id	sid	tid	token	lemma	pos
ejpam-6761	1	1	european	european	PROPN
ejpam-6761	1	2	journal	journal	PROPN
ejpam-6761	1	3	of	of	ADP
ejpam-6761	1	4	pure	pure	ADJ
ejpam-6761	1	5	and	and	CCONJ
ejpam-6761	1	6	applied	applied	ADJ
ejpam-6761	1	7	mathematics	mathematic	NOUN
ejpam-6761	1	8	2025	2025	NUM
ejpam-6761	1	9	,	,	PUNCT
ejpam-6761	1	10	vol	vol	NOUN
ejpam-6761	1	11	.	.	PROPN
ejpam-6761	1	12	18	18	NUM
ejpam-6761	1	13	,	,	PUNCT
ejpam-6761	1	14	issue	issue	NOUN
ejpam-6761	1	15	4	4	NUM
ejpam-6761	1	16	,	,	PUNCT
ejpam-6761	1	17	article	article	NOUN
ejpam-6761	1	18	number	number	NOUN
ejpam-6761	1	19	6761	6761	NUM
ejpam-6761	1	20	issn	issn	PROPN
ejpam-6761	1	21	1307	1307	NUM
ejpam-6761	1	22	-	-	SYM
ejpam-6761	1	23	5543	5543	NUM
ejpam-6761	1	24	–	–	PUNCT
ejpam-6761	1	25	ejpam.com	ejpam.com	X
ejpam-6761	1	26	published	publish	VERB
ejpam-6761	1	27	by	by	ADP
ejpam-6761	1	28	new	new	PROPN
ejpam-6761	1	29	york	york	PROPN
ejpam-6761	1	30	business	business	PROPN
ejpam-6761	1	31	global	global	ADJ
ejpam-6761	1	32	bipolar	bipolar	ADV
ejpam-6761	1	33	-	-	PUNCT
ejpam-6761	1	34	valued	value	VERB
ejpam-6761	1	35	fuzzy	fuzzy	ADJ
ejpam-6761	1	36	subgroups	subgroup	NOUN
ejpam-6761	1	37	,	,	PUNCT
ejpam-6761	1	38	normal	normal	ADJ
ejpam-6761	1	39	subgroups	subgroup	NOUN
ejpam-6761	1	40	,	,	PUNCT
ejpam-6761	1	41	and	and	CCONJ
ejpam-6761	1	42	homomorphisms	homomorphism	NOUN
ejpam-6761	1	43	on	on	ADP
ejpam-6761	1	44	dib	dib	PROPN
ejpam-6761	1	45	’s	’s	PART
ejpam-6761	1	46	fuzzy	fuzzy	ADJ
ejpam-6761	1	47	space	space	NOUN
ejpam-6761	1	48	fadi	fadi	PROPN
ejpam-6761	1	49	al	al	PROPN
ejpam-6761	1	50	-	-	PROPN
ejpam-6761	1	51	zu’bi1,2,∗	zu’bi1,2,∗	PROPN
ejpam-6761	1	52	,	,	PUNCT
ejpam-6761	1	53	abd	abd	PROPN
ejpam-6761	1	54	ghafur	ghafur	NOUN
ejpam-6761	1	55	ahmad1	ahmad1	PROPN
ejpam-6761	1	56	,	,	PUNCT
ejpam-6761	1	57	abd	abd	PROPN
ejpam-6761	1	58	ulazeez	ulazeez	PROPN
ejpam-6761	1	59	alkouri3	alkouri3	PROPN
ejpam-6761	1	60	,	,	PUNCT
ejpam-6761	1	61	maslina	maslina	PROPN
ejpam-6761	1	62	darus1	darus1	PROPN
ejpam-6761	1	63	,	,	PUNCT
ejpam-6761	1	64	sadeq	sadeq	VERB
ejpam-6761	1	65	damrah4	damrah4	PROPN
ejpam-6761	1	66	1	1	NUM
ejpam-6761	1	67	department	department	NOUN
ejpam-6761	1	68	of	of	ADP
ejpam-6761	1	69	mathematical	mathematical	ADJ
ejpam-6761	1	70	sciences	science	NOUN
ejpam-6761	1	71	,	,	PUNCT
ejpam-6761	1	72	faculty	faculty	NOUN
ejpam-6761	1	73	of	of	ADP
ejpam-6761	1	74	science	science	NOUN
ejpam-6761	1	75	and	and	CCONJ
ejpam-6761	1	76	technology	technology	NOUN
ejpam-6761	1	77	,	,	PUNCT
ejpam-6761	1	78	universiti	universiti	PROPN
ejpam-6761	1	79	kebangsaan	kebangsaan	PROPN
ejpam-6761	1	80	malaysia	malaysia	PROPN
ejpam-6761	1	81	,	,	PUNCT
ejpam-6761	1	82	bangi	bangi	VERB
ejpam-6761	1	83	43600	43600	NUM
ejpam-6761	1	84	,	,	PUNCT
ejpam-6761	1	85	malaysia	malaysia	PROPN
ejpam-6761	1	86	2	2	NUM
ejpam-6761	1	87	college	college	NOUN
ejpam-6761	1	88	of	of	ADP
ejpam-6761	1	89	natural	natural	ADJ
ejpam-6761	1	90	and	and	CCONJ
ejpam-6761	1	91	health	health	NOUN
ejpam-6761	1	92	sciences	science	NOUN
ejpam-6761	1	93	,	,	PUNCT
ejpam-6761	1	94	zayed	zayed	PROPN
ejpam-6761	1	95	university	university	PROPN
ejpam-6761	1	96	,	,	PUNCT
ejpam-6761	1	97	abu	abu	PROPN
ejpam-6761	1	98	dhabi	dhabi	PROPN
ejpam-6761	1	99	,	,	PUNCT
ejpam-6761	1	100	united	united	PROPN
ejpam-6761	1	101	arab	arab	PROPN
ejpam-6761	1	102	emirates	emirates	PROPN
ejpam-6761	1	103	3	3	NUM
ejpam-6761	1	104	department	department	NOUN
ejpam-6761	1	105	of	of	ADP
ejpam-6761	1	106	mathematics	mathematic	NOUN
ejpam-6761	1	107	,	,	PUNCT
ejpam-6761	1	108	faculty	faculty	NOUN
ejpam-6761	1	109	of	of	ADP
ejpam-6761	1	110	science	science	NOUN
ejpam-6761	1	111	,	,	PUNCT
ejpam-6761	1	112	ajloun	ajloun	ADJ
ejpam-6761	1	113	national	national	ADJ
ejpam-6761	1	114	university	university	PROPN
ejpam-6761	1	115	,	,	PUNCT
ejpam-6761	1	116	p.o	p.o	PROPN
ejpam-6761	1	117	.	.	PROPN
ejpam-6761	1	118	box	box	PROPN
ejpam-6761	1	119	43	43	NUM
ejpam-6761	1	120	,	,	PUNCT
ejpam-6761	1	121	ajloun-26810	ajloun-26810	NOUN
ejpam-6761	1	122	,	,	PUNCT
ejpam-6761	1	123	jordan	jordan	PROPN
ejpam-6761	1	124	4	4	NUM
ejpam-6761	1	125	department	department	NOUN
ejpam-6761	1	126	of	of	ADP
ejpam-6761	1	127	mathematics	mathematics	PROPN
ejpam-6761	1	128	and	and	CCONJ
ejpam-6761	1	129	physics	physics	PROPN
ejpam-6761	1	130	,	,	PUNCT
ejpam-6761	1	131	college	college	NOUN
ejpam-6761	1	132	of	of	ADP
ejpam-6761	1	133	engineering	engineering	NOUN
ejpam-6761	1	134	,	,	PUNCT
ejpam-6761	1	135	australian	australian	ADJ
ejpam-6761	1	136	university	university	NOUN
ejpam-6761	1	137	,	,	PUNCT
ejpam-6761	1	138	west	west	PROPN
ejpam-6761	1	139	mishref	mishref	PROPN
ejpam-6761	1	140	,	,	PUNCT
ejpam-6761	1	141	safat	safat	NOUN
ejpam-6761	1	142	13015	13015	NUM
ejpam-6761	1	143	,	,	PUNCT
ejpam-6761	1	144	kuwait	kuwait	PROPN
ejpam-6761	1	145	abstract	abstract	NOUN
ejpam-6761	1	146	.	.	PUNCT
ejpam-6761	2	1	fuzzy	fuzzy	ADJ
ejpam-6761	2	2	group	group	NOUN
ejpam-6761	2	3	theory	theory	NOUN
ejpam-6761	2	4	has	have	AUX
ejpam-6761	2	5	evolved	evolve	VERB
ejpam-6761	2	6	beyond	beyond	ADP
ejpam-6761	2	7	single	single	ADV
ejpam-6761	2	8	-	-	PUNCT
ejpam-6761	2	9	valued	value	VERB
ejpam-6761	2	10	memberships	membership	NOUN
ejpam-6761	2	11	to	to	PART
ejpam-6761	2	12	account	account	VERB
ejpam-6761	2	13	for	for	ADP
ejpam-6761	2	14	dual	dual	ADJ
ejpam-6761	2	15	polarity	polarity	NOUN
ejpam-6761	2	16	and	and	CCONJ
ejpam-6761	2	17	uncertainty	uncertainty	NOUN
ejpam-6761	2	18	.	.	PUNCT
ejpam-6761	3	1	building	build	VERB
ejpam-6761	3	2	on	on	ADP
ejpam-6761	3	3	dib	dib	PROPN
ejpam-6761	3	4	’s	’s	PART
ejpam-6761	3	5	fuzzy	fuzzy	ADJ
ejpam-6761	3	6	space	space	NOUN
ejpam-6761	3	7	and	and	CCONJ
ejpam-6761	3	8	bipolar	bipolar	ADV
ejpam-6761	3	9	-	-	PUNCT
ejpam-6761	3	10	valued	value	VERB
ejpam-6761	3	11	fuzzy	fuzzy	ADJ
ejpam-6761	3	12	sets	set	NOUN
ejpam-6761	3	13	,	,	PUNCT
ejpam-6761	3	14	we	we	PRON
ejpam-6761	3	15	develop	develop	VERB
ejpam-6761	3	16	a	a	DET
ejpam-6761	3	17	unified	unified	ADJ
ejpam-6761	3	18	algebraic	algebraic	ADJ
ejpam-6761	3	19	theory	theory	NOUN
ejpam-6761	3	20	of	of	ADP
ejpam-6761	3	21	bipolar	bipolar	ADV
ejpam-6761	3	22	-	-	PUNCT
ejpam-6761	3	23	valued	value	VERB
ejpam-6761	3	24	fuzzy	fuzzy	ADJ
ejpam-6761	3	25	(	(	PUNCT
ejpam-6761	3	26	bvf	bvf	NOUN
ejpam-6761	3	27	)	)	PUNCT
ejpam-6761	3	28	subgroups	subgroup	NOUN
ejpam-6761	3	29	,	,	PUNCT
ejpam-6761	3	30	including	include	VERB
ejpam-6761	3	31	bvf	bvf	VERB
ejpam-6761	3	32	normal	normal	ADJ
ejpam-6761	3	33	subgroups	subgroup	NOUN
ejpam-6761	3	34	and	and	CCONJ
ejpam-6761	3	35	bvf	bvf	NOUN
ejpam-6761	3	36	homomorphisms	homomorphism	NOUN
ejpam-6761	3	37	,	,	PUNCT
ejpam-6761	3	38	via	via	ADP
ejpam-6761	3	39	a	a	DET
ejpam-6761	3	40	bvf	bvf	NOUN
ejpam-6761	3	41	binary	binary	ADJ
ejpam-6761	3	42	operation	operation	NOUN
ejpam-6761	3	43	(	(	PUNCT
ejpam-6761	3	44	bvfbo	bvfbo	X
ejpam-6761	3	45	)	)	PUNCT
ejpam-6761	3	46	on	on	ADP
ejpam-6761	3	47	a	a	DET
ejpam-6761	3	48	bvf	bvf	NOUN
ejpam-6761	3	49	-	-	PUNCT
ejpam-6761	3	50	space	space	NOUN
ejpam-6761	3	51	.	.	PUNCT
ejpam-6761	4	1	we	we	PRON
ejpam-6761	4	2	establish	establish	VERB
ejpam-6761	4	3	necessary	necessary	ADJ
ejpam-6761	4	4	and	and	CCONJ
ejpam-6761	4	5	sufficient	sufficient	ADJ
ejpam-6761	4	6	subgroup	subgroup	NOUN
ejpam-6761	4	7	criteria	criterion	NOUN
ejpam-6761	4	8	,	,	PUNCT
ejpam-6761	4	9	characterize	characterize	VERB
ejpam-6761	4	10	normality	normality	NOUN
ejpam-6761	4	11	through	through	ADP
ejpam-6761	4	12	coset	coset	NOUN
ejpam-6761	4	13	symmetry	symmetry	NOUN
ejpam-6761	4	14	in	in	ADP
ejpam-6761	4	15	bvf	bvf	NOUN
ejpam-6761	4	16	-	-	PUNCT
ejpam-6761	4	17	space	space	NOUN
ejpam-6761	4	18	,	,	PUNCT
ejpam-6761	4	19	and	and	CCONJ
ejpam-6761	4	20	prove	prove	VERB
ejpam-6761	4	21	homomorphism	homomorphism	NOUN
ejpam-6761	4	22	properties	property	NOUN
ejpam-6761	4	23	that	that	PRON
ejpam-6761	4	24	align	align	VERB
ejpam-6761	4	25	bvf	bvf	VERB
ejpam-6761	4	26	structures	structure	NOUN
ejpam-6761	4	27	with	with	ADP
ejpam-6761	4	28	their	their	PRON
ejpam-6761	4	29	classical	classical	ADJ
ejpam-6761	4	30	counterparts	counterpart	NOUN
ejpam-6761	4	31	through	through	ADP
ejpam-6761	4	32	correspondence	correspondence	NOUN
ejpam-6761	4	33	theorems	theorem	NOUN
ejpam-6761	4	34	.	.	PUNCT
ejpam-6761	5	1	the	the	DET
ejpam-6761	5	2	framework	framework	NOUN
ejpam-6761	5	3	clarifies	clarify	VERB
ejpam-6761	5	4	when	when	SCONJ
ejpam-6761	5	5	associativity	associativity	NOUN
ejpam-6761	5	6	holds	hold	VERB
ejpam-6761	5	7	between	between	ADP
ejpam-6761	5	8	subgroup	subgroup	NOUN
ejpam-6761	5	9	elements	element	NOUN
ejpam-6761	5	10	and	and	CCONJ
ejpam-6761	5	11	ambient	ambient	ADJ
ejpam-6761	5	12	bvf	bvf	NOUN
ejpam-6761	5	13	-	-	PUNCT
ejpam-6761	5	14	group	group	NOUN
ejpam-6761	5	15	elements	element	NOUN
ejpam-6761	5	16	and	and	CCONJ
ejpam-6761	5	17	provides	provide	VERB
ejpam-6761	5	18	constructive	constructive	ADJ
ejpam-6761	5	19	examples	example	NOUN
ejpam-6761	5	20	.	.	PUNCT
ejpam-6761	6	1	this	this	DET
ejpam-6761	6	2	generalization	generalization	NOUN
ejpam-6761	6	3	resolves	resolve	VERB
ejpam-6761	6	4	limitations	limitation	NOUN
ejpam-6761	6	5	tied	tie	VERB
ejpam-6761	6	6	to	to	ADP
ejpam-6761	6	7	the	the	DET
ejpam-6761	6	8	absence	absence	NOUN
ejpam-6761	6	9	of	of	ADP
ejpam-6761	6	10	a	a	DET
ejpam-6761	6	11	bipolar	bipolar	ADJ
ejpam-6761	6	12	fuzzy	fuzzy	ADJ
ejpam-6761	6	13	universal	universal	ADJ
ejpam-6761	6	14	set	set	NOUN
ejpam-6761	6	15	and	and	CCONJ
ejpam-6761	6	16	supports	support	VERB
ejpam-6761	6	17	applications	application	NOUN
ejpam-6761	6	18	in	in	ADP
ejpam-6761	6	19	polarity	polarity	NOUN
ejpam-6761	6	20	-	-	PUNCT
ejpam-6761	6	21	sensitive	sensitive	ADJ
ejpam-6761	6	22	decision	decision	NOUN
ejpam-6761	6	23	systems	system	NOUN
ejpam-6761	6	24	and	and	CCONJ
ejpam-6761	6	25	network	network	NOUN
ejpam-6761	6	26	analysis	analysis	NOUN
ejpam-6761	6	27	.	.	PUNCT
ejpam-6761	7	1	2020	2020	NUM
ejpam-6761	7	2	mathematics	mathematic	NOUN
ejpam-6761	7	3	subject	subject	NOUN
ejpam-6761	7	4	classifications	classification	NOUN
ejpam-6761	7	5	:	:	PUNCT
ejpam-6761	7	6	30c45	30c45	NUM
ejpam-6761	7	7	key	key	ADJ
ejpam-6761	7	8	words	word	NOUN
ejpam-6761	7	9	and	and	CCONJ
ejpam-6761	7	10	phrases	phrase	NOUN
ejpam-6761	7	11	:	:	PUNCT
ejpam-6761	7	12	fuzzy	fuzzy	ADJ
ejpam-6761	7	13	group	group	NOUN
ejpam-6761	7	14	,	,	PUNCT
ejpam-6761	7	15	fuzzy	fuzzy	ADJ
ejpam-6761	7	16	space	space	NOUN
ejpam-6761	7	17	,	,	PUNCT
ejpam-6761	7	18	bipolar	bipolar	ADV
ejpam-6761	7	19	-	-	PUNCT
ejpam-6761	7	20	valued	value	VERB
ejpam-6761	7	21	fuzzy	fuzzy	ADJ
ejpam-6761	7	22	space	space	NOUN
ejpam-6761	7	23	,	,	PUNCT
ejpam-6761	7	24	bipolar	bipolar	ADV
ejpam-6761	7	25	-	-	PUNCT
ejpam-6761	7	26	valued	value	VERB
ejpam-6761	7	27	fuzzy	fuzzy	ADJ
ejpam-6761	7	28	subgroup	subgroup	NOUN
ejpam-6761	7	29	,	,	PUNCT
ejpam-6761	7	30	bipolar	bipolar	ADJ
ejpam-6761	7	31	-	-	PUNCT
ejpam-6761	7	32	valued	value	VERB
ejpam-6761	7	33	fuzzy	fuzzy	ADJ
ejpam-6761	7	34	homomorphisms	homomorphism	NOUN
ejpam-6761	7	35	,	,	PUNCT
ejpam-6761	7	36	bipolar	bipolar	ADJ
ejpam-6761	7	37	-	-	PUNCT
ejpam-6761	7	38	valued	value	VERB
ejpam-6761	7	39	fuzzy	fuzzy	ADJ
ejpam-6761	7	40	normal	normal	ADJ
ejpam-6761	7	41	subgroup	subgroup	NOUN
ejpam-6761	7	42	,	,	PUNCT
ejpam-6761	7	43	dib	dib	NOUN
ejpam-6761	7	44	fuzzy	fuzzy	ADJ
ejpam-6761	7	45	group	group	NOUN
ejpam-6761	7	46	theory	theory	NOUN
ejpam-6761	7	47	1	1	NUM
ejpam-6761	7	48	.	.	PUNCT
ejpam-6761	7	49	introduction	introduction	NOUN
ejpam-6761	7	50	the	the	DET
ejpam-6761	7	51	theory	theory	NOUN
ejpam-6761	7	52	of	of	ADP
ejpam-6761	7	53	fuzzy	fuzzy	ADJ
ejpam-6761	7	54	groups	group	NOUN
ejpam-6761	7	55	,	,	PUNCT
ejpam-6761	7	56	first	first	ADV
ejpam-6761	7	57	formulated	formulate	VERB
ejpam-6761	7	58	by	by	ADP
ejpam-6761	7	59	rosenfeld	rosenfeld	PROPN
ejpam-6761	8	1	[	[	X
ejpam-6761	8	2	1	1	NUM
ejpam-6761	8	3	]	]	PUNCT
ejpam-6761	8	4	,	,	PUNCT
ejpam-6761	8	5	marked	mark	VERB
ejpam-6761	8	6	a	a	DET
ejpam-6761	8	7	foundational	foundational	ADJ
ejpam-6761	8	8	shift	shift	NOUN
ejpam-6761	8	9	in	in	ADP
ejpam-6761	8	10	algebraic	algebraic	PROPN
ejpam-6761	8	11	systems	system	NOUN
ejpam-6761	8	12	by	by	ADP
ejpam-6761	8	13	incorporating	incorporate	VERB
ejpam-6761	8	14	uncertainty	uncertainty	NOUN
ejpam-6761	8	15	into	into	ADP
ejpam-6761	8	16	group	group	NOUN
ejpam-6761	8	17	membership	membership	NOUN
ejpam-6761	8	18	.	.	PUNCT
ejpam-6761	9	1	his	his	PRON
ejpam-6761	9	2	seminal	seminal	ADJ
ejpam-6761	9	3	work	work	NOUN
ejpam-6761	9	4	defined	define	VERB
ejpam-6761	9	5	fuzzy	fuzzy	ADJ
ejpam-6761	9	6	subgroups	subgroup	NOUN
ejpam-6761	9	7	using	use	VERB
ejpam-6761	9	8	a	a	DET
ejpam-6761	9	9	single	single	ADJ
ejpam-6761	9	10	-	-	PUNCT
ejpam-6761	9	11	valued	value	VERB
ejpam-6761	9	12	membership	membership	NOUN
ejpam-6761	9	13	function	function	NOUN
ejpam-6761	9	14	ranging	range	VERB
ejpam-6761	9	15	∗corresponding	∗corresponde	VERB
ejpam-6761	9	16	author	author	NOUN
ejpam-6761	9	17	.	.	PUNCT
ejpam-6761	10	1	doi	doi	NOUN
ejpam-6761	10	2	:	:	PUNCT
ejpam-6761	10	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6761	https://doi.org/10.29020/nybg.ejpam.v18i4.6761	NUM
ejpam-6761	10	4	email	email	NOUN
ejpam-6761	10	5	addresses	address	NOUN
ejpam-6761	10	6	:	:	PUNCT
ejpam-6761	10	7	p115916@siswa.ukm.edu.my	p115916@siswa.ukm.edu.my	X
ejpam-6761	10	8	(	(	PUNCT
ejpam-6761	10	9	f.	f.	PROPN
ejpam-6761	10	10	al	al	PROPN
ejpam-6761	10	11	-	-	PROPN
ejpam-6761	10	12	zu’bi	zu’bi	PROPN
ejpam-6761	10	13	)	)	PUNCT
ejpam-6761	10	14	,	,	PUNCT
ejpam-6761	10	15	ghafur@ukm.edu.my	ghafur@ukm.edu.my	X
ejpam-6761	10	16	(	(	PUNCT
ejpam-6761	10	17	a.	a.	NOUN
ejpam-6761	10	18	ahmad	ahmad	PROPN
ejpam-6761	10	19	)	)	PUNCT
ejpam-6761	10	20	,	,	PUNCT
ejpam-6761	10	21	alkouriabdulazeez@anu.edu.jo	alkouriabdulazeez@anu.edu.jo	NOUN
ejpam-6761	10	22	(	(	PUNCT
ejpam-6761	10	23	a.	a.	NOUN
ejpam-6761	10	24	alkouri	alkouri	PROPN
ejpam-6761	10	25	)	)	PUNCT
ejpam-6761	10	26	,	,	PUNCT
ejpam-6761	10	27	maslina@ukm.edu.my	maslina@ukm.edu.my	X
ejpam-6761	10	28	(	(	PUNCT
ejpam-6761	10	29	m.	m.	NOUN
ejpam-6761	10	30	darus	darus	PROPN
ejpam-6761	10	31	)	)	PUNCT
ejpam-6761	10	32	,	,	PUNCT
ejpam-6761	10	33	s.damrah@au.edu.kw	s.damrah@au.edu.kw	PROPN
ejpam-6761	10	34	(	(	PUNCT
ejpam-6761	10	35	s.	s.	PROPN
ejpam-6761	10	36	damrah	damrah	PROPN
ejpam-6761	10	37	)	)	PUNCT
ejpam-6761	10	38	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6761	11	1	1	1	NUM
ejpam-6761	11	2	copyright	copyright	NOUN
ejpam-6761	11	3	:	:	PUNCT
ejpam-6761	11	4	©	©	PROPN
ejpam-6761	11	5	2025	2025	NUM
ejpam-6761	11	6	the	the	DET
ejpam-6761	11	7	author(s	author(s	NOUN
ejpam-6761	11	8	)	)	PUNCT
ejpam-6761	11	9	.	.	PUNCT
ejpam-6761	12	1	(	(	PUNCT
ejpam-6761	12	2	cc	cc	NOUN
ejpam-6761	12	3	by	by	ADP
ejpam-6761	12	4	-	-	PUNCT
ejpam-6761	12	5	nc	nc	PROPN
ejpam-6761	12	6	4.0	4.0	NUM
ejpam-6761	12	7	)	)	PUNCT
ejpam-6761	12	8	f.	f.	PROPN
ejpam-6761	12	9	al	al	PROPN
ejpam-6761	12	10	-	-	PROPN
ejpam-6761	12	11	zu’bi	zu’bi	PROPN
ejpam-6761	12	12	et	et	NOUN
ejpam-6761	12	13	al	al	PROPN
ejpam-6761	12	14	.	.	PUNCT
ejpam-6761	12	15	/	/	SYM
ejpam-6761	12	16	eur	eur	PROPN
ejpam-6761	12	17	.	.	PUNCT
ejpam-6761	13	1	j.	j.	PROPN
ejpam-6761	13	2	pure	pure	PROPN
ejpam-6761	13	3	appl	appl	PROPN
ejpam-6761	13	4	.	.	PROPN
ejpam-6761	13	5	math	math	PROPN
ejpam-6761	13	6	,	,	PUNCT
ejpam-6761	13	7	18	18	NUM
ejpam-6761	13	8	(	(	PUNCT
ejpam-6761	13	9	4	4	NUM
ejpam-6761	13	10	)	)	PUNCT
ejpam-6761	13	11	(	(	PUNCT
ejpam-6761	13	12	2025	2025	NUM
ejpam-6761	13	13	)	)	PUNCT
ejpam-6761	13	14	,	,	PUNCT
ejpam-6761	13	15	6761	6761	NUM
ejpam-6761	13	16	2	2	NUM
ejpam-6761	13	17	of	of	ADP
ejpam-6761	13	18	28	28	NUM
ejpam-6761	13	19	within	within	ADP
ejpam-6761	13	20	the	the	DET
ejpam-6761	13	21	interval	interval	NOUN
ejpam-6761	13	22	[	[	X
ejpam-6761	13	23	0	0	NUM
ejpam-6761	13	24	,	,	PUNCT
ejpam-6761	13	25	1	1	NUM
ejpam-6761	13	26	]	]	PUNCT
ejpam-6761	13	27	,	,	PUNCT
ejpam-6761	13	28	laying	lay	VERB
ejpam-6761	13	29	the	the	DET
ejpam-6761	13	30	groundwork	groundwork	NOUN
ejpam-6761	13	31	for	for	ADP
ejpam-6761	13	32	fuzzy	fuzzy	ADJ
ejpam-6761	13	33	algebraic	algebraic	ADJ
ejpam-6761	13	34	structures	structure	NOUN
ejpam-6761	13	35	.	.	PUNCT
ejpam-6761	14	1	this	this	DET
ejpam-6761	14	2	concept	concept	NOUN
ejpam-6761	14	3	was	be	AUX
ejpam-6761	14	4	later	later	ADV
ejpam-6761	14	5	refined	refine	VERB
ejpam-6761	14	6	by	by	ADP
ejpam-6761	14	7	anthony	anthony	PROPN
ejpam-6761	14	8	and	and	CCONJ
ejpam-6761	14	9	sherwood	sherwood	PROPN
ejpam-6761	15	1	[	[	X
ejpam-6761	15	2	2	2	NUM
ejpam-6761	15	3	]	]	PUNCT
ejpam-6761	15	4	,	,	PUNCT
ejpam-6761	15	5	who	who	PRON
ejpam-6761	15	6	introduced	introduce	VERB
ejpam-6761	15	7	triangular	triangular	NOUN
ejpam-6761	15	8	norms	norm	NOUN
ejpam-6761	15	9	to	to	PART
ejpam-6761	15	10	achieve	achieve	VERB
ejpam-6761	15	11	more	more	ADV
ejpam-6761	15	12	flexible	flexible	ADJ
ejpam-6761	15	13	and	and	CCONJ
ejpam-6761	15	14	expressive	expressive	ADJ
ejpam-6761	15	15	formulations	formulation	NOUN
ejpam-6761	15	16	.	.	PUNCT
ejpam-6761	16	1	a	a	DET
ejpam-6761	16	2	major	major	ADJ
ejpam-6761	16	3	breakthrough	breakthrough	NOUN
ejpam-6761	16	4	came	come	VERB
ejpam-6761	16	5	from	from	ADP
ejpam-6761	16	6	dib	dib	PROPN
ejpam-6761	16	7	[	[	X
ejpam-6761	16	8	3	3	NUM
ejpam-6761	16	9	,	,	PUNCT
ejpam-6761	16	10	4	4	NUM
ejpam-6761	16	11	]	]	PUNCT
ejpam-6761	16	12	,	,	PUNCT
ejpam-6761	16	13	who	who	PRON
ejpam-6761	16	14	proposed	propose	VERB
ejpam-6761	16	15	the	the	DET
ejpam-6761	16	16	concept	concept	NOUN
ejpam-6761	16	17	of	of	ADP
ejpam-6761	16	18	a	a	DET
ejpam-6761	16	19	fuzzy	fuzzy	ADJ
ejpam-6761	16	20	space	space	NOUN
ejpam-6761	16	21	(	(	PUNCT
ejpam-6761	16	22	f	f	NOUN
ejpam-6761	16	23	-	-	PUNCT
ejpam-6761	16	24	space	space	NOUN
ejpam-6761	16	25	)	)	PUNCT
ejpam-6761	16	26	to	to	PART
ejpam-6761	16	27	replace	replace	VERB
ejpam-6761	16	28	the	the	DET
ejpam-6761	16	29	classical	classical	ADJ
ejpam-6761	16	30	universal	universal	ADJ
ejpam-6761	16	31	set	set	NOUN
ejpam-6761	16	32	.	.	PUNCT
ejpam-6761	17	1	dib	dib	PROPN
ejpam-6761	17	2	’s	’s	PART
ejpam-6761	17	3	framework	framework	NOUN
ejpam-6761	17	4	redefined	redefine	VERB
ejpam-6761	17	5	fuzzy	fuzzy	ADJ
ejpam-6761	17	6	groups	group	NOUN
ejpam-6761	17	7	through	through	ADP
ejpam-6761	17	8	fuzzy	fuzzy	ADJ
ejpam-6761	17	9	binary	binary	ADJ
ejpam-6761	17	10	operations	operation	NOUN
ejpam-6761	17	11	acting	act	VERB
ejpam-6761	17	12	on	on	ADP
ejpam-6761	17	13	elements	element	NOUN
ejpam-6761	17	14	of	of	ADP
ejpam-6761	17	15	this	this	DET
ejpam-6761	17	16	f	f	NOUN
ejpam-6761	17	17	-	-	PUNCT
ejpam-6761	17	18	space	space	NOUN
ejpam-6761	17	19	,	,	PUNCT
ejpam-6761	17	20	effectively	effectively	ADV
ejpam-6761	17	21	overcoming	overcome	VERB
ejpam-6761	17	22	limitations	limitation	NOUN
ejpam-6761	17	23	of	of	ADP
ejpam-6761	17	24	earlier	early	ADJ
ejpam-6761	17	25	models	model	NOUN
ejpam-6761	17	26	.	.	PUNCT
ejpam-6761	18	1	his	his	PRON
ejpam-6761	18	2	fuzzy	fuzzy	ADJ
ejpam-6761	18	3	topological	topological	ADJ
ejpam-6761	18	4	space	space	NOUN
ejpam-6761	18	5	enabled	enable	VERB
ejpam-6761	18	6	a	a	DET
ejpam-6761	18	7	more	more	ADV
ejpam-6761	18	8	coherent	coherent	ADJ
ejpam-6761	18	9	foundation	foundation	NOUN
ejpam-6761	18	10	for	for	ADP
ejpam-6761	18	11	defining	define	VERB
ejpam-6761	18	12	fuzzy	fuzzy	ADJ
ejpam-6761	18	13	group	group	NOUN
ejpam-6761	18	14	structures	structure	NOUN
ejpam-6761	18	15	and	and	CCONJ
ejpam-6761	18	16	operations	operation	NOUN
ejpam-6761	18	17	.	.	PUNCT
ejpam-6761	19	1	in	in	ADP
ejpam-6761	19	2	parallel	parallel	NOUN
ejpam-6761	19	3	,	,	PUNCT
ejpam-6761	19	4	salleh	salleh	NOUN
ejpam-6761	20	1	[	[	X
ejpam-6761	20	2	5	5	NUM
ejpam-6761	20	3	]	]	PUNCT
ejpam-6761	20	4	initiated	initiate	VERB
ejpam-6761	20	5	work	work	NOUN
ejpam-6761	20	6	on	on	ADP
ejpam-6761	20	7	fuzzy	fuzzy	ADJ
ejpam-6761	20	8	homomorphisms	homomorphism	NOUN
ejpam-6761	20	9	,	,	PUNCT
ejpam-6761	20	10	followed	follow	VERB
ejpam-6761	20	11	by	by	ADP
ejpam-6761	20	12	the	the	DET
ejpam-6761	20	13	development	development	NOUN
ejpam-6761	20	14	of	of	ADP
ejpam-6761	20	15	intuitionistic	intuitionistic	ADJ
ejpam-6761	20	16	fuzzy	fuzzy	ADJ
ejpam-6761	20	17	groups	group	NOUN
ejpam-6761	20	18	by	by	ADP
ejpam-6761	20	19	marashdeh	marashdeh	NOUN
ejpam-6761	20	20	and	and	CCONJ
ejpam-6761	20	21	salleh	salleh	NOUN
ejpam-6761	21	1	[	[	X
ejpam-6761	21	2	6	6	NUM
ejpam-6761	21	3	]	]	PUNCT
ejpam-6761	21	4	,	,	PUNCT
ejpam-6761	21	5	and	and	CCONJ
ejpam-6761	21	6	their	their	PRON
ejpam-6761	21	7	extension	extension	NOUN
ejpam-6761	21	8	to	to	ADP
ejpam-6761	21	9	intuitionistic	intuitionistic	ADJ
ejpam-6761	21	10	fuzzy	fuzzy	ADJ
ejpam-6761	21	11	normal	normal	ADJ
ejpam-6761	21	12	subgroups	subgroup	NOUN
ejpam-6761	22	1	[	[	X
ejpam-6761	22	2	7	7	NUM
ejpam-6761	22	3	]	]	PUNCT
ejpam-6761	22	4	.	.	PUNCT
ejpam-6761	23	1	these	these	DET
ejpam-6761	23	2	models	model	NOUN
ejpam-6761	23	3	added	add	VERB
ejpam-6761	23	4	nuance	nuance	NOUN
ejpam-6761	23	5	by	by	ADP
ejpam-6761	23	6	capturing	capture	VERB
ejpam-6761	23	7	degrees	degree	NOUN
ejpam-6761	23	8	of	of	ADP
ejpam-6761	23	9	hesitation	hesitation	NOUN
ejpam-6761	23	10	in	in	ADP
ejpam-6761	23	11	membership	membership	NOUN
ejpam-6761	23	12	but	but	CCONJ
ejpam-6761	23	13	did	do	AUX
ejpam-6761	23	14	not	not	PART
ejpam-6761	23	15	fully	fully	ADV
ejpam-6761	23	16	accommodate	accommodate	VERB
ejpam-6761	23	17	negative	negative	ADJ
ejpam-6761	23	18	evaluations	evaluation	NOUN
ejpam-6761	23	19	inherent	inherent	ADJ
ejpam-6761	23	20	in	in	ADP
ejpam-6761	23	21	many	many	ADJ
ejpam-6761	23	22	real	real	ADJ
ejpam-6761	23	23	-	-	PUNCT
ejpam-6761	23	24	world	world	NOUN
ejpam-6761	23	25	systems	system	NOUN
ejpam-6761	23	26	.	.	PUNCT
ejpam-6761	24	1	the	the	DET
ejpam-6761	24	2	formal	formal	ADJ
ejpam-6761	24	3	introduction	introduction	NOUN
ejpam-6761	24	4	of	of	ADP
ejpam-6761	24	5	bipolar	bipolar	ADV
ejpam-6761	24	6	-	-	PUNCT
ejpam-6761	24	7	valued	value	VERB
ejpam-6761	24	8	fuzzy	fuzzy	ADJ
ejpam-6761	24	9	sets	set	NOUN
ejpam-6761	24	10	(	(	PUNCT
ejpam-6761	24	11	bvfs	bvfs	ADJ
ejpam-6761	24	12	)	)	PUNCT
ejpam-6761	24	13	by	by	ADP
ejpam-6761	24	14	lee	lee	PROPN
ejpam-6761	25	1	[	[	X
ejpam-6761	25	2	8	8	NUM
ejpam-6761	25	3	]	]	PUNCT
ejpam-6761	25	4	,	,	PUNCT
ejpam-6761	25	5	and	and	CCONJ
ejpam-6761	25	6	later	later	ADV
ejpam-6761	25	7	expanded	expand	VERB
ejpam-6761	25	8	by	by	ADP
ejpam-6761	25	9	lee	lee	PROPN
ejpam-6761	25	10	,	,	PUNCT
ejpam-6761	25	11	lee	lee	PROPN
ejpam-6761	25	12	,	,	PUNCT
ejpam-6761	25	13	and	and	CCONJ
ejpam-6761	25	14	cios	cio	NOUN
ejpam-6761	26	1	[	[	X
ejpam-6761	26	2	9	9	NUM
ejpam-6761	26	3	]	]	PUNCT
ejpam-6761	26	4	,	,	PUNCT
ejpam-6761	26	5	enabled	enable	VERB
ejpam-6761	26	6	the	the	DET
ejpam-6761	26	7	representation	representation	NOUN
ejpam-6761	26	8	of	of	ADP
ejpam-6761	26	9	both	both	CCONJ
ejpam-6761	26	10	negative	negative	ADJ
ejpam-6761	26	11	and	and	CCONJ
ejpam-6761	26	12	positive	positive	ADJ
ejpam-6761	26	13	membership	membership	NOUN
ejpam-6761	26	14	grades	grade	NOUN
ejpam-6761	26	15	via	via	ADP
ejpam-6761	26	16	a	a	DET
ejpam-6761	26	17	cartesian	cartesian	ADJ
ejpam-6761	26	18	domain	domain	NOUN
ejpam-6761	26	19	[	[	X
ejpam-6761	26	20	−1	−1	NOUN
ejpam-6761	26	21	,	,	PUNCT
ejpam-6761	26	22	0]×	0]×	PROPN
ejpam-6761	27	1	[	[	X
ejpam-6761	27	2	0	0	NUM
ejpam-6761	27	3	,	,	PUNCT
ejpam-6761	27	4	1	1	NUM
ejpam-6761	27	5	]	]	PUNCT
ejpam-6761	27	6	.	.	PUNCT
ejpam-6761	28	1	this	this	DET
ejpam-6761	28	2	duality	duality	NOUN
ejpam-6761	28	3	provided	provide	VERB
ejpam-6761	28	4	the	the	DET
ejpam-6761	28	5	necessary	necessary	ADJ
ejpam-6761	28	6	framework	framework	NOUN
ejpam-6761	28	7	to	to	PART
ejpam-6761	28	8	model	model	VERB
ejpam-6761	28	9	conflicting	conflicting	ADJ
ejpam-6761	28	10	or	or	CCONJ
ejpam-6761	28	11	opposing	oppose	VERB
ejpam-6761	28	12	characteristics	characteristic	NOUN
ejpam-6761	28	13	in	in	ADP
ejpam-6761	28	14	algebraic	algebraic	ADJ
ejpam-6761	28	15	structures	structure	NOUN
ejpam-6761	28	16	.	.	PUNCT
ejpam-6761	29	1	expanding	expand	VERB
ejpam-6761	29	2	these	these	DET
ejpam-6761	29	3	ideas	idea	NOUN
ejpam-6761	29	4	,	,	PUNCT
ejpam-6761	29	5	recent	recent	ADJ
ejpam-6761	29	6	work	work	NOUN
ejpam-6761	29	7	by	by	ADP
ejpam-6761	29	8	al	al	PROPN
ejpam-6761	29	9	-	-	PROPN
ejpam-6761	29	10	zu’bi	zu’bi	PROPN
ejpam-6761	29	11	et	et	NOUN
ejpam-6761	29	12	al	al	PROPN
ejpam-6761	29	13	.	.	PUNCT
ejpam-6761	30	1	[	[	X
ejpam-6761	30	2	10	10	NUM
ejpam-6761	30	3	,	,	PUNCT
ejpam-6761	30	4	11	11	NUM
ejpam-6761	30	5	]	]	PUNCT
ejpam-6761	30	6	introduced	introduce	VERB
ejpam-6761	30	7	bipolar	bipolar	ADV
ejpam-6761	30	8	-	-	PUNCT
ejpam-6761	30	9	valued	value	VERB
ejpam-6761	30	10	fuzzy	fuzzy	ADJ
ejpam-6761	30	11	groups	group	NOUN
ejpam-6761	30	12	(	(	PUNCT
ejpam-6761	30	13	bvf	bvf	NOUN
ejpam-6761	30	14	-	-	PUNCT
ejpam-6761	30	15	groups	group	NOUN
ejpam-6761	30	16	)	)	PUNCT
ejpam-6761	30	17	and	and	CCONJ
ejpam-6761	30	18	formalized	formalize	VERB
ejpam-6761	30	19	bipolar	bipolar	ADV
ejpam-6761	30	20	-	-	PUNCT
ejpam-6761	30	21	valued	value	VERB
ejpam-6761	30	22	fuzzy	fuzzy	ADJ
ejpam-6761	30	23	cartesian	cartesian	ADJ
ejpam-6761	30	24	products	product	NOUN
ejpam-6761	30	25	,	,	PUNCT
ejpam-6761	30	26	relations	relation	NOUN
ejpam-6761	30	27	,	,	PUNCT
ejpam-6761	30	28	and	and	CCONJ
ejpam-6761	30	29	functions	function	NOUN
ejpam-6761	30	30	.	.	PUNCT
ejpam-6761	31	1	these	these	DET
ejpam-6761	31	2	advancements	advancement	NOUN
ejpam-6761	31	3	,	,	PUNCT
ejpam-6761	31	4	built	build	VERB
ejpam-6761	31	5	on	on	ADP
ejpam-6761	31	6	dib	dib	PROPN
ejpam-6761	31	7	’s	’s	PART
ejpam-6761	31	8	algebraic	algebraic	ADJ
ejpam-6761	31	9	philosophy	philosophy	NOUN
ejpam-6761	31	10	,	,	PUNCT
ejpam-6761	31	11	laid	lay	VERB
ejpam-6761	31	12	the	the	DET
ejpam-6761	31	13	groundwork	groundwork	NOUN
ejpam-6761	31	14	for	for	ADP
ejpam-6761	31	15	a	a	DET
ejpam-6761	31	16	more	more	ADV
ejpam-6761	31	17	robust	robust	ADJ
ejpam-6761	31	18	bipolar	bipolar	ADV
ejpam-6761	31	19	-	-	PUNCT
ejpam-6761	31	20	valued	value	VERB
ejpam-6761	31	21	fuzzy	fuzzy	ADJ
ejpam-6761	31	22	universe	universe	NOUN
ejpam-6761	31	23	that	that	PRON
ejpam-6761	31	24	supports	support	VERB
ejpam-6761	31	25	richer	rich	ADJ
ejpam-6761	31	26	algebraic	algebraic	ADJ
ejpam-6761	31	27	properties	property	NOUN
ejpam-6761	31	28	.	.	PUNCT
ejpam-6761	32	1	contemporary	contemporary	ADJ
ejpam-6761	32	2	research	research	NOUN
ejpam-6761	32	3	highlights	highlight	VERB
ejpam-6761	32	4	a	a	DET
ejpam-6761	32	5	growing	grow	VERB
ejpam-6761	32	6	demand	demand	NOUN
ejpam-6761	32	7	for	for	ADP
ejpam-6761	32	8	such	such	ADJ
ejpam-6761	32	9	dual	dual	ADJ
ejpam-6761	32	10	-	-	PUNCT
ejpam-6761	32	11	polarity	polarity	NOUN
ejpam-6761	32	12	fuzzy	fuzzy	ADJ
ejpam-6761	32	13	systems	system	NOUN
ejpam-6761	32	14	.	.	PUNCT
ejpam-6761	33	1	for	for	ADP
ejpam-6761	33	2	instance	instance	NOUN
ejpam-6761	33	3	,	,	PUNCT
ejpam-6761	33	4	akram	akram	PROPN
ejpam-6761	33	5	et	et	PROPN
ejpam-6761	33	6	al	al	PROPN
ejpam-6761	33	7	.	.	PUNCT
ejpam-6761	34	1	[	[	X
ejpam-6761	34	2	12	12	NUM
ejpam-6761	34	3	]	]	PUNCT
ejpam-6761	34	4	proposed	propose	VERB
ejpam-6761	34	5	multi	multi	ADJ
ejpam-6761	34	6	-	-	ADJ
ejpam-6761	34	7	criteria	criterion	NOUN
ejpam-6761	34	8	decision	decision	NOUN
ejpam-6761	34	9	-	-	PUNCT
ejpam-6761	34	10	making	make	VERB
ejpam-6761	34	11	models	model	NOUN
ejpam-6761	34	12	based	base	VERB
ejpam-6761	34	13	on	on	ADP
ejpam-6761	34	14	bvf	bvf	NOUN
ejpam-6761	34	15	sets	set	NOUN
ejpam-6761	34	16	.	.	PUNCT
ejpam-6761	35	1	al	al	PROPN
ejpam-6761	35	2	-	-	PUNCT
ejpam-6761	35	3	quran	quran	PROPN
ejpam-6761	35	4	et	et	PROPN
ejpam-6761	35	5	al	al	PROPN
ejpam-6761	35	6	.	.	PUNCT
ejpam-6761	36	1	[	[	X
ejpam-6761	36	2	13	13	NUM
ejpam-6761	36	3	]	]	PUNCT
ejpam-6761	36	4	applied	apply	VERB
ejpam-6761	36	5	cubic	cubic	ADJ
ejpam-6761	36	6	bipolar	bipolar	ADJ
ejpam-6761	36	7	fuzzy	fuzzy	ADJ
ejpam-6761	36	8	sets	set	NOUN
ejpam-6761	36	9	in	in	ADP
ejpam-6761	36	10	vikor	vikor	ADJ
ejpam-6761	36	11	and	and	CCONJ
ejpam-6761	36	12	electre	electre	NOUN
ejpam-6761	36	13	-	-	PUNCT
ejpam-6761	36	14	ii	ii	NOUN
ejpam-6761	36	15	algorithms	algorithm	NOUN
ejpam-6761	36	16	to	to	PART
ejpam-6761	36	17	optimize	optimize	VERB
ejpam-6761	36	18	logistics	logistic	NOUN
ejpam-6761	36	19	in	in	ADP
ejpam-6761	36	20	industry	industry	NOUN
ejpam-6761	36	21	4.0	4.0	NUM
ejpam-6761	36	22	.	.	PUNCT
ejpam-6761	37	1	gutiérrez	gutiérrez	NOUN
ejpam-6761	37	2	et	et	NOUN
ejpam-6761	37	3	al	al	PROPN
ejpam-6761	37	4	.	.	PUNCT
ejpam-6761	38	1	[	[	X
ejpam-6761	38	2	14	14	NUM
ejpam-6761	38	3	]	]	PUNCT
ejpam-6761	38	4	explored	explore	VERB
ejpam-6761	38	5	bvf	bvf	NOUN
ejpam-6761	38	6	measures	measure	NOUN
ejpam-6761	38	7	for	for	ADP
ejpam-6761	38	8	community	community	NOUN
ejpam-6761	38	9	detection	detection	NOUN
ejpam-6761	38	10	in	in	ADP
ejpam-6761	38	11	enriched	enrich	VERB
ejpam-6761	38	12	social	social	ADJ
ejpam-6761	38	13	networks	network	NOUN
ejpam-6761	38	14	.	.	PUNCT
ejpam-6761	39	1	alqahtani	alqahtani	PROPN
ejpam-6761	39	2	et	et	PROPN
ejpam-6761	39	3	al	al	PROPN
ejpam-6761	39	4	.	.	PUNCT
ejpam-6761	40	1	[	[	X
ejpam-6761	40	2	15	15	NUM
ejpam-6761	40	3	]	]	X
ejpam-6761	40	4	advanced	advanced	ADJ
ejpam-6761	40	5	hesitant	hesitant	ADJ
ejpam-6761	40	6	bvf	bvf	NOUN
ejpam-6761	40	7	intuitionistic	intuitionistic	ADJ
ejpam-6761	40	8	fuzzy	fuzzy	ADJ
ejpam-6761	40	9	graphs	graph	NOUN
ejpam-6761	40	10	for	for	ADP
ejpam-6761	40	11	social	social	ADJ
ejpam-6761	40	12	media	medium	NOUN
ejpam-6761	40	13	analysis	analysis	NOUN
ejpam-6761	40	14	,	,	PUNCT
ejpam-6761	40	15	while	while	SCONJ
ejpam-6761	40	16	mahmood	mahmood	PROPN
ejpam-6761	40	17	et	et	PROPN
ejpam-6761	40	18	al	al	PROPN
ejpam-6761	40	19	.	.	PUNCT
ejpam-6761	41	1	[	[	X
ejpam-6761	41	2	16	16	NUM
ejpam-6761	41	3	]	]	PUNCT
ejpam-6761	41	4	demonstrated	demonstrate	VERB
ejpam-6761	41	5	applications	application	NOUN
ejpam-6761	41	6	of	of	ADP
ejpam-6761	41	7	bvf	bvf	NOUN
ejpam-6761	41	8	soft	soft	ADJ
ejpam-6761	41	9	sets	set	NOUN
ejpam-6761	41	10	in	in	ADP
ejpam-6761	41	11	pattern	pattern	NOUN
ejpam-6761	41	12	recognition	recognition	NOUN
ejpam-6761	41	13	and	and	CCONJ
ejpam-6761	41	14	healthcare	healthcare	PROPN
ejpam-6761	41	15	.	.	PUNCT
ejpam-6761	42	1	further	further	ADJ
ejpam-6761	42	2	generalizations	generalization	NOUN
ejpam-6761	42	3	include	include	VERB
ejpam-6761	42	4	bipolar	bipolar	ADJ
ejpam-6761	42	5	fuzzy	fuzzy	ADJ
ejpam-6761	42	6	subgroups	subgroup	NOUN
ejpam-6761	42	7	[	[	X
ejpam-6761	42	8	17	17	NUM
ejpam-6761	42	9	]	]	PUNCT
ejpam-6761	42	10	,	,	PUNCT
ejpam-6761	42	11	bck	bck	PROPN
ejpam-6761	42	12	/	/	SYM
ejpam-6761	42	13	bci	bci	NOUN
ejpam-6761	42	14	-	-	PUNCT
ejpam-6761	42	15	algebras	algebras	X
ejpam-6761	42	16	[	[	X
ejpam-6761	42	17	18	18	NUM
ejpam-6761	42	18	,	,	PUNCT
ejpam-6761	42	19	19	19	NUM
ejpam-6761	42	20	]	]	PUNCT
ejpam-6761	42	21	,	,	PUNCT
ejpam-6761	42	22	q	q	ADJ
ejpam-6761	42	23	-	-	PUNCT
ejpam-6761	42	24	fuzzy	fuzzy	ADJ
ejpam-6761	42	25	and	and	CCONJ
ejpam-6761	42	26	interval	interval	NOUN
ejpam-6761	42	27	-	-	PUNCT
ejpam-6761	42	28	valued	value	VERB
ejpam-6761	42	29	bipolar	bipolar	ADJ
ejpam-6761	42	30	subgroups	subgroup	NOUN
ejpam-6761	42	31	[	[	X
ejpam-6761	42	32	20	20	NUM
ejpam-6761	42	33	,	,	PUNCT
ejpam-6761	42	34	21	21	NUM
ejpam-6761	42	35	]	]	PUNCT
ejpam-6761	42	36	,	,	PUNCT
ejpam-6761	42	37	fuzzy	fuzzy	ADJ
ejpam-6761	42	38	subsemirings	subsemiring	NOUN
ejpam-6761	42	39	[	[	X
ejpam-6761	42	40	22	22	NUM
ejpam-6761	42	41	]	]	PUNCT
ejpam-6761	42	42	,	,	PUNCT
ejpam-6761	42	43	bchalgebras	bchalgebras	PROPN
ejpam-6761	42	44	[	[	X
ejpam-6761	42	45	23	23	NUM
ejpam-6761	42	46	]	]	PUNCT
ejpam-6761	42	47	,	,	PUNCT
ejpam-6761	42	48	and	and	CCONJ
ejpam-6761	42	49	γ	γ	NOUN
ejpam-6761	42	50	-	-	PUNCT
ejpam-6761	42	51	semigroups	semigroup	NOUN
ejpam-6761	42	52	under	under	ADP
ejpam-6761	42	53	bvf	bvf	NOUN
ejpam-6761	42	54	frameworks	framework	NOUN
ejpam-6761	42	55	[	[	X
ejpam-6761	42	56	24	24	NUM
ejpam-6761	42	57	]	]	PUNCT
ejpam-6761	42	58	.	.	PUNCT
ejpam-6761	43	1	new	new	ADJ
ejpam-6761	43	2	structural	structural	ADJ
ejpam-6761	43	3	models	model	NOUN
ejpam-6761	43	4	such	such	ADJ
ejpam-6761	43	5	asm	asm	ADJ
ejpam-6761	43	6	-	-	ADJ
ejpam-6761	43	7	polar	polar	ADJ
ejpam-6761	43	8	ideals	ideal	NOUN
ejpam-6761	43	9	[	[	X
ejpam-6761	43	10	25	25	NUM
ejpam-6761	43	11	]	]	PUNCT
ejpam-6761	43	12	,	,	PUNCT
ejpam-6761	43	13	k	k	X
ejpam-6761	43	14	-	-	PUNCT
ejpam-6761	43	15	folded	fold	VERB
ejpam-6761	43	16	n	n	CCONJ
ejpam-6761	43	17	-	-	PUNCT
ejpam-6761	43	18	structures	structure	NOUN
ejpam-6761	43	19	[	[	X
ejpam-6761	43	20	26	26	NUM
ejpam-6761	43	21	]	]	PUNCT
ejpam-6761	43	22	,	,	PUNCT
ejpam-6761	43	23	and	and	CCONJ
ejpam-6761	43	24	bvf	bvf	VERB
ejpam-6761	43	25	soft	soft	ADJ
ejpam-6761	43	26	sets	set	NOUN
ejpam-6761	43	27	[	[	X
ejpam-6761	43	28	27	27	NUM
ejpam-6761	43	29	]	]	PUNCT
ejpam-6761	43	30	continue	continue	VERB
ejpam-6761	43	31	to	to	PART
ejpam-6761	43	32	expand	expand	VERB
ejpam-6761	43	33	the	the	DET
ejpam-6761	43	34	field	field	NOUN
ejpam-6761	43	35	’s	’s	PART
ejpam-6761	43	36	boundaries	boundary	NOUN
ejpam-6761	43	37	.	.	PUNCT
ejpam-6761	44	1	notably	notably	ADV
ejpam-6761	44	2	,	,	PUNCT
ejpam-6761	44	3	massa’deh	massa’deh	PROPN
ejpam-6761	44	4	et	et	PROPN
ejpam-6761	44	5	al	al	PROPN
ejpam-6761	44	6	.	.	PUNCT
ejpam-6761	45	1	[	[	X
ejpam-6761	45	2	28	28	NUM
ejpam-6761	45	3	]	]	PUNCT
ejpam-6761	45	4	have	have	AUX
ejpam-6761	45	5	introduced	introduce	VERB
ejpam-6761	45	6	concepts	concept	NOUN
ejpam-6761	45	7	such	such	ADJ
ejpam-6761	45	8	as	as	ADP
ejpam-6761	45	9	antihomomorphisms	antihomomorphism	NOUN
ejpam-6761	45	10	and	and	CCONJ
ejpam-6761	45	11	bvf	bvf	VERB
ejpam-6761	45	12	multi	multi	ADJ
ejpam-6761	45	13	-	-	ADJ
ejpam-6761	45	14	fuzzy	fuzzy	ADJ
ejpam-6761	45	15	subgroups	subgroup	NOUN
ejpam-6761	45	16	,	,	PUNCT
ejpam-6761	45	17	bridging	bridge	VERB
ejpam-6761	45	18	theory	theory	NOUN
ejpam-6761	45	19	with	with	ADP
ejpam-6761	45	20	complex	complex	ADJ
ejpam-6761	45	21	functional	functional	ADJ
ejpam-6761	45	22	systems	system	NOUN
ejpam-6761	45	23	.	.	PUNCT
ejpam-6761	46	1	in	in	ADP
ejpam-6761	46	2	this	this	DET
ejpam-6761	46	3	paper	paper	NOUN
ejpam-6761	46	4	,	,	PUNCT
ejpam-6761	46	5	we	we	PRON
ejpam-6761	46	6	extend	extend	VERB
ejpam-6761	46	7	these	these	DET
ejpam-6761	46	8	developments	development	NOUN
ejpam-6761	46	9	by	by	ADP
ejpam-6761	46	10	proposing	propose	VERB
ejpam-6761	46	11	a	a	DET
ejpam-6761	46	12	complete	complete	ADJ
ejpam-6761	46	13	theory	theory	NOUN
ejpam-6761	46	14	of	of	ADP
ejpam-6761	46	15	bipolarvalued	bipolarvalue	VERB
ejpam-6761	46	16	fuzzy	fuzzy	ADJ
ejpam-6761	46	17	subgroups	subgroup	NOUN
ejpam-6761	46	18	(	(	PUNCT
ejpam-6761	46	19	bvf	bvf	NOUN
ejpam-6761	46	20	-	-	PUNCT
ejpam-6761	46	21	subgroups	subgroup	NOUN
ejpam-6761	46	22	)	)	PUNCT
ejpam-6761	46	23	,	,	PUNCT
ejpam-6761	46	24	and	and	CCONJ
ejpam-6761	46	25	further	far	ADV
ejpam-6761	46	26	advancing	advance	VERB
ejpam-6761	46	27	the	the	DET
ejpam-6761	46	28	structures	structure	NOUN
ejpam-6761	46	29	of	of	ADP
ejpam-6761	46	30	bvfnormal	bvfnormal	NOUN
ejpam-6761	46	31	subgroups	subgroup	NOUN
ejpam-6761	46	32	and	and	CCONJ
ejpam-6761	46	33	bvf	bvf	NOUN
ejpam-6761	46	34	-	-	PUNCT
ejpam-6761	46	35	homomorphisms	homomorphism	NOUN
ejpam-6761	46	36	.	.	PUNCT
ejpam-6761	47	1	our	our	PRON
ejpam-6761	47	2	approach	approach	NOUN
ejpam-6761	47	3	preserves	preserve	VERB
ejpam-6761	47	4	classical	classical	ADJ
ejpam-6761	47	5	group	group	NOUN
ejpam-6761	47	6	axioms	axiom	NOUN
ejpam-6761	47	7	while	while	SCONJ
ejpam-6761	47	8	adapting	adapt	VERB
ejpam-6761	47	9	them	they	PRON
ejpam-6761	47	10	to	to	ADP
ejpam-6761	47	11	the	the	DET
ejpam-6761	47	12	dual	dual	ADV
ejpam-6761	47	13	-	-	PUNCT
ejpam-6761	47	14	valued	value	VERB
ejpam-6761	47	15	bvf	bvf	NOUN
ejpam-6761	47	16	context	context	NOUN
ejpam-6761	47	17	.	.	PUNCT
ejpam-6761	48	1	our	our	PRON
ejpam-6761	48	2	contributions	contribution	NOUN
ejpam-6761	48	3	are	be	AUX
ejpam-6761	48	4	threefold	threefold	ADV
ejpam-6761	48	5	:	:	PUNCT
ejpam-6761	48	6	f.	f.	PROPN
ejpam-6761	48	7	al	al	PROPN
ejpam-6761	48	8	-	-	PROPN
ejpam-6761	48	9	zu’bi	zu’bi	PROPN
ejpam-6761	48	10	et	et	NOUN
ejpam-6761	48	11	al	al	PROPN
ejpam-6761	48	12	.	.	PUNCT
ejpam-6761	48	13	/	/	SYM
ejpam-6761	48	14	eur	eur	PROPN
ejpam-6761	48	15	.	.	PUNCT
ejpam-6761	49	1	j.	j.	PROPN
ejpam-6761	49	2	pure	pure	PROPN
ejpam-6761	49	3	appl	appl	PROPN
ejpam-6761	49	4	.	.	PROPN
ejpam-6761	49	5	math	math	PROPN
ejpam-6761	49	6	,	,	PUNCT
ejpam-6761	49	7	18	18	NUM
ejpam-6761	49	8	(	(	PUNCT
ejpam-6761	49	9	4	4	NUM
ejpam-6761	49	10	)	)	PUNCT
ejpam-6761	49	11	(	(	PUNCT
ejpam-6761	49	12	2025	2025	NUM
ejpam-6761	49	13	)	)	PUNCT
ejpam-6761	49	14	,	,	PUNCT
ejpam-6761	49	15	6761	6761	NUM
ejpam-6761	49	16	3	3	NUM
ejpam-6761	49	17	of	of	ADP
ejpam-6761	49	18	28	28	NUM
ejpam-6761	49	19	(	(	PUNCT
ejpam-6761	49	20	i	i	NOUN
ejpam-6761	49	21	)	)	PUNCT
ejpam-6761	49	22	we	we	PRON
ejpam-6761	49	23	define	define	VERB
ejpam-6761	49	24	and	and	CCONJ
ejpam-6761	49	25	characterize	characterize	VERB
ejpam-6761	49	26	bvf	bvf	NOUN
ejpam-6761	49	27	-	-	PUNCT
ejpam-6761	49	28	subgroups	subgroup	NOUN
ejpam-6761	49	29	using	use	VERB
ejpam-6761	49	30	the	the	DET
ejpam-6761	49	31	bvf	bvf	NOUN
ejpam-6761	49	32	-	-	PUNCT
ejpam-6761	49	33	space	space	NOUN
ejpam-6761	49	34	and	and	CCONJ
ejpam-6761	49	35	bipolar	bipolar	ADV
ejpam-6761	49	36	-	-	PUNCT
ejpam-6761	49	37	valued	value	VERB
ejpam-6761	49	38	fuzzy	fuzzy	ADJ
ejpam-6761	49	39	binary	binary	NOUN
ejpam-6761	49	40	operation	operation	NOUN
ejpam-6761	49	41	(	(	PUNCT
ejpam-6761	49	42	bvfbo	bvfbo	NOUN
ejpam-6761	49	43	)	)	PUNCT
ejpam-6761	49	44	.	.	PUNCT
ejpam-6761	50	1	(	(	PUNCT
ejpam-6761	50	2	ii	ii	X
ejpam-6761	50	3	)	)	PUNCT
ejpam-6761	50	4	we	we	PRON
ejpam-6761	50	5	formulate	formulate	VERB
ejpam-6761	50	6	bvf	bvf	NOUN
ejpam-6761	50	7	-	-	PUNCT
ejpam-6761	50	8	normal	normal	ADJ
ejpam-6761	50	9	subgroups	subgroup	NOUN
ejpam-6761	50	10	and	and	CCONJ
ejpam-6761	50	11	bvf	bvf	NOUN
ejpam-6761	50	12	-	-	PUNCT
ejpam-6761	50	13	homomorphisms	homomorphism	NOUN
ejpam-6761	50	14	,	,	PUNCT
ejpam-6761	50	15	demonstrating	demonstrate	VERB
ejpam-6761	50	16	consistency	consistency	NOUN
ejpam-6761	50	17	with	with	ADP
ejpam-6761	50	18	classical	classical	ADJ
ejpam-6761	50	19	and	and	CCONJ
ejpam-6761	50	20	intuitionistic	intuitionistic	ADJ
ejpam-6761	50	21	subgroup	subgroup	NOUN
ejpam-6761	50	22	theory	theory	NOUN
ejpam-6761	50	23	.	.	PUNCT
ejpam-6761	51	1	(	(	PUNCT
ejpam-6761	51	2	iii	iii	X
ejpam-6761	51	3	)	)	PUNCT
ejpam-6761	51	4	we	we	PRON
ejpam-6761	51	5	establish	establish	VERB
ejpam-6761	51	6	algebraic	algebraic	ADJ
ejpam-6761	51	7	theorems	theorem	NOUN
ejpam-6761	51	8	that	that	SCONJ
ejpam-6761	51	9	validate	validate	VERB
ejpam-6761	51	10	associativity	associativity	NOUN
ejpam-6761	51	11	,	,	PUNCT
ejpam-6761	51	12	structural	structural	ADJ
ejpam-6761	51	13	generalization	generalization	NOUN
ejpam-6761	51	14	,	,	PUNCT
ejpam-6761	51	15	and	and	CCONJ
ejpam-6761	51	16	compatibility	compatibility	NOUN
ejpam-6761	51	17	with	with	ADP
ejpam-6761	51	18	fuzzy	fuzzy	ADJ
ejpam-6761	51	19	group	group	NOUN
ejpam-6761	51	20	frameworks	framework	NOUN
ejpam-6761	51	21	.	.	PUNCT
ejpam-6761	52	1	this	this	DET
ejpam-6761	52	2	expanded	expand	VERB
ejpam-6761	52	3	bvf	bvf	NOUN
ejpam-6761	52	4	-	-	PUNCT
ejpam-6761	52	5	subgroup	subgroup	NOUN
ejpam-6761	52	6	theory	theory	NOUN
ejpam-6761	52	7	is	be	AUX
ejpam-6761	52	8	not	not	PART
ejpam-6761	52	9	only	only	ADV
ejpam-6761	52	10	mathematically	mathematically	ADV
ejpam-6761	52	11	rigorous	rigorous	ADJ
ejpam-6761	52	12	but	but	CCONJ
ejpam-6761	52	13	also	also	ADV
ejpam-6761	52	14	aligns	align	VERB
ejpam-6761	52	15	with	with	ADP
ejpam-6761	52	16	complex	complex	ADJ
ejpam-6761	52	17	real	real	ADJ
ejpam-6761	52	18	-	-	PUNCT
ejpam-6761	52	19	world	world	NOUN
ejpam-6761	52	20	contexts	context	NOUN
ejpam-6761	52	21	that	that	PRON
ejpam-6761	52	22	involve	involve	VERB
ejpam-6761	52	23	positive	positive	ADJ
ejpam-6761	52	24	and	and	CCONJ
ejpam-6761	52	25	negative	negative	ADJ
ejpam-6761	52	26	evaluations	evaluation	NOUN
ejpam-6761	52	27	.	.	PUNCT
ejpam-6761	53	1	applications	application	NOUN
ejpam-6761	53	2	span	span	VERB
ejpam-6761	53	3	control	control	NOUN
ejpam-6761	53	4	systems	system	NOUN
ejpam-6761	53	5	influenced	influence	VERB
ejpam-6761	53	6	by	by	ADP
ejpam-6761	53	7	conflicting	conflicting	ADJ
ejpam-6761	53	8	dynamics	dynamic	NOUN
ejpam-6761	53	9	,	,	PUNCT
ejpam-6761	53	10	decision	decision	NOUN
ejpam-6761	53	11	-	-	PUNCT
ejpam-6761	53	12	making	make	VERB
ejpam-6761	53	13	scenarios	scenario	NOUN
ejpam-6761	53	14	with	with	ADP
ejpam-6761	53	15	trade	trade	NOUN
ejpam-6761	53	16	-	-	PUNCT
ejpam-6761	53	17	offs	off	NOUN
ejpam-6761	53	18	,	,	PUNCT
ejpam-6761	53	19	and	and	CCONJ
ejpam-6761	53	20	medical	medical	ADJ
ejpam-6761	53	21	diagnosis	diagnosis	NOUN
ejpam-6761	53	22	where	where	SCONJ
ejpam-6761	53	23	symptoms	symptom	NOUN
ejpam-6761	53	24	have	have	AUX
ejpam-6761	53	25	both	both	PRON
ejpam-6761	53	26	enhancing	enhance	VERB
ejpam-6761	53	27	and	and	CCONJ
ejpam-6761	53	28	deteriorating	deteriorate	VERB
ejpam-6761	53	29	effects	effect	NOUN
ejpam-6761	53	30	[	[	X
ejpam-6761	53	31	12	12	NUM
ejpam-6761	53	32	,	,	PUNCT
ejpam-6761	53	33	16	16	NUM
ejpam-6761	53	34	,	,	PUNCT
ejpam-6761	53	35	27	27	NUM
ejpam-6761	53	36	]	]	PUNCT
ejpam-6761	53	37	.	.	PUNCT
ejpam-6761	54	1	our	our	PRON
ejpam-6761	54	2	contribution	contribution	NOUN
ejpam-6761	54	3	expands	expand	VERB
ejpam-6761	54	4	on	on	ADP
ejpam-6761	54	5	recent	recent	ADJ
ejpam-6761	54	6	studies	study	NOUN
ejpam-6761	54	7	that	that	PRON
ejpam-6761	54	8	introduced	introduce	VERB
ejpam-6761	54	9	bvf	bvf	NOUN
ejpam-6761	54	10	groups	group	NOUN
ejpam-6761	54	11	and	and	CCONJ
ejpam-6761	54	12	bipolarvalued	bipolarvalue	VERB
ejpam-6761	54	13	fuzzy	fuzzy	ADJ
ejpam-6761	54	14	cartesian	cartesian	ADJ
ejpam-6761	54	15	relations	relation	NOUN
ejpam-6761	54	16	,	,	PUNCT
ejpam-6761	54	17	providing	provide	VERB
ejpam-6761	54	18	a	a	DET
ejpam-6761	54	19	comprehensive	comprehensive	ADJ
ejpam-6761	54	20	algebraic	algebraic	ADJ
ejpam-6761	54	21	system	system	NOUN
ejpam-6761	54	22	.	.	PUNCT
ejpam-6761	55	1	we	we	PRON
ejpam-6761	55	2	prove	prove	VERB
ejpam-6761	55	3	that	that	SCONJ
ejpam-6761	55	4	not	not	PART
ejpam-6761	55	5	every	every	DET
ejpam-6761	55	6	bvf	bvf	NOUN
ejpam-6761	55	7	-	-	PUNCT
ejpam-6761	55	8	subgroup	subgroup	NOUN
ejpam-6761	55	9	is	be	AUX
ejpam-6761	55	10	associative	associative	ADJ
ejpam-6761	55	11	and	and	CCONJ
ejpam-6761	55	12	establish	establish	VERB
ejpam-6761	55	13	theorems	theorem	NOUN
ejpam-6761	55	14	connecting	connect	VERB
ejpam-6761	55	15	bvfsubgroups	bvfsubgroup	NOUN
ejpam-6761	55	16	to	to	ADP
ejpam-6761	55	17	their	their	PRON
ejpam-6761	55	18	fuzzy	fuzzy	ADJ
ejpam-6761	55	19	and	and	CCONJ
ejpam-6761	55	20	intuitionistic	intuitionistic	ADJ
ejpam-6761	55	21	counterparts	counterpart	NOUN
ejpam-6761	55	22	.	.	PUNCT
ejpam-6761	56	1	the	the	DET
ejpam-6761	56	2	proposed	propose	VERB
ejpam-6761	56	3	generalization	generalization	NOUN
ejpam-6761	56	4	has	have	VERB
ejpam-6761	56	5	practical	practical	ADJ
ejpam-6761	56	6	relevance	relevance	NOUN
ejpam-6761	56	7	for	for	ADP
ejpam-6761	56	8	applications	application	NOUN
ejpam-6761	56	9	in	in	ADP
ejpam-6761	56	10	decision	decision	NOUN
ejpam-6761	56	11	-	-	PUNCT
ejpam-6761	56	12	making	making	NOUN
ejpam-6761	56	13	,	,	PUNCT
ejpam-6761	56	14	intelligent	intelligent	ADJ
ejpam-6761	56	15	systems	system	NOUN
ejpam-6761	56	16	,	,	PUNCT
ejpam-6761	56	17	and	and	CCONJ
ejpam-6761	56	18	control	control	NOUN
ejpam-6761	56	19	theory	theory	NOUN
ejpam-6761	56	20	,	,	PUNCT
ejpam-6761	56	21	where	where	SCONJ
ejpam-6761	56	22	positive	positive	ADJ
ejpam-6761	56	23	and	and	CCONJ
ejpam-6761	56	24	negative	negative	ADJ
ejpam-6761	56	25	valuations	valuation	NOUN
ejpam-6761	56	26	must	must	AUX
ejpam-6761	56	27	coexist	coexist	VERB
ejpam-6761	56	28	in	in	ADP
ejpam-6761	56	29	algebraic	algebraic	ADJ
ejpam-6761	56	30	reasoning	reasoning	NOUN
ejpam-6761	56	31	.	.	PUNCT
ejpam-6761	57	1	the	the	DET
ejpam-6761	57	2	remainder	remainder	NOUN
ejpam-6761	57	3	of	of	ADP
ejpam-6761	57	4	this	this	DET
ejpam-6761	57	5	paper	paper	NOUN
ejpam-6761	57	6	presents	present	VERB
ejpam-6761	57	7	a	a	DET
ejpam-6761	57	8	comprehensive	comprehensive	ADJ
ejpam-6761	57	9	theoretical	theoretical	ADJ
ejpam-6761	57	10	formulation	formulation	NOUN
ejpam-6761	57	11	of	of	ADP
ejpam-6761	57	12	bvfsubgroups	bvfsubgroup	NOUN
ejpam-6761	57	13	.	.	PUNCT
ejpam-6761	58	1	we	we	PRON
ejpam-6761	58	2	begin	begin	VERB
ejpam-6761	58	3	with	with	ADP
ejpam-6761	58	4	the	the	DET
ejpam-6761	58	5	necessary	necessary	ADJ
ejpam-6761	58	6	background	background	NOUN
ejpam-6761	58	7	,	,	PUNCT
ejpam-6761	58	8	proceed	proceed	VERB
ejpam-6761	58	9	with	with	ADP
ejpam-6761	58	10	formal	formal	ADJ
ejpam-6761	58	11	definitions	definition	NOUN
ejpam-6761	58	12	and	and	CCONJ
ejpam-6761	58	13	proofs	proof	NOUN
ejpam-6761	58	14	,	,	PUNCT
ejpam-6761	58	15	and	and	CCONJ
ejpam-6761	58	16	conclude	conclude	VERB
ejpam-6761	58	17	with	with	ADP
ejpam-6761	58	18	theoretical	theoretical	ADJ
ejpam-6761	58	19	discussions	discussion	NOUN
ejpam-6761	58	20	and	and	CCONJ
ejpam-6761	58	21	implications	implication	NOUN
ejpam-6761	58	22	that	that	PRON
ejpam-6761	58	23	bridge	bridge	NOUN
ejpam-6761	58	24	abstract	abstract	ADJ
ejpam-6761	58	25	fuzzy	fuzzy	ADJ
ejpam-6761	58	26	logic	logic	NOUN
ejpam-6761	58	27	and	and	CCONJ
ejpam-6761	58	28	applicable	applicable	ADJ
ejpam-6761	58	29	mathematical	mathematical	ADJ
ejpam-6761	58	30	systems	system	NOUN
ejpam-6761	58	31	.	.	PUNCT
ejpam-6761	59	1	1.1	1.1	NUM
ejpam-6761	59	2	.	.	PUNCT
ejpam-6761	59	3	related	relate	VERB
ejpam-6761	59	4	work	work	NOUN
ejpam-6761	59	5	the	the	DET
ejpam-6761	59	6	evolution	evolution	NOUN
ejpam-6761	59	7	of	of	ADP
ejpam-6761	59	8	bipolar	bipolar	ADV
ejpam-6761	59	9	-	-	PUNCT
ejpam-6761	59	10	valued	value	VERB
ejpam-6761	59	11	fuzzy	fuzzy	ADJ
ejpam-6761	59	12	algebraic	algebraic	ADJ
ejpam-6761	59	13	structures	structure	NOUN
ejpam-6761	59	14	has	have	AUX
ejpam-6761	59	15	been	be	AUX
ejpam-6761	59	16	shaped	shape	VERB
ejpam-6761	59	17	by	by	ADP
ejpam-6761	59	18	multiple	multiple	ADJ
ejpam-6761	59	19	foundational	foundational	ADJ
ejpam-6761	59	20	studies	study	NOUN
ejpam-6761	59	21	.	.	PUNCT
ejpam-6761	60	1	anitha	anitha	PROPN
ejpam-6761	60	2	et	et	PROPN
ejpam-6761	60	3	al	al	PROPN
ejpam-6761	60	4	.	.	PUNCT
ejpam-6761	61	1	[	[	X
ejpam-6761	61	2	17	17	NUM
ejpam-6761	61	3	]	]	PUNCT
ejpam-6761	61	4	first	first	ADV
ejpam-6761	61	5	introduced	introduce	VERB
ejpam-6761	61	6	the	the	DET
ejpam-6761	61	7	concept	concept	NOUN
ejpam-6761	61	8	of	of	ADP
ejpam-6761	61	9	bipolar	bipolar	ADJ
ejpam-6761	61	10	fuzzy	fuzzy	ADJ
ejpam-6761	61	11	subgroups	subgroup	NOUN
ejpam-6761	61	12	,	,	PUNCT
ejpam-6761	61	13	laying	lay	VERB
ejpam-6761	61	14	the	the	DET
ejpam-6761	61	15	groundwork	groundwork	NOUN
ejpam-6761	61	16	for	for	ADP
ejpam-6761	61	17	understanding	understand	VERB
ejpam-6761	61	18	subgroup	subgroup	NOUN
ejpam-6761	61	19	properties	property	NOUN
ejpam-6761	61	20	within	within	ADP
ejpam-6761	61	21	a	a	DET
ejpam-6761	61	22	dualvalued	dualvalue	VERB
ejpam-6761	61	23	logic	logic	NOUN
ejpam-6761	61	24	framework	framework	NOUN
ejpam-6761	61	25	.	.	PUNCT
ejpam-6761	62	1	building	build	VERB
ejpam-6761	62	2	on	on	ADP
ejpam-6761	62	3	this	this	PRON
ejpam-6761	62	4	,	,	PUNCT
ejpam-6761	62	5	saeid	saeid	PROPN
ejpam-6761	63	1	[	[	X
ejpam-6761	63	2	18	18	NUM
ejpam-6761	63	3	]	]	PUNCT
ejpam-6761	63	4	and	and	CCONJ
ejpam-6761	63	5	lee	lee	PROPN
ejpam-6761	64	1	[	[	X
ejpam-6761	64	2	19	19	NUM
ejpam-6761	64	3	]	]	PUNCT
ejpam-6761	64	4	expanded	expand	VERB
ejpam-6761	64	5	bipolar	bipolar	ADV
ejpam-6761	64	6	-	-	PUNCT
ejpam-6761	64	7	valued	value	VERB
ejpam-6761	64	8	fuzzy	fuzzy	ADJ
ejpam-6761	64	9	concepts	concept	NOUN
ejpam-6761	64	10	to	to	PART
ejpam-6761	64	11	bck	bck	VERB
ejpam-6761	64	12	/	/	SYM
ejpam-6761	64	13	bci	bci	NOUN
ejpam-6761	64	14	-	-	PUNCT
ejpam-6761	64	15	algebras	algebras	X
ejpam-6761	64	16	,	,	PUNCT
ejpam-6761	64	17	enabling	enable	VERB
ejpam-6761	64	18	algebraic	algebraic	ADJ
ejpam-6761	64	19	reasoning	reasoning	NOUN
ejpam-6761	64	20	in	in	ADP
ejpam-6761	64	21	more	more	ADV
ejpam-6761	64	22	general	general	ADJ
ejpam-6761	64	23	logical	logical	ADJ
ejpam-6761	64	24	structures	structure	NOUN
ejpam-6761	64	25	.	.	PUNCT
ejpam-6761	65	1	similarly	similarly	ADV
ejpam-6761	65	2	,	,	PUNCT
ejpam-6761	65	3	balasubramanian	balasubramanian	PROPN
ejpam-6761	65	4	et	et	PROPN
ejpam-6761	65	5	al	al	PROPN
ejpam-6761	65	6	.	.	PUNCT
ejpam-6761	66	1	[	[	X
ejpam-6761	66	2	20	20	NUM
ejpam-6761	66	3	]	]	PUNCT
ejpam-6761	66	4	examined	examine	VERB
ejpam-6761	66	5	bipolar	bipolar	ADJ
ejpam-6761	66	6	interval	interval	NOUN
ejpam-6761	66	7	-	-	PUNCT
ejpam-6761	66	8	valued	value	VERB
ejpam-6761	66	9	fuzzy	fuzzy	ADJ
ejpam-6761	66	10	subgroups	subgroup	NOUN
ejpam-6761	66	11	,	,	PUNCT
ejpam-6761	66	12	which	which	PRON
ejpam-6761	66	13	accommodate	accommodate	VERB
ejpam-6761	66	14	uncertainty	uncertainty	NOUN
ejpam-6761	66	15	in	in	ADP
ejpam-6761	66	16	both	both	CCONJ
ejpam-6761	66	17	positive	positive	ADJ
ejpam-6761	66	18	and	and	CCONJ
ejpam-6761	66	19	negative	negative	ADJ
ejpam-6761	66	20	evaluations	evaluation	NOUN
ejpam-6761	66	21	.	.	PUNCT
ejpam-6761	67	1	further	further	ADJ
ejpam-6761	67	2	structural	structural	ADJ
ejpam-6761	67	3	generalizations	generalization	NOUN
ejpam-6761	67	4	have	have	AUX
ejpam-6761	67	5	been	be	AUX
ejpam-6761	67	6	introduced	introduce	VERB
ejpam-6761	67	7	by	by	ADP
ejpam-6761	67	8	shanmugapriya	shanmugapriya	PROPN
ejpam-6761	67	9	and	and	CCONJ
ejpam-6761	67	10	arjunan	arjunan	NOUN
ejpam-6761	68	1	[	[	X
ejpam-6761	68	2	22	22	NUM
ejpam-6761	68	3	]	]	PUNCT
ejpam-6761	69	1	who	who	PRON
ejpam-6761	69	2	investigated	investigate	VERB
ejpam-6761	69	3	bipolar	bipolar	ADJ
ejpam-6761	69	4	fuzzy	fuzzy	ADJ
ejpam-6761	69	5	subsemirings	subsemiring	NOUN
ejpam-6761	69	6	,	,	PUNCT
ejpam-6761	69	7	and	and	CCONJ
ejpam-6761	69	8	jun	jun	PROPN
ejpam-6761	69	9	and	and	CCONJ
ejpam-6761	69	10	song	song	NOUN
ejpam-6761	69	11	[	[	X
ejpam-6761	69	12	23	23	NUM
ejpam-6761	69	13	]	]	PUNCT
ejpam-6761	69	14	who	who	PRON
ejpam-6761	69	15	applied	apply	VERB
ejpam-6761	69	16	bipolar	bipolar	ADJ
ejpam-6761	69	17	fuzzy	fuzzy	ADJ
ejpam-6761	69	18	sets	set	NOUN
ejpam-6761	69	19	to	to	ADP
ejpam-6761	69	20	the	the	DET
ejpam-6761	69	21	closed	closed	ADJ
ejpam-6761	69	22	ideals	ideal	NOUN
ejpam-6761	69	23	and	and	CCONJ
ejpam-6761	69	24	subalgebras	subalgebras	PROPN
ejpam-6761	69	25	of	of	ADP
ejpam-6761	69	26	bch	bch	PROPN
ejpam-6761	69	27	-	-	PUNCT
ejpam-6761	69	28	algebras	algebras	PROPN
ejpam-6761	69	29	.	.	PUNCT
ejpam-6761	70	1	these	these	DET
ejpam-6761	70	2	efforts	effort	NOUN
ejpam-6761	70	3	collectively	collectively	ADV
ejpam-6761	70	4	demonstrate	demonstrate	VERB
ejpam-6761	70	5	the	the	DET
ejpam-6761	70	6	expanding	expand	VERB
ejpam-6761	70	7	utility	utility	NOUN
ejpam-6761	70	8	of	of	ADP
ejpam-6761	70	9	bipolar	bipolar	ADJ
ejpam-6761	70	10	-	-	PUNCT
ejpam-6761	70	11	valued	value	VERB
ejpam-6761	70	12	logic	logic	NOUN
ejpam-6761	70	13	in	in	ADP
ejpam-6761	70	14	algebraic	algebraic	PROPN
ejpam-6761	70	15	systems	system	NOUN
ejpam-6761	70	16	.	.	PUNCT
ejpam-6761	71	1	the	the	DET
ejpam-6761	71	2	notion	notion	NOUN
ejpam-6761	71	3	of	of	ADP
ejpam-6761	71	4	q	q	NOUN
ejpam-6761	71	5	-	-	PUNCT
ejpam-6761	71	6	fuzziness	fuzziness	NOUN
ejpam-6761	71	7	was	be	AUX
ejpam-6761	71	8	also	also	ADV
ejpam-6761	71	9	extended	extend	VERB
ejpam-6761	71	10	into	into	ADP
ejpam-6761	71	11	the	the	DET
ejpam-6761	71	12	bipolar	bipolar	ADJ
ejpam-6761	71	13	domain	domain	NOUN
ejpam-6761	71	14	by	by	ADP
ejpam-6761	71	15	sahaya	sahaya	NOUN
ejpam-6761	71	16	et	et	PROPN
ejpam-6761	71	17	al	al	PROPN
ejpam-6761	71	18	.	.	PUNCT
ejpam-6761	72	1	[	[	X
ejpam-6761	72	2	21	21	NUM
ejpam-6761	72	3	]	]	X
ejpam-6761	72	4	,	,	PUNCT
ejpam-6761	72	5	who	who	PRON
ejpam-6761	72	6	defined	define	VERB
ejpam-6761	72	7	bipolar	bipolar	ADV
ejpam-6761	72	8	-	-	PUNCT
ejpam-6761	72	9	valued	value	VERB
ejpam-6761	72	10	q	q	ADJ
ejpam-6761	72	11	-	-	PUNCT
ejpam-6761	72	12	fuzzy	fuzzy	ADJ
ejpam-6761	72	13	subgroups	subgroup	NOUN
ejpam-6761	72	14	,	,	PUNCT
ejpam-6761	72	15	providing	provide	VERB
ejpam-6761	72	16	additional	additional	ADJ
ejpam-6761	72	17	flexibility	flexibility	NOUN
ejpam-6761	72	18	and	and	CCONJ
ejpam-6761	72	19	generalization	generalization	NOUN
ejpam-6761	72	20	.	.	PUNCT
ejpam-6761	73	1	from	from	ADP
ejpam-6761	73	2	an	an	DET
ejpam-6761	73	3	application	application	NOUN
ejpam-6761	73	4	standpoint	standpoint	NOUN
ejpam-6761	73	5	,	,	PUNCT
ejpam-6761	73	6	recent	recent	ADJ
ejpam-6761	73	7	studies	study	NOUN
ejpam-6761	73	8	underscore	underscore	VERB
ejpam-6761	73	9	the	the	DET
ejpam-6761	73	10	versatility	versatility	NOUN
ejpam-6761	73	11	of	of	ADP
ejpam-6761	73	12	bipolar	bipolar	ADJ
ejpam-6761	73	13	fuzzy	fuzzy	ADJ
ejpam-6761	73	14	systems	system	NOUN
ejpam-6761	73	15	.	.	PUNCT
ejpam-6761	74	1	al	al	PROPN
ejpam-6761	74	2	-	-	PROPN
ejpam-6761	74	3	masarwah	masarwah	PROPN
ejpam-6761	74	4	et	et	PROPN
ejpam-6761	74	5	al	al	PROPN
ejpam-6761	74	6	.	.	PUNCT
ejpam-6761	75	1	[	[	X
ejpam-6761	75	2	25	25	NUM
ejpam-6761	75	3	]	]	PUNCT
ejpam-6761	75	4	introduced	introduce	VERB
ejpam-6761	75	5	m	m	ADJ
ejpam-6761	75	6	-	-	ADJ
ejpam-6761	75	7	polar	polar	ADJ
ejpam-6761	75	8	fuzzy	fuzzy	ADJ
ejpam-6761	75	9	ideals	ideal	NOUN
ejpam-6761	75	10	in	in	ADP
ejpam-6761	75	11	bck	bck	NOUN
ejpam-6761	75	12	-	-	PUNCT
ejpam-6761	75	13	algebras	algebra	NOUN
ejpam-6761	75	14	,	,	PUNCT
ejpam-6761	75	15	while	while	SCONJ
ejpam-6761	75	16	also	also	ADV
ejpam-6761	75	17	developing	develop	VERB
ejpam-6761	75	18	k	k	NOUN
ejpam-6761	75	19	-	-	PUNCT
ejpam-6761	75	20	folded	fold	VERB
ejpam-6761	75	21	n	n	CCONJ
ejpam-6761	75	22	-	-	PUNCT
ejpam-6761	75	23	structures	structure	NOUN
ejpam-6761	75	24	in	in	ADP
ejpam-6761	75	25	semigroups	semigroup	NOUN
ejpam-6761	75	26	[	[	X
ejpam-6761	75	27	26	26	NUM
ejpam-6761	75	28	]	]	PUNCT
ejpam-6761	75	29	,	,	PUNCT
ejpam-6761	75	30	enriching	enrich	VERB
ejpam-6761	75	31	the	the	DET
ejpam-6761	75	32	algebraic	algebraic	PROPN
ejpam-6761	75	33	f.	f.	PROPN
ejpam-6761	75	34	al	al	PROPN
ejpam-6761	75	35	-	-	PROPN
ejpam-6761	75	36	zu’bi	zu’bi	PROPN
ejpam-6761	75	37	et	et	NOUN
ejpam-6761	75	38	al	al	PROPN
ejpam-6761	75	39	.	.	PUNCT
ejpam-6761	75	40	/	/	SYM
ejpam-6761	75	41	eur	eur	PROPN
ejpam-6761	75	42	.	.	PUNCT
ejpam-6761	76	1	j.	j.	PROPN
ejpam-6761	76	2	pure	pure	PROPN
ejpam-6761	76	3	appl	appl	PROPN
ejpam-6761	76	4	.	.	PROPN
ejpam-6761	76	5	math	math	PROPN
ejpam-6761	76	6	,	,	PUNCT
ejpam-6761	76	7	18	18	NUM
ejpam-6761	76	8	(	(	PUNCT
ejpam-6761	76	9	4	4	NUM
ejpam-6761	76	10	)	)	PUNCT
ejpam-6761	76	11	(	(	PUNCT
ejpam-6761	76	12	2025	2025	NUM
ejpam-6761	76	13	)	)	PUNCT
ejpam-6761	76	14	,	,	PUNCT
ejpam-6761	76	15	6761	6761	NUM
ejpam-6761	76	16	4	4	NUM
ejpam-6761	76	17	of	of	ADP
ejpam-6761	76	18	28	28	NUM
ejpam-6761	76	19	foundation	foundation	NOUN
ejpam-6761	76	20	for	for	ADP
ejpam-6761	76	21	multipolar	multipolar	ADJ
ejpam-6761	76	22	decision	decision	NOUN
ejpam-6761	76	23	systems	system	NOUN
ejpam-6761	76	24	.	.	PUNCT
ejpam-6761	77	1	alqaraleh	alqaraleh	PROPN
ejpam-6761	77	2	et	et	PROPN
ejpam-6761	77	3	al	al	PROPN
ejpam-6761	77	4	.	.	PUNCT
ejpam-6761	78	1	[	[	X
ejpam-6761	78	2	27	27	NUM
ejpam-6761	78	3	]	]	PUNCT
ejpam-6761	78	4	proposed	propose	VERB
ejpam-6761	78	5	applications	application	NOUN
ejpam-6761	78	6	of	of	ADP
ejpam-6761	78	7	bipolar	bipolar	ADJ
ejpam-6761	78	8	complex	complex	ADJ
ejpam-6761	78	9	fuzzy	fuzzy	ADJ
ejpam-6761	78	10	soft	soft	ADJ
ejpam-6761	78	11	sets	set	NOUN
ejpam-6761	78	12	,	,	PUNCT
ejpam-6761	78	13	particularly	particularly	ADV
ejpam-6761	78	14	in	in	ADP
ejpam-6761	78	15	decision	decision	NOUN
ejpam-6761	78	16	-	-	PUNCT
ejpam-6761	78	17	making	make	VERB
ejpam-6761	78	18	contexts	context	NOUN
ejpam-6761	78	19	,	,	PUNCT
ejpam-6761	78	20	while	while	SCONJ
ejpam-6761	78	21	massa’deh	massa’deh	PROPN
ejpam-6761	78	22	et	et	PROPN
ejpam-6761	78	23	al	al	PROPN
ejpam-6761	78	24	.	.	PUNCT
ejpam-6761	79	1	[	[	X
ejpam-6761	79	2	28	28	NUM
ejpam-6761	79	3	]	]	PUNCT
ejpam-6761	79	4	investigated	investigate	VERB
ejpam-6761	79	5	homomorphisms	homomorphism	NOUN
ejpam-6761	79	6	and	and	CCONJ
ejpam-6761	79	7	anti	anti	ADJ
ejpam-6761	79	8	-	-	ADJ
ejpam-6761	79	9	homomorphisms	homomorphism	NOUN
ejpam-6761	79	10	in	in	ADP
ejpam-6761	79	11	multi	multi	ADJ
ejpam-6761	79	12	fuzzy	fuzzy	ADJ
ejpam-6761	79	13	hxsubgroups	hxsubgroup	NOUN
ejpam-6761	79	14	,	,	PUNCT
ejpam-6761	79	15	thereby	thereby	ADV
ejpam-6761	79	16	extending	extend	VERB
ejpam-6761	79	17	functional	functional	ADJ
ejpam-6761	79	18	operations	operation	NOUN
ejpam-6761	79	19	in	in	ADP
ejpam-6761	79	20	bipolar	bipolar	ADJ
ejpam-6761	79	21	fuzzy	fuzzy	ADJ
ejpam-6761	79	22	algebra	algebra	NOUN
ejpam-6761	79	23	.	.	PUNCT
ejpam-6761	80	1	additional	additional	ADJ
ejpam-6761	80	2	interdisciplinary	interdisciplinary	ADJ
ejpam-6761	80	3	contributions	contribution	NOUN
ejpam-6761	80	4	offer	offer	VERB
ejpam-6761	80	5	further	further	ADJ
ejpam-6761	80	6	support	support	NOUN
ejpam-6761	80	7	for	for	ADP
ejpam-6761	80	8	the	the	DET
ejpam-6761	80	9	practical	practical	ADJ
ejpam-6761	80	10	reach	reach	NOUN
ejpam-6761	80	11	of	of	ADP
ejpam-6761	80	12	fuzzy	fuzzy	ADJ
ejpam-6761	80	13	systems	system	NOUN
ejpam-6761	80	14	.	.	PUNCT
ejpam-6761	81	1	manavalan	manavalan	PROPN
ejpam-6761	81	2	et	et	PROPN
ejpam-6761	81	3	al	al	PROPN
ejpam-6761	81	4	.	.	PUNCT
ejpam-6761	82	1	[	[	X
ejpam-6761	82	2	29	29	NUM
ejpam-6761	82	3	,	,	PUNCT
ejpam-6761	82	4	30	30	NUM
ejpam-6761	82	5	]	]	PUNCT
ejpam-6761	82	6	and	and	CCONJ
ejpam-6761	82	7	damrah	damrah	PROPN
ejpam-6761	82	8	et	et	PROPN
ejpam-6761	82	9	al	al	PROPN
ejpam-6761	82	10	.	.	PUNCT
ejpam-6761	83	1	[	[	X
ejpam-6761	83	2	31	31	NUM
ejpam-6761	83	3	,	,	PUNCT
ejpam-6761	83	4	32	32	NUM
ejpam-6761	83	5	]	]	PUNCT
ejpam-6761	83	6	apply	apply	VERB
ejpam-6761	83	7	neutrosophic	neutrosophic	ADJ
ejpam-6761	83	8	and	and	CCONJ
ejpam-6761	83	9	fuzzy	fuzzy	ADJ
ejpam-6761	83	10	-	-	PUNCT
ejpam-6761	83	11	set	set	VERB
ejpam-6761	83	12	extensions	extension	NOUN
ejpam-6761	83	13	to	to	ADP
ejpam-6761	83	14	real	real	ADJ
ejpam-6761	83	15	-	-	PUNCT
ejpam-6761	83	16	life	life	NOUN
ejpam-6761	83	17	decision	decision	NOUN
ejpam-6761	83	18	-	-	PUNCT
ejpam-6761	83	19	making	making	NOUN
ejpam-6761	83	20	,	,	PUNCT
ejpam-6761	83	21	cybersecurity	cybersecurity	NOUN
ejpam-6761	83	22	,	,	PUNCT
ejpam-6761	83	23	and	and	CCONJ
ejpam-6761	83	24	epidemiological	epidemiological	ADJ
ejpam-6761	83	25	modeling	modeling	NOUN
ejpam-6761	83	26	.	.	PUNCT
ejpam-6761	84	1	firouzkouhi	firouzkouhi	VERB
ejpam-6761	84	2	et	et	PROPN
ejpam-6761	84	3	al	al	PROPN
ejpam-6761	84	4	.	.	PUNCT
ejpam-6761	85	1	[	[	X
ejpam-6761	85	2	33	33	NUM
ejpam-6761	85	3	]	]	PUNCT
ejpam-6761	85	4	employed	employ	VERB
ejpam-6761	85	5	generalized	generalize	VERB
ejpam-6761	85	6	fuzzy	fuzzy	ADJ
ejpam-6761	85	7	hypergraphs	hypergraph	NOUN
ejpam-6761	85	8	for	for	ADP
ejpam-6761	85	9	link	link	NOUN
ejpam-6761	85	10	prediction	prediction	NOUN
ejpam-6761	85	11	and	and	CCONJ
ejpam-6761	85	12	influencer	influencer	NOUN
ejpam-6761	85	13	detection	detection	NOUN
ejpam-6761	85	14	in	in	ADP
ejpam-6761	85	15	dynamic	dynamic	ADJ
ejpam-6761	85	16	social	social	ADJ
ejpam-6761	85	17	networks	network	NOUN
ejpam-6761	85	18	,	,	PUNCT
ejpam-6761	85	19	demonstrating	demonstrate	VERB
ejpam-6761	85	20	the	the	DET
ejpam-6761	85	21	power	power	NOUN
ejpam-6761	85	22	of	of	ADP
ejpam-6761	85	23	fuzzy	fuzzy	ADJ
ejpam-6761	85	24	logic	logic	NOUN
ejpam-6761	85	25	in	in	ADP
ejpam-6761	85	26	complex	complex	ADJ
ejpam-6761	85	27	relational	relational	ADJ
ejpam-6761	85	28	environments	environment	NOUN
ejpam-6761	85	29	.	.	PUNCT
ejpam-6761	86	1	similarly	similarly	ADV
ejpam-6761	86	2	,	,	PUNCT
ejpam-6761	86	3	damrah	damrah	PROPN
ejpam-6761	86	4	et	et	PROPN
ejpam-6761	86	5	al	al	PROPN
ejpam-6761	86	6	.	.	PUNCT
ejpam-6761	87	1	[	[	X
ejpam-6761	87	2	34	34	NUM
ejpam-6761	87	3	,	,	PUNCT
ejpam-6761	87	4	35	35	NUM
ejpam-6761	87	5	]	]	PUNCT
ejpam-6761	87	6	explored	explore	VERB
ejpam-6761	87	7	fuzzy	fuzzy	ADJ
ejpam-6761	87	8	mathematical	mathematical	ADJ
ejpam-6761	87	9	modeling	modeling	NOUN
ejpam-6761	87	10	in	in	ADP
ejpam-6761	87	11	energy	energy	NOUN
ejpam-6761	87	12	-	-	PUNCT
ejpam-6761	87	13	efficient	efficient	ADJ
ejpam-6761	87	14	drilling	drilling	NOUN
ejpam-6761	87	15	and	and	CCONJ
ejpam-6761	87	16	well	well	ADV
ejpam-6761	87	17	design	design	NOUN
ejpam-6761	87	18	validation	validation	NOUN
ejpam-6761	87	19	,	,	PUNCT
ejpam-6761	87	20	illustrating	illustrate	VERB
ejpam-6761	87	21	how	how	SCONJ
ejpam-6761	87	22	fuzzy	fuzzy	ADJ
ejpam-6761	87	23	algebra	algebra	NOUN
ejpam-6761	87	24	can	can	AUX
ejpam-6761	87	25	inform	inform	VERB
ejpam-6761	87	26	industrial	industrial	ADJ
ejpam-6761	87	27	and	and	CCONJ
ejpam-6761	87	28	environmental	environmental	ADJ
ejpam-6761	87	29	challenges	challenge	NOUN
ejpam-6761	87	30	.	.	PUNCT
ejpam-6761	88	1	further	further	ADJ
ejpam-6761	88	2	generalizations	generalization	NOUN
ejpam-6761	88	3	include	include	VERB
ejpam-6761	88	4	a	a	DET
ejpam-6761	88	5	new	new	ADJ
ejpam-6761	88	6	structure	structure	NOUN
ejpam-6761	88	7	of	of	ADP
ejpam-6761	88	8	hesitant	hesitant	ADJ
ejpam-6761	88	9	fuzzy	fuzzy	ADJ
ejpam-6761	88	10	relations	relation	NOUN
ejpam-6761	88	11	by	by	ADP
ejpam-6761	88	12	talafha	talafha	NOUN
ejpam-6761	88	13	et	et	PROPN
ejpam-6761	88	14	al	al	PROPN
ejpam-6761	88	15	.	.	PUNCT
ejpam-6761	89	1	[	[	X
ejpam-6761	89	2	36],an	36],an	NUM
ejpam-6761	89	3	investigation	investigation	NOUN
ejpam-6761	89	4	into	into	ADP
ejpam-6761	89	5	bipolar	bipolar	ADJ
ejpam-6761	89	6	fuzzy	fuzzy	ADJ
ejpam-6761	89	7	hoop	hoop	NOUN
ejpam-6761	89	8	algebras	algebra	NOUN
ejpam-6761	89	9	and	and	CCONJ
ejpam-6761	89	10	their	their	PRON
ejpam-6761	89	11	applications	application	NOUN
ejpam-6761	89	12	[	[	X
ejpam-6761	89	13	37	37	NUM
ejpam-6761	89	14	]	]	PUNCT
ejpam-6761	89	15	,	,	PUNCT
ejpam-6761	89	16	and	and	CCONJ
ejpam-6761	89	17	axiomatic	axiomatic	ADJ
ejpam-6761	89	18	analysis	analysis	NOUN
ejpam-6761	89	19	of	of	ADP
ejpam-6761	89	20	state	state	NOUN
ejpam-6761	89	21	operators	operator	NOUN
ejpam-6761	89	22	in	in	ADP
ejpam-6761	89	23	sheffer	sheffer	PROPN
ejpam-6761	89	24	stroke	stroke	NOUN
ejpam-6761	89	25	bck	bck	PROPN
ejpam-6761	89	26	-	-	PUNCT
ejpam-6761	89	27	algebras	algebras	PROPN
ejpam-6761	89	28	associated	associate	VERB
ejpam-6761	89	29	with	with	ADP
ejpam-6761	89	30	algorithmic	algorithmic	ADJ
ejpam-6761	89	31	approaches	approach	NOUN
ejpam-6761	89	32	[	[	X
ejpam-6761	89	33	38	38	NUM
ejpam-6761	89	34	]	]	PUNCT
ejpam-6761	89	35	.	.	PUNCT
ejpam-6761	90	1	our	our	PRON
ejpam-6761	90	2	bvf	bvf	NOUN
ejpam-6761	90	3	framework	framework	NOUN
ejpam-6761	90	4	generalizes	generalize	VERB
ejpam-6761	90	5	rosenfeld	rosenfeld	PROPN
ejpam-6761	90	6	’s	’s	PART
ejpam-6761	90	7	fuzzy	fuzzy	ADJ
ejpam-6761	90	8	subgroups	subgroup	NOUN
ejpam-6761	90	9	via	via	ADP
ejpam-6761	90	10	dual	dual	ADJ
ejpam-6761	90	11	polarity	polarity	NOUN
ejpam-6761	90	12	and	and	CCONJ
ejpam-6761	90	13	bvf	bvf	NOUN
ejpam-6761	90	14	-	-	PUNCT
ejpam-6761	90	15	space	space	NOUN
ejpam-6761	90	16	semantics	semantic	NOUN
ejpam-6761	90	17	;	;	PUNCT
ejpam-6761	90	18	we	we	PRON
ejpam-6761	90	19	explain	explain	VERB
ejpam-6761	90	20	when	when	SCONJ
ejpam-6761	90	21	they	they	PRON
ejpam-6761	90	22	coincide	coincide	VERB
ejpam-6761	90	23	(	(	PUNCT
ejpam-6761	90	24	via	via	ADP
ejpam-6761	90	25	correspondence	correspondence	NOUN
ejpam-6761	90	26	)	)	PUNCT
ejpam-6761	90	27	and	and	CCONJ
ejpam-6761	90	28	when	when	SCONJ
ejpam-6761	90	29	bvf	bvf	NOUN
ejpam-6761	90	30	adds	add	VERB
ejpam-6761	90	31	expressive	expressive	ADJ
ejpam-6761	90	32	power	power	NOUN
ejpam-6761	90	33	.	.	PUNCT
ejpam-6761	91	1	these	these	DET
ejpam-6761	91	2	contributions	contribution	NOUN
ejpam-6761	91	3	collectively	collectively	ADV
ejpam-6761	91	4	demonstrate	demonstrate	VERB
ejpam-6761	91	5	a	a	DET
ejpam-6761	91	6	vibrant	vibrant	ADJ
ejpam-6761	91	7	and	and	CCONJ
ejpam-6761	91	8	evolving	evolve	VERB
ejpam-6761	91	9	field	field	NOUN
ejpam-6761	91	10	that	that	PRON
ejpam-6761	91	11	bridges	bridge	VERB
ejpam-6761	91	12	theory	theory	NOUN
ejpam-6761	91	13	and	and	CCONJ
ejpam-6761	91	14	application	application	NOUN
ejpam-6761	91	15	.	.	PUNCT
ejpam-6761	92	1	the	the	DET
ejpam-6761	92	2	current	current	ADJ
ejpam-6761	92	3	study	study	NOUN
ejpam-6761	92	4	builds	build	VERB
ejpam-6761	92	5	upon	upon	SCONJ
ejpam-6761	92	6	these	these	DET
ejpam-6761	92	7	insights	insight	NOUN
ejpam-6761	92	8	by	by	ADP
ejpam-6761	92	9	advancing	advance	VERB
ejpam-6761	92	10	a	a	DET
ejpam-6761	92	11	unified	unified	ADJ
ejpam-6761	92	12	framework	framework	NOUN
ejpam-6761	92	13	for	for	ADP
ejpam-6761	92	14	bvf	bvf	NOUN
ejpam-6761	92	15	-	-	PUNCT
ejpam-6761	92	16	subgroups	subgroup	NOUN
ejpam-6761	92	17	,	,	PUNCT
ejpam-6761	92	18	bvf	bvf	NOUN
ejpam-6761	92	19	-	-	PUNCT
ejpam-6761	92	20	normal	normal	ADJ
ejpam-6761	92	21	subgroups	subgroup	NOUN
ejpam-6761	92	22	,	,	PUNCT
ejpam-6761	92	23	and	and	CCONJ
ejpam-6761	92	24	bvf	bvf	NOUN
ejpam-6761	92	25	-	-	PUNCT
ejpam-6761	92	26	homomorphisms	homomorphism	NOUN
ejpam-6761	92	27	,	,	PUNCT
ejpam-6761	92	28	offering	offer	VERB
ejpam-6761	92	29	both	both	PRON
ejpam-6761	92	30	structural	structural	ADJ
ejpam-6761	92	31	clarity	clarity	NOUN
ejpam-6761	92	32	and	and	CCONJ
ejpam-6761	92	33	practical	practical	ADJ
ejpam-6761	92	34	applicability	applicability	NOUN
ejpam-6761	92	35	across	across	ADP
ejpam-6761	92	36	complex	complex	ADJ
ejpam-6761	92	37	,	,	PUNCT
ejpam-6761	92	38	polarity	polarity	NOUN
ejpam-6761	92	39	-	-	PUNCT
ejpam-6761	92	40	sensitive	sensitive	ADJ
ejpam-6761	92	41	domains	domain	NOUN
ejpam-6761	92	42	.	.	PUNCT
ejpam-6761	93	1	1.2	1.2	NUM
ejpam-6761	93	2	.	.	PUNCT
ejpam-6761	93	3	comparative	comparative	ADJ
ejpam-6761	93	4	overview	overview	NOUN
ejpam-6761	93	5	of	of	ADP
ejpam-6761	93	6	previous	previous	ADJ
ejpam-6761	93	7	studies	study	NOUN
ejpam-6761	93	8	and	and	CCONJ
ejpam-6761	93	9	present	present	ADJ
ejpam-6761	93	10	work	work	NOUN
ejpam-6761	93	11	the	the	DET
ejpam-6761	93	12	following	follow	VERB
ejpam-6761	93	13	table	table	NOUN
ejpam-6761	93	14	1	1	NUM
ejpam-6761	93	15	summarizes	summarize	NOUN
ejpam-6761	93	16	the	the	DET
ejpam-6761	93	17	key	key	ADJ
ejpam-6761	93	18	distinctions	distinction	NOUN
ejpam-6761	93	19	and	and	CCONJ
ejpam-6761	93	20	innovations	innovation	NOUN
ejpam-6761	93	21	of	of	ADP
ejpam-6761	93	22	the	the	DET
ejpam-6761	93	23	present	present	ADJ
ejpam-6761	93	24	study	study	NOUN
ejpam-6761	93	25	compared	compare	VERB
ejpam-6761	93	26	to	to	ADP
ejpam-6761	93	27	earlier	early	ADJ
ejpam-6761	93	28	works	work	NOUN
ejpam-6761	93	29	in	in	ADP
ejpam-6761	93	30	the	the	DET
ejpam-6761	93	31	field	field	NOUN
ejpam-6761	93	32	of	of	ADP
ejpam-6761	93	33	bipolar	bipolar	ADV
ejpam-6761	93	34	-	-	PUNCT
ejpam-6761	93	35	valued	value	VERB
ejpam-6761	93	36	fuzzy	fuzzy	ADJ
ejpam-6761	93	37	algebra	algebra	NOUN
ejpam-6761	93	38	.	.	PUNCT
ejpam-6761	94	1	f.	f.	PROPN
ejpam-6761	94	2	al	al	PROPN
ejpam-6761	94	3	-	-	PROPN
ejpam-6761	94	4	zu’bi	zu’bi	PROPN
ejpam-6761	94	5	et	et	NOUN
ejpam-6761	94	6	al	al	PROPN
ejpam-6761	94	7	.	.	PUNCT
ejpam-6761	94	8	/	/	SYM
ejpam-6761	94	9	eur	eur	PROPN
ejpam-6761	94	10	.	.	PUNCT
ejpam-6761	95	1	j.	j.	PROPN
ejpam-6761	95	2	pure	pure	PROPN
ejpam-6761	95	3	appl	appl	PROPN
ejpam-6761	95	4	.	.	PROPN
ejpam-6761	95	5	math	math	PROPN
ejpam-6761	95	6	,	,	PUNCT
ejpam-6761	95	7	18	18	NUM
ejpam-6761	95	8	(	(	PUNCT
ejpam-6761	95	9	4	4	NUM
ejpam-6761	95	10	)	)	PUNCT
ejpam-6761	95	11	(	(	PUNCT
ejpam-6761	95	12	2025	2025	NUM
ejpam-6761	95	13	)	)	PUNCT
ejpam-6761	95	14	,	,	PUNCT
ejpam-6761	95	15	6761	6761	NUM
ejpam-6761	95	16	5	5	NUM
ejpam-6761	95	17	of	of	ADP
ejpam-6761	95	18	28	28	NUM
ejpam-6761	95	19	table	table	NOUN
ejpam-6761	95	20	1	1	NUM
ejpam-6761	95	21	:	:	PUNCT
ejpam-6761	95	22	comparison	comparison	NOUN
ejpam-6761	95	23	of	of	ADP
ejpam-6761	95	24	the	the	DET
ejpam-6761	95	25	current	current	ADJ
ejpam-6761	95	26	study	study	NOUN
ejpam-6761	95	27	with	with	ADP
ejpam-6761	95	28	previous	previous	ADJ
ejpam-6761	95	29	works	work	NOUN
ejpam-6761	95	30	study	study	VERB
ejpam-6761	95	31	main	main	ADJ
ejpam-6761	95	32	contribution	contribution	NOUN
ejpam-6761	95	33	fuzzy	fuzzy	ADJ
ejpam-6761	95	34	structure	structure	NOUN
ejpam-6761	95	35	type	type	NOUN
ejpam-6761	95	36	mathematical	mathematical	ADJ
ejpam-6761	95	37	focus	focus	NOUN
ejpam-6761	95	38	advancement	advancement	NOUN
ejpam-6761	95	39	over	over	ADP
ejpam-6761	95	40	previous	previous	ADJ
ejpam-6761	95	41	work	work	NOUN
ejpam-6761	95	42	rosenfeld	rosenfeld	PROPN
ejpam-6761	95	43	(	(	PUNCT
ejpam-6761	95	44	1971	1971	NUM
ejpam-6761	95	45	)	)	PUNCT
ejpam-6761	96	1	[	[	X
ejpam-6761	96	2	1	1	X
ejpam-6761	96	3	]	]	PUNCT
ejpam-6761	96	4	introduced	introduce	VERB
ejpam-6761	96	5	fuzzy	fuzzy	ADJ
ejpam-6761	96	6	subgroups	subgroup	NOUN
ejpam-6761	96	7	fuzzy	fuzzy	ADJ
ejpam-6761	96	8	set	set	VERB
ejpam-6761	96	9	group	group	NOUN
ejpam-6761	96	10	theory	theory	NOUN
ejpam-6761	96	11	laid	lay	VERB
ejpam-6761	96	12	the	the	DET
ejpam-6761	96	13	foundational	foundational	ADJ
ejpam-6761	96	14	concept	concept	NOUN
ejpam-6761	96	15	of	of	ADP
ejpam-6761	96	16	fuzzy	fuzzy	ADJ
ejpam-6761	96	17	groups	group	NOUN
ejpam-6761	96	18	dib	dib	X
ejpam-6761	96	19	(	(	PUNCT
ejpam-6761	96	20	1994)[3	1994)[3	NUM
ejpam-6761	96	21	]	]	PUNCT
ejpam-6761	96	22	;	;	PUNCT
ejpam-6761	96	23	dib	dib	PROPN
ejpam-6761	96	24	and	and	CCONJ
ejpam-6761	96	25	youssef	youssef	PROPN
ejpam-6761	96	26	(	(	PUNCT
ejpam-6761	96	27	1991	1991	NUM
ejpam-6761	96	28	)	)	PUNCT
ejpam-6761	97	1	[	[	X
ejpam-6761	97	2	4	4	X
ejpam-6761	97	3	]	]	PUNCT
ejpam-6761	97	4	proposed	propose	VERB
ejpam-6761	97	5	fuzzy	fuzzy	ADJ
ejpam-6761	97	6	space	space	NOUN
ejpam-6761	97	7	(	(	PUNCT
ejpam-6761	97	8	f	f	NOUN
ejpam-6761	97	9	-	-	PUNCT
ejpam-6761	97	10	space	space	NOUN
ejpam-6761	97	11	)	)	PUNCT
ejpam-6761	97	12	,	,	PUNCT
ejpam-6761	97	13	fuzzy	fuzzy	ADJ
ejpam-6761	97	14	binary	binary	ADJ
ejpam-6761	97	15	operations	operation	NOUN
ejpam-6761	97	16	fuzzy	fuzzy	ADJ
ejpam-6761	97	17	space	space	NOUN
ejpam-6761	97	18	algebraic	algebraic	PROPN
ejpam-6761	97	19	topology	topology	NOUN
ejpam-6761	97	20	,	,	PUNCT
ejpam-6761	97	21	structure	structure	NOUN
ejpam-6761	97	22	reframed	reframe	VERB
ejpam-6761	97	23	fuzzy	fuzzy	ADJ
ejpam-6761	97	24	groups	group	NOUN
ejpam-6761	97	25	on	on	ADP
ejpam-6761	97	26	a	a	DET
ejpam-6761	97	27	topological	topological	ADJ
ejpam-6761	97	28	space	space	NOUN
ejpam-6761	97	29	lee	lee	PROPN
ejpam-6761	97	30	(	(	PUNCT
ejpam-6761	97	31	2000	2000	NUM
ejpam-6761	97	32	,	,	PUNCT
ejpam-6761	97	33	2001	2001	NUM
ejpam-6761	97	34	)	)	PUNCT
ejpam-6761	98	1	[	[	X
ejpam-6761	98	2	8	8	NUM
ejpam-6761	98	3	,	,	PUNCT
ejpam-6761	98	4	9	9	NUM
ejpam-6761	98	5	]	]	PUNCT
ejpam-6761	98	6	formalized	formalize	VERB
ejpam-6761	98	7	bipolar	bipolar	ADV
ejpam-6761	98	8	-	-	PUNCT
ejpam-6761	98	9	valued	value	VERB
ejpam-6761	98	10	fuzzy	fuzzy	ADJ
ejpam-6761	98	11	sets	set	NOUN
ejpam-6761	98	12	bipolar	bipolar	ADV
ejpam-6761	98	13	-	-	PUNCT
ejpam-6761	98	14	valued	value	VERB
ejpam-6761	98	15	fuzzy	fuzzy	ADJ
ejpam-6761	98	16	set	set	VERB
ejpam-6761	98	17	bvfs	bvfs	ADJ
ejpam-6761	98	18	structure	structure	NOUN
ejpam-6761	98	19	,	,	PUNCT
ejpam-6761	98	20	comparison	comparison	NOUN
ejpam-6761	98	21	expanded	expand	VERB
ejpam-6761	98	22	fuzzy	fuzzy	ADJ
ejpam-6761	98	23	membership	membership	NOUN
ejpam-6761	98	24	to	to	ADP
ejpam-6761	98	25	[	[	X
ejpam-6761	98	26	−1	−1	NOUN
ejpam-6761	98	27	,	,	PUNCT
ejpam-6761	98	28	0]×	0]×	PROPN
ejpam-6761	99	1	[	[	X
ejpam-6761	99	2	0	0	NUM
ejpam-6761	99	3	,	,	PUNCT
ejpam-6761	99	4	1	1	NUM
ejpam-6761	99	5	]	]	PUNCT
ejpam-6761	99	6	anitha	anitha	NOUN
ejpam-6761	99	7	et	et	PROPN
ejpam-6761	99	8	al	al	PROPN
ejpam-6761	99	9	.	.	PROPN
ejpam-6761	100	1	(	(	PUNCT
ejpam-6761	100	2	2013	2013	NUM
ejpam-6761	100	3	)	)	PUNCT
ejpam-6761	101	1	[	[	X
ejpam-6761	101	2	17	17	NUM
ejpam-6761	101	3	]	]	PUNCT
ejpam-6761	101	4	studied	study	VERB
ejpam-6761	101	5	bvfsubgroups	bvfsubgroup	NOUN
ejpam-6761	101	6	structurally	structurally	ADV
ejpam-6761	101	7	bipolar	bipolar	ADV
ejpam-6761	101	8	-	-	PUNCT
ejpam-6761	101	9	valued	value	VERB
ejpam-6761	101	10	fuzzy	fuzzy	ADJ
ejpam-6761	101	11	set	set	VERB
ejpam-6761	101	12	subgroup	subgroup	NOUN
ejpam-6761	101	13	theory	theory	NOUN
ejpam-6761	101	14	first	first	ADV
ejpam-6761	101	15	attempt	attempt	NOUN
ejpam-6761	101	16	to	to	PART
ejpam-6761	101	17	apply	apply	VERB
ejpam-6761	101	18	bvf	bvf	NOUN
ejpam-6761	101	19	to	to	ADP
ejpam-6761	101	20	subgroup	subgroup	PROPN
ejpam-6761	101	21	structure	structure	NOUN
ejpam-6761	101	22	current	current	ADJ
ejpam-6761	101	23	study	study	NOUN
ejpam-6761	101	24	develops	develop	VERB
ejpam-6761	101	25	a	a	DET
ejpam-6761	101	26	complete	complete	ADJ
ejpam-6761	101	27	theory	theory	NOUN
ejpam-6761	101	28	for	for	ADP
ejpam-6761	101	29	bvfsubgroups	bvfsubgroup	NOUN
ejpam-6761	101	30	,	,	PUNCT
ejpam-6761	101	31	normal	normal	ADJ
ejpam-6761	101	32	subgroups	subgroup	NOUN
ejpam-6761	101	33	,	,	PUNCT
ejpam-6761	101	34	and	and	CCONJ
ejpam-6761	101	35	homomorphisms	homomorphism	NOUN
ejpam-6761	101	36	using	use	VERB
ejpam-6761	101	37	bvfbo	bvfbo	NOUN
ejpam-6761	101	38	on	on	ADP
ejpam-6761	101	39	bvf	bvf	NOUN
ejpam-6761	101	40	-	-	PUNCT
ejpam-6761	101	41	space	space	NOUN
ejpam-6761	101	42	.	.	PUNCT
ejpam-6761	102	1	bipolar	bipolar	ADJ
ejpam-6761	102	2	-	-	PUNCT
ejpam-6761	102	3	valued	value	VERB
ejpam-6761	102	4	fuzzy	fuzzy	ADJ
ejpam-6761	102	5	space	space	NOUN
ejpam-6761	102	6	algebraic	algebraic	ADJ
ejpam-6761	102	7	structure	structure	NOUN
ejpam-6761	102	8	,	,	PUNCT
ejpam-6761	102	9	homomorphism	homomorphism	PROPN
ejpam-6761	102	10	,	,	PUNCT
ejpam-6761	102	11	generalization	generalization	NOUN
ejpam-6761	102	12	unified	unify	VERB
ejpam-6761	102	13	,	,	PUNCT
ejpam-6761	102	14	topological	topological	ADJ
ejpam-6761	102	15	,	,	PUNCT
ejpam-6761	102	16	and	and	CCONJ
ejpam-6761	102	17	dual	dual	ADV
ejpam-6761	102	18	-	-	PUNCT
ejpam-6761	102	19	valued	value	VERB
ejpam-6761	102	20	group	group	NOUN
ejpam-6761	102	21	theory	theory	NOUN
ejpam-6761	102	22	in	in	ADP
ejpam-6761	102	23	one	one	NUM
ejpam-6761	102	24	framework	framework	NOUN
ejpam-6761	102	25	2	2	NUM
ejpam-6761	102	26	.	.	PUNCT
ejpam-6761	102	27	preliminaries	preliminary	NOUN
ejpam-6761	102	28	in	in	ADP
ejpam-6761	102	29	this	this	DET
ejpam-6761	102	30	section	section	NOUN
ejpam-6761	102	31	,	,	PUNCT
ejpam-6761	102	32	we	we	PRON
ejpam-6761	102	33	recall	recall	VERB
ejpam-6761	102	34	some	some	PRON
ejpam-6761	102	35	of	of	ADP
ejpam-6761	102	36	the	the	DET
ejpam-6761	102	37	fundamental	fundamental	ADJ
ejpam-6761	102	38	concepts	concept	NOUN
ejpam-6761	102	39	and	and	CCONJ
ejpam-6761	102	40	definitions	definition	NOUN
ejpam-6761	102	41	required	require	VERB
ejpam-6761	102	42	in	in	ADP
ejpam-6761	102	43	the	the	DET
ejpam-6761	102	44	sequel	sequel	NOUN
ejpam-6761	102	45	.	.	PUNCT
ejpam-6761	103	1	definition	definition	NOUN
ejpam-6761	103	2	1	1	NUM
ejpam-6761	103	3	(	(	PUNCT
ejpam-6761	103	4	[	[	X
ejpam-6761	103	5	9	9	NUM
ejpam-6761	103	6	]	]	NUM
ejpam-6761	103	7	)	)	PUNCT
ejpam-6761	103	8	.	.	PUNCT
ejpam-6761	104	1	an	an	DET
ejpam-6761	104	2	intuitionistic	intuitionistic	ADJ
ejpam-6761	104	3	fuzzy	fuzzy	NOUN
ejpam-6761	104	4	set	set	VERB
ejpam-6761	104	5	a	a	PRON
ejpam-6761	104	6	in	in	ADP
ejpam-6761	104	7	a	a	DET
ejpam-6761	104	8	universe	universe	NOUN
ejpam-6761	104	9	℧	℧	NUM
ejpam-6761	104	10	is	be	AUX
ejpam-6761	104	11	defined	define	VERB
ejpam-6761	104	12	by	by	ADP
ejpam-6761	104	13	a	a	DET
ejpam-6761	104	14	membership	membership	NOUN
ejpam-6761	104	15	function	function	NOUN
ejpam-6761	104	16	µa	µa	NOUN
ejpam-6761	104	17	:	:	PUNCT
ejpam-6761	104	18	℧	℧	PROPN
ejpam-6761	104	19	→	→	SYM
ejpam-6761	104	20	[	[	X
ejpam-6761	104	21	0	0	NUM
ejpam-6761	104	22	,	,	PUNCT
ejpam-6761	104	23	1	1	NUM
ejpam-6761	104	24	]	]	PUNCT
ejpam-6761	104	25	and	and	CCONJ
ejpam-6761	104	26	a	a	DET
ejpam-6761	104	27	non	non	ADJ
ejpam-6761	104	28	-	-	ADJ
ejpam-6761	104	29	membership	membership	ADJ
ejpam-6761	104	30	function	function	NOUN
ejpam-6761	104	31	νa	νa	VERB
ejpam-6761	104	32	:	:	PUNCT
ejpam-6761	104	33	℧	℧	PROPN
ejpam-6761	104	34	→	→	SYM
ejpam-6761	104	35	[	[	X
ejpam-6761	104	36	0	0	NUM
ejpam-6761	104	37	,	,	PUNCT
ejpam-6761	104	38	1	1	NUM
ejpam-6761	104	39	]	]	PUNCT
ejpam-6761	104	40	such	such	ADJ
ejpam-6761	104	41	that	that	SCONJ
ejpam-6761	104	42	0	0	NUM
ejpam-6761	104	43	≤	≤	NOUN
ejpam-6761	104	44	µa(x	µa(x	NOUN
ejpam-6761	104	45	)	)	PUNCT
ejpam-6761	105	1	+	+	CCONJ
ejpam-6761	105	2	νa(x	νa(x	NOUN
ejpam-6761	105	3	)	)	PUNCT
ejpam-6761	105	4	≤	≤	NUM
ejpam-6761	105	5	1	1	NUM
ejpam-6761	105	6	for	for	ADP
ejpam-6761	105	7	all	all	DET
ejpam-6761	105	8	x	x	SYM
ejpam-6761	105	9	∈	∈	PROPN
ejpam-6761	105	10	℧	℧	PROPN
ejpam-6761	105	11	.	.	PUNCT
ejpam-6761	105	12	definition	definition	NOUN
ejpam-6761	105	13	2	2	NUM
ejpam-6761	105	14	(	(	PUNCT
ejpam-6761	105	15	[	[	X
ejpam-6761	105	16	8	8	NUM
ejpam-6761	105	17	]	]	NUM
ejpam-6761	105	18	)	)	PUNCT
ejpam-6761	105	19	.	.	PUNCT
ejpam-6761	106	1	a	a	DET
ejpam-6761	106	2	bipolar	bipolar	ADV
ejpam-6761	106	3	-	-	PUNCT
ejpam-6761	106	4	valued	value	VERB
ejpam-6761	106	5	fuzzy	fuzzy	NOUN
ejpam-6761	106	6	set	set	VERB
ejpam-6761	106	7	a	a	PRON
ejpam-6761	106	8	in	in	ADP
ejpam-6761	106	9	a	a	DET
ejpam-6761	106	10	universe	universe	NOUN
ejpam-6761	106	11	℧	℧	NUM
ejpam-6761	106	12	is	be	AUX
ejpam-6761	106	13	defined	define	VERB
ejpam-6761	106	14	by	by	ADP
ejpam-6761	106	15	a	a	DET
ejpam-6761	106	16	memf	memf	NOUN
ejpam-6761	106	17	.	.	PUNCT
ejpam-6761	107	1	al	al	PROPN
ejpam-6761	107	2	-	-	PROPN
ejpam-6761	107	3	zu’bi	zu’bi	PROPN
ejpam-6761	107	4	et	et	NOUN
ejpam-6761	107	5	al	al	PROPN
ejpam-6761	107	6	.	.	PUNCT
ejpam-6761	107	7	/	/	SYM
ejpam-6761	107	8	eur	eur	PROPN
ejpam-6761	107	9	.	.	PUNCT
ejpam-6761	108	1	j.	j.	PROPN
ejpam-6761	108	2	pure	pure	PROPN
ejpam-6761	108	3	appl	appl	PROPN
ejpam-6761	108	4	.	.	PROPN
ejpam-6761	108	5	math	math	PROPN
ejpam-6761	108	6	,	,	PUNCT
ejpam-6761	108	7	18	18	NUM
ejpam-6761	108	8	(	(	PUNCT
ejpam-6761	108	9	4	4	NUM
ejpam-6761	108	10	)	)	PUNCT
ejpam-6761	108	11	(	(	PUNCT
ejpam-6761	108	12	2025	2025	NUM
ejpam-6761	108	13	)	)	PUNCT
ejpam-6761	108	14	,	,	PUNCT
ejpam-6761	108	15	6761	6761	NUM
ejpam-6761	108	16	6	6	NUM
ejpam-6761	108	17	of	of	ADP
ejpam-6761	108	18	28	28	NUM
ejpam-6761	108	19	bership	bership	NOUN
ejpam-6761	108	20	function	function	NOUN
ejpam-6761	108	21	µa	µa	NOUN
ejpam-6761	108	22	:	:	PUNCT
ejpam-6761	108	23	℧	℧	PROPN
ejpam-6761	108	24	→	→	SYM
ejpam-6761	108	25	[	[	X
ejpam-6761	108	26	−1	−1	NOUN
ejpam-6761	108	27	,	,	PUNCT
ejpam-6761	108	28	1	1	NUM
ejpam-6761	108	29	]	]	PUNCT
ejpam-6761	108	30	,	,	PUNCT
ejpam-6761	108	31	which	which	PRON
ejpam-6761	108	32	can	can	AUX
ejpam-6761	108	33	represent	represent	VERB
ejpam-6761	108	34	positive	positive	ADJ
ejpam-6761	108	35	and	and	CCONJ
ejpam-6761	108	36	negative	negative	ADJ
ejpam-6761	108	37	membership	membership	NOUN
ejpam-6761	108	38	degrees	degree	NOUN
ejpam-6761	108	39	:	:	PUNCT
ejpam-6761	108	40	•	•	NOUN
ejpam-6761	108	41	µa(x	µa(x	NOUN
ejpam-6761	108	42	)	)	PUNCT
ejpam-6761	108	43	>	>	X
ejpam-6761	109	1	0	0	NUM
ejpam-6761	109	2	:	:	PUNCT
ejpam-6761	109	3	the	the	DET
ejpam-6761	109	4	extent	extent	NOUN
ejpam-6761	109	5	to	to	PART
ejpam-6761	109	6	which	which	PRON
ejpam-6761	109	7	x	x	PUNCT
ejpam-6761	109	8	is	be	AUX
ejpam-6761	109	9	positively	positively	ADV
ejpam-6761	109	10	part	part	NOUN
ejpam-6761	109	11	of	of	ADP
ejpam-6761	109	12	a.	a.	NOUN
ejpam-6761	109	13	•	•	NUM
ejpam-6761	109	14	µa(x	µa(x	PUNCT
ejpam-6761	109	15	)	)	PUNCT
ejpam-6761	109	16	<	<	X
ejpam-6761	109	17	0	0	NUM
ejpam-6761	109	18	:	:	PUNCT
ejpam-6761	109	19	the	the	DET
ejpam-6761	109	20	degree	degree	NOUN
ejpam-6761	109	21	to	to	PART
ejpam-6761	109	22	which	which	PRON
ejpam-6761	109	23	x	x	PUNCT
ejpam-6761	109	24	is	be	AUX
ejpam-6761	109	25	negatively	negatively	ADV
ejpam-6761	109	26	part	part	NOUN
ejpam-6761	109	27	of	of	ADP
ejpam-6761	109	28	a.	a.	NOUN
ejpam-6761	109	29	remark	remark	NOUN
ejpam-6761	109	30	1	1	NUM
ejpam-6761	109	31	(	(	PUNCT
ejpam-6761	109	32	[	[	X
ejpam-6761	109	33	8	8	NUM
ejpam-6761	109	34	]	]	NUM
ejpam-6761	109	35	)	)	PUNCT
ejpam-6761	109	36	.	.	PUNCT
ejpam-6761	110	1	(	(	PUNCT
ejpam-6761	110	2	bfs	bfs	NOUN
ejpam-6761	110	3	vs.	vs.	X
ejpam-6761	110	4	bvfs	bvfs	NOUN
ejpam-6761	110	5	)	)	PUNCT
ejpam-6761	110	6	.	.	PUNCT
ejpam-6761	111	1	in	in	ADP
ejpam-6761	111	2	a	a	DET
ejpam-6761	111	3	bipolar	bipolar	ADJ
ejpam-6761	111	4	fuzzy	fuzzy	ADJ
ejpam-6761	111	5	set	set	NOUN
ejpam-6761	111	6	(	(	PUNCT
ejpam-6761	111	7	bfs	bfs	NOUN
ejpam-6761	111	8	)	)	PUNCT
ejpam-6761	111	9	one	one	NOUN
ejpam-6761	111	10	typically	typically	ADV
ejpam-6761	111	11	models	model	VERB
ejpam-6761	111	12	two	two	NUM
ejpam-6761	111	13	components	component	NOUN
ejpam-6761	111	14	µ−(x	µ−(x	PROPN
ejpam-6761	111	15	)	)	PUNCT
ejpam-6761	111	16	,	,	PUNCT
ejpam-6761	111	17	µ+(x	µ+(x	PROPN
ejpam-6761	111	18	)	)	PUNCT
ejpam-6761	111	19	∈	∈	PROPN
ejpam-6761	112	1	[	[	X
ejpam-6761	112	2	0	0	NUM
ejpam-6761	112	3	,	,	PUNCT
ejpam-6761	112	4	1	1	NUM
ejpam-6761	112	5	]	]	PUNCT
ejpam-6761	112	6	describing	describe	VERB
ejpam-6761	112	7	the	the	DET
ejpam-6761	112	8	degree	degree	NOUN
ejpam-6761	112	9	to	to	PART
ejpam-6761	112	10	which	which	PRON
ejpam-6761	112	11	x	x	PRON
ejpam-6761	112	12	satisfies	satisfy	VERB
ejpam-6761	112	13	a	a	DET
ejpam-6761	112	14	property	property	NOUN
ejpam-6761	112	15	and	and	CCONJ
ejpam-6761	112	16	its	its	PRON
ejpam-6761	112	17	counter	counter	NOUN
ejpam-6761	112	18	-	-	NOUN
ejpam-6761	112	19	property	property	NOUN
ejpam-6761	112	20	.	.	PUNCT
ejpam-6761	113	1	in	in	ADP
ejpam-6761	113	2	a	a	DET
ejpam-6761	113	3	bipolar	bipolar	ADV
ejpam-6761	113	4	-	-	PUNCT
ejpam-6761	113	5	valued	value	VERB
ejpam-6761	113	6	fuzzy	fuzzy	ADJ
ejpam-6761	113	7	set	set	NOUN
ejpam-6761	113	8	(	(	PUNCT
ejpam-6761	113	9	bvfs	bvfs	ADJ
ejpam-6761	113	10	)	)	PUNCT
ejpam-6761	113	11	a	a	DET
ejpam-6761	113	12	single	single	ADJ
ejpam-6761	113	13	membership	membership	NOUN
ejpam-6761	113	14	map	map	NOUN
ejpam-6761	113	15	µ(x	µ(x	NOUN
ejpam-6761	113	16	)	)	PUNCT
ejpam-6761	113	17	∈	∈	NOUN
ejpam-6761	114	1	[	[	X
ejpam-6761	114	2	−1	−1	NOUN
ejpam-6761	114	3	,	,	PUNCT
ejpam-6761	114	4	1	1	NUM
ejpam-6761	114	5	]	]	PUNCT
ejpam-6761	114	6	carries	carry	VERB
ejpam-6761	114	7	both	both	DET
ejpam-6761	114	8	directions	direction	NOUN
ejpam-6761	114	9	:	:	PUNCT
ejpam-6761	114	10	positive	positive	ADJ
ejpam-6761	114	11	values	value	NOUN
ejpam-6761	114	12	indicate	indicate	VERB
ejpam-6761	114	13	positive	positive	ADJ
ejpam-6761	114	14	membership	membership	NOUN
ejpam-6761	114	15	and	and	CCONJ
ejpam-6761	114	16	negative	negative	ADJ
ejpam-6761	114	17	values	value	NOUN
ejpam-6761	114	18	indicate	indicate	VERB
ejpam-6761	114	19	negative	negative	ADJ
ejpam-6761	114	20	membership	membership	NOUN
ejpam-6761	114	21	.	.	PUNCT
ejpam-6761	115	1	our	our	PRON
ejpam-6761	115	2	bvf	bvf	NOUN
ejpam-6761	115	3	-	-	PUNCT
ejpam-6761	115	4	space	space	NOUN
ejpam-6761	115	5	adopts	adopt	VERB
ejpam-6761	115	6	the	the	DET
ejpam-6761	115	7	latter	latter	ADJ
ejpam-6761	115	8	representation	representation	NOUN
ejpam-6761	115	9	(	(	PUNCT
ejpam-6761	115	10	with	with	ADP
ejpam-6761	115	11	explicit	explicit	ADJ
ejpam-6761	115	12	positive	positive	ADJ
ejpam-6761	115	13	/	/	SYM
ejpam-6761	115	14	negative	negative	ADJ
ejpam-6761	115	15	channels	channel	NOUN
ejpam-6761	115	16	when	when	SCONJ
ejpam-6761	115	17	convenient	convenient	ADJ
ejpam-6761	115	18	)	)	PUNCT
ejpam-6761	115	19	and	and	CCONJ
ejpam-6761	115	20	the	the	DET
ejpam-6761	115	21	bvfbo	bvfbo	NOUN
ejpam-6761	115	22	acts	act	VERB
ejpam-6761	115	23	compatibly	compatibly	ADV
ejpam-6761	115	24	on	on	ADP
ejpam-6761	115	25	[	[	X
ejpam-6761	115	26	−1	−1	NOUN
ejpam-6761	115	27	,	,	PUNCT
ejpam-6761	115	28	0]×	0]×	PROPN
ejpam-6761	116	1	[	[	X
ejpam-6761	116	2	0	0	NUM
ejpam-6761	116	3	,	,	PUNCT
ejpam-6761	116	4	1	1	NUM
ejpam-6761	116	5	]	]	PUNCT
ejpam-6761	116	6	.	.	PUNCT
ejpam-6761	117	1	definition	definition	NOUN
ejpam-6761	117	2	3	3	NUM
ejpam-6761	117	3	(	(	PUNCT
ejpam-6761	117	4	[	[	X
ejpam-6761	117	5	22	22	NUM
ejpam-6761	117	6	]	]	PUNCT
ejpam-6761	117	7	)	)	PUNCT
ejpam-6761	117	8	.	.	PUNCT
ejpam-6761	118	1	a	a	DET
ejpam-6761	118	2	bipolar	bipolar	ADV
ejpam-6761	118	3	-	-	PUNCT
ejpam-6761	118	4	valued	value	VERB
ejpam-6761	118	5	fuzzy	fuzzy	NOUN
ejpam-6761	118	6	set	set	VERB
ejpam-6761	118	7	a	a	PRON
ejpam-6761	118	8	is	be	AUX
ejpam-6761	118	9	called	call	VERB
ejpam-6761	118	10	a	a	DET
ejpam-6761	118	11	bipolar	bipolar	ADV
ejpam-6761	118	12	-	-	PUNCT
ejpam-6761	118	13	valued	value	VERB
ejpam-6761	118	14	fuzzy	fuzzy	ADJ
ejpam-6761	118	15	subsemigroup	subsemigroup	ADV
ejpam-6761	118	16	in	in	ADP
ejpam-6761	118	17	a	a	DET
ejpam-6761	118	18	semigroup	semigroup	NOUN
ejpam-6761	118	19	s	s	X
ejpam-6761	118	20	if	if	SCONJ
ejpam-6761	118	21	µa(x	µa(x	NOUN
ejpam-6761	118	22	·	·	PUNCT
ejpam-6761	118	23	y	y	X
ejpam-6761	118	24	)	)	PUNCT
ejpam-6761	118	25	≥	≥	NOUN
ejpam-6761	118	26	min	min	NOUN
ejpam-6761	118	27	(	(	PUNCT
ejpam-6761	118	28	µa(x	µa(x	NOUN
ejpam-6761	118	29	)	)	PUNCT
ejpam-6761	118	30	,	,	PUNCT
ejpam-6761	118	31	µa(y	µa(y	NOUN
ejpam-6761	118	32	)	)	PUNCT
ejpam-6761	118	33	)	)	PUNCT
ejpam-6761	118	34	for	for	ADP
ejpam-6761	118	35	all	all	DET
ejpam-6761	118	36	x	x	NOUN
ejpam-6761	118	37	,	,	PUNCT
ejpam-6761	118	38	y	y	PROPN
ejpam-6761	118	39	∈	∈	PROPN
ejpam-6761	118	40	s.	s.	PROPN
ejpam-6761	118	41	this	this	PRON
ejpam-6761	118	42	guarantees	guarantee	VERB
ejpam-6761	118	43	that	that	SCONJ
ejpam-6761	118	44	the	the	DET
ejpam-6761	118	45	characteristics	characteristic	NOUN
ejpam-6761	118	46	of	of	ADP
ejpam-6761	118	47	the	the	DET
ejpam-6761	118	48	subsemigroup	subsemigroup	NOUN
ejpam-6761	118	49	are	be	AUX
ejpam-6761	118	50	maintained	maintain	VERB
ejpam-6761	118	51	within	within	ADP
ejpam-6761	118	52	the	the	DET
ejpam-6761	118	53	fuzzy	fuzzy	ADJ
ejpam-6761	118	54	framework	framework	NOUN
ejpam-6761	118	55	.	.	PUNCT
ejpam-6761	119	1	definition	definition	NOUN
ejpam-6761	119	2	4	4	NUM
ejpam-6761	119	3	(	(	PUNCT
ejpam-6761	119	4	[	[	X
ejpam-6761	119	5	1	1	NUM
ejpam-6761	119	6	]	]	NUM
ejpam-6761	119	7	)	)	PUNCT
ejpam-6761	119	8	.	.	PUNCT
ejpam-6761	120	1	rosenfeld	rosenfeld	PROPN
ejpam-6761	120	2	expanded	expand	VERB
ejpam-6761	120	3	the	the	DET
ejpam-6761	120	4	idea	idea	NOUN
ejpam-6761	120	5	of	of	ADP
ejpam-6761	120	6	fuzzy	fuzzy	ADJ
ejpam-6761	120	7	sets	set	NOUN
ejpam-6761	120	8	to	to	ADP
ejpam-6761	120	9	group	group	NOUN
ejpam-6761	120	10	theory	theory	NOUN
ejpam-6761	120	11	through	through	ADP
ejpam-6761	120	12	the	the	DET
ejpam-6761	120	13	introduction	introduction	NOUN
ejpam-6761	120	14	of	of	ADP
ejpam-6761	120	15	fuzzy	fuzzy	ADJ
ejpam-6761	120	16	subgroups	subgroup	NOUN
ejpam-6761	120	17	.	.	PUNCT
ejpam-6761	121	1	a	a	DET
ejpam-6761	121	2	fuzzy	fuzzy	NOUN
ejpam-6761	121	3	subset	subset	VERB
ejpam-6761	121	4	a	a	PRON
ejpam-6761	121	5	in	in	ADP
ejpam-6761	121	6	group	group	NOUN
ejpam-6761	121	7	g	g	PROPN
ejpam-6761	121	8	is	be	AUX
ejpam-6761	121	9	termed	term	VERB
ejpam-6761	121	10	a	a	DET
ejpam-6761	121	11	fuzzy	fuzzy	ADJ
ejpam-6761	121	12	subgroup	subgroup	NOUN
ejpam-6761	121	13	when	when	SCONJ
ejpam-6761	121	14	:	:	PUNCT
ejpam-6761	121	15	(	(	PUNCT
ejpam-6761	121	16	i	i	NOUN
ejpam-6761	121	17	)	)	PUNCT
ejpam-6761	121	18	µa(x	µa(x	PUNCT
ejpam-6761	121	19	·	·	PUNCT
ejpam-6761	121	20	y	y	X
ejpam-6761	121	21	)	)	PUNCT
ejpam-6761	121	22	≥	≥	PROPN
ejpam-6761	121	23	min	min	NOUN
ejpam-6761	121	24	(	(	PUNCT
ejpam-6761	121	25	µa(x	µa(x	NOUN
ejpam-6761	121	26	)	)	PUNCT
ejpam-6761	121	27	,	,	PUNCT
ejpam-6761	121	28	µa(y	µa(y	NOUN
ejpam-6761	121	29	)	)	PUNCT
ejpam-6761	121	30	)	)	PUNCT
ejpam-6761	121	31	for	for	ADP
ejpam-6761	121	32	all	all	DET
ejpam-6761	121	33	x	x	NOUN
ejpam-6761	121	34	,	,	PUNCT
ejpam-6761	121	35	y	y	PROPN
ejpam-6761	121	36	∈	∈	PROPN
ejpam-6761	121	37	g	g	PROPN
ejpam-6761	121	38	,	,	PUNCT
ejpam-6761	121	39	(	(	PUNCT
ejpam-6761	121	40	ii	ii	NOUN
ejpam-6761	121	41	)	)	PUNCT
ejpam-6761	121	42	µa(e	µa(e	X
ejpam-6761	121	43	)	)	PUNCT
ejpam-6761	121	44	=	=	SYM
ejpam-6761	121	45	1	1	NUM
ejpam-6761	121	46	where	where	SCONJ
ejpam-6761	121	47	e	e	NOUN
ejpam-6761	121	48	is	be	AUX
ejpam-6761	121	49	the	the	DET
ejpam-6761	121	50	identity	identity	NOUN
ejpam-6761	121	51	element	element	NOUN
ejpam-6761	121	52	of	of	ADP
ejpam-6761	121	53	g	g	PROPN
ejpam-6761	121	54	,	,	PUNCT
ejpam-6761	121	55	(	(	PUNCT
ejpam-6761	121	56	iii	iii	NOUN
ejpam-6761	121	57	)	)	PUNCT
ejpam-6761	121	58	µa(x	µa(x	NOUN
ejpam-6761	121	59	−1	−1	NOUN
ejpam-6761	121	60	)	)	PUNCT
ejpam-6761	121	61	=	=	NOUN
ejpam-6761	122	1	µa(x	µa(x	X
ejpam-6761	122	2	)	)	PUNCT
ejpam-6761	123	1	for	for	ADP
ejpam-6761	123	2	all	all	DET
ejpam-6761	123	3	x	x	SYM
ejpam-6761	123	4	∈	∈	PROPN
ejpam-6761	123	5	g.	g.	NOUN
ejpam-6761	123	6	these	these	DET
ejpam-6761	123	7	conditions	condition	NOUN
ejpam-6761	123	8	ensure	ensure	VERB
ejpam-6761	123	9	that	that	SCONJ
ejpam-6761	123	10	the	the	DET
ejpam-6761	123	11	fuzziness	fuzziness	NOUN
ejpam-6761	123	12	respects	respect	VERB
ejpam-6761	123	13	the	the	DET
ejpam-6761	123	14	group	group	NOUN
ejpam-6761	123	15	structure	structure	NOUN
ejpam-6761	123	16	.	.	PUNCT
ejpam-6761	124	1	definition	definition	NOUN
ejpam-6761	124	2	5	5	NUM
ejpam-6761	124	3	(	(	PUNCT
ejpam-6761	124	4	[	[	X
ejpam-6761	124	5	4	4	NUM
ejpam-6761	124	6	]	]	NUM
ejpam-6761	124	7	)	)	PUNCT
ejpam-6761	124	8	.	.	PUNCT
ejpam-6761	125	1	a	a	DET
ejpam-6761	125	2	fuzzy	fuzzy	ADJ
ejpam-6761	125	3	relation	relation	NOUN
ejpam-6761	125	4	r	r	NOUN
ejpam-6761	125	5	between	between	ADP
ejpam-6761	125	6	sets	set	NOUN
ejpam-6761	125	7	℧	℧	PROPN
ejpam-6761	125	8	and	and	CCONJ
ejpam-6761	125	9	y	y	PROPN
ejpam-6761	125	10	is	be	AUX
ejpam-6761	125	11	a	a	DET
ejpam-6761	125	12	fuzzy	fuzzy	ADJ
ejpam-6761	125	13	set	set	NOUN
ejpam-6761	125	14	in	in	ADP
ejpam-6761	125	15	the	the	DET
ejpam-6761	125	16	cartesian	cartesian	ADJ
ejpam-6761	125	17	product	product	NOUN
ejpam-6761	125	18	x	x	X
ejpam-6761	125	19	×	×	PROPN
ejpam-6761	125	20	y	y	PROPN
ejpam-6761	125	21	with	with	ADP
ejpam-6761	125	22	a	a	DET
ejpam-6761	125	23	membership	membership	NOUN
ejpam-6761	125	24	function	function	NOUN
ejpam-6761	125	25	µr	µr	ADP
ejpam-6761	125	26	:	:	PUNCT
ejpam-6761	125	27	℧	℧	PROPN
ejpam-6761	125	28	×	×	NOUN
ejpam-6761	125	29	y	y	PROPN
ejpam-6761	125	30	→	→	SYM
ejpam-6761	126	1	[	[	X
ejpam-6761	126	2	0	0	NUM
ejpam-6761	126	3	,	,	PUNCT
ejpam-6761	126	4	1	1	NUM
ejpam-6761	126	5	]	]	PUNCT
ejpam-6761	126	6	.	.	PUNCT
ejpam-6761	127	1	definition	definition	NOUN
ejpam-6761	127	2	6	6	NUM
ejpam-6761	127	3	(	(	PUNCT
ejpam-6761	127	4	[	[	X
ejpam-6761	127	5	4	4	NUM
ejpam-6761	127	6	]	]	NUM
ejpam-6761	127	7	)	)	PUNCT
ejpam-6761	127	8	.	.	PUNCT
ejpam-6761	128	1	a	a	DET
ejpam-6761	128	2	fuzzy	fuzzy	ADJ
ejpam-6761	128	3	function	function	NOUN
ejpam-6761	128	4	from	from	ADP
ejpam-6761	128	5	a	a	DET
ejpam-6761	128	6	fuzzy	fuzzy	ADJ
ejpam-6761	128	7	set	set	NOUN
ejpam-6761	128	8	a	a	PRON
ejpam-6761	128	9	in	in	ADP
ejpam-6761	128	10	℧	℧	PROPN
ejpam-6761	128	11	to	to	ADP
ejpam-6761	128	12	a	a	DET
ejpam-6761	128	13	fuzzy	fuzzy	ADJ
ejpam-6761	128	14	set	set	NOUN
ejpam-6761	128	15	b	b	PROPN
ejpam-6761	128	16	in	in	ADP
ejpam-6761	128	17	y	y	PROPN
ejpam-6761	128	18	is	be	AUX
ejpam-6761	128	19	a	a	DET
ejpam-6761	128	20	function	function	NOUN
ejpam-6761	128	21	f	f	NOUN
ejpam-6761	128	22	:	:	PUNCT
ejpam-6761	128	23	℧	℧	PROPN
ejpam-6761	128	24	→	→	SYM
ejpam-6761	128	25	y	y	PROPN
ejpam-6761	128	26	such	such	ADJ
ejpam-6761	128	27	that	that	SCONJ
ejpam-6761	128	28	the	the	DET
ejpam-6761	128	29	membership	membership	NOUN
ejpam-6761	128	30	value	value	NOUN
ejpam-6761	128	31	of	of	ADP
ejpam-6761	128	32	f(x	f(x	PROPN
ejpam-6761	128	33	)	)	PUNCT
ejpam-6761	128	34	in	in	ADP
ejpam-6761	128	35	b	b	NOUN
ejpam-6761	128	36	is	be	AUX
ejpam-6761	128	37	related	relate	VERB
ejpam-6761	128	38	to	to	ADP
ejpam-6761	128	39	the	the	DET
ejpam-6761	128	40	membership	membership	NOUN
ejpam-6761	128	41	value	value	NOUN
ejpam-6761	128	42	of	of	ADP
ejpam-6761	128	43	x	x	PUNCT
ejpam-6761	128	44	in	in	ADP
ejpam-6761	128	45	a.	a.	NOUN
ejpam-6761	128	46	definition	definition	NOUN
ejpam-6761	128	47	7	7	NUM
ejpam-6761	128	48	(	(	PUNCT
ejpam-6761	128	49	[	[	X
ejpam-6761	128	50	3	3	NUM
ejpam-6761	128	51	]	]	NUM
ejpam-6761	128	52	)	)	PUNCT
ejpam-6761	128	53	.	.	PUNCT
ejpam-6761	129	1	a	a	DET
ejpam-6761	129	2	f	f	NOUN
ejpam-6761	129	3	-	-	PUNCT
ejpam-6761	129	4	space	space	NOUN
ejpam-6761	129	5	(	(	PUNCT
ejpam-6761	129	6	℧	℧	PROPN
ejpam-6761	129	7	,	,	PUNCT
ejpam-6761	129	8	i	i	PRON
ejpam-6761	129	9	=	=	PUNCT
ejpam-6761	130	1	[	[	X
ejpam-6761	130	2	0	0	NUM
ejpam-6761	130	3	,	,	PUNCT
ejpam-6761	130	4	1	1	NUM
ejpam-6761	130	5	]	]	PUNCT
ejpam-6761	130	6	)	)	PUNCT
ejpam-6761	130	7	is	be	AUX
ejpam-6761	130	8	the	the	DET
ejpam-6761	130	9	set	set	NOUN
ejpam-6761	130	10	of	of	ADP
ejpam-6761	130	11	all	all	DET
ejpam-6761	130	12	ordered	order	VERB
ejpam-6761	130	13	pairs	pair	NOUN
ejpam-6761	130	14	(	(	PUNCT
ejpam-6761	130	15	x	x	X
ejpam-6761	130	16	,	,	PUNCT
ejpam-6761	130	17	i	i	PROPN
ejpam-6761	130	18	)	)	PUNCT
ejpam-6761	130	19	,	,	PUNCT
ejpam-6761	130	20	x	x	PUNCT
ejpam-6761	130	21	∈	∈	PROPN
ejpam-6761	130	22	℧	℧	PROPN
ejpam-6761	130	23	,	,	PUNCT
ejpam-6761	130	24	(	(	PUNCT
ejpam-6761	130	25	℧	℧	PROPN
ejpam-6761	130	26	,	,	PUNCT
ejpam-6761	130	27	i	i	NOUN
ejpam-6761	130	28	)	)	PUNCT
ejpam-6761	130	29	=	=	PRON
ejpam-6761	130	30	{	{	PUNCT
ejpam-6761	130	31	(	(	PUNCT
ejpam-6761	130	32	x	x	NOUN
ejpam-6761	130	33	,	,	PUNCT
ejpam-6761	130	34	i	i	PROPN
ejpam-6761	130	35	)	)	PUNCT
ejpam-6761	130	36	:	:	PUNCT
ejpam-6761	131	1	x	x	X
ejpam-6761	131	2	∈	∈	PROPN
ejpam-6761	131	3	℧	℧	NOUN
ejpam-6761	131	4	}	}	PUNCT
ejpam-6761	131	5	where	where	SCONJ
ejpam-6761	131	6	(	(	PUNCT
ejpam-6761	131	7	x	x	X
ejpam-6761	131	8	,	,	PUNCT
ejpam-6761	131	9	i	i	NOUN
ejpam-6761	131	10	)	)	PUNCT
ejpam-6761	131	11	=	=	PRON
ejpam-6761	131	12	{	{	PUNCT
ejpam-6761	131	13	(	(	PUNCT
ejpam-6761	131	14	x	x	NOUN
ejpam-6761	131	15	,	,	PUNCT
ejpam-6761	131	16	r	r	NOUN
ejpam-6761	131	17	)	)	PUNCT
ejpam-6761	131	18	:	:	PUNCT
ejpam-6761	131	19	r	r	X
ejpam-6761	131	20	∈	∈	PROPN
ejpam-6761	131	21	i	i	X
ejpam-6761	131	22	}	}	PUNCT
ejpam-6761	131	23	.	.	PUNCT
ejpam-6761	132	1	the	the	DET
ejpam-6761	132	2	ordered	order	VERB
ejpam-6761	132	3	pair	pair	NOUN
ejpam-6761	132	4	(	(	PUNCT
ejpam-6761	132	5	x	x	NOUN
ejpam-6761	132	6	,	,	PUNCT
ejpam-6761	132	7	i	i	NOUN
ejpam-6761	132	8	)	)	PUNCT
ejpam-6761	132	9	is	be	AUX
ejpam-6761	132	10	called	call	VERB
ejpam-6761	132	11	a	a	DET
ejpam-6761	132	12	fuzzy	fuzzy	ADJ
ejpam-6761	132	13	element	element	NOUN
ejpam-6761	132	14	in	in	ADP
ejpam-6761	132	15	the	the	DET
ejpam-6761	132	16	f	f	NOUN
ejpam-6761	132	17	-	-	PUNCT
ejpam-6761	132	18	space	space	NOUN
ejpam-6761	132	19	(	(	PUNCT
ejpam-6761	132	20	℧	℧	PROPN
ejpam-6761	132	21	,	,	PUNCT
ejpam-6761	132	22	i	i	PROPN
ejpam-6761	132	23	)	)	PUNCT
ejpam-6761	132	24	.	.	PUNCT
ejpam-6761	133	1	f.	f.	PROPN
ejpam-6761	133	2	al	al	PROPN
ejpam-6761	133	3	-	-	PROPN
ejpam-6761	133	4	zu’bi	zu’bi	PROPN
ejpam-6761	133	5	et	et	NOUN
ejpam-6761	133	6	al	al	PROPN
ejpam-6761	133	7	.	.	PUNCT
ejpam-6761	133	8	/	/	SYM
ejpam-6761	133	9	eur	eur	PROPN
ejpam-6761	133	10	.	.	PUNCT
ejpam-6761	134	1	j.	j.	PROPN
ejpam-6761	134	2	pure	pure	PROPN
ejpam-6761	134	3	appl	appl	PROPN
ejpam-6761	134	4	.	.	PROPN
ejpam-6761	134	5	math	math	PROPN
ejpam-6761	134	6	,	,	PUNCT
ejpam-6761	134	7	18	18	NUM
ejpam-6761	134	8	(	(	PUNCT
ejpam-6761	134	9	4	4	NUM
ejpam-6761	134	10	)	)	PUNCT
ejpam-6761	134	11	(	(	PUNCT
ejpam-6761	134	12	2025	2025	NUM
ejpam-6761	134	13	)	)	PUNCT
ejpam-6761	134	14	,	,	PUNCT
ejpam-6761	134	15	6761	6761	NUM
ejpam-6761	134	16	7	7	NUM
ejpam-6761	134	17	of	of	ADP
ejpam-6761	134	18	28	28	NUM
ejpam-6761	134	19	definition	definition	NOUN
ejpam-6761	134	20	8	8	NUM
ejpam-6761	134	21	(	(	PUNCT
ejpam-6761	134	22	[	[	X
ejpam-6761	134	23	3	3	NUM
ejpam-6761	134	24	]	]	NUM
ejpam-6761	134	25	)	)	PUNCT
ejpam-6761	134	26	.	.	PUNCT
ejpam-6761	135	1	a	a	DET
ejpam-6761	135	2	fuzzy	fuzzy	ADJ
ejpam-6761	135	3	group	group	NOUN
ejpam-6761	135	4	(	(	PUNCT
ejpam-6761	135	5	(	(	PUNCT
ejpam-6761	135	6	℧	℧	PROPN
ejpam-6761	135	7	,	,	PUNCT
ejpam-6761	135	8	i	i	PROPN
ejpam-6761	135	9	)	)	PUNCT
ejpam-6761	135	10	,	,	PUNCT
ejpam-6761	135	11	f	f	PROPN
ejpam-6761	135	12	)	)	PUNCT
ejpam-6761	135	13	is	be	AUX
ejpam-6761	135	14	called	call	VERB
ejpam-6761	135	15	a	a	DET
ejpam-6761	135	16	commutative	commutative	ADJ
ejpam-6761	135	17	or	or	CCONJ
ejpam-6761	135	18	abelian	abelian	ADJ
ejpam-6761	135	19	fuzzy	fuzzy	ADJ
ejpam-6761	135	20	group	group	NOUN
ejpam-6761	135	21	if	if	SCONJ
ejpam-6761	135	22	(	(	PUNCT
ejpam-6761	135	23	x	x	X
ejpam-6761	135	24	,	,	PUNCT
ejpam-6761	135	25	i)f	i)f	ADJ
ejpam-6761	135	26	(	(	PUNCT
ejpam-6761	135	27	y	y	NOUN
ejpam-6761	135	28	,	,	PUNCT
ejpam-6761	135	29	i	i	NOUN
ejpam-6761	135	30	)	)	PUNCT
ejpam-6761	135	31	=	=	SYM
ejpam-6761	135	32	(	(	PUNCT
ejpam-6761	135	33	y	y	NOUN
ejpam-6761	135	34	,	,	PUNCT
ejpam-6761	135	35	i)f	i)f	ADJ
ejpam-6761	135	36	(	(	PUNCT
ejpam-6761	135	37	x	x	X
ejpam-6761	135	38	,	,	PUNCT
ejpam-6761	135	39	i	i	PROPN
ejpam-6761	135	40	)	)	PUNCT
ejpam-6761	135	41	,	,	PUNCT
ejpam-6761	135	42	for	for	ADP
ejpam-6761	135	43	all	all	DET
ejpam-6761	135	44	fuzzy	fuzzy	ADJ
ejpam-6761	135	45	elements	element	NOUN
ejpam-6761	135	46	(	(	PUNCT
ejpam-6761	135	47	x	x	X
ejpam-6761	135	48	,	,	PUNCT
ejpam-6761	135	49	i	i	NOUN
ejpam-6761	135	50	)	)	PUNCT
ejpam-6761	135	51	and	and	CCONJ
ejpam-6761	135	52	(	(	PUNCT
ejpam-6761	135	53	y	y	PROPN
ejpam-6761	135	54	,	,	PUNCT
ejpam-6761	135	55	i	i	NOUN
ejpam-6761	135	56	)	)	PUNCT
ejpam-6761	135	57	of	of	ADP
ejpam-6761	135	58	the	the	DET
ejpam-6761	135	59	fspace	fspace	NOUN
ejpam-6761	135	60	(	(	PUNCT
ejpam-6761	135	61	℧	℧	PROPN
ejpam-6761	135	62	,	,	PUNCT
ejpam-6761	135	63	i	i	PROPN
ejpam-6761	135	64	)	)	PUNCT
ejpam-6761	135	65	.	.	PUNCT
ejpam-6761	136	1	it	it	PRON
ejpam-6761	136	2	is	be	AUX
ejpam-6761	136	3	clear	clear	ADJ
ejpam-6761	136	4	that	that	SCONJ
ejpam-6761	136	5	(	(	PUNCT
ejpam-6761	136	6	(	(	PUNCT
ejpam-6761	136	7	℧	℧	PROPN
ejpam-6761	136	8	,	,	PUNCT
ejpam-6761	136	9	i	i	PROPN
ejpam-6761	136	10	)	)	PUNCT
ejpam-6761	136	11	,	,	PUNCT
ejpam-6761	136	12	f	f	PROPN
ejpam-6761	136	13	)	)	PUNCT
ejpam-6761	136	14	is	be	AUX
ejpam-6761	136	15	a	a	DET
ejpam-6761	136	16	commutative	commutative	ADJ
ejpam-6761	136	17	fuzzy	fuzzy	ADJ
ejpam-6761	136	18	group	group	NOUN
ejpam-6761	136	19	iff	iff	PROPN
ejpam-6761	136	20	(	(	PUNCT
ejpam-6761	136	21	℧	℧	PROPN
ejpam-6761	136	22	,	,	PUNCT
ejpam-6761	136	23	f	f	PROPN
ejpam-6761	136	24	)	)	PUNCT
ejpam-6761	136	25	is	be	AUX
ejpam-6761	136	26	an	an	DET
ejpam-6761	136	27	ordinary	ordinary	ADJ
ejpam-6761	136	28	commutative	commutative	ADJ
ejpam-6761	136	29	group	group	NOUN
ejpam-6761	136	30	.	.	PUNCT
ejpam-6761	137	1	definition	definition	NOUN
ejpam-6761	137	2	9	9	NUM
ejpam-6761	137	3	(	(	PUNCT
ejpam-6761	137	4	[	[	X
ejpam-6761	137	5	6	6	NUM
ejpam-6761	137	6	]	]	NUM
ejpam-6761	137	7	)	)	PUNCT
ejpam-6761	137	8	.	.	PUNCT
ejpam-6761	138	1	an	an	DET
ejpam-6761	138	2	intuitionistic	intuitionistic	ADJ
ejpam-6761	138	3	fuzzy	fuzzy	ADJ
ejpam-6761	138	4	binary	binary	ADJ
ejpam-6761	138	5	operation	operation	NOUN
ejpam-6761	138	6	(	(	PUNCT
ejpam-6761	138	7	ifbo	ifbo	PROPN
ejpam-6761	138	8	)	)	PUNCT
ejpam-6761	138	9	f	f	PROPN
ejpam-6761	138	10	on	on	ADP
ejpam-6761	138	11	an	an	DET
ejpam-6761	138	12	intuitionistic	intuitionistic	ADJ
ejpam-6761	138	13	fuzzy	fuzzy	ADJ
ejpam-6761	138	14	space	space	NOUN
ejpam-6761	138	15	(	(	PUNCT
ejpam-6761	138	16	if	if	SCONJ
ejpam-6761	138	17	-	-	PUNCT
ejpam-6761	138	18	space	space	NOUN
ejpam-6761	138	19	)	)	PUNCT
ejpam-6761	138	20	(	(	PUNCT
ejpam-6761	138	21	℧	℧	PROPN
ejpam-6761	138	22	,	,	PUNCT
ejpam-6761	138	23	i	i	PRON
ejpam-6761	138	24	,	,	PUNCT
ejpam-6761	138	25	i	i	PROPN
ejpam-6761	138	26	)	)	PUNCT
ejpam-6761	138	27	is	be	AUX
ejpam-6761	138	28	an	an	DET
ejpam-6761	138	29	intuitionistic	intuitionistic	ADJ
ejpam-6761	138	30	fuzzy	fuzzy	ADJ
ejpam-6761	138	31	function	function	NOUN
ejpam-6761	138	32	f	f	NOUN
ejpam-6761	138	33	:	:	PUNCT
ejpam-6761	138	34	(	(	PUNCT
ejpam-6761	138	35	℧	℧	PROPN
ejpam-6761	138	36	,	,	PUNCT
ejpam-6761	138	37	i	i	PRON
ejpam-6761	138	38	,	,	PUNCT
ejpam-6761	138	39	i)×	i)×	PROPN
ejpam-6761	138	40	(	(	PUNCT
ejpam-6761	138	41	℧	℧	PROPN
ejpam-6761	138	42	,	,	PUNCT
ejpam-6761	138	43	i	i	PRON
ejpam-6761	138	44	,	,	PUNCT
ejpam-6761	138	45	i	i	PROPN
ejpam-6761	138	46	)	)	PUNCT
ejpam-6761	138	47	→	→	PUNCT
ejpam-6761	138	48	(	(	PUNCT
ejpam-6761	138	49	℧	℧	PROPN
ejpam-6761	138	50	,	,	PUNCT
ejpam-6761	138	51	i	i	PRON
ejpam-6761	138	52	,	,	PUNCT
ejpam-6761	138	53	i	i	PROPN
ejpam-6761	138	54	)	)	PUNCT
ejpam-6761	138	55	with	with	ADP
ejpam-6761	138	56	comembership	comembership	NOUN
ejpam-6761	138	57	functions	function	NOUN
ejpam-6761	138	58	f	f	PROPN
ejpam-6761	138	59	xy	xy	PROPN
ejpam-6761	138	60	and	and	CCONJ
ejpam-6761	138	61	cononmembership	cononmembership	NOUN
ejpam-6761	138	62	functions	function	NOUN
ejpam-6761	138	63	fxy	fxy	NOUN
ejpam-6761	138	64	satisfying	satisfying	NOUN
ejpam-6761	138	65	:	:	PUNCT
ejpam-6761	138	66	(	(	PUNCT
ejpam-6761	138	67	1	1	X
ejpam-6761	138	68	)	)	PUNCT
ejpam-6761	138	69	f	f	NOUN
ejpam-6761	138	70	xy	xy	INTJ
ejpam-6761	138	71	(	(	PUNCT
ejpam-6761	138	72	r	r	NOUN
ejpam-6761	138	73	,	,	PUNCT
ejpam-6761	138	74	s	s	PART
ejpam-6761	138	75	)	)	PUNCT
ejpam-6761	138	76	̸=	̸=	PROPN
ejpam-6761	138	77	0	0	NUM
ejpam-6761	138	78	iff	iff	PROPN
ejpam-6761	138	79	r	r	PROPN
ejpam-6761	138	80	̸=	̸=	PROPN
ejpam-6761	138	81	0	0	NUM
ejpam-6761	138	82	,	,	PUNCT
ejpam-6761	138	83	s	s	VERB
ejpam-6761	138	84	̸=	̸=	PROPN
ejpam-6761	138	85	0	0	NUM
ejpam-6761	138	86	and	and	CCONJ
ejpam-6761	138	87	fxy(w	fxy(w	PROPN
ejpam-6761	138	88	,	,	PUNCT
ejpam-6761	138	89	z	z	NOUN
ejpam-6761	138	90	)	)	PUNCT
ejpam-6761	138	91	̸=	̸=	PROPN
ejpam-6761	138	92	1	1	NUM
ejpam-6761	138	93	iff	iff	PROPN
ejpam-6761	138	94	w	w	PROPN
ejpam-6761	138	95	̸=	̸=	PROPN
ejpam-6761	138	96	1	1	NUM
ejpam-6761	138	97	,	,	PUNCT
ejpam-6761	138	98	z	z	NOUN
ejpam-6761	138	99	̸=	̸=	PROPN
ejpam-6761	138	100	1	1	NUM
ejpam-6761	138	101	.	.	PUNCT
ejpam-6761	139	1	(	(	PUNCT
ejpam-6761	139	2	2	2	X
ejpam-6761	139	3	)	)	PUNCT
ejpam-6761	139	4	f	f	NOUN
ejpam-6761	139	5	xy	xy	PROPN
ejpam-6761	139	6	and	and	CCONJ
ejpam-6761	139	7	fxy	fxy	NOUN
ejpam-6761	139	8	are	be	AUX
ejpam-6761	139	9	onto	onto	ADP
ejpam-6761	139	10	.	.	PUNCT
ejpam-6761	140	1	that	that	PRON
ejpam-6761	140	2	is	be	AUX
ejpam-6761	140	3	,	,	PUNCT
ejpam-6761	140	4	f	f	PROPN
ejpam-6761	140	5	xy	xy	INTJ
ejpam-6761	141	1	(	(	PUNCT
ejpam-6761	141	2	i	i	PRON
ejpam-6761	141	3	×	×	VERB
ejpam-6761	141	4	i	i	NOUN
ejpam-6761	141	5	)	)	PUNCT
ejpam-6761	142	1	=	=	SYM
ejpam-6761	142	2	i	i	PRON
ejpam-6761	142	3	and	and	CCONJ
ejpam-6761	142	4	fxy(i	fxy(i	PROPN
ejpam-6761	142	5	×	×	NOUN
ejpam-6761	142	6	i	i	NOUN
ejpam-6761	142	7	)	)	PUNCT
ejpam-6761	143	1	=	=	SYM
ejpam-6761	143	2	i	i	PROPN
ejpam-6761	143	3	,	,	PUNCT
ejpam-6761	143	4	where	where	SCONJ
ejpam-6761	143	5	i	i	PRON
ejpam-6761	143	6	=	=	PUNCT
ejpam-6761	144	1	[	[	X
ejpam-6761	144	2	0	0	NUM
ejpam-6761	144	3	,	,	PUNCT
ejpam-6761	144	4	1	1	NUM
ejpam-6761	144	5	]	]	PUNCT
ejpam-6761	144	6	.	.	PUNCT
ejpam-6761	145	1	thus	thus	ADV
ejpam-6761	145	2	,	,	PUNCT
ejpam-6761	145	3	the	the	DET
ejpam-6761	145	4	intuitionistic	intuitionistic	ADJ
ejpam-6761	145	5	fuzzy	fuzzy	ADJ
ejpam-6761	145	6	binary	binary	ADJ
ejpam-6761	145	7	operation	operation	NOUN
ejpam-6761	145	8	f	f	PROPN
ejpam-6761	145	9	=	=	PUNCT
ejpam-6761	145	10	(	(	PUNCT
ejpam-6761	145	11	f	f	X
ejpam-6761	145	12	,	,	PUNCT
ejpam-6761	145	13	f	f	PROPN
ejpam-6761	145	14	xy	xy	PROPN
ejpam-6761	145	15	,	,	PUNCT
ejpam-6761	145	16	fxy	fxy	NOUN
ejpam-6761	145	17	)	)	PUNCT
ejpam-6761	145	18	over	over	ADP
ejpam-6761	145	19	the	the	DET
ejpam-6761	145	20	if	if	NOUN
ejpam-6761	145	21	-	-	PUNCT
ejpam-6761	145	22	space	space	NOUN
ejpam-6761	145	23	℧	℧	NOUN
ejpam-6761	145	24	is	be	AUX
ejpam-6761	145	25	defined	define	VERB
ejpam-6761	145	26	by	by	ADP
ejpam-6761	145	27	:	:	PUNCT
ejpam-6761	145	28	(	(	PUNCT
ejpam-6761	145	29	3	3	X
ejpam-6761	145	30	)	)	PUNCT
ejpam-6761	145	31	(	(	PUNCT
ejpam-6761	145	32	x	x	X
ejpam-6761	145	33	,	,	PUNCT
ejpam-6761	145	34	i	i	PRON
ejpam-6761	145	35	,	,	PUNCT
ejpam-6761	145	36	i)f	i)f	PROPN
ejpam-6761	145	37	(	(	PUNCT
ejpam-6761	145	38	y	y	PROPN
ejpam-6761	145	39	,	,	PUNCT
ejpam-6761	145	40	i	i	PRON
ejpam-6761	145	41	,	,	PUNCT
ejpam-6761	145	42	i	i	PROPN
ejpam-6761	145	43	)	)	PUNCT
ejpam-6761	146	1	=	=	SYM
ejpam-6761	146	2	f	f	PROPN
ejpam-6761	146	3	(	(	PUNCT
ejpam-6761	146	4	(	(	PUNCT
ejpam-6761	146	5	x	x	X
ejpam-6761	146	6	,	,	PUNCT
ejpam-6761	146	7	i	i	PRON
ejpam-6761	146	8	,	,	PUNCT
ejpam-6761	146	9	i	i	PROPN
ejpam-6761	146	10	)	)	PUNCT
ejpam-6761	146	11	,	,	PUNCT
ejpam-6761	146	12	(	(	PUNCT
ejpam-6761	146	13	y	y	X
ejpam-6761	146	14	,	,	PUNCT
ejpam-6761	146	15	i	i	PRON
ejpam-6761	146	16	,	,	PUNCT
ejpam-6761	146	17	i	i	NOUN
ejpam-6761	146	18	)	)	PUNCT
ejpam-6761	146	19	)	)	PUNCT
ejpam-6761	147	1	=	=	PRON
ejpam-6761	147	2	(	(	PUNCT
ejpam-6761	147	3	f	f	X
ejpam-6761	147	4	(	(	PUNCT
ejpam-6761	147	5	x	x	PROPN
ejpam-6761	147	6	,	,	PUNCT
ejpam-6761	147	7	y	y	PROPN
ejpam-6761	147	8	)	)	PUNCT
ejpam-6761	147	9	,	,	PUNCT
ejpam-6761	147	10	f	f	PROPN
ejpam-6761	147	11	xy	xy	PROPN
ejpam-6761	147	12	(	(	PUNCT
ejpam-6761	147	13	i×i	i×i	PROPN
ejpam-6761	147	14	)	)	PUNCT
ejpam-6761	147	15	,	,	PUNCT
ejpam-6761	147	16	fxy(i×i	fxy(i×i	ADJ
ejpam-6761	147	17	)	)	PUNCT
ejpam-6761	147	18	)	)	PUNCT
ejpam-6761	148	1	=	=	PRON
ejpam-6761	148	2	(	(	PUNCT
ejpam-6761	148	3	f	f	X
ejpam-6761	148	4	(	(	PUNCT
ejpam-6761	148	5	x	x	PROPN
ejpam-6761	148	6	,	,	PUNCT
ejpam-6761	148	7	y	y	PROPN
ejpam-6761	148	8	)	)	PUNCT
ejpam-6761	148	9	,	,	PUNCT
ejpam-6761	148	10	i	i	PRON
ejpam-6761	148	11	,	,	PUNCT
ejpam-6761	148	12	i	i	PROPN
ejpam-6761	148	13	)	)	PUNCT
ejpam-6761	148	14	where	where	SCONJ
ejpam-6761	148	15	(	(	PUNCT
ejpam-6761	148	16	x	x	X
ejpam-6761	148	17	,	,	PUNCT
ejpam-6761	148	18	i	i	PRON
ejpam-6761	148	19	,	,	PUNCT
ejpam-6761	148	20	i	i	PROPN
ejpam-6761	148	21	)	)	PUNCT
ejpam-6761	148	22	,	,	PUNCT
ejpam-6761	148	23	(	(	PUNCT
ejpam-6761	148	24	y	y	X
ejpam-6761	148	25	,	,	PUNCT
ejpam-6761	148	26	i	i	PRON
ejpam-6761	148	27	,	,	PUNCT
ejpam-6761	148	28	i	i	PROPN
ejpam-6761	148	29	)	)	PUNCT
ejpam-6761	148	30	of	of	ADP
ejpam-6761	148	31	the	the	DET
ejpam-6761	148	32	if	if	NOUN
ejpam-6761	148	33	-	-	PUNCT
ejpam-6761	148	34	space	space	NOUN
ejpam-6761	148	35	x	x	NOUN
ejpam-6761	148	36	are	be	AUX
ejpam-6761	148	37	intuitionistic	intuitionistic	ADJ
ejpam-6761	148	38	fuzzy	fuzzy	ADJ
ejpam-6761	148	39	elements	element	NOUN
ejpam-6761	148	40	(	(	PUNCT
ejpam-6761	148	41	if	if	SCONJ
ejpam-6761	148	42	-	-	PUNCT
ejpam-6761	148	43	element	element	NOUN
ejpam-6761	148	44	)	)	PUNCT
ejpam-6761	148	45	,	,	PUNCT
ejpam-6761	148	46	and	and	CCONJ
ejpam-6761	148	47	f	f	X
ejpam-6761	148	48	=	=	SYM
ejpam-6761	148	49	(	(	PUNCT
ejpam-6761	148	50	f	f	X
ejpam-6761	148	51	,	,	PUNCT
ejpam-6761	148	52	f	f	PROPN
ejpam-6761	148	53	xy	xy	PROPN
ejpam-6761	148	54	,	,	PUNCT
ejpam-6761	148	55	fxy	fxy	NOUN
ejpam-6761	148	56	)	)	PUNCT
ejpam-6761	148	57	is	be	AUX
ejpam-6761	148	58	any	any	DET
ejpam-6761	148	59	ifbo	ifbo	NOUN
ejpam-6761	148	60	defined	define	VERB
ejpam-6761	148	61	on	on	ADP
ejpam-6761	148	62	an	an	DET
ejpam-6761	148	63	if	if	NOUN
ejpam-6761	148	64	-	-	PUNCT
ejpam-6761	148	65	space	space	NOUN
ejpam-6761	148	66	℧	℧	PROPN
ejpam-6761	148	67	.	.	PUNCT
ejpam-6761	149	1	an	an	DET
ejpam-6761	149	2	ifbo	ifbo	NOUN
ejpam-6761	149	3	is	be	AUX
ejpam-6761	149	4	identified	identify	VERB
ejpam-6761	149	5	to	to	PART
ejpam-6761	149	6	be	be	AUX
ejpam-6761	149	7	uniform	uniform	ADJ
ejpam-6761	149	8	if	if	SCONJ
ejpam-6761	149	9	both	both	DET
ejpam-6761	149	10	f	f	PROPN
ejpam-6761	149	11	xy	xy	PROPN
ejpam-6761	149	12	and	and	CCONJ
ejpam-6761	149	13	fxy	fxy	NOUN
ejpam-6761	149	14	are	be	AUX
ejpam-6761	149	15	identical	identical	ADJ
ejpam-6761	149	16	.	.	PUNCT
ejpam-6761	150	1	that	that	PRON
ejpam-6761	150	2	is	be	AUX
ejpam-6761	150	3	,	,	PUNCT
ejpam-6761	150	4	f	f	PROPN
ejpam-6761	150	5	xy	xy	NOUN
ejpam-6761	151	1	=	=	SYM
ejpam-6761	151	2	fxy	fxy	X
ejpam-6761	151	3	=	=	SYM
ejpam-6761	151	4	f	f	PROPN
ejpam-6761	151	5	for	for	ADP
ejpam-6761	151	6	all	all	DET
ejpam-6761	151	7	x	x	NOUN
ejpam-6761	151	8	,	,	PUNCT
ejpam-6761	151	9	y	y	PROPN
ejpam-6761	151	10	∈	∈	PROPN
ejpam-6761	151	11	v	v	NOUN
ejpam-6761	151	12	.	.	PUNCT
ejpam-6761	152	1	a	a	DET
ejpam-6761	152	2	left	left	ADJ
ejpam-6761	152	3	uniform	uniform	NOUN
ejpam-6761	152	4	(	(	PUNCT
ejpam-6761	152	5	right	right	ADJ
ejpam-6761	152	6	uniform	uniform	NOUN
ejpam-6761	152	7	)	)	PUNCT
ejpam-6761	152	8	ifbo	ifbo	NOUN
ejpam-6761	152	9	is	be	AUX
ejpam-6761	152	10	ifbo	ifbo	NOUN
ejpam-6761	152	11	having	have	VERB
ejpam-6761	152	12	identical	identical	ADJ
ejpam-6761	152	13	comembership	comembership	NOUN
ejpam-6761	152	14	functions	function	NOUN
ejpam-6761	152	15	(	(	PUNCT
ejpam-6761	152	16	co	co	NOUN
ejpam-6761	152	17	-	-	NOUN
ejpam-6761	152	18	nonmembership	nonmembership	NOUN
ejpam-6761	152	19	functions	function	NOUN
ejpam-6761	152	20	)	)	PUNCT
ejpam-6761	152	21	.	.	PUNCT
ejpam-6761	153	1	definition	definition	NOUN
ejpam-6761	153	2	10	10	NUM
ejpam-6761	153	3	(	(	PUNCT
ejpam-6761	153	4	[	[	X
ejpam-6761	153	5	6	6	NUM
ejpam-6761	153	6	]	]	NUM
ejpam-6761	153	7	)	)	PUNCT
ejpam-6761	153	8	.	.	PUNCT
ejpam-6761	154	1	the	the	DET
ejpam-6761	154	2	structure	structure	NOUN
ejpam-6761	154	3	of	of	ADP
ejpam-6761	154	4	(	(	PUNCT
ejpam-6761	154	5	(	(	PUNCT
ejpam-6761	154	6	g	g	NOUN
ejpam-6761	154	7	,	,	PUNCT
ejpam-6761	154	8	i	i	PRON
ejpam-6761	154	9	,	,	PUNCT
ejpam-6761	154	10	i	i	PROPN
ejpam-6761	154	11	)	)	PUNCT
ejpam-6761	154	12	,	,	PUNCT
ejpam-6761	154	13	f	f	PROPN
ejpam-6761	154	14	)	)	PUNCT
ejpam-6761	154	15	,	,	PUNCT
ejpam-6761	154	16	where	where	SCONJ
ejpam-6761	154	17	if	if	SCONJ
ejpam-6761	154	18	-	-	PUNCT
ejpam-6761	154	19	space	space	NOUN
ejpam-6761	154	20	g	g	NOUN
ejpam-6761	154	21	and	and	CCONJ
ejpam-6761	154	22	i	i	PRON
ejpam-6761	154	23	=	=	PUNCT
ejpam-6761	155	1	[	[	X
ejpam-6761	155	2	0	0	NUM
ejpam-6761	155	3	,	,	PUNCT
ejpam-6761	155	4	1	1	NUM
ejpam-6761	155	5	]	]	PUNCT
ejpam-6761	155	6	,	,	PUNCT
ejpam-6761	155	7	with	with	ADP
ejpam-6761	155	8	ifbo	ifbo	NOUN
ejpam-6761	155	9	f	f	PROPN
ejpam-6761	155	10	defined	define	VERB
ejpam-6761	155	11	on	on	ADP
ejpam-6761	155	12	if	if	SCONJ
ejpam-6761	155	13	-	-	PUNCT
ejpam-6761	155	14	space	space	NOUN
ejpam-6761	155	15	g	g	NOUN
ejpam-6761	155	16	,	,	PUNCT
ejpam-6761	155	17	is	be	AUX
ejpam-6761	155	18	called	call	VERB
ejpam-6761	155	19	an	an	DET
ejpam-6761	155	20	intuitionistic	intuitionistic	ADJ
ejpam-6761	155	21	fuzzy	fuzzy	ADJ
ejpam-6761	155	22	group	group	NOUN
ejpam-6761	155	23	(	(	PUNCT
ejpam-6761	155	24	ifg	ifg	PROPN
ejpam-6761	155	25	)	)	PUNCT
ejpam-6761	155	26	if	if	SCONJ
ejpam-6761	155	27	the	the	DET
ejpam-6761	155	28	following	follow	VERB
ejpam-6761	155	29	conditions	condition	NOUN
ejpam-6761	155	30	are	be	AUX
ejpam-6761	155	31	fulfilled	fulfil	VERB
ejpam-6761	155	32	:	:	PUNCT
ejpam-6761	155	33	(	(	PUNCT
ejpam-6761	155	34	1	1	X
ejpam-6761	155	35	)	)	PUNCT
ejpam-6761	155	36	for	for	ADP
ejpam-6761	155	37	any	any	DET
ejpam-6761	155	38	if	if	NOUN
ejpam-6761	155	39	-	-	PUNCT
ejpam-6761	155	40	element	element	NOUN
ejpam-6761	155	41	(	(	PUNCT
ejpam-6761	155	42	x	x	X
ejpam-6761	155	43	,	,	PUNCT
ejpam-6761	155	44	i	i	PRON
ejpam-6761	155	45	,	,	PUNCT
ejpam-6761	155	46	i	i	PROPN
ejpam-6761	155	47	)	)	PUNCT
ejpam-6761	155	48	,	,	PUNCT
ejpam-6761	155	49	(	(	PUNCT
ejpam-6761	155	50	y	y	X
ejpam-6761	155	51	,	,	PUNCT
ejpam-6761	155	52	i	i	PRON
ejpam-6761	155	53	,	,	PUNCT
ejpam-6761	155	54	i	i	PROPN
ejpam-6761	155	55	)	)	PUNCT
ejpam-6761	155	56	,	,	PUNCT
ejpam-6761	155	57	(	(	PUNCT
ejpam-6761	155	58	z	z	X
ejpam-6761	155	59	,	,	PUNCT
ejpam-6761	155	60	i	i	PRON
ejpam-6761	155	61	,	,	PUNCT
ejpam-6761	155	62	i	i	PROPN
ejpam-6761	155	63	)	)	PUNCT
ejpam-6761	155	64	∈	∈	PROPN
ejpam-6761	155	65	(	(	PUNCT
ejpam-6761	155	66	(	(	PUNCT
ejpam-6761	155	67	g	g	NOUN
ejpam-6761	155	68	,	,	PUNCT
ejpam-6761	155	69	i	i	PRON
ejpam-6761	155	70	,	,	PUNCT
ejpam-6761	155	71	i	i	PROPN
ejpam-6761	155	72	)	)	PUNCT
ejpam-6761	155	73	,	,	PUNCT
ejpam-6761	155	74	f	f	PROPN
ejpam-6761	155	75	)	)	PUNCT
ejpam-6761	155	76	,	,	PUNCT
ejpam-6761	155	77	(	(	PUNCT
ejpam-6761	155	78	(	(	PUNCT
ejpam-6761	155	79	x	x	X
ejpam-6761	155	80	,	,	PUNCT
ejpam-6761	155	81	i	i	PRON
ejpam-6761	155	82	,	,	PUNCT
ejpam-6761	155	83	i)f	i)f	PROPN
ejpam-6761	155	84	(	(	PUNCT
ejpam-6761	155	85	y	y	PROPN
ejpam-6761	155	86	,	,	PUNCT
ejpam-6761	155	87	i	i	PRON
ejpam-6761	155	88	,	,	PUNCT
ejpam-6761	155	89	i))f	i))f	PROPN
ejpam-6761	155	90	(	(	PUNCT
ejpam-6761	155	91	z	z	X
ejpam-6761	155	92	,	,	PUNCT
ejpam-6761	155	93	i	i	PRON
ejpam-6761	155	94	,	,	PUNCT
ejpam-6761	155	95	i	i	PROPN
ejpam-6761	155	96	)	)	PUNCT
ejpam-6761	155	97	=	=	SYM
ejpam-6761	155	98	(	(	PUNCT
ejpam-6761	155	99	x	x	X
ejpam-6761	155	100	,	,	PUNCT
ejpam-6761	155	101	i	i	PRON
ejpam-6761	155	102	,	,	PUNCT
ejpam-6761	155	103	i)f	i)f	ADJ
ejpam-6761	155	104	(	(	PUNCT
ejpam-6761	155	105	(	(	PUNCT
ejpam-6761	155	106	y	y	PROPN
ejpam-6761	155	107	,	,	PUNCT
ejpam-6761	155	108	i	i	PRON
ejpam-6761	155	109	,	,	PUNCT
ejpam-6761	155	110	i)f	i)f	ADJ
ejpam-6761	155	111	(	(	PUNCT
ejpam-6761	155	112	z	z	X
ejpam-6761	155	113	,	,	PUNCT
ejpam-6761	155	114	i	i	PRON
ejpam-6761	155	115	,	,	PUNCT
ejpam-6761	155	116	i	i	PROPN
ejpam-6761	155	117	)	)	PUNCT
ejpam-6761	155	118	)	)	PUNCT
ejpam-6761	155	119	.	.	PUNCT
ejpam-6761	156	1	(	(	PUNCT
ejpam-6761	156	2	2	2	X
ejpam-6761	156	3	)	)	PUNCT
ejpam-6761	156	4	there	there	PRON
ejpam-6761	156	5	exists	exist	VERB
ejpam-6761	156	6	an	an	DET
ejpam-6761	156	7	if	if	NOUN
ejpam-6761	156	8	-	-	PUNCT
ejpam-6761	156	9	element	element	NOUN
ejpam-6761	156	10	(	(	PUNCT
ejpam-6761	156	11	e	e	NOUN
ejpam-6761	156	12	,	,	PUNCT
ejpam-6761	156	13	i	i	PRON
ejpam-6761	156	14	,	,	PUNCT
ejpam-6761	156	15	i	i	PROPN
ejpam-6761	156	16	)	)	PUNCT
ejpam-6761	156	17	∈	∈	PROPN
ejpam-6761	156	18	(	(	PUNCT
ejpam-6761	156	19	g	g	NOUN
ejpam-6761	156	20	,	,	PUNCT
ejpam-6761	156	21	i	i	PRON
ejpam-6761	156	22	,	,	PUNCT
ejpam-6761	156	23	i	i	PROPN
ejpam-6761	156	24	)	)	PUNCT
ejpam-6761	156	25	such	such	ADJ
ejpam-6761	156	26	that	that	PRON
ejpam-6761	156	27	for	for	ADP
ejpam-6761	156	28	all	all	PRON
ejpam-6761	156	29	(	(	PUNCT
ejpam-6761	156	30	x	x	X
ejpam-6761	156	31	,	,	PUNCT
ejpam-6761	156	32	i	i	PRON
ejpam-6761	156	33	,	,	PUNCT
ejpam-6761	156	34	i	i	PROPN
ejpam-6761	156	35	)	)	PUNCT
ejpam-6761	156	36	in	in	ADP
ejpam-6761	156	37	(	(	PUNCT
ejpam-6761	156	38	(	(	PUNCT
ejpam-6761	156	39	g	g	NOUN
ejpam-6761	156	40	,	,	PUNCT
ejpam-6761	156	41	i	i	PRON
ejpam-6761	156	42	,	,	PUNCT
ejpam-6761	156	43	i	i	PROPN
ejpam-6761	156	44	)	)	PUNCT
ejpam-6761	156	45	,	,	PUNCT
ejpam-6761	156	46	f	f	PROPN
ejpam-6761	156	47	):	):	PUNCT
ejpam-6761	156	48	(	(	PUNCT
ejpam-6761	156	49	e	e	X
ejpam-6761	156	50	,	,	PUNCT
ejpam-6761	156	51	i	i	PRON
ejpam-6761	156	52	,	,	PUNCT
ejpam-6761	156	53	i)f	i)f	ADJ
ejpam-6761	156	54	(	(	PUNCT
ejpam-6761	156	55	x	x	X
ejpam-6761	156	56	,	,	PUNCT
ejpam-6761	156	57	i	i	PRON
ejpam-6761	156	58	,	,	PUNCT
ejpam-6761	156	59	i	i	PROPN
ejpam-6761	156	60	)	)	PUNCT
ejpam-6761	156	61	=	=	SYM
ejpam-6761	156	62	(	(	PUNCT
ejpam-6761	156	63	x	x	X
ejpam-6761	156	64	,	,	PUNCT
ejpam-6761	156	65	i	i	PRON
ejpam-6761	156	66	,	,	PUNCT
ejpam-6761	156	67	i)f	i)f	ADJ
ejpam-6761	156	68	(	(	PUNCT
ejpam-6761	156	69	e	e	NOUN
ejpam-6761	156	70	,	,	PUNCT
ejpam-6761	156	71	i	i	PRON
ejpam-6761	156	72	,	,	PUNCT
ejpam-6761	156	73	i	i	PROPN
ejpam-6761	156	74	)	)	PUNCT
ejpam-6761	156	75	=	=	SYM
ejpam-6761	157	1	(	(	PUNCT
ejpam-6761	157	2	x	x	X
ejpam-6761	157	3	,	,	PUNCT
ejpam-6761	157	4	i	i	PRON
ejpam-6761	157	5	,	,	PUNCT
ejpam-6761	157	6	i	i	PROPN
ejpam-6761	157	7	)	)	PUNCT
ejpam-6761	157	8	.	.	PUNCT
ejpam-6761	158	1	(	(	PUNCT
ejpam-6761	158	2	3	3	X
ejpam-6761	158	3	)	)	PUNCT
ejpam-6761	158	4	for	for	ADP
ejpam-6761	158	5	every	every	DET
ejpam-6761	158	6	if	if	NOUN
ejpam-6761	158	7	-	-	PUNCT
ejpam-6761	158	8	element	element	NOUN
ejpam-6761	158	9	(	(	PUNCT
ejpam-6761	158	10	x	x	X
ejpam-6761	158	11	,	,	PUNCT
ejpam-6761	158	12	i	i	PRON
ejpam-6761	158	13	,	,	PUNCT
ejpam-6761	158	14	i	i	PROPN
ejpam-6761	158	15	)	)	PUNCT
ejpam-6761	158	16	in	in	ADP
ejpam-6761	158	17	(	(	PUNCT
ejpam-6761	158	18	(	(	PUNCT
ejpam-6761	158	19	g	g	NOUN
ejpam-6761	158	20	,	,	PUNCT
ejpam-6761	158	21	i	i	PRON
ejpam-6761	158	22	,	,	PUNCT
ejpam-6761	158	23	i	i	PROPN
ejpam-6761	158	24	)	)	PUNCT
ejpam-6761	158	25	,	,	PUNCT
ejpam-6761	158	26	f	f	PROPN
ejpam-6761	158	27	)	)	PUNCT
ejpam-6761	158	28	there	there	PRON
ejpam-6761	158	29	exists	exist	VERB
ejpam-6761	158	30	an	an	DET
ejpam-6761	158	31	if	if	NOUN
ejpam-6761	158	32	-	-	PUNCT
ejpam-6761	158	33	element	element	NOUN
ejpam-6761	158	34	(	(	PUNCT
ejpam-6761	158	35	x−1	x−1	PROPN
ejpam-6761	158	36	,	,	PUNCT
ejpam-6761	158	37	i	i	PRON
ejpam-6761	158	38	,	,	PUNCT
ejpam-6761	158	39	i	i	PROPN
ejpam-6761	158	40	)	)	PUNCT
ejpam-6761	158	41	in	in	ADP
ejpam-6761	158	42	(	(	PUNCT
ejpam-6761	158	43	g	g	NOUN
ejpam-6761	158	44	,	,	PUNCT
ejpam-6761	158	45	i	i	PRON
ejpam-6761	158	46	,	,	PUNCT
ejpam-6761	158	47	i	i	PROPN
ejpam-6761	158	48	)	)	PUNCT
ejpam-6761	158	49	,	,	PUNCT
ejpam-6761	158	50	f	f	PROPN
ejpam-6761	158	51	such	such	ADJ
ejpam-6761	158	52	that	that	SCONJ
ejpam-6761	158	53	:	:	PUNCT
ejpam-6761	158	54	(	(	PUNCT
ejpam-6761	158	55	x	x	X
ejpam-6761	158	56	,	,	PUNCT
ejpam-6761	158	57	i	i	PRON
ejpam-6761	158	58	,	,	PUNCT
ejpam-6761	158	59	i)f	i)f	ADJ
ejpam-6761	158	60	(	(	PUNCT
ejpam-6761	158	61	x−1	x−1	PROPN
ejpam-6761	158	62	,	,	PUNCT
ejpam-6761	158	63	i	i	PRON
ejpam-6761	158	64	,	,	PUNCT
ejpam-6761	158	65	i	i	PROPN
ejpam-6761	158	66	)	)	PUNCT
ejpam-6761	158	67	=	=	SYM
ejpam-6761	159	1	(	(	PUNCT
ejpam-6761	159	2	x−1	x−1	PROPN
ejpam-6761	159	3	,	,	PUNCT
ejpam-6761	159	4	i	i	PRON
ejpam-6761	159	5	,	,	PUNCT
ejpam-6761	159	6	i)f	i)f	ADJ
ejpam-6761	159	7	(	(	PUNCT
ejpam-6761	159	8	x	x	X
ejpam-6761	159	9	,	,	PUNCT
ejpam-6761	159	10	i	i	PRON
ejpam-6761	159	11	,	,	PUNCT
ejpam-6761	159	12	i	i	PROPN
ejpam-6761	159	13	)	)	PUNCT
ejpam-6761	159	14	=	=	SYM
ejpam-6761	160	1	(	(	PUNCT
ejpam-6761	160	2	e	e	NOUN
ejpam-6761	160	3	,	,	PUNCT
ejpam-6761	160	4	i	i	PRON
ejpam-6761	160	5	,	,	PUNCT
ejpam-6761	160	6	i	i	PROPN
ejpam-6761	160	7	)	)	PUNCT
ejpam-6761	160	8	.	.	PUNCT
ejpam-6761	161	1	an	an	DET
ejpam-6761	161	2	ifg	ifg	NOUN
ejpam-6761	161	3	(	(	PUNCT
ejpam-6761	161	4	(	(	PUNCT
ejpam-6761	161	5	g	g	NOUN
ejpam-6761	161	6	,	,	PUNCT
ejpam-6761	161	7	i	i	PRON
ejpam-6761	161	8	,	,	PUNCT
ejpam-6761	161	9	i	i	PROPN
ejpam-6761	161	10	)	)	PUNCT
ejpam-6761	161	11	,	,	PUNCT
ejpam-6761	161	12	f	f	PROPN
ejpam-6761	161	13	)	)	PUNCT
ejpam-6761	161	14	is	be	AUX
ejpam-6761	161	15	called	call	VERB
ejpam-6761	161	16	an	an	DET
ejpam-6761	161	17	abelian	abelian	PROPN
ejpam-6761	161	18	ifg	ifg	VERB
ejpam-6761	161	19	iff	iff	PROPN
ejpam-6761	161	20	for	for	ADP
ejpam-6761	161	21	all	all	PRON
ejpam-6761	161	22	(	(	PUNCT
ejpam-6761	161	23	x	x	X
ejpam-6761	161	24	,	,	PUNCT
ejpam-6761	161	25	i	i	PRON
ejpam-6761	161	26	,	,	PUNCT
ejpam-6761	161	27	i	i	PROPN
ejpam-6761	161	28	)	)	PUNCT
ejpam-6761	161	29	,	,	PUNCT
ejpam-6761	161	30	(	(	PUNCT
ejpam-6761	161	31	y	y	X
ejpam-6761	161	32	,	,	PUNCT
ejpam-6761	161	33	i	i	PRON
ejpam-6761	161	34	,	,	PUNCT
ejpam-6761	161	35	i	i	PROPN
ejpam-6761	161	36	)	)	PUNCT
ejpam-6761	161	37	∈	∈	PROPN
ejpam-6761	161	38	(	(	PUNCT
ejpam-6761	161	39	(	(	PUNCT
ejpam-6761	161	40	g	g	NOUN
ejpam-6761	161	41	,	,	PUNCT
ejpam-6761	161	42	i	i	PRON
ejpam-6761	161	43	,	,	PUNCT
ejpam-6761	161	44	i	i	PROPN
ejpam-6761	161	45	)	)	PUNCT
ejpam-6761	161	46	,	,	PUNCT
ejpam-6761	161	47	f	f	PROPN
ejpam-6761	161	48	)	)	PUNCT
ejpam-6761	161	49	,	,	PUNCT
ejpam-6761	161	50	(	(	PUNCT
ejpam-6761	161	51	x	x	X
ejpam-6761	161	52	,	,	PUNCT
ejpam-6761	161	53	i	i	PRON
ejpam-6761	161	54	,	,	PUNCT
ejpam-6761	161	55	i)f	i)f	PROPN
ejpam-6761	161	56	(	(	PUNCT
ejpam-6761	161	57	y	y	PROPN
ejpam-6761	161	58	,	,	PUNCT
ejpam-6761	161	59	i	i	PRON
ejpam-6761	161	60	,	,	PUNCT
ejpam-6761	161	61	i	i	PROPN
ejpam-6761	161	62	)	)	PUNCT
ejpam-6761	161	63	=	=	SYM
ejpam-6761	162	1	(	(	PUNCT
ejpam-6761	162	2	y	y	PROPN
ejpam-6761	162	3	,	,	PUNCT
ejpam-6761	162	4	i	i	PRON
ejpam-6761	162	5	,	,	PUNCT
ejpam-6761	162	6	i)f	i)f	ADJ
ejpam-6761	162	7	(	(	PUNCT
ejpam-6761	162	8	x	x	X
ejpam-6761	162	9	,	,	PUNCT
ejpam-6761	162	10	i	i	PRON
ejpam-6761	162	11	,	,	PUNCT
ejpam-6761	162	12	i	i	PROPN
ejpam-6761	162	13	)	)	PUNCT
ejpam-6761	162	14	is	be	AUX
ejpam-6761	162	15	true	true	ADJ
ejpam-6761	162	16	.	.	PUNCT
ejpam-6761	163	1	f.	f.	PROPN
ejpam-6761	163	2	al	al	PROPN
ejpam-6761	163	3	-	-	PROPN
ejpam-6761	163	4	zu’bi	zu’bi	PROPN
ejpam-6761	163	5	et	et	NOUN
ejpam-6761	163	6	al	al	PROPN
ejpam-6761	163	7	.	.	PUNCT
ejpam-6761	163	8	/	/	SYM
ejpam-6761	163	9	eur	eur	PROPN
ejpam-6761	163	10	.	.	PUNCT
ejpam-6761	164	1	j.	j.	PROPN
ejpam-6761	164	2	pure	pure	PROPN
ejpam-6761	164	3	appl	appl	PROPN
ejpam-6761	164	4	.	.	PROPN
ejpam-6761	164	5	math	math	PROPN
ejpam-6761	164	6	,	,	PUNCT
ejpam-6761	164	7	18	18	NUM
ejpam-6761	164	8	(	(	PUNCT
ejpam-6761	164	9	4	4	NUM
ejpam-6761	164	10	)	)	PUNCT
ejpam-6761	164	11	(	(	PUNCT
ejpam-6761	164	12	2025	2025	NUM
ejpam-6761	164	13	)	)	PUNCT
ejpam-6761	164	14	,	,	PUNCT
ejpam-6761	164	15	6761	6761	NUM
ejpam-6761	164	16	8	8	NUM
ejpam-6761	164	17	of	of	ADP
ejpam-6761	164	18	28	28	NUM
ejpam-6761	164	19	definition	definition	NOUN
ejpam-6761	164	20	11	11	NUM
ejpam-6761	164	21	(	(	PUNCT
ejpam-6761	164	22	[	[	X
ejpam-6761	164	23	11	11	NUM
ejpam-6761	164	24	]	]	NUM
ejpam-6761	164	25	)	)	PUNCT
ejpam-6761	164	26	.	.	PUNCT
ejpam-6761	165	1	the	the	DET
ejpam-6761	165	2	bvfcp	bvfcp	NOUN
ejpam-6761	165	3	of	of	ADP
ejpam-6761	165	4	two	two	NUM
ejpam-6761	165	5	ordinary	ordinary	ADJ
ejpam-6761	165	6	sets	set	NOUN
ejpam-6761	165	7	u	u	NOUN
ejpam-6761	165	8	and	and	CCONJ
ejpam-6761	165	9	v	v	NOUN
ejpam-6761	165	10	,	,	PUNCT
ejpam-6761	165	11	denoted	denote	VERB
ejpam-6761	165	12	by	by	ADP
ejpam-6761	165	13	u×v	u×v	PROPN
ejpam-6761	165	14	,	,	PUNCT
ejpam-6761	165	15	is	be	AUX
ejpam-6761	165	16	the	the	DET
ejpam-6761	165	17	collection	collection	NOUN
ejpam-6761	165	18	of	of	ADP
ejpam-6761	165	19	all	all	DET
ejpam-6761	165	20	k	k	NOUN
ejpam-6761	165	21	-	-	PUNCT
ejpam-6761	165	22	bvf	bvf	NOUN
ejpam-6761	165	23	subsets	subset	NOUN
ejpam-6761	165	24	of	of	ADP
ejpam-6761	165	25	u	u	NOUN
ejpam-6761	165	26	×	×	PROPN
ejpam-6761	165	27	v	v	NOUN
ejpam-6761	165	28	that	that	PRON
ejpam-6761	165	29	is	be	AUX
ejpam-6761	165	30	u×v	u×v	PROPN
ejpam-6761	165	31	=	=	SYM
ejpam-6761	165	32	k(u×v	k(u×v	PROPN
ejpam-6761	165	33	)	)	PUNCT
ejpam-6761	165	34	,	,	PUNCT
ejpam-6761	165	35	an	an	DET
ejpam-6761	165	36	element	element	NOUN
ejpam-6761	165	37	of	of	ADP
ejpam-6761	165	38	u×v	u×v	PROPN
ejpam-6761	165	39	is	be	AUX
ejpam-6761	165	40	then	then	ADV
ejpam-6761	165	41	a	a	DET
ejpam-6761	165	42	function	function	NOUN
ejpam-6761	165	43	m	m	VERB
ejpam-6761	165	44	:	:	PUNCT
ejpam-6761	165	45	u	u	NOUN
ejpam-6761	165	46	×	×	PROPN
ejpam-6761	165	47	v	v	INTJ
ejpam-6761	165	48	→	→	SYM
ejpam-6761	165	49	k	k	X
ejpam-6761	165	50	,	,	PUNCT
ejpam-6761	165	51	or	or	CCONJ
ejpam-6761	165	52	m	m	PROPN
ejpam-6761	165	53	=	=	X
ejpam-6761	165	54	{	{	PUNCT
ejpam-6761	165	55	(	(	PUNCT
ejpam-6761	165	56	(	(	PUNCT
ejpam-6761	165	57	u	u	NOUN
ejpam-6761	165	58	,	,	PUNCT
ejpam-6761	165	59	v	v	NOUN
ejpam-6761	165	60	)	)	PUNCT
ejpam-6761	165	61	,	,	PUNCT
ejpam-6761	166	1	[	[	X
ejpam-6761	166	2	(	(	PUNCT
ejpam-6761	166	3	δ−	δ−	ADJ
ejpam-6761	166	4	,	,	PUNCT
ejpam-6761	166	5	δ+	δ+	NOUN
ejpam-6761	166	6	)	)	PUNCT
ejpam-6761	166	7	,	,	PUNCT
ejpam-6761	166	8	(	(	PUNCT
ejpam-6761	166	9	ϑ−	ϑ−	PROPN
ejpam-6761	166	10	,	,	PUNCT
ejpam-6761	166	11	ϑ+	ϑ+	NOUN
ejpam-6761	166	12	)	)	PUNCT
ejpam-6761	166	13	]	]	PUNCT
ejpam-6761	166	14	)	)	PUNCT
ejpam-6761	166	15	:	:	PUNCT
ejpam-6761	166	16	(	(	PUNCT
ejpam-6761	166	17	u	u	NOUN
ejpam-6761	166	18	,	,	PUNCT
ejpam-6761	166	19	v	v	NOUN
ejpam-6761	166	20	)	)	PUNCT
ejpam-6761	166	21	∈	∈	PROPN
ejpam-6761	166	22	u	u	NOUN
ejpam-6761	166	23	×	×	PROPN
ejpam-6761	166	24	v	v	NOUN
ejpam-6761	166	25	,	,	PUNCT
ejpam-6761	166	26	[	[	X
ejpam-6761	166	27	(	(	PUNCT
ejpam-6761	166	28	δ−	δ−	ADJ
ejpam-6761	166	29	,	,	PUNCT
ejpam-6761	166	30	δ+	δ+	NOUN
ejpam-6761	166	31	)	)	PUNCT
ejpam-6761	166	32	,	,	PUNCT
ejpam-6761	166	33	(	(	PUNCT
ejpam-6761	166	34	ϑ−	ϑ−	PROPN
ejpam-6761	166	35	,	,	PUNCT
ejpam-6761	166	36	ϑ+	ϑ+	NOUN
ejpam-6761	166	37	)	)	PUNCT
ejpam-6761	166	38	]	]	PUNCT
ejpam-6761	166	39	=	=	SYM
ejpam-6761	166	40	m(u	m(u	PROPN
ejpam-6761	166	41	,	,	PUNCT
ejpam-6761	166	42	v	v	NOUN
ejpam-6761	166	43	)	)	PUNCT
ejpam-6761	166	44	→	→	PUNCT
ejpam-6761	166	45	k	k	X
ejpam-6761	166	46	}	}	PUNCT
ejpam-6761	166	47	.	.	PUNCT
ejpam-6761	167	1	the	the	DET
ejpam-6761	167	2	bvfcp	bvfcp	NOUN
ejpam-6761	167	3	of	of	ADP
ejpam-6761	167	4	a	a	DET
ejpam-6761	167	5	bvf	bvf	NOUN
ejpam-6761	167	6	subset	subset	VERB
ejpam-6761	167	7	h	h	NOUN
ejpam-6761	167	8	=	=	PRON
ejpam-6761	167	9	{	{	PUNCT
ejpam-6761	167	10	(	(	PUNCT
ejpam-6761	167	11	u	u	NOUN
ejpam-6761	167	12	,	,	PUNCT
ejpam-6761	167	13	(	(	PUNCT
ejpam-6761	167	14	δ−	δ−	ADJ
ejpam-6761	167	15	,	,	PUNCT
ejpam-6761	167	16	δ+	δ+	NOUN
ejpam-6761	167	17	)	)	PUNCT
ejpam-6761	167	18	)	)	PUNCT
ejpam-6761	167	19	}	}	PUNCT
ejpam-6761	167	20	of	of	ADP
ejpam-6761	167	21	u	u	NOUN
ejpam-6761	167	22	and	and	CCONJ
ejpam-6761	167	23	a	a	DET
ejpam-6761	167	24	bvf	bvf	NOUN
ejpam-6761	167	25	subset	subset	VERB
ejpam-6761	167	26	t	t	PROPN
ejpam-6761	167	27	=	=	SYM
ejpam-6761	167	28	{	{	PUNCT
ejpam-6761	167	29	(	(	PUNCT
ejpam-6761	167	30	v	v	NOUN
ejpam-6761	167	31	,	,	PUNCT
ejpam-6761	167	32	(	(	PUNCT
ejpam-6761	167	33	ϑ−	ϑ−	PROPN
ejpam-6761	167	34	,	,	PUNCT
ejpam-6761	167	35	ϑ+	ϑ+	NOUN
ejpam-6761	167	36	)	)	PUNCT
ejpam-6761	167	37	)	)	PUNCT
ejpam-6761	167	38	}	}	PUNCT
ejpam-6761	167	39	of	of	ADP
ejpam-6761	167	40	v	v	NUM
ejpam-6761	167	41	is	be	AUX
ejpam-6761	167	42	the	the	DET
ejpam-6761	167	43	k	k	NOUN
ejpam-6761	167	44	-	-	PUNCT
ejpam-6761	167	45	bvf	bvf	NOUN
ejpam-6761	167	46	subset	subset	VERB
ejpam-6761	167	47	h×t	h×t	PROPN
ejpam-6761	167	48	of	of	ADP
ejpam-6761	167	49	u	u	PROPN
ejpam-6761	167	50	×	×	PROPN
ejpam-6761	167	51	v	v	NOUN
ejpam-6761	167	52	defined	define	VERB
ejpam-6761	167	53	by	by	ADP
ejpam-6761	167	54	:	:	PUNCT
ejpam-6761	167	55	h×t	h×t	PROPN
ejpam-6761	167	56	=	=	X
ejpam-6761	167	57	{	{	PUNCT
ejpam-6761	167	58	(	(	PUNCT
ejpam-6761	167	59	(	(	PUNCT
ejpam-6761	167	60	u	u	NOUN
ejpam-6761	167	61	,	,	PUNCT
ejpam-6761	167	62	v	v	NOUN
ejpam-6761	167	63	)	)	PUNCT
ejpam-6761	167	64	,	,	PUNCT
ejpam-6761	167	65	(	(	PUNCT
ejpam-6761	167	66	(	(	PUNCT
ejpam-6761	167	67	h−(u	h−(u	NOUN
ejpam-6761	167	68	)	)	PUNCT
ejpam-6761	167	69	,	,	PUNCT
ejpam-6761	167	70	h+(u	h+(u	NUM
ejpam-6761	167	71	)	)	PUNCT
ejpam-6761	167	72	)	)	PUNCT
ejpam-6761	167	73	,	,	PUNCT
ejpam-6761	167	74	(	(	PUNCT
ejpam-6761	167	75	t−(v	t−(v	PROPN
ejpam-6761	167	76	)	)	PUNCT
ejpam-6761	167	77	,	,	PUNCT
ejpam-6761	167	78	t+(v	t+(v	PROPN
ejpam-6761	167	79	)	)	PUNCT
ejpam-6761	167	80	)	)	PUNCT
ejpam-6761	167	81	)	)	PUNCT
ejpam-6761	167	82	:	:	PUNCT
ejpam-6761	168	1	u	u	PROPN
ejpam-6761	168	2	∈	∈	PROPN
ejpam-6761	168	3	u	u	PROPN
ejpam-6761	168	4	,	,	PUNCT
ejpam-6761	168	5	v	v	PROPN
ejpam-6761	168	6	∈	∈	NOUN
ejpam-6761	168	7	v	v	NOUN
ejpam-6761	168	8	}	}	PUNCT
ejpam-6761	168	9	≡	≡	PROPN
ejpam-6761	168	10	{	{	PUNCT
ejpam-6761	168	11	(	(	PUNCT
ejpam-6761	168	12	(	(	PUNCT
ejpam-6761	168	13	u	u	NOUN
ejpam-6761	168	14	,	,	PUNCT
ejpam-6761	168	15	v	v	NOUN
ejpam-6761	168	16	)	)	PUNCT
ejpam-6761	168	17	,	,	PUNCT
ejpam-6761	168	18	(	(	PUNCT
ejpam-6761	168	19	(	(	PUNCT
ejpam-6761	168	20	δ−	δ−	ADJ
ejpam-6761	168	21	,	,	PUNCT
ejpam-6761	168	22	δ+	δ+	NOUN
ejpam-6761	168	23	)	)	PUNCT
ejpam-6761	168	24	,	,	PUNCT
ejpam-6761	168	25	(	(	PUNCT
ejpam-6761	168	26	ϑ−	ϑ−	PROPN
ejpam-6761	168	27	,	,	PUNCT
ejpam-6761	168	28	ϑ+	ϑ+	NOUN
ejpam-6761	168	29	)	)	PUNCT
ejpam-6761	168	30	)	)	PUNCT
ejpam-6761	168	31	)	)	PUNCT
ejpam-6761	168	32	}	}	PUNCT
ejpam-6761	168	33	.	.	PUNCT
ejpam-6761	169	1	therefore	therefore	ADV
ejpam-6761	169	2	,	,	PUNCT
ejpam-6761	169	3	h×t	h×t	PROPN
ejpam-6761	169	4	is	be	AUX
ejpam-6761	169	5	an	an	DET
ejpam-6761	169	6	element	element	NOUN
ejpam-6761	169	7	of	of	ADP
ejpam-6761	169	8	u×v	u×v	PROPN
ejpam-6761	169	9	,	,	PUNCT
ejpam-6761	169	10	∀h	∀h	PROPN
ejpam-6761	169	11	∈wu	∈wu	NOUN
ejpam-6761	169	12	and	and	CCONJ
ejpam-6761	169	13	∀t	∀t	AUX
ejpam-6761	169	14	∈w	∈w	VERB
ejpam-6761	169	15	v	v	NOUN
ejpam-6761	169	16	.	.	PUNCT
ejpam-6761	170	1	definition	definition	NOUN
ejpam-6761	170	2	12	12	NUM
ejpam-6761	170	3	(	(	PUNCT
ejpam-6761	170	4	[	[	X
ejpam-6761	170	5	11	11	NUM
ejpam-6761	170	6	]	]	NUM
ejpam-6761	170	7	)	)	PUNCT
ejpam-6761	170	8	.	.	PUNCT
ejpam-6761	171	1	a	a	DET
ejpam-6761	171	2	bvfr	bvfr	NOUN
ejpam-6761	171	3	β	β	X
ejpam-6761	171	4	maps	map	VERB
ejpam-6761	171	5	u	u	NOUN
ejpam-6761	171	6	to	to	ADP
ejpam-6761	171	7	v	v	NOUN
ejpam-6761	171	8	is	be	AUX
ejpam-6761	171	9	a	a	DET
ejpam-6761	171	10	subset	subset	NOUN
ejpam-6761	171	11	of	of	ADP
ejpam-6761	171	12	the	the	DET
ejpam-6761	171	13	bvfcp	bvfcp	PROPN
ejpam-6761	171	14	u×v	u×v	PROPN
ejpam-6761	171	15	.	.	PUNCT
ejpam-6761	172	1	in	in	ADP
ejpam-6761	172	2	other	other	ADJ
ejpam-6761	172	3	words	word	NOUN
ejpam-6761	172	4	,	,	PUNCT
ejpam-6761	172	5	β	β	X
ejpam-6761	172	6	is	be	AUX
ejpam-6761	172	7	a	a	DET
ejpam-6761	172	8	member	member	NOUN
ejpam-6761	172	9	of	of	ADP
ejpam-6761	172	10	k	k	PROPN
ejpam-6761	172	11	-	-	PUNCT
ejpam-6761	172	12	bvf	bvf	PROPN
ejpam-6761	172	13	subsets	subset	NOUN
ejpam-6761	172	14	m	m	VERB
ejpam-6761	172	15	:	:	PUNCT
ejpam-6761	172	16	u	u	NOUN
ejpam-6761	172	17	×	×	PROPN
ejpam-6761	172	18	v	v	PROPN
ejpam-6761	172	19	→	→	PUNCT
ejpam-6761	172	20	k.	k.	PROPN
ejpam-6761	172	21	a	a	DET
ejpam-6761	172	22	bvfr	bvfr	NOUN
ejpam-6761	172	23	from	from	ADP
ejpam-6761	172	24	u	u	NOUN
ejpam-6761	172	25	to	to	ADP
ejpam-6761	172	26	u	u	NOUN
ejpam-6761	172	27	is	be	AUX
ejpam-6761	172	28	said	say	VERB
ejpam-6761	172	29	to	to	PART
ejpam-6761	172	30	be	be	AUX
ejpam-6761	172	31	a	a	DET
ejpam-6761	172	32	bvfr	bvfr	NOUN
ejpam-6761	172	33	in	in	ADP
ejpam-6761	172	34	u	u	PROPN
ejpam-6761	172	35	.	.	PUNCT
ejpam-6761	173	1	definition	definition	NOUN
ejpam-6761	173	2	13	13	NUM
ejpam-6761	173	3	(	(	PUNCT
ejpam-6761	173	4	[	[	X
ejpam-6761	173	5	11	11	NUM
ejpam-6761	173	6	]	]	NUM
ejpam-6761	173	7	)	)	PUNCT
ejpam-6761	173	8	.	.	PUNCT
ejpam-6761	174	1	let	let	VERB
ejpam-6761	174	2	β1	β1	PROPN
ejpam-6761	174	3	and	and	CCONJ
ejpam-6761	174	4	β2	β2	NOUN
ejpam-6761	174	5	:	:	PUNCT
ejpam-6761	174	6	u	u	NOUN
ejpam-6761	174	7	→	→	SYM
ejpam-6761	174	8	v	v	NOUN
ejpam-6761	174	9	to	to	ADP
ejpam-6761	174	10	v	v	NOUN
ejpam-6761	174	11	be	be	AUX
ejpam-6761	174	12	two	two	NUM
ejpam-6761	174	13	bvfrs	bvfrs	NOUN
ejpam-6761	174	14	.	.	PUNCT
ejpam-6761	175	1	we	we	PRON
ejpam-6761	175	2	call	call	VERB
ejpam-6761	175	3	that	that	SCONJ
ejpam-6761	175	4	β2	β2	PROPN
ejpam-6761	175	5	is	be	AUX
ejpam-6761	175	6	containing	contain	VERB
ejpam-6761	175	7	β1	β1	NOUN
ejpam-6761	175	8	,	,	PUNCT
ejpam-6761	175	9	denoted	denote	VERB
ejpam-6761	175	10	by	by	ADP
ejpam-6761	175	11	β1	β1	PROPN
ejpam-6761	175	12	⊂	⊂	PROPN
ejpam-6761	175	13	β2	β2	PROPN
ejpam-6761	175	14	,	,	PUNCT
ejpam-6761	175	15	if	if	SCONJ
ejpam-6761	175	16	and	and	CCONJ
ejpam-6761	175	17	only	only	ADV
ejpam-6761	175	18	if	if	SCONJ
ejpam-6761	175	19	when	when	SCONJ
ejpam-6761	175	20	(	(	PUNCT
ejpam-6761	175	21	(	(	PUNCT
ejpam-6761	175	22	u	u	NOUN
ejpam-6761	175	23	,	,	PUNCT
ejpam-6761	175	24	v	v	NOUN
ejpam-6761	175	25	)	)	PUNCT
ejpam-6761	175	26	,	,	PUNCT
ejpam-6761	175	27	(	(	PUNCT
ejpam-6761	175	28	(	(	PUNCT
ejpam-6761	175	29	δ−	δ−	ADJ
ejpam-6761	175	30	,	,	PUNCT
ejpam-6761	175	31	δ+	δ+	NOUN
ejpam-6761	175	32	)	)	PUNCT
ejpam-6761	175	33	,	,	PUNCT
ejpam-6761	175	34	(	(	PUNCT
ejpam-6761	175	35	ϑ−	ϑ−	PROPN
ejpam-6761	175	36	,	,	PUNCT
ejpam-6761	175	37	ϑ+	ϑ+	NOUN
ejpam-6761	175	38	)	)	PUNCT
ejpam-6761	175	39	)	)	PUNCT
ejpam-6761	175	40	)	)	PUNCT
ejpam-6761	176	1	∈	∈	PROPN
ejpam-6761	176	2	h	h	NOUN
ejpam-6761	176	3	∈	∈	PROPN
ejpam-6761	176	4	β1	β1	PROPN
ejpam-6761	176	5	,	,	PUNCT
ejpam-6761	176	6	there	there	PRON
ejpam-6761	176	7	exists	exist	VERB
ejpam-6761	176	8	b	b	PROPN
ejpam-6761	176	9	∈	∈	PROPN
ejpam-6761	176	10	β2	β2	NOUN
ejpam-6761	176	11	such	such	ADJ
ejpam-6761	176	12	that	that	SCONJ
ejpam-6761	176	13	(	(	PUNCT
ejpam-6761	176	14	(	(	PUNCT
ejpam-6761	176	15	u	u	NOUN
ejpam-6761	176	16	,	,	PUNCT
ejpam-6761	176	17	v	v	NOUN
ejpam-6761	176	18	)	)	PUNCT
ejpam-6761	176	19	,	,	PUNCT
ejpam-6761	176	20	(	(	PUNCT
ejpam-6761	176	21	(	(	PUNCT
ejpam-6761	176	22	δ−	δ−	ADJ
ejpam-6761	176	23	,	,	PUNCT
ejpam-6761	176	24	δ+	δ+	NOUN
ejpam-6761	176	25	)	)	PUNCT
ejpam-6761	176	26	,	,	PUNCT
ejpam-6761	176	27	(	(	PUNCT
ejpam-6761	176	28	ϑ−	ϑ−	PROPN
ejpam-6761	176	29	,	,	PUNCT
ejpam-6761	176	30	ϑ+	ϑ+	NOUN
ejpam-6761	176	31	)	)	PUNCT
ejpam-6761	176	32	)	)	PUNCT
ejpam-6761	176	33	)	)	PUNCT
ejpam-6761	177	1	∈	∈	PROPN
ejpam-6761	177	2	t	t	PROPN
ejpam-6761	177	3	∈	∈	PROPN
ejpam-6761	177	4	β2	β2	NOUN
ejpam-6761	177	5	.	.	PUNCT
ejpam-6761	178	1	if	if	SCONJ
ejpam-6761	178	2	β1	β1	PROPN
ejpam-6761	178	3	⊂	⊂	PROPN
ejpam-6761	178	4	β2	β2	PROPN
ejpam-6761	178	5	and	and	CCONJ
ejpam-6761	178	6	β2	β2	PROPN
ejpam-6761	178	7	⊂	⊂	PROPN
ejpam-6761	178	8	β1	β1	PROPN
ejpam-6761	178	9	,	,	PUNCT
ejpam-6761	178	10	then	then	ADV
ejpam-6761	178	11	β1	β1	PROPN
ejpam-6761	178	12	and	and	CCONJ
ejpam-6761	178	13	β2	β2	NOUN
ejpam-6761	178	14	are	be	AUX
ejpam-6761	178	15	equal	equal	ADJ
ejpam-6761	178	16	,	,	PUNCT
ejpam-6761	178	17	that	that	PRON
ejpam-6761	178	18	is	is	ADV
ejpam-6761	178	19	β1	β1	PROPN
ejpam-6761	178	20	=	=	SYM
ejpam-6761	178	21	β2	β2	PROPN
ejpam-6761	178	22	.	.	PUNCT
ejpam-6761	179	1	definition	definition	NOUN
ejpam-6761	179	2	14	14	NUM
ejpam-6761	179	3	(	(	PUNCT
ejpam-6761	179	4	[	[	X
ejpam-6761	179	5	11	11	NUM
ejpam-6761	179	6	]	]	NUM
ejpam-6761	179	7	)	)	PUNCT
ejpam-6761	179	8	.	.	PUNCT
ejpam-6761	180	1	let	let	VERB
ejpam-6761	180	2	β	β	PRON
ejpam-6761	180	3	:	:	PUNCT
ejpam-6761	180	4	u	u	SYM
ejpam-6761	180	5	→	→	SYM
ejpam-6761	180	6	v	v	NUM
ejpam-6761	180	7	be	be	AUX
ejpam-6761	180	8	a	a	DET
ejpam-6761	180	9	bvfr	bvfr	NOUN
ejpam-6761	180	10	.	.	PUNCT
ejpam-6761	181	1	the	the	DET
ejpam-6761	181	2	inverse	inverse	NOUN
ejpam-6761	181	3	of	of	ADP
ejpam-6761	181	4	β	β	X
ejpam-6761	181	5	=	=	PUNCT
ejpam-6761	181	6	β−1	β−1	PUNCT
ejpam-6761	181	7	:	:	PUNCT
ejpam-6761	181	8	v	v	NOUN
ejpam-6761	181	9	→	→	SYM
ejpam-6761	181	10	u	u	NOUN
ejpam-6761	181	11	is	be	AUX
ejpam-6761	181	12	the	the	DET
ejpam-6761	181	13	bvfr	bvfr	NOUN
ejpam-6761	181	14	defined	define	VERB
ejpam-6761	181	15	by	by	ADP
ejpam-6761	181	16	β−1	β−1	PUNCT
ejpam-6761	182	1	=	=	SYM
ejpam-6761	182	2	{	{	PUNCT
ejpam-6761	182	3	m−1	m−1	PROPN
ejpam-6761	182	4	:	:	PUNCT
ejpam-6761	182	5	m	m	VERB
ejpam-6761	182	6	∈	∈	NOUN
ejpam-6761	182	7	β	β	NOUN
ejpam-6761	182	8	}	}	PUNCT
ejpam-6761	182	9	.	.	PUNCT
ejpam-6761	183	1	definition	definition	NOUN
ejpam-6761	183	2	15	15	NUM
ejpam-6761	183	3	(	(	PUNCT
ejpam-6761	183	4	[	[	X
ejpam-6761	183	5	11	11	NUM
ejpam-6761	183	6	]	]	NUM
ejpam-6761	183	7	)	)	PUNCT
ejpam-6761	183	8	.	.	PUNCT
ejpam-6761	184	1	let	let	VERB
ejpam-6761	184	2	β	β	PRON
ejpam-6761	184	3	:	:	PUNCT
ejpam-6761	184	4	u	u	X
ejpam-6761	184	5	→	→	SYM
ejpam-6761	184	6	v	v	PROPN
ejpam-6761	184	7	and	and	CCONJ
ejpam-6761	184	8	γ	γ	X
ejpam-6761	184	9	:	:	PUNCT
ejpam-6761	184	10	v	v	PROPN
ejpam-6761	184	11	→	→	SYM
ejpam-6761	184	12	z	z	X
ejpam-6761	184	13	be	be	AUX
ejpam-6761	184	14	two	two	NUM
ejpam-6761	184	15	bvfrs	bvfrs	NOUN
ejpam-6761	184	16	.	.	PUNCT
ejpam-6761	185	1	the	the	DET
ejpam-6761	185	2	composition	composition	NOUN
ejpam-6761	185	3	of	of	ADP
ejpam-6761	185	4	β	β	X
ejpam-6761	185	5	and	and	CCONJ
ejpam-6761	185	6	γ	γ	PROPN
ejpam-6761	185	7	,	,	PUNCT
ejpam-6761	185	8	denoted	denote	VERB
ejpam-6761	185	9	γ	γ	X
ejpam-6761	185	10	◦	◦	NOUN
ejpam-6761	185	11	β	β	X
ejpam-6761	185	12	:	:	PUNCT
ejpam-6761	185	13	u	u	X
ejpam-6761	185	14	→	→	SYM
ejpam-6761	185	15	z	z	NOUN
ejpam-6761	185	16	,	,	PUNCT
ejpam-6761	185	17	is	be	AUX
ejpam-6761	185	18	a	a	DET
ejpam-6761	185	19	bvfr	bvfr	NOUN
ejpam-6761	185	20	defined	define	VERB
ejpam-6761	185	21	by	by	ADP
ejpam-6761	185	22	γ	γ	NOUN
ejpam-6761	185	23	◦	◦	NOUN
ejpam-6761	185	24	β	β	NOUN
ejpam-6761	185	25	=	=	SYM
ejpam-6761	185	26	(	(	PUNCT
ejpam-6761	185	27	(	(	PUNCT
ejpam-6761	185	28	u	u	NOUN
ejpam-6761	185	29	,	,	PUNCT
ejpam-6761	185	30	z	z	NOUN
ejpam-6761	185	31	)	)	PUNCT
ejpam-6761	185	32	,	,	PUNCT
ejpam-6761	185	33	(	(	PUNCT
ejpam-6761	185	34	(	(	PUNCT
ejpam-6761	185	35	δ−	δ−	ADJ
ejpam-6761	185	36	,	,	PUNCT
ejpam-6761	185	37	δ+	δ+	NOUN
ejpam-6761	185	38	)	)	PUNCT
ejpam-6761	185	39	,	,	PUNCT
ejpam-6761	185	40	(	(	PUNCT
ejpam-6761	185	41	α−	α−	ADP
ejpam-6761	185	42	,	,	PUNCT
ejpam-6761	185	43	α+	α+	NOUN
ejpam-6761	185	44	)	)	PUNCT
ejpam-6761	185	45	)	)	PUNCT
ejpam-6761	185	46	)	)	PUNCT
ejpam-6761	185	47	∈m	∈m	NOUN
ejpam-6761	185	48	:	:	PUNCT
ejpam-6761	185	49	m	m	VERB
ejpam-6761	185	50	∈	∈	PROPN
ejpam-6761	185	51	u×z	u×z	PROPN
ejpam-6761	185	52	.	.	PUNCT
ejpam-6761	185	53	where	where	SCONJ
ejpam-6761	185	54	a	a	DET
ejpam-6761	185	55	k	k	NOUN
ejpam-6761	185	56	-	-	PUNCT
ejpam-6761	185	57	bvf	bvf	NOUN
ejpam-6761	185	58	subset	subset	VERB
ejpam-6761	185	59	m	m	VERB
ejpam-6761	185	60	∈	∈	PROPN
ejpam-6761	185	61	u×z	u×z	PRON
ejpam-6761	185	62	is	be	AUX
ejpam-6761	185	63	defined	define	VERB
ejpam-6761	185	64	by	by	ADP
ejpam-6761	185	65	:	:	PUNCT
ejpam-6761	185	66	(	(	PUNCT
ejpam-6761	185	67	(	(	PUNCT
ejpam-6761	185	68	u	u	NOUN
ejpam-6761	185	69	,	,	PUNCT
ejpam-6761	185	70	z	z	NOUN
ejpam-6761	185	71	)	)	PUNCT
ejpam-6761	185	72	,	,	PUNCT
ejpam-6761	185	73	(	(	PUNCT
ejpam-6761	185	74	(	(	PUNCT
ejpam-6761	185	75	δ−	δ−	ADJ
ejpam-6761	185	76	,	,	PUNCT
ejpam-6761	185	77	δ+	δ+	NOUN
ejpam-6761	185	78	)	)	PUNCT
ejpam-6761	185	79	,	,	PUNCT
ejpam-6761	185	80	(	(	PUNCT
ejpam-6761	185	81	α−	α−	ADP
ejpam-6761	185	82	,	,	PUNCT
ejpam-6761	185	83	α+	α+	NOUN
ejpam-6761	185	84	)	)	PUNCT
ejpam-6761	185	85	)	)	PUNCT
ejpam-6761	185	86	)	)	PUNCT
ejpam-6761	185	87	∈m	∈m	NOUN
ejpam-6761	185	88	if	if	SCONJ
ejpam-6761	185	89	and	and	CCONJ
ejpam-6761	185	90	only	only	ADV
ejpam-6761	185	91	if	if	SCONJ
ejpam-6761	185	92	∃(v	∃(v	PROPN
ejpam-6761	185	93	,	,	PUNCT
ejpam-6761	185	94	(	(	PUNCT
ejpam-6761	185	95	ϑ−	ϑ−	PROPN
ejpam-6761	185	96	,	,	PUNCT
ejpam-6761	185	97	ϑ+	ϑ+	NOUN
ejpam-6761	185	98	)	)	PUNCT
ejpam-6761	185	99	)	)	PUNCT
ejpam-6761	186	1	∈	∈	PROPN
ejpam-6761	186	2	v	v	NOUN
ejpam-6761	186	3	×w	×w	NOUN
ejpam-6761	186	4	such	such	ADJ
ejpam-6761	186	5	that	that	SCONJ
ejpam-6761	186	6	(	(	PUNCT
ejpam-6761	186	7	(	(	PUNCT
ejpam-6761	186	8	u	u	NOUN
ejpam-6761	186	9	,	,	PUNCT
ejpam-6761	186	10	v	v	NOUN
ejpam-6761	186	11	)	)	PUNCT
ejpam-6761	186	12	,	,	PUNCT
ejpam-6761	186	13	(	(	PUNCT
ejpam-6761	186	14	(	(	PUNCT
ejpam-6761	186	15	δ−	δ−	ADJ
ejpam-6761	186	16	,	,	PUNCT
ejpam-6761	186	17	δ+	δ+	NOUN
ejpam-6761	186	18	)	)	PUNCT
ejpam-6761	186	19	,	,	PUNCT
ejpam-6761	186	20	(	(	PUNCT
ejpam-6761	186	21	ϑ−	ϑ−	PROPN
ejpam-6761	186	22	,	,	PUNCT
ejpam-6761	186	23	ϑ+	ϑ+	NOUN
ejpam-6761	186	24	)	)	PUNCT
ejpam-6761	186	25	)	)	PUNCT
ejpam-6761	186	26	)	)	PUNCT
ejpam-6761	187	1	∈	∈	PROPN
ejpam-6761	187	2	a	a	PRON
ejpam-6761	187	3	and	and	CCONJ
ejpam-6761	187	4	(	(	PUNCT
ejpam-6761	187	5	(	(	PUNCT
ejpam-6761	187	6	v	v	NOUN
ejpam-6761	187	7	,	,	PUNCT
ejpam-6761	187	8	z	z	NOUN
ejpam-6761	187	9	)	)	PUNCT
ejpam-6761	187	10	,	,	PUNCT
ejpam-6761	187	11	(	(	PUNCT
ejpam-6761	187	12	(	(	PUNCT
ejpam-6761	187	13	ϑ−	ϑ−	PROPN
ejpam-6761	187	14	,	,	PUNCT
ejpam-6761	187	15	ϑ+	ϑ+	NOUN
ejpam-6761	187	16	)	)	PUNCT
ejpam-6761	187	17	,	,	PUNCT
ejpam-6761	187	18	(	(	PUNCT
ejpam-6761	187	19	α−	α−	ADP
ejpam-6761	187	20	,	,	PUNCT
ejpam-6761	187	21	α+	α+	NOUN
ejpam-6761	187	22	)	)	PUNCT
ejpam-6761	187	23	)	)	PUNCT
ejpam-6761	187	24	)	)	PUNCT
ejpam-6761	188	1	∈	∈	PROPN
ejpam-6761	188	2	b	b	PROPN
ejpam-6761	188	3	for	for	ADP
ejpam-6761	188	4	some	some	DET
ejpam-6761	188	5	β	β	NOUN
ejpam-6761	188	6	and	and	CCONJ
ejpam-6761	188	7	b	b	X
ejpam-6761	188	8	∈	∈	PROPN
ejpam-6761	188	9	γ	γ	PROPN
ejpam-6761	188	10	.	.	PROPN
ejpam-6761	188	11	f.	f.	PROPN
ejpam-6761	188	12	al	al	PROPN
ejpam-6761	188	13	-	-	PROPN
ejpam-6761	188	14	zu’bi	zu’bi	PROPN
ejpam-6761	188	15	et	et	NOUN
ejpam-6761	188	16	al	al	PROPN
ejpam-6761	188	17	.	.	PUNCT
ejpam-6761	188	18	/	/	SYM
ejpam-6761	188	19	eur	eur	PROPN
ejpam-6761	188	20	.	.	PUNCT
ejpam-6761	189	1	j.	j.	PROPN
ejpam-6761	189	2	pure	pure	PROPN
ejpam-6761	189	3	appl	appl	PROPN
ejpam-6761	189	4	.	.	PROPN
ejpam-6761	189	5	math	math	PROPN
ejpam-6761	189	6	,	,	PUNCT
ejpam-6761	189	7	18	18	NUM
ejpam-6761	189	8	(	(	PUNCT
ejpam-6761	189	9	4	4	NUM
ejpam-6761	189	10	)	)	PUNCT
ejpam-6761	189	11	(	(	PUNCT
ejpam-6761	189	12	2025	2025	NUM
ejpam-6761	189	13	)	)	PUNCT
ejpam-6761	189	14	,	,	PUNCT
ejpam-6761	189	15	6761	6761	NUM
ejpam-6761	189	16	9	9	NUM
ejpam-6761	189	17	of	of	ADP
ejpam-6761	189	18	28	28	NUM
ejpam-6761	189	19	definition	definition	NOUN
ejpam-6761	189	20	16	16	NUM
ejpam-6761	189	21	(	(	PUNCT
ejpam-6761	189	22	[	[	X
ejpam-6761	189	23	11	11	NUM
ejpam-6761	189	24	]	]	NUM
ejpam-6761	189	25	)	)	PUNCT
ejpam-6761	189	26	.	.	PUNCT
ejpam-6761	190	1	let	let	VERB
ejpam-6761	190	2	β	β	PRON
ejpam-6761	190	3	be	be	AUX
ejpam-6761	190	4	a	a	DET
ejpam-6761	190	5	bvfr	bvfr	NOUN
ejpam-6761	190	6	in	in	ADP
ejpam-6761	190	7	u	u	PROPN
ejpam-6761	190	8	,	,	PUNCT
ejpam-6761	190	9	i.e.	i.e.	X
ejpam-6761	190	10	,	,	PUNCT
ejpam-6761	190	11	β	β	X
ejpam-6761	190	12	⊂	⊂	X
ejpam-6761	190	13	u×u	u×u	PROPN
ejpam-6761	190	14	.	.	PUNCT
ejpam-6761	191	1	then	then	ADV
ejpam-6761	191	2	:	:	PUNCT
ejpam-6761	191	3	(	(	PUNCT
ejpam-6761	191	4	i	i	NOUN
ejpam-6761	191	5	)	)	PUNCT
ejpam-6761	191	6	β	β	PROPN
ejpam-6761	191	7	is	be	AUX
ejpam-6761	191	8	called	call	VERB
ejpam-6761	191	9	reflexive	reflexive	ADJ
ejpam-6761	191	10	in	in	ADP
ejpam-6761	191	11	u	u	NOUN
ejpam-6761	191	12	if	if	SCONJ
ejpam-6761	192	1	and	and	CCONJ
ejpam-6761	192	2	only	only	ADV
ejpam-6761	192	3	if	if	SCONJ
ejpam-6761	192	4	∀u	∀u	NOUN
ejpam-6761	192	5	∈	∈	NOUN
ejpam-6761	192	6	u	u	NOUN
ejpam-6761	192	7	and	and	CCONJ
ejpam-6761	192	8	∀(δ−	∀(δ−	NOUN
ejpam-6761	192	9	,	,	PUNCT
ejpam-6761	192	10	δ+	δ+	NOUN
ejpam-6761	192	11	)	)	PUNCT
ejpam-6761	192	12	∈	∈	PROPN
ejpam-6761	192	13	w	w	PROPN
ejpam-6761	192	14	,	,	PUNCT
ejpam-6761	192	15	∃h	∃h	NOUN
ejpam-6761	192	16	∈	∈	PROPN
ejpam-6761	192	17	β	β	VERB
ejpam-6761	192	18	such	such	ADJ
ejpam-6761	192	19	that	that	SCONJ
ejpam-6761	192	20	(	(	PUNCT
ejpam-6761	192	21	(	(	PUNCT
ejpam-6761	192	22	u	u	NOUN
ejpam-6761	192	23	,	,	PUNCT
ejpam-6761	192	24	u	u	NOUN
ejpam-6761	192	25	)	)	PUNCT
ejpam-6761	192	26	,	,	PUNCT
ejpam-6761	192	27	(	(	PUNCT
ejpam-6761	192	28	(	(	PUNCT
ejpam-6761	192	29	δ−	δ−	ADJ
ejpam-6761	192	30	,	,	PUNCT
ejpam-6761	192	31	δ+	δ+	NOUN
ejpam-6761	192	32	)	)	PUNCT
ejpam-6761	192	33	,	,	PUNCT
ejpam-6761	192	34	(	(	PUNCT
ejpam-6761	192	35	δ−	δ−	ADJ
ejpam-6761	192	36	,	,	PUNCT
ejpam-6761	192	37	δ+	δ+	NOUN
ejpam-6761	192	38	)	)	PUNCT
ejpam-6761	192	39	)	)	PUNCT
ejpam-6761	192	40	)	)	PUNCT
ejpam-6761	193	1	∈	∈	PROPN
ejpam-6761	193	2	h	h	NOUN
ejpam-6761	193	3	∈	∈	NOUN
ejpam-6761	193	4	β	β	X
ejpam-6761	193	5	,	,	PUNCT
ejpam-6761	193	6	that	that	ADV
ejpam-6761	193	7	is	is	ADV
ejpam-6761	193	8	,	,	PUNCT
ejpam-6761	193	9	if	if	SCONJ
ejpam-6761	193	10	and	and	CCONJ
ejpam-6761	193	11	only	only	ADV
ejpam-6761	193	12	if	if	SCONJ
ejpam-6761	193	13	∆u	∆u	PROPN
ejpam-6761	193	14	⊂	⊂	PROPN
ejpam-6761	193	15	β	β	X
ejpam-6761	193	16	.	.	PUNCT
ejpam-6761	193	17	(	(	PUNCT
ejpam-6761	193	18	ii	ii	NOUN
ejpam-6761	193	19	)	)	PUNCT
ejpam-6761	193	20	β	β	PROPN
ejpam-6761	193	21	is	be	AUX
ejpam-6761	193	22	called	call	VERB
ejpam-6761	193	23	symmetric	symmetric	ADJ
ejpam-6761	193	24	if	if	SCONJ
ejpam-6761	193	25	and	and	CCONJ
ejpam-6761	193	26	only	only	ADV
ejpam-6761	193	27	if	if	SCONJ
ejpam-6761	193	28	whenever	whenever	SCONJ
ejpam-6761	193	29	(	(	PUNCT
ejpam-6761	193	30	(	(	PUNCT
ejpam-6761	193	31	u	u	NOUN
ejpam-6761	193	32	,	,	PUNCT
ejpam-6761	193	33	v	v	NOUN
ejpam-6761	193	34	)	)	PUNCT
ejpam-6761	193	35	,	,	PUNCT
ejpam-6761	193	36	(	(	PUNCT
ejpam-6761	193	37	(	(	PUNCT
ejpam-6761	193	38	δ−	δ−	ADJ
ejpam-6761	193	39	,	,	PUNCT
ejpam-6761	193	40	δ+	δ+	NOUN
ejpam-6761	193	41	)	)	PUNCT
ejpam-6761	193	42	,	,	PUNCT
ejpam-6761	193	43	(	(	PUNCT
ejpam-6761	193	44	n−	n−	NOUN
ejpam-6761	193	45	,	,	PUNCT
ejpam-6761	193	46	n+	n+	NUM
ejpam-6761	193	47	)	)	PUNCT
ejpam-6761	193	48	)	)	PUNCT
ejpam-6761	193	49	)	)	PUNCT
ejpam-6761	194	1	∈	∈	PROPN
ejpam-6761	194	2	h	h	NOUN
ejpam-6761	194	3	∈	∈	PROPN
ejpam-6761	194	4	β	β	X
ejpam-6761	194	5	,	,	PUNCT
ejpam-6761	194	6	∃h	∃h	PROPN
ejpam-6761	194	7	∈	∈	PROPN
ejpam-6761	194	8	ρ	ρ	NOUN
ejpam-6761	194	9	such	such	ADJ
ejpam-6761	194	10	that	that	SCONJ
ejpam-6761	194	11	(	(	PUNCT
ejpam-6761	194	12	(	(	PUNCT
ejpam-6761	194	13	v	v	NOUN
ejpam-6761	194	14	,	,	PUNCT
ejpam-6761	194	15	u	u	NOUN
ejpam-6761	194	16	)	)	PUNCT
ejpam-6761	194	17	,	,	PUNCT
ejpam-6761	194	18	(	(	PUNCT
ejpam-6761	194	19	(	(	PUNCT
ejpam-6761	194	20	n−	n−	NOUN
ejpam-6761	194	21	,	,	PUNCT
ejpam-6761	194	22	n+	n+	NUM
ejpam-6761	194	23	)	)	PUNCT
ejpam-6761	194	24	,	,	PUNCT
ejpam-6761	194	25	(	(	PUNCT
ejpam-6761	194	26	δ−	δ−	ADJ
ejpam-6761	194	27	,	,	PUNCT
ejpam-6761	194	28	δ+	δ+	NOUN
ejpam-6761	194	29	)	)	PUNCT
ejpam-6761	194	30	)	)	PUNCT
ejpam-6761	194	31	)	)	PUNCT
ejpam-6761	195	1	∈	∈	PROPN
ejpam-6761	195	2	t	t	X
ejpam-6761	195	3	∈	∈	PROPN
ejpam-6761	195	4	β	β	X
ejpam-6761	195	5	,	,	PUNCT
ejpam-6761	195	6	that	that	ADV
ejpam-6761	195	7	is	is	ADV
ejpam-6761	195	8	,	,	PUNCT
ejpam-6761	195	9	if	if	SCONJ
ejpam-6761	195	10	and	and	CCONJ
ejpam-6761	195	11	only	only	ADV
ejpam-6761	195	12	if	if	SCONJ
ejpam-6761	195	13	β−1	β−1	ADP
ejpam-6761	195	14	=	=	SYM
ejpam-6761	195	15	β	β	X
ejpam-6761	195	16	.	.	PUNCT
ejpam-6761	195	17	(	(	PUNCT
ejpam-6761	195	18	iii	iii	X
ejpam-6761	195	19	)	)	PUNCT
ejpam-6761	195	20	β	β	PROPN
ejpam-6761	195	21	is	be	AUX
ejpam-6761	195	22	called	call	VERB
ejpam-6761	195	23	transitive	transitive	ADJ
ejpam-6761	195	24	if	if	SCONJ
ejpam-6761	195	25	and	and	CCONJ
ejpam-6761	195	26	only	only	ADV
ejpam-6761	195	27	if	if	SCONJ
ejpam-6761	195	28	whenever	whenever	SCONJ
ejpam-6761	195	29	(	(	PUNCT
ejpam-6761	195	30	(	(	PUNCT
ejpam-6761	195	31	u	u	NOUN
ejpam-6761	195	32	,	,	PUNCT
ejpam-6761	195	33	v	v	NOUN
ejpam-6761	195	34	)	)	PUNCT
ejpam-6761	195	35	,	,	PUNCT
ejpam-6761	195	36	(	(	PUNCT
ejpam-6761	195	37	(	(	PUNCT
ejpam-6761	195	38	δ−	δ−	ADJ
ejpam-6761	195	39	,	,	PUNCT
ejpam-6761	195	40	δ+	δ+	NOUN
ejpam-6761	195	41	)	)	PUNCT
ejpam-6761	195	42	,	,	PUNCT
ejpam-6761	195	43	(	(	PUNCT
ejpam-6761	195	44	ϑ−	ϑ−	PROPN
ejpam-6761	195	45	,	,	PUNCT
ejpam-6761	195	46	ϑ+	ϑ+	NOUN
ejpam-6761	195	47	)	)	PUNCT
ejpam-6761	195	48	)	)	PUNCT
ejpam-6761	195	49	)	)	PUNCT
ejpam-6761	196	1	∈	∈	PROPN
ejpam-6761	196	2	h	h	NOUN
ejpam-6761	196	3	∈	∈	PROPN
ejpam-6761	196	4	β	β	X
ejpam-6761	196	5	and	and	CCONJ
ejpam-6761	196	6	(	(	PUNCT
ejpam-6761	196	7	(	(	PUNCT
ejpam-6761	196	8	v	v	NOUN
ejpam-6761	196	9	,	,	PUNCT
ejpam-6761	196	10	z	z	NOUN
ejpam-6761	196	11	)	)	PUNCT
ejpam-6761	196	12	,	,	PUNCT
ejpam-6761	196	13	(	(	PUNCT
ejpam-6761	196	14	(	(	PUNCT
ejpam-6761	196	15	ϑ−	ϑ−	PROPN
ejpam-6761	196	16	,	,	PUNCT
ejpam-6761	196	17	ϑ+	ϑ+	NOUN
ejpam-6761	196	18	)	)	PUNCT
ejpam-6761	196	19	,	,	PUNCT
ejpam-6761	196	20	(	(	PUNCT
ejpam-6761	196	21	α−	α−	ADP
ejpam-6761	196	22	,	,	PUNCT
ejpam-6761	196	23	α+	α+	NOUN
ejpam-6761	196	24	)	)	PUNCT
ejpam-6761	196	25	)	)	PUNCT
ejpam-6761	196	26	)	)	PUNCT
ejpam-6761	197	1	∈	∈	PROPN
ejpam-6761	197	2	t	t	X
ejpam-6761	197	3	∈	∈	PROPN
ejpam-6761	197	4	β	β	X
ejpam-6761	197	5	,	,	PUNCT
ejpam-6761	197	6	∃c	∃c	PROPN
ejpam-6761	197	7	∈	∈	PROPN
ejpam-6761	197	8	β	β	NOUN
ejpam-6761	197	9	such	such	ADJ
ejpam-6761	197	10	that	that	PRON
ejpam-6761	197	11	(	(	PUNCT
ejpam-6761	197	12	(	(	PUNCT
ejpam-6761	197	13	u	u	NOUN
ejpam-6761	197	14	,	,	PUNCT
ejpam-6761	197	15	z	z	NOUN
ejpam-6761	197	16	)	)	PUNCT
ejpam-6761	197	17	,	,	PUNCT
ejpam-6761	197	18	(	(	PUNCT
ejpam-6761	197	19	(	(	PUNCT
ejpam-6761	197	20	δ−	δ−	ADJ
ejpam-6761	197	21	,	,	PUNCT
ejpam-6761	197	22	δ+	δ+	NOUN
ejpam-6761	197	23	)	)	PUNCT
ejpam-6761	197	24	,	,	PUNCT
ejpam-6761	197	25	(	(	PUNCT
ejpam-6761	197	26	α−	α−	ADP
ejpam-6761	197	27	,	,	PUNCT
ejpam-6761	197	28	α+	α+	NOUN
ejpam-6761	197	29	)	)	PUNCT
ejpam-6761	197	30	)	)	PUNCT
ejpam-6761	197	31	)	)	PUNCT
ejpam-6761	198	1	∈	∈	PROPN
ejpam-6761	198	2	c	c	NOUN
ejpam-6761	198	3	∈	∈	PROPN
ejpam-6761	198	4	β	β	X
ejpam-6761	198	5	,	,	PUNCT
ejpam-6761	198	6	that	that	ADV
ejpam-6761	198	7	is	is	ADV
ejpam-6761	198	8	,	,	PUNCT
ejpam-6761	198	9	if	if	SCONJ
ejpam-6761	198	10	and	and	CCONJ
ejpam-6761	198	11	only	only	ADV
ejpam-6761	198	12	if	if	SCONJ
ejpam-6761	198	13	β	β	X
ejpam-6761	198	14	◦	◦	NOUN
ejpam-6761	198	15	β	β	X
ejpam-6761	198	16	⊂	⊂	NOUN
ejpam-6761	198	17	β	β	X
ejpam-6761	198	18	.	.	PUNCT
ejpam-6761	199	1	a	a	DET
ejpam-6761	199	2	bvfr	bvfr	NOUN
ejpam-6761	199	3	in	in	ADP
ejpam-6761	199	4	u	u	NOUN
ejpam-6761	199	5	is	be	AUX
ejpam-6761	199	6	called	call	VERB
ejpam-6761	199	7	a	a	DET
ejpam-6761	199	8	bvfer	bvfer	NOUN
ejpam-6761	199	9	in	in	ADP
ejpam-6761	199	10	u	u	NOUN
ejpam-6761	199	11	if	if	SCONJ
ejpam-6761	199	12	and	and	CCONJ
ejpam-6761	199	13	only	only	ADV
ejpam-6761	199	14	if	if	SCONJ
ejpam-6761	199	15	it	it	PRON
ejpam-6761	199	16	satisfies	satisfy	VERB
ejpam-6761	199	17	all	all	DET
ejpam-6761	199	18	three	three	NUM
ejpam-6761	199	19	axioms	axiom	NOUN
ejpam-6761	199	20	above	above	ADV
ejpam-6761	199	21	.	.	PUNCT
ejpam-6761	200	1	definition	definition	NOUN
ejpam-6761	200	2	17	17	NUM
ejpam-6761	200	3	(	(	PUNCT
ejpam-6761	200	4	[	[	X
ejpam-6761	200	5	11	11	NUM
ejpam-6761	200	6	]	]	NUM
ejpam-6761	200	7	)	)	PUNCT
ejpam-6761	200	8	.	.	PUNCT
ejpam-6761	201	1	let	let	VERB
ejpam-6761	201	2	u	u	PRON
ejpam-6761	201	3	and	and	CCONJ
ejpam-6761	201	4	v	v	NOUN
ejpam-6761	201	5	be	be	VERB
ejpam-6761	201	6	nonempty	nonempty	ADJ
ejpam-6761	201	7	sets	set	NOUN
ejpam-6761	201	8	.	.	PUNCT
ejpam-6761	202	1	a	a	DET
ejpam-6761	202	2	bvf	bvf	NOUN
ejpam-6761	202	3	function	function	VERB
ejpam-6761	202	4	from	from	ADP
ejpam-6761	202	5	u	u	NOUN
ejpam-6761	202	6	to	to	ADP
ejpam-6761	202	7	v	v	NOUN
ejpam-6761	202	8	can	can	AUX
ejpam-6761	202	9	be	be	AUX
ejpam-6761	202	10	described	describe	VERB
ejpam-6761	202	11	as	as	ADP
ejpam-6761	202	12	a	a	DET
ejpam-6761	202	13	function	function	NOUN
ejpam-6761	202	14	f	f	NOUN
ejpam-6761	202	15	from	from	ADP
ejpam-6761	202	16	wu	wu	PROPN
ejpam-6761	202	17	to	to	ADP
ejpam-6761	202	18	w	w	PROPN
ejpam-6761	202	19	v	v	NOUN
ejpam-6761	202	20	characterized	characterize	VERB
ejpam-6761	202	21	by	by	ADP
ejpam-6761	202	22	the	the	DET
ejpam-6761	202	23	ordered	order	VERB
ejpam-6761	202	24	pair	pair	NOUN
ejpam-6761	202	25	(	(	PUNCT
ejpam-6761	202	26	f	f	X
ejpam-6761	202	27	,	,	PUNCT
ejpam-6761	202	28	{	{	PUNCT
ejpam-6761	202	29	(	(	PUNCT
ejpam-6761	202	30	fu(δ−	fu(δ−	PROPN
ejpam-6761	202	31	)	)	PUNCT
ejpam-6761	202	32	,	,	PUNCT
ejpam-6761	202	33	fu(δ+))}u∈u	fu(δ+))}u∈u	PROPN
ejpam-6761	202	34	)	)	PUNCT
ejpam-6761	202	35	,	,	PUNCT
ejpam-6761	202	36	where	where	SCONJ
ejpam-6761	202	37	f	f	X
ejpam-6761	202	38	:	:	PUNCT
ejpam-6761	202	39	u	u	PROPN
ejpam-6761	202	40	→	→	SYM
ejpam-6761	202	41	v	v	PROPN
ejpam-6761	202	42	is	be	AUX
ejpam-6761	202	43	a	a	DET
ejpam-6761	202	44	function	function	NOUN
ejpam-6761	202	45	from	from	ADP
ejpam-6761	202	46	u	u	NOUN
ejpam-6761	202	47	to	to	ADP
ejpam-6761	202	48	v	v	NOUN
ejpam-6761	202	49	and	and	CCONJ
ejpam-6761	202	50	{	{	PUNCT
ejpam-6761	202	51	(	(	PUNCT
ejpam-6761	202	52	fu(δ−	fu(δ−	PROPN
ejpam-6761	202	53	)	)	PUNCT
ejpam-6761	202	54	,	,	PUNCT
ejpam-6761	202	55	fu(δ+))}u∈u	fu(δ+))}u∈u	PROPN
ejpam-6761	202	56	is	be	AUX
ejpam-6761	202	57	a	a	DET
ejpam-6761	202	58	family	family	NOUN
ejpam-6761	202	59	of	of	ADP
ejpam-6761	202	60	functions	function	NOUN
ejpam-6761	202	61	(	(	PUNCT
ejpam-6761	202	62	fu(δ	fu(δ	NOUN
ejpam-6761	202	63	−	−	NOUN
ejpam-6761	202	64	)	)	PUNCT
ejpam-6761	202	65	,	,	PUNCT
ejpam-6761	202	66	fu(δ	fu(δ	X
ejpam-6761	202	67	+	+	X
ejpam-6761	202	68	)	)	PUNCT
ejpam-6761	202	69	)	)	PUNCT
ejpam-6761	203	1	:	:	PUNCT
ejpam-6761	203	2	w	w	X
ejpam-6761	203	3	→w	→w	PROPN
ejpam-6761	203	4	that	that	PRON
ejpam-6761	203	5	satisfy	satisfy	VERB
ejpam-6761	203	6	the	the	DET
ejpam-6761	203	7	following	follow	VERB
ejpam-6761	203	8	conditions	condition	NOUN
ejpam-6761	203	9	:	:	PUNCT
ejpam-6761	203	10	i.	i.	NOUN
ejpam-6761	203	11	fu(δ	fu(δ	NOUN
ejpam-6761	203	12	−	−	PROPN
ejpam-6761	203	13	)	)	PUNCT
ejpam-6761	203	14	,	,	PUNCT
ejpam-6761	203	15	fu(δ	fu(δ	X
ejpam-6761	203	16	+	+	X
ejpam-6761	203	17	)	)	PUNCT
ejpam-6761	203	18	are	be	AUX
ejpam-6761	203	19	nondecreasing	nondecrease	VERB
ejpam-6761	203	20	on	on	ADP
ejpam-6761	203	21	w	w	PROPN
ejpam-6761	203	22	,	,	PUNCT
ejpam-6761	203	23	and	and	CCONJ
ejpam-6761	203	24	ii	ii	PROPN
ejpam-6761	203	25	.	.	PROPN
ejpam-6761	203	26	fu(δ	fu(δ	PART
ejpam-6761	204	1	−	−	PROPN
ejpam-6761	204	2	=	=	SYM
ejpam-6761	204	3	0	0	X
ejpam-6761	204	4	)	)	PUNCT
ejpam-6761	204	5	=	=	SYM
ejpam-6761	204	6	0	0	PUNCT
ejpam-6761	205	1	=	=	NOUN
ejpam-6761	205	2	fu(δ	fu(δ	NOUN
ejpam-6761	206	1	+	+	PUNCT
ejpam-6761	206	2	=	=	NOUN
ejpam-6761	206	3	0	0	NUM
ejpam-6761	206	4	)	)	PUNCT
ejpam-6761	206	5	,	,	PUNCT
ejpam-6761	206	6	fu(δ	fu(δ	CCONJ
ejpam-6761	206	7	−	−	PROPN
ejpam-6761	206	8	=	=	SYM
ejpam-6761	206	9	−1	−1	NOUN
ejpam-6761	206	10	)	)	PUNCT
ejpam-6761	206	11	=	=	SYM
ejpam-6761	206	12	−1	−1	NOUN
ejpam-6761	206	13	,	,	PUNCT
ejpam-6761	206	14	and	and	CCONJ
ejpam-6761	206	15	fu(δ	fu(δ	X
ejpam-6761	207	1	+	+	CCONJ
ejpam-6761	207	2	=	=	SYM
ejpam-6761	207	3	1	1	X
ejpam-6761	207	4	)	)	PUNCT
ejpam-6761	207	5	=	=	SYM
ejpam-6761	207	6	1	1	X
ejpam-6761	207	7	.	.	X
ejpam-6761	207	8	definition	definition	NOUN
ejpam-6761	207	9	18	18	NUM
ejpam-6761	207	10	(	(	PUNCT
ejpam-6761	207	11	[	[	X
ejpam-6761	207	12	10	10	NUM
ejpam-6761	207	13	]	]	NUM
ejpam-6761	207	14	)	)	PUNCT
ejpam-6761	207	15	.	.	PUNCT
ejpam-6761	208	1	an	an	DET
ejpam-6761	208	2	bipolar	bipolar	ADJ
ejpam-6761	208	3	valued	value	VERB
ejpam-6761	208	4	fuzzy	fuzzy	ADJ
ejpam-6761	208	5	binary	binary	NOUN
ejpam-6761	208	6	operation	operation	NOUN
ejpam-6761	208	7	f	f	PROPN
ejpam-6761	208	8	on	on	ADP
ejpam-6761	208	9	a	a	DET
ejpam-6761	208	10	bvf	bvf	NOUN
ejpam-6761	208	11	-	-	PUNCT
ejpam-6761	208	12	space	space	NOUN
ejpam-6761	208	13	(	(	PUNCT
ejpam-6761	208	14	℧	℧	PROPN
ejpam-6761	208	15	,	,	PUNCT
ejpam-6761	208	16	[	[	X
ejpam-6761	208	17	−1	−1	NOUN
ejpam-6761	208	18	,	,	PUNCT
ejpam-6761	208	19	0	0	NUM
ejpam-6761	208	20	]	]	PUNCT
ejpam-6761	208	21	,	,	PUNCT
ejpam-6761	208	22	[	[	X
ejpam-6761	208	23	0	0	NUM
ejpam-6761	208	24	,	,	PUNCT
ejpam-6761	208	25	1	1	NUM
ejpam-6761	208	26	]	]	PUNCT
ejpam-6761	208	27	)	)	PUNCT
ejpam-6761	208	28	is	be	AUX
ejpam-6761	208	29	a	a	DET
ejpam-6761	208	30	bipolar	bipolar	ADJ
ejpam-6761	208	31	valued	value	VERB
ejpam-6761	208	32	fuzzy	fuzzy	ADJ
ejpam-6761	208	33	function	function	NOUN
ejpam-6761	208	34	f	f	NOUN
ejpam-6761	208	35	:	:	PUNCT
ejpam-6761	208	36	(	(	PUNCT
ejpam-6761	208	37	℧	℧	PROPN
ejpam-6761	208	38	,	,	PUNCT
ejpam-6761	208	39	[	[	X
ejpam-6761	208	40	−1	−1	NOUN
ejpam-6761	208	41	,	,	PUNCT
ejpam-6761	208	42	0	0	NUM
ejpam-6761	208	43	]	]	PUNCT
ejpam-6761	208	44	,	,	PUNCT
ejpam-6761	208	45	[	[	X
ejpam-6761	208	46	0	0	NUM
ejpam-6761	208	47	,	,	PUNCT
ejpam-6761	208	48	1])×	1])×	PRON
ejpam-6761	208	49	(	(	PUNCT
ejpam-6761	208	50	℧	℧	PROPN
ejpam-6761	208	51	,	,	PUNCT
ejpam-6761	208	52	[	[	X
ejpam-6761	208	53	−1	−1	NOUN
ejpam-6761	208	54	,	,	PUNCT
ejpam-6761	208	55	0	0	NUM
ejpam-6761	208	56	]	]	PUNCT
ejpam-6761	208	57	,	,	PUNCT
ejpam-6761	208	58	[	[	X
ejpam-6761	208	59	0	0	NUM
ejpam-6761	208	60	,	,	PUNCT
ejpam-6761	208	61	1	1	NUM
ejpam-6761	208	62	]	]	NUM
ejpam-6761	208	63	)	)	PUNCT
ejpam-6761	208	64	→	→	PUNCT
ejpam-6761	208	65	(	(	PUNCT
ejpam-6761	208	66	℧	℧	PROPN
ejpam-6761	208	67	,	,	PUNCT
ejpam-6761	208	68	[	[	X
ejpam-6761	208	69	−1	−1	NOUN
ejpam-6761	208	70	,	,	PUNCT
ejpam-6761	208	71	0	0	NUM
ejpam-6761	208	72	]	]	PUNCT
ejpam-6761	208	73	,	,	PUNCT
ejpam-6761	208	74	[	[	X
ejpam-6761	208	75	0	0	NUM
ejpam-6761	208	76	,	,	PUNCT
ejpam-6761	208	77	1	1	NUM
ejpam-6761	208	78	]	]	PUNCT
ejpam-6761	208	79	)	)	PUNCT
ejpam-6761	208	80	with	with	ADP
ejpam-6761	208	81	negative	negative	ADJ
ejpam-6761	208	82	comembership	comembership	NOUN
ejpam-6761	208	83	functions	function	NOUN
ejpam-6761	208	84	f−xy	f−xy	NOUN
ejpam-6761	208	85	and	and	CCONJ
ejpam-6761	208	86	positive	positive	ADJ
ejpam-6761	208	87	comembership	comembership	NOUN
ejpam-6761	208	88	functions	function	NOUN
ejpam-6761	209	1	f+xy	f+xy	VERB
ejpam-6761	209	2	satisfying	satisfy	VERB
ejpam-6761	209	3	:	:	PUNCT
ejpam-6761	209	4	f.	f.	PROPN
ejpam-6761	209	5	al	al	PROPN
ejpam-6761	209	6	-	-	PROPN
ejpam-6761	209	7	zu’bi	zu’bi	PROPN
ejpam-6761	209	8	et	et	NOUN
ejpam-6761	209	9	al	al	PROPN
ejpam-6761	209	10	.	.	PUNCT
ejpam-6761	209	11	/	/	SYM
ejpam-6761	209	12	eur	eur	PROPN
ejpam-6761	209	13	.	.	PUNCT
ejpam-6761	210	1	j.	j.	PROPN
ejpam-6761	210	2	pure	pure	PROPN
ejpam-6761	210	3	appl	appl	PROPN
ejpam-6761	210	4	.	.	PROPN
ejpam-6761	210	5	math	math	PROPN
ejpam-6761	210	6	,	,	PUNCT
ejpam-6761	210	7	18	18	NUM
ejpam-6761	210	8	(	(	PUNCT
ejpam-6761	210	9	4	4	NUM
ejpam-6761	210	10	)	)	PUNCT
ejpam-6761	210	11	(	(	PUNCT
ejpam-6761	210	12	2025	2025	NUM
ejpam-6761	210	13	)	)	PUNCT
ejpam-6761	210	14	,	,	PUNCT
ejpam-6761	210	15	6761	6761	NUM
ejpam-6761	210	16	10	10	NUM
ejpam-6761	210	17	of	of	ADP
ejpam-6761	210	18	28	28	NUM
ejpam-6761	210	19	(	(	PUNCT
ejpam-6761	210	20	1	1	NUM
ejpam-6761	210	21	)	)	PUNCT
ejpam-6761	210	22	f−xy(n	f−xy(n	NOUN
ejpam-6761	210	23	−,m−	−,m−	NOUN
ejpam-6761	210	24	)	)	PUNCT
ejpam-6761	210	25	̸=	̸=	PROPN
ejpam-6761	210	26	0	0	NUM
ejpam-6761	210	27	⇐	⇐	ADJ
ejpam-6761	210	28	⇒	⇒	NOUN
ejpam-6761	210	29	n−	n−	NOUN
ejpam-6761	210	30	̸=	̸=	PROPN
ejpam-6761	210	31	0	0	NUM
ejpam-6761	210	32	,	,	PUNCT
ejpam-6761	210	33	m−	m−	PROPN
ejpam-6761	210	34	̸=	̸=	PROPN
ejpam-6761	210	35	0	0	NUM
ejpam-6761	210	36	f−xy(w	f−xy(w	NOUN
ejpam-6761	210	37	−	−	NOUN
ejpam-6761	210	38	,	,	PUNCT
ejpam-6761	210	39	z−	z−	ADJ
ejpam-6761	210	40	)	)	PUNCT
ejpam-6761	210	41	̸=	̸=	PROPN
ejpam-6761	210	42	−1	−1	NOUN
ejpam-6761	210	43	⇐	⇐	ADJ
ejpam-6761	210	44	⇒	⇒	NOUN
ejpam-6761	210	45	w−	w−	NOUN
ejpam-6761	210	46	̸=	̸=	PROPN
ejpam-6761	210	47	−1	−1	NOUN
ejpam-6761	210	48	,	,	PUNCT
ejpam-6761	210	49	z−	z−	PROPN
ejpam-6761	210	50	̸=	̸=	PROPN
ejpam-6761	210	51	−1	−1	NOUN
ejpam-6761	210	52	f+xy(n	f+xy(n	NOUN
ejpam-6761	210	53	+	+	ADJ
ejpam-6761	210	54	,	,	PUNCT
ejpam-6761	210	55	m+	m+	NUM
ejpam-6761	210	56	)	)	PUNCT
ejpam-6761	210	57	̸=	̸=	PROPN
ejpam-6761	210	58	0	0	NUM
ejpam-6761	210	59	⇐	⇐	ADJ
ejpam-6761	210	60	⇒	⇒	NOUN
ejpam-6761	210	61	n+	n+	PUNCT
ejpam-6761	210	62	̸=	̸=	PROPN
ejpam-6761	210	63	0	0	NUM
ejpam-6761	210	64	,	,	PUNCT
ejpam-6761	210	65	m+	m+	NOUN
ejpam-6761	210	66	̸=	̸=	NOUN
ejpam-6761	210	67	0	0	NUM
ejpam-6761	210	68	f+xy(w	f+xy(w	PROPN
ejpam-6761	210	69	+	+	PROPN
ejpam-6761	210	70	,	,	PUNCT
ejpam-6761	210	71	z+	z+	NUM
ejpam-6761	210	72	)	)	PUNCT
ejpam-6761	210	73	̸=	̸=	PROPN
ejpam-6761	210	74	1	1	NUM
ejpam-6761	210	75	⇐	⇐	ADJ
ejpam-6761	210	76	⇒	⇒	NOUN
ejpam-6761	210	77	w+	w+	NUM
ejpam-6761	210	78	̸=	̸=	PROPN
ejpam-6761	210	79	1	1	NUM
ejpam-6761	210	80	,	,	PUNCT
ejpam-6761	210	81	z+	z+	NUM
ejpam-6761	210	82	̸=	̸=	PROPN
ejpam-6761	210	83	1	1	NUM
ejpam-6761	210	84	(	(	PUNCT
ejpam-6761	210	85	2	2	NUM
ejpam-6761	210	86	)	)	PUNCT
ejpam-6761	210	87	f−xy	f−xy	NOUN
ejpam-6761	210	88	,	,	PUNCT
ejpam-6761	210	89	f	f	PROPN
ejpam-6761	211	1	+	+	CCONJ
ejpam-6761	211	2	xy	xy	PROPN
ejpam-6761	211	3	are	be	AUX
ejpam-6761	211	4	onto	onto	ADP
ejpam-6761	211	5	.	.	PUNCT
ejpam-6761	212	1	that	that	PRON
ejpam-6761	212	2	is	be	AUX
ejpam-6761	212	3	,	,	PUNCT
ejpam-6761	212	4	f−xy([−1	f−xy([−1	PROPN
ejpam-6761	212	5	,	,	PUNCT
ejpam-6761	212	6	0	0	NUM
ejpam-6761	212	7	]	]	X
ejpam-6761	212	8	×	×	NOUN
ejpam-6761	213	1	[	[	X
ejpam-6761	213	2	−1	−1	NOUN
ejpam-6761	213	3	,	,	PUNCT
ejpam-6761	213	4	0	0	NUM
ejpam-6761	213	5	]	]	PUNCT
ejpam-6761	213	6	)	)	PUNCT
ejpam-6761	214	1	=	=	PUNCT
ejpam-6761	215	1	[	[	X
ejpam-6761	215	2	−1	−1	NOUN
ejpam-6761	215	3	,	,	PUNCT
ejpam-6761	215	4	0	0	NUM
ejpam-6761	215	5	]	]	PUNCT
ejpam-6761	215	6	and	and	CCONJ
ejpam-6761	215	7	f+xy([0	f+xy([0	NOUN
ejpam-6761	215	8	,	,	PUNCT
ejpam-6761	215	9	1	1	NUM
ejpam-6761	215	10	]	]	SYM
ejpam-6761	215	11	×	×	NOUN
ejpam-6761	215	12	[	[	X
ejpam-6761	215	13	0	0	NUM
ejpam-6761	215	14	,	,	PUNCT
ejpam-6761	215	15	1	1	NUM
ejpam-6761	215	16	]	]	PUNCT
ejpam-6761	215	17	)	)	PUNCT
ejpam-6761	216	1	=	=	PUNCT
ejpam-6761	217	1	[	[	X
ejpam-6761	217	2	0	0	NUM
ejpam-6761	217	3	,	,	PUNCT
ejpam-6761	217	4	1	1	NUM
ejpam-6761	217	5	]	]	PUNCT
ejpam-6761	217	6	.	.	PUNCT
ejpam-6761	218	1	thus	thus	ADV
ejpam-6761	218	2	,	,	PUNCT
ejpam-6761	218	3	for	for	ADP
ejpam-6761	218	4	any	any	DET
ejpam-6761	218	5	two	two	NUM
ejpam-6761	218	6	bvf	bvf	NOUN
ejpam-6761	218	7	-	-	PUNCT
ejpam-6761	218	8	elements	element	NOUN
ejpam-6761	218	9	(	(	PUNCT
ejpam-6761	218	10	x	x	X
ejpam-6761	218	11	,	,	PUNCT
ejpam-6761	218	12	[	[	X
ejpam-6761	218	13	−1	−1	NOUN
ejpam-6761	218	14	,	,	PUNCT
ejpam-6761	218	15	0	0	NUM
ejpam-6761	218	16	]	]	PUNCT
ejpam-6761	218	17	,	,	PUNCT
ejpam-6761	218	18	[	[	X
ejpam-6761	218	19	0	0	NUM
ejpam-6761	218	20	,	,	PUNCT
ejpam-6761	218	21	1	1	NUM
ejpam-6761	218	22	]	]	NUM
ejpam-6761	218	23	)	)	PUNCT
ejpam-6761	218	24	,	,	PUNCT
ejpam-6761	218	25	(	(	PUNCT
ejpam-6761	218	26	y	y	NOUN
ejpam-6761	218	27	,	,	PUNCT
ejpam-6761	218	28	[	[	X
ejpam-6761	218	29	−1	−1	NOUN
ejpam-6761	218	30	,	,	PUNCT
ejpam-6761	218	31	0	0	NUM
ejpam-6761	218	32	]	]	PUNCT
ejpam-6761	218	33	,	,	PUNCT
ejpam-6761	218	34	[	[	X
ejpam-6761	218	35	0	0	NUM
ejpam-6761	218	36	,	,	PUNCT
ejpam-6761	218	37	1	1	NUM
ejpam-6761	218	38	]	]	PUNCT
ejpam-6761	218	39	)	)	PUNCT
ejpam-6761	218	40	of	of	ADP
ejpam-6761	218	41	the	the	DET
ejpam-6761	218	42	bvf	bvf	NOUN
ejpam-6761	218	43	-	-	PUNCT
ejpam-6761	218	44	space	space	NOUN
ejpam-6761	218	45	℧	℧	PROPN
ejpam-6761	218	46	and	and	CCONJ
ejpam-6761	218	47	any	any	DET
ejpam-6761	218	48	bvfbo	bvfbo	NOUN
ejpam-6761	218	49	f	f	X
ejpam-6761	218	50	=	=	SYM
ejpam-6761	218	51	(	(	PUNCT
ejpam-6761	218	52	f	f	PROPN
ejpam-6761	218	53	,	,	PUNCT
ejpam-6761	218	54	f−xy	f−xy	PROPN
ejpam-6761	218	55	,	,	PUNCT
ejpam-6761	218	56	f	f	PROPN
ejpam-6761	218	57	+	+	CCONJ
ejpam-6761	218	58	xy	xy	PROPN
ejpam-6761	218	59	)	)	PUNCT
ejpam-6761	218	60	defined	define	VERB
ejpam-6761	218	61	on	on	ADP
ejpam-6761	218	62	℧	℧	PROPN
ejpam-6761	218	63	,	,	PUNCT
ejpam-6761	218	64	the	the	DET
ejpam-6761	218	65	action	action	NOUN
ejpam-6761	218	66	of	of	ADP
ejpam-6761	218	67	the	the	DET
ejpam-6761	218	68	bvfbo	bvfbo	PROPN
ejpam-6761	218	69	f	f	PROPN
ejpam-6761	218	70	over	over	ADP
ejpam-6761	218	71	℧	℧	PROPN
ejpam-6761	218	72	is	be	AUX
ejpam-6761	218	73	given	give	VERB
ejpam-6761	218	74	by	by	ADP
ejpam-6761	218	75	(	(	PUNCT
ejpam-6761	218	76	x,−i	x,−i	PROPN
ejpam-6761	218	77	,	,	PUNCT
ejpam-6761	218	78	i)f	i)f	ADJ
ejpam-6761	218	79	(	(	PUNCT
ejpam-6761	218	80	y,−i	y,−i	PROPN
ejpam-6761	218	81	,	,	PUNCT
ejpam-6761	218	82	i	i	NOUN
ejpam-6761	218	83	)	)	PUNCT
ejpam-6761	219	1	=	=	SYM
ejpam-6761	219	2	f	f	PROPN
ejpam-6761	219	3	(	(	PUNCT
ejpam-6761	219	4	(	(	PUNCT
ejpam-6761	219	5	x	x	X
ejpam-6761	219	6	,	,	PUNCT
ejpam-6761	219	7	[	[	X
ejpam-6761	219	8	−1	−1	NOUN
ejpam-6761	219	9	,	,	PUNCT
ejpam-6761	219	10	0	0	NUM
ejpam-6761	219	11	]	]	PUNCT
ejpam-6761	219	12	,	,	PUNCT
ejpam-6761	219	13	[	[	X
ejpam-6761	219	14	0	0	NUM
ejpam-6761	219	15	,	,	PUNCT
ejpam-6761	219	16	1	1	NUM
ejpam-6761	219	17	]	]	NUM
ejpam-6761	219	18	)	)	PUNCT
ejpam-6761	219	19	,	,	PUNCT
ejpam-6761	219	20	(	(	PUNCT
ejpam-6761	219	21	y	y	NOUN
ejpam-6761	219	22	,	,	PUNCT
ejpam-6761	219	23	[	[	X
ejpam-6761	219	24	−1	−1	NOUN
ejpam-6761	219	25	,	,	PUNCT
ejpam-6761	219	26	0	0	NUM
ejpam-6761	219	27	]	]	PUNCT
ejpam-6761	219	28	,	,	PUNCT
ejpam-6761	219	29	[	[	X
ejpam-6761	219	30	0	0	NUM
ejpam-6761	219	31	,	,	PUNCT
ejpam-6761	219	32	1	1	NUM
ejpam-6761	219	33	]	]	NUM
ejpam-6761	219	34	)	)	PUNCT
ejpam-6761	219	35	)	)	PUNCT
ejpam-6761	220	1	=	=	PRON
ejpam-6761	220	2	(	(	PUNCT
ejpam-6761	220	3	f	f	X
ejpam-6761	220	4	(	(	PUNCT
ejpam-6761	220	5	x	x	PROPN
ejpam-6761	220	6	,	,	PUNCT
ejpam-6761	220	7	y	y	PROPN
ejpam-6761	220	8	)	)	PUNCT
ejpam-6761	220	9	,	,	PUNCT
ejpam-6761	220	10	f−xy([−1	f−xy([−1	PROPN
ejpam-6761	220	11	,	,	PUNCT
ejpam-6761	220	12	0]×	0]×	NUM
ejpam-6761	221	1	[	[	X
ejpam-6761	221	2	−1	−1	NOUN
ejpam-6761	221	3	,	,	PUNCT
ejpam-6761	221	4	0	0	NUM
ejpam-6761	221	5	]	]	PUNCT
ejpam-6761	221	6	)	)	PUNCT
ejpam-6761	221	7	,	,	PUNCT
ejpam-6761	221	8	f+xy([0	f+xy([0	X
ejpam-6761	221	9	,	,	PUNCT
ejpam-6761	221	10	1]×	1]×	NUM
ejpam-6761	222	1	[	[	X
ejpam-6761	222	2	0	0	NUM
ejpam-6761	222	3	,	,	PUNCT
ejpam-6761	222	4	1	1	NUM
ejpam-6761	222	5	]	]	NUM
ejpam-6761	222	6	)	)	PUNCT
ejpam-6761	222	7	)	)	PUNCT
ejpam-6761	223	1	(	(	PUNCT
ejpam-6761	223	2	f	f	X
ejpam-6761	223	3	(	(	PUNCT
ejpam-6761	223	4	x	x	PROPN
ejpam-6761	223	5	,	,	PUNCT
ejpam-6761	223	6	y	y	PROPN
ejpam-6761	223	7	)	)	PUNCT
ejpam-6761	223	8	,	,	PUNCT
ejpam-6761	224	1	[	[	X
ejpam-6761	224	2	−1	−1	NOUN
ejpam-6761	224	3	,	,	PUNCT
ejpam-6761	224	4	0	0	NUM
ejpam-6761	224	5	]	]	PUNCT
ejpam-6761	224	6	,	,	PUNCT
ejpam-6761	225	1	[	[	X
ejpam-6761	225	2	0	0	NUM
ejpam-6761	225	3	,	,	PUNCT
ejpam-6761	225	4	1	1	NUM
ejpam-6761	225	5	]	]	NUM
ejpam-6761	225	6	)	)	PUNCT
ejpam-6761	225	7	.	.	PUNCT
ejpam-6761	226	1	definition	definition	NOUN
ejpam-6761	226	2	19	19	NUM
ejpam-6761	226	3	(	(	PUNCT
ejpam-6761	226	4	[	[	X
ejpam-6761	226	5	10	10	NUM
ejpam-6761	226	6	]	]	NUM
ejpam-6761	226	7	)	)	PUNCT
ejpam-6761	226	8	.	.	PUNCT
ejpam-6761	227	1	(	(	PUNCT
ejpam-6761	227	2	classical	classical	ADJ
ejpam-6761	227	3	bvf	bvf	NOUN
ejpam-6761	227	4	group	group	NOUN
ejpam-6761	227	5	)	)	PUNCT
ejpam-6761	227	6	.	.	PUNCT
ejpam-6761	228	1	a	a	DET
ejpam-6761	228	2	bvf	bvf	NOUN
ejpam-6761	228	3	-	-	PUNCT
ejpam-6761	228	4	group	group	NOUN
ejpam-6761	228	5	(	(	PUNCT
ejpam-6761	228	6	(	(	PUNCT
ejpam-6761	228	7	g	g	NOUN
ejpam-6761	228	8	,	,	PUNCT
ejpam-6761	228	9	[	[	X
ejpam-6761	228	10	−1	−1	NOUN
ejpam-6761	228	11	,	,	PUNCT
ejpam-6761	228	12	0	0	NUM
ejpam-6761	228	13	]	]	PUNCT
ejpam-6761	228	14	,	,	PUNCT
ejpam-6761	228	15	[	[	X
ejpam-6761	228	16	0	0	NUM
ejpam-6761	228	17	,	,	PUNCT
ejpam-6761	228	18	1	1	NUM
ejpam-6761	228	19	]	]	NUM
ejpam-6761	228	20	)	)	PUNCT
ejpam-6761	228	21	,	,	PUNCT
ejpam-6761	228	22	f	f	PROPN
ejpam-6761	228	23	)	)	PUNCT
ejpam-6761	228	24	consists	consist	VERB
ejpam-6761	228	25	of	of	ADP
ejpam-6761	228	26	a	a	DET
ejpam-6761	228	27	set	set	NOUN
ejpam-6761	228	28	g	g	NOUN
ejpam-6761	228	29	and	and	CCONJ
ejpam-6761	228	30	a	a	DET
ejpam-6761	228	31	bvf	bvf	NOUN
ejpam-6761	228	32	binary	binary	PROPN
ejpam-6761	228	33	operation	operation	PROPN
ejpam-6761	228	34	f	f	PROPN
ejpam-6761	228	35	on	on	ADP
ejpam-6761	228	36	the	the	DET
ejpam-6761	228	37	bvf	bvf	NOUN
ejpam-6761	228	38	-	-	PUNCT
ejpam-6761	228	39	space	space	NOUN
ejpam-6761	228	40	such	such	ADJ
ejpam-6761	228	41	that	that	PRON
ejpam-6761	228	42	:	:	PUNCT
ejpam-6761	228	43	(	(	PUNCT
ejpam-6761	228	44	i	i	NOUN
ejpam-6761	228	45	)	)	PUNCT
ejpam-6761	228	46	associativity	associativity	PROPN
ejpam-6761	228	47	holds	hold	VERB
ejpam-6761	228	48	in	in	ADP
ejpam-6761	228	49	the	the	DET
ejpam-6761	228	50	bvf	bvf	NOUN
ejpam-6761	228	51	sense	sense	NOUN
ejpam-6761	228	52	;	;	PUNCT
ejpam-6761	228	53	(	(	PUNCT
ejpam-6761	228	54	ii	ii	NOUN
ejpam-6761	228	55	)	)	PUNCT
ejpam-6761	228	56	there	there	PRON
ejpam-6761	228	57	exists	exist	VERB
ejpam-6761	228	58	a	a	DET
ejpam-6761	228	59	bvf	bvf	NOUN
ejpam-6761	228	60	identity	identity	NOUN
ejpam-6761	228	61	;	;	PUNCT
ejpam-6761	228	62	(	(	PUNCT
ejpam-6761	228	63	iii	iii	X
ejpam-6761	228	64	)	)	PUNCT
ejpam-6761	228	65	each	each	DET
ejpam-6761	228	66	bvf	bvf	NOUN
ejpam-6761	228	67	element	element	NOUN
ejpam-6761	228	68	has	have	VERB
ejpam-6761	228	69	a	a	DET
ejpam-6761	228	70	bvf	bvf	NOUN
ejpam-6761	228	71	inverse	inverse	NOUN
ejpam-6761	228	72	.	.	PUNCT
ejpam-6761	229	1	this	this	PRON
ejpam-6761	229	2	aligns	align	VERB
ejpam-6761	229	3	with	with	ADP
ejpam-6761	229	4	the	the	DET
ejpam-6761	229	5	classical	classical	ADJ
ejpam-6761	229	6	group	group	NOUN
ejpam-6761	229	7	axioms	axiom	VERB
ejpam-6761	229	8	under	under	ADP
ejpam-6761	229	9	the	the	DET
ejpam-6761	229	10	correspondence	correspondence	NOUN
ejpam-6761	229	11	between	between	ADP
ejpam-6761	229	12	bvf	bvf	NOUN
ejpam-6761	229	13	-	-	PUNCT
ejpam-6761	229	14	elements	element	NOUN
ejpam-6761	229	15	and	and	CCONJ
ejpam-6761	229	16	their	their	PRON
ejpam-6761	229	17	positive	positive	ADJ
ejpam-6761	229	18	/	/	SYM
ejpam-6761	229	19	negative	negative	ADJ
ejpam-6761	229	20	components	component	NOUN
ejpam-6761	229	21	.	.	PUNCT
ejpam-6761	230	1	definition	definition	NOUN
ejpam-6761	230	2	20	20	NUM
ejpam-6761	230	3	(	(	PUNCT
ejpam-6761	230	4	[	[	X
ejpam-6761	230	5	10	10	NUM
ejpam-6761	230	6	]	]	NUM
ejpam-6761	230	7	)	)	PUNCT
ejpam-6761	230	8	.	.	PUNCT
ejpam-6761	231	1	for	for	SCONJ
ejpam-6761	231	2	all	all	DET
ejpam-6761	231	3	bvf	bvf	NOUN
ejpam-6761	231	4	-	-	PUNCT
ejpam-6761	231	5	elements	element	NOUN
ejpam-6761	231	6	have	have	VERB
ejpam-6761	231	7	an	an	DET
ejpam-6761	231	8	inverse	inverse	NOUN
ejpam-6761	231	9	,	,	PUNCT
ejpam-6761	231	10	a	a	DET
ejpam-6761	231	11	bipolar	bipolar	NOUN
ejpam-6761	231	12	valued	value	VERB
ejpam-6761	231	13	fuzzy	fuzzy	ADJ
ejpam-6761	231	14	monoid	monoid	NOUN
ejpam-6761	231	15	is	be	AUX
ejpam-6761	231	16	called	call	VERB
ejpam-6761	231	17	a	a	DET
ejpam-6761	231	18	bipolar	bipolar	ADJ
ejpam-6761	231	19	valued	value	VERB
ejpam-6761	231	20	fuzzy	fuzzy	ADJ
ejpam-6761	231	21	group	group	NOUN
ejpam-6761	231	22	.	.	PUNCT
ejpam-6761	232	1	equivalently	equivalently	ADV
ejpam-6761	232	2	,	,	PUNCT
ejpam-6761	232	3	a	a	DET
ejpam-6761	232	4	bipolar	bipolar	ADJ
ejpam-6761	232	5	valued	value	VERB
ejpam-6761	232	6	fuzzy	fuzzy	ADJ
ejpam-6761	232	7	groupoid	groupoid	NOUN
ejpam-6761	232	8	(	(	PUNCT
ejpam-6761	232	9	g	g	NOUN
ejpam-6761	232	10	,	,	PUNCT
ejpam-6761	232	11	[	[	X
ejpam-6761	232	12	−1	−1	NOUN
ejpam-6761	232	13	,	,	PUNCT
ejpam-6761	232	14	0	0	NUM
ejpam-6761	232	15	]	]	PUNCT
ejpam-6761	232	16	,	,	PUNCT
ejpam-6761	232	17	[	[	X
ejpam-6761	232	18	0	0	NUM
ejpam-6761	232	19	,	,	PUNCT
ejpam-6761	232	20	1	1	NUM
ejpam-6761	232	21	]	]	PUNCT
ejpam-6761	232	22	,	,	PUNCT
ejpam-6761	232	23	f	f	PROPN
ejpam-6761	232	24	)	)	PUNCT
ejpam-6761	232	25	is	be	AUX
ejpam-6761	232	26	a	a	DET
ejpam-6761	232	27	bvf	bvf	NOUN
ejpam-6761	232	28	-	-	PUNCT
ejpam-6761	232	29	group	group	NOUN
ejpam-6761	232	30	iff	iff	NOUN
ejpam-6761	232	31	the	the	DET
ejpam-6761	232	32	following	follow	VERB
ejpam-6761	232	33	restrictions	restriction	NOUN
ejpam-6761	232	34	hold	hold	VERB
ejpam-6761	232	35	:	:	PUNCT
ejpam-6761	232	36	(	(	PUNCT
ejpam-6761	232	37	1	1	X
ejpam-6761	232	38	)	)	PUNCT
ejpam-6761	232	39	for	for	ADP
ejpam-6761	232	40	any	any	DET
ejpam-6761	232	41	bvf	bvf	NOUN
ejpam-6761	232	42	-	-	PUNCT
ejpam-6761	232	43	elements	element	NOUN
ejpam-6761	232	44	(	(	PUNCT
ejpam-6761	232	45	x	x	X
ejpam-6761	232	46	,	,	PUNCT
ejpam-6761	232	47	[	[	X
ejpam-6761	232	48	−1	−1	NOUN
ejpam-6761	232	49	,	,	PUNCT
ejpam-6761	232	50	0	0	NUM
ejpam-6761	232	51	]	]	PUNCT
ejpam-6761	232	52	,	,	PUNCT
ejpam-6761	232	53	[	[	X
ejpam-6761	232	54	0	0	NUM
ejpam-6761	232	55	,	,	PUNCT
ejpam-6761	232	56	1	1	NUM
ejpam-6761	232	57	]	]	NUM
ejpam-6761	232	58	)	)	PUNCT
ejpam-6761	232	59	,	,	PUNCT
ejpam-6761	232	60	(	(	PUNCT
ejpam-6761	232	61	y	y	NOUN
ejpam-6761	232	62	,	,	PUNCT
ejpam-6761	232	63	[	[	X
ejpam-6761	232	64	−1	−1	NOUN
ejpam-6761	232	65	,	,	PUNCT
ejpam-6761	232	66	0	0	NUM
ejpam-6761	232	67	]	]	PUNCT
ejpam-6761	232	68	,	,	PUNCT
ejpam-6761	232	69	[	[	X
ejpam-6761	232	70	0	0	NUM
ejpam-6761	232	71	,	,	PUNCT
ejpam-6761	232	72	1	1	NUM
ejpam-6761	232	73	]	]	NUM
ejpam-6761	232	74	)	)	PUNCT
ejpam-6761	232	75	,	,	PUNCT
ejpam-6761	232	76	(	(	PUNCT
ejpam-6761	232	77	z	z	X
ejpam-6761	232	78	,	,	PUNCT
ejpam-6761	232	79	[	[	X
ejpam-6761	232	80	−1	−1	NOUN
ejpam-6761	232	81	,	,	PUNCT
ejpam-6761	232	82	0	0	NUM
ejpam-6761	232	83	]	]	PUNCT
ejpam-6761	232	84	,	,	PUNCT
ejpam-6761	233	1	[	[	X
ejpam-6761	233	2	0	0	NUM
ejpam-6761	233	3	,	,	PUNCT
ejpam-6761	233	4	1	1	NUM
ejpam-6761	233	5	]	]	PUNCT
ejpam-6761	233	6	)	)	PUNCT
ejpam-6761	233	7	∈	∈	PROPN
ejpam-6761	233	8	(	(	PUNCT
ejpam-6761	233	9	g	g	NOUN
ejpam-6761	233	10	,	,	PUNCT
ejpam-6761	233	11	[	[	X
ejpam-6761	233	12	−1	−1	NOUN
ejpam-6761	233	13	,	,	PUNCT
ejpam-6761	233	14	0	0	NUM
ejpam-6761	233	15	]	]	PUNCT
ejpam-6761	233	16	,	,	PUNCT
ejpam-6761	234	1	[	[	X
ejpam-6761	234	2	0	0	NUM
ejpam-6761	234	3	,	,	PUNCT
ejpam-6761	234	4	1	1	NUM
ejpam-6761	234	5	]	]	PUNCT
ejpam-6761	234	6	,	,	PUNCT
ejpam-6761	234	7	f	f	PROPN
ejpam-6761	234	8	)	)	PUNCT
ejpam-6761	234	9	:	:	PUNCT
ejpam-6761	235	1	(	(	PUNCT
ejpam-6761	235	2	(	(	PUNCT
ejpam-6761	235	3	x	x	X
ejpam-6761	235	4	,	,	PUNCT
ejpam-6761	235	5	[	[	X
ejpam-6761	235	6	−1	−1	NOUN
ejpam-6761	235	7	,	,	PUNCT
ejpam-6761	235	8	0	0	NUM
ejpam-6761	235	9	]	]	PUNCT
ejpam-6761	235	10	,	,	PUNCT
ejpam-6761	235	11	[	[	X
ejpam-6761	235	12	0	0	NUM
ejpam-6761	235	13	,	,	PUNCT
ejpam-6761	235	14	1])f	1])f	NUM
ejpam-6761	235	15	(	(	PUNCT
ejpam-6761	235	16	y	y	NOUN
ejpam-6761	235	17	,	,	PUNCT
ejpam-6761	235	18	[	[	X
ejpam-6761	235	19	−1	−1	NOUN
ejpam-6761	235	20	,	,	PUNCT
ejpam-6761	235	21	0	0	NUM
ejpam-6761	235	22	]	]	PUNCT
ejpam-6761	235	23	,	,	PUNCT
ejpam-6761	235	24	[	[	X
ejpam-6761	235	25	0	0	NUM
ejpam-6761	235	26	,	,	PUNCT
ejpam-6761	235	27	1]))f	1]))f	NUM
ejpam-6761	235	28	(	(	PUNCT
ejpam-6761	235	29	z	z	NOUN
ejpam-6761	235	30	,	,	PUNCT
ejpam-6761	235	31	[	[	X
ejpam-6761	235	32	−1	−1	NOUN
ejpam-6761	235	33	,	,	PUNCT
ejpam-6761	235	34	0	0	NUM
ejpam-6761	235	35	]	]	PUNCT
ejpam-6761	235	36	,	,	PUNCT
ejpam-6761	235	37	[	[	X
ejpam-6761	235	38	0	0	NUM
ejpam-6761	235	39	,	,	PUNCT
ejpam-6761	235	40	1	1	NUM
ejpam-6761	235	41	]	]	PUNCT
ejpam-6761	235	42	)	)	PUNCT
ejpam-6761	236	1	=	=	SYM
ejpam-6761	236	2	(	(	PUNCT
ejpam-6761	236	3	x	x	X
ejpam-6761	236	4	,	,	PUNCT
ejpam-6761	236	5	[	[	X
ejpam-6761	236	6	−1	−1	NOUN
ejpam-6761	236	7	,	,	PUNCT
ejpam-6761	236	8	0	0	NUM
ejpam-6761	236	9	]	]	PUNCT
ejpam-6761	236	10	,	,	PUNCT
ejpam-6761	237	1	[	[	X
ejpam-6761	237	2	0	0	NUM
ejpam-6761	237	3	,	,	PUNCT
ejpam-6761	237	4	1])f	1])f	NUM
ejpam-6761	237	5	(	(	PUNCT
ejpam-6761	237	6	(	(	PUNCT
ejpam-6761	237	7	y	y	NOUN
ejpam-6761	237	8	,	,	PUNCT
ejpam-6761	237	9	[	[	X
ejpam-6761	237	10	−1	−1	NOUN
ejpam-6761	237	11	,	,	PUNCT
ejpam-6761	237	12	0	0	NUM
ejpam-6761	237	13	]	]	PUNCT
ejpam-6761	237	14	,	,	PUNCT
ejpam-6761	237	15	[	[	X
ejpam-6761	237	16	0	0	NUM
ejpam-6761	237	17	,	,	PUNCT
ejpam-6761	237	18	1])f	1])f	NUM
ejpam-6761	237	19	(	(	PUNCT
ejpam-6761	237	20	z	z	NOUN
ejpam-6761	237	21	,	,	PUNCT
ejpam-6761	237	22	[	[	X
ejpam-6761	237	23	−1	−1	NOUN
ejpam-6761	237	24	,	,	PUNCT
ejpam-6761	237	25	0	0	NUM
ejpam-6761	237	26	]	]	PUNCT
ejpam-6761	237	27	,	,	PUNCT
ejpam-6761	237	28	[	[	X
ejpam-6761	237	29	0	0	NUM
ejpam-6761	237	30	,	,	PUNCT
ejpam-6761	237	31	1	1	NUM
ejpam-6761	237	32	]	]	NUM
ejpam-6761	237	33	)	)	PUNCT
ejpam-6761	237	34	)	)	PUNCT
ejpam-6761	237	35	.	.	PUNCT
ejpam-6761	238	1	f.	f.	PROPN
ejpam-6761	238	2	al	al	PROPN
ejpam-6761	238	3	-	-	PROPN
ejpam-6761	238	4	zu’bi	zu’bi	PROPN
ejpam-6761	238	5	et	et	NOUN
ejpam-6761	238	6	al	al	PROPN
ejpam-6761	238	7	.	.	PUNCT
ejpam-6761	238	8	/	/	SYM
ejpam-6761	238	9	eur	eur	PROPN
ejpam-6761	238	10	.	.	PUNCT
ejpam-6761	239	1	j.	j.	PROPN
ejpam-6761	239	2	pure	pure	PROPN
ejpam-6761	239	3	appl	appl	PROPN
ejpam-6761	239	4	.	.	PROPN
ejpam-6761	239	5	math	math	PROPN
ejpam-6761	239	6	,	,	PUNCT
ejpam-6761	239	7	18	18	NUM
ejpam-6761	239	8	(	(	PUNCT
ejpam-6761	239	9	4	4	NUM
ejpam-6761	239	10	)	)	PUNCT
ejpam-6761	239	11	(	(	PUNCT
ejpam-6761	239	12	2025	2025	NUM
ejpam-6761	239	13	)	)	PUNCT
ejpam-6761	239	14	,	,	PUNCT
ejpam-6761	239	15	6761	6761	NUM
ejpam-6761	239	16	11	11	NUM
ejpam-6761	239	17	of	of	ADP
ejpam-6761	239	18	28	28	NUM
ejpam-6761	239	19	(	(	PUNCT
ejpam-6761	239	20	2	2	NUM
ejpam-6761	239	21	)	)	PUNCT
ejpam-6761	239	22	there	there	PRON
ejpam-6761	239	23	exists	exist	VERB
ejpam-6761	239	24	a	a	DET
ejpam-6761	239	25	bvf	bvf	NOUN
ejpam-6761	239	26	-	-	PUNCT
ejpam-6761	239	27	element	element	NOUN
ejpam-6761	239	28	(	(	PUNCT
ejpam-6761	239	29	e	e	NOUN
ejpam-6761	239	30	,	,	PUNCT
ejpam-6761	239	31	[	[	X
ejpam-6761	239	32	−1	−1	NOUN
ejpam-6761	239	33	,	,	PUNCT
ejpam-6761	239	34	0	0	NUM
ejpam-6761	239	35	]	]	PUNCT
ejpam-6761	239	36	,	,	PUNCT
ejpam-6761	239	37	[	[	X
ejpam-6761	239	38	0	0	NUM
ejpam-6761	239	39	,	,	PUNCT
ejpam-6761	239	40	1	1	NUM
ejpam-6761	239	41	]	]	PUNCT
ejpam-6761	239	42	)	)	PUNCT
ejpam-6761	239	43	∈	∈	PROPN
ejpam-6761	239	44	(	(	PUNCT
ejpam-6761	239	45	g	g	NOUN
ejpam-6761	239	46	,	,	PUNCT
ejpam-6761	239	47	[	[	X
ejpam-6761	239	48	−1	−1	NOUN
ejpam-6761	239	49	,	,	PUNCT
ejpam-6761	239	50	0	0	NUM
ejpam-6761	239	51	]	]	PUNCT
ejpam-6761	239	52	,	,	PUNCT
ejpam-6761	240	1	[	[	X
ejpam-6761	240	2	0	0	NUM
ejpam-6761	240	3	,	,	PUNCT
ejpam-6761	240	4	1	1	NUM
ejpam-6761	240	5	]	]	PUNCT
ejpam-6761	240	6	)	)	PUNCT
ejpam-6761	241	1	such	such	ADJ
ejpam-6761	241	2	that	that	PRON
ejpam-6761	241	3	for	for	ADP
ejpam-6761	241	4	all	all	DET
ejpam-6761	241	5	(	(	PUNCT
ejpam-6761	241	6	x	x	NOUN
ejpam-6761	241	7	,	,	PUNCT
ejpam-6761	241	8	[	[	X
ejpam-6761	241	9	−1	−1	NOUN
ejpam-6761	241	10	,	,	PUNCT
ejpam-6761	241	11	0	0	NUM
ejpam-6761	241	12	]	]	PUNCT
ejpam-6761	241	13	,	,	PUNCT
ejpam-6761	242	1	[	[	X
ejpam-6761	242	2	0	0	NUM
ejpam-6761	242	3	,	,	PUNCT
ejpam-6761	242	4	1])in(g	1])in(g	NUM
ejpam-6761	242	5	,	,	PUNCT
ejpam-6761	242	6	[	[	X
ejpam-6761	242	7	−1	−1	NOUN
ejpam-6761	242	8	,	,	PUNCT
ejpam-6761	242	9	0	0	NUM
ejpam-6761	242	10	]	]	PUNCT
ejpam-6761	242	11	,	,	PUNCT
ejpam-6761	242	12	[	[	X
ejpam-6761	242	13	0	0	NUM
ejpam-6761	242	14	,	,	PUNCT
ejpam-6761	242	15	1	1	NUM
ejpam-6761	242	16	]	]	PUNCT
ejpam-6761	242	17	,	,	PUNCT
ejpam-6761	242	18	f	f	PROPN
ejpam-6761	242	19	)	)	PUNCT
ejpam-6761	242	20	:	:	PUNCT
ejpam-6761	243	1	(	(	PUNCT
ejpam-6761	243	2	e	e	X
ejpam-6761	243	3	,	,	PUNCT
ejpam-6761	243	4	[	[	X
ejpam-6761	243	5	−1	−1	NOUN
ejpam-6761	243	6	,	,	PUNCT
ejpam-6761	243	7	0	0	NUM
ejpam-6761	243	8	]	]	PUNCT
ejpam-6761	243	9	,	,	PUNCT
ejpam-6761	243	10	[	[	X
ejpam-6761	243	11	0	0	NUM
ejpam-6761	243	12	,	,	PUNCT
ejpam-6761	243	13	1])f	1])f	NUM
ejpam-6761	243	14	(	(	PUNCT
ejpam-6761	243	15	x	x	X
ejpam-6761	243	16	,	,	PUNCT
ejpam-6761	243	17	[	[	X
ejpam-6761	243	18	−1	−1	NOUN
ejpam-6761	243	19	,	,	PUNCT
ejpam-6761	243	20	0	0	NUM
ejpam-6761	243	21	]	]	PUNCT
ejpam-6761	243	22	,	,	PUNCT
ejpam-6761	243	23	[	[	X
ejpam-6761	243	24	0	0	NUM
ejpam-6761	243	25	,	,	PUNCT
ejpam-6761	243	26	1	1	NUM
ejpam-6761	243	27	]	]	PUNCT
ejpam-6761	243	28	)	)	PUNCT
ejpam-6761	243	29	=	=	SYM
ejpam-6761	243	30	(	(	PUNCT
ejpam-6761	243	31	x	x	X
ejpam-6761	243	32	,	,	PUNCT
ejpam-6761	243	33	[	[	X
ejpam-6761	243	34	−1	−1	NOUN
ejpam-6761	243	35	,	,	PUNCT
ejpam-6761	243	36	0	0	NUM
ejpam-6761	243	37	]	]	PUNCT
ejpam-6761	243	38	,	,	PUNCT
ejpam-6761	243	39	[	[	X
ejpam-6761	243	40	0	0	NUM
ejpam-6761	243	41	,	,	PUNCT
ejpam-6761	243	42	1])f	1])f	NUM
ejpam-6761	243	43	(	(	PUNCT
ejpam-6761	243	44	e	e	NOUN
ejpam-6761	243	45	,	,	PUNCT
ejpam-6761	243	46	[	[	X
ejpam-6761	243	47	−1	−1	NOUN
ejpam-6761	243	48	,	,	PUNCT
ejpam-6761	243	49	0	0	NUM
ejpam-6761	243	50	]	]	PUNCT
ejpam-6761	243	51	,	,	PUNCT
ejpam-6761	243	52	[	[	X
ejpam-6761	243	53	0	0	NUM
ejpam-6761	243	54	,	,	PUNCT
ejpam-6761	243	55	1	1	NUM
ejpam-6761	243	56	]	]	PUNCT
ejpam-6761	243	57	)	)	PUNCT
ejpam-6761	243	58	=	=	SYM
ejpam-6761	243	59	(	(	PUNCT
ejpam-6761	243	60	x	x	X
ejpam-6761	243	61	,	,	PUNCT
ejpam-6761	243	62	[	[	X
ejpam-6761	243	63	−1	−1	NOUN
ejpam-6761	243	64	,	,	PUNCT
ejpam-6761	243	65	0	0	NUM
ejpam-6761	243	66	]	]	PUNCT
ejpam-6761	243	67	,	,	PUNCT
ejpam-6761	243	68	[	[	X
ejpam-6761	243	69	0	0	NUM
ejpam-6761	243	70	,	,	PUNCT
ejpam-6761	243	71	1	1	NUM
ejpam-6761	243	72	]	]	NUM
ejpam-6761	243	73	)	)	PUNCT
ejpam-6761	243	74	.	.	PUNCT
ejpam-6761	244	1	(	(	PUNCT
ejpam-6761	244	2	3	3	X
ejpam-6761	244	3	)	)	PUNCT
ejpam-6761	244	4	for	for	ADP
ejpam-6761	244	5	every	every	DET
ejpam-6761	244	6	bvf	bvf	NOUN
ejpam-6761	244	7	-	-	PUNCT
ejpam-6761	244	8	element	element	NOUN
ejpam-6761	244	9	(	(	PUNCT
ejpam-6761	244	10	x	x	X
ejpam-6761	244	11	,	,	PUNCT
ejpam-6761	244	12	[	[	X
ejpam-6761	244	13	−1	−1	NOUN
ejpam-6761	244	14	,	,	PUNCT
ejpam-6761	244	15	0	0	NUM
ejpam-6761	244	16	]	]	PUNCT
ejpam-6761	244	17	,	,	PUNCT
ejpam-6761	244	18	[	[	X
ejpam-6761	244	19	0	0	NUM
ejpam-6761	244	20	,	,	PUNCT
ejpam-6761	244	21	1])in(g	1])in(g	NUM
ejpam-6761	244	22	,	,	PUNCT
ejpam-6761	244	23	[	[	X
ejpam-6761	244	24	−1	−1	NOUN
ejpam-6761	244	25	,	,	PUNCT
ejpam-6761	244	26	0	0	NUM
ejpam-6761	244	27	]	]	PUNCT
ejpam-6761	244	28	,	,	PUNCT
ejpam-6761	245	1	[	[	X
ejpam-6761	245	2	0	0	NUM
ejpam-6761	245	3	,	,	PUNCT
ejpam-6761	245	4	1	1	NUM
ejpam-6761	245	5	]	]	PUNCT
ejpam-6761	245	6	,	,	PUNCT
ejpam-6761	245	7	f	f	PROPN
ejpam-6761	245	8	)	)	PUNCT
ejpam-6761	245	9	,	,	PUNCT
ejpam-6761	245	10	there	there	PRON
ejpam-6761	245	11	exists	exist	VERB
ejpam-6761	245	12	a	a	DET
ejpam-6761	245	13	bvf	bvf	NOUN
ejpam-6761	245	14	-	-	PUNCT
ejpam-6761	245	15	element	element	NOUN
ejpam-6761	245	16	(	(	PUNCT
ejpam-6761	245	17	x−1	x−1	PROPN
ejpam-6761	245	18	,	,	PUNCT
ejpam-6761	245	19	[	[	X
ejpam-6761	245	20	−1	−1	NOUN
ejpam-6761	245	21	,	,	PUNCT
ejpam-6761	245	22	0	0	NUM
ejpam-6761	245	23	]	]	PUNCT
ejpam-6761	245	24	,	,	PUNCT
ejpam-6761	245	25	[	[	X
ejpam-6761	245	26	0	0	NUM
ejpam-6761	245	27	,	,	PUNCT
ejpam-6761	245	28	1])in(g	1])in(g	NUM
ejpam-6761	245	29	,	,	PUNCT
ejpam-6761	245	30	[	[	X
ejpam-6761	245	31	−1	−1	NOUN
ejpam-6761	245	32	,	,	PUNCT
ejpam-6761	245	33	0	0	NUM
ejpam-6761	245	34	]	]	PUNCT
ejpam-6761	245	35	,	,	PUNCT
ejpam-6761	245	36	[	[	X
ejpam-6761	245	37	0	0	NUM
ejpam-6761	245	38	,	,	PUNCT
ejpam-6761	245	39	1	1	NUM
ejpam-6761	245	40	]	]	PUNCT
ejpam-6761	245	41	,	,	PUNCT
ejpam-6761	245	42	f	f	PROPN
ejpam-6761	245	43	)	)	PUNCT
ejpam-6761	245	44	such	such	ADJ
ejpam-6761	245	45	that	that	SCONJ
ejpam-6761	245	46	:	:	PUNCT
ejpam-6761	245	47	(	(	PUNCT
ejpam-6761	245	48	x	x	X
ejpam-6761	245	49	,	,	PUNCT
ejpam-6761	245	50	[	[	X
ejpam-6761	245	51	−1	−1	NOUN
ejpam-6761	245	52	,	,	PUNCT
ejpam-6761	245	53	0	0	NUM
ejpam-6761	245	54	]	]	PUNCT
ejpam-6761	245	55	,	,	PUNCT
ejpam-6761	245	56	[	[	X
ejpam-6761	245	57	0	0	NUM
ejpam-6761	245	58	,	,	PUNCT
ejpam-6761	245	59	1])f	1])f	NUM
ejpam-6761	245	60	(	(	PUNCT
ejpam-6761	245	61	x−1	x−1	PROPN
ejpam-6761	245	62	,	,	PUNCT
ejpam-6761	245	63	[	[	X
ejpam-6761	245	64	−1	−1	NOUN
ejpam-6761	245	65	,	,	PUNCT
ejpam-6761	245	66	0	0	NUM
ejpam-6761	245	67	]	]	PUNCT
ejpam-6761	245	68	,	,	PUNCT
ejpam-6761	245	69	[	[	X
ejpam-6761	245	70	0	0	NUM
ejpam-6761	245	71	,	,	PUNCT
ejpam-6761	245	72	1	1	NUM
ejpam-6761	245	73	]	]	PUNCT
ejpam-6761	245	74	)	)	PUNCT
ejpam-6761	245	75	=	=	SYM
ejpam-6761	246	1	(	(	PUNCT
ejpam-6761	246	2	x−1	x−1	PROPN
ejpam-6761	246	3	,	,	PUNCT
ejpam-6761	246	4	[	[	X
ejpam-6761	246	5	−1	−1	NOUN
ejpam-6761	246	6	,	,	PUNCT
ejpam-6761	246	7	0	0	NUM
ejpam-6761	246	8	]	]	PUNCT
ejpam-6761	246	9	,	,	PUNCT
ejpam-6761	246	10	[	[	X
ejpam-6761	246	11	0	0	NUM
ejpam-6761	246	12	,	,	PUNCT
ejpam-6761	246	13	1])f	1])f	NUM
ejpam-6761	246	14	(	(	PUNCT
ejpam-6761	246	15	x	x	X
ejpam-6761	246	16	,	,	PUNCT
ejpam-6761	246	17	[	[	X
ejpam-6761	246	18	−1	−1	NOUN
ejpam-6761	246	19	,	,	PUNCT
ejpam-6761	246	20	0	0	NUM
ejpam-6761	246	21	]	]	PUNCT
ejpam-6761	246	22	,	,	PUNCT
ejpam-6761	246	23	[	[	X
ejpam-6761	246	24	0	0	NUM
ejpam-6761	246	25	,	,	PUNCT
ejpam-6761	246	26	1	1	NUM
ejpam-6761	246	27	]	]	PUNCT
ejpam-6761	246	28	)	)	PUNCT
ejpam-6761	246	29	=	=	SYM
ejpam-6761	246	30	(	(	PUNCT
ejpam-6761	246	31	e	e	NOUN
ejpam-6761	246	32	,	,	PUNCT
ejpam-6761	246	33	[	[	X
ejpam-6761	246	34	−1	−1	NOUN
ejpam-6761	246	35	,	,	PUNCT
ejpam-6761	246	36	0	0	NUM
ejpam-6761	246	37	]	]	PUNCT
ejpam-6761	246	38	,	,	PUNCT
ejpam-6761	246	39	[	[	X
ejpam-6761	246	40	0	0	NUM
ejpam-6761	246	41	,	,	PUNCT
ejpam-6761	246	42	1	1	NUM
ejpam-6761	246	43	]	]	NUM
ejpam-6761	246	44	)	)	PUNCT
ejpam-6761	246	45	.	.	PUNCT
ejpam-6761	247	1	a	a	DET
ejpam-6761	247	2	bvf	bvf	NOUN
ejpam-6761	247	3	-	-	PUNCT
ejpam-6761	247	4	group	group	NOUN
ejpam-6761	247	5	(	(	PUNCT
ejpam-6761	247	6	(	(	PUNCT
ejpam-6761	247	7	g	g	NOUN
ejpam-6761	247	8	,	,	PUNCT
ejpam-6761	247	9	[	[	X
ejpam-6761	247	10	−1	−1	NOUN
ejpam-6761	247	11	,	,	PUNCT
ejpam-6761	247	12	0	0	NUM
ejpam-6761	247	13	]	]	PUNCT
ejpam-6761	247	14	,	,	PUNCT
ejpam-6761	247	15	[	[	X
ejpam-6761	247	16	0	0	NUM
ejpam-6761	247	17	,	,	PUNCT
ejpam-6761	247	18	1	1	NUM
ejpam-6761	247	19	]	]	NUM
ejpam-6761	247	20	)	)	PUNCT
ejpam-6761	247	21	,	,	PUNCT
ejpam-6761	247	22	f	f	PROPN
ejpam-6761	247	23	)	)	PUNCT
ejpam-6761	247	24	is	be	AUX
ejpam-6761	247	25	named	name	VERB
ejpam-6761	247	26	an	an	DET
ejpam-6761	247	27	abelian	abelian	ADJ
ejpam-6761	247	28	bvf	bvf	NOUN
ejpam-6761	247	29	-	-	PUNCT
ejpam-6761	247	30	group	group	NOUN
ejpam-6761	247	31	if	if	SCONJ
ejpam-6761	247	32	and	and	CCONJ
ejpam-6761	247	33	only	only	ADV
ejpam-6761	247	34	if	if	SCONJ
ejpam-6761	247	35	for	for	ADP
ejpam-6761	247	36	all	all	DET
ejpam-6761	247	37	(	(	PUNCT
ejpam-6761	247	38	x	x	NOUN
ejpam-6761	247	39	,	,	PUNCT
ejpam-6761	247	40	[	[	X
ejpam-6761	247	41	−1	−1	NOUN
ejpam-6761	247	42	,	,	PUNCT
ejpam-6761	247	43	0	0	NUM
ejpam-6761	247	44	]	]	PUNCT
ejpam-6761	247	45	,	,	PUNCT
ejpam-6761	247	46	[	[	X
ejpam-6761	247	47	0	0	NUM
ejpam-6761	247	48	,	,	PUNCT
ejpam-6761	247	49	1	1	NUM
ejpam-6761	247	50	]	]	NUM
ejpam-6761	247	51	)	)	PUNCT
ejpam-6761	247	52	,	,	PUNCT
ejpam-6761	247	53	(	(	PUNCT
ejpam-6761	247	54	y	y	NOUN
ejpam-6761	247	55	,	,	PUNCT
ejpam-6761	247	56	[	[	X
ejpam-6761	247	57	−1	−1	NOUN
ejpam-6761	247	58	,	,	PUNCT
ejpam-6761	247	59	0	0	NUM
ejpam-6761	247	60	]	]	PUNCT
ejpam-6761	247	61	,	,	PUNCT
ejpam-6761	247	62	[	[	X
ejpam-6761	247	63	0	0	NUM
ejpam-6761	247	64	,	,	PUNCT
ejpam-6761	247	65	1	1	NUM
ejpam-6761	247	66	]	]	PUNCT
ejpam-6761	247	67	)	)	PUNCT
ejpam-6761	247	68	∈	∈	PROPN
ejpam-6761	247	69	(	(	PUNCT
ejpam-6761	247	70	(	(	PUNCT
ejpam-6761	247	71	g	g	NOUN
ejpam-6761	247	72	,	,	PUNCT
ejpam-6761	247	73	[	[	X
ejpam-6761	247	74	−1	−1	NOUN
ejpam-6761	247	75	,	,	PUNCT
ejpam-6761	247	76	0	0	NUM
ejpam-6761	247	77	]	]	PUNCT
ejpam-6761	247	78	,	,	PUNCT
ejpam-6761	248	1	[	[	X
ejpam-6761	248	2	0	0	NUM
ejpam-6761	248	3	,	,	PUNCT
ejpam-6761	248	4	1	1	NUM
ejpam-6761	248	5	]	]	NUM
ejpam-6761	248	6	)	)	PUNCT
ejpam-6761	248	7	,	,	PUNCT
ejpam-6761	248	8	f	f	PROPN
ejpam-6761	248	9	)	)	PUNCT
ejpam-6761	248	10	,	,	PUNCT
ejpam-6761	248	11	(	(	PUNCT
ejpam-6761	248	12	x	x	X
ejpam-6761	248	13	,	,	PUNCT
ejpam-6761	248	14	[	[	X
ejpam-6761	248	15	−1	−1	NOUN
ejpam-6761	248	16	,	,	PUNCT
ejpam-6761	248	17	0	0	NUM
ejpam-6761	248	18	]	]	PUNCT
ejpam-6761	248	19	,	,	PUNCT
ejpam-6761	248	20	[	[	X
ejpam-6761	248	21	0	0	NUM
ejpam-6761	248	22	,	,	PUNCT
ejpam-6761	248	23	1])f	1])f	NUM
ejpam-6761	248	24	(	(	PUNCT
ejpam-6761	248	25	y	y	NOUN
ejpam-6761	248	26	,	,	PUNCT
ejpam-6761	248	27	[	[	X
ejpam-6761	248	28	−1	−1	NOUN
ejpam-6761	248	29	,	,	PUNCT
ejpam-6761	248	30	0	0	NUM
ejpam-6761	248	31	]	]	PUNCT
ejpam-6761	248	32	,	,	PUNCT
ejpam-6761	249	1	[	[	X
ejpam-6761	249	2	0	0	NUM
ejpam-6761	249	3	,	,	PUNCT
ejpam-6761	249	4	1	1	NUM
ejpam-6761	249	5	]	]	PUNCT
ejpam-6761	249	6	)	)	PUNCT
ejpam-6761	249	7	=	=	SYM
ejpam-6761	249	8	(	(	PUNCT
ejpam-6761	249	9	y	y	NOUN
ejpam-6761	249	10	,	,	PUNCT
ejpam-6761	249	11	[	[	X
ejpam-6761	249	12	−1	−1	NOUN
ejpam-6761	249	13	,	,	PUNCT
ejpam-6761	249	14	0	0	NUM
ejpam-6761	249	15	]	]	PUNCT
ejpam-6761	249	16	,	,	PUNCT
ejpam-6761	250	1	[	[	X
ejpam-6761	250	2	0	0	NUM
ejpam-6761	250	3	,	,	PUNCT
ejpam-6761	250	4	1])f	1])f	NUM
ejpam-6761	250	5	(	(	PUNCT
ejpam-6761	250	6	x	x	X
ejpam-6761	250	7	,	,	PUNCT
ejpam-6761	250	8	[	[	X
ejpam-6761	250	9	−1	−1	NOUN
ejpam-6761	250	10	,	,	PUNCT
ejpam-6761	250	11	0	0	NUM
ejpam-6761	250	12	]	]	PUNCT
ejpam-6761	250	13	,	,	PUNCT
ejpam-6761	250	14	[	[	X
ejpam-6761	250	15	0	0	NUM
ejpam-6761	250	16	,	,	PUNCT
ejpam-6761	250	17	1	1	NUM
ejpam-6761	250	18	]	]	NUM
ejpam-6761	250	19	)	)	PUNCT
ejpam-6761	250	20	.	.	PUNCT
ejpam-6761	251	1	identical	identical	ADJ
ejpam-6761	251	2	to	to	ADP
ejpam-6761	251	3	the	the	DET
ejpam-6761	251	4	bipolar	bipolar	PROPN
ejpam-6761	251	5	valued	value	VERB
ejpam-6761	251	6	fuzzy	fuzzy	ADJ
ejpam-6761	251	7	groupoid	groupoid	NOUN
ejpam-6761	251	8	,	,	PUNCT
ejpam-6761	251	9	the	the	DET
ejpam-6761	251	10	following	follow	VERB
ejpam-6761	251	11	theorem	theorem	NOUN
ejpam-6761	251	12	establishes	establish	VERB
ejpam-6761	251	13	a	a	DET
ejpam-6761	251	14	relationship	relationship	NOUN
ejpam-6761	251	15	between	between	ADP
ejpam-6761	251	16	bvf	bvf	NOUN
ejpam-6761	251	17	-	-	PUNCT
ejpam-6761	251	18	groups	group	NOUN
ejpam-6761	251	19	and	and	CCONJ
ejpam-6761	251	20	both	both	CCONJ
ejpam-6761	251	21	ordinary	ordinary	ADJ
ejpam-6761	251	22	and	and	CCONJ
ejpam-6761	251	23	fuzzy	fuzzy	ADJ
ejpam-6761	251	24	groups	group	NOUN
ejpam-6761	251	25	.	.	PUNCT
ejpam-6761	252	1	theorem	theorem	NOUN
ejpam-6761	252	2	1	1	NUM
ejpam-6761	252	3	(	(	PUNCT
ejpam-6761	252	4	[	[	X
ejpam-6761	252	5	10	10	NUM
ejpam-6761	252	6	]	]	NUM
ejpam-6761	252	7	)	)	PUNCT
ejpam-6761	252	8	.	.	PUNCT
ejpam-6761	253	1	(	(	PUNCT
ejpam-6761	253	2	1	1	X
ejpam-6761	253	3	)	)	PUNCT
ejpam-6761	253	4	associated	associate	VERB
ejpam-6761	253	5	to	to	ADP
ejpam-6761	253	6	each	each	DET
ejpam-6761	253	7	bipolar	bipolar	PROPN
ejpam-6761	253	8	valued	value	VERB
ejpam-6761	253	9	fuzzy	fuzzy	ADJ
ejpam-6761	253	10	group	group	NOUN
ejpam-6761	253	11	(	(	PUNCT
ejpam-6761	253	12	(	(	PUNCT
ejpam-6761	253	13	g	g	NOUN
ejpam-6761	253	14	,	,	PUNCT
ejpam-6761	253	15	[	[	X
ejpam-6761	253	16	−1	−1	NOUN
ejpam-6761	253	17	,	,	PUNCT
ejpam-6761	253	18	0	0	NUM
ejpam-6761	253	19	]	]	PUNCT
ejpam-6761	253	20	,	,	PUNCT
ejpam-6761	254	1	[	[	X
ejpam-6761	254	2	0	0	NUM
ejpam-6761	254	3	,	,	PUNCT
ejpam-6761	254	4	1	1	NUM
ejpam-6761	254	5	]	]	NUM
ejpam-6761	254	6	)	)	PUNCT
ejpam-6761	254	7	,	,	PUNCT
ejpam-6761	254	8	f	f	PROPN
ejpam-6761	254	9	)	)	PUNCT
ejpam-6761	254	10	where	where	SCONJ
ejpam-6761	254	11	f	f	X
ejpam-6761	254	12	=	=	PRON
ejpam-6761	254	13	(	(	PUNCT
ejpam-6761	254	14	f	f	PROPN
ejpam-6761	254	15	,	,	PUNCT
ejpam-6761	254	16	f−xy	f−xy	PROPN
ejpam-6761	254	17	,	,	PUNCT
ejpam-6761	254	18	f	f	PROPN
ejpam-6761	255	1	+	+	CCONJ
ejpam-6761	255	2	xy	xy	PROPN
ejpam-6761	255	3	)	)	PUNCT
ejpam-6761	255	4	a	a	DET
ejpam-6761	255	5	fuzzy	fuzzy	ADJ
ejpam-6761	255	6	group	group	NOUN
ejpam-6761	255	7	(	(	PUNCT
ejpam-6761	255	8	(	(	PUNCT
ejpam-6761	255	9	g	g	NOUN
ejpam-6761	255	10	,	,	PUNCT
ejpam-6761	255	11	[	[	X
ejpam-6761	255	12	0	0	NUM
ejpam-6761	255	13	,	,	PUNCT
ejpam-6761	255	14	1	1	NUM
ejpam-6761	255	15	]	]	NUM
ejpam-6761	255	16	)	)	PUNCT
ejpam-6761	255	17	,	,	PUNCT
ejpam-6761	255	18	f̄	f̄	PROPN
ejpam-6761	255	19	)	)	PUNCT
ejpam-6761	255	20	where	where	SCONJ
ejpam-6761	255	21	f̄	f̄	PROPN
ejpam-6761	255	22	=	=	PUNCT
ejpam-6761	255	23	(	(	PUNCT
ejpam-6761	255	24	f	f	X
ejpam-6761	255	25	,	,	PUNCT
ejpam-6761	255	26	f+xy	f+xy	PROPN
ejpam-6761	255	27	)	)	PUNCT
ejpam-6761	255	28	which	which	PRON
ejpam-6761	255	29	is	be	AUX
ejpam-6761	255	30	isomorphic	isomorphic	ADJ
ejpam-6761	255	31	to	to	ADP
ejpam-6761	255	32	the	the	DET
ejpam-6761	255	33	bipolar	bipolar	ADJ
ejpam-6761	255	34	valued	value	VERB
ejpam-6761	255	35	fuzzy	fuzzy	ADJ
ejpam-6761	255	36	group	group	NOUN
ejpam-6761	255	37	(	(	PUNCT
ejpam-6761	255	38	(	(	PUNCT
ejpam-6761	255	39	g	g	NOUN
ejpam-6761	255	40	,	,	PUNCT
ejpam-6761	255	41	[	[	X
ejpam-6761	255	42	−1	−1	NOUN
ejpam-6761	255	43	,	,	PUNCT
ejpam-6761	255	44	0	0	NUM
ejpam-6761	255	45	]	]	PUNCT
ejpam-6761	255	46	,	,	PUNCT
ejpam-6761	255	47	[	[	X
ejpam-6761	255	48	0	0	NUM
ejpam-6761	255	49	,	,	PUNCT
ejpam-6761	255	50	1	1	NUM
ejpam-6761	255	51	]	]	NUM
ejpam-6761	255	52	)	)	PUNCT
ejpam-6761	255	53	,	,	PUNCT
ejpam-6761	255	54	f	f	PROPN
ejpam-6761	255	55	)	)	PUNCT
ejpam-6761	255	56	by	by	ADP
ejpam-6761	255	57	the	the	DET
ejpam-6761	255	58	correspondence	correspondence	NOUN
ejpam-6761	255	59	(	(	PUNCT
ejpam-6761	255	60	x	x	X
ejpam-6761	255	61	,	,	PUNCT
ejpam-6761	255	62	[	[	X
ejpam-6761	255	63	−1	−1	NOUN
ejpam-6761	255	64	,	,	PUNCT
ejpam-6761	255	65	0	0	NUM
ejpam-6761	255	66	]	]	PUNCT
ejpam-6761	255	67	,	,	PUNCT
ejpam-6761	255	68	[	[	X
ejpam-6761	255	69	0	0	NUM
ejpam-6761	255	70	,	,	PUNCT
ejpam-6761	255	71	1	1	NUM
ejpam-6761	255	72	]	]	PUNCT
ejpam-6761	255	73	)	)	PUNCT
ejpam-6761	255	74	↔	↔	PROPN
ejpam-6761	255	75	(	(	PUNCT
ejpam-6761	255	76	x	x	X
ejpam-6761	255	77	,	,	PUNCT
ejpam-6761	255	78	[	[	X
ejpam-6761	255	79	0	0	NUM
ejpam-6761	255	80	,	,	PUNCT
ejpam-6761	255	81	1	1	NUM
ejpam-6761	255	82	]	]	NUM
ejpam-6761	255	83	)	)	PUNCT
ejpam-6761	255	84	.	.	PUNCT
ejpam-6761	256	1	(	(	PUNCT
ejpam-6761	256	2	2	2	X
ejpam-6761	256	3	)	)	PUNCT
ejpam-6761	256	4	there	there	PRON
ejpam-6761	256	5	is	be	VERB
ejpam-6761	256	6	an	an	DET
ejpam-6761	256	7	associated	associate	VERB
ejpam-6761	256	8	(	(	PUNCT
ejpam-6761	256	9	ordinary	ordinary	ADJ
ejpam-6761	256	10	)	)	PUNCT
ejpam-6761	256	11	group	group	NOUN
ejpam-6761	256	12	(	(	PUNCT
ejpam-6761	256	13	g	g	PROPN
ejpam-6761	256	14	,	,	PUNCT
ejpam-6761	256	15	f	f	PROPN
ejpam-6761	256	16	)	)	PUNCT
ejpam-6761	256	17	to	to	ADP
ejpam-6761	256	18	any	any	DET
ejpam-6761	256	19	bipolar	bipolar	ADJ
ejpam-6761	256	20	valued	value	VERB
ejpam-6761	256	21	fuzzy	fuzzy	ADJ
ejpam-6761	256	22	group	group	NOUN
ejpam-6761	256	23	(	(	PUNCT
ejpam-6761	256	24	(	(	PUNCT
ejpam-6761	256	25	g	g	NOUN
ejpam-6761	256	26	,	,	PUNCT
ejpam-6761	256	27	[	[	X
ejpam-6761	256	28	−1	−1	NOUN
ejpam-6761	256	29	,	,	PUNCT
ejpam-6761	256	30	0	0	NUM
ejpam-6761	256	31	]	]	PUNCT
ejpam-6761	256	32	,	,	PUNCT
ejpam-6761	256	33	[	[	X
ejpam-6761	256	34	0	0	NUM
ejpam-6761	256	35	,	,	PUNCT
ejpam-6761	256	36	1	1	NUM
ejpam-6761	256	37	]	]	NUM
ejpam-6761	256	38	)	)	PUNCT
ejpam-6761	256	39	,	,	PUNCT
ejpam-6761	256	40	f	f	PROPN
ejpam-6761	256	41	)	)	PUNCT
ejpam-6761	256	42	that	that	PRON
ejpam-6761	256	43	is	be	AUX
ejpam-6761	256	44	isomorphic	isomorphic	ADJ
ejpam-6761	256	45	to	to	ADP
ejpam-6761	256	46	the	the	DET
ejpam-6761	256	47	bipolar	bipolar	ADJ
ejpam-6761	256	48	valued	value	VERB
ejpam-6761	256	49	fuzzy	fuzzy	ADJ
ejpam-6761	256	50	group	group	NOUN
ejpam-6761	256	51	via	via	ADP
ejpam-6761	256	52	the	the	DET
ejpam-6761	256	53	corresponding	correspond	VERB
ejpam-6761	256	54	(	(	PUNCT
ejpam-6761	256	55	x	x	X
ejpam-6761	256	56	,	,	PUNCT
ejpam-6761	256	57	[	[	X
ejpam-6761	256	58	−1	−1	NOUN
ejpam-6761	256	59	,	,	PUNCT
ejpam-6761	256	60	0	0	NUM
ejpam-6761	256	61	]	]	PUNCT
ejpam-6761	256	62	,	,	PUNCT
ejpam-6761	256	63	[	[	X
ejpam-6761	256	64	0	0	NUM
ejpam-6761	256	65	,	,	PUNCT
ejpam-6761	256	66	1	1	NUM
ejpam-6761	256	67	]	]	PUNCT
ejpam-6761	256	68	)	)	PUNCT
ejpam-6761	256	69	↔	↔	PROPN
ejpam-6761	256	70	x.	x.	NOUN
ejpam-6761	256	71	corollary	corollary	NOUN
ejpam-6761	256	72	1	1	NUM
ejpam-6761	256	73	(	(	PUNCT
ejpam-6761	256	74	[	[	X
ejpam-6761	256	75	10	10	NUM
ejpam-6761	256	76	]	]	NUM
ejpam-6761	256	77	)	)	PUNCT
ejpam-6761	256	78	.	.	PUNCT
ejpam-6761	257	1	let	let	VERB
ejpam-6761	257	2	(	(	PUNCT
ejpam-6761	257	3	℧	℧	PROPN
ejpam-6761	257	4	,	,	PUNCT
ejpam-6761	257	5	[	[	X
ejpam-6761	257	6	−1	−1	NOUN
ejpam-6761	257	7	,	,	PUNCT
ejpam-6761	257	8	0	0	NUM
ejpam-6761	257	9	]	]	PUNCT
ejpam-6761	257	10	,	,	PUNCT
ejpam-6761	257	11	[	[	X
ejpam-6761	257	12	0	0	NUM
ejpam-6761	257	13	,	,	PUNCT
ejpam-6761	257	14	1	1	NUM
ejpam-6761	257	15	]	]	PUNCT
ejpam-6761	257	16	)	)	PUNCT
ejpam-6761	257	17	be	be	AUX
ejpam-6761	257	18	an	an	DET
ejpam-6761	257	19	bvf	bvf	NOUN
ejpam-6761	257	20	-	-	PUNCT
ejpam-6761	257	21	space	space	NOUN
ejpam-6761	257	22	and	and	CCONJ
ejpam-6761	257	23	let	let	VERB
ejpam-6761	257	24	f	f	PROPN
ejpam-6761	257	25	=	=	SYM
ejpam-6761	257	26	(	(	PUNCT
ejpam-6761	257	27	f	f	PROPN
ejpam-6761	257	28	,	,	PUNCT
ejpam-6761	257	29	f−xy	f−xy	PROPN
ejpam-6761	257	30	,	,	PUNCT
ejpam-6761	257	31	f	f	PROPN
ejpam-6761	257	32	+	+	CCONJ
ejpam-6761	257	33	xy	xy	PROPN
ejpam-6761	257	34	)	)	PUNCT
ejpam-6761	257	35	be	be	VERB
ejpam-6761	257	36	an	an	DET
ejpam-6761	257	37	bipolar	bipolar	ADJ
ejpam-6761	257	38	valued	value	VERB
ejpam-6761	257	39	fuzzy	fuzzy	ADJ
ejpam-6761	257	40	binary	binary	ADJ
ejpam-6761	257	41	operation	operation	NOUN
ejpam-6761	257	42	defined	define	VERB
ejpam-6761	257	43	over	over	ADP
ejpam-6761	257	44	(	(	PUNCT
ejpam-6761	257	45	℧	℧	PROPN
ejpam-6761	257	46	,	,	PUNCT
ejpam-6761	257	47	[	[	X
ejpam-6761	257	48	−1	−1	NOUN
ejpam-6761	257	49	,	,	PUNCT
ejpam-6761	257	50	0	0	NUM
ejpam-6761	257	51	]	]	PUNCT
ejpam-6761	257	52	,	,	PUNCT
ejpam-6761	257	53	[	[	X
ejpam-6761	257	54	0	0	NUM
ejpam-6761	257	55	,	,	PUNCT
ejpam-6761	257	56	1	1	NUM
ejpam-6761	257	57	]	]	NUM
ejpam-6761	257	58	)	)	PUNCT
ejpam-6761	257	59	.	.	PUNCT
ejpam-6761	258	1	the	the	DET
ejpam-6761	258	2	algebraic	algebraic	ADJ
ejpam-6761	258	3	structure	structure	NOUN
ejpam-6761	258	4	(	(	PUNCT
ejpam-6761	258	5	(	(	PUNCT
ejpam-6761	258	6	℧	℧	PROPN
ejpam-6761	258	7	,	,	PUNCT
ejpam-6761	258	8	[	[	X
ejpam-6761	258	9	−1	−1	NOUN
ejpam-6761	258	10	,	,	PUNCT
ejpam-6761	258	11	0	0	NUM
ejpam-6761	258	12	]	]	PUNCT
ejpam-6761	258	13	,	,	PUNCT
ejpam-6761	258	14	[	[	X
ejpam-6761	258	15	0	0	NUM
ejpam-6761	258	16	,	,	PUNCT
ejpam-6761	258	17	1	1	NUM
ejpam-6761	258	18	]	]	NUM
ejpam-6761	258	19	)	)	PUNCT
ejpam-6761	258	20	,	,	PUNCT
ejpam-6761	258	21	f	f	PROPN
ejpam-6761	258	22	)	)	PUNCT
ejpam-6761	258	23	defines	define	VERB
ejpam-6761	258	24	an	an	DET
ejpam-6761	258	25	bvf	bvf	NOUN
ejpam-6761	258	26	-	-	PUNCT
ejpam-6761	258	27	group	group	NOUN
ejpam-6761	258	28	iff	iff	PROPN
ejpam-6761	258	29	(	(	PUNCT
ejpam-6761	258	30	(	(	PUNCT
ejpam-6761	258	31	℧	℧	PROPN
ejpam-6761	258	32	,	,	PUNCT
ejpam-6761	258	33	[	[	X
ejpam-6761	258	34	0	0	NUM
ejpam-6761	258	35	,	,	PUNCT
ejpam-6761	258	36	1]),f	1]),f	NUM
ejpam-6761	258	37	)	)	PUNCT
ejpam-6761	258	38	and	and	CCONJ
ejpam-6761	258	39	(	(	PUNCT
ejpam-6761	258	40	(	(	PUNCT
ejpam-6761	258	41	℧	℧	PROPN
ejpam-6761	258	42	,	,	PUNCT
ejpam-6761	258	43	[	[	X
ejpam-6761	258	44	0	0	NUM
ejpam-6761	258	45	,	,	PUNCT
ejpam-6761	258	46	1	1	NUM
ejpam-6761	258	47	]	]	NUM
ejpam-6761	258	48	)	)	PUNCT
ejpam-6761	258	49	,	,	PUNCT
ejpam-6761	258	50	f̄	f̄	PROPN
ejpam-6761	258	51	)	)	PUNCT
ejpam-6761	258	52	are	be	AUX
ejpam-6761	258	53	both	both	PRON
ejpam-6761	258	54	fuzzy	fuzzy	ADJ
ejpam-6761	258	55	groups	group	NOUN
ejpam-6761	258	56	,	,	PUNCT
ejpam-6761	258	57	where	where	SCONJ
ejpam-6761	258	58	f	f	AUX
ejpam-6761	258	59	=	=	PRON
ejpam-6761	258	60	(	(	PUNCT
ejpam-6761	258	61	f	f	X
ejpam-6761	258	62	,	,	PUNCT
ejpam-6761	258	63	f+xy	f+xy	PROPN
ejpam-6761	258	64	)	)	PUNCT
ejpam-6761	258	65	and	and	CCONJ
ejpam-6761	258	66	f̄	f̄	NOUN
ejpam-6761	258	67	=	=	PUNCT
ejpam-6761	258	68	(	(	PUNCT
ejpam-6761	258	69	f	f	X
ejpam-6761	258	70	,	,	PUNCT
ejpam-6761	258	71	|f−xy|	|f−xy|	PROPN
ejpam-6761	258	72	)	)	PUNCT
ejpam-6761	258	73	.	.	PUNCT
ejpam-6761	259	1	theorem	theorem	ADJ
ejpam-6761	259	2	2	2	NUM
ejpam-6761	259	3	(	(	PUNCT
ejpam-6761	259	4	[	[	X
ejpam-6761	259	5	10	10	NUM
ejpam-6761	259	6	]	]	NUM
ejpam-6761	259	7	)	)	PUNCT
ejpam-6761	259	8	.	.	PUNCT
ejpam-6761	260	1	for	for	ADP
ejpam-6761	260	2	any	any	DET
ejpam-6761	260	3	bvf	bvf	NOUN
ejpam-6761	260	4	-	-	PUNCT
ejpam-6761	260	5	group	group	NOUN
ejpam-6761	260	6	(	(	PUNCT
ejpam-6761	260	7	(	(	PUNCT
ejpam-6761	260	8	g	g	NOUN
ejpam-6761	260	9	,	,	PUNCT
ejpam-6761	260	10	[	[	X
ejpam-6761	260	11	−1	−1	NOUN
ejpam-6761	260	12	,	,	PUNCT
ejpam-6761	260	13	0	0	NUM
ejpam-6761	260	14	]	]	PUNCT
ejpam-6761	260	15	,	,	PUNCT
ejpam-6761	260	16	[	[	X
ejpam-6761	260	17	0	0	NUM
ejpam-6761	260	18	,	,	PUNCT
ejpam-6761	260	19	1	1	NUM
ejpam-6761	260	20	]	]	NUM
ejpam-6761	260	21	)	)	PUNCT
ejpam-6761	260	22	,	,	PUNCT
ejpam-6761	260	23	f	f	PROPN
ejpam-6761	260	24	)	)	PUNCT
ejpam-6761	260	25	,	,	PUNCT
ejpam-6761	260	26	the	the	DET
ejpam-6761	260	27	next	next	ADJ
ejpam-6761	260	28	statements	statement	NOUN
ejpam-6761	260	29	are	be	AUX
ejpam-6761	260	30	true	true	ADJ
ejpam-6761	260	31	:	:	PUNCT
ejpam-6761	260	32	f.	f.	PROPN
ejpam-6761	260	33	al	al	PROPN
ejpam-6761	260	34	-	-	PROPN
ejpam-6761	260	35	zu’bi	zu’bi	PROPN
ejpam-6761	260	36	et	et	NOUN
ejpam-6761	260	37	al	al	PROPN
ejpam-6761	260	38	.	.	PUNCT
ejpam-6761	260	39	/	/	SYM
ejpam-6761	260	40	eur	eur	PROPN
ejpam-6761	260	41	.	.	PUNCT
ejpam-6761	261	1	j.	j.	PROPN
ejpam-6761	261	2	pure	pure	PROPN
ejpam-6761	261	3	appl	appl	PROPN
ejpam-6761	261	4	.	.	PROPN
ejpam-6761	261	5	math	math	PROPN
ejpam-6761	261	6	,	,	PUNCT
ejpam-6761	261	7	18	18	NUM
ejpam-6761	261	8	(	(	PUNCT
ejpam-6761	261	9	4	4	NUM
ejpam-6761	261	10	)	)	PUNCT
ejpam-6761	261	11	(	(	PUNCT
ejpam-6761	261	12	2025	2025	NUM
ejpam-6761	261	13	)	)	PUNCT
ejpam-6761	261	14	,	,	PUNCT
ejpam-6761	261	15	6761	6761	NUM
ejpam-6761	261	16	12	12	NUM
ejpam-6761	261	17	of	of	ADP
ejpam-6761	261	18	28	28	NUM
ejpam-6761	261	19	•	•	NOUN
ejpam-6761	261	20	the	the	DET
ejpam-6761	261	21	identity	identity	NOUN
ejpam-6761	261	22	of	of	ADP
ejpam-6761	261	23	element	element	NOUN
ejpam-6761	261	24	of	of	ADP
ejpam-6761	261	25	bvf	bvf	NOUN
ejpam-6761	261	26	-	-	PUNCT
ejpam-6761	261	27	group	group	NOUN
ejpam-6761	261	28	is	be	AUX
ejpam-6761	261	29	unique	unique	ADJ
ejpam-6761	261	30	.	.	PUNCT
ejpam-6761	262	1	•	•	NUM
ejpam-6761	262	2	the	the	DET
ejpam-6761	262	3	inverse	inverse	NOUN
ejpam-6761	262	4	of	of	ADP
ejpam-6761	262	5	each	each	DET
ejpam-6761	262	6	bvf	bvf	NOUN
ejpam-6761	262	7	-	-	PUNCT
ejpam-6761	262	8	element	element	NOUN
ejpam-6761	262	9	(	(	PUNCT
ejpam-6761	262	10	x	x	X
ejpam-6761	262	11	,	,	PUNCT
ejpam-6761	262	12	[	[	X
ejpam-6761	262	13	−1	−1	NOUN
ejpam-6761	262	14	,	,	PUNCT
ejpam-6761	262	15	0	0	NUM
ejpam-6761	262	16	]	]	PUNCT
ejpam-6761	262	17	,	,	PUNCT
ejpam-6761	263	1	[	[	X
ejpam-6761	263	2	0	0	NUM
ejpam-6761	263	3	,	,	PUNCT
ejpam-6761	263	4	1	1	NUM
ejpam-6761	263	5	]	]	PUNCT
ejpam-6761	263	6	)	)	PUNCT
ejpam-6761	263	7	∈	∈	PROPN
ejpam-6761	263	8	(	(	PUNCT
ejpam-6761	263	9	(	(	PUNCT
ejpam-6761	263	10	g	g	NOUN
ejpam-6761	263	11	,	,	PUNCT
ejpam-6761	263	12	[	[	X
ejpam-6761	263	13	−1	−1	NOUN
ejpam-6761	263	14	,	,	PUNCT
ejpam-6761	263	15	0	0	NUM
ejpam-6761	263	16	]	]	PUNCT
ejpam-6761	263	17	,	,	PUNCT
ejpam-6761	264	1	[	[	X
ejpam-6761	264	2	0	0	NUM
ejpam-6761	264	3	,	,	PUNCT
ejpam-6761	264	4	1	1	NUM
ejpam-6761	264	5	]	]	NUM
ejpam-6761	264	6	)	)	PUNCT
ejpam-6761	264	7	,	,	PUNCT
ejpam-6761	264	8	f	f	PROPN
ejpam-6761	264	9	)	)	PUNCT
ejpam-6761	264	10	is	be	AUX
ejpam-6761	264	11	unique	unique	ADJ
ejpam-6761	264	12	.	.	PUNCT
ejpam-6761	265	1	•	•	NUM
ejpam-6761	265	2	(	(	PUNCT
ejpam-6761	265	3	(	(	PUNCT
ejpam-6761	265	4	x−1)−1	x−1)−1	NOUN
ejpam-6761	265	5	,	,	PUNCT
ejpam-6761	265	6	[	[	X
ejpam-6761	265	7	−1	−1	NOUN
ejpam-6761	265	8	,	,	PUNCT
ejpam-6761	265	9	0	0	NUM
ejpam-6761	265	10	]	]	PUNCT
ejpam-6761	265	11	,	,	PUNCT
ejpam-6761	265	12	[	[	X
ejpam-6761	265	13	0	0	NUM
ejpam-6761	265	14	,	,	PUNCT
ejpam-6761	265	15	1	1	NUM
ejpam-6761	265	16	]	]	PUNCT
ejpam-6761	265	17	)	)	PUNCT
ejpam-6761	265	18	=	=	SYM
ejpam-6761	265	19	(	(	PUNCT
ejpam-6761	265	20	x	x	X
ejpam-6761	265	21	,	,	PUNCT
ejpam-6761	265	22	[	[	X
ejpam-6761	265	23	−1	−1	NOUN
ejpam-6761	265	24	,	,	PUNCT
ejpam-6761	265	25	0	0	NUM
ejpam-6761	265	26	]	]	PUNCT
ejpam-6761	265	27	,	,	PUNCT
ejpam-6761	266	1	[	[	X
ejpam-6761	266	2	0	0	NUM
ejpam-6761	266	3	,	,	PUNCT
ejpam-6761	266	4	1	1	NUM
ejpam-6761	266	5	]	]	PUNCT
ejpam-6761	266	6	)	)	PUNCT
ejpam-6761	266	7	•	•	ADP
ejpam-6761	266	8	for	for	ADP
ejpam-6761	266	9	all	all	DET
ejpam-6761	266	10	(	(	PUNCT
ejpam-6761	266	11	x	x	NOUN
ejpam-6761	266	12	,	,	PUNCT
ejpam-6761	266	13	[	[	X
ejpam-6761	266	14	−1	−1	NOUN
ejpam-6761	266	15	,	,	PUNCT
ejpam-6761	266	16	0	0	NUM
ejpam-6761	266	17	]	]	PUNCT
ejpam-6761	266	18	,	,	PUNCT
ejpam-6761	267	1	[	[	X
ejpam-6761	267	2	0	0	NUM
ejpam-6761	267	3	,	,	PUNCT
ejpam-6761	267	4	1	1	NUM
ejpam-6761	267	5	]	]	NUM
ejpam-6761	267	6	)	)	PUNCT
ejpam-6761	267	7	,	,	PUNCT
ejpam-6761	267	8	(	(	PUNCT
ejpam-6761	267	9	y	y	NOUN
ejpam-6761	267	10	,	,	PUNCT
ejpam-6761	267	11	[	[	X
ejpam-6761	267	12	−1	−1	NOUN
ejpam-6761	267	13	,	,	PUNCT
ejpam-6761	267	14	0	0	NUM
ejpam-6761	267	15	]	]	PUNCT
ejpam-6761	267	16	,	,	PUNCT
ejpam-6761	267	17	[	[	X
ejpam-6761	267	18	0	0	NUM
ejpam-6761	267	19	,	,	PUNCT
ejpam-6761	267	20	1	1	NUM
ejpam-6761	267	21	]	]	PUNCT
ejpam-6761	267	22	)	)	PUNCT
ejpam-6761	267	23	∈	∈	PROPN
ejpam-6761	267	24	(	(	PUNCT
ejpam-6761	267	25	(	(	PUNCT
ejpam-6761	267	26	g	g	NOUN
ejpam-6761	267	27	,	,	PUNCT
ejpam-6761	267	28	[	[	X
ejpam-6761	267	29	−1	−1	NOUN
ejpam-6761	267	30	,	,	PUNCT
ejpam-6761	267	31	0	0	NUM
ejpam-6761	267	32	]	]	PUNCT
ejpam-6761	267	33	,	,	PUNCT
ejpam-6761	268	1	[	[	X
ejpam-6761	268	2	0	0	NUM
ejpam-6761	268	3	,	,	PUNCT
ejpam-6761	268	4	1	1	NUM
ejpam-6761	268	5	]	]	NUM
ejpam-6761	268	6	)	)	PUNCT
ejpam-6761	268	7	,	,	PUNCT
ejpam-6761	268	8	f	f	PROPN
ejpam-6761	268	9	):	):	PUNCT
ejpam-6761	268	10	(	(	PUNCT
ejpam-6761	268	11	(	(	PUNCT
ejpam-6761	268	12	x	x	X
ejpam-6761	268	13	,	,	PUNCT
ejpam-6761	268	14	[	[	X
ejpam-6761	268	15	−1	−1	NOUN
ejpam-6761	268	16	,	,	PUNCT
ejpam-6761	268	17	0	0	NUM
ejpam-6761	268	18	]	]	PUNCT
ejpam-6761	268	19	,	,	PUNCT
ejpam-6761	268	20	[	[	X
ejpam-6761	268	21	0	0	NUM
ejpam-6761	268	22	,	,	PUNCT
ejpam-6761	268	23	1])f	1])f	NUM
ejpam-6761	268	24	(	(	PUNCT
ejpam-6761	268	25	y	y	NOUN
ejpam-6761	268	26	,	,	PUNCT
ejpam-6761	268	27	[	[	X
ejpam-6761	268	28	−1	−1	NOUN
ejpam-6761	268	29	,	,	PUNCT
ejpam-6761	268	30	0	0	NUM
ejpam-6761	268	31	]	]	PUNCT
ejpam-6761	268	32	,	,	PUNCT
ejpam-6761	268	33	[	[	X
ejpam-6761	268	34	0	0	NUM
ejpam-6761	268	35	,	,	PUNCT
ejpam-6761	268	36	1]))−1	1]))−1	NOUN
ejpam-6761	268	37	=	=	SYM
ejpam-6761	268	38	(	(	PUNCT
ejpam-6761	268	39	y−1	y−1	PROPN
ejpam-6761	268	40	,	,	PUNCT
ejpam-6761	268	41	[	[	X
ejpam-6761	268	42	−1	−1	NOUN
ejpam-6761	268	43	,	,	PUNCT
ejpam-6761	268	44	0	0	NUM
ejpam-6761	268	45	]	]	PUNCT
ejpam-6761	268	46	,	,	PUNCT
ejpam-6761	269	1	[	[	X
ejpam-6761	269	2	0	0	NUM
ejpam-6761	269	3	,	,	PUNCT
ejpam-6761	269	4	1])f	1])f	NUM
ejpam-6761	269	5	(	(	PUNCT
ejpam-6761	269	6	x−1	x−1	PROPN
ejpam-6761	269	7	,	,	PUNCT
ejpam-6761	269	8	[	[	X
ejpam-6761	269	9	−1	−1	NOUN
ejpam-6761	269	10	,	,	PUNCT
ejpam-6761	269	11	0	0	NUM
ejpam-6761	269	12	]	]	PUNCT
ejpam-6761	269	13	,	,	PUNCT
ejpam-6761	270	1	[	[	X
ejpam-6761	270	2	0	0	NUM
ejpam-6761	270	3	,	,	PUNCT
ejpam-6761	270	4	1	1	NUM
ejpam-6761	270	5	]	]	NUM
ejpam-6761	270	6	)	)	PUNCT
ejpam-6761	270	7	.	.	PUNCT
ejpam-6761	271	1	•	•	NOUN
ejpam-6761	271	2	for	for	ADP
ejpam-6761	271	3	all	all	DET
ejpam-6761	271	4	(	(	PUNCT
ejpam-6761	271	5	x	x	NOUN
ejpam-6761	271	6	,	,	PUNCT
ejpam-6761	271	7	[	[	X
ejpam-6761	271	8	−1	−1	NOUN
ejpam-6761	271	9	,	,	PUNCT
ejpam-6761	271	10	0	0	NUM
ejpam-6761	271	11	]	]	PUNCT
ejpam-6761	271	12	,	,	PUNCT
ejpam-6761	271	13	[	[	X
ejpam-6761	271	14	0	0	NUM
ejpam-6761	271	15	,	,	PUNCT
ejpam-6761	271	16	1	1	NUM
ejpam-6761	271	17	]	]	NUM
ejpam-6761	271	18	)	)	PUNCT
ejpam-6761	271	19	,	,	PUNCT
ejpam-6761	271	20	(	(	PUNCT
ejpam-6761	271	21	y	y	NOUN
ejpam-6761	271	22	,	,	PUNCT
ejpam-6761	271	23	[	[	X
ejpam-6761	271	24	−1	−1	NOUN
ejpam-6761	271	25	,	,	PUNCT
ejpam-6761	271	26	0	0	NUM
ejpam-6761	271	27	]	]	PUNCT
ejpam-6761	271	28	,	,	PUNCT
ejpam-6761	271	29	[	[	X
ejpam-6761	271	30	0	0	NUM
ejpam-6761	271	31	,	,	PUNCT
ejpam-6761	271	32	1	1	NUM
ejpam-6761	271	33	]	]	NUM
ejpam-6761	271	34	)	)	PUNCT
ejpam-6761	271	35	,	,	PUNCT
ejpam-6761	271	36	(	(	PUNCT
ejpam-6761	271	37	z	z	X
ejpam-6761	271	38	,	,	PUNCT
ejpam-6761	271	39	[	[	X
ejpam-6761	271	40	−1	−1	NOUN
ejpam-6761	271	41	,	,	PUNCT
ejpam-6761	271	42	0	0	NUM
ejpam-6761	271	43	]	]	PUNCT
ejpam-6761	271	44	,	,	PUNCT
ejpam-6761	271	45	[	[	X
ejpam-6761	271	46	0	0	NUM
ejpam-6761	271	47	,	,	PUNCT
ejpam-6761	271	48	1	1	NUM
ejpam-6761	271	49	]	]	PUNCT
ejpam-6761	271	50	)	)	PUNCT
ejpam-6761	271	51	∈	∈	PROPN
ejpam-6761	271	52	(	(	PUNCT
ejpam-6761	271	53	(	(	PUNCT
ejpam-6761	271	54	g	g	NOUN
ejpam-6761	271	55	,	,	PUNCT
ejpam-6761	271	56	[	[	X
ejpam-6761	271	57	−1	−1	NOUN
ejpam-6761	271	58	,	,	PUNCT
ejpam-6761	271	59	0	0	NUM
ejpam-6761	271	60	]	]	PUNCT
ejpam-6761	271	61	,	,	PUNCT
ejpam-6761	272	1	[	[	X
ejpam-6761	272	2	0	0	NUM
ejpam-6761	272	3	,	,	PUNCT
ejpam-6761	272	4	1	1	NUM
ejpam-6761	272	5	]	]	NUM
ejpam-6761	272	6	)	)	PUNCT
ejpam-6761	272	7	,	,	PUNCT
ejpam-6761	272	8	f	f	PROPN
ejpam-6761	272	9	):	):	PUNCT
ejpam-6761	272	10	if	if	SCONJ
ejpam-6761	272	11	(	(	PUNCT
ejpam-6761	272	12	x	x	X
ejpam-6761	272	13	,	,	PUNCT
ejpam-6761	272	14	[	[	X
ejpam-6761	272	15	−1	−1	NOUN
ejpam-6761	272	16	,	,	PUNCT
ejpam-6761	272	17	0	0	NUM
ejpam-6761	272	18	]	]	PUNCT
ejpam-6761	272	19	,	,	PUNCT
ejpam-6761	272	20	[	[	X
ejpam-6761	272	21	0	0	NUM
ejpam-6761	272	22	,	,	PUNCT
ejpam-6761	272	23	1])f	1])f	NUM
ejpam-6761	272	24	(	(	PUNCT
ejpam-6761	272	25	y	y	NOUN
ejpam-6761	272	26	,	,	PUNCT
ejpam-6761	272	27	[	[	X
ejpam-6761	272	28	−1	−1	NOUN
ejpam-6761	272	29	,	,	PUNCT
ejpam-6761	272	30	0	0	NUM
ejpam-6761	272	31	]	]	PUNCT
ejpam-6761	272	32	,	,	PUNCT
ejpam-6761	272	33	[	[	X
ejpam-6761	272	34	0	0	NUM
ejpam-6761	272	35	,	,	PUNCT
ejpam-6761	272	36	1	1	NUM
ejpam-6761	272	37	]	]	PUNCT
ejpam-6761	272	38	)	)	PUNCT
ejpam-6761	272	39	=	=	SYM
ejpam-6761	273	1	(	(	PUNCT
ejpam-6761	273	2	z	z	NOUN
ejpam-6761	273	3	,	,	PUNCT
ejpam-6761	273	4	[	[	X
ejpam-6761	273	5	−1	−1	NOUN
ejpam-6761	273	6	,	,	PUNCT
ejpam-6761	273	7	0	0	NUM
ejpam-6761	273	8	]	]	PUNCT
ejpam-6761	273	9	,	,	PUNCT
ejpam-6761	274	1	[	[	X
ejpam-6761	274	2	0	0	NUM
ejpam-6761	274	3	,	,	PUNCT
ejpam-6761	274	4	1])f	1])f	NUM
ejpam-6761	274	5	(	(	PUNCT
ejpam-6761	274	6	y	y	NOUN
ejpam-6761	274	7	,	,	PUNCT
ejpam-6761	274	8	[	[	X
ejpam-6761	274	9	−1	−1	NOUN
ejpam-6761	274	10	,	,	PUNCT
ejpam-6761	274	11	0	0	NUM
ejpam-6761	274	12	]	]	PUNCT
ejpam-6761	274	13	,	,	PUNCT
ejpam-6761	274	14	[	[	X
ejpam-6761	274	15	0	0	NUM
ejpam-6761	274	16	,	,	PUNCT
ejpam-6761	274	17	1	1	NUM
ejpam-6761	274	18	]	]	NUM
ejpam-6761	274	19	)	)	PUNCT
ejpam-6761	274	20	,	,	PUNCT
ejpam-6761	274	21	then	then	ADV
ejpam-6761	274	22	(	(	PUNCT
ejpam-6761	274	23	x	x	X
ejpam-6761	274	24	,	,	PUNCT
ejpam-6761	274	25	[	[	X
ejpam-6761	274	26	−1	−1	NOUN
ejpam-6761	274	27	,	,	PUNCT
ejpam-6761	274	28	0	0	NUM
ejpam-6761	274	29	]	]	PUNCT
ejpam-6761	274	30	,	,	PUNCT
ejpam-6761	274	31	[	[	X
ejpam-6761	274	32	0	0	NUM
ejpam-6761	274	33	,	,	PUNCT
ejpam-6761	274	34	1	1	NUM
ejpam-6761	274	35	]	]	PUNCT
ejpam-6761	274	36	)	)	PUNCT
ejpam-6761	275	1	=	=	SYM
ejpam-6761	275	2	(	(	PUNCT
ejpam-6761	275	3	z	z	NOUN
ejpam-6761	275	4	,	,	PUNCT
ejpam-6761	275	5	[	[	X
ejpam-6761	275	6	−1	−1	NOUN
ejpam-6761	275	7	,	,	PUNCT
ejpam-6761	275	8	0	0	NUM
ejpam-6761	275	9	]	]	PUNCT
ejpam-6761	275	10	,	,	PUNCT
ejpam-6761	276	1	[	[	X
ejpam-6761	276	2	0	0	NUM
ejpam-6761	276	3	,	,	PUNCT
ejpam-6761	276	4	1	1	NUM
ejpam-6761	276	5	]	]	PUNCT
ejpam-6761	276	6	)	)	PUNCT
ejpam-6761	276	7	.	.	PUNCT
ejpam-6761	277	1	if	if	SCONJ
ejpam-6761	277	2	(	(	PUNCT
ejpam-6761	277	3	y	y	NOUN
ejpam-6761	277	4	,	,	PUNCT
ejpam-6761	277	5	[	[	X
ejpam-6761	277	6	−1	−1	NOUN
ejpam-6761	277	7	,	,	PUNCT
ejpam-6761	277	8	0	0	NUM
ejpam-6761	277	9	]	]	PUNCT
ejpam-6761	277	10	,	,	PUNCT
ejpam-6761	277	11	[	[	X
ejpam-6761	277	12	0	0	NUM
ejpam-6761	277	13	,	,	PUNCT
ejpam-6761	277	14	1])f	1])f	NUM
ejpam-6761	277	15	(	(	PUNCT
ejpam-6761	277	16	x	x	X
ejpam-6761	277	17	,	,	PUNCT
ejpam-6761	277	18	[	[	X
ejpam-6761	277	19	−1	−1	NOUN
ejpam-6761	277	20	,	,	PUNCT
ejpam-6761	277	21	0	0	NUM
ejpam-6761	277	22	]	]	PUNCT
ejpam-6761	277	23	,	,	PUNCT
ejpam-6761	277	24	[	[	X
ejpam-6761	277	25	0	0	NUM
ejpam-6761	277	26	,	,	PUNCT
ejpam-6761	277	27	1	1	NUM
ejpam-6761	277	28	]	]	PUNCT
ejpam-6761	277	29	)	)	PUNCT
ejpam-6761	277	30	=	=	SYM
ejpam-6761	277	31	(	(	PUNCT
ejpam-6761	277	32	y	y	NOUN
ejpam-6761	277	33	,	,	PUNCT
ejpam-6761	277	34	[	[	X
ejpam-6761	277	35	−1	−1	NOUN
ejpam-6761	277	36	,	,	PUNCT
ejpam-6761	277	37	0	0	NUM
ejpam-6761	277	38	]	]	PUNCT
ejpam-6761	277	39	,	,	PUNCT
ejpam-6761	277	40	[	[	X
ejpam-6761	277	41	0	0	NUM
ejpam-6761	277	42	,	,	PUNCT
ejpam-6761	277	43	1])f	1])f	NUM
ejpam-6761	277	44	(	(	PUNCT
ejpam-6761	277	45	z	z	NOUN
ejpam-6761	277	46	,	,	PUNCT
ejpam-6761	277	47	[	[	X
ejpam-6761	277	48	−1	−1	NOUN
ejpam-6761	277	49	,	,	PUNCT
ejpam-6761	277	50	0	0	NUM
ejpam-6761	277	51	]	]	PUNCT
ejpam-6761	277	52	,	,	PUNCT
ejpam-6761	277	53	[	[	X
ejpam-6761	277	54	0	0	NUM
ejpam-6761	277	55	,	,	PUNCT
ejpam-6761	277	56	1	1	NUM
ejpam-6761	277	57	]	]	NUM
ejpam-6761	277	58	)	)	PUNCT
ejpam-6761	277	59	,	,	PUNCT
ejpam-6761	277	60	then	then	ADV
ejpam-6761	277	61	(	(	PUNCT
ejpam-6761	277	62	x	x	X
ejpam-6761	277	63	,	,	PUNCT
ejpam-6761	277	64	[	[	X
ejpam-6761	277	65	−1	−1	NOUN
ejpam-6761	277	66	,	,	PUNCT
ejpam-6761	277	67	0	0	NUM
ejpam-6761	277	68	]	]	PUNCT
ejpam-6761	277	69	,	,	PUNCT
ejpam-6761	277	70	[	[	X
ejpam-6761	277	71	0	0	NUM
ejpam-6761	277	72	,	,	PUNCT
ejpam-6761	277	73	1	1	NUM
ejpam-6761	277	74	]	]	PUNCT
ejpam-6761	277	75	)	)	PUNCT
ejpam-6761	277	76	=	=	SYM
ejpam-6761	277	77	(	(	PUNCT
ejpam-6761	277	78	z	z	NOUN
ejpam-6761	277	79	,	,	PUNCT
ejpam-6761	277	80	[	[	X
ejpam-6761	277	81	−1	−1	NOUN
ejpam-6761	277	82	,	,	PUNCT
ejpam-6761	277	83	0	0	NUM
ejpam-6761	277	84	]	]	PUNCT
ejpam-6761	277	85	,	,	PUNCT
ejpam-6761	277	86	[	[	X
ejpam-6761	277	87	0	0	NUM
ejpam-6761	277	88	,	,	PUNCT
ejpam-6761	277	89	1	1	NUM
ejpam-6761	277	90	]	]	NUM
ejpam-6761	277	91	)	)	PUNCT
ejpam-6761	277	92	.	.	PUNCT
ejpam-6761	278	1	3	3	X
ejpam-6761	278	2	.	.	X
ejpam-6761	278	3	bipolar	bipolar	ADJ
ejpam-6761	278	4	valued	value	VERB
ejpam-6761	278	5	fuzzy	fuzzy	ADJ
ejpam-6761	278	6	subgroups	subgroup	NOUN
ejpam-6761	278	7	in	in	ADP
ejpam-6761	278	8	this	this	DET
ejpam-6761	278	9	part	part	NOUN
ejpam-6761	278	10	,	,	PUNCT
ejpam-6761	278	11	the	the	DET
ejpam-6761	278	12	bipolar	bipolar	ADJ
ejpam-6761	278	13	valued	value	VERB
ejpam-6761	278	14	fuzzy	fuzzy	ADJ
ejpam-6761	278	15	subgroup	subgroup	NOUN
ejpam-6761	278	16	is	be	AUX
ejpam-6761	278	17	introduced	introduce	VERB
ejpam-6761	278	18	and	and	CCONJ
ejpam-6761	278	19	related	related	ADJ
ejpam-6761	278	20	results	result	NOUN
ejpam-6761	278	21	are	be	AUX
ejpam-6761	278	22	studied	study	VERB
ejpam-6761	278	23	.	.	PUNCT
ejpam-6761	279	1	also	also	ADV
ejpam-6761	279	2	,	,	PUNCT
ejpam-6761	279	3	the	the	DET
ejpam-6761	279	4	bipolar	bipolar	ADJ
ejpam-6761	279	5	valued	value	VERB
ejpam-6761	279	6	fuzzy	fuzzy	ADJ
ejpam-6761	279	7	subgroups	subgroup	NOUN
ejpam-6761	279	8	are	be	AUX
ejpam-6761	279	9	induced	induce	VERB
ejpam-6761	279	10	by	by	ADP
ejpam-6761	279	11	bipolar	bipolar	ADJ
ejpam-6761	279	12	valued	value	VERB
ejpam-6761	279	13	fuzzy	fuzzy	ADJ
ejpam-6761	279	14	subsets	subset	NOUN
ejpam-6761	279	15	and	and	CCONJ
ejpam-6761	279	16	then	then	ADV
ejpam-6761	279	17	a	a	DET
ejpam-6761	279	18	relationship	relationship	NOUN
ejpam-6761	279	19	between	between	ADP
ejpam-6761	279	20	bipolar	bipolar	ADJ
ejpam-6761	279	21	valued	value	VERB
ejpam-6761	279	22	fuzzy	fuzzy	ADJ
ejpam-6761	279	23	subgroups	subgroup	NOUN
ejpam-6761	279	24	and	and	CCONJ
ejpam-6761	279	25	classical	classical	ADJ
ejpam-6761	279	26	fuzzy	fuzzy	ADJ
ejpam-6761	279	27	subgroups	subgroup	NOUN
ejpam-6761	279	28	in	in	ADP
ejpam-6761	279	29	terms	term	NOUN
ejpam-6761	279	30	of	of	ADP
ejpam-6761	279	31	induction	induction	NOUN
ejpam-6761	279	32	is	be	AUX
ejpam-6761	279	33	demonstrated	demonstrate	VERB
ejpam-6761	279	34	.	.	PUNCT
ejpam-6761	280	1	definition	definition	NOUN
ejpam-6761	280	2	21	21	NUM
ejpam-6761	280	3	.	.	PUNCT
ejpam-6761	281	1	let	let	VERB
ejpam-6761	281	2	s	s	PRON
ejpam-6761	281	3	be	be	AUX
ejpam-6761	281	4	a	a	DET
ejpam-6761	281	5	bipolar	bipolar	ADJ
ejpam-6761	281	6	valued	value	VERB
ejpam-6761	281	7	fuzzy	fuzzy	ADJ
ejpam-6761	281	8	subspace	subspace	NOUN
ejpam-6761	281	9	of	of	ADP
ejpam-6761	281	10	the	the	DET
ejpam-6761	281	11	bipolar	bipolar	PROPN
ejpam-6761	281	12	valued	value	VERB
ejpam-6761	281	13	fuzzy	fuzzy	ADJ
ejpam-6761	281	14	space	space	NOUN
ejpam-6761	281	15	(	(	PUNCT
ejpam-6761	281	16	g	g	NOUN
ejpam-6761	281	17	,	,	PUNCT
ejpam-6761	281	18	[	[	X
ejpam-6761	281	19	−1	−1	NOUN
ejpam-6761	281	20	,	,	PUNCT
ejpam-6761	281	21	0	0	NUM
ejpam-6761	281	22	]	]	PUNCT
ejpam-6761	281	23	,	,	PUNCT
ejpam-6761	281	24	[	[	X
ejpam-6761	281	25	0	0	NUM
ejpam-6761	281	26	,	,	PUNCT
ejpam-6761	281	27	1	1	NUM
ejpam-6761	281	28	]	]	NUM
ejpam-6761	281	29	)	)	PUNCT
ejpam-6761	281	30	.	.	PUNCT
ejpam-6761	282	1	the	the	DET
ejpam-6761	282	2	ordered	order	VERB
ejpam-6761	282	3	pair	pair	NOUN
ejpam-6761	282	4	(	(	PUNCT
ejpam-6761	282	5	s;f	s;f	NOUN
ejpam-6761	282	6	)	)	PUNCT
ejpam-6761	282	7	is	be	AUX
ejpam-6761	282	8	called	call	VERB
ejpam-6761	282	9	a	a	DET
ejpam-6761	282	10	bipolar	bipolar	ADJ
ejpam-6761	282	11	valued	value	VERB
ejpam-6761	282	12	fuzzy	fuzzy	ADJ
ejpam-6761	282	13	subgroup	subgroup	NOUN
ejpam-6761	282	14	of	of	ADP
ejpam-6761	282	15	the	the	DET
ejpam-6761	282	16	bipolar	bipolar	ADJ
ejpam-6761	282	17	valued	value	VERB
ejpam-6761	282	18	fuzzy	fuzzy	ADJ
ejpam-6761	282	19	group	group	NOUN
ejpam-6761	282	20	(	(	PUNCT
ejpam-6761	282	21	g	g	NOUN
ejpam-6761	282	22	,	,	PUNCT
ejpam-6761	282	23	[	[	X
ejpam-6761	282	24	−1	−1	NOUN
ejpam-6761	282	25	,	,	PUNCT
ejpam-6761	282	26	0	0	NUM
ejpam-6761	282	27	]	]	PUNCT
ejpam-6761	282	28	,	,	PUNCT
ejpam-6761	282	29	[	[	X
ejpam-6761	282	30	0	0	NUM
ejpam-6761	282	31	,	,	PUNCT
ejpam-6761	282	32	1	1	NUM
ejpam-6761	282	33	]	]	NUM
ejpam-6761	282	34	)	)	PUNCT
ejpam-6761	282	35	,	,	PUNCT
ejpam-6761	282	36	f	f	PROPN
ejpam-6761	282	37	)	)	PUNCT
ejpam-6761	282	38	,	,	PUNCT
ejpam-6761	282	39	denoted	denote	VERB
ejpam-6761	282	40	by	by	ADP
ejpam-6761	282	41	(	(	PUNCT
ejpam-6761	282	42	s;f	s;f	ADV
ejpam-6761	282	43	)	)	PUNCT
ejpam-6761	282	44	≤	≤	NOUN
ejpam-6761	282	45	(	(	PUNCT
ejpam-6761	282	46	g	g	NOUN
ejpam-6761	282	47	,	,	PUNCT
ejpam-6761	282	48	[	[	X
ejpam-6761	282	49	−1	−1	NOUN
ejpam-6761	282	50	,	,	PUNCT
ejpam-6761	282	51	0	0	NUM
ejpam-6761	282	52	]	]	PUNCT
ejpam-6761	282	53	,	,	PUNCT
ejpam-6761	282	54	[	[	X
ejpam-6761	282	55	0	0	NUM
ejpam-6761	282	56	,	,	PUNCT
ejpam-6761	282	57	1	1	NUM
ejpam-6761	282	58	]	]	NUM
ejpam-6761	282	59	)	)	PUNCT
ejpam-6761	282	60	,	,	PUNCT
ejpam-6761	282	61	f	f	PROPN
ejpam-6761	282	62	)	)	PUNCT
ejpam-6761	282	63	,	,	PUNCT
ejpam-6761	282	64	if	if	SCONJ
ejpam-6761	282	65	(	(	PUNCT
ejpam-6761	282	66	s;f	s;f	NOUN
ejpam-6761	282	67	)	)	PUNCT
ejpam-6761	282	68	states	state	VERB
ejpam-6761	282	69	a	a	DET
ejpam-6761	282	70	bipolar	bipolar	ADJ
ejpam-6761	282	71	valued	value	VERB
ejpam-6761	282	72	fuzzy	fuzzy	ADJ
ejpam-6761	282	73	group	group	NOUN
ejpam-6761	282	74	under	under	ADP
ejpam-6761	282	75	the	the	DET
ejpam-6761	282	76	bipolar	bipolar	PROPN
ejpam-6761	282	77	valued	value	VERB
ejpam-6761	282	78	fuzzy	fuzzy	ADJ
ejpam-6761	282	79	binary	binary	NOUN
ejpam-6761	282	80	operation	operation	PROPN
ejpam-6761	282	81	f	f	PROPN
ejpam-6761	282	82	.	.	PUNCT
ejpam-6761	283	1	clearly	clearly	ADV
ejpam-6761	283	2	,	,	PUNCT
ejpam-6761	283	3	if	if	SCONJ
ejpam-6761	283	4	(	(	PUNCT
ejpam-6761	283	5	s;f	s;f	NOUN
ejpam-6761	283	6	)	)	PUNCT
ejpam-6761	283	7	is	be	AUX
ejpam-6761	283	8	a	a	DET
ejpam-6761	283	9	bipolar	bipolar	ADJ
ejpam-6761	283	10	valued	value	VERB
ejpam-6761	283	11	fuzzy	fuzzy	ADJ
ejpam-6761	283	12	subgroup	subgroup	NOUN
ejpam-6761	283	13	of	of	ADP
ejpam-6761	283	14	(	(	PUNCT
ejpam-6761	283	15	g	g	PROPN
ejpam-6761	283	16	,	,	PUNCT
ejpam-6761	283	17	[	[	X
ejpam-6761	283	18	−1	−1	NOUN
ejpam-6761	283	19	,	,	PUNCT
ejpam-6761	283	20	0	0	NUM
ejpam-6761	283	21	]	]	PUNCT
ejpam-6761	283	22	,	,	PUNCT
ejpam-6761	283	23	[	[	X
ejpam-6761	283	24	0	0	NUM
ejpam-6761	283	25	,	,	PUNCT
ejpam-6761	283	26	1	1	NUM
ejpam-6761	283	27	]	]	NUM
ejpam-6761	283	28	)	)	PUNCT
ejpam-6761	283	29	,	,	PUNCT
ejpam-6761	283	30	f	f	PROPN
ejpam-6761	283	31	)	)	PUNCT
ejpam-6761	283	32	and	and	CCONJ
ejpam-6761	283	33	(	(	PUNCT
ejpam-6761	283	34	n	n	X
ejpam-6761	283	35	;	;	PUNCT
ejpam-6761	283	36	f	f	X
ejpam-6761	283	37	)	)	PUNCT
ejpam-6761	283	38	is	be	AUX
ejpam-6761	283	39	a	a	DET
ejpam-6761	283	40	bipolar	bipolar	ADJ
ejpam-6761	283	41	valued	value	VERB
ejpam-6761	283	42	fuzzy	fuzzy	ADJ
ejpam-6761	283	43	subgroup	subgroup	NOUN
ejpam-6761	283	44	of	of	ADP
ejpam-6761	283	45	(	(	PUNCT
ejpam-6761	283	46	s;f	s;f	PROPN
ejpam-6761	283	47	)	)	PUNCT
ejpam-6761	283	48	,	,	PUNCT
ejpam-6761	283	49	then	then	ADV
ejpam-6761	283	50	(	(	PUNCT
ejpam-6761	283	51	n	n	X
ejpam-6761	283	52	;	;	PUNCT
ejpam-6761	283	53	f	f	X
ejpam-6761	283	54	)	)	PUNCT
ejpam-6761	283	55	is	be	AUX
ejpam-6761	283	56	a	a	DET
ejpam-6761	283	57	bipolar	bipolar	ADJ
ejpam-6761	283	58	valued	value	VERB
ejpam-6761	283	59	fuzzy	fuzzy	ADJ
ejpam-6761	283	60	subgroup	subgroup	NOUN
ejpam-6761	283	61	of	of	ADP
ejpam-6761	283	62	(	(	PUNCT
ejpam-6761	283	63	g	g	PROPN
ejpam-6761	283	64	,	,	PUNCT
ejpam-6761	283	65	[	[	X
ejpam-6761	283	66	−1	−1	NOUN
ejpam-6761	283	67	,	,	PUNCT
ejpam-6761	283	68	0	0	NUM
ejpam-6761	283	69	]	]	PUNCT
ejpam-6761	283	70	,	,	PUNCT
ejpam-6761	284	1	[	[	X
ejpam-6761	284	2	0	0	NUM
ejpam-6761	284	3	,	,	PUNCT
ejpam-6761	284	4	1	1	NUM
ejpam-6761	284	5	]	]	NUM
ejpam-6761	284	6	)	)	PUNCT
ejpam-6761	284	7	,	,	PUNCT
ejpam-6761	284	8	f	f	PROPN
ejpam-6761	284	9	)	)	PUNCT
ejpam-6761	284	10	.	.	PUNCT
ejpam-6761	285	1	also	also	ADV
ejpam-6761	285	2	,	,	PUNCT
ejpam-6761	285	3	if	if	SCONJ
ejpam-6761	285	4	(	(	PUNCT
ejpam-6761	285	5	g	g	NOUN
ejpam-6761	285	6	,	,	PUNCT
ejpam-6761	285	7	[	[	X
ejpam-6761	285	8	−1	−1	NOUN
ejpam-6761	285	9	,	,	PUNCT
ejpam-6761	285	10	0	0	NUM
ejpam-6761	285	11	]	]	PUNCT
ejpam-6761	285	12	,	,	PUNCT
ejpam-6761	285	13	[	[	X
ejpam-6761	285	14	0	0	NUM
ejpam-6761	285	15	,	,	PUNCT
ejpam-6761	285	16	1	1	NUM
ejpam-6761	285	17	]	]	NUM
ejpam-6761	285	18	)	)	PUNCT
ejpam-6761	285	19	,	,	PUNCT
ejpam-6761	285	20	f	f	PROPN
ejpam-6761	285	21	)	)	PUNCT
ejpam-6761	285	22	is	be	AUX
ejpam-6761	285	23	a	a	DET
ejpam-6761	285	24	bvf	bvf	NOUN
ejpam-6761	285	25	group	group	NOUN
ejpam-6761	285	26	with	with	ADP
ejpam-6761	285	27	a	a	DET
ejpam-6761	285	28	bvf	bvf	NOUN
ejpam-6761	285	29	identity	identity	NOUN
ejpam-6761	285	30	(	(	PUNCT
ejpam-6761	285	31	e	e	NOUN
ejpam-6761	285	32	,	,	PUNCT
ejpam-6761	285	33	[	[	X
ejpam-6761	285	34	−1	−1	NOUN
ejpam-6761	285	35	,	,	PUNCT
ejpam-6761	285	36	0	0	NUM
ejpam-6761	285	37	]	]	PUNCT
ejpam-6761	285	38	,	,	PUNCT
ejpam-6761	285	39	[	[	X
ejpam-6761	285	40	0	0	NUM
ejpam-6761	285	41	,	,	PUNCT
ejpam-6761	285	42	1	1	NUM
ejpam-6761	285	43	]	]	NUM
ejpam-6761	285	44	)	)	PUNCT
ejpam-6761	285	45	,	,	PUNCT
ejpam-6761	286	1	then	then	ADV
ejpam-6761	286	2	both	both	DET
ejpam-6761	286	3	{	{	PUNCT
ejpam-6761	286	4	(	(	PUNCT
ejpam-6761	286	5	e	e	NOUN
ejpam-6761	286	6	,	,	PUNCT
ejpam-6761	286	7	[	[	X
ejpam-6761	286	8	−1	−1	NOUN
ejpam-6761	286	9	,	,	PUNCT
ejpam-6761	286	10	0	0	NUM
ejpam-6761	286	11	]	]	PUNCT
ejpam-6761	286	12	,	,	PUNCT
ejpam-6761	286	13	[	[	X
ejpam-6761	286	14	0	0	NUM
ejpam-6761	286	15	,	,	PUNCT
ejpam-6761	286	16	1	1	NUM
ejpam-6761	286	17	]	]	NUM
ejpam-6761	286	18	)	)	PUNCT
ejpam-6761	286	19	}	}	PUNCT
ejpam-6761	286	20	and	and	CCONJ
ejpam-6761	286	21	(	(	PUNCT
ejpam-6761	286	22	g	g	NOUN
ejpam-6761	286	23	,	,	PUNCT
ejpam-6761	286	24	[	[	X
ejpam-6761	286	25	−1	−1	NOUN
ejpam-6761	286	26	,	,	PUNCT
ejpam-6761	286	27	0	0	NUM
ejpam-6761	286	28	]	]	PUNCT
ejpam-6761	286	29	,	,	PUNCT
ejpam-6761	286	30	[	[	X
ejpam-6761	286	31	0	0	NUM
ejpam-6761	286	32	,	,	PUNCT
ejpam-6761	286	33	1	1	NUM
ejpam-6761	286	34	]	]	NUM
ejpam-6761	286	35	)	)	PUNCT
ejpam-6761	286	36	,	,	PUNCT
ejpam-6761	286	37	f	f	PROPN
ejpam-6761	286	38	)	)	PUNCT
ejpam-6761	286	39	are	be	AUX
ejpam-6761	286	40	trivial	trivial	ADJ
ejpam-6761	286	41	bipolar	bipolar	ADJ
ejpam-6761	286	42	valued	value	VERB
ejpam-6761	286	43	fuzzy	fuzzy	ADJ
ejpam-6761	286	44	subgroups	subgroup	NOUN
ejpam-6761	286	45	of	of	ADP
ejpam-6761	286	46	(	(	PUNCT
ejpam-6761	286	47	g	g	PROPN
ejpam-6761	286	48	,	,	PUNCT
ejpam-6761	286	49	[	[	X
ejpam-6761	286	50	−1	−1	NOUN
ejpam-6761	286	51	,	,	PUNCT
ejpam-6761	286	52	0	0	NUM
ejpam-6761	286	53	]	]	PUNCT
ejpam-6761	286	54	,	,	PUNCT
ejpam-6761	286	55	[	[	X
ejpam-6761	286	56	0	0	NUM
ejpam-6761	286	57	,	,	PUNCT
ejpam-6761	286	58	1	1	NUM
ejpam-6761	286	59	]	]	NUM
ejpam-6761	286	60	)	)	PUNCT
ejpam-6761	286	61	,	,	PUNCT
ejpam-6761	286	62	f	f	PROPN
ejpam-6761	286	63	)	)	PUNCT
ejpam-6761	286	64	.	.	PUNCT
ejpam-6761	287	1	the	the	DET
ejpam-6761	287	2	next	next	ADJ
ejpam-6761	287	3	theorem	theorem	NOUN
ejpam-6761	287	4	explains	explain	VERB
ejpam-6761	287	5	exactly	exactly	ADV
ejpam-6761	287	6	when	when	SCONJ
ejpam-6761	287	7	a	a	DET
ejpam-6761	287	8	bipolar	bipolar	ADV
ejpam-6761	287	9	-	-	PUNCT
ejpam-6761	287	10	valued	value	VERB
ejpam-6761	287	11	fuzzy	fuzzy	ADJ
ejpam-6761	287	12	subgroup	subgroup	NOUN
ejpam-6761	287	13	exists	exist	VERB
ejpam-6761	287	14	,	,	PUNCT
ejpam-6761	287	15	giving	give	VERB
ejpam-6761	287	16	both	both	CCONJ
ejpam-6761	287	17	necessary	necessary	ADJ
ejpam-6761	287	18	and	and	CCONJ
ejpam-6761	287	19	sufficient	sufficient	ADJ
ejpam-6761	287	20	conditions	condition	NOUN
ejpam-6761	287	21	.	.	PUNCT
ejpam-6761	288	1	theorem	theorem	NOUN
ejpam-6761	288	2	3	3	X
ejpam-6761	288	3	.	.	PUNCT
ejpam-6761	289	1	let	let	VERB
ejpam-6761	289	2	s	s	PRON
ejpam-6761	289	3	=	=	VERB
ejpam-6761	289	4	{	{	PUNCT
ejpam-6761	289	5	(	(	PUNCT
ejpam-6761	289	6	x	x	NOUN
ejpam-6761	289	7	,	,	PUNCT
ejpam-6761	289	8	s−x	s−x	NOUN
ejpam-6761	289	9	,	,	PUNCT
ejpam-6761	289	10	s+x	s+x	PROPN
ejpam-6761	289	11	)	)	PUNCT
ejpam-6761	289	12	:	:	PUNCT
ejpam-6761	290	1	x	x	PUNCT
ejpam-6761	290	2	∈	∈	PROPN
ejpam-6761	290	3	s	s	X
ejpam-6761	290	4	◦	◦	NOUN
ejpam-6761	290	5	}	}	PUNCT
ejpam-6761	290	6	be	be	AUX
ejpam-6761	290	7	a	a	DET
ejpam-6761	290	8	bipolar	bipolar	ADJ
ejpam-6761	290	9	valued	value	VERB
ejpam-6761	290	10	fuzzy	fuzzy	ADJ
ejpam-6761	290	11	subspace	subspace	NOUN
ejpam-6761	290	12	of	of	ADP
ejpam-6761	290	13	the	the	DET
ejpam-6761	290	14	bipolar	bipolar	PROPN
ejpam-6761	290	15	valued	value	VERB
ejpam-6761	290	16	fuzzy	fuzzy	ADJ
ejpam-6761	290	17	space	space	NOUN
ejpam-6761	290	18	(	(	PUNCT
ejpam-6761	290	19	g	g	NOUN
ejpam-6761	290	20	,	,	PUNCT
ejpam-6761	290	21	[	[	X
ejpam-6761	290	22	−1	−1	NOUN
ejpam-6761	290	23	,	,	PUNCT
ejpam-6761	290	24	0	0	NUM
ejpam-6761	290	25	]	]	PUNCT
ejpam-6761	290	26	,	,	PUNCT
ejpam-6761	291	1	[	[	X
ejpam-6761	291	2	0	0	NUM
ejpam-6761	291	3	,	,	PUNCT
ejpam-6761	291	4	1	1	NUM
ejpam-6761	291	5	]	]	NUM
ejpam-6761	291	6	)	)	PUNCT
ejpam-6761	291	7	.	.	PUNCT
ejpam-6761	292	1	then	then	ADV
ejpam-6761	292	2	(	(	PUNCT
ejpam-6761	292	3	s;f	s;f	NOUN
ejpam-6761	292	4	)	)	PUNCT
ejpam-6761	292	5	is	be	AUX
ejpam-6761	292	6	a	a	DET
ejpam-6761	292	7	bipolar	bipolar	ADJ
ejpam-6761	292	8	valued	value	VERB
ejpam-6761	292	9	fuzzy	fuzzy	ADJ
ejpam-6761	292	10	subgroup	subgroup	NOUN
ejpam-6761	292	11	of	of	ADP
ejpam-6761	292	12	the	the	DET
ejpam-6761	292	13	bvf	bvf	NOUN
ejpam-6761	292	14	group	group	NOUN
ejpam-6761	292	15	(	(	PUNCT
ejpam-6761	292	16	(	(	PUNCT
ejpam-6761	292	17	g	g	NOUN
ejpam-6761	292	18	,	,	PUNCT
ejpam-6761	292	19	[	[	X
ejpam-6761	292	20	−1	−1	NOUN
ejpam-6761	292	21	,	,	PUNCT
ejpam-6761	292	22	0	0	NUM
ejpam-6761	292	23	]	]	PUNCT
ejpam-6761	292	24	,	,	PUNCT
ejpam-6761	292	25	[	[	X
ejpam-6761	292	26	0	0	NUM
ejpam-6761	292	27	,	,	PUNCT
ejpam-6761	292	28	1	1	NUM
ejpam-6761	292	29	]	]	NUM
ejpam-6761	292	30	)	)	PUNCT
ejpam-6761	292	31	,	,	PUNCT
ejpam-6761	292	32	f	f	PROPN
ejpam-6761	292	33	)	)	PUNCT
ejpam-6761	293	1	if	if	SCONJ
ejpam-6761	293	2	and	and	CCONJ
ejpam-6761	293	3	only	only	ADV
ejpam-6761	293	4	if	if	SCONJ
ejpam-6761	293	5	:	:	PUNCT
ejpam-6761	293	6	(	(	PUNCT
ejpam-6761	293	7	1	1	X
ejpam-6761	293	8	)	)	PUNCT
ejpam-6761	293	9	(	(	PUNCT
ejpam-6761	293	10	s	s	NOUN
ejpam-6761	293	11	◦	◦	NOUN
ejpam-6761	293	12	;f	;f	PUNCT
ejpam-6761	293	13	)	)	PUNCT
ejpam-6761	293	14	is	be	AUX
ejpam-6761	293	15	an	an	DET
ejpam-6761	293	16	ordinary	ordinary	ADJ
ejpam-6761	293	17	subgroup	subgroup	NOUN
ejpam-6761	293	18	of	of	ADP
ejpam-6761	293	19	the	the	DET
ejpam-6761	293	20	group	group	NOUN
ejpam-6761	293	21	(	(	PUNCT
ejpam-6761	293	22	g	g	PROPN
ejpam-6761	293	23	,	,	PUNCT
ejpam-6761	293	24	f	f	PROPN
ejpam-6761	293	25	)	)	PUNCT
ejpam-6761	293	26	,	,	PUNCT
ejpam-6761	293	27	f.	f.	PROPN
ejpam-6761	293	28	al	al	PROPN
ejpam-6761	293	29	-	-	PROPN
ejpam-6761	293	30	zu’bi	zu’bi	PROPN
ejpam-6761	293	31	et	et	NOUN
ejpam-6761	293	32	al	al	PROPN
ejpam-6761	293	33	.	.	PUNCT
ejpam-6761	293	34	/	/	SYM
ejpam-6761	293	35	eur	eur	PROPN
ejpam-6761	293	36	.	.	PUNCT
ejpam-6761	294	1	j.	j.	PROPN
ejpam-6761	294	2	pure	pure	PROPN
ejpam-6761	294	3	appl	appl	PROPN
ejpam-6761	294	4	.	.	PROPN
ejpam-6761	294	5	math	math	PROPN
ejpam-6761	294	6	,	,	PUNCT
ejpam-6761	294	7	18	18	NUM
ejpam-6761	294	8	(	(	PUNCT
ejpam-6761	294	9	4	4	NUM
ejpam-6761	294	10	)	)	PUNCT
ejpam-6761	294	11	(	(	PUNCT
ejpam-6761	294	12	2025	2025	NUM
ejpam-6761	294	13	)	)	PUNCT
ejpam-6761	294	14	,	,	PUNCT
ejpam-6761	294	15	6761	6761	NUM
ejpam-6761	294	16	13	13	NUM
ejpam-6761	294	17	of	of	ADP
ejpam-6761	294	18	28	28	NUM
ejpam-6761	294	19	(	(	PUNCT
ejpam-6761	294	20	2	2	NUM
ejpam-6761	294	21	)	)	PUNCT
ejpam-6761	294	22	f−xy(s	f−xy(	VERB
ejpam-6761	294	23	−	−	PROPN
ejpam-6761	294	24	x	x	INTJ
ejpam-6761	294	25	,	,	PUNCT
ejpam-6761	294	26	s	s	PART
ejpam-6761	294	27	−	−	PROPN
ejpam-6761	294	28	y	y	PROPN
ejpam-6761	294	29	)	)	PUNCT
ejpam-6761	294	30	=	=	PUNCT
ejpam-6761	294	31	s−x	s−x	PROPN
ejpam-6761	294	32	f	f	X
ejpam-6761	294	33	−	−	NOUN
ejpam-6761	295	1	xys	xys	NOUN
ejpam-6761	296	1	−	−	PROPN
ejpam-6761	296	2	y	y	PROPN
ejpam-6761	296	3	=	=	PUNCT
ejpam-6761	296	4	sxfy	sxfy	PROPN
ejpam-6761	296	5	−	−	PROPN
ejpam-6761	296	6	,	,	PUNCT
ejpam-6761	296	7	and	and	CCONJ
ejpam-6761	296	8	f+xy(s	f+xy(s	PROPN
ejpam-6761	296	9	+	+	CCONJ
ejpam-6761	296	10	x	x	SYM
ejpam-6761	296	11	,	,	PUNCT
ejpam-6761	296	12	s	s	PART
ejpam-6761	296	13	+	+	X
ejpam-6761	296	14	y	y	NOUN
ejpam-6761	296	15	)	)	PUNCT
ejpam-6761	296	16	=	=	PUNCT
ejpam-6761	297	1	s+x	s+x	PROPN
ejpam-6761	297	2	f	f	PROPN
ejpam-6761	297	3	+	+	CCONJ
ejpam-6761	297	4	xys	xys	PROPN
ejpam-6761	298	1	+	+	CCONJ
ejpam-6761	298	2	y	y	NOUN
ejpam-6761	298	3	=	=	PUNCT
ejpam-6761	298	4	sxfy	sxfy	NOUN
ejpam-6761	298	5	+	+	CCONJ
ejpam-6761	298	6	(	(	PUNCT
ejpam-6761	298	7	1	1	X
ejpam-6761	298	8	)	)	PUNCT
ejpam-6761	298	9	for	for	ADP
ejpam-6761	298	10	all	all	DET
ejpam-6761	298	11	x	x	NOUN
ejpam-6761	298	12	,	,	PUNCT
ejpam-6761	298	13	y	y	PROPN
ejpam-6761	298	14	∈	∈	PROPN
ejpam-6761	298	15	s	s	PART
ejpam-6761	298	16	◦	◦	NOUN
ejpam-6761	298	17	.	.	PUNCT
ejpam-6761	299	1	proof	proof	NOUN
ejpam-6761	299	2	.	.	PUNCT
ejpam-6761	300	1	suppose	suppose	VERB
ejpam-6761	300	2	(	(	PUNCT
ejpam-6761	300	3	1	1	NUM
ejpam-6761	300	4	)	)	PUNCT
ejpam-6761	300	5	and	and	CCONJ
ejpam-6761	300	6	(	(	PUNCT
ejpam-6761	300	7	2	2	X
ejpam-6761	300	8	)	)	PUNCT
ejpam-6761	300	9	are	be	AUX
ejpam-6761	300	10	satisfied	satisfied	ADJ
ejpam-6761	300	11	,	,	PUNCT
ejpam-6761	300	12	then	then	ADV
ejpam-6761	300	13	:	:	PUNCT
ejpam-6761	300	14	(	(	PUNCT
ejpam-6761	300	15	i	i	NOUN
ejpam-6761	300	16	)	)	PUNCT
ejpam-6761	300	17	(	(	PUNCT
ejpam-6761	300	18	closeness	closeness	NOUN
ejpam-6761	300	19	condition	condition	NOUN
ejpam-6761	300	20	)	)	PUNCT
ejpam-6761	300	21	the	the	DET
ejpam-6761	300	22	bipolar	bipolar	ADJ
ejpam-6761	300	23	valued	value	VERB
ejpam-6761	300	24	fuzzy	fuzzy	ADJ
ejpam-6761	300	25	subspace	subspace	NOUN
ejpam-6761	300	26	s	s	PART
ejpam-6761	300	27	is	be	AUX
ejpam-6761	300	28	closed	close	VERB
ejpam-6761	300	29	under	under	ADP
ejpam-6761	300	30	f	f	PROPN
ejpam-6761	300	31	:	:	PUNCT
ejpam-6761	300	32	let	let	VERB
ejpam-6761	300	33	(	(	PUNCT
ejpam-6761	300	34	x	x	NOUN
ejpam-6761	300	35	,	,	PUNCT
ejpam-6761	300	36	s−x	s−x	NOUN
ejpam-6761	300	37	,	,	PUNCT
ejpam-6761	300	38	s	s	PART
ejpam-6761	300	39	+	+	NOUN
ejpam-6761	300	40	x	x	X
ejpam-6761	300	41	)	)	PUNCT
ejpam-6761	300	42	,	,	PUNCT
ejpam-6761	300	43	(	(	PUNCT
ejpam-6761	300	44	y	y	NOUN
ejpam-6761	300	45	,	,	PUNCT
ejpam-6761	300	46	s	s	PART
ejpam-6761	300	47	−	−	PROPN
ejpam-6761	300	48	y	y	PROPN
ejpam-6761	300	49	,	,	PUNCT
ejpam-6761	300	50	s	s	PART
ejpam-6761	300	51	+	+	PROPN
ejpam-6761	300	52	y	y	NOUN
ejpam-6761	300	53	)	)	PUNCT
ejpam-6761	300	54	be	be	AUX
ejpam-6761	300	55	in	in	ADP
ejpam-6761	300	56	s	s	PRON
ejpam-6761	300	57	then	then	ADV
ejpam-6761	300	58	:	:	PUNCT
ejpam-6761	300	59	(	(	PUNCT
ejpam-6761	300	60	x	x	NOUN
ejpam-6761	300	61	,	,	PUNCT
ejpam-6761	300	62	s−x	s−x	NOUN
ejpam-6761	300	63	,	,	PUNCT
ejpam-6761	300	64	s	s	PART
ejpam-6761	300	65	+	+	NOUN
ejpam-6761	300	66	x	x	X
ejpam-6761	300	67	)	)	PUNCT
ejpam-6761	300	68	f	f	NOUN
ejpam-6761	300	69	(	(	PUNCT
ejpam-6761	300	70	y	y	PROPN
ejpam-6761	300	71	,	,	PUNCT
ejpam-6761	300	72	s	s	PART
ejpam-6761	300	73	−	−	PROPN
ejpam-6761	300	74	y	y	PROPN
ejpam-6761	300	75	,	,	PUNCT
ejpam-6761	300	76	s	s	PART
ejpam-6761	300	77	+	+	X
ejpam-6761	300	78	y	y	NOUN
ejpam-6761	300	79	)	)	PUNCT
ejpam-6761	301	1	=	=	SYM
ejpam-6761	301	2	f	f	PROPN
ejpam-6761	301	3	(	(	PUNCT
ejpam-6761	301	4	(	(	PUNCT
ejpam-6761	301	5	x	x	NOUN
ejpam-6761	301	6	,	,	PUNCT
ejpam-6761	301	7	s−x	s−x	NOUN
ejpam-6761	301	8	,	,	PUNCT
ejpam-6761	301	9	s	s	PART
ejpam-6761	301	10	+	+	NOUN
ejpam-6761	301	11	x	x	X
ejpam-6761	301	12	)	)	PUNCT
ejpam-6761	301	13	,	,	PUNCT
ejpam-6761	301	14	(	(	PUNCT
ejpam-6761	301	15	y	y	NOUN
ejpam-6761	301	16	,	,	PUNCT
ejpam-6761	301	17	s	s	PART
ejpam-6761	301	18	−	−	PROPN
ejpam-6761	301	19	y	y	PROPN
ejpam-6761	301	20	,	,	PUNCT
ejpam-6761	301	21	s	s	PART
ejpam-6761	301	22	+	+	X
ejpam-6761	301	23	y	y	PROPN
ejpam-6761	301	24	)	)	PUNCT
ejpam-6761	301	25	)	)	PUNCT
ejpam-6761	302	1	=	=	PRON
ejpam-6761	302	2	(	(	PUNCT
ejpam-6761	302	3	f	f	X
ejpam-6761	302	4	(	(	PUNCT
ejpam-6761	302	5	x	x	PROPN
ejpam-6761	302	6	,	,	PUNCT
ejpam-6761	302	7	y	y	PROPN
ejpam-6761	302	8	)	)	PUNCT
ejpam-6761	302	9	,	,	PUNCT
ejpam-6761	302	10	f−xy(s	f−xy(	VERB
ejpam-6761	302	11	−	−	PROPN
ejpam-6761	302	12	x	x	INTJ
ejpam-6761	302	13	,	,	PUNCT
ejpam-6761	302	14	s	s	PART
ejpam-6761	302	15	−	−	PROPN
ejpam-6761	302	16	y	y	PROPN
ejpam-6761	302	17	)	)	PUNCT
ejpam-6761	302	18	,	,	PUNCT
ejpam-6761	302	19	f	f	PROPN
ejpam-6761	302	20	+	+	CCONJ
ejpam-6761	302	21	xy(s	xy(s	PROPN
ejpam-6761	302	22	+	+	CCONJ
ejpam-6761	302	23	x	x	SYM
ejpam-6761	302	24	,	,	PUNCT
ejpam-6761	302	25	s	s	PART
ejpam-6761	302	26	+	+	X
ejpam-6761	302	27	y	y	PROPN
ejpam-6761	302	28	)	)	PUNCT
ejpam-6761	302	29	)	)	PUNCT
ejpam-6761	303	1	=	=	PRON
ejpam-6761	303	2	(	(	PUNCT
ejpam-6761	303	3	xfy	xfy	PROPN
ejpam-6761	303	4	,	,	PUNCT
ejpam-6761	303	5	sxfy	sxfy	NOUN
ejpam-6761	303	6	−	−	PROPN
ejpam-6761	303	7	,	,	PUNCT
ejpam-6761	303	8	sxfy	sxfy	NOUN
ejpam-6761	303	9	+	+	NOUN
ejpam-6761	303	10	)	)	PUNCT
ejpam-6761	303	11	∈	∈	PROPN
ejpam-6761	303	12	s.	s.	PROPN
ejpam-6761	303	13	(	(	PUNCT
ejpam-6761	303	14	2	2	NUM
ejpam-6761	303	15	)	)	PUNCT
ejpam-6761	303	16	(	(	PUNCT
ejpam-6761	303	17	ii	ii	NOUN
ejpam-6761	303	18	)	)	PUNCT
ejpam-6761	303	19	(	(	PUNCT
ejpam-6761	303	20	s;f	s;f	ADV
ejpam-6761	303	21	)	)	PUNCT
ejpam-6761	303	22	is	be	AUX
ejpam-6761	303	23	itself	itself	PRON
ejpam-6761	303	24	a	a	DET
ejpam-6761	303	25	bvf	bvf	NOUN
ejpam-6761	303	26	group	group	NOUN
ejpam-6761	303	27	:	:	PUNCT
ejpam-6761	303	28	a	a	X
ejpam-6761	303	29	)	)	PUNCT
ejpam-6761	303	30	(	(	PUNCT
ejpam-6761	303	31	associative	associative	ADJ
ejpam-6761	303	32	condition	condition	NOUN
ejpam-6761	303	33	)	)	PUNCT
ejpam-6761	303	34	let	let	VERB
ejpam-6761	303	35	(	(	PUNCT
ejpam-6761	303	36	x	x	NOUN
ejpam-6761	303	37	,	,	PUNCT
ejpam-6761	303	38	s−x	s−x	NOUN
ejpam-6761	303	39	,	,	PUNCT
ejpam-6761	303	40	s	s	PART
ejpam-6761	303	41	+	+	NOUN
ejpam-6761	303	42	x	x	X
ejpam-6761	303	43	)	)	PUNCT
ejpam-6761	303	44	,	,	PUNCT
ejpam-6761	303	45	(	(	PUNCT
ejpam-6761	303	46	y	y	NOUN
ejpam-6761	303	47	,	,	PUNCT
ejpam-6761	303	48	s	s	PART
ejpam-6761	303	49	−	−	PROPN
ejpam-6761	303	50	y	y	PROPN
ejpam-6761	303	51	,	,	PUNCT
ejpam-6761	303	52	s	s	PART
ejpam-6761	303	53	+	+	X
ejpam-6761	303	54	y	y	PROPN
ejpam-6761	303	55	)	)	PUNCT
ejpam-6761	303	56	,	,	PUNCT
ejpam-6761	303	57	(	(	PUNCT
ejpam-6761	303	58	z	z	X
ejpam-6761	303	59	,	,	PUNCT
ejpam-6761	303	60	s	s	PART
ejpam-6761	303	61	−	−	PROPN
ejpam-6761	303	62	z	z	NOUN
ejpam-6761	303	63	,	,	PUNCT
ejpam-6761	303	64	s	s	PART
ejpam-6761	303	65	+	+	X
ejpam-6761	303	66	z	z	NOUN
ejpam-6761	303	67	)	)	PUNCT
ejpam-6761	303	68	be	be	AUX
ejpam-6761	303	69	in	in	ADP
ejpam-6761	303	70	s	s	PRON
ejpam-6761	303	71	then	then	ADV
ejpam-6761	303	72	:	:	PUNCT
ejpam-6761	303	73	(	(	PUNCT
ejpam-6761	303	74	(	(	PUNCT
ejpam-6761	303	75	x	x	NOUN
ejpam-6761	303	76	,	,	PUNCT
ejpam-6761	303	77	s−x	s−x	NOUN
ejpam-6761	303	78	,	,	PUNCT
ejpam-6761	303	79	s	s	PART
ejpam-6761	303	80	+	+	NOUN
ejpam-6761	303	81	x	x	X
ejpam-6761	303	82	)	)	PUNCT
ejpam-6761	303	83	f	f	NOUN
ejpam-6761	303	84	(	(	PUNCT
ejpam-6761	303	85	y	y	PROPN
ejpam-6761	303	86	,	,	PUNCT
ejpam-6761	303	87	s	s	PART
ejpam-6761	303	88	−	−	PROPN
ejpam-6761	303	89	y	y	PROPN
ejpam-6761	303	90	,	,	PUNCT
ejpam-6761	303	91	s	s	PART
ejpam-6761	303	92	+	+	X
ejpam-6761	303	93	y	y	PROPN
ejpam-6761	303	94	)	)	PUNCT
ejpam-6761	303	95	)	)	PUNCT
ejpam-6761	304	1	f	f	X
ejpam-6761	304	2	(	(	PUNCT
ejpam-6761	304	3	z	z	NOUN
ejpam-6761	304	4	,	,	PUNCT
ejpam-6761	304	5	s−z	s−z	NOUN
ejpam-6761	304	6	,	,	PUNCT
ejpam-6761	304	7	s	s	PART
ejpam-6761	304	8	+	+	NOUN
ejpam-6761	304	9	z	z	NOUN
ejpam-6761	304	10	)	)	PUNCT
ejpam-6761	305	1	=	=	PUNCT
ejpam-6761	305	2	(	(	PUNCT
ejpam-6761	305	3	f	f	X
ejpam-6761	305	4	(	(	PUNCT
ejpam-6761	305	5	x	x	PROPN
ejpam-6761	305	6	,	,	PUNCT
ejpam-6761	305	7	y	y	PROPN
ejpam-6761	305	8	)	)	PUNCT
ejpam-6761	305	9	,	,	PUNCT
ejpam-6761	305	10	f−xy(s	f−xy(	VERB
ejpam-6761	305	11	−	−	PROPN
ejpam-6761	305	12	x	x	INTJ
ejpam-6761	305	13	,	,	PUNCT
ejpam-6761	305	14	s	s	PART
ejpam-6761	305	15	−	−	PROPN
ejpam-6761	305	16	y	y	PROPN
ejpam-6761	305	17	)	)	PUNCT
ejpam-6761	305	18	,	,	PUNCT
ejpam-6761	305	19	f	f	PROPN
ejpam-6761	305	20	+	+	CCONJ
ejpam-6761	305	21	xy(s	xy(s	PROPN
ejpam-6761	305	22	+	+	CCONJ
ejpam-6761	305	23	x	x	SYM
ejpam-6761	305	24	,	,	PUNCT
ejpam-6761	305	25	s	s	PART
ejpam-6761	305	26	+	+	X
ejpam-6761	305	27	y	y	PROPN
ejpam-6761	305	28	)	)	PUNCT
ejpam-6761	305	29	)	)	PUNCT
ejpam-6761	306	1	f	f	X
ejpam-6761	306	2	(	(	PUNCT
ejpam-6761	306	3	z	z	NOUN
ejpam-6761	306	4	,	,	PUNCT
ejpam-6761	306	5	s	s	PART
ejpam-6761	306	6	−	−	PROPN
ejpam-6761	306	7	z	z	NOUN
ejpam-6761	306	8	,	,	PUNCT
ejpam-6761	306	9	s	s	PART
ejpam-6761	306	10	+	+	NOUN
ejpam-6761	306	11	z	z	NOUN
ejpam-6761	306	12	)	)	PUNCT
ejpam-6761	307	1	=	=	SYM
ejpam-6761	307	2	(	(	PUNCT
ejpam-6761	307	3	(	(	PUNCT
ejpam-6761	307	4	xfy)fz	xfy)fz	ADJ
ejpam-6761	307	5	,	,	PUNCT
ejpam-6761	307	6	s−(xfy)fz	s−(xfy)fz	NOUN
ejpam-6761	307	7	,	,	PUNCT
ejpam-6761	307	8	s	s	PART
ejpam-6761	307	9	+	+	X
ejpam-6761	307	10	(	(	PUNCT
ejpam-6761	307	11	xfy)fz	xfy)fz	ADJ
ejpam-6761	307	12	)	)	PUNCT
ejpam-6761	307	13	=	=	PRON
ejpam-6761	308	1	(	(	PUNCT
ejpam-6761	308	2	xf	xf	PROPN
ejpam-6761	308	3	(	(	PUNCT
ejpam-6761	308	4	yfz	yfz	PROPN
ejpam-6761	308	5	)	)	PUNCT
ejpam-6761	308	6	,	,	PUNCT
ejpam-6761	308	7	s−xf	s−xf	NOUN
ejpam-6761	308	8	(	(	PUNCT
ejpam-6761	308	9	yfz	yfz	PROPN
ejpam-6761	308	10	)	)	PUNCT
ejpam-6761	308	11	,	,	PUNCT
ejpam-6761	308	12	s	s	PART
ejpam-6761	309	1	+	+	CCONJ
ejpam-6761	309	2	xf	xf	PROPN
ejpam-6761	309	3	(	(	PUNCT
ejpam-6761	309	4	yfz	yfz	PROPN
ejpam-6761	309	5	)	)	PUNCT
ejpam-6761	309	6	)	)	PUNCT
ejpam-6761	310	1	=	=	PUNCT
ejpam-6761	310	2	(	(	PUNCT
ejpam-6761	310	3	x	x	X
ejpam-6761	310	4	,	,	PUNCT
ejpam-6761	310	5	s−x	s−x	NOUN
ejpam-6761	310	6	,	,	PUNCT
ejpam-6761	310	7	s	s	PART
ejpam-6761	310	8	+	+	NOUN
ejpam-6761	310	9	x	x	X
ejpam-6761	310	10	)	)	PUNCT
ejpam-6761	310	11	f	f	NOUN
ejpam-6761	310	12	(	(	PUNCT
ejpam-6761	310	13	(	(	PUNCT
ejpam-6761	310	14	y	y	PROPN
ejpam-6761	310	15	,	,	PUNCT
ejpam-6761	310	16	s−y	s−y	ADJ
ejpam-6761	310	17	,	,	PUNCT
ejpam-6761	310	18	s	s	PART
ejpam-6761	310	19	+	+	X
ejpam-6761	310	20	y	y	PROPN
ejpam-6761	310	21	)	)	PUNCT
ejpam-6761	310	22	f	f	PROPN
ejpam-6761	310	23	(	(	PUNCT
ejpam-6761	310	24	z	z	NOUN
ejpam-6761	310	25	,	,	PUNCT
ejpam-6761	310	26	s	s	PART
ejpam-6761	310	27	−	−	PROPN
ejpam-6761	310	28	z	z	NOUN
ejpam-6761	310	29	,	,	PUNCT
ejpam-6761	310	30	s	s	PART
ejpam-6761	310	31	+	+	X
ejpam-6761	310	32	z	z	NOUN
ejpam-6761	310	33	)	)	PUNCT
ejpam-6761	310	34	)	)	PUNCT
ejpam-6761	310	35	.	.	PUNCT
ejpam-6761	311	1	(	(	PUNCT
ejpam-6761	311	2	3	3	X
ejpam-6761	311	3	)	)	PUNCT
ejpam-6761	311	4	b	b	NOUN
ejpam-6761	311	5	)	)	PUNCT
ejpam-6761	311	6	(	(	PUNCT
ejpam-6761	311	7	identity	identity	NOUN
ejpam-6761	311	8	condition	condition	NOUN
ejpam-6761	311	9	)	)	PUNCT
ejpam-6761	311	10	since	since	SCONJ
ejpam-6761	311	11	(	(	PUNCT
ejpam-6761	311	12	s	s	NOUN
ejpam-6761	311	13	◦	◦	NOUN
ejpam-6761	311	14	;f	;f	PUNCT
ejpam-6761	311	15	)	)	PUNCT
ejpam-6761	311	16	is	be	AUX
ejpam-6761	311	17	an	an	DET
ejpam-6761	311	18	(	(	PUNCT
ejpam-6761	311	19	ordinary	ordinary	ADJ
ejpam-6761	311	20	)	)	PUNCT
ejpam-6761	311	21	subgroup	subgroup	NOUN
ejpam-6761	311	22	of	of	ADP
ejpam-6761	311	23	the	the	DET
ejpam-6761	311	24	group	group	NOUN
ejpam-6761	311	25	(	(	PUNCT
ejpam-6761	311	26	g	g	PROPN
ejpam-6761	311	27	,	,	PUNCT
ejpam-6761	311	28	f	f	PROPN
ejpam-6761	311	29	)	)	PUNCT
ejpam-6761	311	30	then	then	ADV
ejpam-6761	311	31	s	s	AUX
ejpam-6761	311	32	◦	◦	NOUN
ejpam-6761	311	33	contains	contain	VERB
ejpam-6761	311	34	the	the	DET
ejpam-6761	311	35	identity	identity	NOUN
ejpam-6761	311	36	e.	e.	PROPN
ejpam-6761	311	37	that	that	PRON
ejpam-6761	311	38	is	be	AUX
ejpam-6761	311	39	,	,	PUNCT
ejpam-6761	311	40	(	(	PUNCT
ejpam-6761	311	41	e	e	NOUN
ejpam-6761	311	42	,	,	PUNCT
ejpam-6761	311	43	s−e	s−e	PROPN
ejpam-6761	311	44	,	,	PUNCT
ejpam-6761	311	45	s	s	PART
ejpam-6761	311	46	+	+	CCONJ
ejpam-6761	311	47	e	e	NOUN
ejpam-6761	311	48	)	)	PUNCT
ejpam-6761	311	49	∈	∈	PROPN
ejpam-6761	311	50	s	s	PART
ejpam-6761	311	51	thus	thus	ADV
ejpam-6761	311	52	:	:	PUNCT
ejpam-6761	311	53	(	(	PUNCT
ejpam-6761	311	54	x	x	NOUN
ejpam-6761	311	55	,	,	PUNCT
ejpam-6761	311	56	s−x	s−x	NOUN
ejpam-6761	311	57	,	,	PUNCT
ejpam-6761	311	58	s	s	PART
ejpam-6761	311	59	+	+	NOUN
ejpam-6761	311	60	x	x	X
ejpam-6761	311	61	)	)	PUNCT
ejpam-6761	311	62	f	f	NOUN
ejpam-6761	311	63	(	(	PUNCT
ejpam-6761	311	64	e	e	NOUN
ejpam-6761	311	65	,	,	PUNCT
ejpam-6761	311	66	s	s	PART
ejpam-6761	311	67	−	−	PROPN
ejpam-6761	311	68	e	e	NOUN
ejpam-6761	311	69	,	,	PUNCT
ejpam-6761	311	70	s	s	PART
ejpam-6761	311	71	+	+	X
ejpam-6761	311	72	e	e	NOUN
ejpam-6761	311	73	)	)	PUNCT
ejpam-6761	311	74	=	=	PUNCT
ejpam-6761	312	1	(	(	PUNCT
ejpam-6761	312	2	f	f	X
ejpam-6761	312	3	(	(	PUNCT
ejpam-6761	312	4	x	x	NOUN
ejpam-6761	312	5	,	,	PUNCT
ejpam-6761	312	6	e	e	NOUN
ejpam-6761	312	7	)	)	PUNCT
ejpam-6761	312	8	,	,	PUNCT
ejpam-6761	312	9	f−xe(s	f−xe(s	VERB
ejpam-6761	312	10	−	−	PROPN
ejpam-6761	312	11	x	x	INTJ
ejpam-6761	312	12	,	,	PUNCT
ejpam-6761	312	13	s	s	PART
ejpam-6761	312	14	−	−	PROPN
ejpam-6761	312	15	e	e	NOUN
ejpam-6761	312	16	)	)	PUNCT
ejpam-6761	312	17	,	,	PUNCT
ejpam-6761	312	18	f	f	PROPN
ejpam-6761	313	1	+	+	CCONJ
ejpam-6761	313	2	xe(s	xe(s	NUM
ejpam-6761	314	1	+	+	NUM
ejpam-6761	314	2	x	x	SYM
ejpam-6761	314	3	,	,	PUNCT
ejpam-6761	314	4	s	s	PART
ejpam-6761	314	5	+	+	CCONJ
ejpam-6761	314	6	e	e	NOUN
ejpam-6761	314	7	)	)	PUNCT
ejpam-6761	314	8	)	)	PUNCT
ejpam-6761	315	1	=	=	PRON
ejpam-6761	315	2	(	(	PUNCT
ejpam-6761	315	3	xfe	xfe	PROPN
ejpam-6761	315	4	,	,	PUNCT
ejpam-6761	315	5	s−xfe	s−xfe	NOUN
ejpam-6761	315	6	,	,	PUNCT
ejpam-6761	315	7	s	s	PART
ejpam-6761	315	8	+	+	NOUN
ejpam-6761	315	9	xfe	xfe	NUM
ejpam-6761	315	10	)	)	PUNCT
ejpam-6761	315	11	=	=	PRON
ejpam-6761	315	12	(	(	PUNCT
ejpam-6761	315	13	efx	efx	PROPN
ejpam-6761	315	14	,	,	PUNCT
ejpam-6761	315	15	s−efx	s−efx	NOUN
ejpam-6761	315	16	,	,	PUNCT
ejpam-6761	315	17	s	s	PART
ejpam-6761	315	18	+	+	NUM
ejpam-6761	315	19	efx	efx	NOUN
ejpam-6761	315	20	)	)	PUNCT
ejpam-6761	316	1	=	=	PRON
ejpam-6761	316	2	(	(	PUNCT
ejpam-6761	316	3	e	e	NOUN
ejpam-6761	316	4	,	,	PUNCT
ejpam-6761	316	5	s−e	s−e	PROPN
ejpam-6761	316	6	,	,	PUNCT
ejpam-6761	316	7	s	s	PART
ejpam-6761	316	8	+	+	CCONJ
ejpam-6761	316	9	e	e	NOUN
ejpam-6761	316	10	)	)	PUNCT
ejpam-6761	316	11	f	f	PROPN
ejpam-6761	316	12	(	(	PUNCT
ejpam-6761	316	13	x	x	X
ejpam-6761	316	14	,	,	PUNCT
ejpam-6761	316	15	s	s	PART
ejpam-6761	316	16	−	−	NOUN
ejpam-6761	316	17	x	x	INTJ
ejpam-6761	316	18	,	,	PUNCT
ejpam-6761	316	19	s	s	PART
ejpam-6761	316	20	+	+	NOUN
ejpam-6761	316	21	x	x	X
ejpam-6761	316	22	)	)	PUNCT
ejpam-6761	317	1	=	=	SYM
ejpam-6761	317	2	(	(	PUNCT
ejpam-6761	317	3	x	x	X
ejpam-6761	317	4	,	,	PUNCT
ejpam-6761	317	5	s−x	s−x	NOUN
ejpam-6761	317	6	,	,	PUNCT
ejpam-6761	317	7	s	s	PART
ejpam-6761	317	8	+	+	NOUN
ejpam-6761	317	9	x	x	X
ejpam-6761	317	10	)	)	PUNCT
ejpam-6761	317	11	.	.	PUNCT
ejpam-6761	318	1	(	(	PUNCT
ejpam-6761	318	2	4	4	X
ejpam-6761	318	3	)	)	PUNCT
ejpam-6761	318	4	in	in	ADP
ejpam-6761	318	5	the	the	DET
ejpam-6761	318	6	same	same	ADJ
ejpam-6761	318	7	way	way	NOUN
ejpam-6761	318	8	,	,	PUNCT
ejpam-6761	318	9	(	(	PUNCT
ejpam-6761	318	10	e	e	NOUN
ejpam-6761	318	11	,	,	PUNCT
ejpam-6761	318	12	s−e	s−e	PROPN
ejpam-6761	318	13	,	,	PUNCT
ejpam-6761	318	14	s	s	PART
ejpam-6761	318	15	+	+	CCONJ
ejpam-6761	318	16	e	e	NOUN
ejpam-6761	318	17	)	)	PUNCT
ejpam-6761	318	18	f	f	PROPN
ejpam-6761	318	19	(	(	PUNCT
ejpam-6761	318	20	x	x	X
ejpam-6761	318	21	,	,	PUNCT
ejpam-6761	318	22	s	s	PART
ejpam-6761	318	23	−	−	NOUN
ejpam-6761	318	24	x	x	INTJ
ejpam-6761	318	25	,	,	PUNCT
ejpam-6761	318	26	s	s	PART
ejpam-6761	318	27	+	+	NOUN
ejpam-6761	318	28	x	x	X
ejpam-6761	318	29	)	)	PUNCT
ejpam-6761	319	1	=	=	SYM
ejpam-6761	319	2	(	(	PUNCT
ejpam-6761	319	3	x	x	X
ejpam-6761	319	4	,	,	PUNCT
ejpam-6761	319	5	s−x	s−x	NOUN
ejpam-6761	319	6	,	,	PUNCT
ejpam-6761	319	7	s	s	PART
ejpam-6761	319	8	+	+	NOUN
ejpam-6761	319	9	x	x	X
ejpam-6761	319	10	)	)	PUNCT
ejpam-6761	319	11	.	.	PUNCT
ejpam-6761	320	1	c	c	X
ejpam-6761	320	2	)	)	PUNCT
ejpam-6761	320	3	(	(	PUNCT
ejpam-6761	320	4	inverse	inverse	NOUN
ejpam-6761	320	5	condition	condition	NOUN
ejpam-6761	320	6	)	)	PUNCT
ejpam-6761	320	7	since	since	SCONJ
ejpam-6761	320	8	(	(	PUNCT
ejpam-6761	320	9	s	s	NOUN
ejpam-6761	320	10	◦	◦	NOUN
ejpam-6761	320	11	;f	;f	PUNCT
ejpam-6761	320	12	)	)	PUNCT
ejpam-6761	320	13	is	be	AUX
ejpam-6761	320	14	an	an	DET
ejpam-6761	320	15	(	(	PUNCT
ejpam-6761	320	16	ordinary	ordinary	ADJ
ejpam-6761	320	17	)	)	PUNCT
ejpam-6761	320	18	subgroup	subgroup	NOUN
ejpam-6761	320	19	of	of	ADP
ejpam-6761	320	20	the	the	DET
ejpam-6761	320	21	group	group	NOUN
ejpam-6761	320	22	(	(	PUNCT
ejpam-6761	320	23	g	g	PROPN
ejpam-6761	320	24	,	,	PUNCT
ejpam-6761	320	25	f	f	PROPN
ejpam-6761	320	26	)	)	PUNCT
ejpam-6761	320	27	then	then	ADV
ejpam-6761	320	28	s	s	AUX
ejpam-6761	320	29	◦	◦	NOUN
ejpam-6761	320	30	contains	contain	VERB
ejpam-6761	320	31	the	the	DET
ejpam-6761	320	32	inverse	inverse	NOUN
ejpam-6761	320	33	element	element	NOUN
ejpam-6761	320	34	x−1	x−1	PROPN
ejpam-6761	320	35	for	for	ADP
ejpam-6761	320	36	each	each	DET
ejpam-6761	320	37	x	x	PUNCT
ejpam-6761	320	38	∈	∈	PROPN
ejpam-6761	320	39	s	s	NOUN
ejpam-6761	320	40	◦	◦	NOUN
ejpam-6761	320	41	,	,	PUNCT
ejpam-6761	320	42	(	(	PUNCT
ejpam-6761	320	43	i.e.	i.e.	X
ejpam-6761	320	44	∀(x	∀(x	NUM
ejpam-6761	320	45	,	,	PUNCT
ejpam-6761	320	46	s−x	s−x	NOUN
ejpam-6761	320	47	,	,	PUNCT
ejpam-6761	320	48	s+x	s+x	PROPN
ejpam-6761	320	49	)	)	PUNCT
ejpam-6761	320	50	∈	∈	PROPN
ejpam-6761	320	51	s	s	NOUN
ejpam-6761	320	52	,	,	PUNCT
ejpam-6761	320	53	∃(x−1	∃(x−1	PROPN
ejpam-6761	320	54	,	,	PUNCT
ejpam-6761	320	55	s−	s−	PROPN
ejpam-6761	320	56	x−1	x−1	PROPN
ejpam-6761	320	57	,	,	PUNCT
ejpam-6761	320	58	s	s	PART
ejpam-6761	320	59	+	+	PROPN
ejpam-6761	320	60	x−1	x−1	PROPN
ejpam-6761	320	61	)	)	PUNCT
ejpam-6761	320	62	∈	∈	PROPN
ejpam-6761	320	63	s	s	PART
ejpam-6761	320	64	)	)	PUNCT
ejpam-6761	320	65	then	then	ADV
ejpam-6761	320	66	:	:	PUNCT
ejpam-6761	320	67	f.	f.	PROPN
ejpam-6761	320	68	al	al	PROPN
ejpam-6761	320	69	-	-	PROPN
ejpam-6761	320	70	zu’bi	zu’bi	PROPN
ejpam-6761	320	71	et	et	NOUN
ejpam-6761	320	72	al	al	PROPN
ejpam-6761	320	73	.	.	PUNCT
ejpam-6761	320	74	/	/	SYM
ejpam-6761	320	75	eur	eur	PROPN
ejpam-6761	320	76	.	.	PUNCT
ejpam-6761	321	1	j.	j.	PROPN
ejpam-6761	321	2	pure	pure	PROPN
ejpam-6761	321	3	appl	appl	PROPN
ejpam-6761	321	4	.	.	PROPN
ejpam-6761	321	5	math	math	PROPN
ejpam-6761	321	6	,	,	PUNCT
ejpam-6761	321	7	18	18	NUM
ejpam-6761	321	8	(	(	PUNCT
ejpam-6761	321	9	4	4	NUM
ejpam-6761	321	10	)	)	PUNCT
ejpam-6761	321	11	(	(	PUNCT
ejpam-6761	321	12	2025	2025	NUM
ejpam-6761	321	13	)	)	PUNCT
ejpam-6761	321	14	,	,	PUNCT
ejpam-6761	321	15	6761	6761	NUM
ejpam-6761	321	16	14	14	NUM
ejpam-6761	321	17	of	of	ADP
ejpam-6761	321	18	28	28	NUM
ejpam-6761	321	19	(	(	PUNCT
ejpam-6761	321	20	x	x	NOUN
ejpam-6761	321	21	,	,	PUNCT
ejpam-6761	321	22	s−x	s−x	NOUN
ejpam-6761	321	23	,	,	PUNCT
ejpam-6761	321	24	s	s	PART
ejpam-6761	321	25	+	+	NOUN
ejpam-6761	321	26	x	x	X
ejpam-6761	321	27	)	)	PUNCT
ejpam-6761	321	28	f	f	NOUN
ejpam-6761	321	29	(	(	PUNCT
ejpam-6761	321	30	x	x	SYM
ejpam-6761	321	31	−1	−1	NOUN
ejpam-6761	321	32	,	,	PUNCT
ejpam-6761	321	33	s−	s−	PROPN
ejpam-6761	321	34	x−1	x−1	PROPN
ejpam-6761	321	35	,	,	PUNCT
ejpam-6761	321	36	s	s	PART
ejpam-6761	322	1	+	+	PROPN
ejpam-6761	323	1	x−1	x−1	NOUN
ejpam-6761	323	2	)	)	PUNCT
ejpam-6761	324	1	=	=	PUNCT
ejpam-6761	324	2	(	(	PUNCT
ejpam-6761	324	3	f	f	X
ejpam-6761	324	4	(	(	PUNCT
ejpam-6761	324	5	x	x	PROPN
ejpam-6761	324	6	,	,	PUNCT
ejpam-6761	324	7	x−1	x−1	PROPN
ejpam-6761	324	8	)	)	PUNCT
ejpam-6761	324	9	,	,	PUNCT
ejpam-6761	324	10	f−	f−	PROPN
ejpam-6761	324	11	xx−1(s	xx−1(s	INTJ
ejpam-6761	325	1	−	−	PROPN
ejpam-6761	325	2	x	x	INTJ
ejpam-6761	325	3	,	,	PUNCT
ejpam-6761	325	4	s	s	PART
ejpam-6761	325	5	−	−	PROPN
ejpam-6761	325	6	x−1	x−1	PROPN
ejpam-6761	325	7	)	)	PUNCT
ejpam-6761	325	8	,	,	PUNCT
ejpam-6761	326	1	f	f	PROPN
ejpam-6761	327	1	+	+	CCONJ
ejpam-6761	327	2	xx−1(s	xx−1(s	PROPN
ejpam-6761	327	3	+	+	CCONJ
ejpam-6761	327	4	x	x	SYM
ejpam-6761	327	5	,	,	PUNCT
ejpam-6761	327	6	s	s	PART
ejpam-6761	327	7	+	+	PROPN
ejpam-6761	327	8	x−1	x−1	NOUN
ejpam-6761	327	9	)	)	PUNCT
ejpam-6761	327	10	)	)	PUNCT
ejpam-6761	328	1	=	=	SYM
ejpam-6761	328	2	(	(	PUNCT
ejpam-6761	328	3	xfx−1	xfx−1	PROPN
ejpam-6761	328	4	,	,	PUNCT
ejpam-6761	328	5	s−	s−	PROPN
ejpam-6761	328	6	xfx−1	xfx−1	PROPN
ejpam-6761	328	7	,	,	PUNCT
ejpam-6761	328	8	s	s	PART
ejpam-6761	328	9	+	+	X
ejpam-6761	328	10	xfx−1	xfx−1	NUM
ejpam-6761	328	11	)	)	PUNCT
ejpam-6761	328	12	=	=	SYM
ejpam-6761	328	13	(	(	PUNCT
ejpam-6761	328	14	x−1fx	x−1fx	PROPN
ejpam-6761	328	15	,	,	PUNCT
ejpam-6761	328	16	s−	s−	PROPN
ejpam-6761	328	17	x−1fx	x−1fx	PROPN
ejpam-6761	328	18	,	,	PUNCT
ejpam-6761	328	19	s+	s+	X
ejpam-6761	328	20	x−1fx	x−1fx	PROPN
ejpam-6761	328	21	)	)	PUNCT
ejpam-6761	328	22	=	=	SYM
ejpam-6761	328	23	(	(	PUNCT
ejpam-6761	328	24	x−1	x−1	PROPN
ejpam-6761	328	25	,	,	PUNCT
ejpam-6761	328	26	s−	s−	PROPN
ejpam-6761	328	27	x−1	x−1	PROPN
ejpam-6761	328	28	,	,	PUNCT
ejpam-6761	328	29	s	s	PART
ejpam-6761	328	30	+	+	X
ejpam-6761	328	31	x−1)f	x−1)f	NUM
ejpam-6761	328	32	(	(	PUNCT
ejpam-6761	328	33	x	x	X
ejpam-6761	328	34	,	,	PUNCT
ejpam-6761	328	35	s	s	PART
ejpam-6761	328	36	−	−	NOUN
ejpam-6761	328	37	x	x	INTJ
ejpam-6761	328	38	,	,	PUNCT
ejpam-6761	328	39	s	s	PART
ejpam-6761	328	40	+	+	NOUN
ejpam-6761	328	41	x	x	X
ejpam-6761	328	42	)	)	PUNCT
ejpam-6761	328	43	=	=	SYM
ejpam-6761	328	44	(	(	PUNCT
ejpam-6761	328	45	e	e	NOUN
ejpam-6761	328	46	,	,	PUNCT
ejpam-6761	328	47	s−e	s−e	PROPN
ejpam-6761	328	48	,	,	PUNCT
ejpam-6761	328	49	s	s	PART
ejpam-6761	328	50	+	+	NUM
ejpam-6761	328	51	e	e	NOUN
ejpam-6761	328	52	)	)	PUNCT
ejpam-6761	328	53	.	.	PUNCT
ejpam-6761	329	1	(	(	PUNCT
ejpam-6761	329	2	5	5	X
ejpam-6761	329	3	)	)	PUNCT
ejpam-6761	329	4	in	in	ADP
ejpam-6761	329	5	the	the	DET
ejpam-6761	329	6	same	same	ADJ
ejpam-6761	329	7	way	way	NOUN
ejpam-6761	329	8	,	,	PUNCT
ejpam-6761	329	9	(	(	PUNCT
ejpam-6761	329	10	x−1	x−1	PROPN
ejpam-6761	329	11	,	,	PUNCT
ejpam-6761	329	12	s−	s−	PROPN
ejpam-6761	329	13	x−1	x−1	PROPN
ejpam-6761	329	14	,	,	PUNCT
ejpam-6761	329	15	s	s	PART
ejpam-6761	329	16	+	+	X
ejpam-6761	329	17	x−1)f	x−1)f	NUM
ejpam-6761	329	18	(	(	PUNCT
ejpam-6761	329	19	x	x	X
ejpam-6761	329	20	,	,	PUNCT
ejpam-6761	329	21	s	s	PART
ejpam-6761	329	22	−	−	NOUN
ejpam-6761	329	23	x	x	INTJ
ejpam-6761	329	24	,	,	PUNCT
ejpam-6761	329	25	s	s	PART
ejpam-6761	329	26	+	+	NOUN
ejpam-6761	329	27	x	x	X
ejpam-6761	329	28	)	)	PUNCT
ejpam-6761	329	29	=	=	SYM
ejpam-6761	329	30	(	(	PUNCT
ejpam-6761	329	31	e	e	NOUN
ejpam-6761	329	32	,	,	PUNCT
ejpam-6761	329	33	s−e	s−e	PROPN
ejpam-6761	329	34	,	,	PUNCT
ejpam-6761	329	35	s	s	PART
ejpam-6761	329	36	+	+	CCONJ
ejpam-6761	329	37	e	e	NOUN
ejpam-6761	329	38	)	)	PUNCT
ejpam-6761	329	39	.	.	PUNCT
ejpam-6761	330	1	therefore	therefore	ADV
ejpam-6761	330	2	,	,	PUNCT
ejpam-6761	330	3	we	we	PRON
ejpam-6761	330	4	determine	determine	VERB
ejpam-6761	330	5	that	that	SCONJ
ejpam-6761	330	6	(	(	PUNCT
ejpam-6761	330	7	s;f	s;f	NOUN
ejpam-6761	330	8	)	)	PUNCT
ejpam-6761	330	9	is	be	AUX
ejpam-6761	330	10	a	a	DET
ejpam-6761	330	11	bvf	bvf	NOUN
ejpam-6761	330	12	subgroup	subgroup	NOUN
ejpam-6761	330	13	of	of	ADP
ejpam-6761	330	14	(	(	PUNCT
ejpam-6761	330	15	(	(	PUNCT
ejpam-6761	330	16	g	g	NOUN
ejpam-6761	330	17	,	,	PUNCT
ejpam-6761	330	18	[	[	X
ejpam-6761	330	19	−1	−1	NOUN
ejpam-6761	330	20	,	,	PUNCT
ejpam-6761	330	21	0	0	NUM
ejpam-6761	330	22	]	]	PUNCT
ejpam-6761	330	23	,	,	PUNCT
ejpam-6761	331	1	[	[	X
ejpam-6761	331	2	0	0	NUM
ejpam-6761	331	3	,	,	PUNCT
ejpam-6761	331	4	1	1	NUM
ejpam-6761	331	5	]	]	NUM
ejpam-6761	331	6	)	)	PUNCT
ejpam-6761	331	7	,	,	PUNCT
ejpam-6761	331	8	f	f	PROPN
ejpam-6761	331	9	)	)	PUNCT
ejpam-6761	331	10	by	by	ADP
ejpam-6761	331	11	(	(	PUNCT
ejpam-6761	331	12	i	i	NOUN
ejpam-6761	331	13	)	)	PUNCT
ejpam-6761	331	14	and	and	CCONJ
ejpam-6761	331	15	(	(	PUNCT
ejpam-6761	331	16	ii	ii	NOUN
ejpam-6761	331	17	)	)	PUNCT
ejpam-6761	331	18	.	.	PUNCT
ejpam-6761	332	1	conversely	conversely	ADV
ejpam-6761	332	2	,	,	PUNCT
ejpam-6761	332	3	if	if	SCONJ
ejpam-6761	332	4	(	(	PUNCT
ejpam-6761	332	5	s;f	s;f	NOUN
ejpam-6761	332	6	)	)	PUNCT
ejpam-6761	332	7	is	be	AUX
ejpam-6761	332	8	a	a	DET
ejpam-6761	332	9	bvf	bvf	NOUN
ejpam-6761	332	10	subgroup	subgroup	NOUN
ejpam-6761	332	11	of	of	ADP
ejpam-6761	332	12	(	(	PUNCT
ejpam-6761	332	13	(	(	PUNCT
ejpam-6761	332	14	g	g	NOUN
ejpam-6761	332	15	,	,	PUNCT
ejpam-6761	332	16	[	[	X
ejpam-6761	332	17	−1	−1	NOUN
ejpam-6761	332	18	,	,	PUNCT
ejpam-6761	332	19	0	0	NUM
ejpam-6761	332	20	]	]	PUNCT
ejpam-6761	332	21	,	,	PUNCT
ejpam-6761	332	22	[	[	X
ejpam-6761	332	23	0	0	NUM
ejpam-6761	332	24	,	,	PUNCT
ejpam-6761	332	25	1	1	NUM
ejpam-6761	332	26	]	]	NUM
ejpam-6761	332	27	)	)	PUNCT
ejpam-6761	332	28	,	,	PUNCT
ejpam-6761	332	29	f	f	PROPN
ejpam-6761	332	30	)	)	PUNCT
ejpam-6761	332	31	then	then	ADV
ejpam-6761	332	32	(	(	PUNCT
ejpam-6761	332	33	1	1	X
ejpam-6761	332	34	)	)	PUNCT
ejpam-6761	332	35	holds	hold	VERB
ejpam-6761	332	36	by	by	ADP
ejpam-6761	332	37	the	the	DET
ejpam-6761	332	38	associativity	associativity	NOUN
ejpam-6761	332	39	theorem	theorem	VERB
ejpam-6761	332	40	.	.	PUNCT
ejpam-6761	333	1	also	also	ADV
ejpam-6761	333	2	,	,	PUNCT
ejpam-6761	333	3	(	(	PUNCT
ejpam-6761	333	4	2	2	X
ejpam-6761	333	5	)	)	PUNCT
ejpam-6761	333	6	hold	hold	VERB
ejpam-6761	333	7	as	as	ADP
ejpam-6761	333	8	:	:	PUNCT
ejpam-6761	333	9	s−x	s−x	NOUN
ejpam-6761	333	10	f	f	X
ejpam-6761	333	11	−	−	NOUN
ejpam-6761	333	12	xys	xys	NOUN
ejpam-6761	334	1	−	−	PROPN
ejpam-6761	335	1	y	y	PROPN
ejpam-6761	335	2	=	=	PUNCT
ejpam-6761	335	3	f−xy(s	f−xy(	VERB
ejpam-6761	335	4	−	−	PROPN
ejpam-6761	335	5	x	x	SYM
ejpam-6761	335	6	×	×	PROPN
ejpam-6761	335	7	s−y	s−y	ADJ
ejpam-6761	335	8	)	)	PUNCT
ejpam-6761	336	1	=	=	SYM
ejpam-6761	336	2	s−xfy	s−xfy	NOUN
ejpam-6761	336	3	and	and	CCONJ
ejpam-6761	336	4	s+x	s+x	PROPN
ejpam-6761	336	5	f	f	PROPN
ejpam-6761	337	1	+	+	CCONJ
ejpam-6761	337	2	xys	xys	PROPN
ejpam-6761	338	1	+	+	CCONJ
ejpam-6761	338	2	y	y	NOUN
ejpam-6761	338	3	=	=	PUNCT
ejpam-6761	338	4	f+xy(s	f+xy(s	X
ejpam-6761	338	5	+	+	CCONJ
ejpam-6761	338	6	x	x	SYM
ejpam-6761	338	7	×	×	PROPN
ejpam-6761	338	8	s+y	s+y	NUM
ejpam-6761	338	9	)	)	PUNCT
ejpam-6761	339	1	=	=	PUNCT
ejpam-6761	339	2	s+xfy	s+xfy	NOUN
ejpam-6761	339	3	being	be	AUX
ejpam-6761	339	4	onto	onto	ADP
ejpam-6761	339	5	over	over	ADP
ejpam-6761	339	6	the	the	DET
ejpam-6761	339	7	partial	partial	ADJ
ejpam-6761	339	8	ordered	order	VERB
ejpam-6761	339	9	sub	sub	NOUN
ejpam-6761	339	10	-	-	ADJ
ejpam-6761	339	11	lattices	lattice	NOUN
ejpam-6761	339	12	s−x	s−x	NOUN
ejpam-6761	339	13	×	×	NOUN
ejpam-6761	339	14	s−y	s−y	ADJ
ejpam-6761	339	15	and	and	CCONJ
ejpam-6761	339	16	s+x	s+x	PROPN
ejpam-6761	339	17	×	×	NOUN
ejpam-6761	339	18	s+y	s+y	NUM
ejpam-6761	339	19	respectively	respectively	ADV
ejpam-6761	339	20	of	of	ADP
ejpam-6761	339	21	the	the	DET
ejpam-6761	339	22	vector	vector	NOUN
ejpam-6761	339	23	lattice	lattice	NOUN
ejpam-6761	340	1	[	[	X
ejpam-6761	340	2	−1	−1	NOUN
ejpam-6761	340	3	,	,	PUNCT
ejpam-6761	340	4	0]×	0]×	PROPN
ejpam-6761	341	1	[	[	X
ejpam-6761	341	2	0	0	NUM
ejpam-6761	341	3	,	,	PUNCT
ejpam-6761	341	4	1	1	NUM
ejpam-6761	341	5	]	]	PUNCT
ejpam-6761	341	6	.	.	PUNCT
ejpam-6761	341	7	example	example	NOUN
ejpam-6761	342	1	1	1	NUM
ejpam-6761	342	2	.	.	PUNCT
ejpam-6761	342	3	(	(	PUNCT
ejpam-6761	342	4	1	1	X
ejpam-6761	342	5	)	)	PUNCT
ejpam-6761	342	6	let	let	VERB
ejpam-6761	342	7	(	(	PUNCT
ejpam-6761	342	8	(	(	PUNCT
ejpam-6761	342	9	g	g	NOUN
ejpam-6761	342	10	=	=	X
ejpam-6761	342	11	{	{	PUNCT
ejpam-6761	342	12	a	a	NOUN
ejpam-6761	342	13	}	}	PUNCT
ejpam-6761	342	14	,	,	PUNCT
ejpam-6761	342	15	[	[	X
ejpam-6761	342	16	−1	−1	NOUN
ejpam-6761	342	17	,	,	PUNCT
ejpam-6761	342	18	0	0	NUM
ejpam-6761	342	19	]	]	PUNCT
ejpam-6761	342	20	,	,	PUNCT
ejpam-6761	342	21	[	[	X
ejpam-6761	342	22	0	0	NUM
ejpam-6761	342	23	,	,	PUNCT
ejpam-6761	342	24	1]),f	1]),f	NUM
ejpam-6761	342	25	)	)	PUNCT
ejpam-6761	342	26	be	be	AUX
ejpam-6761	342	27	defined	define	VERB
ejpam-6761	342	28	as	as	ADP
ejpam-6761	342	29	the	the	DET
ejpam-6761	342	30	bvf	bvf	NOUN
ejpam-6761	342	31	binary	binary	PROPN
ejpam-6761	342	32	operation	operation	NOUN
ejpam-6761	342	33	f	f	PROPN
ejpam-6761	342	34	=	=	PUNCT
ejpam-6761	342	35	(	(	PUNCT
ejpam-6761	342	36	f	f	PROPN
ejpam-6761	342	37	,	,	PUNCT
ejpam-6761	342	38	f−xy	f−xy	PROPN
ejpam-6761	342	39	,	,	PUNCT
ejpam-6761	342	40	f	f	PROPN
ejpam-6761	343	1	+	+	CCONJ
ejpam-6761	343	2	xy	xy	NOUN
ejpam-6761	343	3	)	)	PUNCT
ejpam-6761	343	4	over	over	ADP
ejpam-6761	343	5	bvf	bvf	NOUN
ejpam-6761	343	6	space	space	NOUN
ejpam-6761	343	7	(	(	PUNCT
ejpam-6761	343	8	g	g	NOUN
ejpam-6761	343	9	,	,	PUNCT
ejpam-6761	343	10	[	[	X
ejpam-6761	343	11	−1	−1	NOUN
ejpam-6761	343	12	,	,	PUNCT
ejpam-6761	343	13	0	0	NUM
ejpam-6761	343	14	]	]	PUNCT
ejpam-6761	343	15	,	,	PUNCT
ejpam-6761	344	1	[	[	X
ejpam-6761	344	2	0	0	NUM
ejpam-6761	344	3	,	,	PUNCT
ejpam-6761	344	4	1	1	NUM
ejpam-6761	344	5	]	]	PUNCT
ejpam-6761	344	6	)	)	PUNCT
ejpam-6761	345	1	such	such	ADJ
ejpam-6761	345	2	that	that	SCONJ
ejpam-6761	345	3	:	:	PUNCT
ejpam-6761	345	4	f	f	X
ejpam-6761	345	5	(	(	PUNCT
ejpam-6761	345	6	a	a	PRON
ejpam-6761	345	7	,	,	PUNCT
ejpam-6761	345	8	a	a	NOUN
ejpam-6761	345	9	)	)	PUNCT
ejpam-6761	345	10	=	=	SYM
ejpam-6761	345	11	a	a	PRON
ejpam-6761	345	12	and	and	CCONJ
ejpam-6761	345	13	f−aa(n	f−aa(n	ADV
ejpam-6761	345	14	−,m−	−,m−	ADJ
ejpam-6761	345	15	)	)	PUNCT
ejpam-6761	345	16	=	=	SYM
ejpam-6761	345	17	min{n−,m−	min{n−,m−	ADJ
ejpam-6761	345	18	}	}	PUNCT
ejpam-6761	345	19	,	,	PUNCT
ejpam-6761	345	20	f+aa(n+,m+	f+aa(n+,m+	NOUN
ejpam-6761	345	21	)	)	PUNCT
ejpam-6761	345	22	=	=	PUNCT
ejpam-6761	345	23	max{n+,m+	max{n+,m+	NOUN
ejpam-6761	345	24	}	}	PUNCT
ejpam-6761	345	25	.	.	PUNCT
ejpam-6761	346	1	consider	consider	VERB
ejpam-6761	346	2	the	the	DET
ejpam-6761	346	3	bvf	bvf	NOUN
ejpam-6761	346	4	subspace	subspace	NOUN
ejpam-6761	346	5	s	s	PART
ejpam-6761	346	6	=	=	PUNCT
ejpam-6761	346	7	{	{	PUNCT
ejpam-6761	346	8	(	(	PUNCT
ejpam-6761	346	9	a	a	NOUN
ejpam-6761	346	10	,	,	PUNCT
ejpam-6761	346	11	[	[	X
ejpam-6761	346	12	−1	−1	NOUN
ejpam-6761	346	13	,	,	PUNCT
ejpam-6761	346	14	α	α	X
ejpam-6761	346	15	]	]	X
ejpam-6761	346	16	∪	∪	X
ejpam-6761	346	17	{	{	PUNCT
ejpam-6761	346	18	0	0	NUM
ejpam-6761	346	19	}	}	PUNCT
ejpam-6761	346	20	,	,	PUNCT
ejpam-6761	346	21	{	{	PUNCT
ejpam-6761	346	22	0	0	NUM
ejpam-6761	346	23	}	}	PUNCT
ejpam-6761	346	24	∪	∪	ADP
ejpam-6761	346	25	[	[	X
ejpam-6761	346	26	β	β	NOUN
ejpam-6761	346	27	,	,	PUNCT
ejpam-6761	346	28	1	1	NUM
ejpam-6761	346	29	]	]	NUM
ejpam-6761	346	30	)	)	PUNCT
ejpam-6761	346	31	}	}	PUNCT
ejpam-6761	346	32	such	such	ADJ
ejpam-6761	346	33	that	that	DET
ejpam-6761	346	34	−1	−1	NOUN
ejpam-6761	346	35	<	<	X
ejpam-6761	346	36	α	α	X
ejpam-6761	346	37	<	<	X
ejpam-6761	346	38	0	0	X
ejpam-6761	346	39	<	<	X
ejpam-6761	346	40	β	β	X
ejpam-6761	346	41	<	<	X
ejpam-6761	346	42	1	1	NUM
ejpam-6761	346	43	.	.	PUNCT
ejpam-6761	347	1	then	then	ADV
ejpam-6761	347	2	(	(	PUNCT
ejpam-6761	347	3	s	s	X
ejpam-6761	347	4	,	,	PUNCT
ejpam-6761	347	5	f	f	X
ejpam-6761	347	6	)	)	PUNCT
ejpam-6761	347	7	defines	define	VERB
ejpam-6761	347	8	a	a	DET
ejpam-6761	347	9	bipolar	bipolar	ADJ
ejpam-6761	347	10	valued	value	VERB
ejpam-6761	347	11	fuzzy	fuzzy	ADJ
ejpam-6761	347	12	subgroup	subgroup	NOUN
ejpam-6761	347	13	of	of	ADP
ejpam-6761	347	14	(	(	PUNCT
ejpam-6761	347	15	(	(	PUNCT
ejpam-6761	347	16	g	g	NOUN
ejpam-6761	347	17	,	,	PUNCT
ejpam-6761	347	18	[	[	X
ejpam-6761	347	19	−1	−1	NOUN
ejpam-6761	347	20	,	,	PUNCT
ejpam-6761	347	21	0	0	NUM
ejpam-6761	347	22	]	]	PUNCT
ejpam-6761	347	23	,	,	PUNCT
ejpam-6761	347	24	[	[	X
ejpam-6761	347	25	0	0	NUM
ejpam-6761	347	26	,	,	PUNCT
ejpam-6761	347	27	1]),f	1]),f	NUM
ejpam-6761	347	28	)	)	PUNCT
ejpam-6761	347	29	.	.	PUNCT
ejpam-6761	348	1	if	if	SCONJ
ejpam-6761	348	2	we	we	PRON
ejpam-6761	348	3	consider	consider	VERB
ejpam-6761	348	4	s′	s′	ADJ
ejpam-6761	348	5	=	=	PUNCT
ejpam-6761	348	6	{	{	PUNCT
ejpam-6761	348	7	(	(	PUNCT
ejpam-6761	348	8	a	a	NOUN
ejpam-6761	348	9	,	,	PUNCT
ejpam-6761	348	10	[	[	X
ejpam-6761	348	11	−1	−1	NOUN
ejpam-6761	348	12	,	,	PUNCT
ejpam-6761	348	13	γ	γ	X
ejpam-6761	348	14	]	]	X
ejpam-6761	348	15	∪	∪	X
ejpam-6761	348	16	{	{	PUNCT
ejpam-6761	348	17	0	0	NUM
ejpam-6761	348	18	}	}	PUNCT
ejpam-6761	348	19	,	,	PUNCT
ejpam-6761	348	20	{	{	PUNCT
ejpam-6761	348	21	0	0	NUM
ejpam-6761	348	22	}	}	PUNCT
ejpam-6761	348	23	∪	∪	NOUN
ejpam-6761	348	24	[	[	X
ejpam-6761	348	25	δ	δ	PROPN
ejpam-6761	348	26	,	,	PUNCT
ejpam-6761	348	27	1	1	NUM
ejpam-6761	348	28	]	]	NUM
ejpam-6761	348	29	)	)	PUNCT
ejpam-6761	348	30	}	}	PUNCT
ejpam-6761	348	31	such	such	ADJ
ejpam-6761	348	32	that	that	DET
ejpam-6761	348	33	−1	−1	NOUN
ejpam-6761	348	34	<	<	X
ejpam-6761	348	35	γ	γ	X
ejpam-6761	348	36	<	<	X
ejpam-6761	348	37	0	0	PUNCT
ejpam-6761	348	38	<	<	X
ejpam-6761	348	39	δ	δ	X
ejpam-6761	348	40	<	<	X
ejpam-6761	348	41	1	1	NUM
ejpam-6761	348	42	and	and	CCONJ
ejpam-6761	348	43	α	α	PROPN
ejpam-6761	348	44	̸=	̸=	PROPN
ejpam-6761	348	45	γ	γ	PROPN
ejpam-6761	348	46	,	,	PUNCT
ejpam-6761	348	47	β	β	PROPN
ejpam-6761	348	48	̸=	̸=	PROPN
ejpam-6761	348	49	δ	δ	PROPN
ejpam-6761	348	50	,	,	PUNCT
ejpam-6761	348	51	then	then	ADV
ejpam-6761	348	52	(	(	PUNCT
ejpam-6761	348	53	s′,f	s′,f	PROPN
ejpam-6761	348	54	)	)	PUNCT
ejpam-6761	348	55	defines	define	VERB
ejpam-6761	348	56	a	a	DET
ejpam-6761	348	57	bipolar	bipolar	ADJ
ejpam-6761	348	58	valued	value	VERB
ejpam-6761	348	59	fuzzy	fuzzy	ADJ
ejpam-6761	348	60	subgroup	subgroup	NOUN
ejpam-6761	348	61	of	of	ADP
ejpam-6761	348	62	(	(	PUNCT
ejpam-6761	348	63	(	(	PUNCT
ejpam-6761	348	64	g	g	NOUN
ejpam-6761	348	65	,	,	PUNCT
ejpam-6761	348	66	[	[	X
ejpam-6761	348	67	−1	−1	NOUN
ejpam-6761	348	68	,	,	PUNCT
ejpam-6761	348	69	0	0	NUM
ejpam-6761	348	70	]	]	PUNCT
ejpam-6761	348	71	,	,	PUNCT
ejpam-6761	348	72	[	[	X
ejpam-6761	348	73	0	0	NUM
ejpam-6761	348	74	,	,	PUNCT
ejpam-6761	348	75	1]),f	1]),f	NUM
ejpam-6761	348	76	)	)	PUNCT
ejpam-6761	348	77	where	where	SCONJ
ejpam-6761	348	78	s	s	AUX
ejpam-6761	348	79	̸=	̸=	PROPN
ejpam-6761	348	80	s′.	s′.	PROPN
ejpam-6761	348	81	that	that	PRON
ejpam-6761	348	82	is	be	AUX
ejpam-6761	348	83	,	,	PUNCT
ejpam-6761	348	84	a	a	DET
ejpam-6761	348	85	trivial	trivial	ADJ
ejpam-6761	348	86	bipolar	bipolar	ADJ
ejpam-6761	348	87	-	-	PUNCT
ejpam-6761	348	88	valued	value	VERB
ejpam-6761	348	89	fuzzy	fuzzy	ADJ
ejpam-6761	348	90	group	group	NOUN
ejpam-6761	348	91	may	may	AUX
ejpam-6761	348	92	admit	admit	VERB
ejpam-6761	348	93	multiple	multiple	ADJ
ejpam-6761	348	94	distinct	distinct	ADJ
ejpam-6761	348	95	bipolar	bipolar	ADJ
ejpam-6761	348	96	-	-	PUNCT
ejpam-6761	348	97	valued	value	VERB
ejpam-6761	348	98	fuzzy	fuzzy	ADJ
ejpam-6761	348	99	subgroups	subgroup	NOUN
ejpam-6761	348	100	,	,	PUNCT
ejpam-6761	348	101	in	in	ADP
ejpam-6761	348	102	contrast	contrast	NOUN
ejpam-6761	348	103	to	to	ADP
ejpam-6761	348	104	the	the	DET
ejpam-6761	348	105	classical	classical	ADJ
ejpam-6761	348	106	case	case	NOUN
ejpam-6761	348	107	wherein	wherein	SCONJ
ejpam-6761	348	108	a	a	DET
ejpam-6761	348	109	trivial	trivial	ADJ
ejpam-6761	348	110	group	group	NOUN
ejpam-6761	348	111	possesses	possess	VERB
ejpam-6761	348	112	a	a	DET
ejpam-6761	348	113	unique	unique	ADJ
ejpam-6761	348	114	subgroup	subgroup	NOUN
ejpam-6761	348	115	—	—	PUNCT
ejpam-6761	348	116	that	that	ADV
ejpam-6761	348	117	is	is	ADV
ejpam-6761	348	118	,	,	PUNCT
ejpam-6761	348	119	the	the	DET
ejpam-6761	348	120	group	group	NOUN
ejpam-6761	348	121	itself	itself	PRON
ejpam-6761	348	122	.	.	PUNCT
ejpam-6761	349	1	(	(	PUNCT
ejpam-6761	349	2	2	2	X
ejpam-6761	349	3	)	)	PUNCT
ejpam-6761	349	4	let	let	VERB
ejpam-6761	349	5	(	(	PUNCT
ejpam-6761	349	6	(	(	PUNCT
ejpam-6761	349	7	z5	z5	X
ejpam-6761	349	8	,	,	PUNCT
ejpam-6761	349	9	[	[	X
ejpam-6761	349	10	−1	−1	NOUN
ejpam-6761	349	11	,	,	PUNCT
ejpam-6761	349	12	0	0	NUM
ejpam-6761	349	13	]	]	PUNCT
ejpam-6761	349	14	,	,	PUNCT
ejpam-6761	349	15	[	[	X
ejpam-6761	349	16	0	0	NUM
ejpam-6761	349	17	,	,	PUNCT
ejpam-6761	349	18	1]),f	1]),f	NUM
ejpam-6761	349	19	)	)	PUNCT
ejpam-6761	349	20	be	be	AUX
ejpam-6761	349	21	defined	define	VERB
ejpam-6761	349	22	as	as	ADP
ejpam-6761	349	23	the	the	DET
ejpam-6761	349	24	bvf	bvf	NOUN
ejpam-6761	349	25	binary	binary	PROPN
ejpam-6761	349	26	operation	operation	NOUN
ejpam-6761	350	1	f	f	PROPN
ejpam-6761	350	2	=	=	PUNCT
ejpam-6761	350	3	(	(	PUNCT
ejpam-6761	350	4	f	f	PROPN
ejpam-6761	350	5	,	,	PUNCT
ejpam-6761	350	6	f−xy	f−xy	PROPN
ejpam-6761	350	7	,	,	PUNCT
ejpam-6761	350	8	f	f	PROPN
ejpam-6761	350	9	+	+	CCONJ
ejpam-6761	350	10	xy	xy	PROPN
ejpam-6761	350	11	)	)	PUNCT
ejpam-6761	350	12	as	as	SCONJ
ejpam-6761	350	13	follows	follow	VERB
ejpam-6761	350	14	:	:	PUNCT
ejpam-6761	350	15	f	f	PROPN
ejpam-6761	350	16	(	(	PUNCT
ejpam-6761	350	17	x	x	X
ejpam-6761	350	18	,	,	PUNCT
ejpam-6761	350	19	y	y	NOUN
ejpam-6761	350	20	)	)	PUNCT
ejpam-6761	350	21	=	=	PUNCT
ejpam-6761	351	1	x+5	x+5	NUM
ejpam-6761	351	2	y	y	NOUN
ejpam-6761	351	3	,	,	PUNCT
ejpam-6761	351	4	where	where	SCONJ
ejpam-6761	351	5	+5	+5	PROPN
ejpam-6761	351	6	refers	refer	VERB
ejpam-6761	351	7	to	to	ADP
ejpam-6761	351	8	addition	addition	NOUN
ejpam-6761	351	9	modulo	modulo	NOUN
ejpam-6761	351	10	5	5	NUM
ejpam-6761	351	11	,	,	PUNCT
ejpam-6761	351	12	and	and	CCONJ
ejpam-6761	351	13	f+xy(n	f+xy(n	PRON
ejpam-6761	352	1	+	+	ADJ
ejpam-6761	352	2	,	,	PUNCT
ejpam-6761	352	3	m+	m+	NUM
ejpam-6761	352	4	)	)	PUNCT
ejpam-6761	352	5	=	=	SYM
ejpam-6761	352	6	n+	n+	X
ejpam-6761	352	7	·	·	PUNCT
ejpam-6761	352	8	m+	m+	NUM
ejpam-6761	352	9	,	,	PUNCT
ejpam-6761	352	10	f−xy(n	f−xy(n	NOUN
ejpam-6761	352	11	−,m−	−,m−	NOUN
ejpam-6761	352	12	)	)	PUNCT
ejpam-6761	352	13	=	=	VERB
ejpam-6761	353	1	−(n−	−(n−	PROPN
ejpam-6761	353	2	·	·	PUNCT
ejpam-6761	353	3	m−	m−	PROPN
ejpam-6761	353	4	)	)	PUNCT
ejpam-6761	353	5	.	.	PUNCT
ejpam-6761	354	1	consider	consider	VERB
ejpam-6761	354	2	the	the	DET
ejpam-6761	354	3	bipolar	bipolar	ADJ
ejpam-6761	354	4	valued	value	VERB
ejpam-6761	354	5	fuzzy	fuzzy	ADJ
ejpam-6761	354	6	subspace	subspace	NOUN
ejpam-6761	354	7	z	z	PROPN
ejpam-6761	354	8	=	=	PRON
ejpam-6761	354	9	{	{	PUNCT
ejpam-6761	354	10	(	(	PUNCT
ejpam-6761	354	11	0	0	NUM
ejpam-6761	354	12	,	,	PUNCT
ejpam-6761	354	13	[	[	X
ejpam-6761	354	14	−1	−1	NOUN
ejpam-6761	354	15	,	,	PUNCT
ejpam-6761	354	16	α	α	X
ejpam-6761	354	17	]	]	X
ejpam-6761	354	18	∪	∪	X
ejpam-6761	354	19	{	{	PUNCT
ejpam-6761	354	20	0	0	NUM
ejpam-6761	354	21	}	}	PUNCT
ejpam-6761	354	22	,	,	PUNCT
ejpam-6761	354	23	{	{	PUNCT
ejpam-6761	354	24	0	0	NUM
ejpam-6761	354	25	}	}	PUNCT
ejpam-6761	354	26	∪	∪	ADP
ejpam-6761	354	27	[	[	X
ejpam-6761	354	28	β	β	NOUN
ejpam-6761	354	29	,	,	PUNCT
ejpam-6761	354	30	1	1	NUM
ejpam-6761	354	31	]	]	NUM
ejpam-6761	354	32	)	)	PUNCT
ejpam-6761	354	33	,	,	PUNCT
ejpam-6761	354	34	(	(	PUNCT
ejpam-6761	354	35	1	1	X
ejpam-6761	354	36	,	,	PUNCT
ejpam-6761	354	37	[	[	X
ejpam-6761	354	38	−1	−1	NOUN
ejpam-6761	354	39	,	,	PUNCT
ejpam-6761	354	40	γ	γ	X
ejpam-6761	354	41	]	]	X
ejpam-6761	354	42	∪	∪	X
ejpam-6761	354	43	{	{	PUNCT
ejpam-6761	354	44	0	0	NUM
ejpam-6761	354	45	}	}	PUNCT
ejpam-6761	354	46	,	,	PUNCT
ejpam-6761	354	47	{	{	PUNCT
ejpam-6761	354	48	0	0	NUM
ejpam-6761	354	49	}	}	PUNCT
ejpam-6761	354	50	∪	∪	NOUN
ejpam-6761	354	51	[	[	X
ejpam-6761	354	52	δ	δ	PROPN
ejpam-6761	354	53	,	,	PUNCT
ejpam-6761	354	54	1	1	NUM
ejpam-6761	354	55	]	]	NUM
ejpam-6761	354	56	)	)	PUNCT
ejpam-6761	354	57	}	}	PUNCT
ejpam-6761	354	58	such	such	ADJ
ejpam-6761	354	59	that	that	DET
ejpam-6761	354	60	−1	−1	NOUN
ejpam-6761	354	61	<	<	X
ejpam-6761	354	62	α	α	X
ejpam-6761	354	63	<	<	X
ejpam-6761	354	64	0	0	X
ejpam-6761	354	65	<	<	X
ejpam-6761	354	66	β	β	X
ejpam-6761	354	67	<	<	X
ejpam-6761	354	68	1	1	NUM
ejpam-6761	354	69	and	and	CCONJ
ejpam-6761	354	70	−1	−1	NOUN
ejpam-6761	354	71	<	<	X
ejpam-6761	354	72	γ	γ	X
ejpam-6761	354	73	<	<	X
ejpam-6761	354	74	0	0	PUNCT
ejpam-6761	354	75	<	<	X
ejpam-6761	354	76	δ	δ	X
ejpam-6761	354	77	<	<	X
ejpam-6761	354	78	1	1	NUM
ejpam-6761	354	79	.	.	PUNCT
ejpam-6761	355	1	f.	f.	PROPN
ejpam-6761	355	2	al	al	PROPN
ejpam-6761	355	3	-	-	PROPN
ejpam-6761	355	4	zu’bi	zu’bi	PROPN
ejpam-6761	355	5	et	et	NOUN
ejpam-6761	355	6	al	al	PROPN
ejpam-6761	355	7	.	.	PUNCT
ejpam-6761	355	8	/	/	SYM
ejpam-6761	355	9	eur	eur	PROPN
ejpam-6761	355	10	.	.	PUNCT
ejpam-6761	356	1	j.	j.	PROPN
ejpam-6761	356	2	pure	pure	PROPN
ejpam-6761	356	3	appl	appl	PROPN
ejpam-6761	356	4	.	.	PROPN
ejpam-6761	356	5	math	math	PROPN
ejpam-6761	356	6	,	,	PUNCT
ejpam-6761	356	7	18	18	NUM
ejpam-6761	356	8	(	(	PUNCT
ejpam-6761	356	9	4	4	NUM
ejpam-6761	356	10	)	)	PUNCT
ejpam-6761	356	11	(	(	PUNCT
ejpam-6761	356	12	2025	2025	NUM
ejpam-6761	356	13	)	)	PUNCT
ejpam-6761	356	14	,	,	PUNCT
ejpam-6761	356	15	6761	6761	NUM
ejpam-6761	356	16	15	15	NUM
ejpam-6761	356	17	of	of	ADP
ejpam-6761	356	18	28	28	NUM
ejpam-6761	356	19	then	then	ADV
ejpam-6761	356	20	(	(	PUNCT
ejpam-6761	356	21	z	z	NOUN
ejpam-6761	356	22	,	,	PUNCT
ejpam-6761	356	23	f	f	X
ejpam-6761	356	24	)	)	PUNCT
ejpam-6761	356	25	is	be	AUX
ejpam-6761	356	26	not	not	PART
ejpam-6761	356	27	a	a	DET
ejpam-6761	356	28	bipolar	bipolar	ADJ
ejpam-6761	356	29	valued	value	VERB
ejpam-6761	356	30	fuzzy	fuzzy	ADJ
ejpam-6761	356	31	subgroup	subgroup	NOUN
ejpam-6761	356	32	of	of	ADP
ejpam-6761	356	33	(	(	PUNCT
ejpam-6761	356	34	(	(	PUNCT
ejpam-6761	356	35	z5	z5	X
ejpam-6761	356	36	,	,	PUNCT
ejpam-6761	356	37	[	[	X
ejpam-6761	356	38	−1	−1	NOUN
ejpam-6761	356	39	,	,	PUNCT
ejpam-6761	356	40	0	0	NUM
ejpam-6761	356	41	]	]	PUNCT
ejpam-6761	356	42	,	,	PUNCT
ejpam-6761	356	43	[	[	X
ejpam-6761	356	44	0	0	NUM
ejpam-6761	356	45	,	,	PUNCT
ejpam-6761	356	46	1]),f	1]),f	NUM
ejpam-6761	356	47	)	)	PUNCT
ejpam-6761	356	48	,	,	PUNCT
ejpam-6761	356	49	since	since	SCONJ
ejpam-6761	356	50	z	z	NOUN
ejpam-6761	356	51	is	be	AUX
ejpam-6761	356	52	not	not	PART
ejpam-6761	356	53	closed	close	VERB
ejpam-6761	356	54	under	under	ADP
ejpam-6761	356	55	f	f	PROPN
ejpam-6761	356	56	.	.	PUNCT
ejpam-6761	357	1	for	for	ADP
ejpam-6761	357	2	instance	instance	NOUN
ejpam-6761	357	3	,	,	PUNCT
ejpam-6761	357	4	(	(	PUNCT
ejpam-6761	357	5	0	0	NUM
ejpam-6761	357	6	,	,	PUNCT
ejpam-6761	357	7	[	[	X
ejpam-6761	357	8	−1	−1	NOUN
ejpam-6761	357	9	,	,	PUNCT
ejpam-6761	357	10	β	β	X
ejpam-6761	357	11	]	]	X
ejpam-6761	357	12	,	,	PUNCT
ejpam-6761	357	13	[	[	X
ejpam-6761	357	14	cα	cα	ADP
ejpam-6761	357	15	,	,	PUNCT
ejpam-6761	357	16	1])f(1	1])f(1	PROPN
ejpam-6761	357	17	,	,	PUNCT
ejpam-6761	357	18	[	[	X
ejpam-6761	357	19	−1	−1	NOUN
ejpam-6761	357	20	,	,	PUNCT
ejpam-6761	357	21	γ	γ	X
ejpam-6761	357	22	]	]	X
ejpam-6761	357	23	,	,	PUNCT
ejpam-6761	357	24	[	[	X
ejpam-6761	357	25	δ	δ	X
ejpam-6761	357	26	,	,	PUNCT
ejpam-6761	357	27	1	1	NUM
ejpam-6761	357	28	]	]	PUNCT
ejpam-6761	357	29	)	)	PUNCT
ejpam-6761	357	30	=	=	SYM
ejpam-6761	358	1	(	(	PUNCT
ejpam-6761	358	2	1	1	NUM
ejpam-6761	358	3	,	,	PUNCT
ejpam-6761	358	4	[	[	X
ejpam-6761	358	5	−1,−α	−1,−α	X
ejpam-6761	358	6	·	·	PUNCT
ejpam-6761	358	7	γ	γ	X
ejpam-6761	358	8	]	]	X
ejpam-6761	358	9	,	,	PUNCT
ejpam-6761	358	10	[	[	X
ejpam-6761	358	11	β	β	X
ejpam-6761	358	12	·	·	PUNCT
ejpam-6761	358	13	δ	δ	PROPN
ejpam-6761	358	14	,	,	PUNCT
ejpam-6761	358	15	1	1	NUM
ejpam-6761	358	16	]	]	PUNCT
ejpam-6761	358	17	)	)	PUNCT
ejpam-6761	358	18	/∈	/∈	PUNCT
ejpam-6761	359	1	z	z	NOUN
ejpam-6761	359	2	,	,	PUNCT
ejpam-6761	359	3	since	since	SCONJ
ejpam-6761	359	4	the	the	DET
ejpam-6761	359	5	value	value	NOUN
ejpam-6761	359	6	{	{	PUNCT
ejpam-6761	359	7	0	0	NUM
ejpam-6761	359	8	}	}	PUNCT
ejpam-6761	359	9	will	will	AUX
ejpam-6761	359	10	not	not	PART
ejpam-6761	359	11	appear	appear	VERB
ejpam-6761	359	12	in	in	ADP
ejpam-6761	359	13	both	both	CCONJ
ejpam-6761	359	14	positive	positive	ADJ
ejpam-6761	359	15	and/or	and/or	CCONJ
ejpam-6761	359	16	negative	negative	ADJ
ejpam-6761	359	17	membership	membership	NOUN
ejpam-6761	359	18	functions	function	NOUN
ejpam-6761	359	19	.	.	PUNCT
ejpam-6761	360	1	if	if	SCONJ
ejpam-6761	360	2	α	α	NOUN
ejpam-6761	360	3	=	=	SYM
ejpam-6761	360	4	γ	γ	X
ejpam-6761	360	5	=	=	SYM
ejpam-6761	360	6	0	0	NUM
ejpam-6761	360	7	and	and	CCONJ
ejpam-6761	360	8	β	β	X
ejpam-6761	360	9	=	=	PUNCT
ejpam-6761	360	10	δ	δ	X
ejpam-6761	360	11	=	=	SYM
ejpam-6761	360	12	0	0	PROPN
ejpam-6761	360	13	,	,	PUNCT
ejpam-6761	360	14	then	then	ADV
ejpam-6761	360	15	z	z	NOUN
ejpam-6761	360	16	=	=	SYM
ejpam-6761	360	17	{	{	PUNCT
ejpam-6761	360	18	(	(	PUNCT
ejpam-6761	360	19	0	0	NUM
ejpam-6761	360	20	,	,	PUNCT
ejpam-6761	360	21	[	[	X
ejpam-6761	360	22	−1	−1	NOUN
ejpam-6761	360	23	,	,	PUNCT
ejpam-6761	360	24	0	0	NUM
ejpam-6761	360	25	]	]	PUNCT
ejpam-6761	360	26	,	,	PUNCT
ejpam-6761	361	1	[	[	X
ejpam-6761	361	2	0	0	NUM
ejpam-6761	361	3	,	,	PUNCT
ejpam-6761	361	4	1	1	NUM
ejpam-6761	361	5	]	]	NUM
ejpam-6761	361	6	)	)	PUNCT
ejpam-6761	361	7	,	,	PUNCT
ejpam-6761	361	8	(	(	PUNCT
ejpam-6761	361	9	1	1	X
ejpam-6761	361	10	,	,	PUNCT
ejpam-6761	361	11	[	[	X
ejpam-6761	361	12	−1	−1	NOUN
ejpam-6761	361	13	,	,	PUNCT
ejpam-6761	361	14	0	0	NUM
ejpam-6761	361	15	]	]	PUNCT
ejpam-6761	361	16	,	,	PUNCT
ejpam-6761	361	17	[	[	X
ejpam-6761	361	18	0	0	NUM
ejpam-6761	361	19	,	,	PUNCT
ejpam-6761	361	20	1	1	NUM
ejpam-6761	361	21	]	]	PUNCT
ejpam-6761	361	22	)	)	PUNCT
ejpam-6761	361	23	}	}	PUNCT
ejpam-6761	361	24	together	together	ADV
ejpam-6761	361	25	with	with	ADP
ejpam-6761	361	26	f	f	PROPN
ejpam-6761	361	27	defines	define	VERB
ejpam-6761	361	28	a	a	DET
ejpam-6761	361	29	bipolar	bipolar	ADJ
ejpam-6761	361	30	valued	value	VERB
ejpam-6761	361	31	fuzzy	fuzzy	ADJ
ejpam-6761	361	32	subgroup	subgroup	NOUN
ejpam-6761	361	33	of	of	ADP
ejpam-6761	361	34	(	(	PUNCT
ejpam-6761	361	35	(	(	PUNCT
ejpam-6761	361	36	z5	z5	X
ejpam-6761	361	37	,	,	PUNCT
ejpam-6761	361	38	[	[	X
ejpam-6761	361	39	−1	−1	NOUN
ejpam-6761	361	40	,	,	PUNCT
ejpam-6761	361	41	0	0	NUM
ejpam-6761	361	42	]	]	PUNCT
ejpam-6761	361	43	,	,	PUNCT
ejpam-6761	361	44	[	[	X
ejpam-6761	361	45	0	0	NUM
ejpam-6761	361	46	,	,	PUNCT
ejpam-6761	361	47	1]),f	1]),f	NUM
ejpam-6761	361	48	)	)	PUNCT
ejpam-6761	361	49	.	.	PUNCT
ejpam-6761	362	1	let	let	VERB
ejpam-6761	362	2	b	b	NOUN
ejpam-6761	362	3	=	=	PRON
ejpam-6761	362	4	{	{	PUNCT
ejpam-6761	362	5	(	(	PUNCT
ejpam-6761	362	6	b−(x	b−(x	PROPN
ejpam-6761	362	7	)	)	PUNCT
ejpam-6761	362	8	,	,	PUNCT
ejpam-6761	362	9	b+(x	b+(x	PROPN
ejpam-6761	362	10	)	)	PUNCT
ejpam-6761	362	11	)	)	PUNCT
ejpam-6761	362	12	:	:	PUNCT
ejpam-6761	363	1	x	x	X
ejpam-6761	363	2	∈	∈	PROPN
ejpam-6761	363	3	b	b	X
ejpam-6761	363	4	◦	◦	NOUN
ejpam-6761	363	5	}	}	PUNCT
ejpam-6761	363	6	be	be	AUX
ejpam-6761	363	7	a	a	DET
ejpam-6761	363	8	bipolar	bipolar	ADJ
ejpam-6761	363	9	valued	value	VERB
ejpam-6761	363	10	fuzzy	fuzzy	ADJ
ejpam-6761	363	11	subset	subset	NOUN
ejpam-6761	363	12	of	of	ADP
ejpam-6761	363	13	the	the	DET
ejpam-6761	363	14	set	set	NOUN
ejpam-6761	363	15	g	g	NOUN
ejpam-6761	363	16	and	and	CCONJ
ejpam-6761	363	17	let	let	VERB
ejpam-6761	363	18	sl(b	sl(b	NOUN
ejpam-6761	363	19	)	)	PUNCT
ejpam-6761	363	20	,	,	PUNCT
ejpam-6761	363	21	su(b	su(b	NUM
ejpam-6761	363	22	)	)	PUNCT
ejpam-6761	363	23	and	and	CCONJ
ejpam-6761	363	24	s	s	AUX
ejpam-6761	363	25	◦	◦	NOUN
ejpam-6761	363	26	(b	(b	X
ejpam-6761	363	27	)	)	PUNCT
ejpam-6761	363	28	be	be	AUX
ejpam-6761	363	29	bipolar	bipolar	ADJ
ejpam-6761	363	30	valued	value	VERB
ejpam-6761	363	31	fuzzy	fuzzy	ADJ
ejpam-6761	363	32	subspaces	subspace	NOUN
ejpam-6761	363	33	induced	induce	VERB
ejpam-6761	363	34	by	by	ADP
ejpam-6761	363	35	the	the	DET
ejpam-6761	363	36	bipolar	bipolar	PROPN
ejpam-6761	363	37	valued	value	VERB
ejpam-6761	363	38	fuzzy	fuzzy	ADJ
ejpam-6761	363	39	subset	subset	PROPN
ejpam-6761	363	40	b.	b.	PROPN
ejpam-6761	363	41	for	for	ADP
ejpam-6761	363	42	these	these	DET
ejpam-6761	363	43	bipolar	bipolar	ADJ
ejpam-6761	363	44	valued	value	VERB
ejpam-6761	363	45	fuzzy	fuzzy	ADJ
ejpam-6761	363	46	spaces	space	NOUN
ejpam-6761	363	47	,	,	PUNCT
ejpam-6761	363	48	we	we	PRON
ejpam-6761	363	49	can	can	AUX
ejpam-6761	363	50	re	re	VERB
ejpam-6761	363	51	-	-	NOUN
ejpam-6761	363	52	state	state	NOUN
ejpam-6761	363	53	theorem	theorem	NOUN
ejpam-6761	363	54	3	3	NUM
ejpam-6761	363	55	in	in	ADP
ejpam-6761	363	56	the	the	DET
ejpam-6761	363	57	following	following	ADJ
ejpam-6761	363	58	manner	manner	NOUN
ejpam-6761	363	59	.	.	PUNCT
ejpam-6761	364	1	theorem	theorem	ADJ
ejpam-6761	364	2	4	4	NUM
ejpam-6761	364	3	.	.	PUNCT
ejpam-6761	364	4	(	(	PUNCT
ejpam-6761	364	5	sl(b	sl(b	NOUN
ejpam-6761	364	6	)	)	PUNCT
ejpam-6761	364	7	,	,	PUNCT
ejpam-6761	364	8	f	f	PROPN
ejpam-6761	364	9	)	)	PUNCT
ejpam-6761	364	10	,	,	PUNCT
ejpam-6761	364	11	(	(	PUNCT
ejpam-6761	364	12	su(b	su(b	NUM
ejpam-6761	364	13	)	)	PUNCT
ejpam-6761	364	14	,	,	PUNCT
ejpam-6761	364	15	f	f	PROPN
ejpam-6761	364	16	)	)	PUNCT
ejpam-6761	364	17	and	and	CCONJ
ejpam-6761	364	18	(	(	PUNCT
ejpam-6761	364	19	s	s	X
ejpam-6761	364	20	◦	◦	NOUN
ejpam-6761	364	21	(b	(b	NOUN
ejpam-6761	364	22	)	)	PUNCT
ejpam-6761	364	23	,	,	PUNCT
ejpam-6761	364	24	f	f	PROPN
ejpam-6761	364	25	)	)	PUNCT
ejpam-6761	364	26	are	be	AUX
ejpam-6761	364	27	bipolar	bipolar	ADJ
ejpam-6761	364	28	valued	value	VERB
ejpam-6761	364	29	fuzzy	fuzzy	ADJ
ejpam-6761	364	30	subgroups	subgroup	NOUN
ejpam-6761	364	31	of	of	ADP
ejpam-6761	364	32	(	(	PUNCT
ejpam-6761	364	33	(	(	PUNCT
ejpam-6761	364	34	g	g	NOUN
ejpam-6761	364	35	,	,	PUNCT
ejpam-6761	364	36	[	[	X
ejpam-6761	364	37	−1	−1	NOUN
ejpam-6761	364	38	,	,	PUNCT
ejpam-6761	364	39	0	0	NUM
ejpam-6761	364	40	]	]	PUNCT
ejpam-6761	364	41	,	,	PUNCT
ejpam-6761	364	42	[	[	X
ejpam-6761	364	43	0	0	NUM
ejpam-6761	364	44	,	,	PUNCT
ejpam-6761	364	45	1	1	NUM
ejpam-6761	364	46	]	]	NUM
ejpam-6761	364	47	)	)	PUNCT
ejpam-6761	364	48	,	,	PUNCT
ejpam-6761	364	49	f	f	X
ejpam-6761	364	50	)	)	PUNCT
ejpam-6761	364	51	iff	iff	PROPN
ejpam-6761	364	52	:	:	PUNCT
ejpam-6761	364	53	(	(	PUNCT
ejpam-6761	365	1	1	1	X
ejpam-6761	365	2	)	)	PUNCT
ejpam-6761	365	3	xfy	xfy	PROPN
ejpam-6761	365	4	∈	∈	PROPN
ejpam-6761	365	5	b	b	X
ejpam-6761	365	6	◦	◦	NOUN
ejpam-6761	365	7	,	,	PUNCT
ejpam-6761	365	8	∀x	∀x	X
ejpam-6761	365	9	,	,	PUNCT
ejpam-6761	365	10	y	y	PROPN
ejpam-6761	365	11	∈	∈	PROPN
ejpam-6761	365	12	b	b	PROPN
ejpam-6761	365	13	◦	◦	NOUN
ejpam-6761	365	14	,	,	PUNCT
ejpam-6761	365	15	(	(	PUNCT
ejpam-6761	365	16	6	6	NUM
ejpam-6761	365	17	)	)	PUNCT
ejpam-6761	365	18	(	(	PUNCT
ejpam-6761	365	19	2	2	NUM
ejpam-6761	365	20	)	)	PUNCT
ejpam-6761	365	21	f−xy(b	f−xy(b	NOUN
ejpam-6761	365	22	−(x	−(x	NOUN
ejpam-6761	365	23	)	)	PUNCT
ejpam-6761	365	24	,	,	PUNCT
ejpam-6761	365	25	b−(y	b−(y	PROPN
ejpam-6761	365	26	)	)	PUNCT
ejpam-6761	365	27	)	)	PUNCT
ejpam-6761	366	1	=	=	SYM
ejpam-6761	366	2	b−(xfy	b−(xfy	NOUN
ejpam-6761	366	3	)	)	PUNCT
ejpam-6761	366	4	,	,	PUNCT
ejpam-6761	366	5	and	and	CCONJ
ejpam-6761	366	6	f+xy(b	f+xy(b	NOUN
ejpam-6761	366	7	+	+	NOUN
ejpam-6761	366	8	(	(	PUNCT
ejpam-6761	366	9	x	x	NOUN
ejpam-6761	366	10	)	)	PUNCT
ejpam-6761	366	11	,	,	PUNCT
ejpam-6761	366	12	b+(y	b+(y	NUM
ejpam-6761	366	13	)	)	PUNCT
ejpam-6761	366	14	)	)	PUNCT
ejpam-6761	367	1	=	=	SYM
ejpam-6761	367	2	b+(xfy	b+(xfy	PROPN
ejpam-6761	367	3	)	)	PUNCT
ejpam-6761	367	4	.	.	PUNCT
ejpam-6761	368	1	(	(	PUNCT
ejpam-6761	368	2	7	7	X
ejpam-6761	368	3	)	)	PUNCT
ejpam-6761	368	4	definition	definition	NOUN
ejpam-6761	368	5	22	22	NUM
ejpam-6761	368	6	.	.	PUNCT
ejpam-6761	369	1	a	a	DET
ejpam-6761	369	2	bipolar	bipolar	ADJ
ejpam-6761	369	3	valued	value	VERB
ejpam-6761	369	4	fuzzy	fuzzy	ADJ
ejpam-6761	369	5	subset	subset	NOUN
ejpam-6761	369	6	b	b	NOUN
ejpam-6761	369	7	of	of	ADP
ejpam-6761	369	8	g	g	PROPN
ejpam-6761	369	9	is	be	AUX
ejpam-6761	369	10	said	say	VERB
ejpam-6761	369	11	to	to	PART
ejpam-6761	369	12	induce	induce	VERB
ejpam-6761	369	13	bipolar	bipolar	ADJ
ejpam-6761	369	14	valued	value	VERB
ejpam-6761	369	15	fuzzy	fuzzy	ADJ
ejpam-6761	369	16	subgroups	subgroup	NOUN
ejpam-6761	369	17	of	of	ADP
ejpam-6761	369	18	(	(	PUNCT
ejpam-6761	369	19	(	(	PUNCT
ejpam-6761	369	20	g	g	NOUN
ejpam-6761	369	21	,	,	PUNCT
ejpam-6761	369	22	[	[	X
ejpam-6761	369	23	−1	−1	NOUN
ejpam-6761	369	24	,	,	PUNCT
ejpam-6761	369	25	0	0	NUM
ejpam-6761	369	26	]	]	PUNCT
ejpam-6761	369	27	,	,	PUNCT
ejpam-6761	369	28	[	[	X
ejpam-6761	369	29	0	0	NUM
ejpam-6761	369	30	,	,	PUNCT
ejpam-6761	369	31	1	1	NUM
ejpam-6761	369	32	]	]	NUM
ejpam-6761	369	33	)	)	PUNCT
ejpam-6761	369	34	,	,	PUNCT
ejpam-6761	369	35	f	f	PROPN
ejpam-6761	369	36	)	)	PUNCT
ejpam-6761	369	37	iff	iff	PROPN
ejpam-6761	369	38	(	(	PUNCT
ejpam-6761	369	39	sl(b	sl(b	PROPN
ejpam-6761	369	40	)	)	PUNCT
ejpam-6761	369	41	,	,	PUNCT
ejpam-6761	369	42	f	f	PROPN
ejpam-6761	369	43	)	)	PUNCT
ejpam-6761	369	44	,	,	PUNCT
ejpam-6761	369	45	(	(	PUNCT
ejpam-6761	369	46	su(b	su(b	NUM
ejpam-6761	369	47	)	)	PUNCT
ejpam-6761	369	48	,	,	PUNCT
ejpam-6761	369	49	f	f	PROPN
ejpam-6761	369	50	)	)	PUNCT
ejpam-6761	369	51	,	,	PUNCT
ejpam-6761	369	52	and	and	CCONJ
ejpam-6761	369	53	(	(	PUNCT
ejpam-6761	369	54	s	s	AUX
ejpam-6761	369	55	◦	◦	NOUN
ejpam-6761	369	56	(b	(b	NOUN
ejpam-6761	369	57	)	)	PUNCT
ejpam-6761	369	58	,	,	PUNCT
ejpam-6761	369	59	f	f	PROPN
ejpam-6761	369	60	)	)	PUNCT
ejpam-6761	369	61	are	be	AUX
ejpam-6761	369	62	bipolar	bipolar	ADJ
ejpam-6761	369	63	valued	value	VERB
ejpam-6761	369	64	fuzzy	fuzzy	ADJ
ejpam-6761	369	65	subgroups	subgroup	NOUN
ejpam-6761	369	66	.	.	PUNCT
ejpam-6761	370	1	let	let	AUX
ejpam-6761	370	2	(	(	PUNCT
ejpam-6761	370	3	(	(	PUNCT
ejpam-6761	370	4	g	g	NOUN
ejpam-6761	370	5	,	,	PUNCT
ejpam-6761	370	6	[	[	X
ejpam-6761	370	7	−1	−1	NOUN
ejpam-6761	370	8	,	,	PUNCT
ejpam-6761	370	9	0	0	NUM
ejpam-6761	370	10	]	]	PUNCT
ejpam-6761	370	11	,	,	PUNCT
ejpam-6761	370	12	[	[	X
ejpam-6761	370	13	0	0	NUM
ejpam-6761	370	14	,	,	PUNCT
ejpam-6761	370	15	1	1	NUM
ejpam-6761	370	16	]	]	NUM
ejpam-6761	370	17	)	)	PUNCT
ejpam-6761	370	18	,	,	PUNCT
ejpam-6761	370	19	f	f	PROPN
ejpam-6761	370	20	)	)	PUNCT
ejpam-6761	370	21	with	with	ADP
ejpam-6761	370	22	f	f	PROPN
ejpam-6761	370	23	=	=	SYM
ejpam-6761	370	24	(	(	PUNCT
ejpam-6761	370	25	f	f	PROPN
ejpam-6761	370	26	,	,	PUNCT
ejpam-6761	370	27	f−xy	f−xy	PROPN
ejpam-6761	370	28	,	,	PUNCT
ejpam-6761	370	29	f	f	PROPN
ejpam-6761	370	30	+	+	CCONJ
ejpam-6761	370	31	xy	xy	PROPN
ejpam-6761	370	32	)	)	PUNCT
ejpam-6761	370	33	be	be	VERB
ejpam-6761	370	34	a	a	DET
ejpam-6761	370	35	uniform	uniform	ADJ
ejpam-6761	370	36	bipolar	bipolar	ADJ
ejpam-6761	370	37	valued	value	VERB
ejpam-6761	370	38	fuzzy	fuzzy	ADJ
ejpam-6761	370	39	group	group	NOUN
ejpam-6761	370	40	with	with	ADP
ejpam-6761	370	41	f−xy	f−xy	PROPN
ejpam-6761	370	42	,	,	PUNCT
ejpam-6761	370	43	f	f	PROPN
ejpam-6761	371	1	+	+	PRON
ejpam-6761	371	2	xy	xy	PROPN
ejpam-6761	371	3	(	(	PUNCT
ejpam-6761	371	4	(	(	PUNCT
ejpam-6761	371	5	i.e.	i.e.	X
ejpam-6761	371	6	,	,	PUNCT
ejpam-6761	371	7	f+	f+	ADJ
ejpam-6761	371	8	=	=	SYM
ejpam-6761	371	9	|f−|	|f−|	NUM
ejpam-6761	371	10	)	)	PUNCT
ejpam-6761	371	11	.	.	PUNCT
ejpam-6761	371	12	)	)	PUNCT
ejpam-6761	371	13	,	,	PUNCT
ejpam-6761	371	14	then	then	ADV
ejpam-6761	371	15	we	we	PRON
ejpam-6761	371	16	have	have	VERB
ejpam-6761	371	17	the	the	DET
ejpam-6761	371	18	following	follow	VERB
ejpam-6761	371	19	theorem	theorem	NOUN
ejpam-6761	371	20	:	:	PUNCT
ejpam-6761	371	21	theorem	theorem	NOUN
ejpam-6761	371	22	5	5	NUM
ejpam-6761	371	23	.	.	PUNCT
ejpam-6761	371	24	(	(	PUNCT
ejpam-6761	371	25	1	1	X
ejpam-6761	371	26	)	)	PUNCT
ejpam-6761	371	27	every	every	DET
ejpam-6761	371	28	bipolar	bipolar	ADJ
ejpam-6761	371	29	valued	value	VERB
ejpam-6761	371	30	fuzzy	fuzzy	ADJ
ejpam-6761	371	31	subset	subset	NOUN
ejpam-6761	371	32	b	b	NOUN
ejpam-6761	371	33	of	of	ADP
ejpam-6761	371	34	g	g	NOUN
ejpam-6761	371	35	which	which	PRON
ejpam-6761	371	36	induces	induce	VERB
ejpam-6761	371	37	bipolar	bipolar	ADJ
ejpam-6761	371	38	valued	value	VERB
ejpam-6761	371	39	fuzzy	fuzzy	ADJ
ejpam-6761	371	40	subgroups	subgroup	NOUN
ejpam-6761	371	41	is	be	AUX
ejpam-6761	371	42	a	a	DET
ejpam-6761	371	43	classical	classical	ADJ
ejpam-6761	371	44	bipolar	bipolar	NOUN
ejpam-6761	371	45	valued	value	VERB
ejpam-6761	371	46	fuzzy	fuzzy	ADJ
ejpam-6761	371	47	subgroup	subgroup	NOUN
ejpam-6761	371	48	of	of	ADP
ejpam-6761	371	49	(	(	PUNCT
ejpam-6761	371	50	g	g	PROPN
ejpam-6761	371	51	,	,	PUNCT
ejpam-6761	371	52	f	f	PROPN
ejpam-6761	371	53	)	)	PUNCT
ejpam-6761	371	54	.	.	PUNCT
ejpam-6761	372	1	(	(	PUNCT
ejpam-6761	372	2	2	2	X
ejpam-6761	372	3	)	)	PUNCT
ejpam-6761	372	4	if	if	SCONJ
ejpam-6761	372	5	(	(	PUNCT
ejpam-6761	372	6	s	s	X
ejpam-6761	372	7	,	,	PUNCT
ejpam-6761	372	8	f	f	PROPN
ejpam-6761	372	9	)	)	PUNCT
ejpam-6761	372	10	is	be	AUX
ejpam-6761	372	11	an	an	DET
ejpam-6761	372	12	ordinary	ordinary	ADJ
ejpam-6761	372	13	subgroup	subgroup	NOUN
ejpam-6761	372	14	of	of	ADP
ejpam-6761	372	15	the	the	DET
ejpam-6761	372	16	group	group	NOUN
ejpam-6761	372	17	(	(	PUNCT
ejpam-6761	372	18	g	g	PROPN
ejpam-6761	372	19	,	,	PUNCT
ejpam-6761	372	20	f	f	PROPN
ejpam-6761	372	21	)	)	PUNCT
ejpam-6761	372	22	,	,	PUNCT
ejpam-6761	372	23	then	then	ADV
ejpam-6761	372	24	every	every	DET
ejpam-6761	372	25	bipolar	bipolar	ADJ
ejpam-6761	372	26	valued	value	VERB
ejpam-6761	372	27	fuzzy	fuzzy	ADJ
ejpam-6761	372	28	subset	subset	NOUN
ejpam-6761	372	29	b	b	NOUN
ejpam-6761	372	30	of	of	ADP
ejpam-6761	372	31	g	g	NOUN
ejpam-6761	372	32	,	,	PUNCT
ejpam-6761	372	33	for	for	ADP
ejpam-6761	372	34	which	which	PRON
ejpam-6761	372	35	b	b	NUM
ejpam-6761	372	36	◦	◦	NOUN
ejpam-6761	372	37	=	=	SYM
ejpam-6761	372	38	s	s	NOUN
ejpam-6761	372	39	,	,	PUNCT
ejpam-6761	372	40	induces	induce	VERB
ejpam-6761	372	41	a	a	DET
ejpam-6761	372	42	bipolar	bipolar	ADJ
ejpam-6761	372	43	valued	value	VERB
ejpam-6761	372	44	fuzzy	fuzzy	ADJ
ejpam-6761	372	45	subgroup	subgroup	NOUN
ejpam-6761	372	46	(	(	PUNCT
ejpam-6761	372	47	(	(	PUNCT
ejpam-6761	372	48	g	g	NOUN
ejpam-6761	372	49	,	,	PUNCT
ejpam-6761	372	50	[	[	X
ejpam-6761	372	51	−1	−1	NOUN
ejpam-6761	372	52	,	,	PUNCT
ejpam-6761	372	53	0	0	NUM
ejpam-6761	372	54	]	]	PUNCT
ejpam-6761	372	55	,	,	PUNCT
ejpam-6761	372	56	[	[	X
ejpam-6761	372	57	0	0	NUM
ejpam-6761	372	58	,	,	PUNCT
ejpam-6761	372	59	1	1	NUM
ejpam-6761	372	60	]	]	NUM
ejpam-6761	372	61	)	)	PUNCT
ejpam-6761	372	62	,	,	PUNCT
ejpam-6761	372	63	p	p	NOUN
ejpam-6761	372	64	)	)	PUNCT
ejpam-6761	372	65	where	where	SCONJ
ejpam-6761	372	66	p	p	NOUN
ejpam-6761	372	67	=	=	X
ejpam-6761	372	68	{	{	PUNCT
ejpam-6761	372	69	p	p	X
ejpam-6761	372	70	,	,	PUNCT
ejpam-6761	372	71	p−xy	p−xy	PROPN
ejpam-6761	372	72	,	,	PUNCT
ejpam-6761	372	73	p+xy	p+xy	ADP
ejpam-6761	372	74	}	}	PUNCT
ejpam-6761	372	75	with	with	ADP
ejpam-6761	372	76	p	p	NOUN
ejpam-6761	372	77	=	=	SYM
ejpam-6761	372	78	f	f	PROPN
ejpam-6761	372	79	and	and	CCONJ
ejpam-6761	372	80	p−xy	p−xy	PROPN
ejpam-6761	372	81	,	,	PUNCT
ejpam-6761	372	82	p	p	X
ejpam-6761	373	1	+	+	X
ejpam-6761	373	2	xy	xy	NOUN
ejpam-6761	373	3	are	be	AUX
ejpam-6761	373	4	suitable	suitable	ADJ
ejpam-6761	373	5	negative	negative	ADJ
ejpam-6761	373	6	and	and	CCONJ
ejpam-6761	373	7	positive	positive	ADJ
ejpam-6761	373	8	comembership	comembership	NOUN
ejpam-6761	373	9	functions	function	NOUN
ejpam-6761	373	10	respectively	respectively	ADV
ejpam-6761	373	11	.	.	PUNCT
ejpam-6761	374	1	proof	proof	NOUN
ejpam-6761	374	2	.	.	PUNCT
ejpam-6761	375	1	(	(	PUNCT
ejpam-6761	375	2	1	1	X
ejpam-6761	375	3	)	)	PUNCT
ejpam-6761	375	4	if	if	SCONJ
ejpam-6761	375	5	the	the	DET
ejpam-6761	375	6	bipolar	bipolar	ADJ
ejpam-6761	375	7	valued	value	VERB
ejpam-6761	375	8	fuzzy	fuzzy	ADJ
ejpam-6761	375	9	subset	subset	VERB
ejpam-6761	375	10	b	b	NOUN
ejpam-6761	375	11	induces	induce	VERB
ejpam-6761	375	12	bipolar	bipolar	ADJ
ejpam-6761	375	13	valued	value	VERB
ejpam-6761	375	14	fuzzy	fuzzy	ADJ
ejpam-6761	375	15	subgroups	subgroup	NOUN
ejpam-6761	375	16	of	of	ADP
ejpam-6761	375	17	(	(	PUNCT
ejpam-6761	375	18	(	(	PUNCT
ejpam-6761	375	19	g	g	NOUN
ejpam-6761	375	20	,	,	PUNCT
ejpam-6761	375	21	[	[	X
ejpam-6761	375	22	−1	−1	NOUN
ejpam-6761	375	23	,	,	PUNCT
ejpam-6761	375	24	0	0	NUM
ejpam-6761	375	25	]	]	PUNCT
ejpam-6761	375	26	,	,	PUNCT
ejpam-6761	376	1	[	[	X
ejpam-6761	376	2	0	0	NUM
ejpam-6761	376	3	,	,	PUNCT
ejpam-6761	376	4	1	1	NUM
ejpam-6761	376	5	]	]	NUM
ejpam-6761	376	6	)	)	PUNCT
ejpam-6761	376	7	,	,	PUNCT
ejpam-6761	376	8	f	f	PROPN
ejpam-6761	376	9	)	)	PUNCT
ejpam-6761	376	10	,	,	PUNCT
ejpam-6761	376	11	then	then	ADV
ejpam-6761	376	12	by	by	ADP
ejpam-6761	376	13	theorem	theorem	NOUN
ejpam-6761	376	14	4	4	NUM
ejpam-6761	376	15	we	we	PRON
ejpam-6761	376	16	have	have	VERB
ejpam-6761	376	17	:	:	PUNCT
ejpam-6761	376	18	f−xy(b	f−xy(b	NOUN
ejpam-6761	376	19	−(x	−(x	NOUN
ejpam-6761	376	20	)	)	PUNCT
ejpam-6761	376	21	,	,	PUNCT
ejpam-6761	376	22	b−(y	b−(y	PROPN
ejpam-6761	376	23	)	)	PUNCT
ejpam-6761	376	24	)	)	PUNCT
ejpam-6761	377	1	=	=	SYM
ejpam-6761	377	2	b−(xfy	b−(xfy	X
ejpam-6761	377	3	)	)	PUNCT
ejpam-6761	377	4	and	and	CCONJ
ejpam-6761	377	5	f+xy(b	f+xy(b	NOUN
ejpam-6761	377	6	+	+	NOUN
ejpam-6761	377	7	(	(	PUNCT
ejpam-6761	377	8	x	x	NOUN
ejpam-6761	377	9	)	)	PUNCT
ejpam-6761	377	10	,	,	PUNCT
ejpam-6761	377	11	b+(y	b+(y	NUM
ejpam-6761	377	12	)	)	PUNCT
ejpam-6761	377	13	)	)	PUNCT
ejpam-6761	378	1	=	=	SYM
ejpam-6761	378	2	b+(xfy	b+(xfy	PROPN
ejpam-6761	378	3	)	)	PUNCT
ejpam-6761	378	4	,	,	PUNCT
ejpam-6761	378	5	for	for	ADP
ejpam-6761	378	6	all	all	DET
ejpam-6761	378	7	b−(x	b−(x	NOUN
ejpam-6761	378	8	)	)	PUNCT
ejpam-6761	378	9	̸=	̸=	PROPN
ejpam-6761	378	10	−1	−1	NOUN
ejpam-6761	378	11	̸=	̸=	PROPN
ejpam-6761	378	12	b−(y	b−(y	PROPN
ejpam-6761	378	13	)	)	PUNCT
ejpam-6761	378	14	and	and	CCONJ
ejpam-6761	378	15	b+(x	b+(x	ADJ
ejpam-6761	378	16	)	)	PUNCT
ejpam-6761	378	17	̸=	̸=	PROPN
ejpam-6761	378	18	1	1	NUM
ejpam-6761	378	19	̸=	̸=	PROPN
ejpam-6761	378	20	b+(y	b+(y	NUM
ejpam-6761	378	21	)	)	PUNCT
ejpam-6761	378	22	.	.	PUNCT
ejpam-6761	379	1	(	(	PUNCT
ejpam-6761	379	2	8)	8)	NUM
ejpam-6761	379	3	f.	f.	PROPN
ejpam-6761	379	4	al	al	PROPN
ejpam-6761	379	5	-	-	PROPN
ejpam-6761	379	6	zu’bi	zu’bi	PROPN
ejpam-6761	379	7	et	et	NOUN
ejpam-6761	379	8	al	al	PROPN
ejpam-6761	379	9	.	.	PUNCT
ejpam-6761	379	10	/	/	SYM
ejpam-6761	379	11	eur	eur	PROPN
ejpam-6761	379	12	.	.	PUNCT
ejpam-6761	380	1	j.	j.	PROPN
ejpam-6761	380	2	pure	pure	PROPN
ejpam-6761	380	3	appl	appl	PROPN
ejpam-6761	380	4	.	.	PROPN
ejpam-6761	380	5	math	math	PROPN
ejpam-6761	380	6	,	,	PUNCT
ejpam-6761	380	7	18	18	NUM
ejpam-6761	380	8	(	(	PUNCT
ejpam-6761	380	9	4	4	NUM
ejpam-6761	380	10	)	)	PUNCT
ejpam-6761	380	11	(	(	PUNCT
ejpam-6761	380	12	2025	2025	NUM
ejpam-6761	380	13	)	)	PUNCT
ejpam-6761	380	14	,	,	PUNCT
ejpam-6761	380	15	6761	6761	NUM
ejpam-6761	380	16	16	16	NUM
ejpam-6761	380	17	of	of	ADP
ejpam-6761	380	18	28	28	NUM
ejpam-6761	380	19	that	that	PRON
ejpam-6761	380	20	is	be	AUX
ejpam-6761	380	21	,	,	PUNCT
ejpam-6761	380	22	if	if	SCONJ
ejpam-6761	380	23	the	the	DET
ejpam-6761	380	24	bipolar	bipolar	ADJ
ejpam-6761	380	25	valued	value	VERB
ejpam-6761	380	26	fuzzy	fuzzy	ADJ
ejpam-6761	380	27	subset	subset	VERB
ejpam-6761	380	28	b	b	NOUN
ejpam-6761	380	29	induces	induce	VERB
ejpam-6761	380	30	bipolar	bipolar	ADJ
ejpam-6761	380	31	valued	value	VERB
ejpam-6761	380	32	fuzzy	fuzzy	ADJ
ejpam-6761	380	33	subgroups	subgroup	NOUN
ejpam-6761	380	34	of	of	ADP
ejpam-6761	380	35	(	(	PUNCT
ejpam-6761	380	36	(	(	PUNCT
ejpam-6761	380	37	g	g	NOUN
ejpam-6761	380	38	,	,	PUNCT
ejpam-6761	380	39	[	[	X
ejpam-6761	380	40	−1	−1	NOUN
ejpam-6761	380	41	,	,	PUNCT
ejpam-6761	380	42	0	0	NUM
ejpam-6761	380	43	]	]	PUNCT
ejpam-6761	380	44	,	,	PUNCT
ejpam-6761	381	1	[	[	X
ejpam-6761	381	2	0	0	NUM
ejpam-6761	381	3	,	,	PUNCT
ejpam-6761	381	4	1	1	NUM
ejpam-6761	381	5	]	]	NUM
ejpam-6761	381	6	)	)	PUNCT
ejpam-6761	381	7	,	,	PUNCT
ejpam-6761	381	8	f	f	PROPN
ejpam-6761	381	9	)	)	PUNCT
ejpam-6761	381	10	,	,	PUNCT
ejpam-6761	381	11	then	then	ADV
ejpam-6761	381	12	it	it	PRON
ejpam-6761	381	13	satisfies	satisfy	VERB
ejpam-6761	381	14	the	the	DET
ejpam-6761	381	15	inequalities	inequality	NOUN
ejpam-6761	381	16	:	:	PUNCT
ejpam-6761	381	17	f−xy(b	f−xy(b	NOUN
ejpam-6761	381	18	−(x	−(x	NOUN
ejpam-6761	381	19	)	)	PUNCT
ejpam-6761	381	20	,	,	PUNCT
ejpam-6761	381	21	b−(y	b−(y	PROPN
ejpam-6761	381	22	)	)	PUNCT
ejpam-6761	381	23	)	)	PUNCT
ejpam-6761	382	1	≤	≤	NUM
ejpam-6761	382	2	b−(xfy	b−(xfy	PROPN
ejpam-6761	382	3	)	)	PUNCT
ejpam-6761	382	4	and	and	CCONJ
ejpam-6761	382	5	f+xy(b	f+xy(b	NOUN
ejpam-6761	382	6	+	+	NOUN
ejpam-6761	382	7	(	(	PUNCT
ejpam-6761	382	8	x	x	NOUN
ejpam-6761	382	9	)	)	PUNCT
ejpam-6761	382	10	,	,	PUNCT
ejpam-6761	382	11	b+(y	b+(y	NUM
ejpam-6761	382	12	)	)	PUNCT
ejpam-6761	382	13	)	)	PUNCT
ejpam-6761	382	14	≥	≥	PROPN
ejpam-6761	382	15	b+(xfy	b+(xfy	PROPN
ejpam-6761	382	16	)	)	PUNCT
ejpam-6761	382	17	,	,	PUNCT
ejpam-6761	382	18	∀x	∀x	X
ejpam-6761	382	19	,	,	PUNCT
ejpam-6761	382	20	y	y	PROPN
ejpam-6761	382	21	∈	∈	PROPN
ejpam-6761	382	22	g.	g.	PROPN
ejpam-6761	382	23	therefore	therefore	ADV
ejpam-6761	382	24	,	,	PUNCT
ejpam-6761	382	25	b	b	PROPN
ejpam-6761	382	26	is	be	AUX
ejpam-6761	382	27	a	a	DET
ejpam-6761	382	28	classical	classical	ADJ
ejpam-6761	382	29	bipolar	bipolar	NOUN
ejpam-6761	382	30	valued	value	VERB
ejpam-6761	382	31	fuzzy	fuzzy	ADJ
ejpam-6761	382	32	subgroup	subgroup	NOUN
ejpam-6761	382	33	.	.	PUNCT
ejpam-6761	383	1	(	(	PUNCT
ejpam-6761	383	2	2	2	X
ejpam-6761	383	3	)	)	PUNCT
ejpam-6761	383	4	let	let	VERB
ejpam-6761	383	5	(	(	PUNCT
ejpam-6761	383	6	s	s	X
ejpam-6761	383	7	,	,	PUNCT
ejpam-6761	383	8	f	f	PROPN
ejpam-6761	383	9	)	)	PUNCT
ejpam-6761	383	10	be	be	AUX
ejpam-6761	383	11	an	an	DET
ejpam-6761	383	12	ordinary	ordinary	ADJ
ejpam-6761	383	13	subgroup	subgroup	NOUN
ejpam-6761	383	14	of	of	ADP
ejpam-6761	383	15	the	the	DET
ejpam-6761	383	16	group	group	NOUN
ejpam-6761	383	17	(	(	PUNCT
ejpam-6761	383	18	g	g	PROPN
ejpam-6761	383	19	,	,	PUNCT
ejpam-6761	383	20	f	f	PROPN
ejpam-6761	383	21	)	)	PUNCT
ejpam-6761	383	22	,	,	PUNCT
ejpam-6761	383	23	and	and	CCONJ
ejpam-6761	383	24	let	let	VERB
ejpam-6761	383	25	b	b	X
ejpam-6761	383	26	be	be	AUX
ejpam-6761	383	27	a	a	DET
ejpam-6761	383	28	bipolar	bipolar	ADJ
ejpam-6761	383	29	valued	value	VERB
ejpam-6761	383	30	fuzzy	fuzzy	ADJ
ejpam-6761	383	31	subset	subset	NOUN
ejpam-6761	383	32	of	of	ADP
ejpam-6761	383	33	g	g	PROPN
ejpam-6761	383	34	for	for	ADP
ejpam-6761	383	35	which	which	PRON
ejpam-6761	383	36	b	b	X
ejpam-6761	383	37	◦	◦	NOUN
ejpam-6761	383	38	=	=	SYM
ejpam-6761	383	39	s	s	X
ejpam-6761	383	40	and	and	CCONJ
ejpam-6761	383	41	let	let	VERB
ejpam-6761	383	42	p−xy	p−xy	PROPN
ejpam-6761	383	43	,	,	PUNCT
ejpam-6761	383	44	p	p	X
ejpam-6761	384	1	+	+	CCONJ
ejpam-6761	384	2	xy	xy	PROPN
ejpam-6761	384	3	be	be	AUX
ejpam-6761	384	4	given	give	VERB
ejpam-6761	384	5	intersection	intersection	NOUN
ejpam-6761	384	6	bvf	bvf	NOUN
ejpam-6761	384	7	functions	function	NOUN
ejpam-6761	384	8	.	.	PUNCT
ejpam-6761	385	1	define	define	VERB
ejpam-6761	385	2	the	the	DET
ejpam-6761	385	3	bipolar	bipolar	ADJ
ejpam-6761	385	4	valued	value	VERB
ejpam-6761	385	5	fuzzy	fuzzy	ADJ
ejpam-6761	385	6	group	group	NOUN
ejpam-6761	385	7	(	(	PUNCT
ejpam-6761	385	8	(	(	PUNCT
ejpam-6761	385	9	g	g	NOUN
ejpam-6761	385	10	,	,	PUNCT
ejpam-6761	385	11	[	[	X
ejpam-6761	385	12	−1	−1	NOUN
ejpam-6761	385	13	,	,	PUNCT
ejpam-6761	385	14	0	0	NUM
ejpam-6761	385	15	]	]	PUNCT
ejpam-6761	385	16	,	,	PUNCT
ejpam-6761	385	17	[	[	X
ejpam-6761	385	18	0	0	NUM
ejpam-6761	385	19	,	,	PUNCT
ejpam-6761	385	20	1	1	NUM
ejpam-6761	385	21	]	]	NUM
ejpam-6761	385	22	)	)	PUNCT
ejpam-6761	385	23	,	,	PUNCT
ejpam-6761	385	24	p	p	NOUN
ejpam-6761	385	25	)	)	PUNCT
ejpam-6761	385	26	as	as	SCONJ
ejpam-6761	385	27	follows	follow	VERB
ejpam-6761	385	28	:	:	PUNCT
ejpam-6761	385	29	p	p	X
ejpam-6761	385	30	=	=	X
ejpam-6761	385	31	{	{	PUNCT
ejpam-6761	385	32	p	p	X
ejpam-6761	385	33	,	,	PUNCT
ejpam-6761	385	34	p−xy	p−xy	PROPN
ejpam-6761	385	35	,	,	PUNCT
ejpam-6761	385	36	p+xy	p+xy	X
ejpam-6761	385	37	}	}	PUNCT
ejpam-6761	385	38	,	,	PUNCT
ejpam-6761	385	39	where	where	SCONJ
ejpam-6761	385	40	p	p	NOUN
ejpam-6761	385	41	=	=	SYM
ejpam-6761	385	42	f	f	PROPN
ejpam-6761	385	43	,	,	PUNCT
ejpam-6761	385	44	and	and	CCONJ
ejpam-6761	385	45	p−xy(n1,m1	p−xy(n1,m1	NOUN
ejpam-6761	385	46	)	)	PUNCT
ejpam-6761	385	47	=	=	VERB
ejpam-6761	385	48	ψ−	ψ−	PROPN
ejpam-6761	385	49	xy(f	xy(f	PUNCT
ejpam-6761	385	50	−(n1,m1	−(n1,m1	VERB
ejpam-6761	385	51	)	)	PUNCT
ejpam-6761	385	52	)	)	PUNCT
ejpam-6761	385	53	,	,	PUNCT
ejpam-6761	385	54	p+xy(n2,m2	p+xy(n2,m2	NOUN
ejpam-6761	385	55	)	)	PUNCT
ejpam-6761	385	56	=	=	PRON
ejpam-6761	385	57	ψ+	ψ+	PUNCT
ejpam-6761	385	58	xy(f	xy(f	PUNCT
ejpam-6761	386	1	+	+	ADJ
ejpam-6761	386	2	(	(	PUNCT
ejpam-6761	386	3	n2,m2	n2,m2	PROPN
ejpam-6761	386	4	)	)	PUNCT
ejpam-6761	386	5	)	)	PUNCT
ejpam-6761	386	6	,	,	PUNCT
ejpam-6761	386	7	such	such	ADJ
ejpam-6761	386	8	that	that	SCONJ
ejpam-6761	386	9	:	:	PUNCT
ejpam-6761	386	10	if	if	SCONJ
ejpam-6761	386	11	f−(b−(x	f−(b−(x	NOUN
ejpam-6761	386	12	)	)	PUNCT
ejpam-6761	386	13	,	,	PUNCT
ejpam-6761	386	14	b−(y	b−(y	PROPN
ejpam-6761	386	15	)	)	PUNCT
ejpam-6761	386	16	)	)	PUNCT
ejpam-6761	387	1	=	=	SYM
ejpam-6761	387	2	−1	−1	NOUN
ejpam-6761	387	3	,	,	PUNCT
ejpam-6761	387	4	then	then	ADV
ejpam-6761	387	5	:	:	PUNCT
ejpam-6761	387	6	ψ−	ψ−	VERB
ejpam-6761	387	7	xy(t	xy(t	PUNCT
ejpam-6761	387	8	)	)	PUNCT
ejpam-6761	387	9	=	=	SYM
ejpam-6761	388	1	t	t	PROPN
ejpam-6761	388	2	for	for	ADP
ejpam-6761	388	3	all	all	DET
ejpam-6761	388	4	t	t	NOUN
ejpam-6761	388	5	∈	∈	PROPN
ejpam-6761	389	1	[	[	X
ejpam-6761	389	2	−1	−1	NOUN
ejpam-6761	389	3	,	,	PUNCT
ejpam-6761	389	4	0	0	NUM
ejpam-6761	389	5	]	]	PUNCT
ejpam-6761	389	6	.	.	PUNCT
ejpam-6761	390	1	if	if	SCONJ
ejpam-6761	390	2	f−(b−(x	f−(b−(x	NOUN
ejpam-6761	390	3	)	)	PUNCT
ejpam-6761	390	4	,	,	PUNCT
ejpam-6761	390	5	b−(y	b−(y	PROPN
ejpam-6761	390	6	)	)	PUNCT
ejpam-6761	390	7	)	)	PUNCT
ejpam-6761	391	1	̸=	̸=	PROPN
ejpam-6761	391	2	−1	−1	NOUN
ejpam-6761	391	3	,	,	PUNCT
ejpam-6761	391	4	then	then	ADV
ejpam-6761	391	5	:	:	PUNCT
ejpam-6761	391	6	ψ−	ψ−	VERB
ejpam-6761	391	7	xy(t	xy(t	PUNCT
ejpam-6761	391	8	)	)	PUNCT
ejpam-6761	391	9	=	=	SYM
ejpam-6761	391	10			NUM
ejpam-6761	391	11	b−(xfy	b−(xfy	NOUN
ejpam-6761	391	12	)	)	PUNCT
ejpam-6761	391	13	f−(b−(x	f−(b−(x	NOUN
ejpam-6761	391	14	)	)	PUNCT
ejpam-6761	391	15	,	,	PUNCT
ejpam-6761	391	16	b−(y	b−(y	PROPN
ejpam-6761	391	17	)	)	PUNCT
ejpam-6761	391	18	)	)	PUNCT
ejpam-6761	391	19	·	·	PUNCT
ejpam-6761	392	1	t	t	X
ejpam-6761	392	2	if	if	SCONJ
ejpam-6761	392	3	t	t	PROPN
ejpam-6761	392	4	≤	≤	NUM
ejpam-6761	392	5	f−(b−(x	f−(b−(x	NOUN
ejpam-6761	392	6	)	)	PUNCT
ejpam-6761	392	7	,	,	PUNCT
ejpam-6761	392	8	b−(y	b−(y	PROPN
ejpam-6761	392	9	)	)	PUNCT
ejpam-6761	392	10	)	)	PUNCT
ejpam-6761	392	11	,	,	PUNCT
ejpam-6761	392	12	−1	−1	NOUN
ejpam-6761	393	1	+	+	CCONJ
ejpam-6761	393	2	1	1	NUM
ejpam-6761	393	3	+	+	ADJ
ejpam-6761	393	4	b−(xfy	b−(xfy	NOUN
ejpam-6761	393	5	)	)	PUNCT
ejpam-6761	393	6	1	1	NUM
ejpam-6761	394	1	+	+	CCONJ
ejpam-6761	394	2	f−(b−(x	f−(b−(x	NUM
ejpam-6761	394	3	)	)	PUNCT
ejpam-6761	394	4	,	,	PUNCT
ejpam-6761	394	5	b−(y	b−(y	PROPN
ejpam-6761	394	6	)	)	PUNCT
ejpam-6761	394	7	)	)	PUNCT
ejpam-6761	394	8	·	·	PUNCT
ejpam-6761	394	9	(	(	PUNCT
ejpam-6761	394	10	t+	t+	NOUN
ejpam-6761	394	11	1	1	X
ejpam-6761	394	12	)	)	PUNCT
ejpam-6761	394	13	if	if	SCONJ
ejpam-6761	394	14	t	t	PROPN
ejpam-6761	394	15	≥	≥	PROPN
ejpam-6761	394	16	f−(b−(x	f−(b−(x	PROPN
ejpam-6761	394	17	)	)	PUNCT
ejpam-6761	394	18	,	,	PUNCT
ejpam-6761	394	19	b−(y	b−(y	PROPN
ejpam-6761	394	20	)	)	PUNCT
ejpam-6761	394	21	)	)	PUNCT
ejpam-6761	394	22	.	.	PUNCT
ejpam-6761	395	1	if	if	SCONJ
ejpam-6761	395	2	f+(b+(x	f+(b+(x	PROPN
ejpam-6761	395	3	)	)	PUNCT
ejpam-6761	395	4	,	,	PUNCT
ejpam-6761	395	5	b+(y	b+(y	NUM
ejpam-6761	395	6	)	)	PUNCT
ejpam-6761	395	7	)	)	PUNCT
ejpam-6761	396	1	=	=	PUNCT
ejpam-6761	396	2	1	1	NUM
ejpam-6761	396	3	,	,	PUNCT
ejpam-6761	396	4	then	then	ADV
ejpam-6761	396	5	:	:	PUNCT
ejpam-6761	396	6	ψ+	ψ+	ADJ
ejpam-6761	396	7	xy(k	xy(k	PUNCT
ejpam-6761	396	8	)	)	PUNCT
ejpam-6761	396	9	=	=	SYM
ejpam-6761	396	10	k	k	PROPN
ejpam-6761	396	11	for	for	ADP
ejpam-6761	396	12	all	all	DET
ejpam-6761	396	13	k	k	PROPN
ejpam-6761	396	14	∈	∈	PROPN
ejpam-6761	397	1	[	[	X
ejpam-6761	397	2	0	0	NUM
ejpam-6761	397	3	,	,	PUNCT
ejpam-6761	397	4	1	1	NUM
ejpam-6761	397	5	]	]	PUNCT
ejpam-6761	397	6	.	.	PUNCT
ejpam-6761	398	1	(	(	PUNCT
ejpam-6761	398	2	9	9	X
ejpam-6761	398	3	)	)	PUNCT
ejpam-6761	398	4	if	if	SCONJ
ejpam-6761	398	5	f+(b+(x	f+(b+(x	VERB
ejpam-6761	398	6	)	)	PUNCT
ejpam-6761	398	7	,	,	PUNCT
ejpam-6761	398	8	b+(y	b+(y	NUM
ejpam-6761	398	9	)	)	PUNCT
ejpam-6761	398	10	)	)	PUNCT
ejpam-6761	399	1	̸=	̸=	PROPN
ejpam-6761	399	2	1	1	NUM
ejpam-6761	399	3	,	,	PUNCT
ejpam-6761	399	4	then	then	ADV
ejpam-6761	399	5	:	:	PUNCT
ejpam-6761	399	6	ψ+	ψ+	ADJ
ejpam-6761	399	7	xy(k	xy(k	PUNCT
ejpam-6761	399	8	)	)	PUNCT
ejpam-6761	399	9	=	=	PUNCT
ejpam-6761	399	10			PUNCT
ejpam-6761	399	11	−1	−1	NOUN
ejpam-6761	399	12	+	+	CCONJ
ejpam-6761	399	13	1	1	NUM
ejpam-6761	399	14	+	+	NOUN
ejpam-6761	399	15	b+(xfy	b+(xfy	NOUN
ejpam-6761	399	16	)	)	PUNCT
ejpam-6761	399	17	1	1	NUM
ejpam-6761	399	18	+	+	CCONJ
ejpam-6761	399	19	f+(b+(x	f+(b+(x	X
ejpam-6761	399	20	)	)	PUNCT
ejpam-6761	399	21	,	,	PUNCT
ejpam-6761	399	22	b+(y	b+(y	NUM
ejpam-6761	399	23	)	)	PUNCT
ejpam-6761	399	24	)	)	PUNCT
ejpam-6761	399	25	·	·	PUNCT
ejpam-6761	400	1	(	(	PUNCT
ejpam-6761	400	2	k	k	X
ejpam-6761	400	3	+	+	PROPN
ejpam-6761	400	4	1	1	X
ejpam-6761	400	5	)	)	PUNCT
ejpam-6761	400	6	if	if	SCONJ
ejpam-6761	400	7	k	k	PROPN
ejpam-6761	400	8	≤	≤	X
ejpam-6761	400	9	f+(b+(x	f+(b+(x	X
ejpam-6761	400	10	)	)	PUNCT
ejpam-6761	400	11	,	,	PUNCT
ejpam-6761	400	12	b+(y	b+(y	NUM
ejpam-6761	400	13	)	)	PUNCT
ejpam-6761	400	14	)	)	PUNCT
ejpam-6761	400	15	,	,	PUNCT
ejpam-6761	400	16	b+(xfy	b+(xfy	PROPN
ejpam-6761	400	17	)	)	PUNCT
ejpam-6761	400	18	f+(b+(x	f+(b+(x	PROPN
ejpam-6761	400	19	)	)	PUNCT
ejpam-6761	400	20	,	,	PUNCT
ejpam-6761	400	21	b+(y	b+(y	NUM
ejpam-6761	400	22	)	)	PUNCT
ejpam-6761	400	23	)	)	PUNCT
ejpam-6761	400	24	·	·	PUNCT
ejpam-6761	401	1	k	k	X
ejpam-6761	402	1	if	if	SCONJ
ejpam-6761	402	2	k	k	PROPN
ejpam-6761	402	3	≥	≥	X
ejpam-6761	402	4	f+(b+(x	f+(b+(x	X
ejpam-6761	402	5	)	)	PUNCT
ejpam-6761	402	6	,	,	PUNCT
ejpam-6761	402	7	b+(y	b+(y	NUM
ejpam-6761	402	8	)	)	PUNCT
ejpam-6761	402	9	)	)	PUNCT
ejpam-6761	402	10	.	.	PUNCT
ejpam-6761	403	1	(	(	PUNCT
ejpam-6761	403	2	10	10	NUM
ejpam-6761	403	3	)	)	PUNCT
ejpam-6761	403	4	it	it	PRON
ejpam-6761	403	5	is	be	AUX
ejpam-6761	403	6	clear	clear	ADJ
ejpam-6761	403	7	that	that	SCONJ
ejpam-6761	403	8	ψ−	ψ−	PROPN
ejpam-6761	403	9	xy(n1,m1	xy(n1,m1	NUM
ejpam-6761	403	10	)	)	PUNCT
ejpam-6761	403	11	,	,	PUNCT
ejpam-6761	403	12	ψ	ψ	X
ejpam-6761	403	13	+	+	X
ejpam-6761	403	14	xy(n2,m2	xy(n2,m2	NUM
ejpam-6761	403	15	)	)	PUNCT
ejpam-6761	403	16	:	:	PUNCT
ejpam-6761	404	1	x	x	X
ejpam-6761	404	2	,	,	PUNCT
ejpam-6761	404	3	y	y	PROPN
ejpam-6761	404	4	∈	∈	PROPN
ejpam-6761	404	5	g	g	PROPN
ejpam-6761	404	6	are	be	AUX
ejpam-6761	404	7	continuous	continuous	ADJ
ejpam-6761	404	8	negative	negative	ADJ
ejpam-6761	404	9	and	and	CCONJ
ejpam-6761	404	10	positive	positive	ADJ
ejpam-6761	404	11	comembership	comembership	NOUN
ejpam-6761	404	12	functions	function	NOUN
ejpam-6761	404	13	respectively	respectively	ADV
ejpam-6761	404	14	.	.	PUNCT
ejpam-6761	405	1	moreover	moreover	ADV
ejpam-6761	405	2	,	,	PUNCT
ejpam-6761	405	3	ψ−	ψ−	VERB
ejpam-6761	405	4	xy(n1,m1	xy(n1,m1	PROPN
ejpam-6761	405	5	)	)	PUNCT
ejpam-6761	406	1	=	=	SYM
ejpam-6761	406	2	−1	−1	NOUN
ejpam-6761	406	3	⇐	⇐	ADJ
ejpam-6761	406	4	⇒	⇒	PROPN
ejpam-6761	406	5	n1	n1	NOUN
ejpam-6761	406	6	=	=	SYM
ejpam-6761	406	7	−1	−1	NOUN
ejpam-6761	406	8	or	or	CCONJ
ejpam-6761	406	9	m1	m1	PROPN
ejpam-6761	406	10	=	=	SYM
ejpam-6761	406	11	−1	−1	NOUN
ejpam-6761	406	12	,	,	PUNCT
ejpam-6761	406	13	ψ+	ψ+	ADJ
ejpam-6761	406	14	xy(n2,m2	xy(n2,m2	NUM
ejpam-6761	406	15	)	)	PUNCT
ejpam-6761	406	16	=	=	SYM
ejpam-6761	406	17	1	1	NUM
ejpam-6761	406	18	⇐	⇐	ADJ
ejpam-6761	406	19	⇒	⇒	NOUN
ejpam-6761	406	20	n2	n2	NOUN
ejpam-6761	406	21	=	=	SYM
ejpam-6761	406	22	1	1	NUM
ejpam-6761	406	23	or	or	CCONJ
ejpam-6761	406	24	m2	m2	PROPN
ejpam-6761	406	25	=	=	SYM
ejpam-6761	406	26	1	1	NUM
ejpam-6761	406	27	.	.	PUNCT
ejpam-6761	407	1	hence	hence	ADV
ejpam-6761	407	2	,	,	PUNCT
ejpam-6761	407	3	p	p	PROPN
ejpam-6761	407	4	is	be	AUX
ejpam-6761	407	5	a	a	DET
ejpam-6761	407	6	bipolar	bipolar	ADJ
ejpam-6761	407	7	valued	value	VERB
ejpam-6761	407	8	fuzzy	fuzzy	ADJ
ejpam-6761	407	9	binary	binary	ADJ
ejpam-6761	407	10	operation	operation	NOUN
ejpam-6761	407	11	on	on	ADP
ejpam-6761	407	12	g.	g.	PROPN
ejpam-6761	407	13	f.	f.	PROPN
ejpam-6761	407	14	al	al	PROPN
ejpam-6761	407	15	-	-	PROPN
ejpam-6761	407	16	zu’bi	zu’bi	PROPN
ejpam-6761	407	17	et	et	NOUN
ejpam-6761	407	18	al	al	PROPN
ejpam-6761	407	19	.	.	PUNCT
ejpam-6761	407	20	/	/	SYM
ejpam-6761	407	21	eur	eur	PROPN
ejpam-6761	407	22	.	.	PUNCT
ejpam-6761	408	1	j.	j.	PROPN
ejpam-6761	408	2	pure	pure	PROPN
ejpam-6761	408	3	appl	appl	PROPN
ejpam-6761	408	4	.	.	PROPN
ejpam-6761	408	5	math	math	PROPN
ejpam-6761	408	6	,	,	PUNCT
ejpam-6761	408	7	18	18	NUM
ejpam-6761	408	8	(	(	PUNCT
ejpam-6761	408	9	4	4	NUM
ejpam-6761	408	10	)	)	PUNCT
ejpam-6761	408	11	(	(	PUNCT
ejpam-6761	408	12	2025	2025	NUM
ejpam-6761	408	13	)	)	PUNCT
ejpam-6761	408	14	,	,	PUNCT
ejpam-6761	408	15	6761	6761	NUM
ejpam-6761	408	16	17	17	NUM
ejpam-6761	408	17	of	of	ADP
ejpam-6761	408	18	28	28	NUM
ejpam-6761	408	19	now	now	ADV
ejpam-6761	408	20	,	,	PUNCT
ejpam-6761	408	21	based	base	VERB
ejpam-6761	408	22	on	on	ADP
ejpam-6761	408	23	the	the	DET
ejpam-6761	408	24	property	property	NOUN
ejpam-6761	408	25	of	of	ADP
ejpam-6761	408	26	the	the	DET
ejpam-6761	408	27	given	give	VERB
ejpam-6761	408	28	intersection	intersection	NOUN
ejpam-6761	408	29	bvf	bvf	NOUN
ejpam-6761	408	30	functions	function	NOUN
ejpam-6761	408	31	f−(n1,m1	f−(n1,m1	PROPN
ejpam-6761	408	32	)	)	PUNCT
ejpam-6761	408	33	,	,	PUNCT
ejpam-6761	408	34	f	f	PROPN
ejpam-6761	409	1	+	+	PROPN
ejpam-6761	409	2	(	(	PUNCT
ejpam-6761	409	3	n2,m2	n2,m2	PROPN
ejpam-6761	409	4	)	)	PUNCT
ejpam-6761	409	5	and	and	CCONJ
ejpam-6761	409	6	the	the	DET
ejpam-6761	409	7	construction	construction	NOUN
ejpam-6761	409	8	of	of	ADP
ejpam-6761	409	9	p−xy(n1,m1	p−xy(n1,m1	NOUN
ejpam-6761	409	10	)	)	PUNCT
ejpam-6761	409	11	,	,	PUNCT
ejpam-6761	409	12	p	p	X
ejpam-6761	409	13	+	+	NOUN
ejpam-6761	409	14	xy(n2,m2	xy(n2,m2	NUM
ejpam-6761	409	15	)	)	PUNCT
ejpam-6761	409	16	,	,	PUNCT
ejpam-6761	409	17	we	we	PRON
ejpam-6761	409	18	notice	notice	VERB
ejpam-6761	409	19	that	that	SCONJ
ejpam-6761	409	20	:	:	PUNCT
ejpam-6761	409	21	f−(b−(x	f−(b−(x	X
ejpam-6761	409	22	)	)	PUNCT
ejpam-6761	409	23	,	,	PUNCT
ejpam-6761	409	24	b−(y	b−(y	PROPN
ejpam-6761	409	25	)	)	PUNCT
ejpam-6761	409	26	)	)	PUNCT
ejpam-6761	410	1	̸=	̸=	PROPN
ejpam-6761	410	2	−1	−1	NOUN
ejpam-6761	410	3	whenever	whenever	SCONJ
ejpam-6761	410	4	both	both	DET
ejpam-6761	410	5	b−(x	b−(x	PROPN
ejpam-6761	410	6	)	)	PUNCT
ejpam-6761	410	7	,	,	PUNCT
ejpam-6761	410	8	b−(y	b−(y	PROPN
ejpam-6761	410	9	)	)	PUNCT
ejpam-6761	410	10	̸=	̸=	PROPN
ejpam-6761	410	11	−1	−1	NOUN
ejpam-6761	410	12	,	,	PUNCT
ejpam-6761	410	13	and	and	CCONJ
ejpam-6761	410	14	f+(b+(x	f+(b+(x	X
ejpam-6761	410	15	)	)	PUNCT
ejpam-6761	410	16	,	,	PUNCT
ejpam-6761	410	17	b+(y	b+(y	NUM
ejpam-6761	410	18	)	)	PUNCT
ejpam-6761	410	19	)	)	PUNCT
ejpam-6761	411	1	̸=	̸=	NOUN
ejpam-6761	411	2	1	1	NUM
ejpam-6761	411	3	whenever	whenever	SCONJ
ejpam-6761	411	4	both	both	DET
ejpam-6761	411	5	b+(x	b+(x	ADJ
ejpam-6761	411	6	)	)	PUNCT
ejpam-6761	411	7	,	,	PUNCT
ejpam-6761	411	8	b+(y	b+(y	NUM
ejpam-6761	411	9	)	)	PUNCT
ejpam-6761	411	10	̸=	̸=	PROPN
ejpam-6761	411	11	1	1	NUM
ejpam-6761	411	12	.	.	PUNCT
ejpam-6761	412	1	that	that	PRON
ejpam-6761	412	2	is	be	AUX
ejpam-6761	412	3	,	,	PUNCT
ejpam-6761	412	4	p−xy(b	p−xy(b	ADJ
ejpam-6761	412	5	−(x	−(x	NOUN
ejpam-6761	412	6	)	)	PUNCT
ejpam-6761	412	7	,	,	PUNCT
ejpam-6761	412	8	b−(y	b−(y	PROPN
ejpam-6761	412	9	)	)	PUNCT
ejpam-6761	412	10	)	)	PUNCT
ejpam-6761	413	1	=	=	PRON
ejpam-6761	413	2	ψ−	ψ−	PROPN
ejpam-6761	413	3	xy(f(b	xy(f(b	X
ejpam-6761	413	4	−(x	−(x	NOUN
ejpam-6761	413	5	)	)	PUNCT
ejpam-6761	413	6	,	,	PUNCT
ejpam-6761	413	7	b−(y	b−(y	PROPN
ejpam-6761	413	8	)	)	PUNCT
ejpam-6761	413	9	)	)	PUNCT
ejpam-6761	413	10	)	)	PUNCT
ejpam-6761	414	1	=	=	SYM
ejpam-6761	414	2	b−(xfy	b−(xfy	NOUN
ejpam-6761	414	3	)	)	PUNCT
ejpam-6761	414	4	,	,	PUNCT
ejpam-6761	414	5	(	(	PUNCT
ejpam-6761	414	6	11	11	X
ejpam-6761	414	7	)	)	PUNCT
ejpam-6761	414	8	p+xy(b	p+xy(b	NOUN
ejpam-6761	414	9	+	+	NOUN
ejpam-6761	414	10	(	(	PUNCT
ejpam-6761	414	11	x	x	NOUN
ejpam-6761	414	12	)	)	PUNCT
ejpam-6761	414	13	,	,	PUNCT
ejpam-6761	414	14	b+(y	b+(y	NUM
ejpam-6761	414	15	)	)	PUNCT
ejpam-6761	414	16	)	)	PUNCT
ejpam-6761	415	1	=	=	PRON
ejpam-6761	415	2	ψ+	ψ+	ADJ
ejpam-6761	415	3	xy(f(b	xy(f(b	PUNCT
ejpam-6761	416	1	+	+	ADJ
ejpam-6761	416	2	(	(	PUNCT
ejpam-6761	416	3	x	x	NOUN
ejpam-6761	416	4	)	)	PUNCT
ejpam-6761	416	5	,	,	PUNCT
ejpam-6761	416	6	b+(y	b+(y	NUM
ejpam-6761	416	7	)	)	PUNCT
ejpam-6761	416	8	)	)	PUNCT
ejpam-6761	416	9	)	)	PUNCT
ejpam-6761	417	1	=	=	SYM
ejpam-6761	417	2	b+(xfy	b+(xfy	PROPN
ejpam-6761	417	3	)	)	PUNCT
ejpam-6761	417	4	.	.	PUNCT
ejpam-6761	418	1	(	(	PUNCT
ejpam-6761	418	2	12	12	NUM
ejpam-6761	418	3	)	)	PUNCT
ejpam-6761	418	4	thus	thus	ADV
ejpam-6761	418	5	,	,	PUNCT
ejpam-6761	418	6	by	by	ADP
ejpam-6761	418	7	theorem	theorem	NOUN
ejpam-6761	418	8	5	5	NUM
ejpam-6761	418	9	and	and	CCONJ
ejpam-6761	418	10	the	the	DET
ejpam-6761	418	11	assumption	assumption	NOUN
ejpam-6761	418	12	that	that	SCONJ
ejpam-6761	418	13	(	(	PUNCT
ejpam-6761	418	14	s	s	PROPN
ejpam-6761	418	15	,	,	PUNCT
ejpam-6761	418	16	f	f	PROPN
ejpam-6761	418	17	)	)	PUNCT
ejpam-6761	418	18	is	be	AUX
ejpam-6761	418	19	an	an	DET
ejpam-6761	418	20	ordinary	ordinary	ADJ
ejpam-6761	418	21	subgroup	subgroup	NOUN
ejpam-6761	418	22	,	,	PUNCT
ejpam-6761	418	23	b	b	PROPN
ejpam-6761	418	24	induces	induce	VERB
ejpam-6761	418	25	a	a	DET
ejpam-6761	418	26	bipolar	bipolar	ADJ
ejpam-6761	418	27	valued	value	VERB
ejpam-6761	418	28	fuzzy	fuzzy	ADJ
ejpam-6761	418	29	subgroup	subgroup	NOUN
ejpam-6761	418	30	of	of	ADP
ejpam-6761	418	31	the	the	DET
ejpam-6761	418	32	bipolar	bipolar	ADJ
ejpam-6761	418	33	valued	value	VERB
ejpam-6761	418	34	fuzzy	fuzzy	ADJ
ejpam-6761	418	35	group	group	NOUN
ejpam-6761	418	36	(	(	PUNCT
ejpam-6761	418	37	(	(	PUNCT
ejpam-6761	418	38	g	g	NOUN
ejpam-6761	418	39	,	,	PUNCT
ejpam-6761	418	40	[	[	X
ejpam-6761	418	41	−1	−1	NOUN
ejpam-6761	418	42	,	,	PUNCT
ejpam-6761	418	43	0	0	NUM
ejpam-6761	418	44	]	]	PUNCT
ejpam-6761	418	45	,	,	PUNCT
ejpam-6761	419	1	[	[	X
ejpam-6761	419	2	0	0	NUM
ejpam-6761	419	3	,	,	PUNCT
ejpam-6761	419	4	1	1	NUM
ejpam-6761	419	5	]	]	NUM
ejpam-6761	419	6	)	)	PUNCT
ejpam-6761	419	7	,	,	PUNCT
ejpam-6761	419	8	p	p	NOUN
ejpam-6761	419	9	)	)	PUNCT
ejpam-6761	419	10	.	.	PUNCT
ejpam-6761	420	1	corollary	corollary	ADJ
ejpam-6761	420	2	2	2	NUM
ejpam-6761	420	3	.	.	PUNCT
ejpam-6761	421	1	every	every	DET
ejpam-6761	421	2	classical	classical	ADJ
ejpam-6761	421	3	bipolar	bipolar	NOUN
ejpam-6761	421	4	valued	value	VERB
ejpam-6761	421	5	fuzzy	fuzzy	ADJ
ejpam-6761	421	6	subgroup	subgroup	PROPN
ejpam-6761	421	7	b	b	PROPN
ejpam-6761	421	8	of	of	ADP
ejpam-6761	421	9	(	(	PUNCT
ejpam-6761	421	10	g	g	PROPN
ejpam-6761	421	11	,	,	PUNCT
ejpam-6761	421	12	f	f	PROPN
ejpam-6761	421	13	)	)	PUNCT
ejpam-6761	421	14	induces	induce	VERB
ejpam-6761	421	15	bipolar	bipolar	ADJ
ejpam-6761	421	16	valued	value	VERB
ejpam-6761	421	17	fuzzy	fuzzy	ADJ
ejpam-6761	421	18	subgroups	subgroup	NOUN
ejpam-6761	421	19	relative	relative	ADJ
ejpam-6761	421	20	to	to	ADP
ejpam-6761	421	21	some	some	DET
ejpam-6761	421	22	bipolar	bipolar	ADJ
ejpam-6761	421	23	valued	value	VERB
ejpam-6761	421	24	fuzzy	fuzzy	ADJ
ejpam-6761	421	25	group	group	NOUN
ejpam-6761	421	26	(	(	PUNCT
ejpam-6761	421	27	g	g	NOUN
ejpam-6761	421	28	,	,	PUNCT
ejpam-6761	421	29	p	p	NOUN
ejpam-6761	421	30	)	)	PUNCT
ejpam-6761	421	31	.	.	PUNCT
ejpam-6761	422	1	4	4	X
ejpam-6761	422	2	.	.	X
ejpam-6761	422	3	the	the	DET
ejpam-6761	422	4	normal	normal	ADJ
ejpam-6761	422	5	bipolar	bipolar	ADJ
ejpam-6761	422	6	valued	value	VERB
ejpam-6761	422	7	fuzzy	fuzzy	ADJ
ejpam-6761	422	8	subgroup	subgroup	NOUN
ejpam-6761	422	9	in	in	ADP
ejpam-6761	422	10	this	this	DET
ejpam-6761	422	11	section	section	NOUN
ejpam-6761	422	12	,	,	PUNCT
ejpam-6761	422	13	we	we	PRON
ejpam-6761	422	14	introduce	introduce	VERB
ejpam-6761	422	15	the	the	DET
ejpam-6761	422	16	notion	notion	NOUN
ejpam-6761	422	17	of	of	ADP
ejpam-6761	422	18	the	the	DET
ejpam-6761	422	19	associated	associated	ADJ
ejpam-6761	422	20	bipolar	bipolar	PROPN
ejpam-6761	422	21	valued	value	VERB
ejpam-6761	422	22	fuzzy	fuzzy	ADJ
ejpam-6761	422	23	subgroup	subgroup	NOUN
ejpam-6761	422	24	,	,	PUNCT
ejpam-6761	422	25	then	then	ADV
ejpam-6761	422	26	we	we	PRON
ejpam-6761	422	27	define	define	VERB
ejpam-6761	422	28	the	the	DET
ejpam-6761	422	29	bipolar	bipolar	ADJ
ejpam-6761	422	30	valued	value	VERB
ejpam-6761	422	31	fuzzy	fuzzy	ADJ
ejpam-6761	422	32	normal	normal	ADJ
ejpam-6761	422	33	subgroup	subgroup	NOUN
ejpam-6761	422	34	based	base	VERB
ejpam-6761	422	35	on	on	ADP
ejpam-6761	422	36	the	the	DET
ejpam-6761	422	37	associated	associated	ADJ
ejpam-6761	422	38	bipolar	bipolar	PROPN
ejpam-6761	422	39	valued	value	VERB
ejpam-6761	422	40	fuzzy	fuzzy	ADJ
ejpam-6761	422	41	subgroup	subgroup	NOUN
ejpam-6761	422	42	to	to	PART
ejpam-6761	422	43	obtain	obtain	VERB
ejpam-6761	422	44	interesting	interesting	ADJ
ejpam-6761	422	45	results	result	NOUN
ejpam-6761	422	46	regarding	regard	VERB
ejpam-6761	422	47	abelian	abelian	ADJ
ejpam-6761	422	48	bipolar	bipolar	PROPN
ejpam-6761	422	49	valued	value	VERB
ejpam-6761	422	50	fuzzy	fuzzy	ADJ
ejpam-6761	422	51	groups	group	NOUN
ejpam-6761	422	52	and	and	CCONJ
ejpam-6761	422	53	related	relate	VERB
ejpam-6761	422	54	bipolar	bipolar	ADJ
ejpam-6761	422	55	valued	value	VERB
ejpam-6761	422	56	fuzzy	fuzzy	ADJ
ejpam-6761	422	57	normal	normal	ADJ
ejpam-6761	422	58	subgroups	subgroup	NOUN
ejpam-6761	422	59	.	.	PUNCT
ejpam-6761	423	1	let	let	AUX
ejpam-6761	423	2	(	(	PUNCT
ejpam-6761	423	3	(	(	PUNCT
ejpam-6761	423	4	g	g	NOUN
ejpam-6761	423	5	,	,	PUNCT
ejpam-6761	423	6	[	[	X
ejpam-6761	423	7	−1	−1	NOUN
ejpam-6761	423	8	,	,	PUNCT
ejpam-6761	423	9	0	0	NUM
ejpam-6761	423	10	]	]	PUNCT
ejpam-6761	423	11	,	,	PUNCT
ejpam-6761	423	12	[	[	X
ejpam-6761	423	13	0	0	NUM
ejpam-6761	423	14	,	,	PUNCT
ejpam-6761	423	15	1	1	NUM
ejpam-6761	423	16	]	]	NUM
ejpam-6761	423	17	)	)	PUNCT
ejpam-6761	423	18	,	,	PUNCT
ejpam-6761	423	19	f	f	PROPN
ejpam-6761	423	20	)	)	PUNCT
ejpam-6761	423	21	be	be	AUX
ejpam-6761	423	22	a	a	DET
ejpam-6761	423	23	bipolar	bipolar	ADJ
ejpam-6761	423	24	valued	value	VERB
ejpam-6761	423	25	fuzzy	fuzzy	ADJ
ejpam-6761	423	26	group	group	NOUN
ejpam-6761	423	27	having	have	VERB
ejpam-6761	423	28	the	the	DET
ejpam-6761	423	29	bipolar	bipolar	ADJ
ejpam-6761	423	30	valued	value	VERB
ejpam-6761	423	31	fuzzy	fuzzy	ADJ
ejpam-6761	423	32	subgroup	subgroup	NOUN
ejpam-6761	423	33	(	(	PUNCT
ejpam-6761	423	34	u	u	NOUN
ejpam-6761	423	35	;	;	PUNCT
ejpam-6761	423	36	f	f	PROPN
ejpam-6761	423	37	)	)	PUNCT
ejpam-6761	423	38	.	.	PUNCT
ejpam-6761	424	1	similar	similar	ADJ
ejpam-6761	424	2	to	to	ADP
ejpam-6761	424	3	the	the	DET
ejpam-6761	424	4	fuzzy	fuzzy	ADJ
ejpam-6761	424	5	and	and	CCONJ
ejpam-6761	424	6	intuitionistic	intuitionistic	ADJ
ejpam-6761	424	7	fuzzy	fuzzy	ADJ
ejpam-6761	424	8	case	case	NOUN
ejpam-6761	424	9	and	and	CCONJ
ejpam-6761	424	10	contrary	contrary	ADJ
ejpam-6761	424	11	to	to	ADP
ejpam-6761	424	12	the	the	DET
ejpam-6761	424	13	ordinary	ordinary	ADJ
ejpam-6761	424	14	case	case	NOUN
ejpam-6761	424	15	,	,	PUNCT
ejpam-6761	424	16	bipolar	bipolar	ADJ
ejpam-6761	424	17	valued	value	VERB
ejpam-6761	424	18	fuzzy	fuzzy	ADJ
ejpam-6761	424	19	elements	element	NOUN
ejpam-6761	424	20	of	of	ADP
ejpam-6761	424	21	the	the	DET
ejpam-6761	424	22	bipolar	bipolar	ADJ
ejpam-6761	424	23	valued	value	VERB
ejpam-6761	424	24	fuzzy	fuzzy	ADJ
ejpam-6761	424	25	subgroup	subgroup	NOUN
ejpam-6761	424	26	(	(	PUNCT
ejpam-6761	424	27	u	u	NOUN
ejpam-6761	424	28	;	;	PUNCT
ejpam-6761	424	29	f	f	PROPN
ejpam-6761	424	30	)	)	PUNCT
ejpam-6761	424	31	are	be	AUX
ejpam-6761	424	32	not	not	PART
ejpam-6761	424	33	necessarily	necessarily	ADV
ejpam-6761	424	34	associative	associative	ADJ
ejpam-6761	424	35	with	with	ADP
ejpam-6761	424	36	bipolar	bipolar	ADJ
ejpam-6761	424	37	valued	value	VERB
ejpam-6761	424	38	fuzzy	fuzzy	ADJ
ejpam-6761	424	39	elements	element	NOUN
ejpam-6761	424	40	of	of	ADP
ejpam-6761	424	41	the	the	DET
ejpam-6761	424	42	bipolar	bipolar	ADJ
ejpam-6761	424	43	valued	value	VERB
ejpam-6761	424	44	fuzzy	fuzzy	ADJ
ejpam-6761	424	45	group	group	NOUN
ejpam-6761	424	46	(	(	PUNCT
ejpam-6761	424	47	(	(	PUNCT
ejpam-6761	424	48	g	g	NOUN
ejpam-6761	424	49	,	,	PUNCT
ejpam-6761	424	50	[	[	X
ejpam-6761	424	51	−1	−1	NOUN
ejpam-6761	424	52	,	,	PUNCT
ejpam-6761	424	53	0	0	NUM
ejpam-6761	424	54	]	]	PUNCT
ejpam-6761	424	55	,	,	PUNCT
ejpam-6761	425	1	[	[	X
ejpam-6761	425	2	0	0	NUM
ejpam-6761	425	3	,	,	PUNCT
ejpam-6761	425	4	1	1	NUM
ejpam-6761	425	5	]	]	NUM
ejpam-6761	425	6	)	)	PUNCT
ejpam-6761	425	7	,	,	PUNCT
ejpam-6761	425	8	f	f	PROPN
ejpam-6761	425	9	)	)	PUNCT
ejpam-6761	425	10	.	.	PUNCT
ejpam-6761	426	1	that	that	PRON
ejpam-6761	426	2	is	be	AUX
ejpam-6761	426	3	:	:	PUNCT
ejpam-6761	426	4	αf	αf	X
ejpam-6761	426	5	(	(	PUNCT
ejpam-6761	426	6	βfγ	βfγ	NOUN
ejpam-6761	426	7	)	)	PUNCT
ejpam-6761	426	8	̸=	̸=	PROPN
ejpam-6761	426	9	(	(	PUNCT
ejpam-6761	426	10	αfβ)fγ	αfβ)fγ	NOUN
ejpam-6761	426	11	(	(	PUNCT
ejpam-6761	426	12	13	13	NUM
ejpam-6761	426	13	)	)	PUNCT
ejpam-6761	426	14	where	where	SCONJ
ejpam-6761	426	15	α	α	X
ejpam-6761	426	16	,	,	PUNCT
ejpam-6761	426	17	β	β	X
ejpam-6761	426	18	,	,	PUNCT
ejpam-6761	426	19	γ	γ	NOUN
ejpam-6761	426	20	are	be	AUX
ejpam-6761	426	21	some	some	DET
ejpam-6761	426	22	bipolar	bipolar	ADJ
ejpam-6761	426	23	valued	value	VERB
ejpam-6761	426	24	fuzzy	fuzzy	ADJ
ejpam-6761	426	25	elements	element	NOUN
ejpam-6761	426	26	of	of	ADP
ejpam-6761	426	27	u	u	NOUN
ejpam-6761	426	28	or	or	CCONJ
ejpam-6761	426	29	(	(	PUNCT
ejpam-6761	426	30	g	g	NOUN
ejpam-6761	426	31	,	,	PUNCT
ejpam-6761	426	32	[	[	X
ejpam-6761	426	33	−1	−1	NOUN
ejpam-6761	426	34	,	,	PUNCT
ejpam-6761	426	35	0	0	NUM
ejpam-6761	426	36	]	]	PUNCT
ejpam-6761	426	37	,	,	PUNCT
ejpam-6761	426	38	[	[	X
ejpam-6761	426	39	0	0	NUM
ejpam-6761	426	40	,	,	PUNCT
ejpam-6761	426	41	1	1	NUM
ejpam-6761	426	42	]	]	PUNCT
ejpam-6761	426	43	)	)	PUNCT
ejpam-6761	426	44	such	such	ADJ
ejpam-6761	426	45	that	that	DET
ejpam-6761	426	46	one	one	NUM
ejpam-6761	426	47	or	or	CCONJ
ejpam-6761	426	48	two	two	NUM
ejpam-6761	426	49	of	of	ADP
ejpam-6761	426	50	these	these	DET
ejpam-6761	426	51	elements	element	NOUN
ejpam-6761	426	52	belong	belong	VERB
ejpam-6761	426	53	to	to	ADP
ejpam-6761	426	54	u	u	PROPN
ejpam-6761	426	55	.	.	PUNCT
ejpam-6761	427	1	example	example	NOUN
ejpam-6761	428	1	2	2	NUM
ejpam-6761	428	2	.	.	PUNCT
ejpam-6761	428	3	let	let	VERB
ejpam-6761	428	4	x	x	PUNCT
ejpam-6761	428	5	=	=	PRON
ejpam-6761	428	6	{	{	PUNCT
ejpam-6761	428	7	−1	−1	NOUN
ejpam-6761	428	8	,	,	PUNCT
ejpam-6761	428	9	1,−i	1,−i	NUM
ejpam-6761	428	10	,	,	PUNCT
ejpam-6761	428	11	i	i	PRON
ejpam-6761	428	12	}	}	PUNCT
ejpam-6761	428	13	.	.	PUNCT
ejpam-6761	429	1	define	define	VERB
ejpam-6761	429	2	the	the	DET
ejpam-6761	429	3	bipolar	bipolar	ADJ
ejpam-6761	429	4	valued	value	VERB
ejpam-6761	429	5	fuzzy	fuzzy	ADJ
ejpam-6761	429	6	binary	binary	PROPN
ejpam-6761	429	7	operation	operation	PROPN
ejpam-6761	429	8	f	f	PROPN
ejpam-6761	429	9	=(	=(	PROPN
ejpam-6761	430	1	f	f	PROPN
ejpam-6761	430	2	,	,	PUNCT
ejpam-6761	430	3	f−xy	f−xy	PROPN
ejpam-6761	430	4	,	,	PUNCT
ejpam-6761	430	5	f	f	PROPN
ejpam-6761	431	1	+	+	X
ejpam-6761	431	2	xy	xy	PROPN
ejpam-6761	431	3	)	)	PUNCT
ejpam-6761	431	4	on	on	ADP
ejpam-6761	431	5	(	(	PUNCT
ejpam-6761	431	6	℧	℧	PROPN
ejpam-6761	431	7	,	,	PUNCT
ejpam-6761	431	8	[	[	X
ejpam-6761	431	9	−1	−1	NOUN
ejpam-6761	431	10	,	,	PUNCT
ejpam-6761	431	11	0	0	NUM
ejpam-6761	431	12	]	]	PUNCT
ejpam-6761	431	13	,	,	PUNCT
ejpam-6761	431	14	[	[	X
ejpam-6761	431	15	0	0	NUM
ejpam-6761	431	16	,	,	PUNCT
ejpam-6761	431	17	1	1	NUM
ejpam-6761	431	18	]	]	PUNCT
ejpam-6761	431	19	)	)	PUNCT
ejpam-6761	431	20	such	such	ADJ
ejpam-6761	431	21	that	that	SCONJ
ejpam-6761	431	22	f	f	X
ejpam-6761	431	23	:	:	PUNCT
ejpam-6761	431	24	(	(	PUNCT
ejpam-6761	431	25	℧	℧	PROPN
ejpam-6761	431	26	,	,	PUNCT
ejpam-6761	431	27	[	[	X
ejpam-6761	431	28	−1	−1	NOUN
ejpam-6761	431	29	,	,	PUNCT
ejpam-6761	431	30	0	0	NUM
ejpam-6761	431	31	]	]	PUNCT
ejpam-6761	431	32	,	,	PUNCT
ejpam-6761	431	33	[	[	X
ejpam-6761	431	34	0	0	NUM
ejpam-6761	431	35	,	,	PUNCT
ejpam-6761	431	36	1])×	1])×	PRON
ejpam-6761	431	37	(	(	PUNCT
ejpam-6761	431	38	℧	℧	PROPN
ejpam-6761	431	39	,	,	PUNCT
ejpam-6761	431	40	[	[	X
ejpam-6761	431	41	−1	−1	NOUN
ejpam-6761	431	42	,	,	PUNCT
ejpam-6761	431	43	0	0	NUM
ejpam-6761	431	44	]	]	PUNCT
ejpam-6761	431	45	,	,	PUNCT
ejpam-6761	431	46	[	[	X
ejpam-6761	431	47	0	0	NUM
ejpam-6761	431	48	,	,	PUNCT
ejpam-6761	431	49	1	1	NUM
ejpam-6761	431	50	]	]	NUM
ejpam-6761	431	51	)	)	PUNCT
ejpam-6761	431	52	→	→	PUNCT
ejpam-6761	431	53	(	(	PUNCT
ejpam-6761	431	54	℧	℧	PROPN
ejpam-6761	431	55	,	,	PUNCT
ejpam-6761	431	56	[	[	X
ejpam-6761	431	57	−1	−1	NOUN
ejpam-6761	431	58	,	,	PUNCT
ejpam-6761	431	59	0	0	NUM
ejpam-6761	431	60	]	]	PUNCT
ejpam-6761	431	61	,	,	PUNCT
ejpam-6761	431	62	[	[	X
ejpam-6761	431	63	0	0	NUM
ejpam-6761	431	64	,	,	PUNCT
ejpam-6761	431	65	1	1	NUM
ejpam-6761	431	66	]	]	PUNCT
ejpam-6761	431	67	)	)	PUNCT
ejpam-6761	431	68	is	be	AUX
ejpam-6761	431	69	the	the	DET
ejpam-6761	431	70	ordinary	ordinary	ADJ
ejpam-6761	431	71	multiplication	multiplication	NOUN
ejpam-6761	431	72	of	of	ADP
ejpam-6761	431	73	complex	complex	ADJ
ejpam-6761	431	74	numbers	number	NOUN
ejpam-6761	431	75	and	and	CCONJ
ejpam-6761	431	76	the	the	DET
ejpam-6761	431	77	(	(	PUNCT
ejpam-6761	431	78	negative	negative	ADJ
ejpam-6761	431	79	and	and	CCONJ
ejpam-6761	431	80	positive	positive	ADJ
ejpam-6761	431	81	)	)	PUNCT
ejpam-6761	431	82	comembership	comembership	NOUN
ejpam-6761	431	83	functions	function	NOUN
ejpam-6761	431	84	have	have	VERB
ejpam-6761	431	85	the	the	DET
ejpam-6761	431	86	following	follow	VERB
ejpam-6761	431	87	form	form	NOUN
ejpam-6761	431	88	:	:	PUNCT
ejpam-6761	431	89	f−11(n	f−11(n	NUM
ejpam-6761	431	90	−,m−	−,m−	NOUN
ejpam-6761	431	91	)	)	PUNCT
ejpam-6761	431	92	=	=	SYM
ejpam-6761	432	1			PUNCT
ejpam-6761	432	2	n−	n−	NOUN
ejpam-6761	432	3	·	·	PUNCT
ejpam-6761	432	4	m−	m−	PROPN
ejpam-6761	432	5	β	β	NOUN
ejpam-6761	432	6	if	if	SCONJ
ejpam-6761	432	7	n−	n−	PROPN
ejpam-6761	432	8	·	·	SYM
ejpam-6761	432	9	m−	m−	PROPN
ejpam-6761	432	10	≤	≤	PROPN
ejpam-6761	432	11	β2	β2	VERB
ejpam-6761	432	12	−1	−1	NOUN
ejpam-6761	432	13	+	+	CCONJ
ejpam-6761	432	14	(	(	PUNCT
ejpam-6761	432	15	1	1	NUM
ejpam-6761	432	16	+	+	CCONJ
ejpam-6761	432	17	β	β	X
ejpam-6761	432	18	)	)	PUNCT
ejpam-6761	432	19	·	·	PUNCT
ejpam-6761	433	1	(	(	PUNCT
ejpam-6761	433	2	n−	n−	NOUN
ejpam-6761	433	3	·	·	PUNCT
ejpam-6761	433	4	m−	m−	PROPN
ejpam-6761	433	5	+	+	X
ejpam-6761	433	6	1	1	X
ejpam-6761	433	7	)	)	SYM
ejpam-6761	433	8	1	1	NUM
ejpam-6761	434	1	+	+	CCONJ
ejpam-6761	434	2	β2	β2	VERB
ejpam-6761	434	3	if	if	SCONJ
ejpam-6761	434	4	n−	n−	PROPN
ejpam-6761	434	5	·	·	PUNCT
ejpam-6761	434	6	m−	m−	PROPN
ejpam-6761	434	7	>	>	X
ejpam-6761	434	8	β2	β2	PROPN
ejpam-6761	434	9	(	(	PUNCT
ejpam-6761	434	10	14	14	NUM
ejpam-6761	434	11	)	)	PUNCT
ejpam-6761	434	12	f.	f.	PROPN
ejpam-6761	434	13	al	al	PROPN
ejpam-6761	434	14	-	-	PROPN
ejpam-6761	434	15	zu’bi	zu’bi	PROPN
ejpam-6761	434	16	et	et	NOUN
ejpam-6761	434	17	al	al	PROPN
ejpam-6761	434	18	.	.	PUNCT
ejpam-6761	434	19	/	/	SYM
ejpam-6761	434	20	eur	eur	PROPN
ejpam-6761	434	21	.	.	PUNCT
ejpam-6761	435	1	j.	j.	PROPN
ejpam-6761	435	2	pure	pure	PROPN
ejpam-6761	435	3	appl	appl	PROPN
ejpam-6761	435	4	.	.	PROPN
ejpam-6761	435	5	math	math	PROPN
ejpam-6761	435	6	,	,	PUNCT
ejpam-6761	435	7	18	18	NUM
ejpam-6761	435	8	(	(	PUNCT
ejpam-6761	435	9	4	4	NUM
ejpam-6761	435	10	)	)	PUNCT
ejpam-6761	435	11	(	(	PUNCT
ejpam-6761	435	12	2025	2025	NUM
ejpam-6761	435	13	)	)	PUNCT
ejpam-6761	435	14	,	,	PUNCT
ejpam-6761	435	15	6761	6761	NUM
ejpam-6761	435	16	18	18	NUM
ejpam-6761	435	17	of	of	ADP
ejpam-6761	435	18	28	28	NUM
ejpam-6761	435	19	f+11(n	f+11(n	NOUN
ejpam-6761	435	20	+	+	ADJ
ejpam-6761	435	21	,	,	PUNCT
ejpam-6761	435	22	m+	m+	NUM
ejpam-6761	435	23	)	)	PUNCT
ejpam-6761	435	24	=	=	PUNCT
ejpam-6761	436	1			PRON
ejpam-6761	436	2	−1	−1	NOUN
ejpam-6761	437	1	+	+	CCONJ
ejpam-6761	438	1	(	(	PUNCT
ejpam-6761	438	2	1	1	NUM
ejpam-6761	438	3	+	+	NUM
ejpam-6761	438	4	α	α	NOUN
ejpam-6761	438	5	)	)	PUNCT
ejpam-6761	438	6	·	·	PUNCT
ejpam-6761	438	7	(	(	PUNCT
ejpam-6761	438	8	n+	n+	X
ejpam-6761	438	9	·	·	PUNCT
ejpam-6761	438	10	m+	m+	NOUN
ejpam-6761	438	11	+	+	NOUN
ejpam-6761	438	12	1	1	X
ejpam-6761	438	13	)	)	SYM
ejpam-6761	438	14	1	1	NUM
ejpam-6761	439	1	+	+	CCONJ
ejpam-6761	439	2	α2	α2	ADJ
ejpam-6761	439	3	if	if	SCONJ
ejpam-6761	439	4	n+	n+	NUM
ejpam-6761	439	5	·	·	PUNCT
ejpam-6761	439	6	m+	m+	NUM
ejpam-6761	439	7	>	>	X
ejpam-6761	439	8	α2	α2	PROPN
ejpam-6761	439	9	n+	n+	NUM
ejpam-6761	439	10	·	·	PUNCT
ejpam-6761	439	11	m+	m+	NUM
ejpam-6761	439	12	α	α	NOUN
ejpam-6761	439	13	if	if	SCONJ
ejpam-6761	439	14	n+	n+	NUM
ejpam-6761	439	15	·	·	PUNCT
ejpam-6761	439	16	m+	m+	NUM
ejpam-6761	439	17	≤	≤	ADV
ejpam-6761	439	18	α2	α2	NOUN
ejpam-6761	439	19	(	(	PUNCT
ejpam-6761	439	20	15	15	NUM
ejpam-6761	439	21	)	)	PUNCT
ejpam-6761	439	22	f−−11(n	f−−11(n	VERB
ejpam-6761	439	23	−,m−	−,m−	NOUN
ejpam-6761	439	24	)	)	PUNCT
ejpam-6761	440	1	=	=	SYM
ejpam-6761	440	2	f−1−1(n	f−1−1(n	NOUN
ejpam-6761	440	3	−,m−	−,m−	PROPN
ejpam-6761	440	4	)	)	PUNCT
ejpam-6761	440	5	=	=	PUNCT
ejpam-6761	441	1			PRON
ejpam-6761	441	2	n−	n−	PROPN
ejpam-6761	441	3	·	·	PUNCT
ejpam-6761	441	4	m−	m−	PROPN
ejpam-6761	441	5	−α	−α	NOUN
ejpam-6761	441	6	if	if	SCONJ
ejpam-6761	441	7	−	−	PROPN
ejpam-6761	441	8	n−	n−	PROPN
ejpam-6761	441	9	·	·	PUNCT
ejpam-6761	441	10	m−	m−	PROPN
ejpam-6761	441	11	≤	≤	NUM
ejpam-6761	441	12	αβ	αβ	DET
ejpam-6761	441	13	−1	−1	NOUN
ejpam-6761	442	1	+	+	CCONJ
ejpam-6761	442	2	(	(	PUNCT
ejpam-6761	442	3	1	1	NUM
ejpam-6761	442	4	+	+	CCONJ
ejpam-6761	442	5	β	β	X
ejpam-6761	442	6	)	)	PUNCT
ejpam-6761	442	7	·	·	PUNCT
ejpam-6761	442	8	(	(	PUNCT
ejpam-6761	442	9	n−	n−	NOUN
ejpam-6761	442	10	·	·	PUNCT
ejpam-6761	442	11	m−	m−	PROPN
ejpam-6761	442	12	+	+	CCONJ
ejpam-6761	443	1	1	1	X
ejpam-6761	443	2	)	)	PUNCT
ejpam-6761	443	3	1−	1−	NUM
ejpam-6761	444	1	αβ	αβ	INTJ
ejpam-6761	444	2	if	if	SCONJ
ejpam-6761	444	3	−	−	PROPN
ejpam-6761	444	4	n−	n−	PROPN
ejpam-6761	444	5	·	·	PUNCT
ejpam-6761	444	6	m−	m−	PROPN
ejpam-6761	444	7	>	>	X
ejpam-6761	445	1	αβ	αβ	INTJ
ejpam-6761	445	2	(	(	PUNCT
ejpam-6761	445	3	16	16	NUM
ejpam-6761	445	4	)	)	PUNCT
ejpam-6761	445	5	f+−11(n	f+−11(n	PROPN
ejpam-6761	445	6	+	+	PROPN
ejpam-6761	445	7	,	,	PUNCT
ejpam-6761	445	8	m+	m+	NUM
ejpam-6761	445	9	)	)	PUNCT
ejpam-6761	445	10	=	=	SYM
ejpam-6761	446	1	f+1−1(n	f+1−1(n	PROPN
ejpam-6761	446	2	+	+	PROPN
ejpam-6761	446	3	,	,	PUNCT
ejpam-6761	446	4	m+	m+	NUM
ejpam-6761	446	5	)	)	PUNCT
ejpam-6761	446	6	=	=	PUNCT
ejpam-6761	446	7			PUNCT
ejpam-6761	446	8	−1	−1	NOUN
ejpam-6761	447	1	+	+	CCONJ
ejpam-6761	447	2	(	(	PUNCT
ejpam-6761	447	3	1	1	NUM
ejpam-6761	447	4	+	+	NUM
ejpam-6761	447	5	α	α	NOUN
ejpam-6761	447	6	)	)	PUNCT
ejpam-6761	447	7	·	·	PUNCT
ejpam-6761	447	8	(	(	PUNCT
ejpam-6761	447	9	n+	n+	X
ejpam-6761	447	10	·	·	PUNCT
ejpam-6761	447	11	m+	m+	NOUN
ejpam-6761	447	12	+	+	NOUN
ejpam-6761	447	13	1	1	NUM
ejpam-6761	447	14	)	)	PUNCT
ejpam-6761	447	15	1−	1−	NUM
ejpam-6761	448	1	αβ	αβ	INTJ
ejpam-6761	448	2	if	if	SCONJ
ejpam-6761	448	3	n+	n+	NUM
ejpam-6761	448	4	·	·	PUNCT
ejpam-6761	448	5	m+	m+	NOUN
ejpam-6761	448	6	>	>	X
ejpam-6761	448	7	−αβ	−αβ	PROPN
ejpam-6761	448	8	n+	n+	PUNCT
ejpam-6761	448	9	·	·	PUNCT
ejpam-6761	448	10	m+	m+	NOUN
ejpam-6761	448	11	−β	−β	NOUN
ejpam-6761	448	12	if	if	SCONJ
ejpam-6761	448	13	n+	n+	NUM
ejpam-6761	448	14	·	·	PUNCT
ejpam-6761	448	15	m+	m+	NUM
ejpam-6761	448	16	≤	≤	NUM
ejpam-6761	448	17	−αβ	−αβ	PROPN
ejpam-6761	448	18	(	(	PUNCT
ejpam-6761	448	19	17	17	NUM
ejpam-6761	448	20	)	)	PUNCT
ejpam-6761	448	21	and	and	CCONJ
ejpam-6761	448	22	the	the	DET
ejpam-6761	448	23	other	other	ADJ
ejpam-6761	448	24	negative	negative	ADJ
ejpam-6761	448	25	and	and	CCONJ
ejpam-6761	448	26	positive	positive	ADJ
ejpam-6761	448	27	comembership	comembership	NOUN
ejpam-6761	448	28	functions	function	NOUN
ejpam-6761	448	29	are	be	AUX
ejpam-6761	448	30	defined	define	VERB
ejpam-6761	448	31	by	by	ADP
ejpam-6761	448	32	the	the	DET
ejpam-6761	448	33	product	product	NOUN
ejpam-6761	448	34	n−·m−	n−·m−	ADV
ejpam-6761	448	35	and	and	CCONJ
ejpam-6761	448	36	n+·m+	n+·m+	NOUN
ejpam-6761	448	37	,	,	PUNCT
ejpam-6761	448	38	where	where	SCONJ
ejpam-6761	448	39	α	α	X
ejpam-6761	448	40	,	,	PUNCT
ejpam-6761	448	41	β	β	X
ejpam-6761	448	42	are	be	AUX
ejpam-6761	448	43	given	give	VERB
ejpam-6761	448	44	fixed	fix	VERB
ejpam-6761	448	45	real	real	ADJ
ejpam-6761	448	46	numbers	number	NOUN
ejpam-6761	448	47	satisfying	satisfy	VERB
ejpam-6761	448	48	−1	−1	NOUN
ejpam-6761	448	49	<	<	X
ejpam-6761	448	50	β	β	X
ejpam-6761	448	51	<	<	X
ejpam-6761	448	52	0	0	PUNCT
ejpam-6761	448	53	<	<	X
ejpam-6761	448	54	α	α	X
ejpam-6761	448	55	<	<	X
ejpam-6761	448	56	1	1	NUM
ejpam-6761	448	57	.	.	PUNCT
ejpam-6761	449	1	clearly	clearly	ADV
ejpam-6761	449	2	(	(	PUNCT
ejpam-6761	449	3	(	(	PUNCT
ejpam-6761	449	4	℧	℧	PROPN
ejpam-6761	449	5	,	,	PUNCT
ejpam-6761	449	6	[	[	X
ejpam-6761	449	7	−1	−1	NOUN
ejpam-6761	449	8	,	,	PUNCT
ejpam-6761	449	9	0	0	NUM
ejpam-6761	449	10	]	]	PUNCT
ejpam-6761	449	11	,	,	PUNCT
ejpam-6761	449	12	[	[	X
ejpam-6761	449	13	0	0	NUM
ejpam-6761	449	14	,	,	PUNCT
ejpam-6761	449	15	1	1	NUM
ejpam-6761	449	16	]	]	NUM
ejpam-6761	449	17	)	)	PUNCT
ejpam-6761	449	18	,	,	PUNCT
ejpam-6761	449	19	f	f	PROPN
ejpam-6761	449	20	)	)	PUNCT
ejpam-6761	449	21	defines	define	VERB
ejpam-6761	449	22	a	a	DET
ejpam-6761	449	23	non	non	ADJ
ejpam-6761	449	24	-	-	ADJ
ejpam-6761	449	25	uniform	uniform	ADJ
ejpam-6761	449	26	bipolar	bipolar	ADJ
ejpam-6761	449	27	valued	value	VERB
ejpam-6761	449	28	fuzzy	fuzzy	ADJ
ejpam-6761	449	29	group	group	NOUN
ejpam-6761	449	30	.	.	PUNCT
ejpam-6761	450	1	also	also	ADV
ejpam-6761	450	2	the	the	DET
ejpam-6761	450	3	bipolar	bipolar	ADJ
ejpam-6761	450	4	valued	value	VERB
ejpam-6761	450	5	fuzzy	fuzzy	ADJ
ejpam-6761	450	6	subspace	subspace	NOUN
ejpam-6761	450	7	u	u	NOUN
ejpam-6761	450	8	=	=	X
ejpam-6761	450	9	{	{	PUNCT
ejpam-6761	450	10	(	(	PUNCT
ejpam-6761	450	11	−1,−0.3	−1,−0.3	PROPN
ejpam-6761	450	12	,	,	PUNCT
ejpam-6761	450	13	0.5	0.5	NUM
ejpam-6761	450	14	)	)	PUNCT
ejpam-6761	450	15	,	,	PUNCT
ejpam-6761	450	16	(	(	PUNCT
ejpam-6761	450	17	1,−0.6	1,−0.6	NUM
ejpam-6761	450	18	,	,	PUNCT
ejpam-6761	450	19	0.7	0.7	NUM
ejpam-6761	450	20	)	)	PUNCT
ejpam-6761	450	21	}	}	PUNCT
ejpam-6761	450	22	together	together	ADV
ejpam-6761	450	23	with	with	ADP
ejpam-6761	450	24	the	the	DET
ejpam-6761	450	25	bipolar	bipolar	PROPN
ejpam-6761	450	26	valued	value	VERB
ejpam-6761	450	27	fuzzy	fuzzy	ADJ
ejpam-6761	450	28	binary	binary	PROPN
ejpam-6761	450	29	operation	operation	NOUN
ejpam-6761	450	30	f	f	PROPN
ejpam-6761	450	31	define	define	VERB
ejpam-6761	450	32	a	a	DET
ejpam-6761	450	33	bipolar	bipolar	ADJ
ejpam-6761	450	34	valued	value	VERB
ejpam-6761	450	35	fuzzy	fuzzy	ADJ
ejpam-6761	450	36	subgroup	subgroup	NOUN
ejpam-6761	450	37	of	of	ADP
ejpam-6761	450	38	(	(	PUNCT
ejpam-6761	450	39	(	(	PUNCT
ejpam-6761	450	40	℧	℧	PROPN
ejpam-6761	450	41	,	,	PUNCT
ejpam-6761	450	42	[	[	X
ejpam-6761	450	43	−1	−1	NOUN
ejpam-6761	450	44	,	,	PUNCT
ejpam-6761	450	45	0	0	NUM
ejpam-6761	450	46	]	]	PUNCT
ejpam-6761	450	47	,	,	PUNCT
ejpam-6761	451	1	[	[	X
ejpam-6761	451	2	0	0	NUM
ejpam-6761	451	3	,	,	PUNCT
ejpam-6761	451	4	1	1	NUM
ejpam-6761	451	5	]	]	NUM
ejpam-6761	451	6	)	)	PUNCT
ejpam-6761	451	7	,	,	PUNCT
ejpam-6761	451	8	f	f	PROPN
ejpam-6761	451	9	)	)	PUNCT
ejpam-6761	451	10	.	.	PUNCT
ejpam-6761	452	1	let	let	VERB
ejpam-6761	452	2	β	β	NOUN
ejpam-6761	452	3	=	=	SYM
ejpam-6761	452	4	−0.3	−0.3	PROPN
ejpam-6761	452	5	and	and	CCONJ
ejpam-6761	452	6	α	α	NOUN
ejpam-6761	452	7	=	=	NOUN
ejpam-6761	452	8	0.4	0.4	NUM
ejpam-6761	452	9	and	and	CCONJ
ejpam-6761	452	10	we	we	PRON
ejpam-6761	452	11	need	need	VERB
ejpam-6761	452	12	to	to	PART
ejpam-6761	452	13	show	show	VERB
ejpam-6761	452	14	that	that	SCONJ
ejpam-6761	452	15	(	(	PUNCT
ejpam-6761	452	16	(	(	PUNCT
ejpam-6761	452	17	1,−0.6	1,−0.6	NUM
ejpam-6761	452	18	,	,	PUNCT
ejpam-6761	452	19	0.7)f	0.7)f	NUM
ejpam-6761	452	20	(	(	PUNCT
ejpam-6761	452	21	1,−0.6	1,−0.6	NUM
ejpam-6761	452	22	,	,	PUNCT
ejpam-6761	452	23	0.7))f	0.7))f	NUM
ejpam-6761	452	24	(	(	PUNCT
ejpam-6761	452	25	−1,−0.3	−1,−0.3	PROPN
ejpam-6761	452	26	,	,	PUNCT
ejpam-6761	452	27	0.5	0.5	NUM
ejpam-6761	452	28	)	)	PUNCT
ejpam-6761	452	29	̸=	̸=	PROPN
ejpam-6761	452	30	(	(	PUNCT
ejpam-6761	452	31	1,−0.6	1,−0.6	NUM
ejpam-6761	452	32	,	,	PUNCT
ejpam-6761	452	33	0.7)f	0.7)f	NUM
ejpam-6761	452	34	(	(	PUNCT
ejpam-6761	452	35	(	(	PUNCT
ejpam-6761	452	36	1,−0.6	1,−0.6	NUM
ejpam-6761	452	37	,	,	PUNCT
ejpam-6761	452	38	0.7)f	0.7)f	NUM
ejpam-6761	452	39	(	(	PUNCT
ejpam-6761	452	40	−1,−0.3	−1,−0.3	NOUN
ejpam-6761	452	41	,	,	PUNCT
ejpam-6761	452	42	0.5	0.5	NUM
ejpam-6761	452	43	)	)	PUNCT
ejpam-6761	452	44	)	)	PUNCT
ejpam-6761	453	1	so	so	ADV
ejpam-6761	453	2	we	we	PRON
ejpam-6761	453	3	have	have	VERB
ejpam-6761	453	4	,	,	PUNCT
ejpam-6761	453	5	f−11(−0.6,−0.6	f−11(−0.6,−0.6	ADJ
ejpam-6761	453	6	)	)	PUNCT
ejpam-6761	453	7	=	=	SYM
ejpam-6761	453	8	−1	−1	NOUN
ejpam-6761	453	9	+	+	CCONJ
ejpam-6761	453	10	(	(	PUNCT
ejpam-6761	453	11	0.7)((0.36	0.7)((0.36	NOUN
ejpam-6761	453	12	)	)	PUNCT
ejpam-6761	454	1	+	+	CCONJ
ejpam-6761	454	2	1	1	X
ejpam-6761	454	3	)	)	PUNCT
ejpam-6761	454	4	1	1	NUM
ejpam-6761	455	1	+	+	NUM
ejpam-6761	455	2	0.09	0.09	NUM
ejpam-6761	455	3	=	=	SYM
ejpam-6761	455	4	−1	−1	NOUN
ejpam-6761	455	5	+	+	NOUN
ejpam-6761	455	6	0.873	0.873	NUM
ejpam-6761	455	7	=	=	SYM
ejpam-6761	455	8	−0.126	−0.126	NOUN
ejpam-6761	455	9	f+11(0.7	f+11(0.7	PROPN
ejpam-6761	455	10	,	,	PUNCT
ejpam-6761	455	11	0.7	0.7	NUM
ejpam-6761	455	12	)	)	PUNCT
ejpam-6761	455	13	=	=	SYM
ejpam-6761	455	14	−1	−1	NOUN
ejpam-6761	455	15	+	+	CCONJ
ejpam-6761	455	16	(	(	PUNCT
ejpam-6761	455	17	1.4)((0.49	1.4)((0.49	NUM
ejpam-6761	455	18	)	)	PUNCT
ejpam-6761	455	19	+	+	NOUN
ejpam-6761	455	20	1	1	X
ejpam-6761	455	21	)	)	PUNCT
ejpam-6761	455	22	1	1	NUM
ejpam-6761	456	1	+	+	CCONJ
ejpam-6761	456	2	0.16	0.16	NUM
ejpam-6761	456	3	=	=	SYM
ejpam-6761	456	4	−1	−1	NOUN
ejpam-6761	456	5	+	+	CCONJ
ejpam-6761	456	6	1.798	1.798	NUM
ejpam-6761	456	7	=	=	NUM
ejpam-6761	456	8	0.798	0.798	NUM
ejpam-6761	456	9	f−−11(−0.3,−0.6	f−−11(−0.3,−0.6	ADJ
ejpam-6761	456	10	)	)	PUNCT
ejpam-6761	456	11	=	=	SYM
ejpam-6761	456	12	f−1−1(−0.6,−0.3	f−1−1(−0.6,−0.3	PROPN
ejpam-6761	456	13	)	)	PUNCT
ejpam-6761	456	14	=	=	SYM
ejpam-6761	456	15	(	(	PUNCT
ejpam-6761	456	16	n−.m−	n−.m−	NOUN
ejpam-6761	456	17	)	)	PUNCT
ejpam-6761	456	18	−α	−α	NOUN
ejpam-6761	456	19	=	=	SYM
ejpam-6761	456	20	(	(	PUNCT
ejpam-6761	456	21	−0.6)(−0.3	−0.6)(−0.3	NOUN
ejpam-6761	456	22	)	)	PUNCT
ejpam-6761	456	23	−0.4	−0.4	NUM
ejpam-6761	457	1	=	=	PUNCT
ejpam-6761	458	1	−0.45	−0.45	NOUN
ejpam-6761	458	2	f+−11(0.5	f+−11(0.5	NOUN
ejpam-6761	458	3	,	,	PUNCT
ejpam-6761	458	4	0.7	0.7	NUM
ejpam-6761	458	5	)	)	PUNCT
ejpam-6761	458	6	=	=	NOUN
ejpam-6761	458	7	f+1−1(0.7	f+1−1(0.7	NOUN
ejpam-6761	458	8	,	,	PUNCT
ejpam-6761	458	9	0.5	0.5	NUM
ejpam-6761	458	10	)	)	PUNCT
ejpam-6761	458	11	=	=	SYM
ejpam-6761	458	12	−1	−1	NOUN
ejpam-6761	458	13	+	+	CCONJ
ejpam-6761	458	14	(	(	PUNCT
ejpam-6761	458	15	1.4)((0.35	1.4)((0.35	NUM
ejpam-6761	458	16	)	)	PUNCT
ejpam-6761	458	17	+	+	CCONJ
ejpam-6761	458	18	1	1	X
ejpam-6761	458	19	)	)	PUNCT
ejpam-6761	458	20	1	1	NUM
ejpam-6761	459	1	+	+	NUM
ejpam-6761	459	2	0.12	0.12	NUM
ejpam-6761	459	3	=	=	SYM
ejpam-6761	459	4	−1	−1	NOUN
ejpam-6761	459	5	+	+	X
ejpam-6761	460	1	1.6875	1.6875	NUM
ejpam-6761	460	2	=	=	SYM
ejpam-6761	460	3	0.6875	0.6875	NUM
ejpam-6761	460	4	f−11,−1(−0.126,−0.3	f−11,−1(−0.126,−0.3	NOUN
ejpam-6761	460	5	)	)	PUNCT
ejpam-6761	460	6	=	=	SYM
ejpam-6761	460	7	−1	−1	NOUN
ejpam-6761	460	8	+	+	CCONJ
ejpam-6761	460	9	(	(	PUNCT
ejpam-6761	460	10	0.7)((0.0378	0.7)((0.0378	NUM
ejpam-6761	460	11	)	)	PUNCT
ejpam-6761	460	12	+	+	CCONJ
ejpam-6761	460	13	1	1	X
ejpam-6761	460	14	)	)	PUNCT
ejpam-6761	460	15	1	1	NUM
ejpam-6761	460	16	+	+	NUM
ejpam-6761	460	17	0.12	0.12	NUM
ejpam-6761	460	18	=	=	SYM
ejpam-6761	460	19	−1	−1	NOUN
ejpam-6761	460	20	+	+	NOUN
ejpam-6761	460	21	0.6486	0.6486	NUM
ejpam-6761	460	22	=	=	SYM
ejpam-6761	460	23	−0.351	−0.351	NOUN
ejpam-6761	460	24	f+11,−1(0.798	f+11,−1(0.798	ADP
ejpam-6761	460	25	,	,	PUNCT
ejpam-6761	460	26	0.5	0.5	NUM
ejpam-6761	460	27	)	)	PUNCT
ejpam-6761	460	28	=	=	SYM
ejpam-6761	460	29	−1	−1	NOUN
ejpam-6761	460	30	+	+	CCONJ
ejpam-6761	460	31	(	(	PUNCT
ejpam-6761	460	32	1.4)((0.399	1.4)((0.399	NUM
ejpam-6761	460	33	)	)	PUNCT
ejpam-6761	461	1	+	+	CCONJ
ejpam-6761	462	1	1	1	X
ejpam-6761	462	2	)	)	PUNCT
ejpam-6761	462	3	1	1	NUM
ejpam-6761	462	4	+	+	NUM
ejpam-6761	462	5	0.12	0.12	NUM
ejpam-6761	462	6	=	=	SYM
ejpam-6761	462	7	−1	−1	NOUN
ejpam-6761	462	8	+	+	NOUN
ejpam-6761	462	9	1.7487	1.7487	NUM
ejpam-6761	462	10	=	=	SYM
ejpam-6761	462	11	0.74875	0.74875	NUM
ejpam-6761	462	12	f−1−1,1(−0.45,−0.6	f−1−1,1(−0.45,−0.6	NOUN
ejpam-6761	462	13	)	)	PUNCT
ejpam-6761	462	14	=	=	SYM
ejpam-6761	462	15	(	(	PUNCT
ejpam-6761	462	16	−0.45)(−0.6	−0.45)(−0.6	NOUN
ejpam-6761	462	17	)	)	PUNCT
ejpam-6761	462	18	−0.4	−0.4	PUNCT
ejpam-6761	463	1	=	=	PUNCT
ejpam-6761	464	1	−0.675	−0.675	NOUN
ejpam-6761	464	2	f+1−1,1(0.6875	f+1−1,1(0.6875	NOUN
ejpam-6761	464	3	,	,	PUNCT
ejpam-6761	464	4	0.7	0.7	NUM
ejpam-6761	464	5	)	)	PUNCT
ejpam-6761	464	6	=	=	SYM
ejpam-6761	464	7	−1	−1	NOUN
ejpam-6761	464	8	+	+	CCONJ
ejpam-6761	464	9	(	(	PUNCT
ejpam-6761	464	10	1.4)((0.481	1.4)((0.481	NUM
ejpam-6761	464	11	)	)	PUNCT
ejpam-6761	465	1	+	+	CCONJ
ejpam-6761	465	2	1	1	X
ejpam-6761	465	3	)	)	PUNCT
ejpam-6761	465	4	1	1	NUM
ejpam-6761	465	5	+	+	NUM
ejpam-6761	465	6	0.12	0.12	NUM
ejpam-6761	465	7	=	=	SYM
ejpam-6761	465	8	−1	−1	NOUN
ejpam-6761	465	9	+	+	NUM
ejpam-6761	465	10	1.851	1.851	NUM
ejpam-6761	465	11	=	=	SYM
ejpam-6761	465	12	0.851	0.851	NUM
ejpam-6761	465	13	f.	f.	PROPN
ejpam-6761	465	14	al	al	PROPN
ejpam-6761	465	15	-	-	PROPN
ejpam-6761	465	16	zu’bi	zu’bi	PROPN
ejpam-6761	465	17	et	et	NOUN
ejpam-6761	465	18	al	al	PROPN
ejpam-6761	465	19	.	.	PUNCT
ejpam-6761	465	20	/	/	SYM
ejpam-6761	465	21	eur	eur	PROPN
ejpam-6761	465	22	.	.	PUNCT
ejpam-6761	466	1	j.	j.	PROPN
ejpam-6761	466	2	pure	pure	PROPN
ejpam-6761	466	3	appl	appl	PROPN
ejpam-6761	466	4	.	.	PROPN
ejpam-6761	466	5	math	math	PROPN
ejpam-6761	466	6	,	,	PUNCT
ejpam-6761	466	7	18	18	NUM
ejpam-6761	466	8	(	(	PUNCT
ejpam-6761	466	9	4	4	NUM
ejpam-6761	466	10	)	)	PUNCT
ejpam-6761	466	11	(	(	PUNCT
ejpam-6761	466	12	2025	2025	NUM
ejpam-6761	466	13	)	)	PUNCT
ejpam-6761	466	14	,	,	PUNCT
ejpam-6761	466	15	6761	6761	NUM
ejpam-6761	466	16	19	19	NUM
ejpam-6761	466	17	of	of	ADP
ejpam-6761	466	18	28	28	NUM
ejpam-6761	466	19	so	so	ADV
ejpam-6761	466	20	,	,	PUNCT
ejpam-6761	466	21	(	(	PUNCT
ejpam-6761	466	22	(	(	PUNCT
ejpam-6761	466	23	(	(	PUNCT
ejpam-6761	466	24	1,−0.6	1,−0.6	NUM
ejpam-6761	466	25	,	,	PUNCT
ejpam-6761	466	26	0.7))f(1,−0.6	0.7))f(1,−0.6	NUM
ejpam-6761	466	27	,	,	PUNCT
ejpam-6761	466	28	0.7))f	0.7))f	NUM
ejpam-6761	466	29	(	(	PUNCT
ejpam-6761	466	30	−1,−0.3	−1,−0.3	PROPN
ejpam-6761	466	31	,	,	PUNCT
ejpam-6761	466	32	0.5	0.5	NUM
ejpam-6761	466	33	)	)	PUNCT
ejpam-6761	466	34	=	=	SYM
ejpam-6761	466	35	(	(	PUNCT
ejpam-6761	466	36	(	(	PUNCT
ejpam-6761	466	37	1f1)f	1f1)f	NUM
ejpam-6761	466	38	−	−	NOUN
ejpam-6761	466	39	1,−0.351	1,−0.351	NUM
ejpam-6761	466	40	,	,	PUNCT
ejpam-6761	466	41	0.74875	0.74875	NUM
ejpam-6761	466	42	)	)	PUNCT
ejpam-6761	466	43	̸=	̸=	PROPN
ejpam-6761	466	44	(	(	PUNCT
ejpam-6761	466	45	(	(	PUNCT
ejpam-6761	466	46	(	(	PUNCT
ejpam-6761	466	47	1,−0.6	1,−0.6	NUM
ejpam-6761	466	48	,	,	PUNCT
ejpam-6761	466	49	0.7))f	0.7))f	NUM
ejpam-6761	466	50	(	(	PUNCT
ejpam-6761	466	51	−1,−0.3	−1,−0.3	PROPN
ejpam-6761	466	52	,	,	PUNCT
ejpam-6761	466	53	0.5))f	0.5))f	PROPN
ejpam-6761	466	54	(	(	PUNCT
ejpam-6761	466	55	−1,−0.6	−1,−0.6	PROPN
ejpam-6761	466	56	,	,	PUNCT
ejpam-6761	466	57	0.7	0.7	NUM
ejpam-6761	466	58	)	)	PUNCT
ejpam-6761	466	59	=	=	SYM
ejpam-6761	466	60	(	(	PUNCT
ejpam-6761	466	61	(	(	PUNCT
ejpam-6761	466	62	1f	1f	NUM
ejpam-6761	466	63	−	−	PROPN
ejpam-6761	467	1	1)f1,−0.675	1)f1,−0.675	NUM
ejpam-6761	467	2	,	,	PUNCT
ejpam-6761	467	3	0.851	0.851	NUM
ejpam-6761	467	4	)	)	PUNCT
ejpam-6761	467	5	that	that	PRON
ejpam-6761	467	6	is	be	AUX
ejpam-6761	467	7	,	,	PUNCT
ejpam-6761	467	8	bipolar	bipolar	ADJ
ejpam-6761	467	9	valued	value	VERB
ejpam-6761	467	10	fuzzy	fuzzy	ADJ
ejpam-6761	467	11	elements	element	NOUN
ejpam-6761	467	12	of	of	ADP
ejpam-6761	467	13	u	u	NOUN
ejpam-6761	467	14	are	be	AUX
ejpam-6761	467	15	not	not	PART
ejpam-6761	467	16	associative	associative	ADJ
ejpam-6761	467	17	with	with	ADP
ejpam-6761	467	18	bipolar	bipolar	ADJ
ejpam-6761	467	19	valued	value	VERB
ejpam-6761	467	20	fuzzy	fuzzy	ADJ
ejpam-6761	467	21	elements	element	NOUN
ejpam-6761	467	22	of	of	ADP
ejpam-6761	467	23	(	(	PUNCT
ejpam-6761	467	24	℧	℧	PROPN
ejpam-6761	467	25	,	,	PUNCT
ejpam-6761	467	26	[	[	X
ejpam-6761	467	27	−1	−1	NOUN
ejpam-6761	467	28	,	,	PUNCT
ejpam-6761	467	29	0	0	NUM
ejpam-6761	467	30	]	]	PUNCT
ejpam-6761	467	31	,	,	PUNCT
ejpam-6761	467	32	[	[	X
ejpam-6761	467	33	0	0	NUM
ejpam-6761	467	34	,	,	PUNCT
ejpam-6761	467	35	1	1	NUM
ejpam-6761	467	36	]	]	NUM
ejpam-6761	467	37	)	)	PUNCT
ejpam-6761	467	38	.	.	PUNCT
ejpam-6761	468	1	definition	definition	NOUN
ejpam-6761	468	2	23	23	NUM
ejpam-6761	468	3	.	.	PUNCT
ejpam-6761	469	1	definition	definition	NOUN
ejpam-6761	469	2	4.2	4.2	NUM
ejpam-6761	469	3	an	an	DET
ejpam-6761	469	4	associative	associative	ADJ
ejpam-6761	469	5	bipolar	bipolar	NOUN
ejpam-6761	469	6	valued	value	VERB
ejpam-6761	469	7	fuzzy	fuzzy	ADJ
ejpam-6761	469	8	subgroup	subgroup	NOUN
ejpam-6761	469	9	(	(	PUNCT
ejpam-6761	469	10	u	u	NOUN
ejpam-6761	469	11	;	;	PUNCT
ejpam-6761	469	12	f	f	PROPN
ejpam-6761	469	13	)	)	PUNCT
ejpam-6761	469	14	of	of	ADP
ejpam-6761	469	15	the	the	DET
ejpam-6761	469	16	bipolar	bipolar	ADJ
ejpam-6761	469	17	valued	value	VERB
ejpam-6761	469	18	fuzzy	fuzzy	ADJ
ejpam-6761	469	19	group	group	NOUN
ejpam-6761	469	20	(	(	PUNCT
ejpam-6761	469	21	(	(	PUNCT
ejpam-6761	469	22	g	g	NOUN
ejpam-6761	469	23	,	,	PUNCT
ejpam-6761	469	24	[	[	X
ejpam-6761	469	25	−1	−1	NOUN
ejpam-6761	469	26	,	,	PUNCT
ejpam-6761	469	27	0	0	NUM
ejpam-6761	469	28	]	]	PUNCT
ejpam-6761	469	29	,	,	PUNCT
ejpam-6761	470	1	[	[	X
ejpam-6761	470	2	0	0	NUM
ejpam-6761	470	3	,	,	PUNCT
ejpam-6761	470	4	1	1	NUM
ejpam-6761	470	5	]	]	NUM
ejpam-6761	470	6	)	)	PUNCT
ejpam-6761	470	7	,	,	PUNCT
ejpam-6761	470	8	f	f	PROPN
ejpam-6761	470	9	)	)	PUNCT
ejpam-6761	470	10	is	be	AUX
ejpam-6761	470	11	a	a	DET
ejpam-6761	470	12	bipolar	bipolar	ADJ
ejpam-6761	470	13	valued	value	VERB
ejpam-6761	470	14	fuzzy	fuzzy	ADJ
ejpam-6761	470	15	group	group	NOUN
ejpam-6761	470	16	(	(	PUNCT
ejpam-6761	470	17	u	u	NOUN
ejpam-6761	470	18	;	;	PUNCT
ejpam-6761	470	19	f	f	PROPN
ejpam-6761	470	20	)	)	PUNCT
ejpam-6761	470	21	of	of	ADP
ejpam-6761	470	22	(	(	PUNCT
ejpam-6761	470	23	(	(	PUNCT
ejpam-6761	470	24	g	g	NOUN
ejpam-6761	470	25	,	,	PUNCT
ejpam-6761	470	26	[	[	X
ejpam-6761	470	27	−1	−1	NOUN
ejpam-6761	470	28	,	,	PUNCT
ejpam-6761	470	29	0	0	NUM
ejpam-6761	470	30	]	]	PUNCT
ejpam-6761	470	31	,	,	PUNCT
ejpam-6761	471	1	[	[	X
ejpam-6761	471	2	0	0	NUM
ejpam-6761	471	3	,	,	PUNCT
ejpam-6761	471	4	1	1	NUM
ejpam-6761	471	5	]	]	NUM
ejpam-6761	471	6	)	)	PUNCT
ejpam-6761	471	7	,	,	PUNCT
ejpam-6761	471	8	f	f	PROPN
ejpam-6761	471	9	)	)	PUNCT
ejpam-6761	471	10	in	in	ADP
ejpam-6761	471	11	which	which	PRON
ejpam-6761	471	12	bipolar	bipolar	ADJ
ejpam-6761	471	13	valued	value	VERB
ejpam-6761	471	14	fuzzy	fuzzy	ADJ
ejpam-6761	471	15	elements	element	NOUN
ejpam-6761	471	16	of	of	ADP
ejpam-6761	471	17	u	u	NOUN
ejpam-6761	471	18	are	be	AUX
ejpam-6761	471	19	associative	associative	ADJ
ejpam-6761	471	20	with	with	ADP
ejpam-6761	471	21	bipolar	bipolar	ADJ
ejpam-6761	471	22	valued	value	VERB
ejpam-6761	471	23	fuzzy	fuzzy	ADJ
ejpam-6761	471	24	elements	element	NOUN
ejpam-6761	471	25	of	of	ADP
ejpam-6761	471	26	(	(	PUNCT
ejpam-6761	471	27	g	g	PROPN
ejpam-6761	471	28	,	,	PUNCT
ejpam-6761	471	29	[	[	X
ejpam-6761	471	30	−1	−1	NOUN
ejpam-6761	471	31	,	,	PUNCT
ejpam-6761	471	32	0	0	NUM
ejpam-6761	471	33	]	]	PUNCT
ejpam-6761	471	34	,	,	PUNCT
ejpam-6761	471	35	[	[	X
ejpam-6761	471	36	0	0	NUM
ejpam-6761	471	37	,	,	PUNCT
ejpam-6761	471	38	1	1	NUM
ejpam-6761	471	39	]	]	PUNCT
ejpam-6761	471	40	)	)	PUNCT
ejpam-6761	471	41	for	for	ADP
ejpam-6761	471	42	any	any	DET
ejpam-6761	471	43	arbitrary	arbitrary	ADJ
ejpam-6761	471	44	choice	choice	NOUN
ejpam-6761	471	45	of	of	ADP
ejpam-6761	471	46	bipolar	bipolar	ADJ
ejpam-6761	471	47	valued	value	VERB
ejpam-6761	471	48	fuzzy	fuzzy	ADJ
ejpam-6761	471	49	elements	element	NOUN
ejpam-6761	471	50	of	of	ADP
ejpam-6761	471	51	u	u	NOUN
ejpam-6761	471	52	and	and	CCONJ
ejpam-6761	471	53	(	(	PUNCT
ejpam-6761	471	54	g	g	NOUN
ejpam-6761	471	55	,	,	PUNCT
ejpam-6761	471	56	[	[	X
ejpam-6761	471	57	−1	−1	NOUN
ejpam-6761	471	58	,	,	PUNCT
ejpam-6761	471	59	0	0	NUM
ejpam-6761	471	60	]	]	PUNCT
ejpam-6761	471	61	,	,	PUNCT
ejpam-6761	471	62	[	[	X
ejpam-6761	471	63	0	0	NUM
ejpam-6761	471	64	,	,	PUNCT
ejpam-6761	471	65	1	1	NUM
ejpam-6761	471	66	]	]	NUM
ejpam-6761	471	67	)	)	PUNCT
ejpam-6761	471	68	.	.	PUNCT
ejpam-6761	472	1	example	example	NOUN
ejpam-6761	473	1	3	3	X
ejpam-6761	473	2	.	.	PUNCT
ejpam-6761	473	3	let	let	VERB
ejpam-6761	473	4	℧	℧	PROPN
ejpam-6761	473	5	=	=	PRON
ejpam-6761	473	6	{	{	PUNCT
ejpam-6761	473	7	−1	−1	NOUN
ejpam-6761	473	8	,	,	PUNCT
ejpam-6761	473	9	1,−i	1,−i	NUM
ejpam-6761	473	10	,	,	PUNCT
ejpam-6761	473	11	i	i	PRON
ejpam-6761	473	12	}	}	PUNCT
ejpam-6761	473	13	.	.	PUNCT
ejpam-6761	474	1	define	define	VERB
ejpam-6761	474	2	the	the	DET
ejpam-6761	474	3	bipolar	bipolar	ADJ
ejpam-6761	474	4	valued	value	VERB
ejpam-6761	474	5	fuzzy	fuzzy	ADJ
ejpam-6761	474	6	binary	binary	PROPN
ejpam-6761	474	7	operation	operation	PROPN
ejpam-6761	474	8	f	f	PROPN
ejpam-6761	474	9	=(	=(	PROPN
ejpam-6761	475	1	f	f	PROPN
ejpam-6761	475	2	,	,	PUNCT
ejpam-6761	475	3	f−xy	f−xy	PROPN
ejpam-6761	475	4	,	,	PUNCT
ejpam-6761	475	5	f	f	PROPN
ejpam-6761	476	1	+	+	X
ejpam-6761	476	2	xy	xy	PROPN
ejpam-6761	476	3	)	)	PUNCT
ejpam-6761	476	4	on	on	ADP
ejpam-6761	476	5	(	(	PUNCT
ejpam-6761	476	6	℧	℧	PROPN
ejpam-6761	476	7	,	,	PUNCT
ejpam-6761	476	8	[	[	X
ejpam-6761	476	9	−1	−1	NOUN
ejpam-6761	476	10	,	,	PUNCT
ejpam-6761	476	11	0	0	NUM
ejpam-6761	476	12	]	]	PUNCT
ejpam-6761	476	13	,	,	PUNCT
ejpam-6761	476	14	[	[	X
ejpam-6761	476	15	0	0	NUM
ejpam-6761	476	16	,	,	PUNCT
ejpam-6761	476	17	1	1	NUM
ejpam-6761	476	18	]	]	PUNCT
ejpam-6761	476	19	)	)	PUNCT
ejpam-6761	476	20	such	such	ADJ
ejpam-6761	476	21	that	that	SCONJ
ejpam-6761	476	22	f	f	X
ejpam-6761	476	23	:	:	PUNCT
ejpam-6761	476	24	(	(	PUNCT
ejpam-6761	476	25	℧	℧	PROPN
ejpam-6761	476	26	,	,	PUNCT
ejpam-6761	476	27	[	[	X
ejpam-6761	476	28	−1	−1	NOUN
ejpam-6761	476	29	,	,	PUNCT
ejpam-6761	476	30	0	0	NUM
ejpam-6761	476	31	]	]	PUNCT
ejpam-6761	476	32	,	,	PUNCT
ejpam-6761	476	33	[	[	X
ejpam-6761	476	34	0	0	NUM
ejpam-6761	476	35	,	,	PUNCT
ejpam-6761	476	36	1])×	1])×	PRON
ejpam-6761	476	37	(	(	PUNCT
ejpam-6761	476	38	℧	℧	PROPN
ejpam-6761	476	39	,	,	PUNCT
ejpam-6761	476	40	[	[	X
ejpam-6761	476	41	−1	−1	NOUN
ejpam-6761	476	42	,	,	PUNCT
ejpam-6761	476	43	0	0	NUM
ejpam-6761	476	44	]	]	PUNCT
ejpam-6761	476	45	,	,	PUNCT
ejpam-6761	476	46	[	[	X
ejpam-6761	476	47	0	0	NUM
ejpam-6761	476	48	,	,	PUNCT
ejpam-6761	476	49	1	1	NUM
ejpam-6761	476	50	]	]	NUM
ejpam-6761	476	51	)	)	PUNCT
ejpam-6761	476	52	→	→	PUNCT
ejpam-6761	476	53	(	(	PUNCT
ejpam-6761	476	54	℧	℧	PROPN
ejpam-6761	476	55	,	,	PUNCT
ejpam-6761	476	56	[	[	X
ejpam-6761	476	57	−1	−1	NOUN
ejpam-6761	476	58	,	,	PUNCT
ejpam-6761	476	59	0	0	NUM
ejpam-6761	476	60	]	]	PUNCT
ejpam-6761	476	61	,	,	PUNCT
ejpam-6761	476	62	[	[	X
ejpam-6761	476	63	0	0	NUM
ejpam-6761	476	64	,	,	PUNCT
ejpam-6761	476	65	1	1	NUM
ejpam-6761	476	66	]	]	PUNCT
ejpam-6761	476	67	)	)	PUNCT
ejpam-6761	476	68	is	be	AUX
ejpam-6761	476	69	the	the	DET
ejpam-6761	476	70	ordinary	ordinary	ADJ
ejpam-6761	476	71	multiplication	multiplication	NOUN
ejpam-6761	476	72	of	of	ADP
ejpam-6761	476	73	complex	complex	ADJ
ejpam-6761	476	74	numbers	number	NOUN
ejpam-6761	476	75	and	and	CCONJ
ejpam-6761	476	76	the	the	DET
ejpam-6761	476	77	negative	negative	ADJ
ejpam-6761	476	78	and	and	CCONJ
ejpam-6761	476	79	positive	positive	ADJ
ejpam-6761	476	80	comembership	comembership	NOUN
ejpam-6761	476	81	functions	function	NOUN
ejpam-6761	476	82	are	be	AUX
ejpam-6761	476	83	given	give	VERB
ejpam-6761	476	84	respectively	respectively	ADV
ejpam-6761	476	85	for	for	ADP
ejpam-6761	476	86	all	all	DET
ejpam-6761	476	87	x	x	NOUN
ejpam-6761	476	88	,	,	PUNCT
ejpam-6761	476	89	y	y	PROPN
ejpam-6761	476	90	∈	∈	PROPN
ejpam-6761	476	91	u	u	NOUN
ejpam-6761	476	92	by	by	ADP
ejpam-6761	476	93	f−xy	f−xy	PROPN
ejpam-6761	476	94	(	(	PUNCT
ejpam-6761	476	95	n−,m−	n−,m−	NUM
ejpam-6761	476	96	)	)	PUNCT
ejpam-6761	476	97	=	=	VERB
ejpam-6761	477	1	n−	n−	NOUN
ejpam-6761	477	2	∨m−	∨m−	ADJ
ejpam-6761	477	3	=	=	VERB
ejpam-6761	477	4	min	min	X
ejpam-6761	477	5	(	(	PUNCT
ejpam-6761	477	6	n−,m−	n−,m−	NUM
ejpam-6761	477	7	)	)	PUNCT
ejpam-6761	477	8	and	and	CCONJ
ejpam-6761	477	9	f+xy	f+xy	X
ejpam-6761	477	10	(	(	PUNCT
ejpam-6761	477	11	n+,m+	n+,m+	X
ejpam-6761	477	12	)	)	PUNCT
ejpam-6761	477	13	=	=	SYM
ejpam-6761	477	14	n+	n+	ADP
ejpam-6761	478	1	∧m+	∧m+	VERB
ejpam-6761	478	2	=	=	SYM
ejpam-6761	478	3	max	max	PROPN
ejpam-6761	478	4	(	(	PUNCT
ejpam-6761	478	5	n+,m+	n+,m+	PROPN
ejpam-6761	478	6	)	)	PUNCT
ejpam-6761	478	7	(	(	PUNCT
ejpam-6761	478	8	18	18	NUM
ejpam-6761	478	9	)	)	PUNCT
ejpam-6761	478	10	obviously	obviously	ADV
ejpam-6761	478	11	the	the	DET
ejpam-6761	478	12	bipolar	bipolar	ADJ
ejpam-6761	478	13	valued	value	VERB
ejpam-6761	478	14	fuzzy	fuzzy	ADJ
ejpam-6761	478	15	subspace	subspace	NOUN
ejpam-6761	478	16	u	u	NOUN
ejpam-6761	478	17	=	=	X
ejpam-6761	478	18	{	{	PUNCT
ejpam-6761	478	19	(	(	PUNCT
ejpam-6761	478	20	−1	−1	NOUN
ejpam-6761	478	21	,	,	PUNCT
ejpam-6761	478	22	[	[	PUNCT
ejpam-6761	478	23	−1,−1	−1,−1	NOUN
ejpam-6761	478	24	2	2	NUM
ejpam-6761	478	25	]	]	PUNCT
ejpam-6761	478	26	∪	∪	X
ejpam-6761	478	27	{	{	PUNCT
ejpam-6761	478	28	0	0	NUM
ejpam-6761	478	29	}	}	PUNCT
ejpam-6761	478	30	,	,	PUNCT
ejpam-6761	478	31	{	{	PUNCT
ejpam-6761	478	32	0	0	NUM
ejpam-6761	478	33	}	}	PUNCT
ejpam-6761	478	34	∪	∪	NOUN
ejpam-6761	478	35	[	[	PUNCT
ejpam-6761	478	36	1	1	NUM
ejpam-6761	478	37	2	2	NUM
ejpam-6761	478	38	,	,	PUNCT
ejpam-6761	478	39	1	1	NUM
ejpam-6761	478	40	]	]	PUNCT
ejpam-6761	478	41	)	)	PUNCT
ejpam-6761	478	42	,	,	PUNCT
ejpam-6761	478	43	(	(	PUNCT
ejpam-6761	478	44	1	1	X
ejpam-6761	478	45	,	,	PUNCT
ejpam-6761	478	46	[	[	PUNCT
ejpam-6761	478	47	−1,−1	−1,−1	NOUN
ejpam-6761	478	48	2	2	NUM
ejpam-6761	478	49	]	]	PUNCT
ejpam-6761	478	50	∪	∪	X
ejpam-6761	478	51	{	{	PUNCT
ejpam-6761	478	52	0	0	NUM
ejpam-6761	478	53	}	}	PUNCT
ejpam-6761	478	54	,	,	PUNCT
ejpam-6761	478	55	{	{	PUNCT
ejpam-6761	478	56	0	0	NUM
ejpam-6761	478	57	}	}	PUNCT
ejpam-6761	478	58	∪	∪	NOUN
ejpam-6761	478	59	[	[	PUNCT
ejpam-6761	478	60	1	1	NUM
ejpam-6761	478	61	2	2	NUM
ejpam-6761	478	62	,	,	PUNCT
ejpam-6761	478	63	1	1	NUM
ejpam-6761	478	64	]	]	PUNCT
ejpam-6761	478	65	)	)	PUNCT
ejpam-6761	478	66	}	}	PUNCT
ejpam-6761	478	67	defines	define	VERB
ejpam-6761	478	68	an	an	DET
ejpam-6761	478	69	associative	associative	ADJ
ejpam-6761	478	70	bipolar	bipolar	NOUN
ejpam-6761	478	71	valued	value	VERB
ejpam-6761	478	72	fuzzy	fuzzy	ADJ
ejpam-6761	478	73	subgroup	subgroup	NOUN
ejpam-6761	478	74	of	of	ADP
ejpam-6761	478	75	(	(	PUNCT
ejpam-6761	478	76	(	(	PUNCT
ejpam-6761	478	77	℧	℧	PROPN
ejpam-6761	478	78	,	,	PUNCT
ejpam-6761	478	79	[	[	X
ejpam-6761	478	80	−1	−1	NOUN
ejpam-6761	478	81	,	,	PUNCT
ejpam-6761	478	82	0	0	NUM
ejpam-6761	478	83	]	]	PUNCT
ejpam-6761	478	84	,	,	PUNCT
ejpam-6761	478	85	[	[	X
ejpam-6761	478	86	0	0	NUM
ejpam-6761	478	87	,	,	PUNCT
ejpam-6761	478	88	1	1	NUM
ejpam-6761	478	89	]	]	NUM
ejpam-6761	478	90	)	)	PUNCT
ejpam-6761	478	91	,	,	PUNCT
ejpam-6761	478	92	f	f	PROPN
ejpam-6761	478	93	)	)	PUNCT
ejpam-6761	478	94	under	under	ADP
ejpam-6761	478	95	f	f	PROPN
ejpam-6761	478	96	.	.	PUNCT
ejpam-6761	479	1	building	build	VERB
ejpam-6761	479	2	upon	upon	SCONJ
ejpam-6761	479	3	the	the	DET
ejpam-6761	479	4	preceding	precede	VERB
ejpam-6761	479	5	definitions	definition	NOUN
ejpam-6761	479	6	and	and	CCONJ
ejpam-6761	479	7	examples	example	NOUN
ejpam-6761	479	8	,	,	PUNCT
ejpam-6761	479	9	we	we	PRON
ejpam-6761	479	10	now	now	ADV
ejpam-6761	479	11	present	present	VERB
ejpam-6761	479	12	a	a	DET
ejpam-6761	479	13	significant	significant	ADJ
ejpam-6761	479	14	result	result	NOUN
ejpam-6761	479	15	pertaining	pertain	VERB
ejpam-6761	479	16	to	to	PART
ejpam-6761	479	17	associative	associative	VERB
ejpam-6761	479	18	bipolar	bipolar	ADV
ejpam-6761	479	19	-	-	PUNCT
ejpam-6761	479	20	valued	value	VERB
ejpam-6761	479	21	fuzzy	fuzzy	ADJ
ejpam-6761	479	22	subgroups	subgroup	NOUN
ejpam-6761	479	23	.	.	PUNCT
ejpam-6761	480	1	theorem	theorem	ADJ
ejpam-6761	480	2	6	6	NUM
ejpam-6761	480	3	.	.	PUNCT
ejpam-6761	481	1	let	let	AUX
ejpam-6761	481	2	(	(	PUNCT
ejpam-6761	481	3	(	(	PUNCT
ejpam-6761	481	4	g	g	NOUN
ejpam-6761	481	5	,	,	PUNCT
ejpam-6761	481	6	[	[	X
ejpam-6761	481	7	−1	−1	NOUN
ejpam-6761	481	8	,	,	PUNCT
ejpam-6761	481	9	0	0	NUM
ejpam-6761	481	10	]	]	PUNCT
ejpam-6761	481	11	,	,	PUNCT
ejpam-6761	481	12	[	[	X
ejpam-6761	481	13	0	0	NUM
ejpam-6761	481	14	,	,	PUNCT
ejpam-6761	481	15	1	1	NUM
ejpam-6761	481	16	]	]	NUM
ejpam-6761	481	17	)	)	PUNCT
ejpam-6761	481	18	,	,	PUNCT
ejpam-6761	481	19	f	f	PROPN
ejpam-6761	481	20	)	)	PUNCT
ejpam-6761	481	21	with	with	ADP
ejpam-6761	481	22	f	f	PROPN
ejpam-6761	481	23	=	=	SYM
ejpam-6761	481	24	(	(	PUNCT
ejpam-6761	481	25	f	f	X
ejpam-6761	481	26	,	,	PUNCT
ejpam-6761	481	27	f−	f−	PROPN
ejpam-6761	481	28	,	,	PUNCT
ejpam-6761	481	29	f+	f+	PROPN
ejpam-6761	481	30	)	)	PUNCT
ejpam-6761	481	31	be	be	VERB
ejpam-6761	481	32	a	a	DET
ejpam-6761	481	33	uniform	uniform	ADJ
ejpam-6761	481	34	bipolar	bipolar	ADJ
ejpam-6761	481	35	valued	value	VERB
ejpam-6761	481	36	fuzzy	fuzzy	ADJ
ejpam-6761	481	37	group	group	NOUN
ejpam-6761	481	38	(	(	PUNCT
ejpam-6761	481	39	i.e.	i.e.	X
ejpam-6761	481	40	,	,	PUNCT
ejpam-6761	481	41	f+	f+	ADJ
ejpam-6761	481	42	=	=	SYM
ejpam-6761	481	43	|f−|	|f−|	NUM
ejpam-6761	481	44	)	)	PUNCT
ejpam-6761	481	45	.	.	PUNCT
ejpam-6761	482	1	if	if	SCONJ
ejpam-6761	482	2	f−(n−,−1	f−(n−,−1	NOUN
ejpam-6761	482	3	)	)	PUNCT
ejpam-6761	483	1	=	=	SYM
ejpam-6761	483	2	f−(−1	f−(−1	NOUN
ejpam-6761	483	3	,	,	PUNCT
ejpam-6761	483	4	n−	n−	NOUN
ejpam-6761	483	5	)	)	PUNCT
ejpam-6761	483	6	=	=	SYM
ejpam-6761	483	7	n−	n−	NOUN
ejpam-6761	483	8	and	and	CCONJ
ejpam-6761	483	9	f+(n+	f+(n+	ADJ
ejpam-6761	483	10	,	,	PUNCT
ejpam-6761	483	11	1	1	X
ejpam-6761	483	12	)	)	PUNCT
ejpam-6761	483	13	=	=	SYM
ejpam-6761	483	14	f+(1	f+(1	NOUN
ejpam-6761	483	15	,	,	PUNCT
ejpam-6761	483	16	n+	n+	PUNCT
ejpam-6761	483	17	)	)	PUNCT
ejpam-6761	483	18	=	=	SYM
ejpam-6761	484	1	n+	n+	PROPN
ejpam-6761	484	2	,	,	PUNCT
ejpam-6761	484	3	then	then	ADV
ejpam-6761	484	4	every	every	DET
ejpam-6761	484	5	bipolar	bipolar	ADJ
ejpam-6761	484	6	valued	value	VERB
ejpam-6761	484	7	fuzzy	fuzzy	ADJ
ejpam-6761	484	8	subgroup	subgroup	NOUN
ejpam-6761	484	9	of	of	ADP
ejpam-6761	484	10	the	the	DET
ejpam-6761	484	11	bipolar	bipolar	ADJ
ejpam-6761	484	12	valued	value	VERB
ejpam-6761	484	13	fuzzy	fuzzy	ADJ
ejpam-6761	484	14	group	group	NOUN
ejpam-6761	484	15	(	(	PUNCT
ejpam-6761	484	16	(	(	PUNCT
ejpam-6761	484	17	g	g	NOUN
ejpam-6761	484	18	,	,	PUNCT
ejpam-6761	484	19	[	[	X
ejpam-6761	484	20	−1	−1	NOUN
ejpam-6761	484	21	,	,	PUNCT
ejpam-6761	484	22	0	0	NUM
ejpam-6761	484	23	]	]	PUNCT
ejpam-6761	484	24	,	,	PUNCT
ejpam-6761	484	25	[	[	X
ejpam-6761	484	26	0	0	NUM
ejpam-6761	484	27	,	,	PUNCT
ejpam-6761	484	28	1	1	NUM
ejpam-6761	484	29	]	]	NUM
ejpam-6761	484	30	)	)	PUNCT
ejpam-6761	484	31	,	,	PUNCT
ejpam-6761	484	32	f	f	PROPN
ejpam-6761	484	33	)	)	PUNCT
ejpam-6761	484	34	is	be	AUX
ejpam-6761	484	35	an	an	DET
ejpam-6761	484	36	associative	associative	ADJ
ejpam-6761	484	37	bipolar	bipolar	NOUN
ejpam-6761	484	38	valued	value	VERB
ejpam-6761	484	39	fuzzy	fuzzy	ADJ
ejpam-6761	484	40	subgroup	subgroup	NOUN
ejpam-6761	484	41	.	.	PUNCT
ejpam-6761	485	1	proof	proof	NOUN
ejpam-6761	485	2	.	.	PUNCT
ejpam-6761	486	1	let	let	VERB
ejpam-6761	486	2	(	(	PUNCT
ejpam-6761	486	3	u	u	NOUN
ejpam-6761	486	4	;	;	PUNCT
ejpam-6761	486	5	f	f	PROPN
ejpam-6761	486	6	)	)	PUNCT
ejpam-6761	486	7	be	be	AUX
ejpam-6761	486	8	a	a	DET
ejpam-6761	486	9	bipolar	bipolar	ADJ
ejpam-6761	486	10	valued	value	VERB
ejpam-6761	486	11	fuzzy	fuzzy	ADJ
ejpam-6761	486	12	subgroup	subgroup	NOUN
ejpam-6761	486	13	of	of	ADP
ejpam-6761	486	14	the	the	DET
ejpam-6761	486	15	bipolar	bipolar	ADJ
ejpam-6761	486	16	valued	value	VERB
ejpam-6761	486	17	fuzzy	fuzzy	ADJ
ejpam-6761	486	18	group	group	NOUN
ejpam-6761	486	19	(	(	PUNCT
ejpam-6761	486	20	(	(	PUNCT
ejpam-6761	486	21	g	g	NOUN
ejpam-6761	486	22	,	,	PUNCT
ejpam-6761	486	23	[	[	X
ejpam-6761	486	24	−1	−1	NOUN
ejpam-6761	486	25	,	,	PUNCT
ejpam-6761	486	26	0	0	NUM
ejpam-6761	486	27	]	]	PUNCT
ejpam-6761	486	28	,	,	PUNCT
ejpam-6761	487	1	[	[	X
ejpam-6761	487	2	0	0	NUM
ejpam-6761	487	3	,	,	PUNCT
ejpam-6761	487	4	1	1	NUM
ejpam-6761	487	5	]	]	NUM
ejpam-6761	487	6	)	)	PUNCT
ejpam-6761	487	7	,	,	PUNCT
ejpam-6761	487	8	f	f	PROPN
ejpam-6761	487	9	)	)	PUNCT
ejpam-6761	487	10	.	.	PUNCT
ejpam-6761	488	1	consider	consider	VERB
ejpam-6761	488	2	the	the	DET
ejpam-6761	488	3	bipolar	bipolar	ADJ
ejpam-6761	488	4	valued	value	VERB
ejpam-6761	488	5	fuzzy	fuzzy	ADJ
ejpam-6761	488	6	elements	element	NOUN
ejpam-6761	488	7	x	x	PUNCT
ejpam-6761	488	8	=	=	SYM
ejpam-6761	488	9	(	(	PUNCT
ejpam-6761	488	10	x	x	X
ejpam-6761	488	11	,	,	PUNCT
ejpam-6761	488	12	[	[	X
ejpam-6761	488	13	−1	−1	NOUN
ejpam-6761	488	14	,	,	PUNCT
ejpam-6761	488	15	0	0	NUM
ejpam-6761	488	16	]	]	PUNCT
ejpam-6761	488	17	,	,	PUNCT
ejpam-6761	488	18	[	[	X
ejpam-6761	488	19	0	0	NUM
ejpam-6761	488	20	,	,	PUNCT
ejpam-6761	488	21	1	1	NUM
ejpam-6761	488	22	]	]	NUM
ejpam-6761	488	23	)	)	PUNCT
ejpam-6761	488	24	,	,	PUNCT
ejpam-6761	488	25	y	y	PROPN
ejpam-6761	488	26	=	=	PRON
ejpam-6761	488	27	(	(	PUNCT
ejpam-6761	488	28	y	y	PROPN
ejpam-6761	488	29	,	,	PUNCT
ejpam-6761	488	30	[	[	X
ejpam-6761	488	31	−1	−1	NOUN
ejpam-6761	488	32	,	,	PUNCT
ejpam-6761	488	33	0	0	NUM
ejpam-6761	488	34	]	]	PUNCT
ejpam-6761	488	35	,	,	PUNCT
ejpam-6761	488	36	[	[	X
ejpam-6761	488	37	0	0	NUM
ejpam-6761	488	38	,	,	PUNCT
ejpam-6761	488	39	1	1	NUM
ejpam-6761	488	40	]	]	NUM
ejpam-6761	488	41	)	)	PUNCT
ejpam-6761	488	42	,	,	PUNCT
ejpam-6761	488	43	z	z	NOUN
ejpam-6761	488	44	=	=	SYM
ejpam-6761	488	45	(	(	PUNCT
ejpam-6761	488	46	z	z	NOUN
ejpam-6761	488	47	,	,	PUNCT
ejpam-6761	488	48	[	[	X
ejpam-6761	488	49	−1	−1	NOUN
ejpam-6761	488	50	,	,	PUNCT
ejpam-6761	488	51	0	0	NUM
ejpam-6761	488	52	]	]	PUNCT
ejpam-6761	488	53	,	,	PUNCT
ejpam-6761	489	1	[	[	X
ejpam-6761	489	2	0	0	NUM
ejpam-6761	489	3	,	,	PUNCT
ejpam-6761	489	4	1	1	NUM
ejpam-6761	489	5	]	]	PUNCT
ejpam-6761	489	6	)	)	PUNCT
ejpam-6761	489	7	f.	f.	PROPN
ejpam-6761	489	8	al	al	PROPN
ejpam-6761	489	9	-	-	PROPN
ejpam-6761	489	10	zu’bi	zu’bi	PROPN
ejpam-6761	489	11	et	et	NOUN
ejpam-6761	489	12	al	al	PROPN
ejpam-6761	489	13	.	.	PUNCT
ejpam-6761	489	14	/	/	SYM
ejpam-6761	489	15	eur	eur	PROPN
ejpam-6761	489	16	.	.	PUNCT
ejpam-6761	490	1	j.	j.	PROPN
ejpam-6761	490	2	pure	pure	PROPN
ejpam-6761	490	3	appl	appl	PROPN
ejpam-6761	490	4	.	.	PROPN
ejpam-6761	490	5	math	math	PROPN
ejpam-6761	490	6	,	,	PUNCT
ejpam-6761	490	7	18	18	NUM
ejpam-6761	490	8	(	(	PUNCT
ejpam-6761	490	9	4	4	NUM
ejpam-6761	490	10	)	)	PUNCT
ejpam-6761	490	11	(	(	PUNCT
ejpam-6761	490	12	2025	2025	NUM
ejpam-6761	490	13	)	)	PUNCT
ejpam-6761	490	14	,	,	PUNCT
ejpam-6761	490	15	6761	6761	NUM
ejpam-6761	490	16	20	20	NUM
ejpam-6761	490	17	of	of	ADP
ejpam-6761	490	18	28	28	NUM
ejpam-6761	490	19	in	in	ADP
ejpam-6761	490	20	u	u	PRON
ejpam-6761	490	21	or	or	CCONJ
ejpam-6761	490	22	(	(	PUNCT
ejpam-6761	490	23	g	g	NOUN
ejpam-6761	490	24	,	,	PUNCT
ejpam-6761	490	25	[	[	X
ejpam-6761	490	26	−1	−1	NOUN
ejpam-6761	490	27	,	,	PUNCT
ejpam-6761	490	28	0	0	NUM
ejpam-6761	490	29	]	]	PUNCT
ejpam-6761	490	30	,	,	PUNCT
ejpam-6761	491	1	[	[	X
ejpam-6761	491	2	0	0	NUM
ejpam-6761	491	3	,	,	PUNCT
ejpam-6761	491	4	1	1	NUM
ejpam-6761	491	5	]	]	NUM
ejpam-6761	491	6	)	)	PUNCT
ejpam-6761	491	7	,	,	PUNCT
ejpam-6761	491	8	such	such	ADJ
ejpam-6761	491	9	that	that	DET
ejpam-6761	491	10	one	one	NUM
ejpam-6761	491	11	or	or	CCONJ
ejpam-6761	491	12	two	two	NUM
ejpam-6761	491	13	of	of	ADP
ejpam-6761	491	14	them	they	PRON
ejpam-6761	491	15	belong	belong	VERB
ejpam-6761	491	16	to	to	ADP
ejpam-6761	491	17	u	u	PRON
ejpam-6761	491	18	.	.	PUNCT
ejpam-6761	492	1	using	use	VERB
ejpam-6761	492	2	the	the	DET
ejpam-6761	492	3	properties	property	NOUN
ejpam-6761	492	4	of	of	ADP
ejpam-6761	492	5	f−	f−	PROPN
ejpam-6761	492	6	,	,	PUNCT
ejpam-6761	492	7	f+	f+	NOUN
ejpam-6761	492	8	,	,	PUNCT
ejpam-6761	492	9	and	and	CCONJ
ejpam-6761	492	10	the	the	DET
ejpam-6761	492	11	associativity	associativity	NOUN
ejpam-6761	492	12	of	of	ADP
ejpam-6761	492	13	f	f	PROPN
ejpam-6761	492	14	,	,	PUNCT
ejpam-6761	492	15	we	we	PRON
ejpam-6761	492	16	have	have	VERB
ejpam-6761	492	17	:	:	PUNCT
ejpam-6761	492	18	xf(yfz	xf(yfz	PROPN
ejpam-6761	492	19	)	)	PUNCT
ejpam-6761	493	1	=	=	SYM
ejpam-6761	493	2	xf	xf	PROPN
ejpam-6761	493	3	(	(	PUNCT
ejpam-6761	493	4	(	(	PUNCT
ejpam-6761	493	5	yfz	yfz	PROPN
ejpam-6761	493	6	,	,	PUNCT
ejpam-6761	493	7	f−([−1	f−([−1	PROPN
ejpam-6761	493	8	,	,	PUNCT
ejpam-6761	493	9	0]×	0]×	PROPN
ejpam-6761	494	1	[	[	X
ejpam-6761	494	2	−1	−1	NOUN
ejpam-6761	494	3	,	,	PUNCT
ejpam-6761	494	4	0	0	NUM
ejpam-6761	494	5	]	]	PUNCT
ejpam-6761	494	6	)	)	PUNCT
ejpam-6761	494	7	,	,	PUNCT
ejpam-6761	494	8	f+([0	f+([0	ADJ
ejpam-6761	494	9	,	,	PUNCT
ejpam-6761	494	10	1]×	1]×	NUM
ejpam-6761	494	11	[	[	X
ejpam-6761	494	12	0	0	NUM
ejpam-6761	494	13	,	,	PUNCT
ejpam-6761	494	14	1	1	NUM
ejpam-6761	494	15	]	]	PUNCT
ejpam-6761	494	16	)	)	PUNCT
ejpam-6761	494	17	)	)	PUNCT
ejpam-6761	495	1	=	=	PUNCT
ejpam-6761	495	2	(	(	PUNCT
ejpam-6761	495	3	xf	xf	PROPN
ejpam-6761	495	4	(	(	PUNCT
ejpam-6761	495	5	yfz	yfz	PROPN
ejpam-6761	495	6	)	)	PUNCT
ejpam-6761	495	7	,	,	PUNCT
ejpam-6761	495	8	f−([−1	f−([−1	PROPN
ejpam-6761	495	9	,	,	PUNCT
ejpam-6761	495	10	0]×	0]×	PROPN
ejpam-6761	496	1	[	[	X
ejpam-6761	496	2	−1	−1	NOUN
ejpam-6761	496	3	,	,	PUNCT
ejpam-6761	496	4	0	0	NUM
ejpam-6761	496	5	]	]	PUNCT
ejpam-6761	496	6	)	)	PUNCT
ejpam-6761	496	7	,	,	PUNCT
ejpam-6761	496	8	f+([0	f+([0	ADJ
ejpam-6761	496	9	,	,	PUNCT
ejpam-6761	496	10	1]×	1]×	NUM
ejpam-6761	496	11	[	[	X
ejpam-6761	496	12	0	0	NUM
ejpam-6761	496	13	,	,	PUNCT
ejpam-6761	496	14	1	1	NUM
ejpam-6761	496	15	]	]	NUM
ejpam-6761	496	16	)	)	PUNCT
ejpam-6761	496	17	)	)	PUNCT
ejpam-6761	497	1	=	=	SYM
ejpam-6761	497	2	(	(	PUNCT
ejpam-6761	497	3	(	(	PUNCT
ejpam-6761	497	4	xfy)fz	xfy)fz	ADJ
ejpam-6761	497	5	,	,	PUNCT
ejpam-6761	497	6	[	[	X
ejpam-6761	497	7	−1	−1	NOUN
ejpam-6761	497	8	,	,	PUNCT
ejpam-6761	497	9	0	0	NUM
ejpam-6761	497	10	]	]	PUNCT
ejpam-6761	497	11	,	,	PUNCT
ejpam-6761	497	12	[	[	X
ejpam-6761	497	13	0	0	NUM
ejpam-6761	497	14	,	,	PUNCT
ejpam-6761	497	15	1	1	NUM
ejpam-6761	497	16	]	]	PUNCT
ejpam-6761	497	17	)	)	PUNCT
ejpam-6761	497	18	=	=	SYM
ejpam-6761	498	1	(	(	PUNCT
ejpam-6761	498	2	xfy)fz	xfy)fz	ADJ
ejpam-6761	498	3	,	,	PUNCT
ejpam-6761	498	4	(	(	PUNCT
ejpam-6761	498	5	19	19	NUM
ejpam-6761	498	6	)	)	PUNCT
ejpam-6761	498	7	which	which	PRON
ejpam-6761	498	8	proves	prove	VERB
ejpam-6761	498	9	the	the	DET
ejpam-6761	498	10	associativity	associativity	NOUN
ejpam-6761	498	11	of	of	ADP
ejpam-6761	498	12	the	the	DET
ejpam-6761	498	13	bipolar	bipolar	ADJ
ejpam-6761	498	14	valued	value	VERB
ejpam-6761	498	15	fuzzy	fuzzy	ADJ
ejpam-6761	498	16	elements	element	NOUN
ejpam-6761	498	17	of	of	ADP
ejpam-6761	498	18	u	u	NOUN
ejpam-6761	498	19	with	with	ADP
ejpam-6761	498	20	those	those	PRON
ejpam-6761	498	21	of	of	ADP
ejpam-6761	498	22	(	(	PUNCT
ejpam-6761	498	23	g	g	PROPN
ejpam-6761	498	24	,	,	PUNCT
ejpam-6761	498	25	[	[	X
ejpam-6761	498	26	−1	−1	NOUN
ejpam-6761	498	27	,	,	PUNCT
ejpam-6761	498	28	0	0	NUM
ejpam-6761	498	29	]	]	PUNCT
ejpam-6761	498	30	,	,	PUNCT
ejpam-6761	498	31	[	[	X
ejpam-6761	498	32	0	0	NUM
ejpam-6761	498	33	,	,	PUNCT
ejpam-6761	498	34	1	1	NUM
ejpam-6761	498	35	]	]	PUNCT
ejpam-6761	498	36	)	)	PUNCT
ejpam-6761	498	37	under	under	ADP
ejpam-6761	498	38	f	f	PROPN
ejpam-6761	498	39	.	.	PUNCT
ejpam-6761	499	1	corollary	corollary	ADJ
ejpam-6761	499	2	3	3	X
ejpam-6761	499	3	.	.	PUNCT
ejpam-6761	500	1	let	let	VERB
ejpam-6761	500	2	(	(	PUNCT
ejpam-6761	500	3	(	(	PUNCT
ejpam-6761	500	4	g	g	NOUN
ejpam-6761	500	5	,	,	PUNCT
ejpam-6761	500	6	[	[	X
ejpam-6761	500	7	−1	−1	NOUN
ejpam-6761	500	8	,	,	PUNCT
ejpam-6761	500	9	0	0	NUM
ejpam-6761	500	10	]	]	PUNCT
ejpam-6761	500	11	,	,	PUNCT
ejpam-6761	500	12	[	[	X
ejpam-6761	500	13	0	0	NUM
ejpam-6761	500	14	,	,	PUNCT
ejpam-6761	500	15	1	1	NUM
ejpam-6761	500	16	]	]	NUM
ejpam-6761	500	17	)	)	PUNCT
ejpam-6761	500	18	,	,	PUNCT
ejpam-6761	500	19	f	f	X
ejpam-6761	501	1	=	=	PRON
ejpam-6761	501	2	(	(	PUNCT
ejpam-6761	501	3	f	f	X
ejpam-6761	501	4	,	,	PUNCT
ejpam-6761	501	5	f−	f−	PROPN
ejpam-6761	501	6	,	,	PUNCT
ejpam-6761	501	7	f+	f+	NOUN
ejpam-6761	501	8	)	)	PUNCT
ejpam-6761	501	9	)	)	PUNCT
ejpam-6761	501	10	be	be	AUX
ejpam-6761	501	11	a	a	DET
ejpam-6761	501	12	uniform	uniform	ADJ
ejpam-6761	501	13	bipolar	bipolar	ADJ
ejpam-6761	501	14	valued	value	VERB
ejpam-6761	501	15	fuzzy	fuzzy	ADJ
ejpam-6761	501	16	group	group	NOUN
ejpam-6761	501	17	.	.	PUNCT
ejpam-6761	502	1	if	if	SCONJ
ejpam-6761	502	2	f−	f−	PROPN
ejpam-6761	502	3	and	and	CCONJ
ejpam-6761	502	4	f+	f+	NOUN
ejpam-6761	502	5	are	be	AUX
ejpam-6761	502	6	intersection	intersection	NOUN
ejpam-6761	502	7	of	of	ADP
ejpam-6761	502	8	bvf	bvf	NOUN
ejpam-6761	502	9	functions	function	NOUN
ejpam-6761	502	10	,	,	PUNCT
ejpam-6761	502	11	then	then	ADV
ejpam-6761	502	12	every	every	DET
ejpam-6761	502	13	bipolar	bipolar	ADJ
ejpam-6761	502	14	valued	value	VERB
ejpam-6761	502	15	fuzzy	fuzzy	ADJ
ejpam-6761	502	16	subgroup	subgroup	NOUN
ejpam-6761	502	17	of	of	ADP
ejpam-6761	502	18	the	the	DET
ejpam-6761	502	19	bipolar	bipolar	ADJ
ejpam-6761	502	20	valued	value	VERB
ejpam-6761	502	21	fuzzy	fuzzy	ADJ
ejpam-6761	502	22	group	group	NOUN
ejpam-6761	502	23	(	(	PUNCT
ejpam-6761	502	24	(	(	PUNCT
ejpam-6761	502	25	g	g	NOUN
ejpam-6761	502	26	,	,	PUNCT
ejpam-6761	502	27	[	[	X
ejpam-6761	502	28	−1	−1	NOUN
ejpam-6761	502	29	,	,	PUNCT
ejpam-6761	502	30	0	0	NUM
ejpam-6761	502	31	]	]	PUNCT
ejpam-6761	502	32	,	,	PUNCT
ejpam-6761	502	33	[	[	X
ejpam-6761	502	34	0	0	NUM
ejpam-6761	502	35	,	,	PUNCT
ejpam-6761	502	36	1	1	NUM
ejpam-6761	502	37	]	]	NUM
ejpam-6761	502	38	)	)	PUNCT
ejpam-6761	502	39	,	,	PUNCT
ejpam-6761	502	40	f	f	PROPN
ejpam-6761	502	41	)	)	PUNCT
ejpam-6761	502	42	is	be	AUX
ejpam-6761	502	43	an	an	DET
ejpam-6761	502	44	associative	associative	ADJ
ejpam-6761	502	45	bipolar	bipolar	NOUN
ejpam-6761	502	46	valued	value	VERB
ejpam-6761	502	47	fuzzy	fuzzy	ADJ
ejpam-6761	502	48	subgroup	subgroup	NOUN
ejpam-6761	502	49	.	.	PUNCT
ejpam-6761	503	1	prior	prior	ADV
ejpam-6761	503	2	to	to	ADP
ejpam-6761	503	3	defining	define	VERB
ejpam-6761	503	4	a	a	DET
ejpam-6761	503	5	normal	normal	ADJ
ejpam-6761	503	6	bipolar	bipolar	ADJ
ejpam-6761	503	7	-	-	PUNCT
ejpam-6761	503	8	valued	value	VERB
ejpam-6761	503	9	fuzzy	fuzzy	ADJ
ejpam-6761	503	10	group	group	NOUN
ejpam-6761	503	11	,	,	PUNCT
ejpam-6761	503	12	we	we	PRON
ejpam-6761	503	13	introduce	introduce	VERB
ejpam-6761	503	14	the	the	DET
ejpam-6761	503	15	concepts	concept	NOUN
ejpam-6761	503	16	of	of	ADP
ejpam-6761	503	17	left	left	ADJ
ejpam-6761	503	18	and	and	CCONJ
ejpam-6761	503	19	right	right	ADJ
ejpam-6761	503	20	cosets	coset	NOUN
ejpam-6761	503	21	associated	associate	VERB
ejpam-6761	503	22	with	with	ADP
ejpam-6761	503	23	a	a	DET
ejpam-6761	503	24	bipolar	bipolar	ADV
ejpam-6761	503	25	-	-	PUNCT
ejpam-6761	503	26	valued	value	VERB
ejpam-6761	503	27	fuzzy	fuzzy	ADJ
ejpam-6761	503	28	subgroup	subgroup	NOUN
ejpam-6761	503	29	.	.	PUNCT
ejpam-6761	504	1	definition	definition	NOUN
ejpam-6761	504	2	24	24	NUM
ejpam-6761	504	3	.	.	PUNCT
ejpam-6761	505	1	if	if	SCONJ
ejpam-6761	505	2	(	(	PUNCT
ejpam-6761	505	3	b;f	b;f	NOUN
ejpam-6761	505	4	)	)	PUNCT
ejpam-6761	505	5	,	,	PUNCT
ejpam-6761	505	6	where	where	SCONJ
ejpam-6761	505	7	b	b	X
ejpam-6761	505	8	=	=	PRON
ejpam-6761	505	9	{	{	PUNCT
ejpam-6761	505	10	(	(	PUNCT
ejpam-6761	505	11	z	z	NOUN
ejpam-6761	505	12	,	,	PUNCT
ejpam-6761	505	13	b−z	b−z	NOUN
ejpam-6761	505	14	,	,	PUNCT
ejpam-6761	505	15	b+z	b+z	PROPN
ejpam-6761	505	16	)	)	PUNCT
ejpam-6761	506	1	|	|	ADV
ejpam-6761	506	2	z	z	PROPN
ejpam-6761	506	3	∈	∈	PROPN
ejpam-6761	506	4	b	b	X
ejpam-6761	506	5	◦	◦	NOUN
ejpam-6761	506	6	}	}	PUNCT
ejpam-6761	506	7	,	,	PUNCT
ejpam-6761	506	8	is	be	AUX
ejpam-6761	506	9	a	a	DET
ejpam-6761	506	10	bipolar	bipolar	ADJ
ejpam-6761	506	11	valued	value	VERB
ejpam-6761	506	12	fuzzy	fuzzy	ADJ
ejpam-6761	506	13	subgroup	subgroup	NOUN
ejpam-6761	506	14	of	of	ADP
ejpam-6761	506	15	the	the	DET
ejpam-6761	506	16	bipolar	bipolar	ADJ
ejpam-6761	506	17	valued	value	VERB
ejpam-6761	506	18	fuzzy	fuzzy	ADJ
ejpam-6761	506	19	group	group	NOUN
ejpam-6761	506	20	(	(	PUNCT
ejpam-6761	506	21	(	(	PUNCT
ejpam-6761	506	22	g	g	NOUN
ejpam-6761	506	23	,	,	PUNCT
ejpam-6761	506	24	[	[	X
ejpam-6761	506	25	−1	−1	NOUN
ejpam-6761	506	26	,	,	PUNCT
ejpam-6761	506	27	0	0	NUM
ejpam-6761	506	28	]	]	PUNCT
ejpam-6761	506	29	,	,	PUNCT
ejpam-6761	506	30	[	[	X
ejpam-6761	506	31	0	0	NUM
ejpam-6761	506	32	,	,	PUNCT
ejpam-6761	506	33	1	1	NUM
ejpam-6761	506	34	]	]	NUM
ejpam-6761	506	35	)	)	PUNCT
ejpam-6761	506	36	,	,	PUNCT
ejpam-6761	506	37	f	f	PROPN
ejpam-6761	506	38	)	)	PUNCT
ejpam-6761	506	39	,	,	PUNCT
ejpam-6761	506	40	then	then	ADV
ejpam-6761	506	41	for	for	ADP
ejpam-6761	506	42	every	every	DET
ejpam-6761	506	43	bipolar	bipolar	ADJ
ejpam-6761	506	44	valued	value	VERB
ejpam-6761	506	45	fuzzy	fuzzy	ADJ
ejpam-6761	506	46	element	element	NOUN
ejpam-6761	506	47	(	(	PUNCT
ejpam-6761	506	48	x	x	X
ejpam-6761	506	49	,	,	PUNCT
ejpam-6761	506	50	[	[	X
ejpam-6761	506	51	−1	−1	NOUN
ejpam-6761	506	52	,	,	PUNCT
ejpam-6761	506	53	0	0	NUM
ejpam-6761	506	54	]	]	PUNCT
ejpam-6761	506	55	,	,	PUNCT
ejpam-6761	506	56	[	[	X
ejpam-6761	506	57	0	0	NUM
ejpam-6761	506	58	,	,	PUNCT
ejpam-6761	506	59	1	1	NUM
ejpam-6761	506	60	]	]	PUNCT
ejpam-6761	506	61	)	)	PUNCT
ejpam-6761	506	62	of	of	ADP
ejpam-6761	506	63	(	(	PUNCT
ejpam-6761	506	64	g	g	NOUN
ejpam-6761	506	65	,	,	PUNCT
ejpam-6761	506	66	[	[	X
ejpam-6761	506	67	−1	−1	NOUN
ejpam-6761	506	68	,	,	PUNCT
ejpam-6761	506	69	0	0	NUM
ejpam-6761	506	70	]	]	PUNCT
ejpam-6761	506	71	,	,	PUNCT
ejpam-6761	506	72	[	[	X
ejpam-6761	506	73	0	0	NUM
ejpam-6761	506	74	,	,	PUNCT
ejpam-6761	506	75	1	1	NUM
ejpam-6761	506	76	]	]	NUM
ejpam-6761	506	77	)	)	PUNCT
ejpam-6761	506	78	,	,	PUNCT
ejpam-6761	506	79	the	the	DET
ejpam-6761	506	80	fuzzy	fuzzy	ADJ
ejpam-6761	506	81	subspace	subspace	NOUN
ejpam-6761	506	82	defined	define	VERB
ejpam-6761	506	83	by	by	ADP
ejpam-6761	506	84	(	(	PUNCT
ejpam-6761	506	85	x	x	X
ejpam-6761	506	86	,	,	PUNCT
ejpam-6761	506	87	[	[	X
ejpam-6761	506	88	−1	−1	NOUN
ejpam-6761	506	89	,	,	PUNCT
ejpam-6761	506	90	0	0	NUM
ejpam-6761	506	91	]	]	PUNCT
ejpam-6761	506	92	,	,	PUNCT
ejpam-6761	506	93	[	[	X
ejpam-6761	506	94	0	0	NUM
ejpam-6761	506	95	,	,	PUNCT
ejpam-6761	506	96	1])b	1])b	NUM
ejpam-6761	506	97	=	=	SYM
ejpam-6761	506	98	(	(	PUNCT
ejpam-6761	506	99	x	x	X
ejpam-6761	506	100	,	,	PUNCT
ejpam-6761	506	101	[	[	X
ejpam-6761	506	102	−1	−1	NOUN
ejpam-6761	506	103	,	,	PUNCT
ejpam-6761	506	104	0	0	NUM
ejpam-6761	506	105	]	]	PUNCT
ejpam-6761	506	106	,	,	PUNCT
ejpam-6761	506	107	[	[	X
ejpam-6761	506	108	0	0	NUM
ejpam-6761	506	109	,	,	PUNCT
ejpam-6761	506	110	1])fb	1])fb	NUM
ejpam-6761	506	111	=	=	SYM
ejpam-6761	506	112	{	{	PUNCT
ejpam-6761	506	113	(	(	PUNCT
ejpam-6761	506	114	xfz	xfz	PROPN
ejpam-6761	506	115	,	,	PUNCT
ejpam-6761	506	116	f−xz([−1	f−xz([−1	PROPN
ejpam-6761	506	117	,	,	PUNCT
ejpam-6761	506	118	0	0	NUM
ejpam-6761	506	119	]	]	PUNCT
ejpam-6761	506	120	,	,	PUNCT
ejpam-6761	506	121	bz	bz	PROPN
ejpam-6761	506	122	)	)	PUNCT
ejpam-6761	506	123	,	,	PUNCT
ejpam-6761	506	124	f	f	PROPN
ejpam-6761	506	125	+	+	CCONJ
ejpam-6761	506	126	xz([0	xz([0	ADJ
ejpam-6761	506	127	,	,	PUNCT
ejpam-6761	506	128	1	1	NUM
ejpam-6761	506	129	]	]	PUNCT
ejpam-6761	506	130	,	,	PUNCT
ejpam-6761	506	131	bz	bz	PROPN
ejpam-6761	506	132	)	)	PUNCT
ejpam-6761	506	133	)	)	PUNCT
ejpam-6761	506	134	}	}	PUNCT
ejpam-6761	506	135	(	(	PUNCT
ejpam-6761	506	136	20	20	NUM
ejpam-6761	506	137	)	)	PUNCT
ejpam-6761	506	138	is	be	AUX
ejpam-6761	506	139	called	call	VERB
ejpam-6761	506	140	a	a	DET
ejpam-6761	506	141	left	left	ADJ
ejpam-6761	506	142	coset	coset	NOUN
ejpam-6761	506	143	of	of	ADP
ejpam-6761	506	144	the	the	DET
ejpam-6761	506	145	bipolar	bipolar	PROPN
ejpam-6761	506	146	valued	value	VERB
ejpam-6761	506	147	fuzzy	fuzzy	ADJ
ejpam-6761	506	148	subgroup	subgroup	NOUN
ejpam-6761	506	149	(	(	PUNCT
ejpam-6761	506	150	b;f	b;f	NOUN
ejpam-6761	506	151	)	)	PUNCT
ejpam-6761	506	152	.	.	PUNCT
ejpam-6761	507	1	a	a	DET
ejpam-6761	507	2	right	right	ADJ
ejpam-6761	507	3	coset	coset	NOUN
ejpam-6761	507	4	of	of	ADP
ejpam-6761	507	5	the	the	DET
ejpam-6761	507	6	bipolar	bipolar	PROPN
ejpam-6761	507	7	valued	value	VERB
ejpam-6761	507	8	fuzzy	fuzzy	ADJ
ejpam-6761	507	9	subgroup	subgroup	NOUN
ejpam-6761	507	10	(	(	PUNCT
ejpam-6761	507	11	b;f	b;f	NOUN
ejpam-6761	507	12	)	)	PUNCT
ejpam-6761	507	13	is	be	AUX
ejpam-6761	507	14	defined	define	VERB
ejpam-6761	507	15	by	by	ADP
ejpam-6761	507	16	the	the	DET
ejpam-6761	507	17	bipolar	bipolar	PROPN
ejpam-6761	507	18	valued	value	VERB
ejpam-6761	507	19	fuzzy	fuzzy	ADJ
ejpam-6761	507	20	subspace	subspace	NOUN
ejpam-6761	507	21	b(x	b(x	NOUN
ejpam-6761	507	22	,	,	PUNCT
ejpam-6761	507	23	[	[	X
ejpam-6761	507	24	−1	−1	NOUN
ejpam-6761	507	25	,	,	PUNCT
ejpam-6761	507	26	0	0	NUM
ejpam-6761	507	27	]	]	PUNCT
ejpam-6761	507	28	,	,	PUNCT
ejpam-6761	507	29	[	[	X
ejpam-6761	507	30	0	0	NUM
ejpam-6761	507	31	,	,	PUNCT
ejpam-6761	507	32	1	1	NUM
ejpam-6761	507	33	]	]	PUNCT
ejpam-6761	507	34	)	)	PUNCT
ejpam-6761	507	35	=	=	SYM
ejpam-6761	507	36	bf	bf	NOUN
ejpam-6761	507	37	(	(	PUNCT
ejpam-6761	507	38	x	x	X
ejpam-6761	507	39	,	,	PUNCT
ejpam-6761	507	40	[	[	X
ejpam-6761	507	41	−1	−1	NOUN
ejpam-6761	507	42	,	,	PUNCT
ejpam-6761	507	43	0	0	NUM
ejpam-6761	507	44	]	]	PUNCT
ejpam-6761	507	45	,	,	PUNCT
ejpam-6761	507	46	[	[	X
ejpam-6761	507	47	0	0	NUM
ejpam-6761	507	48	,	,	PUNCT
ejpam-6761	507	49	1	1	NUM
ejpam-6761	507	50	]	]	PUNCT
ejpam-6761	507	51	)	)	PUNCT
ejpam-6761	507	52	=	=	PRON
ejpam-6761	507	53	{	{	PUNCT
ejpam-6761	507	54	(	(	PUNCT
ejpam-6761	507	55	zfx	zfx	NOUN
ejpam-6761	507	56	,	,	PUNCT
ejpam-6761	507	57	f−zx(bz	f−zx(bz	PROPN
ejpam-6761	507	58	,	,	PUNCT
ejpam-6761	507	59	[	[	X
ejpam-6761	507	60	−1	−1	NOUN
ejpam-6761	507	61	,	,	PUNCT
ejpam-6761	507	62	0	0	NUM
ejpam-6761	507	63	]	]	NUM
ejpam-6761	507	64	)	)	PUNCT
ejpam-6761	507	65	,	,	PUNCT
ejpam-6761	507	66	f+zx(bz	f+zx(bz	X
ejpam-6761	507	67	,	,	PUNCT
ejpam-6761	507	68	[	[	X
ejpam-6761	507	69	0	0	NUM
ejpam-6761	507	70	,	,	PUNCT
ejpam-6761	507	71	1	1	NUM
ejpam-6761	507	72	]	]	NUM
ejpam-6761	507	73	)	)	PUNCT
ejpam-6761	507	74	)	)	PUNCT
ejpam-6761	507	75	}	}	PUNCT
ejpam-6761	507	76	.	.	PUNCT
ejpam-6761	508	1	theorem	theorem	VERB
ejpam-6761	508	2	7	7	NUM
ejpam-6761	508	3	.	.	X
ejpam-6761	508	4	for	for	ADP
ejpam-6761	508	5	any	any	DET
ejpam-6761	508	6	associative	associative	ADJ
ejpam-6761	508	7	bipolar	bipolar	ADJ
ejpam-6761	508	8	valued	value	VERB
ejpam-6761	508	9	fuzzy	fuzzy	ADJ
ejpam-6761	508	10	subgroup	subgroup	NOUN
ejpam-6761	508	11	(	(	PUNCT
ejpam-6761	508	12	b;f	b;f	NOUN
ejpam-6761	508	13	)	)	PUNCT
ejpam-6761	508	14	of	of	ADP
ejpam-6761	508	15	the	the	DET
ejpam-6761	508	16	bipolar	bipolar	ADJ
ejpam-6761	508	17	valued	value	VERB
ejpam-6761	508	18	fuzzy	fuzzy	ADJ
ejpam-6761	508	19	group	group	NOUN
ejpam-6761	508	20	(	(	PUNCT
ejpam-6761	508	21	(	(	PUNCT
ejpam-6761	508	22	g	g	NOUN
ejpam-6761	508	23	,	,	PUNCT
ejpam-6761	508	24	[	[	X
ejpam-6761	508	25	−1	−1	NOUN
ejpam-6761	508	26	,	,	PUNCT
ejpam-6761	508	27	0	0	NUM
ejpam-6761	508	28	]	]	PUNCT
ejpam-6761	508	29	,	,	PUNCT
ejpam-6761	508	30	[	[	X
ejpam-6761	508	31	0	0	NUM
ejpam-6761	508	32	,	,	PUNCT
ejpam-6761	508	33	1	1	NUM
ejpam-6761	508	34	]	]	NUM
ejpam-6761	508	35	)	)	PUNCT
ejpam-6761	508	36	,	,	PUNCT
ejpam-6761	508	37	f	f	PROPN
ejpam-6761	508	38	)	)	PUNCT
ejpam-6761	508	39	,	,	PUNCT
ejpam-6761	508	40	the	the	DET
ejpam-6761	508	41	following	follow	VERB
ejpam-6761	508	42	hold	hold	NOUN
ejpam-6761	508	43	:	:	PUNCT
ejpam-6761	508	44	(	(	PUNCT
ejpam-6761	508	45	1	1	X
ejpam-6761	508	46	)	)	PUNCT
ejpam-6761	508	47	(	(	PUNCT
ejpam-6761	508	48	x	x	X
ejpam-6761	508	49	,	,	PUNCT
ejpam-6761	508	50	[	[	X
ejpam-6761	508	51	−1	−1	NOUN
ejpam-6761	508	52	,	,	PUNCT
ejpam-6761	508	53	0	0	NUM
ejpam-6761	508	54	]	]	PUNCT
ejpam-6761	508	55	,	,	PUNCT
ejpam-6761	509	1	[	[	X
ejpam-6761	509	2	0	0	NUM
ejpam-6761	509	3	,	,	PUNCT
ejpam-6761	509	4	1])b	1])b	NUM
ejpam-6761	509	5	=	=	SYM
ejpam-6761	509	6	(	(	PUNCT
ejpam-6761	509	7	h	h	NOUN
ejpam-6761	509	8	,	,	PUNCT
ejpam-6761	509	9	[	[	X
ejpam-6761	509	10	−1	−1	NOUN
ejpam-6761	509	11	,	,	PUNCT
ejpam-6761	509	12	0]−h	0]−h	NOUN
ejpam-6761	509	13	,	,	PUNCT
ejpam-6761	509	14	[	[	X
ejpam-6761	509	15	0	0	NUM
ejpam-6761	509	16	,	,	PUNCT
ejpam-6761	509	17	1	1	NUM
ejpam-6761	509	18	]	]	PUNCT
ejpam-6761	509	19	+	+	NUM
ejpam-6761	509	20	h	h	NOUN
ejpam-6761	509	21	)	)	PUNCT
ejpam-6761	509	22	b	b	NOUN
ejpam-6761	509	23	for	for	ADP
ejpam-6761	509	24	every	every	DET
ejpam-6761	509	25	bipolar	bipolar	ADJ
ejpam-6761	509	26	valued	value	VERB
ejpam-6761	509	27	fuzzy	fuzzy	ADJ
ejpam-6761	509	28	element	element	NOUN
ejpam-6761	509	29	(	(	PUNCT
ejpam-6761	509	30	h	h	NOUN
ejpam-6761	509	31	,	,	PUNCT
ejpam-6761	509	32	[	[	X
ejpam-6761	509	33	−1	−1	NOUN
ejpam-6761	509	34	,	,	PUNCT
ejpam-6761	509	35	0]−h	0]−h	NOUN
ejpam-6761	509	36	,	,	PUNCT
ejpam-6761	509	37	[	[	X
ejpam-6761	509	38	0	0	NUM
ejpam-6761	509	39	,	,	PUNCT
ejpam-6761	509	40	1	1	NUM
ejpam-6761	509	41	]	]	PUNCT
ejpam-6761	509	42	+	+	NUM
ejpam-6761	509	43	h	h	NOUN
ejpam-6761	509	44	)	)	PUNCT
ejpam-6761	509	45	∈	∈	PROPN
ejpam-6761	509	46	(	(	PUNCT
ejpam-6761	509	47	x	x	X
ejpam-6761	509	48	,	,	PUNCT
ejpam-6761	509	49	[	[	X
ejpam-6761	509	50	−1	−1	NOUN
ejpam-6761	509	51	,	,	PUNCT
ejpam-6761	509	52	0	0	NUM
ejpam-6761	509	53	]	]	PUNCT
ejpam-6761	509	54	,	,	PUNCT
ejpam-6761	509	55	[	[	X
ejpam-6761	509	56	0	0	NUM
ejpam-6761	509	57	,	,	PUNCT
ejpam-6761	509	58	1])b	1])b	NUM
ejpam-6761	509	59	,	,	PUNCT
ejpam-6761	510	1	where	where	SCONJ
ejpam-6761	510	2	[	[	X
ejpam-6761	510	3	−1	−1	NOUN
ejpam-6761	510	4	,	,	PUNCT
ejpam-6761	510	5	0]−h	0]−h	NOUN
ejpam-6761	510	6	,	,	PUNCT
ejpam-6761	510	7	[	[	X
ejpam-6761	510	8	0	0	NUM
ejpam-6761	510	9	,	,	PUNCT
ejpam-6761	510	10	1	1	NUM
ejpam-6761	510	11	]	]	PUNCT
ejpam-6761	510	12	+	+	CCONJ
ejpam-6761	510	13	h	h	NOUN
ejpam-6761	510	14	denote	denote	VERB
ejpam-6761	510	15	the	the	DET
ejpam-6761	510	16	possible	possible	ADJ
ejpam-6761	510	17	negative	negative	ADJ
ejpam-6761	510	18	and	and	CCONJ
ejpam-6761	510	19	positive	positive	ADJ
ejpam-6761	510	20	membership	membership	NOUN
ejpam-6761	510	21	values	value	NOUN
ejpam-6761	510	22	of	of	ADP
ejpam-6761	510	23	h.	h.	PROPN
ejpam-6761	510	24	(	(	PUNCT
ejpam-6761	510	25	2	2	X
ejpam-6761	510	26	)	)	PUNCT
ejpam-6761	510	27	there	there	PRON
ejpam-6761	510	28	is	be	VERB
ejpam-6761	510	29	a	a	DET
ejpam-6761	510	30	one	one	NUM
ejpam-6761	510	31	-	-	PUNCT
ejpam-6761	510	32	to	to	ADP
ejpam-6761	510	33	-	-	PUNCT
ejpam-6761	510	34	one	one	NUM
ejpam-6761	510	35	correspondence	correspondence	NOUN
ejpam-6761	510	36	between	between	ADP
ejpam-6761	510	37	any	any	DET
ejpam-6761	510	38	two	two	NUM
ejpam-6761	510	39	left	left	ADJ
ejpam-6761	510	40	(	(	PUNCT
ejpam-6761	510	41	right	right	ADJ
ejpam-6761	510	42	)	)	PUNCT
ejpam-6761	510	43	cossets	cosset	NOUN
ejpam-6761	510	44	of	of	ADP
ejpam-6761	510	45	the	the	DET
ejpam-6761	510	46	bipolar	bipolar	ADJ
ejpam-6761	510	47	valued	value	VERB
ejpam-6761	510	48	fuzzy	fuzzy	ADJ
ejpam-6761	510	49	subgroup	subgroup	NOUN
ejpam-6761	510	50	(	(	PUNCT
ejpam-6761	510	51	b;f	b;f	NOUN
ejpam-6761	510	52	)	)	PUNCT
ejpam-6761	510	53	.	.	PUNCT
ejpam-6761	511	1	(	(	PUNCT
ejpam-6761	511	2	3	3	X
ejpam-6761	511	3	)	)	PUNCT
ejpam-6761	511	4	there	there	PRON
ejpam-6761	511	5	is	be	VERB
ejpam-6761	511	6	a	a	DET
ejpam-6761	511	7	one	one	NUM
ejpam-6761	511	8	-	-	PUNCT
ejpam-6761	511	9	to	to	ADP
ejpam-6761	511	10	-	-	PUNCT
ejpam-6761	511	11	one	one	NUM
ejpam-6761	511	12	correspondence	correspondence	NOUN
ejpam-6761	511	13	between	between	ADP
ejpam-6761	511	14	the	the	DET
ejpam-6761	511	15	family	family	NOUN
ejpam-6761	511	16	of	of	ADP
ejpam-6761	511	17	right	right	ADJ
ejpam-6761	511	18	cosets	coset	NOUN
ejpam-6761	511	19	and	and	CCONJ
ejpam-6761	511	20	the	the	DET
ejpam-6761	511	21	family	family	NOUN
ejpam-6761	511	22	of	of	ADP
ejpam-6761	511	23	left	leave	VERB
ejpam-6761	511	24	cosets	coset	NOUN
ejpam-6761	511	25	of	of	ADP
ejpam-6761	511	26	the	the	DET
ejpam-6761	511	27	bipolar	bipolar	ADJ
ejpam-6761	511	28	valued	value	VERB
ejpam-6761	511	29	fuzzy	fuzzy	ADJ
ejpam-6761	511	30	subgroup	subgroup	NOUN
ejpam-6761	511	31	(	(	PUNCT
ejpam-6761	511	32	b;f	b;f	NOUN
ejpam-6761	511	33	)	)	PUNCT
ejpam-6761	511	34	.	.	PUNCT
ejpam-6761	512	1	(	(	PUNCT
ejpam-6761	512	2	4	4	X
ejpam-6761	512	3	)	)	PUNCT
ejpam-6761	512	4	any	any	DET
ejpam-6761	512	5	two	two	NUM
ejpam-6761	512	6	right	right	ADJ
ejpam-6761	512	7	cosets	coset	NOUN
ejpam-6761	512	8	(	(	PUNCT
ejpam-6761	512	9	left	leave	VERB
ejpam-6761	512	10	cosets	coset	NOUN
ejpam-6761	512	11	)	)	PUNCT
ejpam-6761	512	12	of	of	ADP
ejpam-6761	512	13	the	the	DET
ejpam-6761	512	14	bipolar	bipolar	PROPN
ejpam-6761	512	15	valued	value	VERB
ejpam-6761	512	16	fuzzy	fuzzy	ADJ
ejpam-6761	512	17	subgroup	subgroup	NOUN
ejpam-6761	512	18	(	(	PUNCT
ejpam-6761	512	19	b;f	b;f	NOUN
ejpam-6761	512	20	)	)	PUNCT
ejpam-6761	512	21	are	be	AUX
ejpam-6761	512	22	either	either	CCONJ
ejpam-6761	512	23	identical	identical	ADJ
ejpam-6761	512	24	or	or	CCONJ
ejpam-6761	512	25	disjoint	disjoint	ADJ
ejpam-6761	512	26	bipolar	bipolar	ADJ
ejpam-6761	512	27	valued	value	VERB
ejpam-6761	512	28	fuzzy	fuzzy	ADJ
ejpam-6761	512	29	subspaces	subspace	NOUN
ejpam-6761	512	30	.	.	PUNCT
ejpam-6761	513	1	f.	f.	PROPN
ejpam-6761	513	2	al	al	PROPN
ejpam-6761	513	3	-	-	PROPN
ejpam-6761	513	4	zu’bi	zu’bi	PROPN
ejpam-6761	513	5	et	et	NOUN
ejpam-6761	513	6	al	al	PROPN
ejpam-6761	513	7	.	.	PUNCT
ejpam-6761	513	8	/	/	SYM
ejpam-6761	513	9	eur	eur	PROPN
ejpam-6761	513	10	.	.	PUNCT
ejpam-6761	514	1	j.	j.	PROPN
ejpam-6761	514	2	pure	pure	PROPN
ejpam-6761	514	3	appl	appl	PROPN
ejpam-6761	514	4	.	.	PROPN
ejpam-6761	514	5	math	math	PROPN
ejpam-6761	514	6	,	,	PUNCT
ejpam-6761	514	7	18	18	NUM
ejpam-6761	514	8	(	(	PUNCT
ejpam-6761	514	9	4	4	NUM
ejpam-6761	514	10	)	)	PUNCT
ejpam-6761	514	11	(	(	PUNCT
ejpam-6761	514	12	2025	2025	NUM
ejpam-6761	514	13	)	)	PUNCT
ejpam-6761	514	14	,	,	PUNCT
ejpam-6761	514	15	6761	6761	NUM
ejpam-6761	514	16	21	21	NUM
ejpam-6761	514	17	of	of	ADP
ejpam-6761	514	18	28	28	NUM
ejpam-6761	514	19	proof	proof	NOUN
ejpam-6761	514	20	.	.	PUNCT
ejpam-6761	515	1	(	(	PUNCT
ejpam-6761	515	2	1	1	X
ejpam-6761	515	3	)	)	PUNCT
ejpam-6761	515	4	let	let	VERB
ejpam-6761	515	5	(	(	PUNCT
ejpam-6761	515	6	h	h	NOUN
ejpam-6761	515	7	,	,	PUNCT
ejpam-6761	515	8	[	[	X
ejpam-6761	515	9	−1	−1	NOUN
ejpam-6761	515	10	,	,	PUNCT
ejpam-6761	515	11	0]−h	0]−h	NOUN
ejpam-6761	515	12	,	,	PUNCT
ejpam-6761	515	13	[	[	X
ejpam-6761	515	14	0	0	NUM
ejpam-6761	515	15	,	,	PUNCT
ejpam-6761	515	16	1	1	NUM
ejpam-6761	515	17	]	]	PUNCT
ejpam-6761	515	18	+	+	NUM
ejpam-6761	515	19	h	h	NOUN
ejpam-6761	515	20	)	)	PUNCT
ejpam-6761	515	21	be	be	VERB
ejpam-6761	515	22	any	any	DET
ejpam-6761	515	23	bipolar	bipolar	ADJ
ejpam-6761	515	24	valued	value	VERB
ejpam-6761	515	25	fuzzy	fuzzy	ADJ
ejpam-6761	515	26	element	element	NOUN
ejpam-6761	515	27	in	in	ADP
ejpam-6761	515	28	(	(	PUNCT
ejpam-6761	515	29	x	x	X
ejpam-6761	515	30	,	,	PUNCT
ejpam-6761	515	31	[	[	X
ejpam-6761	515	32	−1	−1	NOUN
ejpam-6761	515	33	,	,	PUNCT
ejpam-6761	515	34	0	0	NUM
ejpam-6761	515	35	]	]	PUNCT
ejpam-6761	515	36	,	,	PUNCT
ejpam-6761	515	37	[	[	X
ejpam-6761	515	38	0	0	NUM
ejpam-6761	515	39	,	,	PUNCT
ejpam-6761	515	40	1])b	1])b	NUM
ejpam-6761	515	41	,	,	PUNCT
ejpam-6761	515	42	then	then	ADV
ejpam-6761	515	43	(	(	PUNCT
ejpam-6761	515	44	h	h	NOUN
ejpam-6761	515	45	,	,	PUNCT
ejpam-6761	515	46	[	[	X
ejpam-6761	515	47	−1	−1	NOUN
ejpam-6761	515	48	,	,	PUNCT
ejpam-6761	515	49	0]−h	0]−h	NOUN
ejpam-6761	515	50	,	,	PUNCT
ejpam-6761	515	51	[	[	X
ejpam-6761	515	52	0	0	NUM
ejpam-6761	515	53	,	,	PUNCT
ejpam-6761	515	54	1	1	NUM
ejpam-6761	515	55	]	]	PUNCT
ejpam-6761	515	56	+	+	NUM
ejpam-6761	515	57	h	h	NOUN
ejpam-6761	515	58	)	)	PUNCT
ejpam-6761	516	1	=	=	SYM
ejpam-6761	516	2	(	(	PUNCT
ejpam-6761	516	3	x	x	X
ejpam-6761	516	4	,	,	PUNCT
ejpam-6761	516	5	[	[	X
ejpam-6761	516	6	−1	−1	NOUN
ejpam-6761	516	7	,	,	PUNCT
ejpam-6761	516	8	0	0	NUM
ejpam-6761	516	9	]	]	PUNCT
ejpam-6761	516	10	,	,	PUNCT
ejpam-6761	517	1	[	[	X
ejpam-6761	517	2	0	0	NUM
ejpam-6761	517	3	,	,	PUNCT
ejpam-6761	517	4	1])(y	1])(y	PROPN
ejpam-6761	517	5	,	,	PUNCT
ejpam-6761	517	6	b−y	b−y	NOUN
ejpam-6761	517	7	,	,	PUNCT
ejpam-6761	517	8	b	b	PROPN
ejpam-6761	517	9	+	+	CCONJ
ejpam-6761	517	10	y	y	PROPN
ejpam-6761	517	11	)	)	PUNCT
ejpam-6761	517	12	for	for	ADP
ejpam-6761	517	13	some	some	DET
ejpam-6761	517	14	y	y	PROPN
ejpam-6761	517	15	∈	∈	PROPN
ejpam-6761	517	16	b	b	PROPN
ejpam-6761	517	17	◦	◦	NOUN
ejpam-6761	517	18	.	.	PUNCT
ejpam-6761	518	1	if	if	SCONJ
ejpam-6761	518	2	(	(	PUNCT
ejpam-6761	518	3	z	z	NOUN
ejpam-6761	518	4	,	,	PUNCT
ejpam-6761	518	5	b	b	NOUN
ejpam-6761	518	6	−	−	PROPN
ejpam-6761	518	7	z	z	NOUN
ejpam-6761	518	8	,	,	PUNCT
ejpam-6761	518	9	b	b	PROPN
ejpam-6761	518	10	+	+	CCONJ
ejpam-6761	518	11	z	z	NOUN
ejpam-6761	518	12	)	)	PUNCT
ejpam-6761	518	13	is	be	AUX
ejpam-6761	518	14	an	an	DET
ejpam-6761	518	15	arbitrary	arbitrary	ADJ
ejpam-6761	518	16	element	element	NOUN
ejpam-6761	518	17	of	of	ADP
ejpam-6761	518	18	b	b	NOUN
ejpam-6761	518	19	,	,	PUNCT
ejpam-6761	518	20	then	then	ADV
ejpam-6761	518	21	(	(	PUNCT
ejpam-6761	518	22	x	x	X
ejpam-6761	518	23	,	,	PUNCT
ejpam-6761	518	24	[	[	X
ejpam-6761	518	25	−1	−1	NOUN
ejpam-6761	518	26	,	,	PUNCT
ejpam-6761	518	27	0	0	NUM
ejpam-6761	518	28	]	]	PUNCT
ejpam-6761	518	29	,	,	PUNCT
ejpam-6761	518	30	[	[	X
ejpam-6761	518	31	0	0	NUM
ejpam-6761	518	32	,	,	PUNCT
ejpam-6761	518	33	1])(z	1])(z	PROPN
ejpam-6761	518	34	,	,	PUNCT
ejpam-6761	518	35	b−z	b−z	NOUN
ejpam-6761	518	36	,	,	PUNCT
ejpam-6761	518	37	b	b	PROPN
ejpam-6761	519	1	+	+	NOUN
ejpam-6761	519	2	z	z	NOUN
ejpam-6761	519	3	)	)	PUNCT
ejpam-6761	520	1	=	=	SYM
ejpam-6761	520	2	(	(	PUNCT
ejpam-6761	520	3	x	x	X
ejpam-6761	520	4	,	,	PUNCT
ejpam-6761	520	5	[	[	X
ejpam-6761	520	6	−1	−1	NOUN
ejpam-6761	520	7	,	,	PUNCT
ejpam-6761	520	8	0	0	NUM
ejpam-6761	520	9	]	]	PUNCT
ejpam-6761	520	10	,	,	PUNCT
ejpam-6761	521	1	[	[	X
ejpam-6761	521	2	0	0	NUM
ejpam-6761	521	3	,	,	PUNCT
ejpam-6761	521	4	1])((y	1])((y	NUM
ejpam-6761	521	5	,	,	PUNCT
ejpam-6761	521	6	b−y	b−y	NOUN
ejpam-6761	521	7	,	,	PUNCT
ejpam-6761	521	8	b	b	PROPN
ejpam-6761	521	9	+	+	CCONJ
ejpam-6761	521	10	y	y	PROPN
ejpam-6761	521	11	)	)	PUNCT
ejpam-6761	521	12	(	(	PUNCT
ejpam-6761	521	13	y	y	PROPN
ejpam-6761	521	14	−1	−1	NOUN
ejpam-6761	521	15	,	,	PUNCT
ejpam-6761	521	16	b−	b−	PROPN
ejpam-6761	521	17	y−1	y−1	PROPN
ejpam-6761	521	18	,	,	PUNCT
ejpam-6761	521	19	b	b	PROPN
ejpam-6761	521	20	+	+	CCONJ
ejpam-6761	521	21	y−1))(z	y−1))(z	NOUN
ejpam-6761	521	22	,	,	PUNCT
ejpam-6761	521	23	b	b	X
ejpam-6761	521	24	−	−	PROPN
ejpam-6761	522	1	z	z	NOUN
ejpam-6761	522	2	,	,	PUNCT
ejpam-6761	522	3	b	b	PROPN
ejpam-6761	522	4	+	+	NOUN
ejpam-6761	522	5	z	z	NOUN
ejpam-6761	522	6	)	)	PUNCT
ejpam-6761	523	1	=	=	SYM
ejpam-6761	523	2	(	(	PUNCT
ejpam-6761	523	3	(	(	PUNCT
ejpam-6761	523	4	x	x	NOUN
ejpam-6761	523	5	,	,	PUNCT
ejpam-6761	523	6	c)(y	c)(y	PROPN
ejpam-6761	523	7	,	,	PUNCT
ejpam-6761	523	8	b−y	b−y	NOUN
ejpam-6761	523	9	,	,	PUNCT
ejpam-6761	523	10	b	b	PROPN
ejpam-6761	523	11	+	+	CCONJ
ejpam-6761	523	12	y	y	PROPN
ejpam-6761	523	13	)	)	PUNCT
ejpam-6761	523	14	)	)	PUNCT
ejpam-6761	524	1	(	(	PUNCT
ejpam-6761	524	2	(	(	PUNCT
ejpam-6761	524	3	y	y	PROPN
ejpam-6761	524	4	−1	−1	NOUN
ejpam-6761	524	5	,	,	PUNCT
ejpam-6761	524	6	b−	b−	PROPN
ejpam-6761	524	7	y−1	y−1	PROPN
ejpam-6761	524	8	,	,	PUNCT
ejpam-6761	524	9	b	b	PROPN
ejpam-6761	524	10	+	+	NUM
ejpam-6761	524	11	y−1)(z	y−1)(z	PROPN
ejpam-6761	524	12	,	,	PUNCT
ejpam-6761	524	13	b	b	X
ejpam-6761	524	14	−	−	PROPN
ejpam-6761	524	15	z	z	NOUN
ejpam-6761	524	16	,	,	PUNCT
ejpam-6761	524	17	b	b	PROPN
ejpam-6761	524	18	+	+	CCONJ
ejpam-6761	524	19	z	z	NOUN
ejpam-6761	524	20	)	)	PUNCT
ejpam-6761	524	21	)	)	PUNCT
ejpam-6761	525	1	∈	∈	PROPN
ejpam-6761	525	2	(	(	PUNCT
ejpam-6761	525	3	h	h	NOUN
ejpam-6761	525	4	,	,	PUNCT
ejpam-6761	525	5	[	[	X
ejpam-6761	525	6	−1	−1	NOUN
ejpam-6761	525	7	,	,	PUNCT
ejpam-6761	525	8	0]−h	0]−h	NOUN
ejpam-6761	525	9	,	,	PUNCT
ejpam-6761	525	10	[	[	X
ejpam-6761	525	11	0	0	NUM
ejpam-6761	525	12	,	,	PUNCT
ejpam-6761	525	13	1	1	NUM
ejpam-6761	525	14	]	]	PUNCT
ejpam-6761	525	15	+	+	NUM
ejpam-6761	525	16	h	h	NOUN
ejpam-6761	525	17	)	)	PUNCT
ejpam-6761	525	18	b.	b.	PROPN
ejpam-6761	525	19	(	(	PUNCT
ejpam-6761	525	20	21	21	NUM
ejpam-6761	525	21	)	)	PUNCT
ejpam-6761	525	22	(	(	PUNCT
ejpam-6761	525	23	2	2	X
ejpam-6761	525	24	)	)	PUNCT
ejpam-6761	525	25	let	let	VERB
ejpam-6761	525	26	(	(	PUNCT
ejpam-6761	525	27	x	x	X
ejpam-6761	525	28	,	,	PUNCT
ejpam-6761	525	29	[	[	X
ejpam-6761	525	30	−1	−1	NOUN
ejpam-6761	525	31	,	,	PUNCT
ejpam-6761	525	32	0	0	NUM
ejpam-6761	525	33	]	]	PUNCT
ejpam-6761	525	34	,	,	PUNCT
ejpam-6761	525	35	[	[	X
ejpam-6761	525	36	0	0	NUM
ejpam-6761	525	37	,	,	PUNCT
ejpam-6761	525	38	1])b	1])b	NUM
ejpam-6761	525	39	and	and	CCONJ
ejpam-6761	525	40	(	(	PUNCT
ejpam-6761	525	41	y	y	PROPN
ejpam-6761	525	42	,	,	PUNCT
ejpam-6761	525	43	[	[	X
ejpam-6761	525	44	−1	−1	NOUN
ejpam-6761	525	45	,	,	PUNCT
ejpam-6761	525	46	0	0	NUM
ejpam-6761	525	47	]	]	PUNCT
ejpam-6761	525	48	,	,	PUNCT
ejpam-6761	525	49	[	[	X
ejpam-6761	525	50	0	0	NUM
ejpam-6761	525	51	,	,	PUNCT
ejpam-6761	525	52	1])b	1])b	NUM
ejpam-6761	525	53	be	be	AUX
ejpam-6761	525	54	any	any	DET
ejpam-6761	525	55	two	two	NUM
ejpam-6761	525	56	left	leave	VERB
ejpam-6761	525	57	cosets	coset	NOUN
ejpam-6761	525	58	of	of	ADP
ejpam-6761	525	59	the	the	DET
ejpam-6761	525	60	bipolar	bipolar	ADJ
ejpam-6761	525	61	valued	value	VERB
ejpam-6761	525	62	fuzzy	fuzzy	ADJ
ejpam-6761	525	63	group	group	NOUN
ejpam-6761	525	64	b	b	PROPN
ejpam-6761	525	65	,	,	PUNCT
ejpam-6761	525	66	then	then	ADV
ejpam-6761	525	67	(	(	PUNCT
ejpam-6761	525	68	x	x	X
ejpam-6761	525	69	,	,	PUNCT
ejpam-6761	525	70	[	[	X
ejpam-6761	525	71	−1	−1	NOUN
ejpam-6761	525	72	,	,	PUNCT
ejpam-6761	525	73	0	0	NUM
ejpam-6761	525	74	]	]	PUNCT
ejpam-6761	525	75	,	,	PUNCT
ejpam-6761	525	76	[	[	X
ejpam-6761	525	77	0	0	NUM
ejpam-6761	525	78	,	,	PUNCT
ejpam-6761	525	79	1])(z	1])(z	PROPN
ejpam-6761	525	80	,	,	PUNCT
ejpam-6761	525	81	b−z	b−z	NOUN
ejpam-6761	525	82	,	,	PUNCT
ejpam-6761	525	83	b	b	PROPN
ejpam-6761	525	84	+	+	NOUN
ejpam-6761	525	85	z	z	NOUN
ejpam-6761	525	86	)	)	PUNCT
ejpam-6761	526	1	↔	↔	PROPN
ejpam-6761	526	2	(	(	PUNCT
ejpam-6761	526	3	y	y	NOUN
ejpam-6761	526	4	,	,	PUNCT
ejpam-6761	526	5	[	[	X
ejpam-6761	526	6	−1	−1	NOUN
ejpam-6761	526	7	,	,	PUNCT
ejpam-6761	526	8	0	0	NUM
ejpam-6761	526	9	]	]	PUNCT
ejpam-6761	526	10	,	,	PUNCT
ejpam-6761	526	11	[	[	X
ejpam-6761	526	12	0	0	NUM
ejpam-6761	526	13	,	,	PUNCT
ejpam-6761	526	14	1])(z	1])(z	PROPN
ejpam-6761	526	15	,	,	PUNCT
ejpam-6761	526	16	b−z	b−z	NOUN
ejpam-6761	526	17	,	,	PUNCT
ejpam-6761	526	18	b	b	PROPN
ejpam-6761	526	19	+	+	CCONJ
ejpam-6761	526	20	z	z	NOUN
ejpam-6761	526	21	)	)	PUNCT
ejpam-6761	526	22	(	(	PUNCT
ejpam-6761	526	23	22	22	NUM
ejpam-6761	526	24	)	)	PUNCT
ejpam-6761	526	25	is	be	AUX
ejpam-6761	526	26	the	the	DET
ejpam-6761	526	27	required	require	VERB
ejpam-6761	526	28	one	one	NUM
ejpam-6761	526	29	-	-	PUNCT
ejpam-6761	526	30	to	to	ADP
ejpam-6761	526	31	-	-	PUNCT
ejpam-6761	526	32	one	one	NUM
ejpam-6761	526	33	correspondence	correspondence	NOUN
ejpam-6761	526	34	between	between	ADP
ejpam-6761	526	35	(	(	PUNCT
ejpam-6761	526	36	x	x	X
ejpam-6761	526	37	,	,	PUNCT
ejpam-6761	526	38	[	[	X
ejpam-6761	526	39	−1	−1	NOUN
ejpam-6761	526	40	,	,	PUNCT
ejpam-6761	526	41	0	0	NUM
ejpam-6761	526	42	]	]	PUNCT
ejpam-6761	526	43	,	,	PUNCT
ejpam-6761	526	44	[	[	X
ejpam-6761	526	45	0	0	NUM
ejpam-6761	526	46	,	,	PUNCT
ejpam-6761	526	47	1])b	1])b	NUM
ejpam-6761	526	48	and	and	CCONJ
ejpam-6761	526	49	(	(	PUNCT
ejpam-6761	526	50	y	y	PROPN
ejpam-6761	526	51	,	,	PUNCT
ejpam-6761	526	52	[	[	X
ejpam-6761	526	53	−1	−1	NOUN
ejpam-6761	526	54	,	,	PUNCT
ejpam-6761	526	55	0	0	NUM
ejpam-6761	526	56	]	]	PUNCT
ejpam-6761	526	57	,	,	PUNCT
ejpam-6761	526	58	[	[	X
ejpam-6761	526	59	0	0	NUM
ejpam-6761	526	60	,	,	PUNCT
ejpam-6761	526	61	1])b	1])b	NUM
ejpam-6761	526	62	.	.	X
ejpam-6761	527	1	for	for	ADP
ejpam-6761	527	2	the	the	DET
ejpam-6761	527	3	right	right	ADJ
ejpam-6761	527	4	cosets	coset	NOUN
ejpam-6761	527	5	,	,	PUNCT
ejpam-6761	527	6	we	we	PRON
ejpam-6761	527	7	use	use	VERB
ejpam-6761	527	8	the	the	DET
ejpam-6761	527	9	same	same	ADJ
ejpam-6761	527	10	arrangement	arrangement	NOUN
ejpam-6761	527	11	.	.	PUNCT
ejpam-6761	528	1	(	(	PUNCT
ejpam-6761	528	2	3	3	X
ejpam-6761	528	3	)	)	PUNCT
ejpam-6761	528	4	let	let	VERB
ejpam-6761	528	5	{	{	PUNCT
ejpam-6761	528	6	(	(	PUNCT
ejpam-6761	528	7	x	x	X
ejpam-6761	528	8	,	,	PUNCT
ejpam-6761	528	9	[	[	X
ejpam-6761	528	10	−1	−1	NOUN
ejpam-6761	528	11	,	,	PUNCT
ejpam-6761	528	12	0	0	NUM
ejpam-6761	528	13	]	]	PUNCT
ejpam-6761	528	14	,	,	PUNCT
ejpam-6761	528	15	[	[	X
ejpam-6761	528	16	0	0	NUM
ejpam-6761	528	17	,	,	PUNCT
ejpam-6761	528	18	1])b	1])b	NUM
ejpam-6761	528	19	|	|	ADV
ejpam-6761	528	20	x	x	SYM
ejpam-6761	528	21	∈	∈	PROPN
ejpam-6761	528	22	g	g	NOUN
ejpam-6761	528	23	}	}	PUNCT
ejpam-6761	528	24	and	and	CCONJ
ejpam-6761	528	25	{	{	PUNCT
ejpam-6761	528	26	b(x	b(x	NOUN
ejpam-6761	528	27	,	,	PUNCT
ejpam-6761	528	28	[	[	X
ejpam-6761	528	29	−1	−1	NOUN
ejpam-6761	528	30	,	,	PUNCT
ejpam-6761	528	31	0	0	NUM
ejpam-6761	528	32	]	]	PUNCT
ejpam-6761	528	33	,	,	PUNCT
ejpam-6761	528	34	[	[	X
ejpam-6761	528	35	0	0	NUM
ejpam-6761	528	36	,	,	PUNCT
ejpam-6761	528	37	1	1	NUM
ejpam-6761	528	38	]	]	PUNCT
ejpam-6761	528	39	)	)	PUNCT
ejpam-6761	529	1	|	|	ADV
ejpam-6761	529	2	x	x	SYM
ejpam-6761	529	3	∈	∈	PROPN
ejpam-6761	529	4	g	g	PROPN
ejpam-6761	529	5	}	}	PUNCT
ejpam-6761	529	6	denote	denote	VERB
ejpam-6761	529	7	the	the	DET
ejpam-6761	529	8	family	family	NOUN
ejpam-6761	529	9	of	of	ADP
ejpam-6761	529	10	left	left	ADJ
ejpam-6761	529	11	and	and	CCONJ
ejpam-6761	529	12	right	right	ADJ
ejpam-6761	529	13	cosets	coset	NOUN
ejpam-6761	529	14	respectively	respectively	ADV
ejpam-6761	529	15	of	of	ADP
ejpam-6761	529	16	the	the	DET
ejpam-6761	529	17	bipolar	bipolar	ADJ
ejpam-6761	529	18	valued	value	VERB
ejpam-6761	529	19	fuzzy	fuzzy	ADJ
ejpam-6761	529	20	group	group	NOUN
ejpam-6761	529	21	b	b	PROPN
ejpam-6761	529	22	,	,	PUNCT
ejpam-6761	529	23	then	then	ADV
ejpam-6761	529	24	the	the	DET
ejpam-6761	529	25	required	required	ADJ
ejpam-6761	529	26	one	one	NUM
ejpam-6761	529	27	-	-	PUNCT
ejpam-6761	529	28	to	to	ADP
ejpam-6761	529	29	-	-	PUNCT
ejpam-6761	529	30	one	one	NUM
ejpam-6761	529	31	correspondence	correspondence	NOUN
ejpam-6761	529	32	is	be	AUX
ejpam-6761	529	33	defined	define	VERB
ejpam-6761	529	34	by	by	ADP
ejpam-6761	529	35	:	:	PUNCT
ejpam-6761	529	36	(	(	PUNCT
ejpam-6761	529	37	x	x	X
ejpam-6761	529	38	,	,	PUNCT
ejpam-6761	529	39	[	[	X
ejpam-6761	529	40	−1	−1	NOUN
ejpam-6761	529	41	,	,	PUNCT
ejpam-6761	529	42	0	0	NUM
ejpam-6761	529	43	]	]	PUNCT
ejpam-6761	529	44	,	,	PUNCT
ejpam-6761	530	1	[	[	X
ejpam-6761	530	2	0	0	NUM
ejpam-6761	530	3	,	,	PUNCT
ejpam-6761	530	4	1])b	1])b	NUM
ejpam-6761	530	5	↔	↔	PROPN
ejpam-6761	530	6	b(x	b(x	NOUN
ejpam-6761	530	7	,	,	PUNCT
ejpam-6761	530	8	[	[	X
ejpam-6761	530	9	−1	−1	NOUN
ejpam-6761	530	10	,	,	PUNCT
ejpam-6761	530	11	0	0	NUM
ejpam-6761	530	12	]	]	PUNCT
ejpam-6761	530	13	,	,	PUNCT
ejpam-6761	531	1	[	[	X
ejpam-6761	531	2	0	0	NUM
ejpam-6761	531	3	,	,	PUNCT
ejpam-6761	531	4	1	1	NUM
ejpam-6761	531	5	]	]	NUM
ejpam-6761	531	6	)	)	PUNCT
ejpam-6761	531	7	(	(	PUNCT
ejpam-6761	531	8	23	23	NUM
ejpam-6761	531	9	)	)	PUNCT
ejpam-6761	531	10	(	(	PUNCT
ejpam-6761	531	11	4	4	X
ejpam-6761	531	12	)	)	PUNCT
ejpam-6761	531	13	let	let	VERB
ejpam-6761	531	14	(	(	PUNCT
ejpam-6761	531	15	x	x	X
ejpam-6761	531	16	,	,	PUNCT
ejpam-6761	531	17	[	[	X
ejpam-6761	531	18	−1	−1	NOUN
ejpam-6761	531	19	,	,	PUNCT
ejpam-6761	531	20	0	0	NUM
ejpam-6761	531	21	]	]	PUNCT
ejpam-6761	531	22	,	,	PUNCT
ejpam-6761	532	1	[	[	X
ejpam-6761	532	2	0	0	NUM
ejpam-6761	532	3	,	,	PUNCT
ejpam-6761	532	4	1])b	1])b	NUM
ejpam-6761	532	5	and	and	CCONJ
ejpam-6761	532	6	(	(	PUNCT
ejpam-6761	532	7	y	y	PROPN
ejpam-6761	532	8	,	,	PUNCT
ejpam-6761	532	9	[	[	X
ejpam-6761	532	10	−1	−1	NOUN
ejpam-6761	532	11	,	,	PUNCT
ejpam-6761	532	12	0	0	NUM
ejpam-6761	532	13	]	]	PUNCT
ejpam-6761	532	14	,	,	PUNCT
ejpam-6761	532	15	[	[	X
ejpam-6761	532	16	0	0	NUM
ejpam-6761	532	17	,	,	PUNCT
ejpam-6761	532	18	1])b	1])b	NUM
ejpam-6761	532	19	be	be	AUX
ejpam-6761	532	20	any	any	DET
ejpam-6761	532	21	two	two	NUM
ejpam-6761	532	22	intersecting	intersecting	NOUN
ejpam-6761	532	23	left	leave	VERB
ejpam-6761	532	24	cosets	coset	NOUN
ejpam-6761	532	25	of	of	ADP
ejpam-6761	532	26	the	the	DET
ejpam-6761	532	27	bipolar	bipolar	ADJ
ejpam-6761	532	28	valued	value	VERB
ejpam-6761	532	29	fuzzy	fuzzy	ADJ
ejpam-6761	532	30	subgroup	subgroup	PROPN
ejpam-6761	532	31	b	b	PROPN
ejpam-6761	532	32	,	,	PUNCT
ejpam-6761	532	33	then	then	ADV
ejpam-6761	532	34	there	there	PRON
ejpam-6761	532	35	exist	exist	VERB
ejpam-6761	532	36	α	α	PRON
ejpam-6761	532	37	,	,	PUNCT
ejpam-6761	532	38	β	β	X
ejpam-6761	532	39	∈	∈	PROPN
ejpam-6761	533	1	b	b	X
ejpam-6761	533	2	◦	◦	NOUN
ejpam-6761	533	3	such	such	ADJ
ejpam-6761	533	4	that	that	SCONJ
ejpam-6761	533	5	(	(	PUNCT
ejpam-6761	533	6	x	x	X
ejpam-6761	533	7	,	,	PUNCT
ejpam-6761	533	8	[	[	X
ejpam-6761	533	9	−1	−1	NOUN
ejpam-6761	533	10	,	,	PUNCT
ejpam-6761	533	11	0	0	NUM
ejpam-6761	533	12	]	]	PUNCT
ejpam-6761	533	13	,	,	PUNCT
ejpam-6761	533	14	[	[	X
ejpam-6761	533	15	0	0	NUM
ejpam-6761	533	16	,	,	PUNCT
ejpam-6761	533	17	1])(α	1])(α	PROPN
ejpam-6761	533	18	,	,	PUNCT
ejpam-6761	533	19	b−α	b−α	PROPN
ejpam-6761	533	20	,	,	PUNCT
ejpam-6761	533	21	b	b	X
ejpam-6761	533	22	+	+	CCONJ
ejpam-6761	533	23	α	α	NOUN
ejpam-6761	533	24	)	)	PUNCT
ejpam-6761	534	1	=	=	SYM
ejpam-6761	534	2	(	(	PUNCT
ejpam-6761	534	3	y	y	NOUN
ejpam-6761	534	4	,	,	PUNCT
ejpam-6761	534	5	[	[	X
ejpam-6761	534	6	−1	−1	NOUN
ejpam-6761	534	7	,	,	PUNCT
ejpam-6761	534	8	0	0	NUM
ejpam-6761	534	9	]	]	PUNCT
ejpam-6761	534	10	,	,	PUNCT
ejpam-6761	534	11	[	[	X
ejpam-6761	534	12	0	0	NUM
ejpam-6761	534	13	,	,	PUNCT
ejpam-6761	534	14	1])(β	1])(β	PROPN
ejpam-6761	534	15	,	,	PUNCT
ejpam-6761	534	16	b−β	b−β	NOUN
ejpam-6761	534	17	,	,	PUNCT
ejpam-6761	534	18	b	b	X
ejpam-6761	534	19	+	+	CCONJ
ejpam-6761	534	20	β	β	X
ejpam-6761	534	21	)	)	PUNCT
ejpam-6761	534	22	(	(	PUNCT
ejpam-6761	534	23	24	24	NUM
ejpam-6761	534	24	)	)	PUNCT
ejpam-6761	534	25	choose	choose	VERB
ejpam-6761	534	26	any	any	DET
ejpam-6761	534	27	bipolar	bipolar	ADJ
ejpam-6761	534	28	valued	value	VERB
ejpam-6761	534	29	fuzzy	fuzzy	ADJ
ejpam-6761	534	30	element	element	NOUN
ejpam-6761	534	31	(	(	PUNCT
ejpam-6761	534	32	x	x	X
ejpam-6761	534	33	,	,	PUNCT
ejpam-6761	534	34	[	[	X
ejpam-6761	534	35	−1	−1	NOUN
ejpam-6761	534	36	,	,	PUNCT
ejpam-6761	534	37	0	0	NUM
ejpam-6761	534	38	]	]	PUNCT
ejpam-6761	534	39	,	,	PUNCT
ejpam-6761	535	1	[	[	X
ejpam-6761	535	2	0	0	NUM
ejpam-6761	535	3	,	,	PUNCT
ejpam-6761	535	4	1])(z	1])(z	PROPN
ejpam-6761	535	5	,	,	PUNCT
ejpam-6761	535	6	b−z	b−z	NOUN
ejpam-6761	535	7	,	,	PUNCT
ejpam-6761	535	8	b	b	PROPN
ejpam-6761	535	9	+	+	NOUN
ejpam-6761	535	10	z	z	NOUN
ejpam-6761	535	11	)	)	PUNCT
ejpam-6761	535	12	∈	∈	PROPN
ejpam-6761	535	13	(	(	PUNCT
ejpam-6761	535	14	x	x	X
ejpam-6761	535	15	,	,	PUNCT
ejpam-6761	535	16	[	[	X
ejpam-6761	536	1	−1	−1	NOUN
ejpam-6761	536	2	,	,	PUNCT
ejpam-6761	536	3	0	0	NUM
ejpam-6761	536	4	]	]	PUNCT
ejpam-6761	536	5	,	,	PUNCT
ejpam-6761	537	1	[	[	X
ejpam-6761	537	2	0	0	NUM
ejpam-6761	537	3	,	,	PUNCT
ejpam-6761	537	4	1])b	1])b	NUM
ejpam-6761	537	5	,	,	PUNCT
ejpam-6761	537	6	then	then	ADV
ejpam-6761	537	7	(	(	PUNCT
ejpam-6761	537	8	x	x	X
ejpam-6761	537	9	,	,	PUNCT
ejpam-6761	537	10	[	[	X
ejpam-6761	537	11	−1	−1	NOUN
ejpam-6761	537	12	,	,	PUNCT
ejpam-6761	537	13	0	0	NUM
ejpam-6761	537	14	]	]	PUNCT
ejpam-6761	537	15	,	,	PUNCT
ejpam-6761	537	16	[	[	X
ejpam-6761	537	17	0	0	NUM
ejpam-6761	537	18	,	,	PUNCT
ejpam-6761	537	19	1])(z	1])(z	PROPN
ejpam-6761	537	20	,	,	PUNCT
ejpam-6761	537	21	b−z	b−z	NOUN
ejpam-6761	537	22	,	,	PUNCT
ejpam-6761	537	23	b	b	PROPN
ejpam-6761	537	24	+	+	NOUN
ejpam-6761	537	25	z	z	NOUN
ejpam-6761	537	26	)	)	PUNCT
ejpam-6761	538	1	=	=	SYM
ejpam-6761	538	2	(	(	PUNCT
ejpam-6761	538	3	x	x	X
ejpam-6761	538	4	,	,	PUNCT
ejpam-6761	538	5	[	[	X
ejpam-6761	538	6	−1	−1	NOUN
ejpam-6761	538	7	,	,	PUNCT
ejpam-6761	538	8	0	0	NUM
ejpam-6761	538	9	]	]	PUNCT
ejpam-6761	538	10	,	,	PUNCT
ejpam-6761	538	11	[	[	X
ejpam-6761	538	12	0	0	NUM
ejpam-6761	538	13	,	,	PUNCT
ejpam-6761	538	14	1])((α	1])((α	NUM
ejpam-6761	538	15	,	,	PUNCT
ejpam-6761	538	16	b−α	b−α	PROPN
ejpam-6761	538	17	,	,	PUNCT
ejpam-6761	538	18	b	b	PROPN
ejpam-6761	538	19	+	+	CCONJ
ejpam-6761	538	20	α	α	NOUN
ejpam-6761	538	21	)	)	PUNCT
ejpam-6761	538	22	(	(	PUNCT
ejpam-6761	538	23	α	α	NOUN
ejpam-6761	538	24	−1	−1	NOUN
ejpam-6761	538	25	,	,	PUNCT
ejpam-6761	538	26	b−	b−	PROPN
ejpam-6761	538	27	α−1	α−1	PROPN
ejpam-6761	538	28	,	,	PUNCT
ejpam-6761	538	29	b	b	PROPN
ejpam-6761	538	30	+	+	NUM
ejpam-6761	538	31	α−1))(z	α−1))(z	NOUN
ejpam-6761	538	32	,	,	PUNCT
ejpam-6761	538	33	b	b	X
ejpam-6761	539	1	−	−	PROPN
ejpam-6761	539	2	z	z	NOUN
ejpam-6761	539	3	,	,	PUNCT
ejpam-6761	539	4	b	b	PROPN
ejpam-6761	540	1	+	+	NOUN
ejpam-6761	540	2	z	z	NOUN
ejpam-6761	540	3	)	)	PUNCT
ejpam-6761	541	1	=	=	SYM
ejpam-6761	541	2	(	(	PUNCT
ejpam-6761	541	3	(	(	PUNCT
ejpam-6761	541	4	x	x	NOUN
ejpam-6761	541	5	,	,	PUNCT
ejpam-6761	541	6	[	[	X
ejpam-6761	541	7	−1	−1	NOUN
ejpam-6761	541	8	,	,	PUNCT
ejpam-6761	541	9	0	0	NUM
ejpam-6761	541	10	]	]	PUNCT
ejpam-6761	541	11	,	,	PUNCT
ejpam-6761	541	12	[	[	X
ejpam-6761	541	13	0	0	NUM
ejpam-6761	541	14	,	,	PUNCT
ejpam-6761	541	15	1])(α	1])(α	PROPN
ejpam-6761	541	16	,	,	PUNCT
ejpam-6761	541	17	b−α	b−α	PROPN
ejpam-6761	541	18	,	,	PUNCT
ejpam-6761	541	19	b	b	PROPN
ejpam-6761	541	20	+	+	CCONJ
ejpam-6761	541	21	α	α	NOUN
ejpam-6761	541	22	)	)	PUNCT
ejpam-6761	541	23	)	)	PUNCT
ejpam-6761	541	24	(	(	PUNCT
ejpam-6761	541	25	(	(	PUNCT
ejpam-6761	541	26	α	α	NOUN
ejpam-6761	541	27	−1	−1	NOUN
ejpam-6761	541	28	,	,	PUNCT
ejpam-6761	541	29	b−	b−	PROPN
ejpam-6761	541	30	α−1	α−1	PROPN
ejpam-6761	541	31	,	,	PUNCT
ejpam-6761	541	32	b	b	PROPN
ejpam-6761	541	33	+	+	X
ejpam-6761	541	34	α−1)(z	α−1)(z	PROPN
ejpam-6761	541	35	,	,	PUNCT
ejpam-6761	541	36	b	b	X
ejpam-6761	541	37	−	−	PROPN
ejpam-6761	541	38	z	z	NOUN
ejpam-6761	541	39	,	,	PUNCT
ejpam-6761	541	40	b	b	PROPN
ejpam-6761	541	41	+	+	CCONJ
ejpam-6761	541	42	z	z	NOUN
ejpam-6761	541	43	)	)	PUNCT
ejpam-6761	541	44	)	)	PUNCT
ejpam-6761	542	1	=	=	PUNCT
ejpam-6761	542	2	(	(	PUNCT
ejpam-6761	542	3	(	(	PUNCT
ejpam-6761	542	4	y	y	NOUN
ejpam-6761	542	5	,	,	PUNCT
ejpam-6761	542	6	[	[	X
ejpam-6761	542	7	−1	−1	NOUN
ejpam-6761	542	8	,	,	PUNCT
ejpam-6761	542	9	0	0	NUM
ejpam-6761	542	10	]	]	PUNCT
ejpam-6761	542	11	,	,	PUNCT
ejpam-6761	542	12	[	[	X
ejpam-6761	542	13	0	0	NUM
ejpam-6761	542	14	,	,	PUNCT
ejpam-6761	542	15	1])(β	1])(β	PROPN
ejpam-6761	542	16	,	,	PUNCT
ejpam-6761	542	17	b−β	b−β	NOUN
ejpam-6761	542	18	,	,	PUNCT
ejpam-6761	542	19	b	b	X
ejpam-6761	542	20	+	+	CCONJ
ejpam-6761	542	21	β	β	X
ejpam-6761	542	22	)	)	PUNCT
ejpam-6761	542	23	)	)	PUNCT
ejpam-6761	542	24	(	(	PUNCT
ejpam-6761	542	25	(	(	PUNCT
ejpam-6761	542	26	α	α	NOUN
ejpam-6761	542	27	−1	−1	NOUN
ejpam-6761	542	28	,	,	PUNCT
ejpam-6761	542	29	b−	b−	PROPN
ejpam-6761	542	30	α−1	α−1	PROPN
ejpam-6761	542	31	,	,	PUNCT
ejpam-6761	542	32	b	b	PROPN
ejpam-6761	542	33	+	+	X
ejpam-6761	542	34	α−1)(z	α−1)(z	PROPN
ejpam-6761	542	35	,	,	PUNCT
ejpam-6761	542	36	b	b	X
ejpam-6761	542	37	−	−	PROPN
ejpam-6761	542	38	z	z	NOUN
ejpam-6761	542	39	,	,	PUNCT
ejpam-6761	542	40	b	b	PROPN
ejpam-6761	542	41	+	+	CCONJ
ejpam-6761	542	42	z	z	NOUN
ejpam-6761	542	43	)	)	PUNCT
ejpam-6761	542	44	)	)	PUNCT
ejpam-6761	543	1	=	=	PRON
ejpam-6761	543	2	(	(	PUNCT
ejpam-6761	543	3	y	y	NOUN
ejpam-6761	543	4	,	,	PUNCT
ejpam-6761	543	5	[	[	X
ejpam-6761	543	6	−1	−1	NOUN
ejpam-6761	543	7	,	,	PUNCT
ejpam-6761	543	8	0	0	NUM
ejpam-6761	543	9	]	]	PUNCT
ejpam-6761	543	10	,	,	PUNCT
ejpam-6761	543	11	[	[	X
ejpam-6761	543	12	0	0	NUM
ejpam-6761	543	13	,	,	PUNCT
ejpam-6761	543	14	1])((β	1])((β	NUM
ejpam-6761	543	15	,	,	PUNCT
ejpam-6761	543	16	b−β	b−β	NOUN
ejpam-6761	543	17	,	,	PUNCT
ejpam-6761	543	18	b	b	X
ejpam-6761	543	19	+	+	CCONJ
ejpam-6761	543	20	β	β	X
ejpam-6761	543	21	)	)	PUNCT
ejpam-6761	543	22	(	(	PUNCT
ejpam-6761	543	23	α	α	NOUN
ejpam-6761	543	24	−1	−1	NOUN
ejpam-6761	543	25	,	,	PUNCT
ejpam-6761	543	26	b−	b−	PROPN
ejpam-6761	543	27	α−1	α−1	PROPN
ejpam-6761	543	28	,	,	PUNCT
ejpam-6761	543	29	b	b	PROPN
ejpam-6761	543	30	+	+	X
ejpam-6761	543	31	α−1)(z	α−1)(z	PROPN
ejpam-6761	543	32	,	,	PUNCT
ejpam-6761	543	33	b	b	X
ejpam-6761	543	34	−	−	PROPN
ejpam-6761	543	35	z	z	NOUN
ejpam-6761	543	36	,	,	PUNCT
ejpam-6761	543	37	b	b	PROPN
ejpam-6761	543	38	+	+	CCONJ
ejpam-6761	543	39	z	z	NOUN
ejpam-6761	543	40	)	)	PUNCT
ejpam-6761	543	41	)	)	PUNCT
ejpam-6761	544	1	∈	∈	PROPN
ejpam-6761	544	2	(	(	PUNCT
ejpam-6761	544	3	y	y	NOUN
ejpam-6761	544	4	,	,	PUNCT
ejpam-6761	544	5	[	[	X
ejpam-6761	544	6	−1	−1	NOUN
ejpam-6761	544	7	,	,	PUNCT
ejpam-6761	544	8	0	0	NUM
ejpam-6761	544	9	]	]	PUNCT
ejpam-6761	544	10	,	,	PUNCT
ejpam-6761	544	11	[	[	X
ejpam-6761	544	12	0	0	NUM
ejpam-6761	544	13	,	,	PUNCT
ejpam-6761	544	14	1])b	1])b	NUM
ejpam-6761	544	15	.	.	PUNCT
ejpam-6761	545	1	that	that	PRON
ejpam-6761	545	2	is	be	AUX
ejpam-6761	545	3	,	,	PUNCT
ejpam-6761	545	4	(	(	PUNCT
ejpam-6761	545	5	x	x	X
ejpam-6761	545	6	,	,	PUNCT
ejpam-6761	545	7	[	[	X
ejpam-6761	545	8	−1	−1	NOUN
ejpam-6761	545	9	,	,	PUNCT
ejpam-6761	545	10	0	0	NUM
ejpam-6761	545	11	]	]	PUNCT
ejpam-6761	545	12	,	,	PUNCT
ejpam-6761	546	1	[	[	X
ejpam-6761	546	2	0	0	NUM
ejpam-6761	546	3	,	,	PUNCT
ejpam-6761	546	4	1])b	1])b	NUM
ejpam-6761	546	5	⊂	⊂	PROPN
ejpam-6761	546	6	(	(	PUNCT
ejpam-6761	546	7	y	y	NOUN
ejpam-6761	546	8	,	,	PUNCT
ejpam-6761	546	9	[	[	X
ejpam-6761	546	10	−1	−1	NOUN
ejpam-6761	546	11	,	,	PUNCT
ejpam-6761	546	12	0	0	NUM
ejpam-6761	546	13	]	]	PUNCT
ejpam-6761	546	14	,	,	PUNCT
ejpam-6761	546	15	[	[	X
ejpam-6761	546	16	0	0	NUM
ejpam-6761	546	17	,	,	PUNCT
ejpam-6761	546	18	1])b	1])b	NUM
ejpam-6761	546	19	.	.	PUNCT
ejpam-6761	547	1	similarly	similarly	ADV
ejpam-6761	547	2	,	,	PUNCT
ejpam-6761	547	3	we	we	PRON
ejpam-6761	547	4	can	can	AUX
ejpam-6761	547	5	show	show	VERB
ejpam-6761	547	6	that	that	SCONJ
ejpam-6761	547	7	(	(	PUNCT
ejpam-6761	547	8	y	y	NOUN
ejpam-6761	547	9	,	,	PUNCT
ejpam-6761	547	10	[	[	X
ejpam-6761	547	11	−1	−1	NOUN
ejpam-6761	547	12	,	,	PUNCT
ejpam-6761	547	13	0	0	NUM
ejpam-6761	547	14	]	]	PUNCT
ejpam-6761	547	15	,	,	PUNCT
ejpam-6761	547	16	[	[	X
ejpam-6761	547	17	0	0	NUM
ejpam-6761	547	18	,	,	PUNCT
ejpam-6761	547	19	1])b	1])b	NUM
ejpam-6761	547	20	⊂	⊂	X
ejpam-6761	547	21	(	(	PUNCT
ejpam-6761	547	22	x	x	X
ejpam-6761	547	23	,	,	PUNCT
ejpam-6761	547	24	[	[	X
ejpam-6761	547	25	−1	−1	NOUN
ejpam-6761	547	26	,	,	PUNCT
ejpam-6761	547	27	0	0	NUM
ejpam-6761	547	28	]	]	PUNCT
ejpam-6761	547	29	,	,	PUNCT
ejpam-6761	547	30	[	[	X
ejpam-6761	547	31	0	0	NUM
ejpam-6761	547	32	,	,	PUNCT
ejpam-6761	547	33	1])b	1])b	NUM
ejpam-6761	547	34	.	.	PUNCT
ejpam-6761	548	1	also	also	ADV
ejpam-6761	548	2	,	,	PUNCT
ejpam-6761	548	3	we	we	PRON
ejpam-6761	548	4	can	can	AUX
ejpam-6761	548	5	show	show	VERB
ejpam-6761	548	6	the	the	DET
ejpam-6761	548	7	same	same	ADJ
ejpam-6761	548	8	result	result	NOUN
ejpam-6761	548	9	for	for	ADP
ejpam-6761	548	10	the	the	DET
ejpam-6761	548	11	right	right	ADJ
ejpam-6761	548	12	cosets	coset	NOUN
ejpam-6761	548	13	of	of	ADP
ejpam-6761	548	14	b	b	NOUN
ejpam-6761	548	15	,	,	PUNCT
ejpam-6761	548	16	which	which	PRON
ejpam-6761	548	17	proves	prove	VERB
ejpam-6761	548	18	(	(	PUNCT
ejpam-6761	548	19	4	4	NUM
ejpam-6761	548	20	)	)	PUNCT
ejpam-6761	548	21	.	.	PUNCT
ejpam-6761	549	1	definition	definition	NOUN
ejpam-6761	549	2	25	25	NUM
ejpam-6761	549	3	.	.	PUNCT
ejpam-6761	550	1	a	a	DET
ejpam-6761	550	2	bipolar	bipolar	ADJ
ejpam-6761	550	3	valued	value	VERB
ejpam-6761	550	4	fuzzy	fuzzy	ADJ
ejpam-6761	550	5	subgroup	subgroup	PROPN
ejpam-6761	550	6	b	b	PROPN
ejpam-6761	550	7	of	of	ADP
ejpam-6761	550	8	the	the	DET
ejpam-6761	550	9	bipolar	bipolar	ADJ
ejpam-6761	550	10	valued	value	VERB
ejpam-6761	550	11	fuzzy	fuzzy	ADJ
ejpam-6761	550	12	group	group	NOUN
ejpam-6761	550	13	(	(	PUNCT
ejpam-6761	550	14	(	(	PUNCT
ejpam-6761	550	15	g	g	NOUN
ejpam-6761	550	16	,	,	PUNCT
ejpam-6761	550	17	[	[	X
ejpam-6761	550	18	−1	−1	NOUN
ejpam-6761	550	19	,	,	PUNCT
ejpam-6761	550	20	0	0	NUM
ejpam-6761	550	21	]	]	PUNCT
ejpam-6761	550	22	,	,	PUNCT
ejpam-6761	550	23	[	[	X
ejpam-6761	550	24	0	0	NUM
ejpam-6761	550	25	,	,	PUNCT
ejpam-6761	550	26	1]),f	1]),f	NUM
ejpam-6761	550	27	)	)	PUNCT
ejpam-6761	550	28	is	be	AUX
ejpam-6761	550	29	called	call	VERB
ejpam-6761	550	30	a	a	DET
ejpam-6761	550	31	bipolar	bipolar	ADJ
ejpam-6761	550	32	valued	value	VERB
ejpam-6761	550	33	fuzzy	fuzzy	ADJ
ejpam-6761	550	34	normal	normal	ADJ
ejpam-6761	550	35	subgroup	subgroup	NOUN
ejpam-6761	550	36	if	if	SCONJ
ejpam-6761	550	37	:	:	PUNCT
ejpam-6761	550	38	f.	f.	PROPN
ejpam-6761	550	39	al	al	PROPN
ejpam-6761	550	40	-	-	PROPN
ejpam-6761	550	41	zu’bi	zu’bi	PROPN
ejpam-6761	550	42	et	et	NOUN
ejpam-6761	550	43	al	al	PROPN
ejpam-6761	550	44	.	.	PUNCT
ejpam-6761	550	45	/	/	SYM
ejpam-6761	550	46	eur	eur	PROPN
ejpam-6761	550	47	.	.	PUNCT
ejpam-6761	551	1	j.	j.	PROPN
ejpam-6761	551	2	pure	pure	PROPN
ejpam-6761	551	3	appl	appl	PROPN
ejpam-6761	551	4	.	.	PROPN
ejpam-6761	551	5	math	math	PROPN
ejpam-6761	551	6	,	,	PUNCT
ejpam-6761	551	7	18	18	NUM
ejpam-6761	551	8	(	(	PUNCT
ejpam-6761	551	9	4	4	NUM
ejpam-6761	551	10	)	)	PUNCT
ejpam-6761	551	11	(	(	PUNCT
ejpam-6761	551	12	2025	2025	NUM
ejpam-6761	551	13	)	)	PUNCT
ejpam-6761	551	14	,	,	PUNCT
ejpam-6761	551	15	6761	6761	NUM
ejpam-6761	551	16	22	22	NUM
ejpam-6761	551	17	of	of	ADP
ejpam-6761	551	18	28	28	NUM
ejpam-6761	551	19	(	(	PUNCT
ejpam-6761	551	20	1	1	NUM
ejpam-6761	551	21	)	)	PUNCT
ejpam-6761	551	22	b	b	NOUN
ejpam-6761	551	23	is	be	AUX
ejpam-6761	551	24	associative	associative	ADJ
ejpam-6761	551	25	in	in	ADP
ejpam-6761	551	26	(	(	PUNCT
ejpam-6761	551	27	(	(	PUNCT
ejpam-6761	551	28	g	g	NOUN
ejpam-6761	551	29	,	,	PUNCT
ejpam-6761	551	30	[	[	X
ejpam-6761	551	31	−1	−1	NOUN
ejpam-6761	551	32	,	,	PUNCT
ejpam-6761	551	33	0	0	NUM
ejpam-6761	551	34	]	]	PUNCT
ejpam-6761	551	35	,	,	PUNCT
ejpam-6761	551	36	[	[	X
ejpam-6761	551	37	0	0	NUM
ejpam-6761	551	38	,	,	PUNCT
ejpam-6761	551	39	1	1	NUM
ejpam-6761	551	40	]	]	NUM
ejpam-6761	551	41	)	)	PUNCT
ejpam-6761	551	42	,	,	PUNCT
ejpam-6761	551	43	f	f	PROPN
ejpam-6761	551	44	)	)	PUNCT
ejpam-6761	551	45	,	,	PUNCT
ejpam-6761	551	46	(	(	PUNCT
ejpam-6761	551	47	2	2	X
ejpam-6761	551	48	)	)	PUNCT
ejpam-6761	551	49	(	(	PUNCT
ejpam-6761	551	50	x	x	X
ejpam-6761	551	51	,	,	PUNCT
ejpam-6761	551	52	[	[	X
ejpam-6761	551	53	−1	−1	NOUN
ejpam-6761	551	54	,	,	PUNCT
ejpam-6761	551	55	0	0	NUM
ejpam-6761	551	56	]	]	PUNCT
ejpam-6761	551	57	,	,	PUNCT
ejpam-6761	551	58	[	[	X
ejpam-6761	551	59	0	0	NUM
ejpam-6761	551	60	,	,	PUNCT
ejpam-6761	551	61	1])b	1])b	NUM
ejpam-6761	551	62	=	=	SYM
ejpam-6761	551	63	b(x	b(x	PROPN
ejpam-6761	551	64	,	,	PUNCT
ejpam-6761	551	65	[	[	X
ejpam-6761	551	66	−1	−1	NOUN
ejpam-6761	551	67	,	,	PUNCT
ejpam-6761	551	68	0	0	NUM
ejpam-6761	551	69	]	]	PUNCT
ejpam-6761	551	70	,	,	PUNCT
ejpam-6761	552	1	[	[	X
ejpam-6761	552	2	0	0	NUM
ejpam-6761	552	3	,	,	PUNCT
ejpam-6761	552	4	1	1	NUM
ejpam-6761	552	5	]	]	PUNCT
ejpam-6761	552	6	)	)	PUNCT
ejpam-6761	552	7	such	such	ADJ
ejpam-6761	552	8	that	that	SCONJ
ejpam-6761	552	9	x	x	SYM
ejpam-6761	552	10	∈	∈	PROPN
ejpam-6761	552	11	g.	g.	NOUN
ejpam-6761	552	12	the	the	DET
ejpam-6761	552	13	next	next	ADJ
ejpam-6761	552	14	theorem	theorem	NOUN
ejpam-6761	552	15	gives	give	VERB
ejpam-6761	552	16	a	a	DET
ejpam-6761	552	17	necessary	necessary	ADJ
ejpam-6761	552	18	and	and	CCONJ
ejpam-6761	552	19	sufficient	sufficient	ADJ
ejpam-6761	552	20	condition	condition	NOUN
ejpam-6761	552	21	for	for	ADP
ejpam-6761	552	22	bipolar	bipolar	ADJ
ejpam-6761	552	23	valued	value	VERB
ejpam-6761	552	24	fuzzy	fuzzy	ADJ
ejpam-6761	552	25	normal	normal	ADJ
ejpam-6761	552	26	subgroups	subgroup	NOUN
ejpam-6761	552	27	.	.	PUNCT
ejpam-6761	553	1	theorem	theorem	ADJ
ejpam-6761	553	2	8	8	NUM
ejpam-6761	553	3	.	.	PUNCT
ejpam-6761	554	1	a	a	DET
ejpam-6761	554	2	bipolar	bipolar	ADJ
ejpam-6761	554	3	valued	value	VERB
ejpam-6761	554	4	fuzzy	fuzzy	ADJ
ejpam-6761	554	5	subgroup	subgroup	NOUN
ejpam-6761	554	6	(	(	PUNCT
ejpam-6761	554	7	b;f	b;f	PROPN
ejpam-6761	554	8	)	)	PUNCT
ejpam-6761	554	9	,	,	PUNCT
ejpam-6761	554	10	where	where	SCONJ
ejpam-6761	554	11	b	b	X
ejpam-6761	554	12	=	=	PRON
ejpam-6761	554	13	{	{	PUNCT
ejpam-6761	554	14	(	(	PUNCT
ejpam-6761	554	15	z	z	NOUN
ejpam-6761	554	16	,	,	PUNCT
ejpam-6761	554	17	b−z	b−z	NOUN
ejpam-6761	554	18	,	,	PUNCT
ejpam-6761	554	19	b+z	b+z	PROPN
ejpam-6761	554	20	)	)	PUNCT
ejpam-6761	555	1	|	|	ADV
ejpam-6761	555	2	z	z	PROPN
ejpam-6761	555	3	∈	∈	PROPN
ejpam-6761	555	4	b	b	X
ejpam-6761	555	5	◦	◦	NOUN
ejpam-6761	555	6	}	}	PUNCT
ejpam-6761	555	7	,	,	PUNCT
ejpam-6761	555	8	of	of	ADP
ejpam-6761	555	9	the	the	DET
ejpam-6761	555	10	bipolar	bipolar	ADJ
ejpam-6761	555	11	valued	value	VERB
ejpam-6761	555	12	group	group	NOUN
ejpam-6761	555	13	(	(	PUNCT
ejpam-6761	555	14	(	(	PUNCT
ejpam-6761	555	15	g	g	NOUN
ejpam-6761	555	16	,	,	PUNCT
ejpam-6761	555	17	[	[	X
ejpam-6761	555	18	−1	−1	NOUN
ejpam-6761	555	19	,	,	PUNCT
ejpam-6761	555	20	0	0	NUM
ejpam-6761	555	21	]	]	PUNCT
ejpam-6761	555	22	,	,	PUNCT
ejpam-6761	555	23	[	[	X
ejpam-6761	555	24	0	0	NUM
ejpam-6761	555	25	,	,	PUNCT
ejpam-6761	555	26	1	1	NUM
ejpam-6761	555	27	]	]	NUM
ejpam-6761	555	28	)	)	PUNCT
ejpam-6761	555	29	,	,	PUNCT
ejpam-6761	555	30	f	f	PROPN
ejpam-6761	555	31	)	)	PUNCT
ejpam-6761	555	32	is	be	AUX
ejpam-6761	555	33	a	a	DET
ejpam-6761	555	34	bipolar	bipolar	ADJ
ejpam-6761	555	35	valued	value	VERB
ejpam-6761	555	36	fuzzy	fuzzy	ADJ
ejpam-6761	555	37	normal	normal	ADJ
ejpam-6761	555	38	subgroup	subgroup	NOUN
ejpam-6761	555	39	if	if	SCONJ
ejpam-6761	556	1	and	and	CCONJ
ejpam-6761	556	2	only	only	ADV
ejpam-6761	556	3	if	if	SCONJ
ejpam-6761	556	4	:	:	PUNCT
ejpam-6761	556	5	(	(	PUNCT
ejpam-6761	556	6	1	1	X
ejpam-6761	556	7	)	)	PUNCT
ejpam-6761	556	8	(	(	PUNCT
ejpam-6761	556	9	b	b	X
ejpam-6761	556	10	◦	◦	NOUN
ejpam-6761	556	11	,	,	PUNCT
ejpam-6761	556	12	f	f	PROPN
ejpam-6761	556	13	)	)	PUNCT
ejpam-6761	556	14	is	be	AUX
ejpam-6761	556	15	an	an	DET
ejpam-6761	556	16	ordinary	ordinary	ADJ
ejpam-6761	556	17	normal	normal	ADJ
ejpam-6761	556	18	subgroup	subgroup	NOUN
ejpam-6761	556	19	of	of	ADP
ejpam-6761	556	20	the	the	DET
ejpam-6761	556	21	ordinary	ordinary	ADJ
ejpam-6761	556	22	group	group	NOUN
ejpam-6761	556	23	(	(	PUNCT
ejpam-6761	556	24	g	g	PROPN
ejpam-6761	556	25	,	,	PUNCT
ejpam-6761	556	26	f	f	PROPN
ejpam-6761	556	27	)	)	PUNCT
ejpam-6761	556	28	,	,	PUNCT
ejpam-6761	556	29	(	(	PUNCT
ejpam-6761	556	30	2	2	X
ejpam-6761	556	31	)	)	PUNCT
ejpam-6761	556	32	f−xz([−1	f−xz([−1	PROPN
ejpam-6761	556	33	,	,	PUNCT
ejpam-6761	556	34	0	0	NUM
ejpam-6761	556	35	]	]	PUNCT
ejpam-6761	556	36	,	,	PUNCT
ejpam-6761	556	37	b−z	b−z	NOUN
ejpam-6761	556	38	)	)	PUNCT
ejpam-6761	556	39	=	=	PUNCT
ejpam-6761	556	40	f−źx(b	f−źx(b	NUM
ejpam-6761	556	41	−	−	PROPN
ejpam-6761	556	42	ź	ź	PROPN
ejpam-6761	556	43	,	,	PUNCT
ejpam-6761	557	1	[	[	X
ejpam-6761	557	2	−1	−1	NOUN
ejpam-6761	557	3	,	,	PUNCT
ejpam-6761	557	4	0	0	NUM
ejpam-6761	557	5	]	]	PUNCT
ejpam-6761	557	6	)	)	PUNCT
ejpam-6761	557	7	,	,	PUNCT
ejpam-6761	557	8	f+xz([0	f+xz([0	PROPN
ejpam-6761	557	9	,	,	PUNCT
ejpam-6761	557	10	1	1	NUM
ejpam-6761	557	11	]	]	PUNCT
ejpam-6761	557	12	,	,	PUNCT
ejpam-6761	557	13	b	b	X
ejpam-6761	557	14	+	+	NOUN
ejpam-6761	557	15	z	z	NOUN
ejpam-6761	557	16	)	)	PUNCT
ejpam-6761	557	17	=	=	PUNCT
ejpam-6761	557	18	f+źx(b	f+źx(b	VERB
ejpam-6761	557	19	+	+	CCONJ
ejpam-6761	557	20	ź	ź	PROPN
ejpam-6761	557	21	,	,	PUNCT
ejpam-6761	558	1	[	[	X
ejpam-6761	558	2	0	0	NUM
ejpam-6761	558	3	,	,	PUNCT
ejpam-6761	558	4	1	1	NUM
ejpam-6761	558	5	]	]	PUNCT
ejpam-6761	558	6	)	)	PUNCT
ejpam-6761	559	1	where	where	SCONJ
ejpam-6761	559	2	xfz	xfz	NOUN
ejpam-6761	559	3	=	=	SYM
ejpam-6761	559	4	źfx	źfx	PROPN
ejpam-6761	559	5	,	,	PUNCT
ejpam-6761	559	6	x	x	X
ejpam-6761	559	7	∈	∈	PROPN
ejpam-6761	559	8	x	x	X
ejpam-6761	559	9	,	,	PUNCT
ejpam-6761	559	10	z	z	PROPN
ejpam-6761	559	11	,	,	PUNCT
ejpam-6761	559	12	ź	ź	PROPN
ejpam-6761	559	13	∈	∈	PROPN
ejpam-6761	559	14	b	b	X
ejpam-6761	559	15	◦	◦	NOUN
ejpam-6761	559	16	.	.	PUNCT
ejpam-6761	560	1	(	(	PUNCT
ejpam-6761	560	2	25	25	NUM
ejpam-6761	560	3	)	)	PUNCT
ejpam-6761	560	4	proof	proof	NOUN
ejpam-6761	560	5	.	.	PUNCT
ejpam-6761	561	1	assume	assume	VERB
ejpam-6761	561	2	b	b	NOUN
ejpam-6761	561	3	=	=	PRON
ejpam-6761	561	4	{	{	PUNCT
ejpam-6761	561	5	(	(	PUNCT
ejpam-6761	561	6	z	z	NOUN
ejpam-6761	561	7	,	,	PUNCT
ejpam-6761	561	8	b−z	b−z	NOUN
ejpam-6761	561	9	,	,	PUNCT
ejpam-6761	561	10	b+z	b+z	PROPN
ejpam-6761	561	11	)	)	PUNCT
ejpam-6761	562	1	|	|	ADV
ejpam-6761	562	2	z	z	PROPN
ejpam-6761	562	3	∈	∈	PROPN
ejpam-6761	562	4	b	b	X
ejpam-6761	562	5	◦	◦	NOUN
ejpam-6761	562	6	}	}	PUNCT
ejpam-6761	562	7	is	be	AUX
ejpam-6761	562	8	a	a	DET
ejpam-6761	562	9	bipolar	bipolar	ADJ
ejpam-6761	562	10	valued	value	VERB
ejpam-6761	562	11	fuzzy	fuzzy	ADJ
ejpam-6761	562	12	normal	normal	ADJ
ejpam-6761	562	13	subgroup	subgroup	NOUN
ejpam-6761	562	14	of	of	ADP
ejpam-6761	562	15	(	(	PUNCT
ejpam-6761	562	16	(	(	PUNCT
ejpam-6761	562	17	g	g	NOUN
ejpam-6761	562	18	,	,	PUNCT
ejpam-6761	562	19	[	[	X
ejpam-6761	562	20	−1	−1	NOUN
ejpam-6761	562	21	,	,	PUNCT
ejpam-6761	562	22	0	0	NUM
ejpam-6761	562	23	]	]	PUNCT
ejpam-6761	562	24	,	,	PUNCT
ejpam-6761	562	25	[	[	X
ejpam-6761	562	26	0	0	NUM
ejpam-6761	562	27	,	,	PUNCT
ejpam-6761	562	28	1	1	NUM
ejpam-6761	562	29	]	]	NUM
ejpam-6761	562	30	)	)	PUNCT
ejpam-6761	562	31	,	,	PUNCT
ejpam-6761	562	32	f	f	PROPN
ejpam-6761	562	33	)	)	PUNCT
ejpam-6761	562	34	.	.	PUNCT
ejpam-6761	563	1	from	from	ADP
ejpam-6761	563	2	the	the	DET
ejpam-6761	563	3	correspondence	correspondence	NOUN
ejpam-6761	563	4	theorem	theorem	VERB
ejpam-6761	563	5	,	,	PUNCT
ejpam-6761	563	6	we	we	PRON
ejpam-6761	563	7	have	have	VERB
ejpam-6761	563	8	that	that	PRON
ejpam-6761	563	9	(	(	PUNCT
ejpam-6761	563	10	b	b	X
ejpam-6761	563	11	◦	◦	NOUN
ejpam-6761	563	12	,	,	PUNCT
ejpam-6761	563	13	f	f	PROPN
ejpam-6761	563	14	)	)	PUNCT
ejpam-6761	563	15	is	be	AUX
ejpam-6761	563	16	an	an	DET
ejpam-6761	563	17	ordinary	ordinary	ADJ
ejpam-6761	563	18	normal	normal	ADJ
ejpam-6761	563	19	subgroup	subgroup	NOUN
ejpam-6761	563	20	of	of	ADP
ejpam-6761	563	21	the	the	DET
ejpam-6761	563	22	ordinary	ordinary	ADJ
ejpam-6761	563	23	group	group	NOUN
ejpam-6761	563	24	(	(	PUNCT
ejpam-6761	563	25	g	g	PROPN
ejpam-6761	563	26	,	,	PUNCT
ejpam-6761	563	27	f	f	PROPN
ejpam-6761	563	28	)	)	PUNCT
ejpam-6761	563	29	.	.	PUNCT
ejpam-6761	564	1	using	use	VERB
ejpam-6761	564	2	the	the	DET
ejpam-6761	564	3	normality	normality	NOUN
ejpam-6761	564	4	of	of	ADP
ejpam-6761	564	5	b	b	X
ejpam-6761	564	6	,	,	PUNCT
ejpam-6761	564	7	we	we	PRON
ejpam-6761	564	8	have	have	VERB
ejpam-6761	564	9	:	:	PUNCT
ejpam-6761	564	10	(	(	PUNCT
ejpam-6761	564	11	x	x	X
ejpam-6761	564	12	,	,	PUNCT
ejpam-6761	564	13	[	[	X
ejpam-6761	564	14	−1	−1	NOUN
ejpam-6761	564	15	,	,	PUNCT
ejpam-6761	564	16	0	0	NUM
ejpam-6761	564	17	]	]	PUNCT
ejpam-6761	564	18	,	,	PUNCT
ejpam-6761	564	19	[	[	X
ejpam-6761	564	20	0	0	NUM
ejpam-6761	564	21	,	,	PUNCT
ejpam-6761	564	22	1])b	1])b	NUM
ejpam-6761	564	23	=	=	SYM
ejpam-6761	564	24	b(x	b(x	PROPN
ejpam-6761	564	25	,	,	PUNCT
ejpam-6761	564	26	[	[	X
ejpam-6761	564	27	−1	−1	NOUN
ejpam-6761	564	28	,	,	PUNCT
ejpam-6761	564	29	0	0	NUM
ejpam-6761	564	30	]	]	PUNCT
ejpam-6761	564	31	,	,	PUNCT
ejpam-6761	565	1	[	[	X
ejpam-6761	565	2	0	0	NUM
ejpam-6761	565	3	,	,	PUNCT
ejpam-6761	565	4	1	1	NUM
ejpam-6761	565	5	]	]	NUM
ejpam-6761	565	6	)	)	PUNCT
ejpam-6761	565	7	,	,	PUNCT
ejpam-6761	565	8	x	x	PUNCT
ejpam-6761	565	9	∈	∈	PROPN
ejpam-6761	565	10	g.	g.	NOUN
ejpam-6761	565	11	that	that	PRON
ejpam-6761	565	12	is	be	AUX
ejpam-6761	565	13	:	:	PUNCT
ejpam-6761	565	14	{	{	PUNCT
ejpam-6761	565	15	(	(	PUNCT
ejpam-6761	565	16	xfz	xfz	PROPN
ejpam-6761	565	17	,	,	PUNCT
ejpam-6761	565	18	f−xz([−1	f−xz([−1	PROPN
ejpam-6761	565	19	,	,	PUNCT
ejpam-6761	565	20	0	0	NUM
ejpam-6761	565	21	]	]	PUNCT
ejpam-6761	565	22	,	,	PUNCT
ejpam-6761	565	23	b−z	b−z	PROPN
ejpam-6761	565	24	)	)	PUNCT
ejpam-6761	565	25	,	,	PUNCT
ejpam-6761	565	26	f	f	PROPN
ejpam-6761	565	27	+	+	CCONJ
ejpam-6761	565	28	xz([0	xz([0	ADJ
ejpam-6761	565	29	,	,	PUNCT
ejpam-6761	565	30	1	1	NUM
ejpam-6761	565	31	]	]	PUNCT
ejpam-6761	565	32	,	,	PUNCT
ejpam-6761	565	33	b	b	X
ejpam-6761	565	34	+	+	CCONJ
ejpam-6761	565	35	z	z	NOUN
ejpam-6761	565	36	)	)	PUNCT
ejpam-6761	565	37	)	)	PUNCT
ejpam-6761	566	1	|	|	ADV
ejpam-6761	566	2	z	z	NOUN
ejpam-6761	566	3	∈	∈	PROPN
ejpam-6761	566	4	b	b	X
ejpam-6761	566	5	◦	◦	NOUN
ejpam-6761	566	6	}	}	PUNCT
ejpam-6761	566	7	=	=	SYM
ejpam-6761	566	8	{	{	PUNCT
ejpam-6761	566	9	(	(	PUNCT
ejpam-6761	566	10	zfx	zfx	NOUN
ejpam-6761	566	11	,	,	PUNCT
ejpam-6761	566	12	f−zx(b−z	f−zx(b−z	ADJ
ejpam-6761	566	13	,	,	PUNCT
ejpam-6761	566	14	[	[	X
ejpam-6761	566	15	−1	−1	NOUN
ejpam-6761	566	16	,	,	PUNCT
ejpam-6761	566	17	0	0	NUM
ejpam-6761	566	18	]	]	PUNCT
ejpam-6761	566	19	)	)	PUNCT
ejpam-6761	566	20	,	,	PUNCT
ejpam-6761	566	21	f+zx(b	f+zx(b	PROPN
ejpam-6761	566	22	+	+	CCONJ
ejpam-6761	566	23	z	z	NOUN
ejpam-6761	566	24	,	,	PUNCT
ejpam-6761	567	1	[	[	X
ejpam-6761	567	2	0	0	NUM
ejpam-6761	567	3	,	,	PUNCT
ejpam-6761	567	4	1	1	NUM
ejpam-6761	567	5	]	]	NUM
ejpam-6761	567	6	)	)	PUNCT
ejpam-6761	567	7	)	)	PUNCT
ejpam-6761	568	1	|	|	ADV
ejpam-6761	568	2	z	z	NOUN
ejpam-6761	568	3	∈	∈	PROPN
ejpam-6761	568	4	b	b	X
ejpam-6761	568	5	◦	◦	NOUN
ejpam-6761	568	6	}	}	PUNCT
ejpam-6761	568	7	(	(	PUNCT
ejpam-6761	568	8	26	26	NUM
ejpam-6761	568	9	)	)	PUNCT
ejpam-6761	568	10	therefore	therefore	ADV
ejpam-6761	568	11	,	,	PUNCT
ejpam-6761	568	12	for	for	ADP
ejpam-6761	568	13	every	every	DET
ejpam-6761	568	14	z	z	PROPN
ejpam-6761	568	15	∈	∈	PROPN
ejpam-6761	568	16	b	b	PROPN
ejpam-6761	568	17	◦	◦	NOUN
ejpam-6761	568	18	,	,	PUNCT
ejpam-6761	568	19	there	there	PRON
ejpam-6761	568	20	exists	exist	VERB
ejpam-6761	568	21	ź	ź	PROPN
ejpam-6761	568	22	∈	∈	PROPN
ejpam-6761	569	1	b	b	PUNCT
ejpam-6761	569	2	◦	◦	NOUN
ejpam-6761	569	3	such	such	ADJ
ejpam-6761	569	4	that	that	DET
ejpam-6761	569	5	xfz	xfz	NOUN
ejpam-6761	570	1	=	=	SYM
ejpam-6761	570	2	źfx	źfx	PROPN
ejpam-6761	570	3	.	.	PUNCT
ejpam-6761	571	1	in	in	ADP
ejpam-6761	571	2	other	other	ADJ
ejpam-6761	571	3	words	word	NOUN
ejpam-6761	571	4	,	,	PUNCT
ejpam-6761	571	5	xfb	xfb	PUNCT
ejpam-6761	571	6	◦	◦	NOUN
ejpam-6761	571	7	=	=	SYM
ejpam-6761	571	8	b	b	X
ejpam-6761	571	9	◦	◦	NOUN
ejpam-6761	571	10	fx	fx	NOUN
ejpam-6761	571	11	.	.	PUNCT
ejpam-6761	572	1	hence	hence	ADV
ejpam-6761	572	2	,	,	PUNCT
ejpam-6761	572	3	b	b	X
ejpam-6761	572	4	◦	◦	NOUN
ejpam-6761	572	5	is	be	AUX
ejpam-6761	572	6	an	an	DET
ejpam-6761	572	7	ordinary	ordinary	ADJ
ejpam-6761	572	8	normal	normal	ADJ
ejpam-6761	572	9	subgroup	subgroup	NOUN
ejpam-6761	572	10	of	of	ADP
ejpam-6761	572	11	the	the	DET
ejpam-6761	572	12	ordinary	ordinary	ADJ
ejpam-6761	572	13	group	group	NOUN
ejpam-6761	572	14	(	(	PUNCT
ejpam-6761	572	15	g	g	PROPN
ejpam-6761	572	16	,	,	PUNCT
ejpam-6761	572	17	f	f	PROPN
ejpam-6761	572	18	)	)	PUNCT
ejpam-6761	572	19	,	,	PUNCT
ejpam-6761	572	20	which	which	PRON
ejpam-6761	572	21	proves	prove	VERB
ejpam-6761	572	22	(	(	PUNCT
ejpam-6761	572	23	i	i	NOUN
ejpam-6761	572	24	)	)	PUNCT
ejpam-6761	572	25	.	.	PUNCT
ejpam-6761	573	1	condition	condition	NOUN
ejpam-6761	573	2	(	(	PUNCT
ejpam-6761	573	3	ii	ii	NOUN
ejpam-6761	573	4	)	)	PUNCT
ejpam-6761	573	5	follows	follow	VERB
ejpam-6761	573	6	directly	directly	ADV
ejpam-6761	573	7	from	from	ADP
ejpam-6761	573	8	the	the	DET
ejpam-6761	573	9	definition	definition	NOUN
ejpam-6761	573	10	.	.	PUNCT
ejpam-6761	574	1	the	the	DET
ejpam-6761	574	2	other	other	ADJ
ejpam-6761	574	3	part	part	NOUN
ejpam-6761	574	4	of	of	ADP
ejpam-6761	574	5	the	the	DET
ejpam-6761	574	6	proof	proof	NOUN
ejpam-6761	574	7	is	be	AUX
ejpam-6761	574	8	direct	direct	ADJ
ejpam-6761	574	9	.	.	PUNCT
ejpam-6761	575	1	theorem	theorem	NOUN
ejpam-6761	575	2	9	9	NUM
ejpam-6761	575	3	.	.	PUNCT
ejpam-6761	576	1	every	every	DET
ejpam-6761	576	2	bipolar	bipolar	PROPN
ejpam-6761	576	3	valued	value	VERB
ejpam-6761	576	4	fuzzy	fuzzy	ADJ
ejpam-6761	576	5	normal	normal	ADJ
ejpam-6761	576	6	subgroup	subgroup	PROPN
ejpam-6761	576	7	b	b	PROPN
ejpam-6761	576	8	of	of	ADP
ejpam-6761	576	9	(	(	PUNCT
ejpam-6761	576	10	(	(	PUNCT
ejpam-6761	576	11	g	g	NOUN
ejpam-6761	576	12	,	,	PUNCT
ejpam-6761	576	13	[	[	X
ejpam-6761	576	14	−1	−1	NOUN
ejpam-6761	576	15	,	,	PUNCT
ejpam-6761	576	16	0	0	NUM
ejpam-6761	576	17	]	]	PUNCT
ejpam-6761	576	18	,	,	PUNCT
ejpam-6761	576	19	[	[	X
ejpam-6761	576	20	0	0	NUM
ejpam-6761	576	21	,	,	PUNCT
ejpam-6761	576	22	1]),f	1]),f	NUM
ejpam-6761	576	23	)	)	PUNCT
ejpam-6761	576	24	defines	define	VERB
ejpam-6761	576	25	a	a	DET
ejpam-6761	576	26	bipolar	bipolar	ADJ
ejpam-6761	576	27	valued	value	VERB
ejpam-6761	576	28	fuzzy	fuzzy	ADJ
ejpam-6761	576	29	equivalence	equivalence	NOUN
ejpam-6761	576	30	relation	relation	NOUN
ejpam-6761	576	31	on	on	ADP
ejpam-6761	576	32	the	the	DET
ejpam-6761	576	33	bipolar	bipolar	ADJ
ejpam-6761	576	34	valued	value	VERB
ejpam-6761	576	35	fuzzy	fuzzy	ADJ
ejpam-6761	576	36	space	space	NOUN
ejpam-6761	576	37	(	(	PUNCT
ejpam-6761	576	38	g	g	NOUN
ejpam-6761	576	39	,	,	PUNCT
ejpam-6761	576	40	[	[	X
ejpam-6761	576	41	−1	−1	NOUN
ejpam-6761	576	42	,	,	PUNCT
ejpam-6761	576	43	0	0	NUM
ejpam-6761	576	44	]	]	PUNCT
ejpam-6761	576	45	,	,	PUNCT
ejpam-6761	577	1	[	[	X
ejpam-6761	577	2	0	0	NUM
ejpam-6761	577	3	,	,	PUNCT
ejpam-6761	577	4	1	1	NUM
ejpam-6761	577	5	]	]	PUNCT
ejpam-6761	577	6	)	)	PUNCT
ejpam-6761	577	7	given	give	VERB
ejpam-6761	577	8	by	by	ADP
ejpam-6761	577	9	:	:	PUNCT
ejpam-6761	577	10	(	(	PUNCT
ejpam-6761	577	11	x	x	X
ejpam-6761	577	12	,	,	PUNCT
ejpam-6761	577	13	[	[	X
ejpam-6761	577	14	−1	−1	NOUN
ejpam-6761	577	15	,	,	PUNCT
ejpam-6761	577	16	0	0	NUM
ejpam-6761	577	17	]	]	PUNCT
ejpam-6761	577	18	,	,	PUNCT
ejpam-6761	577	19	[	[	X
ejpam-6761	577	20	0	0	NUM
ejpam-6761	577	21	,	,	PUNCT
ejpam-6761	577	22	1])r(y	1])r(y	NUM
ejpam-6761	577	23	,	,	PUNCT
ejpam-6761	577	24	[	[	X
ejpam-6761	577	25	−1	−1	NOUN
ejpam-6761	577	26	,	,	PUNCT
ejpam-6761	577	27	0	0	NUM
ejpam-6761	577	28	]	]	PUNCT
ejpam-6761	577	29	,	,	PUNCT
ejpam-6761	577	30	[	[	X
ejpam-6761	577	31	0	0	NUM
ejpam-6761	577	32	,	,	PUNCT
ejpam-6761	577	33	1	1	NUM
ejpam-6761	577	34	]	]	PUNCT
ejpam-6761	577	35	)	)	PUNCT
ejpam-6761	577	36	⇐	⇐	ADJ
ejpam-6761	577	37	⇒	⇒	NOUN
ejpam-6761	577	38	(	(	PUNCT
ejpam-6761	577	39	x	x	X
ejpam-6761	577	40	,	,	PUNCT
ejpam-6761	577	41	[	[	X
ejpam-6761	577	42	−1	−1	NOUN
ejpam-6761	577	43	,	,	PUNCT
ejpam-6761	577	44	0	0	NUM
ejpam-6761	577	45	]	]	PUNCT
ejpam-6761	577	46	,	,	PUNCT
ejpam-6761	577	47	[	[	X
ejpam-6761	577	48	0	0	NUM
ejpam-6761	577	49	,	,	PUNCT
ejpam-6761	577	50	1])b	1])b	NUM
ejpam-6761	577	51	=	=	SYM
ejpam-6761	577	52	b(y	b(y	PROPN
ejpam-6761	577	53	,	,	PUNCT
ejpam-6761	577	54	[	[	X
ejpam-6761	577	55	−1	−1	NOUN
ejpam-6761	577	56	,	,	PUNCT
ejpam-6761	577	57	0	0	NUM
ejpam-6761	577	58	]	]	PUNCT
ejpam-6761	577	59	,	,	PUNCT
ejpam-6761	578	1	[	[	X
ejpam-6761	578	2	0	0	NUM
ejpam-6761	578	3	,	,	PUNCT
ejpam-6761	578	4	1	1	NUM
ejpam-6761	578	5	]	]	NUM
ejpam-6761	578	6	)	)	PUNCT
ejpam-6761	578	7	(	(	PUNCT
ejpam-6761	578	8	27	27	NUM
ejpam-6761	578	9	)	)	PUNCT
ejpam-6761	578	10	the	the	DET
ejpam-6761	578	11	bipolar	bipolar	ADJ
ejpam-6761	578	12	valued	value	VERB
ejpam-6761	578	13	fuzzy	fuzzy	ADJ
ejpam-6761	578	14	equivalence	equivalence	NOUN
ejpam-6761	578	15	relation	relation	NOUN
ejpam-6761	578	16	r	r	NOUN
ejpam-6761	578	17	on	on	ADP
ejpam-6761	578	18	the	the	DET
ejpam-6761	578	19	bipolar	bipolar	ADJ
ejpam-6761	578	20	valued	value	VERB
ejpam-6761	578	21	fuzzy	fuzzy	ADJ
ejpam-6761	578	22	space	space	NOUN
ejpam-6761	578	23	(	(	PUNCT
ejpam-6761	578	24	g	g	NOUN
ejpam-6761	578	25	,	,	PUNCT
ejpam-6761	578	26	[	[	X
ejpam-6761	578	27	−1	−1	NOUN
ejpam-6761	578	28	,	,	PUNCT
ejpam-6761	578	29	0	0	NUM
ejpam-6761	578	30	]	]	PUNCT
ejpam-6761	578	31	,	,	PUNCT
ejpam-6761	578	32	[	[	X
ejpam-6761	578	33	0	0	NUM
ejpam-6761	578	34	,	,	PUNCT
ejpam-6761	578	35	1	1	NUM
ejpam-6761	578	36	]	]	PUNCT
ejpam-6761	578	37	)	)	PUNCT
ejpam-6761	578	38	induces	induce	VERB
ejpam-6761	578	39	an	an	DET
ejpam-6761	578	40	ordinary	ordinary	ADJ
ejpam-6761	578	41	equivalence	equivalence	NOUN
ejpam-6761	578	42	relation	relation	NOUN
ejpam-6761	578	43	on	on	ADP
ejpam-6761	578	44	g	g	NOUN
ejpam-6761	578	45	by	by	ADP
ejpam-6761	578	46	the	the	DET
ejpam-6761	578	47	correspondence	correspondence	NOUN
ejpam-6761	578	48	:	:	PUNCT
ejpam-6761	578	49	(	(	PUNCT
ejpam-6761	578	50	x	x	X
ejpam-6761	578	51	,	,	PUNCT
ejpam-6761	578	52	[	[	X
ejpam-6761	578	53	−1	−1	NOUN
ejpam-6761	578	54	,	,	PUNCT
ejpam-6761	578	55	0	0	NUM
ejpam-6761	578	56	]	]	PUNCT
ejpam-6761	578	57	,	,	PUNCT
ejpam-6761	578	58	[	[	X
ejpam-6761	578	59	0	0	NUM
ejpam-6761	578	60	,	,	PUNCT
ejpam-6761	578	61	1	1	NUM
ejpam-6761	578	62	]	]	PUNCT
ejpam-6761	578	63	)	)	PUNCT
ejpam-6761	579	1	↔	↔	PROPN
ejpam-6761	579	2	x.	x.	NOUN
ejpam-6761	579	3	that	that	PRON
ejpam-6761	579	4	is	be	AUX
ejpam-6761	579	5	,	,	PUNCT
ejpam-6761	579	6	(	(	PUNCT
ejpam-6761	579	7	x	x	X
ejpam-6761	579	8	,	,	PUNCT
ejpam-6761	579	9	[	[	X
ejpam-6761	579	10	−1	−1	NOUN
ejpam-6761	579	11	,	,	PUNCT
ejpam-6761	579	12	0	0	NUM
ejpam-6761	579	13	]	]	PUNCT
ejpam-6761	579	14	,	,	PUNCT
ejpam-6761	579	15	[	[	X
ejpam-6761	579	16	0	0	NUM
ejpam-6761	579	17	,	,	PUNCT
ejpam-6761	579	18	1])r(y	1])r(y	NUM
ejpam-6761	579	19	,	,	PUNCT
ejpam-6761	579	20	[	[	X
ejpam-6761	579	21	−1	−1	NOUN
ejpam-6761	579	22	,	,	PUNCT
ejpam-6761	579	23	0	0	NUM
ejpam-6761	579	24	]	]	PUNCT
ejpam-6761	579	25	,	,	PUNCT
ejpam-6761	579	26	[	[	X
ejpam-6761	579	27	0	0	NUM
ejpam-6761	579	28	,	,	PUNCT
ejpam-6761	579	29	1	1	NUM
ejpam-6761	579	30	]	]	PUNCT
ejpam-6761	579	31	)	)	PUNCT
ejpam-6761	579	32	⇐	⇐	ADJ
ejpam-6761	579	33	⇒	⇒	PROPN
ejpam-6761	579	34	xry	xry	X
ejpam-6761	579	35	(	(	PUNCT
ejpam-6761	579	36	28	28	NUM
ejpam-6761	579	37	)	)	PUNCT
ejpam-6761	579	38	which	which	PRON
ejpam-6761	579	39	is	be	AUX
ejpam-6761	579	40	equivalent	equivalent	ADJ
ejpam-6761	579	41	to	to	ADP
ejpam-6761	579	42	xb	xb	PROPN
ejpam-6761	579	43	◦	◦	NOUN
ejpam-6761	579	44	=	=	SYM
ejpam-6761	579	45	b	b	X
ejpam-6761	579	46	◦	◦	NOUN
ejpam-6761	579	47	x.	x.	PROPN
ejpam-6761	579	48	f.	f.	PROPN
ejpam-6761	579	49	al	al	PROPN
ejpam-6761	579	50	-	-	PROPN
ejpam-6761	579	51	zu’bi	zu’bi	PROPN
ejpam-6761	579	52	et	et	NOUN
ejpam-6761	579	53	al	al	PROPN
ejpam-6761	579	54	.	.	PUNCT
ejpam-6761	579	55	/	/	SYM
ejpam-6761	579	56	eur	eur	PROPN
ejpam-6761	579	57	.	.	PUNCT
ejpam-6761	580	1	j.	j.	PROPN
ejpam-6761	580	2	pure	pure	PROPN
ejpam-6761	580	3	appl	appl	PROPN
ejpam-6761	580	4	.	.	PROPN
ejpam-6761	580	5	math	math	PROPN
ejpam-6761	580	6	,	,	PUNCT
ejpam-6761	580	7	18	18	NUM
ejpam-6761	580	8	(	(	PUNCT
ejpam-6761	580	9	4	4	NUM
ejpam-6761	580	10	)	)	PUNCT
ejpam-6761	580	11	(	(	PUNCT
ejpam-6761	580	12	2025	2025	NUM
ejpam-6761	580	13	)	)	PUNCT
ejpam-6761	580	14	,	,	PUNCT
ejpam-6761	580	15	6761	6761	NUM
ejpam-6761	580	16	23	23	NUM
ejpam-6761	580	17	of	of	ADP
ejpam-6761	580	18	28	28	NUM
ejpam-6761	580	19	5	5	NUM
ejpam-6761	580	20	.	.	PUNCT
ejpam-6761	581	1	bipolar	bipolar	PROPN
ejpam-6761	581	2	valued	value	VERB
ejpam-6761	581	3	fuzzy	fuzzy	ADJ
ejpam-6761	581	4	homomorphisms	homomorphism	NOUN
ejpam-6761	581	5	in	in	ADP
ejpam-6761	581	6	this	this	DET
ejpam-6761	581	7	section	section	NOUN
ejpam-6761	581	8	we	we	PRON
ejpam-6761	581	9	introduce	introduce	VERB
ejpam-6761	581	10	the	the	DET
ejpam-6761	581	11	notion	notion	NOUN
ejpam-6761	581	12	of	of	ADP
ejpam-6761	581	13	bipolar	bipolar	ADJ
ejpam-6761	581	14	valued	value	VERB
ejpam-6761	581	15	fuzzy	fuzzy	ADJ
ejpam-6761	581	16	homomorphism	homomorphism	NOUN
ejpam-6761	581	17	,	,	PUNCT
ejpam-6761	581	18	bipolar	bipolar	PROPN
ejpam-6761	581	19	valued	value	VERB
ejpam-6761	581	20	isomorphism	isomorphism	NOUN
ejpam-6761	581	21	and	and	CCONJ
ejpam-6761	581	22	bipolar	bipolar	ADJ
ejpam-6761	581	23	valued	value	VERB
ejpam-6761	581	24	fuzzy	fuzzy	ADJ
ejpam-6761	581	25	kernel	kernel	NOUN
ejpam-6761	581	26	.	.	PUNCT
ejpam-6761	582	1	we	we	PRON
ejpam-6761	582	2	also	also	ADV
ejpam-6761	582	3	study	study	VERB
ejpam-6761	582	4	the	the	DET
ejpam-6761	582	5	action	action	NOUN
ejpam-6761	582	6	of	of	ADP
ejpam-6761	582	7	bipolar	bipolar	ADJ
ejpam-6761	582	8	valued	value	VERB
ejpam-6761	582	9	fuzzy	fuzzy	ADJ
ejpam-6761	582	10	normal	normal	ADJ
ejpam-6761	582	11	subgroups	subgroup	NOUN
ejpam-6761	582	12	under	under	ADP
ejpam-6761	582	13	bipolar	bipolar	ADJ
ejpam-6761	582	14	valued	value	VERB
ejpam-6761	582	15	fuzzy	fuzzy	ADJ
ejpam-6761	582	16	homomorphisms	homomorphism	NOUN
ejpam-6761	582	17	.	.	PUNCT
ejpam-6761	583	1	definition	definition	NOUN
ejpam-6761	583	2	26	26	NUM
ejpam-6761	583	3	.	.	PUNCT
ejpam-6761	584	1	let	let	VERB
ejpam-6761	584	2	(	(	PUNCT
ejpam-6761	584	3	(	(	PUNCT
ejpam-6761	584	4	g	g	NOUN
ejpam-6761	584	5	,	,	PUNCT
ejpam-6761	584	6	[	[	X
ejpam-6761	584	7	−1	−1	NOUN
ejpam-6761	584	8	,	,	PUNCT
ejpam-6761	584	9	0	0	NUM
ejpam-6761	584	10	]	]	PUNCT
ejpam-6761	584	11	,	,	PUNCT
ejpam-6761	584	12	[	[	X
ejpam-6761	584	13	0	0	NUM
ejpam-6761	584	14	,	,	PUNCT
ejpam-6761	584	15	1	1	NUM
ejpam-6761	584	16	]	]	NUM
ejpam-6761	584	17	)	)	PUNCT
ejpam-6761	584	18	,	,	PUNCT
ejpam-6761	584	19	f	f	PROPN
ejpam-6761	584	20	)	)	PUNCT
ejpam-6761	584	21	and	and	CCONJ
ejpam-6761	584	22	(	(	PUNCT
ejpam-6761	584	23	(	(	PUNCT
ejpam-6761	584	24	g′	g′	NOUN
ejpam-6761	584	25	,	,	PUNCT
ejpam-6761	584	26	[	[	X
ejpam-6761	584	27	−1	−1	NOUN
ejpam-6761	584	28	,	,	PUNCT
ejpam-6761	584	29	0	0	NUM
ejpam-6761	584	30	]	]	PUNCT
ejpam-6761	584	31	,	,	PUNCT
ejpam-6761	584	32	[	[	X
ejpam-6761	584	33	0	0	NUM
ejpam-6761	584	34	,	,	PUNCT
ejpam-6761	584	35	1	1	NUM
ejpam-6761	584	36	]	]	NUM
ejpam-6761	584	37	)	)	PUNCT
ejpam-6761	584	38	,	,	PUNCT
ejpam-6761	584	39	h	h	X
ejpam-6761	584	40	)	)	PUNCT
ejpam-6761	584	41	be	be	VERB
ejpam-6761	584	42	two	two	NUM
ejpam-6761	584	43	bipolar	bipolar	ADJ
ejpam-6761	584	44	valued	value	VERB
ejpam-6761	584	45	fuzzy	fuzzy	ADJ
ejpam-6761	584	46	groups	group	NOUN
ejpam-6761	584	47	.	.	PUNCT
ejpam-6761	585	1	a	a	DET
ejpam-6761	585	2	bipolar	bipolar	ADJ
ejpam-6761	585	3	valued	value	VERB
ejpam-6761	585	4	fuzzy	fuzzy	ADJ
ejpam-6761	585	5	homomorphism	homomorphism	PROPN
ejpam-6761	585	6	φ	φ	PROPN
ejpam-6761	585	7	of	of	ADP
ejpam-6761	585	8	(	(	PUNCT
ejpam-6761	585	9	(	(	PUNCT
ejpam-6761	585	10	g	g	NOUN
ejpam-6761	585	11	,	,	PUNCT
ejpam-6761	585	12	[	[	X
ejpam-6761	585	13	−1	−1	NOUN
ejpam-6761	585	14	,	,	PUNCT
ejpam-6761	585	15	0	0	NUM
ejpam-6761	585	16	]	]	PUNCT
ejpam-6761	585	17	,	,	PUNCT
ejpam-6761	585	18	[	[	X
ejpam-6761	585	19	0	0	NUM
ejpam-6761	585	20	,	,	PUNCT
ejpam-6761	585	21	1	1	NUM
ejpam-6761	585	22	]	]	NUM
ejpam-6761	585	23	)	)	PUNCT
ejpam-6761	585	24	,	,	PUNCT
ejpam-6761	585	25	f	f	PROPN
ejpam-6761	585	26	)	)	PUNCT
ejpam-6761	585	27	into	into	ADP
ejpam-6761	585	28	(	(	PUNCT
ejpam-6761	585	29	(	(	PUNCT
ejpam-6761	585	30	g′	g′	NOUN
ejpam-6761	585	31	,	,	PUNCT
ejpam-6761	585	32	[	[	X
ejpam-6761	585	33	−1	−1	NOUN
ejpam-6761	585	34	,	,	PUNCT
ejpam-6761	585	35	0	0	NUM
ejpam-6761	585	36	]	]	PUNCT
ejpam-6761	585	37	,	,	PUNCT
ejpam-6761	585	38	[	[	X
ejpam-6761	585	39	0	0	NUM
ejpam-6761	585	40	,	,	PUNCT
ejpam-6761	585	41	1	1	NUM
ejpam-6761	585	42	]	]	NUM
ejpam-6761	585	43	)	)	PUNCT
ejpam-6761	585	44	,	,	PUNCT
ejpam-6761	585	45	h	h	X
ejpam-6761	585	46	)	)	PUNCT
ejpam-6761	585	47	is	be	AUX
ejpam-6761	585	48	a	a	DET
ejpam-6761	585	49	bipolar	bipolar	ADJ
ejpam-6761	585	50	valued	value	VERB
ejpam-6761	585	51	fuzzy	fuzzy	ADJ
ejpam-6761	585	52	function	function	NOUN
ejpam-6761	585	53	having	have	VERB
ejpam-6761	585	54	onto	onto	ADP
ejpam-6761	585	55	negative	negative	ADJ
ejpam-6761	585	56	and	and	CCONJ
ejpam-6761	585	57	positive	positive	ADJ
ejpam-6761	585	58	comembership	comembership	NOUN
ejpam-6761	585	59	functions	function	NOUN
ejpam-6761	585	60	φ	φ	NOUN
ejpam-6761	585	61	=	=	SYM
ejpam-6761	585	62	(	(	PUNCT
ejpam-6761	585	63	ϕ	ϕ	NOUN
ejpam-6761	585	64	,	,	PUNCT
ejpam-6761	585	65	φ−	φ−	PROPN
ejpam-6761	585	66	x	x	X
ejpam-6761	585	67	,	,	PUNCT
ejpam-6761	585	68	φ	φ	PROPN
ejpam-6761	585	69	+	+	CCONJ
ejpam-6761	585	70	x	x	X
ejpam-6761	585	71	)	)	PUNCT
ejpam-6761	585	72	:	:	PUNCT
ejpam-6761	585	73	(	(	PUNCT
ejpam-6761	585	74	(	(	PUNCT
ejpam-6761	585	75	g	g	NOUN
ejpam-6761	585	76	,	,	PUNCT
ejpam-6761	585	77	[	[	X
ejpam-6761	585	78	−1	−1	NOUN
ejpam-6761	585	79	,	,	PUNCT
ejpam-6761	585	80	0	0	NUM
ejpam-6761	585	81	]	]	PUNCT
ejpam-6761	585	82	,	,	PUNCT
ejpam-6761	585	83	[	[	X
ejpam-6761	585	84	0	0	NUM
ejpam-6761	585	85	,	,	PUNCT
ejpam-6761	585	86	1	1	NUM
ejpam-6761	585	87	]	]	NUM
ejpam-6761	585	88	)	)	PUNCT
ejpam-6761	585	89	,	,	PUNCT
ejpam-6761	585	90	f	f	PROPN
ejpam-6761	585	91	)	)	PUNCT
ejpam-6761	585	92	→	→	PUNCT
ejpam-6761	585	93	(	(	PUNCT
ejpam-6761	585	94	(	(	PUNCT
ejpam-6761	585	95	g′	g′	NOUN
ejpam-6761	585	96	,	,	PUNCT
ejpam-6761	585	97	[	[	X
ejpam-6761	585	98	−1	−1	NOUN
ejpam-6761	585	99	,	,	PUNCT
ejpam-6761	585	100	0	0	NUM
ejpam-6761	585	101	]	]	PUNCT
ejpam-6761	585	102	,	,	PUNCT
ejpam-6761	585	103	[	[	X
ejpam-6761	585	104	0	0	NUM
ejpam-6761	585	105	,	,	PUNCT
ejpam-6761	585	106	1	1	NUM
ejpam-6761	585	107	]	]	NUM
ejpam-6761	585	108	)	)	PUNCT
ejpam-6761	585	109	,	,	PUNCT
ejpam-6761	585	110	h	h	NOUN
ejpam-6761	585	111	)	)	PUNCT
ejpam-6761	586	1	such	such	ADJ
ejpam-6761	586	2	that	that	SCONJ
ejpam-6761	586	3	φ	φ	PROPN
ejpam-6761	586	4	(	(	PUNCT
ejpam-6761	586	5	(	(	PUNCT
ejpam-6761	586	6	x	x	X
ejpam-6761	586	7	,	,	PUNCT
ejpam-6761	586	8	[	[	X
ejpam-6761	586	9	−1	−1	NOUN
ejpam-6761	586	10	,	,	PUNCT
ejpam-6761	586	11	0	0	NUM
ejpam-6761	586	12	]	]	PUNCT
ejpam-6761	586	13	,	,	PUNCT
ejpam-6761	587	1	[	[	X
ejpam-6761	587	2	0	0	NUM
ejpam-6761	587	3	,	,	PUNCT
ejpam-6761	587	4	1])f	1])f	NUM
ejpam-6761	587	5	(	(	PUNCT
ejpam-6761	587	6	y	y	NOUN
ejpam-6761	587	7	,	,	PUNCT
ejpam-6761	587	8	[	[	X
ejpam-6761	587	9	−1	−1	NOUN
ejpam-6761	587	10	,	,	PUNCT
ejpam-6761	587	11	0	0	NUM
ejpam-6761	587	12	]	]	PUNCT
ejpam-6761	587	13	,	,	PUNCT
ejpam-6761	587	14	[	[	X
ejpam-6761	587	15	0	0	NUM
ejpam-6761	587	16	,	,	PUNCT
ejpam-6761	587	17	1	1	NUM
ejpam-6761	587	18	]	]	PUNCT
ejpam-6761	587	19	)	)	PUNCT
ejpam-6761	587	20	)	)	PUNCT
ejpam-6761	588	1	=	=	PUNCT
ejpam-6761	588	2	φ(x	φ(x	NOUN
ejpam-6761	588	3	,	,	PUNCT
ejpam-6761	588	4	[	[	X
ejpam-6761	588	5	−1	−1	NOUN
ejpam-6761	588	6	,	,	PUNCT
ejpam-6761	588	7	0	0	NUM
ejpam-6761	588	8	]	]	PUNCT
ejpam-6761	588	9	,	,	PUNCT
ejpam-6761	588	10	[	[	X
ejpam-6761	588	11	0	0	NUM
ejpam-6761	588	12	,	,	PUNCT
ejpam-6761	588	13	1])h	1])h	NUM
ejpam-6761	588	14	φ(y	φ(y	PROPN
ejpam-6761	588	15	,	,	PUNCT
ejpam-6761	588	16	[	[	X
ejpam-6761	588	17	−1	−1	NOUN
ejpam-6761	588	18	,	,	PUNCT
ejpam-6761	588	19	0	0	NUM
ejpam-6761	588	20	]	]	PUNCT
ejpam-6761	588	21	,	,	PUNCT
ejpam-6761	588	22	[	[	X
ejpam-6761	588	23	0	0	NUM
ejpam-6761	588	24	,	,	PUNCT
ejpam-6761	588	25	1	1	NUM
ejpam-6761	588	26	]	]	NUM
ejpam-6761	588	27	)	)	PUNCT
ejpam-6761	588	28	.	.	PUNCT
ejpam-6761	589	1	(	(	PUNCT
ejpam-6761	589	2	29	29	NUM
ejpam-6761	589	3	)	)	PUNCT
ejpam-6761	589	4	the	the	DET
ejpam-6761	589	5	bipolar	bipolar	ADJ
ejpam-6761	589	6	valued	value	VERB
ejpam-6761	589	7	fuzzy	fuzzy	ADJ
ejpam-6761	589	8	groups	group	NOUN
ejpam-6761	589	9	(	(	PUNCT
ejpam-6761	589	10	(	(	PUNCT
ejpam-6761	589	11	g	g	NOUN
ejpam-6761	589	12	,	,	PUNCT
ejpam-6761	589	13	[	[	X
ejpam-6761	589	14	−1	−1	NOUN
ejpam-6761	589	15	,	,	PUNCT
ejpam-6761	589	16	0	0	NUM
ejpam-6761	589	17	]	]	PUNCT
ejpam-6761	589	18	,	,	PUNCT
ejpam-6761	589	19	[	[	X
ejpam-6761	589	20	0	0	NUM
ejpam-6761	589	21	,	,	PUNCT
ejpam-6761	589	22	1	1	NUM
ejpam-6761	589	23	]	]	NUM
ejpam-6761	589	24	)	)	PUNCT
ejpam-6761	589	25	,	,	PUNCT
ejpam-6761	589	26	f	f	PROPN
ejpam-6761	589	27	)	)	PUNCT
ejpam-6761	589	28	and	and	CCONJ
ejpam-6761	589	29	(	(	PUNCT
ejpam-6761	589	30	(	(	PUNCT
ejpam-6761	589	31	g′	g′	NOUN
ejpam-6761	589	32	,	,	PUNCT
ejpam-6761	589	33	[	[	X
ejpam-6761	589	34	−1	−1	NOUN
ejpam-6761	589	35	,	,	PUNCT
ejpam-6761	589	36	0	0	NUM
ejpam-6761	589	37	]	]	PUNCT
ejpam-6761	589	38	,	,	PUNCT
ejpam-6761	589	39	[	[	X
ejpam-6761	589	40	0	0	NUM
ejpam-6761	589	41	,	,	PUNCT
ejpam-6761	589	42	1	1	NUM
ejpam-6761	589	43	]	]	NUM
ejpam-6761	589	44	)	)	PUNCT
ejpam-6761	589	45	,	,	PUNCT
ejpam-6761	589	46	h	h	X
ejpam-6761	589	47	)	)	PUNCT
ejpam-6761	589	48	are	be	AUX
ejpam-6761	589	49	called	call	VERB
ejpam-6761	589	50	homomorphic	homomorphic	ADJ
ejpam-6761	589	51	bipolar	bipolar	ADJ
ejpam-6761	589	52	valued	value	VERB
ejpam-6761	589	53	fuzzy	fuzzy	ADJ
ejpam-6761	589	54	groups	group	NOUN
ejpam-6761	589	55	under	under	ADP
ejpam-6761	589	56	the	the	DET
ejpam-6761	589	57	bipolar	bipolar	PROPN
ejpam-6761	589	58	valued	value	VERB
ejpam-6761	589	59	fuzzy	fuzzy	ADJ
ejpam-6761	589	60	homomorphism	homomorphism	PROPN
ejpam-6761	589	61	φ	φ	X
ejpam-6761	589	62	.	.	PUNCT
ejpam-6761	590	1	if	if	SCONJ
ejpam-6761	590	2	φ	φ	PROPN
ejpam-6761	590	3	:	:	PUNCT
ejpam-6761	590	4	g→	g→	PROPN
ejpam-6761	590	5	g′	g′	NOUN
ejpam-6761	590	6	is	be	AUX
ejpam-6761	590	7	a	a	DET
ejpam-6761	590	8	bijection	bijection	NOUN
ejpam-6761	590	9	(	(	PUNCT
ejpam-6761	590	10	one	one	NUM
ejpam-6761	590	11	-	-	PUNCT
ejpam-6761	590	12	to	to	ADP
ejpam-6761	590	13	-	-	PUNCT
ejpam-6761	590	14	one	one	NUM
ejpam-6761	590	15	and	and	CCONJ
ejpam-6761	590	16	onto	onto	ADP
ejpam-6761	590	17	)	)	PUNCT
ejpam-6761	590	18	then	then	ADV
ejpam-6761	590	19	it	it	PRON
ejpam-6761	590	20	is	be	AUX
ejpam-6761	590	21	called	call	VERB
ejpam-6761	590	22	a	a	DET
ejpam-6761	590	23	bipolar	bipolar	ADJ
ejpam-6761	590	24	valued	value	VERB
ejpam-6761	590	25	fuzzy	fuzzy	ADJ
ejpam-6761	590	26	isomorphism	isomorphism	NOUN
ejpam-6761	590	27	,	,	PUNCT
ejpam-6761	590	28	and	and	CCONJ
ejpam-6761	590	29	the	the	DET
ejpam-6761	590	30	bipolar	bipolar	ADJ
ejpam-6761	590	31	valued	value	VERB
ejpam-6761	590	32	fuzzy	fuzzy	ADJ
ejpam-6761	590	33	groups	group	NOUN
ejpam-6761	590	34	(	(	PUNCT
ejpam-6761	590	35	(	(	PUNCT
ejpam-6761	590	36	g	g	NOUN
ejpam-6761	590	37	,	,	PUNCT
ejpam-6761	590	38	[	[	X
ejpam-6761	590	39	−1	−1	NOUN
ejpam-6761	590	40	,	,	PUNCT
ejpam-6761	590	41	0	0	NUM
ejpam-6761	590	42	]	]	PUNCT
ejpam-6761	590	43	,	,	PUNCT
ejpam-6761	591	1	[	[	X
ejpam-6761	591	2	0	0	NUM
ejpam-6761	591	3	,	,	PUNCT
ejpam-6761	591	4	1	1	NUM
ejpam-6761	591	5	]	]	NUM
ejpam-6761	591	6	)	)	PUNCT
ejpam-6761	591	7	,	,	PUNCT
ejpam-6761	591	8	f	f	PROPN
ejpam-6761	591	9	)	)	PUNCT
ejpam-6761	591	10	,	,	PUNCT
ejpam-6761	591	11	(	(	PUNCT
ejpam-6761	591	12	(	(	PUNCT
ejpam-6761	591	13	g′	g′	NOUN
ejpam-6761	591	14	,	,	PUNCT
ejpam-6761	591	15	[	[	X
ejpam-6761	591	16	−1	−1	NOUN
ejpam-6761	591	17	,	,	PUNCT
ejpam-6761	591	18	0	0	NUM
ejpam-6761	591	19	]	]	PUNCT
ejpam-6761	591	20	,	,	PUNCT
ejpam-6761	591	21	[	[	X
ejpam-6761	591	22	0	0	NUM
ejpam-6761	591	23	,	,	PUNCT
ejpam-6761	591	24	1	1	NUM
ejpam-6761	591	25	]	]	NUM
ejpam-6761	591	26	)	)	PUNCT
ejpam-6761	591	27	,	,	PUNCT
ejpam-6761	591	28	h	h	X
ejpam-6761	591	29	)	)	PUNCT
ejpam-6761	591	30	are	be	AUX
ejpam-6761	591	31	said	say	VERB
ejpam-6761	591	32	to	to	PART
ejpam-6761	591	33	be	be	AUX
ejpam-6761	591	34	isomorphic	isomorphic	ADJ
ejpam-6761	591	35	bipolar	bipolar	ADJ
ejpam-6761	591	36	valued	value	VERB
ejpam-6761	591	37	fuzzy	fuzzy	ADJ
ejpam-6761	591	38	groups	group	NOUN
ejpam-6761	591	39	and	and	CCONJ
ejpam-6761	591	40	will	will	AUX
ejpam-6761	591	41	be	be	AUX
ejpam-6761	591	42	denoted	denote	VERB
ejpam-6761	591	43	by	by	ADP
ejpam-6761	591	44	(	(	PUNCT
ejpam-6761	591	45	(	(	PUNCT
ejpam-6761	591	46	g	g	NOUN
ejpam-6761	591	47	,	,	PUNCT
ejpam-6761	591	48	[	[	X
ejpam-6761	591	49	−1	−1	NOUN
ejpam-6761	591	50	,	,	PUNCT
ejpam-6761	591	51	0	0	NUM
ejpam-6761	591	52	]	]	PUNCT
ejpam-6761	591	53	,	,	PUNCT
ejpam-6761	592	1	[	[	X
ejpam-6761	592	2	0	0	NUM
ejpam-6761	592	3	,	,	PUNCT
ejpam-6761	592	4	1	1	NUM
ejpam-6761	592	5	]	]	NUM
ejpam-6761	592	6	)	)	PUNCT
ejpam-6761	592	7	,	,	PUNCT
ejpam-6761	592	8	f	f	X
ejpam-6761	592	9	)	)	PUNCT
ejpam-6761	592	10	∼=	∼=	PROPN
ejpam-6761	592	11	(	(	PUNCT
ejpam-6761	592	12	(	(	PUNCT
ejpam-6761	592	13	g′	g′	NOUN
ejpam-6761	592	14	,	,	PUNCT
ejpam-6761	592	15	[	[	X
ejpam-6761	592	16	−1	−1	NOUN
ejpam-6761	592	17	,	,	PUNCT
ejpam-6761	592	18	0	0	NUM
ejpam-6761	592	19	]	]	PUNCT
ejpam-6761	592	20	,	,	PUNCT
ejpam-6761	593	1	[	[	X
ejpam-6761	593	2	0	0	NUM
ejpam-6761	593	3	,	,	PUNCT
ejpam-6761	593	4	1	1	NUM
ejpam-6761	593	5	]	]	NUM
ejpam-6761	593	6	)	)	PUNCT
ejpam-6761	593	7	,	,	PUNCT
ejpam-6761	593	8	h	h	NOUN
ejpam-6761	593	9	)	)	PUNCT
ejpam-6761	593	10	.	.	PUNCT
ejpam-6761	594	1	from	from	ADP
ejpam-6761	594	2	the	the	DET
ejpam-6761	594	3	above	above	ADJ
ejpam-6761	594	4	definition	definition	NOUN
ejpam-6761	594	5	,	,	PUNCT
ejpam-6761	594	6	we	we	PRON
ejpam-6761	594	7	can	can	AUX
ejpam-6761	594	8	formulate	formulate	VERB
ejpam-6761	594	9	the	the	DET
ejpam-6761	594	10	action	action	NOUN
ejpam-6761	594	11	of	of	ADP
ejpam-6761	594	12	the	the	DET
ejpam-6761	594	13	bipolar	bipolar	PROPN
ejpam-6761	594	14	valued	value	VERB
ejpam-6761	594	15	fuzzy	fuzzy	ADJ
ejpam-6761	594	16	homomorphism	homomorphism	PROPN
ejpam-6761	594	17	φ	φ	PROPN
ejpam-6761	594	18	=	=	SYM
ejpam-6761	594	19	(	(	PUNCT
ejpam-6761	594	20	ϕ	ϕ	NOUN
ejpam-6761	594	21	,	,	PUNCT
ejpam-6761	594	22	φ−	φ−	PROPN
ejpam-6761	594	23	x	x	X
ejpam-6761	594	24	,	,	PUNCT
ejpam-6761	594	25	φ	φ	PROPN
ejpam-6761	594	26	+	+	CCONJ
ejpam-6761	594	27	x	x	X
ejpam-6761	594	28	)	)	PUNCT
ejpam-6761	594	29	of	of	ADP
ejpam-6761	594	30	(	(	PUNCT
ejpam-6761	594	31	(	(	PUNCT
ejpam-6761	594	32	g	g	NOUN
ejpam-6761	594	33	,	,	PUNCT
ejpam-6761	594	34	[	[	X
ejpam-6761	594	35	−1	−1	NOUN
ejpam-6761	594	36	,	,	PUNCT
ejpam-6761	594	37	0	0	NUM
ejpam-6761	594	38	]	]	PUNCT
ejpam-6761	594	39	,	,	PUNCT
ejpam-6761	595	1	[	[	X
ejpam-6761	595	2	0	0	NUM
ejpam-6761	595	3	,	,	PUNCT
ejpam-6761	595	4	1	1	NUM
ejpam-6761	595	5	]	]	NUM
ejpam-6761	595	6	)	)	PUNCT
ejpam-6761	595	7	,	,	PUNCT
ejpam-6761	595	8	f	f	PROPN
ejpam-6761	595	9	)	)	PUNCT
ejpam-6761	595	10	into	into	ADP
ejpam-6761	595	11	(	(	PUNCT
ejpam-6761	595	12	(	(	PUNCT
ejpam-6761	595	13	g′	g′	NOUN
ejpam-6761	595	14	,	,	PUNCT
ejpam-6761	595	15	[	[	X
ejpam-6761	595	16	−1	−1	NOUN
ejpam-6761	595	17	,	,	PUNCT
ejpam-6761	595	18	0	0	NUM
ejpam-6761	595	19	]	]	PUNCT
ejpam-6761	595	20	,	,	PUNCT
ejpam-6761	595	21	[	[	X
ejpam-6761	595	22	0	0	NUM
ejpam-6761	595	23	,	,	PUNCT
ejpam-6761	595	24	1	1	NUM
ejpam-6761	595	25	]	]	NUM
ejpam-6761	595	26	)	)	PUNCT
ejpam-6761	595	27	,	,	PUNCT
ejpam-6761	595	28	h	h	NOUN
ejpam-6761	595	29	)	)	PUNCT
ejpam-6761	595	30	for	for	ADP
ejpam-6761	595	31	any	any	DET
ejpam-6761	595	32	two	two	NUM
ejpam-6761	595	33	bipolar	bipolar	ADJ
ejpam-6761	595	34	valued	value	VERB
ejpam-6761	595	35	fuzzy	fuzzy	ADJ
ejpam-6761	595	36	elements	element	NOUN
ejpam-6761	595	37	(	(	PUNCT
ejpam-6761	595	38	x	x	X
ejpam-6761	595	39	,	,	PUNCT
ejpam-6761	595	40	[	[	X
ejpam-6761	595	41	−1	−1	NOUN
ejpam-6761	595	42	,	,	PUNCT
ejpam-6761	595	43	0	0	NUM
ejpam-6761	595	44	]	]	PUNCT
ejpam-6761	595	45	,	,	PUNCT
ejpam-6761	595	46	[	[	X
ejpam-6761	595	47	0	0	NUM
ejpam-6761	595	48	,	,	PUNCT
ejpam-6761	595	49	1	1	NUM
ejpam-6761	595	50	]	]	NUM
ejpam-6761	595	51	)	)	PUNCT
ejpam-6761	595	52	,	,	PUNCT
ejpam-6761	595	53	(	(	PUNCT
ejpam-6761	595	54	y	y	NOUN
ejpam-6761	595	55	,	,	PUNCT
ejpam-6761	595	56	[	[	X
ejpam-6761	595	57	−1	−1	NOUN
ejpam-6761	595	58	,	,	PUNCT
ejpam-6761	595	59	0	0	NUM
ejpam-6761	595	60	]	]	PUNCT
ejpam-6761	595	61	,	,	PUNCT
ejpam-6761	595	62	[	[	X
ejpam-6761	595	63	0	0	NUM
ejpam-6761	595	64	,	,	PUNCT
ejpam-6761	595	65	1	1	NUM
ejpam-6761	595	66	]	]	PUNCT
ejpam-6761	595	67	)	)	PUNCT
ejpam-6761	595	68	∈	∈	PROPN
ejpam-6761	595	69	(	(	PUNCT
ejpam-6761	595	70	g	g	NOUN
ejpam-6761	595	71	,	,	PUNCT
ejpam-6761	595	72	[	[	X
ejpam-6761	595	73	−1	−1	NOUN
ejpam-6761	595	74	,	,	PUNCT
ejpam-6761	595	75	0	0	NUM
ejpam-6761	595	76	]	]	PUNCT
ejpam-6761	595	77	,	,	PUNCT
ejpam-6761	595	78	[	[	X
ejpam-6761	595	79	0	0	NUM
ejpam-6761	595	80	,	,	PUNCT
ejpam-6761	595	81	1	1	NUM
ejpam-6761	595	82	]	]	PUNCT
ejpam-6761	595	83	)	)	PUNCT
ejpam-6761	595	84	as	as	SCONJ
ejpam-6761	595	85	follows	follow	VERB
ejpam-6761	595	86	:	:	PUNCT
ejpam-6761	595	87	φ	φ	PROPN
ejpam-6761	595	88	(	(	PUNCT
ejpam-6761	595	89	(	(	PUNCT
ejpam-6761	595	90	x	x	X
ejpam-6761	595	91	,	,	PUNCT
ejpam-6761	595	92	[	[	X
ejpam-6761	595	93	−1	−1	NOUN
ejpam-6761	595	94	,	,	PUNCT
ejpam-6761	595	95	0	0	NUM
ejpam-6761	595	96	]	]	PUNCT
ejpam-6761	595	97	,	,	PUNCT
ejpam-6761	595	98	[	[	X
ejpam-6761	595	99	0	0	NUM
ejpam-6761	595	100	,	,	PUNCT
ejpam-6761	595	101	1])f	1])f	NUM
ejpam-6761	595	102	(	(	PUNCT
ejpam-6761	595	103	y	y	NOUN
ejpam-6761	595	104	,	,	PUNCT
ejpam-6761	595	105	[	[	X
ejpam-6761	595	106	−1	−1	NOUN
ejpam-6761	595	107	,	,	PUNCT
ejpam-6761	595	108	0	0	NUM
ejpam-6761	595	109	]	]	PUNCT
ejpam-6761	595	110	,	,	PUNCT
ejpam-6761	595	111	[	[	X
ejpam-6761	595	112	0	0	NUM
ejpam-6761	595	113	,	,	PUNCT
ejpam-6761	595	114	1	1	NUM
ejpam-6761	595	115	]	]	PUNCT
ejpam-6761	595	116	)	)	PUNCT
ejpam-6761	595	117	)	)	PUNCT
ejpam-6761	596	1	=	=	SYM
ejpam-6761	596	2	φ	φ	PROPN
ejpam-6761	596	3	(	(	PUNCT
ejpam-6761	596	4	(	(	PUNCT
ejpam-6761	596	5	xfy	xfy	PROPN
ejpam-6761	596	6	)	)	PUNCT
ejpam-6761	596	7	,	,	PUNCT
ejpam-6761	597	1	[	[	X
ejpam-6761	597	2	−1	−1	NOUN
ejpam-6761	597	3	,	,	PUNCT
ejpam-6761	597	4	0	0	NUM
ejpam-6761	597	5	]	]	PUNCT
ejpam-6761	597	6	,	,	PUNCT
ejpam-6761	598	1	[	[	X
ejpam-6761	598	2	0	0	NUM
ejpam-6761	598	3	,	,	PUNCT
ejpam-6761	598	4	1	1	NUM
ejpam-6761	598	5	]	]	PUNCT
ejpam-6761	598	6	)	)	PUNCT
ejpam-6761	599	1	=	=	SYM
ejpam-6761	599	2	(	(	PUNCT
ejpam-6761	599	3	φ(x)hφ(y	φ(x)hφ(y	NOUN
ejpam-6761	599	4	)	)	PUNCT
ejpam-6761	599	5	,	,	PUNCT
ejpam-6761	600	1	[	[	X
ejpam-6761	600	2	−1	−1	NOUN
ejpam-6761	600	3	,	,	PUNCT
ejpam-6761	600	4	0	0	NUM
ejpam-6761	600	5	]	]	PUNCT
ejpam-6761	600	6	,	,	PUNCT
ejpam-6761	600	7	[	[	X
ejpam-6761	600	8	0	0	NUM
ejpam-6761	600	9	,	,	PUNCT
ejpam-6761	600	10	1	1	NUM
ejpam-6761	600	11	]	]	NUM
ejpam-6761	600	12	)	)	PUNCT
ejpam-6761	600	13	.	.	PUNCT
ejpam-6761	601	1	(	(	PUNCT
ejpam-6761	601	2	30	30	X
ejpam-6761	601	3	)	)	PUNCT
ejpam-6761	601	4	remark	remark	NOUN
ejpam-6761	601	5	2	2	NUM
ejpam-6761	601	6	.	.	PUNCT
ejpam-6761	602	1	the	the	DET
ejpam-6761	602	2	notions	notion	NOUN
ejpam-6761	602	3	bipolar	bipolar	ADJ
ejpam-6761	602	4	valued	value	VERB
ejpam-6761	602	5	fuzzy	fuzzy	ADJ
ejpam-6761	602	6	monomorphism	monomorphism	NOUN
ejpam-6761	602	7	,	,	PUNCT
ejpam-6761	602	8	epimorphism	epimorphism	NOUN
ejpam-6761	602	9	,	,	PUNCT
ejpam-6761	602	10	automorphism	automorphism	NOUN
ejpam-6761	602	11	and	and	CCONJ
ejpam-6761	602	12	endomorphism	endomorphism	PROPN
ejpam-6761	602	13	are	be	AUX
ejpam-6761	602	14	defined	define	VERB
ejpam-6761	602	15	as	as	ADP
ejpam-6761	602	16	obviously	obviously	ADV
ejpam-6761	602	17	as	as	ADP
ejpam-6761	602	18	in	in	ADP
ejpam-6761	602	19	the	the	DET
ejpam-6761	602	20	ordinary	ordinary	ADJ
ejpam-6761	602	21	case	case	NOUN
ejpam-6761	602	22	.	.	PUNCT
ejpam-6761	603	1	the	the	DET
ejpam-6761	603	2	next	next	ADJ
ejpam-6761	603	3	theorem	theorem	NOUN
ejpam-6761	603	4	is	be	AUX
ejpam-6761	603	5	a	a	DET
ejpam-6761	603	6	direct	direct	ADJ
ejpam-6761	603	7	result	result	NOUN
ejpam-6761	603	8	from	from	ADP
ejpam-6761	603	9	the	the	DET
ejpam-6761	603	10	above	above	ADJ
ejpam-6761	603	11	argument	argument	NOUN
ejpam-6761	603	12	and	and	CCONJ
ejpam-6761	603	13	definition	definition	NOUN
ejpam-6761	603	14	which	which	PRON
ejpam-6761	603	15	relates	relate	VERB
ejpam-6761	603	16	homomorphic	homomorphic	ADJ
ejpam-6761	603	17	bipolar	bipolar	ADJ
ejpam-6761	603	18	valued	value	VERB
ejpam-6761	603	19	groups	group	NOUN
ejpam-6761	603	20	with	with	ADP
ejpam-6761	603	21	their	their	PRON
ejpam-6761	603	22	corresponding	correspond	VERB
ejpam-6761	603	23	ordinary	ordinary	ADJ
ejpam-6761	603	24	groups	group	NOUN
ejpam-6761	603	25	in	in	ADP
ejpam-6761	603	26	terms	term	NOUN
ejpam-6761	603	27	of	of	ADP
ejpam-6761	603	28	necessity	necessity	NOUN
ejpam-6761	603	29	.	.	PUNCT
ejpam-6761	604	1	theorem	theorem	NOUN
ejpam-6761	604	2	10	10	NUM
ejpam-6761	604	3	.	.	PUNCT
ejpam-6761	605	1	if	if	SCONJ
ejpam-6761	605	2	(	(	PUNCT
ejpam-6761	605	3	(	(	PUNCT
ejpam-6761	605	4	g	g	NOUN
ejpam-6761	605	5	,	,	PUNCT
ejpam-6761	605	6	[	[	X
ejpam-6761	605	7	−1	−1	NOUN
ejpam-6761	605	8	,	,	PUNCT
ejpam-6761	605	9	0	0	NUM
ejpam-6761	605	10	]	]	PUNCT
ejpam-6761	605	11	,	,	PUNCT
ejpam-6761	605	12	[	[	X
ejpam-6761	605	13	0	0	NUM
ejpam-6761	605	14	,	,	PUNCT
ejpam-6761	605	15	1	1	NUM
ejpam-6761	605	16	]	]	NUM
ejpam-6761	605	17	)	)	PUNCT
ejpam-6761	605	18	,	,	PUNCT
ejpam-6761	605	19	f	f	PROPN
ejpam-6761	605	20	)	)	PUNCT
ejpam-6761	605	21	and	and	CCONJ
ejpam-6761	605	22	(	(	PUNCT
ejpam-6761	605	23	(	(	PUNCT
ejpam-6761	605	24	g′	g′	NOUN
ejpam-6761	605	25	,	,	PUNCT
ejpam-6761	605	26	[	[	X
ejpam-6761	605	27	−1	−1	NOUN
ejpam-6761	605	28	,	,	PUNCT
ejpam-6761	605	29	0	0	NUM
ejpam-6761	605	30	]	]	PUNCT
ejpam-6761	605	31	,	,	PUNCT
ejpam-6761	605	32	[	[	X
ejpam-6761	605	33	0	0	NUM
ejpam-6761	605	34	,	,	PUNCT
ejpam-6761	605	35	1	1	NUM
ejpam-6761	605	36	]	]	NUM
ejpam-6761	605	37	)	)	PUNCT
ejpam-6761	605	38	,	,	PUNCT
ejpam-6761	605	39	h	h	X
ejpam-6761	605	40	)	)	PUNCT
ejpam-6761	605	41	are	be	AUX
ejpam-6761	605	42	homomorphic	homomorphic	ADJ
ejpam-6761	605	43	bipolar	bipolar	ADJ
ejpam-6761	605	44	valued	value	VERB
ejpam-6761	605	45	fuzzy	fuzzy	ADJ
ejpam-6761	605	46	groups	group	NOUN
ejpam-6761	605	47	,	,	PUNCT
ejpam-6761	605	48	then	then	ADV
ejpam-6761	605	49	the	the	DET
ejpam-6761	605	50	corresponding	corresponding	ADJ
ejpam-6761	605	51	ordinary	ordinary	ADJ
ejpam-6761	605	52	groups	group	NOUN
ejpam-6761	605	53	(	(	PUNCT
ejpam-6761	605	54	g	g	NOUN
ejpam-6761	605	55	,	,	PUNCT
ejpam-6761	605	56	f	f	PROPN
ejpam-6761	605	57	)	)	PUNCT
ejpam-6761	605	58	and	and	CCONJ
ejpam-6761	605	59	(	(	PUNCT
ejpam-6761	605	60	g′	g′	NOUN
ejpam-6761	605	61	,	,	PUNCT
ejpam-6761	605	62	h	h	NOUN
ejpam-6761	605	63	)	)	PUNCT
ejpam-6761	605	64	are	be	AUX
ejpam-6761	605	65	homomorphic	homomorphic	ADJ
ejpam-6761	605	66	.	.	PUNCT
ejpam-6761	606	1	f.	f.	PROPN
ejpam-6761	606	2	al	al	PROPN
ejpam-6761	606	3	-	-	PROPN
ejpam-6761	606	4	zu’bi	zu’bi	PROPN
ejpam-6761	606	5	et	et	NOUN
ejpam-6761	606	6	al	al	PROPN
ejpam-6761	606	7	.	.	PUNCT
ejpam-6761	606	8	/	/	SYM
ejpam-6761	606	9	eur	eur	PROPN
ejpam-6761	606	10	.	.	PUNCT
ejpam-6761	607	1	j.	j.	PROPN
ejpam-6761	607	2	pure	pure	PROPN
ejpam-6761	607	3	appl	appl	PROPN
ejpam-6761	607	4	.	.	PROPN
ejpam-6761	607	5	math	math	PROPN
ejpam-6761	607	6	,	,	PUNCT
ejpam-6761	607	7	18	18	NUM
ejpam-6761	607	8	(	(	PUNCT
ejpam-6761	607	9	4	4	NUM
ejpam-6761	607	10	)	)	PUNCT
ejpam-6761	607	11	(	(	PUNCT
ejpam-6761	607	12	2025	2025	NUM
ejpam-6761	607	13	)	)	PUNCT
ejpam-6761	607	14	,	,	PUNCT
ejpam-6761	607	15	6761	6761	NUM
ejpam-6761	607	16	24	24	NUM
ejpam-6761	607	17	of	of	ADP
ejpam-6761	607	18	28	28	NUM
ejpam-6761	607	19	proof	proof	NOUN
ejpam-6761	607	20	.	.	PUNCT
ejpam-6761	608	1	let	let	VERB
ejpam-6761	608	2	(	(	PUNCT
ejpam-6761	608	3	(	(	PUNCT
ejpam-6761	608	4	g	g	NOUN
ejpam-6761	608	5	,	,	PUNCT
ejpam-6761	608	6	[	[	X
ejpam-6761	608	7	−1	−1	NOUN
ejpam-6761	608	8	,	,	PUNCT
ejpam-6761	608	9	0	0	NUM
ejpam-6761	608	10	]	]	PUNCT
ejpam-6761	608	11	,	,	PUNCT
ejpam-6761	608	12	[	[	X
ejpam-6761	608	13	0	0	NUM
ejpam-6761	608	14	,	,	PUNCT
ejpam-6761	608	15	1	1	NUM
ejpam-6761	608	16	]	]	NUM
ejpam-6761	608	17	)	)	PUNCT
ejpam-6761	608	18	,	,	PUNCT
ejpam-6761	608	19	f	f	PROPN
ejpam-6761	608	20	)	)	PUNCT
ejpam-6761	608	21	and	and	CCONJ
ejpam-6761	608	22	(	(	PUNCT
ejpam-6761	608	23	(	(	PUNCT
ejpam-6761	608	24	g′	g′	NOUN
ejpam-6761	608	25	,	,	PUNCT
ejpam-6761	608	26	[	[	X
ejpam-6761	608	27	−1	−1	NOUN
ejpam-6761	608	28	,	,	PUNCT
ejpam-6761	608	29	0	0	NUM
ejpam-6761	608	30	]	]	PUNCT
ejpam-6761	608	31	,	,	PUNCT
ejpam-6761	608	32	[	[	X
ejpam-6761	608	33	0	0	NUM
ejpam-6761	608	34	,	,	PUNCT
ejpam-6761	608	35	1	1	NUM
ejpam-6761	608	36	]	]	NUM
ejpam-6761	608	37	)	)	PUNCT
ejpam-6761	608	38	,	,	PUNCT
ejpam-6761	608	39	h	h	X
ejpam-6761	608	40	)	)	PUNCT
ejpam-6761	608	41	be	be	AUX
ejpam-6761	608	42	homomorphic	homomorphic	ADJ
ejpam-6761	608	43	bipolar	bipolar	ADJ
ejpam-6761	608	44	valued	value	VERB
ejpam-6761	608	45	fuzzy	fuzzy	ADJ
ejpam-6761	608	46	groups	group	NOUN
ejpam-6761	608	47	under	under	ADP
ejpam-6761	608	48	the	the	DET
ejpam-6761	608	49	bipolar	bipolar	PROPN
ejpam-6761	608	50	valued	value	VERB
ejpam-6761	608	51	fuzzy	fuzzy	ADJ
ejpam-6761	608	52	homomorphism	homomorphism	PROPN
ejpam-6761	608	53	φ	φ	PROPN
ejpam-6761	608	54	=	=	SYM
ejpam-6761	608	55	(	(	PUNCT
ejpam-6761	608	56	ϕ	ϕ	NOUN
ejpam-6761	608	57	,	,	PUNCT
ejpam-6761	608	58	φ−	φ−	PROPN
ejpam-6761	608	59	x	x	X
ejpam-6761	608	60	,	,	PUNCT
ejpam-6761	608	61	φ	φ	PROPN
ejpam-6761	608	62	+	+	CCONJ
ejpam-6761	608	63	x	x	X
ejpam-6761	608	64	)	)	PUNCT
ejpam-6761	608	65	with	with	ADP
ejpam-6761	608	66	corresponding	correspond	VERB
ejpam-6761	608	67	ordinary	ordinary	ADJ
ejpam-6761	608	68	groups	group	NOUN
ejpam-6761	608	69	(	(	PUNCT
ejpam-6761	608	70	g	g	NOUN
ejpam-6761	608	71	,	,	PUNCT
ejpam-6761	608	72	f	f	PROPN
ejpam-6761	608	73	)	)	PUNCT
ejpam-6761	608	74	and	and	CCONJ
ejpam-6761	608	75	(	(	PUNCT
ejpam-6761	608	76	g′	g′	NOUN
ejpam-6761	608	77	,	,	PUNCT
ejpam-6761	608	78	h	h	NOUN
ejpam-6761	608	79	)	)	PUNCT
ejpam-6761	608	80	.	.	PUNCT
ejpam-6761	609	1	now	now	ADV
ejpam-6761	609	2	using	use	VERB
ejpam-6761	609	3	the	the	DET
ejpam-6761	609	4	correspondences	correspondence	NOUN
ejpam-6761	609	5	(	(	PUNCT
ejpam-6761	609	6	x	x	X
ejpam-6761	609	7	,	,	PUNCT
ejpam-6761	609	8	[	[	X
ejpam-6761	609	9	−1	−1	NOUN
ejpam-6761	609	10	,	,	PUNCT
ejpam-6761	609	11	0	0	NUM
ejpam-6761	609	12	]	]	PUNCT
ejpam-6761	609	13	,	,	PUNCT
ejpam-6761	609	14	[	[	X
ejpam-6761	609	15	0	0	NUM
ejpam-6761	609	16	,	,	PUNCT
ejpam-6761	609	17	1	1	NUM
ejpam-6761	609	18	]	]	PUNCT
ejpam-6761	609	19	)	)	PUNCT
ejpam-6761	609	20	7→	7→	NUM
ejpam-6761	609	21	x	x	PUNCT
ejpam-6761	609	22	and	and	CCONJ
ejpam-6761	609	23	(	(	PUNCT
ejpam-6761	609	24	y	y	NOUN
ejpam-6761	609	25	,	,	PUNCT
ejpam-6761	609	26	[	[	X
ejpam-6761	609	27	−1	−1	NOUN
ejpam-6761	609	28	,	,	PUNCT
ejpam-6761	609	29	0	0	NUM
ejpam-6761	609	30	]	]	PUNCT
ejpam-6761	609	31	,	,	PUNCT
ejpam-6761	609	32	[	[	X
ejpam-6761	609	33	0	0	NUM
ejpam-6761	609	34	,	,	PUNCT
ejpam-6761	609	35	1	1	NUM
ejpam-6761	609	36	]	]	PUNCT
ejpam-6761	609	37	)	)	PUNCT
ejpam-6761	610	1	7→	7→	NUM
ejpam-6761	610	2	y	y	NOUN
ejpam-6761	610	3	and	and	CCONJ
ejpam-6761	610	4	the	the	DET
ejpam-6761	610	5	formulation	formulation	NOUN
ejpam-6761	610	6	obtained	obtain	VERB
ejpam-6761	610	7	in	in	ADP
ejpam-6761	610	8	definition	definition	NOUN
ejpam-6761	610	9	5.1	5.1	NUM
ejpam-6761	610	10	,	,	PUNCT
ejpam-6761	610	11	we	we	PRON
ejpam-6761	610	12	have	have	VERB
ejpam-6761	610	13	φ(xfy	φ(xfy	NOUN
ejpam-6761	610	14	)	)	PUNCT
ejpam-6761	610	15	=	=	SYM
ejpam-6761	610	16	φ(x)hφ(y	φ(x)hφ(y	NOUN
ejpam-6761	610	17	)	)	PUNCT
ejpam-6761	610	18	.	.	PUNCT
ejpam-6761	611	1	(	(	PUNCT
ejpam-6761	611	2	31	31	NUM
ejpam-6761	611	3	)	)	PUNCT
ejpam-6761	611	4	two	two	NUM
ejpam-6761	611	5	main	main	ADJ
ejpam-6761	611	6	properties	property	NOUN
ejpam-6761	611	7	of	of	ADP
ejpam-6761	611	8	bipolar	bipolar	ADJ
ejpam-6761	611	9	valued	value	VERB
ejpam-6761	611	10	fuzzy	fuzzy	ADJ
ejpam-6761	611	11	homomorphisms	homomorphism	NOUN
ejpam-6761	611	12	that	that	DET
ejpam-6761	611	13	coincide	coincide	NOUN
ejpam-6761	611	14	with	with	ADP
ejpam-6761	611	15	ordinary	ordinary	ADJ
ejpam-6761	611	16	homomorphisms	homomorphism	NOUN
ejpam-6761	611	17	are	be	AUX
ejpam-6761	611	18	given	give	VERB
ejpam-6761	611	19	in	in	ADP
ejpam-6761	611	20	the	the	DET
ejpam-6761	611	21	next	next	ADJ
ejpam-6761	611	22	lemma	lemma	PROPN
ejpam-6761	611	23	.	.	PUNCT
ejpam-6761	612	1	lemma	lemma	PROPN
ejpam-6761	612	2	1	1	NUM
ejpam-6761	612	3	.	.	PUNCT
ejpam-6761	613	1	if	if	SCONJ
ejpam-6761	613	2	φ	φ	PROPN
ejpam-6761	613	3	=	=	SYM
ejpam-6761	613	4	(	(	PUNCT
ejpam-6761	613	5	ϕ	ϕ	NOUN
ejpam-6761	613	6	,	,	PUNCT
ejpam-6761	613	7	φ−	φ−	PROPN
ejpam-6761	613	8	x	x	X
ejpam-6761	613	9	,	,	PUNCT
ejpam-6761	613	10	φ	φ	PROPN
ejpam-6761	613	11	+	+	CCONJ
ejpam-6761	613	12	x	x	X
ejpam-6761	613	13	)	)	PUNCT
ejpam-6761	613	14	:	:	PUNCT
ejpam-6761	613	15	(	(	PUNCT
ejpam-6761	613	16	(	(	PUNCT
ejpam-6761	613	17	g	g	NOUN
ejpam-6761	613	18	,	,	PUNCT
ejpam-6761	613	19	[	[	X
ejpam-6761	613	20	−1	−1	NOUN
ejpam-6761	613	21	,	,	PUNCT
ejpam-6761	613	22	0	0	NUM
ejpam-6761	613	23	]	]	PUNCT
ejpam-6761	613	24	,	,	PUNCT
ejpam-6761	613	25	[	[	X
ejpam-6761	613	26	0	0	NUM
ejpam-6761	613	27	,	,	PUNCT
ejpam-6761	613	28	1	1	NUM
ejpam-6761	613	29	]	]	NUM
ejpam-6761	613	30	)	)	PUNCT
ejpam-6761	613	31	,	,	PUNCT
ejpam-6761	613	32	f	f	PROPN
ejpam-6761	613	33	)	)	PUNCT
ejpam-6761	613	34	→	→	PUNCT
ejpam-6761	613	35	(	(	PUNCT
ejpam-6761	613	36	(	(	PUNCT
ejpam-6761	613	37	g′	g′	NOUN
ejpam-6761	613	38	,	,	PUNCT
ejpam-6761	613	39	[	[	X
ejpam-6761	613	40	−1	−1	NOUN
ejpam-6761	613	41	,	,	PUNCT
ejpam-6761	613	42	0	0	NUM
ejpam-6761	613	43	]	]	PUNCT
ejpam-6761	613	44	,	,	PUNCT
ejpam-6761	613	45	[	[	X
ejpam-6761	613	46	0	0	NUM
ejpam-6761	613	47	,	,	PUNCT
ejpam-6761	613	48	1	1	NUM
ejpam-6761	613	49	]	]	NUM
ejpam-6761	613	50	)	)	PUNCT
ejpam-6761	613	51	,	,	PUNCT
ejpam-6761	613	52	h	h	X
ejpam-6761	613	53	)	)	PUNCT
ejpam-6761	613	54	is	be	AUX
ejpam-6761	613	55	a	a	DET
ejpam-6761	613	56	bipolar	bipolar	ADJ
ejpam-6761	613	57	valued	value	VERB
ejpam-6761	613	58	fuzzy	fuzzy	ADJ
ejpam-6761	613	59	homomorphism	homomorphism	NOUN
ejpam-6761	613	60	of	of	ADP
ejpam-6761	613	61	bipolar	bipolar	ADJ
ejpam-6761	613	62	valued	value	VERB
ejpam-6761	613	63	fuzzy	fuzzy	ADJ
ejpam-6761	613	64	groups	group	NOUN
ejpam-6761	613	65	(	(	PUNCT
ejpam-6761	613	66	(	(	PUNCT
ejpam-6761	613	67	g	g	NOUN
ejpam-6761	613	68	,	,	PUNCT
ejpam-6761	613	69	[	[	X
ejpam-6761	613	70	−1	−1	NOUN
ejpam-6761	613	71	,	,	PUNCT
ejpam-6761	613	72	0	0	NUM
ejpam-6761	613	73	]	]	PUNCT
ejpam-6761	613	74	,	,	PUNCT
ejpam-6761	613	75	[	[	X
ejpam-6761	613	76	0	0	NUM
ejpam-6761	613	77	,	,	PUNCT
ejpam-6761	613	78	1	1	NUM
ejpam-6761	613	79	]	]	NUM
ejpam-6761	613	80	)	)	PUNCT
ejpam-6761	613	81	,	,	PUNCT
ejpam-6761	613	82	f	f	PROPN
ejpam-6761	613	83	)	)	PUNCT
ejpam-6761	613	84	,	,	PUNCT
ejpam-6761	613	85	(	(	PUNCT
ejpam-6761	613	86	(	(	PUNCT
ejpam-6761	613	87	g′	g′	NOUN
ejpam-6761	613	88	,	,	PUNCT
ejpam-6761	613	89	[	[	X
ejpam-6761	613	90	−1	−1	NOUN
ejpam-6761	613	91	,	,	PUNCT
ejpam-6761	613	92	0	0	NUM
ejpam-6761	613	93	]	]	PUNCT
ejpam-6761	613	94	,	,	PUNCT
ejpam-6761	613	95	[	[	X
ejpam-6761	613	96	0	0	NUM
ejpam-6761	613	97	,	,	PUNCT
ejpam-6761	613	98	1	1	NUM
ejpam-6761	613	99	]	]	NUM
ejpam-6761	613	100	)	)	PUNCT
ejpam-6761	613	101	,	,	PUNCT
ejpam-6761	613	102	h	h	X
ejpam-6761	613	103	)	)	PUNCT
ejpam-6761	613	104	having	have	VERB
ejpam-6761	613	105	bipolar	bipolar	ADJ
ejpam-6761	613	106	valued	value	VERB
ejpam-6761	613	107	fuzzy	fuzzy	ADJ
ejpam-6761	613	108	identities	identity	NOUN
ejpam-6761	613	109	(	(	PUNCT
ejpam-6761	613	110	e	e	NOUN
ejpam-6761	613	111	,	,	PUNCT
ejpam-6761	613	112	[	[	X
ejpam-6761	613	113	−1	−1	NOUN
ejpam-6761	613	114	,	,	PUNCT
ejpam-6761	613	115	0	0	NUM
ejpam-6761	613	116	]	]	PUNCT
ejpam-6761	613	117	,	,	PUNCT
ejpam-6761	613	118	[	[	X
ejpam-6761	613	119	0	0	NUM
ejpam-6761	613	120	,	,	PUNCT
ejpam-6761	613	121	1	1	NUM
ejpam-6761	613	122	]	]	PUNCT
ejpam-6761	613	123	)	)	PUNCT
ejpam-6761	613	124	and	and	CCONJ
ejpam-6761	613	125	(	(	PUNCT
ejpam-6761	613	126	e′	e′	PROPN
ejpam-6761	613	127	,	,	PUNCT
ejpam-6761	613	128	[	[	X
ejpam-6761	613	129	−1	−1	NOUN
ejpam-6761	613	130	,	,	PUNCT
ejpam-6761	613	131	0	0	NUM
ejpam-6761	613	132	]	]	PUNCT
ejpam-6761	613	133	,	,	PUNCT
ejpam-6761	613	134	[	[	X
ejpam-6761	613	135	0	0	NUM
ejpam-6761	613	136	,	,	PUNCT
ejpam-6761	613	137	1	1	NUM
ejpam-6761	613	138	]	]	NUM
ejpam-6761	613	139	)	)	PUNCT
ejpam-6761	613	140	respectively	respectively	ADV
ejpam-6761	613	141	,	,	PUNCT
ejpam-6761	613	142	then	then	ADV
ejpam-6761	613	143	the	the	DET
ejpam-6761	613	144	following	follow	VERB
ejpam-6761	613	145	holds	hold	VERB
ejpam-6761	613	146	:	:	PUNCT
ejpam-6761	613	147	(	(	PUNCT
ejpam-6761	613	148	1	1	X
ejpam-6761	613	149	)	)	PUNCT
ejpam-6761	613	150	φ((e	φ((e	NOUN
ejpam-6761	613	151	,	,	PUNCT
ejpam-6761	613	152	[	[	X
ejpam-6761	613	153	−1	−1	NOUN
ejpam-6761	613	154	,	,	PUNCT
ejpam-6761	613	155	0	0	NUM
ejpam-6761	613	156	]	]	PUNCT
ejpam-6761	613	157	,	,	PUNCT
ejpam-6761	613	158	[	[	X
ejpam-6761	613	159	0	0	NUM
ejpam-6761	613	160	,	,	PUNCT
ejpam-6761	613	161	1	1	NUM
ejpam-6761	613	162	]	]	NUM
ejpam-6761	613	163	)	)	PUNCT
ejpam-6761	613	164	)	)	PUNCT
ejpam-6761	614	1	=	=	SYM
ejpam-6761	614	2	(	(	PUNCT
ejpam-6761	614	3	e′	e′	PROPN
ejpam-6761	614	4	,	,	PUNCT
ejpam-6761	614	5	[	[	X
ejpam-6761	614	6	−1	−1	NOUN
ejpam-6761	614	7	,	,	PUNCT
ejpam-6761	614	8	0	0	NUM
ejpam-6761	614	9	]	]	PUNCT
ejpam-6761	614	10	,	,	PUNCT
ejpam-6761	614	11	[	[	X
ejpam-6761	614	12	0	0	NUM
ejpam-6761	614	13	,	,	PUNCT
ejpam-6761	614	14	1	1	NUM
ejpam-6761	614	15	]	]	NUM
ejpam-6761	614	16	)	)	PUNCT
ejpam-6761	614	17	,	,	PUNCT
ejpam-6761	614	18	(	(	PUNCT
ejpam-6761	614	19	2	2	X
ejpam-6761	614	20	)	)	PUNCT
ejpam-6761	614	21	φ((x−1	φ((x−1	NOUN
ejpam-6761	614	22	,	,	PUNCT
ejpam-6761	614	23	[	[	X
ejpam-6761	614	24	−1	−1	NOUN
ejpam-6761	614	25	,	,	PUNCT
ejpam-6761	614	26	0	0	NUM
ejpam-6761	614	27	]	]	PUNCT
ejpam-6761	614	28	,	,	PUNCT
ejpam-6761	614	29	[	[	X
ejpam-6761	614	30	0	0	NUM
ejpam-6761	614	31	,	,	PUNCT
ejpam-6761	614	32	1	1	NUM
ejpam-6761	614	33	]	]	NUM
ejpam-6761	614	34	)	)	PUNCT
ejpam-6761	614	35	)	)	PUNCT
ejpam-6761	615	1	=	=	SYM
ejpam-6761	615	2	(	(	PUNCT
ejpam-6761	615	3	φ(x	φ(x	PROPN
ejpam-6761	615	4	,	,	PUNCT
ejpam-6761	615	5	[	[	X
ejpam-6761	615	6	−1	−1	NOUN
ejpam-6761	615	7	,	,	PUNCT
ejpam-6761	615	8	0	0	NUM
ejpam-6761	615	9	]	]	PUNCT
ejpam-6761	615	10	,	,	PUNCT
ejpam-6761	615	11	[	[	X
ejpam-6761	615	12	0	0	NUM
ejpam-6761	615	13	,	,	PUNCT
ejpam-6761	615	14	1]))−1	1]))−1	NOUN
ejpam-6761	615	15	.	.	PUNCT
ejpam-6761	616	1	proof	proof	NOUN
ejpam-6761	616	2	.	.	PUNCT
ejpam-6761	617	1	the	the	DET
ejpam-6761	617	2	proof	proof	NOUN
ejpam-6761	617	3	is	be	AUX
ejpam-6761	617	4	straightforward	straightforward	ADJ
ejpam-6761	617	5	using	use	VERB
ejpam-6761	617	6	the	the	DET
ejpam-6761	617	7	properties	property	NOUN
ejpam-6761	617	8	of	of	ADP
ejpam-6761	617	9	bipolar	bipolar	ADJ
ejpam-6761	617	10	valued	value	VERB
ejpam-6761	617	11	fuzzy	fuzzy	ADJ
ejpam-6761	617	12	homomorphism	homomorphism	NOUN
ejpam-6761	617	13	.	.	PUNCT
ejpam-6761	618	1	obviously	obviously	ADV
ejpam-6761	618	2	,	,	PUNCT
ejpam-6761	618	3	if	if	SCONJ
ejpam-6761	618	4	φ	φ	PROPN
ejpam-6761	618	5	=	=	SYM
ejpam-6761	618	6	(	(	PUNCT
ejpam-6761	618	7	ϕ	ϕ	NOUN
ejpam-6761	618	8	,	,	PUNCT
ejpam-6761	618	9	φ−	φ−	PROPN
ejpam-6761	618	10	x	x	X
ejpam-6761	618	11	,	,	PUNCT
ejpam-6761	618	12	φ	φ	PROPN
ejpam-6761	618	13	+	+	CCONJ
ejpam-6761	618	14	x	x	X
ejpam-6761	618	15	)	)	PUNCT
ejpam-6761	618	16	is	be	AUX
ejpam-6761	618	17	a	a	DET
ejpam-6761	618	18	bipolar	bipolar	ADJ
ejpam-6761	618	19	valued	value	VERB
ejpam-6761	618	20	fuzzy	fuzzy	ADJ
ejpam-6761	618	21	homomorphism	homomorphism	NOUN
ejpam-6761	618	22	between	between	ADP
ejpam-6761	618	23	the	the	DET
ejpam-6761	618	24	bipolar	bipolar	PROPN
ejpam-6761	618	25	valued	value	VERB
ejpam-6761	618	26	fuzzy	fuzzy	ADJ
ejpam-6761	618	27	groups	group	NOUN
ejpam-6761	618	28	(	(	PUNCT
ejpam-6761	618	29	(	(	PUNCT
ejpam-6761	618	30	g	g	NOUN
ejpam-6761	618	31	,	,	PUNCT
ejpam-6761	618	32	[	[	X
ejpam-6761	618	33	−1	−1	NOUN
ejpam-6761	618	34	,	,	PUNCT
ejpam-6761	618	35	0	0	NUM
ejpam-6761	618	36	]	]	PUNCT
ejpam-6761	618	37	,	,	PUNCT
ejpam-6761	618	38	[	[	X
ejpam-6761	618	39	0	0	NUM
ejpam-6761	618	40	,	,	PUNCT
ejpam-6761	618	41	1	1	NUM
ejpam-6761	618	42	]	]	NUM
ejpam-6761	618	43	)	)	PUNCT
ejpam-6761	618	44	,	,	PUNCT
ejpam-6761	618	45	f	f	PROPN
ejpam-6761	618	46	)	)	PUNCT
ejpam-6761	618	47	and	and	CCONJ
ejpam-6761	618	48	(	(	PUNCT
ejpam-6761	618	49	(	(	PUNCT
ejpam-6761	618	50	g′	g′	NOUN
ejpam-6761	618	51	,	,	PUNCT
ejpam-6761	618	52	[	[	X
ejpam-6761	618	53	−1	−1	NOUN
ejpam-6761	618	54	,	,	PUNCT
ejpam-6761	618	55	0	0	NUM
ejpam-6761	618	56	]	]	PUNCT
ejpam-6761	618	57	,	,	PUNCT
ejpam-6761	618	58	[	[	X
ejpam-6761	618	59	0	0	NUM
ejpam-6761	618	60	,	,	PUNCT
ejpam-6761	618	61	1	1	NUM
ejpam-6761	618	62	]	]	NUM
ejpam-6761	618	63	)	)	PUNCT
ejpam-6761	618	64	,	,	PUNCT
ejpam-6761	618	65	h	h	NOUN
ejpam-6761	618	66	)	)	PUNCT
ejpam-6761	618	67	then	then	ADV
ejpam-6761	618	68	the	the	DET
ejpam-6761	618	69	image	image	NOUN
ejpam-6761	618	70	of	of	ADP
ejpam-6761	618	71	any	any	DET
ejpam-6761	618	72	bipolar	bipolar	ADJ
ejpam-6761	618	73	valued	value	VERB
ejpam-6761	618	74	fuzzy	fuzzy	ADJ
ejpam-6761	618	75	group	group	NOUN
ejpam-6761	618	76	b	b	PROPN
ejpam-6761	618	77	=	=	SYM
ejpam-6761	618	78	(	(	PUNCT
ejpam-6761	618	79	x	x	X
ejpam-6761	618	80	,	,	PUNCT
ejpam-6761	618	81	b−x	b−x	NOUN
ejpam-6761	618	82	,	,	PUNCT
ejpam-6761	618	83	b	b	X
ejpam-6761	619	1	+	+	CCONJ
ejpam-6761	619	2	x	x	X
ejpam-6761	619	3	)	)	PUNCT
ejpam-6761	620	1	|	|	ADV
ejpam-6761	620	2	x	x	SYM
ejpam-6761	620	3	∈	∈	PROPN
ejpam-6761	621	1	b	b	X
ejpam-6761	621	2	◦	◦	NOUN
ejpam-6761	621	3	of	of	ADP
ejpam-6761	621	4	(	(	PUNCT
ejpam-6761	621	5	(	(	PUNCT
ejpam-6761	621	6	g	g	NOUN
ejpam-6761	621	7	,	,	PUNCT
ejpam-6761	621	8	[	[	X
ejpam-6761	621	9	−1	−1	NOUN
ejpam-6761	621	10	,	,	PUNCT
ejpam-6761	621	11	0	0	NUM
ejpam-6761	621	12	]	]	PUNCT
ejpam-6761	621	13	,	,	PUNCT
ejpam-6761	621	14	[	[	X
ejpam-6761	621	15	0	0	NUM
ejpam-6761	621	16	,	,	PUNCT
ejpam-6761	621	17	1	1	NUM
ejpam-6761	621	18	]	]	NUM
ejpam-6761	621	19	)	)	PUNCT
ejpam-6761	621	20	,	,	PUNCT
ejpam-6761	621	21	f	f	PROPN
ejpam-6761	621	22	)	)	PUNCT
ejpam-6761	621	23	under	under	ADP
ejpam-6761	621	24	φ	φ	PROPN
ejpam-6761	621	25	,	,	PUNCT
ejpam-6761	621	26	denoted	denote	VERB
ejpam-6761	621	27	by	by	ADP
ejpam-6761	621	28	φ(b	φ(b	NOUN
ejpam-6761	621	29	)	)	PUNCT
ejpam-6761	621	30	,	,	PUNCT
ejpam-6761	621	31	is	be	AUX
ejpam-6761	621	32	a	a	DET
ejpam-6761	621	33	bipolar	bipolar	ADJ
ejpam-6761	621	34	valued	value	VERB
ejpam-6761	621	35	fuzzy	fuzzy	ADJ
ejpam-6761	621	36	subgroup	subgroup	NOUN
ejpam-6761	621	37	of	of	ADP
ejpam-6761	621	38	(	(	PUNCT
ejpam-6761	621	39	(	(	PUNCT
ejpam-6761	621	40	g′	g′	NOUN
ejpam-6761	621	41	,	,	PUNCT
ejpam-6761	621	42	[	[	X
ejpam-6761	621	43	−1	−1	NOUN
ejpam-6761	621	44	,	,	PUNCT
ejpam-6761	621	45	0	0	NUM
ejpam-6761	621	46	]	]	PUNCT
ejpam-6761	621	47	,	,	PUNCT
ejpam-6761	621	48	[	[	X
ejpam-6761	621	49	0	0	NUM
ejpam-6761	621	50	,	,	PUNCT
ejpam-6761	621	51	1	1	NUM
ejpam-6761	621	52	]	]	NUM
ejpam-6761	621	53	)	)	PUNCT
ejpam-6761	621	54	,	,	PUNCT
ejpam-6761	621	55	h	h	NOUN
ejpam-6761	621	56	)	)	PUNCT
ejpam-6761	621	57	if	if	SCONJ
ejpam-6761	621	58	for	for	ADP
ejpam-6761	621	59	all	all	DET
ejpam-6761	621	60	φ(x	φ(x	NOUN
ejpam-6761	621	61	)	)	PUNCT
ejpam-6761	621	62	=	=	SYM
ejpam-6761	621	63	φ(x′	φ(x′	NUM
ejpam-6761	621	64	)	)	PUNCT
ejpam-6761	621	65	,	,	PUNCT
ejpam-6761	621	66	φ−	φ−	PROPN
ejpam-6761	621	67	x	x	X
ejpam-6761	621	68	(	(	PUNCT
ejpam-6761	621	69	b	b	NOUN
ejpam-6761	621	70	−	−	NOUN
ejpam-6761	621	71	x	x	SYM
ejpam-6761	621	72	)	)	PUNCT
ejpam-6761	622	1	=	=	SYM
ejpam-6761	622	2	φ−	φ−	PROPN
ejpam-6761	622	3	x′(b	x′(b	PUNCT
ejpam-6761	623	1	−	−	PROPN
ejpam-6761	623	2	x′	x′	NUM
ejpam-6761	623	3	)	)	PUNCT
ejpam-6761	624	1	,	,	PUNCT
ejpam-6761	624	2	φ+	φ+	NOUN
ejpam-6761	624	3	x	x	X
ejpam-6761	624	4	(	(	PUNCT
ejpam-6761	624	5	b	b	NOUN
ejpam-6761	624	6	+	+	CCONJ
ejpam-6761	624	7	x	x	X
ejpam-6761	624	8	)	)	PUNCT
ejpam-6761	625	1	=	=	NOUN
ejpam-6761	625	2	φ+	φ+	NOUN
ejpam-6761	625	3	x′(b	x′(b	PROPN
ejpam-6761	626	1	+	+	CCONJ
ejpam-6761	626	2	x′	x′	NUM
ejpam-6761	626	3	)	)	PUNCT
ejpam-6761	626	4	.	.	PUNCT
ejpam-6761	627	1	(	(	PUNCT
ejpam-6761	627	2	32	32	NUM
ejpam-6761	627	3	)	)	PUNCT
ejpam-6761	627	4	theorem	theorem	VERB
ejpam-6761	627	5	11	11	NUM
ejpam-6761	627	6	.	.	PUNCT
ejpam-6761	628	1	if	if	SCONJ
ejpam-6761	628	2	φ	φ	PROPN
ejpam-6761	628	3	=	=	SYM
ejpam-6761	628	4	(	(	PUNCT
ejpam-6761	628	5	ϕ	ϕ	NOUN
ejpam-6761	628	6	,	,	PUNCT
ejpam-6761	628	7	φ−	φ−	PROPN
ejpam-6761	628	8	x	x	X
ejpam-6761	628	9	,	,	PUNCT
ejpam-6761	628	10	φ	φ	PROPN
ejpam-6761	628	11	+	+	CCONJ
ejpam-6761	628	12	x	x	X
ejpam-6761	628	13	)	)	PUNCT
ejpam-6761	628	14	is	be	AUX
ejpam-6761	628	15	a	a	DET
ejpam-6761	628	16	bipolar	bipolar	ADJ
ejpam-6761	628	17	valued	value	VERB
ejpam-6761	628	18	fuzzy	fuzzy	ADJ
ejpam-6761	628	19	homomorphism	homomorphism	NOUN
ejpam-6761	628	20	between	between	ADP
ejpam-6761	628	21	the	the	DET
ejpam-6761	628	22	bipolar	bipolar	PROPN
ejpam-6761	628	23	valued	value	VERB
ejpam-6761	628	24	fuzzy	fuzzy	ADJ
ejpam-6761	628	25	groups	group	NOUN
ejpam-6761	628	26	(	(	PUNCT
ejpam-6761	628	27	(	(	PUNCT
ejpam-6761	628	28	g	g	NOUN
ejpam-6761	628	29	,	,	PUNCT
ejpam-6761	628	30	[	[	X
ejpam-6761	628	31	−1	−1	NOUN
ejpam-6761	628	32	,	,	PUNCT
ejpam-6761	628	33	0	0	NUM
ejpam-6761	628	34	]	]	PUNCT
ejpam-6761	628	35	,	,	PUNCT
ejpam-6761	628	36	[	[	X
ejpam-6761	628	37	0	0	NUM
ejpam-6761	628	38	,	,	PUNCT
ejpam-6761	628	39	1	1	NUM
ejpam-6761	628	40	]	]	NUM
ejpam-6761	628	41	)	)	PUNCT
ejpam-6761	628	42	,	,	PUNCT
ejpam-6761	628	43	f	f	PROPN
ejpam-6761	628	44	)	)	PUNCT
ejpam-6761	628	45	and	and	CCONJ
ejpam-6761	628	46	(	(	PUNCT
ejpam-6761	628	47	(	(	PUNCT
ejpam-6761	628	48	g′	g′	NOUN
ejpam-6761	628	49	,	,	PUNCT
ejpam-6761	628	50	[	[	X
ejpam-6761	628	51	−1	−1	NOUN
ejpam-6761	628	52	,	,	PUNCT
ejpam-6761	628	53	0	0	NUM
ejpam-6761	628	54	]	]	PUNCT
ejpam-6761	628	55	,	,	PUNCT
ejpam-6761	628	56	[	[	X
ejpam-6761	628	57	0	0	NUM
ejpam-6761	628	58	,	,	PUNCT
ejpam-6761	628	59	1	1	NUM
ejpam-6761	628	60	]	]	NUM
ejpam-6761	628	61	)	)	PUNCT
ejpam-6761	628	62	,	,	PUNCT
ejpam-6761	628	63	h	h	NOUN
ejpam-6761	628	64	)	)	PUNCT
ejpam-6761	628	65	,	,	PUNCT
ejpam-6761	628	66	then	then	ADV
ejpam-6761	628	67	every	every	DET
ejpam-6761	628	68	associative	associative	ADJ
ejpam-6761	628	69	bipolar	bipolar	ADJ
ejpam-6761	628	70	valued	value	VERB
ejpam-6761	628	71	fuzzy	fuzzy	ADJ
ejpam-6761	628	72	subgroup	subgroup	PROPN
ejpam-6761	628	73	b	b	PROPN
ejpam-6761	628	74	=	=	SYM
ejpam-6761	628	75	(	(	PUNCT
ejpam-6761	628	76	x	x	X
ejpam-6761	628	77	,	,	PUNCT
ejpam-6761	628	78	b−x	b−x	NOUN
ejpam-6761	628	79	,	,	PUNCT
ejpam-6761	628	80	b	b	X
ejpam-6761	628	81	+	+	CCONJ
ejpam-6761	628	82	x	x	X
ejpam-6761	628	83	)	)	PUNCT
ejpam-6761	629	1	|	|	ADV
ejpam-6761	629	2	x	x	SYM
ejpam-6761	629	3	∈	∈	PROPN
ejpam-6761	630	1	b	b	X
ejpam-6761	630	2	◦	◦	NOUN
ejpam-6761	630	3	of	of	ADP
ejpam-6761	630	4	(	(	PUNCT
ejpam-6761	630	5	(	(	PUNCT
ejpam-6761	630	6	g	g	NOUN
ejpam-6761	630	7	,	,	PUNCT
ejpam-6761	630	8	[	[	X
ejpam-6761	630	9	−1	−1	NOUN
ejpam-6761	630	10	,	,	PUNCT
ejpam-6761	630	11	0	0	NUM
ejpam-6761	630	12	]	]	PUNCT
ejpam-6761	630	13	,	,	PUNCT
ejpam-6761	630	14	[	[	X
ejpam-6761	630	15	0	0	NUM
ejpam-6761	630	16	,	,	PUNCT
ejpam-6761	630	17	1	1	NUM
ejpam-6761	630	18	]	]	NUM
ejpam-6761	630	19	)	)	PUNCT
ejpam-6761	630	20	,	,	PUNCT
ejpam-6761	630	21	f	f	PROPN
ejpam-6761	630	22	)	)	PUNCT
ejpam-6761	630	23	is	be	AUX
ejpam-6761	630	24	mapped	map	VERB
ejpam-6761	630	25	under	under	ADP
ejpam-6761	630	26	φ	φ	NUM
ejpam-6761	630	27	to	to	ADP
ejpam-6761	630	28	an	an	DET
ejpam-6761	630	29	associative	associative	ADJ
ejpam-6761	630	30	bipolar	bipolar	NOUN
ejpam-6761	630	31	valued	value	VERB
ejpam-6761	630	32	fuzzy	fuzzy	ADJ
ejpam-6761	630	33	subgroup	subgroup	NOUN
ejpam-6761	630	34	φ(b	φ(b	ADP
ejpam-6761	630	35	)	)	PUNCT
ejpam-6761	630	36	of	of	ADP
ejpam-6761	630	37	(	(	PUNCT
ejpam-6761	630	38	(	(	PUNCT
ejpam-6761	630	39	ϕ(g	ϕ(g	PROPN
ejpam-6761	630	40	)	)	PUNCT
ejpam-6761	630	41	,	,	PUNCT
ejpam-6761	631	1	[	[	X
ejpam-6761	631	2	−1	−1	NOUN
ejpam-6761	631	3	,	,	PUNCT
ejpam-6761	631	4	0	0	NUM
ejpam-6761	631	5	]	]	PUNCT
ejpam-6761	631	6	,	,	PUNCT
ejpam-6761	632	1	[	[	X
ejpam-6761	632	2	0	0	NUM
ejpam-6761	632	3	,	,	PUNCT
ejpam-6761	632	4	1	1	NUM
ejpam-6761	632	5	]	]	NUM
ejpam-6761	632	6	)	)	PUNCT
ejpam-6761	632	7	,	,	PUNCT
ejpam-6761	632	8	h	h	NOUN
ejpam-6761	632	9	)	)	PUNCT
ejpam-6761	632	10	.	.	PUNCT
ejpam-6761	633	1	proof	proof	NOUN
ejpam-6761	633	2	.	.	PUNCT
ejpam-6761	634	1	let	let	VERB
ejpam-6761	634	2	φ	φ	PROPN
ejpam-6761	634	3	=	=	SYM
ejpam-6761	634	4	(	(	PUNCT
ejpam-6761	634	5	ϕ	ϕ	NOUN
ejpam-6761	634	6	,	,	PUNCT
ejpam-6761	634	7	φ−	φ−	PROPN
ejpam-6761	634	8	x	x	X
ejpam-6761	634	9	,	,	PUNCT
ejpam-6761	634	10	φ	φ	PROPN
ejpam-6761	634	11	+	+	CCONJ
ejpam-6761	634	12	x	x	X
ejpam-6761	634	13	)	)	PUNCT
ejpam-6761	634	14	be	be	VERB
ejpam-6761	634	15	a	a	DET
ejpam-6761	634	16	bipolar	bipolar	ADJ
ejpam-6761	634	17	valued	value	VERB
ejpam-6761	634	18	fuzzy	fuzzy	ADJ
ejpam-6761	634	19	homomorphism	homomorphism	NOUN
ejpam-6761	634	20	between	between	ADP
ejpam-6761	634	21	(	(	PUNCT
ejpam-6761	634	22	(	(	PUNCT
ejpam-6761	634	23	g	g	NOUN
ejpam-6761	634	24	,	,	PUNCT
ejpam-6761	634	25	[	[	X
ejpam-6761	634	26	−1	−1	NOUN
ejpam-6761	634	27	,	,	PUNCT
ejpam-6761	634	28	0	0	NUM
ejpam-6761	634	29	]	]	PUNCT
ejpam-6761	634	30	,	,	PUNCT
ejpam-6761	634	31	[	[	X
ejpam-6761	634	32	0	0	NUM
ejpam-6761	634	33	,	,	PUNCT
ejpam-6761	634	34	1	1	NUM
ejpam-6761	634	35	]	]	NUM
ejpam-6761	634	36	)	)	PUNCT
ejpam-6761	634	37	,	,	PUNCT
ejpam-6761	634	38	f	f	PROPN
ejpam-6761	634	39	)	)	PUNCT
ejpam-6761	634	40	and	and	CCONJ
ejpam-6761	634	41	(	(	PUNCT
ejpam-6761	634	42	(	(	PUNCT
ejpam-6761	634	43	g′	g′	NOUN
ejpam-6761	634	44	,	,	PUNCT
ejpam-6761	634	45	[	[	X
ejpam-6761	634	46	−1	−1	NOUN
ejpam-6761	634	47	,	,	PUNCT
ejpam-6761	634	48	0	0	NUM
ejpam-6761	634	49	]	]	PUNCT
ejpam-6761	634	50	,	,	PUNCT
ejpam-6761	634	51	[	[	X
ejpam-6761	634	52	0	0	NUM
ejpam-6761	634	53	,	,	PUNCT
ejpam-6761	634	54	1	1	NUM
ejpam-6761	634	55	]	]	NUM
ejpam-6761	634	56	)	)	PUNCT
ejpam-6761	634	57	,	,	PUNCT
ejpam-6761	634	58	h	h	NOUN
ejpam-6761	634	59	)	)	PUNCT
ejpam-6761	634	60	and	and	CCONJ
ejpam-6761	634	61	let	let	VERB
ejpam-6761	634	62	{	{	PUNCT
ejpam-6761	634	63	b	b	NOUN
ejpam-6761	634	64	=	=	SYM
ejpam-6761	634	65	(	(	PUNCT
ejpam-6761	634	66	x	x	X
ejpam-6761	634	67	,	,	PUNCT
ejpam-6761	634	68	b−x	b−x	NOUN
ejpam-6761	634	69	,	,	PUNCT
ejpam-6761	634	70	b	b	X
ejpam-6761	635	1	+	+	CCONJ
ejpam-6761	635	2	x	x	X
ejpam-6761	635	3	)	)	PUNCT
ejpam-6761	635	4	|	|	ADV
ejpam-6761	635	5	x	x	SYM
ejpam-6761	635	6	∈	∈	PROPN
ejpam-6761	635	7	b	b	X
ejpam-6761	635	8	◦	◦	NOUN
ejpam-6761	635	9	}	}	PUNCT
ejpam-6761	635	10	be	be	VERB
ejpam-6761	635	11	any	any	DET
ejpam-6761	635	12	associative	associative	ADJ
ejpam-6761	635	13	bipolar	bipolar	ADJ
ejpam-6761	635	14	valued	value	VERB
ejpam-6761	635	15	fuzzy	fuzzy	ADJ
ejpam-6761	635	16	subgroup	subgroup	NOUN
ejpam-6761	635	17	of	of	ADP
ejpam-6761	635	18	(	(	PUNCT
ejpam-6761	635	19	(	(	PUNCT
ejpam-6761	635	20	g	g	NOUN
ejpam-6761	635	21	,	,	PUNCT
ejpam-6761	635	22	[	[	X
ejpam-6761	635	23	−1	−1	NOUN
ejpam-6761	635	24	,	,	PUNCT
ejpam-6761	635	25	0	0	NUM
ejpam-6761	635	26	]	]	PUNCT
ejpam-6761	635	27	,	,	PUNCT
ejpam-6761	635	28	[	[	X
ejpam-6761	635	29	0	0	NUM
ejpam-6761	635	30	,	,	PUNCT
ejpam-6761	635	31	1	1	NUM
ejpam-6761	635	32	]	]	NUM
ejpam-6761	635	33	)	)	PUNCT
ejpam-6761	635	34	,	,	PUNCT
ejpam-6761	635	35	f	f	PROPN
ejpam-6761	635	36	)	)	PUNCT
ejpam-6761	635	37	.	.	PUNCT
ejpam-6761	636	1	then	then	ADV
ejpam-6761	636	2	(	(	PUNCT
ejpam-6761	636	3	φ(x)hφ(y))hφ(z	φ(x)hφ(y))hφ(z	PROPN
ejpam-6761	636	4	)	)	PUNCT
ejpam-6761	636	5	=	=	SYM
ejpam-6761	636	6	φ((xfy)fz	φ((xfy)fz	NOUN
ejpam-6761	636	7	)	)	PUNCT
ejpam-6761	636	8	=	=	SYM
ejpam-6761	637	1	φ(xf	φ(xf	PROPN
ejpam-6761	637	2	(	(	PUNCT
ejpam-6761	637	3	yfz	yfz	NOUN
ejpam-6761	637	4	)	)	PUNCT
ejpam-6761	637	5	)	)	PUNCT
ejpam-6761	638	1	=	=	SYM
ejpam-6761	638	2	φ(x)h(φ(y)hφ(z	φ(x)h(φ(y)hφ(z	NUM
ejpam-6761	638	3	)	)	PUNCT
ejpam-6761	638	4	)	)	PUNCT
ejpam-6761	638	5	.	.	PUNCT
ejpam-6761	639	1	(	(	PUNCT
ejpam-6761	639	2	33	33	NUM
ejpam-6761	639	3	)	)	PUNCT
ejpam-6761	639	4	if	if	SCONJ
ejpam-6761	639	5	x	x	X
ejpam-6761	639	6	(	(	PUNCT
ejpam-6761	639	7	or	or	CCONJ
ejpam-6761	639	8	y	y	PROPN
ejpam-6761	639	9	or	or	CCONJ
ejpam-6761	639	10	z	z	PROPN
ejpam-6761	639	11	)	)	PUNCT
ejpam-6761	639	12	belongs	belong	VERB
ejpam-6761	639	13	to	to	ADP
ejpam-6761	639	14	(	(	PUNCT
ejpam-6761	639	15	g	g	NOUN
ejpam-6761	639	16	,	,	PUNCT
ejpam-6761	639	17	[	[	X
ejpam-6761	639	18	−1	−1	NOUN
ejpam-6761	639	19	,	,	PUNCT
ejpam-6761	639	20	0	0	NUM
ejpam-6761	639	21	]	]	PUNCT
ejpam-6761	639	22	,	,	PUNCT
ejpam-6761	640	1	[	[	X
ejpam-6761	640	2	0	0	NUM
ejpam-6761	640	3	,	,	PUNCT
ejpam-6761	640	4	1	1	NUM
ejpam-6761	640	5	]	]	NUM
ejpam-6761	640	6	)	)	PUNCT
ejpam-6761	640	7	,	,	PUNCT
ejpam-6761	640	8	then	then	ADV
ejpam-6761	640	9	φ(x	φ(x	PROPN
ejpam-6761	640	10	)	)	PUNCT
ejpam-6761	640	11	∈	∈	PROPN
ejpam-6761	640	12	(	(	PUNCT
ejpam-6761	640	13	ϕ(g	ϕ(g	PROPN
ejpam-6761	640	14	)	)	PUNCT
ejpam-6761	640	15	,	,	PUNCT
ejpam-6761	641	1	[	[	X
ejpam-6761	641	2	−1	−1	NOUN
ejpam-6761	641	3	,	,	PUNCT
ejpam-6761	641	4	0	0	NUM
ejpam-6761	641	5	]	]	PUNCT
ejpam-6761	641	6	,	,	PUNCT
ejpam-6761	642	1	[	[	X
ejpam-6761	642	2	0	0	NUM
ejpam-6761	642	3	,	,	PUNCT
ejpam-6761	642	4	1	1	NUM
ejpam-6761	642	5	]	]	NUM
ejpam-6761	642	6	)	)	PUNCT
ejpam-6761	642	7	,	,	PUNCT
ejpam-6761	642	8	and	and	CCONJ
ejpam-6761	642	9	if	if	SCONJ
ejpam-6761	642	10	x	x	X
ejpam-6761	642	11	(	(	PUNCT
ejpam-6761	642	12	or	or	CCONJ
ejpam-6761	642	13	y	y	PROPN
ejpam-6761	642	14	or	or	CCONJ
ejpam-6761	642	15	z	z	PROPN
ejpam-6761	642	16	)	)	PUNCT
ejpam-6761	642	17	belongs	belong	VERB
ejpam-6761	642	18	to	to	ADP
ejpam-6761	642	19	b	b	NOUN
ejpam-6761	642	20	,	,	PUNCT
ejpam-6761	642	21	then	then	ADV
ejpam-6761	642	22	φ(b	φ(b	NOUN
ejpam-6761	642	23	)	)	PUNCT
ejpam-6761	642	24	is	be	AUX
ejpam-6761	642	25	associative	associative	ADJ
ejpam-6761	642	26	in	in	ADP
ejpam-6761	642	27	(	(	PUNCT
ejpam-6761	642	28	(	(	PUNCT
ejpam-6761	642	29	ϕ(g	ϕ(g	PROPN
ejpam-6761	642	30	)	)	PUNCT
ejpam-6761	642	31	,	,	PUNCT
ejpam-6761	643	1	[	[	X
ejpam-6761	643	2	−1	−1	NOUN
ejpam-6761	643	3	,	,	PUNCT
ejpam-6761	643	4	0	0	NUM
ejpam-6761	643	5	]	]	PUNCT
ejpam-6761	643	6	,	,	PUNCT
ejpam-6761	644	1	[	[	X
ejpam-6761	644	2	0	0	NUM
ejpam-6761	644	3	,	,	PUNCT
ejpam-6761	644	4	1	1	NUM
ejpam-6761	644	5	]	]	NUM
ejpam-6761	644	6	)	)	PUNCT
ejpam-6761	644	7	,	,	PUNCT
ejpam-6761	644	8	h	h	NOUN
ejpam-6761	644	9	)	)	PUNCT
ejpam-6761	644	10	whenever	whenever	SCONJ
ejpam-6761	644	11	b	b	NOUN
ejpam-6761	644	12	is	be	AUX
ejpam-6761	644	13	associative	associative	ADJ
ejpam-6761	644	14	in	in	ADP
ejpam-6761	644	15	(	(	PUNCT
ejpam-6761	644	16	(	(	PUNCT
ejpam-6761	644	17	g	g	NOUN
ejpam-6761	644	18	,	,	PUNCT
ejpam-6761	644	19	[	[	X
ejpam-6761	644	20	−1	−1	NOUN
ejpam-6761	644	21	,	,	PUNCT
ejpam-6761	644	22	0	0	NUM
ejpam-6761	644	23	]	]	PUNCT
ejpam-6761	644	24	,	,	PUNCT
ejpam-6761	644	25	[	[	X
ejpam-6761	644	26	0	0	NUM
ejpam-6761	644	27	,	,	PUNCT
ejpam-6761	644	28	1	1	NUM
ejpam-6761	644	29	]	]	NUM
ejpam-6761	644	30	)	)	PUNCT
ejpam-6761	644	31	,	,	PUNCT
ejpam-6761	644	32	f	f	PROPN
ejpam-6761	644	33	)	)	PUNCT
ejpam-6761	644	34	.	.	PUNCT
ejpam-6761	645	1	f.	f.	PROPN
ejpam-6761	645	2	al	al	PROPN
ejpam-6761	645	3	-	-	PROPN
ejpam-6761	645	4	zu’bi	zu’bi	PROPN
ejpam-6761	645	5	et	et	NOUN
ejpam-6761	645	6	al	al	PROPN
ejpam-6761	645	7	.	.	PUNCT
ejpam-6761	645	8	/	/	SYM
ejpam-6761	645	9	eur	eur	PROPN
ejpam-6761	645	10	.	.	PUNCT
ejpam-6761	646	1	j.	j.	PROPN
ejpam-6761	646	2	pure	pure	PROPN
ejpam-6761	646	3	appl	appl	PROPN
ejpam-6761	646	4	.	.	PROPN
ejpam-6761	646	5	math	math	PROPN
ejpam-6761	646	6	,	,	PUNCT
ejpam-6761	646	7	18	18	NUM
ejpam-6761	646	8	(	(	PUNCT
ejpam-6761	646	9	4	4	NUM
ejpam-6761	646	10	)	)	PUNCT
ejpam-6761	646	11	(	(	PUNCT
ejpam-6761	646	12	2025	2025	NUM
ejpam-6761	646	13	)	)	PUNCT
ejpam-6761	646	14	,	,	PUNCT
ejpam-6761	646	15	6761	6761	NUM
ejpam-6761	646	16	25	25	NUM
ejpam-6761	646	17	of	of	ADP
ejpam-6761	646	18	28	28	NUM
ejpam-6761	646	19	conclusion	conclusion	NOUN
ejpam-6761	646	20	:	:	PUNCT
ejpam-6761	646	21	this	this	DET
ejpam-6761	646	22	study	study	NOUN
ejpam-6761	646	23	presents	present	VERB
ejpam-6761	646	24	a	a	DET
ejpam-6761	646	25	significant	significant	ADJ
ejpam-6761	646	26	extension	extension	NOUN
ejpam-6761	646	27	to	to	ADP
ejpam-6761	646	28	the	the	DET
ejpam-6761	646	29	theory	theory	NOUN
ejpam-6761	646	30	of	of	ADP
ejpam-6761	646	31	fuzzy	fuzzy	ADJ
ejpam-6761	646	32	groups	group	NOUN
ejpam-6761	646	33	by	by	ADP
ejpam-6761	646	34	introducing	introduce	VERB
ejpam-6761	646	35	a	a	DET
ejpam-6761	646	36	complete	complete	ADJ
ejpam-6761	646	37	algebraic	algebraic	ADJ
ejpam-6761	646	38	framework	framework	NOUN
ejpam-6761	646	39	for	for	ADP
ejpam-6761	646	40	bipolar	bipolar	ADV
ejpam-6761	646	41	-	-	PUNCT
ejpam-6761	646	42	valued	value	VERB
ejpam-6761	646	43	fuzzy	fuzzy	ADJ
ejpam-6761	646	44	subgroups	subgroup	NOUN
ejpam-6761	646	45	(	(	PUNCT
ejpam-6761	646	46	bvf	bvf	NOUN
ejpam-6761	646	47	-	-	PUNCT
ejpam-6761	646	48	subgroups	subgroup	NOUN
ejpam-6761	646	49	)	)	PUNCT
ejpam-6761	646	50	,	,	PUNCT
ejpam-6761	646	51	along	along	ADP
ejpam-6761	646	52	with	with	ADP
ejpam-6761	646	53	their	their	PRON
ejpam-6761	646	54	corresponding	correspond	VERB
ejpam-6761	646	55	normal	normal	ADJ
ejpam-6761	646	56	subgroups	subgroup	NOUN
ejpam-6761	646	57	and	and	CCONJ
ejpam-6761	646	58	homomorphisms	homomorphism	NOUN
ejpam-6761	646	59	.	.	PUNCT
ejpam-6761	647	1	rooted	root	VERB
ejpam-6761	647	2	in	in	ADP
ejpam-6761	647	3	dib	dib	PROPN
ejpam-6761	647	4	’s	’s	PART
ejpam-6761	647	5	foundational	foundational	ADJ
ejpam-6761	647	6	work	work	NOUN
ejpam-6761	647	7	on	on	ADP
ejpam-6761	647	8	fuzzy	fuzzy	ADJ
ejpam-6761	647	9	spaces	space	NOUN
ejpam-6761	647	10	[	[	X
ejpam-6761	647	11	3	3	NUM
ejpam-6761	647	12	,	,	PUNCT
ejpam-6761	647	13	4	4	NUM
ejpam-6761	647	14	]	]	PUNCT
ejpam-6761	647	15	,	,	PUNCT
ejpam-6761	647	16	our	our	PRON
ejpam-6761	647	17	approach	approach	NOUN
ejpam-6761	647	18	leverages	leverage	VERB
ejpam-6761	647	19	the	the	DET
ejpam-6761	647	20	bvf	bvf	NOUN
ejpam-6761	647	21	-	-	PUNCT
ejpam-6761	647	22	space	space	NOUN
ejpam-6761	647	23	,	,	PUNCT
ejpam-6761	647	24	where	where	SCONJ
ejpam-6761	647	25	membership	membership	NOUN
ejpam-6761	647	26	values	value	NOUN
ejpam-6761	647	27	span	span	VERB
ejpam-6761	647	28	the	the	DET
ejpam-6761	647	29	cartesian	cartesian	ADJ
ejpam-6761	647	30	product	product	NOUN
ejpam-6761	647	31	[	[	X
ejpam-6761	647	32	−1	−1	NOUN
ejpam-6761	647	33	,	,	PUNCT
ejpam-6761	647	34	0	0	NUM
ejpam-6761	647	35	]	]	X
ejpam-6761	647	36	×	×	NOUN
ejpam-6761	648	1	[	[	X
ejpam-6761	648	2	0	0	NUM
ejpam-6761	648	3	,	,	PUNCT
ejpam-6761	648	4	1	1	NUM
ejpam-6761	648	5	]	]	PUNCT
ejpam-6761	648	6	,	,	PUNCT
ejpam-6761	648	7	thus	thus	ADV
ejpam-6761	648	8	capturing	capture	VERB
ejpam-6761	648	9	both	both	CCONJ
ejpam-6761	648	10	negative	negative	ADJ
ejpam-6761	648	11	and	and	CCONJ
ejpam-6761	648	12	positive	positive	ADJ
ejpam-6761	648	13	evaluations	evaluation	NOUN
ejpam-6761	648	14	in	in	ADP
ejpam-6761	648	15	group	group	NOUN
ejpam-6761	648	16	theory	theory	NOUN
ejpam-6761	648	17	.	.	PUNCT
ejpam-6761	649	1	by	by	ADP
ejpam-6761	649	2	formalizing	formalize	VERB
ejpam-6761	649	3	the	the	DET
ejpam-6761	649	4	bipolar	bipolar	ADV
ejpam-6761	649	5	-	-	PUNCT
ejpam-6761	649	6	valued	value	VERB
ejpam-6761	649	7	fuzzy	fuzzy	ADJ
ejpam-6761	649	8	binary	binary	NOUN
ejpam-6761	649	9	operation	operation	NOUN
ejpam-6761	649	10	(	(	PUNCT
ejpam-6761	649	11	bvfbo	bvfbo	NOUN
ejpam-6761	649	12	)	)	PUNCT
ejpam-6761	649	13	,	,	PUNCT
ejpam-6761	649	14	this	this	DET
ejpam-6761	649	15	research	research	NOUN
ejpam-6761	649	16	ensures	ensure	VERB
ejpam-6761	649	17	compatibility	compatibility	NOUN
ejpam-6761	649	18	with	with	ADP
ejpam-6761	649	19	classical	classical	ADJ
ejpam-6761	649	20	group	group	NOUN
ejpam-6761	649	21	axioms	axiom	NOUN
ejpam-6761	649	22	while	while	SCONJ
ejpam-6761	649	23	enriching	enrich	VERB
ejpam-6761	649	24	the	the	DET
ejpam-6761	649	25	theory	theory	NOUN
ejpam-6761	649	26	to	to	PART
ejpam-6761	649	27	accommodate	accommodate	VERB
ejpam-6761	649	28	dual	dual	ADV
ejpam-6761	649	29	-	-	PUNCT
ejpam-6761	649	30	valued	value	VERB
ejpam-6761	649	31	logic	logic	NOUN
ejpam-6761	649	32	.	.	PUNCT
ejpam-6761	650	1	unlike	unlike	ADP
ejpam-6761	650	2	earlier	early	ADV
ejpam-6761	650	3	fuzzy	fuzzy	ADJ
ejpam-6761	650	4	and	and	CCONJ
ejpam-6761	650	5	intuitionistic	intuitionistic	ADJ
ejpam-6761	650	6	fuzzy	fuzzy	ADJ
ejpam-6761	650	7	subgroup	subgroup	NOUN
ejpam-6761	650	8	models	model	NOUN
ejpam-6761	650	9	[	[	X
ejpam-6761	650	10	1–7	1–7	NUM
ejpam-6761	650	11	]	]	PUNCT
ejpam-6761	650	12	,	,	PUNCT
ejpam-6761	650	13	our	our	PRON
ejpam-6761	650	14	model	model	NOUN
ejpam-6761	650	15	introduces	introduce	VERB
ejpam-6761	650	16	a	a	DET
ejpam-6761	650	17	topologically	topologically	ADV
ejpam-6761	650	18	and	and	CCONJ
ejpam-6761	650	19	algebraically	algebraically	ADV
ejpam-6761	650	20	complete	complete	ADJ
ejpam-6761	650	21	structure	structure	NOUN
ejpam-6761	650	22	that	that	PRON
ejpam-6761	650	23	resolves	resolve	VERB
ejpam-6761	650	24	prior	prior	ADJ
ejpam-6761	650	25	limitations	limitation	NOUN
ejpam-6761	650	26	such	such	ADJ
ejpam-6761	650	27	as	as	ADP
ejpam-6761	650	28	the	the	DET
ejpam-6761	650	29	absence	absence	NOUN
ejpam-6761	650	30	of	of	ADP
ejpam-6761	650	31	a	a	DET
ejpam-6761	650	32	bipolar	bipolar	ADJ
ejpam-6761	650	33	fuzzy	fuzzy	ADJ
ejpam-6761	650	34	universal	universal	ADJ
ejpam-6761	650	35	set	set	NOUN
ejpam-6761	650	36	.	.	PUNCT
ejpam-6761	651	1	our	our	PRON
ejpam-6761	651	2	comparison	comparison	NOUN
ejpam-6761	651	3	with	with	ADP
ejpam-6761	651	4	prior	prior	ADJ
ejpam-6761	651	5	literature	literature	NOUN
ejpam-6761	651	6	confirms	confirm	VERB
ejpam-6761	651	7	the	the	DET
ejpam-6761	651	8	originality	originality	NOUN
ejpam-6761	651	9	and	and	CCONJ
ejpam-6761	651	10	depth	depth	NOUN
ejpam-6761	651	11	of	of	ADP
ejpam-6761	651	12	this	this	DET
ejpam-6761	651	13	contribution	contribution	NOUN
ejpam-6761	651	14	.	.	PUNCT
ejpam-6761	652	1	while	while	SCONJ
ejpam-6761	652	2	earlier	early	ADJ
ejpam-6761	652	3	efforts	effort	NOUN
ejpam-6761	652	4	—	—	PUNCT
ejpam-6761	652	5	such	such	ADJ
ejpam-6761	652	6	as	as	ADP
ejpam-6761	652	7	those	those	PRON
ejpam-6761	652	8	by	by	ADP
ejpam-6761	652	9	lee	lee	PROPN
ejpam-6761	653	1	[	[	X
ejpam-6761	653	2	8	8	NUM
ejpam-6761	653	3	,	,	PUNCT
ejpam-6761	653	4	9	9	NUM
ejpam-6761	653	5	]	]	PUNCT
ejpam-6761	653	6	,	,	PUNCT
ejpam-6761	653	7	anitha	anitha	PROPN
ejpam-6761	653	8	et	et	PROPN
ejpam-6761	653	9	al	al	PROPN
ejpam-6761	653	10	.	.	PUNCT
ejpam-6761	654	1	[	[	X
ejpam-6761	654	2	17	17	NUM
ejpam-6761	654	3	]	]	PUNCT
ejpam-6761	654	4	,	,	PUNCT
ejpam-6761	654	5	and	and	CCONJ
ejpam-6761	654	6	mahmood	mahmood	PROPN
ejpam-6761	654	7	et	et	PROPN
ejpam-6761	654	8	al	al	PROPN
ejpam-6761	654	9	.	.	PUNCT
ejpam-6761	655	1	[	[	X
ejpam-6761	655	2	16	16	NUM
ejpam-6761	655	3	,	,	PUNCT
ejpam-6761	655	4	24	24	NUM
ejpam-6761	655	5	]	]	PUNCT
ejpam-6761	655	6	—	—	PUNCT
ejpam-6761	655	7	offered	offer	VERB
ejpam-6761	655	8	isolated	isolate	VERB
ejpam-6761	655	9	results	result	NOUN
ejpam-6761	655	10	on	on	ADP
ejpam-6761	655	11	bipolar	bipolar	ADJ
ejpam-6761	655	12	fuzzy	fuzzy	ADJ
ejpam-6761	655	13	logic	logic	NOUN
ejpam-6761	655	14	or	or	CCONJ
ejpam-6761	655	15	its	its	PRON
ejpam-6761	655	16	structural	structural	ADJ
ejpam-6761	655	17	applications	application	NOUN
ejpam-6761	655	18	,	,	PUNCT
ejpam-6761	655	19	the	the	DET
ejpam-6761	655	20	current	current	ADJ
ejpam-6761	655	21	work	work	NOUN
ejpam-6761	655	22	integrates	integrate	VERB
ejpam-6761	655	23	these	these	DET
ejpam-6761	655	24	threads	thread	NOUN
ejpam-6761	655	25	into	into	ADP
ejpam-6761	655	26	a	a	DET
ejpam-6761	655	27	unifying	unifying	ADJ
ejpam-6761	655	28	theory	theory	NOUN
ejpam-6761	655	29	that	that	PRON
ejpam-6761	655	30	supports	support	VERB
ejpam-6761	655	31	associativity	associativity	NOUN
ejpam-6761	655	32	,	,	PUNCT
ejpam-6761	655	33	identity	identity	NOUN
ejpam-6761	655	34	,	,	PUNCT
ejpam-6761	655	35	inverse	inverse	NOUN
ejpam-6761	655	36	,	,	PUNCT
ejpam-6761	655	37	and	and	CCONJ
ejpam-6761	655	38	homomorphic	homomorphic	ADJ
ejpam-6761	655	39	mappings	mapping	NOUN
ejpam-6761	655	40	within	within	ADP
ejpam-6761	655	41	the	the	DET
ejpam-6761	655	42	bvf	bvf	NOUN
ejpam-6761	655	43	context	context	NOUN
ejpam-6761	655	44	.	.	PUNCT
ejpam-6761	656	1	practically	practically	ADV
ejpam-6761	656	2	,	,	PUNCT
ejpam-6761	656	3	this	this	DET
ejpam-6761	656	4	generalization	generalization	NOUN
ejpam-6761	656	5	has	have	VERB
ejpam-6761	656	6	implications	implication	NOUN
ejpam-6761	656	7	across	across	ADP
ejpam-6761	656	8	multiple	multiple	ADJ
ejpam-6761	656	9	domains	domain	NOUN
ejpam-6761	656	10	,	,	PUNCT
ejpam-6761	656	11	including	include	VERB
ejpam-6761	656	12	multi	multi	ADJ
ejpam-6761	656	13	-	-	ADJ
ejpam-6761	656	14	criteria	criterion	NOUN
ejpam-6761	656	15	decision	decision	NOUN
ejpam-6761	656	16	-	-	PUNCT
ejpam-6761	656	17	making	making	NOUN
ejpam-6761	656	18	[	[	X
ejpam-6761	656	19	12	12	NUM
ejpam-6761	656	20	]	]	X
ejpam-6761	656	21	,	,	PUNCT
ejpam-6761	656	22	intelligent	intelligent	ADJ
ejpam-6761	656	23	transport	transport	NOUN
ejpam-6761	656	24	systems	system	NOUN
ejpam-6761	656	25	[	[	X
ejpam-6761	656	26	13	13	NUM
ejpam-6761	656	27	]	]	PUNCT
ejpam-6761	656	28	,	,	PUNCT
ejpam-6761	656	29	community	community	NOUN
ejpam-6761	656	30	detection	detection	NOUN
ejpam-6761	656	31	in	in	ADP
ejpam-6761	656	32	complex	complex	ADJ
ejpam-6761	656	33	networks	network	NOUN
ejpam-6761	656	34	[	[	X
ejpam-6761	656	35	14	14	NUM
ejpam-6761	656	36	]	]	PUNCT
ejpam-6761	656	37	,	,	PUNCT
ejpam-6761	656	38	and	and	CCONJ
ejpam-6761	656	39	social	social	ADJ
ejpam-6761	656	40	influence	influence	NOUN
ejpam-6761	656	41	modeling	model	VERB
ejpam-6761	656	42	[	[	X
ejpam-6761	656	43	15	15	NUM
ejpam-6761	656	44	]	]	PUNCT
ejpam-6761	656	45	.	.	PUNCT
ejpam-6761	657	1	additionally	additionally	ADV
ejpam-6761	657	2	,	,	PUNCT
ejpam-6761	657	3	interdisciplinary	interdisciplinary	ADJ
ejpam-6761	657	4	studies	study	NOUN
ejpam-6761	657	5	such	such	ADJ
ejpam-6761	657	6	as	as	ADP
ejpam-6761	657	7	those	those	PRON
ejpam-6761	657	8	on	on	ADP
ejpam-6761	657	9	neutrosophic	neutrosophic	ADJ
ejpam-6761	657	10	set	set	NOUN
ejpam-6761	657	11	-	-	PUNCT
ejpam-6761	657	12	based	base	VERB
ejpam-6761	657	13	selection	selection	NOUN
ejpam-6761	657	14	processes	process	NOUN
ejpam-6761	657	15	[	[	X
ejpam-6761	657	16	29	29	NUM
ejpam-6761	657	17	]	]	PUNCT
ejpam-6761	657	18	,	,	PUNCT
ejpam-6761	657	19	iot	iot	ADJ
ejpam-6761	657	20	-	-	PUNCT
ejpam-6761	657	21	related	relate	VERB
ejpam-6761	657	22	cyberattack	cyberattack	NOUN
ejpam-6761	657	23	modeling	modeling	NOUN
ejpam-6761	657	24	[	[	X
ejpam-6761	657	25	31	31	NUM
ejpam-6761	657	26	]	]	PUNCT
ejpam-6761	657	27	,	,	PUNCT
ejpam-6761	657	28	hypergraph	hypergraph	NOUN
ejpam-6761	657	29	-	-	PUNCT
ejpam-6761	657	30	based	base	VERB
ejpam-6761	657	31	influencer	influencer	NOUN
ejpam-6761	657	32	identification	identification	NOUN
ejpam-6761	657	33	in	in	ADP
ejpam-6761	657	34	dynamic	dynamic	ADJ
ejpam-6761	657	35	networks	network	NOUN
ejpam-6761	657	36	[	[	X
ejpam-6761	657	37	33	33	NUM
ejpam-6761	657	38	]	]	PUNCT
ejpam-6761	657	39	,	,	PUNCT
ejpam-6761	657	40	and	and	CCONJ
ejpam-6761	657	41	decision	decision	NOUN
ejpam-6761	657	42	-	-	PUNCT
ejpam-6761	657	43	making	making	NOUN
ejpam-6761	657	44	under	under	ADP
ejpam-6761	657	45	neutrosophic	neutrosophic	ADJ
ejpam-6761	657	46	uncertainty	uncertainty	NOUN
ejpam-6761	657	47	[	[	X
ejpam-6761	657	48	30	30	NUM
ejpam-6761	657	49	]	]	PUNCT
ejpam-6761	658	1	further	far	ADV
ejpam-6761	658	2	emphasize	emphasize	VERB
ejpam-6761	658	3	the	the	DET
ejpam-6761	658	4	urgent	urgent	ADJ
ejpam-6761	658	5	need	need	NOUN
ejpam-6761	658	6	for	for	ADP
ejpam-6761	658	7	algebraic	algebraic	ADJ
ejpam-6761	658	8	systems	system	NOUN
ejpam-6761	658	9	capable	capable	ADJ
ejpam-6761	658	10	of	of	ADP
ejpam-6761	658	11	modeling	model	VERB
ejpam-6761	658	12	dual	dual	ADJ
ejpam-6761	658	13	polarity	polarity	NOUN
ejpam-6761	658	14	and	and	CCONJ
ejpam-6761	658	15	imprecision	imprecision	NOUN
ejpam-6761	658	16	.	.	PUNCT
ejpam-6761	659	1	these	these	DET
ejpam-6761	659	2	applications	application	NOUN
ejpam-6761	659	3	suggest	suggest	VERB
ejpam-6761	659	4	strong	strong	ADJ
ejpam-6761	659	5	synergies	synergy	NOUN
ejpam-6761	659	6	with	with	ADP
ejpam-6761	659	7	the	the	DET
ejpam-6761	659	8	proposed	propose	VERB
ejpam-6761	659	9	bvf	bvf	NOUN
ejpam-6761	659	10	-	-	PUNCT
ejpam-6761	659	11	subgroup	subgroup	NOUN
ejpam-6761	659	12	theory	theory	NOUN
ejpam-6761	659	13	.	.	PUNCT
ejpam-6761	660	1	the	the	DET
ejpam-6761	660	2	algebraic	algebraic	ADJ
ejpam-6761	660	3	extension	extension	NOUN
ejpam-6761	660	4	proposed	propose	VERB
ejpam-6761	660	5	here	here	ADV
ejpam-6761	660	6	also	also	ADV
ejpam-6761	660	7	opens	open	VERB
ejpam-6761	660	8	promising	promise	VERB
ejpam-6761	660	9	avenues	avenue	NOUN
ejpam-6761	660	10	for	for	ADP
ejpam-6761	660	11	defining	define	VERB
ejpam-6761	660	12	bvfquotient	bvfquotient	NOUN
ejpam-6761	660	13	groups	group	NOUN
ejpam-6761	660	14	,	,	PUNCT
ejpam-6761	660	15	bvf	bvf	NOUN
ejpam-6761	660	16	-	-	PUNCT
ejpam-6761	660	17	rings	ring	NOUN
ejpam-6761	660	18	,	,	PUNCT
ejpam-6761	660	19	and	and	CCONJ
ejpam-6761	660	20	bvf	bvf	NOUN
ejpam-6761	660	21	-	-	PUNCT
ejpam-6761	660	22	ideals	ideal	NOUN
ejpam-6761	660	23	,	,	PUNCT
ejpam-6761	660	24	offering	offer	VERB
ejpam-6761	660	25	a	a	DET
ejpam-6761	660	26	broader	broad	ADJ
ejpam-6761	660	27	mathematical	mathematical	ADJ
ejpam-6761	660	28	toolkit	toolkit	NOUN
ejpam-6761	660	29	for	for	ADP
ejpam-6761	660	30	systems	system	NOUN
ejpam-6761	660	31	characterized	characterize	VERB
ejpam-6761	660	32	by	by	ADP
ejpam-6761	660	33	conflicting	conflicting	ADJ
ejpam-6761	660	34	,	,	PUNCT
ejpam-6761	660	35	uncertain	uncertain	ADJ
ejpam-6761	660	36	,	,	PUNCT
ejpam-6761	660	37	or	or	CCONJ
ejpam-6761	660	38	fuzzy	fuzzy	ADJ
ejpam-6761	660	39	information	information	NOUN
ejpam-6761	660	40	.	.	PUNCT
ejpam-6761	661	1	future	future	ADJ
ejpam-6761	661	2	work	work	NOUN
ejpam-6761	661	3	should	should	AUX
ejpam-6761	661	4	focus	focus	VERB
ejpam-6761	661	5	on	on	ADP
ejpam-6761	661	6	a	a	DET
ejpam-6761	661	7	few	few	ADJ
ejpam-6761	661	8	different	different	ADJ
ejpam-6761	661	9	fields	field	NOUN
ejpam-6761	661	10	.	.	PUNCT
ejpam-6761	662	1	we	we	PRON
ejpam-6761	662	2	presented	present	VERB
ejpam-6761	662	3	a	a	DET
ejpam-6761	662	4	cohesive	cohesive	ADJ
ejpam-6761	662	5	algebraic	algebraic	ADJ
ejpam-6761	662	6	framework	framework	NOUN
ejpam-6761	662	7	for	for	ADP
ejpam-6761	662	8	bvfsubgroups	bvfsubgroup	NOUN
ejpam-6761	662	9	,	,	PUNCT
ejpam-6761	662	10	bvf	bvf	NOUN
ejpam-6761	662	11	-	-	PUNCT
ejpam-6761	662	12	normal	normal	ADJ
ejpam-6761	662	13	subgroups	subgroup	NOUN
ejpam-6761	662	14	,	,	PUNCT
ejpam-6761	662	15	and	and	CCONJ
ejpam-6761	662	16	bvf	bvf	NOUN
ejpam-6761	662	17	-	-	PUNCT
ejpam-6761	662	18	homomorphisms	homomorphism	NOUN
ejpam-6761	662	19	on	on	ADP
ejpam-6761	662	20	a	a	DET
ejpam-6761	662	21	bvf	bvf	NOUN
ejpam-6761	662	22	-	-	PUNCT
ejpam-6761	662	23	space	space	NOUN
ejpam-6761	662	24	with	with	ADP
ejpam-6761	662	25	a	a	DET
ejpam-6761	662	26	bvfbo	bvfbo	NOUN
ejpam-6761	662	27	.	.	PUNCT
ejpam-6761	663	1	the	the	DET
ejpam-6761	663	2	results	result	NOUN
ejpam-6761	663	3	unify	unify	VERB
ejpam-6761	663	4	subgroup	subgroup	NOUN
ejpam-6761	663	5	criteria	criterion	NOUN
ejpam-6761	663	6	,	,	PUNCT
ejpam-6761	663	7	normality	normality	NOUN
ejpam-6761	663	8	via	via	ADP
ejpam-6761	663	9	coset	coset	NOUN
ejpam-6761	663	10	behaviour	behaviour	NOUN
ejpam-6761	663	11	,	,	PUNCT
ejpam-6761	663	12	and	and	CCONJ
ejpam-6761	663	13	homomorphic	homomorphic	ADJ
ejpam-6761	663	14	images	image	NOUN
ejpam-6761	663	15	/	/	SYM
ejpam-6761	663	16	kernels	kernel	NOUN
ejpam-6761	663	17	while	while	SCONJ
ejpam-6761	663	18	clarifying	clarify	VERB
ejpam-6761	663	19	associativity	associativity	NOUN
ejpam-6761	663	20	boundaries	boundary	NOUN
ejpam-6761	663	21	between	between	ADP
ejpam-6761	663	22	subgroup	subgroup	NOUN
ejpam-6761	663	23	and	and	CCONJ
ejpam-6761	663	24	ambient	ambient	ADJ
ejpam-6761	663	25	elements	element	NOUN
ejpam-6761	663	26	.	.	PUNCT
ejpam-6761	664	1	this	this	DET
ejpam-6761	664	2	foundation	foundation	NOUN
ejpam-6761	664	3	is	be	AUX
ejpam-6761	664	4	well	well	ADV
ejpam-6761	664	5	-	-	PUNCT
ejpam-6761	664	6	suited	suit	VERB
ejpam-6761	664	7	for	for	ADP
ejpam-6761	664	8	polarity	polarity	NOUN
ejpam-6761	664	9	-	-	PUNCT
ejpam-6761	664	10	aware	aware	ADJ
ejpam-6761	664	11	decision	decision	NOUN
ejpam-6761	664	12	and	and	CCONJ
ejpam-6761	664	13	network	network	NOUN
ejpam-6761	664	14	models	model	NOUN
ejpam-6761	664	15	.	.	PUNCT
ejpam-6761	665	1	future	future	ADJ
ejpam-6761	665	2	work	work	NOUN
ejpam-6761	665	3	includes	include	VERB
ejpam-6761	665	4	bvf	bvf	NOUN
ejpam-6761	665	5	-	-	PUNCT
ejpam-6761	665	6	quotients	quotient	NOUN
ejpam-6761	665	7	,	,	PUNCT
ejpam-6761	665	8	bvf	bvf	NOUN
ejpam-6761	665	9	-	-	PUNCT
ejpam-6761	665	10	rings	ring	NOUN
ejpam-6761	665	11	/	/	SYM
ejpam-6761	665	12	ideals	ideal	NOUN
ejpam-6761	665	13	,	,	PUNCT
ejpam-6761	665	14	and	and	CCONJ
ejpam-6761	665	15	algorithmic	algorithmic	ADJ
ejpam-6761	665	16	implementations	implementation	NOUN
ejpam-6761	665	17	for	for	ADP
ejpam-6761	665	18	symbolic	symbolic	ADJ
ejpam-6761	665	19	and	and	CCONJ
ejpam-6761	665	20	ai	ai	VERB
ejpam-6761	665	21	inference	inference	NOUN
ejpam-6761	665	22	engines	engine	NOUN
ejpam-6761	665	23	.	.	PUNCT
ejpam-6761	666	1	these	these	DET
ejpam-6761	666	2	directions	direction	NOUN
ejpam-6761	666	3	will	will	AUX
ejpam-6761	666	4	help	help	VERB
ejpam-6761	666	5	translate	translate	VERB
ejpam-6761	666	6	the	the	DET
ejpam-6761	666	7	robust	robust	ADJ
ejpam-6761	666	8	theoretical	theoretical	ADJ
ejpam-6761	666	9	foundation	foundation	NOUN
ejpam-6761	666	10	of	of	ADP
ejpam-6761	666	11	bvf	bvf	NOUN
ejpam-6761	666	12	-	-	PUNCT
ejpam-6761	666	13	subgroups	subgroup	NOUN
ejpam-6761	666	14	into	into	ADP
ejpam-6761	666	15	practical	practical	ADJ
ejpam-6761	666	16	tools	tool	NOUN
ejpam-6761	666	17	for	for	ADP
ejpam-6761	666	18	addressing	address	VERB
ejpam-6761	666	19	ambiguity	ambiguity	NOUN
ejpam-6761	666	20	and	and	CCONJ
ejpam-6761	666	21	dualism	dualism	NOUN
ejpam-6761	666	22	in	in	ADP
ejpam-6761	666	23	uncertain	uncertain	ADJ
ejpam-6761	666	24	systems	system	NOUN
ejpam-6761	666	25	.	.	PUNCT
ejpam-6761	667	1	acknowledgements	acknowledgement	NOUN
ejpam-6761	667	2	we	we	PRON
ejpam-6761	667	3	would	would	AUX
ejpam-6761	667	4	like	like	VERB
ejpam-6761	667	5	to	to	PART
ejpam-6761	667	6	thank	thank	VERB
ejpam-6761	667	7	the	the	DET
ejpam-6761	667	8	editor	editor	NOUN
ejpam-6761	667	9	-	-	PUNCT
ejpam-6761	667	10	in	in	ADP
ejpam-6761	667	11	-	-	PUNCT
ejpam-6761	667	12	chief	chief	NOUN
ejpam-6761	667	13	and	and	CCONJ
ejpam-6761	667	14	reviewers	reviewer	NOUN
ejpam-6761	667	15	for	for	ADP
ejpam-6761	667	16	their	their	PRON
ejpam-6761	667	17	helpful	helpful	ADJ
ejpam-6761	667	18	instructions	instruction	NOUN
ejpam-6761	667	19	and	and	CCONJ
ejpam-6761	667	20	comments	comment	NOUN
ejpam-6761	667	21	.	.	PUNCT
ejpam-6761	668	1	i	i	PRON
ejpam-6761	668	2	want	want	VERB
ejpam-6761	668	3	to	to	PART
ejpam-6761	668	4	express	express	VERB
ejpam-6761	668	5	my	my	PRON
ejpam-6761	668	6	thanks	thank	NOUN
ejpam-6761	668	7	to	to	ADP
ejpam-6761	668	8	all	all	DET
ejpam-6761	668	9	authors	author	NOUN
ejpam-6761	668	10	helping	help	VERB
ejpam-6761	668	11	to	to	PART
ejpam-6761	668	12	complete	complete	VERB
ejpam-6761	668	13	this	this	DET
ejpam-6761	668	14	work	work	NOUN
ejpam-6761	668	15	.	.	PUNCT
ejpam-6761	669	1	f.	f.	PROPN
ejpam-6761	669	2	al	al	PROPN
ejpam-6761	669	3	-	-	PROPN
ejpam-6761	669	4	zu’bi	zu’bi	PROPN
ejpam-6761	669	5	et	et	NOUN
ejpam-6761	669	6	al	al	PROPN
ejpam-6761	669	7	.	.	PUNCT
ejpam-6761	669	8	/	/	SYM
ejpam-6761	669	9	eur	eur	PROPN
ejpam-6761	669	10	.	.	PUNCT
ejpam-6761	670	1	j.	j.	PROPN
ejpam-6761	670	2	pure	pure	PROPN
ejpam-6761	670	3	appl	appl	PROPN
ejpam-6761	670	4	.	.	PROPN
ejpam-6761	670	5	math	math	PROPN
ejpam-6761	670	6	,	,	PUNCT
ejpam-6761	670	7	18	18	NUM
ejpam-6761	670	8	(	(	PUNCT
ejpam-6761	670	9	4	4	NUM
ejpam-6761	670	10	)	)	PUNCT
ejpam-6761	670	11	(	(	PUNCT
ejpam-6761	670	12	2025	2025	NUM
ejpam-6761	670	13	)	)	PUNCT
ejpam-6761	670	14	,	,	PUNCT
ejpam-6761	670	15	6761	6761	NUM
ejpam-6761	670	16	26	26	NUM
ejpam-6761	670	17	of	of	ADP
ejpam-6761	670	18	28	28	NUM
ejpam-6761	670	19	financial	financial	ADJ
ejpam-6761	670	20	support	support	NOUN
ejpam-6761	670	21	:	:	PUNCT
ejpam-6761	670	22	there	there	PRON
ejpam-6761	670	23	is	be	VERB
ejpam-6761	670	24	no	no	DET
ejpam-6761	670	25	funding	funding	NOUN
ejpam-6761	670	26	for	for	ADP
ejpam-6761	670	27	this	this	DET
ejpam-6761	670	28	article	article	NOUN
ejpam-6761	670	29	.	.	PUNCT
ejpam-6761	671	1	references	reference	NOUN
ejpam-6761	671	2	[	[	X
ejpam-6761	671	3	1	1	NUM
ejpam-6761	671	4	]	]	PUNCT
ejpam-6761	671	5	a.	a.	NOUN
ejpam-6761	671	6	rosenfeld	rosenfeld	PROPN
ejpam-6761	671	7	.	.	PUNCT
ejpam-6761	672	1	fuzzy	fuzzy	ADJ
ejpam-6761	672	2	groups	group	NOUN
ejpam-6761	672	3	.	.	PUNCT
ejpam-6761	673	1	j.	j.	PROPN
ejpam-6761	673	2	math	math	PROPN
ejpam-6761	673	3	.	.	PUNCT
ejpam-6761	674	1	anal	anal	PROPN
ejpam-6761	674	2	.	.	PUNCT
ejpam-6761	675	1	appl	appl	PROPN
ejpam-6761	675	2	.	.	PROPN
ejpam-6761	675	3	,	,	PUNCT
ejpam-6761	675	4	35:512–517	35:512–517	PROPN
ejpam-6761	675	5	,	,	PUNCT
ejpam-6761	675	6	1971	1971	NUM
ejpam-6761	675	7	.	.	PUNCT
ejpam-6761	676	1	[	[	X
ejpam-6761	676	2	2	2	X
ejpam-6761	676	3	]	]	PUNCT
ejpam-6761	676	4	j.	j.	PROPN
ejpam-6761	676	5	m.	m.	PROPN
ejpam-6761	676	6	anthony	anthony	PROPN
ejpam-6761	676	7	and	and	CCONJ
ejpam-6761	676	8	h.	h.	PROPN
ejpam-6761	676	9	sherwood	sherwood	PROPN
ejpam-6761	676	10	.	.	PUNCT
ejpam-6761	677	1	fuzzy	fuzzy	ADJ
ejpam-6761	677	2	groups	group	NOUN
ejpam-6761	677	3	redefined	redefine	VERB
ejpam-6761	677	4	.	.	PUNCT
ejpam-6761	678	1	j.	j.	PROPN
ejpam-6761	678	2	math	math	PROPN
ejpam-6761	678	3	.	.	PUNCT
ejpam-6761	679	1	anal	anal	PROPN
ejpam-6761	679	2	.	.	PUNCT
ejpam-6761	680	1	appl	appl	PROPN
ejpam-6761	680	2	.	.	PROPN
ejpam-6761	680	3	,	,	PUNCT
ejpam-6761	680	4	69:124–130	69:124–130	NUM
ejpam-6761	680	5	,	,	PUNCT
ejpam-6761	680	6	1979	1979	NUM
ejpam-6761	680	7	.	.	PUNCT
ejpam-6761	681	1	[	[	X
ejpam-6761	681	2	3	3	X
ejpam-6761	681	3	]	]	X
ejpam-6761	681	4	k.	k.	PROPN
ejpam-6761	681	5	a.	a.	PROPN
ejpam-6761	681	6	dib	dib	PROPN
ejpam-6761	681	7	.	.	PUNCT
ejpam-6761	682	1	on	on	ADP
ejpam-6761	682	2	fuzzy	fuzzy	ADJ
ejpam-6761	682	3	spaces	space	NOUN
ejpam-6761	682	4	and	and	CCONJ
ejpam-6761	682	5	fuzzy	fuzzy	ADJ
ejpam-6761	682	6	group	group	NOUN
ejpam-6761	682	7	theory	theory	NOUN
ejpam-6761	682	8	.	.	PUNCT
ejpam-6761	683	1	inform	inform	NOUN
ejpam-6761	683	2	.	.	PUNCT
ejpam-6761	684	1	sci	sci	PROPN
ejpam-6761	684	2	.	.	PROPN
ejpam-6761	684	3	,	,	PUNCT
ejpam-6761	684	4	80(3	80(3	X
ejpam-6761	684	5	-	-	SYM
ejpam-6761	684	6	4):253–282	4):253–282	NUM
ejpam-6761	684	7	,	,	PUNCT
ejpam-6761	684	8	1994	1994	NUM
ejpam-6761	684	9	.	.	PUNCT
ejpam-6761	685	1	[	[	X
ejpam-6761	685	2	4	4	X
ejpam-6761	685	3	]	]	PUNCT
ejpam-6761	685	4	k.	k.	PROPN
ejpam-6761	685	5	a.	a.	PROPN
ejpam-6761	685	6	dib	dib	PROPN
ejpam-6761	685	7	and	and	CCONJ
ejpam-6761	685	8	n.	n.	PROPN
ejpam-6761	685	9	l.	l.	PROPN
ejpam-6761	685	10	youssef	youssef	PROPN
ejpam-6761	685	11	.	.	PUNCT
ejpam-6761	686	1	fuzzy	fuzzy	ADJ
ejpam-6761	686	2	cartesian	cartesian	ADJ
ejpam-6761	686	3	product	product	NOUN
ejpam-6761	686	4	,	,	PUNCT
ejpam-6761	686	5	fuzzy	fuzzy	ADJ
ejpam-6761	686	6	relations	relation	NOUN
ejpam-6761	686	7	and	and	CCONJ
ejpam-6761	686	8	fuzzy	fuzzy	ADJ
ejpam-6761	686	9	functions	function	NOUN
ejpam-6761	686	10	.	.	PUNCT
ejpam-6761	687	1	fuzzy	fuzzy	ADJ
ejpam-6761	687	2	sets	set	NOUN
ejpam-6761	687	3	and	and	CCONJ
ejpam-6761	687	4	systems	system	NOUN
ejpam-6761	687	5	,	,	PUNCT
ejpam-6761	687	6	41(3):299–315	41(3):299–315	PROPN
ejpam-6761	687	7	,	,	PUNCT
ejpam-6761	687	8	1991	1991	NUM
ejpam-6761	687	9	.	.	PUNCT
ejpam-6761	688	1	[	[	X
ejpam-6761	688	2	5	5	NUM
ejpam-6761	688	3	]	]	PUNCT
ejpam-6761	688	4	a.	a.	PROPN
ejpam-6761	688	5	r.	r.	PROPN
ejpam-6761	688	6	salleh	salleh	PROPN
ejpam-6761	688	7	.	.	PUNCT
ejpam-6761	689	1	sifat	sifat	NOUN
ejpam-6761	689	2	-	-	PUNCT
ejpam-6761	689	3	sifat	sifat	NOUN
ejpam-6761	689	4	homomorfisma	homomorfisma	PROPN
ejpam-6761	689	5	kabur	kabur	PROPN
ejpam-6761	689	6	bagi	bagi	PROPN
ejpam-6761	689	7	kumpulan	kumpulan	PROPN
ejpam-6761	689	8	kabur	kabur	PROPN
ejpam-6761	689	9	.	.	PUNCT
ejpam-6761	690	1	in	in	ADP
ejpam-6761	690	2	prosiding	proside	VERB
ejpam-6761	690	3	simposium	simposium	NOUN
ejpam-6761	690	4	kebangsaan	kebangsaan	PROPN
ejpam-6761	690	5	sains	sains	PROPN
ejpam-6761	690	6	matematik	matematik	PROPN
ejpam-6761	690	7	ke-7	ke-7	NOUN
ejpam-6761	690	8	,	,	PUNCT
ejpam-6761	690	9	shah	shah	PROPN
ejpam-6761	690	10	alam	alam	PROPN
ejpam-6761	690	11	:	:	PUNCT
ejpam-6761	690	12	institut	institut	PROPN
ejpam-6761	690	13	teknologi	teknologi	PROPN
ejpam-6761	690	14	mara	mara	PROPN
ejpam-6761	690	15	,	,	PUNCT
ejpam-6761	690	16	1996	1996	NUM
ejpam-6761	690	17	.	.	PUNCT
ejpam-6761	691	1	[	[	X
ejpam-6761	691	2	6	6	NUM
ejpam-6761	691	3	]	]	PUNCT
ejpam-6761	691	4	m.	m.	PROPN
ejpam-6761	691	5	f.	f.	PROPN
ejpam-6761	691	6	marashdeh	marashdeh	PROPN
ejpam-6761	691	7	and	and	CCONJ
ejpam-6761	691	8	a.	a.	PROPN
ejpam-6761	691	9	r.	r.	PROPN
ejpam-6761	691	10	salleh	salleh	PROPN
ejpam-6761	691	11	.	.	PUNCT
ejpam-6761	692	1	intuitionistic	intuitionistic	ADJ
ejpam-6761	692	2	fuzzy	fuzzy	ADJ
ejpam-6761	692	3	groups	group	NOUN
ejpam-6761	692	4	.	.	PUNCT
ejpam-6761	693	1	asian	asian	ADJ
ejpam-6761	693	2	journal	journal	PROPN
ejpam-6761	693	3	of	of	ADP
ejpam-6761	693	4	algebra	algebra	PROPN
ejpam-6761	693	5	,	,	PUNCT
ejpam-6761	693	6	2(1):1–10	2(1):1–10	NUM
ejpam-6761	693	7	,	,	PUNCT
ejpam-6761	693	8	2009	2009	NUM
ejpam-6761	693	9	.	.	PUNCT
ejpam-6761	694	1	[	[	X
ejpam-6761	694	2	7	7	X
ejpam-6761	694	3	]	]	PUNCT
ejpam-6761	694	4	m.	m.	NOUN
ejpam-6761	694	5	f.	f.	PROPN
ejpam-6761	694	6	marashdeh	marashdeh	PROPN
ejpam-6761	694	7	and	and	CCONJ
ejpam-6761	694	8	a.	a.	PROPN
ejpam-6761	694	9	r.	r.	PROPN
ejpam-6761	694	10	salleh	salleh	PROPN
ejpam-6761	694	11	.	.	PUNCT
ejpam-6761	695	1	the	the	DET
ejpam-6761	695	2	intuitionistic	intuitionistic	ADJ
ejpam-6761	695	3	fuzzy	fuzzy	ADJ
ejpam-6761	695	4	normal	normal	ADJ
ejpam-6761	695	5	subgroup	subgroup	NOUN
ejpam-6761	695	6	.	.	PUNCT
ejpam-6761	696	1	int	int	NOUN
ejpam-6761	696	2	.	.	PUNCT
ejpam-6761	697	1	j.	j.	PROPN
ejpam-6761	697	2	fuzzy	fuzzy	PROPN
ejpam-6761	697	3	log	log	PROPN
ejpam-6761	697	4	.	.	PUNCT
ejpam-6761	698	1	intell	intell	PROPN
ejpam-6761	698	2	.	.	PUNCT
ejpam-6761	699	1	syst	syst	PROPN
ejpam-6761	699	2	.	.	PROPN
ejpam-6761	699	3	,	,	PUNCT
ejpam-6761	699	4	10:82–88	10:82–88	NUM
ejpam-6761	699	5	,	,	PUNCT
ejpam-6761	699	6	2010	2010	NUM
ejpam-6761	699	7	.	.	PUNCT
ejpam-6761	700	1	[	[	X
ejpam-6761	700	2	8	8	NUM
ejpam-6761	700	3	]	]	PUNCT
ejpam-6761	700	4	k.	k.	PROPN
ejpam-6761	700	5	m.	m.	PROPN
ejpam-6761	700	6	lee	lee	PROPN
ejpam-6761	700	7	.	.	PUNCT
ejpam-6761	701	1	bipolar	bipolar	ADJ
ejpam-6761	701	2	-	-	PUNCT
ejpam-6761	701	3	valued	value	VERB
ejpam-6761	701	4	fuzzy	fuzzy	ADJ
ejpam-6761	701	5	sets	set	NOUN
ejpam-6761	701	6	and	and	CCONJ
ejpam-6761	701	7	their	their	PRON
ejpam-6761	701	8	operations	operation	NOUN
ejpam-6761	701	9	.	.	PUNCT
ejpam-6761	702	1	in	in	ADP
ejpam-6761	702	2	proc	proc	PROPN
ejpam-6761	702	3	.	.	PUNCT
ejpam-6761	703	1	int	int	NOUN
ejpam-6761	703	2	.	.	PUNCT
ejpam-6761	703	3	conf	conf	PROPN
ejpam-6761	703	4	.	.	PUNCT
ejpam-6761	704	1	on	on	ADP
ejpam-6761	704	2	intelligent	intelligent	ADJ
ejpam-6761	704	3	technologies	technology	NOUN
ejpam-6761	704	4	,	,	PUNCT
ejpam-6761	704	5	pages	page	NOUN
ejpam-6761	704	6	307–312	307–312	NUM
ejpam-6761	704	7	,	,	PUNCT
ejpam-6761	704	8	bangkok	bangkok	PROPN
ejpam-6761	704	9	,	,	PUNCT
ejpam-6761	704	10	thailand	thailand	PROPN
ejpam-6761	704	11	,	,	PUNCT
ejpam-6761	704	12	2000	2000	NUM
ejpam-6761	704	13	.	.	PUNCT
ejpam-6761	705	1	[	[	X
ejpam-6761	705	2	9	9	NUM
ejpam-6761	705	3	]	]	PUNCT
ejpam-6761	705	4	k.-m	k.-m	PROPN
ejpam-6761	705	5	.	.	PUNCT
ejpam-6761	705	6	lee	lee	PROPN
ejpam-6761	705	7	,	,	PUNCT
ejpam-6761	705	8	k.-m	k.-m	PROPN
ejpam-6761	705	9	.	.	PUNCT
ejpam-6761	705	10	lee	lee	PROPN
ejpam-6761	705	11	,	,	PUNCT
ejpam-6761	705	12	and	and	CCONJ
ejpam-6761	705	13	k.	k.	PROPN
ejpam-6761	705	14	j.	j.	PROPN
ejpam-6761	705	15	cios	cios	PROPN
ejpam-6761	705	16	.	.	PUNCT
ejpam-6761	706	1	comparison	comparison	NOUN
ejpam-6761	706	2	of	of	ADP
ejpam-6761	706	3	interval	interval	NOUN
ejpam-6761	706	4	-	-	PUNCT
ejpam-6761	706	5	valued	value	VERB
ejpam-6761	706	6	fuzzy	fuzzy	ADJ
ejpam-6761	706	7	sets	set	NOUN
ejpam-6761	706	8	,	,	PUNCT
ejpam-6761	706	9	intuitionistic	intuitionistic	ADJ
ejpam-6761	706	10	fuzzy	fuzzy	ADJ
ejpam-6761	706	11	sets	set	NOUN
ejpam-6761	706	12	,	,	PUNCT
ejpam-6761	706	13	and	and	CCONJ
ejpam-6761	706	14	bipolar	bipolar	ADV
ejpam-6761	706	15	-	-	PUNCT
ejpam-6761	706	16	valued	value	VERB
ejpam-6761	706	17	fuzzy	fuzzy	ADJ
ejpam-6761	706	18	sets	set	NOUN
ejpam-6761	706	19	.	.	PUNCT
ejpam-6761	707	1	in	in	ADP
ejpam-6761	707	2	computing	computing	NOUN
ejpam-6761	707	3	and	and	CCONJ
ejpam-6761	707	4	information	information	NOUN
ejpam-6761	707	5	technologies	technology	NOUN
ejpam-6761	707	6	:	:	PUNCT
ejpam-6761	707	7	exploring	explore	VERB
ejpam-6761	707	8	emerging	emerge	VERB
ejpam-6761	707	9	technologies	technology	NOUN
ejpam-6761	707	10	,	,	PUNCT
ejpam-6761	707	11	pages	page	NOUN
ejpam-6761	707	12	433–439	433–439	NUM
ejpam-6761	707	13	.	.	PUNCT
ejpam-6761	707	14	world	world	NOUN
ejpam-6761	707	15	scientific	scientific	ADJ
ejpam-6761	707	16	,	,	PUNCT
ejpam-6761	707	17	2001	2001	NUM
ejpam-6761	707	18	.	.	PUNCT
ejpam-6761	708	1	[	[	X
ejpam-6761	708	2	10	10	NUM
ejpam-6761	708	3	]	]	X
ejpam-6761	708	4	f.	f.	PROPN
ejpam-6761	708	5	m.	m.	PROPN
ejpam-6761	708	6	a.	a.	PROPN
ejpam-6761	708	7	al	al	PROPN
ejpam-6761	708	8	-	-	PUNCT
ejpam-6761	708	9	zu’bi	zu’bi	PROPN
ejpam-6761	708	10	,	,	PUNCT
ejpam-6761	708	11	a.	a.	NOUN
ejpam-6761	708	12	g.	g.	PROPN
ejpam-6761	708	13	ahmad	ahmad	PROPN
ejpam-6761	708	14	,	,	PUNCT
ejpam-6761	708	15	a.	a.	PROPN
ejpam-6761	708	16	u.	u.	PROPN
ejpam-6761	708	17	alkouri	alkouri	PROPN
ejpam-6761	708	18	,	,	PUNCT
ejpam-6761	708	19	and	and	CCONJ
ejpam-6761	708	20	m.	m.	NOUN
ejpam-6761	708	21	darus	darus	NOUN
ejpam-6761	708	22	.	.	PUNCT
ejpam-6761	709	1	a	a	DET
ejpam-6761	709	2	novel	novel	ADJ
ejpam-6761	709	3	bipolar	bipolar	NOUN
ejpam-6761	709	4	valued	value	VERB
ejpam-6761	709	5	fuzzy	fuzzy	ADJ
ejpam-6761	709	6	group	group	NOUN
ejpam-6761	709	7	based	base	VERB
ejpam-6761	709	8	on	on	ADP
ejpam-6761	709	9	dib	dib	PROPN
ejpam-6761	709	10	’s	’s	PART
ejpam-6761	709	11	approach	approach	NOUN
ejpam-6761	709	12	.	.	PUNCT
ejpam-6761	710	1	european	european	PROPN
ejpam-6761	710	2	journal	journal	PROPN
ejpam-6761	710	3	of	of	ADP
ejpam-6761	710	4	pure	pure	ADJ
ejpam-6761	710	5	and	and	CCONJ
ejpam-6761	710	6	applied	applied	ADJ
ejpam-6761	710	7	mathematics	mathematic	NOUN
ejpam-6761	710	8	,	,	PUNCT
ejpam-6761	710	9	17(4):2898–2914	17(4):2898–2914	NUM
ejpam-6761	710	10	,	,	PUNCT
ejpam-6761	710	11	october	october	PROPN
ejpam-6761	710	12	2024	2024	NUM
ejpam-6761	710	13	.	.	PUNCT
ejpam-6761	711	1	[	[	X
ejpam-6761	711	2	11	11	NUM
ejpam-6761	711	3	]	]	X
ejpam-6761	711	4	f.	f.	PROPN
ejpam-6761	711	5	m.	m.	PROPN
ejpam-6761	711	6	a.	a.	PROPN
ejpam-6761	711	7	al	al	PROPN
ejpam-6761	711	8	-	-	PUNCT
ejpam-6761	711	9	zu’bi	zu’bi	PROPN
ejpam-6761	711	10	,	,	PUNCT
ejpam-6761	711	11	a.	a.	NOUN
ejpam-6761	711	12	g.	g.	PROPN
ejpam-6761	711	13	ahmad	ahmad	PROPN
ejpam-6761	711	14	,	,	PUNCT
ejpam-6761	711	15	a.	a.	PROPN
ejpam-6761	711	16	u.	u.	PROPN
ejpam-6761	711	17	alkouri	alkouri	PROPN
ejpam-6761	711	18	,	,	PUNCT
ejpam-6761	711	19	and	and	CCONJ
ejpam-6761	711	20	m.	m.	NOUN
ejpam-6761	711	21	darus	darus	NOUN
ejpam-6761	711	22	.	.	PUNCT
ejpam-6761	712	1	a	a	DET
ejpam-6761	712	2	new	new	ADJ
ejpam-6761	712	3	trend	trend	NOUN
ejpam-6761	712	4	of	of	ADP
ejpam-6761	712	5	bipolarvalued	bipolarvalue	VERB
ejpam-6761	712	6	fuzzy	fuzzy	ADJ
ejpam-6761	712	7	cartesian	cartesian	ADJ
ejpam-6761	712	8	products	product	NOUN
ejpam-6761	712	9	,	,	PUNCT
ejpam-6761	712	10	relations	relation	NOUN
ejpam-6761	712	11	,	,	PUNCT
ejpam-6761	712	12	and	and	CCONJ
ejpam-6761	712	13	functions	function	NOUN
ejpam-6761	712	14	.	.	PUNCT
ejpam-6761	713	1	wseas	wseas	VERB
ejpam-6761	713	2	transactions	transaction	NOUN
ejpam-6761	713	3	on	on	ADP
ejpam-6761	713	4	mathematics	mathematic	NOUN
ejpam-6761	713	5	,	,	PUNCT
ejpam-6761	713	6	23:502–514	23:502–514	NOUN
ejpam-6761	713	7	,	,	PUNCT
ejpam-6761	713	8	2024	2024	NUM
ejpam-6761	713	9	.	.	PUNCT
ejpam-6761	714	1	[	[	X
ejpam-6761	714	2	12	12	NUM
ejpam-6761	714	3	]	]	PUNCT
ejpam-6761	714	4	m.	m.	NOUN
ejpam-6761	714	5	akram	akram	PROPN
ejpam-6761	714	6	,	,	PUNCT
ejpam-6761	714	7	a.	a.	PROPN
ejpam-6761	714	8	j.	j.	PROPN
ejpam-6761	714	9	c.	c.	PROPN
ejpam-6761	714	10	r.	r.	PROPN
ejpam-6761	714	11	shumaiza	shumaiza	PROPN
ejpam-6761	714	12	,	,	PUNCT
ejpam-6761	714	13	and	and	CCONJ
ejpam-6761	714	14	j.	j.	PROPN
ejpam-6761	714	15	c.	c.	PROPN
ejpam-6761	714	16	r.	r.	PROPN
ejpam-6761	714	17	alcantud	alcantud	PROPN
ejpam-6761	714	18	.	.	PUNCT
ejpam-6761	715	1	multi	multi	ADJ
ejpam-6761	715	2	-	-	ADJ
ejpam-6761	715	3	criteria	criterion	NOUN
ejpam-6761	715	4	decision	decision	NOUN
ejpam-6761	715	5	making	make	VERB
ejpam-6761	715	6	methods	method	NOUN
ejpam-6761	715	7	with	with	ADP
ejpam-6761	715	8	bipolar	bipolar	ADJ
ejpam-6761	715	9	fuzzy	fuzzy	ADJ
ejpam-6761	715	10	sets	set	NOUN
ejpam-6761	715	11	,	,	PUNCT
ejpam-6761	715	12	volume	volume	NOUN
ejpam-6761	715	13	2023	2023	NUM
ejpam-6761	715	14	.	.	PUNCT
ejpam-6761	716	1	springer	springer	NOUN
ejpam-6761	716	2	,	,	PUNCT
ejpam-6761	716	3	singapore	singapore	PROPN
ejpam-6761	716	4	,	,	PUNCT
ejpam-6761	716	5	2023	2023	NUM
ejpam-6761	716	6	.	.	PUNCT
ejpam-6761	717	1	[	[	X
ejpam-6761	717	2	13	13	NUM
ejpam-6761	717	3	]	]	PUNCT
ejpam-6761	717	4	a.	a.	PROPN
ejpam-6761	717	5	al	al	PROPN
ejpam-6761	717	6	-	-	PUNCT
ejpam-6761	717	7	quran	quran	PROPN
ejpam-6761	717	8	,	,	PUNCT
ejpam-6761	717	9	n.	n.	PROPN
ejpam-6761	717	10	jamil	jamil	PROPN
ejpam-6761	717	11	,	,	PUNCT
ejpam-6761	717	12	s.	s.	PROPN
ejpam-6761	717	13	t.	t.	PROPN
ejpam-6761	717	14	tehrim	tehrim	PROPN
ejpam-6761	717	15	,	,	PUNCT
ejpam-6761	717	16	and	and	CCONJ
ejpam-6761	717	17	m.	m.	PROPN
ejpam-6761	717	18	riaz	riaz	PROPN
ejpam-6761	717	19	.	.	PUNCT
ejpam-6761	718	1	cubic	cubic	ADJ
ejpam-6761	718	2	bipolar	bipolar	ADJ
ejpam-6761	718	3	fuzzy	fuzzy	ADV
ejpam-6761	718	4	vikor	vikor	ADJ
ejpam-6761	718	5	and	and	CCONJ
ejpam-6761	718	6	electre	electre	NOUN
ejpam-6761	718	7	-	-	PUNCT
ejpam-6761	718	8	ii	ii	NOUN
ejpam-6761	718	9	algorithms	algorithm	NOUN
ejpam-6761	718	10	for	for	ADP
ejpam-6761	718	11	efficient	efficient	ADJ
ejpam-6761	718	12	freight	freight	NOUN
ejpam-6761	718	13	transportation	transportation	NOUN
ejpam-6761	718	14	in	in	ADP
ejpam-6761	718	15	industry	industry	NOUN
ejpam-6761	718	16	4.0	4.0	NUM
ejpam-6761	718	17	.	.	PUNCT
ejpam-6761	718	18	aims	aim	VERB
ejpam-6761	718	19	mathematics	mathematic	NOUN
ejpam-6761	718	20	,	,	PUNCT
ejpam-6761	718	21	8(10):24484–24514	8(10):24484–24514	NOUN
ejpam-6761	718	22	,	,	PUNCT
ejpam-6761	718	23	2023	2023	NUM
ejpam-6761	718	24	.	.	PUNCT
ejpam-6761	719	1	[	[	X
ejpam-6761	719	2	14	14	NUM
ejpam-6761	719	3	]	]	X
ejpam-6761	719	4	i.	i.	PROPN
ejpam-6761	719	5	gutiérrez	gutiérrez	PROPN
ejpam-6761	719	6	,	,	PUNCT
ejpam-6761	719	7	d.	d.	PROPN
ejpam-6761	719	8	gómez	gómez	PROPN
ejpam-6761	719	9	,	,	PUNCT
ejpam-6761	719	10	j.	j.	PROPN
ejpam-6761	719	11	castro	castro	PROPN
ejpam-6761	719	12	,	,	PUNCT
ejpam-6761	719	13	and	and	CCONJ
ejpam-6761	719	14	r.	r.	PROPN
ejpam-6761	719	15	esṕınola	esṕınola	PROPN
ejpam-6761	719	16	.	.	PUNCT
ejpam-6761	720	1	multiple	multiple	ADJ
ejpam-6761	720	2	bipolar	bipolar	ADJ
ejpam-6761	720	3	fuzzy	fuzzy	ADJ
ejpam-6761	720	4	measures	measure	NOUN
ejpam-6761	720	5	:	:	PUNCT
ejpam-6761	720	6	an	an	DET
ejpam-6761	720	7	application	application	NOUN
ejpam-6761	720	8	to	to	ADP
ejpam-6761	720	9	community	community	NOUN
ejpam-6761	720	10	detection	detection	NOUN
ejpam-6761	720	11	problems	problem	NOUN
ejpam-6761	720	12	for	for	ADP
ejpam-6761	720	13	networks	network	NOUN
ejpam-6761	720	14	with	with	ADP
ejpam-6761	720	15	additional	additional	ADJ
ejpam-6761	720	16	information	information	NOUN
ejpam-6761	720	17	.	.	PUNCT
ejpam-6761	721	1	international	international	ADJ
ejpam-6761	721	2	journal	journal	PROPN
ejpam-6761	721	3	of	of	ADP
ejpam-6761	721	4	computational	computational	ADJ
ejpam-6761	721	5	intelligence	intelligence	NOUN
ejpam-6761	721	6	systems	system	NOUN
ejpam-6761	721	7	,	,	PUNCT
ejpam-6761	721	8	13(1):1636–1649	13(1):1636–1649	NUM
ejpam-6761	721	9	,	,	PUNCT
ejpam-6761	721	10	2020	2020	NUM
ejpam-6761	721	11	.	.	PUNCT
ejpam-6761	722	1	[	[	X
ejpam-6761	722	2	15	15	NUM
ejpam-6761	722	3	]	]	X
ejpam-6761	722	4	m.	m.	NOUN
ejpam-6761	722	5	alqahtani	alqahtani	PROPN
ejpam-6761	722	6	,	,	PUNCT
ejpam-6761	722	7	r.	r.	PROPN
ejpam-6761	722	8	keerthana	keerthana	PROPN
ejpam-6761	722	9	,	,	PUNCT
ejpam-6761	722	10	s.	s.	PROPN
ejpam-6761	722	11	venkatesh	venkatesh	PROPN
ejpam-6761	722	12	,	,	PUNCT
ejpam-6761	722	13	and	and	CCONJ
ejpam-6761	722	14	m.	m.	PROPN
ejpam-6761	722	15	kaviyarasu	kaviyarasu	PROPN
ejpam-6761	722	16	.	.	PUNCT
ejpam-6761	723	1	hesitant	hesitant	PROPN
ejpam-6761	723	2	bipolarvalued	bipolarvalue	VERB
ejpam-6761	723	3	intuitionistic	intuitionistic	ADJ
ejpam-6761	723	4	fuzzy	fuzzy	ADJ
ejpam-6761	723	5	graphs	graph	NOUN
ejpam-6761	723	6	for	for	ADP
ejpam-6761	723	7	identifying	identify	VERB
ejpam-6761	723	8	the	the	DET
ejpam-6761	723	9	dominant	dominant	ADJ
ejpam-6761	723	10	person	person	NOUN
ejpam-6761	723	11	in	in	ADP
ejpam-6761	723	12	social	social	ADJ
ejpam-6761	723	13	media	medium	NOUN
ejpam-6761	723	14	groups	group	NOUN
ejpam-6761	723	15	.	.	PUNCT
ejpam-6761	724	1	symmetry	symmetry	NOUN
ejpam-6761	724	2	,	,	PUNCT
ejpam-6761	724	3	16(10):1293	16(10):1293	NUM
ejpam-6761	724	4	,	,	PUNCT
ejpam-6761	724	5	2024	2024	NUM
ejpam-6761	724	6	.	.	PUNCT
ejpam-6761	725	1	[	[	X
ejpam-6761	725	2	16	16	NUM
ejpam-6761	725	3	]	]	PUNCT
ejpam-6761	725	4	t.	t.	PROPN
ejpam-6761	725	5	mahmood	mahmood	PROPN
ejpam-6761	725	6	,	,	PUNCT
ejpam-6761	725	7	a.	a.	NOUN
ejpam-6761	725	8	jaleel	jaleel	PROPN
ejpam-6761	725	9	,	,	PUNCT
ejpam-6761	725	10	and	and	CCONJ
ejpam-6761	725	11	u.	u.	PROPN
ejpam-6761	725	12	u.	u.	PROPN
ejpam-6761	725	13	rehman	rehman	PROPN
ejpam-6761	725	14	.	.	PUNCT
ejpam-6761	725	15	pattern	pattern	NOUN
ejpam-6761	725	16	recognition	recognition	NOUN
ejpam-6761	725	17	and	and	CCONJ
ejpam-6761	725	18	medical	medical	ADJ
ejpam-6761	725	19	diagnosis	diagnosis	NOUN
ejpam-6761	725	20	f.	f.	PROPN
ejpam-6761	725	21	al	al	PROPN
ejpam-6761	725	22	-	-	PROPN
ejpam-6761	725	23	zu’bi	zu’bi	PROPN
ejpam-6761	725	24	et	et	NOUN
ejpam-6761	725	25	al	al	PROPN
ejpam-6761	725	26	.	.	PUNCT
ejpam-6761	725	27	/	/	SYM
ejpam-6761	725	28	eur	eur	PROPN
ejpam-6761	725	29	.	.	PUNCT
ejpam-6761	726	1	j.	j.	PROPN
ejpam-6761	726	2	pure	pure	PROPN
ejpam-6761	726	3	appl	appl	PROPN
ejpam-6761	726	4	.	.	PROPN
ejpam-6761	726	5	math	math	PROPN
ejpam-6761	726	6	,	,	PUNCT
ejpam-6761	726	7	18	18	NUM
ejpam-6761	726	8	(	(	PUNCT
ejpam-6761	726	9	4	4	NUM
ejpam-6761	726	10	)	)	PUNCT
ejpam-6761	726	11	(	(	PUNCT
ejpam-6761	726	12	2025	2025	NUM
ejpam-6761	726	13	)	)	PUNCT
ejpam-6761	726	14	,	,	PUNCT
ejpam-6761	726	15	6761	6761	NUM
ejpam-6761	726	16	27	27	NUM
ejpam-6761	726	17	of	of	ADP
ejpam-6761	726	18	28	28	NUM
ejpam-6761	726	19	based	base	VERB
ejpam-6761	726	20	on	on	ADP
ejpam-6761	726	21	trigonometric	trigonometric	ADJ
ejpam-6761	726	22	similarity	similarity	NOUN
ejpam-6761	726	23	measures	measure	NOUN
ejpam-6761	726	24	for	for	ADP
ejpam-6761	726	25	bipolar	bipolar	ADJ
ejpam-6761	726	26	complex	complex	ADJ
ejpam-6761	726	27	fuzzy	fuzzy	ADJ
ejpam-6761	726	28	soft	soft	ADJ
ejpam-6761	726	29	sets	set	NOUN
ejpam-6761	726	30	.	.	PUNCT
ejpam-6761	727	1	soft	soft	ADJ
ejpam-6761	727	2	computing	computing	NOUN
ejpam-6761	727	3	,	,	PUNCT
ejpam-6761	727	4	27(16):11125–11154	27(16):11125–11154	NUM
ejpam-6761	727	5	,	,	PUNCT
ejpam-6761	727	6	2023	2023	NUM
ejpam-6761	727	7	.	.	PUNCT
ejpam-6761	728	1	[	[	X
ejpam-6761	728	2	17	17	NUM
ejpam-6761	728	3	]	]	PUNCT
ejpam-6761	728	4	m.	m.	PROPN
ejpam-6761	728	5	s.	s.	PROPN
ejpam-6761	728	6	anitha	anitha	PROPN
ejpam-6761	728	7	,	,	PUNCT
ejpam-6761	728	8	k.	k.	PROPN
ejpam-6761	728	9	l.	l.	PROPN
ejpam-6761	728	10	muruganantha	muruganantha	PROPN
ejpam-6761	728	11	prasad	prasad	PROPN
ejpam-6761	728	12	,	,	PUNCT
ejpam-6761	728	13	and	and	CCONJ
ejpam-6761	728	14	k.	k.	PROPN
ejpam-6761	728	15	arjunan	arjunan	PROPN
ejpam-6761	728	16	.	.	PUNCT
ejpam-6761	729	1	notes	note	NOUN
ejpam-6761	729	2	on	on	ADP
ejpam-6761	729	3	bipolar	bipolar	ADJ
ejpam-6761	729	4	valued	value	VERB
ejpam-6761	729	5	fuzzy	fuzzy	ADJ
ejpam-6761	729	6	subgroups	subgroup	NOUN
ejpam-6761	729	7	of	of	ADP
ejpam-6761	729	8	a	a	DET
ejpam-6761	729	9	group	group	NOUN
ejpam-6761	729	10	.	.	PUNCT
ejpam-6761	730	1	the	the	DET
ejpam-6761	730	2	bulletin	bulletin	NOUN
ejpam-6761	730	3	of	of	ADP
ejpam-6761	730	4	society	society	NOUN
ejpam-6761	730	5	for	for	ADP
ejpam-6761	730	6	mathematical	mathematical	ADJ
ejpam-6761	730	7	services	service	NOUN
ejpam-6761	730	8	and	and	CCONJ
ejpam-6761	730	9	standards	standard	NOUN
ejpam-6761	730	10	,	,	PUNCT
ejpam-6761	730	11	7:40–45	7:40–45	NUM
ejpam-6761	730	12	,	,	PUNCT
ejpam-6761	730	13	2013	2013	NUM
ejpam-6761	730	14	.	.	PUNCT
ejpam-6761	731	1	[	[	X
ejpam-6761	731	2	18	18	NUM
ejpam-6761	731	3	]	]	PUNCT
ejpam-6761	731	4	a.	a.	PROPN
ejpam-6761	731	5	b.	b.	PROPN
ejpam-6761	731	6	saeid	saeid	PROPN
ejpam-6761	731	7	.	.	PUNCT
ejpam-6761	732	1	bipolar	bipolar	ADJ
ejpam-6761	732	2	-	-	PUNCT
ejpam-6761	732	3	valued	value	VERB
ejpam-6761	732	4	fuzzy	fuzzy	ADJ
ejpam-6761	732	5	bck	bck	PROPN
ejpam-6761	732	6	/	/	SYM
ejpam-6761	732	7	bci	bci	NOUN
ejpam-6761	732	8	-	-	PUNCT
ejpam-6761	732	9	algebras	algebra	NOUN
ejpam-6761	732	10	.	.	PUNCT
ejpam-6761	733	1	world	world	PROPN
ejpam-6761	733	2	applied	apply	VERB
ejpam-6761	733	3	sciences	science	NOUN
ejpam-6761	733	4	journal	journal	NOUN
ejpam-6761	733	5	,	,	PUNCT
ejpam-6761	733	6	7(11):1404–1411	7(11):1404–1411	NUM
ejpam-6761	733	7	,	,	PUNCT
ejpam-6761	733	8	2009	2009	NUM
ejpam-6761	733	9	.	.	PUNCT
ejpam-6761	734	1	[	[	X
ejpam-6761	734	2	19	19	NUM
ejpam-6761	734	3	]	]	PUNCT
ejpam-6761	734	4	k.	k.	PROPN
ejpam-6761	734	5	j.	j.	PROPN
ejpam-6761	734	6	lee	lee	PROPN
ejpam-6761	734	7	.	.	PUNCT
ejpam-6761	735	1	bipolar	bipolar	ADJ
ejpam-6761	735	2	fuzzy	fuzzy	ADJ
ejpam-6761	735	3	subalgebras	subalgebra	NOUN
ejpam-6761	735	4	and	and	CCONJ
ejpam-6761	735	5	bipolar	bipolar	ADJ
ejpam-6761	735	6	fuzzy	fuzzy	ADJ
ejpam-6761	735	7	ideals	ideal	NOUN
ejpam-6761	735	8	of	of	ADP
ejpam-6761	735	9	bck	bck	PROPN
ejpam-6761	735	10	/	/	SYM
ejpam-6761	735	11	bci	bci	NOUN
ejpam-6761	735	12	-	-	PUNCT
ejpam-6761	735	13	algebras	algebra	NOUN
ejpam-6761	735	14	.	.	PUNCT
ejpam-6761	736	1	bull	bull	NOUN
ejpam-6761	736	2	.	.	PUNCT
ejpam-6761	737	1	malays	malays	PROPN
ejpam-6761	737	2	.	.	PUNCT
ejpam-6761	738	1	math	math	NOUN
ejpam-6761	738	2	.	.	PUNCT
ejpam-6761	739	1	sci	sci	PROPN
ejpam-6761	739	2	.	.	PROPN
ejpam-6761	739	3	soc	soc	PROPN
ejpam-6761	739	4	.	.	PUNCT
ejpam-6761	739	5	,	,	PUNCT
ejpam-6761	740	1	32(3):361–373	32(3):361–373	NUM
ejpam-6761	740	2	,	,	PUNCT
ejpam-6761	740	3	2009	2009	NUM
ejpam-6761	740	4	.	.	PUNCT
ejpam-6761	741	1	[	[	X
ejpam-6761	741	2	20	20	NUM
ejpam-6761	741	3	]	]	PUNCT
ejpam-6761	741	4	a.	a.	NOUN
ejpam-6761	741	5	balasubramanian	balasubramanian	PROPN
ejpam-6761	741	6	,	,	PUNCT
ejpam-6761	741	7	k.	k.	PROPN
ejpam-6761	741	8	m.	m.	PROPN
ejpam-6761	741	9	prasad	prasad	PROPN
ejpam-6761	741	10	,	,	PUNCT
ejpam-6761	741	11	and	and	CCONJ
ejpam-6761	741	12	k.	k.	PROPN
ejpam-6761	741	13	arjunan	arjunan	PROPN
ejpam-6761	741	14	.	.	PUNCT
ejpam-6761	742	1	bipolar	bipolar	ADJ
ejpam-6761	742	2	interval	interval	NOUN
ejpam-6761	742	3	valued	value	VERB
ejpam-6761	742	4	fuzzy	fuzzy	ADJ
ejpam-6761	742	5	subgroups	subgroup	NOUN
ejpam-6761	742	6	of	of	ADP
ejpam-6761	742	7	a	a	DET
ejpam-6761	742	8	group	group	NOUN
ejpam-6761	742	9	.	.	PUNCT
ejpam-6761	743	1	bulletin	bulletin	NOUN
ejpam-6761	743	2	of	of	ADP
ejpam-6761	743	3	mathematics	mathematic	NOUN
ejpam-6761	743	4	and	and	CCONJ
ejpam-6761	743	5	statistics	statistic	NOUN
ejpam-6761	743	6	research	research	PROPN
ejpam-6761	743	7	,	,	PUNCT
ejpam-6761	743	8	3(3):234–239	3(3):234–239	NUM
ejpam-6761	743	9	,	,	PUNCT
ejpam-6761	743	10	2015	2015	NUM
ejpam-6761	743	11	.	.	PUNCT
ejpam-6761	744	1	[	[	X
ejpam-6761	744	2	21	21	NUM
ejpam-6761	744	3	]	]	PUNCT
ejpam-6761	744	4	a.	a.	PROPN
ejpam-6761	744	5	s.	s.	PROPN
ejpam-6761	744	6	sahaya	sahaya	PROPN
ejpam-6761	744	7	,	,	PUNCT
ejpam-6761	744	8	s.	s.	PROPN
ejpam-6761	744	9	naganathan	naganathan	PROPN
ejpam-6761	744	10	,	,	PUNCT
ejpam-6761	744	11	and	and	CCONJ
ejpam-6761	744	12	k.	k.	PROPN
ejpam-6761	744	13	arjunan	arjunan	PROPN
ejpam-6761	744	14	.	.	PUNCT
ejpam-6761	745	1	a	a	DET
ejpam-6761	745	2	study	study	NOUN
ejpam-6761	745	3	on	on	ADP
ejpam-6761	745	4	bipolar	bipolar	ADJ
ejpam-6761	745	5	valued	value	VERB
ejpam-6761	745	6	q	q	ADJ
ejpam-6761	745	7	-	-	PUNCT
ejpam-6761	745	8	fuzzy	fuzzy	ADJ
ejpam-6761	745	9	subgroups	subgroup	NOUN
ejpam-6761	745	10	of	of	ADP
ejpam-6761	745	11	a	a	DET
ejpam-6761	745	12	group	group	NOUN
ejpam-6761	745	13	.	.	PUNCT
ejpam-6761	746	1	bulletin	bulletin	NOUN
ejpam-6761	746	2	of	of	ADP
ejpam-6761	746	3	mathematics	mathematic	NOUN
ejpam-6761	746	4	and	and	CCONJ
ejpam-6761	746	5	statistics	statistic	NOUN
ejpam-6761	746	6	research	research	PROPN
ejpam-6761	746	7	,	,	PUNCT
ejpam-6761	746	8	4(3):97–101	4(3):97–101	NOUN
ejpam-6761	746	9	,	,	PUNCT
ejpam-6761	746	10	2016	2016	NUM
ejpam-6761	746	11	.	.	PUNCT
ejpam-6761	747	1	[	[	X
ejpam-6761	747	2	22	22	NUM
ejpam-6761	747	3	]	]	PUNCT
ejpam-6761	747	4	v.	v.	CCONJ
ejpam-6761	747	5	shanmugapriya	shanmugapriya	PROPN
ejpam-6761	747	6	and	and	CCONJ
ejpam-6761	747	7	k.	k.	PROPN
ejpam-6761	747	8	arjunan	arjunan	PROPN
ejpam-6761	747	9	.	.	PUNCT
ejpam-6761	748	1	some	some	DET
ejpam-6761	748	2	translators	translator	NOUN
ejpam-6761	748	3	in	in	ADP
ejpam-6761	748	4	bipolar	bipolar	ADJ
ejpam-6761	748	5	valued	value	VERB
ejpam-6761	748	6	fuzzy	fuzzy	ADJ
ejpam-6761	748	7	subsemiring	subsemiring	NOUN
ejpam-6761	748	8	of	of	ADP
ejpam-6761	748	9	a	a	DET
ejpam-6761	748	10	semiring	semiring	NOUN
ejpam-6761	748	11	.	.	PUNCT
ejpam-6761	749	1	bulletin	bulletin	NOUN
ejpam-6761	749	2	of	of	ADP
ejpam-6761	749	3	mathematics	mathematic	NOUN
ejpam-6761	749	4	and	and	CCONJ
ejpam-6761	749	5	statistics	statistic	NOUN
ejpam-6761	749	6	research	research	NOUN
ejpam-6761	749	7	,	,	PUNCT
ejpam-6761	749	8	4(4):118–123	4(4):118–123	NUM
ejpam-6761	749	9	,	,	PUNCT
ejpam-6761	749	10	2016	2016	NUM
ejpam-6761	749	11	.	.	PUNCT
ejpam-6761	750	1	[	[	X
ejpam-6761	750	2	23	23	NUM
ejpam-6761	750	3	]	]	X
ejpam-6761	750	4	y.	y.	PROPN
ejpam-6761	750	5	b.	b.	PROPN
ejpam-6761	750	6	jun	jun	PROPN
ejpam-6761	750	7	and	and	CCONJ
ejpam-6761	750	8	s.	s.	PROPN
ejpam-6761	750	9	z.	z.	PROPN
ejpam-6761	750	10	song	song	PROPN
ejpam-6761	750	11	.	.	PUNCT
ejpam-6761	751	1	subalgebras	subalgebras	PROPN
ejpam-6761	751	2	and	and	CCONJ
ejpam-6761	751	3	closed	closed	ADJ
ejpam-6761	751	4	ideals	ideal	NOUN
ejpam-6761	751	5	of	of	ADP
ejpam-6761	751	6	bch	bch	PROPN
ejpam-6761	751	7	-	-	PUNCT
ejpam-6761	751	8	algebras	algebras	PROPN
ejpam-6761	751	9	based	base	VERB
ejpam-6761	751	10	on	on	ADP
ejpam-6761	751	11	bipolar	bipolar	ADV
ejpam-6761	751	12	-	-	PUNCT
ejpam-6761	751	13	valued	value	VERB
ejpam-6761	751	14	fuzzy	fuzzy	ADJ
ejpam-6761	751	15	sets	set	NOUN
ejpam-6761	751	16	.	.	PUNCT
ejpam-6761	752	1	sci	sci	PROPN
ejpam-6761	752	2	.	.	PROPN
ejpam-6761	752	3	math	math	PROPN
ejpam-6761	752	4	.	.	PUNCT
ejpam-6761	753	1	jpn	jpn	PROPN
ejpam-6761	753	2	,	,	PUNCT
ejpam-6761	753	3	68(2):287–297	68(2):287–297	PROPN
ejpam-6761	753	4	,	,	PUNCT
ejpam-6761	753	5	2008	2008	NUM
ejpam-6761	753	6	.	.	PUNCT
ejpam-6761	754	1	[	[	X
ejpam-6761	754	2	24	24	NUM
ejpam-6761	754	3	]	]	PUNCT
ejpam-6761	754	4	t.	t.	PROPN
ejpam-6761	754	5	mahmood	mahmood	PROPN
ejpam-6761	754	6	,	,	PUNCT
ejpam-6761	754	7	u.	u.	PROPN
ejpam-6761	754	8	u.	u.	PROPN
ejpam-6761	754	9	rehman	rehman	PROPN
ejpam-6761	754	10	,	,	PUNCT
ejpam-6761	754	11	and	and	CCONJ
ejpam-6761	754	12	m.	m.	NOUN
ejpam-6761	754	13	albaity	albaity	NOUN
ejpam-6761	754	14	.	.	PUNCT
ejpam-6761	755	1	analysis	analysis	NOUN
ejpam-6761	755	2	of	of	ADP
ejpam-6761	755	3	γ	γ	NOUN
ejpam-6761	755	4	-	-	PUNCT
ejpam-6761	755	5	semigroups	semigroup	NOUN
ejpam-6761	755	6	based	base	VERB
ejpam-6761	755	7	on	on	ADP
ejpam-6761	755	8	bipolar	bipolar	ADJ
ejpam-6761	755	9	complex	complex	ADJ
ejpam-6761	755	10	fuzzy	fuzzy	ADJ
ejpam-6761	755	11	sets	set	NOUN
ejpam-6761	755	12	.	.	PUNCT
ejpam-6761	756	1	computational	computational	ADJ
ejpam-6761	756	2	and	and	CCONJ
ejpam-6761	756	3	applied	applied	ADJ
ejpam-6761	756	4	mathematics	mathematic	NOUN
ejpam-6761	756	5	,	,	PUNCT
ejpam-6761	756	6	42(6):262	42(6):262	PROPN
ejpam-6761	756	7	,	,	PUNCT
ejpam-6761	756	8	2023	2023	NUM
ejpam-6761	756	9	.	.	PUNCT
ejpam-6761	757	1	[	[	X
ejpam-6761	757	2	25	25	NUM
ejpam-6761	757	3	]	]	PUNCT
ejpam-6761	757	4	a.	a.	PROPN
ejpam-6761	757	5	al	al	PROPN
ejpam-6761	757	6	-	-	PROPN
ejpam-6761	757	7	masarwah	masarwah	PROPN
ejpam-6761	757	8	,	,	PUNCT
ejpam-6761	757	9	a.	a.	PROPN
ejpam-6761	757	10	g.	g.	PROPN
ejpam-6761	757	11	ahmad	ahmad	PROPN
ejpam-6761	757	12	,	,	PUNCT
ejpam-6761	757	13	g.	g.	PROPN
ejpam-6761	757	14	muhiuddin	muhiuddin	PROPN
ejpam-6761	757	15	,	,	PUNCT
ejpam-6761	757	16	and	and	CCONJ
ejpam-6761	757	17	d.	d.	PROPN
ejpam-6761	757	18	al	al	PROPN
ejpam-6761	757	19	-	-	PUNCT
ejpam-6761	757	20	kadi	kadi	PROPN
ejpam-6761	757	21	.	.	PUNCT
ejpam-6761	758	1	generalized	generalize	VERB
ejpam-6761	758	2	mpolar	mpolar	ADJ
ejpam-6761	758	3	fuzzy	fuzzy	ADJ
ejpam-6761	758	4	positive	positive	ADJ
ejpam-6761	758	5	implicative	implicative	ADJ
ejpam-6761	758	6	ideals	ideal	NOUN
ejpam-6761	758	7	of	of	ADP
ejpam-6761	758	8	bck	bck	NOUN
ejpam-6761	758	9	-	-	PUNCT
ejpam-6761	758	10	algebras	algebras	PROPN
ejpam-6761	758	11	.	.	PUNCT
ejpam-6761	759	1	journal	journal	PROPN
ejpam-6761	759	2	of	of	ADP
ejpam-6761	759	3	mathematics	mathematic	NOUN
ejpam-6761	759	4	,	,	PUNCT
ejpam-6761	759	5	2021(1):6610009	2021(1):6610009	NUM
ejpam-6761	759	6	,	,	PUNCT
ejpam-6761	759	7	2021	2021	NUM
ejpam-6761	759	8	.	.	PUNCT
ejpam-6761	760	1	[	[	X
ejpam-6761	760	2	26	26	NUM
ejpam-6761	760	3	]	]	PUNCT
ejpam-6761	760	4	a.	a.	PROPN
ejpam-6761	760	5	al	al	PROPN
ejpam-6761	760	6	-	-	PROPN
ejpam-6761	760	7	masarwah	masarwah	PROPN
ejpam-6761	760	8	and	and	CCONJ
ejpam-6761	760	9	m.	m.	NOUN
ejpam-6761	760	10	alqahtani	alqahtani	PROPN
ejpam-6761	760	11	.	.	PUNCT
ejpam-6761	761	1	operational	operational	ADJ
ejpam-6761	761	2	algebraic	algebraic	ADJ
ejpam-6761	761	3	properties	property	NOUN
ejpam-6761	761	4	and	and	CCONJ
ejpam-6761	761	5	subsemigroups	subsemigroup	NOUN
ejpam-6761	761	6	of	of	ADP
ejpam-6761	761	7	semigroups	semigroup	NOUN
ejpam-6761	761	8	in	in	ADP
ejpam-6761	761	9	view	view	NOUN
ejpam-6761	761	10	of	of	ADP
ejpam-6761	761	11	k	k	NOUN
ejpam-6761	761	12	-	-	PUNCT
ejpam-6761	761	13	folded	fold	VERB
ejpam-6761	761	14	n	n	CCONJ
ejpam-6761	761	15	-	-	PUNCT
ejpam-6761	761	16	structures	structure	NOUN
ejpam-6761	761	17	.	.	PUNCT
ejpam-6761	762	1	aims	aim	VERB
ejpam-6761	762	2	mathematics	mathematic	NOUN
ejpam-6761	762	3	,	,	PUNCT
ejpam-6761	762	4	8(9):22081–22096	8(9):22081–22096	NUM
ejpam-6761	762	5	,	,	PUNCT
ejpam-6761	762	6	2023	2023	NUM
ejpam-6761	762	7	.	.	PUNCT
ejpam-6761	763	1	[	[	X
ejpam-6761	763	2	27	27	NUM
ejpam-6761	763	3	]	]	X
ejpam-6761	763	4	s.	s.	PROPN
ejpam-6761	763	5	m.	m.	PROPN
ejpam-6761	763	6	alqaraleh	alqaraleh	PROPN
ejpam-6761	763	7	,	,	PUNCT
ejpam-6761	763	8	m.	m.	PROPN
ejpam-6761	763	9	j.	j.	PROPN
ejpam-6761	763	10	s.	s.	PROPN
ejpam-6761	763	11	abd	abd	PROPN
ejpam-6761	763	12	ulazeez	ulazeez	PROPN
ejpam-6761	763	13	,	,	PUNCT
ejpam-6761	763	14	m.	m.	NOUN
ejpam-6761	763	15	o.	o.	PROPN
ejpam-6761	763	16	massa’deh	massa’deh	PROPN
ejpam-6761	763	17	,	,	PUNCT
ejpam-6761	763	18	a.	a.	NOUN
ejpam-6761	763	19	g.	g.	PROPN
ejpam-6761	763	20	talafha	talafha	PROPN
ejpam-6761	763	21	,	,	PUNCT
ejpam-6761	763	22	and	and	CCONJ
ejpam-6761	763	23	a.	a.	NOUN
ejpam-6761	763	24	bataihah	bataihah	PROPN
ejpam-6761	763	25	.	.	PUNCT
ejpam-6761	764	1	bipolar	bipolar	ADJ
ejpam-6761	764	2	complex	complex	ADJ
ejpam-6761	764	3	fuzzy	fuzzy	ADJ
ejpam-6761	764	4	soft	soft	ADJ
ejpam-6761	764	5	sets	set	NOUN
ejpam-6761	764	6	and	and	CCONJ
ejpam-6761	764	7	their	their	PRON
ejpam-6761	764	8	application	application	NOUN
ejpam-6761	764	9	.	.	PUNCT
ejpam-6761	765	1	international	international	ADJ
ejpam-6761	765	2	journal	journal	NOUN
ejpam-6761	765	3	of	of	ADP
ejpam-6761	765	4	fuzzy	fuzzy	ADJ
ejpam-6761	765	5	system	system	NOUN
ejpam-6761	765	6	applications	application	NOUN
ejpam-6761	765	7	(	(	PUNCT
ejpam-6761	765	8	ijfsa	ijfsa	NOUN
ejpam-6761	765	9	)	)	PUNCT
ejpam-6761	765	10	,	,	PUNCT
ejpam-6761	765	11	11(1):1–23	11(1):1–23	NUM
ejpam-6761	765	12	,	,	PUNCT
ejpam-6761	765	13	2022	2022	NUM
ejpam-6761	765	14	.	.	PUNCT
ejpam-6761	766	1	[	[	X
ejpam-6761	766	2	28	28	NUM
ejpam-6761	766	3	]	]	X
ejpam-6761	766	4	m.	m.	NOUN
ejpam-6761	766	5	o.	o.	PROPN
ejpam-6761	766	6	massa’deh	massa’deh	PROPN
ejpam-6761	766	7	,	,	PUNCT
ejpam-6761	766	8	a.	a.	NOUN
ejpam-6761	766	9	o.	o.	PROPN
ejpam-6761	766	10	fallatah	fallatah	PROPN
ejpam-6761	766	11	,	,	PUNCT
ejpam-6761	766	12	and	and	CCONJ
ejpam-6761	766	13	et	et	PROPN
ejpam-6761	766	14	al	al	PROPN
ejpam-6761	766	15	.	.	PUNCT
ejpam-6761	767	1	anti	anti	PROPN
ejpam-6761	767	2	homomorphism	homomorphism	NOUN
ejpam-6761	767	3	and	and	CCONJ
ejpam-6761	767	4	homomorphism	homomorphism	NOUN
ejpam-6761	767	5	of	of	ADP
ejpam-6761	767	6	bipolar	bipolar	ADJ
ejpam-6761	767	7	valued	value	VERB
ejpam-6761	767	8	multi	multi	X
ejpam-6761	767	9	fuzzy	fuzzy	ADJ
ejpam-6761	767	10	hx	hx	PROPN
ejpam-6761	767	11	-	-	PUNCT
ejpam-6761	767	12	subgroups	subgroup	NOUN
ejpam-6761	767	13	and	and	CCONJ
ejpam-6761	767	14	its	its	PRON
ejpam-6761	767	15	normal	normal	ADJ
ejpam-6761	767	16	.	.	PUNCT
ejpam-6761	768	1	full	full	ADJ
ejpam-6761	768	2	length	length	NOUN
ejpam-6761	768	3	article	article	NOUN
ejpam-6761	768	4	,	,	PUNCT
ejpam-6761	768	5	24(3):165–165	24(3):165–165	PROPN
ejpam-6761	768	6	,	,	PUNCT
ejpam-6761	768	7	2024	2024	NUM
ejpam-6761	768	8	.	.	PUNCT
ejpam-6761	769	1	[	[	X
ejpam-6761	769	2	29	29	NUM
ejpam-6761	769	3	]	]	PUNCT
ejpam-6761	769	4	l.	l.	PROPN
ejpam-6761	769	5	j.	j.	PROPN
ejpam-6761	769	6	manavalan	manavalan	PROPN
ejpam-6761	769	7	,	,	PUNCT
ejpam-6761	769	8	s.	s.	PROPN
ejpam-6761	769	9	damrah	damrah	PROPN
ejpam-6761	769	10	,	,	PUNCT
ejpam-6761	769	11	i.	i.	PROPN
ejpam-6761	769	12	a.	a.	PROPN
ejpam-6761	769	13	falahah	falahah	PROPN
ejpam-6761	769	14	,	,	PUNCT
ejpam-6761	769	15	a.	a.	PROPN
ejpam-6761	769	16	al	al	PROPN
ejpam-6761	769	17	-	-	PUNCT
ejpam-6761	769	18	husban	husban	PROPN
ejpam-6761	769	19	,	,	PUNCT
ejpam-6761	769	20	and	and	CCONJ
ejpam-6761	769	21	m.	m.	NOUN
ejpam-6761	769	22	palanikumar	palanikumar	PROPN
ejpam-6761	769	23	.	.	PUNCT
ejpam-6761	769	24	selection	selection	NOUN
ejpam-6761	769	25	process	process	NOUN
ejpam-6761	769	26	based	base	VERB
ejpam-6761	769	27	on	on	ADP
ejpam-6761	769	28	new	new	ADJ
ejpam-6761	769	29	type	type	NOUN
ejpam-6761	769	30	neutrosophic	neutrosophic	ADJ
ejpam-6761	769	31	interval	interval	NOUN
ejpam-6761	769	32	-	-	PUNCT
ejpam-6761	769	33	valued	value	VERB
ejpam-6761	769	34	set	set	NOUN
ejpam-6761	769	35	applied	apply	VERB
ejpam-6761	769	36	to	to	ADP
ejpam-6761	769	37	logarithm	logarithm	NOUN
ejpam-6761	769	38	operator	operator	NOUN
ejpam-6761	769	39	.	.	PUNCT
ejpam-6761	770	1	international	international	ADJ
ejpam-6761	770	2	journal	journal	PROPN
ejpam-6761	770	3	of	of	ADP
ejpam-6761	770	4	neutrosophic	neutrosophic	ADJ
ejpam-6761	770	5	science	science	NOUN
ejpam-6761	770	6	(	(	PUNCT
ejpam-6761	770	7	ijns	ijns	PROPN
ejpam-6761	770	8	)	)	PUNCT
ejpam-6761	770	9	,	,	PUNCT
ejpam-6761	770	10	24(4	24(4	NUM
ejpam-6761	770	11	)	)	PUNCT
ejpam-6761	770	12	,	,	PUNCT
ejpam-6761	770	13	2024	2024	NUM
ejpam-6761	770	14	.	.	PUNCT
ejpam-6761	771	1	[	[	X
ejpam-6761	771	2	30	30	NUM
ejpam-6761	771	3	]	]	X
ejpam-6761	771	4	l.	l.	PROPN
ejpam-6761	771	5	j.	j.	PROPN
ejpam-6761	771	6	manavalan	manavalan	PROPN
ejpam-6761	771	7	,	,	PUNCT
ejpam-6761	771	8	s.	s.	PROPN
ejpam-6761	771	9	damrah	damrah	PROPN
ejpam-6761	771	10	,	,	PUNCT
ejpam-6761	771	11	m.	m.	NOUN
ejpam-6761	771	12	m.	m.	PROPN
ejpam-6761	771	13	abbas	abbas	PROPN
ejpam-6761	771	14	ali	ali	PROPN
ejpam-6761	771	15	,	,	PUNCT
ejpam-6761	771	16	a.	a.	PROPN
ejpam-6761	771	17	al	al	PROPN
ejpam-6761	771	18	-	-	PUNCT
ejpam-6761	771	19	husban	husban	PROPN
ejpam-6761	771	20	,	,	PUNCT
ejpam-6761	771	21	and	and	CCONJ
ejpam-6761	771	22	m.	m.	NOUN
ejpam-6761	771	23	palanikumar	palanikumar	PROPN
ejpam-6761	771	24	.	.	PUNCT
ejpam-6761	772	1	type	type	NOUN
ejpam-6761	772	2	-	-	PUNCT
ejpam-6761	772	3	i	i	PROPN
ejpam-6761	772	4	extension	extension	NOUN
ejpam-6761	772	5	diophantine	diophantine	VERB
ejpam-6761	772	6	neutrosophic	neutrosophic	ADJ
ejpam-6761	772	7	interval	interval	NOUN
ejpam-6761	772	8	valued	value	VERB
ejpam-6761	772	9	soft	soft	ADJ
ejpam-6761	772	10	set	set	NOUN
ejpam-6761	772	11	in	in	ADP
ejpam-6761	772	12	real	real	ADJ
ejpam-6761	772	13	life	life	NOUN
ejpam-6761	772	14	applications	application	NOUN
ejpam-6761	772	15	for	for	ADP
ejpam-6761	772	16	a	a	DET
ejpam-6761	772	17	decision	decision	NOUN
ejpam-6761	772	18	making	making	NOUN
ejpam-6761	772	19	.	.	PUNCT
ejpam-6761	773	1	international	international	ADJ
ejpam-6761	773	2	journal	journal	PROPN
ejpam-6761	773	3	of	of	ADP
ejpam-6761	773	4	neutrosophic	neutrosophic	ADJ
ejpam-6761	773	5	science	science	NOUN
ejpam-6761	773	6	(	(	PUNCT
ejpam-6761	773	7	ijns	ijns	PROPN
ejpam-6761	773	8	)	)	PUNCT
ejpam-6761	773	9	,	,	PUNCT
ejpam-6761	773	10	24(4	24(4	NUM
ejpam-6761	773	11	)	)	PUNCT
ejpam-6761	773	12	,	,	PUNCT
ejpam-6761	773	13	2024	2024	NUM
ejpam-6761	773	14	.	.	PUNCT
ejpam-6761	774	1	[	[	X
ejpam-6761	774	2	31	31	NUM
ejpam-6761	774	3	]	]	PUNCT
ejpam-6761	774	4	s.	s.	PROPN
ejpam-6761	774	5	damrah	damrah	PROPN
ejpam-6761	774	6	,	,	PUNCT
ejpam-6761	774	7	m.	m.	PROPN
ejpam-6761	774	8	h.	h.	PROPN
ejpam-6761	774	9	darassi	darassi	PROPN
ejpam-6761	774	10	,	,	PUNCT
ejpam-6761	774	11	and	and	CCONJ
ejpam-6761	774	12	y.	y.	PROPN
ejpam-6761	774	13	abuhour	abuhour	PROPN
ejpam-6761	774	14	.	.	PUNCT
ejpam-6761	775	1	mathematical	mathematical	ADJ
ejpam-6761	775	2	modeling	modeling	NOUN
ejpam-6761	775	3	for	for	ADP
ejpam-6761	775	4	exploring	explore	VERB
ejpam-6761	775	5	the	the	DET
ejpam-6761	775	6	spread	spread	NOUN
ejpam-6761	775	7	of	of	ADP
ejpam-6761	775	8	cyberattacks	cyberattack	NOUN
ejpam-6761	775	9	through	through	ADP
ejpam-6761	775	10	iot	iot	NOUN
ejpam-6761	775	11	devices	device	NOUN
ejpam-6761	775	12	.	.	PUNCT
ejpam-6761	776	1	in	in	ADP
ejpam-6761	776	2	international	international	ADJ
ejpam-6761	776	3	conference	conference	NOUN
ejpam-6761	776	4	on	on	ADP
ejpam-6761	776	5	f.	f.	PROPN
ejpam-6761	776	6	al	al	PROPN
ejpam-6761	776	7	-	-	PROPN
ejpam-6761	776	8	zu’bi	zu’bi	PROPN
ejpam-6761	776	9	et	et	NOUN
ejpam-6761	776	10	al	al	PROPN
ejpam-6761	776	11	.	.	PUNCT
ejpam-6761	776	12	/	/	SYM
ejpam-6761	776	13	eur	eur	PROPN
ejpam-6761	776	14	.	.	PUNCT
ejpam-6761	777	1	j.	j.	PROPN
ejpam-6761	777	2	pure	pure	PROPN
ejpam-6761	777	3	appl	appl	PROPN
ejpam-6761	777	4	.	.	PROPN
ejpam-6761	777	5	math	math	PROPN
ejpam-6761	777	6	,	,	PUNCT
ejpam-6761	777	7	18	18	NUM
ejpam-6761	777	8	(	(	PUNCT
ejpam-6761	777	9	4	4	NUM
ejpam-6761	777	10	)	)	PUNCT
ejpam-6761	777	11	(	(	PUNCT
ejpam-6761	777	12	2025	2025	NUM
ejpam-6761	777	13	)	)	PUNCT
ejpam-6761	777	14	,	,	PUNCT
ejpam-6761	777	15	6761	6761	NUM
ejpam-6761	777	16	28	28	NUM
ejpam-6761	777	17	of	of	ADP
ejpam-6761	777	18	28	28	NUM
ejpam-6761	777	19	science	science	NOUN
ejpam-6761	777	20	,	,	PUNCT
ejpam-6761	777	21	engineering	engineering	NOUN
ejpam-6761	777	22	management	management	NOUN
ejpam-6761	777	23	and	and	CCONJ
ejpam-6761	777	24	information	information	NOUN
ejpam-6761	777	25	technology	technology	NOUN
ejpam-6761	777	26	,	,	PUNCT
ejpam-6761	777	27	pages	page	NOUN
ejpam-6761	777	28	17–27	17–27	NUM
ejpam-6761	777	29	,	,	PUNCT
ejpam-6761	777	30	cham	cham	NOUN
ejpam-6761	777	31	,	,	PUNCT
ejpam-6761	777	32	september	september	PROPN
ejpam-6761	777	33	2023	2023	NUM
ejpam-6761	777	34	.	.	PUNCT
ejpam-6761	778	1	springer	springer	NOUN
ejpam-6761	778	2	nature	nature	PROPN
ejpam-6761	778	3	switzerland	switzerland	PROPN
ejpam-6761	778	4	.	.	PUNCT
ejpam-6761	779	1	[	[	X
ejpam-6761	779	2	32	32	NUM
ejpam-6761	779	3	]	]	PUNCT
ejpam-6761	779	4	m.	m.	NOUN
ejpam-6761	779	5	h.	h.	PROPN
ejpam-6761	779	6	darassi	darassi	PROPN
ejpam-6761	779	7	,	,	PUNCT
ejpam-6761	779	8	s.	s.	PROPN
ejpam-6761	779	9	damrah	damrah	PROPN
ejpam-6761	779	10	,	,	PUNCT
ejpam-6761	779	11	and	and	CCONJ
ejpam-6761	779	12	y.	y.	PROPN
ejpam-6761	779	13	abuhour	abuhour	PROPN
ejpam-6761	779	14	.	.	PUNCT
ejpam-6761	780	1	a	a	DET
ejpam-6761	780	2	mathematical	mathematical	ADJ
ejpam-6761	780	3	study	study	NOUN
ejpam-6761	780	4	of	of	ADP
ejpam-6761	780	5	the	the	DET
ejpam-6761	780	6	omicron	omicron	PROPN
ejpam-6761	780	7	variant	variant	NOUN
ejpam-6761	780	8	in	in	ADP
ejpam-6761	780	9	a	a	DET
ejpam-6761	780	10	discrete	discrete	ADJ
ejpam-6761	780	11	-	-	PUNCT
ejpam-6761	780	12	time	time	NOUN
ejpam-6761	780	13	covid-19	covid-19	PROPN
ejpam-6761	780	14	model	model	NOUN
ejpam-6761	780	15	.	.	PUNCT
ejpam-6761	781	1	the	the	DET
ejpam-6761	781	2	european	european	PROPN
ejpam-6761	781	3	physical	physical	PROPN
ejpam-6761	781	4	journal	journal	PROPN
ejpam-6761	781	5	plus	plus	CCONJ
ejpam-6761	781	6	,	,	PUNCT
ejpam-6761	781	7	138(7):1–18	138(7):1–18	NUM
ejpam-6761	781	8	,	,	PUNCT
ejpam-6761	781	9	2023	2023	NUM
ejpam-6761	781	10	.	.	PUNCT
ejpam-6761	782	1	[	[	X
ejpam-6761	782	2	33	33	NUM
ejpam-6761	782	3	]	]	X
ejpam-6761	782	4	n.	n.	NOUN
ejpam-6761	782	5	firouzkouhi	firouzkouhi	PROPN
ejpam-6761	782	6	,	,	PUNCT
ejpam-6761	782	7	a.	a.	PROPN
ejpam-6761	782	8	amini	amini	PROPN
ejpam-6761	782	9	,	,	PUNCT
ejpam-6761	782	10	a.	a.	PROPN
ejpam-6761	782	11	bani	bani	PROPN
ejpam-6761	782	12	-	-	PUNCT
ejpam-6761	782	13	mustafa	mustafa	PROPN
ejpam-6761	782	14	,	,	PUNCT
ejpam-6761	782	15	a.	a.	NOUN
ejpam-6761	782	16	mehdizadeh	mehdizadeh	PROPN
ejpam-6761	782	17	,	,	PUNCT
ejpam-6761	782	18	s.	s.	PROPN
ejpam-6761	782	19	damrah	damrah	PROPN
ejpam-6761	782	20	,	,	PUNCT
ejpam-6761	782	21	a.	a.	NOUN
ejpam-6761	782	22	gholami	gholami	PROPN
ejpam-6761	782	23	,	,	PUNCT
ejpam-6761	782	24	and	and	CCONJ
ejpam-6761	782	25	b.	b.	PROPN
ejpam-6761	782	26	davvaz	davvaz	PROPN
ejpam-6761	782	27	.	.	PUNCT
ejpam-6761	783	1	generalized	generalize	VERB
ejpam-6761	783	2	fuzzy	fuzzy	ADJ
ejpam-6761	783	3	hypergraph	hypergraph	NOUN
ejpam-6761	783	4	for	for	ADP
ejpam-6761	783	5	link	link	NOUN
ejpam-6761	783	6	prediction	prediction	NOUN
ejpam-6761	783	7	and	and	CCONJ
ejpam-6761	783	8	identification	identification	NOUN
ejpam-6761	783	9	of	of	ADP
ejpam-6761	783	10	influencers	influencer	NOUN
ejpam-6761	783	11	in	in	ADP
ejpam-6761	783	12	dynamic	dynamic	ADJ
ejpam-6761	783	13	social	social	ADJ
ejpam-6761	783	14	media	medium	NOUN
ejpam-6761	783	15	networks	network	NOUN
ejpam-6761	783	16	.	.	PUNCT
ejpam-6761	784	1	expert	expert	NOUN
ejpam-6761	784	2	systems	system	NOUN
ejpam-6761	784	3	with	with	ADP
ejpam-6761	784	4	applications	application	NOUN
ejpam-6761	784	5	,	,	PUNCT
ejpam-6761	784	6	238:121736	238:121736	NUM
ejpam-6761	784	7	,	,	PUNCT
ejpam-6761	784	8	2024	2024	NUM
ejpam-6761	784	9	.	.	PUNCT
ejpam-6761	785	1	[	[	X
ejpam-6761	785	2	34	34	NUM
ejpam-6761	785	3	]	]	PUNCT
ejpam-6761	785	4	a.	a.	NOUN
ejpam-6761	785	5	sedaghat	sedaghat	PROPN
ejpam-6761	785	6	,	,	PUNCT
ejpam-6761	785	7	m.	m.	NOUN
ejpam-6761	785	8	a.	a.	PROPN
ejpam-6761	785	9	a.	a.	PROPN
ejpam-6761	785	10	omar	omar	PROPN
ejpam-6761	785	11	,	,	PUNCT
ejpam-6761	785	12	s.	s.	PROPN
ejpam-6761	785	13	damrah	damrah	PROPN
ejpam-6761	785	14	,	,	PUNCT
ejpam-6761	785	15	and	and	CCONJ
ejpam-6761	785	16	m.	m.	NOUN
ejpam-6761	785	17	gaith	gaith	PROPN
ejpam-6761	785	18	.	.	PUNCT
ejpam-6761	786	1	mathematical	mathematical	ADJ
ejpam-6761	786	2	modelling	modelling	NOUN
ejpam-6761	786	3	of	of	ADP
ejpam-6761	786	4	the	the	DET
ejpam-6761	786	5	marsh	marsh	ADJ
ejpam-6761	786	6	funnel	funnel	NOUN
ejpam-6761	786	7	for	for	ADP
ejpam-6761	786	8	measuring	measure	VERB
ejpam-6761	786	9	rheological	rheological	ADJ
ejpam-6761	786	10	properties	property	NOUN
ejpam-6761	786	11	of	of	ADP
ejpam-6761	786	12	drilling	drilling	NOUN
ejpam-6761	786	13	nanofluids	nanofluid	NOUN
ejpam-6761	786	14	for	for	ADP
ejpam-6761	786	15	energy	energy	NOUN
ejpam-6761	786	16	efficient	efficient	ADJ
ejpam-6761	786	17	environment	environment	NOUN
ejpam-6761	786	18	.	.	PUNCT
ejpam-6761	787	1	in	in	ADP
ejpam-6761	787	2	2016	2016	NUM
ejpam-6761	787	3	eleventh	eleventh	ADJ
ejpam-6761	787	4	international	international	ADJ
ejpam-6761	787	5	conference	conference	NOUN
ejpam-6761	787	6	on	on	ADP
ejpam-6761	787	7	ecological	ecological	ADJ
ejpam-6761	787	8	vehicles	vehicle	NOUN
ejpam-6761	787	9	and	and	CCONJ
ejpam-6761	787	10	renewable	renewable	ADJ
ejpam-6761	787	11	energies	energy	NOUN
ejpam-6761	787	12	(	(	PUNCT
ejpam-6761	787	13	ever	ever	ADV
ejpam-6761	787	14	)	)	PUNCT
ejpam-6761	787	15	,	,	PUNCT
ejpam-6761	787	16	pages	page	NOUN
ejpam-6761	787	17	1–4	1–4	PROPN
ejpam-6761	787	18	.	.	PROPN
ejpam-6761	787	19	ieee	ieee	PROPN
ejpam-6761	787	20	,	,	PUNCT
ejpam-6761	787	21	april	april	PROPN
ejpam-6761	787	22	2016	2016	NUM
ejpam-6761	787	23	.	.	PUNCT
ejpam-6761	788	1	[	[	X
ejpam-6761	788	2	35	35	NUM
ejpam-6761	788	3	]	]	X
ejpam-6761	788	4	b.	b.	PROPN
ejpam-6761	788	5	m.	m.	PROPN
ejpam-6761	788	6	biltayib	biltayib	PROPN
ejpam-6761	788	7	,	,	PUNCT
ejpam-6761	788	8	s.	s.	PROPN
ejpam-6761	788	9	damrah	damrah	PROPN
ejpam-6761	788	10	,	,	PUNCT
ejpam-6761	788	11	b.	b.	PROPN
ejpam-6761	788	12	al	al	PROPN
ejpam-6761	788	13	-	-	PUNCT
ejpam-6761	788	14	fakeh	fakeh	PROPN
ejpam-6761	788	15	,	,	PUNCT
ejpam-6761	788	16	and	and	CCONJ
ejpam-6761	788	17	a.	a.	PROPN
ejpam-6761	788	18	al	al	PROPN
ejpam-6761	788	19	-	-	PUNCT
ejpam-6761	788	20	kanderi	kanderi	PROPN
ejpam-6761	788	21	.	.	PUNCT
ejpam-6761	789	1	validation	validation	NOUN
ejpam-6761	789	2	of	of	ADP
ejpam-6761	789	3	directional	directional	ADJ
ejpam-6761	789	4	drilling	drilling	NOUN
ejpam-6761	789	5	well	well	NOUN
ejpam-6761	789	6	design	design	NOUN
ejpam-6761	789	7	trajectory	trajectory	NOUN
ejpam-6761	789	8	with	with	ADP
ejpam-6761	789	9	a	a	DET
ejpam-6761	789	10	case	case	NOUN
ejpam-6761	789	11	study	study	NOUN
ejpam-6761	789	12	in	in	ADP
ejpam-6761	789	13	kuwait	kuwait	PROPN
ejpam-6761	789	14	.	.	PUNCT
ejpam-6761	790	1	in	in	ADP
ejpam-6761	790	2	2015	2015	NUM
ejpam-6761	790	3	international	international	ADJ
ejpam-6761	790	4	conference	conference	NOUN
ejpam-6761	790	5	on	on	ADP
ejpam-6761	790	6	sustainable	sustainable	ADJ
ejpam-6761	790	7	mobility	mobility	NOUN
ejpam-6761	790	8	applications	application	NOUN
ejpam-6761	790	9	,	,	PUNCT
ejpam-6761	790	10	renewables	renewable	NOUN
ejpam-6761	790	11	and	and	CCONJ
ejpam-6761	790	12	technology	technology	NOUN
ejpam-6761	790	13	(	(	PUNCT
ejpam-6761	790	14	smart	smart	ADJ
ejpam-6761	790	15	)	)	PUNCT
ejpam-6761	790	16	,	,	PUNCT
ejpam-6761	790	17	pages	page	NOUN
ejpam-6761	790	18	1–7	1–7	NUM
ejpam-6761	790	19	.	.	PUNCT
ejpam-6761	790	20	ieee	ieee	PROPN
ejpam-6761	790	21	,	,	PUNCT
ejpam-6761	790	22	november	november	PROPN
ejpam-6761	790	23	2015	2015	NUM
ejpam-6761	790	24	.	.	PUNCT
ejpam-6761	791	1	[	[	X
ejpam-6761	791	2	36	36	NUM
ejpam-6761	791	3	]	]	PUNCT
ejpam-6761	791	4	m.	m.	NOUN
ejpam-6761	791	5	talafha	talafha	NOUN
ejpam-6761	791	6	,	,	PUNCT
ejpam-6761	791	7	s.	s.	PROPN
ejpam-6761	791	8	c.	c.	PROPN
ejpam-6761	791	9	dzul	dzul	PROPN
ejpam-6761	791	10	-	-	PUNCT
ejpam-6761	791	11	kifli	kifli	PROPN
ejpam-6761	791	12	,	,	PUNCT
ejpam-6761	791	13	and	and	CCONJ
ejpam-6761	791	14	a.	a.	PROPN
ejpam-6761	791	15	u.	u.	PROPN
ejpam-6761	791	16	alkouri	alkouri	PROPN
ejpam-6761	791	17	.	.	PUNCT
ejpam-6761	792	1	a	a	DET
ejpam-6761	792	2	new	new	ADJ
ejpam-6761	792	3	structure	structure	NOUN
ejpam-6761	792	4	of	of	ADP
ejpam-6761	792	5	hesitant	hesitant	ADJ
ejpam-6761	792	6	fuzzy	fuzzy	ADJ
ejpam-6761	792	7	relations	relation	NOUN
ejpam-6761	792	8	:	:	PUNCT
ejpam-6761	792	9	an	an	DET
ejpam-6761	792	10	extension	extension	NOUN
ejpam-6761	792	11	from	from	ADP
ejpam-6761	792	12	fuzzy	fuzzy	ADJ
ejpam-6761	792	13	and	and	CCONJ
ejpam-6761	792	14	intuitionistic	intuitionistic	ADJ
ejpam-6761	792	15	fuzzy	fuzzy	ADJ
ejpam-6761	792	16	relations	relation	NOUN
ejpam-6761	792	17	with	with	ADP
ejpam-6761	792	18	applications	application	NOUN
ejpam-6761	792	19	.	.	PUNCT
ejpam-6761	793	1	journal	journal	NOUN
ejpam-6761	793	2	of	of	ADP
ejpam-6761	793	3	intelligent	intelligent	ADJ
ejpam-6761	793	4	&	&	CCONJ
ejpam-6761	793	5	fuzzy	fuzzy	ADJ
ejpam-6761	793	6	systems	system	NOUN
ejpam-6761	793	7	,	,	PUNCT
ejpam-6761	793	8	2025	2025	NUM
ejpam-6761	793	9	.	.	PUNCT
ejpam-6761	794	1	[	[	X
ejpam-6761	794	2	37	37	NUM
ejpam-6761	794	3	]	]	PUNCT
ejpam-6761	794	4	t.	t.	NOUN
ejpam-6761	794	5	oner	oner	PROPN
ejpam-6761	794	6	,	,	PUNCT
ejpam-6761	794	7	r.	r.	PROPN
ejpam-6761	794	8	neelamegarajan	neelamegarajan	PROPN
ejpam-6761	794	9	,	,	PUNCT
ejpam-6761	794	10	r.	r.	PROPN
ejpam-6761	794	11	k.	k.	PROPN
ejpam-6761	794	12	bandaru	bandaru	PROPN
ejpam-6761	794	13	,	,	PUNCT
ejpam-6761	794	14	and	and	CCONJ
ejpam-6761	794	15	h.	h.	PROPN
ejpam-6761	794	16	bordbar	bordbar	PROPN
ejpam-6761	794	17	.	.	PUNCT
ejpam-6761	795	1	an	an	DET
ejpam-6761	795	2	investigation	investigation	NOUN
ejpam-6761	795	3	into	into	ADP
ejpam-6761	795	4	bipolar	bipolar	ADJ
ejpam-6761	795	5	fuzzy	fuzzy	ADJ
ejpam-6761	795	6	hoop	hoop	NOUN
ejpam-6761	795	7	algebras	algebra	NOUN
ejpam-6761	795	8	and	and	CCONJ
ejpam-6761	795	9	their	their	PRON
ejpam-6761	795	10	applications	application	NOUN
ejpam-6761	795	11	.	.	PUNCT
ejpam-6761	796	1	axioms	axiom	NOUN
ejpam-6761	796	2	,	,	PUNCT
ejpam-6761	796	3	14(5):338	14(5):338	NUM
ejpam-6761	796	4	,	,	PUNCT
ejpam-6761	796	5	2025	2025	NUM
ejpam-6761	796	6	.	.	PUNCT
ejpam-6761	797	1	[	[	X
ejpam-6761	797	2	38	38	NUM
ejpam-6761	797	3	]	]	PUNCT
ejpam-6761	797	4	i.	i.	NOUN
ejpam-6761	797	5	senturk	senturk	PROPN
ejpam-6761	797	6	,	,	PUNCT
ejpam-6761	797	7	t.	t.	PROPN
ejpam-6761	797	8	oner	oner	PROPN
ejpam-6761	797	9	,	,	PUNCT
ejpam-6761	797	10	d.	d.	PROPN
ejpam-6761	797	11	s.	s.	PROPN
ejpam-6761	797	12	turan	turan	PROPN
ejpam-6761	797	13	,	,	PUNCT
ejpam-6761	797	14	g.	g.	PROPN
ejpam-6761	797	15	n.	n.	PROPN
ejpam-6761	797	16	gurbuz	gurbuz	PROPN
ejpam-6761	797	17	,	,	PUNCT
ejpam-6761	797	18	and	and	CCONJ
ejpam-6761	797	19	b.	b.	PROPN
ejpam-6761	797	20	ordin	ordin	PROPN
ejpam-6761	797	21	.	.	PUNCT
ejpam-6761	798	1	axiomatic	axiomatic	ADJ
ejpam-6761	798	2	analysis	analysis	NOUN
ejpam-6761	798	3	of	of	ADP
ejpam-6761	798	4	state	state	NOUN
ejpam-6761	798	5	operators	operator	NOUN
ejpam-6761	798	6	in	in	ADP
ejpam-6761	798	7	sheffer	sheffer	PROPN
ejpam-6761	798	8	stroke	stroke	NOUN
ejpam-6761	798	9	bck	bck	PROPN
ejpam-6761	798	10	-	-	PUNCT
ejpam-6761	798	11	algebras	algebras	PROPN
ejpam-6761	798	12	associated	associate	VERB
ejpam-6761	798	13	with	with	ADP
ejpam-6761	798	14	algorithmic	algorithmic	ADJ
ejpam-6761	798	15	approaches	approach	NOUN
ejpam-6761	798	16	.	.	PUNCT
ejpam-6761	799	1	aims	aim	VERB
ejpam-6761	799	2	mathematics	mathematic	NOUN
ejpam-6761	799	3	,	,	PUNCT
ejpam-6761	799	4	10(1):1555–1588	10(1):1555–1588	NUM
ejpam-6761	799	5	,	,	PUNCT
ejpam-6761	799	6	2025	2025	NUM
ejpam-6761	799	7	.	.	PUNCT