id	sid	tid	token	lemma	pos
ejpam-3844	1	1	european	european	PROPN
ejpam-3844	1	2	journal	journal	PROPN
ejpam-3844	1	3	of	of	ADP
ejpam-3844	1	4	pure	pure	ADJ
ejpam-3844	1	5	and	and	CCONJ
ejpam-3844	1	6	applied	apply	VERB
ejpam-3844	1	7	mathematics	mathematic	NOUN
ejpam-3844	1	8	vol	vol	NOUN
ejpam-3844	1	9	.	.	PROPN
ejpam-3844	2	1	13	13	NUM
ejpam-3844	2	2	,	,	PUNCT
ejpam-3844	2	3	no	no	INTJ
ejpam-3844	2	4	.	.	NOUN
ejpam-3844	2	5	4	4	NUM
ejpam-3844	2	6	,	,	PUNCT
ejpam-3844	2	7	2020	2020	NUM
ejpam-3844	2	8	,	,	PUNCT
ejpam-3844	2	9	939	939	NUM
ejpam-3844	2	10	-	-	SYM
ejpam-3844	2	11	947	947	NUM
ejpam-3844	2	12	issn	issn	PROPN
ejpam-3844	2	13	1307	1307	NUM
ejpam-3844	2	14	-	-	SYM
ejpam-3844	2	15	5543	5543	NUM
ejpam-3844	2	16	–	–	PUNCT
ejpam-3844	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3844	2	18	published	publish	VERB
ejpam-3844	2	19	by	by	ADP
ejpam-3844	2	20	new	new	PROPN
ejpam-3844	2	21	york	york	PROPN
ejpam-3844	2	22	business	business	PROPN
ejpam-3844	2	23	global	global	ADJ
ejpam-3844	2	24	further	further	ADJ
ejpam-3844	2	25	results	result	NOUN
ejpam-3844	2	26	on	on	ADP
ejpam-3844	2	27	fuzzy	fuzzy	ADJ
ejpam-3844	2	28	soft	soft	ADJ
ejpam-3844	2	29	bck	bck	NOUN
ejpam-3844	2	30	/	/	SYM
ejpam-3844	2	31	bci	bci	NOUN
ejpam-3844	2	32	-	-	PUNCT
ejpam-3844	3	1	algebras	algebras	X
ejpam-3844	3	2	deena	deena	PROPN
ejpam-3844	3	3	s.	s.	PROPN
ejpam-3844	3	4	al	al	PROPN
ejpam-3844	3	5	-	-	PUNCT
ejpam-3844	3	6	kadi1	kadi1	PROPN
ejpam-3844	3	7	,	,	PUNCT
ejpam-3844	3	8	g.	g.	PROPN
ejpam-3844	3	9	muhiuddin2,∗	muhiuddin2,∗	PROPN
ejpam-3844	3	10	1	1	NUM
ejpam-3844	3	11	department	department	NOUN
ejpam-3844	3	12	of	of	ADP
ejpam-3844	3	13	mathematics	mathematic	NOUN
ejpam-3844	3	14	and	and	CCONJ
ejpam-3844	3	15	statistics	statistic	NOUN
ejpam-3844	3	16	,	,	PUNCT
ejpam-3844	3	17	taif	taif	PROPN
ejpam-3844	3	18	university	university	PROPN
ejpam-3844	3	19	,	,	PUNCT
ejpam-3844	3	20	taif	taif	PROPN
ejpam-3844	3	21	21974	21974	NUM
ejpam-3844	3	22	,	,	PUNCT
ejpam-3844	3	23	saudi	saudi	PROPN
ejpam-3844	3	24	arabia	arabia	PROPN
ejpam-3844	3	25	2	2	NUM
ejpam-3844	3	26	department	department	NOUN
ejpam-3844	3	27	of	of	ADP
ejpam-3844	3	28	mathematics	mathematic	NOUN
ejpam-3844	3	29	,	,	PUNCT
ejpam-3844	3	30	university	university	PROPN
ejpam-3844	3	31	of	of	ADP
ejpam-3844	3	32	tabuk	tabuk	PROPN
ejpam-3844	3	33	,	,	PUNCT
ejpam-3844	3	34	tabuk	tabuk	NOUN
ejpam-3844	3	35	71491	71491	NUM
ejpam-3844	3	36	,	,	PUNCT
ejpam-3844	3	37	saudi	saudi	PROPN
ejpam-3844	3	38	arabia	arabia	PROPN
ejpam-3844	3	39	abstract	abstract	NOUN
ejpam-3844	3	40	.	.	PUNCT
ejpam-3844	4	1	in	in	ADP
ejpam-3844	4	2	this	this	DET
ejpam-3844	4	3	paper	paper	NOUN
ejpam-3844	4	4	,	,	PUNCT
ejpam-3844	4	5	we	we	PRON
ejpam-3844	4	6	obtain	obtain	VERB
ejpam-3844	4	7	further	further	ADJ
ejpam-3844	4	8	results	result	NOUN
ejpam-3844	4	9	on	on	ADP
ejpam-3844	4	10	fuzzy	fuzzy	ADJ
ejpam-3844	4	11	soft	soft	ADJ
ejpam-3844	4	12	bck	bck	NOUN
ejpam-3844	4	13	/	/	SYM
ejpam-3844	4	14	bci	bci	NOUN
ejpam-3844	4	15	-	-	PUNCT
ejpam-3844	4	16	algebras	algebras	X
ejpam-3844	4	17	.	.	PUNCT
ejpam-3844	5	1	in	in	ADP
ejpam-3844	5	2	fact	fact	NOUN
ejpam-3844	5	3	,	,	PUNCT
ejpam-3844	5	4	we	we	PRON
ejpam-3844	5	5	introduce	introduce	VERB
ejpam-3844	5	6	the	the	DET
ejpam-3844	5	7	notion	notion	NOUN
ejpam-3844	5	8	of	of	ADP
ejpam-3844	5	9	fuzzy	fuzzy	ADJ
ejpam-3844	5	10	soft	soft	ADJ
ejpam-3844	5	11	sub	sub	NOUN
ejpam-3844	5	12	-	-	ADJ
ejpam-3844	5	13	bck	bck	ADJ
ejpam-3844	5	14	/	/	SYM
ejpam-3844	5	15	bci	bci	NOUN
ejpam-3844	5	16	-	-	NOUN
ejpam-3844	5	17	algebra	algebra	NOUN
ejpam-3844	5	18	and	and	CCONJ
ejpam-3844	5	19	investigate	investigate	VERB
ejpam-3844	5	20	related	related	ADJ
ejpam-3844	5	21	properties	property	NOUN
ejpam-3844	5	22	.	.	PUNCT
ejpam-3844	6	1	2020	2020	NUM
ejpam-3844	6	2	mathematics	mathematic	NOUN
ejpam-3844	6	3	subject	subject	NOUN
ejpam-3844	6	4	classifications	classification	NOUN
ejpam-3844	6	5	:	:	PUNCT
ejpam-3844	6	6	06f35	06f35	NUM
ejpam-3844	6	7	,	,	PUNCT
ejpam-3844	6	8	03g25	03g25	NUM
ejpam-3844	6	9	,	,	PUNCT
ejpam-3844	6	10	06d72	06d72	VERB
ejpam-3844	6	11	key	key	ADJ
ejpam-3844	6	12	words	word	NOUN
ejpam-3844	6	13	and	and	CCONJ
ejpam-3844	6	14	phrases	phrase	NOUN
ejpam-3844	6	15	:	:	PUNCT
ejpam-3844	6	16	bck	bck	VERB
ejpam-3844	6	17	/	/	SYM
ejpam-3844	6	18	bci	bci	NOUN
ejpam-3844	6	19	-	-	NOUN
ejpam-3844	6	20	algebra	algebra	ADJ
ejpam-3844	6	21	,	,	PUNCT
ejpam-3844	6	22	fuzzy	fuzzy	ADJ
ejpam-3844	6	23	bck	bck	PROPN
ejpam-3844	6	24	/	/	SYM
ejpam-3844	6	25	bci	bci	NOUN
ejpam-3844	6	26	-	-	NOUN
ejpam-3844	6	27	algebra	algebra	ADJ
ejpam-3844	6	28	,	,	PUNCT
ejpam-3844	6	29	soft	soft	ADJ
ejpam-3844	6	30	bck	bck	NOUN
ejpam-3844	6	31	/	/	SYM
ejpam-3844	6	32	bcialgebra	bcialgebra	NOUN
ejpam-3844	6	33	,	,	PUNCT
ejpam-3844	6	34	fuzzy	fuzzy	ADJ
ejpam-3844	6	35	soft	soft	ADJ
ejpam-3844	6	36	bck	bck	NOUN
ejpam-3844	6	37	/	/	SYM
ejpam-3844	6	38	bci	bci	NOUN
ejpam-3844	6	39	-	-	NOUN
ejpam-3844	6	40	algebra	algebra	NOUN
ejpam-3844	6	41	.	.	PUNCT
ejpam-3844	7	1	1	1	X
ejpam-3844	7	2	.	.	X
ejpam-3844	7	3	introduction	introduction	NOUN
ejpam-3844	7	4	soft	soft	ADJ
ejpam-3844	7	5	set	set	NOUN
ejpam-3844	7	6	theory	theory	NOUN
ejpam-3844	7	7	was	be	AUX
ejpam-3844	7	8	introduced	introduce	VERB
ejpam-3844	7	9	initially	initially	ADV
ejpam-3844	7	10	by	by	ADP
ejpam-3844	7	11	molodtsov	molodtsov	NOUN
ejpam-3844	7	12	in	in	ADP
ejpam-3844	7	13	1999	1999	NUM
ejpam-3844	7	14	[	[	X
ejpam-3844	7	15	12	12	NUM
ejpam-3844	7	16	]	]	PUNCT
ejpam-3844	7	17	as	as	ADP
ejpam-3844	7	18	a	a	DET
ejpam-3844	7	19	mathematical	mathematical	ADJ
ejpam-3844	7	20	tool	tool	NOUN
ejpam-3844	7	21	to	to	PART
ejpam-3844	7	22	model	model	VERB
ejpam-3844	7	23	uncertainty	uncertainty	NOUN
ejpam-3844	7	24	and	and	CCONJ
ejpam-3844	7	25	vagueness	vagueness	NOUN
ejpam-3844	7	26	.	.	PUNCT
ejpam-3844	8	1	in	in	ADP
ejpam-3844	8	2	[	[	X
ejpam-3844	8	3	1	1	NUM
ejpam-3844	8	4	]	]	PUNCT
ejpam-3844	8	5	,	,	PUNCT
ejpam-3844	8	6	ali	ali	PROPN
ejpam-3844	8	7	et	et	PROPN
ejpam-3844	8	8	al	al	PROPN
ejpam-3844	8	9	.	.	PROPN
ejpam-3844	8	10	studied	study	VERB
ejpam-3844	8	11	some	some	DET
ejpam-3844	8	12	operations	operation	NOUN
ejpam-3844	8	13	between	between	ADP
ejpam-3844	8	14	two	two	NUM
ejpam-3844	8	15	soft	soft	ADJ
ejpam-3844	8	16	sets	set	NOUN
ejpam-3844	8	17	.	.	PUNCT
ejpam-3844	9	1	furthermore	furthermore	ADV
ejpam-3844	9	2	,	,	PUNCT
ejpam-3844	9	3	they	they	PRON
ejpam-3844	9	4	improved	improve	VERB
ejpam-3844	9	5	the	the	DET
ejpam-3844	9	6	definition	definition	NOUN
ejpam-3844	9	7	of	of	ADP
ejpam-3844	9	8	the	the	DET
ejpam-3844	9	9	complement	complement	NOUN
ejpam-3844	9	10	of	of	ADP
ejpam-3844	9	11	a	a	DET
ejpam-3844	9	12	soft	soft	ADJ
ejpam-3844	9	13	set	set	NOUN
ejpam-3844	9	14	then	then	ADV
ejpam-3844	9	15	studied	study	VERB
ejpam-3844	9	16	demorgan	demorgan	NOUN
ejpam-3844	9	17	’s	’s	PART
ejpam-3844	9	18	type	type	NOUN
ejpam-3844	9	19	results	result	NOUN
ejpam-3844	9	20	in	in	ADP
ejpam-3844	9	21	soft	soft	ADJ
ejpam-3844	9	22	set	set	NOUN
ejpam-3844	9	23	theory	theory	NOUN
ejpam-3844	9	24	.	.	PUNCT
ejpam-3844	10	1	soft	soft	ADJ
ejpam-3844	10	2	set	set	NOUN
ejpam-3844	10	3	theory	theory	NOUN
ejpam-3844	10	4	has	have	AUX
ejpam-3844	10	5	been	be	AUX
ejpam-3844	10	6	applied	apply	VERB
ejpam-3844	10	7	in	in	ADP
ejpam-3844	10	8	different	different	ADJ
ejpam-3844	10	9	directions	direction	NOUN
ejpam-3844	10	10	some	some	PRON
ejpam-3844	10	11	are	be	AUX
ejpam-3844	10	12	shown	show	VERB
ejpam-3844	10	13	in	in	ADP
ejpam-3844	10	14	[	[	X
ejpam-3844	10	15	12	12	NUM
ejpam-3844	10	16	]	]	PUNCT
ejpam-3844	10	17	and	and	CCONJ
ejpam-3844	10	18	other	other	ADJ
ejpam-3844	10	19	applications	application	NOUN
ejpam-3844	10	20	are	be	AUX
ejpam-3844	10	21	shown	show	VERB
ejpam-3844	10	22	in	in	ADP
ejpam-3844	10	23	[	[	X
ejpam-3844	10	24	5	5	NUM
ejpam-3844	10	25	]	]	PUNCT
ejpam-3844	10	26	and	and	CCONJ
ejpam-3844	10	27	[	[	X
ejpam-3844	10	28	11	11	NUM
ejpam-3844	10	29	]	]	PUNCT
ejpam-3844	10	30	.	.	PUNCT
ejpam-3844	11	1	based	base	VERB
ejpam-3844	11	2	on	on	ADP
ejpam-3844	11	3	soft	soft	ADJ
ejpam-3844	11	4	set	set	NOUN
ejpam-3844	11	5	theory	theory	NOUN
ejpam-3844	11	6	many	many	ADJ
ejpam-3844	11	7	researches	research	NOUN
ejpam-3844	11	8	has	have	AUX
ejpam-3844	11	9	been	be	AUX
ejpam-3844	11	10	done	do	VERB
ejpam-3844	11	11	(	(	PUNCT
ejpam-3844	11	12	see	see	VERB
ejpam-3844	11	13	for	for	ADP
ejpam-3844	11	14	example	example	NOUN
ejpam-3844	11	15	[	[	X
ejpam-3844	11	16	3	3	NUM
ejpam-3844	11	17	,	,	PUNCT
ejpam-3844	11	18	7	7	NUM
ejpam-3844	11	19	,	,	PUNCT
ejpam-3844	11	20	9	9	NUM
ejpam-3844	11	21	,	,	PUNCT
ejpam-3844	11	22	14	14	NUM
ejpam-3844	11	23	–	–	PUNCT
ejpam-3844	11	24	18	18	NUM
ejpam-3844	11	25	]	]	PUNCT
ejpam-3844	11	26	)	)	PUNCT
ejpam-3844	11	27	.	.	PUNCT
ejpam-3844	12	1	wong	wong	PROPN
ejpam-3844	13	1	[	[	X
ejpam-3844	13	2	20	20	NUM
ejpam-3844	13	3	]	]	PUNCT
ejpam-3844	13	4	used	use	VERB
ejpam-3844	13	5	fuzzy	fuzzy	ADJ
ejpam-3844	13	6	set	set	NOUN
ejpam-3844	13	7	theory	theory	NOUN
ejpam-3844	13	8	introduced	introduce	VERB
ejpam-3844	13	9	by	by	ADP
ejpam-3844	13	10	zadeh	zadeh	PROPN
ejpam-3844	14	1	[	[	X
ejpam-3844	14	2	21	21	NUM
ejpam-3844	14	3	]	]	PUNCT
ejpam-3844	14	4	to	to	PART
ejpam-3844	14	5	extend	extend	VERB
ejpam-3844	14	6	general	general	ADJ
ejpam-3844	14	7	topology	topology	NOUN
ejpam-3844	14	8	to	to	ADP
ejpam-3844	14	9	fuzzy	fuzzy	ADJ
ejpam-3844	14	10	topology	topology	NOUN
ejpam-3844	14	11	.	.	PUNCT
ejpam-3844	15	1	jun	jun	PROPN
ejpam-3844	16	1	[	[	X
ejpam-3844	16	2	6	6	NUM
ejpam-3844	16	3	]	]	PUNCT
ejpam-3844	16	4	studied	study	VERB
ejpam-3844	16	5	fuzzy	fuzzy	ADJ
ejpam-3844	16	6	subalgebras	subalgebra	NOUN
ejpam-3844	16	7	of	of	ADP
ejpam-3844	16	8	bck	bck	PROPN
ejpam-3844	16	9	/	/	SYM
ejpam-3844	16	10	bci	bci	NOUN
ejpam-3844	16	11	-	-	PUNCT
ejpam-3844	16	12	algebras	algebras	PROPN
ejpam-3844	16	13	based	base	VERB
ejpam-3844	16	14	on	on	ADP
ejpam-3844	16	15	the	the	DET
ejpam-3844	16	16	relations	relation	NOUN
ejpam-3844	16	17	belongs	belong	VERB
ejpam-3844	16	18	to	to	ADP
ejpam-3844	16	19	and	and	CCONJ
ejpam-3844	16	20	quasi	quasi	NOUN
ejpam-3844	16	21	-	-	NOUN
ejpam-3844	16	22	coincidence	coincidence	NOUN
ejpam-3844	16	23	with	with	ADP
ejpam-3844	16	24	.	.	PUNCT
ejpam-3844	17	1	the	the	DET
ejpam-3844	17	2	authors	author	NOUN
ejpam-3844	17	3	in	in	ADP
ejpam-3844	17	4	[	[	X
ejpam-3844	17	5	4	4	NUM
ejpam-3844	17	6	]	]	PUNCT
ejpam-3844	17	7	introduced	introduce	VERB
ejpam-3844	17	8	and	and	CCONJ
ejpam-3844	17	9	studied	study	VERB
ejpam-3844	17	10	fuzzy	fuzzy	ADJ
ejpam-3844	17	11	soft	soft	ADJ
ejpam-3844	17	12	groups	group	NOUN
ejpam-3844	17	13	and	and	CCONJ
ejpam-3844	17	14	fuzzy	fuzzy	ADJ
ejpam-3844	17	15	soft	soft	ADJ
ejpam-3844	17	16	homomorphisms	homomorphism	NOUN
ejpam-3844	17	17	.	.	PUNCT
ejpam-3844	18	1	maji	maji	PROPN
ejpam-3844	18	2	et	et	PROPN
ejpam-3844	18	3	al	al	PROPN
ejpam-3844	18	4	.	.	PUNCT
ejpam-3844	19	1	[	[	X
ejpam-3844	19	2	10	10	NUM
ejpam-3844	19	3	]	]	PUNCT
ejpam-3844	19	4	defined	define	VERB
ejpam-3844	19	5	and	and	CCONJ
ejpam-3844	19	6	studied	study	VERB
ejpam-3844	19	7	fuzzy	fuzzy	ADJ
ejpam-3844	19	8	soft	soft	ADJ
ejpam-3844	19	9	sets	set	NOUN
ejpam-3844	19	10	.	.	PUNCT
ejpam-3844	20	1	roy	roy	PROPN
ejpam-3844	20	2	and	and	CCONJ
ejpam-3844	20	3	maji	maji	PROPN
ejpam-3844	21	1	[	[	X
ejpam-3844	21	2	19	19	NUM
ejpam-3844	21	3	]	]	PUNCT
ejpam-3844	21	4	considered	consider	VERB
ejpam-3844	21	5	the	the	DET
ejpam-3844	21	6	notion	notion	NOUN
ejpam-3844	21	7	of	of	ADP
ejpam-3844	21	8	fuzzy	fuzzy	ADJ
ejpam-3844	21	9	soft	soft	ADJ
ejpam-3844	21	10	set	set	NOUN
ejpam-3844	21	11	and	and	CCONJ
ejpam-3844	21	12	used	use	VERB
ejpam-3844	21	13	it	it	PRON
ejpam-3844	21	14	to	to	PART
ejpam-3844	21	15	present	present	VERB
ejpam-3844	21	16	a	a	DET
ejpam-3844	21	17	theoretic	theoretic	ADJ
ejpam-3844	21	18	approach	approach	NOUN
ejpam-3844	21	19	to	to	ADP
ejpam-3844	21	20	decision	decision	NOUN
ejpam-3844	21	21	making	make	VERB
ejpam-3844	21	22	problems	problem	NOUN
ejpam-3844	21	23	and	and	CCONJ
ejpam-3844	21	24	jun	jun	PROPN
ejpam-3844	21	25	et	et	PROPN
ejpam-3844	21	26	al	al	PROPN
ejpam-3844	21	27	.	.	PUNCT
ejpam-3844	22	1	[	[	X
ejpam-3844	22	2	8	8	NUM
ejpam-3844	22	3	]	]	PUNCT
ejpam-3844	22	4	applied	apply	VERB
ejpam-3844	22	5	the	the	DET
ejpam-3844	22	6	same	same	ADJ
ejpam-3844	22	7	notion	notion	NOUN
ejpam-3844	22	8	to	to	PART
ejpam-3844	22	9	bck	bck	VERB
ejpam-3844	22	10	/	/	SYM
ejpam-3844	22	11	bci	bci	NOUN
ejpam-3844	22	12	-	-	PUNCT
ejpam-3844	22	13	algebras	algebras	X
ejpam-3844	22	14	.	.	PUNCT
ejpam-3844	23	1	recently	recently	ADV
ejpam-3844	23	2	,	,	PUNCT
ejpam-3844	23	3	almasarwah	almasarwah	PROPN
ejpam-3844	23	4	and	and	CCONJ
ejpam-3844	23	5	ahmad	ahmad	PROPN
ejpam-3844	23	6	[	[	X
ejpam-3844	23	7	2	2	NUM
ejpam-3844	23	8	]	]	PUNCT
ejpam-3844	23	9	applied	apply	VERB
ejpam-3844	23	10	the	the	DET
ejpam-3844	23	11	notion	notion	NOUN
ejpam-3844	23	12	of	of	ADP
ejpam-3844	23	13	m	m	ADJ
ejpam-3844	23	14	-	-	ADJ
ejpam-3844	23	15	polar	polar	ADJ
ejpam-3844	23	16	fuzzy	fuzzy	ADJ
ejpam-3844	23	17	sets	set	NOUN
ejpam-3844	23	18	to	to	PART
ejpam-3844	23	19	bck	bck	VERB
ejpam-3844	23	20	/	/	SYM
ejpam-3844	23	21	bci	bci	NOUN
ejpam-3844	23	22	-	-	PUNCT
ejpam-3844	23	23	algebras	algebras	X
ejpam-3844	23	24	.	.	PUNCT
ejpam-3844	24	1	as	as	SCONJ
ejpam-3844	24	2	shown	show	VERB
ejpam-3844	24	3	above	above	ADV
ejpam-3844	24	4	,	,	PUNCT
ejpam-3844	24	5	the	the	DET
ejpam-3844	24	6	bck	bck	PROPN
ejpam-3844	24	7	/	/	SYM
ejpam-3844	24	8	bci	bci	NOUN
ejpam-3844	24	9	-	-	NOUN
ejpam-3844	24	10	algebra	algebra	NOUN
ejpam-3844	24	11	which	which	PRON
ejpam-3844	24	12	is	be	AUX
ejpam-3844	24	13	introduced	introduce	VERB
ejpam-3844	24	14	by	by	ADP
ejpam-3844	24	15	iséki	iséki	PROPN
ejpam-3844	24	16	was	be	AUX
ejpam-3844	24	17	extensively	extensively	ADV
ejpam-3844	24	18	investigated	investigate	VERB
ejpam-3844	24	19	by	by	ADP
ejpam-3844	24	20	several	several	ADJ
ejpam-3844	24	21	researchers	researcher	NOUN
ejpam-3844	24	22	and	and	CCONJ
ejpam-3844	24	23	this	this	DET
ejpam-3844	24	24	paper	paper	NOUN
ejpam-3844	24	25	gives	give	VERB
ejpam-3844	24	26	further	further	ADJ
ejpam-3844	24	27	results	result	NOUN
ejpam-3844	24	28	on	on	ADP
ejpam-3844	24	29	fuzzy	fuzzy	ADJ
ejpam-3844	24	30	soft	soft	ADJ
ejpam-3844	24	31	bck	bck	NOUN
ejpam-3844	24	32	/	/	SYM
ejpam-3844	24	33	bci	bci	NOUN
ejpam-3844	24	34	-	-	PUNCT
ejpam-3844	24	35	algebras	algebras	X
ejpam-3844	24	36	.	.	PUNCT
ejpam-3844	25	1	we	we	PRON
ejpam-3844	25	2	start	start	VERB
ejpam-3844	25	3	by	by	ADP
ejpam-3844	25	4	recalling	recall	VERB
ejpam-3844	25	5	the	the	DET
ejpam-3844	25	6	definition	definition	NOUN
ejpam-3844	25	7	of	of	ADP
ejpam-3844	25	8	the	the	DET
ejpam-3844	25	9	algebras	algebra	NOUN
ejpam-3844	25	10	we	we	PRON
ejpam-3844	25	11	are	be	AUX
ejpam-3844	25	12	studying	study	VERB
ejpam-3844	25	13	and	and	CCONJ
ejpam-3844	25	14	the	the	DET
ejpam-3844	25	15	basic	basic	ADJ
ejpam-3844	25	16	definitions	definition	NOUN
ejpam-3844	25	17	of	of	ADP
ejpam-3844	25	18	soft	soft	ADJ
ejpam-3844	25	19	sets	set	NOUN
ejpam-3844	25	20	and	and	CCONJ
ejpam-3844	25	21	fuzzy	fuzzy	ADJ
ejpam-3844	25	22	soft	soft	ADJ
ejpam-3844	25	23	sets	set	NOUN
ejpam-3844	25	24	and	and	CCONJ
ejpam-3844	25	25	the	the	DET
ejpam-3844	25	26	definition	definition	NOUN
ejpam-3844	25	27	of	of	ADP
ejpam-3844	25	28	some	some	DET
ejpam-3844	25	29	operations	operation	NOUN
ejpam-3844	25	30	related	relate	VERB
ejpam-3844	25	31	.	.	PUNCT
ejpam-3844	26	1	then	then	ADV
ejpam-3844	26	2	we	we	PRON
ejpam-3844	26	3	investigate	investigate	VERB
ejpam-3844	26	4	further	further	ADJ
ejpam-3844	26	5	results	result	NOUN
ejpam-3844	26	6	that	that	PRON
ejpam-3844	26	7	are	be	AUX
ejpam-3844	26	8	not	not	PART
ejpam-3844	26	9	studied	study	VERB
ejpam-3844	26	10	in	in	ADP
ejpam-3844	26	11	[	[	X
ejpam-3844	26	12	8	8	NUM
ejpam-3844	26	13	]	]	PUNCT
ejpam-3844	26	14	.	.	PUNCT
ejpam-3844	27	1	∗corresponding	∗corresponde	VERB
ejpam-3844	27	2	author	author	NOUN
ejpam-3844	27	3	.	.	PUNCT
ejpam-3844	28	1	doi	doi	NOUN
ejpam-3844	28	2	:	:	PUNCT
ejpam-3844	28	3	https://doi.org/10.29020/nybg.ejpam.v13i4.3844	https://doi.org/10.29020/nybg.ejpam.v13i4.3844	ADJ
ejpam-3844	28	4	email	email	NOUN
ejpam-3844	28	5	addresses	address	NOUN
ejpam-3844	28	6	:	:	PUNCT
ejpam-3844	28	7	dak12le@hotmail.co.uk	dak12le@hotmail.co.uk	PROPN
ejpam-3844	28	8	(	(	PUNCT
ejpam-3844	28	9	d.	d.	PROPN
ejpam-3844	28	10	al	al	PROPN
ejpam-3844	28	11	-	-	PUNCT
ejpam-3844	28	12	kadi	kadi	PROPN
ejpam-3844	28	13	)	)	PUNCT
ejpam-3844	28	14	,	,	PUNCT
ejpam-3844	28	15	chishtygm@gmail.com	chishtygm@gmail.com	X
ejpam-3844	28	16	(	(	PUNCT
ejpam-3844	28	17	g.	g.	PROPN
ejpam-3844	28	18	muhiuddin	muhiuddin	PROPN
ejpam-3844	28	19	)	)	PUNCT
ejpam-3844	28	20	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-3844	29	1	939	939	NUM
ejpam-3844	29	2	c	c	X
ejpam-3844	29	3	©	©	NOUN
ejpam-3844	29	4	2020	2020	NUM
ejpam-3844	29	5	ejpam	ejpam	VERB
ejpam-3844	29	6	all	all	DET
ejpam-3844	29	7	rights	right	NOUN
ejpam-3844	29	8	reserved	reserve	VERB
ejpam-3844	29	9	.	.	PUNCT
ejpam-3844	30	1	al	al	PROPN
ejpam-3844	30	2	-	-	PUNCT
ejpam-3844	30	3	kadi	kadi	PROPN
ejpam-3844	30	4	,	,	PUNCT
ejpam-3844	30	5	muhiuddin	muhiuddin	NOUN
ejpam-3844	30	6	/	/	SYM
ejpam-3844	30	7	eur	eur	PROPN
ejpam-3844	30	8	.	.	PUNCT
ejpam-3844	31	1	j.	j.	PROPN
ejpam-3844	31	2	pure	pure	PROPN
ejpam-3844	31	3	appl	appl	PROPN
ejpam-3844	31	4	.	.	PROPN
ejpam-3844	31	5	math	math	PROPN
ejpam-3844	31	6	,	,	PUNCT
ejpam-3844	31	7	13	13	NUM
ejpam-3844	31	8	(	(	PUNCT
ejpam-3844	31	9	4	4	NUM
ejpam-3844	31	10	)	)	PUNCT
ejpam-3844	31	11	(	(	PUNCT
ejpam-3844	31	12	2020	2020	NUM
ejpam-3844	31	13	)	)	PUNCT
ejpam-3844	31	14	,	,	PUNCT
ejpam-3844	31	15	939	939	NUM
ejpam-3844	31	16	-	-	SYM
ejpam-3844	31	17	947	947	NUM
ejpam-3844	31	18	940	940	NUM
ejpam-3844	31	19	2	2	NUM
ejpam-3844	31	20	.	.	PUNCT
ejpam-3844	31	21	preliminaries	preliminary	NOUN
ejpam-3844	31	22	an	an	DET
ejpam-3844	31	23	algebra	algebra	NOUN
ejpam-3844	31	24	(	(	PUNCT
ejpam-3844	31	25	b	b	NOUN
ejpam-3844	31	26	;	;	PUNCT
ejpam-3844	31	27	∗	∗	NOUN
ejpam-3844	31	28	,	,	PUNCT
ejpam-3844	31	29	0	0	NUM
ejpam-3844	31	30	)	)	PUNCT
ejpam-3844	31	31	of	of	ADP
ejpam-3844	31	32	type	type	NOUN
ejpam-3844	31	33	(	(	PUNCT
ejpam-3844	31	34	2	2	NUM
ejpam-3844	31	35	,	,	PUNCT
ejpam-3844	31	36	0	0	NUM
ejpam-3844	31	37	)	)	PUNCT
ejpam-3844	31	38	is	be	AUX
ejpam-3844	31	39	called	call	VERB
ejpam-3844	31	40	a	a	DET
ejpam-3844	31	41	bci	bci	NOUN
ejpam-3844	31	42	-	-	NOUN
ejpam-3844	31	43	algebra	algebra	NOUN
ejpam-3844	31	44	if	if	SCONJ
ejpam-3844	31	45	it	it	PRON
ejpam-3844	31	46	satisfies	satisfy	VERB
ejpam-3844	31	47	the	the	DET
ejpam-3844	31	48	following	follow	VERB
ejpam-3844	31	49	conditions	condition	NOUN
ejpam-3844	31	50	:	:	PUNCT
ejpam-3844	32	1	1	1	X
ejpam-3844	32	2	.	.	PUNCT
ejpam-3844	32	3	(	(	PUNCT
ejpam-3844	32	4	∀β	∀β	PROPN
ejpam-3844	32	5	,	,	PUNCT
ejpam-3844	32	6	γ	γ	X
ejpam-3844	32	7	,	,	PUNCT
ejpam-3844	32	8	δ	δ	PROPN
ejpam-3844	32	9	∈	∈	PROPN
ejpam-3844	32	10	b	b	PROPN
ejpam-3844	32	11	)	)	PUNCT
ejpam-3844	32	12	(	(	PUNCT
ejpam-3844	32	13	(	(	PUNCT
ejpam-3844	32	14	(	(	PUNCT
ejpam-3844	32	15	β	β	X
ejpam-3844	32	16	∗	∗	X
ejpam-3844	32	17	γ	γ	PROPN
ejpam-3844	32	18	)	)	PUNCT
ejpam-3844	32	19	∗	∗	NOUN
ejpam-3844	32	20	(	(	PUNCT
ejpam-3844	32	21	β	β	X
ejpam-3844	32	22	∗	∗	X
ejpam-3844	32	23	δ	δ	PROPN
ejpam-3844	32	24	)	)	PUNCT
ejpam-3844	32	25	)	)	PUNCT
ejpam-3844	32	26	∗	∗	NOUN
ejpam-3844	32	27	(	(	PUNCT
ejpam-3844	32	28	δ	δ	PROPN
ejpam-3844	32	29	∗	∗	X
ejpam-3844	32	30	γ	γ	X
ejpam-3844	32	31	)	)	PUNCT
ejpam-3844	32	32	=	=	SYM
ejpam-3844	32	33	0	0	NUM
ejpam-3844	32	34	)	)	PUNCT
ejpam-3844	32	35	,	,	PUNCT
ejpam-3844	32	36	2	2	X
ejpam-3844	32	37	.	.	PUNCT
ejpam-3844	32	38	(	(	PUNCT
ejpam-3844	32	39	∀β	∀β	PROPN
ejpam-3844	32	40	,	,	PUNCT
ejpam-3844	32	41	γ	γ	PROPN
ejpam-3844	32	42	∈	∈	PROPN
ejpam-3844	32	43	b	b	X
ejpam-3844	32	44	)	)	PUNCT
ejpam-3844	32	45	(	(	PUNCT
ejpam-3844	32	46	(	(	PUNCT
ejpam-3844	32	47	β	β	X
ejpam-3844	32	48	∗	∗	X
ejpam-3844	32	49	(	(	PUNCT
ejpam-3844	32	50	β	β	X
ejpam-3844	32	51	∗	∗	X
ejpam-3844	32	52	γ	γ	PROPN
ejpam-3844	32	53	)	)	PUNCT
ejpam-3844	32	54	)	)	PUNCT
ejpam-3844	32	55	∗	∗	NOUN
ejpam-3844	32	56	γ	γ	X
ejpam-3844	32	57	=	=	SYM
ejpam-3844	32	58	0	0	NUM
ejpam-3844	32	59	)	)	PUNCT
ejpam-3844	32	60	,	,	PUNCT
ejpam-3844	32	61	3	3	X
ejpam-3844	32	62	.	.	PUNCT
ejpam-3844	32	63	(	(	PUNCT
ejpam-3844	32	64	∀β	∀β	PROPN
ejpam-3844	32	65	∈	∈	PROPN
ejpam-3844	32	66	b	b	X
ejpam-3844	32	67	)	)	PUNCT
ejpam-3844	32	68	β	β	NOUN
ejpam-3844	32	69	∗	∗	X
ejpam-3844	32	70	β	β	X
ejpam-3844	32	71	=	=	NOUN
ejpam-3844	32	72	0	0	NUM
ejpam-3844	32	73	)	)	PUNCT
ejpam-3844	32	74	,	,	PUNCT
ejpam-3844	32	75	4	4	X
ejpam-3844	32	76	.	.	PUNCT
ejpam-3844	32	77	(	(	PUNCT
ejpam-3844	32	78	∀β	∀β	PROPN
ejpam-3844	32	79	,	,	PUNCT
ejpam-3844	32	80	γ	γ	PROPN
ejpam-3844	32	81	∈	∈	PROPN
ejpam-3844	32	82	b	b	X
ejpam-3844	32	83	)	)	PUNCT
ejpam-3844	32	84	(	(	PUNCT
ejpam-3844	32	85	β	β	X
ejpam-3844	32	86	∗	∗	X
ejpam-3844	32	87	γ	γ	X
ejpam-3844	32	88	=	=	SYM
ejpam-3844	32	89	0	0	NUM
ejpam-3844	32	90	,	,	PUNCT
ejpam-3844	32	91	γ	γ	X
ejpam-3844	32	92	∗	∗	NOUN
ejpam-3844	32	93	β	β	X
ejpam-3844	32	94	=	=	SYM
ejpam-3844	32	95	0	0	NUM
ejpam-3844	32	96	⇒	⇒	NOUN
ejpam-3844	32	97	β	β	X
ejpam-3844	32	98	=	=	SYM
ejpam-3844	32	99	γ	γ	X
ejpam-3844	32	100	)	)	PUNCT
ejpam-3844	32	101	.	.	PUNCT
ejpam-3844	33	1	if	if	SCONJ
ejpam-3844	33	2	a	a	DET
ejpam-3844	33	3	bci	bci	NOUN
ejpam-3844	33	4	-	-	NOUN
ejpam-3844	33	5	algebra	algebra	ADJ
ejpam-3844	33	6	b	b	NOUN
ejpam-3844	33	7	satisfies	satisfie	NOUN
ejpam-3844	33	8	(	(	PUNCT
ejpam-3844	33	9	0	0	NUM
ejpam-3844	33	10	∗	∗	NOUN
ejpam-3844	33	11	β	β	X
ejpam-3844	33	12	=	=	NOUN
ejpam-3844	33	13	0	0	NUM
ejpam-3844	33	14	)	)	PUNCT
ejpam-3844	33	15	,	,	PUNCT
ejpam-3844	33	16	(	(	PUNCT
ejpam-3844	33	17	∀β	∀β	PROPN
ejpam-3844	33	18	∈	∈	PROPN
ejpam-3844	33	19	b	b	X
ejpam-3844	33	20	)	)	PUNCT
ejpam-3844	33	21	then	then	ADV
ejpam-3844	33	22	b	b	PROPN
ejpam-3844	33	23	is	be	AUX
ejpam-3844	33	24	called	call	VERB
ejpam-3844	33	25	a	a	DET
ejpam-3844	33	26	bck	bck	NOUN
ejpam-3844	33	27	-	-	PUNCT
ejpam-3844	33	28	algebra	algebra	NOUN
ejpam-3844	33	29	.	.	PUNCT
ejpam-3844	34	1	any	any	DET
ejpam-3844	34	2	bck	bck	NOUN
ejpam-3844	34	3	-	-	PUNCT
ejpam-3844	34	4	algebra	algebra	NOUN
ejpam-3844	34	5	b	b	NOUN
ejpam-3844	34	6	satisfies	satisfy	VERB
ejpam-3844	34	7	the	the	DET
ejpam-3844	34	8	following	follow	VERB
ejpam-3844	34	9	properties	property	NOUN
ejpam-3844	34	10	:	:	PUNCT
ejpam-3844	34	11	•	•	NUM
ejpam-3844	34	12	(	(	PUNCT
ejpam-3844	34	13	∀β	∀β	PROPN
ejpam-3844	34	14	∈	∈	PROPN
ejpam-3844	34	15	b	b	X
ejpam-3844	34	16	)	)	PUNCT
ejpam-3844	34	17	(	(	PUNCT
ejpam-3844	34	18	β	β	X
ejpam-3844	34	19	∗	∗	NOUN
ejpam-3844	34	20	0	0	NUM
ejpam-3844	35	1	=	=	SYM
ejpam-3844	35	2	β	β	X
ejpam-3844	35	3	)	)	PUNCT
ejpam-3844	35	4	,	,	PUNCT
ejpam-3844	35	5	•	•	X
ejpam-3844	35	6	(	(	PUNCT
ejpam-3844	35	7	∀β	∀β	PROPN
ejpam-3844	35	8	,	,	PUNCT
ejpam-3844	35	9	γ	γ	X
ejpam-3844	35	10	,	,	PUNCT
ejpam-3844	35	11	δ	δ	PROPN
ejpam-3844	35	12	∈	∈	PROPN
ejpam-3844	35	13	b	b	PROPN
ejpam-3844	35	14	)	)	PUNCT
ejpam-3844	35	15	(	(	PUNCT
ejpam-3844	35	16	β	β	NOUN
ejpam-3844	35	17	≤	≤	NUM
ejpam-3844	35	18	γ	γ	PROPN
ejpam-3844	35	19	⇒	⇒	PROPN
ejpam-3844	35	20	β	β	PROPN
ejpam-3844	35	21	∗	∗	X
ejpam-3844	35	22	δ	δ	PROPN
ejpam-3844	35	23	≤	≤	ADV
ejpam-3844	35	24	γ	γ	PROPN
ejpam-3844	35	25	∗	∗	PROPN
ejpam-3844	35	26	δ	δ	PROPN
ejpam-3844	35	27	,	,	PUNCT
ejpam-3844	35	28	δ	δ	PROPN
ejpam-3844	35	29	∗	∗	NOUN
ejpam-3844	35	30	γ	γ	PROPN
ejpam-3844	35	31	≤	≤	PROPN
ejpam-3844	35	32	δ	δ	PROPN
ejpam-3844	35	33	∗	∗	NOUN
ejpam-3844	35	34	β	β	NOUN
ejpam-3844	35	35	)	)	PUNCT
ejpam-3844	35	36	,	,	PUNCT
ejpam-3844	35	37	•	•	X
ejpam-3844	35	38	(	(	PUNCT
ejpam-3844	35	39	∀β	∀β	PROPN
ejpam-3844	35	40	,	,	PUNCT
ejpam-3844	35	41	γ	γ	X
ejpam-3844	35	42	,	,	PUNCT
ejpam-3844	35	43	δ	δ	PROPN
ejpam-3844	35	44	∈	∈	PROPN
ejpam-3844	35	45	b	b	PROPN
ejpam-3844	35	46	)	)	PUNCT
ejpam-3844	35	47	(	(	PUNCT
ejpam-3844	35	48	(	(	PUNCT
ejpam-3844	35	49	β	β	X
ejpam-3844	35	50	∗	∗	X
ejpam-3844	35	51	γ	γ	PROPN
ejpam-3844	35	52	)	)	PUNCT
ejpam-3844	35	53	∗	∗	NOUN
ejpam-3844	35	54	δ	δ	NOUN
ejpam-3844	35	55	=	=	PRON
ejpam-3844	35	56	(	(	PUNCT
ejpam-3844	35	57	β	β	X
ejpam-3844	35	58	∗	∗	X
ejpam-3844	35	59	δ	δ	PROPN
ejpam-3844	35	60	)	)	PUNCT
ejpam-3844	35	61	∗	∗	PROPN
ejpam-3844	35	62	γ	γ	PROPN
ejpam-3844	35	63	)	)	PUNCT
ejpam-3844	35	64	,	,	PUNCT
ejpam-3844	35	65	•	•	X
ejpam-3844	35	66	(	(	PUNCT
ejpam-3844	35	67	∀β	∀β	PROPN
ejpam-3844	35	68	,	,	PUNCT
ejpam-3844	35	69	γ	γ	X
ejpam-3844	35	70	,	,	PUNCT
ejpam-3844	35	71	δ	δ	PROPN
ejpam-3844	35	72	∈	∈	PROPN
ejpam-3844	35	73	b	b	PROPN
ejpam-3844	35	74	)	)	PUNCT
ejpam-3844	35	75	(	(	PUNCT
ejpam-3844	35	76	(	(	PUNCT
ejpam-3844	35	77	β	β	X
ejpam-3844	35	78	∗	∗	X
ejpam-3844	35	79	δ	δ	PROPN
ejpam-3844	35	80	)	)	PUNCT
ejpam-3844	35	81	∗	∗	NOUN
ejpam-3844	35	82	(	(	PUNCT
ejpam-3844	35	83	γ	γ	X
ejpam-3844	35	84	∗	∗	X
ejpam-3844	35	85	δ	δ	PROPN
ejpam-3844	35	86	)	)	PUNCT
ejpam-3844	35	87	≤	≤	PUNCT
ejpam-3844	35	88	β	β	X
ejpam-3844	35	89	∗	∗	X
ejpam-3844	35	90	γ	γ	PROPN
ejpam-3844	35	91	)	)	PUNCT
ejpam-3844	35	92	where	where	SCONJ
ejpam-3844	35	93	β	β	X
ejpam-3844	35	94	≤	≤	X
ejpam-3844	35	95	γ	γ	PROPN
ejpam-3844	35	96	if	if	SCONJ
ejpam-3844	35	97	and	and	CCONJ
ejpam-3844	35	98	only	only	ADV
ejpam-3844	35	99	if	if	SCONJ
ejpam-3844	35	100	β	β	PROPN
ejpam-3844	35	101	∗	∗	X
ejpam-3844	35	102	γ	γ	X
ejpam-3844	35	103	=	=	SYM
ejpam-3844	35	104	0	0	NUM
ejpam-3844	35	105	.	.	PUNCT
ejpam-3844	36	1	any	any	DET
ejpam-3844	36	2	bci	bci	NOUN
ejpam-3844	36	3	-	-	NOUN
ejpam-3844	36	4	algebra	algebra	NOUN
ejpam-3844	36	5	b	b	NOUN
ejpam-3844	36	6	satisfies	satisfy	VERB
ejpam-3844	36	7	the	the	DET
ejpam-3844	36	8	properties	property	NOUN
ejpam-3844	36	9	:	:	PUNCT
ejpam-3844	36	10	•	•	X
ejpam-3844	36	11	(	(	PUNCT
ejpam-3844	36	12	∀β	∀β	PROPN
ejpam-3844	36	13	,	,	PUNCT
ejpam-3844	36	14	γ	γ	X
ejpam-3844	36	15	,	,	PUNCT
ejpam-3844	36	16	δ	δ	PROPN
ejpam-3844	36	17	∈	∈	PROPN
ejpam-3844	36	18	b	b	PROPN
ejpam-3844	36	19	)	)	PUNCT
ejpam-3844	36	20	(	(	PUNCT
ejpam-3844	36	21	0	0	NUM
ejpam-3844	36	22	∗	∗	NOUN
ejpam-3844	36	23	(	(	PUNCT
ejpam-3844	36	24	0	0	NUM
ejpam-3844	36	25	∗	∗	NOUN
ejpam-3844	36	26	(	(	PUNCT
ejpam-3844	36	27	(	(	PUNCT
ejpam-3844	36	28	β	β	X
ejpam-3844	36	29	∗	∗	X
ejpam-3844	36	30	δ	δ	PROPN
ejpam-3844	36	31	)	)	PUNCT
ejpam-3844	36	32	∗	∗	NOUN
ejpam-3844	36	33	(	(	PUNCT
ejpam-3844	36	34	γ	γ	X
ejpam-3844	36	35	∗	∗	X
ejpam-3844	36	36	δ	δ	PROPN
ejpam-3844	36	37	)	)	PUNCT
ejpam-3844	36	38	)	)	PUNCT
ejpam-3844	36	39	)	)	PUNCT
ejpam-3844	37	1	=	=	PUNCT
ejpam-3844	37	2	(	(	PUNCT
ejpam-3844	37	3	0	0	NUM
ejpam-3844	37	4	∗	∗	NUM
ejpam-3844	37	5	γ	γ	NOUN
ejpam-3844	37	6	)	)	PUNCT
ejpam-3844	37	7	∗	∗	NOUN
ejpam-3844	37	8	(	(	PUNCT
ejpam-3844	37	9	0	0	NUM
ejpam-3844	37	10	∗	∗	NOUN
ejpam-3844	37	11	β	β	NOUN
ejpam-3844	37	12	)	)	PUNCT
ejpam-3844	37	13	)	)	PUNCT
ejpam-3844	37	14	,	,	PUNCT
ejpam-3844	37	15	•	•	X
ejpam-3844	37	16	(	(	PUNCT
ejpam-3844	37	17	∀β	∀β	PROPN
ejpam-3844	37	18	,	,	PUNCT
ejpam-3844	37	19	γ	γ	PROPN
ejpam-3844	37	20	∈	∈	PROPN
ejpam-3844	37	21	b	b	X
ejpam-3844	37	22	)	)	PUNCT
ejpam-3844	37	23	(	(	PUNCT
ejpam-3844	37	24	0	0	NUM
ejpam-3844	37	25	∗	∗	NOUN
ejpam-3844	37	26	(	(	PUNCT
ejpam-3844	37	27	0	0	NUM
ejpam-3844	37	28	∗	∗	NOUN
ejpam-3844	37	29	(	(	PUNCT
ejpam-3844	37	30	β	β	X
ejpam-3844	37	31	∗	∗	X
ejpam-3844	37	32	γ	γ	NOUN
ejpam-3844	37	33	)	)	PUNCT
ejpam-3844	37	34	)	)	PUNCT
ejpam-3844	37	35	=	=	SYM
ejpam-3844	38	1	(	(	PUNCT
ejpam-3844	38	2	0	0	NUM
ejpam-3844	38	3	∗	∗	NUM
ejpam-3844	38	4	γ	γ	NOUN
ejpam-3844	38	5	)	)	PUNCT
ejpam-3844	38	6	∗	∗	NOUN
ejpam-3844	38	7	(	(	PUNCT
ejpam-3844	38	8	0	0	NUM
ejpam-3844	38	9	∗	∗	NOUN
ejpam-3844	38	10	β	β	NOUN
ejpam-3844	38	11	)	)	PUNCT
ejpam-3844	38	12	)	)	PUNCT
ejpam-3844	38	13	.	.	PUNCT
ejpam-3844	39	1	for	for	ADP
ejpam-3844	39	2	a	a	DET
ejpam-3844	39	3	nonempty	nonempty	NOUN
ejpam-3844	39	4	subset	subset	VERB
ejpam-3844	39	5	a	a	PRON
ejpam-3844	39	6	of	of	ADP
ejpam-3844	39	7	a	a	DET
ejpam-3844	39	8	bck	bck	PROPN
ejpam-3844	39	9	/	/	SYM
ejpam-3844	39	10	bci	bci	NOUN
ejpam-3844	39	11	-	-	NOUN
ejpam-3844	39	12	algebra	algebra	NOUN
ejpam-3844	39	13	b	b	NOUN
ejpam-3844	39	14	,	,	PUNCT
ejpam-3844	39	15	if	if	SCONJ
ejpam-3844	39	16	β	β	PROPN
ejpam-3844	39	17	∗	∗	VERB
ejpam-3844	39	18	γ	γ	PROPN
ejpam-3844	39	19	∈	∈	PROPN
ejpam-3844	39	20	a	a	PRON
ejpam-3844	39	21	for	for	ADP
ejpam-3844	39	22	all	all	DET
ejpam-3844	39	23	β	β	NOUN
ejpam-3844	39	24	,	,	PUNCT
ejpam-3844	39	25	γ	γ	PROPN
ejpam-3844	39	26	∈	∈	PROPN
ejpam-3844	39	27	a	a	DET
ejpam-3844	39	28	then	then	ADV
ejpam-3844	39	29	a	a	PRON
ejpam-3844	39	30	is	be	AUX
ejpam-3844	39	31	said	say	VERB
ejpam-3844	39	32	to	to	PART
ejpam-3844	39	33	be	be	AUX
ejpam-3844	39	34	a	a	DET
ejpam-3844	39	35	bck	bck	VERB
ejpam-3844	39	36	/	/	SYM
ejpam-3844	39	37	bci	bci	NOUN
ejpam-3844	39	38	-	-	PUNCT
ejpam-3844	39	39	subalgebra	subalgebra	NOUN
ejpam-3844	39	40	of	of	ADP
ejpam-3844	39	41	b.	b.	PROPN
ejpam-3844	39	42	a	a	DET
ejpam-3844	39	43	fuzzy	fuzzy	ADJ
ejpam-3844	39	44	set	set	VERB
ejpam-3844	39	45	%	%	NOUN
ejpam-3844	39	46	in	in	ADP
ejpam-3844	39	47	a	a	DET
ejpam-3844	39	48	bck	bck	VERB
ejpam-3844	39	49	/	/	SYM
ejpam-3844	39	50	bci	bci	NOUN
ejpam-3844	39	51	-	-	NOUN
ejpam-3844	39	52	algebra	algebra	NOUN
ejpam-3844	39	53	b	b	NUM
ejpam-3844	39	54	which	which	PRON
ejpam-3844	39	55	satisfies	satisfy	VERB
ejpam-3844	39	56	(	(	PUNCT
ejpam-3844	39	57	∀β	∀β	PROPN
ejpam-3844	39	58	,	,	PUNCT
ejpam-3844	39	59	γ	γ	PROPN
ejpam-3844	39	60	∈	∈	PROPN
ejpam-3844	39	61	b	b	X
ejpam-3844	39	62	)	)	PUNCT
ejpam-3844	39	63	(	(	PUNCT
ejpam-3844	39	64	%	%	INTJ
ejpam-3844	39	65	(	(	PUNCT
ejpam-3844	39	66	β	β	X
ejpam-3844	39	67	∗	∗	X
ejpam-3844	39	68	γ	γ	PROPN
ejpam-3844	39	69	)	)	PUNCT
ejpam-3844	39	70	≥	≥	NOUN
ejpam-3844	39	71	min{%(β	min{%(β	PROPN
ejpam-3844	39	72	)	)	PUNCT
ejpam-3844	39	73	,	,	PUNCT
ejpam-3844	39	74	%	%	INTJ
ejpam-3844	39	75	(	(	PUNCT
ejpam-3844	39	76	γ	γ	NOUN
ejpam-3844	39	77	)	)	PUNCT
ejpam-3844	39	78	}	}	PUNCT
ejpam-3844	39	79	)	)	PUNCT
ejpam-3844	39	80	(	(	PUNCT
ejpam-3844	39	81	1	1	X
ejpam-3844	39	82	)	)	PUNCT
ejpam-3844	39	83	is	be	AUX
ejpam-3844	39	84	said	say	VERB
ejpam-3844	39	85	to	to	PART
ejpam-3844	39	86	be	be	AUX
ejpam-3844	39	87	a	a	DET
ejpam-3844	39	88	fuzzy	fuzzy	ADJ
ejpam-3844	39	89	bck	bck	NOUN
ejpam-3844	39	90	/	/	SYM
ejpam-3844	39	91	bci	bci	NOUN
ejpam-3844	39	92	-	-	NOUN
ejpam-3844	39	93	algebra	algebra	NOUN
ejpam-3844	39	94	.	.	PUNCT
ejpam-3844	40	1	let	let	VERB
ejpam-3844	40	2	%	%	INTJ
ejpam-3844	40	3	be	be	AUX
ejpam-3844	40	4	a	a	DET
ejpam-3844	40	5	fuzzy	fuzzy	ADJ
ejpam-3844	40	6	set	set	NOUN
ejpam-3844	40	7	in	in	ADP
ejpam-3844	40	8	a	a	DET
ejpam-3844	40	9	set	set	NOUN
ejpam-3844	40	10	b	b	NOUN
ejpam-3844	40	11	defined	define	VERB
ejpam-3844	40	12	by	by	ADP
ejpam-3844	40	13	:	:	PUNCT
ejpam-3844	40	14	%	%	INTJ
ejpam-3844	40	15	(	(	PUNCT
ejpam-3844	40	16	γ	γ	NOUN
ejpam-3844	40	17	)	)	PUNCT
ejpam-3844	40	18	:	:	PUNCT
ejpam-3844	41	1	=	=	SYM
ejpam-3844	41	2	{	{	PUNCT
ejpam-3844	41	3	k	k	PROPN
ejpam-3844	41	4	∈	∈	PROPN
ejpam-3844	41	5	(	(	PUNCT
ejpam-3844	41	6	0	0	NUM
ejpam-3844	41	7	,	,	PUNCT
ejpam-3844	41	8	1	1	NUM
ejpam-3844	41	9	]	]	PUNCT
ejpam-3844	41	10	if	if	SCONJ
ejpam-3844	41	11	γ	γ	X
ejpam-3844	41	12	=	=	SYM
ejpam-3844	41	13	β	β	X
ejpam-3844	41	14	,	,	PUNCT
ejpam-3844	41	15	0	0	PUNCT
ejpam-3844	42	1	if	if	SCONJ
ejpam-3844	42	2	γ	γ	PROPN
ejpam-3844	42	3	6=	6=	ADP
ejpam-3844	42	4	β	β	PROPN
ejpam-3844	42	5	.	.	PUNCT
ejpam-3844	43	1	then	then	ADV
ejpam-3844	43	2	%	%	INTJ
ejpam-3844	43	3	is	be	AUX
ejpam-3844	43	4	called	call	VERB
ejpam-3844	43	5	a	a	DET
ejpam-3844	43	6	fuzzy	fuzzy	ADJ
ejpam-3844	43	7	point	point	NOUN
ejpam-3844	43	8	with	with	ADP
ejpam-3844	43	9	support	support	NOUN
ejpam-3844	43	10	β	β	NOUN
ejpam-3844	43	11	and	and	CCONJ
ejpam-3844	43	12	value	value	PROPN
ejpam-3844	43	13	k	k	PROPN
ejpam-3844	43	14	and	and	CCONJ
ejpam-3844	43	15	is	be	AUX
ejpam-3844	43	16	denoted	denote	VERB
ejpam-3844	43	17	by	by	ADP
ejpam-3844	43	18	βk	βk	NOUN
ejpam-3844	43	19	.	.	PROPN
ejpam-3844	44	1	for	for	ADP
ejpam-3844	44	2	an	an	DET
ejpam-3844	44	3	initial	initial	ADJ
ejpam-3844	44	4	universe	universe	NOUN
ejpam-3844	44	5	set	set	VERB
ejpam-3844	44	6	u	u	NOUN
ejpam-3844	44	7	,	,	PUNCT
ejpam-3844	44	8	let	let	VERB
ejpam-3844	44	9	p(u	p(u	ADJ
ejpam-3844	44	10	)	)	PUNCT
ejpam-3844	44	11	denotes	denote	VERB
ejpam-3844	44	12	the	the	DET
ejpam-3844	44	13	power	power	NOUN
ejpam-3844	44	14	set	set	NOUN
ejpam-3844	44	15	of	of	ADP
ejpam-3844	44	16	u	u	NOUN
ejpam-3844	44	17	and	and	CCONJ
ejpam-3844	44	18	for	for	ADP
ejpam-3844	44	19	a	a	DET
ejpam-3844	44	20	set	set	NOUN
ejpam-3844	44	21	of	of	ADP
ejpam-3844	44	22	parameters	parameter	NOUN
ejpam-3844	44	23	e	e	NOUN
ejpam-3844	44	24	,	,	PUNCT
ejpam-3844	44	25	let	let	VERB
ejpam-3844	44	26	m	m	PROPN
ejpam-3844	44	27	⊂	⊂	PROPN
ejpam-3844	44	28	e.	e.	PROPN
ejpam-3844	44	29	molodtsov	molodtsov	PROPN
ejpam-3844	45	1	[	[	X
ejpam-3844	45	2	12	12	NUM
ejpam-3844	45	3	]	]	PUNCT
ejpam-3844	45	4	defined	define	VERB
ejpam-3844	45	5	the	the	DET
ejpam-3844	45	6	soft	soft	ADJ
ejpam-3844	45	7	set	set	NOUN
ejpam-3844	45	8	as	as	SCONJ
ejpam-3844	45	9	follows	follow	VERB
ejpam-3844	45	10	.	.	PUNCT
ejpam-3844	46	1	definition	definition	NOUN
ejpam-3844	46	2	1	1	NUM
ejpam-3844	46	3	(	(	PUNCT
ejpam-3844	46	4	[	[	X
ejpam-3844	46	5	12	12	NUM
ejpam-3844	46	6	]	]	NUM
ejpam-3844	46	7	)	)	PUNCT
ejpam-3844	46	8	.	.	PUNCT
ejpam-3844	47	1	a	a	DET
ejpam-3844	47	2	soft	soft	ADJ
ejpam-3844	47	3	set	set	NOUN
ejpam-3844	47	4	over	over	ADP
ejpam-3844	47	5	u	u	NOUN
ejpam-3844	47	6	,	,	PUNCT
ejpam-3844	47	7	is	be	AUX
ejpam-3844	47	8	a	a	DET
ejpam-3844	47	9	pair	pair	NOUN
ejpam-3844	47	10	(	(	PUNCT
ejpam-3844	47	11	µ,m	µ,m	NOUN
ejpam-3844	47	12	)	)	PUNCT
ejpam-3844	47	13	where	where	SCONJ
ejpam-3844	47	14	µ	µ	NOUN
ejpam-3844	47	15	is	be	AUX
ejpam-3844	47	16	a	a	DET
ejpam-3844	47	17	mapping	mapping	NOUN
ejpam-3844	47	18	given	give	VERB
ejpam-3844	47	19	by	by	ADP
ejpam-3844	47	20	µ	µ	X
ejpam-3844	47	21	:	:	PUNCT
ejpam-3844	47	22	m	m	VERB
ejpam-3844	47	23	→	→	SYM
ejpam-3844	47	24	p(u	p(u	ADJ
ejpam-3844	47	25	)	)	PUNCT
ejpam-3844	47	26	.	.	PUNCT
ejpam-3844	48	1	al	al	PROPN
ejpam-3844	48	2	-	-	PUNCT
ejpam-3844	48	3	kadi	kadi	PROPN
ejpam-3844	48	4	,	,	PUNCT
ejpam-3844	48	5	muhiuddin	muhiuddin	NOUN
ejpam-3844	48	6	/	/	SYM
ejpam-3844	48	7	eur	eur	PROPN
ejpam-3844	48	8	.	.	PUNCT
ejpam-3844	49	1	j.	j.	PROPN
ejpam-3844	49	2	pure	pure	PROPN
ejpam-3844	49	3	appl	appl	PROPN
ejpam-3844	49	4	.	.	PROPN
ejpam-3844	49	5	math	math	PROPN
ejpam-3844	49	6	,	,	PUNCT
ejpam-3844	49	7	13	13	NUM
ejpam-3844	49	8	(	(	PUNCT
ejpam-3844	49	9	4	4	NUM
ejpam-3844	49	10	)	)	PUNCT
ejpam-3844	49	11	(	(	PUNCT
ejpam-3844	49	12	2020	2020	NUM
ejpam-3844	49	13	)	)	PUNCT
ejpam-3844	49	14	,	,	PUNCT
ejpam-3844	49	15	939	939	NUM
ejpam-3844	49	16	-	-	SYM
ejpam-3844	49	17	947	947	NUM
ejpam-3844	49	18	941	941	NUM
ejpam-3844	49	19	clearly	clearly	ADV
ejpam-3844	49	20	,	,	PUNCT
ejpam-3844	49	21	a	a	DET
ejpam-3844	49	22	soft	soft	ADJ
ejpam-3844	49	23	set	set	NOUN
ejpam-3844	49	24	is	be	AUX
ejpam-3844	49	25	not	not	PART
ejpam-3844	49	26	a	a	DET
ejpam-3844	49	27	set	set	NOUN
ejpam-3844	49	28	.	.	PUNCT
ejpam-3844	50	1	several	several	ADJ
ejpam-3844	50	2	examples	example	NOUN
ejpam-3844	50	3	have	have	AUX
ejpam-3844	50	4	been	be	AUX
ejpam-3844	50	5	considered	consider	VERB
ejpam-3844	50	6	by	by	ADP
ejpam-3844	50	7	molodtsov	molodtsov	NOUN
ejpam-3844	50	8	in	in	ADP
ejpam-3844	50	9	[	[	X
ejpam-3844	50	10	12	12	NUM
ejpam-3844	50	11	]	]	PUNCT
ejpam-3844	50	12	.	.	PUNCT
ejpam-3844	51	1	definition	definition	NOUN
ejpam-3844	51	2	2	2	NUM
ejpam-3844	51	3	(	(	PUNCT
ejpam-3844	51	4	[	[	X
ejpam-3844	51	5	10	10	NUM
ejpam-3844	51	6	]	]	NUM
ejpam-3844	51	7	)	)	PUNCT
ejpam-3844	51	8	.	.	PUNCT
ejpam-3844	52	1	let	let	VERB
ejpam-3844	52	2	e	e	PRON
ejpam-3844	52	3	be	be	AUX
ejpam-3844	52	4	a	a	DET
ejpam-3844	52	5	set	set	NOUN
ejpam-3844	52	6	of	of	ADP
ejpam-3844	52	7	parameters	parameter	NOUN
ejpam-3844	52	8	and	and	CCONJ
ejpam-3844	52	9	m	m	PROPN
ejpam-3844	52	10	⊆	⊆	NUM
ejpam-3844	52	11	e.	e.	PROPN
ejpam-3844	52	12	a	a	DET
ejpam-3844	52	13	fuzzy	fuzzy	ADJ
ejpam-3844	52	14	soft	soft	ADJ
ejpam-3844	52	15	set	set	NOUN
ejpam-3844	52	16	over	over	ADP
ejpam-3844	52	17	an	an	DET
ejpam-3844	52	18	initial	initial	ADJ
ejpam-3844	52	19	universe	universe	NOUN
ejpam-3844	52	20	set	set	NOUN
ejpam-3844	52	21	u	u	NOUN
ejpam-3844	52	22	is	be	AUX
ejpam-3844	52	23	a	a	DET
ejpam-3844	52	24	pair	pair	NOUN
ejpam-3844	52	25	(	(	PUNCT
ejpam-3844	52	26	µ̃,m	µ̃,m	PROPN
ejpam-3844	52	27	)	)	PUNCT
ejpam-3844	52	28	where	where	SCONJ
ejpam-3844	52	29	µ̃	µ̃	PROPN
ejpam-3844	52	30	is	be	AUX
ejpam-3844	52	31	a	a	DET
ejpam-3844	52	32	mapping	mapping	NOUN
ejpam-3844	52	33	from	from	ADP
ejpam-3844	52	34	m	m	PROPN
ejpam-3844	52	35	to	to	ADP
ejpam-3844	52	36	the	the	DET
ejpam-3844	52	37	set	set	NOUN
ejpam-3844	52	38	of	of	ADP
ejpam-3844	52	39	all	all	DET
ejpam-3844	52	40	fuzzy	fuzzy	ADJ
ejpam-3844	52	41	sets	set	NOUN
ejpam-3844	52	42	in	in	ADP
ejpam-3844	52	43	u	u	PROPN
ejpam-3844	52	44	.	.	PUNCT
ejpam-3844	53	1	in	in	ADP
ejpam-3844	53	2	general	general	ADJ
ejpam-3844	53	3	,	,	PUNCT
ejpam-3844	53	4	for	for	ADP
ejpam-3844	53	5	every	every	DET
ejpam-3844	53	6	m	m	NOUN
ejpam-3844	53	7	∈m	∈m	NOUN
ejpam-3844	53	8	,	,	PUNCT
ejpam-3844	53	9	µ̃[m	µ̃[m	X
ejpam-3844	53	10	]	]	PUNCT
ejpam-3844	53	11	is	be	AUX
ejpam-3844	53	12	a	a	DET
ejpam-3844	53	13	fuzzy	fuzzy	ADJ
ejpam-3844	53	14	set	set	NOUN
ejpam-3844	53	15	in	in	ADP
ejpam-3844	53	16	u	u	NOUN
ejpam-3844	53	17	and	and	CCONJ
ejpam-3844	53	18	it	it	PRON
ejpam-3844	53	19	is	be	AUX
ejpam-3844	53	20	called	call	VERB
ejpam-3844	53	21	fuzzy	fuzzy	ADJ
ejpam-3844	53	22	value	value	NOUN
ejpam-3844	53	23	set	set	NOUN
ejpam-3844	53	24	of	of	ADP
ejpam-3844	53	25	parameter	parameter	NOUN
ejpam-3844	53	26	m.	m.	NOUN
ejpam-3844	53	27	definition	definition	NOUN
ejpam-3844	53	28	3	3	NUM
ejpam-3844	53	29	(	(	PUNCT
ejpam-3844	53	30	[	[	X
ejpam-3844	53	31	10	10	NUM
ejpam-3844	53	32	]	]	NUM
ejpam-3844	53	33	)	)	PUNCT
ejpam-3844	53	34	.	.	PUNCT
ejpam-3844	54	1	the	the	DET
ejpam-3844	54	2	“	"	PUNCT
ejpam-3844	54	3	union	union	NOUN
ejpam-3844	54	4	”	"	PUNCT
ejpam-3844	54	5	of	of	ADP
ejpam-3844	54	6	two	two	NUM
ejpam-3844	54	7	fuzzy	fuzzy	ADJ
ejpam-3844	54	8	soft	soft	ADJ
ejpam-3844	54	9	sets	set	NOUN
ejpam-3844	54	10	(	(	PUNCT
ejpam-3844	54	11	µ̃,m	µ̃,m	PROPN
ejpam-3844	54	12	)	)	PUNCT
ejpam-3844	54	13	and	and	CCONJ
ejpam-3844	54	14	(	(	PUNCT
ejpam-3844	54	15	η̃	η̃	PROPN
ejpam-3844	54	16	,	,	PUNCT
ejpam-3844	54	17	n	n	CCONJ
ejpam-3844	54	18	)	)	PUNCT
ejpam-3844	54	19	over	over	ADP
ejpam-3844	54	20	a	a	DET
ejpam-3844	54	21	common	common	ADJ
ejpam-3844	54	22	universe	universe	NOUN
ejpam-3844	54	23	u	u	NOUN
ejpam-3844	54	24	,	,	PUNCT
ejpam-3844	54	25	is	be	AUX
ejpam-3844	54	26	the	the	DET
ejpam-3844	54	27	fuzzy	fuzzy	ADJ
ejpam-3844	54	28	soft	soft	ADJ
ejpam-3844	54	29	set	set	NOUN
ejpam-3844	54	30	(	(	PUNCT
ejpam-3844	54	31	ξ̃	ξ̃	PROPN
ejpam-3844	54	32	,	,	PUNCT
ejpam-3844	54	33	q	q	NOUN
ejpam-3844	54	34	)	)	PUNCT
ejpam-3844	54	35	satisfying	satisfy	VERB
ejpam-3844	54	36	the	the	DET
ejpam-3844	54	37	following	follow	VERB
ejpam-3844	54	38	conditions	condition	NOUN
ejpam-3844	54	39	:	:	PUNCT
ejpam-3844	54	40	(	(	PUNCT
ejpam-3844	54	41	i	i	NOUN
ejpam-3844	54	42	)	)	PUNCT
ejpam-3844	54	43	q	q	PROPN
ejpam-3844	55	1	=	=	PUNCT
ejpam-3844	55	2	m	m	VERB
ejpam-3844	55	3	∪n	∪n	NUM
ejpam-3844	55	4	,	,	PUNCT
ejpam-3844	55	5	(	(	PUNCT
ejpam-3844	55	6	ii	ii	NOUN
ejpam-3844	55	7	)	)	PUNCT
ejpam-3844	55	8	for	for	ADP
ejpam-3844	55	9	all	all	DET
ejpam-3844	55	10	q	q	PROPN
ejpam-3844	55	11	∈	∈	PROPN
ejpam-3844	55	12	q	q	NOUN
ejpam-3844	55	13	,	,	PUNCT
ejpam-3844	55	14	ξ̃[q	ξ̃[q	PROPN
ejpam-3844	55	15	]	]	X
ejpam-3844	55	16	=	=	PUNCT
ejpam-3844	55	17			PUNCT
ejpam-3844	55	18	µ̃[q	µ̃[q	X
ejpam-3844	55	19	]	]	X
ejpam-3844	55	20	if	if	SCONJ
ejpam-3844	55	21	q	q	X
ejpam-3844	55	22	∈m	∈m	NOUN
ejpam-3844	55	23	\n	\n	PROPN
ejpam-3844	55	24	,	,	PUNCT
ejpam-3844	55	25	η̃[q	η̃[q	NOUN
ejpam-3844	55	26	]	]	PUNCT
ejpam-3844	55	27	if	if	SCONJ
ejpam-3844	55	28	q	q	PROPN
ejpam-3844	55	29	∈	∈	PROPN
ejpam-3844	55	30	n	n	PRON
ejpam-3844	55	31	\m	\m	NOUN
ejpam-3844	55	32	,	,	PUNCT
ejpam-3844	55	33	µ̃[q	µ̃[q	PROPN
ejpam-3844	55	34	]	]	X
ejpam-3844	55	35	∪	∪	ADP
ejpam-3844	55	36	η̃[q	η̃[q	NOUN
ejpam-3844	55	37	]	]	PUNCT
ejpam-3844	55	38	if	if	SCONJ
ejpam-3844	55	39	q	q	X
ejpam-3844	55	40	∈m	∈m	NOUN
ejpam-3844	55	41	∩n	∩n	NOUN
ejpam-3844	55	42	.	.	PUNCT
ejpam-3844	56	1	we	we	PRON
ejpam-3844	56	2	write	write	VERB
ejpam-3844	56	3	(	(	PUNCT
ejpam-3844	56	4	µ̃,m	µ̃,m	PROPN
ejpam-3844	56	5	)	)	PUNCT
ejpam-3844	56	6	∪̃	∪̃	PROPN
ejpam-3844	56	7	(	(	PUNCT
ejpam-3844	56	8	η̃	η̃	PROPN
ejpam-3844	56	9	,	,	PUNCT
ejpam-3844	56	10	n	n	CCONJ
ejpam-3844	56	11	)	)	PUNCT
ejpam-3844	56	12	=	=	SYM
ejpam-3844	56	13	(	(	PUNCT
ejpam-3844	56	14	ξ̃	ξ̃	PROPN
ejpam-3844	56	15	,	,	PUNCT
ejpam-3844	56	16	q	q	NOUN
ejpam-3844	56	17	)	)	PUNCT
ejpam-3844	56	18	.	.	PUNCT
ejpam-3844	57	1	definition	definition	NOUN
ejpam-3844	57	2	4	4	NUM
ejpam-3844	57	3	(	(	PUNCT
ejpam-3844	57	4	[	[	X
ejpam-3844	57	5	10	10	NUM
ejpam-3844	57	6	]	]	NUM
ejpam-3844	57	7	)	)	PUNCT
ejpam-3844	57	8	.	.	PUNCT
ejpam-3844	58	1	for	for	ADP
ejpam-3844	58	2	two	two	NUM
ejpam-3844	58	3	fuzzy	fuzzy	ADJ
ejpam-3844	58	4	soft	soft	ADJ
ejpam-3844	58	5	sets	set	NOUN
ejpam-3844	58	6	(	(	PUNCT
ejpam-3844	58	7	µ̃,m	µ̃,m	PROPN
ejpam-3844	58	8	)	)	PUNCT
ejpam-3844	58	9	and	and	CCONJ
ejpam-3844	58	10	(	(	PUNCT
ejpam-3844	58	11	η̃	η̃	PROPN
ejpam-3844	58	12	,	,	PUNCT
ejpam-3844	58	13	n	n	CCONJ
ejpam-3844	58	14	)	)	PUNCT
ejpam-3844	58	15	over	over	ADP
ejpam-3844	58	16	a	a	DET
ejpam-3844	58	17	common	common	ADJ
ejpam-3844	58	18	universe	universe	NOUN
ejpam-3844	58	19	u	u	NOUN
ejpam-3844	58	20	,	,	PUNCT
ejpam-3844	58	21	the	the	DET
ejpam-3844	58	22	(	(	PUNCT
ejpam-3844	58	23	µ̃,m	µ̃,m	PROPN
ejpam-3844	58	24	)	)	PUNCT
ejpam-3844	58	25	“	"	PUNCT
ejpam-3844	58	26	and	and	CCONJ
ejpam-3844	58	27	”	"	PUNCT
ejpam-3844	58	28	(	(	PUNCT
ejpam-3844	58	29	η̃	η̃	PROPN
ejpam-3844	58	30	,	,	PUNCT
ejpam-3844	58	31	n	n	CCONJ
ejpam-3844	58	32	)	)	PUNCT
ejpam-3844	58	33	denoted	denote	VERB
ejpam-3844	58	34	by	by	ADP
ejpam-3844	58	35	(	(	PUNCT
ejpam-3844	58	36	µ̃,m	µ̃,m	PROPN
ejpam-3844	58	37	)	)	PUNCT
ejpam-3844	58	38	∧̃	∧̃	PROPN
ejpam-3844	58	39	(	(	PUNCT
ejpam-3844	58	40	η̃	η̃	PROPN
ejpam-3844	58	41	,	,	PUNCT
ejpam-3844	58	42	n	n	CCONJ
ejpam-3844	58	43	)	)	PUNCT
ejpam-3844	58	44	is	be	AUX
ejpam-3844	58	45	defined	define	VERB
ejpam-3844	58	46	by	by	ADP
ejpam-3844	58	47	(	(	PUNCT
ejpam-3844	58	48	µ̃,m	µ̃,m	PROPN
ejpam-3844	58	49	)	)	PUNCT
ejpam-3844	58	50	∧̃	∧̃	PROPN
ejpam-3844	58	51	(	(	PUNCT
ejpam-3844	58	52	η̃	η̃	PROPN
ejpam-3844	58	53	,	,	PUNCT
ejpam-3844	58	54	n	n	CCONJ
ejpam-3844	58	55	)	)	PUNCT
ejpam-3844	58	56	=	=	SYM
ejpam-3844	58	57	(	(	PUNCT
ejpam-3844	58	58	ξ̃,m	ξ̃,m	PROPN
ejpam-3844	58	59	×n	×n	PROPN
ejpam-3844	58	60	)	)	PUNCT
ejpam-3844	58	61	,	,	PUNCT
ejpam-3844	58	62	where	where	SCONJ
ejpam-3844	58	63	ξ̃[m	ξ̃[m	X
ejpam-3844	58	64	,	,	PUNCT
ejpam-3844	58	65	n	n	CCONJ
ejpam-3844	58	66	]	]	PUNCT
ejpam-3844	58	67	=	=	SYM
ejpam-3844	58	68	µ̃[m	µ̃[m	X
ejpam-3844	58	69	]	]	PUNCT
ejpam-3844	58	70	∩	∩	NOUN
ejpam-3844	58	71	η̃[n	η̃[n	NOUN
ejpam-3844	58	72	]	]	PUNCT
ejpam-3844	58	73	for	for	ADP
ejpam-3844	58	74	all	all	PRON
ejpam-3844	58	75	(	(	PUNCT
ejpam-3844	58	76	m	m	PROPN
ejpam-3844	58	77	,	,	PUNCT
ejpam-3844	58	78	n	n	CCONJ
ejpam-3844	58	79	)	)	PUNCT
ejpam-3844	58	80	∈m	∈m	ADP
ejpam-3844	58	81	×n	×n	NUM
ejpam-3844	58	82	.	.	PUNCT
ejpam-3844	59	1	definition	definition	NOUN
ejpam-3844	59	2	5	5	NUM
ejpam-3844	59	3	(	(	PUNCT
ejpam-3844	59	4	[	[	X
ejpam-3844	59	5	1	1	NUM
ejpam-3844	59	6	]	]	NUM
ejpam-3844	59	7	)	)	PUNCT
ejpam-3844	59	8	.	.	PUNCT
ejpam-3844	60	1	the	the	DET
ejpam-3844	60	2	“	"	PUNCT
ejpam-3844	60	3	extended	extended	ADJ
ejpam-3844	60	4	intersection	intersection	NOUN
ejpam-3844	60	5	”	"	PUNCT
ejpam-3844	60	6	of	of	ADP
ejpam-3844	60	7	two	two	NUM
ejpam-3844	60	8	soft	soft	ADJ
ejpam-3844	60	9	sets	set	NOUN
ejpam-3844	60	10	(	(	PUNCT
ejpam-3844	60	11	µ̃,m	µ̃,m	PROPN
ejpam-3844	60	12	)	)	PUNCT
ejpam-3844	60	13	and	and	CCONJ
ejpam-3844	60	14	(	(	PUNCT
ejpam-3844	60	15	η̃	η̃	PROPN
ejpam-3844	60	16	,	,	PUNCT
ejpam-3844	60	17	n	n	CCONJ
ejpam-3844	60	18	)	)	PUNCT
ejpam-3844	60	19	over	over	ADP
ejpam-3844	60	20	a	a	DET
ejpam-3844	60	21	common	common	ADJ
ejpam-3844	60	22	universe	universe	NOUN
ejpam-3844	60	23	u	u	NOUN
ejpam-3844	60	24	,	,	PUNCT
ejpam-3844	60	25	is	be	AUX
ejpam-3844	60	26	the	the	DET
ejpam-3844	60	27	soft	soft	ADJ
ejpam-3844	60	28	set	set	NOUN
ejpam-3844	60	29	(	(	PUNCT
ejpam-3844	60	30	ξ̃	ξ̃	PROPN
ejpam-3844	60	31	,	,	PUNCT
ejpam-3844	60	32	q	q	NOUN
ejpam-3844	60	33	)	)	PUNCT
ejpam-3844	60	34	satisfying	satisfy	VERB
ejpam-3844	60	35	the	the	DET
ejpam-3844	60	36	following	follow	VERB
ejpam-3844	60	37	conditions	condition	NOUN
ejpam-3844	60	38	:	:	PUNCT
ejpam-3844	60	39	(	(	PUNCT
ejpam-3844	60	40	i	i	NOUN
ejpam-3844	60	41	)	)	PUNCT
ejpam-3844	60	42	q	q	PROPN
ejpam-3844	61	1	=	=	PUNCT
ejpam-3844	61	2	m	m	VERB
ejpam-3844	61	3	∪n	∪n	NUM
ejpam-3844	61	4	,	,	PUNCT
ejpam-3844	61	5	(	(	PUNCT
ejpam-3844	61	6	ii	ii	NOUN
ejpam-3844	61	7	)	)	PUNCT
ejpam-3844	61	8	for	for	ADP
ejpam-3844	61	9	all	all	DET
ejpam-3844	61	10	q	q	PROPN
ejpam-3844	61	11	∈	∈	PROPN
ejpam-3844	61	12	q	q	NOUN
ejpam-3844	61	13	,	,	PUNCT
ejpam-3844	61	14	ξ̃[q	ξ̃[q	PROPN
ejpam-3844	61	15	]	]	X
ejpam-3844	61	16	=	=	PUNCT
ejpam-3844	61	17			PUNCT
ejpam-3844	61	18	µ̃[q	µ̃[q	X
ejpam-3844	61	19	]	]	X
ejpam-3844	61	20	if	if	SCONJ
ejpam-3844	61	21	q	q	X
ejpam-3844	61	22	∈m	∈m	NOUN
ejpam-3844	61	23	\n	\n	PROPN
ejpam-3844	61	24	,	,	PUNCT
ejpam-3844	61	25	η̃[q	η̃[q	NOUN
ejpam-3844	61	26	]	]	PUNCT
ejpam-3844	61	27	if	if	SCONJ
ejpam-3844	61	28	q	q	PROPN
ejpam-3844	61	29	∈	∈	PROPN
ejpam-3844	61	30	n	n	PRON
ejpam-3844	61	31	\m	\m	NOUN
ejpam-3844	61	32	,	,	PUNCT
ejpam-3844	61	33	µ̃[q	µ̃[q	PROPN
ejpam-3844	61	34	]	]	X
ejpam-3844	61	35	∩	∩	ADJ
ejpam-3844	61	36	η̃[q	η̃[q	NOUN
ejpam-3844	61	37	]	]	X
ejpam-3844	61	38	if	if	SCONJ
ejpam-3844	61	39	q	q	X
ejpam-3844	61	40	∈m	∈m	NOUN
ejpam-3844	61	41	∩n	∩n	NOUN
ejpam-3844	61	42	.	.	PUNCT
ejpam-3844	62	1	we	we	PRON
ejpam-3844	62	2	write	write	VERB
ejpam-3844	62	3	(	(	PUNCT
ejpam-3844	62	4	µ̃,m	µ̃,m	PROPN
ejpam-3844	62	5	)	)	PUNCT
ejpam-3844	62	6	∩̃	∩̃	PUNCT
ejpam-3844	63	1	e	e	X
ejpam-3844	63	2	(	(	PUNCT
ejpam-3844	63	3	η̃	η̃	PROPN
ejpam-3844	63	4	,	,	PUNCT
ejpam-3844	63	5	n	n	CCONJ
ejpam-3844	63	6	)	)	PUNCT
ejpam-3844	63	7	=	=	SYM
ejpam-3844	63	8	(	(	PUNCT
ejpam-3844	63	9	ξ̃	ξ̃	PROPN
ejpam-3844	63	10	,	,	PUNCT
ejpam-3844	63	11	q	q	NOUN
ejpam-3844	63	12	)	)	PUNCT
ejpam-3844	63	13	.	.	PUNCT
ejpam-3844	64	1	definition	definition	NOUN
ejpam-3844	64	2	6	6	NUM
ejpam-3844	64	3	(	(	PUNCT
ejpam-3844	64	4	[	[	X
ejpam-3844	64	5	1	1	NUM
ejpam-3844	64	6	]	]	NUM
ejpam-3844	64	7	)	)	PUNCT
ejpam-3844	64	8	.	.	PUNCT
ejpam-3844	65	1	the	the	DET
ejpam-3844	65	2	“	"	PUNCT
ejpam-3844	65	3	restricted	restricted	ADJ
ejpam-3844	65	4	intersection	intersection	NOUN
ejpam-3844	65	5	”	"	PUNCT
ejpam-3844	65	6	of	of	ADP
ejpam-3844	65	7	two	two	NUM
ejpam-3844	65	8	soft	soft	ADJ
ejpam-3844	65	9	sets	set	NOUN
ejpam-3844	65	10	(	(	PUNCT
ejpam-3844	65	11	µ̃,m	µ̃,m	PROPN
ejpam-3844	65	12	)	)	PUNCT
ejpam-3844	65	13	and	and	CCONJ
ejpam-3844	65	14	(	(	PUNCT
ejpam-3844	65	15	η̃	η̃	PROPN
ejpam-3844	65	16	,	,	PUNCT
ejpam-3844	65	17	n	n	CCONJ
ejpam-3844	65	18	)	)	PUNCT
ejpam-3844	65	19	over	over	ADP
ejpam-3844	65	20	a	a	DET
ejpam-3844	65	21	common	common	ADJ
ejpam-3844	65	22	universe	universe	NOUN
ejpam-3844	65	23	u	u	NOUN
ejpam-3844	65	24	where	where	SCONJ
ejpam-3844	65	25	m	m	VERB
ejpam-3844	65	26	∩n	∩n	NOUN
ejpam-3844	65	27	6=	6=	NUM
ejpam-3844	65	28	∅	∅	NOUN
ejpam-3844	65	29	is	be	AUX
ejpam-3844	65	30	denoted	denote	VERB
ejpam-3844	65	31	by	by	ADP
ejpam-3844	65	32	(	(	PUNCT
ejpam-3844	65	33	µ̃,m	µ̃,m	PROPN
ejpam-3844	65	34	)	)	PUNCT
ejpam-3844	65	35	∩̃	∩̃	PUNCT
ejpam-3844	66	1	r	r	NOUN
ejpam-3844	66	2	(	(	PUNCT
ejpam-3844	66	3	η̃	η̃	PROPN
ejpam-3844	66	4	,	,	PUNCT
ejpam-3844	66	5	n	n	CCONJ
ejpam-3844	66	6	)	)	PUNCT
ejpam-3844	66	7	and	and	CCONJ
ejpam-3844	66	8	is	be	AUX
ejpam-3844	66	9	defined	define	VERB
ejpam-3844	66	10	as	as	ADP
ejpam-3844	66	11	(	(	PUNCT
ejpam-3844	66	12	µ̃,m	µ̃,m	PROPN
ejpam-3844	66	13	)	)	PUNCT
ejpam-3844	66	14	∩̃	∩̃	PUNCT
ejpam-3844	67	1	r	r	NOUN
ejpam-3844	67	2	(	(	PUNCT
ejpam-3844	67	3	η̃	η̃	PROPN
ejpam-3844	67	4	,	,	PUNCT
ejpam-3844	67	5	n	n	CCONJ
ejpam-3844	67	6	)	)	PUNCT
ejpam-3844	67	7	=	=	SYM
ejpam-3844	67	8	(	(	PUNCT
ejpam-3844	67	9	ξ̃	ξ̃	PROPN
ejpam-3844	67	10	,	,	PUNCT
ejpam-3844	67	11	q	q	NOUN
ejpam-3844	67	12	)	)	PUNCT
ejpam-3844	67	13	,	,	PUNCT
ejpam-3844	68	1	where	where	SCONJ
ejpam-3844	68	2	q	q	NOUN
ejpam-3844	68	3	=	=	NOUN
ejpam-3844	68	4	m	m	NOUN
ejpam-3844	68	5	∩n	∩n	NOUN
ejpam-3844	68	6	and	and	CCONJ
ejpam-3844	68	7	for	for	ADP
ejpam-3844	68	8	all	all	DET
ejpam-3844	68	9	q	q	PROPN
ejpam-3844	68	10	∈	∈	PROPN
ejpam-3844	68	11	q	q	NOUN
ejpam-3844	68	12	,	,	PUNCT
ejpam-3844	68	13	ξ̃[q	ξ̃[q	PROPN
ejpam-3844	68	14	]	]	X
ejpam-3844	68	15	=	=	SYM
ejpam-3844	68	16	µ̃[q	µ̃[q	X
ejpam-3844	68	17	]	]	X
ejpam-3844	68	18	∩	∩	ADJ
ejpam-3844	68	19	η̃[q	η̃[q	NOUN
ejpam-3844	68	20	]	]	PUNCT
ejpam-3844	68	21	.	.	PUNCT
ejpam-3844	69	1	al	al	PROPN
ejpam-3844	69	2	-	-	PUNCT
ejpam-3844	69	3	kadi	kadi	PROPN
ejpam-3844	69	4	,	,	PUNCT
ejpam-3844	69	5	muhiuddin	muhiuddin	NOUN
ejpam-3844	69	6	/	/	SYM
ejpam-3844	69	7	eur	eur	PROPN
ejpam-3844	69	8	.	.	PUNCT
ejpam-3844	70	1	j.	j.	PROPN
ejpam-3844	70	2	pure	pure	PROPN
ejpam-3844	70	3	appl	appl	PROPN
ejpam-3844	70	4	.	.	PROPN
ejpam-3844	70	5	math	math	PROPN
ejpam-3844	70	6	,	,	PUNCT
ejpam-3844	70	7	13	13	NUM
ejpam-3844	70	8	(	(	PUNCT
ejpam-3844	70	9	4	4	NUM
ejpam-3844	70	10	)	)	PUNCT
ejpam-3844	70	11	(	(	PUNCT
ejpam-3844	70	12	2020	2020	NUM
ejpam-3844	70	13	)	)	PUNCT
ejpam-3844	70	14	,	,	PUNCT
ejpam-3844	70	15	939	939	NUM
ejpam-3844	70	16	-	-	SYM
ejpam-3844	70	17	947	947	NUM
ejpam-3844	70	18	942	942	NUM
ejpam-3844	70	19	3	3	NUM
ejpam-3844	70	20	.	.	PUNCT
ejpam-3844	70	21	fuzzy	fuzzy	ADJ
ejpam-3844	70	22	soft	soft	ADJ
ejpam-3844	70	23	bck	bck	NOUN
ejpam-3844	70	24	/	/	SYM
ejpam-3844	70	25	bci	bci	NOUN
ejpam-3844	70	26	-	-	PUNCT
ejpam-3844	70	27	algebras	algebra	NOUN
ejpam-3844	70	28	in	in	ADP
ejpam-3844	70	29	what	what	PRON
ejpam-3844	70	30	follows	follow	VERB
ejpam-3844	70	31	,	,	PUNCT
ejpam-3844	70	32	b	b	PRON
ejpam-3844	70	33	is	be	AUX
ejpam-3844	70	34	a	a	DET
ejpam-3844	70	35	bck	bck	VERB
ejpam-3844	70	36	/	/	SYM
ejpam-3844	70	37	bci	bci	NOUN
ejpam-3844	70	38	-	-	NOUN
ejpam-3844	70	39	algebra	algebra	NOUN
ejpam-3844	70	40	and	and	CCONJ
ejpam-3844	70	41	e	e	NOUN
ejpam-3844	70	42	is	be	AUX
ejpam-3844	70	43	a	a	DET
ejpam-3844	70	44	set	set	NOUN
ejpam-3844	70	45	of	of	ADP
ejpam-3844	70	46	parameters	parameter	NOUN
ejpam-3844	70	47	.	.	PUNCT
ejpam-3844	71	1	definition	definition	NOUN
ejpam-3844	71	2	7	7	NUM
ejpam-3844	71	3	(	(	PUNCT
ejpam-3844	71	4	[	[	X
ejpam-3844	71	5	8	8	NUM
ejpam-3844	71	6	]	]	NUM
ejpam-3844	71	7	)	)	PUNCT
ejpam-3844	71	8	.	.	PUNCT
ejpam-3844	72	1	for	for	ADP
ejpam-3844	72	2	a	a	DET
ejpam-3844	72	3	fuzzy	fuzzy	ADJ
ejpam-3844	72	4	soft	soft	ADJ
ejpam-3844	72	5	set	set	NOUN
ejpam-3844	72	6	(	(	PUNCT
ejpam-3844	72	7	µ̃,m	µ̃,m	PROPN
ejpam-3844	72	8	)	)	PUNCT
ejpam-3844	72	9	over	over	ADP
ejpam-3844	72	10	b	b	NOUN
ejpam-3844	72	11	where	where	SCONJ
ejpam-3844	72	12	m	m	NOUN
ejpam-3844	72	13	is	be	AUX
ejpam-3844	72	14	a	a	DET
ejpam-3844	72	15	subset	subset	NOUN
ejpam-3844	72	16	of	of	ADP
ejpam-3844	72	17	e	e	NOUN
ejpam-3844	72	18	,	,	PUNCT
ejpam-3844	72	19	we	we	PRON
ejpam-3844	72	20	say	say	VERB
ejpam-3844	72	21	that	that	SCONJ
ejpam-3844	72	22	(	(	PUNCT
ejpam-3844	72	23	µ̃,m	µ̃,m	PROPN
ejpam-3844	72	24	)	)	PUNCT
ejpam-3844	72	25	is	be	AUX
ejpam-3844	72	26	a	a	DET
ejpam-3844	72	27	fuzzy	fuzzy	ADJ
ejpam-3844	72	28	soft	soft	ADJ
ejpam-3844	72	29	bck	bck	NOUN
ejpam-3844	72	30	/	/	SYM
ejpam-3844	72	31	bci	bci	NOUN
ejpam-3844	72	32	-	-	NOUN
ejpam-3844	72	33	algebra	algebra	NOUN
ejpam-3844	72	34	based	base	VERB
ejpam-3844	72	35	on	on	ADP
ejpam-3844	72	36	a	a	DET
ejpam-3844	72	37	parameter	parameter	NOUN
ejpam-3844	72	38	m	m	VERB
ejpam-3844	72	39	over	over	ADP
ejpam-3844	72	40	b	b	NOUN
ejpam-3844	72	41	if	if	SCONJ
ejpam-3844	72	42	there	there	PRON
ejpam-3844	72	43	exists	exist	VERB
ejpam-3844	72	44	m	m	VERB
ejpam-3844	72	45	∈m	∈m	NOUN
ejpam-3844	72	46	such	such	ADJ
ejpam-3844	72	47	that	that	SCONJ
ejpam-3844	72	48	µ̃[m	µ̃[m	X
ejpam-3844	72	49	]	]	PUNCT
ejpam-3844	72	50	is	be	AUX
ejpam-3844	72	51	a	a	DET
ejpam-3844	72	52	fuzzy	fuzzy	ADJ
ejpam-3844	72	53	bck	bck	NOUN
ejpam-3844	72	54	/	/	SYM
ejpam-3844	72	55	bci	bci	NOUN
ejpam-3844	72	56	-	-	NOUN
ejpam-3844	72	57	algebra	algebra	NOUN
ejpam-3844	72	58	in	in	ADP
ejpam-3844	72	59	b.	b.	PROPN
ejpam-3844	72	60	if	if	SCONJ
ejpam-3844	72	61	(	(	PUNCT
ejpam-3844	72	62	µ̃,m	µ̃,m	PROPN
ejpam-3844	72	63	)	)	PUNCT
ejpam-3844	72	64	is	be	AUX
ejpam-3844	72	65	a	a	DET
ejpam-3844	72	66	fuzzy	fuzzy	ADJ
ejpam-3844	72	67	soft	soft	ADJ
ejpam-3844	72	68	bck	bck	NOUN
ejpam-3844	72	69	/	/	SYM
ejpam-3844	72	70	bci	bci	NOUN
ejpam-3844	72	71	-	-	NOUN
ejpam-3844	72	72	algebra	algebra	NOUN
ejpam-3844	72	73	based	base	VERB
ejpam-3844	72	74	on	on	ADP
ejpam-3844	72	75	a	a	DET
ejpam-3844	72	76	parameter	parameter	NOUN
ejpam-3844	72	77	m	m	VERB
ejpam-3844	72	78	over	over	ADP
ejpam-3844	72	79	b	b	NOUN
ejpam-3844	72	80	for	for	ADP
ejpam-3844	72	81	all	all	DET
ejpam-3844	72	82	m	m	NOUN
ejpam-3844	72	83	∈m	∈m	NOUN
ejpam-3844	72	84	,	,	PUNCT
ejpam-3844	72	85	we	we	PRON
ejpam-3844	72	86	say	say	VERB
ejpam-3844	72	87	that	that	SCONJ
ejpam-3844	72	88	(	(	PUNCT
ejpam-3844	72	89	µ̃,m	µ̃,m	PROPN
ejpam-3844	72	90	)	)	PUNCT
ejpam-3844	72	91	is	be	AUX
ejpam-3844	72	92	a	a	DET
ejpam-3844	72	93	fuzzy	fuzzy	ADJ
ejpam-3844	72	94	soft	soft	ADJ
ejpam-3844	72	95	bck	bck	NOUN
ejpam-3844	72	96	/	/	SYM
ejpam-3844	72	97	bci	bci	NOUN
ejpam-3844	72	98	-	-	NOUN
ejpam-3844	72	99	algebra	algebra	NOUN
ejpam-3844	72	100	over	over	ADP
ejpam-3844	72	101	b.	b.	PROPN
ejpam-3844	72	102	definition	definition	NOUN
ejpam-3844	72	103	8	8	NUM
ejpam-3844	72	104	.	.	PUNCT
ejpam-3844	73	1	let	let	VERB
ejpam-3844	73	2	(	(	PUNCT
ejpam-3844	73	3	µ̃,m	µ̃,m	PROPN
ejpam-3844	73	4	)	)	PUNCT
ejpam-3844	73	5	be	be	VERB
ejpam-3844	73	6	a	a	DET
ejpam-3844	73	7	fuzzy	fuzzy	ADJ
ejpam-3844	73	8	soft	soft	ADJ
ejpam-3844	73	9	bck	bck	NOUN
ejpam-3844	73	10	/	/	SYM
ejpam-3844	73	11	bci	bci	NOUN
ejpam-3844	73	12	-	-	NOUN
ejpam-3844	73	13	algebra	algebra	NOUN
ejpam-3844	73	14	over	over	ADP
ejpam-3844	73	15	b.	b.	PROPN
ejpam-3844	74	1	then	then	ADV
ejpam-3844	74	2	(	(	PUNCT
ejpam-3844	74	3	1	1	X
ejpam-3844	74	4	)	)	PUNCT
ejpam-3844	74	5	(	(	PUNCT
ejpam-3844	74	6	µ̃,m	µ̃,m	PROPN
ejpam-3844	74	7	)	)	PUNCT
ejpam-3844	74	8	is	be	AUX
ejpam-3844	74	9	said	say	VERB
ejpam-3844	74	10	to	to	PART
ejpam-3844	74	11	be	be	AUX
ejpam-3844	74	12	θ	θ	NOUN
ejpam-3844	74	13	-	-	NOUN
ejpam-3844	74	14	identity	identity	NOUN
ejpam-3844	74	15	,	,	PUNCT
ejpam-3844	74	16	where	where	SCONJ
ejpam-3844	74	17	θ	θ	PROPN
ejpam-3844	74	18	∈	∈	PROPN
ejpam-3844	74	19	(	(	PUNCT
ejpam-3844	74	20	0	0	NUM
ejpam-3844	74	21	,	,	PUNCT
ejpam-3844	74	22	1	1	NUM
ejpam-3844	74	23	]	]	PUNCT
ejpam-3844	74	24	,	,	PUNCT
ejpam-3844	74	25	if	if	SCONJ
ejpam-3844	74	26	it	it	PRON
ejpam-3844	74	27	satisfies	satisfy	VERB
ejpam-3844	74	28	:	:	PUNCT
ejpam-3844	74	29	(	(	PUNCT
ejpam-3844	74	30	∀m	∀m	PROPN
ejpam-3844	74	31	∈m)(∀β	∈m)(∀β	PROPN
ejpam-3844	74	32	∈	∈	PROPN
ejpam-3844	74	33	b	b	PROPN
ejpam-3844	74	34	)	)	PUNCT
ejpam-3844	74	35	(	(	PUNCT
ejpam-3844	74	36	µ̃[m](β	µ̃[m](β	NOUN
ejpam-3844	74	37	)	)	PUNCT
ejpam-3844	74	38	=	=	SYM
ejpam-3844	74	39	{	{	PUNCT
ejpam-3844	74	40	θ	θ	NOUN
ejpam-3844	74	41	if	if	SCONJ
ejpam-3844	74	42	β	β	X
ejpam-3844	74	43	=	=	SYM
ejpam-3844	74	44	0	0	NUM
ejpam-3844	74	45	,	,	PUNCT
ejpam-3844	74	46	0	0	NUM
ejpam-3844	74	47	otherwise	otherwise	ADV
ejpam-3844	74	48	)	)	PUNCT
ejpam-3844	74	49	.	.	PUNCT
ejpam-3844	75	1	(	(	PUNCT
ejpam-3844	75	2	2	2	X
ejpam-3844	75	3	)	)	PUNCT
ejpam-3844	75	4	(	(	PUNCT
ejpam-3844	75	5	µ̃,m	µ̃,m	PROPN
ejpam-3844	75	6	)	)	PUNCT
ejpam-3844	75	7	is	be	AUX
ejpam-3844	75	8	said	say	VERB
ejpam-3844	75	9	to	to	PART
ejpam-3844	75	10	be	be	AUX
ejpam-3844	75	11	θ	θ	NOUN
ejpam-3844	75	12	-	-	ADJ
ejpam-3844	75	13	absolute	absolute	ADJ
ejpam-3844	75	14	,	,	PUNCT
ejpam-3844	75	15	where	where	SCONJ
ejpam-3844	75	16	θ	θ	PROPN
ejpam-3844	75	17	∈	∈	PROPN
ejpam-3844	75	18	(	(	PUNCT
ejpam-3844	75	19	0	0	NUM
ejpam-3844	75	20	,	,	PUNCT
ejpam-3844	75	21	1	1	NUM
ejpam-3844	75	22	]	]	PUNCT
ejpam-3844	75	23	,	,	PUNCT
ejpam-3844	75	24	if	if	SCONJ
ejpam-3844	75	25	µ̃[m](β	µ̃[m](β	NOUN
ejpam-3844	75	26	)	)	PUNCT
ejpam-3844	75	27	=	=	SYM
ejpam-3844	75	28	θ	θ	PROPN
ejpam-3844	75	29	for	for	ADP
ejpam-3844	75	30	all	all	DET
ejpam-3844	75	31	β	β	X
ejpam-3844	75	32	∈	∈	PROPN
ejpam-3844	75	33	b	b	PROPN
ejpam-3844	75	34	and	and	CCONJ
ejpam-3844	75	35	m	m	PROPN
ejpam-3844	75	36	∈m	∈m	NOUN
ejpam-3844	75	37	.	.	PUNCT
ejpam-3844	75	38	example	example	NOUN
ejpam-3844	76	1	1	1	NUM
ejpam-3844	76	2	.	.	X
ejpam-3844	76	3	consider	consider	VERB
ejpam-3844	76	4	a	a	DET
ejpam-3844	76	5	bci	bci	NOUN
ejpam-3844	76	6	-	-	NOUN
ejpam-3844	76	7	algebra	algebra	NOUN
ejpam-3844	76	8	b	b	NOUN
ejpam-3844	76	9	=	=	SYM
ejpam-3844	76	10	{	{	PUNCT
ejpam-3844	76	11	0	0	NUM
ejpam-3844	76	12	,	,	PUNCT
ejpam-3844	76	13	1	1	NUM
ejpam-3844	76	14	,	,	PUNCT
ejpam-3844	76	15	2	2	NUM
ejpam-3844	76	16	,	,	PUNCT
ejpam-3844	76	17	β	β	X
ejpam-3844	76	18	,	,	PUNCT
ejpam-3844	76	19	γ	γ	X
ejpam-3844	76	20	}	}	PUNCT
ejpam-3844	76	21	with	with	ADP
ejpam-3844	76	22	the	the	DET
ejpam-3844	76	23	following	follow	VERB
ejpam-3844	76	24	cayley	cayley	ADJ
ejpam-3844	76	25	table	table	NOUN
ejpam-3844	76	26	:	:	PUNCT
ejpam-3844	76	27	∗	∗	NOUN
ejpam-3844	76	28	0	0	NUM
ejpam-3844	76	29	1	1	NUM
ejpam-3844	76	30	2	2	NUM
ejpam-3844	76	31	β	β	X
ejpam-3844	76	32	γ	γ	X
ejpam-3844	76	33	0	0	PROPN
ejpam-3844	76	34	0	0	NUM
ejpam-3844	76	35	0	0	NUM
ejpam-3844	76	36	0	0	NUM
ejpam-3844	76	37	β	β	X
ejpam-3844	76	38	β	β	VERB
ejpam-3844	76	39	1	1	NUM
ejpam-3844	76	40	1	1	NUM
ejpam-3844	76	41	0	0	NUM
ejpam-3844	76	42	1	1	NUM
ejpam-3844	76	43	γ	γ	X
ejpam-3844	76	44	β	β	NOUN
ejpam-3844	76	45	2	2	NUM
ejpam-3844	76	46	2	2	NUM
ejpam-3844	76	47	2	2	NUM
ejpam-3844	76	48	0	0	NUM
ejpam-3844	76	49	β	β	NOUN
ejpam-3844	76	50	β	β	X
ejpam-3844	76	51	β	β	X
ejpam-3844	76	52	β	β	X
ejpam-3844	76	53	β	β	X
ejpam-3844	76	54	β	β	X
ejpam-3844	76	55	0	0	NUM
ejpam-3844	76	56	0	0	NUM
ejpam-3844	76	57	γ	γ	PROPN
ejpam-3844	76	58	γ	γ	X
ejpam-3844	76	59	β	β	X
ejpam-3844	76	60	γ	γ	X
ejpam-3844	76	61	1	1	NUM
ejpam-3844	76	62	0	0	NUM
ejpam-3844	76	63	(	(	PUNCT
ejpam-3844	76	64	1	1	X
ejpam-3844	76	65	)	)	PUNCT
ejpam-3844	76	66	let	let	VERB
ejpam-3844	76	67	m	m	VERB
ejpam-3844	76	68	=	=	VERB
ejpam-3844	76	69	{	{	PUNCT
ejpam-3844	76	70	m1,m2,m3,m4	m1,m2,m3,m4	AUX
ejpam-3844	76	71	}	}	PUNCT
ejpam-3844	76	72	be	be	AUX
ejpam-3844	76	73	a	a	DET
ejpam-3844	76	74	set	set	NOUN
ejpam-3844	76	75	of	of	ADP
ejpam-3844	76	76	parameters	parameter	NOUN
ejpam-3844	76	77	and	and	CCONJ
ejpam-3844	76	78	define	define	VERB
ejpam-3844	76	79	a	a	DET
ejpam-3844	76	80	fuzzy	fuzzy	ADJ
ejpam-3844	76	81	soft	soft	ADJ
ejpam-3844	76	82	set	set	NOUN
ejpam-3844	76	83	(	(	PUNCT
ejpam-3844	76	84	µ̃,m	µ̃,m	PROPN
ejpam-3844	76	85	)	)	PUNCT
ejpam-3844	76	86	as	as	SCONJ
ejpam-3844	76	87	follows	follow	VERB
ejpam-3844	76	88	:	:	PUNCT
ejpam-3844	76	89	µ̃	µ̃	PROPN
ejpam-3844	76	90	0	0	NUM
ejpam-3844	76	91	1	1	NUM
ejpam-3844	76	92	2	2	NUM
ejpam-3844	76	93	β	β	X
ejpam-3844	76	94	γ	γ	X
ejpam-3844	76	95	m1	m1	PROPN
ejpam-3844	76	96	0.03	0.03	NUM
ejpam-3844	76	97	0	0	NUM
ejpam-3844	76	98	0	0	NUM
ejpam-3844	76	99	0	0	NUM
ejpam-3844	76	100	0	0	NUM
ejpam-3844	76	101	m2	m2	PROPN
ejpam-3844	76	102	0.03	0.03	NUM
ejpam-3844	76	103	0	0	NUM
ejpam-3844	76	104	0	0	NUM
ejpam-3844	76	105	0	0	NUM
ejpam-3844	76	106	0	0	NUM
ejpam-3844	76	107	m3	m3	PROPN
ejpam-3844	76	108	0.03	0.03	NUM
ejpam-3844	76	109	0	0	NUM
ejpam-3844	76	110	0	0	NUM
ejpam-3844	76	111	0	0	NUM
ejpam-3844	76	112	0	0	NUM
ejpam-3844	76	113	m4	m4	PROPN
ejpam-3844	76	114	0.03	0.03	NUM
ejpam-3844	76	115	0	0	NUM
ejpam-3844	76	116	0	0	NUM
ejpam-3844	76	117	0	0	NUM
ejpam-3844	76	118	0	0	NUM
ejpam-3844	77	1	then	then	ADV
ejpam-3844	77	2	(	(	PUNCT
ejpam-3844	77	3	µ̃,m	µ̃,m	PROPN
ejpam-3844	77	4	)	)	PUNCT
ejpam-3844	77	5	is	be	AUX
ejpam-3844	77	6	a	a	DET
ejpam-3844	77	7	0.03	0.03	NUM
ejpam-3844	77	8	-	-	PUNCT
ejpam-3844	77	9	identity	identity	NOUN
ejpam-3844	77	10	fuzzy	fuzzy	ADJ
ejpam-3844	77	11	soft	soft	ADJ
ejpam-3844	77	12	bci	bci	NOUN
ejpam-3844	77	13	-	-	NOUN
ejpam-3844	77	14	algebra	algebra	NOUN
ejpam-3844	77	15	over	over	ADP
ejpam-3844	77	16	b.	b.	PROPN
ejpam-3844	77	17	(	(	PUNCT
ejpam-3844	77	18	2	2	X
ejpam-3844	77	19	)	)	PUNCT
ejpam-3844	77	20	let	let	VERB
ejpam-3844	77	21	n	n	X
ejpam-3844	77	22	=	=	VERB
ejpam-3844	77	23	{	{	PUNCT
ejpam-3844	77	24	n1	n1	PROPN
ejpam-3844	77	25	,	,	PUNCT
ejpam-3844	77	26	n2	n2	NOUN
ejpam-3844	77	27	,	,	PUNCT
ejpam-3844	77	28	n3	n3	NOUN
ejpam-3844	77	29	}	}	PUNCT
ejpam-3844	77	30	be	be	AUX
ejpam-3844	77	31	a	a	DET
ejpam-3844	77	32	set	set	NOUN
ejpam-3844	77	33	of	of	ADP
ejpam-3844	77	34	parameters	parameter	NOUN
ejpam-3844	77	35	and	and	CCONJ
ejpam-3844	77	36	define	define	VERB
ejpam-3844	77	37	a	a	DET
ejpam-3844	77	38	fuzzy	fuzzy	ADJ
ejpam-3844	77	39	soft	soft	ADJ
ejpam-3844	77	40	set	set	NOUN
ejpam-3844	77	41	(	(	PUNCT
ejpam-3844	77	42	η̃	η̃	PROPN
ejpam-3844	77	43	,	,	PUNCT
ejpam-3844	77	44	n	n	CCONJ
ejpam-3844	77	45	)	)	PUNCT
ejpam-3844	77	46	as	as	SCONJ
ejpam-3844	77	47	follows	follow	VERB
ejpam-3844	77	48	:	:	PUNCT
ejpam-3844	77	49	η̃	η̃	PROPN
ejpam-3844	77	50	0	0	NUM
ejpam-3844	77	51	1	1	NUM
ejpam-3844	77	52	2	2	NUM
ejpam-3844	77	53	β	β	X
ejpam-3844	77	54	γ	γ	X
ejpam-3844	77	55	n1	n1	PROPN
ejpam-3844	77	56	0.4	0.4	NUM
ejpam-3844	77	57	0.4	0.4	NUM
ejpam-3844	77	58	0.4	0.4	NUM
ejpam-3844	77	59	0.4	0.4	NUM
ejpam-3844	77	60	0.4	0.4	NUM
ejpam-3844	77	61	n2	n2	NOUN
ejpam-3844	77	62	0.4	0.4	NUM
ejpam-3844	77	63	0.4	0.4	NUM
ejpam-3844	77	64	0.4	0.4	NUM
ejpam-3844	77	65	0.4	0.4	NUM
ejpam-3844	77	66	0.4	0.4	NUM
ejpam-3844	77	67	n3	n3	NOUN
ejpam-3844	77	68	0.4	0.4	NUM
ejpam-3844	77	69	0.4	0.4	NUM
ejpam-3844	77	70	0.4	0.4	NUM
ejpam-3844	77	71	0.4	0.4	NUM
ejpam-3844	77	72	0.4	0.4	NUM
ejpam-3844	78	1	then	then	ADV
ejpam-3844	78	2	(	(	PUNCT
ejpam-3844	78	3	η̃	η̃	PROPN
ejpam-3844	78	4	,	,	PUNCT
ejpam-3844	78	5	n	n	CCONJ
ejpam-3844	78	6	)	)	PUNCT
ejpam-3844	78	7	is	be	AUX
ejpam-3844	78	8	a	a	DET
ejpam-3844	78	9	0.4	0.4	NUM
ejpam-3844	78	10	-	-	PUNCT
ejpam-3844	78	11	absolute	absolute	ADJ
ejpam-3844	78	12	fuzzy	fuzzy	ADJ
ejpam-3844	78	13	soft	soft	ADJ
ejpam-3844	78	14	bci	bci	NOUN
ejpam-3844	78	15	-	-	NOUN
ejpam-3844	78	16	algebra	algebra	NOUN
ejpam-3844	78	17	over	over	ADP
ejpam-3844	78	18	b.	b.	PROPN
ejpam-3844	78	19	al	al	PROPN
ejpam-3844	78	20	-	-	PUNCT
ejpam-3844	78	21	kadi	kadi	PROPN
ejpam-3844	78	22	,	,	PUNCT
ejpam-3844	78	23	muhiuddin	muhiuddin	NOUN
ejpam-3844	78	24	/	/	SYM
ejpam-3844	78	25	eur	eur	PROPN
ejpam-3844	78	26	.	.	PUNCT
ejpam-3844	79	1	j.	j.	PROPN
ejpam-3844	79	2	pure	pure	PROPN
ejpam-3844	79	3	appl	appl	PROPN
ejpam-3844	79	4	.	.	PROPN
ejpam-3844	79	5	math	math	PROPN
ejpam-3844	79	6	,	,	PUNCT
ejpam-3844	79	7	13	13	NUM
ejpam-3844	79	8	(	(	PUNCT
ejpam-3844	79	9	4	4	NUM
ejpam-3844	79	10	)	)	PUNCT
ejpam-3844	79	11	(	(	PUNCT
ejpam-3844	79	12	2020	2020	NUM
ejpam-3844	79	13	)	)	PUNCT
ejpam-3844	79	14	,	,	PUNCT
ejpam-3844	79	15	939	939	NUM
ejpam-3844	79	16	-	-	SYM
ejpam-3844	79	17	947	947	NUM
ejpam-3844	79	18	943	943	NUM
ejpam-3844	79	19	theorem	theorem	NOUN
ejpam-3844	79	20	1	1	NUM
ejpam-3844	79	21	.	.	PUNCT
ejpam-3844	80	1	let	let	VERB
ejpam-3844	80	2	π	π	NOUN
ejpam-3844	80	3	:	:	PUNCT
ejpam-3844	80	4	b	b	X
ejpam-3844	80	5	→	→	SYM
ejpam-3844	80	6	c	c	AUX
ejpam-3844	80	7	be	be	AUX
ejpam-3844	80	8	a	a	DET
ejpam-3844	80	9	homomorphism	homomorphism	NOUN
ejpam-3844	80	10	of	of	ADP
ejpam-3844	80	11	bck	bck	PROPN
ejpam-3844	80	12	/	/	SYM
ejpam-3844	80	13	bci	bci	NOUN
ejpam-3844	80	14	-	-	PUNCT
ejpam-3844	80	15	algebras	algebra	NOUN
ejpam-3844	80	16	.	.	PUNCT
ejpam-3844	81	1	if	if	SCONJ
ejpam-3844	81	2	a	a	DET
ejpam-3844	81	3	fuzzy	fuzzy	ADJ
ejpam-3844	81	4	soft	soft	ADJ
ejpam-3844	81	5	bck	bck	NOUN
ejpam-3844	81	6	/	/	SYM
ejpam-3844	81	7	bci	bci	NOUN
ejpam-3844	81	8	-	-	NOUN
ejpam-3844	81	9	algebra	algebra	NOUN
ejpam-3844	81	10	(	(	PUNCT
ejpam-3844	81	11	µ̃,m	µ̃,m	PROPN
ejpam-3844	81	12	)	)	PUNCT
ejpam-3844	81	13	over	over	ADP
ejpam-3844	81	14	b	b	NOUN
ejpam-3844	81	15	satisfies	satisfie	NOUN
ejpam-3844	81	16	:	:	PUNCT
ejpam-3844	81	17	(	(	PUNCT
ejpam-3844	81	18	∀m	∀m	PROPN
ejpam-3844	81	19	∈m)(∀β	∈m)(∀β	PROPN
ejpam-3844	81	20	∈	∈	PROPN
ejpam-3844	81	21	b	b	PROPN
ejpam-3844	81	22	)	)	PUNCT
ejpam-3844	81	23	(	(	PUNCT
ejpam-3844	81	24	µ̃[m](β	µ̃[m](β	NOUN
ejpam-3844	81	25	)	)	PUNCT
ejpam-3844	81	26	=	=	SYM
ejpam-3844	81	27	{	{	PUNCT
ejpam-3844	81	28	θ	θ	NOUN
ejpam-3844	81	29	if	if	SCONJ
ejpam-3844	81	30	β	β	X
ejpam-3844	81	31	∈	∈	PROPN
ejpam-3844	81	32	kerπ	kerπ	PROPN
ejpam-3844	81	33	,	,	PUNCT
ejpam-3844	81	34	0	0	NUM
ejpam-3844	81	35	otherwise	otherwise	ADV
ejpam-3844	81	36	,	,	PUNCT
ejpam-3844	81	37	)	)	PUNCT
ejpam-3844	81	38	(	(	PUNCT
ejpam-3844	81	39	2	2	X
ejpam-3844	81	40	)	)	PUNCT
ejpam-3844	81	41	then	then	ADV
ejpam-3844	81	42	(	(	PUNCT
ejpam-3844	81	43	π(µ̃),m	π(µ̃),m	ADJ
ejpam-3844	81	44	)	)	PUNCT
ejpam-3844	81	45	is	be	AUX
ejpam-3844	81	46	a	a	DET
ejpam-3844	81	47	θ	θ	NOUN
ejpam-3844	81	48	-	-	PUNCT
ejpam-3844	81	49	identity	identity	NOUN
ejpam-3844	81	50	fuzzy	fuzzy	ADJ
ejpam-3844	81	51	soft	soft	ADJ
ejpam-3844	81	52	bck	bck	NOUN
ejpam-3844	81	53	/	/	SYM
ejpam-3844	81	54	bci	bci	NOUN
ejpam-3844	81	55	-	-	NOUN
ejpam-3844	81	56	algebra	algebra	NOUN
ejpam-3844	81	57	over	over	ADP
ejpam-3844	81	58	c.	c.	NOUN
ejpam-3844	81	59	proof	proof	NOUN
ejpam-3844	81	60	.	.	PUNCT
ejpam-3844	82	1	let	let	VERB
ejpam-3844	82	2	m	m	PRON
ejpam-3844	82	3	∈	∈	VERB
ejpam-3844	82	4	m	m	NOUN
ejpam-3844	82	5	and	and	CCONJ
ejpam-3844	82	6	γ	γ	PROPN
ejpam-3844	82	7	∈	∈	PROPN
ejpam-3844	82	8	c.	c.	NOUN
ejpam-3844	82	9	if	if	SCONJ
ejpam-3844	82	10	γ	γ	PROPN
ejpam-3844	82	11	=	=	SYM
ejpam-3844	82	12	0c	0c	X
ejpam-3844	82	13	(	(	PUNCT
ejpam-3844	82	14	the	the	DET
ejpam-3844	82	15	zero	zero	NUM
ejpam-3844	82	16	element	element	NOUN
ejpam-3844	82	17	of	of	ADP
ejpam-3844	82	18	c	c	PROPN
ejpam-3844	82	19	)	)	PUNCT
ejpam-3844	82	20	,	,	PUNCT
ejpam-3844	82	21	then	then	ADV
ejpam-3844	82	22	0b	0b	PROPN
ejpam-3844	82	23	∈	∈	PROPN
ejpam-3844	82	24	kerπ	kerπ	PROPN
ejpam-3844	82	25	where	where	SCONJ
ejpam-3844	82	26	0b	0b	NOUN
ejpam-3844	82	27	is	be	AUX
ejpam-3844	82	28	the	the	DET
ejpam-3844	82	29	zero	zero	NUM
ejpam-3844	82	30	element	element	NOUN
ejpam-3844	82	31	of	of	ADP
ejpam-3844	82	32	b	b	PROPN
ejpam-3844	82	33	and	and	CCONJ
ejpam-3844	82	34	so	so	ADV
ejpam-3844	82	35	π(µ̃)[m](γ	π(µ̃)[m](γ	ADJ
ejpam-3844	82	36	)	)	PUNCT
ejpam-3844	82	37	=	=	SYM
ejpam-3844	83	1	π(µ̃[m])(0c	π(µ̃[m])(0c	PROPN
ejpam-3844	83	2	)	)	PUNCT
ejpam-3844	83	3	=	=	NOUN
ejpam-3844	83	4	sup	sup	NOUN
ejpam-3844	83	5	β∈π−1(0c	β∈π−1(0c	NOUN
ejpam-3844	83	6	)	)	PUNCT
ejpam-3844	83	7	µ̃[m](β	µ̃[m](β	NOUN
ejpam-3844	83	8	)	)	PUNCT
ejpam-3844	83	9	=	=	SYM
ejpam-3844	83	10	sup	sup	NOUN
ejpam-3844	83	11	β∈kerπ	β∈kerπ	PROPN
ejpam-3844	83	12	µ̃[m](β	µ̃[m](β	NOUN
ejpam-3844	83	13	)	)	PUNCT
ejpam-3844	83	14	=	=	SYM
ejpam-3844	83	15	θ	θ	PROPN
ejpam-3844	83	16	.	.	PUNCT
ejpam-3844	84	1	if	if	SCONJ
ejpam-3844	84	2	γ	γ	PROPN
ejpam-3844	84	3	6=	6=	PROPN
ejpam-3844	84	4	0c	0c	NOUN
ejpam-3844	84	5	,	,	PUNCT
ejpam-3844	84	6	then	then	ADV
ejpam-3844	84	7	π(µ̃)[m](γ	π(µ̃)[m](γ	ADJ
ejpam-3844	84	8	)	)	PUNCT
ejpam-3844	84	9	=	=	SYM
ejpam-3844	84	10	0	0	X
ejpam-3844	84	11	.	.	PUNCT
ejpam-3844	85	1	therefore	therefore	ADV
ejpam-3844	85	2	,	,	PUNCT
ejpam-3844	85	3	(	(	PUNCT
ejpam-3844	85	4	π(µ̃),m	π(µ̃),m	ADJ
ejpam-3844	85	5	)	)	PUNCT
ejpam-3844	85	6	is	be	AUX
ejpam-3844	85	7	a	a	DET
ejpam-3844	85	8	θ	θ	NOUN
ejpam-3844	85	9	-	-	PUNCT
ejpam-3844	85	10	identity	identity	NOUN
ejpam-3844	85	11	fuzzy	fuzzy	ADJ
ejpam-3844	85	12	soft	soft	ADJ
ejpam-3844	85	13	bck	bck	NOUN
ejpam-3844	85	14	/	/	SYM
ejpam-3844	85	15	bcialgebra	bcialgebra	NOUN
ejpam-3844	85	16	over	over	ADP
ejpam-3844	85	17	c.	c.	PROPN
ejpam-3844	85	18	theorem	theorem	PROPN
ejpam-3844	85	19	2	2	X
ejpam-3844	85	20	.	.	PUNCT
ejpam-3844	86	1	let	let	VERB
ejpam-3844	86	2	π	π	NOUN
ejpam-3844	86	3	:	:	PUNCT
ejpam-3844	86	4	b	b	X
ejpam-3844	86	5	→	→	SYM
ejpam-3844	86	6	c	c	AUX
ejpam-3844	86	7	be	be	AUX
ejpam-3844	86	8	a	a	DET
ejpam-3844	86	9	homomorphism	homomorphism	NOUN
ejpam-3844	86	10	of	of	ADP
ejpam-3844	86	11	bck	bck	PROPN
ejpam-3844	86	12	/	/	SYM
ejpam-3844	86	13	bci	bci	NOUN
ejpam-3844	86	14	-	-	PUNCT
ejpam-3844	86	15	algebras	algebra	NOUN
ejpam-3844	86	16	.	.	PUNCT
ejpam-3844	87	1	if	if	SCONJ
ejpam-3844	87	2	(	(	PUNCT
ejpam-3844	87	3	µ̃,m	µ̃,m	PROPN
ejpam-3844	87	4	)	)	PUNCT
ejpam-3844	87	5	is	be	AUX
ejpam-3844	87	6	a	a	DET
ejpam-3844	87	7	θ	θ	ADJ
ejpam-3844	87	8	-	-	ADJ
ejpam-3844	87	9	absolute	absolute	ADJ
ejpam-3844	87	10	fuzzy	fuzzy	ADJ
ejpam-3844	87	11	soft	soft	ADJ
ejpam-3844	87	12	bck	bck	NOUN
ejpam-3844	87	13	/	/	SYM
ejpam-3844	87	14	bci	bci	NOUN
ejpam-3844	87	15	-	-	NOUN
ejpam-3844	87	16	algebra	algebra	NOUN
ejpam-3844	87	17	over	over	ADP
ejpam-3844	87	18	b	b	NOUN
ejpam-3844	87	19	,	,	PUNCT
ejpam-3844	87	20	then	then	ADV
ejpam-3844	87	21	(	(	PUNCT
ejpam-3844	87	22	π(µ̃),m	π(µ̃),m	ADJ
ejpam-3844	87	23	)	)	PUNCT
ejpam-3844	87	24	is	be	AUX
ejpam-3844	87	25	a	a	DET
ejpam-3844	87	26	θ	θ	ADJ
ejpam-3844	87	27	-	-	ADJ
ejpam-3844	87	28	absolute	absolute	ADJ
ejpam-3844	87	29	fuzzy	fuzzy	ADJ
ejpam-3844	87	30	soft	soft	ADJ
ejpam-3844	87	31	bck	bck	NOUN
ejpam-3844	87	32	/	/	SYM
ejpam-3844	87	33	bci	bci	NOUN
ejpam-3844	87	34	-	-	NOUN
ejpam-3844	87	35	algebra	algebra	NOUN
ejpam-3844	87	36	over	over	ADP
ejpam-3844	87	37	c.	c.	NOUN
ejpam-3844	87	38	proof	proof	NOUN
ejpam-3844	87	39	.	.	PUNCT
ejpam-3844	88	1	direct	direct	ADJ
ejpam-3844	88	2	.	.	PUNCT
ejpam-3844	88	3	definition	definition	NOUN
ejpam-3844	88	4	9	9	NUM
ejpam-3844	88	5	.	.	PUNCT
ejpam-3844	89	1	let	let	AUX
ejpam-3844	89	2	(	(	PUNCT
ejpam-3844	89	3	µ̃,m	µ̃,m	PROPN
ejpam-3844	89	4	)	)	PUNCT
ejpam-3844	89	5	and	and	CCONJ
ejpam-3844	89	6	(	(	PUNCT
ejpam-3844	89	7	η̃	η̃	PROPN
ejpam-3844	89	8	,	,	PUNCT
ejpam-3844	89	9	n	n	CCONJ
ejpam-3844	89	10	)	)	PUNCT
ejpam-3844	89	11	be	be	AUX
ejpam-3844	89	12	two	two	NUM
ejpam-3844	89	13	fuzzy	fuzzy	ADJ
ejpam-3844	89	14	soft	soft	ADJ
ejpam-3844	89	15	bck	bck	NOUN
ejpam-3844	89	16	/	/	SYM
ejpam-3844	89	17	bci	bci	NOUN
ejpam-3844	89	18	-	-	PUNCT
ejpam-3844	89	19	algebras	algebras	PROPN
ejpam-3844	89	20	over	over	ADP
ejpam-3844	89	21	b.	b.	PROPN
ejpam-3844	90	1	we	we	PRON
ejpam-3844	90	2	say	say	VERB
ejpam-3844	90	3	that	that	SCONJ
ejpam-3844	90	4	(	(	PUNCT
ejpam-3844	90	5	µ̃,m	µ̃,m	PROPN
ejpam-3844	90	6	)	)	PUNCT
ejpam-3844	90	7	is	be	AUX
ejpam-3844	90	8	a	a	DET
ejpam-3844	90	9	fuzzy	fuzzy	ADJ
ejpam-3844	90	10	soft	soft	ADJ
ejpam-3844	90	11	sub	sub	NOUN
ejpam-3844	90	12	-	-	ADJ
ejpam-3844	90	13	bck	bck	ADJ
ejpam-3844	90	14	/	/	SYM
ejpam-3844	90	15	bci	bci	NOUN
ejpam-3844	90	16	-	-	NOUN
ejpam-3844	90	17	algebra	algebra	NOUN
ejpam-3844	90	18	of	of	ADP
ejpam-3844	90	19	(	(	PUNCT
ejpam-3844	90	20	η̃	η̃	PROPN
ejpam-3844	90	21	,	,	PUNCT
ejpam-3844	90	22	n	n	CCONJ
ejpam-3844	90	23	)	)	PUNCT
ejpam-3844	90	24	if	if	SCONJ
ejpam-3844	90	25	(	(	PUNCT
ejpam-3844	90	26	1	1	X
ejpam-3844	90	27	)	)	PUNCT
ejpam-3844	90	28	m	m	PROPN
ejpam-3844	90	29	⊆	⊆	NUM
ejpam-3844	90	30	n	n	CCONJ
ejpam-3844	90	31	,	,	PUNCT
ejpam-3844	90	32	(	(	PUNCT
ejpam-3844	90	33	2	2	NUM
ejpam-3844	90	34	)	)	PUNCT
ejpam-3844	90	35	µ̃[m	µ̃[m	X
ejpam-3844	90	36	]	]	PUNCT
ejpam-3844	90	37	is	be	AUX
ejpam-3844	90	38	a	a	DET
ejpam-3844	90	39	fuzzy	fuzzy	ADJ
ejpam-3844	90	40	sub	sub	NOUN
ejpam-3844	90	41	-	-	ADJ
ejpam-3844	90	42	bck	bck	ADJ
ejpam-3844	90	43	/	/	SYM
ejpam-3844	90	44	bci	bci	NOUN
ejpam-3844	90	45	-	-	NOUN
ejpam-3844	90	46	algebra	algebra	NOUN
ejpam-3844	90	47	of	of	ADP
ejpam-3844	90	48	η̃[m	η̃[m	X
ejpam-3844	90	49	]	]	PUNCT
ejpam-3844	90	50	for	for	ADP
ejpam-3844	90	51	all	all	DET
ejpam-3844	90	52	m	m	NOUN
ejpam-3844	90	53	∈	∈	NOUN
ejpam-3844	90	54	m	m	NOUN
ejpam-3844	90	55	,	,	PUNCT
ejpam-3844	90	56	that	that	ADV
ejpam-3844	90	57	is	is	ADV
ejpam-3844	90	58	,	,	PUNCT
ejpam-3844	90	59	µ̃[m	µ̃[m	X
ejpam-3844	90	60	]	]	PUNCT
ejpam-3844	90	61	is	be	AUX
ejpam-3844	90	62	a	a	DET
ejpam-3844	90	63	fuzzy	fuzzy	ADJ
ejpam-3844	90	64	bck	bck	NOUN
ejpam-3844	90	65	/	/	SYM
ejpam-3844	90	66	bci	bci	NOUN
ejpam-3844	90	67	-	-	NOUN
ejpam-3844	90	68	algebra	algebra	NOUN
ejpam-3844	90	69	satisfying	satisfy	VERB
ejpam-3844	90	70	the	the	DET
ejpam-3844	90	71	condition	condition	NOUN
ejpam-3844	90	72	:	:	PUNCT
ejpam-3844	90	73	(	(	PUNCT
ejpam-3844	90	74	∀β	∀β	PROPN
ejpam-3844	90	75	∈	∈	PROPN
ejpam-3844	90	76	b	b	X
ejpam-3844	90	77	)	)	PUNCT
ejpam-3844	90	78	(	(	PUNCT
ejpam-3844	90	79	µ̃[m](β	µ̃[m](β	NOUN
ejpam-3844	90	80	)	)	PUNCT
ejpam-3844	90	81	≤	≤	NUM
ejpam-3844	90	82	η̃[m](β	η̃[m](β	NOUN
ejpam-3844	90	83	)	)	PUNCT
ejpam-3844	90	84	)	)	PUNCT
ejpam-3844	90	85	.	.	PUNCT
ejpam-3844	91	1	example	example	NOUN
ejpam-3844	92	1	2	2	NUM
ejpam-3844	92	2	.	.	X
ejpam-3844	92	3	consider	consider	VERB
ejpam-3844	92	4	a	a	DET
ejpam-3844	92	5	bck	bck	NOUN
ejpam-3844	92	6	-	-	PUNCT
ejpam-3844	92	7	algebra	algebra	NOUN
ejpam-3844	92	8	b	b	NOUN
ejpam-3844	92	9	=	=	SYM
ejpam-3844	92	10	{	{	PUNCT
ejpam-3844	92	11	0	0	NUM
ejpam-3844	92	12	,	,	PUNCT
ejpam-3844	92	13	1	1	NUM
ejpam-3844	92	14	,	,	PUNCT
ejpam-3844	92	15	2	2	NUM
ejpam-3844	92	16	,	,	PUNCT
ejpam-3844	92	17	3	3	NUM
ejpam-3844	92	18	,	,	PUNCT
ejpam-3844	92	19	4	4	NUM
ejpam-3844	92	20	}	}	PUNCT
ejpam-3844	92	21	with	with	ADP
ejpam-3844	92	22	the	the	DET
ejpam-3844	92	23	following	follow	VERB
ejpam-3844	92	24	cayley	cayley	ADJ
ejpam-3844	92	25	table	table	NOUN
ejpam-3844	92	26	:	:	PUNCT
ejpam-3844	92	27	∗	∗	NOUN
ejpam-3844	92	28	0	0	NUM
ejpam-3844	93	1	1	1	NUM
ejpam-3844	93	2	2	2	NUM
ejpam-3844	93	3	3	3	NUM
ejpam-3844	93	4	4	4	NUM
ejpam-3844	93	5	0	0	NUM
ejpam-3844	93	6	0	0	NUM
ejpam-3844	93	7	0	0	NUM
ejpam-3844	93	8	0	0	NUM
ejpam-3844	93	9	0	0	NUM
ejpam-3844	93	10	0	0	NUM
ejpam-3844	93	11	1	1	NUM
ejpam-3844	93	12	1	1	NUM
ejpam-3844	93	13	0	0	NUM
ejpam-3844	93	14	1	1	NUM
ejpam-3844	93	15	1	1	NUM
ejpam-3844	93	16	0	0	NUM
ejpam-3844	93	17	2	2	NUM
ejpam-3844	93	18	2	2	NUM
ejpam-3844	93	19	2	2	NUM
ejpam-3844	93	20	0	0	NUM
ejpam-3844	93	21	2	2	NUM
ejpam-3844	93	22	0	0	NUM
ejpam-3844	93	23	3	3	NUM
ejpam-3844	93	24	3	3	NUM
ejpam-3844	93	25	3	3	NUM
ejpam-3844	93	26	3	3	NUM
ejpam-3844	93	27	0	0	NUM
ejpam-3844	93	28	0	0	NUM
ejpam-3844	93	29	4	4	NUM
ejpam-3844	93	30	4	4	NUM
ejpam-3844	93	31	4	4	NUM
ejpam-3844	93	32	4	4	NUM
ejpam-3844	93	33	4	4	NUM
ejpam-3844	93	34	0	0	NUM
ejpam-3844	93	35	let	let	VERB
ejpam-3844	93	36	n	n	NOUN
ejpam-3844	93	37	=	=	SYM
ejpam-3844	93	38	{	{	PUNCT
ejpam-3844	93	39	n1	n1	PROPN
ejpam-3844	93	40	,	,	PUNCT
ejpam-3844	93	41	n2	n2	NOUN
ejpam-3844	93	42	,	,	PUNCT
ejpam-3844	93	43	n3	n3	PROPN
ejpam-3844	93	44	,	,	PUNCT
ejpam-3844	93	45	n4	n4	PROPN
ejpam-3844	93	46	,	,	PUNCT
ejpam-3844	93	47	n5	n5	PROPN
ejpam-3844	93	48	}	}	PUNCT
ejpam-3844	93	49	be	be	VERB
ejpam-3844	93	50	a	a	DET
ejpam-3844	93	51	set	set	NOUN
ejpam-3844	93	52	of	of	ADP
ejpam-3844	93	53	parameters	parameter	NOUN
ejpam-3844	93	54	and	and	CCONJ
ejpam-3844	93	55	let	let	VERB
ejpam-3844	93	56	(	(	PUNCT
ejpam-3844	93	57	η̃	η̃	PROPN
ejpam-3844	93	58	,	,	PUNCT
ejpam-3844	93	59	n	n	CCONJ
ejpam-3844	93	60	)	)	PUNCT
ejpam-3844	93	61	be	be	AUX
ejpam-3844	93	62	a	a	DET
ejpam-3844	93	63	fuzzy	fuzzy	ADJ
ejpam-3844	93	64	soft	soft	ADJ
ejpam-3844	93	65	set	set	NOUN
ejpam-3844	93	66	over	over	ADP
ejpam-3844	93	67	b	b	NOUN
ejpam-3844	93	68	given	give	VERB
ejpam-3844	93	69	as	as	SCONJ
ejpam-3844	93	70	follows	follow	VERB
ejpam-3844	93	71	:	:	PUNCT
ejpam-3844	93	72	η̃	η̃	PROPN
ejpam-3844	93	73	0	0	NUM
ejpam-3844	93	74	1	1	NUM
ejpam-3844	93	75	2	2	NUM
ejpam-3844	93	76	3	3	NUM
ejpam-3844	93	77	4	4	NUM
ejpam-3844	93	78	n1	n1	NOUN
ejpam-3844	93	79	0.9	0.9	NUM
ejpam-3844	93	80	0.7	0.7	NUM
ejpam-3844	93	81	0.5	0.5	NUM
ejpam-3844	93	82	0.4	0.4	NUM
ejpam-3844	93	83	0.2	0.2	NUM
ejpam-3844	93	84	n2	n2	NOUN
ejpam-3844	93	85	0.8	0.8	NUM
ejpam-3844	93	86	0.7	0.7	NUM
ejpam-3844	93	87	0.6	0.6	NUM
ejpam-3844	93	88	0.4	0.4	NUM
ejpam-3844	93	89	0.3	0.3	NUM
ejpam-3844	93	90	n3	n3	ADJ
ejpam-3844	93	91	0.9	0.9	NUM
ejpam-3844	93	92	0.8	0.8	NUM
ejpam-3844	93	93	0.6	0.6	NUM
ejpam-3844	93	94	0.5	0.5	NUM
ejpam-3844	93	95	0.3	0.3	NUM
ejpam-3844	93	96	n4	n4	PROPN
ejpam-3844	93	97	0.7	0.7	NUM
ejpam-3844	93	98	0.6	0.6	NUM
ejpam-3844	93	99	0.4	0.4	NUM
ejpam-3844	93	100	0.3	0.3	NUM
ejpam-3844	93	101	0.1	0.1	NUM
ejpam-3844	93	102	n5	n5	PROPN
ejpam-3844	93	103	0.9	0.9	NUM
ejpam-3844	93	104	0.6	0.6	NUM
ejpam-3844	93	105	0.5	0.5	NUM
ejpam-3844	93	106	0.6	0.6	NUM
ejpam-3844	93	107	0.5	0.5	NUM
ejpam-3844	93	108	al	al	PROPN
ejpam-3844	93	109	-	-	PUNCT
ejpam-3844	93	110	kadi	kadi	NOUN
ejpam-3844	93	111	,	,	PUNCT
ejpam-3844	93	112	muhiuddin	muhiuddin	NOUN
ejpam-3844	93	113	/	/	SYM
ejpam-3844	93	114	eur	eur	PROPN
ejpam-3844	93	115	.	.	PUNCT
ejpam-3844	94	1	j.	j.	PROPN
ejpam-3844	94	2	pure	pure	PROPN
ejpam-3844	94	3	appl	appl	PROPN
ejpam-3844	94	4	.	.	PROPN
ejpam-3844	94	5	math	math	PROPN
ejpam-3844	94	6	,	,	PUNCT
ejpam-3844	94	7	13	13	NUM
ejpam-3844	94	8	(	(	PUNCT
ejpam-3844	94	9	4	4	NUM
ejpam-3844	94	10	)	)	PUNCT
ejpam-3844	94	11	(	(	PUNCT
ejpam-3844	94	12	2020	2020	NUM
ejpam-3844	94	13	)	)	PUNCT
ejpam-3844	94	14	,	,	PUNCT
ejpam-3844	94	15	939	939	NUM
ejpam-3844	94	16	-	-	SYM
ejpam-3844	94	17	947	947	NUM
ejpam-3844	94	18	944	944	NUM
ejpam-3844	94	19	then	then	ADV
ejpam-3844	94	20	,	,	PUNCT
ejpam-3844	94	21	(	(	PUNCT
ejpam-3844	94	22	η̃	η̃	PROPN
ejpam-3844	94	23	,	,	PUNCT
ejpam-3844	94	24	n	n	CCONJ
ejpam-3844	94	25	)	)	PUNCT
ejpam-3844	94	26	is	be	AUX
ejpam-3844	94	27	a	a	DET
ejpam-3844	94	28	fuzzy	fuzzy	ADJ
ejpam-3844	94	29	soft	soft	ADJ
ejpam-3844	94	30	bck	bck	NOUN
ejpam-3844	94	31	-	-	PUNCT
ejpam-3844	94	32	algebra	algebra	NOUN
ejpam-3844	94	33	over	over	ADP
ejpam-3844	94	34	b.	b.	PROPN
ejpam-3844	94	35	now	now	ADV
ejpam-3844	94	36	let	let	VERB
ejpam-3844	94	37	m	m	VERB
ejpam-3844	94	38	=	=	SYM
ejpam-3844	94	39	{	{	PUNCT
ejpam-3844	94	40	n2	n2	PROPN
ejpam-3844	94	41	,	,	PUNCT
ejpam-3844	94	42	n5	n5	PROPN
ejpam-3844	94	43	}	}	PUNCT
ejpam-3844	94	44	be	be	VERB
ejpam-3844	94	45	a	a	DET
ejpam-3844	94	46	subset	subset	NOUN
ejpam-3844	94	47	of	of	ADP
ejpam-3844	94	48	n.	n.	NOUN
ejpam-3844	94	49	define	define	VERB
ejpam-3844	94	50	a	a	DET
ejpam-3844	94	51	soft	soft	ADJ
ejpam-3844	94	52	set	set	NOUN
ejpam-3844	94	53	(	(	PUNCT
ejpam-3844	94	54	µ̃,m	µ̃,m	PROPN
ejpam-3844	94	55	)	)	PUNCT
ejpam-3844	94	56	over	over	ADP
ejpam-3844	94	57	b	b	NOUN
ejpam-3844	94	58	as	as	SCONJ
ejpam-3844	94	59	follows	follow	VERB
ejpam-3844	94	60	:	:	PUNCT
ejpam-3844	94	61	µ̃	µ̃	PROPN
ejpam-3844	94	62	0	0	NUM
ejpam-3844	94	63	1	1	NUM
ejpam-3844	94	64	2	2	NUM
ejpam-3844	94	65	3	3	NUM
ejpam-3844	94	66	4	4	NUM
ejpam-3844	94	67	n2	n2	NOUN
ejpam-3844	94	68	0.78	0.78	NUM
ejpam-3844	94	69	0.67	0.67	NUM
ejpam-3844	94	70	0.56	0.56	NUM
ejpam-3844	94	71	0.34	0.34	NUM
ejpam-3844	94	72	0.23	0.23	NUM
ejpam-3844	94	73	n5	n5	PROPN
ejpam-3844	94	74	0.89	0.89	NUM
ejpam-3844	94	75	0.56	0.56	NUM
ejpam-3844	94	76	0.45	0.45	NUM
ejpam-3844	94	77	0.56	0.56	NUM
ejpam-3844	94	78	0.45	0.45	NUM
ejpam-3844	94	79	then	then	ADV
ejpam-3844	94	80	,	,	PUNCT
ejpam-3844	94	81	(	(	PUNCT
ejpam-3844	94	82	µ̃,m	µ̃,m	PROPN
ejpam-3844	94	83	)	)	PUNCT
ejpam-3844	94	84	is	be	AUX
ejpam-3844	94	85	a	a	DET
ejpam-3844	94	86	fuzzy	fuzzy	ADJ
ejpam-3844	94	87	soft	soft	ADJ
ejpam-3844	94	88	sub	sub	ADJ
ejpam-3844	94	89	-	-	ADJ
ejpam-3844	94	90	bck	bck	ADJ
ejpam-3844	94	91	-	-	PUNCT
ejpam-3844	94	92	algebra	algebra	NOUN
ejpam-3844	94	93	of	of	ADP
ejpam-3844	94	94	(	(	PUNCT
ejpam-3844	94	95	η̃	η̃	PROPN
ejpam-3844	94	96	,	,	PUNCT
ejpam-3844	94	97	n	n	CCONJ
ejpam-3844	94	98	)	)	PUNCT
ejpam-3844	94	99	.	.	PUNCT
ejpam-3844	95	1	the	the	DET
ejpam-3844	95	2	following	follow	VERB
ejpam-3844	95	3	theorem	theorem	NOUN
ejpam-3844	95	4	is	be	AUX
ejpam-3844	95	5	obvious	obvious	ADJ
ejpam-3844	95	6	.	.	PUNCT
ejpam-3844	96	1	theorem	theorem	NOUN
ejpam-3844	96	2	3	3	X
ejpam-3844	96	3	.	.	PUNCT
ejpam-3844	97	1	let	let	AUX
ejpam-3844	97	2	(	(	PUNCT
ejpam-3844	97	3	µ̃,m	µ̃,m	PROPN
ejpam-3844	97	4	)	)	PUNCT
ejpam-3844	97	5	and	and	CCONJ
ejpam-3844	97	6	(	(	PUNCT
ejpam-3844	97	7	η̃,m	η̃,m	X
ejpam-3844	97	8	)	)	PUNCT
ejpam-3844	97	9	be	be	AUX
ejpam-3844	97	10	fuzzy	fuzzy	ADJ
ejpam-3844	97	11	soft	soft	ADJ
ejpam-3844	97	12	bck	bck	NOUN
ejpam-3844	97	13	/	/	SYM
ejpam-3844	97	14	bci	bci	NOUN
ejpam-3844	97	15	-	-	PUNCT
ejpam-3844	97	16	algebras	algebras	PROPN
ejpam-3844	97	17	over	over	ADP
ejpam-3844	97	18	b.	b.	PROPN
ejpam-3844	97	19	if	if	SCONJ
ejpam-3844	97	20	µ̃[m	µ̃[m	X
ejpam-3844	97	21	]	]	X
ejpam-3844	97	22	⊆	⊆	NUM
ejpam-3844	97	23	η̃[m	η̃[m	X
ejpam-3844	97	24	]	]	PUNCT
ejpam-3844	97	25	for	for	ADP
ejpam-3844	97	26	all	all	DET
ejpam-3844	97	27	m	m	NOUN
ejpam-3844	97	28	∈m	∈m	NOUN
ejpam-3844	97	29	,	,	PUNCT
ejpam-3844	97	30	then	then	ADV
ejpam-3844	97	31	(	(	PUNCT
ejpam-3844	97	32	µ̃,m	µ̃,m	PROPN
ejpam-3844	97	33	)	)	PUNCT
ejpam-3844	97	34	is	be	AUX
ejpam-3844	97	35	a	a	DET
ejpam-3844	97	36	fuzzy	fuzzy	ADJ
ejpam-3844	97	37	soft	soft	ADJ
ejpam-3844	97	38	sub	sub	NOUN
ejpam-3844	97	39	-	-	ADJ
ejpam-3844	97	40	bck	bck	ADJ
ejpam-3844	97	41	/	/	SYM
ejpam-3844	97	42	bci	bci	NOUN
ejpam-3844	97	43	-	-	NOUN
ejpam-3844	97	44	algebra	algebra	NOUN
ejpam-3844	97	45	of	of	ADP
ejpam-3844	97	46	(	(	PUNCT
ejpam-3844	97	47	η̃,m	η̃,m	PROPN
ejpam-3844	97	48	)	)	PUNCT
ejpam-3844	97	49	.	.	PUNCT
ejpam-3844	98	1	lemma	lemma	PROPN
ejpam-3844	98	2	1	1	NUM
ejpam-3844	98	3	(	(	PUNCT
ejpam-3844	98	4	[	[	X
ejpam-3844	98	5	8	8	NUM
ejpam-3844	98	6	]	]	PUNCT
ejpam-3844	98	7	)	)	PUNCT
ejpam-3844	98	8	.	.	PUNCT
ejpam-3844	99	1	if	if	SCONJ
ejpam-3844	99	2	(	(	PUNCT
ejpam-3844	99	3	µ̃,m	µ̃,m	PROPN
ejpam-3844	99	4	)	)	PUNCT
ejpam-3844	99	5	and	and	CCONJ
ejpam-3844	99	6	(	(	PUNCT
ejpam-3844	99	7	η̃	η̃	PROPN
ejpam-3844	99	8	,	,	PUNCT
ejpam-3844	99	9	n	n	CCONJ
ejpam-3844	99	10	)	)	PUNCT
ejpam-3844	99	11	are	be	AUX
ejpam-3844	99	12	fuzzy	fuzzy	ADJ
ejpam-3844	99	13	soft	soft	ADJ
ejpam-3844	99	14	bck	bck	NOUN
ejpam-3844	99	15	/	/	SYM
ejpam-3844	99	16	bci	bci	NOUN
ejpam-3844	99	17	-	-	PUNCT
ejpam-3844	99	18	algebras	algebra	NOUN
ejpam-3844	99	19	over	over	ADP
ejpam-3844	99	20	b	b	PROPN
ejpam-3844	99	21	,	,	PUNCT
ejpam-3844	99	22	then	then	ADV
ejpam-3844	99	23	the	the	DET
ejpam-3844	99	24	extended	extended	ADJ
ejpam-3844	99	25	intersection	intersection	NOUN
ejpam-3844	99	26	of	of	ADP
ejpam-3844	99	27	(	(	PUNCT
ejpam-3844	99	28	µ̃,m	µ̃,m	PROPN
ejpam-3844	99	29	)	)	PUNCT
ejpam-3844	99	30	and	and	CCONJ
ejpam-3844	99	31	(	(	PUNCT
ejpam-3844	99	32	η̃	η̃	PROPN
ejpam-3844	99	33	,	,	PUNCT
ejpam-3844	99	34	n	n	CCONJ
ejpam-3844	99	35	)	)	PUNCT
ejpam-3844	99	36	is	be	AUX
ejpam-3844	99	37	a	a	DET
ejpam-3844	99	38	fuzzy	fuzzy	ADJ
ejpam-3844	99	39	soft	soft	ADJ
ejpam-3844	99	40	bck	bck	NOUN
ejpam-3844	99	41	/	/	SYM
ejpam-3844	99	42	bci	bci	NOUN
ejpam-3844	99	43	-	-	NOUN
ejpam-3844	99	44	algebra	algebra	NOUN
ejpam-3844	99	45	over	over	ADP
ejpam-3844	99	46	b.	b.	PROPN
ejpam-3844	99	47	theorem	theorem	PROPN
ejpam-3844	99	48	4	4	X
ejpam-3844	99	49	.	.	PUNCT
ejpam-3844	100	1	let	let	AUX
ejpam-3844	100	2	(	(	PUNCT
ejpam-3844	100	3	ξ̃	ξ̃	PROPN
ejpam-3844	100	4	,	,	PUNCT
ejpam-3844	100	5	q	q	PUNCT
ejpam-3844	100	6	)	)	PUNCT
ejpam-3844	100	7	be	be	AUX
ejpam-3844	100	8	a	a	DET
ejpam-3844	100	9	fuzzy	fuzzy	ADJ
ejpam-3844	100	10	soft	soft	ADJ
ejpam-3844	100	11	bck	bck	NOUN
ejpam-3844	100	12	/	/	SYM
ejpam-3844	100	13	bci	bci	NOUN
ejpam-3844	100	14	-	-	NOUN
ejpam-3844	100	15	algebra	algebra	NOUN
ejpam-3844	100	16	over	over	ADP
ejpam-3844	100	17	b.	b.	PROPN
ejpam-3844	101	1	if	if	SCONJ
ejpam-3844	101	2	(	(	PUNCT
ejpam-3844	101	3	µ̃,m	µ̃,m	PROPN
ejpam-3844	101	4	)	)	PUNCT
ejpam-3844	101	5	and	and	CCONJ
ejpam-3844	101	6	(	(	PUNCT
ejpam-3844	101	7	η̃	η̃	PROPN
ejpam-3844	101	8	,	,	PUNCT
ejpam-3844	101	9	n	n	CCONJ
ejpam-3844	101	10	)	)	PUNCT
ejpam-3844	101	11	are	be	AUX
ejpam-3844	101	12	fuzzy	fuzzy	ADJ
ejpam-3844	101	13	soft	soft	ADJ
ejpam-3844	101	14	sub	sub	NOUN
ejpam-3844	101	15	-	-	ADJ
ejpam-3844	101	16	bck	bck	ADJ
ejpam-3844	101	17	/	/	SYM
ejpam-3844	101	18	bci	bci	NOUN
ejpam-3844	101	19	-	-	PUNCT
ejpam-3844	101	20	algebras	algebra	NOUN
ejpam-3844	101	21	of	of	ADP
ejpam-3844	101	22	(	(	PUNCT
ejpam-3844	101	23	ξ̃	ξ̃	PROPN
ejpam-3844	101	24	,	,	PUNCT
ejpam-3844	101	25	q	q	NOUN
ejpam-3844	101	26	)	)	PUNCT
ejpam-3844	101	27	,	,	PUNCT
ejpam-3844	101	28	then	then	ADV
ejpam-3844	101	29	so	so	ADV
ejpam-3844	101	30	is	be	AUX
ejpam-3844	101	31	the	the	DET
ejpam-3844	101	32	extended	extended	ADJ
ejpam-3844	101	33	intersection	intersection	NOUN
ejpam-3844	101	34	of	of	ADP
ejpam-3844	101	35	(	(	PUNCT
ejpam-3844	101	36	µ̃,m	µ̃,m	PROPN
ejpam-3844	101	37	)	)	PUNCT
ejpam-3844	101	38	and	and	CCONJ
ejpam-3844	101	39	(	(	PUNCT
ejpam-3844	101	40	η̃	η̃	PROPN
ejpam-3844	101	41	,	,	PUNCT
ejpam-3844	101	42	n	n	CCONJ
ejpam-3844	101	43	)	)	PUNCT
ejpam-3844	101	44	.	.	PUNCT
ejpam-3844	102	1	proof	proof	NOUN
ejpam-3844	102	2	.	.	PUNCT
ejpam-3844	103	1	it	it	PRON
ejpam-3844	103	2	is	be	AUX
ejpam-3844	103	3	proved	prove	VERB
ejpam-3844	103	4	by	by	ADP
ejpam-3844	103	5	definition	definition	NOUN
ejpam-3844	103	6	9	9	NUM
ejpam-3844	103	7	and	and	CCONJ
ejpam-3844	103	8	lemma	lemma	PROPN
ejpam-3844	103	9	1	1	X
ejpam-3844	103	10	.	.	PUNCT
ejpam-3844	104	1	lemma	lemma	PROPN
ejpam-3844	104	2	2	2	NUM
ejpam-3844	104	3	(	(	PUNCT
ejpam-3844	104	4	[	[	X
ejpam-3844	104	5	8	8	NUM
ejpam-3844	104	6	]	]	PUNCT
ejpam-3844	104	7	)	)	PUNCT
ejpam-3844	104	8	.	.	PUNCT
ejpam-3844	105	1	let	let	VERB
ejpam-3844	105	2	(	(	PUNCT
ejpam-3844	105	3	µ̃,m	µ̃,m	PROPN
ejpam-3844	105	4	)	)	PUNCT
ejpam-3844	105	5	and	and	CCONJ
ejpam-3844	105	6	(	(	PUNCT
ejpam-3844	105	7	η̃	η̃	PROPN
ejpam-3844	105	8	,	,	PUNCT
ejpam-3844	105	9	n	n	CCONJ
ejpam-3844	105	10	)	)	PUNCT
ejpam-3844	105	11	be	be	AUX
ejpam-3844	105	12	fuzzy	fuzzy	ADJ
ejpam-3844	105	13	soft	soft	ADJ
ejpam-3844	105	14	bck	bck	NOUN
ejpam-3844	105	15	/	/	SYM
ejpam-3844	105	16	bci	bci	NOUN
ejpam-3844	105	17	-	-	PUNCT
ejpam-3844	105	18	algebras	algebras	PROPN
ejpam-3844	105	19	over	over	ADP
ejpam-3844	105	20	b.	b.	PROPN
ejpam-3844	106	1	if	if	SCONJ
ejpam-3844	106	2	m	m	PROPN
ejpam-3844	106	3	and	and	CCONJ
ejpam-3844	106	4	n	n	PROPN
ejpam-3844	106	5	are	be	AUX
ejpam-3844	106	6	disjoint	disjoint	ADJ
ejpam-3844	106	7	,	,	PUNCT
ejpam-3844	106	8	then	then	ADV
ejpam-3844	106	9	the	the	DET
ejpam-3844	106	10	union	union	NOUN
ejpam-3844	106	11	(	(	PUNCT
ejpam-3844	106	12	µ̃,m	µ̃,m	PROPN
ejpam-3844	106	13	)	)	PUNCT
ejpam-3844	106	14	∪̃	∪̃	PROPN
ejpam-3844	106	15	(	(	PUNCT
ejpam-3844	106	16	η̃	η̃	PROPN
ejpam-3844	106	17	,	,	PUNCT
ejpam-3844	106	18	n	n	CCONJ
ejpam-3844	106	19	)	)	PUNCT
ejpam-3844	106	20	is	be	AUX
ejpam-3844	106	21	a	a	DET
ejpam-3844	106	22	fuzzy	fuzzy	ADJ
ejpam-3844	106	23	soft	soft	ADJ
ejpam-3844	106	24	bck	bck	NOUN
ejpam-3844	106	25	/	/	SYM
ejpam-3844	106	26	bci	bci	NOUN
ejpam-3844	106	27	-	-	NOUN
ejpam-3844	106	28	algebra	algebra	NOUN
ejpam-3844	106	29	over	over	ADP
ejpam-3844	106	30	b.	b.	PROPN
ejpam-3844	106	31	theorem	theorem	PROPN
ejpam-3844	106	32	5	5	X
ejpam-3844	106	33	.	.	PUNCT
ejpam-3844	107	1	let	let	AUX
ejpam-3844	107	2	(	(	PUNCT
ejpam-3844	107	3	ξ̃	ξ̃	PROPN
ejpam-3844	107	4	,	,	PUNCT
ejpam-3844	107	5	q	q	PUNCT
ejpam-3844	107	6	)	)	PUNCT
ejpam-3844	107	7	be	be	AUX
ejpam-3844	107	8	a	a	DET
ejpam-3844	107	9	fuzzy	fuzzy	ADJ
ejpam-3844	107	10	soft	soft	ADJ
ejpam-3844	107	11	bck	bck	NOUN
ejpam-3844	107	12	/	/	SYM
ejpam-3844	107	13	bci	bci	NOUN
ejpam-3844	107	14	-	-	NOUN
ejpam-3844	107	15	algebra	algebra	NOUN
ejpam-3844	107	16	over	over	ADP
ejpam-3844	107	17	b.	b.	PROPN
ejpam-3844	108	1	if	if	SCONJ
ejpam-3844	108	2	(	(	PUNCT
ejpam-3844	108	3	µ̃,m	µ̃,m	PROPN
ejpam-3844	108	4	)	)	PUNCT
ejpam-3844	108	5	and	and	CCONJ
ejpam-3844	108	6	(	(	PUNCT
ejpam-3844	108	7	η̃	η̃	PROPN
ejpam-3844	108	8	,	,	PUNCT
ejpam-3844	108	9	n	n	CCONJ
ejpam-3844	108	10	)	)	PUNCT
ejpam-3844	108	11	are	be	AUX
ejpam-3844	108	12	fuzzy	fuzzy	ADJ
ejpam-3844	108	13	soft	soft	ADJ
ejpam-3844	108	14	sub	sub	NOUN
ejpam-3844	108	15	-	-	ADJ
ejpam-3844	108	16	bck	bck	ADJ
ejpam-3844	108	17	/	/	SYM
ejpam-3844	108	18	bci	bci	NOUN
ejpam-3844	108	19	-	-	PUNCT
ejpam-3844	108	20	algebras	algebra	NOUN
ejpam-3844	108	21	of	of	ADP
ejpam-3844	108	22	(	(	PUNCT
ejpam-3844	108	23	ξ̃	ξ̃	PROPN
ejpam-3844	108	24	,	,	PUNCT
ejpam-3844	108	25	q	q	NOUN
ejpam-3844	108	26	)	)	PUNCT
ejpam-3844	108	27	,	,	PUNCT
ejpam-3844	108	28	then	then	ADV
ejpam-3844	108	29	so	so	ADV
ejpam-3844	108	30	is	be	AUX
ejpam-3844	108	31	the	the	DET
ejpam-3844	108	32	union	union	NOUN
ejpam-3844	108	33	of	of	ADP
ejpam-3844	108	34	(	(	PUNCT
ejpam-3844	108	35	µ̃,m	µ̃,m	PROPN
ejpam-3844	108	36	)	)	PUNCT
ejpam-3844	108	37	and	and	CCONJ
ejpam-3844	108	38	(	(	PUNCT
ejpam-3844	108	39	η̃	η̃	PROPN
ejpam-3844	108	40	,	,	PUNCT
ejpam-3844	108	41	n	n	CCONJ
ejpam-3844	108	42	)	)	PUNCT
ejpam-3844	108	43	whenever	whenever	SCONJ
ejpam-3844	108	44	m	m	VERB
ejpam-3844	108	45	and	and	CCONJ
ejpam-3844	108	46	n	n	PROPN
ejpam-3844	108	47	are	be	AUX
ejpam-3844	108	48	disjoint	disjoint	ADJ
ejpam-3844	108	49	.	.	PUNCT
ejpam-3844	109	1	proof	proof	NOUN
ejpam-3844	109	2	.	.	PUNCT
ejpam-3844	110	1	it	it	PRON
ejpam-3844	110	2	is	be	AUX
ejpam-3844	110	3	proved	prove	VERB
ejpam-3844	110	4	by	by	ADP
ejpam-3844	110	5	definition	definition	NOUN
ejpam-3844	110	6	9	9	NUM
ejpam-3844	110	7	and	and	CCONJ
ejpam-3844	110	8	lemma	lemma	PROPN
ejpam-3844	110	9	2	2	PROPN
ejpam-3844	110	10	.	.	PUNCT
ejpam-3844	111	1	lemma	lemma	PROPN
ejpam-3844	111	2	3	3	NUM
ejpam-3844	111	3	(	(	PUNCT
ejpam-3844	111	4	[	[	X
ejpam-3844	111	5	8	8	NUM
ejpam-3844	111	6	]	]	PUNCT
ejpam-3844	111	7	)	)	PUNCT
ejpam-3844	111	8	.	.	PUNCT
ejpam-3844	112	1	if	if	SCONJ
ejpam-3844	112	2	(	(	PUNCT
ejpam-3844	112	3	µ̃,m	µ̃,m	PROPN
ejpam-3844	112	4	)	)	PUNCT
ejpam-3844	112	5	and	and	CCONJ
ejpam-3844	112	6	(	(	PUNCT
ejpam-3844	112	7	η̃	η̃	PROPN
ejpam-3844	112	8	,	,	PUNCT
ejpam-3844	112	9	n	n	CCONJ
ejpam-3844	112	10	)	)	PUNCT
ejpam-3844	112	11	are	be	AUX
ejpam-3844	112	12	two	two	NUM
ejpam-3844	112	13	fuzzy	fuzzy	ADJ
ejpam-3844	112	14	soft	soft	ADJ
ejpam-3844	112	15	bck	bck	NOUN
ejpam-3844	112	16	/	/	SYM
ejpam-3844	112	17	bci	bci	NOUN
ejpam-3844	112	18	-	-	PUNCT
ejpam-3844	112	19	algebras	algebra	NOUN
ejpam-3844	112	20	over	over	ADP
ejpam-3844	112	21	b	b	PROPN
ejpam-3844	112	22	,	,	PUNCT
ejpam-3844	112	23	then	then	ADV
ejpam-3844	112	24	(	(	PUNCT
ejpam-3844	112	25	µ̃,m	µ̃,m	PROPN
ejpam-3844	112	26	)	)	PUNCT
ejpam-3844	112	27	∧̃	∧̃	PROPN
ejpam-3844	112	28	(	(	PUNCT
ejpam-3844	112	29	η̃	η̃	PROPN
ejpam-3844	112	30	,	,	PUNCT
ejpam-3844	112	31	n	n	CCONJ
ejpam-3844	112	32	)	)	PUNCT
ejpam-3844	112	33	is	be	AUX
ejpam-3844	112	34	a	a	DET
ejpam-3844	112	35	fuzzy	fuzzy	ADJ
ejpam-3844	112	36	soft	soft	ADJ
ejpam-3844	112	37	bck	bck	NOUN
ejpam-3844	112	38	/	/	SYM
ejpam-3844	112	39	bci	bci	NOUN
ejpam-3844	112	40	-	-	NOUN
ejpam-3844	112	41	algebra	algebra	NOUN
ejpam-3844	112	42	over	over	ADP
ejpam-3844	112	43	b.	b.	PROPN
ejpam-3844	112	44	theorem	theorem	PROPN
ejpam-3844	112	45	6	6	NUM
ejpam-3844	112	46	.	.	PUNCT
ejpam-3844	113	1	let	let	AUX
ejpam-3844	113	2	(	(	PUNCT
ejpam-3844	113	3	ξ̃	ξ̃	PROPN
ejpam-3844	113	4	,	,	PUNCT
ejpam-3844	113	5	q	q	PUNCT
ejpam-3844	113	6	)	)	PUNCT
ejpam-3844	113	7	be	be	AUX
ejpam-3844	113	8	a	a	DET
ejpam-3844	113	9	fuzzy	fuzzy	ADJ
ejpam-3844	113	10	soft	soft	ADJ
ejpam-3844	113	11	bck	bck	NOUN
ejpam-3844	113	12	/	/	SYM
ejpam-3844	113	13	bci	bci	NOUN
ejpam-3844	113	14	-	-	NOUN
ejpam-3844	113	15	algebra	algebra	NOUN
ejpam-3844	113	16	over	over	ADP
ejpam-3844	113	17	b.	b.	PROPN
ejpam-3844	114	1	if	if	SCONJ
ejpam-3844	114	2	(	(	PUNCT
ejpam-3844	114	3	µ̃,m	µ̃,m	PROPN
ejpam-3844	114	4	)	)	PUNCT
ejpam-3844	114	5	and	and	CCONJ
ejpam-3844	114	6	(	(	PUNCT
ejpam-3844	114	7	η̃	η̃	PROPN
ejpam-3844	114	8	,	,	PUNCT
ejpam-3844	114	9	n	n	CCONJ
ejpam-3844	114	10	)	)	PUNCT
ejpam-3844	114	11	are	be	AUX
ejpam-3844	114	12	fuzzy	fuzzy	ADJ
ejpam-3844	114	13	soft	soft	ADJ
ejpam-3844	114	14	sub	sub	NOUN
ejpam-3844	114	15	-	-	ADJ
ejpam-3844	114	16	bck	bck	ADJ
ejpam-3844	114	17	/	/	SYM
ejpam-3844	114	18	bci	bci	NOUN
ejpam-3844	114	19	-	-	PUNCT
ejpam-3844	114	20	algebras	algebra	NOUN
ejpam-3844	114	21	of	of	ADP
ejpam-3844	114	22	(	(	PUNCT
ejpam-3844	114	23	ξ̃	ξ̃	PROPN
ejpam-3844	114	24	,	,	PUNCT
ejpam-3844	114	25	q	q	NOUN
ejpam-3844	114	26	)	)	PUNCT
ejpam-3844	114	27	,	,	PUNCT
ejpam-3844	114	28	then	then	ADV
ejpam-3844	114	29	(	(	PUNCT
ejpam-3844	114	30	µ̃,m	µ̃,m	PROPN
ejpam-3844	114	31	)	)	PUNCT
ejpam-3844	114	32	∧̃	∧̃	PROPN
ejpam-3844	114	33	(	(	PUNCT
ejpam-3844	114	34	η̃	η̃	PROPN
ejpam-3844	114	35	,	,	PUNCT
ejpam-3844	114	36	n	n	CCONJ
ejpam-3844	114	37	)	)	PUNCT
ejpam-3844	114	38	is	be	AUX
ejpam-3844	114	39	a	a	DET
ejpam-3844	114	40	fuzzy	fuzzy	ADJ
ejpam-3844	114	41	soft	soft	ADJ
ejpam-3844	114	42	subbck	subbck	NOUN
ejpam-3844	114	43	/	/	SYM
ejpam-3844	114	44	bci	bci	NOUN
ejpam-3844	114	45	-	-	NOUN
ejpam-3844	114	46	algebra	algebra	NOUN
ejpam-3844	114	47	of	of	ADP
ejpam-3844	114	48	(	(	PUNCT
ejpam-3844	114	49	ξ̃	ξ̃	PROPN
ejpam-3844	114	50	,	,	PUNCT
ejpam-3844	114	51	q	q	NOUN
ejpam-3844	114	52	)	)	PUNCT
ejpam-3844	114	53	.	.	PUNCT
ejpam-3844	115	1	proof	proof	NOUN
ejpam-3844	115	2	.	.	PUNCT
ejpam-3844	116	1	it	it	PRON
ejpam-3844	116	2	is	be	AUX
ejpam-3844	116	3	proved	prove	VERB
ejpam-3844	116	4	by	by	ADP
ejpam-3844	116	5	definition	definition	NOUN
ejpam-3844	116	6	9	9	NUM
ejpam-3844	116	7	and	and	CCONJ
ejpam-3844	116	8	lemma	lemma	PROPN
ejpam-3844	116	9	3	3	X
ejpam-3844	116	10	.	.	PUNCT
ejpam-3844	117	1	let	let	VERB
ejpam-3844	117	2	(	(	PUNCT
ejpam-3844	117	3	µ̃,m	µ̃,m	PROPN
ejpam-3844	117	4	)	)	PUNCT
ejpam-3844	117	5	be	be	VERB
ejpam-3844	117	6	a	a	DET
ejpam-3844	117	7	fuzzy	fuzzy	ADJ
ejpam-3844	117	8	soft	soft	ADJ
ejpam-3844	117	9	set	set	NOUN
ejpam-3844	117	10	over	over	ADP
ejpam-3844	117	11	b	b	NOUN
ejpam-3844	117	12	and	and	CCONJ
ejpam-3844	117	13	let	let	VERB
ejpam-3844	118	1	k	k	PROPN
ejpam-3844	118	2	∈	∈	PROPN
ejpam-3844	118	3	[	[	X
ejpam-3844	118	4	0	0	NUM
ejpam-3844	118	5	,	,	PUNCT
ejpam-3844	118	6	1	1	NUM
ejpam-3844	118	7	]	]	PUNCT
ejpam-3844	118	8	.	.	PUNCT
ejpam-3844	119	1	for	for	ADP
ejpam-3844	119	2	a	a	DET
ejpam-3844	119	3	parameter	parameter	NOUN
ejpam-3844	119	4	m	m	VERB
ejpam-3844	119	5	in	in	ADP
ejpam-3844	119	6	m	m	PROPN
ejpam-3844	119	7	,	,	PUNCT
ejpam-3844	119	8	consider	consider	VERB
ejpam-3844	119	9	the	the	DET
ejpam-3844	119	10	following	follow	VERB
ejpam-3844	119	11	sets	set	NOUN
ejpam-3844	119	12	:	:	PUNCT
ejpam-3844	119	13	al	al	PROPN
ejpam-3844	119	14	-	-	PUNCT
ejpam-3844	119	15	kadi	kadi	PROPN
ejpam-3844	119	16	,	,	PUNCT
ejpam-3844	119	17	muhiuddin	muhiuddin	NOUN
ejpam-3844	119	18	/	/	SYM
ejpam-3844	119	19	eur	eur	PROPN
ejpam-3844	119	20	.	.	PUNCT
ejpam-3844	120	1	j.	j.	PROPN
ejpam-3844	120	2	pure	pure	PROPN
ejpam-3844	120	3	appl	appl	PROPN
ejpam-3844	120	4	.	.	PROPN
ejpam-3844	120	5	math	math	PROPN
ejpam-3844	120	6	,	,	PUNCT
ejpam-3844	120	7	13	13	NUM
ejpam-3844	120	8	(	(	PUNCT
ejpam-3844	120	9	4	4	NUM
ejpam-3844	120	10	)	)	PUNCT
ejpam-3844	120	11	(	(	PUNCT
ejpam-3844	120	12	2020	2020	NUM
ejpam-3844	120	13	)	)	PUNCT
ejpam-3844	120	14	,	,	PUNCT
ejpam-3844	120	15	939	939	NUM
ejpam-3844	120	16	-	-	SYM
ejpam-3844	120	17	947	947	NUM
ejpam-3844	120	18	945	945	NUM
ejpam-3844	120	19	(	(	PUNCT
ejpam-3844	120	20	µ̃,m)≥km	µ̃,m)≥km	PUNCT
ejpam-3844	120	21	:	:	PUNCT
ejpam-3844	120	22	=	=	SYM
ejpam-3844	120	23	{	{	PUNCT
ejpam-3844	120	24	β	β	X
ejpam-3844	120	25	∈	∈	PROPN
ejpam-3844	120	26	b	b	PROPN
ejpam-3844	120	27	|	|	ADV
ejpam-3844	120	28	µ̃[m](β	µ̃[m](β	NOUN
ejpam-3844	120	29	)	)	PUNCT
ejpam-3844	120	30	≥	≥	NOUN
ejpam-3844	120	31	k	k	NOUN
ejpam-3844	120	32	}	}	PUNCT
ejpam-3844	120	33	,	,	PUNCT
ejpam-3844	120	34	and	and	CCONJ
ejpam-3844	120	35	(	(	PUNCT
ejpam-3844	120	36	µ̃,m)≥k	µ̃,m)≥k	NOUN
ejpam-3844	120	37	:	:	PUNCT
ejpam-3844	120	38	=	=	SYM
ejpam-3844	120	39	{	{	PUNCT
ejpam-3844	120	40	β	β	X
ejpam-3844	120	41	∈	∈	PROPN
ejpam-3844	120	42	b	b	PROPN
ejpam-3844	120	43	|	|	ADV
ejpam-3844	120	44	µ̃[m](β	µ̃[m](β	NOUN
ejpam-3844	120	45	)	)	PUNCT
ejpam-3844	120	46	≥	≥	NOUN
ejpam-3844	120	47	k	k	NOUN
ejpam-3844	120	48	for	for	ADP
ejpam-3844	120	49	all	all	DET
ejpam-3844	120	50	m	m	NOUN
ejpam-3844	120	51	∈m	∈m	NOUN
ejpam-3844	120	52	}	}	PUNCT
ejpam-3844	120	53	.	.	PUNCT
ejpam-3844	121	1	obviously	obviously	ADV
ejpam-3844	121	2	,	,	PUNCT
ejpam-3844	121	3	(	(	PUNCT
ejpam-3844	121	4	µ̃,m)≥k	µ̃,m)≥k	NOUN
ejpam-3844	121	5	=	=	SYM
ejpam-3844	121	6	⋂	⋂	PROPN
ejpam-3844	121	7	m∈m	m∈m	NOUN
ejpam-3844	121	8	(	(	PUNCT
ejpam-3844	121	9	µ̃,m)≥km	µ̃,m)≥km	PRON
ejpam-3844	121	10	.	.	PUNCT
ejpam-3844	122	1	theorem	theorem	VERB
ejpam-3844	122	2	7	7	NUM
ejpam-3844	122	3	.	.	X
ejpam-3844	122	4	for	for	ADP
ejpam-3844	122	5	a	a	DET
ejpam-3844	122	6	fuzzy	fuzzy	ADJ
ejpam-3844	122	7	soft	soft	ADJ
ejpam-3844	122	8	set	set	NOUN
ejpam-3844	122	9	(	(	PUNCT
ejpam-3844	122	10	µ̃,m	µ̃,m	PROPN
ejpam-3844	122	11	)	)	PUNCT
ejpam-3844	122	12	over	over	ADP
ejpam-3844	122	13	b	b	PROPN
ejpam-3844	122	14	,	,	PUNCT
ejpam-3844	122	15	the	the	DET
ejpam-3844	122	16	following	follow	VERB
ejpam-3844	122	17	two	two	NUM
ejpam-3844	122	18	statements	statement	NOUN
ejpam-3844	122	19	are	be	AUX
ejpam-3844	122	20	equivalent	equivalent	ADJ
ejpam-3844	122	21	:	:	PUNCT
ejpam-3844	122	22	(	(	PUNCT
ejpam-3844	122	23	1	1	X
ejpam-3844	122	24	)	)	PUNCT
ejpam-3844	122	25	(	(	PUNCT
ejpam-3844	122	26	µ̃,m	µ̃,m	PROPN
ejpam-3844	122	27	)	)	PUNCT
ejpam-3844	122	28	is	be	AUX
ejpam-3844	122	29	a	a	DET
ejpam-3844	122	30	fuzzy	fuzzy	ADJ
ejpam-3844	122	31	soft	soft	ADJ
ejpam-3844	122	32	bck	bck	NOUN
ejpam-3844	122	33	/	/	SYM
ejpam-3844	122	34	bci	bci	NOUN
ejpam-3844	122	35	-	-	NOUN
ejpam-3844	122	36	algebra	algebra	NOUN
ejpam-3844	122	37	over	over	ADP
ejpam-3844	122	38	b	b	NOUN
ejpam-3844	122	39	based	base	VERB
ejpam-3844	122	40	on	on	ADP
ejpam-3844	122	41	a	a	DET
ejpam-3844	122	42	parameter	parameter	NOUN
ejpam-3844	122	43	m	m	NOUN
ejpam-3844	122	44	∈m	∈m	NOUN
ejpam-3844	122	45	.	.	PUNCT
ejpam-3844	123	1	(	(	PUNCT
ejpam-3844	123	2	2	2	NUM
ejpam-3844	123	3	)	)	PUNCT
ejpam-3844	123	4	(	(	PUNCT
ejpam-3844	123	5	µ̃,m)≥km	µ̃,m)≥km	ADV
ejpam-3844	123	6	is	be	AUX
ejpam-3844	123	7	a	a	DET
ejpam-3844	123	8	subalgebra	subalgebra	NOUN
ejpam-3844	123	9	of	of	ADP
ejpam-3844	123	10	b	b	NOUN
ejpam-3844	123	11	for	for	ADP
ejpam-3844	123	12	all	all	DET
ejpam-3844	123	13	k	k	PROPN
ejpam-3844	123	14	∈	∈	PROPN
ejpam-3844	124	1	[	[	X
ejpam-3844	124	2	0	0	NUM
ejpam-3844	124	3	,	,	PUNCT
ejpam-3844	124	4	1	1	NUM
ejpam-3844	124	5	]	]	PUNCT
ejpam-3844	124	6	with	with	ADP
ejpam-3844	124	7	(	(	PUNCT
ejpam-3844	124	8	µ̃,m)≥km	µ̃,m)≥km	PRON
ejpam-3844	124	9	6=	6=	X
ejpam-3844	124	10	∅.	∅.	NOUN
ejpam-3844	124	11	proof	proof	NOUN
ejpam-3844	124	12	.	.	PUNCT
ejpam-3844	125	1	(	(	PUNCT
ejpam-3844	125	2	1)⇒	1)⇒	NUM
ejpam-3844	125	3	(	(	PUNCT
ejpam-3844	125	4	2	2	NUM
ejpam-3844	125	5	)	)	PUNCT
ejpam-3844	125	6	.	.	PUNCT
ejpam-3844	126	1	assume	assume	VERB
ejpam-3844	126	2	that	that	SCONJ
ejpam-3844	126	3	(	(	PUNCT
ejpam-3844	126	4	µ̃,m	µ̃,m	PROPN
ejpam-3844	126	5	)	)	PUNCT
ejpam-3844	126	6	is	be	AUX
ejpam-3844	126	7	a	a	DET
ejpam-3844	126	8	fuzzy	fuzzy	ADJ
ejpam-3844	126	9	soft	soft	ADJ
ejpam-3844	126	10	bck	bck	NOUN
ejpam-3844	126	11	/	/	SYM
ejpam-3844	126	12	bci	bci	NOUN
ejpam-3844	126	13	-	-	NOUN
ejpam-3844	126	14	algebra	algebra	NOUN
ejpam-3844	126	15	over	over	ADP
ejpam-3844	126	16	b	b	NOUN
ejpam-3844	126	17	based	base	VERB
ejpam-3844	126	18	on	on	ADP
ejpam-3844	126	19	a	a	DET
ejpam-3844	126	20	parameter	parameter	NOUN
ejpam-3844	126	21	m	m	NOUN
ejpam-3844	126	22	∈m	∈m	NOUN
ejpam-3844	126	23	.	.	PUNCT
ejpam-3844	127	1	let	let	VERB
ejpam-3844	127	2	k	k	PROPN
ejpam-3844	127	3	∈	∈	PROPN
ejpam-3844	128	1	[	[	X
ejpam-3844	128	2	0	0	NUM
ejpam-3844	128	3	,	,	PUNCT
ejpam-3844	128	4	1	1	NUM
ejpam-3844	128	5	]	]	PUNCT
ejpam-3844	129	1	such	such	ADJ
ejpam-3844	129	2	that	that	SCONJ
ejpam-3844	129	3	(	(	PUNCT
ejpam-3844	129	4	µ̃,m)≥km	µ̃,m)≥km	X
ejpam-3844	129	5	6=	6=	PUNCT
ejpam-3844	129	6	∅.	∅.	NOUN
ejpam-3844	129	7	let	let	VERB
ejpam-3844	129	8	β	β	X
ejpam-3844	129	9	,	,	PUNCT
ejpam-3844	129	10	γ	γ	PROPN
ejpam-3844	129	11	∈	∈	PROPN
ejpam-3844	129	12	(	(	PUNCT
ejpam-3844	129	13	µ̃,m)≥km	µ̃,m)≥km	PUNCT
ejpam-3844	129	14	.	.	PUNCT
ejpam-3844	130	1	then	then	ADV
ejpam-3844	130	2	,	,	PUNCT
ejpam-3844	130	3	µ̃[m](β	µ̃[m](β	NOUN
ejpam-3844	130	4	)	)	PUNCT
ejpam-3844	130	5	≥	≥	NOUN
ejpam-3844	130	6	k	k	NOUN
ejpam-3844	130	7	and	and	CCONJ
ejpam-3844	130	8	µ̃[m](γ	µ̃[m](γ	PROPN
ejpam-3844	130	9	)	)	PUNCT
ejpam-3844	130	10	≥	≥	NOUN
ejpam-3844	130	11	k.	k.	PUNCT
ejpam-3844	131	1	thus	thus	ADV
ejpam-3844	131	2	,	,	PUNCT
ejpam-3844	131	3	µ̃[m](β	µ̃[m](β	PROPN
ejpam-3844	131	4	∗	∗	X
ejpam-3844	131	5	γ	γ	PROPN
ejpam-3844	131	6	)	)	PUNCT
ejpam-3844	131	7	≥	≥	PROPN
ejpam-3844	131	8	min	min	PROPN
ejpam-3844	131	9	{	{	PUNCT
ejpam-3844	131	10	µ̃[m](β	µ̃[m](β	NOUN
ejpam-3844	131	11	)	)	PUNCT
ejpam-3844	131	12	,	,	PUNCT
ejpam-3844	131	13	µ̃[m](γ	µ̃[m](γ	PROPN
ejpam-3844	131	14	)	)	PUNCT
ejpam-3844	131	15	}	}	PUNCT
ejpam-3844	131	16	≥	≥	PROPN
ejpam-3844	131	17	k	k	NOUN
ejpam-3844	131	18	which	which	PRON
ejpam-3844	131	19	implies	imply	VERB
ejpam-3844	131	20	that	that	SCONJ
ejpam-3844	131	21	β	β	PROPN
ejpam-3844	131	22	∗	∗	NOUN
ejpam-3844	131	23	γ	γ	X
ejpam-3844	131	24	∈	∈	PROPN
ejpam-3844	131	25	(	(	PUNCT
ejpam-3844	131	26	µ̃,m)≥km	µ̃,m)≥km	PUNCT
ejpam-3844	131	27	.	.	PUNCT
ejpam-3844	132	1	therefore	therefore	ADV
ejpam-3844	132	2	,	,	PUNCT
ejpam-3844	132	3	(	(	PUNCT
ejpam-3844	132	4	µ̃,m)≥km	µ̃,m)≥km	ADV
ejpam-3844	132	5	is	be	AUX
ejpam-3844	132	6	a	a	DET
ejpam-3844	132	7	subalgebra	subalgebra	NOUN
ejpam-3844	132	8	of	of	ADP
ejpam-3844	132	9	b.	b.	PROPN
ejpam-3844	132	10	(	(	PUNCT
ejpam-3844	132	11	2	2	NUM
ejpam-3844	132	12	)	)	PUNCT
ejpam-3844	132	13	⇒	⇒	NOUN
ejpam-3844	132	14	(	(	PUNCT
ejpam-3844	132	15	1	1	NUM
ejpam-3844	132	16	)	)	PUNCT
ejpam-3844	132	17	.	.	PUNCT
ejpam-3844	133	1	suppose	suppose	VERB
ejpam-3844	133	2	that	that	SCONJ
ejpam-3844	133	3	the	the	DET
ejpam-3844	133	4	second	second	ADJ
ejpam-3844	133	5	assertion	assertion	NOUN
ejpam-3844	133	6	is	be	AUX
ejpam-3844	133	7	valid	valid	ADJ
ejpam-3844	133	8	and	and	CCONJ
ejpam-3844	133	9	that	that	SCONJ
ejpam-3844	133	10	(	(	PUNCT
ejpam-3844	133	11	µ̃,m	µ̃,m	PROPN
ejpam-3844	133	12	)	)	PUNCT
ejpam-3844	133	13	is	be	AUX
ejpam-3844	133	14	not	not	PART
ejpam-3844	133	15	a	a	DET
ejpam-3844	133	16	fuzzy	fuzzy	ADJ
ejpam-3844	133	17	soft	soft	ADJ
ejpam-3844	133	18	bck	bck	NOUN
ejpam-3844	133	19	/	/	SYM
ejpam-3844	133	20	bci	bci	NOUN
ejpam-3844	133	21	-	-	NOUN
ejpam-3844	133	22	algebra	algebra	NOUN
ejpam-3844	133	23	over	over	ADP
ejpam-3844	133	24	b	b	NOUN
ejpam-3844	133	25	based	base	VERB
ejpam-3844	133	26	on	on	ADP
ejpam-3844	133	27	a	a	DET
ejpam-3844	133	28	parameter	parameter	NOUN
ejpam-3844	133	29	m	m	NOUN
ejpam-3844	133	30	∈m	∈m	NOUN
ejpam-3844	133	31	.	.	PUNCT
ejpam-3844	134	1	then	then	ADV
ejpam-3844	134	2	,	,	PUNCT
ejpam-3844	134	3	µ̃[m](β	µ̃[m](β	PROPN
ejpam-3844	134	4	∗	∗	X
ejpam-3844	134	5	γ	γ	PROPN
ejpam-3844	134	6	)	)	PUNCT
ejpam-3844	134	7	<	<	X
ejpam-3844	134	8	k0	k0	PROPN
ejpam-3844	134	9	≤	≤	PROPN
ejpam-3844	134	10	min	min	PROPN
ejpam-3844	134	11	{	{	PUNCT
ejpam-3844	134	12	µ̃[m](β	µ̃[m](β	NOUN
ejpam-3844	134	13	)	)	PUNCT
ejpam-3844	134	14	,	,	PUNCT
ejpam-3844	134	15	µ̃[m](γ	µ̃[m](γ	NOUN
ejpam-3844	134	16	)	)	PUNCT
ejpam-3844	134	17	}	}	PUNCT
ejpam-3844	134	18	for	for	ADP
ejpam-3844	134	19	some	some	DET
ejpam-3844	134	20	β	β	NOUN
ejpam-3844	134	21	,	,	PUNCT
ejpam-3844	134	22	γ	γ	PROPN
ejpam-3844	134	23	∈	∈	PROPN
ejpam-3844	134	24	b	b	PROPN
ejpam-3844	134	25	and	and	CCONJ
ejpam-3844	134	26	k0	k0	PROPN
ejpam-3844	134	27	∈	∈	PROPN
ejpam-3844	134	28	(	(	PUNCT
ejpam-3844	134	29	0	0	NUM
ejpam-3844	134	30	,	,	PUNCT
ejpam-3844	134	31	1	1	NUM
ejpam-3844	134	32	]	]	PUNCT
ejpam-3844	134	33	.	.	PUNCT
ejpam-3844	135	1	it	it	PRON
ejpam-3844	135	2	follows	follow	VERB
ejpam-3844	135	3	that	that	SCONJ
ejpam-3844	135	4	β	β	X
ejpam-3844	135	5	,	,	PUNCT
ejpam-3844	135	6	γ	γ	PROPN
ejpam-3844	135	7	∈	∈	PROPN
ejpam-3844	135	8	(	(	PUNCT
ejpam-3844	135	9	µ̃,m)≥k0	µ̃,m)≥k0	NOUN
ejpam-3844	135	10	m	m	VERB
ejpam-3844	135	11	but	but	CCONJ
ejpam-3844	135	12	β	β	X
ejpam-3844	135	13	∗	∗	X
ejpam-3844	135	14	γ	γ	X
ejpam-3844	135	15	/∈	/∈	PUNCT
ejpam-3844	135	16	(	(	PUNCT
ejpam-3844	135	17	µ̃,m)≥k0	µ̃,m)≥k0	NOUN
ejpam-3844	135	18	m	m	NOUN
ejpam-3844	135	19	,	,	PUNCT
ejpam-3844	135	20	which	which	PRON
ejpam-3844	135	21	is	be	AUX
ejpam-3844	135	22	a	a	DET
ejpam-3844	135	23	contradiction	contradiction	NOUN
ejpam-3844	135	24	.	.	PUNCT
ejpam-3844	136	1	hence	hence	ADV
ejpam-3844	136	2	,	,	PUNCT
ejpam-3844	136	3	(	(	PUNCT
ejpam-3844	136	4	µ̃,m	µ̃,m	PROPN
ejpam-3844	136	5	)	)	PUNCT
ejpam-3844	136	6	is	be	AUX
ejpam-3844	136	7	a	a	DET
ejpam-3844	136	8	fuzzy	fuzzy	ADJ
ejpam-3844	136	9	soft	soft	ADJ
ejpam-3844	136	10	bck	bck	NOUN
ejpam-3844	136	11	/	/	SYM
ejpam-3844	136	12	bci	bci	NOUN
ejpam-3844	136	13	-	-	NOUN
ejpam-3844	136	14	algebra	algebra	NOUN
ejpam-3844	136	15	over	over	ADP
ejpam-3844	136	16	b	b	NOUN
ejpam-3844	136	17	based	base	VERB
ejpam-3844	136	18	on	on	ADP
ejpam-3844	136	19	a	a	DET
ejpam-3844	136	20	parameter	parameter	NOUN
ejpam-3844	136	21	m	m	NOUN
ejpam-3844	136	22	∈m	∈m	NOUN
ejpam-3844	136	23	.	.	PUNCT
ejpam-3844	136	24	corollary	corollary	ADJ
ejpam-3844	136	25	1	1	NUM
ejpam-3844	136	26	.	.	PUNCT
ejpam-3844	137	1	a	a	DET
ejpam-3844	137	2	fuzzy	fuzzy	ADJ
ejpam-3844	137	3	soft	soft	ADJ
ejpam-3844	137	4	set	set	NOUN
ejpam-3844	137	5	(	(	PUNCT
ejpam-3844	137	6	µ̃,m	µ̃,m	PROPN
ejpam-3844	137	7	)	)	PUNCT
ejpam-3844	137	8	over	over	ADP
ejpam-3844	137	9	b	b	PROPN
ejpam-3844	137	10	is	be	AUX
ejpam-3844	137	11	a	a	DET
ejpam-3844	137	12	fuzzy	fuzzy	ADJ
ejpam-3844	137	13	soft	soft	ADJ
ejpam-3844	137	14	bck	bck	NOUN
ejpam-3844	137	15	/	/	SYM
ejpam-3844	137	16	bci	bci	NOUN
ejpam-3844	137	17	-	-	NOUN
ejpam-3844	137	18	algebra	algebra	NOUN
ejpam-3844	137	19	over	over	ADP
ejpam-3844	137	20	b	b	NOUN
ejpam-3844	137	21	if	if	SCONJ
ejpam-3844	137	22	and	and	CCONJ
ejpam-3844	137	23	only	only	ADV
ejpam-3844	137	24	if	if	SCONJ
ejpam-3844	137	25	(	(	PUNCT
ejpam-3844	137	26	µ̃,m)≥k	µ̃,m)≥k	NOUN
ejpam-3844	137	27	is	be	AUX
ejpam-3844	137	28	a	a	DET
ejpam-3844	137	29	subalgebra	subalgebra	NOUN
ejpam-3844	137	30	of	of	ADP
ejpam-3844	137	31	b	b	NOUN
ejpam-3844	137	32	for	for	ADP
ejpam-3844	137	33	all	all	DET
ejpam-3844	137	34	k	k	PROPN
ejpam-3844	137	35	∈	∈	PROPN
ejpam-3844	138	1	[	[	X
ejpam-3844	138	2	0	0	NUM
ejpam-3844	138	3	,	,	PUNCT
ejpam-3844	138	4	1	1	NUM
ejpam-3844	138	5	]	]	PUNCT
ejpam-3844	138	6	with	with	ADP
ejpam-3844	138	7	(	(	PUNCT
ejpam-3844	138	8	µ̃,m)≥k	µ̃,m)≥k	PROPN
ejpam-3844	138	9	6=	6=	ADP
ejpam-3844	138	10	∅.	∅.	PRON
ejpam-3844	138	11	4	4	NUM
ejpam-3844	138	12	.	.	PUNCT
ejpam-3844	139	1	conclusion	conclusion	VERB
ejpam-3844	139	2	the	the	DET
ejpam-3844	139	3	main	main	ADJ
ejpam-3844	139	4	goal	goal	NOUN
ejpam-3844	139	5	of	of	ADP
ejpam-3844	139	6	the	the	DET
ejpam-3844	139	7	present	present	ADJ
ejpam-3844	139	8	paper	paper	NOUN
ejpam-3844	139	9	is	be	AUX
ejpam-3844	139	10	to	to	PART
ejpam-3844	139	11	obtain	obtain	VERB
ejpam-3844	139	12	further	further	ADJ
ejpam-3844	139	13	results	result	NOUN
ejpam-3844	139	14	on	on	ADP
ejpam-3844	139	15	fuzzy	fuzzy	ADJ
ejpam-3844	139	16	softbck	softbck	ADJ
ejpam-3844	139	17	/	/	SYM
ejpam-3844	139	18	bcialgebras	bcialgebras	NOUN
ejpam-3844	139	19	.	.	PUNCT
ejpam-3844	140	1	in	in	ADP
ejpam-3844	140	2	fact	fact	NOUN
ejpam-3844	140	3	,	,	PUNCT
ejpam-3844	140	4	the	the	DET
ejpam-3844	140	5	notion	notion	NOUN
ejpam-3844	140	6	of	of	ADP
ejpam-3844	140	7	fuzzy	fuzzy	ADJ
ejpam-3844	140	8	soft	soft	ADJ
ejpam-3844	140	9	sub	sub	NOUN
ejpam-3844	140	10	-	-	ADJ
ejpam-3844	140	11	bck	bck	ADJ
ejpam-3844	140	12	/	/	SYM
ejpam-3844	140	13	bci	bci	NOUN
ejpam-3844	140	14	-	-	NOUN
ejpam-3844	140	15	algebra	algebra	NOUN
ejpam-3844	140	16	is	be	AUX
ejpam-3844	140	17	introduced	introduce	VERB
ejpam-3844	140	18	and	and	CCONJ
ejpam-3844	140	19	related	related	ADJ
ejpam-3844	140	20	properties	property	NOUN
ejpam-3844	140	21	are	be	AUX
ejpam-3844	140	22	investigated	investigate	VERB
ejpam-3844	140	23	.	.	PUNCT
ejpam-3844	141	1	in	in	ADP
ejpam-3844	141	2	our	our	PRON
ejpam-3844	141	3	future	future	ADJ
ejpam-3844	141	4	study	study	NOUN
ejpam-3844	141	5	,	,	PUNCT
ejpam-3844	141	6	we	we	PRON
ejpam-3844	141	7	intend	intend	VERB
ejpam-3844	141	8	to	to	PART
ejpam-3844	141	9	apply	apply	VERB
ejpam-3844	141	10	the	the	DET
ejpam-3844	141	11	notions	notion	NOUN
ejpam-3844	141	12	of	of	ADP
ejpam-3844	141	13	the	the	DET
ejpam-3844	141	14	present	present	ADJ
ejpam-3844	141	15	paper	paper	NOUN
ejpam-3844	141	16	to	to	ADP
ejpam-3844	141	17	different	different	ADJ
ejpam-3844	141	18	algebras	algebra	NOUN
ejpam-3844	141	19	such	such	ADJ
ejpam-3844	141	20	as	as	ADP
ejpam-3844	141	21	bl	bl	NOUN
ejpam-3844	141	22	-	-	PUNCT
ejpam-3844	141	23	algebras	algebras	PROPN
ejpam-3844	141	24	,	,	PUNCT
ejpam-3844	141	25	mtl	mtl	PROPN
ejpam-3844	141	26	-	-	PUNCT
ejpam-3844	141	27	algebras	algebras	PROPN
ejpam-3844	141	28	,	,	PUNCT
ejpam-3844	141	29	r0	r0	NOUN
ejpam-3844	141	30	-algebras	-algebras	PROPN
ejpam-3844	141	31	,	,	PUNCT
ejpam-3844	141	32	mv	mv	PROPN
ejpam-3844	141	33	-algebras	-algebras	PROPN
ejpam-3844	141	34	,	,	PUNCT
ejpam-3844	141	35	eq	eq	NOUN
ejpam-3844	141	36	-	-	PUNCT
ejpam-3844	141	37	algebras	algebras	PROPN
ejpam-3844	141	38	and	and	CCONJ
ejpam-3844	141	39	lattice	lattice	PROPN
ejpam-3844	141	40	implication	implication	NOUN
ejpam-3844	141	41	algebras	algebra	NOUN
ejpam-3844	141	42	etc	etc	X
ejpam-3844	141	43	.	.	X
ejpam-3844	141	44	acknowledgements	acknowledgement	VERB
ejpam-3844	141	45	the	the	DET
ejpam-3844	141	46	authors	author	NOUN
ejpam-3844	141	47	would	would	AUX
ejpam-3844	141	48	like	like	VERB
ejpam-3844	141	49	to	to	PART
ejpam-3844	141	50	express	express	VERB
ejpam-3844	141	51	their	their	PRON
ejpam-3844	141	52	sincere	sincere	ADJ
ejpam-3844	141	53	thanks	thank	NOUN
ejpam-3844	141	54	to	to	ADP
ejpam-3844	141	55	the	the	DET
ejpam-3844	141	56	learned	learn	VERB
ejpam-3844	141	57	referee(s	referee(s	PROPN
ejpam-3844	141	58	)	)	PUNCT
ejpam-3844	141	59	for	for	ADP
ejpam-3844	141	60	valuable	valuable	ADJ
ejpam-3844	141	61	comments	comment	NOUN
ejpam-3844	141	62	and	and	CCONJ
ejpam-3844	141	63	several	several	ADJ
ejpam-3844	141	64	useful	useful	ADJ
ejpam-3844	141	65	suggestions	suggestion	NOUN
ejpam-3844	141	66	.	.	PUNCT
ejpam-3844	142	1	references	reference	NOUN
ejpam-3844	142	2	946	946	NUM
ejpam-3844	142	3	references	reference	NOUN
ejpam-3844	142	4	[	[	X
ejpam-3844	142	5	1	1	NUM
ejpam-3844	142	6	]	]	PUNCT
ejpam-3844	142	7	m.	m.	PROPN
ejpam-3844	142	8	i.	i.	PROPN
ejpam-3844	142	9	ali	ali	PROPN
ejpam-3844	142	10	,	,	PUNCT
ejpam-3844	142	11	f.	f.	PROPN
ejpam-3844	142	12	feng	feng	PROPN
ejpam-3844	142	13	,	,	PUNCT
ejpam-3844	142	14	x	x	PROPN
ejpam-3844	142	15	,	,	PUNCT
ejpam-3844	142	16	liu	liu	PROPN
ejpam-3844	142	17	,	,	PUNCT
ejpam-3844	142	18	w.	w.	PROPN
ejpam-3844	142	19	k.	k.	PROPN
ejpam-3844	142	20	min	min	PROPN
ejpam-3844	142	21	and	and	CCONJ
ejpam-3844	142	22	m.	m.	NOUN
ejpam-3844	142	23	shabir	shabir	PROPN
ejpam-3844	142	24	,	,	PUNCT
ejpam-3844	142	25	on	on	ADP
ejpam-3844	142	26	some	some	DET
ejpam-3844	142	27	new	new	ADJ
ejpam-3844	142	28	operations	operation	NOUN
ejpam-3844	142	29	in	in	ADP
ejpam-3844	142	30	soft	soft	ADJ
ejpam-3844	142	31	set	set	NOUN
ejpam-3844	142	32	theory	theory	NOUN
ejpam-3844	142	33	.	.	PUNCT
ejpam-3844	143	1	comput	comput	NOUN
ejpam-3844	143	2	.	.	PUNCT
ejpam-3844	144	1	math	math	NOUN
ejpam-3844	144	2	.	.	PUNCT
ejpam-3844	145	1	appl	appl	PROPN
ejpam-3844	145	2	.	.	PROPN
ejpam-3844	145	3	,	,	PUNCT
ejpam-3844	145	4	57	57	NUM
ejpam-3844	145	5	(	(	PUNCT
ejpam-3844	145	6	2009	2009	NUM
ejpam-3844	145	7	)	)	PUNCT
ejpam-3844	145	8	1547	1547	NUM
ejpam-3844	145	9	-	-	SYM
ejpam-3844	145	10	1553	1553	NUM
ejpam-3844	145	11	.	.	PUNCT
ejpam-3844	146	1	https://doi.org/10.1016/j.camwa.2008.11.009	https://doi.org/10.1016/j.camwa.2008.11.009	X
ejpam-3844	147	1	[	[	X
ejpam-3844	147	2	2	2	NUM
ejpam-3844	147	3	]	]	PUNCT
ejpam-3844	147	4	a.	a.	PROPN
ejpam-3844	147	5	al	al	PROPN
ejpam-3844	147	6	-	-	PROPN
ejpam-3844	147	7	masarwah	masarwah	PROPN
ejpam-3844	147	8	and	and	CCONJ
ejpam-3844	147	9	a.g	a.g	PROPN
ejpam-3844	147	10	.	.	PROPN
ejpam-3844	147	11	ahmad	ahmad	PROPN
ejpam-3844	147	12	,	,	PUNCT
ejpam-3844	147	13	m	m	NOUN
ejpam-3844	147	14	-	-	ADJ
ejpam-3844	147	15	polar	polar	ADJ
ejpam-3844	147	16	fuzzy	fuzzy	ADJ
ejpam-3844	147	17	ideals	ideal	NOUN
ejpam-3844	147	18	of	of	ADP
ejpam-3844	147	19	bck	bck	PROPN
ejpam-3844	147	20	/	/	SYM
ejpam-3844	147	21	bci	bci	NOUN
ejpam-3844	147	22	-	-	PUNCT
ejpam-3844	147	23	algebras	algebras	X
ejpam-3844	147	24	.	.	PUNCT
ejpam-3844	148	1	j.	j.	PROPN
ejpam-3844	148	2	king	king	PROPN
ejpam-3844	148	3	saud	saud	VERB
ejpam-3844	148	4	univ.-sci	univ.-sci	PRON
ejpam-3844	148	5	.	.	PUNCT
ejpam-3844	149	1	,	,	PUNCT
ejpam-3844	149	2	31	31	NUM
ejpam-3844	149	3	(	(	PUNCT
ejpam-3844	149	4	4	4	NUM
ejpam-3844	149	5	)	)	PUNCT
ejpam-3844	149	6	(	(	PUNCT
ejpam-3844	149	7	2019	2019	NUM
ejpam-3844	149	8	)	)	PUNCT
ejpam-3844	149	9	1220	1220	NUM
ejpam-3844	149	10	-	-	SYM
ejpam-3844	149	11	1226	1226	NUM
ejpam-3844	149	12	.	.	PUNCT
ejpam-3844	150	1	[	[	X
ejpam-3844	150	2	3	3	NUM
ejpam-3844	150	3	]	]	PUNCT
ejpam-3844	150	4	a.	a.	NOUN
ejpam-3844	150	5	al	al	PROPN
ejpam-3844	150	6	-	-	PUNCT
ejpam-3844	150	7	roqi	roqi	ADV
ejpam-3844	150	8	,	,	PUNCT
ejpam-3844	150	9	g.	g.	PROPN
ejpam-3844	150	10	muhiuddin	muhiuddin	PROPN
ejpam-3844	150	11	and	and	CCONJ
ejpam-3844	150	12	s.	s.	PROPN
ejpam-3844	150	13	aldhafeeri	aldhafeeri	PROPN
ejpam-3844	150	14	,	,	PUNCT
ejpam-3844	150	15	normal	normal	ADJ
ejpam-3844	150	16	unisoft	unisoft	ADJ
ejpam-3844	150	17	filters	filter	NOUN
ejpam-3844	150	18	in	in	ADP
ejpam-3844	150	19	r0	r0	NOUN
ejpam-3844	150	20	-	-	PUNCT
ejpam-3844	150	21	algebras	algebras	PROPN
ejpam-3844	150	22	.	.	PUNCT
ejpam-3844	151	1	cogent	cogent	NOUN
ejpam-3844	151	2	mathematics	mathematic	NOUN
ejpam-3844	151	3	,	,	PUNCT
ejpam-3844	151	4	1	1	NUM
ejpam-3844	151	5	(	(	PUNCT
ejpam-3844	151	6	4	4	NUM
ejpam-3844	151	7	)	)	PUNCT
ejpam-3844	151	8	(	(	PUNCT
ejpam-3844	151	9	2017	2017	NUM
ejpam-3844	151	10	)	)	PUNCT
ejpam-3844	151	11	1	1	NUM
ejpam-3844	151	12	-	-	SYM
ejpam-3844	151	13	9	9	NUM
ejpam-3844	151	14	.	.	PUNCT
ejpam-3844	152	1	[	[	X
ejpam-3844	152	2	4	4	NUM
ejpam-3844	152	3	]	]	PUNCT
ejpam-3844	152	4	a.	a.	NOUN
ejpam-3844	152	5	aygünoǧlu	aygünoǧlu	PROPN
ejpam-3844	152	6	and	and	CCONJ
ejpam-3844	152	7	h.	h.	PROPN
ejpam-3844	152	8	aygün	aygün	PROPN
ejpam-3844	152	9	,	,	PUNCT
ejpam-3844	152	10	introduction	introduction	NOUN
ejpam-3844	152	11	to	to	ADP
ejpam-3844	152	12	fuzzy	fuzzy	ADJ
ejpam-3844	152	13	soft	soft	ADJ
ejpam-3844	152	14	groups	group	NOUN
ejpam-3844	152	15	.	.	PUNCT
ejpam-3844	153	1	comput	comput	NOUN
ejpam-3844	153	2	.	.	PUNCT
ejpam-3844	154	1	math	math	NOUN
ejpam-3844	154	2	.	.	PUNCT
ejpam-3844	155	1	appl	appl	PROPN
ejpam-3844	155	2	.	.	PROPN
ejpam-3844	156	1	,	,	PUNCT
ejpam-3844	156	2	58	58	NUM
ejpam-3844	156	3	(	(	PUNCT
ejpam-3844	156	4	2009	2009	NUM
ejpam-3844	156	5	)	)	PUNCT
ejpam-3844	156	6	1279	1279	NUM
ejpam-3844	156	7	-	-	SYM
ejpam-3844	156	8	1286	1286	NUM
ejpam-3844	156	9	.	.	PUNCT
ejpam-3844	157	1	[	[	X
ejpam-3844	157	2	5	5	X
ejpam-3844	157	3	]	]	PUNCT
ejpam-3844	157	4	d.	d.	PROPN
ejpam-3844	157	5	chen	chen	PROPN
ejpam-3844	157	6	,	,	PUNCT
ejpam-3844	157	7	e.	e.	PROPN
ejpam-3844	157	8	c.c	c.c	PROPN
ejpam-3844	157	9	.	.	PROPN
ejpam-3844	157	10	tsang	tsang	PROPN
ejpam-3844	157	11	,	,	PUNCT
ejpam-3844	157	12	d.	d.	PROPN
ejpam-3844	157	13	s.	s.	PROPN
ejpam-3844	157	14	yeung	yeung	PROPN
ejpam-3844	157	15	,	,	PUNCT
ejpam-3844	157	16	x.	x.	PROPN
ejpam-3844	157	17	wang	wang	PROPN
ejpam-3844	157	18	,	,	PUNCT
ejpam-3844	157	19	the	the	DET
ejpam-3844	157	20	parameterization	parameterization	NOUN
ejpam-3844	157	21	reduction	reduction	NOUN
ejpam-3844	157	22	of	of	ADP
ejpam-3844	157	23	soft	soft	ADJ
ejpam-3844	157	24	set	set	NOUN
ejpam-3844	157	25	and	and	CCONJ
ejpam-3844	157	26	its	its	PRON
ejpam-3844	157	27	applications	application	NOUN
ejpam-3844	157	28	.	.	PUNCT
ejpam-3844	158	1	computers	computer	NOUN
ejpam-3844	158	2	and	and	CCONJ
ejpam-3844	158	3	mathematics	mathematic	NOUN
ejpam-3844	158	4	with	with	ADP
ejpam-3844	158	5	applications	application	NOUN
ejpam-3844	158	6	,	,	PUNCT
ejpam-3844	158	7	49	49	NUM
ejpam-3844	158	8	(	(	PUNCT
ejpam-3844	158	9	2005	2005	NUM
ejpam-3844	158	10	)	)	PUNCT
ejpam-3844	158	11	757	757	PROPN
ejpam-3844	158	12	-	-	SYM
ejpam-3844	158	13	763	763	NUM
ejpam-3844	158	14	.	.	PUNCT
ejpam-3844	159	1	[	[	X
ejpam-3844	159	2	6	6	NUM
ejpam-3844	159	3	]	]	X
ejpam-3844	159	4	y.	y.	PROPN
ejpam-3844	159	5	b.	b.	PROPN
ejpam-3844	159	6	jun	jun	PROPN
ejpam-3844	159	7	,	,	PUNCT
ejpam-3844	159	8	on	on	ADP
ejpam-3844	159	9	(	(	PUNCT
ejpam-3844	159	10	α	α	NOUN
ejpam-3844	159	11	,	,	PUNCT
ejpam-3844	159	12	β)-fuzzy	β)-fuzzy	PUNCT
ejpam-3844	159	13	subalgebras	subalgebras	PROPN
ejpam-3844	159	14	of	of	ADP
ejpam-3844	159	15	bck	bck	PROPN
ejpam-3844	159	16	/	/	SYM
ejpam-3844	159	17	bci	bci	NOUN
ejpam-3844	159	18	-	-	PUNCT
ejpam-3844	159	19	algebras	algebra	NOUN
ejpam-3844	159	20	.	.	PUNCT
ejpam-3844	160	1	bull	bull	NOUN
ejpam-3844	160	2	.	.	PUNCT
ejpam-3844	161	1	korean	korean	ADJ
ejpam-3844	161	2	math	math	PROPN
ejpam-3844	161	3	.	.	PUNCT
ejpam-3844	162	1	soc	soc	PROPN
ejpam-3844	162	2	.	.	PUNCT
ejpam-3844	162	3	,	,	PUNCT
ejpam-3844	162	4	42	42	NUM
ejpam-3844	162	5	(	(	PUNCT
ejpam-3844	162	6	2005	2005	NUM
ejpam-3844	162	7	)	)	PUNCT
ejpam-3844	162	8	703	703	NUM
ejpam-3844	162	9	-	-	SYM
ejpam-3844	162	10	711	711	NUM
ejpam-3844	162	11	.	.	PUNCT
ejpam-3844	163	1	https://doi.org/10.4134/bkms.2005.42.4.703	https://doi.org/10.4134/bkms.2005.42.4.703	NOUN
ejpam-3844	164	1	[	[	X
ejpam-3844	164	2	7	7	NUM
ejpam-3844	164	3	]	]	X
ejpam-3844	164	4	y.	y.	PROPN
ejpam-3844	164	5	b.	b.	PROPN
ejpam-3844	164	6	jun	jun	PROPN
ejpam-3844	164	7	,	,	PUNCT
ejpam-3844	164	8	s.	s.	PROPN
ejpam-3844	164	9	s.	s.	PROPN
ejpam-3844	164	10	ahn	ahn	PROPN
ejpam-3844	164	11	and	and	CCONJ
ejpam-3844	164	12	k.	k.	PROPN
ejpam-3844	164	13	j.	j.	PROPN
ejpam-3844	164	14	lee	lee	PROPN
ejpam-3844	164	15	,	,	PUNCT
ejpam-3844	164	16	intersection	intersection	NOUN
ejpam-3844	164	17	-	-	PUNCT
ejpam-3844	164	18	soft	soft	ADJ
ejpam-3844	164	19	filters	filter	NOUN
ejpam-3844	164	20	in	in	ADP
ejpam-3844	164	21	r0	r0	NOUN
ejpam-3844	164	22	-	-	PUNCT
ejpam-3844	164	23	algberas	algberas	ADJ
ejpam-3844	164	24	.	.	PUNCT
ejpam-3844	164	25	discrete	discrete	ADJ
ejpam-3844	164	26	dynamics	dynamic	NOUN
ejpam-3844	164	27	nature	nature	NOUN
ejpam-3844	164	28	and	and	CCONJ
ejpam-3844	164	29	society	society	NOUN
ejpam-3844	164	30	,	,	PUNCT
ejpam-3844	164	31	2013	2013	NUM
ejpam-3844	164	32	,	,	PUNCT
ejpam-3844	164	33	article	article	NOUN
ejpam-3844	164	34	i	i	PROPN
ejpam-3844	164	35	d	d	PROPN
ejpam-3844	164	36	950897	950897	NUM
ejpam-3844	164	37	,	,	PUNCT
ejpam-3844	164	38	7	7	NUM
ejpam-3844	164	39	pages	page	NOUN
ejpam-3844	164	40	.	.	PUNCT
ejpam-3844	165	1	https://doi.org/10.1155/2013/950897	https://doi.org/10.1155/2013/950897	PROPN
ejpam-3844	166	1	[	[	X
ejpam-3844	166	2	8	8	X
ejpam-3844	166	3	]	]	X
ejpam-3844	166	4	y.	y.	PROPN
ejpam-3844	166	5	b.	b.	PROPN
ejpam-3844	166	6	jun	jun	PROPN
ejpam-3844	166	7	,	,	PUNCT
ejpam-3844	166	8	k.	k.	PROPN
ejpam-3844	166	9	j.	j.	PROPN
ejpam-3844	166	10	lee	lee	PROPN
ejpam-3844	166	11	and	and	CCONJ
ejpam-3844	166	12	c.	c.	PROPN
ejpam-3844	166	13	h.	h.	PROPN
ejpam-3844	166	14	park	park	PROPN
ejpam-3844	166	15	,	,	PUNCT
ejpam-3844	166	16	fuzzy	fuzzy	ADJ
ejpam-3844	166	17	soft	soft	ADJ
ejpam-3844	166	18	set	set	NOUN
ejpam-3844	166	19	theory	theory	NOUN
ejpam-3844	166	20	applied	apply	VERB
ejpam-3844	166	21	to	to	PART
ejpam-3844	166	22	bck	bck	VERB
ejpam-3844	166	23	/	/	SYM
ejpam-3844	166	24	bci	bci	NOUN
ejpam-3844	166	25	-	-	PUNCT
ejpam-3844	166	26	algebras	algebra	NOUN
ejpam-3844	166	27	.	.	PUNCT
ejpam-3844	167	1	comput	comput	PROPN
ejpam-3844	167	2	.	.	PUNCT
ejpam-3844	168	1	math	math	NOUN
ejpam-3844	168	2	.	.	PUNCT
ejpam-3844	169	1	appl	appl	PROPN
ejpam-3844	169	2	.	.	PROPN
ejpam-3844	169	3	,	,	PUNCT
ejpam-3844	169	4	59	59	NUM
ejpam-3844	169	5	(	(	PUNCT
ejpam-3844	169	6	2010	2010	NUM
ejpam-3844	169	7	)	)	PUNCT
ejpam-3844	169	8	3180	3180	NUM
ejpam-3844	169	9	-	-	SYM
ejpam-3844	169	10	3192	3192	NUM
ejpam-3844	169	11	.	.	PUNCT
ejpam-3844	170	1	https://doi.org/10.1016/j.camwa.2010.03.004	https://doi.org/10.1016/j.camwa.2010.03.004	NOUN
ejpam-3844	170	2	[	[	X
ejpam-3844	170	3	9	9	X
ejpam-3844	170	4	]	]	X
ejpam-3844	170	5	y.	y.	PROPN
ejpam-3844	170	6	b.	b.	PROPN
ejpam-3844	170	7	jun	jun	PROPN
ejpam-3844	170	8	,	,	PUNCT
ejpam-3844	170	9	g.	g.	PROPN
ejpam-3844	170	10	muhiuddin	muhiuddin	PROPN
ejpam-3844	170	11	,	,	PUNCT
ejpam-3844	170	12	m.	m.	NOUN
ejpam-3844	170	13	a.	a.	NOUN
ejpam-3844	170	14	ozturk	ozturk	PROPN
ejpam-3844	170	15	and	and	CCONJ
ejpam-3844	170	16	e.	e.	PROPN
ejpam-3844	170	17	h.	h.	PROPN
ejpam-3844	170	18	roh	roh	PROPN
ejpam-3844	170	19	,	,	PUNCT
ejpam-3844	170	20	cubic	cubic	ADJ
ejpam-3844	170	21	soft	soft	ADJ
ejpam-3844	170	22	ideals	ideal	NOUN
ejpam-3844	170	23	in	in	ADP
ejpam-3844	170	24	bck	bck	PROPN
ejpam-3844	170	25	/	/	SYM
ejpam-3844	170	26	bci	bci	NOUN
ejpam-3844	170	27	-	-	PUNCT
ejpam-3844	170	28	algebras	algebras	PROPN
ejpam-3844	170	29	.	.	PUNCT
ejpam-3844	170	30	journal	journal	PROPN
ejpam-3844	170	31	of	of	ADP
ejpam-3844	170	32	computational	computational	ADJ
ejpam-3844	170	33	analysis	analysis	NOUN
ejpam-3844	170	34	and	and	CCONJ
ejpam-3844	170	35	applications	application	NOUN
ejpam-3844	170	36	,	,	PUNCT
ejpam-3844	170	37	22	22	NUM
ejpam-3844	170	38	(	(	PUNCT
ejpam-3844	170	39	5	5	NUM
ejpam-3844	170	40	)	)	PUNCT
ejpam-3844	170	41	(	(	PUNCT
ejpam-3844	170	42	2017	2017	NUM
ejpam-3844	170	43	)	)	PUNCT
ejpam-3844	170	44	929	929	NUM
ejpam-3844	170	45	-	-	SYM
ejpam-3844	170	46	940	940	NUM
ejpam-3844	170	47	.	.	PUNCT
ejpam-3844	171	1	[	[	X
ejpam-3844	171	2	10	10	NUM
ejpam-3844	171	3	]	]	PUNCT
ejpam-3844	171	4	p.	p.	PROPN
ejpam-3844	171	5	k.	k.	PROPN
ejpam-3844	172	1	maji	maji	PROPN
ejpam-3844	172	2	,	,	PUNCT
ejpam-3844	172	3	r.	r.	PROPN
ejpam-3844	172	4	biswas	biswas	PROPN
ejpam-3844	172	5	and	and	CCONJ
ejpam-3844	172	6	a.	a.	PROPN
ejpam-3844	172	7	r.	r.	PROPN
ejpam-3844	172	8	roy	roy	PROPN
ejpam-3844	172	9	,	,	PUNCT
ejpam-3844	172	10	fuzzy	fuzzy	ADJ
ejpam-3844	172	11	soft	soft	ADJ
ejpam-3844	172	12	sets	set	NOUN
ejpam-3844	172	13	.	.	PUNCT
ejpam-3844	173	1	j.	j.	PROPN
ejpam-3844	173	2	fuzzy	fuzzy	PROPN
ejpam-3844	173	3	math	math	PROPN
ejpam-3844	173	4	.	.	PUNCT
ejpam-3844	173	5	,	,	PUNCT
ejpam-3844	173	6	9(3	9(3	NUM
ejpam-3844	173	7	)	)	PUNCT
ejpam-3844	173	8	(	(	PUNCT
ejpam-3844	173	9	2001	2001	NUM
ejpam-3844	173	10	)	)	PUNCT
ejpam-3844	173	11	589	589	NUM
ejpam-3844	173	12	-	-	SYM
ejpam-3844	173	13	602	602	NUM
ejpam-3844	173	14	.	.	PUNCT
ejpam-3844	174	1	[	[	X
ejpam-3844	174	2	11	11	NUM
ejpam-3844	174	3	]	]	PUNCT
ejpam-3844	174	4	p.	p.	PROPN
ejpam-3844	174	5	k.	k.	PROPN
ejpam-3844	175	1	maji	maji	PROPN
ejpam-3844	175	2	,	,	PUNCT
ejpam-3844	175	3	a.	a.	PROPN
ejpam-3844	175	4	r.	r.	PROPN
ejpam-3844	175	5	roy	roy	PROPN
ejpam-3844	175	6	and	and	CCONJ
ejpam-3844	175	7	r.	r.	PROPN
ejpam-3844	175	8	biswas	biswas	PROPN
ejpam-3844	175	9	,	,	PUNCT
ejpam-3844	175	10	an	an	DET
ejpam-3844	175	11	application	application	NOUN
ejpam-3844	175	12	of	of	ADP
ejpam-3844	175	13	soft	soft	ADJ
ejpam-3844	175	14	sets	set	NOUN
ejpam-3844	175	15	in	in	ADP
ejpam-3844	175	16	a	a	DET
ejpam-3844	175	17	decision	decision	NOUN
ejpam-3844	175	18	making	make	VERB
ejpam-3844	175	19	problem	problem	NOUN
ejpam-3844	175	20	.	.	PUNCT
ejpam-3844	176	1	comput	comput	NOUN
ejpam-3844	176	2	.	.	PUNCT
ejpam-3844	177	1	math	math	NOUN
ejpam-3844	177	2	.	.	PUNCT
ejpam-3844	178	1	appl	appl	PROPN
ejpam-3844	178	2	.	.	PROPN
ejpam-3844	178	3	,	,	PUNCT
ejpam-3844	178	4	44	44	NUM
ejpam-3844	178	5	(	(	PUNCT
ejpam-3844	178	6	2002	2002	NUM
ejpam-3844	178	7	)	)	PUNCT
ejpam-3844	178	8	1077	1077	NUM
ejpam-3844	178	9	-	-	SYM
ejpam-3844	178	10	1083	1083	NUM
ejpam-3844	178	11	.	.	PUNCT
ejpam-3844	179	1	https://doi.org/10.1016/s08981221(02)00216-x	https://doi.org/10.1016/s08981221(02)00216-x	PROPN
ejpam-3844	180	1	[	[	X
ejpam-3844	180	2	12	12	NUM
ejpam-3844	180	3	]	]	X
ejpam-3844	180	4	d.	d.	PROPN
ejpam-3844	180	5	molodtsov	molodtsov	PROPN
ejpam-3844	180	6	,	,	PUNCT
ejpam-3844	180	7	soft	soft	ADJ
ejpam-3844	180	8	set	set	NOUN
ejpam-3844	180	9	theory	theory	NOUN
ejpam-3844	180	10	first	first	ADJ
ejpam-3844	180	11	results	result	NOUN
ejpam-3844	180	12	.	.	PUNCT
ejpam-3844	181	1	comput	comput	NOUN
ejpam-3844	181	2	.	.	PUNCT
ejpam-3844	182	1	math	math	NOUN
ejpam-3844	182	2	.	.	PUNCT
ejpam-3844	183	1	appl	appl	PROPN
ejpam-3844	183	2	.	.	PROPN
ejpam-3844	183	3	,	,	PUNCT
ejpam-3844	183	4	37	37	NUM
ejpam-3844	183	5	(	(	PUNCT
ejpam-3844	183	6	1999	1999	NUM
ejpam-3844	183	7	)	)	PUNCT
ejpam-3844	183	8	19	19	NUM
ejpam-3844	183	9	-	-	SYM
ejpam-3844	183	10	31	31	NUM
ejpam-3844	183	11	.	.	PUNCT
ejpam-3844	184	1	[	[	X
ejpam-3844	184	2	13	13	NUM
ejpam-3844	184	3	]	]	X
ejpam-3844	184	4	g.	g.	PROPN
ejpam-3844	184	5	muhiuddin	muhiuddin	PROPN
ejpam-3844	184	6	and	and	CCONJ
ejpam-3844	184	7	a.	a.	PROPN
ejpam-3844	184	8	m.	m.	PROPN
ejpam-3844	184	9	al	al	PROPN
ejpam-3844	184	10	-	-	PUNCT
ejpam-3844	184	11	roqi	roqi	ADJ
ejpam-3844	184	12	,	,	PUNCT
ejpam-3844	184	13	cubic	cubic	ADJ
ejpam-3844	184	14	soft	soft	ADJ
ejpam-3844	184	15	sets	set	NOUN
ejpam-3844	184	16	with	with	ADP
ejpam-3844	184	17	applications	application	NOUN
ejpam-3844	184	18	in	in	ADP
ejpam-3844	184	19	bck	bck	PROPN
ejpam-3844	184	20	/	/	SYM
ejpam-3844	184	21	bcialgebras	bcialgebra	NOUN
ejpam-3844	184	22	.	.	PUNCT
ejpam-3844	185	1	annals	annal	NOUN
ejpam-3844	185	2	of	of	ADP
ejpam-3844	185	3	fuzzy	fuzzy	ADJ
ejpam-3844	185	4	mathematics	mathematic	NOUN
ejpam-3844	185	5	and	and	CCONJ
ejpam-3844	185	6	informatics	informatic	NOUN
ejpam-3844	185	7	,	,	PUNCT
ejpam-3844	185	8	8	8	NUM
ejpam-3844	185	9	(	(	PUNCT
ejpam-3844	185	10	2	2	NUM
ejpam-3844	185	11	)	)	PUNCT
ejpam-3844	185	12	(	(	PUNCT
ejpam-3844	185	13	2014	2014	NUM
ejpam-3844	185	14	)	)	PUNCT
ejpam-3844	185	15	291	291	NUM
ejpam-3844	185	16	-	-	SYM
ejpam-3844	185	17	304	304	NUM
ejpam-3844	185	18	.	.	PUNCT
ejpam-3844	186	1	[	[	X
ejpam-3844	186	2	14	14	NUM
ejpam-3844	186	3	]	]	X
ejpam-3844	186	4	g.	g.	PROPN
ejpam-3844	186	5	muhiuddin	muhiuddin	PROPN
ejpam-3844	186	6	and	and	CCONJ
ejpam-3844	186	7	a.	a.	PROPN
ejpam-3844	186	8	m.	m.	PROPN
ejpam-3844	186	9	al	al	PROPN
ejpam-3844	186	10	-	-	PUNCT
ejpam-3844	186	11	roqi	roqi	PROPN
ejpam-3844	186	12	,	,	PUNCT
ejpam-3844	186	13	unisoft	unisoft	ADJ
ejpam-3844	186	14	filters	filter	NOUN
ejpam-3844	186	15	in	in	ADP
ejpam-3844	186	16	r0	r0	NOUN
ejpam-3844	186	17	-	-	PUNCT
ejpam-3844	186	18	algebras	algebras	PROPN
ejpam-3844	186	19	,	,	PUNCT
ejpam-3844	186	20	journal	journal	NOUN
ejpam-3844	186	21	of	of	ADP
ejpam-3844	186	22	computational	computational	ADJ
ejpam-3844	186	23	analysis	analysis	NOUN
ejpam-3844	186	24	and	and	CCONJ
ejpam-3844	186	25	applications	application	NOUN
ejpam-3844	186	26	,	,	PUNCT
ejpam-3844	186	27	19	19	NUM
ejpam-3844	186	28	(	(	PUNCT
ejpam-3844	186	29	1	1	NUM
ejpam-3844	186	30	)	)	PUNCT
ejpam-3844	186	31	(	(	PUNCT
ejpam-3844	186	32	2015	2015	NUM
ejpam-3844	186	33	)	)	PUNCT
ejpam-3844	186	34	133	133	NUM
ejpam-3844	186	35	-	-	SYM
ejpam-3844	186	36	143	143	NUM
ejpam-3844	186	37	.	.	PUNCT
ejpam-3844	187	1	references	reference	NOUN
ejpam-3844	187	2	947	947	NUM
ejpam-3844	188	1	[	[	X
ejpam-3844	188	2	15	15	NUM
ejpam-3844	188	3	]	]	X
ejpam-3844	188	4	g.	g.	PROPN
ejpam-3844	188	5	muhiuddin	muhiuddin	PROPN
ejpam-3844	188	6	,	,	PUNCT
ejpam-3844	188	7	a.	a.	PROPN
ejpam-3844	188	8	m.	m.	PROPN
ejpam-3844	188	9	al	al	PROPN
ejpam-3844	188	10	-	-	PUNCT
ejpam-3844	188	11	roqi	roqi	PROPN
ejpam-3844	188	12	and	and	CCONJ
ejpam-3844	188	13	s.	s.	PROPN
ejpam-3844	188	14	aldhafeeri	aldhafeeri	PROPN
ejpam-3844	188	15	,	,	PUNCT
ejpam-3844	188	16	filter	filter	NOUN
ejpam-3844	188	17	theory	theory	NOUN
ejpam-3844	188	18	in	in	ADP
ejpam-3844	188	19	mtl	mtl	PROPN
ejpam-3844	188	20	-	-	PUNCT
ejpam-3844	188	21	algebras	algebras	PROPN
ejpam-3844	188	22	based	base	VERB
ejpam-3844	188	23	on	on	ADP
ejpam-3844	188	24	uni	uni	ADJ
ejpam-3844	188	25	-	-	ADJ
ejpam-3844	188	26	soft	soft	ADJ
ejpam-3844	188	27	property	property	NOUN
ejpam-3844	188	28	.	.	PUNCT
ejpam-3844	189	1	bulletin	bulletin	NOUN
ejpam-3844	189	2	of	of	ADP
ejpam-3844	189	3	the	the	DET
ejpam-3844	189	4	iranian	iranian	PROPN
ejpam-3844	189	5	mathematical	mathematical	PROPN
ejpam-3844	189	6	society	society	NOUN
ejpam-3844	189	7	,	,	PUNCT
ejpam-3844	189	8	43	43	NUM
ejpam-3844	189	9	(	(	PUNCT
ejpam-3844	189	10	7	7	NUM
ejpam-3844	189	11	)	)	PUNCT
ejpam-3844	189	12	(	(	PUNCT
ejpam-3844	189	13	2017	2017	NUM
ejpam-3844	189	14	)	)	PUNCT
ejpam-3844	189	15	2293	2293	NUM
ejpam-3844	189	16	-	-	SYM
ejpam-3844	189	17	2306	2306	NUM
ejpam-3844	189	18	.	.	PUNCT
ejpam-3844	190	1	[	[	X
ejpam-3844	190	2	16	16	NUM
ejpam-3844	190	3	]	]	X
ejpam-3844	190	4	g.	g.	PROPN
ejpam-3844	190	5	muhiuddin	muhiuddin	PROPN
ejpam-3844	190	6	and	and	CCONJ
ejpam-3844	190	7	m.	m.	NOUN
ejpam-3844	190	8	balamurugan	balamurugan	PROPN
ejpam-3844	190	9	,	,	PUNCT
ejpam-3844	190	10	hesitant	hesitant	ADJ
ejpam-3844	190	11	intuitionistic	intuitionistic	ADJ
ejpam-3844	190	12	fuzzy	fuzzy	ADJ
ejpam-3844	190	13	soft	soft	ADJ
ejpam-3844	190	14	b	b	NOUN
ejpam-3844	190	15	-	-	PUNCT
ejpam-3844	190	16	ideals	ideal	NOUN
ejpam-3844	190	17	of	of	ADP
ejpam-3844	190	18	bck	bck	NOUN
ejpam-3844	190	19	-	-	PUNCT
ejpam-3844	190	20	algebras	algebra	NOUN
ejpam-3844	190	21	,	,	PUNCT
ejpam-3844	190	22	annals	annal	NOUN
ejpam-3844	190	23	of	of	ADP
ejpam-3844	190	24	communications	communication	NOUN
ejpam-3844	190	25	in	in	ADP
ejpam-3844	190	26	mathematics	mathematic	NOUN
ejpam-3844	190	27	,	,	PUNCT
ejpam-3844	190	28	3	3	NUM
ejpam-3844	190	29	(	(	PUNCT
ejpam-3844	190	30	1	1	NUM
ejpam-3844	190	31	)	)	PUNCT
ejpam-3844	190	32	(	(	PUNCT
ejpam-3844	190	33	2020	2020	NUM
ejpam-3844	190	34	)	)	PUNCT
ejpam-3844	190	35	26–34	26–34	NUM
ejpam-3844	191	1	[	[	X
ejpam-3844	191	2	17	17	NUM
ejpam-3844	191	3	]	]	X
ejpam-3844	191	4	g.	g.	PROPN
ejpam-3844	191	5	muhiuddin	muhiuddin	PROPN
ejpam-3844	191	6	,	,	PUNCT
ejpam-3844	191	7	f.	f.	PROPN
ejpam-3844	191	8	feng	feng	PROPN
ejpam-3844	191	9	and	and	CCONJ
ejpam-3844	191	10	y.	y.	PROPN
ejpam-3844	191	11	b.	b.	PROPN
ejpam-3844	191	12	jun	jun	PROPN
ejpam-3844	191	13	,	,	PUNCT
ejpam-3844	191	14	subalgebras	subalgebras	PROPN
ejpam-3844	191	15	of	of	ADP
ejpam-3844	191	16	bck	bck	PROPN
ejpam-3844	191	17	/	/	SYM
ejpam-3844	191	18	bci	bci	NOUN
ejpam-3844	191	19	-	-	PUNCT
ejpam-3844	191	20	algebras	algebras	PROPN
ejpam-3844	191	21	based	base	VERB
ejpam-3844	191	22	on	on	ADP
ejpam-3844	191	23	cubic	cubic	ADJ
ejpam-3844	191	24	soft	soft	ADJ
ejpam-3844	191	25	sets	set	NOUN
ejpam-3844	191	26	.	.	PUNCT
ejpam-3844	192	1	the	the	DET
ejpam-3844	192	2	scientific	scientific	ADJ
ejpam-3844	192	3	world	world	NOUN
ejpam-3844	192	4	journal	journal	NOUN
ejpam-3844	192	5	,	,	PUNCT
ejpam-3844	192	6	2014	2014	NUM
ejpam-3844	192	7	,	,	PUNCT
ejpam-3844	192	8	article	article	NOUN
ejpam-3844	192	9	i	i	PROPN
ejpam-3844	192	10	d	d	PROPN
ejpam-3844	192	11	458638	458638	NUM
ejpam-3844	192	12	(	(	PUNCT
ejpam-3844	192	13	2014	2014	NUM
ejpam-3844	192	14	)	)	PUNCT
ejpam-3844	192	15	9	9	NUM
ejpam-3844	192	16	pages	page	NOUN
ejpam-3844	192	17	.	.	PUNCT
ejpam-3844	193	1	[	[	X
ejpam-3844	193	2	18	18	NUM
ejpam-3844	193	3	]	]	X
ejpam-3844	194	1	e.	e.	PROPN
ejpam-3844	194	2	h.	h.	PROPN
ejpam-3844	194	3	roh	roh	PROPN
ejpam-3844	194	4	and	and	CCONJ
ejpam-3844	194	5	y.	y.	PROPN
ejpam-3844	194	6	b.	b.	PROPN
ejpam-3844	194	7	jun	jun	PROPN
ejpam-3844	194	8	,	,	PUNCT
ejpam-3844	194	9	positive	positive	ADJ
ejpam-3844	194	10	implicative	implicative	ADJ
ejpam-3844	194	11	ideals	ideal	NOUN
ejpam-3844	194	12	of	of	ADP
ejpam-3844	194	13	bck	bck	NOUN
ejpam-3844	194	14	-	-	PUNCT
ejpam-3844	194	15	algebras	algebras	PROPN
ejpam-3844	194	16	based	base	VERB
ejpam-3844	194	17	on	on	ADP
ejpam-3844	194	18	intersectional	intersectional	ADJ
ejpam-3844	194	19	soft	soft	ADJ
ejpam-3844	194	20	sets	set	NOUN
ejpam-3844	194	21	.	.	PUNCT
ejpam-3844	195	1	j.	j.	PROPN
ejpam-3844	195	2	appl	appl	PROPN
ejpam-3844	195	3	.	.	PROPN
ejpam-3844	195	4	math	math	PROPN
ejpam-3844	195	5	.	.	PUNCT
ejpam-3844	195	6	,	,	PUNCT
ejpam-3844	195	7	2013	2013	NUM
ejpam-3844	195	8	,	,	PUNCT
ejpam-3844	195	9	article	article	NOUN
ejpam-3844	195	10	i	i	PROPN
ejpam-3844	195	11	d	d	PROPN
ejpam-3844	195	12	853907	853907	NUM
ejpam-3844	195	13	,	,	PUNCT
ejpam-3844	195	14	9	9	NUM
ejpam-3844	195	15	pages	page	NOUN
ejpam-3844	195	16	.	.	PUNCT
ejpam-3844	196	1	http://dx.doi.org/10.1155/2013/853907	http://dx.doi.org/10.1155/2013/853907	PROPN
ejpam-3844	197	1	[	[	X
ejpam-3844	197	2	19	19	NUM
ejpam-3844	197	3	]	]	PUNCT
ejpam-3844	197	4	a.	a.	PROPN
ejpam-3844	197	5	r.	r.	PROPN
ejpam-3844	197	6	roy	roy	PROPN
ejpam-3844	197	7	and	and	CCONJ
ejpam-3844	197	8	p.	p.	PROPN
ejpam-3844	197	9	k.	k.	PROPN
ejpam-3844	198	1	maji	maji	PROPN
ejpam-3844	198	2	,	,	PUNCT
ejpam-3844	198	3	a	a	DET
ejpam-3844	198	4	fuzzy	fuzzy	ADJ
ejpam-3844	198	5	soft	soft	ADJ
ejpam-3844	198	6	set	set	ADJ
ejpam-3844	198	7	theoretic	theoretic	ADJ
ejpam-3844	198	8	approach	approach	NOUN
ejpam-3844	198	9	to	to	ADP
ejpam-3844	198	10	decision	decision	NOUN
ejpam-3844	198	11	making	make	VERB
ejpam-3844	198	12	problems	problem	NOUN
ejpam-3844	198	13	.	.	PUNCT
ejpam-3844	199	1	j.	j.	PROPN
ejpam-3844	199	2	comput	comput	PROPN
ejpam-3844	199	3	.	.	PUNCT
ejpam-3844	200	1	appl	appl	PROPN
ejpam-3844	200	2	.	.	PROPN
ejpam-3844	200	3	math	math	PROPN
ejpam-3844	200	4	.	.	PUNCT
ejpam-3844	201	1	,	,	PUNCT
ejpam-3844	201	2	203	203	NUM
ejpam-3844	201	3	(	(	PUNCT
ejpam-3844	201	4	2007	2007	NUM
ejpam-3844	201	5	)	)	PUNCT
ejpam-3844	201	6	412	412	NUM
ejpam-3844	201	7	-	-	SYM
ejpam-3844	201	8	418	418	NUM
ejpam-3844	201	9	.	.	PUNCT
ejpam-3844	202	1	https://doi.org/10.1016/j.cam.2006.04.008	https://doi.org/10.1016/j.cam.2006.04.008	NOUN
ejpam-3844	203	1	[	[	X
ejpam-3844	203	2	20	20	NUM
ejpam-3844	203	3	]	]	X
ejpam-3844	203	4	c.k	c.k	PROPN
ejpam-3844	203	5	.	.	PROPN
ejpam-3844	203	6	wong	wong	PROPN
ejpam-3844	203	7	,	,	PUNCT
ejpam-3844	203	8	fuzzy	fuzzy	ADJ
ejpam-3844	203	9	topology	topology	NOUN
ejpam-3844	203	10	.	.	PUNCT
ejpam-3844	204	1	fuzzy	fuzzy	ADJ
ejpam-3844	204	2	sets	set	NOUN
ejpam-3844	204	3	and	and	CCONJ
ejpam-3844	204	4	their	their	PRON
ejpam-3844	204	5	applications	application	NOUN
ejpam-3844	204	6	to	to	PART
ejpam-3844	204	7	cognitive	cognitive	VERB
ejpam-3844	204	8	and	and	CCONJ
ejpam-3844	204	9	decision	decision	NOUN
ejpam-3844	204	10	processes	process	NOUN
ejpam-3844	204	11	,	,	PUNCT
ejpam-3844	204	12	elsevier	elsevier	NOUN
ejpam-3844	204	13	,	,	PUNCT
ejpam-3844	204	14	(	(	PUNCT
ejpam-3844	204	15	1975	1975	NUM
ejpam-3844	204	16	)	)	PUNCT
ejpam-3844	204	17	171	171	NUM
ejpam-3844	204	18	-	-	SYM
ejpam-3844	204	19	190	190	NUM
ejpam-3844	204	20	.	.	PUNCT
ejpam-3844	205	1	[	[	X
ejpam-3844	205	2	21	21	NUM
ejpam-3844	205	3	]	]	X
ejpam-3844	205	4	l.	l.	PROPN
ejpam-3844	205	5	a.	a.	PROPN
ejpam-3844	205	6	zadeh	zadeh	PROPN
ejpam-3844	205	7	,	,	PUNCT
ejpam-3844	205	8	fuzzy	fuzzy	ADJ
ejpam-3844	205	9	sets	set	NOUN
ejpam-3844	205	10	.	.	PUNCT
ejpam-3844	206	1	inform	inform	NOUN
ejpam-3844	206	2	.	.	PUNCT
ejpam-3844	207	1	control	control	NOUN
ejpam-3844	207	2	,	,	PUNCT
ejpam-3844	207	3	8	8	NUM
ejpam-3844	207	4	(	(	PUNCT
ejpam-3844	207	5	1965	1965	NUM
ejpam-3844	207	6	)	)	PUNCT
ejpam-3844	207	7	338	338	NUM
ejpam-3844	207	8	-	-	SYM
ejpam-3844	207	9	353	353	NUM
ejpam-3844	207	10	.	.	PUNCT