id	sid	tid	token	lemma	pos
ejpam-5450	1	1	european	european	PROPN
ejpam-5450	1	2	journal	journal	PROPN
ejpam-5450	1	3	of	of	ADP
ejpam-5450	1	4	pure	pure	ADJ
ejpam-5450	1	5	and	and	CCONJ
ejpam-5450	1	6	applied	apply	VERB
ejpam-5450	1	7	mathematics	mathematic	NOUN
ejpam-5450	1	8	vol	vol	NOUN
ejpam-5450	1	9	.	.	PROPN
ejpam-5450	2	1	17	17	NUM
ejpam-5450	2	2	,	,	PUNCT
ejpam-5450	2	3	no	no	INTJ
ejpam-5450	2	4	.	.	NOUN
ejpam-5450	2	5	4	4	NUM
ejpam-5450	2	6	,	,	PUNCT
ejpam-5450	2	7	2024	2024	NUM
ejpam-5450	2	8	,	,	PUNCT
ejpam-5450	2	9	3209	3209	NUM
ejpam-5450	2	10	-	-	SYM
ejpam-5450	2	11	3222	3222	NUM
ejpam-5450	2	12	issn	issn	VERB
ejpam-5450	2	13	1307	1307	NUM
ejpam-5450	2	14	-	-	SYM
ejpam-5450	2	15	5543	5543	NUM
ejpam-5450	2	16	–	–	PUNCT
ejpam-5450	2	17	ejpam.com	ejpam.com	X
ejpam-5450	2	18	published	publish	VERB
ejpam-5450	2	19	by	by	ADP
ejpam-5450	2	20	new	new	PROPN
ejpam-5450	2	21	york	york	PROPN
ejpam-5450	2	22	business	business	PROPN
ejpam-5450	2	23	global	global	ADJ
ejpam-5450	2	24	εlukasiewicz	εlukasiewicz	NOUN
ejpam-5450	2	25	fuzzy	fuzzy	ADJ
ejpam-5450	2	26	up	up	ADP
ejpam-5450	2	27	(	(	PUNCT
ejpam-5450	2	28	bcc)-ideals	bcc)-ideal	NOUN
ejpam-5450	2	29	:	:	PUNCT
ejpam-5450	2	30	a	a	DET
ejpam-5450	2	31	new	new	ADJ
ejpam-5450	2	32	frontier	frontier	NOUN
ejpam-5450	2	33	in	in	ADP
ejpam-5450	2	34	up	up	ADP
ejpam-5450	2	35	(	(	PUNCT
ejpam-5450	2	36	bcc)-algebras	bcc)-algebra	NOUN
ejpam-5450	2	37	aiyared	aiyare	VERB
ejpam-5450	2	38	iampan1,∗	iampan1,∗	NOUN
ejpam-5450	2	39	,	,	PUNCT
ejpam-5450	2	40	ramasamy	ramasamy	NOUN
ejpam-5450	2	41	subasini2	subasini2	NOUN
ejpam-5450	2	42	,	,	PUNCT
ejpam-5450	2	43	neelamegarajan	neelamegarajan	ADJ
ejpam-5450	2	44	rajesh3	rajesh3	PROPN
ejpam-5450	2	45	1	1	NUM
ejpam-5450	2	46	department	department	NOUN
ejpam-5450	2	47	of	of	ADP
ejpam-5450	2	48	mathematics	mathematic	NOUN
ejpam-5450	2	49	,	,	PUNCT
ejpam-5450	2	50	school	school	NOUN
ejpam-5450	2	51	of	of	ADP
ejpam-5450	2	52	science	science	NOUN
ejpam-5450	2	53	,	,	PUNCT
ejpam-5450	2	54	university	university	NOUN
ejpam-5450	2	55	of	of	ADP
ejpam-5450	2	56	phayao	phayao	NOUN
ejpam-5450	2	57	,	,	PUNCT
ejpam-5450	2	58	mae	mae	PROPN
ejpam-5450	2	59	ka	ka	PROPN
ejpam-5450	2	60	,	,	PUNCT
ejpam-5450	2	61	mueang	mueang	PROPN
ejpam-5450	2	62	,	,	PUNCT
ejpam-5450	2	63	phayao	phayao	NOUN
ejpam-5450	2	64	56000	56000	NUM
ejpam-5450	2	65	,	,	PUNCT
ejpam-5450	2	66	thailand	thailand	PROPN
ejpam-5450	2	67	2	2	NUM
ejpam-5450	2	68	department	department	NOUN
ejpam-5450	2	69	of	of	ADP
ejpam-5450	2	70	mathematics	mathematics	PROPN
ejpam-5450	2	71	,	,	PUNCT
ejpam-5450	2	72	pollachi	pollachi	PROPN
ejpam-5450	2	73	institute	institute	PROPN
ejpam-5450	2	74	of	of	ADP
ejpam-5450	2	75	engineering	engineering	NOUN
ejpam-5450	2	76	and	and	CCONJ
ejpam-5450	2	77	technology	technology	NOUN
ejpam-5450	2	78	,	,	PUNCT
ejpam-5450	2	79	pollachi642205	pollachi642205	NOUN
ejpam-5450	2	80	,	,	PUNCT
ejpam-5450	2	81	tamilnadu	tamilnadu	NOUN
ejpam-5450	2	82	,	,	PUNCT
ejpam-5450	2	83	india	india	PROPN
ejpam-5450	2	84	3	3	PROPN
ejpam-5450	2	85	department	department	PROPN
ejpam-5450	2	86	of	of	ADP
ejpam-5450	2	87	mathematics	mathematics	PROPN
ejpam-5450	2	88	,	,	PUNCT
ejpam-5450	2	89	rajah	rajah	NOUN
ejpam-5450	2	90	serfoji	serfoji	ADJ
ejpam-5450	2	91	government	government	NOUN
ejpam-5450	2	92	college	college	NOUN
ejpam-5450	2	93	(	(	PUNCT
ejpam-5450	2	94	affiliated	affiliate	VERB
ejpam-5450	2	95	to	to	PART
ejpam-5450	2	96	bharathidasan	bharathidasan	VERB
ejpam-5450	2	97	university	university	NOUN
ejpam-5450	2	98	)	)	PUNCT
ejpam-5450	2	99	,	,	PUNCT
ejpam-5450	2	100	thanjavur-613005	thanjavur-613005	NOUN
ejpam-5450	2	101	,	,	PUNCT
ejpam-5450	2	102	tamilnadu	tamilnadu	ADJ
ejpam-5450	2	103	,	,	PUNCT
ejpam-5450	2	104	india	india	PROPN
ejpam-5450	2	105	abstract	abstract	NOUN
ejpam-5450	2	106	.	.	PUNCT
ejpam-5450	3	1	this	this	DET
ejpam-5450	3	2	paper	paper	NOUN
ejpam-5450	3	3	presents	present	VERB
ejpam-5450	3	4	the	the	DET
ejpam-5450	3	5	development	development	NOUN
ejpam-5450	3	6	of	of	ADP
ejpam-5450	3	7	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	3	8	fuzzy	fuzzy	ADJ
ejpam-5450	3	9	sets	set	NOUN
ejpam-5450	3	10	using	use	VERB
ejpam-5450	3	11	the	the	DET
ejpam-5450	3	12	lukasiewicz	lukasiewicz	ADJ
ejpam-5450	3	13	t	t	PROPN
ejpam-5450	3	14	-	-	PUNCT
ejpam-5450	3	15	norm	norm	NOUN
ejpam-5450	3	16	derived	derive	VERB
ejpam-5450	3	17	from	from	ADP
ejpam-5450	3	18	a	a	DET
ejpam-5450	3	19	given	give	VERB
ejpam-5450	3	20	fuzzy	fuzzy	ADJ
ejpam-5450	3	21	set	set	NOUN
ejpam-5450	3	22	.	.	PUNCT
ejpam-5450	4	1	these	these	DET
ejpam-5450	4	2	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	4	3	fuzzy	fuzzy	ADJ
ejpam-5450	4	4	sets	set	NOUN
ejpam-5450	4	5	are	be	AUX
ejpam-5450	4	6	subsequently	subsequently	ADV
ejpam-5450	4	7	applied	apply	VERB
ejpam-5450	4	8	to	to	ADP
ejpam-5450	4	9	up	up	ADP
ejpam-5450	4	10	(	(	PUNCT
ejpam-5450	4	11	bcc)-algebras	bcc)-algebra	NOUN
ejpam-5450	4	12	.	.	NOUN
ejpam-5450	4	13	in	in	ADP
ejpam-5450	4	14	addition	addition	NOUN
ejpam-5450	4	15	,	,	PUNCT
ejpam-5450	4	16	the	the	DET
ejpam-5450	4	17	paper	paper	NOUN
ejpam-5450	4	18	introduces	introduce	VERB
ejpam-5450	4	19	the	the	DET
ejpam-5450	4	20	concept	concept	NOUN
ejpam-5450	4	21	of	of	ADP
ejpam-5450	4	22	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	4	23	fuzzy	fuzzy	ADJ
ejpam-5450	4	24	up	up	ADP
ejpam-5450	4	25	(	(	PUNCT
ejpam-5450	4	26	bcc)-ideals	bcc)-ideal	NOUN
ejpam-5450	4	27	and	and	CCONJ
ejpam-5450	4	28	examines	examine	VERB
ejpam-5450	4	29	their	their	PRON
ejpam-5450	4	30	various	various	ADJ
ejpam-5450	4	31	properties	property	NOUN
ejpam-5450	4	32	.	.	PUNCT
ejpam-5450	5	1	three	three	NUM
ejpam-5450	5	2	specific	specific	ADJ
ejpam-5450	5	3	subsets	subset	NOUN
ejpam-5450	5	4	,	,	PUNCT
ejpam-5450	5	5	termed	term	VERB
ejpam-5450	5	6	the	the	DET
ejpam-5450	5	7	∈-set	∈-set	NOUN
ejpam-5450	5	8	,	,	PUNCT
ejpam-5450	5	9	qset	qset	NOUN
ejpam-5450	5	10	,	,	PUNCT
ejpam-5450	5	11	and	and	CCONJ
ejpam-5450	5	12	o	o	X
ejpam-5450	5	13	-	-	NOUN
ejpam-5450	5	14	set	set	ADJ
ejpam-5450	5	15	,	,	PUNCT
ejpam-5450	5	16	are	be	AUX
ejpam-5450	5	17	constructed	construct	VERB
ejpam-5450	5	18	,	,	PUNCT
ejpam-5450	5	19	with	with	ADP
ejpam-5450	5	20	an	an	DET
ejpam-5450	5	21	exploration	exploration	NOUN
ejpam-5450	5	22	of	of	ADP
ejpam-5450	5	23	the	the	DET
ejpam-5450	5	24	conditions	condition	NOUN
ejpam-5450	5	25	under	under	ADP
ejpam-5450	5	26	which	which	PRON
ejpam-5450	5	27	these	these	DET
ejpam-5450	5	28	subsets	subset	NOUN
ejpam-5450	5	29	qualify	qualify	VERB
ejpam-5450	5	30	as	as	ADP
ejpam-5450	5	31	up	up	ADV
ejpam-5450	5	32	(	(	PUNCT
ejpam-5450	5	33	bcc)-ideals	bcc)-ideal	NOUN
ejpam-5450	5	34	.	.	PUNCT
ejpam-5450	6	1	2020	2020	NUM
ejpam-5450	6	2	mathematics	mathematic	NOUN
ejpam-5450	6	3	subject	subject	NOUN
ejpam-5450	6	4	classifications	classification	NOUN
ejpam-5450	6	5	:	:	PUNCT
ejpam-5450	6	6	03g25	03g25	NUM
ejpam-5450	6	7	,	,	PUNCT
ejpam-5450	6	8	08a72	08a72	NOUN
ejpam-5450	6	9	key	key	ADJ
ejpam-5450	6	10	words	word	NOUN
ejpam-5450	6	11	and	and	CCONJ
ejpam-5450	6	12	phrases	phrase	NOUN
ejpam-5450	6	13	:	:	PUNCT
ejpam-5450	6	14	up	up	ADV
ejpam-5450	6	15	(	(	PUNCT
ejpam-5450	6	16	bcc)-algebra	bcc)-algebra	PROPN
ejpam-5450	6	17	,	,	PUNCT
ejpam-5450	6	18	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	6	19	fuzzy	fuzzy	ADJ
ejpam-5450	6	20	set	set	NOUN
ejpam-5450	6	21	,	,	PUNCT
ejpam-5450	6	22	εlukasiewicz	εlukasiewicz	VERB
ejpam-5450	6	23	fuzzy	fuzzy	ADJ
ejpam-5450	6	24	up	up	ADP
ejpam-5450	6	25	(	(	PUNCT
ejpam-5450	6	26	bcc)-ideal	bcc)-ideal	NOUN
ejpam-5450	6	27	,	,	PUNCT
ejpam-5450	6	28	∈-set	∈-set	NOUN
ejpam-5450	6	29	,	,	PUNCT
ejpam-5450	6	30	q	q	NOUN
ejpam-5450	6	31	-	-	PUNCT
ejpam-5450	6	32	set	set	ADJ
ejpam-5450	6	33	,	,	PUNCT
ejpam-5450	6	34	o	o	NOUN
ejpam-5450	6	35	-	-	PUNCT
ejpam-5450	6	36	set	set	ADJ
ejpam-5450	6	37	1	1	NUM
ejpam-5450	6	38	.	.	PUNCT
ejpam-5450	7	1	introduction	introduction	NOUN
ejpam-5450	7	2	zadeh	zadeh	PROPN
ejpam-5450	7	3	[	[	X
ejpam-5450	7	4	21	21	NUM
ejpam-5450	7	5	]	]	PUNCT
ejpam-5450	7	6	originally	originally	ADV
ejpam-5450	7	7	proposed	propose	VERB
ejpam-5450	7	8	the	the	DET
ejpam-5450	7	9	concept	concept	NOUN
ejpam-5450	7	10	of	of	ADP
ejpam-5450	7	11	fuzzy	fuzzy	ADJ
ejpam-5450	7	12	sets	set	NOUN
ejpam-5450	7	13	.	.	PUNCT
ejpam-5450	8	1	fuzzy	fuzzy	ADJ
ejpam-5450	8	2	set	set	NOUN
ejpam-5450	8	3	theory	theory	NOUN
ejpam-5450	8	4	finds	find	VERB
ejpam-5450	8	5	numerous	numerous	ADJ
ejpam-5450	8	6	real	real	ADJ
ejpam-5450	8	7	-	-	PUNCT
ejpam-5450	8	8	world	world	NOUN
ejpam-5450	8	9	applications	application	NOUN
ejpam-5450	8	10	,	,	PUNCT
ejpam-5450	8	11	and	and	CCONJ
ejpam-5450	8	12	many	many	ADJ
ejpam-5450	8	13	researchers	researcher	NOUN
ejpam-5450	8	14	have	have	AUX
ejpam-5450	8	15	extensively	extensively	ADV
ejpam-5450	8	16	explored	explore	VERB
ejpam-5450	8	17	its	its	PRON
ejpam-5450	8	18	principles	principle	NOUN
ejpam-5450	8	19	.	.	PUNCT
ejpam-5450	9	1	following	follow	VERB
ejpam-5450	9	2	the	the	DET
ejpam-5450	9	3	introduction	introduction	NOUN
ejpam-5450	9	4	of	of	ADP
ejpam-5450	9	5	fuzzy	fuzzy	ADJ
ejpam-5450	9	6	sets	set	NOUN
ejpam-5450	9	7	,	,	PUNCT
ejpam-5450	9	8	various	various	ADJ
ejpam-5450	9	9	studies	study	NOUN
ejpam-5450	9	10	have	have	AUX
ejpam-5450	9	11	focused	focus	VERB
ejpam-5450	9	12	on	on	ADP
ejpam-5450	9	13	their	their	PRON
ejpam-5450	9	14	generalizations	generalization	NOUN
ejpam-5450	9	15	.	.	PUNCT
ejpam-5450	10	1	the	the	DET
ejpam-5450	10	2	intersection	intersection	NOUN
ejpam-5450	10	3	of	of	ADP
ejpam-5450	10	4	fuzzy	fuzzy	ADJ
ejpam-5450	10	5	sets	set	NOUN
ejpam-5450	10	6	with	with	ADP
ejpam-5450	10	7	other	other	ADJ
ejpam-5450	10	8	uncertainty	uncertainty	NOUN
ejpam-5450	10	9	models	model	NOUN
ejpam-5450	10	10	,	,	PUNCT
ejpam-5450	10	11	such	such	ADJ
ejpam-5450	10	12	as	as	ADP
ejpam-5450	10	13	soft	soft	ADJ
ejpam-5450	10	14	and	and	CCONJ
ejpam-5450	10	15	rough	rough	ADJ
ejpam-5450	10	16	sets	set	NOUN
ejpam-5450	10	17	,	,	PUNCT
ejpam-5450	10	18	has	have	AUX
ejpam-5450	10	19	been	be	AUX
ejpam-5450	10	20	explored	explore	VERB
ejpam-5450	10	21	in	in	ADP
ejpam-5450	10	22	[	[	X
ejpam-5450	10	23	1–3	1–3	NOUN
ejpam-5450	10	24	]	]	X
ejpam-5450	10	25	.	.	PUNCT
ejpam-5450	11	1	modern	modern	ADJ
ejpam-5450	11	2	technology	technology	NOUN
ejpam-5450	11	3	enables	enable	VERB
ejpam-5450	11	4	sophisticated	sophisticated	ADJ
ejpam-5450	11	5	inferences	inference	NOUN
ejpam-5450	11	6	and	and	CCONJ
ejpam-5450	11	7	problem	problem	NOUN
ejpam-5450	11	8	-	-	PUNCT
ejpam-5450	11	9	solving	solve	VERB
ejpam-5450	11	10	capabilities	capability	NOUN
ejpam-5450	11	11	,	,	PUNCT
ejpam-5450	11	12	particularly	particularly	ADV
ejpam-5450	11	13	in	in	ADP
ejpam-5450	11	14	handling	handle	VERB
ejpam-5450	11	15	theme	theme	NOUN
ejpam-5450	11	16	variations	variation	NOUN
ejpam-5450	11	17	through	through	ADP
ejpam-5450	11	18	programming	programming	NOUN
ejpam-5450	11	19	.	.	PUNCT
ejpam-5450	12	1	lukasiewicz	lukasiewicz	ADJ
ejpam-5450	12	2	logic	logic	NOUN
ejpam-5450	12	3	,	,	PUNCT
ejpam-5450	12	4	governed	govern	VERB
ejpam-5450	12	5	by	by	ADP
ejpam-5450	12	6	the	the	DET
ejpam-5450	12	7	lukasiewicz	lukasiewicz	ADJ
ejpam-5450	12	8	t	t	PROPN
ejpam-5450	12	9	-	-	PUNCT
ejpam-5450	12	10	norm	norm	NOUN
ejpam-5450	12	11	,	,	PUNCT
ejpam-5450	12	12	represents	represent	VERB
ejpam-5450	12	13	a	a	DET
ejpam-5450	12	14	non	non	ADJ
ejpam-5450	12	15	-	-	ADJ
ejpam-5450	12	16	classical	classical	ADJ
ejpam-5450	12	17	,	,	PUNCT
ejpam-5450	12	18	multi	multi	ADJ
ejpam-5450	12	19	-	-	ADJ
ejpam-5450	12	20	valued	value	VERB
ejpam-5450	12	21	logic	logic	NOUN
ejpam-5450	12	22	initially	initially	ADV
ejpam-5450	12	23	formulated	formulate	VERB
ejpam-5450	12	24	in	in	ADP
ejpam-5450	12	25	the	the	DET
ejpam-5450	12	26	early	early	ADJ
ejpam-5450	12	27	20th	20th	ADJ
ejpam-5450	12	28	century	century	NOUN
ejpam-5450	12	29	with	with	ADP
ejpam-5450	12	30	three	three	NUM
ejpam-5450	12	31	truth	truth	NOUN
ejpam-5450	12	32	values	value	NOUN
ejpam-5450	12	33	.	.	PUNCT
ejpam-5450	13	1	one	one	NUM
ejpam-5450	13	2	significant	significant	ADJ
ejpam-5450	13	3	extension	extension	NOUN
ejpam-5450	13	4	is	be	AUX
ejpam-5450	13	5	the	the	DET
ejpam-5450	13	6	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	13	7	fuzzy	fuzzy	ADJ
ejpam-5450	13	8	set	set	NOUN
ejpam-5450	13	9	,	,	PUNCT
ejpam-5450	13	10	derived	derive	VERB
ejpam-5450	13	11	from	from	ADP
ejpam-5450	13	12	the	the	DET
ejpam-5450	13	13	lukasiewicz	lukasiewicz	ADJ
ejpam-5450	13	14	logic	logic	NOUN
ejpam-5450	13	15	,	,	PUNCT
ejpam-5450	13	16	a	a	DET
ejpam-5450	13	17	non	non	ADJ
ejpam-5450	13	18	-	-	ADJ
ejpam-5450	13	19	classical	classical	ADJ
ejpam-5450	13	20	,	,	PUNCT
ejpam-5450	13	21	many	many	ADV
ejpam-5450	13	22	-	-	PUNCT
ejpam-5450	13	23	valued	value	VERB
ejpam-5450	13	24	logic	logic	NOUN
ejpam-5450	13	25	.	.	PUNCT
ejpam-5450	14	1	the	the	DET
ejpam-5450	14	2	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	14	3	fuzzy	fuzzy	ADJ
ejpam-5450	14	4	set	set	NOUN
ejpam-5450	14	5	is	be	AUX
ejpam-5450	14	6	based	base	VERB
ejpam-5450	14	7	on	on	ADP
ejpam-5450	14	8	the	the	DET
ejpam-5450	14	9	lukasiewicz	lukasiewicz	NOUN
ejpam-5450	14	10	∗corresponding	∗corresponde	VERB
ejpam-5450	14	11	author	author	NOUN
ejpam-5450	14	12	.	.	PUNCT
ejpam-5450	15	1	doi	doi	NOUN
ejpam-5450	15	2	:	:	PUNCT
ejpam-5450	15	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5450	https://doi.org/10.29020/nybg.ejpam.v17i4.5450	PRON
ejpam-5450	15	4	email	email	NOUN
ejpam-5450	15	5	addresses	address	NOUN
ejpam-5450	15	6	:	:	PUNCT
ejpam-5450	15	7	aiyared.ia@up.ac.th	aiyared.ia@up.ac.th	NOUN
ejpam-5450	15	8	(	(	PUNCT
ejpam-5450	15	9	a.	a.	NOUN
ejpam-5450	15	10	iampan	iampan	PROPN
ejpam-5450	15	11	)	)	PUNCT
ejpam-5450	15	12	,	,	PUNCT
ejpam-5450	15	13	subasinimaths@gmail.com	subasinimaths@gmail.com	PROPN
ejpam-5450	15	14	(	(	PUNCT
ejpam-5450	15	15	r.	r.	PROPN
ejpam-5450	15	16	subasini	subasini	PROPN
ejpam-5450	15	17	)	)	PUNCT
ejpam-5450	15	18	,	,	PUNCT
ejpam-5450	15	19	nrajesh	nrajesh	PROPN
ejpam-5450	15	20	topology@yahoo.co.in	topology@yahoo.co.in	PROPN
ejpam-5450	15	21	(	(	PUNCT
ejpam-5450	15	22	n.	n.	PROPN
ejpam-5450	15	23	rajesh	rajesh	PROPN
ejpam-5450	15	24	)	)	PUNCT
ejpam-5450	15	25	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5450	16	1	3209	3209	NUM
ejpam-5450	16	2	copyright	copyright	NOUN
ejpam-5450	16	3	:	:	PUNCT
ejpam-5450	16	4	©	©	PROPN
ejpam-5450	16	5	2024	2024	NUM
ejpam-5450	16	6	the	the	DET
ejpam-5450	16	7	author(s	author(s	NOUN
ejpam-5450	16	8	)	)	PUNCT
ejpam-5450	16	9	.	.	PUNCT
ejpam-5450	17	1	(	(	PUNCT
ejpam-5450	17	2	cc	cc	NOUN
ejpam-5450	17	3	by	by	ADP
ejpam-5450	17	4	-	-	PUNCT
ejpam-5450	17	5	nc	nc	PROPN
ejpam-5450	17	6	4.0	4.0	NUM
ejpam-5450	17	7	)	)	PUNCT
ejpam-5450	17	8	a.	a.	NOUN
ejpam-5450	17	9	iampan	iampan	PROPN
ejpam-5450	17	10	,	,	PUNCT
ejpam-5450	17	11	r.	r.	PROPN
ejpam-5450	17	12	subasini	subasini	PROPN
ejpam-5450	17	13	,	,	PUNCT
ejpam-5450	17	14	n.	n.	PROPN
ejpam-5450	17	15	rajesh	rajesh	PROPN
ejpam-5450	17	16	/	/	SYM
ejpam-5450	17	17	eur	eur	PROPN
ejpam-5450	17	18	.	.	PUNCT
ejpam-5450	18	1	j.	j.	PROPN
ejpam-5450	18	2	pure	pure	PROPN
ejpam-5450	18	3	appl	appl	PROPN
ejpam-5450	18	4	.	.	PROPN
ejpam-5450	18	5	math	math	PROPN
ejpam-5450	18	6	,	,	PUNCT
ejpam-5450	18	7	17	17	NUM
ejpam-5450	18	8	(	(	PUNCT
ejpam-5450	18	9	4	4	NUM
ejpam-5450	18	10	)	)	PUNCT
ejpam-5450	18	11	(	(	PUNCT
ejpam-5450	18	12	2024	2024	NUM
ejpam-5450	18	13	)	)	PUNCT
ejpam-5450	18	14	,	,	PUNCT
ejpam-5450	18	15	3209	3209	NUM
ejpam-5450	18	16	-	-	SYM
ejpam-5450	18	17	3222	3222	NUM
ejpam-5450	18	18	3210	3210	NUM
ejpam-5450	18	19	t	t	PROPN
ejpam-5450	18	20	-	-	PUNCT
ejpam-5450	18	21	norm	norm	NOUN
ejpam-5450	18	22	and	and	CCONJ
ejpam-5450	18	23	t	t	NOUN
ejpam-5450	18	24	-	-	PUNCT
ejpam-5450	18	25	conorm	conorm	NOUN
ejpam-5450	18	26	,	,	PUNCT
ejpam-5450	18	27	which	which	PRON
ejpam-5450	18	28	define	define	VERB
ejpam-5450	18	29	fuzzy	fuzzy	ADJ
ejpam-5450	18	30	operations	operation	NOUN
ejpam-5450	18	31	such	such	ADJ
ejpam-5450	18	32	as	as	ADP
ejpam-5450	18	33	intersection	intersection	NOUN
ejpam-5450	18	34	,	,	PUNCT
ejpam-5450	18	35	union	union	NOUN
ejpam-5450	18	36	,	,	PUNCT
ejpam-5450	18	37	and	and	CCONJ
ejpam-5450	18	38	complement	complement	NOUN
ejpam-5450	18	39	.	.	PUNCT
ejpam-5450	19	1	the	the	DET
ejpam-5450	19	2	parameter	parameter	NOUN
ejpam-5450	19	3	ε	ε	PROPN
ejpam-5450	19	4	is	be	AUX
ejpam-5450	19	5	introduced	introduce	VERB
ejpam-5450	19	6	to	to	PART
ejpam-5450	19	7	provide	provide	VERB
ejpam-5450	19	8	additional	additional	ADJ
ejpam-5450	19	9	flexibility	flexibility	NOUN
ejpam-5450	19	10	and	and	CCONJ
ejpam-5450	19	11	control	control	NOUN
ejpam-5450	19	12	over	over	ADP
ejpam-5450	19	13	the	the	DET
ejpam-5450	19	14	set	set	NOUN
ejpam-5450	19	15	’s	’s	PART
ejpam-5450	19	16	fuzziness	fuzziness	NOUN
ejpam-5450	19	17	level	level	NOUN
ejpam-5450	19	18	.	.	PUNCT
ejpam-5450	20	1	fundamental	fundamental	ADJ
ejpam-5450	20	2	concepts	concept	NOUN
ejpam-5450	20	3	of	of	ADP
ejpam-5450	20	4	the	the	DET
ejpam-5450	20	5	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	20	6	fuzzy	fuzzy	ADJ
ejpam-5450	20	7	set	set	NOUN
ejpam-5450	20	8	can	can	AUX
ejpam-5450	20	9	be	be	AUX
ejpam-5450	20	10	found	find	VERB
ejpam-5450	20	11	in	in	ADP
ejpam-5450	20	12	[	[	X
ejpam-5450	20	13	5	5	NUM
ejpam-5450	20	14	,	,	PUNCT
ejpam-5450	20	15	6	6	NUM
ejpam-5450	20	16	,	,	PUNCT
ejpam-5450	20	17	14	14	NUM
ejpam-5450	20	18	]	]	PUNCT
ejpam-5450	20	19	.	.	PUNCT
ejpam-5450	21	1	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	21	2	fuzzy	fuzzy	ADJ
ejpam-5450	21	3	sets	set	NOUN
ejpam-5450	21	4	are	be	AUX
ejpam-5450	21	5	highly	highly	ADV
ejpam-5450	21	6	applicable	applicable	ADJ
ejpam-5450	21	7	across	across	ADP
ejpam-5450	21	8	various	various	ADJ
ejpam-5450	21	9	fields	field	NOUN
ejpam-5450	21	10	by	by	ADP
ejpam-5450	21	11	effectively	effectively	ADV
ejpam-5450	21	12	modelling	model	VERB
ejpam-5450	21	13	uncertainty	uncertainty	NOUN
ejpam-5450	21	14	and	and	CCONJ
ejpam-5450	21	15	imprecision	imprecision	NOUN
ejpam-5450	21	16	.	.	PUNCT
ejpam-5450	22	1	in	in	ADP
ejpam-5450	22	2	decision	decision	NOUN
ejpam-5450	22	3	-	-	PUNCT
ejpam-5450	22	4	making	make	VERB
ejpam-5450	22	5	systems	system	NOUN
ejpam-5450	22	6	,	,	PUNCT
ejpam-5450	22	7	they	they	PRON
ejpam-5450	22	8	enable	enable	VERB
ejpam-5450	22	9	the	the	DET
ejpam-5450	22	10	incorporation	incorporation	NOUN
ejpam-5450	22	11	of	of	ADP
ejpam-5450	22	12	ambiguous	ambiguous	ADJ
ejpam-5450	22	13	information	information	NOUN
ejpam-5450	22	14	,	,	PUNCT
ejpam-5450	22	15	allowing	allow	VERB
ejpam-5450	22	16	for	for	ADP
ejpam-5450	22	17	more	more	ADV
ejpam-5450	22	18	nuanced	nuanced	ADJ
ejpam-5450	22	19	evaluations	evaluation	NOUN
ejpam-5450	22	20	of	of	ADP
ejpam-5450	22	21	alternatives	alternative	NOUN
ejpam-5450	22	22	.	.	PUNCT
ejpam-5450	23	1	in	in	ADP
ejpam-5450	23	2	medical	medical	ADJ
ejpam-5450	23	3	diagnosis	diagnosis	NOUN
ejpam-5450	23	4	,	,	PUNCT
ejpam-5450	23	5	these	these	DET
ejpam-5450	23	6	fuzzy	fuzzy	ADJ
ejpam-5450	23	7	sets	set	NOUN
ejpam-5450	23	8	help	help	VERB
ejpam-5450	23	9	assess	assess	VERB
ejpam-5450	23	10	unclear	unclear	ADJ
ejpam-5450	23	11	symptoms	symptom	NOUN
ejpam-5450	23	12	and	and	CCONJ
ejpam-5450	23	13	test	test	NOUN
ejpam-5450	23	14	results	result	NOUN
ejpam-5450	23	15	,	,	PUNCT
ejpam-5450	23	16	leading	lead	VERB
ejpam-5450	23	17	to	to	ADP
ejpam-5450	23	18	personalized	personalize	VERB
ejpam-5450	23	19	treatment	treatment	NOUN
ejpam-5450	23	20	plans	plan	NOUN
ejpam-5450	23	21	.	.	PUNCT
ejpam-5450	24	1	in	in	ADP
ejpam-5450	24	2	financial	financial	ADJ
ejpam-5450	24	3	analysis	analysis	NOUN
ejpam-5450	24	4	,	,	PUNCT
ejpam-5450	24	5	they	they	PRON
ejpam-5450	24	6	enhance	enhance	VERB
ejpam-5450	24	7	risk	risk	NOUN
ejpam-5450	24	8	assessment	assessment	NOUN
ejpam-5450	24	9	by	by	ADP
ejpam-5450	24	10	capturing	capture	VERB
ejpam-5450	24	11	market	market	NOUN
ejpam-5450	24	12	uncertainties	uncertainty	NOUN
ejpam-5450	24	13	,	,	PUNCT
ejpam-5450	24	14	while	while	SCONJ
ejpam-5450	24	15	in	in	ADP
ejpam-5450	24	16	artificial	artificial	ADJ
ejpam-5450	24	17	intelligence	intelligence	NOUN
ejpam-5450	24	18	,	,	PUNCT
ejpam-5450	24	19	they	they	PRON
ejpam-5450	24	20	improve	improve	VERB
ejpam-5450	24	21	knowledge	knowledge	NOUN
ejpam-5450	24	22	representation	representation	NOUN
ejpam-5450	24	23	and	and	CCONJ
ejpam-5450	24	24	reasoning	reasoning	NOUN
ejpam-5450	24	25	,	,	PUNCT
ejpam-5450	24	26	enabling	enable	VERB
ejpam-5450	24	27	ai	ai	VERB
ejpam-5450	24	28	systems	system	NOUN
ejpam-5450	24	29	to	to	PART
ejpam-5450	24	30	make	make	VERB
ejpam-5450	24	31	human	human	ADJ
ejpam-5450	24	32	-	-	PUNCT
ejpam-5450	24	33	like	like	ADJ
ejpam-5450	24	34	decisions	decision	NOUN
ejpam-5450	24	35	.	.	PUNCT
ejpam-5450	25	1	overall	overall	ADJ
ejpam-5450	25	2	,	,	PUNCT
ejpam-5450	25	3	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	25	4	fuzzy	fuzzy	ADJ
ejpam-5450	25	5	sets	set	NOUN
ejpam-5450	25	6	offer	offer	VERB
ejpam-5450	25	7	valuable	valuable	ADJ
ejpam-5450	25	8	insights	insight	NOUN
ejpam-5450	25	9	and	and	CCONJ
ejpam-5450	25	10	practical	practical	ADJ
ejpam-5450	25	11	solutions	solution	NOUN
ejpam-5450	25	12	in	in	ADP
ejpam-5450	25	13	uncertain	uncertain	ADJ
ejpam-5450	25	14	environments	environment	NOUN
ejpam-5450	25	15	across	across	ADP
ejpam-5450	25	16	multiple	multiple	ADJ
ejpam-5450	25	17	disciplines	discipline	NOUN
ejpam-5450	25	18	.	.	PUNCT
ejpam-5450	26	1	iampan	iampan	NOUN
ejpam-5450	26	2	[	[	X
ejpam-5450	26	3	9	9	X
ejpam-5450	26	4	]	]	PUNCT
ejpam-5450	26	5	introduced	introduce	VERB
ejpam-5450	26	6	up	up	ADV
ejpam-5450	26	7	-	-	PUNCT
ejpam-5450	26	8	algebras	algebra	NOUN
ejpam-5450	26	9	as	as	ADP
ejpam-5450	26	10	a	a	DET
ejpam-5450	26	11	novel	novel	ADJ
ejpam-5450	26	12	algebraic	algebraic	ADJ
ejpam-5450	26	13	structure	structure	NOUN
ejpam-5450	26	14	.	.	PUNCT
ejpam-5450	27	1	somjanta	somjanta	PROPN
ejpam-5450	27	2	et	et	PROPN
ejpam-5450	27	3	al	al	PROPN
ejpam-5450	27	4	.	.	PUNCT
ejpam-5450	28	1	[	[	X
ejpam-5450	28	2	20	20	NUM
ejpam-5450	28	3	]	]	PUNCT
ejpam-5450	28	4	and	and	CCONJ
ejpam-5450	28	5	guntasow	guntasow	VERB
ejpam-5450	28	6	et	et	PROPN
ejpam-5450	28	7	al	al	PROPN
ejpam-5450	28	8	.	.	PUNCT
ejpam-5450	29	1	[	[	X
ejpam-5450	29	2	7	7	NUM
ejpam-5450	29	3	]	]	PUNCT
ejpam-5450	29	4	applied	apply	VERB
ejpam-5450	29	5	fuzzy	fuzzy	ADJ
ejpam-5450	29	6	set	set	NOUN
ejpam-5450	29	7	theory	theory	NOUN
ejpam-5450	29	8	within	within	ADP
ejpam-5450	29	9	the	the	DET
ejpam-5450	29	10	framework	framework	NOUN
ejpam-5450	29	11	of	of	ADP
ejpam-5450	29	12	up	up	ADP
ejpam-5450	29	13	-	-	PUNCT
ejpam-5450	29	14	algebras	algebras	X
ejpam-5450	29	15	.	.	PUNCT
ejpam-5450	30	1	dokkhamdang	dokkhamdang	PROPN
ejpam-5450	30	2	et	et	PROPN
ejpam-5450	30	3	al	al	PROPN
ejpam-5450	30	4	.	.	PUNCT
ejpam-5450	31	1	[	[	X
ejpam-5450	31	2	4	4	X
ejpam-5450	31	3	]	]	PUNCT
ejpam-5450	31	4	introduced	introduce	VERB
ejpam-5450	31	5	the	the	DET
ejpam-5450	31	6	concept	concept	NOUN
ejpam-5450	31	7	of	of	ADP
ejpam-5450	31	8	fuzzy	fuzzy	ADJ
ejpam-5450	31	9	up	up	NOUN
ejpam-5450	31	10	-	-	PUNCT
ejpam-5450	31	11	subalgebras	subalgebras	PROPN
ejpam-5450	31	12	with	with	ADP
ejpam-5450	31	13	thresholds	threshold	NOUN
ejpam-5450	31	14	in	in	ADP
ejpam-5450	31	15	up	up	ADP
ejpam-5450	31	16	-	-	PUNCT
ejpam-5450	31	17	algebras	algebras	X
ejpam-5450	31	18	.	.	PUNCT
ejpam-5450	32	1	poungsumpao	poungsumpao	PROPN
ejpam-5450	32	2	et	et	PROPN
ejpam-5450	32	3	al	al	PROPN
ejpam-5450	32	4	.	.	PUNCT
ejpam-5450	33	1	[	[	X
ejpam-5450	33	2	16	16	NUM
ejpam-5450	33	3	]	]	PUNCT
ejpam-5450	33	4	studied	study	VERB
ejpam-5450	33	5	fuzzy	fuzzy	ADJ
ejpam-5450	33	6	up	up	ADP
ejpam-5450	33	7	-	-	PUNCT
ejpam-5450	33	8	subalgebras	subalgebra	NOUN
ejpam-5450	33	9	and	and	CCONJ
ejpam-5450	33	10	fuzzy	fuzzy	ADJ
ejpam-5450	33	11	up	up	NOUN
ejpam-5450	33	12	-	-	PUNCT
ejpam-5450	33	13	ideals	ideal	NOUN
ejpam-5450	33	14	of	of	ADP
ejpam-5450	33	15	up	up	ADV
ejpam-5450	33	16	-	-	PUNCT
ejpam-5450	33	17	algebras	algebras	NOUN
ejpam-5450	33	18	in	in	ADP
ejpam-5450	33	19	terms	term	NOUN
ejpam-5450	33	20	of	of	ADP
ejpam-5450	33	21	upper	upper	ADJ
ejpam-5450	33	22	t-(strong	t-(strong	PROPN
ejpam-5450	33	23	)	)	PUNCT
ejpam-5450	33	24	level	level	NOUN
ejpam-5450	33	25	subsets	subset	NOUN
ejpam-5450	33	26	and	and	CCONJ
ejpam-5450	33	27	lower	low	ADJ
ejpam-5450	33	28	t-(strong	t-(strong	NOUN
ejpam-5450	33	29	)	)	PUNCT
ejpam-5450	33	30	level	level	NOUN
ejpam-5450	33	31	subsets	subset	NOUN
ejpam-5450	33	32	.	.	PUNCT
ejpam-5450	34	1	senapati	senapati	PROPN
ejpam-5450	34	2	et	et	PROPN
ejpam-5450	34	3	al	al	PROPN
ejpam-5450	34	4	.	.	PUNCT
ejpam-5450	35	1	[	[	X
ejpam-5450	35	2	18	18	NUM
ejpam-5450	35	3	]	]	PUNCT
ejpam-5450	35	4	pioneered	pioneer	VERB
ejpam-5450	35	5	the	the	DET
ejpam-5450	35	6	concept	concept	NOUN
ejpam-5450	35	7	of	of	ADP
ejpam-5450	35	8	cubic	cubic	ADJ
ejpam-5450	35	9	sets	set	NOUN
ejpam-5450	35	10	within	within	ADP
ejpam-5450	35	11	up	up	ADV
ejpam-5450	35	12	-	-	PUNCT
ejpam-5450	35	13	subalgebras	subalgebra	NOUN
ejpam-5450	35	14	and	and	CCONJ
ejpam-5450	35	15	up	up	ADP
ejpam-5450	35	16	-	-	PUNCT
ejpam-5450	35	17	ideals	ideal	NOUN
ejpam-5450	35	18	in	in	ADP
ejpam-5450	35	19	the	the	DET
ejpam-5450	35	20	framework	framework	NOUN
ejpam-5450	35	21	of	of	ADP
ejpam-5450	35	22	up	up	ADP
ejpam-5450	35	23	-	-	PUNCT
ejpam-5450	35	24	algebras	algebras	X
ejpam-5450	35	25	.	.	PUNCT
ejpam-5450	36	1	their	their	PRON
ejpam-5450	36	2	research	research	NOUN
ejpam-5450	36	3	delved	delve	VERB
ejpam-5450	36	4	into	into	ADP
ejpam-5450	36	5	the	the	DET
ejpam-5450	36	6	intricate	intricate	ADJ
ejpam-5450	36	7	relationships	relationship	NOUN
ejpam-5450	36	8	between	between	ADP
ejpam-5450	36	9	cubic	cubic	ADJ
ejpam-5450	36	10	up	up	ADP
ejpam-5450	36	11	-	-	PUNCT
ejpam-5450	36	12	subalgebras	subalgebra	NOUN
ejpam-5450	36	13	and	and	CCONJ
ejpam-5450	36	14	cubic	cubic	ADJ
ejpam-5450	36	15	up	up	ADP
ejpam-5450	36	16	-	-	PUNCT
ejpam-5450	36	17	ideals	ideal	NOUN
ejpam-5450	36	18	,	,	PUNCT
ejpam-5450	36	19	revealing	reveal	VERB
ejpam-5450	36	20	new	new	ADJ
ejpam-5450	36	21	insights	insight	NOUN
ejpam-5450	36	22	into	into	ADP
ejpam-5450	36	23	their	their	PRON
ejpam-5450	36	24	structural	structural	ADJ
ejpam-5450	36	25	connections	connection	NOUN
ejpam-5450	36	26	.	.	PUNCT
ejpam-5450	37	1	senapati	senapati	PROPN
ejpam-5450	37	2	et	et	PROPN
ejpam-5450	37	3	al	al	PROPN
ejpam-5450	37	4	.	.	PUNCT
ejpam-5450	38	1	[	[	X
ejpam-5450	38	2	19	19	NUM
ejpam-5450	38	3	]	]	PUNCT
ejpam-5450	38	4	explored	explore	VERB
ejpam-5450	38	5	the	the	DET
ejpam-5450	38	6	concept	concept	NOUN
ejpam-5450	38	7	of	of	ADP
ejpam-5450	38	8	interval	interval	NOUN
ejpam-5450	38	9	-	-	PUNCT
ejpam-5450	38	10	valued	value	VERB
ejpam-5450	38	11	intuitionistic	intuitionistic	ADJ
ejpam-5450	38	12	fuzzy	fuzzy	ADJ
ejpam-5450	38	13	sets	set	NOUN
ejpam-5450	38	14	,	,	PUNCT
ejpam-5450	38	15	applying	apply	VERB
ejpam-5450	38	16	it	it	PRON
ejpam-5450	38	17	to	to	ADP
ejpam-5450	38	18	both	both	CCONJ
ejpam-5450	38	19	up	up	ADP
ejpam-5450	38	20	-	-	PUNCT
ejpam-5450	38	21	subalgebras	subalgebra	NOUN
ejpam-5450	38	22	and	and	CCONJ
ejpam-5450	38	23	up	up	ADP
ejpam-5450	38	24	-	-	PUNCT
ejpam-5450	38	25	ideals	ideal	NOUN
ejpam-5450	38	26	in	in	ADP
ejpam-5450	38	27	up	up	ADP
ejpam-5450	38	28	-	-	PUNCT
ejpam-5450	38	29	algebras	algebras	X
ejpam-5450	38	30	.	.	PUNCT
ejpam-5450	39	1	their	their	PRON
ejpam-5450	39	2	work	work	NOUN
ejpam-5450	39	3	examined	examine	VERB
ejpam-5450	39	4	the	the	DET
ejpam-5450	39	5	homomorphic	homomorphic	ADJ
ejpam-5450	39	6	images	image	NOUN
ejpam-5450	39	7	and	and	CCONJ
ejpam-5450	39	8	inverse	inverse	NOUN
ejpam-5450	39	9	images	image	NOUN
ejpam-5450	39	10	of	of	ADP
ejpam-5450	39	11	these	these	DET
ejpam-5450	39	12	interval	interval	NOUN
ejpam-5450	39	13	-	-	PUNCT
ejpam-5450	39	14	valued	value	VERB
ejpam-5450	39	15	intuitionistic	intuitionistic	ADJ
ejpam-5450	39	16	fuzzy	fuzzy	ADJ
ejpam-5450	39	17	up	up	ADV
ejpam-5450	39	18	-	-	PUNCT
ejpam-5450	39	19	subalgebras	subalgebra	NOUN
ejpam-5450	39	20	and	and	CCONJ
ejpam-5450	39	21	up	up	ADP
ejpam-5450	39	22	-	-	PUNCT
ejpam-5450	39	23	ideals	ideal	NOUN
ejpam-5450	39	24	,	,	PUNCT
ejpam-5450	39	25	providing	provide	VERB
ejpam-5450	39	26	deeper	deep	ADJ
ejpam-5450	39	27	insights	insight	NOUN
ejpam-5450	39	28	into	into	ADP
ejpam-5450	39	29	their	their	PRON
ejpam-5450	39	30	structural	structural	ADJ
ejpam-5450	39	31	behaviour	behaviour	NOUN
ejpam-5450	39	32	.	.	PUNCT
ejpam-5450	40	1	jana	jana	PROPN
ejpam-5450	40	2	et	et	PROPN
ejpam-5450	40	3	al	al	PROPN
ejpam-5450	40	4	.	.	PUNCT
ejpam-5450	41	1	[	[	X
ejpam-5450	41	2	11	11	NUM
ejpam-5450	41	3	]	]	PUNCT
ejpam-5450	41	4	introduced	introduce	VERB
ejpam-5450	41	5	the	the	DET
ejpam-5450	41	6	concept	concept	NOUN
ejpam-5450	41	7	of	of	ADP
ejpam-5450	41	8	quasi	quasi	NOUN
ejpam-5450	41	9	-	-	NOUN
ejpam-5450	41	10	coincidence	coincidence	NOUN
ejpam-5450	41	11	between	between	ADP
ejpam-5450	41	12	an	an	DET
ejpam-5450	41	13	intuitionistic	intuitionistic	ADJ
ejpam-5450	41	14	fuzzy	fuzzy	ADJ
ejpam-5450	41	15	point	point	NOUN
ejpam-5450	41	16	and	and	CCONJ
ejpam-5450	41	17	an	an	DET
ejpam-5450	41	18	intuitionistic	intuitionistic	ADJ
ejpam-5450	41	19	fuzzy	fuzzy	ADJ
ejpam-5450	41	20	set	set	NOUN
ejpam-5450	41	21	.	.	PUNCT
ejpam-5450	42	1	they	they	PRON
ejpam-5450	42	2	further	far	ADV
ejpam-5450	42	3	developed	develop	VERB
ejpam-5450	42	4	and	and	CCONJ
ejpam-5450	42	5	explored	explore	VERB
ejpam-5450	42	6	the	the	DET
ejpam-5450	42	7	notions	notion	NOUN
ejpam-5450	42	8	of	of	ADP
ejpam-5450	42	9	(	(	PUNCT
ejpam-5450	42	10	∈,∈	∈,∈	X
ejpam-5450	42	11	∨q)-intuitionistic	∨q)-intuitionistic	ADJ
ejpam-5450	42	12	fuzzy	fuzzy	ADJ
ejpam-5450	42	13	bci	bci	NOUN
ejpam-5450	42	14	-	-	PUNCT
ejpam-5450	42	15	subalgebras	subalgebras	PROPN
ejpam-5450	42	16	within	within	ADP
ejpam-5450	42	17	the	the	DET
ejpam-5450	42	18	framework	framework	NOUN
ejpam-5450	42	19	of	of	ADP
ejpam-5450	42	20	bci	bci	PROPN
ejpam-5450	42	21	-	-	PUNCT
ejpam-5450	42	22	algebras	algebras	X
ejpam-5450	42	23	,	,	PUNCT
ejpam-5450	42	24	offering	offer	VERB
ejpam-5450	42	25	new	new	ADJ
ejpam-5450	42	26	perspectives	perspective	NOUN
ejpam-5450	42	27	on	on	ADP
ejpam-5450	42	28	their	their	PRON
ejpam-5450	42	29	structure	structure	NOUN
ejpam-5450	42	30	and	and	CCONJ
ejpam-5450	42	31	properties	property	NOUN
ejpam-5450	42	32	.	.	PUNCT
ejpam-5450	43	1	up	up	ADP
ejpam-5450	43	2	-	-	PUNCT
ejpam-5450	43	3	algebras	algebras	X
ejpam-5450	43	4	(	(	PUNCT
ejpam-5450	43	5	see	see	VERB
ejpam-5450	43	6	[	[	X
ejpam-5450	43	7	9	9	NUM
ejpam-5450	43	8	]	]	PUNCT
ejpam-5450	43	9	)	)	PUNCT
ejpam-5450	43	10	and	and	CCONJ
ejpam-5450	43	11	bcc	bcc	PROPN
ejpam-5450	43	12	-	-	PUNCT
ejpam-5450	43	13	algebras	algebras	PROPN
ejpam-5450	43	14	(	(	PUNCT
ejpam-5450	43	15	see	see	VERB
ejpam-5450	43	16	[	[	X
ejpam-5450	43	17	15	15	NUM
ejpam-5450	43	18	]	]	PUNCT
ejpam-5450	43	19	)	)	PUNCT
ejpam-5450	43	20	are	be	AUX
ejpam-5450	43	21	identified	identify	VERB
ejpam-5450	43	22	as	as	ADP
ejpam-5450	43	23	the	the	DET
ejpam-5450	43	24	same	same	ADJ
ejpam-5450	43	25	concept	concept	NOUN
ejpam-5450	43	26	,	,	PUNCT
ejpam-5450	43	27	as	as	SCONJ
ejpam-5450	43	28	demonstrated	demonstrate	VERB
ejpam-5450	43	29	by	by	ADP
ejpam-5450	43	30	jun	jun	PROPN
ejpam-5450	43	31	et	et	PROPN
ejpam-5450	43	32	al	al	PROPN
ejpam-5450	43	33	.	.	PUNCT
ejpam-5450	44	1	[	[	X
ejpam-5450	44	2	13	13	NUM
ejpam-5450	44	3	]	]	PUNCT
ejpam-5450	44	4	in	in	ADP
ejpam-5450	44	5	2022	2022	NUM
ejpam-5450	44	6	.	.	PUNCT
ejpam-5450	45	1	for	for	ADP
ejpam-5450	45	2	consistency	consistency	NOUN
ejpam-5450	45	3	with	with	ADP
ejpam-5450	45	4	komori	komori	PROPN
ejpam-5450	45	5	’s	’s	PART
ejpam-5450	45	6	initial	initial	ADJ
ejpam-5450	45	7	characterization	characterization	NOUN
ejpam-5450	45	8	in	in	ADP
ejpam-5450	45	9	1984	1984	NUM
ejpam-5450	45	10	,	,	PUNCT
ejpam-5450	45	11	our	our	PRON
ejpam-5450	45	12	research	research	NOUN
ejpam-5450	45	13	team	team	NOUN
ejpam-5450	45	14	will	will	AUX
ejpam-5450	45	15	adopt	adopt	VERB
ejpam-5450	45	16	the	the	DET
ejpam-5450	45	17	term	term	NOUN
ejpam-5450	45	18	bcc	bcc	PROPN
ejpam-5450	45	19	rather	rather	ADV
ejpam-5450	45	20	than	than	ADP
ejpam-5450	45	21	up	up	ADP
ejpam-5450	45	22	in	in	ADP
ejpam-5450	45	23	subsequent	subsequent	ADJ
ejpam-5450	45	24	investigations	investigation	NOUN
ejpam-5450	45	25	and	and	CCONJ
ejpam-5450	45	26	publications	publication	NOUN
ejpam-5450	45	27	.	.	PUNCT
ejpam-5450	46	1	in	in	ADP
ejpam-5450	46	2	this	this	DET
ejpam-5450	46	3	paper	paper	NOUN
ejpam-5450	46	4	,	,	PUNCT
ejpam-5450	46	5	we	we	PRON
ejpam-5450	46	6	utilize	utilize	VERB
ejpam-5450	46	7	the	the	DET
ejpam-5450	46	8	lukasiewicz	lukasiewicz	ADJ
ejpam-5450	46	9	t	t	PROPN
ejpam-5450	46	10	-	-	PUNCT
ejpam-5450	46	11	norm	norm	NOUN
ejpam-5450	46	12	to	to	PART
ejpam-5450	46	13	introduce	introduce	VERB
ejpam-5450	46	14	the	the	DET
ejpam-5450	46	15	concept	concept	NOUN
ejpam-5450	46	16	of	of	ADP
ejpam-5450	46	17	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	46	18	fuzzy	fuzzy	ADJ
ejpam-5450	46	19	sets	set	NOUN
ejpam-5450	46	20	derived	derive	VERB
ejpam-5450	46	21	from	from	ADP
ejpam-5450	46	22	a	a	DET
ejpam-5450	46	23	given	give	VERB
ejpam-5450	46	24	fuzzy	fuzzy	ADJ
ejpam-5450	46	25	set	set	NOUN
ejpam-5450	46	26	,	,	PUNCT
ejpam-5450	46	27	applying	apply	VERB
ejpam-5450	46	28	this	this	DET
ejpam-5450	46	29	framework	framework	NOUN
ejpam-5450	46	30	to	to	ADP
ejpam-5450	46	31	bcc	bcc	PROPN
ejpam-5450	46	32	-	-	PUNCT
ejpam-5450	46	33	algebras	algebras	PROPN
ejpam-5450	46	34	.	.	PUNCT
ejpam-5450	47	1	we	we	PRON
ejpam-5450	47	2	define	define	VERB
ejpam-5450	47	3	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	47	4	fuzzy	fuzzy	ADJ
ejpam-5450	47	5	bcc	bcc	PROPN
ejpam-5450	47	6	-	-	PUNCT
ejpam-5450	47	7	ideals	ideal	NOUN
ejpam-5450	47	8	and	and	CCONJ
ejpam-5450	47	9	explore	explore	VERB
ejpam-5450	47	10	their	their	PRON
ejpam-5450	47	11	properties	property	NOUN
ejpam-5450	47	12	.	.	PUNCT
ejpam-5450	48	1	conditions	condition	NOUN
ejpam-5450	48	2	are	be	AUX
ejpam-5450	48	3	established	establish	VERB
ejpam-5450	48	4	for	for	ADP
ejpam-5450	48	5	an	an	DET
ejpam-5450	48	6	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	48	7	fuzzy	fuzzy	NOUN
ejpam-5450	48	8	set	set	VERB
ejpam-5450	48	9	to	to	PART
ejpam-5450	48	10	qualify	qualify	VERB
ejpam-5450	48	11	as	as	ADP
ejpam-5450	48	12	an	an	DET
ejpam-5450	48	13	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	48	14	fuzzy	fuzzy	ADJ
ejpam-5450	48	15	bccsubalgebra	bccsubalgebra	NOUN
ejpam-5450	48	16	,	,	PUNCT
ejpam-5450	48	17	and	and	CCONJ
ejpam-5450	48	18	we	we	PRON
ejpam-5450	48	19	characterize	characterize	VERB
ejpam-5450	48	20	these	these	DET
ejpam-5450	48	21	structures	structure	NOUN
ejpam-5450	48	22	.	.	PUNCT
ejpam-5450	49	1	additionally	additionally	ADV
ejpam-5450	49	2	,	,	PUNCT
ejpam-5450	49	3	we	we	PRON
ejpam-5450	49	4	introduce	introduce	VERB
ejpam-5450	49	5	three	three	NUM
ejpam-5450	49	6	specific	specific	ADJ
ejpam-5450	49	7	subsets	subset	NOUN
ejpam-5450	49	8	—	—	PUNCT
ejpam-5450	49	9	referred	refer	VERB
ejpam-5450	49	10	to	to	ADP
ejpam-5450	49	11	as	as	ADP
ejpam-5450	49	12	∈-set	∈-set	NOUN
ejpam-5450	49	13	,	,	PUNCT
ejpam-5450	49	14	q	q	NOUN
ejpam-5450	49	15	-	-	PUNCT
ejpam-5450	49	16	set	set	NOUN
ejpam-5450	49	17	,	,	PUNCT
ejpam-5450	49	18	and	and	CCONJ
ejpam-5450	49	19	o	o	X
ejpam-5450	49	20	-	-	NOUN
ejpam-5450	49	21	set	set	NOUN
ejpam-5450	49	22	—	—	PUNCT
ejpam-5450	49	23	and	and	CCONJ
ejpam-5450	49	24	determine	determine	VERB
ejpam-5450	49	25	the	the	DET
ejpam-5450	49	26	conditions	condition	NOUN
ejpam-5450	49	27	under	under	ADP
ejpam-5450	49	28	which	which	PRON
ejpam-5450	49	29	they	they	PRON
ejpam-5450	49	30	can	can	AUX
ejpam-5450	49	31	function	function	VERB
ejpam-5450	49	32	as	as	ADP
ejpam-5450	49	33	bcc	bcc	NOUN
ejpam-5450	49	34	-	-	PUNCT
ejpam-5450	49	35	ideals	ideal	NOUN
ejpam-5450	49	36	.	.	PUNCT
ejpam-5450	50	1	a.	a.	PROPN
ejpam-5450	50	2	iampan	iampan	PROPN
ejpam-5450	50	3	,	,	PUNCT
ejpam-5450	50	4	r.	r.	PROPN
ejpam-5450	50	5	subasini	subasini	PROPN
ejpam-5450	50	6	,	,	PUNCT
ejpam-5450	50	7	n.	n.	PROPN
ejpam-5450	50	8	rajesh	rajesh	PROPN
ejpam-5450	50	9	/	/	SYM
ejpam-5450	50	10	eur	eur	PROPN
ejpam-5450	50	11	.	.	PUNCT
ejpam-5450	51	1	j.	j.	PROPN
ejpam-5450	51	2	pure	pure	PROPN
ejpam-5450	51	3	appl	appl	PROPN
ejpam-5450	51	4	.	.	PROPN
ejpam-5450	51	5	math	math	PROPN
ejpam-5450	51	6	,	,	PUNCT
ejpam-5450	51	7	17	17	NUM
ejpam-5450	51	8	(	(	PUNCT
ejpam-5450	51	9	4	4	NUM
ejpam-5450	51	10	)	)	PUNCT
ejpam-5450	51	11	(	(	PUNCT
ejpam-5450	51	12	2024	2024	NUM
ejpam-5450	51	13	)	)	PUNCT
ejpam-5450	51	14	,	,	PUNCT
ejpam-5450	51	15	3209	3209	NUM
ejpam-5450	51	16	-	-	SYM
ejpam-5450	51	17	3222	3222	NUM
ejpam-5450	51	18	3211	3211	NUM
ejpam-5450	51	19	2	2	NUM
ejpam-5450	51	20	.	.	PUNCT
ejpam-5450	51	21	preliminaries	preliminary	NOUN
ejpam-5450	51	22	the	the	DET
ejpam-5450	51	23	concept	concept	NOUN
ejpam-5450	51	24	of	of	ADP
ejpam-5450	51	25	bcc	bcc	PROPN
ejpam-5450	51	26	-	-	PUNCT
ejpam-5450	51	27	algebras	algebras	PROPN
ejpam-5450	51	28	(	(	PUNCT
ejpam-5450	51	29	referenced	reference	VERB
ejpam-5450	51	30	in	in	ADP
ejpam-5450	51	31	[	[	X
ejpam-5450	51	32	15	15	NUM
ejpam-5450	51	33	]	]	PUNCT
ejpam-5450	51	34	)	)	PUNCT
ejpam-5450	51	35	can	can	AUX
ejpam-5450	51	36	be	be	AUX
ejpam-5450	51	37	reformulated	reformulate	VERB
ejpam-5450	51	38	without	without	ADP
ejpam-5450	51	39	the	the	DET
ejpam-5450	51	40	condition	condition	NOUN
ejpam-5450	51	41	(	(	PUNCT
ejpam-5450	51	42	2.6	2.6	NUM
ejpam-5450	51	43	)	)	PUNCT
ejpam-5450	51	44	as	as	SCONJ
ejpam-5450	51	45	follows	follow	VERB
ejpam-5450	51	46	:	:	PUNCT
ejpam-5450	51	47	an	an	DET
ejpam-5450	51	48	algebra	algebra	NOUN
ejpam-5450	51	49	x	x	X
ejpam-5450	51	50	=	=	SYM
ejpam-5450	51	51	(	(	PUNCT
ejpam-5450	51	52	x	x	NOUN
ejpam-5450	51	53	,	,	PUNCT
ejpam-5450	51	54	◦	◦	NOUN
ejpam-5450	51	55	,	,	PUNCT
ejpam-5450	51	56	0	0	NUM
ejpam-5450	51	57	)	)	PUNCT
ejpam-5450	51	58	of	of	ADP
ejpam-5450	51	59	type	type	NOUN
ejpam-5450	51	60	(	(	PUNCT
ejpam-5450	51	61	2	2	NUM
ejpam-5450	51	62	,	,	PUNCT
ejpam-5450	51	63	0	0	NUM
ejpam-5450	51	64	)	)	PUNCT
ejpam-5450	51	65	is	be	AUX
ejpam-5450	51	66	called	call	VERB
ejpam-5450	51	67	a	a	DET
ejpam-5450	51	68	bcc	bcc	PROPN
ejpam-5450	51	69	-	-	PUNCT
ejpam-5450	51	70	algebra	algebra	PROPN
ejpam-5450	51	71	(	(	PUNCT
ejpam-5450	51	72	see	see	VERB
ejpam-5450	51	73	[	[	X
ejpam-5450	51	74	8	8	NUM
ejpam-5450	51	75	]	]	PUNCT
ejpam-5450	51	76	)	)	PUNCT
ejpam-5450	51	77	if	if	SCONJ
ejpam-5450	51	78	it	it	PRON
ejpam-5450	51	79	satisfies	satisfy	VERB
ejpam-5450	51	80	the	the	DET
ejpam-5450	51	81	following	follow	VERB
ejpam-5450	51	82	conditions	condition	NOUN
ejpam-5450	51	83	:	:	PUNCT
ejpam-5450	51	84	(	(	PUNCT
ejpam-5450	51	85	∀x	∀x	X
ejpam-5450	51	86	,	,	PUNCT
ejpam-5450	51	87	y	y	PROPN
ejpam-5450	51	88	,	,	PUNCT
ejpam-5450	51	89	z	z	NOUN
ejpam-5450	51	90	∈	∈	PROPN
ejpam-5450	51	91	x)((y	x)((y	PROPN
ejpam-5450	52	1	◦	◦	PROPN
ejpam-5450	52	2	z	z	NOUN
ejpam-5450	52	3	)	)	PUNCT
ejpam-5450	52	4	◦	◦	NOUN
ejpam-5450	52	5	(	(	PUNCT
ejpam-5450	52	6	(	(	PUNCT
ejpam-5450	52	7	x	x	SYM
ejpam-5450	52	8	◦	◦	VERB
ejpam-5450	52	9	y	y	NOUN
ejpam-5450	52	10	)	)	PUNCT
ejpam-5450	52	11	◦	◦	NOUN
ejpam-5450	53	1	(	(	PUNCT
ejpam-5450	53	2	x	x	PART
ejpam-5450	53	3	◦	◦	NOUN
ejpam-5450	53	4	z	z	NOUN
ejpam-5450	53	5	)	)	PUNCT
ejpam-5450	53	6	)	)	PUNCT
ejpam-5450	54	1	=	=	SYM
ejpam-5450	54	2	0	0	X
ejpam-5450	54	3	)	)	PUNCT
ejpam-5450	54	4	(	(	PUNCT
ejpam-5450	54	5	2.1	2.1	NUM
ejpam-5450	54	6	)	)	PUNCT
ejpam-5450	54	7	(	(	PUNCT
ejpam-5450	54	8	∀x	∀x	X
ejpam-5450	54	9	∈	∈	NOUN
ejpam-5450	54	10	x)(0	x)(0	X
ejpam-5450	55	1	◦	◦	NOUN
ejpam-5450	55	2	x	x	X
ejpam-5450	56	1	=	=	SYM
ejpam-5450	56	2	x	x	X
ejpam-5450	56	3	)	)	PUNCT
ejpam-5450	56	4	(	(	PUNCT
ejpam-5450	56	5	2.2	2.2	NUM
ejpam-5450	56	6	)	)	PUNCT
ejpam-5450	56	7	(	(	PUNCT
ejpam-5450	56	8	∀x	∀x	X
ejpam-5450	56	9	∈	∈	PROPN
ejpam-5450	56	10	x)(x	x)(x	PROPN
ejpam-5450	56	11	◦	◦	NOUN
ejpam-5450	56	12	0	0	NUM
ejpam-5450	57	1	=	=	SYM
ejpam-5450	57	2	0	0	NUM
ejpam-5450	57	3	)	)	PUNCT
ejpam-5450	57	4	(	(	PUNCT
ejpam-5450	57	5	2.3	2.3	NUM
ejpam-5450	57	6	)	)	PUNCT
ejpam-5450	57	7	(	(	PUNCT
ejpam-5450	57	8	∀x	∀x	X
ejpam-5450	57	9	,	,	PUNCT
ejpam-5450	57	10	y	y	PROPN
ejpam-5450	57	11	∈	∈	PROPN
ejpam-5450	57	12	x)(x	x)(x	PROPN
ejpam-5450	57	13	◦	◦	NOUN
ejpam-5450	57	14	y	y	PROPN
ejpam-5450	57	15	=	=	SYM
ejpam-5450	57	16	0	0	PROPN
ejpam-5450	57	17	,	,	PUNCT
ejpam-5450	57	18	y	y	PROPN
ejpam-5450	57	19	◦	◦	NOUN
ejpam-5450	57	20	x	x	X
ejpam-5450	57	21	=	=	SYM
ejpam-5450	57	22	0	0	NUM
ejpam-5450	57	23	⇒	⇒	NOUN
ejpam-5450	57	24	x	x	PUNCT
ejpam-5450	57	25	=	=	SYM
ejpam-5450	57	26	y	y	NOUN
ejpam-5450	57	27	)	)	PUNCT
ejpam-5450	57	28	(	(	PUNCT
ejpam-5450	57	29	2.4	2.4	NUM
ejpam-5450	57	30	)	)	PUNCT
ejpam-5450	57	31	following	follow	VERB
ejpam-5450	57	32	this	this	PRON
ejpam-5450	58	1	,	,	PUNCT
ejpam-5450	58	2	we	we	PRON
ejpam-5450	58	3	will	will	AUX
ejpam-5450	58	4	denote	denote	VERB
ejpam-5450	58	5	x	x	PUNCT
ejpam-5450	58	6	as	as	ADP
ejpam-5450	58	7	a	a	DET
ejpam-5450	58	8	bcc	bcc	PROPN
ejpam-5450	58	9	-	-	PUNCT
ejpam-5450	58	10	algebra	algebra	PROPN
ejpam-5450	58	11	(	(	PUNCT
ejpam-5450	58	12	x	x	NOUN
ejpam-5450	58	13	,	,	PUNCT
ejpam-5450	58	14	◦	◦	NOUN
ejpam-5450	58	15	,	,	PUNCT
ejpam-5450	58	16	0	0	NUM
ejpam-5450	58	17	)	)	PUNCT
ejpam-5450	58	18	unless	unless	SCONJ
ejpam-5450	58	19	stated	state	VERB
ejpam-5450	58	20	otherwise	otherwise	ADV
ejpam-5450	58	21	.	.	PUNCT
ejpam-5450	59	1	we	we	PRON
ejpam-5450	59	2	define	define	VERB
ejpam-5450	59	3	a	a	DET
ejpam-5450	59	4	binary	binary	ADJ
ejpam-5450	59	5	relation	relation	NOUN
ejpam-5450	59	6	≤	≤	NOUN
ejpam-5450	59	7	on	on	ADP
ejpam-5450	59	8	x	x	PUNCT
ejpam-5450	59	9	as	as	SCONJ
ejpam-5450	59	10	follows	follow	VERB
ejpam-5450	59	11	:	:	PUNCT
ejpam-5450	59	12	(	(	PUNCT
ejpam-5450	59	13	∀x	∀x	X
ejpam-5450	59	14	,	,	PUNCT
ejpam-5450	59	15	y	y	PROPN
ejpam-5450	59	16	∈	∈	PROPN
ejpam-5450	59	17	x)(x	x)(x	PROPN
ejpam-5450	59	18	≤	≤	PROPN
ejpam-5450	60	1	y	y	PROPN
ejpam-5450	60	2	⇔	⇔	X
ejpam-5450	60	3	x	x	PUNCT
ejpam-5450	60	4	◦	◦	NOUN
ejpam-5450	60	5	y	y	NOUN
ejpam-5450	60	6	=	=	SYM
ejpam-5450	60	7	0	0	NUM
ejpam-5450	60	8	)	)	PUNCT
ejpam-5450	60	9	(	(	PUNCT
ejpam-5450	60	10	2.5	2.5	NUM
ejpam-5450	60	11	)	)	PUNCT
ejpam-5450	60	12	in	in	ADP
ejpam-5450	60	13	x	x	PRON
ejpam-5450	60	14	,	,	PUNCT
ejpam-5450	60	15	the	the	DET
ejpam-5450	60	16	following	follow	VERB
ejpam-5450	60	17	assertions	assertion	NOUN
ejpam-5450	60	18	are	be	AUX
ejpam-5450	60	19	valid	valid	ADJ
ejpam-5450	60	20	(	(	PUNCT
ejpam-5450	60	21	see	see	VERB
ejpam-5450	60	22	[	[	X
ejpam-5450	60	23	9	9	NUM
ejpam-5450	60	24	]	]	NUM
ejpam-5450	60	25	)	)	PUNCT
ejpam-5450	60	26	.	.	PUNCT
ejpam-5450	61	1	(	(	PUNCT
ejpam-5450	61	2	∀x	∀x	X
ejpam-5450	61	3	∈	∈	PROPN
ejpam-5450	61	4	x)(x	x)(x	PROPN
ejpam-5450	61	5	≤	≤	NUM
ejpam-5450	61	6	x	x	X
ejpam-5450	61	7	)	)	PUNCT
ejpam-5450	61	8	(	(	PUNCT
ejpam-5450	61	9	2.6	2.6	NUM
ejpam-5450	61	10	)	)	PUNCT
ejpam-5450	61	11	(	(	PUNCT
ejpam-5450	61	12	∀x	∀x	X
ejpam-5450	61	13	,	,	PUNCT
ejpam-5450	61	14	y	y	PROPN
ejpam-5450	61	15	,	,	PUNCT
ejpam-5450	61	16	z	z	PROPN
ejpam-5450	61	17	∈	∈	PROPN
ejpam-5450	61	18	x)(x	x)(x	PROPN
ejpam-5450	61	19	≤	≤	PROPN
ejpam-5450	61	20	y	y	PROPN
ejpam-5450	61	21	,	,	PUNCT
ejpam-5450	61	22	y	y	PROPN
ejpam-5450	61	23	≤	≤	PROPN
ejpam-5450	61	24	z	z	NOUN
ejpam-5450	61	25	⇒	⇒	NOUN
ejpam-5450	61	26	x	x	PUNCT
ejpam-5450	61	27	≤	≤	NUM
ejpam-5450	61	28	z	z	NOUN
ejpam-5450	61	29	)	)	PUNCT
ejpam-5450	61	30	(	(	PUNCT
ejpam-5450	61	31	2.7	2.7	NUM
ejpam-5450	61	32	)	)	PUNCT
ejpam-5450	61	33	(	(	PUNCT
ejpam-5450	61	34	∀x	∀x	X
ejpam-5450	61	35	,	,	PUNCT
ejpam-5450	61	36	y	y	PROPN
ejpam-5450	61	37	,	,	PUNCT
ejpam-5450	61	38	z	z	PROPN
ejpam-5450	61	39	∈	∈	PROPN
ejpam-5450	61	40	x)(x	x)(x	PROPN
ejpam-5450	61	41	≤	≤	ADV
ejpam-5450	61	42	y	y	PROPN
ejpam-5450	61	43	⇒	⇒	NOUN
ejpam-5450	61	44	z	z	PROPN
ejpam-5450	61	45	◦	◦	NOUN
ejpam-5450	61	46	x	x	SYM
ejpam-5450	61	47	≤	≤	NUM
ejpam-5450	61	48	z	z	NOUN
ejpam-5450	61	49	◦	◦	NOUN
ejpam-5450	61	50	y	y	PROPN
ejpam-5450	61	51	)	)	PUNCT
ejpam-5450	61	52	(	(	PUNCT
ejpam-5450	61	53	2.8	2.8	NUM
ejpam-5450	61	54	)	)	PUNCT
ejpam-5450	61	55	(	(	PUNCT
ejpam-5450	61	56	∀x	∀x	X
ejpam-5450	61	57	,	,	PUNCT
ejpam-5450	61	58	y	y	PROPN
ejpam-5450	61	59	,	,	PUNCT
ejpam-5450	61	60	z	z	PROPN
ejpam-5450	61	61	∈	∈	PROPN
ejpam-5450	61	62	x)(x	x)(x	PROPN
ejpam-5450	61	63	≤	≤	ADV
ejpam-5450	61	64	y	y	PROPN
ejpam-5450	61	65	⇒	⇒	VERB
ejpam-5450	61	66	y	y	PROPN
ejpam-5450	61	67	◦	◦	NOUN
ejpam-5450	61	68	z	z	NOUN
ejpam-5450	61	69	≤	≤	NUM
ejpam-5450	61	70	x	x	PUNCT
ejpam-5450	61	71	◦	◦	NOUN
ejpam-5450	61	72	z	z	NOUN
ejpam-5450	61	73	)	)	PUNCT
ejpam-5450	61	74	(	(	PUNCT
ejpam-5450	61	75	2.9	2.9	NUM
ejpam-5450	61	76	)	)	PUNCT
ejpam-5450	61	77	(	(	PUNCT
ejpam-5450	61	78	∀x	∀x	X
ejpam-5450	61	79	,	,	PUNCT
ejpam-5450	61	80	y	y	PROPN
ejpam-5450	61	81	,	,	PUNCT
ejpam-5450	61	82	z	z	PROPN
ejpam-5450	61	83	∈	∈	PROPN
ejpam-5450	61	84	x)(x	x)(x	PROPN
ejpam-5450	61	85	≤	≤	ADV
ejpam-5450	61	86	y	y	PROPN
ejpam-5450	61	87	◦	◦	NOUN
ejpam-5450	61	88	x	x	SYM
ejpam-5450	61	89	,	,	PUNCT
ejpam-5450	61	90	in	in	ADP
ejpam-5450	61	91	particular	particular	ADJ
ejpam-5450	61	92	,	,	PUNCT
ejpam-5450	61	93	y	y	PROPN
ejpam-5450	61	94	◦	◦	NOUN
ejpam-5450	61	95	z	z	NOUN
ejpam-5450	61	96	≤	≤	NUM
ejpam-5450	61	97	x	x	PUNCT
ejpam-5450	61	98	◦	◦	NOUN
ejpam-5450	61	99	(	(	PUNCT
ejpam-5450	61	100	y	y	PROPN
ejpam-5450	61	101	◦	◦	PROPN
ejpam-5450	61	102	z	z	PROPN
ejpam-5450	61	103	)	)	PUNCT
ejpam-5450	61	104	)	)	PUNCT
ejpam-5450	61	105	(	(	PUNCT
ejpam-5450	61	106	2.10	2.10	NUM
ejpam-5450	61	107	)	)	PUNCT
ejpam-5450	61	108	(	(	PUNCT
ejpam-5450	61	109	∀x	∀x	X
ejpam-5450	61	110	,	,	PUNCT
ejpam-5450	61	111	y	y	PROPN
ejpam-5450	61	112	∈	∈	PROPN
ejpam-5450	61	113	x)(y	x)(y	PUNCT
ejpam-5450	62	1	◦	◦	NOUN
ejpam-5450	62	2	x	x	SYM
ejpam-5450	62	3	≤	≤	NUM
ejpam-5450	62	4	x	x	PUNCT
ejpam-5450	62	5	⇔	⇔	NOUN
ejpam-5450	62	6	x	x	X
ejpam-5450	62	7	=	=	PUNCT
ejpam-5450	62	8	y	y	PROPN
ejpam-5450	62	9	◦	◦	NOUN
ejpam-5450	62	10	x	x	X
ejpam-5450	62	11	)	)	PUNCT
ejpam-5450	62	12	(	(	PUNCT
ejpam-5450	62	13	2.11	2.11	NUM
ejpam-5450	62	14	)	)	PUNCT
ejpam-5450	62	15	(	(	PUNCT
ejpam-5450	62	16	∀x	∀x	X
ejpam-5450	62	17	,	,	PUNCT
ejpam-5450	62	18	y	y	PROPN
ejpam-5450	62	19	∈	∈	PROPN
ejpam-5450	62	20	x)(x	x)(x	PROPN
ejpam-5450	62	21	≤	≤	ADV
ejpam-5450	62	22	y	y	PROPN
ejpam-5450	62	23	◦	◦	NOUN
ejpam-5450	62	24	y	y	PROPN
ejpam-5450	62	25	)	)	PUNCT
ejpam-5450	62	26	(	(	PUNCT
ejpam-5450	62	27	2.12	2.12	NUM
ejpam-5450	62	28	)	)	PUNCT
ejpam-5450	62	29	(	(	PUNCT
ejpam-5450	62	30	∀a	∀a	X
ejpam-5450	62	31	,	,	PUNCT
ejpam-5450	62	32	x	x	X
ejpam-5450	62	33	,	,	PUNCT
ejpam-5450	62	34	y	y	PROPN
ejpam-5450	62	35	,	,	PUNCT
ejpam-5450	62	36	z	z	PROPN
ejpam-5450	62	37	∈	∈	PROPN
ejpam-5450	62	38	x)(x	x)(x	PROPN
ejpam-5450	62	39	◦	◦	NOUN
ejpam-5450	62	40	(	(	PUNCT
ejpam-5450	62	41	y	y	PROPN
ejpam-5450	62	42	◦	◦	PROPN
ejpam-5450	62	43	z	z	PROPN
ejpam-5450	62	44	)	)	PUNCT
ejpam-5450	62	45	≤	≤	NUM
ejpam-5450	62	46	x	x	PUNCT
ejpam-5450	62	47	◦	◦	NOUN
ejpam-5450	62	48	(	(	PUNCT
ejpam-5450	62	49	(	(	PUNCT
ejpam-5450	62	50	a	a	DET
ejpam-5450	62	51	◦	◦	NOUN
ejpam-5450	62	52	y	y	NOUN
ejpam-5450	62	53	)	)	PUNCT
ejpam-5450	62	54	◦	◦	NOUN
ejpam-5450	62	55	(	(	PUNCT
ejpam-5450	62	56	a	a	DET
ejpam-5450	62	57	◦	◦	NOUN
ejpam-5450	62	58	z	z	NOUN
ejpam-5450	62	59	)	)	PUNCT
ejpam-5450	62	60	)	)	PUNCT
ejpam-5450	62	61	)	)	PUNCT
ejpam-5450	62	62	(	(	PUNCT
ejpam-5450	62	63	2.13	2.13	NUM
ejpam-5450	62	64	)	)	PUNCT
ejpam-5450	62	65	(	(	PUNCT
ejpam-5450	62	66	∀a	∀a	X
ejpam-5450	62	67	,	,	PUNCT
ejpam-5450	62	68	x	x	X
ejpam-5450	62	69	,	,	PUNCT
ejpam-5450	62	70	y	y	PROPN
ejpam-5450	62	71	,	,	PUNCT
ejpam-5450	62	72	z	z	PROPN
ejpam-5450	62	73	∈	∈	PROPN
ejpam-5450	62	74	x)(((a	x)(((a	PROPN
ejpam-5450	62	75	◦	◦	NOUN
ejpam-5450	62	76	x	x	SYM
ejpam-5450	62	77	)	)	PUNCT
ejpam-5450	62	78	◦	◦	NOUN
ejpam-5450	62	79	(	(	PUNCT
ejpam-5450	62	80	a	a	DET
ejpam-5450	62	81	◦	◦	NOUN
ejpam-5450	62	82	y	y	NOUN
ejpam-5450	62	83	)	)	PUNCT
ejpam-5450	62	84	)	)	PUNCT
ejpam-5450	63	1	◦	◦	NOUN
ejpam-5450	63	2	z	z	NOUN
ejpam-5450	63	3	≤	≤	NOUN
ejpam-5450	63	4	(	(	PUNCT
ejpam-5450	63	5	x	x	SYM
ejpam-5450	63	6	◦	◦	VERB
ejpam-5450	63	7	y	y	NOUN
ejpam-5450	63	8	)	)	PUNCT
ejpam-5450	63	9	◦	◦	NOUN
ejpam-5450	63	10	z	z	NOUN
ejpam-5450	63	11	)	)	PUNCT
ejpam-5450	63	12	(	(	PUNCT
ejpam-5450	63	13	2.14	2.14	NUM
ejpam-5450	63	14	)	)	PUNCT
ejpam-5450	63	15	(	(	PUNCT
ejpam-5450	63	16	∀x	∀x	X
ejpam-5450	63	17	,	,	PUNCT
ejpam-5450	63	18	y	y	PROPN
ejpam-5450	63	19	,	,	PUNCT
ejpam-5450	63	20	z	z	PROPN
ejpam-5450	63	21	∈	∈	PROPN
ejpam-5450	63	22	x)((x	x)((x	PUNCT
ejpam-5450	64	1	◦	◦	NOUN
ejpam-5450	64	2	y	y	PROPN
ejpam-5450	64	3	)	)	PUNCT
ejpam-5450	64	4	◦	◦	NOUN
ejpam-5450	64	5	z	z	NOUN
ejpam-5450	65	1	≤	≤	NOUN
ejpam-5450	65	2	y	y	PROPN
ejpam-5450	65	3	◦	◦	PROPN
ejpam-5450	65	4	z	z	PROPN
ejpam-5450	65	5	)	)	PUNCT
ejpam-5450	65	6	(	(	PUNCT
ejpam-5450	65	7	2.15	2.15	NUM
ejpam-5450	65	8	)	)	PUNCT
ejpam-5450	65	9	(	(	PUNCT
ejpam-5450	65	10	∀x	∀x	X
ejpam-5450	65	11	,	,	PUNCT
ejpam-5450	65	12	y	y	PROPN
ejpam-5450	65	13	,	,	PUNCT
ejpam-5450	65	14	z	z	PROPN
ejpam-5450	65	15	∈	∈	PROPN
ejpam-5450	65	16	x)(x	x)(x	PROPN
ejpam-5450	65	17	≤	≤	ADV
ejpam-5450	65	18	y	y	PROPN
ejpam-5450	65	19	⇒	⇒	NOUN
ejpam-5450	65	20	x	x	PUNCT
ejpam-5450	65	21	≤	≤	NUM
ejpam-5450	65	22	z	z	NOUN
ejpam-5450	65	23	◦	◦	NOUN
ejpam-5450	65	24	y	y	PROPN
ejpam-5450	65	25	)	)	PUNCT
ejpam-5450	65	26	(	(	PUNCT
ejpam-5450	65	27	2.16	2.16	NUM
ejpam-5450	65	28	)	)	PUNCT
ejpam-5450	65	29	(	(	PUNCT
ejpam-5450	65	30	∀x	∀x	X
ejpam-5450	65	31	,	,	PUNCT
ejpam-5450	65	32	y	y	PROPN
ejpam-5450	65	33	,	,	PUNCT
ejpam-5450	65	34	z	z	PROPN
ejpam-5450	65	35	∈	∈	PROPN
ejpam-5450	65	36	x)((x	x)((x	PUNCT
ejpam-5450	66	1	◦	◦	NOUN
ejpam-5450	66	2	y	y	PROPN
ejpam-5450	66	3	)	)	PUNCT
ejpam-5450	66	4	◦	◦	NOUN
ejpam-5450	66	5	z	z	NOUN
ejpam-5450	66	6	≤	≤	NOUN
ejpam-5450	67	1	x	x	PUNCT
ejpam-5450	67	2	◦	◦	NOUN
ejpam-5450	67	3	(	(	PUNCT
ejpam-5450	67	4	y	y	PROPN
ejpam-5450	67	5	◦	◦	PROPN
ejpam-5450	67	6	z	z	PROPN
ejpam-5450	67	7	)	)	PUNCT
ejpam-5450	67	8	)	)	PUNCT
ejpam-5450	67	9	(	(	PUNCT
ejpam-5450	67	10	2.17	2.17	NUM
ejpam-5450	67	11	)	)	PUNCT
ejpam-5450	67	12	(	(	PUNCT
ejpam-5450	67	13	∀a	∀a	X
ejpam-5450	67	14	,	,	PUNCT
ejpam-5450	67	15	x	x	X
ejpam-5450	67	16	,	,	PUNCT
ejpam-5450	67	17	y	y	PROPN
ejpam-5450	67	18	,	,	PUNCT
ejpam-5450	67	19	z	z	PROPN
ejpam-5450	67	20	∈	∈	PROPN
ejpam-5450	67	21	x)((x	x)((x	PUNCT
ejpam-5450	68	1	◦	◦	NOUN
ejpam-5450	68	2	y	y	PROPN
ejpam-5450	68	3	)	)	PUNCT
ejpam-5450	68	4	◦	◦	NOUN
ejpam-5450	68	5	z	z	NOUN
ejpam-5450	69	1	≤	≤	NOUN
ejpam-5450	69	2	y	y	PROPN
ejpam-5450	69	3	◦	◦	NOUN
ejpam-5450	69	4	(	(	PUNCT
ejpam-5450	69	5	a	a	DET
ejpam-5450	69	6	◦	◦	NOUN
ejpam-5450	69	7	z	z	NOUN
ejpam-5450	69	8	)	)	PUNCT
ejpam-5450	69	9	)	)	PUNCT
ejpam-5450	69	10	(	(	PUNCT
ejpam-5450	69	11	2.18	2.18	NUM
ejpam-5450	69	12	)	)	PUNCT
ejpam-5450	69	13	definition	definition	NOUN
ejpam-5450	69	14	1	1	NUM
ejpam-5450	69	15	.	.	PUNCT
ejpam-5450	70	1	[	[	X
ejpam-5450	70	2	9	9	NUM
ejpam-5450	70	3	]	]	PUNCT
ejpam-5450	70	4	a	a	DET
ejpam-5450	70	5	nonempty	nonempty	NOUN
ejpam-5450	70	6	subset	subset	VERB
ejpam-5450	70	7	s	s	NOUN
ejpam-5450	70	8	of	of	ADP
ejpam-5450	70	9	x	x	PRON
ejpam-5450	70	10	is	be	AUX
ejpam-5450	70	11	called	call	VERB
ejpam-5450	70	12	(	(	PUNCT
ejpam-5450	70	13	1	1	NUM
ejpam-5450	70	14	)	)	PUNCT
ejpam-5450	70	15	a	a	DET
ejpam-5450	70	16	bcc	bcc	PROPN
ejpam-5450	70	17	-	-	PUNCT
ejpam-5450	70	18	subalgebra	subalgebra	NOUN
ejpam-5450	70	19	of	of	ADP
ejpam-5450	70	20	x	x	PRON
ejpam-5450	70	21	if	if	SCONJ
ejpam-5450	70	22	it	it	PRON
ejpam-5450	70	23	satisfies	satisfy	VERB
ejpam-5450	70	24	the	the	DET
ejpam-5450	70	25	following	follow	VERB
ejpam-5450	70	26	property	property	NOUN
ejpam-5450	70	27	:	:	PUNCT
ejpam-5450	70	28	(	(	PUNCT
ejpam-5450	70	29	∀x	∀x	X
ejpam-5450	70	30	,	,	PUNCT
ejpam-5450	70	31	y	y	PROPN
ejpam-5450	70	32	∈	∈	PROPN
ejpam-5450	70	33	s)(x	s)(x	PROPN
ejpam-5450	70	34	◦	◦	NOUN
ejpam-5450	70	35	y	y	PROPN
ejpam-5450	70	36	∈	∈	PROPN
ejpam-5450	70	37	s	s	PART
ejpam-5450	70	38	)	)	PUNCT
ejpam-5450	70	39	(	(	PUNCT
ejpam-5450	70	40	2.19	2.19	NUM
ejpam-5450	70	41	)	)	PUNCT
ejpam-5450	70	42	(	(	PUNCT
ejpam-5450	70	43	2	2	X
ejpam-5450	70	44	)	)	PUNCT
ejpam-5450	70	45	a	a	DET
ejpam-5450	70	46	bcc	bcc	PROPN
ejpam-5450	70	47	-	-	PUNCT
ejpam-5450	70	48	ideal	ideal	NOUN
ejpam-5450	70	49	of	of	ADP
ejpam-5450	70	50	x	x	PRON
ejpam-5450	70	51	if	if	SCONJ
ejpam-5450	70	52	it	it	PRON
ejpam-5450	70	53	satisfies	satisfy	VERB
ejpam-5450	70	54	the	the	DET
ejpam-5450	70	55	following	follow	VERB
ejpam-5450	70	56	properties	property	NOUN
ejpam-5450	70	57	:	:	PUNCT
ejpam-5450	70	58	0	0	NUM
ejpam-5450	70	59	∈	∈	NOUN
ejpam-5450	70	60	s	s	X
ejpam-5450	70	61	(	(	PUNCT
ejpam-5450	70	62	2.20	2.20	NUM
ejpam-5450	70	63	)	)	PUNCT
ejpam-5450	70	64	(	(	PUNCT
ejpam-5450	70	65	∀x	∀x	X
ejpam-5450	70	66	,	,	PUNCT
ejpam-5450	70	67	y	y	PROPN
ejpam-5450	70	68	,	,	PUNCT
ejpam-5450	70	69	z	z	PROPN
ejpam-5450	70	70	∈	∈	PROPN
ejpam-5450	70	71	x)(x	x)(x	PROPN
ejpam-5450	71	1	◦	◦	NOUN
ejpam-5450	71	2	(	(	PUNCT
ejpam-5450	71	3	y	y	PROPN
ejpam-5450	71	4	◦	◦	PROPN
ejpam-5450	71	5	z	z	PROPN
ejpam-5450	71	6	)	)	PUNCT
ejpam-5450	71	7	,	,	PUNCT
ejpam-5450	71	8	y	y	PROPN
ejpam-5450	71	9	∈	∈	PROPN
ejpam-5450	71	10	s	s	PART
ejpam-5450	71	11	⇒	⇒	NOUN
ejpam-5450	71	12	x	x	PUNCT
ejpam-5450	71	13	◦	◦	NOUN
ejpam-5450	71	14	z	z	NOUN
ejpam-5450	71	15	∈	∈	NOUN
ejpam-5450	71	16	s	s	PART
ejpam-5450	71	17	)	)	PUNCT
ejpam-5450	71	18	(	(	PUNCT
ejpam-5450	71	19	2.21	2.21	NUM
ejpam-5450	71	20	)	)	PUNCT
ejpam-5450	71	21	a.	a.	NOUN
ejpam-5450	71	22	iampan	iampan	PROPN
ejpam-5450	71	23	,	,	PUNCT
ejpam-5450	71	24	r.	r.	PROPN
ejpam-5450	71	25	subasini	subasini	PROPN
ejpam-5450	71	26	,	,	PUNCT
ejpam-5450	71	27	n.	n.	PROPN
ejpam-5450	71	28	rajesh	rajesh	PROPN
ejpam-5450	71	29	/	/	SYM
ejpam-5450	71	30	eur	eur	PROPN
ejpam-5450	71	31	.	.	PUNCT
ejpam-5450	72	1	j.	j.	PROPN
ejpam-5450	72	2	pure	pure	PROPN
ejpam-5450	72	3	appl	appl	PROPN
ejpam-5450	72	4	.	.	PROPN
ejpam-5450	72	5	math	math	PROPN
ejpam-5450	72	6	,	,	PUNCT
ejpam-5450	72	7	17	17	NUM
ejpam-5450	72	8	(	(	PUNCT
ejpam-5450	72	9	4	4	NUM
ejpam-5450	72	10	)	)	PUNCT
ejpam-5450	72	11	(	(	PUNCT
ejpam-5450	72	12	2024	2024	NUM
ejpam-5450	72	13	)	)	PUNCT
ejpam-5450	72	14	,	,	PUNCT
ejpam-5450	72	15	3209	3209	NUM
ejpam-5450	72	16	-	-	SYM
ejpam-5450	72	17	3222	3222	NUM
ejpam-5450	72	18	3212	3212	NUM
ejpam-5450	72	19	a	a	DET
ejpam-5450	72	20	fuzzy	fuzzy	ADJ
ejpam-5450	72	21	set	set	NOUN
ejpam-5450	72	22	[	[	X
ejpam-5450	72	23	21	21	NUM
ejpam-5450	72	24	]	]	PUNCT
ejpam-5450	72	25	in	in	ADP
ejpam-5450	72	26	a	a	DET
ejpam-5450	72	27	nonempty	nonempty	ADV
ejpam-5450	72	28	set	set	VERB
ejpam-5450	72	29	x	x	SYM
ejpam-5450	72	30	is	be	AUX
ejpam-5450	72	31	defined	define	VERB
ejpam-5450	72	32	to	to	PART
ejpam-5450	72	33	be	be	AUX
ejpam-5450	72	34	a	a	DET
ejpam-5450	72	35	function	function	NOUN
ejpam-5450	72	36	µ	µ	NOUN
ejpam-5450	72	37	:	:	PUNCT
ejpam-5450	72	38	x	x	SYM
ejpam-5450	72	39	→	→	SYM
ejpam-5450	73	1	[	[	X
ejpam-5450	73	2	0	0	NUM
ejpam-5450	73	3	,	,	PUNCT
ejpam-5450	73	4	1	1	NUM
ejpam-5450	73	5	]	]	PUNCT
ejpam-5450	73	6	,	,	PUNCT
ejpam-5450	73	7	where	where	SCONJ
ejpam-5450	73	8	[	[	X
ejpam-5450	73	9	0	0	NUM
ejpam-5450	73	10	,	,	PUNCT
ejpam-5450	73	11	1	1	NUM
ejpam-5450	73	12	]	]	PUNCT
ejpam-5450	73	13	is	be	AUX
ejpam-5450	73	14	the	the	DET
ejpam-5450	73	15	unit	unit	NOUN
ejpam-5450	73	16	closed	close	VERB
ejpam-5450	73	17	interval	interval	NOUN
ejpam-5450	73	18	of	of	ADP
ejpam-5450	73	19	real	real	ADJ
ejpam-5450	73	20	numbers	number	NOUN
ejpam-5450	73	21	.	.	PUNCT
ejpam-5450	74	1	definition	definition	NOUN
ejpam-5450	74	2	2	2	NUM
ejpam-5450	74	3	.	.	PUNCT
ejpam-5450	75	1	[	[	X
ejpam-5450	75	2	20	20	NUM
ejpam-5450	75	3	]	]	PUNCT
ejpam-5450	75	4	a	a	DET
ejpam-5450	75	5	fuzzy	fuzzy	ADJ
ejpam-5450	75	6	set	set	VERB
ejpam-5450	75	7	µ	µ	NOUN
ejpam-5450	75	8	in	in	ADP
ejpam-5450	75	9	x	x	VERB
ejpam-5450	75	10	is	be	AUX
ejpam-5450	75	11	said	say	VERB
ejpam-5450	75	12	to	to	PART
ejpam-5450	75	13	be	be	AUX
ejpam-5450	75	14	(	(	PUNCT
ejpam-5450	75	15	1	1	X
ejpam-5450	75	16	)	)	PUNCT
ejpam-5450	75	17	a	a	DET
ejpam-5450	75	18	fuzzy	fuzzy	ADJ
ejpam-5450	75	19	bcc	bcc	NOUN
ejpam-5450	75	20	-	-	PUNCT
ejpam-5450	75	21	subalgebra	subalgebra	NOUN
ejpam-5450	75	22	of	of	ADP
ejpam-5450	75	23	x	x	PRON
ejpam-5450	75	24	if	if	SCONJ
ejpam-5450	75	25	it	it	PRON
ejpam-5450	75	26	satisfies	satisfy	VERB
ejpam-5450	75	27	the	the	DET
ejpam-5450	75	28	following	follow	VERB
ejpam-5450	75	29	property	property	NOUN
ejpam-5450	75	30	:	:	PUNCT
ejpam-5450	75	31	(	(	PUNCT
ejpam-5450	75	32	∀x	∀x	X
ejpam-5450	75	33	,	,	PUNCT
ejpam-5450	75	34	y	y	PROPN
ejpam-5450	75	35	∈	∈	PROPN
ejpam-5450	75	36	x)(µ(x	x)(µ(x	PUNCT
ejpam-5450	76	1	◦	◦	VERB
ejpam-5450	76	2	y	y	NOUN
ejpam-5450	76	3	)	)	PUNCT
ejpam-5450	76	4	≥	≥	NOUN
ejpam-5450	76	5	min{µ(x	min{µ(x	NOUN
ejpam-5450	76	6	)	)	PUNCT
ejpam-5450	76	7	,	,	PUNCT
ejpam-5450	76	8	µ(y	µ(y	PROPN
ejpam-5450	76	9	)	)	PUNCT
ejpam-5450	76	10	}	}	PUNCT
ejpam-5450	76	11	)	)	PUNCT
ejpam-5450	77	1	(	(	PUNCT
ejpam-5450	77	2	2.22	2.22	NUM
ejpam-5450	77	3	)	)	PUNCT
ejpam-5450	77	4	(	(	PUNCT
ejpam-5450	77	5	2	2	X
ejpam-5450	77	6	)	)	PUNCT
ejpam-5450	77	7	a	a	DET
ejpam-5450	77	8	fuzzy	fuzzy	ADJ
ejpam-5450	77	9	bcc	bcc	NOUN
ejpam-5450	77	10	-	-	PUNCT
ejpam-5450	77	11	ideal	ideal	NOUN
ejpam-5450	77	12	of	of	ADP
ejpam-5450	77	13	x	x	PRON
ejpam-5450	77	14	if	if	SCONJ
ejpam-5450	77	15	it	it	PRON
ejpam-5450	77	16	satisfies	satisfy	VERB
ejpam-5450	77	17	the	the	DET
ejpam-5450	77	18	following	follow	VERB
ejpam-5450	77	19	properties	property	NOUN
ejpam-5450	77	20	:	:	PUNCT
ejpam-5450	77	21	(	(	PUNCT
ejpam-5450	77	22	∀x	∀x	X
ejpam-5450	77	23	∈	∈	PROPN
ejpam-5450	77	24	x)(µ(0	x)(µ(0	PROPN
ejpam-5450	77	25	)	)	PUNCT
ejpam-5450	77	26	≥	≥	NOUN
ejpam-5450	77	27	µ(x	µ(x	VERB
ejpam-5450	77	28	)	)	PUNCT
ejpam-5450	77	29	)	)	PUNCT
ejpam-5450	77	30	(	(	PUNCT
ejpam-5450	77	31	2.23	2.23	NUM
ejpam-5450	77	32	)	)	PUNCT
ejpam-5450	77	33	(	(	PUNCT
ejpam-5450	77	34	∀x	∀x	X
ejpam-5450	77	35	,	,	PUNCT
ejpam-5450	77	36	y	y	PROPN
ejpam-5450	77	37	,	,	PUNCT
ejpam-5450	77	38	z	z	PROPN
ejpam-5450	77	39	∈	∈	PROPN
ejpam-5450	77	40	x)(µ(x	x)(µ(x	PUNCT
ejpam-5450	77	41	◦	◦	NOUN
ejpam-5450	77	42	z	z	NOUN
ejpam-5450	77	43	)	)	PUNCT
ejpam-5450	77	44	≥	≥	NOUN
ejpam-5450	78	1	min{µ(x	min{µ(x	NOUN
ejpam-5450	78	2	◦	◦	NOUN
ejpam-5450	78	3	(	(	PUNCT
ejpam-5450	78	4	y	y	PROPN
ejpam-5450	78	5	◦	◦	PROPN
ejpam-5450	78	6	z	z	PROPN
ejpam-5450	78	7	)	)	PUNCT
ejpam-5450	78	8	)	)	PUNCT
ejpam-5450	78	9	,	,	PUNCT
ejpam-5450	78	10	µ(y	µ(y	PROPN
ejpam-5450	78	11	)	)	PUNCT
ejpam-5450	78	12	}	}	PUNCT
ejpam-5450	78	13	)	)	PUNCT
ejpam-5450	78	14	(	(	PUNCT
ejpam-5450	78	15	2.24	2.24	NUM
ejpam-5450	78	16	)	)	PUNCT
ejpam-5450	78	17	a	a	DET
ejpam-5450	78	18	fuzzy	fuzzy	ADJ
ejpam-5450	78	19	set	set	VERB
ejpam-5450	78	20	µ	µ	NOUN
ejpam-5450	78	21	in	in	ADP
ejpam-5450	78	22	a	a	DET
ejpam-5450	78	23	set	set	NOUN
ejpam-5450	78	24	x	x	X
ejpam-5450	78	25	of	of	ADP
ejpam-5450	78	26	the	the	DET
ejpam-5450	78	27	form	form	NOUN
ejpam-5450	78	28	µ(x	µ(x	VERB
ejpam-5450	78	29	)	)	PUNCT
ejpam-5450	78	30	=	=	PRON
ejpam-5450	78	31	{	{	PUNCT
ejpam-5450	78	32	t	t	PROPN
ejpam-5450	78	33	∈	∈	PROPN
ejpam-5450	78	34	(	(	PUNCT
ejpam-5450	78	35	0	0	NUM
ejpam-5450	78	36	,	,	PUNCT
ejpam-5450	78	37	1	1	NUM
ejpam-5450	78	38	]	]	PUNCT
ejpam-5450	78	39	if	if	SCONJ
ejpam-5450	78	40	x	x	X
ejpam-5450	78	41	=	=	PUNCT
ejpam-5450	78	42	a	a	DET
ejpam-5450	78	43	0	0	NUM
ejpam-5450	78	44	otherwise	otherwise	ADV
ejpam-5450	78	45	,	,	PUNCT
ejpam-5450	78	46	is	be	AUX
ejpam-5450	78	47	said	say	VERB
ejpam-5450	78	48	to	to	PART
ejpam-5450	78	49	be	be	AUX
ejpam-5450	78	50	a	a	DET
ejpam-5450	78	51	fuzzy	fuzzy	ADJ
ejpam-5450	78	52	point	point	NOUN
ejpam-5450	78	53	with	with	ADP
ejpam-5450	78	54	support	support	NOUN
ejpam-5450	78	55	a	a	PRON
ejpam-5450	78	56	and	and	CCONJ
ejpam-5450	78	57	value	value	NOUN
ejpam-5450	78	58	t	t	NOUN
ejpam-5450	78	59	and	and	CCONJ
ejpam-5450	78	60	is	be	AUX
ejpam-5450	78	61	denoted	denote	VERB
ejpam-5450	78	62	by	by	ADP
ejpam-5450	78	63	[	[	PUNCT
ejpam-5450	78	64	a	a	X
ejpam-5450	78	65	/	/	SYM
ejpam-5450	78	66	t	t	NOUN
ejpam-5450	78	67	]	]	PUNCT
ejpam-5450	78	68	.	.	PUNCT
ejpam-5450	79	1	for	for	ADP
ejpam-5450	79	2	a	a	DET
ejpam-5450	79	3	fuzzy	fuzzy	ADJ
ejpam-5450	79	4	set	set	VERB
ejpam-5450	79	5	µ	µ	NOUN
ejpam-5450	79	6	in	in	ADP
ejpam-5450	79	7	a	a	DET
ejpam-5450	79	8	set	set	NOUN
ejpam-5450	79	9	x	x	NOUN
ejpam-5450	79	10	,	,	PUNCT
ejpam-5450	79	11	we	we	PRON
ejpam-5450	79	12	say	say	VERB
ejpam-5450	79	13	that	that	SCONJ
ejpam-5450	79	14	a	a	DET
ejpam-5450	79	15	fuzzy	fuzzy	ADJ
ejpam-5450	79	16	point	point	NOUN
ejpam-5450	79	17	[	[	X
ejpam-5450	79	18	a	a	X
ejpam-5450	79	19	/	/	SYM
ejpam-5450	79	20	t	t	NOUN
ejpam-5450	79	21	]	]	PUNCT
ejpam-5450	79	22	is	be	AUX
ejpam-5450	79	23	(	(	PUNCT
ejpam-5450	79	24	1	1	NUM
ejpam-5450	79	25	)	)	PUNCT
ejpam-5450	79	26	contained	contain	VERB
ejpam-5450	79	27	in	in	ADP
ejpam-5450	79	28	µ	µ	NUM
ejpam-5450	79	29	,	,	PUNCT
ejpam-5450	79	30	denoted	denote	VERB
ejpam-5450	79	31	by	by	ADP
ejpam-5450	79	32	[	[	PUNCT
ejpam-5450	79	33	a	a	X
ejpam-5450	79	34	/	/	SYM
ejpam-5450	79	35	t	t	NOUN
ejpam-5450	79	36	]	]	X
ejpam-5450	79	37	∈	∈	PROPN
ejpam-5450	79	38	µ	µ	PROPN
ejpam-5450	79	39	,	,	PUNCT
ejpam-5450	79	40	(	(	PUNCT
ejpam-5450	79	41	see	see	VERB
ejpam-5450	79	42	[	[	X
ejpam-5450	79	43	17	17	NUM
ejpam-5450	79	44	]	]	SYM
ejpam-5450	79	45	)	)	PUNCT
ejpam-5450	79	46	if	if	SCONJ
ejpam-5450	79	47	µ(a	µ(a	PROPN
ejpam-5450	79	48	)	)	PUNCT
ejpam-5450	79	49	≥	≥	PROPN
ejpam-5450	79	50	t	t	PROPN
ejpam-5450	79	51	,	,	PUNCT
ejpam-5450	79	52	(	(	PUNCT
ejpam-5450	79	53	2	2	X
ejpam-5450	79	54	)	)	PUNCT
ejpam-5450	79	55	quasi	quasi	NOUN
ejpam-5450	79	56	-	-	VERB
ejpam-5450	79	57	coincident	coincident	ADJ
ejpam-5450	79	58	with	with	ADP
ejpam-5450	79	59	µ	µ	NUM
ejpam-5450	79	60	,	,	PUNCT
ejpam-5450	79	61	denoted	denote	VERB
ejpam-5450	79	62	by	by	ADP
ejpam-5450	79	63	[	[	PUNCT
ejpam-5450	79	64	a	a	X
ejpam-5450	79	65	/	/	SYM
ejpam-5450	79	66	t]qµ	t]qµ	PROPN
ejpam-5450	79	67	,	,	PUNCT
ejpam-5450	79	68	(	(	PUNCT
ejpam-5450	79	69	see	see	VERB
ejpam-5450	79	70	[	[	X
ejpam-5450	79	71	17	17	NUM
ejpam-5450	79	72	]	]	SYM
ejpam-5450	79	73	)	)	PUNCT
ejpam-5450	79	74	if	if	SCONJ
ejpam-5450	79	75	µ(a	µ(a	PROPN
ejpam-5450	79	76	)	)	PUNCT
ejpam-5450	80	1	+	+	CCONJ
ejpam-5450	80	2	t	t	X
ejpam-5450	80	3	>	>	X
ejpam-5450	80	4	1	1	X
ejpam-5450	80	5	.	.	PUNCT
ejpam-5450	80	6	proposition	proposition	NOUN
ejpam-5450	80	7	1	1	NUM
ejpam-5450	80	8	.	.	PUNCT
ejpam-5450	81	1	if	if	SCONJ
ejpam-5450	81	2	µ	µ	NOUN
ejpam-5450	81	3	is	be	AUX
ejpam-5450	81	4	a	a	DET
ejpam-5450	81	5	fuzzy	fuzzy	ADJ
ejpam-5450	81	6	set	set	NOUN
ejpam-5450	81	7	in	in	ADP
ejpam-5450	81	8	a	a	DET
ejpam-5450	81	9	set	set	NOUN
ejpam-5450	81	10	x	x	PUNCT
ejpam-5450	81	11	and	and	CCONJ
ejpam-5450	81	12	ε	ε	PROPN
ejpam-5450	81	13	∈	∈	PROPN
ejpam-5450	81	14	(	(	PUNCT
ejpam-5450	81	15	0	0	NUM
ejpam-5450	81	16	,	,	PUNCT
ejpam-5450	81	17	1	1	NUM
ejpam-5450	81	18	)	)	PUNCT
ejpam-5450	81	19	,	,	PUNCT
ejpam-5450	81	20	then	then	ADV
ejpam-5450	81	21	its	its	PRON
ejpam-5450	81	22	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	81	23	fuzzy	fuzzy	NOUN
ejpam-5450	81	24	set	set	VERB
ejpam-5450	81	25	lε	lε	PRON
ejpam-5450	81	26	µ	µ	PRON
ejpam-5450	81	27	satisfies	satisfie	NOUN
ejpam-5450	81	28	the	the	DET
ejpam-5450	81	29	following	follow	VERB
ejpam-5450	81	30	property	property	NOUN
ejpam-5450	81	31	:	:	PUNCT
ejpam-5450	81	32	(	(	PUNCT
ejpam-5450	81	33	1	1	X
ejpam-5450	81	34	)	)	PUNCT
ejpam-5450	81	35	(	(	PUNCT
ejpam-5450	81	36	∀x	∀x	X
ejpam-5450	81	37	,	,	PUNCT
ejpam-5450	81	38	y	y	PROPN
ejpam-5450	81	39	∈	∈	PROPN
ejpam-5450	81	40	x)(µ(x	x)(µ(x	PUNCT
ejpam-5450	81	41	)	)	PUNCT
ejpam-5450	81	42	≥	≥	PROPN
ejpam-5450	81	43	µ(y	µ(y	NOUN
ejpam-5450	81	44	)	)	PUNCT
ejpam-5450	81	45	⇒	⇒	NOUN
ejpam-5450	81	46	lε	lε	VERB
ejpam-5450	81	47	µ(x	µ(x	NOUN
ejpam-5450	81	48	)	)	PUNCT
ejpam-5450	81	49	≥	≥	NOUN
ejpam-5450	81	50	lε	lε	X
ejpam-5450	81	51	µ(y	µ(y	PROPN
ejpam-5450	81	52	)	)	PUNCT
ejpam-5450	81	53	)	)	PUNCT
ejpam-5450	81	54	(	(	PUNCT
ejpam-5450	81	55	2	2	X
ejpam-5450	81	56	)	)	PUNCT
ejpam-5450	81	57	(	(	PUNCT
ejpam-5450	81	58	∀x	∀x	X
ejpam-5450	81	59	∈	∈	PROPN
ejpam-5450	81	60	x)([x	x)([x	PROPN
ejpam-5450	81	61	/	/	SYM
ejpam-5450	81	62	ε]qµ	ε]qµ	ADJ
ejpam-5450	81	63	⇒	⇒	NOUN
ejpam-5450	81	64	lε	lε	ADP
ejpam-5450	81	65	µ(x	µ(x	NOUN
ejpam-5450	81	66	)	)	PUNCT
ejpam-5450	81	67	=	=	SYM
ejpam-5450	81	68	µ(x	µ(x	X
ejpam-5450	81	69	)	)	PUNCT
ejpam-5450	81	70	+	+	CCONJ
ejpam-5450	81	71	ε−	ε−	PROPN
ejpam-5450	81	72	1	1	NUM
ejpam-5450	81	73	)	)	PUNCT
ejpam-5450	81	74	(	(	PUNCT
ejpam-5450	81	75	3	3	X
ejpam-5450	81	76	)	)	PUNCT
ejpam-5450	81	77	(	(	PUNCT
ejpam-5450	81	78	∀x	∀x	X
ejpam-5450	81	79	∈	∈	PROPN
ejpam-5450	81	80	x,∀δ	x,∀δ	ADP
ejpam-5450	81	81	∈	∈	PROPN
ejpam-5450	81	82	(	(	PUNCT
ejpam-5450	81	83	0	0	NUM
ejpam-5450	81	84	,	,	PUNCT
ejpam-5450	81	85	1))(ε	1))(ε	NUM
ejpam-5450	81	86	≥	≥	NOUN
ejpam-5450	81	87	δ	δ	PROPN
ejpam-5450	81	88	⇒	⇒	NOUN
ejpam-5450	81	89	lε	lε	VERB
ejpam-5450	81	90	µ(x	µ(x	NOUN
ejpam-5450	81	91	)	)	PUNCT
ejpam-5450	81	92	≥	≥	NOUN
ejpam-5450	81	93	lδ	lδ	X
ejpam-5450	81	94	µ(x	µ(x	NOUN
ejpam-5450	81	95	)	)	PUNCT
ejpam-5450	81	96	)	)	PUNCT
ejpam-5450	81	97	3	3	X
ejpam-5450	81	98	.	.	X
ejpam-5450	81	99	εlukasiewicz	εlukasiewicz	VERB
ejpam-5450	81	100	fuzzy	fuzzy	ADJ
ejpam-5450	81	101	bcc	bcc	PROPN
ejpam-5450	81	102	-	-	PUNCT
ejpam-5450	81	103	ideals	ideal	NOUN
ejpam-5450	81	104	of	of	ADP
ejpam-5450	81	105	bcc	bcc	PROPN
ejpam-5450	81	106	-	-	PUNCT
ejpam-5450	81	107	algebras	algebras	PROPN
ejpam-5450	81	108	in	in	ADP
ejpam-5450	81	109	this	this	DET
ejpam-5450	81	110	section	section	NOUN
ejpam-5450	81	111	,	,	PUNCT
ejpam-5450	81	112	we	we	PRON
ejpam-5450	81	113	revisit	revisit	VERB
ejpam-5450	81	114	the	the	DET
ejpam-5450	81	115	concept	concept	NOUN
ejpam-5450	81	116	of	of	ADP
ejpam-5450	81	117	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	81	118	fuzzy	fuzzy	ADJ
ejpam-5450	81	119	sets	set	NOUN
ejpam-5450	81	120	and	and	CCONJ
ejpam-5450	81	121	introduce	introduce	VERB
ejpam-5450	81	122	an	an	DET
ejpam-5450	81	123	innovative	innovative	ADJ
ejpam-5450	81	124	idea	idea	NOUN
ejpam-5450	81	125	:	:	PUNCT
ejpam-5450	81	126	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	81	127	fuzzy	fuzzy	ADJ
ejpam-5450	81	128	bcc	bcc	PROPN
ejpam-5450	81	129	-	-	PUNCT
ejpam-5450	81	130	ideals	ideal	NOUN
ejpam-5450	81	131	.	.	PUNCT
ejpam-5450	82	1	definition	definition	NOUN
ejpam-5450	82	2	3	3	NUM
ejpam-5450	82	3	.	.	PUNCT
ejpam-5450	83	1	let	let	VERB
ejpam-5450	83	2	µ	µ	X
ejpam-5450	83	3	be	be	AUX
ejpam-5450	83	4	a	a	DET
ejpam-5450	83	5	fuzzy	fuzzy	ADJ
ejpam-5450	83	6	set	set	NOUN
ejpam-5450	83	7	in	in	ADP
ejpam-5450	83	8	a	a	DET
ejpam-5450	83	9	set	set	NOUN
ejpam-5450	83	10	x	x	PUNCT
ejpam-5450	83	11	and	and	CCONJ
ejpam-5450	83	12	let	let	VERB
ejpam-5450	83	13	ε	ε	PROPN
ejpam-5450	83	14	∈	∈	PROPN
ejpam-5450	84	1	[	[	X
ejpam-5450	84	2	0	0	NUM
ejpam-5450	84	3	,	,	PUNCT
ejpam-5450	84	4	1	1	NUM
ejpam-5450	84	5	]	]	PUNCT
ejpam-5450	84	6	.	.	PUNCT
ejpam-5450	85	1	a	a	DET
ejpam-5450	85	2	function	function	NOUN
ejpam-5450	85	3	lε	lε	ADP
ejpam-5450	85	4	µ	µ	NOUN
ejpam-5450	85	5	:	:	PUNCT
ejpam-5450	85	6	x	x	SYM
ejpam-5450	85	7	→	→	SYM
ejpam-5450	86	1	[	[	X
ejpam-5450	86	2	0	0	NUM
ejpam-5450	86	3	,	,	PUNCT
ejpam-5450	86	4	1	1	NUM
ejpam-5450	86	5	]	]	PUNCT
ejpam-5450	86	6	;	;	PUNCT
ejpam-5450	86	7	x	x	X
ejpam-5450	86	8	7→	7→	NUM
ejpam-5450	86	9	max{0	max{0	NOUN
ejpam-5450	86	10	,	,	PUNCT
ejpam-5450	86	11	µ(x	µ(x	X
ejpam-5450	86	12	)	)	PUNCT
ejpam-5450	86	13	+	+	CCONJ
ejpam-5450	86	14	ε−	ε−	PROPN
ejpam-5450	86	15	1	1	NUM
ejpam-5450	86	16	}	}	PUNCT
ejpam-5450	86	17	is	be	AUX
ejpam-5450	86	18	called	call	VERB
ejpam-5450	86	19	an	an	DET
ejpam-5450	86	20	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	86	21	fuzzy	fuzzy	ADJ
ejpam-5450	86	22	set	set	NOUN
ejpam-5450	86	23	of	of	ADP
ejpam-5450	86	24	µ	µ	NOUN
ejpam-5450	86	25	in	in	ADP
ejpam-5450	86	26	x.	x.	NOUN
ejpam-5450	86	27	definition	definition	NOUN
ejpam-5450	86	28	4	4	NUM
ejpam-5450	86	29	.	.	PUNCT
ejpam-5450	87	1	[	[	X
ejpam-5450	87	2	10	10	NUM
ejpam-5450	87	3	]	]	PUNCT
ejpam-5450	87	4	let	let	VERB
ejpam-5450	87	5	µ	µ	X
ejpam-5450	87	6	be	be	AUX
ejpam-5450	87	7	a	a	DET
ejpam-5450	87	8	fuzzy	fuzzy	ADJ
ejpam-5450	87	9	set	set	NOUN
ejpam-5450	87	10	in	in	ADP
ejpam-5450	87	11	x.	x.	NOUN
ejpam-5450	87	12	then	then	ADV
ejpam-5450	87	13	its	its	PRON
ejpam-5450	87	14	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	87	15	fuzzy	fuzzy	NOUN
ejpam-5450	87	16	set	set	VERB
ejpam-5450	87	17	lε	lε	PRON
ejpam-5450	87	18	µ	µ	NOUN
ejpam-5450	87	19	in	in	ADP
ejpam-5450	87	20	x	x	AUX
ejpam-5450	87	21	is	be	AUX
ejpam-5450	87	22	called	call	VERB
ejpam-5450	87	23	an	an	DET
ejpam-5450	87	24	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	87	25	fuzzy	fuzzy	ADJ
ejpam-5450	87	26	bcc	bcc	PROPN
ejpam-5450	87	27	-	-	PUNCT
ejpam-5450	87	28	subalgebra	subalgebra	NOUN
ejpam-5450	87	29	of	of	ADP
ejpam-5450	87	30	x	x	PRON
ejpam-5450	87	31	if	if	SCONJ
ejpam-5450	87	32	it	it	PRON
ejpam-5450	87	33	satisfies	satisfy	VERB
ejpam-5450	87	34	the	the	DET
ejpam-5450	87	35	following	follow	VERB
ejpam-5450	87	36	property	property	NOUN
ejpam-5450	87	37	:	:	PUNCT
ejpam-5450	87	38	(	(	PUNCT
ejpam-5450	87	39	∀x	∀x	X
ejpam-5450	87	40	,	,	PUNCT
ejpam-5450	87	41	y	y	PROPN
ejpam-5450	87	42	∈	∈	PROPN
ejpam-5450	87	43	x,∀ta	x,∀ta	PROPN
ejpam-5450	87	44	,	,	PUNCT
ejpam-5450	87	45	tb	tb	ADP
ejpam-5450	87	46	∈	∈	PROPN
ejpam-5450	87	47	(	(	PUNCT
ejpam-5450	87	48	0	0	NUM
ejpam-5450	87	49	,	,	PUNCT
ejpam-5450	87	50	1])([x	1])([x	NUM
ejpam-5450	87	51	/	/	SYM
ejpam-5450	87	52	ta	ta	X
ejpam-5450	87	53	]	]	X
ejpam-5450	87	54	∈	∈	PROPN
ejpam-5450	87	55	lε	lε	ADP
ejpam-5450	87	56	µ	µ	NOUN
ejpam-5450	87	57	,	,	PUNCT
ejpam-5450	87	58	[	[	X
ejpam-5450	87	59	y	y	X
ejpam-5450	87	60	/	/	SYM
ejpam-5450	87	61	tb	tb	NOUN
ejpam-5450	87	62	]	]	PUNCT
ejpam-5450	87	63	∈	∈	PROPN
ejpam-5450	87	64	lε	lε	X
ejpam-5450	87	65	µ	µ	X
ejpam-5450	87	66	⇒	⇒	NOUN
ejpam-5450	88	1	[	[	X
ejpam-5450	88	2	(	(	PUNCT
ejpam-5450	88	3	x	x	SYM
ejpam-5450	88	4	◦	◦	NOUN
ejpam-5450	88	5	y)/min{ta	y)/min{ta	NOUN
ejpam-5450	88	6	,	,	PUNCT
ejpam-5450	88	7	tb	tb	NOUN
ejpam-5450	88	8	}	}	PUNCT
ejpam-5450	88	9	]	]	PUNCT
ejpam-5450	88	10	∈	∈	PROPN
ejpam-5450	88	11	lε	lε	ADP
ejpam-5450	88	12	µ	µ	NUM
ejpam-5450	88	13	)	)	PUNCT
ejpam-5450	88	14	(	(	PUNCT
ejpam-5450	88	15	3.1	3.1	NUM
ejpam-5450	88	16	)	)	PUNCT
ejpam-5450	88	17	a.	a.	NOUN
ejpam-5450	88	18	iampan	iampan	PROPN
ejpam-5450	88	19	,	,	PUNCT
ejpam-5450	88	20	r.	r.	PROPN
ejpam-5450	88	21	subasini	subasini	PROPN
ejpam-5450	88	22	,	,	PUNCT
ejpam-5450	88	23	n.	n.	PROPN
ejpam-5450	88	24	rajesh	rajesh	PROPN
ejpam-5450	88	25	/	/	SYM
ejpam-5450	88	26	eur	eur	PROPN
ejpam-5450	88	27	.	.	PUNCT
ejpam-5450	89	1	j.	j.	PROPN
ejpam-5450	89	2	pure	pure	PROPN
ejpam-5450	89	3	appl	appl	PROPN
ejpam-5450	89	4	.	.	PROPN
ejpam-5450	89	5	math	math	PROPN
ejpam-5450	89	6	,	,	PUNCT
ejpam-5450	89	7	17	17	NUM
ejpam-5450	89	8	(	(	PUNCT
ejpam-5450	89	9	4	4	NUM
ejpam-5450	89	10	)	)	PUNCT
ejpam-5450	89	11	(	(	PUNCT
ejpam-5450	89	12	2024	2024	NUM
ejpam-5450	89	13	)	)	PUNCT
ejpam-5450	89	14	,	,	PUNCT
ejpam-5450	89	15	3209	3209	NUM
ejpam-5450	89	16	-	-	SYM
ejpam-5450	89	17	3222	3222	NUM
ejpam-5450	89	18	3213	3213	NUM
ejpam-5450	89	19	definition	definition	NOUN
ejpam-5450	89	20	5	5	NUM
ejpam-5450	89	21	.	.	PUNCT
ejpam-5450	90	1	let	let	VERB
ejpam-5450	90	2	µ	µ	X
ejpam-5450	90	3	be	be	AUX
ejpam-5450	90	4	a	a	DET
ejpam-5450	90	5	fuzzy	fuzzy	ADJ
ejpam-5450	90	6	set	set	NOUN
ejpam-5450	90	7	in	in	ADP
ejpam-5450	90	8	x.	x.	NOUN
ejpam-5450	90	9	then	then	ADV
ejpam-5450	90	10	its	its	PRON
ejpam-5450	90	11	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	90	12	fuzzy	fuzzy	NOUN
ejpam-5450	90	13	set	set	VERB
ejpam-5450	90	14	lε	lε	PRON
ejpam-5450	90	15	µ	µ	NOUN
ejpam-5450	90	16	in	in	ADP
ejpam-5450	90	17	x	x	AUX
ejpam-5450	90	18	is	be	AUX
ejpam-5450	90	19	called	call	VERB
ejpam-5450	90	20	an	an	DET
ejpam-5450	90	21	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	90	22	fuzzy	fuzzy	ADJ
ejpam-5450	90	23	bcc	bcc	PROPN
ejpam-5450	90	24	-	-	PUNCT
ejpam-5450	90	25	ideal	ideal	NOUN
ejpam-5450	90	26	of	of	ADP
ejpam-5450	90	27	x	x	PRON
ejpam-5450	90	28	if	if	SCONJ
ejpam-5450	90	29	it	it	PRON
ejpam-5450	90	30	satisfies	satisfy	VERB
ejpam-5450	90	31	the	the	DET
ejpam-5450	90	32	following	follow	VERB
ejpam-5450	90	33	properties	property	NOUN
ejpam-5450	90	34	:	:	PUNCT
ejpam-5450	90	35	(	(	PUNCT
ejpam-5450	90	36	∀x	∀x	X
ejpam-5450	90	37	∈	∈	PROPN
ejpam-5450	90	38	x,∀ta	x,∀ta	PROPN
ejpam-5450	90	39	∈	∈	PROPN
ejpam-5450	90	40	(	(	PUNCT
ejpam-5450	90	41	0	0	NUM
ejpam-5450	90	42	,	,	PUNCT
ejpam-5450	90	43	1])([x	1])([x	NUM
ejpam-5450	90	44	/	/	SYM
ejpam-5450	90	45	ta	ta	X
ejpam-5450	90	46	]	]	X
ejpam-5450	90	47	∈	∈	PROPN
ejpam-5450	90	48	lε	lε	X
ejpam-5450	90	49	µ	µ	X
ejpam-5450	90	50	⇒	⇒	NOUN
ejpam-5450	90	51	[	[	X
ejpam-5450	90	52	0	0	NUM
ejpam-5450	90	53	/	/	SYM
ejpam-5450	90	54	ta	ta	X
ejpam-5450	90	55	]	]	X
ejpam-5450	90	56	∈	∈	PROPN
ejpam-5450	90	57	lε	lε	X
ejpam-5450	90	58	µ	µ	NUM
ejpam-5450	90	59	)	)	PUNCT
ejpam-5450	90	60	(	(	PUNCT
ejpam-5450	90	61	3.2	3.2	NUM
ejpam-5450	90	62	)	)	PUNCT
ejpam-5450	90	63	(	(	PUNCT
ejpam-5450	90	64	∀x	∀x	X
ejpam-5450	90	65	,	,	PUNCT
ejpam-5450	90	66	y	y	PROPN
ejpam-5450	90	67	,	,	PUNCT
ejpam-5450	90	68	z	z	PROPN
ejpam-5450	90	69	∈	∈	PROPN
ejpam-5450	90	70	x,∀ta	x,∀ta	NOUN
ejpam-5450	90	71	,	,	PUNCT
ejpam-5450	90	72	tb	tb	ADP
ejpam-5450	90	73	∈	∈	PROPN
ejpam-5450	90	74	(	(	PUNCT
ejpam-5450	90	75	0	0	NUM
ejpam-5450	90	76	,	,	PUNCT
ejpam-5450	90	77	1	1	NUM
ejpam-5450	90	78	]	]	NUM
ejpam-5450	90	79	)	)	PUNCT
ejpam-5450	91	1	(	(	PUNCT
ejpam-5450	91	2	[	[	X
ejpam-5450	91	3	(	(	PUNCT
ejpam-5450	91	4	x	x	SYM
ejpam-5450	91	5	◦	◦	NOUN
ejpam-5450	91	6	(	(	PUNCT
ejpam-5450	91	7	y	y	PROPN
ejpam-5450	91	8	◦	◦	NOUN
ejpam-5450	91	9	z))/ta	z))/ta	NOUN
ejpam-5450	91	10	]	]	X
ejpam-5450	91	11	∈	∈	PROPN
ejpam-5450	91	12	lε	lε	X
ejpam-5450	91	13	µ	µ	NOUN
ejpam-5450	91	14	,	,	PUNCT
ejpam-5450	91	15	[	[	X
ejpam-5450	91	16	y	y	X
ejpam-5450	91	17	/	/	SYM
ejpam-5450	91	18	tb	tb	NOUN
ejpam-5450	91	19	]	]	PUNCT
ejpam-5450	91	20	∈	∈	PROPN
ejpam-5450	91	21	lε	lε	X
ejpam-5450	91	22	µ	µ	X
ejpam-5450	91	23	⇒	⇒	NOUN
ejpam-5450	91	24	[	[	X
ejpam-5450	91	25	(	(	PUNCT
ejpam-5450	91	26	x	x	SYM
ejpam-5450	91	27	◦	◦	NOUN
ejpam-5450	91	28	z)/min{ta	z)/min{ta	PROPN
ejpam-5450	91	29	,	,	PUNCT
ejpam-5450	91	30	tb	tb	NOUN
ejpam-5450	91	31	}	}	PUNCT
ejpam-5450	91	32	]	]	PUNCT
ejpam-5450	91	33	∈	∈	PROPN
ejpam-5450	91	34	lε	lε	ADP
ejpam-5450	91	35	µ	µ	NOUN
ejpam-5450	91	36	)	)	PUNCT
ejpam-5450	91	37	(	(	PUNCT
ejpam-5450	91	38	3.3	3.3	NUM
ejpam-5450	91	39	)	)	PUNCT
ejpam-5450	91	40	example	example	NOUN
ejpam-5450	91	41	1	1	NUM
ejpam-5450	91	42	.	.	PUNCT
ejpam-5450	92	1	[	[	X
ejpam-5450	92	2	7	7	X
ejpam-5450	92	3	]	]	X
ejpam-5450	92	4	let	let	NOUN
ejpam-5450	92	5	x	x	PUNCT
ejpam-5450	92	6	=	=	PUNCT
ejpam-5450	92	7	{	{	PUNCT
ejpam-5450	92	8	0	0	NUM
ejpam-5450	92	9	,	,	PUNCT
ejpam-5450	92	10	1	1	NUM
ejpam-5450	92	11	,	,	PUNCT
ejpam-5450	92	12	2	2	NUM
ejpam-5450	92	13	,	,	PUNCT
ejpam-5450	92	14	3	3	NUM
ejpam-5450	92	15	}	}	PUNCT
ejpam-5450	92	16	with	with	ADP
ejpam-5450	92	17	the	the	DET
ejpam-5450	92	18	following	follow	VERB
ejpam-5450	92	19	cayley	cayley	ADJ
ejpam-5450	92	20	table	table	NOUN
ejpam-5450	92	21	:	:	PUNCT
ejpam-5450	92	22	◦	◦	NOUN
ejpam-5450	92	23	0	0	NUM
ejpam-5450	92	24	1	1	NUM
ejpam-5450	92	25	2	2	NUM
ejpam-5450	92	26	3	3	NUM
ejpam-5450	92	27	0	0	NUM
ejpam-5450	92	28	0	0	NUM
ejpam-5450	92	29	1	1	NUM
ejpam-5450	92	30	2	2	NUM
ejpam-5450	92	31	3	3	NUM
ejpam-5450	92	32	1	1	NUM
ejpam-5450	92	33	0	0	NUM
ejpam-5450	92	34	0	0	NUM
ejpam-5450	92	35	2	2	NUM
ejpam-5450	92	36	3	3	NUM
ejpam-5450	92	37	2	2	NUM
ejpam-5450	92	38	0	0	NUM
ejpam-5450	92	39	1	1	NUM
ejpam-5450	92	40	0	0	NUM
ejpam-5450	92	41	3	3	NUM
ejpam-5450	92	42	3	3	NUM
ejpam-5450	92	43	0	0	NUM
ejpam-5450	92	44	1	1	NUM
ejpam-5450	92	45	2	2	NUM
ejpam-5450	92	46	0	0	NUM
ejpam-5450	92	47	then	then	ADV
ejpam-5450	92	48	x	x	PUNCT
ejpam-5450	92	49	is	be	AUX
ejpam-5450	92	50	a	a	DET
ejpam-5450	92	51	bcc	bcc	PROPN
ejpam-5450	92	52	-	-	PUNCT
ejpam-5450	92	53	algebra	algebra	PROPN
ejpam-5450	92	54	.	.	PUNCT
ejpam-5450	93	1	define	define	VERB
ejpam-5450	93	2	a	a	DET
ejpam-5450	93	3	fuzzy	fuzzy	ADJ
ejpam-5450	93	4	set	set	VERB
ejpam-5450	93	5	µ	µ	NOUN
ejpam-5450	93	6	as	as	SCONJ
ejpam-5450	93	7	follows	follow	VERB
ejpam-5450	93	8	:	:	PUNCT
ejpam-5450	93	9	µ	µ	X
ejpam-5450	93	10	:	:	PUNCT
ejpam-5450	93	11	x	x	SYM
ejpam-5450	93	12	→	→	SYM
ejpam-5450	93	13	[	[	X
ejpam-5450	93	14	0	0	NUM
ejpam-5450	93	15	,	,	PUNCT
ejpam-5450	93	16	1];x	1];x	NUM
ejpam-5450	93	17	7→	7→	NUM
ejpam-5450	93	18			NUM
ejpam-5450	93	19	0.6	0.6	NUM
ejpam-5450	93	20	if	if	SCONJ
ejpam-5450	93	21	x	x	PROPN
ejpam-5450	93	22	=	=	SYM
ejpam-5450	93	23	0	0	NUM
ejpam-5450	93	24	0.4	0.4	NUM
ejpam-5450	93	25	if	if	SCONJ
ejpam-5450	93	26	x	x	SYM
ejpam-5450	93	27	=	=	SYM
ejpam-5450	93	28	1	1	NUM
ejpam-5450	93	29	0.3	0.3	NUM
ejpam-5450	93	30	if	if	SCONJ
ejpam-5450	93	31	x	x	NOUN
ejpam-5450	93	32	=	=	SYM
ejpam-5450	93	33	2	2	NUM
ejpam-5450	93	34	0.2	0.2	NUM
ejpam-5450	93	35	if	if	SCONJ
ejpam-5450	93	36	x	x	SYM
ejpam-5450	93	37	=	=	SYM
ejpam-5450	93	38	3	3	NUM
ejpam-5450	93	39	given	give	VERB
ejpam-5450	93	40	ε	ε	PROPN
ejpam-5450	93	41	=	=	SYM
ejpam-5450	93	42	0.85	0.85	NUM
ejpam-5450	93	43	,	,	PUNCT
ejpam-5450	93	44	the	the	DET
ejpam-5450	93	45	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	93	46	fuzzy	fuzzy	NOUN
ejpam-5450	93	47	set	set	VERB
ejpam-5450	93	48	lε	lε	PRON
ejpam-5450	93	49	µ	µ	PROPN
ejpam-5450	93	50	of	of	ADP
ejpam-5450	93	51	µ	µ	NOUN
ejpam-5450	93	52	in	in	ADP
ejpam-5450	93	53	x	x	AUX
ejpam-5450	93	54	is	be	AUX
ejpam-5450	93	55	given	give	VERB
ejpam-5450	93	56	as	as	SCONJ
ejpam-5450	93	57	follows	follow	VERB
ejpam-5450	93	58	:	:	PUNCT
ejpam-5450	93	59	lε	lε	ADP
ejpam-5450	93	60	µ	µ	NOUN
ejpam-5450	93	61	:	:	PUNCT
ejpam-5450	93	62	x	x	SYM
ejpam-5450	93	63	→	→	SYM
ejpam-5450	94	1	[	[	X
ejpam-5450	94	2	0	0	NUM
ejpam-5450	94	3	,	,	PUNCT
ejpam-5450	94	4	1];x	1];x	NUM
ejpam-5450	94	5	7→	7→	NUM
ejpam-5450	94	6			NUM
ejpam-5450	94	7	0.45	0.45	NUM
ejpam-5450	94	8	if	if	SCONJ
ejpam-5450	94	9	x	x	X
ejpam-5450	94	10	=	=	SYM
ejpam-5450	94	11	0	0	NUM
ejpam-5450	94	12	0.25	0.25	NUM
ejpam-5450	94	13	if	if	SCONJ
ejpam-5450	94	14	x	x	NOUN
ejpam-5450	94	15	=	=	SYM
ejpam-5450	94	16	1	1	NUM
ejpam-5450	94	17	0.15	0.15	NUM
ejpam-5450	94	18	if	if	SCONJ
ejpam-5450	94	19	x	x	NOUN
ejpam-5450	94	20	=	=	SYM
ejpam-5450	94	21	2	2	NUM
ejpam-5450	94	22	0.05	0.05	NUM
ejpam-5450	94	23	if	if	SCONJ
ejpam-5450	94	24	x	x	PROPN
ejpam-5450	94	25	=	=	SYM
ejpam-5450	94	26	3	3	NUM
ejpam-5450	94	27	then	then	ADV
ejpam-5450	94	28	lε	lε	PROPN
ejpam-5450	94	29	µ	µ	PROPN
ejpam-5450	94	30	is	be	AUX
ejpam-5450	94	31	an	an	DET
ejpam-5450	94	32	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	94	33	fuzzy	fuzzy	ADJ
ejpam-5450	94	34	bcc	bcc	PROPN
ejpam-5450	94	35	-	-	PUNCT
ejpam-5450	94	36	ideal	ideal	NOUN
ejpam-5450	94	37	of	of	ADP
ejpam-5450	94	38	x.	x.	PROPN
ejpam-5450	94	39	theorem	theorem	NOUN
ejpam-5450	94	40	1	1	X
ejpam-5450	94	41	.	.	PUNCT
ejpam-5450	95	1	let	let	VERB
ejpam-5450	95	2	µ	µ	X
ejpam-5450	95	3	be	be	AUX
ejpam-5450	95	4	a	a	DET
ejpam-5450	95	5	fuzzy	fuzzy	ADJ
ejpam-5450	95	6	set	set	NOUN
ejpam-5450	95	7	in	in	ADP
ejpam-5450	95	8	x.	x.	NOUN
ejpam-5450	95	9	then	then	ADV
ejpam-5450	95	10	its	its	PRON
ejpam-5450	95	11	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	95	12	fuzzy	fuzzy	NOUN
ejpam-5450	95	13	set	set	VERB
ejpam-5450	95	14	lε	lε	PRON
ejpam-5450	95	15	µ	µ	NOUN
ejpam-5450	95	16	in	in	ADP
ejpam-5450	95	17	x	x	VERB
ejpam-5450	95	18	is	be	AUX
ejpam-5450	95	19	an	an	DET
ejpam-5450	95	20	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	95	21	fuzzy	fuzzy	ADJ
ejpam-5450	95	22	bcc	bcc	PROPN
ejpam-5450	95	23	-	-	PUNCT
ejpam-5450	95	24	ideal	ideal	NOUN
ejpam-5450	95	25	of	of	ADP
ejpam-5450	95	26	x	x	SYM
ejpam-5450	95	27	if	if	SCONJ
ejpam-5450	95	28	and	and	CCONJ
ejpam-5450	95	29	only	only	ADV
ejpam-5450	95	30	if	if	SCONJ
ejpam-5450	95	31	it	it	PRON
ejpam-5450	95	32	satisfies	satisfy	VERB
ejpam-5450	95	33	the	the	DET
ejpam-5450	95	34	following	follow	VERB
ejpam-5450	95	35	properties	property	NOUN
ejpam-5450	95	36	:	:	PUNCT
ejpam-5450	95	37	(	(	PUNCT
ejpam-5450	95	38	∀x	∀x	X
ejpam-5450	95	39	∈	∈	PROPN
ejpam-5450	95	40	x)(lε	x)(lε	NOUN
ejpam-5450	95	41	µ(0	µ(0	NOUN
ejpam-5450	95	42	)	)	PUNCT
ejpam-5450	95	43	≥	≥	NOUN
ejpam-5450	95	44	lε	lε	X
ejpam-5450	95	45	µ(x	µ(x	NOUN
ejpam-5450	95	46	)	)	PUNCT
ejpam-5450	95	47	)	)	PUNCT
ejpam-5450	95	48	(	(	PUNCT
ejpam-5450	95	49	3.4	3.4	NUM
ejpam-5450	95	50	)	)	PUNCT
ejpam-5450	95	51	(	(	PUNCT
ejpam-5450	95	52	∀x	∀x	X
ejpam-5450	95	53	,	,	PUNCT
ejpam-5450	95	54	y	y	PROPN
ejpam-5450	95	55	,	,	PUNCT
ejpam-5450	95	56	z	z	PROPN
ejpam-5450	95	57	∈	∈	PROPN
ejpam-5450	95	58	x)(lε	x)(lε	NOUN
ejpam-5450	95	59	µ(x	µ(x	PUNCT
ejpam-5450	95	60	◦	◦	NOUN
ejpam-5450	95	61	z	z	NOUN
ejpam-5450	95	62	)	)	PUNCT
ejpam-5450	95	63	≥	≥	NOUN
ejpam-5450	95	64	min{lε	min{lε	NUM
ejpam-5450	95	65	µ(x	µ(x	ADJ
ejpam-5450	95	66	◦	◦	NOUN
ejpam-5450	95	67	(	(	PUNCT
ejpam-5450	95	68	y	y	PROPN
ejpam-5450	95	69	◦	◦	PROPN
ejpam-5450	95	70	z	z	PROPN
ejpam-5450	95	71	)	)	PUNCT
ejpam-5450	95	72	)	)	PUNCT
ejpam-5450	95	73	,	,	PUNCT
ejpam-5450	95	74	lε	lε	X
ejpam-5450	95	75	µ(y	µ(y	PROPN
ejpam-5450	95	76	)	)	PUNCT
ejpam-5450	95	77	}	}	PUNCT
ejpam-5450	95	78	)	)	PUNCT
ejpam-5450	95	79	(	(	PUNCT
ejpam-5450	95	80	3.5	3.5	NUM
ejpam-5450	95	81	)	)	PUNCT
ejpam-5450	95	82	proof	proof	NOUN
ejpam-5450	95	83	.	.	PUNCT
ejpam-5450	96	1	assume	assume	VERB
ejpam-5450	96	2	that	that	SCONJ
ejpam-5450	96	3	lε	lε	PROPN
ejpam-5450	96	4	µ	µ	PROPN
ejpam-5450	96	5	is	be	AUX
ejpam-5450	96	6	an	an	DET
ejpam-5450	96	7	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	96	8	fuzzy	fuzzy	ADJ
ejpam-5450	96	9	bcc	bcc	PROPN
ejpam-5450	96	10	-	-	PUNCT
ejpam-5450	96	11	ideal	ideal	NOUN
ejpam-5450	96	12	of	of	ADP
ejpam-5450	96	13	x.	x.	NOUN
ejpam-5450	96	14	let	let	VERB
ejpam-5450	96	15	x	x	X
ejpam-5450	96	16	∈	∈	PROPN
ejpam-5450	96	17	x.	x.	NOUN
ejpam-5450	96	18	since	since	SCONJ
ejpam-5450	96	19	[	[	X
ejpam-5450	96	20	x	x	X
ejpam-5450	96	21	/	/	X
ejpam-5450	96	22	lε	lε	X
ejpam-5450	96	23	µ(x	µ(x	NOUN
ejpam-5450	96	24	)	)	PUNCT
ejpam-5450	96	25	]	]	PUNCT
ejpam-5450	97	1	∈	∈	PROPN
ejpam-5450	97	2	lε	lε	ADP
ejpam-5450	97	3	µ	µ	NUM
ejpam-5450	97	4	,	,	PUNCT
ejpam-5450	97	5	we	we	PRON
ejpam-5450	97	6	have	have	VERB
ejpam-5450	97	7	[	[	X
ejpam-5450	97	8	0	0	NUM
ejpam-5450	97	9	/	/	SYM
ejpam-5450	97	10	lε	lε	X
ejpam-5450	97	11	µ(x	µ(x	NOUN
ejpam-5450	97	12	)	)	PUNCT
ejpam-5450	97	13	]	]	PUNCT
ejpam-5450	98	1	∈	∈	PROPN
ejpam-5450	98	2	lε	lε	PRON
ejpam-5450	98	3	µ	µ	X
ejpam-5450	98	4	by	by	ADP
ejpam-5450	98	5	(	(	PUNCT
ejpam-5450	98	6	3.2	3.2	NUM
ejpam-5450	98	7	)	)	PUNCT
ejpam-5450	98	8	,	,	PUNCT
ejpam-5450	98	9	and	and	CCONJ
ejpam-5450	98	10	so	so	ADV
ejpam-5450	98	11	lε	lε	ADP
ejpam-5450	98	12	µ(0	µ(0	NOUN
ejpam-5450	98	13	)	)	PUNCT
ejpam-5450	98	14	≥	≥	NOUN
ejpam-5450	98	15	lε	lε	X
ejpam-5450	98	16	µ(x	µ(x	NOUN
ejpam-5450	98	17	)	)	PUNCT
ejpam-5450	98	18	.	.	PUNCT
ejpam-5450	99	1	note	note	VERB
ejpam-5450	99	2	that	that	SCONJ
ejpam-5450	100	1	[	[	X
ejpam-5450	100	2	(	(	PUNCT
ejpam-5450	100	3	x	x	NOUN
ejpam-5450	100	4	◦	◦	NOUN
ejpam-5450	100	5	(y	(y	NOUN
ejpam-5450	100	6	◦	◦	NOUN
ejpam-5450	100	7	z))/lε	z))/lε	X
ejpam-5450	100	8	µ(x	µ(x	ADJ
ejpam-5450	100	9	◦	◦	NOUN
ejpam-5450	100	10	(y	(y	NOUN
ejpam-5450	100	11	◦	◦	NOUN
ejpam-5450	100	12	z	z	NOUN
ejpam-5450	100	13	)	)	PUNCT
ejpam-5450	100	14	)	)	PUNCT
ejpam-5450	100	15	]	]	PUNCT
ejpam-5450	101	1	∈	∈	PROPN
ejpam-5450	101	2	lε	lε	ADP
ejpam-5450	101	3	µ	µ	PRON
ejpam-5450	101	4	,	,	PUNCT
ejpam-5450	101	5	[	[	X
ejpam-5450	101	6	y	y	X
ejpam-5450	101	7	/	/	SYM
ejpam-5450	101	8	l	l	PROPN
ejpam-5450	101	9	ε	ε	PROPN
ejpam-5450	101	10	µ(y	µ(y	PROPN
ejpam-5450	101	11	)	)	PUNCT
ejpam-5450	101	12	]	]	PUNCT
ejpam-5450	102	1	∈	∈	PROPN
ejpam-5450	102	2	lε	lε	VERB
ejpam-5450	102	3	µ	µ	NOUN
ejpam-5450	102	4	for	for	ADP
ejpam-5450	102	5	all	all	DET
ejpam-5450	102	6	x	x	NOUN
ejpam-5450	102	7	,	,	PUNCT
ejpam-5450	102	8	y	y	PROPN
ejpam-5450	102	9	,	,	PUNCT
ejpam-5450	102	10	z	z	NOUN
ejpam-5450	102	11	∈	∈	PROPN
ejpam-5450	102	12	x.	x.	NOUN
ejpam-5450	103	1	it	it	PRON
ejpam-5450	103	2	follows	follow	VERB
ejpam-5450	103	3	from	from	ADP
ejpam-5450	103	4	(	(	PUNCT
ejpam-5450	103	5	3.3	3.3	NUM
ejpam-5450	103	6	)	)	PUNCT
ejpam-5450	103	7	that	that	SCONJ
ejpam-5450	104	1	[	[	X
ejpam-5450	104	2	lε	lε	ADP
ejpam-5450	104	3	µ(x	µ(x	ADJ
ejpam-5450	104	4	◦	◦	NOUN
ejpam-5450	104	5	z)/min{lε	z)/min{lε	NOUN
ejpam-5450	104	6	µ(x	µ(x	VERB
ejpam-5450	104	7	◦	◦	NOUN
ejpam-5450	104	8	(y	(y	NOUN
ejpam-5450	104	9	◦	◦	NOUN
ejpam-5450	104	10	z	z	NOUN
ejpam-5450	104	11	)	)	PUNCT
ejpam-5450	104	12	)	)	PUNCT
ejpam-5450	104	13	,	,	PUNCT
ejpam-5450	104	14	lε	lε	X
ejpam-5450	104	15	µ(y	µ(y	PROPN
ejpam-5450	104	16	)	)	PUNCT
ejpam-5450	104	17	}	}	PUNCT
ejpam-5450	104	18	]	]	PUNCT
ejpam-5450	105	1	∈	∈	PROPN
ejpam-5450	105	2	lε	lε	ADP
ejpam-5450	105	3	µ	µ	NOUN
ejpam-5450	105	4	,	,	PUNCT
ejpam-5450	105	5	that	that	ADV
ejpam-5450	105	6	is	is	ADV
ejpam-5450	105	7	,	,	PUNCT
ejpam-5450	105	8	lε	lε	X
ejpam-5450	105	9	µ(x	µ(x	ADJ
ejpam-5450	105	10	◦	◦	NOUN
ejpam-5450	105	11	z	z	NOUN
ejpam-5450	105	12	)	)	PUNCT
ejpam-5450	105	13	≥	≥	NOUN
ejpam-5450	105	14	min{lε	min{lε	NUM
ejpam-5450	105	15	µ(x	µ(x	ADJ
ejpam-5450	105	16	◦	◦	NOUN
ejpam-5450	105	17	(y	(y	NOUN
ejpam-5450	105	18	◦	◦	NOUN
ejpam-5450	105	19	z	z	NOUN
ejpam-5450	105	20	)	)	PUNCT
ejpam-5450	105	21	)	)	PUNCT
ejpam-5450	105	22	,	,	PUNCT
ejpam-5450	105	23	lε	lε	X
ejpam-5450	105	24	µ(y	µ(y	PROPN
ejpam-5450	105	25	)	)	PUNCT
ejpam-5450	105	26	}	}	PUNCT
ejpam-5450	105	27	for	for	ADP
ejpam-5450	105	28	all	all	DET
ejpam-5450	105	29	x	x	NOUN
ejpam-5450	105	30	,	,	PUNCT
ejpam-5450	105	31	y	y	PROPN
ejpam-5450	105	32	,	,	PUNCT
ejpam-5450	105	33	z	z	NOUN
ejpam-5450	105	34	∈	∈	NOUN
ejpam-5450	105	35	x.	x.	NOUN
ejpam-5450	105	36	conversely	conversely	ADV
ejpam-5450	105	37	,	,	PUNCT
ejpam-5450	105	38	let	let	VERB
ejpam-5450	105	39	lε	lε	PART
ejpam-5450	105	40	µ	µ	PART
ejpam-5450	105	41	be	be	AUX
ejpam-5450	105	42	an	an	DET
ejpam-5450	105	43	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	105	44	fuzzy	fuzzy	ADJ
ejpam-5450	105	45	set	set	NOUN
ejpam-5450	105	46	satisfying	satisfy	VERB
ejpam-5450	105	47	the	the	DET
ejpam-5450	105	48	conditions	condition	NOUN
ejpam-5450	105	49	(	(	PUNCT
ejpam-5450	105	50	3.4	3.4	NUM
ejpam-5450	105	51	)	)	PUNCT
ejpam-5450	105	52	and	and	CCONJ
ejpam-5450	105	53	(	(	PUNCT
ejpam-5450	105	54	3.5	3.5	NUM
ejpam-5450	105	55	)	)	PUNCT
ejpam-5450	105	56	.	.	PUNCT
ejpam-5450	106	1	if	if	SCONJ
ejpam-5450	106	2	[	[	X
ejpam-5450	106	3	x	x	X
ejpam-5450	106	4	/	/	SYM
ejpam-5450	106	5	t	t	PROPN
ejpam-5450	106	6	]	]	X
ejpam-5450	106	7	∈	∈	PROPN
ejpam-5450	106	8	lε	lε	VERB
ejpam-5450	106	9	µ	µ	NOUN
ejpam-5450	106	10	for	for	ADP
ejpam-5450	106	11	all	all	DET
ejpam-5450	106	12	x	x	SYM
ejpam-5450	106	13	∈	∈	PROPN
ejpam-5450	106	14	x	x	X
ejpam-5450	106	15	and	and	CCONJ
ejpam-5450	106	16	t	t	PROPN
ejpam-5450	106	17	∈	∈	PROPN
ejpam-5450	106	18	(	(	PUNCT
ejpam-5450	106	19	0	0	NUM
ejpam-5450	106	20	,	,	PUNCT
ejpam-5450	106	21	1	1	NUM
ejpam-5450	106	22	]	]	PUNCT
ejpam-5450	106	23	,	,	PUNCT
ejpam-5450	106	24	then	then	ADV
ejpam-5450	106	25	lε	lε	X
ejpam-5450	106	26	µ(0	µ(0	NOUN
ejpam-5450	106	27	)	)	PUNCT
ejpam-5450	106	28	≥	≥	NOUN
ejpam-5450	106	29	lε	lε	X
ejpam-5450	106	30	µ(x	µ(x	NOUN
ejpam-5450	106	31	)	)	PUNCT
ejpam-5450	106	32	≥	≥	NOUN
ejpam-5450	106	33	t	t	NOUN
ejpam-5450	106	34	for	for	ADP
ejpam-5450	106	35	all	all	DET
ejpam-5450	106	36	x	x	SYM
ejpam-5450	106	37	∈	∈	PROPN
ejpam-5450	106	38	x	x	PUNCT
ejpam-5450	106	39	by	by	ADP
ejpam-5450	106	40	(	(	PUNCT
ejpam-5450	106	41	3.4	3.4	NUM
ejpam-5450	106	42	)	)	PUNCT
ejpam-5450	106	43	.	.	PUNCT
ejpam-5450	107	1	hence	hence	ADV
ejpam-5450	107	2	,	,	PUNCT
ejpam-5450	107	3	[	[	X
ejpam-5450	107	4	0	0	NUM
ejpam-5450	107	5	/	/	SYM
ejpam-5450	107	6	t	t	PROPN
ejpam-5450	107	7	]	]	X
ejpam-5450	107	8	∈	∈	PROPN
ejpam-5450	107	9	lε	lε	AUX
ejpam-5450	107	10	µ.	µ.	NOUN
ejpam-5450	107	11	let	let	VERB
ejpam-5450	107	12	x	x	PRON
ejpam-5450	107	13	,	,	PUNCT
ejpam-5450	107	14	y	y	PROPN
ejpam-5450	107	15	,	,	PUNCT
ejpam-5450	107	16	z	z	NOUN
ejpam-5450	107	17	∈	∈	PROPN
ejpam-5450	107	18	x	x	X
ejpam-5450	107	19	and	and	CCONJ
ejpam-5450	107	20	ta	ta	PROPN
ejpam-5450	107	21	,	,	PUNCT
ejpam-5450	107	22	tb	tb	ADP
ejpam-5450	107	23	∈	∈	PROPN
ejpam-5450	107	24	(	(	PUNCT
ejpam-5450	107	25	0	0	NUM
ejpam-5450	107	26	,	,	PUNCT
ejpam-5450	107	27	1	1	NUM
ejpam-5450	107	28	]	]	PUNCT
ejpam-5450	107	29	be	be	AUX
ejpam-5450	107	30	such	such	ADJ
ejpam-5450	107	31	that	that	SCONJ
ejpam-5450	107	32	[	[	X
ejpam-5450	107	33	(	(	PUNCT
ejpam-5450	107	34	x	x	NOUN
ejpam-5450	107	35	◦	◦	NOUN
ejpam-5450	107	36	(y	(y	NOUN
ejpam-5450	107	37	◦	◦	NOUN
ejpam-5450	107	38	z))/ta	z))/ta	NOUN
ejpam-5450	107	39	]	]	X
ejpam-5450	107	40	∈	∈	PROPN
ejpam-5450	107	41	lε	lε	ADP
ejpam-5450	107	42	µ	µ	NOUN
ejpam-5450	107	43	and	and	CCONJ
ejpam-5450	107	44	[	[	X
ejpam-5450	107	45	y	y	X
ejpam-5450	107	46	/	/	SYM
ejpam-5450	107	47	tb	tb	NOUN
ejpam-5450	107	48	]	]	PUNCT
ejpam-5450	107	49	∈	∈	PROPN
ejpam-5450	108	1	lε	lε	X
ejpam-5450	108	2	µ.	µ.	NOUN
ejpam-5450	108	3	then	then	ADV
ejpam-5450	108	4	lε	lε	ADP
ejpam-5450	108	5	µ(x	µ(x	ADJ
ejpam-5450	108	6	◦	◦	NOUN
ejpam-5450	108	7	(	(	PUNCT
ejpam-5450	108	8	y	y	PROPN
ejpam-5450	108	9	◦	◦	PROPN
ejpam-5450	108	10	z	z	PROPN
ejpam-5450	108	11	)	)	PUNCT
ejpam-5450	108	12	)	)	PUNCT
ejpam-5450	108	13	≥	≥	PROPN
ejpam-5450	108	14	ta	ta	X
ejpam-5450	108	15	and	and	CCONJ
ejpam-5450	108	16	lε	lε	INTJ
ejpam-5450	108	17	µ(y	µ(y	PROPN
ejpam-5450	108	18	)	)	PUNCT
ejpam-5450	108	19	≥	≥	NOUN
ejpam-5450	108	20	tb	tb	NOUN
ejpam-5450	108	21	.	.	PUNCT
ejpam-5450	109	1	it	it	PRON
ejpam-5450	109	2	follows	follow	VERB
ejpam-5450	109	3	from	from	ADP
ejpam-5450	109	4	(	(	PUNCT
ejpam-5450	109	5	3.5	3.5	NUM
ejpam-5450	109	6	)	)	PUNCT
ejpam-5450	109	7	that	that	PRON
ejpam-5450	109	8	lε	lε	ADP
ejpam-5450	109	9	µ(x	µ(x	ADJ
ejpam-5450	109	10	◦	◦	NOUN
ejpam-5450	109	11	z	z	NOUN
ejpam-5450	109	12	)	)	PUNCT
ejpam-5450	109	13	≥	≥	NOUN
ejpam-5450	109	14	min{lε	min{lε	NUM
ejpam-5450	109	15	µ(x	µ(x	ADJ
ejpam-5450	109	16	◦	◦	NOUN
ejpam-5450	109	17	(	(	PUNCT
ejpam-5450	109	18	y	y	PROPN
ejpam-5450	109	19	◦	◦	PROPN
ejpam-5450	109	20	z	z	PROPN
ejpam-5450	109	21	)	)	PUNCT
ejpam-5450	109	22	)	)	PUNCT
ejpam-5450	109	23	,	,	PUNCT
ejpam-5450	109	24	lε	lε	X
ejpam-5450	109	25	µ(y	µ(y	PROPN
ejpam-5450	109	26	)	)	PUNCT
ejpam-5450	109	27	}	}	PUNCT
ejpam-5450	109	28	≥	≥	NOUN
ejpam-5450	109	29	min{ta	min{ta	X
ejpam-5450	109	30	,	,	PUNCT
ejpam-5450	109	31	tb	tb	NOUN
ejpam-5450	109	32	}	}	PUNCT
ejpam-5450	109	33	.	.	PUNCT
ejpam-5450	110	1	hence	hence	ADV
ejpam-5450	110	2	,	,	PUNCT
ejpam-5450	110	3	[	[	X
ejpam-5450	110	4	(	(	PUNCT
ejpam-5450	110	5	(	(	PUNCT
ejpam-5450	110	6	x	x	SYM
ejpam-5450	110	7	◦	◦	NOUN
ejpam-5450	110	8	z)/min{ta	z)/min{ta	PROPN
ejpam-5450	110	9	,	,	PUNCT
ejpam-5450	110	10	tb	tb	NOUN
ejpam-5450	110	11	}	}	PUNCT
ejpam-5450	110	12	∈	∈	PROPN
ejpam-5450	110	13	lε	lε	ADP
ejpam-5450	110	14	µ.	µ.	NOUN
ejpam-5450	110	15	therefore	therefore	ADV
ejpam-5450	110	16	,	,	PUNCT
ejpam-5450	110	17	lε	lε	PROPN
ejpam-5450	110	18	µ	µ	PROPN
ejpam-5450	110	19	is	be	AUX
ejpam-5450	110	20	an	an	DET
ejpam-5450	110	21	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	110	22	fuzzy	fuzzy	ADJ
ejpam-5450	110	23	bcc	bcc	PROPN
ejpam-5450	110	24	-	-	PUNCT
ejpam-5450	110	25	ideal	ideal	NOUN
ejpam-5450	110	26	of	of	ADP
ejpam-5450	110	27	x.	x.	PROPN
ejpam-5450	110	28	a.	a.	PROPN
ejpam-5450	110	29	iampan	iampan	PROPN
ejpam-5450	110	30	,	,	PUNCT
ejpam-5450	110	31	r.	r.	PROPN
ejpam-5450	110	32	subasini	subasini	PROPN
ejpam-5450	110	33	,	,	PUNCT
ejpam-5450	110	34	n.	n.	PROPN
ejpam-5450	110	35	rajesh	rajesh	PROPN
ejpam-5450	110	36	/	/	SYM
ejpam-5450	110	37	eur	eur	PROPN
ejpam-5450	110	38	.	.	PUNCT
ejpam-5450	111	1	j.	j.	PROPN
ejpam-5450	111	2	pure	pure	PROPN
ejpam-5450	111	3	appl	appl	PROPN
ejpam-5450	111	4	.	.	PROPN
ejpam-5450	111	5	math	math	PROPN
ejpam-5450	111	6	,	,	PUNCT
ejpam-5450	111	7	17	17	NUM
ejpam-5450	111	8	(	(	PUNCT
ejpam-5450	111	9	4	4	NUM
ejpam-5450	111	10	)	)	PUNCT
ejpam-5450	111	11	(	(	PUNCT
ejpam-5450	111	12	2024	2024	NUM
ejpam-5450	111	13	)	)	PUNCT
ejpam-5450	111	14	,	,	PUNCT
ejpam-5450	111	15	3209	3209	NUM
ejpam-5450	111	16	-	-	SYM
ejpam-5450	111	17	3222	3222	NUM
ejpam-5450	111	18	3214	3214	NUM
ejpam-5450	111	19	proposition	proposition	NOUN
ejpam-5450	111	20	2	2	NUM
ejpam-5450	111	21	.	.	PUNCT
ejpam-5450	112	1	if	if	SCONJ
ejpam-5450	112	2	lε	lε	PROPN
ejpam-5450	112	3	µ	µ	PROPN
ejpam-5450	112	4	is	be	AUX
ejpam-5450	112	5	an	an	DET
ejpam-5450	112	6	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	112	7	fuzzy	fuzzy	ADJ
ejpam-5450	112	8	bcc	bcc	PROPN
ejpam-5450	112	9	-	-	PUNCT
ejpam-5450	112	10	ideal	ideal	NOUN
ejpam-5450	112	11	of	of	ADP
ejpam-5450	112	12	x	x	PRON
ejpam-5450	112	13	,	,	PUNCT
ejpam-5450	112	14	then	then	ADV
ejpam-5450	112	15	(	(	PUNCT
ejpam-5450	112	16	∀x	∀x	X
ejpam-5450	112	17	,	,	PUNCT
ejpam-5450	112	18	y	y	PROPN
ejpam-5450	112	19	∈	∈	PROPN
ejpam-5450	112	20	x)(y	x)(y	PUNCT
ejpam-5450	112	21	≤	≤	NUM
ejpam-5450	112	22	x	x	PUNCT
ejpam-5450	112	23	⇒	⇒	NOUN
ejpam-5450	112	24	lε	lε	X
ejpam-5450	112	25	µ(y	µ(y	PROPN
ejpam-5450	112	26	)	)	PUNCT
ejpam-5450	112	27	≤	≤	NUM
ejpam-5450	112	28	lε	lε	ADP
ejpam-5450	112	29	µ(x	µ(x	NOUN
ejpam-5450	112	30	)	)	PUNCT
ejpam-5450	112	31	)	)	PUNCT
ejpam-5450	112	32	.	.	PUNCT
ejpam-5450	113	1	(	(	PUNCT
ejpam-5450	113	2	3.6	3.6	NUM
ejpam-5450	113	3	)	)	PUNCT
ejpam-5450	113	4	proof	proof	NOUN
ejpam-5450	113	5	.	.	PUNCT
ejpam-5450	114	1	let	let	VERB
ejpam-5450	114	2	lε	lε	PART
ejpam-5450	114	3	µ	µ	X
ejpam-5450	114	4	be	be	AUX
ejpam-5450	114	5	an	an	DET
ejpam-5450	114	6	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	114	7	fuzzy	fuzzy	ADJ
ejpam-5450	114	8	bcc	bcc	PROPN
ejpam-5450	114	9	-	-	PUNCT
ejpam-5450	114	10	ideal	ideal	NOUN
ejpam-5450	114	11	of	of	ADP
ejpam-5450	114	12	x.	x.	NOUN
ejpam-5450	114	13	let	let	VERB
ejpam-5450	114	14	x	x	PRON
ejpam-5450	114	15	,	,	PUNCT
ejpam-5450	114	16	y	y	PROPN
ejpam-5450	114	17	∈	∈	PROPN
ejpam-5450	114	18	x	x	AUX
ejpam-5450	114	19	be	be	AUX
ejpam-5450	114	20	such	such	ADJ
ejpam-5450	114	21	that	that	SCONJ
ejpam-5450	114	22	y	y	PROPN
ejpam-5450	114	23	≤	≤	PROPN
ejpam-5450	114	24	x.	x.	NOUN
ejpam-5450	114	25	then	then	ADV
ejpam-5450	114	26	lε	lε	X
ejpam-5450	114	27	µ(x	µ(x	NOUN
ejpam-5450	114	28	)	)	PUNCT
ejpam-5450	114	29	=	=	PRON
ejpam-5450	114	30	lε	lε	PART
ejpam-5450	114	31	µ(0	µ(0	NOUN
ejpam-5450	114	32	◦	◦	NOUN
ejpam-5450	114	33	x	x	X
ejpam-5450	114	34	)	)	PUNCT
ejpam-5450	114	35	=	=	SYM
ejpam-5450	114	36	max{0	max{0	PROPN
ejpam-5450	114	37	,	,	PUNCT
ejpam-5450	114	38	µ(0	µ(0	PROPN
ejpam-5450	114	39	◦	◦	NOUN
ejpam-5450	114	40	x	x	X
ejpam-5450	114	41	)	)	PUNCT
ejpam-5450	115	1	+	+	CCONJ
ejpam-5450	115	2	ε−	ε−	PROPN
ejpam-5450	115	3	1	1	NUM
ejpam-5450	115	4	}	}	PUNCT
ejpam-5450	115	5	≥	≥	NUM
ejpam-5450	115	6	max{0,min{µ(0	max{0,min{µ(0	PROPN
ejpam-5450	115	7	◦	◦	NOUN
ejpam-5450	115	8	(	(	PUNCT
ejpam-5450	115	9	y	y	PROPN
ejpam-5450	115	10	◦	◦	NOUN
ejpam-5450	115	11	x	x	X
ejpam-5450	115	12	)	)	PUNCT
ejpam-5450	115	13	)	)	PUNCT
ejpam-5450	115	14	,	,	PUNCT
ejpam-5450	115	15	µ(y	µ(y	PROPN
ejpam-5450	115	16	)	)	PUNCT
ejpam-5450	115	17	}	}	PUNCT
ejpam-5450	116	1	+	+	CCONJ
ejpam-5450	116	2	ε−	ε−	PROPN
ejpam-5450	116	3	1	1	NUM
ejpam-5450	116	4	}	}	PUNCT
ejpam-5450	116	5	=	=	PUNCT
ejpam-5450	116	6	max{0,min{µ(y	max{0,min{µ(y	PROPN
ejpam-5450	116	7	◦	◦	NOUN
ejpam-5450	116	8	x	x	X
ejpam-5450	116	9	)	)	PUNCT
ejpam-5450	116	10	+	+	CCONJ
ejpam-5450	116	11	ε−	ε−	PROPN
ejpam-5450	116	12	1	1	NUM
ejpam-5450	116	13	,	,	PUNCT
ejpam-5450	116	14	µ(y	µ(y	PROPN
ejpam-5450	116	15	)	)	PUNCT
ejpam-5450	116	16	+	+	CCONJ
ejpam-5450	116	17	ε−	ε−	PROPN
ejpam-5450	116	18	1	1	NUM
ejpam-5450	116	19	}	}	PUNCT
ejpam-5450	116	20	}	}	PUNCT
ejpam-5450	116	21	=	=	SYM
ejpam-5450	116	22	min{max{0	min{max{0	X
ejpam-5450	116	23	,	,	PUNCT
ejpam-5450	116	24	µ(0	µ(0	NOUN
ejpam-5450	116	25	)	)	PUNCT
ejpam-5450	116	26	+	+	CCONJ
ejpam-5450	116	27	ε−	ε−	PROPN
ejpam-5450	116	28	1},max{0	1},max{0	NUM
ejpam-5450	116	29	,	,	PUNCT
ejpam-5450	116	30	µ(y	µ(y	PROPN
ejpam-5450	116	31	)	)	PUNCT
ejpam-5450	116	32	+	+	CCONJ
ejpam-5450	116	33	ε−	ε−	PROPN
ejpam-5450	116	34	1	1	NUM
ejpam-5450	116	35	}	}	PUNCT
ejpam-5450	116	36	}	}	PUNCT
ejpam-5450	116	37	=	=	NOUN
ejpam-5450	116	38	min{lε	min{lε	NUM
ejpam-5450	116	39	µ(0	µ(0	NOUN
ejpam-5450	116	40	)	)	PUNCT
ejpam-5450	116	41	,	,	PUNCT
ejpam-5450	116	42	lε	lε	X
ejpam-5450	116	43	µ(y	µ(y	PROPN
ejpam-5450	116	44	)	)	PUNCT
ejpam-5450	116	45	}	}	PUNCT
ejpam-5450	116	46	=	=	SYM
ejpam-5450	116	47	lε	lε	X
ejpam-5450	116	48	µ(y	µ(y	PROPN
ejpam-5450	116	49	)	)	PUNCT
ejpam-5450	116	50	.	.	PUNCT
ejpam-5450	117	1	proposition	proposition	NOUN
ejpam-5450	117	2	3	3	NUM
ejpam-5450	117	3	.	.	PUNCT
ejpam-5450	118	1	if	if	SCONJ
ejpam-5450	118	2	lε	lε	PROPN
ejpam-5450	118	3	µ	µ	PROPN
ejpam-5450	118	4	is	be	AUX
ejpam-5450	118	5	an	an	DET
ejpam-5450	118	6	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	118	7	fuzzy	fuzzy	ADJ
ejpam-5450	118	8	bcc	bcc	PROPN
ejpam-5450	118	9	-	-	PUNCT
ejpam-5450	118	10	ideal	ideal	NOUN
ejpam-5450	118	11	of	of	ADP
ejpam-5450	118	12	x	x	PRON
ejpam-5450	118	13	,	,	PUNCT
ejpam-5450	118	14	then	then	ADV
ejpam-5450	118	15	(	(	PUNCT
ejpam-5450	118	16	∀w	∀w	PROPN
ejpam-5450	118	17	,	,	PUNCT
ejpam-5450	118	18	x	x	PRON
ejpam-5450	118	19	,	,	PUNCT
ejpam-5450	118	20	y	y	PROPN
ejpam-5450	118	21	,	,	PUNCT
ejpam-5450	118	22	z	z	PROPN
ejpam-5450	118	23	∈	∈	PROPN
ejpam-5450	118	24	x)(x	x)(x	PROPN
ejpam-5450	118	25	≤	≤	NUM
ejpam-5450	118	26	w	w	PROPN
ejpam-5450	118	27	◦	◦	NOUN
ejpam-5450	118	28	(	(	PUNCT
ejpam-5450	118	29	y	y	PROPN
ejpam-5450	118	30	◦	◦	PROPN
ejpam-5450	118	31	z	z	NOUN
ejpam-5450	118	32	)	)	PUNCT
ejpam-5450	118	33	⇒	⇒	NOUN
ejpam-5450	118	34	lε	lε	ADP
ejpam-5450	118	35	µ(x	µ(x	ADJ
ejpam-5450	118	36	◦	◦	NOUN
ejpam-5450	118	37	z	z	NOUN
ejpam-5450	118	38	)	)	PUNCT
ejpam-5450	118	39	≥	≥	NOUN
ejpam-5450	118	40	min{lε	min{lε	NUM
ejpam-5450	118	41	µ(w	µ(w	PROPN
ejpam-5450	118	42	)	)	PUNCT
ejpam-5450	118	43	,	,	PUNCT
ejpam-5450	118	44	lε	lε	X
ejpam-5450	118	45	µ(y	µ(y	PROPN
ejpam-5450	118	46	)	)	PUNCT
ejpam-5450	118	47	}	}	PUNCT
ejpam-5450	118	48	)	)	PUNCT
ejpam-5450	118	49	.	.	PUNCT
ejpam-5450	119	1	(	(	PUNCT
ejpam-5450	119	2	3.7	3.7	NUM
ejpam-5450	119	3	)	)	PUNCT
ejpam-5450	119	4	proof	proof	NOUN
ejpam-5450	119	5	.	.	PUNCT
ejpam-5450	120	1	let	let	VERB
ejpam-5450	120	2	lε	lε	PART
ejpam-5450	120	3	µ	µ	X
ejpam-5450	120	4	be	be	AUX
ejpam-5450	120	5	an	an	DET
ejpam-5450	120	6	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	120	7	fuzzy	fuzzy	ADJ
ejpam-5450	120	8	bcc	bcc	PROPN
ejpam-5450	120	9	-	-	PUNCT
ejpam-5450	120	10	ideal	ideal	NOUN
ejpam-5450	120	11	of	of	ADP
ejpam-5450	120	12	x.	x.	NOUN
ejpam-5450	120	13	let	let	VERB
ejpam-5450	120	14	w	w	NOUN
ejpam-5450	120	15	,	,	PUNCT
ejpam-5450	120	16	x	x	NOUN
ejpam-5450	120	17	,	,	PUNCT
ejpam-5450	120	18	y	y	PROPN
ejpam-5450	120	19	,	,	PUNCT
ejpam-5450	120	20	z	z	NOUN
ejpam-5450	120	21	∈	∈	PROPN
ejpam-5450	120	22	x	x	AUX
ejpam-5450	120	23	be	be	AUX
ejpam-5450	120	24	such	such	ADJ
ejpam-5450	120	25	that	that	SCONJ
ejpam-5450	120	26	x	x	SYM
ejpam-5450	120	27	≤	≤	PROPN
ejpam-5450	120	28	w	w	ADP
ejpam-5450	120	29	◦	◦	NOUN
ejpam-5450	120	30	(	(	PUNCT
ejpam-5450	120	31	y	y	PROPN
ejpam-5450	120	32	◦	◦	PROPN
ejpam-5450	120	33	z	z	PROPN
ejpam-5450	120	34	)	)	PUNCT
ejpam-5450	120	35	.	.	PUNCT
ejpam-5450	121	1	then	then	ADV
ejpam-5450	121	2	lε	lε	X
ejpam-5450	121	3	µ(x	µ(x	ADJ
ejpam-5450	121	4	◦	◦	NOUN
ejpam-5450	121	5	z	z	NOUN
ejpam-5450	121	6	)	)	PUNCT
ejpam-5450	121	7	=	=	SYM
ejpam-5450	121	8	max{0	max{0	PROPN
ejpam-5450	121	9	,	,	PUNCT
ejpam-5450	121	10	µ(x	µ(x	X
ejpam-5450	121	11	◦	◦	NOUN
ejpam-5450	121	12	z	z	NOUN
ejpam-5450	121	13	)	)	PUNCT
ejpam-5450	121	14	+	+	CCONJ
ejpam-5450	121	15	ε−	ε−	PROPN
ejpam-5450	121	16	1	1	NUM
ejpam-5450	121	17	}	}	PUNCT
ejpam-5450	121	18	≥	≥	NOUN
ejpam-5450	121	19	max{0,min{µ(x	max{0,min{µ(x	VERB
ejpam-5450	121	20	◦	◦	NOUN
ejpam-5450	121	21	(	(	PUNCT
ejpam-5450	121	22	y	y	PROPN
ejpam-5450	121	23	◦	◦	PROPN
ejpam-5450	121	24	z	z	PROPN
ejpam-5450	121	25	)	)	PUNCT
ejpam-5450	121	26	)	)	PUNCT
ejpam-5450	121	27	,	,	PUNCT
ejpam-5450	121	28	µ(y	µ(y	PROPN
ejpam-5450	121	29	)	)	PUNCT
ejpam-5450	121	30	}	}	PUNCT
ejpam-5450	121	31	+	+	CCONJ
ejpam-5450	121	32	ε−	ε−	PROPN
ejpam-5450	121	33	1	1	NUM
ejpam-5450	121	34	}	}	PUNCT
ejpam-5450	121	35	≥	≥	NOUN
ejpam-5450	121	36	max{0,min{min{µ(x	max{0,min{min{µ(x	NOUN
ejpam-5450	121	37	◦	◦	NOUN
ejpam-5450	121	38	(	(	PUNCT
ejpam-5450	121	39	w	w	NOUN
ejpam-5450	121	40	◦	◦	NOUN
ejpam-5450	121	41	(	(	PUNCT
ejpam-5450	121	42	y	y	PROPN
ejpam-5450	121	43	◦	◦	PROPN
ejpam-5450	121	44	z	z	PROPN
ejpam-5450	121	45	)	)	PUNCT
ejpam-5450	121	46	)	)	PUNCT
ejpam-5450	121	47	)	)	PUNCT
ejpam-5450	121	48	,	,	PUNCT
ejpam-5450	121	49	µ(w	µ(w	NUM
ejpam-5450	121	50	)	)	PUNCT
ejpam-5450	121	51	}	}	PUNCT
ejpam-5450	121	52	,	,	PUNCT
ejpam-5450	121	53	µ(y	µ(y	PROPN
ejpam-5450	121	54	)	)	PUNCT
ejpam-5450	121	55	}	}	PUNCT
ejpam-5450	121	56	+	+	CCONJ
ejpam-5450	121	57	ε−	ε−	PROPN
ejpam-5450	121	58	1	1	NUM
ejpam-5450	121	59	}	}	PUNCT
ejpam-5450	121	60	=	=	SYM
ejpam-5450	121	61	max{0,min{min{µ(0	max{0,min{min{µ(0	NOUN
ejpam-5450	121	62	)	)	PUNCT
ejpam-5450	121	63	,	,	PUNCT
ejpam-5450	121	64	µ(w	µ(w	NUM
ejpam-5450	121	65	)	)	PUNCT
ejpam-5450	121	66	}	}	PUNCT
ejpam-5450	121	67	,	,	PUNCT
ejpam-5450	121	68	µ(y	µ(y	PROPN
ejpam-5450	121	69	)	)	PUNCT
ejpam-5450	121	70	}	}	PUNCT
ejpam-5450	121	71	+	+	CCONJ
ejpam-5450	121	72	ε−	ε−	PROPN
ejpam-5450	121	73	1	1	NUM
ejpam-5450	121	74	}	}	PUNCT
ejpam-5450	121	75	=	=	SYM
ejpam-5450	121	76	max{0,min{µ(w	max{0,min{µ(w	NUM
ejpam-5450	121	77	)	)	PUNCT
ejpam-5450	121	78	,	,	PUNCT
ejpam-5450	121	79	µ(y	µ(y	PROPN
ejpam-5450	121	80	)	)	PUNCT
ejpam-5450	121	81	}	}	PUNCT
ejpam-5450	121	82	+	+	CCONJ
ejpam-5450	121	83	ε−	ε−	PROPN
ejpam-5450	121	84	1	1	NUM
ejpam-5450	121	85	}	}	PUNCT
ejpam-5450	121	86	=	=	SYM
ejpam-5450	121	87	max{0,min{µ(w	max{0,min{µ(w	NUM
ejpam-5450	121	88	)	)	PUNCT
ejpam-5450	121	89	+	+	CCONJ
ejpam-5450	121	90	ε−	ε−	PROPN
ejpam-5450	121	91	1	1	NUM
ejpam-5450	121	92	,	,	PUNCT
ejpam-5450	121	93	µ(y	µ(y	PROPN
ejpam-5450	121	94	)	)	PUNCT
ejpam-5450	121	95	+	+	CCONJ
ejpam-5450	121	96	ε−	ε−	PROPN
ejpam-5450	121	97	1	1	NUM
ejpam-5450	121	98	}	}	PUNCT
ejpam-5450	121	99	}	}	PUNCT
ejpam-5450	121	100	=	=	SYM
ejpam-5450	121	101	min{max{0	min{max{0	X
ejpam-5450	121	102	,	,	PUNCT
ejpam-5450	121	103	µ(w	µ(w	NUM
ejpam-5450	121	104	)	)	PUNCT
ejpam-5450	121	105	+	+	CCONJ
ejpam-5450	121	106	ε−	ε−	PROPN
ejpam-5450	121	107	1},max{0	1},max{0	NUM
ejpam-5450	121	108	,	,	PUNCT
ejpam-5450	121	109	µ(y	µ(y	PROPN
ejpam-5450	121	110	)	)	PUNCT
ejpam-5450	121	111	+	+	CCONJ
ejpam-5450	121	112	ε−	ε−	PROPN
ejpam-5450	121	113	1	1	NUM
ejpam-5450	121	114	}	}	PUNCT
ejpam-5450	121	115	}	}	PUNCT
ejpam-5450	121	116	=	=	SYM
ejpam-5450	121	117	min{lε	min{lε	NUM
ejpam-5450	121	118	µ(w	µ(w	PROPN
ejpam-5450	121	119	)	)	PUNCT
ejpam-5450	121	120	,	,	PUNCT
ejpam-5450	121	121	lε	lε	X
ejpam-5450	121	122	µ(y	µ(y	PROPN
ejpam-5450	121	123	)	)	PUNCT
ejpam-5450	121	124	}	}	PUNCT
ejpam-5450	121	125	.	.	PUNCT
ejpam-5450	122	1	proposition	proposition	NOUN
ejpam-5450	122	2	4	4	NUM
ejpam-5450	122	3	.	.	PUNCT
ejpam-5450	123	1	if	if	SCONJ
ejpam-5450	123	2	lε	lε	PROPN
ejpam-5450	123	3	µ	µ	PROPN
ejpam-5450	123	4	is	be	AUX
ejpam-5450	123	5	an	an	DET
ejpam-5450	123	6	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	123	7	fuzzy	fuzzy	ADJ
ejpam-5450	123	8	bcc	bcc	PROPN
ejpam-5450	123	9	-	-	PUNCT
ejpam-5450	123	10	ideal	ideal	NOUN
ejpam-5450	123	11	of	of	ADP
ejpam-5450	123	12	x	x	PRON
ejpam-5450	123	13	,	,	PUNCT
ejpam-5450	123	14	then	then	ADV
ejpam-5450	123	15	(	(	PUNCT
ejpam-5450	123	16	∀x	∀x	X
ejpam-5450	123	17	,	,	PUNCT
ejpam-5450	123	18	y	y	PROPN
ejpam-5450	123	19	,	,	PUNCT
ejpam-5450	123	20	z	z	PROPN
ejpam-5450	123	21	∈	∈	PROPN
ejpam-5450	123	22	x)(x	x)(x	PROPN
ejpam-5450	123	23	≤	≤	ADV
ejpam-5450	123	24	y	y	PROPN
ejpam-5450	123	25	◦	◦	NOUN
ejpam-5450	123	26	z	z	NOUN
ejpam-5450	123	27	⇒	⇒	NOUN
ejpam-5450	123	28	lε	lε	ADP
ejpam-5450	123	29	µ(x	µ(x	ADJ
ejpam-5450	123	30	◦	◦	NOUN
ejpam-5450	123	31	z	z	NOUN
ejpam-5450	123	32	)	)	PUNCT
ejpam-5450	123	33	≥	≥	NOUN
ejpam-5450	123	34	lε	lε	X
ejpam-5450	123	35	µ(y	µ(y	PROPN
ejpam-5450	123	36	)	)	PUNCT
ejpam-5450	123	37	)	)	PUNCT
ejpam-5450	123	38	.	.	PUNCT
ejpam-5450	124	1	(	(	PUNCT
ejpam-5450	124	2	3.8	3.8	NUM
ejpam-5450	124	3	)	)	PUNCT
ejpam-5450	124	4	proof	proof	NOUN
ejpam-5450	124	5	.	.	PUNCT
ejpam-5450	125	1	let	let	VERB
ejpam-5450	125	2	lε	lε	PART
ejpam-5450	125	3	µ	µ	X
ejpam-5450	125	4	be	be	AUX
ejpam-5450	125	5	an	an	DET
ejpam-5450	125	6	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	125	7	fuzzy	fuzzy	ADJ
ejpam-5450	125	8	bcc	bcc	PROPN
ejpam-5450	125	9	-	-	PUNCT
ejpam-5450	125	10	ideal	ideal	NOUN
ejpam-5450	125	11	of	of	ADP
ejpam-5450	125	12	x.	x.	NOUN
ejpam-5450	125	13	let	let	VERB
ejpam-5450	125	14	x	x	PRON
ejpam-5450	125	15	,	,	PUNCT
ejpam-5450	125	16	y	y	PROPN
ejpam-5450	125	17	,	,	PUNCT
ejpam-5450	125	18	z	z	NOUN
ejpam-5450	125	19	∈	∈	PROPN
ejpam-5450	125	20	x	x	AUX
ejpam-5450	125	21	be	be	AUX
ejpam-5450	125	22	such	such	ADJ
ejpam-5450	125	23	that	that	SCONJ
ejpam-5450	125	24	x	x	SYM
ejpam-5450	125	25	≤	≤	NUM
ejpam-5450	125	26	y	y	PROPN
ejpam-5450	125	27	◦	◦	PROPN
ejpam-5450	125	28	z	z	NOUN
ejpam-5450	125	29	in	in	ADP
ejpam-5450	125	30	x.	x.	NOUN
ejpam-5450	125	31	by	by	ADP
ejpam-5450	125	32	proposition	proposition	NOUN
ejpam-5450	125	33	3	3	NUM
ejpam-5450	125	34	,	,	PUNCT
ejpam-5450	125	35	put	put	VERB
ejpam-5450	125	36	w	w	NOUN
ejpam-5450	125	37	=	=	NOUN
ejpam-5450	125	38	0	0	NUM
ejpam-5450	125	39	.	.	PUNCT
ejpam-5450	126	1	by	by	ADP
ejpam-5450	126	2	(	(	PUNCT
ejpam-5450	126	3	3.7	3.7	NUM
ejpam-5450	126	4	)	)	PUNCT
ejpam-5450	126	5	,	,	PUNCT
ejpam-5450	126	6	we	we	PRON
ejpam-5450	126	7	have	have	VERB
ejpam-5450	126	8	x	x	NOUN
ejpam-5450	126	9	≤	≤	X
ejpam-5450	126	10	0	0	NUM
ejpam-5450	127	1	◦	◦	NOUN
ejpam-5450	127	2	(	(	PUNCT
ejpam-5450	127	3	y	y	PROPN
ejpam-5450	127	4	◦	◦	PROPN
ejpam-5450	127	5	z	z	PROPN
ejpam-5450	127	6	)	)	PUNCT
ejpam-5450	127	7	.	.	PUNCT
ejpam-5450	128	1	hence	hence	ADV
ejpam-5450	128	2	,	,	PUNCT
ejpam-5450	128	3	lε	lε	ADP
ejpam-5450	128	4	µ(x	µ(x	ADJ
ejpam-5450	128	5	◦	◦	NOUN
ejpam-5450	128	6	z	z	NOUN
ejpam-5450	128	7	)	)	PUNCT
ejpam-5450	128	8	≥	≥	NOUN
ejpam-5450	128	9	min{lε	min{lε	X
ejpam-5450	128	10	µ(0	µ(0	NOUN
ejpam-5450	128	11	)	)	PUNCT
ejpam-5450	128	12	,	,	PUNCT
ejpam-5450	128	13	lε	lε	X
ejpam-5450	128	14	µ(y	µ(y	PROPN
ejpam-5450	128	15	)	)	PUNCT
ejpam-5450	128	16	}	}	PUNCT
ejpam-5450	128	17	=	=	SYM
ejpam-5450	128	18	lε	lε	X
ejpam-5450	128	19	µ(y	µ(y	PROPN
ejpam-5450	128	20	)	)	PUNCT
ejpam-5450	128	21	.	.	PUNCT
ejpam-5450	129	1	proposition	proposition	NOUN
ejpam-5450	129	2	5	5	NUM
ejpam-5450	129	3	.	.	PUNCT
ejpam-5450	130	1	every	every	DET
ejpam-5450	130	2	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	130	3	fuzzy	fuzzy	ADJ
ejpam-5450	130	4	bcc	bcc	PROPN
ejpam-5450	130	5	-	-	PUNCT
ejpam-5450	130	6	ideal	ideal	NOUN
ejpam-5450	130	7	of	of	ADP
ejpam-5450	130	8	x	x	PUNCT
ejpam-5450	130	9	is	be	AUX
ejpam-5450	130	10	an	an	DET
ejpam-5450	130	11	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	130	12	fuzzy	fuzzy	ADJ
ejpam-5450	130	13	bcc	bcc	PROPN
ejpam-5450	130	14	-	-	PUNCT
ejpam-5450	130	15	subalgebra	subalgebra	NOUN
ejpam-5450	130	16	of	of	ADP
ejpam-5450	130	17	x.	x.	NOUN
ejpam-5450	130	18	proof	proof	NOUN
ejpam-5450	130	19	.	.	PUNCT
ejpam-5450	131	1	let	let	VERB
ejpam-5450	131	2	lε	lε	PRON
ejpam-5450	131	3	µ	µ	VERB
ejpam-5450	131	4	ba	ba	PROPN
ejpam-5450	131	5	an	an	DET
ejpam-5450	131	6	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	131	7	fuzzy	fuzzy	ADJ
ejpam-5450	131	8	bcc	bcc	PROPN
ejpam-5450	131	9	-	-	PUNCT
ejpam-5450	131	10	ideal	ideal	NOUN
ejpam-5450	131	11	of	of	ADP
ejpam-5450	131	12	x	x	PUNCT
ejpam-5450	131	13	and	and	CCONJ
ejpam-5450	131	14	let	let	VERB
ejpam-5450	131	15	x	x	PRON
ejpam-5450	131	16	,	,	PUNCT
ejpam-5450	131	17	y	y	PROPN
ejpam-5450	131	18	∈	∈	PROPN
ejpam-5450	131	19	x.	x.	NOUN
ejpam-5450	131	20	by	by	ADP
ejpam-5450	131	21	(	(	PUNCT
ejpam-5450	131	22	2.10	2.10	NUM
ejpam-5450	131	23	)	)	PUNCT
ejpam-5450	131	24	,	,	PUNCT
ejpam-5450	131	25	we	we	PRON
ejpam-5450	131	26	have	have	VERB
ejpam-5450	131	27	x	x	NOUN
ejpam-5450	131	28	≤	≤	NOUN
ejpam-5450	131	29	y	y	PROPN
ejpam-5450	131	30	◦	◦	NOUN
ejpam-5450	131	31	x.	x.	NOUN
ejpam-5450	132	1	it	it	PRON
ejpam-5450	132	2	follows	follow	VERB
ejpam-5450	132	3	from	from	ADP
ejpam-5450	132	4	(	(	PUNCT
ejpam-5450	132	5	3.6	3.6	NUM
ejpam-5450	132	6	)	)	PUNCT
ejpam-5450	132	7	that	that	PRON
ejpam-5450	132	8	lε	lε	ADP
ejpam-5450	132	9	µ(y	µ(y	PROPN
ejpam-5450	132	10	◦	◦	PROPN
ejpam-5450	132	11	x	x	SYM
ejpam-5450	132	12	)	)	PUNCT
ejpam-5450	132	13	≥	≥	NOUN
ejpam-5450	132	14	lε	lε	X
ejpam-5450	132	15	µ(x	µ(x	NOUN
ejpam-5450	132	16	)	)	PUNCT
ejpam-5450	132	17	≥	≥	NOUN
ejpam-5450	132	18	min{lε	min{lε	NUM
ejpam-5450	132	19	µ(y	µ(y	PROPN
ejpam-5450	132	20	)	)	PUNCT
ejpam-5450	132	21	,	,	PUNCT
ejpam-5450	132	22	lε	lε	ADP
ejpam-5450	132	23	µ(x	µ(x	NOUN
ejpam-5450	132	24	)	)	PUNCT
ejpam-5450	132	25	}	}	PUNCT
ejpam-5450	132	26	.	.	PUNCT
ejpam-5450	133	1	the	the	DET
ejpam-5450	133	2	following	follow	VERB
ejpam-5450	133	3	example	example	NOUN
ejpam-5450	133	4	shows	show	VERB
ejpam-5450	133	5	that	that	SCONJ
ejpam-5450	133	6	the	the	DET
ejpam-5450	133	7	converse	converse	NOUN
ejpam-5450	133	8	of	of	ADP
ejpam-5450	133	9	proposition	proposition	NOUN
ejpam-5450	133	10	5	5	NUM
ejpam-5450	133	11	is	be	AUX
ejpam-5450	133	12	not	not	PART
ejpam-5450	133	13	generally	generally	ADV
ejpam-5450	133	14	true	true	ADJ
ejpam-5450	133	15	.	.	PUNCT
ejpam-5450	134	1	a.	a.	PROPN
ejpam-5450	134	2	iampan	iampan	PROPN
ejpam-5450	134	3	,	,	PUNCT
ejpam-5450	134	4	r.	r.	PROPN
ejpam-5450	134	5	subasini	subasini	PROPN
ejpam-5450	134	6	,	,	PUNCT
ejpam-5450	134	7	n.	n.	PROPN
ejpam-5450	134	8	rajesh	rajesh	PROPN
ejpam-5450	134	9	/	/	SYM
ejpam-5450	134	10	eur	eur	PROPN
ejpam-5450	134	11	.	.	PUNCT
ejpam-5450	135	1	j.	j.	PROPN
ejpam-5450	135	2	pure	pure	PROPN
ejpam-5450	135	3	appl	appl	PROPN
ejpam-5450	135	4	.	.	PROPN
ejpam-5450	135	5	math	math	PROPN
ejpam-5450	135	6	,	,	PUNCT
ejpam-5450	135	7	17	17	NUM
ejpam-5450	135	8	(	(	PUNCT
ejpam-5450	135	9	4	4	NUM
ejpam-5450	135	10	)	)	PUNCT
ejpam-5450	135	11	(	(	PUNCT
ejpam-5450	135	12	2024	2024	NUM
ejpam-5450	135	13	)	)	PUNCT
ejpam-5450	135	14	,	,	PUNCT
ejpam-5450	135	15	3209	3209	NUM
ejpam-5450	135	16	-	-	SYM
ejpam-5450	135	17	3222	3222	NUM
ejpam-5450	135	18	3215	3215	NUM
ejpam-5450	135	19	example	example	NOUN
ejpam-5450	135	20	2	2	NUM
ejpam-5450	135	21	.	.	PUNCT
ejpam-5450	136	1	[	[	X
ejpam-5450	136	2	7	7	X
ejpam-5450	136	3	]	]	X
ejpam-5450	136	4	let	let	NOUN
ejpam-5450	136	5	x	x	PUNCT
ejpam-5450	136	6	=	=	PUNCT
ejpam-5450	136	7	{	{	PUNCT
ejpam-5450	136	8	0	0	NUM
ejpam-5450	136	9	,	,	PUNCT
ejpam-5450	136	10	1	1	NUM
ejpam-5450	136	11	,	,	PUNCT
ejpam-5450	136	12	2	2	NUM
ejpam-5450	136	13	,	,	PUNCT
ejpam-5450	136	14	3	3	NUM
ejpam-5450	136	15	}	}	PUNCT
ejpam-5450	136	16	with	with	ADP
ejpam-5450	136	17	the	the	DET
ejpam-5450	136	18	following	follow	VERB
ejpam-5450	136	19	cayley	cayley	ADJ
ejpam-5450	136	20	table	table	NOUN
ejpam-5450	136	21	:	:	PUNCT
ejpam-5450	136	22	◦	◦	NOUN
ejpam-5450	136	23	0	0	NUM
ejpam-5450	136	24	1	1	NUM
ejpam-5450	136	25	2	2	NUM
ejpam-5450	136	26	3	3	NUM
ejpam-5450	136	27	0	0	NUM
ejpam-5450	136	28	0	0	NUM
ejpam-5450	136	29	1	1	NUM
ejpam-5450	136	30	2	2	NUM
ejpam-5450	136	31	3	3	NUM
ejpam-5450	136	32	1	1	NUM
ejpam-5450	136	33	0	0	NUM
ejpam-5450	136	34	0	0	NUM
ejpam-5450	136	35	1	1	NUM
ejpam-5450	136	36	2	2	NUM
ejpam-5450	136	37	2	2	NUM
ejpam-5450	136	38	0	0	NUM
ejpam-5450	136	39	0	0	NUM
ejpam-5450	136	40	0	0	NUM
ejpam-5450	136	41	1	1	NUM
ejpam-5450	136	42	3	3	NUM
ejpam-5450	136	43	0	0	NUM
ejpam-5450	136	44	0	0	NUM
ejpam-5450	136	45	0	0	NUM
ejpam-5450	136	46	0	0	PUNCT
ejpam-5450	137	1	then	then	ADV
ejpam-5450	137	2	x	x	PUNCT
ejpam-5450	137	3	is	be	AUX
ejpam-5450	137	4	a	a	DET
ejpam-5450	137	5	bcc	bcc	PROPN
ejpam-5450	137	6	-	-	PUNCT
ejpam-5450	137	7	algebra	algebra	PROPN
ejpam-5450	137	8	.	.	PUNCT
ejpam-5450	138	1	define	define	VERB
ejpam-5450	138	2	a	a	DET
ejpam-5450	138	3	fuzzy	fuzzy	ADJ
ejpam-5450	138	4	set	set	VERB
ejpam-5450	138	5	µ	µ	NOUN
ejpam-5450	138	6	as	as	SCONJ
ejpam-5450	138	7	follows	follow	VERB
ejpam-5450	138	8	:	:	PUNCT
ejpam-5450	138	9	µ	µ	X
ejpam-5450	138	10	:	:	PUNCT
ejpam-5450	138	11	x	x	SYM
ejpam-5450	138	12	→	→	SYM
ejpam-5450	139	1	[	[	X
ejpam-5450	139	2	0	0	NUM
ejpam-5450	139	3	,	,	PUNCT
ejpam-5450	139	4	1];x	1];x	NUM
ejpam-5450	139	5	7→	7→	NUM
ejpam-5450	139	6			NUM
ejpam-5450	139	7	1	1	NUM
ejpam-5450	139	8	if	if	SCONJ
ejpam-5450	139	9	x	x	PROPN
ejpam-5450	139	10	=	=	SYM
ejpam-5450	139	11	0	0	NUM
ejpam-5450	139	12	0.6	0.6	NUM
ejpam-5450	139	13	if	if	SCONJ
ejpam-5450	139	14	x	x	NOUN
ejpam-5450	140	1	=	=	SYM
ejpam-5450	140	2	1	1	NUM
ejpam-5450	140	3	0.4	0.4	NUM
ejpam-5450	140	4	if	if	SCONJ
ejpam-5450	140	5	x	x	NOUN
ejpam-5450	140	6	=	=	SYM
ejpam-5450	140	7	2	2	NUM
ejpam-5450	140	8	0.1	0.1	NUM
ejpam-5450	140	9	if	if	SCONJ
ejpam-5450	140	10	x	x	SYM
ejpam-5450	140	11	=	=	SYM
ejpam-5450	140	12	3	3	NUM
ejpam-5450	140	13	given	give	VERB
ejpam-5450	140	14	ε	ε	PROPN
ejpam-5450	140	15	=	=	SYM
ejpam-5450	140	16	0.9	0.9	NUM
ejpam-5450	140	17	,	,	PUNCT
ejpam-5450	140	18	the	the	DET
ejpam-5450	140	19	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	140	20	fuzzy	fuzzy	NOUN
ejpam-5450	140	21	set	set	VERB
ejpam-5450	140	22	lε	lε	PRON
ejpam-5450	140	23	µ	µ	PROPN
ejpam-5450	140	24	of	of	ADP
ejpam-5450	140	25	µ	µ	NOUN
ejpam-5450	140	26	in	in	ADP
ejpam-5450	140	27	x	x	AUX
ejpam-5450	140	28	is	be	AUX
ejpam-5450	140	29	given	give	VERB
ejpam-5450	140	30	as	as	SCONJ
ejpam-5450	140	31	follows	follow	VERB
ejpam-5450	140	32	:	:	PUNCT
ejpam-5450	140	33	lε	lε	ADP
ejpam-5450	140	34	µ	µ	NOUN
ejpam-5450	140	35	:	:	PUNCT
ejpam-5450	140	36	x	x	SYM
ejpam-5450	140	37	→	→	SYM
ejpam-5450	141	1	[	[	X
ejpam-5450	141	2	0	0	NUM
ejpam-5450	141	3	,	,	PUNCT
ejpam-5450	141	4	1];x	1];x	NUM
ejpam-5450	141	5	7→	7→	NUM
ejpam-5450	141	6			NUM
ejpam-5450	141	7	0.9	0.9	NUM
ejpam-5450	141	8	if	if	SCONJ
ejpam-5450	141	9	x	x	PROPN
ejpam-5450	141	10	=	=	SYM
ejpam-5450	141	11	0	0	NUM
ejpam-5450	141	12	0.5	0.5	NUM
ejpam-5450	141	13	if	if	SCONJ
ejpam-5450	141	14	x	x	NOUN
ejpam-5450	141	15	=	=	SYM
ejpam-5450	141	16	1	1	NUM
ejpam-5450	141	17	0.3	0.3	NUM
ejpam-5450	141	18	if	if	SCONJ
ejpam-5450	141	19	x	x	PROPN
ejpam-5450	141	20	=	=	SYM
ejpam-5450	141	21	2	2	NUM
ejpam-5450	141	22	0	0	NUM
ejpam-5450	141	23	if	if	SCONJ
ejpam-5450	141	24	x	x	PROPN
ejpam-5450	141	25	=	=	SYM
ejpam-5450	141	26	3	3	NUM
ejpam-5450	141	27	then	then	ADV
ejpam-5450	141	28	lε	lε	PROPN
ejpam-5450	141	29	µ	µ	PROPN
ejpam-5450	141	30	is	be	AUX
ejpam-5450	141	31	an	an	DET
ejpam-5450	141	32	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	141	33	fuzzy	fuzzy	ADJ
ejpam-5450	141	34	bcc	bcc	PROPN
ejpam-5450	141	35	-	-	PUNCT
ejpam-5450	141	36	subalgebra	subalgebra	NOUN
ejpam-5450	141	37	of	of	ADP
ejpam-5450	141	38	x	x	X
ejpam-5450	141	39	but	but	CCONJ
ejpam-5450	141	40	not	not	PART
ejpam-5450	141	41	an	an	DET
ejpam-5450	141	42	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	141	43	fuzzy	fuzzy	ADJ
ejpam-5450	141	44	bcc	bcc	PROPN
ejpam-5450	141	45	-	-	PUNCT
ejpam-5450	141	46	ideal	ideal	NOUN
ejpam-5450	141	47	of	of	ADP
ejpam-5450	141	48	x	x	PRON
ejpam-5450	141	49	because	because	SCONJ
ejpam-5450	141	50	lε	lε	PART
ejpam-5450	141	51	µ(0	µ(0	VERB
ejpam-5450	141	52	◦	◦	VERB
ejpam-5450	141	53	3	3	NUM
ejpam-5450	141	54	)	)	PUNCT
ejpam-5450	141	55	=	=	PRON
ejpam-5450	141	56	lε	lε	ADP
ejpam-5450	141	57	µ(3	µ(3	PROPN
ejpam-5450	141	58	)	)	PUNCT
ejpam-5450	141	59	=	=	PUNCT
ejpam-5450	141	60	0	0	NUM
ejpam-5450	141	61	≱	≱	PROPN
ejpam-5450	141	62	0.3	0.3	NUM
ejpam-5450	141	63	=	=	SYM
ejpam-5450	141	64	min{0.3	min{0.3	PROPN
ejpam-5450	141	65	,	,	PUNCT
ejpam-5450	141	66	0.5	0.5	NUM
ejpam-5450	141	67	}	}	PUNCT
ejpam-5450	141	68	=	=	NUM
ejpam-5450	141	69	min{lε	min{lε	NUM
ejpam-5450	141	70	µ(0	µ(0	NOUN
ejpam-5450	141	71	◦	◦	NOUN
ejpam-5450	141	72	(	(	PUNCT
ejpam-5450	141	73	1	1	NUM
ejpam-5450	141	74	◦	◦	NOUN
ejpam-5450	141	75	3	3	NUM
ejpam-5450	141	76	)	)	PUNCT
ejpam-5450	141	77	)	)	PUNCT
ejpam-5450	141	78	,	,	PUNCT
ejpam-5450	141	79	lε	lε	X
ejpam-5450	141	80	µ(1	µ(1	NOUN
ejpam-5450	141	81	)	)	PUNCT
ejpam-5450	141	82	}	}	PUNCT
ejpam-5450	141	83	by	by	ADP
ejpam-5450	141	84	theorem	theorem	NOUN
ejpam-5450	141	85	1	1	NUM
ejpam-5450	141	86	.	.	PUNCT
ejpam-5450	141	87	theorem	theorem	NOUN
ejpam-5450	141	88	2	2	NUM
ejpam-5450	141	89	.	.	PUNCT
ejpam-5450	141	90	if	if	SCONJ
ejpam-5450	141	91	µ	µ	NOUN
ejpam-5450	141	92	is	be	AUX
ejpam-5450	141	93	a	a	DET
ejpam-5450	141	94	fuzzy	fuzzy	ADJ
ejpam-5450	141	95	bcc	bcc	NOUN
ejpam-5450	141	96	-	-	PUNCT
ejpam-5450	141	97	ideal	ideal	NOUN
ejpam-5450	141	98	of	of	ADP
ejpam-5450	141	99	x	x	PRON
ejpam-5450	141	100	,	,	PUNCT
ejpam-5450	141	101	then	then	ADV
ejpam-5450	141	102	its	its	PRON
ejpam-5450	141	103	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	141	104	fuzzy	fuzzy	NOUN
ejpam-5450	141	105	set	set	VERB
ejpam-5450	141	106	lε	lε	PRON
ejpam-5450	141	107	µ	µ	NOUN
ejpam-5450	141	108	in	in	ADP
ejpam-5450	141	109	x	x	VERB
ejpam-5450	141	110	is	be	AUX
ejpam-5450	141	111	an	an	DET
ejpam-5450	141	112	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	141	113	fuzzy	fuzzy	ADJ
ejpam-5450	141	114	bcc	bcc	PROPN
ejpam-5450	141	115	-	-	PUNCT
ejpam-5450	141	116	ideal	ideal	NOUN
ejpam-5450	141	117	of	of	ADP
ejpam-5450	141	118	x.	x.	NOUN
ejpam-5450	141	119	proof	proof	PROPN
ejpam-5450	141	120	.	.	PUNCT
ejpam-5450	142	1	assume	assume	VERB
ejpam-5450	142	2	that	that	SCONJ
ejpam-5450	142	3	µ	µ	NOUN
ejpam-5450	142	4	is	be	AUX
ejpam-5450	142	5	a	a	DET
ejpam-5450	142	6	fuzzy	fuzzy	ADJ
ejpam-5450	142	7	bcc	bcc	NOUN
ejpam-5450	142	8	-	-	PUNCT
ejpam-5450	142	9	ideal	ideal	NOUN
ejpam-5450	142	10	of	of	ADP
ejpam-5450	142	11	x.	x.	NOUN
ejpam-5450	142	12	let	let	VERB
ejpam-5450	143	1	x	x	X
ejpam-5450	143	2	∈	∈	PROPN
ejpam-5450	143	3	x	x	X
ejpam-5450	143	4	and	and	CCONJ
ejpam-5450	143	5	ta	ta	ADP
ejpam-5450	143	6	∈	∈	PROPN
ejpam-5450	143	7	(	(	PUNCT
ejpam-5450	143	8	0	0	NUM
ejpam-5450	143	9	,	,	PUNCT
ejpam-5450	143	10	1	1	NUM
ejpam-5450	143	11	]	]	PUNCT
ejpam-5450	143	12	be	be	AUX
ejpam-5450	143	13	such	such	ADJ
ejpam-5450	143	14	that	that	SCONJ
ejpam-5450	143	15	[	[	X
ejpam-5450	143	16	x	x	X
ejpam-5450	143	17	/	/	SYM
ejpam-5450	143	18	ta	ta	X
ejpam-5450	143	19	]	]	X
ejpam-5450	143	20	∈	∈	PROPN
ejpam-5450	143	21	lε	lε	ADP
ejpam-5450	143	22	µ.	µ.	NOUN
ejpam-5450	143	23	then	then	ADV
ejpam-5450	143	24	lε	lε	ADP
ejpam-5450	143	25	µ(x	µ(x	NOUN
ejpam-5450	143	26	)	)	PUNCT
ejpam-5450	143	27	≥	≥	NOUN
ejpam-5450	143	28	ta	ta	NOUN
ejpam-5450	143	29	.	.	PUNCT
ejpam-5450	144	1	thus	thus	ADV
ejpam-5450	144	2	lε	lε	ADP
ejpam-5450	144	3	µ(0	µ(0	NOUN
ejpam-5450	144	4	)	)	PUNCT
ejpam-5450	144	5	=	=	SYM
ejpam-5450	144	6	max{0	max{0	PROPN
ejpam-5450	144	7	,	,	PUNCT
ejpam-5450	144	8	µ(0	µ(0	NOUN
ejpam-5450	144	9	)	)	PUNCT
ejpam-5450	144	10	+	+	CCONJ
ejpam-5450	144	11	ε−	ε−	PROPN
ejpam-5450	144	12	1	1	NUM
ejpam-5450	144	13	}	}	PUNCT
ejpam-5450	144	14	≥	≥	X
ejpam-5450	144	15	max{0	max{0	NUM
ejpam-5450	144	16	,	,	PUNCT
ejpam-5450	144	17	µ(x	µ(x	X
ejpam-5450	144	18	)	)	PUNCT
ejpam-5450	144	19	+	+	CCONJ
ejpam-5450	144	20	ε−	ε−	PROPN
ejpam-5450	144	21	1	1	NUM
ejpam-5450	144	22	}	}	PUNCT
ejpam-5450	144	23	=	=	PUNCT
ejpam-5450	144	24	lε	lε	X
ejpam-5450	144	25	µ(x	µ(x	NOUN
ejpam-5450	144	26	)	)	PUNCT
ejpam-5450	144	27	≥	≥	NOUN
ejpam-5450	144	28	ta	ta	PROPN
ejpam-5450	144	29	.	.	PUNCT
ejpam-5450	145	1	then	then	ADV
ejpam-5450	145	2	[	[	X
ejpam-5450	145	3	0	0	NUM
ejpam-5450	145	4	/	/	SYM
ejpam-5450	145	5	ta	ta	X
ejpam-5450	145	6	]	]	X
ejpam-5450	145	7	∈	∈	PROPN
ejpam-5450	145	8	lε	lε	AUX
ejpam-5450	145	9	µ.	µ.	NOUN
ejpam-5450	145	10	let	let	VERB
ejpam-5450	145	11	x	x	PRON
ejpam-5450	145	12	,	,	PUNCT
ejpam-5450	145	13	y	y	PROPN
ejpam-5450	145	14	,	,	PUNCT
ejpam-5450	145	15	z	z	NOUN
ejpam-5450	145	16	∈	∈	PROPN
ejpam-5450	145	17	x	x	X
ejpam-5450	145	18	and	and	CCONJ
ejpam-5450	145	19	ta	ta	PROPN
ejpam-5450	145	20	,	,	PUNCT
ejpam-5450	145	21	tb	tb	ADP
ejpam-5450	145	22	∈	∈	PROPN
ejpam-5450	145	23	(	(	PUNCT
ejpam-5450	145	24	0	0	NUM
ejpam-5450	145	25	,	,	PUNCT
ejpam-5450	145	26	1	1	NUM
ejpam-5450	145	27	]	]	PUNCT
ejpam-5450	145	28	be	be	AUX
ejpam-5450	145	29	such	such	ADJ
ejpam-5450	145	30	that	that	SCONJ
ejpam-5450	145	31	[	[	X
ejpam-5450	145	32	x	x	X
ejpam-5450	145	33	◦	◦	NOUN
ejpam-5450	145	34	(	(	PUNCT
ejpam-5450	145	35	y	y	NOUN
ejpam-5450	145	36	◦	◦	NOUN
ejpam-5450	145	37	z)/ta	z)/ta	NOUN
ejpam-5450	145	38	]	]	X
ejpam-5450	145	39	∈	∈	NOUN
ejpam-5450	145	40	lε	lε	ADP
ejpam-5450	145	41	µ	µ	NOUN
ejpam-5450	145	42	and	and	CCONJ
ejpam-5450	145	43	[	[	X
ejpam-5450	145	44	y	y	X
ejpam-5450	145	45	/	/	SYM
ejpam-5450	145	46	tb	tb	NOUN
ejpam-5450	145	47	]	]	PUNCT
ejpam-5450	145	48	∈	∈	PROPN
ejpam-5450	146	1	lε	lε	X
ejpam-5450	146	2	µ.	µ.	NOUN
ejpam-5450	146	3	then	then	ADV
ejpam-5450	146	4	lε	lε	ADP
ejpam-5450	146	5	µ(x	µ(x	ADJ
ejpam-5450	146	6	◦	◦	NOUN
ejpam-5450	146	7	(	(	PUNCT
ejpam-5450	146	8	y	y	PROPN
ejpam-5450	146	9	◦	◦	PROPN
ejpam-5450	146	10	z	z	PROPN
ejpam-5450	146	11	)	)	PUNCT
ejpam-5450	146	12	)	)	PUNCT
ejpam-5450	146	13	≥	≥	PROPN
ejpam-5450	146	14	ta	ta	X
ejpam-5450	146	15	and	and	CCONJ
ejpam-5450	146	16	lε	lε	INTJ
ejpam-5450	146	17	µ(y	µ(y	PROPN
ejpam-5450	146	18	)	)	PUNCT
ejpam-5450	146	19	≥	≥	NOUN
ejpam-5450	146	20	tb	tb	NOUN
ejpam-5450	146	21	.	.	PUNCT
ejpam-5450	147	1	thus	thus	ADV
ejpam-5450	147	2	lε	lε	ADP
ejpam-5450	147	3	µ(x	µ(x	ADJ
ejpam-5450	147	4	◦	◦	NOUN
ejpam-5450	147	5	z	z	NOUN
ejpam-5450	147	6	)	)	PUNCT
ejpam-5450	147	7	=	=	SYM
ejpam-5450	147	8	max{0	max{0	PROPN
ejpam-5450	147	9	,	,	PUNCT
ejpam-5450	147	10	µ(x	µ(x	X
ejpam-5450	147	11	◦	◦	NOUN
ejpam-5450	147	12	z	z	NOUN
ejpam-5450	147	13	)	)	PUNCT
ejpam-5450	147	14	+	+	CCONJ
ejpam-5450	147	15	ε−	ε−	PROPN
ejpam-5450	147	16	1	1	NUM
ejpam-5450	147	17	}	}	PUNCT
ejpam-5450	147	18	≥	≥	NOUN
ejpam-5450	147	19	max{0,min{µ(x	max{0,min{µ(x	VERB
ejpam-5450	147	20	◦	◦	NOUN
ejpam-5450	147	21	(	(	PUNCT
ejpam-5450	147	22	y	y	PROPN
ejpam-5450	147	23	◦	◦	PROPN
ejpam-5450	147	24	z	z	PROPN
ejpam-5450	147	25	)	)	PUNCT
ejpam-5450	147	26	)	)	PUNCT
ejpam-5450	147	27	,	,	PUNCT
ejpam-5450	147	28	µ(y	µ(y	PROPN
ejpam-5450	147	29	)	)	PUNCT
ejpam-5450	147	30	}	}	PUNCT
ejpam-5450	147	31	+	+	CCONJ
ejpam-5450	147	32	ε−	ε−	PROPN
ejpam-5450	147	33	1	1	NUM
ejpam-5450	147	34	}	}	PUNCT
ejpam-5450	147	35	=	=	SYM
ejpam-5450	147	36	max{0,min{µ(x	max{0,min{µ(x	ADJ
ejpam-5450	147	37	◦	◦	NOUN
ejpam-5450	147	38	(	(	PUNCT
ejpam-5450	147	39	y	y	PROPN
ejpam-5450	147	40	◦	◦	PROPN
ejpam-5450	147	41	z	z	PROPN
ejpam-5450	147	42	)	)	PUNCT
ejpam-5450	147	43	)	)	PUNCT
ejpam-5450	148	1	+	+	CCONJ
ejpam-5450	148	2	ε−	ε−	PROPN
ejpam-5450	148	3	1	1	NUM
ejpam-5450	148	4	,	,	PUNCT
ejpam-5450	148	5	µ(y	µ(y	PROPN
ejpam-5450	148	6	)	)	PUNCT
ejpam-5450	148	7	+	+	CCONJ
ejpam-5450	148	8	ε−	ε−	PROPN
ejpam-5450	148	9	1	1	NUM
ejpam-5450	148	10	}	}	PUNCT
ejpam-5450	148	11	}	}	PUNCT
ejpam-5450	148	12	=	=	SYM
ejpam-5450	148	13	min{max{µ(x	min{max{µ(x	PROPN
ejpam-5450	148	14	◦	◦	NOUN
ejpam-5450	148	15	(	(	PUNCT
ejpam-5450	148	16	y	y	PROPN
ejpam-5450	148	17	◦	◦	PROPN
ejpam-5450	148	18	z	z	PROPN
ejpam-5450	148	19	)	)	PUNCT
ejpam-5450	148	20	)	)	PUNCT
ejpam-5450	149	1	+	+	CCONJ
ejpam-5450	149	2	ε−	ε−	PROPN
ejpam-5450	149	3	1},max{µ(y	1},max{µ(y	NUM
ejpam-5450	149	4	)	)	PUNCT
ejpam-5450	150	1	+	+	CCONJ
ejpam-5450	150	2	ε−	ε−	PROPN
ejpam-5450	150	3	1	1	NUM
ejpam-5450	150	4	}	}	PUNCT
ejpam-5450	150	5	}	}	PUNCT
ejpam-5450	150	6	=	=	SYM
ejpam-5450	150	7	min{lε	min{lε	NUM
ejpam-5450	150	8	µ(x	µ(x	PUNCT
ejpam-5450	150	9	◦	◦	NOUN
ejpam-5450	150	10	(	(	PUNCT
ejpam-5450	150	11	y	y	PROPN
ejpam-5450	150	12	◦	◦	PROPN
ejpam-5450	150	13	z	z	PROPN
ejpam-5450	150	14	)	)	PUNCT
ejpam-5450	150	15	)	)	PUNCT
ejpam-5450	150	16	,	,	PUNCT
ejpam-5450	150	17	lε	lε	X
ejpam-5450	150	18	µ(y	µ(y	PROPN
ejpam-5450	150	19	)	)	PUNCT
ejpam-5450	150	20	}	}	PUNCT
ejpam-5450	150	21	≥	≥	NOUN
ejpam-5450	150	22	min{ta	min{ta	X
ejpam-5450	150	23	,	,	PUNCT
ejpam-5450	150	24	tb	tb	NOUN
ejpam-5450	150	25	}	}	PUNCT
ejpam-5450	150	26	.	.	PUNCT
ejpam-5450	151	1	a.	a.	PROPN
ejpam-5450	151	2	iampan	iampan	PROPN
ejpam-5450	151	3	,	,	PUNCT
ejpam-5450	151	4	r.	r.	PROPN
ejpam-5450	151	5	subasini	subasini	PROPN
ejpam-5450	151	6	,	,	PUNCT
ejpam-5450	151	7	n.	n.	PROPN
ejpam-5450	151	8	rajesh	rajesh	PROPN
ejpam-5450	151	9	/	/	SYM
ejpam-5450	151	10	eur	eur	PROPN
ejpam-5450	151	11	.	.	PUNCT
ejpam-5450	152	1	j.	j.	PROPN
ejpam-5450	152	2	pure	pure	PROPN
ejpam-5450	152	3	appl	appl	PROPN
ejpam-5450	152	4	.	.	PROPN
ejpam-5450	152	5	math	math	PROPN
ejpam-5450	152	6	,	,	PUNCT
ejpam-5450	152	7	17	17	NUM
ejpam-5450	152	8	(	(	PUNCT
ejpam-5450	152	9	4	4	NUM
ejpam-5450	152	10	)	)	PUNCT
ejpam-5450	152	11	(	(	PUNCT
ejpam-5450	152	12	2024	2024	NUM
ejpam-5450	152	13	)	)	PUNCT
ejpam-5450	152	14	,	,	PUNCT
ejpam-5450	152	15	3209	3209	NUM
ejpam-5450	152	16	-	-	SYM
ejpam-5450	152	17	3222	3222	NUM
ejpam-5450	152	18	3216	3216	NUM
ejpam-5450	152	19	then	then	ADV
ejpam-5450	152	20	[	[	X
ejpam-5450	152	21	(	(	PUNCT
ejpam-5450	152	22	x	x	SYM
ejpam-5450	152	23	◦	◦	NOUN
ejpam-5450	152	24	z)/min{ta	z)/min{ta	PROPN
ejpam-5450	152	25	,	,	PUNCT
ejpam-5450	152	26	tb	tb	NOUN
ejpam-5450	152	27	}	}	PUNCT
ejpam-5450	152	28	]	]	PUNCT
ejpam-5450	153	1	∈	∈	PROPN
ejpam-5450	153	2	lε	lε	VERB
ejpam-5450	153	3	µ.	µ.	NOUN
ejpam-5450	153	4	hence	hence	ADV
ejpam-5450	153	5	,	,	PUNCT
ejpam-5450	153	6	lε	lε	PROPN
ejpam-5450	153	7	µ	µ	PROPN
ejpam-5450	153	8	is	be	AUX
ejpam-5450	153	9	an	an	DET
ejpam-5450	153	10	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	153	11	fuzzy	fuzzy	ADJ
ejpam-5450	153	12	bcc	bcc	PROPN
ejpam-5450	153	13	-	-	PUNCT
ejpam-5450	153	14	ideal	ideal	NOUN
ejpam-5450	153	15	of	of	ADP
ejpam-5450	153	16	x.	x.	NOUN
ejpam-5450	153	17	let	let	VERB
ejpam-5450	153	18	µ	µ	X
ejpam-5450	153	19	be	be	AUX
ejpam-5450	153	20	a	a	DET
ejpam-5450	153	21	fuzzy	fuzzy	ADJ
ejpam-5450	153	22	set	set	NOUN
ejpam-5450	153	23	in	in	ADP
ejpam-5450	153	24	x.	x.	NOUN
ejpam-5450	153	25	for	for	ADP
ejpam-5450	153	26	an	an	DET
ejpam-5450	153	27	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	153	28	fuzzy	fuzzy	NOUN
ejpam-5450	153	29	set	set	VERB
ejpam-5450	153	30	lε	lε	PRON
ejpam-5450	153	31	µ	µ	PROPN
ejpam-5450	153	32	of	of	ADP
ejpam-5450	153	33	µ	µ	NOUN
ejpam-5450	153	34	in	in	ADP
ejpam-5450	153	35	x	x	X
ejpam-5450	153	36	and	and	CCONJ
ejpam-5450	153	37	t	t	PROPN
ejpam-5450	153	38	∈	∈	PROPN
ejpam-5450	153	39	(	(	PUNCT
ejpam-5450	153	40	0	0	NUM
ejpam-5450	153	41	,	,	PUNCT
ejpam-5450	153	42	1	1	NUM
ejpam-5450	153	43	]	]	PUNCT
ejpam-5450	153	44	,	,	PUNCT
ejpam-5450	153	45	consider	consider	VERB
ejpam-5450	153	46	the	the	DET
ejpam-5450	153	47	sets	set	NOUN
ejpam-5450	153	48	(	(	PUNCT
ejpam-5450	153	49	lε	lε	X
ejpam-5450	153	50	µ	µ	NUM
ejpam-5450	153	51	,	,	PUNCT
ejpam-5450	153	52	t)∈	t)∈	PUNCT
ejpam-5450	153	53	=	=	SYM
ejpam-5450	153	54	{	{	PUNCT
ejpam-5450	153	55	x	x	SYM
ejpam-5450	153	56	∈	∈	PROPN
ejpam-5450	153	57	x	x	X
ejpam-5450	153	58	:	:	PUNCT
ejpam-5450	154	1	[	[	X
ejpam-5450	154	2	x	x	X
ejpam-5450	154	3	/	/	SYM
ejpam-5450	154	4	t	t	PROPN
ejpam-5450	154	5	]	]	X
ejpam-5450	154	6	∈	∈	PROPN
ejpam-5450	154	7	lε	lε	ADP
ejpam-5450	154	8	µ	µ	NOUN
ejpam-5450	154	9	}	}	PUNCT
ejpam-5450	154	10	,	,	PUNCT
ejpam-5450	154	11	(	(	PUNCT
ejpam-5450	154	12	lε	lε	X
ejpam-5450	154	13	µ	µ	NUM
ejpam-5450	154	14	,	,	PUNCT
ejpam-5450	154	15	t)q	t)q	PUNCT
ejpam-5450	154	16	=	=	SYM
ejpam-5450	154	17	{	{	PUNCT
ejpam-5450	154	18	x	x	SYM
ejpam-5450	154	19	∈	∈	PROPN
ejpam-5450	154	20	x	x	X
ejpam-5450	154	21	:	:	PUNCT
ejpam-5450	155	1	[	[	X
ejpam-5450	155	2	x	x	X
ejpam-5450	155	3	/	/	SYM
ejpam-5450	155	4	t]qlε	t]qlε	X
ejpam-5450	155	5	µ	µ	X
ejpam-5450	155	6	}	}	PUNCT
ejpam-5450	155	7	,	,	PUNCT
ejpam-5450	155	8	which	which	PRON
ejpam-5450	155	9	are	be	AUX
ejpam-5450	155	10	called	call	VERB
ejpam-5450	155	11	the	the	DET
ejpam-5450	155	12	∈-set	∈-set	NOUN
ejpam-5450	155	13	and	and	CCONJ
ejpam-5450	155	14	q	q	NOUN
ejpam-5450	155	15	-	-	PUNCT
ejpam-5450	155	16	set	set	VERB
ejpam-5450	155	17	,	,	PUNCT
ejpam-5450	155	18	respectively	respectively	ADV
ejpam-5450	155	19	,	,	PUNCT
ejpam-5450	155	20	of	of	ADP
ejpam-5450	155	21	lε	lε	X
ejpam-5450	155	22	µ	µ	X
ejpam-5450	155	23	(	(	PUNCT
ejpam-5450	155	24	with	with	ADP
ejpam-5450	155	25	value	value	NOUN
ejpam-5450	155	26	t	t	PROPN
ejpam-5450	155	27	)	)	PUNCT
ejpam-5450	155	28	.	.	PUNCT
ejpam-5450	156	1	we	we	PRON
ejpam-5450	156	2	explore	explore	VERB
ejpam-5450	156	3	the	the	DET
ejpam-5450	156	4	conditions	condition	NOUN
ejpam-5450	156	5	under	under	ADP
ejpam-5450	156	6	which	which	PRON
ejpam-5450	156	7	the	the	DET
ejpam-5450	156	8	∈-set	∈-set	NOUN
ejpam-5450	156	9	and	and	CCONJ
ejpam-5450	156	10	q	q	NOUN
ejpam-5450	156	11	-	-	PUNCT
ejpam-5450	156	12	set	set	NOUN
ejpam-5450	156	13	of	of	ADP
ejpam-5450	156	14	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	156	15	fuzzy	fuzzy	ADJ
ejpam-5450	156	16	sets	set	NOUN
ejpam-5450	156	17	can	can	AUX
ejpam-5450	156	18	be	be	AUX
ejpam-5450	156	19	a	a	DET
ejpam-5450	156	20	bcc	bcc	PROPN
ejpam-5450	156	21	-	-	PUNCT
ejpam-5450	156	22	ideal	ideal	NOUN
ejpam-5450	156	23	.	.	PUNCT
ejpam-5450	157	1	theorem	theorem	NOUN
ejpam-5450	157	2	3	3	X
ejpam-5450	157	3	.	.	PUNCT
ejpam-5450	158	1	let	let	VERB
ejpam-5450	158	2	lε	lε	PART
ejpam-5450	158	3	µ	µ	X
ejpam-5450	158	4	be	be	AUX
ejpam-5450	158	5	an	an	DET
ejpam-5450	158	6	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	158	7	fuzzy	fuzzy	ADJ
ejpam-5450	158	8	set	set	NOUN
ejpam-5450	158	9	of	of	ADP
ejpam-5450	158	10	a	a	DET
ejpam-5450	158	11	fuzzy	fuzzy	ADJ
ejpam-5450	158	12	set	set	VERB
ejpam-5450	158	13	µ	µ	NOUN
ejpam-5450	158	14	in	in	ADP
ejpam-5450	158	15	x.	x.	NOUN
ejpam-5450	158	16	then	then	ADV
ejpam-5450	158	17	the	the	DET
ejpam-5450	158	18	∈-set	∈-set	NOUN
ejpam-5450	158	19	(	(	PUNCT
ejpam-5450	158	20	lε	lε	X
ejpam-5450	158	21	µ	µ	NUM
ejpam-5450	158	22	,	,	PUNCT
ejpam-5450	158	23	t)∈	t)∈	NUM
ejpam-5450	158	24	of	of	ADP
ejpam-5450	158	25	lε	lε	X
ejpam-5450	158	26	µ	µ	X
ejpam-5450	158	27	with	with	ADP
ejpam-5450	158	28	value	value	NOUN
ejpam-5450	158	29	t	t	PROPN
ejpam-5450	158	30	∈	∈	PROPN
ejpam-5450	158	31	(	(	PUNCT
ejpam-5450	158	32	0.5	0.5	NUM
ejpam-5450	158	33	,	,	PUNCT
ejpam-5450	158	34	1	1	NUM
ejpam-5450	158	35	]	]	PUNCT
ejpam-5450	158	36	is	be	AUX
ejpam-5450	158	37	a	a	DET
ejpam-5450	158	38	bcc	bcc	PROPN
ejpam-5450	158	39	-	-	PUNCT
ejpam-5450	158	40	ideal	ideal	NOUN
ejpam-5450	158	41	of	of	ADP
ejpam-5450	158	42	x	x	SYM
ejpam-5450	158	43	if	if	SCONJ
ejpam-5450	158	44	and	and	CCONJ
ejpam-5450	158	45	only	only	ADV
ejpam-5450	158	46	if	if	SCONJ
ejpam-5450	158	47	the	the	DET
ejpam-5450	158	48	following	follow	VERB
ejpam-5450	158	49	assertions	assertion	NOUN
ejpam-5450	158	50	are	be	AUX
ejpam-5450	158	51	valid	valid	ADJ
ejpam-5450	158	52	:	:	PUNCT
ejpam-5450	158	53	(	(	PUNCT
ejpam-5450	159	1	∀x	∀x	X
ejpam-5450	159	2	∈	∈	PROPN
ejpam-5450	159	3	x)(max{lε	x)(max{lε	PUNCT
ejpam-5450	159	4	µ(0	µ(0	NOUN
ejpam-5450	159	5	)	)	PUNCT
ejpam-5450	159	6	,	,	PUNCT
ejpam-5450	159	7	0.5	0.5	NUM
ejpam-5450	159	8	}	}	PUNCT
ejpam-5450	159	9	≥	≥	NOUN
ejpam-5450	159	10	lε	lε	X
ejpam-5450	159	11	µ(x	µ(x	NOUN
ejpam-5450	159	12	)	)	PUNCT
ejpam-5450	159	13	)	)	PUNCT
ejpam-5450	159	14	(	(	PUNCT
ejpam-5450	159	15	3.9	3.9	NUM
ejpam-5450	159	16	)	)	PUNCT
ejpam-5450	159	17	(	(	PUNCT
ejpam-5450	159	18	∀x	∀x	X
ejpam-5450	159	19	,	,	PUNCT
ejpam-5450	159	20	y	y	PROPN
ejpam-5450	159	21	,	,	PUNCT
ejpam-5450	159	22	z	z	PROPN
ejpam-5450	159	23	∈	∈	PROPN
ejpam-5450	159	24	x)(max{lε	x)(max{lε	NUM
ejpam-5450	159	25	µ(x	µ(x	PUNCT
ejpam-5450	159	26	◦	◦	NOUN
ejpam-5450	159	27	z	z	NOUN
ejpam-5450	159	28	)	)	PUNCT
ejpam-5450	159	29	,	,	PUNCT
ejpam-5450	159	30	0.5	0.5	NUM
ejpam-5450	159	31	}	}	PUNCT
ejpam-5450	159	32	≥	≥	PROPN
ejpam-5450	159	33	min{lε	min{lε	NUM
ejpam-5450	159	34	µ(x	µ(x	ADJ
ejpam-5450	159	35	◦	◦	NOUN
ejpam-5450	159	36	(	(	PUNCT
ejpam-5450	159	37	y	y	PROPN
ejpam-5450	159	38	◦	◦	PROPN
ejpam-5450	159	39	z	z	PROPN
ejpam-5450	159	40	)	)	PUNCT
ejpam-5450	159	41	)	)	PUNCT
ejpam-5450	159	42	,	,	PUNCT
ejpam-5450	159	43	lε	lε	X
ejpam-5450	159	44	µ(y	µ(y	PROPN
ejpam-5450	159	45	)	)	PUNCT
ejpam-5450	159	46	}	}	PUNCT
ejpam-5450	159	47	)	)	PUNCT
ejpam-5450	159	48	(	(	PUNCT
ejpam-5450	159	49	3.10	3.10	NUM
ejpam-5450	159	50	)	)	PUNCT
ejpam-5450	159	51	proof	proof	NOUN
ejpam-5450	159	52	.	.	PUNCT
ejpam-5450	160	1	assume	assume	VERB
ejpam-5450	160	2	that	that	SCONJ
ejpam-5450	160	3	the	the	DET
ejpam-5450	160	4	∈-set	∈-set	NOUN
ejpam-5450	160	5	(	(	PUNCT
ejpam-5450	160	6	lε	lε	X
ejpam-5450	160	7	µ	µ	NUM
ejpam-5450	160	8	,	,	PUNCT
ejpam-5450	160	9	t)∈	t)∈	NUM
ejpam-5450	160	10	of	of	ADP
ejpam-5450	160	11	lε	lε	X
ejpam-5450	160	12	µ	µ	X
ejpam-5450	160	13	with	with	ADP
ejpam-5450	160	14	value	value	NOUN
ejpam-5450	160	15	t	t	PROPN
ejpam-5450	160	16	∈	∈	PROPN
ejpam-5450	160	17	(	(	PUNCT
ejpam-5450	160	18	0.5	0.5	NUM
ejpam-5450	160	19	,	,	PUNCT
ejpam-5450	160	20	1	1	NUM
ejpam-5450	160	21	]	]	PUNCT
ejpam-5450	160	22	is	be	AUX
ejpam-5450	160	23	a	a	DET
ejpam-5450	160	24	bcc	bcc	PROPN
ejpam-5450	160	25	-	-	PUNCT
ejpam-5450	160	26	ideal	ideal	NOUN
ejpam-5450	160	27	of	of	ADP
ejpam-5450	160	28	x.	x.	NOUN
ejpam-5450	160	29	if	if	SCONJ
ejpam-5450	160	30	the	the	DET
ejpam-5450	160	31	condition	condition	NOUN
ejpam-5450	160	32	(	(	PUNCT
ejpam-5450	160	33	3.9	3.9	NUM
ejpam-5450	160	34	)	)	PUNCT
ejpam-5450	160	35	is	be	AUX
ejpam-5450	160	36	not	not	PART
ejpam-5450	160	37	valid	valid	ADJ
ejpam-5450	160	38	,	,	PUNCT
ejpam-5450	160	39	then	then	ADV
ejpam-5450	160	40	there	there	PRON
ejpam-5450	160	41	exists	exist	VERB
ejpam-5450	160	42	a	a	DET
ejpam-5450	160	43	∈	∈	NOUN
ejpam-5450	160	44	x	x	PUNCT
ejpam-5450	160	45	such	such	ADJ
ejpam-5450	160	46	that	that	SCONJ
ejpam-5450	160	47	max{lε	max{lε	ADJ
ejpam-5450	160	48	µ(0	µ(0	NOUN
ejpam-5450	160	49	)	)	PUNCT
ejpam-5450	160	50	,	,	PUNCT
ejpam-5450	160	51	0.5	0.5	NUM
ejpam-5450	160	52	}	}	PUNCT
ejpam-5450	160	53	<	<	X
ejpam-5450	160	54	lε	lε	X
ejpam-5450	160	55	µ(a	µ(a	PROPN
ejpam-5450	160	56	)	)	PUNCT
ejpam-5450	160	57	.	.	PUNCT
ejpam-5450	161	1	thus	thus	ADV
ejpam-5450	161	2	lε	lε	ADP
ejpam-5450	161	3	µ(a	µ(a	PROPN
ejpam-5450	161	4	)	)	PUNCT
ejpam-5450	161	5	∈	∈	PROPN
ejpam-5450	161	6	(	(	PUNCT
ejpam-5450	161	7	0.5	0.5	NUM
ejpam-5450	161	8	,	,	PUNCT
ejpam-5450	161	9	1	1	NUM
ejpam-5450	161	10	]	]	PUNCT
ejpam-5450	161	11	and	and	CCONJ
ejpam-5450	161	12	lε	lε	INTJ
ejpam-5450	161	13	µ(a	µ(a	PROPN
ejpam-5450	161	14	)	)	PUNCT
ejpam-5450	161	15	>	>	X
ejpam-5450	161	16	lε	lε	X
ejpam-5450	161	17	µ(0	µ(0	NOUN
ejpam-5450	161	18	)	)	PUNCT
ejpam-5450	161	19	.	.	PUNCT
ejpam-5450	162	1	if	if	SCONJ
ejpam-5450	162	2	we	we	PRON
ejpam-5450	162	3	take	take	VERB
ejpam-5450	162	4	t	t	NOUN
ejpam-5450	162	5	=	=	PUNCT
ejpam-5450	162	6	lε	lε	ADP
ejpam-5450	162	7	µ(a	µ(a	PROPN
ejpam-5450	162	8	)	)	PUNCT
ejpam-5450	162	9	,	,	PUNCT
ejpam-5450	162	10	then	then	ADV
ejpam-5450	162	11	[	[	X
ejpam-5450	162	12	a	a	X
ejpam-5450	162	13	/	/	SYM
ejpam-5450	162	14	t	t	NOUN
ejpam-5450	162	15	]	]	X
ejpam-5450	162	16	∈	∈	PROPN
ejpam-5450	162	17	lε	lε	X
ejpam-5450	162	18	µ	µ	NOUN
ejpam-5450	162	19	,	,	PUNCT
ejpam-5450	162	20	that	that	ADV
ejpam-5450	162	21	is	is	ADV
ejpam-5450	162	22	,	,	PUNCT
ejpam-5450	162	23	a	a	DET
ejpam-5450	162	24	∈	∈	PROPN
ejpam-5450	162	25	(	(	PUNCT
ejpam-5450	162	26	lε	lε	X
ejpam-5450	162	27	µ	µ	NUM
ejpam-5450	162	28	,	,	PUNCT
ejpam-5450	162	29	s)∈	s)∈	NUM
ejpam-5450	162	30	and	and	CCONJ
ejpam-5450	162	31	0	0	NUM
ejpam-5450	162	32	/∈	/∈	INTJ
ejpam-5450	162	33	(	(	PUNCT
ejpam-5450	162	34	lε	lε	ADP
ejpam-5450	162	35	µ	µ	NUM
ejpam-5450	162	36	,	,	PUNCT
ejpam-5450	162	37	t)∈.	t)∈.	PROPN
ejpam-5450	162	38	this	this	PRON
ejpam-5450	162	39	is	be	AUX
ejpam-5450	162	40	a	a	DET
ejpam-5450	162	41	contradiction	contradiction	NOUN
ejpam-5450	162	42	and	and	CCONJ
ejpam-5450	162	43	so	so	ADV
ejpam-5450	162	44	lε	lε	ADP
ejpam-5450	162	45	µ(x	µ(x	NOUN
ejpam-5450	162	46	)	)	PUNCT
ejpam-5450	162	47	≤	≤	NOUN
ejpam-5450	162	48	max{lε	max{lε	NOUN
ejpam-5450	162	49	µ(0	µ(0	NOUN
ejpam-5450	162	50	)	)	PUNCT
ejpam-5450	162	51	,	,	PUNCT
ejpam-5450	162	52	0.5	0.5	NUM
ejpam-5450	162	53	}	}	PUNCT
ejpam-5450	162	54	for	for	ADP
ejpam-5450	162	55	all	all	PRON
ejpam-5450	162	56	x	x	SYM
ejpam-5450	162	57	∈	∈	NOUN
ejpam-5450	162	58	x.	x.	NOUN
ejpam-5450	163	1	now	now	ADV
ejpam-5450	163	2	,	,	PUNCT
ejpam-5450	163	3	if	if	SCONJ
ejpam-5450	163	4	the	the	DET
ejpam-5450	163	5	condition	condition	NOUN
ejpam-5450	163	6	(	(	PUNCT
ejpam-5450	163	7	3.10	3.10	NUM
ejpam-5450	163	8	)	)	PUNCT
ejpam-5450	163	9	is	be	AUX
ejpam-5450	163	10	not	not	PART
ejpam-5450	163	11	valid	valid	ADJ
ejpam-5450	163	12	,	,	PUNCT
ejpam-5450	163	13	then	then	ADV
ejpam-5450	163	14	there	there	PRON
ejpam-5450	163	15	exist	exist	VERB
ejpam-5450	163	16	a	a	DET
ejpam-5450	163	17	,	,	PUNCT
ejpam-5450	163	18	b	b	NOUN
ejpam-5450	163	19	,	,	PUNCT
ejpam-5450	163	20	c	c	PROPN
ejpam-5450	163	21	∈	∈	PROPN
ejpam-5450	163	22	x	x	PUNCT
ejpam-5450	163	23	such	such	ADJ
ejpam-5450	163	24	that	that	SCONJ
ejpam-5450	163	25	max{lε	max{lε	X
ejpam-5450	163	26	µ(a	µ(a	PROPN
ejpam-5450	163	27	◦	◦	NOUN
ejpam-5450	163	28	c	c	NOUN
ejpam-5450	163	29	)	)	PUNCT
ejpam-5450	163	30	,	,	PUNCT
ejpam-5450	163	31	0.5	0.5	NUM
ejpam-5450	163	32	}	}	PUNCT
ejpam-5450	163	33	<	<	X
ejpam-5450	163	34	min{lε	min{lε	NUM
ejpam-5450	163	35	µ(a	µ(a	PROPN
ejpam-5450	163	36	◦	◦	NOUN
ejpam-5450	163	37	(	(	PUNCT
ejpam-5450	163	38	b	b	X
ejpam-5450	163	39	◦	◦	NOUN
ejpam-5450	163	40	c	c	NOUN
ejpam-5450	163	41	)	)	PUNCT
ejpam-5450	163	42	)	)	PUNCT
ejpam-5450	163	43	,	,	PUNCT
ejpam-5450	163	44	lε	lε	X
ejpam-5450	163	45	µ(b	µ(b	NOUN
ejpam-5450	163	46	)	)	PUNCT
ejpam-5450	163	47	}	}	PUNCT
ejpam-5450	163	48	.	.	PUNCT
ejpam-5450	164	1	if	if	SCONJ
ejpam-5450	164	2	we	we	PRON
ejpam-5450	164	3	take	take	VERB
ejpam-5450	164	4	s	s	VERB
ejpam-5450	164	5	=	=	PUNCT
ejpam-5450	164	6	min{lε	min{lε	NUM
ejpam-5450	164	7	µ(a	µ(a	PROPN
ejpam-5450	164	8	◦	◦	NOUN
ejpam-5450	164	9	(	(	PUNCT
ejpam-5450	164	10	b	b	X
ejpam-5450	164	11	◦	◦	NOUN
ejpam-5450	164	12	c	c	NOUN
ejpam-5450	164	13	)	)	PUNCT
ejpam-5450	164	14	)	)	PUNCT
ejpam-5450	164	15	,	,	PUNCT
ejpam-5450	164	16	lε	lε	X
ejpam-5450	164	17	µ(b	µ(b	NOUN
ejpam-5450	164	18	)	)	PUNCT
ejpam-5450	164	19	}	}	PUNCT
ejpam-5450	164	20	,	,	PUNCT
ejpam-5450	164	21	then	then	ADV
ejpam-5450	164	22	s	s	VERB
ejpam-5450	164	23	∈	∈	PROPN
ejpam-5450	164	24	(	(	PUNCT
ejpam-5450	164	25	0.5	0.5	NUM
ejpam-5450	164	26	,	,	PUNCT
ejpam-5450	164	27	1	1	NUM
ejpam-5450	164	28	]	]	PUNCT
ejpam-5450	164	29	and	and	CCONJ
ejpam-5450	164	30	[	[	X
ejpam-5450	164	31	a	a	DET
ejpam-5450	164	32	◦	◦	NOUN
ejpam-5450	164	33	(	(	PUNCT
ejpam-5450	164	34	b	b	X
ejpam-5450	164	35	◦	◦	PROPN
ejpam-5450	164	36	c)/s	c)/s	PROPN
ejpam-5450	164	37	]	]	PUNCT
ejpam-5450	164	38	,	,	PUNCT
ejpam-5450	164	39	[	[	X
ejpam-5450	164	40	b	b	X
ejpam-5450	164	41	/	/	SYM
ejpam-5450	164	42	s	s	NOUN
ejpam-5450	164	43	]	]	X
ejpam-5450	164	44	∈	∈	PROPN
ejpam-5450	164	45	lε	lε	X
ejpam-5450	164	46	µ	µ	NOUN
ejpam-5450	164	47	,	,	PUNCT
ejpam-5450	164	48	that	that	ADV
ejpam-5450	164	49	is	is	ADV
ejpam-5450	164	50	,	,	PUNCT
ejpam-5450	164	51	a	a	DET
ejpam-5450	164	52	◦	◦	NOUN
ejpam-5450	164	53	(	(	PUNCT
ejpam-5450	164	54	b	b	X
ejpam-5450	164	55	◦	◦	NOUN
ejpam-5450	164	56	c	c	NOUN
ejpam-5450	164	57	)	)	PUNCT
ejpam-5450	164	58	,	,	PUNCT
ejpam-5450	164	59	b	b	X
ejpam-5450	164	60	∈	∈	PROPN
ejpam-5450	164	61	(	(	PUNCT
ejpam-5450	164	62	lε	lε	ADP
ejpam-5450	164	63	µ	µ	NOUN
ejpam-5450	164	64	,	,	PUNCT
ejpam-5450	164	65	s)∈.	s)∈.	PROPN
ejpam-5450	164	66	since	since	SCONJ
ejpam-5450	164	67	(	(	PUNCT
ejpam-5450	164	68	lε	lε	X
ejpam-5450	164	69	µ	µ	NUM
ejpam-5450	164	70	,	,	PUNCT
ejpam-5450	164	71	s)∈	s)∈	NUM
ejpam-5450	164	72	is	be	AUX
ejpam-5450	164	73	a	a	DET
ejpam-5450	164	74	bcc	bcc	PROPN
ejpam-5450	164	75	-	-	PUNCT
ejpam-5450	164	76	ideal	ideal	NOUN
ejpam-5450	164	77	of	of	ADP
ejpam-5450	164	78	x	x	PRON
ejpam-5450	164	79	,	,	PUNCT
ejpam-5450	164	80	we	we	PRON
ejpam-5450	164	81	have	have	VERB
ejpam-5450	164	82	a	a	DET
ejpam-5450	164	83	◦	◦	NOUN
ejpam-5450	164	84	c	c	NOUN
ejpam-5450	165	1	∈	∈	NOUN
ejpam-5450	165	2	(	(	PUNCT
ejpam-5450	165	3	lε	lε	ADP
ejpam-5450	165	4	µ	µ	NOUN
ejpam-5450	165	5	,	,	PUNCT
ejpam-5450	165	6	s)∈.	s)∈.	PROPN
ejpam-5450	165	7	but	but	CCONJ
ejpam-5450	165	8	[	[	X
ejpam-5450	165	9	(	(	PUNCT
ejpam-5450	165	10	a	a	DET
ejpam-5450	165	11	◦	◦	NOUN
ejpam-5450	165	12	c)/s]∈lε	c)/s]∈lε	PROPN
ejpam-5450	165	13	µ	µ	PRON
ejpam-5450	165	14	implies	imply	VERB
ejpam-5450	165	15	a	a	DET
ejpam-5450	165	16	◦	◦	NOUN
ejpam-5450	165	17	c	c	NOUN
ejpam-5450	165	18	/∈	/∈	PUNCT
ejpam-5450	166	1	(	(	PUNCT
ejpam-5450	166	2	lε	lε	ADP
ejpam-5450	166	3	µ	µ	NUM
ejpam-5450	166	4	,	,	PUNCT
ejpam-5450	166	5	s)∈	s)∈	PROPN
ejpam-5450	166	6	,	,	PUNCT
ejpam-5450	166	7	a	a	DET
ejpam-5450	166	8	contradiction	contradiction	NOUN
ejpam-5450	166	9	.	.	PUNCT
ejpam-5450	167	1	thus	thus	ADV
ejpam-5450	167	2	,	,	PUNCT
ejpam-5450	167	3	max{lε	max{lε	NOUN
ejpam-5450	167	4	µ(x	µ(x	VERB
ejpam-5450	167	5	◦	◦	NOUN
ejpam-5450	167	6	z	z	NOUN
ejpam-5450	167	7	)	)	PUNCT
ejpam-5450	167	8	,	,	PUNCT
ejpam-5450	167	9	0.5	0.5	NUM
ejpam-5450	167	10	}	}	PUNCT
ejpam-5450	167	11	≥	≥	PROPN
ejpam-5450	167	12	min{lε	min{lε	NUM
ejpam-5450	167	13	µ(x	µ(x	ADJ
ejpam-5450	167	14	◦	◦	NOUN
ejpam-5450	167	15	(	(	PUNCT
ejpam-5450	167	16	y	y	PROPN
ejpam-5450	167	17	◦	◦	PROPN
ejpam-5450	167	18	z	z	PROPN
ejpam-5450	167	19	)	)	PUNCT
ejpam-5450	167	20	)	)	PUNCT
ejpam-5450	167	21	,	,	PUNCT
ejpam-5450	167	22	lε	lε	X
ejpam-5450	167	23	µ(y	µ(y	PROPN
ejpam-5450	167	24	)	)	PUNCT
ejpam-5450	167	25	}	}	PUNCT
ejpam-5450	167	26	for	for	ADP
ejpam-5450	167	27	all	all	DET
ejpam-5450	167	28	x	x	NOUN
ejpam-5450	167	29	,	,	PUNCT
ejpam-5450	167	30	y	y	PROPN
ejpam-5450	167	31	,	,	PUNCT
ejpam-5450	167	32	z	z	NOUN
ejpam-5450	167	33	∈	∈	NOUN
ejpam-5450	167	34	x.	x.	NOUN
ejpam-5450	167	35	conversely	conversely	ADV
ejpam-5450	167	36	,	,	PUNCT
ejpam-5450	167	37	suppose	suppose	VERB
ejpam-5450	167	38	that	that	SCONJ
ejpam-5450	167	39	lε	lε	AUX
ejpam-5450	167	40	µ	µ	PRON
ejpam-5450	167	41	satisfies	satisfy	VERB
ejpam-5450	167	42	the	the	DET
ejpam-5450	167	43	conditions	condition	NOUN
ejpam-5450	167	44	(	(	PUNCT
ejpam-5450	167	45	3.9	3.9	NUM
ejpam-5450	167	46	)	)	PUNCT
ejpam-5450	167	47	and	and	CCONJ
ejpam-5450	167	48	(	(	PUNCT
ejpam-5450	167	49	3.10	3.10	NUM
ejpam-5450	167	50	)	)	PUNCT
ejpam-5450	167	51	.	.	PUNCT
ejpam-5450	168	1	for	for	ADP
ejpam-5450	168	2	every	every	DET
ejpam-5450	168	3	t	t	NOUN
ejpam-5450	168	4	∈	∈	PROPN
ejpam-5450	168	5	(	(	PUNCT
ejpam-5450	168	6	0.5	0.5	NUM
ejpam-5450	168	7	,	,	PUNCT
ejpam-5450	168	8	1	1	NUM
ejpam-5450	168	9	]	]	PUNCT
ejpam-5450	168	10	,	,	PUNCT
ejpam-5450	168	11	we	we	PRON
ejpam-5450	168	12	have	have	VERB
ejpam-5450	168	13	0.5	0.5	NUM
ejpam-5450	168	14	<	<	X
ejpam-5450	168	15	t	t	NOUN
ejpam-5450	168	16	≤	≤	NUM
ejpam-5450	168	17	lε	lε	ADP
ejpam-5450	168	18	µ(x	µ(x	NOUN
ejpam-5450	168	19	)	)	PUNCT
ejpam-5450	168	20	≤	≤	NOUN
ejpam-5450	168	21	max{lε	max{lε	NOUN
ejpam-5450	168	22	µ(0	µ(0	NOUN
ejpam-5450	168	23	)	)	PUNCT
ejpam-5450	168	24	,	,	PUNCT
ejpam-5450	168	25	0.5	0.5	NUM
ejpam-5450	168	26	}	}	PUNCT
ejpam-5450	168	27	for	for	ADP
ejpam-5450	168	28	all	all	DET
ejpam-5450	168	29	x	x	SYM
ejpam-5450	168	30	∈	∈	PROPN
ejpam-5450	168	31	(	(	PUNCT
ejpam-5450	168	32	lε	lε	X
ejpam-5450	168	33	µ	µ	NUM
ejpam-5450	168	34	,	,	PUNCT
ejpam-5450	168	35	t)∈	t)∈	VERB
ejpam-5450	168	36	by	by	ADP
ejpam-5450	168	37	(	(	PUNCT
ejpam-5450	168	38	3.9	3.9	NUM
ejpam-5450	168	39	)	)	PUNCT
ejpam-5450	168	40	.	.	PUNCT
ejpam-5450	169	1	then	then	ADV
ejpam-5450	169	2	0	0	NUM
ejpam-5450	169	3	∈	∈	PROPN
ejpam-5450	169	4	(	(	PUNCT
ejpam-5450	169	5	lε	lε	ADP
ejpam-5450	169	6	µ	µ	NUM
ejpam-5450	169	7	,	,	PUNCT
ejpam-5450	169	8	t)∈.	t)∈.	PROPN
ejpam-5450	169	9	let	let	VERB
ejpam-5450	169	10	t	t	PROPN
ejpam-5450	169	11	∈	∈	PROPN
ejpam-5450	169	12	(	(	PUNCT
ejpam-5450	169	13	0.5	0.5	NUM
ejpam-5450	169	14	,	,	PUNCT
ejpam-5450	169	15	1	1	NUM
ejpam-5450	169	16	]	]	PUNCT
ejpam-5450	169	17	and	and	CCONJ
ejpam-5450	169	18	x	x	NOUN
ejpam-5450	169	19	,	,	PUNCT
ejpam-5450	169	20	y	y	PROPN
ejpam-5450	169	21	,	,	PUNCT
ejpam-5450	169	22	z	z	NOUN
ejpam-5450	169	23	∈	∈	PROPN
ejpam-5450	169	24	x	x	AUX
ejpam-5450	169	25	be	be	AUX
ejpam-5450	169	26	such	such	ADJ
ejpam-5450	169	27	that	that	SCONJ
ejpam-5450	169	28	x	x	X
ejpam-5450	169	29	◦	◦	NOUN
ejpam-5450	169	30	(	(	PUNCT
ejpam-5450	169	31	y	y	PROPN
ejpam-5450	169	32	◦	◦	PROPN
ejpam-5450	169	33	z	z	PROPN
ejpam-5450	169	34	)	)	PUNCT
ejpam-5450	169	35	∈	∈	PROPN
ejpam-5450	169	36	(	(	PUNCT
ejpam-5450	169	37	lε	lε	X
ejpam-5450	169	38	µ	µ	NUM
ejpam-5450	169	39	,	,	PUNCT
ejpam-5450	169	40	t)∈	t)∈	PROPN
ejpam-5450	169	41	and	and	CCONJ
ejpam-5450	169	42	y	y	PROPN
ejpam-5450	169	43	∈	∈	PROPN
ejpam-5450	169	44	(	(	PUNCT
ejpam-5450	169	45	lε	lε	ADP
ejpam-5450	169	46	µ	µ	NUM
ejpam-5450	169	47	,	,	PUNCT
ejpam-5450	169	48	t)∈.	t)∈.	PROPN
ejpam-5450	169	49	then	then	ADV
ejpam-5450	169	50	lε	lε	ADP
ejpam-5450	169	51	µ(x	µ(x	ADJ
ejpam-5450	169	52	◦	◦	NOUN
ejpam-5450	169	53	(	(	PUNCT
ejpam-5450	169	54	y	y	PROPN
ejpam-5450	169	55	◦	◦	PROPN
ejpam-5450	169	56	z	z	PROPN
ejpam-5450	169	57	)	)	PUNCT
ejpam-5450	169	58	)	)	PUNCT
ejpam-5450	169	59	≥	≥	PROPN
ejpam-5450	169	60	t	t	NOUN
ejpam-5450	169	61	and	and	CCONJ
ejpam-5450	169	62	lε	lε	ADP
ejpam-5450	169	63	µ(y	µ(y	PROPN
ejpam-5450	169	64	)	)	PUNCT
ejpam-5450	169	65	≥	≥	PROPN
ejpam-5450	169	66	t	t	PROPN
ejpam-5450	169	67	,	,	PUNCT
ejpam-5450	169	68	which	which	PRON
ejpam-5450	169	69	imply	imply	VERB
ejpam-5450	169	70	from	from	ADP
ejpam-5450	169	71	(	(	PUNCT
ejpam-5450	169	72	3.10	3.10	NUM
ejpam-5450	169	73	)	)	PUNCT
ejpam-5450	169	74	that	that	PRON
ejpam-5450	169	75	0.5	0.5	NUM
ejpam-5450	169	76	<	<	X
ejpam-5450	169	77	t	t	NOUN
ejpam-5450	169	78	≤	≤	NOUN
ejpam-5450	169	79	min{lε	min{lε	NUM
ejpam-5450	169	80	µ(x	µ(x	ADJ
ejpam-5450	169	81	◦	◦	NOUN
ejpam-5450	169	82	(	(	PUNCT
ejpam-5450	169	83	y	y	PROPN
ejpam-5450	169	84	◦	◦	PROPN
ejpam-5450	169	85	z	z	PROPN
ejpam-5450	169	86	)	)	PUNCT
ejpam-5450	169	87	)	)	PUNCT
ejpam-5450	169	88	,	,	PUNCT
ejpam-5450	169	89	lε	lε	X
ejpam-5450	169	90	µ(y	µ(y	PROPN
ejpam-5450	169	91	)	)	PUNCT
ejpam-5450	169	92	}	}	PUNCT
ejpam-5450	169	93	≤	≤	NOUN
ejpam-5450	169	94	max{lε	max{lε	PUNCT
ejpam-5450	169	95	µ(x	µ(x	ADJ
ejpam-5450	169	96	◦	◦	NOUN
ejpam-5450	169	97	z	z	NOUN
ejpam-5450	169	98	)	)	PUNCT
ejpam-5450	169	99	,	,	PUNCT
ejpam-5450	169	100	0.5	0.5	NUM
ejpam-5450	169	101	}	}	PUNCT
ejpam-5450	169	102	.	.	PUNCT
ejpam-5450	170	1	thus	thus	ADV
ejpam-5450	170	2	,	,	PUNCT
ejpam-5450	170	3	[	[	X
ejpam-5450	170	4	(	(	PUNCT
ejpam-5450	170	5	x	x	SYM
ejpam-5450	170	6	◦	◦	NOUN
ejpam-5450	170	7	z)/t	z)/t	NOUN
ejpam-5450	170	8	]	]	X
ejpam-5450	170	9	∈	∈	PROPN
ejpam-5450	170	10	lε	lε	ADP
ejpam-5450	170	11	µ	µ	NOUN
ejpam-5450	170	12	,	,	PUNCT
ejpam-5450	170	13	that	that	ADV
ejpam-5450	170	14	is	is	ADV
ejpam-5450	170	15	,	,	PUNCT
ejpam-5450	170	16	x	x	PUNCT
ejpam-5450	170	17	◦	◦	NOUN
ejpam-5450	170	18	z	z	NOUN
ejpam-5450	170	19	∈	∈	PROPN
ejpam-5450	170	20	(	(	PUNCT
ejpam-5450	170	21	lε	lε	ADP
ejpam-5450	170	22	µ	µ	NUM
ejpam-5450	170	23	,	,	PUNCT
ejpam-5450	170	24	t)∈.	t)∈.	PROPN
ejpam-5450	170	25	hence	hence	ADV
ejpam-5450	170	26	,	,	PUNCT
ejpam-5450	170	27	(	(	PUNCT
ejpam-5450	170	28	lε	lε	X
ejpam-5450	170	29	µ	µ	NUM
ejpam-5450	170	30	,	,	PUNCT
ejpam-5450	170	31	t)∈	t)∈	NUM
ejpam-5450	170	32	is	be	AUX
ejpam-5450	170	33	a	a	DET
ejpam-5450	170	34	bcc	bcc	PROPN
ejpam-5450	170	35	-	-	PUNCT
ejpam-5450	170	36	ideal	ideal	NOUN
ejpam-5450	170	37	of	of	ADP
ejpam-5450	170	38	x	x	PUNCT
ejpam-5450	170	39	for	for	ADP
ejpam-5450	170	40	t	t	PROPN
ejpam-5450	170	41	∈	∈	PROPN
ejpam-5450	170	42	(	(	PUNCT
ejpam-5450	170	43	0.5	0.5	NUM
ejpam-5450	170	44	,	,	PUNCT
ejpam-5450	170	45	1	1	NUM
ejpam-5450	170	46	]	]	PUNCT
ejpam-5450	170	47	.	.	PUNCT
ejpam-5450	171	1	in	in	ADP
ejpam-5450	171	2	theorem	theorem	NOUN
ejpam-5450	171	3	3	3	NUM
ejpam-5450	171	4	,	,	PUNCT
ejpam-5450	171	5	if	if	SCONJ
ejpam-5450	171	6	t	t	PROPN
ejpam-5450	171	7	/∈	/∈	PUNCT
ejpam-5450	171	8	(	(	PUNCT
ejpam-5450	171	9	0.5	0.5	NUM
ejpam-5450	171	10	,	,	PUNCT
ejpam-5450	171	11	1	1	NUM
ejpam-5450	171	12	]	]	PUNCT
ejpam-5450	171	13	,	,	PUNCT
ejpam-5450	171	14	that	that	ADV
ejpam-5450	171	15	is	is	ADV
ejpam-5450	171	16	,	,	PUNCT
ejpam-5450	171	17	there	there	PRON
ejpam-5450	171	18	exists	exist	VERB
ejpam-5450	171	19	at	at	ADP
ejpam-5450	171	20	least	least	ADV
ejpam-5450	171	21	one	one	NUM
ejpam-5450	171	22	t	t	NOUN
ejpam-5450	171	23	≤	≤	NUM
ejpam-5450	171	24	0.5	0.5	NUM
ejpam-5450	171	25	,	,	PUNCT
ejpam-5450	171	26	then	then	ADV
ejpam-5450	171	27	theorem	theorem	VERB
ejpam-5450	171	28	3	3	NUM
ejpam-5450	171	29	is	be	AUX
ejpam-5450	171	30	incorrect	incorrect	ADJ
ejpam-5450	171	31	,	,	PUNCT
ejpam-5450	171	32	as	as	SCONJ
ejpam-5450	171	33	shown	show	VERB
ejpam-5450	171	34	in	in	ADP
ejpam-5450	171	35	the	the	DET
ejpam-5450	171	36	following	follow	VERB
ejpam-5450	171	37	example	example	NOUN
ejpam-5450	171	38	.	.	PUNCT
ejpam-5450	172	1	example	example	NOUN
ejpam-5450	173	1	3	3	X
ejpam-5450	173	2	.	.	PUNCT
ejpam-5450	173	3	let	let	VERB
ejpam-5450	173	4	x	x	PUNCT
ejpam-5450	173	5	=	=	PUNCT
ejpam-5450	173	6	{	{	PUNCT
ejpam-5450	173	7	0	0	NUM
ejpam-5450	173	8	,	,	PUNCT
ejpam-5450	173	9	1	1	NUM
ejpam-5450	173	10	,	,	PUNCT
ejpam-5450	173	11	2	2	NUM
ejpam-5450	173	12	,	,	PUNCT
ejpam-5450	173	13	3	3	NUM
ejpam-5450	173	14	}	}	PUNCT
ejpam-5450	173	15	with	with	ADP
ejpam-5450	173	16	the	the	DET
ejpam-5450	173	17	following	follow	VERB
ejpam-5450	173	18	cayley	cayley	ADJ
ejpam-5450	173	19	table	table	NOUN
ejpam-5450	173	20	:	:	PUNCT
ejpam-5450	173	21	◦	◦	NOUN
ejpam-5450	173	22	0	0	NUM
ejpam-5450	173	23	1	1	NUM
ejpam-5450	173	24	2	2	NUM
ejpam-5450	173	25	3	3	NUM
ejpam-5450	173	26	0	0	NUM
ejpam-5450	173	27	0	0	NUM
ejpam-5450	173	28	1	1	NUM
ejpam-5450	173	29	2	2	NUM
ejpam-5450	173	30	3	3	NUM
ejpam-5450	173	31	1	1	NUM
ejpam-5450	173	32	0	0	NUM
ejpam-5450	173	33	0	0	NUM
ejpam-5450	173	34	2	2	NUM
ejpam-5450	173	35	3	3	NUM
ejpam-5450	173	36	2	2	NUM
ejpam-5450	173	37	0	0	NUM
ejpam-5450	173	38	1	1	NUM
ejpam-5450	173	39	0	0	NUM
ejpam-5450	173	40	0	0	NUM
ejpam-5450	173	41	3	3	NUM
ejpam-5450	173	42	0	0	NUM
ejpam-5450	173	43	1	1	NUM
ejpam-5450	173	44	2	2	NUM
ejpam-5450	173	45	0	0	NUM
ejpam-5450	173	46	a.	a.	NOUN
ejpam-5450	173	47	iampan	iampan	PROPN
ejpam-5450	173	48	,	,	PUNCT
ejpam-5450	173	49	r.	r.	PROPN
ejpam-5450	173	50	subasini	subasini	PROPN
ejpam-5450	173	51	,	,	PUNCT
ejpam-5450	173	52	n.	n.	PROPN
ejpam-5450	173	53	rajesh	rajesh	PROPN
ejpam-5450	173	54	/	/	SYM
ejpam-5450	173	55	eur	eur	PROPN
ejpam-5450	173	56	.	.	PUNCT
ejpam-5450	174	1	j.	j.	PROPN
ejpam-5450	174	2	pure	pure	PROPN
ejpam-5450	174	3	appl	appl	PROPN
ejpam-5450	174	4	.	.	PROPN
ejpam-5450	174	5	math	math	PROPN
ejpam-5450	174	6	,	,	PUNCT
ejpam-5450	174	7	17	17	NUM
ejpam-5450	174	8	(	(	PUNCT
ejpam-5450	174	9	4	4	NUM
ejpam-5450	174	10	)	)	PUNCT
ejpam-5450	174	11	(	(	PUNCT
ejpam-5450	174	12	2024	2024	NUM
ejpam-5450	174	13	)	)	PUNCT
ejpam-5450	174	14	,	,	PUNCT
ejpam-5450	174	15	3209	3209	NUM
ejpam-5450	174	16	-	-	SYM
ejpam-5450	174	17	3222	3222	NUM
ejpam-5450	174	18	3217	3217	NUM
ejpam-5450	174	19	then	then	ADV
ejpam-5450	174	20	x	x	PUNCT
ejpam-5450	174	21	is	be	AUX
ejpam-5450	174	22	a	a	DET
ejpam-5450	174	23	bcc	bcc	PROPN
ejpam-5450	174	24	-	-	PUNCT
ejpam-5450	174	25	algebra	algebra	PROPN
ejpam-5450	174	26	.	.	PUNCT
ejpam-5450	175	1	define	define	VERB
ejpam-5450	175	2	a	a	DET
ejpam-5450	175	3	fuzzy	fuzzy	ADJ
ejpam-5450	175	4	set	set	VERB
ejpam-5450	175	5	µ	µ	NOUN
ejpam-5450	175	6	as	as	SCONJ
ejpam-5450	175	7	follows	follow	VERB
ejpam-5450	175	8	:	:	PUNCT
ejpam-5450	175	9	µ	µ	X
ejpam-5450	175	10	:	:	PUNCT
ejpam-5450	175	11	x	x	SYM
ejpam-5450	175	12	→	→	SYM
ejpam-5450	176	1	[	[	X
ejpam-5450	176	2	0	0	NUM
ejpam-5450	176	3	,	,	PUNCT
ejpam-5450	176	4	1];x	1];x	NUM
ejpam-5450	176	5	7→	7→	NUM
ejpam-5450	176	6			NUM
ejpam-5450	176	7	0.72	0.72	NUM
ejpam-5450	176	8	if	if	SCONJ
ejpam-5450	176	9	x	x	NOUN
ejpam-5450	176	10	=	=	SYM
ejpam-5450	176	11	0	0	NUM
ejpam-5450	176	12	0.68	0.68	NUM
ejpam-5450	177	1	if	if	SCONJ
ejpam-5450	177	2	x	x	NOUN
ejpam-5450	177	3	=	=	SYM
ejpam-5450	177	4	1	1	NUM
ejpam-5450	177	5	0.61	0.61	NUM
ejpam-5450	177	6	if	if	SCONJ
ejpam-5450	177	7	x	x	NOUN
ejpam-5450	177	8	=	=	SYM
ejpam-5450	177	9	2	2	NUM
ejpam-5450	177	10	0.57	0.57	NUM
ejpam-5450	177	11	if	if	SCONJ
ejpam-5450	177	12	x	x	SYM
ejpam-5450	177	13	=	=	SYM
ejpam-5450	177	14	3	3	NUM
ejpam-5450	177	15	given	give	VERB
ejpam-5450	177	16	ε	ε	PROPN
ejpam-5450	177	17	=	=	PUNCT
ejpam-5450	177	18	0.42	0.42	NUM
ejpam-5450	177	19	,	,	PUNCT
ejpam-5450	177	20	the	the	DET
ejpam-5450	177	21	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	177	22	fuzzy	fuzzy	NOUN
ejpam-5450	177	23	set	set	VERB
ejpam-5450	177	24	lε	lε	PRON
ejpam-5450	177	25	µ	µ	PROPN
ejpam-5450	177	26	of	of	ADP
ejpam-5450	177	27	µ	µ	NOUN
ejpam-5450	177	28	in	in	ADP
ejpam-5450	177	29	x	x	AUX
ejpam-5450	177	30	is	be	AUX
ejpam-5450	177	31	given	give	VERB
ejpam-5450	177	32	as	as	SCONJ
ejpam-5450	177	33	follows	follow	VERB
ejpam-5450	177	34	:	:	PUNCT
ejpam-5450	177	35	lε	lε	ADP
ejpam-5450	177	36	µ	µ	NOUN
ejpam-5450	177	37	:	:	PUNCT
ejpam-5450	177	38	x	x	SYM
ejpam-5450	177	39	→	→	SYM
ejpam-5450	178	1	[	[	X
ejpam-5450	178	2	0	0	NUM
ejpam-5450	178	3	,	,	PUNCT
ejpam-5450	178	4	1];x	1];x	NUM
ejpam-5450	178	5	7→	7→	NUM
ejpam-5450	178	6			NUM
ejpam-5450	178	7	0.14	0.14	NUM
ejpam-5450	178	8	if	if	SCONJ
ejpam-5450	178	9	x	x	PROPN
ejpam-5450	179	1	=	=	SYM
ejpam-5450	179	2	0	0	NUM
ejpam-5450	179	3	0.10	0.10	NUM
ejpam-5450	179	4	if	if	SCONJ
ejpam-5450	179	5	x	x	NOUN
ejpam-5450	179	6	=	=	SYM
ejpam-5450	179	7	1	1	NUM
ejpam-5450	179	8	0.03	0.03	NUM
ejpam-5450	179	9	if	if	SCONJ
ejpam-5450	179	10	x	x	PROPN
ejpam-5450	179	11	=	=	SYM
ejpam-5450	179	12	2	2	NUM
ejpam-5450	179	13	0	0	NUM
ejpam-5450	179	14	if	if	SCONJ
ejpam-5450	179	15	x	x	PROPN
ejpam-5450	179	16	=	=	SYM
ejpam-5450	179	17	3	3	NUM
ejpam-5450	179	18	then	then	ADV
ejpam-5450	179	19	(	(	PUNCT
ejpam-5450	179	20	lε	lε	X
ejpam-5450	179	21	µ	µ	NUM
ejpam-5450	179	22	,	,	PUNCT
ejpam-5450	179	23	0.25)∈	0.25)∈	PRON
ejpam-5450	179	24	=	=	NOUN
ejpam-5450	180	1	∅	∅	NOUN
ejpam-5450	180	2	is	be	AUX
ejpam-5450	180	3	not	not	PART
ejpam-5450	180	4	a	a	DET
ejpam-5450	180	5	bcc	bcc	PROPN
ejpam-5450	180	6	-	-	PUNCT
ejpam-5450	180	7	ideal	ideal	NOUN
ejpam-5450	180	8	of	of	ADP
ejpam-5450	180	9	x.	x.	PROPN
ejpam-5450	180	10	theorem	theorem	VERB
ejpam-5450	180	11	4	4	NUM
ejpam-5450	180	12	.	.	PUNCT
ejpam-5450	181	1	let	let	VERB
ejpam-5450	181	2	lε	lε	PART
ejpam-5450	181	3	µ	µ	X
ejpam-5450	181	4	be	be	AUX
ejpam-5450	181	5	an	an	DET
ejpam-5450	181	6	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	181	7	fuzzy	fuzzy	ADJ
ejpam-5450	181	8	set	set	NOUN
ejpam-5450	181	9	of	of	ADP
ejpam-5450	181	10	a	a	DET
ejpam-5450	181	11	fuzzy	fuzzy	ADJ
ejpam-5450	181	12	set	set	VERB
ejpam-5450	181	13	µ	µ	NOUN
ejpam-5450	181	14	in	in	ADP
ejpam-5450	181	15	x.	x.	NOUN
ejpam-5450	181	16	if	if	SCONJ
ejpam-5450	181	17	µ	µ	PRON
ejpam-5450	181	18	is	be	AUX
ejpam-5450	181	19	a	a	DET
ejpam-5450	181	20	fuzzy	fuzzy	ADJ
ejpam-5450	181	21	bcc	bcc	NOUN
ejpam-5450	181	22	-	-	PUNCT
ejpam-5450	181	23	ideal	ideal	NOUN
ejpam-5450	181	24	of	of	ADP
ejpam-5450	181	25	x	x	PRON
ejpam-5450	181	26	,	,	PUNCT
ejpam-5450	181	27	then	then	ADV
ejpam-5450	181	28	the	the	DET
ejpam-5450	181	29	q	q	NOUN
ejpam-5450	181	30	-	-	PUNCT
ejpam-5450	181	31	set	set	ADJ
ejpam-5450	181	32	(	(	PUNCT
ejpam-5450	181	33	lε	lε	X
ejpam-5450	181	34	µ	µ	NUM
ejpam-5450	181	35	,	,	PUNCT
ejpam-5450	181	36	t)q	t)q	PRON
ejpam-5450	181	37	of	of	ADP
ejpam-5450	181	38	lε	lε	ADP
ejpam-5450	181	39	µ	µ	X
ejpam-5450	181	40	with	with	ADP
ejpam-5450	181	41	value	value	NOUN
ejpam-5450	181	42	t	t	X
ejpam-5450	181	43	∈	∈	PROPN
ejpam-5450	181	44	(	(	PUNCT
ejpam-5450	181	45	0	0	NUM
ejpam-5450	181	46	,	,	PUNCT
ejpam-5450	181	47	1	1	NUM
ejpam-5450	181	48	]	]	PUNCT
ejpam-5450	181	49	is	be	AUX
ejpam-5450	181	50	a	a	DET
ejpam-5450	181	51	bcc	bcc	PROPN
ejpam-5450	181	52	-	-	PUNCT
ejpam-5450	181	53	ideal	ideal	NOUN
ejpam-5450	181	54	of	of	ADP
ejpam-5450	181	55	x.	x.	NOUN
ejpam-5450	181	56	proof	proof	PROPN
ejpam-5450	181	57	.	.	PUNCT
ejpam-5450	182	1	assume	assume	VERB
ejpam-5450	182	2	that	that	SCONJ
ejpam-5450	182	3	µ	µ	NOUN
ejpam-5450	182	4	is	be	AUX
ejpam-5450	182	5	a	a	DET
ejpam-5450	182	6	fuzzy	fuzzy	ADJ
ejpam-5450	182	7	bcc	bcc	NOUN
ejpam-5450	182	8	-	-	PUNCT
ejpam-5450	182	9	ideal	ideal	NOUN
ejpam-5450	182	10	of	of	ADP
ejpam-5450	182	11	x	x	PUNCT
ejpam-5450	182	12	and	and	CCONJ
ejpam-5450	182	13	let	let	VERB
ejpam-5450	182	14	t	t	PROPN
ejpam-5450	182	15	∈	∈	PROPN
ejpam-5450	182	16	(	(	PUNCT
ejpam-5450	182	17	0	0	NUM
ejpam-5450	182	18	,	,	PUNCT
ejpam-5450	182	19	1	1	NUM
ejpam-5450	182	20	]	]	PUNCT
ejpam-5450	182	21	.	.	PUNCT
ejpam-5450	183	1	if	if	SCONJ
ejpam-5450	183	2	0	0	NUM
ejpam-5450	183	3	/∈	/∈	INTJ
ejpam-5450	183	4	(	(	PUNCT
ejpam-5450	183	5	lε	lε	ADP
ejpam-5450	183	6	µ	µ	NUM
ejpam-5450	183	7	,	,	PUNCT
ejpam-5450	183	8	t)q	t)q	PRON
ejpam-5450	183	9	,	,	PUNCT
ejpam-5450	183	10	then	then	ADV
ejpam-5450	183	11	[	[	X
ejpam-5450	183	12	0	0	NUM
ejpam-5450	183	13	/	/	SYM
ejpam-5450	183	14	t]qlε	t]qlε	X
ejpam-5450	183	15	µ	µ	NOUN
ejpam-5450	183	16	,	,	PUNCT
ejpam-5450	183	17	that	that	ADV
ejpam-5450	183	18	is	is	ADV
ejpam-5450	183	19	,	,	PUNCT
ejpam-5450	183	20	lε	lε	X
ejpam-5450	183	21	µ(0	µ(0	NOUN
ejpam-5450	183	22	)	)	PUNCT
ejpam-5450	184	1	+	+	NUM
ejpam-5450	184	2	t	t	X
ejpam-5450	184	3	≤	≤	NUM
ejpam-5450	184	4	1	1	NUM
ejpam-5450	184	5	.	.	PUNCT
ejpam-5450	185	1	since	since	SCONJ
ejpam-5450	185	2	lε	lε	X
ejpam-5450	185	3	µ(0	µ(0	NOUN
ejpam-5450	185	4	)	)	PUNCT
ejpam-5450	185	5	≥	≥	NOUN
ejpam-5450	185	6	lε	lε	X
ejpam-5450	185	7	µ(x	µ(x	NOUN
ejpam-5450	185	8	)	)	PUNCT
ejpam-5450	185	9	for	for	ADP
ejpam-5450	185	10	x	x	PROPN
ejpam-5450	185	11	∈	∈	PROPN
ejpam-5450	185	12	(	(	PUNCT
ejpam-5450	185	13	lε	lε	X
ejpam-5450	185	14	µ	µ	NUM
ejpam-5450	185	15	,	,	PUNCT
ejpam-5450	185	16	t)q	t)q	NUM
ejpam-5450	185	17	,	,	PUNCT
ejpam-5450	185	18	it	it	PRON
ejpam-5450	185	19	follows	follow	VERB
ejpam-5450	185	20	that	that	SCONJ
ejpam-5450	185	21	lε	lε	ADP
ejpam-5450	185	22	µ(x	µ(x	NOUN
ejpam-5450	185	23	)	)	PUNCT
ejpam-5450	185	24	≤	≤	NUM
ejpam-5450	185	25	lε	lε	ADP
ejpam-5450	185	26	µ(0	µ(0	NOUN
ejpam-5450	185	27	)	)	PUNCT
ejpam-5450	185	28	≤	≤	NOUN
ejpam-5450	185	29	1	1	NUM
ejpam-5450	185	30	−	−	NOUN
ejpam-5450	185	31	t.	t.	NOUN
ejpam-5450	185	32	hence	hence	ADV
ejpam-5450	185	33	,	,	PUNCT
ejpam-5450	185	34	[	[	X
ejpam-5450	185	35	x	x	X
ejpam-5450	185	36	/	/	SYM
ejpam-5450	185	37	t]qlε	t]qlε	X
ejpam-5450	185	38	µ	µ	NOUN
ejpam-5450	185	39	,	,	PUNCT
ejpam-5450	185	40	and	and	CCONJ
ejpam-5450	185	41	so	so	ADV
ejpam-5450	185	42	x	x	X
ejpam-5450	185	43	/∈	/∈	PUNCT
ejpam-5450	186	1	(	(	PUNCT
ejpam-5450	186	2	lε	lε	ADP
ejpam-5450	186	3	µ	µ	NUM
ejpam-5450	186	4	,	,	PUNCT
ejpam-5450	186	5	t)q	t)q	PUNCT
ejpam-5450	186	6	.	.	PUNCT
ejpam-5450	187	1	this	this	DET
ejpam-5450	187	2	contradiction	contradiction	NOUN
ejpam-5450	187	3	is	be	AUX
ejpam-5450	187	4	thus	thus	ADV
ejpam-5450	187	5	0	0	NUM
ejpam-5450	187	6	∈	∈	NOUN
ejpam-5450	187	7	(	(	PUNCT
ejpam-5450	187	8	lε	lε	X
ejpam-5450	187	9	µ	µ	NUM
ejpam-5450	187	10	,	,	PUNCT
ejpam-5450	187	11	t)q	t)q	PUNCT
ejpam-5450	187	12	.	.	PUNCT
ejpam-5450	188	1	let	let	VERB
ejpam-5450	188	2	t	t	PROPN
ejpam-5450	188	3	∈	∈	PROPN
ejpam-5450	188	4	(	(	PUNCT
ejpam-5450	188	5	0	0	NUM
ejpam-5450	188	6	,	,	PUNCT
ejpam-5450	188	7	1	1	NUM
ejpam-5450	188	8	]	]	PUNCT
ejpam-5450	188	9	and	and	CCONJ
ejpam-5450	188	10	x	x	NOUN
ejpam-5450	188	11	,	,	PUNCT
ejpam-5450	188	12	y	y	PROPN
ejpam-5450	188	13	,	,	PUNCT
ejpam-5450	188	14	z	z	NOUN
ejpam-5450	188	15	∈	∈	PROPN
ejpam-5450	188	16	(	(	PUNCT
ejpam-5450	188	17	lε	lε	X
ejpam-5450	188	18	µ	µ	NUM
ejpam-5450	188	19	,	,	PUNCT
ejpam-5450	188	20	t)q	t)q	PUNCT
ejpam-5450	188	21	be	be	AUX
ejpam-5450	188	22	such	such	ADJ
ejpam-5450	188	23	that	that	SCONJ
ejpam-5450	188	24	x	x	X
ejpam-5450	188	25	◦	◦	NOUN
ejpam-5450	188	26	(	(	PUNCT
ejpam-5450	188	27	y	y	PROPN
ejpam-5450	188	28	◦	◦	PROPN
ejpam-5450	188	29	z	z	PROPN
ejpam-5450	188	30	)	)	PUNCT
ejpam-5450	188	31	∈	∈	PROPN
ejpam-5450	188	32	(	(	PUNCT
ejpam-5450	188	33	lε	lε	X
ejpam-5450	188	34	µ	µ	NUM
ejpam-5450	188	35	,	,	PUNCT
ejpam-5450	188	36	t)q	t)q	PUNCT
ejpam-5450	188	37	and	and	CCONJ
ejpam-5450	188	38	y	y	PROPN
ejpam-5450	188	39	∈	∈	PROPN
ejpam-5450	188	40	(	(	PUNCT
ejpam-5450	188	41	lε	lε	X
ejpam-5450	188	42	µ	µ	NUM
ejpam-5450	188	43	,	,	PUNCT
ejpam-5450	188	44	t)q	t)q	PUNCT
ejpam-5450	188	45	.	.	PUNCT
ejpam-5450	189	1	then	then	ADV
ejpam-5450	189	2	[	[	X
ejpam-5450	189	3	x	x	X
ejpam-5450	189	4	◦	◦	NOUN
ejpam-5450	189	5	(	(	PUNCT
ejpam-5450	189	6	y	y	NOUN
ejpam-5450	189	7	◦	◦	NOUN
ejpam-5450	189	8	z)/t]ql	z)/t]ql	PROPN
ejpam-5450	189	9	ε	ε	PROPN
ejpam-5450	189	10	µ	µ	PROPN
ejpam-5450	189	11	and	and	CCONJ
ejpam-5450	189	12	[	[	X
ejpam-5450	189	13	y	y	NOUN
ejpam-5450	189	14	/	/	SYM
ejpam-5450	189	15	t]ql	t]ql	PROPN
ejpam-5450	189	16	ε	ε	PROPN
ejpam-5450	189	17	µ	µ	NUM
ejpam-5450	189	18	,	,	PUNCT
ejpam-5450	189	19	that	that	ADV
ejpam-5450	189	20	is	is	ADV
ejpam-5450	189	21	,	,	PUNCT
ejpam-5450	189	22	lε	lε	ADP
ejpam-5450	189	23	µ(x	µ(x	ADJ
ejpam-5450	189	24	◦	◦	NOUN
ejpam-5450	189	25	(	(	PUNCT
ejpam-5450	189	26	y	y	PROPN
ejpam-5450	189	27	◦	◦	PROPN
ejpam-5450	189	28	z	z	PROPN
ejpam-5450	189	29	)	)	PUNCT
ejpam-5450	189	30	)	)	PUNCT
ejpam-5450	190	1	+	+	CCONJ
ejpam-5450	190	2	t	t	X
ejpam-5450	190	3	>	>	X
ejpam-5450	190	4	1	1	NUM
ejpam-5450	190	5	and	and	CCONJ
ejpam-5450	190	6	lε	lε	ADP
ejpam-5450	190	7	µ(y	µ(y	PROPN
ejpam-5450	190	8	)	)	PUNCT
ejpam-5450	191	1	+	+	CCONJ
ejpam-5450	191	2	t	t	X
ejpam-5450	191	3	>	>	X
ejpam-5450	191	4	1	1	X
ejpam-5450	191	5	.	.	PUNCT
ejpam-5450	192	1	it	it	PRON
ejpam-5450	192	2	follows	follow	VERB
ejpam-5450	192	3	from	from	ADP
ejpam-5450	192	4	theorem	theorem	ADJ
ejpam-5450	192	5	1	1	NUM
ejpam-5450	192	6	and	and	CCONJ
ejpam-5450	192	7	theorem	theorem	VERB
ejpam-5450	192	8	2	2	NUM
ejpam-5450	193	1	that	that	PRON
ejpam-5450	193	2	lε	lε	ADP
ejpam-5450	193	3	µ(x	µ(x	ADJ
ejpam-5450	193	4	◦	◦	NOUN
ejpam-5450	193	5	z	z	NOUN
ejpam-5450	193	6	)	)	PUNCT
ejpam-5450	194	1	+	+	CCONJ
ejpam-5450	194	2	t	t	X
ejpam-5450	194	3	≥	≥	X
ejpam-5450	194	4	min{lε	min{lε	PRON
ejpam-5450	194	5	µ(x	µ(x	ADJ
ejpam-5450	194	6	◦	◦	NOUN
ejpam-5450	194	7	(y	(y	NOUN
ejpam-5450	194	8	◦	◦	NOUN
ejpam-5450	194	9	z	z	NOUN
ejpam-5450	194	10	)	)	PUNCT
ejpam-5450	194	11	)	)	PUNCT
ejpam-5450	194	12	,	,	PUNCT
ejpam-5450	194	13	lε	lε	ADP
ejpam-5450	194	14	µ(y)}+t	µ(y)}+t	NOUN
ejpam-5450	194	15	=	=	SYM
ejpam-5450	194	16	min{lε	min{lε	NUM
ejpam-5450	194	17	µ(x	µ(x	ADJ
ejpam-5450	194	18	◦	◦	NOUN
ejpam-5450	194	19	(y	(y	NOUN
ejpam-5450	194	20	◦	◦	NOUN
ejpam-5450	194	21	z))+t	z))+t	NOUN
ejpam-5450	194	22	,	,	PUNCT
ejpam-5450	194	23	lε	lε	X
ejpam-5450	194	24	µ(y)+t	µ(y)+t	ADP
ejpam-5450	194	25	}	}	PUNCT
ejpam-5450	194	26	>	>	X
ejpam-5450	194	27	1	1	NUM
ejpam-5450	194	28	.	.	PUNCT
ejpam-5450	194	29	thus	thus	ADV
ejpam-5450	194	30	,	,	PUNCT
ejpam-5450	194	31	[	[	X
ejpam-5450	194	32	(	(	PUNCT
ejpam-5450	194	33	x	x	SYM
ejpam-5450	194	34	◦	◦	NOUN
ejpam-5450	194	35	z)/t]qlε	z)/t]qlε	ADJ
ejpam-5450	194	36	µ.	µ.	NOUN
ejpam-5450	194	37	so	so	SCONJ
ejpam-5450	194	38	x	x	SYM
ejpam-5450	194	39	◦	◦	NOUN
ejpam-5450	194	40	z	z	NOUN
ejpam-5450	194	41	∈	∈	PROPN
ejpam-5450	194	42	(	(	PUNCT
ejpam-5450	194	43	lε	lε	X
ejpam-5450	194	44	µ	µ	NUM
ejpam-5450	194	45	,	,	PUNCT
ejpam-5450	194	46	t)q	t)q	PUNCT
ejpam-5450	194	47	.	.	PUNCT
ejpam-5450	195	1	hence	hence	ADV
ejpam-5450	195	2	,	,	PUNCT
ejpam-5450	195	3	(	(	PUNCT
ejpam-5450	195	4	lε	lε	X
ejpam-5450	195	5	µ	µ	NUM
ejpam-5450	195	6	,	,	PUNCT
ejpam-5450	195	7	t)q	t)q	PUNCT
ejpam-5450	195	8	is	be	AUX
ejpam-5450	195	9	a	a	DET
ejpam-5450	195	10	bcc	bcc	PROPN
ejpam-5450	195	11	-	-	PUNCT
ejpam-5450	195	12	ideal	ideal	NOUN
ejpam-5450	195	13	of	of	ADP
ejpam-5450	195	14	x.	x.	PROPN
ejpam-5450	195	15	theorem	theorem	VERB
ejpam-5450	195	16	5	5	NUM
ejpam-5450	195	17	.	.	PUNCT
ejpam-5450	196	1	let	let	VERB
ejpam-5450	196	2	µ	µ	X
ejpam-5450	196	3	be	be	AUX
ejpam-5450	196	4	a	a	DET
ejpam-5450	196	5	fuzzy	fuzzy	ADJ
ejpam-5450	196	6	set	set	NOUN
ejpam-5450	196	7	in	in	ADP
ejpam-5450	196	8	x.	x.	NOUN
ejpam-5450	196	9	for	for	ADP
ejpam-5450	196	10	an	an	DET
ejpam-5450	196	11	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	196	12	fuzzy	fuzzy	NOUN
ejpam-5450	196	13	set	set	VERB
ejpam-5450	196	14	lε	lε	PRON
ejpam-5450	196	15	µ	µ	PROPN
ejpam-5450	196	16	of	of	ADP
ejpam-5450	196	17	µ	µ	NOUN
ejpam-5450	196	18	in	in	ADP
ejpam-5450	196	19	x	x	SYM
ejpam-5450	196	20	,	,	PUNCT
ejpam-5450	196	21	if	if	SCONJ
ejpam-5450	196	22	the	the	DET
ejpam-5450	196	23	q	q	NOUN
ejpam-5450	196	24	-	-	PUNCT
ejpam-5450	196	25	set	set	ADJ
ejpam-5450	196	26	(	(	PUNCT
ejpam-5450	196	27	lε	lε	X
ejpam-5450	196	28	µ	µ	NUM
ejpam-5450	196	29	,	,	PUNCT
ejpam-5450	196	30	t)q	t)q	PUNCT
ejpam-5450	196	31	is	be	AUX
ejpam-5450	196	32	a	a	DET
ejpam-5450	196	33	bcc	bcc	PROPN
ejpam-5450	196	34	-	-	PUNCT
ejpam-5450	196	35	ideal	ideal	NOUN
ejpam-5450	196	36	of	of	ADP
ejpam-5450	196	37	x	x	PRON
ejpam-5450	196	38	,	,	PUNCT
ejpam-5450	196	39	then	then	ADV
ejpam-5450	196	40	lε	lε	X
ejpam-5450	196	41	µ	µ	PRON
ejpam-5450	196	42	satisfies	satisfy	VERB
ejpam-5450	196	43	the	the	DET
ejpam-5450	196	44	following	follow	VERB
ejpam-5450	196	45	properties	property	NOUN
ejpam-5450	196	46	:	:	PUNCT
ejpam-5450	196	47	(	(	PUNCT
ejpam-5450	196	48	∀ta	∀ta	PROPN
ejpam-5450	196	49	∈	∈	PROPN
ejpam-5450	196	50	(	(	PUNCT
ejpam-5450	196	51	0	0	NUM
ejpam-5450	196	52	,	,	PUNCT
ejpam-5450	196	53	0.5])(0	0.5])(0	PRON
ejpam-5450	196	54	∈	∈	PROPN
ejpam-5450	196	55	(	(	PUNCT
ejpam-5450	196	56	lε	lε	ADP
ejpam-5450	196	57	µ	µ	NOUN
ejpam-5450	196	58	,	,	PUNCT
ejpam-5450	196	59	ta)∈	ta)∈	PROPN
ejpam-5450	196	60	)	)	PUNCT
ejpam-5450	196	61	(	(	PUNCT
ejpam-5450	196	62	3.11	3.11	NUM
ejpam-5450	196	63	)	)	PUNCT
ejpam-5450	196	64	(	(	PUNCT
ejpam-5450	196	65	∀x	∀x	X
ejpam-5450	196	66	,	,	PUNCT
ejpam-5450	196	67	y	y	PROPN
ejpam-5450	196	68	,	,	PUNCT
ejpam-5450	196	69	z	z	PROPN
ejpam-5450	196	70	∈	∈	PROPN
ejpam-5450	196	71	x,∀ta	x,∀ta	NOUN
ejpam-5450	196	72	,	,	PUNCT
ejpam-5450	196	73	tb	tb	ADP
ejpam-5450	196	74	∈	∈	PROPN
ejpam-5450	196	75	(	(	PUNCT
ejpam-5450	196	76	0	0	NUM
ejpam-5450	196	77	,	,	PUNCT
ejpam-5450	196	78	0.5	0.5	NUM
ejpam-5450	196	79	]	]	PUNCT
ejpam-5450	196	80	)	)	PUNCT
ejpam-5450	196	81	(	(	PUNCT
ejpam-5450	196	82	[	[	X
ejpam-5450	196	83	x	x	X
ejpam-5450	196	84	◦	◦	NOUN
ejpam-5450	196	85	(	(	PUNCT
ejpam-5450	196	86	y	y	NOUN
ejpam-5450	196	87	◦	◦	VERB
ejpam-5450	196	88	z)/ta]qlε	z)/ta]qlε	NOUN
ejpam-5450	196	89	µ	µ	X
ejpam-5450	196	90	,	,	PUNCT
ejpam-5450	196	91	[	[	X
ejpam-5450	196	92	y	y	X
ejpam-5450	196	93	/	/	SYM
ejpam-5450	196	94	tb]ql	tb]ql	NOUN
ejpam-5450	196	95	ε	ε	PROPN
ejpam-5450	196	96	µ	µ	PROPN
ejpam-5450	196	97	⇒	⇒	NOUN
ejpam-5450	196	98	(	(	PUNCT
ejpam-5450	196	99	x	x	SYM
ejpam-5450	196	100	◦	◦	NOUN
ejpam-5450	196	101	z	z	NOUN
ejpam-5450	196	102	)	)	PUNCT
ejpam-5450	196	103	∈	∈	PROPN
ejpam-5450	196	104	(	(	PUNCT
ejpam-5450	196	105	lε	lε	X
ejpam-5450	196	106	µ,max{ta	µ,max{ta	PROPN
ejpam-5450	196	107	,	,	PUNCT
ejpam-5450	196	108	tb})∈	tb})∈	ADJ
ejpam-5450	196	109	)	)	PUNCT
ejpam-5450	196	110	(	(	PUNCT
ejpam-5450	196	111	3.12	3.12	NUM
ejpam-5450	196	112	)	)	PUNCT
ejpam-5450	196	113	proof	proof	NOUN
ejpam-5450	196	114	.	.	PUNCT
ejpam-5450	197	1	let	let	VERB
ejpam-5450	197	2	x	x	PRON
ejpam-5450	197	3	,	,	PUNCT
ejpam-5450	197	4	y	y	PROPN
ejpam-5450	197	5	,	,	PUNCT
ejpam-5450	197	6	z	z	NOUN
ejpam-5450	197	7	∈	∈	PROPN
ejpam-5450	197	8	x	x	X
ejpam-5450	197	9	and	and	CCONJ
ejpam-5450	197	10	ta	ta	PROPN
ejpam-5450	197	11	,	,	PUNCT
ejpam-5450	197	12	tb	tb	ADP
ejpam-5450	197	13	∈	∈	PROPN
ejpam-5450	197	14	(	(	PUNCT
ejpam-5450	197	15	0	0	NUM
ejpam-5450	197	16	,	,	PUNCT
ejpam-5450	197	17	0.5	0.5	NUM
ejpam-5450	197	18	]	]	PUNCT
ejpam-5450	197	19	.	.	PUNCT
ejpam-5450	198	1	if	if	SCONJ
ejpam-5450	198	2	0	0	NUM
ejpam-5450	198	3	/∈	/∈	INTJ
ejpam-5450	198	4	(	(	PUNCT
ejpam-5450	198	5	lε	lε	ADP
ejpam-5450	198	6	µ	µ	NOUN
ejpam-5450	198	7	,	,	PUNCT
ejpam-5450	198	8	ta)∈	ta)∈	PROPN
ejpam-5450	198	9	,	,	PUNCT
ejpam-5450	198	10	then	then	ADV
ejpam-5450	198	11	[	[	X
ejpam-5450	198	12	0	0	NUM
ejpam-5450	198	13	/	/	SYM
ejpam-5450	198	14	ta]∈lε	ta]∈lε	NOUN
ejpam-5450	198	15	µ	µ	NOUN
ejpam-5450	198	16	and	and	CCONJ
ejpam-5450	198	17	so	so	ADV
ejpam-5450	198	18	lε	lε	ADP
ejpam-5450	198	19	µ(0	µ(0	NOUN
ejpam-5450	198	20	)	)	PUNCT
ejpam-5450	198	21	<	<	X
ejpam-5450	198	22	ta	ta	X
ejpam-5450	198	23	≤	≤	ADV
ejpam-5450	198	24	1	1	NUM
ejpam-5450	198	25	−	−	NOUN
ejpam-5450	198	26	ta	ta	X
ejpam-5450	198	27	since	since	SCONJ
ejpam-5450	198	28	ta	ta	ADP
ejpam-5450	198	29	≤	≤	ADV
ejpam-5450	198	30	0.5	0.5	NUM
ejpam-5450	198	31	.	.	PUNCT
ejpam-5450	199	1	hence	hence	ADV
ejpam-5450	199	2	,	,	PUNCT
ejpam-5450	199	3	[	[	X
ejpam-5450	199	4	0	0	NUM
ejpam-5450	199	5	/	/	SYM
ejpam-5450	199	6	ta]qlε	ta]qlε	NOUN
ejpam-5450	199	7	µ.	µ.	NOUN
ejpam-5450	199	8	this	this	DET
ejpam-5450	199	9	contradiction	contradiction	NOUN
ejpam-5450	199	10	is	be	AUX
ejpam-5450	199	11	hence	hence	ADV
ejpam-5450	199	12	0	0	NUM
ejpam-5450	200	1	∈	∈	NOUN
ejpam-5450	201	1	(	(	PUNCT
ejpam-5450	201	2	lε	lε	X
ejpam-5450	201	3	µ	µ	NUM
ejpam-5450	201	4	,	,	PUNCT
ejpam-5450	202	1	ta)∈.	ta)∈.	AUX
ejpam-5450	202	2	let	let	VERB
ejpam-5450	202	3	x	x	PRON
ejpam-5450	202	4	,	,	PUNCT
ejpam-5450	202	5	y	y	PROPN
ejpam-5450	202	6	,	,	PUNCT
ejpam-5450	202	7	z	z	NOUN
ejpam-5450	202	8	∈	∈	PROPN
ejpam-5450	202	9	x	x	AUX
ejpam-5450	202	10	be	be	AUX
ejpam-5450	203	1	such	such	ADJ
ejpam-5450	203	2	that	that	SCONJ
ejpam-5450	203	3	x	x	X
ejpam-5450	203	4	◦	◦	NOUN
ejpam-5450	203	5	(	(	PUNCT
ejpam-5450	203	6	y	y	PROPN
ejpam-5450	203	7	◦	◦	PROPN
ejpam-5450	203	8	z	z	PROPN
ejpam-5450	203	9	)	)	PUNCT
ejpam-5450	203	10	∈	∈	PROPN
ejpam-5450	203	11	(	(	PUNCT
ejpam-5450	203	12	lε	lε	X
ejpam-5450	203	13	µ	µ	NUM
ejpam-5450	203	14	,	,	PUNCT
ejpam-5450	203	15	t)q	t)q	PUNCT
ejpam-5450	203	16	and	and	CCONJ
ejpam-5450	203	17	y	y	PROPN
ejpam-5450	203	18	∈	∈	PROPN
ejpam-5450	203	19	(	(	PUNCT
ejpam-5450	203	20	lε	lε	X
ejpam-5450	203	21	µ	µ	NUM
ejpam-5450	203	22	,	,	PUNCT
ejpam-5450	203	23	t)q	t)q	PUNCT
ejpam-5450	203	24	.	.	PUNCT
ejpam-5450	204	1	then	then	ADV
ejpam-5450	204	2	[	[	X
ejpam-5450	204	3	x	x	X
ejpam-5450	204	4	◦	◦	NOUN
ejpam-5450	204	5	(	(	PUNCT
ejpam-5450	204	6	y	y	NOUN
ejpam-5450	204	7	◦	◦	NOUN
ejpam-5450	204	8	z)/t]qlε	z)/t]qlε	X
ejpam-5450	204	9	µ	µ	X
ejpam-5450	204	10	and	and	CCONJ
ejpam-5450	204	11	[	[	X
ejpam-5450	204	12	y	y	X
ejpam-5450	204	13	/	/	SYM
ejpam-5450	204	14	t]qlε	t]qlε	X
ejpam-5450	204	15	µ	µ	NOUN
ejpam-5450	204	16	,	,	PUNCT
ejpam-5450	204	17	that	that	ADV
ejpam-5450	204	18	is	is	ADV
ejpam-5450	204	19	,	,	PUNCT
ejpam-5450	204	20	lε	lε	ADP
ejpam-5450	204	21	µ(x	µ(x	ADJ
ejpam-5450	204	22	◦	◦	NOUN
ejpam-5450	204	23	(	(	PUNCT
ejpam-5450	204	24	y	y	PROPN
ejpam-5450	204	25	◦	◦	PROPN
ejpam-5450	204	26	z	z	PROPN
ejpam-5450	204	27	)	)	PUNCT
ejpam-5450	204	28	)	)	PUNCT
ejpam-5450	204	29	>	>	X
ejpam-5450	205	1	1	1	NUM
ejpam-5450	205	2	−	−	PROPN
ejpam-5450	205	3	t	t	NOUN
ejpam-5450	205	4	and	and	CCONJ
ejpam-5450	205	5	lε	lε	ADP
ejpam-5450	205	6	µ(y	µ(y	PROPN
ejpam-5450	205	7	)	)	PUNCT
ejpam-5450	205	8	>	>	X
ejpam-5450	206	1	1	1	NUM
ejpam-5450	206	2	−	−	NOUN
ejpam-5450	206	3	t.	t.	NOUN
ejpam-5450	206	4	it	it	PRON
ejpam-5450	206	5	follows	follow	VERB
ejpam-5450	206	6	that	that	SCONJ
ejpam-5450	206	7	lε	lε	ADP
ejpam-5450	206	8	µ(x	µ(x	ADJ
ejpam-5450	206	9	◦	◦	NOUN
ejpam-5450	206	10	z	z	NOUN
ejpam-5450	206	11	)	)	PUNCT
ejpam-5450	206	12	≥	≥	NOUN
ejpam-5450	206	13	min{lε	min{lε	NUM
ejpam-5450	206	14	µ(x	µ(x	ADJ
ejpam-5450	206	15	◦	◦	NOUN
ejpam-5450	206	16	(	(	PUNCT
ejpam-5450	206	17	y	y	PROPN
ejpam-5450	206	18	◦	◦	PROPN
ejpam-5450	206	19	z	z	PROPN
ejpam-5450	206	20	)	)	PUNCT
ejpam-5450	206	21	)	)	PUNCT
ejpam-5450	206	22	,	,	PUNCT
ejpam-5450	206	23	lε	lε	X
ejpam-5450	206	24	µ(y	µ(y	PROPN
ejpam-5450	206	25	)	)	PUNCT
ejpam-5450	206	26	}	}	PUNCT
ejpam-5450	206	27	>	>	X
ejpam-5450	206	28	1	1	NUM
ejpam-5450	206	29	−	−	NOUN
ejpam-5450	206	30	t.	t.	NOUN
ejpam-5450	206	31	thus	thus	ADV
ejpam-5450	206	32	,	,	PUNCT
ejpam-5450	206	33	[	[	X
ejpam-5450	206	34	x	x	X
ejpam-5450	206	35	◦	◦	NOUN
ejpam-5450	206	36	z	z	NOUN
ejpam-5450	206	37	/	/	SYM
ejpam-5450	206	38	t]qlε	t]qlε	X
ejpam-5450	206	39	µ	µ	NOUN
ejpam-5450	206	40	and	and	CCONJ
ejpam-5450	206	41	so	so	ADV
ejpam-5450	206	42	x	x	PART
ejpam-5450	206	43	◦	◦	NOUN
ejpam-5450	206	44	z	z	NOUN
ejpam-5450	206	45	∈	∈	PROPN
ejpam-5450	206	46	(	(	PUNCT
ejpam-5450	206	47	lε	lε	X
ejpam-5450	206	48	µ	µ	NUM
ejpam-5450	206	49	,	,	PUNCT
ejpam-5450	206	50	t)q	t)q	PUNCT
ejpam-5450	206	51	.	.	PUNCT
ejpam-5450	207	1	hence	hence	ADV
ejpam-5450	207	2	,	,	PUNCT
ejpam-5450	207	3	(	(	PUNCT
ejpam-5450	207	4	lε	lε	X
ejpam-5450	207	5	µ	µ	NUM
ejpam-5450	207	6	,	,	PUNCT
ejpam-5450	207	7	t)q	t)q	PUNCT
ejpam-5450	207	8	is	be	AUX
ejpam-5450	207	9	a	a	DET
ejpam-5450	207	10	bcc	bcc	PROPN
ejpam-5450	207	11	-	-	PUNCT
ejpam-5450	207	12	ideal	ideal	NOUN
ejpam-5450	207	13	of	of	ADP
ejpam-5450	207	14	x.	x.	PROPN
ejpam-5450	207	15	theorem	theorem	VERB
ejpam-5450	207	16	6	6	NUM
ejpam-5450	207	17	.	.	PUNCT
ejpam-5450	208	1	if	if	SCONJ
ejpam-5450	208	2	an	an	DET
ejpam-5450	208	3	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	208	4	fuzzy	fuzzy	ADJ
ejpam-5450	208	5	set	set	VERB
ejpam-5450	208	6	lε	lε	PRON
ejpam-5450	208	7	µ	µ	NOUN
ejpam-5450	208	8	in	in	ADP
ejpam-5450	208	9	x	x	PART
ejpam-5450	208	10	satisfies	satisfie	NOUN
ejpam-5450	208	11	the	the	DET
ejpam-5450	208	12	following	follow	VERB
ejpam-5450	208	13	properties	property	NOUN
ejpam-5450	208	14	:	:	PUNCT
ejpam-5450	208	15	(	(	PUNCT
ejpam-5450	208	16	∀x	∀x	X
ejpam-5450	208	17	∈	∈	PROPN
ejpam-5450	208	18	x,∀t	x,∀t	X
ejpam-5450	208	19	∈	∈	PROPN
ejpam-5450	208	20	(	(	PUNCT
ejpam-5450	208	21	0.5	0.5	NUM
ejpam-5450	208	22	,	,	PUNCT
ejpam-5450	208	23	1])([x	1])([x	NUM
ejpam-5450	208	24	/	/	SYM
ejpam-5450	208	25	t]qlε	t]qlε	X
ejpam-5450	208	26	µ	µ	ADJ
ejpam-5450	208	27	⇒	⇒	NOUN
ejpam-5450	208	28	[	[	X
ejpam-5450	208	29	0	0	NUM
ejpam-5450	208	30	/	/	SYM
ejpam-5450	208	31	t	t	PROPN
ejpam-5450	208	32	]	]	X
ejpam-5450	208	33	∈	∈	PROPN
ejpam-5450	208	34	(	(	PUNCT
ejpam-5450	208	35	lε	lε	X
ejpam-5450	208	36	µ	µ	NUM
ejpam-5450	208	37	)	)	PUNCT
ejpam-5450	208	38	)	)	PUNCT
ejpam-5450	208	39	(	(	PUNCT
ejpam-5450	208	40	3.13	3.13	NUM
ejpam-5450	208	41	)	)	PUNCT
ejpam-5450	208	42	a.	a.	NOUN
ejpam-5450	208	43	iampan	iampan	PROPN
ejpam-5450	208	44	,	,	PUNCT
ejpam-5450	208	45	r.	r.	PROPN
ejpam-5450	208	46	subasini	subasini	PROPN
ejpam-5450	208	47	,	,	PUNCT
ejpam-5450	208	48	n.	n.	PROPN
ejpam-5450	208	49	rajesh	rajesh	PROPN
ejpam-5450	208	50	/	/	SYM
ejpam-5450	208	51	eur	eur	PROPN
ejpam-5450	208	52	.	.	PUNCT
ejpam-5450	209	1	j.	j.	PROPN
ejpam-5450	209	2	pure	pure	PROPN
ejpam-5450	209	3	appl	appl	PROPN
ejpam-5450	209	4	.	.	PROPN
ejpam-5450	209	5	math	math	PROPN
ejpam-5450	209	6	,	,	PUNCT
ejpam-5450	209	7	17	17	NUM
ejpam-5450	209	8	(	(	PUNCT
ejpam-5450	209	9	4	4	NUM
ejpam-5450	209	10	)	)	PUNCT
ejpam-5450	209	11	(	(	PUNCT
ejpam-5450	209	12	2024	2024	NUM
ejpam-5450	209	13	)	)	PUNCT
ejpam-5450	209	14	,	,	PUNCT
ejpam-5450	209	15	3209	3209	NUM
ejpam-5450	209	16	-	-	SYM
ejpam-5450	209	17	3222	3222	NUM
ejpam-5450	209	18	3218	3218	NUM
ejpam-5450	209	19	(	(	PUNCT
ejpam-5450	209	20	∀x	∀x	NUM
ejpam-5450	209	21	,	,	PUNCT
ejpam-5450	209	22	y	y	PROPN
ejpam-5450	209	23	,	,	PUNCT
ejpam-5450	209	24	z	z	PROPN
ejpam-5450	209	25	∈	∈	PROPN
ejpam-5450	209	26	x,∀ta	x,∀ta	NOUN
ejpam-5450	209	27	,	,	PUNCT
ejpam-5450	209	28	tb	tb	ADP
ejpam-5450	209	29	∈	∈	PROPN
ejpam-5450	209	30	(	(	PUNCT
ejpam-5450	209	31	0.5	0.5	NUM
ejpam-5450	209	32	,	,	PUNCT
ejpam-5450	209	33	1	1	NUM
ejpam-5450	209	34	]	]	PUNCT
ejpam-5450	209	35	)	)	PUNCT
ejpam-5450	209	36	(	(	PUNCT
ejpam-5450	209	37	[	[	X
ejpam-5450	209	38	x	x	X
ejpam-5450	209	39	◦	◦	NOUN
ejpam-5450	209	40	(	(	PUNCT
ejpam-5450	209	41	y	y	NOUN
ejpam-5450	209	42	◦	◦	VERB
ejpam-5450	209	43	z)/ta]qlε	z)/ta]qlε	NOUN
ejpam-5450	209	44	µ	µ	X
ejpam-5450	209	45	,	,	PUNCT
ejpam-5450	209	46	[	[	X
ejpam-5450	209	47	y	y	X
ejpam-5450	209	48	/	/	SYM
ejpam-5450	209	49	tb]ql	tb]ql	NOUN
ejpam-5450	209	50	ε	ε	PROPN
ejpam-5450	209	51	µ	µ	PRON
ejpam-5450	209	52	⇒	⇒	NOUN
ejpam-5450	210	1	[	[	X
ejpam-5450	210	2	(	(	PUNCT
ejpam-5450	210	3	x	x	SYM
ejpam-5450	210	4	◦	◦	NOUN
ejpam-5450	210	5	z)/max{ta	z)/max{ta	NUM
ejpam-5450	210	6	,	,	PUNCT
ejpam-5450	210	7	tb	tb	NOUN
ejpam-5450	210	8	}	}	PUNCT
ejpam-5450	210	9	]	]	PUNCT
ejpam-5450	211	1	∈	∈	PROPN
ejpam-5450	211	2	lε	lε	ADP
ejpam-5450	211	3	µ	µ	NOUN
ejpam-5450	211	4	)	)	PUNCT
ejpam-5450	211	5	(	(	PUNCT
ejpam-5450	211	6	3.14	3.14	NUM
ejpam-5450	211	7	)	)	PUNCT
ejpam-5450	211	8	then	then	ADV
ejpam-5450	211	9	the	the	DET
ejpam-5450	211	10	nonempty	nonempty	ADJ
ejpam-5450	211	11	∈-set	∈-set	NOUN
ejpam-5450	211	12	(	(	PUNCT
ejpam-5450	211	13	lε	lε	X
ejpam-5450	211	14	µ,max{ta	µ,max{ta	PROPN
ejpam-5450	211	15	,	,	PUNCT
ejpam-5450	211	16	tb})∈	tb})∈	PROPN
ejpam-5450	211	17	of	of	ADP
ejpam-5450	211	18	lε	lε	X
ejpam-5450	211	19	µ	µ	PROPN
ejpam-5450	211	20	is	be	AUX
ejpam-5450	211	21	a	a	DET
ejpam-5450	211	22	bcc	bcc	PROPN
ejpam-5450	211	23	-	-	PUNCT
ejpam-5450	211	24	ideal	ideal	NOUN
ejpam-5450	211	25	of	of	ADP
ejpam-5450	211	26	x	x	PUNCT
ejpam-5450	211	27	for	for	ADP
ejpam-5450	211	28	all	all	DET
ejpam-5450	211	29	ta	ta	NOUN
ejpam-5450	211	30	,	,	PUNCT
ejpam-5450	211	31	tb	tb	ADP
ejpam-5450	211	32	∈	∈	PROPN
ejpam-5450	211	33	(	(	PUNCT
ejpam-5450	211	34	0.5	0.5	NUM
ejpam-5450	211	35	,	,	PUNCT
ejpam-5450	211	36	1	1	NUM
ejpam-5450	211	37	]	]	PUNCT
ejpam-5450	211	38	.	.	PUNCT
ejpam-5450	212	1	proof	proof	NOUN
ejpam-5450	212	2	.	.	PUNCT
ejpam-5450	213	1	let	let	VERB
ejpam-5450	213	2	ta	ta	PART
ejpam-5450	213	3	,	,	PUNCT
ejpam-5450	213	4	tb	tb	ADP
ejpam-5450	213	5	∈	∈	PROPN
ejpam-5450	213	6	(	(	PUNCT
ejpam-5450	213	7	0.5	0.5	NUM
ejpam-5450	213	8	,	,	PUNCT
ejpam-5450	213	9	1	1	NUM
ejpam-5450	213	10	]	]	PUNCT
ejpam-5450	213	11	and	and	CCONJ
ejpam-5450	213	12	assume	assume	VERB
ejpam-5450	213	13	that	that	SCONJ
ejpam-5450	213	14	the	the	DET
ejpam-5450	213	15	∈-set	∈-set	NOUN
ejpam-5450	213	16	(	(	PUNCT
ejpam-5450	213	17	lε	lε	X
ejpam-5450	213	18	µ,max{ta	µ,max{ta	PROPN
ejpam-5450	213	19	,	,	PUNCT
ejpam-5450	213	20	tb})∈	tb})∈	PROPN
ejpam-5450	213	21	of	of	ADP
ejpam-5450	213	22	lε	lε	X
ejpam-5450	213	23	µ	µ	PROPN
ejpam-5450	213	24	is	be	AUX
ejpam-5450	213	25	nonempty	nonempty	ADJ
ejpam-5450	213	26	.	.	PUNCT
ejpam-5450	214	1	then	then	ADV
ejpam-5450	214	2	there	there	PRON
ejpam-5450	214	3	exists	exist	VERB
ejpam-5450	214	4	x	x	X
ejpam-5450	214	5	∈	∈	PROPN
ejpam-5450	214	6	(	(	PUNCT
ejpam-5450	214	7	lε	lε	X
ejpam-5450	214	8	µ,max{ta	µ,max{ta	PROPN
ejpam-5450	214	9	,	,	PUNCT
ejpam-5450	214	10	tb})∈	tb})∈	ADJ
ejpam-5450	214	11	,	,	PUNCT
ejpam-5450	214	12	and	and	CCONJ
ejpam-5450	214	13	so	so	ADV
ejpam-5450	214	14	lε	lε	ADP
ejpam-5450	214	15	µ(x	µ(x	NOUN
ejpam-5450	214	16	)	)	PUNCT
ejpam-5450	214	17	≥	≥	NOUN
ejpam-5450	214	18	max{ta	max{ta	NOUN
ejpam-5450	214	19	,	,	PUNCT
ejpam-5450	214	20	tb	tb	NOUN
ejpam-5450	214	21	}	}	PUNCT
ejpam-5450	214	22	>	>	X
ejpam-5450	214	23	1	1	NUM
ejpam-5450	214	24	−	−	NOUN
ejpam-5450	214	25	max{ta	max{ta	NOUN
ejpam-5450	214	26	,	,	PUNCT
ejpam-5450	214	27	tb	tb	NOUN
ejpam-5450	214	28	}	}	PUNCT
ejpam-5450	214	29	,	,	PUNCT
ejpam-5450	214	30	that	that	ADV
ejpam-5450	214	31	is	is	ADV
ejpam-5450	214	32	,	,	PUNCT
ejpam-5450	214	33	[	[	X
ejpam-5450	214	34	x	x	X
ejpam-5450	214	35	/	/	SYM
ejpam-5450	214	36	max{ta	max{ta	ADJ
ejpam-5450	214	37	,	,	PUNCT
ejpam-5450	214	38	tb}]qlε	tb}]qlε	NOUN
ejpam-5450	214	39	µ.	µ.	NOUN
ejpam-5450	214	40	hence	hence	ADV
ejpam-5450	214	41	,	,	PUNCT
ejpam-5450	214	42	[	[	X
ejpam-5450	214	43	0	0	NUM
ejpam-5450	214	44	/	/	SYM
ejpam-5450	214	45	max{ta	max{ta	NOUN
ejpam-5450	214	46	,	,	PUNCT
ejpam-5450	214	47	tb	tb	NOUN
ejpam-5450	214	48	}	}	PUNCT
ejpam-5450	214	49	]	]	PUNCT
ejpam-5450	214	50	∈	∈	PROPN
ejpam-5450	214	51	lε	lε	PRON
ejpam-5450	214	52	µ	µ	X
ejpam-5450	214	53	by	by	ADP
ejpam-5450	214	54	(	(	PUNCT
ejpam-5450	214	55	3.13	3.13	NUM
ejpam-5450	214	56	)	)	PUNCT
ejpam-5450	214	57	,	,	PUNCT
ejpam-5450	214	58	and	and	CCONJ
ejpam-5450	214	59	thus	thus	ADV
ejpam-5450	214	60	0	0	X
ejpam-5450	214	61	∈	∈	NOUN
ejpam-5450	214	62	(	(	PUNCT
ejpam-5450	214	63	lε	lε	X
ejpam-5450	214	64	µ,max{ta	µ,max{ta	PROPN
ejpam-5450	214	65	,	,	PUNCT
ejpam-5450	214	66	tb})∈.	tb})∈.	NUM
ejpam-5450	214	67	let	let	VERB
ejpam-5450	214	68	x	x	PRON
ejpam-5450	214	69	,	,	PUNCT
ejpam-5450	214	70	y	y	PROPN
ejpam-5450	214	71	,	,	PUNCT
ejpam-5450	214	72	z	z	NOUN
ejpam-5450	214	73	∈	∈	PROPN
ejpam-5450	214	74	x	x	AUX
ejpam-5450	214	75	be	be	AUX
ejpam-5450	214	76	such	such	ADJ
ejpam-5450	214	77	that	that	SCONJ
ejpam-5450	214	78	x	x	X
ejpam-5450	214	79	◦	◦	NOUN
ejpam-5450	214	80	(	(	PUNCT
ejpam-5450	214	81	y	y	PROPN
ejpam-5450	214	82	◦	◦	PROPN
ejpam-5450	214	83	z	z	PROPN
ejpam-5450	214	84	)	)	PUNCT
ejpam-5450	214	85	∈	∈	PROPN
ejpam-5450	214	86	(	(	PUNCT
ejpam-5450	214	87	lε	lε	X
ejpam-5450	214	88	µ,max{ta	µ,max{ta	PROPN
ejpam-5450	214	89	,	,	PUNCT
ejpam-5450	214	90	tb})∈	tb})∈	ADJ
ejpam-5450	214	91	and	and	CCONJ
ejpam-5450	214	92	y	y	PROPN
ejpam-5450	214	93	∈	∈	PROPN
ejpam-5450	214	94	(	(	PUNCT
ejpam-5450	214	95	lε	lε	X
ejpam-5450	214	96	µ,max{ta	µ,max{ta	PROPN
ejpam-5450	214	97	,	,	PUNCT
ejpam-5450	214	98	tb})∈.	tb})∈.	ADJ
ejpam-5450	214	99	then	then	ADV
ejpam-5450	214	100	lε	lε	ADP
ejpam-5450	214	101	µ(x	µ(x	ADJ
ejpam-5450	214	102	◦	◦	NOUN
ejpam-5450	214	103	(	(	PUNCT
ejpam-5450	214	104	y	y	PROPN
ejpam-5450	214	105	◦	◦	PROPN
ejpam-5450	214	106	z	z	PROPN
ejpam-5450	214	107	)	)	PUNCT
ejpam-5450	214	108	)	)	PUNCT
ejpam-5450	214	109	≥	≥	NOUN
ejpam-5450	214	110	max{ta	max{ta	NOUN
ejpam-5450	214	111	,	,	PUNCT
ejpam-5450	214	112	tb	tb	NOUN
ejpam-5450	214	113	}	}	PUNCT
ejpam-5450	214	114	>	>	X
ejpam-5450	214	115	1	1	NUM
ejpam-5450	214	116	−	−	NOUN
ejpam-5450	214	117	max{ta	max{ta	NOUN
ejpam-5450	214	118	,	,	PUNCT
ejpam-5450	214	119	tb	tb	NOUN
ejpam-5450	214	120	}	}	PUNCT
ejpam-5450	214	121	and	and	CCONJ
ejpam-5450	214	122	lε	lε	ADP
ejpam-5450	214	123	µ(y	µ(y	PROPN
ejpam-5450	214	124	)	)	PUNCT
ejpam-5450	214	125	≥	≥	NOUN
ejpam-5450	214	126	max{ta	max{ta	NOUN
ejpam-5450	214	127	,	,	PUNCT
ejpam-5450	214	128	tb	tb	NOUN
ejpam-5450	214	129	}	}	PUNCT
ejpam-5450	214	130	>	>	X
ejpam-5450	214	131	1	1	NUM
ejpam-5450	214	132	−	−	NOUN
ejpam-5450	214	133	max{ta	max{ta	NOUN
ejpam-5450	214	134	,	,	PUNCT
ejpam-5450	214	135	tb	tb	NOUN
ejpam-5450	214	136	}	}	PUNCT
ejpam-5450	214	137	,	,	PUNCT
ejpam-5450	214	138	that	that	ADV
ejpam-5450	214	139	is	is	ADV
ejpam-5450	214	140	,	,	PUNCT
ejpam-5450	214	141	[	[	X
ejpam-5450	214	142	(	(	PUNCT
ejpam-5450	214	143	x	x	SYM
ejpam-5450	214	144	◦	◦	NOUN
ejpam-5450	214	145	(	(	PUNCT
ejpam-5450	214	146	y	y	PROPN
ejpam-5450	214	147	◦	◦	PROPN
ejpam-5450	214	148	z))/max{ta	z))/max{ta	NUM
ejpam-5450	214	149	,	,	PUNCT
ejpam-5450	214	150	tb}]qlε	tb}]qlε	NOUN
ejpam-5450	214	151	µ	µ	NOUN
ejpam-5450	214	152	and	and	CCONJ
ejpam-5450	214	153	[	[	X
ejpam-5450	214	154	y	y	NOUN
ejpam-5450	214	155	/	/	SYM
ejpam-5450	214	156	max{ta	max{ta	NOUN
ejpam-5450	214	157	,	,	PUNCT
ejpam-5450	214	158	tb}]qlε	tb}]qlε	ADJ
ejpam-5450	214	159	µ.	µ.	NOUN
ejpam-5450	214	160	it	it	PRON
ejpam-5450	214	161	follows	follow	VERB
ejpam-5450	214	162	from	from	ADP
ejpam-5450	214	163	(	(	PUNCT
ejpam-5450	214	164	3.14	3.14	NUM
ejpam-5450	214	165	)	)	PUNCT
ejpam-5450	214	166	that	that	SCONJ
ejpam-5450	214	167	[	[	X
ejpam-5450	214	168	(	(	PUNCT
ejpam-5450	214	169	x	x	SYM
ejpam-5450	214	170	◦	◦	NOUN
ejpam-5450	214	171	z)/max{ta	z)/max{ta	NUM
ejpam-5450	214	172	,	,	PUNCT
ejpam-5450	214	173	tb	tb	NOUN
ejpam-5450	214	174	}	}	PUNCT
ejpam-5450	214	175	]	]	PUNCT
ejpam-5450	214	176	∈	∈	PROPN
ejpam-5450	214	177	lε	lε	VERB
ejpam-5450	214	178	µ.	µ.	NOUN
ejpam-5450	214	179	hence	hence	ADV
ejpam-5450	214	180	,	,	PUNCT
ejpam-5450	214	181	x	x	PUNCT
ejpam-5450	214	182	◦	◦	NOUN
ejpam-5450	214	183	z	z	NOUN
ejpam-5450	214	184	∈	∈	PROPN
ejpam-5450	214	185	(	(	PUNCT
ejpam-5450	214	186	lε	lε	X
ejpam-5450	214	187	µ,max{ta	µ,max{ta	PROPN
ejpam-5450	214	188	,	,	PUNCT
ejpam-5450	214	189	tb})∈	tb})∈	ADJ
ejpam-5450	214	190	,	,	PUNCT
ejpam-5450	214	191	and	and	CCONJ
ejpam-5450	214	192	therefore	therefore	ADV
ejpam-5450	214	193	(	(	PUNCT
ejpam-5450	214	194	lε	lε	X
ejpam-5450	214	195	µ,max{ta	µ,max{ta	PROPN
ejpam-5450	214	196	,	,	PUNCT
ejpam-5450	214	197	tb})∈	tb})∈	PROPN
ejpam-5450	214	198	is	be	AUX
ejpam-5450	214	199	a	a	DET
ejpam-5450	214	200	bcc	bcc	PROPN
ejpam-5450	214	201	-	-	PUNCT
ejpam-5450	214	202	ideal	ideal	NOUN
ejpam-5450	214	203	of	of	ADP
ejpam-5450	214	204	x	x	PUNCT
ejpam-5450	214	205	for	for	ADP
ejpam-5450	214	206	all	all	DET
ejpam-5450	214	207	ta	ta	NOUN
ejpam-5450	214	208	,	,	PUNCT
ejpam-5450	214	209	tb	tb	ADP
ejpam-5450	214	210	∈	∈	PROPN
ejpam-5450	214	211	(	(	PUNCT
ejpam-5450	214	212	0.5	0.5	NUM
ejpam-5450	214	213	,	,	PUNCT
ejpam-5450	214	214	1	1	NUM
ejpam-5450	214	215	]	]	PUNCT
ejpam-5450	214	216	.	.	PUNCT
ejpam-5450	215	1	theorem	theorem	VERB
ejpam-5450	215	2	7	7	NUM
ejpam-5450	215	3	.	.	PUNCT
ejpam-5450	216	1	if	if	SCONJ
ejpam-5450	216	2	an	an	DET
ejpam-5450	216	3	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	216	4	fuzzy	fuzzy	ADJ
ejpam-5450	216	5	set	set	VERB
ejpam-5450	216	6	lε	lε	PRON
ejpam-5450	216	7	µ	µ	NOUN
ejpam-5450	216	8	in	in	ADP
ejpam-5450	216	9	x	x	PART
ejpam-5450	216	10	satisfies	satisfie	NOUN
ejpam-5450	216	11	the	the	DET
ejpam-5450	216	12	conditions	condition	NOUN
ejpam-5450	216	13	(	(	PUNCT
ejpam-5450	216	14	3.13	3.13	NUM
ejpam-5450	216	15	)	)	PUNCT
ejpam-5450	216	16	and	and	CCONJ
ejpam-5450	216	17	(	(	PUNCT
ejpam-5450	216	18	∀x	∀x	NUM
ejpam-5450	216	19	,	,	PUNCT
ejpam-5450	216	20	y	y	PROPN
ejpam-5450	216	21	,	,	PUNCT
ejpam-5450	216	22	z	z	PROPN
ejpam-5450	216	23	∈	∈	PROPN
ejpam-5450	216	24	x,∀ta	x,∀ta	NOUN
ejpam-5450	216	25	,	,	PUNCT
ejpam-5450	216	26	tb	tb	ADP
ejpam-5450	216	27	∈	∈	PROPN
ejpam-5450	216	28	(	(	PUNCT
ejpam-5450	216	29	0.5	0.5	NUM
ejpam-5450	216	30	,	,	PUNCT
ejpam-5450	216	31	1	1	NUM
ejpam-5450	216	32	]	]	PUNCT
ejpam-5450	216	33	)	)	PUNCT
ejpam-5450	217	1	(	(	PUNCT
ejpam-5450	217	2	[	[	X
ejpam-5450	217	3	x	x	X
ejpam-5450	217	4	◦	◦	NOUN
ejpam-5450	217	5	(	(	PUNCT
ejpam-5450	217	6	y	y	NOUN
ejpam-5450	217	7	◦	◦	VERB
ejpam-5450	217	8	z)/ta]qlε	z)/ta]qlε	NOUN
ejpam-5450	217	9	µ	µ	X
ejpam-5450	217	10	,	,	PUNCT
ejpam-5450	217	11	[	[	X
ejpam-5450	217	12	y	y	X
ejpam-5450	217	13	/	/	SYM
ejpam-5450	217	14	tb]ql	tb]ql	NOUN
ejpam-5450	217	15	ε	ε	PROPN
ejpam-5450	217	16	µ	µ	PRON
ejpam-5450	217	17	⇒	⇒	NOUN
ejpam-5450	217	18	[	[	X
ejpam-5450	217	19	(	(	PUNCT
ejpam-5450	217	20	x	x	SYM
ejpam-5450	217	21	◦	◦	NOUN
ejpam-5450	217	22	z)/min{ta	z)/min{ta	PROPN
ejpam-5450	217	23	,	,	PUNCT
ejpam-5450	217	24	tb	tb	NOUN
ejpam-5450	217	25	}	}	PUNCT
ejpam-5450	217	26	]	]	PUNCT
ejpam-5450	217	27	∈	∈	PROPN
ejpam-5450	217	28	lε	lε	ADP
ejpam-5450	217	29	µ	µ	NOUN
ejpam-5450	217	30	)	)	PUNCT
ejpam-5450	217	31	,	,	PUNCT
ejpam-5450	217	32	(	(	PUNCT
ejpam-5450	217	33	3.15	3.15	NUM
ejpam-5450	217	34	)	)	PUNCT
ejpam-5450	217	35	then	then	ADV
ejpam-5450	217	36	the	the	DET
ejpam-5450	217	37	nonempty	nonempty	ADJ
ejpam-5450	217	38	∈-set	∈-set	NOUN
ejpam-5450	217	39	(	(	PUNCT
ejpam-5450	217	40	lε	lε	X
ejpam-5450	217	41	µ,min{ta	µ,min{ta	PROPN
ejpam-5450	217	42	,	,	PUNCT
ejpam-5450	217	43	tb})∈	tb})∈	PROPN
ejpam-5450	217	44	of	of	ADP
ejpam-5450	217	45	lε	lε	PRON
ejpam-5450	217	46	µ	µ	PROPN
ejpam-5450	217	47	is	be	AUX
ejpam-5450	217	48	a	a	DET
ejpam-5450	217	49	bcc	bcc	PROPN
ejpam-5450	217	50	-	-	PUNCT
ejpam-5450	217	51	ideal	ideal	NOUN
ejpam-5450	217	52	of	of	ADP
ejpam-5450	217	53	x	x	PUNCT
ejpam-5450	217	54	for	for	ADP
ejpam-5450	217	55	all	all	DET
ejpam-5450	217	56	ta	ta	NOUN
ejpam-5450	217	57	,	,	PUNCT
ejpam-5450	217	58	tb	tb	ADP
ejpam-5450	217	59	∈	∈	PROPN
ejpam-5450	217	60	(	(	PUNCT
ejpam-5450	217	61	0.5	0.5	NUM
ejpam-5450	217	62	,	,	PUNCT
ejpam-5450	217	63	1	1	NUM
ejpam-5450	217	64	]	]	PUNCT
ejpam-5450	217	65	.	.	PUNCT
ejpam-5450	218	1	proof	proof	NOUN
ejpam-5450	218	2	.	.	PUNCT
ejpam-5450	219	1	let	let	VERB
ejpam-5450	219	2	ta	ta	PART
ejpam-5450	219	3	,	,	PUNCT
ejpam-5450	219	4	tb	tb	ADP
ejpam-5450	219	5	∈	∈	PROPN
ejpam-5450	219	6	(	(	PUNCT
ejpam-5450	219	7	0.5	0.5	NUM
ejpam-5450	219	8	,	,	PUNCT
ejpam-5450	219	9	1	1	NUM
ejpam-5450	219	10	]	]	PUNCT
ejpam-5450	219	11	and	and	CCONJ
ejpam-5450	219	12	assume	assume	VERB
ejpam-5450	219	13	that	that	SCONJ
ejpam-5450	219	14	the	the	DET
ejpam-5450	219	15	∈-set	∈-set	NOUN
ejpam-5450	219	16	(	(	PUNCT
ejpam-5450	219	17	lε	lε	X
ejpam-5450	219	18	µ,min{ta	µ,min{ta	PROPN
ejpam-5450	219	19	,	,	PUNCT
ejpam-5450	219	20	tb})∈	tb})∈	PROPN
ejpam-5450	219	21	of	of	ADP
ejpam-5450	219	22	lε	lε	X
ejpam-5450	219	23	µ	µ	PROPN
ejpam-5450	219	24	is	be	AUX
ejpam-5450	219	25	nonempty	nonempty	ADJ
ejpam-5450	219	26	.	.	PUNCT
ejpam-5450	220	1	then	then	ADV
ejpam-5450	220	2	there	there	PRON
ejpam-5450	220	3	exists	exist	VERB
ejpam-5450	220	4	x	x	X
ejpam-5450	220	5	∈	∈	PROPN
ejpam-5450	220	6	(	(	PUNCT
ejpam-5450	220	7	lε	lε	X
ejpam-5450	220	8	µ,min{ta	µ,min{ta	PROPN
ejpam-5450	220	9	,	,	PUNCT
ejpam-5450	220	10	tb})∈	tb})∈	ADJ
ejpam-5450	220	11	,	,	PUNCT
ejpam-5450	220	12	and	and	CCONJ
ejpam-5450	221	1	so	so	ADV
ejpam-5450	221	2	lε	lε	ADP
ejpam-5450	221	3	µ(x	µ(x	NOUN
ejpam-5450	221	4	)	)	PUNCT
ejpam-5450	221	5	≥	≥	NOUN
ejpam-5450	221	6	min{ta	min{ta	X
ejpam-5450	221	7	,	,	PUNCT
ejpam-5450	221	8	tb	tb	ADP
ejpam-5450	221	9	}	}	PUNCT
ejpam-5450	221	10	>	>	X
ejpam-5450	221	11	1	1	NUM
ejpam-5450	221	12	−	−	NOUN
ejpam-5450	221	13	min{ta	min{ta	NOUN
ejpam-5450	221	14	,	,	PUNCT
ejpam-5450	221	15	tb	tb	NOUN
ejpam-5450	221	16	}	}	PUNCT
ejpam-5450	221	17	,	,	PUNCT
ejpam-5450	221	18	that	that	ADV
ejpam-5450	221	19	is	is	ADV
ejpam-5450	221	20	,	,	PUNCT
ejpam-5450	221	21	[	[	X
ejpam-5450	221	22	x	x	X
ejpam-5450	221	23	/	/	SYM
ejpam-5450	221	24	min{ta	min{ta	NUM
ejpam-5450	221	25	,	,	PUNCT
ejpam-5450	221	26	tb}]qlε	tb}]qlε	NOUN
ejpam-5450	221	27	µ.	µ.	NOUN
ejpam-5450	221	28	hence	hence	ADV
ejpam-5450	221	29	,	,	PUNCT
ejpam-5450	221	30	[	[	X
ejpam-5450	221	31	0	0	NUM
ejpam-5450	221	32	/	/	SYM
ejpam-5450	221	33	min{ta	min{ta	NUM
ejpam-5450	221	34	,	,	PUNCT
ejpam-5450	221	35	tb	tb	NOUN
ejpam-5450	221	36	}	}	PUNCT
ejpam-5450	221	37	]	]	PUNCT
ejpam-5450	221	38	∈	∈	PROPN
ejpam-5450	221	39	lε	lε	PRON
ejpam-5450	221	40	µ	µ	X
ejpam-5450	221	41	by	by	ADP
ejpam-5450	221	42	(	(	PUNCT
ejpam-5450	221	43	3.13	3.13	NUM
ejpam-5450	221	44	)	)	PUNCT
ejpam-5450	221	45	,	,	PUNCT
ejpam-5450	221	46	and	and	CCONJ
ejpam-5450	221	47	thus	thus	ADV
ejpam-5450	221	48	0	0	X
ejpam-5450	221	49	∈	∈	NOUN
ejpam-5450	221	50	(	(	PUNCT
ejpam-5450	221	51	lε	lε	X
ejpam-5450	221	52	µ,min{ta	µ,min{ta	PROPN
ejpam-5450	221	53	,	,	PUNCT
ejpam-5450	221	54	tb})∈.	tb})∈.	NUM
ejpam-5450	221	55	let	let	VERB
ejpam-5450	221	56	x	x	PRON
ejpam-5450	221	57	,	,	PUNCT
ejpam-5450	221	58	y	y	PROPN
ejpam-5450	221	59	,	,	PUNCT
ejpam-5450	221	60	z	z	NOUN
ejpam-5450	221	61	∈	∈	PROPN
ejpam-5450	221	62	x	x	AUX
ejpam-5450	221	63	be	be	AUX
ejpam-5450	221	64	such	such	ADJ
ejpam-5450	221	65	that	that	SCONJ
ejpam-5450	221	66	x	x	X
ejpam-5450	221	67	◦	◦	NOUN
ejpam-5450	221	68	(y	(y	NOUN
ejpam-5450	221	69	◦	◦	NOUN
ejpam-5450	221	70	z	z	NOUN
ejpam-5450	221	71	)	)	PUNCT
ejpam-5450	221	72	∈	∈	PROPN
ejpam-5450	221	73	(	(	PUNCT
ejpam-5450	221	74	lε	lε	X
ejpam-5450	221	75	µ,min{ta	µ,min{ta	PROPN
ejpam-5450	221	76	,	,	PUNCT
ejpam-5450	221	77	tb})∈	tb})∈	ADJ
ejpam-5450	221	78	and	and	CCONJ
ejpam-5450	221	79	y	y	PROPN
ejpam-5450	221	80	∈	∈	PROPN
ejpam-5450	221	81	(	(	PUNCT
ejpam-5450	221	82	lε	lε	X
ejpam-5450	221	83	µ,min{ta	µ,min{ta	PROPN
ejpam-5450	221	84	,	,	PUNCT
ejpam-5450	221	85	tb})∈.	tb})∈.	ADJ
ejpam-5450	221	86	then	then	ADV
ejpam-5450	221	87	lε	lε	ADP
ejpam-5450	221	88	µ(x	µ(x	ADJ
ejpam-5450	221	89	◦	◦	NOUN
ejpam-5450	221	90	(	(	PUNCT
ejpam-5450	221	91	y	y	PROPN
ejpam-5450	221	92	◦	◦	PROPN
ejpam-5450	221	93	z	z	PROPN
ejpam-5450	221	94	)	)	PUNCT
ejpam-5450	221	95	)	)	PUNCT
ejpam-5450	221	96	≥	≥	NOUN
ejpam-5450	221	97	min{ta	min{ta	X
ejpam-5450	221	98	,	,	PUNCT
ejpam-5450	221	99	tb	tb	ADP
ejpam-5450	221	100	}	}	PUNCT
ejpam-5450	221	101	>	>	X
ejpam-5450	221	102	1	1	NUM
ejpam-5450	221	103	−	−	NOUN
ejpam-5450	221	104	min{ta	min{ta	NOUN
ejpam-5450	221	105	,	,	PUNCT
ejpam-5450	221	106	tb	tb	NOUN
ejpam-5450	221	107	}	}	PUNCT
ejpam-5450	221	108	and	and	CCONJ
ejpam-5450	221	109	lε	lε	ADP
ejpam-5450	221	110	µ(y	µ(y	PROPN
ejpam-5450	221	111	)	)	PUNCT
ejpam-5450	221	112	≥	≥	NOUN
ejpam-5450	221	113	min{ta	min{ta	X
ejpam-5450	221	114	,	,	PUNCT
ejpam-5450	221	115	tb	tb	ADP
ejpam-5450	221	116	}	}	PUNCT
ejpam-5450	221	117	>	>	X
ejpam-5450	221	118	1−min{ta	1−min{ta	NUM
ejpam-5450	221	119	,	,	PUNCT
ejpam-5450	221	120	tb	tb	NOUN
ejpam-5450	221	121	}	}	PUNCT
ejpam-5450	221	122	,	,	PUNCT
ejpam-5450	221	123	that	that	ADV
ejpam-5450	221	124	is	is	ADV
ejpam-5450	221	125	,	,	PUNCT
ejpam-5450	221	126	[	[	X
ejpam-5450	221	127	(	(	PUNCT
ejpam-5450	221	128	x	x	X
ejpam-5450	221	129	◦	◦	NOUN
ejpam-5450	221	130	(	(	PUNCT
ejpam-5450	221	131	y	y	PROPN
ejpam-5450	221	132	◦	◦	NOUN
ejpam-5450	221	133	z))/min{ta	z))/min{ta	NUM
ejpam-5450	221	134	,	,	PUNCT
ejpam-5450	221	135	tb}]qlε	tb}]qlε	NOUN
ejpam-5450	221	136	µ	µ	NOUN
ejpam-5450	221	137	and	and	CCONJ
ejpam-5450	221	138	[	[	X
ejpam-5450	221	139	y	y	X
ejpam-5450	221	140	/	/	SYM
ejpam-5450	221	141	min{ta	min{ta	VERB
ejpam-5450	221	142	,	,	PUNCT
ejpam-5450	221	143	tb}]qlε	tb}]qlε	ADJ
ejpam-5450	221	144	µ.	µ.	NOUN
ejpam-5450	221	145	it	it	PRON
ejpam-5450	221	146	follows	follow	VERB
ejpam-5450	221	147	from	from	ADP
ejpam-5450	221	148	(	(	PUNCT
ejpam-5450	221	149	3.15	3.15	NUM
ejpam-5450	221	150	)	)	PUNCT
ejpam-5450	221	151	that	that	SCONJ
ejpam-5450	221	152	[	[	X
ejpam-5450	221	153	(	(	PUNCT
ejpam-5450	221	154	x	x	SYM
ejpam-5450	221	155	◦	◦	NOUN
ejpam-5450	221	156	z)/min{ta	z)/min{ta	PROPN
ejpam-5450	221	157	,	,	PUNCT
ejpam-5450	221	158	tb	tb	NOUN
ejpam-5450	221	159	}	}	PUNCT
ejpam-5450	221	160	]	]	PUNCT
ejpam-5450	221	161	∈	∈	PROPN
ejpam-5450	221	162	lε	lε	VERB
ejpam-5450	221	163	µ.	µ.	NOUN
ejpam-5450	221	164	hence	hence	ADV
ejpam-5450	221	165	,	,	PUNCT
ejpam-5450	221	166	x	x	PUNCT
ejpam-5450	221	167	◦	◦	NOUN
ejpam-5450	221	168	z	z	NOUN
ejpam-5450	221	169	∈	∈	PROPN
ejpam-5450	221	170	(	(	PUNCT
ejpam-5450	221	171	lε	lε	X
ejpam-5450	221	172	µ,min{ta	µ,min{ta	PROPN
ejpam-5450	221	173	,	,	PUNCT
ejpam-5450	221	174	tb})∈	tb})∈	ADJ
ejpam-5450	221	175	,	,	PUNCT
ejpam-5450	221	176	and	and	CCONJ
ejpam-5450	221	177	therefore	therefore	ADV
ejpam-5450	221	178	(	(	PUNCT
ejpam-5450	221	179	lε	lε	X
ejpam-5450	221	180	µ,min{ta	µ,min{ta	PROPN
ejpam-5450	221	181	,	,	PUNCT
ejpam-5450	221	182	tb})∈	tb})∈	PROPN
ejpam-5450	221	183	is	be	AUX
ejpam-5450	221	184	a	a	DET
ejpam-5450	221	185	bcc	bcc	PROPN
ejpam-5450	221	186	-	-	PUNCT
ejpam-5450	221	187	ideal	ideal	NOUN
ejpam-5450	221	188	of	of	ADP
ejpam-5450	221	189	x	x	PUNCT
ejpam-5450	221	190	for	for	ADP
ejpam-5450	221	191	all	all	DET
ejpam-5450	221	192	ta	ta	NOUN
ejpam-5450	221	193	,	,	PUNCT
ejpam-5450	221	194	tb	tb	ADP
ejpam-5450	221	195	∈	∈	PROPN
ejpam-5450	221	196	(	(	PUNCT
ejpam-5450	221	197	0.5	0.5	NUM
ejpam-5450	221	198	,	,	PUNCT
ejpam-5450	221	199	1	1	NUM
ejpam-5450	221	200	]	]	PUNCT
ejpam-5450	221	201	.	.	PUNCT
ejpam-5450	222	1	theorem	theorem	ADJ
ejpam-5450	222	2	8	8	NUM
ejpam-5450	222	3	.	.	PUNCT
ejpam-5450	223	1	if	if	SCONJ
ejpam-5450	223	2	an	an	DET
ejpam-5450	223	3	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	223	4	fuzzy	fuzzy	ADJ
ejpam-5450	223	5	set	set	VERB
ejpam-5450	223	6	lε	lε	PRON
ejpam-5450	223	7	µ	µ	NOUN
ejpam-5450	223	8	in	in	ADP
ejpam-5450	223	9	x	x	PART
ejpam-5450	223	10	satisfies	satisfie	NOUN
ejpam-5450	223	11	the	the	DET
ejpam-5450	223	12	conditions	condition	NOUN
ejpam-5450	223	13	(	(	PUNCT
ejpam-5450	223	14	3.13	3.13	NUM
ejpam-5450	223	15	)	)	PUNCT
ejpam-5450	223	16	and	and	CCONJ
ejpam-5450	223	17	(	(	PUNCT
ejpam-5450	223	18	∀x	∀x	X
ejpam-5450	223	19	∈	∈	PROPN
ejpam-5450	223	20	x,∀t	x,∀t	X
ejpam-5450	223	21	∈	∈	PROPN
ejpam-5450	223	22	(	(	PUNCT
ejpam-5450	223	23	0.5	0.5	NUM
ejpam-5450	223	24	,	,	PUNCT
ejpam-5450	223	25	1])([x	1])([x	NUM
ejpam-5450	223	26	/	/	SYM
ejpam-5450	223	27	t]qlε	t]qlε	X
ejpam-5450	223	28	µ	µ	ADJ
ejpam-5450	223	29	⇒	⇒	NOUN
ejpam-5450	224	1	[	[	X
ejpam-5450	224	2	0	0	NUM
ejpam-5450	224	3	/	/	SYM
ejpam-5450	224	4	t	t	PROPN
ejpam-5450	224	5	]	]	X
ejpam-5450	224	6	∈	∈	PROPN
ejpam-5450	224	7	(	(	PUNCT
ejpam-5450	224	8	lε	lε	X
ejpam-5450	224	9	µ	µ	NUM
ejpam-5450	224	10	)	)	PUNCT
ejpam-5450	224	11	)	)	PUNCT
ejpam-5450	224	12	(	(	PUNCT
ejpam-5450	224	13	3.16	3.16	NUM
ejpam-5450	224	14	)	)	PUNCT
ejpam-5450	224	15	(	(	PUNCT
ejpam-5450	224	16	∀x	∀x	X
ejpam-5450	224	17	,	,	PUNCT
ejpam-5450	224	18	y	y	PROPN
ejpam-5450	224	19	,	,	PUNCT
ejpam-5450	224	20	z	z	PROPN
ejpam-5450	224	21	∈	∈	PROPN
ejpam-5450	224	22	x,∀ta	x,∀ta	NOUN
ejpam-5450	224	23	,	,	PUNCT
ejpam-5450	224	24	tb	tb	ADP
ejpam-5450	224	25	∈	∈	PROPN
ejpam-5450	224	26	(	(	PUNCT
ejpam-5450	224	27	0.5	0.5	NUM
ejpam-5450	224	28	,	,	PUNCT
ejpam-5450	224	29	1	1	NUM
ejpam-5450	224	30	]	]	PUNCT
ejpam-5450	224	31	)	)	PUNCT
ejpam-5450	224	32	(	(	PUNCT
ejpam-5450	224	33	[	[	X
ejpam-5450	224	34	x	x	X
ejpam-5450	224	35	◦	◦	NOUN
ejpam-5450	224	36	(	(	PUNCT
ejpam-5450	224	37	y	y	NOUN
ejpam-5450	224	38	◦	◦	VERB
ejpam-5450	224	39	z)/ta]qlε	z)/ta]qlε	NOUN
ejpam-5450	224	40	µ	µ	X
ejpam-5450	224	41	,	,	PUNCT
ejpam-5450	224	42	[	[	X
ejpam-5450	224	43	y	y	X
ejpam-5450	224	44	/	/	SYM
ejpam-5450	224	45	tb]ql	tb]ql	NOUN
ejpam-5450	224	46	ε	ε	PROPN
ejpam-5450	224	47	µ	µ	PRON
ejpam-5450	224	48	⇒	⇒	NOUN
ejpam-5450	225	1	[	[	X
ejpam-5450	225	2	(	(	PUNCT
ejpam-5450	225	3	x	x	SYM
ejpam-5450	225	4	◦	◦	NOUN
ejpam-5450	225	5	z)/min{ta	z)/min{ta	PROPN
ejpam-5450	225	6	,	,	PUNCT
ejpam-5450	225	7	tb	tb	NOUN
ejpam-5450	225	8	}	}	PUNCT
ejpam-5450	225	9	]	]	PUNCT
ejpam-5450	225	10	∈	∈	PROPN
ejpam-5450	225	11	lε	lε	ADP
ejpam-5450	225	12	µ	µ	NOUN
ejpam-5450	225	13	)	)	PUNCT
ejpam-5450	225	14	(	(	PUNCT
ejpam-5450	225	15	3.17	3.17	NUM
ejpam-5450	225	16	)	)	PUNCT
ejpam-5450	225	17	then	then	ADV
ejpam-5450	225	18	the	the	DET
ejpam-5450	225	19	nonempty	nonempty	ADJ
ejpam-5450	225	20	∈-set	∈-set	NOUN
ejpam-5450	225	21	(	(	PUNCT
ejpam-5450	225	22	lε	lε	X
ejpam-5450	225	23	µ,max{ta	µ,max{ta	PROPN
ejpam-5450	225	24	,	,	PUNCT
ejpam-5450	225	25	tb})∈	tb})∈	PROPN
ejpam-5450	225	26	of	of	ADP
ejpam-5450	225	27	lε	lε	X
ejpam-5450	225	28	µ	µ	PROPN
ejpam-5450	225	29	is	be	AUX
ejpam-5450	225	30	a	a	DET
ejpam-5450	225	31	bcc	bcc	PROPN
ejpam-5450	225	32	-	-	PUNCT
ejpam-5450	225	33	ideal	ideal	NOUN
ejpam-5450	225	34	of	of	ADP
ejpam-5450	225	35	x	x	PUNCT
ejpam-5450	225	36	for	for	ADP
ejpam-5450	225	37	all	all	DET
ejpam-5450	225	38	ta	ta	NOUN
ejpam-5450	225	39	,	,	PUNCT
ejpam-5450	225	40	tb	tb	ADP
ejpam-5450	225	41	∈	∈	PROPN
ejpam-5450	225	42	(	(	PUNCT
ejpam-5450	225	43	0.5	0.5	NUM
ejpam-5450	225	44	,	,	PUNCT
ejpam-5450	225	45	1	1	NUM
ejpam-5450	225	46	]	]	PUNCT
ejpam-5450	225	47	.	.	PUNCT
ejpam-5450	226	1	proof	proof	NOUN
ejpam-5450	226	2	.	.	PUNCT
ejpam-5450	227	1	let	let	VERB
ejpam-5450	227	2	y	y	PROPN
ejpam-5450	227	3	∈	∈	PROPN
ejpam-5450	227	4	(	(	PUNCT
ejpam-5450	227	5	lε	lε	X
ejpam-5450	227	6	µ,max{ta	µ,max{ta	PROPN
ejpam-5450	227	7	,	,	PUNCT
ejpam-5450	227	8	tb})∈	tb})∈	ADJ
ejpam-5450	227	9	for	for	ADP
ejpam-5450	227	10	ta	ta	PROPN
ejpam-5450	227	11	,	,	PUNCT
ejpam-5450	227	12	tb	tb	ADP
ejpam-5450	227	13	∈	∈	PROPN
ejpam-5450	227	14	(	(	PUNCT
ejpam-5450	227	15	0.5	0.5	NUM
ejpam-5450	227	16	,	,	PUNCT
ejpam-5450	227	17	1	1	NUM
ejpam-5450	227	18	]	]	PUNCT
ejpam-5450	227	19	.	.	PUNCT
ejpam-5450	228	1	then	then	ADV
ejpam-5450	228	2	lε	lε	PROPN
ejpam-5450	228	3	µ(y	µ(y	PROPN
ejpam-5450	228	4	)	)	PUNCT
ejpam-5450	228	5	≥	≥	NOUN
ejpam-5450	228	6	max{ta	max{ta	NOUN
ejpam-5450	228	7	,	,	PUNCT
ejpam-5450	228	8	tb	tb	NOUN
ejpam-5450	228	9	}	}	PUNCT
ejpam-5450	228	10	>	>	X
ejpam-5450	228	11	1	1	NUM
ejpam-5450	228	12	−	−	NOUN
ejpam-5450	228	13	max{ta	max{ta	NOUN
ejpam-5450	228	14	,	,	PUNCT
ejpam-5450	228	15	tb	tb	NOUN
ejpam-5450	228	16	}	}	PUNCT
ejpam-5450	228	17	,	,	PUNCT
ejpam-5450	228	18	and	and	CCONJ
ejpam-5450	228	19	so	so	ADV
ejpam-5450	228	20	[	[	X
ejpam-5450	228	21	y	y	NOUN
ejpam-5450	228	22	/	/	SYM
ejpam-5450	228	23	max{ta	max{ta	NOUN
ejpam-5450	228	24	,	,	PUNCT
ejpam-5450	228	25	tb}]qlε	tb}]qlε	NOUN
ejpam-5450	228	26	µ.	µ.	NOUN
ejpam-5450	228	27	hence	hence	ADV
ejpam-5450	228	28	,	,	PUNCT
ejpam-5450	228	29	[	[	X
ejpam-5450	228	30	(	(	PUNCT
ejpam-5450	228	31	x	x	SYM
ejpam-5450	228	32	◦	◦	NOUN
ejpam-5450	228	33	y)/max{ta	y)/max{ta	X
ejpam-5450	228	34	,	,	PUNCT
ejpam-5450	228	35	tb	tb	NOUN
ejpam-5450	228	36	}	}	PUNCT
ejpam-5450	228	37	]	]	PUNCT
ejpam-5450	228	38	∈	∈	PROPN
ejpam-5450	228	39	lε	lε	VERB
ejpam-5450	228	40	µ	µ	NOUN
ejpam-5450	228	41	for	for	ADP
ejpam-5450	228	42	all	all	DET
ejpam-5450	228	43	x	x	SYM
ejpam-5450	228	44	∈	∈	PROPN
ejpam-5450	228	45	x	x	PUNCT
ejpam-5450	228	46	by	by	ADP
ejpam-5450	228	47	(	(	PUNCT
ejpam-5450	228	48	3.16	3.16	NUM
ejpam-5450	228	49	)	)	PUNCT
ejpam-5450	228	50	,	,	PUNCT
ejpam-5450	228	51	which	which	PRON
ejpam-5450	228	52	implies	imply	VERB
ejpam-5450	228	53	that	that	SCONJ
ejpam-5450	228	54	x	x	PUNCT
ejpam-5450	228	55	◦	◦	VERB
ejpam-5450	228	56	y	y	PROPN
ejpam-5450	228	57	∈	∈	PROPN
ejpam-5450	228	58	(	(	PUNCT
ejpam-5450	228	59	lε	lε	X
ejpam-5450	228	60	µ,max{ta	µ,max{ta	PROPN
ejpam-5450	228	61	,	,	PUNCT
ejpam-5450	228	62	tb})∈	tb})∈	ADJ
ejpam-5450	228	63	for	for	ADP
ejpam-5450	228	64	all	all	DET
ejpam-5450	228	65	x	x	SYM
ejpam-5450	228	66	∈	∈	NOUN
ejpam-5450	228	67	x.	x.	NOUN
ejpam-5450	228	68	let	let	VERB
ejpam-5450	228	69	x	x	PRON
ejpam-5450	228	70	,	,	PUNCT
ejpam-5450	228	71	y	y	PROPN
ejpam-5450	228	72	∈	∈	PROPN
ejpam-5450	228	73	a.	a.	NOUN
ejpam-5450	228	74	iampan	iampan	PROPN
ejpam-5450	228	75	,	,	PUNCT
ejpam-5450	228	76	r.	r.	PROPN
ejpam-5450	228	77	subasini	subasini	PROPN
ejpam-5450	228	78	,	,	PUNCT
ejpam-5450	228	79	n.	n.	PROPN
ejpam-5450	228	80	rajesh	rajesh	PROPN
ejpam-5450	228	81	/	/	SYM
ejpam-5450	228	82	eur	eur	PROPN
ejpam-5450	228	83	.	.	PUNCT
ejpam-5450	229	1	j.	j.	PROPN
ejpam-5450	229	2	pure	pure	PROPN
ejpam-5450	229	3	appl	appl	PROPN
ejpam-5450	229	4	.	.	PROPN
ejpam-5450	229	5	math	math	PROPN
ejpam-5450	229	6	,	,	PUNCT
ejpam-5450	229	7	17	17	NUM
ejpam-5450	229	8	(	(	PUNCT
ejpam-5450	229	9	4	4	NUM
ejpam-5450	229	10	)	)	PUNCT
ejpam-5450	229	11	(	(	PUNCT
ejpam-5450	229	12	2024	2024	NUM
ejpam-5450	229	13	)	)	PUNCT
ejpam-5450	229	14	,	,	PUNCT
ejpam-5450	229	15	3209	3209	NUM
ejpam-5450	229	16	-	-	SYM
ejpam-5450	229	17	3222	3222	NUM
ejpam-5450	229	18	3219	3219	NUM
ejpam-5450	229	19	(	(	PUNCT
ejpam-5450	229	20	lε	lε	X
ejpam-5450	229	21	µ,max{ta	µ,max{ta	PROPN
ejpam-5450	229	22	,	,	PUNCT
ejpam-5450	229	23	tb})∈	tb})∈	ADJ
ejpam-5450	229	24	for	for	ADP
ejpam-5450	229	25	ta	ta	PROPN
ejpam-5450	229	26	,	,	PUNCT
ejpam-5450	229	27	tb	tb	ADP
ejpam-5450	229	28	∈	∈	PROPN
ejpam-5450	229	29	(	(	PUNCT
ejpam-5450	229	30	0.5	0.5	NUM
ejpam-5450	229	31	,	,	PUNCT
ejpam-5450	229	32	1	1	NUM
ejpam-5450	229	33	]	]	PUNCT
ejpam-5450	229	34	.	.	PUNCT
ejpam-5450	230	1	then	then	ADV
ejpam-5450	230	2	lε	lε	X
ejpam-5450	230	3	µ(x	µ(x	NOUN
ejpam-5450	230	4	)	)	PUNCT
ejpam-5450	230	5	≥	≥	NOUN
ejpam-5450	230	6	max{ta	max{ta	NOUN
ejpam-5450	230	7	,	,	PUNCT
ejpam-5450	230	8	tb	tb	NOUN
ejpam-5450	230	9	}	}	PUNCT
ejpam-5450	230	10	>	>	X
ejpam-5450	230	11	1	1	NUM
ejpam-5450	230	12	−	−	NOUN
ejpam-5450	230	13	max{ta	max{ta	NOUN
ejpam-5450	230	14	,	,	PUNCT
ejpam-5450	230	15	tb	tb	NOUN
ejpam-5450	230	16	}	}	PUNCT
ejpam-5450	230	17	and	and	CCONJ
ejpam-5450	230	18	lε	lε	ADP
ejpam-5450	230	19	µ(y	µ(y	PROPN
ejpam-5450	230	20	)	)	PUNCT
ejpam-5450	230	21	≥	≥	NOUN
ejpam-5450	230	22	max{ta	max{ta	NOUN
ejpam-5450	230	23	,	,	PUNCT
ejpam-5450	230	24	tb	tb	ADP
ejpam-5450	230	25	}	}	PUNCT
ejpam-5450	230	26	>	>	X
ejpam-5450	230	27	1−max{ta	1−max{ta	PROPN
ejpam-5450	230	28	,	,	PUNCT
ejpam-5450	230	29	tb	tb	NOUN
ejpam-5450	230	30	}	}	PUNCT
ejpam-5450	230	31	,	,	PUNCT
ejpam-5450	230	32	that	that	ADV
ejpam-5450	230	33	is	is	ADV
ejpam-5450	230	34	,	,	PUNCT
ejpam-5450	230	35	[	[	X
ejpam-5450	230	36	x	x	X
ejpam-5450	230	37	/	/	SYM
ejpam-5450	230	38	max{ta	max{ta	ADJ
ejpam-5450	230	39	,	,	PUNCT
ejpam-5450	230	40	tb}]qlε	tb}]qlε	NOUN
ejpam-5450	230	41	µ	µ	NOUN
ejpam-5450	230	42	and	and	CCONJ
ejpam-5450	230	43	[	[	X
ejpam-5450	230	44	y	y	NOUN
ejpam-5450	230	45	/	/	SYM
ejpam-5450	230	46	max{ta	max{ta	NOUN
ejpam-5450	230	47	,	,	PUNCT
ejpam-5450	230	48	tb}]qlε	tb}]qlε	ADJ
ejpam-5450	230	49	µ.	µ.	NOUN
ejpam-5450	230	50	it	it	PRON
ejpam-5450	230	51	follows	follow	VERB
ejpam-5450	230	52	from	from	ADP
ejpam-5450	230	53	(	(	PUNCT
ejpam-5450	230	54	3.17	3.17	NUM
ejpam-5450	230	55	)	)	PUNCT
ejpam-5450	230	56	that	that	SCONJ
ejpam-5450	231	1	[	[	X
ejpam-5450	231	2	(	(	PUNCT
ejpam-5450	231	3	x	x	X
ejpam-5450	231	4	◦	◦	NOUN
ejpam-5450	231	5	(	(	PUNCT
ejpam-5450	231	6	y	y	PROPN
ejpam-5450	231	7	◦	◦	NOUN
ejpam-5450	231	8	z)/max{ta	z)/max{ta	PROPN
ejpam-5450	231	9	,	,	PUNCT
ejpam-5450	231	10	tb	tb	NOUN
ejpam-5450	231	11	}	}	PUNCT
ejpam-5450	231	12	]	]	PUNCT
ejpam-5450	231	13	∈	∈	PROPN
ejpam-5450	231	14	lε	lε	VERB
ejpam-5450	231	15	µ	µ	NOUN
ejpam-5450	231	16	for	for	ADP
ejpam-5450	231	17	all	all	DET
ejpam-5450	231	18	z	z	NOUN
ejpam-5450	231	19	∈	∈	NOUN
ejpam-5450	231	20	x.	x.	NOUN
ejpam-5450	231	21	hence	hence	ADV
ejpam-5450	231	22	,	,	PUNCT
ejpam-5450	231	23	x	x	X
ejpam-5450	231	24	◦	◦	NOUN
ejpam-5450	231	25	(	(	PUNCT
ejpam-5450	231	26	y	y	PROPN
ejpam-5450	231	27	◦	◦	PROPN
ejpam-5450	231	28	z	z	NOUN
ejpam-5450	231	29	)	)	PUNCT
ejpam-5450	231	30	∈	∈	PROPN
ejpam-5450	231	31	(	(	PUNCT
ejpam-5450	231	32	lε	lε	X
ejpam-5450	231	33	µ,max{ta	µ,max{ta	PROPN
ejpam-5450	231	34	,	,	PUNCT
ejpam-5450	231	35	tb})∈	tb})∈	ADJ
ejpam-5450	231	36	for	for	ADP
ejpam-5450	231	37	all	all	DET
ejpam-5450	231	38	z	z	NOUN
ejpam-5450	231	39	∈	∈	NOUN
ejpam-5450	231	40	x.	x.	NOUN
ejpam-5450	231	41	therefore	therefore	ADV
ejpam-5450	231	42	,	,	PUNCT
ejpam-5450	231	43	(	(	PUNCT
ejpam-5450	231	44	lε	lε	X
ejpam-5450	231	45	µ,max{ta	µ,max{ta	PROPN
ejpam-5450	231	46	,	,	PUNCT
ejpam-5450	231	47	tb})∈	tb})∈	PROPN
ejpam-5450	231	48	of	of	ADP
ejpam-5450	231	49	lε	lε	X
ejpam-5450	231	50	µ	µ	PROPN
ejpam-5450	231	51	is	be	AUX
ejpam-5450	231	52	a	a	DET
ejpam-5450	231	53	bcc	bcc	PROPN
ejpam-5450	231	54	-	-	PUNCT
ejpam-5450	231	55	ideal	ideal	NOUN
ejpam-5450	231	56	of	of	ADP
ejpam-5450	231	57	x	x	PUNCT
ejpam-5450	231	58	for	for	ADP
ejpam-5450	231	59	all	all	DET
ejpam-5450	231	60	ta	ta	NOUN
ejpam-5450	231	61	,	,	PUNCT
ejpam-5450	231	62	tb	tb	ADP
ejpam-5450	231	63	∈	∈	PROPN
ejpam-5450	231	64	(	(	PUNCT
ejpam-5450	231	65	0.5	0.5	NUM
ejpam-5450	231	66	,	,	PUNCT
ejpam-5450	231	67	1	1	NUM
ejpam-5450	231	68	]	]	PUNCT
ejpam-5450	231	69	.	.	PUNCT
ejpam-5450	232	1	lemma	lemma	PROPN
ejpam-5450	232	2	1	1	NUM
ejpam-5450	232	3	.	.	PUNCT
ejpam-5450	233	1	every	every	DET
ejpam-5450	233	2	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	233	3	fuzzy	fuzzy	ADJ
ejpam-5450	233	4	ideal	ideal	NOUN
ejpam-5450	233	5	lε	lε	ADP
ejpam-5450	233	6	µ	µ	PROPN
ejpam-5450	233	7	of	of	ADP
ejpam-5450	233	8	x	x	VERB
ejpam-5450	233	9	satisfies	satisfie	NOUN
ejpam-5450	233	10	the	the	DET
ejpam-5450	233	11	following	follow	VERB
ejpam-5450	233	12	property	property	NOUN
ejpam-5450	233	13	:	:	PUNCT
ejpam-5450	233	14	(	(	PUNCT
ejpam-5450	233	15	∀x	∀x	X
ejpam-5450	233	16	,	,	PUNCT
ejpam-5450	233	17	y	y	PROPN
ejpam-5450	233	18	,	,	PUNCT
ejpam-5450	233	19	z	z	PROPN
ejpam-5450	233	20	∈	∈	PROPN
ejpam-5450	233	21	x)(lε	x)(lε	NOUN
ejpam-5450	233	22	µ(x	µ(x	PUNCT
ejpam-5450	233	23	◦	◦	NOUN
ejpam-5450	233	24	z	z	NOUN
ejpam-5450	233	25	)	)	PUNCT
ejpam-5450	233	26	≥	≥	NOUN
ejpam-5450	233	27	max{lε	max{lε	PUNCT
ejpam-5450	233	28	µ(x	µ(x	VERB
ejpam-5450	233	29	◦	◦	NOUN
ejpam-5450	233	30	(	(	PUNCT
ejpam-5450	233	31	y	y	PROPN
ejpam-5450	233	32	◦	◦	PROPN
ejpam-5450	233	33	z	z	PROPN
ejpam-5450	233	34	)	)	PUNCT
ejpam-5450	233	35	)	)	PUNCT
ejpam-5450	233	36	,	,	PUNCT
ejpam-5450	233	37	lε	lε	X
ejpam-5450	233	38	µ(y	µ(y	PROPN
ejpam-5450	233	39	)	)	PUNCT
ejpam-5450	233	40	}	}	PUNCT
ejpam-5450	233	41	)	)	PUNCT
ejpam-5450	233	42	proof	proof	NOUN
ejpam-5450	233	43	.	.	PUNCT
ejpam-5450	234	1	note	note	VERB
ejpam-5450	234	2	that	that	SCONJ
ejpam-5450	234	3	[	[	X
ejpam-5450	234	4	(	(	PUNCT
ejpam-5450	234	5	x	x	SYM
ejpam-5450	234	6	◦	◦	NOUN
ejpam-5450	234	7	(	(	PUNCT
ejpam-5450	234	8	y	y	PROPN
ejpam-5450	234	9	◦	◦	NOUN
ejpam-5450	234	10	z))/lε	z))/lε	PUNCT
ejpam-5450	234	11	µ(x	µ(x	ADJ
ejpam-5450	234	12	◦	◦	NOUN
ejpam-5450	234	13	(	(	PUNCT
ejpam-5450	234	14	y	y	PROPN
ejpam-5450	234	15	◦	◦	PROPN
ejpam-5450	234	16	z	z	PROPN
ejpam-5450	234	17	)	)	PUNCT
ejpam-5450	234	18	)	)	PUNCT
ejpam-5450	234	19	]	]	PUNCT
ejpam-5450	235	1	∈	∈	PROPN
ejpam-5450	235	2	lε	lε	ADP
ejpam-5450	235	3	µ	µ	NOUN
ejpam-5450	235	4	and	and	CCONJ
ejpam-5450	235	5	[	[	X
ejpam-5450	235	6	y	y	X
ejpam-5450	235	7	/	/	SYM
ejpam-5450	235	8	lε	lε	X
ejpam-5450	235	9	µ(y	µ(y	PROPN
ejpam-5450	235	10	)	)	PUNCT
ejpam-5450	235	11	]	]	PUNCT
ejpam-5450	236	1	∈	∈	PROPN
ejpam-5450	236	2	lε	lε	VERB
ejpam-5450	236	3	µ	µ	NOUN
ejpam-5450	236	4	for	for	ADP
ejpam-5450	236	5	all	all	DET
ejpam-5450	236	6	x	x	NOUN
ejpam-5450	236	7	,	,	PUNCT
ejpam-5450	236	8	y	y	PROPN
ejpam-5450	236	9	,	,	PUNCT
ejpam-5450	236	10	z	z	NOUN
ejpam-5450	236	11	∈	∈	PROPN
ejpam-5450	236	12	x.	x.	NOUN
ejpam-5450	237	1	it	it	PRON
ejpam-5450	237	2	follows	follow	VERB
ejpam-5450	237	3	that	that	SCONJ
ejpam-5450	237	4	[	[	X
ejpam-5450	237	5	(	(	PUNCT
ejpam-5450	237	6	x	x	SYM
ejpam-5450	237	7	◦	◦	NOUN
ejpam-5450	237	8	z)/min{lε	z)/min{lε	NOUN
ejpam-5450	237	9	µ(x	µ(x	ADJ
ejpam-5450	237	10	◦	◦	NOUN
ejpam-5450	237	11	(	(	PUNCT
ejpam-5450	237	12	y	y	PROPN
ejpam-5450	237	13	◦	◦	PROPN
ejpam-5450	237	14	z	z	PROPN
ejpam-5450	237	15	)	)	PUNCT
ejpam-5450	237	16	)	)	PUNCT
ejpam-5450	237	17	,	,	PUNCT
ejpam-5450	237	18	lε	lε	X
ejpam-5450	237	19	µ(y	µ(y	PROPN
ejpam-5450	237	20	)	)	PUNCT
ejpam-5450	237	21	}	}	PUNCT
ejpam-5450	237	22	]	]	PUNCT
ejpam-5450	238	1	∈	∈	PROPN
ejpam-5450	238	2	lε	lε	ADP
ejpam-5450	238	3	µ	µ	NOUN
ejpam-5450	238	4	,	,	PUNCT
ejpam-5450	238	5	that	that	ADV
ejpam-5450	238	6	is	is	ADV
ejpam-5450	238	7	,	,	PUNCT
ejpam-5450	238	8	lε	lε	ADP
ejpam-5450	238	9	µ(x	µ(x	PUNCT
ejpam-5450	238	10	◦	◦	NOUN
ejpam-5450	238	11	z	z	NOUN
ejpam-5450	238	12	)	)	PUNCT
ejpam-5450	238	13	≥	≥	NOUN
ejpam-5450	238	14	min{lε	min{lε	NUM
ejpam-5450	238	15	µ(x	µ(x	ADJ
ejpam-5450	238	16	◦	◦	NOUN
ejpam-5450	238	17	(	(	PUNCT
ejpam-5450	238	18	y	y	PROPN
ejpam-5450	238	19	◦	◦	PROPN
ejpam-5450	238	20	z	z	PROPN
ejpam-5450	238	21	)	)	PUNCT
ejpam-5450	238	22	)	)	PUNCT
ejpam-5450	238	23	,	,	PUNCT
ejpam-5450	238	24	lε	lε	X
ejpam-5450	238	25	µ(y	µ(y	PROPN
ejpam-5450	238	26	)	)	PUNCT
ejpam-5450	238	27	}	}	PUNCT
ejpam-5450	238	28	for	for	ADP
ejpam-5450	238	29	all	all	DET
ejpam-5450	238	30	x	x	NOUN
ejpam-5450	238	31	,	,	PUNCT
ejpam-5450	238	32	y	y	PROPN
ejpam-5450	238	33	,	,	PUNCT
ejpam-5450	238	34	z	z	PROPN
ejpam-5450	238	35	∈	∈	PROPN
ejpam-5450	238	36	x.	x.	NOUN
ejpam-5450	238	37	theorem	theorem	VERB
ejpam-5450	238	38	9	9	NUM
ejpam-5450	238	39	.	.	PUNCT
ejpam-5450	239	1	if	if	SCONJ
ejpam-5450	239	2	an	an	DET
ejpam-5450	239	3	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	239	4	fuzzy	fuzzy	ADJ
ejpam-5450	239	5	set	set	VERB
ejpam-5450	239	6	lε	lε	PRON
ejpam-5450	239	7	µ	µ	NOUN
ejpam-5450	239	8	in	in	ADP
ejpam-5450	239	9	x	x	PART
ejpam-5450	239	10	satisfies	satisfie	NOUN
ejpam-5450	239	11	the	the	DET
ejpam-5450	239	12	following	follow	VERB
ejpam-5450	239	13	properties	property	NOUN
ejpam-5450	239	14	:	:	PUNCT
ejpam-5450	239	15	(	(	PUNCT
ejpam-5450	239	16	∀x	∀x	X
ejpam-5450	239	17	∈	∈	PROPN
ejpam-5450	239	18	x,∀t	x,∀t	X
ejpam-5450	239	19	∈	∈	PROPN
ejpam-5450	239	20	(	(	PUNCT
ejpam-5450	239	21	0.5	0.5	NUM
ejpam-5450	239	22	,	,	PUNCT
ejpam-5450	239	23	1])([x	1])([x	NUM
ejpam-5450	239	24	/	/	SYM
ejpam-5450	239	25	t]qlε	t]qlε	X
ejpam-5450	239	26	µ	µ	ADJ
ejpam-5450	239	27	⇒	⇒	NOUN
ejpam-5450	239	28	[	[	X
ejpam-5450	239	29	0	0	NUM
ejpam-5450	239	30	/	/	SYM
ejpam-5450	239	31	t	t	PROPN
ejpam-5450	239	32	]	]	X
ejpam-5450	239	33	∈	∈	PROPN
ejpam-5450	239	34	(	(	PUNCT
ejpam-5450	239	35	lε	lε	X
ejpam-5450	239	36	µ	µ	NUM
ejpam-5450	239	37	)	)	PUNCT
ejpam-5450	239	38	)	)	PUNCT
ejpam-5450	239	39	(	(	PUNCT
ejpam-5450	239	40	3.18	3.18	NUM
ejpam-5450	239	41	)	)	PUNCT
ejpam-5450	239	42	(	(	PUNCT
ejpam-5450	239	43	∀x	∀x	X
ejpam-5450	239	44	,	,	PUNCT
ejpam-5450	239	45	y	y	PROPN
ejpam-5450	239	46	,	,	PUNCT
ejpam-5450	239	47	z	z	PROPN
ejpam-5450	239	48	∈	∈	PROPN
ejpam-5450	239	49	x,∀ta	x,∀ta	NOUN
ejpam-5450	239	50	,	,	PUNCT
ejpam-5450	239	51	tb	tb	ADP
ejpam-5450	239	52	∈	∈	PROPN
ejpam-5450	239	53	(	(	PUNCT
ejpam-5450	239	54	0.5	0.5	NUM
ejpam-5450	239	55	,	,	PUNCT
ejpam-5450	239	56	1	1	NUM
ejpam-5450	239	57	]	]	PUNCT
ejpam-5450	239	58	)	)	PUNCT
ejpam-5450	240	1	(	(	PUNCT
ejpam-5450	240	2	[	[	X
ejpam-5450	240	3	x	x	X
ejpam-5450	240	4	◦	◦	NOUN
ejpam-5450	240	5	(	(	PUNCT
ejpam-5450	240	6	y	y	NOUN
ejpam-5450	240	7	◦	◦	NOUN
ejpam-5450	240	8	z)/ta	z)/ta	NOUN
ejpam-5450	240	9	]	]	X
ejpam-5450	240	10	∈	∈	PROPN
ejpam-5450	240	11	lε	lε	X
ejpam-5450	240	12	µ	µ	NOUN
ejpam-5450	240	13	,	,	PUNCT
ejpam-5450	240	14	[	[	X
ejpam-5450	240	15	y	y	X
ejpam-5450	240	16	/	/	SYM
ejpam-5450	240	17	tb	tb	NOUN
ejpam-5450	240	18	]	]	PUNCT
ejpam-5450	240	19	∈	∈	PROPN
ejpam-5450	240	20	lε	lε	X
ejpam-5450	240	21	µ	µ	X
ejpam-5450	240	22	⇒	⇒	NOUN
ejpam-5450	240	23	[	[	X
ejpam-5450	240	24	(	(	PUNCT
ejpam-5450	240	25	x	x	SYM
ejpam-5450	240	26	◦	◦	NOUN
ejpam-5450	240	27	z)/min{ta	z)/min{ta	PROPN
ejpam-5450	240	28	,	,	PUNCT
ejpam-5450	240	29	tb}]qlε	tb}]qlε	NOUN
ejpam-5450	240	30	µ	µ	NOUN
ejpam-5450	240	31	)	)	PUNCT
ejpam-5450	240	32	(	(	PUNCT
ejpam-5450	240	33	3.19	3.19	NUM
ejpam-5450	240	34	)	)	PUNCT
ejpam-5450	240	35	then	then	ADV
ejpam-5450	240	36	the	the	DET
ejpam-5450	240	37	nonempty	nonempty	ADJ
ejpam-5450	240	38	q	q	NOUN
ejpam-5450	240	39	-	-	PUNCT
ejpam-5450	240	40	set	set	ADJ
ejpam-5450	240	41	(	(	PUNCT
ejpam-5450	240	42	lε	lε	X
ejpam-5450	240	43	µ,min{ta	µ,min{ta	PROPN
ejpam-5450	240	44	,	,	PUNCT
ejpam-5450	240	45	tb})q	tb})q	PROPN
ejpam-5450	240	46	of	of	ADP
ejpam-5450	240	47	lε	lε	PRON
ejpam-5450	240	48	µ	µ	PROPN
ejpam-5450	240	49	is	be	AUX
ejpam-5450	240	50	a	a	DET
ejpam-5450	240	51	bcc	bcc	PROPN
ejpam-5450	240	52	-	-	PUNCT
ejpam-5450	240	53	ideal	ideal	NOUN
ejpam-5450	240	54	of	of	ADP
ejpam-5450	240	55	x	x	PUNCT
ejpam-5450	240	56	for	for	ADP
ejpam-5450	240	57	all	all	DET
ejpam-5450	240	58	ta	ta	NOUN
ejpam-5450	240	59	,	,	PUNCT
ejpam-5450	240	60	tb	tb	ADP
ejpam-5450	240	61	∈	∈	PROPN
ejpam-5450	240	62	(	(	PUNCT
ejpam-5450	240	63	0	0	NUM
ejpam-5450	240	64	,	,	PUNCT
ejpam-5450	240	65	0.5	0.5	NUM
ejpam-5450	240	66	]	]	PUNCT
ejpam-5450	240	67	.	.	PUNCT
ejpam-5450	241	1	proof	proof	NOUN
ejpam-5450	241	2	.	.	PUNCT
ejpam-5450	242	1	let	let	VERB
ejpam-5450	242	2	ta	ta	PART
ejpam-5450	242	3	,	,	PUNCT
ejpam-5450	242	4	tb	tb	ADP
ejpam-5450	242	5	∈	∈	PROPN
ejpam-5450	242	6	(	(	PUNCT
ejpam-5450	242	7	0	0	NUM
ejpam-5450	242	8	,	,	PUNCT
ejpam-5450	242	9	0.5	0.5	NUM
ejpam-5450	242	10	]	]	PUNCT
ejpam-5450	242	11	.	.	PUNCT
ejpam-5450	243	1	if	if	SCONJ
ejpam-5450	243	2	(	(	PUNCT
ejpam-5450	243	3	lε	lε	X
ejpam-5450	243	4	µ,min{ta	µ,min{ta	PROPN
ejpam-5450	243	5	,	,	PUNCT
ejpam-5450	243	6	tb})q	tb})q	PROPN
ejpam-5450	243	7	is	be	AUX
ejpam-5450	243	8	nonempty	nonempty	ADJ
ejpam-5450	243	9	,	,	PUNCT
ejpam-5450	243	10	then	then	ADV
ejpam-5450	243	11	there	there	PRON
ejpam-5450	243	12	exists	exist	VERB
ejpam-5450	243	13	x	x	X
ejpam-5450	243	14	∈	∈	PROPN
ejpam-5450	243	15	(	(	PUNCT
ejpam-5450	243	16	lε	lε	X
ejpam-5450	243	17	µ,min{ta	µ,min{ta	PROPN
ejpam-5450	243	18	,	,	PUNCT
ejpam-5450	243	19	tb})q	tb})q	PROPN
ejpam-5450	243	20	.	.	PUNCT
ejpam-5450	244	1	hence	hence	ADV
ejpam-5450	244	2	,	,	PUNCT
ejpam-5450	244	3	lε	lε	X
ejpam-5450	244	4	µ(x	µ(x	NOUN
ejpam-5450	244	5	)	)	PUNCT
ejpam-5450	244	6	>	>	X
ejpam-5450	244	7	1	1	NUM
ejpam-5450	244	8	−	−	NOUN
ejpam-5450	244	9	min{ta	min{ta	NOUN
ejpam-5450	244	10	,	,	PUNCT
ejpam-5450	244	11	tb	tb	ADP
ejpam-5450	244	12	}	}	PUNCT
ejpam-5450	244	13	≥	≥	X
ejpam-5450	244	14	min{ta	min{ta	NOUN
ejpam-5450	244	15	,	,	PUNCT
ejpam-5450	244	16	tb	tb	NOUN
ejpam-5450	244	17	}	}	PUNCT
ejpam-5450	244	18	,	,	PUNCT
ejpam-5450	244	19	which	which	PRON
ejpam-5450	244	20	shows	show	VERB
ejpam-5450	244	21	that	that	SCONJ
ejpam-5450	244	22	[	[	X
ejpam-5450	244	23	x	x	X
ejpam-5450	244	24	/	/	SYM
ejpam-5450	244	25	min{ta	min{ta	X
ejpam-5450	244	26	,	,	PUNCT
ejpam-5450	244	27	tb	tb	NOUN
ejpam-5450	244	28	}	}	PUNCT
ejpam-5450	244	29	]	]	PUNCT
ejpam-5450	244	30	∈	∈	PROPN
ejpam-5450	244	31	lε	lε	ADP
ejpam-5450	244	32	µ.	µ.	NOUN
ejpam-5450	244	33	it	it	PRON
ejpam-5450	244	34	follows	follow	VERB
ejpam-5450	244	35	from	from	ADP
ejpam-5450	244	36	(	(	PUNCT
ejpam-5450	244	37	3.18	3.18	NUM
ejpam-5450	244	38	)	)	PUNCT
ejpam-5450	244	39	that	that	SCONJ
ejpam-5450	244	40	[	[	X
ejpam-5450	244	41	0	0	NUM
ejpam-5450	244	42	/	/	SYM
ejpam-5450	244	43	min{ta	min{ta	VERB
ejpam-5450	244	44	,	,	PUNCT
ejpam-5450	244	45	tb}]qlε	tb}]qlε	NOUN
ejpam-5450	244	46	µ.	µ.	NOUN
ejpam-5450	244	47	thus	thus	ADV
ejpam-5450	244	48	,	,	PUNCT
ejpam-5450	244	49	0	0	NUM
ejpam-5450	244	50	∈	∈	PROPN
ejpam-5450	244	51	(	(	PUNCT
ejpam-5450	244	52	lε	lε	X
ejpam-5450	244	53	µ,min{ta	µ,min{ta	PROPN
ejpam-5450	244	54	,	,	PUNCT
ejpam-5450	244	55	tb})q	tb})q	PROPN
ejpam-5450	244	56	.	.	PUNCT
ejpam-5450	245	1	let	let	VERB
ejpam-5450	245	2	x	x	PRON
ejpam-5450	245	3	,	,	PUNCT
ejpam-5450	245	4	y	y	PROPN
ejpam-5450	245	5	,	,	PUNCT
ejpam-5450	245	6	z	z	NOUN
ejpam-5450	245	7	∈	∈	PROPN
ejpam-5450	245	8	x	x	AUX
ejpam-5450	245	9	be	be	AUX
ejpam-5450	245	10	such	such	ADJ
ejpam-5450	245	11	that	that	SCONJ
ejpam-5450	245	12	x	x	X
ejpam-5450	245	13	◦	◦	NOUN
ejpam-5450	245	14	(y	(y	NOUN
ejpam-5450	245	15	◦	◦	NOUN
ejpam-5450	245	16	z	z	NOUN
ejpam-5450	245	17	)	)	PUNCT
ejpam-5450	245	18	∈	∈	PROPN
ejpam-5450	245	19	(	(	PUNCT
ejpam-5450	245	20	lε	lε	X
ejpam-5450	245	21	µ,min{ta	µ,min{ta	PROPN
ejpam-5450	245	22	,	,	PUNCT
ejpam-5450	245	23	tb})q	tb})q	PROPN
ejpam-5450	245	24	and	and	CCONJ
ejpam-5450	245	25	y	y	PROPN
ejpam-5450	245	26	∈	∈	PROPN
ejpam-5450	245	27	(	(	PUNCT
ejpam-5450	245	28	lε	lε	X
ejpam-5450	245	29	µ,min{ta	µ,min{ta	PROPN
ejpam-5450	245	30	,	,	PUNCT
ejpam-5450	245	31	tb})q	tb})q	PROPN
ejpam-5450	245	32	.	.	PUNCT
ejpam-5450	246	1	then	then	ADV
ejpam-5450	246	2	lε	lε	ADP
ejpam-5450	246	3	µ(x	µ(x	ADJ
ejpam-5450	246	4	◦	◦	NOUN
ejpam-5450	246	5	(	(	PUNCT
ejpam-5450	246	6	y	y	PROPN
ejpam-5450	246	7	◦	◦	PROPN
ejpam-5450	246	8	z	z	PROPN
ejpam-5450	246	9	)	)	PUNCT
ejpam-5450	246	10	)	)	PUNCT
ejpam-5450	246	11	>	>	X
ejpam-5450	247	1	1	1	NUM
ejpam-5450	247	2	−	−	NOUN
ejpam-5450	247	3	min{ta	min{ta	NOUN
ejpam-5450	247	4	,	,	PUNCT
ejpam-5450	247	5	tb	tb	ADP
ejpam-5450	247	6	}	}	PUNCT
ejpam-5450	247	7	≥	≥	X
ejpam-5450	247	8	min{ta	min{ta	NOUN
ejpam-5450	247	9	,	,	PUNCT
ejpam-5450	247	10	tb	tb	NOUN
ejpam-5450	247	11	}	}	PUNCT
ejpam-5450	247	12	and	and	CCONJ
ejpam-5450	247	13	lε	lε	ADP
ejpam-5450	247	14	µ(y	µ(y	PROPN
ejpam-5450	247	15	)	)	PUNCT
ejpam-5450	247	16	>	>	X
ejpam-5450	247	17	1	1	NUM
ejpam-5450	247	18	−	−	NOUN
ejpam-5450	247	19	min{ta	min{ta	NOUN
ejpam-5450	247	20	,	,	PUNCT
ejpam-5450	247	21	tb	tb	ADP
ejpam-5450	247	22	}	}	PUNCT
ejpam-5450	247	23	≥	≥	X
ejpam-5450	247	24	min{ta	min{ta	NOUN
ejpam-5450	247	25	,	,	PUNCT
ejpam-5450	247	26	tb	tb	NOUN
ejpam-5450	247	27	}	}	PUNCT
ejpam-5450	247	28	.	.	PUNCT
ejpam-5450	248	1	thus	thus	ADV
ejpam-5450	248	2	,	,	PUNCT
ejpam-5450	248	3	[	[	X
ejpam-5450	248	4	(	(	PUNCT
ejpam-5450	248	5	x	x	SYM
ejpam-5450	248	6	◦	◦	NOUN
ejpam-5450	248	7	(	(	PUNCT
ejpam-5450	248	8	y	y	PROPN
ejpam-5450	248	9	◦	◦	NOUN
ejpam-5450	248	10	z))/min{ta	z))/min{ta	NUM
ejpam-5450	248	11	,	,	PUNCT
ejpam-5450	248	12	tb	tb	NOUN
ejpam-5450	248	13	}	}	PUNCT
ejpam-5450	248	14	]	]	PUNCT
ejpam-5450	248	15	∈	∈	PROPN
ejpam-5450	248	16	lε	lε	ADP
ejpam-5450	248	17	µ	µ	NOUN
ejpam-5450	248	18	and	and	CCONJ
ejpam-5450	248	19	[	[	X
ejpam-5450	248	20	y	y	X
ejpam-5450	248	21	/	/	SYM
ejpam-5450	248	22	min{ta	min{ta	NUM
ejpam-5450	248	23	,	,	PUNCT
ejpam-5450	248	24	tb	tb	NOUN
ejpam-5450	248	25	}	}	PUNCT
ejpam-5450	248	26	]	]	PUNCT
ejpam-5450	249	1	∈	∈	PROPN
ejpam-5450	249	2	lε	lε	ADP
ejpam-5450	249	3	µ.	µ.	NOUN
ejpam-5450	249	4	it	it	PRON
ejpam-5450	249	5	follows	follow	VERB
ejpam-5450	249	6	from	from	ADP
ejpam-5450	249	7	(	(	PUNCT
ejpam-5450	249	8	3.19	3.19	NUM
ejpam-5450	249	9	)	)	PUNCT
ejpam-5450	249	10	that	that	SCONJ
ejpam-5450	250	1	[	[	X
ejpam-5450	250	2	(	(	PUNCT
ejpam-5450	250	3	x	x	SYM
ejpam-5450	250	4	◦	◦	NOUN
ejpam-5450	250	5	z)/min{ta	z)/min{ta	PROPN
ejpam-5450	250	6	,	,	PUNCT
ejpam-5450	250	7	tb}]qlε	tb}]qlε	NOUN
ejpam-5450	250	8	µ	µ	NOUN
ejpam-5450	250	9	,	,	PUNCT
ejpam-5450	250	10	that	that	ADV
ejpam-5450	250	11	is	is	ADV
ejpam-5450	250	12	,	,	PUNCT
ejpam-5450	250	13	x	x	PUNCT
ejpam-5450	250	14	◦	◦	NOUN
ejpam-5450	250	15	z	z	NOUN
ejpam-5450	250	16	∈	∈	PROPN
ejpam-5450	250	17	(	(	PUNCT
ejpam-5450	250	18	lε	lε	X
ejpam-5450	250	19	µ,min{ta	µ,min{ta	PROPN
ejpam-5450	250	20	,	,	PUNCT
ejpam-5450	250	21	tb})q	tb})q	PROPN
ejpam-5450	250	22	.	.	PUNCT
ejpam-5450	251	1	therefore	therefore	ADV
ejpam-5450	251	2	,	,	PUNCT
ejpam-5450	251	3	(	(	PUNCT
ejpam-5450	251	4	lε	lε	X
ejpam-5450	251	5	µ,min{ta	µ,min{ta	PROPN
ejpam-5450	251	6	,	,	PUNCT
ejpam-5450	251	7	tb})q	tb})q	PROPN
ejpam-5450	251	8	is	be	AUX
ejpam-5450	251	9	a	a	DET
ejpam-5450	251	10	bcc	bcc	PROPN
ejpam-5450	251	11	-	-	PUNCT
ejpam-5450	251	12	ideal	ideal	NOUN
ejpam-5450	251	13	of	of	ADP
ejpam-5450	251	14	x.	x.	PROPN
ejpam-5450	251	15	theorem	theorem	VERB
ejpam-5450	251	16	10	10	NUM
ejpam-5450	251	17	.	.	PUNCT
ejpam-5450	252	1	if	if	SCONJ
ejpam-5450	252	2	an	an	DET
ejpam-5450	252	3	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	252	4	fuzzy	fuzzy	ADJ
ejpam-5450	252	5	set	set	VERB
ejpam-5450	252	6	lε	lε	PRON
ejpam-5450	252	7	µ	µ	NOUN
ejpam-5450	252	8	in	in	ADP
ejpam-5450	252	9	x	x	PART
ejpam-5450	252	10	satisfies	satisfie	NOUN
ejpam-5450	252	11	the	the	DET
ejpam-5450	252	12	conditions	condition	NOUN
ejpam-5450	252	13	(	(	PUNCT
ejpam-5450	252	14	3.11	3.11	NUM
ejpam-5450	252	15	)	)	PUNCT
ejpam-5450	252	16	and	and	CCONJ
ejpam-5450	252	17	(	(	PUNCT
ejpam-5450	252	18	3.12	3.12	NUM
ejpam-5450	252	19	)	)	PUNCT
ejpam-5450	252	20	,	,	PUNCT
ejpam-5450	252	21	then	then	ADV
ejpam-5450	252	22	the	the	DET
ejpam-5450	252	23	q	q	NOUN
ejpam-5450	252	24	-	-	PUNCT
ejpam-5450	252	25	set	set	ADJ
ejpam-5450	252	26	(	(	PUNCT
ejpam-5450	252	27	lε	lε	X
ejpam-5450	252	28	µ	µ	NUM
ejpam-5450	252	29	,	,	PUNCT
ejpam-5450	252	30	t)q	t)q	PRON
ejpam-5450	252	31	of	of	ADP
ejpam-5450	252	32	lε	lε	PRON
ejpam-5450	252	33	µ	µ	PROPN
ejpam-5450	252	34	is	be	AUX
ejpam-5450	252	35	a	a	DET
ejpam-5450	252	36	bcc	bcc	PROPN
ejpam-5450	252	37	-	-	PUNCT
ejpam-5450	252	38	ideal	ideal	NOUN
ejpam-5450	252	39	of	of	ADP
ejpam-5450	252	40	x	x	PUNCT
ejpam-5450	252	41	for	for	ADP
ejpam-5450	252	42	all	all	DET
ejpam-5450	252	43	t	t	NOUN
ejpam-5450	252	44	∈	∈	PROPN
ejpam-5450	252	45	(	(	PUNCT
ejpam-5450	252	46	0.5	0.5	NUM
ejpam-5450	252	47	,	,	PUNCT
ejpam-5450	252	48	1	1	NUM
ejpam-5450	252	49	]	]	PUNCT
ejpam-5450	252	50	.	.	PUNCT
ejpam-5450	253	1	proof	proof	NOUN
ejpam-5450	253	2	.	.	PUNCT
ejpam-5450	254	1	assume	assume	VERB
ejpam-5450	254	2	that	that	SCONJ
ejpam-5450	254	3	lε	lε	PART
ejpam-5450	254	4	µ	µ	PRON
ejpam-5450	254	5	satisfies	satisfy	VERB
ejpam-5450	254	6	the	the	DET
ejpam-5450	254	7	conditions	condition	NOUN
ejpam-5450	254	8	(	(	PUNCT
ejpam-5450	254	9	3.11	3.11	NUM
ejpam-5450	254	10	)	)	PUNCT
ejpam-5450	254	11	and	and	CCONJ
ejpam-5450	254	12	(	(	PUNCT
ejpam-5450	254	13	3.12	3.12	NUM
ejpam-5450	254	14	)	)	PUNCT
ejpam-5450	254	15	.	.	PUNCT
ejpam-5450	255	1	the	the	DET
ejpam-5450	255	2	condition	condition	NOUN
ejpam-5450	255	3	(	(	PUNCT
ejpam-5450	255	4	3.11	3.11	NUM
ejpam-5450	255	5	)	)	PUNCT
ejpam-5450	255	6	induces	induce	VERB
ejpam-5450	255	7	lε	lε	X
ejpam-5450	255	8	µ(0	µ(0	NOUN
ejpam-5450	255	9	)	)	PUNCT
ejpam-5450	256	1	+	+	NOUN
ejpam-5450	256	2	t	t	X
ejpam-5450	256	3	≥	≥	NUM
ejpam-5450	256	4	2	2	NUM
ejpam-5450	256	5	t	t	NOUN
ejpam-5450	256	6	>	>	X
ejpam-5450	256	7	1	1	NUM
ejpam-5450	256	8	,	,	PUNCT
ejpam-5450	256	9	that	that	ADV
ejpam-5450	256	10	is	is	ADV
ejpam-5450	256	11	,	,	PUNCT
ejpam-5450	256	12	[	[	X
ejpam-5450	256	13	0	0	NUM
ejpam-5450	256	14	/	/	SYM
ejpam-5450	256	15	t]qlε	t]qlε	NOUN
ejpam-5450	256	16	µ.	µ.	NOUN
ejpam-5450	256	17	hence	hence	ADV
ejpam-5450	256	18	,	,	PUNCT
ejpam-5450	256	19	0	0	NUM
ejpam-5450	256	20	∈	∈	PROPN
ejpam-5450	256	21	(	(	PUNCT
ejpam-5450	256	22	lε	lε	X
ejpam-5450	256	23	µ	µ	NUM
ejpam-5450	256	24	,	,	PUNCT
ejpam-5450	256	25	t)q	t)q	PUNCT
ejpam-5450	256	26	.	.	PUNCT
ejpam-5450	257	1	let	let	VERB
ejpam-5450	257	2	x	x	PRON
ejpam-5450	257	3	,	,	PUNCT
ejpam-5450	257	4	y	y	PROPN
ejpam-5450	257	5	,	,	PUNCT
ejpam-5450	257	6	z	z	NOUN
ejpam-5450	257	7	∈	∈	PROPN
ejpam-5450	257	8	x	x	AUX
ejpam-5450	257	9	be	be	AUX
ejpam-5450	257	10	such	such	ADJ
ejpam-5450	257	11	that	that	SCONJ
ejpam-5450	257	12	x	x	X
ejpam-5450	257	13	◦	◦	NOUN
ejpam-5450	257	14	(	(	PUNCT
ejpam-5450	257	15	y	y	PROPN
ejpam-5450	257	16	◦	◦	PROPN
ejpam-5450	257	17	z	z	NOUN
ejpam-5450	257	18	)	)	PUNCT
ejpam-5450	257	19	∈	∈	PROPN
ejpam-5450	257	20	(	(	PUNCT
ejpam-5450	257	21	lε	lε	X
ejpam-5450	257	22	µ	µ	NUM
ejpam-5450	257	23	,	,	PUNCT
ejpam-5450	257	24	t)q	t)q	PUNCT
ejpam-5450	257	25	and	and	CCONJ
ejpam-5450	257	26	y	y	PROPN
ejpam-5450	257	27	∈	∈	PROPN
ejpam-5450	257	28	(	(	PUNCT
ejpam-5450	257	29	lε	lε	X
ejpam-5450	257	30	µ	µ	NUM
ejpam-5450	257	31	,	,	PUNCT
ejpam-5450	257	32	t)q	t)q	PUNCT
ejpam-5450	257	33	.	.	PUNCT
ejpam-5450	258	1	then	then	ADV
ejpam-5450	258	2	[	[	X
ejpam-5450	258	3	(	(	PUNCT
ejpam-5450	258	4	x	x	X
ejpam-5450	258	5	◦	◦	NOUN
ejpam-5450	258	6	(	(	PUNCT
ejpam-5450	258	7	y	y	PROPN
ejpam-5450	258	8	◦	◦	PROPN
ejpam-5450	258	9	z))/t]qlε	z))/t]qlε	PROPN
ejpam-5450	258	10	µ	µ	NOUN
ejpam-5450	258	11	and	and	CCONJ
ejpam-5450	258	12	[	[	X
ejpam-5450	258	13	y	y	NOUN
ejpam-5450	258	14	/	/	SYM
ejpam-5450	258	15	t]qlε	t]qlε	NOUN
ejpam-5450	258	16	µ.	µ.	NOUN
ejpam-5450	258	17	it	it	PRON
ejpam-5450	258	18	follows	follow	VERB
ejpam-5450	258	19	from	from	ADP
ejpam-5450	258	20	(	(	PUNCT
ejpam-5450	258	21	3.12	3.12	NUM
ejpam-5450	258	22	)	)	PUNCT
ejpam-5450	258	23	that	that	PRON
ejpam-5450	258	24	x	x	PUNCT
ejpam-5450	258	25	◦	◦	NOUN
ejpam-5450	258	26	z	z	NOUN
ejpam-5450	258	27	∈	∈	PROPN
ejpam-5450	258	28	(	(	PUNCT
ejpam-5450	258	29	lε	lε	X
ejpam-5450	258	30	µ,min{t	µ,min{t	PROPN
ejpam-5450	258	31	,	,	PUNCT
ejpam-5450	258	32	t})∈	t})∈	PROPN
ejpam-5450	258	33	=	=	PUNCT
ejpam-5450	258	34	(	(	PUNCT
ejpam-5450	258	35	lε	lε	X
ejpam-5450	258	36	µ	µ	NUM
ejpam-5450	258	37	,	,	PUNCT
ejpam-5450	258	38	t)∈.	t)∈.	PROPN
ejpam-5450	258	39	hence	hence	ADV
ejpam-5450	258	40	,	,	PUNCT
ejpam-5450	258	41	lε	lε	ADP
ejpam-5450	258	42	µ(x	µ(x	ADJ
ejpam-5450	258	43	◦	◦	NOUN
ejpam-5450	258	44	z	z	NOUN
ejpam-5450	258	45	)	)	PUNCT
ejpam-5450	258	46	≥	≥	PROPN
ejpam-5450	258	47	t	t	X
ejpam-5450	258	48	>	>	X
ejpam-5450	258	49	1	1	NUM
ejpam-5450	258	50	−	−	PROPN
ejpam-5450	258	51	t	t	PROPN
ejpam-5450	258	52	,	,	PUNCT
ejpam-5450	258	53	that	that	ADV
ejpam-5450	258	54	is	is	ADV
ejpam-5450	258	55	,	,	PUNCT
ejpam-5450	258	56	x	x	PUNCT
ejpam-5450	258	57	◦	◦	NOUN
ejpam-5450	258	58	z	z	NOUN
ejpam-5450	258	59	∈	∈	PROPN
ejpam-5450	258	60	(	(	PUNCT
ejpam-5450	258	61	lε	lε	X
ejpam-5450	258	62	µ	µ	NUM
ejpam-5450	258	63	,	,	PUNCT
ejpam-5450	258	64	t)q	t)q	PUNCT
ejpam-5450	258	65	.	.	PUNCT
ejpam-5450	259	1	therefore	therefore	ADV
ejpam-5450	259	2	,	,	PUNCT
ejpam-5450	259	3	(	(	PUNCT
ejpam-5450	259	4	lε	lε	X
ejpam-5450	259	5	µ	µ	NUM
ejpam-5450	259	6	,	,	PUNCT
ejpam-5450	259	7	t)q	t)q	PUNCT
ejpam-5450	259	8	is	be	AUX
ejpam-5450	259	9	a	a	DET
ejpam-5450	259	10	bcc	bcc	PROPN
ejpam-5450	259	11	-	-	PUNCT
ejpam-5450	259	12	ideal	ideal	NOUN
ejpam-5450	259	13	of	of	ADP
ejpam-5450	259	14	x	x	PUNCT
ejpam-5450	259	15	for	for	ADP
ejpam-5450	259	16	all	all	DET
ejpam-5450	259	17	t	t	NOUN
ejpam-5450	259	18	∈	∈	PROPN
ejpam-5450	259	19	(	(	PUNCT
ejpam-5450	259	20	0.5	0.5	NUM
ejpam-5450	259	21	,	,	PUNCT
ejpam-5450	259	22	1	1	NUM
ejpam-5450	259	23	]	]	PUNCT
ejpam-5450	259	24	.	.	PUNCT
ejpam-5450	260	1	let	let	VERB
ejpam-5450	260	2	µ	µ	X
ejpam-5450	260	3	be	be	AUX
ejpam-5450	260	4	a	a	DET
ejpam-5450	260	5	fuzzy	fuzzy	ADJ
ejpam-5450	260	6	set	set	NOUN
ejpam-5450	260	7	in	in	ADP
ejpam-5450	260	8	x.	x.	NOUN
ejpam-5450	260	9	consider	consider	VERB
ejpam-5450	260	10	an	an	DET
ejpam-5450	260	11	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	260	12	fuzzy	fuzzy	ADJ
ejpam-5450	260	13	set	set	VERB
ejpam-5450	260	14	lε	lε	PRON
ejpam-5450	260	15	µ	µ	PRON
ejpam-5450	260	16	associated	associate	VERB
ejpam-5450	260	17	with	with	ADP
ejpam-5450	260	18	µ	µ	NOUN
ejpam-5450	260	19	in	in	ADP
ejpam-5450	260	20	x.	x.	NOUN
ejpam-5450	260	21	define	define	VERB
ejpam-5450	260	22	the	the	DET
ejpam-5450	260	23	set	set	VERB
ejpam-5450	260	24	o(lε	o(lε	PROPN
ejpam-5450	260	25	µ	µ	NOUN
ejpam-5450	260	26	)	)	PUNCT
ejpam-5450	260	27	=	=	PRON
ejpam-5450	261	1	{	{	PUNCT
ejpam-5450	261	2	x	x	PUNCT
ejpam-5450	261	3	∈	∈	PROPN
ejpam-5450	261	4	x	x	X
ejpam-5450	261	5	:	:	PUNCT
ejpam-5450	261	6	lε	lε	X
ejpam-5450	261	7	µ(x	µ(x	NOUN
ejpam-5450	261	8	)	)	PUNCT
ejpam-5450	261	9	>	>	X
ejpam-5450	261	10	0	0	NUM
ejpam-5450	261	11	}	}	PUNCT
ejpam-5450	261	12	,	,	PUNCT
ejpam-5450	261	13	known	know	VERB
ejpam-5450	261	14	as	as	ADP
ejpam-5450	261	15	the	the	DET
ejpam-5450	261	16	o	o	NOUN
ejpam-5450	261	17	-	-	NOUN
ejpam-5450	261	18	set	set	NOUN
ejpam-5450	261	19	of	of	ADP
ejpam-5450	261	20	lε	lε	INTJ
ejpam-5450	261	21	µ.	µ.	PROPN
ejpam-5450	261	22	it	it	PRON
ejpam-5450	261	23	is	be	AUX
ejpam-5450	261	24	noted	note	VERB
ejpam-5450	261	25	that	that	SCONJ
ejpam-5450	261	26	o(lε	o(lε	PROPN
ejpam-5450	261	27	µ	µ	X
ejpam-5450	261	28	)	)	PUNCT
ejpam-5450	261	29	can	can	AUX
ejpam-5450	261	30	be	be	AUX
ejpam-5450	261	31	expressed	express	VERB
ejpam-5450	261	32	as	as	ADP
ejpam-5450	261	33	o(lε	o(lε	PROPN
ejpam-5450	261	34	µ	µ	X
ejpam-5450	261	35	)	)	PUNCT
ejpam-5450	261	36	=	=	PRON
ejpam-5450	261	37	{	{	PUNCT
ejpam-5450	261	38	x	x	PUNCT
ejpam-5450	261	39	∈	∈	NOUN
ejpam-5450	261	40	x	x	X
ejpam-5450	261	41	:	:	PUNCT
ejpam-5450	261	42	µ(x	µ(x	X
ejpam-5450	261	43	)	)	PUNCT
ejpam-5450	262	1	+	+	CCONJ
ejpam-5450	262	2	ε−	ε−	PROPN
ejpam-5450	262	3	1	1	NUM
ejpam-5450	262	4	>	>	PUNCT
ejpam-5450	262	5	0	0	NUM
ejpam-5450	262	6	}	}	PUNCT
ejpam-5450	262	7	.	.	PUNCT
ejpam-5450	263	1	theorem	theorem	VERB
ejpam-5450	263	2	11	11	NUM
ejpam-5450	263	3	.	.	PUNCT
ejpam-5450	264	1	let	let	VERB
ejpam-5450	264	2	lε	lε	PART
ejpam-5450	264	3	µ	µ	X
ejpam-5450	264	4	be	be	AUX
ejpam-5450	264	5	an	an	DET
ejpam-5450	264	6	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	264	7	fuzzy	fuzzy	ADJ
ejpam-5450	264	8	set	set	NOUN
ejpam-5450	264	9	of	of	ADP
ejpam-5450	264	10	a	a	DET
ejpam-5450	264	11	fuzzy	fuzzy	ADJ
ejpam-5450	264	12	set	set	VERB
ejpam-5450	264	13	µ	µ	NOUN
ejpam-5450	264	14	in	in	ADP
ejpam-5450	264	15	x.	x.	NOUN
ejpam-5450	264	16	if	if	SCONJ
ejpam-5450	264	17	µ	µ	PRON
ejpam-5450	264	18	is	be	AUX
ejpam-5450	264	19	a	a	DET
ejpam-5450	264	20	fuzzy	fuzzy	ADJ
ejpam-5450	264	21	bcc	bcc	NOUN
ejpam-5450	264	22	-	-	PUNCT
ejpam-5450	264	23	ideal	ideal	NOUN
ejpam-5450	264	24	of	of	ADP
ejpam-5450	264	25	x	x	PRON
ejpam-5450	264	26	,	,	PUNCT
ejpam-5450	264	27	then	then	ADV
ejpam-5450	264	28	the	the	DET
ejpam-5450	264	29	o	o	NOUN
ejpam-5450	264	30	-	-	ADJ
ejpam-5450	264	31	set	set	VERB
ejpam-5450	264	32	o(lε	o(lε	PROPN
ejpam-5450	264	33	µ	µ	NOUN
ejpam-5450	264	34	)	)	PUNCT
ejpam-5450	264	35	of	of	ADP
ejpam-5450	264	36	lε	lε	PRON
ejpam-5450	264	37	µ	µ	PROPN
ejpam-5450	264	38	is	be	AUX
ejpam-5450	264	39	a	a	DET
ejpam-5450	264	40	bcc	bcc	PROPN
ejpam-5450	264	41	-	-	PUNCT
ejpam-5450	264	42	ideal	ideal	NOUN
ejpam-5450	264	43	of	of	ADP
ejpam-5450	264	44	x.	x.	PROPN
ejpam-5450	264	45	a.	a.	PROPN
ejpam-5450	264	46	iampan	iampan	PROPN
ejpam-5450	264	47	,	,	PUNCT
ejpam-5450	264	48	r.	r.	PROPN
ejpam-5450	264	49	subasini	subasini	PROPN
ejpam-5450	264	50	,	,	PUNCT
ejpam-5450	264	51	n.	n.	PROPN
ejpam-5450	264	52	rajesh	rajesh	PROPN
ejpam-5450	264	53	/	/	SYM
ejpam-5450	264	54	eur	eur	PROPN
ejpam-5450	264	55	.	.	PUNCT
ejpam-5450	265	1	j.	j.	PROPN
ejpam-5450	265	2	pure	pure	PROPN
ejpam-5450	265	3	appl	appl	PROPN
ejpam-5450	265	4	.	.	PROPN
ejpam-5450	265	5	math	math	PROPN
ejpam-5450	265	6	,	,	PUNCT
ejpam-5450	265	7	17	17	NUM
ejpam-5450	265	8	(	(	PUNCT
ejpam-5450	265	9	4	4	NUM
ejpam-5450	265	10	)	)	PUNCT
ejpam-5450	265	11	(	(	PUNCT
ejpam-5450	265	12	2024	2024	NUM
ejpam-5450	265	13	)	)	PUNCT
ejpam-5450	265	14	,	,	PUNCT
ejpam-5450	265	15	3209	3209	NUM
ejpam-5450	265	16	-	-	SYM
ejpam-5450	265	17	3222	3222	NUM
ejpam-5450	265	18	3220	3220	NUM
ejpam-5450	265	19	proof	proof	NOUN
ejpam-5450	265	20	.	.	PUNCT
ejpam-5450	266	1	assume	assume	VERB
ejpam-5450	266	2	that	that	SCONJ
ejpam-5450	266	3	µ	µ	NOUN
ejpam-5450	266	4	is	be	AUX
ejpam-5450	266	5	a	a	DET
ejpam-5450	266	6	fuzzy	fuzzy	ADJ
ejpam-5450	266	7	bcc	bcc	NOUN
ejpam-5450	266	8	-	-	PUNCT
ejpam-5450	266	9	ideal	ideal	NOUN
ejpam-5450	266	10	of	of	ADP
ejpam-5450	266	11	x.	x.	NOUN
ejpam-5450	266	12	then	then	ADV
ejpam-5450	266	13	lε	lε	PROPN
ejpam-5450	266	14	µ	µ	PROPN
ejpam-5450	266	15	is	be	AUX
ejpam-5450	266	16	an	an	DET
ejpam-5450	266	17	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	266	18	fuzzy	fuzzy	ADJ
ejpam-5450	266	19	bcc	bcc	PROPN
ejpam-5450	266	20	-	-	PUNCT
ejpam-5450	266	21	ideal	ideal	NOUN
ejpam-5450	266	22	of	of	ADP
ejpam-5450	266	23	x	x	PUNCT
ejpam-5450	266	24	by	by	ADP
ejpam-5450	266	25	theorem	theorem	NOUN
ejpam-5450	266	26	2	2	NUM
ejpam-5450	266	27	.	.	PUNCT
ejpam-5450	267	1	it	it	PRON
ejpam-5450	267	2	is	be	AUX
ejpam-5450	267	3	clear	clear	ADJ
ejpam-5450	267	4	that	that	SCONJ
ejpam-5450	267	5	0	0	NUM
ejpam-5450	267	6	∈	∈	NOUN
ejpam-5450	267	7	lε	lε	AUX
ejpam-5450	267	8	µ.	µ.	NOUN
ejpam-5450	267	9	let	let	VERB
ejpam-5450	267	10	x	x	PRON
ejpam-5450	267	11	,	,	PUNCT
ejpam-5450	267	12	y	y	PROPN
ejpam-5450	267	13	,	,	PUNCT
ejpam-5450	267	14	z	z	PROPN
ejpam-5450	267	15	∈	∈	PROPN
ejpam-5450	267	16	o(lε	o(lε	PROPN
ejpam-5450	267	17	µ	µ	NOUN
ejpam-5450	267	18	)	)	PUNCT
ejpam-5450	267	19	be	be	AUX
ejpam-5450	267	20	such	such	ADJ
ejpam-5450	267	21	that	that	SCONJ
ejpam-5450	267	22	µ(x	µ(x	ADJ
ejpam-5450	267	23	◦	◦	NOUN
ejpam-5450	267	24	(	(	PUNCT
ejpam-5450	267	25	y	y	PROPN
ejpam-5450	267	26	◦	◦	PROPN
ejpam-5450	267	27	z	z	PROPN
ejpam-5450	267	28	)	)	PUNCT
ejpam-5450	267	29	)	)	PUNCT
ejpam-5450	268	1	+	+	CCONJ
ejpam-5450	268	2	ε	ε	PROPN
ejpam-5450	268	3	−	−	NOUN
ejpam-5450	268	4	1	1	NUM
ejpam-5450	268	5	>	>	SYM
ejpam-5450	268	6	0	0	NUM
ejpam-5450	268	7	and	and	CCONJ
ejpam-5450	268	8	µ(y	µ(y	NUM
ejpam-5450	268	9	)	)	PUNCT
ejpam-5450	269	1	+	+	CCONJ
ejpam-5450	269	2	ε	ε	PROPN
ejpam-5450	269	3	−	−	PROPN
ejpam-5450	269	4	1	1	NUM
ejpam-5450	269	5	>	>	X
ejpam-5450	269	6	0	0	X
ejpam-5450	269	7	.	.	PUNCT
ejpam-5450	270	1	it	it	PRON
ejpam-5450	270	2	follows	follow	VERB
ejpam-5450	270	3	from	from	ADP
ejpam-5450	270	4	(	(	PUNCT
ejpam-5450	270	5	3.5	3.5	NUM
ejpam-5450	270	6	)	)	PUNCT
ejpam-5450	271	1	that	that	PRON
ejpam-5450	271	2	lε	lε	ADP
ejpam-5450	271	3	µ(x	µ(x	ADJ
ejpam-5450	271	4	◦	◦	NOUN
ejpam-5450	271	5	z	z	NOUN
ejpam-5450	271	6	)	)	PUNCT
ejpam-5450	271	7	≥	≥	NOUN
ejpam-5450	271	8	min{lε	min{lε	NUM
ejpam-5450	271	9	µ(x	µ(x	ADJ
ejpam-5450	271	10	◦	◦	NOUN
ejpam-5450	271	11	(	(	PUNCT
ejpam-5450	271	12	y	y	PROPN
ejpam-5450	271	13	◦	◦	PROPN
ejpam-5450	271	14	z	z	PROPN
ejpam-5450	271	15	)	)	PUNCT
ejpam-5450	271	16	)	)	PUNCT
ejpam-5450	271	17	,	,	PUNCT
ejpam-5450	271	18	lε	lε	X
ejpam-5450	271	19	µ(y	µ(y	PROPN
ejpam-5450	271	20	)	)	PUNCT
ejpam-5450	271	21	}	}	PUNCT
ejpam-5450	272	1	=	=	SYM
ejpam-5450	272	2	min{µ(x	min{µ(x	PROPN
ejpam-5450	272	3	◦	◦	NOUN
ejpam-5450	272	4	(	(	PUNCT
ejpam-5450	272	5	y	y	PROPN
ejpam-5450	272	6	◦	◦	PROPN
ejpam-5450	272	7	z	z	PROPN
ejpam-5450	272	8	)	)	PUNCT
ejpam-5450	272	9	)	)	PUNCT
ejpam-5450	273	1	+	+	CCONJ
ejpam-5450	273	2	ε	ε	PROPN
ejpam-5450	273	3	−	−	PROPN
ejpam-5450	273	4	1	1	NUM
ejpam-5450	273	5	,	,	PUNCT
ejpam-5450	273	6	µ(y	µ(y	PROPN
ejpam-5450	273	7	)	)	PUNCT
ejpam-5450	273	8	+	+	CCONJ
ejpam-5450	273	9	ε	ε	PROPN
ejpam-5450	273	10	−	−	NOUN
ejpam-5450	273	11	1	1	NUM
ejpam-5450	273	12	}	}	PUNCT
ejpam-5450	273	13	>	>	X
ejpam-5450	273	14	0	0	X
ejpam-5450	273	15	.	.	PUNCT
ejpam-5450	274	1	thus	thus	ADV
ejpam-5450	274	2	,	,	PUNCT
ejpam-5450	274	3	x	x	PUNCT
ejpam-5450	274	4	◦	◦	NOUN
ejpam-5450	274	5	z	z	NOUN
ejpam-5450	274	6	∈	∈	PROPN
ejpam-5450	274	7	o(lε	o(lε	PROPN
ejpam-5450	274	8	µ	µ	NOUN
ejpam-5450	274	9	)	)	PUNCT
ejpam-5450	274	10	.	.	PUNCT
ejpam-5450	275	1	hence	hence	ADV
ejpam-5450	275	2	,	,	PUNCT
ejpam-5450	275	3	o(lε	o(lε	PROPN
ejpam-5450	275	4	µ	µ	NOUN
ejpam-5450	275	5	)	)	PUNCT
ejpam-5450	275	6	is	be	AUX
ejpam-5450	275	7	a	a	DET
ejpam-5450	275	8	bcc	bcc	PROPN
ejpam-5450	275	9	-	-	PUNCT
ejpam-5450	275	10	ideal	ideal	NOUN
ejpam-5450	275	11	of	of	ADP
ejpam-5450	275	12	x.	x.	PROPN
ejpam-5450	275	13	theorem	theorem	VERB
ejpam-5450	275	14	12	12	NUM
ejpam-5450	275	15	.	.	PUNCT
ejpam-5450	276	1	let	let	VERB
ejpam-5450	276	2	µ	µ	X
ejpam-5450	276	3	be	be	AUX
ejpam-5450	276	4	a	a	DET
ejpam-5450	276	5	fuzzy	fuzzy	ADJ
ejpam-5450	276	6	set	set	NOUN
ejpam-5450	276	7	in	in	ADP
ejpam-5450	276	8	x.	x.	NOUN
ejpam-5450	276	9	if	if	SCONJ
ejpam-5450	276	10	an	an	DET
ejpam-5450	276	11	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	276	12	fuzzy	fuzzy	ADJ
ejpam-5450	276	13	set	set	VERB
ejpam-5450	276	14	lε	lε	PRON
ejpam-5450	276	15	µ	µ	PROPN
ejpam-5450	276	16	of	of	ADP
ejpam-5450	276	17	µ	µ	NOUN
ejpam-5450	276	18	in	in	ADP
ejpam-5450	276	19	x	x	PART
ejpam-5450	276	20	satisfies	satisfie	NOUN
ejpam-5450	276	21	the	the	DET
ejpam-5450	276	22	following	follow	VERB
ejpam-5450	276	23	properties	property	NOUN
ejpam-5450	276	24	:	:	PUNCT
ejpam-5450	276	25	(	(	PUNCT
ejpam-5450	276	26	∀x	∀x	X
ejpam-5450	276	27	∈	∈	PROPN
ejpam-5450	276	28	x,∀t	x,∀t	X
ejpam-5450	276	29	∈	∈	PROPN
ejpam-5450	276	30	(	(	PUNCT
ejpam-5450	276	31	0	0	NUM
ejpam-5450	276	32	,	,	PUNCT
ejpam-5450	276	33	1])([x	1])([x	NUM
ejpam-5450	276	34	/	/	SYM
ejpam-5450	276	35	t]qlε	t]qlε	X
ejpam-5450	276	36	µ	µ	ADJ
ejpam-5450	276	37	⇒	⇒	NOUN
ejpam-5450	276	38	[	[	X
ejpam-5450	276	39	0	0	NUM
ejpam-5450	276	40	/	/	SYM
ejpam-5450	276	41	t]qlε	t]qlε	X
ejpam-5450	276	42	µ	µ	NUM
ejpam-5450	276	43	)	)	PUNCT
ejpam-5450	276	44	(	(	PUNCT
ejpam-5450	276	45	3.20	3.20	NUM
ejpam-5450	276	46	)	)	PUNCT
ejpam-5450	276	47	(	(	PUNCT
ejpam-5450	276	48	∀x	∀x	X
ejpam-5450	276	49	,	,	PUNCT
ejpam-5450	276	50	y	y	PROPN
ejpam-5450	276	51	,	,	PUNCT
ejpam-5450	276	52	z	z	PROPN
ejpam-5450	276	53	∈	∈	PROPN
ejpam-5450	276	54	x,∀ta	x,∀ta	NOUN
ejpam-5450	276	55	,	,	PUNCT
ejpam-5450	276	56	tb	tb	ADP
ejpam-5450	276	57	∈	∈	PROPN
ejpam-5450	276	58	(	(	PUNCT
ejpam-5450	276	59	0.5	0.5	NUM
ejpam-5450	276	60	,	,	PUNCT
ejpam-5450	276	61	1	1	NUM
ejpam-5450	276	62	]	]	PUNCT
ejpam-5450	276	63	)	)	PUNCT
ejpam-5450	276	64	(	(	PUNCT
ejpam-5450	276	65	[	[	X
ejpam-5450	276	66	x	x	X
ejpam-5450	276	67	◦	◦	NOUN
ejpam-5450	276	68	(	(	PUNCT
ejpam-5450	276	69	y	y	NOUN
ejpam-5450	276	70	◦	◦	NOUN
ejpam-5450	276	71	z)/ta	z)/ta	NOUN
ejpam-5450	276	72	]	]	X
ejpam-5450	276	73	∈	∈	PROPN
ejpam-5450	276	74	lε	lε	X
ejpam-5450	276	75	µ	µ	NOUN
ejpam-5450	276	76	,	,	PUNCT
ejpam-5450	276	77	[	[	X
ejpam-5450	276	78	y	y	X
ejpam-5450	276	79	/	/	SYM
ejpam-5450	276	80	tb	tb	NOUN
ejpam-5450	276	81	]	]	PUNCT
ejpam-5450	276	82	∈	∈	PROPN
ejpam-5450	276	83	lε	lε	X
ejpam-5450	276	84	µ	µ	X
ejpam-5450	276	85	⇒	⇒	NOUN
ejpam-5450	276	86	[	[	X
ejpam-5450	276	87	(	(	PUNCT
ejpam-5450	276	88	x	x	SYM
ejpam-5450	276	89	◦	◦	NOUN
ejpam-5450	276	90	z)/min{ta	z)/min{ta	PROPN
ejpam-5450	276	91	,	,	PUNCT
ejpam-5450	276	92	tb}]qlε	tb}]qlε	NOUN
ejpam-5450	276	93	µ	µ	NOUN
ejpam-5450	276	94	)	)	PUNCT
ejpam-5450	276	95	(	(	PUNCT
ejpam-5450	276	96	3.21	3.21	NUM
ejpam-5450	276	97	)	)	PUNCT
ejpam-5450	276	98	then	then	ADV
ejpam-5450	276	99	the	the	DET
ejpam-5450	276	100	o	o	NOUN
ejpam-5450	276	101	-	-	ADJ
ejpam-5450	276	102	set	set	VERB
ejpam-5450	276	103	o(lε	o(lε	PROPN
ejpam-5450	276	104	µ	µ	NOUN
ejpam-5450	276	105	)	)	PUNCT
ejpam-5450	276	106	of	of	ADP
ejpam-5450	276	107	lε	lε	PRON
ejpam-5450	276	108	µ	µ	PROPN
ejpam-5450	276	109	is	be	AUX
ejpam-5450	276	110	a	a	DET
ejpam-5450	276	111	bcc	bcc	PROPN
ejpam-5450	276	112	-	-	PUNCT
ejpam-5450	276	113	ideal	ideal	NOUN
ejpam-5450	276	114	of	of	ADP
ejpam-5450	276	115	x.	x.	NOUN
ejpam-5450	276	116	proof	proof	NOUN
ejpam-5450	276	117	.	.	PUNCT
ejpam-5450	277	1	if	if	SCONJ
ejpam-5450	277	2	y	y	PROPN
ejpam-5450	277	3	∈	∈	PROPN
ejpam-5450	277	4	o(lε	o(lε	PROPN
ejpam-5450	277	5	µ	µ	NOUN
ejpam-5450	277	6	)	)	PUNCT
ejpam-5450	277	7	,	,	PUNCT
ejpam-5450	277	8	then	then	ADV
ejpam-5450	277	9	µ(y	µ(y	PROPN
ejpam-5450	277	10	)	)	PUNCT
ejpam-5450	277	11	>	>	X
ejpam-5450	278	1	1−ε	1−ε	NUM
ejpam-5450	278	2	,	,	PUNCT
ejpam-5450	278	3	that	that	ADV
ejpam-5450	278	4	is	is	ADV
ejpam-5450	278	5	,	,	PUNCT
ejpam-5450	278	6	[	[	X
ejpam-5450	278	7	y/(1−ε	y/(1−ε	NOUN
ejpam-5450	278	8	)	)	PUNCT
ejpam-5450	278	9	]	]	PUNCT
ejpam-5450	279	1	∈	∈	PROPN
ejpam-5450	279	2	µ.	µ.	NOUN
ejpam-5450	279	3	hence	hence	ADV
ejpam-5450	279	4	,	,	PUNCT
ejpam-5450	279	5	[	[	X
ejpam-5450	279	6	0/(1−ε)]qlε	0/(1−ε)]qlε	X
ejpam-5450	279	7	µ	µ	X
ejpam-5450	279	8	by	by	ADP
ejpam-5450	279	9	(	(	PUNCT
ejpam-5450	279	10	3.20	3.20	NUM
ejpam-5450	279	11	)	)	PUNCT
ejpam-5450	279	12	,	,	PUNCT
ejpam-5450	279	13	and	and	CCONJ
ejpam-5450	279	14	thus	thus	ADV
ejpam-5450	279	15	lε	lε	VERB
ejpam-5450	279	16	µ(0)+1−ε	µ(0)+1−ε	NOUN
ejpam-5450	279	17	>	>	X
ejpam-5450	279	18	1	1	X
ejpam-5450	279	19	.	.	PUNCT
ejpam-5450	280	1	thus	thus	ADV
ejpam-5450	280	2	,	,	PUNCT
ejpam-5450	280	3	lε	lε	X
ejpam-5450	280	4	µ(0	µ(0	NOUN
ejpam-5450	280	5	)	)	PUNCT
ejpam-5450	280	6	>	>	X
ejpam-5450	280	7	ε	ε	PROPN
ejpam-5450	280	8	>	>	X
ejpam-5450	280	9	0	0	PROPN
ejpam-5450	280	10	,	,	PUNCT
ejpam-5450	280	11	which	which	PRON
ejpam-5450	280	12	shows	show	VERB
ejpam-5450	280	13	that	that	SCONJ
ejpam-5450	280	14	0	0	NUM
ejpam-5450	280	15	∈	∈	PROPN
ejpam-5450	280	16	o(lε	o(lε	PROPN
ejpam-5450	280	17	µ	µ	NOUN
ejpam-5450	280	18	)	)	PUNCT
ejpam-5450	280	19	.	.	PUNCT
ejpam-5450	281	1	let	let	VERB
ejpam-5450	281	2	x	x	PRON
ejpam-5450	281	3	,	,	PUNCT
ejpam-5450	281	4	y	y	PROPN
ejpam-5450	281	5	,	,	PUNCT
ejpam-5450	281	6	z	z	NOUN
ejpam-5450	281	7	∈	∈	PROPN
ejpam-5450	281	8	x	x	AUX
ejpam-5450	281	9	be	be	AUX
ejpam-5450	281	10	such	such	ADJ
ejpam-5450	281	11	that	that	SCONJ
ejpam-5450	281	12	x	x	X
ejpam-5450	281	13	◦	◦	NOUN
ejpam-5450	281	14	(	(	PUNCT
ejpam-5450	281	15	y	y	PROPN
ejpam-5450	281	16	◦	◦	PROPN
ejpam-5450	281	17	z	z	PROPN
ejpam-5450	281	18	)	)	PUNCT
ejpam-5450	281	19	∈	∈	PROPN
ejpam-5450	281	20	o(lε	o(lε	PROPN
ejpam-5450	281	21	µ	µ	NOUN
ejpam-5450	281	22	)	)	PUNCT
ejpam-5450	281	23	and	and	CCONJ
ejpam-5450	281	24	y	y	PROPN
ejpam-5450	281	25	∈	∈	PROPN
ejpam-5450	281	26	o(lε	o(lε	PROPN
ejpam-5450	281	27	µ	µ	NOUN
ejpam-5450	281	28	)	)	PUNCT
ejpam-5450	281	29	.	.	PUNCT
ejpam-5450	282	1	then	then	ADV
ejpam-5450	282	2	µ(x	µ(x	ADJ
ejpam-5450	282	3	◦	◦	NOUN
ejpam-5450	282	4	(	(	PUNCT
ejpam-5450	282	5	y	y	PROPN
ejpam-5450	282	6	◦	◦	PROPN
ejpam-5450	282	7	z	z	PROPN
ejpam-5450	282	8	)	)	PUNCT
ejpam-5450	282	9	)	)	PUNCT
ejpam-5450	283	1	+	+	CCONJ
ejpam-5450	283	2	ε−	ε−	PROPN
ejpam-5450	283	3	1	1	NUM
ejpam-5450	283	4	>	>	SYM
ejpam-5450	283	5	0	0	NUM
ejpam-5450	283	6	and	and	CCONJ
ejpam-5450	283	7	µ(y	µ(y	NUM
ejpam-5450	283	8	)	)	PUNCT
ejpam-5450	284	1	+	+	CCONJ
ejpam-5450	284	2	ε−	ε−	PROPN
ejpam-5450	284	3	1	1	NUM
ejpam-5450	284	4	>	>	X
ejpam-5450	284	5	0	0	X
ejpam-5450	284	6	.	.	PUNCT
ejpam-5450	285	1	since	since	SCONJ
ejpam-5450	285	2	[	[	X
ejpam-5450	285	3	x	x	PART
ejpam-5450	285	4	◦	◦	NOUN
ejpam-5450	285	5	(	(	PUNCT
ejpam-5450	285	6	y	y	PROPN
ejpam-5450	285	7	◦	◦	NOUN
ejpam-5450	285	8	z)/lε	z)/lε	PROPN
ejpam-5450	285	9	µ(x	µ(x	ADJ
ejpam-5450	285	10	◦	◦	NOUN
ejpam-5450	285	11	(	(	PUNCT
ejpam-5450	285	12	y	y	PROPN
ejpam-5450	285	13	◦	◦	PROPN
ejpam-5450	285	14	z	z	PROPN
ejpam-5450	285	15	)	)	PUNCT
ejpam-5450	285	16	)	)	PUNCT
ejpam-5450	285	17	]	]	PUNCT
ejpam-5450	286	1	∈	∈	PROPN
ejpam-5450	286	2	lε	lε	ADP
ejpam-5450	286	3	µ	µ	NOUN
ejpam-5450	286	4	and	and	CCONJ
ejpam-5450	286	5	[	[	X
ejpam-5450	286	6	y	y	X
ejpam-5450	286	7	/	/	SYM
ejpam-5450	286	8	lε	lε	X
ejpam-5450	286	9	µ(y	µ(y	PROPN
ejpam-5450	286	10	)	)	PUNCT
ejpam-5450	286	11	]	]	PUNCT
ejpam-5450	287	1	∈	∈	PROPN
ejpam-5450	287	2	lε	lε	VERB
ejpam-5450	287	3	µ.	µ.	PROPN
ejpam-5450	287	4	it	it	PRON
ejpam-5450	287	5	follows	follow	VERB
ejpam-5450	287	6	from	from	ADP
ejpam-5450	287	7	(	(	PUNCT
ejpam-5450	287	8	3.21	3.21	NUM
ejpam-5450	287	9	)	)	PUNCT
ejpam-5450	287	10	that	that	SCONJ
ejpam-5450	287	11	[	[	X
ejpam-5450	287	12	(	(	PUNCT
ejpam-5450	287	13	x	x	SYM
ejpam-5450	287	14	◦	◦	NOUN
ejpam-5450	287	15	z)/max{lε	z)/max{lε	PROPN
ejpam-5450	287	16	µ(x	µ(x	PUNCT
ejpam-5450	287	17	◦	◦	NOUN
ejpam-5450	287	18	(	(	PUNCT
ejpam-5450	287	19	y	y	PROPN
ejpam-5450	287	20	◦	◦	PROPN
ejpam-5450	287	21	z	z	PROPN
ejpam-5450	287	22	)	)	PUNCT
ejpam-5450	287	23	)	)	PUNCT
ejpam-5450	287	24	,	,	PUNCT
ejpam-5450	287	25	lε	lε	ADP
ejpam-5450	287	26	µ(y)}]qlε	µ(y)}]qlε	VERB
ejpam-5450	287	27	µ.	µ.	NOUN
ejpam-5450	287	28	(	(	PUNCT
ejpam-5450	287	29	3.22	3.22	NUM
ejpam-5450	287	30	)	)	PUNCT
ejpam-5450	287	31	if	if	SCONJ
ejpam-5450	287	32	x	x	PART
ejpam-5450	287	33	◦	◦	NOUN
ejpam-5450	287	34	z	z	NOUN
ejpam-5450	287	35	/∈	/∈	PUNCT
ejpam-5450	287	36	o(lε	o(lε	PROPN
ejpam-5450	287	37	µ	µ	X
ejpam-5450	287	38	)	)	PUNCT
ejpam-5450	287	39	,	,	PUNCT
ejpam-5450	287	40	then	then	ADV
ejpam-5450	287	41	lε	lε	ADP
ejpam-5450	287	42	µ(x	µ(x	ADJ
ejpam-5450	287	43	◦	◦	NOUN
ejpam-5450	287	44	z	z	NOUN
ejpam-5450	287	45	)	)	PUNCT
ejpam-5450	287	46	=	=	SYM
ejpam-5450	287	47	0	0	X
ejpam-5450	287	48	.	.	PUNCT
ejpam-5450	288	1	thus	thus	ADV
ejpam-5450	288	2	,	,	PUNCT
ejpam-5450	288	3	lε	lε	ADP
ejpam-5450	288	4	µ(x	µ(x	ADJ
ejpam-5450	288	5	◦	◦	NOUN
ejpam-5450	288	6	z	z	NOUN
ejpam-5450	288	7	)	)	PUNCT
ejpam-5450	288	8	+	+	NUM
ejpam-5450	288	9	max{lε	max{lε	PUNCT
ejpam-5450	288	10	µ(x	µ(x	ADJ
ejpam-5450	288	11	◦	◦	NOUN
ejpam-5450	288	12	(	(	PUNCT
ejpam-5450	288	13	y	y	PROPN
ejpam-5450	288	14	◦	◦	PROPN
ejpam-5450	288	15	z	z	PROPN
ejpam-5450	288	16	)	)	PUNCT
ejpam-5450	288	17	)	)	PUNCT
ejpam-5450	288	18	,	,	PUNCT
ejpam-5450	288	19	lε	lε	X
ejpam-5450	288	20	µ(y	µ(y	PROPN
ejpam-5450	288	21	)	)	PUNCT
ejpam-5450	288	22	}	}	PUNCT
ejpam-5450	288	23	=	=	SYM
ejpam-5450	288	24	max{lε	max{lε	NUM
ejpam-5450	288	25	µ(x	µ(x	VERB
ejpam-5450	288	26	◦	◦	NOUN
ejpam-5450	288	27	(	(	PUNCT
ejpam-5450	288	28	y	y	PROPN
ejpam-5450	288	29	◦	◦	PROPN
ejpam-5450	288	30	z	z	PROPN
ejpam-5450	288	31	)	)	PUNCT
ejpam-5450	288	32	)	)	PUNCT
ejpam-5450	288	33	,	,	PUNCT
ejpam-5450	288	34	lε	lε	X
ejpam-5450	288	35	µ(y	µ(y	PROPN
ejpam-5450	288	36	)	)	PUNCT
ejpam-5450	288	37	}	}	PUNCT
ejpam-5450	288	38	=	=	SYM
ejpam-5450	288	39	max{max{0	max{max{0	VERB
ejpam-5450	288	40	,	,	PUNCT
ejpam-5450	288	41	µ(x	µ(x	ADJ
ejpam-5450	288	42	◦	◦	NOUN
ejpam-5450	288	43	(	(	PUNCT
ejpam-5450	288	44	y	y	PROPN
ejpam-5450	288	45	◦	◦	PROPN
ejpam-5450	288	46	z	z	PROPN
ejpam-5450	288	47	)	)	PUNCT
ejpam-5450	288	48	)	)	PUNCT
ejpam-5450	289	1	+	+	CCONJ
ejpam-5450	289	2	ε−	ε−	PROPN
ejpam-5450	289	3	1},max{0	1},max{0	NUM
ejpam-5450	289	4	,	,	PUNCT
ejpam-5450	289	5	µ(y	µ(y	PROPN
ejpam-5450	289	6	)	)	PUNCT
ejpam-5450	289	7	+	+	CCONJ
ejpam-5450	289	8	ε−	ε−	PROPN
ejpam-5450	289	9	1	1	NUM
ejpam-5450	289	10	}	}	PUNCT
ejpam-5450	289	11	}	}	PUNCT
ejpam-5450	289	12	=	=	SYM
ejpam-5450	289	13	max{µ(x	max{µ(x	PROPN
ejpam-5450	289	14	◦	◦	NOUN
ejpam-5450	289	15	(	(	PUNCT
ejpam-5450	289	16	y	y	PROPN
ejpam-5450	289	17	◦	◦	PROPN
ejpam-5450	289	18	z	z	PROPN
ejpam-5450	289	19	)	)	PUNCT
ejpam-5450	289	20	)	)	PUNCT
ejpam-5450	290	1	+	+	CCONJ
ejpam-5450	290	2	ε−	ε−	PROPN
ejpam-5450	290	3	1	1	NUM
ejpam-5450	290	4	,	,	PUNCT
ejpam-5450	290	5	µ(y	µ(y	PROPN
ejpam-5450	290	6	)	)	PUNCT
ejpam-5450	290	7	+	+	CCONJ
ejpam-5450	290	8	ε−	ε−	PROPN
ejpam-5450	290	9	1	1	NUM
ejpam-5450	290	10	}	}	PUNCT
ejpam-5450	290	11	=	=	SYM
ejpam-5450	290	12	max{µ(x	max{µ(x	PROPN
ejpam-5450	290	13	◦	◦	NOUN
ejpam-5450	290	14	(	(	PUNCT
ejpam-5450	290	15	y	y	PROPN
ejpam-5450	290	16	◦	◦	PROPN
ejpam-5450	290	17	z	z	PROPN
ejpam-5450	290	18	)	)	PUNCT
ejpam-5450	290	19	)	)	PUNCT
ejpam-5450	290	20	,	,	PUNCT
ejpam-5450	290	21	µ(y	µ(y	PROPN
ejpam-5450	290	22	)	)	PUNCT
ejpam-5450	290	23	}	}	PUNCT
ejpam-5450	290	24	+	+	CCONJ
ejpam-5450	290	25	ε−	ε−	PROPN
ejpam-5450	290	26	1	1	NUM
ejpam-5450	290	27	≤	≤	NUM
ejpam-5450	290	28	1	1	NUM
ejpam-5450	290	29	+	+	CCONJ
ejpam-5450	290	30	ε−	ε−	PROPN
ejpam-5450	290	31	1	1	NUM
ejpam-5450	290	32	=	=	SYM
ejpam-5450	290	33	ε	ε	PROPN
ejpam-5450	290	34	≤	≤	ADJ
ejpam-5450	290	35	1	1	NUM
ejpam-5450	290	36	,	,	PUNCT
ejpam-5450	290	37	which	which	PRON
ejpam-5450	290	38	shows	show	VERB
ejpam-5450	290	39	that	that	SCONJ
ejpam-5450	290	40	(	(	PUNCT
ejpam-5450	290	41	3.22	3.22	NUM
ejpam-5450	290	42	)	)	PUNCT
ejpam-5450	290	43	is	be	AUX
ejpam-5450	290	44	not	not	PART
ejpam-5450	290	45	valid	valid	ADJ
ejpam-5450	290	46	.	.	PUNCT
ejpam-5450	291	1	this	this	PRON
ejpam-5450	291	2	is	be	AUX
ejpam-5450	291	3	a	a	DET
ejpam-5450	291	4	contradiction	contradiction	NOUN
ejpam-5450	291	5	.	.	PUNCT
ejpam-5450	292	1	so	so	ADV
ejpam-5450	292	2	x	x	PUNCT
ejpam-5450	292	3	◦	◦	NOUN
ejpam-5450	292	4	z	z	NOUN
ejpam-5450	292	5	∈	∈	PROPN
ejpam-5450	292	6	o(lε	o(lε	PROPN
ejpam-5450	292	7	µ	µ	NOUN
ejpam-5450	292	8	)	)	PUNCT
ejpam-5450	292	9	.	.	PUNCT
ejpam-5450	293	1	hence	hence	ADV
ejpam-5450	293	2	,	,	PUNCT
ejpam-5450	293	3	o(lε	o(lε	PROPN
ejpam-5450	293	4	µ	µ	NOUN
ejpam-5450	293	5	)	)	PUNCT
ejpam-5450	293	6	is	be	AUX
ejpam-5450	293	7	a	a	DET
ejpam-5450	293	8	bcc	bcc	PROPN
ejpam-5450	293	9	-	-	PUNCT
ejpam-5450	293	10	ideal	ideal	NOUN
ejpam-5450	293	11	of	of	ADP
ejpam-5450	293	12	x.	x.	PROPN
ejpam-5450	293	13	theorem	theorem	VERB
ejpam-5450	293	14	13	13	NUM
ejpam-5450	293	15	.	.	PUNCT
ejpam-5450	294	1	let	let	VERB
ejpam-5450	294	2	µ	µ	X
ejpam-5450	294	3	be	be	AUX
ejpam-5450	294	4	a	a	DET
ejpam-5450	294	5	fuzzy	fuzzy	ADJ
ejpam-5450	294	6	set	set	NOUN
ejpam-5450	294	7	in	in	ADP
ejpam-5450	294	8	x.	x.	NOUN
ejpam-5450	294	9	if	if	SCONJ
ejpam-5450	294	10	an	an	DET
ejpam-5450	294	11	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	294	12	fuzzy	fuzzy	ADJ
ejpam-5450	294	13	set	set	VERB
ejpam-5450	294	14	lε	lε	PRON
ejpam-5450	294	15	µ	µ	PROPN
ejpam-5450	294	16	of	of	ADP
ejpam-5450	294	17	µ	µ	NOUN
ejpam-5450	294	18	in	in	ADP
ejpam-5450	294	19	x	x	X
ejpam-5450	294	20	satisfies	satisfie	NOUN
ejpam-5450	294	21	[	[	X
ejpam-5450	294	22	0	0	NUM
ejpam-5450	294	23	/	/	SYM
ejpam-5450	294	24	ε]qµ	ε]qµ	NOUN
ejpam-5450	294	25	and	and	CCONJ
ejpam-5450	294	26	the	the	DET
ejpam-5450	294	27	following	follow	VERB
ejpam-5450	294	28	property	property	NOUN
ejpam-5450	294	29	:	:	PUNCT
ejpam-5450	294	30	(	(	PUNCT
ejpam-5450	294	31	∀x	∀x	X
ejpam-5450	294	32	,	,	PUNCT
ejpam-5450	294	33	y	y	PROPN
ejpam-5450	294	34	,	,	PUNCT
ejpam-5450	294	35	z	z	NOUN
ejpam-5450	294	36	∈	∈	PROPN
ejpam-5450	294	37	x	x	X
ejpam-5450	294	38	)	)	PUNCT
ejpam-5450	294	39	(	(	PUNCT
ejpam-5450	294	40	[	[	X
ejpam-5450	294	41	x	x	X
ejpam-5450	294	42	◦	◦	NOUN
ejpam-5450	294	43	(	(	PUNCT
ejpam-5450	294	44	y	y	PROPN
ejpam-5450	294	45	◦	◦	PROPN
ejpam-5450	294	46	z)/ε]qµ	z)/ε]qµ	PROPN
ejpam-5450	294	47	,	,	PUNCT
ejpam-5450	294	48	[	[	X
ejpam-5450	294	49	y	y	X
ejpam-5450	294	50	/	/	SYM
ejpam-5450	294	51	ε]qµ	ε]qµ	ADJ
ejpam-5450	294	52	⇒	⇒	NOUN
ejpam-5450	294	53	[	[	X
ejpam-5450	294	54	(	(	PUNCT
ejpam-5450	294	55	x	x	SYM
ejpam-5450	294	56	◦	◦	NOUN
ejpam-5450	294	57	z)/ε]qlε	z)/ε]qlε	X
ejpam-5450	294	58	µ	µ	X
ejpam-5450	294	59	)	)	PUNCT
ejpam-5450	294	60	,	,	PUNCT
ejpam-5450	294	61	(	(	PUNCT
ejpam-5450	294	62	3.23	3.23	NUM
ejpam-5450	294	63	)	)	PUNCT
ejpam-5450	294	64	then	then	ADV
ejpam-5450	294	65	the	the	DET
ejpam-5450	294	66	o	o	NOUN
ejpam-5450	294	67	-	-	ADJ
ejpam-5450	294	68	set	set	VERB
ejpam-5450	294	69	o(lε	o(lε	PROPN
ejpam-5450	294	70	µ	µ	NOUN
ejpam-5450	294	71	)	)	PUNCT
ejpam-5450	294	72	of	of	ADP
ejpam-5450	294	73	lε	lε	PRON
ejpam-5450	294	74	µ	µ	PROPN
ejpam-5450	294	75	is	be	AUX
ejpam-5450	294	76	a	a	DET
ejpam-5450	294	77	bcc	bcc	PROPN
ejpam-5450	294	78	-	-	PUNCT
ejpam-5450	294	79	ideal	ideal	NOUN
ejpam-5450	294	80	of	of	ADP
ejpam-5450	294	81	x.	x.	PROPN
ejpam-5450	294	82	references	reference	NOUN
ejpam-5450	294	83	3221	3221	NUM
ejpam-5450	294	84	proof	proof	NOUN
ejpam-5450	294	85	.	.	PUNCT
ejpam-5450	295	1	if	if	SCONJ
ejpam-5450	295	2	[	[	X
ejpam-5450	295	3	0	0	NUM
ejpam-5450	295	4	/	/	SYM
ejpam-5450	295	5	ε]qµ	ε]qµ	PROPN
ejpam-5450	295	6	,	,	PUNCT
ejpam-5450	295	7	then	then	ADV
ejpam-5450	295	8	µ(0)+ε	µ(0)+ε	CCONJ
ejpam-5450	295	9	>	>	SYM
ejpam-5450	295	10	1	1	NUM
ejpam-5450	296	1	and	and	CCONJ
ejpam-5450	296	2	so	so	ADV
ejpam-5450	296	3	lε	lε	ADP
ejpam-5450	296	4	µ(0	µ(0	NOUN
ejpam-5450	296	5	)	)	PUNCT
ejpam-5450	296	6	=	=	SYM
ejpam-5450	296	7	max{0	max{0	PROPN
ejpam-5450	296	8	,	,	PUNCT
ejpam-5450	296	9	µ(0)+ε−1	µ(0)+ε−1	PROPN
ejpam-5450	296	10	}	}	PUNCT
ejpam-5450	296	11	=	=	SYM
ejpam-5450	296	12	µ(0)+ε−1	µ(0)+ε−1	PROPN
ejpam-5450	296	13	>	>	X
ejpam-5450	296	14	0	0	PROPN
ejpam-5450	296	15	.	.	PUNCT
ejpam-5450	297	1	hence	hence	ADV
ejpam-5450	297	2	,	,	PUNCT
ejpam-5450	297	3	0	0	NUM
ejpam-5450	297	4	∈	∈	PROPN
ejpam-5450	297	5	o(lε	o(lε	PROPN
ejpam-5450	297	6	µ	µ	NOUN
ejpam-5450	297	7	)	)	PUNCT
ejpam-5450	297	8	.	.	PUNCT
ejpam-5450	298	1	let	let	VERB
ejpam-5450	298	2	x	x	PRON
ejpam-5450	298	3	,	,	PUNCT
ejpam-5450	298	4	y	y	PROPN
ejpam-5450	298	5	,	,	PUNCT
ejpam-5450	298	6	z	z	NOUN
ejpam-5450	298	7	∈	∈	PROPN
ejpam-5450	298	8	x	x	AUX
ejpam-5450	298	9	be	be	AUX
ejpam-5450	298	10	such	such	ADJ
ejpam-5450	298	11	that	that	SCONJ
ejpam-5450	298	12	x	x	X
ejpam-5450	298	13	◦	◦	NOUN
ejpam-5450	298	14	(	(	PUNCT
ejpam-5450	298	15	y	y	PROPN
ejpam-5450	298	16	◦	◦	PROPN
ejpam-5450	298	17	z	z	PROPN
ejpam-5450	298	18	)	)	PUNCT
ejpam-5450	298	19	∈	∈	PROPN
ejpam-5450	298	20	o(lε	o(lε	PROPN
ejpam-5450	298	21	µ	µ	NOUN
ejpam-5450	298	22	)	)	PUNCT
ejpam-5450	298	23	and	and	CCONJ
ejpam-5450	298	24	y	y	PROPN
ejpam-5450	298	25	∈	∈	PROPN
ejpam-5450	298	26	o(lε	o(lε	PROPN
ejpam-5450	298	27	µ	µ	NOUN
ejpam-5450	298	28	)	)	PUNCT
ejpam-5450	298	29	.	.	PUNCT
ejpam-5450	299	1	then	then	ADV
ejpam-5450	299	2	µ(x	µ(x	ADJ
ejpam-5450	299	3	◦	◦	NOUN
ejpam-5450	299	4	(	(	PUNCT
ejpam-5450	299	5	y	y	PROPN
ejpam-5450	299	6	◦	◦	PROPN
ejpam-5450	299	7	z	z	PROPN
ejpam-5450	299	8	)	)	PUNCT
ejpam-5450	299	9	)	)	PUNCT
ejpam-5450	300	1	+	+	CCONJ
ejpam-5450	300	2	ε	ε	PROPN
ejpam-5450	300	3	−	−	NOUN
ejpam-5450	300	4	1	1	NUM
ejpam-5450	300	5	>	>	SYM
ejpam-5450	300	6	0	0	NUM
ejpam-5450	300	7	and	and	CCONJ
ejpam-5450	300	8	µ(y	µ(y	NUM
ejpam-5450	300	9	)	)	PUNCT
ejpam-5450	301	1	+	+	CCONJ
ejpam-5450	301	2	ε	ε	PROPN
ejpam-5450	301	3	−	−	PROPN
ejpam-5450	301	4	1	1	NUM
ejpam-5450	301	5	>	>	X
ejpam-5450	301	6	0	0	NUM
ejpam-5450	301	7	.	.	PUNCT
ejpam-5450	302	1	hence	hence	ADV
ejpam-5450	302	2	,	,	PUNCT
ejpam-5450	302	3	lε	lε	ADP
ejpam-5450	302	4	µ(x	µ(x	ADJ
ejpam-5450	302	5	◦	◦	NOUN
ejpam-5450	302	6	(	(	PUNCT
ejpam-5450	302	7	y	y	PROPN
ejpam-5450	302	8	◦	◦	PROPN
ejpam-5450	302	9	z	z	PROPN
ejpam-5450	302	10	)	)	PUNCT
ejpam-5450	302	11	)	)	PUNCT
ejpam-5450	303	1	+	+	CCONJ
ejpam-5450	303	2	1	1	NUM
ejpam-5450	303	3	=	=	SYM
ejpam-5450	303	4	max{0	max{0	PROPN
ejpam-5450	303	5	,	,	PUNCT
ejpam-5450	303	6	µ(x	µ(x	ADJ
ejpam-5450	303	7	◦	◦	NOUN
ejpam-5450	303	8	(	(	PUNCT
ejpam-5450	303	9	y	y	PROPN
ejpam-5450	303	10	◦	◦	PROPN
ejpam-5450	303	11	z	z	PROPN
ejpam-5450	303	12	)	)	PUNCT
ejpam-5450	303	13	)	)	PUNCT
ejpam-5450	304	1	+	+	CCONJ
ejpam-5450	304	2	ε	ε	PROPN
ejpam-5450	304	3	−	−	NOUN
ejpam-5450	304	4	1	1	NUM
ejpam-5450	304	5	}	}	PUNCT
ejpam-5450	304	6	+	+	CCONJ
ejpam-5450	304	7	1	1	NUM
ejpam-5450	304	8	=	=	NOUN
ejpam-5450	304	9	µ(x	µ(x	PUNCT
ejpam-5450	304	10	◦	◦	NOUN
ejpam-5450	304	11	(	(	PUNCT
ejpam-5450	304	12	y	y	PROPN
ejpam-5450	304	13	◦	◦	PROPN
ejpam-5450	304	14	z	z	PROPN
ejpam-5450	304	15	)	)	PUNCT
ejpam-5450	304	16	)	)	PUNCT
ejpam-5450	305	1	+	+	CCONJ
ejpam-5450	305	2	ε	ε	PROPN
ejpam-5450	305	3	−	−	NUM
ejpam-5450	305	4	1	1	NUM
ejpam-5450	305	5	+	+	CCONJ
ejpam-5450	305	6	1	1	NUM
ejpam-5450	305	7	=	=	NOUN
ejpam-5450	305	8	µ(x	µ(x	PUNCT
ejpam-5450	305	9	◦	◦	NOUN
ejpam-5450	305	10	(	(	PUNCT
ejpam-5450	305	11	y	y	PROPN
ejpam-5450	305	12	◦	◦	PROPN
ejpam-5450	305	13	z	z	PROPN
ejpam-5450	305	14	)	)	PUNCT
ejpam-5450	305	15	)	)	PUNCT
ejpam-5450	306	1	+	+	CCONJ
ejpam-5450	306	2	ε	ε	X
ejpam-5450	306	3	>	>	X
ejpam-5450	306	4	1	1	NUM
ejpam-5450	306	5	and	and	CCONJ
ejpam-5450	306	6	lε	lε	ADP
ejpam-5450	306	7	µ(y	µ(y	PROPN
ejpam-5450	306	8	)	)	PUNCT
ejpam-5450	306	9	+	+	CCONJ
ejpam-5450	306	10	1	1	NUM
ejpam-5450	306	11	=	=	SYM
ejpam-5450	306	12	max{0	max{0	PROPN
ejpam-5450	306	13	,	,	PUNCT
ejpam-5450	306	14	µ(y	µ(y	PROPN
ejpam-5450	306	15	)	)	PUNCT
ejpam-5450	307	1	+	+	CCONJ
ejpam-5450	307	2	ε	ε	PROPN
ejpam-5450	307	3	−	−	NOUN
ejpam-5450	307	4	1	1	NUM
ejpam-5450	307	5	}	}	PUNCT
ejpam-5450	307	6	+	+	CCONJ
ejpam-5450	307	7	1	1	NUM
ejpam-5450	307	8	=	=	SYM
ejpam-5450	307	9	µ(y	µ(y	NOUN
ejpam-5450	307	10	)	)	PUNCT
ejpam-5450	308	1	+	+	CCONJ
ejpam-5450	308	2	ε	ε	PROPN
ejpam-5450	308	3	−	−	NUM
ejpam-5450	308	4	1	1	NUM
ejpam-5450	308	5	+	+	SYM
ejpam-5450	308	6	1	1	NUM
ejpam-5450	308	7	=	=	SYM
ejpam-5450	308	8	µ(y	µ(y	NOUN
ejpam-5450	308	9	)	)	PUNCT
ejpam-5450	308	10	+	+	CCONJ
ejpam-5450	308	11	ε	ε	PROPN
ejpam-5450	308	12	>	>	X
ejpam-5450	308	13	1	1	NUM
ejpam-5450	308	14	,	,	PUNCT
ejpam-5450	308	15	that	that	ADV
ejpam-5450	308	16	is	is	ADV
ejpam-5450	308	17	,	,	PUNCT
ejpam-5450	308	18	[	[	X
ejpam-5450	308	19	x	x	X
ejpam-5450	308	20	◦	◦	NOUN
ejpam-5450	308	21	(	(	PUNCT
ejpam-5450	308	22	y	y	NOUN
ejpam-5450	308	23	◦	◦	NOUN
ejpam-5450	308	24	z)/ε]qlε	z)/ε]qlε	ADJ
ejpam-5450	308	25	µ	µ	NOUN
ejpam-5450	308	26	and	and	CCONJ
ejpam-5450	308	27	[	[	X
ejpam-5450	308	28	y	y	NOUN
ejpam-5450	308	29	/	/	SYM
ejpam-5450	308	30	ε]qlε	ε]qlε	NOUN
ejpam-5450	308	31	µ.	µ.	NOUN
ejpam-5450	308	32	it	it	PRON
ejpam-5450	308	33	follows	follow	VERB
ejpam-5450	308	34	from	from	ADP
ejpam-5450	308	35	(	(	PUNCT
ejpam-5450	308	36	3.23	3.23	NUM
ejpam-5450	308	37	)	)	PUNCT
ejpam-5450	308	38	that	that	SCONJ
ejpam-5450	309	1	[	[	X
ejpam-5450	309	2	(	(	PUNCT
ejpam-5450	309	3	x	x	SYM
ejpam-5450	309	4	◦	◦	NOUN
ejpam-5450	309	5	z)/ε	z)/ε	PROPN
ejpam-5450	309	6	]	]	X
ejpam-5450	310	1	=	=	PUNCT
ejpam-5450	311	1	[	[	X
ejpam-5450	311	2	(	(	PUNCT
ejpam-5450	311	3	x	x	SYM
ejpam-5450	311	4	◦	◦	NOUN
ejpam-5450	311	5	z)/ε	z)/ε	PROPN
ejpam-5450	311	6	]	]	X
ejpam-5450	311	7	∈	∈	PROPN
ejpam-5450	311	8	lε	lε	X
ejpam-5450	311	9	µ	µ	NUM
ejpam-5450	311	10	,	,	PUNCT
ejpam-5450	311	11	which	which	PRON
ejpam-5450	311	12	shows	show	VERB
ejpam-5450	311	13	that	that	SCONJ
ejpam-5450	311	14	lε	lε	ADP
ejpam-5450	311	15	µ(x	µ(x	ADJ
ejpam-5450	311	16	◦	◦	NOUN
ejpam-5450	311	17	z	z	NOUN
ejpam-5450	311	18	)	)	PUNCT
ejpam-5450	311	19	≥	≥	X
ejpam-5450	311	20	ε	ε	PROPN
ejpam-5450	311	21	>	>	X
ejpam-5450	311	22	0	0	PROPN
ejpam-5450	311	23	.	.	PUNCT
ejpam-5450	312	1	hence	hence	ADV
ejpam-5450	312	2	,	,	PUNCT
ejpam-5450	312	3	x	x	PUNCT
ejpam-5450	312	4	◦	◦	NOUN
ejpam-5450	312	5	z	z	NOUN
ejpam-5450	312	6	∈	∈	PROPN
ejpam-5450	312	7	o(lε	o(lε	PROPN
ejpam-5450	312	8	µ	µ	NOUN
ejpam-5450	312	9	)	)	PUNCT
ejpam-5450	312	10	.	.	PUNCT
ejpam-5450	313	1	therefore	therefore	ADV
ejpam-5450	313	2	,	,	PUNCT
ejpam-5450	313	3	o(lε	o(lε	PROPN
ejpam-5450	313	4	µ	µ	NOUN
ejpam-5450	313	5	)	)	PUNCT
ejpam-5450	313	6	is	be	AUX
ejpam-5450	313	7	a	a	DET
ejpam-5450	313	8	bcc	bcc	PROPN
ejpam-5450	313	9	-	-	PUNCT
ejpam-5450	313	10	ideal	ideal	NOUN
ejpam-5450	313	11	of	of	ADP
ejpam-5450	313	12	x.	x.	NOUN
ejpam-5450	313	13	4	4	NUM
ejpam-5450	313	14	.	.	PUNCT
ejpam-5450	313	15	conclusions	conclusion	NOUN
ejpam-5450	313	16	the	the	DET
ejpam-5450	313	17	concept	concept	NOUN
ejpam-5450	313	18	of	of	ADP
ejpam-5450	313	19	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	313	20	fuzzy	fuzzy	ADJ
ejpam-5450	313	21	sets	set	NOUN
ejpam-5450	313	22	utilizing	utilize	VERB
ejpam-5450	313	23	the	the	DET
ejpam-5450	313	24	lukasiewicz	lukasiewicz	ADJ
ejpam-5450	313	25	t	t	PROPN
ejpam-5450	313	26	-	-	PUNCT
ejpam-5450	313	27	norm	norm	NOUN
ejpam-5450	313	28	was	be	AUX
ejpam-5450	313	29	introduced	introduce	VERB
ejpam-5450	313	30	by	by	ADP
ejpam-5450	313	31	jun	jun	PROPN
ejpam-5450	314	1	[	[	X
ejpam-5450	314	2	12	12	NUM
ejpam-5450	314	3	]	]	PUNCT
ejpam-5450	314	4	.	.	PUNCT
ejpam-5450	315	1	this	this	DET
ejpam-5450	315	2	paper	paper	NOUN
ejpam-5450	315	3	applies	apply	VERB
ejpam-5450	315	4	εlukasiewicz	εlukasiewicz	VERB
ejpam-5450	315	5	fuzzy	fuzzy	ADJ
ejpam-5450	315	6	sets	set	NOUN
ejpam-5450	315	7	to	to	ADP
ejpam-5450	315	8	bcc	bcc	PROPN
ejpam-5450	315	9	-	-	PUNCT
ejpam-5450	315	10	ideals	ideal	NOUN
ejpam-5450	315	11	within	within	ADP
ejpam-5450	315	12	bcc	bcc	PROPN
ejpam-5450	315	13	-	-	PUNCT
ejpam-5450	315	14	algebras	algebras	X
ejpam-5450	315	15	,	,	PUNCT
ejpam-5450	315	16	introducing	introduce	VERB
ejpam-5450	315	17	the	the	DET
ejpam-5450	315	18	concept	concept	NOUN
ejpam-5450	315	19	of	of	ADP
ejpam-5450	315	20	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	315	21	fuzzy	fuzzy	ADJ
ejpam-5450	315	22	bcc	bcc	PROPN
ejpam-5450	315	23	-	-	PUNCT
ejpam-5450	315	24	ideals	ideal	NOUN
ejpam-5450	315	25	and	and	CCONJ
ejpam-5450	315	26	exploring	explore	VERB
ejpam-5450	315	27	their	their	PRON
ejpam-5450	315	28	properties	property	NOUN
ejpam-5450	315	29	.	.	PUNCT
ejpam-5450	316	1	the	the	DET
ejpam-5450	316	2	characterization	characterization	NOUN
ejpam-5450	316	3	of	of	ADP
ejpam-5450	316	4	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	316	5	fuzzy	fuzzy	ADJ
ejpam-5450	316	6	bcc	bcc	PROPN
ejpam-5450	316	7	-	-	PUNCT
ejpam-5450	316	8	ideals	ideal	NOUN
ejpam-5450	316	9	is	be	AUX
ejpam-5450	316	10	discussed	discuss	VERB
ejpam-5450	316	11	,	,	PUNCT
ejpam-5450	316	12	along	along	ADP
ejpam-5450	316	13	with	with	ADP
ejpam-5450	316	14	the	the	DET
ejpam-5450	316	15	relationship	relationship	NOUN
ejpam-5450	316	16	between	between	ADP
ejpam-5450	316	17	fuzzy	fuzzy	ADJ
ejpam-5450	316	18	bcc	bcc	PROPN
ejpam-5450	316	19	-	-	PUNCT
ejpam-5450	316	20	ideals	ideal	NOUN
ejpam-5450	316	21	and	and	CCONJ
ejpam-5450	316	22	εlukasiewicz	εlukasiewicz	VERB
ejpam-5450	316	23	fuzzy	fuzzy	ADJ
ejpam-5450	316	24	bcc	bcc	PROPN
ejpam-5450	316	25	-	-	PUNCT
ejpam-5450	316	26	ideals	ideal	NOUN
ejpam-5450	316	27	.	.	PUNCT
ejpam-5450	317	1	conditions	condition	NOUN
ejpam-5450	317	2	are	be	AUX
ejpam-5450	317	3	provided	provide	VERB
ejpam-5450	317	4	under	under	ADP
ejpam-5450	317	5	which	which	PRON
ejpam-5450	317	6	εlukasiewicz	εlukasiewicz	VERB
ejpam-5450	317	7	fuzzy	fuzzy	ADJ
ejpam-5450	317	8	sets	set	NOUN
ejpam-5450	317	9	qualify	qualify	VERB
ejpam-5450	317	10	as	as	ADP
ejpam-5450	317	11	εlukasiewicz	εlukasiewicz	ADJ
ejpam-5450	317	12	fuzzy	fuzzy	ADJ
ejpam-5450	317	13	bcc	bcc	PROPN
ejpam-5450	317	14	-	-	PUNCT
ejpam-5450	317	15	ideals	ideal	NOUN
ejpam-5450	317	16	.	.	PUNCT
ejpam-5450	318	1	furthermore	furthermore	ADV
ejpam-5450	318	2	,	,	PUNCT
ejpam-5450	318	3	conditions	condition	NOUN
ejpam-5450	318	4	under	under	ADP
ejpam-5450	318	5	which	which	PRON
ejpam-5450	318	6	three	three	NUM
ejpam-5450	318	7	subsets—∈-set	subsets—∈-set	ADJ
ejpam-5450	318	8	,	,	PUNCT
ejpam-5450	318	9	q	q	NOUN
ejpam-5450	318	10	-	-	PUNCT
ejpam-5450	318	11	set	set	NOUN
ejpam-5450	318	12	,	,	PUNCT
ejpam-5450	318	13	and	and	CCONJ
ejpam-5450	318	14	o	o	X
ejpam-5450	318	15	-	-	NOUN
ejpam-5450	318	16	set	set	NOUN
ejpam-5450	318	17	—	—	PUNCT
ejpam-5450	318	18	can	can	AUX
ejpam-5450	318	19	be	be	AUX
ejpam-5450	318	20	bcc	bcc	PROPN
ejpam-5450	318	21	-	-	PUNCT
ejpam-5450	318	22	ideals	ideal	NOUN
ejpam-5450	318	23	are	be	AUX
ejpam-5450	318	24	explored	explore	VERB
ejpam-5450	318	25	.	.	PUNCT
ejpam-5450	319	1	this	this	DET
ejpam-5450	319	2	study	study	NOUN
ejpam-5450	319	3	’s	’s	PART
ejpam-5450	319	4	insights	insight	NOUN
ejpam-5450	319	5	and	and	CCONJ
ejpam-5450	319	6	findings	finding	NOUN
ejpam-5450	319	7	are	be	AUX
ejpam-5450	319	8	anticipated	anticipate	VERB
ejpam-5450	319	9	to	to	PART
ejpam-5450	319	10	be	be	AUX
ejpam-5450	319	11	applied	apply	VERB
ejpam-5450	319	12	in	in	ADP
ejpam-5450	319	13	future	future	ADJ
ejpam-5450	319	14	research	research	NOUN
ejpam-5450	319	15	concerning	concern	VERB
ejpam-5450	319	16	relevant	relevant	ADJ
ejpam-5450	319	17	algebraic	algebraic	ADJ
ejpam-5450	319	18	systems	system	NOUN
ejpam-5450	319	19	.	.	PUNCT
ejpam-5450	320	1	this	this	PRON
ejpam-5450	320	2	includes	include	VERB
ejpam-5450	320	3	exploring	explore	VERB
ejpam-5450	320	4	their	their	PRON
ejpam-5450	320	5	utility	utility	NOUN
ejpam-5450	320	6	as	as	ADP
ejpam-5450	320	7	mathematical	mathematical	ADJ
ejpam-5450	320	8	tools	tool	NOUN
ejpam-5450	320	9	applicable	applicable	ADJ
ejpam-5450	320	10	to	to	ADP
ejpam-5450	320	11	decision	decision	NOUN
ejpam-5450	320	12	theory	theory	NOUN
ejpam-5450	320	13	,	,	PUNCT
ejpam-5450	320	14	medical	medical	ADJ
ejpam-5450	320	15	diagnosis	diagnosis	NOUN
ejpam-5450	320	16	systems	system	NOUN
ejpam-5450	320	17	,	,	PUNCT
ejpam-5450	320	18	automation	automation	NOUN
ejpam-5450	320	19	systems	system	NOUN
ejpam-5450	320	20	,	,	PUNCT
ejpam-5450	320	21	and	and	CCONJ
ejpam-5450	320	22	other	other	ADJ
ejpam-5450	320	23	fields	field	NOUN
ejpam-5450	320	24	.	.	PUNCT
ejpam-5450	321	1	acknowledgements	acknowledgement	NOUN
ejpam-5450	321	2	this	this	DET
ejpam-5450	321	3	research	research	NOUN
ejpam-5450	321	4	was	be	AUX
ejpam-5450	321	5	supported	support	VERB
ejpam-5450	321	6	by	by	ADP
ejpam-5450	321	7	university	university	NOUN
ejpam-5450	321	8	of	of	ADP
ejpam-5450	321	9	phayao	phayao	NOUN
ejpam-5450	321	10	and	and	CCONJ
ejpam-5450	321	11	thailand	thailand	PROPN
ejpam-5450	321	12	science	science	PROPN
ejpam-5450	321	13	research	research	PROPN
ejpam-5450	321	14	and	and	CCONJ
ejpam-5450	321	15	innovation	innovation	NOUN
ejpam-5450	321	16	fund	fund	NOUN
ejpam-5450	321	17	(	(	PUNCT
ejpam-5450	321	18	fundamental	fundamental	ADJ
ejpam-5450	321	19	fund	fund	NOUN
ejpam-5450	321	20	2025	2025	NUM
ejpam-5450	321	21	,	,	PUNCT
ejpam-5450	321	22	grant	grant	VERB
ejpam-5450	321	23	no	no	NOUN
ejpam-5450	321	24	.	.	PROPN
ejpam-5450	322	1	5027/2567	5027/2567	NUM
ejpam-5450	322	2	)	)	PUNCT
ejpam-5450	322	3	.	.	PUNCT
ejpam-5450	323	1	references	reference	NOUN
ejpam-5450	323	2	[	[	X
ejpam-5450	323	3	1	1	NUM
ejpam-5450	323	4	]	]	PUNCT
ejpam-5450	323	5	b.	b.	PROPN
ejpam-5450	323	6	ahmad	ahmad	PROPN
ejpam-5450	323	7	and	and	CCONJ
ejpam-5450	323	8	a.	a.	PROPN
ejpam-5450	323	9	kharal	kharal	PROPN
ejpam-5450	323	10	.	.	PUNCT
ejpam-5450	324	1	on	on	ADP
ejpam-5450	324	2	fuzzy	fuzzy	ADJ
ejpam-5450	324	3	soft	soft	ADJ
ejpam-5450	324	4	sets	set	NOUN
ejpam-5450	324	5	.	.	PUNCT
ejpam-5450	325	1	adv	adv	PROPN
ejpam-5450	325	2	.	.	PUNCT
ejpam-5450	325	3	fuzzy	fuzzy	ADJ
ejpam-5450	325	4	syst	syst	PROPN
ejpam-5450	325	5	.	.	PUNCT
ejpam-5450	325	6	,	,	PUNCT
ejpam-5450	325	7	2009	2009	NUM
ejpam-5450	325	8	:	:	PUNCT
ejpam-5450	325	9	article	article	NOUN
ejpam-5450	325	10	i	i	PROPN
ejpam-5450	325	11	d	d	PROPN
ejpam-5450	325	12	586507	586507	NUM
ejpam-5450	325	13	,	,	PUNCT
ejpam-5450	325	14	6	6	NUM
ejpam-5450	325	15	pages	page	NOUN
ejpam-5450	325	16	,	,	PUNCT
ejpam-5450	325	17	2009	2009	NUM
ejpam-5450	325	18	.	.	PUNCT
ejpam-5450	326	1	[	[	X
ejpam-5450	326	2	2	2	NUM
ejpam-5450	326	3	]	]	PUNCT
ejpam-5450	326	4	m.	m.	NOUN
ejpam-5450	326	5	atef	atef	PROPN
ejpam-5450	326	6	,	,	PUNCT
ejpam-5450	326	7	m.	m.	PROPN
ejpam-5450	326	8	i.	i.	PROPN
ejpam-5450	326	9	ali	ali	PROPN
ejpam-5450	326	10	,	,	PUNCT
ejpam-5450	326	11	and	and	CCONJ
ejpam-5450	326	12	t.	t.	PROPN
ejpam-5450	326	13	al	al	PROPN
ejpam-5450	326	14	-	-	PUNCT
ejpam-5450	326	15	shami	shami	PROPN
ejpam-5450	326	16	.	.	PUNCT
ejpam-5450	327	1	fuzzy	fuzzy	ADJ
ejpam-5450	327	2	soft	soft	ADJ
ejpam-5450	327	3	covering	covering	NOUN
ejpam-5450	327	4	based	base	VERB
ejpam-5450	327	5	multi	multi	ADJ
ejpam-5450	327	6	-	-	ADJ
ejpam-5450	327	7	granulation	granulation	ADJ
ejpam-5450	327	8	fuzzy	fuzzy	ADJ
ejpam-5450	327	9	rough	rough	ADJ
ejpam-5450	327	10	sets	set	NOUN
ejpam-5450	327	11	and	and	CCONJ
ejpam-5450	327	12	their	their	PRON
ejpam-5450	327	13	applications	application	NOUN
ejpam-5450	327	14	.	.	PUNCT
ejpam-5450	328	1	comput	comput	NOUN
ejpam-5450	328	2	.	.	PUNCT
ejpam-5450	329	1	appl	appl	PROPN
ejpam-5450	329	2	.	.	PROPN
ejpam-5450	329	3	math	math	PROPN
ejpam-5450	329	4	.	.	PUNCT
ejpam-5450	329	5	,	,	PUNCT
ejpam-5450	329	6	40(4):115	40(4):115	PROPN
ejpam-5450	329	7	,	,	PUNCT
ejpam-5450	329	8	2021	2021	NUM
ejpam-5450	329	9	.	.	PUNCT
ejpam-5450	330	1	[	[	X
ejpam-5450	330	2	3	3	NUM
ejpam-5450	330	3	]	]	X
ejpam-5450	330	4	n.	n.	NOUN
ejpam-5450	330	5	caǧman	caǧman	PROPN
ejpam-5450	330	6	,	,	PUNCT
ejpam-5450	330	7	s.	s.	PROPN
ejpam-5450	330	8	enginoǧlu	enginoǧlu	PROPN
ejpam-5450	330	9	,	,	PUNCT
ejpam-5450	330	10	and	and	CCONJ
ejpam-5450	330	11	f.	f.	PROPN
ejpam-5450	330	12	citak	citak	PROPN
ejpam-5450	330	13	.	.	PUNCT
ejpam-5450	331	1	fuzzy	fuzzy	ADJ
ejpam-5450	331	2	soft	soft	ADJ
ejpam-5450	331	3	set	set	NOUN
ejpam-5450	331	4	theory	theory	NOUN
ejpam-5450	331	5	and	and	CCONJ
ejpam-5450	331	6	its	its	PRON
ejpam-5450	331	7	application	application	NOUN
ejpam-5450	331	8	.	.	PUNCT
ejpam-5450	332	1	iran	iran	PROPN
ejpam-5450	332	2	.	.	PUNCT
ejpam-5450	333	1	j.	j.	PROPN
ejpam-5450	333	2	fuzzy	fuzzy	PROPN
ejpam-5450	333	3	syst	syst	PROPN
ejpam-5450	333	4	.	.	PROPN
ejpam-5450	333	5	,	,	PUNCT
ejpam-5450	333	6	8(3):137–147	8(3):137–147	NUM
ejpam-5450	333	7	,	,	PUNCT
ejpam-5450	333	8	2011	2011	NUM
ejpam-5450	333	9	.	.	PUNCT
ejpam-5450	334	1	[	[	X
ejpam-5450	334	2	4	4	NUM
ejpam-5450	334	3	]	]	X
ejpam-5450	334	4	n.	n.	PROPN
ejpam-5450	334	5	dokkhamdang	dokkhamdang	PROPN
ejpam-5450	334	6	,	,	PUNCT
ejpam-5450	334	7	a.	a.	PROPN
ejpam-5450	334	8	kesorn	kesorn	PROPN
ejpam-5450	334	9	,	,	PUNCT
ejpam-5450	334	10	and	and	CCONJ
ejpam-5450	334	11	a.	a.	NOUN
ejpam-5450	334	12	iampan	iampan	PROPN
ejpam-5450	334	13	.	.	PUNCT
ejpam-5450	335	1	generalized	generalize	VERB
ejpam-5450	335	2	fuzzy	fuzzy	ADJ
ejpam-5450	335	3	sets	set	NOUN
ejpam-5450	335	4	in	in	ADP
ejpam-5450	335	5	up	up	ADP
ejpam-5450	335	6	-	-	PUNCT
ejpam-5450	335	7	algebras	algebras	X
ejpam-5450	335	8	.	.	PUNCT
ejpam-5450	336	1	ann	ann	PROPN
ejpam-5450	336	2	.	.	PUNCT
ejpam-5450	336	3	fuzzy	fuzzy	ADJ
ejpam-5450	336	4	math	math	NOUN
ejpam-5450	336	5	.	.	PUNCT
ejpam-5450	337	1	inform	inform	NOUN
ejpam-5450	337	2	.	.	PUNCT
ejpam-5450	337	3	,	,	PUNCT
ejpam-5450	337	4	16(2):171–190	16(2):171–190	NUM
ejpam-5450	337	5	,	,	PUNCT
ejpam-5450	337	6	2018	2018	NUM
ejpam-5450	337	7	.	.	PUNCT
ejpam-5450	338	1	references	reference	NOUN
ejpam-5450	338	2	3222	3222	NUM
ejpam-5450	338	3	[	[	X
ejpam-5450	338	4	5	5	NUM
ejpam-5450	338	5	]	]	X
ejpam-5450	338	6	d.	d.	PROPN
ejpam-5450	338	7	dubois	dubois	PROPN
ejpam-5450	338	8	and	and	CCONJ
ejpam-5450	338	9	h.	h.	PROPN
ejpam-5450	338	10	prade	prade	PROPN
ejpam-5450	338	11	.	.	PUNCT
ejpam-5450	339	1	fuzzy	fuzzy	ADJ
ejpam-5450	339	2	sets	set	NOUN
ejpam-5450	339	3	and	and	CCONJ
ejpam-5450	339	4	systems	system	NOUN
ejpam-5450	339	5	:	:	PUNCT
ejpam-5450	339	6	theory	theory	NOUN
ejpam-5450	339	7	and	and	CCONJ
ejpam-5450	339	8	applications	application	NOUN
ejpam-5450	339	9	.	.	PUNCT
ejpam-5450	340	1	academic	academic	ADJ
ejpam-5450	340	2	press	press	PROPN
ejpam-5450	340	3	,	,	PUNCT
ejpam-5450	340	4	inc	inc	PROPN
ejpam-5450	340	5	.	.	PROPN
ejpam-5450	340	6	,	,	PUNCT
ejpam-5450	340	7	1980	1980	NUM
ejpam-5450	340	8	.	.	PUNCT
ejpam-5450	341	1	[	[	X
ejpam-5450	341	2	6	6	NUM
ejpam-5450	341	3	]	]	PUNCT
ejpam-5450	341	4	j.	j.	PROPN
ejpam-5450	341	5	a.	a.	PROPN
ejpam-5450	341	6	goguen	goguen	PROPN
ejpam-5450	341	7	.	.	PUNCT
ejpam-5450	342	1	the	the	DET
ejpam-5450	342	2	logic	logic	NOUN
ejpam-5450	342	3	of	of	ADP
ejpam-5450	342	4	inexact	inexact	ADJ
ejpam-5450	342	5	concepts	concept	NOUN
ejpam-5450	342	6	.	.	PUNCT
ejpam-5450	343	1	synthese	synthese	ADJ
ejpam-5450	343	2	,	,	PUNCT
ejpam-5450	343	3	19(3	19(3	NUM
ejpam-5450	343	4	-	-	SYM
ejpam-5450	343	5	4):325–373	4):325–373	NOUN
ejpam-5450	343	6	,	,	PUNCT
ejpam-5450	343	7	1969	1969	NUM
ejpam-5450	343	8	.	.	PUNCT
ejpam-5450	344	1	[	[	X
ejpam-5450	344	2	7	7	X
ejpam-5450	344	3	]	]	X
ejpam-5450	344	4	t.	t.	NOUN
ejpam-5450	344	5	guntasow	guntasow	NOUN
ejpam-5450	344	6	,	,	PUNCT
ejpam-5450	344	7	s.	s.	PROPN
ejpam-5450	344	8	sajak	sajak	PROPN
ejpam-5450	344	9	,	,	PUNCT
ejpam-5450	344	10	a.	a.	PROPN
ejpam-5450	344	11	jomkham	jomkham	PROPN
ejpam-5450	344	12	,	,	PUNCT
ejpam-5450	344	13	and	and	CCONJ
ejpam-5450	344	14	a.	a.	NOUN
ejpam-5450	344	15	iampan	iampan	PROPN
ejpam-5450	344	16	.	.	PUNCT
ejpam-5450	345	1	fuzzy	fuzzy	ADJ
ejpam-5450	345	2	translations	translation	NOUN
ejpam-5450	345	3	of	of	ADP
ejpam-5450	345	4	a	a	DET
ejpam-5450	345	5	fuzzy	fuzzy	ADJ
ejpam-5450	345	6	set	set	NOUN
ejpam-5450	345	7	in	in	ADP
ejpam-5450	345	8	up	up	ADP
ejpam-5450	345	9	-	-	PUNCT
ejpam-5450	345	10	algebras	algebras	X
ejpam-5450	345	11	.	.	PUNCT
ejpam-5450	346	1	j.	j.	PROPN
ejpam-5450	346	2	indones	indones	PROPN
ejpam-5450	346	3	.	.	PUNCT
ejpam-5450	347	1	math	math	NOUN
ejpam-5450	347	2	.	.	PUNCT
ejpam-5450	348	1	soc	soc	PROPN
ejpam-5450	348	2	.	.	PROPN
ejpam-5450	348	3	,	,	PUNCT
ejpam-5450	348	4	23(2):1–19	23(2):1–19	NUM
ejpam-5450	348	5	,	,	PUNCT
ejpam-5450	348	6	2017	2017	NUM
ejpam-5450	348	7	.	.	PUNCT
ejpam-5450	349	1	[	[	X
ejpam-5450	349	2	8	8	NUM
ejpam-5450	349	3	]	]	X
ejpam-5450	349	4	y.	y.	PROPN
ejpam-5450	349	5	huang	huang	PROPN
ejpam-5450	349	6	.	.	PUNCT
ejpam-5450	350	1	bci	bci	PROPN
ejpam-5450	350	2	-	-	NOUN
ejpam-5450	350	3	algebra	algebra	NOUN
ejpam-5450	350	4	.	.	PUNCT
ejpam-5450	351	1	science	science	NOUN
ejpam-5450	351	2	press	press	PROPN
ejpam-5450	351	3	,	,	PUNCT
ejpam-5450	351	4	beijing	beijing	PROPN
ejpam-5450	351	5	,	,	PUNCT
ejpam-5450	351	6	china	china	PROPN
ejpam-5450	351	7	,	,	PUNCT
ejpam-5450	351	8	2006	2006	NUM
ejpam-5450	351	9	.	.	PUNCT
ejpam-5450	352	1	[	[	X
ejpam-5450	352	2	9	9	NUM
ejpam-5450	352	3	]	]	PUNCT
ejpam-5450	352	4	a.	a.	NOUN
ejpam-5450	352	5	iampan	iampan	PROPN
ejpam-5450	352	6	.	.	PUNCT
ejpam-5450	353	1	a	a	DET
ejpam-5450	353	2	new	new	ADJ
ejpam-5450	353	3	branch	branch	NOUN
ejpam-5450	353	4	of	of	ADP
ejpam-5450	353	5	the	the	DET
ejpam-5450	353	6	logical	logical	ADJ
ejpam-5450	353	7	algebra	algebra	NOUN
ejpam-5450	353	8	:	:	PUNCT
ejpam-5450	353	9	up	up	ADP
ejpam-5450	353	10	-	-	PUNCT
ejpam-5450	353	11	algebras	algebras	X
ejpam-5450	353	12	.	.	PUNCT
ejpam-5450	354	1	j.	j.	PROPN
ejpam-5450	354	2	algebra	algebra	PROPN
ejpam-5450	354	3	relat	relat	PROPN
ejpam-5450	354	4	.	.	PUNCT
ejpam-5450	355	1	top	top	PROPN
ejpam-5450	355	2	.	.	PROPN
ejpam-5450	355	3	,	,	PUNCT
ejpam-5450	355	4	5(1):35–54	5(1):35–54	NUM
ejpam-5450	355	5	,	,	PUNCT
ejpam-5450	355	6	2017	2017	NUM
ejpam-5450	355	7	.	.	PUNCT
ejpam-5450	356	1	[	[	X
ejpam-5450	356	2	10	10	NUM
ejpam-5450	356	3	]	]	PUNCT
ejpam-5450	356	4	a.	a.	NOUN
ejpam-5450	356	5	iampan	iampan	PROPN
ejpam-5450	356	6	,	,	PUNCT
ejpam-5450	356	7	r.	r.	PROPN
ejpam-5450	356	8	subasini	subasini	PROPN
ejpam-5450	356	9	,	,	PUNCT
ejpam-5450	356	10	and	and	CCONJ
ejpam-5450	356	11	n.	n.	PROPN
ejpam-5450	356	12	rajesh	rajesh	PROPN
ejpam-5450	356	13	.	.	PUNCT
ejpam-5450	357	1	εlukasiewicz	εlukasiewicz	VERB
ejpam-5450	357	2	fuzzy	fuzzy	ADJ
ejpam-5450	357	3	up	up	ADP
ejpam-5450	357	4	(	(	PUNCT
ejpam-5450	357	5	bcc)-subalgebras	bcc)-subalgebras	NUM
ejpam-5450	357	6	of	of	ADP
ejpam-5450	357	7	up	up	ADV
ejpam-5450	357	8	(	(	PUNCT
ejpam-5450	357	9	bcc)-algebras	bcc)-algebra	NOUN
ejpam-5450	357	10	.	.	PROPN
ejpam-5450	357	11	eur	eur	PROPN
ejpam-5450	357	12	.	.	PUNCT
ejpam-5450	358	1	j.	j.	PROPN
ejpam-5450	358	2	pure	pure	PROPN
ejpam-5450	358	3	appl	appl	PROPN
ejpam-5450	358	4	.	.	PUNCT
ejpam-5450	358	5	math	math	PROPN
ejpam-5450	358	6	.	.	PUNCT
ejpam-5450	358	7	,	,	PUNCT
ejpam-5450	358	8	17(3):2235–2245	17(3):2235–2245	NUM
ejpam-5450	358	9	,	,	PUNCT
ejpam-5450	358	10	2024	2024	NUM
ejpam-5450	358	11	.	.	PUNCT
ejpam-5450	359	1	[	[	X
ejpam-5450	359	2	11	11	NUM
ejpam-5450	359	3	]	]	X
ejpam-5450	359	4	c.	c.	PROPN
ejpam-5450	359	5	jana	jana	PROPN
ejpam-5450	359	6	,	,	PUNCT
ejpam-5450	359	7	t.	t.	PROPN
ejpam-5450	359	8	senapati	senapati	PROPN
ejpam-5450	359	9	,	,	PUNCT
ejpam-5450	359	10	and	and	CCONJ
ejpam-5450	359	11	m.	m.	NOUN
ejpam-5450	359	12	pal	pal	NOUN
ejpam-5450	359	13	.	.	PUNCT
ejpam-5450	360	1	(	(	PUNCT
ejpam-5450	360	2	∈,∈	∈,∈	X
ejpam-5450	360	3	∨q)-intuitionistic	∨q)-intuitionistic	ADJ
ejpam-5450	360	4	fuzzy	fuzzy	ADJ
ejpam-5450	360	5	bci	bci	NOUN
ejpam-5450	360	6	-	-	PUNCT
ejpam-5450	360	7	subalgebras	subalgebras	PROPN
ejpam-5450	360	8	of	of	ADP
ejpam-5450	360	9	a	a	DET
ejpam-5450	360	10	bci	bci	NOUN
ejpam-5450	360	11	-	-	NOUN
ejpam-5450	360	12	algebra	algebra	NOUN
ejpam-5450	360	13	.	.	PUNCT
ejpam-5450	361	1	j.	j.	PROPN
ejpam-5450	361	2	intell	intell	PROPN
ejpam-5450	361	3	.	.	PUNCT
ejpam-5450	362	1	fuzzy	fuzzy	ADJ
ejpam-5450	362	2	syst	syst	PROPN
ejpam-5450	362	3	.	.	PUNCT
ejpam-5450	362	4	,	,	PUNCT
ejpam-5450	362	5	31(1):613–621	31(1):613–621	PROPN
ejpam-5450	362	6	,	,	PUNCT
ejpam-5450	362	7	2016	2016	NUM
ejpam-5450	362	8	.	.	PUNCT
ejpam-5450	363	1	[	[	X
ejpam-5450	363	2	12	12	NUM
ejpam-5450	363	3	]	]	X
ejpam-5450	363	4	y.	y.	PROPN
ejpam-5450	363	5	b.	b.	PROPN
ejpam-5450	363	6	jun	jun	PROPN
ejpam-5450	363	7	.	.	PROPN
ejpam-5450	363	8	lukasiewicz	lukasiewicz	ADJ
ejpam-5450	363	9	fuzzy	fuzzy	ADJ
ejpam-5450	363	10	subalgebras	subalgebras	PROPN
ejpam-5450	363	11	in	in	ADP
ejpam-5450	363	12	bck	bck	PROPN
ejpam-5450	363	13	-	-	PUNCT
ejpam-5450	363	14	algebras	algebras	PROPN
ejpam-5450	363	15	and	and	CCONJ
ejpam-5450	363	16	bci	bci	NOUN
ejpam-5450	363	17	-	-	PUNCT
ejpam-5450	363	18	algebras	algebras	PROPN
ejpam-5450	363	19	.	.	PUNCT
ejpam-5450	364	1	ann	ann	PROPN
ejpam-5450	364	2	.	.	PUNCT
ejpam-5450	364	3	fuzzy	fuzzy	ADJ
ejpam-5450	364	4	math	math	NOUN
ejpam-5450	364	5	.	.	PUNCT
ejpam-5450	365	1	inform	inform	NOUN
ejpam-5450	365	2	.	.	PUNCT
ejpam-5450	365	3	,	,	PUNCT
ejpam-5450	365	4	23(2):213–223	23(2):213–223	NOUN
ejpam-5450	365	5	,	,	PUNCT
ejpam-5450	365	6	2022	2022	NUM
ejpam-5450	365	7	.	.	PUNCT
ejpam-5450	366	1	[	[	X
ejpam-5450	366	2	13	13	NUM
ejpam-5450	366	3	]	]	X
ejpam-5450	366	4	y.	y.	PROPN
ejpam-5450	366	5	b.	b.	PROPN
ejpam-5450	366	6	jun	jun	PROPN
ejpam-5450	366	7	,	,	PUNCT
ejpam-5450	366	8	b.	b.	PROPN
ejpam-5450	366	9	brundha	brundha	PROPN
ejpam-5450	366	10	,	,	PUNCT
ejpam-5450	366	11	n.	n.	PROPN
ejpam-5450	366	12	rajesh	rajesh	PROPN
ejpam-5450	366	13	,	,	PUNCT
ejpam-5450	366	14	and	and	CCONJ
ejpam-5450	366	15	r.	r.	PROPN
ejpam-5450	366	16	k.	k.	PROPN
ejpam-5450	366	17	bandaru	bandaru	PROPN
ejpam-5450	366	18	.	.	PUNCT
ejpam-5450	367	1	(	(	PUNCT
ejpam-5450	367	2	3	3	NUM
ejpam-5450	367	3	,	,	PUNCT
ejpam-5450	367	4	2)-fuzzy	2)-fuzzy	NUM
ejpam-5450	367	5	up	up	ADP
ejpam-5450	367	6	(	(	PUNCT
ejpam-5450	367	7	bcc)subalgebras	bcc)subalgebras	PROPN
ejpam-5450	367	8	and	and	CCONJ
ejpam-5450	367	9	(	(	PUNCT
ejpam-5450	367	10	3	3	NUM
ejpam-5450	367	11	,	,	PUNCT
ejpam-5450	367	12	2)-fuzzy	2)-fuzzy	NUM
ejpam-5450	367	13	up	up	ADP
ejpam-5450	367	14	(	(	PUNCT
ejpam-5450	367	15	bcc)-filters	bcc)-filter	NOUN
ejpam-5450	367	16	.	.	PUNCT
ejpam-5450	368	1	j.	j.	PROPN
ejpam-5450	368	2	mahani	mahani	PROPN
ejpam-5450	368	3	math	math	PROPN
ejpam-5450	368	4	.	.	PUNCT
ejpam-5450	369	1	res	re	NOUN
ejpam-5450	369	2	.	.	PUNCT
ejpam-5450	370	1	cent	cent	NOUN
ejpam-5450	370	2	.	.	PUNCT
ejpam-5450	370	3	,	,	PUNCT
ejpam-5450	370	4	11(3):1	11(3):1	NUM
ejpam-5450	370	5	–	–	PUNCT
ejpam-5450	370	6	14	14	NUM
ejpam-5450	370	7	,	,	PUNCT
ejpam-5450	370	8	2022	2022	NUM
ejpam-5450	370	9	.	.	PUNCT
ejpam-5450	371	1	[	[	X
ejpam-5450	371	2	14	14	NUM
ejpam-5450	371	3	]	]	PUNCT
ejpam-5450	371	4	e.	e.	PROPN
ejpam-5450	371	5	p.	p.	PROPN
ejpam-5450	371	6	klement	klement	PROPN
ejpam-5450	371	7	,	,	PUNCT
ejpam-5450	371	8	r.	r.	PROPN
ejpam-5450	371	9	mesiar	mesiar	PROPN
ejpam-5450	371	10	,	,	PUNCT
ejpam-5450	371	11	and	and	CCONJ
ejpam-5450	371	12	e.	e.	PROPN
ejpam-5450	371	13	pap	pap	PROPN
ejpam-5450	371	14	.	.	PUNCT
ejpam-5450	372	1	triangular	triangular	NOUN
ejpam-5450	372	2	norms	norm	NOUN
ejpam-5450	372	3	.	.	PUNCT
ejpam-5450	373	1	springer	springer	NOUN
ejpam-5450	373	2	,	,	PUNCT
ejpam-5450	373	3	2000	2000	NUM
ejpam-5450	373	4	.	.	PUNCT
ejpam-5450	374	1	[	[	X
ejpam-5450	374	2	15	15	NUM
ejpam-5450	374	3	]	]	X
ejpam-5450	374	4	y.	y.	PROPN
ejpam-5450	374	5	komori	komori	PROPN
ejpam-5450	374	6	.	.	PUNCT
ejpam-5450	375	1	the	the	DET
ejpam-5450	375	2	class	class	NOUN
ejpam-5450	375	3	of	of	ADP
ejpam-5450	375	4	bcc	bcc	PROPN
ejpam-5450	375	5	-	-	PUNCT
ejpam-5450	375	6	algebras	algebras	PROPN
ejpam-5450	375	7	is	be	AUX
ejpam-5450	375	8	not	not	PART
ejpam-5450	375	9	a	a	DET
ejpam-5450	375	10	variety	variety	NOUN
ejpam-5450	375	11	.	.	PUNCT
ejpam-5450	376	1	math	math	NOUN
ejpam-5450	376	2	.	.	PUNCT
ejpam-5450	377	1	japon	japon	PROPN
ejpam-5450	377	2	.	.	PROPN
ejpam-5450	377	3	,	,	PUNCT
ejpam-5450	377	4	29(3):391–394	29(3):391–394	NOUN
ejpam-5450	377	5	,	,	PUNCT
ejpam-5450	377	6	1984	1984	NUM
ejpam-5450	377	7	.	.	PUNCT
ejpam-5450	378	1	[	[	X
ejpam-5450	378	2	16	16	NUM
ejpam-5450	378	3	]	]	X
ejpam-5450	378	4	p.	p.	PROPN
ejpam-5450	378	5	poungsumpao	poungsumpao	PROPN
ejpam-5450	378	6	,	,	PUNCT
ejpam-5450	378	7	w.	w.	PROPN
ejpam-5450	378	8	kaijae	kaijae	PROPN
ejpam-5450	378	9	,	,	PUNCT
ejpam-5450	378	10	s.	s.	PROPN
ejpam-5450	378	11	arayarangsi	arayarangsi	PROPN
ejpam-5450	378	12	,	,	PUNCT
ejpam-5450	378	13	and	and	CCONJ
ejpam-5450	378	14	a.	a.	NOUN
ejpam-5450	378	15	iampan	iampan	PROPN
ejpam-5450	378	16	.	.	PUNCT
ejpam-5450	379	1	fuzzy	fuzzy	ADJ
ejpam-5450	379	2	up	up	ADJ
ejpam-5450	379	3	-	-	PUNCT
ejpam-5450	379	4	ideals	ideal	NOUN
ejpam-5450	379	5	and	and	CCONJ
ejpam-5450	379	6	fuzzy	fuzzy	ADJ
ejpam-5450	379	7	up	up	ADP
ejpam-5450	379	8	-	-	PUNCT
ejpam-5450	379	9	subalgebras	subalgebra	NOUN
ejpam-5450	379	10	of	of	ADP
ejpam-5450	379	11	up	up	ADV
ejpam-5450	379	12	-	-	PUNCT
ejpam-5450	379	13	algebras	algebras	NOUN
ejpam-5450	379	14	in	in	ADP
ejpam-5450	379	15	term	term	NOUN
ejpam-5450	379	16	of	of	ADP
ejpam-5450	379	17	level	level	NOUN
ejpam-5450	379	18	subsets	subset	NOUN
ejpam-5450	379	19	.	.	PUNCT
ejpam-5450	380	1	int	int	NOUN
ejpam-5450	380	2	.	.	PUNCT
ejpam-5450	381	1	j.	j.	PROPN
ejpam-5450	381	2	math	math	PROPN
ejpam-5450	381	3	.	.	PUNCT
ejpam-5450	382	1	comput	comput	NOUN
ejpam-5450	382	2	.	.	PUNCT
ejpam-5450	383	1	sci	sci	PROPN
ejpam-5450	383	2	.	.	PROPN
ejpam-5450	383	3	,	,	PUNCT
ejpam-5450	383	4	14(3):647–674	14(3):647–674	NUM
ejpam-5450	383	5	,	,	PUNCT
ejpam-5450	383	6	2019	2019	NUM
ejpam-5450	383	7	.	.	PUNCT
ejpam-5450	384	1	[	[	X
ejpam-5450	384	2	17	17	NUM
ejpam-5450	384	3	]	]	X
ejpam-5450	384	4	p.	p.	NOUN
ejpam-5450	384	5	m.	m.	NOUN
ejpam-5450	384	6	pu	pu	PROPN
ejpam-5450	384	7	and	and	CCONJ
ejpam-5450	384	8	y.	y.	PROPN
ejpam-5450	384	9	m.	m.	PROPN
ejpam-5450	384	10	liu	liu	PROPN
ejpam-5450	384	11	.	.	PROPN
ejpam-5450	385	1	fuzzy	fuzzy	ADJ
ejpam-5450	385	2	topology	topology	PROPN
ejpam-5450	385	3	i.	i.	PROPN
ejpam-5450	385	4	neighborhood	neighborhood	PROPN
ejpam-5450	385	5	structure	structure	NOUN
ejpam-5450	385	6	of	of	ADP
ejpam-5450	385	7	a	a	DET
ejpam-5450	385	8	fuzzy	fuzzy	ADJ
ejpam-5450	385	9	point	point	NOUN
ejpam-5450	385	10	and	and	CCONJ
ejpam-5450	385	11	moore	moore	PROPN
ejpam-5450	385	12	-	-	PUNCT
ejpam-5450	385	13	smith	smith	PROPN
ejpam-5450	385	14	convergence	convergence	NOUN
ejpam-5450	385	15	.	.	PUNCT
ejpam-5450	386	1	j.	j.	PROPN
ejpam-5450	386	2	math	math	PROPN
ejpam-5450	386	3	.	.	PUNCT
ejpam-5450	387	1	anal	anal	PROPN
ejpam-5450	387	2	.	.	PUNCT
ejpam-5450	388	1	appl	appl	PROPN
ejpam-5450	388	2	.	.	PROPN
ejpam-5450	389	1	,	,	PUNCT
ejpam-5450	389	2	76(2):571–599	76(2):571–599	PROPN
ejpam-5450	389	3	,	,	PUNCT
ejpam-5450	389	4	1980	1980	NUM
ejpam-5450	389	5	.	.	PUNCT
ejpam-5450	390	1	[	[	X
ejpam-5450	390	2	18	18	NUM
ejpam-5450	390	3	]	]	PUNCT
ejpam-5450	390	4	t.	t.	NOUN
ejpam-5450	390	5	senapati	senapati	PROPN
ejpam-5450	390	6	,	,	PUNCT
ejpam-5450	390	7	y.	y.	PROPN
ejpam-5450	390	8	b.	b.	PROPN
ejpam-5450	390	9	jun	jun	PROPN
ejpam-5450	390	10	,	,	PUNCT
ejpam-5450	390	11	and	and	CCONJ
ejpam-5450	390	12	k.	k.	PROPN
ejpam-5450	390	13	p.	p.	PROPN
ejpam-5450	390	14	shum	shum	PROPN
ejpam-5450	390	15	.	.	PUNCT
ejpam-5450	391	1	cubic	cubic	ADJ
ejpam-5450	391	2	set	set	VERB
ejpam-5450	391	3	structure	structure	NOUN
ejpam-5450	391	4	applied	apply	VERB
ejpam-5450	391	5	in	in	ADP
ejpam-5450	391	6	up	up	ADP
ejpam-5450	391	7	-	-	PUNCT
ejpam-5450	391	8	algebras	algebras	X
ejpam-5450	391	9	.	.	PUNCT
ejpam-5450	392	1	discrete	discrete	ADJ
ejpam-5450	392	2	math	math	NOUN
ejpam-5450	392	3	.	.	PUNCT
ejpam-5450	393	1	algorithms	algorithms	PROPN
ejpam-5450	393	2	appl	appl	PROPN
ejpam-5450	393	3	.	.	PROPN
ejpam-5450	393	4	,	,	PUNCT
ejpam-5450	393	5	10(4):1850049	10(4):1850049	NUM
ejpam-5450	393	6	,	,	PUNCT
ejpam-5450	393	7	2018	2018	NUM
ejpam-5450	393	8	.	.	PUNCT
ejpam-5450	394	1	[	[	X
ejpam-5450	394	2	19	19	NUM
ejpam-5450	394	3	]	]	PUNCT
ejpam-5450	394	4	t.	t.	NOUN
ejpam-5450	394	5	senapati	senapati	PROPN
ejpam-5450	394	6	,	,	PUNCT
ejpam-5450	394	7	g.	g.	PROPN
ejpam-5450	394	8	muhiuddin	muhiuddin	PROPN
ejpam-5450	394	9	,	,	PUNCT
ejpam-5450	394	10	and	and	CCONJ
ejpam-5450	394	11	k.	k.	PROPN
ejpam-5450	394	12	p.	p.	PROPN
ejpam-5450	394	13	shum	shum	PROPN
ejpam-5450	394	14	.	.	PUNCT
ejpam-5450	395	1	representation	representation	NOUN
ejpam-5450	395	2	of	of	ADP
ejpam-5450	395	3	up	up	ADV
ejpam-5450	395	4	-	-	PUNCT
ejpam-5450	395	5	algebras	algebras	NOUN
ejpam-5450	395	6	in	in	ADP
ejpam-5450	395	7	interval	interval	NOUN
ejpam-5450	395	8	-	-	PUNCT
ejpam-5450	395	9	valued	value	VERB
ejpam-5450	395	10	intuitionistic	intuitionistic	ADJ
ejpam-5450	395	11	fuzzy	fuzzy	ADJ
ejpam-5450	395	12	environment	environment	NOUN
ejpam-5450	395	13	.	.	PUNCT
ejpam-5450	396	1	ital	ital	PROPN
ejpam-5450	396	2	.	.	PUNCT
ejpam-5450	397	1	j.	j.	PROPN
ejpam-5450	397	2	pure	pure	PROPN
ejpam-5450	397	3	appl	appl	PROPN
ejpam-5450	397	4	.	.	PUNCT
ejpam-5450	397	5	math	math	PROPN
ejpam-5450	397	6	.	.	PUNCT
ejpam-5450	397	7	,	,	PUNCT
ejpam-5450	397	8	38:497	38:497	NUM
ejpam-5450	397	9	–	–	PUNCT
ejpam-5450	397	10	518	518	NUM
ejpam-5450	397	11	,	,	PUNCT
ejpam-5450	397	12	2017	2017	NUM
ejpam-5450	397	13	.	.	PUNCT
ejpam-5450	398	1	[	[	X
ejpam-5450	398	2	20	20	NUM
ejpam-5450	398	3	]	]	PUNCT
ejpam-5450	398	4	j.	j.	PROPN
ejpam-5450	398	5	somjanta	somjanta	PROPN
ejpam-5450	398	6	,	,	PUNCT
ejpam-5450	398	7	n.	n.	PROPN
ejpam-5450	398	8	thuekaew	thuekaew	PROPN
ejpam-5450	398	9	,	,	PUNCT
ejpam-5450	398	10	p.	p.	NOUN
ejpam-5450	398	11	kumpeangkeaw	kumpeangkeaw	PROPN
ejpam-5450	398	12	,	,	PUNCT
ejpam-5450	398	13	and	and	CCONJ
ejpam-5450	398	14	a.	a.	NOUN
ejpam-5450	398	15	iampan	iampan	PROPN
ejpam-5450	398	16	.	.	PUNCT
ejpam-5450	399	1	fuzzy	fuzzy	ADJ
ejpam-5450	399	2	sets	set	NOUN
ejpam-5450	399	3	in	in	ADP
ejpam-5450	399	4	upalgebras	upalgebra	NOUN
ejpam-5450	399	5	.	.	PUNCT
ejpam-5450	400	1	ann	ann	PROPN
ejpam-5450	400	2	.	.	PUNCT
ejpam-5450	400	3	fuzzy	fuzzy	ADJ
ejpam-5450	400	4	math	math	NOUN
ejpam-5450	400	5	.	.	PUNCT
ejpam-5450	401	1	inform	inform	NOUN
ejpam-5450	401	2	.	.	PUNCT
ejpam-5450	401	3	,	,	PUNCT
ejpam-5450	401	4	12(6):739–756	12(6):739–756	PROPN
ejpam-5450	401	5	,	,	PUNCT
ejpam-5450	401	6	2016	2016	NUM
ejpam-5450	401	7	.	.	PUNCT
ejpam-5450	402	1	[	[	X
ejpam-5450	402	2	21	21	NUM
ejpam-5450	402	3	]	]	X
ejpam-5450	402	4	l.	l.	PROPN
ejpam-5450	402	5	a.	a.	PROPN
ejpam-5450	402	6	zadeh	zadeh	PROPN
ejpam-5450	402	7	.	.	PUNCT
ejpam-5450	402	8	fuzzy	fuzzy	ADJ
ejpam-5450	402	9	sets	set	NOUN
ejpam-5450	402	10	.	.	PUNCT
ejpam-5450	403	1	inf	inf	PROPN
ejpam-5450	403	2	.	.	PUNCT
ejpam-5450	403	3	control	control	PROPN
ejpam-5450	403	4	,	,	PUNCT
ejpam-5450	403	5	8(3):338–353	8(3):338–353	NUM
ejpam-5450	403	6	,	,	PUNCT
ejpam-5450	403	7	1965	1965	NUM
ejpam-5450	403	8	.	.	PUNCT