id	sid	tid	token	lemma	pos
ejpam-5311	1	1	european	european	PROPN
ejpam-5311	1	2	journal	journal	PROPN
ejpam-5311	1	3	of	of	ADP
ejpam-5311	1	4	pure	pure	ADJ
ejpam-5311	1	5	and	and	CCONJ
ejpam-5311	1	6	applied	apply	VERB
ejpam-5311	1	7	mathematics	mathematic	NOUN
ejpam-5311	1	8	vol	vol	NOUN
ejpam-5311	1	9	.	.	PROPN
ejpam-5311	2	1	17	17	NUM
ejpam-5311	2	2	,	,	PUNCT
ejpam-5311	2	3	no	no	INTJ
ejpam-5311	2	4	.	.	NOUN
ejpam-5311	2	5	3	3	NUM
ejpam-5311	2	6	,	,	PUNCT
ejpam-5311	2	7	2024	2024	NUM
ejpam-5311	2	8	,	,	PUNCT
ejpam-5311	2	9	2235	2235	NUM
ejpam-5311	2	10	-	-	SYM
ejpam-5311	2	11	2245	2245	NUM
ejpam-5311	2	12	issn	issn	PROPN
ejpam-5311	2	13	1307	1307	NUM
ejpam-5311	2	14	-	-	SYM
ejpam-5311	2	15	5543	5543	NUM
ejpam-5311	2	16	–	–	PUNCT
ejpam-5311	3	1	ejpam.com	ejpam.com	X
ejpam-5311	3	2	published	publish	VERB
ejpam-5311	3	3	by	by	ADP
ejpam-5311	3	4	new	new	PROPN
ejpam-5311	3	5	york	york	PROPN
ejpam-5311	3	6	business	business	PROPN
ejpam-5311	3	7	global	global	ADJ
ejpam-5311	3	8	εlukasiewicz	εlukasiewicz	NOUN
ejpam-5311	3	9	fuzzy	fuzzy	ADJ
ejpam-5311	3	10	up	up	ADP
ejpam-5311	3	11	(	(	PUNCT
ejpam-5311	3	12	bcc)-subalgebras	bcc)-subalgebras	NUM
ejpam-5311	3	13	of	of	ADP
ejpam-5311	3	14	up	up	ADV
ejpam-5311	3	15	(	(	PUNCT
ejpam-5311	3	16	bcc)-algebras	bcc)-algebra	NOUN
ejpam-5311	3	17	aiyared	aiyare	VERB
ejpam-5311	3	18	iampan1,∗	iampan1,∗	NOUN
ejpam-5311	3	19	,	,	PUNCT
ejpam-5311	3	20	ramasamy	ramasamy	NOUN
ejpam-5311	3	21	subasini2	subasini2	NOUN
ejpam-5311	3	22	,	,	PUNCT
ejpam-5311	3	23	neelamegarajan	neelamegarajan	ADJ
ejpam-5311	3	24	rajesh3	rajesh3	PROPN
ejpam-5311	3	25	1	1	NUM
ejpam-5311	3	26	department	department	NOUN
ejpam-5311	3	27	of	of	ADP
ejpam-5311	3	28	mathematics	mathematic	NOUN
ejpam-5311	3	29	,	,	PUNCT
ejpam-5311	3	30	school	school	NOUN
ejpam-5311	3	31	of	of	ADP
ejpam-5311	3	32	science	science	NOUN
ejpam-5311	3	33	,	,	PUNCT
ejpam-5311	3	34	university	university	NOUN
ejpam-5311	3	35	of	of	ADP
ejpam-5311	3	36	phayao	phayao	NOUN
ejpam-5311	3	37	,	,	PUNCT
ejpam-5311	3	38	mae	mae	PROPN
ejpam-5311	3	39	ka	ka	PROPN
ejpam-5311	3	40	,	,	PUNCT
ejpam-5311	3	41	mueang	mueang	PROPN
ejpam-5311	3	42	,	,	PUNCT
ejpam-5311	3	43	phayao	phayao	NOUN
ejpam-5311	3	44	56000	56000	NUM
ejpam-5311	3	45	,	,	PUNCT
ejpam-5311	3	46	thailand	thailand	PROPN
ejpam-5311	3	47	2	2	NUM
ejpam-5311	3	48	department	department	NOUN
ejpam-5311	3	49	of	of	ADP
ejpam-5311	3	50	mathematics	mathematics	PROPN
ejpam-5311	3	51	,	,	PUNCT
ejpam-5311	3	52	pollachi	pollachi	PROPN
ejpam-5311	3	53	institute	institute	PROPN
ejpam-5311	3	54	of	of	ADP
ejpam-5311	3	55	engineering	engineering	NOUN
ejpam-5311	3	56	and	and	CCONJ
ejpam-5311	3	57	technology	technology	NOUN
ejpam-5311	3	58	,	,	PUNCT
ejpam-5311	3	59	pollachi-642205	pollachi-642205	ADV
ejpam-5311	3	60	,	,	PUNCT
ejpam-5311	3	61	tamilnadu	tamilnadu	ADJ
ejpam-5311	3	62	,	,	PUNCT
ejpam-5311	3	63	india	india	PROPN
ejpam-5311	3	64	3	3	PROPN
ejpam-5311	3	65	department	department	PROPN
ejpam-5311	3	66	of	of	ADP
ejpam-5311	3	67	mathematics	mathematics	PROPN
ejpam-5311	3	68	,	,	PUNCT
ejpam-5311	3	69	rajah	rajah	NOUN
ejpam-5311	3	70	serfoji	serfoji	ADJ
ejpam-5311	3	71	government	government	NOUN
ejpam-5311	3	72	college	college	NOUN
ejpam-5311	3	73	(	(	PUNCT
ejpam-5311	3	74	affiliated	affiliate	VERB
ejpam-5311	3	75	to	to	PART
ejpam-5311	3	76	bharathidasan	bharathidasan	VERB
ejpam-5311	3	77	university	university	NOUN
ejpam-5311	3	78	)	)	PUNCT
ejpam-5311	3	79	,	,	PUNCT
ejpam-5311	3	80	thanjavur-613005	thanjavur-613005	NOUN
ejpam-5311	3	81	,	,	PUNCT
ejpam-5311	3	82	tamilnadu	tamilnadu	ADJ
ejpam-5311	3	83	,	,	PUNCT
ejpam-5311	3	84	india	india	PROPN
ejpam-5311	3	85	abstract	abstract	NOUN
ejpam-5311	3	86	.	.	PUNCT
ejpam-5311	4	1	the	the	DET
ejpam-5311	4	2	idea	idea	NOUN
ejpam-5311	4	3	of	of	ADP
ejpam-5311	4	4	lukasiewicz	lukasiewicz	ADJ
ejpam-5311	4	5	t	t	PROPN
ejpam-5311	4	6	-	-	PUNCT
ejpam-5311	4	7	norm	norm	NOUN
ejpam-5311	4	8	is	be	AUX
ejpam-5311	4	9	used	use	VERB
ejpam-5311	4	10	to	to	PART
ejpam-5311	4	11	construct	construct	VERB
ejpam-5311	4	12	the	the	DET
ejpam-5311	4	13	concept	concept	NOUN
ejpam-5311	4	14	of	of	ADP
ejpam-5311	4	15	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	4	16	fuzzy	fuzzy	ADJ
ejpam-5311	4	17	sets	set	NOUN
ejpam-5311	4	18	based	base	VERB
ejpam-5311	4	19	on	on	ADP
ejpam-5311	4	20	a	a	DET
ejpam-5311	4	21	given	give	VERB
ejpam-5311	4	22	fuzzy	fuzzy	ADJ
ejpam-5311	4	23	set	set	NOUN
ejpam-5311	4	24	.	.	PUNCT
ejpam-5311	5	1	the	the	DET
ejpam-5311	5	2	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	5	3	fuzzy	fuzzy	ADJ
ejpam-5311	5	4	sets	set	NOUN
ejpam-5311	5	5	are	be	AUX
ejpam-5311	5	6	applied	apply	VERB
ejpam-5311	5	7	to	to	ADP
ejpam-5311	5	8	up	up	ADP
ejpam-5311	5	9	(	(	PUNCT
ejpam-5311	5	10	bcc)-algebras	bcc)-algebra	NOUN
ejpam-5311	5	11	.	.	PUNCT
ejpam-5311	6	1	moreover	moreover	ADV
ejpam-5311	6	2	,	,	PUNCT
ejpam-5311	6	3	the	the	DET
ejpam-5311	6	4	notion	notion	NOUN
ejpam-5311	6	5	of	of	ADP
ejpam-5311	6	6	εlukasiewicz	εlukasiewicz	NOUN
ejpam-5311	6	7	fuzzy	fuzzy	ADJ
ejpam-5311	6	8	up	up	ADP
ejpam-5311	6	9	(	(	PUNCT
ejpam-5311	6	10	bcc)-subalgebras	bcc)-subalgebras	PROPN
ejpam-5311	6	11	is	be	AUX
ejpam-5311	6	12	introduced	introduce	VERB
ejpam-5311	6	13	,	,	PUNCT
ejpam-5311	6	14	and	and	CCONJ
ejpam-5311	6	15	its	its	PRON
ejpam-5311	6	16	various	various	ADJ
ejpam-5311	6	17	properties	property	NOUN
ejpam-5311	6	18	are	be	AUX
ejpam-5311	6	19	investigated	investigate	VERB
ejpam-5311	6	20	.	.	PUNCT
ejpam-5311	7	1	three	three	NUM
ejpam-5311	7	2	subsets	subset	NOUN
ejpam-5311	7	3	,	,	PUNCT
ejpam-5311	7	4	so	so	ADV
ejpam-5311	7	5	-	-	PUNCT
ejpam-5311	7	6	called	call	VERB
ejpam-5311	7	7	∈-set	∈-set	NOUN
ejpam-5311	7	8	,	,	PUNCT
ejpam-5311	7	9	q	q	NOUN
ejpam-5311	7	10	-	-	PUNCT
ejpam-5311	7	11	set	set	NOUN
ejpam-5311	7	12	,	,	PUNCT
ejpam-5311	7	13	and	and	CCONJ
ejpam-5311	7	14	o	o	X
ejpam-5311	7	15	-	-	NOUN
ejpam-5311	7	16	set	set	ADJ
ejpam-5311	7	17	,	,	PUNCT
ejpam-5311	7	18	are	be	AUX
ejpam-5311	7	19	constructed	construct	VERB
ejpam-5311	7	20	,	,	PUNCT
ejpam-5311	7	21	and	and	CCONJ
ejpam-5311	7	22	the	the	DET
ejpam-5311	7	23	conditions	condition	NOUN
ejpam-5311	7	24	under	under	ADP
ejpam-5311	7	25	which	which	PRON
ejpam-5311	7	26	they	they	PRON
ejpam-5311	7	27	can	can	AUX
ejpam-5311	7	28	be	be	AUX
ejpam-5311	7	29	up	up	ADV
ejpam-5311	7	30	(	(	PUNCT
ejpam-5311	7	31	bcc)-subalgebras	bcc)-subalgebra	NOUN
ejpam-5311	7	32	are	be	AUX
ejpam-5311	7	33	explored	explore	VERB
ejpam-5311	7	34	.	.	PUNCT
ejpam-5311	8	1	2020	2020	NUM
ejpam-5311	8	2	mathematics	mathematics	PROPN
ejpam-5311	8	3	subject	subject	NOUN
ejpam-5311	8	4	classifications	classification	NOUN
ejpam-5311	8	5	:	:	PUNCT
ejpam-5311	8	6	03g25	03g25	NUM
ejpam-5311	8	7	;	;	PUNCT
ejpam-5311	8	8	08a72	08a72	NUM
ejpam-5311	8	9	key	key	ADJ
ejpam-5311	8	10	words	word	NOUN
ejpam-5311	8	11	and	and	CCONJ
ejpam-5311	8	12	phrases	phrase	NOUN
ejpam-5311	8	13	:	:	PUNCT
ejpam-5311	8	14	up	up	ADV
ejpam-5311	8	15	(	(	PUNCT
ejpam-5311	8	16	bcc)-algebra	bcc)-algebra	PROPN
ejpam-5311	8	17	,	,	PUNCT
ejpam-5311	8	18	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	8	19	fuzzy	fuzzy	ADJ
ejpam-5311	8	20	set	set	NOUN
ejpam-5311	8	21	,	,	PUNCT
ejpam-5311	8	22	εlukasiewicz	εlukasiewicz	VERB
ejpam-5311	8	23	fuzzy	fuzzy	ADJ
ejpam-5311	8	24	up	up	ADP
ejpam-5311	8	25	(	(	PUNCT
ejpam-5311	8	26	bcc)-subalgebra	bcc)-subalgebra	PROPN
ejpam-5311	8	27	,	,	PUNCT
ejpam-5311	8	28	∈-set	∈-set	NOUN
ejpam-5311	8	29	,	,	PUNCT
ejpam-5311	8	30	q	q	NOUN
ejpam-5311	8	31	-	-	PUNCT
ejpam-5311	8	32	set	set	ADJ
ejpam-5311	8	33	,	,	PUNCT
ejpam-5311	8	34	o	o	NOUN
ejpam-5311	8	35	-	-	PUNCT
ejpam-5311	8	36	set	set	ADJ
ejpam-5311	8	37	.	.	PUNCT
ejpam-5311	9	1	1	1	X
ejpam-5311	9	2	.	.	X
ejpam-5311	9	3	introduction	introduction	NOUN
ejpam-5311	9	4	zadeh	zadeh	PROPN
ejpam-5311	9	5	[	[	X
ejpam-5311	9	6	12	12	NUM
ejpam-5311	9	7	]	]	PUNCT
ejpam-5311	9	8	first	first	ADV
ejpam-5311	9	9	proposed	propose	VERB
ejpam-5311	9	10	the	the	DET
ejpam-5311	9	11	idea	idea	NOUN
ejpam-5311	9	12	of	of	ADP
ejpam-5311	9	13	fuzzy	fuzzy	ADJ
ejpam-5311	9	14	sets	set	NOUN
ejpam-5311	9	15	.	.	PUNCT
ejpam-5311	10	1	the	the	DET
ejpam-5311	10	2	theory	theory	NOUN
ejpam-5311	10	3	of	of	ADP
ejpam-5311	10	4	fuzzy	fuzzy	ADJ
ejpam-5311	10	5	sets	set	NOUN
ejpam-5311	10	6	has	have	VERB
ejpam-5311	10	7	several	several	ADJ
ejpam-5311	10	8	applications	application	NOUN
ejpam-5311	10	9	in	in	ADP
ejpam-5311	10	10	real	real	ADJ
ejpam-5311	10	11	-	-	PUNCT
ejpam-5311	10	12	life	life	NOUN
ejpam-5311	10	13	situations	situation	NOUN
ejpam-5311	10	14	,	,	PUNCT
ejpam-5311	10	15	and	and	CCONJ
ejpam-5311	10	16	many	many	ADJ
ejpam-5311	10	17	scholars	scholar	NOUN
ejpam-5311	10	18	have	have	AUX
ejpam-5311	10	19	researched	research	VERB
ejpam-5311	10	20	fuzzy	fuzzy	ADJ
ejpam-5311	10	21	set	set	NOUN
ejpam-5311	10	22	theory	theory	NOUN
ejpam-5311	10	23	.	.	PUNCT
ejpam-5311	11	1	after	after	ADP
ejpam-5311	11	2	introducing	introduce	VERB
ejpam-5311	11	3	the	the	DET
ejpam-5311	11	4	concept	concept	NOUN
ejpam-5311	11	5	of	of	ADP
ejpam-5311	11	6	fuzzy	fuzzy	ADJ
ejpam-5311	11	7	sets	set	NOUN
ejpam-5311	11	8	,	,	PUNCT
ejpam-5311	11	9	several	several	ADJ
ejpam-5311	11	10	research	research	NOUN
ejpam-5311	11	11	studies	study	NOUN
ejpam-5311	11	12	were	be	AUX
ejpam-5311	11	13	conducted	conduct	VERB
ejpam-5311	11	14	on	on	ADP
ejpam-5311	11	15	the	the	DET
ejpam-5311	11	16	generalizations	generalization	NOUN
ejpam-5311	11	17	of	of	ADP
ejpam-5311	11	18	fuzzy	fuzzy	ADJ
ejpam-5311	11	19	sets	set	NOUN
ejpam-5311	11	20	.	.	PUNCT
ejpam-5311	12	1	the	the	DET
ejpam-5311	12	2	integration	integration	NOUN
ejpam-5311	12	3	between	between	ADP
ejpam-5311	12	4	fuzzy	fuzzy	ADJ
ejpam-5311	12	5	sets	set	NOUN
ejpam-5311	12	6	and	and	CCONJ
ejpam-5311	12	7	some	some	DET
ejpam-5311	12	8	uncertainty	uncertainty	NOUN
ejpam-5311	12	9	approaches	approach	VERB
ejpam-5311	12	10	,	,	PUNCT
ejpam-5311	12	11	such	such	ADJ
ejpam-5311	12	12	as	as	ADP
ejpam-5311	12	13	soft	soft	ADJ
ejpam-5311	12	14	sets	set	NOUN
ejpam-5311	12	15	and	and	CCONJ
ejpam-5311	12	16	rough	rough	ADJ
ejpam-5311	12	17	sets	set	NOUN
ejpam-5311	12	18	,	,	PUNCT
ejpam-5311	12	19	has	have	AUX
ejpam-5311	12	20	been	be	AUX
ejpam-5311	12	21	discussed	discuss	VERB
ejpam-5311	12	22	in	in	ADP
ejpam-5311	12	23	[	[	X
ejpam-5311	12	24	1–3	1–3	NOUN
ejpam-5311	12	25	]	]	X
ejpam-5311	12	26	.	.	PUNCT
ejpam-5311	13	1	the	the	DET
ejpam-5311	13	2	new	new	ADJ
ejpam-5311	13	3	technology	technology	NOUN
ejpam-5311	13	4	allows	allow	VERB
ejpam-5311	13	5	very	very	ADV
ejpam-5311	13	6	complex	complex	ADJ
ejpam-5311	13	7	inferences	inference	NOUN
ejpam-5311	13	8	about	about	ADP
ejpam-5311	13	9	variations	variation	NOUN
ejpam-5311	13	10	on	on	ADP
ejpam-5311	13	11	a	a	DET
ejpam-5311	13	12	theme	theme	NOUN
ejpam-5311	13	13	to	to	PART
ejpam-5311	13	14	be	be	AUX
ejpam-5311	13	15	anticipated	anticipate	VERB
ejpam-5311	13	16	and	and	CCONJ
ejpam-5311	13	17	fixed	fix	VERB
ejpam-5311	13	18	in	in	ADP
ejpam-5311	13	19	a	a	DET
ejpam-5311	13	20	program	program	NOUN
ejpam-5311	13	21	.	.	PUNCT
ejpam-5311	14	1	lukasiewicz	lukasiewicz	ADJ
ejpam-5311	14	2	logic	logic	NOUN
ejpam-5311	14	3	,	,	PUNCT
ejpam-5311	14	4	which	which	PRON
ejpam-5311	14	5	is	be	AUX
ejpam-5311	14	6	the	the	DET
ejpam-5311	14	7	logic	logic	NOUN
ejpam-5311	14	8	of	of	ADP
ejpam-5311	14	9	the	the	DET
ejpam-5311	14	10	lukasiewicz	lukasiewicz	ADJ
ejpam-5311	14	11	t	t	PROPN
ejpam-5311	14	12	-	-	PUNCT
ejpam-5311	14	13	norm	norm	NOUN
ejpam-5311	14	14	,	,	PUNCT
ejpam-5311	14	15	is	be	AUX
ejpam-5311	14	16	a	a	DET
ejpam-5311	14	17	non	non	ADJ
ejpam-5311	14	18	-	-	ADJ
ejpam-5311	14	19	classical	classical	ADJ
ejpam-5311	14	20	and	and	CCONJ
ejpam-5311	14	21	many	many	ADV
ejpam-5311	14	22	-	-	PUNCT
ejpam-5311	14	23	valued	value	VERB
ejpam-5311	14	24	logic	logic	NOUN
ejpam-5311	14	25	.	.	PUNCT
ejpam-5311	15	1	it	it	PRON
ejpam-5311	15	2	was	be	AUX
ejpam-5311	15	3	originally	originally	ADV
ejpam-5311	15	4	defined	define	VERB
ejpam-5311	15	5	in	in	ADP
ejpam-5311	15	6	the	the	DET
ejpam-5311	15	7	early	early	ADJ
ejpam-5311	15	8	20th	20th	ADJ
ejpam-5311	15	9	century	century	NOUN
ejpam-5311	15	10	by	by	ADP
ejpam-5311	15	11	lukasiewicz	lukasiewicz	NOUN
ejpam-5311	15	12	as	as	ADP
ejpam-5311	15	13	a	a	DET
ejpam-5311	15	14	three	three	NUM
ejpam-5311	15	15	-	-	PUNCT
ejpam-5311	15	16	valued	value	VERB
ejpam-5311	15	17	logic	logic	NOUN
ejpam-5311	15	18	.	.	PUNCT
ejpam-5311	16	1	iampan	iampan	NOUN
ejpam-5311	16	2	[	[	X
ejpam-5311	16	3	7	7	X
ejpam-5311	16	4	]	]	PUNCT
ejpam-5311	16	5	introduced	introduce	VERB
ejpam-5311	16	6	a	a	DET
ejpam-5311	16	7	new	new	ADJ
ejpam-5311	16	8	algebraic	algebraic	ADJ
ejpam-5311	16	9	structure	structure	NOUN
ejpam-5311	16	10	called	call	VERB
ejpam-5311	16	11	up	up	ADP
ejpam-5311	16	12	-	-	PUNCT
ejpam-5311	16	13	algebra	algebra	NOUN
ejpam-5311	16	14	.	.	PUNCT
ejpam-5311	17	1	somjanta	somjanta	NOUN
ejpam-5311	17	2	et	et	PROPN
ejpam-5311	17	3	al	al	PROPN
ejpam-5311	17	4	.	.	PUNCT
ejpam-5311	18	1	[	[	X
ejpam-5311	18	2	11	11	NUM
ejpam-5311	18	3	]	]	PUNCT
ejpam-5311	18	4	and	and	CCONJ
ejpam-5311	18	5	guntasow	guntasow	VERB
ejpam-5311	18	6	et	et	PROPN
ejpam-5311	18	7	al	al	PROPN
ejpam-5311	18	8	.	.	PUNCT
ejpam-5311	19	1	[	[	X
ejpam-5311	19	2	5	5	NUM
ejpam-5311	19	3	]	]	PUNCT
ejpam-5311	19	4	applied	apply	VERB
ejpam-5311	19	5	fuzzy	fuzzy	ADJ
ejpam-5311	19	6	set	set	NOUN
ejpam-5311	19	7	theory	theory	NOUN
ejpam-5311	19	8	in	in	ADP
ejpam-5311	19	9	up	up	ADP
ejpam-5311	19	10	-	-	PUNCT
ejpam-5311	19	11	algebras	algebras	X
ejpam-5311	19	12	.	.	PUNCT
ejpam-5311	20	1	dokkhamdang	dokkhamdang	PROPN
ejpam-5311	20	2	et	et	PROPN
ejpam-5311	20	3	al	al	PROPN
ejpam-5311	20	4	.	.	PUNCT
ejpam-5311	21	1	[	[	X
ejpam-5311	21	2	4	4	X
ejpam-5311	21	3	]	]	PUNCT
ejpam-5311	21	4	introduced	introduce	VERB
ejpam-5311	21	5	the	the	DET
ejpam-5311	21	6	notion	notion	NOUN
ejpam-5311	21	7	of	of	ADP
ejpam-5311	21	8	fuzzy	fuzzy	ADJ
ejpam-5311	21	9	up	up	ADP
ejpam-5311	21	10	-	-	PUNCT
ejpam-5311	21	11	subalgebras	subalgebras	NOUN
ejpam-5311	21	12	∗corresponding	∗corresponde	VERB
ejpam-5311	21	13	author	author	NOUN
ejpam-5311	21	14	.	.	PUNCT
ejpam-5311	22	1	doi	doi	NOUN
ejpam-5311	22	2	:	:	PUNCT
ejpam-5311	22	3	https://doi.org/10.29020/nybg.ejpam.v17i3.5311	https://doi.org/10.29020/nybg.ejpam.v17i3.5311	NOUN
ejpam-5311	22	4	email	email	NOUN
ejpam-5311	22	5	addresses	address	NOUN
ejpam-5311	22	6	:	:	PUNCT
ejpam-5311	22	7	aiyared.ia@up.ac.th	aiyared.ia@up.ac.th	NOUN
ejpam-5311	22	8	(	(	PUNCT
ejpam-5311	22	9	a.	a.	NOUN
ejpam-5311	22	10	iampan	iampan	PROPN
ejpam-5311	22	11	)	)	PUNCT
ejpam-5311	22	12	,	,	PUNCT
ejpam-5311	22	13	subasinimaths@gmail.com	subasinimaths@gmail.com	PROPN
ejpam-5311	22	14	(	(	PUNCT
ejpam-5311	22	15	r.	r.	PROPN
ejpam-5311	22	16	subasini	subasini	PROPN
ejpam-5311	22	17	)	)	PUNCT
ejpam-5311	22	18	,	,	PUNCT
ejpam-5311	22	19	nrajesh	nrajesh	PROPN
ejpam-5311	22	20	topology@yahoo.co.in	topology@yahoo.co.in	PROPN
ejpam-5311	22	21	(	(	PUNCT
ejpam-5311	22	22	n.	n.	PROPN
ejpam-5311	22	23	rajesh	rajesh	PROPN
ejpam-5311	22	24	)	)	PUNCT
ejpam-5311	22	25	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5311	22	26	2235	2235	NUM
ejpam-5311	23	1	©	©	PROPN
ejpam-5311	23	2	2024	2024	NUM
ejpam-5311	23	3	ejpam	ejpam	NOUN
ejpam-5311	23	4	all	all	DET
ejpam-5311	23	5	rights	right	NOUN
ejpam-5311	23	6	reserved	reserve	VERB
ejpam-5311	23	7	.	.	PUNCT
ejpam-5311	24	1	a.	a.	PROPN
ejpam-5311	24	2	iampan	iampan	PROPN
ejpam-5311	24	3	,	,	PUNCT
ejpam-5311	24	4	r.	r.	PROPN
ejpam-5311	24	5	subasini	subasini	PROPN
ejpam-5311	24	6	,	,	PUNCT
ejpam-5311	24	7	n.	n.	PROPN
ejpam-5311	24	8	rajesh	rajesh	PROPN
ejpam-5311	24	9	/	/	SYM
ejpam-5311	24	10	eur	eur	PROPN
ejpam-5311	24	11	.	.	PUNCT
ejpam-5311	25	1	j.	j.	PROPN
ejpam-5311	25	2	pure	pure	PROPN
ejpam-5311	25	3	appl	appl	PROPN
ejpam-5311	25	4	.	.	PROPN
ejpam-5311	25	5	math	math	PROPN
ejpam-5311	25	6	,	,	PUNCT
ejpam-5311	25	7	17	17	NUM
ejpam-5311	25	8	(	(	PUNCT
ejpam-5311	25	9	3	3	NUM
ejpam-5311	25	10	)	)	PUNCT
ejpam-5311	25	11	(	(	PUNCT
ejpam-5311	25	12	2024	2024	NUM
ejpam-5311	25	13	)	)	PUNCT
ejpam-5311	25	14	,	,	PUNCT
ejpam-5311	25	15	2235	2235	NUM
ejpam-5311	25	16	-	-	SYM
ejpam-5311	25	17	2245	2245	NUM
ejpam-5311	25	18	2236	2236	NUM
ejpam-5311	25	19	with	with	ADP
ejpam-5311	25	20	thresholds	threshold	NOUN
ejpam-5311	25	21	of	of	ADP
ejpam-5311	25	22	up	up	ADP
ejpam-5311	25	23	-	-	PUNCT
ejpam-5311	25	24	algebras	algebras	X
ejpam-5311	25	25	.	.	PUNCT
ejpam-5311	26	1	the	the	DET
ejpam-5311	26	2	concepts	concept	NOUN
ejpam-5311	26	3	of	of	ADP
ejpam-5311	26	4	up	up	ADP
ejpam-5311	26	5	-	-	PUNCT
ejpam-5311	26	6	algebras	algebras	X
ejpam-5311	26	7	(	(	PUNCT
ejpam-5311	26	8	see	see	VERB
ejpam-5311	26	9	[	[	X
ejpam-5311	26	10	7	7	NUM
ejpam-5311	26	11	]	]	PUNCT
ejpam-5311	26	12	)	)	PUNCT
ejpam-5311	26	13	and	and	CCONJ
ejpam-5311	26	14	bcc	bcc	PROPN
ejpam-5311	26	15	-	-	PUNCT
ejpam-5311	26	16	algebras	algebras	PROPN
ejpam-5311	26	17	(	(	PUNCT
ejpam-5311	26	18	see	see	VERB
ejpam-5311	26	19	[	[	X
ejpam-5311	26	20	9	9	NUM
ejpam-5311	26	21	]	]	PUNCT
ejpam-5311	26	22	)	)	PUNCT
ejpam-5311	26	23	are	be	AUX
ejpam-5311	26	24	the	the	DET
ejpam-5311	26	25	same	same	ADJ
ejpam-5311	26	26	concept	concept	NOUN
ejpam-5311	26	27	,	,	PUNCT
ejpam-5311	26	28	as	as	SCONJ
ejpam-5311	26	29	shown	show	VERB
ejpam-5311	26	30	by	by	ADP
ejpam-5311	26	31	jun	jun	PROPN
ejpam-5311	26	32	et	et	PROPN
ejpam-5311	26	33	al	al	PROPN
ejpam-5311	26	34	.	.	PUNCT
ejpam-5311	27	1	[	[	X
ejpam-5311	27	2	8	8	NUM
ejpam-5311	27	3	]	]	PUNCT
ejpam-5311	27	4	in	in	ADP
ejpam-5311	27	5	2022	2022	NUM
ejpam-5311	27	6	.	.	PUNCT
ejpam-5311	28	1	in	in	ADP
ejpam-5311	28	2	this	this	DET
ejpam-5311	28	3	publication	publication	NOUN
ejpam-5311	28	4	and	and	CCONJ
ejpam-5311	28	5	following	follow	VERB
ejpam-5311	28	6	investigations	investigation	NOUN
ejpam-5311	28	7	,	,	PUNCT
ejpam-5311	28	8	our	our	PRON
ejpam-5311	28	9	research	research	NOUN
ejpam-5311	28	10	team	team	NOUN
ejpam-5311	28	11	will	will	AUX
ejpam-5311	28	12	refer	refer	VERB
ejpam-5311	28	13	to	to	ADP
ejpam-5311	28	14	it	it	PRON
ejpam-5311	28	15	as	as	ADP
ejpam-5311	28	16	bcc	bcc	PROPN
ejpam-5311	28	17	rather	rather	ADV
ejpam-5311	28	18	than	than	ADP
ejpam-5311	28	19	up	up	ADV
ejpam-5311	28	20	out	out	ADP
ejpam-5311	28	21	of	of	ADP
ejpam-5311	28	22	respect	respect	NOUN
ejpam-5311	28	23	for	for	ADP
ejpam-5311	28	24	komori	komori	PROPN
ejpam-5311	28	25	,	,	PUNCT
ejpam-5311	28	26	who	who	PRON
ejpam-5311	28	27	first	first	ADV
ejpam-5311	28	28	characterized	characterize	VERB
ejpam-5311	28	29	it	it	PRON
ejpam-5311	28	30	in	in	ADP
ejpam-5311	28	31	1984	1984	NUM
ejpam-5311	28	32	.	.	PUNCT
ejpam-5311	29	1	in	in	ADP
ejpam-5311	29	2	this	this	DET
ejpam-5311	29	3	paper	paper	NOUN
ejpam-5311	29	4	,	,	PUNCT
ejpam-5311	29	5	using	use	VERB
ejpam-5311	29	6	the	the	DET
ejpam-5311	29	7	idea	idea	NOUN
ejpam-5311	29	8	of	of	ADP
ejpam-5311	29	9	lukasiewicz	lukasiewicz	ADJ
ejpam-5311	29	10	t	t	PROPN
ejpam-5311	29	11	-	-	PUNCT
ejpam-5311	29	12	norm	norm	NOUN
ejpam-5311	29	13	,	,	PUNCT
ejpam-5311	29	14	we	we	PRON
ejpam-5311	29	15	construct	construct	VERB
ejpam-5311	29	16	the	the	DET
ejpam-5311	29	17	concept	concept	NOUN
ejpam-5311	29	18	of	of	ADP
ejpam-5311	29	19	ε	ε	PROPN
ejpam-5311	29	20	lukasiewicz	lukasiewicz	VERB
ejpam-5311	29	21	fuzzy	fuzzy	ADJ
ejpam-5311	29	22	sets	set	NOUN
ejpam-5311	29	23	based	base	VERB
ejpam-5311	29	24	on	on	ADP
ejpam-5311	29	25	a	a	DET
ejpam-5311	29	26	given	give	VERB
ejpam-5311	29	27	fuzzy	fuzzy	ADJ
ejpam-5311	29	28	set	set	NOUN
ejpam-5311	29	29	and	and	CCONJ
ejpam-5311	29	30	apply	apply	VERB
ejpam-5311	29	31	it	it	PRON
ejpam-5311	29	32	to	to	ADP
ejpam-5311	29	33	bcc	bcc	PROPN
ejpam-5311	29	34	-	-	PUNCT
ejpam-5311	29	35	algebras	algebras	PROPN
ejpam-5311	29	36	.	.	PUNCT
ejpam-5311	30	1	we	we	PRON
ejpam-5311	30	2	define	define	VERB
ejpam-5311	30	3	the	the	DET
ejpam-5311	30	4	concepts	concept	NOUN
ejpam-5311	30	5	of	of	ADP
ejpam-5311	30	6	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	30	7	fuzzy	fuzzy	ADJ
ejpam-5311	30	8	bcc	bcc	PROPN
ejpam-5311	30	9	-	-	PUNCT
ejpam-5311	30	10	subalgebras	subalgebras	PROPN
ejpam-5311	30	11	and	and	CCONJ
ejpam-5311	30	12	investigate	investigate	VERB
ejpam-5311	30	13	several	several	ADJ
ejpam-5311	30	14	properties	property	NOUN
ejpam-5311	30	15	.	.	PUNCT
ejpam-5311	31	1	we	we	PRON
ejpam-5311	31	2	provide	provide	VERB
ejpam-5311	31	3	conditions	condition	NOUN
ejpam-5311	31	4	for	for	SCONJ
ejpam-5311	31	5	an	an	DET
ejpam-5311	31	6	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	31	7	fuzzy	fuzzy	ADJ
ejpam-5311	31	8	set	set	VERB
ejpam-5311	31	9	to	to	PART
ejpam-5311	31	10	be	be	AUX
ejpam-5311	31	11	an	an	DET
ejpam-5311	31	12	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	31	13	fuzzy	fuzzy	ADJ
ejpam-5311	31	14	bccsubalgebra	bccsubalgebra	NOUN
ejpam-5311	31	15	.	.	PUNCT
ejpam-5311	32	1	we	we	PRON
ejpam-5311	32	2	discuss	discuss	VERB
ejpam-5311	32	3	the	the	DET
ejpam-5311	32	4	characterizations	characterization	NOUN
ejpam-5311	32	5	of	of	ADP
ejpam-5311	32	6	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	32	7	fuzzy	fuzzy	ADJ
ejpam-5311	32	8	bcc	bcc	PROPN
ejpam-5311	32	9	-	-	PUNCT
ejpam-5311	32	10	subalgebras	subalgebras	PROPN
ejpam-5311	32	11	.	.	PUNCT
ejpam-5311	33	1	we	we	PRON
ejpam-5311	33	2	construct	construct	VERB
ejpam-5311	33	3	three	three	NUM
ejpam-5311	33	4	kinds	kind	NOUN
ejpam-5311	33	5	of	of	ADP
ejpam-5311	33	6	subsets	subset	NOUN
ejpam-5311	33	7	,	,	PUNCT
ejpam-5311	33	8	so	so	ADV
ejpam-5311	33	9	-	-	PUNCT
ejpam-5311	33	10	called	call	VERB
ejpam-5311	33	11	∈-set	∈-set	NOUN
ejpam-5311	33	12	,	,	PUNCT
ejpam-5311	33	13	q	q	NOUN
ejpam-5311	33	14	-	-	PUNCT
ejpam-5311	33	15	set	set	NOUN
ejpam-5311	33	16	,	,	PUNCT
ejpam-5311	33	17	and	and	CCONJ
ejpam-5311	33	18	o	o	NOUN
ejpam-5311	33	19	-	-	NOUN
ejpam-5311	33	20	set	set	NOUN
ejpam-5311	33	21	,	,	PUNCT
ejpam-5311	33	22	and	and	CCONJ
ejpam-5311	33	23	we	we	PRON
ejpam-5311	33	24	find	find	VERB
ejpam-5311	33	25	the	the	DET
ejpam-5311	33	26	conditions	condition	NOUN
ejpam-5311	33	27	under	under	ADP
ejpam-5311	33	28	which	which	PRON
ejpam-5311	33	29	they	they	PRON
ejpam-5311	33	30	can	can	AUX
ejpam-5311	33	31	be	be	AUX
ejpam-5311	33	32	bcc	bcc	PROPN
ejpam-5311	33	33	-	-	PUNCT
ejpam-5311	33	34	subalgebras	subalgebras	PROPN
ejpam-5311	33	35	.	.	PUNCT
ejpam-5311	34	1	2	2	X
ejpam-5311	34	2	.	.	X
ejpam-5311	34	3	preliminaries	preliminary	NOUN
ejpam-5311	34	4	the	the	DET
ejpam-5311	34	5	concept	concept	NOUN
ejpam-5311	34	6	of	of	ADP
ejpam-5311	34	7	bcc	bcc	PROPN
ejpam-5311	34	8	-	-	PUNCT
ejpam-5311	34	9	algebras	algebras	PROPN
ejpam-5311	34	10	(	(	PUNCT
ejpam-5311	34	11	see	see	VERB
ejpam-5311	34	12	[	[	X
ejpam-5311	34	13	9	9	NUM
ejpam-5311	34	14	]	]	PUNCT
ejpam-5311	34	15	)	)	PUNCT
ejpam-5311	34	16	can	can	AUX
ejpam-5311	34	17	be	be	AUX
ejpam-5311	34	18	redefined	redefine	VERB
ejpam-5311	34	19	without	without	ADP
ejpam-5311	34	20	the	the	DET
ejpam-5311	34	21	condition	condition	NOUN
ejpam-5311	34	22	(	(	PUNCT
ejpam-5311	34	23	2.6	2.6	NUM
ejpam-5311	34	24	)	)	PUNCT
ejpam-5311	34	25	as	as	SCONJ
ejpam-5311	34	26	follows	follow	VERB
ejpam-5311	34	27	:	:	PUNCT
ejpam-5311	34	28	an	an	DET
ejpam-5311	34	29	algebra	algebra	NOUN
ejpam-5311	34	30	x	x	X
ejpam-5311	34	31	=	=	SYM
ejpam-5311	34	32	(	(	PUNCT
ejpam-5311	34	33	x	x	X
ejpam-5311	34	34	,	,	PUNCT
ejpam-5311	34	35	∗	∗	NOUN
ejpam-5311	34	36	,	,	PUNCT
ejpam-5311	34	37	0	0	NUM
ejpam-5311	34	38	)	)	PUNCT
ejpam-5311	34	39	of	of	ADP
ejpam-5311	34	40	type	type	NOUN
ejpam-5311	34	41	(	(	PUNCT
ejpam-5311	34	42	2	2	NUM
ejpam-5311	34	43	,	,	PUNCT
ejpam-5311	34	44	0	0	NUM
ejpam-5311	34	45	)	)	PUNCT
ejpam-5311	34	46	is	be	AUX
ejpam-5311	34	47	called	call	VERB
ejpam-5311	34	48	a	a	DET
ejpam-5311	34	49	bcc	bcc	PROPN
ejpam-5311	34	50	-	-	PUNCT
ejpam-5311	34	51	algebra	algebra	PROPN
ejpam-5311	34	52	(	(	PUNCT
ejpam-5311	34	53	see	see	VERB
ejpam-5311	34	54	[	[	X
ejpam-5311	34	55	6	6	NUM
ejpam-5311	34	56	]	]	PUNCT
ejpam-5311	34	57	)	)	PUNCT
ejpam-5311	34	58	if	if	SCONJ
ejpam-5311	34	59	it	it	PRON
ejpam-5311	34	60	satisfies	satisfy	VERB
ejpam-5311	34	61	the	the	DET
ejpam-5311	34	62	following	follow	VERB
ejpam-5311	34	63	conditions	condition	NOUN
ejpam-5311	34	64	:	:	PUNCT
ejpam-5311	34	65	(	(	PUNCT
ejpam-5311	34	66	∀x	∀x	X
ejpam-5311	34	67	,	,	PUNCT
ejpam-5311	34	68	y	y	PROPN
ejpam-5311	34	69	,	,	PUNCT
ejpam-5311	34	70	z	z	PROPN
ejpam-5311	34	71	∈	∈	PROPN
ejpam-5311	34	72	x)((y	x)((y	PROPN
ejpam-5311	34	73	∗	∗	PROPN
ejpam-5311	34	74	z	z	PROPN
ejpam-5311	34	75	)	)	PUNCT
ejpam-5311	34	76	∗	∗	NOUN
ejpam-5311	34	77	(	(	PUNCT
ejpam-5311	34	78	(	(	PUNCT
ejpam-5311	34	79	x	x	SYM
ejpam-5311	34	80	∗	∗	PROPN
ejpam-5311	34	81	y	y	NOUN
ejpam-5311	34	82	)	)	PUNCT
ejpam-5311	34	83	∗	∗	NOUN
ejpam-5311	34	84	(	(	PUNCT
ejpam-5311	34	85	x	x	X
ejpam-5311	34	86	∗	∗	PROPN
ejpam-5311	34	87	z	z	NOUN
ejpam-5311	34	88	)	)	PUNCT
ejpam-5311	34	89	)	)	PUNCT
ejpam-5311	35	1	=	=	SYM
ejpam-5311	35	2	0	0	X
ejpam-5311	35	3	)	)	PUNCT
ejpam-5311	35	4	(	(	PUNCT
ejpam-5311	35	5	2.1	2.1	NUM
ejpam-5311	35	6	)	)	PUNCT
ejpam-5311	35	7	(	(	PUNCT
ejpam-5311	35	8	∀x	∀x	X
ejpam-5311	35	9	∈	∈	PROPN
ejpam-5311	35	10	x)(0	x)(0	X
ejpam-5311	36	1	∗	∗	NOUN
ejpam-5311	36	2	x	x	X
ejpam-5311	37	1	=	=	SYM
ejpam-5311	37	2	x	x	X
ejpam-5311	37	3	)	)	PUNCT
ejpam-5311	37	4	(	(	PUNCT
ejpam-5311	37	5	2.2	2.2	NUM
ejpam-5311	37	6	)	)	PUNCT
ejpam-5311	37	7	(	(	PUNCT
ejpam-5311	37	8	∀x	∀x	X
ejpam-5311	37	9	∈	∈	PROPN
ejpam-5311	37	10	x)(x	x)(x	PROPN
ejpam-5311	37	11	∗	∗	NOUN
ejpam-5311	37	12	0	0	NUM
ejpam-5311	38	1	=	=	SYM
ejpam-5311	38	2	0	0	NUM
ejpam-5311	38	3	)	)	PUNCT
ejpam-5311	38	4	(	(	PUNCT
ejpam-5311	38	5	2.3	2.3	NUM
ejpam-5311	38	6	)	)	PUNCT
ejpam-5311	38	7	(	(	PUNCT
ejpam-5311	38	8	∀x	∀x	X
ejpam-5311	38	9	,	,	PUNCT
ejpam-5311	38	10	y	y	PROPN
ejpam-5311	38	11	∈	∈	PROPN
ejpam-5311	38	12	x)(x	x)(x	PROPN
ejpam-5311	38	13	∗	∗	VERB
ejpam-5311	38	14	y	y	NOUN
ejpam-5311	38	15	=	=	SYM
ejpam-5311	38	16	0	0	PUNCT
ejpam-5311	39	1	=	=	SYM
ejpam-5311	39	2	y	y	PROPN
ejpam-5311	39	3	∗	∗	X
ejpam-5311	39	4	x	x	X
ejpam-5311	39	5	⇒	⇒	NOUN
ejpam-5311	39	6	x	x	PUNCT
ejpam-5311	39	7	=	=	SYM
ejpam-5311	39	8	y	y	PROPN
ejpam-5311	39	9	)	)	PUNCT
ejpam-5311	39	10	(	(	PUNCT
ejpam-5311	39	11	2.4	2.4	NUM
ejpam-5311	39	12	)	)	PUNCT
ejpam-5311	39	13	after	after	ADP
ejpam-5311	39	14	this	this	PRON
ejpam-5311	39	15	,	,	PUNCT
ejpam-5311	39	16	we	we	PRON
ejpam-5311	39	17	assign	assign	VERB
ejpam-5311	39	18	x	x	PUNCT
ejpam-5311	39	19	instead	instead	ADV
ejpam-5311	39	20	of	of	ADP
ejpam-5311	39	21	a	a	DET
ejpam-5311	39	22	bcc	bcc	NOUN
ejpam-5311	39	23	-	-	PUNCT
ejpam-5311	39	24	algebra	algebra	PROPN
ejpam-5311	39	25	(	(	PUNCT
ejpam-5311	39	26	x	x	X
ejpam-5311	39	27	,	,	PUNCT
ejpam-5311	39	28	∗	∗	NOUN
ejpam-5311	39	29	,	,	PUNCT
ejpam-5311	39	30	0	0	NUM
ejpam-5311	39	31	)	)	PUNCT
ejpam-5311	39	32	until	until	SCONJ
ejpam-5311	39	33	otherwise	otherwise	ADV
ejpam-5311	39	34	specified	specify	VERB
ejpam-5311	39	35	.	.	PUNCT
ejpam-5311	40	1	we	we	PRON
ejpam-5311	40	2	define	define	VERB
ejpam-5311	40	3	a	a	DET
ejpam-5311	40	4	binary	binary	ADJ
ejpam-5311	40	5	relation	relation	NOUN
ejpam-5311	40	6	≤	≤	NOUN
ejpam-5311	40	7	on	on	ADP
ejpam-5311	40	8	x	x	PUNCT
ejpam-5311	40	9	as	as	SCONJ
ejpam-5311	40	10	follows	follow	VERB
ejpam-5311	40	11	:	:	PUNCT
ejpam-5311	40	12	(	(	PUNCT
ejpam-5311	40	13	∀x	∀x	X
ejpam-5311	40	14	,	,	PUNCT
ejpam-5311	40	15	y	y	PROPN
ejpam-5311	40	16	∈	∈	PROPN
ejpam-5311	40	17	x)(x	x)(x	PROPN
ejpam-5311	40	18	≤	≤	PROPN
ejpam-5311	40	19	y	y	PROPN
ejpam-5311	40	20	⇔	⇔	PROPN
ejpam-5311	40	21	x	x	PROPN
ejpam-5311	40	22	∗	∗	NOUN
ejpam-5311	40	23	y	y	NOUN
ejpam-5311	40	24	=	=	SYM
ejpam-5311	40	25	0	0	NUM
ejpam-5311	40	26	)	)	PUNCT
ejpam-5311	40	27	(	(	PUNCT
ejpam-5311	40	28	2.5	2.5	NUM
ejpam-5311	40	29	)	)	PUNCT
ejpam-5311	40	30	in	in	ADP
ejpam-5311	40	31	x	x	PRON
ejpam-5311	40	32	,	,	PUNCT
ejpam-5311	40	33	the	the	DET
ejpam-5311	40	34	following	follow	VERB
ejpam-5311	40	35	assertions	assertion	NOUN
ejpam-5311	40	36	are	be	AUX
ejpam-5311	40	37	valid	valid	ADJ
ejpam-5311	40	38	(	(	PUNCT
ejpam-5311	40	39	see	see	VERB
ejpam-5311	40	40	[	[	X
ejpam-5311	40	41	7	7	NUM
ejpam-5311	40	42	]	]	NUM
ejpam-5311	40	43	)	)	PUNCT
ejpam-5311	40	44	.	.	PUNCT
ejpam-5311	41	1	(	(	PUNCT
ejpam-5311	41	2	∀x	∀x	X
ejpam-5311	41	3	∈	∈	PROPN
ejpam-5311	41	4	x)(x	x)(x	PROPN
ejpam-5311	41	5	≤	≤	NUM
ejpam-5311	41	6	x	x	X
ejpam-5311	41	7	)	)	PUNCT
ejpam-5311	41	8	(	(	PUNCT
ejpam-5311	41	9	2.6	2.6	NUM
ejpam-5311	41	10	)	)	PUNCT
ejpam-5311	41	11	(	(	PUNCT
ejpam-5311	41	12	∀x	∀x	X
ejpam-5311	41	13	,	,	PUNCT
ejpam-5311	41	14	y	y	PROPN
ejpam-5311	41	15	,	,	PUNCT
ejpam-5311	41	16	z	z	PROPN
ejpam-5311	41	17	∈	∈	PROPN
ejpam-5311	41	18	x)(x	x)(x	PROPN
ejpam-5311	41	19	≤	≤	PROPN
ejpam-5311	41	20	y	y	PROPN
ejpam-5311	41	21	,	,	PUNCT
ejpam-5311	41	22	y	y	PROPN
ejpam-5311	41	23	≤	≤	PROPN
ejpam-5311	41	24	z	z	NOUN
ejpam-5311	41	25	⇒	⇒	NOUN
ejpam-5311	41	26	x	x	PUNCT
ejpam-5311	41	27	≤	≤	NUM
ejpam-5311	41	28	z	z	NOUN
ejpam-5311	41	29	)	)	PUNCT
ejpam-5311	41	30	(	(	PUNCT
ejpam-5311	41	31	2.7	2.7	NUM
ejpam-5311	41	32	)	)	PUNCT
ejpam-5311	41	33	(	(	PUNCT
ejpam-5311	41	34	∀x	∀x	X
ejpam-5311	41	35	,	,	PUNCT
ejpam-5311	41	36	y	y	PROPN
ejpam-5311	41	37	,	,	PUNCT
ejpam-5311	41	38	z	z	PROPN
ejpam-5311	41	39	∈	∈	PROPN
ejpam-5311	41	40	x)(x	x)(x	PROPN
ejpam-5311	41	41	≤	≤	ADV
ejpam-5311	41	42	y	y	PROPN
ejpam-5311	41	43	⇒	⇒	PROPN
ejpam-5311	41	44	z	z	PROPN
ejpam-5311	41	45	∗	∗	X
ejpam-5311	41	46	x	x	PUNCT
ejpam-5311	41	47	≤	≤	NUM
ejpam-5311	41	48	z	z	NOUN
ejpam-5311	41	49	∗	∗	NOUN
ejpam-5311	41	50	y	y	PROPN
ejpam-5311	41	51	)	)	PUNCT
ejpam-5311	41	52	(	(	PUNCT
ejpam-5311	41	53	2.8	2.8	NUM
ejpam-5311	41	54	)	)	PUNCT
ejpam-5311	41	55	(	(	PUNCT
ejpam-5311	41	56	∀x	∀x	X
ejpam-5311	41	57	,	,	PUNCT
ejpam-5311	41	58	y	y	PROPN
ejpam-5311	41	59	,	,	PUNCT
ejpam-5311	41	60	z	z	PROPN
ejpam-5311	41	61	∈	∈	PROPN
ejpam-5311	41	62	x)(x	x)(x	PROPN
ejpam-5311	41	63	≤	≤	ADV
ejpam-5311	41	64	y	y	PROPN
ejpam-5311	41	65	⇒	⇒	VERB
ejpam-5311	41	66	y	y	PROPN
ejpam-5311	41	67	∗	∗	NOUN
ejpam-5311	41	68	z	z	NOUN
ejpam-5311	41	69	≤	≤	NUM
ejpam-5311	41	70	x	x	PUNCT
ejpam-5311	41	71	∗	∗	NOUN
ejpam-5311	41	72	z	z	NOUN
ejpam-5311	41	73	)	)	PUNCT
ejpam-5311	41	74	(	(	PUNCT
ejpam-5311	41	75	2.9	2.9	NUM
ejpam-5311	41	76	)	)	PUNCT
ejpam-5311	41	77	(	(	PUNCT
ejpam-5311	41	78	∀x	∀x	X
ejpam-5311	41	79	,	,	PUNCT
ejpam-5311	41	80	y	y	PROPN
ejpam-5311	41	81	,	,	PUNCT
ejpam-5311	41	82	z	z	PROPN
ejpam-5311	41	83	∈	∈	PROPN
ejpam-5311	41	84	x)(x	x)(x	PROPN
ejpam-5311	41	85	≤	≤	ADV
ejpam-5311	41	86	y	y	PROPN
ejpam-5311	41	87	∗	∗	NOUN
ejpam-5311	41	88	x	x	NOUN
ejpam-5311	41	89	,	,	PUNCT
ejpam-5311	41	90	in	in	ADP
ejpam-5311	41	91	particular	particular	ADJ
ejpam-5311	41	92	,	,	PUNCT
ejpam-5311	41	93	y	y	PROPN
ejpam-5311	41	94	∗	∗	NOUN
ejpam-5311	41	95	z	z	NOUN
ejpam-5311	41	96	≤	≤	NUM
ejpam-5311	41	97	x	x	PUNCT
ejpam-5311	41	98	∗	∗	NOUN
ejpam-5311	41	99	(	(	PUNCT
ejpam-5311	41	100	y	y	PROPN
ejpam-5311	41	101	∗	∗	PROPN
ejpam-5311	41	102	z	z	PROPN
ejpam-5311	41	103	)	)	PUNCT
ejpam-5311	41	104	)	)	PUNCT
ejpam-5311	41	105	(	(	PUNCT
ejpam-5311	41	106	2.10	2.10	NUM
ejpam-5311	41	107	)	)	PUNCT
ejpam-5311	41	108	(	(	PUNCT
ejpam-5311	41	109	∀x	∀x	X
ejpam-5311	41	110	,	,	PUNCT
ejpam-5311	41	111	y	y	PROPN
ejpam-5311	41	112	∈	∈	PROPN
ejpam-5311	41	113	x)(y	x)(y	PUNCT
ejpam-5311	42	1	∗	∗	NOUN
ejpam-5311	42	2	x	x	PUNCT
ejpam-5311	42	3	≤	≤	NUM
ejpam-5311	42	4	x	x	PUNCT
ejpam-5311	42	5	⇔	⇔	NOUN
ejpam-5311	42	6	x	x	X
ejpam-5311	42	7	=	=	SYM
ejpam-5311	42	8	y	y	PROPN
ejpam-5311	42	9	∗	∗	NOUN
ejpam-5311	42	10	x	x	NOUN
ejpam-5311	42	11	)	)	PUNCT
ejpam-5311	42	12	(	(	PUNCT
ejpam-5311	42	13	2.11	2.11	NUM
ejpam-5311	42	14	)	)	PUNCT
ejpam-5311	42	15	(	(	PUNCT
ejpam-5311	42	16	∀x	∀x	X
ejpam-5311	42	17	,	,	PUNCT
ejpam-5311	42	18	y	y	PROPN
ejpam-5311	42	19	∈	∈	PROPN
ejpam-5311	42	20	x)(x	x)(x	PROPN
ejpam-5311	42	21	≤	≤	ADV
ejpam-5311	42	22	y	y	PROPN
ejpam-5311	42	23	∗	∗	PROPN
ejpam-5311	42	24	y	y	PROPN
ejpam-5311	42	25	)	)	PUNCT
ejpam-5311	42	26	(	(	PUNCT
ejpam-5311	42	27	2.12	2.12	NUM
ejpam-5311	42	28	)	)	PUNCT
ejpam-5311	42	29	(	(	PUNCT
ejpam-5311	42	30	∀a	∀a	X
ejpam-5311	42	31	,	,	PUNCT
ejpam-5311	42	32	x	x	X
ejpam-5311	42	33	,	,	PUNCT
ejpam-5311	42	34	y	y	PROPN
ejpam-5311	42	35	,	,	PUNCT
ejpam-5311	42	36	z	z	PROPN
ejpam-5311	42	37	∈	∈	PROPN
ejpam-5311	42	38	x)(x	x)(x	PROPN
ejpam-5311	42	39	∗	∗	NOUN
ejpam-5311	42	40	(	(	PUNCT
ejpam-5311	42	41	y	y	PROPN
ejpam-5311	42	42	∗	∗	PROPN
ejpam-5311	42	43	z	z	NOUN
ejpam-5311	42	44	)	)	PUNCT
ejpam-5311	42	45	≤	≤	NUM
ejpam-5311	42	46	x	x	X
ejpam-5311	42	47	∗	∗	NOUN
ejpam-5311	42	48	(	(	PUNCT
ejpam-5311	42	49	(	(	PUNCT
ejpam-5311	42	50	a	a	DET
ejpam-5311	42	51	∗	∗	NOUN
ejpam-5311	42	52	y	y	NOUN
ejpam-5311	42	53	)	)	PUNCT
ejpam-5311	42	54	∗	∗	NOUN
ejpam-5311	42	55	(	(	PUNCT
ejpam-5311	42	56	a	a	DET
ejpam-5311	42	57	∗	∗	NOUN
ejpam-5311	42	58	z	z	NOUN
ejpam-5311	42	59	)	)	PUNCT
ejpam-5311	42	60	)	)	PUNCT
ejpam-5311	42	61	)	)	PUNCT
ejpam-5311	42	62	(	(	PUNCT
ejpam-5311	42	63	2.13	2.13	NUM
ejpam-5311	42	64	)	)	PUNCT
ejpam-5311	42	65	(	(	PUNCT
ejpam-5311	42	66	∀a	∀a	X
ejpam-5311	42	67	,	,	PUNCT
ejpam-5311	42	68	x	x	X
ejpam-5311	42	69	,	,	PUNCT
ejpam-5311	42	70	y	y	PROPN
ejpam-5311	42	71	,	,	PUNCT
ejpam-5311	42	72	z	z	PROPN
ejpam-5311	42	73	∈	∈	PROPN
ejpam-5311	42	74	x)(((a	x)(((a	PROPN
ejpam-5311	42	75	∗	∗	NOUN
ejpam-5311	42	76	x	x	NOUN
ejpam-5311	42	77	)	)	PUNCT
ejpam-5311	42	78	∗	∗	NOUN
ejpam-5311	42	79	(	(	PUNCT
ejpam-5311	42	80	a	a	DET
ejpam-5311	42	81	∗	∗	NOUN
ejpam-5311	42	82	y	y	NOUN
ejpam-5311	42	83	)	)	PUNCT
ejpam-5311	42	84	)	)	PUNCT
ejpam-5311	42	85	∗	∗	NOUN
ejpam-5311	42	86	z	z	NOUN
ejpam-5311	42	87	≤	≤	NOUN
ejpam-5311	42	88	(	(	PUNCT
ejpam-5311	42	89	x	x	X
ejpam-5311	42	90	∗	∗	PROPN
ejpam-5311	42	91	y	y	NOUN
ejpam-5311	42	92	)	)	PUNCT
ejpam-5311	42	93	∗	∗	NOUN
ejpam-5311	42	94	z	z	NOUN
ejpam-5311	42	95	)	)	PUNCT
ejpam-5311	42	96	(	(	PUNCT
ejpam-5311	42	97	2.14	2.14	NUM
ejpam-5311	42	98	)	)	PUNCT
ejpam-5311	42	99	(	(	PUNCT
ejpam-5311	42	100	∀x	∀x	X
ejpam-5311	42	101	,	,	PUNCT
ejpam-5311	42	102	y	y	PROPN
ejpam-5311	42	103	,	,	PUNCT
ejpam-5311	42	104	z	z	PROPN
ejpam-5311	42	105	∈	∈	PROPN
ejpam-5311	42	106	x)((x	x)((x	NOUN
ejpam-5311	42	107	∗	∗	PROPN
ejpam-5311	42	108	y	y	PROPN
ejpam-5311	42	109	)	)	PUNCT
ejpam-5311	42	110	∗	∗	NOUN
ejpam-5311	42	111	z	z	NOUN
ejpam-5311	42	112	≤	≤	NOUN
ejpam-5311	42	113	y	y	PROPN
ejpam-5311	42	114	∗	∗	PROPN
ejpam-5311	42	115	z	z	PROPN
ejpam-5311	42	116	)	)	PUNCT
ejpam-5311	42	117	(	(	PUNCT
ejpam-5311	42	118	2.15	2.15	NUM
ejpam-5311	42	119	)	)	PUNCT
ejpam-5311	42	120	a.	a.	NOUN
ejpam-5311	42	121	iampan	iampan	PROPN
ejpam-5311	42	122	,	,	PUNCT
ejpam-5311	42	123	r.	r.	PROPN
ejpam-5311	42	124	subasini	subasini	PROPN
ejpam-5311	42	125	,	,	PUNCT
ejpam-5311	42	126	n.	n.	PROPN
ejpam-5311	42	127	rajesh	rajesh	PROPN
ejpam-5311	42	128	/	/	SYM
ejpam-5311	42	129	eur	eur	PROPN
ejpam-5311	42	130	.	.	PUNCT
ejpam-5311	43	1	j.	j.	PROPN
ejpam-5311	43	2	pure	pure	PROPN
ejpam-5311	43	3	appl	appl	PROPN
ejpam-5311	43	4	.	.	PROPN
ejpam-5311	43	5	math	math	PROPN
ejpam-5311	43	6	,	,	PUNCT
ejpam-5311	43	7	17	17	NUM
ejpam-5311	43	8	(	(	PUNCT
ejpam-5311	43	9	3	3	NUM
ejpam-5311	43	10	)	)	PUNCT
ejpam-5311	43	11	(	(	PUNCT
ejpam-5311	43	12	2024	2024	NUM
ejpam-5311	43	13	)	)	PUNCT
ejpam-5311	43	14	,	,	PUNCT
ejpam-5311	43	15	2235	2235	NUM
ejpam-5311	43	16	-	-	SYM
ejpam-5311	43	17	2245	2245	NUM
ejpam-5311	43	18	2237	2237	NUM
ejpam-5311	43	19	(	(	PUNCT
ejpam-5311	43	20	∀x	∀x	NUM
ejpam-5311	43	21	,	,	PUNCT
ejpam-5311	43	22	y	y	PROPN
ejpam-5311	43	23	,	,	PUNCT
ejpam-5311	43	24	z	z	PROPN
ejpam-5311	43	25	∈	∈	PROPN
ejpam-5311	43	26	x)(x	x)(x	PROPN
ejpam-5311	43	27	≤	≤	ADV
ejpam-5311	43	28	y	y	PROPN
ejpam-5311	43	29	⇒	⇒	NOUN
ejpam-5311	43	30	x	x	PUNCT
ejpam-5311	43	31	≤	≤	ADJ
ejpam-5311	43	32	z	z	NOUN
ejpam-5311	43	33	∗	∗	NOUN
ejpam-5311	43	34	y	y	PROPN
ejpam-5311	43	35	)	)	PUNCT
ejpam-5311	43	36	(	(	PUNCT
ejpam-5311	43	37	2.16	2.16	NUM
ejpam-5311	43	38	)	)	PUNCT
ejpam-5311	43	39	(	(	PUNCT
ejpam-5311	43	40	∀x	∀x	X
ejpam-5311	43	41	,	,	PUNCT
ejpam-5311	43	42	y	y	PROPN
ejpam-5311	43	43	,	,	PUNCT
ejpam-5311	43	44	z	z	PROPN
ejpam-5311	43	45	∈	∈	PROPN
ejpam-5311	43	46	x)((x	x)((x	NOUN
ejpam-5311	43	47	∗	∗	PROPN
ejpam-5311	43	48	y	y	PROPN
ejpam-5311	43	49	)	)	PUNCT
ejpam-5311	43	50	∗	∗	NOUN
ejpam-5311	43	51	z	z	NOUN
ejpam-5311	43	52	≤	≤	NUM
ejpam-5311	43	53	x	x	PUNCT
ejpam-5311	43	54	∗	∗	NOUN
ejpam-5311	43	55	(	(	PUNCT
ejpam-5311	43	56	y	y	PROPN
ejpam-5311	43	57	∗	∗	PROPN
ejpam-5311	43	58	z	z	PROPN
ejpam-5311	43	59	)	)	PUNCT
ejpam-5311	43	60	)	)	PUNCT
ejpam-5311	43	61	(	(	PUNCT
ejpam-5311	43	62	2.17	2.17	NUM
ejpam-5311	43	63	)	)	PUNCT
ejpam-5311	43	64	(	(	PUNCT
ejpam-5311	43	65	∀a	∀a	X
ejpam-5311	43	66	,	,	PUNCT
ejpam-5311	43	67	x	x	X
ejpam-5311	43	68	,	,	PUNCT
ejpam-5311	43	69	y	y	PROPN
ejpam-5311	43	70	,	,	PUNCT
ejpam-5311	43	71	z	z	PROPN
ejpam-5311	43	72	∈	∈	PROPN
ejpam-5311	43	73	x)((x	x)((x	NOUN
ejpam-5311	43	74	∗	∗	PROPN
ejpam-5311	43	75	y	y	PROPN
ejpam-5311	43	76	)	)	PUNCT
ejpam-5311	43	77	∗	∗	NOUN
ejpam-5311	43	78	z	z	NOUN
ejpam-5311	43	79	≤	≤	NOUN
ejpam-5311	44	1	y	y	PROPN
ejpam-5311	44	2	∗	∗	NOUN
ejpam-5311	44	3	(	(	PUNCT
ejpam-5311	44	4	a	a	DET
ejpam-5311	44	5	∗	∗	NOUN
ejpam-5311	44	6	z	z	NOUN
ejpam-5311	44	7	)	)	PUNCT
ejpam-5311	44	8	)	)	PUNCT
ejpam-5311	44	9	(	(	PUNCT
ejpam-5311	44	10	2.18	2.18	NUM
ejpam-5311	44	11	)	)	PUNCT
ejpam-5311	44	12	definition	definition	NOUN
ejpam-5311	44	13	1	1	NUM
ejpam-5311	44	14	.	.	PUNCT
ejpam-5311	45	1	[	[	X
ejpam-5311	45	2	7	7	X
ejpam-5311	45	3	]	]	X
ejpam-5311	45	4	a	a	DET
ejpam-5311	45	5	nonempty	nonempty	NOUN
ejpam-5311	45	6	subset	subset	VERB
ejpam-5311	45	7	s	s	NOUN
ejpam-5311	45	8	of	of	ADP
ejpam-5311	45	9	x	x	PRON
ejpam-5311	45	10	is	be	AUX
ejpam-5311	45	11	called	call	VERB
ejpam-5311	45	12	a	a	DET
ejpam-5311	45	13	bcc	bcc	PROPN
ejpam-5311	45	14	-	-	PUNCT
ejpam-5311	45	15	subalgebra	subalgebra	NOUN
ejpam-5311	45	16	of	of	ADP
ejpam-5311	45	17	x	x	PRON
ejpam-5311	45	18	if	if	SCONJ
ejpam-5311	45	19	it	it	PRON
ejpam-5311	45	20	satisfies	satisfy	VERB
ejpam-5311	45	21	the	the	DET
ejpam-5311	45	22	following	follow	VERB
ejpam-5311	45	23	properties	property	NOUN
ejpam-5311	45	24	:	:	PUNCT
ejpam-5311	45	25	(	(	PUNCT
ejpam-5311	45	26	∀x	∀x	X
ejpam-5311	45	27	,	,	PUNCT
ejpam-5311	45	28	y	y	PROPN
ejpam-5311	45	29	∈	∈	PROPN
ejpam-5311	45	30	s)(x	s)(x	PROPN
ejpam-5311	45	31	∗	∗	VERB
ejpam-5311	45	32	y	y	PROPN
ejpam-5311	45	33	∈	∈	PROPN
ejpam-5311	45	34	s	s	PART
ejpam-5311	45	35	)	)	PUNCT
ejpam-5311	45	36	(	(	PUNCT
ejpam-5311	45	37	2.19	2.19	NUM
ejpam-5311	45	38	)	)	PUNCT
ejpam-5311	45	39	a	a	DET
ejpam-5311	45	40	fuzzy	fuzzy	ADJ
ejpam-5311	45	41	set	set	NOUN
ejpam-5311	45	42	[	[	X
ejpam-5311	45	43	12	12	NUM
ejpam-5311	45	44	]	]	PUNCT
ejpam-5311	45	45	in	in	ADP
ejpam-5311	45	46	a	a	DET
ejpam-5311	45	47	nonempty	nonempty	ADV
ejpam-5311	45	48	set	set	VERB
ejpam-5311	45	49	x	x	SYM
ejpam-5311	45	50	is	be	AUX
ejpam-5311	45	51	defined	define	VERB
ejpam-5311	45	52	to	to	PART
ejpam-5311	45	53	be	be	AUX
ejpam-5311	45	54	a	a	DET
ejpam-5311	45	55	function	function	NOUN
ejpam-5311	45	56	µ	µ	NOUN
ejpam-5311	45	57	:	:	PUNCT
ejpam-5311	45	58	x	x	SYM
ejpam-5311	45	59	→	→	SYM
ejpam-5311	45	60	[	[	X
ejpam-5311	45	61	0	0	NUM
ejpam-5311	45	62	,	,	PUNCT
ejpam-5311	45	63	1	1	NUM
ejpam-5311	45	64	]	]	PUNCT
ejpam-5311	45	65	,	,	PUNCT
ejpam-5311	45	66	where	where	SCONJ
ejpam-5311	45	67	[	[	X
ejpam-5311	45	68	0	0	NUM
ejpam-5311	45	69	,	,	PUNCT
ejpam-5311	45	70	1	1	NUM
ejpam-5311	45	71	]	]	PUNCT
ejpam-5311	45	72	is	be	AUX
ejpam-5311	45	73	the	the	DET
ejpam-5311	45	74	unit	unit	NOUN
ejpam-5311	45	75	closed	close	VERB
ejpam-5311	45	76	interval	interval	NOUN
ejpam-5311	45	77	of	of	ADP
ejpam-5311	45	78	real	real	ADJ
ejpam-5311	45	79	numbers	number	NOUN
ejpam-5311	45	80	.	.	PUNCT
ejpam-5311	46	1	definition	definition	NOUN
ejpam-5311	46	2	2	2	NUM
ejpam-5311	46	3	.	.	PUNCT
ejpam-5311	47	1	[	[	X
ejpam-5311	47	2	11	11	NUM
ejpam-5311	47	3	]	]	PUNCT
ejpam-5311	47	4	a	a	DET
ejpam-5311	47	5	fuzzy	fuzzy	ADJ
ejpam-5311	47	6	set	set	VERB
ejpam-5311	47	7	µ	µ	NOUN
ejpam-5311	47	8	in	in	ADP
ejpam-5311	47	9	x	x	AUX
ejpam-5311	47	10	is	be	AUX
ejpam-5311	47	11	called	call	VERB
ejpam-5311	47	12	a	a	DET
ejpam-5311	47	13	fuzzy	fuzzy	ADJ
ejpam-5311	47	14	bcc	bcc	NOUN
ejpam-5311	47	15	-	-	PUNCT
ejpam-5311	47	16	subalgebra	subalgebra	NOUN
ejpam-5311	47	17	of	of	ADP
ejpam-5311	47	18	x	x	PRON
ejpam-5311	47	19	if	if	SCONJ
ejpam-5311	47	20	it	it	PRON
ejpam-5311	47	21	satisfies	satisfy	VERB
ejpam-5311	47	22	the	the	DET
ejpam-5311	47	23	following	follow	VERB
ejpam-5311	47	24	property	property	NOUN
ejpam-5311	47	25	:	:	PUNCT
ejpam-5311	47	26	(	(	PUNCT
ejpam-5311	47	27	∀x	∀x	X
ejpam-5311	47	28	,	,	PUNCT
ejpam-5311	47	29	y	y	PROPN
ejpam-5311	47	30	∈	∈	PROPN
ejpam-5311	47	31	x)(µ(x	x)(µ(x	PUNCT
ejpam-5311	47	32	∗	∗	PROPN
ejpam-5311	47	33	y	y	PROPN
ejpam-5311	47	34	)	)	PUNCT
ejpam-5311	47	35	≥	≥	NOUN
ejpam-5311	47	36	min{µ(x	min{µ(x	NOUN
ejpam-5311	47	37	)	)	PUNCT
ejpam-5311	47	38	,	,	PUNCT
ejpam-5311	47	39	µ(y	µ(y	PROPN
ejpam-5311	47	40	)	)	PUNCT
ejpam-5311	47	41	}	}	PUNCT
ejpam-5311	47	42	)	)	PUNCT
ejpam-5311	47	43	.	.	PUNCT
ejpam-5311	48	1	(	(	PUNCT
ejpam-5311	48	2	2.20	2.20	NUM
ejpam-5311	48	3	)	)	PUNCT
ejpam-5311	48	4	a	a	DET
ejpam-5311	48	5	fuzzy	fuzzy	ADJ
ejpam-5311	48	6	set	set	VERB
ejpam-5311	48	7	µ	µ	NOUN
ejpam-5311	48	8	in	in	ADP
ejpam-5311	48	9	a	a	DET
ejpam-5311	48	10	set	set	NOUN
ejpam-5311	48	11	x	x	X
ejpam-5311	48	12	of	of	ADP
ejpam-5311	48	13	the	the	DET
ejpam-5311	48	14	form	form	NOUN
ejpam-5311	48	15	µ(x	µ(x	VERB
ejpam-5311	48	16	)	)	PUNCT
ejpam-5311	48	17	=	=	PRON
ejpam-5311	48	18	{	{	PUNCT
ejpam-5311	48	19	t	t	PROPN
ejpam-5311	48	20	∈	∈	PROPN
ejpam-5311	48	21	(	(	PUNCT
ejpam-5311	48	22	0	0	NUM
ejpam-5311	48	23	,	,	PUNCT
ejpam-5311	48	24	1	1	NUM
ejpam-5311	48	25	]	]	PUNCT
ejpam-5311	48	26	if	if	SCONJ
ejpam-5311	48	27	x	x	X
ejpam-5311	48	28	=	=	PUNCT
ejpam-5311	48	29	a	a	DET
ejpam-5311	48	30	0	0	X
ejpam-5311	48	31	if	if	SCONJ
ejpam-5311	48	32	x	x	PROPN
ejpam-5311	48	33	̸=	̸=	PROPN
ejpam-5311	48	34	a	a	PRON
ejpam-5311	48	35	,	,	PUNCT
ejpam-5311	48	36	is	be	AUX
ejpam-5311	48	37	said	say	VERB
ejpam-5311	48	38	to	to	PART
ejpam-5311	48	39	be	be	AUX
ejpam-5311	48	40	a	a	DET
ejpam-5311	48	41	fuzzy	fuzzy	ADJ
ejpam-5311	48	42	point	point	NOUN
ejpam-5311	48	43	with	with	ADP
ejpam-5311	48	44	support	support	NOUN
ejpam-5311	48	45	a	a	PRON
ejpam-5311	48	46	and	and	CCONJ
ejpam-5311	48	47	value	value	NOUN
ejpam-5311	48	48	t	t	NOUN
ejpam-5311	48	49	and	and	CCONJ
ejpam-5311	48	50	is	be	AUX
ejpam-5311	48	51	denoted	denote	VERB
ejpam-5311	48	52	by	by	ADP
ejpam-5311	48	53	[	[	PUNCT
ejpam-5311	48	54	a	a	X
ejpam-5311	48	55	/	/	SYM
ejpam-5311	48	56	t	t	NOUN
ejpam-5311	48	57	]	]	PUNCT
ejpam-5311	48	58	.	.	PUNCT
ejpam-5311	49	1	for	for	ADP
ejpam-5311	49	2	a	a	DET
ejpam-5311	49	3	fuzzy	fuzzy	ADJ
ejpam-5311	49	4	set	set	VERB
ejpam-5311	49	5	µ	µ	NOUN
ejpam-5311	49	6	in	in	ADP
ejpam-5311	49	7	a	a	DET
ejpam-5311	49	8	set	set	NOUN
ejpam-5311	49	9	x	x	NOUN
ejpam-5311	49	10	,	,	PUNCT
ejpam-5311	49	11	we	we	PRON
ejpam-5311	49	12	say	say	VERB
ejpam-5311	49	13	that	that	SCONJ
ejpam-5311	49	14	a	a	DET
ejpam-5311	49	15	fuzzy	fuzzy	ADJ
ejpam-5311	49	16	point	point	NOUN
ejpam-5311	49	17	[	[	X
ejpam-5311	49	18	a	a	X
ejpam-5311	49	19	/	/	SYM
ejpam-5311	49	20	t	t	NOUN
ejpam-5311	49	21	]	]	PUNCT
ejpam-5311	49	22	is	be	AUX
ejpam-5311	49	23	(	(	PUNCT
ejpam-5311	49	24	1	1	NUM
ejpam-5311	49	25	)	)	PUNCT
ejpam-5311	49	26	contained	contain	VERB
ejpam-5311	49	27	in	in	ADP
ejpam-5311	49	28	µ	µ	NUM
ejpam-5311	49	29	,	,	PUNCT
ejpam-5311	49	30	denoted	denote	VERB
ejpam-5311	49	31	by	by	ADP
ejpam-5311	49	32	[	[	PUNCT
ejpam-5311	49	33	a	a	X
ejpam-5311	49	34	/	/	SYM
ejpam-5311	49	35	t	t	NOUN
ejpam-5311	49	36	]	]	X
ejpam-5311	49	37	∈	∈	PROPN
ejpam-5311	49	38	µ	µ	PROPN
ejpam-5311	49	39	,	,	PUNCT
ejpam-5311	49	40	(	(	PUNCT
ejpam-5311	49	41	see	see	VERB
ejpam-5311	49	42	[	[	X
ejpam-5311	49	43	10	10	NUM
ejpam-5311	49	44	]	]	SYM
ejpam-5311	49	45	)	)	PUNCT
ejpam-5311	49	46	if	if	SCONJ
ejpam-5311	49	47	µ(a	µ(a	PROPN
ejpam-5311	49	48	)	)	PUNCT
ejpam-5311	49	49	≥	≥	PROPN
ejpam-5311	49	50	t	t	PROPN
ejpam-5311	49	51	,	,	PUNCT
ejpam-5311	49	52	(	(	PUNCT
ejpam-5311	49	53	2	2	X
ejpam-5311	49	54	)	)	PUNCT
ejpam-5311	49	55	quasi	quasi	NOUN
ejpam-5311	49	56	-	-	VERB
ejpam-5311	49	57	coincident	coincident	ADJ
ejpam-5311	49	58	with	with	ADP
ejpam-5311	49	59	µ	µ	NUM
ejpam-5311	49	60	,	,	PUNCT
ejpam-5311	49	61	denoted	denote	VERB
ejpam-5311	49	62	by	by	ADP
ejpam-5311	49	63	[	[	PUNCT
ejpam-5311	49	64	a	a	X
ejpam-5311	49	65	/	/	SYM
ejpam-5311	49	66	t]qµ	t]qµ	PROPN
ejpam-5311	49	67	,	,	PUNCT
ejpam-5311	49	68	(	(	PUNCT
ejpam-5311	49	69	see	see	VERB
ejpam-5311	49	70	[	[	X
ejpam-5311	49	71	10	10	NUM
ejpam-5311	49	72	]	]	SYM
ejpam-5311	49	73	)	)	PUNCT
ejpam-5311	49	74	if	if	SCONJ
ejpam-5311	49	75	µ(a	µ(a	PROPN
ejpam-5311	49	76	)	)	PUNCT
ejpam-5311	50	1	+	+	CCONJ
ejpam-5311	50	2	t	t	X
ejpam-5311	50	3	>	>	X
ejpam-5311	50	4	1	1	X
ejpam-5311	50	5	.	.	PUNCT
ejpam-5311	50	6	proposition	proposition	NOUN
ejpam-5311	50	7	1	1	NUM
ejpam-5311	50	8	.	.	PUNCT
ejpam-5311	51	1	if	if	SCONJ
ejpam-5311	51	2	µ	µ	NOUN
ejpam-5311	51	3	is	be	AUX
ejpam-5311	51	4	a	a	DET
ejpam-5311	51	5	fuzzy	fuzzy	ADJ
ejpam-5311	51	6	set	set	NOUN
ejpam-5311	51	7	in	in	ADP
ejpam-5311	51	8	a	a	DET
ejpam-5311	51	9	set	set	NOUN
ejpam-5311	51	10	x	x	PUNCT
ejpam-5311	51	11	and	and	CCONJ
ejpam-5311	51	12	ε	ε	PROPN
ejpam-5311	51	13	∈	∈	PROPN
ejpam-5311	51	14	(	(	PUNCT
ejpam-5311	51	15	0	0	NUM
ejpam-5311	51	16	,	,	PUNCT
ejpam-5311	51	17	1	1	NUM
ejpam-5311	51	18	)	)	PUNCT
ejpam-5311	51	19	,	,	PUNCT
ejpam-5311	51	20	then	then	ADV
ejpam-5311	51	21	its	its	PRON
ejpam-5311	51	22	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	51	23	fuzzy	fuzzy	NOUN
ejpam-5311	51	24	set	set	VERB
ejpam-5311	51	25	lε	lε	PRON
ejpam-5311	51	26	µ	µ	PRON
ejpam-5311	51	27	satisfies	satisfie	NOUN
ejpam-5311	51	28	the	the	DET
ejpam-5311	51	29	following	follow	VERB
ejpam-5311	51	30	property	property	NOUN
ejpam-5311	51	31	:	:	PUNCT
ejpam-5311	51	32	(	(	PUNCT
ejpam-5311	51	33	1	1	X
ejpam-5311	51	34	)	)	PUNCT
ejpam-5311	51	35	(	(	PUNCT
ejpam-5311	51	36	∀x	∀x	X
ejpam-5311	51	37	,	,	PUNCT
ejpam-5311	51	38	y	y	PROPN
ejpam-5311	51	39	∈	∈	PROPN
ejpam-5311	51	40	x)(µ(x	x)(µ(x	PUNCT
ejpam-5311	51	41	)	)	PUNCT
ejpam-5311	51	42	≥	≥	PROPN
ejpam-5311	51	43	µ(y	µ(y	NOUN
ejpam-5311	51	44	)	)	PUNCT
ejpam-5311	51	45	⇒	⇒	NOUN
ejpam-5311	51	46	lε	lε	VERB
ejpam-5311	51	47	µ(x	µ(x	NOUN
ejpam-5311	51	48	)	)	PUNCT
ejpam-5311	51	49	≥	≥	NOUN
ejpam-5311	51	50	lε	lε	X
ejpam-5311	51	51	µ(y	µ(y	PROPN
ejpam-5311	51	52	)	)	PUNCT
ejpam-5311	51	53	)	)	PUNCT
ejpam-5311	51	54	(	(	PUNCT
ejpam-5311	51	55	2	2	X
ejpam-5311	51	56	)	)	PUNCT
ejpam-5311	51	57	(	(	PUNCT
ejpam-5311	51	58	∀x	∀x	X
ejpam-5311	51	59	∈	∈	PROPN
ejpam-5311	51	60	x)([x	x)([x	PROPN
ejpam-5311	51	61	/	/	SYM
ejpam-5311	51	62	ε]qµ	ε]qµ	ADJ
ejpam-5311	51	63	⇒	⇒	NOUN
ejpam-5311	51	64	lε	lε	ADP
ejpam-5311	51	65	µ(x	µ(x	NOUN
ejpam-5311	51	66	)	)	PUNCT
ejpam-5311	51	67	=	=	SYM
ejpam-5311	51	68	µ(x	µ(x	X
ejpam-5311	51	69	)	)	PUNCT
ejpam-5311	51	70	+	+	CCONJ
ejpam-5311	51	71	ε−	ε−	PROPN
ejpam-5311	51	72	1	1	NUM
ejpam-5311	51	73	)	)	PUNCT
ejpam-5311	51	74	(	(	PUNCT
ejpam-5311	51	75	3	3	X
ejpam-5311	51	76	)	)	PUNCT
ejpam-5311	51	77	(	(	PUNCT
ejpam-5311	51	78	∀x	∀x	X
ejpam-5311	51	79	∈	∈	PROPN
ejpam-5311	51	80	x,∀δ	x,∀δ	ADP
ejpam-5311	51	81	∈	∈	PROPN
ejpam-5311	51	82	(	(	PUNCT
ejpam-5311	51	83	0	0	NUM
ejpam-5311	51	84	,	,	PUNCT
ejpam-5311	51	85	1))(ε	1))(ε	NUM
ejpam-5311	51	86	≥	≥	NOUN
ejpam-5311	51	87	δ	δ	PROPN
ejpam-5311	51	88	⇒	⇒	NOUN
ejpam-5311	51	89	lε	lε	VERB
ejpam-5311	51	90	µ(x	µ(x	NOUN
ejpam-5311	51	91	)	)	PUNCT
ejpam-5311	51	92	≥	≥	NOUN
ejpam-5311	51	93	lδ	lδ	X
ejpam-5311	51	94	µ(x	µ(x	NOUN
ejpam-5311	51	95	)	)	PUNCT
ejpam-5311	51	96	)	)	PUNCT
ejpam-5311	51	97	3	3	X
ejpam-5311	51	98	.	.	X
ejpam-5311	51	99	εlukasiewicz	εlukasiewicz	VERB
ejpam-5311	51	100	fuzzy	fuzzy	ADJ
ejpam-5311	51	101	bcc	bcc	PROPN
ejpam-5311	51	102	-	-	PUNCT
ejpam-5311	51	103	subalgebra	subalgebra	NOUN
ejpam-5311	51	104	of	of	ADP
ejpam-5311	51	105	a	a	DET
ejpam-5311	51	106	bcc	bcc	PROPN
ejpam-5311	51	107	-	-	PUNCT
ejpam-5311	51	108	algebra	algebra	NOUN
ejpam-5311	51	109	in	in	ADP
ejpam-5311	51	110	this	this	DET
ejpam-5311	51	111	section	section	NOUN
ejpam-5311	51	112	,	,	PUNCT
ejpam-5311	51	113	we	we	PRON
ejpam-5311	51	114	will	will	AUX
ejpam-5311	51	115	recall	recall	VERB
ejpam-5311	51	116	the	the	DET
ejpam-5311	51	117	definition	definition	NOUN
ejpam-5311	51	118	of	of	ADP
ejpam-5311	51	119	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	51	120	fuzzy	fuzzy	ADJ
ejpam-5311	51	121	sets	set	NOUN
ejpam-5311	51	122	and	and	CCONJ
ejpam-5311	51	123	introduce	introduce	VERB
ejpam-5311	51	124	a	a	DET
ejpam-5311	51	125	new	new	ADJ
ejpam-5311	51	126	concept	concept	NOUN
ejpam-5311	51	127	called	call	VERB
ejpam-5311	51	128	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	51	129	fuzzy	fuzzy	ADJ
ejpam-5311	51	130	bcc	bcc	PROPN
ejpam-5311	51	131	-	-	PUNCT
ejpam-5311	51	132	subalgebras	subalgebras	PROPN
ejpam-5311	51	133	.	.	PUNCT
ejpam-5311	52	1	definition	definition	NOUN
ejpam-5311	52	2	3	3	X
ejpam-5311	52	3	.	.	PUNCT
ejpam-5311	53	1	let	let	VERB
ejpam-5311	53	2	µ	µ	X
ejpam-5311	53	3	be	be	AUX
ejpam-5311	53	4	a	a	DET
ejpam-5311	53	5	fuzzy	fuzzy	ADJ
ejpam-5311	53	6	set	set	NOUN
ejpam-5311	53	7	in	in	ADP
ejpam-5311	53	8	a	a	DET
ejpam-5311	53	9	set	set	NOUN
ejpam-5311	53	10	x	x	PUNCT
ejpam-5311	53	11	and	and	CCONJ
ejpam-5311	53	12	let	let	VERB
ejpam-5311	53	13	ε	ε	PROPN
ejpam-5311	53	14	∈	∈	PROPN
ejpam-5311	54	1	[	[	X
ejpam-5311	54	2	0	0	NUM
ejpam-5311	54	3	,	,	PUNCT
ejpam-5311	54	4	1	1	NUM
ejpam-5311	54	5	]	]	PUNCT
ejpam-5311	54	6	.	.	PUNCT
ejpam-5311	55	1	a	a	DET
ejpam-5311	55	2	function	function	NOUN
ejpam-5311	55	3	lε	lε	ADP
ejpam-5311	55	4	µ	µ	NOUN
ejpam-5311	55	5	:	:	PUNCT
ejpam-5311	55	6	x	x	SYM
ejpam-5311	55	7	→	→	SYM
ejpam-5311	56	1	[	[	X
ejpam-5311	56	2	0	0	NUM
ejpam-5311	56	3	,	,	PUNCT
ejpam-5311	56	4	1	1	NUM
ejpam-5311	56	5	]	]	PUNCT
ejpam-5311	56	6	;	;	PUNCT
ejpam-5311	56	7	x	x	X
ejpam-5311	56	8	7→	7→	NUM
ejpam-5311	56	9	max{0	max{0	NOUN
ejpam-5311	56	10	,	,	PUNCT
ejpam-5311	56	11	µ(x	µ(x	X
ejpam-5311	56	12	)	)	PUNCT
ejpam-5311	56	13	+	+	CCONJ
ejpam-5311	56	14	ε−	ε−	PROPN
ejpam-5311	56	15	1	1	NUM
ejpam-5311	56	16	}	}	PUNCT
ejpam-5311	56	17	is	be	AUX
ejpam-5311	56	18	called	call	VERB
ejpam-5311	56	19	an	an	DET
ejpam-5311	56	20	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	56	21	fuzzy	fuzzy	ADJ
ejpam-5311	56	22	set	set	NOUN
ejpam-5311	56	23	of	of	ADP
ejpam-5311	56	24	µ	µ	NOUN
ejpam-5311	56	25	in	in	ADP
ejpam-5311	56	26	x.	x.	PROPN
ejpam-5311	56	27	a.	a.	PROPN
ejpam-5311	56	28	iampan	iampan	PROPN
ejpam-5311	56	29	,	,	PUNCT
ejpam-5311	56	30	r.	r.	PROPN
ejpam-5311	56	31	subasini	subasini	PROPN
ejpam-5311	56	32	,	,	PUNCT
ejpam-5311	56	33	n.	n.	PROPN
ejpam-5311	56	34	rajesh	rajesh	PROPN
ejpam-5311	56	35	/	/	SYM
ejpam-5311	56	36	eur	eur	PROPN
ejpam-5311	56	37	.	.	PUNCT
ejpam-5311	57	1	j.	j.	PROPN
ejpam-5311	57	2	pure	pure	PROPN
ejpam-5311	57	3	appl	appl	PROPN
ejpam-5311	57	4	.	.	PROPN
ejpam-5311	57	5	math	math	PROPN
ejpam-5311	57	6	,	,	PUNCT
ejpam-5311	57	7	17	17	NUM
ejpam-5311	57	8	(	(	PUNCT
ejpam-5311	57	9	3	3	NUM
ejpam-5311	57	10	)	)	PUNCT
ejpam-5311	57	11	(	(	PUNCT
ejpam-5311	57	12	2024	2024	NUM
ejpam-5311	57	13	)	)	PUNCT
ejpam-5311	57	14	,	,	PUNCT
ejpam-5311	57	15	2235	2235	NUM
ejpam-5311	57	16	-	-	SYM
ejpam-5311	57	17	2245	2245	NUM
ejpam-5311	57	18	2238	2238	NUM
ejpam-5311	57	19	definition	definition	NOUN
ejpam-5311	57	20	4	4	NUM
ejpam-5311	57	21	.	.	PUNCT
ejpam-5311	58	1	let	let	VERB
ejpam-5311	58	2	µ	µ	X
ejpam-5311	58	3	be	be	AUX
ejpam-5311	58	4	a	a	DET
ejpam-5311	58	5	fuzzy	fuzzy	ADJ
ejpam-5311	58	6	set	set	NOUN
ejpam-5311	58	7	in	in	ADP
ejpam-5311	58	8	x.	x.	NOUN
ejpam-5311	58	9	then	then	ADV
ejpam-5311	58	10	its	its	PRON
ejpam-5311	58	11	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	58	12	fuzzy	fuzzy	NOUN
ejpam-5311	58	13	set	set	VERB
ejpam-5311	58	14	lε	lε	PRON
ejpam-5311	58	15	µ	µ	NOUN
ejpam-5311	58	16	in	in	ADP
ejpam-5311	58	17	x	x	AUX
ejpam-5311	58	18	is	be	AUX
ejpam-5311	58	19	called	call	VERB
ejpam-5311	58	20	an	an	DET
ejpam-5311	58	21	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	58	22	fuzzy	fuzzy	ADJ
ejpam-5311	58	23	bcc	bcc	PROPN
ejpam-5311	58	24	-	-	PUNCT
ejpam-5311	58	25	subalgebra	subalgebra	NOUN
ejpam-5311	58	26	of	of	ADP
ejpam-5311	58	27	x	x	PRON
ejpam-5311	58	28	if	if	SCONJ
ejpam-5311	58	29	it	it	PRON
ejpam-5311	58	30	satisfies	satisfy	VERB
ejpam-5311	58	31	the	the	DET
ejpam-5311	58	32	following	follow	VERB
ejpam-5311	58	33	property	property	NOUN
ejpam-5311	58	34	:	:	PUNCT
ejpam-5311	58	35	(	(	PUNCT
ejpam-5311	58	36	∀x	∀x	X
ejpam-5311	58	37	,	,	PUNCT
ejpam-5311	58	38	y	y	PROPN
ejpam-5311	58	39	∈	∈	PROPN
ejpam-5311	58	40	x,∀ta	x,∀ta	PROPN
ejpam-5311	58	41	,	,	PUNCT
ejpam-5311	58	42	tb	tb	ADP
ejpam-5311	58	43	∈	∈	PROPN
ejpam-5311	58	44	(	(	PUNCT
ejpam-5311	58	45	0	0	NUM
ejpam-5311	58	46	,	,	PUNCT
ejpam-5311	58	47	1])([x	1])([x	NUM
ejpam-5311	58	48	/	/	SYM
ejpam-5311	58	49	ta	ta	X
ejpam-5311	58	50	]	]	X
ejpam-5311	58	51	∈	∈	PROPN
ejpam-5311	58	52	lε	lε	ADP
ejpam-5311	58	53	µ	µ	NOUN
ejpam-5311	58	54	,	,	PUNCT
ejpam-5311	58	55	[	[	X
ejpam-5311	58	56	y	y	X
ejpam-5311	58	57	/	/	SYM
ejpam-5311	58	58	tb	tb	NOUN
ejpam-5311	58	59	]	]	PUNCT
ejpam-5311	58	60	∈	∈	PROPN
ejpam-5311	58	61	lε	lε	X
ejpam-5311	58	62	µ	µ	X
ejpam-5311	58	63	⇒	⇒	NOUN
ejpam-5311	59	1	[	[	X
ejpam-5311	59	2	(	(	PUNCT
ejpam-5311	59	3	x	x	X
ejpam-5311	59	4	∗	∗	NOUN
ejpam-5311	59	5	y)/min{ta	y)/min{ta	NOUN
ejpam-5311	59	6	,	,	PUNCT
ejpam-5311	59	7	tb	tb	NOUN
ejpam-5311	59	8	}	}	PUNCT
ejpam-5311	59	9	]	]	PUNCT
ejpam-5311	59	10	∈	∈	PROPN
ejpam-5311	59	11	lε	lε	ADP
ejpam-5311	59	12	µ	µ	NUM
ejpam-5311	59	13	)	)	PUNCT
ejpam-5311	59	14	(	(	PUNCT
ejpam-5311	59	15	3.1	3.1	NUM
ejpam-5311	59	16	)	)	PUNCT
ejpam-5311	59	17	theorem	theorem	NOUN
ejpam-5311	59	18	1	1	NUM
ejpam-5311	59	19	.	.	PUNCT
ejpam-5311	60	1	if	if	SCONJ
ejpam-5311	60	2	µ	µ	NOUN
ejpam-5311	60	3	is	be	AUX
ejpam-5311	60	4	a	a	DET
ejpam-5311	60	5	fuzzy	fuzzy	ADJ
ejpam-5311	60	6	bcc	bcc	NOUN
ejpam-5311	60	7	-	-	PUNCT
ejpam-5311	60	8	subalgebra	subalgebra	NOUN
ejpam-5311	60	9	of	of	ADP
ejpam-5311	60	10	x	x	PRON
ejpam-5311	60	11	,	,	PUNCT
ejpam-5311	60	12	then	then	ADV
ejpam-5311	60	13	its	its	PRON
ejpam-5311	60	14	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	60	15	fuzzy	fuzzy	NOUN
ejpam-5311	60	16	set	set	VERB
ejpam-5311	60	17	lε	lε	PRON
ejpam-5311	60	18	µ	µ	NOUN
ejpam-5311	60	19	in	in	ADP
ejpam-5311	60	20	x	x	VERB
ejpam-5311	60	21	is	be	AUX
ejpam-5311	60	22	an	an	DET
ejpam-5311	60	23	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	60	24	fuzzy	fuzzy	ADJ
ejpam-5311	60	25	bcc	bcc	PROPN
ejpam-5311	60	26	-	-	PUNCT
ejpam-5311	60	27	subalgebra	subalgebra	NOUN
ejpam-5311	60	28	of	of	ADP
ejpam-5311	60	29	x.	x.	NOUN
ejpam-5311	60	30	proof	proof	PROPN
ejpam-5311	60	31	.	.	PUNCT
ejpam-5311	61	1	assume	assume	VERB
ejpam-5311	61	2	that	that	SCONJ
ejpam-5311	61	3	µ	µ	NOUN
ejpam-5311	61	4	is	be	AUX
ejpam-5311	61	5	a	a	DET
ejpam-5311	61	6	fuzzy	fuzzy	ADJ
ejpam-5311	61	7	bcc	bcc	NOUN
ejpam-5311	61	8	-	-	PUNCT
ejpam-5311	61	9	subalgebra	subalgebra	PROPN
ejpam-5311	61	10	of	of	ADP
ejpam-5311	61	11	x.	x.	NOUN
ejpam-5311	61	12	let	let	VERB
ejpam-5311	61	13	x	x	PRON
ejpam-5311	61	14	,	,	PUNCT
ejpam-5311	61	15	y	y	PROPN
ejpam-5311	61	16	∈	∈	PROPN
ejpam-5311	61	17	x	x	X
ejpam-5311	61	18	and	and	CCONJ
ejpam-5311	61	19	ta	ta	PROPN
ejpam-5311	61	20	,	,	PUNCT
ejpam-5311	61	21	tb	tb	ADP
ejpam-5311	61	22	∈	∈	PROPN
ejpam-5311	61	23	(	(	PUNCT
ejpam-5311	61	24	0	0	NUM
ejpam-5311	61	25	,	,	PUNCT
ejpam-5311	61	26	1	1	NUM
ejpam-5311	61	27	]	]	PUNCT
ejpam-5311	61	28	be	be	AUX
ejpam-5311	61	29	such	such	ADJ
ejpam-5311	61	30	that	that	SCONJ
ejpam-5311	61	31	[	[	X
ejpam-5311	61	32	x	x	X
ejpam-5311	61	33	/	/	SYM
ejpam-5311	61	34	ta	ta	X
ejpam-5311	61	35	]	]	X
ejpam-5311	61	36	∈	∈	PROPN
ejpam-5311	61	37	lε	lε	ADP
ejpam-5311	61	38	µ	µ	NOUN
ejpam-5311	61	39	and	and	CCONJ
ejpam-5311	61	40	[	[	X
ejpam-5311	61	41	y	y	X
ejpam-5311	61	42	/	/	SYM
ejpam-5311	61	43	tb	tb	NOUN
ejpam-5311	61	44	]	]	PUNCT
ejpam-5311	61	45	∈	∈	PROPN
ejpam-5311	61	46	lε	lε	X
ejpam-5311	61	47	µ.	µ.	NOUN
ejpam-5311	61	48	then	then	ADV
ejpam-5311	61	49	lε	lε	ADP
ejpam-5311	61	50	µ(x	µ(x	NOUN
ejpam-5311	61	51	)	)	PUNCT
ejpam-5311	61	52	≥	≥	NOUN
ejpam-5311	61	53	ta	ta	X
ejpam-5311	61	54	and	and	CCONJ
ejpam-5311	61	55	lε	lε	INTJ
ejpam-5311	61	56	µ(y	µ(y	PROPN
ejpam-5311	61	57	)	)	PUNCT
ejpam-5311	61	58	≥	≥	NOUN
ejpam-5311	61	59	tb	tb	NOUN
ejpam-5311	61	60	.	.	PUNCT
ejpam-5311	62	1	thus	thus	ADV
ejpam-5311	62	2	lε	lε	ADP
ejpam-5311	62	3	µ(x	µ(x	ADJ
ejpam-5311	62	4	∗	∗	NOUN
ejpam-5311	62	5	y	y	NOUN
ejpam-5311	62	6	)	)	PUNCT
ejpam-5311	62	7	=	=	SYM
ejpam-5311	62	8	max{0	max{0	PROPN
ejpam-5311	62	9	,	,	PUNCT
ejpam-5311	62	10	µ(x	µ(x	X
ejpam-5311	62	11	∗	∗	NOUN
ejpam-5311	62	12	y	y	NOUN
ejpam-5311	62	13	)	)	PUNCT
ejpam-5311	62	14	+	+	CCONJ
ejpam-5311	62	15	ε−	ε−	PROPN
ejpam-5311	62	16	1	1	NUM
ejpam-5311	62	17	}	}	PUNCT
ejpam-5311	62	18	≥	≥	NOUN
ejpam-5311	62	19	max{0,min{µ(x	max{0,min{µ(x	NUM
ejpam-5311	62	20	)	)	PUNCT
ejpam-5311	62	21	,	,	PUNCT
ejpam-5311	62	22	µ(y	µ(y	PROPN
ejpam-5311	62	23	)	)	PUNCT
ejpam-5311	62	24	}	}	PUNCT
ejpam-5311	62	25	+	+	CCONJ
ejpam-5311	62	26	ε−	ε−	PROPN
ejpam-5311	62	27	1	1	NUM
ejpam-5311	62	28	}	}	PUNCT
ejpam-5311	62	29	=	=	PUNCT
ejpam-5311	62	30	max{0,min{µ(x	max{0,min{µ(x	NOUN
ejpam-5311	62	31	)	)	PUNCT
ejpam-5311	62	32	+	+	CCONJ
ejpam-5311	62	33	ε−	ε−	PROPN
ejpam-5311	62	34	1	1	NUM
ejpam-5311	62	35	,	,	PUNCT
ejpam-5311	62	36	µ(y	µ(y	PROPN
ejpam-5311	62	37	)	)	PUNCT
ejpam-5311	62	38	+	+	CCONJ
ejpam-5311	62	39	ε−	ε−	PROPN
ejpam-5311	62	40	1	1	NUM
ejpam-5311	62	41	}	}	PUNCT
ejpam-5311	62	42	}	}	PUNCT
ejpam-5311	62	43	=	=	SYM
ejpam-5311	62	44	min{max{0	min{max{0	NOUN
ejpam-5311	62	45	,	,	PUNCT
ejpam-5311	62	46	µ(x	µ(x	X
ejpam-5311	62	47	)	)	PUNCT
ejpam-5311	62	48	+	+	CCONJ
ejpam-5311	62	49	ε−	ε−	PROPN
ejpam-5311	62	50	1},max{0	1},max{0	NUM
ejpam-5311	62	51	,	,	PUNCT
ejpam-5311	62	52	µ(y	µ(y	PROPN
ejpam-5311	62	53	)	)	PUNCT
ejpam-5311	62	54	+	+	CCONJ
ejpam-5311	62	55	ε−	ε−	PROPN
ejpam-5311	62	56	1	1	NUM
ejpam-5311	62	57	}	}	PUNCT
ejpam-5311	62	58	}	}	PUNCT
ejpam-5311	62	59	=	=	NOUN
ejpam-5311	62	60	min{lε	min{lε	NUM
ejpam-5311	62	61	µ(x	µ(x	PROPN
ejpam-5311	62	62	)	)	PUNCT
ejpam-5311	62	63	,	,	PUNCT
ejpam-5311	62	64	lε	lε	X
ejpam-5311	62	65	µ(y	µ(y	PROPN
ejpam-5311	62	66	)	)	PUNCT
ejpam-5311	62	67	}	}	PUNCT
ejpam-5311	62	68	≥	≥	NOUN
ejpam-5311	62	69	min{ta	min{ta	X
ejpam-5311	62	70	,	,	PUNCT
ejpam-5311	62	71	tb	tb	NOUN
ejpam-5311	62	72	}	}	PUNCT
ejpam-5311	62	73	.	.	PUNCT
ejpam-5311	63	1	hence	hence	ADV
ejpam-5311	63	2	,	,	PUNCT
ejpam-5311	63	3	[	[	X
ejpam-5311	63	4	(	(	PUNCT
ejpam-5311	63	5	x∗y)/min{ta	x∗y)/min{ta	ADJ
ejpam-5311	63	6	,	,	PUNCT
ejpam-5311	63	7	tb	tb	X
ejpam-5311	63	8	}	}	PUNCT
ejpam-5311	63	9	]	]	PUNCT
ejpam-5311	63	10	∈	∈	PROPN
ejpam-5311	63	11	lε	lε	VERB
ejpam-5311	63	12	µ.	µ.	PROPN
ejpam-5311	63	13	therefore	therefore	ADV
ejpam-5311	63	14	,	,	PUNCT
ejpam-5311	63	15	lε	lε	PROPN
ejpam-5311	63	16	µ	µ	PROPN
ejpam-5311	63	17	is	be	AUX
ejpam-5311	63	18	an	an	DET
ejpam-5311	63	19	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	63	20	fuzzy	fuzzy	ADJ
ejpam-5311	63	21	bcc	bcc	PROPN
ejpam-5311	63	22	-	-	PUNCT
ejpam-5311	63	23	subalgebra	subalgebra	NOUN
ejpam-5311	63	24	of	of	ADP
ejpam-5311	63	25	x.	x.	NOUN
ejpam-5311	63	26	the	the	DET
ejpam-5311	63	27	following	follow	VERB
ejpam-5311	63	28	example	example	NOUN
ejpam-5311	63	29	shows	show	VERB
ejpam-5311	63	30	that	that	SCONJ
ejpam-5311	63	31	the	the	DET
ejpam-5311	63	32	converse	converse	NOUN
ejpam-5311	63	33	of	of	ADP
ejpam-5311	63	34	theorem	theorem	NOUN
ejpam-5311	63	35	1	1	NUM
ejpam-5311	63	36	may	may	AUX
ejpam-5311	63	37	not	not	PART
ejpam-5311	63	38	be	be	AUX
ejpam-5311	63	39	true	true	ADJ
ejpam-5311	63	40	.	.	PUNCT
ejpam-5311	64	1	example	example	NOUN
ejpam-5311	65	1	1	1	NUM
ejpam-5311	65	2	.	.	PUNCT
ejpam-5311	65	3	let	let	VERB
ejpam-5311	65	4	x	x	PUNCT
ejpam-5311	65	5	=	=	PUNCT
ejpam-5311	65	6	{	{	PUNCT
ejpam-5311	65	7	0	0	NUM
ejpam-5311	65	8	,	,	PUNCT
ejpam-5311	65	9	1	1	NUM
ejpam-5311	65	10	,	,	PUNCT
ejpam-5311	65	11	2	2	NUM
ejpam-5311	65	12	,	,	PUNCT
ejpam-5311	65	13	3	3	NUM
ejpam-5311	65	14	,	,	PUNCT
ejpam-5311	65	15	4	4	NUM
ejpam-5311	65	16	}	}	PUNCT
ejpam-5311	65	17	with	with	ADP
ejpam-5311	65	18	the	the	DET
ejpam-5311	65	19	following	follow	VERB
ejpam-5311	65	20	cayley	cayley	ADJ
ejpam-5311	65	21	table	table	NOUN
ejpam-5311	65	22	:	:	PUNCT
ejpam-5311	65	23	∗	∗	NOUN
ejpam-5311	65	24	0	0	NUM
ejpam-5311	66	1	1	1	NUM
ejpam-5311	66	2	2	2	NUM
ejpam-5311	66	3	3	3	NUM
ejpam-5311	66	4	4	4	NUM
ejpam-5311	66	5	0	0	NUM
ejpam-5311	66	6	0	0	NUM
ejpam-5311	66	7	1	1	NUM
ejpam-5311	66	8	2	2	NUM
ejpam-5311	66	9	3	3	NUM
ejpam-5311	66	10	4	4	NUM
ejpam-5311	66	11	1	1	NUM
ejpam-5311	66	12	0	0	NUM
ejpam-5311	66	13	0	0	NUM
ejpam-5311	66	14	2	2	NUM
ejpam-5311	66	15	3	3	NUM
ejpam-5311	66	16	0	0	NUM
ejpam-5311	66	17	2	2	NUM
ejpam-5311	66	18	0	0	NUM
ejpam-5311	66	19	1	1	NUM
ejpam-5311	66	20	0	0	NUM
ejpam-5311	66	21	0	0	NUM
ejpam-5311	66	22	4	4	NUM
ejpam-5311	66	23	3	3	NUM
ejpam-5311	66	24	0	0	NUM
ejpam-5311	66	25	1	1	NUM
ejpam-5311	66	26	2	2	NUM
ejpam-5311	66	27	0	0	NUM
ejpam-5311	66	28	4	4	NUM
ejpam-5311	66	29	4	4	NUM
ejpam-5311	66	30	0	0	NUM
ejpam-5311	66	31	4	4	NUM
ejpam-5311	66	32	2	2	NUM
ejpam-5311	66	33	3	3	NUM
ejpam-5311	66	34	0	0	NUM
ejpam-5311	66	35	then	then	ADV
ejpam-5311	66	36	x	x	PUNCT
ejpam-5311	66	37	is	be	AUX
ejpam-5311	66	38	a	a	DET
ejpam-5311	66	39	bcc	bcc	PROPN
ejpam-5311	66	40	-	-	PUNCT
ejpam-5311	66	41	algebra	algebra	PROPN
ejpam-5311	66	42	.	.	PUNCT
ejpam-5311	67	1	define	define	VERB
ejpam-5311	67	2	a	a	DET
ejpam-5311	67	3	fuzzy	fuzzy	ADJ
ejpam-5311	67	4	set	set	VERB
ejpam-5311	67	5	µ	µ	NOUN
ejpam-5311	67	6	as	as	SCONJ
ejpam-5311	67	7	follows	follow	VERB
ejpam-5311	67	8	:	:	PUNCT
ejpam-5311	67	9	µ(x	µ(x	X
ejpam-5311	67	10	)	)	PUNCT
ejpam-5311	67	11	=	=	PUNCT
ejpam-5311	67	12			VERB
ejpam-5311	67	13	1.0	1.0	NUM
ejpam-5311	68	1	if	if	SCONJ
ejpam-5311	68	2	x	x	PROPN
ejpam-5311	68	3	=	=	SYM
ejpam-5311	68	4	0	0	NUM
ejpam-5311	68	5	0.4	0.4	NUM
ejpam-5311	68	6	if	if	SCONJ
ejpam-5311	68	7	x	x	SYM
ejpam-5311	68	8	=	=	SYM
ejpam-5311	68	9	1	1	NUM
ejpam-5311	68	10	0.2	0.2	NUM
ejpam-5311	68	11	if	if	SCONJ
ejpam-5311	68	12	x	x	NOUN
ejpam-5311	68	13	=	=	SYM
ejpam-5311	68	14	2	2	NUM
ejpam-5311	68	15	0.3	0.3	NUM
ejpam-5311	68	16	if	if	SCONJ
ejpam-5311	68	17	x	x	ADP
ejpam-5311	68	18	=	=	SYM
ejpam-5311	68	19	3	3	NUM
ejpam-5311	68	20	0.6	0.6	NUM
ejpam-5311	68	21	if	if	SCONJ
ejpam-5311	68	22	x	x	X
ejpam-5311	68	23	=	=	SYM
ejpam-5311	68	24	4	4	X
ejpam-5311	68	25	.	.	PUNCT
ejpam-5311	68	26	given	give	VERB
ejpam-5311	68	27	ε	ε	PROPN
ejpam-5311	68	28	=	=	SYM
ejpam-5311	68	29	0.9	0.9	NUM
ejpam-5311	68	30	,	,	PUNCT
ejpam-5311	68	31	the	the	DET
ejpam-5311	68	32	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	68	33	fuzzy	fuzzy	NOUN
ejpam-5311	68	34	set	set	VERB
ejpam-5311	68	35	lε	lε	PRON
ejpam-5311	68	36	µ	µ	PROPN
ejpam-5311	68	37	of	of	ADP
ejpam-5311	68	38	µ	µ	NOUN
ejpam-5311	68	39	in	in	ADP
ejpam-5311	68	40	x	x	AUX
ejpam-5311	68	41	is	be	AUX
ejpam-5311	68	42	given	give	VERB
ejpam-5311	68	43	as	as	SCONJ
ejpam-5311	68	44	follows	follow	VERB
ejpam-5311	68	45	:	:	PUNCT
ejpam-5311	68	46	lε	lε	X
ejpam-5311	68	47	µ(x	µ(x	NOUN
ejpam-5311	68	48	)	)	PUNCT
ejpam-5311	68	49	=	=	PUNCT
ejpam-5311	68	50			NOUN
ejpam-5311	68	51	0.9	0.9	NUM
ejpam-5311	69	1	if	if	SCONJ
ejpam-5311	69	2	x	x	NOUN
ejpam-5311	69	3	=	=	SYM
ejpam-5311	69	4	0	0	NUM
ejpam-5311	69	5	0.3	0.3	NUM
ejpam-5311	69	6	if	if	SCONJ
ejpam-5311	69	7	x	x	NOUN
ejpam-5311	69	8	=	=	SYM
ejpam-5311	69	9	1	1	NUM
ejpam-5311	69	10	0.1	0.1	NUM
ejpam-5311	69	11	if	if	SCONJ
ejpam-5311	69	12	x	x	NOUN
ejpam-5311	69	13	=	=	SYM
ejpam-5311	69	14	2	2	NUM
ejpam-5311	69	15	0.2	0.2	NUM
ejpam-5311	69	16	if	if	SCONJ
ejpam-5311	69	17	x	x	X
ejpam-5311	69	18	=	=	SYM
ejpam-5311	69	19	3	3	NUM
ejpam-5311	69	20	.	.	NOUN
ejpam-5311	69	21	0.5	0.5	NUM
ejpam-5311	69	22	if	if	SCONJ
ejpam-5311	69	23	x	x	X
ejpam-5311	69	24	=	=	SYM
ejpam-5311	69	25	4	4	X
ejpam-5311	69	26	.	.	PUNCT
ejpam-5311	69	27	then	then	ADV
ejpam-5311	69	28	lε	lε	PROPN
ejpam-5311	69	29	µ	µ	PROPN
ejpam-5311	69	30	is	be	AUX
ejpam-5311	69	31	an	an	DET
ejpam-5311	69	32	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	69	33	fuzzy	fuzzy	ADJ
ejpam-5311	69	34	bcc	bcc	PROPN
ejpam-5311	69	35	-	-	PUNCT
ejpam-5311	69	36	subalgebra	subalgebra	PROPN
ejpam-5311	69	37	of	of	ADP
ejpam-5311	69	38	x.	x.	PROPN
ejpam-5311	69	39	a.	a.	PROPN
ejpam-5311	69	40	iampan	iampan	PROPN
ejpam-5311	69	41	,	,	PUNCT
ejpam-5311	69	42	r.	r.	PROPN
ejpam-5311	69	43	subasini	subasini	PROPN
ejpam-5311	69	44	,	,	PUNCT
ejpam-5311	69	45	n.	n.	PROPN
ejpam-5311	69	46	rajesh	rajesh	PROPN
ejpam-5311	69	47	/	/	SYM
ejpam-5311	69	48	eur	eur	PROPN
ejpam-5311	69	49	.	.	PUNCT
ejpam-5311	70	1	j.	j.	PROPN
ejpam-5311	70	2	pure	pure	PROPN
ejpam-5311	70	3	appl	appl	PROPN
ejpam-5311	70	4	.	.	PROPN
ejpam-5311	70	5	math	math	PROPN
ejpam-5311	70	6	,	,	PUNCT
ejpam-5311	70	7	17	17	NUM
ejpam-5311	70	8	(	(	PUNCT
ejpam-5311	70	9	3	3	NUM
ejpam-5311	70	10	)	)	PUNCT
ejpam-5311	70	11	(	(	PUNCT
ejpam-5311	70	12	2024	2024	NUM
ejpam-5311	70	13	)	)	PUNCT
ejpam-5311	70	14	,	,	PUNCT
ejpam-5311	70	15	2235	2235	NUM
ejpam-5311	70	16	-	-	SYM
ejpam-5311	70	17	2245	2245	NUM
ejpam-5311	70	18	2239	2239	NUM
ejpam-5311	70	19	theorem	theorem	NOUN
ejpam-5311	70	20	2	2	NUM
ejpam-5311	70	21	.	.	PUNCT
ejpam-5311	70	22	let	let	VERB
ejpam-5311	70	23	µ	µ	X
ejpam-5311	70	24	be	be	AUX
ejpam-5311	70	25	a	a	DET
ejpam-5311	70	26	fuzzy	fuzzy	ADJ
ejpam-5311	70	27	set	set	NOUN
ejpam-5311	70	28	in	in	ADP
ejpam-5311	70	29	x.	x.	NOUN
ejpam-5311	70	30	then	then	ADV
ejpam-5311	70	31	its	its	PRON
ejpam-5311	70	32	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	70	33	fuzzy	fuzzy	NOUN
ejpam-5311	70	34	set	set	VERB
ejpam-5311	70	35	lε	lε	PRON
ejpam-5311	70	36	µ	µ	NOUN
ejpam-5311	70	37	in	in	ADP
ejpam-5311	70	38	x	x	VERB
ejpam-5311	70	39	is	be	AUX
ejpam-5311	70	40	an	an	DET
ejpam-5311	70	41	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	70	42	fuzzy	fuzzy	ADJ
ejpam-5311	70	43	bcc	bcc	PROPN
ejpam-5311	70	44	-	-	PUNCT
ejpam-5311	70	45	subalgebra	subalgebra	NOUN
ejpam-5311	70	46	of	of	ADP
ejpam-5311	70	47	x	x	PRON
ejpam-5311	70	48	if	if	SCONJ
ejpam-5311	70	49	and	and	CCONJ
ejpam-5311	70	50	only	only	ADV
ejpam-5311	70	51	if	if	SCONJ
ejpam-5311	70	52	it	it	PRON
ejpam-5311	70	53	satisfies	satisfy	VERB
ejpam-5311	70	54	the	the	DET
ejpam-5311	70	55	following	follow	VERB
ejpam-5311	70	56	property	property	NOUN
ejpam-5311	70	57	:	:	PUNCT
ejpam-5311	70	58	(	(	PUNCT
ejpam-5311	70	59	∀x	∀x	X
ejpam-5311	70	60	,	,	PUNCT
ejpam-5311	70	61	y	y	PROPN
ejpam-5311	70	62	∈	∈	PROPN
ejpam-5311	70	63	x)(lε	x)(lε	X
ejpam-5311	70	64	µ(x	µ(x	X
ejpam-5311	70	65	∗	∗	NOUN
ejpam-5311	70	66	y	y	NOUN
ejpam-5311	70	67	)	)	PUNCT
ejpam-5311	70	68	≥	≥	PROPN
ejpam-5311	70	69	min{lε	min{lε	NUM
ejpam-5311	70	70	µ(x	µ(x	PROPN
ejpam-5311	70	71	)	)	PUNCT
ejpam-5311	70	72	,	,	PUNCT
ejpam-5311	70	73	lε	lε	X
ejpam-5311	70	74	µ(y	µ(y	PROPN
ejpam-5311	70	75	)	)	PUNCT
ejpam-5311	70	76	}	}	PUNCT
ejpam-5311	70	77	)	)	PUNCT
ejpam-5311	70	78	(	(	PUNCT
ejpam-5311	70	79	3.2	3.2	NUM
ejpam-5311	70	80	)	)	PUNCT
ejpam-5311	70	81	proof	proof	NOUN
ejpam-5311	70	82	.	.	PUNCT
ejpam-5311	71	1	suppose	suppose	VERB
ejpam-5311	71	2	lε	lε	X
ejpam-5311	71	3	µ	µ	PROPN
ejpam-5311	71	4	is	be	AUX
ejpam-5311	71	5	an	an	DET
ejpam-5311	71	6	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	71	7	fuzzy	fuzzy	ADJ
ejpam-5311	71	8	bcc	bcc	PROPN
ejpam-5311	71	9	-	-	PUNCT
ejpam-5311	71	10	subalgebra	subalgebra	PROPN
ejpam-5311	71	11	of	of	ADP
ejpam-5311	71	12	x.	x.	NOUN
ejpam-5311	71	13	let	let	VERB
ejpam-5311	71	14	x	x	PRON
ejpam-5311	71	15	,	,	PUNCT
ejpam-5311	71	16	y	y	PROPN
ejpam-5311	71	17	∈	∈	PROPN
ejpam-5311	71	18	x.	x.	NOUN
ejpam-5311	72	1	then	then	ADV
ejpam-5311	72	2	[	[	X
ejpam-5311	72	3	x	x	X
ejpam-5311	72	4	/	/	SYM
ejpam-5311	72	5	lε	lε	X
ejpam-5311	72	6	µ(x	µ(x	NOUN
ejpam-5311	72	7	)	)	PUNCT
ejpam-5311	72	8	]	]	PUNCT
ejpam-5311	72	9	∈	∈	PROPN
ejpam-5311	72	10	lε	lε	ADP
ejpam-5311	72	11	µ	µ	NOUN
ejpam-5311	72	12	and	and	CCONJ
ejpam-5311	72	13	[	[	X
ejpam-5311	72	14	y	y	X
ejpam-5311	72	15	/	/	SYM
ejpam-5311	72	16	lε	lε	X
ejpam-5311	72	17	µ(y	µ(y	PROPN
ejpam-5311	72	18	)	)	PUNCT
ejpam-5311	72	19	]	]	PUNCT
ejpam-5311	73	1	∈	∈	PROPN
ejpam-5311	73	2	lε	lε	VERB
ejpam-5311	73	3	µ.	µ.	PROPN
ejpam-5311	73	4	thus	thus	ADV
ejpam-5311	73	5	,	,	PUNCT
ejpam-5311	73	6	[	[	X
ejpam-5311	73	7	(	(	PUNCT
ejpam-5311	73	8	x	x	SYM
ejpam-5311	73	9	∗	∗	VERB
ejpam-5311	73	10	y)/min{lε	y)/min{lε	NOUN
ejpam-5311	73	11	µ(x	µ(x	NOUN
ejpam-5311	73	12	)	)	PUNCT
ejpam-5311	73	13	,	,	PUNCT
ejpam-5311	73	14	lε	lε	X
ejpam-5311	73	15	µ(y	µ(y	PROPN
ejpam-5311	73	16	)	)	PUNCT
ejpam-5311	73	17	}	}	PUNCT
ejpam-5311	73	18	]	]	PUNCT
ejpam-5311	74	1	∈	∈	PROPN
ejpam-5311	74	2	lε	lε	PRON
ejpam-5311	74	3	µ	µ	X
ejpam-5311	74	4	by	by	ADP
ejpam-5311	74	5	(	(	PUNCT
ejpam-5311	74	6	3.1	3.1	NUM
ejpam-5311	74	7	)	)	PUNCT
ejpam-5311	74	8	,	,	PUNCT
ejpam-5311	74	9	which	which	PRON
ejpam-5311	74	10	implies	imply	VERB
ejpam-5311	74	11	that	that	SCONJ
ejpam-5311	74	12	lε	lε	ADP
ejpam-5311	74	13	µ(x	µ(x	PROPN
ejpam-5311	74	14	∗	∗	NOUN
ejpam-5311	74	15	y	y	NOUN
ejpam-5311	74	16	)	)	PUNCT
ejpam-5311	74	17	≥	≥	PROPN
ejpam-5311	74	18	min{lε	min{lε	NUM
ejpam-5311	74	19	µ(x	µ(x	PROPN
ejpam-5311	74	20	)	)	PUNCT
ejpam-5311	74	21	,	,	PUNCT
ejpam-5311	74	22	lε	lε	X
ejpam-5311	74	23	µ(y	µ(y	PROPN
ejpam-5311	74	24	)	)	PUNCT
ejpam-5311	74	25	}	}	PUNCT
ejpam-5311	74	26	.	.	PUNCT
ejpam-5311	75	1	conversely	conversely	ADV
ejpam-5311	75	2	,	,	PUNCT
ejpam-5311	75	3	suppose	suppose	VERB
ejpam-5311	75	4	that	that	SCONJ
ejpam-5311	75	5	lε	lε	AUX
ejpam-5311	75	6	µ	µ	PRON
ejpam-5311	75	7	satisfies	satisfy	VERB
ejpam-5311	75	8	the	the	DET
ejpam-5311	75	9	condition	condition	NOUN
ejpam-5311	75	10	(	(	PUNCT
ejpam-5311	75	11	3.2	3.2	NUM
ejpam-5311	75	12	)	)	PUNCT
ejpam-5311	75	13	.	.	PUNCT
ejpam-5311	76	1	let	let	VERB
ejpam-5311	76	2	x	x	PRON
ejpam-5311	76	3	,	,	PUNCT
ejpam-5311	76	4	y	y	PROPN
ejpam-5311	76	5	∈	∈	PROPN
ejpam-5311	76	6	x	x	X
ejpam-5311	76	7	and	and	CCONJ
ejpam-5311	76	8	ta	ta	PROPN
ejpam-5311	76	9	,	,	PUNCT
ejpam-5311	76	10	tb	tb	ADP
ejpam-5311	76	11	∈	∈	PROPN
ejpam-5311	76	12	(	(	PUNCT
ejpam-5311	76	13	0	0	NUM
ejpam-5311	76	14	,	,	PUNCT
ejpam-5311	76	15	1	1	NUM
ejpam-5311	76	16	]	]	PUNCT
ejpam-5311	76	17	be	be	AUX
ejpam-5311	76	18	such	such	ADJ
ejpam-5311	76	19	that	that	SCONJ
ejpam-5311	76	20	[	[	X
ejpam-5311	76	21	x	x	X
ejpam-5311	76	22	/	/	SYM
ejpam-5311	76	23	ta	ta	X
ejpam-5311	76	24	]	]	X
ejpam-5311	76	25	∈	∈	PROPN
ejpam-5311	76	26	lε	lε	ADP
ejpam-5311	76	27	µ	µ	NOUN
ejpam-5311	76	28	and	and	CCONJ
ejpam-5311	76	29	[	[	X
ejpam-5311	76	30	y	y	X
ejpam-5311	76	31	/	/	SYM
ejpam-5311	76	32	tb	tb	NOUN
ejpam-5311	76	33	]	]	PUNCT
ejpam-5311	76	34	∈	∈	PROPN
ejpam-5311	76	35	lε	lε	X
ejpam-5311	76	36	µ.	µ.	NOUN
ejpam-5311	76	37	then	then	ADV
ejpam-5311	76	38	lε	lε	ADP
ejpam-5311	76	39	µ(x	µ(x	NOUN
ejpam-5311	76	40	)	)	PUNCT
ejpam-5311	76	41	≥	≥	NOUN
ejpam-5311	76	42	ta	ta	X
ejpam-5311	76	43	and	and	CCONJ
ejpam-5311	76	44	lε	lε	INTJ
ejpam-5311	76	45	µ(y	µ(y	PROPN
ejpam-5311	76	46	)	)	PUNCT
ejpam-5311	76	47	≥	≥	NOUN
ejpam-5311	76	48	tb	tb	NOUN
ejpam-5311	76	49	,	,	PUNCT
ejpam-5311	76	50	which	which	PRON
ejpam-5311	76	51	implies	imply	VERB
ejpam-5311	76	52	from	from	ADP
ejpam-5311	76	53	(	(	PUNCT
ejpam-5311	76	54	3.2	3.2	NUM
ejpam-5311	76	55	)	)	PUNCT
ejpam-5311	76	56	that	that	PRON
ejpam-5311	76	57	lε	lε	ADP
ejpam-5311	76	58	µ(x∗y	µ(x∗y	NOUN
ejpam-5311	76	59	)	)	PUNCT
ejpam-5311	76	60	≥	≥	PROPN
ejpam-5311	76	61	min{lε	min{lε	NUM
ejpam-5311	76	62	µ(x	µ(x	PROPN
ejpam-5311	76	63	)	)	PUNCT
ejpam-5311	76	64	,	,	PUNCT
ejpam-5311	76	65	lε	lε	X
ejpam-5311	76	66	µ(y	µ(y	PROPN
ejpam-5311	76	67	)	)	PUNCT
ejpam-5311	76	68	}	}	PUNCT
ejpam-5311	76	69	≥	≥	NOUN
ejpam-5311	76	70	min{ta	min{ta	X
ejpam-5311	76	71	,	,	PUNCT
ejpam-5311	76	72	tb	tb	NOUN
ejpam-5311	76	73	}	}	PUNCT
ejpam-5311	76	74	.	.	PUNCT
ejpam-5311	77	1	thus	thus	ADV
ejpam-5311	77	2	,	,	PUNCT
ejpam-5311	77	3	[	[	X
ejpam-5311	77	4	(	(	PUNCT
ejpam-5311	77	5	x∗y)/min{ta	x∗y)/min{ta	ADJ
ejpam-5311	77	6	,	,	PUNCT
ejpam-5311	77	7	tb	tb	X
ejpam-5311	77	8	}	}	PUNCT
ejpam-5311	77	9	]	]	PUNCT
ejpam-5311	77	10	∈	∈	PROPN
ejpam-5311	77	11	lε	lε	VERB
ejpam-5311	77	12	µ.	µ.	NOUN
ejpam-5311	77	13	hence	hence	ADV
ejpam-5311	77	14	,	,	PUNCT
ejpam-5311	77	15	lε	lε	PROPN
ejpam-5311	77	16	µ	µ	PROPN
ejpam-5311	77	17	is	be	AUX
ejpam-5311	77	18	an	an	DET
ejpam-5311	77	19	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	77	20	fuzzy	fuzzy	ADJ
ejpam-5311	77	21	bcc	bcc	PROPN
ejpam-5311	77	22	-	-	PUNCT
ejpam-5311	77	23	subalgebra	subalgebra	PROPN
ejpam-5311	77	24	of	of	ADP
ejpam-5311	77	25	x.	x.	NOUN
ejpam-5311	77	26	proposition	proposition	NOUN
ejpam-5311	77	27	2	2	NUM
ejpam-5311	77	28	.	.	PUNCT
ejpam-5311	78	1	if	if	SCONJ
ejpam-5311	78	2	µ	µ	NOUN
ejpam-5311	78	3	is	be	AUX
ejpam-5311	78	4	a	a	DET
ejpam-5311	78	5	fuzzy	fuzzy	ADJ
ejpam-5311	78	6	bcc	bcc	NOUN
ejpam-5311	78	7	-	-	PUNCT
ejpam-5311	78	8	subalgebra	subalgebra	NOUN
ejpam-5311	78	9	of	of	ADP
ejpam-5311	78	10	x	x	PRON
ejpam-5311	78	11	,	,	PUNCT
ejpam-5311	78	12	then	then	ADV
ejpam-5311	78	13	its	its	PRON
ejpam-5311	78	14	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	78	15	fuzzy	fuzzy	NOUN
ejpam-5311	78	16	set	set	VERB
ejpam-5311	78	17	lε	lε	PRON
ejpam-5311	78	18	µ	µ	PRON
ejpam-5311	78	19	satisfies	satisfie	NOUN
ejpam-5311	78	20	the	the	DET
ejpam-5311	78	21	following	follow	VERB
ejpam-5311	78	22	property	property	NOUN
ejpam-5311	78	23	:	:	PUNCT
ejpam-5311	78	24	(	(	PUNCT
ejpam-5311	78	25	∀x	∀x	X
ejpam-5311	78	26	∈	∈	PROPN
ejpam-5311	78	27	x)(lε	x)(lε	NOUN
ejpam-5311	78	28	µ(0	µ(0	NOUN
ejpam-5311	78	29	)	)	PUNCT
ejpam-5311	78	30	≥	≥	NOUN
ejpam-5311	78	31	lε	lε	X
ejpam-5311	78	32	µ(x	µ(x	NOUN
ejpam-5311	78	33	)	)	PUNCT
ejpam-5311	78	34	)	)	PUNCT
ejpam-5311	78	35	(	(	PUNCT
ejpam-5311	78	36	3.3	3.3	NUM
ejpam-5311	78	37	)	)	PUNCT
ejpam-5311	78	38	proof	proof	NOUN
ejpam-5311	78	39	.	.	PUNCT
ejpam-5311	79	1	if	if	SCONJ
ejpam-5311	79	2	µ	µ	NOUN
ejpam-5311	79	3	is	be	AUX
ejpam-5311	79	4	a	a	DET
ejpam-5311	79	5	fuzzy	fuzzy	ADJ
ejpam-5311	79	6	bcc	bcc	NOUN
ejpam-5311	79	7	-	-	PUNCT
ejpam-5311	79	8	subalgebra	subalgebra	NOUN
ejpam-5311	79	9	of	of	ADP
ejpam-5311	79	10	x	x	PRON
ejpam-5311	79	11	,	,	PUNCT
ejpam-5311	79	12	then	then	ADV
ejpam-5311	79	13	µ(0	µ(0	PROPN
ejpam-5311	79	14	)	)	PUNCT
ejpam-5311	79	15	=	=	SYM
ejpam-5311	79	16	µ(x∗x	µ(x∗x	ADJ
ejpam-5311	79	17	)	)	PUNCT
ejpam-5311	79	18	≥	≥	NOUN
ejpam-5311	79	19	min{µ(x	min{µ(x	NOUN
ejpam-5311	79	20	)	)	PUNCT
ejpam-5311	79	21	,	,	PUNCT
ejpam-5311	79	22	µ(x	µ(x	NOUN
ejpam-5311	79	23	)	)	PUNCT
ejpam-5311	79	24	}	}	PUNCT
ejpam-5311	79	25	=	=	SYM
ejpam-5311	79	26	µ(x	µ(x	X
ejpam-5311	79	27	)	)	PUNCT
ejpam-5311	79	28	for	for	ADP
ejpam-5311	79	29	all	all	PRON
ejpam-5311	79	30	x	x	SYM
ejpam-5311	79	31	∈	∈	ADJ
ejpam-5311	79	32	x.	x.	NOUN
ejpam-5311	79	33	it	it	PRON
ejpam-5311	79	34	follows	follow	VERB
ejpam-5311	79	35	from	from	ADP
ejpam-5311	79	36	proposition	proposition	NOUN
ejpam-5311	79	37	1	1	NUM
ejpam-5311	79	38	(	(	PUNCT
ejpam-5311	79	39	1	1	NUM
ejpam-5311	79	40	)	)	PUNCT
ejpam-5311	79	41	that	that	PRON
ejpam-5311	79	42	lε	lε	ADP
ejpam-5311	79	43	µ(0	µ(0	NOUN
ejpam-5311	79	44	)	)	PUNCT
ejpam-5311	79	45	≥	≥	NOUN
ejpam-5311	79	46	lε	lε	X
ejpam-5311	79	47	µ(x	µ(x	NOUN
ejpam-5311	79	48	)	)	PUNCT
ejpam-5311	79	49	for	for	ADP
ejpam-5311	79	50	all	all	PRON
ejpam-5311	79	51	x	x	SYM
ejpam-5311	79	52	∈	∈	NOUN
ejpam-5311	79	53	x.	x.	NOUN
ejpam-5311	80	1	the	the	DET
ejpam-5311	80	2	following	follow	VERB
ejpam-5311	80	3	example	example	NOUN
ejpam-5311	80	4	shows	show	VERB
ejpam-5311	80	5	that	that	SCONJ
ejpam-5311	80	6	the	the	DET
ejpam-5311	80	7	converse	converse	NOUN
ejpam-5311	80	8	of	of	ADP
ejpam-5311	80	9	proposition	proposition	NOUN
ejpam-5311	80	10	2	2	NUM
ejpam-5311	80	11	is	be	AUX
ejpam-5311	80	12	not	not	PART
ejpam-5311	80	13	true	true	ADJ
ejpam-5311	80	14	in	in	ADP
ejpam-5311	80	15	general	general	ADJ
ejpam-5311	80	16	.	.	PUNCT
ejpam-5311	80	17	example	example	NOUN
ejpam-5311	81	1	2	2	NUM
ejpam-5311	81	2	.	.	PUNCT
ejpam-5311	82	1	[	[	X
ejpam-5311	82	2	5	5	X
ejpam-5311	82	3	]	]	PUNCT
ejpam-5311	82	4	let	let	VERB
ejpam-5311	82	5	x	x	PUNCT
ejpam-5311	82	6	=	=	PUNCT
ejpam-5311	82	7	{	{	PUNCT
ejpam-5311	82	8	0	0	NUM
ejpam-5311	82	9	,	,	PUNCT
ejpam-5311	82	10	1	1	NUM
ejpam-5311	82	11	,	,	PUNCT
ejpam-5311	82	12	2	2	NUM
ejpam-5311	82	13	,	,	PUNCT
ejpam-5311	82	14	3	3	NUM
ejpam-5311	82	15	}	}	PUNCT
ejpam-5311	82	16	with	with	ADP
ejpam-5311	82	17	the	the	DET
ejpam-5311	82	18	following	follow	VERB
ejpam-5311	82	19	cayley	cayley	ADJ
ejpam-5311	82	20	table	table	NOUN
ejpam-5311	82	21	:	:	PUNCT
ejpam-5311	82	22	∗	∗	NOUN
ejpam-5311	82	23	0	0	NUM
ejpam-5311	83	1	1	1	NUM
ejpam-5311	83	2	2	2	NUM
ejpam-5311	83	3	3	3	NUM
ejpam-5311	83	4	0	0	NUM
ejpam-5311	83	5	0	0	NUM
ejpam-5311	83	6	1	1	NUM
ejpam-5311	83	7	2	2	NUM
ejpam-5311	83	8	3	3	NUM
ejpam-5311	83	9	1	1	NUM
ejpam-5311	83	10	0	0	NUM
ejpam-5311	83	11	0	0	NUM
ejpam-5311	83	12	1	1	NUM
ejpam-5311	83	13	2	2	NUM
ejpam-5311	83	14	2	2	NUM
ejpam-5311	83	15	0	0	NUM
ejpam-5311	83	16	0	0	NUM
ejpam-5311	83	17	0	0	NUM
ejpam-5311	83	18	1	1	NUM
ejpam-5311	83	19	3	3	NUM
ejpam-5311	83	20	0	0	NUM
ejpam-5311	83	21	0	0	NUM
ejpam-5311	83	22	0	0	NUM
ejpam-5311	83	23	0	0	PUNCT
ejpam-5311	84	1	then	then	ADV
ejpam-5311	84	2	x	x	PUNCT
ejpam-5311	84	3	is	be	AUX
ejpam-5311	84	4	a	a	DET
ejpam-5311	84	5	bcc	bcc	PROPN
ejpam-5311	84	6	-	-	PUNCT
ejpam-5311	84	7	algebra	algebra	PROPN
ejpam-5311	84	8	.	.	PUNCT
ejpam-5311	85	1	define	define	VERB
ejpam-5311	85	2	a	a	DET
ejpam-5311	85	3	fuzzy	fuzzy	ADJ
ejpam-5311	85	4	set	set	VERB
ejpam-5311	85	5	µ	µ	NOUN
ejpam-5311	85	6	as	as	SCONJ
ejpam-5311	85	7	follows	follow	VERB
ejpam-5311	85	8	:	:	PUNCT
ejpam-5311	85	9	µ	µ	X
ejpam-5311	85	10	:	:	PUNCT
ejpam-5311	85	11	x	x	SYM
ejpam-5311	85	12	→	→	SYM
ejpam-5311	86	1	[	[	X
ejpam-5311	86	2	0	0	NUM
ejpam-5311	86	3	,	,	PUNCT
ejpam-5311	86	4	1];x	1];x	NUM
ejpam-5311	86	5	7→	7→	NUM
ejpam-5311	86	6			NUM
ejpam-5311	86	7	1	1	NUM
ejpam-5311	86	8	if	if	SCONJ
ejpam-5311	86	9	x	x	X
ejpam-5311	86	10	=	=	NOUN
ejpam-5311	86	11	0	0	NUM
ejpam-5311	86	12	0	0	PUNCT
ejpam-5311	87	1	if	if	SCONJ
ejpam-5311	87	2	x	x	SYM
ejpam-5311	87	3	=	=	SYM
ejpam-5311	87	4	1	1	NUM
ejpam-5311	87	5	1	1	NUM
ejpam-5311	87	6	if	if	SCONJ
ejpam-5311	87	7	x	x	SYM
ejpam-5311	87	8	=	=	SYM
ejpam-5311	87	9	2	2	NUM
ejpam-5311	87	10	1	1	NUM
ejpam-5311	87	11	if	if	SCONJ
ejpam-5311	87	12	x	x	SYM
ejpam-5311	87	13	=	=	SYM
ejpam-5311	87	14	3	3	NUM
ejpam-5311	87	15	given	give	VERB
ejpam-5311	87	16	ε	ε	PROPN
ejpam-5311	87	17	=	=	SYM
ejpam-5311	87	18	0.9	0.9	NUM
ejpam-5311	87	19	,	,	PUNCT
ejpam-5311	87	20	the	the	DET
ejpam-5311	87	21	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	87	22	fuzzy	fuzzy	NOUN
ejpam-5311	87	23	set	set	VERB
ejpam-5311	87	24	lε	lε	PRON
ejpam-5311	87	25	µ	µ	PROPN
ejpam-5311	87	26	of	of	ADP
ejpam-5311	87	27	µ	µ	NOUN
ejpam-5311	87	28	in	in	ADP
ejpam-5311	87	29	x	x	AUX
ejpam-5311	87	30	is	be	AUX
ejpam-5311	87	31	given	give	VERB
ejpam-5311	87	32	as	as	SCONJ
ejpam-5311	87	33	follows	follow	VERB
ejpam-5311	87	34	:	:	PUNCT
ejpam-5311	87	35	lε	lε	ADP
ejpam-5311	87	36	µ	µ	NOUN
ejpam-5311	87	37	:	:	PUNCT
ejpam-5311	87	38	x	x	SYM
ejpam-5311	87	39	→	→	SYM
ejpam-5311	88	1	[	[	X
ejpam-5311	88	2	0	0	NUM
ejpam-5311	88	3	,	,	PUNCT
ejpam-5311	88	4	1];x	1];x	NUM
ejpam-5311	88	5	7→	7→	NUM
ejpam-5311	88	6			NUM
ejpam-5311	88	7	0.9	0.9	NUM
ejpam-5311	88	8	if	if	SCONJ
ejpam-5311	88	9	x	x	PROPN
ejpam-5311	89	1	=	=	SYM
ejpam-5311	89	2	0	0	NUM
ejpam-5311	89	3	0	0	PUNCT
ejpam-5311	90	1	if	if	SCONJ
ejpam-5311	90	2	x	x	SYM
ejpam-5311	90	3	=	=	NOUN
ejpam-5311	90	4	1	1	NUM
ejpam-5311	90	5	0.9	0.9	NUM
ejpam-5311	90	6	if	if	SCONJ
ejpam-5311	90	7	x	x	NOUN
ejpam-5311	90	8	=	=	SYM
ejpam-5311	90	9	2	2	NUM
ejpam-5311	90	10	0.9	0.9	NUM
ejpam-5311	90	11	if	if	SCONJ
ejpam-5311	90	12	x	x	PROPN
ejpam-5311	90	13	=	=	SYM
ejpam-5311	90	14	3	3	NUM
ejpam-5311	90	15	then	then	ADV
ejpam-5311	90	16	lε	lε	X
ejpam-5311	90	17	µ(0	µ(0	NOUN
ejpam-5311	90	18	)	)	PUNCT
ejpam-5311	90	19	≥=	≥=	PROPN
ejpam-5311	90	20	lε	lε	ADP
ejpam-5311	90	21	µ(x	µ(x	NOUN
ejpam-5311	90	22	)	)	PUNCT
ejpam-5311	90	23	for	for	ADP
ejpam-5311	90	24	all	all	DET
ejpam-5311	90	25	x	x	SYM
ejpam-5311	90	26	∈	∈	PROPN
ejpam-5311	90	27	x	x	X
ejpam-5311	90	28	but	but	CCONJ
ejpam-5311	90	29	µ	µ	X
ejpam-5311	90	30	is	be	AUX
ejpam-5311	90	31	not	not	PART
ejpam-5311	90	32	a	a	DET
ejpam-5311	90	33	fuzzy	fuzzy	ADJ
ejpam-5311	90	34	bcc	bcc	NOUN
ejpam-5311	90	35	-	-	PUNCT
ejpam-5311	90	36	subalgebra	subalgebra	NOUN
ejpam-5311	90	37	of	of	ADP
ejpam-5311	90	38	x	x	PRON
ejpam-5311	90	39	because	because	SCONJ
ejpam-5311	90	40	µ(2	µ(2	PROPN
ejpam-5311	90	41	∗	∗	NOUN
ejpam-5311	90	42	3	3	NUM
ejpam-5311	90	43	)	)	PUNCT
ejpam-5311	90	44	=	=	PUNCT
ejpam-5311	90	45	µ(1	µ(1	PROPN
ejpam-5311	90	46	)	)	PUNCT
ejpam-5311	90	47	=	=	SYM
ejpam-5311	91	1	0	0	NUM
ejpam-5311	91	2	≱	≱	PROPN
ejpam-5311	91	3	1	1	NUM
ejpam-5311	91	4	=	=	SYM
ejpam-5311	91	5	min{µ(2	min{µ(2	NOUN
ejpam-5311	91	6	)	)	PUNCT
ejpam-5311	91	7	,	,	PUNCT
ejpam-5311	91	8	µ(3	µ(3	PROPN
ejpam-5311	91	9	)	)	PUNCT
ejpam-5311	91	10	}	}	PUNCT
ejpam-5311	91	11	.	.	PUNCT
ejpam-5311	92	1	a.	a.	PROPN
ejpam-5311	92	2	iampan	iampan	PROPN
ejpam-5311	92	3	,	,	PUNCT
ejpam-5311	92	4	r.	r.	PROPN
ejpam-5311	92	5	subasini	subasini	PROPN
ejpam-5311	92	6	,	,	PUNCT
ejpam-5311	92	7	n.	n.	PROPN
ejpam-5311	92	8	rajesh	rajesh	PROPN
ejpam-5311	92	9	/	/	SYM
ejpam-5311	92	10	eur	eur	PROPN
ejpam-5311	92	11	.	.	PUNCT
ejpam-5311	93	1	j.	j.	PROPN
ejpam-5311	93	2	pure	pure	PROPN
ejpam-5311	93	3	appl	appl	PROPN
ejpam-5311	93	4	.	.	PROPN
ejpam-5311	93	5	math	math	PROPN
ejpam-5311	93	6	,	,	PUNCT
ejpam-5311	93	7	17	17	NUM
ejpam-5311	93	8	(	(	PUNCT
ejpam-5311	93	9	3	3	NUM
ejpam-5311	93	10	)	)	PUNCT
ejpam-5311	93	11	(	(	PUNCT
ejpam-5311	93	12	2024	2024	NUM
ejpam-5311	93	13	)	)	PUNCT
ejpam-5311	93	14	,	,	PUNCT
ejpam-5311	93	15	2235	2235	NUM
ejpam-5311	93	16	-	-	SYM
ejpam-5311	93	17	2245	2245	NUM
ejpam-5311	93	18	2240	2240	NUM
ejpam-5311	93	19	proposition	proposition	NOUN
ejpam-5311	93	20	3	3	X
ejpam-5311	93	21	.	.	PUNCT
ejpam-5311	94	1	if	if	SCONJ
ejpam-5311	94	2	µ	µ	NOUN
ejpam-5311	94	3	is	be	AUX
ejpam-5311	94	4	a	a	DET
ejpam-5311	94	5	fuzzy	fuzzy	ADJ
ejpam-5311	94	6	bcc	bcc	NOUN
ejpam-5311	94	7	-	-	PUNCT
ejpam-5311	94	8	subalgebra	subalgebra	NOUN
ejpam-5311	94	9	of	of	ADP
ejpam-5311	94	10	x	x	PRON
ejpam-5311	94	11	,	,	PUNCT
ejpam-5311	94	12	then	then	ADV
ejpam-5311	94	13	its	its	PRON
ejpam-5311	94	14	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	94	15	fuzzy	fuzzy	NOUN
ejpam-5311	94	16	set	set	VERB
ejpam-5311	94	17	lε	lε	PRON
ejpam-5311	94	18	µ	µ	PRON
ejpam-5311	94	19	satisfies	satisfie	NOUN
ejpam-5311	94	20	the	the	DET
ejpam-5311	94	21	following	follow	VERB
ejpam-5311	94	22	property	property	NOUN
ejpam-5311	94	23	:	:	PUNCT
ejpam-5311	94	24	(	(	PUNCT
ejpam-5311	94	25	∀x	∀x	X
ejpam-5311	94	26	,	,	PUNCT
ejpam-5311	94	27	y	y	PROPN
ejpam-5311	94	28	∈	∈	PROPN
ejpam-5311	94	29	x)(lε	x)(lε	PROPN
ejpam-5311	94	30	µ(y	µ(y	PROPN
ejpam-5311	94	31	)	)	PUNCT
ejpam-5311	95	1	=	=	PRON
ejpam-5311	95	2	lε	lε	X
ejpam-5311	95	3	µ(0	µ(0	NOUN
ejpam-5311	95	4	)	)	PUNCT
ejpam-5311	95	5	⇔	⇔	NOUN
ejpam-5311	95	6	lε	lε	ADP
ejpam-5311	95	7	µ(x	µ(x	PROPN
ejpam-5311	95	8	∗	∗	NOUN
ejpam-5311	95	9	y	y	NOUN
ejpam-5311	95	10	)	)	PUNCT
ejpam-5311	95	11	≥	≥	NOUN
ejpam-5311	95	12	lε	lε	X
ejpam-5311	95	13	µ(x	µ(x	NOUN
ejpam-5311	95	14	)	)	PUNCT
ejpam-5311	95	15	)	)	PUNCT
ejpam-5311	95	16	(	(	PUNCT
ejpam-5311	95	17	3.4	3.4	NUM
ejpam-5311	95	18	)	)	PUNCT
ejpam-5311	95	19	proof	proof	NOUN
ejpam-5311	95	20	.	.	PUNCT
ejpam-5311	96	1	assume	assume	VERB
ejpam-5311	96	2	that	that	SCONJ
ejpam-5311	96	3	lε	lε	ADP
ejpam-5311	96	4	µ(y	µ(y	PROPN
ejpam-5311	96	5	)	)	PUNCT
ejpam-5311	96	6	=	=	PRON
ejpam-5311	96	7	lε	lε	X
ejpam-5311	96	8	µ(0	µ(0	NOUN
ejpam-5311	96	9	)	)	PUNCT
ejpam-5311	96	10	for	for	ADP
ejpam-5311	96	11	all	all	DET
ejpam-5311	96	12	y	y	PROPN
ejpam-5311	96	13	∈	∈	PROPN
ejpam-5311	96	14	x.	x.	NOUN
ejpam-5311	96	15	then	then	ADV
ejpam-5311	96	16	lε	lε	ADP
ejpam-5311	96	17	µ(x∗y	µ(x∗y	NOUN
ejpam-5311	96	18	)	)	PUNCT
ejpam-5311	96	19	≥	≥	PROPN
ejpam-5311	96	20	min{lε	min{lε	NUM
ejpam-5311	96	21	µ(x	µ(x	PROPN
ejpam-5311	96	22	)	)	PUNCT
ejpam-5311	96	23	,	,	PUNCT
ejpam-5311	96	24	lε	lε	X
ejpam-5311	96	25	µ(y	µ(y	PROPN
ejpam-5311	96	26	)	)	PUNCT
ejpam-5311	96	27	}	}	PUNCT
ejpam-5311	96	28	=	=	NOUN
ejpam-5311	96	29	min{lε	min{lε	NUM
ejpam-5311	96	30	µ(x	µ(x	PROPN
ejpam-5311	96	31	)	)	PUNCT
ejpam-5311	96	32	,	,	PUNCT
ejpam-5311	96	33	lε	lε	X
ejpam-5311	96	34	µ(0	µ(0	NOUN
ejpam-5311	96	35	)	)	PUNCT
ejpam-5311	96	36	}	}	PUNCT
ejpam-5311	96	37	=	=	SYM
ejpam-5311	96	38	lε	lε	X
ejpam-5311	96	39	µ(x	µ(x	NOUN
ejpam-5311	96	40	)	)	PUNCT
ejpam-5311	96	41	for	for	ADP
ejpam-5311	96	42	all	all	DET
ejpam-5311	96	43	x	x	NOUN
ejpam-5311	96	44	,	,	PUNCT
ejpam-5311	96	45	y	y	PROPN
ejpam-5311	96	46	∈	∈	PROPN
ejpam-5311	96	47	x	x	PUNCT
ejpam-5311	96	48	by	by	ADP
ejpam-5311	96	49	the	the	DET
ejpam-5311	96	50	combination	combination	NOUN
ejpam-5311	96	51	of	of	ADP
ejpam-5311	96	52	theorem	theorem	ADJ
ejpam-5311	96	53	1	1	NUM
ejpam-5311	96	54	and	and	CCONJ
ejpam-5311	96	55	proposition	proposition	NOUN
ejpam-5311	96	56	2	2	NUM
ejpam-5311	96	57	.	.	PUNCT
ejpam-5311	96	58	conversely	conversely	ADV
ejpam-5311	96	59	,	,	PUNCT
ejpam-5311	96	60	suppose	suppose	VERB
ejpam-5311	96	61	that	that	SCONJ
ejpam-5311	96	62	lε	lε	ADP
ejpam-5311	96	63	µ(x	µ(x	PROPN
ejpam-5311	96	64	∗	∗	NOUN
ejpam-5311	96	65	y	y	NOUN
ejpam-5311	96	66	)	)	PUNCT
ejpam-5311	96	67	≥	≥	NOUN
ejpam-5311	96	68	lε	lε	X
ejpam-5311	96	69	µ(x	µ(x	NOUN
ejpam-5311	96	70	)	)	PUNCT
ejpam-5311	96	71	for	for	ADP
ejpam-5311	96	72	all	all	DET
ejpam-5311	96	73	x	x	NOUN
ejpam-5311	96	74	,	,	PUNCT
ejpam-5311	96	75	y	y	PROPN
ejpam-5311	96	76	∈	∈	PROPN
ejpam-5311	96	77	x.	x.	NOUN
ejpam-5311	96	78	using	use	VERB
ejpam-5311	96	79	(	(	PUNCT
ejpam-5311	96	80	2.2	2.2	NUM
ejpam-5311	96	81	)	)	PUNCT
ejpam-5311	96	82	induces	induce	VERB
ejpam-5311	96	83	lε	lε	ADP
ejpam-5311	96	84	µ(y	µ(y	PROPN
ejpam-5311	96	85	)	)	PUNCT
ejpam-5311	96	86	=	=	PRON
ejpam-5311	97	1	lε	lε	PART
ejpam-5311	97	2	µ(0	µ(0	PROPN
ejpam-5311	97	3	∗	∗	PROPN
ejpam-5311	97	4	y	y	PROPN
ejpam-5311	97	5	)	)	PUNCT
ejpam-5311	97	6	≥	≥	NOUN
ejpam-5311	97	7	lε	lε	X
ejpam-5311	97	8	µ(0	µ(0	NUM
ejpam-5311	97	9	)	)	PUNCT
ejpam-5311	97	10	.	.	PUNCT
ejpam-5311	98	1	the	the	DET
ejpam-5311	98	2	combination	combination	NOUN
ejpam-5311	98	3	of	of	ADP
ejpam-5311	98	4	this	this	PRON
ejpam-5311	98	5	and	and	CCONJ
ejpam-5311	98	6	proposition	proposition	NOUN
ejpam-5311	98	7	2	2	NUM
ejpam-5311	98	8	leads	lead	VERB
ejpam-5311	98	9	to	to	ADP
ejpam-5311	98	10	lε	lε	PROPN
ejpam-5311	98	11	µ(y	µ(y	PROPN
ejpam-5311	98	12	)	)	PUNCT
ejpam-5311	98	13	=	=	PRON
ejpam-5311	98	14	lε	lε	X
ejpam-5311	98	15	µ(0	µ(0	NOUN
ejpam-5311	98	16	)	)	PUNCT
ejpam-5311	98	17	for	for	ADP
ejpam-5311	98	18	all	all	DET
ejpam-5311	98	19	y	y	PROPN
ejpam-5311	98	20	∈	∈	PROPN
ejpam-5311	98	21	x.	x.	NOUN
ejpam-5311	98	22	proposition	proposition	NOUN
ejpam-5311	98	23	4	4	NUM
ejpam-5311	98	24	.	.	PUNCT
ejpam-5311	99	1	if	if	SCONJ
ejpam-5311	99	2	µ	µ	NOUN
ejpam-5311	99	3	is	be	AUX
ejpam-5311	99	4	a	a	DET
ejpam-5311	99	5	fuzzy	fuzzy	ADJ
ejpam-5311	99	6	bcc	bcc	NOUN
ejpam-5311	99	7	-	-	PUNCT
ejpam-5311	99	8	subalgebra	subalgebra	NOUN
ejpam-5311	99	9	of	of	ADP
ejpam-5311	99	10	x	x	PRON
ejpam-5311	99	11	,	,	PUNCT
ejpam-5311	99	12	then	then	ADV
ejpam-5311	99	13	its	its	PRON
ejpam-5311	99	14	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	99	15	fuzzy	fuzzy	NOUN
ejpam-5311	99	16	set	set	VERB
ejpam-5311	99	17	lε	lε	PRON
ejpam-5311	99	18	µ	µ	PRON
ejpam-5311	99	19	satisfies	satisfie	NOUN
ejpam-5311	99	20	the	the	DET
ejpam-5311	99	21	following	follow	VERB
ejpam-5311	99	22	property	property	NOUN
ejpam-5311	99	23	:	:	PUNCT
ejpam-5311	99	24	(	(	PUNCT
ejpam-5311	99	25	∀x	∀x	X
ejpam-5311	99	26	,	,	PUNCT
ejpam-5311	99	27	y	y	PROPN
ejpam-5311	99	28	∈	∈	PROPN
ejpam-5311	99	29	x,∀ta	x,∀ta	PROPN
ejpam-5311	99	30	,	,	PUNCT
ejpam-5311	99	31	tb	tb	ADP
ejpam-5311	99	32	∈	∈	PROPN
ejpam-5311	99	33	(	(	PUNCT
ejpam-5311	99	34	0	0	NUM
ejpam-5311	99	35	,	,	PUNCT
ejpam-5311	99	36	1	1	NUM
ejpam-5311	99	37	]	]	NUM
ejpam-5311	99	38	)	)	PUNCT
ejpam-5311	100	1	(	(	PUNCT
ejpam-5311	100	2	[	[	X
ejpam-5311	100	3	x	x	X
ejpam-5311	100	4	/	/	SYM
ejpam-5311	100	5	ta	ta	X
ejpam-5311	100	6	]	]	X
ejpam-5311	100	7	∈	∈	PROPN
ejpam-5311	100	8	lε	lε	ADP
ejpam-5311	100	9	µ	µ	NOUN
ejpam-5311	100	10	,	,	PUNCT
ejpam-5311	100	11	[	[	X
ejpam-5311	100	12	y	y	X
ejpam-5311	100	13	/	/	SYM
ejpam-5311	100	14	tb	tb	NOUN
ejpam-5311	100	15	]	]	PUNCT
ejpam-5311	100	16	∈	∈	PROPN
ejpam-5311	100	17	lε	lε	X
ejpam-5311	100	18	µ	µ	X
ejpam-5311	100	19	⇒	⇒	NOUN
ejpam-5311	100	20	[	[	X
ejpam-5311	100	21	(	(	PUNCT
ejpam-5311	100	22	x	x	SYM
ejpam-5311	100	23	∗	∗	NOUN
ejpam-5311	100	24	(	(	PUNCT
ejpam-5311	100	25	0	0	NUM
ejpam-5311	100	26	∗	∗	NOUN
ejpam-5311	100	27	y))/min{ta	y))/min{ta	NOUN
ejpam-5311	100	28	,	,	PUNCT
ejpam-5311	100	29	tb	tb	NOUN
ejpam-5311	100	30	}	}	PUNCT
ejpam-5311	100	31	]	]	PUNCT
ejpam-5311	100	32	∈	∈	PROPN
ejpam-5311	100	33	lε	lε	ADP
ejpam-5311	100	34	µ	µ	NOUN
ejpam-5311	100	35	)	)	PUNCT
ejpam-5311	100	36	(	(	PUNCT
ejpam-5311	100	37	3.5	3.5	NUM
ejpam-5311	100	38	)	)	PUNCT
ejpam-5311	100	39	proof	proof	NOUN
ejpam-5311	100	40	.	.	PUNCT
ejpam-5311	101	1	let	let	VERB
ejpam-5311	101	2	x	x	PRON
ejpam-5311	101	3	,	,	PUNCT
ejpam-5311	101	4	y	y	PROPN
ejpam-5311	101	5	∈	∈	PROPN
ejpam-5311	101	6	x	x	X
ejpam-5311	101	7	and	and	CCONJ
ejpam-5311	101	8	ta	ta	PROPN
ejpam-5311	101	9	,	,	PUNCT
ejpam-5311	101	10	tb	tb	ADP
ejpam-5311	101	11	∈	∈	PROPN
ejpam-5311	101	12	(	(	PUNCT
ejpam-5311	101	13	0	0	NUM
ejpam-5311	101	14	,	,	PUNCT
ejpam-5311	101	15	1	1	NUM
ejpam-5311	101	16	]	]	PUNCT
ejpam-5311	101	17	be	be	AUX
ejpam-5311	101	18	such	such	ADJ
ejpam-5311	101	19	that	that	SCONJ
ejpam-5311	101	20	[	[	X
ejpam-5311	101	21	x	x	X
ejpam-5311	101	22	/	/	SYM
ejpam-5311	101	23	ta	ta	X
ejpam-5311	101	24	]	]	X
ejpam-5311	101	25	∈	∈	PROPN
ejpam-5311	101	26	lε	lε	ADP
ejpam-5311	101	27	µ	µ	NOUN
ejpam-5311	101	28	and	and	CCONJ
ejpam-5311	101	29	[	[	X
ejpam-5311	101	30	y	y	X
ejpam-5311	101	31	/	/	SYM
ejpam-5311	101	32	tb	tb	NOUN
ejpam-5311	101	33	]	]	PUNCT
ejpam-5311	101	34	∈	∈	PROPN
ejpam-5311	101	35	lε	lε	X
ejpam-5311	101	36	µ.	µ.	NOUN
ejpam-5311	101	37	then	then	ADV
ejpam-5311	101	38	lε	lε	ADP
ejpam-5311	101	39	µ(x	µ(x	NOUN
ejpam-5311	101	40	)	)	PUNCT
ejpam-5311	101	41	≥	≥	NOUN
ejpam-5311	101	42	ta	ta	X
ejpam-5311	101	43	and	and	CCONJ
ejpam-5311	101	44	lε	lε	INTJ
ejpam-5311	101	45	µ(y	µ(y	PROPN
ejpam-5311	101	46	)	)	PUNCT
ejpam-5311	101	47	≥	≥	NOUN
ejpam-5311	101	48	tb	tb	NOUN
ejpam-5311	101	49	.	.	PUNCT
ejpam-5311	102	1	thus	thus	ADV
ejpam-5311	102	2	lε	lε	ADP
ejpam-5311	102	3	µ(x	µ(x	ADJ
ejpam-5311	102	4	∗	∗	NOUN
ejpam-5311	102	5	(	(	PUNCT
ejpam-5311	102	6	0	0	NUM
ejpam-5311	102	7	∗	∗	NOUN
ejpam-5311	102	8	y	y	PROPN
ejpam-5311	102	9	)	)	PUNCT
ejpam-5311	102	10	)	)	PUNCT
ejpam-5311	103	1	=	=	SYM
ejpam-5311	103	2	max{0	max{0	PROPN
ejpam-5311	103	3	,	,	PUNCT
ejpam-5311	103	4	µ(x	µ(x	X
ejpam-5311	103	5	∗	∗	NOUN
ejpam-5311	103	6	(	(	PUNCT
ejpam-5311	103	7	0	0	NUM
ejpam-5311	103	8	∗	∗	NOUN
ejpam-5311	103	9	y	y	PROPN
ejpam-5311	103	10	)	)	PUNCT
ejpam-5311	103	11	)	)	PUNCT
ejpam-5311	104	1	+	+	CCONJ
ejpam-5311	104	2	ε−	ε−	PROPN
ejpam-5311	104	3	1	1	NUM
ejpam-5311	104	4	}	}	PUNCT
ejpam-5311	104	5	≥	≥	NOUN
ejpam-5311	104	6	max{0,min{µ(x	max{0,min{µ(x	NUM
ejpam-5311	104	7	)	)	PUNCT
ejpam-5311	104	8	,	,	PUNCT
ejpam-5311	104	9	µ(0	µ(0	PROPN
ejpam-5311	104	10	∗	∗	PROPN
ejpam-5311	104	11	y	y	NOUN
ejpam-5311	104	12	)	)	PUNCT
ejpam-5311	104	13	}	}	PUNCT
ejpam-5311	105	1	+	+	CCONJ
ejpam-5311	105	2	ε−	ε−	PROPN
ejpam-5311	105	3	1	1	NUM
ejpam-5311	105	4	}	}	PUNCT
ejpam-5311	105	5	≥	≥	NOUN
ejpam-5311	105	6	max{0,min{µ(x),min{µ(0	max{0,min{µ(x),min{µ(0	NOUN
ejpam-5311	105	7	)	)	PUNCT
ejpam-5311	105	8	,	,	PUNCT
ejpam-5311	105	9	µ(y	µ(y	PROPN
ejpam-5311	105	10	)	)	PUNCT
ejpam-5311	105	11	}	}	PUNCT
ejpam-5311	105	12	}	}	PUNCT
ejpam-5311	106	1	+	+	CCONJ
ejpam-5311	106	2	ε−	ε−	PROPN
ejpam-5311	106	3	1	1	NUM
ejpam-5311	106	4	}	}	PUNCT
ejpam-5311	106	5	=	=	SYM
ejpam-5311	106	6	max{0,min{µ(x	max{0,min{µ(x	NOUN
ejpam-5311	106	7	)	)	PUNCT
ejpam-5311	106	8	,	,	PUNCT
ejpam-5311	106	9	µ(y	µ(y	PROPN
ejpam-5311	106	10	)	)	PUNCT
ejpam-5311	106	11	}	}	PUNCT
ejpam-5311	106	12	+	+	CCONJ
ejpam-5311	106	13	ε−	ε−	PROPN
ejpam-5311	106	14	1	1	NUM
ejpam-5311	106	15	}	}	PUNCT
ejpam-5311	106	16	=	=	PUNCT
ejpam-5311	106	17	max{0,min{µ(x	max{0,min{µ(x	NOUN
ejpam-5311	106	18	)	)	PUNCT
ejpam-5311	107	1	+	+	CCONJ
ejpam-5311	107	2	ε−	ε−	PROPN
ejpam-5311	107	3	1	1	NUM
ejpam-5311	107	4	,	,	PUNCT
ejpam-5311	107	5	µ(y	µ(y	PROPN
ejpam-5311	107	6	)	)	PUNCT
ejpam-5311	107	7	+	+	CCONJ
ejpam-5311	108	1	ε−	ε−	PROPN
ejpam-5311	108	2	1	1	NUM
ejpam-5311	108	3	}	}	PUNCT
ejpam-5311	108	4	}	}	PUNCT
ejpam-5311	108	5	=	=	SYM
ejpam-5311	108	6	min{max{0	min{max{0	NOUN
ejpam-5311	108	7	,	,	PUNCT
ejpam-5311	108	8	µ(x	µ(x	X
ejpam-5311	108	9	)	)	PUNCT
ejpam-5311	108	10	+	+	CCONJ
ejpam-5311	108	11	ε−	ε−	PROPN
ejpam-5311	108	12	1},max{0	1},max{0	NUM
ejpam-5311	108	13	,	,	PUNCT
ejpam-5311	108	14	µ(y	µ(y	PROPN
ejpam-5311	108	15	)	)	PUNCT
ejpam-5311	108	16	+	+	CCONJ
ejpam-5311	108	17	ε−	ε−	PROPN
ejpam-5311	108	18	1	1	NUM
ejpam-5311	108	19	}	}	PUNCT
ejpam-5311	108	20	}	}	PUNCT
ejpam-5311	108	21	=	=	NOUN
ejpam-5311	108	22	min{lε	min{lε	NUM
ejpam-5311	108	23	µ(x	µ(x	PROPN
ejpam-5311	108	24	)	)	PUNCT
ejpam-5311	108	25	,	,	PUNCT
ejpam-5311	108	26	lε	lε	X
ejpam-5311	108	27	µ(y	µ(y	PROPN
ejpam-5311	108	28	)	)	PUNCT
ejpam-5311	108	29	}	}	PUNCT
ejpam-5311	108	30	≥	≥	NOUN
ejpam-5311	108	31	min{ta	min{ta	X
ejpam-5311	108	32	,	,	PUNCT
ejpam-5311	108	33	tb	tb	NOUN
ejpam-5311	108	34	}	}	PUNCT
ejpam-5311	108	35	.	.	PUNCT
ejpam-5311	109	1	hence	hence	ADV
ejpam-5311	109	2	,	,	PUNCT
ejpam-5311	109	3	[	[	X
ejpam-5311	109	4	(	(	PUNCT
ejpam-5311	109	5	x	x	SYM
ejpam-5311	109	6	∗	∗	NOUN
ejpam-5311	109	7	(	(	PUNCT
ejpam-5311	109	8	0	0	NUM
ejpam-5311	109	9	∗	∗	NOUN
ejpam-5311	109	10	y))/min{ta	y))/min{ta	NOUN
ejpam-5311	109	11	,	,	PUNCT
ejpam-5311	109	12	tb	tb	NOUN
ejpam-5311	109	13	}	}	PUNCT
ejpam-5311	109	14	]	]	PUNCT
ejpam-5311	109	15	∈	∈	PROPN
ejpam-5311	109	16	lε	lε	VERB
ejpam-5311	109	17	µ.	µ.	NOUN
ejpam-5311	109	18	we	we	PRON
ejpam-5311	109	19	provide	provide	VERB
ejpam-5311	109	20	conditions	condition	NOUN
ejpam-5311	109	21	for	for	SCONJ
ejpam-5311	109	22	an	an	DET
ejpam-5311	109	23	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	109	24	fuzzy	fuzzy	ADJ
ejpam-5311	109	25	set	set	VERB
ejpam-5311	109	26	to	to	PART
ejpam-5311	109	27	be	be	AUX
ejpam-5311	109	28	an	an	DET
ejpam-5311	109	29	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	109	30	fuzzy	fuzzy	ADJ
ejpam-5311	109	31	bcc	bcc	PROPN
ejpam-5311	109	32	-	-	PUNCT
ejpam-5311	109	33	subalgebra	subalgebra	PROPN
ejpam-5311	109	34	.	.	PUNCT
ejpam-5311	110	1	theorem	theorem	NOUN
ejpam-5311	110	2	3	3	X
ejpam-5311	110	3	.	.	PUNCT
ejpam-5311	111	1	let	let	VERB
ejpam-5311	111	2	µ	µ	X
ejpam-5311	111	3	be	be	AUX
ejpam-5311	111	4	a	a	DET
ejpam-5311	111	5	fuzzy	fuzzy	ADJ
ejpam-5311	111	6	set	set	NOUN
ejpam-5311	111	7	in	in	ADP
ejpam-5311	111	8	x.	x.	NOUN
ejpam-5311	111	9	if	if	SCONJ
ejpam-5311	111	10	its	its	PRON
ejpam-5311	111	11	εlukasiewicz	εlukasiewicz	NOUN
ejpam-5311	111	12	fuzzy	fuzzy	NOUN
ejpam-5311	111	13	set	set	VERB
ejpam-5311	111	14	lε	lε	PRON
ejpam-5311	111	15	µ	µ	PRON
ejpam-5311	111	16	satisfies	satisfie	NOUN
ejpam-5311	111	17	the	the	DET
ejpam-5311	111	18	following	follow	VERB
ejpam-5311	111	19	property	property	NOUN
ejpam-5311	111	20	:	:	PUNCT
ejpam-5311	112	1	[	[	X
ejpam-5311	112	2	y	y	X
ejpam-5311	112	3	/	/	SYM
ejpam-5311	112	4	tb	tb	NOUN
ejpam-5311	112	5	]	]	PUNCT
ejpam-5311	112	6	∈	∈	PROPN
ejpam-5311	112	7	lε	lε	ADP
ejpam-5311	112	8	µ	µ	NOUN
ejpam-5311	112	9	,	,	PUNCT
ejpam-5311	112	10	[	[	X
ejpam-5311	112	11	z	z	X
ejpam-5311	112	12	/	/	SYM
ejpam-5311	112	13	tc	tc	NOUN
ejpam-5311	112	14	]	]	X
ejpam-5311	112	15	∈	∈	PROPN
ejpam-5311	112	16	lε	lε	X
ejpam-5311	112	17	µ	µ	X
ejpam-5311	112	18	⇒	⇒	NOUN
ejpam-5311	112	19	[	[	X
ejpam-5311	112	20	(	(	PUNCT
ejpam-5311	112	21	x	x	SYM
ejpam-5311	112	22	∗	∗	NOUN
ejpam-5311	112	23	y)/min{tb	y)/min{tb	PROPN
ejpam-5311	112	24	,	,	PUNCT
ejpam-5311	112	25	tc	tc	NOUN
ejpam-5311	112	26	}	}	PUNCT
ejpam-5311	112	27	]	]	PUNCT
ejpam-5311	112	28	∈	∈	PROPN
ejpam-5311	112	29	lε	lε	ADP
ejpam-5311	112	30	µ	µ	X
ejpam-5311	112	31	(	(	PUNCT
ejpam-5311	112	32	3.6	3.6	NUM
ejpam-5311	112	33	)	)	PUNCT
ejpam-5311	112	34	for	for	ADP
ejpam-5311	112	35	all	all	DET
ejpam-5311	112	36	tb	tb	NOUN
ejpam-5311	112	37	,	,	PUNCT
ejpam-5311	112	38	tc	tc	NOUN
ejpam-5311	112	39	∈	∈	PROPN
ejpam-5311	112	40	(	(	PUNCT
ejpam-5311	112	41	0	0	NUM
ejpam-5311	112	42	,	,	PUNCT
ejpam-5311	112	43	1	1	NUM
ejpam-5311	112	44	]	]	PUNCT
ejpam-5311	112	45	and	and	CCONJ
ejpam-5311	112	46	x	x	NOUN
ejpam-5311	112	47	,	,	PUNCT
ejpam-5311	112	48	y	y	PROPN
ejpam-5311	112	49	,	,	PUNCT
ejpam-5311	112	50	z	z	NOUN
ejpam-5311	112	51	∈	∈	PROPN
ejpam-5311	112	52	x	x	PUNCT
ejpam-5311	112	53	with	with	ADP
ejpam-5311	112	54	z	z	NOUN
ejpam-5311	112	55	≤	≤	NUM
ejpam-5311	112	56	x	x	PUNCT
ejpam-5311	112	57	,	,	PUNCT
ejpam-5311	112	58	then	then	ADV
ejpam-5311	112	59	lε	lε	PROPN
ejpam-5311	112	60	µ	µ	PROPN
ejpam-5311	112	61	is	be	AUX
ejpam-5311	112	62	an	an	DET
ejpam-5311	112	63	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	112	64	fuzzy	fuzzy	ADJ
ejpam-5311	112	65	bccsubalgebra	bccsubalgebra	NOUN
ejpam-5311	112	66	of	of	ADP
ejpam-5311	112	67	x.	x.	NOUN
ejpam-5311	112	68	proof	proof	PROPN
ejpam-5311	112	69	.	.	PUNCT
ejpam-5311	113	1	let	let	VERB
ejpam-5311	113	2	x	x	PRON
ejpam-5311	113	3	,	,	PUNCT
ejpam-5311	113	4	y	y	PROPN
ejpam-5311	113	5	∈	∈	PROPN
ejpam-5311	113	6	x	x	X
ejpam-5311	113	7	and	and	CCONJ
ejpam-5311	113	8	ta	ta	PROPN
ejpam-5311	113	9	,	,	PUNCT
ejpam-5311	113	10	tb	tb	ADP
ejpam-5311	113	11	∈	∈	PROPN
ejpam-5311	113	12	(	(	PUNCT
ejpam-5311	113	13	0	0	NUM
ejpam-5311	113	14	,	,	PUNCT
ejpam-5311	113	15	1	1	NUM
ejpam-5311	113	16	]	]	PUNCT
ejpam-5311	113	17	be	be	AUX
ejpam-5311	113	18	such	such	ADJ
ejpam-5311	113	19	that	that	SCONJ
ejpam-5311	113	20	[	[	X
ejpam-5311	113	21	x	x	X
ejpam-5311	113	22	/	/	SYM
ejpam-5311	113	23	ta	ta	X
ejpam-5311	113	24	]	]	X
ejpam-5311	113	25	∈	∈	PROPN
ejpam-5311	113	26	lε	lε	ADP
ejpam-5311	113	27	µ	µ	NOUN
ejpam-5311	113	28	and	and	CCONJ
ejpam-5311	113	29	[	[	X
ejpam-5311	113	30	y	y	X
ejpam-5311	113	31	/	/	SYM
ejpam-5311	113	32	tb	tb	NOUN
ejpam-5311	113	33	]	]	PUNCT
ejpam-5311	113	34	∈	∈	NOUN
ejpam-5311	113	35	lε	lε	VERB
ejpam-5311	113	36	µ.	µ.	NOUN
ejpam-5311	113	37	since	since	SCONJ
ejpam-5311	113	38	x	x	PROPN
ejpam-5311	113	39	≤	≤	X
ejpam-5311	113	40	x	x	PUNCT
ejpam-5311	113	41	for	for	ADP
ejpam-5311	113	42	all	all	DET
ejpam-5311	113	43	x	x	SYM
ejpam-5311	113	44	∈	∈	NOUN
ejpam-5311	113	45	x	x	X
ejpam-5311	113	46	,	,	PUNCT
ejpam-5311	113	47	it	it	PRON
ejpam-5311	113	48	follows	follow	VERB
ejpam-5311	113	49	from	from	ADP
ejpam-5311	113	50	(	(	PUNCT
ejpam-5311	113	51	3.6	3.6	NUM
ejpam-5311	113	52	)	)	PUNCT
ejpam-5311	113	53	that	that	SCONJ
ejpam-5311	113	54	[	[	X
ejpam-5311	113	55	(	(	PUNCT
ejpam-5311	113	56	x	x	X
ejpam-5311	113	57	∗	∗	NOUN
ejpam-5311	113	58	y)/min{ta	y)/min{ta	NOUN
ejpam-5311	113	59	,	,	PUNCT
ejpam-5311	113	60	tb	tb	NOUN
ejpam-5311	113	61	}	}	PUNCT
ejpam-5311	113	62	]	]	PUNCT
ejpam-5311	113	63	∈	∈	PROPN
ejpam-5311	113	64	lε	lε	VERB
ejpam-5311	113	65	µ.	µ.	NOUN
ejpam-5311	113	66	hence	hence	ADV
ejpam-5311	113	67	,	,	PUNCT
ejpam-5311	113	68	lε	lε	PROPN
ejpam-5311	113	69	µ	µ	PROPN
ejpam-5311	113	70	is	be	AUX
ejpam-5311	113	71	an	an	DET
ejpam-5311	113	72	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	113	73	fuzzy	fuzzy	ADJ
ejpam-5311	113	74	bcc	bcc	PROPN
ejpam-5311	113	75	-	-	PUNCT
ejpam-5311	113	76	subalgebra	subalgebra	PROPN
ejpam-5311	113	77	of	of	ADP
ejpam-5311	113	78	x.	x.	PROPN
ejpam-5311	113	79	a.	a.	PROPN
ejpam-5311	113	80	iampan	iampan	PROPN
ejpam-5311	113	81	,	,	PUNCT
ejpam-5311	113	82	r.	r.	PROPN
ejpam-5311	113	83	subasini	subasini	PROPN
ejpam-5311	113	84	,	,	PUNCT
ejpam-5311	113	85	n.	n.	PROPN
ejpam-5311	113	86	rajesh	rajesh	PROPN
ejpam-5311	113	87	/	/	SYM
ejpam-5311	113	88	eur	eur	PROPN
ejpam-5311	113	89	.	.	PUNCT
ejpam-5311	114	1	j.	j.	PROPN
ejpam-5311	114	2	pure	pure	PROPN
ejpam-5311	114	3	appl	appl	PROPN
ejpam-5311	114	4	.	.	PROPN
ejpam-5311	114	5	math	math	PROPN
ejpam-5311	114	6	,	,	PUNCT
ejpam-5311	114	7	17	17	NUM
ejpam-5311	114	8	(	(	PUNCT
ejpam-5311	114	9	3	3	NUM
ejpam-5311	114	10	)	)	PUNCT
ejpam-5311	114	11	(	(	PUNCT
ejpam-5311	114	12	2024	2024	NUM
ejpam-5311	114	13	)	)	PUNCT
ejpam-5311	114	14	,	,	PUNCT
ejpam-5311	114	15	2235	2235	NUM
ejpam-5311	114	16	-	-	SYM
ejpam-5311	114	17	2245	2245	NUM
ejpam-5311	114	18	2241	2241	NUM
ejpam-5311	114	19	proposition	proposition	NOUN
ejpam-5311	114	20	5	5	NUM
ejpam-5311	114	21	.	.	PUNCT
ejpam-5311	115	1	let	let	VERB
ejpam-5311	115	2	µ	µ	X
ejpam-5311	115	3	be	be	AUX
ejpam-5311	115	4	a	a	DET
ejpam-5311	115	5	fuzzy	fuzzy	ADJ
ejpam-5311	115	6	set	set	NOUN
ejpam-5311	115	7	in	in	ADP
ejpam-5311	115	8	x.	x.	NOUN
ejpam-5311	115	9	then	then	ADV
ejpam-5311	115	10	every	every	DET
ejpam-5311	115	11	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	115	12	fuzzy	fuzzy	ADJ
ejpam-5311	115	13	bcc	bcc	PROPN
ejpam-5311	115	14	-	-	PUNCT
ejpam-5311	115	15	subalgebra	subalgebra	PROPN
ejpam-5311	115	16	lε	lε	ADP
ejpam-5311	115	17	µ	µ	PRON
ejpam-5311	115	18	of	of	ADP
ejpam-5311	115	19	x	x	VERB
ejpam-5311	115	20	satisfies	satisfie	NOUN
ejpam-5311	115	21	the	the	DET
ejpam-5311	115	22	following	follow	VERB
ejpam-5311	115	23	property	property	NOUN
ejpam-5311	115	24	:	:	PUNCT
ejpam-5311	115	25	(	(	PUNCT
ejpam-5311	115	26	∀x	∀x	X
ejpam-5311	115	27	,	,	PUNCT
ejpam-5311	115	28	y	y	PROPN
ejpam-5311	115	29	∈	∈	PROPN
ejpam-5311	115	30	x,∀ta	x,∀ta	PROPN
ejpam-5311	115	31	,	,	PUNCT
ejpam-5311	115	32	tb	tb	ADP
ejpam-5311	115	33	∈	∈	PROPN
ejpam-5311	115	34	(	(	PUNCT
ejpam-5311	115	35	0	0	NUM
ejpam-5311	115	36	,	,	PUNCT
ejpam-5311	115	37	1])([x	1])([x	NUM
ejpam-5311	115	38	/	/	SYM
ejpam-5311	115	39	ta	ta	X
ejpam-5311	115	40	]	]	X
ejpam-5311	115	41	∈	∈	PROPN
ejpam-5311	115	42	lε	lε	ADP
ejpam-5311	115	43	µ	µ	NOUN
ejpam-5311	115	44	,	,	PUNCT
ejpam-5311	115	45	[	[	X
ejpam-5311	115	46	y	y	X
ejpam-5311	115	47	/	/	SYM
ejpam-5311	115	48	tb	tb	NOUN
ejpam-5311	115	49	]	]	PUNCT
ejpam-5311	115	50	∈	∈	PROPN
ejpam-5311	115	51	lε	lε	X
ejpam-5311	115	52	µ	µ	X
ejpam-5311	115	53	⇒	⇒	NOUN
ejpam-5311	115	54	[	[	X
ejpam-5311	115	55	(	(	PUNCT
ejpam-5311	115	56	x	x	SYM
ejpam-5311	115	57	∗	∗	NOUN
ejpam-5311	115	58	(	(	PUNCT
ejpam-5311	115	59	0	0	NUM
ejpam-5311	115	60	∗	∗	NOUN
ejpam-5311	115	61	y))/min{tb	y))/min{tb	NOUN
ejpam-5311	115	62	,	,	PUNCT
ejpam-5311	115	63	tc	tc	PRON
ejpam-5311	115	64	}	}	PUNCT
ejpam-5311	115	65	]	]	PUNCT
ejpam-5311	115	66	∈	∈	PROPN
ejpam-5311	115	67	lε	lε	ADP
ejpam-5311	115	68	µ	µ	NUM
ejpam-5311	115	69	)	)	PUNCT
ejpam-5311	115	70	(	(	PUNCT
ejpam-5311	115	71	3.7	3.7	NUM
ejpam-5311	115	72	)	)	PUNCT
ejpam-5311	115	73	proof	proof	NOUN
ejpam-5311	115	74	.	.	PUNCT
ejpam-5311	116	1	let	let	VERB
ejpam-5311	116	2	x	x	PRON
ejpam-5311	116	3	,	,	PUNCT
ejpam-5311	116	4	y	y	PROPN
ejpam-5311	116	5	∈	∈	PROPN
ejpam-5311	116	6	x	x	X
ejpam-5311	116	7	and	and	CCONJ
ejpam-5311	116	8	ta	ta	PROPN
ejpam-5311	116	9	,	,	PUNCT
ejpam-5311	116	10	tb	tb	ADP
ejpam-5311	116	11	∈	∈	PROPN
ejpam-5311	116	12	(	(	PUNCT
ejpam-5311	116	13	0	0	NUM
ejpam-5311	116	14	,	,	PUNCT
ejpam-5311	116	15	1	1	NUM
ejpam-5311	116	16	]	]	PUNCT
ejpam-5311	116	17	be	be	AUX
ejpam-5311	116	18	such	such	ADJ
ejpam-5311	116	19	that	that	SCONJ
ejpam-5311	116	20	[	[	X
ejpam-5311	116	21	x	x	X
ejpam-5311	116	22	/	/	SYM
ejpam-5311	116	23	ta	ta	X
ejpam-5311	116	24	]	]	X
ejpam-5311	116	25	∈	∈	PROPN
ejpam-5311	116	26	lε	lε	ADP
ejpam-5311	116	27	µ	µ	NOUN
ejpam-5311	116	28	and	and	CCONJ
ejpam-5311	116	29	[	[	X
ejpam-5311	116	30	y	y	X
ejpam-5311	116	31	/	/	SYM
ejpam-5311	116	32	tb	tb	NOUN
ejpam-5311	116	33	]	]	PUNCT
ejpam-5311	116	34	∈	∈	PROPN
ejpam-5311	116	35	lε	lε	X
ejpam-5311	116	36	µ.	µ.	NOUN
ejpam-5311	116	37	then	then	ADV
ejpam-5311	116	38	lε	lε	ADP
ejpam-5311	116	39	µ(x	µ(x	NOUN
ejpam-5311	116	40	)	)	PUNCT
ejpam-5311	116	41	≥	≥	NOUN
ejpam-5311	116	42	ta	ta	X
ejpam-5311	116	43	and	and	CCONJ
ejpam-5311	116	44	lε	lε	INTJ
ejpam-5311	116	45	µ(y	µ(y	PROPN
ejpam-5311	116	46	)	)	PUNCT
ejpam-5311	116	47	≥	≥	NOUN
ejpam-5311	116	48	tb	tb	NOUN
ejpam-5311	116	49	.	.	PUNCT
ejpam-5311	117	1	it	it	PRON
ejpam-5311	117	2	follows	follow	VERB
ejpam-5311	117	3	from	from	ADP
ejpam-5311	117	4	theorem	theorem	ADJ
ejpam-5311	117	5	2	2	NUM
ejpam-5311	117	6	and	and	CCONJ
ejpam-5311	117	7	proposition	proposition	NOUN
ejpam-5311	117	8	2	2	NUM
ejpam-5311	117	9	that	that	PRON
ejpam-5311	117	10	lε	lε	ADP
ejpam-5311	117	11	µ(x	µ(x	ADJ
ejpam-5311	117	12	∗	∗	NOUN
ejpam-5311	117	13	(	(	PUNCT
ejpam-5311	117	14	0	0	NUM
ejpam-5311	117	15	∗	∗	PROPN
ejpam-5311	117	16	y	y	PROPN
ejpam-5311	117	17	)	)	PUNCT
ejpam-5311	117	18	)	)	PUNCT
ejpam-5311	117	19	≥	≥	PROPN
ejpam-5311	117	20	min{lε	min{lε	PUNCT
ejpam-5311	117	21	µ(x	µ(x	PROPN
ejpam-5311	117	22	)	)	PUNCT
ejpam-5311	117	23	,	,	PUNCT
ejpam-5311	117	24	lε	lε	AUX
ejpam-5311	117	25	µ(0	µ(0	PROPN
ejpam-5311	117	26	∗	∗	PROPN
ejpam-5311	117	27	y	y	PROPN
ejpam-5311	117	28	)	)	PUNCT
ejpam-5311	117	29	}	}	PUNCT
ejpam-5311	117	30	≥	≥	NOUN
ejpam-5311	117	31	min{lε	min{lε	NUM
ejpam-5311	117	32	µ(x),min{lε	µ(x),min{lε	PROPN
ejpam-5311	117	33	µ(0	µ(0	NOUN
ejpam-5311	117	34	)	)	PUNCT
ejpam-5311	117	35	,	,	PUNCT
ejpam-5311	117	36	lε	lε	X
ejpam-5311	117	37	µ(y	µ(y	PROPN
ejpam-5311	117	38	)	)	PUNCT
ejpam-5311	117	39	}	}	PUNCT
ejpam-5311	117	40	}	}	PUNCT
ejpam-5311	118	1	=	=	NOUN
ejpam-5311	118	2	min{lε	min{lε	NUM
ejpam-5311	118	3	µ(x	µ(x	PROPN
ejpam-5311	118	4	)	)	PUNCT
ejpam-5311	118	5	,	,	PUNCT
ejpam-5311	118	6	lε	lε	X
ejpam-5311	118	7	µ(y	µ(y	PROPN
ejpam-5311	118	8	)	)	PUNCT
ejpam-5311	118	9	}	}	PUNCT
ejpam-5311	118	10	≥	≥	NOUN
ejpam-5311	118	11	min{ta	min{ta	X
ejpam-5311	118	12	,	,	PUNCT
ejpam-5311	118	13	tb	tb	NOUN
ejpam-5311	118	14	}	}	PUNCT
ejpam-5311	118	15	.	.	PUNCT
ejpam-5311	119	1	hence	hence	ADV
ejpam-5311	119	2	,	,	PUNCT
ejpam-5311	119	3	[	[	X
ejpam-5311	119	4	(	(	PUNCT
ejpam-5311	119	5	x	x	SYM
ejpam-5311	119	6	∗	∗	NOUN
ejpam-5311	119	7	(	(	PUNCT
ejpam-5311	119	8	0	0	NUM
ejpam-5311	119	9	∗	∗	NOUN
ejpam-5311	119	10	y))/min{ta	y))/min{ta	NOUN
ejpam-5311	119	11	,	,	PUNCT
ejpam-5311	119	12	tb	tb	NOUN
ejpam-5311	119	13	}	}	PUNCT
ejpam-5311	119	14	]	]	PUNCT
ejpam-5311	119	15	∈	∈	PROPN
ejpam-5311	119	16	lε	lε	AUX
ejpam-5311	119	17	µ.	µ.	NOUN
ejpam-5311	119	18	let	let	VERB
ejpam-5311	119	19	µ	µ	X
ejpam-5311	119	20	be	be	AUX
ejpam-5311	119	21	a	a	DET
ejpam-5311	119	22	fuzzy	fuzzy	ADJ
ejpam-5311	119	23	set	set	NOUN
ejpam-5311	119	24	in	in	ADP
ejpam-5311	119	25	x.	x.	NOUN
ejpam-5311	119	26	for	for	ADP
ejpam-5311	119	27	an	an	DET
ejpam-5311	119	28	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	119	29	fuzzy	fuzzy	NOUN
ejpam-5311	119	30	set	set	VERB
ejpam-5311	119	31	lε	lε	PRON
ejpam-5311	119	32	µ	µ	PROPN
ejpam-5311	119	33	of	of	ADP
ejpam-5311	119	34	µ	µ	NOUN
ejpam-5311	119	35	in	in	ADP
ejpam-5311	119	36	x	x	X
ejpam-5311	119	37	and	and	CCONJ
ejpam-5311	119	38	t	t	PROPN
ejpam-5311	119	39	∈	∈	PROPN
ejpam-5311	119	40	(	(	PUNCT
ejpam-5311	119	41	0	0	NUM
ejpam-5311	119	42	,	,	PUNCT
ejpam-5311	119	43	1	1	NUM
ejpam-5311	119	44	]	]	PUNCT
ejpam-5311	119	45	,	,	PUNCT
ejpam-5311	119	46	consider	consider	VERB
ejpam-5311	119	47	the	the	DET
ejpam-5311	119	48	sets	set	NOUN
ejpam-5311	119	49	(	(	PUNCT
ejpam-5311	119	50	lε	lε	X
ejpam-5311	119	51	µ	µ	NUM
ejpam-5311	119	52	,	,	PUNCT
ejpam-5311	119	53	t)∈	t)∈	PUNCT
ejpam-5311	119	54	=	=	SYM
ejpam-5311	119	55	{	{	PUNCT
ejpam-5311	119	56	x	x	SYM
ejpam-5311	119	57	∈	∈	PROPN
ejpam-5311	119	58	x	x	X
ejpam-5311	119	59	:	:	PUNCT
ejpam-5311	120	1	[	[	X
ejpam-5311	120	2	x	x	X
ejpam-5311	120	3	/	/	SYM
ejpam-5311	120	4	t	t	PROPN
ejpam-5311	120	5	]	]	X
ejpam-5311	120	6	∈	∈	PROPN
ejpam-5311	120	7	lε	lε	ADP
ejpam-5311	120	8	µ	µ	NOUN
ejpam-5311	120	9	}	}	PUNCT
ejpam-5311	120	10	,	,	PUNCT
ejpam-5311	120	11	(	(	PUNCT
ejpam-5311	120	12	lε	lε	X
ejpam-5311	120	13	µ	µ	NUM
ejpam-5311	120	14	,	,	PUNCT
ejpam-5311	120	15	t)q	t)q	PUNCT
ejpam-5311	120	16	=	=	SYM
ejpam-5311	120	17	{	{	PUNCT
ejpam-5311	120	18	x	x	SYM
ejpam-5311	120	19	∈	∈	PROPN
ejpam-5311	120	20	x	x	X
ejpam-5311	120	21	:	:	PUNCT
ejpam-5311	121	1	[	[	X
ejpam-5311	121	2	x	x	X
ejpam-5311	121	3	/	/	SYM
ejpam-5311	121	4	t]qlε	t]qlε	X
ejpam-5311	121	5	µ	µ	X
ejpam-5311	121	6	}	}	PUNCT
ejpam-5311	121	7	,	,	PUNCT
ejpam-5311	121	8	which	which	PRON
ejpam-5311	121	9	are	be	AUX
ejpam-5311	121	10	called	call	VERB
ejpam-5311	121	11	the	the	DET
ejpam-5311	121	12	∈-set	∈-set	NOUN
ejpam-5311	121	13	and	and	CCONJ
ejpam-5311	121	14	q	q	NOUN
ejpam-5311	121	15	-	-	PUNCT
ejpam-5311	121	16	set	set	VERB
ejpam-5311	121	17	,	,	PUNCT
ejpam-5311	121	18	respectively	respectively	ADV
ejpam-5311	121	19	,	,	PUNCT
ejpam-5311	121	20	of	of	ADP
ejpam-5311	121	21	lε	lε	X
ejpam-5311	121	22	µ	µ	X
ejpam-5311	121	23	(	(	PUNCT
ejpam-5311	121	24	with	with	ADP
ejpam-5311	121	25	value	value	NOUN
ejpam-5311	121	26	t	t	PROPN
ejpam-5311	121	27	)	)	PUNCT
ejpam-5311	121	28	.	.	PUNCT
ejpam-5311	122	1	we	we	PRON
ejpam-5311	122	2	explore	explore	VERB
ejpam-5311	122	3	the	the	DET
ejpam-5311	122	4	conditions	condition	NOUN
ejpam-5311	122	5	under	under	ADP
ejpam-5311	122	6	which	which	PRON
ejpam-5311	122	7	the	the	DET
ejpam-5311	122	8	∈-set	∈-set	NOUN
ejpam-5311	122	9	and	and	CCONJ
ejpam-5311	122	10	q	q	NOUN
ejpam-5311	122	11	-	-	PUNCT
ejpam-5311	122	12	set	set	NOUN
ejpam-5311	122	13	of	of	ADP
ejpam-5311	122	14	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	122	15	fuzzy	fuzzy	ADJ
ejpam-5311	122	16	sets	set	NOUN
ejpam-5311	122	17	can	can	AUX
ejpam-5311	122	18	be	be	AUX
ejpam-5311	122	19	bcc	bcc	PROPN
ejpam-5311	122	20	-	-	PUNCT
ejpam-5311	122	21	subalgebras	subalgebras	PROPN
ejpam-5311	122	22	.	.	PUNCT
ejpam-5311	123	1	theorem	theorem	ADJ
ejpam-5311	123	2	4	4	NUM
ejpam-5311	123	3	.	.	PUNCT
ejpam-5311	124	1	let	let	VERB
ejpam-5311	124	2	lε	lε	PART
ejpam-5311	124	3	µ	µ	X
ejpam-5311	124	4	be	be	AUX
ejpam-5311	124	5	an	an	DET
ejpam-5311	124	6	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	124	7	fuzzy	fuzzy	ADJ
ejpam-5311	124	8	set	set	NOUN
ejpam-5311	124	9	of	of	ADP
ejpam-5311	124	10	a	a	DET
ejpam-5311	124	11	fuzzy	fuzzy	ADJ
ejpam-5311	124	12	set	set	VERB
ejpam-5311	124	13	µ	µ	NOUN
ejpam-5311	124	14	in	in	ADP
ejpam-5311	124	15	x.	x.	NOUN
ejpam-5311	124	16	then	then	ADV
ejpam-5311	124	17	the	the	DET
ejpam-5311	124	18	∈-set	∈-set	NOUN
ejpam-5311	124	19	(	(	PUNCT
ejpam-5311	124	20	lε	lε	X
ejpam-5311	124	21	µ	µ	NUM
ejpam-5311	124	22	,	,	PUNCT
ejpam-5311	124	23	t)∈	t)∈	NUM
ejpam-5311	124	24	of	of	ADP
ejpam-5311	124	25	lε	lε	X
ejpam-5311	124	26	µ	µ	X
ejpam-5311	124	27	with	with	ADP
ejpam-5311	124	28	value	value	NOUN
ejpam-5311	124	29	t	t	PROPN
ejpam-5311	124	30	∈	∈	PROPN
ejpam-5311	124	31	(	(	PUNCT
ejpam-5311	124	32	0.5	0.5	NUM
ejpam-5311	124	33	,	,	PUNCT
ejpam-5311	124	34	1	1	NUM
ejpam-5311	124	35	]	]	PUNCT
ejpam-5311	124	36	is	be	AUX
ejpam-5311	124	37	a	a	DET
ejpam-5311	124	38	bcc	bcc	NOUN
ejpam-5311	124	39	-	-	PUNCT
ejpam-5311	124	40	subalgebra	subalgebra	NOUN
ejpam-5311	124	41	of	of	ADP
ejpam-5311	124	42	x	x	PRON
ejpam-5311	124	43	if	if	SCONJ
ejpam-5311	124	44	and	and	CCONJ
ejpam-5311	124	45	only	only	ADV
ejpam-5311	124	46	if	if	SCONJ
ejpam-5311	124	47	the	the	DET
ejpam-5311	124	48	following	follow	VERB
ejpam-5311	124	49	assertion	assertion	NOUN
ejpam-5311	124	50	is	be	AUX
ejpam-5311	124	51	valid	valid	ADJ
ejpam-5311	124	52	:	:	PUNCT
ejpam-5311	124	53	(	(	PUNCT
ejpam-5311	124	54	∀x	∀x	X
ejpam-5311	124	55	,	,	PUNCT
ejpam-5311	124	56	y	y	PROPN
ejpam-5311	124	57	∈	∈	PROPN
ejpam-5311	124	58	x)(min{lε	x)(min{lε	NUM
ejpam-5311	124	59	µ(x	µ(x	PROPN
ejpam-5311	124	60	)	)	PUNCT
ejpam-5311	124	61	,	,	PUNCT
ejpam-5311	124	62	lε	lε	X
ejpam-5311	124	63	µ(y	µ(y	PROPN
ejpam-5311	124	64	)	)	PUNCT
ejpam-5311	124	65	}	}	PUNCT
ejpam-5311	124	66	≤	≤	NOUN
ejpam-5311	124	67	max{lε	max{lε	PUNCT
ejpam-5311	124	68	µ(x	µ(x	ADJ
ejpam-5311	124	69	∗	∗	NOUN
ejpam-5311	124	70	y	y	NOUN
ejpam-5311	124	71	)	)	PUNCT
ejpam-5311	124	72	,	,	PUNCT
ejpam-5311	124	73	0.5	0.5	NUM
ejpam-5311	124	74	}	}	PUNCT
ejpam-5311	124	75	)	)	PUNCT
ejpam-5311	124	76	(	(	PUNCT
ejpam-5311	124	77	3.8	3.8	NUM
ejpam-5311	124	78	)	)	PUNCT
ejpam-5311	124	79	proof	proof	NOUN
ejpam-5311	124	80	.	.	PUNCT
ejpam-5311	125	1	assume	assume	VERB
ejpam-5311	125	2	that	that	SCONJ
ejpam-5311	125	3	the	the	DET
ejpam-5311	125	4	∈-set	∈-set	NOUN
ejpam-5311	125	5	(	(	PUNCT
ejpam-5311	125	6	lε	lε	X
ejpam-5311	125	7	µ	µ	NUM
ejpam-5311	125	8	,	,	PUNCT
ejpam-5311	125	9	t)∈	t)∈	NUM
ejpam-5311	125	10	of	of	ADP
ejpam-5311	125	11	lε	lε	X
ejpam-5311	125	12	µ	µ	X
ejpam-5311	125	13	with	with	ADP
ejpam-5311	125	14	value	value	NOUN
ejpam-5311	125	15	t	t	PROPN
ejpam-5311	125	16	∈	∈	PROPN
ejpam-5311	125	17	(	(	PUNCT
ejpam-5311	125	18	0.5	0.5	NUM
ejpam-5311	125	19	,	,	PUNCT
ejpam-5311	125	20	1	1	NUM
ejpam-5311	125	21	]	]	PUNCT
ejpam-5311	125	22	is	be	AUX
ejpam-5311	125	23	a	a	DET
ejpam-5311	125	24	bcc	bcc	PROPN
ejpam-5311	125	25	-	-	PUNCT
ejpam-5311	125	26	subalgebra	subalgebra	NOUN
ejpam-5311	125	27	of	of	ADP
ejpam-5311	125	28	x.	x.	NOUN
ejpam-5311	125	29	if	if	SCONJ
ejpam-5311	125	30	the	the	DET
ejpam-5311	125	31	condition	condition	NOUN
ejpam-5311	125	32	(	(	PUNCT
ejpam-5311	125	33	3.8	3.8	NUM
ejpam-5311	125	34	)	)	PUNCT
ejpam-5311	125	35	is	be	AUX
ejpam-5311	125	36	not	not	PART
ejpam-5311	125	37	valid	valid	ADJ
ejpam-5311	125	38	,	,	PUNCT
ejpam-5311	125	39	then	then	ADV
ejpam-5311	125	40	there	there	PRON
ejpam-5311	125	41	exist	exist	VERB
ejpam-5311	125	42	a	a	DET
ejpam-5311	125	43	,	,	PUNCT
ejpam-5311	125	44	b	b	X
ejpam-5311	125	45	∈	∈	PROPN
ejpam-5311	125	46	x	x	X
ejpam-5311	125	47	such	such	ADJ
ejpam-5311	125	48	that	that	SCONJ
ejpam-5311	125	49	min{lε	min{lε	NUM
ejpam-5311	125	50	µ(a	µ(a	PROPN
ejpam-5311	125	51	)	)	PUNCT
ejpam-5311	125	52	,	,	PUNCT
ejpam-5311	125	53	lε	lε	X
ejpam-5311	125	54	µ(b	µ(b	NOUN
ejpam-5311	125	55	)	)	PUNCT
ejpam-5311	125	56	}	}	PUNCT
ejpam-5311	125	57	>	>	X
ejpam-5311	125	58	max{lε	max{lε	X
ejpam-5311	126	1	µ(a	µ(a	PROPN
ejpam-5311	126	2	∗	∗	PROPN
ejpam-5311	126	3	b	b	NOUN
ejpam-5311	126	4	)	)	PUNCT
ejpam-5311	126	5	,	,	PUNCT
ejpam-5311	126	6	0.5	0.5	NUM
ejpam-5311	126	7	}	}	PUNCT
ejpam-5311	126	8	.	.	PUNCT
ejpam-5311	127	1	if	if	SCONJ
ejpam-5311	127	2	we	we	PRON
ejpam-5311	127	3	take	take	VERB
ejpam-5311	127	4	s	s	VERB
ejpam-5311	127	5	=	=	PUNCT
ejpam-5311	127	6	min{lε	min{lε	X
ejpam-5311	127	7	µ(a	µ(a	PROPN
ejpam-5311	127	8	)	)	PUNCT
ejpam-5311	127	9	,	,	PUNCT
ejpam-5311	127	10	lε	lε	X
ejpam-5311	127	11	µ(b	µ(b	NOUN
ejpam-5311	127	12	)	)	PUNCT
ejpam-5311	127	13	}	}	PUNCT
ejpam-5311	127	14	,	,	PUNCT
ejpam-5311	127	15	then	then	ADV
ejpam-5311	127	16	s	s	VERB
ejpam-5311	127	17	∈	∈	PROPN
ejpam-5311	127	18	(	(	PUNCT
ejpam-5311	127	19	0.5	0.5	NUM
ejpam-5311	127	20	,	,	PUNCT
ejpam-5311	127	21	1	1	NUM
ejpam-5311	127	22	]	]	PUNCT
ejpam-5311	127	23	and	and	CCONJ
ejpam-5311	127	24	[	[	X
ejpam-5311	127	25	a	a	X
ejpam-5311	127	26	/	/	SYM
ejpam-5311	127	27	s	s	NOUN
ejpam-5311	127	28	]	]	X
ejpam-5311	127	29	,	,	PUNCT
ejpam-5311	127	30	[	[	X
ejpam-5311	127	31	b	b	X
ejpam-5311	127	32	/	/	SYM
ejpam-5311	127	33	s	s	NOUN
ejpam-5311	127	34	]	]	X
ejpam-5311	127	35	∈	∈	PROPN
ejpam-5311	127	36	lε	lε	X
ejpam-5311	127	37	µ	µ	NOUN
ejpam-5311	127	38	,	,	PUNCT
ejpam-5311	127	39	that	that	ADV
ejpam-5311	127	40	is	is	ADV
ejpam-5311	127	41	,	,	PUNCT
ejpam-5311	127	42	a	a	PRON
ejpam-5311	127	43	,	,	PUNCT
ejpam-5311	127	44	b	b	X
ejpam-5311	127	45	∈	∈	PROPN
ejpam-5311	127	46	(	(	PUNCT
ejpam-5311	127	47	lε	lε	ADP
ejpam-5311	127	48	µ	µ	NOUN
ejpam-5311	127	49	,	,	PUNCT
ejpam-5311	127	50	s)∈.	s)∈.	PROPN
ejpam-5311	127	51	since	since	SCONJ
ejpam-5311	127	52	(	(	PUNCT
ejpam-5311	127	53	lε	lε	X
ejpam-5311	127	54	µ	µ	NUM
ejpam-5311	127	55	,	,	PUNCT
ejpam-5311	127	56	s)∈	s)∈	NUM
ejpam-5311	127	57	is	be	AUX
ejpam-5311	127	58	a	a	DET
ejpam-5311	127	59	bcc	bcc	NOUN
ejpam-5311	127	60	-	-	PUNCT
ejpam-5311	127	61	subalgebra	subalgebra	NOUN
ejpam-5311	127	62	of	of	ADP
ejpam-5311	127	63	x	x	PRON
ejpam-5311	127	64	,	,	PUNCT
ejpam-5311	127	65	we	we	PRON
ejpam-5311	127	66	have	have	VERB
ejpam-5311	127	67	a	a	DET
ejpam-5311	127	68	∗	∗	NOUN
ejpam-5311	127	69	b	b	NOUN
ejpam-5311	127	70	∈	∈	PROPN
ejpam-5311	127	71	(	(	PUNCT
ejpam-5311	127	72	lε	lε	ADP
ejpam-5311	127	73	µ	µ	NOUN
ejpam-5311	127	74	,	,	PUNCT
ejpam-5311	127	75	s)∈.	s)∈.	PROPN
ejpam-5311	127	76	but	but	CCONJ
ejpam-5311	127	77	[	[	X
ejpam-5311	127	78	(	(	PUNCT
ejpam-5311	127	79	a	a	DET
ejpam-5311	127	80	∗	∗	X
ejpam-5311	127	81	b)/s	b)/s	PROPN
ejpam-5311	127	82	]	]	PUNCT
ejpam-5311	127	83	/∈	/∈	PUNCT
ejpam-5311	128	1	lε	lε	ADP
ejpam-5311	128	2	µ	µ	PROPN
ejpam-5311	128	3	implies	imply	VERB
ejpam-5311	128	4	a	a	DET
ejpam-5311	128	5	∗	∗	NOUN
ejpam-5311	128	6	b	b	NOUN
ejpam-5311	128	7	/∈	/∈	PUNCT
ejpam-5311	128	8	(	(	PUNCT
ejpam-5311	128	9	lε	lε	ADP
ejpam-5311	128	10	µ	µ	NUM
ejpam-5311	128	11	,	,	PUNCT
ejpam-5311	128	12	s)∈	s)∈	PROPN
ejpam-5311	128	13	,	,	PUNCT
ejpam-5311	128	14	a	a	DET
ejpam-5311	128	15	contradiction	contradiction	NOUN
ejpam-5311	128	16	.	.	PUNCT
ejpam-5311	129	1	thus	thus	ADV
ejpam-5311	129	2	,	,	PUNCT
ejpam-5311	129	3	min{lε	min{lε	PRON
ejpam-5311	129	4	µ(x	µ(x	PROPN
ejpam-5311	129	5	)	)	PUNCT
ejpam-5311	129	6	,	,	PUNCT
ejpam-5311	129	7	lε	lε	X
ejpam-5311	129	8	µ(y	µ(y	PROPN
ejpam-5311	129	9	)	)	PUNCT
ejpam-5311	129	10	}	}	PUNCT
ejpam-5311	129	11	≤	≤	NOUN
ejpam-5311	129	12	max{lε	max{lε	PUNCT
ejpam-5311	129	13	µ(x	µ(x	ADJ
ejpam-5311	129	14	∗	∗	NOUN
ejpam-5311	129	15	y	y	NOUN
ejpam-5311	129	16	)	)	PUNCT
ejpam-5311	129	17	,	,	PUNCT
ejpam-5311	129	18	0.5	0.5	NUM
ejpam-5311	129	19	}	}	PUNCT
ejpam-5311	129	20	for	for	ADP
ejpam-5311	129	21	all	all	DET
ejpam-5311	129	22	x	x	NOUN
ejpam-5311	129	23	,	,	PUNCT
ejpam-5311	129	24	y	y	PROPN
ejpam-5311	129	25	∈	∈	PROPN
ejpam-5311	129	26	x.	x.	NOUN
ejpam-5311	129	27	conversely	conversely	ADV
ejpam-5311	129	28	,	,	PUNCT
ejpam-5311	129	29	suppose	suppose	VERB
ejpam-5311	129	30	that	that	SCONJ
ejpam-5311	129	31	lε	lε	AUX
ejpam-5311	129	32	µ	µ	PRON
ejpam-5311	129	33	satisfies	satisfy	VERB
ejpam-5311	129	34	the	the	DET
ejpam-5311	129	35	condition	condition	NOUN
ejpam-5311	129	36	(	(	PUNCT
ejpam-5311	129	37	3.8	3.8	NUM
ejpam-5311	129	38	)	)	PUNCT
ejpam-5311	129	39	.	.	PUNCT
ejpam-5311	130	1	let	let	VERB
ejpam-5311	130	2	t	t	PROPN
ejpam-5311	130	3	∈	∈	PROPN
ejpam-5311	130	4	(	(	PUNCT
ejpam-5311	130	5	0.5	0.5	NUM
ejpam-5311	130	6	,	,	PUNCT
ejpam-5311	130	7	1	1	NUM
ejpam-5311	130	8	]	]	PUNCT
ejpam-5311	130	9	and	and	CCONJ
ejpam-5311	130	10	x	x	X
ejpam-5311	130	11	,	,	PUNCT
ejpam-5311	130	12	y	y	PROPN
ejpam-5311	130	13	∈	∈	PROPN
ejpam-5311	130	14	x	x	AUX
ejpam-5311	130	15	be	be	AUX
ejpam-5311	130	16	such	such	ADJ
ejpam-5311	130	17	that	that	SCONJ
ejpam-5311	130	18	x	x	SYM
ejpam-5311	130	19	∈	∈	PROPN
ejpam-5311	130	20	(	(	PUNCT
ejpam-5311	130	21	lε	lε	X
ejpam-5311	130	22	µ	µ	NUM
ejpam-5311	130	23	,	,	PUNCT
ejpam-5311	130	24	t)∈	t)∈	PROPN
ejpam-5311	130	25	and	and	CCONJ
ejpam-5311	130	26	y	y	PROPN
ejpam-5311	130	27	∈	∈	PROPN
ejpam-5311	130	28	(	(	PUNCT
ejpam-5311	130	29	lε	lε	ADP
ejpam-5311	130	30	µ	µ	NUM
ejpam-5311	130	31	,	,	PUNCT
ejpam-5311	130	32	t)∈.	t)∈.	PROPN
ejpam-5311	130	33	then	then	ADV
ejpam-5311	130	34	lε	lε	ADP
ejpam-5311	130	35	µ(x	µ(x	NOUN
ejpam-5311	130	36	)	)	PUNCT
ejpam-5311	130	37	≥	≥	NOUN
ejpam-5311	130	38	t	t	NOUN
ejpam-5311	130	39	and	and	CCONJ
ejpam-5311	130	40	lε	lε	ADP
ejpam-5311	130	41	µ(y	µ(y	PROPN
ejpam-5311	130	42	)	)	PUNCT
ejpam-5311	130	43	≥	≥	PROPN
ejpam-5311	130	44	t	t	PROPN
ejpam-5311	130	45	,	,	PUNCT
ejpam-5311	130	46	which	which	PRON
ejpam-5311	130	47	imply	imply	VERB
ejpam-5311	130	48	from	from	ADP
ejpam-5311	130	49	(	(	PUNCT
ejpam-5311	130	50	3.8	3.8	NUM
ejpam-5311	130	51	)	)	PUNCT
ejpam-5311	130	52	that	that	PRON
ejpam-5311	130	53	0.5	0.5	NUM
ejpam-5311	130	54	<	<	X
ejpam-5311	130	55	t	t	NOUN
ejpam-5311	130	56	≤	≤	NOUN
ejpam-5311	130	57	min{lε	min{lε	PRON
ejpam-5311	130	58	µ(x	µ(x	PROPN
ejpam-5311	130	59	)	)	PUNCT
ejpam-5311	130	60	,	,	PUNCT
ejpam-5311	130	61	lε	lε	X
ejpam-5311	130	62	µ(y	µ(y	PROPN
ejpam-5311	130	63	)	)	PUNCT
ejpam-5311	130	64	}	}	PUNCT
ejpam-5311	130	65	≤	≤	NOUN
ejpam-5311	130	66	max{lε	max{lε	PUNCT
ejpam-5311	130	67	µ(x∗y	µ(x∗y	PROPN
ejpam-5311	130	68	)	)	PUNCT
ejpam-5311	130	69	,	,	PUNCT
ejpam-5311	130	70	0.5	0.5	NUM
ejpam-5311	130	71	}	}	PUNCT
ejpam-5311	130	72	.	.	PUNCT
ejpam-5311	131	1	thus	thus	ADV
ejpam-5311	131	2	,	,	PUNCT
ejpam-5311	131	3	[	[	X
ejpam-5311	131	4	(	(	PUNCT
ejpam-5311	131	5	x∗y)/t	x∗y)/t	X
ejpam-5311	131	6	]	]	X
ejpam-5311	131	7	∈	∈	PROPN
ejpam-5311	131	8	lε	lε	ADP
ejpam-5311	131	9	µ	µ	NOUN
ejpam-5311	131	10	,	,	PUNCT
ejpam-5311	131	11	that	that	ADV
ejpam-5311	131	12	is	is	ADV
ejpam-5311	131	13	,	,	PUNCT
ejpam-5311	131	14	x	x	SYM
ejpam-5311	131	15	∗	∗	NOUN
ejpam-5311	131	16	y	y	PROPN
ejpam-5311	131	17	∈	∈	PROPN
ejpam-5311	131	18	(	(	PUNCT
ejpam-5311	131	19	lε	lε	ADP
ejpam-5311	131	20	µ	µ	NUM
ejpam-5311	131	21	,	,	PUNCT
ejpam-5311	131	22	t)∈.	t)∈.	PROPN
ejpam-5311	131	23	so	so	ADV
ejpam-5311	131	24	,	,	PUNCT
ejpam-5311	131	25	(	(	PUNCT
ejpam-5311	131	26	lε	lε	X
ejpam-5311	131	27	µ	µ	NUM
ejpam-5311	131	28	,	,	PUNCT
ejpam-5311	131	29	t)∈	t)∈	NUM
ejpam-5311	131	30	is	be	AUX
ejpam-5311	131	31	a	a	DET
ejpam-5311	131	32	bcc	bcc	NOUN
ejpam-5311	131	33	-	-	PUNCT
ejpam-5311	131	34	subalgebra	subalgebra	NOUN
ejpam-5311	131	35	of	of	ADP
ejpam-5311	131	36	x	x	PUNCT
ejpam-5311	131	37	for	for	ADP
ejpam-5311	131	38	t	t	PROPN
ejpam-5311	131	39	∈	∈	PROPN
ejpam-5311	131	40	(	(	PUNCT
ejpam-5311	131	41	0.5	0.5	NUM
ejpam-5311	131	42	,	,	PUNCT
ejpam-5311	131	43	1	1	NUM
ejpam-5311	131	44	]	]	PUNCT
ejpam-5311	131	45	.	.	PUNCT
ejpam-5311	132	1	theorem	theorem	NOUN
ejpam-5311	132	2	5	5	NUM
ejpam-5311	132	3	.	.	PUNCT
ejpam-5311	133	1	let	let	VERB
ejpam-5311	133	2	lε	lε	PART
ejpam-5311	133	3	µ	µ	X
ejpam-5311	133	4	be	be	AUX
ejpam-5311	133	5	an	an	DET
ejpam-5311	133	6	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	133	7	fuzzy	fuzzy	ADJ
ejpam-5311	133	8	set	set	NOUN
ejpam-5311	133	9	of	of	ADP
ejpam-5311	133	10	a	a	DET
ejpam-5311	133	11	fuzzy	fuzzy	ADJ
ejpam-5311	133	12	set	set	VERB
ejpam-5311	133	13	µ	µ	NOUN
ejpam-5311	133	14	in	in	ADP
ejpam-5311	133	15	x.	x.	NOUN
ejpam-5311	133	16	if	if	SCONJ
ejpam-5311	133	17	µ	µ	PRON
ejpam-5311	133	18	is	be	AUX
ejpam-5311	133	19	a	a	DET
ejpam-5311	133	20	fuzzy	fuzzy	ADJ
ejpam-5311	133	21	bcc	bcc	NOUN
ejpam-5311	133	22	-	-	PUNCT
ejpam-5311	133	23	subalgebra	subalgebra	NOUN
ejpam-5311	133	24	of	of	ADP
ejpam-5311	133	25	x	x	PRON
ejpam-5311	133	26	,	,	PUNCT
ejpam-5311	133	27	then	then	ADV
ejpam-5311	133	28	the	the	DET
ejpam-5311	133	29	nonempty	nonempty	ADJ
ejpam-5311	133	30	q	q	NOUN
ejpam-5311	133	31	-	-	PUNCT
ejpam-5311	133	32	set	set	ADJ
ejpam-5311	133	33	(	(	PUNCT
ejpam-5311	133	34	lε	lε	X
ejpam-5311	133	35	µ	µ	NUM
ejpam-5311	133	36	,	,	PUNCT
ejpam-5311	133	37	t)q	t)q	PRON
ejpam-5311	133	38	of	of	ADP
ejpam-5311	133	39	lε	lε	ADP
ejpam-5311	133	40	µ	µ	X
ejpam-5311	133	41	with	with	ADP
ejpam-5311	133	42	value	value	NOUN
ejpam-5311	133	43	t	t	X
ejpam-5311	133	44	∈	∈	PROPN
ejpam-5311	133	45	(	(	PUNCT
ejpam-5311	133	46	0	0	NUM
ejpam-5311	133	47	,	,	PUNCT
ejpam-5311	133	48	1	1	NUM
ejpam-5311	133	49	]	]	PUNCT
ejpam-5311	133	50	is	be	AUX
ejpam-5311	133	51	a	a	DET
ejpam-5311	133	52	bcc	bcc	PROPN
ejpam-5311	133	53	-	-	PUNCT
ejpam-5311	133	54	subalgebra	subalgebra	NOUN
ejpam-5311	133	55	of	of	ADP
ejpam-5311	133	56	x.	x.	PROPN
ejpam-5311	133	57	a.	a.	PROPN
ejpam-5311	133	58	iampan	iampan	PROPN
ejpam-5311	133	59	,	,	PUNCT
ejpam-5311	133	60	r.	r.	PROPN
ejpam-5311	133	61	subasini	subasini	PROPN
ejpam-5311	133	62	,	,	PUNCT
ejpam-5311	133	63	n.	n.	PROPN
ejpam-5311	133	64	rajesh	rajesh	PROPN
ejpam-5311	133	65	/	/	SYM
ejpam-5311	133	66	eur	eur	PROPN
ejpam-5311	133	67	.	.	PUNCT
ejpam-5311	134	1	j.	j.	PROPN
ejpam-5311	134	2	pure	pure	PROPN
ejpam-5311	134	3	appl	appl	PROPN
ejpam-5311	134	4	.	.	PROPN
ejpam-5311	134	5	math	math	PROPN
ejpam-5311	134	6	,	,	PUNCT
ejpam-5311	134	7	17	17	NUM
ejpam-5311	134	8	(	(	PUNCT
ejpam-5311	134	9	3	3	NUM
ejpam-5311	134	10	)	)	PUNCT
ejpam-5311	134	11	(	(	PUNCT
ejpam-5311	134	12	2024	2024	NUM
ejpam-5311	134	13	)	)	PUNCT
ejpam-5311	134	14	,	,	PUNCT
ejpam-5311	134	15	2235	2235	NUM
ejpam-5311	134	16	-	-	SYM
ejpam-5311	134	17	2245	2245	NUM
ejpam-5311	134	18	2242	2242	NUM
ejpam-5311	134	19	proof	proof	NOUN
ejpam-5311	134	20	.	.	PUNCT
ejpam-5311	135	1	let	let	VERB
ejpam-5311	135	2	t	t	PROPN
ejpam-5311	135	3	∈	∈	PROPN
ejpam-5311	135	4	(	(	PUNCT
ejpam-5311	135	5	0	0	NUM
ejpam-5311	135	6	,	,	PUNCT
ejpam-5311	135	7	1	1	NUM
ejpam-5311	135	8	]	]	PUNCT
ejpam-5311	135	9	and	and	CCONJ
ejpam-5311	135	10	x	x	X
ejpam-5311	135	11	,	,	PUNCT
ejpam-5311	135	12	y	y	PROPN
ejpam-5311	135	13	∈	∈	PROPN
ejpam-5311	135	14	(	(	PUNCT
ejpam-5311	135	15	lε	lε	X
ejpam-5311	135	16	µ	µ	NUM
ejpam-5311	135	17	,	,	PUNCT
ejpam-5311	135	18	t)q	t)q	PUNCT
ejpam-5311	135	19	.	.	PUNCT
ejpam-5311	136	1	then	then	ADV
ejpam-5311	136	2	[	[	X
ejpam-5311	136	3	x	x	X
ejpam-5311	136	4	/	/	SYM
ejpam-5311	136	5	t]qlε	t]qlε	X
ejpam-5311	136	6	µ	µ	NOUN
ejpam-5311	136	7	and	and	CCONJ
ejpam-5311	136	8	[	[	X
ejpam-5311	136	9	y	y	X
ejpam-5311	136	10	/	/	SYM
ejpam-5311	136	11	t]qlε	t]qlε	X
ejpam-5311	136	12	µ	µ	NOUN
ejpam-5311	136	13	,	,	PUNCT
ejpam-5311	136	14	that	that	ADV
ejpam-5311	136	15	is	is	ADV
ejpam-5311	136	16	,	,	PUNCT
ejpam-5311	136	17	lε	lε	X
ejpam-5311	136	18	µ(x	µ(x	NOUN
ejpam-5311	136	19	)	)	PUNCT
ejpam-5311	137	1	+	+	NUM
ejpam-5311	137	2	t	t	X
ejpam-5311	137	3	>	>	X
ejpam-5311	137	4	1	1	NUM
ejpam-5311	137	5	and	and	CCONJ
ejpam-5311	137	6	lε	lε	ADP
ejpam-5311	137	7	µ(y	µ(y	PROPN
ejpam-5311	137	8	)	)	PUNCT
ejpam-5311	138	1	+	+	CCONJ
ejpam-5311	138	2	t	t	X
ejpam-5311	138	3	>	>	X
ejpam-5311	138	4	1	1	X
ejpam-5311	138	5	.	.	PUNCT
ejpam-5311	139	1	it	it	PRON
ejpam-5311	139	2	follows	follow	VERB
ejpam-5311	139	3	from	from	ADP
ejpam-5311	139	4	theorems	theorem	NOUN
ejpam-5311	139	5	1	1	NUM
ejpam-5311	139	6	and	and	CCONJ
ejpam-5311	139	7	2	2	NUM
ejpam-5311	139	8	that	that	PRON
ejpam-5311	139	9	lε	lε	ADP
ejpam-5311	139	10	µ(x	µ(x	PROPN
ejpam-5311	139	11	∗	∗	NOUN
ejpam-5311	139	12	y	y	NOUN
ejpam-5311	139	13	)	)	PUNCT
ejpam-5311	140	1	+	+	CCONJ
ejpam-5311	140	2	t	t	X
ejpam-5311	140	3	≥	≥	X
ejpam-5311	140	4	min{lε	min{lε	PRON
ejpam-5311	140	5	µ(x	µ(x	PROPN
ejpam-5311	140	6	)	)	PUNCT
ejpam-5311	140	7	,	,	PUNCT
ejpam-5311	140	8	lε	lε	X
ejpam-5311	140	9	µ(y	µ(y	PROPN
ejpam-5311	140	10	)	)	PUNCT
ejpam-5311	140	11	}	}	PUNCT
ejpam-5311	141	1	+	+	NUM
ejpam-5311	141	2	t	t	X
ejpam-5311	141	3	=	=	SYM
ejpam-5311	141	4	min{lε	min{lε	NUM
ejpam-5311	141	5	µ(x	µ(x	PROPN
ejpam-5311	141	6	)	)	PUNCT
ejpam-5311	141	7	+	+	SYM
ejpam-5311	141	8	t	t	PROPN
ejpam-5311	141	9	,	,	PUNCT
ejpam-5311	141	10	lε	lε	X
ejpam-5311	141	11	µ(y	µ(y	PROPN
ejpam-5311	141	12	)	)	PUNCT
ejpam-5311	141	13	+	+	NUM
ejpam-5311	141	14	t	t	X
ejpam-5311	141	15	}	}	PUNCT
ejpam-5311	141	16	>	>	X
ejpam-5311	141	17	1	1	NUM
ejpam-5311	141	18	.	.	PUNCT
ejpam-5311	141	19	thus	thus	ADV
ejpam-5311	141	20	,	,	PUNCT
ejpam-5311	141	21	[	[	X
ejpam-5311	141	22	(	(	PUNCT
ejpam-5311	141	23	x	x	SYM
ejpam-5311	141	24	∗	∗	NOUN
ejpam-5311	141	25	y)/t]qlε	y)/t]qlε	NOUN
ejpam-5311	141	26	µ.	µ.	NOUN
ejpam-5311	142	1	so	so	ADV
ejpam-5311	142	2	,	,	PUNCT
ejpam-5311	142	3	x	x	PUNCT
ejpam-5311	142	4	∗	∗	NOUN
ejpam-5311	142	5	y	y	PROPN
ejpam-5311	142	6	∈	∈	PROPN
ejpam-5311	142	7	(	(	PUNCT
ejpam-5311	142	8	lε	lε	X
ejpam-5311	142	9	µ	µ	NUM
ejpam-5311	142	10	,	,	PUNCT
ejpam-5311	142	11	t)q	t)q	PUNCT
ejpam-5311	142	12	.	.	PUNCT
ejpam-5311	143	1	hence	hence	ADV
ejpam-5311	143	2	,	,	PUNCT
ejpam-5311	143	3	(	(	PUNCT
ejpam-5311	143	4	lε	lε	X
ejpam-5311	143	5	µ	µ	NUM
ejpam-5311	143	6	,	,	PUNCT
ejpam-5311	143	7	t)q	t)q	PUNCT
ejpam-5311	143	8	is	be	AUX
ejpam-5311	143	9	a	a	DET
ejpam-5311	143	10	bcc	bcc	NOUN
ejpam-5311	143	11	-	-	PUNCT
ejpam-5311	143	12	subalgebra	subalgebra	NOUN
ejpam-5311	143	13	of	of	ADP
ejpam-5311	143	14	x.	x.	NOUN
ejpam-5311	143	15	the	the	DET
ejpam-5311	143	16	following	follow	VERB
ejpam-5311	143	17	example	example	NOUN
ejpam-5311	143	18	shows	show	VERB
ejpam-5311	143	19	that	that	SCONJ
ejpam-5311	143	20	the	the	DET
ejpam-5311	143	21	converse	converse	NOUN
ejpam-5311	143	22	of	of	ADP
ejpam-5311	143	23	theorem	theorem	NOUN
ejpam-5311	143	24	5	5	NUM
ejpam-5311	143	25	is	be	AUX
ejpam-5311	143	26	not	not	PART
ejpam-5311	143	27	true	true	ADJ
ejpam-5311	143	28	in	in	ADP
ejpam-5311	143	29	general	general	ADJ
ejpam-5311	143	30	.	.	PUNCT
ejpam-5311	144	1	example	example	NOUN
ejpam-5311	145	1	3	3	NUM
ejpam-5311	145	2	.	.	X
ejpam-5311	145	3	from	from	ADP
ejpam-5311	145	4	the	the	DET
ejpam-5311	145	5	bcc	bcc	PROPN
ejpam-5311	145	6	-	-	PUNCT
ejpam-5311	145	7	algebra	algebra	PROPN
ejpam-5311	145	8	x	x	PUNCT
ejpam-5311	145	9	in	in	ADP
ejpam-5311	145	10	example	example	NOUN
ejpam-5311	145	11	2	2	NUM
ejpam-5311	145	12	,	,	PUNCT
ejpam-5311	145	13	define	define	VERB
ejpam-5311	145	14	a	a	DET
ejpam-5311	145	15	fuzzy	fuzzy	ADJ
ejpam-5311	145	16	set	set	VERB
ejpam-5311	145	17	µ	µ	NOUN
ejpam-5311	145	18	as	as	SCONJ
ejpam-5311	145	19	follows	follow	VERB
ejpam-5311	145	20	:	:	PUNCT
ejpam-5311	145	21	µ	µ	X
ejpam-5311	145	22	:	:	PUNCT
ejpam-5311	145	23	x	x	SYM
ejpam-5311	145	24	→	→	SYM
ejpam-5311	145	25	[	[	X
ejpam-5311	145	26	0	0	NUM
ejpam-5311	145	27	,	,	PUNCT
ejpam-5311	145	28	1];x	1];x	NUM
ejpam-5311	145	29	7→	7→	NUM
ejpam-5311	145	30			NUM
ejpam-5311	145	31	0.1	0.1	NUM
ejpam-5311	145	32	if	if	SCONJ
ejpam-5311	145	33	x	x	X
ejpam-5311	146	1	=	=	SYM
ejpam-5311	146	2	0	0	NUM
ejpam-5311	146	3	0	0	PUNCT
ejpam-5311	147	1	if	if	SCONJ
ejpam-5311	147	2	x	x	X
ejpam-5311	147	3	=	=	SYM
ejpam-5311	147	4	1	1	NUM
ejpam-5311	147	5	0.1	0.1	NUM
ejpam-5311	147	6	if	if	SCONJ
ejpam-5311	147	7	x	x	NOUN
ejpam-5311	147	8	=	=	SYM
ejpam-5311	147	9	2	2	NUM
ejpam-5311	147	10	0.1	0.1	NUM
ejpam-5311	147	11	if	if	SCONJ
ejpam-5311	147	12	x	x	SYM
ejpam-5311	147	13	=	=	SYM
ejpam-5311	147	14	3	3	NUM
ejpam-5311	147	15	given	give	VERB
ejpam-5311	147	16	ε	ε	PROPN
ejpam-5311	147	17	=	=	PUNCT
ejpam-5311	147	18	0.2	0.2	NUM
ejpam-5311	147	19	,	,	PUNCT
ejpam-5311	147	20	the	the	DET
ejpam-5311	147	21	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	147	22	fuzzy	fuzzy	NOUN
ejpam-5311	147	23	set	set	VERB
ejpam-5311	147	24	lε	lε	PRON
ejpam-5311	147	25	µ	µ	PROPN
ejpam-5311	147	26	of	of	ADP
ejpam-5311	147	27	µ	µ	NOUN
ejpam-5311	147	28	in	in	ADP
ejpam-5311	147	29	x	x	AUX
ejpam-5311	147	30	is	be	AUX
ejpam-5311	147	31	given	give	VERB
ejpam-5311	147	32	as	as	SCONJ
ejpam-5311	147	33	follows	follow	VERB
ejpam-5311	147	34	:	:	PUNCT
ejpam-5311	147	35	lε	lε	ADP
ejpam-5311	147	36	µ	µ	NOUN
ejpam-5311	147	37	:	:	PUNCT
ejpam-5311	147	38	x	x	SYM
ejpam-5311	147	39	→	→	SYM
ejpam-5311	148	1	[	[	X
ejpam-5311	148	2	0	0	NUM
ejpam-5311	148	3	,	,	PUNCT
ejpam-5311	148	4	1];x	1];x	NUM
ejpam-5311	148	5	7→	7→	NUM
ejpam-5311	148	6			NUM
ejpam-5311	148	7	0	0	NUM
ejpam-5311	149	1	if	if	SCONJ
ejpam-5311	149	2	x	x	X
ejpam-5311	149	3	=	=	NOUN
ejpam-5311	149	4	0	0	NUM
ejpam-5311	149	5	0	0	PUNCT
ejpam-5311	150	1	if	if	SCONJ
ejpam-5311	150	2	x	x	X
ejpam-5311	150	3	=	=	NOUN
ejpam-5311	150	4	1	1	NUM
ejpam-5311	150	5	0	0	NUM
ejpam-5311	150	6	if	if	SCONJ
ejpam-5311	150	7	x	x	X
ejpam-5311	150	8	=	=	SYM
ejpam-5311	150	9	2	2	NUM
ejpam-5311	150	10	0	0	NUM
ejpam-5311	150	11	if	if	SCONJ
ejpam-5311	150	12	x	x	PROPN
ejpam-5311	150	13	=	=	SYM
ejpam-5311	150	14	3	3	NUM
ejpam-5311	150	15	then	then	ADV
ejpam-5311	151	1	the	the	DET
ejpam-5311	151	2	q	q	NOUN
ejpam-5311	151	3	-	-	PUNCT
ejpam-5311	151	4	set	set	ADJ
ejpam-5311	151	5	(	(	PUNCT
ejpam-5311	151	6	lε	lε	X
ejpam-5311	151	7	µ	µ	NUM
ejpam-5311	151	8	,	,	PUNCT
ejpam-5311	151	9	t)q	t)q	PRON
ejpam-5311	151	10	of	of	ADP
ejpam-5311	151	11	lε	lε	ADP
ejpam-5311	151	12	µ	µ	X
ejpam-5311	151	13	with	with	ADP
ejpam-5311	151	14	value	value	NOUN
ejpam-5311	151	15	t	t	X
ejpam-5311	151	16	∈	∈	PROPN
ejpam-5311	151	17	(	(	PUNCT
ejpam-5311	151	18	0	0	NUM
ejpam-5311	151	19	,	,	PUNCT
ejpam-5311	151	20	1	1	NUM
ejpam-5311	151	21	]	]	PUNCT
ejpam-5311	151	22	is	be	AUX
ejpam-5311	151	23	empty	empty	ADJ
ejpam-5311	151	24	but	but	CCONJ
ejpam-5311	151	25	µ	µ	NOUN
ejpam-5311	151	26	is	be	AUX
ejpam-5311	151	27	not	not	PART
ejpam-5311	151	28	a	a	DET
ejpam-5311	151	29	fuzzy	fuzzy	ADJ
ejpam-5311	151	30	bccsubalgebra	bccsubalgebra	NOUN
ejpam-5311	151	31	of	of	ADP
ejpam-5311	151	32	x	x	PRON
ejpam-5311	151	33	because	because	SCONJ
ejpam-5311	151	34	µ(2	µ(2	PROPN
ejpam-5311	151	35	∗	∗	NOUN
ejpam-5311	151	36	3	3	NUM
ejpam-5311	151	37	)	)	PUNCT
ejpam-5311	152	1	=	=	PUNCT
ejpam-5311	152	2	µ(1	µ(1	PROPN
ejpam-5311	152	3	)	)	PUNCT
ejpam-5311	152	4	=	=	PUNCT
ejpam-5311	152	5	0	0	NUM
ejpam-5311	152	6	≱	≱	PROPN
ejpam-5311	152	7	0.1	0.1	NUM
ejpam-5311	152	8	=	=	SYM
ejpam-5311	152	9	min{µ(2	min{µ(2	ADJ
ejpam-5311	152	10	)	)	PUNCT
ejpam-5311	152	11	,	,	PUNCT
ejpam-5311	152	12	µ(3	µ(3	PROPN
ejpam-5311	152	13	)	)	PUNCT
ejpam-5311	152	14	}	}	PUNCT
ejpam-5311	152	15	.	.	PUNCT
ejpam-5311	153	1	theorem	theorem	VERB
ejpam-5311	153	2	6	6	NUM
ejpam-5311	153	3	.	.	PUNCT
ejpam-5311	154	1	let	let	VERB
ejpam-5311	154	2	µ	µ	X
ejpam-5311	154	3	be	be	AUX
ejpam-5311	154	4	a	a	DET
ejpam-5311	154	5	fuzzy	fuzzy	ADJ
ejpam-5311	154	6	set	set	NOUN
ejpam-5311	154	7	in	in	ADP
ejpam-5311	154	8	x.	x.	NOUN
ejpam-5311	154	9	for	for	ADP
ejpam-5311	154	10	an	an	DET
ejpam-5311	154	11	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	154	12	fuzzy	fuzzy	NOUN
ejpam-5311	154	13	set	set	VERB
ejpam-5311	154	14	lε	lε	PRON
ejpam-5311	154	15	µ	µ	PROPN
ejpam-5311	154	16	of	of	ADP
ejpam-5311	154	17	µ	µ	NOUN
ejpam-5311	154	18	in	in	ADP
ejpam-5311	154	19	x	x	SYM
ejpam-5311	154	20	,	,	PUNCT
ejpam-5311	154	21	if	if	SCONJ
ejpam-5311	154	22	the	the	DET
ejpam-5311	154	23	q	q	NOUN
ejpam-5311	154	24	-	-	PUNCT
ejpam-5311	154	25	set	set	ADJ
ejpam-5311	154	26	(	(	PUNCT
ejpam-5311	154	27	lε	lε	X
ejpam-5311	154	28	µ	µ	NUM
ejpam-5311	154	29	,	,	PUNCT
ejpam-5311	154	30	t)q	t)q	PUNCT
ejpam-5311	154	31	is	be	AUX
ejpam-5311	154	32	a	a	DET
ejpam-5311	154	33	bcc	bcc	NOUN
ejpam-5311	154	34	-	-	PUNCT
ejpam-5311	154	35	subalgebra	subalgebra	NOUN
ejpam-5311	154	36	of	of	ADP
ejpam-5311	154	37	x	x	PRON
ejpam-5311	154	38	,	,	PUNCT
ejpam-5311	154	39	then	then	ADV
ejpam-5311	154	40	lε	lε	X
ejpam-5311	154	41	µ	µ	PRON
ejpam-5311	154	42	satisfies	satisfy	VERB
ejpam-5311	154	43	the	the	DET
ejpam-5311	154	44	following	follow	VERB
ejpam-5311	154	45	property	property	NOUN
ejpam-5311	154	46	:	:	PUNCT
ejpam-5311	154	47	(	(	PUNCT
ejpam-5311	154	48	∀x	∀x	X
ejpam-5311	154	49	,	,	PUNCT
ejpam-5311	154	50	y	y	PROPN
ejpam-5311	154	51	∈	∈	PROPN
ejpam-5311	154	52	x,∀ta	x,∀ta	PROPN
ejpam-5311	154	53	,	,	PUNCT
ejpam-5311	154	54	tb	tb	ADP
ejpam-5311	154	55	∈	∈	PROPN
ejpam-5311	154	56	(	(	PUNCT
ejpam-5311	154	57	0	0	NUM
ejpam-5311	154	58	,	,	PUNCT
ejpam-5311	154	59	0.5	0.5	NUM
ejpam-5311	154	60	]	]	PUNCT
ejpam-5311	154	61	)	)	PUNCT
ejpam-5311	154	62	(	(	PUNCT
ejpam-5311	154	63	[	[	X
ejpam-5311	154	64	x	x	X
ejpam-5311	154	65	/	/	SYM
ejpam-5311	154	66	ta]qlε	ta]qlε	ADP
ejpam-5311	154	67	µ	µ	NOUN
ejpam-5311	154	68	,	,	PUNCT
ejpam-5311	154	69	[	[	X
ejpam-5311	154	70	y	y	X
ejpam-5311	154	71	/	/	SYM
ejpam-5311	154	72	tb]ql	tb]ql	NOUN
ejpam-5311	154	73	ε	ε	PROPN
ejpam-5311	154	74	µ	µ	PRON
ejpam-5311	154	75	⇒	⇒	NOUN
ejpam-5311	154	76	[	[	X
ejpam-5311	154	77	(	(	PUNCT
ejpam-5311	154	78	x	x	SYM
ejpam-5311	154	79	∗	∗	NOUN
ejpam-5311	154	80	y)/max{ta	y)/max{ta	NOUN
ejpam-5311	154	81	,	,	PUNCT
ejpam-5311	154	82	tb	tb	NOUN
ejpam-5311	154	83	}	}	PUNCT
ejpam-5311	154	84	]	]	PUNCT
ejpam-5311	154	85	∈	∈	PROPN
ejpam-5311	154	86	lε	lε	ADP
ejpam-5311	154	87	µ	µ	NOUN
ejpam-5311	154	88	)	)	PUNCT
ejpam-5311	154	89	(	(	PUNCT
ejpam-5311	154	90	3.9	3.9	NUM
ejpam-5311	154	91	)	)	PUNCT
ejpam-5311	154	92	proof	proof	NOUN
ejpam-5311	154	93	.	.	PUNCT
ejpam-5311	155	1	let	let	VERB
ejpam-5311	155	2	x	x	PRON
ejpam-5311	155	3	,	,	PUNCT
ejpam-5311	155	4	y	y	PROPN
ejpam-5311	155	5	∈	∈	PROPN
ejpam-5311	155	6	x	x	X
ejpam-5311	155	7	and	and	CCONJ
ejpam-5311	155	8	ta	ta	PROPN
ejpam-5311	155	9	,	,	PUNCT
ejpam-5311	155	10	tb	tb	ADP
ejpam-5311	155	11	∈	∈	PROPN
ejpam-5311	155	12	(	(	PUNCT
ejpam-5311	155	13	0	0	NUM
ejpam-5311	155	14	,	,	PUNCT
ejpam-5311	155	15	0.5	0.5	NUM
ejpam-5311	155	16	]	]	PUNCT
ejpam-5311	155	17	be	be	VERB
ejpam-5311	155	18	such	such	ADJ
ejpam-5311	156	1	that	that	SCONJ
ejpam-5311	156	2	[	[	X
ejpam-5311	156	3	x	x	X
ejpam-5311	156	4	/	/	SYM
ejpam-5311	156	5	ta]qlε	ta]qlε	ADP
ejpam-5311	156	6	µ	µ	NOUN
ejpam-5311	156	7	and	and	CCONJ
ejpam-5311	156	8	[	[	X
ejpam-5311	156	9	y	y	X
ejpam-5311	156	10	/	/	SYM
ejpam-5311	156	11	tb]ql	tb]ql	NOUN
ejpam-5311	156	12	ε	ε	PROPN
ejpam-5311	156	13	µ.	µ.	NOUN
ejpam-5311	156	14	then	then	ADV
ejpam-5311	156	15	x	x	SYM
ejpam-5311	156	16	∈	∈	PROPN
ejpam-5311	156	17	(	(	PUNCT
ejpam-5311	156	18	lε	lε	X
ejpam-5311	156	19	µ	µ	NOUN
ejpam-5311	156	20	,	,	PUNCT
ejpam-5311	156	21	ta)q	ta)q	NUM
ejpam-5311	156	22	⊆	⊆	NUM
ejpam-5311	156	23	(	(	PUNCT
ejpam-5311	156	24	lε	lε	X
ejpam-5311	156	25	µ,max{ta	µ,max{ta	PROPN
ejpam-5311	156	26	,	,	PUNCT
ejpam-5311	156	27	tb})q	tb})q	PROPN
ejpam-5311	156	28	and	and	CCONJ
ejpam-5311	156	29	y	y	PROPN
ejpam-5311	156	30	∈	∈	PROPN
ejpam-5311	156	31	(	(	PUNCT
ejpam-5311	156	32	lε	lε	ADP
ejpam-5311	156	33	µ	µ	NOUN
ejpam-5311	156	34	,	,	PUNCT
ejpam-5311	156	35	tb)q	tb)q	PROPN
ejpam-5311	156	36	⊆	⊆	NUM
ejpam-5311	156	37	(	(	PUNCT
ejpam-5311	156	38	lε	lε	X
ejpam-5311	156	39	µ,max{ta	µ,max{ta	PROPN
ejpam-5311	156	40	,	,	PUNCT
ejpam-5311	156	41	tb})q	tb})q	PROPN
ejpam-5311	156	42	.	.	PUNCT
ejpam-5311	157	1	thus	thus	ADV
ejpam-5311	157	2	,	,	PUNCT
ejpam-5311	157	3	x	x	PUNCT
ejpam-5311	157	4	∗	∗	NOUN
ejpam-5311	157	5	y	y	PROPN
ejpam-5311	157	6	∈	∈	PROPN
ejpam-5311	157	7	(	(	PUNCT
ejpam-5311	157	8	lε	lε	X
ejpam-5311	157	9	µ,max{ta	µ,max{ta	PROPN
ejpam-5311	157	10	,	,	PUNCT
ejpam-5311	157	11	tb})q	tb})q	PROPN
ejpam-5311	157	12	.	.	PUNCT
ejpam-5311	158	1	since	since	SCONJ
ejpam-5311	158	2	max{ta	max{ta	NOUN
ejpam-5311	158	3	,	,	PUNCT
ejpam-5311	158	4	tb	tb	NOUN
ejpam-5311	158	5	}	}	PUNCT
ejpam-5311	158	6	≤	≤	NUM
ejpam-5311	158	7	0.5	0.5	NUM
ejpam-5311	158	8	,	,	PUNCT
ejpam-5311	158	9	we	we	PRON
ejpam-5311	158	10	have	have	VERB
ejpam-5311	158	11	lε	lε	ADP
ejpam-5311	158	12	µ(x	µ(x	ADJ
ejpam-5311	158	13	∗	∗	NOUN
ejpam-5311	158	14	y	y	NOUN
ejpam-5311	158	15	)	)	PUNCT
ejpam-5311	158	16	>	>	X
ejpam-5311	159	1	1	1	NUM
ejpam-5311	159	2	−	−	NOUN
ejpam-5311	159	3	max{ta	max{ta	NOUN
ejpam-5311	159	4	,	,	PUNCT
ejpam-5311	159	5	tb	tb	NOUN
ejpam-5311	159	6	}	}	PUNCT
ejpam-5311	159	7	≥	≥	X
ejpam-5311	159	8	max{ta	max{ta	NOUN
ejpam-5311	159	9	,	,	PUNCT
ejpam-5311	159	10	tb	tb	NOUN
ejpam-5311	159	11	}	}	PUNCT
ejpam-5311	159	12	.	.	PUNCT
ejpam-5311	160	1	hence	hence	ADV
ejpam-5311	160	2	,	,	PUNCT
ejpam-5311	160	3	[	[	X
ejpam-5311	160	4	(	(	PUNCT
ejpam-5311	160	5	x	x	NOUN
ejpam-5311	160	6	∗	∗	NOUN
ejpam-5311	160	7	y)/max{ta	y)/max{ta	NOUN
ejpam-5311	160	8	,	,	PUNCT
ejpam-5311	160	9	tb	tb	NOUN
ejpam-5311	160	10	}	}	PUNCT
ejpam-5311	160	11	]	]	PUNCT
ejpam-5311	161	1	∈	∈	PROPN
ejpam-5311	161	2	lε	lε	AUX
ejpam-5311	161	3	µ.	µ.	NOUN
ejpam-5311	161	4	let	let	VERB
ejpam-5311	161	5	µ	µ	X
ejpam-5311	161	6	be	be	AUX
ejpam-5311	161	7	a	a	DET
ejpam-5311	161	8	fuzzy	fuzzy	ADJ
ejpam-5311	161	9	set	set	NOUN
ejpam-5311	161	10	in	in	ADP
ejpam-5311	161	11	x.	x.	NOUN
ejpam-5311	161	12	for	for	ADP
ejpam-5311	161	13	an	an	DET
ejpam-5311	161	14	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	161	15	fuzzy	fuzzy	NOUN
ejpam-5311	161	16	set	set	VERB
ejpam-5311	161	17	lε	lε	PRON
ejpam-5311	161	18	µ	µ	PROPN
ejpam-5311	161	19	of	of	ADP
ejpam-5311	161	20	µ	µ	NOUN
ejpam-5311	161	21	in	in	ADP
ejpam-5311	161	22	x	x	X
ejpam-5311	161	23	,	,	PUNCT
ejpam-5311	161	24	consider	consider	VERB
ejpam-5311	161	25	the	the	DET
ejpam-5311	161	26	set	set	NOUN
ejpam-5311	161	27	:	:	PUNCT
ejpam-5311	161	28	o(lε	o(lε	PROPN
ejpam-5311	161	29	µ	µ	X
ejpam-5311	161	30	)	)	PUNCT
ejpam-5311	161	31	=	=	PRON
ejpam-5311	161	32	{	{	PUNCT
ejpam-5311	161	33	x	x	PUNCT
ejpam-5311	161	34	∈	∈	PROPN
ejpam-5311	161	35	x	x	X
ejpam-5311	161	36	:	:	PUNCT
ejpam-5311	161	37	lε	lε	X
ejpam-5311	161	38	µ(x	µ(x	NOUN
ejpam-5311	161	39	)	)	PUNCT
ejpam-5311	161	40	>	>	X
ejpam-5311	161	41	0	0	NUM
ejpam-5311	161	42	}	}	PUNCT
ejpam-5311	161	43	,	,	PUNCT
ejpam-5311	161	44	which	which	PRON
ejpam-5311	161	45	is	be	AUX
ejpam-5311	161	46	called	call	VERB
ejpam-5311	161	47	the	the	DET
ejpam-5311	161	48	o	o	NOUN
ejpam-5311	161	49	-	-	NOUN
ejpam-5311	161	50	set	set	NOUN
ejpam-5311	161	51	of	of	ADP
ejpam-5311	161	52	lε	lε	INTJ
ejpam-5311	161	53	µ.	µ.	PROPN
ejpam-5311	161	54	it	it	PRON
ejpam-5311	161	55	is	be	AUX
ejpam-5311	161	56	observed	observe	VERB
ejpam-5311	161	57	that	that	SCONJ
ejpam-5311	161	58	o(lε	o(lε	PROPN
ejpam-5311	161	59	µ	µ	X
ejpam-5311	161	60	)	)	PUNCT
ejpam-5311	161	61	=	=	PRON
ejpam-5311	161	62	{	{	PUNCT
ejpam-5311	161	63	x	x	PUNCT
ejpam-5311	161	64	∈	∈	NOUN
ejpam-5311	161	65	x	x	X
ejpam-5311	161	66	:	:	PUNCT
ejpam-5311	161	67	µ(x	µ(x	X
ejpam-5311	161	68	)	)	PUNCT
ejpam-5311	161	69	+	+	CCONJ
ejpam-5311	161	70	ε−	ε−	PROPN
ejpam-5311	161	71	1	1	NUM
ejpam-5311	161	72	>	>	PUNCT
ejpam-5311	161	73	0	0	NUM
ejpam-5311	161	74	}	}	PUNCT
ejpam-5311	161	75	.	.	PUNCT
ejpam-5311	162	1	theorem	theorem	VERB
ejpam-5311	162	2	7	7	NUM
ejpam-5311	162	3	.	.	PUNCT
ejpam-5311	163	1	let	let	VERB
ejpam-5311	163	2	lε	lε	PART
ejpam-5311	163	3	µ	µ	X
ejpam-5311	163	4	be	be	AUX
ejpam-5311	163	5	an	an	DET
ejpam-5311	163	6	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	163	7	fuzzy	fuzzy	ADJ
ejpam-5311	163	8	set	set	NOUN
ejpam-5311	163	9	of	of	ADP
ejpam-5311	163	10	a	a	DET
ejpam-5311	163	11	fuzzy	fuzzy	ADJ
ejpam-5311	163	12	set	set	VERB
ejpam-5311	163	13	µ	µ	NOUN
ejpam-5311	163	14	in	in	ADP
ejpam-5311	163	15	x.	x.	NOUN
ejpam-5311	163	16	if	if	SCONJ
ejpam-5311	163	17	µ	µ	PRON
ejpam-5311	163	18	is	be	AUX
ejpam-5311	163	19	a	a	DET
ejpam-5311	163	20	fuzzy	fuzzy	ADJ
ejpam-5311	163	21	bcc	bcc	NOUN
ejpam-5311	163	22	-	-	PUNCT
ejpam-5311	163	23	subalgebra	subalgebra	NOUN
ejpam-5311	163	24	of	of	ADP
ejpam-5311	163	25	x	x	PRON
ejpam-5311	163	26	,	,	PUNCT
ejpam-5311	163	27	then	then	ADV
ejpam-5311	163	28	the	the	DET
ejpam-5311	163	29	nonempty	nonempty	ADJ
ejpam-5311	163	30	o	o	NOUN
ejpam-5311	163	31	-	-	ADJ
ejpam-5311	163	32	set	set	VERB
ejpam-5311	163	33	o(lε	o(lε	PROPN
ejpam-5311	163	34	µ	µ	NOUN
ejpam-5311	163	35	)	)	PUNCT
ejpam-5311	163	36	of	of	ADP
ejpam-5311	163	37	lε	lε	PRON
ejpam-5311	163	38	µ	µ	PROPN
ejpam-5311	163	39	is	be	AUX
ejpam-5311	163	40	a	a	DET
ejpam-5311	163	41	bcc	bcc	PROPN
ejpam-5311	163	42	-	-	PUNCT
ejpam-5311	163	43	subalgebra	subalgebra	NOUN
ejpam-5311	163	44	of	of	ADP
ejpam-5311	163	45	x.	x.	NOUN
ejpam-5311	163	46	proof	proof	NOUN
ejpam-5311	163	47	.	.	PUNCT
ejpam-5311	164	1	let	let	VERB
ejpam-5311	164	2	x	x	PRON
ejpam-5311	164	3	,	,	PUNCT
ejpam-5311	164	4	y	y	PROPN
ejpam-5311	164	5	∈	∈	PROPN
ejpam-5311	164	6	o(lε	o(lε	PROPN
ejpam-5311	164	7	µ	µ	NOUN
ejpam-5311	164	8	)	)	PUNCT
ejpam-5311	164	9	.	.	PUNCT
ejpam-5311	165	1	then	then	ADV
ejpam-5311	165	2	µ(x	µ(x	NOUN
ejpam-5311	165	3	)	)	PUNCT
ejpam-5311	165	4	+	+	CCONJ
ejpam-5311	165	5	ε	ε	PROPN
ejpam-5311	165	6	−	−	PROPN
ejpam-5311	165	7	1	1	NUM
ejpam-5311	165	8	>	>	SYM
ejpam-5311	165	9	0	0	NUM
ejpam-5311	165	10	and	and	CCONJ
ejpam-5311	165	11	µ(y	µ(y	NUM
ejpam-5311	165	12	)	)	PUNCT
ejpam-5311	166	1	+	+	CCONJ
ejpam-5311	166	2	ε	ε	PROPN
ejpam-5311	166	3	−	−	PROPN
ejpam-5311	166	4	1	1	NUM
ejpam-5311	166	5	>	>	X
ejpam-5311	166	6	0	0	X
ejpam-5311	166	7	.	.	PUNCT
ejpam-5311	167	1	if	if	SCONJ
ejpam-5311	167	2	µ	µ	NOUN
ejpam-5311	167	3	is	be	AUX
ejpam-5311	167	4	a	a	DET
ejpam-5311	167	5	fuzzy	fuzzy	ADJ
ejpam-5311	167	6	bcc	bcc	NOUN
ejpam-5311	167	7	-	-	PUNCT
ejpam-5311	167	8	subalgebra	subalgebra	NOUN
ejpam-5311	167	9	of	of	ADP
ejpam-5311	167	10	x	x	PRON
ejpam-5311	167	11	,	,	PUNCT
ejpam-5311	167	12	then	then	ADV
ejpam-5311	167	13	lε	lε	PROPN
ejpam-5311	167	14	µ	µ	PROPN
ejpam-5311	167	15	is	be	AUX
ejpam-5311	167	16	an	an	DET
ejpam-5311	167	17	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	167	18	fuzzy	fuzzy	ADJ
ejpam-5311	167	19	bcc	bcc	PROPN
ejpam-5311	167	20	-	-	PUNCT
ejpam-5311	167	21	subalgebra	subalgebra	NOUN
ejpam-5311	167	22	of	of	ADP
ejpam-5311	167	23	x	x	PUNCT
ejpam-5311	167	24	by	by	ADP
ejpam-5311	167	25	theorem	theorem	NOUN
ejpam-5311	167	26	1	1	NUM
ejpam-5311	167	27	.	.	PUNCT
ejpam-5311	168	1	it	it	PRON
ejpam-5311	168	2	follows	follow	VERB
ejpam-5311	168	3	from	from	ADP
ejpam-5311	168	4	theorem	theorem	ADJ
ejpam-5311	168	5	2	2	NUM
ejpam-5311	168	6	that	that	PRON
ejpam-5311	168	7	lε	lε	ADP
ejpam-5311	168	8	µ(x	µ(x	PROPN
ejpam-5311	168	9	∗	∗	NOUN
ejpam-5311	168	10	y	y	NOUN
ejpam-5311	168	11	)	)	PUNCT
ejpam-5311	168	12	≥	≥	PROPN
ejpam-5311	168	13	min{lε	min{lε	NUM
ejpam-5311	168	14	µ(x	µ(x	PROPN
ejpam-5311	168	15	)	)	PUNCT
ejpam-5311	168	16	,	,	PUNCT
ejpam-5311	168	17	lε	lε	X
ejpam-5311	168	18	µ(y	µ(y	PROPN
ejpam-5311	168	19	)	)	PUNCT
ejpam-5311	168	20	}	}	PUNCT
ejpam-5311	168	21	=	=	SYM
ejpam-5311	168	22	min{µ(x	min{µ(x	NOUN
ejpam-5311	168	23	)	)	PUNCT
ejpam-5311	169	1	+	+	CCONJ
ejpam-5311	169	2	ε	ε	PROPN
ejpam-5311	169	3	−	−	PROPN
ejpam-5311	169	4	1	1	NUM
ejpam-5311	169	5	,	,	PUNCT
ejpam-5311	169	6	µ(y	µ(y	PROPN
ejpam-5311	169	7	)	)	PUNCT
ejpam-5311	170	1	+	+	CCONJ
ejpam-5311	170	2	ε	ε	PROPN
ejpam-5311	170	3	−	−	NOUN
ejpam-5311	170	4	1	1	NUM
ejpam-5311	170	5	}	}	PUNCT
ejpam-5311	170	6	>	>	X
ejpam-5311	170	7	0	0	X
ejpam-5311	170	8	.	.	PUNCT
ejpam-5311	171	1	thus	thus	ADV
ejpam-5311	171	2	,	,	PUNCT
ejpam-5311	171	3	x	x	PUNCT
ejpam-5311	171	4	∗	∗	NOUN
ejpam-5311	171	5	y	y	PROPN
ejpam-5311	171	6	∈	∈	PROPN
ejpam-5311	171	7	o(lε	o(lε	PROPN
ejpam-5311	171	8	µ	µ	NOUN
ejpam-5311	171	9	)	)	PUNCT
ejpam-5311	171	10	.	.	PUNCT
ejpam-5311	172	1	hence	hence	ADV
ejpam-5311	172	2	,	,	PUNCT
ejpam-5311	172	3	o(lε	o(lε	PROPN
ejpam-5311	172	4	µ	µ	NOUN
ejpam-5311	172	5	)	)	PUNCT
ejpam-5311	172	6	is	be	AUX
ejpam-5311	172	7	a	a	DET
ejpam-5311	172	8	bccsubalgebra	bccsubalgebra	NOUN
ejpam-5311	172	9	of	of	ADP
ejpam-5311	172	10	x.	x.	PROPN
ejpam-5311	172	11	a.	a.	PROPN
ejpam-5311	172	12	iampan	iampan	PROPN
ejpam-5311	172	13	,	,	PUNCT
ejpam-5311	172	14	r.	r.	PROPN
ejpam-5311	172	15	subasini	subasini	PROPN
ejpam-5311	172	16	,	,	PUNCT
ejpam-5311	172	17	n.	n.	PROPN
ejpam-5311	172	18	rajesh	rajesh	PROPN
ejpam-5311	172	19	/	/	SYM
ejpam-5311	172	20	eur	eur	PROPN
ejpam-5311	172	21	.	.	PUNCT
ejpam-5311	173	1	j.	j.	PROPN
ejpam-5311	173	2	pure	pure	PROPN
ejpam-5311	173	3	appl	appl	PROPN
ejpam-5311	173	4	.	.	PROPN
ejpam-5311	173	5	math	math	PROPN
ejpam-5311	173	6	,	,	PUNCT
ejpam-5311	173	7	17	17	NUM
ejpam-5311	173	8	(	(	PUNCT
ejpam-5311	173	9	3	3	NUM
ejpam-5311	173	10	)	)	PUNCT
ejpam-5311	173	11	(	(	PUNCT
ejpam-5311	173	12	2024	2024	NUM
ejpam-5311	173	13	)	)	PUNCT
ejpam-5311	173	14	,	,	PUNCT
ejpam-5311	173	15	2235	2235	NUM
ejpam-5311	173	16	-	-	SYM
ejpam-5311	173	17	2245	2245	NUM
ejpam-5311	173	18	2243	2243	NUM
ejpam-5311	173	19	theorem	theorem	VERB
ejpam-5311	173	20	8	8	NUM
ejpam-5311	173	21	.	.	PUNCT
ejpam-5311	174	1	let	let	VERB
ejpam-5311	174	2	µ	µ	X
ejpam-5311	174	3	be	be	AUX
ejpam-5311	174	4	a	a	DET
ejpam-5311	174	5	fuzzy	fuzzy	ADJ
ejpam-5311	174	6	set	set	NOUN
ejpam-5311	174	7	in	in	ADP
ejpam-5311	174	8	x.	x.	NOUN
ejpam-5311	174	9	if	if	SCONJ
ejpam-5311	174	10	an	an	DET
ejpam-5311	174	11	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	174	12	fuzzy	fuzzy	ADJ
ejpam-5311	174	13	set	set	VERB
ejpam-5311	174	14	lε	lε	PRON
ejpam-5311	174	15	µ	µ	PROPN
ejpam-5311	174	16	of	of	ADP
ejpam-5311	174	17	µ	µ	NOUN
ejpam-5311	174	18	in	in	ADP
ejpam-5311	174	19	x	x	PART
ejpam-5311	174	20	satisfies	satisfie	NOUN
ejpam-5311	174	21	the	the	DET
ejpam-5311	174	22	following	follow	VERB
ejpam-5311	174	23	property	property	NOUN
ejpam-5311	174	24	:	:	PUNCT
ejpam-5311	175	1	[	[	X
ejpam-5311	175	2	x	x	X
ejpam-5311	175	3	/	/	SYM
ejpam-5311	175	4	ta	ta	X
ejpam-5311	175	5	]	]	X
ejpam-5311	175	6	∈	∈	PROPN
ejpam-5311	175	7	lε	lε	ADP
ejpam-5311	175	8	µ	µ	NOUN
ejpam-5311	175	9	,	,	PUNCT
ejpam-5311	175	10	[	[	X
ejpam-5311	175	11	y	y	X
ejpam-5311	175	12	/	/	SYM
ejpam-5311	175	13	tb	tb	NOUN
ejpam-5311	175	14	]	]	PUNCT
ejpam-5311	175	15	∈	∈	PROPN
ejpam-5311	175	16	lε	lε	X
ejpam-5311	175	17	µ	µ	X
ejpam-5311	175	18	⇒	⇒	NOUN
ejpam-5311	175	19	[	[	X
ejpam-5311	175	20	(	(	PUNCT
ejpam-5311	175	21	x	x	SYM
ejpam-5311	175	22	∗	∗	NOUN
ejpam-5311	175	23	y)/max{ta	y)/max{ta	NOUN
ejpam-5311	175	24	,	,	PUNCT
ejpam-5311	175	25	tb}]qlε	tb}]qlε	NOUN
ejpam-5311	175	26	µ	µ	NOUN
ejpam-5311	175	27	(	(	PUNCT
ejpam-5311	175	28	3.10	3.10	NUM
ejpam-5311	175	29	)	)	PUNCT
ejpam-5311	175	30	for	for	ADP
ejpam-5311	175	31	all	all	DET
ejpam-5311	175	32	x	x	NOUN
ejpam-5311	175	33	,	,	PUNCT
ejpam-5311	175	34	y	y	PROPN
ejpam-5311	175	35	∈	∈	PROPN
ejpam-5311	175	36	x	x	X
ejpam-5311	175	37	and	and	CCONJ
ejpam-5311	175	38	ta	ta	PROPN
ejpam-5311	175	39	,	,	PUNCT
ejpam-5311	175	40	tb	tb	ADP
ejpam-5311	175	41	∈	∈	PROPN
ejpam-5311	175	42	(	(	PUNCT
ejpam-5311	175	43	0	0	NUM
ejpam-5311	175	44	,	,	PUNCT
ejpam-5311	175	45	1	1	NUM
ejpam-5311	175	46	]	]	PUNCT
ejpam-5311	175	47	,	,	PUNCT
ejpam-5311	175	48	then	then	ADV
ejpam-5311	175	49	the	the	DET
ejpam-5311	175	50	nonempty	nonempty	ADJ
ejpam-5311	175	51	o	o	NOUN
ejpam-5311	175	52	-	-	ADJ
ejpam-5311	175	53	set	set	VERB
ejpam-5311	175	54	o(lε	o(lε	PROPN
ejpam-5311	175	55	µ	µ	NOUN
ejpam-5311	175	56	)	)	PUNCT
ejpam-5311	175	57	of	of	ADP
ejpam-5311	175	58	lε	lε	PRON
ejpam-5311	175	59	µ	µ	PROPN
ejpam-5311	175	60	is	be	AUX
ejpam-5311	175	61	a	a	DET
ejpam-5311	175	62	bccsubalgebra	bccsubalgebra	NOUN
ejpam-5311	175	63	of	of	ADP
ejpam-5311	175	64	x.	x.	NOUN
ejpam-5311	175	65	proof	proof	PROPN
ejpam-5311	175	66	.	.	PUNCT
ejpam-5311	176	1	assume	assume	VERB
ejpam-5311	176	2	that	that	SCONJ
ejpam-5311	176	3	lε	lε	PART
ejpam-5311	176	4	µ	µ	PRON
ejpam-5311	176	5	satisfies	satisfy	VERB
ejpam-5311	176	6	the	the	DET
ejpam-5311	176	7	condition	condition	NOUN
ejpam-5311	176	8	(	(	PUNCT
ejpam-5311	176	9	3.10	3.10	NUM
ejpam-5311	176	10	)	)	PUNCT
ejpam-5311	176	11	for	for	ADP
ejpam-5311	176	12	all	all	DET
ejpam-5311	176	13	x	x	NOUN
ejpam-5311	176	14	,	,	PUNCT
ejpam-5311	176	15	y	y	PROPN
ejpam-5311	176	16	∈	∈	PROPN
ejpam-5311	176	17	x	x	X
ejpam-5311	176	18	and	and	CCONJ
ejpam-5311	176	19	ta	ta	PROPN
ejpam-5311	176	20	,	,	PUNCT
ejpam-5311	176	21	tb	tb	ADP
ejpam-5311	176	22	∈	∈	PROPN
ejpam-5311	176	23	(	(	PUNCT
ejpam-5311	176	24	0	0	NUM
ejpam-5311	176	25	,	,	PUNCT
ejpam-5311	176	26	1	1	NUM
ejpam-5311	176	27	]	]	PUNCT
ejpam-5311	176	28	.	.	PUNCT
ejpam-5311	177	1	let	let	VERB
ejpam-5311	177	2	x	x	PRON
ejpam-5311	177	3	,	,	PUNCT
ejpam-5311	177	4	y	y	PROPN
ejpam-5311	177	5	∈	∈	PROPN
ejpam-5311	177	6	o(lε	o(lε	PROPN
ejpam-5311	177	7	µ	µ	NOUN
ejpam-5311	177	8	)	)	PUNCT
ejpam-5311	177	9	.	.	PUNCT
ejpam-5311	178	1	then	then	ADV
ejpam-5311	178	2	µ(x	µ(x	NOUN
ejpam-5311	178	3	)	)	PUNCT
ejpam-5311	178	4	+	+	CCONJ
ejpam-5311	178	5	ε−	ε−	PROPN
ejpam-5311	178	6	1	1	NUM
ejpam-5311	178	7	>	>	SYM
ejpam-5311	178	8	0	0	NUM
ejpam-5311	178	9	and	and	CCONJ
ejpam-5311	178	10	µ(y	µ(y	NUM
ejpam-5311	178	11	)	)	PUNCT
ejpam-5311	178	12	+	+	CCONJ
ejpam-5311	178	13	ε−	ε−	PROPN
ejpam-5311	178	14	1	1	NUM
ejpam-5311	178	15	>	>	X
ejpam-5311	178	16	0	0	X
ejpam-5311	178	17	.	.	PUNCT
ejpam-5311	179	1	since	since	SCONJ
ejpam-5311	179	2	[	[	X
ejpam-5311	179	3	x	x	X
ejpam-5311	179	4	/	/	X
ejpam-5311	179	5	lε	lε	X
ejpam-5311	179	6	µ(x	µ(x	NOUN
ejpam-5311	179	7	)	)	PUNCT
ejpam-5311	179	8	]	]	PUNCT
ejpam-5311	179	9	∈	∈	PROPN
ejpam-5311	179	10	lε	lε	ADP
ejpam-5311	179	11	µ	µ	NOUN
ejpam-5311	179	12	and	and	CCONJ
ejpam-5311	179	13	[	[	X
ejpam-5311	179	14	y	y	X
ejpam-5311	179	15	/	/	SYM
ejpam-5311	179	16	lε	lε	X
ejpam-5311	179	17	µ(y	µ(y	PROPN
ejpam-5311	179	18	)	)	PUNCT
ejpam-5311	179	19	]	]	PUNCT
ejpam-5311	179	20	∈	∈	PROPN
ejpam-5311	179	21	lε	lε	ADP
ejpam-5311	179	22	µ	µ	NUM
ejpam-5311	179	23	,	,	PUNCT
ejpam-5311	179	24	it	it	PRON
ejpam-5311	179	25	follows	follow	VERB
ejpam-5311	179	26	from	from	ADP
ejpam-5311	179	27	(	(	PUNCT
ejpam-5311	179	28	3.10	3.10	NUM
ejpam-5311	179	29	)	)	PUNCT
ejpam-5311	179	30	that	that	SCONJ
ejpam-5311	180	1	[	[	X
ejpam-5311	180	2	(	(	PUNCT
ejpam-5311	180	3	x	x	SYM
ejpam-5311	180	4	∗	∗	NOUN
ejpam-5311	180	5	y)/max{lε	y)/max{lε	NOUN
ejpam-5311	180	6	µ(x	µ(x	VERB
ejpam-5311	180	7	∗	∗	NOUN
ejpam-5311	180	8	(	(	PUNCT
ejpam-5311	180	9	y	y	PROPN
ejpam-5311	180	10	∗	∗	PROPN
ejpam-5311	180	11	z	z	PROPN
ejpam-5311	180	12	)	)	PUNCT
ejpam-5311	180	13	)	)	PUNCT
ejpam-5311	180	14	,	,	PUNCT
ejpam-5311	180	15	lε	lε	ADP
ejpam-5311	180	16	µ(y)}]qlε	µ(y)}]qlε	VERB
ejpam-5311	180	17	µ.	µ.	NOUN
ejpam-5311	180	18	(	(	PUNCT
ejpam-5311	180	19	3.11	3.11	NUM
ejpam-5311	180	20	)	)	PUNCT
ejpam-5311	180	21	if	if	SCONJ
ejpam-5311	180	22	x	x	PROPN
ejpam-5311	180	23	∗	∗	VERB
ejpam-5311	180	24	y	y	PROPN
ejpam-5311	180	25	/∈	/∈	PROPN
ejpam-5311	180	26	o(lε	o(lε	PROPN
ejpam-5311	180	27	µ	µ	X
ejpam-5311	180	28	)	)	PUNCT
ejpam-5311	180	29	,	,	PUNCT
ejpam-5311	180	30	then	then	ADV
ejpam-5311	180	31	lε	lε	ADP
ejpam-5311	180	32	µ(x	µ(x	ADJ
ejpam-5311	180	33	∗	∗	NOUN
ejpam-5311	180	34	y	y	NOUN
ejpam-5311	180	35	)	)	PUNCT
ejpam-5311	180	36	=	=	SYM
ejpam-5311	181	1	0	0	X
ejpam-5311	181	2	.	.	PUNCT
ejpam-5311	182	1	thus	thus	ADV
ejpam-5311	182	2	,	,	PUNCT
ejpam-5311	182	3	lε	lε	ADP
ejpam-5311	182	4	µ(x	µ(x	PROPN
ejpam-5311	182	5	∗	∗	NOUN
ejpam-5311	182	6	y	y	NOUN
ejpam-5311	182	7	)	)	PUNCT
ejpam-5311	183	1	+	+	CCONJ
ejpam-5311	183	2	max{lε	max{lε	PUNCT
ejpam-5311	183	3	µ(x	µ(x	NOUN
ejpam-5311	183	4	)	)	PUNCT
ejpam-5311	183	5	,	,	PUNCT
ejpam-5311	183	6	lε	lε	X
ejpam-5311	183	7	µ(y	µ(y	PROPN
ejpam-5311	183	8	)	)	PUNCT
ejpam-5311	183	9	}	}	PUNCT
ejpam-5311	183	10	=	=	SYM
ejpam-5311	183	11	max{lε	max{lε	NOUN
ejpam-5311	183	12	µ(x	µ(x	NOUN
ejpam-5311	183	13	)	)	PUNCT
ejpam-5311	183	14	,	,	PUNCT
ejpam-5311	183	15	lε	lε	X
ejpam-5311	183	16	µ(y	µ(y	PROPN
ejpam-5311	183	17	)	)	PUNCT
ejpam-5311	183	18	}	}	PUNCT
ejpam-5311	183	19	=	=	SYM
ejpam-5311	183	20	max{max{0	max{max{0	NOUN
ejpam-5311	183	21	,	,	PUNCT
ejpam-5311	183	22	µ(x	µ(x	X
ejpam-5311	183	23	)	)	PUNCT
ejpam-5311	183	24	+	+	CCONJ
ejpam-5311	183	25	ε−	ε−	PROPN
ejpam-5311	183	26	1},max{0	1},max{0	NUM
ejpam-5311	183	27	,	,	PUNCT
ejpam-5311	183	28	µ(y	µ(y	PROPN
ejpam-5311	183	29	)	)	PUNCT
ejpam-5311	183	30	+	+	CCONJ
ejpam-5311	183	31	ε−	ε−	PROPN
ejpam-5311	183	32	1	1	NUM
ejpam-5311	183	33	}	}	PUNCT
ejpam-5311	183	34	}	}	PUNCT
ejpam-5311	183	35	=	=	SYM
ejpam-5311	183	36	max{µ(x	max{µ(x	PROPN
ejpam-5311	183	37	)	)	PUNCT
ejpam-5311	183	38	+	+	CCONJ
ejpam-5311	183	39	ε−	ε−	PROPN
ejpam-5311	183	40	1	1	NUM
ejpam-5311	183	41	,	,	PUNCT
ejpam-5311	183	42	µ(y	µ(y	PROPN
ejpam-5311	183	43	)	)	PUNCT
ejpam-5311	183	44	+	+	CCONJ
ejpam-5311	183	45	ε−	ε−	PROPN
ejpam-5311	183	46	1	1	NUM
ejpam-5311	183	47	}	}	PUNCT
ejpam-5311	183	48	=	=	SYM
ejpam-5311	183	49	max{µ(x	max{µ(x	PROPN
ejpam-5311	183	50	)	)	PUNCT
ejpam-5311	183	51	,	,	PUNCT
ejpam-5311	183	52	µ(y	µ(y	PROPN
ejpam-5311	183	53	)	)	PUNCT
ejpam-5311	183	54	}	}	PUNCT
ejpam-5311	183	55	+	+	CCONJ
ejpam-5311	183	56	ε−	ε−	PROPN
ejpam-5311	183	57	1	1	NUM
ejpam-5311	183	58	≤	≤	NUM
ejpam-5311	183	59	1	1	NUM
ejpam-5311	183	60	+	+	CCONJ
ejpam-5311	183	61	ε−	ε−	PROPN
ejpam-5311	183	62	1	1	NUM
ejpam-5311	183	63	=	=	SYM
ejpam-5311	183	64	ε	ε	PROPN
ejpam-5311	183	65	≤	≤	ADJ
ejpam-5311	183	66	1	1	NUM
ejpam-5311	183	67	,	,	PUNCT
ejpam-5311	183	68	which	which	PRON
ejpam-5311	183	69	shows	show	VERB
ejpam-5311	183	70	that	that	SCONJ
ejpam-5311	183	71	(	(	PUNCT
ejpam-5311	183	72	3.11	3.11	NUM
ejpam-5311	183	73	)	)	PUNCT
ejpam-5311	183	74	is	be	AUX
ejpam-5311	183	75	not	not	PART
ejpam-5311	183	76	valid	valid	ADJ
ejpam-5311	183	77	.	.	PUNCT
ejpam-5311	184	1	this	this	PRON
ejpam-5311	184	2	is	be	AUX
ejpam-5311	184	3	a	a	DET
ejpam-5311	184	4	contradiction	contradiction	NOUN
ejpam-5311	184	5	.	.	PUNCT
ejpam-5311	185	1	hence	hence	ADV
ejpam-5311	185	2	,	,	PUNCT
ejpam-5311	185	3	x	x	PROPN
ejpam-5311	185	4	∗	∗	NOUN
ejpam-5311	185	5	y	y	PROPN
ejpam-5311	185	6	∈	∈	PROPN
ejpam-5311	185	7	o(lε	o(lε	PROPN
ejpam-5311	185	8	µ	µ	NOUN
ejpam-5311	185	9	)	)	PUNCT
ejpam-5311	185	10	.	.	PUNCT
ejpam-5311	186	1	therefore	therefore	ADV
ejpam-5311	186	2	,	,	PUNCT
ejpam-5311	186	3	o(lε	o(lε	PROPN
ejpam-5311	186	4	µ	µ	NOUN
ejpam-5311	186	5	)	)	PUNCT
ejpam-5311	186	6	is	be	AUX
ejpam-5311	186	7	a	a	DET
ejpam-5311	186	8	bcc	bcc	PROPN
ejpam-5311	186	9	-	-	PUNCT
ejpam-5311	186	10	subalgebra	subalgebra	NOUN
ejpam-5311	186	11	of	of	ADP
ejpam-5311	186	12	x.	x.	NOUN
ejpam-5311	186	13	theorem	theorem	VERB
ejpam-5311	186	14	9	9	NUM
ejpam-5311	186	15	.	.	PUNCT
ejpam-5311	187	1	let	let	VERB
ejpam-5311	187	2	µ	µ	X
ejpam-5311	187	3	be	be	AUX
ejpam-5311	187	4	a	a	DET
ejpam-5311	187	5	fuzzy	fuzzy	ADJ
ejpam-5311	187	6	set	set	NOUN
ejpam-5311	187	7	in	in	ADP
ejpam-5311	187	8	x.	x.	NOUN
ejpam-5311	187	9	if	if	SCONJ
ejpam-5311	187	10	an	an	DET
ejpam-5311	187	11	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	187	12	fuzzy	fuzzy	ADJ
ejpam-5311	187	13	set	set	VERB
ejpam-5311	187	14	lε	lε	PRON
ejpam-5311	187	15	µ	µ	PROPN
ejpam-5311	187	16	of	of	ADP
ejpam-5311	187	17	µ	µ	NOUN
ejpam-5311	187	18	in	in	ADP
ejpam-5311	187	19	x	x	PART
ejpam-5311	187	20	satisfies	satisfie	NOUN
ejpam-5311	187	21	the	the	DET
ejpam-5311	187	22	condition	condition	NOUN
ejpam-5311	187	23	(	(	PUNCT
ejpam-5311	187	24	3.9	3.9	NUM
ejpam-5311	187	25	)	)	PUNCT
ejpam-5311	187	26	for	for	ADP
ejpam-5311	187	27	all	all	DET
ejpam-5311	187	28	x	x	NOUN
ejpam-5311	187	29	,	,	PUNCT
ejpam-5311	187	30	y	y	PROPN
ejpam-5311	187	31	∈	∈	PROPN
ejpam-5311	187	32	x	x	X
ejpam-5311	187	33	and	and	CCONJ
ejpam-5311	187	34	ta	ta	PROPN
ejpam-5311	187	35	,	,	PUNCT
ejpam-5311	187	36	tb	tb	ADP
ejpam-5311	187	37	∈	∈	PROPN
ejpam-5311	187	38	(	(	PUNCT
ejpam-5311	187	39	0	0	NUM
ejpam-5311	187	40	,	,	PUNCT
ejpam-5311	187	41	1	1	NUM
ejpam-5311	187	42	]	]	PUNCT
ejpam-5311	187	43	,	,	PUNCT
ejpam-5311	187	44	then	then	ADV
ejpam-5311	187	45	the	the	DET
ejpam-5311	187	46	nonempty	nonempty	ADJ
ejpam-5311	187	47	o	o	NOUN
ejpam-5311	187	48	-	-	ADJ
ejpam-5311	187	49	set	set	VERB
ejpam-5311	187	50	o(lε	o(lε	PROPN
ejpam-5311	187	51	µ	µ	NOUN
ejpam-5311	187	52	)	)	PUNCT
ejpam-5311	187	53	of	of	ADP
ejpam-5311	187	54	lε	lε	PRON
ejpam-5311	187	55	µ	µ	PROPN
ejpam-5311	187	56	is	be	AUX
ejpam-5311	187	57	a	a	DET
ejpam-5311	187	58	bcc	bcc	PROPN
ejpam-5311	187	59	-	-	PUNCT
ejpam-5311	187	60	subalgebra	subalgebra	NOUN
ejpam-5311	187	61	of	of	ADP
ejpam-5311	187	62	x.	x.	NOUN
ejpam-5311	187	63	proof	proof	NOUN
ejpam-5311	187	64	.	.	PUNCT
ejpam-5311	188	1	let	let	VERB
ejpam-5311	188	2	x	x	PRON
ejpam-5311	188	3	,	,	PUNCT
ejpam-5311	188	4	y	y	PROPN
ejpam-5311	188	5	∈	∈	PROPN
ejpam-5311	188	6	o(lε	o(lε	PROPN
ejpam-5311	188	7	µ	µ	NOUN
ejpam-5311	188	8	)	)	PUNCT
ejpam-5311	188	9	.	.	PUNCT
ejpam-5311	189	1	then	then	ADV
ejpam-5311	189	2	µ(x	µ(x	NOUN
ejpam-5311	189	3	)	)	PUNCT
ejpam-5311	189	4	+	+	CCONJ
ejpam-5311	189	5	ε	ε	PROPN
ejpam-5311	189	6	−	−	PROPN
ejpam-5311	189	7	1	1	NUM
ejpam-5311	189	8	>	>	SYM
ejpam-5311	189	9	0	0	NUM
ejpam-5311	189	10	and	and	CCONJ
ejpam-5311	189	11	µ(y	µ(y	NUM
ejpam-5311	189	12	)	)	PUNCT
ejpam-5311	190	1	+	+	CCONJ
ejpam-5311	190	2	ε	ε	PROPN
ejpam-5311	190	3	−	−	PROPN
ejpam-5311	190	4	1	1	NUM
ejpam-5311	190	5	>	>	X
ejpam-5311	190	6	0	0	NUM
ejpam-5311	190	7	.	.	PUNCT
ejpam-5311	191	1	thus	thus	ADV
ejpam-5311	191	2	,	,	PUNCT
ejpam-5311	191	3	lε	lε	X
ejpam-5311	191	4	µ(x	µ(x	NOUN
ejpam-5311	191	5	)	)	PUNCT
ejpam-5311	191	6	+	+	CCONJ
ejpam-5311	191	7	1	1	NUM
ejpam-5311	191	8	=	=	SYM
ejpam-5311	191	9	max{0	max{0	PROPN
ejpam-5311	191	10	,	,	PUNCT
ejpam-5311	191	11	µ(x	µ(x	X
ejpam-5311	191	12	)	)	PUNCT
ejpam-5311	191	13	+	+	CCONJ
ejpam-5311	191	14	ε−	ε−	PROPN
ejpam-5311	191	15	1	1	NUM
ejpam-5311	191	16	}	}	PUNCT
ejpam-5311	191	17	+	+	CCONJ
ejpam-5311	191	18	1	1	NUM
ejpam-5311	191	19	=	=	SYM
ejpam-5311	191	20	µ(x	µ(x	X
ejpam-5311	191	21	)	)	PUNCT
ejpam-5311	191	22	+	+	CCONJ
ejpam-5311	191	23	ε−	ε−	X
ejpam-5311	191	24	1	1	NUM
ejpam-5311	191	25	+	+	SYM
ejpam-5311	191	26	1	1	NUM
ejpam-5311	191	27	=	=	SYM
ejpam-5311	191	28	µ(x	µ(x	X
ejpam-5311	191	29	)	)	PUNCT
ejpam-5311	191	30	+	+	CCONJ
ejpam-5311	191	31	ε	ε	PROPN
ejpam-5311	191	32	>	>	X
ejpam-5311	191	33	1	1	NUM
ejpam-5311	191	34	and	and	CCONJ
ejpam-5311	191	35	lε	lε	ADP
ejpam-5311	191	36	µ(y	µ(y	PROPN
ejpam-5311	191	37	)	)	PUNCT
ejpam-5311	192	1	+	+	CCONJ
ejpam-5311	192	2	1	1	NUM
ejpam-5311	192	3	=	=	SYM
ejpam-5311	192	4	max{0	max{0	PROPN
ejpam-5311	192	5	,	,	PUNCT
ejpam-5311	192	6	µ(y	µ(y	PROPN
ejpam-5311	192	7	)	)	PUNCT
ejpam-5311	192	8	+	+	CCONJ
ejpam-5311	192	9	ε−1}+	ε−1}+	NOUN
ejpam-5311	192	10	1	1	X
ejpam-5311	192	11	=	=	SYM
ejpam-5311	192	12	µ(y	µ(y	NOUN
ejpam-5311	192	13	)	)	PUNCT
ejpam-5311	193	1	+	+	CCONJ
ejpam-5311	193	2	ε−1	ε−1	PROPN
ejpam-5311	193	3	+	+	CCONJ
ejpam-5311	193	4	1	1	NUM
ejpam-5311	193	5	=	=	SYM
ejpam-5311	193	6	µ(y	µ(y	NOUN
ejpam-5311	193	7	)	)	PUNCT
ejpam-5311	194	1	+	+	CCONJ
ejpam-5311	194	2	ε	ε	PROPN
ejpam-5311	194	3	>	>	X
ejpam-5311	194	4	1	1	NUM
ejpam-5311	194	5	,	,	PUNCT
ejpam-5311	194	6	that	that	ADV
ejpam-5311	194	7	is	is	ADV
ejpam-5311	194	8	,	,	PUNCT
ejpam-5311	194	9	[	[	X
ejpam-5311	194	10	x/1]qlε	x/1]qlε	X
ejpam-5311	194	11	µ	µ	X
ejpam-5311	194	12	and	and	CCONJ
ejpam-5311	194	13	[	[	X
ejpam-5311	194	14	y/1]qlε	y/1]qlε	NOUN
ejpam-5311	194	15	µ.	µ.	NOUN
ejpam-5311	194	16	it	it	PRON
ejpam-5311	194	17	follows	follow	VERB
ejpam-5311	194	18	from	from	ADP
ejpam-5311	194	19	(	(	PUNCT
ejpam-5311	194	20	3.9	3.9	NUM
ejpam-5311	194	21	)	)	PUNCT
ejpam-5311	195	1	that	that	SCONJ
ejpam-5311	196	1	[	[	X
ejpam-5311	196	2	(	(	PUNCT
ejpam-5311	196	3	x	x	X
ejpam-5311	196	4	∗	∗	NOUN
ejpam-5311	196	5	y)/1	y)/1	PROPN
ejpam-5311	196	6	]	]	PUNCT
ejpam-5311	197	1	=	=	PUNCT
ejpam-5311	198	1	[	[	X
ejpam-5311	198	2	(	(	PUNCT
ejpam-5311	198	3	x	x	X
ejpam-5311	198	4	∗	∗	NOUN
ejpam-5311	198	5	y)/max{1	y)/max{1	NOUN
ejpam-5311	198	6	,	,	PUNCT
ejpam-5311	198	7	1	1	NUM
ejpam-5311	198	8	}	}	PUNCT
ejpam-5311	198	9	]	]	PUNCT
ejpam-5311	198	10	∈	∈	PROPN
ejpam-5311	198	11	lε	lε	X
ejpam-5311	198	12	µ.	µ.	NOUN
ejpam-5311	198	13	(	(	PUNCT
ejpam-5311	198	14	3.12	3.12	NUM
ejpam-5311	198	15	)	)	PUNCT
ejpam-5311	198	16	if	if	SCONJ
ejpam-5311	198	17	x∗	x∗	PROPN
ejpam-5311	198	18	y	y	PROPN
ejpam-5311	198	19	/∈	/∈	PROPN
ejpam-5311	198	20	o(lε	o(lε	PROPN
ejpam-5311	198	21	µ	µ	X
ejpam-5311	198	22	)	)	PUNCT
ejpam-5311	198	23	,	,	PUNCT
ejpam-5311	198	24	then	then	ADV
ejpam-5311	198	25	lε	lε	ADP
ejpam-5311	198	26	µ(x∗	µ(x∗	NOUN
ejpam-5311	198	27	y	y	PROPN
ejpam-5311	198	28	)	)	PUNCT
ejpam-5311	198	29	=	=	SYM
ejpam-5311	198	30	0	0	PUNCT
ejpam-5311	198	31	<	<	X
ejpam-5311	198	32	1	1	NUM
ejpam-5311	198	33	and	and	CCONJ
ejpam-5311	198	34	so	so	ADV
ejpam-5311	198	35	(	(	PUNCT
ejpam-5311	198	36	3.12	3.12	NUM
ejpam-5311	198	37	)	)	PUNCT
ejpam-5311	198	38	is	be	AUX
ejpam-5311	198	39	not	not	PART
ejpam-5311	198	40	valid	valid	ADJ
ejpam-5311	198	41	.	.	PUNCT
ejpam-5311	199	1	this	this	PRON
ejpam-5311	199	2	is	be	AUX
ejpam-5311	199	3	a	a	DET
ejpam-5311	199	4	contradiction	contradiction	NOUN
ejpam-5311	199	5	.	.	PUNCT
ejpam-5311	200	1	thus	thus	ADV
ejpam-5311	200	2	,	,	PUNCT
ejpam-5311	200	3	x	x	PUNCT
ejpam-5311	200	4	∗	∗	NOUN
ejpam-5311	200	5	y	y	PROPN
ejpam-5311	200	6	∈	∈	PROPN
ejpam-5311	200	7	o(lε	o(lε	PROPN
ejpam-5311	200	8	µ	µ	NOUN
ejpam-5311	200	9	)	)	PUNCT
ejpam-5311	200	10	.	.	PUNCT
ejpam-5311	201	1	hence	hence	ADV
ejpam-5311	201	2	,	,	PUNCT
ejpam-5311	201	3	o(lε	o(lε	PROPN
ejpam-5311	201	4	µ	µ	NOUN
ejpam-5311	201	5	)	)	PUNCT
ejpam-5311	201	6	is	be	AUX
ejpam-5311	201	7	a	a	DET
ejpam-5311	201	8	bcc	bcc	PROPN
ejpam-5311	201	9	-	-	PUNCT
ejpam-5311	201	10	subalgebra	subalgebra	NOUN
ejpam-5311	201	11	of	of	ADP
ejpam-5311	201	12	x.	x.	NOUN
ejpam-5311	201	13	references	reference	NOUN
ejpam-5311	201	14	2244	2244	NUM
ejpam-5311	201	15	4	4	NUM
ejpam-5311	201	16	.	.	PUNCT
ejpam-5311	202	1	conclusions	conclusion	NOUN
ejpam-5311	202	2	the	the	DET
ejpam-5311	202	3	concept	concept	NOUN
ejpam-5311	202	4	of	of	ADP
ejpam-5311	202	5	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	202	6	fuzzy	fuzzy	ADJ
ejpam-5311	202	7	sets	set	NOUN
ejpam-5311	202	8	using	use	VERB
ejpam-5311	202	9	lukasiewicz	lukasiewicz	PROPN
ejpam-5311	202	10	t	t	PROPN
ejpam-5311	202	11	-	-	PUNCT
ejpam-5311	202	12	norm	norm	NOUN
ejpam-5311	202	13	was	be	AUX
ejpam-5311	202	14	introduced	introduce	VERB
ejpam-5311	202	15	by	by	ADP
ejpam-5311	202	16	jun	jun	PROPN
ejpam-5311	203	1	[	[	X
ejpam-5311	203	2	8	8	NUM
ejpam-5311	203	3	]	]	PUNCT
ejpam-5311	203	4	.	.	PUNCT
ejpam-5311	204	1	in	in	ADP
ejpam-5311	204	2	this	this	DET
ejpam-5311	204	3	paper	paper	NOUN
ejpam-5311	204	4	,	,	PUNCT
ejpam-5311	204	5	the	the	DET
ejpam-5311	204	6	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	204	7	fuzzy	fuzzy	ADJ
ejpam-5311	204	8	set	set	NOUN
ejpam-5311	204	9	has	have	AUX
ejpam-5311	204	10	been	be	AUX
ejpam-5311	204	11	applied	apply	VERB
ejpam-5311	204	12	to	to	ADP
ejpam-5311	204	13	bcc	bcc	PROPN
ejpam-5311	204	14	-	-	PUNCT
ejpam-5311	204	15	subalgebras	subalgebras	PROPN
ejpam-5311	204	16	in	in	ADP
ejpam-5311	204	17	bcc	bcc	PROPN
ejpam-5311	204	18	-	-	PUNCT
ejpam-5311	204	19	algebras	algebras	X
ejpam-5311	204	20	,	,	PUNCT
ejpam-5311	204	21	introducing	introduce	VERB
ejpam-5311	204	22	the	the	DET
ejpam-5311	204	23	concept	concept	NOUN
ejpam-5311	204	24	of	of	ADP
ejpam-5311	204	25	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	204	26	fuzzy	fuzzy	ADJ
ejpam-5311	204	27	bcc	bcc	PROPN
ejpam-5311	204	28	-	-	PUNCT
ejpam-5311	204	29	subalgebras	subalgebras	PROPN
ejpam-5311	204	30	,	,	PUNCT
ejpam-5311	204	31	and	and	CCONJ
ejpam-5311	204	32	examining	examine	VERB
ejpam-5311	204	33	several	several	ADJ
ejpam-5311	204	34	properties	property	NOUN
ejpam-5311	204	35	.	.	PUNCT
ejpam-5311	205	1	we	we	PRON
ejpam-5311	205	2	discussed	discuss	VERB
ejpam-5311	205	3	the	the	DET
ejpam-5311	205	4	characterization	characterization	NOUN
ejpam-5311	205	5	of	of	ADP
ejpam-5311	205	6	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5311	205	7	fuzzy	fuzzy	ADJ
ejpam-5311	205	8	bcc	bcc	PROPN
ejpam-5311	205	9	-	-	PUNCT
ejpam-5311	205	10	subalgebras	subalgebras	PROPN
ejpam-5311	205	11	and	and	CCONJ
ejpam-5311	205	12	considered	consider	VERB
ejpam-5311	205	13	the	the	DET
ejpam-5311	205	14	relationship	relationship	NOUN
ejpam-5311	205	15	between	between	ADP
ejpam-5311	205	16	fuzzy	fuzzy	ADJ
ejpam-5311	205	17	bcc	bcc	PROPN
ejpam-5311	205	18	-	-	PUNCT
ejpam-5311	205	19	subalgebras	subalgebras	PROPN
ejpam-5311	205	20	and	and	CCONJ
ejpam-5311	205	21	ε	ε	PROPN
ejpam-5311	205	22	lukasiewicz	lukasiewicz	VERB
ejpam-5311	205	23	fuzzy	fuzzy	ADJ
ejpam-5311	205	24	bcc	bcc	PROPN
ejpam-5311	205	25	-	-	PUNCT
ejpam-5311	205	26	subalgebras	subalgebras	PROPN
ejpam-5311	205	27	.	.	PUNCT
ejpam-5311	206	1	we	we	PRON
ejpam-5311	206	2	provided	provide	VERB
ejpam-5311	206	3	conditions	condition	NOUN
ejpam-5311	206	4	under	under	ADP
ejpam-5311	206	5	which	which	PRON
ejpam-5311	206	6	εlukasiewicz	εlukasiewicz	VERB
ejpam-5311	206	7	fuzzy	fuzzy	ADJ
ejpam-5311	206	8	sets	set	NOUN
ejpam-5311	206	9	can	can	AUX
ejpam-5311	206	10	be	be	AUX
ejpam-5311	206	11	εlukasiewicz	εlukasiewicz	VERB
ejpam-5311	206	12	fuzzy	fuzzy	ADJ
ejpam-5311	206	13	bcc	bcc	PROPN
ejpam-5311	206	14	-	-	PUNCT
ejpam-5311	206	15	subalgebras	subalgebras	PROPN
ejpam-5311	206	16	and	and	CCONJ
ejpam-5311	206	17	further	far	ADV
ejpam-5311	206	18	explored	explore	VERB
ejpam-5311	206	19	conditions	condition	NOUN
ejpam-5311	206	20	under	under	ADP
ejpam-5311	206	21	which	which	PRON
ejpam-5311	206	22	three	three	NUM
ejpam-5311	206	23	subsets	subset	NOUN
ejpam-5311	206	24	:	:	PUNCT
ejpam-5311	206	25	∈-set	∈-set	NOUN
ejpam-5311	206	26	,	,	PUNCT
ejpam-5311	206	27	q	q	NOUN
ejpam-5311	206	28	-	-	PUNCT
ejpam-5311	206	29	set	set	NOUN
ejpam-5311	206	30	,	,	PUNCT
ejpam-5311	206	31	and	and	CCONJ
ejpam-5311	206	32	o	o	X
ejpam-5311	206	33	-	-	NOUN
ejpam-5311	206	34	set	set	ADJ
ejpam-5311	206	35	,	,	PUNCT
ejpam-5311	206	36	will	will	AUX
ejpam-5311	206	37	be	be	AUX
ejpam-5311	206	38	bcc	bcc	PROPN
ejpam-5311	206	39	-	-	PUNCT
ejpam-5311	206	40	subalgebras	subalgebras	PROPN
ejpam-5311	206	41	.	.	PUNCT
ejpam-5311	207	1	the	the	DET
ejpam-5311	207	2	ideas	idea	NOUN
ejpam-5311	207	3	and	and	CCONJ
ejpam-5311	207	4	results	result	NOUN
ejpam-5311	207	5	obtained	obtain	VERB
ejpam-5311	207	6	in	in	ADP
ejpam-5311	207	7	this	this	DET
ejpam-5311	207	8	paper	paper	NOUN
ejpam-5311	207	9	will	will	AUX
ejpam-5311	207	10	be	be	AUX
ejpam-5311	207	11	applied	apply	VERB
ejpam-5311	207	12	to	to	ADP
ejpam-5311	207	13	the	the	DET
ejpam-5311	207	14	relevant	relevant	ADJ
ejpam-5311	207	15	algebraic	algebraic	ADJ
ejpam-5311	207	16	systems	system	NOUN
ejpam-5311	207	17	in	in	ADP
ejpam-5311	207	18	the	the	DET
ejpam-5311	207	19	future	future	NOUN
ejpam-5311	207	20	,	,	PUNCT
ejpam-5311	207	21	further	far	ADV
ejpam-5311	207	22	examining	examine	VERB
ejpam-5311	207	23	their	their	PRON
ejpam-5311	207	24	usability	usability	NOUN
ejpam-5311	207	25	as	as	ADP
ejpam-5311	207	26	a	a	DET
ejpam-5311	207	27	mathematical	mathematical	ADJ
ejpam-5311	207	28	tool	tool	NOUN
ejpam-5311	207	29	applicable	applicable	ADJ
ejpam-5311	207	30	to	to	ADP
ejpam-5311	207	31	decision	decision	NOUN
ejpam-5311	207	32	theory	theory	NOUN
ejpam-5311	207	33	,	,	PUNCT
ejpam-5311	207	34	medical	medical	ADJ
ejpam-5311	207	35	diagnosis	diagnosis	NOUN
ejpam-5311	207	36	systems	system	NOUN
ejpam-5311	207	37	,	,	PUNCT
ejpam-5311	207	38	automation	automation	NOUN
ejpam-5311	207	39	systems	system	NOUN
ejpam-5311	207	40	,	,	PUNCT
ejpam-5311	207	41	etc	etc	X
ejpam-5311	207	42	.	.	X
ejpam-5311	208	1	acknowledgements	acknowledgement	VERB
ejpam-5311	208	2	this	this	DET
ejpam-5311	208	3	research	research	NOUN
ejpam-5311	208	4	was	be	AUX
ejpam-5311	208	5	supported	support	VERB
ejpam-5311	208	6	by	by	ADP
ejpam-5311	208	7	the	the	DET
ejpam-5311	208	8	university	university	NOUN
ejpam-5311	208	9	of	of	ADP
ejpam-5311	208	10	phayao	phayao	NOUN
ejpam-5311	208	11	and	and	CCONJ
ejpam-5311	208	12	the	the	DET
ejpam-5311	208	13	thailand	thailand	PROPN
ejpam-5311	208	14	science	science	PROPN
ejpam-5311	208	15	research	research	PROPN
ejpam-5311	208	16	and	and	CCONJ
ejpam-5311	208	17	innovation	innovation	NOUN
ejpam-5311	208	18	fund	fund	NOUN
ejpam-5311	208	19	(	(	PUNCT
ejpam-5311	208	20	fundamental	fundamental	ADJ
ejpam-5311	208	21	fund	fund	NOUN
ejpam-5311	208	22	2024	2024	NUM
ejpam-5311	208	23	)	)	PUNCT
ejpam-5311	208	24	.	.	PUNCT
ejpam-5311	209	1	references	reference	NOUN
ejpam-5311	209	2	[	[	X
ejpam-5311	209	3	1	1	NUM
ejpam-5311	209	4	]	]	PUNCT
ejpam-5311	209	5	b.	b.	PROPN
ejpam-5311	209	6	ahmad	ahmad	PROPN
ejpam-5311	209	7	and	and	CCONJ
ejpam-5311	209	8	a.	a.	PROPN
ejpam-5311	209	9	kharal	kharal	PROPN
ejpam-5311	209	10	.	.	PUNCT
ejpam-5311	210	1	on	on	ADP
ejpam-5311	210	2	fuzzy	fuzzy	ADJ
ejpam-5311	210	3	soft	soft	ADJ
ejpam-5311	210	4	sets	set	NOUN
ejpam-5311	210	5	.	.	PUNCT
ejpam-5311	211	1	adv	adv	PROPN
ejpam-5311	211	2	.	.	PUNCT
ejpam-5311	211	3	fuzzy	fuzzy	ADJ
ejpam-5311	211	4	syst	syst	PROPN
ejpam-5311	211	5	.	.	PUNCT
ejpam-5311	211	6	,	,	PUNCT
ejpam-5311	211	7	2009	2009	NUM
ejpam-5311	211	8	:	:	PUNCT
ejpam-5311	211	9	article	article	NOUN
ejpam-5311	211	10	i	i	PROPN
ejpam-5311	211	11	d	d	PROPN
ejpam-5311	211	12	586507	586507	NUM
ejpam-5311	211	13	,	,	PUNCT
ejpam-5311	211	14	6	6	NUM
ejpam-5311	211	15	pages	page	NOUN
ejpam-5311	211	16	,	,	PUNCT
ejpam-5311	211	17	2009	2009	NUM
ejpam-5311	211	18	.	.	PUNCT
ejpam-5311	212	1	[	[	X
ejpam-5311	212	2	2	2	NUM
ejpam-5311	212	3	]	]	PUNCT
ejpam-5311	212	4	m.	m.	NOUN
ejpam-5311	212	5	atef	atef	PROPN
ejpam-5311	212	6	,	,	PUNCT
ejpam-5311	212	7	m.	m.	PROPN
ejpam-5311	212	8	i.	i.	PROPN
ejpam-5311	212	9	ali	ali	PROPN
ejpam-5311	212	10	,	,	PUNCT
ejpam-5311	212	11	and	and	CCONJ
ejpam-5311	212	12	t.	t.	PROPN
ejpam-5311	212	13	al	al	PROPN
ejpam-5311	212	14	-	-	PUNCT
ejpam-5311	212	15	shami	shami	PROPN
ejpam-5311	212	16	.	.	PUNCT
ejpam-5311	213	1	fuzzy	fuzzy	ADJ
ejpam-5311	213	2	soft	soft	ADJ
ejpam-5311	213	3	covering	covering	NOUN
ejpam-5311	213	4	based	base	VERB
ejpam-5311	213	5	multi	multi	ADJ
ejpam-5311	213	6	-	-	ADJ
ejpam-5311	213	7	granulation	granulation	ADJ
ejpam-5311	213	8	fuzzy	fuzzy	ADJ
ejpam-5311	213	9	rough	rough	ADJ
ejpam-5311	213	10	sets	set	NOUN
ejpam-5311	213	11	and	and	CCONJ
ejpam-5311	213	12	their	their	PRON
ejpam-5311	213	13	applications	application	NOUN
ejpam-5311	213	14	.	.	PUNCT
ejpam-5311	214	1	comput	comput	NOUN
ejpam-5311	214	2	.	.	PUNCT
ejpam-5311	215	1	appl	appl	PROPN
ejpam-5311	215	2	.	.	PROPN
ejpam-5311	215	3	math	math	PROPN
ejpam-5311	215	4	.	.	PUNCT
ejpam-5311	215	5	,	,	PUNCT
ejpam-5311	215	6	40(4):115	40(4):115	PROPN
ejpam-5311	215	7	,	,	PUNCT
ejpam-5311	215	8	2021	2021	NUM
ejpam-5311	215	9	.	.	PUNCT
ejpam-5311	216	1	[	[	X
ejpam-5311	216	2	3	3	NUM
ejpam-5311	216	3	]	]	X
ejpam-5311	216	4	n.	n.	NOUN
ejpam-5311	216	5	caǧman	caǧman	PROPN
ejpam-5311	216	6	,	,	PUNCT
ejpam-5311	216	7	s.	s.	PROPN
ejpam-5311	216	8	enginoǧlu	enginoǧlu	PROPN
ejpam-5311	216	9	,	,	PUNCT
ejpam-5311	216	10	and	and	CCONJ
ejpam-5311	216	11	f.	f.	PROPN
ejpam-5311	216	12	citak	citak	PROPN
ejpam-5311	216	13	.	.	PUNCT
ejpam-5311	217	1	fuzzy	fuzzy	ADJ
ejpam-5311	217	2	soft	soft	ADJ
ejpam-5311	217	3	set	set	NOUN
ejpam-5311	217	4	theory	theory	NOUN
ejpam-5311	217	5	and	and	CCONJ
ejpam-5311	217	6	its	its	PRON
ejpam-5311	217	7	application	application	NOUN
ejpam-5311	217	8	.	.	PUNCT
ejpam-5311	218	1	iran	iran	PROPN
ejpam-5311	218	2	.	.	PUNCT
ejpam-5311	219	1	j.	j.	PROPN
ejpam-5311	219	2	fuzzy	fuzzy	PROPN
ejpam-5311	219	3	syst	syst	PROPN
ejpam-5311	219	4	.	.	PROPN
ejpam-5311	219	5	,	,	PUNCT
ejpam-5311	219	6	8(3):137–147	8(3):137–147	NUM
ejpam-5311	219	7	,	,	PUNCT
ejpam-5311	219	8	2011	2011	NUM
ejpam-5311	219	9	.	.	PUNCT
ejpam-5311	220	1	[	[	X
ejpam-5311	220	2	4	4	NUM
ejpam-5311	220	3	]	]	X
ejpam-5311	220	4	n.	n.	PROPN
ejpam-5311	220	5	dokkhamdang	dokkhamdang	PROPN
ejpam-5311	220	6	,	,	PUNCT
ejpam-5311	220	7	a.	a.	PROPN
ejpam-5311	220	8	kesorn	kesorn	PROPN
ejpam-5311	220	9	,	,	PUNCT
ejpam-5311	220	10	and	and	CCONJ
ejpam-5311	220	11	a.	a.	NOUN
ejpam-5311	220	12	iampan	iampan	PROPN
ejpam-5311	220	13	.	.	PUNCT
ejpam-5311	221	1	generalized	generalize	VERB
ejpam-5311	221	2	fuzzy	fuzzy	ADJ
ejpam-5311	221	3	sets	set	NOUN
ejpam-5311	221	4	in	in	ADP
ejpam-5311	221	5	up	up	ADP
ejpam-5311	221	6	-	-	PUNCT
ejpam-5311	221	7	algebras	algebras	X
ejpam-5311	221	8	.	.	PUNCT
ejpam-5311	222	1	ann	ann	PROPN
ejpam-5311	222	2	.	.	PUNCT
ejpam-5311	222	3	fuzzy	fuzzy	ADJ
ejpam-5311	222	4	math	math	NOUN
ejpam-5311	222	5	.	.	PUNCT
ejpam-5311	223	1	inform	inform	NOUN
ejpam-5311	223	2	.	.	PUNCT
ejpam-5311	223	3	,	,	PUNCT
ejpam-5311	223	4	16(2):171–190	16(2):171–190	NUM
ejpam-5311	223	5	,	,	PUNCT
ejpam-5311	223	6	2018	2018	NUM
ejpam-5311	223	7	.	.	PUNCT
ejpam-5311	224	1	[	[	X
ejpam-5311	224	2	5	5	X
ejpam-5311	224	3	]	]	PUNCT
ejpam-5311	224	4	t.	t.	NOUN
ejpam-5311	224	5	guntasow	guntasow	NOUN
ejpam-5311	224	6	,	,	PUNCT
ejpam-5311	224	7	s.	s.	PROPN
ejpam-5311	224	8	sajak	sajak	PROPN
ejpam-5311	224	9	,	,	PUNCT
ejpam-5311	224	10	a.	a.	PROPN
ejpam-5311	224	11	jomkham	jomkham	PROPN
ejpam-5311	224	12	,	,	PUNCT
ejpam-5311	224	13	and	and	CCONJ
ejpam-5311	224	14	a.	a.	NOUN
ejpam-5311	224	15	iampan	iampan	PROPN
ejpam-5311	224	16	.	.	PUNCT
ejpam-5311	225	1	fuzzy	fuzzy	ADJ
ejpam-5311	225	2	translations	translation	NOUN
ejpam-5311	225	3	of	of	ADP
ejpam-5311	225	4	a	a	DET
ejpam-5311	225	5	fuzzy	fuzzy	ADJ
ejpam-5311	225	6	set	set	NOUN
ejpam-5311	225	7	in	in	ADP
ejpam-5311	225	8	up	up	ADP
ejpam-5311	225	9	-	-	PUNCT
ejpam-5311	225	10	algebras	algebras	X
ejpam-5311	225	11	.	.	PUNCT
ejpam-5311	226	1	j.	j.	PROPN
ejpam-5311	226	2	indones	indones	PROPN
ejpam-5311	226	3	.	.	PUNCT
ejpam-5311	227	1	math	math	NOUN
ejpam-5311	227	2	.	.	PUNCT
ejpam-5311	228	1	soc	soc	PROPN
ejpam-5311	228	2	.	.	PROPN
ejpam-5311	228	3	,	,	PUNCT
ejpam-5311	228	4	23(2):1–19	23(2):1–19	NUM
ejpam-5311	228	5	,	,	PUNCT
ejpam-5311	228	6	2017	2017	NUM
ejpam-5311	228	7	.	.	PUNCT
ejpam-5311	229	1	[	[	X
ejpam-5311	229	2	6	6	NUM
ejpam-5311	229	3	]	]	X
ejpam-5311	229	4	y.	y.	PROPN
ejpam-5311	229	5	huang	huang	PROPN
ejpam-5311	229	6	.	.	PUNCT
ejpam-5311	230	1	bci	bci	PROPN
ejpam-5311	230	2	-	-	NOUN
ejpam-5311	230	3	algebra	algebra	NOUN
ejpam-5311	230	4	.	.	PUNCT
ejpam-5311	231	1	science	science	NOUN
ejpam-5311	231	2	press	press	PROPN
ejpam-5311	231	3	,	,	PUNCT
ejpam-5311	231	4	beijing	beijing	PROPN
ejpam-5311	231	5	,	,	PUNCT
ejpam-5311	231	6	china	china	PROPN
ejpam-5311	231	7	,	,	PUNCT
ejpam-5311	231	8	2006	2006	NUM
ejpam-5311	231	9	.	.	PUNCT
ejpam-5311	232	1	[	[	X
ejpam-5311	232	2	7	7	NUM
ejpam-5311	232	3	]	]	PUNCT
ejpam-5311	232	4	a.	a.	NOUN
ejpam-5311	232	5	iampan	iampan	PROPN
ejpam-5311	232	6	.	.	PUNCT
ejpam-5311	233	1	a	a	DET
ejpam-5311	233	2	new	new	ADJ
ejpam-5311	233	3	branch	branch	NOUN
ejpam-5311	233	4	of	of	ADP
ejpam-5311	233	5	the	the	DET
ejpam-5311	233	6	logical	logical	ADJ
ejpam-5311	233	7	algebra	algebra	NOUN
ejpam-5311	233	8	:	:	PUNCT
ejpam-5311	233	9	up	up	ADP
ejpam-5311	233	10	-	-	PUNCT
ejpam-5311	233	11	algebras	algebras	X
ejpam-5311	233	12	.	.	PUNCT
ejpam-5311	234	1	j.	j.	PROPN
ejpam-5311	234	2	algebra	algebra	PROPN
ejpam-5311	234	3	relat	relat	PROPN
ejpam-5311	234	4	.	.	PUNCT
ejpam-5311	235	1	top	top	PROPN
ejpam-5311	235	2	.	.	PROPN
ejpam-5311	235	3	,	,	PUNCT
ejpam-5311	235	4	5(1):35–54	5(1):35–54	NUM
ejpam-5311	235	5	,	,	PUNCT
ejpam-5311	235	6	2017	2017	NUM
ejpam-5311	235	7	.	.	PUNCT
ejpam-5311	236	1	[	[	X
ejpam-5311	236	2	8	8	NUM
ejpam-5311	236	3	]	]	X
ejpam-5311	236	4	y.	y.	PROPN
ejpam-5311	236	5	b.	b.	PROPN
ejpam-5311	236	6	jun	jun	PROPN
ejpam-5311	236	7	,	,	PUNCT
ejpam-5311	236	8	b.	b.	PROPN
ejpam-5311	236	9	brundha	brundha	PROPN
ejpam-5311	236	10	,	,	PUNCT
ejpam-5311	236	11	n.	n.	PROPN
ejpam-5311	236	12	rajesh	rajesh	PROPN
ejpam-5311	236	13	,	,	PUNCT
ejpam-5311	236	14	and	and	CCONJ
ejpam-5311	236	15	r.	r.	PROPN
ejpam-5311	236	16	k.	k.	PROPN
ejpam-5311	236	17	bandaru	bandaru	PROPN
ejpam-5311	236	18	.	.	PUNCT
ejpam-5311	237	1	(	(	PUNCT
ejpam-5311	237	2	3	3	NUM
ejpam-5311	237	3	,	,	PUNCT
ejpam-5311	237	4	2)-fuzzy	2)-fuzzy	NUM
ejpam-5311	237	5	up	up	ADP
ejpam-5311	237	6	(	(	PUNCT
ejpam-5311	237	7	bcc)subalgebras	bcc)subalgebras	PROPN
ejpam-5311	237	8	and	and	CCONJ
ejpam-5311	237	9	(	(	PUNCT
ejpam-5311	237	10	3	3	NUM
ejpam-5311	237	11	,	,	PUNCT
ejpam-5311	237	12	2)-fuzzy	2)-fuzzy	NUM
ejpam-5311	237	13	up	up	ADP
ejpam-5311	237	14	(	(	PUNCT
ejpam-5311	237	15	bcc)-filters	bcc)-filter	NOUN
ejpam-5311	237	16	.	.	PUNCT
ejpam-5311	238	1	j.	j.	PROPN
ejpam-5311	238	2	mahani	mahani	PROPN
ejpam-5311	238	3	math	math	PROPN
ejpam-5311	238	4	.	.	PUNCT
ejpam-5311	239	1	res	re	NOUN
ejpam-5311	239	2	.	.	PUNCT
ejpam-5311	240	1	cent	cent	NOUN
ejpam-5311	240	2	.	.	PUNCT
ejpam-5311	240	3	,	,	PUNCT
ejpam-5311	240	4	11(3):1	11(3):1	NUM
ejpam-5311	240	5	–	–	PUNCT
ejpam-5311	240	6	14	14	NUM
ejpam-5311	240	7	,	,	PUNCT
ejpam-5311	240	8	2022	2022	NUM
ejpam-5311	240	9	.	.	PUNCT
ejpam-5311	241	1	references	reference	NOUN
ejpam-5311	241	2	2245	2245	NUM
ejpam-5311	241	3	[	[	X
ejpam-5311	241	4	9	9	NUM
ejpam-5311	241	5	]	]	X
ejpam-5311	241	6	y.	y.	PROPN
ejpam-5311	241	7	komori	komori	PROPN
ejpam-5311	241	8	.	.	PUNCT
ejpam-5311	242	1	the	the	DET
ejpam-5311	242	2	class	class	NOUN
ejpam-5311	242	3	of	of	ADP
ejpam-5311	242	4	bcc	bcc	PROPN
ejpam-5311	242	5	-	-	PUNCT
ejpam-5311	242	6	algebras	algebras	PROPN
ejpam-5311	242	7	is	be	AUX
ejpam-5311	242	8	not	not	PART
ejpam-5311	242	9	a	a	DET
ejpam-5311	242	10	variety	variety	NOUN
ejpam-5311	242	11	.	.	PUNCT
ejpam-5311	243	1	math	math	NOUN
ejpam-5311	243	2	.	.	PUNCT
ejpam-5311	244	1	japon	japon	PROPN
ejpam-5311	244	2	.	.	PROPN
ejpam-5311	244	3	,	,	PUNCT
ejpam-5311	244	4	29(3):391–394	29(3):391–394	NOUN
ejpam-5311	244	5	,	,	PUNCT
ejpam-5311	244	6	1984	1984	NUM
ejpam-5311	244	7	.	.	PUNCT
ejpam-5311	245	1	[	[	X
ejpam-5311	245	2	10	10	NUM
ejpam-5311	245	3	]	]	X
ejpam-5311	245	4	p.	p.	NOUN
ejpam-5311	245	5	m.	m.	NOUN
ejpam-5311	245	6	pu	pu	PROPN
ejpam-5311	245	7	and	and	CCONJ
ejpam-5311	245	8	y.	y.	PROPN
ejpam-5311	245	9	m.	m.	PROPN
ejpam-5311	245	10	liu	liu	PROPN
ejpam-5311	245	11	.	.	PROPN
ejpam-5311	246	1	fuzzy	fuzzy	ADJ
ejpam-5311	246	2	topology	topology	PROPN
ejpam-5311	246	3	i.	i.	PROPN
ejpam-5311	246	4	neighborhood	neighborhood	PROPN
ejpam-5311	246	5	structure	structure	NOUN
ejpam-5311	246	6	of	of	ADP
ejpam-5311	246	7	a	a	DET
ejpam-5311	246	8	fuzzy	fuzzy	ADJ
ejpam-5311	246	9	point	point	NOUN
ejpam-5311	246	10	and	and	CCONJ
ejpam-5311	246	11	moore	moore	PROPN
ejpam-5311	246	12	-	-	PUNCT
ejpam-5311	246	13	smith	smith	PROPN
ejpam-5311	246	14	convergence	convergence	NOUN
ejpam-5311	246	15	.	.	PUNCT
ejpam-5311	247	1	j.	j.	PROPN
ejpam-5311	247	2	math	math	PROPN
ejpam-5311	247	3	.	.	PUNCT
ejpam-5311	248	1	anal	anal	PROPN
ejpam-5311	248	2	.	.	PUNCT
ejpam-5311	249	1	appl	appl	PROPN
ejpam-5311	249	2	.	.	PROPN
ejpam-5311	250	1	,	,	PUNCT
ejpam-5311	250	2	76(2):571–599	76(2):571–599	PROPN
ejpam-5311	250	3	,	,	PUNCT
ejpam-5311	250	4	1980	1980	NUM
ejpam-5311	250	5	.	.	PUNCT
ejpam-5311	251	1	[	[	X
ejpam-5311	251	2	11	11	NUM
ejpam-5311	251	3	]	]	PUNCT
ejpam-5311	251	4	j.	j.	PROPN
ejpam-5311	251	5	somjanta	somjanta	PROPN
ejpam-5311	251	6	,	,	PUNCT
ejpam-5311	251	7	n.	n.	PROPN
ejpam-5311	251	8	thuekaew	thuekaew	PROPN
ejpam-5311	251	9	,	,	PUNCT
ejpam-5311	251	10	p.	p.	NOUN
ejpam-5311	251	11	kumpeangkeaw	kumpeangkeaw	PROPN
ejpam-5311	251	12	,	,	PUNCT
ejpam-5311	251	13	and	and	CCONJ
ejpam-5311	251	14	a.	a.	NOUN
ejpam-5311	251	15	iampan	iampan	PROPN
ejpam-5311	251	16	.	.	PUNCT
ejpam-5311	252	1	fuzzy	fuzzy	ADJ
ejpam-5311	252	2	sets	set	NOUN
ejpam-5311	252	3	in	in	ADP
ejpam-5311	252	4	upalgebras	upalgebra	NOUN
ejpam-5311	252	5	.	.	PUNCT
ejpam-5311	253	1	ann	ann	PROPN
ejpam-5311	253	2	.	.	PUNCT
ejpam-5311	253	3	fuzzy	fuzzy	ADJ
ejpam-5311	253	4	math	math	NOUN
ejpam-5311	253	5	.	.	PUNCT
ejpam-5311	254	1	inform	inform	NOUN
ejpam-5311	254	2	.	.	PUNCT
ejpam-5311	254	3	,	,	PUNCT
ejpam-5311	254	4	12(6):739–756	12(6):739–756	PROPN
ejpam-5311	254	5	,	,	PUNCT
ejpam-5311	254	6	2016	2016	NUM
ejpam-5311	254	7	.	.	PUNCT
ejpam-5311	255	1	[	[	X
ejpam-5311	255	2	12	12	NUM
ejpam-5311	255	3	]	]	PUNCT
ejpam-5311	255	4	l.	l.	PROPN
ejpam-5311	255	5	a.	a.	PROPN
ejpam-5311	255	6	zadeh	zadeh	PROPN
ejpam-5311	255	7	.	.	PUNCT
ejpam-5311	255	8	fuzzy	fuzzy	ADJ
ejpam-5311	255	9	sets	set	NOUN
ejpam-5311	255	10	.	.	PUNCT
ejpam-5311	256	1	inf	inf	PROPN
ejpam-5311	256	2	.	.	PUNCT
ejpam-5311	256	3	control	control	PROPN
ejpam-5311	256	4	,	,	PUNCT
ejpam-5311	256	5	8(3):338–353	8(3):338–353	NUM
ejpam-5311	256	6	,	,	PUNCT
ejpam-5311	256	7	1965	1965	NUM
ejpam-5311	256	8	.	.	PUNCT