id	sid	tid	token	lemma	pos
ejpam-5536	1	1	european	european	PROPN
ejpam-5536	1	2	journal	journal	PROPN
ejpam-5536	1	3	of	of	ADP
ejpam-5536	1	4	pure	pure	ADJ
ejpam-5536	1	5	and	and	CCONJ
ejpam-5536	1	6	applied	apply	VERB
ejpam-5536	1	7	mathematics	mathematic	NOUN
ejpam-5536	1	8	vol	vol	NOUN
ejpam-5536	1	9	.	.	PROPN
ejpam-5536	2	1	17	17	NUM
ejpam-5536	2	2	,	,	PUNCT
ejpam-5536	2	3	no	no	INTJ
ejpam-5536	2	4	.	.	NOUN
ejpam-5536	2	5	4	4	NUM
ejpam-5536	2	6	,	,	PUNCT
ejpam-5536	2	7	2024	2024	NUM
ejpam-5536	2	8	,	,	PUNCT
ejpam-5536	2	9	4059	4059	NUM
ejpam-5536	2	10	-	-	SYM
ejpam-5536	2	11	4070	4070	NUM
ejpam-5536	2	12	issn	issn	PROPN
ejpam-5536	2	13	1307	1307	NUM
ejpam-5536	2	14	-	-	SYM
ejpam-5536	2	15	5543	5543	NUM
ejpam-5536	2	16	–	–	PUNCT
ejpam-5536	2	17	ejpam.com	ejpam.com	X
ejpam-5536	2	18	published	publish	VERB
ejpam-5536	2	19	by	by	ADP
ejpam-5536	2	20	new	new	PROPN
ejpam-5536	2	21	york	york	PROPN
ejpam-5536	2	22	business	business	PROPN
ejpam-5536	2	23	global	global	ADJ
ejpam-5536	2	24	translation	translation	NOUN
ejpam-5536	2	25	of	of	ADP
ejpam-5536	2	26	a	a	DET
ejpam-5536	2	27	bipolar	bipolar	ADJ
ejpam-5536	2	28	fuzzy	fuzzy	ADJ
ejpam-5536	2	29	set	set	NOUN
ejpam-5536	2	30	in	in	ADP
ejpam-5536	2	31	hilbert	hilbert	PROPN
ejpam-5536	2	32	algebras	algebras	PROPN
ejpam-5536	2	33	aiyared	aiyare	VERB
ejpam-5536	2	34	iampan1,∗	iampan1,∗	NOUN
ejpam-5536	2	35	,	,	PUNCT
ejpam-5536	2	36	neelamegarajan	neelamegarajan	NOUN
ejpam-5536	2	37	rajesh2	rajesh2	PROPN
ejpam-5536	2	38	,	,	PUNCT
ejpam-5536	2	39	j.	j.	PROPN
ejpam-5536	2	40	princivishvamalar2	princivishvamalar2	PROPN
ejpam-5536	2	41	,	,	PUNCT
ejpam-5536	2	42	c.	c.	PROPN
ejpam-5536	2	43	arivazhagi3	arivazhagi3	PROPN
ejpam-5536	2	44	1	1	NUM
ejpam-5536	2	45	department	department	NOUN
ejpam-5536	2	46	of	of	ADP
ejpam-5536	2	47	mathematics	mathematic	NOUN
ejpam-5536	2	48	,	,	PUNCT
ejpam-5536	2	49	school	school	NOUN
ejpam-5536	2	50	of	of	ADP
ejpam-5536	2	51	science	science	NOUN
ejpam-5536	2	52	,	,	PUNCT
ejpam-5536	2	53	university	university	NOUN
ejpam-5536	2	54	of	of	ADP
ejpam-5536	2	55	phayao	phayao	NOUN
ejpam-5536	2	56	,	,	PUNCT
ejpam-5536	2	57	mae	mae	PROPN
ejpam-5536	2	58	ka	ka	PROPN
ejpam-5536	2	59	,	,	PUNCT
ejpam-5536	2	60	mueang	mueang	PROPN
ejpam-5536	2	61	,	,	PUNCT
ejpam-5536	2	62	phayao	phayao	NOUN
ejpam-5536	2	63	56000	56000	NUM
ejpam-5536	2	64	,	,	PUNCT
ejpam-5536	2	65	thailand	thailand	PROPN
ejpam-5536	2	66	2	2	NUM
ejpam-5536	2	67	department	department	NOUN
ejpam-5536	2	68	of	of	ADP
ejpam-5536	2	69	mathematics	mathematic	NOUN
ejpam-5536	2	70	,	,	PUNCT
ejpam-5536	2	71	rajah	rajah	NOUN
ejpam-5536	2	72	serfoji	serfoji	ADJ
ejpam-5536	2	73	government	government	NOUN
ejpam-5536	2	74	college	college	NOUN
ejpam-5536	2	75	(	(	PUNCT
ejpam-5536	2	76	affiliated	affiliate	VERB
ejpam-5536	2	77	to	to	PART
ejpam-5536	2	78	bharathidasan	bharathidasan	VERB
ejpam-5536	2	79	university	university	NOUN
ejpam-5536	2	80	)	)	PUNCT
ejpam-5536	2	81	,	,	PUNCT
ejpam-5536	2	82	thanjavur-613005	thanjavur-613005	NOUN
ejpam-5536	2	83	,	,	PUNCT
ejpam-5536	2	84	tamilnadu	tamilnadu	ADJ
ejpam-5536	2	85	,	,	PUNCT
ejpam-5536	2	86	india	india	PROPN
ejpam-5536	2	87	3	3	PROPN
ejpam-5536	2	88	department	department	PROPN
ejpam-5536	2	89	of	of	ADP
ejpam-5536	2	90	mathematics	mathematic	NOUN
ejpam-5536	2	91	,	,	PUNCT
ejpam-5536	2	92	kunthavai	kunthavai	NOUN
ejpam-5536	2	93	naacchiyaar	naacchiyaar	PROPN
ejpam-5536	2	94	government	government	NOUN
ejpam-5536	2	95	arts	arts	PROPN
ejpam-5536	2	96	college	college	PROPN
ejpam-5536	2	97	for	for	ADP
ejpam-5536	2	98	women	woman	NOUN
ejpam-5536	2	99	(	(	PUNCT
ejpam-5536	2	100	autonomous	autonomous	ADJ
ejpam-5536	2	101	)	)	PUNCT
ejpam-5536	2	102	,	,	PUNCT
ejpam-5536	2	103	thanjavur-613007	thanjavur-613007	ADJ
ejpam-5536	2	104	,	,	PUNCT
ejpam-5536	2	105	tamilnadu	tamilnadu	ADJ
ejpam-5536	2	106	,	,	PUNCT
ejpam-5536	2	107	india	india	PROPN
ejpam-5536	2	108	abstract	abstract	NOUN
ejpam-5536	2	109	.	.	PUNCT
ejpam-5536	3	1	this	this	DET
ejpam-5536	3	2	study	study	NOUN
ejpam-5536	3	3	explores	explore	VERB
ejpam-5536	3	4	the	the	DET
ejpam-5536	3	5	application	application	NOUN
ejpam-5536	3	6	of	of	ADP
ejpam-5536	3	7	bipolar	bipolar	ADJ
ejpam-5536	3	8	fuzzy	fuzzy	ADJ
ejpam-5536	3	9	set	set	NOUN
ejpam-5536	3	10	theory	theory	NOUN
ejpam-5536	3	11	within	within	ADP
ejpam-5536	3	12	hilbert	hilbert	PROPN
ejpam-5536	3	13	algebras	algebras	PROPN
ejpam-5536	3	14	,	,	PUNCT
ejpam-5536	3	15	introducing	introduce	VERB
ejpam-5536	3	16	and	and	CCONJ
ejpam-5536	3	17	examining	examine	VERB
ejpam-5536	3	18	the	the	DET
ejpam-5536	3	19	concept	concept	NOUN
ejpam-5536	3	20	of	of	ADP
ejpam-5536	3	21	bipolar	bipolar	ADJ
ejpam-5536	3	22	fuzzy	fuzzy	ADJ
ejpam-5536	3	23	(	(	PUNCT
ejpam-5536	3	24	β	β	X
ejpam-5536	3	25	,	,	PUNCT
ejpam-5536	3	26	α)-translations	α)-translation	NOUN
ejpam-5536	3	27	of	of	ADP
ejpam-5536	3	28	a	a	DET
ejpam-5536	3	29	bipolar	bipolar	ADJ
ejpam-5536	3	30	fuzzy	fuzzy	NOUN
ejpam-5536	3	31	set	set	VERB
ejpam-5536	3	32	φ	φ	PROPN
ejpam-5536	3	33	=	=	SYM
ejpam-5536	3	34	(	(	PUNCT
ejpam-5536	3	35	φ+	φ+	NOUN
ejpam-5536	3	36	,	,	PUNCT
ejpam-5536	3	37	φ−	φ−	PROPN
ejpam-5536	3	38	)	)	PUNCT
ejpam-5536	3	39	in	in	ADP
ejpam-5536	3	40	two	two	NUM
ejpam-5536	3	41	distinct	distinct	ADJ
ejpam-5536	3	42	forms	form	NOUN
ejpam-5536	3	43	:	:	PUNCT
ejpam-5536	3	44	type	type	NOUN
ejpam-5536	3	45	i	i	PRON
ejpam-5536	3	46	and	and	CCONJ
ejpam-5536	3	47	type	type	PROPN
ejpam-5536	3	48	ii	ii	PROPN
ejpam-5536	3	49	.	.	PUNCT
ejpam-5536	4	1	fundamental	fundamental	ADJ
ejpam-5536	4	2	properties	property	NOUN
ejpam-5536	4	3	of	of	ADP
ejpam-5536	4	4	these	these	DET
ejpam-5536	4	5	bipolar	bipolar	ADJ
ejpam-5536	4	6	fuzzy	fuzzy	ADJ
ejpam-5536	4	7	translations	translation	NOUN
ejpam-5536	4	8	are	be	AUX
ejpam-5536	4	9	investigated	investigate	VERB
ejpam-5536	4	10	in	in	ADP
ejpam-5536	4	11	depth	depth	NOUN
ejpam-5536	4	12	,	,	PUNCT
ejpam-5536	4	13	alongside	alongside	ADP
ejpam-5536	4	14	the	the	DET
ejpam-5536	4	15	introduction	introduction	NOUN
ejpam-5536	4	16	of	of	ADP
ejpam-5536	4	17	bipolar	bipolar	ADJ
ejpam-5536	4	18	fuzzy	fuzzy	ADJ
ejpam-5536	4	19	extensions	extension	NOUN
ejpam-5536	4	20	and	and	CCONJ
ejpam-5536	4	21	intensities	intensity	NOUN
ejpam-5536	4	22	,	,	PUNCT
ejpam-5536	4	23	broadening	broaden	VERB
ejpam-5536	4	24	the	the	DET
ejpam-5536	4	25	utility	utility	NOUN
ejpam-5536	4	26	and	and	CCONJ
ejpam-5536	4	27	flexibility	flexibility	NOUN
ejpam-5536	4	28	of	of	ADP
ejpam-5536	4	29	bipolar	bipolar	ADJ
ejpam-5536	4	30	fuzzy	fuzzy	ADJ
ejpam-5536	4	31	sets	set	NOUN
ejpam-5536	4	32	in	in	ADP
ejpam-5536	4	33	capturing	capture	VERB
ejpam-5536	4	34	nuanced	nuanced	ADJ
ejpam-5536	4	35	bipolar	bipolar	ADJ
ejpam-5536	4	36	information	information	NOUN
ejpam-5536	4	37	.	.	PUNCT
ejpam-5536	5	1	moreover	moreover	ADV
ejpam-5536	5	2	,	,	PUNCT
ejpam-5536	5	3	this	this	DET
ejpam-5536	5	4	work	work	NOUN
ejpam-5536	5	5	addresses	address	VERB
ejpam-5536	5	6	the	the	DET
ejpam-5536	5	7	intricate	intricate	ADJ
ejpam-5536	5	8	relationships	relationship	NOUN
ejpam-5536	5	9	between	between	ADP
ejpam-5536	5	10	the	the	DET
ejpam-5536	5	11	complement	complement	NOUN
ejpam-5536	5	12	of	of	ADP
ejpam-5536	5	13	a	a	DET
ejpam-5536	5	14	bipolar	bipolar	ADJ
ejpam-5536	5	15	fuzzy	fuzzy	ADJ
ejpam-5536	5	16	subalgebra	subalgebra	NOUN
ejpam-5536	5	17	,	,	PUNCT
ejpam-5536	5	18	bipolar	bipolar	ADJ
ejpam-5536	5	19	fuzzy	fuzzy	ADJ
ejpam-5536	5	20	ideal	ideal	NOUN
ejpam-5536	5	21	,	,	PUNCT
ejpam-5536	5	22	and	and	CCONJ
ejpam-5536	5	23	bipolar	bipolar	ADJ
ejpam-5536	5	24	fuzzy	fuzzy	ADJ
ejpam-5536	5	25	deductive	deductive	ADJ
ejpam-5536	5	26	system	system	NOUN
ejpam-5536	5	27	with	with	ADP
ejpam-5536	5	28	respect	respect	NOUN
ejpam-5536	5	29	to	to	ADP
ejpam-5536	5	30	their	their	PRON
ejpam-5536	5	31	level	level	NOUN
ejpam-5536	5	32	cuts	cut	NOUN
ejpam-5536	5	33	.	.	PUNCT
ejpam-5536	6	1	the	the	DET
ejpam-5536	6	2	findings	finding	NOUN
ejpam-5536	6	3	significantly	significantly	ADV
ejpam-5536	6	4	contribute	contribute	VERB
ejpam-5536	6	5	to	to	ADP
ejpam-5536	6	6	the	the	DET
ejpam-5536	6	7	broader	broad	ADJ
ejpam-5536	6	8	theoretical	theoretical	ADJ
ejpam-5536	6	9	foundation	foundation	NOUN
ejpam-5536	6	10	and	and	CCONJ
ejpam-5536	6	11	potential	potential	ADJ
ejpam-5536	6	12	applications	application	NOUN
ejpam-5536	6	13	of	of	ADP
ejpam-5536	6	14	bipolar	bipolar	ADJ
ejpam-5536	6	15	fuzzy	fuzzy	ADJ
ejpam-5536	6	16	logic	logic	NOUN
ejpam-5536	6	17	in	in	ADP
ejpam-5536	6	18	hilbert	hilbert	PROPN
ejpam-5536	6	19	algebras	algebras	PROPN
ejpam-5536	6	20	,	,	PUNCT
ejpam-5536	6	21	offering	offer	VERB
ejpam-5536	6	22	valuable	valuable	ADJ
ejpam-5536	6	23	insights	insight	NOUN
ejpam-5536	6	24	for	for	ADP
ejpam-5536	6	25	managing	manage	VERB
ejpam-5536	6	26	complex	complex	ADJ
ejpam-5536	6	27	bipolar	bipolar	ADJ
ejpam-5536	6	28	information	information	NOUN
ejpam-5536	6	29	in	in	ADP
ejpam-5536	6	30	uncertain	uncertain	ADJ
ejpam-5536	6	31	environments	environment	NOUN
ejpam-5536	6	32	.	.	PUNCT
ejpam-5536	7	1	2020	2020	NUM
ejpam-5536	7	2	mathematics	mathematic	NOUN
ejpam-5536	7	3	subject	subject	NOUN
ejpam-5536	7	4	classifications	classification	NOUN
ejpam-5536	7	5	:	:	PUNCT
ejpam-5536	7	6	03g25	03g25	NUM
ejpam-5536	7	7	,	,	PUNCT
ejpam-5536	7	8	03e72	03e72	AUX
ejpam-5536	7	9	key	key	ADJ
ejpam-5536	7	10	words	word	NOUN
ejpam-5536	7	11	and	and	CCONJ
ejpam-5536	7	12	phrases	phrase	NOUN
ejpam-5536	7	13	:	:	PUNCT
ejpam-5536	7	14	hilbert	hilbert	NOUN
ejpam-5536	7	15	algebra	algebra	PROPN
ejpam-5536	7	16	,	,	PUNCT
ejpam-5536	7	17	bipolar	bipolar	ADJ
ejpam-5536	7	18	fuzzy	fuzzy	ADJ
ejpam-5536	7	19	subalgebra	subalgebra	NOUN
ejpam-5536	7	20	,	,	PUNCT
ejpam-5536	7	21	bipolar	bipolar	ADJ
ejpam-5536	7	22	fuzzy	fuzzy	ADJ
ejpam-5536	7	23	ideal	ideal	NOUN
ejpam-5536	7	24	,	,	PUNCT
ejpam-5536	7	25	bipolar	bipolar	ADJ
ejpam-5536	7	26	fuzzy	fuzzy	ADJ
ejpam-5536	7	27	deductive	deductive	ADJ
ejpam-5536	7	28	system	system	NOUN
ejpam-5536	7	29	.	.	PUNCT
ejpam-5536	8	1	1	1	X
ejpam-5536	8	2	.	.	X
ejpam-5536	8	3	introduction	introduction	NOUN
ejpam-5536	8	4	the	the	DET
ejpam-5536	8	5	concept	concept	NOUN
ejpam-5536	8	6	of	of	ADP
ejpam-5536	8	7	fuzzy	fuzzy	ADJ
ejpam-5536	8	8	sets	set	NOUN
ejpam-5536	8	9	was	be	AUX
ejpam-5536	8	10	proposed	propose	VERB
ejpam-5536	8	11	by	by	ADP
ejpam-5536	8	12	zadeh	zadeh	PROPN
ejpam-5536	9	1	[	[	X
ejpam-5536	9	2	19	19	NUM
ejpam-5536	9	3	]	]	PUNCT
ejpam-5536	9	4	.	.	PUNCT
ejpam-5536	10	1	the	the	DET
ejpam-5536	10	2	theory	theory	NOUN
ejpam-5536	10	3	of	of	ADP
ejpam-5536	10	4	fuzzy	fuzzy	ADJ
ejpam-5536	10	5	sets	set	NOUN
ejpam-5536	10	6	has	have	VERB
ejpam-5536	10	7	several	several	ADJ
ejpam-5536	10	8	applications	application	NOUN
ejpam-5536	10	9	in	in	ADP
ejpam-5536	10	10	real	real	ADJ
ejpam-5536	10	11	-	-	PUNCT
ejpam-5536	10	12	life	life	NOUN
ejpam-5536	10	13	situations	situation	NOUN
ejpam-5536	10	14	,	,	PUNCT
ejpam-5536	10	15	and	and	CCONJ
ejpam-5536	10	16	many	many	ADJ
ejpam-5536	10	17	scholars	scholar	NOUN
ejpam-5536	10	18	have	have	AUX
ejpam-5536	10	19	researched	research	VERB
ejpam-5536	10	20	fuzzy	fuzzy	ADJ
ejpam-5536	10	21	set	set	NOUN
ejpam-5536	10	22	theory	theory	NOUN
ejpam-5536	10	23	.	.	PUNCT
ejpam-5536	11	1	after	after	ADP
ejpam-5536	11	2	introducing	introduce	VERB
ejpam-5536	11	3	the	the	DET
ejpam-5536	11	4	concept	concept	NOUN
ejpam-5536	11	5	of	of	ADP
ejpam-5536	11	6	fuzzy	fuzzy	ADJ
ejpam-5536	11	7	sets	set	NOUN
ejpam-5536	11	8	,	,	PUNCT
ejpam-5536	11	9	several	several	ADJ
ejpam-5536	11	10	research	research	NOUN
ejpam-5536	11	11	studies	study	NOUN
ejpam-5536	11	12	were	be	AUX
ejpam-5536	11	13	conducted	conduct	VERB
ejpam-5536	11	14	on	on	ADP
ejpam-5536	11	15	the	the	DET
ejpam-5536	11	16	generalizations	generalization	NOUN
ejpam-5536	11	17	of	of	ADP
ejpam-5536	11	18	fuzzy	fuzzy	ADJ
ejpam-5536	11	19	sets	set	NOUN
ejpam-5536	11	20	.	.	PUNCT
ejpam-5536	12	1	in	in	ADP
ejpam-5536	12	2	1994	1994	NUM
ejpam-5536	12	3	,	,	PUNCT
ejpam-5536	12	4	zhang	zhang	PROPN
ejpam-5536	13	1	[	[	X
ejpam-5536	13	2	21	21	NUM
ejpam-5536	13	3	]	]	PUNCT
ejpam-5536	13	4	initiated	initiate	VERB
ejpam-5536	13	5	the	the	DET
ejpam-5536	13	6	concept	concept	NOUN
ejpam-5536	13	7	of	of	ADP
ejpam-5536	13	8	bipolar	bipolar	ADJ
ejpam-5536	13	9	fuzzy	fuzzy	ADJ
ejpam-5536	13	10	sets	set	NOUN
ejpam-5536	13	11	(	(	PUNCT
ejpam-5536	13	12	bfss	bfss	NOUN
ejpam-5536	13	13	)	)	PUNCT
ejpam-5536	13	14	as	as	ADP
ejpam-5536	13	15	a	a	DET
ejpam-5536	13	16	generalization	generalization	NOUN
ejpam-5536	13	17	of	of	ADP
ejpam-5536	13	18	fuzzy	fuzzy	ADJ
ejpam-5536	13	19	sets	set	NOUN
ejpam-5536	13	20	.	.	PUNCT
ejpam-5536	14	1	bfss	bfss	NOUN
ejpam-5536	14	2	are	be	AUX
ejpam-5536	14	3	an	an	DET
ejpam-5536	14	4	extension	extension	NOUN
ejpam-5536	14	5	of	of	ADP
ejpam-5536	14	6	fuzzy	fuzzy	ADJ
ejpam-5536	14	7	sets	set	NOUN
ejpam-5536	14	8	whose	whose	DET
ejpam-5536	14	9	membership	membership	NOUN
ejpam-5536	14	10	degree	degree	NOUN
ejpam-5536	14	11	range	range	NOUN
ejpam-5536	14	12	is	be	AUX
ejpam-5536	14	13	[	[	X
ejpam-5536	14	14	−1	−1	NOUN
ejpam-5536	14	15	,	,	PUNCT
ejpam-5536	14	16	1	1	NUM
ejpam-5536	14	17	]	]	PUNCT
ejpam-5536	14	18	.	.	PUNCT
ejpam-5536	15	1	in	in	ADP
ejpam-5536	15	2	a	a	DET
ejpam-5536	15	3	bfs	bfs	NOUN
ejpam-5536	15	4	,	,	PUNCT
ejpam-5536	15	5	the	the	DET
ejpam-5536	15	6	membership	membership	NOUN
ejpam-5536	15	7	degree	degree	NOUN
ejpam-5536	15	8	0	0	NUM
ejpam-5536	15	9	of	of	ADP
ejpam-5536	15	10	an	an	DET
ejpam-5536	15	11	element	element	NOUN
ejpam-5536	15	12	means	mean	VERB
ejpam-5536	15	13	that	that	SCONJ
ejpam-5536	15	14	the	the	DET
ejpam-5536	15	15	element	element	NOUN
ejpam-5536	15	16	is	be	AUX
ejpam-5536	15	17	irrelevant	irrelevant	ADJ
ejpam-5536	15	18	to	to	ADP
ejpam-5536	15	19	the	the	DET
ejpam-5536	15	20	corresponding	corresponding	ADJ
ejpam-5536	15	21	property	property	NOUN
ejpam-5536	15	22	,	,	PUNCT
ejpam-5536	15	23	the	the	DET
ejpam-5536	15	24	membership	membership	NOUN
ejpam-5536	15	25	degree	degree	NOUN
ejpam-5536	15	26	(	(	PUNCT
ejpam-5536	15	27	0	0	NUM
ejpam-5536	15	28	,	,	PUNCT
ejpam-5536	15	29	1	1	NUM
ejpam-5536	15	30	]	]	PUNCT
ejpam-5536	15	31	of	of	ADP
ejpam-5536	15	32	an	an	DET
ejpam-5536	15	33	element	element	NOUN
ejpam-5536	15	34	indicates	indicate	VERB
ejpam-5536	15	35	that	that	SCONJ
ejpam-5536	15	36	the	the	DET
ejpam-5536	15	37	element	element	NOUN
ejpam-5536	15	38	somewhat	somewhat	ADV
ejpam-5536	15	39	satisfies	satisfy	VERB
ejpam-5536	15	40	the	the	DET
ejpam-5536	15	41	∗corresponding	∗corresponding	NOUN
ejpam-5536	15	42	author	author	NOUN
ejpam-5536	15	43	.	.	PUNCT
ejpam-5536	16	1	doi	doi	NOUN
ejpam-5536	16	2	:	:	PUNCT
ejpam-5536	16	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5536	https://doi.org/10.29020/nybg.ejpam.v17i4.5536	VERB
ejpam-5536	16	4	email	email	NOUN
ejpam-5536	16	5	addresses	address	NOUN
ejpam-5536	16	6	:	:	PUNCT
ejpam-5536	16	7	aiyared.ia@up.ac.th	aiyared.ia@up.ac.th	NOUN
ejpam-5536	16	8	(	(	PUNCT
ejpam-5536	16	9	a.	a.	NOUN
ejpam-5536	16	10	iampan	iampan	PROPN
ejpam-5536	16	11	)	)	PUNCT
ejpam-5536	16	12	,	,	PUNCT
ejpam-5536	16	13	nrajesh	nrajesh	PROPN
ejpam-5536	16	14	topology@yahoo.co.in	topology@yahoo.co.in	PROPN
ejpam-5536	16	15	(	(	PUNCT
ejpam-5536	16	16	n.	n.	PROPN
ejpam-5536	16	17	rajesh	rajesh	PROPN
ejpam-5536	16	18	)	)	PUNCT
ejpam-5536	16	19	,	,	PUNCT
ejpam-5536	16	20	mathsprincy@gmail.com	mathsprincy@gmail.com	PROPN
ejpam-5536	16	21	(	(	PUNCT
ejpam-5536	16	22	j.	j.	PROPN
ejpam-5536	16	23	princivishvamalar	princivishvamalar	PROPN
ejpam-5536	16	24	)	)	PUNCT
ejpam-5536	16	25	,	,	PUNCT
ejpam-5536	16	26	arivuniralya@gmail.com	arivuniralya@gmail.com	X
ejpam-5536	16	27	(	(	PUNCT
ejpam-5536	16	28	c.	c.	PROPN
ejpam-5536	16	29	arivazhagi	arivazhagi	PROPN
ejpam-5536	16	30	)	)	PUNCT
ejpam-5536	16	31	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5536	16	32	4059	4059	NUM
ejpam-5536	17	1	copyright	copyright	NOUN
ejpam-5536	17	2	:	:	PUNCT
ejpam-5536	17	3	©	©	PROPN
ejpam-5536	17	4	2024	2024	NUM
ejpam-5536	17	5	the	the	DET
ejpam-5536	17	6	author(s	author(s	NOUN
ejpam-5536	17	7	)	)	PUNCT
ejpam-5536	17	8	.	.	PUNCT
ejpam-5536	18	1	(	(	PUNCT
ejpam-5536	18	2	cc	cc	NOUN
ejpam-5536	18	3	by	by	ADP
ejpam-5536	18	4	-	-	PUNCT
ejpam-5536	18	5	nc	nc	PROPN
ejpam-5536	18	6	4.0	4.0	NUM
ejpam-5536	18	7	)	)	PUNCT
ejpam-5536	18	8	a.	a.	NOUN
ejpam-5536	18	9	iampan	iampan	NOUN
ejpam-5536	18	10	et	et	PROPN
ejpam-5536	18	11	al	al	PROPN
ejpam-5536	18	12	.	.	PUNCT
ejpam-5536	18	13	/	/	SYM
ejpam-5536	18	14	eur	eur	PROPN
ejpam-5536	18	15	.	.	PUNCT
ejpam-5536	19	1	j.	j.	PROPN
ejpam-5536	19	2	pure	pure	PROPN
ejpam-5536	19	3	appl	appl	PROPN
ejpam-5536	19	4	.	.	PROPN
ejpam-5536	19	5	math	math	PROPN
ejpam-5536	19	6	,	,	PUNCT
ejpam-5536	19	7	17	17	NUM
ejpam-5536	19	8	(	(	PUNCT
ejpam-5536	19	9	4	4	NUM
ejpam-5536	19	10	)	)	PUNCT
ejpam-5536	19	11	(	(	PUNCT
ejpam-5536	19	12	2024	2024	NUM
ejpam-5536	19	13	)	)	PUNCT
ejpam-5536	19	14	,	,	PUNCT
ejpam-5536	19	15	4059	4059	NUM
ejpam-5536	19	16	-	-	SYM
ejpam-5536	19	17	4070	4070	NUM
ejpam-5536	19	18	4060	4060	NUM
ejpam-5536	19	19	property	property	NOUN
ejpam-5536	19	20	,	,	PUNCT
ejpam-5536	19	21	and	and	CCONJ
ejpam-5536	19	22	the	the	DET
ejpam-5536	19	23	membership	membership	NOUN
ejpam-5536	19	24	degree	degree	NOUN
ejpam-5536	20	1	[	[	X
ejpam-5536	20	2	−1	−1	NOUN
ejpam-5536	20	3	,	,	PUNCT
ejpam-5536	20	4	0	0	NUM
ejpam-5536	20	5	)	)	PUNCT
ejpam-5536	20	6	of	of	ADP
ejpam-5536	20	7	an	an	DET
ejpam-5536	20	8	element	element	NOUN
ejpam-5536	20	9	indicates	indicate	VERB
ejpam-5536	20	10	that	that	SCONJ
ejpam-5536	20	11	the	the	DET
ejpam-5536	20	12	element	element	NOUN
ejpam-5536	20	13	somewhat	somewhat	ADV
ejpam-5536	20	14	satisfies	satisfy	VERB
ejpam-5536	20	15	the	the	DET
ejpam-5536	20	16	implicit	implicit	ADJ
ejpam-5536	20	17	counter	counter	NOUN
ejpam-5536	20	18	-	-	NOUN
ejpam-5536	20	19	property	property	NOUN
ejpam-5536	20	20	.	.	PUNCT
ejpam-5536	21	1	although	although	SCONJ
ejpam-5536	21	2	bfss	bfss	NUM
ejpam-5536	21	3	and	and	CCONJ
ejpam-5536	21	4	intuitionistic	intuitionistic	ADJ
ejpam-5536	21	5	fuzzy	fuzzy	ADJ
ejpam-5536	21	6	sets	set	NOUN
ejpam-5536	21	7	[	[	X
ejpam-5536	21	8	2	2	NUM
ejpam-5536	21	9	]	]	PUNCT
ejpam-5536	21	10	look	look	VERB
ejpam-5536	21	11	similar	similar	ADJ
ejpam-5536	21	12	to	to	ADP
ejpam-5536	21	13	each	each	DET
ejpam-5536	21	14	other	other	ADJ
ejpam-5536	21	15	,	,	PUNCT
ejpam-5536	21	16	they	they	PRON
ejpam-5536	21	17	are	be	AUX
ejpam-5536	21	18	essentially	essentially	ADV
ejpam-5536	21	19	different	different	ADJ
ejpam-5536	21	20	sets	set	NOUN
ejpam-5536	21	21	.	.	PUNCT
ejpam-5536	22	1	in	in	ADP
ejpam-5536	22	2	many	many	ADJ
ejpam-5536	22	3	domains	domain	NOUN
ejpam-5536	22	4	,	,	PUNCT
ejpam-5536	22	5	it	it	PRON
ejpam-5536	22	6	is	be	AUX
ejpam-5536	22	7	important	important	ADJ
ejpam-5536	22	8	to	to	PART
ejpam-5536	22	9	be	be	AUX
ejpam-5536	22	10	able	able	ADJ
ejpam-5536	22	11	to	to	PART
ejpam-5536	22	12	deal	deal	VERB
ejpam-5536	22	13	with	with	ADP
ejpam-5536	22	14	bipolar	bipolar	ADJ
ejpam-5536	22	15	information	information	NOUN
ejpam-5536	22	16	.	.	PUNCT
ejpam-5536	23	1	it	it	PRON
ejpam-5536	23	2	is	be	AUX
ejpam-5536	23	3	noted	note	VERB
ejpam-5536	23	4	that	that	SCONJ
ejpam-5536	23	5	positive	positive	ADJ
ejpam-5536	23	6	information	information	NOUN
ejpam-5536	23	7	represents	represent	VERB
ejpam-5536	23	8	what	what	PRON
ejpam-5536	23	9	is	be	AUX
ejpam-5536	23	10	granted	grant	VERB
ejpam-5536	23	11	to	to	PART
ejpam-5536	23	12	be	be	AUX
ejpam-5536	23	13	possible	possible	ADJ
ejpam-5536	23	14	,	,	PUNCT
ejpam-5536	23	15	while	while	SCONJ
ejpam-5536	23	16	negative	negative	ADJ
ejpam-5536	23	17	information	information	NOUN
ejpam-5536	23	18	represents	represent	VERB
ejpam-5536	23	19	what	what	PRON
ejpam-5536	23	20	is	be	AUX
ejpam-5536	23	21	considered	consider	VERB
ejpam-5536	23	22	to	to	PART
ejpam-5536	23	23	be	be	AUX
ejpam-5536	23	24	impossible	impossible	ADJ
ejpam-5536	23	25	.	.	PUNCT
ejpam-5536	24	1	this	this	DET
ejpam-5536	24	2	domain	domain	NOUN
ejpam-5536	24	3	has	have	AUX
ejpam-5536	24	4	recently	recently	ADV
ejpam-5536	24	5	motivated	motivate	VERB
ejpam-5536	24	6	new	new	ADJ
ejpam-5536	24	7	research	research	NOUN
ejpam-5536	24	8	in	in	ADP
ejpam-5536	24	9	several	several	ADJ
ejpam-5536	24	10	directions	direction	NOUN
ejpam-5536	24	11	.	.	PUNCT
ejpam-5536	25	1	in	in	ADP
ejpam-5536	25	2	particular	particular	ADJ
ejpam-5536	25	3	,	,	PUNCT
ejpam-5536	25	4	fuzzy	fuzzy	ADJ
ejpam-5536	25	5	and	and	CCONJ
ejpam-5536	25	6	probabilistic	probabilistic	ADJ
ejpam-5536	25	7	formalisms	formalism	NOUN
ejpam-5536	25	8	for	for	ADP
ejpam-5536	25	9	bipolar	bipolar	ADJ
ejpam-5536	25	10	information	information	NOUN
ejpam-5536	25	11	have	have	AUX
ejpam-5536	25	12	been	be	AUX
ejpam-5536	25	13	proposed	propose	VERB
ejpam-5536	25	14	because	because	SCONJ
ejpam-5536	25	15	when	when	SCONJ
ejpam-5536	25	16	we	we	PRON
ejpam-5536	25	17	deal	deal	VERB
ejpam-5536	25	18	with	with	ADP
ejpam-5536	25	19	spatial	spatial	ADJ
ejpam-5536	25	20	information	information	NOUN
ejpam-5536	25	21	in	in	ADP
ejpam-5536	25	22	image	image	NOUN
ejpam-5536	25	23	processing	processing	NOUN
ejpam-5536	25	24	or	or	CCONJ
ejpam-5536	25	25	in	in	ADP
ejpam-5536	25	26	spatial	spatial	ADJ
ejpam-5536	25	27	reasoning	reasoning	NOUN
ejpam-5536	25	28	applications	application	NOUN
ejpam-5536	25	29	,	,	PUNCT
ejpam-5536	25	30	this	this	DET
ejpam-5536	25	31	bipolarity	bipolarity	NOUN
ejpam-5536	25	32	also	also	ADV
ejpam-5536	25	33	occurs	occur	VERB
ejpam-5536	25	34	.	.	PUNCT
ejpam-5536	26	1	for	for	ADP
ejpam-5536	26	2	instance	instance	NOUN
ejpam-5536	26	3	,	,	PUNCT
ejpam-5536	26	4	when	when	SCONJ
ejpam-5536	26	5	we	we	PRON
ejpam-5536	26	6	assess	assess	VERB
ejpam-5536	26	7	the	the	DET
ejpam-5536	26	8	position	position	NOUN
ejpam-5536	26	9	of	of	ADP
ejpam-5536	26	10	an	an	DET
ejpam-5536	26	11	object	object	NOUN
ejpam-5536	26	12	in	in	ADP
ejpam-5536	26	13	a	a	DET
ejpam-5536	26	14	space	space	NOUN
ejpam-5536	26	15	,	,	PUNCT
ejpam-5536	26	16	we	we	PRON
ejpam-5536	26	17	may	may	AUX
ejpam-5536	26	18	have	have	VERB
ejpam-5536	26	19	positive	positive	ADJ
ejpam-5536	26	20	information	information	NOUN
ejpam-5536	26	21	expressed	express	VERB
ejpam-5536	26	22	as	as	ADP
ejpam-5536	26	23	a	a	DET
ejpam-5536	26	24	set	set	NOUN
ejpam-5536	26	25	of	of	ADP
ejpam-5536	26	26	possible	possible	ADJ
ejpam-5536	26	27	places	place	NOUN
ejpam-5536	26	28	and	and	CCONJ
ejpam-5536	26	29	negative	negative	ADJ
ejpam-5536	26	30	information	information	NOUN
ejpam-5536	26	31	expressed	express	VERB
ejpam-5536	26	32	as	as	ADP
ejpam-5536	26	33	a	a	DET
ejpam-5536	26	34	set	set	NOUN
ejpam-5536	26	35	of	of	ADP
ejpam-5536	26	36	impossible	impossible	ADJ
ejpam-5536	26	37	places	place	NOUN
ejpam-5536	26	38	.	.	PUNCT
ejpam-5536	27	1	as	as	ADP
ejpam-5536	27	2	another	another	DET
ejpam-5536	27	3	example	example	NOUN
ejpam-5536	27	4	,	,	PUNCT
ejpam-5536	27	5	let	let	VERB
ejpam-5536	27	6	us	we	PRON
ejpam-5536	27	7	consider	consider	VERB
ejpam-5536	27	8	the	the	DET
ejpam-5536	27	9	spatial	spatial	ADJ
ejpam-5536	27	10	relations	relation	NOUN
ejpam-5536	27	11	.	.	PUNCT
ejpam-5536	28	1	human	human	ADJ
ejpam-5536	28	2	beings	being	NOUN
ejpam-5536	28	3	consider	consider	VERB
ejpam-5536	28	4	“	"	PUNCT
ejpam-5536	28	5	left	leave	VERB
ejpam-5536	28	6	”	"	PUNCT
ejpam-5536	28	7	and	and	CCONJ
ejpam-5536	28	8	“	"	PUNCT
ejpam-5536	28	9	right	right	ADJ
ejpam-5536	28	10	”	"	PUNCT
ejpam-5536	28	11	in	in	ADP
ejpam-5536	28	12	opposite	opposite	ADJ
ejpam-5536	28	13	directions	direction	NOUN
ejpam-5536	28	14	.	.	PUNCT
ejpam-5536	29	1	but	but	CCONJ
ejpam-5536	29	2	this	this	PRON
ejpam-5536	29	3	does	do	AUX
ejpam-5536	29	4	not	not	PART
ejpam-5536	29	5	mean	mean	VERB
ejpam-5536	29	6	that	that	SCONJ
ejpam-5536	29	7	one	one	NUM
ejpam-5536	29	8	of	of	ADP
ejpam-5536	29	9	them	they	PRON
ejpam-5536	29	10	is	be	AUX
ejpam-5536	29	11	the	the	DET
ejpam-5536	29	12	negation	negation	NOUN
ejpam-5536	29	13	of	of	ADP
ejpam-5536	29	14	the	the	DET
ejpam-5536	29	15	other	other	ADJ
ejpam-5536	29	16	.	.	PUNCT
ejpam-5536	30	1	the	the	DET
ejpam-5536	30	2	semantics	semantic	NOUN
ejpam-5536	30	3	of	of	ADP
ejpam-5536	30	4	“	"	PUNCT
ejpam-5536	30	5	opposite	opposite	ADJ
ejpam-5536	30	6	”	"	PUNCT
ejpam-5536	30	7	capture	capture	NOUN
ejpam-5536	30	8	a	a	DET
ejpam-5536	30	9	notion	notion	NOUN
ejpam-5536	30	10	of	of	ADP
ejpam-5536	30	11	symmetry	symmetry	NOUN
ejpam-5536	30	12	rather	rather	ADV
ejpam-5536	30	13	than	than	ADP
ejpam-5536	30	14	a	a	DET
ejpam-5536	30	15	strict	strict	ADJ
ejpam-5536	30	16	complementation	complementation	NOUN
ejpam-5536	30	17	.	.	PUNCT
ejpam-5536	31	1	in	in	ADP
ejpam-5536	31	2	particular	particular	ADJ
ejpam-5536	31	3	,	,	PUNCT
ejpam-5536	31	4	there	there	PRON
ejpam-5536	31	5	may	may	AUX
ejpam-5536	31	6	be	be	AUX
ejpam-5536	31	7	positions	position	NOUN
ejpam-5536	31	8	considered	consider	VERB
ejpam-5536	31	9	neither	neither	CCONJ
ejpam-5536	31	10	to	to	ADP
ejpam-5536	31	11	the	the	DET
ejpam-5536	31	12	right	right	NOUN
ejpam-5536	31	13	nor	nor	CCONJ
ejpam-5536	31	14	to	to	ADP
ejpam-5536	31	15	the	the	DET
ejpam-5536	31	16	left	left	NOUN
ejpam-5536	31	17	of	of	ADP
ejpam-5536	31	18	some	some	DET
ejpam-5536	31	19	reference	reference	NOUN
ejpam-5536	31	20	object	object	NOUN
ejpam-5536	31	21	,	,	PUNCT
ejpam-5536	31	22	thus	thus	ADV
ejpam-5536	31	23	leaving	leave	VERB
ejpam-5536	31	24	some	some	DET
ejpam-5536	31	25	room	room	NOUN
ejpam-5536	31	26	for	for	ADP
ejpam-5536	31	27	indetermination	indetermination	NOUN
ejpam-5536	31	28	.	.	PUNCT
ejpam-5536	32	1	this	this	PRON
ejpam-5536	32	2	corresponds	correspond	VERB
ejpam-5536	32	3	to	to	ADP
ejpam-5536	32	4	the	the	DET
ejpam-5536	32	5	idea	idea	NOUN
ejpam-5536	32	6	that	that	SCONJ
ejpam-5536	32	7	the	the	DET
ejpam-5536	32	8	union	union	NOUN
ejpam-5536	32	9	of	of	ADP
ejpam-5536	32	10	positive	positive	ADJ
ejpam-5536	32	11	and	and	CCONJ
ejpam-5536	32	12	negative	negative	ADJ
ejpam-5536	32	13	information	information	NOUN
ejpam-5536	32	14	does	do	AUX
ejpam-5536	32	15	not	not	PART
ejpam-5536	32	16	cover	cover	VERB
ejpam-5536	32	17	the	the	DET
ejpam-5536	32	18	whole	whole	ADJ
ejpam-5536	32	19	space	space	NOUN
ejpam-5536	32	20	.	.	PUNCT
ejpam-5536	33	1	the	the	DET
ejpam-5536	33	2	development	development	NOUN
ejpam-5536	33	3	of	of	ADP
ejpam-5536	33	4	bfs	bfs	NOUN
ejpam-5536	33	5	theory	theory	NOUN
ejpam-5536	33	6	has	have	AUX
ejpam-5536	33	7	seen	see	VERB
ejpam-5536	33	8	continuous	continuous	ADJ
ejpam-5536	33	9	advancements	advancement	NOUN
ejpam-5536	33	10	,	,	PUNCT
ejpam-5536	33	11	particularly	particularly	ADV
ejpam-5536	33	12	in	in	ADP
ejpam-5536	33	13	its	its	PRON
ejpam-5536	33	14	expansion	expansion	NOUN
ejpam-5536	33	15	to	to	PART
ejpam-5536	33	16	complex	complex	ADJ
ejpam-5536	33	17	algebraic	algebraic	ADJ
ejpam-5536	33	18	structures	structure	NOUN
ejpam-5536	33	19	and	and	CCONJ
ejpam-5536	33	20	applications	application	NOUN
ejpam-5536	33	21	in	in	ADP
ejpam-5536	33	22	managing	manage	VERB
ejpam-5536	33	23	nuanced	nuanced	ADJ
ejpam-5536	33	24	uncertainties	uncertainty	NOUN
ejpam-5536	33	25	.	.	PUNCT
ejpam-5536	34	1	recent	recent	ADJ
ejpam-5536	34	2	works	work	NOUN
ejpam-5536	34	3	,	,	PUNCT
ejpam-5536	34	4	such	such	ADJ
ejpam-5536	34	5	as	as	ADP
ejpam-5536	34	6	those	those	PRON
ejpam-5536	34	7	in	in	ADP
ejpam-5536	34	8	[	[	X
ejpam-5536	34	9	1	1	NUM
ejpam-5536	34	10	,	,	PUNCT
ejpam-5536	34	11	14–16	14–16	NUM
ejpam-5536	34	12	,	,	PUNCT
ejpam-5536	34	13	18	18	NUM
ejpam-5536	34	14	]	]	PUNCT
ejpam-5536	34	15	,	,	PUNCT
ejpam-5536	34	16	have	have	AUX
ejpam-5536	34	17	played	play	VERB
ejpam-5536	34	18	a	a	DET
ejpam-5536	34	19	significant	significant	ADJ
ejpam-5536	34	20	role	role	NOUN
ejpam-5536	34	21	in	in	ADP
ejpam-5536	34	22	pushing	push	VERB
ejpam-5536	34	23	the	the	DET
ejpam-5536	34	24	boundaries	boundary	NOUN
ejpam-5536	34	25	of	of	ADP
ejpam-5536	34	26	this	this	DET
ejpam-5536	34	27	field	field	NOUN
ejpam-5536	34	28	.	.	PUNCT
ejpam-5536	35	1	for	for	ADP
ejpam-5536	35	2	instance	instance	NOUN
ejpam-5536	35	3	,	,	PUNCT
ejpam-5536	35	4	yang	yang	PROPN
ejpam-5536	35	5	et	et	PROPN
ejpam-5536	35	6	al	al	PROPN
ejpam-5536	35	7	.	.	PUNCT
ejpam-5536	36	1	[	[	X
ejpam-5536	36	2	18	18	NUM
ejpam-5536	36	3	]	]	PUNCT
ejpam-5536	36	4	introduced	introduce	VERB
ejpam-5536	36	5	the	the	DET
ejpam-5536	36	6	concept	concept	NOUN
ejpam-5536	36	7	of	of	ADP
ejpam-5536	36	8	bipolar	bipolar	ADJ
ejpam-5536	36	9	complex	complex	ADJ
ejpam-5536	36	10	fuzzy	fuzzy	ADJ
ejpam-5536	36	11	subgroups	subgroup	NOUN
ejpam-5536	36	12	,	,	PUNCT
ejpam-5536	36	13	which	which	PRON
ejpam-5536	36	14	integrates	integrate	VERB
ejpam-5536	36	15	the	the	DET
ejpam-5536	36	16	bfs	bfs	NOUN
ejpam-5536	36	17	framework	framework	NOUN
ejpam-5536	36	18	within	within	ADP
ejpam-5536	36	19	subgroup	subgroup	NOUN
ejpam-5536	36	20	structures	structure	NOUN
ejpam-5536	36	21	,	,	PUNCT
ejpam-5536	36	22	facilitating	facilitate	VERB
ejpam-5536	36	23	refined	refined	ADJ
ejpam-5536	36	24	control	control	NOUN
ejpam-5536	36	25	over	over	ADP
ejpam-5536	36	26	positive	positive	ADJ
ejpam-5536	36	27	and	and	CCONJ
ejpam-5536	36	28	negative	negative	ADJ
ejpam-5536	36	29	membership	membership	NOUN
ejpam-5536	36	30	degrees	degree	NOUN
ejpam-5536	36	31	across	across	ADP
ejpam-5536	36	32	group	group	NOUN
ejpam-5536	36	33	operations	operation	NOUN
ejpam-5536	36	34	.	.	PUNCT
ejpam-5536	37	1	following	follow	VERB
ejpam-5536	37	2	this	this	PRON
ejpam-5536	37	3	,	,	PUNCT
ejpam-5536	37	4	rehman	rehman	NOUN
ejpam-5536	37	5	et	et	PROPN
ejpam-5536	37	6	al	al	PROPN
ejpam-5536	37	7	.	.	PUNCT
ejpam-5536	38	1	[	[	X
ejpam-5536	38	2	16	16	NUM
ejpam-5536	38	3	]	]	PUNCT
ejpam-5536	38	4	extended	extend	VERB
ejpam-5536	38	5	this	this	DET
ejpam-5536	38	6	approach	approach	NOUN
ejpam-5536	38	7	to	to	ADP
ejpam-5536	38	8	bipolar	bipolar	ADJ
ejpam-5536	38	9	complex	complex	ADJ
ejpam-5536	38	10	fuzzy	fuzzy	ADJ
ejpam-5536	38	11	semigroups	semigroup	NOUN
ejpam-5536	38	12	,	,	PUNCT
ejpam-5536	38	13	where	where	SCONJ
ejpam-5536	38	14	bipolar	bipolar	ADJ
ejpam-5536	38	15	fuzzy	fuzzy	ADJ
ejpam-5536	38	16	logic	logic	NOUN
ejpam-5536	38	17	enables	enable	VERB
ejpam-5536	38	18	a	a	DET
ejpam-5536	38	19	robust	robust	ADJ
ejpam-5536	38	20	representation	representation	NOUN
ejpam-5536	38	21	of	of	ADP
ejpam-5536	38	22	dual	dual	ADV
ejpam-5536	38	23	-	-	PUNCT
ejpam-5536	38	24	valued	value	VERB
ejpam-5536	38	25	uncertainties	uncertainty	NOUN
ejpam-5536	38	26	within	within	ADP
ejpam-5536	38	27	semigroup	semigroup	ADJ
ejpam-5536	38	28	operations	operation	NOUN
ejpam-5536	38	29	,	,	PUNCT
ejpam-5536	38	30	broadening	broaden	VERB
ejpam-5536	38	31	the	the	DET
ejpam-5536	38	32	algebraic	algebraic	ADJ
ejpam-5536	38	33	contexts	context	NOUN
ejpam-5536	38	34	where	where	SCONJ
ejpam-5536	38	35	bipolar	bipolar	ADJ
ejpam-5536	38	36	fuzzy	fuzzy	ADJ
ejpam-5536	38	37	information	information	NOUN
ejpam-5536	38	38	can	can	AUX
ejpam-5536	38	39	be	be	AUX
ejpam-5536	38	40	systematically	systematically	ADV
ejpam-5536	38	41	applied	apply	VERB
ejpam-5536	38	42	.	.	PUNCT
ejpam-5536	39	1	further	far	ADV
ejpam-5536	39	2	,	,	PUNCT
ejpam-5536	39	3	mahmood	mahmood	PROPN
ejpam-5536	39	4	et	et	PROPN
ejpam-5536	39	5	al	al	PROPN
ejpam-5536	39	6	.	.	PUNCT
ejpam-5536	40	1	[	[	X
ejpam-5536	40	2	15	15	NUM
ejpam-5536	40	3	]	]	PUNCT
ejpam-5536	40	4	explored	explore	VERB
ejpam-5536	40	5	γ	γ	NOUN
ejpam-5536	40	6	-	-	PUNCT
ejpam-5536	40	7	semigroups	semigroup	NOUN
ejpam-5536	40	8	under	under	ADP
ejpam-5536	40	9	the	the	DET
ejpam-5536	40	10	lens	lens	NOUN
ejpam-5536	40	11	of	of	ADP
ejpam-5536	40	12	bipolar	bipolar	ADJ
ejpam-5536	40	13	complex	complex	ADJ
ejpam-5536	40	14	fuzzy	fuzzy	ADJ
ejpam-5536	40	15	sets	set	NOUN
ejpam-5536	40	16	,	,	PUNCT
ejpam-5536	40	17	advancing	advance	VERB
ejpam-5536	40	18	the	the	DET
ejpam-5536	40	19	formalism	formalism	NOUN
ejpam-5536	40	20	needed	need	VERB
ejpam-5536	40	21	for	for	ADP
ejpam-5536	40	22	multi	multi	ADJ
ejpam-5536	40	23	-	-	ADJ
ejpam-5536	40	24	dimensional	dimensional	ADJ
ejpam-5536	40	25	decision	decision	NOUN
ejpam-5536	40	26	-	-	PUNCT
ejpam-5536	40	27	making	make	VERB
ejpam-5536	40	28	scenarios	scenario	NOUN
ejpam-5536	40	29	,	,	PUNCT
ejpam-5536	40	30	where	where	SCONJ
ejpam-5536	40	31	bipolar	bipolar	ADJ
ejpam-5536	40	32	attributes	attribute	NOUN
ejpam-5536	40	33	play	play	VERB
ejpam-5536	40	34	a	a	DET
ejpam-5536	40	35	crucial	crucial	ADJ
ejpam-5536	40	36	role	role	NOUN
ejpam-5536	40	37	.	.	PUNCT
ejpam-5536	41	1	similarly	similarly	ADV
ejpam-5536	41	2	,	,	PUNCT
ejpam-5536	41	3	research	research	NOUN
ejpam-5536	41	4	in	in	ADP
ejpam-5536	41	5	[	[	X
ejpam-5536	41	6	14	14	NUM
ejpam-5536	41	7	]	]	PUNCT
ejpam-5536	41	8	delves	delf	NOUN
ejpam-5536	41	9	into	into	ADP
ejpam-5536	41	10	bipolar	bipolar	ADJ
ejpam-5536	41	11	soft	soft	ADJ
ejpam-5536	41	12	groups	group	NOUN
ejpam-5536	41	13	,	,	PUNCT
ejpam-5536	41	14	an	an	DET
ejpam-5536	41	15	extension	extension	NOUN
ejpam-5536	41	16	that	that	PRON
ejpam-5536	41	17	allows	allow	VERB
ejpam-5536	41	18	for	for	ADP
ejpam-5536	41	19	flexible	flexible	ADJ
ejpam-5536	41	20	representation	representation	NOUN
ejpam-5536	41	21	and	and	CCONJ
ejpam-5536	41	22	manipulation	manipulation	NOUN
ejpam-5536	41	23	of	of	ADP
ejpam-5536	41	24	bipolar	bipolar	ADJ
ejpam-5536	41	25	attributes	attribute	NOUN
ejpam-5536	41	26	,	,	PUNCT
ejpam-5536	41	27	thus	thus	ADV
ejpam-5536	41	28	supporting	support	VERB
ejpam-5536	41	29	fundamental	fundamental	ADJ
ejpam-5536	41	30	operations	operation	NOUN
ejpam-5536	41	31	in	in	ADP
ejpam-5536	41	32	fuzzy	fuzzy	ADJ
ejpam-5536	41	33	group	group	NOUN
ejpam-5536	41	34	theory	theory	NOUN
ejpam-5536	41	35	.	.	PUNCT
ejpam-5536	42	1	lastly	lastly	ADV
ejpam-5536	42	2	,	,	PUNCT
ejpam-5536	42	3	alsuraiheed	alsuraiheed	VERB
ejpam-5536	42	4	et	et	PROPN
ejpam-5536	42	5	al	al	PROPN
ejpam-5536	42	6	.	.	PUNCT
ejpam-5536	43	1	[	[	X
ejpam-5536	43	2	1	1	NUM
ejpam-5536	43	3	]	]	PUNCT
ejpam-5536	43	4	investigated	investigate	VERB
ejpam-5536	43	5	bipolar	bipolar	ADJ
ejpam-5536	43	6	complex	complex	ADJ
ejpam-5536	43	7	fuzzy	fuzzy	ADJ
ejpam-5536	43	8	submodules	submodule	NOUN
ejpam-5536	43	9	,	,	PUNCT
ejpam-5536	43	10	highlighting	highlight	VERB
ejpam-5536	43	11	their	their	PRON
ejpam-5536	43	12	relevance	relevance	NOUN
ejpam-5536	43	13	in	in	ADP
ejpam-5536	43	14	module	module	NOUN
ejpam-5536	43	15	theory	theory	NOUN
ejpam-5536	43	16	and	and	CCONJ
ejpam-5536	43	17	reinforcing	reinforce	VERB
ejpam-5536	43	18	the	the	DET
ejpam-5536	43	19	versatility	versatility	NOUN
ejpam-5536	43	20	of	of	ADP
ejpam-5536	43	21	bfss	bfss	NOUN
ejpam-5536	43	22	in	in	ADP
ejpam-5536	43	23	higher	high	ADJ
ejpam-5536	43	24	algebraic	algebraic	ADJ
ejpam-5536	43	25	structures	structure	NOUN
ejpam-5536	43	26	.	.	PUNCT
ejpam-5536	44	1	these	these	DET
ejpam-5536	44	2	studies	study	NOUN
ejpam-5536	44	3	collectively	collectively	ADV
ejpam-5536	44	4	contribute	contribute	VERB
ejpam-5536	44	5	to	to	ADP
ejpam-5536	44	6	a	a	DET
ejpam-5536	44	7	more	more	ADV
ejpam-5536	44	8	robust	robust	ADJ
ejpam-5536	44	9	framework	framework	NOUN
ejpam-5536	44	10	for	for	ADP
ejpam-5536	44	11	applying	apply	VERB
ejpam-5536	44	12	bfss	bfss	NOUN
ejpam-5536	44	13	,	,	PUNCT
ejpam-5536	44	14	enabling	enable	VERB
ejpam-5536	44	15	their	their	PRON
ejpam-5536	44	16	use	use	NOUN
ejpam-5536	44	17	in	in	ADP
ejpam-5536	44	18	increasingly	increasingly	ADV
ejpam-5536	44	19	complex	complex	ADJ
ejpam-5536	44	20	and	and	CCONJ
ejpam-5536	44	21	multi	multi	ADJ
ejpam-5536	44	22	-	-	ADJ
ejpam-5536	44	23	valued	value	VERB
ejpam-5536	44	24	systems	system	NOUN
ejpam-5536	44	25	across	across	ADP
ejpam-5536	44	26	various	various	ADJ
ejpam-5536	44	27	mathematical	mathematical	ADJ
ejpam-5536	44	28	domains	domain	NOUN
ejpam-5536	44	29	.	.	PUNCT
ejpam-5536	45	1	the	the	DET
ejpam-5536	45	2	concept	concept	NOUN
ejpam-5536	45	3	of	of	ADP
ejpam-5536	45	4	hilbert	hilbert	PROPN
ejpam-5536	45	5	algebras	algebras	PROPN
ejpam-5536	45	6	was	be	AUX
ejpam-5536	45	7	introduced	introduce	VERB
ejpam-5536	45	8	in	in	ADP
ejpam-5536	45	9	the	the	DET
ejpam-5536	45	10	early	early	ADJ
ejpam-5536	45	11	50	50	NUM
ejpam-5536	45	12	-	-	PUNCT
ejpam-5536	45	13	ties	tie	NOUN
ejpam-5536	45	14	by	by	ADP
ejpam-5536	45	15	henkin	henkin	PROPN
ejpam-5536	46	1	[	[	X
ejpam-5536	46	2	10	10	NUM
ejpam-5536	46	3	]	]	PUNCT
ejpam-5536	46	4	for	for	ADP
ejpam-5536	46	5	some	some	DET
ejpam-5536	46	6	investigations	investigation	NOUN
ejpam-5536	46	7	of	of	ADP
ejpam-5536	46	8	implication	implication	NOUN
ejpam-5536	46	9	in	in	ADP
ejpam-5536	46	10	intuitionistic	intuitionistic	ADJ
ejpam-5536	46	11	and	and	CCONJ
ejpam-5536	46	12	other	other	ADJ
ejpam-5536	46	13	non	non	ADJ
ejpam-5536	46	14	-	-	ADJ
ejpam-5536	46	15	classical	classical	ADJ
ejpam-5536	46	16	logics	logic	NOUN
ejpam-5536	46	17	.	.	PUNCT
ejpam-5536	47	1	in	in	ADP
ejpam-5536	47	2	the	the	DET
ejpam-5536	47	3	60	60	NUM
ejpam-5536	47	4	-	-	PUNCT
ejpam-5536	47	5	ties	tie	NOUN
ejpam-5536	47	6	,	,	PUNCT
ejpam-5536	47	7	these	these	DET
ejpam-5536	47	8	algebras	algebra	NOUN
ejpam-5536	47	9	were	be	AUX
ejpam-5536	47	10	studied	study	VERB
ejpam-5536	47	11	especially	especially	ADV
ejpam-5536	47	12	by	by	ADP
ejpam-5536	47	13	diego	diego	PROPN
ejpam-5536	48	1	[	[	X
ejpam-5536	48	2	6	6	NUM
ejpam-5536	48	3	]	]	PUNCT
ejpam-5536	48	4	from	from	ADP
ejpam-5536	48	5	an	an	DET
ejpam-5536	48	6	algebraic	algebraic	ADJ
ejpam-5536	48	7	point	point	NOUN
ejpam-5536	48	8	of	of	ADP
ejpam-5536	48	9	view	view	NOUN
ejpam-5536	48	10	.	.	PUNCT
ejpam-5536	49	1	diego	diego	PROPN
ejpam-5536	50	1	[	[	X
ejpam-5536	50	2	6	6	NUM
ejpam-5536	50	3	]	]	PUNCT
ejpam-5536	50	4	proved	prove	VERB
ejpam-5536	50	5	that	that	SCONJ
ejpam-5536	50	6	hilbert	hilbert	PROPN
ejpam-5536	50	7	algebras	algebras	PROPN
ejpam-5536	50	8	form	form	VERB
ejpam-5536	50	9	a	a	DET
ejpam-5536	50	10	variety	variety	NOUN
ejpam-5536	50	11	which	which	PRON
ejpam-5536	50	12	is	be	AUX
ejpam-5536	50	13	locally	locally	ADV
ejpam-5536	50	14	finite	finite	ADJ
ejpam-5536	50	15	.	.	PUNCT
ejpam-5536	51	1	hilbert	hilbert	PROPN
ejpam-5536	51	2	algebras	algebras	PROPN
ejpam-5536	51	3	were	be	AUX
ejpam-5536	51	4	studied	study	VERB
ejpam-5536	51	5	by	by	ADP
ejpam-5536	51	6	busneag	busneag	NOUN
ejpam-5536	51	7	[	[	X
ejpam-5536	51	8	3	3	NUM
ejpam-5536	51	9	,	,	PUNCT
ejpam-5536	51	10	4	4	NUM
ejpam-5536	51	11	]	]	PUNCT
ejpam-5536	51	12	and	and	CCONJ
ejpam-5536	51	13	jun	jun	PROPN
ejpam-5536	52	1	[	[	X
ejpam-5536	52	2	12	12	NUM
ejpam-5536	52	3	]	]	X
ejpam-5536	52	4	,	,	PUNCT
ejpam-5536	52	5	who	who	PRON
ejpam-5536	52	6	recognized	recognize	VERB
ejpam-5536	52	7	some	some	PRON
ejpam-5536	52	8	of	of	ADP
ejpam-5536	52	9	their	their	PRON
ejpam-5536	52	10	a.	a.	NOUN
ejpam-5536	52	11	iampan	iampan	NOUN
ejpam-5536	52	12	et	et	PROPN
ejpam-5536	52	13	al	al	PROPN
ejpam-5536	52	14	.	.	PUNCT
ejpam-5536	52	15	/	/	SYM
ejpam-5536	52	16	eur	eur	PROPN
ejpam-5536	52	17	.	.	PUNCT
ejpam-5536	53	1	j.	j.	PROPN
ejpam-5536	53	2	pure	pure	PROPN
ejpam-5536	53	3	appl	appl	PROPN
ejpam-5536	53	4	.	.	PROPN
ejpam-5536	53	5	math	math	PROPN
ejpam-5536	53	6	,	,	PUNCT
ejpam-5536	53	7	17	17	NUM
ejpam-5536	53	8	(	(	PUNCT
ejpam-5536	53	9	4	4	NUM
ejpam-5536	53	10	)	)	PUNCT
ejpam-5536	53	11	(	(	PUNCT
ejpam-5536	53	12	2024	2024	NUM
ejpam-5536	53	13	)	)	PUNCT
ejpam-5536	53	14	,	,	PUNCT
ejpam-5536	53	15	4059	4059	NUM
ejpam-5536	53	16	-	-	SYM
ejpam-5536	53	17	4070	4070	NUM
ejpam-5536	53	18	4061	4061	NUM
ejpam-5536	53	19	filters	filter	NOUN
ejpam-5536	53	20	as	as	ADP
ejpam-5536	53	21	forming	form	VERB
ejpam-5536	53	22	deductive	deductive	ADJ
ejpam-5536	53	23	systems	system	NOUN
ejpam-5536	53	24	.	.	PUNCT
ejpam-5536	54	1	dudek	dudek	PROPN
ejpam-5536	55	1	[	[	X
ejpam-5536	55	2	7–9	7–9	X
ejpam-5536	55	3	]	]	PUNCT
ejpam-5536	55	4	explored	explore	VERB
ejpam-5536	55	5	the	the	DET
ejpam-5536	55	6	concept	concept	NOUN
ejpam-5536	55	7	of	of	ADP
ejpam-5536	55	8	fuzzification	fuzzification	NOUN
ejpam-5536	55	9	in	in	ADP
ejpam-5536	55	10	subalgebras	subalgebras	PROPN
ejpam-5536	55	11	,	,	PUNCT
ejpam-5536	55	12	ideals	ideal	NOUN
ejpam-5536	55	13	,	,	PUNCT
ejpam-5536	55	14	and	and	CCONJ
ejpam-5536	55	15	deductive	deductive	ADJ
ejpam-5536	55	16	systems	system	NOUN
ejpam-5536	55	17	within	within	ADP
ejpam-5536	55	18	the	the	DET
ejpam-5536	55	19	framework	framework	NOUN
ejpam-5536	55	20	of	of	ADP
ejpam-5536	55	21	hilbert	hilbert	PROPN
ejpam-5536	55	22	algebras	algebras	PROPN
ejpam-5536	55	23	.	.	PUNCT
ejpam-5536	56	1	this	this	DET
ejpam-5536	56	2	research	research	NOUN
ejpam-5536	56	3	delves	delve	VERB
ejpam-5536	56	4	into	into	ADP
ejpam-5536	56	5	the	the	DET
ejpam-5536	56	6	application	application	NOUN
ejpam-5536	56	7	of	of	ADP
ejpam-5536	56	8	bfs	bfs	NOUN
ejpam-5536	56	9	theory	theory	NOUN
ejpam-5536	56	10	within	within	ADP
ejpam-5536	56	11	hilbert	hilbert	PROPN
ejpam-5536	56	12	algebras	algebras	PROPN
ejpam-5536	56	13	,	,	PUNCT
ejpam-5536	56	14	specifically	specifically	ADV
ejpam-5536	56	15	introducing	introduce	VERB
ejpam-5536	56	16	the	the	DET
ejpam-5536	56	17	bipolar	bipolar	ADJ
ejpam-5536	56	18	fuzzy	fuzzy	ADJ
ejpam-5536	56	19	(	(	PUNCT
ejpam-5536	56	20	β	β	X
ejpam-5536	56	21	,	,	PUNCT
ejpam-5536	56	22	α)-translations	α)-translation	NOUN
ejpam-5536	56	23	of	of	ADP
ejpam-5536	56	24	a	a	DET
ejpam-5536	56	25	bfs	bfs	NOUN
ejpam-5536	56	26	φ	φ	NOUN
ejpam-5536	56	27	=	=	SYM
ejpam-5536	56	28	(	(	PUNCT
ejpam-5536	56	29	φ+	φ+	NOUN
ejpam-5536	56	30	,	,	PUNCT
ejpam-5536	56	31	φ−	φ−	PROPN
ejpam-5536	56	32	)	)	PUNCT
ejpam-5536	56	33	in	in	ADP
ejpam-5536	56	34	two	two	NUM
ejpam-5536	56	35	distinct	distinct	ADJ
ejpam-5536	56	36	forms	form	NOUN
ejpam-5536	56	37	:	:	PUNCT
ejpam-5536	56	38	type	type	NOUN
ejpam-5536	56	39	i	i	PRON
ejpam-5536	56	40	and	and	CCONJ
ejpam-5536	56	41	type	type	PROPN
ejpam-5536	56	42	ii	ii	PROPN
ejpam-5536	56	43	.	.	PUNCT
ejpam-5536	57	1	through	through	ADP
ejpam-5536	57	2	a	a	DET
ejpam-5536	57	3	detailed	detailed	ADJ
ejpam-5536	57	4	investigation	investigation	NOUN
ejpam-5536	57	5	of	of	ADP
ejpam-5536	57	6	the	the	DET
ejpam-5536	57	7	fundamental	fundamental	ADJ
ejpam-5536	57	8	properties	property	NOUN
ejpam-5536	57	9	of	of	ADP
ejpam-5536	57	10	these	these	DET
ejpam-5536	57	11	translations	translation	NOUN
ejpam-5536	57	12	,	,	PUNCT
ejpam-5536	57	13	along	along	ADP
ejpam-5536	57	14	with	with	ADP
ejpam-5536	57	15	the	the	DET
ejpam-5536	57	16	concepts	concept	NOUN
ejpam-5536	57	17	of	of	ADP
ejpam-5536	57	18	bipolar	bipolar	ADJ
ejpam-5536	57	19	fuzzy	fuzzy	ADJ
ejpam-5536	57	20	extensions	extension	NOUN
ejpam-5536	57	21	and	and	CCONJ
ejpam-5536	57	22	intensities	intensity	NOUN
ejpam-5536	57	23	,	,	PUNCT
ejpam-5536	57	24	the	the	DET
ejpam-5536	57	25	study	study	NOUN
ejpam-5536	57	26	enhances	enhance	VERB
ejpam-5536	57	27	the	the	DET
ejpam-5536	57	28	flexibility	flexibility	NOUN
ejpam-5536	57	29	and	and	CCONJ
ejpam-5536	57	30	efficacy	efficacy	NOUN
ejpam-5536	57	31	of	of	ADP
ejpam-5536	57	32	bfss	bfss	NOUN
ejpam-5536	57	33	in	in	ADP
ejpam-5536	57	34	representing	represent	VERB
ejpam-5536	57	35	intricate	intricate	ADJ
ejpam-5536	57	36	bipolar	bipolar	ADJ
ejpam-5536	57	37	information	information	NOUN
ejpam-5536	57	38	.	.	PUNCT
ejpam-5536	58	1	additionally	additionally	ADV
ejpam-5536	58	2	,	,	PUNCT
ejpam-5536	58	3	it	it	PRON
ejpam-5536	58	4	explores	explore	VERB
ejpam-5536	58	5	the	the	DET
ejpam-5536	58	6	complex	complex	ADJ
ejpam-5536	58	7	relationships	relationship	NOUN
ejpam-5536	58	8	among	among	ADP
ejpam-5536	58	9	the	the	DET
ejpam-5536	58	10	complements	complement	NOUN
ejpam-5536	58	11	of	of	ADP
ejpam-5536	58	12	bipolar	bipolar	ADJ
ejpam-5536	58	13	fuzzy	fuzzy	ADJ
ejpam-5536	58	14	subalgebras	subalgebra	NOUN
ejpam-5536	58	15	,	,	PUNCT
ejpam-5536	58	16	ideals	ideal	NOUN
ejpam-5536	58	17	,	,	PUNCT
ejpam-5536	58	18	and	and	CCONJ
ejpam-5536	58	19	deductive	deductive	ADJ
ejpam-5536	58	20	systems	system	NOUN
ejpam-5536	58	21	concerning	concern	VERB
ejpam-5536	58	22	their	their	PRON
ejpam-5536	58	23	level	level	NOUN
ejpam-5536	58	24	cuts	cut	NOUN
ejpam-5536	58	25	.	.	PUNCT
ejpam-5536	59	1	together	together	ADV
ejpam-5536	59	2	,	,	PUNCT
ejpam-5536	59	3	these	these	DET
ejpam-5536	59	4	findings	finding	NOUN
ejpam-5536	59	5	lay	lie	VERB
ejpam-5536	59	6	a	a	DET
ejpam-5536	59	7	strengthened	strengthen	VERB
ejpam-5536	59	8	theoretical	theoretical	ADJ
ejpam-5536	59	9	groundwork	groundwork	NOUN
ejpam-5536	59	10	for	for	ADP
ejpam-5536	59	11	bipolar	bipolar	ADJ
ejpam-5536	59	12	fuzzy	fuzzy	ADJ
ejpam-5536	59	13	logic	logic	NOUN
ejpam-5536	59	14	in	in	ADP
ejpam-5536	59	15	hilbert	hilbert	PROPN
ejpam-5536	59	16	algebras	algebras	PROPN
ejpam-5536	59	17	and	and	CCONJ
ejpam-5536	59	18	suggest	suggest	VERB
ejpam-5536	59	19	promising	promising	ADJ
ejpam-5536	59	20	applications	application	NOUN
ejpam-5536	59	21	in	in	ADP
ejpam-5536	59	22	the	the	DET
ejpam-5536	59	23	management	management	NOUN
ejpam-5536	59	24	of	of	ADP
ejpam-5536	59	25	nuanced	nuanced	ADJ
ejpam-5536	59	26	bipolar	bipolar	ADJ
ejpam-5536	59	27	information	information	NOUN
ejpam-5536	59	28	within	within	ADP
ejpam-5536	59	29	uncertain	uncertain	ADJ
ejpam-5536	59	30	systems	system	NOUN
ejpam-5536	59	31	.	.	PUNCT
ejpam-5536	60	1	2	2	X
ejpam-5536	60	2	.	.	X
ejpam-5536	60	3	preliminaries	preliminary	NOUN
ejpam-5536	60	4	to	to	PART
ejpam-5536	60	5	establish	establish	VERB
ejpam-5536	60	6	a	a	DET
ejpam-5536	60	7	solid	solid	ADJ
ejpam-5536	60	8	foundation	foundation	NOUN
ejpam-5536	60	9	for	for	ADP
ejpam-5536	60	10	our	our	PRON
ejpam-5536	60	11	discussion	discussion	NOUN
ejpam-5536	60	12	,	,	PUNCT
ejpam-5536	60	13	we	we	PRON
ejpam-5536	60	14	begin	begin	VERB
ejpam-5536	60	15	by	by	ADP
ejpam-5536	60	16	formally	formally	ADV
ejpam-5536	60	17	defining	define	VERB
ejpam-5536	60	18	the	the	DET
ejpam-5536	60	19	structure	structure	NOUN
ejpam-5536	60	20	and	and	CCONJ
ejpam-5536	60	21	properties	property	NOUN
ejpam-5536	60	22	of	of	ADP
ejpam-5536	60	23	a	a	DET
ejpam-5536	60	24	hilbert	hilbert	NOUN
ejpam-5536	60	25	algebra	algebra	NOUN
ejpam-5536	60	26	.	.	PUNCT
ejpam-5536	61	1	definition	definition	NOUN
ejpam-5536	61	2	1	1	NUM
ejpam-5536	61	3	.	.	PUNCT
ejpam-5536	62	1	[	[	X
ejpam-5536	62	2	6	6	NUM
ejpam-5536	62	3	]	]	PUNCT
ejpam-5536	62	4	a	a	DET
ejpam-5536	62	5	hilbert	hilbert	NOUN
ejpam-5536	62	6	algebra	algebra	NOUN
ejpam-5536	62	7	is	be	AUX
ejpam-5536	62	8	a	a	DET
ejpam-5536	62	9	triplet	triplet	NOUN
ejpam-5536	62	10	with	with	ADP
ejpam-5536	62	11	the	the	DET
ejpam-5536	62	12	formula	formula	NOUN
ejpam-5536	62	13	x	x	PUNCT
ejpam-5536	63	1	=	=	PUNCT
ejpam-5536	63	2	(	(	PUNCT
ejpam-5536	63	3	x	x	NOUN
ejpam-5536	63	4	,	,	PUNCT
ejpam-5536	63	5	·	·	PUNCT
ejpam-5536	63	6	,	,	PUNCT
ejpam-5536	63	7	1x	1x	NUM
ejpam-5536	63	8	)	)	PUNCT
ejpam-5536	63	9	,	,	PUNCT
ejpam-5536	63	10	where	where	SCONJ
ejpam-5536	63	11	x	x	PRON
ejpam-5536	63	12	is	be	AUX
ejpam-5536	63	13	a	a	DET
ejpam-5536	63	14	nonempty	nonempty	ADJ
ejpam-5536	63	15	set	set	VERB
ejpam-5536	63	16	,	,	PUNCT
ejpam-5536	63	17	·	·	PUNCT
ejpam-5536	63	18	is	be	AUX
ejpam-5536	63	19	a	a	DET
ejpam-5536	63	20	binary	binary	ADJ
ejpam-5536	63	21	operation	operation	NOUN
ejpam-5536	63	22	,	,	PUNCT
ejpam-5536	63	23	and	and	CCONJ
ejpam-5536	63	24	1x	1x	NUM
ejpam-5536	63	25	is	be	AUX
ejpam-5536	63	26	a	a	DET
ejpam-5536	63	27	fixed	fix	VERB
ejpam-5536	63	28	member	member	NOUN
ejpam-5536	63	29	of	of	ADP
ejpam-5536	63	30	x	x	PRON
ejpam-5536	63	31	that	that	PRON
ejpam-5536	63	32	is	be	AUX
ejpam-5536	63	33	true	true	ADJ
ejpam-5536	63	34	according	accord	VERB
ejpam-5536	63	35	to	to	ADP
ejpam-5536	63	36	the	the	DET
ejpam-5536	63	37	axioms	axiom	NOUN
ejpam-5536	63	38	mentioned	mention	VERB
ejpam-5536	63	39	below	below	ADV
ejpam-5536	63	40	:	:	PUNCT
ejpam-5536	63	41	(	(	PUNCT
ejpam-5536	63	42	1	1	X
ejpam-5536	63	43	)	)	PUNCT
ejpam-5536	63	44	(	(	PUNCT
ejpam-5536	63	45	∀x	∀x	X
ejpam-5536	63	46	,	,	PUNCT
ejpam-5536	63	47	y	y	PROPN
ejpam-5536	63	48	∈	∈	PROPN
ejpam-5536	63	49	x)(x	x)(x	PROPN
ejpam-5536	63	50	·	·	PUNCT
ejpam-5536	63	51	(	(	PUNCT
ejpam-5536	63	52	y	y	PROPN
ejpam-5536	63	53	·	·	PUNCT
ejpam-5536	63	54	x	x	X
ejpam-5536	63	55	)	)	PUNCT
ejpam-5536	63	56	=	=	SYM
ejpam-5536	63	57	1x	1x	NUM
ejpam-5536	63	58	)	)	PUNCT
ejpam-5536	63	59	(	(	PUNCT
ejpam-5536	63	60	2	2	NUM
ejpam-5536	63	61	)	)	PUNCT
ejpam-5536	63	62	(	(	PUNCT
ejpam-5536	63	63	∀x	∀x	X
ejpam-5536	63	64	,	,	PUNCT
ejpam-5536	63	65	y	y	PROPN
ejpam-5536	63	66	,	,	PUNCT
ejpam-5536	63	67	z	z	PROPN
ejpam-5536	63	68	∈	∈	PROPN
ejpam-5536	63	69	x)((x	x)((x	NOUN
ejpam-5536	63	70	·	·	PUNCT
ejpam-5536	63	71	(	(	PUNCT
ejpam-5536	63	72	y	y	PROPN
ejpam-5536	63	73	·	·	PUNCT
ejpam-5536	63	74	z	z	NOUN
ejpam-5536	63	75	)	)	PUNCT
ejpam-5536	63	76	)	)	PUNCT
ejpam-5536	63	77	·	·	PUNCT
ejpam-5536	64	1	(	(	PUNCT
ejpam-5536	64	2	(	(	PUNCT
ejpam-5536	64	3	x	x	SYM
ejpam-5536	64	4	·	·	PUNCT
ejpam-5536	64	5	y	y	X
ejpam-5536	64	6	)	)	PUNCT
ejpam-5536	64	7	·	·	PUNCT
ejpam-5536	65	1	(	(	PUNCT
ejpam-5536	65	2	x	x	X
ejpam-5536	65	3	·	·	PUNCT
ejpam-5536	65	4	z	z	NOUN
ejpam-5536	65	5	)	)	PUNCT
ejpam-5536	65	6	)	)	PUNCT
ejpam-5536	65	7	=	=	SYM
ejpam-5536	65	8	1x	1x	NUM
ejpam-5536	65	9	)	)	PUNCT
ejpam-5536	65	10	(	(	PUNCT
ejpam-5536	65	11	3	3	X
ejpam-5536	65	12	)	)	PUNCT
ejpam-5536	65	13	(	(	PUNCT
ejpam-5536	65	14	∀x	∀x	X
ejpam-5536	65	15	,	,	PUNCT
ejpam-5536	65	16	y	y	PROPN
ejpam-5536	65	17	∈	∈	PROPN
ejpam-5536	65	18	x)(x	x)(x	PROPN
ejpam-5536	65	19	·	·	PUNCT
ejpam-5536	66	1	y	y	X
ejpam-5536	66	2	=	=	PUNCT
ejpam-5536	66	3	1x	1x	PROPN
ejpam-5536	66	4	,	,	PUNCT
ejpam-5536	66	5	y	y	PROPN
ejpam-5536	66	6	·	·	PUNCT
ejpam-5536	66	7	x	x	PUNCT
ejpam-5536	67	1	=	=	PUNCT
ejpam-5536	67	2	1x	1x	PROPN
ejpam-5536	67	3	⇒	⇒	VERB
ejpam-5536	67	4	x	x	PUNCT
ejpam-5536	67	5	=	=	SYM
ejpam-5536	67	6	y	y	NOUN
ejpam-5536	67	7	)	)	PUNCT
ejpam-5536	67	8	in	in	ADP
ejpam-5536	67	9	[	[	X
ejpam-5536	67	10	7	7	NUM
ejpam-5536	67	11	]	]	PUNCT
ejpam-5536	67	12	,	,	PUNCT
ejpam-5536	67	13	the	the	DET
ejpam-5536	67	14	following	follow	VERB
ejpam-5536	67	15	conclusion	conclusion	NOUN
ejpam-5536	67	16	was	be	AUX
ejpam-5536	67	17	established	establish	VERB
ejpam-5536	67	18	.	.	PUNCT
ejpam-5536	68	1	lemma	lemma	PROPN
ejpam-5536	68	2	1	1	X
ejpam-5536	68	3	.	.	PUNCT
ejpam-5536	69	1	let	let	VERB
ejpam-5536	69	2	x	x	PUNCT
ejpam-5536	69	3	=	=	PUNCT
ejpam-5536	69	4	(	(	PUNCT
ejpam-5536	69	5	x	x	NOUN
ejpam-5536	69	6	,	,	PUNCT
ejpam-5536	69	7	·	·	PUNCT
ejpam-5536	69	8	,	,	PUNCT
ejpam-5536	69	9	1x	1x	NUM
ejpam-5536	69	10	)	)	PUNCT
ejpam-5536	69	11	be	be	AUX
ejpam-5536	69	12	a	a	DET
ejpam-5536	69	13	hilbert	hilbert	NOUN
ejpam-5536	69	14	algebra	algebra	NOUN
ejpam-5536	69	15	.	.	PUNCT
ejpam-5536	70	1	then	then	ADV
ejpam-5536	70	2	(	(	PUNCT
ejpam-5536	70	3	1	1	X
ejpam-5536	70	4	)	)	PUNCT
ejpam-5536	70	5	(	(	PUNCT
ejpam-5536	70	6	∀x	∀x	X
ejpam-5536	70	7	∈	∈	PROPN
ejpam-5536	70	8	x)(x	x)(x	PROPN
ejpam-5536	70	9	·	·	PUNCT
ejpam-5536	70	10	x	x	PUNCT
ejpam-5536	70	11	=	=	SYM
ejpam-5536	70	12	1x	1x	NUM
ejpam-5536	70	13	)	)	PUNCT
ejpam-5536	70	14	(	(	PUNCT
ejpam-5536	70	15	2	2	X
ejpam-5536	70	16	)	)	PUNCT
ejpam-5536	70	17	(	(	PUNCT
ejpam-5536	70	18	∀x	∀x	X
ejpam-5536	70	19	∈	∈	PROPN
ejpam-5536	70	20	x)(1x	x)(1x	NOUN
ejpam-5536	70	21	·	·	PUNCT
ejpam-5536	70	22	x	x	PUNCT
ejpam-5536	70	23	=	=	PUNCT
ejpam-5536	70	24	x	x	X
ejpam-5536	70	25	)	)	PUNCT
ejpam-5536	70	26	(	(	PUNCT
ejpam-5536	70	27	3	3	X
ejpam-5536	70	28	)	)	PUNCT
ejpam-5536	70	29	(	(	PUNCT
ejpam-5536	70	30	∀x	∀x	X
ejpam-5536	70	31	∈	∈	PROPN
ejpam-5536	70	32	x)(x	x)(x	PROPN
ejpam-5536	70	33	·	·	PUNCT
ejpam-5536	70	34	1x	1x	NUM
ejpam-5536	70	35	=	=	SYM
ejpam-5536	70	36	1x	1x	NUM
ejpam-5536	70	37	)	)	PUNCT
ejpam-5536	70	38	(	(	PUNCT
ejpam-5536	70	39	4	4	NUM
ejpam-5536	70	40	)	)	PUNCT
ejpam-5536	70	41	(	(	PUNCT
ejpam-5536	70	42	∀x	∀x	X
ejpam-5536	70	43	,	,	PUNCT
ejpam-5536	70	44	y	y	PROPN
ejpam-5536	70	45	,	,	PUNCT
ejpam-5536	70	46	z	z	PROPN
ejpam-5536	70	47	∈	∈	PROPN
ejpam-5536	70	48	x)(x	x)(x	PROPN
ejpam-5536	70	49	·	·	PUNCT
ejpam-5536	70	50	(	(	PUNCT
ejpam-5536	70	51	y	y	PROPN
ejpam-5536	70	52	·	·	PUNCT
ejpam-5536	71	1	z	z	X
ejpam-5536	71	2	)	)	PUNCT
ejpam-5536	71	3	=	=	SYM
ejpam-5536	71	4	y	y	PROPN
ejpam-5536	71	5	·	·	PUNCT
ejpam-5536	71	6	(	(	PUNCT
ejpam-5536	71	7	x	x	X
ejpam-5536	71	8	·	·	PUNCT
ejpam-5536	71	9	z	z	NOUN
ejpam-5536	71	10	)	)	PUNCT
ejpam-5536	71	11	)	)	PUNCT
ejpam-5536	71	12	(	(	PUNCT
ejpam-5536	71	13	5	5	X
ejpam-5536	71	14	)	)	PUNCT
ejpam-5536	71	15	(	(	PUNCT
ejpam-5536	71	16	∀x	∀x	X
ejpam-5536	71	17	,	,	PUNCT
ejpam-5536	71	18	y	y	PROPN
ejpam-5536	71	19	,	,	PUNCT
ejpam-5536	71	20	z	z	PROPN
ejpam-5536	71	21	∈	∈	PROPN
ejpam-5536	71	22	x)((x	x)((x	NOUN
ejpam-5536	71	23	·	·	PUNCT
ejpam-5536	71	24	z	z	X
ejpam-5536	71	25	)	)	PUNCT
ejpam-5536	71	26	·	·	PUNCT
ejpam-5536	71	27	(	(	PUNCT
ejpam-5536	71	28	(	(	PUNCT
ejpam-5536	71	29	z	z	NOUN
ejpam-5536	71	30	·	·	PUNCT
ejpam-5536	71	31	y	y	X
ejpam-5536	71	32	)	)	PUNCT
ejpam-5536	71	33	·	·	PUNCT
ejpam-5536	72	1	(	(	PUNCT
ejpam-5536	72	2	x	x	X
ejpam-5536	72	3	·	·	PUNCT
ejpam-5536	72	4	y	y	NOUN
ejpam-5536	72	5	)	)	PUNCT
ejpam-5536	72	6	)	)	PUNCT
ejpam-5536	73	1	=	=	SYM
ejpam-5536	73	2	1x	1x	NUM
ejpam-5536	73	3	)	)	PUNCT
ejpam-5536	73	4	.	.	PUNCT
ejpam-5536	74	1	in	in	ADP
ejpam-5536	74	2	a	a	DET
ejpam-5536	74	3	hilbert	hilbert	NOUN
ejpam-5536	74	4	algebra	algebra	NOUN
ejpam-5536	74	5	x	x	PUNCT
ejpam-5536	74	6	=	=	SYM
ejpam-5536	74	7	(	(	PUNCT
ejpam-5536	74	8	x	x	NOUN
ejpam-5536	74	9	,	,	PUNCT
ejpam-5536	74	10	·	·	PUNCT
ejpam-5536	74	11	,	,	PUNCT
ejpam-5536	74	12	1x	1x	NUM
ejpam-5536	74	13	)	)	PUNCT
ejpam-5536	74	14	,	,	PUNCT
ejpam-5536	74	15	the	the	DET
ejpam-5536	74	16	binary	binary	PROPN
ejpam-5536	74	17	relation	relation	PROPN
ejpam-5536	74	18	≤	≤	NUM
ejpam-5536	74	19	is	be	AUX
ejpam-5536	74	20	defined	define	VERB
ejpam-5536	74	21	by	by	ADP
ejpam-5536	74	22	(	(	PUNCT
ejpam-5536	74	23	∀x	∀x	NUM
ejpam-5536	74	24	,	,	PUNCT
ejpam-5536	74	25	y	y	PROPN
ejpam-5536	74	26	∈	∈	PROPN
ejpam-5536	74	27	x)(x	x)(x	PROPN
ejpam-5536	74	28	≤	≤	PROPN
ejpam-5536	74	29	y	y	PROPN
ejpam-5536	74	30	⇔	⇔	PROPN
ejpam-5536	74	31	x	x	PROPN
ejpam-5536	74	32	·	·	PUNCT
ejpam-5536	74	33	y	y	SYM
ejpam-5536	74	34	=	=	SYM
ejpam-5536	74	35	1x	1x	NUM
ejpam-5536	74	36	)	)	PUNCT
ejpam-5536	74	37	,	,	PUNCT
ejpam-5536	74	38	which	which	PRON
ejpam-5536	74	39	is	be	AUX
ejpam-5536	74	40	a	a	DET
ejpam-5536	74	41	partial	partial	ADJ
ejpam-5536	74	42	order	order	NOUN
ejpam-5536	74	43	on	on	ADP
ejpam-5536	74	44	x	x	PUNCT
ejpam-5536	74	45	with	with	ADP
ejpam-5536	74	46	1x	1x	NUM
ejpam-5536	74	47	as	as	ADP
ejpam-5536	74	48	the	the	DET
ejpam-5536	74	49	largest	large	ADJ
ejpam-5536	74	50	element	element	NOUN
ejpam-5536	74	51	.	.	PUNCT
ejpam-5536	75	1	a.	a.	PROPN
ejpam-5536	75	2	iampan	iampan	PROPN
ejpam-5536	75	3	et	et	PROPN
ejpam-5536	75	4	al	al	PROPN
ejpam-5536	75	5	.	.	PUNCT
ejpam-5536	75	6	/	/	SYM
ejpam-5536	75	7	eur	eur	PROPN
ejpam-5536	75	8	.	.	PUNCT
ejpam-5536	76	1	j.	j.	PROPN
ejpam-5536	76	2	pure	pure	PROPN
ejpam-5536	76	3	appl	appl	PROPN
ejpam-5536	76	4	.	.	PROPN
ejpam-5536	76	5	math	math	PROPN
ejpam-5536	76	6	,	,	PUNCT
ejpam-5536	76	7	17	17	NUM
ejpam-5536	76	8	(	(	PUNCT
ejpam-5536	76	9	4	4	NUM
ejpam-5536	76	10	)	)	PUNCT
ejpam-5536	76	11	(	(	PUNCT
ejpam-5536	76	12	2024	2024	NUM
ejpam-5536	76	13	)	)	PUNCT
ejpam-5536	76	14	,	,	PUNCT
ejpam-5536	76	15	4059	4059	NUM
ejpam-5536	76	16	-	-	SYM
ejpam-5536	76	17	4070	4070	NUM
ejpam-5536	76	18	4062	4062	NUM
ejpam-5536	76	19	definition	definition	NOUN
ejpam-5536	76	20	2	2	NUM
ejpam-5536	76	21	.	.	PUNCT
ejpam-5536	77	1	[	[	X
ejpam-5536	77	2	20	20	NUM
ejpam-5536	77	3	]	]	PUNCT
ejpam-5536	77	4	a	a	DET
ejpam-5536	77	5	nonempty	nonempty	NOUN
ejpam-5536	77	6	subset	subset	VERB
ejpam-5536	77	7	d	d	NOUN
ejpam-5536	77	8	of	of	ADP
ejpam-5536	77	9	a	a	DET
ejpam-5536	77	10	hilbert	hilbert	NOUN
ejpam-5536	77	11	algebra	algebra	NOUN
ejpam-5536	77	12	x	x	PUNCT
ejpam-5536	77	13	=	=	SYM
ejpam-5536	77	14	(	(	PUNCT
ejpam-5536	77	15	x	x	NOUN
ejpam-5536	77	16	,	,	PUNCT
ejpam-5536	77	17	·	·	PUNCT
ejpam-5536	77	18	,	,	PUNCT
ejpam-5536	77	19	1x	1x	NUM
ejpam-5536	77	20	)	)	PUNCT
ejpam-5536	77	21	is	be	AUX
ejpam-5536	77	22	called	call	VERB
ejpam-5536	77	23	a	a	DET
ejpam-5536	77	24	subalgebra	subalgebra	NOUN
ejpam-5536	77	25	of	of	ADP
ejpam-5536	77	26	x	x	PUNCT
ejpam-5536	77	27	if	if	SCONJ
ejpam-5536	77	28	x	x	X
ejpam-5536	77	29	·	·	PUNCT
ejpam-5536	77	30	y	y	X
ejpam-5536	77	31	∈	∈	PROPN
ejpam-5536	77	32	d	d	NOUN
ejpam-5536	77	33	for	for	ADP
ejpam-5536	77	34	all	all	DET
ejpam-5536	77	35	x	x	NOUN
ejpam-5536	77	36	,	,	PUNCT
ejpam-5536	77	37	y	y	PROPN
ejpam-5536	77	38	∈	∈	PROPN
ejpam-5536	77	39	d.	d.	PROPN
ejpam-5536	77	40	definition	definition	NOUN
ejpam-5536	77	41	3	3	NUM
ejpam-5536	77	42	.	.	PUNCT
ejpam-5536	78	1	[	[	X
ejpam-5536	78	2	5	5	NUM
ejpam-5536	78	3	,	,	PUNCT
ejpam-5536	78	4	8	8	NUM
ejpam-5536	78	5	]	]	PUNCT
ejpam-5536	78	6	a	a	DET
ejpam-5536	78	7	nonempty	nonempty	NOUN
ejpam-5536	78	8	subset	subset	VERB
ejpam-5536	78	9	d	d	NOUN
ejpam-5536	78	10	of	of	ADP
ejpam-5536	78	11	a	a	DET
ejpam-5536	78	12	hilbert	hilbert	NOUN
ejpam-5536	78	13	algebra	algebra	NOUN
ejpam-5536	78	14	x	x	PUNCT
ejpam-5536	78	15	=	=	SYM
ejpam-5536	78	16	(	(	PUNCT
ejpam-5536	78	17	x	x	NOUN
ejpam-5536	78	18	,	,	PUNCT
ejpam-5536	78	19	·	·	PUNCT
ejpam-5536	78	20	,	,	PUNCT
ejpam-5536	78	21	1x	1x	NUM
ejpam-5536	78	22	)	)	PUNCT
ejpam-5536	78	23	is	be	AUX
ejpam-5536	78	24	called	call	VERB
ejpam-5536	78	25	an	an	DET
ejpam-5536	78	26	ideal	ideal	NOUN
ejpam-5536	78	27	of	of	ADP
ejpam-5536	78	28	x	x	PRON
ejpam-5536	78	29	if	if	SCONJ
ejpam-5536	78	30	the	the	DET
ejpam-5536	78	31	following	follow	VERB
ejpam-5536	78	32	conditions	condition	NOUN
ejpam-5536	78	33	hold	hold	VERB
ejpam-5536	78	34	:	:	PUNCT
ejpam-5536	78	35	(	(	PUNCT
ejpam-5536	78	36	1	1	X
ejpam-5536	78	37	)	)	PUNCT
ejpam-5536	79	1	1x	1x	NOUN
ejpam-5536	79	2	∈	∈	PROPN
ejpam-5536	80	1	d	d	X
ejpam-5536	80	2	(	(	PUNCT
ejpam-5536	80	3	2	2	NUM
ejpam-5536	80	4	)	)	PUNCT
ejpam-5536	80	5	(	(	PUNCT
ejpam-5536	80	6	∀x	∀x	X
ejpam-5536	80	7	,	,	PUNCT
ejpam-5536	80	8	y	y	PROPN
ejpam-5536	80	9	∈	∈	PROPN
ejpam-5536	80	10	x)(y	x)(y	PUNCT
ejpam-5536	80	11	∈	∈	PROPN
ejpam-5536	81	1	d	d	NOUN
ejpam-5536	81	2	⇒	⇒	NOUN
ejpam-5536	81	3	x	x	X
ejpam-5536	81	4	·	·	PUNCT
ejpam-5536	81	5	y	y	X
ejpam-5536	81	6	∈	∈	PROPN
ejpam-5536	81	7	d	d	X
ejpam-5536	81	8	)	)	PUNCT
ejpam-5536	81	9	(	(	PUNCT
ejpam-5536	81	10	3	3	X
ejpam-5536	81	11	)	)	PUNCT
ejpam-5536	81	12	(	(	PUNCT
ejpam-5536	81	13	∀x	∀x	X
ejpam-5536	81	14	,	,	PUNCT
ejpam-5536	81	15	y1	y1	X
ejpam-5536	81	16	,	,	PUNCT
ejpam-5536	81	17	y2	y2	PROPN
ejpam-5536	81	18	∈	∈	PROPN
ejpam-5536	81	19	x)(y1	x)(y1	PROPN
ejpam-5536	81	20	,	,	PUNCT
ejpam-5536	81	21	y2	y2	NOUN
ejpam-5536	81	22	∈	∈	PROPN
ejpam-5536	81	23	d	d	X
ejpam-5536	81	24	⇒	⇒	NOUN
ejpam-5536	81	25	(	(	PUNCT
ejpam-5536	81	26	y1	y1	INTJ
ejpam-5536	81	27	·	·	PUNCT
ejpam-5536	81	28	(	(	PUNCT
ejpam-5536	81	29	y2	y2	INTJ
ejpam-5536	81	30	·	·	PUNCT
ejpam-5536	81	31	x	x	X
ejpam-5536	81	32	)	)	PUNCT
ejpam-5536	81	33	)	)	PUNCT
ejpam-5536	81	34	·	·	PUNCT
ejpam-5536	82	1	x	x	PUNCT
ejpam-5536	82	2	∈	∈	PROPN
ejpam-5536	82	3	d	d	X
ejpam-5536	82	4	)	)	PUNCT
ejpam-5536	82	5	definition	definition	NOUN
ejpam-5536	82	6	4	4	NUM
ejpam-5536	82	7	.	.	PUNCT
ejpam-5536	83	1	[	[	X
ejpam-5536	83	2	8	8	X
ejpam-5536	83	3	]	]	PUNCT
ejpam-5536	83	4	a	a	DET
ejpam-5536	83	5	nonempty	nonempty	NOUN
ejpam-5536	83	6	subset	subset	VERB
ejpam-5536	83	7	d	d	NOUN
ejpam-5536	83	8	of	of	ADP
ejpam-5536	83	9	a	a	DET
ejpam-5536	83	10	hilbert	hilbert	NOUN
ejpam-5536	83	11	algebra	algebra	NOUN
ejpam-5536	83	12	x	x	PUNCT
ejpam-5536	83	13	=	=	SYM
ejpam-5536	83	14	(	(	PUNCT
ejpam-5536	83	15	x	x	NOUN
ejpam-5536	83	16	,	,	PUNCT
ejpam-5536	83	17	·	·	PUNCT
ejpam-5536	83	18	,	,	PUNCT
ejpam-5536	83	19	1x	1x	NUM
ejpam-5536	83	20	)	)	PUNCT
ejpam-5536	83	21	is	be	AUX
ejpam-5536	83	22	called	call	VERB
ejpam-5536	83	23	a	a	DET
ejpam-5536	83	24	deductive	deductive	ADJ
ejpam-5536	83	25	system	system	NOUN
ejpam-5536	83	26	of	of	ADP
ejpam-5536	83	27	x	x	PRON
ejpam-5536	83	28	if	if	SCONJ
ejpam-5536	83	29	(	(	PUNCT
ejpam-5536	83	30	1	1	NUM
ejpam-5536	83	31	)	)	PUNCT
ejpam-5536	83	32	1x	1x	NOUN
ejpam-5536	84	1	∈	∈	PROPN
ejpam-5536	84	2	d	d	X
ejpam-5536	84	3	(	(	PUNCT
ejpam-5536	84	4	2	2	NUM
ejpam-5536	84	5	)	)	PUNCT
ejpam-5536	84	6	(	(	PUNCT
ejpam-5536	84	7	∀x	∀x	X
ejpam-5536	84	8	,	,	PUNCT
ejpam-5536	84	9	y	y	PROPN
ejpam-5536	84	10	∈	∈	PROPN
ejpam-5536	84	11	x)(x	x)(x	PROPN
ejpam-5536	84	12	·	·	PUNCT
ejpam-5536	84	13	y	y	X
ejpam-5536	84	14	∈	∈	PROPN
ejpam-5536	85	1	d	d	NOUN
ejpam-5536	85	2	,	,	PUNCT
ejpam-5536	85	3	x	x	SYM
ejpam-5536	85	4	∈	∈	PROPN
ejpam-5536	85	5	d	d	X
ejpam-5536	85	6	⇒	⇒	NOUN
ejpam-5536	85	7	y	y	PROPN
ejpam-5536	85	8	∈	∈	PROPN
ejpam-5536	86	1	d	d	X
ejpam-5536	86	2	)	)	PUNCT
ejpam-5536	86	3	a	a	DET
ejpam-5536	86	4	fuzzy	fuzzy	ADJ
ejpam-5536	86	5	set	set	NOUN
ejpam-5536	86	6	[	[	X
ejpam-5536	86	7	19	19	NUM
ejpam-5536	86	8	]	]	PUNCT
ejpam-5536	86	9	in	in	ADP
ejpam-5536	86	10	a	a	DET
ejpam-5536	86	11	nonempty	nonempty	ADV
ejpam-5536	86	12	set	set	VERB
ejpam-5536	86	13	x	x	SYM
ejpam-5536	86	14	is	be	AUX
ejpam-5536	86	15	defined	define	VERB
ejpam-5536	86	16	to	to	PART
ejpam-5536	86	17	be	be	AUX
ejpam-5536	86	18	a	a	DET
ejpam-5536	86	19	function	function	NOUN
ejpam-5536	86	20	µ	µ	NOUN
ejpam-5536	86	21	:	:	PUNCT
ejpam-5536	86	22	x	x	SYM
ejpam-5536	86	23	→	→	SYM
ejpam-5536	87	1	[	[	X
ejpam-5536	87	2	0	0	NUM
ejpam-5536	87	3	,	,	PUNCT
ejpam-5536	87	4	1	1	NUM
ejpam-5536	87	5	]	]	PUNCT
ejpam-5536	87	6	,	,	PUNCT
ejpam-5536	87	7	where	where	SCONJ
ejpam-5536	87	8	[	[	X
ejpam-5536	87	9	0	0	NUM
ejpam-5536	87	10	,	,	PUNCT
ejpam-5536	87	11	1	1	NUM
ejpam-5536	87	12	]	]	PUNCT
ejpam-5536	87	13	is	be	AUX
ejpam-5536	87	14	the	the	DET
ejpam-5536	87	15	unit	unit	NOUN
ejpam-5536	87	16	closed	close	VERB
ejpam-5536	87	17	interval	interval	NOUN
ejpam-5536	87	18	of	of	ADP
ejpam-5536	87	19	real	real	ADJ
ejpam-5536	87	20	numbers	number	NOUN
ejpam-5536	87	21	.	.	PUNCT
ejpam-5536	88	1	definition	definition	NOUN
ejpam-5536	88	2	5	5	NUM
ejpam-5536	88	3	.	.	PUNCT
ejpam-5536	89	1	[	[	X
ejpam-5536	89	2	13	13	NUM
ejpam-5536	89	3	]	]	PUNCT
ejpam-5536	89	4	a	a	DET
ejpam-5536	89	5	fuzzy	fuzzy	ADJ
ejpam-5536	89	6	set	set	VERB
ejpam-5536	89	7	µ	µ	NOUN
ejpam-5536	89	8	in	in	ADP
ejpam-5536	89	9	a	a	DET
ejpam-5536	89	10	hilbert	hilbert	NOUN
ejpam-5536	89	11	algebra	algebra	NOUN
ejpam-5536	89	12	x	x	PUNCT
ejpam-5536	89	13	=	=	SYM
ejpam-5536	89	14	(	(	PUNCT
ejpam-5536	89	15	x	x	NOUN
ejpam-5536	89	16	,	,	PUNCT
ejpam-5536	89	17	·	·	PUNCT
ejpam-5536	89	18	,	,	PUNCT
ejpam-5536	89	19	1x	1x	NUM
ejpam-5536	89	20	)	)	PUNCT
ejpam-5536	89	21	is	be	AUX
ejpam-5536	89	22	said	say	VERB
ejpam-5536	89	23	to	to	PART
ejpam-5536	89	24	be	be	AUX
ejpam-5536	89	25	a	a	DET
ejpam-5536	89	26	fuzzy	fuzzy	ADJ
ejpam-5536	89	27	subalgebra	subalgebra	NOUN
ejpam-5536	89	28	of	of	ADP
ejpam-5536	89	29	x	x	PRON
ejpam-5536	89	30	if	if	SCONJ
ejpam-5536	89	31	the	the	DET
ejpam-5536	89	32	following	follow	VERB
ejpam-5536	89	33	condition	condition	NOUN
ejpam-5536	89	34	holds	hold	VERB
ejpam-5536	89	35	:	:	PUNCT
ejpam-5536	89	36	(	(	PUNCT
ejpam-5536	89	37	∀x	∀x	X
ejpam-5536	89	38	,	,	PUNCT
ejpam-5536	89	39	y	y	PROPN
ejpam-5536	89	40	∈	∈	PROPN
ejpam-5536	89	41	x)(µ(x	x)(µ(x	PUNCT
ejpam-5536	89	42	·	·	PUNCT
ejpam-5536	89	43	y	y	X
ejpam-5536	89	44	)	)	PUNCT
ejpam-5536	89	45	≥	≥	NOUN
ejpam-5536	89	46	min{µ(x	min{µ(x	NOUN
ejpam-5536	89	47	)	)	PUNCT
ejpam-5536	89	48	,	,	PUNCT
ejpam-5536	89	49	µ(y	µ(y	PROPN
ejpam-5536	89	50	)	)	PUNCT
ejpam-5536	89	51	}	}	PUNCT
ejpam-5536	89	52	)	)	PUNCT
ejpam-5536	89	53	definition	definition	NOUN
ejpam-5536	89	54	6	6	NUM
ejpam-5536	89	55	.	.	PUNCT
ejpam-5536	90	1	[	[	X
ejpam-5536	90	2	9	9	NUM
ejpam-5536	90	3	]	]	PUNCT
ejpam-5536	90	4	a	a	DET
ejpam-5536	90	5	fuzzy	fuzzy	ADJ
ejpam-5536	90	6	set	set	VERB
ejpam-5536	90	7	µ	µ	NOUN
ejpam-5536	90	8	in	in	ADP
ejpam-5536	90	9	a	a	DET
ejpam-5536	90	10	hilbert	hilbert	NOUN
ejpam-5536	90	11	algebra	algebra	NOUN
ejpam-5536	90	12	x	x	PUNCT
ejpam-5536	90	13	=	=	SYM
ejpam-5536	90	14	(	(	PUNCT
ejpam-5536	90	15	x	x	NOUN
ejpam-5536	90	16	,	,	PUNCT
ejpam-5536	90	17	·	·	PUNCT
ejpam-5536	90	18	,	,	PUNCT
ejpam-5536	90	19	1x	1x	NUM
ejpam-5536	90	20	)	)	PUNCT
ejpam-5536	90	21	is	be	AUX
ejpam-5536	90	22	said	say	VERB
ejpam-5536	90	23	to	to	PART
ejpam-5536	90	24	be	be	AUX
ejpam-5536	90	25	a	a	DET
ejpam-5536	90	26	fuzzy	fuzzy	ADJ
ejpam-5536	90	27	ideal	ideal	NOUN
ejpam-5536	90	28	of	of	ADP
ejpam-5536	90	29	x	x	PRON
ejpam-5536	90	30	if	if	SCONJ
ejpam-5536	90	31	the	the	DET
ejpam-5536	90	32	following	follow	VERB
ejpam-5536	90	33	conditions	condition	NOUN
ejpam-5536	90	34	hold	hold	VERB
ejpam-5536	90	35	:	:	PUNCT
ejpam-5536	90	36	(	(	PUNCT
ejpam-5536	90	37	1	1	X
ejpam-5536	90	38	)	)	PUNCT
ejpam-5536	90	39	(	(	PUNCT
ejpam-5536	90	40	∀x	∀x	X
ejpam-5536	90	41	∈	∈	PROPN
ejpam-5536	90	42	x)(µ(1x	x)(µ(1x	PROPN
ejpam-5536	90	43	)	)	PUNCT
ejpam-5536	90	44	≥	≥	NOUN
ejpam-5536	90	45	µ(x	µ(x	VERB
ejpam-5536	90	46	)	)	PUNCT
ejpam-5536	90	47	)	)	PUNCT
ejpam-5536	90	48	(	(	PUNCT
ejpam-5536	90	49	2	2	X
ejpam-5536	90	50	)	)	PUNCT
ejpam-5536	90	51	(	(	PUNCT
ejpam-5536	90	52	∀x	∀x	X
ejpam-5536	90	53	,	,	PUNCT
ejpam-5536	90	54	y	y	PROPN
ejpam-5536	90	55	∈	∈	PROPN
ejpam-5536	90	56	x)(µ(x	x)(µ(x	PUNCT
ejpam-5536	90	57	·	·	PUNCT
ejpam-5536	90	58	y	y	X
ejpam-5536	90	59	)	)	PUNCT
ejpam-5536	90	60	≥	≥	NOUN
ejpam-5536	90	61	µ(y	µ(y	PROPN
ejpam-5536	90	62	)	)	PUNCT
ejpam-5536	90	63	)	)	PUNCT
ejpam-5536	90	64	(	(	PUNCT
ejpam-5536	90	65	3	3	X
ejpam-5536	90	66	)	)	PUNCT
ejpam-5536	90	67	(	(	PUNCT
ejpam-5536	90	68	∀x	∀x	X
ejpam-5536	90	69	,	,	PUNCT
ejpam-5536	90	70	y1	y1	X
ejpam-5536	90	71	,	,	PUNCT
ejpam-5536	90	72	y2	y2	PROPN
ejpam-5536	90	73	∈	∈	PROPN
ejpam-5536	90	74	x)(µ((y1	x)(µ((y1	PROPN
ejpam-5536	90	75	·	·	PUNCT
ejpam-5536	90	76	(	(	PUNCT
ejpam-5536	90	77	y2	y2	INTJ
ejpam-5536	90	78	·	·	PUNCT
ejpam-5536	90	79	x	x	X
ejpam-5536	90	80	)	)	PUNCT
ejpam-5536	90	81	)	)	PUNCT
ejpam-5536	90	82	·	·	PUNCT
ejpam-5536	91	1	x	x	X
ejpam-5536	91	2	)	)	PUNCT
ejpam-5536	91	3	≥	≥	NOUN
ejpam-5536	91	4	min{µ(y1	min{µ(y1	NOUN
ejpam-5536	91	5	)	)	PUNCT
ejpam-5536	91	6	,	,	PUNCT
ejpam-5536	91	7	µ(y2	µ(y2	NOUN
ejpam-5536	91	8	)	)	PUNCT
ejpam-5536	91	9	}	}	PUNCT
ejpam-5536	91	10	)	)	PUNCT
ejpam-5536	91	11	definition	definition	NOUN
ejpam-5536	91	12	7	7	NUM
ejpam-5536	91	13	.	.	PUNCT
ejpam-5536	92	1	[	[	X
ejpam-5536	92	2	22	22	NUM
ejpam-5536	92	3	]	]	PUNCT
ejpam-5536	92	4	let	let	VERB
ejpam-5536	92	5	x	x	PRON
ejpam-5536	92	6	be	be	AUX
ejpam-5536	92	7	a	a	DET
ejpam-5536	92	8	nonempty	nonempty	ADV
ejpam-5536	92	9	set	set	VERB
ejpam-5536	92	10	.	.	PUNCT
ejpam-5536	93	1	a	a	DET
ejpam-5536	93	2	bipolar	bipolar	ADJ
ejpam-5536	93	3	fuzzy	fuzzy	ADJ
ejpam-5536	93	4	set	set	NOUN
ejpam-5536	93	5	(	(	PUNCT
ejpam-5536	93	6	bfs	bfs	NOUN
ejpam-5536	93	7	)	)	PUNCT
ejpam-5536	93	8	φ	φ	PROPN
ejpam-5536	93	9	in	in	ADP
ejpam-5536	93	10	x	x	PROPN
ejpam-5536	93	11	is	be	AUX
ejpam-5536	93	12	an	an	DET
ejpam-5536	93	13	object	object	NOUN
ejpam-5536	93	14	having	have	VERB
ejpam-5536	93	15	the	the	DET
ejpam-5536	93	16	form	form	NOUN
ejpam-5536	93	17	φ	φ	NOUN
ejpam-5536	93	18	=	=	SYM
ejpam-5536	93	19	{	{	PUNCT
ejpam-5536	93	20	(	(	PUNCT
ejpam-5536	93	21	x	x	NOUN
ejpam-5536	93	22	,	,	PUNCT
ejpam-5536	93	23	φ+(x	φ+(x	NOUN
ejpam-5536	93	24	)	)	PUNCT
ejpam-5536	93	25	,	,	PUNCT
ejpam-5536	93	26	φ−(x	φ−(x	PROPN
ejpam-5536	93	27	)	)	PUNCT
ejpam-5536	93	28	)	)	PUNCT
ejpam-5536	94	1	|	|	ADV
ejpam-5536	94	2	x	x	SYM
ejpam-5536	94	3	∈	∈	NOUN
ejpam-5536	94	4	x	x	X
ejpam-5536	94	5	}	}	PUNCT
ejpam-5536	94	6	,	,	PUNCT
ejpam-5536	94	7	where	where	SCONJ
ejpam-5536	94	8	φ+	φ+	NOUN
ejpam-5536	94	9	:	:	PUNCT
ejpam-5536	94	10	x	x	X
ejpam-5536	94	11	→	→	PUNCT
ejpam-5536	95	1	[	[	X
ejpam-5536	95	2	0	0	NUM
ejpam-5536	95	3	,	,	PUNCT
ejpam-5536	95	4	1	1	NUM
ejpam-5536	95	5	]	]	PUNCT
ejpam-5536	95	6	and	and	CCONJ
ejpam-5536	95	7	φ−	φ−	PROPN
ejpam-5536	95	8	:	:	PUNCT
ejpam-5536	95	9	x	x	X
ejpam-5536	95	10	→	→	PUNCT
ejpam-5536	95	11	[	[	X
ejpam-5536	95	12	−1	−1	NOUN
ejpam-5536	95	13	,	,	PUNCT
ejpam-5536	95	14	0	0	NUM
ejpam-5536	95	15	]	]	PUNCT
ejpam-5536	95	16	are	be	AUX
ejpam-5536	95	17	mappings	mapping	NOUN
ejpam-5536	95	18	.	.	PUNCT
ejpam-5536	96	1	we	we	PRON
ejpam-5536	96	2	use	use	VERB
ejpam-5536	96	3	the	the	DET
ejpam-5536	96	4	positive	positive	ADJ
ejpam-5536	96	5	membership	membership	NOUN
ejpam-5536	96	6	degree	degree	NOUN
ejpam-5536	96	7	φ+(x	φ+(x	NOUN
ejpam-5536	96	8	)	)	PUNCT
ejpam-5536	96	9	to	to	PART
ejpam-5536	96	10	denote	denote	VERB
ejpam-5536	96	11	the	the	DET
ejpam-5536	96	12	satisfaction	satisfaction	NOUN
ejpam-5536	96	13	degree	degree	NOUN
ejpam-5536	96	14	of	of	ADP
ejpam-5536	96	15	an	an	DET
ejpam-5536	96	16	element	element	NOUN
ejpam-5536	96	17	x	x	X
ejpam-5536	96	18	to	to	ADP
ejpam-5536	96	19	the	the	DET
ejpam-5536	96	20	property	property	NOUN
ejpam-5536	96	21	corresponding	correspond	VERB
ejpam-5536	96	22	to	to	ADP
ejpam-5536	96	23	a	a	DET
ejpam-5536	96	24	bfs	bfs	NOUN
ejpam-5536	96	25	φ	φ	NOUN
ejpam-5536	96	26	,	,	PUNCT
ejpam-5536	96	27	and	and	CCONJ
ejpam-5536	96	28	the	the	DET
ejpam-5536	96	29	negative	negative	ADJ
ejpam-5536	96	30	membership	membership	NOUN
ejpam-5536	96	31	degree	degree	NOUN
ejpam-5536	96	32	φ−(x	φ−(x	PROPN
ejpam-5536	96	33	)	)	PUNCT
ejpam-5536	96	34	to	to	PART
ejpam-5536	96	35	denote	denote	VERB
ejpam-5536	96	36	the	the	DET
ejpam-5536	96	37	satisfaction	satisfaction	NOUN
ejpam-5536	96	38	degree	degree	NOUN
ejpam-5536	96	39	of	of	ADP
ejpam-5536	96	40	an	an	DET
ejpam-5536	96	41	element	element	NOUN
ejpam-5536	96	42	x	x	PUNCT
ejpam-5536	96	43	to	to	ADP
ejpam-5536	96	44	some	some	DET
ejpam-5536	96	45	implicit	implicit	ADJ
ejpam-5536	96	46	counter	counter	ADJ
ejpam-5536	96	47	-	-	NOUN
ejpam-5536	96	48	property	property	NOUN
ejpam-5536	96	49	corresponding	corresponding	NOUN
ejpam-5536	96	50	to	to	ADP
ejpam-5536	96	51	a	a	DET
ejpam-5536	96	52	bfs	bfs	NOUN
ejpam-5536	96	53	φ	φ	NOUN
ejpam-5536	96	54	.	.	PUNCT
ejpam-5536	97	1	if	if	SCONJ
ejpam-5536	97	2	φ+(x	φ+(x	X
ejpam-5536	97	3	)	)	PUNCT
ejpam-5536	97	4	̸=	̸=	PROPN
ejpam-5536	97	5	0	0	NUM
ejpam-5536	97	6	and	and	CCONJ
ejpam-5536	97	7	φ−(x	φ−(x	PROPN
ejpam-5536	97	8	)	)	PUNCT
ejpam-5536	98	1	=	=	SYM
ejpam-5536	98	2	0	0	NUM
ejpam-5536	98	3	,	,	PUNCT
ejpam-5536	98	4	it	it	PRON
ejpam-5536	98	5	is	be	AUX
ejpam-5536	98	6	the	the	DET
ejpam-5536	98	7	situation	situation	NOUN
ejpam-5536	98	8	that	that	PRON
ejpam-5536	98	9	x	x	PRON
ejpam-5536	98	10	is	be	AUX
ejpam-5536	98	11	regarded	regard	VERB
ejpam-5536	98	12	as	as	ADP
ejpam-5536	98	13	having	have	VERB
ejpam-5536	98	14	only	only	ADV
ejpam-5536	98	15	positive	positive	ADJ
ejpam-5536	98	16	satisfaction	satisfaction	NOUN
ejpam-5536	98	17	for	for	ADP
ejpam-5536	98	18	φ	φ	PROPN
ejpam-5536	98	19	.	.	PUNCT
ejpam-5536	99	1	if	if	SCONJ
ejpam-5536	99	2	φ+(x	φ+(x	VERB
ejpam-5536	99	3	)	)	PUNCT
ejpam-5536	99	4	=	=	SYM
ejpam-5536	99	5	0	0	NUM
ejpam-5536	99	6	and	and	CCONJ
ejpam-5536	99	7	φ−(x	φ−(x	PROPN
ejpam-5536	99	8	)	)	PUNCT
ejpam-5536	100	1	̸=	̸=	PROPN
ejpam-5536	100	2	0	0	NUM
ejpam-5536	100	3	,	,	PUNCT
ejpam-5536	100	4	it	it	PRON
ejpam-5536	100	5	is	be	AUX
ejpam-5536	100	6	the	the	DET
ejpam-5536	100	7	situation	situation	NOUN
ejpam-5536	100	8	that	that	PRON
ejpam-5536	100	9	x	x	PRON
ejpam-5536	100	10	does	do	AUX
ejpam-5536	100	11	not	not	PART
ejpam-5536	100	12	satisfy	satisfy	VERB
ejpam-5536	100	13	the	the	DET
ejpam-5536	100	14	property	property	NOUN
ejpam-5536	100	15	of	of	ADP
ejpam-5536	100	16	φ	φ	PROPN
ejpam-5536	100	17	but	but	CCONJ
ejpam-5536	100	18	somewhat	somewhat	ADV
ejpam-5536	100	19	satisfies	satisfy	VERB
ejpam-5536	100	20	the	the	DET
ejpam-5536	100	21	counter	counter	ADJ
ejpam-5536	100	22	property	property	NOUN
ejpam-5536	100	23	of	of	ADP
ejpam-5536	100	24	φ	φ	PROPN
ejpam-5536	100	25	.	.	PUNCT
ejpam-5536	101	1	it	it	PRON
ejpam-5536	101	2	is	be	AUX
ejpam-5536	101	3	possible	possible	ADJ
ejpam-5536	101	4	for	for	SCONJ
ejpam-5536	101	5	an	an	DET
ejpam-5536	101	6	element	element	NOUN
ejpam-5536	101	7	x	x	PART
ejpam-5536	101	8	to	to	PART
ejpam-5536	101	9	be	be	AUX
ejpam-5536	101	10	such	such	ADJ
ejpam-5536	101	11	that	that	PRON
ejpam-5536	101	12	φ+(x	φ+(x	NOUN
ejpam-5536	101	13	)	)	PUNCT
ejpam-5536	101	14	=	=	SYM
ejpam-5536	101	15	0	0	NUM
ejpam-5536	101	16	and	and	CCONJ
ejpam-5536	101	17	φ−(x	φ−(x	PROPN
ejpam-5536	101	18	)	)	PUNCT
ejpam-5536	102	1	=	=	SYM
ejpam-5536	102	2	0	0	NUM
ejpam-5536	102	3	,	,	PUNCT
ejpam-5536	102	4	when	when	SCONJ
ejpam-5536	102	5	the	the	DET
ejpam-5536	102	6	membership	membership	NOUN
ejpam-5536	102	7	function	function	NOUN
ejpam-5536	102	8	of	of	ADP
ejpam-5536	102	9	the	the	DET
ejpam-5536	102	10	property	property	NOUN
ejpam-5536	102	11	overlaps	overlap	VERB
ejpam-5536	102	12	that	that	PRON
ejpam-5536	102	13	of	of	ADP
ejpam-5536	102	14	its	its	PRON
ejpam-5536	102	15	counter	counter	ADJ
ejpam-5536	102	16	property	property	NOUN
ejpam-5536	102	17	over	over	ADP
ejpam-5536	102	18	some	some	DET
ejpam-5536	102	19	portion	portion	NOUN
ejpam-5536	102	20	of	of	ADP
ejpam-5536	102	21	x.	x.	NOUN
ejpam-5536	102	22	for	for	ADP
ejpam-5536	102	23	the	the	DET
ejpam-5536	102	24	sake	sake	NOUN
ejpam-5536	102	25	of	of	ADP
ejpam-5536	102	26	simplicity	simplicity	NOUN
ejpam-5536	102	27	,	,	PUNCT
ejpam-5536	102	28	we	we	PRON
ejpam-5536	102	29	shall	shall	AUX
ejpam-5536	102	30	use	use	VERB
ejpam-5536	102	31	the	the	DET
ejpam-5536	102	32	symbol	symbol	NOUN
ejpam-5536	102	33	φ	φ	NOUN
ejpam-5536	102	34	=	=	SYM
ejpam-5536	102	35	(	(	PUNCT
ejpam-5536	102	36	φ+	φ+	NOUN
ejpam-5536	102	37	,	,	PUNCT
ejpam-5536	102	38	φ−	φ−	PROPN
ejpam-5536	102	39	)	)	PUNCT
ejpam-5536	102	40	for	for	SCONJ
ejpam-5536	102	41	the	the	DET
ejpam-5536	102	42	bipolar	bipolar	ADJ
ejpam-5536	102	43	fuzzy	fuzzy	NOUN
ejpam-5536	102	44	set	set	VERB
ejpam-5536	102	45	φ	φ	NOUN
ejpam-5536	102	46	=	=	SYM
ejpam-5536	102	47	{	{	PUNCT
ejpam-5536	102	48	(	(	PUNCT
ejpam-5536	102	49	x	x	NOUN
ejpam-5536	102	50	,	,	PUNCT
ejpam-5536	102	51	φ+(x	φ+(x	NOUN
ejpam-5536	102	52	)	)	PUNCT
ejpam-5536	102	53	,	,	PUNCT
ejpam-5536	102	54	φ−(x	φ−(x	PROPN
ejpam-5536	102	55	)	)	PUNCT
ejpam-5536	102	56	)	)	PUNCT
ejpam-5536	103	1	|	|	ADV
ejpam-5536	103	2	x	x	SYM
ejpam-5536	103	3	∈	∈	NOUN
ejpam-5536	103	4	x	x	X
ejpam-5536	103	5	}	}	PUNCT
ejpam-5536	103	6	.	.	PUNCT
ejpam-5536	104	1	a.	a.	NOUN
ejpam-5536	104	2	iampan	iampan	PROPN
ejpam-5536	104	3	et	et	PROPN
ejpam-5536	104	4	al	al	PROPN
ejpam-5536	104	5	.	.	PUNCT
ejpam-5536	104	6	/	/	SYM
ejpam-5536	104	7	eur	eur	PROPN
ejpam-5536	104	8	.	.	PUNCT
ejpam-5536	105	1	j.	j.	PROPN
ejpam-5536	105	2	pure	pure	PROPN
ejpam-5536	105	3	appl	appl	PROPN
ejpam-5536	105	4	.	.	PROPN
ejpam-5536	105	5	math	math	PROPN
ejpam-5536	105	6	,	,	PUNCT
ejpam-5536	105	7	17	17	NUM
ejpam-5536	105	8	(	(	PUNCT
ejpam-5536	105	9	4	4	NUM
ejpam-5536	105	10	)	)	PUNCT
ejpam-5536	105	11	(	(	PUNCT
ejpam-5536	105	12	2024	2024	NUM
ejpam-5536	105	13	)	)	PUNCT
ejpam-5536	105	14	,	,	PUNCT
ejpam-5536	105	15	4059	4059	NUM
ejpam-5536	105	16	-	-	SYM
ejpam-5536	105	17	4070	4070	NUM
ejpam-5536	105	18	4063	4063	NUM
ejpam-5536	105	19	definition	definition	NOUN
ejpam-5536	105	20	8	8	NUM
ejpam-5536	105	21	.	.	PUNCT
ejpam-5536	106	1	[	[	X
ejpam-5536	106	2	11	11	NUM
ejpam-5536	106	3	]	]	PUNCT
ejpam-5536	106	4	a	a	DET
ejpam-5536	106	5	bfs	bfs	NOUN
ejpam-5536	106	6	φ	φ	NOUN
ejpam-5536	106	7	=	=	SYM
ejpam-5536	106	8	(	(	PUNCT
ejpam-5536	106	9	φ+	φ+	NOUN
ejpam-5536	106	10	,	,	PUNCT
ejpam-5536	106	11	φ−	φ−	PROPN
ejpam-5536	106	12	)	)	PUNCT
ejpam-5536	106	13	in	in	ADP
ejpam-5536	106	14	a	a	DET
ejpam-5536	106	15	hilbert	hilbert	NOUN
ejpam-5536	106	16	algebra	algebra	NOUN
ejpam-5536	106	17	x	x	PUNCT
ejpam-5536	106	18	=	=	SYM
ejpam-5536	106	19	(	(	PUNCT
ejpam-5536	106	20	x	x	NOUN
ejpam-5536	106	21	,	,	PUNCT
ejpam-5536	106	22	·	·	PUNCT
ejpam-5536	106	23	,	,	PUNCT
ejpam-5536	106	24	1x	1x	NUM
ejpam-5536	106	25	)	)	PUNCT
ejpam-5536	106	26	is	be	AUX
ejpam-5536	106	27	called	call	VERB
ejpam-5536	106	28	a	a	DET
ejpam-5536	106	29	bipolar	bipolar	ADJ
ejpam-5536	106	30	fuzzy	fuzzy	ADJ
ejpam-5536	106	31	subalgebra	subalgebra	NOUN
ejpam-5536	106	32	of	of	ADP
ejpam-5536	106	33	x	x	PRON
ejpam-5536	106	34	if	if	SCONJ
ejpam-5536	106	35	the	the	DET
ejpam-5536	106	36	following	follow	VERB
ejpam-5536	106	37	condition	condition	NOUN
ejpam-5536	106	38	holds	hold	VERB
ejpam-5536	106	39	:	:	PUNCT
ejpam-5536	106	40	(	(	PUNCT
ejpam-5536	106	41	∀x	∀x	X
ejpam-5536	106	42	,	,	PUNCT
ejpam-5536	106	43	y	y	PROPN
ejpam-5536	106	44	∈	∈	PROPN
ejpam-5536	106	45	x	x	X
ejpam-5536	106	46	)	)	PUNCT
ejpam-5536	106	47	(	(	PUNCT
ejpam-5536	106	48	φ+(x	φ+(x	X
ejpam-5536	106	49	·	·	SYM
ejpam-5536	106	50	y	y	X
ejpam-5536	106	51	)	)	PUNCT
ejpam-5536	106	52	≥	≥	NOUN
ejpam-5536	106	53	min{φ+(x	min{φ+(x	PROPN
ejpam-5536	106	54	)	)	PUNCT
ejpam-5536	106	55	,	,	PUNCT
ejpam-5536	106	56	φ+(y	φ+(y	CCONJ
ejpam-5536	106	57	)	)	PUNCT
ejpam-5536	106	58	}	}	PUNCT
ejpam-5536	106	59	φ−(x	φ−(x	PROPN
ejpam-5536	106	60	·	·	PUNCT
ejpam-5536	106	61	y	y	X
ejpam-5536	106	62	)	)	PUNCT
ejpam-5536	106	63	≤	≤	NOUN
ejpam-5536	106	64	max{φ−(x	max{φ−(x	PROPN
ejpam-5536	106	65	)	)	PUNCT
ejpam-5536	106	66	,	,	PUNCT
ejpam-5536	106	67	φ−(y	φ−(y	PROPN
ejpam-5536	106	68	)	)	PUNCT
ejpam-5536	106	69	}	}	PUNCT
ejpam-5536	106	70	)	)	PUNCT
ejpam-5536	107	1	(	(	PUNCT
ejpam-5536	107	2	1	1	X
ejpam-5536	107	3	)	)	PUNCT
ejpam-5536	107	4	definition	definition	NOUN
ejpam-5536	107	5	9	9	NUM
ejpam-5536	107	6	.	.	PUNCT
ejpam-5536	108	1	[	[	X
ejpam-5536	108	2	11	11	NUM
ejpam-5536	108	3	]	]	PUNCT
ejpam-5536	108	4	a	a	DET
ejpam-5536	108	5	bfs	bfs	NOUN
ejpam-5536	108	6	φ	φ	NOUN
ejpam-5536	108	7	=	=	SYM
ejpam-5536	108	8	(	(	PUNCT
ejpam-5536	108	9	φ+	φ+	NOUN
ejpam-5536	108	10	,	,	PUNCT
ejpam-5536	108	11	φ−	φ−	PROPN
ejpam-5536	108	12	)	)	PUNCT
ejpam-5536	108	13	in	in	ADP
ejpam-5536	108	14	a	a	DET
ejpam-5536	108	15	hilbert	hilbert	NOUN
ejpam-5536	108	16	algebra	algebra	NOUN
ejpam-5536	108	17	x	x	PUNCT
ejpam-5536	108	18	=	=	SYM
ejpam-5536	108	19	(	(	PUNCT
ejpam-5536	108	20	x	x	NOUN
ejpam-5536	108	21	,	,	PUNCT
ejpam-5536	108	22	·	·	PUNCT
ejpam-5536	108	23	,	,	PUNCT
ejpam-5536	108	24	1x	1x	NUM
ejpam-5536	108	25	)	)	PUNCT
ejpam-5536	108	26	is	be	AUX
ejpam-5536	108	27	called	call	VERB
ejpam-5536	108	28	a	a	DET
ejpam-5536	108	29	bipolar	bipolar	ADJ
ejpam-5536	108	30	fuzzy	fuzzy	ADJ
ejpam-5536	108	31	ideal	ideal	NOUN
ejpam-5536	108	32	of	of	ADP
ejpam-5536	108	33	x	x	PRON
ejpam-5536	108	34	if	if	SCONJ
ejpam-5536	108	35	the	the	DET
ejpam-5536	108	36	following	follow	VERB
ejpam-5536	108	37	conditions	condition	NOUN
ejpam-5536	108	38	hold	hold	VERB
ejpam-5536	108	39	:	:	PUNCT
ejpam-5536	108	40	(	(	PUNCT
ejpam-5536	108	41	∀x	∀x	X
ejpam-5536	108	42	∈	∈	PROPN
ejpam-5536	108	43	x	x	NOUN
ejpam-5536	108	44	)	)	PUNCT
ejpam-5536	108	45	(	(	PUNCT
ejpam-5536	108	46	φ+(1x	φ+(1x	PROPN
ejpam-5536	108	47	)	)	PUNCT
ejpam-5536	108	48	≥	≥	NOUN
ejpam-5536	108	49	φ+(x	φ+(x	X
ejpam-5536	108	50	)	)	PUNCT
ejpam-5536	108	51	φ−(1x	φ−(1x	NOUN
ejpam-5536	108	52	)	)	PUNCT
ejpam-5536	108	53	≤	≤	NUM
ejpam-5536	108	54	φ−(x	φ−(x	PROPN
ejpam-5536	108	55	)	)	PUNCT
ejpam-5536	108	56	)	)	PUNCT
ejpam-5536	109	1	(	(	PUNCT
ejpam-5536	109	2	2	2	X
ejpam-5536	109	3	)	)	PUNCT
ejpam-5536	109	4	(	(	PUNCT
ejpam-5536	109	5	∀x	∀x	X
ejpam-5536	109	6	,	,	PUNCT
ejpam-5536	109	7	y	y	PROPN
ejpam-5536	109	8	∈	∈	PROPN
ejpam-5536	109	9	x	x	X
ejpam-5536	109	10	)	)	PUNCT
ejpam-5536	109	11	(	(	PUNCT
ejpam-5536	109	12	φ+(x	φ+(x	X
ejpam-5536	109	13	·	·	SYM
ejpam-5536	109	14	y	y	X
ejpam-5536	109	15	)	)	PUNCT
ejpam-5536	109	16	≥	≥	NOUN
ejpam-5536	109	17	φ+(y	φ+(y	SYM
ejpam-5536	109	18	)	)	PUNCT
ejpam-5536	110	1	φ−(x	φ−(x	PROPN
ejpam-5536	110	2	·	·	PUNCT
ejpam-5536	110	3	y	y	X
ejpam-5536	110	4	)	)	PUNCT
ejpam-5536	110	5	≤	≤	NOUN
ejpam-5536	110	6	φ−(y	φ−(y	PROPN
ejpam-5536	110	7	)	)	PUNCT
ejpam-5536	110	8	)	)	PUNCT
ejpam-5536	111	1	(	(	PUNCT
ejpam-5536	111	2	3	3	X
ejpam-5536	111	3	)	)	PUNCT
ejpam-5536	111	4	(	(	PUNCT
ejpam-5536	111	5	∀x	∀x	X
ejpam-5536	111	6	,	,	PUNCT
ejpam-5536	111	7	y1	y1	X
ejpam-5536	111	8	,	,	PUNCT
ejpam-5536	111	9	y2	y2	NOUN
ejpam-5536	111	10	∈	∈	PROPN
ejpam-5536	111	11	x	x	X
ejpam-5536	111	12	)	)	PUNCT
ejpam-5536	111	13	(	(	PUNCT
ejpam-5536	111	14	φ+((y1	φ+((y1	X
ejpam-5536	111	15	·	·	PUNCT
ejpam-5536	111	16	(	(	PUNCT
ejpam-5536	111	17	y2	y2	INTJ
ejpam-5536	111	18	·	·	PUNCT
ejpam-5536	111	19	x	x	X
ejpam-5536	111	20	)	)	PUNCT
ejpam-5536	111	21	)	)	PUNCT
ejpam-5536	111	22	·	·	PUNCT
ejpam-5536	112	1	x	x	X
ejpam-5536	112	2	)	)	PUNCT
ejpam-5536	112	3	≥	≥	NOUN
ejpam-5536	112	4	min{φ+(y1	min{φ+(y1	NOUN
ejpam-5536	112	5	)	)	PUNCT
ejpam-5536	112	6	,	,	PUNCT
ejpam-5536	112	7	φ	φ	PROPN
ejpam-5536	112	8	+	+	PROPN
ejpam-5536	112	9	(	(	PUNCT
ejpam-5536	112	10	y2	y2	NOUN
ejpam-5536	112	11	)	)	PUNCT
ejpam-5536	112	12	}	}	PUNCT
ejpam-5536	112	13	φ−((y1	φ−((y1	PROPN
ejpam-5536	112	14	·	·	PUNCT
ejpam-5536	112	15	(	(	PUNCT
ejpam-5536	112	16	y2	y2	INTJ
ejpam-5536	112	17	·	·	PUNCT
ejpam-5536	112	18	x	x	X
ejpam-5536	112	19	)	)	PUNCT
ejpam-5536	112	20	)	)	PUNCT
ejpam-5536	112	21	·	·	PUNCT
ejpam-5536	113	1	x	x	X
ejpam-5536	113	2	)	)	PUNCT
ejpam-5536	113	3	≤	≤	NUM
ejpam-5536	113	4	max{φ−(y1	max{φ−(y1	PROPN
ejpam-5536	113	5	)	)	PUNCT
ejpam-5536	113	6	,	,	PUNCT
ejpam-5536	113	7	φ	φ	PROPN
ejpam-5536	113	8	−(y2	−(y2	PROPN
ejpam-5536	113	9	)	)	PUNCT
ejpam-5536	113	10	}	}	PUNCT
ejpam-5536	113	11	)	)	PUNCT
ejpam-5536	113	12	(	(	PUNCT
ejpam-5536	113	13	4	4	X
ejpam-5536	113	14	)	)	PUNCT
ejpam-5536	113	15	definition	definition	NOUN
ejpam-5536	113	16	10	10	NUM
ejpam-5536	113	17	.	.	PUNCT
ejpam-5536	114	1	[	[	X
ejpam-5536	114	2	11	11	NUM
ejpam-5536	114	3	]	]	PUNCT
ejpam-5536	114	4	a	a	DET
ejpam-5536	114	5	bfs	bfs	NOUN
ejpam-5536	114	6	φ	φ	NOUN
ejpam-5536	114	7	=	=	SYM
ejpam-5536	114	8	(	(	PUNCT
ejpam-5536	114	9	φ+	φ+	NOUN
ejpam-5536	114	10	,	,	PUNCT
ejpam-5536	114	11	φ−	φ−	PROPN
ejpam-5536	114	12	)	)	PUNCT
ejpam-5536	114	13	in	in	ADP
ejpam-5536	114	14	a	a	DET
ejpam-5536	114	15	hilbert	hilbert	NOUN
ejpam-5536	114	16	algebra	algebra	NOUN
ejpam-5536	114	17	x	x	PUNCT
ejpam-5536	114	18	=	=	SYM
ejpam-5536	114	19	(	(	PUNCT
ejpam-5536	114	20	x	x	NOUN
ejpam-5536	114	21	,	,	PUNCT
ejpam-5536	114	22	·	·	PUNCT
ejpam-5536	114	23	,	,	PUNCT
ejpam-5536	114	24	1x	1x	NUM
ejpam-5536	114	25	)	)	PUNCT
ejpam-5536	114	26	is	be	AUX
ejpam-5536	114	27	called	call	VERB
ejpam-5536	114	28	a	a	DET
ejpam-5536	114	29	bipolar	bipolar	ADJ
ejpam-5536	114	30	fuzzy	fuzzy	ADJ
ejpam-5536	114	31	deductive	deductive	ADJ
ejpam-5536	114	32	system	system	NOUN
ejpam-5536	114	33	of	of	ADP
ejpam-5536	114	34	x	x	PRON
ejpam-5536	114	35	if	if	SCONJ
ejpam-5536	114	36	the	the	DET
ejpam-5536	114	37	following	follow	VERB
ejpam-5536	114	38	conditions	condition	NOUN
ejpam-5536	114	39	hold	hold	VERB
ejpam-5536	114	40	:	:	PUNCT
ejpam-5536	114	41	(	(	PUNCT
ejpam-5536	114	42	2	2	X
ejpam-5536	114	43	)	)	PUNCT
ejpam-5536	114	44	and	and	CCONJ
ejpam-5536	114	45	(	(	PUNCT
ejpam-5536	114	46	∀x	∀x	X
ejpam-5536	114	47	,	,	PUNCT
ejpam-5536	114	48	y	y	PROPN
ejpam-5536	114	49	∈	∈	PROPN
ejpam-5536	114	50	x	x	X
ejpam-5536	114	51	)	)	PUNCT
ejpam-5536	114	52	(	(	PUNCT
ejpam-5536	114	53	φ+(y	φ+(y	PUNCT
ejpam-5536	114	54	)	)	PUNCT
ejpam-5536	114	55	≥	≥	NOUN
ejpam-5536	114	56	min{φ+(x	min{φ+(x	NOUN
ejpam-5536	114	57	·	·	PUNCT
ejpam-5536	114	58	y	y	X
ejpam-5536	114	59	)	)	PUNCT
ejpam-5536	114	60	,	,	PUNCT
ejpam-5536	114	61	φ+(x	φ+(x	NOUN
ejpam-5536	114	62	)	)	PUNCT
ejpam-5536	114	63	}	}	PUNCT
ejpam-5536	114	64	φ−(y	φ−(y	PROPN
ejpam-5536	114	65	)	)	PUNCT
ejpam-5536	114	66	≤	≤	PUNCT
ejpam-5536	114	67	max{φ−(x	max{φ−(x	PROPN
ejpam-5536	114	68	·	·	PUNCT
ejpam-5536	114	69	y	y	X
ejpam-5536	114	70	)	)	PUNCT
ejpam-5536	114	71	,	,	PUNCT
ejpam-5536	114	72	φ−(x	φ−(x	PROPN
ejpam-5536	114	73	)	)	PUNCT
ejpam-5536	114	74	}	}	PUNCT
ejpam-5536	114	75	)	)	PUNCT
ejpam-5536	115	1	(	(	PUNCT
ejpam-5536	115	2	5	5	X
ejpam-5536	115	3	)	)	SYM
ejpam-5536	115	4	3	3	NUM
ejpam-5536	115	5	.	.	X
ejpam-5536	115	6	bipolar	bipolar	ADJ
ejpam-5536	115	7	fuzzy	fuzzy	ADJ
ejpam-5536	115	8	(	(	PUNCT
ejpam-5536	115	9	β	β	X
ejpam-5536	115	10	,	,	PUNCT
ejpam-5536	115	11	α)-translations	α)-translation	NOUN
ejpam-5536	115	12	in	in	ADP
ejpam-5536	115	13	hilbert	hilbert	PROPN
ejpam-5536	115	14	algebras	algebras	PROPN
ejpam-5536	115	15	building	build	VERB
ejpam-5536	115	16	upon	upon	SCONJ
ejpam-5536	115	17	the	the	DET
ejpam-5536	115	18	foundational	foundational	ADJ
ejpam-5536	115	19	concepts	concept	NOUN
ejpam-5536	115	20	and	and	CCONJ
ejpam-5536	115	21	preliminary	preliminary	ADJ
ejpam-5536	115	22	definitions	definition	NOUN
ejpam-5536	115	23	of	of	ADP
ejpam-5536	115	24	bfss	bfss	NOUN
ejpam-5536	115	25	and	and	CCONJ
ejpam-5536	115	26	hilbert	hilbert	PROPN
ejpam-5536	115	27	algebras	algebras	PROPN
ejpam-5536	115	28	,	,	PUNCT
ejpam-5536	115	29	we	we	PRON
ejpam-5536	115	30	now	now	ADV
ejpam-5536	115	31	delve	delve	VERB
ejpam-5536	115	32	into	into	ADP
ejpam-5536	115	33	the	the	DET
ejpam-5536	115	34	specific	specific	ADJ
ejpam-5536	115	35	framework	framework	NOUN
ejpam-5536	115	36	of	of	ADP
ejpam-5536	115	37	bipolar	bipolar	ADJ
ejpam-5536	115	38	fuzzy	fuzzy	ADJ
ejpam-5536	115	39	(	(	PUNCT
ejpam-5536	115	40	β	β	X
ejpam-5536	115	41	,	,	PUNCT
ejpam-5536	115	42	α)-translations	α)-translation	NOUN
ejpam-5536	115	43	.	.	PUNCT
ejpam-5536	116	1	this	this	DET
ejpam-5536	116	2	section	section	NOUN
ejpam-5536	116	3	introduces	introduce	VERB
ejpam-5536	116	4	two	two	NUM
ejpam-5536	116	5	types	type	NOUN
ejpam-5536	116	6	of	of	ADP
ejpam-5536	116	7	bipolar	bipolar	ADJ
ejpam-5536	116	8	fuzzy	fuzzy	ADJ
ejpam-5536	116	9	translations	translation	NOUN
ejpam-5536	116	10	,	,	PUNCT
ejpam-5536	116	11	type	type	NOUN
ejpam-5536	116	12	i	i	PRON
ejpam-5536	116	13	and	and	CCONJ
ejpam-5536	116	14	type	type	PROPN
ejpam-5536	116	15	ii	ii	PROPN
ejpam-5536	116	16	,	,	PUNCT
ejpam-5536	116	17	designed	design	VERB
ejpam-5536	116	18	to	to	PART
ejpam-5536	116	19	extend	extend	VERB
ejpam-5536	116	20	the	the	DET
ejpam-5536	116	21	flexibility	flexibility	NOUN
ejpam-5536	116	22	of	of	ADP
ejpam-5536	116	23	bfss	bfss	NOUN
ejpam-5536	116	24	in	in	ADP
ejpam-5536	116	25	hilbert	hilbert	NOUN
ejpam-5536	116	26	algebras	algebras	PROPN
ejpam-5536	116	27	by	by	ADP
ejpam-5536	116	28	capturing	capture	VERB
ejpam-5536	116	29	additional	additional	ADJ
ejpam-5536	116	30	layers	layer	NOUN
ejpam-5536	116	31	of	of	ADP
ejpam-5536	116	32	nuanced	nuanced	ADJ
ejpam-5536	116	33	information	information	NOUN
ejpam-5536	116	34	.	.	PUNCT
ejpam-5536	117	1	through	through	ADP
ejpam-5536	117	2	these	these	DET
ejpam-5536	117	3	translations	translation	NOUN
ejpam-5536	117	4	,	,	PUNCT
ejpam-5536	117	5	we	we	PRON
ejpam-5536	117	6	examine	examine	VERB
ejpam-5536	117	7	the	the	DET
ejpam-5536	117	8	structural	structural	ADJ
ejpam-5536	117	9	adjustments	adjustment	NOUN
ejpam-5536	117	10	within	within	ADP
ejpam-5536	117	11	bipolar	bipolar	ADJ
ejpam-5536	117	12	fuzzy	fuzzy	ADJ
ejpam-5536	117	13	subalgebras	subalgebra	NOUN
ejpam-5536	117	14	,	,	PUNCT
ejpam-5536	117	15	ideals	ideal	NOUN
ejpam-5536	117	16	,	,	PUNCT
ejpam-5536	117	17	and	and	CCONJ
ejpam-5536	117	18	deductive	deductive	ADJ
ejpam-5536	117	19	systems	system	NOUN
ejpam-5536	117	20	,	,	PUNCT
ejpam-5536	117	21	highlighting	highlight	VERB
ejpam-5536	117	22	their	their	PRON
ejpam-5536	117	23	adaptability	adaptability	NOUN
ejpam-5536	117	24	in	in	ADP
ejpam-5536	117	25	algebraic	algebraic	ADJ
ejpam-5536	117	26	systems	system	NOUN
ejpam-5536	117	27	that	that	PRON
ejpam-5536	117	28	require	require	VERB
ejpam-5536	117	29	the	the	DET
ejpam-5536	117	30	representation	representation	NOUN
ejpam-5536	117	31	of	of	ADP
ejpam-5536	117	32	both	both	CCONJ
ejpam-5536	117	33	positive	positive	ADJ
ejpam-5536	117	34	and	and	CCONJ
ejpam-5536	117	35	negative	negative	ADJ
ejpam-5536	117	36	membership	membership	NOUN
ejpam-5536	117	37	.	.	PUNCT
ejpam-5536	118	1	the	the	DET
ejpam-5536	118	2	following	follow	VERB
ejpam-5536	118	3	analysis	analysis	NOUN
ejpam-5536	118	4	in	in	ADP
ejpam-5536	118	5	section	section	NOUN
ejpam-5536	118	6	3	3	NUM
ejpam-5536	118	7	provides	provide	VERB
ejpam-5536	118	8	a	a	DET
ejpam-5536	118	9	detailed	detailed	ADJ
ejpam-5536	118	10	examination	examination	NOUN
ejpam-5536	118	11	of	of	ADP
ejpam-5536	118	12	the	the	DET
ejpam-5536	118	13	properties	property	NOUN
ejpam-5536	118	14	and	and	CCONJ
ejpam-5536	118	15	applications	application	NOUN
ejpam-5536	118	16	of	of	ADP
ejpam-5536	118	17	these	these	DET
ejpam-5536	118	18	translations	translation	NOUN
ejpam-5536	118	19	,	,	PUNCT
ejpam-5536	118	20	setting	set	VERB
ejpam-5536	118	21	the	the	DET
ejpam-5536	118	22	stage	stage	NOUN
ejpam-5536	118	23	for	for	ADP
ejpam-5536	118	24	further	further	ADJ
ejpam-5536	118	25	exploration	exploration	NOUN
ejpam-5536	118	26	into	into	ADP
ejpam-5536	118	27	their	their	PRON
ejpam-5536	118	28	theoretical	theoretical	ADJ
ejpam-5536	118	29	implications	implication	NOUN
ejpam-5536	118	30	and	and	CCONJ
ejpam-5536	118	31	practical	practical	ADJ
ejpam-5536	118	32	applications	application	NOUN
ejpam-5536	118	33	.	.	PUNCT
ejpam-5536	119	1	definition	definition	NOUN
ejpam-5536	119	2	11	11	NUM
ejpam-5536	119	3	.	.	PUNCT
ejpam-5536	120	1	the	the	DET
ejpam-5536	120	2	inclusion	inclusion	NOUN
ejpam-5536	120	3	⊆	⊆	NUM
ejpam-5536	120	4	is	be	AUX
ejpam-5536	120	5	defined	define	VERB
ejpam-5536	120	6	by	by	ADP
ejpam-5536	120	7	setting	set	VERB
ejpam-5536	120	8	,	,	PUNCT
ejpam-5536	120	9	for	for	ADP
ejpam-5536	120	10	any	any	DET
ejpam-5536	120	11	bfss	bfss	NOUN
ejpam-5536	120	12	φ	φ	NOUN
ejpam-5536	120	13	=	=	SYM
ejpam-5536	120	14	(	(	PUNCT
ejpam-5536	120	15	φ+	φ+	NOUN
ejpam-5536	120	16	,	,	PUNCT
ejpam-5536	120	17	φ−	φ−	PROPN
ejpam-5536	120	18	)	)	PUNCT
ejpam-5536	120	19	and	and	CCONJ
ejpam-5536	120	20	ψ	ψ	X
ejpam-5536	121	1	=	=	X
ejpam-5536	121	2	(	(	PUNCT
ejpam-5536	121	3	ψ+	ψ+	ADJ
ejpam-5536	121	4	,	,	PUNCT
ejpam-5536	121	5	ψ−	ψ−	NOUN
ejpam-5536	121	6	)	)	PUNCT
ejpam-5536	121	7	in	in	ADP
ejpam-5536	121	8	a	a	DET
ejpam-5536	121	9	nonempty	nonempty	ADV
ejpam-5536	121	10	set	set	VERB
ejpam-5536	121	11	x	x	SYM
ejpam-5536	121	12	,	,	PUNCT
ejpam-5536	121	13	φ	φ	PROPN
ejpam-5536	121	14	⊆	⊆	NUM
ejpam-5536	121	15	ψ	ψ	X
ejpam-5536	121	16	⇔	⇔	X
ejpam-5536	121	17	(	(	PUNCT
ejpam-5536	121	18	∀x	∀x	X
ejpam-5536	121	19	∈	∈	PROPN
ejpam-5536	121	20	x)(φ+(x	x)(φ+(x	PROPN
ejpam-5536	121	21	)	)	PUNCT
ejpam-5536	121	22	≤	≤	NUM
ejpam-5536	121	23	ψ+(x	ψ+(x	NUM
ejpam-5536	121	24	)	)	PUNCT
ejpam-5536	121	25	and	and	CCONJ
ejpam-5536	121	26	φ−(x	φ−(x	PROPN
ejpam-5536	121	27	)	)	PUNCT
ejpam-5536	121	28	≥	≥	NOUN
ejpam-5536	121	29	ψ−(x	ψ−(x	PROPN
ejpam-5536	121	30	)	)	PUNCT
ejpam-5536	121	31	)	)	PUNCT
ejpam-5536	121	32	.	.	PUNCT
ejpam-5536	122	1	we	we	PRON
ejpam-5536	122	2	say	say	VERB
ejpam-5536	122	3	that	that	SCONJ
ejpam-5536	122	4	ψ	ψ	X
ejpam-5536	122	5	=	=	X
ejpam-5536	122	6	(	(	PUNCT
ejpam-5536	122	7	ψ+	ψ+	ADJ
ejpam-5536	122	8	,	,	PUNCT
ejpam-5536	122	9	ψ−	ψ−	PROPN
ejpam-5536	122	10	)	)	PUNCT
ejpam-5536	122	11	is	be	AUX
ejpam-5536	122	12	a	a	DET
ejpam-5536	122	13	bipolar	bipolar	ADJ
ejpam-5536	122	14	fuzzy	fuzzy	ADJ
ejpam-5536	122	15	extension	extension	NOUN
ejpam-5536	122	16	of	of	ADP
ejpam-5536	122	17	φ	φ	PROPN
ejpam-5536	122	18	=	=	SYM
ejpam-5536	122	19	(	(	PUNCT
ejpam-5536	122	20	φ+	φ+	NOUN
ejpam-5536	122	21	,	,	PUNCT
ejpam-5536	122	22	φ−	φ−	PROPN
ejpam-5536	122	23	)	)	PUNCT
ejpam-5536	122	24	,	,	PUNCT
ejpam-5536	122	25	and	and	CCONJ
ejpam-5536	122	26	φ	φ	NUM
ejpam-5536	122	27	=	=	SYM
ejpam-5536	122	28	(	(	PUNCT
ejpam-5536	122	29	φ+	φ+	NOUN
ejpam-5536	122	30	,	,	PUNCT
ejpam-5536	122	31	φ−	φ−	PROPN
ejpam-5536	122	32	)	)	PUNCT
ejpam-5536	122	33	is	be	AUX
ejpam-5536	122	34	a	a	DET
ejpam-5536	122	35	bipolar	bipolar	ADJ
ejpam-5536	122	36	fuzzy	fuzzy	ADJ
ejpam-5536	122	37	intensity	intensity	NOUN
ejpam-5536	122	38	of	of	ADP
ejpam-5536	122	39	ψ	ψ	NOUN
ejpam-5536	122	40	=	=	PUNCT
ejpam-5536	122	41	(	(	PUNCT
ejpam-5536	122	42	ψ+	ψ+	ADJ
ejpam-5536	122	43	,	,	PUNCT
ejpam-5536	122	44	ψ−	ψ−	PROPN
ejpam-5536	122	45	)	)	PUNCT
ejpam-5536	122	46	.	.	PUNCT
ejpam-5536	123	1	definition	definition	NOUN
ejpam-5536	123	2	12	12	NUM
ejpam-5536	123	3	.	.	PUNCT
ejpam-5536	124	1	for	for	ADP
ejpam-5536	124	2	any	any	DET
ejpam-5536	124	3	bfs	bfs	NOUN
ejpam-5536	124	4	φ	φ	NOUN
ejpam-5536	124	5	=	=	SYM
ejpam-5536	124	6	(	(	PUNCT
ejpam-5536	124	7	φ+	φ+	NOUN
ejpam-5536	124	8	,	,	PUNCT
ejpam-5536	124	9	φ−	φ−	PROPN
ejpam-5536	124	10	)	)	PUNCT
ejpam-5536	124	11	in	in	ADP
ejpam-5536	124	12	a	a	DET
ejpam-5536	124	13	nonempty	nonempty	ADV
ejpam-5536	124	14	set	set	VERB
ejpam-5536	124	15	x	x	NOUN
ejpam-5536	124	16	,	,	PUNCT
ejpam-5536	124	17	we	we	PRON
ejpam-5536	124	18	denote	denote	VERB
ejpam-5536	124	19	⊤	⊤	NOUN
ejpam-5536	124	20	=	=	SYM
ejpam-5536	124	21	1−	1−	NUM
ejpam-5536	124	22	sup{φ+(x	sup{φ+(x	NOUN
ejpam-5536	124	23	)	)	PUNCT
ejpam-5536	124	24	|	|	ADV
ejpam-5536	124	25	x	x	SYM
ejpam-5536	124	26	∈	∈	NOUN
ejpam-5536	124	27	x	x	X
ejpam-5536	124	28	}	}	PUNCT
ejpam-5536	124	29	,	,	PUNCT
ejpam-5536	124	30	a.	a.	NOUN
ejpam-5536	124	31	iampan	iampan	NOUN
ejpam-5536	124	32	et	et	PROPN
ejpam-5536	125	1	al	al	PROPN
ejpam-5536	125	2	.	.	PUNCT
ejpam-5536	125	3	/	/	SYM
ejpam-5536	125	4	eur	eur	PROPN
ejpam-5536	125	5	.	.	PUNCT
ejpam-5536	126	1	j.	j.	PROPN
ejpam-5536	126	2	pure	pure	PROPN
ejpam-5536	126	3	appl	appl	PROPN
ejpam-5536	126	4	.	.	PROPN
ejpam-5536	126	5	math	math	PROPN
ejpam-5536	126	6	,	,	PUNCT
ejpam-5536	126	7	17	17	NUM
ejpam-5536	126	8	(	(	PUNCT
ejpam-5536	126	9	4	4	NUM
ejpam-5536	126	10	)	)	PUNCT
ejpam-5536	126	11	(	(	PUNCT
ejpam-5536	126	12	2024	2024	NUM
ejpam-5536	126	13	)	)	PUNCT
ejpam-5536	126	14	,	,	PUNCT
ejpam-5536	126	15	4059	4059	NUM
ejpam-5536	126	16	-	-	SYM
ejpam-5536	126	17	4070	4070	NUM
ejpam-5536	126	18	4064	4064	NUM
ejpam-5536	126	19	⊥	⊥	NOUN
ejpam-5536	126	20	=	=	SYM
ejpam-5536	126	21	−1−	−1−	PROPN
ejpam-5536	126	22	inf{φ−(x	inf{φ−(x	PROPN
ejpam-5536	126	23	)	)	PUNCT
ejpam-5536	127	1	|	|	ADV
ejpam-5536	127	2	x	x	SYM
ejpam-5536	127	3	∈	∈	NOUN
ejpam-5536	127	4	x	x	X
ejpam-5536	127	5	}	}	PUNCT
ejpam-5536	127	6	.	.	PUNCT
ejpam-5536	128	1	let	let	VERB
ejpam-5536	128	2	φ	φ	PROPN
ejpam-5536	128	3	=	=	SYM
ejpam-5536	128	4	(	(	PUNCT
ejpam-5536	128	5	φ+	φ+	PROPN
ejpam-5536	128	6	,	,	PUNCT
ejpam-5536	128	7	φ−	φ−	PROPN
ejpam-5536	128	8	)	)	PUNCT
ejpam-5536	128	9	be	be	VERB
ejpam-5536	128	10	a	a	DET
ejpam-5536	128	11	bfs	bfs	NOUN
ejpam-5536	128	12	in	in	ADP
ejpam-5536	128	13	a	a	DET
ejpam-5536	128	14	nonempty	nonempty	ADV
ejpam-5536	128	15	set	set	VERB
ejpam-5536	128	16	x	x	PUNCT
ejpam-5536	128	17	and	and	CCONJ
ejpam-5536	128	18	(	(	PUNCT
ejpam-5536	128	19	β	β	X
ejpam-5536	128	20	,	,	PUNCT
ejpam-5536	128	21	α	α	NOUN
ejpam-5536	128	22	)	)	PUNCT
ejpam-5536	128	23	∈	∈	PROPN
ejpam-5536	129	1	[	[	X
ejpam-5536	129	2	0,⊤	0,⊤	NOUN
ejpam-5536	129	3	]	]	X
ejpam-5536	129	4	×	×	NOUN
ejpam-5536	130	1	[	[	X
ejpam-5536	130	2	⊥	⊥	NOUN
ejpam-5536	130	3	,	,	PUNCT
ejpam-5536	130	4	0	0	NUM
ejpam-5536	130	5	]	]	PUNCT
ejpam-5536	130	6	.	.	PUNCT
ejpam-5536	131	1	by	by	ADP
ejpam-5536	131	2	a	a	DET
ejpam-5536	131	3	bipolar	bipolar	ADJ
ejpam-5536	131	4	fuzzy	fuzzy	NOUN
ejpam-5536	131	5	(	(	PUNCT
ejpam-5536	131	6	β	β	NOUN
ejpam-5536	131	7	,	,	PUNCT
ejpam-5536	131	8	α)-translation	α)-translation	NOUN
ejpam-5536	131	9	of	of	ADP
ejpam-5536	131	10	φ	φ	PROPN
ejpam-5536	131	11	=	=	SYM
ejpam-5536	131	12	(	(	PUNCT
ejpam-5536	131	13	φ+	φ+	NOUN
ejpam-5536	131	14	,	,	PUNCT
ejpam-5536	131	15	φ−	φ−	PROPN
ejpam-5536	131	16	)	)	PUNCT
ejpam-5536	131	17	of	of	ADP
ejpam-5536	131	18	type	type	NOUN
ejpam-5536	131	19	i	i	PRON
ejpam-5536	131	20	,	,	PUNCT
ejpam-5536	131	21	we	we	PRON
ejpam-5536	131	22	mean	mean	VERB
ejpam-5536	131	23	a	a	DET
ejpam-5536	131	24	bfs	bfs	NOUN
ejpam-5536	131	25	φt1	φt1	X
ejpam-5536	131	26	(	(	PUNCT
ejpam-5536	131	27	β	β	X
ejpam-5536	131	28	,	,	PUNCT
ejpam-5536	131	29	α	α	NOUN
ejpam-5536	131	30	)	)	PUNCT
ejpam-5536	131	31	=	=	SYM
ejpam-5536	132	1	(	(	PUNCT
ejpam-5536	132	2	φ+	φ+	X
ejpam-5536	132	3	(	(	PUNCT
ejpam-5536	132	4	β	β	X
ejpam-5536	132	5	,	,	PUNCT
ejpam-5536	132	6	t1	t1	NOUN
ejpam-5536	132	7	)	)	PUNCT
ejpam-5536	132	8	,	,	PUNCT
ejpam-5536	132	9	φ−	φ−	PROPN
ejpam-5536	132	10	(	(	PUNCT
ejpam-5536	132	11	α	α	NOUN
ejpam-5536	132	12	,	,	PUNCT
ejpam-5536	132	13	t1	t1	NOUN
ejpam-5536	132	14	)	)	PUNCT
ejpam-5536	132	15	)	)	PUNCT
ejpam-5536	132	16	,	,	PUNCT
ejpam-5536	132	17	where	where	SCONJ
ejpam-5536	132	18	φ+	φ+	X
ejpam-5536	132	19	(	(	PUNCT
ejpam-5536	132	20	β	β	X
ejpam-5536	132	21	,	,	PUNCT
ejpam-5536	132	22	t1	t1	NOUN
ejpam-5536	132	23	)	)	PUNCT
ejpam-5536	132	24	:	:	PUNCT
ejpam-5536	133	1	x	x	X
ejpam-5536	133	2	→	→	PUNCT
ejpam-5536	134	1	[	[	X
ejpam-5536	134	2	0	0	NUM
ejpam-5536	134	3	,	,	PUNCT
ejpam-5536	134	4	1	1	NUM
ejpam-5536	134	5	]	]	PUNCT
ejpam-5536	134	6	,	,	PUNCT
ejpam-5536	134	7	x	x	SYM
ejpam-5536	134	8	7→	7→	NUM
ejpam-5536	134	9	φ+(x	φ+(x	NUM
ejpam-5536	134	10	)	)	PUNCT
ejpam-5536	135	1	+	+	CCONJ
ejpam-5536	135	2	β	β	X
ejpam-5536	135	3	,	,	PUNCT
ejpam-5536	135	4	φ−	φ−	PROPN
ejpam-5536	135	5	(	(	PUNCT
ejpam-5536	135	6	α	α	NOUN
ejpam-5536	135	7	,	,	PUNCT
ejpam-5536	135	8	t1	t1	NOUN
ejpam-5536	135	9	)	)	PUNCT
ejpam-5536	135	10	:	:	PUNCT
ejpam-5536	135	11	x	x	X
ejpam-5536	135	12	→	→	PUNCT
ejpam-5536	135	13	[	[	X
ejpam-5536	135	14	−1	−1	NOUN
ejpam-5536	135	15	,	,	PUNCT
ejpam-5536	135	16	0	0	NUM
ejpam-5536	135	17	]	]	PUNCT
ejpam-5536	135	18	,	,	PUNCT
ejpam-5536	135	19	x	x	PROPN
ejpam-5536	135	20	7→	7→	NUM
ejpam-5536	135	21	φ−(x	φ−(x	PROPN
ejpam-5536	135	22	)	)	PUNCT
ejpam-5536	136	1	+	+	CCONJ
ejpam-5536	136	2	α	α	X
ejpam-5536	136	3	.	.	PUNCT
ejpam-5536	136	4	theorem	theorem	NOUN
ejpam-5536	136	5	1	1	NUM
ejpam-5536	136	6	.	.	PUNCT
ejpam-5536	137	1	if	if	SCONJ
ejpam-5536	137	2	a	a	DET
ejpam-5536	137	3	bfs	bfs	NOUN
ejpam-5536	137	4	φ	φ	X
ejpam-5536	137	5	=	=	SYM
ejpam-5536	137	6	(	(	PUNCT
ejpam-5536	137	7	φ+	φ+	NOUN
ejpam-5536	137	8	,	,	PUNCT
ejpam-5536	137	9	φ−	φ−	PROPN
ejpam-5536	137	10	)	)	PUNCT
ejpam-5536	137	11	in	in	ADP
ejpam-5536	137	12	a	a	DET
ejpam-5536	137	13	hilbert	hilbert	NOUN
ejpam-5536	137	14	algebra	algebra	NOUN
ejpam-5536	137	15	x	x	PUNCT
ejpam-5536	137	16	=	=	SYM
ejpam-5536	137	17	(	(	PUNCT
ejpam-5536	137	18	x	x	NOUN
ejpam-5536	137	19	,	,	PUNCT
ejpam-5536	137	20	·	·	PUNCT
ejpam-5536	137	21	,	,	PUNCT
ejpam-5536	137	22	1x	1x	NUM
ejpam-5536	137	23	)	)	PUNCT
ejpam-5536	137	24	is	be	AUX
ejpam-5536	137	25	a	a	DET
ejpam-5536	137	26	bipolar	bipolar	ADJ
ejpam-5536	137	27	fuzzy	fuzzy	ADJ
ejpam-5536	137	28	subalgebra	subalgebra	NOUN
ejpam-5536	137	29	of	of	ADP
ejpam-5536	137	30	x	x	PRON
ejpam-5536	137	31	,	,	PUNCT
ejpam-5536	137	32	then	then	ADV
ejpam-5536	137	33	for	for	ADP
ejpam-5536	137	34	all	all	DET
ejpam-5536	137	35	(	(	PUNCT
ejpam-5536	137	36	β	β	X
ejpam-5536	137	37	,	,	PUNCT
ejpam-5536	137	38	α	α	NOUN
ejpam-5536	137	39	)	)	PUNCT
ejpam-5536	137	40	∈	∈	PROPN
ejpam-5536	138	1	[	[	X
ejpam-5536	138	2	0,⊤	0,⊤	NOUN
ejpam-5536	138	3	]	]	X
ejpam-5536	138	4	×	×	NOUN
ejpam-5536	139	1	[	[	X
ejpam-5536	139	2	⊥	⊥	NOUN
ejpam-5536	139	3	,	,	PUNCT
ejpam-5536	139	4	0	0	NUM
ejpam-5536	139	5	]	]	PUNCT
ejpam-5536	139	6	,	,	PUNCT
ejpam-5536	139	7	the	the	DET
ejpam-5536	139	8	bipolar	bipolar	ADJ
ejpam-5536	139	9	fuzzy	fuzzy	NOUN
ejpam-5536	139	10	(	(	PUNCT
ejpam-5536	139	11	β	β	NOUN
ejpam-5536	139	12	,	,	PUNCT
ejpam-5536	139	13	α)-translation	α)-translation	NOUN
ejpam-5536	139	14	φt1	φt1	X
ejpam-5536	139	15	(	(	PUNCT
ejpam-5536	139	16	β	β	X
ejpam-5536	139	17	,	,	PUNCT
ejpam-5536	139	18	α	α	NOUN
ejpam-5536	139	19	)	)	PUNCT
ejpam-5536	139	20	=	=	SYM
ejpam-5536	139	21	(	(	PUNCT
ejpam-5536	139	22	φ+	φ+	X
ejpam-5536	139	23	(	(	PUNCT
ejpam-5536	139	24	β	β	X
ejpam-5536	139	25	,	,	PUNCT
ejpam-5536	139	26	t1	t1	NOUN
ejpam-5536	139	27	)	)	PUNCT
ejpam-5536	139	28	,	,	PUNCT
ejpam-5536	139	29	φ−	φ−	PROPN
ejpam-5536	139	30	(	(	PUNCT
ejpam-5536	139	31	α	α	NOUN
ejpam-5536	139	32	,	,	PUNCT
ejpam-5536	139	33	t1	t1	NOUN
ejpam-5536	139	34	)	)	PUNCT
ejpam-5536	139	35	)	)	PUNCT
ejpam-5536	139	36	of	of	ADP
ejpam-5536	139	37	φ	φ	PROPN
ejpam-5536	139	38	=	=	SYM
ejpam-5536	139	39	(	(	PUNCT
ejpam-5536	139	40	φ+	φ+	NOUN
ejpam-5536	139	41	,	,	PUNCT
ejpam-5536	139	42	φ−	φ−	PROPN
ejpam-5536	139	43	)	)	PUNCT
ejpam-5536	139	44	is	be	AUX
ejpam-5536	139	45	a	a	DET
ejpam-5536	139	46	bipolar	bipolar	ADJ
ejpam-5536	139	47	fuzzy	fuzzy	ADJ
ejpam-5536	139	48	subalgebra	subalgebra	NOUN
ejpam-5536	139	49	of	of	ADP
ejpam-5536	139	50	x.	x.	NOUN
ejpam-5536	139	51	proof	proof	PROPN
ejpam-5536	139	52	.	.	PUNCT
ejpam-5536	140	1	assume	assume	VERB
ejpam-5536	140	2	that	that	SCONJ
ejpam-5536	140	3	φ	φ	PROPN
ejpam-5536	140	4	=	=	SYM
ejpam-5536	140	5	(	(	PUNCT
ejpam-5536	140	6	φ+	φ+	NOUN
ejpam-5536	140	7	,	,	PUNCT
ejpam-5536	140	8	φ−	φ−	PROPN
ejpam-5536	140	9	)	)	PUNCT
ejpam-5536	140	10	is	be	AUX
ejpam-5536	140	11	a	a	DET
ejpam-5536	140	12	bipolar	bipolar	ADJ
ejpam-5536	140	13	fuzzy	fuzzy	ADJ
ejpam-5536	140	14	subalgebra	subalgebra	NOUN
ejpam-5536	140	15	of	of	ADP
ejpam-5536	140	16	x.	x.	NOUN
ejpam-5536	140	17	for	for	ADP
ejpam-5536	140	18	any	any	DET
ejpam-5536	140	19	(	(	PUNCT
ejpam-5536	140	20	β	β	X
ejpam-5536	140	21	,	,	PUNCT
ejpam-5536	140	22	α	α	NOUN
ejpam-5536	140	23	)	)	PUNCT
ejpam-5536	140	24	∈	∈	PROPN
ejpam-5536	141	1	[	[	X
ejpam-5536	141	2	0,⊤]×	0,⊤]×	X
ejpam-5536	141	3	[	[	X
ejpam-5536	141	4	⊥	⊥	X
ejpam-5536	141	5	,	,	PUNCT
ejpam-5536	141	6	0	0	NUM
ejpam-5536	141	7	]	]	PUNCT
ejpam-5536	141	8	and	and	CCONJ
ejpam-5536	141	9	for	for	ADP
ejpam-5536	141	10	all	all	DET
ejpam-5536	141	11	x	x	NOUN
ejpam-5536	141	12	,	,	PUNCT
ejpam-5536	141	13	y	y	PROPN
ejpam-5536	141	14	∈	∈	PROPN
ejpam-5536	141	15	x	x	X
ejpam-5536	141	16	,	,	PUNCT
ejpam-5536	141	17	we	we	PRON
ejpam-5536	141	18	have	have	VERB
ejpam-5536	141	19	φ+	φ+	NOUN
ejpam-5536	141	20	(	(	PUNCT
ejpam-5536	141	21	β	β	X
ejpam-5536	141	22	,	,	PUNCT
ejpam-5536	141	23	t1	t1	NOUN
ejpam-5536	141	24	)	)	PUNCT
ejpam-5536	141	25	(	(	PUNCT
ejpam-5536	141	26	x	x	X
ejpam-5536	141	27	·	·	PUNCT
ejpam-5536	141	28	y	y	X
ejpam-5536	141	29	)	)	PUNCT
ejpam-5536	141	30	=	=	SYM
ejpam-5536	141	31	φ+(x	φ+(x	X
ejpam-5536	141	32	·	·	PUNCT
ejpam-5536	141	33	y	y	X
ejpam-5536	141	34	)	)	PUNCT
ejpam-5536	141	35	+	+	CCONJ
ejpam-5536	141	36	β	β	X
ejpam-5536	141	37	≥	≥	NOUN
ejpam-5536	141	38	min{φ+(x	min{φ+(x	PROPN
ejpam-5536	141	39	)	)	PUNCT
ejpam-5536	141	40	,	,	PUNCT
ejpam-5536	141	41	φ+(y)}+	φ+(y)}+	NOUN
ejpam-5536	141	42	β	β	X
ejpam-5536	141	43	=	=	SYM
ejpam-5536	141	44	min{φ+(x	min{φ+(x	PROPN
ejpam-5536	141	45	)	)	PUNCT
ejpam-5536	142	1	+	+	CCONJ
ejpam-5536	142	2	β	β	X
ejpam-5536	142	3	,	,	PUNCT
ejpam-5536	142	4	φ+(y	φ+(y	PUNCT
ejpam-5536	142	5	)	)	PUNCT
ejpam-5536	142	6	+	+	CCONJ
ejpam-5536	142	7	β	β	X
ejpam-5536	142	8	}	}	PUNCT
ejpam-5536	142	9	=	=	SYM
ejpam-5536	142	10	min{φ+	min{φ+	NOUN
ejpam-5536	142	11	(	(	PUNCT
ejpam-5536	142	12	β	β	X
ejpam-5536	142	13	,	,	PUNCT
ejpam-5536	142	14	t1	t1	NOUN
ejpam-5536	142	15	)	)	PUNCT
ejpam-5536	142	16	(	(	PUNCT
ejpam-5536	142	17	x	x	X
ejpam-5536	142	18	)	)	PUNCT
ejpam-5536	142	19	,	,	PUNCT
ejpam-5536	142	20	φ+	φ+	X
ejpam-5536	142	21	(	(	PUNCT
ejpam-5536	142	22	β	β	X
ejpam-5536	142	23	,	,	PUNCT
ejpam-5536	142	24	t1	t1	NOUN
ejpam-5536	142	25	)	)	PUNCT
ejpam-5536	142	26	(	(	PUNCT
ejpam-5536	142	27	y	y	NOUN
ejpam-5536	142	28	)	)	PUNCT
ejpam-5536	142	29	}	}	PUNCT
ejpam-5536	142	30	,	,	PUNCT
ejpam-5536	142	31	φ−	φ−	PROPN
ejpam-5536	142	32	(	(	PUNCT
ejpam-5536	142	33	α	α	NOUN
ejpam-5536	142	34	,	,	PUNCT
ejpam-5536	142	35	t1	t1	NOUN
ejpam-5536	142	36	)	)	PUNCT
ejpam-5536	142	37	(	(	PUNCT
ejpam-5536	142	38	x	x	X
ejpam-5536	142	39	·	·	PUNCT
ejpam-5536	142	40	y	y	X
ejpam-5536	142	41	)	)	PUNCT
ejpam-5536	143	1	=	=	SYM
ejpam-5536	143	2	φ−(x	φ−(x	PROPN
ejpam-5536	143	3	·	·	PUNCT
ejpam-5536	143	4	y	y	X
ejpam-5536	143	5	)	)	PUNCT
ejpam-5536	143	6	+	+	CCONJ
ejpam-5536	143	7	α	α	PROPN
ejpam-5536	143	8	≤	≤	NUM
ejpam-5536	143	9	max{φ−(x	max{φ−(x	PROPN
ejpam-5536	143	10	)	)	PUNCT
ejpam-5536	143	11	,	,	PUNCT
ejpam-5536	143	12	φ−(y)}+	φ−(y)}+	PROPN
ejpam-5536	143	13	α	α	NOUN
ejpam-5536	143	14	=	=	SYM
ejpam-5536	143	15	max{φ−(x	max{φ−(x	PROPN
ejpam-5536	143	16	)	)	PUNCT
ejpam-5536	144	1	+	+	CCONJ
ejpam-5536	144	2	α	α	NOUN
ejpam-5536	144	3	,	,	PUNCT
ejpam-5536	144	4	φ−(y	φ−(y	PROPN
ejpam-5536	144	5	)	)	PUNCT
ejpam-5536	144	6	+	+	CCONJ
ejpam-5536	144	7	α	α	X
ejpam-5536	144	8	}	}	PUNCT
ejpam-5536	144	9	=	=	SYM
ejpam-5536	144	10	max{φ−	max{φ−	PROPN
ejpam-5536	144	11	(	(	PUNCT
ejpam-5536	144	12	α	α	NOUN
ejpam-5536	144	13	,	,	PUNCT
ejpam-5536	144	14	t1	t1	NOUN
ejpam-5536	144	15	)	)	PUNCT
ejpam-5536	144	16	(	(	PUNCT
ejpam-5536	144	17	x	x	X
ejpam-5536	144	18	)	)	PUNCT
ejpam-5536	144	19	,	,	PUNCT
ejpam-5536	144	20	φ−	φ−	PROPN
ejpam-5536	144	21	(	(	PUNCT
ejpam-5536	144	22	α	α	NOUN
ejpam-5536	144	23	,	,	PUNCT
ejpam-5536	144	24	t1	t1	NOUN
ejpam-5536	144	25	)	)	PUNCT
ejpam-5536	144	26	(	(	PUNCT
ejpam-5536	144	27	y	y	NOUN
ejpam-5536	144	28	)	)	PUNCT
ejpam-5536	144	29	}	}	PUNCT
ejpam-5536	144	30	.	.	PUNCT
ejpam-5536	145	1	hence	hence	ADV
ejpam-5536	145	2	,	,	PUNCT
ejpam-5536	145	3	φt1	φt1	X
ejpam-5536	145	4	(	(	PUNCT
ejpam-5536	145	5	β	β	X
ejpam-5536	145	6	,	,	PUNCT
ejpam-5536	145	7	α	α	NOUN
ejpam-5536	145	8	)	)	PUNCT
ejpam-5536	145	9	=	=	SYM
ejpam-5536	145	10	(	(	PUNCT
ejpam-5536	145	11	φ+	φ+	X
ejpam-5536	145	12	(	(	PUNCT
ejpam-5536	145	13	β	β	X
ejpam-5536	145	14	,	,	PUNCT
ejpam-5536	145	15	t1	t1	NOUN
ejpam-5536	145	16	)	)	PUNCT
ejpam-5536	145	17	,	,	PUNCT
ejpam-5536	145	18	φ−	φ−	PROPN
ejpam-5536	145	19	(	(	PUNCT
ejpam-5536	145	20	α	α	NOUN
ejpam-5536	145	21	,	,	PUNCT
ejpam-5536	145	22	t1	t1	NOUN
ejpam-5536	145	23	)	)	PUNCT
ejpam-5536	145	24	)	)	PUNCT
ejpam-5536	145	25	is	be	AUX
ejpam-5536	145	26	a	a	DET
ejpam-5536	145	27	bipolar	bipolar	ADJ
ejpam-5536	145	28	fuzzy	fuzzy	ADJ
ejpam-5536	145	29	subalgebra	subalgebra	NOUN
ejpam-5536	145	30	of	of	ADP
ejpam-5536	145	31	x.	x.	NOUN
ejpam-5536	145	32	theorem	theorem	VERB
ejpam-5536	145	33	2	2	NUM
ejpam-5536	145	34	.	.	PUNCT
ejpam-5536	145	35	if	if	SCONJ
ejpam-5536	145	36	there	there	PRON
ejpam-5536	145	37	exists	exist	VERB
ejpam-5536	145	38	(	(	PUNCT
ejpam-5536	145	39	β	β	X
ejpam-5536	145	40	,	,	PUNCT
ejpam-5536	145	41	α	α	NOUN
ejpam-5536	145	42	)	)	PUNCT
ejpam-5536	145	43	∈	∈	PROPN
ejpam-5536	146	1	[	[	X
ejpam-5536	146	2	0,⊤	0,⊤	NOUN
ejpam-5536	146	3	]	]	X
ejpam-5536	146	4	×	×	NOUN
ejpam-5536	147	1	[	[	X
ejpam-5536	147	2	⊥	⊥	NOUN
ejpam-5536	147	3	,	,	PUNCT
ejpam-5536	147	4	0	0	NUM
ejpam-5536	147	5	]	]	PUNCT
ejpam-5536	147	6	such	such	ADJ
ejpam-5536	147	7	that	that	SCONJ
ejpam-5536	147	8	the	the	DET
ejpam-5536	147	9	bipolar	bipolar	ADJ
ejpam-5536	147	10	fuzzy	fuzzy	NOUN
ejpam-5536	147	11	(	(	PUNCT
ejpam-5536	147	12	β	β	NOUN
ejpam-5536	147	13	,	,	PUNCT
ejpam-5536	147	14	α)translation	α)translation	NOUN
ejpam-5536	147	15	φt1	φt1	X
ejpam-5536	147	16	(	(	PUNCT
ejpam-5536	147	17	β	β	X
ejpam-5536	147	18	,	,	PUNCT
ejpam-5536	147	19	α	α	NOUN
ejpam-5536	147	20	)	)	PUNCT
ejpam-5536	147	21	=	=	SYM
ejpam-5536	147	22	(	(	PUNCT
ejpam-5536	147	23	φ+	φ+	X
ejpam-5536	147	24	(	(	PUNCT
ejpam-5536	147	25	β	β	X
ejpam-5536	147	26	,	,	PUNCT
ejpam-5536	147	27	t1	t1	NOUN
ejpam-5536	147	28	)	)	PUNCT
ejpam-5536	147	29	,	,	PUNCT
ejpam-5536	147	30	φ−	φ−	PROPN
ejpam-5536	147	31	(	(	PUNCT
ejpam-5536	147	32	α	α	NOUN
ejpam-5536	147	33	,	,	PUNCT
ejpam-5536	147	34	t1	t1	NOUN
ejpam-5536	147	35	)	)	PUNCT
ejpam-5536	147	36	)	)	PUNCT
ejpam-5536	147	37	of	of	ADP
ejpam-5536	147	38	a	a	DET
ejpam-5536	147	39	bfs	bfs	NOUN
ejpam-5536	147	40	φ	φ	NOUN
ejpam-5536	147	41	=	=	SYM
ejpam-5536	147	42	(	(	PUNCT
ejpam-5536	147	43	φ+	φ+	NOUN
ejpam-5536	147	44	,	,	PUNCT
ejpam-5536	147	45	φ−	φ−	PROPN
ejpam-5536	147	46	)	)	PUNCT
ejpam-5536	147	47	is	be	AUX
ejpam-5536	147	48	a	a	DET
ejpam-5536	147	49	bipolar	bipolar	ADJ
ejpam-5536	147	50	fuzzy	fuzzy	ADJ
ejpam-5536	147	51	subalgebra	subalgebra	NOUN
ejpam-5536	147	52	of	of	ADP
ejpam-5536	147	53	a	a	DET
ejpam-5536	147	54	hilbert	hilbert	NOUN
ejpam-5536	147	55	algebra	algebra	NOUN
ejpam-5536	147	56	x	x	PUNCT
ejpam-5536	148	1	=	=	SYM
ejpam-5536	148	2	(	(	PUNCT
ejpam-5536	148	3	x	x	NOUN
ejpam-5536	148	4	,	,	PUNCT
ejpam-5536	148	5	·	·	PUNCT
ejpam-5536	148	6	,	,	PUNCT
ejpam-5536	148	7	1x	1x	NUM
ejpam-5536	148	8	)	)	PUNCT
ejpam-5536	148	9	,	,	PUNCT
ejpam-5536	148	10	then	then	ADV
ejpam-5536	148	11	φ	φ	PROPN
ejpam-5536	148	12	=	=	SYM
ejpam-5536	148	13	(	(	PUNCT
ejpam-5536	148	14	φ+	φ+	NOUN
ejpam-5536	148	15	,	,	PUNCT
ejpam-5536	148	16	φ−	φ−	PROPN
ejpam-5536	148	17	)	)	PUNCT
ejpam-5536	148	18	is	be	AUX
ejpam-5536	148	19	a	a	DET
ejpam-5536	148	20	bipolar	bipolar	ADJ
ejpam-5536	148	21	fuzzy	fuzzy	ADJ
ejpam-5536	148	22	subalgebra	subalgebra	NOUN
ejpam-5536	148	23	of	of	ADP
ejpam-5536	148	24	x.	x.	NOUN
ejpam-5536	148	25	proof	proof	PROPN
ejpam-5536	148	26	.	.	PUNCT
ejpam-5536	149	1	assume	assume	VERB
ejpam-5536	149	2	that	that	SCONJ
ejpam-5536	149	3	φt1	φt1	X
ejpam-5536	149	4	(	(	PUNCT
ejpam-5536	149	5	β	β	X
ejpam-5536	149	6	,	,	PUNCT
ejpam-5536	149	7	α	α	NOUN
ejpam-5536	149	8	)	)	PUNCT
ejpam-5536	149	9	=	=	SYM
ejpam-5536	149	10	(	(	PUNCT
ejpam-5536	149	11	φ+	φ+	X
ejpam-5536	149	12	(	(	PUNCT
ejpam-5536	149	13	β	β	X
ejpam-5536	149	14	,	,	PUNCT
ejpam-5536	149	15	t1	t1	NOUN
ejpam-5536	149	16	)	)	PUNCT
ejpam-5536	149	17	,	,	PUNCT
ejpam-5536	149	18	φ−	φ−	PROPN
ejpam-5536	149	19	(	(	PUNCT
ejpam-5536	149	20	α	α	NOUN
ejpam-5536	149	21	,	,	PUNCT
ejpam-5536	149	22	t1	t1	NOUN
ejpam-5536	149	23	)	)	PUNCT
ejpam-5536	149	24	)	)	PUNCT
ejpam-5536	149	25	is	be	AUX
ejpam-5536	149	26	a	a	DET
ejpam-5536	149	27	bipolar	bipolar	ADJ
ejpam-5536	149	28	fuzzy	fuzzy	ADJ
ejpam-5536	149	29	subalgebra	subalgebra	NOUN
ejpam-5536	149	30	of	of	ADP
ejpam-5536	149	31	x	x	PUNCT
ejpam-5536	149	32	for	for	ADP
ejpam-5536	149	33	(	(	PUNCT
ejpam-5536	149	34	β	β	X
ejpam-5536	149	35	,	,	PUNCT
ejpam-5536	149	36	α	α	NOUN
ejpam-5536	149	37	)	)	PUNCT
ejpam-5536	149	38	∈	∈	PROPN
ejpam-5536	150	1	[	[	X
ejpam-5536	150	2	0,⊤]×	0,⊤]×	X
ejpam-5536	151	1	[	[	X
ejpam-5536	151	2	⊥	⊥	X
ejpam-5536	151	3	,	,	PUNCT
ejpam-5536	151	4	0	0	NUM
ejpam-5536	151	5	]	]	PUNCT
ejpam-5536	151	6	.	.	PUNCT
ejpam-5536	152	1	for	for	ADP
ejpam-5536	152	2	all	all	DET
ejpam-5536	152	3	x	x	NOUN
ejpam-5536	152	4	,	,	PUNCT
ejpam-5536	152	5	y	y	PROPN
ejpam-5536	152	6	∈	∈	PROPN
ejpam-5536	152	7	x	x	X
ejpam-5536	152	8	,	,	PUNCT
ejpam-5536	152	9	we	we	PRON
ejpam-5536	152	10	have	have	VERB
ejpam-5536	152	11	φ+(x	φ+(x	NOUN
ejpam-5536	152	12	·	·	PUNCT
ejpam-5536	152	13	y	y	X
ejpam-5536	152	14	)	)	PUNCT
ejpam-5536	153	1	+	+	CCONJ
ejpam-5536	153	2	β	β	X
ejpam-5536	153	3	=	=	SYM
ejpam-5536	153	4	φ+	φ+	X
ejpam-5536	153	5	(	(	PUNCT
ejpam-5536	153	6	β	β	X
ejpam-5536	153	7	,	,	PUNCT
ejpam-5536	153	8	t1	t1	NOUN
ejpam-5536	153	9	)	)	PUNCT
ejpam-5536	153	10	(	(	PUNCT
ejpam-5536	153	11	x	x	X
ejpam-5536	153	12	·	·	PUNCT
ejpam-5536	153	13	y	y	X
ejpam-5536	153	14	)	)	PUNCT
ejpam-5536	153	15	≥	≥	NOUN
ejpam-5536	153	16	min{φ+	min{φ+	NOUN
ejpam-5536	153	17	(	(	PUNCT
ejpam-5536	153	18	β	β	X
ejpam-5536	153	19	,	,	PUNCT
ejpam-5536	153	20	t1	t1	NOUN
ejpam-5536	153	21	)	)	PUNCT
ejpam-5536	153	22	(	(	PUNCT
ejpam-5536	153	23	x	x	X
ejpam-5536	153	24	)	)	PUNCT
ejpam-5536	153	25	,	,	PUNCT
ejpam-5536	153	26	φ+	φ+	X
ejpam-5536	153	27	(	(	PUNCT
ejpam-5536	153	28	β	β	X
ejpam-5536	153	29	,	,	PUNCT
ejpam-5536	153	30	t1	t1	NOUN
ejpam-5536	153	31	)	)	PUNCT
ejpam-5536	153	32	(	(	PUNCT
ejpam-5536	153	33	y	y	NOUN
ejpam-5536	153	34	)	)	PUNCT
ejpam-5536	153	35	}	}	PUNCT
ejpam-5536	153	36	=	=	SYM
ejpam-5536	153	37	min{φ+(x	min{φ+(x	PROPN
ejpam-5536	153	38	)	)	PUNCT
ejpam-5536	154	1	+	+	CCONJ
ejpam-5536	154	2	β	β	X
ejpam-5536	154	3	,	,	PUNCT
ejpam-5536	154	4	φ+(y	φ+(y	PUNCT
ejpam-5536	154	5	)	)	PUNCT
ejpam-5536	154	6	+	+	CCONJ
ejpam-5536	154	7	β	β	X
ejpam-5536	154	8	}	}	PUNCT
ejpam-5536	154	9	=	=	SYM
ejpam-5536	154	10	min{φ+(x	min{φ+(x	PROPN
ejpam-5536	154	11	)	)	PUNCT
ejpam-5536	154	12	,	,	PUNCT
ejpam-5536	154	13	φ+(y)}+	φ+(y)}+	NOUN
ejpam-5536	154	14	β	β	X
ejpam-5536	154	15	,	,	PUNCT
ejpam-5536	154	16	φ−(x	φ−(x	PROPN
ejpam-5536	154	17	·	·	PUNCT
ejpam-5536	154	18	y	y	X
ejpam-5536	154	19	)	)	PUNCT
ejpam-5536	155	1	+	+	CCONJ
ejpam-5536	155	2	α	α	NOUN
ejpam-5536	155	3	=	=	SYM
ejpam-5536	155	4	φ−	φ−	PROPN
ejpam-5536	155	5	(	(	PUNCT
ejpam-5536	155	6	α	α	NOUN
ejpam-5536	155	7	,	,	PUNCT
ejpam-5536	155	8	t1	t1	NOUN
ejpam-5536	155	9	)	)	PUNCT
ejpam-5536	155	10	(	(	PUNCT
ejpam-5536	155	11	x	x	X
ejpam-5536	155	12	·	·	PUNCT
ejpam-5536	155	13	y	y	X
ejpam-5536	155	14	)	)	PUNCT
ejpam-5536	155	15	≤	≤	NOUN
ejpam-5536	156	1	max{φ−	max{φ−	PROPN
ejpam-5536	156	2	(	(	PUNCT
ejpam-5536	156	3	α	α	PROPN
ejpam-5536	156	4	,	,	PUNCT
ejpam-5536	156	5	t1	t1	NOUN
ejpam-5536	156	6	)	)	PUNCT
ejpam-5536	156	7	(	(	PUNCT
ejpam-5536	156	8	x	x	X
ejpam-5536	156	9	)	)	PUNCT
ejpam-5536	156	10	,	,	PUNCT
ejpam-5536	156	11	φ−	φ−	PROPN
ejpam-5536	156	12	(	(	PUNCT
ejpam-5536	156	13	α	α	NOUN
ejpam-5536	156	14	,	,	PUNCT
ejpam-5536	156	15	t1	t1	NOUN
ejpam-5536	156	16	)	)	PUNCT
ejpam-5536	156	17	(	(	PUNCT
ejpam-5536	156	18	y	y	NOUN
ejpam-5536	156	19	)	)	PUNCT
ejpam-5536	156	20	}	}	PUNCT
ejpam-5536	156	21	=	=	SYM
ejpam-5536	156	22	max{φ−(x	max{φ−(x	PROPN
ejpam-5536	156	23	)	)	PUNCT
ejpam-5536	156	24	+	+	CCONJ
ejpam-5536	156	25	α	α	NOUN
ejpam-5536	156	26	,	,	PUNCT
ejpam-5536	156	27	φ−(y	φ−(y	PROPN
ejpam-5536	156	28	)	)	PUNCT
ejpam-5536	157	1	+	+	CCONJ
ejpam-5536	157	2	α	α	X
ejpam-5536	157	3	}	}	PUNCT
ejpam-5536	157	4	=	=	SYM
ejpam-5536	157	5	max{φ−(x	max{φ−(x	PROPN
ejpam-5536	157	6	)	)	PUNCT
ejpam-5536	157	7	,	,	PUNCT
ejpam-5536	158	1	φ−(y)}+	φ−(y)}+	PROPN
ejpam-5536	158	2	α	α	X
ejpam-5536	158	3	.	.	PUNCT
ejpam-5536	158	4	a.	a.	PROPN
ejpam-5536	158	5	iampan	iampan	PROPN
ejpam-5536	158	6	et	et	PROPN
ejpam-5536	158	7	al	al	PROPN
ejpam-5536	158	8	.	.	PUNCT
ejpam-5536	158	9	/	/	SYM
ejpam-5536	158	10	eur	eur	PROPN
ejpam-5536	158	11	.	.	PUNCT
ejpam-5536	159	1	j.	j.	PROPN
ejpam-5536	159	2	pure	pure	PROPN
ejpam-5536	159	3	appl	appl	PROPN
ejpam-5536	159	4	.	.	PROPN
ejpam-5536	159	5	math	math	PROPN
ejpam-5536	159	6	,	,	PUNCT
ejpam-5536	159	7	17	17	NUM
ejpam-5536	159	8	(	(	PUNCT
ejpam-5536	159	9	4	4	NUM
ejpam-5536	159	10	)	)	PUNCT
ejpam-5536	159	11	(	(	PUNCT
ejpam-5536	159	12	2024	2024	NUM
ejpam-5536	159	13	)	)	PUNCT
ejpam-5536	159	14	,	,	PUNCT
ejpam-5536	159	15	4059	4059	NUM
ejpam-5536	159	16	-	-	SYM
ejpam-5536	159	17	4070	4070	NUM
ejpam-5536	159	18	4065	4065	NUM
ejpam-5536	159	19	thus	thus	ADV
ejpam-5536	159	20	,	,	PUNCT
ejpam-5536	159	21	φ+(x	φ+(x	X
ejpam-5536	159	22	·	·	PUNCT
ejpam-5536	159	23	y	y	X
ejpam-5536	159	24	)	)	PUNCT
ejpam-5536	159	25	≥	≥	NOUN
ejpam-5536	159	26	min{φ+(x	min{φ+(x	PROPN
ejpam-5536	159	27	)	)	PUNCT
ejpam-5536	159	28	,	,	PUNCT
ejpam-5536	159	29	φ+(y	φ+(y	CCONJ
ejpam-5536	159	30	)	)	PUNCT
ejpam-5536	159	31	}	}	PUNCT
ejpam-5536	159	32	and	and	CCONJ
ejpam-5536	159	33	φ−(x	φ−(x	PROPN
ejpam-5536	159	34	·	·	PUNCT
ejpam-5536	159	35	y	y	X
ejpam-5536	159	36	)	)	PUNCT
ejpam-5536	159	37	≤	≤	NOUN
ejpam-5536	159	38	max{φ−(x	max{φ−(x	PROPN
ejpam-5536	159	39	)	)	PUNCT
ejpam-5536	159	40	,	,	PUNCT
ejpam-5536	159	41	φ−(y	φ−(y	PROPN
ejpam-5536	159	42	)	)	PUNCT
ejpam-5536	159	43	}	}	PUNCT
ejpam-5536	159	44	.	.	PUNCT
ejpam-5536	160	1	hence	hence	ADV
ejpam-5536	160	2	,	,	PUNCT
ejpam-5536	160	3	φ	φ	PROPN
ejpam-5536	160	4	=	=	SYM
ejpam-5536	160	5	(	(	PUNCT
ejpam-5536	160	6	φ+	φ+	NOUN
ejpam-5536	160	7	,	,	PUNCT
ejpam-5536	160	8	φ−	φ−	PROPN
ejpam-5536	160	9	)	)	PUNCT
ejpam-5536	160	10	is	be	AUX
ejpam-5536	160	11	a	a	DET
ejpam-5536	160	12	bipolar	bipolar	ADJ
ejpam-5536	160	13	fuzzy	fuzzy	ADJ
ejpam-5536	160	14	subalgebra	subalgebra	NOUN
ejpam-5536	160	15	of	of	ADP
ejpam-5536	160	16	x.	x.	PROPN
ejpam-5536	160	17	theorem	theorem	VERB
ejpam-5536	160	18	3	3	X
ejpam-5536	160	19	.	.	PUNCT
ejpam-5536	161	1	if	if	SCONJ
ejpam-5536	161	2	a	a	DET
ejpam-5536	161	3	bfs	bfs	NOUN
ejpam-5536	161	4	φ	φ	X
ejpam-5536	161	5	=	=	SYM
ejpam-5536	161	6	(	(	PUNCT
ejpam-5536	161	7	φ+	φ+	NOUN
ejpam-5536	161	8	,	,	PUNCT
ejpam-5536	161	9	φ−	φ−	PROPN
ejpam-5536	161	10	)	)	PUNCT
ejpam-5536	161	11	in	in	ADP
ejpam-5536	161	12	a	a	DET
ejpam-5536	161	13	hilbert	hilbert	NOUN
ejpam-5536	161	14	algebra	algebra	NOUN
ejpam-5536	161	15	x	x	PUNCT
ejpam-5536	161	16	=	=	SYM
ejpam-5536	161	17	(	(	PUNCT
ejpam-5536	161	18	x	x	NOUN
ejpam-5536	161	19	,	,	PUNCT
ejpam-5536	161	20	·	·	PUNCT
ejpam-5536	161	21	,	,	PUNCT
ejpam-5536	161	22	1x	1x	NUM
ejpam-5536	161	23	)	)	PUNCT
ejpam-5536	161	24	is	be	AUX
ejpam-5536	161	25	a	a	DET
ejpam-5536	161	26	bipolar	bipolar	ADJ
ejpam-5536	161	27	fuzzy	fuzzy	ADJ
ejpam-5536	161	28	ideal	ideal	NOUN
ejpam-5536	161	29	(	(	PUNCT
ejpam-5536	161	30	resp	resp	NOUN
ejpam-5536	161	31	.	.	PUNCT
ejpam-5536	161	32	,	,	PUNCT
ejpam-5536	161	33	deductive	deductive	ADJ
ejpam-5536	161	34	system	system	NOUN
ejpam-5536	161	35	)	)	PUNCT
ejpam-5536	161	36	of	of	ADP
ejpam-5536	161	37	x	x	PRON
ejpam-5536	161	38	,	,	PUNCT
ejpam-5536	161	39	then	then	ADV
ejpam-5536	161	40	for	for	ADP
ejpam-5536	161	41	all	all	DET
ejpam-5536	161	42	(	(	PUNCT
ejpam-5536	161	43	β	β	X
ejpam-5536	161	44	,	,	PUNCT
ejpam-5536	161	45	α	α	NOUN
ejpam-5536	161	46	)	)	PUNCT
ejpam-5536	161	47	∈	∈	PROPN
ejpam-5536	162	1	[	[	X
ejpam-5536	162	2	0,⊤]×	0,⊤]×	X
ejpam-5536	163	1	[	[	X
ejpam-5536	163	2	⊥	⊥	X
ejpam-5536	163	3	,	,	PUNCT
ejpam-5536	163	4	0	0	NUM
ejpam-5536	163	5	]	]	PUNCT
ejpam-5536	163	6	,	,	PUNCT
ejpam-5536	163	7	the	the	DET
ejpam-5536	163	8	bipolar	bipolar	ADJ
ejpam-5536	163	9	fuzzy	fuzzy	NOUN
ejpam-5536	163	10	(	(	PUNCT
ejpam-5536	163	11	β	β	NOUN
ejpam-5536	163	12	,	,	PUNCT
ejpam-5536	163	13	α)-translation	α)-translation	NOUN
ejpam-5536	163	14	φt1	φt1	X
ejpam-5536	163	15	(	(	PUNCT
ejpam-5536	163	16	β	β	X
ejpam-5536	163	17	,	,	PUNCT
ejpam-5536	163	18	α	α	NOUN
ejpam-5536	163	19	)	)	PUNCT
ejpam-5536	163	20	=	=	SYM
ejpam-5536	164	1	(	(	PUNCT
ejpam-5536	164	2	φ+	φ+	X
ejpam-5536	164	3	(	(	PUNCT
ejpam-5536	164	4	β	β	X
ejpam-5536	164	5	,	,	PUNCT
ejpam-5536	164	6	t1	t1	NOUN
ejpam-5536	164	7	)	)	PUNCT
ejpam-5536	164	8	,	,	PUNCT
ejpam-5536	164	9	φ−	φ−	PROPN
ejpam-5536	164	10	(	(	PUNCT
ejpam-5536	164	11	α	α	NOUN
ejpam-5536	164	12	,	,	PUNCT
ejpam-5536	164	13	t1	t1	NOUN
ejpam-5536	164	14	)	)	PUNCT
ejpam-5536	164	15	)	)	PUNCT
ejpam-5536	164	16	of	of	ADP
ejpam-5536	164	17	φ	φ	PROPN
ejpam-5536	164	18	=	=	SYM
ejpam-5536	164	19	(	(	PUNCT
ejpam-5536	164	20	φ+	φ+	NOUN
ejpam-5536	164	21	,	,	PUNCT
ejpam-5536	164	22	φ−	φ−	PROPN
ejpam-5536	164	23	)	)	PUNCT
ejpam-5536	164	24	is	be	AUX
ejpam-5536	164	25	a	a	DET
ejpam-5536	164	26	bipolar	bipolar	ADJ
ejpam-5536	164	27	fuzzy	fuzzy	ADJ
ejpam-5536	164	28	ideal	ideal	NOUN
ejpam-5536	164	29	(	(	PUNCT
ejpam-5536	164	30	resp	resp	NOUN
ejpam-5536	164	31	.	.	PUNCT
ejpam-5536	164	32	,	,	PUNCT
ejpam-5536	164	33	deductive	deductive	ADJ
ejpam-5536	164	34	system	system	NOUN
ejpam-5536	164	35	)	)	PUNCT
ejpam-5536	164	36	of	of	ADP
ejpam-5536	164	37	x.	x.	NOUN
ejpam-5536	164	38	proof	proof	NOUN
ejpam-5536	164	39	.	.	PUNCT
ejpam-5536	165	1	the	the	DET
ejpam-5536	165	2	proof	proof	NOUN
ejpam-5536	165	3	is	be	AUX
ejpam-5536	165	4	similar	similar	ADJ
ejpam-5536	165	5	to	to	ADP
ejpam-5536	165	6	theorem	theorem	VERB
ejpam-5536	165	7	1	1	NUM
ejpam-5536	165	8	.	.	PUNCT
ejpam-5536	165	9	theorem	theorem	NOUN
ejpam-5536	165	10	4	4	NUM
ejpam-5536	165	11	.	.	PUNCT
ejpam-5536	166	1	if	if	SCONJ
ejpam-5536	166	2	there	there	PRON
ejpam-5536	166	3	exists	exist	VERB
ejpam-5536	166	4	(	(	PUNCT
ejpam-5536	166	5	β	β	X
ejpam-5536	166	6	,	,	PUNCT
ejpam-5536	166	7	α	α	NOUN
ejpam-5536	166	8	)	)	PUNCT
ejpam-5536	166	9	∈	∈	PROPN
ejpam-5536	167	1	[	[	X
ejpam-5536	167	2	0,⊤	0,⊤	NOUN
ejpam-5536	167	3	]	]	X
ejpam-5536	167	4	×	×	NOUN
ejpam-5536	168	1	[	[	X
ejpam-5536	168	2	⊥	⊥	NOUN
ejpam-5536	168	3	,	,	PUNCT
ejpam-5536	168	4	0	0	NUM
ejpam-5536	168	5	]	]	PUNCT
ejpam-5536	168	6	such	such	ADJ
ejpam-5536	168	7	that	that	SCONJ
ejpam-5536	168	8	the	the	DET
ejpam-5536	168	9	bipolar	bipolar	ADJ
ejpam-5536	168	10	fuzzy	fuzzy	NOUN
ejpam-5536	168	11	(	(	PUNCT
ejpam-5536	168	12	β	β	NOUN
ejpam-5536	168	13	,	,	PUNCT
ejpam-5536	168	14	α)translation	α)translation	NOUN
ejpam-5536	168	15	φt1	φt1	X
ejpam-5536	168	16	(	(	PUNCT
ejpam-5536	168	17	β	β	X
ejpam-5536	168	18	,	,	PUNCT
ejpam-5536	168	19	α	α	NOUN
ejpam-5536	168	20	)	)	PUNCT
ejpam-5536	168	21	=	=	SYM
ejpam-5536	168	22	(	(	PUNCT
ejpam-5536	168	23	φ+	φ+	X
ejpam-5536	168	24	(	(	PUNCT
ejpam-5536	168	25	β	β	X
ejpam-5536	168	26	,	,	PUNCT
ejpam-5536	168	27	t1	t1	NOUN
ejpam-5536	168	28	)	)	PUNCT
ejpam-5536	168	29	,	,	PUNCT
ejpam-5536	168	30	φ−	φ−	PROPN
ejpam-5536	168	31	(	(	PUNCT
ejpam-5536	168	32	α	α	NOUN
ejpam-5536	168	33	,	,	PUNCT
ejpam-5536	168	34	t1	t1	NOUN
ejpam-5536	168	35	)	)	PUNCT
ejpam-5536	168	36	)	)	PUNCT
ejpam-5536	168	37	of	of	ADP
ejpam-5536	168	38	a	a	DET
ejpam-5536	168	39	bfs	bfs	NOUN
ejpam-5536	168	40	φ	φ	NOUN
ejpam-5536	168	41	=	=	SYM
ejpam-5536	168	42	(	(	PUNCT
ejpam-5536	168	43	φ+	φ+	NOUN
ejpam-5536	168	44	,	,	PUNCT
ejpam-5536	168	45	φ−	φ−	PROPN
ejpam-5536	168	46	)	)	PUNCT
ejpam-5536	168	47	is	be	AUX
ejpam-5536	168	48	a	a	DET
ejpam-5536	168	49	bipolar	bipolar	ADJ
ejpam-5536	168	50	fuzzy	fuzzy	ADJ
ejpam-5536	168	51	ideal	ideal	NOUN
ejpam-5536	168	52	(	(	PUNCT
ejpam-5536	168	53	resp	resp	NOUN
ejpam-5536	168	54	.	.	PUNCT
ejpam-5536	168	55	,	,	PUNCT
ejpam-5536	168	56	deductive	deductive	ADJ
ejpam-5536	168	57	system	system	NOUN
ejpam-5536	168	58	)	)	PUNCT
ejpam-5536	168	59	of	of	ADP
ejpam-5536	168	60	a	a	DET
ejpam-5536	168	61	hilbert	hilbert	NOUN
ejpam-5536	168	62	algebra	algebra	NOUN
ejpam-5536	168	63	x	x	PUNCT
ejpam-5536	169	1	=	=	SYM
ejpam-5536	169	2	(	(	PUNCT
ejpam-5536	169	3	x	x	NOUN
ejpam-5536	169	4	,	,	PUNCT
ejpam-5536	169	5	·	·	PUNCT
ejpam-5536	169	6	,	,	PUNCT
ejpam-5536	169	7	1x	1x	NUM
ejpam-5536	169	8	)	)	PUNCT
ejpam-5536	169	9	,	,	PUNCT
ejpam-5536	169	10	then	then	ADV
ejpam-5536	169	11	φ	φ	PROPN
ejpam-5536	169	12	=	=	SYM
ejpam-5536	169	13	(	(	PUNCT
ejpam-5536	169	14	φ+	φ+	NOUN
ejpam-5536	169	15	,	,	PUNCT
ejpam-5536	169	16	φ−	φ−	PROPN
ejpam-5536	169	17	)	)	PUNCT
ejpam-5536	169	18	is	be	AUX
ejpam-5536	169	19	a	a	DET
ejpam-5536	169	20	bipolar	bipolar	ADJ
ejpam-5536	169	21	fuzzy	fuzzy	ADJ
ejpam-5536	169	22	ideal	ideal	NOUN
ejpam-5536	169	23	(	(	PUNCT
ejpam-5536	169	24	resp	resp	NOUN
ejpam-5536	169	25	.	.	PUNCT
ejpam-5536	169	26	,	,	PUNCT
ejpam-5536	169	27	deductive	deductive	ADJ
ejpam-5536	169	28	system	system	NOUN
ejpam-5536	169	29	)	)	PUNCT
ejpam-5536	169	30	of	of	ADP
ejpam-5536	169	31	x.	x.	NOUN
ejpam-5536	169	32	proof	proof	NOUN
ejpam-5536	169	33	.	.	PUNCT
ejpam-5536	170	1	the	the	DET
ejpam-5536	170	2	proof	proof	NOUN
ejpam-5536	170	3	is	be	AUX
ejpam-5536	170	4	similar	similar	ADJ
ejpam-5536	170	5	to	to	ADP
ejpam-5536	170	6	theorem	theorem	NOUN
ejpam-5536	170	7	2	2	NUM
ejpam-5536	170	8	.	.	NOUN
ejpam-5536	170	9	remark	remark	NOUN
ejpam-5536	170	10	1	1	NUM
ejpam-5536	170	11	.	.	PUNCT
ejpam-5536	171	1	if	if	SCONJ
ejpam-5536	171	2	φ	φ	PROPN
ejpam-5536	171	3	=	=	SYM
ejpam-5536	171	4	(	(	PUNCT
ejpam-5536	171	5	φ+	φ+	NOUN
ejpam-5536	171	6	,	,	PUNCT
ejpam-5536	171	7	φ−	φ−	PROPN
ejpam-5536	171	8	)	)	PUNCT
ejpam-5536	171	9	is	be	AUX
ejpam-5536	171	10	a	a	DET
ejpam-5536	171	11	bfs	bfs	NOUN
ejpam-5536	171	12	in	in	ADP
ejpam-5536	171	13	a	a	DET
ejpam-5536	171	14	nonempty	nonempty	ADV
ejpam-5536	171	15	set	set	VERB
ejpam-5536	171	16	x	x	NOUN
ejpam-5536	171	17	,	,	PUNCT
ejpam-5536	171	18	then	then	ADV
ejpam-5536	171	19	for	for	ADP
ejpam-5536	171	20	all	all	DET
ejpam-5536	171	21	(	(	PUNCT
ejpam-5536	171	22	β	β	X
ejpam-5536	171	23	,	,	PUNCT
ejpam-5536	171	24	α	α	NOUN
ejpam-5536	171	25	)	)	PUNCT
ejpam-5536	171	26	∈	∈	PROPN
ejpam-5536	172	1	[	[	X
ejpam-5536	172	2	0,⊤]×	0,⊤]×	X
ejpam-5536	173	1	[	[	X
ejpam-5536	173	2	⊥	⊥	X
ejpam-5536	173	3	,	,	PUNCT
ejpam-5536	173	4	0	0	NUM
ejpam-5536	173	5	]	]	PUNCT
ejpam-5536	173	6	,	,	PUNCT
ejpam-5536	173	7	φ+	φ+	X
ejpam-5536	173	8	(	(	PUNCT
ejpam-5536	173	9	β	β	X
ejpam-5536	173	10	,	,	PUNCT
ejpam-5536	173	11	t1	t1	NOUN
ejpam-5536	173	12	)	)	PUNCT
ejpam-5536	173	13	(	(	PUNCT
ejpam-5536	173	14	x	x	X
ejpam-5536	173	15	)	)	PUNCT
ejpam-5536	173	16	=	=	SYM
ejpam-5536	173	17	φ+(x)+β	φ+(x)+β	VERB
ejpam-5536	173	18	≥	≥	X
ejpam-5536	173	19	φ+(x	φ+(x	X
ejpam-5536	173	20	)	)	PUNCT
ejpam-5536	173	21	and	and	CCONJ
ejpam-5536	173	22	φ−	φ−	PROPN
ejpam-5536	173	23	(	(	PUNCT
ejpam-5536	173	24	α	α	NOUN
ejpam-5536	173	25	,	,	PUNCT
ejpam-5536	173	26	t1	t1	NOUN
ejpam-5536	173	27	)	)	PUNCT
ejpam-5536	173	28	(	(	PUNCT
ejpam-5536	173	29	x	x	X
ejpam-5536	173	30	)	)	PUNCT
ejpam-5536	173	31	=	=	NOUN
ejpam-5536	173	32	φ−(x)+α	φ−(x)+α	NOUN
ejpam-5536	173	33	≤	≤	NUM
ejpam-5536	173	34	φ−(x	φ−(x	PROPN
ejpam-5536	173	35	)	)	PUNCT
ejpam-5536	173	36	for	for	ADP
ejpam-5536	173	37	all	all	PRON
ejpam-5536	173	38	x	x	SYM
ejpam-5536	173	39	∈	∈	ADJ
ejpam-5536	173	40	x.	x.	NOUN
ejpam-5536	173	41	hence	hence	ADV
ejpam-5536	173	42	,	,	PUNCT
ejpam-5536	173	43	the	the	DET
ejpam-5536	173	44	bipolar	bipolar	ADJ
ejpam-5536	173	45	fuzzy	fuzzy	NOUN
ejpam-5536	173	46	(	(	PUNCT
ejpam-5536	173	47	β	β	NOUN
ejpam-5536	173	48	,	,	PUNCT
ejpam-5536	173	49	α)-translation	α)-translation	NOUN
ejpam-5536	173	50	φt1	φt1	X
ejpam-5536	173	51	(	(	PUNCT
ejpam-5536	173	52	β	β	X
ejpam-5536	173	53	,	,	PUNCT
ejpam-5536	173	54	α	α	NOUN
ejpam-5536	173	55	)	)	PUNCT
ejpam-5536	173	56	=	=	SYM
ejpam-5536	173	57	(	(	PUNCT
ejpam-5536	173	58	φ+	φ+	X
ejpam-5536	173	59	(	(	PUNCT
ejpam-5536	173	60	β	β	X
ejpam-5536	173	61	,	,	PUNCT
ejpam-5536	173	62	t1	t1	NOUN
ejpam-5536	173	63	)	)	PUNCT
ejpam-5536	173	64	,	,	PUNCT
ejpam-5536	173	65	φ−	φ−	PROPN
ejpam-5536	173	66	(	(	PUNCT
ejpam-5536	173	67	α	α	NOUN
ejpam-5536	173	68	,	,	PUNCT
ejpam-5536	173	69	t1	t1	NOUN
ejpam-5536	173	70	)	)	PUNCT
ejpam-5536	173	71	)	)	PUNCT
ejpam-5536	173	72	of	of	ADP
ejpam-5536	173	73	φ	φ	PROPN
ejpam-5536	173	74	=	=	SYM
ejpam-5536	173	75	(	(	PUNCT
ejpam-5536	173	76	φ+	φ+	NOUN
ejpam-5536	173	77	,	,	PUNCT
ejpam-5536	173	78	φ−	φ−	PROPN
ejpam-5536	173	79	)	)	PUNCT
ejpam-5536	173	80	is	be	AUX
ejpam-5536	173	81	a	a	DET
ejpam-5536	173	82	bipolar	bipolar	ADJ
ejpam-5536	173	83	fuzzy	fuzzy	ADJ
ejpam-5536	173	84	extension	extension	NOUN
ejpam-5536	173	85	of	of	ADP
ejpam-5536	173	86	φ	φ	PROPN
ejpam-5536	173	87	=	=	SYM
ejpam-5536	173	88	(	(	PUNCT
ejpam-5536	173	89	φ+	φ+	NOUN
ejpam-5536	173	90	,	,	PUNCT
ejpam-5536	173	91	φ−	φ−	PROPN
ejpam-5536	173	92	)	)	PUNCT
ejpam-5536	173	93	for	for	ADP
ejpam-5536	173	94	all	all	DET
ejpam-5536	173	95	(	(	PUNCT
ejpam-5536	173	96	β	β	X
ejpam-5536	173	97	,	,	PUNCT
ejpam-5536	173	98	α	α	NOUN
ejpam-5536	173	99	)	)	PUNCT
ejpam-5536	173	100	∈	∈	PROPN
ejpam-5536	174	1	[	[	X
ejpam-5536	174	2	0,⊤]×	0,⊤]×	X
ejpam-5536	175	1	[	[	X
ejpam-5536	175	2	⊥	⊥	X
ejpam-5536	175	3	,	,	PUNCT
ejpam-5536	175	4	0	0	NUM
ejpam-5536	175	5	]	]	PUNCT
ejpam-5536	175	6	.	.	PUNCT
ejpam-5536	176	1	definition	definition	NOUN
ejpam-5536	176	2	13	13	NUM
ejpam-5536	176	3	.	.	PUNCT
ejpam-5536	177	1	for	for	ADP
ejpam-5536	177	2	any	any	DET
ejpam-5536	177	3	bfs	bfs	NOUN
ejpam-5536	177	4	φ	φ	NOUN
ejpam-5536	177	5	=	=	SYM
ejpam-5536	177	6	(	(	PUNCT
ejpam-5536	177	7	φ+	φ+	NOUN
ejpam-5536	177	8	,	,	PUNCT
ejpam-5536	177	9	φ−	φ−	PROPN
ejpam-5536	177	10	)	)	PUNCT
ejpam-5536	177	11	in	in	ADP
ejpam-5536	177	12	a	a	DET
ejpam-5536	177	13	nonempty	nonempty	ADV
ejpam-5536	177	14	set	set	VERB
ejpam-5536	177	15	x	x	NOUN
ejpam-5536	177	16	,	,	PUNCT
ejpam-5536	177	17	we	we	PRON
ejpam-5536	177	18	denote	denote	VERB
ejpam-5536	177	19	∓	∓	NOUN
ejpam-5536	178	1	=	=	PUNCT
ejpam-5536	178	2	inf{φ+(x	inf{φ+(x	ADJ
ejpam-5536	178	3	)	)	PUNCT
ejpam-5536	179	1	|	|	ADV
ejpam-5536	179	2	x	x	SYM
ejpam-5536	179	3	∈	∈	NOUN
ejpam-5536	179	4	x	x	X
ejpam-5536	179	5	}	}	PUNCT
ejpam-5536	179	6	,	,	PUNCT
ejpam-5536	179	7	±	±	NUM
ejpam-5536	179	8	=	=	SYM
ejpam-5536	179	9	sup{φ−(x	sup{φ−(x	PROPN
ejpam-5536	179	10	)	)	PUNCT
ejpam-5536	180	1	|	|	ADV
ejpam-5536	180	2	x	x	SYM
ejpam-5536	180	3	∈	∈	NOUN
ejpam-5536	180	4	x	x	X
ejpam-5536	180	5	}	}	PUNCT
ejpam-5536	180	6	.	.	PUNCT
ejpam-5536	181	1	let	let	VERB
ejpam-5536	181	2	φ	φ	PROPN
ejpam-5536	181	3	=	=	SYM
ejpam-5536	181	4	(	(	PUNCT
ejpam-5536	181	5	φ+	φ+	PROPN
ejpam-5536	181	6	,	,	PUNCT
ejpam-5536	181	7	φ−	φ−	PROPN
ejpam-5536	181	8	)	)	PUNCT
ejpam-5536	181	9	be	be	VERB
ejpam-5536	181	10	a	a	DET
ejpam-5536	181	11	bfs	bfs	NOUN
ejpam-5536	181	12	in	in	ADP
ejpam-5536	181	13	a	a	DET
ejpam-5536	181	14	nonempty	nonempty	ADV
ejpam-5536	181	15	set	set	VERB
ejpam-5536	181	16	x	x	PUNCT
ejpam-5536	181	17	and	and	CCONJ
ejpam-5536	181	18	(	(	PUNCT
ejpam-5536	181	19	β	β	X
ejpam-5536	181	20	,	,	PUNCT
ejpam-5536	181	21	α	α	NOUN
ejpam-5536	181	22	)	)	PUNCT
ejpam-5536	181	23	∈	∈	NOUN
ejpam-5536	182	1	[	[	X
ejpam-5536	182	2	0,∓	0,∓	X
ejpam-5536	182	3	]	]	X
ejpam-5536	182	4	×	×	PROPN
ejpam-5536	182	5	[	[	X
ejpam-5536	182	6	±	±	NUM
ejpam-5536	182	7	,	,	PUNCT
ejpam-5536	182	8	0	0	NUM
ejpam-5536	182	9	]	]	PUNCT
ejpam-5536	182	10	.	.	PUNCT
ejpam-5536	183	1	by	by	ADP
ejpam-5536	183	2	a	a	DET
ejpam-5536	183	3	bipolar	bipolar	ADJ
ejpam-5536	183	4	fuzzy	fuzzy	NOUN
ejpam-5536	183	5	(	(	PUNCT
ejpam-5536	183	6	β	β	NOUN
ejpam-5536	183	7	,	,	PUNCT
ejpam-5536	183	8	α)-translation	α)-translation	NOUN
ejpam-5536	183	9	of	of	ADP
ejpam-5536	183	10	φ	φ	PROPN
ejpam-5536	183	11	=	=	SYM
ejpam-5536	183	12	(	(	PUNCT
ejpam-5536	183	13	φ+	φ+	NOUN
ejpam-5536	183	14	,	,	PUNCT
ejpam-5536	183	15	φ−	φ−	PROPN
ejpam-5536	183	16	)	)	PUNCT
ejpam-5536	183	17	of	of	ADP
ejpam-5536	183	18	type	type	NOUN
ejpam-5536	183	19	ii	ii	PROPN
ejpam-5536	183	20	,	,	PUNCT
ejpam-5536	183	21	we	we	PRON
ejpam-5536	183	22	mean	mean	VERB
ejpam-5536	183	23	a	a	DET
ejpam-5536	183	24	bfs	bfs	NOUN
ejpam-5536	183	25	φt2	φt2	NOUN
ejpam-5536	183	26	(	(	PUNCT
ejpam-5536	183	27	β	β	X
ejpam-5536	183	28	,	,	PUNCT
ejpam-5536	183	29	α	α	NOUN
ejpam-5536	183	30	)	)	PUNCT
ejpam-5536	183	31	=	=	SYM
ejpam-5536	184	1	(	(	PUNCT
ejpam-5536	184	2	φ+	φ+	X
ejpam-5536	184	3	(	(	PUNCT
ejpam-5536	184	4	β	β	X
ejpam-5536	184	5	,	,	PUNCT
ejpam-5536	184	6	t2	t2	NOUN
ejpam-5536	184	7	)	)	PUNCT
ejpam-5536	184	8	,	,	PUNCT
ejpam-5536	184	9	φ−	φ−	PROPN
ejpam-5536	184	10	(	(	PUNCT
ejpam-5536	184	11	α	α	NOUN
ejpam-5536	184	12	,	,	PUNCT
ejpam-5536	184	13	t2	t2	NOUN
ejpam-5536	184	14	)	)	PUNCT
ejpam-5536	184	15	)	)	PUNCT
ejpam-5536	184	16	,	,	PUNCT
ejpam-5536	184	17	where	where	SCONJ
ejpam-5536	184	18	φ+	φ+	X
ejpam-5536	184	19	(	(	PUNCT
ejpam-5536	184	20	β	β	X
ejpam-5536	184	21	,	,	PUNCT
ejpam-5536	184	22	t2	t2	NOUN
ejpam-5536	184	23	)	)	PUNCT
ejpam-5536	184	24	:	:	PUNCT
ejpam-5536	185	1	x	x	X
ejpam-5536	185	2	→	→	PUNCT
ejpam-5536	186	1	[	[	X
ejpam-5536	186	2	0	0	NUM
ejpam-5536	186	3	,	,	PUNCT
ejpam-5536	186	4	1	1	NUM
ejpam-5536	186	5	]	]	PUNCT
ejpam-5536	186	6	,	,	PUNCT
ejpam-5536	186	7	x	x	SYM
ejpam-5536	186	8	7→	7→	NUM
ejpam-5536	186	9	φ+(x)−	φ+(x)−	NOUN
ejpam-5536	186	10	β	β	NOUN
ejpam-5536	186	11	,	,	PUNCT
ejpam-5536	186	12	φ−	φ−	PROPN
ejpam-5536	186	13	(	(	PUNCT
ejpam-5536	186	14	α	α	NOUN
ejpam-5536	186	15	,	,	PUNCT
ejpam-5536	186	16	t2	t2	NOUN
ejpam-5536	186	17	)	)	PUNCT
ejpam-5536	186	18	:	:	PUNCT
ejpam-5536	187	1	x	x	X
ejpam-5536	187	2	→	→	PUNCT
ejpam-5536	187	3	[	[	X
ejpam-5536	187	4	−1	−1	NOUN
ejpam-5536	187	5	,	,	PUNCT
ejpam-5536	187	6	0	0	NUM
ejpam-5536	187	7	]	]	PUNCT
ejpam-5536	187	8	,	,	PUNCT
ejpam-5536	187	9	x	x	SYM
ejpam-5536	187	10	7→	7→	NUM
ejpam-5536	187	11	φ−(x)−	φ−(x)−	NOUN
ejpam-5536	187	12	α	α	NOUN
ejpam-5536	187	13	.	.	PUNCT
ejpam-5536	187	14	theorem	theorem	NOUN
ejpam-5536	187	15	5	5	NUM
ejpam-5536	187	16	.	.	PUNCT
ejpam-5536	188	1	if	if	SCONJ
ejpam-5536	188	2	a	a	DET
ejpam-5536	188	3	bfs	bfs	NOUN
ejpam-5536	188	4	φ	φ	X
ejpam-5536	188	5	=	=	SYM
ejpam-5536	188	6	(	(	PUNCT
ejpam-5536	188	7	φ+	φ+	NOUN
ejpam-5536	188	8	,	,	PUNCT
ejpam-5536	188	9	φ−	φ−	PROPN
ejpam-5536	188	10	)	)	PUNCT
ejpam-5536	188	11	in	in	ADP
ejpam-5536	188	12	a	a	DET
ejpam-5536	188	13	hilbert	hilbert	NOUN
ejpam-5536	188	14	algebra	algebra	NOUN
ejpam-5536	188	15	x	x	PUNCT
ejpam-5536	188	16	=	=	SYM
ejpam-5536	188	17	(	(	PUNCT
ejpam-5536	188	18	x	x	NOUN
ejpam-5536	188	19	,	,	PUNCT
ejpam-5536	188	20	·	·	PUNCT
ejpam-5536	188	21	,	,	PUNCT
ejpam-5536	188	22	1x	1x	NUM
ejpam-5536	188	23	)	)	PUNCT
ejpam-5536	188	24	is	be	AUX
ejpam-5536	188	25	a	a	DET
ejpam-5536	188	26	bipolar	bipolar	ADJ
ejpam-5536	188	27	fuzzy	fuzzy	ADJ
ejpam-5536	188	28	subalgebra	subalgebra	NOUN
ejpam-5536	188	29	of	of	ADP
ejpam-5536	188	30	x	x	PRON
ejpam-5536	188	31	,	,	PUNCT
ejpam-5536	188	32	then	then	ADV
ejpam-5536	188	33	for	for	ADP
ejpam-5536	188	34	all	all	PRON
ejpam-5536	188	35	(	(	PUNCT
ejpam-5536	188	36	β	β	X
ejpam-5536	188	37	,	,	PUNCT
ejpam-5536	188	38	α	α	NOUN
ejpam-5536	188	39	)	)	PUNCT
ejpam-5536	188	40	∈	∈	NOUN
ejpam-5536	189	1	[	[	X
ejpam-5536	189	2	0,∓	0,∓	X
ejpam-5536	189	3	]	]	X
ejpam-5536	189	4	×	×	PROPN
ejpam-5536	189	5	[	[	X
ejpam-5536	189	6	±	±	NUM
ejpam-5536	189	7	,	,	PUNCT
ejpam-5536	189	8	0	0	NUM
ejpam-5536	189	9	]	]	PUNCT
ejpam-5536	189	10	,	,	PUNCT
ejpam-5536	189	11	the	the	DET
ejpam-5536	189	12	bipolar	bipolar	ADJ
ejpam-5536	189	13	fuzzy	fuzzy	NOUN
ejpam-5536	189	14	(	(	PUNCT
ejpam-5536	189	15	β	β	NOUN
ejpam-5536	189	16	,	,	PUNCT
ejpam-5536	189	17	α)-translation	α)-translation	NOUN
ejpam-5536	189	18	φt2	φt2	NOUN
ejpam-5536	189	19	(	(	PUNCT
ejpam-5536	189	20	β	β	X
ejpam-5536	189	21	,	,	PUNCT
ejpam-5536	189	22	α	α	NOUN
ejpam-5536	189	23	)	)	PUNCT
ejpam-5536	189	24	=	=	SYM
ejpam-5536	189	25	(	(	PUNCT
ejpam-5536	189	26	φ+	φ+	X
ejpam-5536	189	27	(	(	PUNCT
ejpam-5536	189	28	β	β	X
ejpam-5536	189	29	,	,	PUNCT
ejpam-5536	189	30	t2	t2	NOUN
ejpam-5536	189	31	)	)	PUNCT
ejpam-5536	189	32	,	,	PUNCT
ejpam-5536	189	33	φ−	φ−	PROPN
ejpam-5536	189	34	(	(	PUNCT
ejpam-5536	189	35	α	α	NOUN
ejpam-5536	189	36	,	,	PUNCT
ejpam-5536	189	37	t2	t2	NOUN
ejpam-5536	189	38	)	)	PUNCT
ejpam-5536	189	39	)	)	PUNCT
ejpam-5536	189	40	of	of	ADP
ejpam-5536	189	41	φ	φ	PROPN
ejpam-5536	189	42	=	=	SYM
ejpam-5536	189	43	(	(	PUNCT
ejpam-5536	189	44	φ+	φ+	NOUN
ejpam-5536	189	45	,	,	PUNCT
ejpam-5536	189	46	φ−	φ−	PROPN
ejpam-5536	189	47	)	)	PUNCT
ejpam-5536	189	48	is	be	AUX
ejpam-5536	189	49	a	a	DET
ejpam-5536	189	50	bipolar	bipolar	ADJ
ejpam-5536	189	51	fuzzy	fuzzy	ADJ
ejpam-5536	189	52	subalgebra	subalgebra	NOUN
ejpam-5536	189	53	of	of	ADP
ejpam-5536	189	54	x.	x.	NOUN
ejpam-5536	189	55	proof	proof	PROPN
ejpam-5536	189	56	.	.	PUNCT
ejpam-5536	190	1	assume	assume	VERB
ejpam-5536	190	2	that	that	SCONJ
ejpam-5536	190	3	φ	φ	PROPN
ejpam-5536	190	4	=	=	SYM
ejpam-5536	190	5	(	(	PUNCT
ejpam-5536	190	6	φ+	φ+	NOUN
ejpam-5536	190	7	,	,	PUNCT
ejpam-5536	190	8	φ−	φ−	PROPN
ejpam-5536	190	9	)	)	PUNCT
ejpam-5536	190	10	is	be	AUX
ejpam-5536	190	11	a	a	DET
ejpam-5536	190	12	bipolar	bipolar	ADJ
ejpam-5536	190	13	fuzzy	fuzzy	ADJ
ejpam-5536	190	14	subalgebra	subalgebra	NOUN
ejpam-5536	190	15	of	of	ADP
ejpam-5536	190	16	x.	x.	NOUN
ejpam-5536	190	17	for	for	ADP
ejpam-5536	190	18	any	any	DET
ejpam-5536	190	19	(	(	PUNCT
ejpam-5536	190	20	β	β	X
ejpam-5536	190	21	,	,	PUNCT
ejpam-5536	190	22	α	α	NOUN
ejpam-5536	190	23	)	)	PUNCT
ejpam-5536	190	24	∈	∈	PROPN
ejpam-5536	191	1	[	[	X
ejpam-5536	191	2	0,∓]×	0,∓]×	PROPN
ejpam-5536	192	1	[	[	X
ejpam-5536	192	2	±	±	NUM
ejpam-5536	192	3	,	,	PUNCT
ejpam-5536	192	4	0	0	NUM
ejpam-5536	192	5	]	]	PUNCT
ejpam-5536	192	6	and	and	CCONJ
ejpam-5536	192	7	for	for	ADP
ejpam-5536	192	8	all	all	DET
ejpam-5536	192	9	x	x	NOUN
ejpam-5536	192	10	,	,	PUNCT
ejpam-5536	192	11	y	y	PROPN
ejpam-5536	192	12	∈	∈	PROPN
ejpam-5536	192	13	x	x	X
ejpam-5536	192	14	,	,	PUNCT
ejpam-5536	192	15	we	we	PRON
ejpam-5536	192	16	have	have	VERB
ejpam-5536	192	17	φ+	φ+	NOUN
ejpam-5536	192	18	(	(	PUNCT
ejpam-5536	192	19	β	β	X
ejpam-5536	192	20	,	,	PUNCT
ejpam-5536	192	21	t2	t2	NOUN
ejpam-5536	192	22	)	)	PUNCT
ejpam-5536	192	23	(	(	PUNCT
ejpam-5536	192	24	x	x	X
ejpam-5536	192	25	·	·	PUNCT
ejpam-5536	192	26	y	y	X
ejpam-5536	192	27	)	)	PUNCT
ejpam-5536	192	28	=	=	SYM
ejpam-5536	192	29	φ+(x	φ+(x	X
ejpam-5536	192	30	·	·	PUNCT
ejpam-5536	192	31	y)−	y)−	PROPN
ejpam-5536	192	32	β	β	X
ejpam-5536	192	33	≥	≥	NOUN
ejpam-5536	192	34	min{φ+(x	min{φ+(x	PROPN
ejpam-5536	192	35	)	)	PUNCT
ejpam-5536	192	36	,	,	PUNCT
ejpam-5536	192	37	φ+(y	φ+(y	CCONJ
ejpam-5536	192	38	)	)	PUNCT
ejpam-5536	192	39	}	}	PUNCT
ejpam-5536	192	40	−	−	NOUN
ejpam-5536	192	41	β	β	X
ejpam-5536	192	42	=	=	PUNCT
ejpam-5536	192	43	min{φ+(x)−	min{φ+(x)−	PROPN
ejpam-5536	192	44	β	β	NOUN
ejpam-5536	192	45	,	,	PUNCT
ejpam-5536	192	46	φ+(y)−	φ+(y)−	NOUN
ejpam-5536	193	1	β	β	NOUN
ejpam-5536	193	2	}	}	PUNCT
ejpam-5536	193	3	=	=	SYM
ejpam-5536	193	4	min{φ+	min{φ+	NOUN
ejpam-5536	193	5	(	(	PUNCT
ejpam-5536	193	6	β	β	X
ejpam-5536	193	7	,	,	PUNCT
ejpam-5536	193	8	t2	t2	NOUN
ejpam-5536	193	9	)	)	PUNCT
ejpam-5536	193	10	(	(	PUNCT
ejpam-5536	193	11	x	x	X
ejpam-5536	193	12	)	)	PUNCT
ejpam-5536	193	13	,	,	PUNCT
ejpam-5536	193	14	φ+	φ+	X
ejpam-5536	193	15	(	(	PUNCT
ejpam-5536	193	16	β	β	X
ejpam-5536	193	17	,	,	PUNCT
ejpam-5536	193	18	t2	t2	NOUN
ejpam-5536	193	19	)	)	PUNCT
ejpam-5536	193	20	(	(	PUNCT
ejpam-5536	193	21	y	y	NOUN
ejpam-5536	193	22	)	)	PUNCT
ejpam-5536	193	23	}	}	PUNCT
ejpam-5536	193	24	,	,	PUNCT
ejpam-5536	193	25	a.	a.	NOUN
ejpam-5536	193	26	iampan	iampan	NOUN
ejpam-5536	193	27	et	et	PROPN
ejpam-5536	193	28	al	al	PROPN
ejpam-5536	193	29	.	.	PUNCT
ejpam-5536	193	30	/	/	SYM
ejpam-5536	193	31	eur	eur	PROPN
ejpam-5536	193	32	.	.	PUNCT
ejpam-5536	194	1	j.	j.	PROPN
ejpam-5536	194	2	pure	pure	PROPN
ejpam-5536	194	3	appl	appl	PROPN
ejpam-5536	194	4	.	.	PROPN
ejpam-5536	194	5	math	math	PROPN
ejpam-5536	194	6	,	,	PUNCT
ejpam-5536	194	7	17	17	NUM
ejpam-5536	194	8	(	(	PUNCT
ejpam-5536	194	9	4	4	NUM
ejpam-5536	194	10	)	)	PUNCT
ejpam-5536	194	11	(	(	PUNCT
ejpam-5536	194	12	2024	2024	NUM
ejpam-5536	194	13	)	)	PUNCT
ejpam-5536	194	14	,	,	PUNCT
ejpam-5536	194	15	4059	4059	NUM
ejpam-5536	194	16	-	-	SYM
ejpam-5536	194	17	4070	4070	NUM
ejpam-5536	194	18	4066	4066	NUM
ejpam-5536	194	19	φ−	φ−	PROPN
ejpam-5536	194	20	(	(	PUNCT
ejpam-5536	194	21	α	α	NOUN
ejpam-5536	194	22	,	,	PUNCT
ejpam-5536	194	23	t2	t2	NOUN
ejpam-5536	194	24	)	)	PUNCT
ejpam-5536	194	25	(	(	PUNCT
ejpam-5536	194	26	x	x	X
ejpam-5536	194	27	·	·	PUNCT
ejpam-5536	194	28	y	y	X
ejpam-5536	194	29	)	)	PUNCT
ejpam-5536	195	1	=	=	SYM
ejpam-5536	196	1	φ−(x	φ−(x	PROPN
ejpam-5536	196	2	·	·	PUNCT
ejpam-5536	196	3	y)−	y)−	PROPN
ejpam-5536	196	4	α	α	NOUN
ejpam-5536	196	5	≤	≤	NUM
ejpam-5536	196	6	max{φ−(x	max{φ−(x	PROPN
ejpam-5536	196	7	)	)	PUNCT
ejpam-5536	196	8	,	,	PUNCT
ejpam-5536	196	9	φ−(y	φ−(y	PROPN
ejpam-5536	196	10	)	)	PUNCT
ejpam-5536	196	11	}	}	PUNCT
ejpam-5536	197	1	−	−	PROPN
ejpam-5536	197	2	α	α	X
ejpam-5536	197	3	=	=	PUNCT
ejpam-5536	197	4	max{φ−(x)−	max{φ−(x)−	PROPN
ejpam-5536	197	5	α	α	NOUN
ejpam-5536	197	6	,	,	PUNCT
ejpam-5536	197	7	φ−(y)−	φ−(y)−	NOUN
ejpam-5536	197	8	α	α	NOUN
ejpam-5536	197	9	}	}	PUNCT
ejpam-5536	197	10	=	=	SYM
ejpam-5536	197	11	max{φ−	max{φ−	PROPN
ejpam-5536	197	12	(	(	PUNCT
ejpam-5536	197	13	α	α	NOUN
ejpam-5536	197	14	,	,	PUNCT
ejpam-5536	197	15	t2	t2	NOUN
ejpam-5536	197	16	)	)	PUNCT
ejpam-5536	197	17	(	(	PUNCT
ejpam-5536	198	1	x	x	X
ejpam-5536	198	2	)	)	PUNCT
ejpam-5536	198	3	,	,	PUNCT
ejpam-5536	198	4	φ−	φ−	PROPN
ejpam-5536	198	5	(	(	PUNCT
ejpam-5536	198	6	α	α	NOUN
ejpam-5536	198	7	,	,	PUNCT
ejpam-5536	198	8	t2	t2	NOUN
ejpam-5536	198	9	)	)	PUNCT
ejpam-5536	198	10	(	(	PUNCT
ejpam-5536	198	11	y	y	NOUN
ejpam-5536	198	12	)	)	PUNCT
ejpam-5536	198	13	}	}	PUNCT
ejpam-5536	198	14	.	.	PUNCT
ejpam-5536	199	1	hence	hence	ADV
ejpam-5536	199	2	,	,	PUNCT
ejpam-5536	199	3	φt2	φt2	NOUN
ejpam-5536	199	4	(	(	PUNCT
ejpam-5536	199	5	β	β	X
ejpam-5536	199	6	,	,	PUNCT
ejpam-5536	199	7	α	α	NOUN
ejpam-5536	199	8	)	)	PUNCT
ejpam-5536	199	9	=	=	SYM
ejpam-5536	199	10	(	(	PUNCT
ejpam-5536	199	11	φ+	φ+	X
ejpam-5536	199	12	(	(	PUNCT
ejpam-5536	199	13	β	β	X
ejpam-5536	199	14	,	,	PUNCT
ejpam-5536	199	15	t2	t2	NOUN
ejpam-5536	199	16	)	)	PUNCT
ejpam-5536	199	17	,	,	PUNCT
ejpam-5536	199	18	φ−	φ−	PROPN
ejpam-5536	199	19	(	(	PUNCT
ejpam-5536	199	20	α	α	NOUN
ejpam-5536	199	21	,	,	PUNCT
ejpam-5536	199	22	t2	t2	NOUN
ejpam-5536	199	23	)	)	PUNCT
ejpam-5536	199	24	)	)	PUNCT
ejpam-5536	199	25	is	be	AUX
ejpam-5536	199	26	a	a	DET
ejpam-5536	199	27	bipolar	bipolar	ADJ
ejpam-5536	199	28	fuzzy	fuzzy	ADJ
ejpam-5536	199	29	subalgebra	subalgebra	NOUN
ejpam-5536	199	30	of	of	ADP
ejpam-5536	199	31	x.	x.	PROPN
ejpam-5536	199	32	theorem	theorem	VERB
ejpam-5536	199	33	6	6	NUM
ejpam-5536	199	34	.	.	PUNCT
ejpam-5536	200	1	if	if	SCONJ
ejpam-5536	200	2	there	there	PRON
ejpam-5536	200	3	exists	exist	VERB
ejpam-5536	200	4	(	(	PUNCT
ejpam-5536	200	5	β	β	X
ejpam-5536	200	6	,	,	PUNCT
ejpam-5536	200	7	α	α	NOUN
ejpam-5536	200	8	)	)	PUNCT
ejpam-5536	200	9	∈	∈	NOUN
ejpam-5536	201	1	[	[	X
ejpam-5536	201	2	0,∓	0,∓	X
ejpam-5536	201	3	]	]	X
ejpam-5536	201	4	×	×	PROPN
ejpam-5536	201	5	[	[	X
ejpam-5536	201	6	±	±	NUM
ejpam-5536	201	7	,	,	PUNCT
ejpam-5536	201	8	0	0	NUM
ejpam-5536	201	9	]	]	PUNCT
ejpam-5536	201	10	such	such	ADJ
ejpam-5536	201	11	that	that	SCONJ
ejpam-5536	201	12	the	the	DET
ejpam-5536	201	13	bipolar	bipolar	ADJ
ejpam-5536	201	14	fuzzy	fuzzy	NOUN
ejpam-5536	201	15	(	(	PUNCT
ejpam-5536	201	16	β	β	NOUN
ejpam-5536	201	17	,	,	PUNCT
ejpam-5536	201	18	α)translation	α)translation	PROPN
ejpam-5536	201	19	φt2	φt2	NOUN
ejpam-5536	201	20	(	(	PUNCT
ejpam-5536	201	21	β	β	X
ejpam-5536	201	22	,	,	PUNCT
ejpam-5536	201	23	α	α	NOUN
ejpam-5536	201	24	)	)	PUNCT
ejpam-5536	201	25	=	=	SYM
ejpam-5536	201	26	(	(	PUNCT
ejpam-5536	201	27	φ+	φ+	X
ejpam-5536	201	28	(	(	PUNCT
ejpam-5536	201	29	β	β	X
ejpam-5536	201	30	,	,	PUNCT
ejpam-5536	201	31	t2	t2	NOUN
ejpam-5536	201	32	)	)	PUNCT
ejpam-5536	201	33	,	,	PUNCT
ejpam-5536	201	34	φ−	φ−	PROPN
ejpam-5536	201	35	(	(	PUNCT
ejpam-5536	201	36	α	α	NOUN
ejpam-5536	201	37	,	,	PUNCT
ejpam-5536	201	38	t2	t2	NOUN
ejpam-5536	201	39	)	)	PUNCT
ejpam-5536	201	40	)	)	PUNCT
ejpam-5536	201	41	of	of	ADP
ejpam-5536	201	42	φ	φ	PROPN
ejpam-5536	201	43	=	=	SYM
ejpam-5536	201	44	(	(	PUNCT
ejpam-5536	201	45	φ+	φ+	NOUN
ejpam-5536	201	46	,	,	PUNCT
ejpam-5536	201	47	φ−	φ−	PROPN
ejpam-5536	201	48	)	)	PUNCT
ejpam-5536	201	49	is	be	AUX
ejpam-5536	201	50	a	a	DET
ejpam-5536	201	51	bipolar	bipolar	ADJ
ejpam-5536	201	52	fuzzy	fuzzy	ADJ
ejpam-5536	201	53	subalgebra	subalgebra	NOUN
ejpam-5536	201	54	of	of	ADP
ejpam-5536	201	55	a	a	DET
ejpam-5536	201	56	hilbert	hilbert	NOUN
ejpam-5536	201	57	algebra	algebra	NOUN
ejpam-5536	201	58	x	x	PUNCT
ejpam-5536	202	1	=	=	SYM
ejpam-5536	202	2	(	(	PUNCT
ejpam-5536	202	3	x	x	NOUN
ejpam-5536	202	4	,	,	PUNCT
ejpam-5536	202	5	·	·	PUNCT
ejpam-5536	202	6	,	,	PUNCT
ejpam-5536	202	7	1x	1x	NUM
ejpam-5536	202	8	)	)	PUNCT
ejpam-5536	202	9	,	,	PUNCT
ejpam-5536	202	10	then	then	ADV
ejpam-5536	202	11	φ	φ	PROPN
ejpam-5536	202	12	=	=	SYM
ejpam-5536	202	13	(	(	PUNCT
ejpam-5536	202	14	φ+	φ+	NOUN
ejpam-5536	202	15	,	,	PUNCT
ejpam-5536	202	16	φ−	φ−	PROPN
ejpam-5536	202	17	)	)	PUNCT
ejpam-5536	202	18	is	be	AUX
ejpam-5536	202	19	a	a	DET
ejpam-5536	202	20	bipolar	bipolar	ADJ
ejpam-5536	202	21	fuzzy	fuzzy	ADJ
ejpam-5536	202	22	subalgebra	subalgebra	NOUN
ejpam-5536	202	23	of	of	ADP
ejpam-5536	202	24	x.	x.	NOUN
ejpam-5536	202	25	proof	proof	PROPN
ejpam-5536	202	26	.	.	PUNCT
ejpam-5536	203	1	assume	assume	VERB
ejpam-5536	203	2	that	that	SCONJ
ejpam-5536	203	3	φt2	φt2	NOUN
ejpam-5536	203	4	(	(	PUNCT
ejpam-5536	203	5	β	β	X
ejpam-5536	203	6	,	,	PUNCT
ejpam-5536	203	7	α	α	NOUN
ejpam-5536	203	8	)	)	PUNCT
ejpam-5536	203	9	=	=	SYM
ejpam-5536	203	10	(	(	PUNCT
ejpam-5536	203	11	φ+	φ+	X
ejpam-5536	203	12	(	(	PUNCT
ejpam-5536	203	13	β	β	X
ejpam-5536	203	14	,	,	PUNCT
ejpam-5536	203	15	t2	t2	NOUN
ejpam-5536	203	16	)	)	PUNCT
ejpam-5536	203	17	,	,	PUNCT
ejpam-5536	203	18	φ−	φ−	PROPN
ejpam-5536	203	19	(	(	PUNCT
ejpam-5536	203	20	α	α	NOUN
ejpam-5536	203	21	,	,	PUNCT
ejpam-5536	203	22	t2	t2	NOUN
ejpam-5536	203	23	)	)	PUNCT
ejpam-5536	203	24	)	)	PUNCT
ejpam-5536	203	25	is	be	AUX
ejpam-5536	203	26	a	a	DET
ejpam-5536	203	27	bipolar	bipolar	ADJ
ejpam-5536	203	28	fuzzy	fuzzy	ADJ
ejpam-5536	203	29	subalgebra	subalgebra	NOUN
ejpam-5536	203	30	of	of	ADP
ejpam-5536	203	31	x	x	PUNCT
ejpam-5536	203	32	for	for	ADP
ejpam-5536	203	33	(	(	PUNCT
ejpam-5536	203	34	β	β	X
ejpam-5536	203	35	,	,	PUNCT
ejpam-5536	203	36	α	α	NOUN
ejpam-5536	203	37	)	)	PUNCT
ejpam-5536	203	38	∈	∈	PROPN
ejpam-5536	204	1	[	[	X
ejpam-5536	204	2	0,∓]×	0,∓]×	PROPN
ejpam-5536	205	1	[	[	X
ejpam-5536	205	2	±	±	NUM
ejpam-5536	205	3	,	,	PUNCT
ejpam-5536	205	4	0	0	NUM
ejpam-5536	205	5	]	]	PUNCT
ejpam-5536	205	6	.	.	PUNCT
ejpam-5536	206	1	for	for	ADP
ejpam-5536	206	2	all	all	DET
ejpam-5536	206	3	x	x	NOUN
ejpam-5536	206	4	,	,	PUNCT
ejpam-5536	206	5	y	y	PROPN
ejpam-5536	206	6	∈	∈	PROPN
ejpam-5536	206	7	x	x	X
ejpam-5536	206	8	,	,	PUNCT
ejpam-5536	206	9	we	we	PRON
ejpam-5536	206	10	have	have	VERB
ejpam-5536	206	11	φ+(x	φ+(x	ADJ
ejpam-5536	206	12	·	·	PUNCT
ejpam-5536	206	13	y)−	y)−	NUM
ejpam-5536	206	14	β	β	X
ejpam-5536	206	15	=	=	X
ejpam-5536	206	16	φ+	φ+	X
ejpam-5536	206	17	(	(	PUNCT
ejpam-5536	206	18	β	β	X
ejpam-5536	206	19	,	,	PUNCT
ejpam-5536	206	20	t2	t2	NOUN
ejpam-5536	206	21	)	)	PUNCT
ejpam-5536	206	22	(	(	PUNCT
ejpam-5536	206	23	x	x	X
ejpam-5536	206	24	·	·	PUNCT
ejpam-5536	206	25	y	y	X
ejpam-5536	206	26	)	)	PUNCT
ejpam-5536	206	27	≥	≥	NOUN
ejpam-5536	206	28	min{φ+	min{φ+	NOUN
ejpam-5536	206	29	(	(	PUNCT
ejpam-5536	206	30	β	β	NOUN
ejpam-5536	206	31	,	,	PUNCT
ejpam-5536	206	32	t2	t2	NOUN
ejpam-5536	206	33	)	)	PUNCT
ejpam-5536	206	34	(	(	PUNCT
ejpam-5536	206	35	x	x	X
ejpam-5536	206	36	)	)	PUNCT
ejpam-5536	206	37	,	,	PUNCT
ejpam-5536	206	38	φ+	φ+	X
ejpam-5536	206	39	(	(	PUNCT
ejpam-5536	206	40	β	β	X
ejpam-5536	206	41	,	,	PUNCT
ejpam-5536	206	42	t2	t2	NOUN
ejpam-5536	206	43	)	)	PUNCT
ejpam-5536	206	44	(	(	PUNCT
ejpam-5536	206	45	y	y	NOUN
ejpam-5536	206	46	)	)	PUNCT
ejpam-5536	206	47	}	}	PUNCT
ejpam-5536	207	1	=	=	PUNCT
ejpam-5536	208	1	min{φ+(x)−	min{φ+(x)−	PROPN
ejpam-5536	208	2	β	β	NOUN
ejpam-5536	208	3	,	,	PUNCT
ejpam-5536	208	4	φ+(y)−	φ+(y)−	NOUN
ejpam-5536	208	5	β	β	NOUN
ejpam-5536	208	6	}	}	PUNCT
ejpam-5536	208	7	=	=	SYM
ejpam-5536	208	8	min{φ+(x	min{φ+(x	PROPN
ejpam-5536	208	9	)	)	PUNCT
ejpam-5536	208	10	,	,	PUNCT
ejpam-5536	208	11	φ+(y	φ+(y	CCONJ
ejpam-5536	208	12	)	)	PUNCT
ejpam-5536	208	13	}	}	PUNCT
ejpam-5536	208	14	−	−	ADP
ejpam-5536	208	15	β	β	X
ejpam-5536	208	16	,	,	PUNCT
ejpam-5536	208	17	φ−(x	φ−(x	PROPN
ejpam-5536	208	18	·	·	PUNCT
ejpam-5536	209	1	y)−	y)−	NUM
ejpam-5536	209	2	α	α	NOUN
ejpam-5536	209	3	=	=	SYM
ejpam-5536	209	4	φ−	φ−	PROPN
ejpam-5536	209	5	(	(	PUNCT
ejpam-5536	209	6	α	α	NOUN
ejpam-5536	209	7	,	,	PUNCT
ejpam-5536	209	8	t2	t2	NOUN
ejpam-5536	209	9	)	)	PUNCT
ejpam-5536	209	10	(	(	PUNCT
ejpam-5536	209	11	x	x	X
ejpam-5536	209	12	·	·	PUNCT
ejpam-5536	209	13	y	y	X
ejpam-5536	209	14	)	)	PUNCT
ejpam-5536	209	15	≤	≤	NOUN
ejpam-5536	210	1	max{φ−	max{φ−	PROPN
ejpam-5536	210	2	(	(	PUNCT
ejpam-5536	210	3	α	α	NOUN
ejpam-5536	210	4	,	,	PUNCT
ejpam-5536	210	5	t2	t2	NOUN
ejpam-5536	210	6	)	)	PUNCT
ejpam-5536	210	7	(	(	PUNCT
ejpam-5536	210	8	x	x	X
ejpam-5536	210	9	)	)	PUNCT
ejpam-5536	210	10	,	,	PUNCT
ejpam-5536	210	11	φ−	φ−	PROPN
ejpam-5536	210	12	(	(	PUNCT
ejpam-5536	210	13	α	α	NOUN
ejpam-5536	210	14	,	,	PUNCT
ejpam-5536	210	15	t2	t2	NOUN
ejpam-5536	210	16	)	)	PUNCT
ejpam-5536	210	17	(	(	PUNCT
ejpam-5536	210	18	y	y	NOUN
ejpam-5536	210	19	)	)	PUNCT
ejpam-5536	210	20	}	}	PUNCT
ejpam-5536	211	1	=	=	SYM
ejpam-5536	211	2	max{φ−(x)−	max{φ−(x)−	PROPN
ejpam-5536	211	3	α	α	NOUN
ejpam-5536	211	4	,	,	PUNCT
ejpam-5536	211	5	φ−(y)−	φ−(y)−	NOUN
ejpam-5536	211	6	α	α	NOUN
ejpam-5536	211	7	}	}	PUNCT
ejpam-5536	211	8	=	=	SYM
ejpam-5536	211	9	max{φ−(x	max{φ−(x	NOUN
ejpam-5536	211	10	)	)	PUNCT
ejpam-5536	211	11	,	,	PUNCT
ejpam-5536	211	12	φ−(y	φ−(y	PROPN
ejpam-5536	211	13	)	)	PUNCT
ejpam-5536	211	14	}	}	PUNCT
ejpam-5536	212	1	−	−	PROPN
ejpam-5536	212	2	α	α	X
ejpam-5536	212	3	.	.	PUNCT
ejpam-5536	213	1	thus	thus	ADV
ejpam-5536	213	2	,	,	PUNCT
ejpam-5536	213	3	φ+(x	φ+(x	X
ejpam-5536	213	4	·	·	PUNCT
ejpam-5536	213	5	y	y	X
ejpam-5536	213	6	)	)	PUNCT
ejpam-5536	213	7	≥	≥	NOUN
ejpam-5536	213	8	min{φ+(x	min{φ+(x	PROPN
ejpam-5536	213	9	)	)	PUNCT
ejpam-5536	213	10	,	,	PUNCT
ejpam-5536	213	11	φ+(y	φ+(y	CCONJ
ejpam-5536	213	12	)	)	PUNCT
ejpam-5536	213	13	}	}	PUNCT
ejpam-5536	213	14	and	and	CCONJ
ejpam-5536	213	15	φ−(x	φ−(x	PROPN
ejpam-5536	213	16	·	·	PUNCT
ejpam-5536	213	17	y	y	X
ejpam-5536	213	18	)	)	PUNCT
ejpam-5536	213	19	≤	≤	NOUN
ejpam-5536	213	20	max{φ−(x	max{φ−(x	PROPN
ejpam-5536	213	21	)	)	PUNCT
ejpam-5536	213	22	,	,	PUNCT
ejpam-5536	213	23	φ−(y	φ−(y	PROPN
ejpam-5536	213	24	)	)	PUNCT
ejpam-5536	213	25	}	}	PUNCT
ejpam-5536	213	26	.	.	PUNCT
ejpam-5536	214	1	hence	hence	ADV
ejpam-5536	214	2	,	,	PUNCT
ejpam-5536	214	3	φ	φ	PROPN
ejpam-5536	214	4	=	=	SYM
ejpam-5536	214	5	(	(	PUNCT
ejpam-5536	214	6	φ+	φ+	NOUN
ejpam-5536	214	7	,	,	PUNCT
ejpam-5536	214	8	φ−	φ−	PROPN
ejpam-5536	214	9	)	)	PUNCT
ejpam-5536	214	10	is	be	AUX
ejpam-5536	214	11	a	a	DET
ejpam-5536	214	12	bipolar	bipolar	ADJ
ejpam-5536	214	13	fuzzy	fuzzy	ADJ
ejpam-5536	214	14	subalgebra	subalgebra	NOUN
ejpam-5536	214	15	of	of	ADP
ejpam-5536	214	16	x.	x.	NOUN
ejpam-5536	214	17	theorem	theorem	VERB
ejpam-5536	214	18	7	7	NUM
ejpam-5536	214	19	.	.	PUNCT
ejpam-5536	215	1	if	if	SCONJ
ejpam-5536	215	2	a	a	DET
ejpam-5536	215	3	bfs	bfs	NOUN
ejpam-5536	215	4	φ	φ	X
ejpam-5536	215	5	=	=	SYM
ejpam-5536	215	6	(	(	PUNCT
ejpam-5536	215	7	φ+	φ+	NOUN
ejpam-5536	215	8	,	,	PUNCT
ejpam-5536	215	9	φ−	φ−	PROPN
ejpam-5536	215	10	)	)	PUNCT
ejpam-5536	215	11	in	in	ADP
ejpam-5536	215	12	a	a	DET
ejpam-5536	215	13	hilbert	hilbert	NOUN
ejpam-5536	215	14	algebra	algebra	NOUN
ejpam-5536	215	15	x	x	PUNCT
ejpam-5536	215	16	=	=	SYM
ejpam-5536	215	17	(	(	PUNCT
ejpam-5536	215	18	x	x	NOUN
ejpam-5536	215	19	,	,	PUNCT
ejpam-5536	215	20	·	·	PUNCT
ejpam-5536	215	21	,	,	PUNCT
ejpam-5536	215	22	1x	1x	NUM
ejpam-5536	215	23	)	)	PUNCT
ejpam-5536	215	24	is	be	AUX
ejpam-5536	215	25	a	a	DET
ejpam-5536	215	26	bipolar	bipolar	ADJ
ejpam-5536	215	27	fuzzy	fuzzy	ADJ
ejpam-5536	215	28	ideal	ideal	NOUN
ejpam-5536	215	29	(	(	PUNCT
ejpam-5536	215	30	resp	resp	NOUN
ejpam-5536	215	31	.	.	PUNCT
ejpam-5536	215	32	,	,	PUNCT
ejpam-5536	215	33	deductive	deductive	ADJ
ejpam-5536	215	34	system	system	NOUN
ejpam-5536	215	35	)	)	PUNCT
ejpam-5536	215	36	of	of	ADP
ejpam-5536	215	37	x	x	PRON
ejpam-5536	215	38	,	,	PUNCT
ejpam-5536	215	39	then	then	ADV
ejpam-5536	215	40	for	for	SCONJ
ejpam-5536	215	41	all	all	PRON
ejpam-5536	215	42	(	(	PUNCT
ejpam-5536	215	43	β	β	X
ejpam-5536	215	44	,	,	PUNCT
ejpam-5536	215	45	α	α	NOUN
ejpam-5536	215	46	)	)	PUNCT
ejpam-5536	215	47	∈	∈	PROPN
ejpam-5536	216	1	[	[	X
ejpam-5536	216	2	0,∓]×	0,∓]×	PROPN
ejpam-5536	217	1	[	[	X
ejpam-5536	217	2	±	±	NUM
ejpam-5536	217	3	,	,	PUNCT
ejpam-5536	217	4	0	0	NUM
ejpam-5536	217	5	]	]	PUNCT
ejpam-5536	217	6	,	,	PUNCT
ejpam-5536	217	7	the	the	DET
ejpam-5536	217	8	bipolar	bipolar	ADJ
ejpam-5536	217	9	fuzzy	fuzzy	NOUN
ejpam-5536	217	10	(	(	PUNCT
ejpam-5536	217	11	β	β	NOUN
ejpam-5536	217	12	,	,	PUNCT
ejpam-5536	217	13	α)-translation	α)-translation	NOUN
ejpam-5536	217	14	φt2	φt2	NOUN
ejpam-5536	217	15	(	(	PUNCT
ejpam-5536	217	16	β	β	X
ejpam-5536	217	17	,	,	PUNCT
ejpam-5536	217	18	α	α	NOUN
ejpam-5536	217	19	)	)	PUNCT
ejpam-5536	217	20	=	=	SYM
ejpam-5536	218	1	(	(	PUNCT
ejpam-5536	218	2	φ+	φ+	X
ejpam-5536	218	3	(	(	PUNCT
ejpam-5536	218	4	β	β	X
ejpam-5536	218	5	,	,	PUNCT
ejpam-5536	218	6	t2	t2	NOUN
ejpam-5536	218	7	)	)	PUNCT
ejpam-5536	218	8	,	,	PUNCT
ejpam-5536	218	9	φ−	φ−	PROPN
ejpam-5536	218	10	(	(	PUNCT
ejpam-5536	218	11	α	α	NOUN
ejpam-5536	218	12	,	,	PUNCT
ejpam-5536	218	13	t2	t2	NOUN
ejpam-5536	218	14	)	)	PUNCT
ejpam-5536	218	15	)	)	PUNCT
ejpam-5536	218	16	of	of	ADP
ejpam-5536	218	17	φ	φ	PROPN
ejpam-5536	218	18	=	=	SYM
ejpam-5536	218	19	(	(	PUNCT
ejpam-5536	218	20	φ+	φ+	NOUN
ejpam-5536	218	21	,	,	PUNCT
ejpam-5536	218	22	φ−	φ−	PROPN
ejpam-5536	218	23	)	)	PUNCT
ejpam-5536	218	24	is	be	AUX
ejpam-5536	218	25	a	a	DET
ejpam-5536	218	26	bipolar	bipolar	ADJ
ejpam-5536	218	27	fuzzy	fuzzy	ADJ
ejpam-5536	218	28	ideal	ideal	NOUN
ejpam-5536	218	29	(	(	PUNCT
ejpam-5536	218	30	resp	resp	NOUN
ejpam-5536	218	31	.	.	PUNCT
ejpam-5536	218	32	,	,	PUNCT
ejpam-5536	218	33	deductive	deductive	ADJ
ejpam-5536	218	34	system	system	NOUN
ejpam-5536	218	35	)	)	PUNCT
ejpam-5536	218	36	of	of	ADP
ejpam-5536	218	37	x.	x.	NOUN
ejpam-5536	218	38	proof	proof	NOUN
ejpam-5536	218	39	.	.	PUNCT
ejpam-5536	219	1	the	the	DET
ejpam-5536	219	2	proof	proof	NOUN
ejpam-5536	219	3	is	be	AUX
ejpam-5536	219	4	similar	similar	ADJ
ejpam-5536	219	5	to	to	ADP
ejpam-5536	219	6	theorem	theorem	VERB
ejpam-5536	219	7	5	5	NUM
ejpam-5536	219	8	.	.	PUNCT
ejpam-5536	219	9	theorem	theorem	NOUN
ejpam-5536	219	10	8	8	NUM
ejpam-5536	219	11	.	.	PUNCT
ejpam-5536	220	1	if	if	SCONJ
ejpam-5536	220	2	there	there	PRON
ejpam-5536	220	3	exists	exist	VERB
ejpam-5536	220	4	(	(	PUNCT
ejpam-5536	220	5	β	β	X
ejpam-5536	220	6	,	,	PUNCT
ejpam-5536	220	7	α	α	NOUN
ejpam-5536	220	8	)	)	PUNCT
ejpam-5536	220	9	∈	∈	NOUN
ejpam-5536	221	1	[	[	X
ejpam-5536	221	2	0,∓	0,∓	X
ejpam-5536	221	3	]	]	X
ejpam-5536	221	4	×	×	PROPN
ejpam-5536	221	5	[	[	X
ejpam-5536	221	6	±	±	NUM
ejpam-5536	221	7	,	,	PUNCT
ejpam-5536	221	8	0	0	NUM
ejpam-5536	221	9	]	]	PUNCT
ejpam-5536	221	10	such	such	ADJ
ejpam-5536	221	11	that	that	SCONJ
ejpam-5536	221	12	the	the	DET
ejpam-5536	221	13	bipolar	bipolar	ADJ
ejpam-5536	221	14	fuzzy	fuzzy	NOUN
ejpam-5536	221	15	(	(	PUNCT
ejpam-5536	221	16	β	β	NOUN
ejpam-5536	221	17	,	,	PUNCT
ejpam-5536	221	18	α)translation	α)translation	PROPN
ejpam-5536	221	19	φt2	φt2	NOUN
ejpam-5536	221	20	(	(	PUNCT
ejpam-5536	221	21	β	β	X
ejpam-5536	221	22	,	,	PUNCT
ejpam-5536	221	23	α	α	NOUN
ejpam-5536	221	24	)	)	PUNCT
ejpam-5536	221	25	=	=	SYM
ejpam-5536	221	26	(	(	PUNCT
ejpam-5536	221	27	φ+	φ+	X
ejpam-5536	221	28	(	(	PUNCT
ejpam-5536	221	29	β	β	X
ejpam-5536	221	30	,	,	PUNCT
ejpam-5536	221	31	t2	t2	NOUN
ejpam-5536	221	32	)	)	PUNCT
ejpam-5536	221	33	,	,	PUNCT
ejpam-5536	221	34	φ−	φ−	PROPN
ejpam-5536	221	35	(	(	PUNCT
ejpam-5536	221	36	α	α	NOUN
ejpam-5536	221	37	,	,	PUNCT
ejpam-5536	221	38	t2	t2	NOUN
ejpam-5536	221	39	)	)	PUNCT
ejpam-5536	221	40	)	)	PUNCT
ejpam-5536	221	41	of	of	ADP
ejpam-5536	221	42	φ	φ	PROPN
ejpam-5536	221	43	=	=	SYM
ejpam-5536	221	44	(	(	PUNCT
ejpam-5536	221	45	φ+	φ+	NOUN
ejpam-5536	221	46	,	,	PUNCT
ejpam-5536	221	47	φ−	φ−	PROPN
ejpam-5536	221	48	)	)	PUNCT
ejpam-5536	221	49	is	be	AUX
ejpam-5536	221	50	a	a	DET
ejpam-5536	221	51	bipolar	bipolar	ADJ
ejpam-5536	221	52	fuzzy	fuzzy	ADJ
ejpam-5536	221	53	ideal	ideal	NOUN
ejpam-5536	221	54	(	(	PUNCT
ejpam-5536	221	55	resp	resp	NOUN
ejpam-5536	221	56	.	.	PUNCT
ejpam-5536	221	57	,	,	PUNCT
ejpam-5536	221	58	deductive	deductive	ADJ
ejpam-5536	221	59	system	system	NOUN
ejpam-5536	221	60	)	)	PUNCT
ejpam-5536	221	61	of	of	ADP
ejpam-5536	221	62	a	a	DET
ejpam-5536	221	63	hilbert	hilbert	NOUN
ejpam-5536	221	64	algebra	algebra	NOUN
ejpam-5536	221	65	x	x	PUNCT
ejpam-5536	222	1	=	=	SYM
ejpam-5536	222	2	(	(	PUNCT
ejpam-5536	222	3	x	x	NOUN
ejpam-5536	222	4	,	,	PUNCT
ejpam-5536	222	5	·	·	PUNCT
ejpam-5536	222	6	,	,	PUNCT
ejpam-5536	222	7	1x	1x	NUM
ejpam-5536	222	8	)	)	PUNCT
ejpam-5536	222	9	,	,	PUNCT
ejpam-5536	222	10	then	then	ADV
ejpam-5536	222	11	φ	φ	PROPN
ejpam-5536	222	12	=	=	SYM
ejpam-5536	222	13	(	(	PUNCT
ejpam-5536	222	14	φ+	φ+	NOUN
ejpam-5536	222	15	,	,	PUNCT
ejpam-5536	222	16	φ−	φ−	PROPN
ejpam-5536	222	17	)	)	PUNCT
ejpam-5536	222	18	is	be	AUX
ejpam-5536	222	19	a	a	DET
ejpam-5536	222	20	bipolar	bipolar	ADJ
ejpam-5536	222	21	fuzzy	fuzzy	ADJ
ejpam-5536	222	22	ideal	ideal	NOUN
ejpam-5536	222	23	(	(	PUNCT
ejpam-5536	222	24	resp	resp	NOUN
ejpam-5536	222	25	.	.	PUNCT
ejpam-5536	222	26	,	,	PUNCT
ejpam-5536	222	27	deductive	deductive	ADJ
ejpam-5536	222	28	system	system	NOUN
ejpam-5536	222	29	)	)	PUNCT
ejpam-5536	222	30	of	of	ADP
ejpam-5536	222	31	x.	x.	NOUN
ejpam-5536	222	32	proof	proof	NOUN
ejpam-5536	222	33	.	.	PUNCT
ejpam-5536	223	1	the	the	DET
ejpam-5536	223	2	proof	proof	NOUN
ejpam-5536	223	3	is	be	AUX
ejpam-5536	223	4	similar	similar	ADJ
ejpam-5536	223	5	to	to	AUX
ejpam-5536	223	6	theorem	theorem	VERB
ejpam-5536	223	7	6	6	NUM
ejpam-5536	223	8	.	.	PUNCT
ejpam-5536	223	9	remark	remark	NOUN
ejpam-5536	223	10	2	2	NUM
ejpam-5536	223	11	.	.	PUNCT
ejpam-5536	224	1	if	if	SCONJ
ejpam-5536	224	2	φ	φ	PROPN
ejpam-5536	224	3	=	=	SYM
ejpam-5536	224	4	(	(	PUNCT
ejpam-5536	224	5	φ+	φ+	NOUN
ejpam-5536	224	6	,	,	PUNCT
ejpam-5536	224	7	φ−	φ−	PROPN
ejpam-5536	224	8	)	)	PUNCT
ejpam-5536	224	9	is	be	AUX
ejpam-5536	224	10	a	a	DET
ejpam-5536	224	11	bfs	bfs	NOUN
ejpam-5536	224	12	in	in	ADP
ejpam-5536	224	13	a	a	DET
ejpam-5536	224	14	nonempty	nonempty	ADV
ejpam-5536	224	15	set	set	VERB
ejpam-5536	224	16	x	x	NOUN
ejpam-5536	224	17	,	,	PUNCT
ejpam-5536	224	18	then	then	ADV
ejpam-5536	224	19	for	for	SCONJ
ejpam-5536	224	20	all	all	PRON
ejpam-5536	224	21	(	(	PUNCT
ejpam-5536	224	22	β	β	X
ejpam-5536	224	23	,	,	PUNCT
ejpam-5536	224	24	α	α	NOUN
ejpam-5536	224	25	)	)	PUNCT
ejpam-5536	224	26	∈	∈	PROPN
ejpam-5536	225	1	[	[	X
ejpam-5536	225	2	0,∓]×	0,∓]×	PROPN
ejpam-5536	226	1	[	[	X
ejpam-5536	226	2	±	±	NUM
ejpam-5536	226	3	,	,	PUNCT
ejpam-5536	226	4	0	0	NUM
ejpam-5536	226	5	]	]	PUNCT
ejpam-5536	226	6	,	,	PUNCT
ejpam-5536	226	7	φ+	φ+	X
ejpam-5536	226	8	(	(	PUNCT
ejpam-5536	226	9	β	β	X
ejpam-5536	226	10	,	,	PUNCT
ejpam-5536	226	11	t2	t2	NOUN
ejpam-5536	226	12	)	)	PUNCT
ejpam-5536	226	13	(	(	PUNCT
ejpam-5536	226	14	x	x	X
ejpam-5536	226	15	)	)	PUNCT
ejpam-5536	226	16	=	=	SYM
ejpam-5536	226	17	φ+(x)−β	φ+(x)−β	X
ejpam-5536	226	18	≤	≤	NOUN
ejpam-5536	226	19	φ+(x	φ+(x	NUM
ejpam-5536	226	20	)	)	PUNCT
ejpam-5536	226	21	and	and	CCONJ
ejpam-5536	226	22	φ−	φ−	PROPN
ejpam-5536	226	23	(	(	PUNCT
ejpam-5536	226	24	α	α	NOUN
ejpam-5536	226	25	,	,	PUNCT
ejpam-5536	226	26	t2	t2	NOUN
ejpam-5536	226	27	)	)	PUNCT
ejpam-5536	226	28	(	(	PUNCT
ejpam-5536	226	29	x	x	X
ejpam-5536	226	30	)	)	PUNCT
ejpam-5536	226	31	=	=	PRON
ejpam-5536	226	32	φ−(x)−α	φ−(x)−α	VERB
ejpam-5536	226	33	≥	≥	PRON
ejpam-5536	226	34	φ−(x	φ−(x	NUM
ejpam-5536	226	35	)	)	PUNCT
ejpam-5536	226	36	for	for	ADP
ejpam-5536	226	37	all	all	PRON
ejpam-5536	226	38	x	x	SYM
ejpam-5536	226	39	∈	∈	ADJ
ejpam-5536	226	40	x.	x.	NOUN
ejpam-5536	226	41	hence	hence	ADV
ejpam-5536	226	42	,	,	PUNCT
ejpam-5536	226	43	the	the	DET
ejpam-5536	226	44	bipolar	bipolar	ADJ
ejpam-5536	226	45	fuzzy	fuzzy	NOUN
ejpam-5536	226	46	(	(	PUNCT
ejpam-5536	226	47	β	β	NOUN
ejpam-5536	226	48	,	,	PUNCT
ejpam-5536	226	49	α)-translation	α)-translation	NOUN
ejpam-5536	226	50	φt2	φt2	NOUN
ejpam-5536	226	51	(	(	PUNCT
ejpam-5536	226	52	β	β	X
ejpam-5536	226	53	,	,	PUNCT
ejpam-5536	226	54	α	α	NOUN
ejpam-5536	226	55	)	)	PUNCT
ejpam-5536	226	56	=	=	SYM
ejpam-5536	226	57	(	(	PUNCT
ejpam-5536	226	58	φ+	φ+	X
ejpam-5536	226	59	(	(	PUNCT
ejpam-5536	226	60	β	β	X
ejpam-5536	226	61	,	,	PUNCT
ejpam-5536	226	62	t2	t2	NOUN
ejpam-5536	226	63	)	)	PUNCT
ejpam-5536	226	64	,	,	PUNCT
ejpam-5536	226	65	φ−	φ−	PROPN
ejpam-5536	226	66	(	(	PUNCT
ejpam-5536	226	67	α	α	NOUN
ejpam-5536	226	68	,	,	PUNCT
ejpam-5536	226	69	t2	t2	NOUN
ejpam-5536	226	70	)	)	PUNCT
ejpam-5536	226	71	)	)	PUNCT
ejpam-5536	226	72	of	of	ADP
ejpam-5536	226	73	φ	φ	PROPN
ejpam-5536	226	74	=	=	SYM
ejpam-5536	226	75	(	(	PUNCT
ejpam-5536	226	76	φ+	φ+	NOUN
ejpam-5536	226	77	,	,	PUNCT
ejpam-5536	226	78	φ−	φ−	PROPN
ejpam-5536	226	79	)	)	PUNCT
ejpam-5536	226	80	is	be	AUX
ejpam-5536	226	81	a	a	DET
ejpam-5536	226	82	bipolar	bipolar	ADJ
ejpam-5536	226	83	fuzzy	fuzzy	ADJ
ejpam-5536	226	84	intensity	intensity	NOUN
ejpam-5536	226	85	of	of	ADP
ejpam-5536	226	86	φ	φ	PROPN
ejpam-5536	226	87	=	=	SYM
ejpam-5536	226	88	(	(	PUNCT
ejpam-5536	226	89	φ+	φ+	NOUN
ejpam-5536	226	90	,	,	PUNCT
ejpam-5536	226	91	φ−	φ−	PROPN
ejpam-5536	226	92	)	)	PUNCT
ejpam-5536	226	93	for	for	ADP
ejpam-5536	226	94	all	all	DET
ejpam-5536	226	95	(	(	PUNCT
ejpam-5536	226	96	β	β	X
ejpam-5536	226	97	,	,	PUNCT
ejpam-5536	226	98	α	α	NOUN
ejpam-5536	226	99	)	)	PUNCT
ejpam-5536	226	100	∈	∈	PROPN
ejpam-5536	227	1	[	[	X
ejpam-5536	227	2	0,∓]×	0,∓]×	PROPN
ejpam-5536	228	1	[	[	X
ejpam-5536	228	2	±	±	NUM
ejpam-5536	228	3	,	,	PUNCT
ejpam-5536	228	4	0	0	NUM
ejpam-5536	228	5	]	]	PUNCT
ejpam-5536	228	6	.	.	PUNCT
ejpam-5536	229	1	a.	a.	PROPN
ejpam-5536	229	2	iampan	iampan	PROPN
ejpam-5536	229	3	et	et	PROPN
ejpam-5536	229	4	al	al	PROPN
ejpam-5536	229	5	.	.	PUNCT
ejpam-5536	229	6	/	/	SYM
ejpam-5536	229	7	eur	eur	PROPN
ejpam-5536	229	8	.	.	PUNCT
ejpam-5536	230	1	j.	j.	PROPN
ejpam-5536	230	2	pure	pure	PROPN
ejpam-5536	230	3	appl	appl	PROPN
ejpam-5536	230	4	.	.	PROPN
ejpam-5536	230	5	math	math	PROPN
ejpam-5536	230	6	,	,	PUNCT
ejpam-5536	230	7	17	17	NUM
ejpam-5536	230	8	(	(	PUNCT
ejpam-5536	230	9	4	4	NUM
ejpam-5536	230	10	)	)	PUNCT
ejpam-5536	230	11	(	(	PUNCT
ejpam-5536	230	12	2024	2024	NUM
ejpam-5536	230	13	)	)	PUNCT
ejpam-5536	230	14	,	,	PUNCT
ejpam-5536	230	15	4059	4059	NUM
ejpam-5536	230	16	-	-	SYM
ejpam-5536	230	17	4070	4070	NUM
ejpam-5536	230	18	4067	4067	NUM
ejpam-5536	230	19	definition	definition	NOUN
ejpam-5536	230	20	14	14	NUM
ejpam-5536	230	21	.	.	PUNCT
ejpam-5536	231	1	let	let	VERB
ejpam-5536	231	2	φ	φ	PROPN
ejpam-5536	231	3	=	=	SYM
ejpam-5536	231	4	(	(	PUNCT
ejpam-5536	231	5	φ+	φ+	PROPN
ejpam-5536	231	6	,	,	PUNCT
ejpam-5536	231	7	φ−	φ−	PROPN
ejpam-5536	231	8	)	)	PUNCT
ejpam-5536	231	9	be	be	VERB
ejpam-5536	231	10	a	a	DET
ejpam-5536	231	11	bfs	bfs	NOUN
ejpam-5536	231	12	in	in	ADP
ejpam-5536	231	13	a	a	DET
ejpam-5536	231	14	nonempty	nonempty	ADV
ejpam-5536	231	15	set	set	VERB
ejpam-5536	231	16	x.	x.	NOUN
ejpam-5536	231	17	the	the	DET
ejpam-5536	231	18	bfs	bfs	PROPN
ejpam-5536	231	19	φ	φ	PROPN
ejpam-5536	231	20	=	=	SYM
ejpam-5536	231	21	(	(	PUNCT
ejpam-5536	231	22	φ+	φ+	NOUN
ejpam-5536	231	23	,	,	PUNCT
ejpam-5536	231	24	φ−	φ−	PROPN
ejpam-5536	231	25	)	)	PUNCT
ejpam-5536	231	26	in	in	ADP
ejpam-5536	231	27	x	x	PUNCT
ejpam-5536	231	28	defined	define	VERB
ejpam-5536	231	29	by	by	ADP
ejpam-5536	231	30	:	:	PUNCT
ejpam-5536	231	31	for	for	ADP
ejpam-5536	231	32	all	all	PRON
ejpam-5536	231	33	x	x	SYM
ejpam-5536	231	34	∈	∈	PROPN
ejpam-5536	231	35	x	x	NOUN
ejpam-5536	231	36	,	,	PUNCT
ejpam-5536	231	37	φ+(x	φ+(x	X
ejpam-5536	231	38	)	)	PUNCT
ejpam-5536	231	39	=	=	SYM
ejpam-5536	231	40	1−	1−	NUM
ejpam-5536	231	41	φ+(x	φ+(x	NOUN
ejpam-5536	231	42	)	)	PUNCT
ejpam-5536	231	43	,	,	PUNCT
ejpam-5536	231	44	φ−(x	φ−(x	PROPN
ejpam-5536	231	45	)	)	PUNCT
ejpam-5536	232	1	=	=	PROPN
ejpam-5536	232	2	−1−	−1−	PROPN
ejpam-5536	232	3	φ−(x	φ−(x	PROPN
ejpam-5536	232	4	)	)	PUNCT
ejpam-5536	232	5	,	,	PUNCT
ejpam-5536	232	6	is	be	AUX
ejpam-5536	232	7	called	call	VERB
ejpam-5536	232	8	the	the	DET
ejpam-5536	232	9	complement	complement	NOUN
ejpam-5536	232	10	of	of	ADP
ejpam-5536	232	11	φ	φ	PROPN
ejpam-5536	232	12	=	=	SYM
ejpam-5536	232	13	(	(	PUNCT
ejpam-5536	232	14	φ+	φ+	NOUN
ejpam-5536	232	15	,	,	PUNCT
ejpam-5536	232	16	φ−	φ−	PROPN
ejpam-5536	232	17	)	)	PUNCT
ejpam-5536	232	18	in	in	ADP
ejpam-5536	232	19	x.	x.	NOUN
ejpam-5536	232	20	definition	definition	NOUN
ejpam-5536	232	21	15	15	NUM
ejpam-5536	232	22	.	.	PUNCT
ejpam-5536	233	1	[	[	X
ejpam-5536	233	2	17	17	NUM
ejpam-5536	233	3	]	]	PUNCT
ejpam-5536	233	4	let	let	VERB
ejpam-5536	233	5	φ	φ	PROPN
ejpam-5536	233	6	=	=	SYM
ejpam-5536	233	7	(	(	PUNCT
ejpam-5536	233	8	φ+	φ+	PROPN
ejpam-5536	233	9	,	,	PUNCT
ejpam-5536	233	10	φ−	φ−	PROPN
ejpam-5536	233	11	)	)	PUNCT
ejpam-5536	233	12	be	be	VERB
ejpam-5536	233	13	a	a	DET
ejpam-5536	233	14	bfs	bfs	NOUN
ejpam-5536	233	15	in	in	ADP
ejpam-5536	233	16	a	a	DET
ejpam-5536	233	17	nonempty	nonempty	ADV
ejpam-5536	233	18	set	set	VERB
ejpam-5536	233	19	x.	x.	NOUN
ejpam-5536	233	20	for	for	ADP
ejpam-5536	233	21	(	(	PUNCT
ejpam-5536	233	22	t+	t+	NOUN
ejpam-5536	233	23	,	,	PUNCT
ejpam-5536	233	24	t−	t−	ADJ
ejpam-5536	233	25	)	)	PUNCT
ejpam-5536	233	26	∈	∈	PROPN
ejpam-5536	234	1	[	[	X
ejpam-5536	234	2	0	0	NUM
ejpam-5536	234	3	,	,	PUNCT
ejpam-5536	234	4	1]×	1]×	NUM
ejpam-5536	234	5	[	[	X
ejpam-5536	234	6	−1	−1	NOUN
ejpam-5536	234	7	,	,	PUNCT
ejpam-5536	234	8	0	0	NUM
ejpam-5536	234	9	]	]	PUNCT
ejpam-5536	234	10	,	,	PUNCT
ejpam-5536	234	11	the	the	DET
ejpam-5536	234	12	sets	set	NOUN
ejpam-5536	234	13	pl(φ	pl(φ	VERB
ejpam-5536	234	14	,	,	PUNCT
ejpam-5536	234	15	t	t	PROPN
ejpam-5536	234	16	+	+	NOUN
ejpam-5536	234	17	)	)	PUNCT
ejpam-5536	234	18	=	=	PRON
ejpam-5536	234	19	{	{	PUNCT
ejpam-5536	234	20	x	x	PUNCT
ejpam-5536	234	21	∈	∈	PROPN
ejpam-5536	234	22	x	x	X
ejpam-5536	234	23	|	|	ADV
ejpam-5536	234	24	φ+(x	φ+(x	NOUN
ejpam-5536	234	25	)	)	PUNCT
ejpam-5536	234	26	≤	≤	NOUN
ejpam-5536	234	27	t+	t+	PUNCT
ejpam-5536	234	28	}	}	PUNCT
ejpam-5536	234	29	,	,	PUNCT
ejpam-5536	234	30	pu	pu	PROPN
ejpam-5536	234	31	(	(	PUNCT
ejpam-5536	234	32	φ	φ	PROPN
ejpam-5536	234	33	,	,	PUNCT
ejpam-5536	234	34	t	t	PROPN
ejpam-5536	234	35	+	+	NOUN
ejpam-5536	234	36	)	)	PUNCT
ejpam-5536	234	37	=	=	PRON
ejpam-5536	234	38	{	{	PUNCT
ejpam-5536	234	39	x	x	PUNCT
ejpam-5536	234	40	∈	∈	PROPN
ejpam-5536	234	41	x	x	X
ejpam-5536	234	42	|	|	ADV
ejpam-5536	234	43	φ+(x	φ+(x	NOUN
ejpam-5536	234	44	)	)	PUNCT
ejpam-5536	234	45	≥	≥	NOUN
ejpam-5536	234	46	t+	t+	VERB
ejpam-5536	234	47	}	}	PUNCT
ejpam-5536	234	48	are	be	AUX
ejpam-5536	234	49	called	call	VERB
ejpam-5536	234	50	the	the	DET
ejpam-5536	234	51	positive	positive	ADJ
ejpam-5536	234	52	lower	low	ADJ
ejpam-5536	234	53	t−-cut	t−-cut	VERB
ejpam-5536	234	54	and	and	CCONJ
ejpam-5536	234	55	the	the	DET
ejpam-5536	234	56	positive	positive	ADJ
ejpam-5536	234	57	upper	upper	ADJ
ejpam-5536	234	58	t+-cut	t+-cut	NOUN
ejpam-5536	234	59	of	of	ADP
ejpam-5536	234	60	φ	φ	PROPN
ejpam-5536	234	61	=	=	SYM
ejpam-5536	234	62	(	(	PUNCT
ejpam-5536	234	63	φ+	φ+	NOUN
ejpam-5536	234	64	,	,	PUNCT
ejpam-5536	234	65	φ−	φ−	PROPN
ejpam-5536	234	66	)	)	PUNCT
ejpam-5536	234	67	,	,	PUNCT
ejpam-5536	234	68	respectively	respectively	ADV
ejpam-5536	234	69	.	.	PUNCT
ejpam-5536	235	1	the	the	DET
ejpam-5536	235	2	sets	set	NOUN
ejpam-5536	235	3	nl(φ	nl(φ	ADV
ejpam-5536	235	4	,	,	PUNCT
ejpam-5536	235	5	t	t	PROPN
ejpam-5536	235	6	−	−	NOUN
ejpam-5536	235	7	)	)	PUNCT
ejpam-5536	236	1	=	=	PRON
ejpam-5536	236	2	{	{	PUNCT
ejpam-5536	236	3	x	x	PUNCT
ejpam-5536	236	4	∈	∈	PROPN
ejpam-5536	236	5	x	x	X
ejpam-5536	236	6	|	|	ADV
ejpam-5536	236	7	φ−(x	φ−(x	PROPN
ejpam-5536	236	8	)	)	PUNCT
ejpam-5536	236	9	≤	≤	NOUN
ejpam-5536	236	10	t−	t−	PROPN
ejpam-5536	236	11	}	}	PUNCT
ejpam-5536	236	12	,	,	PUNCT
ejpam-5536	236	13	nu	nu	INTJ
ejpam-5536	236	14	(	(	PUNCT
ejpam-5536	236	15	φ	φ	PROPN
ejpam-5536	236	16	,	,	PUNCT
ejpam-5536	236	17	t	t	PROPN
ejpam-5536	236	18	−	−	PROPN
ejpam-5536	236	19	)	)	PUNCT
ejpam-5536	236	20	=	=	PRON
ejpam-5536	237	1	{	{	PUNCT
ejpam-5536	237	2	x	x	PUNCT
ejpam-5536	237	3	∈	∈	PROPN
ejpam-5536	237	4	x	x	SYM
ejpam-5536	237	5	|	|	ADV
ejpam-5536	237	6	φ−(x	φ−(x	PROPN
ejpam-5536	237	7	)	)	PUNCT
ejpam-5536	237	8	≥	≥	NOUN
ejpam-5536	237	9	t−	t−	NOUN
ejpam-5536	237	10	}	}	PUNCT
ejpam-5536	237	11	are	be	AUX
ejpam-5536	237	12	called	call	VERB
ejpam-5536	237	13	the	the	DET
ejpam-5536	237	14	negative	negative	ADJ
ejpam-5536	237	15	lower	low	ADJ
ejpam-5536	237	16	t−-cut	t−-cut	PROPN
ejpam-5536	237	17	and	and	CCONJ
ejpam-5536	237	18	the	the	DET
ejpam-5536	237	19	negative	negative	ADJ
ejpam-5536	237	20	upper	upper	ADJ
ejpam-5536	237	21	t+-cut	t+-cut	NOUN
ejpam-5536	237	22	of	of	ADP
ejpam-5536	237	23	φ	φ	PROPN
ejpam-5536	237	24	=	=	SYM
ejpam-5536	237	25	(	(	PUNCT
ejpam-5536	237	26	φ+	φ+	NOUN
ejpam-5536	237	27	,	,	PUNCT
ejpam-5536	237	28	φ−	φ−	PROPN
ejpam-5536	237	29	)	)	PUNCT
ejpam-5536	237	30	,	,	PUNCT
ejpam-5536	237	31	respectively	respectively	ADV
ejpam-5536	237	32	.	.	PUNCT
ejpam-5536	238	1	theorem	theorem	VERB
ejpam-5536	238	2	9	9	NUM
ejpam-5536	238	3	.	.	PUNCT
ejpam-5536	239	1	let	let	VERB
ejpam-5536	239	2	φ	φ	PROPN
ejpam-5536	239	3	=	=	SYM
ejpam-5536	239	4	(	(	PUNCT
ejpam-5536	239	5	φ+	φ+	PROPN
ejpam-5536	239	6	,	,	PUNCT
ejpam-5536	239	7	φ−	φ−	PROPN
ejpam-5536	239	8	)	)	PUNCT
ejpam-5536	239	9	be	be	VERB
ejpam-5536	239	10	a	a	DET
ejpam-5536	239	11	bfs	bfs	NOUN
ejpam-5536	239	12	in	in	ADP
ejpam-5536	239	13	a	a	DET
ejpam-5536	239	14	hilbert	hilbert	NOUN
ejpam-5536	239	15	algebra	algebra	NOUN
ejpam-5536	239	16	x	x	PUNCT
ejpam-5536	239	17	=	=	SYM
ejpam-5536	239	18	(	(	PUNCT
ejpam-5536	239	19	x	x	NOUN
ejpam-5536	239	20	,	,	PUNCT
ejpam-5536	239	21	·	·	PUNCT
ejpam-5536	239	22	,	,	PUNCT
ejpam-5536	239	23	1x	1x	NUM
ejpam-5536	239	24	)	)	PUNCT
ejpam-5536	239	25	.	.	PUNCT
ejpam-5536	240	1	then	then	ADV
ejpam-5536	240	2	φ	φ	PROPN
ejpam-5536	240	3	=	=	SYM
ejpam-5536	240	4	(	(	PUNCT
ejpam-5536	240	5	φ+	φ+	NOUN
ejpam-5536	240	6	,	,	PUNCT
ejpam-5536	240	7	φ−	φ−	PROPN
ejpam-5536	240	8	)	)	PUNCT
ejpam-5536	240	9	is	be	AUX
ejpam-5536	240	10	a	a	DET
ejpam-5536	240	11	bipolar	bipolar	ADJ
ejpam-5536	240	12	fuzzy	fuzzy	ADJ
ejpam-5536	240	13	subalgebra	subalgebra	NOUN
ejpam-5536	240	14	of	of	ADP
ejpam-5536	240	15	x	x	PUNCT
ejpam-5536	240	16	if	if	SCONJ
ejpam-5536	240	17	and	and	CCONJ
ejpam-5536	240	18	only	only	ADV
ejpam-5536	240	19	if	if	SCONJ
ejpam-5536	240	20	for	for	ADP
ejpam-5536	240	21	all	all	DET
ejpam-5536	240	22	(	(	PUNCT
ejpam-5536	240	23	t+	t+	NOUN
ejpam-5536	240	24	,	,	PUNCT
ejpam-5536	240	25	t−	t−	ADJ
ejpam-5536	240	26	)	)	PUNCT
ejpam-5536	240	27	∈	∈	PROPN
ejpam-5536	241	1	[	[	X
ejpam-5536	241	2	0	0	NUM
ejpam-5536	241	3	,	,	PUNCT
ejpam-5536	241	4	1]×	1]×	NUM
ejpam-5536	241	5	[	[	X
ejpam-5536	241	6	−1	−1	NOUN
ejpam-5536	241	7	,	,	PUNCT
ejpam-5536	241	8	0	0	NUM
ejpam-5536	241	9	]	]	PUNCT
ejpam-5536	241	10	,	,	PUNCT
ejpam-5536	241	11	pl(φ	pl(φ	NOUN
ejpam-5536	241	12	,	,	PUNCT
ejpam-5536	241	13	t	t	PROPN
ejpam-5536	241	14	+	+	NOUN
ejpam-5536	241	15	)	)	PUNCT
ejpam-5536	241	16	and	and	CCONJ
ejpam-5536	241	17	nu	nu	INTJ
ejpam-5536	241	18	(	(	PUNCT
ejpam-5536	241	19	φ	φ	PROPN
ejpam-5536	241	20	,	,	PUNCT
ejpam-5536	241	21	t	t	PROPN
ejpam-5536	241	22	−	−	PROPN
ejpam-5536	241	23	)	)	PUNCT
ejpam-5536	241	24	are	be	AUX
ejpam-5536	241	25	subalgebras	subalgebra	NOUN
ejpam-5536	241	26	of	of	ADP
ejpam-5536	241	27	x	x	PRON
ejpam-5536	241	28	if	if	SCONJ
ejpam-5536	241	29	pl(φ	pl(φ	NOUN
ejpam-5536	241	30	,	,	PUNCT
ejpam-5536	241	31	t	t	PROPN
ejpam-5536	241	32	+	+	NOUN
ejpam-5536	241	33	)	)	PUNCT
ejpam-5536	241	34	and	and	CCONJ
ejpam-5536	241	35	nu	nu	INTJ
ejpam-5536	241	36	(	(	PUNCT
ejpam-5536	241	37	φ	φ	PROPN
ejpam-5536	241	38	,	,	PUNCT
ejpam-5536	241	39	t	t	PROPN
ejpam-5536	241	40	−	−	PROPN
ejpam-5536	241	41	)	)	PUNCT
ejpam-5536	241	42	are	be	AUX
ejpam-5536	241	43	nonempty	nonempty	ADJ
ejpam-5536	241	44	.	.	PUNCT
ejpam-5536	242	1	proof	proof	NOUN
ejpam-5536	242	2	.	.	PUNCT
ejpam-5536	243	1	assume	assume	VERB
ejpam-5536	243	2	that	that	SCONJ
ejpam-5536	243	3	φ	φ	PROPN
ejpam-5536	243	4	=	=	SYM
ejpam-5536	243	5	(	(	PUNCT
ejpam-5536	243	6	φ+	φ+	NOUN
ejpam-5536	243	7	,	,	PUNCT
ejpam-5536	243	8	φ−	φ−	PROPN
ejpam-5536	243	9	)	)	PUNCT
ejpam-5536	243	10	is	be	AUX
ejpam-5536	243	11	a	a	DET
ejpam-5536	243	12	bipolar	bipolar	ADJ
ejpam-5536	243	13	fuzzy	fuzzy	ADJ
ejpam-5536	243	14	subalgebra	subalgebra	NOUN
ejpam-5536	243	15	of	of	ADP
ejpam-5536	243	16	x.	x.	NOUN
ejpam-5536	243	17	let	let	VERB
ejpam-5536	243	18	(	(	PUNCT
ejpam-5536	243	19	t+	t+	NOUN
ejpam-5536	243	20	,	,	PUNCT
ejpam-5536	243	21	t−	t−	ADJ
ejpam-5536	243	22	)	)	PUNCT
ejpam-5536	243	23	∈	∈	PROPN
ejpam-5536	244	1	[	[	X
ejpam-5536	244	2	0	0	NUM
ejpam-5536	244	3	,	,	PUNCT
ejpam-5536	244	4	1]×	1]×	NUM
ejpam-5536	244	5	[	[	X
ejpam-5536	244	6	−1	−1	NOUN
ejpam-5536	244	7	,	,	PUNCT
ejpam-5536	244	8	0	0	NUM
ejpam-5536	244	9	]	]	PUNCT
ejpam-5536	244	10	be	be	VERB
ejpam-5536	244	11	such	such	ADJ
ejpam-5536	244	12	that	that	DET
ejpam-5536	244	13	pl(φ	pl(φ	NOUN
ejpam-5536	244	14	,	,	PUNCT
ejpam-5536	244	15	t	t	PROPN
ejpam-5536	244	16	+	+	NOUN
ejpam-5536	244	17	)	)	PUNCT
ejpam-5536	244	18	and	and	CCONJ
ejpam-5536	244	19	nu	nu	INTJ
ejpam-5536	244	20	(	(	PUNCT
ejpam-5536	244	21	φ	φ	PROPN
ejpam-5536	244	22	,	,	PUNCT
ejpam-5536	244	23	t	t	PROPN
ejpam-5536	244	24	−	−	PROPN
ejpam-5536	244	25	)	)	PUNCT
ejpam-5536	244	26	are	be	AUX
ejpam-5536	244	27	nonempty	nonempty	ADJ
ejpam-5536	244	28	.	.	PUNCT
ejpam-5536	245	1	let	let	VERB
ejpam-5536	245	2	x	x	PRON
ejpam-5536	245	3	,	,	PUNCT
ejpam-5536	245	4	y	y	PROPN
ejpam-5536	245	5	∈	∈	PROPN
ejpam-5536	245	6	pl(φ	pl(φ	NOUN
ejpam-5536	245	7	,	,	PUNCT
ejpam-5536	245	8	t	t	PROPN
ejpam-5536	245	9	+	+	NOUN
ejpam-5536	245	10	)	)	PUNCT
ejpam-5536	245	11	.	.	PUNCT
ejpam-5536	246	1	then	then	ADV
ejpam-5536	246	2	φ+(x	φ+(x	X
ejpam-5536	246	3	)	)	PUNCT
ejpam-5536	246	4	≤	≤	NOUN
ejpam-5536	246	5	t+	t+	PUNCT
ejpam-5536	246	6	and	and	CCONJ
ejpam-5536	246	7	φ+(y	φ+(y	SYM
ejpam-5536	246	8	)	)	PUNCT
ejpam-5536	246	9	≤	≤	NOUN
ejpam-5536	246	10	t+	t+	PUNCT
ejpam-5536	246	11	,	,	PUNCT
ejpam-5536	246	12	so	so	CCONJ
ejpam-5536	246	13	t+	t+	NOUN
ejpam-5536	246	14	is	be	AUX
ejpam-5536	246	15	an	an	DET
ejpam-5536	246	16	upper	upper	ADJ
ejpam-5536	246	17	bound	bind	VERB
ejpam-5536	246	18	of	of	ADP
ejpam-5536	246	19	{	{	PUNCT
ejpam-5536	246	20	φ+(x	φ+(x	NOUN
ejpam-5536	246	21	)	)	PUNCT
ejpam-5536	246	22	,	,	PUNCT
ejpam-5536	246	23	φ+(y	φ+(y	PUNCT
ejpam-5536	246	24	)	)	PUNCT
ejpam-5536	246	25	}	}	PUNCT
ejpam-5536	246	26	.	.	PUNCT
ejpam-5536	247	1	by	by	ADP
ejpam-5536	247	2	(	(	PUNCT
ejpam-5536	247	3	1	1	NUM
ejpam-5536	247	4	)	)	PUNCT
ejpam-5536	247	5	,	,	PUNCT
ejpam-5536	247	6	we	we	PRON
ejpam-5536	247	7	have	have	VERB
ejpam-5536	247	8	φ+(x	φ+(x	NOUN
ejpam-5536	247	9	·	·	SYM
ejpam-5536	247	10	y	y	X
ejpam-5536	247	11	)	)	PUNCT
ejpam-5536	247	12	≥	≥	NOUN
ejpam-5536	247	13	min{φ+(x	min{φ+(x	PROPN
ejpam-5536	247	14	)	)	PUNCT
ejpam-5536	247	15	,	,	PUNCT
ejpam-5536	247	16	φ+(y	φ+(y	PUNCT
ejpam-5536	247	17	)	)	PUNCT
ejpam-5536	247	18	}	}	PUNCT
ejpam-5536	247	19	.	.	PUNCT
ejpam-5536	248	1	so	so	ADV
ejpam-5536	248	2	,	,	PUNCT
ejpam-5536	248	3	1−	1−	NUM
ejpam-5536	248	4	φ+(x	φ+(x	X
ejpam-5536	248	5	·	·	PUNCT
ejpam-5536	248	6	y	y	X
ejpam-5536	248	7	)	)	PUNCT
ejpam-5536	248	8	≥	≥	NOUN
ejpam-5536	248	9	min{1−	min{1−	VERB
ejpam-5536	248	10	φ+(x	φ+(x	NOUN
ejpam-5536	248	11	)	)	PUNCT
ejpam-5536	248	12	,	,	PUNCT
ejpam-5536	248	13	1−	1−	NUM
ejpam-5536	248	14	φ+(y	φ+(y	NOUN
ejpam-5536	248	15	)	)	PUNCT
ejpam-5536	248	16	}	}	PUNCT
ejpam-5536	248	17	=	=	SYM
ejpam-5536	248	18	1−max{φ+(x	1−max{φ+(x	NUM
ejpam-5536	248	19	)	)	PUNCT
ejpam-5536	248	20	,	,	PUNCT
ejpam-5536	248	21	φ+(y	φ+(y	PUNCT
ejpam-5536	248	22	)	)	PUNCT
ejpam-5536	248	23	}	}	PUNCT
ejpam-5536	248	24	.	.	PUNCT
ejpam-5536	249	1	thus	thus	ADV
ejpam-5536	249	2	,	,	PUNCT
ejpam-5536	249	3	φ+(x	φ+(x	X
ejpam-5536	249	4	·	·	PUNCT
ejpam-5536	249	5	y	y	X
ejpam-5536	249	6	)	)	PUNCT
ejpam-5536	249	7	≤	≤	NOUN
ejpam-5536	249	8	max{φ+(x	max{φ+(x	PROPN
ejpam-5536	249	9	)	)	PUNCT
ejpam-5536	249	10	,	,	PUNCT
ejpam-5536	249	11	φ+(y	φ+(y	CCONJ
ejpam-5536	249	12	)	)	PUNCT
ejpam-5536	249	13	}	}	PUNCT
ejpam-5536	249	14	≤	≤	NOUN
ejpam-5536	249	15	t+	t+	PUNCT
ejpam-5536	249	16	and	and	CCONJ
ejpam-5536	249	17	so	so	ADV
ejpam-5536	249	18	x	x	SYM
ejpam-5536	249	19	·	·	PUNCT
ejpam-5536	249	20	y	y	PROPN
ejpam-5536	249	21	∈	∈	PROPN
ejpam-5536	249	22	pl(φ	pl(φ	NOUN
ejpam-5536	249	23	,	,	PUNCT
ejpam-5536	249	24	t	t	PROPN
ejpam-5536	249	25	+	+	NOUN
ejpam-5536	249	26	)	)	PUNCT
ejpam-5536	249	27	.	.	PUNCT
ejpam-5536	250	1	therefore	therefore	ADV
ejpam-5536	250	2	,	,	PUNCT
ejpam-5536	250	3	pl(φ	pl(φ	NOUN
ejpam-5536	250	4	,	,	PUNCT
ejpam-5536	250	5	t	t	PROPN
ejpam-5536	250	6	+	+	CCONJ
ejpam-5536	250	7	)	)	PUNCT
ejpam-5536	250	8	is	be	AUX
ejpam-5536	250	9	a	a	DET
ejpam-5536	250	10	subalgebra	subalgebra	NOUN
ejpam-5536	250	11	of	of	ADP
ejpam-5536	250	12	x.	x.	NOUN
ejpam-5536	250	13	let	let	VERB
ejpam-5536	250	14	x	x	PRON
ejpam-5536	250	15	,	,	PUNCT
ejpam-5536	250	16	y	y	PROPN
ejpam-5536	250	17	∈	∈	PROPN
ejpam-5536	250	18	nu	nu	PROPN
ejpam-5536	250	19	(	(	PUNCT
ejpam-5536	250	20	φ	φ	PROPN
ejpam-5536	250	21	,	,	PUNCT
ejpam-5536	250	22	t	t	PROPN
ejpam-5536	250	23	−	−	PROPN
ejpam-5536	250	24	)	)	PUNCT
ejpam-5536	250	25	.	.	PUNCT
ejpam-5536	251	1	then	then	ADV
ejpam-5536	251	2	φ−(x	φ−(x	PROPN
ejpam-5536	251	3	)	)	PUNCT
ejpam-5536	251	4	≥	≥	NOUN
ejpam-5536	251	5	t−	t−	PROPN
ejpam-5536	251	6	and	and	CCONJ
ejpam-5536	251	7	φ−(y	φ−(y	PROPN
ejpam-5536	251	8	)	)	PUNCT
ejpam-5536	251	9	≥	≥	NOUN
ejpam-5536	251	10	t−	t−	PROPN
ejpam-5536	251	11	,	,	PUNCT
ejpam-5536	251	12	so	so	SCONJ
ejpam-5536	251	13	t−	t−	PROPN
ejpam-5536	251	14	is	be	AUX
ejpam-5536	251	15	a	a	DET
ejpam-5536	251	16	lower	low	ADJ
ejpam-5536	251	17	bound	bind	VERB
ejpam-5536	251	18	of	of	ADP
ejpam-5536	251	19	{	{	PUNCT
ejpam-5536	251	20	φ−(x	φ−(x	PROPN
ejpam-5536	251	21	)	)	PUNCT
ejpam-5536	251	22	,	,	PUNCT
ejpam-5536	251	23	φ−(y	φ−(y	PROPN
ejpam-5536	251	24	)	)	PUNCT
ejpam-5536	251	25	}	}	PUNCT
ejpam-5536	251	26	.	.	PUNCT
ejpam-5536	252	1	by	by	ADP
ejpam-5536	252	2	(	(	PUNCT
ejpam-5536	252	3	1	1	NUM
ejpam-5536	252	4	)	)	PUNCT
ejpam-5536	252	5	,	,	PUNCT
ejpam-5536	252	6	we	we	PRON
ejpam-5536	252	7	have	have	VERB
ejpam-5536	252	8	φ−(x	φ−(x	PROPN
ejpam-5536	252	9	·	·	PUNCT
ejpam-5536	252	10	y	y	X
ejpam-5536	252	11	)	)	PUNCT
ejpam-5536	252	12	≤	≤	NOUN
ejpam-5536	252	13	max{φ−(x	max{φ−(x	PROPN
ejpam-5536	252	14	)	)	PUNCT
ejpam-5536	252	15	,	,	PUNCT
ejpam-5536	252	16	φ−(y	φ−(y	PROPN
ejpam-5536	252	17	)	)	PUNCT
ejpam-5536	252	18	}	}	PUNCT
ejpam-5536	252	19	.	.	PUNCT
ejpam-5536	253	1	so	so	ADV
ejpam-5536	253	2	,	,	PUNCT
ejpam-5536	253	3	−1−	−1−	PROPN
ejpam-5536	253	4	φ−(x	φ−(x	PROPN
ejpam-5536	253	5	·	·	PUNCT
ejpam-5536	253	6	y	y	X
ejpam-5536	253	7	)	)	PUNCT
ejpam-5536	253	8	≤	≤	NOUN
ejpam-5536	253	9	max{−1−	max{−1−	NOUN
ejpam-5536	253	10	φ−(x),−1−	φ−(x),−1−	NOUN
ejpam-5536	253	11	φ−(y	φ−(y	NOUN
ejpam-5536	253	12	)	)	PUNCT
ejpam-5536	253	13	}	}	PUNCT
ejpam-5536	253	14	=	=	SYM
ejpam-5536	253	15	−1−min{φ−(x	−1−min{φ−(x	X
ejpam-5536	253	16	)	)	PUNCT
ejpam-5536	253	17	,	,	PUNCT
ejpam-5536	253	18	φ−(y	φ−(y	PROPN
ejpam-5536	253	19	)	)	PUNCT
ejpam-5536	253	20	}	}	PUNCT
ejpam-5536	253	21	.	.	PUNCT
ejpam-5536	254	1	thus	thus	ADV
ejpam-5536	254	2	,	,	PUNCT
ejpam-5536	254	3	φ−(x	φ−(x	PROPN
ejpam-5536	254	4	·	·	PUNCT
ejpam-5536	254	5	y	y	X
ejpam-5536	254	6	)	)	PUNCT
ejpam-5536	254	7	≥	≥	NOUN
ejpam-5536	254	8	min{φ−(x	min{φ−(x	PROPN
ejpam-5536	254	9	)	)	PUNCT
ejpam-5536	254	10	,	,	PUNCT
ejpam-5536	254	11	φ−(y	φ−(y	PROPN
ejpam-5536	254	12	)	)	PUNCT
ejpam-5536	254	13	}	}	PUNCT
ejpam-5536	254	14	≥	≥	X
ejpam-5536	255	1	t−	t−	PROPN
ejpam-5536	256	1	and	and	CCONJ
ejpam-5536	256	2	so	so	ADV
ejpam-5536	256	3	x	x	SYM
ejpam-5536	256	4	·	·	PUNCT
ejpam-5536	256	5	y	y	PROPN
ejpam-5536	256	6	∈	∈	PROPN
ejpam-5536	256	7	nu	nu	PROPN
ejpam-5536	256	8	(	(	PUNCT
ejpam-5536	256	9	φ	φ	PROPN
ejpam-5536	256	10	,	,	PUNCT
ejpam-5536	256	11	t	t	PROPN
ejpam-5536	256	12	−	−	NUM
ejpam-5536	256	13	)	)	PUNCT
ejpam-5536	256	14	.	.	PUNCT
ejpam-5536	257	1	therefore	therefore	ADV
ejpam-5536	257	2	,	,	PUNCT
ejpam-5536	257	3	nu	nu	X
ejpam-5536	257	4	(	(	PUNCT
ejpam-5536	257	5	φ	φ	PROPN
ejpam-5536	257	6	,	,	PUNCT
ejpam-5536	257	7	t	t	PROPN
ejpam-5536	257	8	−	−	PROPN
ejpam-5536	257	9	)	)	PUNCT
ejpam-5536	257	10	is	be	AUX
ejpam-5536	257	11	a	a	DET
ejpam-5536	257	12	subalgebra	subalgebra	NOUN
ejpam-5536	257	13	of	of	ADP
ejpam-5536	257	14	x.	x.	PROPN
ejpam-5536	257	15	a.	a.	PROPN
ejpam-5536	257	16	iampan	iampan	PROPN
ejpam-5536	257	17	et	et	PROPN
ejpam-5536	257	18	al	al	PROPN
ejpam-5536	257	19	.	.	PUNCT
ejpam-5536	257	20	/	/	SYM
ejpam-5536	257	21	eur	eur	PROPN
ejpam-5536	257	22	.	.	PUNCT
ejpam-5536	258	1	j.	j.	PROPN
ejpam-5536	258	2	pure	pure	PROPN
ejpam-5536	258	3	appl	appl	PROPN
ejpam-5536	258	4	.	.	PROPN
ejpam-5536	258	5	math	math	PROPN
ejpam-5536	258	6	,	,	PUNCT
ejpam-5536	258	7	17	17	NUM
ejpam-5536	258	8	(	(	PUNCT
ejpam-5536	258	9	4	4	NUM
ejpam-5536	258	10	)	)	PUNCT
ejpam-5536	258	11	(	(	PUNCT
ejpam-5536	258	12	2024	2024	NUM
ejpam-5536	258	13	)	)	PUNCT
ejpam-5536	258	14	,	,	PUNCT
ejpam-5536	258	15	4059	4059	NUM
ejpam-5536	258	16	-	-	SYM
ejpam-5536	258	17	4070	4070	NUM
ejpam-5536	258	18	4068	4068	NUM
ejpam-5536	258	19	conversely	conversely	ADV
ejpam-5536	258	20	,	,	PUNCT
ejpam-5536	258	21	assume	assume	VERB
ejpam-5536	258	22	that	that	SCONJ
ejpam-5536	258	23	for	for	ADP
ejpam-5536	258	24	all	all	DET
ejpam-5536	258	25	(	(	PUNCT
ejpam-5536	258	26	t+	t+	NOUN
ejpam-5536	258	27	,	,	PUNCT
ejpam-5536	258	28	t−	t−	ADJ
ejpam-5536	258	29	)	)	PUNCT
ejpam-5536	258	30	∈	∈	PROPN
ejpam-5536	259	1	[	[	X
ejpam-5536	259	2	0	0	NUM
ejpam-5536	259	3	,	,	PUNCT
ejpam-5536	259	4	1]×	1]×	NUM
ejpam-5536	259	5	[	[	X
ejpam-5536	259	6	−1	−1	NOUN
ejpam-5536	259	7	,	,	PUNCT
ejpam-5536	259	8	0	0	NUM
ejpam-5536	259	9	]	]	PUNCT
ejpam-5536	259	10	,	,	PUNCT
ejpam-5536	259	11	pl(φ	pl(φ	NOUN
ejpam-5536	259	12	,	,	PUNCT
ejpam-5536	259	13	t	t	PROPN
ejpam-5536	259	14	+	+	NOUN
ejpam-5536	259	15	)	)	PUNCT
ejpam-5536	259	16	and	and	CCONJ
ejpam-5536	259	17	nu	nu	INTJ
ejpam-5536	259	18	(	(	PUNCT
ejpam-5536	259	19	φ	φ	PROPN
ejpam-5536	259	20	,	,	PUNCT
ejpam-5536	259	21	t	t	PROPN
ejpam-5536	259	22	−	−	PROPN
ejpam-5536	259	23	)	)	PUNCT
ejpam-5536	259	24	are	be	AUX
ejpam-5536	259	25	subalgebras	subalgebra	NOUN
ejpam-5536	259	26	of	of	ADP
ejpam-5536	259	27	x	x	PRON
ejpam-5536	259	28	if	if	SCONJ
ejpam-5536	259	29	pl(φ	pl(φ	NOUN
ejpam-5536	259	30	,	,	PUNCT
ejpam-5536	259	31	t	t	PROPN
ejpam-5536	259	32	+	+	NOUN
ejpam-5536	259	33	)	)	PUNCT
ejpam-5536	259	34	and	and	CCONJ
ejpam-5536	259	35	nu	nu	INTJ
ejpam-5536	259	36	(	(	PUNCT
ejpam-5536	259	37	φ	φ	PROPN
ejpam-5536	259	38	,	,	PUNCT
ejpam-5536	259	39	t	t	PROPN
ejpam-5536	259	40	−	−	PROPN
ejpam-5536	259	41	)	)	PUNCT
ejpam-5536	259	42	are	be	AUX
ejpam-5536	259	43	nonempty	nonempty	ADJ
ejpam-5536	259	44	.	.	PUNCT
ejpam-5536	260	1	let	let	VERB
ejpam-5536	260	2	x	x	PRON
ejpam-5536	260	3	,	,	PUNCT
ejpam-5536	260	4	y	y	PROPN
ejpam-5536	260	5	∈	∈	PROPN
ejpam-5536	260	6	x.	x.	NOUN
ejpam-5536	260	7	then	then	ADV
ejpam-5536	260	8	φ+(x	φ+(x	NUM
ejpam-5536	260	9	)	)	PUNCT
ejpam-5536	260	10	,	,	PUNCT
ejpam-5536	260	11	φ+(y	φ+(y	CCONJ
ejpam-5536	260	12	)	)	PUNCT
ejpam-5536	260	13	∈	∈	PROPN
ejpam-5536	261	1	[	[	X
ejpam-5536	261	2	0	0	NUM
ejpam-5536	261	3	,	,	PUNCT
ejpam-5536	261	4	1	1	NUM
ejpam-5536	261	5	]	]	PUNCT
ejpam-5536	261	6	.	.	PUNCT
ejpam-5536	262	1	choose	choose	VERB
ejpam-5536	262	2	t+	t+	NOUN
ejpam-5536	262	3	=	=	PROPN
ejpam-5536	262	4	max{φ+(x	max{φ+(x	PROPN
ejpam-5536	262	5	)	)	PUNCT
ejpam-5536	262	6	,	,	PUNCT
ejpam-5536	262	7	φ+(y	φ+(y	PUNCT
ejpam-5536	262	8	)	)	PUNCT
ejpam-5536	262	9	}	}	PUNCT
ejpam-5536	262	10	.	.	PUNCT
ejpam-5536	263	1	thus	thus	ADV
ejpam-5536	263	2	,	,	PUNCT
ejpam-5536	263	3	φ+(x	φ+(x	NOUN
ejpam-5536	263	4	)	)	PUNCT
ejpam-5536	263	5	≤	≤	NOUN
ejpam-5536	263	6	t+	t+	PUNCT
ejpam-5536	263	7	and	and	CCONJ
ejpam-5536	263	8	φ+(y	φ+(y	SYM
ejpam-5536	263	9	)	)	PUNCT
ejpam-5536	263	10	≤	≤	NOUN
ejpam-5536	263	11	t+	t+	PUNCT
ejpam-5536	263	12	,	,	PUNCT
ejpam-5536	263	13	so	so	SCONJ
ejpam-5536	263	14	x	x	SYM
ejpam-5536	263	15	,	,	PUNCT
ejpam-5536	263	16	y	y	PROPN
ejpam-5536	263	17	∈	∈	PROPN
ejpam-5536	263	18	pl(φ	pl(φ	NOUN
ejpam-5536	263	19	,	,	PUNCT
ejpam-5536	263	20	t	t	PROPN
ejpam-5536	263	21	+	+	NOUN
ejpam-5536	263	22	)	)	PUNCT
ejpam-5536	263	23	̸=	̸=	PROPN
ejpam-5536	263	24	∅.	∅.	NOUN
ejpam-5536	263	25	by	by	ADP
ejpam-5536	263	26	the	the	DET
ejpam-5536	263	27	assumption	assumption	NOUN
ejpam-5536	263	28	,	,	PUNCT
ejpam-5536	263	29	we	we	PRON
ejpam-5536	263	30	have	have	VERB
ejpam-5536	263	31	pl(φ	pl(φ	NOUN
ejpam-5536	263	32	,	,	PUNCT
ejpam-5536	263	33	t	t	PROPN
ejpam-5536	264	1	+	+	CCONJ
ejpam-5536	264	2	)	)	PUNCT
ejpam-5536	264	3	is	be	AUX
ejpam-5536	264	4	a	a	DET
ejpam-5536	264	5	subalgebra	subalgebra	NOUN
ejpam-5536	264	6	of	of	ADP
ejpam-5536	264	7	x	x	PUNCT
ejpam-5536	264	8	and	and	CCONJ
ejpam-5536	264	9	so	so	ADV
ejpam-5536	264	10	x	x	SYM
ejpam-5536	264	11	·	·	PUNCT
ejpam-5536	264	12	y	y	PROPN
ejpam-5536	264	13	∈	∈	PROPN
ejpam-5536	264	14	pl(φ	pl(φ	NOUN
ejpam-5536	264	15	,	,	PUNCT
ejpam-5536	264	16	t	t	PROPN
ejpam-5536	264	17	+	+	NOUN
ejpam-5536	264	18	)	)	PUNCT
ejpam-5536	264	19	.	.	PUNCT
ejpam-5536	265	1	thus	thus	ADV
ejpam-5536	265	2	,	,	PUNCT
ejpam-5536	265	3	φ+(x	φ+(x	X
ejpam-5536	265	4	·	·	PUNCT
ejpam-5536	265	5	y	y	X
ejpam-5536	265	6	)	)	PUNCT
ejpam-5536	265	7	≤	≤	NOUN
ejpam-5536	265	8	t+	t+	X
ejpam-5536	265	9	=	=	SYM
ejpam-5536	265	10	max{φ+(x	max{φ+(x	PROPN
ejpam-5536	265	11	)	)	PUNCT
ejpam-5536	265	12	,	,	PUNCT
ejpam-5536	265	13	φ+(y	φ+(y	PUNCT
ejpam-5536	265	14	)	)	PUNCT
ejpam-5536	265	15	}	}	PUNCT
ejpam-5536	265	16	.	.	PUNCT
ejpam-5536	266	1	so	so	ADV
ejpam-5536	266	2	,	,	PUNCT
ejpam-5536	266	3	φ+(x	φ+(x	X
ejpam-5536	266	4	·	·	PUNCT
ejpam-5536	266	5	y	y	X
ejpam-5536	266	6	)	)	PUNCT
ejpam-5536	266	7	=	=	SYM
ejpam-5536	266	8	1−	1−	NUM
ejpam-5536	266	9	φ+(x	φ+(x	X
ejpam-5536	266	10	·	·	PUNCT
ejpam-5536	266	11	y	y	X
ejpam-5536	266	12	)	)	PUNCT
ejpam-5536	266	13	≥	≥	NOUN
ejpam-5536	266	14	1−max{φ+(x	1−max{φ+(x	NUM
ejpam-5536	266	15	)	)	PUNCT
ejpam-5536	266	16	,	,	PUNCT
ejpam-5536	266	17	φ+(y	φ+(y	CCONJ
ejpam-5536	266	18	)	)	PUNCT
ejpam-5536	266	19	}	}	PUNCT
ejpam-5536	266	20	=	=	SYM
ejpam-5536	266	21	min{1−	min{1−	VERB
ejpam-5536	266	22	φ+(x	φ+(x	NOUN
ejpam-5536	266	23	)	)	PUNCT
ejpam-5536	266	24	,	,	PUNCT
ejpam-5536	266	25	1−	1−	NUM
ejpam-5536	266	26	φ+(y	φ+(y	NOUN
ejpam-5536	266	27	)	)	PUNCT
ejpam-5536	266	28	}	}	PUNCT
ejpam-5536	266	29	=	=	SYM
ejpam-5536	266	30	min{φ+(x	min{φ+(x	PROPN
ejpam-5536	266	31	)	)	PUNCT
ejpam-5536	266	32	,	,	PUNCT
ejpam-5536	266	33	φ+(y	φ+(y	PUNCT
ejpam-5536	266	34	)	)	PUNCT
ejpam-5536	266	35	}	}	PUNCT
ejpam-5536	266	36	.	.	PUNCT
ejpam-5536	267	1	let	let	VERB
ejpam-5536	267	2	x	x	PRON
ejpam-5536	267	3	,	,	PUNCT
ejpam-5536	267	4	y	y	PROPN
ejpam-5536	267	5	∈	∈	PROPN
ejpam-5536	267	6	x.	x.	NOUN
ejpam-5536	267	7	then	then	ADV
ejpam-5536	267	8	φ−(x	φ−(x	PROPN
ejpam-5536	267	9	)	)	PUNCT
ejpam-5536	267	10	,	,	PUNCT
ejpam-5536	268	1	φ−(y	φ−(y	PROPN
ejpam-5536	268	2	)	)	PUNCT
ejpam-5536	268	3	∈	∈	PROPN
ejpam-5536	269	1	[	[	X
ejpam-5536	269	2	−1	−1	NOUN
ejpam-5536	269	3	,	,	PUNCT
ejpam-5536	269	4	0	0	NUM
ejpam-5536	269	5	]	]	PUNCT
ejpam-5536	269	6	.	.	PUNCT
ejpam-5536	270	1	choose	choose	VERB
ejpam-5536	270	2	t−	t−	PROPN
ejpam-5536	270	3	=	=	PUNCT
ejpam-5536	270	4	min{φ−(x	min{φ−(x	PROPN
ejpam-5536	270	5	)	)	PUNCT
ejpam-5536	270	6	,	,	PUNCT
ejpam-5536	270	7	φ−(y	φ−(y	PROPN
ejpam-5536	270	8	)	)	PUNCT
ejpam-5536	270	9	}	}	PUNCT
ejpam-5536	270	10	.	.	PUNCT
ejpam-5536	271	1	thus	thus	ADV
ejpam-5536	271	2	,	,	PUNCT
ejpam-5536	271	3	φ−(x	φ−(x	PROPN
ejpam-5536	271	4	)	)	PUNCT
ejpam-5536	271	5	≥	≥	NOUN
ejpam-5536	271	6	t−	t−	PROPN
ejpam-5536	271	7	and	and	CCONJ
ejpam-5536	271	8	φ−(y	φ−(y	PROPN
ejpam-5536	271	9	)	)	PUNCT
ejpam-5536	271	10	≥	≥	NOUN
ejpam-5536	271	11	t−	t−	PROPN
ejpam-5536	271	12	,	,	PUNCT
ejpam-5536	271	13	so	so	SCONJ
ejpam-5536	271	14	x	x	X
ejpam-5536	271	15	,	,	PUNCT
ejpam-5536	271	16	y	y	PROPN
ejpam-5536	271	17	∈	∈	PROPN
ejpam-5536	271	18	nu	nu	PROPN
ejpam-5536	271	19	(	(	PUNCT
ejpam-5536	271	20	φ	φ	PROPN
ejpam-5536	271	21	,	,	PUNCT
ejpam-5536	271	22	t	t	PROPN
ejpam-5536	271	23	−	−	NOUN
ejpam-5536	271	24	)	)	PUNCT
ejpam-5536	271	25	̸=	̸=	PROPN
ejpam-5536	271	26	∅.	∅.	NOUN
ejpam-5536	271	27	by	by	ADP
ejpam-5536	271	28	the	the	DET
ejpam-5536	271	29	assumption	assumption	NOUN
ejpam-5536	271	30	,	,	PUNCT
ejpam-5536	271	31	we	we	PRON
ejpam-5536	271	32	have	have	VERB
ejpam-5536	271	33	nu	nu	PROPN
ejpam-5536	271	34	(	(	PUNCT
ejpam-5536	271	35	φ	φ	PROPN
ejpam-5536	271	36	,	,	PUNCT
ejpam-5536	271	37	t	t	PROPN
ejpam-5536	271	38	−	−	PROPN
ejpam-5536	271	39	)	)	PUNCT
ejpam-5536	271	40	is	be	AUX
ejpam-5536	271	41	a	a	DET
ejpam-5536	271	42	subalgebra	subalgebra	NOUN
ejpam-5536	271	43	of	of	ADP
ejpam-5536	271	44	x	x	PUNCT
ejpam-5536	271	45	and	and	CCONJ
ejpam-5536	271	46	so	so	ADV
ejpam-5536	271	47	x	x	SYM
ejpam-5536	271	48	·	·	PUNCT
ejpam-5536	271	49	y	y	PROPN
ejpam-5536	271	50	∈	∈	PROPN
ejpam-5536	271	51	nu	nu	PROPN
ejpam-5536	271	52	(	(	PUNCT
ejpam-5536	271	53	φ	φ	PROPN
ejpam-5536	271	54	,	,	PUNCT
ejpam-5536	271	55	t	t	PROPN
ejpam-5536	271	56	−	−	NUM
ejpam-5536	271	57	)	)	PUNCT
ejpam-5536	271	58	.	.	PUNCT
ejpam-5536	272	1	thus	thus	ADV
ejpam-5536	272	2	,	,	PUNCT
ejpam-5536	272	3	φ−(x	φ−(x	PROPN
ejpam-5536	272	4	·	·	PUNCT
ejpam-5536	272	5	y	y	X
ejpam-5536	272	6	)	)	PUNCT
ejpam-5536	272	7	≥	≥	NOUN
ejpam-5536	272	8	t−	t−	PROPN
ejpam-5536	272	9	=	=	SYM
ejpam-5536	272	10	min{φ−(x	min{φ−(x	PROPN
ejpam-5536	272	11	)	)	PUNCT
ejpam-5536	272	12	,	,	PUNCT
ejpam-5536	272	13	φ−(y	φ−(y	PROPN
ejpam-5536	272	14	)	)	PUNCT
ejpam-5536	272	15	}	}	PUNCT
ejpam-5536	272	16	.	.	PUNCT
ejpam-5536	273	1	so	so	ADV
ejpam-5536	273	2	,	,	PUNCT
ejpam-5536	273	3	φ−(x	φ−(x	PROPN
ejpam-5536	273	4	·	·	PUNCT
ejpam-5536	273	5	y	y	X
ejpam-5536	273	6	)	)	PUNCT
ejpam-5536	273	7	=	=	PUNCT
ejpam-5536	274	1	−1−	−1−	PROPN
ejpam-5536	274	2	φ−(x	φ−(x	PROPN
ejpam-5536	274	3	·	·	PUNCT
ejpam-5536	274	4	y	y	X
ejpam-5536	274	5	)	)	PUNCT
ejpam-5536	274	6	≤	≤	NOUN
ejpam-5536	274	7	−1−min{φ−	−1−min{φ−	PROPN
ejpam-5536	274	8	(	(	PUNCT
ejpam-5536	274	9	x	x	NOUN
ejpam-5536	274	10	)	)	PUNCT
ejpam-5536	274	11	,	,	PUNCT
ejpam-5536	274	12	φ−(y	φ−(y	PROPN
ejpam-5536	274	13	)	)	PUNCT
ejpam-5536	274	14	}	}	PUNCT
ejpam-5536	275	1	=	=	SYM
ejpam-5536	275	2	max{−1−	max{−1−	NOUN
ejpam-5536	275	3	φ−(x),−1−	φ−(x),−1−	NOUN
ejpam-5536	275	4	φ−(y	φ−(y	NOUN
ejpam-5536	275	5	)	)	PUNCT
ejpam-5536	275	6	}	}	PUNCT
ejpam-5536	275	7	=	=	SYM
ejpam-5536	275	8	max{φ−(x	max{φ−(x	PROPN
ejpam-5536	275	9	)	)	PUNCT
ejpam-5536	275	10	,	,	PUNCT
ejpam-5536	275	11	φ−(y	φ−(y	PROPN
ejpam-5536	275	12	)	)	PUNCT
ejpam-5536	275	13	}	}	PUNCT
ejpam-5536	275	14	.	.	PUNCT
ejpam-5536	276	1	hence	hence	ADV
ejpam-5536	276	2	,	,	PUNCT
ejpam-5536	276	3	φ	φ	PROPN
ejpam-5536	276	4	=	=	SYM
ejpam-5536	276	5	(	(	PUNCT
ejpam-5536	276	6	φ+	φ+	NOUN
ejpam-5536	276	7	,	,	PUNCT
ejpam-5536	276	8	φ−	φ−	PROPN
ejpam-5536	276	9	)	)	PUNCT
ejpam-5536	276	10	is	be	AUX
ejpam-5536	276	11	a	a	DET
ejpam-5536	276	12	bipolar	bipolar	ADJ
ejpam-5536	276	13	fuzzy	fuzzy	ADJ
ejpam-5536	276	14	subalgebra	subalgebra	NOUN
ejpam-5536	276	15	of	of	ADP
ejpam-5536	276	16	x.	x.	PROPN
ejpam-5536	276	17	theorem	theorem	VERB
ejpam-5536	276	18	10	10	NUM
ejpam-5536	276	19	.	.	PUNCT
ejpam-5536	277	1	let	let	VERB
ejpam-5536	277	2	φ	φ	PROPN
ejpam-5536	277	3	=	=	SYM
ejpam-5536	277	4	(	(	PUNCT
ejpam-5536	277	5	φ+	φ+	PROPN
ejpam-5536	277	6	,	,	PUNCT
ejpam-5536	277	7	φ−	φ−	PROPN
ejpam-5536	277	8	)	)	PUNCT
ejpam-5536	277	9	be	be	VERB
ejpam-5536	277	10	a	a	DET
ejpam-5536	277	11	bfs	bfs	NOUN
ejpam-5536	277	12	in	in	ADP
ejpam-5536	277	13	a	a	DET
ejpam-5536	277	14	hilbert	hilbert	NOUN
ejpam-5536	277	15	algebra	algebra	NOUN
ejpam-5536	277	16	x	x	PUNCT
ejpam-5536	277	17	=	=	SYM
ejpam-5536	277	18	(	(	PUNCT
ejpam-5536	277	19	x	x	NOUN
ejpam-5536	277	20	,	,	PUNCT
ejpam-5536	277	21	·	·	PUNCT
ejpam-5536	277	22	,	,	PUNCT
ejpam-5536	277	23	1x	1x	NUM
ejpam-5536	277	24	)	)	PUNCT
ejpam-5536	277	25	.	.	PUNCT
ejpam-5536	278	1	then	then	ADV
ejpam-5536	278	2	φ	φ	PROPN
ejpam-5536	278	3	=	=	SYM
ejpam-5536	278	4	(	(	PUNCT
ejpam-5536	278	5	φ+	φ+	NOUN
ejpam-5536	278	6	,	,	PUNCT
ejpam-5536	278	7	φ−	φ−	PROPN
ejpam-5536	278	8	)	)	PUNCT
ejpam-5536	278	9	is	be	AUX
ejpam-5536	278	10	a	a	DET
ejpam-5536	278	11	bipolar	bipolar	ADJ
ejpam-5536	278	12	fuzzy	fuzzy	ADJ
ejpam-5536	278	13	ideal	ideal	NOUN
ejpam-5536	278	14	(	(	PUNCT
ejpam-5536	278	15	resp	resp	NOUN
ejpam-5536	278	16	.	.	PUNCT
ejpam-5536	278	17	,	,	PUNCT
ejpam-5536	278	18	deductive	deductive	ADJ
ejpam-5536	278	19	system	system	NOUN
ejpam-5536	278	20	)	)	PUNCT
ejpam-5536	278	21	of	of	ADP
ejpam-5536	278	22	x	x	PRON
ejpam-5536	278	23	if	if	SCONJ
ejpam-5536	278	24	and	and	CCONJ
ejpam-5536	278	25	only	only	ADV
ejpam-5536	278	26	if	if	SCONJ
ejpam-5536	278	27	for	for	ADP
ejpam-5536	278	28	all	all	DET
ejpam-5536	278	29	(	(	PUNCT
ejpam-5536	278	30	t+	t+	NOUN
ejpam-5536	278	31	,	,	PUNCT
ejpam-5536	278	32	t−	t−	ADJ
ejpam-5536	278	33	)	)	PUNCT
ejpam-5536	278	34	∈	∈	PROPN
ejpam-5536	279	1	[	[	X
ejpam-5536	279	2	0	0	NUM
ejpam-5536	279	3	,	,	PUNCT
ejpam-5536	279	4	1]×	1]×	NUM
ejpam-5536	279	5	[	[	X
ejpam-5536	279	6	−1	−1	NOUN
ejpam-5536	279	7	,	,	PUNCT
ejpam-5536	279	8	0	0	NUM
ejpam-5536	279	9	]	]	PUNCT
ejpam-5536	279	10	,	,	PUNCT
ejpam-5536	279	11	pl(φ	pl(φ	NOUN
ejpam-5536	279	12	,	,	PUNCT
ejpam-5536	279	13	t	t	PROPN
ejpam-5536	279	14	+	+	NOUN
ejpam-5536	279	15	)	)	PUNCT
ejpam-5536	279	16	and	and	CCONJ
ejpam-5536	279	17	nu	nu	INTJ
ejpam-5536	279	18	(	(	PUNCT
ejpam-5536	279	19	φ	φ	PROPN
ejpam-5536	279	20	,	,	PUNCT
ejpam-5536	279	21	t	t	PROPN
ejpam-5536	279	22	−	−	PROPN
ejpam-5536	279	23	)	)	PUNCT
ejpam-5536	279	24	are	be	AUX
ejpam-5536	279	25	ideals	ideal	NOUN
ejpam-5536	279	26	(	(	PUNCT
ejpam-5536	279	27	resp	resp	NOUN
ejpam-5536	279	28	.	.	PUNCT
ejpam-5536	279	29	,	,	PUNCT
ejpam-5536	279	30	deductive	deductive	ADJ
ejpam-5536	279	31	systems	system	NOUN
ejpam-5536	279	32	)	)	PUNCT
ejpam-5536	279	33	of	of	ADP
ejpam-5536	279	34	x	x	PRON
ejpam-5536	279	35	if	if	SCONJ
ejpam-5536	279	36	pl(φ	pl(φ	NOUN
ejpam-5536	279	37	,	,	PUNCT
ejpam-5536	279	38	t	t	PROPN
ejpam-5536	279	39	+	+	NOUN
ejpam-5536	279	40	)	)	PUNCT
ejpam-5536	279	41	and	and	CCONJ
ejpam-5536	279	42	nu	nu	INTJ
ejpam-5536	279	43	(	(	PUNCT
ejpam-5536	279	44	φ	φ	PROPN
ejpam-5536	279	45	,	,	PUNCT
ejpam-5536	279	46	t	t	PROPN
ejpam-5536	279	47	−	−	PROPN
ejpam-5536	279	48	)	)	PUNCT
ejpam-5536	279	49	are	be	AUX
ejpam-5536	279	50	nonempty	nonempty	ADJ
ejpam-5536	279	51	.	.	PUNCT
ejpam-5536	280	1	proof	proof	NOUN
ejpam-5536	280	2	.	.	PUNCT
ejpam-5536	281	1	the	the	DET
ejpam-5536	281	2	proof	proof	NOUN
ejpam-5536	281	3	is	be	AUX
ejpam-5536	281	4	similar	similar	ADJ
ejpam-5536	281	5	to	to	ADP
ejpam-5536	281	6	theorem	theorem	VERB
ejpam-5536	281	7	9	9	NUM
ejpam-5536	281	8	.	.	NOUN
ejpam-5536	281	9	4	4	NUM
ejpam-5536	281	10	.	.	X
ejpam-5536	281	11	conclusion	conclusion	NOUN
ejpam-5536	281	12	this	this	DET
ejpam-5536	281	13	study	study	NOUN
ejpam-5536	281	14	has	have	AUX
ejpam-5536	281	15	advanced	advance	VERB
ejpam-5536	281	16	the	the	DET
ejpam-5536	281	17	application	application	NOUN
ejpam-5536	281	18	of	of	ADP
ejpam-5536	281	19	bfs	bfs	NOUN
ejpam-5536	281	20	theory	theory	NOUN
ejpam-5536	281	21	within	within	ADP
ejpam-5536	281	22	hilbert	hilbert	PROPN
ejpam-5536	281	23	algebras	algebras	PROPN
ejpam-5536	281	24	by	by	ADP
ejpam-5536	281	25	introducing	introduce	VERB
ejpam-5536	281	26	and	and	CCONJ
ejpam-5536	281	27	rigorously	rigorously	ADV
ejpam-5536	281	28	analyzing	analyze	VERB
ejpam-5536	281	29	bipolar	bipolar	ADJ
ejpam-5536	281	30	fuzzy	fuzzy	ADJ
ejpam-5536	281	31	(	(	PUNCT
ejpam-5536	281	32	β	β	X
ejpam-5536	281	33	,	,	PUNCT
ejpam-5536	281	34	α)-translations	α)-translation	NOUN
ejpam-5536	281	35	of	of	ADP
ejpam-5536	281	36	a	a	DET
ejpam-5536	281	37	bfs	bfs	NOUN
ejpam-5536	281	38	φ	φ	NOUN
ejpam-5536	281	39	=	=	SYM
ejpam-5536	281	40	(	(	PUNCT
ejpam-5536	281	41	φ+	φ+	NOUN
ejpam-5536	281	42	,	,	PUNCT
ejpam-5536	281	43	φ−	φ−	PROPN
ejpam-5536	281	44	)	)	PUNCT
ejpam-5536	281	45	in	in	ADP
ejpam-5536	281	46	two	two	NUM
ejpam-5536	281	47	distinct	distinct	ADJ
ejpam-5536	281	48	forms	form	NOUN
ejpam-5536	281	49	:	:	PUNCT
ejpam-5536	281	50	type	type	NOUN
ejpam-5536	281	51	i	i	PRON
ejpam-5536	281	52	and	and	CCONJ
ejpam-5536	281	53	type	type	PROPN
ejpam-5536	281	54	ii	ii	PROPN
ejpam-5536	281	55	.	.	PUNCT
ejpam-5536	282	1	the	the	DET
ejpam-5536	282	2	in	in	ADP
ejpam-5536	282	3	-	-	PUNCT
ejpam-5536	282	4	depth	depth	NOUN
ejpam-5536	282	5	investigation	investigation	NOUN
ejpam-5536	282	6	of	of	ADP
ejpam-5536	282	7	the	the	DET
ejpam-5536	282	8	fundamental	fundamental	ADJ
ejpam-5536	282	9	properties	property	NOUN
ejpam-5536	282	10	of	of	ADP
ejpam-5536	282	11	these	these	DET
ejpam-5536	282	12	translations	translation	NOUN
ejpam-5536	282	13	,	,	PUNCT
ejpam-5536	282	14	along	along	ADP
ejpam-5536	282	15	with	with	ADP
ejpam-5536	282	16	the	the	DET
ejpam-5536	282	17	development	development	NOUN
ejpam-5536	282	18	of	of	ADP
ejpam-5536	282	19	bipolar	bipolar	ADJ
ejpam-5536	282	20	fuzzy	fuzzy	ADJ
ejpam-5536	282	21	extensions	extension	NOUN
ejpam-5536	282	22	and	and	CCONJ
ejpam-5536	282	23	intensities	intensity	NOUN
ejpam-5536	282	24	,	,	PUNCT
ejpam-5536	282	25	has	have	AUX
ejpam-5536	282	26	broadened	broaden	VERB
ejpam-5536	282	27	the	the	DET
ejpam-5536	282	28	theoretical	theoretical	ADJ
ejpam-5536	282	29	and	and	CCONJ
ejpam-5536	282	30	practical	practical	ADJ
ejpam-5536	282	31	utility	utility	NOUN
ejpam-5536	282	32	of	of	ADP
ejpam-5536	282	33	bfss	bfss	NOUN
ejpam-5536	282	34	in	in	ADP
ejpam-5536	282	35	capturing	capture	VERB
ejpam-5536	282	36	complex	complex	ADJ
ejpam-5536	282	37	bipolar	bipolar	ADJ
ejpam-5536	282	38	information	information	NOUN
ejpam-5536	282	39	.	.	PUNCT
ejpam-5536	283	1	further	far	ADV
ejpam-5536	283	2	,	,	PUNCT
ejpam-5536	283	3	the	the	DET
ejpam-5536	283	4	study	study	NOUN
ejpam-5536	283	5	elucidates	elucidate	VERB
ejpam-5536	283	6	intricate	intricate	ADJ
ejpam-5536	283	7	relationships	relationship	NOUN
ejpam-5536	283	8	among	among	ADP
ejpam-5536	283	9	the	the	DET
ejpam-5536	283	10	complement	complement	NOUN
ejpam-5536	283	11	of	of	ADP
ejpam-5536	283	12	a	a	DET
ejpam-5536	283	13	bipolar	bipolar	ADJ
ejpam-5536	283	14	fuzzy	fuzzy	ADJ
ejpam-5536	283	15	subalgebra	subalgebra	NOUN
ejpam-5536	283	16	,	,	PUNCT
ejpam-5536	283	17	bipolar	bipolar	ADJ
ejpam-5536	283	18	fuzzy	fuzzy	ADJ
ejpam-5536	283	19	ideals	ideal	NOUN
ejpam-5536	283	20	,	,	PUNCT
ejpam-5536	283	21	and	and	CCONJ
ejpam-5536	283	22	bipolar	bipolar	ADJ
ejpam-5536	283	23	fuzzy	fuzzy	ADJ
ejpam-5536	283	24	deductive	deductive	ADJ
ejpam-5536	283	25	systems	system	NOUN
ejpam-5536	283	26	through	through	ADP
ejpam-5536	283	27	their	their	PRON
ejpam-5536	283	28	level	level	NOUN
ejpam-5536	283	29	cuts	cut	NOUN
ejpam-5536	283	30	,	,	PUNCT
ejpam-5536	283	31	offering	offer	VERB
ejpam-5536	283	32	a	a	DET
ejpam-5536	283	33	deeper	deep	ADJ
ejpam-5536	283	34	structural	structural	ADJ
ejpam-5536	283	35	understanding	understanding	NOUN
ejpam-5536	283	36	of	of	ADP
ejpam-5536	283	37	hilbert	hilbert	PROPN
ejpam-5536	283	38	algebras	algebras	PROPN
ejpam-5536	283	39	under	under	ADP
ejpam-5536	283	40	bipolar	bipolar	ADJ
ejpam-5536	283	41	fuzzy	fuzzy	ADJ
ejpam-5536	283	42	logic	logic	NOUN
ejpam-5536	283	43	.	.	PUNCT
ejpam-5536	284	1	these	these	DET
ejpam-5536	284	2	findings	finding	NOUN
ejpam-5536	284	3	contribute	contribute	VERB
ejpam-5536	284	4	significantly	significantly	ADV
ejpam-5536	284	5	to	to	ADP
ejpam-5536	284	6	the	the	DET
ejpam-5536	284	7	references	reference	NOUN
ejpam-5536	284	8	4069	4069	NUM
ejpam-5536	284	9	theoretical	theoretical	ADJ
ejpam-5536	284	10	framework	framework	NOUN
ejpam-5536	284	11	supporting	support	VERB
ejpam-5536	284	12	bipolar	bipolar	ADJ
ejpam-5536	284	13	fuzzy	fuzzy	ADJ
ejpam-5536	284	14	systems	system	NOUN
ejpam-5536	284	15	,	,	PUNCT
ejpam-5536	284	16	which	which	PRON
ejpam-5536	284	17	hold	hold	VERB
ejpam-5536	284	18	promise	promise	NOUN
ejpam-5536	284	19	for	for	ADP
ejpam-5536	284	20	handling	handle	VERB
ejpam-5536	284	21	nuanced	nuanced	ADJ
ejpam-5536	284	22	and	and	CCONJ
ejpam-5536	284	23	uncertain	uncertain	ADJ
ejpam-5536	284	24	information	information	NOUN
ejpam-5536	284	25	across	across	ADP
ejpam-5536	284	26	diverse	diverse	ADJ
ejpam-5536	284	27	applications	application	NOUN
ejpam-5536	284	28	.	.	PUNCT
ejpam-5536	285	1	building	build	VERB
ejpam-5536	285	2	on	on	ADP
ejpam-5536	285	3	this	this	DET
ejpam-5536	285	4	work	work	NOUN
ejpam-5536	285	5	,	,	PUNCT
ejpam-5536	285	6	future	future	ADJ
ejpam-5536	285	7	research	research	NOUN
ejpam-5536	285	8	can	can	AUX
ejpam-5536	285	9	explore	explore	VERB
ejpam-5536	285	10	the	the	DET
ejpam-5536	285	11	extended	extended	ADJ
ejpam-5536	285	12	use	use	NOUN
ejpam-5536	285	13	of	of	ADP
ejpam-5536	285	14	bfss	bfss	NOUN
ejpam-5536	285	15	within	within	ADP
ejpam-5536	285	16	complex	complex	ADJ
ejpam-5536	285	17	structures	structure	NOUN
ejpam-5536	285	18	such	such	ADJ
ejpam-5536	285	19	as	as	ADP
ejpam-5536	285	20	bipolar	bipolar	ADJ
ejpam-5536	285	21	complex	complex	ADJ
ejpam-5536	285	22	fuzzy	fuzzy	ADJ
ejpam-5536	285	23	subgroups	subgroup	NOUN
ejpam-5536	285	24	and	and	CCONJ
ejpam-5536	285	25	semigroups	semigroup	NOUN
ejpam-5536	285	26	,	,	PUNCT
ejpam-5536	285	27	as	as	SCONJ
ejpam-5536	285	28	demonstrated	demonstrate	VERB
ejpam-5536	285	29	in	in	ADP
ejpam-5536	285	30	[	[	X
ejpam-5536	285	31	1	1	NUM
ejpam-5536	285	32	,	,	PUNCT
ejpam-5536	285	33	14–16	14–16	NUM
ejpam-5536	285	34	,	,	PUNCT
ejpam-5536	285	35	18	18	NUM
ejpam-5536	285	36	]	]	PUNCT
ejpam-5536	285	37	.	.	PUNCT
ejpam-5536	286	1	these	these	DET
ejpam-5536	286	2	directions	direction	NOUN
ejpam-5536	286	3	will	will	AUX
ejpam-5536	286	4	likely	likely	ADV
ejpam-5536	286	5	open	open	VERB
ejpam-5536	286	6	new	new	ADJ
ejpam-5536	286	7	pathways	pathway	NOUN
ejpam-5536	286	8	in	in	ADP
ejpam-5536	286	9	the	the	DET
ejpam-5536	286	10	algebraic	algebraic	ADJ
ejpam-5536	286	11	modeling	modeling	NOUN
ejpam-5536	286	12	of	of	ADP
ejpam-5536	286	13	systems	system	NOUN
ejpam-5536	286	14	characterized	characterize	VERB
ejpam-5536	286	15	by	by	ADP
ejpam-5536	286	16	multifaceted	multifaceted	ADJ
ejpam-5536	286	17	uncertainties	uncertainty	NOUN
ejpam-5536	286	18	,	,	PUNCT
ejpam-5536	286	19	further	far	ADV
ejpam-5536	286	20	enriching	enrich	VERB
ejpam-5536	286	21	the	the	DET
ejpam-5536	286	22	versatility	versatility	NOUN
ejpam-5536	286	23	of	of	ADP
ejpam-5536	286	24	bipolar	bipolar	ADJ
ejpam-5536	286	25	fuzzy	fuzzy	ADJ
ejpam-5536	286	26	logic	logic	NOUN
ejpam-5536	286	27	in	in	ADP
ejpam-5536	286	28	advanced	advanced	ADJ
ejpam-5536	286	29	mathematical	mathematical	ADJ
ejpam-5536	286	30	and	and	CCONJ
ejpam-5536	286	31	applied	applied	ADJ
ejpam-5536	286	32	contexts	contexts	NOUN
ejpam-5536	286	33	.	.	PUNCT
ejpam-5536	287	1	acknowledgements	acknowledgement	NOUN
ejpam-5536	287	2	this	this	DET
ejpam-5536	287	3	research	research	NOUN
ejpam-5536	287	4	was	be	AUX
ejpam-5536	287	5	supported	support	VERB
ejpam-5536	287	6	by	by	ADP
ejpam-5536	287	7	university	university	NOUN
ejpam-5536	287	8	of	of	ADP
ejpam-5536	287	9	phayao	phayao	NOUN
ejpam-5536	287	10	and	and	CCONJ
ejpam-5536	287	11	thailand	thailand	PROPN
ejpam-5536	287	12	science	science	PROPN
ejpam-5536	287	13	research	research	PROPN
ejpam-5536	287	14	and	and	CCONJ
ejpam-5536	287	15	innovation	innovation	NOUN
ejpam-5536	287	16	fund	fund	NOUN
ejpam-5536	287	17	(	(	PUNCT
ejpam-5536	287	18	fundamental	fundamental	ADJ
ejpam-5536	287	19	fund	fund	NOUN
ejpam-5536	287	20	2025	2025	NUM
ejpam-5536	287	21	,	,	PUNCT
ejpam-5536	287	22	grant	grant	VERB
ejpam-5536	287	23	no	no	NOUN
ejpam-5536	287	24	.	.	PROPN
ejpam-5536	288	1	5027/2567	5027/2567	NUM
ejpam-5536	288	2	)	)	PUNCT
ejpam-5536	288	3	.	.	PUNCT
ejpam-5536	289	1	references	reference	NOUN
ejpam-5536	289	2	[	[	X
ejpam-5536	289	3	1	1	X
ejpam-5536	289	4	]	]	PUNCT
ejpam-5536	289	5	t.	t.	NOUN
ejpam-5536	289	6	alsuraiheed	alsuraiheed	NOUN
ejpam-5536	289	7	,	,	PUNCT
ejpam-5536	289	8	u.	u.	PROPN
ejpam-5536	289	9	u.	u.	PROPN
ejpam-5536	289	10	rehman	rehman	PROPN
ejpam-5536	289	11	,	,	PUNCT
ejpam-5536	289	12	m.	m.	NOUN
ejpam-5536	289	13	a.	a.	PROPN
ejpam-5536	289	14	khan	khan	PROPN
ejpam-5536	289	15	,	,	PUNCT
ejpam-5536	289	16	and	and	CCONJ
ejpam-5536	289	17	t.	t.	PROPN
ejpam-5536	289	18	mahmood	mahmood	PROPN
ejpam-5536	289	19	.	.	PUNCT
ejpam-5536	290	1	bipolar	bipolar	ADJ
ejpam-5536	290	2	complex	complex	ADJ
ejpam-5536	290	3	fuzzy	fuzzy	ADJ
ejpam-5536	290	4	submodules	submodule	NOUN
ejpam-5536	290	5	.	.	PUNCT
ejpam-5536	291	1	physica	physica	PROPN
ejpam-5536	291	2	scripta	scripta	PROPN
ejpam-5536	291	3	,	,	PUNCT
ejpam-5536	291	4	99(6):065225	99(6):065225	NUM
ejpam-5536	291	5	,	,	PUNCT
ejpam-5536	291	6	2024	2024	NUM
ejpam-5536	291	7	.	.	PUNCT
ejpam-5536	292	1	[	[	X
ejpam-5536	292	2	2	2	NUM
ejpam-5536	292	3	]	]	PUNCT
ejpam-5536	292	4	k.	k.	PROPN
ejpam-5536	292	5	t.	t.	PROPN
ejpam-5536	292	6	atanassov	atanassov	PROPN
ejpam-5536	292	7	.	.	PUNCT
ejpam-5536	293	1	intuitionistic	intuitionistic	ADJ
ejpam-5536	293	2	fuzzy	fuzzy	ADJ
ejpam-5536	293	3	sets	set	NOUN
ejpam-5536	293	4	.	.	PUNCT
ejpam-5536	294	1	fuzzy	fuzzy	ADJ
ejpam-5536	294	2	sets	set	NOUN
ejpam-5536	294	3	syst	syst	PROPN
ejpam-5536	294	4	.	.	PUNCT
ejpam-5536	294	5	,	,	PUNCT
ejpam-5536	294	6	20(1):87–96	20(1):87–96	NUM
ejpam-5536	294	7	,	,	PUNCT
ejpam-5536	294	8	1986	1986	NUM
ejpam-5536	294	9	.	.	PUNCT
ejpam-5536	295	1	[	[	X
ejpam-5536	295	2	3	3	X
ejpam-5536	295	3	]	]	X
ejpam-5536	295	4	d.	d.	PROPN
ejpam-5536	295	5	busneag	busneag	PROPN
ejpam-5536	295	6	.	.	PUNCT
ejpam-5536	296	1	a	a	DET
ejpam-5536	296	2	note	note	NOUN
ejpam-5536	296	3	on	on	ADP
ejpam-5536	296	4	deductive	deductive	ADJ
ejpam-5536	296	5	systems	system	NOUN
ejpam-5536	296	6	of	of	ADP
ejpam-5536	296	7	a	a	DET
ejpam-5536	296	8	hilbert	hilbert	NOUN
ejpam-5536	296	9	algebra	algebra	NOUN
ejpam-5536	296	10	.	.	PUNCT
ejpam-5536	297	1	kobe	kobe	PROPN
ejpam-5536	297	2	j.	j.	PROPN
ejpam-5536	297	3	math	math	PROPN
ejpam-5536	297	4	.	.	PROPN
ejpam-5536	297	5	,	,	PUNCT
ejpam-5536	297	6	2:29–35	2:29–35	NUM
ejpam-5536	297	7	,	,	PUNCT
ejpam-5536	297	8	1985	1985	NUM
ejpam-5536	297	9	.	.	PUNCT
ejpam-5536	298	1	[	[	X
ejpam-5536	298	2	4	4	X
ejpam-5536	298	3	]	]	X
ejpam-5536	298	4	d.	d.	PROPN
ejpam-5536	298	5	busneag	busneag	PROPN
ejpam-5536	298	6	.	.	PUNCT
ejpam-5536	299	1	hilbert	hilbert	PROPN
ejpam-5536	299	2	algebras	algebras	PROPN
ejpam-5536	299	3	of	of	ADP
ejpam-5536	299	4	fractions	fraction	NOUN
ejpam-5536	299	5	and	and	CCONJ
ejpam-5536	299	6	maximal	maximal	ADJ
ejpam-5536	299	7	hilbert	hilbert	NOUN
ejpam-5536	299	8	algebras	algebra	NOUN
ejpam-5536	299	9	of	of	ADP
ejpam-5536	299	10	quotients	quotient	NOUN
ejpam-5536	299	11	.	.	PUNCT
ejpam-5536	300	1	kobe	kobe	PROPN
ejpam-5536	300	2	j.	j.	PROPN
ejpam-5536	300	3	math	math	PROPN
ejpam-5536	300	4	.	.	PUNCT
ejpam-5536	300	5	,	,	PUNCT
ejpam-5536	300	6	5:161–172	5:161–172	NOUN
ejpam-5536	300	7	,	,	PUNCT
ejpam-5536	300	8	1988	1988	NUM
ejpam-5536	300	9	.	.	PUNCT
ejpam-5536	301	1	[	[	X
ejpam-5536	301	2	5	5	NUM
ejpam-5536	301	3	]	]	PUNCT
ejpam-5536	301	4	i.	i.	NOUN
ejpam-5536	301	5	chajda	chajda	PROPN
ejpam-5536	301	6	and	and	CCONJ
ejpam-5536	301	7	r.	r.	PROPN
ejpam-5536	301	8	halas	halas	PROPN
ejpam-5536	301	9	.	.	PUNCT
ejpam-5536	302	1	congruences	congruence	NOUN
ejpam-5536	302	2	and	and	CCONJ
ejpam-5536	302	3	ideals	ideal	NOUN
ejpam-5536	302	4	in	in	ADP
ejpam-5536	302	5	hilbert	hilbert	PROPN
ejpam-5536	302	6	algebras	algebras	PROPN
ejpam-5536	302	7	.	.	PUNCT
ejpam-5536	303	1	kyungpook	kyungpook	PROPN
ejpam-5536	303	2	math	math	PROPN
ejpam-5536	303	3	.	.	PUNCT
ejpam-5536	304	1	j.	j.	PROPN
ejpam-5536	304	2	,	,	PUNCT
ejpam-5536	304	3	39(2):429–432	39(2):429–432	PROPN
ejpam-5536	304	4	,	,	PUNCT
ejpam-5536	304	5	1999	1999	NUM
ejpam-5536	304	6	.	.	PUNCT
ejpam-5536	305	1	[	[	X
ejpam-5536	305	2	6	6	NUM
ejpam-5536	305	3	]	]	PUNCT
ejpam-5536	305	4	a.	a.	NOUN
ejpam-5536	305	5	diego	diego	PROPN
ejpam-5536	305	6	.	.	PUNCT
ejpam-5536	306	1	sur	sur	PROPN
ejpam-5536	306	2	les	les	PROPN
ejpam-5536	306	3	algébres	algébres	PROPN
ejpam-5536	306	4	de	de	X
ejpam-5536	306	5	hilbert	hilbert	PROPN
ejpam-5536	306	6	.	.	PUNCT
ejpam-5536	307	1	collection	collection	PROPN
ejpam-5536	307	2	de	de	X
ejpam-5536	307	3	logique	logique	X
ejpam-5536	307	4	math	math	PROPN
ejpam-5536	307	5	.	.	PUNCT
ejpam-5536	308	1	ser	ser	PROPN
ejpam-5536	308	2	.	.	PUNCT
ejpam-5536	309	1	a	a	DET
ejpam-5536	309	2	(	(	PUNCT
ejpam-5536	309	3	ed	ed	NOUN
ejpam-5536	309	4	.	.	PUNCT
ejpam-5536	309	5	hermann	hermann	PROPN
ejpam-5536	309	6	,	,	PUNCT
ejpam-5536	309	7	paris	paris	PROPN
ejpam-5536	309	8	)	)	PUNCT
ejpam-5536	309	9	,	,	PUNCT
ejpam-5536	309	10	21:1–52	21:1–52	NUM
ejpam-5536	309	11	,	,	PUNCT
ejpam-5536	309	12	1966	1966	NUM
ejpam-5536	309	13	.	.	PUNCT
ejpam-5536	310	1	[	[	X
ejpam-5536	310	2	7	7	X
ejpam-5536	310	3	]	]	PUNCT
ejpam-5536	310	4	w.	w.	PROPN
ejpam-5536	310	5	a.	a.	PROPN
ejpam-5536	310	6	dudek	dudek	PROPN
ejpam-5536	310	7	.	.	PUNCT
ejpam-5536	311	1	on	on	ADP
ejpam-5536	311	2	fuzzification	fuzzification	NOUN
ejpam-5536	311	3	in	in	ADP
ejpam-5536	311	4	hilbert	hilbert	PROPN
ejpam-5536	311	5	algebras	algebras	PROPN
ejpam-5536	311	6	.	.	PUNCT
ejpam-5536	312	1	contrib	contrib	PROPN
ejpam-5536	312	2	.	.	PUNCT
ejpam-5536	312	3	gen	gen	PROPN
ejpam-5536	312	4	.	.	PROPN
ejpam-5536	312	5	algebra	algebra	PROPN
ejpam-5536	312	6	,	,	PUNCT
ejpam-5536	312	7	11:77–83	11:77–83	NUM
ejpam-5536	312	8	,	,	PUNCT
ejpam-5536	312	9	1999	1999	NUM
ejpam-5536	312	10	.	.	PUNCT
ejpam-5536	313	1	[	[	X
ejpam-5536	313	2	8	8	NUM
ejpam-5536	313	3	]	]	X
ejpam-5536	313	4	w.	w.	PROPN
ejpam-5536	313	5	a.	a.	PROPN
ejpam-5536	313	6	dudek	dudek	PROPN
ejpam-5536	313	7	.	.	PUNCT
ejpam-5536	314	1	on	on	ADP
ejpam-5536	314	2	ideals	ideal	NOUN
ejpam-5536	314	3	in	in	ADP
ejpam-5536	314	4	hilbert	hilbert	PROPN
ejpam-5536	314	5	algebras	algebras	PROPN
ejpam-5536	314	6	.	.	PUNCT
ejpam-5536	315	1	acta	acta	PROPN
ejpam-5536	315	2	universitatis	universitatis	PROPN
ejpam-5536	315	3	palackianae	palackianae	VERB
ejpam-5536	315	4	olomuciensis	olomuciensis	PROPN
ejpam-5536	315	5	fac	fac	PROPN
ejpam-5536	315	6	.	.	PUNCT
ejpam-5536	316	1	rer	rer	PROPN
ejpam-5536	316	2	.	.	PUNCT
ejpam-5536	317	1	nat	nat	PROPN
ejpam-5536	317	2	.	.	PUNCT
ejpam-5536	318	1	ser	ser	PROPN
ejpam-5536	318	2	.	.	PUNCT
ejpam-5536	318	3	math	math	PROPN
ejpam-5536	318	4	.	.	PUNCT
ejpam-5536	318	5	,	,	PUNCT
ejpam-5536	319	1	38:31–34	38:31–34	NUM
ejpam-5536	319	2	,	,	PUNCT
ejpam-5536	319	3	1999	1999	NUM
ejpam-5536	319	4	.	.	PUNCT
ejpam-5536	320	1	[	[	X
ejpam-5536	320	2	9	9	NUM
ejpam-5536	320	3	]	]	PUNCT
ejpam-5536	320	4	w.	w.	PROPN
ejpam-5536	320	5	a.	a.	PROPN
ejpam-5536	320	6	dudek	dudek	PROPN
ejpam-5536	320	7	and	and	CCONJ
ejpam-5536	320	8	y.	y.	PROPN
ejpam-5536	320	9	b.	b.	PROPN
ejpam-5536	320	10	jun	jun	PROPN
ejpam-5536	320	11	.	.	PROPN
ejpam-5536	321	1	on	on	ADP
ejpam-5536	321	2	fuzzy	fuzzy	ADJ
ejpam-5536	321	3	ideals	ideal	NOUN
ejpam-5536	321	4	in	in	ADP
ejpam-5536	321	5	hilbert	hilbert	PROPN
ejpam-5536	321	6	algebra	algebra	PROPN
ejpam-5536	321	7	.	.	PUNCT
ejpam-5536	322	1	novi	novi	PROPN
ejpam-5536	322	2	sad	sad	PROPN
ejpam-5536	322	3	j.	j.	PROPN
ejpam-5536	322	4	math	math	PROPN
ejpam-5536	322	5	.	.	PUNCT
ejpam-5536	322	6	,	,	PUNCT
ejpam-5536	322	7	29(2):193–207	29(2):193–207	PROPN
ejpam-5536	322	8	,	,	PUNCT
ejpam-5536	322	9	1999	1999	NUM
ejpam-5536	322	10	.	.	PUNCT
ejpam-5536	323	1	[	[	X
ejpam-5536	323	2	10	10	NUM
ejpam-5536	323	3	]	]	X
ejpam-5536	323	4	l.	l.	PROPN
ejpam-5536	323	5	henkin	henkin	PROPN
ejpam-5536	323	6	.	.	PUNCT
ejpam-5536	324	1	an	an	DET
ejpam-5536	324	2	algebraic	algebraic	ADJ
ejpam-5536	324	3	characterization	characterization	NOUN
ejpam-5536	324	4	of	of	ADP
ejpam-5536	324	5	quantifiers	quantifier	NOUN
ejpam-5536	324	6	.	.	PUNCT
ejpam-5536	325	1	fund	fund	NOUN
ejpam-5536	325	2	.	.	PUNCT
ejpam-5536	326	1	math	math	NOUN
ejpam-5536	326	2	.	.	PUNCT
ejpam-5536	326	3	,	,	PUNCT
ejpam-5536	327	1	37:63–74	37:63–74	NUM
ejpam-5536	327	2	,	,	PUNCT
ejpam-5536	327	3	1950	1950	NUM
ejpam-5536	327	4	.	.	PUNCT
ejpam-5536	328	1	[	[	X
ejpam-5536	328	2	11	11	NUM
ejpam-5536	328	3	]	]	PUNCT
ejpam-5536	328	4	a.	a.	NOUN
ejpam-5536	328	5	iampan	iampan	PROPN
ejpam-5536	328	6	,	,	PUNCT
ejpam-5536	328	7	n.	n.	PROPN
ejpam-5536	328	8	rajesh	rajesh	PROPN
ejpam-5536	328	9	,	,	PUNCT
ejpam-5536	328	10	and	and	CCONJ
ejpam-5536	328	11	j.	j.	PROPN
ejpam-5536	328	12	princivishvamalar	princivishvamalar	PROPN
ejpam-5536	328	13	.	.	PUNCT
ejpam-5536	329	1	bipolar	bipolar	ADJ
ejpam-5536	329	2	fuzzy	fuzzy	ADJ
ejpam-5536	329	3	hilbert	hilbert	PROPN
ejpam-5536	329	4	algebras	algebras	PROPN
ejpam-5536	329	5	.	.	PUNCT
ejpam-5536	330	1	proyecciones	proyecciones	PROPN
ejpam-5536	330	2	(	(	PUNCT
ejpam-5536	330	3	revised	revise	VERB
ejpam-5536	330	4	)	)	PUNCT
ejpam-5536	330	5	,	,	PUNCT
ejpam-5536	330	6	march	march	PROPN
ejpam-5536	330	7	2024	2024	NUM
ejpam-5536	330	8	.	.	PUNCT
ejpam-5536	331	1	[	[	X
ejpam-5536	331	2	12	12	NUM
ejpam-5536	331	3	]	]	X
ejpam-5536	331	4	y.	y.	PROPN
ejpam-5536	331	5	b.	b.	PROPN
ejpam-5536	331	6	jun	jun	PROPN
ejpam-5536	331	7	.	.	PROPN
ejpam-5536	331	8	deductive	deductive	ADJ
ejpam-5536	331	9	systems	system	NOUN
ejpam-5536	331	10	of	of	ADP
ejpam-5536	331	11	hilbert	hilbert	PROPN
ejpam-5536	331	12	algebras	algebras	PROPN
ejpam-5536	331	13	.	.	PUNCT
ejpam-5536	332	1	math	math	PROPN
ejpam-5536	332	2	.	.	PUNCT
ejpam-5536	333	1	japon	japon	PROPN
ejpam-5536	333	2	.	.	PROPN
ejpam-5536	333	3	,	,	PUNCT
ejpam-5536	333	4	43:51–54	43:51–54	NUM
ejpam-5536	333	5	,	,	PUNCT
ejpam-5536	333	6	1996	1996	NUM
ejpam-5536	333	7	.	.	PUNCT
ejpam-5536	334	1	references	reference	NOUN
ejpam-5536	334	2	4070	4070	NUM
ejpam-5536	335	1	[	[	X
ejpam-5536	335	2	13	13	NUM
ejpam-5536	335	3	]	]	PUNCT
ejpam-5536	335	4	k.	k.	PROPN
ejpam-5536	336	1	h.	h.	PROPN
ejpam-5536	336	2	kim	kim	PROPN
ejpam-5536	336	3	.	.	PUNCT
ejpam-5536	337	1	on	on	ADP
ejpam-5536	337	2	t	t	PROPN
ejpam-5536	337	3	-fuzzy	-fuzzy	PROPN
ejpam-5536	337	4	ideals	ideal	NOUN
ejpam-5536	337	5	in	in	ADP
ejpam-5536	337	6	hilbert	hilbert	PROPN
ejpam-5536	337	7	algebras	algebras	PROPN
ejpam-5536	337	8	.	.	PUNCT
ejpam-5536	338	1	sci	sci	PROPN
ejpam-5536	338	2	.	.	PROPN
ejpam-5536	338	3	math	math	PROPN
ejpam-5536	338	4	.	.	PUNCT
ejpam-5536	339	1	jpn	jpn	PROPN
ejpam-5536	339	2	.	.	PROPN
ejpam-5536	339	3	,	,	PUNCT
ejpam-5536	340	1	70(1):7–15	70(1):7–15	NUM
ejpam-5536	340	2	,	,	PUNCT
ejpam-5536	340	3	2009	2009	NUM
ejpam-5536	340	4	.	.	PUNCT
ejpam-5536	341	1	[	[	X
ejpam-5536	341	2	14	14	NUM
ejpam-5536	341	3	]	]	PUNCT
ejpam-5536	341	4	t.	t.	PROPN
ejpam-5536	341	5	mahmood	mahmood	PROPN
ejpam-5536	341	6	,	,	PUNCT
ejpam-5536	341	7	k.	k.	PROPN
ejpam-5536	341	8	hussain	hussain	PROPN
ejpam-5536	341	9	,	,	PUNCT
ejpam-5536	341	10	j.	j.	PROPN
ejpam-5536	341	11	ahmmad	ahmmad	PROPN
ejpam-5536	341	12	,	,	PUNCT
ejpam-5536	341	13	s.	s.	PROPN
ejpam-5536	341	14	shahab	shahab	PROPN
ejpam-5536	341	15	,	,	PUNCT
ejpam-5536	341	16	u.	u.	PROPN
ejpam-5536	341	17	u.	u.	PROPN
ejpam-5536	341	18	rehman	rehman	PROPN
ejpam-5536	341	19	,	,	PUNCT
ejpam-5536	341	20	and	and	CCONJ
ejpam-5536	341	21	m.	m.	PROPN
ejpam-5536	341	22	anjum	anjum	PROPN
ejpam-5536	341	23	.	.	PUNCT
ejpam-5536	342	1	t	t	PROPN
ejpam-5536	342	2	-bipolar	-bipolar	ADJ
ejpam-5536	342	3	soft	soft	ADJ
ejpam-5536	342	4	groups	group	NOUN
ejpam-5536	342	5	and	and	CCONJ
ejpam-5536	342	6	their	their	PRON
ejpam-5536	342	7	fundamental	fundamental	ADJ
ejpam-5536	342	8	laws	law	NOUN
ejpam-5536	342	9	.	.	PUNCT
ejpam-5536	343	1	j.	j.	PROPN
ejpam-5536	343	2	intell	intell	PROPN
ejpam-5536	343	3	.	.	PUNCT
ejpam-5536	344	1	fuzzy	fuzzy	ADJ
ejpam-5536	344	2	syst	syst	PROPN
ejpam-5536	344	3	.	.	PUNCT
ejpam-5536	344	4	,	,	PUNCT
ejpam-5536	344	5	46(4):9479	46(4):9479	NUM
ejpam-5536	344	6	–	–	PUNCT
ejpam-5536	344	7	9490	9490	NUM
ejpam-5536	344	8	,	,	PUNCT
ejpam-5536	344	9	2024	2024	NUM
ejpam-5536	344	10	.	.	PUNCT
ejpam-5536	345	1	[	[	X
ejpam-5536	345	2	15	15	NUM
ejpam-5536	345	3	]	]	PUNCT
ejpam-5536	345	4	t.	t.	PROPN
ejpam-5536	345	5	mahmood	mahmood	PROPN
ejpam-5536	345	6	,	,	PUNCT
ejpam-5536	345	7	u.	u.	PROPN
ejpam-5536	345	8	u.	u.	PROPN
ejpam-5536	345	9	rehman	rehman	PROPN
ejpam-5536	345	10	,	,	PUNCT
ejpam-5536	345	11	and	and	CCONJ
ejpam-5536	345	12	m.	m.	NOUN
ejpam-5536	345	13	albaity	albaity	NOUN
ejpam-5536	345	14	.	.	PUNCT
ejpam-5536	346	1	analysis	analysis	NOUN
ejpam-5536	346	2	of	of	ADP
ejpam-5536	346	3	γ	γ	NOUN
ejpam-5536	346	4	-	-	PUNCT
ejpam-5536	346	5	semigroups	semigroup	NOUN
ejpam-5536	346	6	based	base	VERB
ejpam-5536	346	7	on	on	ADP
ejpam-5536	346	8	bipolar	bipolar	ADJ
ejpam-5536	346	9	complex	complex	ADJ
ejpam-5536	346	10	fuzzy	fuzzy	ADJ
ejpam-5536	346	11	sets	set	NOUN
ejpam-5536	346	12	.	.	PUNCT
ejpam-5536	347	1	comp	comp	NOUN
ejpam-5536	347	2	.	.	PUNCT
ejpam-5536	348	1	appl	appl	PROPN
ejpam-5536	348	2	.	.	PROPN
ejpam-5536	348	3	math	math	PROPN
ejpam-5536	348	4	.	.	PUNCT
ejpam-5536	348	5	,	,	PUNCT
ejpam-5536	348	6	42:262	42:262	NUM
ejpam-5536	348	7	,	,	PUNCT
ejpam-5536	348	8	2023	2023	NUM
ejpam-5536	348	9	.	.	PUNCT
ejpam-5536	349	1	[	[	X
ejpam-5536	349	2	16	16	NUM
ejpam-5536	349	3	]	]	X
ejpam-5536	349	4	u.	u.	PROPN
ejpam-5536	349	5	u.	u.	PROPN
ejpam-5536	349	6	rehman	rehman	PROPN
ejpam-5536	349	7	,	,	PUNCT
ejpam-5536	349	8	t.	t.	PROPN
ejpam-5536	349	9	mahmood	mahmood	PROPN
ejpam-5536	349	10	,	,	PUNCT
ejpam-5536	349	11	and	and	CCONJ
ejpam-5536	349	12	m.	m.	PROPN
ejpam-5536	349	13	naeem	naeem	PROPN
ejpam-5536	349	14	.	.	PUNCT
ejpam-5536	350	1	bipolar	bipolar	ADJ
ejpam-5536	350	2	complex	complex	ADJ
ejpam-5536	350	3	fuzzy	fuzzy	ADJ
ejpam-5536	350	4	semigroups	semigroup	NOUN
ejpam-5536	350	5	.	.	PUNCT
ejpam-5536	351	1	aims	aim	VERB
ejpam-5536	351	2	math	math	NOUN
ejpam-5536	351	3	.	.	PUNCT
ejpam-5536	351	4	,	,	PUNCT
ejpam-5536	351	5	8(2):3997–4021	8(2):3997–4021	PROPN
ejpam-5536	351	6	,	,	PUNCT
ejpam-5536	351	7	2023	2023	NUM
ejpam-5536	351	8	.	.	PUNCT
ejpam-5536	352	1	[	[	X
ejpam-5536	352	2	17	17	NUM
ejpam-5536	352	3	]	]	X
ejpam-5536	352	4	n.	n.	NOUN
ejpam-5536	352	5	udten	udten	PROPN
ejpam-5536	352	6	,	,	PUNCT
ejpam-5536	352	7	n.	n.	PROPN
ejpam-5536	352	8	songseang	songseang	PROPN
ejpam-5536	352	9	,	,	PUNCT
ejpam-5536	352	10	and	and	CCONJ
ejpam-5536	352	11	a.	a.	NOUN
ejpam-5536	352	12	iampan	iampan	PROPN
ejpam-5536	352	13	.	.	PUNCT
ejpam-5536	353	1	translation	translation	NOUN
ejpam-5536	353	2	and	and	CCONJ
ejpam-5536	353	3	density	density	NOUN
ejpam-5536	353	4	of	of	ADP
ejpam-5536	353	5	a	a	DET
ejpam-5536	353	6	bipolar	bipolar	ADV
ejpam-5536	353	7	-	-	PUNCT
ejpam-5536	353	8	valued	value	VERB
ejpam-5536	353	9	fuzzy	fuzzy	ADJ
ejpam-5536	353	10	set	set	VERB
ejpam-5536	353	11	in	in	ADP
ejpam-5536	353	12	up	up	ADP
ejpam-5536	353	13	-	-	PUNCT
ejpam-5536	353	14	algebras	algebras	X
ejpam-5536	353	15	.	.	PUNCT
ejpam-5536	354	1	ital	ital	PROPN
ejpam-5536	354	2	.	.	PUNCT
ejpam-5536	355	1	j.	j.	PROPN
ejpam-5536	355	2	pure	pure	PROPN
ejpam-5536	355	3	appl	appl	PROPN
ejpam-5536	355	4	.	.	PUNCT
ejpam-5536	355	5	math	math	PROPN
ejpam-5536	355	6	.	.	PUNCT
ejpam-5536	355	7	,	,	PUNCT
ejpam-5536	355	8	41:469–496	41:469–496	PROPN
ejpam-5536	355	9	,	,	PUNCT
ejpam-5536	355	10	2019	2019	NUM
ejpam-5536	355	11	.	.	PUNCT
ejpam-5536	356	1	[	[	X
ejpam-5536	356	2	18	18	NUM
ejpam-5536	356	3	]	]	PUNCT
ejpam-5536	356	4	x.	x.	PROPN
ejpam-5536	356	5	yang	yang	PROPN
ejpam-5536	356	6	,	,	PUNCT
ejpam-5536	356	7	t.	t.	PROPN
ejpam-5536	356	8	mahmood	mahmood	PROPN
ejpam-5536	356	9	,	,	PUNCT
ejpam-5536	356	10	and	and	CCONJ
ejpam-5536	356	11	u.	u.	PROPN
ejpam-5536	356	12	u.	u.	PROPN
ejpam-5536	356	13	rehman	rehman	PROPN
ejpam-5536	356	14	.	.	PUNCT
ejpam-5536	357	1	bipolar	bipolar	ADJ
ejpam-5536	357	2	complex	complex	ADJ
ejpam-5536	357	3	fuzzy	fuzzy	ADJ
ejpam-5536	357	4	subgroups	subgroup	NOUN
ejpam-5536	357	5	.	.	PUNCT
ejpam-5536	358	1	mathematics	mathematic	NOUN
ejpam-5536	358	2	,	,	PUNCT
ejpam-5536	358	3	10(16):2882	10(16):2882	NUM
ejpam-5536	358	4	,	,	PUNCT
ejpam-5536	358	5	2022	2022	NUM
ejpam-5536	358	6	.	.	PUNCT
ejpam-5536	359	1	[	[	X
ejpam-5536	359	2	19	19	NUM
ejpam-5536	359	3	]	]	PUNCT
ejpam-5536	359	4	l.	l.	PROPN
ejpam-5536	359	5	a.	a.	PROPN
ejpam-5536	359	6	zadeh	zadeh	PROPN
ejpam-5536	359	7	.	.	PUNCT
ejpam-5536	359	8	fuzzy	fuzzy	ADJ
ejpam-5536	359	9	sets	set	NOUN
ejpam-5536	359	10	.	.	PUNCT
ejpam-5536	360	1	inf	inf	PROPN
ejpam-5536	360	2	.	.	PUNCT
ejpam-5536	360	3	control	control	PROPN
ejpam-5536	360	4	,	,	PUNCT
ejpam-5536	360	5	8(3):338–353	8(3):338–353	NUM
ejpam-5536	360	6	,	,	PUNCT
ejpam-5536	360	7	1965	1965	NUM
ejpam-5536	360	8	.	.	PUNCT
ejpam-5536	361	1	[	[	X
ejpam-5536	361	2	20	20	NUM
ejpam-5536	361	3	]	]	X
ejpam-5536	361	4	j.	j.	PROPN
ejpam-5536	361	5	zhan	zhan	PROPN
ejpam-5536	361	6	and	and	CCONJ
ejpam-5536	361	7	z.	z.	PROPN
ejpam-5536	361	8	tan	tan	PROPN
ejpam-5536	361	9	.	.	PUNCT
ejpam-5536	362	1	intuitionistic	intuitionistic	ADJ
ejpam-5536	362	2	fuzzy	fuzzy	ADJ
ejpam-5536	362	3	deductive	deductive	ADJ
ejpam-5536	362	4	systems	system	NOUN
ejpam-5536	362	5	in	in	ADP
ejpam-5536	362	6	hilbert	hilbert	PROPN
ejpam-5536	362	7	algebras	algebras	PROPN
ejpam-5536	362	8	.	.	PUNCT
ejpam-5536	363	1	southeast	southeast	ADJ
ejpam-5536	363	2	asian	asian	ADJ
ejpam-5536	363	3	bull	bull	PROPN
ejpam-5536	363	4	.	.	PUNCT
ejpam-5536	364	1	math	math	NOUN
ejpam-5536	364	2	.	.	PUNCT
ejpam-5536	364	3	,	,	PUNCT
ejpam-5536	365	1	29(4):813–826	29(4):813–826	PROPN
ejpam-5536	365	2	,	,	PUNCT
ejpam-5536	365	3	2005	2005	NUM
ejpam-5536	365	4	.	.	PUNCT
ejpam-5536	366	1	[	[	X
ejpam-5536	366	2	21	21	NUM
ejpam-5536	366	3	]	]	X
ejpam-5536	366	4	w.-r	w.-r	PROPN
ejpam-5536	366	5	.	.	PUNCT
ejpam-5536	367	1	zhang	zhang	PROPN
ejpam-5536	367	2	.	.	PUNCT
ejpam-5536	367	3	bipolar	bipolar	ADJ
ejpam-5536	367	4	fuzzy	fuzzy	ADJ
ejpam-5536	367	5	sets	set	NOUN
ejpam-5536	367	6	and	and	CCONJ
ejpam-5536	367	7	relations	relation	NOUN
ejpam-5536	367	8	:	:	PUNCT
ejpam-5536	367	9	a	a	DET
ejpam-5536	367	10	computational	computational	ADJ
ejpam-5536	367	11	framework	framework	NOUN
ejpam-5536	367	12	for	for	ADP
ejpam-5536	367	13	cognitive	cognitive	ADJ
ejpam-5536	367	14	modelling	modelling	NOUN
ejpam-5536	367	15	and	and	CCONJ
ejpam-5536	367	16	multiagent	multiagent	ADJ
ejpam-5536	367	17	decision	decision	NOUN
ejpam-5536	367	18	analysis	analysis	NOUN
ejpam-5536	367	19	.	.	PUNCT
ejpam-5536	368	1	in	in	ADP
ejpam-5536	368	2	nafips	nafip	NOUN
ejpam-5536	368	3	/	/	SYM
ejpam-5536	368	4	ifis	ifis	PROPN
ejpam-5536	368	5	/	/	SYM
ejpam-5536	368	6	nasa’94	nasa’94	PROPN
ejpam-5536	368	7	.	.	PUNCT
ejpam-5536	368	8	proc	proc	NOUN
ejpam-5536	368	9	.	.	PUNCT
ejpam-5536	369	1	first	first	ADJ
ejpam-5536	369	2	int	int	NOUN
ejpam-5536	369	3	.	.	PUNCT
ejpam-5536	370	1	joint	joint	ADJ
ejpam-5536	370	2	conf	conf	NOUN
ejpam-5536	370	3	.	.	PUNCT
ejpam-5536	371	1	n.	n.	PROPN
ejpam-5536	371	2	am	am	PROPN
ejpam-5536	371	3	.	.	PUNCT
ejpam-5536	372	1	fuzzy	fuzzy	PROPN
ejpam-5536	372	2	inf	inf	PROPN
ejpam-5536	372	3	.	.	PUNCT
ejpam-5536	372	4	process	process	NOUN
ejpam-5536	372	5	.	.	PUNCT
ejpam-5536	373	1	soc	soc	PROPN
ejpam-5536	373	2	.	.	PUNCT
ejpam-5536	374	1	biannu	biannu	PROPN
ejpam-5536	374	2	.	.	PUNCT
ejpam-5536	374	3	conf	conf	PROPN
ejpam-5536	374	4	.	.	PUNCT
ejpam-5536	375	1	ind	ind	PROPN
ejpam-5536	375	2	.	.	PUNCT
ejpam-5536	376	1	fuzzy	fuzzy	PROPN
ejpam-5536	376	2	control	control	PROPN
ejpam-5536	376	3	intell	intell	PROPN
ejpam-5536	376	4	.	.	PUNCT
ejpam-5536	377	1	,	,	PUNCT
ejpam-5536	377	2	pages	page	NOUN
ejpam-5536	377	3	305–309	305–309	NUM
ejpam-5536	377	4	,	,	PUNCT
ejpam-5536	377	5	1994	1994	NUM
ejpam-5536	377	6	.	.	PUNCT
ejpam-5536	378	1	[	[	X
ejpam-5536	378	2	22	22	NUM
ejpam-5536	378	3	]	]	X
ejpam-5536	378	4	w.-r	w.-r	PROPN
ejpam-5536	378	5	.	.	PUNCT
ejpam-5536	379	1	zhang	zhang	PROPN
ejpam-5536	379	2	.	.	PUNCT
ejpam-5536	380	1	(	(	PUNCT
ejpam-5536	380	2	yin	yin	PROPN
ejpam-5536	380	3	)	)	PUNCT
ejpam-5536	380	4	(	(	PUNCT
ejpam-5536	380	5	yang	yang	NOUN
ejpam-5536	380	6	)	)	PUNCT
ejpam-5536	380	7	bipolar	bipolar	ADJ
ejpam-5536	380	8	fuzzy	fuzzy	ADJ
ejpam-5536	380	9	sets	set	NOUN
ejpam-5536	380	10	.	.	PUNCT
ejpam-5536	381	1	1998	1998	NUM
ejpam-5536	381	2	ieee	ieee	PROPN
ejpam-5536	381	3	international	international	PROPN
ejpam-5536	381	4	conference	conference	NOUN
ejpam-5536	381	5	on	on	ADP
ejpam-5536	381	6	fuzzy	fuzzy	ADJ
ejpam-5536	381	7	systems	system	NOUN
ejpam-5536	381	8	proceedings	proceeding	NOUN
ejpam-5536	381	9	.	.	PUNCT
ejpam-5536	382	1	ieee	ieee	PROPN
ejpam-5536	382	2	world	world	PROPN
ejpam-5536	382	3	congress	congress	PROPN
ejpam-5536	382	4	on	on	ADP
ejpam-5536	382	5	computational	computational	ADJ
ejpam-5536	382	6	intelligence	intelligence	NOUN
ejpam-5536	382	7	(	(	PUNCT
ejpam-5536	382	8	cat	cat	NOUN
ejpam-5536	382	9	.	.	PUNCT
ejpam-5536	383	1	no	no	INTJ
ejpam-5536	383	2	.	.	PUNCT
ejpam-5536	384	1	98ch36228	98ch36228	NUM
ejpam-5536	384	2	)	)	PUNCT
ejpam-5536	385	1	,	,	PUNCT
ejpam-5536	385	2	anchorage	anchorage	PROPN
ejpam-5536	385	3	,	,	PUNCT
ejpam-5536	385	4	ak	ak	PROPN
ejpam-5536	385	5	,	,	PUNCT
ejpam-5536	385	6	usa	usa	PROPN
ejpam-5536	385	7	,	,	PUNCT
ejpam-5536	385	8	1:835–840	1:835–840	NUM
ejpam-5536	385	9	,	,	PUNCT
ejpam-5536	385	10	1998	1998	NUM
ejpam-5536	385	11	.	.	PUNCT