id	sid	tid	token	lemma	pos
ejpam-3288	1	1	european	european	PROPN
ejpam-3288	1	2	journal	journal	PROPN
ejpam-3288	1	3	of	of	ADP
ejpam-3288	1	4	pure	pure	ADJ
ejpam-3288	1	5	and	and	CCONJ
ejpam-3288	1	6	applied	apply	VERB
ejpam-3288	1	7	mathematics	mathematic	NOUN
ejpam-3288	1	8	vol	vol	NOUN
ejpam-3288	1	9	.	.	PUNCT
ejpam-3288	2	1	11	11	NUM
ejpam-3288	2	2	,	,	PUNCT
ejpam-3288	2	3	no	no	INTJ
ejpam-3288	2	4	.	.	NOUN
ejpam-3288	2	5	3	3	NUM
ejpam-3288	2	6	,	,	PUNCT
ejpam-3288	2	7	2018	2018	NUM
ejpam-3288	2	8	,	,	PUNCT
ejpam-3288	2	9	652	652	NUM
ejpam-3288	2	10	-	-	SYM
ejpam-3288	2	11	670	670	NUM
ejpam-3288	2	12	issn	issn	PROPN
ejpam-3288	2	13	1307	1307	NUM
ejpam-3288	2	14	-	-	SYM
ejpam-3288	2	15	5543	5543	NUM
ejpam-3288	2	16	–	–	PUNCT
ejpam-3288	3	1	www.ejpam.com	www.ejpam.com	X
ejpam-3288	3	2	published	publish	VERB
ejpam-3288	3	3	by	by	ADP
ejpam-3288	3	4	new	new	PROPN
ejpam-3288	3	5	york	york	PROPN
ejpam-3288	3	6	business	business	PROPN
ejpam-3288	3	7	global	global	ADJ
ejpam-3288	3	8	on	on	ADP
ejpam-3288	3	9	some	some	DET
ejpam-3288	3	10	properties	property	NOUN
ejpam-3288	3	11	of	of	ADP
ejpam-3288	3	12	doubt	doubt	NOUN
ejpam-3288	3	13	bipolar	bipolar	ADJ
ejpam-3288	3	14	fuzzy	fuzzy	ADJ
ejpam-3288	3	15	h	h	NOUN
ejpam-3288	3	16	-	-	PUNCT
ejpam-3288	3	17	ideals	ideal	NOUN
ejpam-3288	3	18	in	in	ADP
ejpam-3288	3	19	bck	bck	PROPN
ejpam-3288	3	20	/	/	SYM
ejpam-3288	3	21	bci	bci	NOUN
ejpam-3288	3	22	-	-	PUNCT
ejpam-3288	3	23	algebras	algebras	PROPN
ejpam-3288	3	24	anas	anas	PROPN
ejpam-3288	3	25	al	al	PROPN
ejpam-3288	3	26	-	-	PUNCT
ejpam-3288	3	27	masarwah1,∗	masarwah1,∗	PROPN
ejpam-3288	3	28	,	,	PUNCT
ejpam-3288	3	29	abd	abd	NOUN
ejpam-3288	3	30	ghafur	ghafur	NOUN
ejpam-3288	3	31	ahmad1	ahmad1	NOUN
ejpam-3288	3	32	1	1	NUM
ejpam-3288	3	33	school	school	NOUN
ejpam-3288	3	34	of	of	ADP
ejpam-3288	3	35	mathematical	mathematical	ADJ
ejpam-3288	3	36	sciences	science	NOUN
ejpam-3288	3	37	,	,	PUNCT
ejpam-3288	3	38	faculty	faculty	NOUN
ejpam-3288	3	39	of	of	ADP
ejpam-3288	3	40	science	science	NOUN
ejpam-3288	3	41	and	and	CCONJ
ejpam-3288	3	42	technology	technology	NOUN
ejpam-3288	3	43	,	,	PUNCT
ejpam-3288	3	44	universiti	universiti	PROPN
ejpam-3288	3	45	kebangsaan	kebangsaan	PROPN
ejpam-3288	3	46	malaysia	malaysia	PROPN
ejpam-3288	3	47	,	,	PUNCT
ejpam-3288	3	48	43600	43600	NUM
ejpam-3288	3	49	ukm	ukm	PROPN
ejpam-3288	3	50	bangi	bangi	PROPN
ejpam-3288	3	51	,	,	PUNCT
ejpam-3288	3	52	selangor	selangor	PROPN
ejpam-3288	3	53	de	de	PROPN
ejpam-3288	3	54	,	,	PUNCT
ejpam-3288	3	55	malaysia	malaysia	PROPN
ejpam-3288	3	56	abstract	abstract	NOUN
ejpam-3288	3	57	.	.	PUNCT
ejpam-3288	4	1	in	in	ADP
ejpam-3288	4	2	this	this	DET
ejpam-3288	4	3	research	research	NOUN
ejpam-3288	4	4	article	article	NOUN
ejpam-3288	4	5	,	,	PUNCT
ejpam-3288	4	6	we	we	PRON
ejpam-3288	4	7	study	study	VERB
ejpam-3288	4	8	some	some	DET
ejpam-3288	4	9	properties	property	NOUN
ejpam-3288	4	10	of	of	ADP
ejpam-3288	4	11	doubt	doubt	NOUN
ejpam-3288	4	12	bipolar	bipolar	ADJ
ejpam-3288	4	13	fuzzy	fuzzy	ADJ
ejpam-3288	4	14	h	h	NOUN
ejpam-3288	4	15	-	-	PUNCT
ejpam-3288	4	16	ideals	ideal	NOUN
ejpam-3288	4	17	in	in	ADP
ejpam-3288	4	18	bck/	bck/	VERB
ejpam-3288	4	19	bci	bci	NOUN
ejpam-3288	4	20	-	-	PUNCT
ejpam-3288	4	21	algebras	algebra	NOUN
ejpam-3288	4	22	.	.	PUNCT
ejpam-3288	5	1	doubt	doubt	VERB
ejpam-3288	5	2	bipolar	bipolar	ADJ
ejpam-3288	5	3	fuzzy	fuzzy	ADJ
ejpam-3288	5	4	h	h	NOUN
ejpam-3288	5	5	-	-	PUNCT
ejpam-3288	5	6	ideals	ideal	NOUN
ejpam-3288	5	7	are	be	AUX
ejpam-3288	5	8	connected	connect	VERB
ejpam-3288	5	9	with	with	ADP
ejpam-3288	5	10	doubt	doubt	ADV
ejpam-3288	5	11	bipolar	bipolar	ADJ
ejpam-3288	5	12	fuzzy	fuzzy	ADJ
ejpam-3288	5	13	subalgebras	subalgebra	NOUN
ejpam-3288	5	14	and	and	CCONJ
ejpam-3288	5	15	doubt	doubt	VERB
ejpam-3288	5	16	bipolar	bipolar	ADJ
ejpam-3288	5	17	fuzzy	fuzzy	ADJ
ejpam-3288	5	18	ideals	ideal	NOUN
ejpam-3288	5	19	.	.	PUNCT
ejpam-3288	6	1	moreover	moreover	ADV
ejpam-3288	6	2	,	,	PUNCT
ejpam-3288	6	3	doubt	doubt	VERB
ejpam-3288	6	4	bipolar	bipolar	ADJ
ejpam-3288	6	5	fuzzy	fuzzy	ADJ
ejpam-3288	6	6	h	h	NOUN
ejpam-3288	6	7	-	-	PUNCT
ejpam-3288	6	8	ideals	ideal	NOUN
ejpam-3288	6	9	are	be	AUX
ejpam-3288	6	10	characterized	characterize	VERB
ejpam-3288	6	11	using	use	VERB
ejpam-3288	6	12	doubt	doubt	NOUN
ejpam-3288	6	13	positive	positive	ADJ
ejpam-3288	6	14	t	t	NOUN
ejpam-3288	6	15	-	-	PUNCT
ejpam-3288	6	16	level	level	NOUN
ejpam-3288	6	17	cut	cut	NOUN
ejpam-3288	6	18	set	set	NOUN
ejpam-3288	6	19	,	,	PUNCT
ejpam-3288	6	20	doubt	doubt	VERB
ejpam-3288	6	21	negative	negative	ADJ
ejpam-3288	6	22	s	s	NOUN
ejpam-3288	6	23	-	-	PUNCT
ejpam-3288	6	24	level	level	NOUN
ejpam-3288	6	25	cut	cut	NOUN
ejpam-3288	6	26	set	set	VERB
ejpam-3288	6	27	and	and	CCONJ
ejpam-3288	6	28	h	h	NOUN
ejpam-3288	6	29	-	-	PUNCT
ejpam-3288	6	30	artin	artin	NOUN
ejpam-3288	6	31	bck	bck	PROPN
ejpam-3288	6	32	/	/	SYM
ejpam-3288	6	33	bci	bci	NOUN
ejpam-3288	6	34	-	-	PUNCT
ejpam-3288	6	35	algebras	algebras	X
ejpam-3288	6	36	.	.	PUNCT
ejpam-3288	7	1	2010	2010	NUM
ejpam-3288	7	2	mathematics	mathematic	NOUN
ejpam-3288	7	3	subject	subject	NOUN
ejpam-3288	7	4	classifications	classification	NOUN
ejpam-3288	7	5	:	:	PUNCT
ejpam-3288	7	6	03g25	03g25	NUM
ejpam-3288	7	7	,	,	PUNCT
ejpam-3288	7	8	06f35	06f35	NUM
ejpam-3288	7	9	,	,	PUNCT
ejpam-3288	7	10	08a72	08a72	NOUN
ejpam-3288	7	11	key	key	ADJ
ejpam-3288	7	12	words	word	NOUN
ejpam-3288	7	13	and	and	CCONJ
ejpam-3288	7	14	phrases	phrase	NOUN
ejpam-3288	7	15	:	:	PUNCT
ejpam-3288	7	16	bck	bck	VERB
ejpam-3288	7	17	/	/	SYM
ejpam-3288	7	18	bci	bci	NOUN
ejpam-3288	7	19	-	-	PUNCT
ejpam-3288	7	20	algebras	algebra	NOUN
ejpam-3288	7	21	,	,	PUNCT
ejpam-3288	7	22	doubt	doubt	VERB
ejpam-3288	7	23	fuzzy	fuzzy	ADJ
ejpam-3288	7	24	ideals	ideal	NOUN
ejpam-3288	7	25	,	,	PUNCT
ejpam-3288	7	26	doubt	doubt	VERB
ejpam-3288	7	27	fuzzy	fuzzy	ADJ
ejpam-3288	7	28	h	h	NOUN
ejpam-3288	7	29	-	-	PUNCT
ejpam-3288	7	30	ideals	ideal	NOUN
ejpam-3288	7	31	,	,	PUNCT
ejpam-3288	7	32	doubt	doubt	VERB
ejpam-3288	7	33	bipolar	bipolar	ADJ
ejpam-3288	7	34	fuzzy	fuzzy	ADJ
ejpam-3288	7	35	subalgebras	subalgebra	NOUN
ejpam-3288	7	36	,	,	PUNCT
ejpam-3288	7	37	doubt	doubt	VERB
ejpam-3288	7	38	bipolar	bipolar	ADJ
ejpam-3288	7	39	fuzzy	fuzzy	ADJ
ejpam-3288	7	40	ideals	ideal	NOUN
ejpam-3288	7	41	,	,	PUNCT
ejpam-3288	7	42	doubt	doubt	VERB
ejpam-3288	7	43	bipolar	bipolar	ADJ
ejpam-3288	7	44	fuzzy	fuzzy	ADJ
ejpam-3288	7	45	h	h	NOUN
ejpam-3288	7	46	-	-	PUNCT
ejpam-3288	7	47	ideals	ideal	NOUN
ejpam-3288	7	48	1	1	NUM
ejpam-3288	7	49	.	.	PUNCT
ejpam-3288	7	50	introduction	introduction	NOUN
ejpam-3288	7	51	in	in	ADP
ejpam-3288	7	52	1965	1965	NUM
ejpam-3288	7	53	,	,	PUNCT
ejpam-3288	7	54	zadeh	zadeh	PROPN
ejpam-3288	8	1	[	[	X
ejpam-3288	8	2	30	30	NUM
ejpam-3288	8	3	]	]	PUNCT
ejpam-3288	8	4	introduced	introduce	VERB
ejpam-3288	8	5	the	the	DET
ejpam-3288	8	6	concept	concept	NOUN
ejpam-3288	8	7	of	of	ADP
ejpam-3288	8	8	fuzzy	fuzzy	ADJ
ejpam-3288	8	9	set	set	NOUN
ejpam-3288	8	10	to	to	PART
ejpam-3288	8	11	handle	handle	VERB
ejpam-3288	8	12	the	the	DET
ejpam-3288	8	13	uncertainties	uncertainty	NOUN
ejpam-3288	8	14	in	in	ADP
ejpam-3288	8	15	our	our	PRON
ejpam-3288	8	16	daily	daily	ADJ
ejpam-3288	8	17	life	life	NOUN
ejpam-3288	8	18	.	.	PUNCT
ejpam-3288	9	1	fuzzy	fuzzy	ADJ
ejpam-3288	9	2	sets	set	NOUN
ejpam-3288	9	3	are	be	AUX
ejpam-3288	9	4	extremely	extremely	ADV
ejpam-3288	9	5	useful	useful	ADJ
ejpam-3288	9	6	to	to	PART
ejpam-3288	9	7	solve	solve	VERB
ejpam-3288	9	8	many	many	ADJ
ejpam-3288	9	9	problems	problem	NOUN
ejpam-3288	9	10	in	in	ADP
ejpam-3288	9	11	applied	applied	ADJ
ejpam-3288	9	12	mathematics	mathematic	NOUN
ejpam-3288	9	13	,	,	PUNCT
ejpam-3288	9	14	information	information	NOUN
ejpam-3288	9	15	sciences	science	NOUN
ejpam-3288	9	16	and	and	CCONJ
ejpam-3288	9	17	decision	decision	NOUN
ejpam-3288	9	18	making	making	NOUN
ejpam-3288	9	19	.	.	PUNCT
ejpam-3288	10	1	after	after	SCONJ
ejpam-3288	10	2	that	that	DET
ejpam-3288	10	3	many	many	ADJ
ejpam-3288	10	4	generalizations	generalization	NOUN
ejpam-3288	10	5	of	of	ADP
ejpam-3288	10	6	fuzzy	fuzzy	ADJ
ejpam-3288	10	7	sets	set	NOUN
ejpam-3288	10	8	are	be	AUX
ejpam-3288	10	9	presented	present	VERB
ejpam-3288	10	10	,	,	PUNCT
ejpam-3288	10	11	for	for	ADP
ejpam-3288	10	12	example	example	NOUN
ejpam-3288	10	13	,	,	PUNCT
ejpam-3288	10	14	interval	interval	NOUN
ejpam-3288	10	15	valued	value	VERB
ejpam-3288	10	16	fuzzy	fuzzy	ADJ
ejpam-3288	10	17	sets	set	NOUN
ejpam-3288	10	18	[	[	X
ejpam-3288	10	19	31	31	NUM
ejpam-3288	10	20	]	]	PUNCT
ejpam-3288	10	21	and	and	CCONJ
ejpam-3288	10	22	intuitionistic	intuitionistic	ADJ
ejpam-3288	10	23	fuzzy	fuzzy	ADJ
ejpam-3288	10	24	sets	set	NOUN
ejpam-3288	10	25	[	[	X
ejpam-3288	10	26	7	7	NUM
ejpam-3288	10	27	]	]	PUNCT
ejpam-3288	10	28	.	.	PUNCT
ejpam-3288	11	1	lee	lee	PROPN
ejpam-3288	12	1	[	[	X
ejpam-3288	12	2	22	22	NUM
ejpam-3288	12	3	]	]	PUNCT
ejpam-3288	12	4	introduced	introduce	VERB
ejpam-3288	12	5	the	the	DET
ejpam-3288	12	6	notion	notion	NOUN
ejpam-3288	12	7	of	of	ADP
ejpam-3288	12	8	bipolar	bipolar	ADJ
ejpam-3288	12	9	fuzzy	fuzzy	ADJ
ejpam-3288	12	10	sets	set	NOUN
ejpam-3288	12	11	which	which	PRON
ejpam-3288	12	12	is	be	AUX
ejpam-3288	12	13	an	an	DET
ejpam-3288	12	14	extension	extension	NOUN
ejpam-3288	12	15	of	of	ADP
ejpam-3288	12	16	fuzzy	fuzzy	ADJ
ejpam-3288	12	17	sets	set	NOUN
ejpam-3288	12	18	.	.	PUNCT
ejpam-3288	13	1	fuzzy	fuzzy	ADJ
ejpam-3288	13	2	sets	set	NOUN
ejpam-3288	13	3	give	give	VERB
ejpam-3288	13	4	a	a	DET
ejpam-3288	13	5	degree	degree	NOUN
ejpam-3288	13	6	of	of	ADP
ejpam-3288	13	7	membership	membership	NOUN
ejpam-3288	13	8	of	of	ADP
ejpam-3288	13	9	an	an	DET
ejpam-3288	13	10	element	element	NOUN
ejpam-3288	13	11	in	in	ADP
ejpam-3288	13	12	a	a	DET
ejpam-3288	13	13	given	give	VERB
ejpam-3288	13	14	set	set	NOUN
ejpam-3288	13	15	,	,	PUNCT
ejpam-3288	13	16	whereas	whereas	SCONJ
ejpam-3288	13	17	bipolar	bipolar	ADJ
ejpam-3288	13	18	fuzzy	fuzzy	ADJ
ejpam-3288	13	19	sets	set	NOUN
ejpam-3288	13	20	give	give	VERB
ejpam-3288	13	21	both	both	DET
ejpam-3288	13	22	a	a	DET
ejpam-3288	13	23	positive	positive	ADJ
ejpam-3288	13	24	membership	membership	NOUN
ejpam-3288	13	25	degree	degree	NOUN
ejpam-3288	13	26	belongs	belong	VERB
ejpam-3288	13	27	to	to	ADP
ejpam-3288	13	28	the	the	DET
ejpam-3288	13	29	interval	interval	NOUN
ejpam-3288	13	30	[	[	X
ejpam-3288	13	31	0	0	NUM
ejpam-3288	13	32	,	,	PUNCT
ejpam-3288	13	33	1	1	NUM
ejpam-3288	13	34	]	]	PUNCT
ejpam-3288	13	35	and	and	CCONJ
ejpam-3288	13	36	a	a	DET
ejpam-3288	13	37	negative	negative	ADJ
ejpam-3288	13	38	membership	membership	NOUN
ejpam-3288	13	39	degree	degree	NOUN
ejpam-3288	13	40	belongs	belong	VERB
ejpam-3288	13	41	to	to	ADP
ejpam-3288	13	42	the	the	DET
ejpam-3288	13	43	interval	interval	NOUN
ejpam-3288	13	44	[	[	X
ejpam-3288	13	45	-1	-1	X
ejpam-3288	13	46	,	,	PUNCT
ejpam-3288	13	47	0	0	NUM
ejpam-3288	13	48	]	]	PUNCT
ejpam-3288	13	49	.	.	PUNCT
ejpam-3288	14	1	in	in	ADP
ejpam-3288	14	2	the	the	DET
ejpam-3288	14	3	case	case	NOUN
ejpam-3288	14	4	of	of	ADP
ejpam-3288	14	5	bipolar	bipolar	ADJ
ejpam-3288	14	6	fuzzy	fuzzy	ADJ
ejpam-3288	14	7	sets	set	NOUN
ejpam-3288	14	8	,	,	PUNCT
ejpam-3288	14	9	the	the	DET
ejpam-3288	14	10	membership	membership	NOUN
ejpam-3288	14	11	degrees	degree	NOUN
ejpam-3288	14	12	range	range	NOUN
ejpam-3288	14	13	is	be	AUX
ejpam-3288	14	14	enlarged	enlarge	VERB
ejpam-3288	14	15	from	from	ADP
ejpam-3288	14	16	the	the	DET
ejpam-3288	14	17	interval	interval	NOUN
ejpam-3288	14	18	[	[	X
ejpam-3288	14	19	0	0	NUM
ejpam-3288	14	20	,	,	PUNCT
ejpam-3288	14	21	1	1	NUM
ejpam-3288	14	22	]	]	PUNCT
ejpam-3288	14	23	to	to	ADP
ejpam-3288	14	24	the	the	DET
ejpam-3288	14	25	interval	interval	NOUN
ejpam-3288	14	26	[	[	X
ejpam-3288	14	27	-1	-1	X
ejpam-3288	14	28	,	,	PUNCT
ejpam-3288	14	29	1	1	NUM
ejpam-3288	14	30	]	]	PUNCT
ejpam-3288	14	31	.	.	PUNCT
ejpam-3288	15	1	recently	recently	ADV
ejpam-3288	15	2	,	,	PUNCT
ejpam-3288	15	3	the	the	DET
ejpam-3288	15	4	theory	theory	NOUN
ejpam-3288	15	5	of	of	ADP
ejpam-3288	15	6	bipolar	bipolar	ADJ
ejpam-3288	15	7	fuzzy	fuzzy	ADJ
ejpam-3288	15	8	sets	set	NOUN
ejpam-3288	15	9	becomes	become	VERB
ejpam-3288	15	10	a	a	DET
ejpam-3288	15	11	vigorous	vigorous	ADJ
ejpam-3288	15	12	area	area	NOUN
ejpam-3288	15	13	of	of	ADP
ejpam-3288	15	14	research	research	NOUN
ejpam-3288	15	15	in	in	ADP
ejpam-3288	15	16	different	different	ADJ
ejpam-3288	15	17	domains	domain	NOUN
ejpam-3288	15	18	such	such	ADJ
ejpam-3288	15	19	as	as	ADP
ejpam-3288	15	20	group	group	NOUN
ejpam-3288	15	21	theory	theory	NOUN
ejpam-3288	15	22	,	,	PUNCT
ejpam-3288	15	23	semigroup	semigroup	PROPN
ejpam-3288	15	24	theory	theory	NOUN
ejpam-3288	15	25	,	,	PUNCT
ejpam-3288	15	26	ring	ring	NOUN
ejpam-3288	15	27	theory	theory	NOUN
ejpam-3288	15	28	,	,	PUNCT
ejpam-3288	15	29	semiring	semire	VERB
ejpam-3288	15	30	theory	theory	NOUN
ejpam-3288	15	31	,	,	PUNCT
ejpam-3288	15	32	graph	graph	NOUN
ejpam-3288	15	33	theory	theory	NOUN
ejpam-3288	15	34	,	,	PUNCT
ejpam-3288	15	35	engineering	engineering	NOUN
ejpam-3288	15	36	,	,	PUNCT
ejpam-3288	15	37	physics	physics	PROPN
ejpam-3288	15	38	,	,	PUNCT
ejpam-3288	15	39	statics	statics	PROPN
ejpam-3288	15	40	,	,	PUNCT
ejpam-3288	15	41	medical	medical	ADJ
ejpam-3288	15	42	science	science	NOUN
ejpam-3288	15	43	,	,	PUNCT
ejpam-3288	15	44	social	social	ADJ
ejpam-3288	15	45	science	science	NOUN
ejpam-3288	15	46	,	,	PUNCT
ejpam-3288	15	47	artificial	artificial	ADJ
ejpam-3288	15	48	intelligent	intelligent	ADJ
ejpam-3288	15	49	,	,	PUNCT
ejpam-3288	15	50	computer	computer	NOUN
ejpam-3288	15	51	networks	network	NOUN
ejpam-3288	15	52	,	,	PUNCT
ejpam-3288	15	53	expert	expert	NOUN
ejpam-3288	15	54	systems	system	NOUN
ejpam-3288	15	55	,	,	PUNCT
ejpam-3288	15	56	decision	decision	NOUN
ejpam-3288	15	57	making	making	NOUN
ejpam-3288	15	58	and	and	CCONJ
ejpam-3288	15	59	so	so	ADV
ejpam-3288	15	60	on	on	ADV
ejpam-3288	15	61	.	.	PUNCT
ejpam-3288	16	1	bck	bck	VERB
ejpam-3288	16	2	-	-	PUNCT
ejpam-3288	16	3	algebras	algebras	PROPN
ejpam-3288	16	4	introduced	introduce	VERB
ejpam-3288	16	5	by	by	ADP
ejpam-3288	16	6	imai	imai	PROPN
ejpam-3288	16	7	and	and	CCONJ
ejpam-3288	16	8	iséki	iséki	NUM
ejpam-3288	17	1	[	[	X
ejpam-3288	17	2	11	11	NUM
ejpam-3288	17	3	]	]	PUNCT
ejpam-3288	17	4	as	as	ADP
ejpam-3288	17	5	a	a	DET
ejpam-3288	17	6	generalization	generalization	NOUN
ejpam-3288	17	7	of	of	ADP
ejpam-3288	17	8	notion	notion	NOUN
ejpam-3288	17	9	of	of	ADP
ejpam-3288	17	10	the	the	DET
ejpam-3288	17	11	concept	concept	NOUN
ejpam-3288	17	12	of	of	ADP
ejpam-3288	17	13	set	set	VERB
ejpam-3288	17	14	theoretic	theoretic	ADJ
ejpam-3288	17	15	difference	difference	NOUN
ejpam-3288	17	16	and	and	CCONJ
ejpam-3288	17	17	propositional	propositional	ADJ
ejpam-3288	17	18	calculus	calculus	NOUN
ejpam-3288	17	19	and	and	CCONJ
ejpam-3288	17	20	then	then	ADV
ejpam-3288	17	21	iséki	iséki	PUNCT
ejpam-3288	18	1	[	[	X
ejpam-3288	18	2	12	12	NUM
ejpam-3288	18	3	]	]	PUNCT
ejpam-3288	18	4	introduced	introduce	VERB
ejpam-3288	18	5	∗corresponding	∗corresponde	VERB
ejpam-3288	18	6	author	author	NOUN
ejpam-3288	18	7	.	.	PUNCT
ejpam-3288	19	1	doi	doi	NOUN
ejpam-3288	19	2	:	:	PUNCT
ejpam-3288	19	3	https://doi.org/10.29020/nybg.ejpam.v11i3.3288	https://doi.org/10.29020/nybg.ejpam.v11i3.3288	ADJ
ejpam-3288	19	4	email	email	NOUN
ejpam-3288	19	5	addresses	address	NOUN
ejpam-3288	19	6	:	:	PUNCT
ejpam-3288	19	7	almasarwah85@gmail.com	almasarwah85@gmail.com	X
ejpam-3288	19	8	(	(	PUNCT
ejpam-3288	19	9	a.	a.	PROPN
ejpam-3288	19	10	al	al	PROPN
ejpam-3288	19	11	-	-	PROPN
ejpam-3288	19	12	masarwah	masarwah	NOUN
ejpam-3288	19	13	)	)	PUNCT
ejpam-3288	19	14	,	,	PUNCT
ejpam-3288	19	15	ghafur@ukm.edu.my	ghafur@ukm.edu.my	NOUN
ejpam-3288	19	16	(	(	PUNCT
ejpam-3288	19	17	a.	a.	NOUN
ejpam-3288	19	18	g.	g.	PROPN
ejpam-3288	19	19	ahmad	ahmad	PROPN
ejpam-3288	19	20	)	)	PUNCT
ejpam-3288	19	21	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3288	20	1	652	652	NUM
ejpam-3288	20	2	c	c	NOUN
ejpam-3288	20	3	©	©	PROPN
ejpam-3288	20	4	2018	2018	NUM
ejpam-3288	20	5	ejpam	ejpam	VERB
ejpam-3288	20	6	all	all	DET
ejpam-3288	20	7	rights	right	NOUN
ejpam-3288	20	8	reserved	reserve	VERB
ejpam-3288	20	9	.	.	PUNCT
ejpam-3288	21	1	a.	a.	PROPN
ejpam-3288	21	2	al	al	PROPN
ejpam-3288	21	3	-	-	PROPN
ejpam-3288	21	4	masarwah	masarwah	PROPN
ejpam-3288	21	5	,	,	PUNCT
ejpam-3288	21	6	a.	a.	NOUN
ejpam-3288	21	7	g.	g.	PROPN
ejpam-3288	21	8	ahmad	ahmad	PROPN
ejpam-3288	21	9	/	/	SYM
ejpam-3288	21	10	eur	eur	PROPN
ejpam-3288	21	11	.	.	PUNCT
ejpam-3288	22	1	j.	j.	PROPN
ejpam-3288	22	2	pure	pure	PROPN
ejpam-3288	22	3	appl	appl	PROPN
ejpam-3288	22	4	.	.	PROPN
ejpam-3288	22	5	math	math	PROPN
ejpam-3288	22	6	,	,	PUNCT
ejpam-3288	22	7	11	11	NUM
ejpam-3288	22	8	(	(	PUNCT
ejpam-3288	22	9	3	3	NUM
ejpam-3288	22	10	)	)	PUNCT
ejpam-3288	22	11	(	(	PUNCT
ejpam-3288	22	12	2018	2018	NUM
ejpam-3288	22	13	)	)	PUNCT
ejpam-3288	22	14	,	,	PUNCT
ejpam-3288	22	15	652	652	NUM
ejpam-3288	22	16	-	-	SYM
ejpam-3288	22	17	670	670	NUM
ejpam-3288	22	18	653	653	NUM
ejpam-3288	22	19	the	the	DET
ejpam-3288	22	20	notion	notion	NOUN
ejpam-3288	22	21	of	of	ADP
ejpam-3288	22	22	bci	bci	NOUN
ejpam-3288	22	23	-	-	PUNCT
ejpam-3288	22	24	algebras	algebra	NOUN
ejpam-3288	22	25	which	which	PRON
ejpam-3288	22	26	is	be	AUX
ejpam-3288	22	27	a	a	DET
ejpam-3288	22	28	generalization	generalization	NOUN
ejpam-3288	22	29	of	of	ADP
ejpam-3288	22	30	bck	bck	PROPN
ejpam-3288	22	31	-	-	PUNCT
ejpam-3288	22	32	algebras	algebras	PROPN
ejpam-3288	22	33	.	.	PUNCT
ejpam-3288	23	1	it	it	PRON
ejpam-3288	23	2	is	be	AUX
ejpam-3288	23	3	known	know	VERB
ejpam-3288	23	4	that	that	SCONJ
ejpam-3288	23	5	the	the	DET
ejpam-3288	23	6	class	class	NOUN
ejpam-3288	23	7	of	of	ADP
ejpam-3288	23	8	bck	bck	PROPN
ejpam-3288	23	9	-	-	PUNCT
ejpam-3288	23	10	algebras	algebras	PROPN
ejpam-3288	23	11	is	be	AUX
ejpam-3288	23	12	a	a	DET
ejpam-3288	23	13	proper	proper	ADJ
ejpam-3288	23	14	subclass	subclass	NOUN
ejpam-3288	23	15	of	of	ADP
ejpam-3288	23	16	the	the	DET
ejpam-3288	23	17	class	class	NOUN
ejpam-3288	23	18	of	of	ADP
ejpam-3288	23	19	bci	bci	PROPN
ejpam-3288	23	20	-	-	PUNCT
ejpam-3288	23	21	algebras	algebras	X
ejpam-3288	23	22	.	.	PUNCT
ejpam-3288	24	1	the	the	DET
ejpam-3288	24	2	study	study	NOUN
ejpam-3288	24	3	of	of	ADP
ejpam-3288	24	4	fuzzy	fuzzy	ADJ
ejpam-3288	24	5	algebraic	algebraic	ADJ
ejpam-3288	24	6	structures	structure	NOUN
ejpam-3288	24	7	was	be	AUX
ejpam-3288	24	8	started	start	VERB
ejpam-3288	24	9	with	with	ADP
ejpam-3288	24	10	the	the	DET
ejpam-3288	24	11	introduction	introduction	NOUN
ejpam-3288	24	12	of	of	ADP
ejpam-3288	24	13	the	the	DET
ejpam-3288	24	14	concept	concept	NOUN
ejpam-3288	24	15	of	of	ADP
ejpam-3288	24	16	fuzzy	fuzzy	ADJ
ejpam-3288	24	17	subgroups	subgroup	NOUN
ejpam-3288	24	18	in	in	ADP
ejpam-3288	24	19	1971	1971	NUM
ejpam-3288	24	20	by	by	ADP
ejpam-3288	24	21	rosenfeld	rosenfeld	PROPN
ejpam-3288	25	1	[	[	X
ejpam-3288	25	2	26	26	NUM
ejpam-3288	25	3	]	]	PUNCT
ejpam-3288	25	4	and	and	CCONJ
ejpam-3288	25	5	later	later	ADV
ejpam-3288	25	6	these	these	DET
ejpam-3288	25	7	ideas	idea	NOUN
ejpam-3288	25	8	have	have	AUX
ejpam-3288	25	9	been	be	AUX
ejpam-3288	25	10	applied	apply	VERB
ejpam-3288	25	11	to	to	ADP
ejpam-3288	25	12	other	other	ADJ
ejpam-3288	25	13	algebraic	algebraic	ADJ
ejpam-3288	25	14	structures	structure	NOUN
ejpam-3288	25	15	such	such	ADJ
ejpam-3288	25	16	as	as	ADP
ejpam-3288	25	17	semigroups	semigroup	NOUN
ejpam-3288	25	18	,	,	PUNCT
ejpam-3288	25	19	rings	ring	NOUN
ejpam-3288	25	20	,	,	PUNCT
ejpam-3288	25	21	semirings	semiring	NOUN
ejpam-3288	25	22	,	,	PUNCT
ejpam-3288	25	23	hemirings	hemiring	NOUN
ejpam-3288	25	24	,	,	PUNCT
ejpam-3288	25	25	ideals	ideal	NOUN
ejpam-3288	25	26	,	,	PUNCT
ejpam-3288	25	27	modules	module	NOUN
ejpam-3288	25	28	and	and	CCONJ
ejpam-3288	25	29	vector	vector	NOUN
ejpam-3288	25	30	spaces	space	NOUN
ejpam-3288	25	31	.	.	PUNCT
ejpam-3288	26	1	in	in	ADP
ejpam-3288	26	2	1991	1991	NUM
ejpam-3288	26	3	,	,	PUNCT
ejpam-3288	26	4	xi	xi	X
ejpam-3288	27	1	[	[	X
ejpam-3288	27	2	29	29	NUM
ejpam-3288	27	3	]	]	PUNCT
ejpam-3288	27	4	applied	apply	VERB
ejpam-3288	27	5	the	the	DET
ejpam-3288	27	6	concept	concept	NOUN
ejpam-3288	27	7	of	of	ADP
ejpam-3288	27	8	fuzzy	fuzzy	ADJ
ejpam-3288	27	9	sets	set	NOUN
ejpam-3288	27	10	to	to	PART
ejpam-3288	27	11	bck	bck	VERB
ejpam-3288	27	12	-	-	PUNCT
ejpam-3288	27	13	algebras	algebras	PROPN
ejpam-3288	27	14	.	.	PUNCT
ejpam-3288	28	1	after	after	ADP
ejpam-3288	28	2	that	that	PRON
ejpam-3288	28	3	,	,	PUNCT
ejpam-3288	28	4	jun	jun	PROPN
ejpam-3288	29	1	[	[	X
ejpam-3288	29	2	15	15	NUM
ejpam-3288	29	3	]	]	PUNCT
ejpam-3288	29	4	and	and	CCONJ
ejpam-3288	29	5	ahmad	ahmad	NOUN
ejpam-3288	29	6	[	[	X
ejpam-3288	29	7	1	1	NUM
ejpam-3288	29	8	]	]	PUNCT
ejpam-3288	29	9	applied	apply	VERB
ejpam-3288	29	10	the	the	DET
ejpam-3288	29	11	concept	concept	NOUN
ejpam-3288	29	12	of	of	ADP
ejpam-3288	29	13	fuzzy	fuzzy	ADJ
ejpam-3288	29	14	sets	set	NOUN
ejpam-3288	29	15	to	to	ADP
ejpam-3288	29	16	bci	bci	NOUN
ejpam-3288	29	17	-	-	PUNCT
ejpam-3288	29	18	algebras	algebras	X
ejpam-3288	29	19	.	.	PUNCT
ejpam-3288	30	1	jun	jun	PROPN
ejpam-3288	31	1	[	[	X
ejpam-3288	31	2	14	14	NUM
ejpam-3288	31	3	]	]	PUNCT
ejpam-3288	31	4	provided	provide	VERB
ejpam-3288	31	5	characterizations	characterization	NOUN
ejpam-3288	31	6	of	of	ADP
ejpam-3288	31	7	noetherian	noetherian	ADJ
ejpam-3288	31	8	bck	bck	NOUN
ejpam-3288	31	9	-	-	PUNCT
ejpam-3288	31	10	algebras	algebras	PROPN
ejpam-3288	31	11	in	in	ADP
ejpam-3288	31	12	terms	term	NOUN
ejpam-3288	31	13	of	of	ADP
ejpam-3288	31	14	fuzzy	fuzzy	ADJ
ejpam-3288	31	15	ideals	ideal	NOUN
ejpam-3288	31	16	.	.	PUNCT
ejpam-3288	32	1	fuzzy	fuzzy	ADJ
ejpam-3288	32	2	h	h	NOUN
ejpam-3288	32	3	-	-	PUNCT
ejpam-3288	32	4	ideals	ideal	NOUN
ejpam-3288	32	5	of	of	ADP
ejpam-3288	32	6	bci	bci	NOUN
ejpam-3288	32	7	-	-	PUNCT
ejpam-3288	32	8	algebras	algebras	PROPN
ejpam-3288	32	9	introduced	introduce	VERB
ejpam-3288	32	10	in	in	ADP
ejpam-3288	32	11	[	[	X
ejpam-3288	32	12	20	20	NUM
ejpam-3288	32	13	]	]	PUNCT
ejpam-3288	32	14	by	by	ADP
ejpam-3288	32	15	khalid	khalid	PROPN
ejpam-3288	32	16	and	and	CCONJ
ejpam-3288	32	17	ahmad	ahmad	PROPN
ejpam-3288	32	18	and	and	CCONJ
ejpam-3288	32	19	the	the	DET
ejpam-3288	32	20	concept	concept	NOUN
ejpam-3288	32	21	of	of	ADP
ejpam-3288	32	22	h	h	NOUN
ejpam-3288	32	23	-	-	PUNCT
ejpam-3288	32	24	noetherian	noetherian	ADJ
ejpam-3288	32	25	bck	bck	NOUN
ejpam-3288	32	26	-	-	PUNCT
ejpam-3288	32	27	algebras	algebras	PROPN
ejpam-3288	32	28	was	be	AUX
ejpam-3288	32	29	studied	study	VERB
ejpam-3288	32	30	in	in	ADP
ejpam-3288	32	31	[	[	X
ejpam-3288	32	32	33	33	NUM
ejpam-3288	32	33	]	]	PUNCT
ejpam-3288	32	34	by	by	ADP
ejpam-3288	32	35	zhan	zhan	PROPN
ejpam-3288	32	36	and	and	CCONJ
ejpam-3288	32	37	tan	tan	PROPN
ejpam-3288	32	38	.	.	PUNCT
ejpam-3288	33	1	huang	huang	PROPN
ejpam-3288	34	1	[	[	X
ejpam-3288	34	2	9	9	NUM
ejpam-3288	34	3	]	]	PUNCT
ejpam-3288	34	4	fuzzified	fuzzifie	VERB
ejpam-3288	34	5	bci	bci	NOUN
ejpam-3288	34	6	-	-	PUNCT
ejpam-3288	34	7	algebras	algebra	NOUN
ejpam-3288	34	8	in	in	ADP
ejpam-3288	34	9	little	little	ADJ
ejpam-3288	34	10	different	different	ADJ
ejpam-3288	34	11	ways	way	NOUN
ejpam-3288	34	12	.	.	PUNCT
ejpam-3288	35	1	jun	jun	PROPN
ejpam-3288	36	1	[	[	X
ejpam-3288	36	2	16	16	NUM
ejpam-3288	36	3	]	]	PUNCT
ejpam-3288	36	4	renamed	rename	VERB
ejpam-3288	36	5	huanǵs	huanǵs	PROPN
ejpam-3288	36	6	definition	definition	NOUN
ejpam-3288	36	7	as	as	SCONJ
ejpam-3288	36	8	doubt	doubt	ADV
ejpam-3288	36	9	fuzzy	fuzzy	ADJ
ejpam-3288	36	10	ideals	ideal	NOUN
ejpam-3288	36	11	in	in	ADP
ejpam-3288	36	12	bck	bck	PROPN
ejpam-3288	36	13	/	/	SYM
ejpam-3288	36	14	bci	bci	NOUN
ejpam-3288	36	15	-	-	PUNCT
ejpam-3288	36	16	algebras	algebras	PROPN
ejpam-3288	36	17	and	and	CCONJ
ejpam-3288	36	18	introduced	introduce	VERB
ejpam-3288	36	19	the	the	DET
ejpam-3288	36	20	concepts	concept	NOUN
ejpam-3288	36	21	of	of	ADP
ejpam-3288	36	22	doubt	doubt	ADV
ejpam-3288	36	23	fuzzy	fuzzy	ADJ
ejpam-3288	36	24	subalgebras	subalgebra	NOUN
ejpam-3288	36	25	and	and	CCONJ
ejpam-3288	36	26	doubt	doubt	VERB
ejpam-3288	36	27	fuzzy	fuzzy	ADJ
ejpam-3288	36	28	ideals	ideal	NOUN
ejpam-3288	36	29	in	in	ADP
ejpam-3288	36	30	bck	bck	PROPN
ejpam-3288	36	31	/	/	SYM
ejpam-3288	36	32	bci	bci	NOUN
ejpam-3288	36	33	-	-	PUNCT
ejpam-3288	36	34	algebras	algebras	X
ejpam-3288	36	35	.	.	PUNCT
ejpam-3288	37	1	zhan	zhan	PROPN
ejpam-3288	37	2	and	and	CCONJ
ejpam-3288	37	3	tan	tan	PROPN
ejpam-3288	38	1	[	[	X
ejpam-3288	38	2	32	32	NUM
ejpam-3288	38	3	]	]	PUNCT
ejpam-3288	38	4	introduced	introduce	VERB
ejpam-3288	38	5	the	the	DET
ejpam-3288	38	6	concept	concept	NOUN
ejpam-3288	38	7	of	of	ADP
ejpam-3288	38	8	doubt	doubt	ADV
ejpam-3288	38	9	fuzzy	fuzzy	ADJ
ejpam-3288	38	10	h	h	NOUN
ejpam-3288	38	11	-	-	PUNCT
ejpam-3288	38	12	ideals	ideal	NOUN
ejpam-3288	38	13	and	and	CCONJ
ejpam-3288	38	14	provided	provide	VERB
ejpam-3288	38	15	characterizations	characterization	NOUN
ejpam-3288	38	16	of	of	ADP
ejpam-3288	38	17	h	h	NOUN
ejpam-3288	38	18	-	-	PUNCT
ejpam-3288	38	19	artin	artin	NOUN
ejpam-3288	38	20	bck	bck	NOUN
ejpam-3288	38	21	-	-	PUNCT
ejpam-3288	38	22	algebras	algebras	PROPN
ejpam-3288	38	23	in	in	ADP
ejpam-3288	38	24	terms	term	NOUN
ejpam-3288	38	25	of	of	ADP
ejpam-3288	38	26	doubt	doubt	ADV
ejpam-3288	38	27	fuzzy	fuzzy	ADJ
ejpam-3288	38	28	h	h	NOUN
ejpam-3288	38	29	-	-	PUNCT
ejpam-3288	38	30	ideals	ideal	NOUN
ejpam-3288	38	31	.	.	PUNCT
ejpam-3288	39	1	muhiuddin	muhiuddin	VERB
ejpam-3288	39	2	and	and	CCONJ
ejpam-3288	39	3	aldhafeeri	aldhafeeri	VERB
ejpam-3288	39	4	[	[	X
ejpam-3288	39	5	24	24	NUM
ejpam-3288	39	6	]	]	PUNCT
ejpam-3288	39	7	introduced	introduce	VERB
ejpam-3288	39	8	the	the	DET
ejpam-3288	39	9	notions	notion	NOUN
ejpam-3288	39	10	of	of	ADP
ejpam-3288	39	11	unihesitant	unihesitant	ADJ
ejpam-3288	39	12	fuzzy	fuzzy	ADJ
ejpam-3288	39	13	algebras	algebra	NOUN
ejpam-3288	39	14	and	and	CCONJ
ejpam-3288	39	15	uni	uni	ADJ
ejpam-3288	39	16	-	-	ADJ
ejpam-3288	39	17	hesitant	hesitant	ADJ
ejpam-3288	39	18	fuzzy	fuzzy	ADJ
ejpam-3288	39	19	(	(	PUNCT
ejpam-3288	39	20	closed	closed	ADJ
ejpam-3288	39	21	)	)	PUNCT
ejpam-3288	39	22	ideals	ideal	NOUN
ejpam-3288	39	23	in	in	ADP
ejpam-3288	39	24	bck	bck	NOUN
ejpam-3288	39	25	-	-	PUNCT
ejpam-3288	39	26	algebras	algebra	NOUN
ejpam-3288	39	27	and	and	CCONJ
ejpam-3288	39	28	bcialgebras	bcialgebra	NOUN
ejpam-3288	39	29	.	.	PUNCT
ejpam-3288	40	1	muhiuddin	muhiuddin	PROPN
ejpam-3288	40	2	et	et	PROPN
ejpam-3288	40	3	al	al	PROPN
ejpam-3288	40	4	.	.	PUNCT
ejpam-3288	41	1	[	[	X
ejpam-3288	41	2	25	25	NUM
ejpam-3288	41	3	]	]	PUNCT
ejpam-3288	41	4	introduced	introduce	VERB
ejpam-3288	41	5	hesitant	hesitant	ADJ
ejpam-3288	41	6	fuzzy	fuzzy	ADJ
ejpam-3288	41	7	translations	translation	NOUN
ejpam-3288	41	8	and	and	CCONJ
ejpam-3288	41	9	extensions	extension	NOUN
ejpam-3288	41	10	of	of	ADP
ejpam-3288	41	11	subalgebras	subalgebra	NOUN
ejpam-3288	41	12	and	and	CCONJ
ejpam-3288	41	13	ideals	ideal	NOUN
ejpam-3288	41	14	in	in	ADP
ejpam-3288	41	15	bck	bck	PROPN
ejpam-3288	41	16	/	/	SYM
ejpam-3288	41	17	bci	bci	NOUN
ejpam-3288	41	18	-	-	PUNCT
ejpam-3288	41	19	algebras	algebra	NOUN
ejpam-3288	41	20	.	.	PUNCT
ejpam-3288	42	1	also	also	ADV
ejpam-3288	42	2	,	,	PUNCT
ejpam-3288	42	3	jun	jun	PROPN
ejpam-3288	42	4	et	et	PROPN
ejpam-3288	42	5	al	al	PROPN
ejpam-3288	42	6	.	.	PUNCT
ejpam-3288	43	1	[	[	X
ejpam-3288	43	2	17–19	17–19	NUM
ejpam-3288	43	3	]	]	PUNCT
ejpam-3288	43	4	studied	study	VERB
ejpam-3288	43	5	the	the	DET
ejpam-3288	43	6	notions	notion	NOUN
ejpam-3288	43	7	of	of	ADP
ejpam-3288	43	8	subalgebras	subalgebra	NOUN
ejpam-3288	43	9	and	and	CCONJ
ejpam-3288	43	10	ideals	ideal	NOUN
ejpam-3288	43	11	of	of	ADP
ejpam-3288	43	12	bck	bck	PROPN
ejpam-3288	43	13	/	/	SYM
ejpam-3288	43	14	bci	bci	NOUN
ejpam-3288	43	15	-	-	PUNCT
ejpam-3288	43	16	algebras	algebras	PROPN
ejpam-3288	43	17	based	base	VERB
ejpam-3288	43	18	on	on	ADP
ejpam-3288	43	19	hesitant	hesitant	ADJ
ejpam-3288	43	20	fuzzy	fuzzy	ADJ
ejpam-3288	43	21	soft	soft	ADJ
ejpam-3288	43	22	sets	set	NOUN
ejpam-3288	43	23	,	,	PUNCT
ejpam-3288	43	24	double	double	ADJ
ejpam-3288	43	25	-	-	PUNCT
ejpam-3288	43	26	framed	frame	VERB
ejpam-3288	43	27	soft	soft	ADJ
ejpam-3288	43	28	sets	set	NOUN
ejpam-3288	43	29	and	and	CCONJ
ejpam-3288	43	30	cubic	cubic	ADJ
ejpam-3288	43	31	soft	soft	ADJ
ejpam-3288	43	32	sets	set	NOUN
ejpam-3288	43	33	.	.	PUNCT
ejpam-3288	44	1	in	in	ADP
ejpam-3288	44	2	2009	2009	NUM
ejpam-3288	44	3	,	,	PUNCT
ejpam-3288	44	4	lee	lee	PROPN
ejpam-3288	45	1	[	[	X
ejpam-3288	45	2	21	21	NUM
ejpam-3288	45	3	]	]	PUNCT
ejpam-3288	45	4	applied	apply	VERB
ejpam-3288	45	5	the	the	DET
ejpam-3288	45	6	concept	concept	NOUN
ejpam-3288	45	7	of	of	ADP
ejpam-3288	45	8	bipolar	bipolar	ADJ
ejpam-3288	45	9	fuzzy	fuzzy	ADJ
ejpam-3288	45	10	set	set	NOUN
ejpam-3288	45	11	theory	theory	NOUN
ejpam-3288	45	12	to	to	PART
ejpam-3288	45	13	bck	bck	VERB
ejpam-3288	45	14	/	/	SYM
ejpam-3288	45	15	bcialgebras	bcialgebra	NOUN
ejpam-3288	45	16	,	,	PUNCT
ejpam-3288	45	17	and	and	CCONJ
ejpam-3288	45	18	introduced	introduce	VERB
ejpam-3288	45	19	the	the	DET
ejpam-3288	45	20	notions	notion	NOUN
ejpam-3288	45	21	of	of	ADP
ejpam-3288	45	22	bipolar	bipolar	ADJ
ejpam-3288	45	23	fuzzy	fuzzy	ADJ
ejpam-3288	45	24	subalgebras	subalgebra	NOUN
ejpam-3288	45	25	and	and	CCONJ
ejpam-3288	45	26	bipolar	bipolar	ADJ
ejpam-3288	45	27	fuzzy	fuzzy	ADJ
ejpam-3288	45	28	ideals	ideal	NOUN
ejpam-3288	45	29	of	of	ADP
ejpam-3288	45	30	bck	bck	PROPN
ejpam-3288	45	31	/	/	SYM
ejpam-3288	45	32	bci	bci	NOUN
ejpam-3288	45	33	-	-	PUNCT
ejpam-3288	45	34	algebras	algebras	X
ejpam-3288	45	35	.	.	PUNCT
ejpam-3288	46	1	recently	recently	ADV
ejpam-3288	46	2	,	,	PUNCT
ejpam-3288	46	3	the	the	DET
ejpam-3288	46	4	notion	notion	NOUN
ejpam-3288	46	5	of	of	ADP
ejpam-3288	46	6	bipolar	bipolar	ADJ
ejpam-3288	46	7	fuzzy	fuzzy	ADJ
ejpam-3288	46	8	set	set	NOUN
ejpam-3288	46	9	theory	theory	NOUN
ejpam-3288	46	10	was	be	AUX
ejpam-3288	46	11	applied	apply	VERB
ejpam-3288	46	12	to	to	PART
ejpam-3288	46	13	bck	bck	VERB
ejpam-3288	46	14	/	/	SYM
ejpam-3288	46	15	bci	bci	NOUN
ejpam-3288	46	16	-	-	PUNCT
ejpam-3288	46	17	algebras	algebras	X
ejpam-3288	47	1	[	[	X
ejpam-3288	47	2	4	4	NUM
ejpam-3288	47	3	,	,	PUNCT
ejpam-3288	47	4	23	23	NUM
ejpam-3288	47	5	]	]	PUNCT
ejpam-3288	47	6	and	and	CCONJ
ejpam-3288	47	7	other	other	ADJ
ejpam-3288	47	8	algebraic	algebraic	ADJ
ejpam-3288	47	9	structures	structure	NOUN
ejpam-3288	47	10	such	such	ADJ
ejpam-3288	47	11	that	that	DET
ejpam-3288	47	12	lie	lie	NOUN
ejpam-3288	47	13	algebras	algebra	VERB
ejpam-3288	48	1	[	[	X
ejpam-3288	48	2	2	2	NUM
ejpam-3288	48	3	]	]	PUNCT
ejpam-3288	48	4	,	,	PUNCT
ejpam-3288	48	5	lie	lie	VERB
ejpam-3288	48	6	superalgebras	superalgebra	NOUN
ejpam-3288	48	7	[	[	X
ejpam-3288	48	8	3	3	NUM
ejpam-3288	48	9	]	]	PUNCT
ejpam-3288	48	10	,	,	PUNCT
ejpam-3288	48	11	hemirings	hemiring	NOUN
ejpam-3288	48	12	[	[	X
ejpam-3288	48	13	8	8	NUM
ejpam-3288	48	14	]	]	PUNCT
ejpam-3288	48	15	and	and	CCONJ
ejpam-3288	48	16	bf	bf	NOUN
ejpam-3288	48	17	-algebras	-algebras	PROPN
ejpam-3288	48	18	[	[	X
ejpam-3288	48	19	27	27	NUM
ejpam-3288	48	20	,	,	PUNCT
ejpam-3288	48	21	28	28	NUM
ejpam-3288	48	22	]	]	PUNCT
ejpam-3288	48	23	,	,	PUNCT
ejpam-3288	48	24	etc	etc	X
ejpam-3288	48	25	.	.	X
ejpam-3288	49	1	al	al	PROPN
ejpam-3288	49	2	-	-	PROPN
ejpam-3288	49	3	masarwah	masarwah	PROPN
ejpam-3288	49	4	and	and	CCONJ
ejpam-3288	49	5	ahmad	ahmad	PROPN
ejpam-3288	49	6	[	[	X
ejpam-3288	49	7	5	5	NUM
ejpam-3288	49	8	]	]	PUNCT
ejpam-3288	49	9	introduced	introduce	VERB
ejpam-3288	49	10	the	the	DET
ejpam-3288	49	11	notions	notion	NOUN
ejpam-3288	49	12	of	of	ADP
ejpam-3288	49	13	doubt	doubt	NOUN
ejpam-3288	49	14	bipolar	bipolar	ADJ
ejpam-3288	49	15	fuzzy	fuzzy	ADJ
ejpam-3288	49	16	subalgebras	subalgebra	NOUN
ejpam-3288	49	17	and	and	CCONJ
ejpam-3288	49	18	doubt	doubt	VERB
ejpam-3288	49	19	bipolar	bipolar	ADJ
ejpam-3288	49	20	fuzzy	fuzzy	ADJ
ejpam-3288	49	21	ideals	ideal	NOUN
ejpam-3288	49	22	in	in	ADP
ejpam-3288	49	23	bck	bck	PROPN
ejpam-3288	49	24	/	/	SYM
ejpam-3288	49	25	bci	bci	NOUN
ejpam-3288	49	26	-	-	PUNCT
ejpam-3288	49	27	algebras	algebra	NOUN
ejpam-3288	49	28	.	.	PUNCT
ejpam-3288	50	1	also	also	ADV
ejpam-3288	50	2	,	,	PUNCT
ejpam-3288	50	3	they	they	PRON
ejpam-3288	50	4	introduced	introduce	VERB
ejpam-3288	50	5	the	the	DET
ejpam-3288	50	6	concept	concept	NOUN
ejpam-3288	50	7	of	of	ADP
ejpam-3288	50	8	doubt	doubt	NOUN
ejpam-3288	50	9	bipolar	bipolar	ADJ
ejpam-3288	50	10	fuzzy	fuzzy	ADJ
ejpam-3288	50	11	h	h	NOUN
ejpam-3288	50	12	-	-	PUNCT
ejpam-3288	50	13	ideals	ideal	NOUN
ejpam-3288	50	14	in	in	ADP
ejpam-3288	50	15	bck	bck	PROPN
ejpam-3288	50	16	/	/	SYM
ejpam-3288	50	17	bci	bci	NOUN
ejpam-3288	50	18	-	-	PUNCT
ejpam-3288	50	19	algebras	algebras	PROPN
ejpam-3288	50	20	and	and	CCONJ
ejpam-3288	50	21	investigated	investigate	VERB
ejpam-3288	50	22	some	some	DET
ejpam-3288	50	23	interesting	interesting	ADJ
ejpam-3288	50	24	properties	property	NOUN
ejpam-3288	50	25	[	[	X
ejpam-3288	50	26	6	6	NUM
ejpam-3288	50	27	]	]	PUNCT
ejpam-3288	50	28	.	.	PUNCT
ejpam-3288	51	1	this	this	DET
ejpam-3288	51	2	paper	paper	NOUN
ejpam-3288	51	3	is	be	AUX
ejpam-3288	51	4	a	a	DET
ejpam-3288	51	5	continuation	continuation	NOUN
ejpam-3288	51	6	of	of	ADP
ejpam-3288	51	7	the	the	DET
ejpam-3288	51	8	papers	paper	NOUN
ejpam-3288	51	9	[	[	X
ejpam-3288	51	10	5	5	NUM
ejpam-3288	51	11	]	]	PUNCT
ejpam-3288	51	12	and	and	CCONJ
ejpam-3288	51	13	[	[	X
ejpam-3288	51	14	6	6	NUM
ejpam-3288	51	15	]	]	PUNCT
ejpam-3288	51	16	.	.	PUNCT
ejpam-3288	52	1	we	we	PRON
ejpam-3288	52	2	study	study	VERB
ejpam-3288	52	3	some	some	DET
ejpam-3288	52	4	properties	property	NOUN
ejpam-3288	52	5	of	of	ADP
ejpam-3288	52	6	doubt	doubt	NOUN
ejpam-3288	52	7	bipolar	bipolar	ADJ
ejpam-3288	52	8	fuzzy	fuzzy	ADJ
ejpam-3288	52	9	h	h	NOUN
ejpam-3288	52	10	-	-	PUNCT
ejpam-3288	52	11	ideals	ideal	NOUN
ejpam-3288	52	12	in	in	ADP
ejpam-3288	52	13	bck/	bck/	VERB
ejpam-3288	52	14	bci	bci	NOUN
ejpam-3288	52	15	-	-	PUNCT
ejpam-3288	52	16	algebras	algebras	X
ejpam-3288	52	17	.	.	PUNCT
ejpam-3288	53	1	we	we	PRON
ejpam-3288	53	2	provide	provide	VERB
ejpam-3288	53	3	relations	relation	NOUN
ejpam-3288	53	4	between	between	ADP
ejpam-3288	53	5	a	a	DET
ejpam-3288	53	6	doubt	doubt	ADV
ejpam-3288	53	7	bipolar	bipolar	ADJ
ejpam-3288	53	8	fuzzy	fuzzy	ADJ
ejpam-3288	53	9	h	h	NOUN
ejpam-3288	53	10	-	-	PUNCT
ejpam-3288	53	11	ideal	ideal	NOUN
ejpam-3288	53	12	and	and	CCONJ
ejpam-3288	53	13	a	a	DET
ejpam-3288	53	14	doubt	doubt	ADV
ejpam-3288	53	15	bipolar	bipolar	ADJ
ejpam-3288	53	16	fuzzy	fuzzy	ADJ
ejpam-3288	53	17	ideal	ideal	NOUN
ejpam-3288	53	18	.	.	PUNCT
ejpam-3288	54	1	we	we	PRON
ejpam-3288	54	2	give	give	VERB
ejpam-3288	54	3	conditions	condition	NOUN
ejpam-3288	54	4	for	for	ADP
ejpam-3288	54	5	a	a	DET
ejpam-3288	54	6	doubt	doubt	ADV
ejpam-3288	54	7	bipolar	bipolar	ADJ
ejpam-3288	54	8	fuzzy	fuzzy	ADJ
ejpam-3288	54	9	ideal	ideal	NOUN
ejpam-3288	54	10	to	to	PART
ejpam-3288	54	11	be	be	AUX
ejpam-3288	54	12	a	a	DET
ejpam-3288	54	13	doubt	doubt	ADV
ejpam-3288	54	14	bipolar	bipolar	ADJ
ejpam-3288	54	15	fuzzy	fuzzy	ADJ
ejpam-3288	54	16	h	h	NOUN
ejpam-3288	54	17	-	-	PUNCT
ejpam-3288	54	18	ideal	ideal	ADJ
ejpam-3288	54	19	.	.	PUNCT
ejpam-3288	55	1	we	we	PRON
ejpam-3288	55	2	investigate	investigate	VERB
ejpam-3288	55	3	characterizations	characterization	NOUN
ejpam-3288	55	4	of	of	ADP
ejpam-3288	55	5	doubt	doubt	NOUN
ejpam-3288	55	6	bipolar	bipolar	ADJ
ejpam-3288	55	7	fuzzy	fuzzy	ADJ
ejpam-3288	55	8	h	h	NOUN
ejpam-3288	55	9	-	-	PUNCT
ejpam-3288	55	10	ideals	ideal	NOUN
ejpam-3288	55	11	by	by	ADP
ejpam-3288	55	12	means	mean	NOUN
ejpam-3288	55	13	of	of	ADP
ejpam-3288	55	14	doubt	doubt	NOUN
ejpam-3288	55	15	positive	positive	ADJ
ejpam-3288	55	16	t	t	NOUN
ejpam-3288	55	17	-	-	PUNCT
ejpam-3288	55	18	level	level	NOUN
ejpam-3288	55	19	cut	cut	NOUN
ejpam-3288	55	20	set	set	NOUN
ejpam-3288	55	21	,	,	PUNCT
ejpam-3288	55	22	doubt	doubt	VERB
ejpam-3288	55	23	negative	negative	ADJ
ejpam-3288	55	24	s	s	NOUN
ejpam-3288	55	25	-	-	PUNCT
ejpam-3288	55	26	level	level	NOUN
ejpam-3288	55	27	cut	cut	NOUN
ejpam-3288	55	28	set	set	VERB
ejpam-3288	55	29	and	and	CCONJ
ejpam-3288	55	30	h	h	NOUN
ejpam-3288	55	31	-	-	PUNCT
ejpam-3288	55	32	artin	artin	NOUN
ejpam-3288	55	33	bck	bck	PROPN
ejpam-3288	55	34	/	/	SYM
ejpam-3288	55	35	bci	bci	NOUN
ejpam-3288	55	36	-	-	PUNCT
ejpam-3288	55	37	algebras	algebra	NOUN
ejpam-3288	55	38	.	.	PUNCT
ejpam-3288	56	1	2	2	X
ejpam-3288	56	2	.	.	X
ejpam-3288	56	3	preliminaries	preliminary	NOUN
ejpam-3288	56	4	we	we	PRON
ejpam-3288	56	5	first	first	ADV
ejpam-3288	56	6	recall	recall	VERB
ejpam-3288	56	7	some	some	DET
ejpam-3288	56	8	elementary	elementary	ADJ
ejpam-3288	56	9	aspects	aspect	NOUN
ejpam-3288	56	10	which	which	PRON
ejpam-3288	56	11	are	be	AUX
ejpam-3288	56	12	used	use	VERB
ejpam-3288	56	13	to	to	PART
ejpam-3288	56	14	present	present	VERB
ejpam-3288	56	15	the	the	DET
ejpam-3288	56	16	paper	paper	NOUN
ejpam-3288	56	17	.	.	PUNCT
ejpam-3288	57	1	a	a	DET
ejpam-3288	57	2	bck	bck	VERB
ejpam-3288	57	3	/	/	SYM
ejpam-3288	57	4	bci	bci	NOUN
ejpam-3288	57	5	-	-	NOUN
ejpam-3288	57	6	algebra	algebra	NOUN
ejpam-3288	57	7	is	be	AUX
ejpam-3288	57	8	an	an	DET
ejpam-3288	57	9	important	important	ADJ
ejpam-3288	57	10	class	class	NOUN
ejpam-3288	57	11	of	of	ADP
ejpam-3288	57	12	logical	logical	ADJ
ejpam-3288	57	13	algebras	algebra	NOUN
ejpam-3288	57	14	introduced	introduce	VERB
ejpam-3288	57	15	by	by	ADP
ejpam-3288	57	16	imai	imai	PROPN
ejpam-3288	57	17	and	and	CCONJ
ejpam-3288	57	18	iséki	iséki	NUM
ejpam-3288	58	1	[	[	X
ejpam-3288	58	2	11	11	NUM
ejpam-3288	58	3	,	,	PUNCT
ejpam-3288	58	4	12	12	NUM
ejpam-3288	58	5	]	]	PUNCT
ejpam-3288	58	6	and	and	CCONJ
ejpam-3288	58	7	was	be	AUX
ejpam-3288	58	8	extensively	extensively	ADV
ejpam-3288	58	9	investigated	investigate	VERB
ejpam-3288	58	10	by	by	ADP
ejpam-3288	58	11	several	several	ADJ
ejpam-3288	58	12	researchers	researcher	NOUN
ejpam-3288	58	13	.	.	PUNCT
ejpam-3288	59	1	this	this	DET
ejpam-3288	59	2	algebra	algebra	NOUN
ejpam-3288	59	3	is	be	AUX
ejpam-3288	59	4	defined	define	VERB
ejpam-3288	59	5	as	as	ADP
ejpam-3288	59	6	follows	follow	VERB
ejpam-3288	59	7	.	.	PUNCT
ejpam-3288	60	1	by	by	ADP
ejpam-3288	60	2	a	a	DET
ejpam-3288	60	3	bci	bci	NOUN
ejpam-3288	60	4	-	-	NOUN
ejpam-3288	60	5	algebra	algebra	NOUN
ejpam-3288	60	6	,	,	PUNCT
ejpam-3288	60	7	we	we	PRON
ejpam-3288	60	8	mean	mean	VERB
ejpam-3288	60	9	an	an	DET
ejpam-3288	60	10	algebra	algebra	NOUN
ejpam-3288	60	11	(	(	PUNCT
ejpam-3288	60	12	x	x	NOUN
ejpam-3288	60	13	;	;	PUNCT
ejpam-3288	60	14	∗	∗	NOUN
ejpam-3288	60	15	,	,	PUNCT
ejpam-3288	60	16	0	0	NUM
ejpam-3288	60	17	)	)	PUNCT
ejpam-3288	60	18	of	of	ADP
ejpam-3288	60	19	type	type	NOUN
ejpam-3288	60	20	(	(	PUNCT
ejpam-3288	60	21	2	2	NUM
ejpam-3288	60	22	,	,	PUNCT
ejpam-3288	60	23	0	0	NUM
ejpam-3288	60	24	)	)	PUNCT
ejpam-3288	60	25	satisfying	satisfy	VERB
ejpam-3288	60	26	the	the	DET
ejpam-3288	60	27	following	follow	VERB
ejpam-3288	60	28	axioms	axiom	NOUN
ejpam-3288	60	29	for	for	ADP
ejpam-3288	60	30	all	all	DET
ejpam-3288	60	31	x	x	NOUN
ejpam-3288	60	32	,	,	PUNCT
ejpam-3288	60	33	y	y	PROPN
ejpam-3288	60	34	,	,	PUNCT
ejpam-3288	60	35	z	z	NOUN
ejpam-3288	60	36	∈	∈	PROPN
ejpam-3288	60	37	x	x	X
ejpam-3288	60	38	:	:	PUNCT
ejpam-3288	60	39	a.	a.	PROPN
ejpam-3288	60	40	al	al	PROPN
ejpam-3288	60	41	-	-	PROPN
ejpam-3288	60	42	masarwah	masarwah	PROPN
ejpam-3288	60	43	,	,	PUNCT
ejpam-3288	60	44	a.	a.	NOUN
ejpam-3288	60	45	g.	g.	PROPN
ejpam-3288	60	46	ahmad	ahmad	PROPN
ejpam-3288	60	47	/	/	SYM
ejpam-3288	60	48	eur	eur	PROPN
ejpam-3288	60	49	.	.	PUNCT
ejpam-3288	61	1	j.	j.	PROPN
ejpam-3288	61	2	pure	pure	PROPN
ejpam-3288	61	3	appl	appl	PROPN
ejpam-3288	61	4	.	.	PROPN
ejpam-3288	61	5	math	math	PROPN
ejpam-3288	61	6	,	,	PUNCT
ejpam-3288	61	7	11	11	NUM
ejpam-3288	61	8	(	(	PUNCT
ejpam-3288	61	9	3	3	NUM
ejpam-3288	61	10	)	)	PUNCT
ejpam-3288	61	11	(	(	PUNCT
ejpam-3288	61	12	2018	2018	NUM
ejpam-3288	61	13	)	)	PUNCT
ejpam-3288	61	14	,	,	PUNCT
ejpam-3288	61	15	652	652	NUM
ejpam-3288	61	16	-	-	SYM
ejpam-3288	61	17	670	670	NUM
ejpam-3288	61	18	654	654	NUM
ejpam-3288	61	19	(	(	PUNCT
ejpam-3288	61	20	i	i	NOUN
ejpam-3288	61	21	)	)	PUNCT
ejpam-3288	61	22	(	(	PUNCT
ejpam-3288	61	23	(	(	PUNCT
ejpam-3288	61	24	x	x	SYM
ejpam-3288	61	25	∗	∗	PROPN
ejpam-3288	61	26	y	y	NOUN
ejpam-3288	61	27	)	)	PUNCT
ejpam-3288	61	28	∗	∗	NOUN
ejpam-3288	61	29	(	(	PUNCT
ejpam-3288	61	30	x	x	X
ejpam-3288	61	31	∗	∗	PROPN
ejpam-3288	61	32	z	z	NOUN
ejpam-3288	61	33	)	)	PUNCT
ejpam-3288	61	34	)	)	PUNCT
ejpam-3288	61	35	∗	∗	NOUN
ejpam-3288	61	36	(	(	PUNCT
ejpam-3288	61	37	z	z	NOUN
ejpam-3288	61	38	∗	∗	NOUN
ejpam-3288	61	39	y	y	NOUN
ejpam-3288	61	40	)	)	PUNCT
ejpam-3288	62	1	=	=	SYM
ejpam-3288	62	2	0	0	NUM
ejpam-3288	62	3	,	,	PUNCT
ejpam-3288	62	4	(	(	PUNCT
ejpam-3288	62	5	ii	ii	NOUN
ejpam-3288	62	6	)	)	PUNCT
ejpam-3288	62	7	(	(	PUNCT
ejpam-3288	62	8	x	x	SYM
ejpam-3288	62	9	∗	∗	NOUN
ejpam-3288	62	10	(	(	PUNCT
ejpam-3288	62	11	x	x	X
ejpam-3288	62	12	∗	∗	PROPN
ejpam-3288	62	13	y	y	NOUN
ejpam-3288	62	14	)	)	PUNCT
ejpam-3288	62	15	)	)	PUNCT
ejpam-3288	63	1	∗	∗	NOUN
ejpam-3288	63	2	y	y	NOUN
ejpam-3288	63	3	=	=	SYM
ejpam-3288	63	4	0	0	PROPN
ejpam-3288	63	5	,	,	PUNCT
ejpam-3288	63	6	(	(	PUNCT
ejpam-3288	63	7	iii	iii	NOUN
ejpam-3288	63	8	)	)	PUNCT
ejpam-3288	63	9	x	x	SYM
ejpam-3288	63	10	∗	∗	NOUN
ejpam-3288	63	11	x	x	SYM
ejpam-3288	64	1	=	=	SYM
ejpam-3288	64	2	0	0	NUM
ejpam-3288	64	3	,	,	PUNCT
ejpam-3288	64	4	(	(	PUNCT
ejpam-3288	64	5	iv	iv	X
ejpam-3288	64	6	)	)	PUNCT
ejpam-3288	65	1	x	x	PROPN
ejpam-3288	65	2	∗	∗	NOUN
ejpam-3288	65	3	y	y	NOUN
ejpam-3288	65	4	=	=	SYM
ejpam-3288	65	5	0	0	PROPN
ejpam-3288	66	1	and	and	CCONJ
ejpam-3288	66	2	y	y	PROPN
ejpam-3288	66	3	∗	∗	NOUN
ejpam-3288	66	4	x	x	PUNCT
ejpam-3288	67	1	=	=	SYM
ejpam-3288	67	2	0	0	NUM
ejpam-3288	67	3	imply	imply	VERB
ejpam-3288	67	4	x	x	X
ejpam-3288	68	1	=	=	PUNCT
ejpam-3288	68	2	y.	y.	NOUN
ejpam-3288	68	3	if	if	SCONJ
ejpam-3288	68	4	a	a	DET
ejpam-3288	68	5	bci	bci	NOUN
ejpam-3288	68	6	-	-	NOUN
ejpam-3288	68	7	algebra	algebra	NOUN
ejpam-3288	68	8	x	x	SYM
ejpam-3288	68	9	satisfies	satisfie	NOUN
ejpam-3288	68	10	0	0	NUM
ejpam-3288	68	11	∗	∗	NOUN
ejpam-3288	68	12	x	x	PUNCT
ejpam-3288	68	13	=	=	SYM
ejpam-3288	68	14	0	0	NUM
ejpam-3288	68	15	,	,	PUNCT
ejpam-3288	68	16	then	then	ADV
ejpam-3288	68	17	x	x	PUNCT
ejpam-3288	68	18	is	be	AUX
ejpam-3288	68	19	called	call	VERB
ejpam-3288	68	20	a	a	DET
ejpam-3288	68	21	bck	bck	NOUN
ejpam-3288	68	22	-	-	PUNCT
ejpam-3288	68	23	algebra	algebra	NOUN
ejpam-3288	68	24	.	.	PUNCT
ejpam-3288	69	1	in	in	ADP
ejpam-3288	69	2	a	a	DET
ejpam-3288	69	3	bck	bck	VERB
ejpam-3288	69	4	/	/	SYM
ejpam-3288	69	5	bci	bci	NOUN
ejpam-3288	69	6	-	-	NOUN
ejpam-3288	69	7	algebra	algebra	NOUN
ejpam-3288	69	8	,	,	PUNCT
ejpam-3288	69	9	x∗0	x∗0	NOUN
ejpam-3288	69	10	=	=	PUNCT
ejpam-3288	69	11	x	x	PUNCT
ejpam-3288	69	12	hold	hold	VERB
ejpam-3288	69	13	.	.	PUNCT
ejpam-3288	70	1	a	a	DET
ejpam-3288	70	2	bci	bci	NOUN
ejpam-3288	70	3	-	-	NOUN
ejpam-3288	70	4	algebra	algebra	NOUN
ejpam-3288	70	5	is	be	AUX
ejpam-3288	70	6	said	say	VERB
ejpam-3288	70	7	to	to	PART
ejpam-3288	70	8	be	be	AUX
ejpam-3288	70	9	associative	associative	ADJ
ejpam-3288	70	10	if	if	SCONJ
ejpam-3288	70	11	(	(	PUNCT
ejpam-3288	70	12	x∗y)∗z	x∗y)∗z	NOUN
ejpam-3288	70	13	=	=	PUNCT
ejpam-3288	70	14	x	x	SYM
ejpam-3288	70	15	∗	∗	NOUN
ejpam-3288	70	16	(	(	PUNCT
ejpam-3288	70	17	y	y	PROPN
ejpam-3288	70	18	∗	∗	PROPN
ejpam-3288	70	19	z	z	PROPN
ejpam-3288	70	20	)	)	PUNCT
ejpam-3288	70	21	for	for	ADP
ejpam-3288	70	22	all	all	DET
ejpam-3288	70	23	x	x	NOUN
ejpam-3288	70	24	,	,	PUNCT
ejpam-3288	70	25	y	y	PROPN
ejpam-3288	70	26	,	,	PUNCT
ejpam-3288	70	27	z	z	PROPN
ejpam-3288	70	28	∈	∈	PROPN
ejpam-3288	70	29	x.	x.	NOUN
ejpam-3288	70	30	a	a	DET
ejpam-3288	70	31	partial	partial	ADJ
ejpam-3288	70	32	ordering	order	VERB
ejpam-3288	70	33	≤	≤	NOUN
ejpam-3288	70	34	on	on	ADP
ejpam-3288	70	35	a	a	DET
ejpam-3288	70	36	bck	bck	VERB
ejpam-3288	70	37	/	/	SYM
ejpam-3288	70	38	bci	bci	NOUN
ejpam-3288	70	39	-	-	NOUN
ejpam-3288	70	40	algebra	algebra	NOUN
ejpam-3288	70	41	x	x	PUNCT
ejpam-3288	70	42	can	can	AUX
ejpam-3288	70	43	be	be	AUX
ejpam-3288	70	44	defined	define	VERB
ejpam-3288	70	45	by	by	ADP
ejpam-3288	70	46	x	x	PROPN
ejpam-3288	70	47	≤	≤	NUM
ejpam-3288	70	48	y	y	NOUN
ejpam-3288	71	1	if	if	SCONJ
ejpam-3288	71	2	and	and	CCONJ
ejpam-3288	71	3	only	only	ADV
ejpam-3288	71	4	if	if	SCONJ
ejpam-3288	71	5	x∗y	x∗y	PROPN
ejpam-3288	71	6	=	=	SYM
ejpam-3288	71	7	0	0	X
ejpam-3288	71	8	.	.	PUNCT
ejpam-3288	72	1	any	any	DET
ejpam-3288	72	2	bck	bck	PROPN
ejpam-3288	72	3	/	/	SYM
ejpam-3288	72	4	bci	bci	NOUN
ejpam-3288	72	5	-	-	NOUN
ejpam-3288	72	6	algebra	algebra	NOUN
ejpam-3288	72	7	x	x	PRON
ejpam-3288	72	8	satisfies	satisfy	VERB
ejpam-3288	72	9	the	the	DET
ejpam-3288	72	10	following	following	ADJ
ejpam-3288	72	11	axioms	axiom	NOUN
ejpam-3288	72	12	for	for	ADP
ejpam-3288	72	13	all	all	DET
ejpam-3288	72	14	x	x	NOUN
ejpam-3288	72	15	,	,	PUNCT
ejpam-3288	72	16	y	y	PROPN
ejpam-3288	72	17	,	,	PUNCT
ejpam-3288	72	18	z	z	PROPN
ejpam-3288	72	19	∈	∈	PROPN
ejpam-3288	73	1	x	x	X
ejpam-3288	73	2	:	:	PUNCT
ejpam-3288	73	3	(	(	PUNCT
ejpam-3288	73	4	1	1	X
ejpam-3288	73	5	)	)	PUNCT
ejpam-3288	73	6	x	x	NOUN
ejpam-3288	74	1	∗	∗	NOUN
ejpam-3288	74	2	0	0	NUM
ejpam-3288	75	1	=	=	SYM
ejpam-3288	75	2	x	x	NOUN
ejpam-3288	75	3	,	,	PUNCT
ejpam-3288	75	4	(	(	PUNCT
ejpam-3288	75	5	2	2	NUM
ejpam-3288	75	6	)	)	PUNCT
ejpam-3288	75	7	(	(	PUNCT
ejpam-3288	75	8	x	x	SYM
ejpam-3288	75	9	∗	∗	PROPN
ejpam-3288	75	10	y	y	NOUN
ejpam-3288	75	11	)	)	PUNCT
ejpam-3288	75	12	∗	∗	NOUN
ejpam-3288	75	13	z	z	NOUN
ejpam-3288	75	14	=	=	SYM
ejpam-3288	75	15	(	(	PUNCT
ejpam-3288	75	16	x	x	X
ejpam-3288	75	17	∗	∗	PROPN
ejpam-3288	75	18	z	z	NOUN
ejpam-3288	75	19	)	)	PUNCT
ejpam-3288	75	20	∗	∗	PROPN
ejpam-3288	75	21	y	y	PROPN
ejpam-3288	75	22	,	,	PUNCT
ejpam-3288	75	23	(	(	PUNCT
ejpam-3288	75	24	3	3	X
ejpam-3288	75	25	)	)	PUNCT
ejpam-3288	75	26	x	x	NOUN
ejpam-3288	75	27	∗	∗	NOUN
ejpam-3288	75	28	y	y	NOUN
ejpam-3288	75	29	≤	≤	NUM
ejpam-3288	75	30	x	x	X
ejpam-3288	75	31	,	,	PUNCT
ejpam-3288	75	32	(	(	PUNCT
ejpam-3288	75	33	4	4	NUM
ejpam-3288	75	34	)	)	PUNCT
ejpam-3288	75	35	(	(	PUNCT
ejpam-3288	75	36	x	x	SYM
ejpam-3288	75	37	∗	∗	PROPN
ejpam-3288	75	38	y	y	NOUN
ejpam-3288	75	39	)	)	PUNCT
ejpam-3288	75	40	∗	∗	NOUN
ejpam-3288	75	41	z	z	NOUN
ejpam-3288	75	42	≤	≤	NOUN
ejpam-3288	75	43	(	(	PUNCT
ejpam-3288	75	44	x	x	X
ejpam-3288	75	45	∗	∗	PROPN
ejpam-3288	75	46	z	z	NOUN
ejpam-3288	75	47	)	)	PUNCT
ejpam-3288	75	48	∗	∗	NOUN
ejpam-3288	75	49	(	(	PUNCT
ejpam-3288	75	50	y	y	PROPN
ejpam-3288	75	51	∗	∗	PROPN
ejpam-3288	75	52	z	z	PROPN
ejpam-3288	75	53	)	)	PUNCT
ejpam-3288	75	54	,	,	PUNCT
ejpam-3288	75	55	(	(	PUNCT
ejpam-3288	75	56	5	5	X
ejpam-3288	75	57	)	)	PUNCT
ejpam-3288	75	58	x	x	PUNCT
ejpam-3288	75	59	≤	≤	X
ejpam-3288	75	60	y	y	PROPN
ejpam-3288	75	61	⇒	⇒	NOUN
ejpam-3288	75	62	x	x	PUNCT
ejpam-3288	75	63	∗	∗	NOUN
ejpam-3288	75	64	z	z	NOUN
ejpam-3288	75	65	≤	≤	NOUN
ejpam-3288	75	66	y	y	PROPN
ejpam-3288	75	67	∗	∗	PROPN
ejpam-3288	75	68	z	z	PROPN
ejpam-3288	75	69	,	,	PUNCT
ejpam-3288	75	70	z	z	PROPN
ejpam-3288	75	71	∗	∗	NOUN
ejpam-3288	75	72	y	y	PROPN
ejpam-3288	75	73	≤	≤	PROPN
ejpam-3288	75	74	z	z	NOUN
ejpam-3288	75	75	∗	∗	NOUN
ejpam-3288	75	76	x.	x.	NOUN
ejpam-3288	76	1	definition	definition	NOUN
ejpam-3288	76	2	1	1	NUM
ejpam-3288	76	3	.	.	PUNCT
ejpam-3288	77	1	[	[	X
ejpam-3288	77	2	29	29	NUM
ejpam-3288	77	3	]	]	X
ejpam-3288	77	4	a	a	DET
ejpam-3288	77	5	non	non	ADJ
ejpam-3288	77	6	-	-	ADJ
ejpam-3288	77	7	empty	empty	ADJ
ejpam-3288	77	8	subset	subset	NOUN
ejpam-3288	77	9	s	s	NOUN
ejpam-3288	77	10	of	of	ADP
ejpam-3288	77	11	a	a	DET
ejpam-3288	77	12	bck	bck	PROPN
ejpam-3288	77	13	/	/	SYM
ejpam-3288	77	14	bci	bci	NOUN
ejpam-3288	77	15	-	-	NOUN
ejpam-3288	77	16	algebra	algebra	NOUN
ejpam-3288	77	17	x	x	PUNCT
ejpam-3288	77	18	is	be	AUX
ejpam-3288	77	19	called	call	VERB
ejpam-3288	77	20	an	an	DET
ejpam-3288	77	21	ideal	ideal	NOUN
ejpam-3288	77	22	of	of	ADP
ejpam-3288	77	23	x	x	PRON
ejpam-3288	77	24	if	if	SCONJ
ejpam-3288	77	25	(	(	PUNCT
ejpam-3288	77	26	i	i	NOUN
ejpam-3288	77	27	)	)	PUNCT
ejpam-3288	77	28	0	0	PUNCT
ejpam-3288	78	1	∈	∈	NOUN
ejpam-3288	78	2	s	s	X
ejpam-3288	78	3	(	(	PUNCT
ejpam-3288	78	4	ii	ii	NOUN
ejpam-3288	78	5	)	)	PUNCT
ejpam-3288	78	6	x	x	SYM
ejpam-3288	79	1	∗	∗	NOUN
ejpam-3288	79	2	y	y	PROPN
ejpam-3288	79	3	∈	∈	PROPN
ejpam-3288	79	4	s	s	PART
ejpam-3288	79	5	and	and	CCONJ
ejpam-3288	79	6	y	y	PROPN
ejpam-3288	79	7	∈	∈	PROPN
ejpam-3288	80	1	s	s	VERB
ejpam-3288	80	2	then	then	ADV
ejpam-3288	80	3	x	x	SYM
ejpam-3288	80	4	∈	∈	PROPN
ejpam-3288	80	5	s	s	NOUN
ejpam-3288	80	6	,	,	PUNCT
ejpam-3288	80	7	for	for	ADP
ejpam-3288	80	8	all	all	DET
ejpam-3288	80	9	x	x	NOUN
ejpam-3288	80	10	,	,	PUNCT
ejpam-3288	80	11	y	y	PROPN
ejpam-3288	80	12	∈	∈	PROPN
ejpam-3288	80	13	x.	x.	NOUN
ejpam-3288	80	14	definition	definition	NOUN
ejpam-3288	80	15	2	2	NUM
ejpam-3288	80	16	.	.	PUNCT
ejpam-3288	81	1	[	[	X
ejpam-3288	81	2	20	20	NUM
ejpam-3288	81	3	]	]	PUNCT
ejpam-3288	81	4	a	a	DET
ejpam-3288	81	5	non	non	ADJ
ejpam-3288	81	6	-	-	ADJ
ejpam-3288	81	7	empty	empty	ADJ
ejpam-3288	81	8	subset	subset	NOUN
ejpam-3288	81	9	s	s	NOUN
ejpam-3288	81	10	of	of	ADP
ejpam-3288	81	11	a	a	DET
ejpam-3288	81	12	bck	bck	PROPN
ejpam-3288	81	13	/	/	SYM
ejpam-3288	81	14	bci	bci	NOUN
ejpam-3288	81	15	-	-	NOUN
ejpam-3288	81	16	algebra	algebra	NOUN
ejpam-3288	81	17	x	x	PUNCT
ejpam-3288	81	18	is	be	AUX
ejpam-3288	81	19	called	call	VERB
ejpam-3288	81	20	an	an	DET
ejpam-3288	81	21	h	h	NOUN
ejpam-3288	81	22	-	-	PUNCT
ejpam-3288	81	23	ideal	ideal	NOUN
ejpam-3288	81	24	of	of	ADP
ejpam-3288	81	25	x	x	PRON
ejpam-3288	81	26	if	if	SCONJ
ejpam-3288	81	27	(	(	PUNCT
ejpam-3288	81	28	i	i	NOUN
ejpam-3288	81	29	)	)	PUNCT
ejpam-3288	81	30	0	0	PUNCT
ejpam-3288	82	1	∈	∈	NOUN
ejpam-3288	82	2	s	s	X
ejpam-3288	82	3	(	(	PUNCT
ejpam-3288	82	4	ii	ii	NOUN
ejpam-3288	82	5	)	)	PUNCT
ejpam-3288	82	6	x	x	SYM
ejpam-3288	82	7	∗	∗	NOUN
ejpam-3288	82	8	(	(	PUNCT
ejpam-3288	82	9	y	y	PROPN
ejpam-3288	82	10	∗	∗	PROPN
ejpam-3288	82	11	z	z	PROPN
ejpam-3288	82	12	)	)	PUNCT
ejpam-3288	82	13	∈	∈	PROPN
ejpam-3288	82	14	s	s	PART
ejpam-3288	82	15	and	and	CCONJ
ejpam-3288	82	16	y	y	PROPN
ejpam-3288	82	17	∈	∈	PROPN
ejpam-3288	82	18	s	s	VERB
ejpam-3288	82	19	then	then	ADV
ejpam-3288	82	20	x	x	X
ejpam-3288	82	21	∗	∗	NOUN
ejpam-3288	82	22	z	z	PROPN
ejpam-3288	82	23	∈	∈	PROPN
ejpam-3288	82	24	s	s	NOUN
ejpam-3288	82	25	,	,	PUNCT
ejpam-3288	82	26	for	for	ADP
ejpam-3288	82	27	all	all	DET
ejpam-3288	82	28	x	x	NOUN
ejpam-3288	82	29	,	,	PUNCT
ejpam-3288	82	30	y	y	PROPN
ejpam-3288	82	31	,	,	PUNCT
ejpam-3288	82	32	z	z	NOUN
ejpam-3288	82	33	∈	∈	PROPN
ejpam-3288	82	34	x.	x.	NOUN
ejpam-3288	82	35	we	we	PRON
ejpam-3288	82	36	refer	refer	VERB
ejpam-3288	82	37	the	the	DET
ejpam-3288	82	38	reader	reader	NOUN
ejpam-3288	82	39	to	to	ADP
ejpam-3288	82	40	[	[	X
ejpam-3288	82	41	10	10	NUM
ejpam-3288	82	42	,	,	PUNCT
ejpam-3288	82	43	13	13	NUM
ejpam-3288	82	44	]	]	PUNCT
ejpam-3288	82	45	for	for	ADP
ejpam-3288	82	46	further	further	ADJ
ejpam-3288	82	47	information	information	NOUN
ejpam-3288	82	48	regarding	regard	VERB
ejpam-3288	82	49	bck	bck	PROPN
ejpam-3288	82	50	/	/	SYM
ejpam-3288	82	51	bci	bci	NOUN
ejpam-3288	82	52	-	-	PUNCT
ejpam-3288	82	53	algebras	algebras	X
ejpam-3288	82	54	.	.	PUNCT
ejpam-3288	83	1	in	in	ADP
ejpam-3288	83	2	what	what	PRON
ejpam-3288	83	3	follows	follow	VERB
ejpam-3288	83	4	,	,	PUNCT
ejpam-3288	83	5	we	we	PRON
ejpam-3288	83	6	use	use	VERB
ejpam-3288	83	7	(	(	PUNCT
ejpam-3288	83	8	x	x	NOUN
ejpam-3288	83	9	;	;	PUNCT
ejpam-3288	83	10	∗	∗	NOUN
ejpam-3288	83	11	,	,	PUNCT
ejpam-3288	83	12	0	0	NUM
ejpam-3288	83	13	)	)	PUNCT
ejpam-3288	83	14	to	to	PART
ejpam-3288	83	15	denote	denote	VERB
ejpam-3288	83	16	a	a	DET
ejpam-3288	83	17	bck	bck	NOUN
ejpam-3288	83	18	/	/	SYM
ejpam-3288	83	19	bci	bci	NOUN
ejpam-3288	83	20	-	-	NOUN
ejpam-3288	83	21	algebra	algebra	NOUN
ejpam-3288	83	22	unless	unless	SCONJ
ejpam-3288	83	23	otherwise	otherwise	ADV
ejpam-3288	83	24	specified	specify	VERB
ejpam-3288	83	25	.	.	PUNCT
ejpam-3288	84	1	for	for	ADP
ejpam-3288	84	2	the	the	DET
ejpam-3288	84	3	sake	sake	NOUN
ejpam-3288	84	4	of	of	ADP
ejpam-3288	84	5	brevity	brevity	NOUN
ejpam-3288	84	6	,	,	PUNCT
ejpam-3288	84	7	we	we	PRON
ejpam-3288	84	8	call	call	VERB
ejpam-3288	84	9	x	x	DET
ejpam-3288	84	10	a	a	DET
ejpam-3288	84	11	bck	bck	PROPN
ejpam-3288	84	12	/	/	SYM
ejpam-3288	84	13	bci	bci	NOUN
ejpam-3288	84	14	-	-	NOUN
ejpam-3288	84	15	algebra	algebra	NOUN
ejpam-3288	84	16	.	.	PUNCT
ejpam-3288	85	1	definition	definition	NOUN
ejpam-3288	85	2	3	3	NUM
ejpam-3288	85	3	.	.	PUNCT
ejpam-3288	86	1	[	[	X
ejpam-3288	86	2	16	16	NUM
ejpam-3288	86	3	]	]	X
ejpam-3288	86	4	a	a	DET
ejpam-3288	86	5	fuzzy	fuzzy	ADJ
ejpam-3288	86	6	set	set	VERB
ejpam-3288	86	7	a	a	PRON
ejpam-3288	86	8	=	=	X
ejpam-3288	86	9	{	{	PUNCT
ejpam-3288	86	10	(	(	PUNCT
ejpam-3288	86	11	x	x	NOUN
ejpam-3288	86	12	,	,	PUNCT
ejpam-3288	86	13	µa(x	µa(x	NOUN
ejpam-3288	86	14	)	)	PUNCT
ejpam-3288	86	15	)	)	PUNCT
ejpam-3288	87	1	|	|	ADV
ejpam-3288	87	2	x	x	SYM
ejpam-3288	87	3	∈	∈	NOUN
ejpam-3288	87	4	x	x	X
ejpam-3288	87	5	}	}	PUNCT
ejpam-3288	87	6	in	in	ADP
ejpam-3288	87	7	x	x	PROPN
ejpam-3288	87	8	is	be	AUX
ejpam-3288	87	9	called	call	VERB
ejpam-3288	87	10	a	a	DET
ejpam-3288	87	11	doubt	doubt	ADV
ejpam-3288	87	12	fuzzy	fuzzy	ADJ
ejpam-3288	87	13	ideal	ideal	NOUN
ejpam-3288	87	14	of	of	ADP
ejpam-3288	87	15	x	x	PRON
ejpam-3288	87	16	if	if	SCONJ
ejpam-3288	87	17	(	(	PUNCT
ejpam-3288	87	18	i	i	NOUN
ejpam-3288	87	19	)	)	PUNCT
ejpam-3288	87	20	µa(0	µa(0	NOUN
ejpam-3288	87	21	)	)	PUNCT
ejpam-3288	87	22	≤	≤	NOUN
ejpam-3288	87	23	µa(x	µa(x	NOUN
ejpam-3288	87	24	)	)	PUNCT
ejpam-3288	87	25	,	,	PUNCT
ejpam-3288	87	26	(	(	PUNCT
ejpam-3288	87	27	ii	ii	NOUN
ejpam-3288	87	28	)	)	PUNCT
ejpam-3288	87	29	µa(x	µa(x	PROPN
ejpam-3288	87	30	)	)	PUNCT
ejpam-3288	87	31	≤	≤	NUM
ejpam-3288	87	32	max{µa(x	max{µa(x	NOUN
ejpam-3288	87	33	∗	∗	NOUN
ejpam-3288	87	34	y	y	NOUN
ejpam-3288	87	35	)	)	PUNCT
ejpam-3288	87	36	,	,	PUNCT
ejpam-3288	87	37	µa(y	µa(y	NOUN
ejpam-3288	87	38	)	)	PUNCT
ejpam-3288	87	39	}	}	PUNCT
ejpam-3288	87	40	,	,	PUNCT
ejpam-3288	87	41	for	for	ADP
ejpam-3288	87	42	all	all	DET
ejpam-3288	87	43	x	x	NOUN
ejpam-3288	87	44	,	,	PUNCT
ejpam-3288	87	45	y	y	PROPN
ejpam-3288	87	46	∈	∈	PROPN
ejpam-3288	87	47	x.	x.	NOUN
ejpam-3288	87	48	definition	definition	NOUN
ejpam-3288	87	49	4	4	NUM
ejpam-3288	87	50	.	.	PUNCT
ejpam-3288	88	1	[	[	X
ejpam-3288	88	2	32	32	NUM
ejpam-3288	88	3	]	]	PUNCT
ejpam-3288	88	4	a	a	DET
ejpam-3288	88	5	fuzzy	fuzzy	ADJ
ejpam-3288	88	6	set	set	VERB
ejpam-3288	88	7	a	a	PRON
ejpam-3288	88	8	=	=	X
ejpam-3288	88	9	{	{	PUNCT
ejpam-3288	88	10	(	(	PUNCT
ejpam-3288	88	11	x	x	NOUN
ejpam-3288	88	12	,	,	PUNCT
ejpam-3288	88	13	µa(x	µa(x	NOUN
ejpam-3288	88	14	)	)	PUNCT
ejpam-3288	88	15	)	)	PUNCT
ejpam-3288	89	1	|	|	ADV
ejpam-3288	89	2	x	x	SYM
ejpam-3288	89	3	∈	∈	NOUN
ejpam-3288	89	4	x	x	X
ejpam-3288	89	5	}	}	PUNCT
ejpam-3288	89	6	in	in	ADP
ejpam-3288	89	7	x	x	PROPN
ejpam-3288	89	8	is	be	AUX
ejpam-3288	89	9	called	call	VERB
ejpam-3288	89	10	a	a	DET
ejpam-3288	89	11	doubt	doubt	ADV
ejpam-3288	89	12	fuzzy	fuzzy	ADJ
ejpam-3288	89	13	h	h	NOUN
ejpam-3288	89	14	-	-	PUNCT
ejpam-3288	89	15	ideal	ideal	NOUN
ejpam-3288	89	16	of	of	ADP
ejpam-3288	89	17	x	x	PRON
ejpam-3288	89	18	if	if	SCONJ
ejpam-3288	89	19	a.	a.	PROPN
ejpam-3288	89	20	al	al	PROPN
ejpam-3288	89	21	-	-	PROPN
ejpam-3288	89	22	masarwah	masarwah	PROPN
ejpam-3288	89	23	,	,	PUNCT
ejpam-3288	89	24	a.	a.	NOUN
ejpam-3288	89	25	g.	g.	PROPN
ejpam-3288	89	26	ahmad	ahmad	PROPN
ejpam-3288	89	27	/	/	SYM
ejpam-3288	89	28	eur	eur	PROPN
ejpam-3288	89	29	.	.	PUNCT
ejpam-3288	90	1	j.	j.	PROPN
ejpam-3288	90	2	pure	pure	PROPN
ejpam-3288	90	3	appl	appl	PROPN
ejpam-3288	90	4	.	.	PROPN
ejpam-3288	90	5	math	math	PROPN
ejpam-3288	90	6	,	,	PUNCT
ejpam-3288	90	7	11	11	NUM
ejpam-3288	90	8	(	(	PUNCT
ejpam-3288	90	9	3	3	NUM
ejpam-3288	90	10	)	)	PUNCT
ejpam-3288	90	11	(	(	PUNCT
ejpam-3288	90	12	2018	2018	NUM
ejpam-3288	90	13	)	)	PUNCT
ejpam-3288	90	14	,	,	PUNCT
ejpam-3288	90	15	652	652	NUM
ejpam-3288	90	16	-	-	SYM
ejpam-3288	90	17	670	670	NUM
ejpam-3288	90	18	655	655	NUM
ejpam-3288	90	19	(	(	PUNCT
ejpam-3288	90	20	i	i	NOUN
ejpam-3288	90	21	)	)	PUNCT
ejpam-3288	90	22	µa(0	µa(0	NOUN
ejpam-3288	90	23	)	)	PUNCT
ejpam-3288	90	24	≤	≤	NOUN
ejpam-3288	90	25	µa(x	µa(x	NOUN
ejpam-3288	90	26	)	)	PUNCT
ejpam-3288	90	27	,	,	PUNCT
ejpam-3288	90	28	(	(	PUNCT
ejpam-3288	90	29	ii	ii	NOUN
ejpam-3288	90	30	)	)	PUNCT
ejpam-3288	90	31	µa(x	µa(x	PUNCT
ejpam-3288	90	32	∗	∗	PROPN
ejpam-3288	90	33	z	z	NOUN
ejpam-3288	90	34	)	)	PUNCT
ejpam-3288	90	35	≤	≤	NUM
ejpam-3288	90	36	max{µa(x	max{µa(x	NOUN
ejpam-3288	90	37	∗	∗	NOUN
ejpam-3288	90	38	(	(	PUNCT
ejpam-3288	90	39	y	y	PROPN
ejpam-3288	90	40	∗	∗	PROPN
ejpam-3288	90	41	z	z	PROPN
ejpam-3288	90	42	)	)	PUNCT
ejpam-3288	90	43	)	)	PUNCT
ejpam-3288	90	44	,	,	PUNCT
ejpam-3288	90	45	µa(y	µa(y	NOUN
ejpam-3288	90	46	)	)	PUNCT
ejpam-3288	90	47	}	}	PUNCT
ejpam-3288	90	48	,	,	PUNCT
ejpam-3288	90	49	for	for	ADP
ejpam-3288	90	50	all	all	DET
ejpam-3288	90	51	x	x	NOUN
ejpam-3288	90	52	,	,	PUNCT
ejpam-3288	90	53	y	y	PROPN
ejpam-3288	90	54	,	,	PUNCT
ejpam-3288	90	55	z	z	PROPN
ejpam-3288	90	56	∈	∈	PROPN
ejpam-3288	90	57	x.	x.	NOUN
ejpam-3288	91	1	the	the	DET
ejpam-3288	91	2	proposed	propose	VERB
ejpam-3288	91	3	work	work	NOUN
ejpam-3288	91	4	is	be	AUX
ejpam-3288	91	5	done	do	VERB
ejpam-3288	91	6	on	on	ADP
ejpam-3288	91	7	a	a	DET
ejpam-3288	91	8	bipolar	bipolar	ADJ
ejpam-3288	91	9	fuzzy	fuzzy	ADJ
ejpam-3288	91	10	set	set	NOUN
ejpam-3288	91	11	.	.	PUNCT
ejpam-3288	92	1	the	the	DET
ejpam-3288	92	2	formal	formal	ADJ
ejpam-3288	92	3	definition	definition	NOUN
ejpam-3288	92	4	of	of	ADP
ejpam-3288	92	5	a	a	DET
ejpam-3288	92	6	bipolar	bipolar	ADJ
ejpam-3288	92	7	fuzzy	fuzzy	ADJ
ejpam-3288	92	8	set	set	NOUN
ejpam-3288	92	9	is	be	AUX
ejpam-3288	92	10	given	give	VERB
ejpam-3288	92	11	below	below	ADP
ejpam-3288	92	12	:	:	PUNCT
ejpam-3288	92	13	definition	definition	NOUN
ejpam-3288	92	14	5	5	NUM
ejpam-3288	92	15	.	.	PUNCT
ejpam-3288	93	1	[	[	X
ejpam-3288	93	2	22	22	NUM
ejpam-3288	93	3	]	]	PUNCT
ejpam-3288	93	4	let	let	VERB
ejpam-3288	93	5	x	x	PRON
ejpam-3288	93	6	be	be	AUX
ejpam-3288	93	7	a	a	DET
ejpam-3288	93	8	non	non	ADJ
ejpam-3288	93	9	-	-	ADJ
ejpam-3288	93	10	empty	empty	ADJ
ejpam-3288	93	11	set	set	NOUN
ejpam-3288	93	12	.	.	PUNCT
ejpam-3288	94	1	a	a	DET
ejpam-3288	94	2	bipolar	bipolar	ADJ
ejpam-3288	94	3	fuzzy	fuzzy	NOUN
ejpam-3288	94	4	set	set	VERB
ejpam-3288	94	5	a	a	DET
ejpam-3288	94	6	in	in	NOUN
ejpam-3288	94	7	x	x	SYM
ejpam-3288	94	8	is	be	AUX
ejpam-3288	94	9	an	an	DET
ejpam-3288	94	10	object	object	NOUN
ejpam-3288	94	11	having	have	VERB
ejpam-3288	94	12	the	the	DET
ejpam-3288	94	13	form	form	NOUN
ejpam-3288	94	14	a	a	PRON
ejpam-3288	94	15	=	=	X
ejpam-3288	94	16	{	{	PUNCT
ejpam-3288	94	17	(	(	PUNCT
ejpam-3288	94	18	x	x	NOUN
ejpam-3288	94	19	,	,	PUNCT
ejpam-3288	94	20	µpa(x	µpa(x	PRON
ejpam-3288	94	21	)	)	PUNCT
ejpam-3288	94	22	,	,	PUNCT
ejpam-3288	94	23	µna	µna	PROPN
ejpam-3288	94	24	(	(	PUNCT
ejpam-3288	94	25	x))|x	x))|x	PROPN
ejpam-3288	94	26	∈	∈	PROPN
ejpam-3288	94	27	x	x	NOUN
ejpam-3288	94	28	}	}	PUNCT
ejpam-3288	94	29	where	where	SCONJ
ejpam-3288	94	30	µpa	µpa	NOUN
ejpam-3288	94	31	:	:	PUNCT
ejpam-3288	94	32	x	x	PUNCT
ejpam-3288	94	33	−→	−→	NOUN
ejpam-3288	94	34	[	[	X
ejpam-3288	94	35	0	0	NUM
ejpam-3288	94	36	,	,	PUNCT
ejpam-3288	94	37	1	1	NUM
ejpam-3288	94	38	]	]	PUNCT
ejpam-3288	94	39	and	and	CCONJ
ejpam-3288	94	40	µna	µna	ADJ
ejpam-3288	94	41	:	:	PUNCT
ejpam-3288	94	42	x	x	PUNCT
ejpam-3288	94	43	−→	−→	NOUN
ejpam-3288	94	44	[	[	X
ejpam-3288	94	45	−1	−1	NOUN
ejpam-3288	94	46	,	,	PUNCT
ejpam-3288	94	47	0	0	NUM
ejpam-3288	94	48	]	]	PUNCT
ejpam-3288	94	49	are	be	AUX
ejpam-3288	94	50	mappings	mapping	NOUN
ejpam-3288	94	51	.	.	PUNCT
ejpam-3288	95	1	we	we	PRON
ejpam-3288	95	2	use	use	VERB
ejpam-3288	95	3	the	the	DET
ejpam-3288	95	4	positive	positive	ADJ
ejpam-3288	95	5	membership	membership	NOUN
ejpam-3288	95	6	degree	degree	NOUN
ejpam-3288	95	7	µpa(x	µpa(x	PRON
ejpam-3288	95	8	)	)	PUNCT
ejpam-3288	95	9	to	to	PART
ejpam-3288	95	10	denote	denote	VERB
ejpam-3288	95	11	the	the	DET
ejpam-3288	95	12	satisfaction	satisfaction	NOUN
ejpam-3288	95	13	degree	degree	NOUN
ejpam-3288	95	14	of	of	ADP
ejpam-3288	95	15	an	an	DET
ejpam-3288	95	16	element	element	NOUN
ejpam-3288	95	17	x	x	X
ejpam-3288	95	18	to	to	ADP
ejpam-3288	95	19	the	the	DET
ejpam-3288	95	20	property	property	NOUN
ejpam-3288	95	21	corresponding	correspond	VERB
ejpam-3288	95	22	to	to	ADP
ejpam-3288	95	23	a	a	DET
ejpam-3288	95	24	bipolar	bipolar	ADJ
ejpam-3288	95	25	fuzzy	fuzzy	NOUN
ejpam-3288	95	26	set	set	VERB
ejpam-3288	95	27	a	a	PRON
ejpam-3288	95	28	,	,	PUNCT
ejpam-3288	95	29	and	and	CCONJ
ejpam-3288	95	30	the	the	DET
ejpam-3288	95	31	negative	negative	ADJ
ejpam-3288	95	32	membership	membership	NOUN
ejpam-3288	95	33	degree	degree	NOUN
ejpam-3288	95	34	µna	µna	ADJ
ejpam-3288	95	35	(	(	PUNCT
ejpam-3288	95	36	x	x	X
ejpam-3288	95	37	)	)	PUNCT
ejpam-3288	95	38	to	to	PART
ejpam-3288	95	39	denote	denote	VERB
ejpam-3288	95	40	the	the	DET
ejpam-3288	95	41	satisfaction	satisfaction	NOUN
ejpam-3288	95	42	degree	degree	NOUN
ejpam-3288	95	43	of	of	ADP
ejpam-3288	95	44	an	an	DET
ejpam-3288	95	45	element	element	NOUN
ejpam-3288	95	46	x	x	PUNCT
ejpam-3288	95	47	to	to	ADP
ejpam-3288	95	48	some	some	DET
ejpam-3288	95	49	implicit	implicit	ADJ
ejpam-3288	95	50	counter	counter	ADJ
ejpam-3288	95	51	-	-	NOUN
ejpam-3288	95	52	property	property	NOUN
ejpam-3288	95	53	corresponding	corresponding	NOUN
ejpam-3288	95	54	to	to	ADP
ejpam-3288	95	55	a	a	DET
ejpam-3288	95	56	bipolar	bipolar	ADJ
ejpam-3288	95	57	fuzzy	fuzzy	ADJ
ejpam-3288	95	58	set	set	VERB
ejpam-3288	95	59	a.	a.	NOUN
ejpam-3288	95	60	if	if	SCONJ
ejpam-3288	95	61	µpa(x	µpa(x	PRON
ejpam-3288	95	62	)	)	PUNCT
ejpam-3288	95	63	6=	6=	ADP
ejpam-3288	95	64	0	0	NUM
ejpam-3288	95	65	and	and	CCONJ
ejpam-3288	95	66	µna	µna	ADJ
ejpam-3288	95	67	(	(	PUNCT
ejpam-3288	95	68	x	x	NOUN
ejpam-3288	95	69	)	)	PUNCT
ejpam-3288	95	70	=	=	SYM
ejpam-3288	95	71	0	0	NUM
ejpam-3288	95	72	,	,	PUNCT
ejpam-3288	95	73	it	it	PRON
ejpam-3288	95	74	is	be	AUX
ejpam-3288	95	75	the	the	DET
ejpam-3288	95	76	situation	situation	NOUN
ejpam-3288	95	77	that	that	PRON
ejpam-3288	95	78	x	x	PRON
ejpam-3288	95	79	is	be	AUX
ejpam-3288	95	80	regarded	regard	VERB
ejpam-3288	95	81	as	as	ADP
ejpam-3288	95	82	having	have	VERB
ejpam-3288	95	83	only	only	ADV
ejpam-3288	95	84	positive	positive	ADJ
ejpam-3288	95	85	satisfaction	satisfaction	NOUN
ejpam-3288	95	86	for	for	ADP
ejpam-3288	95	87	a.	a.	NOUN
ejpam-3288	95	88	if	if	SCONJ
ejpam-3288	95	89	µpa(x	µpa(x	PRON
ejpam-3288	95	90	)	)	PUNCT
ejpam-3288	95	91	=	=	SYM
ejpam-3288	95	92	0	0	NUM
ejpam-3288	95	93	and	and	CCONJ
ejpam-3288	95	94	µna	µna	ADJ
ejpam-3288	95	95	(	(	PUNCT
ejpam-3288	95	96	x	x	NOUN
ejpam-3288	95	97	)	)	PUNCT
ejpam-3288	95	98	6=	6=	ADP
ejpam-3288	95	99	0	0	NUM
ejpam-3288	95	100	,	,	PUNCT
ejpam-3288	95	101	it	it	PRON
ejpam-3288	95	102	is	be	AUX
ejpam-3288	95	103	the	the	DET
ejpam-3288	95	104	situation	situation	NOUN
ejpam-3288	95	105	that	that	PRON
ejpam-3288	95	106	x	x	PRON
ejpam-3288	95	107	does	do	AUX
ejpam-3288	95	108	not	not	PART
ejpam-3288	95	109	satisfy	satisfy	VERB
ejpam-3288	95	110	the	the	DET
ejpam-3288	95	111	property	property	NOUN
ejpam-3288	95	112	of	of	ADP
ejpam-3288	95	113	a	a	PRON
ejpam-3288	95	114	but	but	CCONJ
ejpam-3288	95	115	somewhat	somewhat	ADV
ejpam-3288	95	116	satisfies	satisfy	VERB
ejpam-3288	95	117	the	the	DET
ejpam-3288	95	118	counter	counter	ADJ
ejpam-3288	95	119	property	property	NOUN
ejpam-3288	95	120	of	of	ADP
ejpam-3288	95	121	a.	a.	NOUN
ejpam-3288	95	122	it	it	PRON
ejpam-3288	95	123	is	be	AUX
ejpam-3288	95	124	possible	possible	ADJ
ejpam-3288	95	125	for	for	SCONJ
ejpam-3288	95	126	an	an	DET
ejpam-3288	95	127	element	element	NOUN
ejpam-3288	95	128	x	x	PART
ejpam-3288	95	129	to	to	PART
ejpam-3288	95	130	be	be	AUX
ejpam-3288	95	131	such	such	ADJ
ejpam-3288	95	132	that	that	SCONJ
ejpam-3288	95	133	µpa(x	µpa(x	NOUN
ejpam-3288	95	134	)	)	PUNCT
ejpam-3288	95	135	6=	6=	ADP
ejpam-3288	95	136	0	0	NUM
ejpam-3288	95	137	and	and	CCONJ
ejpam-3288	95	138	µna	µna	ADJ
ejpam-3288	95	139	(	(	PUNCT
ejpam-3288	95	140	x	x	NOUN
ejpam-3288	95	141	)	)	PUNCT
ejpam-3288	95	142	6=	6=	ADP
ejpam-3288	95	143	0	0	NUM
ejpam-3288	95	144	when	when	SCONJ
ejpam-3288	95	145	the	the	DET
ejpam-3288	95	146	membership	membership	NOUN
ejpam-3288	95	147	function	function	NOUN
ejpam-3288	95	148	of	of	ADP
ejpam-3288	95	149	the	the	DET
ejpam-3288	95	150	property	property	NOUN
ejpam-3288	95	151	overlaps	overlap	VERB
ejpam-3288	95	152	that	that	PRON
ejpam-3288	95	153	of	of	ADP
ejpam-3288	95	154	its	its	PRON
ejpam-3288	95	155	counter	counter	ADJ
ejpam-3288	95	156	property	property	NOUN
ejpam-3288	95	157	over	over	ADP
ejpam-3288	95	158	some	some	DET
ejpam-3288	95	159	portion	portion	NOUN
ejpam-3288	95	160	of	of	ADP
ejpam-3288	95	161	x.	x.	NOUN
ejpam-3288	95	162	for	for	ADP
ejpam-3288	95	163	the	the	DET
ejpam-3288	95	164	sake	sake	NOUN
ejpam-3288	95	165	of	of	ADP
ejpam-3288	95	166	simplicity	simplicity	NOUN
ejpam-3288	95	167	,	,	PUNCT
ejpam-3288	95	168	we	we	PRON
ejpam-3288	95	169	shall	shall	AUX
ejpam-3288	95	170	use	use	VERB
ejpam-3288	95	171	the	the	DET
ejpam-3288	95	172	symbol	symbol	NOUN
ejpam-3288	95	173	a	a	DET
ejpam-3288	95	174	=	=	X
ejpam-3288	95	175	(	(	PUNCT
ejpam-3288	95	176	µpa	µpa	PROPN
ejpam-3288	95	177	,	,	PUNCT
ejpam-3288	95	178	µ	µ	X
ejpam-3288	95	179	n	n	PRON
ejpam-3288	95	180	a	a	NOUN
ejpam-3288	95	181	)	)	PUNCT
ejpam-3288	95	182	for	for	SCONJ
ejpam-3288	95	183	the	the	DET
ejpam-3288	95	184	bipolar	bipolar	ADJ
ejpam-3288	95	185	fuzzy	fuzzy	NOUN
ejpam-3288	95	186	set	set	VERB
ejpam-3288	95	187	a	a	PRON
ejpam-3288	95	188	=	=	X
ejpam-3288	95	189	{	{	PUNCT
ejpam-3288	95	190	(	(	PUNCT
ejpam-3288	95	191	x	x	NOUN
ejpam-3288	95	192	,	,	PUNCT
ejpam-3288	95	193	µpa(x	µpa(x	PRON
ejpam-3288	95	194	)	)	PUNCT
ejpam-3288	95	195	,	,	PUNCT
ejpam-3288	95	196	µna	µna	PROPN
ejpam-3288	95	197	(	(	PUNCT
ejpam-3288	95	198	x))|x	x))|x	PROPN
ejpam-3288	95	199	∈	∈	PROPN
ejpam-3288	95	200	x	x	NOUN
ejpam-3288	95	201	}	}	PUNCT
ejpam-3288	95	202	.	.	PUNCT
ejpam-3288	96	1	definition	definition	NOUN
ejpam-3288	96	2	6	6	NUM
ejpam-3288	96	3	.	.	PUNCT
ejpam-3288	97	1	[	[	X
ejpam-3288	97	2	22	22	NUM
ejpam-3288	97	3	]	]	PUNCT
ejpam-3288	97	4	let	let	VERB
ejpam-3288	97	5	a	a	DET
ejpam-3288	97	6	=	=	SYM
ejpam-3288	97	7	(	(	PUNCT
ejpam-3288	97	8	µpa(x	µpa(x	PROPN
ejpam-3288	97	9	)	)	PUNCT
ejpam-3288	97	10	,	,	PUNCT
ejpam-3288	97	11	µna	µna	ADJ
ejpam-3288	97	12	(	(	PUNCT
ejpam-3288	97	13	x	x	NOUN
ejpam-3288	97	14	)	)	PUNCT
ejpam-3288	97	15	)	)	PUNCT
ejpam-3288	97	16	and	and	CCONJ
ejpam-3288	97	17	b	b	X
ejpam-3288	97	18	=	=	SYM
ejpam-3288	97	19	(	(	PUNCT
ejpam-3288	97	20	µpb(x	µpb(x	PROPN
ejpam-3288	97	21	)	)	PUNCT
ejpam-3288	97	22	,	,	PUNCT
ejpam-3288	97	23	µnb	µnb	X
ejpam-3288	97	24	(	(	PUNCT
ejpam-3288	97	25	x	x	NOUN
ejpam-3288	97	26	)	)	PUNCT
ejpam-3288	97	27	)	)	PUNCT
ejpam-3288	97	28	be	be	AUX
ejpam-3288	97	29	two	two	NUM
ejpam-3288	97	30	bipolar	bipolar	ADJ
ejpam-3288	97	31	fuzzy	fuzzy	ADJ
ejpam-3288	97	32	sets	set	NOUN
ejpam-3288	97	33	in	in	ADP
ejpam-3288	97	34	x.	x.	NOUN
ejpam-3288	97	35	then	then	ADV
ejpam-3288	97	36	a	a	DET
ejpam-3288	97	37	⊆	⊆	NUM
ejpam-3288	97	38	b	b	NOUN
ejpam-3288	97	39	if	if	SCONJ
ejpam-3288	97	40	and	and	CCONJ
ejpam-3288	97	41	only	only	ADV
ejpam-3288	97	42	if	if	SCONJ
ejpam-3288	97	43	µpa(x	µpa(x	PRON
ejpam-3288	97	44	)	)	PUNCT
ejpam-3288	97	45	≤	≤	NOUN
ejpam-3288	97	46	µpb(x	µpb(x	PROPN
ejpam-3288	97	47	)	)	PUNCT
ejpam-3288	97	48	and	and	CCONJ
ejpam-3288	97	49	µna	µna	ADJ
ejpam-3288	97	50	(	(	PUNCT
ejpam-3288	97	51	x	x	NOUN
ejpam-3288	97	52	)	)	PUNCT
ejpam-3288	97	53	≥	≥	NOUN
ejpam-3288	97	54	µnb	µnb	NOUN
ejpam-3288	97	55	(	(	PUNCT
ejpam-3288	97	56	x	x	X
ejpam-3288	97	57	)	)	PUNCT
ejpam-3288	97	58	,	,	PUNCT
ejpam-3288	97	59	for	for	ADP
ejpam-3288	97	60	all	all	PRON
ejpam-3288	97	61	x	x	SYM
ejpam-3288	97	62	∈	∈	ADJ
ejpam-3288	97	63	x.	x.	NOUN
ejpam-3288	97	64	doubt	doubt	VERB
ejpam-3288	97	65	bipolar	bipolar	ADJ
ejpam-3288	97	66	fuzzy	fuzzy	ADJ
ejpam-3288	97	67	subalgebras	subalgebra	NOUN
ejpam-3288	97	68	and	and	CCONJ
ejpam-3288	97	69	doubt	doubt	VERB
ejpam-3288	97	70	bipolar	bipolar	ADJ
ejpam-3288	97	71	fuzzy	fuzzy	ADJ
ejpam-3288	97	72	ideals	ideal	NOUN
ejpam-3288	97	73	are	be	AUX
ejpam-3288	97	74	extensions	extension	NOUN
ejpam-3288	97	75	of	of	ADP
ejpam-3288	97	76	doubt	doubt	NOUN
ejpam-3288	97	77	fuzzy	fuzzy	ADJ
ejpam-3288	97	78	subalgebras	subalgebra	NOUN
ejpam-3288	97	79	and	and	CCONJ
ejpam-3288	97	80	doubt	doubt	VERB
ejpam-3288	97	81	fuzzy	fuzzy	ADJ
ejpam-3288	97	82	ideals	ideal	NOUN
ejpam-3288	97	83	which	which	PRON
ejpam-3288	97	84	are	be	AUX
ejpam-3288	97	85	defined	define	VERB
ejpam-3288	97	86	by	by	ADP
ejpam-3288	97	87	al	al	PROPN
ejpam-3288	97	88	-	-	PROPN
ejpam-3288	97	89	masarwah	masarwah	PROPN
ejpam-3288	97	90	and	and	CCONJ
ejpam-3288	97	91	ahmad	ahmad	PROPN
ejpam-3288	98	1	[	[	X
ejpam-3288	98	2	5	5	NUM
ejpam-3288	98	3	]	]	PUNCT
ejpam-3288	98	4	as	as	SCONJ
ejpam-3288	98	5	follows	follow	VERB
ejpam-3288	98	6	:	:	PUNCT
ejpam-3288	98	7	definition	definition	NOUN
ejpam-3288	98	8	7	7	NUM
ejpam-3288	98	9	.	.	PUNCT
ejpam-3288	99	1	[	[	X
ejpam-3288	99	2	5	5	NUM
ejpam-3288	99	3	]	]	PUNCT
ejpam-3288	99	4	a	a	DET
ejpam-3288	99	5	bipolar	bipolar	ADJ
ejpam-3288	99	6	fuzzy	fuzzy	NOUN
ejpam-3288	99	7	set	set	VERB
ejpam-3288	99	8	a	a	PRON
ejpam-3288	99	9	=	=	X
ejpam-3288	99	10	(	(	PUNCT
ejpam-3288	99	11	µpa	µpa	PROPN
ejpam-3288	99	12	,	,	PUNCT
ejpam-3288	99	13	µ	µ	X
ejpam-3288	99	14	n	n	PRON
ejpam-3288	99	15	a	a	NOUN
ejpam-3288	99	16	)	)	PUNCT
ejpam-3288	99	17	in	in	ADP
ejpam-3288	99	18	x	x	PROPN
ejpam-3288	99	19	is	be	AUX
ejpam-3288	99	20	called	call	VERB
ejpam-3288	99	21	a	a	DET
ejpam-3288	99	22	doubt	doubt	ADV
ejpam-3288	99	23	bipolar	bipolar	ADJ
ejpam-3288	99	24	fuzzy	fuzzy	ADJ
ejpam-3288	99	25	subalgebra	subalgebra	NOUN
ejpam-3288	99	26	of	of	ADP
ejpam-3288	99	27	x	x	PRON
ejpam-3288	99	28	if	if	SCONJ
ejpam-3288	99	29	it	it	PRON
ejpam-3288	99	30	satisfies	satisfy	VERB
ejpam-3288	99	31	:	:	PUNCT
ejpam-3288	99	32	(	(	PUNCT
ejpam-3288	99	33	i	i	NOUN
ejpam-3288	99	34	)	)	PUNCT
ejpam-3288	99	35	µpa(x	µpa(x	PROPN
ejpam-3288	99	36	∗	∗	NOUN
ejpam-3288	99	37	y	y	PROPN
ejpam-3288	99	38	)	)	PUNCT
ejpam-3288	99	39	≤	≤	PROPN
ejpam-3288	99	40	max{µpa(x	max{µpa(x	PROPN
ejpam-3288	99	41	)	)	PUNCT
ejpam-3288	99	42	,	,	PUNCT
ejpam-3288	99	43	µpa(y	µpa(y	PROPN
ejpam-3288	99	44	)	)	PUNCT
ejpam-3288	99	45	}	}	PUNCT
ejpam-3288	99	46	,	,	PUNCT
ejpam-3288	99	47	(	(	PUNCT
ejpam-3288	99	48	ii	ii	NOUN
ejpam-3288	99	49	)	)	PUNCT
ejpam-3288	99	50	µna	µna	NOUN
ejpam-3288	99	51	(	(	PUNCT
ejpam-3288	99	52	x	x	PROPN
ejpam-3288	99	53	∗	∗	PROPN
ejpam-3288	99	54	y	y	PROPN
ejpam-3288	99	55	)	)	PUNCT
ejpam-3288	99	56	≥	≥	NOUN
ejpam-3288	99	57	min{µna	min{µna	NOUN
ejpam-3288	99	58	(	(	PUNCT
ejpam-3288	99	59	x	x	NOUN
ejpam-3288	99	60	)	)	PUNCT
ejpam-3288	99	61	,	,	PUNCT
ejpam-3288	99	62	µna	µna	ADJ
ejpam-3288	99	63	(	(	PUNCT
ejpam-3288	99	64	y	y	NOUN
ejpam-3288	99	65	)	)	PUNCT
ejpam-3288	99	66	}	}	PUNCT
ejpam-3288	99	67	,	,	PUNCT
ejpam-3288	99	68	for	for	ADP
ejpam-3288	99	69	all	all	DET
ejpam-3288	99	70	x	x	NOUN
ejpam-3288	99	71	,	,	PUNCT
ejpam-3288	99	72	y	y	PROPN
ejpam-3288	99	73	∈	∈	PROPN
ejpam-3288	99	74	x.	x.	NOUN
ejpam-3288	99	75	definition	definition	NOUN
ejpam-3288	99	76	8	8	NUM
ejpam-3288	99	77	.	.	PUNCT
ejpam-3288	100	1	[	[	X
ejpam-3288	100	2	5	5	NUM
ejpam-3288	100	3	]	]	PUNCT
ejpam-3288	100	4	a	a	DET
ejpam-3288	100	5	bipolar	bipolar	ADJ
ejpam-3288	100	6	fuzzy	fuzzy	NOUN
ejpam-3288	100	7	set	set	VERB
ejpam-3288	100	8	a	a	PRON
ejpam-3288	100	9	=	=	X
ejpam-3288	100	10	(	(	PUNCT
ejpam-3288	100	11	µpa	µpa	PROPN
ejpam-3288	100	12	,	,	PUNCT
ejpam-3288	100	13	µ	µ	X
ejpam-3288	100	14	n	n	PRON
ejpam-3288	100	15	a	a	NOUN
ejpam-3288	100	16	)	)	PUNCT
ejpam-3288	100	17	in	in	ADP
ejpam-3288	100	18	x	x	PROPN
ejpam-3288	100	19	is	be	AUX
ejpam-3288	100	20	called	call	VERB
ejpam-3288	100	21	a	a	DET
ejpam-3288	100	22	doubt	doubt	ADV
ejpam-3288	100	23	bipolar	bipolar	ADJ
ejpam-3288	100	24	fuzzy	fuzzy	ADJ
ejpam-3288	100	25	ideal	ideal	NOUN
ejpam-3288	100	26	of	of	ADP
ejpam-3288	100	27	x	x	PRON
ejpam-3288	100	28	if	if	SCONJ
ejpam-3288	100	29	it	it	PRON
ejpam-3288	100	30	satisfies	satisfy	VERB
ejpam-3288	100	31	:	:	PUNCT
ejpam-3288	100	32	(	(	PUNCT
ejpam-3288	100	33	i	i	NOUN
ejpam-3288	100	34	)	)	PUNCT
ejpam-3288	100	35	µpa(0	µpa(0	NOUN
ejpam-3288	100	36	)	)	PUNCT
ejpam-3288	100	37	≤	≤	NUM
ejpam-3288	100	38	µpa(x	µpa(x	NOUN
ejpam-3288	100	39	)	)	PUNCT
ejpam-3288	100	40	and	and	CCONJ
ejpam-3288	100	41	µna	µna	ADJ
ejpam-3288	100	42	(	(	PUNCT
ejpam-3288	100	43	0	0	NUM
ejpam-3288	100	44	)	)	PUNCT
ejpam-3288	100	45	≥	≥	NOUN
ejpam-3288	100	46	µna	µna	ADJ
ejpam-3288	100	47	(	(	PUNCT
ejpam-3288	100	48	x	x	NOUN
ejpam-3288	100	49	)	)	PUNCT
ejpam-3288	100	50	,	,	PUNCT
ejpam-3288	100	51	(	(	PUNCT
ejpam-3288	100	52	ii	ii	NOUN
ejpam-3288	100	53	)	)	PUNCT
ejpam-3288	100	54	µpa(x	µpa(x	PROPN
ejpam-3288	100	55	)	)	PUNCT
ejpam-3288	100	56	≤	≤	PUNCT
ejpam-3288	101	1	max{µpa(x	max{µpa(x	PROPN
ejpam-3288	101	2	∗	∗	NOUN
ejpam-3288	101	3	y	y	NOUN
ejpam-3288	101	4	)	)	PUNCT
ejpam-3288	101	5	,	,	PUNCT
ejpam-3288	101	6	µpa(y	µpa(y	PROPN
ejpam-3288	101	7	)	)	PUNCT
ejpam-3288	101	8	}	}	PUNCT
ejpam-3288	101	9	,	,	PUNCT
ejpam-3288	101	10	(	(	PUNCT
ejpam-3288	101	11	iii	iii	X
ejpam-3288	101	12	)	)	PUNCT
ejpam-3288	101	13	µna	µna	ADJ
ejpam-3288	101	14	(	(	PUNCT
ejpam-3288	101	15	x	x	NOUN
ejpam-3288	101	16	)	)	PUNCT
ejpam-3288	101	17	≥	≥	X
ejpam-3288	101	18	min{µna	min{µna	NOUN
ejpam-3288	101	19	(	(	PUNCT
ejpam-3288	101	20	x	x	PROPN
ejpam-3288	101	21	∗	∗	PROPN
ejpam-3288	101	22	y	y	PROPN
ejpam-3288	101	23	)	)	PUNCT
ejpam-3288	101	24	,	,	PUNCT
ejpam-3288	101	25	µna	µna	PROPN
ejpam-3288	101	26	(	(	PUNCT
ejpam-3288	101	27	y	y	NOUN
ejpam-3288	101	28	)	)	PUNCT
ejpam-3288	101	29	}	}	PUNCT
ejpam-3288	101	30	,	,	PUNCT
ejpam-3288	101	31	for	for	ADP
ejpam-3288	101	32	all	all	DET
ejpam-3288	101	33	x	x	NOUN
ejpam-3288	101	34	,	,	PUNCT
ejpam-3288	101	35	y	y	PROPN
ejpam-3288	101	36	∈	∈	PROPN
ejpam-3288	101	37	x.	x.	NOUN
ejpam-3288	101	38	a.	a.	PROPN
ejpam-3288	101	39	al	al	PROPN
ejpam-3288	101	40	-	-	PROPN
ejpam-3288	101	41	masarwah	masarwah	PROPN
ejpam-3288	101	42	,	,	PUNCT
ejpam-3288	101	43	a.	a.	NOUN
ejpam-3288	101	44	g.	g.	PROPN
ejpam-3288	101	45	ahmad	ahmad	PROPN
ejpam-3288	101	46	/	/	SYM
ejpam-3288	101	47	eur	eur	PROPN
ejpam-3288	101	48	.	.	PUNCT
ejpam-3288	102	1	j.	j.	PROPN
ejpam-3288	102	2	pure	pure	PROPN
ejpam-3288	102	3	appl	appl	PROPN
ejpam-3288	102	4	.	.	PROPN
ejpam-3288	102	5	math	math	PROPN
ejpam-3288	102	6	,	,	PUNCT
ejpam-3288	102	7	11	11	NUM
ejpam-3288	102	8	(	(	PUNCT
ejpam-3288	102	9	3	3	NUM
ejpam-3288	102	10	)	)	PUNCT
ejpam-3288	102	11	(	(	PUNCT
ejpam-3288	102	12	2018	2018	NUM
ejpam-3288	102	13	)	)	PUNCT
ejpam-3288	102	14	,	,	PUNCT
ejpam-3288	102	15	652	652	NUM
ejpam-3288	102	16	-	-	SYM
ejpam-3288	102	17	670	670	NUM
ejpam-3288	102	18	656	656	NUM
ejpam-3288	102	19	3	3	NUM
ejpam-3288	102	20	.	.	PUNCT
ejpam-3288	103	1	doubt	doubt	VERB
ejpam-3288	103	2	bipolar	bipolar	ADJ
ejpam-3288	103	3	fuzzy	fuzzy	ADJ
ejpam-3288	103	4	h	h	NOUN
ejpam-3288	103	5	-	-	PUNCT
ejpam-3288	103	6	ideals	ideal	NOUN
ejpam-3288	103	7	in	in	ADP
ejpam-3288	103	8	this	this	DET
ejpam-3288	103	9	section	section	NOUN
ejpam-3288	103	10	,	,	PUNCT
ejpam-3288	103	11	the	the	DET
ejpam-3288	103	12	concepts	concept	NOUN
ejpam-3288	103	13	of	of	ADP
ejpam-3288	103	14	doubt	doubt	ADV
ejpam-3288	103	15	bipolar	bipolar	ADJ
ejpam-3288	103	16	fuzzy	fuzzy	ADJ
ejpam-3288	103	17	h	h	NOUN
ejpam-3288	103	18	-	-	PUNCT
ejpam-3288	103	19	ideals	ideal	NOUN
ejpam-3288	103	20	were	be	AUX
ejpam-3288	103	21	introduced	introduce	VERB
ejpam-3288	103	22	by	by	ADP
ejpam-3288	103	23	almasarwah	almasarwah	NOUN
ejpam-3288	103	24	and	and	CCONJ
ejpam-3288	103	25	ahmad	ahmad	PROPN
ejpam-3288	103	26	[	[	X
ejpam-3288	103	27	6	6	NUM
ejpam-3288	103	28	]	]	PUNCT
ejpam-3288	103	29	will	will	AUX
ejpam-3288	103	30	be	be	AUX
ejpam-3288	103	31	used	use	VERB
ejpam-3288	103	32	to	to	PART
ejpam-3288	103	33	study	study	VERB
ejpam-3288	103	34	and	and	CCONJ
ejpam-3288	103	35	investigate	investigate	VERB
ejpam-3288	103	36	several	several	ADJ
ejpam-3288	103	37	properties	property	NOUN
ejpam-3288	103	38	of	of	ADP
ejpam-3288	103	39	doubt	doubt	NOUN
ejpam-3288	103	40	bipolar	bipolar	ADJ
ejpam-3288	103	41	fuzzy	fuzzy	ADJ
ejpam-3288	103	42	h	h	NOUN
ejpam-3288	103	43	-	-	PUNCT
ejpam-3288	103	44	ideals	ideal	NOUN
ejpam-3288	103	45	in	in	ADP
ejpam-3288	103	46	bck	bck	PROPN
ejpam-3288	103	47	/	/	SYM
ejpam-3288	103	48	bci	bci	NOUN
ejpam-3288	103	49	-	-	PUNCT
ejpam-3288	103	50	algebras	algebras	X
ejpam-3288	103	51	.	.	PUNCT
ejpam-3288	104	1	definition	definition	NOUN
ejpam-3288	104	2	9	9	NUM
ejpam-3288	104	3	.	.	PUNCT
ejpam-3288	105	1	[	[	X
ejpam-3288	105	2	6	6	NUM
ejpam-3288	105	3	]	]	PUNCT
ejpam-3288	105	4	let	let	VERB
ejpam-3288	105	5	a	a	DET
ejpam-3288	105	6	=	=	X
ejpam-3288	105	7	(	(	PUNCT
ejpam-3288	105	8	µpa	µpa	PROPN
ejpam-3288	105	9	,	,	PUNCT
ejpam-3288	105	10	µ	µ	NOUN
ejpam-3288	105	11	n	n	ADV
ejpam-3288	105	12	a	a	PRON
ejpam-3288	105	13	)	)	PUNCT
ejpam-3288	105	14	be	be	AUX
ejpam-3288	105	15	a	a	DET
ejpam-3288	105	16	bipolar	bipolar	ADJ
ejpam-3288	105	17	fuzzy	fuzzy	ADJ
ejpam-3288	105	18	subset	subset	NOUN
ejpam-3288	105	19	of	of	ADP
ejpam-3288	105	20	x	x	PRON
ejpam-3288	105	21	,	,	PUNCT
ejpam-3288	105	22	then	then	ADV
ejpam-3288	105	23	a	a	PRON
ejpam-3288	105	24	is	be	AUX
ejpam-3288	105	25	called	call	VERB
ejpam-3288	105	26	a	a	DET
ejpam-3288	105	27	doubt	doubt	ADV
ejpam-3288	105	28	bipolar	bipolar	ADJ
ejpam-3288	105	29	fuzzy	fuzzy	ADJ
ejpam-3288	105	30	h	h	NOUN
ejpam-3288	105	31	-	-	PUNCT
ejpam-3288	105	32	ideal	ideal	NOUN
ejpam-3288	105	33	of	of	ADP
ejpam-3288	105	34	x	x	PRON
ejpam-3288	105	35	if	if	SCONJ
ejpam-3288	105	36	it	it	PRON
ejpam-3288	105	37	satisfies	satisfy	VERB
ejpam-3288	105	38	:	:	PUNCT
ejpam-3288	105	39	(	(	PUNCT
ejpam-3288	105	40	i	i	NOUN
ejpam-3288	105	41	)	)	PUNCT
ejpam-3288	105	42	µpa(0	µpa(0	NOUN
ejpam-3288	105	43	)	)	PUNCT
ejpam-3288	105	44	≤	≤	NUM
ejpam-3288	105	45	µpa(x	µpa(x	NOUN
ejpam-3288	105	46	)	)	PUNCT
ejpam-3288	105	47	and	and	CCONJ
ejpam-3288	105	48	µna	µna	ADJ
ejpam-3288	105	49	(	(	PUNCT
ejpam-3288	105	50	0	0	NUM
ejpam-3288	105	51	)	)	PUNCT
ejpam-3288	105	52	≥	≥	NOUN
ejpam-3288	106	1	µna	µna	ADJ
ejpam-3288	106	2	(	(	PUNCT
ejpam-3288	106	3	x	x	NOUN
ejpam-3288	106	4	)	)	PUNCT
ejpam-3288	106	5	,	,	PUNCT
ejpam-3288	106	6	(	(	PUNCT
ejpam-3288	106	7	ii	ii	X
ejpam-3288	106	8	)	)	PUNCT
ejpam-3288	106	9	µpa(x	µpa(x	PROPN
ejpam-3288	106	10	∗	∗	NOUN
ejpam-3288	106	11	z	z	NOUN
ejpam-3288	106	12	)	)	PUNCT
ejpam-3288	106	13	≤	≤	PROPN
ejpam-3288	106	14	max{µpa(x	max{µpa(x	PROPN
ejpam-3288	106	15	∗	∗	NOUN
ejpam-3288	106	16	(	(	PUNCT
ejpam-3288	106	17	y	y	PROPN
ejpam-3288	106	18	∗	∗	PROPN
ejpam-3288	106	19	z	z	PROPN
ejpam-3288	106	20	)	)	PUNCT
ejpam-3288	106	21	)	)	PUNCT
ejpam-3288	106	22	,	,	PUNCT
ejpam-3288	106	23	µpa(y	µpa(y	PROPN
ejpam-3288	106	24	)	)	PUNCT
ejpam-3288	106	25	}	}	PUNCT
ejpam-3288	106	26	,	,	PUNCT
ejpam-3288	106	27	(	(	PUNCT
ejpam-3288	106	28	iii	iii	X
ejpam-3288	106	29	)	)	PUNCT
ejpam-3288	106	30	µna	µna	NOUN
ejpam-3288	106	31	(	(	PUNCT
ejpam-3288	106	32	x	x	NOUN
ejpam-3288	106	33	∗	∗	PROPN
ejpam-3288	106	34	z	z	NOUN
ejpam-3288	106	35	)	)	PUNCT
ejpam-3288	106	36	≥	≥	X
ejpam-3288	106	37	min{µna	min{µna	NOUN
ejpam-3288	106	38	(	(	PUNCT
ejpam-3288	106	39	x	x	NOUN
ejpam-3288	106	40	∗	∗	NOUN
ejpam-3288	106	41	(	(	PUNCT
ejpam-3288	106	42	y	y	PROPN
ejpam-3288	106	43	∗	∗	PROPN
ejpam-3288	106	44	z	z	PROPN
ejpam-3288	106	45	)	)	PUNCT
ejpam-3288	106	46	)	)	PUNCT
ejpam-3288	106	47	,	,	PUNCT
ejpam-3288	106	48	µna	µna	PROPN
ejpam-3288	106	49	(	(	PUNCT
ejpam-3288	106	50	y	y	NOUN
ejpam-3288	106	51	)	)	PUNCT
ejpam-3288	106	52	}	}	PUNCT
ejpam-3288	106	53	,	,	PUNCT
ejpam-3288	106	54	for	for	ADP
ejpam-3288	106	55	all	all	DET
ejpam-3288	106	56	x	x	NOUN
ejpam-3288	106	57	,	,	PUNCT
ejpam-3288	106	58	y	y	PROPN
ejpam-3288	106	59	,	,	PUNCT
ejpam-3288	106	60	z	z	PROPN
ejpam-3288	106	61	∈	∈	PROPN
ejpam-3288	106	62	x.	x.	NOUN
ejpam-3288	106	63	definition	definition	NOUN
ejpam-3288	106	64	10	10	NUM
ejpam-3288	106	65	.	.	PUNCT
ejpam-3288	107	1	let	let	VERB
ejpam-3288	107	2	m	m	PRON
ejpam-3288	107	3	be	be	AUX
ejpam-3288	107	4	a	a	DET
ejpam-3288	107	5	nonempty	nonempty	ADJ
ejpam-3288	107	6	subset	subset	NOUN
ejpam-3288	107	7	of	of	ADP
ejpam-3288	107	8	x.	x.	PROPN
ejpam-3288	107	9	a	a	DET
ejpam-3288	107	10	bipolar	bipolar	ADJ
ejpam-3288	107	11	fuzzy	fuzzy	ADJ
ejpam-3288	107	12	set	set	VERB
ejpam-3288	107	13	c̃m	c̃m	NOUN
ejpam-3288	107	14	=	=	PUNCT
ejpam-3288	107	15	(	(	PUNCT
ejpam-3288	107	16	c̃pm	c̃pm	NOUN
ejpam-3288	107	17	,	,	PUNCT
ejpam-3288	107	18	c̃	c̃	PROPN
ejpam-3288	107	19	n	n	PROPN
ejpam-3288	107	20	m	m	VERB
ejpam-3288	107	21	)	)	PUNCT
ejpam-3288	107	22	expressed	express	VERB
ejpam-3288	107	23	by	by	ADP
ejpam-3288	107	24	c̃pm	c̃pm	X
ejpam-3288	107	25	(	(	PUNCT
ejpam-3288	107	26	x	x	NOUN
ejpam-3288	107	27	)	)	PUNCT
ejpam-3288	107	28	=	=	SYM
ejpam-3288	107	29	{	{	PUNCT
ejpam-3288	107	30	0	0	NUM
ejpam-3288	107	31	,	,	PUNCT
ejpam-3288	107	32	x	x	SYM
ejpam-3288	107	33	∈m	∈m	NOUN
ejpam-3288	107	34	,	,	PUNCT
ejpam-3288	107	35	1	1	NUM
ejpam-3288	107	36	,	,	PUNCT
ejpam-3288	107	37	x	x	X
ejpam-3288	107	38	6∈m	6∈m	NOUN
ejpam-3288	107	39	,	,	PUNCT
ejpam-3288	107	40	and	and	CCONJ
ejpam-3288	107	41	c̃pm	c̃pm	X
ejpam-3288	107	42	(	(	PUNCT
ejpam-3288	107	43	x	x	X
ejpam-3288	107	44	)	)	PUNCT
ejpam-3288	107	45	=	=	SYM
ejpam-3288	107	46	{	{	PUNCT
ejpam-3288	107	47	0	0	NUM
ejpam-3288	107	48	,	,	PUNCT
ejpam-3288	107	49	x	x	SYM
ejpam-3288	107	50	∈m	∈m	NOUN
ejpam-3288	107	51	,	,	PUNCT
ejpam-3288	107	52	−1	−1	NOUN
ejpam-3288	107	53	,	,	PUNCT
ejpam-3288	107	54	x	x	X
ejpam-3288	107	55	6∈m	6∈m	NOUN
ejpam-3288	107	56	.	.	PUNCT
ejpam-3288	108	1	is	be	AUX
ejpam-3288	108	2	called	call	VERB
ejpam-3288	108	3	a	a	DET
ejpam-3288	108	4	doubt	doubt	ADV
ejpam-3288	108	5	bipolar	bipolar	ADJ
ejpam-3288	108	6	fuzzy	fuzzy	ADJ
ejpam-3288	108	7	characteristic	characteristic	ADJ
ejpam-3288	108	8	function	function	NOUN
ejpam-3288	108	9	.	.	PUNCT
ejpam-3288	109	1	lemma	lemma	PROPN
ejpam-3288	109	2	1	1	X
ejpam-3288	109	3	.	.	PUNCT
ejpam-3288	110	1	let	let	VERB
ejpam-3288	110	2	m	m	PRON
ejpam-3288	110	3	be	be	AUX
ejpam-3288	110	4	a	a	DET
ejpam-3288	110	5	nonempty	nonempty	ADJ
ejpam-3288	110	6	subset	subset	NOUN
ejpam-3288	110	7	of	of	ADP
ejpam-3288	110	8	x.	x.	NOUN
ejpam-3288	110	9	then	then	ADV
ejpam-3288	110	10	the	the	DET
ejpam-3288	110	11	constant	constant	ADJ
ejpam-3288	110	12	0	0	NUM
ejpam-3288	110	13	of	of	ADP
ejpam-3288	110	14	x	x	PRON
ejpam-3288	110	15	is	be	AUX
ejpam-3288	110	16	in	in	ADP
ejpam-3288	110	17	m	m	PROPN
ejpam-3288	110	18	if	if	SCONJ
ejpam-3288	111	1	and	and	CCONJ
ejpam-3288	111	2	only	only	ADV
ejpam-3288	111	3	if	if	SCONJ
ejpam-3288	111	4	c̃pm	c̃pm	X
ejpam-3288	111	5	(	(	PUNCT
ejpam-3288	111	6	0	0	NUM
ejpam-3288	111	7	)	)	PUNCT
ejpam-3288	111	8	≤	≤	NUM
ejpam-3288	111	9	c̃pm	c̃pm	X
ejpam-3288	111	10	(	(	PUNCT
ejpam-3288	111	11	x	x	NOUN
ejpam-3288	111	12	)	)	PUNCT
ejpam-3288	111	13	and	and	CCONJ
ejpam-3288	111	14	c̃nm	c̃nm	PROPN
ejpam-3288	111	15	(	(	PUNCT
ejpam-3288	111	16	0	0	NUM
ejpam-3288	111	17	)	)	PUNCT
ejpam-3288	111	18	≥	≥	NOUN
ejpam-3288	111	19	c̃nm	c̃nm	PROPN
ejpam-3288	111	20	(	(	PUNCT
ejpam-3288	111	21	x	x	NOUN
ejpam-3288	111	22	)	)	PUNCT
ejpam-3288	111	23	,	,	PUNCT
ejpam-3288	111	24	for	for	ADP
ejpam-3288	111	25	all	all	DET
ejpam-3288	111	26	x	x	SYM
ejpam-3288	111	27	∈	∈	ADJ
ejpam-3288	111	28	x.	x.	NOUN
ejpam-3288	111	29	proof	proof	NOUN
ejpam-3288	111	30	.	.	PUNCT
ejpam-3288	112	1	if	if	SCONJ
ejpam-3288	112	2	0	0	NUM
ejpam-3288	112	3	∈	∈	PROPN
ejpam-3288	112	4	m	m	NOUN
ejpam-3288	112	5	,	,	PUNCT
ejpam-3288	112	6	then	then	ADV
ejpam-3288	112	7	c̃pm	c̃pm	X
ejpam-3288	112	8	(	(	PUNCT
ejpam-3288	112	9	0	0	NUM
ejpam-3288	112	10	)	)	PUNCT
ejpam-3288	112	11	=	=	SYM
ejpam-3288	112	12	0	0	NUM
ejpam-3288	112	13	and	and	CCONJ
ejpam-3288	112	14	c̃nm	c̃nm	PROPN
ejpam-3288	112	15	(	(	PUNCT
ejpam-3288	112	16	0	0	NUM
ejpam-3288	112	17	)	)	PUNCT
ejpam-3288	112	18	=	=	SYM
ejpam-3288	112	19	0	0	X
ejpam-3288	112	20	.	.	PUNCT
ejpam-3288	113	1	thus	thus	ADV
ejpam-3288	113	2	,	,	PUNCT
ejpam-3288	113	3	c̃pm	c̃pm	X
ejpam-3288	113	4	(	(	PUNCT
ejpam-3288	113	5	0	0	NUM
ejpam-3288	113	6	)	)	PUNCT
ejpam-3288	113	7	=	=	SYM
ejpam-3288	114	1	0	0	NUM
ejpam-3288	114	2	≤	≤	NOUN
ejpam-3288	114	3	c̃pm	c̃pm	X
ejpam-3288	114	4	(	(	PUNCT
ejpam-3288	114	5	x	x	NOUN
ejpam-3288	114	6	)	)	PUNCT
ejpam-3288	114	7	and	and	CCONJ
ejpam-3288	114	8	c̃nm	c̃nm	PROPN
ejpam-3288	114	9	(	(	PUNCT
ejpam-3288	114	10	0	0	NUM
ejpam-3288	114	11	)	)	PUNCT
ejpam-3288	114	12	=	=	SYM
ejpam-3288	114	13	0	0	NUM
ejpam-3288	114	14	≥	≥	NOUN
ejpam-3288	114	15	c̃nm	c̃nm	PROPN
ejpam-3288	114	16	(	(	PUNCT
ejpam-3288	114	17	x	x	NOUN
ejpam-3288	114	18	)	)	PUNCT
ejpam-3288	114	19	,	,	PUNCT
ejpam-3288	114	20	for	for	ADP
ejpam-3288	114	21	all	all	PRON
ejpam-3288	114	22	x	x	SYM
ejpam-3288	114	23	∈	∈	NOUN
ejpam-3288	114	24	x.	x.	NOUN
ejpam-3288	114	25	conversely	conversely	ADV
ejpam-3288	114	26	,	,	PUNCT
ejpam-3288	114	27	assume	assume	VERB
ejpam-3288	114	28	that	that	SCONJ
ejpam-3288	114	29	c̃pm	c̃pm	X
ejpam-3288	114	30	(	(	PUNCT
ejpam-3288	114	31	0	0	NUM
ejpam-3288	114	32	)	)	PUNCT
ejpam-3288	114	33	≤	≤	NUM
ejpam-3288	114	34	c̃pm	c̃pm	X
ejpam-3288	114	35	(	(	PUNCT
ejpam-3288	114	36	x	x	NOUN
ejpam-3288	114	37	)	)	PUNCT
ejpam-3288	114	38	and	and	CCONJ
ejpam-3288	114	39	c̃nm	c̃nm	PROPN
ejpam-3288	114	40	(	(	PUNCT
ejpam-3288	114	41	0	0	NUM
ejpam-3288	114	42	)	)	PUNCT
ejpam-3288	114	43	≥	≥	NOUN
ejpam-3288	114	44	c̃nm	c̃nm	PROPN
ejpam-3288	114	45	(	(	PUNCT
ejpam-3288	114	46	x	x	NOUN
ejpam-3288	114	47	)	)	PUNCT
ejpam-3288	114	48	,	,	PUNCT
ejpam-3288	114	49	for	for	ADP
ejpam-3288	114	50	all	all	DET
ejpam-3288	114	51	x	x	SYM
ejpam-3288	114	52	∈	∈	PROPN
ejpam-3288	114	53	x.	x.	NOUN
ejpam-3288	114	54	since	since	SCONJ
ejpam-3288	114	55	m	m	PROPN
ejpam-3288	114	56	is	be	AUX
ejpam-3288	114	57	a	a	DET
ejpam-3288	114	58	nonempty	nonempty	ADJ
ejpam-3288	114	59	subset	subset	NOUN
ejpam-3288	114	60	of	of	ADP
ejpam-3288	114	61	x	x	PRON
ejpam-3288	114	62	,	,	PUNCT
ejpam-3288	114	63	we	we	PRON
ejpam-3288	114	64	have	have	VERB
ejpam-3288	114	65	m	m	NOUN
ejpam-3288	114	66	∈m	∈m	NOUN
ejpam-3288	114	67	for	for	ADP
ejpam-3288	114	68	some	some	DET
ejpam-3288	114	69	m	m	NOUN
ejpam-3288	114	70	∈	∈	NOUN
ejpam-3288	114	71	x.	x.	NOUN
ejpam-3288	114	72	then	then	ADV
ejpam-3288	114	73	c̃pm	c̃pm	X
ejpam-3288	114	74	(	(	PUNCT
ejpam-3288	114	75	0	0	NUM
ejpam-3288	114	76	)	)	PUNCT
ejpam-3288	114	77	≤	≤	NUM
ejpam-3288	115	1	c̃pm	c̃pm	X
ejpam-3288	115	2	(	(	PUNCT
ejpam-3288	115	3	m	m	NOUN
ejpam-3288	115	4	)	)	PUNCT
ejpam-3288	115	5	=	=	SYM
ejpam-3288	115	6	0	0	NUM
ejpam-3288	115	7	and	and	CCONJ
ejpam-3288	115	8	c̃nm	c̃nm	PROPN
ejpam-3288	115	9	(	(	PUNCT
ejpam-3288	115	10	0	0	NUM
ejpam-3288	115	11	)	)	PUNCT
ejpam-3288	115	12	≥	≥	NOUN
ejpam-3288	115	13	c̃pm	c̃pm	X
ejpam-3288	115	14	(	(	PUNCT
ejpam-3288	115	15	m	m	NOUN
ejpam-3288	115	16	)	)	PUNCT
ejpam-3288	115	17	=	=	SYM
ejpam-3288	115	18	0	0	X
ejpam-3288	115	19	.	.	PUNCT
ejpam-3288	116	1	thus	thus	ADV
ejpam-3288	116	2	,	,	PUNCT
ejpam-3288	116	3	c̃pm	c̃pm	X
ejpam-3288	116	4	(	(	PUNCT
ejpam-3288	116	5	0	0	NUM
ejpam-3288	116	6	)	)	PUNCT
ejpam-3288	116	7	=	=	SYM
ejpam-3288	116	8	0	0	NUM
ejpam-3288	116	9	and	and	CCONJ
ejpam-3288	116	10	c̃nm	c̃nm	PROPN
ejpam-3288	116	11	(	(	PUNCT
ejpam-3288	116	12	0	0	NUM
ejpam-3288	116	13	)	)	PUNCT
ejpam-3288	116	14	=	=	SYM
ejpam-3288	116	15	0	0	X
ejpam-3288	116	16	.	.	PUNCT
ejpam-3288	117	1	so	so	ADV
ejpam-3288	117	2	0	0	NUM
ejpam-3288	117	3	∈m	∈m	NOUN
ejpam-3288	117	4	.	.	PUNCT
ejpam-3288	117	5	theorem	theorem	NOUN
ejpam-3288	117	6	1	1	NUM
ejpam-3288	117	7	.	.	PUNCT
ejpam-3288	118	1	let	let	VERB
ejpam-3288	118	2	m	m	PRON
ejpam-3288	118	3	be	be	AUX
ejpam-3288	118	4	a	a	DET
ejpam-3288	118	5	nonempty	nonempty	ADJ
ejpam-3288	118	6	subset	subset	NOUN
ejpam-3288	118	7	of	of	ADP
ejpam-3288	118	8	x.	x.	NOUN
ejpam-3288	118	9	then	then	ADV
ejpam-3288	118	10	m	m	PROPN
ejpam-3288	118	11	is	be	AUX
ejpam-3288	118	12	an	an	DET
ejpam-3288	118	13	h	h	NOUN
ejpam-3288	118	14	-	-	PUNCT
ejpam-3288	118	15	ideal	ideal	NOUN
ejpam-3288	118	16	of	of	ADP
ejpam-3288	118	17	x	x	SYM
ejpam-3288	118	18	if	if	SCONJ
ejpam-3288	118	19	and	and	CCONJ
ejpam-3288	118	20	only	only	ADV
ejpam-3288	118	21	if	if	SCONJ
ejpam-3288	118	22	the	the	DET
ejpam-3288	118	23	doubt	doubt	ADV
ejpam-3288	118	24	bipolar	bipolar	ADJ
ejpam-3288	118	25	fuzzy	fuzzy	ADJ
ejpam-3288	118	26	characteristic	characteristic	ADJ
ejpam-3288	118	27	function	function	NOUN
ejpam-3288	118	28	c̃m	c̃m	NOUN
ejpam-3288	118	29	=	=	PUNCT
ejpam-3288	118	30	(	(	PUNCT
ejpam-3288	118	31	c̃pm	c̃pm	NOUN
ejpam-3288	118	32	,	,	PUNCT
ejpam-3288	118	33	c̃	c̃	PROPN
ejpam-3288	118	34	n	n	PROPN
ejpam-3288	118	35	m	m	PROPN
ejpam-3288	118	36	)	)	PUNCT
ejpam-3288	118	37	is	be	AUX
ejpam-3288	118	38	a	a	DET
ejpam-3288	118	39	doubt	doubt	ADV
ejpam-3288	118	40	bipolar	bipolar	ADJ
ejpam-3288	118	41	fuzzy	fuzzy	ADJ
ejpam-3288	118	42	h	h	NOUN
ejpam-3288	118	43	-	-	PUNCT
ejpam-3288	118	44	ideal	ideal	NOUN
ejpam-3288	118	45	of	of	ADP
ejpam-3288	118	46	x.	x.	NOUN
ejpam-3288	118	47	proof	proof	PROPN
ejpam-3288	118	48	.	.	PUNCT
ejpam-3288	119	1	assume	assume	VERB
ejpam-3288	119	2	that	that	SCONJ
ejpam-3288	119	3	m	m	PROPN
ejpam-3288	119	4	is	be	AUX
ejpam-3288	119	5	an	an	DET
ejpam-3288	119	6	h	h	NOUN
ejpam-3288	119	7	-	-	PUNCT
ejpam-3288	119	8	ideal	ideal	NOUN
ejpam-3288	119	9	of	of	ADP
ejpam-3288	119	10	x.	x.	NOUN
ejpam-3288	119	11	since	since	SCONJ
ejpam-3288	119	12	0	0	NUM
ejpam-3288	119	13	∈m	∈m	NUM
ejpam-3288	119	14	,	,	PUNCT
ejpam-3288	119	15	it	it	PRON
ejpam-3288	119	16	follows	follow	VERB
ejpam-3288	119	17	from	from	ADP
ejpam-3288	119	18	lemma	lemma	PROPN
ejpam-3288	119	19	1	1	NUM
ejpam-3288	119	20	that	that	PRON
ejpam-3288	119	21	c̃pm	c̃pm	X
ejpam-3288	119	22	(	(	PUNCT
ejpam-3288	119	23	0	0	NUM
ejpam-3288	119	24	)	)	PUNCT
ejpam-3288	119	25	≤	≤	NUM
ejpam-3288	119	26	c̃pm	c̃pm	X
ejpam-3288	119	27	(	(	PUNCT
ejpam-3288	119	28	x	x	NOUN
ejpam-3288	119	29	)	)	PUNCT
ejpam-3288	119	30	and	and	CCONJ
ejpam-3288	119	31	c̃nm	c̃nm	PROPN
ejpam-3288	119	32	(	(	PUNCT
ejpam-3288	119	33	0	0	NUM
ejpam-3288	119	34	)	)	PUNCT
ejpam-3288	119	35	≥	≥	NOUN
ejpam-3288	119	36	c̃nm	c̃nm	PROPN
ejpam-3288	119	37	(	(	PUNCT
ejpam-3288	119	38	x	x	NOUN
ejpam-3288	119	39	)	)	PUNCT
ejpam-3288	119	40	,	,	PUNCT
ejpam-3288	119	41	for	for	ADP
ejpam-3288	119	42	all	all	PRON
ejpam-3288	119	43	x	x	SYM
ejpam-3288	119	44	∈	∈	NOUN
ejpam-3288	119	45	x.	x.	NOUN
ejpam-3288	119	46	next	next	ADV
ejpam-3288	119	47	,	,	PUNCT
ejpam-3288	119	48	let	let	VERB
ejpam-3288	119	49	x	x	PRON
ejpam-3288	119	50	,	,	PUNCT
ejpam-3288	119	51	y	y	PROPN
ejpam-3288	119	52	,	,	PUNCT
ejpam-3288	119	53	z	z	PROPN
ejpam-3288	119	54	∈	∈	PROPN
ejpam-3288	120	1	x.	x.	NOUN
ejpam-3288	121	1	then	then	ADV
ejpam-3288	121	2	we	we	PRON
ejpam-3288	121	3	have	have	VERB
ejpam-3288	121	4	the	the	DET
ejpam-3288	121	5	following	follow	VERB
ejpam-3288	121	6	cases	case	NOUN
ejpam-3288	121	7	:	:	PUNCT
ejpam-3288	121	8	case(1	case(1	NUM
ejpam-3288	121	9	)	)	PUNCT
ejpam-3288	121	10	.	.	PUNCT
ejpam-3288	122	1	suppose	suppose	VERB
ejpam-3288	122	2	that	that	SCONJ
ejpam-3288	122	3	x	x	PROPN
ejpam-3288	122	4	∗	∗	NOUN
ejpam-3288	122	5	(	(	PUNCT
ejpam-3288	122	6	y	y	PROPN
ejpam-3288	122	7	∗	∗	PROPN
ejpam-3288	122	8	z	z	PROPN
ejpam-3288	122	9	)	)	PUNCT
ejpam-3288	122	10	∈	∈	PROPN
ejpam-3288	122	11	m	m	PROPN
ejpam-3288	122	12	and	and	CCONJ
ejpam-3288	122	13	y	y	PROPN
ejpam-3288	122	14	∈	∈	PROPN
ejpam-3288	122	15	m	m	PROPN
ejpam-3288	122	16	,	,	PUNCT
ejpam-3288	122	17	then	then	ADV
ejpam-3288	122	18	c̃pm	c̃pm	X
ejpam-3288	122	19	(	(	PUNCT
ejpam-3288	122	20	x	x	SYM
ejpam-3288	122	21	∗	∗	NOUN
ejpam-3288	122	22	(	(	PUNCT
ejpam-3288	122	23	y	y	PROPN
ejpam-3288	122	24	∗	∗	PROPN
ejpam-3288	122	25	z	z	NOUN
ejpam-3288	122	26	)	)	PUNCT
ejpam-3288	122	27	)	)	PUNCT
ejpam-3288	123	1	=	=	SYM
ejpam-3288	123	2	0	0	NUM
ejpam-3288	123	3	,	,	PUNCT
ejpam-3288	123	4	c̃pm	c̃pm	X
ejpam-3288	123	5	(	(	PUNCT
ejpam-3288	123	6	y	y	NOUN
ejpam-3288	123	7	)	)	PUNCT
ejpam-3288	123	8	=	=	SYM
ejpam-3288	123	9	0	0	NUM
ejpam-3288	123	10	,	,	PUNCT
ejpam-3288	123	11	c̃nm	c̃nm	PROPN
ejpam-3288	123	12	(	(	PUNCT
ejpam-3288	123	13	x	x	SYM
ejpam-3288	123	14	∗	∗	NOUN
ejpam-3288	123	15	(	(	PUNCT
ejpam-3288	123	16	y	y	PROPN
ejpam-3288	123	17	∗	∗	PROPN
ejpam-3288	123	18	z	z	NOUN
ejpam-3288	123	19	)	)	PUNCT
ejpam-3288	123	20	)	)	PUNCT
ejpam-3288	124	1	=	=	PUNCT
ejpam-3288	124	2	0	0	NUM
ejpam-3288	124	3	,	,	PUNCT
ejpam-3288	124	4	and	and	CCONJ
ejpam-3288	124	5	c̃nm	c̃nm	PROPN
ejpam-3288	124	6	(	(	PUNCT
ejpam-3288	124	7	y	y	NOUN
ejpam-3288	124	8	)	)	PUNCT
ejpam-3288	124	9	=	=	SYM
ejpam-3288	125	1	0	0	X
ejpam-3288	125	2	.	.	PUNCT
ejpam-3288	126	1	therefore	therefore	ADV
ejpam-3288	126	2	,	,	PUNCT
ejpam-3288	126	3	max{c̃pm	max{c̃pm	NOUN
ejpam-3288	126	4	(	(	PUNCT
ejpam-3288	126	5	x	x	SYM
ejpam-3288	126	6	∗	∗	NOUN
ejpam-3288	126	7	(	(	PUNCT
ejpam-3288	126	8	y	y	PROPN
ejpam-3288	126	9	∗	∗	PROPN
ejpam-3288	126	10	z	z	PROPN
ejpam-3288	126	11	)	)	PUNCT
ejpam-3288	126	12	)	)	PUNCT
ejpam-3288	126	13	,	,	PUNCT
ejpam-3288	126	14	c̃pm	c̃pm	X
ejpam-3288	126	15	(	(	PUNCT
ejpam-3288	126	16	y	y	NOUN
ejpam-3288	126	17	)	)	PUNCT
ejpam-3288	126	18	}	}	PUNCT
ejpam-3288	126	19	=	=	SYM
ejpam-3288	126	20	max{0	max{0	PROPN
ejpam-3288	126	21	,	,	PUNCT
ejpam-3288	126	22	0	0	NUM
ejpam-3288	126	23	}	}	PUNCT
ejpam-3288	126	24	=	=	SYM
ejpam-3288	126	25	0	0	NUM
ejpam-3288	126	26	,	,	PUNCT
ejpam-3288	126	27	and	and	CCONJ
ejpam-3288	126	28	min{c̃nm	min{c̃nm	NOUN
ejpam-3288	126	29	(	(	PUNCT
ejpam-3288	126	30	x	x	SYM
ejpam-3288	126	31	∗	∗	NOUN
ejpam-3288	126	32	(	(	PUNCT
ejpam-3288	126	33	y	y	PROPN
ejpam-3288	126	34	∗	∗	PROPN
ejpam-3288	126	35	z	z	PROPN
ejpam-3288	126	36	)	)	PUNCT
ejpam-3288	126	37	)	)	PUNCT
ejpam-3288	126	38	,	,	PUNCT
ejpam-3288	126	39	c̃nm	c̃nm	PROPN
ejpam-3288	126	40	(	(	PUNCT
ejpam-3288	126	41	y	y	NOUN
ejpam-3288	126	42	)	)	PUNCT
ejpam-3288	126	43	}	}	PUNCT
ejpam-3288	126	44	=	=	SYM
ejpam-3288	126	45	min{0	min{0	PROPN
ejpam-3288	126	46	,	,	PUNCT
ejpam-3288	126	47	0	0	NUM
ejpam-3288	126	48	}	}	PUNCT
ejpam-3288	126	49	=	=	SYM
ejpam-3288	126	50	0	0	X
ejpam-3288	126	51	.	.	PUNCT
ejpam-3288	126	52	a.	a.	PROPN
ejpam-3288	126	53	al	al	PROPN
ejpam-3288	126	54	-	-	PROPN
ejpam-3288	126	55	masarwah	masarwah	PROPN
ejpam-3288	126	56	,	,	PUNCT
ejpam-3288	126	57	a.	a.	NOUN
ejpam-3288	126	58	g.	g.	PROPN
ejpam-3288	126	59	ahmad	ahmad	PROPN
ejpam-3288	126	60	/	/	SYM
ejpam-3288	126	61	eur	eur	PROPN
ejpam-3288	126	62	.	.	PUNCT
ejpam-3288	127	1	j.	j.	PROPN
ejpam-3288	127	2	pure	pure	PROPN
ejpam-3288	127	3	appl	appl	PROPN
ejpam-3288	127	4	.	.	PROPN
ejpam-3288	127	5	math	math	PROPN
ejpam-3288	127	6	,	,	PUNCT
ejpam-3288	127	7	11	11	NUM
ejpam-3288	127	8	(	(	PUNCT
ejpam-3288	127	9	3	3	NUM
ejpam-3288	127	10	)	)	PUNCT
ejpam-3288	127	11	(	(	PUNCT
ejpam-3288	127	12	2018	2018	NUM
ejpam-3288	127	13	)	)	PUNCT
ejpam-3288	127	14	,	,	PUNCT
ejpam-3288	127	15	652	652	NUM
ejpam-3288	127	16	-	-	SYM
ejpam-3288	127	17	670	670	NUM
ejpam-3288	127	18	657	657	NUM
ejpam-3288	127	19	since	since	SCONJ
ejpam-3288	127	20	x	x	PROPN
ejpam-3288	127	21	∗	∗	NOUN
ejpam-3288	127	22	(	(	PUNCT
ejpam-3288	127	23	y	y	PROPN
ejpam-3288	127	24	∗	∗	PROPN
ejpam-3288	127	25	z	z	NOUN
ejpam-3288	127	26	)	)	PUNCT
ejpam-3288	127	27	∈m	∈m	NOUN
ejpam-3288	127	28	and	and	CCONJ
ejpam-3288	127	29	y	y	PROPN
ejpam-3288	127	30	∈m	∈m	NOUN
ejpam-3288	127	31	,	,	PUNCT
ejpam-3288	127	32	we	we	PRON
ejpam-3288	127	33	have	have	AUX
ejpam-3288	127	34	x	x	PROPN
ejpam-3288	127	35	∗	∗	NOUN
ejpam-3288	127	36	z	z	NOUN
ejpam-3288	127	37	∈m	∈m	NOUN
ejpam-3288	127	38	.	.	PUNCT
ejpam-3288	128	1	so	so	ADV
ejpam-3288	128	2	c̃pm	c̃pm	X
ejpam-3288	128	3	(	(	PUNCT
ejpam-3288	128	4	x	x	NOUN
ejpam-3288	128	5	∗	∗	NOUN
ejpam-3288	128	6	z	z	NOUN
ejpam-3288	128	7	)	)	PUNCT
ejpam-3288	128	8	=	=	SYM
ejpam-3288	128	9	0	0	NUM
ejpam-3288	128	10	and	and	CCONJ
ejpam-3288	128	11	c̃nm	c̃nm	PROPN
ejpam-3288	128	12	(	(	PUNCT
ejpam-3288	128	13	x	x	X
ejpam-3288	128	14	∗	∗	PROPN
ejpam-3288	128	15	z	z	NOUN
ejpam-3288	128	16	)	)	PUNCT
ejpam-3288	128	17	=	=	SYM
ejpam-3288	129	1	0	0	X
ejpam-3288	129	2	.	.	PUNCT
ejpam-3288	130	1	therefore	therefore	ADV
ejpam-3288	130	2	,	,	PUNCT
ejpam-3288	130	3	c̃pm	c̃pm	X
ejpam-3288	130	4	(	(	PUNCT
ejpam-3288	130	5	x	x	NOUN
ejpam-3288	130	6	∗	∗	PROPN
ejpam-3288	130	7	z	z	NOUN
ejpam-3288	130	8	)	)	PUNCT
ejpam-3288	130	9	=	=	SYM
ejpam-3288	130	10	0	0	NUM
ejpam-3288	130	11	≤	≤	NUM
ejpam-3288	130	12	0	0	NUM
ejpam-3288	131	1	=	=	NOUN
ejpam-3288	131	2	max{c̃pm	max{c̃pm	NOUN
ejpam-3288	131	3	(	(	PUNCT
ejpam-3288	131	4	x	x	X
ejpam-3288	131	5	∗	∗	NOUN
ejpam-3288	131	6	(	(	PUNCT
ejpam-3288	131	7	y	y	PROPN
ejpam-3288	131	8	∗	∗	PROPN
ejpam-3288	131	9	z	z	PROPN
ejpam-3288	131	10	)	)	PUNCT
ejpam-3288	131	11	)	)	PUNCT
ejpam-3288	131	12	,	,	PUNCT
ejpam-3288	131	13	c̃pm	c̃pm	X
ejpam-3288	131	14	(	(	PUNCT
ejpam-3288	131	15	y	y	NOUN
ejpam-3288	131	16	)	)	PUNCT
ejpam-3288	131	17	}	}	PUNCT
ejpam-3288	131	18	,	,	PUNCT
ejpam-3288	131	19	and	and	CCONJ
ejpam-3288	131	20	c̃nm	c̃nm	PROPN
ejpam-3288	131	21	(	(	PUNCT
ejpam-3288	131	22	x	x	X
ejpam-3288	131	23	∗	∗	PROPN
ejpam-3288	131	24	z	z	NOUN
ejpam-3288	131	25	)	)	PUNCT
ejpam-3288	131	26	=	=	SYM
ejpam-3288	131	27	0	0	NUM
ejpam-3288	131	28	≥	≥	NOUN
ejpam-3288	131	29	0	0	NUM
ejpam-3288	132	1	=	=	PUNCT
ejpam-3288	132	2	min{c̃nm	min{c̃nm	NOUN
ejpam-3288	132	3	(	(	PUNCT
ejpam-3288	132	4	x	x	SYM
ejpam-3288	132	5	∗	∗	NOUN
ejpam-3288	132	6	(	(	PUNCT
ejpam-3288	132	7	y	y	PROPN
ejpam-3288	132	8	∗	∗	PROPN
ejpam-3288	132	9	z	z	PROPN
ejpam-3288	132	10	)	)	PUNCT
ejpam-3288	132	11	)	)	PUNCT
ejpam-3288	132	12	,	,	PUNCT
ejpam-3288	132	13	c̃nm	c̃nm	PROPN
ejpam-3288	132	14	(	(	PUNCT
ejpam-3288	132	15	y	y	NOUN
ejpam-3288	132	16	)	)	PUNCT
ejpam-3288	132	17	}	}	PUNCT
ejpam-3288	132	18	.	.	PUNCT
ejpam-3288	133	1	case(2	case(2	NOUN
ejpam-3288	133	2	)	)	PUNCT
ejpam-3288	133	3	.	.	PUNCT
ejpam-3288	133	4	suppose	suppose	VERB
ejpam-3288	133	5	that	that	SCONJ
ejpam-3288	133	6	x	x	PROPN
ejpam-3288	133	7	∗	∗	NOUN
ejpam-3288	133	8	(	(	PUNCT
ejpam-3288	133	9	y	y	PROPN
ejpam-3288	133	10	∗	∗	PROPN
ejpam-3288	133	11	z	z	PROPN
ejpam-3288	133	12	)	)	PUNCT
ejpam-3288	133	13	6∈	6∈	PROPN
ejpam-3288	133	14	m	m	PROPN
ejpam-3288	133	15	and	and	CCONJ
ejpam-3288	133	16	y	y	PROPN
ejpam-3288	133	17	6∈	6∈	PROPN
ejpam-3288	133	18	m	m	PROPN
ejpam-3288	133	19	,	,	PUNCT
ejpam-3288	133	20	then	then	ADV
ejpam-3288	133	21	c̃pm	c̃pm	X
ejpam-3288	133	22	(	(	PUNCT
ejpam-3288	133	23	x	x	SYM
ejpam-3288	133	24	∗	∗	NOUN
ejpam-3288	133	25	(	(	PUNCT
ejpam-3288	133	26	y	y	PROPN
ejpam-3288	133	27	∗	∗	PROPN
ejpam-3288	133	28	z	z	NOUN
ejpam-3288	133	29	)	)	PUNCT
ejpam-3288	133	30	)	)	PUNCT
ejpam-3288	134	1	=	=	SYM
ejpam-3288	134	2	1	1	NUM
ejpam-3288	134	3	,	,	PUNCT
ejpam-3288	134	4	c̃pm	c̃pm	X
ejpam-3288	134	5	(	(	PUNCT
ejpam-3288	134	6	y	y	NOUN
ejpam-3288	134	7	)	)	PUNCT
ejpam-3288	134	8	=	=	SYM
ejpam-3288	134	9	1	1	NUM
ejpam-3288	134	10	,	,	PUNCT
ejpam-3288	134	11	c̃nm	c̃nm	PROPN
ejpam-3288	134	12	(	(	PUNCT
ejpam-3288	134	13	x	x	SYM
ejpam-3288	134	14	∗	∗	NOUN
ejpam-3288	134	15	(	(	PUNCT
ejpam-3288	134	16	y	y	PROPN
ejpam-3288	134	17	∗	∗	PROPN
ejpam-3288	134	18	z	z	NOUN
ejpam-3288	134	19	)	)	PUNCT
ejpam-3288	134	20	)	)	PUNCT
ejpam-3288	135	1	=	=	SYM
ejpam-3288	135	2	−1	−1	NOUN
ejpam-3288	135	3	,	,	PUNCT
ejpam-3288	135	4	and	and	CCONJ
ejpam-3288	135	5	c̃nm	c̃nm	PROPN
ejpam-3288	135	6	(	(	PUNCT
ejpam-3288	135	7	y	y	NOUN
ejpam-3288	135	8	)	)	PUNCT
ejpam-3288	135	9	=	=	PUNCT
ejpam-3288	135	10	−1	−1	NOUN
ejpam-3288	135	11	.	.	PUNCT
ejpam-3288	136	1	so	so	ADV
ejpam-3288	136	2	,	,	PUNCT
ejpam-3288	136	3	max{c̃pm	max{c̃pm	NOUN
ejpam-3288	136	4	(	(	PUNCT
ejpam-3288	136	5	x	x	SYM
ejpam-3288	136	6	∗	∗	NOUN
ejpam-3288	136	7	(	(	PUNCT
ejpam-3288	136	8	y	y	PROPN
ejpam-3288	136	9	∗	∗	PROPN
ejpam-3288	136	10	z	z	PROPN
ejpam-3288	136	11	)	)	PUNCT
ejpam-3288	136	12	)	)	PUNCT
ejpam-3288	136	13	,	,	PUNCT
ejpam-3288	136	14	c̃pm	c̃pm	X
ejpam-3288	136	15	(	(	PUNCT
ejpam-3288	136	16	y	y	NOUN
ejpam-3288	136	17	)	)	PUNCT
ejpam-3288	136	18	}	}	PUNCT
ejpam-3288	136	19	=	=	SYM
ejpam-3288	136	20	max{1	max{1	NOUN
ejpam-3288	136	21	,	,	PUNCT
ejpam-3288	136	22	1	1	NUM
ejpam-3288	136	23	}	}	PUNCT
ejpam-3288	136	24	=	=	SYM
ejpam-3288	136	25	1	1	NUM
ejpam-3288	136	26	,	,	PUNCT
ejpam-3288	136	27	and	and	CCONJ
ejpam-3288	136	28	min{c̃nm	min{c̃nm	NOUN
ejpam-3288	136	29	(	(	PUNCT
ejpam-3288	136	30	x	x	SYM
ejpam-3288	136	31	∗	∗	NOUN
ejpam-3288	136	32	(	(	PUNCT
ejpam-3288	136	33	y	y	PROPN
ejpam-3288	136	34	∗	∗	PROPN
ejpam-3288	136	35	z	z	PROPN
ejpam-3288	136	36	)	)	PUNCT
ejpam-3288	136	37	)	)	PUNCT
ejpam-3288	136	38	,	,	PUNCT
ejpam-3288	136	39	c̃nm	c̃nm	PROPN
ejpam-3288	136	40	(	(	PUNCT
ejpam-3288	136	41	y	y	NOUN
ejpam-3288	136	42	)	)	PUNCT
ejpam-3288	136	43	}	}	PUNCT
ejpam-3288	137	1	=	=	PUNCT
ejpam-3288	137	2	min{−1,−1	min{−1,−1	ADJ
ejpam-3288	137	3	}	}	PUNCT
ejpam-3288	137	4	=	=	SYM
ejpam-3288	137	5	−1	−1	NOUN
ejpam-3288	137	6	.	.	PUNCT
ejpam-3288	138	1	therefore	therefore	ADV
ejpam-3288	138	2	,	,	PUNCT
ejpam-3288	138	3	c̃pm	c̃pm	X
ejpam-3288	138	4	(	(	PUNCT
ejpam-3288	138	5	x	x	NOUN
ejpam-3288	138	6	∗	∗	PROPN
ejpam-3288	138	7	z	z	NOUN
ejpam-3288	138	8	)	)	PUNCT
ejpam-3288	138	9	≤	≤	NOUN
ejpam-3288	138	10	1	1	NUM
ejpam-3288	138	11	=	=	SYM
ejpam-3288	138	12	max{c̃pm	max{c̃pm	NOUN
ejpam-3288	138	13	(	(	PUNCT
ejpam-3288	138	14	x	x	X
ejpam-3288	138	15	∗	∗	NOUN
ejpam-3288	138	16	(	(	PUNCT
ejpam-3288	138	17	y	y	PROPN
ejpam-3288	138	18	∗	∗	PROPN
ejpam-3288	138	19	z	z	PROPN
ejpam-3288	138	20	)	)	PUNCT
ejpam-3288	138	21	)	)	PUNCT
ejpam-3288	138	22	,	,	PUNCT
ejpam-3288	138	23	c̃pm	c̃pm	X
ejpam-3288	138	24	(	(	PUNCT
ejpam-3288	138	25	y	y	NOUN
ejpam-3288	138	26	)	)	PUNCT
ejpam-3288	138	27	}	}	PUNCT
ejpam-3288	138	28	,	,	PUNCT
ejpam-3288	138	29	and	and	CCONJ
ejpam-3288	138	30	c̃nm	c̃nm	PROPN
ejpam-3288	138	31	(	(	PUNCT
ejpam-3288	138	32	x	x	X
ejpam-3288	138	33	∗	∗	PROPN
ejpam-3288	138	34	z	z	NOUN
ejpam-3288	138	35	)	)	PUNCT
ejpam-3288	138	36	≥	≥	X
ejpam-3288	138	37	−1	−1	NOUN
ejpam-3288	138	38	=	=	PUNCT
ejpam-3288	138	39	min{c̃nm	min{c̃nm	NOUN
ejpam-3288	138	40	(	(	PUNCT
ejpam-3288	138	41	x	x	SYM
ejpam-3288	138	42	∗	∗	NOUN
ejpam-3288	138	43	(	(	PUNCT
ejpam-3288	138	44	y	y	PROPN
ejpam-3288	138	45	∗	∗	PROPN
ejpam-3288	138	46	z	z	PROPN
ejpam-3288	138	47	)	)	PUNCT
ejpam-3288	138	48	)	)	PUNCT
ejpam-3288	138	49	,	,	PUNCT
ejpam-3288	138	50	c̃nm	c̃nm	PROPN
ejpam-3288	138	51	(	(	PUNCT
ejpam-3288	138	52	y	y	NOUN
ejpam-3288	138	53	)	)	PUNCT
ejpam-3288	138	54	}	}	PUNCT
ejpam-3288	138	55	.	.	PUNCT
ejpam-3288	139	1	case(3	case(3	NOUN
ejpam-3288	139	2	)	)	PUNCT
ejpam-3288	139	3	.	.	PUNCT
ejpam-3288	140	1	suppose	suppose	VERB
ejpam-3288	140	2	that	that	SCONJ
ejpam-3288	140	3	x	x	PROPN
ejpam-3288	140	4	∗	∗	NOUN
ejpam-3288	140	5	(	(	PUNCT
ejpam-3288	140	6	y	y	PROPN
ejpam-3288	140	7	∗	∗	PROPN
ejpam-3288	140	8	z	z	NOUN
ejpam-3288	140	9	)	)	PUNCT
ejpam-3288	140	10	∈m	∈m	NOUN
ejpam-3288	140	11	or	or	CCONJ
ejpam-3288	140	12	y	y	NOUN
ejpam-3288	140	13	∈m	∈m	NOUN
ejpam-3288	140	14	.	.	PUNCT
ejpam-3288	141	1	then	then	ADV
ejpam-3288	141	2	we	we	PRON
ejpam-3288	141	3	have	have	VERB
ejpam-3288	141	4	two	two	NUM
ejpam-3288	141	5	subcases	subcase	NOUN
ejpam-3288	141	6	:	:	PUNCT
ejpam-3288	141	7	subcase	subcase	PROPN
ejpam-3288	141	8	(	(	PUNCT
ejpam-3288	141	9	3a	3a	NUM
ejpam-3288	141	10	)	)	PUNCT
ejpam-3288	141	11	.	.	PUNCT
ejpam-3288	142	1	if	if	SCONJ
ejpam-3288	142	2	x	x	PRON
ejpam-3288	142	3	∗	∗	NOUN
ejpam-3288	142	4	(	(	PUNCT
ejpam-3288	142	5	y	y	PROPN
ejpam-3288	142	6	∗	∗	PROPN
ejpam-3288	142	7	z	z	PROPN
ejpam-3288	142	8	)	)	PUNCT
ejpam-3288	142	9	∈	∈	PROPN
ejpam-3288	142	10	m	m	PROPN
ejpam-3288	142	11	and	and	CCONJ
ejpam-3288	142	12	y	y	PROPN
ejpam-3288	142	13	6∈	6∈	PROPN
ejpam-3288	142	14	m	m	PROPN
ejpam-3288	142	15	,	,	PUNCT
ejpam-3288	142	16	then	then	ADV
ejpam-3288	142	17	c̃pm	c̃pm	X
ejpam-3288	142	18	(	(	PUNCT
ejpam-3288	142	19	x	x	SYM
ejpam-3288	142	20	∗	∗	NOUN
ejpam-3288	142	21	(	(	PUNCT
ejpam-3288	142	22	y	y	PROPN
ejpam-3288	142	23	∗	∗	PROPN
ejpam-3288	142	24	z	z	NOUN
ejpam-3288	142	25	)	)	PUNCT
ejpam-3288	142	26	)	)	PUNCT
ejpam-3288	143	1	=	=	SYM
ejpam-3288	143	2	0	0	NUM
ejpam-3288	143	3	,	,	PUNCT
ejpam-3288	143	4	c̃pm	c̃pm	X
ejpam-3288	143	5	(	(	PUNCT
ejpam-3288	143	6	y	y	NOUN
ejpam-3288	143	7	)	)	PUNCT
ejpam-3288	143	8	=	=	SYM
ejpam-3288	143	9	1	1	NUM
ejpam-3288	143	10	,	,	PUNCT
ejpam-3288	143	11	c̃nm	c̃nm	PROPN
ejpam-3288	143	12	(	(	PUNCT
ejpam-3288	143	13	x	x	SYM
ejpam-3288	143	14	∗	∗	NOUN
ejpam-3288	143	15	(	(	PUNCT
ejpam-3288	143	16	y	y	PROPN
ejpam-3288	143	17	∗	∗	PROPN
ejpam-3288	143	18	z	z	NOUN
ejpam-3288	143	19	)	)	PUNCT
ejpam-3288	143	20	)	)	PUNCT
ejpam-3288	144	1	=	=	PUNCT
ejpam-3288	144	2	0	0	NUM
ejpam-3288	144	3	,	,	PUNCT
ejpam-3288	144	4	and	and	CCONJ
ejpam-3288	144	5	c̃nm	c̃nm	PROPN
ejpam-3288	144	6	(	(	PUNCT
ejpam-3288	144	7	y	y	NOUN
ejpam-3288	144	8	)	)	PUNCT
ejpam-3288	144	9	=	=	PUNCT
ejpam-3288	144	10	−1	−1	NOUN
ejpam-3288	144	11	.	.	PUNCT
ejpam-3288	145	1	so	so	ADV
ejpam-3288	145	2	,	,	PUNCT
ejpam-3288	145	3	max{c̃pm	max{c̃pm	NOUN
ejpam-3288	145	4	(	(	PUNCT
ejpam-3288	145	5	x	x	SYM
ejpam-3288	145	6	∗	∗	NOUN
ejpam-3288	145	7	(	(	PUNCT
ejpam-3288	145	8	y	y	PROPN
ejpam-3288	145	9	∗	∗	PROPN
ejpam-3288	145	10	z	z	PROPN
ejpam-3288	145	11	)	)	PUNCT
ejpam-3288	145	12	)	)	PUNCT
ejpam-3288	145	13	,	,	PUNCT
ejpam-3288	145	14	c̃pm	c̃pm	X
ejpam-3288	145	15	(	(	PUNCT
ejpam-3288	145	16	y	y	NOUN
ejpam-3288	145	17	)	)	PUNCT
ejpam-3288	145	18	}	}	PUNCT
ejpam-3288	145	19	=	=	SYM
ejpam-3288	145	20	max{0	max{0	NUM
ejpam-3288	145	21	,	,	PUNCT
ejpam-3288	145	22	1	1	NUM
ejpam-3288	145	23	}	}	PUNCT
ejpam-3288	145	24	=	=	SYM
ejpam-3288	145	25	1	1	NUM
ejpam-3288	145	26	,	,	PUNCT
ejpam-3288	145	27	and	and	CCONJ
ejpam-3288	145	28	min{c̃nm	min{c̃nm	NOUN
ejpam-3288	145	29	(	(	PUNCT
ejpam-3288	145	30	x	x	SYM
ejpam-3288	145	31	∗	∗	NOUN
ejpam-3288	145	32	(	(	PUNCT
ejpam-3288	145	33	y	y	PROPN
ejpam-3288	145	34	∗	∗	PROPN
ejpam-3288	145	35	z	z	PROPN
ejpam-3288	145	36	)	)	PUNCT
ejpam-3288	145	37	)	)	PUNCT
ejpam-3288	145	38	,	,	PUNCT
ejpam-3288	145	39	c̃nm	c̃nm	PROPN
ejpam-3288	145	40	(	(	PUNCT
ejpam-3288	145	41	y	y	NOUN
ejpam-3288	145	42	)	)	PUNCT
ejpam-3288	145	43	}	}	PUNCT
ejpam-3288	145	44	=	=	PUNCT
ejpam-3288	145	45	min{0,−1	min{0,−1	NOUN
ejpam-3288	145	46	}	}	PUNCT
ejpam-3288	145	47	=	=	SYM
ejpam-3288	145	48	−1	−1	NOUN
ejpam-3288	145	49	.	.	PUNCT
ejpam-3288	146	1	therefore	therefore	ADV
ejpam-3288	146	2	,	,	PUNCT
ejpam-3288	146	3	c̃pm	c̃pm	X
ejpam-3288	146	4	(	(	PUNCT
ejpam-3288	146	5	x	x	NOUN
ejpam-3288	146	6	∗	∗	PROPN
ejpam-3288	146	7	z	z	NOUN
ejpam-3288	146	8	)	)	PUNCT
ejpam-3288	146	9	≤	≤	NOUN
ejpam-3288	146	10	1	1	NUM
ejpam-3288	146	11	=	=	SYM
ejpam-3288	146	12	max{c̃pm	max{c̃pm	NOUN
ejpam-3288	146	13	(	(	PUNCT
ejpam-3288	146	14	x	x	X
ejpam-3288	146	15	∗	∗	NOUN
ejpam-3288	146	16	(	(	PUNCT
ejpam-3288	146	17	y	y	PROPN
ejpam-3288	146	18	∗	∗	PROPN
ejpam-3288	146	19	z	z	PROPN
ejpam-3288	146	20	)	)	PUNCT
ejpam-3288	146	21	)	)	PUNCT
ejpam-3288	146	22	,	,	PUNCT
ejpam-3288	146	23	c̃pm	c̃pm	X
ejpam-3288	146	24	(	(	PUNCT
ejpam-3288	146	25	y	y	NOUN
ejpam-3288	146	26	)	)	PUNCT
ejpam-3288	146	27	}	}	PUNCT
ejpam-3288	146	28	,	,	PUNCT
ejpam-3288	146	29	and	and	CCONJ
ejpam-3288	146	30	c̃nm	c̃nm	PROPN
ejpam-3288	146	31	(	(	PUNCT
ejpam-3288	146	32	x	x	X
ejpam-3288	146	33	∗	∗	PROPN
ejpam-3288	146	34	z	z	NOUN
ejpam-3288	146	35	)	)	PUNCT
ejpam-3288	146	36	≥	≥	X
ejpam-3288	146	37	−1	−1	NOUN
ejpam-3288	146	38	=	=	PUNCT
ejpam-3288	146	39	min{c̃nm	min{c̃nm	NOUN
ejpam-3288	146	40	(	(	PUNCT
ejpam-3288	146	41	x	x	SYM
ejpam-3288	146	42	∗	∗	NOUN
ejpam-3288	146	43	(	(	PUNCT
ejpam-3288	146	44	y	y	PROPN
ejpam-3288	146	45	∗	∗	PROPN
ejpam-3288	146	46	z	z	PROPN
ejpam-3288	146	47	)	)	PUNCT
ejpam-3288	146	48	)	)	PUNCT
ejpam-3288	146	49	,	,	PUNCT
ejpam-3288	146	50	c̃nm	c̃nm	PROPN
ejpam-3288	146	51	(	(	PUNCT
ejpam-3288	146	52	y	y	NOUN
ejpam-3288	146	53	)	)	PUNCT
ejpam-3288	146	54	}	}	PUNCT
ejpam-3288	146	55	.	.	PUNCT
ejpam-3288	147	1	subcase	subcase	PROPN
ejpam-3288	147	2	(	(	PUNCT
ejpam-3288	147	3	3b	3b	NUM
ejpam-3288	147	4	)	)	PUNCT
ejpam-3288	147	5	.	.	PUNCT
ejpam-3288	148	1	if	if	SCONJ
ejpam-3288	148	2	x	x	PRON
ejpam-3288	148	3	∗	∗	NOUN
ejpam-3288	148	4	(	(	PUNCT
ejpam-3288	148	5	y	y	PROPN
ejpam-3288	148	6	∗	∗	PROPN
ejpam-3288	148	7	z	z	PROPN
ejpam-3288	148	8	)	)	PUNCT
ejpam-3288	148	9	6∈	6∈	PROPN
ejpam-3288	148	10	m	m	PROPN
ejpam-3288	148	11	and	and	CCONJ
ejpam-3288	148	12	y	y	PROPN
ejpam-3288	148	13	∈	∈	PROPN
ejpam-3288	148	14	m	m	PROPN
ejpam-3288	148	15	,	,	PUNCT
ejpam-3288	148	16	then	then	ADV
ejpam-3288	148	17	c̃pm	c̃pm	X
ejpam-3288	148	18	(	(	PUNCT
ejpam-3288	148	19	x	x	SYM
ejpam-3288	148	20	∗	∗	NOUN
ejpam-3288	148	21	(	(	PUNCT
ejpam-3288	148	22	y	y	PROPN
ejpam-3288	148	23	∗	∗	PROPN
ejpam-3288	148	24	z	z	NOUN
ejpam-3288	148	25	)	)	PUNCT
ejpam-3288	148	26	)	)	PUNCT
ejpam-3288	149	1	=	=	SYM
ejpam-3288	149	2	1	1	NUM
ejpam-3288	149	3	,	,	PUNCT
ejpam-3288	149	4	c̃pm	c̃pm	X
ejpam-3288	149	5	(	(	PUNCT
ejpam-3288	149	6	y	y	NOUN
ejpam-3288	149	7	)	)	PUNCT
ejpam-3288	149	8	=	=	SYM
ejpam-3288	149	9	0	0	NUM
ejpam-3288	149	10	,	,	PUNCT
ejpam-3288	149	11	c̃nm	c̃nm	PROPN
ejpam-3288	149	12	(	(	PUNCT
ejpam-3288	149	13	x	x	SYM
ejpam-3288	149	14	∗	∗	NOUN
ejpam-3288	149	15	(	(	PUNCT
ejpam-3288	149	16	y	y	PROPN
ejpam-3288	149	17	∗	∗	PROPN
ejpam-3288	149	18	z	z	NOUN
ejpam-3288	149	19	)	)	PUNCT
ejpam-3288	149	20	)	)	PUNCT
ejpam-3288	150	1	=	=	SYM
ejpam-3288	150	2	−1	−1	NOUN
ejpam-3288	150	3	,	,	PUNCT
ejpam-3288	150	4	and	and	CCONJ
ejpam-3288	150	5	c̃nm	c̃nm	PROPN
ejpam-3288	150	6	(	(	PUNCT
ejpam-3288	150	7	y	y	NOUN
ejpam-3288	150	8	)	)	PUNCT
ejpam-3288	150	9	=	=	SYM
ejpam-3288	151	1	0	0	X
ejpam-3288	151	2	.	.	PUNCT
ejpam-3288	152	1	so	so	ADV
ejpam-3288	152	2	,	,	PUNCT
ejpam-3288	152	3	max{c̃pm	max{c̃pm	X
ejpam-3288	152	4	(	(	PUNCT
ejpam-3288	152	5	x	x	SYM
ejpam-3288	152	6	∗	∗	NOUN
ejpam-3288	152	7	(	(	PUNCT
ejpam-3288	152	8	y	y	PROPN
ejpam-3288	152	9	∗	∗	PROPN
ejpam-3288	152	10	z	z	PROPN
ejpam-3288	152	11	)	)	PUNCT
ejpam-3288	152	12	)	)	PUNCT
ejpam-3288	152	13	,	,	PUNCT
ejpam-3288	152	14	c̃pm	c̃pm	X
ejpam-3288	152	15	(	(	PUNCT
ejpam-3288	152	16	y	y	NOUN
ejpam-3288	152	17	)	)	PUNCT
ejpam-3288	152	18	}	}	PUNCT
ejpam-3288	152	19	=	=	SYM
ejpam-3288	152	20	max{1	max{1	NOUN
ejpam-3288	152	21	,	,	PUNCT
ejpam-3288	152	22	0	0	NUM
ejpam-3288	152	23	}	}	PUNCT
ejpam-3288	152	24	=	=	SYM
ejpam-3288	152	25	1	1	NUM
ejpam-3288	152	26	,	,	PUNCT
ejpam-3288	152	27	and	and	CCONJ
ejpam-3288	152	28	min{c̃nm	min{c̃nm	NOUN
ejpam-3288	152	29	(	(	PUNCT
ejpam-3288	152	30	x	x	SYM
ejpam-3288	152	31	∗	∗	NOUN
ejpam-3288	152	32	(	(	PUNCT
ejpam-3288	152	33	y	y	PROPN
ejpam-3288	152	34	∗	∗	PROPN
ejpam-3288	152	35	z	z	PROPN
ejpam-3288	152	36	)	)	PUNCT
ejpam-3288	152	37	)	)	PUNCT
ejpam-3288	152	38	,	,	PUNCT
ejpam-3288	152	39	c̃nm	c̃nm	PROPN
ejpam-3288	152	40	(	(	PUNCT
ejpam-3288	152	41	y	y	NOUN
ejpam-3288	152	42	)	)	PUNCT
ejpam-3288	152	43	}	}	PUNCT
ejpam-3288	152	44	=	=	SYM
ejpam-3288	152	45	min{−1	min{−1	NOUN
ejpam-3288	152	46	,	,	PUNCT
ejpam-3288	152	47	0	0	NUM
ejpam-3288	152	48	}	}	PUNCT
ejpam-3288	152	49	=	=	SYM
ejpam-3288	152	50	−1	−1	NOUN
ejpam-3288	152	51	.	.	PUNCT
ejpam-3288	153	1	therefore	therefore	ADV
ejpam-3288	153	2	,	,	PUNCT
ejpam-3288	153	3	c̃pm	c̃pm	X
ejpam-3288	153	4	(	(	PUNCT
ejpam-3288	153	5	x	x	NOUN
ejpam-3288	153	6	∗	∗	PROPN
ejpam-3288	153	7	z	z	NOUN
ejpam-3288	153	8	)	)	PUNCT
ejpam-3288	153	9	≤	≤	NOUN
ejpam-3288	153	10	1	1	NUM
ejpam-3288	153	11	=	=	SYM
ejpam-3288	153	12	max{c̃pm	max{c̃pm	NOUN
ejpam-3288	153	13	(	(	PUNCT
ejpam-3288	153	14	x	x	X
ejpam-3288	153	15	∗	∗	NOUN
ejpam-3288	153	16	(	(	PUNCT
ejpam-3288	153	17	y	y	PROPN
ejpam-3288	153	18	∗	∗	PROPN
ejpam-3288	153	19	z	z	PROPN
ejpam-3288	153	20	)	)	PUNCT
ejpam-3288	153	21	)	)	PUNCT
ejpam-3288	153	22	,	,	PUNCT
ejpam-3288	153	23	c̃pm	c̃pm	X
ejpam-3288	153	24	(	(	PUNCT
ejpam-3288	153	25	y	y	NOUN
ejpam-3288	153	26	)	)	PUNCT
ejpam-3288	153	27	}	}	PUNCT
ejpam-3288	153	28	,	,	PUNCT
ejpam-3288	153	29	and	and	CCONJ
ejpam-3288	153	30	c̃nm	c̃nm	PROPN
ejpam-3288	153	31	(	(	PUNCT
ejpam-3288	153	32	x	x	X
ejpam-3288	153	33	∗	∗	PROPN
ejpam-3288	153	34	z	z	NOUN
ejpam-3288	153	35	)	)	PUNCT
ejpam-3288	153	36	≥	≥	X
ejpam-3288	153	37	−1	−1	NOUN
ejpam-3288	153	38	=	=	PUNCT
ejpam-3288	153	39	min{c̃nm	min{c̃nm	NOUN
ejpam-3288	153	40	(	(	PUNCT
ejpam-3288	153	41	x	x	SYM
ejpam-3288	153	42	∗	∗	NOUN
ejpam-3288	153	43	(	(	PUNCT
ejpam-3288	153	44	y	y	PROPN
ejpam-3288	153	45	∗	∗	PROPN
ejpam-3288	153	46	z	z	PROPN
ejpam-3288	153	47	)	)	PUNCT
ejpam-3288	153	48	)	)	PUNCT
ejpam-3288	153	49	,	,	PUNCT
ejpam-3288	153	50	c̃nm	c̃nm	PROPN
ejpam-3288	153	51	(	(	PUNCT
ejpam-3288	153	52	y	y	NOUN
ejpam-3288	153	53	)	)	PUNCT
ejpam-3288	153	54	}	}	PUNCT
ejpam-3288	153	55	.	.	PUNCT
ejpam-3288	154	1	hence	hence	ADV
ejpam-3288	154	2	,	,	PUNCT
ejpam-3288	154	3	c̃m	c̃m	NOUN
ejpam-3288	154	4	=	=	PUNCT
ejpam-3288	154	5	(	(	PUNCT
ejpam-3288	154	6	c̃pm	c̃pm	NOUN
ejpam-3288	154	7	,	,	PUNCT
ejpam-3288	154	8	c̃	c̃	PROPN
ejpam-3288	154	9	n	n	PROPN
ejpam-3288	154	10	m	m	PROPN
ejpam-3288	154	11	)	)	PUNCT
ejpam-3288	154	12	is	be	AUX
ejpam-3288	154	13	a	a	DET
ejpam-3288	154	14	doubt	doubt	ADV
ejpam-3288	154	15	bipolar	bipolar	ADJ
ejpam-3288	154	16	fuzzy	fuzzy	ADJ
ejpam-3288	154	17	h	h	NOUN
ejpam-3288	154	18	-	-	PUNCT
ejpam-3288	154	19	ideal	ideal	NOUN
ejpam-3288	154	20	of	of	ADP
ejpam-3288	154	21	x.	x.	NOUN
ejpam-3288	154	22	conversely	conversely	ADV
ejpam-3288	154	23	,	,	PUNCT
ejpam-3288	154	24	assume	assume	VERB
ejpam-3288	154	25	that	that	SCONJ
ejpam-3288	154	26	c̃m	c̃m	VERB
ejpam-3288	154	27	=	=	PUNCT
ejpam-3288	154	28	(	(	PUNCT
ejpam-3288	154	29	c̃pm	c̃pm	NOUN
ejpam-3288	154	30	,	,	PUNCT
ejpam-3288	154	31	c̃	c̃	PROPN
ejpam-3288	154	32	n	n	PROPN
ejpam-3288	154	33	m	m	PROPN
ejpam-3288	154	34	)	)	PUNCT
ejpam-3288	154	35	is	be	AUX
ejpam-3288	154	36	a	a	DET
ejpam-3288	154	37	doubt	doubt	ADV
ejpam-3288	154	38	bipolar	bipolar	ADJ
ejpam-3288	154	39	fuzzy	fuzzy	ADJ
ejpam-3288	154	40	h	h	NOUN
ejpam-3288	154	41	-	-	PUNCT
ejpam-3288	154	42	ideal	ideal	NOUN
ejpam-3288	154	43	of	of	ADP
ejpam-3288	154	44	x.	x.	NOUN
ejpam-3288	154	45	since	since	SCONJ
ejpam-3288	154	46	c̃pm	c̃pm	X
ejpam-3288	154	47	(	(	PUNCT
ejpam-3288	154	48	0	0	NUM
ejpam-3288	154	49	)	)	PUNCT
ejpam-3288	154	50	≤	≤	NUM
ejpam-3288	154	51	c̃pm	c̃pm	X
ejpam-3288	154	52	(	(	PUNCT
ejpam-3288	154	53	x	x	NOUN
ejpam-3288	154	54	)	)	PUNCT
ejpam-3288	154	55	and	and	CCONJ
ejpam-3288	154	56	c̃nm	c̃nm	PROPN
ejpam-3288	154	57	(	(	PUNCT
ejpam-3288	154	58	0	0	NUM
ejpam-3288	154	59	)	)	PUNCT
ejpam-3288	154	60	≥	≥	NOUN
ejpam-3288	155	1	c̃nm	c̃nm	PROPN
ejpam-3288	155	2	(	(	PUNCT
ejpam-3288	155	3	x	x	NOUN
ejpam-3288	155	4	)	)	PUNCT
ejpam-3288	155	5	,	,	PUNCT
ejpam-3288	155	6	for	for	ADP
ejpam-3288	155	7	all	all	PRON
ejpam-3288	155	8	x	x	SYM
ejpam-3288	155	9	∈	∈	ADJ
ejpam-3288	155	10	x.	x.	NOUN
ejpam-3288	155	11	it	it	PRON
ejpam-3288	155	12	follows	follow	VERB
ejpam-3288	155	13	that	that	SCONJ
ejpam-3288	155	14	from	from	ADP
ejpam-3288	155	15	lemma	lemma	PROPN
ejpam-3288	155	16	1	1	NUM
ejpam-3288	155	17	that	that	SCONJ
ejpam-3288	155	18	a.	a.	PROPN
ejpam-3288	155	19	al	al	PROPN
ejpam-3288	155	20	-	-	PROPN
ejpam-3288	155	21	masarwah	masarwah	PROPN
ejpam-3288	155	22	,	,	PUNCT
ejpam-3288	155	23	a.	a.	NOUN
ejpam-3288	155	24	g.	g.	PROPN
ejpam-3288	155	25	ahmad	ahmad	PROPN
ejpam-3288	155	26	/	/	SYM
ejpam-3288	155	27	eur	eur	PROPN
ejpam-3288	155	28	.	.	PUNCT
ejpam-3288	156	1	j.	j.	PROPN
ejpam-3288	156	2	pure	pure	PROPN
ejpam-3288	156	3	appl	appl	PROPN
ejpam-3288	156	4	.	.	PROPN
ejpam-3288	156	5	math	math	PROPN
ejpam-3288	156	6	,	,	PUNCT
ejpam-3288	156	7	11	11	NUM
ejpam-3288	156	8	(	(	PUNCT
ejpam-3288	156	9	3	3	NUM
ejpam-3288	156	10	)	)	PUNCT
ejpam-3288	156	11	(	(	PUNCT
ejpam-3288	156	12	2018	2018	NUM
ejpam-3288	156	13	)	)	PUNCT
ejpam-3288	156	14	,	,	PUNCT
ejpam-3288	156	15	652	652	NUM
ejpam-3288	156	16	-	-	SYM
ejpam-3288	156	17	670	670	NUM
ejpam-3288	156	18	658	658	NUM
ejpam-3288	156	19	0	0	NUM
ejpam-3288	156	20	∈m	∈m	NOUN
ejpam-3288	156	21	.	.	PUNCT
ejpam-3288	157	1	next	next	ADV
ejpam-3288	157	2	,	,	PUNCT
ejpam-3288	157	3	let	let	VERB
ejpam-3288	157	4	x	x	PRON
ejpam-3288	157	5	,	,	PUNCT
ejpam-3288	157	6	y	y	PROPN
ejpam-3288	157	7	,	,	PUNCT
ejpam-3288	157	8	z	z	NOUN
ejpam-3288	157	9	∈	∈	PROPN
ejpam-3288	157	10	x	x	PUNCT
ejpam-3288	157	11	such	such	ADJ
ejpam-3288	157	12	that	that	SCONJ
ejpam-3288	157	13	x	x	SYM
ejpam-3288	157	14	∗	∗	NOUN
ejpam-3288	157	15	(	(	PUNCT
ejpam-3288	157	16	y	y	PROPN
ejpam-3288	157	17	∗	∗	PROPN
ejpam-3288	157	18	z	z	NOUN
ejpam-3288	157	19	)	)	PUNCT
ejpam-3288	157	20	∈m	∈m	NOUN
ejpam-3288	157	21	and	and	CCONJ
ejpam-3288	157	22	y	y	NOUN
ejpam-3288	157	23	∈m	∈m	NOUN
ejpam-3288	157	24	.	.	PUNCT
ejpam-3288	158	1	to	to	PART
ejpam-3288	158	2	show	show	VERB
ejpam-3288	158	3	that	that	SCONJ
ejpam-3288	158	4	x	x	PROPN
ejpam-3288	158	5	∗	∗	NOUN
ejpam-3288	158	6	z	z	NOUN
ejpam-3288	158	7	∈m	∈m	NOUN
ejpam-3288	158	8	,	,	PUNCT
ejpam-3288	158	9	assume	assume	VERB
ejpam-3288	158	10	that	that	SCONJ
ejpam-3288	158	11	x	x	PROPN
ejpam-3288	158	12	∗	∗	NOUN
ejpam-3288	158	13	z	z	NOUN
ejpam-3288	158	14	6∈m	6∈m	NOUN
ejpam-3288	158	15	.	.	PUNCT
ejpam-3288	159	1	then	then	ADV
ejpam-3288	159	2	c̃pm	c̃pm	X
ejpam-3288	159	3	(	(	PUNCT
ejpam-3288	159	4	x	x	NOUN
ejpam-3288	159	5	∗	∗	PROPN
ejpam-3288	159	6	z	z	NOUN
ejpam-3288	159	7	)	)	PUNCT
ejpam-3288	159	8	=	=	SYM
ejpam-3288	159	9	1	1	NUM
ejpam-3288	159	10	and	and	CCONJ
ejpam-3288	159	11	c̃nm	c̃nm	PROPN
ejpam-3288	159	12	(	(	PUNCT
ejpam-3288	159	13	x	x	X
ejpam-3288	159	14	∗	∗	PROPN
ejpam-3288	159	15	z	z	NOUN
ejpam-3288	159	16	)	)	PUNCT
ejpam-3288	159	17	=	=	SYM
ejpam-3288	159	18	−1	−1	NOUN
ejpam-3288	159	19	.	.	PUNCT
ejpam-3288	160	1	so	so	ADV
ejpam-3288	160	2	1	1	NUM
ejpam-3288	160	3	=	=	SYM
ejpam-3288	160	4	c̃pm	c̃pm	X
ejpam-3288	160	5	(	(	PUNCT
ejpam-3288	160	6	x	x	NOUN
ejpam-3288	160	7	∗	∗	PROPN
ejpam-3288	160	8	z	z	NOUN
ejpam-3288	160	9	)	)	PUNCT
ejpam-3288	160	10	≤	≤	NOUN
ejpam-3288	160	11	max{c̃pm	max{c̃pm	NOUN
ejpam-3288	160	12	(	(	PUNCT
ejpam-3288	160	13	x	x	SYM
ejpam-3288	160	14	∗	∗	NOUN
ejpam-3288	160	15	(	(	PUNCT
ejpam-3288	160	16	y	y	PROPN
ejpam-3288	160	17	∗	∗	PROPN
ejpam-3288	160	18	z	z	PROPN
ejpam-3288	160	19	)	)	PUNCT
ejpam-3288	160	20	)	)	PUNCT
ejpam-3288	160	21	,	,	PUNCT
ejpam-3288	160	22	c̃pm	c̃pm	X
ejpam-3288	160	23	(	(	PUNCT
ejpam-3288	160	24	y	y	NOUN
ejpam-3288	160	25	)	)	PUNCT
ejpam-3288	160	26	}	}	PUNCT
ejpam-3288	160	27	,	,	PUNCT
ejpam-3288	160	28	and	and	CCONJ
ejpam-3288	160	29	−1	−1	NOUN
ejpam-3288	160	30	=	=	SYM
ejpam-3288	161	1	c̃nm	c̃nm	PROPN
ejpam-3288	161	2	(	(	PUNCT
ejpam-3288	161	3	x	x	X
ejpam-3288	161	4	∗	∗	PROPN
ejpam-3288	161	5	z	z	NOUN
ejpam-3288	161	6	)	)	PUNCT
ejpam-3288	161	7	≥	≥	NOUN
ejpam-3288	161	8	min{c̃nm	min{c̃nm	NOUN
ejpam-3288	161	9	(	(	PUNCT
ejpam-3288	161	10	x	x	SYM
ejpam-3288	161	11	∗	∗	NOUN
ejpam-3288	161	12	(	(	PUNCT
ejpam-3288	161	13	y	y	PROPN
ejpam-3288	161	14	∗	∗	PROPN
ejpam-3288	161	15	z	z	PROPN
ejpam-3288	161	16	)	)	PUNCT
ejpam-3288	161	17	)	)	PUNCT
ejpam-3288	161	18	,	,	PUNCT
ejpam-3288	161	19	c̃nm	c̃nm	PROPN
ejpam-3288	161	20	(	(	PUNCT
ejpam-3288	161	21	y	y	NOUN
ejpam-3288	161	22	)	)	PUNCT
ejpam-3288	161	23	}	}	PUNCT
ejpam-3288	161	24	.	.	PUNCT
ejpam-3288	162	1	thus	thus	ADV
ejpam-3288	162	2	,	,	PUNCT
ejpam-3288	162	3	max{c̃pm	max{c̃pm	NOUN
ejpam-3288	162	4	(	(	PUNCT
ejpam-3288	162	5	x	x	SYM
ejpam-3288	162	6	∗	∗	NOUN
ejpam-3288	162	7	(	(	PUNCT
ejpam-3288	162	8	y	y	PROPN
ejpam-3288	162	9	∗	∗	PROPN
ejpam-3288	162	10	z	z	PROPN
ejpam-3288	162	11	)	)	PUNCT
ejpam-3288	162	12	)	)	PUNCT
ejpam-3288	162	13	,	,	PUNCT
ejpam-3288	162	14	c̃pm	c̃pm	X
ejpam-3288	162	15	(	(	PUNCT
ejpam-3288	162	16	y	y	NOUN
ejpam-3288	162	17	)	)	PUNCT
ejpam-3288	162	18	}	}	PUNCT
ejpam-3288	162	19	=	=	SYM
ejpam-3288	162	20	1	1	NUM
ejpam-3288	162	21	,	,	PUNCT
ejpam-3288	162	22	and	and	CCONJ
ejpam-3288	162	23	min{c̃nm	min{c̃nm	NOUN
ejpam-3288	162	24	(	(	PUNCT
ejpam-3288	162	25	x	x	SYM
ejpam-3288	162	26	∗	∗	NOUN
ejpam-3288	162	27	(	(	PUNCT
ejpam-3288	162	28	y	y	PROPN
ejpam-3288	162	29	∗	∗	PROPN
ejpam-3288	162	30	z	z	PROPN
ejpam-3288	162	31	)	)	PUNCT
ejpam-3288	162	32	)	)	PUNCT
ejpam-3288	162	33	,	,	PUNCT
ejpam-3288	162	34	c̃nm	c̃nm	PROPN
ejpam-3288	162	35	(	(	PUNCT
ejpam-3288	162	36	y	y	NOUN
ejpam-3288	162	37	)	)	PUNCT
ejpam-3288	162	38	}	}	PUNCT
ejpam-3288	162	39	=	=	PUNCT
ejpam-3288	162	40	−1	−1	NOUN
ejpam-3288	162	41	.	.	PUNCT
ejpam-3288	163	1	this	this	PRON
ejpam-3288	163	2	implies	imply	VERB
ejpam-3288	163	3	that	that	PRON
ejpam-3288	163	4	c̃pm	c̃pm	X
ejpam-3288	163	5	(	(	PUNCT
ejpam-3288	163	6	x∗(y∗z	x∗(y∗z	NUM
ejpam-3288	163	7	)	)	PUNCT
ejpam-3288	163	8	)	)	PUNCT
ejpam-3288	164	1	=	=	SYM
ejpam-3288	164	2	1	1	NUM
ejpam-3288	164	3	or	or	CCONJ
ejpam-3288	164	4	c̃pm	c̃pm	X
ejpam-3288	164	5	(	(	PUNCT
ejpam-3288	164	6	y	y	NOUN
ejpam-3288	164	7	)	)	PUNCT
ejpam-3288	164	8	=	=	SYM
ejpam-3288	164	9	1	1	NUM
ejpam-3288	164	10	and	and	CCONJ
ejpam-3288	164	11	c̃nm	c̃nm	PROPN
ejpam-3288	164	12	(	(	PUNCT
ejpam-3288	164	13	x∗(y∗z	x∗(y∗z	NUM
ejpam-3288	164	14	)	)	PUNCT
ejpam-3288	164	15	)	)	PUNCT
ejpam-3288	165	1	=	=	PUNCT
ejpam-3288	165	2	−1	−1	NOUN
ejpam-3288	165	3	or	or	CCONJ
ejpam-3288	165	4	c̃nm	c̃nm	PROPN
ejpam-3288	165	5	(	(	PUNCT
ejpam-3288	165	6	y	y	NOUN
ejpam-3288	165	7	)	)	PUNCT
ejpam-3288	165	8	=	=	PUNCT
ejpam-3288	165	9	−1	−1	NOUN
ejpam-3288	165	10	.	.	PUNCT
ejpam-3288	166	1	so	so	ADV
ejpam-3288	166	2	,	,	PUNCT
ejpam-3288	166	3	x	x	X
ejpam-3288	166	4	∗	∗	NOUN
ejpam-3288	166	5	(	(	PUNCT
ejpam-3288	166	6	y	y	PROPN
ejpam-3288	166	7	∗	∗	PROPN
ejpam-3288	166	8	z	z	NOUN
ejpam-3288	166	9	)	)	PUNCT
ejpam-3288	166	10	6∈m	6∈m	NOUN
ejpam-3288	166	11	or	or	CCONJ
ejpam-3288	166	12	y	y	PRON
ejpam-3288	166	13	6∈m	6∈m	NOUN
ejpam-3288	166	14	,	,	PUNCT
ejpam-3288	166	15	a	a	DET
ejpam-3288	166	16	contradiction	contradiction	NOUN
ejpam-3288	166	17	.	.	PUNCT
ejpam-3288	167	1	hence	hence	ADV
ejpam-3288	167	2	,	,	PUNCT
ejpam-3288	167	3	x	x	X
ejpam-3288	167	4	∗	∗	NOUN
ejpam-3288	167	5	z	z	NOUN
ejpam-3288	167	6	∈m	∈m	NOUN
ejpam-3288	167	7	,	,	PUNCT
ejpam-3288	167	8	and	and	CCONJ
ejpam-3288	167	9	thus	thus	ADV
ejpam-3288	167	10	m	m	VERB
ejpam-3288	167	11	is	be	AUX
ejpam-3288	167	12	an	an	DET
ejpam-3288	167	13	h	h	NOUN
ejpam-3288	167	14	-	-	PUNCT
ejpam-3288	167	15	ideal	ideal	NOUN
ejpam-3288	167	16	of	of	ADP
ejpam-3288	167	17	x.	x.	PROPN
ejpam-3288	167	18	theorem	theorem	NOUN
ejpam-3288	167	19	2	2	X
ejpam-3288	167	20	.	.	PUNCT
ejpam-3288	168	1	let	let	VERB
ejpam-3288	168	2	a	a	DET
ejpam-3288	168	3	=	=	X
ejpam-3288	168	4	(	(	PUNCT
ejpam-3288	168	5	µpa	µpa	PROPN
ejpam-3288	168	6	,	,	PUNCT
ejpam-3288	168	7	µ	µ	NOUN
ejpam-3288	168	8	n	n	ADV
ejpam-3288	168	9	a	a	PRON
ejpam-3288	168	10	)	)	PUNCT
ejpam-3288	168	11	be	be	AUX
ejpam-3288	168	12	a	a	DET
ejpam-3288	168	13	doubt	doubt	ADV
ejpam-3288	168	14	bipolar	bipolar	ADJ
ejpam-3288	168	15	fuzzy	fuzzy	ADJ
ejpam-3288	168	16	h	h	NOUN
ejpam-3288	168	17	-	-	PUNCT
ejpam-3288	168	18	ideal	ideal	NOUN
ejpam-3288	168	19	of	of	ADP
ejpam-3288	168	20	associative	associative	ADJ
ejpam-3288	168	21	bck	bck	PROPN
ejpam-3288	168	22	/	/	SYM
ejpam-3288	168	23	bcialgebras	bcialgebra	NOUN
ejpam-3288	168	24	x.	x.	NOUN
ejpam-3288	169	1	if	if	SCONJ
ejpam-3288	169	2	the	the	DET
ejpam-3288	169	3	inequality	inequality	NOUN
ejpam-3288	169	4	x	x	PUNCT
ejpam-3288	169	5	∗	∗	VERB
ejpam-3288	169	6	y	y	PROPN
ejpam-3288	169	7	≤	≤	PROPN
ejpam-3288	169	8	z	z	NOUN
ejpam-3288	169	9	holds	hold	VERB
ejpam-3288	169	10	in	in	ADP
ejpam-3288	169	11	x	x	NOUN
ejpam-3288	169	12	,	,	PUNCT
ejpam-3288	169	13	then	then	ADV
ejpam-3288	169	14	µpa(x	µpa(x	PROPN
ejpam-3288	169	15	∗	∗	PROPN
ejpam-3288	169	16	y	y	NOUN
ejpam-3288	169	17	)	)	PUNCT
ejpam-3288	169	18	≤	≤	PUNCT
ejpam-3288	169	19	µpa(z	µpa(z	PROPN
ejpam-3288	169	20	)	)	PUNCT
ejpam-3288	169	21	and	and	CCONJ
ejpam-3288	169	22	µna	µna	ADJ
ejpam-3288	169	23	(	(	PUNCT
ejpam-3288	169	24	x	x	PROPN
ejpam-3288	169	25	∗	∗	PROPN
ejpam-3288	169	26	y	y	PROPN
ejpam-3288	169	27	)	)	PUNCT
ejpam-3288	169	28	≥	≥	AUX
ejpam-3288	169	29	µna	µna	ADJ
ejpam-3288	169	30	(	(	PUNCT
ejpam-3288	169	31	z	z	NOUN
ejpam-3288	169	32	)	)	PUNCT
ejpam-3288	169	33	for	for	ADP
ejpam-3288	169	34	all	all	DET
ejpam-3288	169	35	x	x	NOUN
ejpam-3288	169	36	,	,	PUNCT
ejpam-3288	169	37	y	y	PROPN
ejpam-3288	169	38	,	,	PUNCT
ejpam-3288	169	39	z	z	NOUN
ejpam-3288	169	40	∈	∈	NOUN
ejpam-3288	169	41	x.	x.	NOUN
ejpam-3288	169	42	proof	proof	NOUN
ejpam-3288	169	43	.	.	PUNCT
ejpam-3288	170	1	let	let	VERB
ejpam-3288	170	2	x	x	PRON
ejpam-3288	170	3	,	,	PUNCT
ejpam-3288	170	4	y	y	PROPN
ejpam-3288	170	5	,	,	PUNCT
ejpam-3288	170	6	z	z	NOUN
ejpam-3288	170	7	∈	∈	PROPN
ejpam-3288	170	8	x	x	PUNCT
ejpam-3288	170	9	such	such	ADJ
ejpam-3288	170	10	that	that	SCONJ
ejpam-3288	170	11	x	x	PROPN
ejpam-3288	170	12	∗	∗	NOUN
ejpam-3288	170	13	y	y	PROPN
ejpam-3288	170	14	≤	≤	PROPN
ejpam-3288	170	15	z.	z.	PROPN
ejpam-3288	171	1	then	then	ADV
ejpam-3288	171	2	(	(	PUNCT
ejpam-3288	171	3	x	x	X
ejpam-3288	171	4	∗	∗	PROPN
ejpam-3288	171	5	y	y	NOUN
ejpam-3288	171	6	)	)	PUNCT
ejpam-3288	171	7	∗	∗	NOUN
ejpam-3288	171	8	z	z	NOUN
ejpam-3288	171	9	=	=	SYM
ejpam-3288	171	10	0	0	NUM
ejpam-3288	172	1	and	and	CCONJ
ejpam-3288	172	2	since	since	SCONJ
ejpam-3288	172	3	a	a	PRON
ejpam-3288	172	4	is	be	AUX
ejpam-3288	172	5	a	a	DET
ejpam-3288	172	6	doubt	doubt	ADV
ejpam-3288	172	7	bipolar	bipolar	ADJ
ejpam-3288	172	8	fuzzy	fuzzy	ADJ
ejpam-3288	172	9	h	h	NOUN
ejpam-3288	172	10	-	-	PUNCT
ejpam-3288	172	11	ideal	ideal	NOUN
ejpam-3288	172	12	of	of	ADP
ejpam-3288	172	13	x	x	PRON
ejpam-3288	172	14	,	,	PUNCT
ejpam-3288	172	15	so	so	ADV
ejpam-3288	172	16	µpa(x	µpa(x	PRON
ejpam-3288	172	17	∗	∗	NOUN
ejpam-3288	172	18	y	y	NOUN
ejpam-3288	172	19	)	)	PUNCT
ejpam-3288	172	20	≤	≤	PROPN
ejpam-3288	173	1	max{µpa(x	max{µpa(x	PROPN
ejpam-3288	173	2	∗	∗	NOUN
ejpam-3288	173	3	(	(	PUNCT
ejpam-3288	173	4	z	z	NOUN
ejpam-3288	173	5	∗	∗	NOUN
ejpam-3288	173	6	y	y	PROPN
ejpam-3288	173	7	)	)	PUNCT
ejpam-3288	173	8	)	)	PUNCT
ejpam-3288	173	9	,	,	PUNCT
ejpam-3288	173	10	µpa(z	µpa(z	PROPN
ejpam-3288	173	11	)	)	PUNCT
ejpam-3288	173	12	}	}	PUNCT
ejpam-3288	173	13	=	=	SYM
ejpam-3288	173	14	max{µpa((x	max{µpa((x	NOUN
ejpam-3288	173	15	∗	∗	NOUN
ejpam-3288	173	16	z	z	NOUN
ejpam-3288	173	17	)	)	PUNCT
ejpam-3288	173	18	∗	∗	PROPN
ejpam-3288	173	19	y	y	PROPN
ejpam-3288	173	20	)	)	PUNCT
ejpam-3288	173	21	,	,	PUNCT
ejpam-3288	173	22	µpa(z	µpa(z	PROPN
ejpam-3288	173	23	)	)	PUNCT
ejpam-3288	173	24	}	}	PUNCT
ejpam-3288	173	25	=	=	SYM
ejpam-3288	173	26	max{µpa((x	max{µpa((x	NOUN
ejpam-3288	173	27	∗	∗	X
ejpam-3288	173	28	y	y	NOUN
ejpam-3288	173	29	)	)	PUNCT
ejpam-3288	173	30	∗	∗	NOUN
ejpam-3288	173	31	z	z	NOUN
ejpam-3288	173	32	)	)	PUNCT
ejpam-3288	173	33	,	,	PUNCT
ejpam-3288	173	34	µpa(z	µpa(z	PROPN
ejpam-3288	173	35	)	)	PUNCT
ejpam-3288	173	36	}	}	PUNCT
ejpam-3288	173	37	=	=	SYM
ejpam-3288	173	38	max{µpa(0	max{µpa(0	NUM
ejpam-3288	173	39	)	)	PUNCT
ejpam-3288	173	40	,	,	PUNCT
ejpam-3288	173	41	µpa(z	µpa(z	PROPN
ejpam-3288	173	42	)	)	PUNCT
ejpam-3288	173	43	}	}	PUNCT
ejpam-3288	173	44	=	=	SYM
ejpam-3288	173	45	µpa(z	µpa(z	PROPN
ejpam-3288	173	46	)	)	PUNCT
ejpam-3288	173	47	.	.	PUNCT
ejpam-3288	174	1	therefore	therefore	ADV
ejpam-3288	174	2	,	,	PUNCT
ejpam-3288	174	3	µpa(x	µpa(x	PROPN
ejpam-3288	174	4	∗	∗	NOUN
ejpam-3288	174	5	y	y	NOUN
ejpam-3288	174	6	)	)	PUNCT
ejpam-3288	174	7	≤	≤	PUNCT
ejpam-3288	174	8	µpa(z	µpa(z	PROPN
ejpam-3288	174	9	)	)	PUNCT
ejpam-3288	174	10	for	for	ADP
ejpam-3288	174	11	all	all	DET
ejpam-3288	174	12	x	x	NOUN
ejpam-3288	174	13	,	,	PUNCT
ejpam-3288	174	14	y	y	PROPN
ejpam-3288	174	15	,	,	PUNCT
ejpam-3288	174	16	z	z	PROPN
ejpam-3288	174	17	∈	∈	NOUN
ejpam-3288	174	18	x.	x.	NOUN
ejpam-3288	174	19	again	again	ADV
ejpam-3288	174	20	,	,	PUNCT
ejpam-3288	174	21	µna	µna	ADJ
ejpam-3288	174	22	(	(	PUNCT
ejpam-3288	174	23	x	x	NOUN
ejpam-3288	174	24	∗	∗	PROPN
ejpam-3288	174	25	y	y	PROPN
ejpam-3288	174	26	)	)	PUNCT
ejpam-3288	174	27	≥	≥	NOUN
ejpam-3288	174	28	min{µna	min{µna	NOUN
ejpam-3288	174	29	(	(	PUNCT
ejpam-3288	174	30	x	x	NOUN
ejpam-3288	174	31	∗	∗	NOUN
ejpam-3288	174	32	(	(	PUNCT
ejpam-3288	174	33	z	z	NOUN
ejpam-3288	174	34	∗	∗	NOUN
ejpam-3288	174	35	y	y	PROPN
ejpam-3288	174	36	)	)	PUNCT
ejpam-3288	174	37	)	)	PUNCT
ejpam-3288	174	38	,	,	PUNCT
ejpam-3288	174	39	µna	µna	ADJ
ejpam-3288	174	40	(	(	PUNCT
ejpam-3288	174	41	z	z	NOUN
ejpam-3288	174	42	)	)	PUNCT
ejpam-3288	174	43	}	}	PUNCT
ejpam-3288	174	44	=	=	PUNCT
ejpam-3288	174	45	min{µna	min{µna	NOUN
ejpam-3288	174	46	(	(	PUNCT
ejpam-3288	174	47	(	(	PUNCT
ejpam-3288	174	48	x	x	SYM
ejpam-3288	174	49	∗	∗	PROPN
ejpam-3288	174	50	z	z	NOUN
ejpam-3288	174	51	)	)	PUNCT
ejpam-3288	174	52	∗	∗	PROPN
ejpam-3288	174	53	y	y	PROPN
ejpam-3288	174	54	)	)	PUNCT
ejpam-3288	174	55	,	,	PUNCT
ejpam-3288	174	56	µna	µna	ADJ
ejpam-3288	174	57	(	(	PUNCT
ejpam-3288	174	58	z	z	NOUN
ejpam-3288	174	59	)	)	PUNCT
ejpam-3288	174	60	}	}	PUNCT
ejpam-3288	174	61	=	=	PUNCT
ejpam-3288	174	62	min{µna	min{µna	NOUN
ejpam-3288	174	63	(	(	PUNCT
ejpam-3288	174	64	(	(	PUNCT
ejpam-3288	174	65	x	x	SYM
ejpam-3288	174	66	∗	∗	PROPN
ejpam-3288	174	67	y	y	NOUN
ejpam-3288	174	68	)	)	PUNCT
ejpam-3288	174	69	∗	∗	NOUN
ejpam-3288	174	70	z	z	PROPN
ejpam-3288	174	71	)	)	PUNCT
ejpam-3288	174	72	,	,	PUNCT
ejpam-3288	174	73	µna	µna	ADJ
ejpam-3288	174	74	(	(	PUNCT
ejpam-3288	174	75	z	z	NOUN
ejpam-3288	174	76	)	)	PUNCT
ejpam-3288	174	77	}	}	PUNCT
ejpam-3288	174	78	=	=	PUNCT
ejpam-3288	174	79	min{µna	min{µna	NOUN
ejpam-3288	174	80	(	(	PUNCT
ejpam-3288	174	81	0	0	NUM
ejpam-3288	174	82	)	)	PUNCT
ejpam-3288	174	83	,	,	PUNCT
ejpam-3288	174	84	µna	µna	ADJ
ejpam-3288	174	85	(	(	PUNCT
ejpam-3288	174	86	z	z	NOUN
ejpam-3288	174	87	)	)	PUNCT
ejpam-3288	174	88	}	}	PUNCT
ejpam-3288	174	89	=	=	SYM
ejpam-3288	174	90	µna	µna	ADJ
ejpam-3288	174	91	(	(	PUNCT
ejpam-3288	174	92	z	z	NOUN
ejpam-3288	174	93	)	)	PUNCT
ejpam-3288	174	94	.	.	PUNCT
ejpam-3288	175	1	therefore	therefore	ADV
ejpam-3288	175	2	,	,	PUNCT
ejpam-3288	175	3	µna	µna	ADJ
ejpam-3288	175	4	(	(	PUNCT
ejpam-3288	175	5	x	x	NOUN
ejpam-3288	175	6	∗	∗	PROPN
ejpam-3288	175	7	y	y	PROPN
ejpam-3288	175	8	)	)	PUNCT
ejpam-3288	175	9	≥	≥	AUX
ejpam-3288	175	10	µna	µna	ADJ
ejpam-3288	175	11	(	(	PUNCT
ejpam-3288	175	12	z	z	NOUN
ejpam-3288	175	13	)	)	PUNCT
ejpam-3288	175	14	for	for	ADP
ejpam-3288	175	15	all	all	DET
ejpam-3288	175	16	x	x	NOUN
ejpam-3288	175	17	,	,	PUNCT
ejpam-3288	175	18	y	y	PROPN
ejpam-3288	175	19	,	,	PUNCT
ejpam-3288	175	20	z	z	PROPN
ejpam-3288	175	21	∈	∈	NOUN
ejpam-3288	175	22	x.	x.	NOUN
ejpam-3288	175	23	proposition	proposition	NOUN
ejpam-3288	175	24	1	1	NUM
ejpam-3288	175	25	.	.	PUNCT
ejpam-3288	176	1	let	let	VERB
ejpam-3288	176	2	a	a	DET
ejpam-3288	176	3	=	=	X
ejpam-3288	176	4	(	(	PUNCT
ejpam-3288	176	5	µpa	µpa	PROPN
ejpam-3288	176	6	,	,	PUNCT
ejpam-3288	176	7	µ	µ	NOUN
ejpam-3288	176	8	n	n	ADV
ejpam-3288	176	9	a	a	PRON
ejpam-3288	176	10	)	)	PUNCT
ejpam-3288	176	11	be	be	AUX
ejpam-3288	176	12	a	a	DET
ejpam-3288	176	13	doubt	doubt	ADV
ejpam-3288	176	14	bipolar	bipolar	ADJ
ejpam-3288	176	15	fuzzy	fuzzy	ADJ
ejpam-3288	176	16	h	h	NOUN
ejpam-3288	176	17	-	-	PUNCT
ejpam-3288	176	18	ideal	ideal	NOUN
ejpam-3288	176	19	of	of	ADP
ejpam-3288	176	20	x.	x.	NOUN
ejpam-3288	176	21	if	if	SCONJ
ejpam-3288	176	22	the	the	DET
ejpam-3288	176	23	inequality	inequality	NOUN
ejpam-3288	176	24	x	x	PUNCT
ejpam-3288	176	25	≤	≤	NOUN
ejpam-3288	176	26	y	y	NOUN
ejpam-3288	176	27	holds	hold	VERB
ejpam-3288	176	28	in	in	ADP
ejpam-3288	176	29	x	x	NOUN
ejpam-3288	176	30	,	,	PUNCT
ejpam-3288	176	31	then	then	ADV
ejpam-3288	176	32	µpa(x	µpa(x	PRON
ejpam-3288	176	33	)	)	PUNCT
ejpam-3288	176	34	≤	≤	NUM
ejpam-3288	176	35	µpa(y	µpa(y	NOUN
ejpam-3288	176	36	)	)	PUNCT
ejpam-3288	176	37	and	and	CCONJ
ejpam-3288	176	38	µna	µna	ADJ
ejpam-3288	176	39	(	(	PUNCT
ejpam-3288	176	40	x	x	NOUN
ejpam-3288	176	41	)	)	PUNCT
ejpam-3288	176	42	≥	≥	X
ejpam-3288	176	43	µna	µna	ADJ
ejpam-3288	176	44	(	(	PUNCT
ejpam-3288	176	45	y	y	NOUN
ejpam-3288	176	46	)	)	PUNCT
ejpam-3288	176	47	for	for	ADP
ejpam-3288	176	48	all	all	DET
ejpam-3288	176	49	x	x	NOUN
ejpam-3288	176	50	,	,	PUNCT
ejpam-3288	176	51	y	y	PROPN
ejpam-3288	176	52	∈	∈	PROPN
ejpam-3288	176	53	x.	x.	NOUN
ejpam-3288	176	54	a.	a.	PROPN
ejpam-3288	176	55	al	al	PROPN
ejpam-3288	176	56	-	-	PROPN
ejpam-3288	176	57	masarwah	masarwah	PROPN
ejpam-3288	176	58	,	,	PUNCT
ejpam-3288	176	59	a.	a.	NOUN
ejpam-3288	176	60	g.	g.	PROPN
ejpam-3288	176	61	ahmad	ahmad	PROPN
ejpam-3288	176	62	/	/	SYM
ejpam-3288	176	63	eur	eur	PROPN
ejpam-3288	176	64	.	.	PUNCT
ejpam-3288	177	1	j.	j.	PROPN
ejpam-3288	177	2	pure	pure	PROPN
ejpam-3288	177	3	appl	appl	PROPN
ejpam-3288	177	4	.	.	PROPN
ejpam-3288	177	5	math	math	PROPN
ejpam-3288	177	6	,	,	PUNCT
ejpam-3288	177	7	11	11	NUM
ejpam-3288	177	8	(	(	PUNCT
ejpam-3288	177	9	3	3	NUM
ejpam-3288	177	10	)	)	PUNCT
ejpam-3288	177	11	(	(	PUNCT
ejpam-3288	177	12	2018	2018	NUM
ejpam-3288	177	13	)	)	PUNCT
ejpam-3288	177	14	,	,	PUNCT
ejpam-3288	177	15	652	652	NUM
ejpam-3288	177	16	-	-	SYM
ejpam-3288	177	17	670	670	NUM
ejpam-3288	177	18	659	659	NUM
ejpam-3288	177	19	proof	proof	NOUN
ejpam-3288	177	20	.	.	PUNCT
ejpam-3288	178	1	let	let	VERB
ejpam-3288	178	2	x	x	PRON
ejpam-3288	178	3	,	,	PUNCT
ejpam-3288	178	4	y	y	PROPN
ejpam-3288	178	5	∈	∈	PROPN
ejpam-3288	178	6	x	x	PUNCT
ejpam-3288	178	7	such	such	ADJ
ejpam-3288	178	8	that	that	SCONJ
ejpam-3288	178	9	x	x	X
ejpam-3288	178	10	≤	≤	X
ejpam-3288	178	11	y.	y.	NOUN
ejpam-3288	178	12	then	then	ADV
ejpam-3288	178	13	x	x	X
ejpam-3288	178	14	∗	∗	NOUN
ejpam-3288	178	15	y	y	NOUN
ejpam-3288	178	16	=	=	SYM
ejpam-3288	178	17	0	0	PROPN
ejpam-3288	178	18	.	.	PUNCT
ejpam-3288	179	1	now	now	ADV
ejpam-3288	179	2	µpa(x	µpa(x	PRON
ejpam-3288	179	3	)	)	PUNCT
ejpam-3288	179	4	=	=	PUNCT
ejpam-3288	180	1	µpa(x	µpa(x	PROPN
ejpam-3288	180	2	∗	∗	NOUN
ejpam-3288	180	3	0	0	NUM
ejpam-3288	180	4	)	)	PUNCT
ejpam-3288	180	5	≤	≤	NUM
ejpam-3288	180	6	max{µpa(x	max{µpa(x	PROPN
ejpam-3288	180	7	∗	∗	NOUN
ejpam-3288	180	8	(	(	PUNCT
ejpam-3288	180	9	y	y	PROPN
ejpam-3288	180	10	∗	∗	NOUN
ejpam-3288	180	11	0	0	NUM
ejpam-3288	180	12	)	)	PUNCT
ejpam-3288	180	13	)	)	PUNCT
ejpam-3288	180	14	,	,	PUNCT
ejpam-3288	180	15	µpa(y	µpa(y	PROPN
ejpam-3288	180	16	)	)	PUNCT
ejpam-3288	180	17	}	}	PUNCT
ejpam-3288	180	18	=	=	SYM
ejpam-3288	180	19	max{µpa(x	max{µpa(x	PROPN
ejpam-3288	180	20	∗	∗	NOUN
ejpam-3288	180	21	y	y	NOUN
ejpam-3288	180	22	)	)	PUNCT
ejpam-3288	180	23	,	,	PUNCT
ejpam-3288	180	24	µpa(y	µpa(y	PROPN
ejpam-3288	180	25	)	)	PUNCT
ejpam-3288	180	26	}	}	PUNCT
ejpam-3288	180	27	=	=	SYM
ejpam-3288	180	28	max{µpa(0	max{µpa(0	NUM
ejpam-3288	180	29	)	)	PUNCT
ejpam-3288	180	30	,	,	PUNCT
ejpam-3288	180	31	µpa(y	µpa(y	PROPN
ejpam-3288	180	32	)	)	PUNCT
ejpam-3288	180	33	}	}	PUNCT
ejpam-3288	180	34	=	=	SYM
ejpam-3288	180	35	µpa(y	µpa(y	PROPN
ejpam-3288	180	36	)	)	PUNCT
ejpam-3288	180	37	.	.	PUNCT
ejpam-3288	181	1	therefore	therefore	ADV
ejpam-3288	181	2	,	,	PUNCT
ejpam-3288	181	3	µpa(x	µpa(x	PROPN
ejpam-3288	181	4	)	)	PUNCT
ejpam-3288	181	5	≤	≤	NUM
ejpam-3288	181	6	µpa(y	µpa(y	NOUN
ejpam-3288	181	7	)	)	PUNCT
ejpam-3288	181	8	for	for	ADP
ejpam-3288	181	9	all	all	DET
ejpam-3288	181	10	x	x	NOUN
ejpam-3288	181	11	,	,	PUNCT
ejpam-3288	181	12	y	y	PROPN
ejpam-3288	181	13	∈	∈	PROPN
ejpam-3288	181	14	x.	x.	NOUN
ejpam-3288	181	15	again	again	ADV
ejpam-3288	181	16	,	,	PUNCT
ejpam-3288	181	17	µna	µna	ADJ
ejpam-3288	181	18	(	(	PUNCT
ejpam-3288	181	19	x	x	NOUN
ejpam-3288	181	20	)	)	PUNCT
ejpam-3288	181	21	=	=	SYM
ejpam-3288	181	22	µna	µna	ADJ
ejpam-3288	181	23	(	(	PUNCT
ejpam-3288	181	24	x	x	NOUN
ejpam-3288	181	25	∗	∗	NOUN
ejpam-3288	181	26	0	0	NUM
ejpam-3288	181	27	)	)	PUNCT
ejpam-3288	181	28	≥	≥	NOUN
ejpam-3288	181	29	min{µna	min{µna	NOUN
ejpam-3288	181	30	(	(	PUNCT
ejpam-3288	181	31	x	x	NOUN
ejpam-3288	181	32	∗	∗	NOUN
ejpam-3288	181	33	(	(	PUNCT
ejpam-3288	181	34	y	y	PROPN
ejpam-3288	181	35	∗	∗	NOUN
ejpam-3288	181	36	0	0	NUM
ejpam-3288	181	37	)	)	PUNCT
ejpam-3288	181	38	)	)	PUNCT
ejpam-3288	181	39	,	,	PUNCT
ejpam-3288	181	40	µna	µna	PROPN
ejpam-3288	181	41	(	(	PUNCT
ejpam-3288	181	42	y	y	NOUN
ejpam-3288	181	43	)	)	PUNCT
ejpam-3288	181	44	}	}	PUNCT
ejpam-3288	181	45	=	=	PUNCT
ejpam-3288	181	46	min{µna	min{µna	NOUN
ejpam-3288	181	47	(	(	PUNCT
ejpam-3288	181	48	x	x	NOUN
ejpam-3288	181	49	∗	∗	PROPN
ejpam-3288	181	50	y	y	PROPN
ejpam-3288	181	51	)	)	PUNCT
ejpam-3288	181	52	,	,	PUNCT
ejpam-3288	181	53	µna	µna	PROPN
ejpam-3288	181	54	(	(	PUNCT
ejpam-3288	181	55	y	y	NOUN
ejpam-3288	181	56	)	)	PUNCT
ejpam-3288	181	57	}	}	PUNCT
ejpam-3288	181	58	=	=	PUNCT
ejpam-3288	181	59	min{µna	min{µna	NOUN
ejpam-3288	181	60	(	(	PUNCT
ejpam-3288	181	61	0	0	NUM
ejpam-3288	181	62	)	)	PUNCT
ejpam-3288	181	63	,	,	PUNCT
ejpam-3288	181	64	µna	µna	PROPN
ejpam-3288	181	65	(	(	PUNCT
ejpam-3288	181	66	y	y	NOUN
ejpam-3288	181	67	)	)	PUNCT
ejpam-3288	181	68	}	}	PUNCT
ejpam-3288	181	69	=	=	SYM
ejpam-3288	181	70	µna	µna	ADJ
ejpam-3288	181	71	(	(	PUNCT
ejpam-3288	181	72	y	y	NOUN
ejpam-3288	181	73	)	)	PUNCT
ejpam-3288	181	74	.	.	PUNCT
ejpam-3288	182	1	therefore	therefore	ADV
ejpam-3288	182	2	,	,	PUNCT
ejpam-3288	182	3	µna	µna	ADJ
ejpam-3288	182	4	(	(	PUNCT
ejpam-3288	182	5	x	x	NOUN
ejpam-3288	182	6	)	)	PUNCT
ejpam-3288	182	7	≥	≥	X
ejpam-3288	182	8	µna	µna	ADJ
ejpam-3288	182	9	(	(	PUNCT
ejpam-3288	182	10	y	y	NOUN
ejpam-3288	182	11	)	)	PUNCT
ejpam-3288	182	12	for	for	ADP
ejpam-3288	182	13	all	all	DET
ejpam-3288	182	14	x	x	NOUN
ejpam-3288	182	15	,	,	PUNCT
ejpam-3288	182	16	y	y	PROPN
ejpam-3288	182	17	∈	∈	PROPN
ejpam-3288	182	18	x.	x.	NOUN
ejpam-3288	182	19	proposition	proposition	NOUN
ejpam-3288	182	20	2	2	NUM
ejpam-3288	182	21	.	.	PUNCT
ejpam-3288	183	1	let	let	VERB
ejpam-3288	183	2	a	a	PRON
ejpam-3288	183	3	=	=	X
ejpam-3288	183	4	(	(	PUNCT
ejpam-3288	183	5	µpa	µpa	PROPN
ejpam-3288	183	6	,	,	PUNCT
ejpam-3288	183	7	µ	µ	NOUN
ejpam-3288	183	8	n	n	ADV
ejpam-3288	183	9	a	a	PRON
ejpam-3288	183	10	)	)	PUNCT
ejpam-3288	183	11	be	be	AUX
ejpam-3288	183	12	a	a	DET
ejpam-3288	183	13	doubt	doubt	ADV
ejpam-3288	183	14	bipolar	bipolar	ADJ
ejpam-3288	183	15	fuzzy	fuzzy	ADJ
ejpam-3288	183	16	h	h	NOUN
ejpam-3288	183	17	-	-	PUNCT
ejpam-3288	183	18	ideal	ideal	NOUN
ejpam-3288	183	19	of	of	ADP
ejpam-3288	183	20	a	a	DET
ejpam-3288	183	21	bck	bck	NOUN
ejpam-3288	183	22	-	-	PUNCT
ejpam-3288	183	23	algebra	algebra	NOUN
ejpam-3288	183	24	x	x	NOUN
ejpam-3288	183	25	,	,	PUNCT
ejpam-3288	183	26	then	then	ADV
ejpam-3288	183	27	µpa(0	µpa(0	ADJ
ejpam-3288	183	28	∗	∗	NOUN
ejpam-3288	183	29	(	(	PUNCT
ejpam-3288	183	30	0	0	NUM
ejpam-3288	183	31	∗	∗	NOUN
ejpam-3288	183	32	x	x	NOUN
ejpam-3288	183	33	)	)	PUNCT
ejpam-3288	183	34	)	)	PUNCT
ejpam-3288	183	35	≤	≤	PUNCT
ejpam-3288	183	36	µpa(x	µpa(x	NOUN
ejpam-3288	183	37	)	)	PUNCT
ejpam-3288	183	38	and	and	CCONJ
ejpam-3288	183	39	µna	µna	ADJ
ejpam-3288	183	40	(	(	PUNCT
ejpam-3288	183	41	0	0	NUM
ejpam-3288	183	42	∗	∗	NOUN
ejpam-3288	183	43	(	(	PUNCT
ejpam-3288	183	44	0	0	NUM
ejpam-3288	183	45	∗	∗	NOUN
ejpam-3288	183	46	x	x	NOUN
ejpam-3288	183	47	)	)	PUNCT
ejpam-3288	183	48	)	)	PUNCT
ejpam-3288	183	49	≥	≥	AUX
ejpam-3288	183	50	µna	µna	ADJ
ejpam-3288	183	51	(	(	PUNCT
ejpam-3288	183	52	x	x	NOUN
ejpam-3288	183	53	)	)	PUNCT
ejpam-3288	183	54	for	for	ADP
ejpam-3288	183	55	all	all	DET
ejpam-3288	183	56	x	x	SYM
ejpam-3288	183	57	∈	∈	ADJ
ejpam-3288	183	58	x.	x.	NOUN
ejpam-3288	183	59	proof	proof	NOUN
ejpam-3288	183	60	.	.	PUNCT
ejpam-3288	184	1	note	note	VERB
ejpam-3288	184	2	that	that	SCONJ
ejpam-3288	184	3	µpa(0	µpa(0	ADJ
ejpam-3288	184	4	∗	∗	NOUN
ejpam-3288	184	5	(	(	PUNCT
ejpam-3288	184	6	0	0	NUM
ejpam-3288	184	7	∗	∗	NOUN
ejpam-3288	184	8	x	x	NOUN
ejpam-3288	184	9	)	)	PUNCT
ejpam-3288	184	10	)	)	PUNCT
ejpam-3288	184	11	≤	≤	NOUN
ejpam-3288	184	12	max{µpa(0	max{µpa(0	NUM
ejpam-3288	184	13	∗	∗	NOUN
ejpam-3288	184	14	(	(	PUNCT
ejpam-3288	184	15	x	x	X
ejpam-3288	184	16	∗	∗	NOUN
ejpam-3288	184	17	(	(	PUNCT
ejpam-3288	184	18	0	0	NUM
ejpam-3288	184	19	∗	∗	NOUN
ejpam-3288	184	20	x	x	NOUN
ejpam-3288	184	21	)	)	PUNCT
ejpam-3288	184	22	)	)	PUNCT
ejpam-3288	184	23	)	)	PUNCT
ejpam-3288	184	24	,	,	PUNCT
ejpam-3288	184	25	µpa(x	µpa(x	PROPN
ejpam-3288	184	26	)	)	PUNCT
ejpam-3288	184	27	}	}	PUNCT
ejpam-3288	184	28	=	=	SYM
ejpam-3288	184	29	max{µpa(0	max{µpa(0	NUM
ejpam-3288	184	30	∗	∗	NOUN
ejpam-3288	184	31	(	(	PUNCT
ejpam-3288	184	32	x	x	X
ejpam-3288	184	33	∗	∗	NOUN
ejpam-3288	184	34	0	0	NUM
ejpam-3288	184	35	)	)	PUNCT
ejpam-3288	184	36	)	)	PUNCT
ejpam-3288	184	37	,	,	PUNCT
ejpam-3288	184	38	µpa(x	µpa(x	PROPN
ejpam-3288	184	39	)	)	PUNCT
ejpam-3288	184	40	}	}	PUNCT
ejpam-3288	184	41	=	=	SYM
ejpam-3288	184	42	max{µpa(0	max{µpa(0	NUM
ejpam-3288	184	43	∗	∗	NOUN
ejpam-3288	184	44	x	x	X
ejpam-3288	184	45	)	)	PUNCT
ejpam-3288	184	46	,	,	PUNCT
ejpam-3288	184	47	µpa(x	µpa(x	PROPN
ejpam-3288	184	48	)	)	PUNCT
ejpam-3288	184	49	}	}	PUNCT
ejpam-3288	184	50	=	=	SYM
ejpam-3288	184	51	max{µpa(0	max{µpa(0	NUM
ejpam-3288	184	52	)	)	PUNCT
ejpam-3288	184	53	,	,	PUNCT
ejpam-3288	184	54	µpa(x	µpa(x	X
ejpam-3288	184	55	)	)	PUNCT
ejpam-3288	184	56	}	}	PUNCT
ejpam-3288	184	57	=	=	SYM
ejpam-3288	184	58	µpa(x	µpa(x	NOUN
ejpam-3288	184	59	)	)	PUNCT
ejpam-3288	184	60	,	,	PUNCT
ejpam-3288	184	61	for	for	ADP
ejpam-3288	184	62	all	all	DET
ejpam-3288	184	63	x	x	SYM
ejpam-3288	184	64	∈	∈	PROPN
ejpam-3288	184	65	x.	x.	NOUN
ejpam-3288	184	66	therefore	therefore	ADV
ejpam-3288	184	67	,	,	PUNCT
ejpam-3288	184	68	µpa(0	µpa(0	ADJ
ejpam-3288	184	69	∗	∗	NOUN
ejpam-3288	184	70	(	(	PUNCT
ejpam-3288	184	71	0	0	NUM
ejpam-3288	184	72	∗	∗	NOUN
ejpam-3288	184	73	x	x	NOUN
ejpam-3288	184	74	)	)	PUNCT
ejpam-3288	184	75	)	)	PUNCT
ejpam-3288	184	76	≤	≤	PUNCT
ejpam-3288	184	77	µpa(x	µpa(x	NOUN
ejpam-3288	184	78	)	)	PUNCT
ejpam-3288	184	79	for	for	ADP
ejpam-3288	184	80	all	all	PRON
ejpam-3288	184	81	x	x	SYM
ejpam-3288	184	82	∈	∈	NOUN
ejpam-3288	184	83	x.	x.	NOUN
ejpam-3288	184	84	again	again	ADV
ejpam-3288	184	85	,	,	PUNCT
ejpam-3288	184	86	µna	µna	ADJ
ejpam-3288	184	87	(	(	PUNCT
ejpam-3288	184	88	0	0	NUM
ejpam-3288	184	89	∗	∗	NOUN
ejpam-3288	184	90	(	(	PUNCT
ejpam-3288	184	91	0	0	NUM
ejpam-3288	184	92	∗	∗	NOUN
ejpam-3288	184	93	x	x	NOUN
ejpam-3288	184	94	)	)	PUNCT
ejpam-3288	184	95	)	)	PUNCT
ejpam-3288	184	96	≥	≥	NOUN
ejpam-3288	184	97	min{µna	min{µna	NOUN
ejpam-3288	184	98	(	(	PUNCT
ejpam-3288	184	99	0	0	NUM
ejpam-3288	184	100	∗	∗	NOUN
ejpam-3288	184	101	(	(	PUNCT
ejpam-3288	184	102	x	x	X
ejpam-3288	184	103	∗	∗	NOUN
ejpam-3288	184	104	(	(	PUNCT
ejpam-3288	184	105	0	0	NUM
ejpam-3288	184	106	∗	∗	NOUN
ejpam-3288	184	107	x	x	NOUN
ejpam-3288	184	108	)	)	PUNCT
ejpam-3288	184	109	)	)	PUNCT
ejpam-3288	184	110	)	)	PUNCT
ejpam-3288	184	111	,	,	PUNCT
ejpam-3288	184	112	µna	µna	ADJ
ejpam-3288	184	113	(	(	PUNCT
ejpam-3288	184	114	x	x	NOUN
ejpam-3288	184	115	)	)	PUNCT
ejpam-3288	184	116	}	}	PUNCT
ejpam-3288	184	117	=	=	PUNCT
ejpam-3288	184	118	min{µna	min{µna	ADJ
ejpam-3288	184	119	(	(	PUNCT
ejpam-3288	184	120	0	0	NUM
ejpam-3288	184	121	∗	∗	NOUN
ejpam-3288	184	122	(	(	PUNCT
ejpam-3288	184	123	x	x	X
ejpam-3288	184	124	∗	∗	NOUN
ejpam-3288	184	125	0	0	NUM
ejpam-3288	184	126	)	)	PUNCT
ejpam-3288	184	127	)	)	PUNCT
ejpam-3288	184	128	,	,	PUNCT
ejpam-3288	184	129	µna	µna	ADJ
ejpam-3288	184	130	(	(	PUNCT
ejpam-3288	184	131	x	x	NOUN
ejpam-3288	184	132	)	)	PUNCT
ejpam-3288	184	133	}	}	PUNCT
ejpam-3288	184	134	=	=	PUNCT
ejpam-3288	184	135	min{µna	min{µna	NOUN
ejpam-3288	184	136	(	(	PUNCT
ejpam-3288	184	137	0	0	NUM
ejpam-3288	184	138	∗	∗	NOUN
ejpam-3288	184	139	x	x	NOUN
ejpam-3288	184	140	)	)	PUNCT
ejpam-3288	184	141	,	,	PUNCT
ejpam-3288	184	142	µna	µna	ADJ
ejpam-3288	184	143	(	(	PUNCT
ejpam-3288	184	144	x	x	NOUN
ejpam-3288	184	145	)	)	PUNCT
ejpam-3288	184	146	}	}	PUNCT
ejpam-3288	184	147	=	=	PUNCT
ejpam-3288	184	148	min{µna	min{µna	NOUN
ejpam-3288	184	149	(	(	PUNCT
ejpam-3288	184	150	0	0	NUM
ejpam-3288	184	151	)	)	PUNCT
ejpam-3288	184	152	,	,	PUNCT
ejpam-3288	184	153	µna	µna	ADJ
ejpam-3288	184	154	(	(	PUNCT
ejpam-3288	184	155	x	x	NOUN
ejpam-3288	184	156	)	)	PUNCT
ejpam-3288	184	157	}	}	PUNCT
ejpam-3288	184	158	=	=	SYM
ejpam-3288	184	159	µna	µna	ADJ
ejpam-3288	184	160	(	(	PUNCT
ejpam-3288	184	161	x	x	NOUN
ejpam-3288	184	162	)	)	PUNCT
ejpam-3288	184	163	,	,	PUNCT
ejpam-3288	184	164	for	for	ADP
ejpam-3288	184	165	all	all	DET
ejpam-3288	184	166	x	x	SYM
ejpam-3288	184	167	∈	∈	PROPN
ejpam-3288	184	168	x.	x.	NOUN
ejpam-3288	184	169	therefore	therefore	ADV
ejpam-3288	184	170	,	,	PUNCT
ejpam-3288	184	171	µna	µna	ADJ
ejpam-3288	184	172	(	(	PUNCT
ejpam-3288	184	173	0	0	NUM
ejpam-3288	184	174	∗	∗	NOUN
ejpam-3288	184	175	(	(	PUNCT
ejpam-3288	184	176	0	0	NUM
ejpam-3288	184	177	∗	∗	NOUN
ejpam-3288	184	178	x	x	NOUN
ejpam-3288	184	179	)	)	PUNCT
ejpam-3288	184	180	)	)	PUNCT
ejpam-3288	184	181	≥	≥	AUX
ejpam-3288	184	182	µna	µna	ADJ
ejpam-3288	184	183	(	(	PUNCT
ejpam-3288	184	184	x	x	NOUN
ejpam-3288	184	185	)	)	PUNCT
ejpam-3288	184	186	for	for	ADP
ejpam-3288	184	187	all	all	PRON
ejpam-3288	184	188	x	x	SYM
ejpam-3288	184	189	∈	∈	PROPN
ejpam-3288	184	190	x.	x.	NOUN
ejpam-3288	184	191	theorem	theorem	VERB
ejpam-3288	184	192	3	3	NUM
ejpam-3288	184	193	.	.	PUNCT
ejpam-3288	184	194	every	every	DET
ejpam-3288	184	195	doubt	doubt	ADV
ejpam-3288	184	196	bipolar	bipolar	ADJ
ejpam-3288	184	197	fuzzy	fuzzy	ADJ
ejpam-3288	184	198	h	h	NOUN
ejpam-3288	184	199	-	-	PUNCT
ejpam-3288	184	200	ideal	ideal	NOUN
ejpam-3288	184	201	of	of	ADP
ejpam-3288	184	202	x	x	SYM
ejpam-3288	184	203	is	be	AUX
ejpam-3288	184	204	both	both	CCONJ
ejpam-3288	184	205	a	a	DET
ejpam-3288	184	206	doubt	doubt	ADV
ejpam-3288	184	207	bipolar	bipolar	ADJ
ejpam-3288	184	208	fuzzy	fuzzy	ADJ
ejpam-3288	184	209	subalgebra	subalgebra	NOUN
ejpam-3288	184	210	of	of	ADP
ejpam-3288	184	211	x	x	X
ejpam-3288	184	212	and	and	CCONJ
ejpam-3288	184	213	a	a	DET
ejpam-3288	184	214	doubt	doubt	ADV
ejpam-3288	184	215	bipolar	bipolar	ADJ
ejpam-3288	184	216	fuzzy	fuzzy	ADJ
ejpam-3288	184	217	ideal	ideal	NOUN
ejpam-3288	184	218	of	of	ADP
ejpam-3288	184	219	x.	x.	PROPN
ejpam-3288	184	220	a.	a.	PROPN
ejpam-3288	184	221	al	al	PROPN
ejpam-3288	184	222	-	-	PROPN
ejpam-3288	184	223	masarwah	masarwah	PROPN
ejpam-3288	184	224	,	,	PUNCT
ejpam-3288	184	225	a.	a.	NOUN
ejpam-3288	184	226	g.	g.	PROPN
ejpam-3288	184	227	ahmad	ahmad	PROPN
ejpam-3288	184	228	/	/	SYM
ejpam-3288	184	229	eur	eur	PROPN
ejpam-3288	184	230	.	.	PUNCT
ejpam-3288	185	1	j.	j.	PROPN
ejpam-3288	185	2	pure	pure	PROPN
ejpam-3288	185	3	appl	appl	PROPN
ejpam-3288	185	4	.	.	PROPN
ejpam-3288	185	5	math	math	PROPN
ejpam-3288	185	6	,	,	PUNCT
ejpam-3288	185	7	11	11	NUM
ejpam-3288	185	8	(	(	PUNCT
ejpam-3288	185	9	3	3	NUM
ejpam-3288	185	10	)	)	PUNCT
ejpam-3288	185	11	(	(	PUNCT
ejpam-3288	185	12	2018	2018	NUM
ejpam-3288	185	13	)	)	PUNCT
ejpam-3288	185	14	,	,	PUNCT
ejpam-3288	185	15	652	652	NUM
ejpam-3288	185	16	-	-	SYM
ejpam-3288	185	17	670	670	NUM
ejpam-3288	185	18	660	660	NUM
ejpam-3288	185	19	proof	proof	NOUN
ejpam-3288	185	20	.	.	PUNCT
ejpam-3288	186	1	let	let	VERB
ejpam-3288	186	2	a	a	PRON
ejpam-3288	186	3	=	=	X
ejpam-3288	186	4	(	(	PUNCT
ejpam-3288	186	5	µpa	µpa	PROPN
ejpam-3288	186	6	,	,	PUNCT
ejpam-3288	186	7	µ	µ	NOUN
ejpam-3288	186	8	n	n	ADV
ejpam-3288	186	9	a	a	PRON
ejpam-3288	186	10	)	)	PUNCT
ejpam-3288	186	11	be	be	AUX
ejpam-3288	186	12	a	a	DET
ejpam-3288	186	13	doubt	doubt	ADV
ejpam-3288	186	14	bipolar	bipolar	ADJ
ejpam-3288	186	15	fuzzy	fuzzy	ADJ
ejpam-3288	186	16	h	h	NOUN
ejpam-3288	186	17	-	-	PUNCT
ejpam-3288	186	18	ideal	ideal	NOUN
ejpam-3288	186	19	of	of	ADP
ejpam-3288	186	20	x	x	NOUN
ejpam-3288	186	21	,	,	PUNCT
ejpam-3288	186	22	then	then	ADV
ejpam-3288	186	23	for	for	ADP
ejpam-3288	186	24	any	any	DET
ejpam-3288	186	25	x	x	NOUN
ejpam-3288	186	26	,	,	PUNCT
ejpam-3288	186	27	y	y	PROPN
ejpam-3288	186	28	∈	∈	PROPN
ejpam-3288	187	1	x	x	X
ejpam-3288	187	2	,	,	PUNCT
ejpam-3288	187	3	we	we	PRON
ejpam-3288	187	4	have	have	VERB
ejpam-3288	187	5	µpa(x	µpa(x	PROPN
ejpam-3288	187	6	∗	∗	NOUN
ejpam-3288	187	7	y	y	NOUN
ejpam-3288	187	8	)	)	PUNCT
ejpam-3288	187	9	≤	≤	PROPN
ejpam-3288	187	10	max{µpa(x	max{µpa(x	PROPN
ejpam-3288	187	11	∗	∗	NOUN
ejpam-3288	187	12	(	(	PUNCT
ejpam-3288	187	13	y	y	PROPN
ejpam-3288	187	14	∗	∗	PROPN
ejpam-3288	187	15	y	y	PROPN
ejpam-3288	187	16	)	)	PUNCT
ejpam-3288	187	17	)	)	PUNCT
ejpam-3288	187	18	,	,	PUNCT
ejpam-3288	187	19	µpa(y	µpa(y	PROPN
ejpam-3288	187	20	)	)	PUNCT
ejpam-3288	187	21	}	}	PUNCT
ejpam-3288	187	22	=	=	SYM
ejpam-3288	187	23	max{µpa(x	max{µpa(x	PROPN
ejpam-3288	187	24	∗	∗	NOUN
ejpam-3288	187	25	0	0	NUM
ejpam-3288	187	26	)	)	PUNCT
ejpam-3288	187	27	,	,	PUNCT
ejpam-3288	187	28	µpa(y	µpa(y	PROPN
ejpam-3288	187	29	)	)	PUNCT
ejpam-3288	187	30	}	}	PUNCT
ejpam-3288	187	31	=	=	SYM
ejpam-3288	187	32	max{µpa(x	max{µpa(x	PROPN
ejpam-3288	187	33	)	)	PUNCT
ejpam-3288	187	34	,	,	PUNCT
ejpam-3288	187	35	µpa(y	µpa(y	PROPN
ejpam-3288	187	36	)	)	PUNCT
ejpam-3288	187	37	}	}	PUNCT
ejpam-3288	187	38	,	,	PUNCT
ejpam-3288	187	39	and	and	CCONJ
ejpam-3288	187	40	µna	µna	ADJ
ejpam-3288	187	41	(	(	PUNCT
ejpam-3288	187	42	x	x	PROPN
ejpam-3288	187	43	∗	∗	PROPN
ejpam-3288	187	44	y	y	PROPN
ejpam-3288	187	45	)	)	PUNCT
ejpam-3288	187	46	≥	≥	NOUN
ejpam-3288	187	47	min{µna	min{µna	NOUN
ejpam-3288	187	48	(	(	PUNCT
ejpam-3288	187	49	x	x	NOUN
ejpam-3288	187	50	∗	∗	NOUN
ejpam-3288	187	51	(	(	PUNCT
ejpam-3288	187	52	y	y	PROPN
ejpam-3288	187	53	∗	∗	PROPN
ejpam-3288	187	54	y	y	PROPN
ejpam-3288	187	55	)	)	PUNCT
ejpam-3288	187	56	)	)	PUNCT
ejpam-3288	187	57	,	,	PUNCT
ejpam-3288	187	58	µna	µna	PROPN
ejpam-3288	187	59	(	(	PUNCT
ejpam-3288	187	60	y	y	NOUN
ejpam-3288	187	61	)	)	PUNCT
ejpam-3288	187	62	}	}	PUNCT
ejpam-3288	187	63	=	=	PUNCT
ejpam-3288	187	64	min{µna	min{µna	NOUN
ejpam-3288	187	65	(	(	PUNCT
ejpam-3288	187	66	x	x	NOUN
ejpam-3288	187	67	∗	∗	NOUN
ejpam-3288	187	68	0	0	NUM
ejpam-3288	187	69	)	)	PUNCT
ejpam-3288	187	70	,	,	PUNCT
ejpam-3288	187	71	µna	µna	PROPN
ejpam-3288	187	72	(	(	PUNCT
ejpam-3288	187	73	y	y	NOUN
ejpam-3288	187	74	)	)	PUNCT
ejpam-3288	187	75	}	}	PUNCT
ejpam-3288	187	76	=	=	PUNCT
ejpam-3288	187	77	min{µna	min{µna	ADJ
ejpam-3288	187	78	(	(	PUNCT
ejpam-3288	187	79	x	x	NOUN
ejpam-3288	187	80	)	)	PUNCT
ejpam-3288	187	81	,	,	PUNCT
ejpam-3288	187	82	µna	µna	ADJ
ejpam-3288	187	83	(	(	PUNCT
ejpam-3288	187	84	y	y	NOUN
ejpam-3288	187	85	)	)	PUNCT
ejpam-3288	187	86	}	}	PUNCT
ejpam-3288	187	87	.	.	PUNCT
ejpam-3288	188	1	hence	hence	ADV
ejpam-3288	188	2	,	,	PUNCT
ejpam-3288	188	3	a	a	DET
ejpam-3288	188	4	=	=	X
ejpam-3288	188	5	(	(	PUNCT
ejpam-3288	188	6	µpa	µpa	PROPN
ejpam-3288	188	7	,	,	PUNCT
ejpam-3288	188	8	µ	µ	X
ejpam-3288	188	9	n	n	PRON
ejpam-3288	188	10	a	a	PRON
ejpam-3288	188	11	)	)	PUNCT
ejpam-3288	188	12	is	be	AUX
ejpam-3288	188	13	a	a	DET
ejpam-3288	188	14	doubt	doubt	ADV
ejpam-3288	188	15	bipolar	bipolar	ADJ
ejpam-3288	188	16	fuzzy	fuzzy	ADJ
ejpam-3288	188	17	subalgebra	subalgebra	NOUN
ejpam-3288	188	18	of	of	ADP
ejpam-3288	188	19	x.	x.	NOUN
ejpam-3288	188	20	also	also	ADV
ejpam-3288	188	21	,	,	PUNCT
ejpam-3288	188	22	since	since	SCONJ
ejpam-3288	188	23	a	a	DET
ejpam-3288	188	24	=	=	X
ejpam-3288	188	25	(	(	PUNCT
ejpam-3288	188	26	µpa	µpa	PROPN
ejpam-3288	188	27	,	,	PUNCT
ejpam-3288	188	28	µ	µ	X
ejpam-3288	188	29	n	n	PRON
ejpam-3288	188	30	a	a	PRON
ejpam-3288	188	31	)	)	PUNCT
ejpam-3288	188	32	is	be	AUX
ejpam-3288	188	33	a	a	DET
ejpam-3288	188	34	doubt	doubt	ADV
ejpam-3288	188	35	bipolar	bipolar	ADJ
ejpam-3288	188	36	fuzzy	fuzzy	ADJ
ejpam-3288	188	37	h	h	NOUN
ejpam-3288	188	38	-	-	PUNCT
ejpam-3288	188	39	ideal	ideal	NOUN
ejpam-3288	188	40	of	of	ADP
ejpam-3288	188	41	x.	x.	NOUN
ejpam-3288	188	42	then	then	ADV
ejpam-3288	188	43	µpa(0	µpa(0	NOUN
ejpam-3288	188	44	)	)	PUNCT
ejpam-3288	188	45	≤	≤	NUM
ejpam-3288	188	46	µpa(x	µpa(x	NOUN
ejpam-3288	188	47	)	)	PUNCT
ejpam-3288	188	48	and	and	CCONJ
ejpam-3288	188	49	µna	µna	ADJ
ejpam-3288	188	50	(	(	PUNCT
ejpam-3288	188	51	0	0	NUM
ejpam-3288	188	52	)	)	PUNCT
ejpam-3288	188	53	≥	≥	NOUN
ejpam-3288	188	54	µna	µna	ADJ
ejpam-3288	188	55	(	(	PUNCT
ejpam-3288	188	56	x	x	NOUN
ejpam-3288	188	57	)	)	PUNCT
ejpam-3288	188	58	.	.	PUNCT
ejpam-3288	189	1	now	now	ADV
ejpam-3288	189	2	,	,	PUNCT
ejpam-3288	189	3	since	since	SCONJ
ejpam-3288	189	4	x	x	X
ejpam-3288	189	5	∗	∗	NOUN
ejpam-3288	189	6	0	0	NUM
ejpam-3288	190	1	=	=	NOUN
ejpam-3288	190	2	x	x	PROPN
ejpam-3288	190	3	for	for	ADP
ejpam-3288	190	4	all	all	DET
ejpam-3288	190	5	x	x	SYM
ejpam-3288	190	6	∈	∈	PROPN
ejpam-3288	190	7	x	x	X
ejpam-3288	190	8	,	,	PUNCT
ejpam-3288	190	9	we	we	PRON
ejpam-3288	190	10	obtain	obtain	VERB
ejpam-3288	190	11	µpa(x	µpa(x	PRON
ejpam-3288	190	12	)	)	PUNCT
ejpam-3288	190	13	=	=	PUNCT
ejpam-3288	191	1	µpa(x	µpa(x	PROPN
ejpam-3288	191	2	∗	∗	NOUN
ejpam-3288	191	3	0	0	NUM
ejpam-3288	191	4	)	)	PUNCT
ejpam-3288	191	5	≤	≤	NUM
ejpam-3288	191	6	max{µpa(x	max{µpa(x	PROPN
ejpam-3288	191	7	∗	∗	NOUN
ejpam-3288	191	8	(	(	PUNCT
ejpam-3288	191	9	y	y	PROPN
ejpam-3288	191	10	∗	∗	NOUN
ejpam-3288	191	11	0	0	NUM
ejpam-3288	191	12	)	)	PUNCT
ejpam-3288	191	13	)	)	PUNCT
ejpam-3288	191	14	,	,	PUNCT
ejpam-3288	191	15	µpa(y	µpa(y	PROPN
ejpam-3288	191	16	)	)	PUNCT
ejpam-3288	191	17	}	}	PUNCT
ejpam-3288	191	18	=	=	SYM
ejpam-3288	191	19	max{µpa(x	max{µpa(x	PROPN
ejpam-3288	191	20	∗	∗	NOUN
ejpam-3288	191	21	y	y	NOUN
ejpam-3288	191	22	)	)	PUNCT
ejpam-3288	191	23	,	,	PUNCT
ejpam-3288	191	24	µpa(y	µpa(y	PROPN
ejpam-3288	191	25	)	)	PUNCT
ejpam-3288	191	26	}	}	PUNCT
ejpam-3288	191	27	,	,	PUNCT
ejpam-3288	191	28	and	and	CCONJ
ejpam-3288	191	29	µna	µna	ADJ
ejpam-3288	191	30	(	(	PUNCT
ejpam-3288	191	31	x	x	NOUN
ejpam-3288	191	32	)	)	PUNCT
ejpam-3288	191	33	=	=	SYM
ejpam-3288	191	34	µna	µna	ADJ
ejpam-3288	191	35	(	(	PUNCT
ejpam-3288	191	36	x	x	NOUN
ejpam-3288	191	37	∗	∗	NOUN
ejpam-3288	191	38	0	0	NUM
ejpam-3288	191	39	)	)	PUNCT
ejpam-3288	191	40	≥	≥	NOUN
ejpam-3288	191	41	min{µna	min{µna	NOUN
ejpam-3288	191	42	(	(	PUNCT
ejpam-3288	191	43	x	x	NOUN
ejpam-3288	191	44	∗	∗	NOUN
ejpam-3288	191	45	(	(	PUNCT
ejpam-3288	191	46	y	y	PROPN
ejpam-3288	191	47	∗	∗	NOUN
ejpam-3288	191	48	0	0	NUM
ejpam-3288	191	49	)	)	PUNCT
ejpam-3288	191	50	)	)	PUNCT
ejpam-3288	191	51	,	,	PUNCT
ejpam-3288	191	52	µna	µna	PROPN
ejpam-3288	191	53	(	(	PUNCT
ejpam-3288	191	54	y	y	NOUN
ejpam-3288	191	55	)	)	PUNCT
ejpam-3288	191	56	}	}	PUNCT
ejpam-3288	191	57	=	=	PUNCT
ejpam-3288	191	58	min{µna	min{µna	NOUN
ejpam-3288	191	59	(	(	PUNCT
ejpam-3288	191	60	x	x	NOUN
ejpam-3288	191	61	∗	∗	PROPN
ejpam-3288	191	62	y	y	PROPN
ejpam-3288	191	63	)	)	PUNCT
ejpam-3288	191	64	,	,	PUNCT
ejpam-3288	191	65	µna	µna	PROPN
ejpam-3288	191	66	(	(	PUNCT
ejpam-3288	191	67	y	y	NOUN
ejpam-3288	191	68	)	)	PUNCT
ejpam-3288	191	69	}	}	PUNCT
ejpam-3288	191	70	.	.	PUNCT
ejpam-3288	192	1	therefore	therefore	ADV
ejpam-3288	192	2	,	,	PUNCT
ejpam-3288	192	3	a	a	PRON
ejpam-3288	192	4	=	=	X
ejpam-3288	192	5	(	(	PUNCT
ejpam-3288	192	6	µpa	µpa	PROPN
ejpam-3288	192	7	,	,	PUNCT
ejpam-3288	192	8	µ	µ	X
ejpam-3288	192	9	n	n	PRON
ejpam-3288	192	10	a	a	PRON
ejpam-3288	192	11	)	)	PUNCT
ejpam-3288	192	12	is	be	AUX
ejpam-3288	192	13	a	a	DET
ejpam-3288	192	14	doubt	doubt	ADV
ejpam-3288	192	15	bipolar	bipolar	ADJ
ejpam-3288	192	16	fuzzy	fuzzy	ADJ
ejpam-3288	192	17	ideal	ideal	NOUN
ejpam-3288	192	18	of	of	ADP
ejpam-3288	192	19	x.	x.	NOUN
ejpam-3288	192	20	the	the	DET
ejpam-3288	192	21	converse	converse	NOUN
ejpam-3288	192	22	of	of	ADP
ejpam-3288	192	23	theorem	theorem	NOUN
ejpam-3288	192	24	3	3	NUM
ejpam-3288	192	25	is	be	AUX
ejpam-3288	192	26	not	not	PART
ejpam-3288	192	27	true	true	ADJ
ejpam-3288	192	28	.	.	PUNCT
ejpam-3288	193	1	that	that	PRON
ejpam-3288	193	2	is	be	AUX
ejpam-3288	193	3	every	every	PRON
ejpam-3288	193	4	doubt	doubt	ADV
ejpam-3288	193	5	bipolar	bipolar	ADJ
ejpam-3288	193	6	fuzzy	fuzzy	ADJ
ejpam-3288	193	7	subalgebra	subalgebra	NOUN
ejpam-3288	193	8	of	of	ADP
ejpam-3288	193	9	x	x	PUNCT
ejpam-3288	193	10	and	and	CCONJ
ejpam-3288	193	11	doubt	doubt	VERB
ejpam-3288	193	12	bipolar	bipolar	ADJ
ejpam-3288	193	13	fuzzy	fuzzy	ADJ
ejpam-3288	193	14	ideal	ideal	NOUN
ejpam-3288	193	15	of	of	ADP
ejpam-3288	193	16	x	x	PUNCT
ejpam-3288	193	17	is	be	AUX
ejpam-3288	193	18	not	not	PART
ejpam-3288	193	19	necessarily	necessarily	ADV
ejpam-3288	193	20	to	to	PART
ejpam-3288	193	21	be	be	AUX
ejpam-3288	193	22	a	a	DET
ejpam-3288	193	23	doubt	doubt	ADV
ejpam-3288	193	24	bipolar	bipolar	ADJ
ejpam-3288	193	25	fuzzy	fuzzy	ADJ
ejpam-3288	193	26	h	h	NOUN
ejpam-3288	193	27	-	-	PUNCT
ejpam-3288	193	28	ideal	ideal	NOUN
ejpam-3288	193	29	of	of	ADP
ejpam-3288	193	30	x.	x.	NOUN
ejpam-3288	193	31	it	it	PRON
ejpam-3288	193	32	can	can	AUX
ejpam-3288	193	33	be	be	AUX
ejpam-3288	193	34	verified	verify	VERB
ejpam-3288	193	35	by	by	ADP
ejpam-3288	193	36	the	the	DET
ejpam-3288	193	37	following	follow	VERB
ejpam-3288	193	38	example	example	NOUN
ejpam-3288	193	39	:	:	PUNCT
ejpam-3288	193	40	example	example	NOUN
ejpam-3288	193	41	1	1	X
ejpam-3288	193	42	.	.	PUNCT
ejpam-3288	194	1	let	let	VERB
ejpam-3288	194	2	x	x	PUNCT
ejpam-3288	194	3	=	=	PUNCT
ejpam-3288	194	4	{	{	PUNCT
ejpam-3288	194	5	0	0	NUM
ejpam-3288	194	6	,	,	PUNCT
ejpam-3288	194	7	a	a	PRON
ejpam-3288	194	8	,	,	PUNCT
ejpam-3288	194	9	b	b	X
ejpam-3288	194	10	}	}	PUNCT
ejpam-3288	194	11	be	be	AUX
ejpam-3288	194	12	a	a	DET
ejpam-3288	194	13	bci	bci	NOUN
ejpam-3288	194	14	-	-	NOUN
ejpam-3288	194	15	algebra	algebra	NOUN
ejpam-3288	194	16	with	with	ADP
ejpam-3288	194	17	the	the	DET
ejpam-3288	194	18	cayley	cayley	ADJ
ejpam-3288	194	19	table	table	NOUN
ejpam-3288	194	20	which	which	PRON
ejpam-3288	194	21	is	be	AUX
ejpam-3288	194	22	appeared	appear	VERB
ejpam-3288	194	23	in	in	ADP
ejpam-3288	194	24	table	table	NOUN
ejpam-3288	194	25	1	1	NUM
ejpam-3288	194	26	.	.	PUNCT
ejpam-3288	194	27	table	table	NOUN
ejpam-3288	194	28	1	1	NUM
ejpam-3288	194	29	:	:	PUNCT
ejpam-3288	194	30	cayley	cayley	ADJ
ejpam-3288	194	31	table	table	NOUN
ejpam-3288	194	32	for	for	ADP
ejpam-3288	194	33	the	the	DET
ejpam-3288	194	34	∗-operation	∗-operation	NOUN
ejpam-3288	194	35	.	.	PUNCT
ejpam-3288	195	1	∗	∗	NOUN
ejpam-3288	195	2	0	0	NUM
ejpam-3288	196	1	a	a	DET
ejpam-3288	196	2	b	b	NOUN
ejpam-3288	196	3	0	0	NUM
ejpam-3288	196	4	0	0	NUM
ejpam-3288	196	5	b	b	PROPN
ejpam-3288	196	6	a	a	DET
ejpam-3288	196	7	a	a	DET
ejpam-3288	196	8	a	a	DET
ejpam-3288	196	9	0	0	NUM
ejpam-3288	196	10	b	b	PROPN
ejpam-3288	196	11	b	b	PROPN
ejpam-3288	196	12	b	b	PROPN
ejpam-3288	196	13	a	a	DET
ejpam-3288	196	14	0	0	NUM
ejpam-3288	196	15	define	define	VERB
ejpam-3288	196	16	a	a	DET
ejpam-3288	196	17	bipolar	bipolar	ADJ
ejpam-3288	196	18	fuzzy	fuzzy	NOUN
ejpam-3288	196	19	set	set	VERB
ejpam-3288	196	20	a	a	DET
ejpam-3288	196	21	=	=	X
ejpam-3288	196	22	(	(	PUNCT
ejpam-3288	196	23	µpa	µpa	PROPN
ejpam-3288	196	24	,	,	PUNCT
ejpam-3288	196	25	µ	µ	X
ejpam-3288	196	26	n	n	PRON
ejpam-3288	196	27	a	a	NOUN
ejpam-3288	196	28	)	)	PUNCT
ejpam-3288	196	29	in	in	ADP
ejpam-3288	196	30	x	x	PUNCT
ejpam-3288	196	31	as	as	SCONJ
ejpam-3288	196	32	follows	follow	VERB
ejpam-3288	196	33	:	:	PUNCT
ejpam-3288	196	34	µpa(x	µpa(x	X
ejpam-3288	196	35	)	)	PUNCT
ejpam-3288	196	36	=	=	SYM
ejpam-3288	196	37	{	{	PUNCT
ejpam-3288	196	38	0	0	NUM
ejpam-3288	196	39	,	,	PUNCT
ejpam-3288	196	40	if	if	SCONJ
ejpam-3288	196	41	x	x	ADP
ejpam-3288	196	42	=	=	SYM
ejpam-3288	196	43	0	0	NUM
ejpam-3288	196	44	0.8	0.8	NUM
ejpam-3288	196	45	,	,	PUNCT
ejpam-3288	196	46	if	if	SCONJ
ejpam-3288	196	47	x	x	X
ejpam-3288	196	48	=	=	SYM
ejpam-3288	196	49	a	a	PROPN
ejpam-3288	196	50	,	,	PUNCT
ejpam-3288	196	51	b	b	NOUN
ejpam-3288	196	52	,	,	PUNCT
ejpam-3288	196	53	and	and	CCONJ
ejpam-3288	196	54	µna	µna	ADJ
ejpam-3288	196	55	(	(	PUNCT
ejpam-3288	196	56	x	x	NOUN
ejpam-3288	196	57	)	)	PUNCT
ejpam-3288	196	58	=	=	PRON
ejpam-3288	196	59	{	{	PUNCT
ejpam-3288	196	60	−0.2	−0.2	PROPN
ejpam-3288	196	61	,	,	PUNCT
ejpam-3288	196	62	if	if	SCONJ
ejpam-3288	196	63	x	x	ADP
ejpam-3288	196	64	=	=	SYM
ejpam-3288	196	65	0	0	NUM
ejpam-3288	196	66	−0.4	−0.4	NUM
ejpam-3288	196	67	,	,	PUNCT
ejpam-3288	196	68	if	if	SCONJ
ejpam-3288	196	69	x	x	X
ejpam-3288	196	70	=	=	SYM
ejpam-3288	196	71	a	a	PROPN
ejpam-3288	196	72	,	,	PUNCT
ejpam-3288	196	73	b.	b.	PROPN
ejpam-3288	196	74	then	then	ADV
ejpam-3288	196	75	,	,	PUNCT
ejpam-3288	196	76	a	a	PRON
ejpam-3288	196	77	=	=	X
ejpam-3288	196	78	(	(	PUNCT
ejpam-3288	196	79	µpa	µpa	PROPN
ejpam-3288	196	80	,	,	PUNCT
ejpam-3288	196	81	µ	µ	X
ejpam-3288	196	82	n	n	PRON
ejpam-3288	196	83	a	a	PRON
ejpam-3288	196	84	)	)	PUNCT
ejpam-3288	196	85	is	be	AUX
ejpam-3288	196	86	a	a	DET
ejpam-3288	196	87	doubt	doubt	ADV
ejpam-3288	196	88	bipolar	bipolar	ADJ
ejpam-3288	196	89	fuzzy	fuzzy	ADJ
ejpam-3288	196	90	subalgebra	subalgebra	NOUN
ejpam-3288	196	91	of	of	ADP
ejpam-3288	196	92	x	x	X
ejpam-3288	196	93	and	and	CCONJ
ejpam-3288	196	94	a	a	DET
ejpam-3288	196	95	doubt	doubt	ADV
ejpam-3288	196	96	bipolar	bipolar	ADJ
ejpam-3288	196	97	fuzzy	fuzzy	ADJ
ejpam-3288	196	98	ideal	ideal	NOUN
ejpam-3288	196	99	of	of	ADP
ejpam-3288	196	100	x.	x.	NOUN
ejpam-3288	196	101	but	but	CCONJ
ejpam-3288	196	102	a	a	DET
ejpam-3288	196	103	=	=	X
ejpam-3288	196	104	(	(	PUNCT
ejpam-3288	196	105	µpa	µpa	PROPN
ejpam-3288	196	106	,	,	PUNCT
ejpam-3288	196	107	µ	µ	X
ejpam-3288	196	108	n	n	PRON
ejpam-3288	196	109	a	a	PRON
ejpam-3288	196	110	)	)	PUNCT
ejpam-3288	196	111	is	be	AUX
ejpam-3288	196	112	not	not	PART
ejpam-3288	196	113	a	a	DET
ejpam-3288	196	114	doubt	doubt	ADV
ejpam-3288	196	115	bipolar	bipolar	ADJ
ejpam-3288	196	116	fuzzy	fuzzy	ADJ
ejpam-3288	196	117	h	h	NOUN
ejpam-3288	196	118	-	-	PUNCT
ejpam-3288	196	119	ideal	ideal	NOUN
ejpam-3288	196	120	of	of	ADP
ejpam-3288	196	121	x	x	PRON
ejpam-3288	196	122	,	,	PUNCT
ejpam-3288	196	123	since	since	SCONJ
ejpam-3288	196	124	µpa(a	µpa(a	PROPN
ejpam-3288	196	125	∗	∗	NOUN
ejpam-3288	196	126	b	b	NOUN
ejpam-3288	196	127	)	)	PUNCT
ejpam-3288	196	128	=	=	SYM
ejpam-3288	196	129	0.8	0.8	NUM
ejpam-3288	196	130	max{µpa(a	max{µpa(a	NOUN
ejpam-3288	196	131	∗	∗	NOUN
ejpam-3288	196	132	(	(	PUNCT
ejpam-3288	196	133	0	0	NUM
ejpam-3288	196	134	∗	∗	NUM
ejpam-3288	196	135	b	b	NOUN
ejpam-3288	196	136	)	)	PUNCT
ejpam-3288	196	137	)	)	PUNCT
ejpam-3288	196	138	,	,	PUNCT
ejpam-3288	196	139	µpa(0	µpa(0	NOUN
ejpam-3288	196	140	)	)	PUNCT
ejpam-3288	196	141	}	}	PUNCT
ejpam-3288	196	142	=	=	SYM
ejpam-3288	196	143	µpa(0	µpa(0	X
ejpam-3288	196	144	)	)	PUNCT
ejpam-3288	197	1	=	=	SYM
ejpam-3288	197	2	0	0	X
ejpam-3288	197	3	.	.	PUNCT
ejpam-3288	197	4	a.	a.	PROPN
ejpam-3288	197	5	al	al	PROPN
ejpam-3288	197	6	-	-	PROPN
ejpam-3288	197	7	masarwah	masarwah	PROPN
ejpam-3288	197	8	,	,	PUNCT
ejpam-3288	197	9	a.	a.	NOUN
ejpam-3288	197	10	g.	g.	PROPN
ejpam-3288	197	11	ahmad	ahmad	PROPN
ejpam-3288	197	12	/	/	SYM
ejpam-3288	197	13	eur	eur	PROPN
ejpam-3288	197	14	.	.	PUNCT
ejpam-3288	198	1	j.	j.	PROPN
ejpam-3288	198	2	pure	pure	PROPN
ejpam-3288	198	3	appl	appl	PROPN
ejpam-3288	198	4	.	.	PROPN
ejpam-3288	198	5	math	math	PROPN
ejpam-3288	198	6	,	,	PUNCT
ejpam-3288	198	7	11	11	NUM
ejpam-3288	198	8	(	(	PUNCT
ejpam-3288	198	9	3	3	NUM
ejpam-3288	198	10	)	)	PUNCT
ejpam-3288	198	11	(	(	PUNCT
ejpam-3288	198	12	2018	2018	NUM
ejpam-3288	198	13	)	)	PUNCT
ejpam-3288	198	14	,	,	PUNCT
ejpam-3288	198	15	652	652	NUM
ejpam-3288	198	16	-	-	SYM
ejpam-3288	198	17	670	670	NUM
ejpam-3288	198	18	661	661	NUM
ejpam-3288	198	19	in	in	ADP
ejpam-3288	198	20	the	the	DET
ejpam-3288	198	21	following	follow	VERB
ejpam-3288	198	22	example	example	NOUN
ejpam-3288	199	1	,	,	PUNCT
ejpam-3288	199	2	we	we	PRON
ejpam-3288	199	3	have	have	VERB
ejpam-3288	199	4	a	a	DET
ejpam-3288	199	5	doubt	doubt	ADV
ejpam-3288	199	6	bipolar	bipolar	ADJ
ejpam-3288	199	7	fuzzy	fuzzy	ADJ
ejpam-3288	199	8	subalgebra	subalgebra	NOUN
ejpam-3288	199	9	of	of	ADP
ejpam-3288	199	10	x	x	PUNCT
ejpam-3288	200	1	but	but	CCONJ
ejpam-3288	200	2	it	it	PRON
ejpam-3288	200	3	is	be	AUX
ejpam-3288	200	4	neither	neither	CCONJ
ejpam-3288	200	5	a	a	DET
ejpam-3288	200	6	doubt	doubt	ADV
ejpam-3288	200	7	bipolar	bipolar	ADJ
ejpam-3288	200	8	fuzzy	fuzzy	ADJ
ejpam-3288	200	9	ideal	ideal	NOUN
ejpam-3288	200	10	of	of	ADP
ejpam-3288	200	11	x	x	X
ejpam-3288	200	12	nor	nor	CCONJ
ejpam-3288	200	13	a	a	PRON
ejpam-3288	200	14	doubt	doubt	ADV
ejpam-3288	200	15	bipolar	bipolar	ADJ
ejpam-3288	200	16	fuzzy	fuzzy	ADJ
ejpam-3288	200	17	h	h	NOUN
ejpam-3288	200	18	-	-	PUNCT
ejpam-3288	200	19	ideal	ideal	NOUN
ejpam-3288	200	20	of	of	ADP
ejpam-3288	200	21	x.	x.	PROPN
ejpam-3288	200	22	example	example	NOUN
ejpam-3288	201	1	2	2	X
ejpam-3288	201	2	.	.	PUNCT
ejpam-3288	202	1	let	let	VERB
ejpam-3288	202	2	x	x	PUNCT
ejpam-3288	202	3	=	=	PUNCT
ejpam-3288	202	4	{	{	PUNCT
ejpam-3288	202	5	0	0	NUM
ejpam-3288	202	6	,	,	PUNCT
ejpam-3288	202	7	a	a	DET
ejpam-3288	202	8	,	,	PUNCT
ejpam-3288	202	9	b	b	NOUN
ejpam-3288	202	10	,	,	PUNCT
ejpam-3288	202	11	c	c	AUX
ejpam-3288	202	12	}	}	PUNCT
ejpam-3288	202	13	be	be	AUX
ejpam-3288	202	14	a	a	DET
ejpam-3288	202	15	bck	bck	NOUN
ejpam-3288	202	16	-	-	PUNCT
ejpam-3288	202	17	algebra	algebra	NOUN
ejpam-3288	202	18	with	with	ADP
ejpam-3288	202	19	the	the	DET
ejpam-3288	202	20	cayley	cayley	ADJ
ejpam-3288	202	21	table	table	NOUN
ejpam-3288	202	22	which	which	PRON
ejpam-3288	202	23	is	be	AUX
ejpam-3288	202	24	appeared	appear	VERB
ejpam-3288	202	25	in	in	ADP
ejpam-3288	202	26	table	table	NOUN
ejpam-3288	202	27	2	2	NUM
ejpam-3288	202	28	.	.	PUNCT
ejpam-3288	202	29	table	table	NOUN
ejpam-3288	202	30	2	2	NUM
ejpam-3288	202	31	:	:	PUNCT
ejpam-3288	202	32	cayley	cayley	ADJ
ejpam-3288	202	33	table	table	NOUN
ejpam-3288	202	34	for	for	ADP
ejpam-3288	202	35	the	the	DET
ejpam-3288	202	36	∗-operation	∗-operation	NOUN
ejpam-3288	202	37	.	.	PUNCT
ejpam-3288	203	1	∗	∗	NOUN
ejpam-3288	203	2	0	0	NUM
ejpam-3288	204	1	a	a	DET
ejpam-3288	204	2	b	b	NOUN
ejpam-3288	204	3	c	c	NOUN
ejpam-3288	204	4	0	0	NUM
ejpam-3288	204	5	0	0	NUM
ejpam-3288	204	6	0	0	NUM
ejpam-3288	204	7	0	0	NUM
ejpam-3288	204	8	0	0	NUM
ejpam-3288	204	9	a	a	DET
ejpam-3288	204	10	a	a	DET
ejpam-3288	204	11	0	0	NUM
ejpam-3288	204	12	0	0	NUM
ejpam-3288	204	13	a	a	DET
ejpam-3288	204	14	b	b	PROPN
ejpam-3288	204	15	b	b	PROPN
ejpam-3288	204	16	a	a	PRON
ejpam-3288	204	17	0	0	NUM
ejpam-3288	204	18	b	b	NOUN
ejpam-3288	204	19	c	c	NOUN
ejpam-3288	204	20	c	c	NOUN
ejpam-3288	204	21	c	c	NOUN
ejpam-3288	204	22	c	c	SYM
ejpam-3288	204	23	0	0	PUNCT
ejpam-3288	204	24	define	define	VERB
ejpam-3288	204	25	a	a	DET
ejpam-3288	204	26	bipolar	bipolar	ADJ
ejpam-3288	204	27	fuzzy	fuzzy	NOUN
ejpam-3288	204	28	set	set	VERB
ejpam-3288	204	29	a	a	PRON
ejpam-3288	204	30	=	=	X
ejpam-3288	204	31	(	(	PUNCT
ejpam-3288	204	32	µpa	µpa	PROPN
ejpam-3288	204	33	,	,	PUNCT
ejpam-3288	204	34	µ	µ	X
ejpam-3288	204	35	n	n	PRON
ejpam-3288	204	36	a	a	NOUN
ejpam-3288	204	37	)	)	PUNCT
ejpam-3288	204	38	in	in	ADP
ejpam-3288	204	39	x	x	PUNCT
ejpam-3288	204	40	as	as	SCONJ
ejpam-3288	204	41	follows	follow	VERB
ejpam-3288	204	42	:	:	PUNCT
ejpam-3288	204	43	µpa(x	µpa(x	X
ejpam-3288	204	44	)	)	PUNCT
ejpam-3288	204	45	=	=	SYM
ejpam-3288	204	46	{	{	PUNCT
ejpam-3288	204	47	0.5	0.5	NUM
ejpam-3288	204	48	,	,	PUNCT
ejpam-3288	204	49	if	if	SCONJ
ejpam-3288	204	50	x	x	ADP
ejpam-3288	204	51	=	=	SYM
ejpam-3288	204	52	0	0	NUM
ejpam-3288	204	53	,	,	PUNCT
ejpam-3288	204	54	a	a	PRON
ejpam-3288	204	55	,	,	PUNCT
ejpam-3288	204	56	c	c	NOUN
ejpam-3288	204	57	0.6	0.6	NUM
ejpam-3288	204	58	,	,	PUNCT
ejpam-3288	204	59	if	if	SCONJ
ejpam-3288	204	60	x	x	ADP
ejpam-3288	204	61	=	=	SYM
ejpam-3288	204	62	b	b	PROPN
ejpam-3288	204	63	,	,	PUNCT
ejpam-3288	204	64	and	and	CCONJ
ejpam-3288	204	65	µna	µna	ADJ
ejpam-3288	204	66	(	(	PUNCT
ejpam-3288	204	67	0	0	NUM
ejpam-3288	204	68	)	)	PUNCT
ejpam-3288	205	1	=	=	NOUN
ejpam-3288	205	2	µna	µna	ADJ
ejpam-3288	205	3	(	(	PUNCT
ejpam-3288	205	4	a	a	NOUN
ejpam-3288	205	5	)	)	PUNCT
ejpam-3288	205	6	=	=	VERB
ejpam-3288	205	7	µna	µna	ADJ
ejpam-3288	205	8	(	(	PUNCT
ejpam-3288	205	9	b	b	NOUN
ejpam-3288	205	10	)	)	PUNCT
ejpam-3288	205	11	=	=	NOUN
ejpam-3288	205	12	µna	µna	ADJ
ejpam-3288	205	13	(	(	PUNCT
ejpam-3288	205	14	c	c	NOUN
ejpam-3288	205	15	)	)	PUNCT
ejpam-3288	205	16	=	=	PUNCT
ejpam-3288	206	1	−0.5	−0.5	PROPN
ejpam-3288	206	2	.	.	PUNCT
ejpam-3288	206	3	then	then	ADV
ejpam-3288	206	4	by	by	ADP
ejpam-3288	206	5	routine	routine	ADJ
ejpam-3288	206	6	calculation	calculation	NOUN
ejpam-3288	206	7	we	we	PRON
ejpam-3288	206	8	know	know	VERB
ejpam-3288	206	9	that	that	SCONJ
ejpam-3288	206	10	a	a	DET
ejpam-3288	206	11	=	=	X
ejpam-3288	206	12	(	(	PUNCT
ejpam-3288	206	13	µpa	µpa	PROPN
ejpam-3288	206	14	,	,	PUNCT
ejpam-3288	206	15	µ	µ	X
ejpam-3288	206	16	n	n	PRON
ejpam-3288	206	17	a	a	PRON
ejpam-3288	206	18	)	)	PUNCT
ejpam-3288	206	19	is	be	AUX
ejpam-3288	206	20	a	a	DET
ejpam-3288	206	21	doubt	doubt	ADV
ejpam-3288	206	22	bipolar	bipolar	ADJ
ejpam-3288	206	23	fuzzy	fuzzy	ADJ
ejpam-3288	206	24	subalgebra	subalgebra	NOUN
ejpam-3288	206	25	of	of	ADP
ejpam-3288	206	26	x.	x.	NOUN
ejpam-3288	206	27	but	but	CCONJ
ejpam-3288	206	28	,	,	PUNCT
ejpam-3288	206	29	it	it	PRON
ejpam-3288	206	30	is	be	AUX
ejpam-3288	206	31	not	not	PART
ejpam-3288	206	32	a	a	DET
ejpam-3288	206	33	doubt	doubt	ADV
ejpam-3288	206	34	bipolar	bipolar	ADJ
ejpam-3288	206	35	fuzzy	fuzzy	ADJ
ejpam-3288	206	36	ideal	ideal	NOUN
ejpam-3288	206	37	of	of	ADP
ejpam-3288	206	38	x	x	PRON
ejpam-3288	206	39	,	,	PUNCT
ejpam-3288	206	40	since	since	SCONJ
ejpam-3288	206	41	µpa(b	µpa(b	PROPN
ejpam-3288	206	42	)	)	PUNCT
ejpam-3288	206	43	=	=	SYM
ejpam-3288	206	44	0.6	0.6	NUM
ejpam-3288	206	45	,	,	PUNCT
ejpam-3288	206	46	µpa(b	µpa(b	PROPN
ejpam-3288	206	47	)	)	PUNCT
ejpam-3288	206	48	=	=	SYM
ejpam-3288	206	49	0.6	0.6	NUM
ejpam-3288	206	50	�	�	PROPN
ejpam-3288	206	51	0.5	0.5	NUM
ejpam-3288	206	52	=	=	PROPN
ejpam-3288	206	53	max{µpa(b	max{µpa(b	PROPN
ejpam-3288	206	54	∗a	∗a	PROPN
ejpam-3288	206	55	)	)	PUNCT
ejpam-3288	206	56	,	,	PUNCT
ejpam-3288	206	57	µpa(a	µpa(a	PROPN
ejpam-3288	206	58	)	)	PUNCT
ejpam-3288	206	59	}	}	PUNCT
ejpam-3288	206	60	,	,	PUNCT
ejpam-3288	206	61	and	and	CCONJ
ejpam-3288	206	62	hence	hence	ADV
ejpam-3288	206	63	it	it	PRON
ejpam-3288	206	64	is	be	AUX
ejpam-3288	206	65	not	not	PART
ejpam-3288	206	66	a	a	DET
ejpam-3288	206	67	doubt	doubt	ADV
ejpam-3288	206	68	bipolar	bipolar	ADJ
ejpam-3288	206	69	fuzzy	fuzzy	ADJ
ejpam-3288	206	70	hideal	hideal	NOUN
ejpam-3288	206	71	of	of	ADP
ejpam-3288	206	72	x	x	PRON
ejpam-3288	206	73	,	,	PUNCT
ejpam-3288	206	74	since	since	SCONJ
ejpam-3288	206	75	µpa(b	µpa(b	PRON
ejpam-3288	206	76	∗	∗	VERB
ejpam-3288	206	77	c	c	NOUN
ejpam-3288	206	78	)	)	PUNCT
ejpam-3288	206	79	=	=	SYM
ejpam-3288	206	80	µpa(b	µpa(b	ADJ
ejpam-3288	206	81	)	)	PUNCT
ejpam-3288	206	82	=	=	SYM
ejpam-3288	206	83	0.6	0.6	NUM
ejpam-3288	206	84	,	,	PUNCT
ejpam-3288	206	85	µpa(b	µpa(b	PROPN
ejpam-3288	206	86	)	)	PUNCT
ejpam-3288	206	87	=	=	SYM
ejpam-3288	206	88	0.6	0.6	NUM
ejpam-3288	206	89	�	�	PROPN
ejpam-3288	206	90	0.5	0.5	NUM
ejpam-3288	206	91	=	=	SYM
ejpam-3288	206	92	max{µpa(b	max{µpa(b	PROPN
ejpam-3288	206	93	∗	∗	NOUN
ejpam-3288	206	94	(	(	PUNCT
ejpam-3288	206	95	a	a	DET
ejpam-3288	206	96	∗	∗	NOUN
ejpam-3288	206	97	c	c	NOUN
ejpam-3288	206	98	)	)	PUNCT
ejpam-3288	206	99	)	)	PUNCT
ejpam-3288	206	100	,	,	PUNCT
ejpam-3288	206	101	µpa(a	µpa(a	PROPN
ejpam-3288	206	102	)	)	PUNCT
ejpam-3288	206	103	}	}	PUNCT
ejpam-3288	206	104	.	.	PUNCT
ejpam-3288	207	1	now	now	ADV
ejpam-3288	207	2	,	,	PUNCT
ejpam-3288	207	3	we	we	PRON
ejpam-3288	207	4	give	give	VERB
ejpam-3288	207	5	a	a	DET
ejpam-3288	207	6	condition	condition	NOUN
ejpam-3288	207	7	for	for	ADP
ejpam-3288	207	8	the	the	DET
ejpam-3288	207	9	bipolar	bipolar	ADJ
ejpam-3288	207	10	fuzzy	fuzzy	NOUN
ejpam-3288	207	11	set	set	VERB
ejpam-3288	207	12	a	a	DET
ejpam-3288	207	13	=	=	X
ejpam-3288	207	14	(	(	PUNCT
ejpam-3288	207	15	µpa	µpa	PROPN
ejpam-3288	207	16	,	,	PUNCT
ejpam-3288	207	17	µ	µ	NOUN
ejpam-3288	207	18	n	n	PRON
ejpam-3288	207	19	a	a	NOUN
ejpam-3288	207	20	)	)	PUNCT
ejpam-3288	207	21	,	,	PUNCT
ejpam-3288	207	22	which	which	PRON
ejpam-3288	207	23	is	be	AUX
ejpam-3288	207	24	a	a	DET
ejpam-3288	207	25	doubt	doubt	ADV
ejpam-3288	207	26	bipolar	bipolar	ADJ
ejpam-3288	207	27	fuzzy	fuzzy	ADJ
ejpam-3288	207	28	ideal	ideal	NOUN
ejpam-3288	207	29	of	of	ADP
ejpam-3288	207	30	x	x	PUNCT
ejpam-3288	207	31	to	to	PART
ejpam-3288	207	32	be	be	AUX
ejpam-3288	207	33	a	a	DET
ejpam-3288	207	34	doubt	doubt	ADV
ejpam-3288	207	35	bipolar	bipolar	ADJ
ejpam-3288	207	36	fuzzy	fuzzy	ADJ
ejpam-3288	207	37	h	h	NOUN
ejpam-3288	207	38	-	-	PUNCT
ejpam-3288	207	39	ideal	ideal	NOUN
ejpam-3288	207	40	of	of	ADP
ejpam-3288	207	41	x.	x.	PROPN
ejpam-3288	207	42	theorem	theorem	VERB
ejpam-3288	207	43	4	4	NUM
ejpam-3288	207	44	.	.	PUNCT
ejpam-3288	208	1	in	in	ADP
ejpam-3288	208	2	associative	associative	ADJ
ejpam-3288	208	3	bck	bck	PROPN
ejpam-3288	208	4	/	/	SYM
ejpam-3288	208	5	bci	bci	NOUN
ejpam-3288	208	6	-	-	PUNCT
ejpam-3288	208	7	algebras	algebras	ADJ
ejpam-3288	208	8	x	x	SYM
ejpam-3288	208	9	,	,	PUNCT
ejpam-3288	208	10	every	every	PRON
ejpam-3288	208	11	doubt	doubt	ADV
ejpam-3288	208	12	bipolar	bipolar	ADJ
ejpam-3288	208	13	fuzzy	fuzzy	ADJ
ejpam-3288	208	14	ideal	ideal	NOUN
ejpam-3288	208	15	is	be	AUX
ejpam-3288	208	16	a	a	DET
ejpam-3288	208	17	doubt	doubt	ADV
ejpam-3288	208	18	bipolar	bipolar	ADJ
ejpam-3288	208	19	fuzzy	fuzzy	ADJ
ejpam-3288	208	20	h	h	NOUN
ejpam-3288	208	21	-	-	PUNCT
ejpam-3288	208	22	ideal	ideal	NOUN
ejpam-3288	208	23	of	of	ADP
ejpam-3288	208	24	x.	x.	NOUN
ejpam-3288	208	25	proof	proof	NOUN
ejpam-3288	208	26	.	.	PUNCT
ejpam-3288	209	1	let	let	VERB
ejpam-3288	209	2	a	a	PRON
ejpam-3288	209	3	=	=	X
ejpam-3288	209	4	(	(	PUNCT
ejpam-3288	209	5	µpa	µpa	PROPN
ejpam-3288	209	6	,	,	PUNCT
ejpam-3288	209	7	µ	µ	NOUN
ejpam-3288	209	8	n	n	ADV
ejpam-3288	209	9	a	a	PRON
ejpam-3288	209	10	)	)	PUNCT
ejpam-3288	209	11	be	be	AUX
ejpam-3288	209	12	a	a	DET
ejpam-3288	209	13	doubt	doubt	ADV
ejpam-3288	209	14	bipolar	bipolar	ADJ
ejpam-3288	209	15	fuzzy	fuzzy	ADJ
ejpam-3288	209	16	ideal	ideal	NOUN
ejpam-3288	209	17	of	of	ADP
ejpam-3288	209	18	x.	x.	NOUN
ejpam-3288	209	19	then	then	ADV
ejpam-3288	209	20	µpa(0	µpa(0	NOUN
ejpam-3288	209	21	)	)	PUNCT
ejpam-3288	209	22	≤	≤	NUM
ejpam-3288	209	23	µpa(x	µpa(x	NOUN
ejpam-3288	209	24	)	)	PUNCT
ejpam-3288	209	25	and	and	CCONJ
ejpam-3288	209	26	µna	µna	ADJ
ejpam-3288	209	27	(	(	PUNCT
ejpam-3288	209	28	0	0	NUM
ejpam-3288	209	29	)	)	PUNCT
ejpam-3288	209	30	≥	≥	NOUN
ejpam-3288	209	31	µna	µna	ADJ
ejpam-3288	209	32	(	(	PUNCT
ejpam-3288	209	33	x	x	NOUN
ejpam-3288	209	34	)	)	PUNCT
ejpam-3288	209	35	,	,	PUNCT
ejpam-3288	209	36	for	for	ADP
ejpam-3288	209	37	all	all	PRON
ejpam-3288	209	38	x	x	SYM
ejpam-3288	209	39	∈	∈	NOUN
ejpam-3288	209	40	x.	x.	NOUN
ejpam-3288	209	41	now	now	ADV
ejpam-3288	209	42	,	,	PUNCT
ejpam-3288	209	43	since	since	SCONJ
ejpam-3288	209	44	x	x	PRON
ejpam-3288	209	45	is	be	AUX
ejpam-3288	209	46	an	an	DET
ejpam-3288	209	47	associative	associative	NOUN
ejpam-3288	209	48	,	,	PUNCT
ejpam-3288	209	49	then	then	ADV
ejpam-3288	209	50	x	x	X
ejpam-3288	209	51	∗	∗	NOUN
ejpam-3288	209	52	(	(	PUNCT
ejpam-3288	209	53	y	y	PROPN
ejpam-3288	209	54	∗	∗	PROPN
ejpam-3288	209	55	z	z	NOUN
ejpam-3288	209	56	)	)	PUNCT
ejpam-3288	209	57	=	=	SYM
ejpam-3288	209	58	(	(	PUNCT
ejpam-3288	209	59	x	x	X
ejpam-3288	209	60	∗	∗	PROPN
ejpam-3288	209	61	y	y	NOUN
ejpam-3288	209	62	)	)	PUNCT
ejpam-3288	209	63	∗	∗	NOUN
ejpam-3288	209	64	z	z	PROPN
ejpam-3288	209	65	,	,	PUNCT
ejpam-3288	209	66	for	for	ADP
ejpam-3288	209	67	x	x	SYM
ejpam-3288	209	68	,	,	PUNCT
ejpam-3288	209	69	y	y	PROPN
ejpam-3288	209	70	,	,	PUNCT
ejpam-3288	209	71	z	z	PROPN
ejpam-3288	209	72	∈	∈	PROPN
ejpam-3288	209	73	x.	x.	NOUN
ejpam-3288	210	1	now	now	ADV
ejpam-3288	210	2	,	,	PUNCT
ejpam-3288	210	3	max{µpa(x	max{µpa(x	PROPN
ejpam-3288	210	4	∗	∗	NOUN
ejpam-3288	210	5	(	(	PUNCT
ejpam-3288	210	6	y	y	PROPN
ejpam-3288	210	7	∗	∗	PROPN
ejpam-3288	210	8	z	z	PROPN
ejpam-3288	210	9	)	)	PUNCT
ejpam-3288	210	10	)	)	PUNCT
ejpam-3288	210	11	,	,	PUNCT
ejpam-3288	210	12	µpa(y	µpa(y	PROPN
ejpam-3288	210	13	)	)	PUNCT
ejpam-3288	210	14	}	}	PUNCT
ejpam-3288	210	15	=	=	SYM
ejpam-3288	210	16	max{µpa((x	max{µpa((x	NOUN
ejpam-3288	210	17	∗	∗	X
ejpam-3288	210	18	y	y	NOUN
ejpam-3288	210	19	)	)	PUNCT
ejpam-3288	210	20	∗	∗	NOUN
ejpam-3288	210	21	z	z	NOUN
ejpam-3288	210	22	)	)	PUNCT
ejpam-3288	210	23	,	,	PUNCT
ejpam-3288	210	24	µpa(y	µpa(y	PROPN
ejpam-3288	210	25	)	)	PUNCT
ejpam-3288	210	26	}	}	PUNCT
ejpam-3288	210	27	=	=	SYM
ejpam-3288	210	28	max{µpa((x	max{µpa((x	NOUN
ejpam-3288	210	29	∗	∗	NOUN
ejpam-3288	210	30	z	z	NOUN
ejpam-3288	210	31	)	)	PUNCT
ejpam-3288	210	32	∗	∗	PROPN
ejpam-3288	210	33	y	y	PROPN
ejpam-3288	210	34	)	)	PUNCT
ejpam-3288	210	35	,	,	PUNCT
ejpam-3288	210	36	µpa(y	µpa(y	PROPN
ejpam-3288	210	37	)	)	PUNCT
ejpam-3288	210	38	}	}	PUNCT
ejpam-3288	210	39	≥	≥	VERB
ejpam-3288	210	40	µpa(x	µpa(x	PROPN
ejpam-3288	210	41	∗	∗	NOUN
ejpam-3288	210	42	z	z	PROPN
ejpam-3288	210	43	)	)	PUNCT
ejpam-3288	210	44	.	.	PUNCT
ejpam-3288	211	1	therefore	therefore	ADV
ejpam-3288	211	2	,	,	PUNCT
ejpam-3288	211	3	µpa(x	µpa(x	PROPN
ejpam-3288	211	4	∗	∗	NOUN
ejpam-3288	211	5	z	z	NOUN
ejpam-3288	211	6	)	)	PUNCT
ejpam-3288	211	7	≤	≤	PROPN
ejpam-3288	211	8	max{µpa(x	max{µpa(x	PROPN
ejpam-3288	211	9	∗	∗	NOUN
ejpam-3288	211	10	(	(	PUNCT
ejpam-3288	211	11	y	y	PROPN
ejpam-3288	211	12	∗	∗	PROPN
ejpam-3288	211	13	z	z	PROPN
ejpam-3288	211	14	)	)	PUNCT
ejpam-3288	211	15	)	)	PUNCT
ejpam-3288	211	16	,	,	PUNCT
ejpam-3288	211	17	µpa(y	µpa(y	PROPN
ejpam-3288	211	18	)	)	PUNCT
ejpam-3288	211	19	}	}	PUNCT
ejpam-3288	211	20	for	for	ADP
ejpam-3288	211	21	all	all	DET
ejpam-3288	211	22	x	x	NOUN
ejpam-3288	211	23	,	,	PUNCT
ejpam-3288	211	24	y	y	PROPN
ejpam-3288	211	25	,	,	PUNCT
ejpam-3288	211	26	z	z	PROPN
ejpam-3288	211	27	∈	∈	NOUN
ejpam-3288	211	28	x.	x.	NOUN
ejpam-3288	211	29	again	again	ADV
ejpam-3288	211	30	,	,	PUNCT
ejpam-3288	211	31	min{µna	min{µna	PROPN
ejpam-3288	211	32	(	(	PUNCT
ejpam-3288	211	33	x	x	NOUN
ejpam-3288	211	34	∗	∗	NOUN
ejpam-3288	211	35	(	(	PUNCT
ejpam-3288	211	36	y	y	PROPN
ejpam-3288	211	37	∗	∗	PROPN
ejpam-3288	211	38	z	z	PROPN
ejpam-3288	211	39	)	)	PUNCT
ejpam-3288	211	40	)	)	PUNCT
ejpam-3288	211	41	,	,	PUNCT
ejpam-3288	211	42	µna	µna	PROPN
ejpam-3288	211	43	(	(	PUNCT
ejpam-3288	211	44	y	y	NOUN
ejpam-3288	211	45	)	)	PUNCT
ejpam-3288	211	46	}	}	PUNCT
ejpam-3288	211	47	=	=	PUNCT
ejpam-3288	211	48	min{µna	min{µna	NOUN
ejpam-3288	211	49	(	(	PUNCT
ejpam-3288	211	50	(	(	PUNCT
ejpam-3288	211	51	x	x	SYM
ejpam-3288	211	52	∗	∗	PROPN
ejpam-3288	211	53	y	y	NOUN
ejpam-3288	211	54	)	)	PUNCT
ejpam-3288	211	55	∗	∗	NOUN
ejpam-3288	211	56	z	z	PROPN
ejpam-3288	211	57	)	)	PUNCT
ejpam-3288	211	58	,	,	PUNCT
ejpam-3288	211	59	µna	µna	PROPN
ejpam-3288	211	60	(	(	PUNCT
ejpam-3288	211	61	y	y	NOUN
ejpam-3288	211	62	)	)	PUNCT
ejpam-3288	211	63	}	}	PUNCT
ejpam-3288	211	64	=	=	PUNCT
ejpam-3288	211	65	min{µna	min{µna	NOUN
ejpam-3288	211	66	(	(	PUNCT
ejpam-3288	211	67	(	(	PUNCT
ejpam-3288	211	68	x	x	SYM
ejpam-3288	211	69	∗	∗	PROPN
ejpam-3288	211	70	z	z	NOUN
ejpam-3288	211	71	)	)	PUNCT
ejpam-3288	211	72	∗	∗	PROPN
ejpam-3288	211	73	y	y	PROPN
ejpam-3288	211	74	)	)	PUNCT
ejpam-3288	211	75	,	,	PUNCT
ejpam-3288	211	76	µna	µna	PROPN
ejpam-3288	211	77	(	(	PUNCT
ejpam-3288	211	78	y	y	NOUN
ejpam-3288	211	79	)	)	PUNCT
ejpam-3288	211	80	}	}	PUNCT
ejpam-3288	211	81	≤	≤	ADV
ejpam-3288	211	82	µna	µna	ADJ
ejpam-3288	211	83	(	(	PUNCT
ejpam-3288	211	84	x	x	NOUN
ejpam-3288	211	85	∗	∗	PROPN
ejpam-3288	211	86	z	z	NOUN
ejpam-3288	211	87	)	)	PUNCT
ejpam-3288	211	88	.	.	PUNCT
ejpam-3288	212	1	a.	a.	PROPN
ejpam-3288	212	2	al	al	PROPN
ejpam-3288	212	3	-	-	PROPN
ejpam-3288	212	4	masarwah	masarwah	PROPN
ejpam-3288	212	5	,	,	PUNCT
ejpam-3288	212	6	a.	a.	NOUN
ejpam-3288	212	7	g.	g.	PROPN
ejpam-3288	212	8	ahmad	ahmad	PROPN
ejpam-3288	212	9	/	/	SYM
ejpam-3288	212	10	eur	eur	PROPN
ejpam-3288	212	11	.	.	PUNCT
ejpam-3288	213	1	j.	j.	PROPN
ejpam-3288	213	2	pure	pure	PROPN
ejpam-3288	213	3	appl	appl	PROPN
ejpam-3288	213	4	.	.	PROPN
ejpam-3288	213	5	math	math	PROPN
ejpam-3288	213	6	,	,	PUNCT
ejpam-3288	213	7	11	11	NUM
ejpam-3288	213	8	(	(	PUNCT
ejpam-3288	213	9	3	3	NUM
ejpam-3288	213	10	)	)	PUNCT
ejpam-3288	213	11	(	(	PUNCT
ejpam-3288	213	12	2018	2018	NUM
ejpam-3288	213	13	)	)	PUNCT
ejpam-3288	213	14	,	,	PUNCT
ejpam-3288	213	15	652	652	NUM
ejpam-3288	213	16	-	-	SYM
ejpam-3288	213	17	670	670	NUM
ejpam-3288	213	18	662	662	NUM
ejpam-3288	213	19	therefore	therefore	ADV
ejpam-3288	213	20	,	,	PUNCT
ejpam-3288	213	21	µna	µna	ADJ
ejpam-3288	213	22	(	(	PUNCT
ejpam-3288	213	23	x∗z	x∗z	NUM
ejpam-3288	213	24	)	)	PUNCT
ejpam-3288	213	25	≥	≥	NOUN
ejpam-3288	213	26	min{µna	min{µna	NOUN
ejpam-3288	213	27	(	(	PUNCT
ejpam-3288	213	28	x∗(y∗z	x∗(y∗z	PROPN
ejpam-3288	213	29	)	)	PUNCT
ejpam-3288	213	30	)	)	PUNCT
ejpam-3288	213	31	,	,	PUNCT
ejpam-3288	213	32	µna	µna	PROPN
ejpam-3288	213	33	(	(	PUNCT
ejpam-3288	213	34	y	y	NOUN
ejpam-3288	213	35	)	)	PUNCT
ejpam-3288	213	36	}	}	PUNCT
ejpam-3288	213	37	for	for	ADP
ejpam-3288	213	38	all	all	DET
ejpam-3288	213	39	x	x	NOUN
ejpam-3288	213	40	,	,	PUNCT
ejpam-3288	213	41	y	y	PROPN
ejpam-3288	213	42	,	,	PUNCT
ejpam-3288	213	43	z	z	PROPN
ejpam-3288	213	44	∈	∈	PROPN
ejpam-3288	213	45	x.	x.	NOUN
ejpam-3288	213	46	hence	hence	ADV
ejpam-3288	213	47	,	,	PUNCT
ejpam-3288	213	48	a	a	DET
ejpam-3288	213	49	=	=	X
ejpam-3288	213	50	(	(	PUNCT
ejpam-3288	213	51	µpa	µpa	PROPN
ejpam-3288	213	52	,	,	PUNCT
ejpam-3288	213	53	µ	µ	X
ejpam-3288	213	54	n	n	PRON
ejpam-3288	213	55	a	a	PRON
ejpam-3288	213	56	)	)	PUNCT
ejpam-3288	213	57	is	be	AUX
ejpam-3288	213	58	a	a	DET
ejpam-3288	213	59	doubt	doubt	ADV
ejpam-3288	213	60	bipolar	bipolar	ADJ
ejpam-3288	213	61	fuzzy	fuzzy	ADJ
ejpam-3288	213	62	h	h	NOUN
ejpam-3288	213	63	-	-	PUNCT
ejpam-3288	213	64	ideal	ideal	NOUN
ejpam-3288	213	65	of	of	ADP
ejpam-3288	213	66	x.	x.	PROPN
ejpam-3288	213	67	example	example	NOUN
ejpam-3288	214	1	3	3	X
ejpam-3288	214	2	.	.	PUNCT
ejpam-3288	214	3	let	let	VERB
ejpam-3288	214	4	x	x	PUNCT
ejpam-3288	214	5	=	=	PUNCT
ejpam-3288	214	6	{	{	PUNCT
ejpam-3288	214	7	0	0	NUM
ejpam-3288	214	8	,	,	PUNCT
ejpam-3288	214	9	a	a	DET
ejpam-3288	214	10	,	,	PUNCT
ejpam-3288	214	11	b	b	NOUN
ejpam-3288	214	12	,	,	PUNCT
ejpam-3288	214	13	c	c	NOUN
ejpam-3288	214	14	,	,	PUNCT
ejpam-3288	214	15	d	d	AUX
ejpam-3288	214	16	}	}	PUNCT
ejpam-3288	214	17	be	be	AUX
ejpam-3288	214	18	a	a	DET
ejpam-3288	214	19	bck	bck	NOUN
ejpam-3288	214	20	-	-	PUNCT
ejpam-3288	214	21	algebra	algebra	NOUN
ejpam-3288	214	22	with	with	ADP
ejpam-3288	214	23	the	the	DET
ejpam-3288	214	24	cayley	cayley	ADJ
ejpam-3288	214	25	table	table	NOUN
ejpam-3288	214	26	which	which	PRON
ejpam-3288	214	27	is	be	AUX
ejpam-3288	214	28	appeared	appear	VERB
ejpam-3288	214	29	in	in	ADP
ejpam-3288	214	30	table	table	NOUN
ejpam-3288	214	31	3	3	NUM
ejpam-3288	214	32	.	.	PUNCT
ejpam-3288	214	33	table	table	NOUN
ejpam-3288	214	34	3	3	NUM
ejpam-3288	214	35	:	:	PUNCT
ejpam-3288	214	36	cayley	cayley	ADJ
ejpam-3288	214	37	table	table	NOUN
ejpam-3288	214	38	for	for	ADP
ejpam-3288	214	39	the	the	DET
ejpam-3288	214	40	∗-operation	∗-operation	NOUN
ejpam-3288	214	41	.	.	PUNCT
ejpam-3288	215	1	∗	∗	NOUN
ejpam-3288	215	2	0	0	NUM
ejpam-3288	216	1	a	a	DET
ejpam-3288	216	2	b	b	NOUN
ejpam-3288	216	3	c	c	NOUN
ejpam-3288	216	4	d	d	NOUN
ejpam-3288	216	5	0	0	NUM
ejpam-3288	216	6	0	0	NUM
ejpam-3288	216	7	0	0	NUM
ejpam-3288	216	8	0	0	NUM
ejpam-3288	216	9	0	0	NUM
ejpam-3288	216	10	0	0	NUM
ejpam-3288	216	11	a	a	DET
ejpam-3288	216	12	a	a	DET
ejpam-3288	216	13	0	0	PUNCT
ejpam-3288	217	1	a	a	DET
ejpam-3288	217	2	a	a	PRON
ejpam-3288	217	3	a	a	DET
ejpam-3288	217	4	b	b	PROPN
ejpam-3288	217	5	b	b	PROPN
ejpam-3288	217	6	b	b	PROPN
ejpam-3288	217	7	0	0	NUM
ejpam-3288	217	8	b	b	PROPN
ejpam-3288	217	9	b	b	PROPN
ejpam-3288	217	10	c	c	NOUN
ejpam-3288	217	11	c	c	NOUN
ejpam-3288	217	12	c	c	NOUN
ejpam-3288	217	13	c	c	NOUN
ejpam-3288	217	14	0	0	PUNCT
ejpam-3288	217	15	c	c	NOUN
ejpam-3288	217	16	d	d	PROPN
ejpam-3288	217	17	d	d	PROPN
ejpam-3288	217	18	d	d	PROPN
ejpam-3288	217	19	d	d	PROPN
ejpam-3288	217	20	d	d	PROPN
ejpam-3288	217	21	0	0	PUNCT
ejpam-3288	217	22	here	here	ADV
ejpam-3288	217	23	,	,	PUNCT
ejpam-3288	217	24	x	x	X
ejpam-3288	217	25	is	be	AUX
ejpam-3288	217	26	an	an	DET
ejpam-3288	217	27	associative	associative	ADJ
ejpam-3288	217	28	bck	bck	NOUN
ejpam-3288	217	29	-	-	PUNCT
ejpam-3288	217	30	algebra	algebra	NOUN
ejpam-3288	217	31	.	.	PUNCT
ejpam-3288	218	1	define	define	VERB
ejpam-3288	218	2	a	a	DET
ejpam-3288	218	3	bipolar	bipolar	ADJ
ejpam-3288	218	4	fuzzy	fuzzy	NOUN
ejpam-3288	218	5	set	set	VERB
ejpam-3288	218	6	a	a	DET
ejpam-3288	218	7	=	=	X
ejpam-3288	218	8	(	(	PUNCT
ejpam-3288	218	9	µpa	µpa	PROPN
ejpam-3288	218	10	,	,	PUNCT
ejpam-3288	218	11	µ	µ	X
ejpam-3288	218	12	n	n	PRON
ejpam-3288	218	13	a	a	NOUN
ejpam-3288	218	14	)	)	PUNCT
ejpam-3288	218	15	in	in	ADP
ejpam-3288	218	16	x	x	PUNCT
ejpam-3288	218	17	as	as	SCONJ
ejpam-3288	218	18	follows	follow	VERB
ejpam-3288	218	19	:	:	PUNCT
ejpam-3288	218	20	µpa(x	µpa(x	X
ejpam-3288	218	21	)	)	PUNCT
ejpam-3288	218	22	=	=	PUNCT
ejpam-3288	218	23			NOUN
ejpam-3288	218	24	0	0	NUM
ejpam-3288	218	25	,	,	PUNCT
ejpam-3288	218	26	if	if	SCONJ
ejpam-3288	218	27	x	x	ADP
ejpam-3288	218	28	=	=	SYM
ejpam-3288	218	29	0	0	NUM
ejpam-3288	218	30	0.6	0.6	NUM
ejpam-3288	218	31	,	,	PUNCT
ejpam-3288	218	32	if	if	SCONJ
ejpam-3288	218	33	x	x	ADP
ejpam-3288	218	34	=	=	PUNCT
ejpam-3288	218	35	a	a	DET
ejpam-3288	218	36	0.4	0.4	NUM
ejpam-3288	218	37	,	,	PUNCT
ejpam-3288	218	38	if	if	SCONJ
ejpam-3288	218	39	x	x	X
ejpam-3288	218	40	=	=	SYM
ejpam-3288	218	41	b	b	PROPN
ejpam-3288	218	42	0.8	0.8	NUM
ejpam-3288	218	43	,	,	PUNCT
ejpam-3288	218	44	if	if	SCONJ
ejpam-3288	218	45	x	x	X
ejpam-3288	218	46	=	=	SYM
ejpam-3288	218	47	c	c	NOUN
ejpam-3288	218	48	0.9	0.9	NUM
ejpam-3288	218	49	,	,	PUNCT
ejpam-3288	218	50	if	if	SCONJ
ejpam-3288	218	51	x	x	X
ejpam-3288	218	52	=	=	SYM
ejpam-3288	218	53	d	d	NOUN
ejpam-3288	218	54	,	,	PUNCT
ejpam-3288	218	55	and	and	CCONJ
ejpam-3288	218	56	µna	µna	ADJ
ejpam-3288	218	57	(	(	PUNCT
ejpam-3288	218	58	0	0	NUM
ejpam-3288	218	59	)	)	PUNCT
ejpam-3288	218	60	=	=	NOUN
ejpam-3288	218	61	µna	µna	ADJ
ejpam-3288	218	62	(	(	PUNCT
ejpam-3288	218	63	a	a	NOUN
ejpam-3288	218	64	)	)	PUNCT
ejpam-3288	218	65	=	=	VERB
ejpam-3288	218	66	µna	µna	ADJ
ejpam-3288	218	67	(	(	PUNCT
ejpam-3288	218	68	b	b	NOUN
ejpam-3288	218	69	)	)	PUNCT
ejpam-3288	218	70	=	=	NOUN
ejpam-3288	218	71	µna	µna	ADJ
ejpam-3288	218	72	(	(	PUNCT
ejpam-3288	218	73	c	c	NOUN
ejpam-3288	218	74	)	)	PUNCT
ejpam-3288	219	1	=	=	NOUN
ejpam-3288	219	2	µna	µna	ADJ
ejpam-3288	219	3	(	(	PUNCT
ejpam-3288	219	4	d	d	NOUN
ejpam-3288	219	5	)	)	PUNCT
ejpam-3288	219	6	=	=	SYM
ejpam-3288	219	7	r	r	NOUN
ejpam-3288	219	8	,	,	PUNCT
ejpam-3288	219	9	where	where	SCONJ
ejpam-3288	219	10	r	r	NOUN
ejpam-3288	219	11	∈	∈	PROPN
ejpam-3288	220	1	[	[	X
ejpam-3288	220	2	−1	−1	NOUN
ejpam-3288	220	3	,	,	PUNCT
ejpam-3288	220	4	0	0	NUM
ejpam-3288	220	5	]	]	PUNCT
ejpam-3288	220	6	.	.	PUNCT
ejpam-3288	221	1	hence	hence	ADV
ejpam-3288	221	2	,	,	PUNCT
ejpam-3288	221	3	a	a	DET
ejpam-3288	221	4	=	=	X
ejpam-3288	221	5	(	(	PUNCT
ejpam-3288	221	6	µpa	µpa	PROPN
ejpam-3288	221	7	,	,	PUNCT
ejpam-3288	221	8	µ	µ	X
ejpam-3288	221	9	n	n	PRON
ejpam-3288	221	10	a	a	PRON
ejpam-3288	221	11	)	)	PUNCT
ejpam-3288	221	12	is	be	AUX
ejpam-3288	221	13	a	a	DET
ejpam-3288	221	14	doubt	doubt	ADV
ejpam-3288	221	15	bipolar	bipolar	ADJ
ejpam-3288	221	16	fuzzy	fuzzy	ADJ
ejpam-3288	221	17	ideal	ideal	NOUN
ejpam-3288	221	18	as	as	ADV
ejpam-3288	221	19	well	well	ADV
ejpam-3288	221	20	as	as	ADP
ejpam-3288	221	21	a	a	DET
ejpam-3288	221	22	doubt	doubt	ADV
ejpam-3288	221	23	bipolar	bipolar	ADJ
ejpam-3288	221	24	fuzzy	fuzzy	ADJ
ejpam-3288	221	25	h	h	NOUN
ejpam-3288	221	26	-	-	PUNCT
ejpam-3288	221	27	ideal	ideal	NOUN
ejpam-3288	221	28	of	of	ADP
ejpam-3288	221	29	x.	x.	PROPN
ejpam-3288	221	30	corollary	corollary	NOUN
ejpam-3288	222	1	1	1	X
ejpam-3288	222	2	.	.	PUNCT
ejpam-3288	223	1	let	let	VERB
ejpam-3288	223	2	a	a	DET
ejpam-3288	223	3	=	=	X
ejpam-3288	223	4	(	(	PUNCT
ejpam-3288	223	5	µpa	µpa	PROPN
ejpam-3288	223	6	,	,	PUNCT
ejpam-3288	223	7	µ	µ	NOUN
ejpam-3288	223	8	n	n	ADV
ejpam-3288	223	9	a	a	PRON
ejpam-3288	223	10	)	)	PUNCT
ejpam-3288	223	11	be	be	AUX
ejpam-3288	223	12	a	a	DET
ejpam-3288	223	13	doubt	doubt	ADV
ejpam-3288	223	14	bipolar	bipolar	ADJ
ejpam-3288	223	15	fuzzy	fuzzy	ADJ
ejpam-3288	223	16	h	h	NOUN
ejpam-3288	223	17	-	-	PUNCT
ejpam-3288	223	18	ideal	ideal	NOUN
ejpam-3288	223	19	of	of	ADP
ejpam-3288	223	20	x.	x.	NOUN
ejpam-3288	223	21	then	then	ADV
ejpam-3288	223	22	the	the	DET
ejpam-3288	223	23	sets	set	NOUN
ejpam-3288	223	24	dµpa	dµpa	VERB
ejpam-3288	223	25	=	=	SYM
ejpam-3288	223	26	{	{	PUNCT
ejpam-3288	223	27	x	x	SYM
ejpam-3288	223	28	∈	∈	PROPN
ejpam-3288	223	29	x	x	X
ejpam-3288	223	30	:	:	PUNCT
ejpam-3288	223	31	µpa(x	µpa(x	X
ejpam-3288	223	32	)	)	PUNCT
ejpam-3288	223	33	=	=	PUNCT
ejpam-3288	223	34	µpa(0	µpa(0	ADJ
ejpam-3288	223	35	)	)	PUNCT
ejpam-3288	223	36	}	}	PUNCT
ejpam-3288	223	37	and	and	CCONJ
ejpam-3288	223	38	dµna	dµna	ADJ
ejpam-3288	223	39	=	=	SYM
ejpam-3288	223	40	{	{	PUNCT
ejpam-3288	223	41	x	x	SYM
ejpam-3288	223	42	∈	∈	PROPN
ejpam-3288	223	43	x	x	X
ejpam-3288	223	44	:	:	PUNCT
ejpam-3288	223	45	µna	µna	ADJ
ejpam-3288	223	46	(	(	PUNCT
ejpam-3288	223	47	x	x	X
ejpam-3288	223	48	)	)	PUNCT
ejpam-3288	223	49	=	=	PRON
ejpam-3288	223	50	µpn	µpn	X
ejpam-3288	223	51	(	(	PUNCT
ejpam-3288	223	52	0	0	NUM
ejpam-3288	223	53	)	)	PUNCT
ejpam-3288	223	54	}	}	PUNCT
ejpam-3288	223	55	are	be	AUX
ejpam-3288	223	56	h	h	NOUN
ejpam-3288	223	57	-	-	PUNCT
ejpam-3288	223	58	ideals	ideal	NOUN
ejpam-3288	223	59	of	of	ADP
ejpam-3288	223	60	x.	x.	NOUN
ejpam-3288	223	61	proof	proof	NOUN
ejpam-3288	223	62	.	.	PUNCT
ejpam-3288	224	1	let	let	VERB
ejpam-3288	224	2	a	a	PRON
ejpam-3288	224	3	=	=	X
ejpam-3288	224	4	(	(	PUNCT
ejpam-3288	224	5	µpa	µpa	PROPN
ejpam-3288	224	6	,	,	PUNCT
ejpam-3288	224	7	µ	µ	NOUN
ejpam-3288	224	8	n	n	ADV
ejpam-3288	224	9	a	a	PRON
ejpam-3288	224	10	)	)	PUNCT
ejpam-3288	224	11	be	be	AUX
ejpam-3288	224	12	a	a	DET
ejpam-3288	224	13	doubt	doubt	ADV
ejpam-3288	224	14	bipolar	bipolar	ADJ
ejpam-3288	224	15	fuzzy	fuzzy	ADJ
ejpam-3288	224	16	h	h	NOUN
ejpam-3288	224	17	-	-	PUNCT
ejpam-3288	224	18	ideal	ideal	NOUN
ejpam-3288	224	19	of	of	ADP
ejpam-3288	224	20	x.	x.	NOUN
ejpam-3288	224	21	obviously	obviously	ADV
ejpam-3288	224	22	,	,	PUNCT
ejpam-3288	224	23	0	0	NUM
ejpam-3288	224	24	∈	∈	PROPN
ejpam-3288	224	25	dµpa	dµpa	NOUN
ejpam-3288	224	26	and	and	CCONJ
ejpam-3288	224	27	0	0	NUM
ejpam-3288	224	28	∈	∈	PROPN
ejpam-3288	224	29	dµna	dµna	NOUN
ejpam-3288	224	30	.	.	PUNCT
ejpam-3288	225	1	now	now	ADV
ejpam-3288	225	2	,	,	PUNCT
ejpam-3288	225	3	let	let	VERB
ejpam-3288	225	4	x	x	PRON
ejpam-3288	225	5	,	,	PUNCT
ejpam-3288	225	6	y	y	PROPN
ejpam-3288	225	7	,	,	PUNCT
ejpam-3288	225	8	z	z	PROPN
ejpam-3288	225	9	∈	∈	PROPN
ejpam-3288	225	10	dµpa	dµpa	VERB
ejpam-3288	225	11	such	such	ADJ
ejpam-3288	225	12	that	that	SCONJ
ejpam-3288	225	13	x	x	SYM
ejpam-3288	225	14	∗	∗	NOUN
ejpam-3288	225	15	(	(	PUNCT
ejpam-3288	225	16	y	y	PROPN
ejpam-3288	225	17	∗	∗	PROPN
ejpam-3288	225	18	z	z	PROPN
ejpam-3288	225	19	)	)	PUNCT
ejpam-3288	225	20	,	,	PUNCT
ejpam-3288	225	21	y	y	PROPN
ejpam-3288	225	22	∈	∈	PROPN
ejpam-3288	225	23	dµpa	dµpa	VERB
ejpam-3288	225	24	.	.	PUNCT
ejpam-3288	226	1	then	then	ADV
ejpam-3288	226	2	µpa(x	µpa(x	PRON
ejpam-3288	226	3	∗	∗	NOUN
ejpam-3288	226	4	(	(	PUNCT
ejpam-3288	226	5	y	y	PROPN
ejpam-3288	226	6	∗	∗	PROPN
ejpam-3288	226	7	z	z	NOUN
ejpam-3288	226	8	)	)	PUNCT
ejpam-3288	226	9	)	)	PUNCT
ejpam-3288	226	10	=	=	PUNCT
ejpam-3288	226	11	µpa(0	µpa(0	X
ejpam-3288	226	12	)	)	PUNCT
ejpam-3288	226	13	=	=	SYM
ejpam-3288	226	14	µpa(y	µpa(y	PROPN
ejpam-3288	226	15	)	)	PUNCT
ejpam-3288	226	16	.	.	PUNCT
ejpam-3288	227	1	now	now	ADV
ejpam-3288	227	2	,	,	PUNCT
ejpam-3288	227	3	µpa(x	µpa(x	PROPN
ejpam-3288	227	4	∗	∗	NOUN
ejpam-3288	227	5	z	z	NOUN
ejpam-3288	227	6	)	)	PUNCT
ejpam-3288	227	7	≤	≤	PROPN
ejpam-3288	227	8	max{µpa(x	max{µpa(x	PROPN
ejpam-3288	227	9	∗	∗	NOUN
ejpam-3288	227	10	(	(	PUNCT
ejpam-3288	227	11	y	y	PROPN
ejpam-3288	227	12	∗	∗	PROPN
ejpam-3288	227	13	z	z	PROPN
ejpam-3288	227	14	)	)	PUNCT
ejpam-3288	227	15	)	)	PUNCT
ejpam-3288	227	16	,	,	PUNCT
ejpam-3288	227	17	µpa(y	µpa(y	PROPN
ejpam-3288	227	18	)	)	PUNCT
ejpam-3288	227	19	}	}	PUNCT
ejpam-3288	227	20	=	=	SYM
ejpam-3288	227	21	µpa(0	µpa(0	NOUN
ejpam-3288	227	22	)	)	PUNCT
ejpam-3288	227	23	.	.	PUNCT
ejpam-3288	228	1	again	again	ADV
ejpam-3288	228	2	,	,	PUNCT
ejpam-3288	228	3	since	since	SCONJ
ejpam-3288	228	4	a	a	DET
ejpam-3288	228	5	=	=	X
ejpam-3288	228	6	(	(	PUNCT
ejpam-3288	228	7	µpa	µpa	PROPN
ejpam-3288	228	8	,	,	PUNCT
ejpam-3288	228	9	µ	µ	X
ejpam-3288	228	10	n	n	PRON
ejpam-3288	228	11	a	a	PRON
ejpam-3288	228	12	)	)	PUNCT
ejpam-3288	228	13	is	be	AUX
ejpam-3288	228	14	a	a	DET
ejpam-3288	228	15	doubt	doubt	ADV
ejpam-3288	228	16	bipolar	bipolar	ADJ
ejpam-3288	228	17	fuzzy	fuzzy	ADJ
ejpam-3288	228	18	h	h	NOUN
ejpam-3288	228	19	-	-	PUNCT
ejpam-3288	228	20	ideal	ideal	NOUN
ejpam-3288	228	21	of	of	ADP
ejpam-3288	228	22	x,µpa(0	x,µpa(0	NOUN
ejpam-3288	228	23	)	)	PUNCT
ejpam-3288	228	24	≤	≤	PUNCT
ejpam-3288	228	25	µpa(x	µpa(x	PRON
ejpam-3288	228	26	∗	∗	NOUN
ejpam-3288	228	27	z	z	PROPN
ejpam-3288	228	28	)	)	PUNCT
ejpam-3288	228	29	.	.	PUNCT
ejpam-3288	229	1	therefore	therefore	ADV
ejpam-3288	229	2	,	,	PUNCT
ejpam-3288	229	3	µpa(0	µpa(0	ADJ
ejpam-3288	229	4	)	)	PUNCT
ejpam-3288	230	1	=	=	SYM
ejpam-3288	230	2	µpa(x	µpa(x	PROPN
ejpam-3288	230	3	∗	∗	NOUN
ejpam-3288	230	4	z	z	PROPN
ejpam-3288	230	5	)	)	PUNCT
ejpam-3288	230	6	.	.	PUNCT
ejpam-3288	231	1	it	it	PRON
ejpam-3288	231	2	follows	follow	VERB
ejpam-3288	231	3	that	that	SCONJ
ejpam-3288	231	4	x	x	SYM
ejpam-3288	231	5	∗	∗	PROPN
ejpam-3288	231	6	z	z	PROPN
ejpam-3288	231	7	∈	∈	PROPN
ejpam-3288	231	8	dµpa	dµpa	NOUN
ejpam-3288	231	9	,	,	PUNCT
ejpam-3288	231	10	for	for	ADP
ejpam-3288	231	11	all	all	DET
ejpam-3288	231	12	x	x	NOUN
ejpam-3288	231	13	,	,	PUNCT
ejpam-3288	231	14	y	y	PROPN
ejpam-3288	231	15	,	,	PUNCT
ejpam-3288	231	16	z	z	PROPN
ejpam-3288	231	17	∈	∈	PROPN
ejpam-3288	231	18	x.	x.	NOUN
ejpam-3288	231	19	therefore	therefore	ADV
ejpam-3288	231	20	,	,	PUNCT
ejpam-3288	231	21	dµpa	dµpa	PROPN
ejpam-3288	231	22	is	be	AUX
ejpam-3288	231	23	an	an	DET
ejpam-3288	231	24	h	h	NOUN
ejpam-3288	231	25	-	-	PUNCT
ejpam-3288	231	26	ideal	ideal	NOUN
ejpam-3288	231	27	of	of	ADP
ejpam-3288	231	28	x.	x.	NOUN
ejpam-3288	231	29	also	also	ADV
ejpam-3288	231	30	,	,	PUNCT
ejpam-3288	231	31	let	let	VERB
ejpam-3288	231	32	x	x	PRON
ejpam-3288	231	33	,	,	PUNCT
ejpam-3288	231	34	y	y	PROPN
ejpam-3288	231	35	,	,	PUNCT
ejpam-3288	231	36	z	z	PROPN
ejpam-3288	231	37	∈	∈	PROPN
ejpam-3288	231	38	dµna	dµna	NOUN
ejpam-3288	231	39	such	such	ADJ
ejpam-3288	231	40	that	that	SCONJ
ejpam-3288	231	41	x	x	SYM
ejpam-3288	231	42	∗	∗	NOUN
ejpam-3288	231	43	(	(	PUNCT
ejpam-3288	231	44	y	y	PROPN
ejpam-3288	231	45	∗	∗	PROPN
ejpam-3288	231	46	z	z	PROPN
ejpam-3288	231	47	)	)	PUNCT
ejpam-3288	231	48	,	,	PUNCT
ejpam-3288	231	49	y	y	PROPN
ejpam-3288	231	50	∈	∈	PROPN
ejpam-3288	231	51	dµna	dµna	NOUN
ejpam-3288	231	52	.	.	PUNCT
ejpam-3288	232	1	then	then	ADV
ejpam-3288	232	2	µna	µna	ADJ
ejpam-3288	232	3	(	(	PUNCT
ejpam-3288	232	4	x	x	SYM
ejpam-3288	232	5	∗	∗	NOUN
ejpam-3288	232	6	(	(	PUNCT
ejpam-3288	232	7	y	y	PROPN
ejpam-3288	232	8	∗	∗	PROPN
ejpam-3288	232	9	z	z	NOUN
ejpam-3288	232	10	)	)	PUNCT
ejpam-3288	232	11	=	=	SYM
ejpam-3288	232	12	µna	µna	ADJ
ejpam-3288	232	13	(	(	PUNCT
ejpam-3288	232	14	0	0	NUM
ejpam-3288	232	15	)	)	PUNCT
ejpam-3288	232	16	=	=	NOUN
ejpam-3288	232	17	µna	µna	ADJ
ejpam-3288	232	18	(	(	PUNCT
ejpam-3288	232	19	y	y	NOUN
ejpam-3288	232	20	)	)	PUNCT
ejpam-3288	232	21	.	.	PUNCT
ejpam-3288	233	1	now	now	ADV
ejpam-3288	233	2	,	,	PUNCT
ejpam-3288	233	3	µna	µna	ADJ
ejpam-3288	233	4	(	(	PUNCT
ejpam-3288	233	5	x	x	NOUN
ejpam-3288	233	6	∗	∗	PROPN
ejpam-3288	233	7	z	z	NOUN
ejpam-3288	233	8	)	)	PUNCT
ejpam-3288	233	9	≥	≥	X
ejpam-3288	233	10	min{µna	min{µna	NOUN
ejpam-3288	233	11	(	(	PUNCT
ejpam-3288	233	12	x	x	NOUN
ejpam-3288	233	13	∗	∗	NOUN
ejpam-3288	233	14	(	(	PUNCT
ejpam-3288	233	15	y	y	PROPN
ejpam-3288	233	16	∗	∗	PROPN
ejpam-3288	233	17	z	z	PROPN
ejpam-3288	233	18	)	)	PUNCT
ejpam-3288	233	19	)	)	PUNCT
ejpam-3288	233	20	,	,	PUNCT
ejpam-3288	233	21	µna	µna	PROPN
ejpam-3288	233	22	(	(	PUNCT
ejpam-3288	233	23	y	y	NOUN
ejpam-3288	233	24	)	)	PUNCT
ejpam-3288	233	25	}	}	PUNCT
ejpam-3288	233	26	=	=	SYM
ejpam-3288	233	27	µna	µna	ADJ
ejpam-3288	233	28	(	(	PUNCT
ejpam-3288	233	29	0	0	NUM
ejpam-3288	233	30	)	)	PUNCT
ejpam-3288	233	31	.	.	PUNCT
ejpam-3288	234	1	again	again	ADV
ejpam-3288	234	2	,	,	PUNCT
ejpam-3288	234	3	since	since	SCONJ
ejpam-3288	234	4	a	a	DET
ejpam-3288	234	5	=	=	X
ejpam-3288	234	6	(	(	PUNCT
ejpam-3288	234	7	µpa	µpa	PROPN
ejpam-3288	234	8	,	,	PUNCT
ejpam-3288	234	9	µ	µ	X
ejpam-3288	234	10	n	n	PRON
ejpam-3288	234	11	a	a	PRON
ejpam-3288	234	12	)	)	PUNCT
ejpam-3288	234	13	is	be	AUX
ejpam-3288	234	14	a	a	DET
ejpam-3288	234	15	doubt	doubt	ADV
ejpam-3288	234	16	bipolar	bipolar	ADJ
ejpam-3288	234	17	fuzzy	fuzzy	ADJ
ejpam-3288	234	18	h	h	NOUN
ejpam-3288	234	19	-	-	PUNCT
ejpam-3288	234	20	ideal	ideal	NOUN
ejpam-3288	234	21	of	of	ADP
ejpam-3288	234	22	x,µna	x,µna	PROPN
ejpam-3288	234	23	(	(	PUNCT
ejpam-3288	234	24	0	0	NUM
ejpam-3288	234	25	)	)	PUNCT
ejpam-3288	234	26	≥	≥	NOUN
ejpam-3288	234	27	µna	µna	ADJ
ejpam-3288	234	28	(	(	PUNCT
ejpam-3288	234	29	x	x	NOUN
ejpam-3288	234	30	∗	∗	PROPN
ejpam-3288	234	31	z	z	NOUN
ejpam-3288	234	32	)	)	PUNCT
ejpam-3288	234	33	.	.	PUNCT
ejpam-3288	235	1	therefore	therefore	ADV
ejpam-3288	235	2	,	,	PUNCT
ejpam-3288	235	3	µna	µna	ADJ
ejpam-3288	235	4	(	(	PUNCT
ejpam-3288	235	5	0	0	NUM
ejpam-3288	235	6	)	)	PUNCT
ejpam-3288	235	7	=	=	NOUN
ejpam-3288	235	8	µna	µna	ADJ
ejpam-3288	235	9	(	(	PUNCT
ejpam-3288	235	10	x	x	NOUN
ejpam-3288	235	11	∗	∗	PROPN
ejpam-3288	235	12	z	z	NOUN
ejpam-3288	235	13	)	)	PUNCT
ejpam-3288	235	14	.	.	PUNCT
ejpam-3288	236	1	it	it	PRON
ejpam-3288	236	2	follows	follow	VERB
ejpam-3288	236	3	that	that	SCONJ
ejpam-3288	236	4	x	x	NOUN
ejpam-3288	236	5	∗	∗	NOUN
ejpam-3288	236	6	z	z	PROPN
ejpam-3288	236	7	∈	∈	PROPN
ejpam-3288	236	8	dµna	dµna	NOUN
ejpam-3288	236	9	,	,	PUNCT
ejpam-3288	236	10	for	for	ADP
ejpam-3288	236	11	all	all	DET
ejpam-3288	236	12	x	x	NOUN
ejpam-3288	236	13	,	,	PUNCT
ejpam-3288	236	14	y	y	PROPN
ejpam-3288	236	15	,	,	PUNCT
ejpam-3288	236	16	z	z	PROPN
ejpam-3288	236	17	∈	∈	PROPN
ejpam-3288	236	18	x.	x.	NOUN
ejpam-3288	236	19	therefore	therefore	ADV
ejpam-3288	236	20	,	,	PUNCT
ejpam-3288	236	21	dµna	dµna	PROPN
ejpam-3288	236	22	is	be	AUX
ejpam-3288	236	23	an	an	DET
ejpam-3288	236	24	h	h	NOUN
ejpam-3288	236	25	-	-	PUNCT
ejpam-3288	236	26	ideal	ideal	NOUN
ejpam-3288	236	27	of	of	ADP
ejpam-3288	236	28	x.	x.	PROPN
ejpam-3288	236	29	lemma	lemma	PROPN
ejpam-3288	237	1	2	2	X
ejpam-3288	237	2	.	.	PUNCT
ejpam-3288	237	3	let	let	VERB
ejpam-3288	237	4	µ	µ	X
ejpam-3288	237	5	be	be	AUX
ejpam-3288	237	6	a	a	DET
ejpam-3288	237	7	fuzzy	fuzzy	ADJ
ejpam-3288	237	8	set	set	NOUN
ejpam-3288	237	9	in	in	ADP
ejpam-3288	237	10	x.	x.	NOUN
ejpam-3288	237	11	then	then	ADV
ejpam-3288	237	12	the	the	DET
ejpam-3288	237	13	following	follow	VERB
ejpam-3288	237	14	statements	statement	NOUN
ejpam-3288	237	15	holds	hold	VERB
ejpam-3288	237	16	,	,	PUNCT
ejpam-3288	237	17	for	for	ADP
ejpam-3288	237	18	all	all	DET
ejpam-3288	237	19	x	x	NOUN
ejpam-3288	237	20	,	,	PUNCT
ejpam-3288	237	21	y	y	PROPN
ejpam-3288	237	22	∈	∈	PROPN
ejpam-3288	237	23	x	x	PROPN
ejpam-3288	237	24	,	,	PUNCT
ejpam-3288	237	25	a.	a.	PROPN
ejpam-3288	237	26	al	al	PROPN
ejpam-3288	237	27	-	-	PROPN
ejpam-3288	237	28	masarwah	masarwah	PROPN
ejpam-3288	237	29	,	,	PUNCT
ejpam-3288	237	30	a.	a.	NOUN
ejpam-3288	237	31	g.	g.	PROPN
ejpam-3288	237	32	ahmad	ahmad	PROPN
ejpam-3288	237	33	/	/	SYM
ejpam-3288	237	34	eur	eur	PROPN
ejpam-3288	237	35	.	.	PUNCT
ejpam-3288	238	1	j.	j.	PROPN
ejpam-3288	238	2	pure	pure	PROPN
ejpam-3288	238	3	appl	appl	PROPN
ejpam-3288	238	4	.	.	PROPN
ejpam-3288	238	5	math	math	PROPN
ejpam-3288	238	6	,	,	PUNCT
ejpam-3288	238	7	11	11	NUM
ejpam-3288	238	8	(	(	PUNCT
ejpam-3288	238	9	3	3	NUM
ejpam-3288	238	10	)	)	PUNCT
ejpam-3288	238	11	(	(	PUNCT
ejpam-3288	238	12	2018	2018	NUM
ejpam-3288	238	13	)	)	PUNCT
ejpam-3288	238	14	,	,	PUNCT
ejpam-3288	238	15	652	652	NUM
ejpam-3288	238	16	-	-	SYM
ejpam-3288	238	17	670	670	NUM
ejpam-3288	238	18	663	663	NUM
ejpam-3288	238	19	(	(	PUNCT
ejpam-3288	238	20	1	1	NUM
ejpam-3288	238	21	)	)	PUNCT
ejpam-3288	238	22	1−max{µ(x	1−max{µ(x	NUM
ejpam-3288	238	23	)	)	PUNCT
ejpam-3288	238	24	,	,	PUNCT
ejpam-3288	238	25	µ(y	µ(y	PROPN
ejpam-3288	238	26	)	)	PUNCT
ejpam-3288	238	27	}	}	PUNCT
ejpam-3288	238	28	=	=	SYM
ejpam-3288	239	1	min{1−	min{1−	ADJ
ejpam-3288	239	2	µ(x	µ(x	NOUN
ejpam-3288	239	3	)	)	PUNCT
ejpam-3288	239	4	,	,	PUNCT
ejpam-3288	239	5	1−	1−	NUM
ejpam-3288	239	6	µ(y	µ(y	NOUN
ejpam-3288	239	7	)	)	PUNCT
ejpam-3288	239	8	}	}	PUNCT
ejpam-3288	239	9	,	,	PUNCT
ejpam-3288	239	10	(	(	PUNCT
ejpam-3288	239	11	2	2	X
ejpam-3288	239	12	)	)	PUNCT
ejpam-3288	239	13	1−min{µ(x	1−min{µ(x	NUM
ejpam-3288	239	14	)	)	PUNCT
ejpam-3288	239	15	,	,	PUNCT
ejpam-3288	239	16	µ(y	µ(y	PROPN
ejpam-3288	239	17	)	)	PUNCT
ejpam-3288	239	18	}	}	PUNCT
ejpam-3288	239	19	=	=	SYM
ejpam-3288	239	20	max{1−	max{1−	NOUN
ejpam-3288	239	21	µ(x	µ(x	NUM
ejpam-3288	239	22	)	)	PUNCT
ejpam-3288	239	23	,	,	PUNCT
ejpam-3288	239	24	1−	1−	NUM
ejpam-3288	239	25	µ(y	µ(y	NOUN
ejpam-3288	239	26	)	)	PUNCT
ejpam-3288	239	27	}	}	PUNCT
ejpam-3288	239	28	.	.	PUNCT
ejpam-3288	240	1	proof	proof	NOUN
ejpam-3288	240	2	.	.	PUNCT
ejpam-3288	241	1	(	(	PUNCT
ejpam-3288	241	2	1	1	X
ejpam-3288	241	3	)	)	PUNCT
ejpam-3288	241	4	if	if	SCONJ
ejpam-3288	241	5	max{µ(x	max{µ(x	PROPN
ejpam-3288	241	6	)	)	PUNCT
ejpam-3288	241	7	,	,	PUNCT
ejpam-3288	241	8	µ(y	µ(y	PROPN
ejpam-3288	241	9	)	)	PUNCT
ejpam-3288	241	10	}	}	PUNCT
ejpam-3288	241	11	=	=	SYM
ejpam-3288	241	12	µ(x	µ(x	NUM
ejpam-3288	241	13	)	)	PUNCT
ejpam-3288	241	14	,	,	PUNCT
ejpam-3288	241	15	then	then	ADV
ejpam-3288	241	16	µ(y	µ(y	PROPN
ejpam-3288	241	17	)	)	PUNCT
ejpam-3288	241	18	≤	≤	NOUN
ejpam-3288	241	19	µ(x	µ(x	NOUN
ejpam-3288	241	20	)	)	PUNCT
ejpam-3288	241	21	.	.	PUNCT
ejpam-3288	242	1	thus	thus	ADV
ejpam-3288	242	2	,	,	PUNCT
ejpam-3288	242	3	1−µ(y	1−µ(y	NUM
ejpam-3288	242	4	)	)	PUNCT
ejpam-3288	242	5	≥	≥	NOUN
ejpam-3288	242	6	1−µ(x	1−µ(x	NUM
ejpam-3288	242	7	)	)	PUNCT
ejpam-3288	242	8	,	,	PUNCT
ejpam-3288	242	9	so	so	ADV
ejpam-3288	242	10	min{1−µ(x	min{1−µ(x	NOUN
ejpam-3288	242	11	)	)	PUNCT
ejpam-3288	242	12	,	,	PUNCT
ejpam-3288	242	13	1−µ(y	1−µ(y	NUM
ejpam-3288	242	14	)	)	PUNCT
ejpam-3288	242	15	}	}	PUNCT
ejpam-3288	243	1	=	=	SYM
ejpam-3288	243	2	1−µ(x	1−µ(x	X
ejpam-3288	243	3	)	)	PUNCT
ejpam-3288	243	4	=	=	SYM
ejpam-3288	243	5	1−max{µ(x	1−max{µ(x	NUM
ejpam-3288	243	6	)	)	PUNCT
ejpam-3288	243	7	,	,	PUNCT
ejpam-3288	243	8	µ(y	µ(y	PROPN
ejpam-3288	243	9	)	)	PUNCT
ejpam-3288	243	10	}	}	PUNCT
ejpam-3288	243	11	.	.	PUNCT
ejpam-3288	244	1	similarly	similarly	ADV
ejpam-3288	244	2	,	,	PUNCT
ejpam-3288	244	3	if	if	SCONJ
ejpam-3288	244	4	max{µ(x	max{µ(x	PROPN
ejpam-3288	244	5	)	)	PUNCT
ejpam-3288	244	6	,	,	PUNCT
ejpam-3288	244	7	µ(y	µ(y	PROPN
ejpam-3288	244	8	)	)	PUNCT
ejpam-3288	244	9	}	}	PUNCT
ejpam-3288	244	10	=	=	SYM
ejpam-3288	244	11	µ(y	µ(y	PROPN
ejpam-3288	244	12	)	)	PUNCT
ejpam-3288	244	13	,	,	PUNCT
ejpam-3288	244	14	then	then	ADV
ejpam-3288	244	15	min{1−	min{1−	VERB
ejpam-3288	244	16	µ(x	µ(x	NOUN
ejpam-3288	244	17	)	)	PUNCT
ejpam-3288	244	18	,	,	PUNCT
ejpam-3288	244	19	1−	1−	NUM
ejpam-3288	244	20	µ(y	µ(y	NOUN
ejpam-3288	244	21	)	)	PUNCT
ejpam-3288	244	22	}	}	PUNCT
ejpam-3288	244	23	=	=	SYM
ejpam-3288	244	24	1−	1−	NUM
ejpam-3288	244	25	µ(y	µ(y	PROPN
ejpam-3288	244	26	)	)	PUNCT
ejpam-3288	244	27	=	=	SYM
ejpam-3288	244	28	1−max{µ(x	1−max{µ(x	NUM
ejpam-3288	244	29	)	)	PUNCT
ejpam-3288	244	30	,	,	PUNCT
ejpam-3288	244	31	µ(y	µ(y	PROPN
ejpam-3288	244	32	)	)	PUNCT
ejpam-3288	244	33	}	}	PUNCT
ejpam-3288	244	34	.	.	PUNCT
ejpam-3288	245	1	(	(	PUNCT
ejpam-3288	245	2	2	2	X
ejpam-3288	245	3	)	)	PUNCT
ejpam-3288	245	4	if	if	SCONJ
ejpam-3288	245	5	min{µ(x	min{µ(x	PROPN
ejpam-3288	245	6	)	)	PUNCT
ejpam-3288	245	7	,	,	PUNCT
ejpam-3288	245	8	µ(y	µ(y	PROPN
ejpam-3288	245	9	)	)	PUNCT
ejpam-3288	245	10	}	}	PUNCT
ejpam-3288	245	11	=	=	SYM
ejpam-3288	245	12	µ(x	µ(x	NUM
ejpam-3288	245	13	)	)	PUNCT
ejpam-3288	245	14	,	,	PUNCT
ejpam-3288	245	15	then	then	ADV
ejpam-3288	245	16	µ(x	µ(x	NOUN
ejpam-3288	245	17	)	)	PUNCT
ejpam-3288	245	18	≤	≤	NUM
ejpam-3288	245	19	µ(y	µ(y	NUM
ejpam-3288	245	20	)	)	PUNCT
ejpam-3288	245	21	.	.	PUNCT
ejpam-3288	246	1	thus	thus	ADV
ejpam-3288	246	2	,	,	PUNCT
ejpam-3288	246	3	1−	1−	NUM
ejpam-3288	246	4	µ(x	µ(x	X
ejpam-3288	246	5	)	)	PUNCT
ejpam-3288	246	6	≥	≥	NOUN
ejpam-3288	246	7	1−	1−	NUM
ejpam-3288	246	8	µ(y	µ(y	NUM
ejpam-3288	246	9	)	)	PUNCT
ejpam-3288	246	10	,	,	PUNCT
ejpam-3288	246	11	so	so	ADV
ejpam-3288	246	12	max{1−	max{1−	ADJ
ejpam-3288	246	13	µ(x	µ(x	NUM
ejpam-3288	246	14	)	)	PUNCT
ejpam-3288	246	15	,	,	PUNCT
ejpam-3288	246	16	1	1	NUM
ejpam-3288	246	17	−	−	PROPN
ejpam-3288	246	18	µ(y	µ(y	NOUN
ejpam-3288	246	19	)	)	PUNCT
ejpam-3288	246	20	}	}	PUNCT
ejpam-3288	247	1	=	=	SYM
ejpam-3288	247	2	1	1	NUM
ejpam-3288	247	3	−	−	NOUN
ejpam-3288	247	4	µ(x	µ(x	NOUN
ejpam-3288	247	5	)	)	PUNCT
ejpam-3288	247	6	=	=	SYM
ejpam-3288	247	7	1	1	NUM
ejpam-3288	247	8	−	−	PROPN
ejpam-3288	247	9	min{µ(x	min{µ(x	PROPN
ejpam-3288	247	10	)	)	PUNCT
ejpam-3288	247	11	,	,	PUNCT
ejpam-3288	247	12	µ(y	µ(y	PROPN
ejpam-3288	247	13	)	)	PUNCT
ejpam-3288	247	14	}	}	PUNCT
ejpam-3288	247	15	.	.	PUNCT
ejpam-3288	248	1	similarly	similarly	ADV
ejpam-3288	248	2	,	,	PUNCT
ejpam-3288	248	3	if	if	SCONJ
ejpam-3288	248	4	min{µ(x	min{µ(x	PROPN
ejpam-3288	248	5	)	)	PUNCT
ejpam-3288	248	6	,	,	PUNCT
ejpam-3288	248	7	µ(y	µ(y	PROPN
ejpam-3288	248	8	)	)	PUNCT
ejpam-3288	248	9	}	}	PUNCT
ejpam-3288	248	10	=	=	SYM
ejpam-3288	248	11	µ(y	µ(y	PROPN
ejpam-3288	248	12	)	)	PUNCT
ejpam-3288	248	13	,	,	PUNCT
ejpam-3288	248	14	then	then	ADV
ejpam-3288	248	15	max{1−	max{1−	PROPN
ejpam-3288	248	16	µ(x	µ(x	NOUN
ejpam-3288	248	17	)	)	PUNCT
ejpam-3288	248	18	,	,	PUNCT
ejpam-3288	248	19	1−	1−	NUM
ejpam-3288	248	20	µ(y	µ(y	NOUN
ejpam-3288	248	21	)	)	PUNCT
ejpam-3288	248	22	}	}	PUNCT
ejpam-3288	248	23	=	=	SYM
ejpam-3288	248	24	1−	1−	NUM
ejpam-3288	248	25	µ(y	µ(y	PROPN
ejpam-3288	248	26	)	)	PUNCT
ejpam-3288	248	27	=	=	PUNCT
ejpam-3288	249	1	1−min{µ(x	1−min{µ(x	NUM
ejpam-3288	249	2	)	)	PUNCT
ejpam-3288	249	3	,	,	PUNCT
ejpam-3288	249	4	µ(y	µ(y	PROPN
ejpam-3288	249	5	)	)	PUNCT
ejpam-3288	249	6	}	}	PUNCT
ejpam-3288	249	7	.	.	PUNCT
ejpam-3288	250	1	remark	remark	NOUN
ejpam-3288	250	2	1	1	NUM
ejpam-3288	250	3	.	.	PUNCT
ejpam-3288	251	1	a	a	PRON
ejpam-3288	251	2	=	=	X
ejpam-3288	251	3	(	(	PUNCT
ejpam-3288	251	4	µpa	µpa	PROPN
ejpam-3288	251	5	,	,	PUNCT
ejpam-3288	251	6	µ	µ	X
ejpam-3288	251	7	n	n	PRON
ejpam-3288	251	8	a	a	PRON
ejpam-3288	251	9	)	)	PUNCT
ejpam-3288	251	10	is	be	AUX
ejpam-3288	251	11	a	a	DET
ejpam-3288	251	12	bipolar	bipolar	ADJ
ejpam-3288	251	13	fuzzy	fuzzy	ADJ
ejpam-3288	251	14	set	set	NOUN
ejpam-3288	251	15	defined	define	VERB
ejpam-3288	251	16	on	on	ADP
ejpam-3288	251	17	any	any	DET
ejpam-3288	251	18	universe	universe	NOUN
ejpam-3288	251	19	set	set	NOUN
ejpam-3288	251	20	x	x	PUNCT
ejpam-3288	251	21	if	if	SCONJ
ejpam-3288	252	1	and	and	CCONJ
ejpam-3288	252	2	only	only	ADV
ejpam-3288	252	3	if	if	SCONJ
ejpam-3288	252	4	µpa	µpa	PROPN
ejpam-3288	252	5	and	and	CCONJ
ejpam-3288	252	6	−µna	−µna	NOUN
ejpam-3288	252	7	are	be	AUX
ejpam-3288	252	8	fuzzy	fuzzy	ADJ
ejpam-3288	252	9	subsets	subset	NOUN
ejpam-3288	252	10	of	of	ADP
ejpam-3288	252	11	x.	x.	PROPN
ejpam-3288	252	12	theorem	theorem	VERB
ejpam-3288	252	13	5	5	NUM
ejpam-3288	252	14	.	.	PUNCT
ejpam-3288	253	1	a	a	DET
ejpam-3288	253	2	bipolar	bipolar	ADJ
ejpam-3288	253	3	fuzzy	fuzzy	NOUN
ejpam-3288	253	4	set	set	VERB
ejpam-3288	253	5	a	a	PRON
ejpam-3288	253	6	=	=	X
ejpam-3288	253	7	(	(	PUNCT
ejpam-3288	253	8	µpa	µpa	PROPN
ejpam-3288	253	9	,	,	PUNCT
ejpam-3288	253	10	µ	µ	X
ejpam-3288	253	11	n	n	PRON
ejpam-3288	253	12	a	a	PRON
ejpam-3288	253	13	)	)	PUNCT
ejpam-3288	253	14	is	be	AUX
ejpam-3288	253	15	a	a	DET
ejpam-3288	253	16	doubt	doubt	ADV
ejpam-3288	253	17	bipolar	bipolar	ADJ
ejpam-3288	253	18	fuzzy	fuzzy	ADJ
ejpam-3288	253	19	h	h	NOUN
ejpam-3288	253	20	-	-	PUNCT
ejpam-3288	253	21	ideal	ideal	NOUN
ejpam-3288	253	22	of	of	ADP
ejpam-3288	253	23	x	x	SYM
ejpam-3288	253	24	if	if	SCONJ
ejpam-3288	253	25	and	and	CCONJ
ejpam-3288	253	26	only	only	ADV
ejpam-3288	253	27	if	if	SCONJ
ejpam-3288	253	28	the	the	DET
ejpam-3288	253	29	fuzzy	fuzzy	ADJ
ejpam-3288	253	30	subsets	subset	NOUN
ejpam-3288	253	31	µpa	µpa	PROPN
ejpam-3288	253	32	and	and	CCONJ
ejpam-3288	253	33	−µna	−µna	NOUN
ejpam-3288	253	34	are	be	AUX
ejpam-3288	253	35	doubt	doubt	ADV
ejpam-3288	253	36	fuzzy	fuzzy	ADJ
ejpam-3288	253	37	h	h	NOUN
ejpam-3288	253	38	-	-	PUNCT
ejpam-3288	253	39	ideals	ideal	NOUN
ejpam-3288	253	40	of	of	ADP
ejpam-3288	253	41	x.	x.	NOUN
ejpam-3288	253	42	proof	proof	NOUN
ejpam-3288	253	43	.	.	PUNCT
ejpam-3288	254	1	let	let	VERB
ejpam-3288	254	2	a	a	PRON
ejpam-3288	254	3	=	=	X
ejpam-3288	254	4	(	(	PUNCT
ejpam-3288	254	5	µpa	µpa	PROPN
ejpam-3288	254	6	,	,	PUNCT
ejpam-3288	254	7	µ	µ	NOUN
ejpam-3288	254	8	n	n	ADV
ejpam-3288	254	9	a	a	PRON
ejpam-3288	254	10	)	)	PUNCT
ejpam-3288	254	11	be	be	AUX
ejpam-3288	254	12	a	a	DET
ejpam-3288	254	13	doubt	doubt	ADV
ejpam-3288	254	14	bipolar	bipolar	ADJ
ejpam-3288	254	15	fuzzy	fuzzy	ADJ
ejpam-3288	254	16	h	h	NOUN
ejpam-3288	254	17	-	-	PUNCT
ejpam-3288	254	18	ideal	ideal	NOUN
ejpam-3288	254	19	of	of	ADP
ejpam-3288	254	20	x.	x.	NOUN
ejpam-3288	254	21	then	then	ADV
ejpam-3288	254	22	clearly	clearly	ADV
ejpam-3288	254	23	µpa	µpa	PROPN
ejpam-3288	254	24	is	be	AUX
ejpam-3288	254	25	a	a	DET
ejpam-3288	254	26	doubt	doubt	ADV
ejpam-3288	254	27	fuzzy	fuzzy	ADJ
ejpam-3288	254	28	h	h	NOUN
ejpam-3288	254	29	-	-	PUNCT
ejpam-3288	254	30	ideal	ideal	NOUN
ejpam-3288	254	31	ofx.also	ofx.also	ADV
ejpam-3288	254	32	,	,	PUNCT
ejpam-3288	254	33	µna	µna	ADJ
ejpam-3288	254	34	(	(	PUNCT
ejpam-3288	254	35	0	0	NUM
ejpam-3288	254	36	)	)	PUNCT
ejpam-3288	254	37	≥	≥	NOUN
ejpam-3288	254	38	µna	µna	ADJ
ejpam-3288	254	39	(	(	PUNCT
ejpam-3288	254	40	x	x	NOUN
ejpam-3288	254	41	)	)	PUNCT
ejpam-3288	254	42	and	and	CCONJ
ejpam-3288	254	43	µna	µna	ADJ
ejpam-3288	254	44	(	(	PUNCT
ejpam-3288	254	45	x∗z	x∗z	NUM
ejpam-3288	254	46	)	)	PUNCT
ejpam-3288	254	47	≥	≥	NOUN
ejpam-3288	254	48	min{µna	min{µna	NOUN
ejpam-3288	254	49	(	(	PUNCT
ejpam-3288	254	50	x∗(y∗z	x∗(y∗z	PROPN
ejpam-3288	254	51	)	)	PUNCT
ejpam-3288	254	52	)	)	PUNCT
ejpam-3288	254	53	,	,	PUNCT
ejpam-3288	254	54	µna	µna	PROPN
ejpam-3288	254	55	(	(	PUNCT
ejpam-3288	254	56	y	y	NOUN
ejpam-3288	254	57	)	)	PUNCT
ejpam-3288	254	58	}	}	PUNCT
ejpam-3288	254	59	,	,	PUNCT
ejpam-3288	254	60	implies	imply	VERB
ejpam-3288	254	61	that	that	SCONJ
ejpam-3288	254	62	,	,	PUNCT
ejpam-3288	254	63	−µna	−µna	X
ejpam-3288	254	64	(	(	PUNCT
ejpam-3288	254	65	0	0	NUM
ejpam-3288	254	66	)	)	PUNCT
ejpam-3288	254	67	≤	≤	NUM
ejpam-3288	254	68	−µna	−µna	NOUN
ejpam-3288	254	69	(	(	PUNCT
ejpam-3288	254	70	x	x	X
ejpam-3288	254	71	)	)	PUNCT
ejpam-3288	254	72	and	and	CCONJ
ejpam-3288	254	73	−µna	−µna	NOUN
ejpam-3288	254	74	(	(	PUNCT
ejpam-3288	254	75	x	x	X
ejpam-3288	254	76	∗	∗	PROPN
ejpam-3288	254	77	z	z	NOUN
ejpam-3288	254	78	)	)	PUNCT
ejpam-3288	254	79	≤	≤	NUM
ejpam-3288	254	80	−min{µna	−min{µna	ADJ
ejpam-3288	254	81	(	(	PUNCT
ejpam-3288	254	82	x	x	SYM
ejpam-3288	254	83	∗	∗	NOUN
ejpam-3288	254	84	(	(	PUNCT
ejpam-3288	254	85	y	y	PROPN
ejpam-3288	254	86	∗	∗	PROPN
ejpam-3288	254	87	z	z	PROPN
ejpam-3288	254	88	)	)	PUNCT
ejpam-3288	254	89	)	)	PUNCT
ejpam-3288	254	90	,	,	PUNCT
ejpam-3288	254	91	µna	µna	PROPN
ejpam-3288	254	92	(	(	PUNCT
ejpam-3288	254	93	y	y	NOUN
ejpam-3288	254	94	)	)	PUNCT
ejpam-3288	254	95	}	}	PUNCT
ejpam-3288	255	1	=	=	SYM
ejpam-3288	255	2	max{−µna	max{−µna	PROPN
ejpam-3288	255	3	(	(	PUNCT
ejpam-3288	255	4	x	x	NOUN
ejpam-3288	255	5	∗	∗	NOUN
ejpam-3288	255	6	(	(	PUNCT
ejpam-3288	255	7	y	y	PROPN
ejpam-3288	255	8	∗	∗	X
ejpam-3288	255	9	z)),−µna	z)),−µna	NOUN
ejpam-3288	255	10	(	(	PUNCT
ejpam-3288	255	11	y	y	NOUN
ejpam-3288	255	12	)	)	PUNCT
ejpam-3288	255	13	}	}	PUNCT
ejpam-3288	255	14	.	.	PUNCT
ejpam-3288	256	1	therefore	therefore	ADV
ejpam-3288	256	2	,	,	PUNCT
ejpam-3288	256	3	−µna	−µna	NOUN
ejpam-3288	256	4	is	be	AUX
ejpam-3288	256	5	a	a	DET
ejpam-3288	256	6	doubt	doubt	ADV
ejpam-3288	256	7	fuzzy	fuzzy	ADJ
ejpam-3288	256	8	h	h	NOUN
ejpam-3288	256	9	-	-	PUNCT
ejpam-3288	256	10	ideal	ideal	NOUN
ejpam-3288	256	11	of	of	ADP
ejpam-3288	256	12	x.	x.	NOUN
ejpam-3288	256	13	conversely	conversely	ADV
ejpam-3288	256	14	,	,	PUNCT
ejpam-3288	256	15	assume	assume	VERB
ejpam-3288	256	16	that	that	SCONJ
ejpam-3288	256	17	µpa	µpa	NOUN
ejpam-3288	256	18	and	and	CCONJ
ejpam-3288	256	19	−µna	−µna	NOUN
ejpam-3288	256	20	are	be	AUX
ejpam-3288	256	21	doubt	doubt	ADV
ejpam-3288	256	22	fuzzy	fuzzy	ADJ
ejpam-3288	256	23	h	h	NOUN
ejpam-3288	256	24	-	-	PUNCT
ejpam-3288	256	25	ideals	ideal	NOUN
ejpam-3288	256	26	of	of	ADP
ejpam-3288	256	27	x.	x.	NOUN
ejpam-3288	256	28	so	so	SCONJ
ejpam-3288	256	29	that	that	SCONJ
ejpam-3288	256	30	µpa(0	µpa(0	ADV
ejpam-3288	256	31	)	)	PUNCT
ejpam-3288	256	32	≤	≤	NUM
ejpam-3288	256	33	µpa(x	µpa(x	NOUN
ejpam-3288	256	34	)	)	PUNCT
ejpam-3288	256	35	and	and	CCONJ
ejpam-3288	256	36	µpa(x∗z	µpa(x∗z	PROPN
ejpam-3288	256	37	)	)	PUNCT
ejpam-3288	256	38	≤	≤	NOUN
ejpam-3288	256	39	max{µpa(x∗(y∗z	max{µpa(x∗(y∗z	ADJ
ejpam-3288	256	40	)	)	PUNCT
ejpam-3288	256	41	)	)	PUNCT
ejpam-3288	256	42	,	,	PUNCT
ejpam-3288	256	43	µpa(y	µpa(y	PROPN
ejpam-3288	256	44	)	)	PUNCT
ejpam-3288	256	45	}	}	PUNCT
ejpam-3288	256	46	,	,	PUNCT
ejpam-3288	256	47	for	for	ADP
ejpam-3288	256	48	all	all	DET
ejpam-3288	256	49	x	x	NOUN
ejpam-3288	256	50	,	,	PUNCT
ejpam-3288	256	51	y	y	PROPN
ejpam-3288	256	52	,	,	PUNCT
ejpam-3288	256	53	z	z	PROPN
ejpam-3288	256	54	∈	∈	PROPN
ejpam-3288	256	55	x.	x.	NOUN
ejpam-3288	256	56	now	now	ADV
ejpam-3288	256	57	,	,	PUNCT
ejpam-3288	256	58	we	we	PRON
ejpam-3288	256	59	prove	prove	VERB
ejpam-3288	256	60	that	that	SCONJ
ejpam-3288	256	61	µna	µna	ADJ
ejpam-3288	256	62	(	(	PUNCT
ejpam-3288	256	63	0	0	NUM
ejpam-3288	256	64	)	)	PUNCT
ejpam-3288	256	65	≥	≥	NOUN
ejpam-3288	256	66	µna	µna	ADJ
ejpam-3288	256	67	(	(	PUNCT
ejpam-3288	256	68	x	x	NOUN
ejpam-3288	256	69	)	)	PUNCT
ejpam-3288	256	70	and	and	CCONJ
ejpam-3288	256	71	µna	µna	ADJ
ejpam-3288	256	72	(	(	PUNCT
ejpam-3288	256	73	x	x	NOUN
ejpam-3288	256	74	∗	∗	PROPN
ejpam-3288	256	75	z	z	NOUN
ejpam-3288	256	76	)	)	PUNCT
ejpam-3288	256	77	≥	≥	X
ejpam-3288	256	78	min{µna	min{µna	NOUN
ejpam-3288	256	79	(	(	PUNCT
ejpam-3288	256	80	x	x	NOUN
ejpam-3288	256	81	∗	∗	NOUN
ejpam-3288	256	82	(	(	PUNCT
ejpam-3288	256	83	y	y	PROPN
ejpam-3288	256	84	∗	∗	PROPN
ejpam-3288	256	85	z	z	PROPN
ejpam-3288	256	86	)	)	PUNCT
ejpam-3288	256	87	)	)	PUNCT
ejpam-3288	256	88	,	,	PUNCT
ejpam-3288	256	89	µna	µna	PROPN
ejpam-3288	256	90	(	(	PUNCT
ejpam-3288	256	91	y	y	NOUN
ejpam-3288	256	92	)	)	PUNCT
ejpam-3288	256	93	}	}	PUNCT
ejpam-3288	256	94	for	for	ADP
ejpam-3288	256	95	all	all	DET
ejpam-3288	256	96	x	x	NOUN
ejpam-3288	256	97	,	,	PUNCT
ejpam-3288	256	98	y	y	PROPN
ejpam-3288	256	99	,	,	PUNCT
ejpam-3288	256	100	z	z	PROPN
ejpam-3288	256	101	∈	∈	PROPN
ejpam-3288	256	102	x.	x.	NOUN
ejpam-3288	256	103	since	since	SCONJ
ejpam-3288	256	104	−µna	−µna	NOUN
ejpam-3288	256	105	is	be	AUX
ejpam-3288	256	106	a	a	DET
ejpam-3288	256	107	doubt	doubt	ADV
ejpam-3288	256	108	fuzzy	fuzzy	ADJ
ejpam-3288	256	109	h	h	NOUN
ejpam-3288	256	110	-	-	PUNCT
ejpam-3288	256	111	ideal	ideal	NOUN
ejpam-3288	256	112	of	of	ADP
ejpam-3288	256	113	x	x	PRON
ejpam-3288	256	114	,	,	PUNCT
ejpam-3288	256	115	so	so	SCONJ
ejpam-3288	256	116	that	that	SCONJ
ejpam-3288	256	117	−µna	−µna	NOUN
ejpam-3288	256	118	(	(	PUNCT
ejpam-3288	256	119	0	0	NUM
ejpam-3288	256	120	)	)	PUNCT
ejpam-3288	256	121	≤	≤	NUM
ejpam-3288	256	122	−µna	−µna	NOUN
ejpam-3288	256	123	(	(	PUNCT
ejpam-3288	256	124	x	x	X
ejpam-3288	256	125	)	)	PUNCT
ejpam-3288	256	126	and	and	CCONJ
ejpam-3288	256	127	−µna	−µna	NOUN
ejpam-3288	256	128	(	(	PUNCT
ejpam-3288	256	129	x	x	X
ejpam-3288	256	130	∗	∗	X
ejpam-3288	256	131	z	z	NOUN
ejpam-3288	256	132	)	)	PUNCT
ejpam-3288	256	133	≤	≤	NOUN
ejpam-3288	256	134	max{−µna	max{−µna	PROPN
ejpam-3288	256	135	(	(	PUNCT
ejpam-3288	256	136	x	x	NOUN
ejpam-3288	256	137	∗	∗	NOUN
ejpam-3288	256	138	(	(	PUNCT
ejpam-3288	256	139	y	y	PROPN
ejpam-3288	256	140	∗	∗	X
ejpam-3288	256	141	z)),−µna	z)),−µna	NOUN
ejpam-3288	256	142	(	(	PUNCT
ejpam-3288	256	143	y	y	NOUN
ejpam-3288	256	144	)	)	PUNCT
ejpam-3288	256	145	}	}	PUNCT
ejpam-3288	257	1	=	=	SYM
ejpam-3288	257	2	−min{µna	−min{µna	ADJ
ejpam-3288	257	3	(	(	PUNCT
ejpam-3288	257	4	x	x	SYM
ejpam-3288	257	5	∗	∗	NOUN
ejpam-3288	257	6	(	(	PUNCT
ejpam-3288	257	7	y	y	PROPN
ejpam-3288	257	8	∗	∗	PROPN
ejpam-3288	257	9	z	z	PROPN
ejpam-3288	257	10	)	)	PUNCT
ejpam-3288	257	11	)	)	PUNCT
ejpam-3288	257	12	,	,	PUNCT
ejpam-3288	257	13	µna	µna	PROPN
ejpam-3288	257	14	(	(	PUNCT
ejpam-3288	257	15	y	y	NOUN
ejpam-3288	257	16	)	)	PUNCT
ejpam-3288	257	17	}	}	PUNCT
ejpam-3288	257	18	,	,	PUNCT
ejpam-3288	257	19	implies	imply	VERB
ejpam-3288	257	20	that	that	SCONJ
ejpam-3288	257	21	,	,	PUNCT
ejpam-3288	257	22	µna	µna	ADJ
ejpam-3288	257	23	(	(	PUNCT
ejpam-3288	257	24	0	0	NUM
ejpam-3288	257	25	)	)	PUNCT
ejpam-3288	257	26	≥	≥	NOUN
ejpam-3288	257	27	µna	µna	ADJ
ejpam-3288	257	28	(	(	PUNCT
ejpam-3288	257	29	x	x	NOUN
ejpam-3288	257	30	)	)	PUNCT
ejpam-3288	257	31	and	and	CCONJ
ejpam-3288	257	32	µna	µna	ADJ
ejpam-3288	257	33	(	(	PUNCT
ejpam-3288	257	34	x∗z	x∗z	NUM
ejpam-3288	257	35	)	)	PUNCT
ejpam-3288	257	36	≥	≥	NOUN
ejpam-3288	257	37	min{µna	min{µna	NOUN
ejpam-3288	257	38	(	(	PUNCT
ejpam-3288	257	39	x∗(y∗z	x∗(y∗z	PROPN
ejpam-3288	257	40	)	)	PUNCT
ejpam-3288	257	41	)	)	PUNCT
ejpam-3288	257	42	,	,	PUNCT
ejpam-3288	257	43	µna	µna	PROPN
ejpam-3288	257	44	(	(	PUNCT
ejpam-3288	257	45	y	y	NOUN
ejpam-3288	257	46	)	)	PUNCT
ejpam-3288	257	47	}	}	PUNCT
ejpam-3288	257	48	for	for	ADP
ejpam-3288	257	49	all	all	DET
ejpam-3288	257	50	x	x	NOUN
ejpam-3288	257	51	,	,	PUNCT
ejpam-3288	257	52	y	y	PROPN
ejpam-3288	257	53	,	,	PUNCT
ejpam-3288	257	54	z	z	PROPN
ejpam-3288	257	55	∈	∈	PROPN
ejpam-3288	257	56	x.	x.	NOUN
ejpam-3288	257	57	therefore	therefore	ADV
ejpam-3288	257	58	,	,	PUNCT
ejpam-3288	257	59	a	a	DET
ejpam-3288	257	60	=	=	X
ejpam-3288	257	61	(	(	PUNCT
ejpam-3288	257	62	µpa	µpa	PROPN
ejpam-3288	257	63	,	,	PUNCT
ejpam-3288	257	64	µ	µ	X
ejpam-3288	257	65	n	n	PRON
ejpam-3288	257	66	a	a	PRON
ejpam-3288	257	67	)	)	PUNCT
ejpam-3288	257	68	is	be	AUX
ejpam-3288	257	69	a	a	DET
ejpam-3288	257	70	doubt	doubt	ADV
ejpam-3288	257	71	bipolar	bipolar	ADJ
ejpam-3288	257	72	fuzzy	fuzzy	ADJ
ejpam-3288	257	73	h	h	NOUN
ejpam-3288	257	74	-	-	PUNCT
ejpam-3288	257	75	ideal	ideal	NOUN
ejpam-3288	257	76	of	of	ADP
ejpam-3288	257	77	x.	x.	PROPN
ejpam-3288	257	78	theorem	theorem	VERB
ejpam-3288	257	79	6	6	NUM
ejpam-3288	257	80	.	.	PUNCT
ejpam-3288	258	1	a	a	DET
ejpam-3288	258	2	bipolar	bipolar	ADJ
ejpam-3288	258	3	fuzzy	fuzzy	NOUN
ejpam-3288	258	4	set	set	VERB
ejpam-3288	258	5	a	a	PRON
ejpam-3288	258	6	=	=	X
ejpam-3288	258	7	(	(	PUNCT
ejpam-3288	258	8	µpa	µpa	PROPN
ejpam-3288	258	9	,	,	PUNCT
ejpam-3288	258	10	µ	µ	X
ejpam-3288	258	11	n	n	PRON
ejpam-3288	258	12	a	a	PRON
ejpam-3288	258	13	)	)	PUNCT
ejpam-3288	258	14	is	be	AUX
ejpam-3288	258	15	a	a	DET
ejpam-3288	258	16	doubt	doubt	ADV
ejpam-3288	258	17	bipolar	bipolar	ADJ
ejpam-3288	258	18	fuzzy	fuzzy	ADJ
ejpam-3288	258	19	h	h	NOUN
ejpam-3288	258	20	-	-	PUNCT
ejpam-3288	258	21	ideal	ideal	NOUN
ejpam-3288	258	22	of	of	ADP
ejpam-3288	258	23	x	x	SYM
ejpam-3288	258	24	if	if	SCONJ
ejpam-3288	258	25	and	and	CCONJ
ejpam-3288	258	26	only	only	ADV
ejpam-3288	258	27	if	if	SCONJ
ejpam-3288	258	28	4a	4a	NUM
ejpam-3288	258	29	=	=	SYM
ejpam-3288	258	30	(	(	PUNCT
ejpam-3288	258	31	µpa,−µpa	µpa,−µpa	PROPN
ejpam-3288	258	32	)	)	PUNCT
ejpam-3288	258	33	and	and	CCONJ
ejpam-3288	258	34	5a	5a	NUM
ejpam-3288	258	35	=	=	SYM
ejpam-3288	258	36	(	(	PUNCT
ejpam-3288	258	37	−µna	−µna	NOUN
ejpam-3288	258	38	,	,	PUNCT
ejpam-3288	258	39	µna	µna	ADJ
ejpam-3288	258	40	)	)	PUNCT
ejpam-3288	258	41	are	be	AUX
ejpam-3288	258	42	also	also	ADV
ejpam-3288	258	43	doubt	doubt	ADV
ejpam-3288	258	44	bipolar	bipolar	ADJ
ejpam-3288	258	45	fuzzy	fuzzy	ADJ
ejpam-3288	258	46	h	h	NOUN
ejpam-3288	258	47	-	-	PUNCT
ejpam-3288	258	48	ideals	ideal	NOUN
ejpam-3288	258	49	of	of	ADP
ejpam-3288	258	50	x.	x.	NOUN
ejpam-3288	258	51	proof	proof	NOUN
ejpam-3288	258	52	.	.	PUNCT
ejpam-3288	259	1	a	a	PRON
ejpam-3288	259	2	=	=	X
ejpam-3288	259	3	(	(	PUNCT
ejpam-3288	259	4	µpa	µpa	PROPN
ejpam-3288	259	5	,	,	PUNCT
ejpam-3288	259	6	µ	µ	X
ejpam-3288	259	7	n	n	PRON
ejpam-3288	259	8	a	a	PRON
ejpam-3288	259	9	)	)	PUNCT
ejpam-3288	259	10	is	be	AUX
ejpam-3288	259	11	a	a	DET
ejpam-3288	259	12	doubt	doubt	ADV
ejpam-3288	259	13	bipolar	bipolar	ADJ
ejpam-3288	259	14	fuzzy	fuzzy	ADJ
ejpam-3288	259	15	h	h	NOUN
ejpam-3288	259	16	-	-	PUNCT
ejpam-3288	259	17	ideal	ideal	NOUN
ejpam-3288	259	18	of	of	ADP
ejpam-3288	259	19	x	x	SYM
ejpam-3288	259	20	if	if	SCONJ
ejpam-3288	259	21	and	and	CCONJ
ejpam-3288	259	22	only	only	ADV
ejpam-3288	259	23	if	if	SCONJ
ejpam-3288	259	24	the	the	DET
ejpam-3288	259	25	fuzzy	fuzzy	ADJ
ejpam-3288	259	26	subsets	subset	NOUN
ejpam-3288	259	27	µpa	µpa	PROPN
ejpam-3288	259	28	and	and	CCONJ
ejpam-3288	259	29	−µna	−µna	NOUN
ejpam-3288	259	30	are	be	AUX
ejpam-3288	259	31	doubt	doubt	ADV
ejpam-3288	259	32	fuzzy	fuzzy	ADJ
ejpam-3288	259	33	h	h	NOUN
ejpam-3288	259	34	-	-	PUNCT
ejpam-3288	259	35	ideals	ideal	NOUN
ejpam-3288	259	36	of	of	ADP
ejpam-3288	259	37	x	x	PUNCT
ejpam-3288	259	38	by	by	ADP
ejpam-3288	259	39	theorem	theorem	NOUN
ejpam-3288	259	40	5	5	NUM
ejpam-3288	259	41	.	.	PUNCT
ejpam-3288	259	42	that	that	PRON
ejpam-3288	259	43	is	be	AUX
ejpam-3288	259	44	,	,	PUNCT
ejpam-3288	259	45	if	if	SCONJ
ejpam-3288	259	46	and	and	CCONJ
ejpam-3288	259	47	only	only	ADV
ejpam-3288	259	48	if	if	SCONJ
ejpam-3288	259	49	4a	4a	NUM
ejpam-3288	259	50	=	=	SYM
ejpam-3288	259	51	(	(	PUNCT
ejpam-3288	259	52	µpa,−µpa	µpa,−µpa	PROPN
ejpam-3288	259	53	)	)	PUNCT
ejpam-3288	259	54	and	and	CCONJ
ejpam-3288	259	55	5a	5a	NUM
ejpam-3288	259	56	=	=	SYM
ejpam-3288	259	57	(	(	PUNCT
ejpam-3288	259	58	−µna	−µna	NOUN
ejpam-3288	259	59	,	,	PUNCT
ejpam-3288	259	60	µna	µna	ADJ
ejpam-3288	259	61	)	)	PUNCT
ejpam-3288	259	62	are	be	AUX
ejpam-3288	259	63	also	also	ADV
ejpam-3288	259	64	doubt	doubt	ADV
ejpam-3288	259	65	bipolar	bipolar	ADJ
ejpam-3288	259	66	fuzzy	fuzzy	ADJ
ejpam-3288	259	67	h	h	NOUN
ejpam-3288	259	68	-	-	PUNCT
ejpam-3288	259	69	ideals	ideal	NOUN
ejpam-3288	259	70	of	of	ADP
ejpam-3288	259	71	x	x	PUNCT
ejpam-3288	259	72	by	by	ADP
ejpam-3288	259	73	definition	definition	NOUN
ejpam-3288	259	74	of	of	ADP
ejpam-3288	259	75	4a	4a	NUM
ejpam-3288	259	76	and	and	CCONJ
ejpam-3288	259	77	5a	5a	NUM
ejpam-3288	259	78	.	.	PUNCT
ejpam-3288	260	1	a.	a.	PROPN
ejpam-3288	260	2	al	al	PROPN
ejpam-3288	260	3	-	-	PROPN
ejpam-3288	260	4	masarwah	masarwah	PROPN
ejpam-3288	260	5	,	,	PUNCT
ejpam-3288	260	6	a.	a.	NOUN
ejpam-3288	260	7	g.	g.	PROPN
ejpam-3288	260	8	ahmad	ahmad	PROPN
ejpam-3288	260	9	/	/	SYM
ejpam-3288	260	10	eur	eur	PROPN
ejpam-3288	260	11	.	.	PUNCT
ejpam-3288	261	1	j.	j.	PROPN
ejpam-3288	261	2	pure	pure	PROPN
ejpam-3288	261	3	appl	appl	PROPN
ejpam-3288	261	4	.	.	PROPN
ejpam-3288	261	5	math	math	PROPN
ejpam-3288	261	6	,	,	PUNCT
ejpam-3288	261	7	11	11	NUM
ejpam-3288	261	8	(	(	PUNCT
ejpam-3288	261	9	3	3	NUM
ejpam-3288	261	10	)	)	PUNCT
ejpam-3288	261	11	(	(	PUNCT
ejpam-3288	261	12	2018	2018	NUM
ejpam-3288	261	13	)	)	PUNCT
ejpam-3288	261	14	,	,	PUNCT
ejpam-3288	261	15	652	652	NUM
ejpam-3288	261	16	-	-	SYM
ejpam-3288	261	17	670	670	NUM
ejpam-3288	261	18	664	664	NUM
ejpam-3288	261	19	4	4	NUM
ejpam-3288	261	20	.	.	PUNCT
ejpam-3288	261	21	characterizations	characterization	NOUN
ejpam-3288	261	22	of	of	ADP
ejpam-3288	261	23	doubt	doubt	NOUN
ejpam-3288	261	24	bipolar	bipolar	ADJ
ejpam-3288	261	25	fuzzy	fuzzy	ADJ
ejpam-3288	261	26	h	h	NOUN
ejpam-3288	261	27	-	-	PUNCT
ejpam-3288	261	28	ideals	ideal	NOUN
ejpam-3288	261	29	in	in	ADP
ejpam-3288	261	30	this	this	DET
ejpam-3288	261	31	section	section	NOUN
ejpam-3288	261	32	,	,	PUNCT
ejpam-3288	261	33	we	we	PRON
ejpam-3288	261	34	define	define	VERB
ejpam-3288	261	35	a	a	DET
ejpam-3288	261	36	doubt	doubt	ADV
ejpam-3288	261	37	positive	positive	ADJ
ejpam-3288	261	38	t	t	NOUN
ejpam-3288	261	39	-	-	PUNCT
ejpam-3288	261	40	level	level	NOUN
ejpam-3288	261	41	cut	cut	NOUN
ejpam-3288	261	42	set	set	VERB
ejpam-3288	261	43	and	and	CCONJ
ejpam-3288	261	44	a	a	DET
ejpam-3288	261	45	doubt	doubt	ADV
ejpam-3288	261	46	negative	negative	ADJ
ejpam-3288	261	47	s	s	NOUN
ejpam-3288	261	48	-	-	PUNCT
ejpam-3288	261	49	level	level	NOUN
ejpam-3288	261	50	cut	cut	NOUN
ejpam-3288	261	51	set	set	NOUN
ejpam-3288	261	52	of	of	ADP
ejpam-3288	261	53	doubt	doubt	NOUN
ejpam-3288	261	54	bipolar	bipolar	ADJ
ejpam-3288	261	55	fuzzy	fuzzy	ADJ
ejpam-3288	261	56	h	h	NOUN
ejpam-3288	261	57	-	-	PUNCT
ejpam-3288	261	58	ideals	ideal	NOUN
ejpam-3288	261	59	in	in	ADP
ejpam-3288	261	60	bck	bck	PROPN
ejpam-3288	261	61	/	/	SYM
ejpam-3288	261	62	bci	bci	NOUN
ejpam-3288	261	63	-	-	PUNCT
ejpam-3288	261	64	algebras	algebras	X
ejpam-3288	261	65	.	.	PUNCT
ejpam-3288	262	1	we	we	PRON
ejpam-3288	262	2	investigate	investigate	VERB
ejpam-3288	262	3	characterizations	characterization	NOUN
ejpam-3288	262	4	of	of	ADP
ejpam-3288	262	5	doubt	doubt	NOUN
ejpam-3288	262	6	bipolar	bipolar	ADJ
ejpam-3288	262	7	fuzzy	fuzzy	ADJ
ejpam-3288	262	8	h	h	NOUN
ejpam-3288	262	9	-	-	PUNCT
ejpam-3288	262	10	ideals	ideal	NOUN
ejpam-3288	262	11	in	in	ADP
ejpam-3288	262	12	bck	bck	PROPN
ejpam-3288	262	13	/	/	SYM
ejpam-3288	262	14	bci	bci	NOUN
ejpam-3288	262	15	-	-	PUNCT
ejpam-3288	262	16	algebras	algebra	VERB
ejpam-3288	262	17	by	by	ADP
ejpam-3288	262	18	means	mean	NOUN
ejpam-3288	262	19	of	of	ADP
ejpam-3288	262	20	doubt	doubt	NOUN
ejpam-3288	262	21	positive	positive	ADJ
ejpam-3288	262	22	t	t	NOUN
ejpam-3288	262	23	-	-	PUNCT
ejpam-3288	262	24	level	level	NOUN
ejpam-3288	262	25	cut	cut	NOUN
ejpam-3288	262	26	set	set	NOUN
ejpam-3288	262	27	,	,	PUNCT
ejpam-3288	262	28	doubt	doubt	VERB
ejpam-3288	262	29	negative	negative	ADJ
ejpam-3288	262	30	s	s	NOUN
ejpam-3288	262	31	-	-	PUNCT
ejpam-3288	262	32	level	level	NOUN
ejpam-3288	262	33	cut	cut	NOUN
ejpam-3288	262	34	set	set	VERB
ejpam-3288	262	35	and	and	CCONJ
ejpam-3288	262	36	h	h	NOUN
ejpam-3288	262	37	-	-	PUNCT
ejpam-3288	262	38	artin	artin	NOUN
ejpam-3288	262	39	bck	bck	PROPN
ejpam-3288	262	40	/	/	SYM
ejpam-3288	262	41	bci	bci	NOUN
ejpam-3288	262	42	-	-	PUNCT
ejpam-3288	262	43	algebras	algebras	X
ejpam-3288	262	44	.	.	PUNCT
ejpam-3288	263	1	definition	definition	NOUN
ejpam-3288	263	2	11	11	NUM
ejpam-3288	263	3	.	.	PUNCT
ejpam-3288	264	1	let	let	VERB
ejpam-3288	264	2	a	a	DET
ejpam-3288	264	3	=	=	X
ejpam-3288	264	4	(	(	PUNCT
ejpam-3288	264	5	µpa	µpa	PROPN
ejpam-3288	264	6	,	,	PUNCT
ejpam-3288	264	7	µ	µ	NOUN
ejpam-3288	264	8	n	n	ADV
ejpam-3288	264	9	a	a	PRON
ejpam-3288	264	10	)	)	PUNCT
ejpam-3288	264	11	be	be	AUX
ejpam-3288	264	12	a	a	DET
ejpam-3288	264	13	doubt	doubt	ADV
ejpam-3288	264	14	bipolar	bipolar	ADJ
ejpam-3288	264	15	fuzzy	fuzzy	ADJ
ejpam-3288	264	16	h	h	NOUN
ejpam-3288	264	17	-	-	PUNCT
ejpam-3288	264	18	ideal	ideal	NOUN
ejpam-3288	264	19	of	of	ADP
ejpam-3288	264	20	a	a	DET
ejpam-3288	264	21	bck	bck	PROPN
ejpam-3288	264	22	/	/	SYM
ejpam-3288	264	23	bci	bci	NOUN
ejpam-3288	264	24	-	-	NOUN
ejpam-3288	264	25	algebra	algebra	NOUN
ejpam-3288	264	26	x	x	NOUN
ejpam-3288	264	27	,	,	PUNCT
ejpam-3288	264	28	and	and	CCONJ
ejpam-3288	264	29	(	(	PUNCT
ejpam-3288	264	30	s	s	PROPN
ejpam-3288	264	31	,	,	PUNCT
ejpam-3288	264	32	t	t	PROPN
ejpam-3288	264	33	)	)	PUNCT
ejpam-3288	264	34	∈	∈	PROPN
ejpam-3288	265	1	[	[	X
ejpam-3288	265	2	−1	−1	NOUN
ejpam-3288	265	3	,	,	PUNCT
ejpam-3288	265	4	0]×	0]×	PROPN
ejpam-3288	266	1	[	[	X
ejpam-3288	266	2	0	0	NUM
ejpam-3288	266	3	,	,	PUNCT
ejpam-3288	266	4	1	1	NUM
ejpam-3288	266	5	]	]	PUNCT
ejpam-3288	266	6	.	.	PUNCT
ejpam-3288	267	1	then	then	ADV
ejpam-3288	267	2	the	the	DET
ejpam-3288	267	3	doubt	doubt	ADV
ejpam-3288	267	4	positive	positive	ADJ
ejpam-3288	267	5	t	t	NOUN
ejpam-3288	267	6	-	-	PUNCT
ejpam-3288	267	7	level	level	NOUN
ejpam-3288	267	8	cut	cut	NOUN
ejpam-3288	267	9	set	set	VERB
ejpam-3288	267	10	and	and	CCONJ
ejpam-3288	267	11	the	the	DET
ejpam-3288	267	12	doubt	doubt	ADV
ejpam-3288	267	13	negative	negative	ADJ
ejpam-3288	267	14	s	s	NOUN
ejpam-3288	267	15	-	-	PUNCT
ejpam-3288	267	16	level	level	NOUN
ejpam-3288	267	17	cut	cut	NOUN
ejpam-3288	267	18	set	set	NOUN
ejpam-3288	267	19	of	of	ADP
ejpam-3288	267	20	a	a	PRON
ejpam-3288	267	21	are	be	AUX
ejpam-3288	267	22	as	as	SCONJ
ejpam-3288	267	23	follows	follow	VERB
ejpam-3288	267	24	:	:	PUNCT
ejpam-3288	267	25	apt	apt	ADJ
ejpam-3288	267	26	=	=	PRON
ejpam-3288	267	27	{	{	PUNCT
ejpam-3288	267	28	x	x	SYM
ejpam-3288	267	29	∈	∈	PROPN
ejpam-3288	267	30	x	x	X
ejpam-3288	267	31	:	:	PUNCT
ejpam-3288	267	32	µpa(x	µpa(x	X
ejpam-3288	267	33	)	)	PUNCT
ejpam-3288	267	34	≤	≤	NOUN
ejpam-3288	267	35	t	t	PROPN
ejpam-3288	267	36	}	}	PUNCT
ejpam-3288	267	37	and	and	CCONJ
ejpam-3288	267	38	ant	ant	ADJ
ejpam-3288	267	39	=	=	SYM
ejpam-3288	267	40	{	{	PUNCT
ejpam-3288	267	41	x	x	SYM
ejpam-3288	267	42	∈	∈	PROPN
ejpam-3288	267	43	x	x	X
ejpam-3288	267	44	:	:	PUNCT
ejpam-3288	267	45	µna	µna	ADJ
ejpam-3288	267	46	(	(	PUNCT
ejpam-3288	267	47	x	x	NOUN
ejpam-3288	267	48	)	)	PUNCT
ejpam-3288	267	49	≥	≥	NUM
ejpam-3288	267	50	s	s	PART
ejpam-3288	267	51	}	}	PUNCT
ejpam-3288	267	52	.	.	PUNCT
ejpam-3288	268	1	the	the	DET
ejpam-3288	268	2	set	set	PROPN
ejpam-3288	268	3	s(s	s(s	PROPN
ejpam-3288	268	4	,	,	PUNCT
ejpam-3288	268	5	t	t	PROPN
ejpam-3288	268	6	)	)	PUNCT
ejpam-3288	268	7	=	=	PRON
ejpam-3288	268	8	{	{	PUNCT
ejpam-3288	268	9	x	x	PUNCT
ejpam-3288	268	10	∈	∈	PROPN
ejpam-3288	268	11	x	x	X
ejpam-3288	268	12	:	:	PUNCT
ejpam-3288	268	13	µpa(x	µpa(x	X
ejpam-3288	268	14	)	)	PUNCT
ejpam-3288	268	15	≤	≤	NOUN
ejpam-3288	268	16	t	t	NOUN
ejpam-3288	268	17	and	and	CCONJ
ejpam-3288	268	18	µna	µna	ADJ
ejpam-3288	268	19	(	(	PUNCT
ejpam-3288	268	20	x	x	NOUN
ejpam-3288	268	21	)	)	PUNCT
ejpam-3288	268	22	≥	≥	PRON
ejpam-3288	268	23	s	s	PART
ejpam-3288	268	24	}	}	PUNCT
ejpam-3288	268	25	is	be	AUX
ejpam-3288	268	26	called	call	VERB
ejpam-3288	268	27	a	a	DET
ejpam-3288	268	28	doubt	doubt	NOUN
ejpam-3288	268	29	(	(	PUNCT
ejpam-3288	268	30	s	s	NOUN
ejpam-3288	268	31	,	,	PUNCT
ejpam-3288	268	32	t)-level	t)-level	NOUN
ejpam-3288	268	33	cut	cut	VERB
ejpam-3288	268	34	set	set	NOUN
ejpam-3288	268	35	of	of	ADP
ejpam-3288	268	36	a.	a.	NOUN
ejpam-3288	268	37	for	for	ADP
ejpam-3288	268	38	every	every	DET
ejpam-3288	268	39	γ	γ	X
ejpam-3288	268	40	∈	∈	PROPN
ejpam-3288	269	1	[	[	X
ejpam-3288	269	2	0	0	NUM
ejpam-3288	269	3	,	,	PUNCT
ejpam-3288	269	4	1	1	NUM
ejpam-3288	269	5	]	]	PUNCT
ejpam-3288	269	6	,	,	PUNCT
ejpam-3288	269	7	the	the	DET
ejpam-3288	269	8	set	set	NOUN
ejpam-3288	269	9	apγ	apγ	PROPN
ejpam-3288	269	10	∩an−γ	∩an−γ	PROPN
ejpam-3288	269	11	is	be	AUX
ejpam-3288	269	12	called	call	VERB
ejpam-3288	269	13	a	a	DET
ejpam-3288	269	14	doubt	doubt	NOUN
ejpam-3288	269	15	γ	γ	X
ejpam-3288	269	16	-	-	PUNCT
ejpam-3288	269	17	level	level	NOUN
ejpam-3288	269	18	cut	cut	NOUN
ejpam-3288	269	19	set	set	NOUN
ejpam-3288	269	20	of	of	ADP
ejpam-3288	269	21	a.	a.	NOUN
ejpam-3288	269	22	from	from	ADP
ejpam-3288	269	23	definition	definition	NOUN
ejpam-3288	269	24	11	11	NUM
ejpam-3288	269	25	,	,	PUNCT
ejpam-3288	269	26	we	we	PRON
ejpam-3288	269	27	can	can	AUX
ejpam-3288	269	28	easily	easily	ADV
ejpam-3288	269	29	obtained	obtain	VERB
ejpam-3288	269	30	the	the	DET
ejpam-3288	269	31	relation	relation	NOUN
ejpam-3288	269	32	between	between	ADP
ejpam-3288	269	33	a	a	DET
ejpam-3288	269	34	doubt	doubt	ADV
ejpam-3288	269	35	bipolar	bipolar	ADJ
ejpam-3288	269	36	fuzzy	fuzzy	ADJ
ejpam-3288	269	37	h	h	NOUN
ejpam-3288	269	38	-	-	PUNCT
ejpam-3288	269	39	ideal	ideal	ADJ
ejpam-3288	269	40	and	and	CCONJ
ejpam-3288	269	41	h	h	NOUN
ejpam-3288	269	42	-	-	PUNCT
ejpam-3288	269	43	ideal	ideal	NOUN
ejpam-3288	269	44	in	in	ADP
ejpam-3288	269	45	bck	bck	PROPN
ejpam-3288	269	46	/	/	SYM
ejpam-3288	269	47	bci	bci	NOUN
ejpam-3288	269	48	-	-	PUNCT
ejpam-3288	269	49	algebras	algebra	NOUN
ejpam-3288	269	50	.	.	PUNCT
ejpam-3288	270	1	theorem	theorem	NOUN
ejpam-3288	270	2	7	7	NUM
ejpam-3288	270	3	.	.	X
ejpam-3288	270	4	for	for	ADP
ejpam-3288	270	5	a	a	DET
ejpam-3288	270	6	bipolar	bipolar	ADJ
ejpam-3288	270	7	fuzzy	fuzzy	NOUN
ejpam-3288	270	8	set	set	VERB
ejpam-3288	270	9	a	a	PRON
ejpam-3288	270	10	=	=	X
ejpam-3288	270	11	(	(	PUNCT
ejpam-3288	270	12	µpa	µpa	PROPN
ejpam-3288	270	13	,	,	PUNCT
ejpam-3288	270	14	µ	µ	X
ejpam-3288	270	15	n	n	PRON
ejpam-3288	270	16	a	a	NOUN
ejpam-3288	270	17	)	)	PUNCT
ejpam-3288	270	18	in	in	ADP
ejpam-3288	270	19	x	x	PRON
ejpam-3288	270	20	,	,	PUNCT
ejpam-3288	270	21	the	the	DET
ejpam-3288	270	22	following	follow	VERB
ejpam-3288	270	23	are	be	AUX
ejpam-3288	270	24	equivalent	equivalent	ADJ
ejpam-3288	270	25	:	:	PUNCT
ejpam-3288	270	26	1	1	X
ejpam-3288	270	27	.	.	X
ejpam-3288	270	28	a	a	PRON
ejpam-3288	270	29	=	=	X
ejpam-3288	270	30	(	(	PUNCT
ejpam-3288	270	31	µpa	µpa	PROPN
ejpam-3288	270	32	,	,	PUNCT
ejpam-3288	270	33	µ	µ	X
ejpam-3288	270	34	n	n	PRON
ejpam-3288	270	35	a	a	PRON
ejpam-3288	270	36	)	)	PUNCT
ejpam-3288	270	37	is	be	AUX
ejpam-3288	270	38	a	a	DET
ejpam-3288	270	39	doubt	doubt	ADV
ejpam-3288	270	40	bipolar	bipolar	ADJ
ejpam-3288	270	41	fuzzy	fuzzy	ADJ
ejpam-3288	270	42	h	h	NOUN
ejpam-3288	270	43	-	-	PUNCT
ejpam-3288	270	44	ideal	ideal	NOUN
ejpam-3288	270	45	of	of	ADP
ejpam-3288	270	46	x.	x.	NOUN
ejpam-3288	270	47	2	2	NUM
ejpam-3288	270	48	.	.	PUNCT
ejpam-3288	271	1	a	a	DET
ejpam-3288	271	2	=	=	X
ejpam-3288	271	3	(	(	PUNCT
ejpam-3288	271	4	µpa	µpa	PROPN
ejpam-3288	271	5	,	,	PUNCT
ejpam-3288	271	6	µ	µ	X
ejpam-3288	271	7	n	n	PRON
ejpam-3288	271	8	a	a	PRON
ejpam-3288	271	9	)	)	PUNCT
ejpam-3288	271	10	satisfies	satisfy	VERB
ejpam-3288	271	11	the	the	DET
ejpam-3288	271	12	following	follow	VERB
ejpam-3288	271	13	assertions	assertion	NOUN
ejpam-3288	271	14	:	:	PUNCT
ejpam-3288	271	15	i.	i.	NOUN
ejpam-3288	271	16	(	(	PUNCT
ejpam-3288	271	17	∀t	∀t	PROPN
ejpam-3288	271	18	∈	∈	PROPN
ejpam-3288	272	1	[	[	X
ejpam-3288	272	2	0	0	NUM
ejpam-3288	272	3	,	,	PUNCT
ejpam-3288	272	4	1])(apt	1])(apt	NUM
ejpam-3288	272	5	6=	6=	SYM
ejpam-3288	272	6	∅	∅	NOUN
ejpam-3288	272	7	⇒	⇒	NOUN
ejpam-3288	272	8	apt	apt	ADJ
ejpam-3288	272	9	=	=	SYM
ejpam-3288	272	10	{	{	PUNCT
ejpam-3288	272	11	x	x	SYM
ejpam-3288	272	12	∈	∈	PROPN
ejpam-3288	272	13	x	x	X
ejpam-3288	272	14	:	:	PUNCT
ejpam-3288	272	15	µpa(x	µpa(x	X
ejpam-3288	272	16	)	)	PUNCT
ejpam-3288	272	17	≤	≤	NOUN
ejpam-3288	272	18	t	t	PROPN
ejpam-3288	272	19	}	}	PUNCT
ejpam-3288	272	20	is	be	AUX
ejpam-3288	272	21	an	an	DET
ejpam-3288	272	22	h	h	NOUN
ejpam-3288	272	23	-	-	PUNCT
ejpam-3288	272	24	ideal	ideal	NOUN
ejpam-3288	272	25	of	of	ADP
ejpam-3288	272	26	x	x	NOUN
ejpam-3288	272	27	)	)	PUNCT
ejpam-3288	272	28	.	.	PUNCT
ejpam-3288	273	1	ii	ii	PROPN
ejpam-3288	273	2	.	.	PUNCT
ejpam-3288	274	1	(	(	PUNCT
ejpam-3288	274	2	∀s	∀s	PROPN
ejpam-3288	274	3	∈	∈	PROPN
ejpam-3288	275	1	[	[	X
ejpam-3288	275	2	−1	−1	NOUN
ejpam-3288	275	3	,	,	PUNCT
ejpam-3288	275	4	0])(ant	0])(ant	PROPN
ejpam-3288	275	5	6=	6=	SYM
ejpam-3288	275	6	∅	∅	NOUN
ejpam-3288	275	7	⇒	⇒	NOUN
ejpam-3288	275	8	ans	ans	X
ejpam-3288	275	9	=	=	PUNCT
ejpam-3288	275	10	{	{	PUNCT
ejpam-3288	275	11	x	x	PUNCT
ejpam-3288	275	12	∈	∈	PROPN
ejpam-3288	275	13	x	x	X
ejpam-3288	275	14	:	:	PUNCT
ejpam-3288	275	15	µna	µna	ADJ
ejpam-3288	275	16	(	(	PUNCT
ejpam-3288	275	17	x	x	NOUN
ejpam-3288	275	18	)	)	PUNCT
ejpam-3288	275	19	≥	≥	PRON
ejpam-3288	275	20	s	s	PART
ejpam-3288	275	21	}	}	PUNCT
ejpam-3288	275	22	is	be	AUX
ejpam-3288	275	23	an	an	DET
ejpam-3288	275	24	h	h	NOUN
ejpam-3288	275	25	-	-	PUNCT
ejpam-3288	275	26	ideal	ideal	NOUN
ejpam-3288	275	27	of	of	ADP
ejpam-3288	275	28	x	x	NOUN
ejpam-3288	275	29	)	)	PUNCT
ejpam-3288	275	30	.	.	PUNCT
ejpam-3288	276	1	proof	proof	NOUN
ejpam-3288	276	2	.	.	PUNCT
ejpam-3288	277	1	(	(	PUNCT
ejpam-3288	277	2	1⇒	1⇒	NOUN
ejpam-3288	277	3	2	2	X
ejpam-3288	277	4	)	)	PUNCT
ejpam-3288	277	5	let	let	VERB
ejpam-3288	277	6	a	a	PRON
ejpam-3288	277	7	=	=	X
ejpam-3288	277	8	(	(	PUNCT
ejpam-3288	277	9	µpa	µpa	PROPN
ejpam-3288	277	10	,	,	PUNCT
ejpam-3288	277	11	µ	µ	NOUN
ejpam-3288	277	12	n	n	ADV
ejpam-3288	277	13	a	a	PRON
ejpam-3288	277	14	)	)	PUNCT
ejpam-3288	277	15	be	be	AUX
ejpam-3288	277	16	a	a	DET
ejpam-3288	277	17	doubt	doubt	ADV
ejpam-3288	277	18	bipolar	bipolar	ADJ
ejpam-3288	277	19	fuzzy	fuzzy	ADJ
ejpam-3288	277	20	h	h	NOUN
ejpam-3288	277	21	-	-	PUNCT
ejpam-3288	277	22	ideal	ideal	NOUN
ejpam-3288	277	23	of	of	ADP
ejpam-3288	277	24	x.	x.	NOUN
ejpam-3288	277	25	let	let	VERB
ejpam-3288	277	26	t	t	PROPN
ejpam-3288	277	27	∈	∈	PROPN
ejpam-3288	278	1	[	[	X
ejpam-3288	278	2	0	0	NUM
ejpam-3288	278	3	,	,	PUNCT
ejpam-3288	278	4	1	1	NUM
ejpam-3288	278	5	]	]	PUNCT
ejpam-3288	278	6	and	and	CCONJ
ejpam-3288	278	7	s	s	X
ejpam-3288	278	8	∈	∈	PROPN
ejpam-3288	278	9	[	[	X
ejpam-3288	278	10	−1	−1	NOUN
ejpam-3288	278	11	,	,	PUNCT
ejpam-3288	278	12	0	0	NUM
ejpam-3288	278	13	]	]	PUNCT
ejpam-3288	278	14	such	such	ADJ
ejpam-3288	278	15	that	that	SCONJ
ejpam-3288	278	16	apt	apt	ADJ
ejpam-3288	278	17	6=	6=	NUM
ejpam-3288	278	18	∅	∅	NOUN
ejpam-3288	278	19	and	and	CCONJ
ejpam-3288	278	20	ans	an	NOUN
ejpam-3288	278	21	6=	6=	ADP
ejpam-3288	278	22	∅.	∅.	NOUN
ejpam-3288	278	23	then	then	ADV
ejpam-3288	278	24	there	there	PRON
ejpam-3288	278	25	exists	exist	VERB
ejpam-3288	278	26	a	a	DET
ejpam-3288	278	27	∈	∈	NOUN
ejpam-3288	278	28	apt	apt	ADJ
ejpam-3288	278	29	and	and	CCONJ
ejpam-3288	278	30	b	b	PROPN
ejpam-3288	278	31	∈	∈	PROPN
ejpam-3288	278	32	ans	an	NOUN
ejpam-3288	278	33	,	,	PUNCT
ejpam-3288	278	34	that	that	ADV
ejpam-3288	278	35	is	is	ADV
ejpam-3288	278	36	µpa(a	µpa(a	NUM
ejpam-3288	278	37	)	)	PUNCT
ejpam-3288	278	38	≤	≤	NOUN
ejpam-3288	278	39	t	t	NOUN
ejpam-3288	278	40	and	and	CCONJ
ejpam-3288	278	41	µna	µna	ADJ
ejpam-3288	278	42	(	(	PUNCT
ejpam-3288	278	43	b	b	NOUN
ejpam-3288	278	44	)	)	PUNCT
ejpam-3288	278	45	≥	≥	NOUN
ejpam-3288	278	46	s.	s.	PROPN
ejpam-3288	278	47	since	since	SCONJ
ejpam-3288	278	48	a	a	PRON
ejpam-3288	278	49	=	=	X
ejpam-3288	278	50	(	(	PUNCT
ejpam-3288	278	51	µpa	µpa	PROPN
ejpam-3288	278	52	,	,	PUNCT
ejpam-3288	278	53	µ	µ	X
ejpam-3288	278	54	n	n	PRON
ejpam-3288	278	55	a	a	PRON
ejpam-3288	278	56	)	)	PUNCT
ejpam-3288	278	57	is	be	AUX
ejpam-3288	278	58	a	a	DET
ejpam-3288	278	59	doubt	doubt	ADV
ejpam-3288	278	60	bipolar	bipolar	ADJ
ejpam-3288	278	61	fuzzy	fuzzy	ADJ
ejpam-3288	278	62	h	h	NOUN
ejpam-3288	278	63	-	-	PUNCT
ejpam-3288	278	64	ideal	ideal	NOUN
ejpam-3288	278	65	of	of	ADP
ejpam-3288	278	66	x	x	SYM
ejpam-3288	278	67	,	,	PUNCT
ejpam-3288	278	68	we	we	PRON
ejpam-3288	278	69	have	have	VERB
ejpam-3288	278	70	µpa(0	µpa(0	NOUN
ejpam-3288	278	71	)	)	PUNCT
ejpam-3288	278	72	≤	≤	NUM
ejpam-3288	278	73	µpa(x	µpa(x	NOUN
ejpam-3288	278	74	)	)	PUNCT
ejpam-3288	278	75	and	and	CCONJ
ejpam-3288	278	76	µna	µna	ADJ
ejpam-3288	278	77	(	(	PUNCT
ejpam-3288	278	78	0	0	NUM
ejpam-3288	278	79	)	)	PUNCT
ejpam-3288	278	80	≥	≥	NOUN
ejpam-3288	278	81	µna	µna	ADJ
ejpam-3288	278	82	(	(	PUNCT
ejpam-3288	278	83	x	x	NOUN
ejpam-3288	278	84	)	)	PUNCT
ejpam-3288	278	85	,	,	PUNCT
ejpam-3288	278	86	for	for	ADP
ejpam-3288	278	87	all	all	PRON
ejpam-3288	278	88	x	x	SYM
ejpam-3288	278	89	∈	∈	NOUN
ejpam-3288	278	90	x.	x.	NOUN
ejpam-3288	279	1	thus	thus	ADV
ejpam-3288	279	2	,	,	PUNCT
ejpam-3288	279	3	µpa(0	µpa(0	NOUN
ejpam-3288	279	4	)	)	PUNCT
ejpam-3288	280	1	≤	≤	NUM
ejpam-3288	280	2	µpa(a	µpa(a	NUM
ejpam-3288	280	3	)	)	PUNCT
ejpam-3288	280	4	≤	≤	NOUN
ejpam-3288	280	5	t	t	NOUN
ejpam-3288	280	6	and	and	CCONJ
ejpam-3288	280	7	µna	µna	ADJ
ejpam-3288	280	8	(	(	PUNCT
ejpam-3288	280	9	0	0	NUM
ejpam-3288	280	10	)	)	PUNCT
ejpam-3288	280	11	≥	≥	NOUN
ejpam-3288	280	12	µna	µna	ADJ
ejpam-3288	280	13	(	(	PUNCT
ejpam-3288	280	14	b	b	NOUN
ejpam-3288	280	15	)	)	PUNCT
ejpam-3288	280	16	≥	≥	NOUN
ejpam-3288	280	17	s	s	NOUN
ejpam-3288	280	18	,	,	PUNCT
ejpam-3288	280	19	so	so	ADV
ejpam-3288	280	20	0	0	NUM
ejpam-3288	280	21	∈	∈	NOUN
ejpam-3288	280	22	apt	apt	ADJ
ejpam-3288	280	23	and	and	CCONJ
ejpam-3288	280	24	0	0	NUM
ejpam-3288	280	25	∈	∈	PROPN
ejpam-3288	280	26	ans	an	NOUN
ejpam-3288	280	27	.	.	PUNCT
ejpam-3288	281	1	let	let	VERB
ejpam-3288	281	2	x	x	PRON
ejpam-3288	281	3	,	,	PUNCT
ejpam-3288	281	4	y	y	PROPN
ejpam-3288	281	5	,	,	PUNCT
ejpam-3288	281	6	z	z	NOUN
ejpam-3288	281	7	∈	∈	PROPN
ejpam-3288	281	8	x	x	PUNCT
ejpam-3288	281	9	such	such	ADJ
ejpam-3288	281	10	that	that	SCONJ
ejpam-3288	281	11	x	x	SYM
ejpam-3288	281	12	∗	∗	NOUN
ejpam-3288	281	13	(	(	PUNCT
ejpam-3288	281	14	y	y	PROPN
ejpam-3288	281	15	∗	∗	PROPN
ejpam-3288	281	16	z	z	NOUN
ejpam-3288	281	17	)	)	PUNCT
ejpam-3288	281	18	∈	∈	PROPN
ejpam-3288	281	19	apt	apt	ADJ
ejpam-3288	281	20	and	and	CCONJ
ejpam-3288	281	21	y	y	PROPN
ejpam-3288	281	22	∈	∈	PROPN
ejpam-3288	281	23	apt	apt	ADJ
ejpam-3288	281	24	.	.	PUNCT
ejpam-3288	282	1	then	then	ADV
ejpam-3288	282	2	µpa(x	µpa(x	PRON
ejpam-3288	282	3	∗	∗	NOUN
ejpam-3288	282	4	(	(	PUNCT
ejpam-3288	282	5	y	y	PROPN
ejpam-3288	282	6	∗	∗	PROPN
ejpam-3288	282	7	z	z	NOUN
ejpam-3288	282	8	)	)	PUNCT
ejpam-3288	282	9	)	)	PUNCT
ejpam-3288	282	10	≤	≤	NOUN
ejpam-3288	282	11	t	t	NOUN
ejpam-3288	282	12	and	and	CCONJ
ejpam-3288	282	13	µpa(y	µpa(y	NOUN
ejpam-3288	282	14	)	)	PUNCT
ejpam-3288	282	15	≤	≤	NOUN
ejpam-3288	282	16	t.	t.	NOUN
ejpam-3288	282	17	using	use	VERB
ejpam-3288	282	18	definition	definition	NOUN
ejpam-3288	282	19	9	9	NUM
ejpam-3288	282	20	,	,	PUNCT
ejpam-3288	282	21	we	we	PRON
ejpam-3288	282	22	have	have	VERB
ejpam-3288	282	23	µpa(x	µpa(x	PROPN
ejpam-3288	282	24	∗	∗	NOUN
ejpam-3288	282	25	z	z	NOUN
ejpam-3288	282	26	)	)	PUNCT
ejpam-3288	282	27	≤	≤	PROPN
ejpam-3288	282	28	max{µpa(x	max{µpa(x	PROPN
ejpam-3288	282	29	∗	∗	NOUN
ejpam-3288	282	30	(	(	PUNCT
ejpam-3288	282	31	y	y	PROPN
ejpam-3288	282	32	∗	∗	PROPN
ejpam-3288	282	33	z	z	PROPN
ejpam-3288	282	34	)	)	PUNCT
ejpam-3288	282	35	)	)	PUNCT
ejpam-3288	282	36	,	,	PUNCT
ejpam-3288	282	37	µpa(y	µpa(y	PROPN
ejpam-3288	282	38	)	)	PUNCT
ejpam-3288	282	39	}	}	PUNCT
ejpam-3288	282	40	≤	≤	NUM
ejpam-3288	282	41	max{t	max{t	NOUN
ejpam-3288	282	42	,	,	PUNCT
ejpam-3288	282	43	t	t	PROPN
ejpam-3288	282	44	}	}	PUNCT
ejpam-3288	282	45	=	=	SYM
ejpam-3288	282	46	t	t	PROPN
ejpam-3288	282	47	,	,	PUNCT
ejpam-3288	282	48	so	so	ADV
ejpam-3288	282	49	x∗z	x∗z	PUNCT
ejpam-3288	282	50	∈	∈	PROPN
ejpam-3288	282	51	apt	apt	ADJ
ejpam-3288	282	52	.	.	PUNCT
ejpam-3288	283	1	hence	hence	ADV
ejpam-3288	283	2	,	,	PUNCT
ejpam-3288	283	3	apt	apt	ADJ
ejpam-3288	283	4	is	be	AUX
ejpam-3288	283	5	an	an	DET
ejpam-3288	283	6	h	h	NOUN
ejpam-3288	283	7	-	-	PUNCT
ejpam-3288	283	8	ideal	ideal	ADJ
ejpam-3288	283	9	ofx	ofx	NOUN
ejpam-3288	283	10	.	.	PUNCT
ejpam-3288	284	1	finally	finally	ADV
ejpam-3288	284	2	,	,	PUNCT
ejpam-3288	284	3	let	let	VERB
ejpam-3288	284	4	x	x	PRON
ejpam-3288	284	5	,	,	PUNCT
ejpam-3288	284	6	y	y	PROPN
ejpam-3288	284	7	,	,	PUNCT
ejpam-3288	284	8	z	z	NOUN
ejpam-3288	284	9	∈	∈	PROPN
ejpam-3288	284	10	x	x	PUNCT
ejpam-3288	284	11	such	such	ADJ
ejpam-3288	284	12	that	that	SCONJ
ejpam-3288	284	13	x∗(y∗z	x∗(y∗z	X
ejpam-3288	284	14	)	)	PUNCT
ejpam-3288	284	15	∈	∈	PROPN
ejpam-3288	284	16	ans	an	NOUN
ejpam-3288	284	17	and	and	CCONJ
ejpam-3288	284	18	y	y	PROPN
ejpam-3288	284	19	∈	∈	PROPN
ejpam-3288	284	20	ans	ans	X
ejpam-3288	284	21	.	.	PUNCT
ejpam-3288	285	1	then	then	ADV
ejpam-3288	285	2	µna	µna	ADJ
ejpam-3288	285	3	(	(	PUNCT
ejpam-3288	285	4	x	x	SYM
ejpam-3288	285	5	∗	∗	NOUN
ejpam-3288	285	6	(	(	PUNCT
ejpam-3288	285	7	y	y	PROPN
ejpam-3288	285	8	∗	∗	PROPN
ejpam-3288	285	9	z	z	PROPN
ejpam-3288	285	10	)	)	PUNCT
ejpam-3288	285	11	≥	≥	NOUN
ejpam-3288	285	12	s	s	NOUN
ejpam-3288	285	13	and	and	CCONJ
ejpam-3288	285	14	µna	µna	ADJ
ejpam-3288	285	15	(	(	PUNCT
ejpam-3288	285	16	y	y	NOUN
ejpam-3288	285	17	)	)	PUNCT
ejpam-3288	285	18	)	)	PUNCT
ejpam-3288	285	19	≥	≥	PROPN
ejpam-3288	285	20	s.	s.	PROPN
ejpam-3288	286	1	it	it	PRON
ejpam-3288	286	2	follows	follow	VERB
ejpam-3288	286	3	that	that	SCONJ
ejpam-3288	286	4	µna	µna	ADJ
ejpam-3288	286	5	(	(	PUNCT
ejpam-3288	286	6	x	x	NOUN
ejpam-3288	286	7	∗	∗	PROPN
ejpam-3288	286	8	z	z	NOUN
ejpam-3288	286	9	)	)	PUNCT
ejpam-3288	286	10	≥	≥	X
ejpam-3288	286	11	min{µna	min{µna	NOUN
ejpam-3288	286	12	(	(	PUNCT
ejpam-3288	286	13	x	x	NOUN
ejpam-3288	286	14	∗	∗	NOUN
ejpam-3288	286	15	(	(	PUNCT
ejpam-3288	286	16	y	y	PROPN
ejpam-3288	286	17	∗	∗	PROPN
ejpam-3288	286	18	z	z	PROPN
ejpam-3288	286	19	)	)	PUNCT
ejpam-3288	286	20	)	)	PUNCT
ejpam-3288	286	21	,	,	PUNCT
ejpam-3288	286	22	µna	µna	PROPN
ejpam-3288	286	23	(	(	PUNCT
ejpam-3288	286	24	y	y	NOUN
ejpam-3288	286	25	)	)	PUNCT
ejpam-3288	286	26	}	}	PUNCT
ejpam-3288	286	27	≥	≥	NOUN
ejpam-3288	286	28	min{s	min{s	PROPN
ejpam-3288	286	29	,	,	PUNCT
ejpam-3288	286	30	s	s	NOUN
ejpam-3288	286	31	}	}	PUNCT
ejpam-3288	286	32	=	=	SYM
ejpam-3288	286	33	s	s	NOUN
ejpam-3288	286	34	,	,	PUNCT
ejpam-3288	286	35	so	so	ADV
ejpam-3288	286	36	x	x	SYM
ejpam-3288	286	37	∗	∗	NOUN
ejpam-3288	286	38	z	z	PROPN
ejpam-3288	286	39	∈	∈	PROPN
ejpam-3288	286	40	ans	an	NOUN
ejpam-3288	286	41	.	.	PUNCT
ejpam-3288	287	1	hence	hence	ADV
ejpam-3288	287	2	,	,	PUNCT
ejpam-3288	287	3	ans	ans	X
ejpam-3288	287	4	is	be	AUX
ejpam-3288	287	5	an	an	DET
ejpam-3288	287	6	h	h	NOUN
ejpam-3288	287	7	-	-	PUNCT
ejpam-3288	287	8	ideal	ideal	NOUN
ejpam-3288	287	9	of	of	ADP
ejpam-3288	287	10	x.	x.	PROPN
ejpam-3288	287	11	a.	a.	PROPN
ejpam-3288	287	12	al	al	PROPN
ejpam-3288	287	13	-	-	PROPN
ejpam-3288	287	14	masarwah	masarwah	PROPN
ejpam-3288	287	15	,	,	PUNCT
ejpam-3288	287	16	a.	a.	NOUN
ejpam-3288	287	17	g.	g.	PROPN
ejpam-3288	287	18	ahmad	ahmad	PROPN
ejpam-3288	287	19	/	/	SYM
ejpam-3288	287	20	eur	eur	PROPN
ejpam-3288	287	21	.	.	PUNCT
ejpam-3288	288	1	j.	j.	PROPN
ejpam-3288	288	2	pure	pure	PROPN
ejpam-3288	288	3	appl	appl	PROPN
ejpam-3288	288	4	.	.	PROPN
ejpam-3288	288	5	math	math	PROPN
ejpam-3288	288	6	,	,	PUNCT
ejpam-3288	288	7	11	11	NUM
ejpam-3288	288	8	(	(	PUNCT
ejpam-3288	288	9	3	3	NUM
ejpam-3288	288	10	)	)	PUNCT
ejpam-3288	288	11	(	(	PUNCT
ejpam-3288	288	12	2018	2018	NUM
ejpam-3288	288	13	)	)	PUNCT
ejpam-3288	288	14	,	,	PUNCT
ejpam-3288	288	15	652	652	NUM
ejpam-3288	288	16	-	-	SYM
ejpam-3288	288	17	670	670	NUM
ejpam-3288	288	18	665	665	NUM
ejpam-3288	288	19	(	(	PUNCT
ejpam-3288	288	20	2	2	NUM
ejpam-3288	288	21	⇒	⇒	NOUN
ejpam-3288	288	22	1	1	NUM
ejpam-3288	288	23	)	)	PUNCT
ejpam-3288	288	24	suppose	suppose	VERB
ejpam-3288	288	25	that	that	SCONJ
ejpam-3288	288	26	apt	apt	ADJ
ejpam-3288	288	27	6=	6=	NUM
ejpam-3288	288	28	∅	∅	NOUN
ejpam-3288	288	29	and	and	CCONJ
ejpam-3288	288	30	ant	ant	ADJ
ejpam-3288	288	31	6=	6=	PUNCT
ejpam-3288	288	32	∅	∅	NOUN
ejpam-3288	288	33	are	be	AUX
ejpam-3288	288	34	h	h	NOUN
ejpam-3288	288	35	-	-	PUNCT
ejpam-3288	288	36	ideals	ideal	NOUN
ejpam-3288	288	37	of	of	ADP
ejpam-3288	288	38	x	x	PUNCT
ejpam-3288	288	39	for	for	ADP
ejpam-3288	288	40	all	all	DET
ejpam-3288	288	41	t	t	NOUN
ejpam-3288	288	42	∈	∈	PROPN
ejpam-3288	289	1	[	[	X
ejpam-3288	289	2	0	0	NUM
ejpam-3288	289	3	,	,	PUNCT
ejpam-3288	289	4	1	1	NUM
ejpam-3288	289	5	]	]	PUNCT
ejpam-3288	289	6	and	and	CCONJ
ejpam-3288	289	7	s	s	X
ejpam-3288	289	8	∈	∈	PROPN
ejpam-3288	289	9	[	[	X
ejpam-3288	289	10	−1	−1	NOUN
ejpam-3288	289	11	,	,	PUNCT
ejpam-3288	289	12	0	0	NUM
ejpam-3288	289	13	]	]	PUNCT
ejpam-3288	289	14	.	.	PUNCT
ejpam-3288	290	1	assume	assume	VERB
ejpam-3288	290	2	that	that	SCONJ
ejpam-3288	290	3	there	there	PRON
ejpam-3288	290	4	exists	exist	VERB
ejpam-3288	290	5	a	a	DET
ejpam-3288	290	6	∈	∈	NOUN
ejpam-3288	290	7	x	x	PUNCT
ejpam-3288	290	8	such	such	ADJ
ejpam-3288	290	9	that	that	SCONJ
ejpam-3288	290	10	µpa(0	µpa(0	NOUN
ejpam-3288	290	11	)	)	PUNCT
ejpam-3288	290	12	>	>	PUNCT
ejpam-3288	291	1	µpa(a	µpa(a	PROPN
ejpam-3288	291	2	)	)	PUNCT
ejpam-3288	291	3	and	and	CCONJ
ejpam-3288	291	4	µna	µna	ADJ
ejpam-3288	291	5	(	(	PUNCT
ejpam-3288	291	6	0	0	NUM
ejpam-3288	291	7	)	)	PUNCT
ejpam-3288	291	8	<	<	X
ejpam-3288	291	9	µna	µna	ADJ
ejpam-3288	291	10	(	(	PUNCT
ejpam-3288	291	11	a	a	NOUN
ejpam-3288	291	12	)	)	PUNCT
ejpam-3288	291	13	.	.	PUNCT
ejpam-3288	292	1	taking	take	VERB
ejpam-3288	292	2	to	to	ADP
ejpam-3288	292	3	=	=	SYM
ejpam-3288	292	4	1	1	NUM
ejpam-3288	292	5	2	2	NUM
ejpam-3288	292	6	(	(	PUNCT
ejpam-3288	292	7	µpa(0	µpa(0	ADJ
ejpam-3288	292	8	)	)	PUNCT
ejpam-3288	292	9	+	+	NUM
ejpam-3288	292	10	µpa(a	µpa(a	NUM
ejpam-3288	292	11	)	)	PUNCT
ejpam-3288	292	12	)	)	PUNCT
ejpam-3288	292	13	,	,	PUNCT
ejpam-3288	292	14	so	so	CCONJ
ejpam-3288	292	15	=	=	SYM
ejpam-3288	292	16	1	1	NUM
ejpam-3288	292	17	2	2	NUM
ejpam-3288	292	18	(	(	PUNCT
ejpam-3288	292	19	µna	µna	ADJ
ejpam-3288	292	20	(	(	PUNCT
ejpam-3288	292	21	0	0	NUM
ejpam-3288	292	22	)	)	PUNCT
ejpam-3288	292	23	+	+	CCONJ
ejpam-3288	292	24	µna	µna	ADJ
ejpam-3288	292	25	(	(	PUNCT
ejpam-3288	292	26	a	a	NOUN
ejpam-3288	292	27	)	)	PUNCT
ejpam-3288	292	28	)	)	PUNCT
ejpam-3288	292	29	,	,	PUNCT
ejpam-3288	292	30	implies	imply	VERB
ejpam-3288	292	31	that	that	SCONJ
ejpam-3288	292	32	µpa(a	µpa(a	PROPN
ejpam-3288	292	33	)	)	PUNCT
ejpam-3288	292	34	<	<	X
ejpam-3288	292	35	to	to	ADP
ejpam-3288	292	36	<	<	X
ejpam-3288	292	37	µpa(0	µpa(0	ADJ
ejpam-3288	292	38	)	)	PUNCT
ejpam-3288	292	39	and	and	CCONJ
ejpam-3288	292	40	µna	µna	ADJ
ejpam-3288	292	41	(	(	PUNCT
ejpam-3288	292	42	a	a	NOUN
ejpam-3288	292	43	)	)	PUNCT
ejpam-3288	292	44	>	>	X
ejpam-3288	292	45	so	so	CCONJ
ejpam-3288	292	46	>	>	X
ejpam-3288	292	47	µna	µna	ADJ
ejpam-3288	292	48	(	(	PUNCT
ejpam-3288	292	49	0	0	NUM
ejpam-3288	292	50	)	)	PUNCT
ejpam-3288	292	51	.	.	PUNCT
ejpam-3288	293	1	this	this	PRON
ejpam-3288	293	2	shows	show	VERB
ejpam-3288	293	3	that	that	SCONJ
ejpam-3288	293	4	0	0	NUM
ejpam-3288	293	5	/∈	/∈	SYM
ejpam-3288	293	6	apt	apt	ADJ
ejpam-3288	293	7	and	and	CCONJ
ejpam-3288	293	8	0	0	NUM
ejpam-3288	293	9	/∈	/∈	PUNCT
ejpam-3288	293	10	ans	an	NOUN
ejpam-3288	293	11	,	,	PUNCT
ejpam-3288	293	12	which	which	PRON
ejpam-3288	293	13	leads	lead	VERB
ejpam-3288	293	14	to	to	ADP
ejpam-3288	293	15	a	a	DET
ejpam-3288	293	16	contradiction	contradiction	NOUN
ejpam-3288	293	17	.	.	PUNCT
ejpam-3288	294	1	therefore	therefore	ADV
ejpam-3288	294	2	,	,	PUNCT
ejpam-3288	294	3	µpa(0	µpa(0	NOUN
ejpam-3288	294	4	)	)	PUNCT
ejpam-3288	294	5	≤	≤	NUM
ejpam-3288	294	6	µpa(x	µpa(x	NOUN
ejpam-3288	294	7	)	)	PUNCT
ejpam-3288	294	8	and	and	CCONJ
ejpam-3288	294	9	µna	µna	ADJ
ejpam-3288	294	10	(	(	PUNCT
ejpam-3288	294	11	0	0	NUM
ejpam-3288	294	12	)	)	PUNCT
ejpam-3288	294	13	≥	≥	NOUN
ejpam-3288	294	14	µna	µna	ADJ
ejpam-3288	294	15	(	(	PUNCT
ejpam-3288	294	16	x	x	NOUN
ejpam-3288	294	17	)	)	PUNCT
ejpam-3288	294	18	for	for	ADP
ejpam-3288	294	19	all	all	PRON
ejpam-3288	294	20	x	x	SYM
ejpam-3288	294	21	∈	∈	NOUN
ejpam-3288	294	22	x.	x.	NOUN
ejpam-3288	294	23	now	now	ADV
ejpam-3288	294	24	,	,	PUNCT
ejpam-3288	294	25	suppose	suppose	VERB
ejpam-3288	294	26	that	that	SCONJ
ejpam-3288	294	27	there	there	PRON
ejpam-3288	294	28	are	be	VERB
ejpam-3288	294	29	a	a	DET
ejpam-3288	294	30	,	,	PUNCT
ejpam-3288	294	31	b	b	NOUN
ejpam-3288	294	32	,	,	PUNCT
ejpam-3288	294	33	c	c	PROPN
ejpam-3288	294	34	∈	∈	PROPN
ejpam-3288	294	35	x	x	PUNCT
ejpam-3288	294	36	such	such	ADJ
ejpam-3288	294	37	that	that	SCONJ
ejpam-3288	294	38	µpa(a	µpa(a	PROPN
ejpam-3288	294	39	∗	∗	NOUN
ejpam-3288	294	40	c	c	NOUN
ejpam-3288	294	41	)	)	PUNCT
ejpam-3288	294	42	>	>	X
ejpam-3288	295	1	max{µpa(a	max{µpa(a	PROPN
ejpam-3288	295	2	∗	∗	NOUN
ejpam-3288	295	3	(	(	PUNCT
ejpam-3288	295	4	b	b	NOUN
ejpam-3288	295	5	∗	∗	NOUN
ejpam-3288	295	6	c	c	NOUN
ejpam-3288	295	7	)	)	PUNCT
ejpam-3288	295	8	)	)	PUNCT
ejpam-3288	295	9	,	,	PUNCT
ejpam-3288	295	10	µpa(b	µpa(b	PROPN
ejpam-3288	295	11	)	)	PUNCT
ejpam-3288	295	12	}	}	PUNCT
ejpam-3288	295	13	.	.	PUNCT
ejpam-3288	296	1	then	then	ADV
ejpam-3288	296	2	by	by	ADP
ejpam-3288	296	3	taking	take	VERB
ejpam-3288	296	4	t1	t1	NOUN
ejpam-3288	296	5	=	=	NOUN
ejpam-3288	296	6	1	1	NUM
ejpam-3288	296	7	2	2	NUM
ejpam-3288	296	8	(	(	PUNCT
ejpam-3288	296	9	µpa(a	µpa(a	PROPN
ejpam-3288	296	10	∗	∗	NOUN
ejpam-3288	296	11	c	c	NOUN
ejpam-3288	296	12	)	)	PUNCT
ejpam-3288	296	13	+	+	CCONJ
ejpam-3288	296	14	max{µpa(a	max{µpa(a	NOUN
ejpam-3288	296	15	∗	∗	NOUN
ejpam-3288	296	16	(	(	PUNCT
ejpam-3288	296	17	b	b	NOUN
ejpam-3288	296	18	∗	∗	NOUN
ejpam-3288	296	19	c	c	NOUN
ejpam-3288	296	20	)	)	PUNCT
ejpam-3288	296	21	)	)	PUNCT
ejpam-3288	296	22	,	,	PUNCT
ejpam-3288	296	23	µpa(b	µpa(b	PROPN
ejpam-3288	296	24	)	)	PUNCT
ejpam-3288	296	25	}	}	PUNCT
ejpam-3288	296	26	)	)	PUNCT
ejpam-3288	296	27	,	,	PUNCT
ejpam-3288	296	28	we	we	PRON
ejpam-3288	296	29	have	have	VERB
ejpam-3288	296	30	max{µpa(a∗	max{µpa(a∗	NOUN
ejpam-3288	296	31	(	(	PUNCT
ejpam-3288	296	32	b∗	b∗	ADJ
ejpam-3288	296	33	c	c	NOUN
ejpam-3288	296	34	)	)	PUNCT
ejpam-3288	296	35	,	,	PUNCT
ejpam-3288	296	36	µpa(b	µpa(b	PROPN
ejpam-3288	296	37	)	)	PUNCT
ejpam-3288	296	38	}	}	PUNCT
ejpam-3288	296	39	<	<	X
ejpam-3288	297	1	t1	t1	NOUN
ejpam-3288	297	2	<	<	X
ejpam-3288	297	3	µpa(a∗	µpa(a∗	X
ejpam-3288	297	4	c	c	NOUN
ejpam-3288	297	5	)	)	PUNCT
ejpam-3288	297	6	.	.	PUNCT
ejpam-3288	298	1	hence	hence	ADV
ejpam-3288	298	2	a∗	a∗	PROPN
ejpam-3288	298	3	c	c	PROPN
ejpam-3288	298	4	/∈	/∈	PUNCT
ejpam-3288	299	1	apt1	apt1	PROPN
ejpam-3288	299	2	,	,	PUNCT
ejpam-3288	299	3	a∗	a∗	PROPN
ejpam-3288	299	4	(	(	PUNCT
ejpam-3288	299	5	b∗	b∗	ADJ
ejpam-3288	299	6	c	c	NOUN
ejpam-3288	299	7	)	)	PUNCT
ejpam-3288	299	8	)	)	PUNCT
ejpam-3288	300	1	∈	∈	PROPN
ejpam-3288	300	2	apt1	apt1	NOUN
ejpam-3288	300	3	and	and	CCONJ
ejpam-3288	300	4	b	b	X
ejpam-3288	300	5	∈	∈	PROPN
ejpam-3288	300	6	apt1	apt1	NOUN
ejpam-3288	300	7	,	,	PUNCT
ejpam-3288	300	8	that	that	PRON
ejpam-3288	300	9	is	be	AUX
ejpam-3288	300	10	apt1	apt1	NOUN
ejpam-3288	300	11	is	be	AUX
ejpam-3288	300	12	not	not	PART
ejpam-3288	300	13	hideal	hideal	ADJ
ejpam-3288	300	14	of	of	ADP
ejpam-3288	300	15	x	x	X
ejpam-3288	300	16	,	,	PUNCT
ejpam-3288	300	17	which	which	PRON
ejpam-3288	300	18	a	a	DET
ejpam-3288	300	19	contradiction	contradiction	NOUN
ejpam-3288	300	20	.	.	PUNCT
ejpam-3288	301	1	therefore	therefore	ADV
ejpam-3288	301	2	,	,	PUNCT
ejpam-3288	301	3	µpa(x	µpa(x	PROPN
ejpam-3288	301	4	∗	∗	NOUN
ejpam-3288	301	5	y	y	NOUN
ejpam-3288	301	6	)	)	PUNCT
ejpam-3288	301	7	≤	≤	PROPN
ejpam-3288	301	8	max{µpa(x	max{µpa(x	PROPN
ejpam-3288	301	9	∗	∗	NOUN
ejpam-3288	301	10	(	(	PUNCT
ejpam-3288	301	11	y	y	PROPN
ejpam-3288	301	12	∗	∗	PROPN
ejpam-3288	301	13	z	z	PROPN
ejpam-3288	301	14	)	)	PUNCT
ejpam-3288	301	15	)	)	PUNCT
ejpam-3288	301	16	,	,	PUNCT
ejpam-3288	301	17	µpa(y	µpa(y	PROPN
ejpam-3288	301	18	)	)	PUNCT
ejpam-3288	301	19	}	}	PUNCT
ejpam-3288	301	20	for	for	ADP
ejpam-3288	301	21	all	all	DET
ejpam-3288	301	22	x	x	NOUN
ejpam-3288	301	23	,	,	PUNCT
ejpam-3288	301	24	y	y	PROPN
ejpam-3288	301	25	,	,	PUNCT
ejpam-3288	301	26	z	z	PROPN
ejpam-3288	301	27	∈	∈	PROPN
ejpam-3288	301	28	x.	x.	NOUN
ejpam-3288	301	29	finally	finally	ADV
ejpam-3288	301	30	,	,	PUNCT
ejpam-3288	301	31	assume	assume	VERB
ejpam-3288	301	32	that	that	SCONJ
ejpam-3288	301	33	p	p	X
ejpam-3288	301	34	,	,	PUNCT
ejpam-3288	301	35	q	q	ADJ
ejpam-3288	301	36	,	,	PUNCT
ejpam-3288	301	37	r	r	NOUN
ejpam-3288	301	38	∈	∈	PROPN
ejpam-3288	301	39	x	x	PUNCT
ejpam-3288	301	40	such	such	ADJ
ejpam-3288	301	41	that	that	DET
ejpam-3288	301	42	µna	µna	ADJ
ejpam-3288	301	43	(	(	PUNCT
ejpam-3288	301	44	p	p	NOUN
ejpam-3288	301	45	∗	∗	NOUN
ejpam-3288	301	46	r	r	NOUN
ejpam-3288	301	47	)	)	PUNCT
ejpam-3288	301	48	<	<	X
ejpam-3288	301	49	min{µna	min{µna	PROPN
ejpam-3288	301	50	(	(	PUNCT
ejpam-3288	301	51	p	p	NOUN
ejpam-3288	301	52	∗	∗	NOUN
ejpam-3288	301	53	(	(	PUNCT
ejpam-3288	301	54	q	q	NOUN
ejpam-3288	301	55	∗	∗	NOUN
ejpam-3288	301	56	r	r	NOUN
ejpam-3288	301	57	)	)	PUNCT
ejpam-3288	301	58	)	)	PUNCT
ejpam-3288	301	59	,	,	PUNCT
ejpam-3288	301	60	µna	µna	ADJ
ejpam-3288	301	61	(	(	PUNCT
ejpam-3288	301	62	q	q	NOUN
ejpam-3288	301	63	)	)	PUNCT
ejpam-3288	301	64	}	}	PUNCT
ejpam-3288	301	65	.	.	PUNCT
ejpam-3288	302	1	taking	take	VERB
ejpam-3288	302	2	s1	s1	NOUN
ejpam-3288	302	3	=	=	SYM
ejpam-3288	302	4	1	1	NUM
ejpam-3288	302	5	2	2	NUM
ejpam-3288	302	6	(	(	PUNCT
ejpam-3288	302	7	µna	µna	ADJ
ejpam-3288	302	8	(	(	PUNCT
ejpam-3288	302	9	p	p	NOUN
ejpam-3288	302	10	∗	∗	NOUN
ejpam-3288	302	11	r	r	NOUN
ejpam-3288	302	12	)	)	PUNCT
ejpam-3288	303	1	+	+	NUM
ejpam-3288	303	2	min{µna	min{µna	NOUN
ejpam-3288	303	3	(	(	PUNCT
ejpam-3288	303	4	p	p	NOUN
ejpam-3288	303	5	∗	∗	NOUN
ejpam-3288	303	6	(	(	PUNCT
ejpam-3288	303	7	q	q	NOUN
ejpam-3288	303	8	∗	∗	NOUN
ejpam-3288	303	9	r	r	NOUN
ejpam-3288	303	10	)	)	PUNCT
ejpam-3288	303	11	)	)	PUNCT
ejpam-3288	303	12	,	,	PUNCT
ejpam-3288	303	13	µna	µna	ADJ
ejpam-3288	303	14	(	(	PUNCT
ejpam-3288	303	15	q	q	NOUN
ejpam-3288	303	16	)	)	PUNCT
ejpam-3288	303	17	}	}	PUNCT
ejpam-3288	303	18	)	)	PUNCT
ejpam-3288	303	19	,	,	PUNCT
ejpam-3288	303	20	then	then	ADV
ejpam-3288	303	21	µna	µna	ADJ
ejpam-3288	303	22	(	(	PUNCT
ejpam-3288	303	23	p	p	NOUN
ejpam-3288	303	24	∗	∗	NOUN
ejpam-3288	303	25	r	r	NOUN
ejpam-3288	303	26	)	)	PUNCT
ejpam-3288	303	27	<	<	X
ejpam-3288	303	28	s1	s1	PROPN
ejpam-3288	303	29	<	<	X
ejpam-3288	303	30	min{µna	min{µna	PROPN
ejpam-3288	303	31	(	(	PUNCT
ejpam-3288	303	32	p	p	NOUN
ejpam-3288	303	33	∗	∗	NOUN
ejpam-3288	303	34	(	(	PUNCT
ejpam-3288	303	35	q	q	NOUN
ejpam-3288	303	36	∗	∗	NOUN
ejpam-3288	303	37	r	r	NOUN
ejpam-3288	303	38	)	)	PUNCT
ejpam-3288	303	39	)	)	PUNCT
ejpam-3288	303	40	,	,	PUNCT
ejpam-3288	303	41	µna	µna	ADJ
ejpam-3288	303	42	(	(	PUNCT
ejpam-3288	303	43	q	q	NOUN
ejpam-3288	303	44	)	)	PUNCT
ejpam-3288	303	45	}	}	PUNCT
ejpam-3288	303	46	.	.	PUNCT
ejpam-3288	304	1	therefore	therefore	ADV
ejpam-3288	304	2	,	,	PUNCT
ejpam-3288	304	3	p	p	NOUN
ejpam-3288	304	4	∗	∗	NOUN
ejpam-3288	304	5	(	(	PUNCT
ejpam-3288	304	6	q	q	NOUN
ejpam-3288	304	7	∗	∗	NOUN
ejpam-3288	304	8	r	r	NOUN
ejpam-3288	304	9	)	)	PUNCT
ejpam-3288	304	10	∈	∈	NOUN
ejpam-3288	304	11	ans1	ans1	NOUN
ejpam-3288	304	12	and	and	CCONJ
ejpam-3288	304	13	q	q	PROPN
ejpam-3288	304	14	∈	∈	PROPN
ejpam-3288	304	15	ant1	ant1	PROPN
ejpam-3288	304	16	but	but	CCONJ
ejpam-3288	304	17	p	p	NOUN
ejpam-3288	304	18	∗	∗	NOUN
ejpam-3288	304	19	r	r	NOUN
ejpam-3288	304	20	/∈	/∈	PUNCT
ejpam-3288	304	21	ant1	ant1	PROPN
ejpam-3288	304	22	.	.	PUNCT
ejpam-3288	305	1	again	again	ADV
ejpam-3288	305	2	a	a	DET
ejpam-3288	305	3	contradiction	contradiction	NOUN
ejpam-3288	305	4	.	.	PUNCT
ejpam-3288	306	1	thus	thus	ADV
ejpam-3288	306	2	,	,	PUNCT
ejpam-3288	306	3	µna	µna	ADJ
ejpam-3288	306	4	(	(	PUNCT
ejpam-3288	306	5	x	x	NOUN
ejpam-3288	306	6	∗	∗	PROPN
ejpam-3288	306	7	z	z	NOUN
ejpam-3288	306	8	)	)	PUNCT
ejpam-3288	306	9	≥	≥	X
ejpam-3288	306	10	min{µna	min{µna	NOUN
ejpam-3288	306	11	(	(	PUNCT
ejpam-3288	306	12	x	x	NOUN
ejpam-3288	306	13	∗	∗	NOUN
ejpam-3288	306	14	(	(	PUNCT
ejpam-3288	306	15	y	y	PROPN
ejpam-3288	306	16	∗	∗	PROPN
ejpam-3288	306	17	z	z	PROPN
ejpam-3288	306	18	)	)	PUNCT
ejpam-3288	306	19	)	)	PUNCT
ejpam-3288	306	20	,	,	PUNCT
ejpam-3288	306	21	µna	µna	PROPN
ejpam-3288	306	22	(	(	PUNCT
ejpam-3288	306	23	y	y	NOUN
ejpam-3288	306	24	)	)	PUNCT
ejpam-3288	306	25	}	}	PUNCT
ejpam-3288	306	26	for	for	ADP
ejpam-3288	306	27	all	all	DET
ejpam-3288	306	28	x	x	NOUN
ejpam-3288	306	29	,	,	PUNCT
ejpam-3288	306	30	y	y	PROPN
ejpam-3288	306	31	,	,	PUNCT
ejpam-3288	306	32	z	z	PROPN
ejpam-3288	306	33	∈	∈	PROPN
ejpam-3288	306	34	x.	x.	NOUN
ejpam-3288	306	35	hence	hence	ADV
ejpam-3288	306	36	,	,	PUNCT
ejpam-3288	306	37	a	a	PRON
ejpam-3288	306	38	=	=	X
ejpam-3288	306	39	(	(	PUNCT
ejpam-3288	306	40	µpa	µpa	PROPN
ejpam-3288	306	41	,	,	PUNCT
ejpam-3288	306	42	µ	µ	X
ejpam-3288	306	43	n	n	PRON
ejpam-3288	306	44	a	a	PRON
ejpam-3288	306	45	)	)	PUNCT
ejpam-3288	306	46	is	be	AUX
ejpam-3288	306	47	a	a	DET
ejpam-3288	306	48	doubt	doubt	ADV
ejpam-3288	306	49	bipolar	bipolar	ADJ
ejpam-3288	306	50	fuzzy	fuzzy	ADJ
ejpam-3288	306	51	h	h	NOUN
ejpam-3288	306	52	-	-	PUNCT
ejpam-3288	306	53	ideal	ideal	NOUN
ejpam-3288	306	54	of	of	ADP
ejpam-3288	306	55	x.	x.	NOUN
ejpam-3288	306	56	example	example	NOUN
ejpam-3288	307	1	4	4	X
ejpam-3288	307	2	.	.	PUNCT
ejpam-3288	308	1	let	let	VERB
ejpam-3288	308	2	x	x	PUNCT
ejpam-3288	308	3	=	=	PUNCT
ejpam-3288	308	4	{	{	PUNCT
ejpam-3288	308	5	0	0	NUM
ejpam-3288	308	6	,	,	PUNCT
ejpam-3288	308	7	a	a	DET
ejpam-3288	308	8	,	,	PUNCT
ejpam-3288	308	9	b	b	NOUN
ejpam-3288	308	10	,	,	PUNCT
ejpam-3288	308	11	c	c	AUX
ejpam-3288	308	12	}	}	PUNCT
ejpam-3288	308	13	be	be	AUX
ejpam-3288	308	14	a	a	DET
ejpam-3288	308	15	bck	bck	NOUN
ejpam-3288	308	16	-	-	PUNCT
ejpam-3288	308	17	algebra	algebra	NOUN
ejpam-3288	308	18	with	with	ADP
ejpam-3288	308	19	the	the	DET
ejpam-3288	308	20	cayley	cayley	ADJ
ejpam-3288	308	21	table	table	NOUN
ejpam-3288	308	22	which	which	PRON
ejpam-3288	308	23	is	be	AUX
ejpam-3288	308	24	appeared	appear	VERB
ejpam-3288	308	25	in	in	ADP
ejpam-3288	308	26	table	table	NOUN
ejpam-3288	308	27	4	4	NUM
ejpam-3288	308	28	.	.	PUNCT
ejpam-3288	308	29	table	table	NOUN
ejpam-3288	308	30	4	4	NUM
ejpam-3288	308	31	:	:	PUNCT
ejpam-3288	308	32	cayley	cayley	ADJ
ejpam-3288	308	33	table	table	NOUN
ejpam-3288	308	34	for	for	ADP
ejpam-3288	308	35	the	the	DET
ejpam-3288	308	36	∗-operation	∗-operation	NOUN
ejpam-3288	308	37	.	.	PUNCT
ejpam-3288	309	1	∗	∗	NOUN
ejpam-3288	309	2	0	0	NUM
ejpam-3288	310	1	a	a	DET
ejpam-3288	310	2	b	b	NOUN
ejpam-3288	310	3	c	c	NOUN
ejpam-3288	310	4	0	0	NUM
ejpam-3288	310	5	0	0	NUM
ejpam-3288	310	6	0	0	NUM
ejpam-3288	310	7	0	0	NUM
ejpam-3288	310	8	0	0	NUM
ejpam-3288	310	9	a	a	DET
ejpam-3288	310	10	a	a	DET
ejpam-3288	310	11	0	0	PUNCT
ejpam-3288	310	12	a	a	DET
ejpam-3288	310	13	a	a	DET
ejpam-3288	310	14	b	b	NOUN
ejpam-3288	310	15	b	b	NOUN
ejpam-3288	310	16	a	a	DET
ejpam-3288	310	17	0	0	NUM
ejpam-3288	310	18	0	0	NUM
ejpam-3288	310	19	c	c	NOUN
ejpam-3288	310	20	c	c	PROPN
ejpam-3288	310	21	a	a	DET
ejpam-3288	310	22	c	c	NOUN
ejpam-3288	310	23	0	0	PUNCT
ejpam-3288	310	24	define	define	VERB
ejpam-3288	310	25	a	a	DET
ejpam-3288	310	26	bipolar	bipolar	ADJ
ejpam-3288	310	27	fuzzy	fuzzy	NOUN
ejpam-3288	310	28	set	set	VERB
ejpam-3288	310	29	a	a	DET
ejpam-3288	310	30	=	=	X
ejpam-3288	310	31	(	(	PUNCT
ejpam-3288	310	32	µpa	µpa	PROPN
ejpam-3288	310	33	,	,	PUNCT
ejpam-3288	310	34	µ	µ	X
ejpam-3288	310	35	n	n	PRON
ejpam-3288	310	36	a	a	NOUN
ejpam-3288	310	37	)	)	PUNCT
ejpam-3288	310	38	in	in	ADP
ejpam-3288	310	39	x	x	PUNCT
ejpam-3288	310	40	as	as	SCONJ
ejpam-3288	310	41	follows	follow	VERB
ejpam-3288	310	42	:	:	PUNCT
ejpam-3288	310	43	µpa(x	µpa(x	X
ejpam-3288	310	44	)	)	PUNCT
ejpam-3288	310	45	=	=	PUNCT
ejpam-3288	311	1			NUM
ejpam-3288	311	2	0.2	0.2	NUM
ejpam-3288	311	3	,	,	PUNCT
ejpam-3288	311	4	if	if	SCONJ
ejpam-3288	311	5	x	x	ADP
ejpam-3288	311	6	=	=	SYM
ejpam-3288	311	7	0	0	NUM
ejpam-3288	311	8	0.6	0.6	NUM
ejpam-3288	311	9	,	,	PUNCT
ejpam-3288	311	10	if	if	SCONJ
ejpam-3288	311	11	x	x	ADP
ejpam-3288	311	12	=	=	PUNCT
ejpam-3288	311	13	a	a	DET
ejpam-3288	311	14	0.8	0.8	NUM
ejpam-3288	311	15	,	,	PUNCT
ejpam-3288	311	16	if	if	SCONJ
ejpam-3288	311	17	x	x	ADP
ejpam-3288	311	18	=	=	SYM
ejpam-3288	311	19	b	b	PROPN
ejpam-3288	311	20	0.7	0.7	NUM
ejpam-3288	311	21	,	,	PUNCT
ejpam-3288	311	22	if	if	SCONJ
ejpam-3288	311	23	x	x	X
ejpam-3288	311	24	=	=	SYM
ejpam-3288	311	25	c	c	NOUN
ejpam-3288	311	26	,	,	PUNCT
ejpam-3288	311	27	and	and	CCONJ
ejpam-3288	311	28	µna	µna	ADJ
ejpam-3288	311	29	(	(	PUNCT
ejpam-3288	311	30	x	x	NOUN
ejpam-3288	311	31	)	)	PUNCT
ejpam-3288	311	32	=	=	SYM
ejpam-3288	311	33	{	{	PUNCT
ejpam-3288	311	34	−0.3	−0.3	PROPN
ejpam-3288	311	35	,	,	PUNCT
ejpam-3288	311	36	if	if	SCONJ
ejpam-3288	311	37	x	x	ADP
ejpam-3288	311	38	=	=	SYM
ejpam-3288	311	39	0	0	NUM
ejpam-3288	311	40	,	,	PUNCT
ejpam-3288	311	41	a	a	PRON
ejpam-3288	311	42	,	,	PUNCT
ejpam-3288	311	43	c	c	PROPN
ejpam-3288	312	1	−0.5	−0.5	PROPN
ejpam-3288	312	2	,	,	PUNCT
ejpam-3288	312	3	if	if	SCONJ
ejpam-3288	312	4	x	x	ADP
ejpam-3288	312	5	=	=	SYM
ejpam-3288	312	6	b	b	PROPN
ejpam-3288	312	7	,	,	PUNCT
ejpam-3288	312	8	a.	a.	PROPN
ejpam-3288	312	9	al	al	PROPN
ejpam-3288	312	10	-	-	PROPN
ejpam-3288	312	11	masarwah	masarwah	PROPN
ejpam-3288	312	12	,	,	PUNCT
ejpam-3288	312	13	a.	a.	NOUN
ejpam-3288	312	14	g.	g.	PROPN
ejpam-3288	312	15	ahmad	ahmad	PROPN
ejpam-3288	312	16	/	/	SYM
ejpam-3288	312	17	eur	eur	PROPN
ejpam-3288	312	18	.	.	PUNCT
ejpam-3288	313	1	j.	j.	PROPN
ejpam-3288	313	2	pure	pure	PROPN
ejpam-3288	313	3	appl	appl	PROPN
ejpam-3288	313	4	.	.	PROPN
ejpam-3288	313	5	math	math	PROPN
ejpam-3288	313	6	,	,	PUNCT
ejpam-3288	313	7	11	11	NUM
ejpam-3288	313	8	(	(	PUNCT
ejpam-3288	313	9	3	3	NUM
ejpam-3288	313	10	)	)	PUNCT
ejpam-3288	313	11	(	(	PUNCT
ejpam-3288	313	12	2018	2018	NUM
ejpam-3288	313	13	)	)	PUNCT
ejpam-3288	313	14	,	,	PUNCT
ejpam-3288	313	15	652	652	NUM
ejpam-3288	313	16	-	-	SYM
ejpam-3288	313	17	670	670	NUM
ejpam-3288	313	18	666	666	NUM
ejpam-3288	313	19	which	which	PRON
ejpam-3288	313	20	is	be	AUX
ejpam-3288	313	21	not	not	PART
ejpam-3288	313	22	a	a	DET
ejpam-3288	313	23	doubt	doubt	ADV
ejpam-3288	313	24	bipolar	bipolar	ADJ
ejpam-3288	313	25	fuzzy	fuzzy	ADJ
ejpam-3288	313	26	hideal	hideal	NOUN
ejpam-3288	313	27	of	of	ADP
ejpam-3288	313	28	x	x	PRON
ejpam-3288	313	29	,	,	PUNCT
ejpam-3288	313	30	since	since	SCONJ
ejpam-3288	313	31	µpa(b	µpa(b	PRON
ejpam-3288	313	32	∗	∗	NOUN
ejpam-3288	313	33	0	0	NUM
ejpam-3288	313	34	)	)	PUNCT
ejpam-3288	313	35	=	=	SYM
ejpam-3288	314	1	µpa(b	µpa(b	ADJ
ejpam-3288	314	2	)	)	PUNCT
ejpam-3288	314	3	=	=	SYM
ejpam-3288	314	4	0.8	0.8	NUM
ejpam-3288	314	5	max{µpa((b	max{µpa((b	NOUN
ejpam-3288	314	6	∗	∗	NOUN
ejpam-3288	314	7	(	(	PUNCT
ejpam-3288	314	8	a	a	DET
ejpam-3288	314	9	∗	∗	NOUN
ejpam-3288	314	10	0	0	NUM
ejpam-3288	314	11	)	)	PUNCT
ejpam-3288	314	12	)	)	PUNCT
ejpam-3288	314	13	)	)	PUNCT
ejpam-3288	314	14	,	,	PUNCT
ejpam-3288	314	15	µpa(a	µpa(a	PROPN
ejpam-3288	314	16	)	)	PUNCT
ejpam-3288	314	17	}	}	PUNCT
ejpam-3288	314	18	=	=	SYM
ejpam-3288	314	19	max{µpa(a	max{µpa(a	PROPN
ejpam-3288	314	20	)	)	PUNCT
ejpam-3288	314	21	,	,	PUNCT
ejpam-3288	314	22	µpa(a	µpa(a	PROPN
ejpam-3288	314	23	)	)	PUNCT
ejpam-3288	314	24	}	}	PUNCT
ejpam-3288	314	25	=	=	SYM
ejpam-3288	314	26	0.6	0.6	X
ejpam-3288	314	27	.	.	PUNCT
ejpam-3288	315	1	now	now	ADV
ejpam-3288	315	2	,	,	PUNCT
ejpam-3288	315	3	for	for	ADP
ejpam-3288	315	4	t	t	NOUN
ejpam-3288	315	5	=	=	SYM
ejpam-3288	315	6	0.75	0.75	NUM
ejpam-3288	315	7	and	and	CCONJ
ejpam-3288	315	8	s	s	X
ejpam-3288	315	9	=	=	NOUN
ejpam-3288	315	10	−0.45	−0.45	NOUN
ejpam-3288	315	11	,	,	PUNCT
ejpam-3288	315	12	we	we	PRON
ejpam-3288	315	13	get	get	VERB
ejpam-3288	315	14	apt	apt	ADJ
ejpam-3288	315	15	=	=	SYM
ejpam-3288	315	16	ans	ans	X
ejpam-3288	315	17	=	=	PUNCT
ejpam-3288	315	18	{	{	PUNCT
ejpam-3288	315	19	0	0	NUM
ejpam-3288	315	20	,	,	PUNCT
ejpam-3288	315	21	a	a	PRON
ejpam-3288	315	22	,	,	PUNCT
ejpam-3288	315	23	c	c	NOUN
ejpam-3288	315	24	}	}	PUNCT
ejpam-3288	315	25	which	which	PRON
ejpam-3288	315	26	are	be	AUX
ejpam-3288	315	27	not	not	PART
ejpam-3288	315	28	h	h	NOUN
ejpam-3288	315	29	-	-	PUNCT
ejpam-3288	315	30	ideals	ideal	NOUN
ejpam-3288	315	31	of	of	ADP
ejpam-3288	315	32	x	x	PRON
ejpam-3288	315	33	,	,	PUNCT
ejpam-3288	315	34	since	since	SCONJ
ejpam-3288	315	35	a	a	DET
ejpam-3288	315	36	∈	∈	PROPN
ejpam-3288	315	37	{	{	PUNCT
ejpam-3288	315	38	0	0	NUM
ejpam-3288	315	39	,	,	PUNCT
ejpam-3288	315	40	a	a	PRON
ejpam-3288	315	41	,	,	PUNCT
ejpam-3288	315	42	c	c	NOUN
ejpam-3288	315	43	}	}	PUNCT
ejpam-3288	315	44	and	and	CCONJ
ejpam-3288	315	45	b	b	NOUN
ejpam-3288	315	46	∗	∗	NOUN
ejpam-3288	315	47	(	(	PUNCT
ejpam-3288	315	48	a	a	DET
ejpam-3288	315	49	∗	∗	NOUN
ejpam-3288	315	50	0	0	NUM
ejpam-3288	315	51	)	)	PUNCT
ejpam-3288	315	52	=	=	SYM
ejpam-3288	315	53	b	b	PROPN
ejpam-3288	315	54	∗	∗	NOUN
ejpam-3288	315	55	a	a	PRON
ejpam-3288	315	56	=	=	NOUN
ejpam-3288	315	57	a	a	DET
ejpam-3288	315	58	∈	∈	PROPN
ejpam-3288	315	59	{	{	PUNCT
ejpam-3288	315	60	0	0	NUM
ejpam-3288	315	61	,	,	PUNCT
ejpam-3288	315	62	a	a	DET
ejpam-3288	315	63	,	,	PUNCT
ejpam-3288	315	64	c	c	NOUN
ejpam-3288	315	65	}	}	PUNCT
ejpam-3288	315	66	,	,	PUNCT
ejpam-3288	315	67	but	but	CCONJ
ejpam-3288	315	68	b	b	X
ejpam-3288	315	69	∗	∗	NOUN
ejpam-3288	315	70	0	0	NUM
ejpam-3288	316	1	=	=	SYM
ejpam-3288	316	2	b	b	SYM
ejpam-3288	316	3	6∈	6∈	NUM
ejpam-3288	316	4	{	{	PUNCT
ejpam-3288	316	5	0	0	NUM
ejpam-3288	316	6	,	,	PUNCT
ejpam-3288	316	7	a	a	DET
ejpam-3288	316	8	,	,	PUNCT
ejpam-3288	316	9	c	c	NOUN
ejpam-3288	316	10	}	}	PUNCT
ejpam-3288	316	11	.	.	PUNCT
ejpam-3288	317	1	corollary	corollary	ADJ
ejpam-3288	317	2	2	2	NUM
ejpam-3288	317	3	.	.	PUNCT
ejpam-3288	318	1	if	if	SCONJ
ejpam-3288	318	2	a	a	PRON
ejpam-3288	318	3	=	=	X
ejpam-3288	318	4	(	(	PUNCT
ejpam-3288	318	5	µpa	µpa	PROPN
ejpam-3288	318	6	,	,	PUNCT
ejpam-3288	318	7	µ	µ	X
ejpam-3288	318	8	n	n	PRON
ejpam-3288	318	9	a	a	PRON
ejpam-3288	318	10	)	)	PUNCT
ejpam-3288	318	11	is	be	AUX
ejpam-3288	318	12	a	a	DET
ejpam-3288	318	13	doubt	doubt	ADV
ejpam-3288	318	14	bipolar	bipolar	ADJ
ejpam-3288	318	15	fuzzy	fuzzy	ADJ
ejpam-3288	318	16	h	h	NOUN
ejpam-3288	318	17	-	-	PUNCT
ejpam-3288	318	18	ideal	ideal	NOUN
ejpam-3288	318	19	of	of	ADP
ejpam-3288	318	20	x	x	PRON
ejpam-3288	318	21	,	,	PUNCT
ejpam-3288	318	22	then	then	ADV
ejpam-3288	318	23	the	the	DET
ejpam-3288	318	24	doubt	doubt	ADV
ejpam-3288	318	25	γ	γ	ADJ
ejpam-3288	318	26	-	-	PUNCT
ejpam-3288	318	27	level	level	NOUN
ejpam-3288	318	28	cut	cut	NOUN
ejpam-3288	318	29	set	set	NOUN
ejpam-3288	318	30	of	of	ADP
ejpam-3288	318	31	a	a	DET
ejpam-3288	318	32	=	=	X
ejpam-3288	318	33	(	(	PUNCT
ejpam-3288	318	34	µpa	µpa	PROPN
ejpam-3288	318	35	,	,	PUNCT
ejpam-3288	318	36	µ	µ	X
ejpam-3288	318	37	n	n	PRON
ejpam-3288	318	38	a	a	PRON
ejpam-3288	318	39	)	)	PUNCT
ejpam-3288	318	40	is	be	AUX
ejpam-3288	318	41	a	a	DET
ejpam-3288	318	42	doubt	doubt	ADV
ejpam-3288	318	43	bipolar	bipolar	ADJ
ejpam-3288	318	44	fuzzy	fuzzy	ADJ
ejpam-3288	318	45	h	h	NOUN
ejpam-3288	318	46	-	-	PUNCT
ejpam-3288	318	47	ideal	ideal	NOUN
ejpam-3288	318	48	of	of	ADP
ejpam-3288	318	49	x	x	PRON
ejpam-3288	318	50	,	,	PUNCT
ejpam-3288	318	51	for	for	ADP
ejpam-3288	318	52	all	all	DET
ejpam-3288	318	53	γ	γ	X
ejpam-3288	318	54	∈	∈	PROPN
ejpam-3288	319	1	[	[	X
ejpam-3288	319	2	0	0	NUM
ejpam-3288	319	3	,	,	PUNCT
ejpam-3288	319	4	1	1	NUM
ejpam-3288	319	5	]	]	PUNCT
ejpam-3288	319	6	.	.	PUNCT
ejpam-3288	320	1	corollary	corollary	ADJ
ejpam-3288	320	2	3	3	X
ejpam-3288	320	3	.	.	PUNCT
ejpam-3288	321	1	if	if	SCONJ
ejpam-3288	321	2	a	a	PRON
ejpam-3288	321	3	=	=	X
ejpam-3288	321	4	(	(	PUNCT
ejpam-3288	321	5	µpa	µpa	PROPN
ejpam-3288	321	6	,	,	PUNCT
ejpam-3288	321	7	µ	µ	X
ejpam-3288	321	8	n	n	PRON
ejpam-3288	321	9	a	a	PRON
ejpam-3288	321	10	)	)	PUNCT
ejpam-3288	321	11	is	be	AUX
ejpam-3288	321	12	a	a	DET
ejpam-3288	321	13	doubt	doubt	ADV
ejpam-3288	321	14	bipolar	bipolar	ADJ
ejpam-3288	321	15	fuzzy	fuzzy	ADJ
ejpam-3288	321	16	h	h	NOUN
ejpam-3288	321	17	-	-	PUNCT
ejpam-3288	321	18	ideal	ideal	NOUN
ejpam-3288	321	19	of	of	ADP
ejpam-3288	321	20	x.	x.	PROPN
ejpam-3288	321	21	then	then	ADV
ejpam-3288	321	22	s(s	s(s	PROPN
ejpam-3288	321	23	,	,	PUNCT
ejpam-3288	321	24	t	t	PROPN
ejpam-3288	321	25	)	)	PUNCT
ejpam-3288	321	26	is	be	AUX
ejpam-3288	321	27	an	an	DET
ejpam-3288	321	28	h	h	NOUN
ejpam-3288	321	29	-	-	PUNCT
ejpam-3288	321	30	ideal	ideal	NOUN
ejpam-3288	321	31	of	of	ADP
ejpam-3288	321	32	x	x	PUNCT
ejpam-3288	321	33	for	for	ADP
ejpam-3288	321	34	all	all	DET
ejpam-3288	321	35	(	(	PUNCT
ejpam-3288	321	36	s	s	PROPN
ejpam-3288	321	37	,	,	PUNCT
ejpam-3288	321	38	t	t	PROPN
ejpam-3288	321	39	)	)	PUNCT
ejpam-3288	321	40	∈	∈	PROPN
ejpam-3288	322	1	[	[	X
ejpam-3288	322	2	−1	−1	NOUN
ejpam-3288	322	3	,	,	PUNCT
ejpam-3288	322	4	0	0	NUM
ejpam-3288	322	5	]	]	X
ejpam-3288	322	6	×	×	NOUN
ejpam-3288	323	1	[	[	X
ejpam-3288	323	2	0	0	NUM
ejpam-3288	323	3	,	,	PUNCT
ejpam-3288	323	4	1	1	NUM
ejpam-3288	323	5	]	]	PUNCT
ejpam-3288	323	6	.	.	PUNCT
ejpam-3288	324	1	in	in	ADP
ejpam-3288	324	2	particular	particular	ADJ
ejpam-3288	324	3	,	,	PUNCT
ejpam-3288	324	4	the	the	DET
ejpam-3288	324	5	nonempty	nonempty	NOUN
ejpam-3288	324	6	doubt	doubt	VERB
ejpam-3288	324	7	γ	γ	NOUN
ejpam-3288	324	8	-	-	PUNCT
ejpam-3288	324	9	level	level	NOUN
ejpam-3288	324	10	cut	cut	NOUN
ejpam-3288	324	11	set	set	NOUN
ejpam-3288	324	12	of	of	ADP
ejpam-3288	324	13	a	a	DET
ejpam-3288	324	14	=	=	X
ejpam-3288	324	15	(	(	PUNCT
ejpam-3288	324	16	µpa	µpa	PROPN
ejpam-3288	324	17	,	,	PUNCT
ejpam-3288	324	18	µ	µ	X
ejpam-3288	324	19	n	n	PRON
ejpam-3288	324	20	a	a	PRON
ejpam-3288	324	21	)	)	PUNCT
ejpam-3288	324	22	is	be	AUX
ejpam-3288	324	23	an	an	DET
ejpam-3288	324	24	h	h	NOUN
ejpam-3288	324	25	-	-	PUNCT
ejpam-3288	324	26	ideal	ideal	NOUN
ejpam-3288	324	27	of	of	ADP
ejpam-3288	324	28	x	x	PUNCT
ejpam-3288	324	29	for	for	ADP
ejpam-3288	324	30	all	all	DET
ejpam-3288	324	31	γ	γ	X
ejpam-3288	324	32	∈	∈	PROPN
ejpam-3288	325	1	[	[	X
ejpam-3288	325	2	0	0	NUM
ejpam-3288	325	3	,	,	PUNCT
ejpam-3288	325	4	1	1	NUM
ejpam-3288	325	5	]	]	PUNCT
ejpam-3288	325	6	.	.	PUNCT
ejpam-3288	326	1	theorem	theorem	ADJ
ejpam-3288	326	2	8	8	NUM
ejpam-3288	326	3	.	.	PUNCT
ejpam-3288	327	1	if	if	SCONJ
ejpam-3288	327	2	a	a	PRON
ejpam-3288	327	3	=	=	X
ejpam-3288	327	4	(	(	PUNCT
ejpam-3288	327	5	µpa	µpa	PROPN
ejpam-3288	327	6	,	,	PUNCT
ejpam-3288	327	7	µ	µ	X
ejpam-3288	327	8	n	n	PRON
ejpam-3288	327	9	a	a	PRON
ejpam-3288	327	10	)	)	PUNCT
ejpam-3288	327	11	is	be	AUX
ejpam-3288	327	12	a	a	DET
ejpam-3288	327	13	doubt	doubt	ADV
ejpam-3288	327	14	bipolar	bipolar	ADJ
ejpam-3288	327	15	fuzzy	fuzzy	ADJ
ejpam-3288	327	16	h	h	NOUN
ejpam-3288	327	17	-	-	PUNCT
ejpam-3288	327	18	ideal	ideal	NOUN
ejpam-3288	327	19	of	of	ADP
ejpam-3288	327	20	x	x	X
ejpam-3288	327	21	and	and	CCONJ
ejpam-3288	327	22	µpa(z)+µna	µpa(z)+µna	PROPN
ejpam-3288	327	23	(	(	PUNCT
ejpam-3288	327	24	z	z	NOUN
ejpam-3288	327	25	)	)	PUNCT
ejpam-3288	327	26	≤	≤	NOUN
ejpam-3288	327	27	0	0	NUM
ejpam-3288	327	28	for	for	ADP
ejpam-3288	327	29	all	all	DET
ejpam-3288	327	30	z	z	NOUN
ejpam-3288	327	31	∈	∈	PROPN
ejpam-3288	327	32	x	x	X
ejpam-3288	327	33	,	,	PUNCT
ejpam-3288	327	34	then	then	ADV
ejpam-3288	327	35	apγ	apγ	PROPN
ejpam-3288	327	36	∪an−γ	∪an−γ	PROPN
ejpam-3288	327	37	is	be	AUX
ejpam-3288	327	38	an	an	DET
ejpam-3288	327	39	hideal	hideal	NOUN
ejpam-3288	327	40	of	of	ADP
ejpam-3288	327	41	x	x	PUNCT
ejpam-3288	327	42	for	for	ADP
ejpam-3288	327	43	all	all	DET
ejpam-3288	327	44	γ	γ	X
ejpam-3288	327	45	∈	∈	PROPN
ejpam-3288	328	1	[	[	X
ejpam-3288	328	2	0	0	NUM
ejpam-3288	328	3	,	,	PUNCT
ejpam-3288	328	4	1	1	NUM
ejpam-3288	328	5	]	]	PUNCT
ejpam-3288	328	6	.	.	PUNCT
ejpam-3288	329	1	proof	proof	NOUN
ejpam-3288	329	2	.	.	PUNCT
ejpam-3288	330	1	given	give	VERB
ejpam-3288	330	2	that	that	PRON
ejpam-3288	330	3	a	a	PRON
ejpam-3288	330	4	=	=	SYM
ejpam-3288	330	5	(	(	PUNCT
ejpam-3288	330	6	µpa	µpa	PROPN
ejpam-3288	330	7	,	,	PUNCT
ejpam-3288	330	8	µ	µ	X
ejpam-3288	330	9	n	n	PRON
ejpam-3288	330	10	a	a	PRON
ejpam-3288	330	11	)	)	PUNCT
ejpam-3288	330	12	is	be	AUX
ejpam-3288	330	13	a	a	DET
ejpam-3288	330	14	doubt	doubt	ADV
ejpam-3288	330	15	bipolar	bipolar	ADJ
ejpam-3288	330	16	fuzzy	fuzzy	ADJ
ejpam-3288	330	17	h	h	NOUN
ejpam-3288	330	18	-	-	PUNCT
ejpam-3288	330	19	ideal	ideal	NOUN
ejpam-3288	330	20	of	of	ADP
ejpam-3288	330	21	x	x	X
ejpam-3288	330	22	and	and	CCONJ
ejpam-3288	330	23	µpa(z	µpa(z	PROPN
ejpam-3288	330	24	)	)	PUNCT
ejpam-3288	331	1	+	+	CCONJ
ejpam-3288	331	2	µna	µna	ADJ
ejpam-3288	331	3	(	(	PUNCT
ejpam-3288	331	4	z	z	NOUN
ejpam-3288	331	5	)	)	PUNCT
ejpam-3288	331	6	≤	≤	NOUN
ejpam-3288	331	7	0	0	NUM
ejpam-3288	331	8	for	for	ADP
ejpam-3288	331	9	all	all	DET
ejpam-3288	331	10	z	z	NOUN
ejpam-3288	331	11	∈	∈	NOUN
ejpam-3288	331	12	x.	x.	NOUN
ejpam-3288	331	13	assume	assume	VERB
ejpam-3288	331	14	that	that	SCONJ
ejpam-3288	331	15	apγ	apγ	PROPN
ejpam-3288	331	16	and	and	CCONJ
ejpam-3288	331	17	an−γ	an−γ	NOUN
ejpam-3288	331	18	are	be	AUX
ejpam-3288	331	19	nonempty	nonempty	ADJ
ejpam-3288	331	20	for	for	ADP
ejpam-3288	331	21	all	all	DET
ejpam-3288	331	22	γ	γ	X
ejpam-3288	331	23	∈	∈	PROPN
ejpam-3288	332	1	[	[	X
ejpam-3288	332	2	0	0	NUM
ejpam-3288	332	3	,	,	PUNCT
ejpam-3288	332	4	1	1	NUM
ejpam-3288	332	5	]	]	PUNCT
ejpam-3288	332	6	.	.	PUNCT
ejpam-3288	333	1	then	then	ADV
ejpam-3288	333	2	by	by	ADP
ejpam-3288	333	3	theorem	theorem	NOUN
ejpam-3288	333	4	7	7	NUM
ejpam-3288	333	5	,	,	PUNCT
ejpam-3288	333	6	apγ	apγ	NOUN
ejpam-3288	333	7	and	and	CCONJ
ejpam-3288	333	8	an−γ	an−γ	NOUN
ejpam-3288	333	9	are	be	AUX
ejpam-3288	333	10	h	h	NOUN
ejpam-3288	333	11	-	-	PUNCT
ejpam-3288	333	12	ideals	ideal	NOUN
ejpam-3288	333	13	of	of	ADP
ejpam-3288	333	14	x.	x.	NOUN
ejpam-3288	333	15	let	let	VERB
ejpam-3288	333	16	x	x	PRON
ejpam-3288	333	17	,	,	PUNCT
ejpam-3288	333	18	y	y	PROPN
ejpam-3288	333	19	,	,	PUNCT
ejpam-3288	333	20	z	z	NOUN
ejpam-3288	333	21	∈	∈	PROPN
ejpam-3288	334	1	x	x	PUNCT
ejpam-3288	334	2	such	such	ADJ
ejpam-3288	334	3	that	that	SCONJ
ejpam-3288	334	4	x	x	SYM
ejpam-3288	334	5	∗	∗	NOUN
ejpam-3288	334	6	(	(	PUNCT
ejpam-3288	334	7	y	y	PROPN
ejpam-3288	334	8	∗	∗	PROPN
ejpam-3288	334	9	z	z	PROPN
ejpam-3288	334	10	)	)	PUNCT
ejpam-3288	334	11	∈	∈	PROPN
ejpam-3288	334	12	apγ	apγ	PROPN
ejpam-3288	334	13	∪an−γ	∪an−γ	PROPN
ejpam-3288	334	14	and	and	CCONJ
ejpam-3288	334	15	y	y	PROPN
ejpam-3288	334	16	∈	∈	PROPN
ejpam-3288	334	17	apγ	apγ	PROPN
ejpam-3288	334	18	∪an−γ	∪an−γ	PROPN
ejpam-3288	334	19	.	.	PUNCT
ejpam-3288	335	1	here	here	ADV
ejpam-3288	335	2	we	we	PRON
ejpam-3288	335	3	have	have	VERB
ejpam-3288	335	4	four	four	NUM
ejpam-3288	335	5	cases	case	NOUN
ejpam-3288	335	6	to	to	PART
ejpam-3288	335	7	prove	prove	VERB
ejpam-3288	335	8	the	the	DET
ejpam-3288	335	9	theorem	theorem	NOUN
ejpam-3288	335	10	:	:	PUNCT
ejpam-3288	335	11	(	(	PUNCT
ejpam-3288	335	12	i	i	NOUN
ejpam-3288	335	13	)	)	PUNCT
ejpam-3288	335	14	x	x	SYM
ejpam-3288	335	15	∗	∗	NOUN
ejpam-3288	335	16	(	(	PUNCT
ejpam-3288	335	17	y	y	PROPN
ejpam-3288	335	18	∗	∗	PROPN
ejpam-3288	335	19	z	z	PROPN
ejpam-3288	335	20	)	)	PUNCT
ejpam-3288	335	21	∈	∈	PROPN
ejpam-3288	335	22	apγ	apγ	NOUN
ejpam-3288	335	23	and	and	CCONJ
ejpam-3288	335	24	y	y	PROPN
ejpam-3288	335	25	∈	∈	PROPN
ejpam-3288	335	26	apγ	apγ	PROPN
ejpam-3288	335	27	,	,	PUNCT
ejpam-3288	335	28	(	(	PUNCT
ejpam-3288	335	29	ii	ii	NOUN
ejpam-3288	335	30	)	)	PUNCT
ejpam-3288	336	1	x	x	SYM
ejpam-3288	336	2	∗	∗	NOUN
ejpam-3288	336	3	(	(	PUNCT
ejpam-3288	336	4	y	y	PROPN
ejpam-3288	336	5	∗	∗	PROPN
ejpam-3288	336	6	z	z	PROPN
ejpam-3288	336	7	)	)	PUNCT
ejpam-3288	336	8	∈	∈	PROPN
ejpam-3288	336	9	apγ	apγ	NOUN
ejpam-3288	336	10	and	and	CCONJ
ejpam-3288	336	11	y	y	PROPN
ejpam-3288	336	12	∈	∈	PROPN
ejpam-3288	336	13	an−γ	an−γ	NOUN
ejpam-3288	336	14	,	,	PUNCT
ejpam-3288	336	15	(	(	PUNCT
ejpam-3288	336	16	iii	iii	NOUN
ejpam-3288	336	17	)	)	PUNCT
ejpam-3288	336	18	x	x	SYM
ejpam-3288	336	19	∗	∗	NOUN
ejpam-3288	336	20	(	(	PUNCT
ejpam-3288	336	21	y	y	PROPN
ejpam-3288	336	22	∗	∗	PROPN
ejpam-3288	336	23	z	z	NOUN
ejpam-3288	336	24	)	)	PUNCT
ejpam-3288	336	25	∈	∈	PROPN
ejpam-3288	336	26	an−γ	an−γ	NOUN
ejpam-3288	336	27	and	and	CCONJ
ejpam-3288	336	28	y	y	PROPN
ejpam-3288	336	29	∈	∈	PROPN
ejpam-3288	336	30	apγ	apγ	PROPN
ejpam-3288	336	31	,	,	PUNCT
ejpam-3288	336	32	(	(	PUNCT
ejpam-3288	336	33	iv	iv	X
ejpam-3288	336	34	)	)	PUNCT
ejpam-3288	336	35	x	x	SYM
ejpam-3288	336	36	∗	∗	NOUN
ejpam-3288	336	37	(	(	PUNCT
ejpam-3288	336	38	y	y	PROPN
ejpam-3288	336	39	∗	∗	PROPN
ejpam-3288	336	40	z	z	NOUN
ejpam-3288	336	41	)	)	PUNCT
ejpam-3288	336	42	∈	∈	PROPN
ejpam-3288	336	43	an−γ	an−γ	NOUN
ejpam-3288	336	44	and	and	CCONJ
ejpam-3288	336	45	y	y	PROPN
ejpam-3288	336	46	∈	∈	PROPN
ejpam-3288	336	47	an−γ	an−γ	NOUN
ejpam-3288	336	48	.	.	PUNCT
ejpam-3288	337	1	case(i	case(i	PROPN
ejpam-3288	337	2	)	)	PUNCT
ejpam-3288	337	3	.	.	PUNCT
ejpam-3288	338	1	if	if	SCONJ
ejpam-3288	338	2	x	x	PRON
ejpam-3288	338	3	∗	∗	NOUN
ejpam-3288	338	4	(	(	PUNCT
ejpam-3288	338	5	y	y	PROPN
ejpam-3288	338	6	∗	∗	PROPN
ejpam-3288	338	7	z	z	PROPN
ejpam-3288	338	8	)	)	PUNCT
ejpam-3288	338	9	∈	∈	PROPN
ejpam-3288	338	10	apγ	apγ	NOUN
ejpam-3288	338	11	and	and	CCONJ
ejpam-3288	338	12	y	y	PROPN
ejpam-3288	338	13	∈	∈	PROPN
ejpam-3288	338	14	apγ	apγ	PROPN
ejpam-3288	338	15	,	,	PUNCT
ejpam-3288	338	16	implies	imply	VERB
ejpam-3288	338	17	that	that	SCONJ
ejpam-3288	338	18	µpa(x	µpa(x	PRON
ejpam-3288	338	19	∗	∗	NOUN
ejpam-3288	338	20	(	(	PUNCT
ejpam-3288	338	21	y	y	PROPN
ejpam-3288	338	22	∗	∗	PROPN
ejpam-3288	338	23	z	z	NOUN
ejpam-3288	338	24	)	)	PUNCT
ejpam-3288	338	25	)	)	PUNCT
ejpam-3288	338	26	≤	≤	NUM
ejpam-3288	338	27	γ	γ	X
ejpam-3288	338	28	and	and	CCONJ
ejpam-3288	338	29	µpa(y	µpa(y	PROPN
ejpam-3288	338	30	)	)	PUNCT
ejpam-3288	338	31	≤	≤	NUM
ejpam-3288	338	32	γ	γ	PROPN
ejpam-3288	338	33	.	.	PROPN
ejpam-3288	338	34	since	since	SCONJ
ejpam-3288	338	35	a	a	DET
ejpam-3288	338	36	=	=	X
ejpam-3288	338	37	(	(	PUNCT
ejpam-3288	338	38	µpa	µpa	PROPN
ejpam-3288	338	39	,	,	PUNCT
ejpam-3288	338	40	µ	µ	X
ejpam-3288	338	41	n	n	PRON
ejpam-3288	338	42	a	a	PRON
ejpam-3288	338	43	)	)	PUNCT
ejpam-3288	338	44	is	be	AUX
ejpam-3288	338	45	a	a	DET
ejpam-3288	338	46	doubt	doubt	ADV
ejpam-3288	338	47	bipolar	bipolar	ADJ
ejpam-3288	338	48	fuzzy	fuzzy	ADJ
ejpam-3288	338	49	h	h	NOUN
ejpam-3288	338	50	-	-	PUNCT
ejpam-3288	338	51	ideal	ideal	NOUN
ejpam-3288	338	52	of	of	ADP
ejpam-3288	338	53	x	x	PRON
ejpam-3288	338	54	,	,	PUNCT
ejpam-3288	338	55	it	it	PRON
ejpam-3288	338	56	follows	follow	VERB
ejpam-3288	338	57	that	that	SCONJ
ejpam-3288	338	58	µpa(x	µpa(x	PRON
ejpam-3288	338	59	∗	∗	NOUN
ejpam-3288	338	60	z	z	NOUN
ejpam-3288	338	61	)	)	PUNCT
ejpam-3288	338	62	≤	≤	PROPN
ejpam-3288	339	1	max{µpa(x	max{µpa(x	PROPN
ejpam-3288	339	2	∗	∗	NOUN
ejpam-3288	339	3	(	(	PUNCT
ejpam-3288	339	4	y	y	PROPN
ejpam-3288	339	5	∗	∗	PROPN
ejpam-3288	339	6	z	z	PROPN
ejpam-3288	339	7	)	)	PUNCT
ejpam-3288	339	8	)	)	PUNCT
ejpam-3288	339	9	,	,	PUNCT
ejpam-3288	339	10	µpa(y	µpa(y	PROPN
ejpam-3288	339	11	)	)	PUNCT
ejpam-3288	339	12	}	}	PUNCT
ejpam-3288	339	13	≤	≤	NUM
ejpam-3288	339	14	γ	γ	X
ejpam-3288	339	15	.	.	PUNCT
ejpam-3288	339	16	therefore	therefore	ADV
ejpam-3288	339	17	,	,	PUNCT
ejpam-3288	339	18	x	x	X
ejpam-3288	339	19	∗	∗	NOUN
ejpam-3288	339	20	z	z	PROPN
ejpam-3288	339	21	∈	∈	PROPN
ejpam-3288	339	22	apγ	apγ	PROPN
ejpam-3288	339	23	⊆	⊆	NUM
ejpam-3288	339	24	apγ	apγ	PROPN
ejpam-3288	339	25	∪an−γ	∪an−γ	PROPN
ejpam-3288	339	26	.	.	PUNCT
ejpam-3288	340	1	case(ii	case(ii	ADJ
ejpam-3288	340	2	)	)	PUNCT
ejpam-3288	340	3	.	.	PUNCT
ejpam-3288	341	1	if	if	SCONJ
ejpam-3288	341	2	x∗(y∗z	x∗(y∗z	NUM
ejpam-3288	341	3	)	)	PUNCT
ejpam-3288	341	4	∈	∈	PROPN
ejpam-3288	341	5	apγ	apγ	PROPN
ejpam-3288	341	6	and	and	CCONJ
ejpam-3288	341	7	y	y	PROPN
ejpam-3288	341	8	∈	∈	PROPN
ejpam-3288	341	9	an−γ	an−γ	NOUN
ejpam-3288	341	10	,	,	PUNCT
ejpam-3288	341	11	implies	imply	VERB
ejpam-3288	341	12	that	that	SCONJ
ejpam-3288	341	13	µpa(x∗(y∗z	µpa(x∗(y∗z	VERB
ejpam-3288	341	14	)	)	PUNCT
ejpam-3288	341	15	)	)	PUNCT
ejpam-3288	341	16	≤	≤	NUM
ejpam-3288	341	17	γ	γ	NOUN
ejpam-3288	341	18	and	and	CCONJ
ejpam-3288	341	19	µna	µna	ADJ
ejpam-3288	341	20	(	(	PUNCT
ejpam-3288	341	21	y	y	NOUN
ejpam-3288	341	22	)	)	PUNCT
ejpam-3288	341	23	≥	≥	NOUN
ejpam-3288	341	24	−γ	−γ	NOUN
ejpam-3288	341	25	.	.	PUNCT
ejpam-3288	342	1	since	since	SCONJ
ejpam-3288	342	2	µpa(y	µpa(y	PROPN
ejpam-3288	342	3	)	)	PUNCT
ejpam-3288	343	1	+	+	CCONJ
ejpam-3288	343	2	µna	µna	ADJ
ejpam-3288	343	3	(	(	PUNCT
ejpam-3288	343	4	y	y	NOUN
ejpam-3288	343	5	)	)	PUNCT
ejpam-3288	343	6	≤	≤	NOUN
ejpam-3288	343	7	0	0	NUM
ejpam-3288	343	8	,	,	PUNCT
ejpam-3288	343	9	so	so	ADV
ejpam-3288	343	10	µpa(y	µpa(y	NOUN
ejpam-3288	343	11	)	)	PUNCT
ejpam-3288	343	12	≤	≤	NUM
ejpam-3288	343	13	−µna	−µna	NOUN
ejpam-3288	343	14	(	(	PUNCT
ejpam-3288	343	15	y	y	NOUN
ejpam-3288	343	16	)	)	PUNCT
ejpam-3288	343	17	≤	≤	NOUN
ejpam-3288	343	18	γ	γ	PROPN
ejpam-3288	343	19	,	,	PUNCT
ejpam-3288	343	20	it	it	PRON
ejpam-3288	343	21	follows	follow	VERB
ejpam-3288	343	22	that	that	SCONJ
ejpam-3288	343	23	µpa(x	µpa(x	PRON
ejpam-3288	343	24	∗	∗	NOUN
ejpam-3288	343	25	z	z	NOUN
ejpam-3288	343	26	)	)	PUNCT
ejpam-3288	343	27	≤	≤	PROPN
ejpam-3288	344	1	max{µpa(x	max{µpa(x	PROPN
ejpam-3288	344	2	∗	∗	NOUN
ejpam-3288	344	3	(	(	PUNCT
ejpam-3288	344	4	y	y	PROPN
ejpam-3288	344	5	∗	∗	PROPN
ejpam-3288	344	6	z	z	PROPN
ejpam-3288	344	7	)	)	PUNCT
ejpam-3288	344	8	)	)	PUNCT
ejpam-3288	344	9	,	,	PUNCT
ejpam-3288	344	10	µpa(y	µpa(y	PROPN
ejpam-3288	344	11	)	)	PUNCT
ejpam-3288	344	12	}	}	PUNCT
ejpam-3288	344	13	≤	≤	NUM
ejpam-3288	345	1	max{µpa(x	max{µpa(x	PROPN
ejpam-3288	345	2	∗	∗	NOUN
ejpam-3288	345	3	(	(	PUNCT
ejpam-3288	345	4	y	y	PROPN
ejpam-3288	345	5	∗	∗	X
ejpam-3288	345	6	z)),−µna	z)),−µna	NOUN
ejpam-3288	345	7	(	(	PUNCT
ejpam-3288	345	8	y	y	NOUN
ejpam-3288	345	9	)	)	PUNCT
ejpam-3288	345	10	}	}	PUNCT
ejpam-3288	345	11	≤	≤	NUM
ejpam-3288	345	12	γ	γ	X
ejpam-3288	345	13	.	.	PUNCT
ejpam-3288	345	14	therefore	therefore	ADV
ejpam-3288	345	15	,	,	PUNCT
ejpam-3288	345	16	x	x	X
ejpam-3288	345	17	∗	∗	NOUN
ejpam-3288	345	18	z	z	PROPN
ejpam-3288	345	19	∈	∈	PROPN
ejpam-3288	345	20	apγ	apγ	PROPN
ejpam-3288	345	21	⊆	⊆	NUM
ejpam-3288	345	22	apγ	apγ	PROPN
ejpam-3288	345	23	∪an−γ	∪an−γ	PROPN
ejpam-3288	345	24	.	.	PUNCT
ejpam-3288	346	1	case(iii	case(iii	PROPN
ejpam-3288	346	2	)	)	PUNCT
ejpam-3288	346	3	.	.	PUNCT
ejpam-3288	347	1	if	if	SCONJ
ejpam-3288	347	2	x∗(y∗z	x∗(y∗z	NUM
ejpam-3288	347	3	)	)	PUNCT
ejpam-3288	348	1	∈	∈	PROPN
ejpam-3288	348	2	an−γ	an−γ	NOUN
ejpam-3288	348	3	and	and	CCONJ
ejpam-3288	348	4	y	y	PROPN
ejpam-3288	348	5	∈	∈	PROPN
ejpam-3288	348	6	apγ	apγ	PROPN
ejpam-3288	348	7	,	,	PUNCT
ejpam-3288	348	8	implies	imply	VERB
ejpam-3288	348	9	that	that	SCONJ
ejpam-3288	348	10	µna	µna	ADJ
ejpam-3288	348	11	(	(	PUNCT
ejpam-3288	348	12	x∗(y∗z	x∗(y∗z	NUM
ejpam-3288	348	13	)	)	PUNCT
ejpam-3288	348	14	)	)	PUNCT
ejpam-3288	348	15	≥	≥	NOUN
ejpam-3288	348	16	−γ	−γ	NOUN
ejpam-3288	348	17	and	and	CCONJ
ejpam-3288	348	18	µpa(y	µpa(y	NOUN
ejpam-3288	348	19	)	)	PUNCT
ejpam-3288	348	20	≤	≤	NUM
ejpam-3288	348	21	γ	γ	PROPN
ejpam-3288	348	22	.	.	PROPN
ejpam-3288	349	1	since	since	SCONJ
ejpam-3288	349	2	µpa(x	µpa(x	PRON
ejpam-3288	349	3	∗	∗	NOUN
ejpam-3288	349	4	(	(	PUNCT
ejpam-3288	349	5	y	y	PROPN
ejpam-3288	349	6	∗	∗	PROPN
ejpam-3288	349	7	z	z	PROPN
ejpam-3288	349	8	)	)	PUNCT
ejpam-3288	349	9	)	)	PUNCT
ejpam-3288	350	1	+	+	CCONJ
ejpam-3288	350	2	µna	µna	ADJ
ejpam-3288	350	3	(	(	PUNCT
ejpam-3288	350	4	x	x	SYM
ejpam-3288	350	5	∗	∗	NOUN
ejpam-3288	350	6	(	(	PUNCT
ejpam-3288	350	7	y	y	PROPN
ejpam-3288	350	8	∗	∗	PROPN
ejpam-3288	350	9	z	z	NOUN
ejpam-3288	350	10	)	)	PUNCT
ejpam-3288	350	11	)	)	PUNCT
ejpam-3288	350	12	≤	≤	ADV
ejpam-3288	350	13	0	0	NUM
ejpam-3288	350	14	,	,	PUNCT
ejpam-3288	350	15	so	so	SCONJ
ejpam-3288	350	16	µpa(x	µpa(x	PRON
ejpam-3288	350	17	∗	∗	NOUN
ejpam-3288	350	18	(	(	PUNCT
ejpam-3288	350	19	y	y	PROPN
ejpam-3288	350	20	∗	∗	PROPN
ejpam-3288	350	21	z	z	NOUN
ejpam-3288	350	22	)	)	PUNCT
ejpam-3288	350	23	)	)	PUNCT
ejpam-3288	350	24	≤	≤	NUM
ejpam-3288	350	25	−µna	−µna	NOUN
ejpam-3288	350	26	(	(	PUNCT
ejpam-3288	350	27	x	x	SYM
ejpam-3288	350	28	∗	∗	NOUN
ejpam-3288	350	29	(	(	PUNCT
ejpam-3288	350	30	y	y	PROPN
ejpam-3288	350	31	∗	∗	PROPN
ejpam-3288	350	32	z	z	PROPN
ejpam-3288	350	33	)	)	PUNCT
ejpam-3288	350	34	)	)	PUNCT
ejpam-3288	350	35	≤	≤	NUM
ejpam-3288	350	36	γ	γ	X
ejpam-3288	350	37	,	,	PUNCT
ejpam-3288	350	38	it	it	PRON
ejpam-3288	350	39	follows	follow	VERB
ejpam-3288	350	40	that	that	SCONJ
ejpam-3288	350	41	µpa(x	µpa(x	PRON
ejpam-3288	350	42	∗	∗	NOUN
ejpam-3288	350	43	z	z	NOUN
ejpam-3288	350	44	)	)	PUNCT
ejpam-3288	350	45	≤	≤	PROPN
ejpam-3288	351	1	max{µpa(x	max{µpa(x	PROPN
ejpam-3288	351	2	∗	∗	NOUN
ejpam-3288	351	3	(	(	PUNCT
ejpam-3288	351	4	y	y	PROPN
ejpam-3288	351	5	∗	∗	PROPN
ejpam-3288	351	6	z	z	PROPN
ejpam-3288	351	7	)	)	PUNCT
ejpam-3288	351	8	)	)	PUNCT
ejpam-3288	351	9	,	,	PUNCT
ejpam-3288	351	10	µpa(y	µpa(y	PROPN
ejpam-3288	351	11	)	)	PUNCT
ejpam-3288	351	12	}	}	PUNCT
ejpam-3288	351	13	a.	a.	PROPN
ejpam-3288	351	14	al	al	PROPN
ejpam-3288	351	15	-	-	PROPN
ejpam-3288	351	16	masarwah	masarwah	PROPN
ejpam-3288	351	17	,	,	PUNCT
ejpam-3288	351	18	a.	a.	NOUN
ejpam-3288	351	19	g.	g.	PROPN
ejpam-3288	351	20	ahmad	ahmad	PROPN
ejpam-3288	351	21	/	/	SYM
ejpam-3288	351	22	eur	eur	PROPN
ejpam-3288	351	23	.	.	PUNCT
ejpam-3288	352	1	j.	j.	PROPN
ejpam-3288	352	2	pure	pure	PROPN
ejpam-3288	352	3	appl	appl	PROPN
ejpam-3288	352	4	.	.	PROPN
ejpam-3288	352	5	math	math	PROPN
ejpam-3288	352	6	,	,	PUNCT
ejpam-3288	352	7	11	11	NUM
ejpam-3288	352	8	(	(	PUNCT
ejpam-3288	352	9	3	3	NUM
ejpam-3288	352	10	)	)	PUNCT
ejpam-3288	352	11	(	(	PUNCT
ejpam-3288	352	12	2018	2018	NUM
ejpam-3288	352	13	)	)	PUNCT
ejpam-3288	352	14	,	,	PUNCT
ejpam-3288	352	15	652	652	NUM
ejpam-3288	352	16	-	-	SYM
ejpam-3288	352	17	670	670	NUM
ejpam-3288	352	18	667	667	NUM
ejpam-3288	352	19	≤	≤	NOUN
ejpam-3288	352	20	max{−µna	max{−µna	PROPN
ejpam-3288	352	21	(	(	PUNCT
ejpam-3288	352	22	x	x	NOUN
ejpam-3288	352	23	∗	∗	NOUN
ejpam-3288	352	24	(	(	PUNCT
ejpam-3288	352	25	y	y	PROPN
ejpam-3288	352	26	∗	∗	PROPN
ejpam-3288	352	27	z	z	PROPN
ejpam-3288	352	28	)	)	PUNCT
ejpam-3288	352	29	)	)	PUNCT
ejpam-3288	352	30	,	,	PUNCT
ejpam-3288	352	31	µpa(y	µpa(y	PROPN
ejpam-3288	352	32	)	)	PUNCT
ejpam-3288	352	33	}	}	PUNCT
ejpam-3288	352	34	≤	≤	NUM
ejpam-3288	352	35	γ	γ	X
ejpam-3288	352	36	.	.	PUNCT
ejpam-3288	353	1	therefore	therefore	ADV
ejpam-3288	353	2	,	,	PUNCT
ejpam-3288	353	3	x	x	X
ejpam-3288	353	4	∗	∗	NOUN
ejpam-3288	353	5	z	z	PROPN
ejpam-3288	353	6	∈	∈	PROPN
ejpam-3288	353	7	apγ	apγ	PROPN
ejpam-3288	353	8	⊆	⊆	NUM
ejpam-3288	353	9	apγ	apγ	PROPN
ejpam-3288	353	10	∪an−γ	∪an−γ	PROPN
ejpam-3288	353	11	.	.	PUNCT
ejpam-3288	354	1	case(iv	case(iv	X
ejpam-3288	354	2	)	)	PUNCT
ejpam-3288	354	3	.	.	PUNCT
ejpam-3288	355	1	if	if	SCONJ
ejpam-3288	355	2	x	x	PRON
ejpam-3288	355	3	∗	∗	NOUN
ejpam-3288	355	4	(	(	PUNCT
ejpam-3288	355	5	y	y	PROPN
ejpam-3288	355	6	∗	∗	PROPN
ejpam-3288	355	7	z	z	NOUN
ejpam-3288	355	8	)	)	PUNCT
ejpam-3288	355	9	∈	∈	PROPN
ejpam-3288	355	10	an−γ	an−γ	NOUN
ejpam-3288	355	11	and	and	CCONJ
ejpam-3288	355	12	y	y	PROPN
ejpam-3288	355	13	∈	∈	PROPN
ejpam-3288	355	14	an−γ	an−γ	NOUN
ejpam-3288	355	15	,	,	PUNCT
ejpam-3288	355	16	implies	imply	VERB
ejpam-3288	355	17	that	that	SCONJ
ejpam-3288	355	18	µna	µna	ADJ
ejpam-3288	355	19	(	(	PUNCT
ejpam-3288	355	20	x	x	SYM
ejpam-3288	355	21	∗	∗	NOUN
ejpam-3288	355	22	(	(	PUNCT
ejpam-3288	355	23	y	y	PROPN
ejpam-3288	355	24	∗	∗	PROPN
ejpam-3288	355	25	z	z	NOUN
ejpam-3288	355	26	)	)	PUNCT
ejpam-3288	355	27	)	)	PUNCT
ejpam-3288	355	28	≥	≥	NOUN
ejpam-3288	355	29	−γ	−γ	NOUN
ejpam-3288	355	30	and	and	CCONJ
ejpam-3288	355	31	µna	µna	ADJ
ejpam-3288	355	32	(	(	PUNCT
ejpam-3288	355	33	y	y	NOUN
ejpam-3288	355	34	)	)	PUNCT
ejpam-3288	355	35	≥	≥	NOUN
ejpam-3288	355	36	−γ	−γ	NOUN
ejpam-3288	355	37	.	.	PUNCT
ejpam-3288	356	1	since	since	SCONJ
ejpam-3288	356	2	a	a	PRON
ejpam-3288	356	3	=	=	X
ejpam-3288	356	4	(	(	PUNCT
ejpam-3288	356	5	µpa	µpa	PROPN
ejpam-3288	356	6	,	,	PUNCT
ejpam-3288	356	7	µ	µ	X
ejpam-3288	356	8	n	n	PRON
ejpam-3288	356	9	a	a	PRON
ejpam-3288	356	10	)	)	PUNCT
ejpam-3288	356	11	is	be	AUX
ejpam-3288	356	12	a	a	DET
ejpam-3288	356	13	doubt	doubt	ADV
ejpam-3288	356	14	bipolar	bipolar	ADJ
ejpam-3288	356	15	fuzzy	fuzzy	ADJ
ejpam-3288	356	16	h	h	NOUN
ejpam-3288	356	17	-	-	PUNCT
ejpam-3288	356	18	ideal	ideal	NOUN
ejpam-3288	356	19	of	of	ADP
ejpam-3288	356	20	x	x	PRON
ejpam-3288	356	21	,	,	PUNCT
ejpam-3288	356	22	it	it	PRON
ejpam-3288	356	23	follows	follow	VERB
ejpam-3288	356	24	that	that	SCONJ
ejpam-3288	356	25	µna	µna	ADJ
ejpam-3288	356	26	(	(	PUNCT
ejpam-3288	356	27	x	x	NOUN
ejpam-3288	356	28	∗	∗	PROPN
ejpam-3288	356	29	z	z	NOUN
ejpam-3288	356	30	)	)	PUNCT
ejpam-3288	356	31	≥	≥	X
ejpam-3288	356	32	min{µna	min{µna	NOUN
ejpam-3288	356	33	(	(	PUNCT
ejpam-3288	356	34	x	x	NOUN
ejpam-3288	356	35	∗	∗	NOUN
ejpam-3288	356	36	(	(	PUNCT
ejpam-3288	356	37	y	y	PROPN
ejpam-3288	356	38	∗	∗	PROPN
ejpam-3288	356	39	z	z	PROPN
ejpam-3288	356	40	)	)	PUNCT
ejpam-3288	356	41	)	)	PUNCT
ejpam-3288	356	42	,	,	PUNCT
ejpam-3288	356	43	µna	µna	PROPN
ejpam-3288	356	44	(	(	PUNCT
ejpam-3288	356	45	y	y	NOUN
ejpam-3288	356	46	)	)	PUNCT
ejpam-3288	356	47	}	}	PUNCT
ejpam-3288	356	48	≥	≥	NOUN
ejpam-3288	356	49	−γ	−γ	NOUN
ejpam-3288	356	50	.	.	PUNCT
ejpam-3288	357	1	therefore	therefore	ADV
ejpam-3288	357	2	,	,	PUNCT
ejpam-3288	357	3	x	x	X
ejpam-3288	357	4	∗	∗	NOUN
ejpam-3288	357	5	z	z	NOUN
ejpam-3288	357	6	∈	∈	NOUN
ejpam-3288	357	7	an−γ	an−γ	NOUN
ejpam-3288	357	8	⊆	⊆	NUM
ejpam-3288	357	9	apγ	apγ	PROPN
ejpam-3288	357	10	∪an−γ	∪an−γ	PROPN
ejpam-3288	357	11	.	.	PUNCT
ejpam-3288	358	1	hence	hence	ADV
ejpam-3288	358	2	,	,	PUNCT
ejpam-3288	358	3	apγ	apγ	PROPN
ejpam-3288	358	4	∪an−γ	∪an−γ	PROPN
ejpam-3288	358	5	is	be	AUX
ejpam-3288	358	6	an	an	DET
ejpam-3288	358	7	h	h	NOUN
ejpam-3288	358	8	-	-	PUNCT
ejpam-3288	358	9	ideal	ideal	NOUN
ejpam-3288	358	10	of	of	ADP
ejpam-3288	358	11	x.	x.	NOUN
ejpam-3288	358	12	definition	definition	NOUN
ejpam-3288	358	13	12	12	NUM
ejpam-3288	358	14	.	.	PUNCT
ejpam-3288	359	1	[	[	X
ejpam-3288	359	2	33	33	NUM
ejpam-3288	359	3	]	]	PUNCT
ejpam-3288	359	4	a	a	DET
ejpam-3288	359	5	bck	bck	PROPN
ejpam-3288	359	6	/	/	SYM
ejpam-3288	359	7	bci	bci	NOUN
ejpam-3288	359	8	-	-	NOUN
ejpam-3288	359	9	algebra	algebra	NOUN
ejpam-3288	359	10	x	x	PUNCT
ejpam-3288	359	11	is	be	AUX
ejpam-3288	359	12	said	say	VERB
ejpam-3288	359	13	to	to	PART
ejpam-3288	359	14	satisfy	satisfy	VERB
ejpam-3288	359	15	the	the	DET
ejpam-3288	359	16	h	h	NOUN
ejpam-3288	359	17	-	-	PUNCT
ejpam-3288	359	18	ascending	ascend	VERB
ejpam-3288	359	19	(	(	PUNCT
ejpam-3288	359	20	resp	resp	NOUN
ejpam-3288	359	21	.	.	PUNCT
ejpam-3288	360	1	h	h	NOUN
ejpam-3288	360	2	-	-	PUNCT
ejpam-3288	360	3	descending	descend	VERB
ejpam-3288	360	4	)	)	PUNCT
ejpam-3288	360	5	chain	chain	NOUN
ejpam-3288	360	6	condition	condition	NOUN
ejpam-3288	360	7	(	(	PUNCT
ejpam-3288	360	8	briefly	briefly	ADV
ejpam-3288	360	9	,	,	PUNCT
ejpam-3288	360	10	h	h	NOUN
ejpam-3288	360	11	-	-	PUNCT
ejpam-3288	360	12	acc	acc	PROPN
ejpam-3288	360	13	(	(	PUNCT
ejpam-3288	360	14	resp	resp	NOUN
ejpam-3288	360	15	.	.	PUNCT
ejpam-3288	361	1	h	h	NOUN
ejpam-3288	361	2	-	-	PUNCT
ejpam-3288	361	3	dcc	dcc	NOUN
ejpam-3288	361	4	)	)	PUNCT
ejpam-3288	361	5	)	)	PUNCT
ejpam-3288	362	1	if	if	SCONJ
ejpam-3288	362	2	for	for	ADP
ejpam-3288	362	3	every	every	DET
ejpam-3288	362	4	ascending	ascend	VERB
ejpam-3288	362	5	(	(	PUNCT
ejpam-3288	362	6	resp	resp	NOUN
ejpam-3288	362	7	.	.	PUNCT
ejpam-3288	363	1	descending	descend	VERB
ejpam-3288	363	2	)	)	PUNCT
ejpam-3288	363	3	sequence	sequence	NOUN
ejpam-3288	363	4	i1	i1	PROPN
ejpam-3288	363	5	⊆	⊆	NUM
ejpam-3288	363	6	i2	i2	PROPN
ejpam-3288	363	7	⊆	⊆	NUM
ejpam-3288	363	8	i3	i3	NOUN
ejpam-3288	363	9	⊆	⊆	NUM
ejpam-3288	363	10	...	...	PUNCT
ejpam-3288	363	11	(	(	PUNCT
ejpam-3288	363	12	resp	resp	NOUN
ejpam-3288	363	13	.	.	PUNCT
ejpam-3288	364	1	i1	i1	PROPN
ejpam-3288	364	2	⊇	⊇	PROPN
ejpam-3288	364	3	i2	i2	PROPN
ejpam-3288	364	4	⊇	⊇	PROPN
ejpam-3288	364	5	i3	i3	PROPN
ejpam-3288	364	6	⊇	⊇	PROPN
ejpam-3288	364	7	...	...	PUNCT
ejpam-3288	364	8	)	)	PUNCT
ejpam-3288	364	9	of	of	ADP
ejpam-3288	364	10	h	h	NOUN
ejpam-3288	364	11	-	-	PUNCT
ejpam-3288	364	12	ideals	ideal	NOUN
ejpam-3288	364	13	of	of	ADP
ejpam-3288	364	14	x	x	SYM
ejpam-3288	364	15	there	there	PRON
ejpam-3288	364	16	exists	exist	VERB
ejpam-3288	364	17	a	a	DET
ejpam-3288	364	18	natural	natural	ADJ
ejpam-3288	364	19	number	number	NOUN
ejpam-3288	364	20	n	n	ADP
ejpam-3288	364	21	such	such	ADJ
ejpam-3288	364	22	that	that	SCONJ
ejpam-3288	364	23	in	in	ADP
ejpam-3288	364	24	=	=	PUNCT
ejpam-3288	364	25	ik	ik	PROPN
ejpam-3288	364	26	for	for	ADP
ejpam-3288	364	27	all	all	DET
ejpam-3288	364	28	n	n	DET
ejpam-3288	364	29	≥	≥	NOUN
ejpam-3288	364	30	k.	k.	PUNCT
ejpam-3288	365	1	if	if	SCONJ
ejpam-3288	365	2	x	x	PRON
ejpam-3288	365	3	satisfies	satisfy	VERB
ejpam-3288	365	4	h	h	NOUN
ejpam-3288	365	5	-	-	PUNCT
ejpam-3288	365	6	dcc	dcc	NOUN
ejpam-3288	365	7	,	,	PUNCT
ejpam-3288	365	8	we	we	PRON
ejpam-3288	365	9	say	say	VERB
ejpam-3288	365	10	that	that	SCONJ
ejpam-3288	365	11	x	x	PRON
ejpam-3288	365	12	is	be	AUX
ejpam-3288	365	13	an	an	DET
ejpam-3288	365	14	h	h	NOUN
ejpam-3288	365	15	-	-	PUNCT
ejpam-3288	365	16	artin	artin	NOUN
ejpam-3288	365	17	bck	bck	PROPN
ejpam-3288	365	18	/	/	SYM
ejpam-3288	365	19	bci	bci	NOUN
ejpam-3288	365	20	-	-	PUNCT
ejpam-3288	365	21	algebras	algebra	NOUN
ejpam-3288	365	22	.	.	PUNCT
ejpam-3288	366	1	in	in	ADP
ejpam-3288	366	2	the	the	DET
ejpam-3288	366	3	next	next	ADJ
ejpam-3288	366	4	two	two	NUM
ejpam-3288	366	5	theorems	theorem	NOUN
ejpam-3288	366	6	,	,	PUNCT
ejpam-3288	366	7	we	we	PRON
ejpam-3288	366	8	investigate	investigate	VERB
ejpam-3288	366	9	characterizations	characterization	NOUN
ejpam-3288	366	10	of	of	ADP
ejpam-3288	366	11	h	h	NOUN
ejpam-3288	366	12	-	-	PUNCT
ejpam-3288	366	13	artin	artin	NOUN
ejpam-3288	366	14	bck	bck	PROPN
ejpam-3288	366	15	/	/	SYM
ejpam-3288	366	16	bcialgebras	bcialgebra	NOUN
ejpam-3288	366	17	in	in	ADP
ejpam-3288	366	18	terms	term	NOUN
ejpam-3288	366	19	of	of	ADP
ejpam-3288	366	20	doubt	doubt	NOUN
ejpam-3288	366	21	bipolar	bipolar	ADJ
ejpam-3288	366	22	fuzzy	fuzzy	ADJ
ejpam-3288	366	23	h	h	NOUN
ejpam-3288	366	24	-	-	PUNCT
ejpam-3288	366	25	ideals	ideal	NOUN
ejpam-3288	366	26	.	.	PUNCT
ejpam-3288	367	1	theorem	theorem	NOUN
ejpam-3288	367	2	9	9	NUM
ejpam-3288	367	3	.	.	PUNCT
ejpam-3288	368	1	let	let	VERB
ejpam-3288	368	2	x	x	PRON
ejpam-3288	368	3	be	be	AUX
ejpam-3288	368	4	a	a	DET
ejpam-3288	368	5	bck	bck	VERB
ejpam-3288	368	6	/	/	SYM
ejpam-3288	368	7	bci	bci	NOUN
ejpam-3288	368	8	-	-	NOUN
ejpam-3288	368	9	algebra	algebra	NOUN
ejpam-3288	368	10	satisfying	satisfying	ADJ
ejpam-3288	368	11	h	h	NOUN
ejpam-3288	368	12	-	-	PUNCT
ejpam-3288	368	13	dcc	dcc	PROPN
ejpam-3288	368	14	and	and	CCONJ
ejpam-3288	368	15	a	a	DET
ejpam-3288	368	16	=	=	X
ejpam-3288	368	17	(	(	PUNCT
ejpam-3288	368	18	µpa	µpa	PROPN
ejpam-3288	368	19	,	,	PUNCT
ejpam-3288	368	20	µ	µ	X
ejpam-3288	368	21	n	n	PRON
ejpam-3288	368	22	a	a	PRON
ejpam-3288	368	23	)	)	PUNCT
ejpam-3288	368	24	is	be	AUX
ejpam-3288	368	25	a	a	DET
ejpam-3288	368	26	doubt	doubt	ADV
ejpam-3288	368	27	bipolar	bipolar	ADJ
ejpam-3288	368	28	fuzzy	fuzzy	ADJ
ejpam-3288	368	29	h	h	NOUN
ejpam-3288	368	30	-	-	PUNCT
ejpam-3288	368	31	ideal	ideal	NOUN
ejpam-3288	368	32	of	of	ADP
ejpam-3288	368	33	x.	x.	NOUN
ejpam-3288	368	34	if	if	SCONJ
ejpam-3288	368	35	a	a	DET
ejpam-3288	368	36	sequence	sequence	NOUN
ejpam-3288	368	37	of	of	ADP
ejpam-3288	368	38	elements	element	NOUN
ejpam-3288	368	39	of	of	ADP
ejpam-3288	368	40	im(µpa	im(µpa	NOUN
ejpam-3288	368	41	)	)	PUNCT
ejpam-3288	368	42	is	be	AUX
ejpam-3288	368	43	strictly	strictly	ADV
ejpam-3288	368	44	decreasing	decrease	VERB
ejpam-3288	368	45	and	and	CCONJ
ejpam-3288	368	46	a	a	DET
ejpam-3288	368	47	sequence	sequence	NOUN
ejpam-3288	368	48	of	of	ADP
ejpam-3288	368	49	elements	element	NOUN
ejpam-3288	368	50	of	of	ADP
ejpam-3288	368	51	im(µna	im(µna	NOUN
ejpam-3288	368	52	)	)	PUNCT
ejpam-3288	368	53	is	be	AUX
ejpam-3288	368	54	strictly	strictly	ADV
ejpam-3288	368	55	increasing	increase	VERB
ejpam-3288	368	56	,	,	PUNCT
ejpam-3288	368	57	then	then	ADV
ejpam-3288	368	58	a	a	DET
ejpam-3288	368	59	=	=	X
ejpam-3288	368	60	(	(	PUNCT
ejpam-3288	368	61	µpa	µpa	PROPN
ejpam-3288	368	62	,	,	PUNCT
ejpam-3288	368	63	µ	µ	X
ejpam-3288	368	64	n	n	PRON
ejpam-3288	368	65	a	a	PRON
ejpam-3288	368	66	)	)	PUNCT
ejpam-3288	368	67	has	have	VERB
ejpam-3288	368	68	finite	finite	ADJ
ejpam-3288	368	69	number	number	NOUN
ejpam-3288	368	70	of	of	ADP
ejpam-3288	368	71	values	value	NOUN
ejpam-3288	368	72	.	.	PUNCT
ejpam-3288	369	1	proof	proof	NOUN
ejpam-3288	369	2	.	.	PUNCT
ejpam-3288	370	1	let	let	VERB
ejpam-3288	370	2	{	{	PUNCT
ejpam-3288	370	3	tn	tn	NOUN
ejpam-3288	370	4	}	}	PUNCT
ejpam-3288	370	5	be	be	AUX
ejpam-3288	370	6	a	a	DET
ejpam-3288	370	7	strictly	strictly	ADV
ejpam-3288	370	8	decreasing	decrease	VERB
ejpam-3288	370	9	sequence	sequence	NOUN
ejpam-3288	370	10	of	of	ADP
ejpam-3288	370	11	im(µpa	im(µpa	NOUN
ejpam-3288	370	12	)	)	PUNCT
ejpam-3288	370	13	,	,	PUNCT
ejpam-3288	370	14	then	then	ADV
ejpam-3288	370	15	0	0	NUM
ejpam-3288	370	16	≤	≤	NUM
ejpam-3288	370	17	...	...	PUNCT
ejpam-3288	371	1	<	<	X
ejpam-3288	371	2	t2	t2	PROPN
ejpam-3288	371	3	<	<	X
ejpam-3288	371	4	t1	t1	PROPN
ejpam-3288	371	5	≤	≤	NUM
ejpam-3288	371	6	1	1	NUM
ejpam-3288	371	7	.	.	PUNCT
ejpam-3288	371	8	define	define	VERB
ejpam-3288	371	9	aptr	aptr	VERB
ejpam-3288	371	10	=	=	SYM
ejpam-3288	371	11	{	{	PUNCT
ejpam-3288	371	12	x	x	SYM
ejpam-3288	371	13	∈	∈	PROPN
ejpam-3288	371	14	x	x	X
ejpam-3288	371	15	|	|	ADV
ejpam-3288	371	16	µpa(x	µpa(x	PRON
ejpam-3288	371	17	)	)	PUNCT
ejpam-3288	371	18	≤	≤	NUM
ejpam-3288	371	19	tr	tr	VERB
ejpam-3288	371	20	}	}	PUNCT
ejpam-3288	371	21	,	,	PUNCT
ejpam-3288	371	22	r	r	NOUN
ejpam-3288	371	23	=	=	SYM
ejpam-3288	371	24	1	1	NUM
ejpam-3288	371	25	,	,	PUNCT
ejpam-3288	371	26	2	2	NUM
ejpam-3288	371	27	,	,	PUNCT
ejpam-3288	371	28	3	3	NUM
ejpam-3288	371	29	,	,	PUNCT
ejpam-3288	371	30	...	...	PUNCT
ejpam-3288	371	31	.	.	PUNCT
ejpam-3288	372	1	then	then	ADV
ejpam-3288	372	2	aptr	aptr	PROPN
ejpam-3288	372	3	is	be	AUX
ejpam-3288	372	4	an	an	DET
ejpam-3288	372	5	h	h	NOUN
ejpam-3288	372	6	-	-	PUNCT
ejpam-3288	372	7	ideal	ideal	NOUN
ejpam-3288	372	8	by	by	ADP
ejpam-3288	372	9	theorem	theorem	NOUN
ejpam-3288	372	10	7	7	NUM
ejpam-3288	372	11	.	.	PUNCT
ejpam-3288	373	1	let	let	VERB
ejpam-3288	373	2	x	x	X
ejpam-3288	373	3	∈	∈	PROPN
ejpam-3288	373	4	aptr	aptr	VERB
ejpam-3288	373	5	,	,	PUNCT
ejpam-3288	373	6	then	then	ADV
ejpam-3288	373	7	µpa(x	µpa(x	PRON
ejpam-3288	373	8	)	)	PUNCT
ejpam-3288	373	9	≤	≤	NUM
ejpam-3288	373	10	tr	tr	VERB
ejpam-3288	373	11	<	<	X
ejpam-3288	373	12	tr−1	tr−1	PROPN
ejpam-3288	373	13	,	,	PUNCT
ejpam-3288	373	14	which	which	PRON
ejpam-3288	373	15	implies	imply	VERB
ejpam-3288	373	16	that	that	SCONJ
ejpam-3288	373	17	x	x	SYM
ejpam-3288	373	18	∈	∈	PROPN
ejpam-3288	373	19	aptr−1	aptr−1	INTJ
ejpam-3288	373	20	.	.	PUNCT
ejpam-3288	374	1	hence	hence	ADV
ejpam-3288	374	2	,	,	PUNCT
ejpam-3288	374	3	aptr	aptr	VERB
ejpam-3288	374	4	⊆	⊆	NUM
ejpam-3288	374	5	aptr−1	aptr−1	PROPN
ejpam-3288	374	6	.	.	PUNCT
ejpam-3288	375	1	since	since	SCONJ
ejpam-3288	375	2	tr−1	tr−1	PROPN
ejpam-3288	375	3	∈	∈	PROPN
ejpam-3288	375	4	im(µpa	im(µpa	PROPN
ejpam-3288	375	5	)	)	PUNCT
ejpam-3288	375	6	,	,	PUNCT
ejpam-3288	375	7	there	there	PRON
ejpam-3288	375	8	exists	exist	VERB
ejpam-3288	375	9	xr−1	xr−1	PROPN
ejpam-3288	375	10	∈	∈	PROPN
ejpam-3288	375	11	x	x	PUNCT
ejpam-3288	376	1	such	such	ADJ
ejpam-3288	376	2	that	that	SCONJ
ejpam-3288	376	3	µpa(xr−1	µpa(xr−1	ADJ
ejpam-3288	376	4	)	)	PUNCT
ejpam-3288	376	5	=	=	SYM
ejpam-3288	376	6	tr−1	tr−1	PROPN
ejpam-3288	376	7	.	.	PUNCT
ejpam-3288	377	1	it	it	PRON
ejpam-3288	377	2	follows	follow	VERB
ejpam-3288	377	3	that	that	SCONJ
ejpam-3288	377	4	xr−1	xr−1	PROPN
ejpam-3288	377	5	∈	∈	PROPN
ejpam-3288	378	1	aptr−1	aptr−1	INTJ
ejpam-3288	378	2	,	,	PUNCT
ejpam-3288	378	3	but	but	CCONJ
ejpam-3288	378	4	xr−1	xr−1	PROPN
ejpam-3288	378	5	6∈	6∈	PROPN
ejpam-3288	378	6	aptr	aptr	VERB
ejpam-3288	378	7	.	.	PUNCT
ejpam-3288	379	1	thus	thus	ADV
ejpam-3288	379	2	,	,	PUNCT
ejpam-3288	379	3	aptr	aptr	VERB
ejpam-3288	379	4	⊂	⊂	PRON
ejpam-3288	379	5	aptr−1	aptr−1	INTJ
ejpam-3288	379	6	,	,	PUNCT
ejpam-3288	379	7	and	and	CCONJ
ejpam-3288	379	8	so	so	ADV
ejpam-3288	379	9	we	we	PRON
ejpam-3288	379	10	obtain	obtain	VERB
ejpam-3288	379	11	a	a	DET
ejpam-3288	379	12	strictly	strictly	ADV
ejpam-3288	379	13	decreasing	decrease	VERB
ejpam-3288	379	14	sequence	sequence	NOUN
ejpam-3288	379	15	apt1	apt1	PROPN
ejpam-3288	379	16	⊃	⊃	PROPN
ejpam-3288	379	17	a	a	DET
ejpam-3288	379	18	p	p	X
ejpam-3288	379	19	t2	t2	PROPN
ejpam-3288	379	20	⊃	⊃	PROPN
ejpam-3288	379	21	a	a	DET
ejpam-3288	379	22	p	p	PROPN
ejpam-3288	379	23	t3	t3	PROPN
ejpam-3288	379	24	⊃	⊃	PROPN
ejpam-3288	379	25	...	...	PUNCT
ejpam-3288	379	26	of	of	ADP
ejpam-3288	379	27	h	h	NOUN
ejpam-3288	379	28	-	-	PUNCT
ejpam-3288	379	29	ideals	ideal	NOUN
ejpam-3288	379	30	of	of	ADP
ejpam-3288	379	31	x	x	PUNCT
ejpam-3288	379	32	which	which	PRON
ejpam-3288	379	33	is	be	AUX
ejpam-3288	379	34	not	not	PART
ejpam-3288	379	35	terminating	terminate	VERB
ejpam-3288	379	36	.	.	PUNCT
ejpam-3288	380	1	a	a	DET
ejpam-3288	380	2	contradiction	contradiction	NOUN
ejpam-3288	380	3	.	.	PUNCT
ejpam-3288	381	1	similar	similar	ADJ
ejpam-3288	381	2	for	for	ADP
ejpam-3288	381	3	im(µna	im(µna	PROPN
ejpam-3288	381	4	)	)	PUNCT
ejpam-3288	381	5	.	.	PUNCT
ejpam-3288	382	1	this	this	PRON
ejpam-3288	382	2	completes	complete	VERB
ejpam-3288	382	3	the	the	DET
ejpam-3288	382	4	proof	proof	NOUN
ejpam-3288	382	5	.	.	PUNCT
ejpam-3288	383	1	now	now	ADV
ejpam-3288	383	2	we	we	PRON
ejpam-3288	383	3	consider	consider	VERB
ejpam-3288	383	4	the	the	DET
ejpam-3288	383	5	converse	converse	NOUN
ejpam-3288	383	6	of	of	ADP
ejpam-3288	383	7	theorem	theorem	ADJ
ejpam-3288	383	8	9	9	NUM
ejpam-3288	383	9	.	.	PUNCT
ejpam-3288	383	10	theorem	theorem	NOUN
ejpam-3288	383	11	10	10	NUM
ejpam-3288	383	12	.	.	PUNCT
ejpam-3288	384	1	let	let	VERB
ejpam-3288	384	2	x	x	PRON
ejpam-3288	384	3	be	be	AUX
ejpam-3288	384	4	a	a	DET
ejpam-3288	384	5	bck	bck	VERB
ejpam-3288	384	6	/	/	SYM
ejpam-3288	384	7	bci	bci	NOUN
ejpam-3288	384	8	-	-	NOUN
ejpam-3288	384	9	algebra	algebra	NOUN
ejpam-3288	384	10	.	.	PUNCT
ejpam-3288	385	1	if	if	SCONJ
ejpam-3288	385	2	every	every	DET
ejpam-3288	385	3	doubt	doubt	ADV
ejpam-3288	385	4	bipolar	bipolar	ADJ
ejpam-3288	385	5	fuzzy	fuzzy	ADJ
ejpam-3288	385	6	h	h	NOUN
ejpam-3288	385	7	-	-	PUNCT
ejpam-3288	385	8	ideal	ideal	NOUN
ejpam-3288	385	9	of	of	ADP
ejpam-3288	385	10	x	x	PUNCT
ejpam-3288	385	11	has	have	VERB
ejpam-3288	385	12	finite	finite	ADJ
ejpam-3288	385	13	number	number	NOUN
ejpam-3288	385	14	of	of	ADP
ejpam-3288	385	15	values	value	NOUN
ejpam-3288	385	16	,	,	PUNCT
ejpam-3288	385	17	then	then	ADV
ejpam-3288	385	18	x	x	PRON
ejpam-3288	385	19	satisfies	satisfy	VERB
ejpam-3288	385	20	h	h	NOUN
ejpam-3288	385	21	-	-	PUNCT
ejpam-3288	385	22	dcc	dcc	NOUN
ejpam-3288	385	23	.	.	PUNCT
ejpam-3288	386	1	proof	proof	NOUN
ejpam-3288	386	2	.	.	PUNCT
ejpam-3288	387	1	suppose	suppose	VERB
ejpam-3288	387	2	that	that	SCONJ
ejpam-3288	387	3	x	x	PRON
ejpam-3288	387	4	does	do	AUX
ejpam-3288	387	5	not	not	PART
ejpam-3288	387	6	satisfy	satisfy	VERB
ejpam-3288	387	7	h	h	NOUN
ejpam-3288	387	8	-	-	PUNCT
ejpam-3288	387	9	dcc	dcc	NOUN
ejpam-3288	387	10	,	,	PUNCT
ejpam-3288	387	11	then	then	ADV
ejpam-3288	387	12	there	there	PRON
ejpam-3288	387	13	exists	exist	VERB
ejpam-3288	387	14	a	a	DET
ejpam-3288	387	15	strictly	strictly	ADV
ejpam-3288	387	16	descending	descend	VERB
ejpam-3288	387	17	chain	chain	NOUN
ejpam-3288	387	18	i	i	PRON
ejpam-3288	387	19	◦	◦	VERB
ejpam-3288	387	20	⊃	⊃	PROPN
ejpam-3288	387	21	i1	i1	PROPN
ejpam-3288	387	22	⊃	⊃	PROPN
ejpam-3288	387	23	i2	i2	PROPN
ejpam-3288	387	24	⊃	⊃	PROPN
ejpam-3288	387	25	...	...	PUNCT
ejpam-3288	387	26	of	of	ADP
ejpam-3288	387	27	h	h	NOUN
ejpam-3288	387	28	-	-	PUNCT
ejpam-3288	387	29	ideals	ideal	NOUN
ejpam-3288	387	30	of	of	ADP
ejpam-3288	387	31	x.	x.	NOUN
ejpam-3288	387	32	define	define	VERB
ejpam-3288	387	33	a	a	DET
ejpam-3288	387	34	bipolar	bipolar	ADJ
ejpam-3288	387	35	fuzzy	fuzzy	NOUN
ejpam-3288	387	36	set	set	VERB
ejpam-3288	387	37	a	a	PRON
ejpam-3288	387	38	=	=	X
ejpam-3288	387	39	(	(	PUNCT
ejpam-3288	387	40	µpa	µpa	PROPN
ejpam-3288	387	41	,	,	PUNCT
ejpam-3288	387	42	µ	µ	X
ejpam-3288	387	43	n	n	PRON
ejpam-3288	387	44	a	a	NOUN
ejpam-3288	387	45	)	)	PUNCT
ejpam-3288	387	46	in	in	ADP
ejpam-3288	387	47	x	x	PUNCT
ejpam-3288	387	48	by	by	ADP
ejpam-3288	387	49	µpa(x	µpa(x	PRON
ejpam-3288	387	50	)	)	PUNCT
ejpam-3288	387	51	=	=	PRON
ejpam-3288	387	52	{	{	PUNCT
ejpam-3288	387	53	1	1	NUM
ejpam-3288	387	54	n+1	n+1	PRON
ejpam-3288	387	55	,	,	PUNCT
ejpam-3288	387	56	if	if	SCONJ
ejpam-3288	387	57	x	x	SYM
ejpam-3288	387	58	∈	∈	NOUN
ejpam-3288	387	59	in	in	ADP
ejpam-3288	387	60	−	−	PROPN
ejpam-3288	387	61	in+1	in+1	NOUN
ejpam-3288	387	62	,	,	PUNCT
ejpam-3288	387	63	n	n	PROPN
ejpam-3288	387	64	=	=	SYM
ejpam-3288	387	65	0	0	NUM
ejpam-3288	387	66	,	,	PUNCT
ejpam-3288	387	67	1	1	NUM
ejpam-3288	387	68	,	,	PUNCT
ejpam-3288	387	69	2	2	NUM
ejpam-3288	387	70	,	,	PUNCT
ejpam-3288	387	71	...	...	PUNCT
ejpam-3288	388	1	0	0	X
ejpam-3288	388	2	,	,	PUNCT
ejpam-3288	388	3	if	if	SCONJ
ejpam-3288	388	4	x	x	SYM
ejpam-3288	388	5	∈	∈	NOUN
ejpam-3288	388	6	⋂∞	⋂∞	NOUN
ejpam-3288	388	7	n=0	n=0	X
ejpam-3288	388	8	in	in	ADP
ejpam-3288	388	9	,	,	PUNCT
ejpam-3288	388	10	µna	µna	ADJ
ejpam-3288	388	11	(	(	PUNCT
ejpam-3288	388	12	x	x	NOUN
ejpam-3288	388	13	)	)	PUNCT
ejpam-3288	388	14	=	=	SYM
ejpam-3288	388	15	−µpa(x	−µpa(x	NOUN
ejpam-3288	388	16	)	)	PUNCT
ejpam-3288	388	17	.	.	PUNCT
ejpam-3288	389	1	where	where	SCONJ
ejpam-3288	389	2	i	i	PRON
ejpam-3288	389	3	◦	◦	NOUN
ejpam-3288	389	4	stands	stand	VERB
ejpam-3288	389	5	for	for	ADP
ejpam-3288	389	6	x.	x.	PROPN
ejpam-3288	389	7	a.	a.	PROPN
ejpam-3288	389	8	al	al	PROPN
ejpam-3288	389	9	-	-	PROPN
ejpam-3288	389	10	masarwah	masarwah	PROPN
ejpam-3288	389	11	,	,	PUNCT
ejpam-3288	389	12	a.	a.	NOUN
ejpam-3288	389	13	g.	g.	PROPN
ejpam-3288	389	14	ahmad	ahmad	PROPN
ejpam-3288	389	15	/	/	SYM
ejpam-3288	389	16	eur	eur	PROPN
ejpam-3288	389	17	.	.	PUNCT
ejpam-3288	390	1	j.	j.	PROPN
ejpam-3288	390	2	pure	pure	PROPN
ejpam-3288	390	3	appl	appl	PROPN
ejpam-3288	390	4	.	.	PROPN
ejpam-3288	390	5	math	math	PROPN
ejpam-3288	390	6	,	,	PUNCT
ejpam-3288	390	7	11	11	NUM
ejpam-3288	390	8	(	(	PUNCT
ejpam-3288	390	9	3	3	NUM
ejpam-3288	390	10	)	)	PUNCT
ejpam-3288	390	11	(	(	PUNCT
ejpam-3288	390	12	2018	2018	NUM
ejpam-3288	390	13	)	)	PUNCT
ejpam-3288	390	14	,	,	PUNCT
ejpam-3288	390	15	652	652	NUM
ejpam-3288	390	16	-	-	SYM
ejpam-3288	390	17	670	670	NUM
ejpam-3288	390	18	668	668	NUM
ejpam-3288	391	1	we	we	PRON
ejpam-3288	391	2	prove	prove	VERB
ejpam-3288	391	3	that	that	SCONJ
ejpam-3288	391	4	a	a	DET
ejpam-3288	391	5	=	=	X
ejpam-3288	391	6	(	(	PUNCT
ejpam-3288	391	7	µpa	µpa	PROPN
ejpam-3288	391	8	,	,	PUNCT
ejpam-3288	391	9	µ	µ	X
ejpam-3288	391	10	n	n	PRON
ejpam-3288	391	11	a	a	PRON
ejpam-3288	391	12	)	)	PUNCT
ejpam-3288	391	13	is	be	AUX
ejpam-3288	391	14	a	a	DET
ejpam-3288	391	15	doubt	doubt	ADV
ejpam-3288	391	16	bipolar	bipolar	ADJ
ejpam-3288	391	17	fuzzy	fuzzy	ADJ
ejpam-3288	391	18	h	h	NOUN
ejpam-3288	391	19	-	-	PUNCT
ejpam-3288	391	20	ideal	ideal	NOUN
ejpam-3288	391	21	of	of	ADP
ejpam-3288	391	22	x.	x.	NOUN
ejpam-3288	391	23	clearly	clearly	ADV
ejpam-3288	391	24	,	,	PUNCT
ejpam-3288	391	25	µpa(0	µpa(0	ADJ
ejpam-3288	391	26	)	)	PUNCT
ejpam-3288	392	1	=	=	SYM
ejpam-3288	392	2	0	0	X
ejpam-3288	392	3	≤	≤	NUM
ejpam-3288	392	4	µpa(x	µpa(x	NOUN
ejpam-3288	392	5	)	)	PUNCT
ejpam-3288	392	6	and	and	CCONJ
ejpam-3288	392	7	µna	µna	ADJ
ejpam-3288	392	8	(	(	PUNCT
ejpam-3288	392	9	0	0	NUM
ejpam-3288	392	10	)	)	PUNCT
ejpam-3288	392	11	=	=	SYM
ejpam-3288	392	12	0	0	NUM
ejpam-3288	392	13	≥	≥	NOUN
ejpam-3288	392	14	µna	µna	ADJ
ejpam-3288	392	15	(	(	PUNCT
ejpam-3288	392	16	x	x	NOUN
ejpam-3288	392	17	)	)	PUNCT
ejpam-3288	392	18	for	for	ADP
ejpam-3288	392	19	all	all	PRON
ejpam-3288	392	20	x	x	SYM
ejpam-3288	392	21	∈	∈	NOUN
ejpam-3288	392	22	x.	x.	NOUN
ejpam-3288	392	23	let	let	VERB
ejpam-3288	392	24	x	x	PRON
ejpam-3288	392	25	,	,	PUNCT
ejpam-3288	392	26	y	y	PROPN
ejpam-3288	392	27	,	,	PUNCT
ejpam-3288	392	28	z	z	PROPN
ejpam-3288	392	29	∈	∈	PROPN
ejpam-3288	392	30	x.	x.	NOUN
ejpam-3288	392	31	assume	assume	VERB
ejpam-3288	392	32	that	that	SCONJ
ejpam-3288	392	33	x∗	x∗	PROPN
ejpam-3288	392	34	(	(	PUNCT
ejpam-3288	392	35	y	y	PROPN
ejpam-3288	392	36	∗z	∗z	PROPN
ejpam-3288	392	37	)	)	PUNCT
ejpam-3288	392	38	∈	∈	NOUN
ejpam-3288	392	39	in	in	ADP
ejpam-3288	392	40	−	−	PROPN
ejpam-3288	392	41	in+1	in+1	NOUN
ejpam-3288	392	42	and	and	CCONJ
ejpam-3288	392	43	y	y	PROPN
ejpam-3288	392	44	∈	∈	PROPN
ejpam-3288	392	45	ik	ik	INTJ
ejpam-3288	392	46	−	−	PROPN
ejpam-3288	392	47	ik+1	ik+1	X
ejpam-3288	392	48	for	for	ADP
ejpam-3288	392	49	n	n	NOUN
ejpam-3288	392	50	=	=	SYM
ejpam-3288	392	51	0	0	NUM
ejpam-3288	392	52	,	,	PUNCT
ejpam-3288	392	53	1	1	NUM
ejpam-3288	392	54	,	,	PUNCT
ejpam-3288	392	55	2	2	NUM
ejpam-3288	392	56	,	,	PUNCT
ejpam-3288	392	57	...	...	PUNCT
ejpam-3288	392	58	;	;	PUNCT
ejpam-3288	392	59	k	k	X
ejpam-3288	392	60	=	=	SYM
ejpam-3288	392	61	0	0	NUM
ejpam-3288	392	62	,	,	PUNCT
ejpam-3288	392	63	1	1	NUM
ejpam-3288	392	64	,	,	PUNCT
ejpam-3288	392	65	2	2	NUM
ejpam-3288	392	66	,	,	PUNCT
ejpam-3288	392	67	...	...	PUNCT
ejpam-3288	392	68	.	.	PUNCT
ejpam-3288	393	1	without	without	ADP
ejpam-3288	393	2	loss	loss	NOUN
ejpam-3288	393	3	of	of	ADP
ejpam-3288	393	4	generality	generality	NOUN
ejpam-3288	393	5	,	,	PUNCT
ejpam-3288	393	6	we	we	PRON
ejpam-3288	393	7	may	may	AUX
ejpam-3288	393	8	assume	assume	VERB
ejpam-3288	393	9	that	that	SCONJ
ejpam-3288	393	10	n	n	PROPN
ejpam-3288	393	11	≤	≤	PROPN
ejpam-3288	393	12	k.	k.	NOUN
ejpam-3288	394	1	then	then	ADV
ejpam-3288	394	2	clearly	clearly	ADV
ejpam-3288	394	3	y	y	PROPN
ejpam-3288	394	4	∈	∈	PROPN
ejpam-3288	394	5	in	in	ADP
ejpam-3288	394	6	.	.	PUNCT
ejpam-3288	395	1	since	since	SCONJ
ejpam-3288	395	2	in	in	ADV
ejpam-3288	395	3	is	be	AUX
ejpam-3288	395	4	an	an	DET
ejpam-3288	395	5	h	h	NOUN
ejpam-3288	395	6	-	-	PUNCT
ejpam-3288	395	7	ideal	ideal	ADJ
ejpam-3288	395	8	,	,	PUNCT
ejpam-3288	395	9	we	we	PRON
ejpam-3288	395	10	have	have	VERB
ejpam-3288	395	11	x∗z	x∗z	PROPN
ejpam-3288	395	12	∈	∈	PROPN
ejpam-3288	395	13	in	in	ADP
ejpam-3288	395	14	.	.	PUNCT
ejpam-3288	396	1	hence	hence	ADV
ejpam-3288	396	2	,	,	PUNCT
ejpam-3288	396	3	µpa(x	µpa(x	PROPN
ejpam-3288	396	4	∗	∗	NOUN
ejpam-3288	396	5	z	z	NOUN
ejpam-3288	396	6	)	)	PUNCT
ejpam-3288	396	7	≤	≤	NUM
ejpam-3288	396	8	1	1	NUM
ejpam-3288	396	9	n+1	n+1	PROPN
ejpam-3288	396	10	=	=	SYM
ejpam-3288	396	11	max{µpa(x	max{µpa(x	PROPN
ejpam-3288	396	12	∗	∗	NOUN
ejpam-3288	396	13	(	(	PUNCT
ejpam-3288	396	14	y	y	PROPN
ejpam-3288	396	15	∗	∗	PROPN
ejpam-3288	396	16	z	z	PROPN
ejpam-3288	396	17	)	)	PUNCT
ejpam-3288	396	18	)	)	PUNCT
ejpam-3288	396	19	,	,	PUNCT
ejpam-3288	396	20	µpa(y	µpa(y	PROPN
ejpam-3288	396	21	)	)	PUNCT
ejpam-3288	396	22	}	}	PUNCT
ejpam-3288	396	23	and	and	CCONJ
ejpam-3288	396	24	µna	µna	ADJ
ejpam-3288	396	25	(	(	PUNCT
ejpam-3288	396	26	x	x	NOUN
ejpam-3288	396	27	∗	∗	PROPN
ejpam-3288	396	28	z	z	NOUN
ejpam-3288	396	29	)	)	PUNCT
ejpam-3288	396	30	≥	≥	X
ejpam-3288	396	31	−1	−1	NOUN
ejpam-3288	396	32	n+1	n+1	PRON
ejpam-3288	396	33	=	=	SYM
ejpam-3288	396	34	min{µna	min{µna	NOUN
ejpam-3288	396	35	(	(	PUNCT
ejpam-3288	396	36	x	x	NOUN
ejpam-3288	396	37	∗	∗	NOUN
ejpam-3288	396	38	(	(	PUNCT
ejpam-3288	396	39	y	y	PROPN
ejpam-3288	396	40	∗	∗	PROPN
ejpam-3288	396	41	z	z	PROPN
ejpam-3288	396	42	)	)	PUNCT
ejpam-3288	396	43	)	)	PUNCT
ejpam-3288	396	44	,	,	PUNCT
ejpam-3288	396	45	µna	µna	PROPN
ejpam-3288	396	46	(	(	PUNCT
ejpam-3288	396	47	y	y	NOUN
ejpam-3288	396	48	)	)	PUNCT
ejpam-3288	396	49	}	}	PUNCT
ejpam-3288	396	50	.	.	PUNCT
ejpam-3288	397	1	if	if	SCONJ
ejpam-3288	397	2	x	x	PROPN
ejpam-3288	397	3	∗	∗	NOUN
ejpam-3288	397	4	(	(	PUNCT
ejpam-3288	397	5	y	y	PROPN
ejpam-3288	397	6	∗	∗	PROPN
ejpam-3288	397	7	z	z	PROPN
ejpam-3288	397	8	)	)	PUNCT
ejpam-3288	397	9	,	,	PUNCT
ejpam-3288	397	10	y	y	PROPN
ejpam-3288	397	11	∈	∈	PROPN
ejpam-3288	397	12	⋂∞	⋂∞	NOUN
ejpam-3288	397	13	n=0	n=0	X
ejpam-3288	397	14	in	in	ADP
ejpam-3288	397	15	,	,	PUNCT
ejpam-3288	397	16	then	then	ADV
ejpam-3288	397	17	x	x	X
ejpam-3288	397	18	∗	∗	PROPN
ejpam-3288	397	19	z	z	NOUN
ejpam-3288	397	20	∈	∈	NOUN
ejpam-3288	397	21	⋂∞	⋂∞	NOUN
ejpam-3288	397	22	n=0	n=0	X
ejpam-3288	397	23	in	in	ADP
ejpam-3288	397	24	.	.	PUNCT
ejpam-3288	398	1	thus	thus	ADV
ejpam-3288	398	2	,	,	PUNCT
ejpam-3288	398	3	µpa(x	µpa(x	PROPN
ejpam-3288	398	4	∗	∗	NOUN
ejpam-3288	398	5	z	z	NOUN
ejpam-3288	398	6	)	)	PUNCT
ejpam-3288	398	7	=	=	SYM
ejpam-3288	398	8	0	0	PUNCT
ejpam-3288	398	9	=	=	SYM
ejpam-3288	398	10	max{µpa(x	max{µpa(x	PROPN
ejpam-3288	398	11	∗	∗	NOUN
ejpam-3288	398	12	(	(	PUNCT
ejpam-3288	398	13	y	y	PROPN
ejpam-3288	398	14	∗	∗	PROPN
ejpam-3288	398	15	z	z	PROPN
ejpam-3288	398	16	)	)	PUNCT
ejpam-3288	398	17	)	)	PUNCT
ejpam-3288	398	18	,	,	PUNCT
ejpam-3288	398	19	µpa(y	µpa(y	PROPN
ejpam-3288	398	20	)	)	PUNCT
ejpam-3288	398	21	}	}	PUNCT
ejpam-3288	398	22	and	and	CCONJ
ejpam-3288	398	23	µna	µna	ADJ
ejpam-3288	398	24	(	(	PUNCT
ejpam-3288	398	25	x	x	NOUN
ejpam-3288	398	26	∗	∗	PROPN
ejpam-3288	398	27	z	z	NOUN
ejpam-3288	398	28	)	)	PUNCT
ejpam-3288	398	29	=	=	SYM
ejpam-3288	398	30	0	0	PUNCT
ejpam-3288	398	31	=	=	SYM
ejpam-3288	398	32	min{µna	min{µna	NOUN
ejpam-3288	398	33	(	(	PUNCT
ejpam-3288	398	34	x	x	NOUN
ejpam-3288	398	35	∗	∗	NOUN
ejpam-3288	398	36	(	(	PUNCT
ejpam-3288	398	37	y	y	PROPN
ejpam-3288	398	38	∗	∗	PROPN
ejpam-3288	398	39	z	z	PROPN
ejpam-3288	398	40	)	)	PUNCT
ejpam-3288	398	41	)	)	PUNCT
ejpam-3288	398	42	,	,	PUNCT
ejpam-3288	398	43	µna	µna	PROPN
ejpam-3288	398	44	(	(	PUNCT
ejpam-3288	398	45	y	y	NOUN
ejpam-3288	398	46	)	)	PUNCT
ejpam-3288	398	47	}	}	PUNCT
ejpam-3288	398	48	.	.	PUNCT
ejpam-3288	399	1	if	if	SCONJ
ejpam-3288	399	2	x	x	PROPN
ejpam-3288	399	3	∗	∗	NOUN
ejpam-3288	399	4	(	(	PUNCT
ejpam-3288	399	5	y	y	PROPN
ejpam-3288	399	6	∗	∗	PROPN
ejpam-3288	399	7	z	z	PROPN
ejpam-3288	399	8	)	)	PUNCT
ejpam-3288	399	9	6∈	6∈	NOUN
ejpam-3288	399	10	⋂∞	⋂∞	NOUN
ejpam-3288	399	11	n=0	n=0	PROPN
ejpam-3288	399	12	in	in	ADP
ejpam-3288	399	13	and	and	CCONJ
ejpam-3288	399	14	y	y	PROPN
ejpam-3288	399	15	∈	∈	PROPN
ejpam-3288	399	16	⋂∞	⋂∞	NOUN
ejpam-3288	399	17	n=0	n=0	X
ejpam-3288	399	18	in	in	ADP
ejpam-3288	399	19	,	,	PUNCT
ejpam-3288	399	20	then	then	ADV
ejpam-3288	399	21	there	there	PRON
ejpam-3288	399	22	exists	exist	VERB
ejpam-3288	399	23	k	k	PROPN
ejpam-3288	399	24	∈	∈	PROPN
ejpam-3288	399	25	n	n	PRON
ejpam-3288	399	26	such	such	ADJ
ejpam-3288	399	27	that	that	SCONJ
ejpam-3288	399	28	x	x	SYM
ejpam-3288	399	29	∗	∗	NOUN
ejpam-3288	399	30	(	(	PUNCT
ejpam-3288	399	31	y	y	PROPN
ejpam-3288	399	32	∗	∗	PROPN
ejpam-3288	399	33	z	z	PROPN
ejpam-3288	399	34	)	)	PUNCT
ejpam-3288	399	35	6∈	6∈	PROPN
ejpam-3288	399	36	ik	ik	INTJ
ejpam-3288	399	37	−	−	PROPN
ejpam-3288	399	38	ik+1	ik+1	PROPN
ejpam-3288	399	39	.	.	PUNCT
ejpam-3288	400	1	it	it	PRON
ejpam-3288	400	2	follows	follow	VERB
ejpam-3288	400	3	that	that	SCONJ
ejpam-3288	400	4	x	x	NOUN
ejpam-3288	400	5	∗	∗	NOUN
ejpam-3288	400	6	z	z	PROPN
ejpam-3288	400	7	∈	∈	PROPN
ejpam-3288	400	8	ik	ik	NOUN
ejpam-3288	400	9	,	,	PUNCT
ejpam-3288	400	10	so	so	SCONJ
ejpam-3288	400	11	that	that	SCONJ
ejpam-3288	400	12	µpa(x	µpa(x	PRON
ejpam-3288	400	13	∗	∗	NOUN
ejpam-3288	400	14	z	z	NOUN
ejpam-3288	400	15	)	)	PUNCT
ejpam-3288	400	16	≤	≤	NUM
ejpam-3288	400	17	1	1	NUM
ejpam-3288	400	18	k+1	k+1	NOUN
ejpam-3288	400	19	=	=	SYM
ejpam-3288	400	20	max{µpa(x	max{µpa(x	PROPN
ejpam-3288	400	21	∗	∗	NOUN
ejpam-3288	400	22	(	(	PUNCT
ejpam-3288	400	23	y	y	PROPN
ejpam-3288	400	24	∗	∗	PROPN
ejpam-3288	400	25	z	z	PROPN
ejpam-3288	400	26	)	)	PUNCT
ejpam-3288	400	27	)	)	PUNCT
ejpam-3288	400	28	,	,	PUNCT
ejpam-3288	400	29	µpa(y	µpa(y	PROPN
ejpam-3288	400	30	)	)	PUNCT
ejpam-3288	400	31	}	}	PUNCT
ejpam-3288	400	32	and	and	CCONJ
ejpam-3288	400	33	µna	µna	ADJ
ejpam-3288	400	34	(	(	PUNCT
ejpam-3288	400	35	x	x	NOUN
ejpam-3288	400	36	∗	∗	PROPN
ejpam-3288	400	37	z	z	NOUN
ejpam-3288	400	38	)	)	PUNCT
ejpam-3288	400	39	≥	≥	X
ejpam-3288	400	40	−1	−1	NOUN
ejpam-3288	400	41	k+1	k+1	NOUN
ejpam-3288	400	42	=	=	PUNCT
ejpam-3288	400	43	min{µna	min{µna	NOUN
ejpam-3288	400	44	(	(	PUNCT
ejpam-3288	400	45	x	x	NOUN
ejpam-3288	400	46	∗	∗	NOUN
ejpam-3288	400	47	(	(	PUNCT
ejpam-3288	400	48	y	y	PROPN
ejpam-3288	400	49	∗	∗	PROPN
ejpam-3288	400	50	z	z	PROPN
ejpam-3288	400	51	)	)	PUNCT
ejpam-3288	400	52	)	)	PUNCT
ejpam-3288	400	53	,	,	PUNCT
ejpam-3288	400	54	µna	µna	PROPN
ejpam-3288	400	55	(	(	PUNCT
ejpam-3288	400	56	y	y	NOUN
ejpam-3288	400	57	)	)	PUNCT
ejpam-3288	400	58	}	}	PUNCT
ejpam-3288	400	59	.	.	PUNCT
ejpam-3288	401	1	finally	finally	ADV
ejpam-3288	401	2	,	,	PUNCT
ejpam-3288	401	3	assume	assume	VERB
ejpam-3288	401	4	that	that	SCONJ
ejpam-3288	401	5	x	x	SYM
ejpam-3288	401	6	∗	∗	NOUN
ejpam-3288	401	7	(	(	PUNCT
ejpam-3288	401	8	y	y	PROPN
ejpam-3288	401	9	∗	∗	PROPN
ejpam-3288	401	10	z	z	NOUN
ejpam-3288	401	11	)	)	PUNCT
ejpam-3288	401	12	∈	∈	NOUN
ejpam-3288	401	13	⋂∞	⋂∞	NOUN
ejpam-3288	401	14	n=0	n=0	X
ejpam-3288	401	15	in	in	ADP
ejpam-3288	401	16	and	and	CCONJ
ejpam-3288	401	17	y	y	PROPN
ejpam-3288	401	18	6∈	6∈	PROPN
ejpam-3288	401	19	⋂∞	⋂∞	NOUN
ejpam-3288	401	20	n=0	n=0	PROPN
ejpam-3288	401	21	in	in	ADP
ejpam-3288	401	22	,	,	PUNCT
ejpam-3288	401	23	then	then	ADV
ejpam-3288	401	24	y	y	PROPN
ejpam-3288	401	25	∈	∈	PROPN
ejpam-3288	401	26	ir	ir	PROPN
ejpam-3288	402	1	−	−	PROPN
ejpam-3288	402	2	ir+1	ir+1	NOUN
ejpam-3288	402	3	for	for	ADP
ejpam-3288	402	4	some	some	DET
ejpam-3288	402	5	r	r	NOUN
ejpam-3288	402	6	∈	∈	PROPN
ejpam-3288	402	7	n.	n.	NOUN
ejpam-3288	402	8	it	it	PRON
ejpam-3288	402	9	follows	follow	VERB
ejpam-3288	402	10	that	that	SCONJ
ejpam-3288	402	11	x	x	NOUN
ejpam-3288	402	12	∗	∗	NOUN
ejpam-3288	402	13	z	z	PROPN
ejpam-3288	402	14	∈	∈	PROPN
ejpam-3288	402	15	ir	ir	NOUN
ejpam-3288	402	16	and	and	CCONJ
ejpam-3288	402	17	hence	hence	ADV
ejpam-3288	402	18	µpa(x	µpa(x	PRON
ejpam-3288	402	19	∗	∗	NOUN
ejpam-3288	402	20	z	z	NOUN
ejpam-3288	402	21	)	)	PUNCT
ejpam-3288	402	22	≤	≤	NUM
ejpam-3288	402	23	1	1	NUM
ejpam-3288	402	24	r+1	r+1	PROPN
ejpam-3288	402	25	=	=	SYM
ejpam-3288	402	26	max{µpa(x	max{µpa(x	PROPN
ejpam-3288	402	27	∗	∗	NOUN
ejpam-3288	402	28	(	(	PUNCT
ejpam-3288	402	29	y	y	PROPN
ejpam-3288	402	30	∗	∗	PROPN
ejpam-3288	402	31	z	z	PROPN
ejpam-3288	402	32	)	)	PUNCT
ejpam-3288	402	33	)	)	PUNCT
ejpam-3288	402	34	,	,	PUNCT
ejpam-3288	402	35	µpa(y	µpa(y	PROPN
ejpam-3288	402	36	)	)	PUNCT
ejpam-3288	402	37	}	}	PUNCT
ejpam-3288	402	38	and	and	CCONJ
ejpam-3288	402	39	µna	µna	ADJ
ejpam-3288	402	40	(	(	PUNCT
ejpam-3288	402	41	x	x	NOUN
ejpam-3288	402	42	∗	∗	PROPN
ejpam-3288	402	43	z	z	NOUN
ejpam-3288	402	44	)	)	PUNCT
ejpam-3288	402	45	≥	≥	NOUN
ejpam-3288	402	46	−1	−1	NOUN
ejpam-3288	403	1	r+1	r+1	NOUN
ejpam-3288	403	2	=	=	PUNCT
ejpam-3288	403	3	min{µna	min{µna	NOUN
ejpam-3288	403	4	(	(	PUNCT
ejpam-3288	403	5	x	x	NOUN
ejpam-3288	403	6	∗	∗	NOUN
ejpam-3288	403	7	(	(	PUNCT
ejpam-3288	403	8	y	y	PROPN
ejpam-3288	403	9	∗	∗	PROPN
ejpam-3288	403	10	z	z	PROPN
ejpam-3288	403	11	)	)	PUNCT
ejpam-3288	403	12	)	)	PUNCT
ejpam-3288	403	13	,	,	PUNCT
ejpam-3288	403	14	µna	µna	PROPN
ejpam-3288	403	15	(	(	PUNCT
ejpam-3288	403	16	y	y	NOUN
ejpam-3288	403	17	)	)	PUNCT
ejpam-3288	403	18	}	}	PUNCT
ejpam-3288	403	19	.	.	PUNCT
ejpam-3288	404	1	consequently	consequently	ADV
ejpam-3288	404	2	,	,	PUNCT
ejpam-3288	404	3	we	we	PRON
ejpam-3288	404	4	find	find	VERB
ejpam-3288	404	5	that	that	SCONJ
ejpam-3288	404	6	a	a	DET
ejpam-3288	404	7	=	=	X
ejpam-3288	404	8	(	(	PUNCT
ejpam-3288	404	9	µpa	µpa	PROPN
ejpam-3288	404	10	,	,	PUNCT
ejpam-3288	404	11	µ	µ	X
ejpam-3288	404	12	n	n	PRON
ejpam-3288	404	13	a	a	PRON
ejpam-3288	404	14	)	)	PUNCT
ejpam-3288	404	15	is	be	AUX
ejpam-3288	404	16	a	a	DET
ejpam-3288	404	17	doubt	doubt	ADV
ejpam-3288	404	18	bipolar	bipolar	ADJ
ejpam-3288	404	19	fuzzy	fuzzy	ADJ
ejpam-3288	404	20	h	h	NOUN
ejpam-3288	404	21	-	-	PUNCT
ejpam-3288	404	22	ideal	ideal	NOUN
ejpam-3288	404	23	and	and	CCONJ
ejpam-3288	404	24	a	a	DET
ejpam-3288	404	25	=	=	X
ejpam-3288	404	26	(	(	PUNCT
ejpam-3288	404	27	µpa	µpa	PROPN
ejpam-3288	404	28	,	,	PUNCT
ejpam-3288	404	29	µ	µ	X
ejpam-3288	404	30	n	n	PRON
ejpam-3288	404	31	a	a	PRON
ejpam-3288	404	32	)	)	PUNCT
ejpam-3288	404	33	has	have	VERB
ejpam-3288	404	34	infinite	infinite	ADJ
ejpam-3288	404	35	number	number	NOUN
ejpam-3288	404	36	of	of	ADP
ejpam-3288	404	37	different	different	ADJ
ejpam-3288	404	38	values	value	NOUN
ejpam-3288	404	39	.	.	PUNCT
ejpam-3288	405	1	this	this	PRON
ejpam-3288	405	2	is	be	AUX
ejpam-3288	405	3	a	a	DET
ejpam-3288	405	4	contradiction	contradiction	NOUN
ejpam-3288	405	5	and	and	CCONJ
ejpam-3288	405	6	the	the	DET
ejpam-3288	405	7	proof	proof	NOUN
ejpam-3288	405	8	is	be	AUX
ejpam-3288	405	9	complete	complete	ADJ
ejpam-3288	405	10	.	.	PUNCT
ejpam-3288	406	1	5	5	X
ejpam-3288	406	2	.	.	X
ejpam-3288	406	3	conclusions	conclusion	NOUN
ejpam-3288	406	4	in	in	ADP
ejpam-3288	406	5	the	the	DET
ejpam-3288	406	6	study	study	NOUN
ejpam-3288	406	7	of	of	ADP
ejpam-3288	406	8	a	a	DET
ejpam-3288	406	9	bck	bck	PROPN
ejpam-3288	406	10	/	/	SYM
ejpam-3288	406	11	bci	bci	NOUN
ejpam-3288	406	12	-	-	NOUN
ejpam-3288	406	13	algebra	algebra	NOUN
ejpam-3288	406	14	,	,	PUNCT
ejpam-3288	406	15	we	we	PRON
ejpam-3288	406	16	know	know	VERB
ejpam-3288	406	17	that	that	PRON
ejpam-3288	406	18	doubt	doubt	VERB
ejpam-3288	406	19	bipolar	bipolar	ADJ
ejpam-3288	406	20	fuzzy	fuzzy	ADJ
ejpam-3288	406	21	h	h	NOUN
ejpam-3288	406	22	-	-	PUNCT
ejpam-3288	406	23	ideals	ideal	NOUN
ejpam-3288	406	24	with	with	ADP
ejpam-3288	406	25	special	special	ADJ
ejpam-3288	406	26	properties	property	NOUN
ejpam-3288	406	27	always	always	ADV
ejpam-3288	406	28	play	play	VERB
ejpam-3288	406	29	a	a	DET
ejpam-3288	406	30	vital	vital	ADJ
ejpam-3288	406	31	role	role	NOUN
ejpam-3288	406	32	in	in	ADP
ejpam-3288	406	33	the	the	DET
ejpam-3288	406	34	structure	structure	NOUN
ejpam-3288	406	35	theory	theory	NOUN
ejpam-3288	406	36	of	of	ADP
ejpam-3288	406	37	a	a	DET
ejpam-3288	406	38	bck	bck	NOUN
ejpam-3288	406	39	/	/	SYM
ejpam-3288	406	40	bcialgebra	bcialgebra	NOUN
ejpam-3288	406	41	.	.	PUNCT
ejpam-3288	407	1	in	in	ADP
ejpam-3288	407	2	this	this	DET
ejpam-3288	407	3	paper	paper	NOUN
ejpam-3288	407	4	,	,	PUNCT
ejpam-3288	407	5	we	we	PRON
ejpam-3288	407	6	have	have	AUX
ejpam-3288	407	7	studied	study	VERB
ejpam-3288	407	8	some	some	DET
ejpam-3288	407	9	properties	property	NOUN
ejpam-3288	407	10	of	of	ADP
ejpam-3288	407	11	doubt	doubt	NOUN
ejpam-3288	407	12	bipolar	bipolar	ADJ
ejpam-3288	407	13	fuzzy	fuzzy	ADJ
ejpam-3288	407	14	h	h	NOUN
ejpam-3288	407	15	-	-	PUNCT
ejpam-3288	407	16	ideals	ideal	NOUN
ejpam-3288	407	17	in	in	ADP
ejpam-3288	407	18	bck/	bck/	VERB
ejpam-3288	407	19	bci	bci	NOUN
ejpam-3288	407	20	-	-	PUNCT
ejpam-3288	407	21	algebras	algebra	NOUN
ejpam-3288	407	22	.	.	PUNCT
ejpam-3288	408	1	also	also	ADV
ejpam-3288	408	2	,	,	PUNCT
ejpam-3288	408	3	we	we	PRON
ejpam-3288	408	4	have	have	AUX
ejpam-3288	408	5	discussed	discuss	VERB
ejpam-3288	408	6	relations	relation	NOUN
ejpam-3288	408	7	between	between	ADP
ejpam-3288	408	8	a	a	DET
ejpam-3288	408	9	doubt	doubt	ADV
ejpam-3288	408	10	bipolar	bipolar	ADJ
ejpam-3288	408	11	fuzzy	fuzzy	ADJ
ejpam-3288	408	12	h	h	NOUN
ejpam-3288	408	13	-	-	PUNCT
ejpam-3288	408	14	ideal	ideal	NOUN
ejpam-3288	408	15	and	and	CCONJ
ejpam-3288	408	16	a	a	DET
ejpam-3288	408	17	doubt	doubt	ADV
ejpam-3288	408	18	bipolar	bipolar	ADJ
ejpam-3288	408	19	fuzzy	fuzzy	ADJ
ejpam-3288	408	20	ideal	ideal	NOUN
ejpam-3288	408	21	and	and	CCONJ
ejpam-3288	408	22	we	we	PRON
ejpam-3288	408	23	have	have	AUX
ejpam-3288	408	24	provided	provide	VERB
ejpam-3288	408	25	conditions	condition	NOUN
ejpam-3288	408	26	for	for	ADP
ejpam-3288	408	27	a	a	DET
ejpam-3288	408	28	doubt	doubt	ADV
ejpam-3288	408	29	bipolar	bipolar	ADJ
ejpam-3288	408	30	fuzzy	fuzzy	ADJ
ejpam-3288	408	31	ideal	ideal	NOUN
ejpam-3288	408	32	to	to	PART
ejpam-3288	408	33	be	be	AUX
ejpam-3288	408	34	a	a	DET
ejpam-3288	408	35	doubt	doubt	ADV
ejpam-3288	408	36	bipolar	bipolar	ADJ
ejpam-3288	408	37	fuzzy	fuzzy	ADJ
ejpam-3288	408	38	h	h	NOUN
ejpam-3288	408	39	-	-	PUNCT
ejpam-3288	408	40	ideal	ideal	ADJ
ejpam-3288	408	41	.	.	PUNCT
ejpam-3288	409	1	in	in	ADP
ejpam-3288	409	2	addition	addition	NOUN
ejpam-3288	409	3	,	,	PUNCT
ejpam-3288	409	4	we	we	PRON
ejpam-3288	409	5	have	have	AUX
ejpam-3288	409	6	investigated	investigate	VERB
ejpam-3288	409	7	characterizations	characterization	NOUN
ejpam-3288	409	8	of	of	ADP
ejpam-3288	409	9	doubt	doubt	NOUN
ejpam-3288	409	10	bipolar	bipolar	ADJ
ejpam-3288	409	11	fuzzy	fuzzy	ADJ
ejpam-3288	409	12	h	h	NOUN
ejpam-3288	409	13	-	-	PUNCT
ejpam-3288	409	14	ideals	ideal	NOUN
ejpam-3288	409	15	by	by	ADP
ejpam-3288	409	16	means	mean	NOUN
ejpam-3288	409	17	of	of	ADP
ejpam-3288	409	18	doubt	doubt	NOUN
ejpam-3288	409	19	positive	positive	ADJ
ejpam-3288	409	20	t	t	NOUN
ejpam-3288	409	21	-	-	PUNCT
ejpam-3288	409	22	level	level	NOUN
ejpam-3288	409	23	cut	cut	NOUN
ejpam-3288	409	24	set	set	NOUN
ejpam-3288	409	25	,	,	PUNCT
ejpam-3288	409	26	doubt	doubt	VERB
ejpam-3288	409	27	negative	negative	ADJ
ejpam-3288	409	28	s	s	NOUN
ejpam-3288	409	29	-	-	PUNCT
ejpam-3288	409	30	level	level	NOUN
ejpam-3288	409	31	cut	cut	NOUN
ejpam-3288	409	32	set	set	VERB
ejpam-3288	409	33	and	and	CCONJ
ejpam-3288	409	34	h	h	NOUN
ejpam-3288	409	35	-	-	PUNCT
ejpam-3288	409	36	artin	artin	NOUN
ejpam-3288	409	37	bck	bck	PROPN
ejpam-3288	409	38	/	/	SYM
ejpam-3288	409	39	bci	bci	NOUN
ejpam-3288	409	40	-	-	PUNCT
ejpam-3288	409	41	algebras	algebras	X
ejpam-3288	409	42	.	.	PUNCT
ejpam-3288	410	1	in	in	ADP
ejpam-3288	410	2	the	the	DET
ejpam-3288	410	3	future	future	ADJ
ejpam-3288	410	4	study	study	NOUN
ejpam-3288	410	5	of	of	ADP
ejpam-3288	410	6	doubt	doubt	NOUN
ejpam-3288	410	7	bipolar	bipolar	ADJ
ejpam-3288	410	8	fuzzy	fuzzy	ADJ
ejpam-3288	410	9	h	h	NOUN
ejpam-3288	410	10	-	-	PUNCT
ejpam-3288	410	11	ideals	ideal	NOUN
ejpam-3288	410	12	in	in	ADP
ejpam-3288	410	13	bck	bck	PROPN
ejpam-3288	410	14	/	/	SYM
ejpam-3288	410	15	bci	bci	NOUN
ejpam-3288	410	16	-	-	PUNCT
ejpam-3288	410	17	algebras	algebra	NOUN
ejpam-3288	410	18	,	,	PUNCT
ejpam-3288	410	19	perhaps	perhaps	ADV
ejpam-3288	410	20	the	the	DET
ejpam-3288	410	21	following	follow	VERB
ejpam-3288	410	22	topics	topic	NOUN
ejpam-3288	410	23	are	be	AUX
ejpam-3288	410	24	worth	worth	ADJ
ejpam-3288	410	25	to	to	PART
ejpam-3288	410	26	be	be	AUX
ejpam-3288	410	27	considered	consider	VERB
ejpam-3288	410	28	:	:	PUNCT
ejpam-3288	410	29	references	reference	NOUN
ejpam-3288	410	30	669	669	NUM
ejpam-3288	410	31	(	(	PUNCT
ejpam-3288	410	32	1	1	NUM
ejpam-3288	410	33	)	)	PUNCT
ejpam-3288	410	34	to	to	PART
ejpam-3288	410	35	characterize	characterize	VERB
ejpam-3288	410	36	other	other	ADJ
ejpam-3288	410	37	classes	class	NOUN
ejpam-3288	410	38	of	of	ADP
ejpam-3288	410	39	bck	bck	PROPN
ejpam-3288	410	40	/	/	SYM
ejpam-3288	410	41	bci	bci	NOUN
ejpam-3288	410	42	-	-	PUNCT
ejpam-3288	410	43	algebras	algebra	VERB
ejpam-3288	410	44	by	by	ADP
ejpam-3288	410	45	using	use	VERB
ejpam-3288	410	46	this	this	DET
ejpam-3288	410	47	notion	notion	NOUN
ejpam-3288	410	48	;	;	PUNCT
ejpam-3288	410	49	(	(	PUNCT
ejpam-3288	410	50	2	2	X
ejpam-3288	410	51	)	)	PUNCT
ejpam-3288	410	52	to	to	PART
ejpam-3288	410	53	apply	apply	VERB
ejpam-3288	410	54	this	this	DET
ejpam-3288	410	55	notion	notion	NOUN
ejpam-3288	410	56	to	to	ADP
ejpam-3288	410	57	some	some	DET
ejpam-3288	410	58	other	other	ADJ
ejpam-3288	410	59	algebraic	algebraic	ADJ
ejpam-3288	410	60	structures	structure	NOUN
ejpam-3288	410	61	for	for	ADP
ejpam-3288	410	62	example	example	NOUN
ejpam-3288	410	63	,	,	PUNCT
ejpam-3288	410	64	bch	bch	PROPN
ejpam-3288	410	65	-	-	PUNCT
ejpam-3288	410	66	algebras	algebras	PROPN
ejpam-3288	410	67	,	,	PUNCT
ejpam-3288	410	68	bcc	bcc	PROPN
ejpam-3288	410	69	-	-	PUNCT
ejpam-3288	410	70	algebras	algebras	PROPN
ejpam-3288	410	71	,	,	PUNCT
ejpam-3288	410	72	b	b	X
ejpam-3288	410	73	-	-	PUNCT
ejpam-3288	410	74	algebras	algebras	PROPN
ejpam-3288	410	75	,	,	PUNCT
ejpam-3288	410	76	brk	brk	PROPN
ejpam-3288	410	77	-	-	PUNCT
ejpam-3288	410	78	algebras	algebras	PROPN
ejpam-3288	410	79	,	,	PUNCT
ejpam-3288	410	80	semigroups	semigroup	NOUN
ejpam-3288	410	81	,	,	PUNCT
ejpam-3288	410	82	semirings	semiring	NOUN
ejpam-3288	410	83	and	and	CCONJ
ejpam-3288	410	84	lattice	lattice	PROPN
ejpam-3288	410	85	implication	implication	NOUN
ejpam-3288	410	86	algebras	algebra	NOUN
ejpam-3288	410	87	,	,	PUNCT
ejpam-3288	410	88	etc	etc	X
ejpam-3288	410	89	.	.	X
ejpam-3288	410	90	references	reference	NOUN
ejpam-3288	410	91	[	[	X
ejpam-3288	410	92	1	1	NUM
ejpam-3288	410	93	]	]	PUNCT
ejpam-3288	410	94	b.	b.	PROPN
ejpam-3288	410	95	ahmad	ahmad	PROPN
ejpam-3288	410	96	,	,	PUNCT
ejpam-3288	410	97	fuzzy	fuzzy	ADJ
ejpam-3288	410	98	bci	bci	NOUN
ejpam-3288	410	99	-	-	PUNCT
ejpam-3288	410	100	algebras	algebra	NOUN
ejpam-3288	410	101	,	,	PUNCT
ejpam-3288	410	102	j.	j.	PROPN
ejpam-3288	410	103	fuzzy	fuzzy	PROPN
ejpam-3288	410	104	math	math	PROPN
ejpam-3288	410	105	.	.	PUNCT
ejpam-3288	411	1	1:445	1:445	NUM
ejpam-3288	411	2	-	-	SYM
ejpam-3288	411	3	452	452	NUM
ejpam-3288	411	4	,	,	PUNCT
ejpam-3288	411	5	1993	1993	NUM
ejpam-3288	411	6	.	.	PUNCT
ejpam-3288	412	1	[	[	X
ejpam-3288	412	2	2	2	NUM
ejpam-3288	412	3	]	]	PUNCT
ejpam-3288	412	4	m.	m.	NOUN
ejpam-3288	412	5	akram	akram	PROPN
ejpam-3288	412	6	and	and	CCONJ
ejpam-3288	412	7	n.o	n.o	PROPN
ejpam-3288	412	8	.	.	PROPN
ejpam-3288	412	9	alshehri	alshehri	PROPN
ejpam-3288	412	10	,	,	PUNCT
ejpam-3288	412	11	bipolar	bipolar	ADJ
ejpam-3288	412	12	fuzzy	fuzzy	ADJ
ejpam-3288	412	13	lie	lie	NOUN
ejpam-3288	412	14	ideals	ideal	NOUN
ejpam-3288	412	15	,	,	PUNCT
ejpam-3288	412	16	utilitas	utilitas	PROPN
ejpam-3288	412	17	mathematica	mathematica	PROPN
ejpam-3288	412	18	,	,	PUNCT
ejpam-3288	412	19	87:265278	87:265278	NOUN
ejpam-3288	412	20	,	,	PUNCT
ejpam-3288	412	21	2012	2012	NUM
ejpam-3288	412	22	.	.	PUNCT
ejpam-3288	413	1	[	[	X
ejpam-3288	413	2	3	3	NUM
ejpam-3288	413	3	]	]	X
ejpam-3288	413	4	m.	m.	NOUN
ejpam-3288	413	5	akram	akram	PROPN
ejpam-3288	413	6	,	,	PUNCT
ejpam-3288	413	7	w.	w.	PROPN
ejpam-3288	413	8	chen	chen	PROPN
ejpam-3288	413	9	,	,	PUNCT
ejpam-3288	413	10	and	and	CCONJ
ejpam-3288	413	11	y.	y.	PROPN
ejpam-3288	413	12	lin	lin	PROPN
ejpam-3288	413	13	,	,	PUNCT
ejpam-3288	413	14	bipolar	bipolar	ADJ
ejpam-3288	413	15	fuzzy	fuzzy	ADJ
ejpam-3288	413	16	lie	lie	NOUN
ejpam-3288	413	17	superalgebras	superalgebra	NOUN
ejpam-3288	413	18	,	,	PUNCT
ejpam-3288	413	19	quasigroups	quasigroup	VERB
ejpam-3288	413	20	related	related	ADJ
ejpam-3288	413	21	systems	system	NOUN
ejpam-3288	413	22	,	,	PUNCT
ejpam-3288	413	23	20:139	20:139	NUM
ejpam-3288	413	24	-	-	SYM
ejpam-3288	413	25	156	156	NUM
ejpam-3288	413	26	,	,	PUNCT
ejpam-3288	413	27	2012	2012	NUM
ejpam-3288	413	28	.	.	PUNCT
ejpam-3288	414	1	[	[	X
ejpam-3288	414	2	4	4	NUM
ejpam-3288	414	3	]	]	X
ejpam-3288	414	4	m.a	m.a	PROPN
ejpam-3288	414	5	.	.	PROPN
ejpam-3288	414	6	alghamdi	alghamdi	PROPN
ejpam-3288	414	7	,	,	PUNCT
ejpam-3288	414	8	n.m	n.m	PROPN
ejpam-3288	414	9	.	.	PROPN
ejpam-3288	414	10	muthana	muthana	PROPN
ejpam-3288	414	11	and	and	CCONJ
ejpam-3288	414	12	n.o	n.o	PROPN
ejpam-3288	414	13	.	.	PROPN
ejpam-3288	414	14	alshehri	alshehri	PROPN
ejpam-3288	414	15	,	,	PUNCT
ejpam-3288	414	16	novel	novel	ADJ
ejpam-3288	414	17	concepts	concept	NOUN
ejpam-3288	414	18	of	of	ADP
ejpam-3288	414	19	bipolar	bipolar	ADJ
ejpam-3288	414	20	fuzzy	fuzzy	ADJ
ejpam-3288	414	21	bcksubmodules	bcksubmodule	NOUN
ejpam-3288	414	22	,	,	PUNCT
ejpam-3288	414	23	discrete	discrete	ADJ
ejpam-3288	414	24	dyn	dyn	NOUN
ejpam-3288	414	25	.	.	PUNCT
ejpam-3288	415	1	nat	nat	PROPN
ejpam-3288	415	2	.	.	PUNCT
ejpam-3288	416	1	soc	soc	PROPN
ejpam-3288	416	2	.	.	PUNCT
ejpam-3288	417	1	2017	2017	NUM
ejpam-3288	417	2	,	,	PUNCT
ejpam-3288	417	3	article	article	NOUN
ejpam-3288	417	4	i	i	PROPN
ejpam-3288	417	5	d	d	PROPN
ejpam-3288	417	6	2084191	2084191	NUM
ejpam-3288	417	7	,	,	PUNCT
ejpam-3288	417	8	7	7	NUM
ejpam-3288	417	9	pages	page	NOUN
ejpam-3288	417	10	,	,	PUNCT
ejpam-3288	417	11	2017	2017	NUM
ejpam-3288	417	12	.	.	PUNCT
ejpam-3288	418	1	[	[	X
ejpam-3288	418	2	5	5	NUM
ejpam-3288	418	3	]	]	PUNCT
ejpam-3288	418	4	a.	a.	PROPN
ejpam-3288	418	5	al	al	PROPN
ejpam-3288	418	6	-	-	PUNCT
ejpam-3288	418	7	masarwah	masarwah	PROPN
ejpam-3288	418	8	,	,	PUNCT
ejpam-3288	418	9	a.g	a.g	PROPN
ejpam-3288	418	10	.	.	PROPN
ejpam-3288	418	11	ahmad	ahmad	PROPN
ejpam-3288	418	12	,	,	PUNCT
ejpam-3288	418	13	doubt	doubt	VERB
ejpam-3288	418	14	bipolar	bipolar	ADJ
ejpam-3288	418	15	fuzzy	fuzzy	ADJ
ejpam-3288	418	16	subalgebra	subalgebra	NOUN
ejpam-3288	418	17	and	and	CCONJ
ejpam-3288	418	18	ideals	ideal	NOUN
ejpam-3288	418	19	in	in	ADP
ejpam-3288	418	20	bck	bck	PROPN
ejpam-3288	418	21	/	/	SYM
ejpam-3288	418	22	bci	bci	NOUN
ejpam-3288	418	23	-	-	PUNCT
ejpam-3288	418	24	algebras	algebra	NOUN
ejpam-3288	418	25	,	,	PUNCT
ejpam-3288	418	26	j.	j.	PROPN
ejpam-3288	418	27	math	math	PROPN
ejpam-3288	418	28	.	.	PUNCT
ejpam-3288	419	1	anal	anal	PROPN
ejpam-3288	419	2	.	.	PUNCT
ejpam-3288	420	1	(	(	PUNCT
ejpam-3288	420	2	accepted	accept	VERB
ejpam-3288	420	3	)	)	PUNCT
ejpam-3288	420	4	,	,	PUNCT
ejpam-3288	420	5	2018	2018	NUM
ejpam-3288	420	6	.	.	PUNCT
ejpam-3288	421	1	[	[	X
ejpam-3288	421	2	6	6	NUM
ejpam-3288	421	3	]	]	PUNCT
ejpam-3288	421	4	a.	a.	PROPN
ejpam-3288	421	5	al	al	PROPN
ejpam-3288	421	6	-	-	PUNCT
ejpam-3288	421	7	masarwah	masarwah	PROPN
ejpam-3288	421	8	,	,	PUNCT
ejpam-3288	421	9	a.g	a.g	PROPN
ejpam-3288	421	10	.	.	PROPN
ejpam-3288	421	11	ahmad	ahmad	PROPN
ejpam-3288	421	12	,	,	PUNCT
ejpam-3288	421	13	novel	novel	ADJ
ejpam-3288	421	14	concepts	concept	NOUN
ejpam-3288	421	15	of	of	ADP
ejpam-3288	421	16	doubt	doubt	ADV
ejpam-3288	421	17	bipolar	bipolar	ADJ
ejpam-3288	421	18	fuzzy	fuzzy	ADJ
ejpam-3288	421	19	h	h	NOUN
ejpam-3288	421	20	-	-	PUNCT
ejpam-3288	421	21	ideals	ideal	NOUN
ejpam-3288	421	22	of	of	ADP
ejpam-3288	421	23	bck	bck	PROPN
ejpam-3288	421	24	/	/	SYM
ejpam-3288	421	25	bci	bci	NOUN
ejpam-3288	421	26	-	-	PUNCT
ejpam-3288	421	27	algebras	algebra	NOUN
ejpam-3288	421	28	,	,	PUNCT
ejpam-3288	421	29	international	international	ADJ
ejpam-3288	421	30	journal	journal	NOUN
ejpam-3288	421	31	of	of	ADP
ejpam-3288	421	32	innovative	innovative	ADJ
ejpam-3288	421	33	computing	computing	NOUN
ejpam-3288	421	34	,	,	PUNCT
ejpam-3288	421	35	information	information	NOUN
ejpam-3288	421	36	and	and	CCONJ
ejpam-3288	421	37	control	control	NOUN
ejpam-3288	421	38	,	,	PUNCT
ejpam-3288	421	39	(	(	PUNCT
ejpam-3288	421	40	accepted	accept	VERB
ejpam-3288	421	41	)	)	PUNCT
ejpam-3288	421	42	,	,	PUNCT
ejpam-3288	421	43	2018	2018	NUM
ejpam-3288	421	44	.	.	PUNCT
ejpam-3288	422	1	[	[	X
ejpam-3288	422	2	7	7	X
ejpam-3288	422	3	]	]	X
ejpam-3288	422	4	k.t	k.t	PROPN
ejpam-3288	422	5	.	.	PROPN
ejpam-3288	422	6	atanassov	atanassov	PROPN
ejpam-3288	422	7	,	,	PUNCT
ejpam-3288	422	8	intuitionistic	intuitionistic	ADJ
ejpam-3288	422	9	fuzzy	fuzzy	ADJ
ejpam-3288	422	10	sets	set	NOUN
ejpam-3288	422	11	,	,	PUNCT
ejpam-3288	422	12	fuzzy	fuzzy	ADJ
ejpam-3288	422	13	sets	set	NOUN
ejpam-3288	422	14	syst	syst	NOUN
ejpam-3288	422	15	.	.	PUNCT
ejpam-3288	423	1	20(1):87	20(1):87	NUM
ejpam-3288	423	2	-	-	SYM
ejpam-3288	423	3	96	96	NUM
ejpam-3288	423	4	,	,	PUNCT
ejpam-3288	423	5	1986	1986	NUM
ejpam-3288	423	6	.	.	PUNCT
ejpam-3288	424	1	[	[	X
ejpam-3288	424	2	8	8	X
ejpam-3288	424	3	]	]	PUNCT
ejpam-3288	424	4	k.	k.	PROPN
ejpam-3288	424	5	hayat	hayat	PROPN
ejpam-3288	424	6	,	,	PUNCT
ejpam-3288	424	7	t.	t.	PROPN
ejpam-3288	424	8	mahmood	mahmood	PROPN
ejpam-3288	424	9	and	and	CCONJ
ejpam-3288	424	10	b.y	b.y	PROPN
ejpam-3288	424	11	.	.	PROPN
ejpam-3288	424	12	cao	cao	PROPN
ejpam-3288	424	13	,	,	PUNCT
ejpam-3288	424	14	on	on	ADP
ejpam-3288	424	15	bipolar	bipolar	ADJ
ejpam-3288	424	16	anti	anti	ADJ
ejpam-3288	424	17	fuzzy	fuzzy	ADJ
ejpam-3288	424	18	h	h	NOUN
ejpam-3288	424	19	-	-	PUNCT
ejpam-3288	424	20	ideals	ideal	NOUN
ejpam-3288	424	21	in	in	ADP
ejpam-3288	424	22	hemirings	hemiring	NOUN
ejpam-3288	424	23	,	,	PUNCT
ejpam-3288	424	24	fuzzy	fuzzy	ADJ
ejpam-3288	424	25	inf	inf	NOUN
ejpam-3288	424	26	.	.	PUNCT
ejpam-3288	425	1	eng	eng	PROPN
ejpam-3288	425	2	.	.	PUNCT
ejpam-3288	426	1	9(1):1	9(1):1	PROPN
ejpam-3288	426	2	-	-	PUNCT
ejpam-3288	426	3	19	19	NUM
ejpam-3288	426	4	,	,	PUNCT
ejpam-3288	426	5	2017	2017	NUM
ejpam-3288	426	6	.	.	PUNCT
ejpam-3288	427	1	[	[	X
ejpam-3288	427	2	9	9	NUM
ejpam-3288	427	3	]	]	X
ejpam-3288	427	4	f.y	f.y	PROPN
ejpam-3288	427	5	.	.	PROPN
ejpam-3288	427	6	huang	huang	PROPN
ejpam-3288	427	7	,	,	PUNCT
ejpam-3288	427	8	another	another	DET
ejpam-3288	427	9	definition	definition	NOUN
ejpam-3288	427	10	of	of	ADP
ejpam-3288	427	11	fuzzy	fuzzy	ADJ
ejpam-3288	427	12	bci	bci	NOUN
ejpam-3288	427	13	-	-	PUNCT
ejpam-3288	427	14	algebras	algebra	NOUN
ejpam-3288	427	15	,	,	PUNCT
ejpam-3288	427	16	selected	select	VERB
ejpam-3288	427	17	papers	paper	NOUN
ejpam-3288	427	18	on	on	ADP
ejpam-3288	427	19	bck	bck	PROPN
ejpam-3288	427	20	/	/	SYM
ejpam-3288	427	21	bci	bci	NOUN
ejpam-3288	427	22	-	-	PUNCT
ejpam-3288	427	23	algebras	algebra	NOUN
ejpam-3288	427	24	,	,	PUNCT
ejpam-3288	427	25	china	china	PROPN
ejpam-3288	427	26	,	,	PUNCT
ejpam-3288	427	27	1:91	1:91	NUM
ejpam-3288	427	28	-	-	SYM
ejpam-3288	427	29	92	92	NUM
ejpam-3288	427	30	,	,	PUNCT
ejpam-3288	427	31	1991	1991	NUM
ejpam-3288	427	32	.	.	PUNCT
ejpam-3288	428	1	[	[	X
ejpam-3288	428	2	10	10	NUM
ejpam-3288	428	3	]	]	X
ejpam-3288	428	4	y.s	y.s	PROPN
ejpam-3288	428	5	.	.	PROPN
ejpam-3288	428	6	huang	huang	PROPN
ejpam-3288	428	7	,	,	PUNCT
ejpam-3288	428	8	bci	bci	PROPN
ejpam-3288	428	9	-	-	NOUN
ejpam-3288	428	10	algebra	algebra	NOUN
ejpam-3288	428	11	,	,	PUNCT
ejpam-3288	428	12	science	science	NOUN
ejpam-3288	428	13	press	press	NOUN
ejpam-3288	428	14	,	,	PUNCT
ejpam-3288	428	15	beijing	beijing	PROPN
ejpam-3288	428	16	,	,	PUNCT
ejpam-3288	428	17	china	china	PROPN
ejpam-3288	428	18	,	,	PUNCT
ejpam-3288	428	19	2006	2006	NUM
ejpam-3288	428	20	.	.	PUNCT
ejpam-3288	429	1	[	[	X
ejpam-3288	429	2	11	11	NUM
ejpam-3288	429	3	]	]	X
ejpam-3288	429	4	y.	y.	PROPN
ejpam-3288	429	5	imai	imai	PROPN
ejpam-3288	429	6	,	,	PUNCT
ejpam-3288	429	7	k.	k.	PROPN
ejpam-3288	429	8	iséki	iséki	PROPN
ejpam-3288	429	9	,	,	PUNCT
ejpam-3288	429	10	on	on	ADP
ejpam-3288	429	11	axiom	axiom	NOUN
ejpam-3288	429	12	systems	system	NOUN
ejpam-3288	429	13	of	of	ADP
ejpam-3288	429	14	propositional	propositional	ADJ
ejpam-3288	429	15	calculi	calculi	PROPN
ejpam-3288	429	16	,	,	PUNCT
ejpam-3288	429	17	proc	proc	PROPN
ejpam-3288	429	18	.	.	PUNCT
ejpam-3288	430	1	japan	japan	PROPN
ejpam-3288	430	2	academy	academy	PROPN
ejpam-3288	430	3	,	,	PUNCT
ejpam-3288	430	4	42:19	42:19	NUM
ejpam-3288	430	5	-	-	SYM
ejpam-3288	430	6	22	22	NUM
ejpam-3288	430	7	,	,	PUNCT
ejpam-3288	430	8	1966	1966	NUM
ejpam-3288	430	9	.	.	PUNCT
ejpam-3288	431	1	[	[	X
ejpam-3288	431	2	12	12	NUM
ejpam-3288	431	3	]	]	PUNCT
ejpam-3288	431	4	k.	k.	PROPN
ejpam-3288	431	5	iséki	iséki	PROPN
ejpam-3288	431	6	,	,	PUNCT
ejpam-3288	431	7	an	an	DET
ejpam-3288	431	8	algebra	algebra	NOUN
ejpam-3288	431	9	related	relate	VERB
ejpam-3288	431	10	with	with	ADP
ejpam-3288	431	11	a	a	DET
ejpam-3288	431	12	propositional	propositional	ADJ
ejpam-3288	431	13	calculus	calculus	NOUN
ejpam-3288	431	14	,	,	PUNCT
ejpam-3288	431	15	proc	proc	NOUN
ejpam-3288	431	16	.	.	PUNCT
ejpam-3288	432	1	japan	japan	PROPN
ejpam-3288	432	2	academy	academy	PROPN
ejpam-3288	432	3	,	,	PUNCT
ejpam-3288	432	4	42:26	42:26	NUM
ejpam-3288	432	5	-	-	SYM
ejpam-3288	432	6	29	29	NUM
ejpam-3288	432	7	,	,	PUNCT
ejpam-3288	432	8	1966	1966	NUM
ejpam-3288	432	9	.	.	PUNCT
ejpam-3288	433	1	[	[	X
ejpam-3288	433	2	13	13	NUM
ejpam-3288	433	3	]	]	PUNCT
ejpam-3288	433	4	k.	k.	PROPN
ejpam-3288	433	5	iséki	iséki	PROPN
ejpam-3288	433	6	,	,	PUNCT
ejpam-3288	433	7	on	on	ADP
ejpam-3288	433	8	bci	bci	NOUN
ejpam-3288	433	9	-	-	PUNCT
ejpam-3288	433	10	algebras	algebra	NOUN
ejpam-3288	433	11	,	,	PUNCT
ejpam-3288	433	12	math	math	NOUN
ejpam-3288	433	13	.	.	PUNCT
ejpam-3288	434	1	seminar	seminar	NOUN
ejpam-3288	434	2	notes	note	NOUN
ejpam-3288	434	3	(	(	PUNCT
ejpam-3288	434	4	kobe	kobe	PROPN
ejpam-3288	434	5	university	university	PROPN
ejpam-3288	434	6	)	)	PUNCT
ejpam-3288	434	7	,	,	PUNCT
ejpam-3288	434	8	8:125	8:125	NOUN
ejpam-3288	434	9	-	-	SYM
ejpam-3288	434	10	130	130	NUM
ejpam-3288	434	11	,	,	PUNCT
ejpam-3288	434	12	1980	1980	NUM
ejpam-3288	434	13	.	.	PUNCT
ejpam-3288	435	1	[	[	X
ejpam-3288	435	2	14	14	NUM
ejpam-3288	435	3	]	]	X
ejpam-3288	435	4	y.b	y.b	PROPN
ejpam-3288	435	5	.	.	PROPN
ejpam-3288	435	6	jun	jun	PROPN
ejpam-3288	435	7	,	,	PUNCT
ejpam-3288	435	8	characterizations	characterization	NOUN
ejpam-3288	435	9	of	of	ADP
ejpam-3288	435	10	noetherian	noetherian	ADJ
ejpam-3288	435	11	bck	bck	NOUN
ejpam-3288	435	12	-	-	PUNCT
ejpam-3288	435	13	algebras	algebras	PROPN
ejpam-3288	435	14	via	via	ADP
ejpam-3288	435	15	fuzzy	fuzzy	ADJ
ejpam-3288	435	16	ideals	ideal	NOUN
ejpam-3288	435	17	,	,	PUNCT
ejpam-3288	435	18	fuzzy	fuzzy	ADJ
ejpam-3288	435	19	sets	set	VERB
ejpam-3288	435	20	syst	syst	NOUN
ejpam-3288	435	21	.	.	PUNCT
ejpam-3288	436	1	108:231	108:231	X
ejpam-3288	436	2	-	-	SYM
ejpam-3288	436	3	234	234	NUM
ejpam-3288	436	4	,	,	PUNCT
ejpam-3288	436	5	1999	1999	NUM
ejpam-3288	436	6	.	.	PUNCT
ejpam-3288	437	1	[	[	X
ejpam-3288	437	2	15	15	NUM
ejpam-3288	437	3	]	]	X
ejpam-3288	437	4	y.b	y.b	PROPN
ejpam-3288	437	5	.	.	PROPN
ejpam-3288	437	6	jun	jun	PROPN
ejpam-3288	437	7	,	,	PUNCT
ejpam-3288	437	8	closed	close	VERB
ejpam-3288	437	9	fuzzy	fuzzy	ADJ
ejpam-3288	437	10	ideals	ideal	NOUN
ejpam-3288	437	11	in	in	ADP
ejpam-3288	437	12	bci	bci	NOUN
ejpam-3288	437	13	-	-	PUNCT
ejpam-3288	437	14	algebras	algebra	NOUN
ejpam-3288	437	15	,	,	PUNCT
ejpam-3288	437	16	math	math	NOUN
ejpam-3288	437	17	.	.	PUNCT
ejpam-3288	438	1	japon	japon	PROPN
ejpam-3288	438	2	.	.	PUNCT
ejpam-3288	439	1	38:199	38:199	NUM
ejpam-3288	439	2	-	-	PUNCT
ejpam-3288	439	3	202	202	NUM
ejpam-3288	439	4	,	,	PUNCT
ejpam-3288	439	5	1993	1993	NUM
ejpam-3288	439	6	.	.	PUNCT
ejpam-3288	440	1	references	reference	NOUN
ejpam-3288	440	2	670	670	NUM
ejpam-3288	440	3	[	[	X
ejpam-3288	440	4	16	16	NUM
ejpam-3288	440	5	]	]	X
ejpam-3288	440	6	y.b	y.b	PROPN
ejpam-3288	440	7	.	.	PROPN
ejpam-3288	440	8	jun	jun	PROPN
ejpam-3288	440	9	,	,	PUNCT
ejpam-3288	440	10	doubt	doubt	VERB
ejpam-3288	440	11	fuzzy	fuzzy	ADJ
ejpam-3288	440	12	bck	bck	PROPN
ejpam-3288	440	13	/	/	SYM
ejpam-3288	440	14	bci	bci	NOUN
ejpam-3288	440	15	-	-	PUNCT
ejpam-3288	440	16	algebras	algebra	NOUN
ejpam-3288	440	17	,	,	PUNCT
ejpam-3288	440	18	soochow	soochow	PROPN
ejpam-3288	440	19	j.	j.	PROPN
ejpam-3288	440	20	math	math	PROPN
ejpam-3288	440	21	.	.	PUNCT
ejpam-3288	441	1	20(3):351	20(3):351	NOUN
ejpam-3288	441	2	-	-	SYM
ejpam-3288	441	3	358	358	NUM
ejpam-3288	441	4	,	,	PUNCT
ejpam-3288	441	5	1994	1994	NUM
ejpam-3288	441	6	.	.	PUNCT
ejpam-3288	442	1	[	[	X
ejpam-3288	442	2	17	17	NUM
ejpam-3288	442	3	]	]	X
ejpam-3288	442	4	y.b	y.b	PROPN
ejpam-3288	442	5	.	.	PROPN
ejpam-3288	442	6	jun	jun	PROPN
ejpam-3288	442	7	,	,	PUNCT
ejpam-3288	442	8	g.	g.	PROPN
ejpam-3288	442	9	muhiuddin	muhiuddin	PROPN
ejpam-3288	442	10	and	and	CCONJ
ejpam-3288	442	11	a.m.	a.m.	PROPN
ejpam-3288	442	12	al	al	PROPN
ejpam-3288	442	13	-	-	PUNCT
ejpam-3288	442	14	roqi	roqi	ADJ
ejpam-3288	442	15	,	,	PUNCT
ejpam-3288	442	16	ideal	ideal	ADJ
ejpam-3288	442	17	theory	theory	NOUN
ejpam-3288	442	18	of	of	ADP
ejpam-3288	442	19	bck	bck	PROPN
ejpam-3288	442	20	/	/	SYM
ejpam-3288	442	21	bci	bci	NOUN
ejpam-3288	442	22	-	-	PUNCT
ejpam-3288	442	23	algebras	algebra	NOUN
ejpam-3288	442	24	based	base	VERB
ejpam-3288	442	25	on	on	ADP
ejpam-3288	442	26	double	double	ADJ
ejpam-3288	442	27	-	-	PUNCT
ejpam-3288	442	28	framed	frame	VERB
ejpam-3288	442	29	soft	soft	ADJ
ejpam-3288	442	30	sets	set	NOUN
ejpam-3288	442	31	,	,	PUNCT
ejpam-3288	442	32	appl	appl	PROPN
ejpam-3288	442	33	.	.	PROPN
ejpam-3288	442	34	math	math	PROPN
ejpam-3288	442	35	.	.	PUNCT
ejpam-3288	443	1	inf	inf	PROPN
ejpam-3288	443	2	.	.	PUNCT
ejpam-3288	444	1	sci	sci	PROPN
ejpam-3288	444	2	.	.	PUNCT
ejpam-3288	445	1	7(5):1879	7(5):1879	NUM
ejpam-3288	445	2	-	-	SYM
ejpam-3288	445	3	1887	1887	NUM
ejpam-3288	445	4	,	,	PUNCT
ejpam-3288	445	5	2013	2013	NUM
ejpam-3288	445	6	.	.	PUNCT
ejpam-3288	446	1	[	[	X
ejpam-3288	446	2	18	18	NUM
ejpam-3288	446	3	]	]	X
ejpam-3288	446	4	y.b	y.b	PROPN
ejpam-3288	446	5	.	.	PROPN
ejpam-3288	446	6	jun	jun	PROPN
ejpam-3288	446	7	,	,	PUNCT
ejpam-3288	446	8	g.	g.	PROPN
ejpam-3288	446	9	muhiuddin	muhiuddin	PROPN
ejpam-3288	446	10	,	,	PUNCT
ejpam-3288	446	11	m.a	m.a	PROPN
ejpam-3288	446	12	.	.	PROPN
ejpam-3288	446	13	ozturk	ozturk	PROPN
ejpam-3288	446	14	and	and	CCONJ
ejpam-3288	446	15	e.h	e.h	PROPN
ejpam-3288	446	16	.	.	PROPN
ejpam-3288	446	17	roh	roh	PROPN
ejpam-3288	446	18	,	,	PUNCT
ejpam-3288	446	19	cubic	cubic	ADJ
ejpam-3288	446	20	soft	soft	ADJ
ejpam-3288	446	21	ideals	ideal	NOUN
ejpam-3288	446	22	in	in	ADP
ejpam-3288	446	23	bck	bck	PROPN
ejpam-3288	446	24	/	/	SYM
ejpam-3288	446	25	bcialgebras	bcialgebras	PROPN
ejpam-3288	446	26	,	,	PUNCT
ejpam-3288	446	27	j.	j.	PROPN
ejpam-3288	446	28	comput	comput	PROPN
ejpam-3288	446	29	.	.	PUNCT
ejpam-3288	447	1	anal	anal	PROPN
ejpam-3288	447	2	.	.	PUNCT
ejpam-3288	447	3	appl	appl	PROPN
ejpam-3288	447	4	.	.	PUNCT
ejpam-3288	448	1	22(5):929	22(5):929	NOUN
ejpam-3288	448	2	-	-	SYM
ejpam-3288	448	3	940	940	NUM
ejpam-3288	448	4	,	,	PUNCT
ejpam-3288	448	5	2017	2017	NUM
ejpam-3288	448	6	.	.	PUNCT
ejpam-3288	449	1	[	[	X
ejpam-3288	449	2	19	19	NUM
ejpam-3288	449	3	]	]	X
ejpam-3288	449	4	y.b	y.b	PROPN
ejpam-3288	449	5	.	.	PROPN
ejpam-3288	449	6	jun	jun	PROPN
ejpam-3288	449	7	,	,	PUNCT
ejpam-3288	449	8	s.s	s.s	PROPN
ejpam-3288	449	9	.	.	PROPN
ejpam-3288	449	10	ahn	ahn	PROPN
ejpam-3288	449	11	and	and	CCONJ
ejpam-3288	449	12	g.	g.	PROPN
ejpam-3288	449	13	muhiuddin	muhiuddin	PROPN
ejpam-3288	449	14	,	,	PUNCT
ejpam-3288	449	15	hesitant	hesitant	ADJ
ejpam-3288	449	16	fuzzy	fuzzy	ADJ
ejpam-3288	449	17	soft	soft	ADJ
ejpam-3288	449	18	subalgebras	subalgebra	NOUN
ejpam-3288	449	19	and	and	CCONJ
ejpam-3288	449	20	ideals	ideal	NOUN
ejpam-3288	449	21	in	in	ADP
ejpam-3288	449	22	bck	bck	PROPN
ejpam-3288	449	23	/	/	SYM
ejpam-3288	449	24	bci	bci	NOUN
ejpam-3288	449	25	-	-	PUNCT
ejpam-3288	449	26	algebras	algebra	NOUN
ejpam-3288	449	27	,	,	PUNCT
ejpam-3288	449	28	the	the	DET
ejpam-3288	449	29	scientific	scientific	ADJ
ejpam-3288	449	30	world	world	NOUN
ejpam-3288	449	31	journal	journal	NOUN
ejpam-3288	449	32	,	,	PUNCT
ejpam-3288	449	33	2014	2014	NUM
ejpam-3288	449	34	,	,	PUNCT
ejpam-3288	449	35	article	article	NOUN
ejpam-3288	449	36	i	i	PROPN
ejpam-3288	449	37	d	d	PROPN
ejpam-3288	449	38	763929	763929	NUM
ejpam-3288	449	39	,	,	PUNCT
ejpam-3288	449	40	7	7	NUM
ejpam-3288	449	41	pages	page	NOUN
ejpam-3288	449	42	,	,	PUNCT
ejpam-3288	449	43	2014	2014	NUM
ejpam-3288	449	44	.	.	PUNCT
ejpam-3288	450	1	[	[	X
ejpam-3288	450	2	20	20	NUM
ejpam-3288	450	3	]	]	X
ejpam-3288	450	4	h.m	h.m	PROPN
ejpam-3288	450	5	.	.	PROPN
ejpam-3288	450	6	khalid	khalid	PROPN
ejpam-3288	450	7	,	,	PUNCT
ejpam-3288	450	8	b.	b.	PROPN
ejpam-3288	450	9	ahmad	ahmad	PROPN
ejpam-3288	450	10	,	,	PUNCT
ejpam-3288	450	11	fuzzy	fuzzy	ADJ
ejpam-3288	450	12	h	h	NOUN
ejpam-3288	450	13	-	-	PUNCT
ejpam-3288	450	14	ideals	ideal	NOUN
ejpam-3288	450	15	in	in	ADP
ejpam-3288	450	16	bci	bci	NOUN
ejpam-3288	450	17	-	-	PUNCT
ejpam-3288	450	18	algebras	algebra	NOUN
ejpam-3288	450	19	,	,	PUNCT
ejpam-3288	450	20	fuzzy	fuzzy	ADJ
ejpam-3288	450	21	sets	set	NOUN
ejpam-3288	450	22	syst	syst	NOUN
ejpam-3288	450	23	.	.	PUNCT
ejpam-3288	451	1	101(1):153	101(1):153	PROPN
ejpam-3288	451	2	-	-	SYM
ejpam-3288	451	3	158	158	NUM
ejpam-3288	451	4	,	,	PUNCT
ejpam-3288	451	5	1999	1999	NUM
ejpam-3288	451	6	.	.	PUNCT
ejpam-3288	452	1	[	[	X
ejpam-3288	452	2	21	21	NUM
ejpam-3288	452	3	]	]	X
ejpam-3288	452	4	k.j	k.j	PROPN
ejpam-3288	452	5	.	.	PROPN
ejpam-3288	452	6	lee	lee	PROPN
ejpam-3288	452	7	,	,	PUNCT
ejpam-3288	452	8	bipolar	bipolar	ADJ
ejpam-3288	452	9	fuzzy	fuzzy	ADJ
ejpam-3288	452	10	subalgerbas	subalgerbas	NOUN
ejpam-3288	452	11	and	and	CCONJ
ejpam-3288	452	12	bipolar	bipolar	ADJ
ejpam-3288	452	13	fuzzy	fuzzy	ADJ
ejpam-3288	452	14	ideals	ideal	NOUN
ejpam-3288	452	15	of	of	ADP
ejpam-3288	452	16	bck	bck	PROPN
ejpam-3288	452	17	/	/	SYM
ejpam-3288	452	18	bci	bci	PROPN
ejpam-3288	452	19	-	-	PUNCT
ejpam-3288	452	20	algerbas	algerbas	ADJ
ejpam-3288	452	21	,	,	PUNCT
ejpam-3288	452	22	bull	bull	NOUN
ejpam-3288	452	23	.	.	PUNCT
ejpam-3288	453	1	malays	malays	PROPN
ejpam-3288	453	2	.	.	PUNCT
ejpam-3288	454	1	math	math	NOUN
ejpam-3288	454	2	.	.	PUNCT
ejpam-3288	455	1	sci	sci	PROPN
ejpam-3288	455	2	.	.	PROPN
ejpam-3288	455	3	soc	soc	PROPN
ejpam-3288	455	4	.	.	PUNCT
ejpam-3288	456	1	32(3):361	32(3):361	NOUN
ejpam-3288	456	2	-	-	SYM
ejpam-3288	456	3	373	373	NUM
ejpam-3288	456	4	,	,	PUNCT
ejpam-3288	456	5	2009	2009	NUM
ejpam-3288	456	6	.	.	PUNCT
ejpam-3288	457	1	[	[	X
ejpam-3288	457	2	22	22	NUM
ejpam-3288	457	3	]	]	X
ejpam-3288	457	4	k.m	k.m	PROPN
ejpam-3288	457	5	.	.	PROPN
ejpam-3288	457	6	lee	lee	PROPN
ejpam-3288	457	7	,	,	PUNCT
ejpam-3288	457	8	bipolar	bipolar	ADV
ejpam-3288	457	9	-	-	PUNCT
ejpam-3288	457	10	valued	value	VERB
ejpam-3288	457	11	fuzzy	fuzzy	ADJ
ejpam-3288	457	12	sets	set	NOUN
ejpam-3288	457	13	and	and	CCONJ
ejpam-3288	457	14	their	their	PRON
ejpam-3288	457	15	operations	operation	NOUN
ejpam-3288	457	16	,	,	PUNCT
ejpam-3288	457	17	proc	proc	NOUN
ejpam-3288	457	18	.	.	PUNCT
ejpam-3288	458	1	int	int	NOUN
ejpam-3288	458	2	.	.	PUNCT
ejpam-3288	458	3	conf	conf	PROPN
ejpam-3288	458	4	.	.	PUNCT
ejpam-3288	459	1	intelligent	intelligent	ADJ
ejpam-3288	459	2	technologies	technologies	PROPN
ejpam-3288	459	3	bangkok	bangkok	PROPN
ejpam-3288	459	4	,	,	PUNCT
ejpam-3288	459	5	thailand	thailand	PROPN
ejpam-3288	459	6	,	,	PUNCT
ejpam-3288	459	7	307	307	NUM
ejpam-3288	459	8	-	-	SYM
ejpam-3288	459	9	312	312	NUM
ejpam-3288	459	10	,	,	PUNCT
ejpam-3288	459	11	2000	2000	NUM
ejpam-3288	459	12	.	.	PUNCT
ejpam-3288	460	1	[	[	X
ejpam-3288	460	2	23	23	NUM
ejpam-3288	460	3	]	]	X
ejpam-3288	460	4	k.j	k.j	PROPN
ejpam-3288	460	5	.	.	PROPN
ejpam-3288	460	6	lee	lee	PROPN
ejpam-3288	460	7	and	and	CCONJ
ejpam-3288	460	8	y.	y.	PROPN
ejpam-3288	460	9	b.	b.	PROPN
ejpam-3288	460	10	jun	jun	PROPN
ejpam-3288	460	11	,	,	PUNCT
ejpam-3288	460	12	bipolar	bipolar	ADJ
ejpam-3288	460	13	fuzzy	fuzzy	ADJ
ejpam-3288	460	14	a	a	NOUN
ejpam-3288	460	15	-	-	PUNCT
ejpam-3288	460	16	ideals	ideal	NOUN
ejpam-3288	460	17	of	of	ADP
ejpam-3288	460	18	bci	bci	NOUN
ejpam-3288	460	19	-	-	PUNCT
ejpam-3288	460	20	algebras	algebra	NOUN
ejpam-3288	460	21	,	,	PUNCT
ejpam-3288	460	22	commun	commun	PROPN
ejpam-3288	460	23	.	.	PUNCT
ejpam-3288	461	1	korean	korean	ADJ
ejpam-3288	461	2	math	math	PROPN
ejpam-3288	461	3	.	.	PUNCT
ejpam-3288	462	1	soc	soc	PROPN
ejpam-3288	462	2	.	.	PUNCT
ejpam-3288	463	1	26(4):531	26(4):531	NUM
ejpam-3288	463	2	-	-	SYM
ejpam-3288	463	3	542	542	NUM
ejpam-3288	463	4	,	,	PUNCT
ejpam-3288	463	5	2011	2011	NUM
ejpam-3288	463	6	.	.	PUNCT
ejpam-3288	464	1	[	[	X
ejpam-3288	464	2	24	24	NUM
ejpam-3288	464	3	]	]	X
ejpam-3288	464	4	g.	g.	PROPN
ejpam-3288	464	5	muhiuddin	muhiuddin	PROPN
ejpam-3288	464	6	and	and	CCONJ
ejpam-3288	464	7	s.	s.	PROPN
ejpam-3288	464	8	aldhafeeri	aldhafeeri	PROPN
ejpam-3288	464	9	,	,	PUNCT
ejpam-3288	464	10	subalgebras	subalgebras	PROPN
ejpam-3288	464	11	and	and	CCONJ
ejpam-3288	464	12	ideals	ideal	NOUN
ejpam-3288	464	13	inbck	inbck	ADV
ejpam-3288	464	14	/	/	SYM
ejpam-3288	464	15	bci	bci	NOUN
ejpam-3288	464	16	-	-	PUNCT
ejpam-3288	464	17	algebras	algebras	PROPN
ejpam-3288	464	18	based	base	VERB
ejpam-3288	464	19	on	on	ADP
ejpam-3288	464	20	uni	uni	ADJ
ejpam-3288	464	21	-	-	ADJ
ejpam-3288	464	22	hesitant	hesitant	ADJ
ejpam-3288	464	23	fuzzy	fuzzy	ADJ
ejpam-3288	464	24	set	set	NOUN
ejpam-3288	464	25	theory	theory	NOUN
ejpam-3288	464	26	,	,	PUNCT
ejpam-3288	464	27	eur	eur	PROPN
ejpam-3288	464	28	.	.	PUNCT
ejpam-3288	465	1	j.	j.	PROPN
ejpam-3288	465	2	pure	pure	PROPN
ejpam-3288	465	3	appl	appl	PROPN
ejpam-3288	465	4	.	.	PUNCT
ejpam-3288	465	5	math	math	PROPN
ejpam-3288	465	6	.	.	PUNCT
ejpam-3288	465	7	,	,	PUNCT
ejpam-3288	465	8	11(2):417	11(2):417	NUM
ejpam-3288	465	9	-	-	SYM
ejpam-3288	465	10	430	430	NUM
ejpam-3288	465	11	,	,	PUNCT
ejpam-3288	465	12	2018	2018	NUM
ejpam-3288	465	13	.	.	PUNCT
ejpam-3288	466	1	[	[	X
ejpam-3288	466	2	25	25	NUM
ejpam-3288	466	3	]	]	X
ejpam-3288	466	4	g.	g.	PROPN
ejpam-3288	466	5	muhiuddin	muhiuddin	PROPN
ejpam-3288	466	6	,	,	PUNCT
ejpam-3288	466	7	h.s	h.s	PROPN
ejpam-3288	466	8	.	.	PROPN
ejpam-3288	466	9	kim	kim	PROPN
ejpam-3288	466	10	,	,	PUNCT
ejpam-3288	466	11	s.z	s.z	PROPN
ejpam-3288	466	12	.	.	PROPN
ejpam-3288	466	13	song	song	NOUN
ejpam-3288	466	14	and	and	CCONJ
ejpam-3288	466	15	y.b	y.b	PROPN
ejpam-3288	466	16	.	.	PROPN
ejpam-3288	466	17	jun	jun	PROPN
ejpam-3288	466	18	,	,	PUNCT
ejpam-3288	466	19	hesitant	hesitant	ADJ
ejpam-3288	466	20	fuzzy	fuzzy	ADJ
ejpam-3288	466	21	translations	translation	NOUN
ejpam-3288	466	22	and	and	CCONJ
ejpam-3288	466	23	extensions	extension	NOUN
ejpam-3288	466	24	of	of	ADP
ejpam-3288	466	25	subalgebras	subalgebra	NOUN
ejpam-3288	466	26	and	and	CCONJ
ejpam-3288	466	27	ideals	ideal	NOUN
ejpam-3288	466	28	in	in	ADP
ejpam-3288	466	29	bck	bck	PROPN
ejpam-3288	466	30	/	/	SYM
ejpam-3288	466	31	bci	bci	NOUN
ejpam-3288	466	32	-	-	PUNCT
ejpam-3288	466	33	algebras	algebra	NOUN
ejpam-3288	466	34	,	,	PUNCT
ejpam-3288	466	35	j.	j.	PROPN
ejpam-3288	466	36	intell	intell	PROPN
ejpam-3288	466	37	.	.	PUNCT
ejpam-3288	467	1	fuzzy	fuzzy	ADJ
ejpam-3288	467	2	systems	system	NOUN
ejpam-3288	467	3	,	,	PUNCT
ejpam-3288	467	4	32(1):43	32(1):43	PROPN
ejpam-3288	467	5	-	-	SYM
ejpam-3288	467	6	48	48	NUM
ejpam-3288	467	7	,	,	PUNCT
ejpam-3288	467	8	2017	2017	NUM
ejpam-3288	467	9	.	.	PUNCT
ejpam-3288	468	1	[	[	X
ejpam-3288	468	2	26	26	NUM
ejpam-3288	468	3	]	]	PUNCT
ejpam-3288	468	4	a.	a.	NOUN
ejpam-3288	468	5	rosenfeld	rosenfeld	PROPN
ejpam-3288	468	6	,	,	PUNCT
ejpam-3288	468	7	fuzzy	fuzzy	ADJ
ejpam-3288	468	8	groups	group	NOUN
ejpam-3288	468	9	,	,	PUNCT
ejpam-3288	468	10	j.	j.	PROPN
ejpam-3288	468	11	math	math	PROPN
ejpam-3288	468	12	.	.	PUNCT
ejpam-3288	469	1	anal	anal	PROPN
ejpam-3288	469	2	.	.	PUNCT
ejpam-3288	469	3	appl	appl	PROPN
ejpam-3288	469	4	.	.	PUNCT
ejpam-3288	470	1	35(3):512	35(3):512	PROPN
ejpam-3288	470	2	-	-	SYM
ejpam-3288	470	3	517	517	NUM
ejpam-3288	470	4	,	,	PUNCT
ejpam-3288	470	5	1971	1971	NUM
ejpam-3288	470	6	.	.	PUNCT
ejpam-3288	471	1	[	[	X
ejpam-3288	471	2	27	27	NUM
ejpam-3288	471	3	]	]	X
ejpam-3288	471	4	s.	s.	PROPN
ejpam-3288	471	5	sabarinathan	sabarinathan	PROPN
ejpam-3288	471	6	,	,	PUNCT
ejpam-3288	471	7	d.c	d.c	PROPN
ejpam-3288	471	8	.	.	PROPN
ejpam-3288	471	9	kumar	kumar	PROPN
ejpam-3288	471	10	and	and	CCONJ
ejpam-3288	471	11	p.	p.	PROPN
ejpam-3288	471	12	muralikrishna	muralikrishna	NOUN
ejpam-3288	471	13	,	,	PUNCT
ejpam-3288	471	14	bipolar	bipolar	PROPN
ejpam-3288	471	15	valued	value	VERB
ejpam-3288	471	16	fuzzy	fuzzy	ADJ
ejpam-3288	471	17	α	α	NOUN
ejpam-3288	471	18	-	-	NOUN
ejpam-3288	471	19	ideals	ideal	NOUN
ejpam-3288	471	20	of	of	ADP
ejpam-3288	471	21	bf	bf	NOUN
ejpam-3288	471	22	algebras	algebra	NOUN
ejpam-3288	471	23	,	,	PUNCT
ejpam-3288	471	24	circuits	circuit	NOUN
ejpam-3288	471	25	and	and	CCONJ
ejpam-3288	471	26	systems	system	NOUN
ejpam-3288	471	27	,	,	PUNCT
ejpam-3288	471	28	7:3054	7:3054	PROPN
ejpam-3288	471	29	-	-	SYM
ejpam-3288	471	30	3092	3092	NUM
ejpam-3288	471	31	,	,	PUNCT
ejpam-3288	471	32	2016	2016	NUM
ejpam-3288	471	33	.	.	PUNCT
ejpam-3288	472	1	[	[	X
ejpam-3288	472	2	28	28	NUM
ejpam-3288	472	3	]	]	X
ejpam-3288	472	4	s.	s.	PROPN
ejpam-3288	472	5	sabarinathan	sabarinathan	PROPN
ejpam-3288	472	6	,	,	PUNCT
ejpam-3288	472	7	p.	p.	NOUN
ejpam-3288	472	8	muralikrishna	muralikrishna	NOUN
ejpam-3288	472	9	,	,	PUNCT
ejpam-3288	472	10	and	and	CCONJ
ejpam-3288	472	11	d.c	d.c	PROPN
ejpam-3288	472	12	.	.	PUNCT
ejpam-3288	472	13	kumar	kumar	PROPN
ejpam-3288	472	14	,	,	PUNCT
ejpam-3288	472	15	bipolar	bipolar	PROPN
ejpam-3288	472	16	valued	value	VERB
ejpam-3288	472	17	fuzzy	fuzzy	ADJ
ejpam-3288	472	18	h	h	NOUN
ejpam-3288	472	19	-	-	PUNCT
ejpam-3288	472	20	ideals	ideal	NOUN
ejpam-3288	472	21	of	of	ADP
ejpam-3288	472	22	bf	bf	NOUN
ejpam-3288	472	23	algebras	algebra	NOUN
ejpam-3288	472	24	,	,	PUNCT
ejpam-3288	472	25	int	int	PROPN
ejpam-3288	472	26	.	.	PUNCT
ejpam-3288	473	1	j.	j.	PROPN
ejpam-3288	473	2	pure	pure	PROPN
ejpam-3288	473	3	appl	appl	PROPN
ejpam-3288	473	4	.	.	PUNCT
ejpam-3288	473	5	math	math	NOUN
ejpam-3288	473	6	.	.	PUNCT
ejpam-3288	474	1	112(5):87	112(5):87	NUM
ejpam-3288	474	2	-	-	SYM
ejpam-3288	474	3	92	92	NUM
ejpam-3288	474	4	,	,	PUNCT
ejpam-3288	474	5	2017	2017	NUM
ejpam-3288	474	6	.	.	PUNCT
ejpam-3288	475	1	[	[	X
ejpam-3288	475	2	29	29	NUM
ejpam-3288	475	3	]	]	X
ejpam-3288	475	4	o.g	o.g	PROPN
ejpam-3288	475	5	.	.	PROPN
ejpam-3288	475	6	xi	xi	PROPN
ejpam-3288	475	7	,	,	PUNCT
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ejpam-3288	475	9	bck	bck	NOUN
ejpam-3288	475	10	-	-	PUNCT
ejpam-3288	475	11	algebras	algebra	NOUN
ejpam-3288	475	12	,	,	PUNCT
ejpam-3288	475	13	math	math	NOUN
ejpam-3288	475	14	.	.	PUNCT
ejpam-3288	476	1	japon	japon	PROPN
ejpam-3288	476	2	.	.	PUNCT
ejpam-3288	477	1	24(36):935	24(36):935	NUM
ejpam-3288	477	2	-	-	SYM
ejpam-3288	477	3	942	942	NUM
ejpam-3288	477	4	,	,	PUNCT
ejpam-3288	477	5	1991	1991	NUM
ejpam-3288	477	6	.	.	PUNCT
ejpam-3288	478	1	[	[	X
ejpam-3288	478	2	30	30	NUM
ejpam-3288	478	3	]	]	X
ejpam-3288	478	4	l.a	l.a	PROPN
ejpam-3288	478	5	.	.	PROPN
ejpam-3288	478	6	zadeh	zadeh	PROPN
ejpam-3288	478	7	,	,	PUNCT
ejpam-3288	478	8	fuzzy	fuzzy	ADJ
ejpam-3288	478	9	sets	set	NOUN
ejpam-3288	478	10	,	,	PUNCT
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ejpam-3288	478	12	and	and	CCONJ
ejpam-3288	478	13	control	control	NOUN
ejpam-3288	478	14	,	,	PUNCT
ejpam-3288	478	15	8:338	8:338	NUM
ejpam-3288	478	16	-	-	SYM
ejpam-3288	478	17	353	353	NUM
ejpam-3288	478	18	,	,	PUNCT
ejpam-3288	478	19	1965	1965	NUM
ejpam-3288	478	20	.	.	PUNCT
ejpam-3288	479	1	[	[	X
ejpam-3288	479	2	31	31	NUM
ejpam-3288	479	3	]	]	X
ejpam-3288	479	4	l.a	l.a	PROPN
ejpam-3288	479	5	.	.	PROPN
ejpam-3288	479	6	zadeh	zadeh	PROPN
ejpam-3288	479	7	,	,	PUNCT
ejpam-3288	479	8	the	the	DET
ejpam-3288	479	9	concept	concept	NOUN
ejpam-3288	479	10	of	of	ADP
ejpam-3288	479	11	a	a	DET
ejpam-3288	479	12	linguistic	linguistic	ADJ
ejpam-3288	479	13	variable	variable	NOUN
ejpam-3288	479	14	and	and	CCONJ
ejpam-3288	479	15	its	its	PRON
ejpam-3288	479	16	application	application	NOUN
ejpam-3288	479	17	to	to	PART
ejpam-3288	479	18	approximate	approximate	ADJ
ejpam-3288	479	19	reasoning	reasoning	NOUN
ejpam-3288	479	20	-	-	PUNCT
ejpam-3288	479	21	i	i	PROPN
ejpam-3288	479	22	,	,	PUNCT
ejpam-3288	479	23	information	information	NOUN
ejpam-3288	479	24	and	and	CCONJ
ejpam-3288	479	25	control	control	NOUN
ejpam-3288	479	26	,	,	PUNCT
ejpam-3288	479	27	8:199	8:199	NUM
ejpam-3288	479	28	-	-	SYM
ejpam-3288	479	29	249	249	NUM
ejpam-3288	479	30	,	,	PUNCT
ejpam-3288	479	31	1975	1975	NUM
ejpam-3288	479	32	.	.	PUNCT
ejpam-3288	480	1	[	[	X
ejpam-3288	480	2	32	32	NUM
ejpam-3288	480	3	]	]	PUNCT
ejpam-3288	480	4	j.	j.	PROPN
ejpam-3288	480	5	zhan	zhan	PROPN
ejpam-3288	480	6	and	and	CCONJ
ejpam-3288	480	7	z.	z.	PROPN
ejpam-3288	480	8	tan	tan	PROPN
ejpam-3288	480	9	,	,	PUNCT
ejpam-3288	480	10	characterization	characterization	NOUN
ejpam-3288	480	11	of	of	ADP
ejpam-3288	480	12	doubt	doubt	ADV
ejpam-3288	480	13	fuzzy	fuzzy	ADJ
ejpam-3288	480	14	h	h	NOUN
ejpam-3288	480	15	-	-	PUNCT
ejpam-3288	480	16	ideals	ideal	NOUN
ejpam-3288	480	17	in	in	ADP
ejpam-3288	480	18	bck	bck	NOUN
ejpam-3288	480	19	-	-	PUNCT
ejpam-3288	480	20	algebras	algebras	PROPN
ejpam-3288	480	21	,	,	PUNCT
ejpam-3288	480	22	soochow	soochow	PROPN
ejpam-3288	480	23	j.	j.	PROPN
ejpam-3288	480	24	math	math	PROPN
ejpam-3288	480	25	.	.	PUNCT
ejpam-3288	481	1	29(3):293	29(3):293	NUM
ejpam-3288	481	2	-	-	SYM
ejpam-3288	481	3	298	298	NUM
ejpam-3288	481	4	,	,	PUNCT
ejpam-3288	481	5	2003	2003	NUM
ejpam-3288	481	6	.	.	PUNCT
ejpam-3288	482	1	[	[	X
ejpam-3288	482	2	33	33	NUM
ejpam-3288	482	3	]	]	X
ejpam-3288	482	4	j.	j.	PROPN
ejpam-3288	482	5	zhan	zhan	PROPN
ejpam-3288	482	6	,	,	PUNCT
ejpam-3288	482	7	z.	z.	PROPN
ejpam-3288	482	8	tan	tan	PROPN
ejpam-3288	482	9	,	,	PUNCT
ejpam-3288	482	10	fuzzy	fuzzy	ADJ
ejpam-3288	482	11	h	h	NOUN
ejpam-3288	482	12	-	-	PUNCT
ejpam-3288	482	13	ideals	ideal	NOUN
ejpam-3288	482	14	in	in	ADP
ejpam-3288	482	15	bck	bck	NOUN
ejpam-3288	482	16	-	-	PUNCT
ejpam-3288	482	17	algebras	algebras	PROPN
ejpam-3288	482	18	,	,	PUNCT
ejpam-3288	482	19	southeast	southeast	ADJ
ejpam-3288	482	20	asian	asian	ADJ
ejpam-3288	482	21	bull	bull	NOUN
ejpam-3288	482	22	.	.	PUNCT
ejpam-3288	482	23	math	math	NOUN
ejpam-3288	482	24	.	.	PUNCT
ejpam-3288	483	1	29(6):1165	29(6):1165	NUM
ejpam-3288	483	2	-	-	SYM
ejpam-3288	483	3	1173	1173	NUM
ejpam-3288	483	4	,	,	PUNCT
ejpam-3288	483	5	2005	2005	NUM
ejpam-3288	483	6	.	.	PUNCT