473	453	3	]	]	X
ejpam-5473	453	4	ms	ms	PROPN
ejpam-5473	453	5	anitha	anitha	PROPN
ejpam-5473	453	6	,	,	PUNCT
ejpam-5473	453	7	kl	kl	PROPN
ejpam-5473	453	8	muruganantha	muruganantha	PROPN
ejpam-5473	453	9	prasad	prasad	PROPN
ejpam-5473	453	10	,	,	PUNCT
ejpam-5473	453	11	and	and	CCONJ
ejpam-5473	453	12	k	k	PROPN
ejpam-5473	453	13	arjunan	arjunan	PROPN
ejpam-5473	453	14	.	.	PUNCT
ejpam-5473	454	1	notes	note	NOUN
ejpam-5473	454	2	on	on	ADP
ejpam-5473	454	3	bipolar	bipolar	ADJ
ejpam-5473	454	4	valued	value	VERB
ejpam-5473	454	5	fuzzy	fuzzy	ADJ
ejpam-5473	454	6	subgroups	subgroup	NOUN
ejpam-5473	454	7	of	of	ADP
ejpam-5473	454	8	a	a	DET
ejpam-5473	454	9	group	group	NOUN
ejpam-5473	454	10	.	.	PUNCT
ejpam-5473	455	1	the	the	DET
ejpam-5473	455	2	bulletin	bulletin	NOUN
ejpam-5473	455	3	of	of	ADP
ejpam-5473	455	4	society	society	NOUN
ejpam-5473	455	5	for	for	ADP
ejpam-5473	455	6	mathematical	mathematical	ADJ
ejpam-5473	455	7	services	service	NOUN
ejpam-5473	455	8	and	and	CCONJ
ejpam-5473	455	9	standards	standard	NOUN
ejpam-5473	455	10	,	,	PUNCT
ejpam-5473	455	11	7:40–45	7:40–45	NUM
ejpam-5473	455	12	,	,	PUNCT
ejpam-5473	455	13	2013	2013	NUM
ejpam-5473	455	14	.	.	PUNCT
ejpam-5473	456	1	[	[	X
ejpam-5473	456	2	13	13	NUM
ejpam-5473	456	3	]	]	X
ejpam-5473	456	4	ms	ms	PROPN
ejpam-5473	456	5	anitha	anitha	PROPN
ejpam-5473	456	6	and	and	CCONJ
ejpam-5473	456	7	b	b	NOUN
ejpam-5473	456	8	yasodara	yasodara	NOUN
ejpam-5473	456	9	.	.	PUNCT
ejpam-5473	457	1	properties	property	NOUN
ejpam-5473	457	2	of	of	ADP
ejpam-5473	457	3	bipolar	bipolar	ADV
ejpam-5473	457	4	-	-	PUNCT
ejpam-5473	457	5	valued	value	VERB
ejpam-5473	457	6	fuzzy	fuzzy	ADJ
ejpam-5473	457	7	subsemigroups	subsemigroup	NOUN
ejpam-5473	457	8	of	of	ADP
ejpam-5473	457	9	a	a	DET
ejpam-5473	457	10	semigroup	semigroup	PROPN
ejpam-5473	457	11	.	.	PUNCT
ejpam-5473	458	1	journal	journal	PROPN
ejpam-5473	458	2	of	of	ADP
ejpam-5473	458	3	discrete	discrete	ADJ
ejpam-5473	458	4	mathematical	mathematical	ADJ
ejpam-5473	458	5	sciences	science	NOUN
ejpam-5473	458	6	and	and	CCONJ
ejpam-5473	458	7	cryptography	cryptography	NOUN
ejpam-5473	458	8	,	,	PUNCT
ejpam-5473	458	9	22(5):711	22(5):711	NOUN
ejpam-5473	458	10	–	–	PUNCT
ejpam-5473	458	11	717	717	NUM
ejpam-5473	458	12	,	,	PUNCT
ejpam-5473	458	13	2019	2019	NUM
ejpam-5473	458	14	.	.	PUNCT
ejpam-5473	459	1	[	[	X
ejpam-5473	459	2	14	14	NUM
ejpam-5473	459	3	]	]	X
ejpam-5473	459	4	manivannan	manivannan	NOUN
ejpam-5473	459	5	balamurugan	balamurugan	VERB
ejpam-5473	459	6	,	,	PUNCT
ejpam-5473	459	7	thukkaraman	thukkaraman	PROPN
ejpam-5473	459	8	ramesh	ramesh	PROPN
ejpam-5473	459	9	,	,	PUNCT
ejpam-5473	459	10	anas	anas	PROPN
ejpam-5473	459	11	al	al	PROPN
ejpam-5473	459	12	-	-	PROPN
ejpam-5473	459	13	masarwah	masarwah	PROPN
ejpam-5473	459	14	,	,	PUNCT
ejpam-5473	459	15	and	and	CCONJ
ejpam-5473	459	16	kholood	kholood	NOUN
ejpam-5473	459	17	alsager	alsager	NOUN
ejpam-5473	459	18	.	.	PUNCT
ejpam-5473	460	1	a	a	DET
ejpam-5473	460	2	new	new	ADJ
ejpam-5473	460	3	approach	approach	NOUN
ejpam-5473	460	4	of	of	ADP
ejpam-5473	460	5	complex	complex	ADJ
ejpam-5473	460	6	fuzzy	fuzzy	ADJ
ejpam-5473	460	7	ideals	ideal	NOUN
ejpam-5473	460	8	in	in	ADP
ejpam-5473	460	9	bck	bck	PROPN
ejpam-5473	460	10	/	/	SYM
ejpam-5473	460	11	bci	bci	NOUN
ejpam-5473	460	12	-	-	PUNCT
ejpam-5473	460	13	algebras	algebra	NOUN
ejpam-5473	460	14	.	.	PUNCT
ejpam-5473	461	1	mathematics	mathematic	NOUN
ejpam-5473	461	2	,	,	PUNCT
ejpam-5473	461	3	12(10):1583	12(10):1583	NUM
ejpam-5473	461	4	,	,	PUNCT
ejpam-5473	461	5	2024	2024	NUM
ejpam-5473	461	6	.	.	PUNCT
ejpam-5473	462	1	[	[	X
ejpam-5473	462	2	15	15	NUM
ejpam-5473	462	3	]	]	X
ejpam-5473	462	4	a	a	DET
ejpam-5473	462	5	balasubramanian	balasubramanian	PROPN
ejpam-5473	462	6	,	,	PUNCT
ejpam-5473	462	7	km	km	NOUN
ejpam-5473	462	8	prasad	prasad	NOUN
ejpam-5473	462	9	,	,	PUNCT
ejpam-5473	462	10	and	and	CCONJ
ejpam-5473	462	11	k	k	PROPN
ejpam-5473	462	12	arjunan	arjunan	NOUN
ejpam-5473	462	13	.	.	PUNCT
ejpam-5473	463	1	bipolar	bipolar	ADJ
ejpam-5473	463	2	interval	interval	NOUN
ejpam-5473	463	3	valued	value	VERB
ejpam-5473	463	4	fuzzy	fuzzy	ADJ
ejpam-5473	463	5	subgroups	subgroup	NOUN
ejpam-5473	463	6	of	of	ADP
ejpam-5473	463	7	a	a	DET
ejpam-5473	463	8	group	group	NOUN
ejpam-5473	463	9	.	.	PUNCT
ejpam-5473	464	1	bulletin	bulletin	NOUN
ejpam-5473	464	2	of	of	ADP
ejpam-5473	464	3	mathematics	mathematic	NOUN
ejpam-5473	464	4	and	and	CCONJ
ejpam-5473	464	5	statistics	statistic	NOUN
ejpam-5473	464	6	research	research	NOUN
ejpam-5473	464	7	,	,	PUNCT
ejpam-5473	464	8	3(3):234	3(3):234	NUM
ejpam-5473	464	9	–	–	PUNCT
ejpam-5473	464	10	239	239	NUM
ejpam-5473	464	11	,	,	PUNCT
ejpam-5473	464	12	2015	2015	NUM
ejpam-5473	464	13	.	.	PUNCT
ejpam-5473	465	1	[	[	X
ejpam-5473	465	2	16	16	NUM
ejpam-5473	465	3	]	]	X
ejpam-5473	465	4	k.a	k.a	PROPN
ejpam-5473	465	5	dib	dib	PROPN
ejpam-5473	465	6	.	.	PUNCT
ejpam-5473	466	1	on	on	ADP
ejpam-5473	466	2	fuzzy	fuzzy	ADJ
ejpam-5473	466	3	spaces	space	NOUN
ejpam-5473	466	4	and	and	CCONJ
ejpam-5473	466	5	fuzzy	fuzzy	ADJ
ejpam-5473	466	6	group	group	NOUN
ejpam-5473	466	7	theory	theory	NOUN
ejpam-5473	466	8	.	.	PUNCT
ejpam-5473	467	1	information	information	NOUN
ejpam-5473	467	2	sciences	sciences	PROPN
ejpam-5473	467	3	,	,	PUNCT
ejpam-5473	467	4	80(3	80(3	X
ejpam-5473	467	5	-	-	SYM
ejpam-5473	467	6	4):253	4):253	NUM
ejpam-5473	467	7	–	–	PUNCT
ejpam-5473	467	8	282	282	NUM
ejpam-5473	467	9	,	,	PUNCT
ejpam-5473	467	10	1994	1994	NUM
ejpam-5473	467	11	.	.	PUNCT
ejpam-5473	468	1	[	[	X
ejpam-5473	468	2	17	17	NUM
ejpam-5473	468	3	]	]	X
ejpam-5473	468	4	k.a	k.a	PROPN
ejpam-5473	468	5	dib	dib	PROPN
ejpam-5473	468	6	and	and	CCONJ
ejpam-5473	468	7	nabil	nabil	PROPN
ejpam-5473	468	8	l	l	PROPN
ejpam-5473	468	9	youssef	youssef	PROPN
ejpam-5473	468	10	.	.	PUNCT
ejpam-5473	469	1	fuzzy	fuzzy	ADJ
ejpam-5473	469	2	cartesian	cartesian	ADJ
ejpam-5473	469	3	product	product	NOUN
ejpam-5473	469	4	,	,	PUNCT
ejpam-5473	469	5	fuzzy	fuzzy	ADJ
ejpam-5473	469	6	relations	relation	NOUN
ejpam-5473	469	7	and	and	CCONJ
ejpam-5473	469	8	fuzzy	fuzzy	ADJ
ejpam-5473	469	9	functions	function	NOUN
ejpam-5473	469	10	.	.	PUNCT
ejpam-5473	470	1	fuzzy	fuzzy	ADJ
ejpam-5473	470	2	sets	set	NOUN
ejpam-5473	470	3	and	and	CCONJ
ejpam-5473	470	4	systems	system	NOUN
ejpam-5473	470	5	,	,	PUNCT
ejpam-5473	470	6	41(3):299–315	41(3):299–315	PROPN
ejpam-5473	470	7	,	,	PUNCT
ejpam-5473	470	8	1991	1991	NUM
ejpam-5473	470	9	.	.	PUNCT
ejpam-5473	471	1	[	[	X
ejpam-5473	471	2	18	18	NUM
ejpam-5473	471	3	]	]	X
ejpam-5473	471	4	m	m	VERB
ejpam-5473	471	5	fathi	fathi	PROPN
ejpam-5473	471	6	and	and	CCONJ
ejpam-5473	471	7	abdul	abdul	PROPN
ejpam-5473	471	8	razak	razak	PROPN
ejpam-5473	471	9	salleh	salleh	PROPN
ejpam-5473	471	10	.	.	PUNCT
ejpam-5473	472	1	intuitionistic	intuitionistic	ADJ
ejpam-5473	472	2	fuzzy	fuzzy	ADJ
ejpam-5473	472	3	groups	group	NOUN
ejpam-5473	472	4	.	.	PUNCT
ejpam-5473	473	1	asian	asian	ADJ
ejpam-5473	473	2	journal	journal	PROPN
ejpam-5473	473	3	of	of	ADP
ejpam-5473	473	4	algebra	algebra	PROPN
ejpam-5473	473	5	,	,	PUNCT
ejpam-5473	473	6	2(1):1–10	2(1):1–10	NUM
ejpam-5473	473	7	,	,	PUNCT
ejpam-5473	473	8	2009	2009	NUM
ejpam-5473	473	9	.	.	PUNCT
ejpam-5473	474	1	[	[	X
ejpam-5473	474	2	19	19	NUM
ejpam-5473	474	3	]	]	X
ejpam-5473	474	4	bao	bao	PROPN
ejpam-5473	474	5	qing	qe	VERB
ejpam-5473	474	6	hu	hu	PROPN
ejpam-5473	474	7	and	and	CCONJ
ejpam-5473	474	8	ka	ka	PROPN
ejpam-5473	474	9	-	-	PUNCT
ejpam-5473	474	10	fai	fai	PROPN
ejpam-5473	474	11	cedric	cedric	PROPN
ejpam-5473	474	12	yiu	yiu	PROPN
ejpam-5473	474	13	.	.	PUNCT
ejpam-5473	475	1	a	a	DET
ejpam-5473	475	2	bipolar	bipolar	ADV
ejpam-5473	475	3	-	-	PUNCT
ejpam-5473	475	4	valued	value	VERB
ejpam-5473	475	5	fuzzy	fuzzy	ADJ
ejpam-5473	475	6	set	set	NOUN
ejpam-5473	475	7	is	be	AUX
ejpam-5473	475	8	an	an	DET
ejpam-5473	475	9	intersected	intersect	VERB
ejpam-5473	475	10	interval	interval	NOUN
ejpam-5473	475	11	-	-	PUNCT
ejpam-5473	475	12	valued	value	VERB
ejpam-5473	475	13	fuzzy	fuzzy	ADJ
ejpam-5473	475	14	set	set	NOUN
ejpam-5473	475	15	.	.	PUNCT
ejpam-5473	476	1	information	information	NOUN
ejpam-5473	476	2	sciences	sciences	PROPN
ejpam-5473	476	3	,	,	PUNCT
ejpam-5473	476	4	657:119980	657:119980	NUM
ejpam-5473	476	5	,	,	PUNCT
ejpam-5473	476	6	2024	2024	NUM
ejpam-5473	476	7	.	.	PUNCT
ejpam-5473	477	1	[	[	X
ejpam-5473	477	2	20	20	NUM
ejpam-5473	477	3	]	]	X
ejpam-5473	477	4	ra	ra	PROPN
ejpam-5473	477	5	husban	husban	PROPN
ejpam-5473	477	6	,	,	PUNCT
ejpam-5473	477	7	abdul	abdul	PROPN
ejpam-5473	477	8	razak	razak	PROPN
ejpam-5473	477	9	salleh	salleh	PROPN
ejpam-5473	477	10	,	,	PUNCT
ejpam-5473	477	11	and	and	CCONJ
ejpam-5473	477	12	agb	agb	PROPN
ejpam-5473	477	13	ahmed	ahmed	PROPN
ejpam-5473	477	14	.	.	PUNCT
ejpam-5473	478	1	complex	complex	ADJ
ejpam-5473	478	2	intuitionistic	intuitionistic	ADJ
ejpam-5473	478	3	fuzzy	fuzzy	ADJ
ejpam-5473	478	4	group	group	NOUN
ejpam-5473	478	5	.	.	PUNCT
ejpam-5473	479	1	global	global	ADJ
ejpam-5473	479	2	journal	journal	PROPN
ejpam-5473	479	3	of	of	ADP
ejpam-5473	479	4	pure	pure	ADJ
ejpam-5473	479	5	and	and	CCONJ
ejpam-5473	479	6	applied	applied	ADJ
ejpam-5473	479	7	mathematics	mathematic	NOUN
ejpam-5473	479	8	,	,	PUNCT
ejpam-5473	479	9	12:4929–4949	12:4929–4949	NUM
ejpam-5473	479	10	,	,	PUNCT
ejpam-5473	479	11	2016	2016	NUM
ejpam-5473	479	12	.	.	PUNCT
ejpam-5473	480	1	[	[	X
ejpam-5473	480	2	21	21	NUM
ejpam-5473	480	3	]	]	X
ejpam-5473	480	4	abdul	abdul	PROPN
ejpam-5473	480	5	jaleel	jaleel	PROPN
ejpam-5473	480	6	,	,	PUNCT
ejpam-5473	480	7	tahir	tahir	PROPN
ejpam-5473	480	8	mahmood	mahmood	PROPN
ejpam-5473	480	9	,	,	PUNCT
ejpam-5473	480	10	walid	walid	PROPN
ejpam-5473	480	11	emam	emam	PROPN
ejpam-5473	480	12	,	,	PUNCT
ejpam-5473	480	13	and	and	CCONJ
ejpam-5473	480	14	shi	shi	PROPN
ejpam-5473	480	15	yin	yin	PROPN
ejpam-5473	480	16	.	.	PUNCT
ejpam-5473	481	1	interval	interval	NOUN
ejpam-5473	481	2	-	-	PUNCT
ejpam-5473	481	3	valued	value	VERB
ejpam-5473	481	4	bipolar	bipolar	ADJ
ejpam-5473	481	5	complex	complex	ADJ
ejpam-5473	481	6	fuzzy	fuzzy	ADJ
ejpam-5473	481	7	soft	soft	ADJ
ejpam-5473	481	8	sets	set	NOUN
ejpam-5473	481	9	and	and	CCONJ
ejpam-5473	481	10	their	their	PRON
ejpam-5473	481	11	applications	application	NOUN
ejpam-5473	481	12	in	in	ADP
ejpam-5473	481	13	decision	decision	NOUN
ejpam-5473	481	14	making	making	NOUN
ejpam-5473	481	15	.	.	PUNCT
ejpam-5473	482	1	scientific	scientific	ADJ
ejpam-5473	482	2	reports	report	NOUN
ejpam-5473	482	3	,	,	PUNCT
ejpam-5473	482	4	14(1):11589	14(1):11589	NUM
ejpam-5473	482	5	,	,	PUNCT
ejpam-5473	482	6	2024	2024	NUM
ejpam-5473	482	7	.	.	PUNCT
ejpam-5473	483	1	references	reference	NOUN
ejpam-5473	483	2	2913	2913	NUM
ejpam-5473	483	3	[	[	X
ejpam-5473	483	4	22	22	NUM
ejpam-5473	483	5	]	]	X
ejpam-5473	483	6	young	young	ADJ
ejpam-5473	483	7	bae	bae	PROPN
ejpam-5473	483	8	jun	jun	PROPN
ejpam-5473	483	9	and	and	CCONJ
ejpam-5473	483	10	seok	seok	PROPN
ejpam-5473	483	11	zun	zun	PROPN
ejpam-5473	483	12	song	song	PROPN
ejpam-5473	483	13	.	.	PUNCT
ejpam-5473	484	1	subalgebras	subalgebras	PROPN
ejpam-5473	484	2	and	and	CCONJ
ejpam-5473	484	3	closed	closed	ADJ
ejpam-5473	484	4	ideals	ideal	NOUN
ejpam-5473	484	5	of	of	ADP
ejpam-5473	484	6	bch	bch	PROPN
ejpam-5473	484	7	-	-	PUNCT
ejpam-5473	484	8	algebras	algebras	PROPN
ejpam-5473	484	9	based	base	VERB
ejpam-5473	484	10	on	on	ADP
ejpam-5473	484	11	bipolar	bipolar	ADV
ejpam-5473	484	12	-	-	PUNCT
ejpam-5473	484	13	valued	value	VERB
ejpam-5473	484	14	fuzzy	fuzzy	ADJ
ejpam-5473	484	15	sets	set	NOUN
ejpam-5473	484	16	.	.	PUNCT
ejpam-5473	485	1	sci	sci	PROPN
ejpam-5473	485	2	.	.	PROPN
ejpam-5473	485	3	math	math	PROPN
ejpam-5473	485	4	.	.	PUNCT
ejpam-5473	486	1	jpn	jpn	PROPN
ejpam-5473	486	2	,	,	PUNCT
ejpam-5473	486	3	68(2):287–297	68(2):287–297	PROPN
ejpam-5473	486	4	,	,	PUNCT
ejpam-5473	486	5	2008	2008	NUM
ejpam-5473	486	6	.	.	PUNCT
ejpam-5473	487	1	[	[	X
ejpam-5473	487	2	23	23	NUM
ejpam-5473	487	3	]	]	X
ejpam-5473	487	4	keon	keon	PROPN
ejpam-5473	487	5	myung	myung	PROPN
ejpam-5473	487	6	lee	lee	PROPN
ejpam-5473	487	7	.	.	PUNCT
ejpam-5473	488	1	bipolar	bipolar	ADJ
ejpam-5473	488	2	-	-	PUNCT
ejpam-5473	488	3	valued	value	VERB
ejpam-5473	488	4	fuzzy	fuzzy	ADJ
ejpam-5473	488	5	sets	set	NOUN
ejpam-5473	488	6	and	and	CCONJ
ejpam-5473	488	7	their	their	PRON
ejpam-5473	488	8	operations	operation	NOUN
ejpam-5473	488	9	.	.	PUNCT
ejpam-5473	489	1	in	in	ADP
ejpam-5473	489	2	proc	proc	PROPN
ejpam-5473	489	3	.	.	PUNCT
ejpam-5473	490	1	int	int	NOUN
ejpam-5473	490	2	.	.	PUNCT
ejpam-5473	490	3	conf	conf	PROPN
ejpam-5473	490	4	.	.	PUNCT
ejpam-5473	491	1	on	on	ADP
ejpam-5473	491	2	intelligent	intelligent	ADJ
ejpam-5473	491	3	technologies	technology	NOUN
ejpam-5473	491	4	,	,	PUNCT
ejpam-5473	491	5	bangkok	bangkok	PROPN
ejpam-5473	491	6	,	,	PUNCT
ejpam-5473	491	7	thailand	thailand	PROPN
ejpam-5473	491	8	,	,	PUNCT
ejpam-5473	491	9	2000	2000	NUM
ejpam-5473	491	10	,	,	PUNCT
ejpam-5473	491	11	pages	page	NOUN
ejpam-5473	491	12	307–312	307–312	NUM
ejpam-5473	491	13	,	,	PUNCT
ejpam-5473	491	14	2000	2000	NUM
ejpam-5473	491	15	.	.	PUNCT
ejpam-5473	492	1	[	[	X
ejpam-5473	492	2	24	24	NUM
ejpam-5473	492	3	]	]	X
ejpam-5473	492	4	keon	keon	PROPN
ejpam-5473	492	5	-	-	PUNCT
ejpam-5473	492	6	myung	myung	PROPN
ejpam-5473	492	7	lee	lee	PROPN
ejpam-5473	492	8	,	,	PUNCT
ejpam-5473	492	9	kyung	kyung	PROPN
ejpam-5473	492	10	-	-	PUNCT
ejpam-5473	492	11	mi	mi	PROPN
ejpam-5473	492	12	lee	lee	PROPN
ejpam-5473	492	13	,	,	PUNCT
ejpam-5473	492	14	and	and	CCONJ
ejpam-5473	492	15	krzysztof	krzysztof	PROPN
ejpam-5473	492	16	j	j	PROPN
ejpam-5473	492	17	cios	cio	NOUN
ejpam-5473	492	18	.	.	PUNCT
ejpam-5473	493	1	comparison	comparison	NOUN
ejpam-5473	493	2	of	of	ADP
ejpam-5473	493	3	interval	interval	NOUN
ejpam-5473	493	4	-	-	PUNCT
ejpam-5473	493	5	valued	value	VERB
ejpam-5473	493	6	fuzzy	fuzzy	ADJ
ejpam-5473	493	7	sets	set	NOUN
ejpam-5473	493	8	,	,	PUNCT
ejpam-5473	493	9	intuitionistic	intuitionistic	ADJ
ejpam-5473	493	10	fuzzy	fuzzy	ADJ
ejpam-5473	493	11	sets	set	NOUN
ejpam-5473	493	12	,	,	PUNCT
ejpam-5473	493	13	and	and	CCONJ
ejpam-5473	493	14	bipolar	bipolar	ADV
ejpam-5473	493	15	-	-	PUNCT
ejpam-5473	493	16	valued	value	VERB
ejpam-5473	493	17	fuzzy	fuzzy	ADJ
ejpam-5473	493	18	sets	set	NOUN
ejpam-5473	493	19	.	.	PUNCT
ejpam-5473	494	1	in	in	ADP
ejpam-5473	494	2	computing	computing	NOUN
ejpam-5473	494	3	and	and	CCONJ
ejpam-5473	494	4	information	information	NOUN
ejpam-5473	494	5	technologies	technology	NOUN
ejpam-5473	494	6	:	:	PUNCT
ejpam-5473	494	7	exploring	explore	VERB
ejpam-5473	494	8	emerging	emerge	VERB
ejpam-5473	494	9	technologies	technology	NOUN
ejpam-5473	494	10	,	,	PUNCT
ejpam-5473	494	11	pages	page	NOUN
ejpam-5473	494	12	433	433	NUM
ejpam-5473	494	13	–	–	PUNCT
ejpam-5473	494	14	439	439	NUM
ejpam-5473	494	15	.	.	PUNCT
ejpam-5473	494	16	world	world	PROPN
ejpam-5473	494	17	scientific	scientific	PROPN
ejpam-5473	494	18	,	,	PUNCT
ejpam-5473	494	19	2001	2001	NUM
ejpam-5473	494	20	.	.	PUNCT
ejpam-5473	495	1	[	[	X
ejpam-5473	495	2	25	25	NUM
ejpam-5473	495	3	]	]	X
ejpam-5473	495	4	kyoung	kyoung	PROPN
ejpam-5473	495	5	ja	ja	PROPN
ejpam-5473	495	6	lee	lee	PROPN
ejpam-5473	495	7	.	.	PUNCT
ejpam-5473	496	1	bipolar	bipolar	ADJ
ejpam-5473	496	2	fuzzy	fuzzy	ADJ
ejpam-5473	496	3	subalgebras	subalgebra	NOUN
ejpam-5473	496	4	and	and	CCONJ
ejpam-5473	496	5	bipolar	bipolar	ADJ
ejpam-5473	496	6	fuzzy	fuzzy	ADJ
ejpam-5473	496	7	ideals	ideal	NOUN
ejpam-5473	496	8	of	of	ADP
ejpam-5473	496	9	bck	bck	PROPN
ejpam-5473	496	10	/	/	SYM
ejpam-5473	496	11	bcialgebras	bcialgebra	NOUN
ejpam-5473	496	12	.	.	PUNCT
ejpam-5473	497	1	bull	bull	NOUN
ejpam-5473	497	2	.	.	PUNCT
ejpam-5473	498	1	malays	malays	PROPN
ejpam-5473	498	2	.	.	PUNCT
ejpam-5473	499	1	math	math	NOUN
ejpam-5473	499	2	.	.	PUNCT
ejpam-5473	500	1	sci	sci	PROPN
ejpam-5473	500	2	.	.	PROPN
ejpam-5473	500	3	soc	soc	PROPN
ejpam-5473	500	4	,	,	PUNCT
ejpam-5473	500	5	32(3):361–373	32(3):361–373	PROPN
ejpam-5473	500	6	,	,	PUNCT
ejpam-5473	500	7	2009	2009	NUM
ejpam-5473	500	8	.	.	PUNCT
ejpam-5473	501	1	[	[	X
ejpam-5473	501	2	26	26	NUM
ejpam-5473	501	3	]	]	X
ejpam-5473	501	4	tahir	tahir	PROPN
ejpam-5473	501	5	mahmood	mahmood	PROPN
ejpam-5473	501	6	,	,	PUNCT
ejpam-5473	501	7	abdul	abdul	PROPN
ejpam-5473	501	8	jaleel	jaleel	PROPN
ejpam-5473	501	9	,	,	PUNCT
ejpam-5473	501	10	and	and	CCONJ
ejpam-5473	501	11	ubaid	ubaid	VERB
ejpam-5473	501	12	ur	ur	PROPN
ejpam-5473	501	13	rehman	rehman	PROPN
ejpam-5473	501	14	.	.	PUNCT
ejpam-5473	502	1	pattern	pattern	NOUN
ejpam-5473	502	2	recognition	recognition	NOUN
ejpam-5473	502	3	and	and	CCONJ
ejpam-5473	502	4	medical	medical	ADJ
ejpam-5473	502	5	diagnosis	diagnosis	NOUN
ejpam-5473	502	6	based	base	VERB
ejpam-5473	502	7	on	on	ADP
ejpam-5473	502	8	trigonometric	trigonometric	ADJ
ejpam-5473	502	9	similarity	similarity	NOUN
ejpam-5473	502	10	measures	measure	NOUN
ejpam-5473	502	11	for	for	ADP
ejpam-5473	502	12	bipolar	bipolar	ADJ
ejpam-5473	502	13	complex	complex	ADJ
ejpam-5473	502	14	fuzzy	fuzzy	ADJ
ejpam-5473	502	15	soft	soft	ADJ
ejpam-5473	502	16	sets	set	NOUN
ejpam-5473	502	17	.	.	PUNCT
ejpam-5473	503	1	soft	soft	ADJ
ejpam-5473	503	2	computing	computing	NOUN
ejpam-5473	503	3	,	,	PUNCT
ejpam-5473	503	4	27(16):11125–11154	27(16):11125–11154	NUM
ejpam-5473	503	5	,	,	PUNCT
ejpam-5473	503	6	2023	2023	NUM
ejpam-5473	503	7	.	.	PUNCT
ejpam-5473	504	1	[	[	X
ejpam-5473	504	2	27	27	NUM
ejpam-5473	504	3	]	]	X
ejpam-5473	504	4	tahir	tahir	PROPN
ejpam-5473	504	5	mahmood	mahmood	PROPN
ejpam-5473	504	6	,	,	PUNCT
ejpam-5473	504	7	ubaid	ubaid	VERB
ejpam-5473	504	8	ur	ur	PROPN
ejpam-5473	504	9	rehman	rehman	PROPN
ejpam-5473	504	10	,	,	PUNCT
ejpam-5473	504	11	and	and	CCONJ
ejpam-5473	504	12	majed	majed	PROPN
ejpam-5473	504	13	albaity	albaity	NOUN
ejpam-5473	504	14	.	.	PUNCT
ejpam-5473	505	1	analysis	analysis	NOUN
ejpam-5473	505	2	of	of	ADP
ejpam-5473	505	3	γ	γ	NOUN
ejpam-5473	505	4	-	-	PUNCT
ejpam-5473	505	5	semigroups	semigroup	NOUN
ejpam-5473	505	6	based	base	VERB
ejpam-5473	505	7	on	on	ADP
ejpam-5473	505	8	bipolar	bipolar	ADJ
ejpam-5473	505	9	complex	complex	ADJ
ejpam-5473	505	10	fuzzy	fuzzy	ADJ
ejpam-5473	505	11	sets	set	NOUN
ejpam-5473	505	12	.	.	PUNCT
ejpam-5473	506	1	computational	computational	ADJ
ejpam-5473	506	2	and	and	CCONJ
ejpam-5473	506	3	applied	applied	ADJ
ejpam-5473	506	4	mathematics	mathematic	NOUN
ejpam-5473	506	5	,	,	PUNCT
ejpam-5473	506	6	42(6):262	42(6):262	PROPN
ejpam-5473	506	7	,	,	PUNCT
ejpam-5473	506	8	2023	2023	NUM
ejpam-5473	506	9	.	.	PUNCT
ejpam-5473	507	1	[	[	X
ejpam-5473	507	2	28	28	NUM
ejpam-5473	507	3	]	]	X
ejpam-5473	507	4	mourad	mourad	PROPN
ejpam-5473	507	5	oqla	oqla	PROPN
ejpam-5473	507	6	massa’deh	massa’deh	PROPN
ejpam-5473	507	7	,	,	PUNCT
ejpam-5473	507	8	ahlam	ahlam	PROPN
ejpam-5473	507	9	omar	omar	PROPN
ejpam-5473	507	10	fallatah	fallatah	PROPN
ejpam-5473	507	11	,	,	PUNCT
ejpam-5473	507	12	et	et	PROPN
ejpam-5473	507	13	al	al	PROPN
ejpam-5473	507	14	.	.	PUNCT
ejpam-5473	508	1	anti	anti	PROPN
ejpam-5473	508	2	homomorphism	homomorphism	NOUN
ejpam-5473	508	3	and	and	CCONJ
ejpam-5473	508	4	homomorphism	homomorphism	NOUN
ejpam-5473	508	5	of	of	ADP
ejpam-5473	508	6	bipolar	bipolar	ADJ
ejpam-5473	508	7	valued	value	VERB
ejpam-5473	508	8	multi	multi	X
ejpam-5473	508	9	fuzzy	fuzzy	ADJ
ejpam-5473	508	10	hx	hx	PROPN
ejpam-5473	508	11	-	-	PUNCT
ejpam-5473	508	12	subgroups	subgroup	NOUN
ejpam-5473	508	13	and	and	CCONJ
ejpam-5473	508	14	it	it	PRON
ejpam-5473	508	15	’s	’	VERB
ejpam-5473	508	16	normal	normal	ADJ
ejpam-5473	508	17	.	.	PUNCT
ejpam-5473	509	1	full	full	ADJ
ejpam-5473	509	2	length	length	NOUN
ejpam-5473	509	3	article	article	NOUN
ejpam-5473	509	4	,	,	PUNCT
ejpam-5473	509	5	24(3):165–65	24(3):165–65	NUM
ejpam-5473	509	6	,	,	PUNCT
ejpam-5473	509	7	2024	2024	NUM
ejpam-5473	509	8	.	.	PUNCT
ejpam-5473	510	1	[	[	X
ejpam-5473	510	2	29	29	NUM
ejpam-5473	510	3	]	]	X
ejpam-5473	510	4	azriel	azriel	PROPN
ejpam-5473	510	5	rosenfeld	rosenfeld	PROPN
ejpam-5473	510	6	.	.	PUNCT
ejpam-5473	511	1	fuzzy	fuzzy	ADJ
ejpam-5473	511	2	groups	group	NOUN
ejpam-5473	511	3	.	.	PUNCT
ejpam-5473	512	1	journal	journal	PROPN
ejpam-5473	512	2	of	of	ADP
ejpam-5473	512	3	mathematical	mathematical	ADJ
ejpam-5473	512	4	analysis	analysis	NOUN
ejpam-5473	512	5	and	and	CCONJ
ejpam-5473	512	6	applications	application	NOUN
ejpam-5473	512	7	,	,	PUNCT
ejpam-5473	512	8	35(3):512–517	35(3):512–517	PROPN
ejpam-5473	512	9	,	,	PUNCT
ejpam-5473	512	10	1971	1971	NUM
ejpam-5473	512	11	.	.	PUNCT
ejpam-5473	513	1	[	[	X
ejpam-5473	513	2	30	30	NUM
ejpam-5473	513	3	]	]	SYM
ejpam-5473	513	4	arsham	arsham	PROPN
ejpam-5473	513	5	borumand	borumand	PROPN
ejpam-5473	513	6	saeid	saeid	PROPN
ejpam-5473	513	7	.	.	PUNCT
ejpam-5473	514	1	bipolar	bipolar	ADJ
ejpam-5473	514	2	-	-	PUNCT
ejpam-5473	514	3	valued	value	VERB
ejpam-5473	514	4	fuzzy	fuzzy	ADJ
ejpam-5473	514	5	bck	bck	PROPN
ejpam-5473	514	6	/	/	SYM
ejpam-5473	514	7	bci	bci	NOUN
ejpam-5473	514	8	-	-	PUNCT
ejpam-5473	514	9	algebras	algebra	NOUN
ejpam-5473	514	10	.	.	PUNCT
ejpam-5473	515	1	world	world	PROPN
ejpam-5473	515	2	applied	apply	VERB
ejpam-5473	515	3	sciences	science	NOUN
ejpam-5473	515	4	journal	journal	NOUN
ejpam-5473	515	5	,	,	PUNCT
ejpam-5473	515	6	7(11):1404–1411	7(11):1404–1411	NUM
ejpam-5473	515	7	,	,	PUNCT
ejpam-5473	515	8	2009	2009	NUM
ejpam-5473	515	9	.	.	PUNCT
ejpam-5473	516	1	[	[	X
ejpam-5473	516	2	31	31	NUM
ejpam-5473	516	3	]	]	X
ejpam-5473	516	4	a.s	a.s	PROPN
ejpam-5473	516	5	.	.	PROPN
ejpam-5473	516	6	sahaya	sahaya	PROPN
ejpam-5473	516	7	,	,	PUNCT
ejpam-5473	516	8	s	s	VERB
ejpam-5473	516	9	naganathan	naganathan	NOUN
ejpam-5473	516	10	,	,	PUNCT
ejpam-5473	516	11	and	and	CCONJ
ejpam-5473	516	12	k	k	PROPN
ejpam-5473	516	13	arjunan	arjunan	PROPN
ejpam-5473	516	14	.	.	PUNCT
ejpam-5473	517	1	a	a	DET
ejpam-5473	517	2	study	study	NOUN
ejpam-5473	517	3	on	on	ADP
ejpam-5473	517	4	bipolar	bipolar	ADJ
ejpam-5473	517	5	valued	value	VERB
ejpam-5473	517	6	q	q	ADJ
ejpam-5473	517	7	-	-	PUNCT
ejpam-5473	517	8	fuzzy	fuzzy	ADJ
ejpam-5473	517	9	subgroups	subgroup	NOUN
ejpam-5473	517	10	of	of	ADP
ejpam-5473	517	11	a	a	DET
ejpam-5473	517	12	group	group	NOUN
ejpam-5473	517	13	.	.	PUNCT
ejpam-5473	518	1	bulletin	bulletin	NOUN
ejpam-5473	518	2	of	of	ADP
ejpam-5473	518	3	mathematics	mathematic	NOUN
ejpam-5473	518	4	and	and	CCONJ
ejpam-5473	518	5	statistics	statistic	NOUN
ejpam-5473	518	6	research	research	PROPN
ejpam-5473	518	7	,	,	PUNCT
ejpam-5473	518	8	4(3):97–101	4(3):97–101	NOUN
ejpam-5473	518	9	,	,	PUNCT
ejpam-5473	518	10	2016	2016	NUM
ejpam-5473	518	11	.	.	PUNCT
ejpam-5473	519	1	[	[	X
ejpam-5473	519	2	32	32	NUM
ejpam-5473	519	3	]	]	X
ejpam-5473	519	4	aa	aa	PROPN
ejpam-5473	519	5	salama	salama	PROPN
ejpam-5473	519	6	,	,	PUNCT
ejpam-5473	519	7	mahmoud	mahmoud	PROPN
ejpam-5473	519	8	y	y	PROPN
ejpam-5473	519	9	shams	sham	NOUN
ejpam-5473	519	10	,	,	PUNCT
ejpam-5473	519	11	huda	huda	PROPN
ejpam-5473	519	12	e	e	PROPN
ejpam-5473	519	13	khalid	khalid	PROPN
ejpam-5473	519	14	,	,	PUNCT
ejpam-5473	519	15	and	and	CCONJ
ejpam-5473	519	16	doaa	doaa	VERB
ejpam-5473	519	17	e	e	PROPN
ejpam-5473	519	18	mousa	mousa	PROPN
ejpam-5473	519	19	.	.	PUNCT
ejpam-5473	520	1	enhancing	enhance	VERB
ejpam-5473	520	2	medical	medical	ADJ
ejpam-5473	520	3	image	image	NOUN
ejpam-5473	520	4	quality	quality	NOUN
ejpam-5473	520	5	using	use	VERB
ejpam-5473	520	6	neutrosophic	neutrosophic	ADJ
ejpam-5473	520	7	fuzzy	fuzzy	ADJ
ejpam-5473	520	8	domain	domain	NOUN
ejpam-5473	520	9	and	and	CCONJ
ejpam-5473	520	10	multi	multi	ADJ
ejpam-5473	520	11	-	-	ADJ
ejpam-5473	520	12	level	level	ADJ
ejpam-5473	520	13	enhancement	enhancement	NOUN
ejpam-5473	520	14	transforms	transform	VERB
ejpam-5473	520	15	:	:	PUNCT
ejpam-5473	520	16	a	a	DET
ejpam-5473	520	17	comparative	comparative	ADJ
ejpam-5473	520	18	study	study	NOUN
ejpam-5473	520	19	for	for	ADP
ejpam-5473	520	20	leukemia	leukemia	NOUN
ejpam-5473	520	21	detection	detection	NOUN
ejpam-5473	520	22	and	and	CCONJ
ejpam-5473	520	23	classification	classification	NOUN
ejpam-5473	520	24	.	.	PUNCT
ejpam-5473	521	1	neutrosophic	neutrosophic	ADJ
ejpam-5473	521	2	sets	set	NOUN
ejpam-5473	521	3	and	and	CCONJ
ejpam-5473	521	4	systems	system	NOUN
ejpam-5473	521	5	,	,	PUNCT
ejpam-5473	521	6	65(1):3	65(1):3	PROPN
ejpam-5473	521	7	,	,	PUNCT
ejpam-5473	521	8	2024	2024	NUM
ejpam-5473	521	9	.	.	PUNCT
ejpam-5473	522	1	[	[	X
ejpam-5473	522	2	33	33	NUM
ejpam-5473	522	3	]	]	SYM
ejpam-5473	522	4	v	v	NUM
ejpam-5473	522	5	shanmugapriya	shanmugapriya	PROPN
ejpam-5473	522	6	and	and	CCONJ
ejpam-5473	522	7	k	k	PROPN
ejpam-5473	522	8	arjunan	arjunan	PROPN
ejpam-5473	522	9	.	.	PUNCT
ejpam-5473	523	1	some	some	DET
ejpam-5473	523	2	translators	translator	NOUN
ejpam-5473	523	3	in	in	ADP
ejpam-5473	523	4	bipolar	bipolar	ADJ
ejpam-5473	523	5	valued	value	VERB
ejpam-5473	523	6	fuzzy	fuzzy	ADJ
ejpam-5473	523	7	subsemiring	subsemiring	NOUN
ejpam-5473	523	8	of	of	ADP
ejpam-5473	523	9	a	a	DET
ejpam-5473	523	10	semiring	semiring	NOUN
ejpam-5473	523	11	.	.	PUNCT
ejpam-5473	524	1	bulletin	bulletin	NOUN
ejpam-5473	524	2	of	of	ADP
ejpam-5473	524	3	mathematics	mathematic	NOUN
ejpam-5473	524	4	and	and	CCONJ
ejpam-5473	524	5	statistics	statistic	NOUN
ejpam-5473	524	6	research	research	NOUN
ejpam-5473	524	7	,	,	PUNCT
ejpam-5473	524	8	4(4):118–123	4(4):118–123	NUM
ejpam-5473	524	9	,	,	PUNCT
ejpam-5473	524	10	2016	2016	NUM
ejpam-5473	524	11	.	.	PUNCT
ejpam-5473	525	1	[	[	X
ejpam-5473	525	2	34	34	NUM
ejpam-5473	525	3	]	]	X
ejpam-5473	525	4	sharifeh	sharifeh	X
ejpam-5473	525	5	soofizadeh	soofizadeh	PROPN
ejpam-5473	525	6	and	and	CCONJ
ejpam-5473	525	7	reza	reza	PROPN
ejpam-5473	525	8	fallahnejad	fallahnejad	PROPN
ejpam-5473	525	9	.	.	PUNCT
ejpam-5473	526	1	evaluation	evaluation	NOUN
ejpam-5473	526	2	of	of	ADP
ejpam-5473	526	3	groups	group	NOUN
ejpam-5473	526	4	using	use	VERB
ejpam-5473	526	5	cooperative	cooperative	ADJ
ejpam-5473	526	6	game	game	NOUN
ejpam-5473	526	7	with	with	ADP
ejpam-5473	526	8	fuzzy	fuzzy	ADJ
ejpam-5473	526	9	data	datum	NOUN
ejpam-5473	526	10	envelopment	envelopment	ADJ
ejpam-5473	526	11	analysis	analysis	NOUN
ejpam-5473	526	12	.	.	PUNCT
ejpam-5473	527	1	aims	aim	VERB
ejpam-5473	527	2	math	math	NOUN
ejpam-5473	527	3	,	,	PUNCT
ejpam-5473	527	4	8(4):8661–8679	8(4):8661–8679	PROPN
ejpam-5473	527	5	,	,	PUNCT
ejpam-5473	527	6	2023	2023	NUM
ejpam-5473	527	7	.	.	PUNCT
ejpam-5473	528	1	references	reference	NOUN
ejpam-5473	528	2	2914	2914	NUM
ejpam-5473	528	3	[	[	X
ejpam-5473	528	4	35	35	NUM
ejpam-5473	528	5	]	]	X
ejpam-5473	528	6	yuhua	yuhua	PROPN
ejpam-5473	528	7	xu	xu	PROPN
ejpam-5473	528	8	,	,	PUNCT
ejpam-5473	528	9	yang	yang	PROPN
ejpam-5473	528	10	liu	liu	PROPN
ejpam-5473	528	11	,	,	PUNCT
ejpam-5473	528	12	zhixin	zhixin	PROPN
ejpam-5473	528	13	sun	sun	PROPN
ejpam-5473	528	14	,	,	PUNCT
ejpam-5473	528	15	yucheng	yucheng	PROPN
ejpam-5473	528	16	xue	xue	PROPN
ejpam-5473	528	17	,	,	PUNCT
ejpam-5473	528	18	weiliang	weiliang	PROPN
ejpam-5473	528	19	liao	liao	PROPN
ejpam-5473	528	20	,	,	PUNCT
ejpam-5473	528	21	chenlei	chenlei	VERB
ejpam-5473	528	22	liu	liu	PROPN
ejpam-5473	528	23	,	,	PUNCT
ejpam-5473	528	24	and	and	CCONJ
ejpam-5473	528	25	zhe	zhe	PROPN
ejpam-5473	528	26	sun	sun	PROPN
ejpam-5473	528	27	.	.	PUNCT
ejpam-5473	529	1	key	key	ADJ
ejpam-5473	529	2	vulnerable	vulnerable	ADJ
ejpam-5473	529	3	nodes	node	NOUN
ejpam-5473	529	4	discovery	discovery	NOUN
ejpam-5473	529	5	based	base	VERB
ejpam-5473	529	6	on	on	ADP
ejpam-5473	529	7	bayesian	bayesian	NOUN
ejpam-5473	529	8	attack	attack	NOUN
ejpam-5473	529	9	subgraphs	subgraph	NOUN
ejpam-5473	529	10	and	and	CCONJ
ejpam-5473	529	11	improved	improve	VERB
ejpam-5473	529	12	fuzzy	fuzzy	ADJ
ejpam-5473	529	13	c	c	NOUN
ejpam-5473	529	14	-	-	PUNCT
ejpam-5473	529	15	means	means	NOUN
ejpam-5473	529	16	clustering	clustering	NOUN
ejpam-5473	529	17	.	.	PUNCT
ejpam-5473	530	1	mathematics	mathematic	NOUN
ejpam-5473	530	2	,	,	PUNCT
ejpam-5473	530	3	12(10):1447	12(10):1447	NUM
ejpam-5473	530	4	,	,	PUNCT
ejpam-5473	530	5	2024	2024	NUM
ejpam-5473	530	6	.	.	PUNCT
ejpam-5473	531	1	[	[	X
ejpam-5473	531	2	36	36	NUM
ejpam-5473	531	3	]	]	X
ejpam-5473	531	4	pairote	pairote	ADJ
ejpam-5473	531	5	yiarayong	yiarayong	NOUN
ejpam-5473	531	6	.	.	PUNCT
ejpam-5473	532	1	a	a	DET
ejpam-5473	532	2	new	new	ADJ
ejpam-5473	532	3	approach	approach	NOUN
ejpam-5473	532	4	of	of	ADP
ejpam-5473	532	5	bipolar	bipolar	ADJ
ejpam-5473	532	6	valued	value	VERB
ejpam-5473	532	7	fuzzy	fuzzy	ADJ
ejpam-5473	532	8	set	set	NOUN
ejpam-5473	532	9	theory	theory	NOUN
ejpam-5473	532	10	applied	apply	VERB
ejpam-5473	532	11	on	on	ADP
ejpam-5473	532	12	semigroups	semigroup	NOUN
ejpam-5473	532	13	.	.	PUNCT
ejpam-5473	533	1	international	international	ADJ
ejpam-5473	533	2	journal	journal	NOUN
ejpam-5473	533	3	of	of	ADP
ejpam-5473	533	4	intelligent	intelligent	ADJ
ejpam-5473	533	5	systems	system	NOUN
ejpam-5473	533	6	,	,	PUNCT
ejpam-5473	533	7	36(8):4415–4438	36(8):4415–4438	NUM
ejpam-5473	533	8	,	,	PUNCT
ejpam-5473	533	9	2021	2021	NUM
ejpam-5473	533	10	.	.	PUNCT
ejpam-5473	534	1	[	[	X
ejpam-5473	534	2	37	37	NUM
ejpam-5473	534	3	]	]	X
ejpam-5473	534	4	l.a	l.a	PROPN
ejpam-5473	534	5	zadeh	zadeh	PROPN
ejpam-5473	534	6	.	.	PUNCT
ejpam-5473	534	7	fuzzy	fuzzy	ADJ
ejpam-5473	534	8	sets	set	NOUN
ejpam-5473	534	9	.	.	PUNCT
ejpam-5473	535	1	information	information	NOUN
ejpam-5473	535	2	and	and	CCONJ
ejpam-5473	535	3	control	control	NOUN
ejpam-5473	535	4	,	,	PUNCT
ejpam-5473	535	5	8(3):338–353	8(3):338–353	NUM
ejpam-5473	535	6	,	,	PUNCT
ejpam-5473	535	7	1965	1965	NUM
ejpam-5473	535	8	.	.	PUNCT