id	sid	tid	token	lemma	pos
ejpam-3412	1	1	european	european	PROPN
ejpam-3412	1	2	journal	journal	PROPN
ejpam-3412	1	3	of	of	ADP
ejpam-3412	1	4	pure	pure	ADJ
ejpam-3412	1	5	and	and	CCONJ
ejpam-3412	1	6	applied	apply	VERB
ejpam-3412	1	7	mathematics	mathematic	NOUN
ejpam-3412	1	8	vol	vol	NOUN
ejpam-3412	1	9	.	.	PROPN
ejpam-3412	2	1	12	12	NUM
ejpam-3412	2	2	,	,	PUNCT
ejpam-3412	2	3	no	no	INTJ
ejpam-3412	2	4	.	.	NOUN
ejpam-3412	2	5	2	2	NUM
ejpam-3412	2	6	,	,	PUNCT
ejpam-3412	2	7	2019	2019	NUM
ejpam-3412	2	8	,	,	PUNCT
ejpam-3412	2	9	294	294	NUM
ejpam-3412	2	10	-	-	SYM
ejpam-3412	2	11	331	331	NUM
ejpam-3412	2	12	issn	issn	PROPN
ejpam-3412	2	13	1307	1307	NUM
ejpam-3412	2	14	-	-	SYM
ejpam-3412	2	15	5543	5543	NUM
ejpam-3412	2	16	–	–	PUNCT
ejpam-3412	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3412	2	18	published	publish	VERB
ejpam-3412	2	19	by	by	ADP
ejpam-3412	2	20	new	new	PROPN
ejpam-3412	2	21	york	york	PROPN
ejpam-3412	2	22	business	business	PROPN
ejpam-3412	2	23	global	global	ADJ
ejpam-3412	2	24	fuzzy	fuzzy	ADJ
ejpam-3412	2	25	soft	soft	ADJ
ejpam-3412	2	26	sets	set	NOUN
ejpam-3412	2	27	over	over	ADP
ejpam-3412	2	28	fully	fully	ADV
ejpam-3412	2	29	up	up	ADV
ejpam-3412	2	30	-	-	PUNCT
ejpam-3412	2	31	semigroups∗	semigroups∗	ADV
ejpam-3412	2	32	akarachai	akarachai	NOUN
ejpam-3412	2	33	satirad1	satirad1	PROPN
ejpam-3412	2	34	,	,	PUNCT
ejpam-3412	2	35	aiyared	aiyare	VERB
ejpam-3412	2	36	iampan1,†	iampan1,†	PROPN
ejpam-3412	2	37	1	1	NUM
ejpam-3412	2	38	department	department	NOUN
ejpam-3412	2	39	of	of	ADP
ejpam-3412	2	40	mathematics	mathematic	NOUN
ejpam-3412	2	41	,	,	PUNCT
ejpam-3412	2	42	school	school	NOUN
ejpam-3412	2	43	of	of	ADP
ejpam-3412	2	44	science	science	NOUN
ejpam-3412	2	45	,	,	PUNCT
ejpam-3412	2	46	university	university	NOUN
ejpam-3412	2	47	of	of	ADP
ejpam-3412	2	48	phayao	phayao	NOUN
ejpam-3412	2	49	,	,	PUNCT
ejpam-3412	2	50	phayao	phayao	NOUN
ejpam-3412	2	51	56000	56000	NUM
ejpam-3412	2	52	,	,	PUNCT
ejpam-3412	2	53	thailand	thailand	PROPN
ejpam-3412	2	54	abstract	abstract	NOUN
ejpam-3412	2	55	.	.	PUNCT
ejpam-3412	3	1	in	in	ADP
ejpam-3412	3	2	this	this	DET
ejpam-3412	3	3	paper	paper	NOUN
ejpam-3412	3	4	,	,	PUNCT
ejpam-3412	3	5	we	we	PRON
ejpam-3412	3	6	introduce	introduce	VERB
ejpam-3412	3	7	ten	ten	NUM
ejpam-3412	3	8	types	type	NOUN
ejpam-3412	3	9	of	of	ADP
ejpam-3412	3	10	fuzzy	fuzzy	ADJ
ejpam-3412	3	11	soft	soft	ADJ
ejpam-3412	3	12	sets	set	NOUN
ejpam-3412	3	13	over	over	ADP
ejpam-3412	3	14	fully	fully	ADV
ejpam-3412	3	15	up	up	ADP
ejpam-3412	3	16	-	-	PUNCT
ejpam-3412	3	17	semigroups	semigroup	NOUN
ejpam-3412	3	18	,	,	PUNCT
ejpam-3412	3	19	and	and	CCONJ
ejpam-3412	3	20	investigate	investigate	VERB
ejpam-3412	3	21	the	the	DET
ejpam-3412	3	22	algebraic	algebraic	ADJ
ejpam-3412	3	23	properties	property	NOUN
ejpam-3412	3	24	of	of	ADP
ejpam-3412	3	25	fuzzy	fuzzy	ADJ
ejpam-3412	3	26	soft	soft	ADJ
ejpam-3412	3	27	sets	set	NOUN
ejpam-3412	3	28	under	under	ADP
ejpam-3412	3	29	the	the	DET
ejpam-3412	3	30	operations	operation	NOUN
ejpam-3412	3	31	of	of	ADP
ejpam-3412	3	32	(	(	PUNCT
ejpam-3412	3	33	extended	extended	ADJ
ejpam-3412	3	34	)	)	PUNCT
ejpam-3412	3	35	intersection	intersection	NOUN
ejpam-3412	3	36	and	and	CCONJ
ejpam-3412	3	37	(	(	PUNCT
ejpam-3412	3	38	restricted	restrict	VERB
ejpam-3412	3	39	)	)	PUNCT
ejpam-3412	3	40	union	union	NOUN
ejpam-3412	3	41	.	.	PUNCT
ejpam-3412	4	1	further	far	ADV
ejpam-3412	4	2	,	,	PUNCT
ejpam-3412	4	3	we	we	PRON
ejpam-3412	4	4	discuss	discuss	VERB
ejpam-3412	4	5	the	the	DET
ejpam-3412	4	6	relation	relation	NOUN
ejpam-3412	4	7	between	between	ADP
ejpam-3412	4	8	some	some	DET
ejpam-3412	4	9	conditions	condition	NOUN
ejpam-3412	4	10	of	of	ADP
ejpam-3412	4	11	fuzzy	fuzzy	ADJ
ejpam-3412	4	12	soft	soft	ADJ
ejpam-3412	4	13	sets	set	NOUN
ejpam-3412	4	14	and	and	CCONJ
ejpam-3412	4	15	fuzzy	fuzzy	ADJ
ejpam-3412	4	16	soft	soft	ADJ
ejpam-3412	4	17	ups	up	NOUN
ejpam-3412	4	18	-	-	PUNCT
ejpam-3412	4	19	subalgebras	subalgebras	PROPN
ejpam-3412	4	20	(	(	PUNCT
ejpam-3412	4	21	resp	resp	PROPN
ejpam-3412	4	22	.	.	PUNCT
ejpam-3412	4	23	,	,	PUNCT
ejpam-3412	4	24	fuzzy	fuzzy	ADJ
ejpam-3412	4	25	soft	soft	ADJ
ejpam-3412	4	26	upi	upi	PROPN
ejpam-3412	4	27	-	-	PUNCT
ejpam-3412	4	28	subalgebras	subalgebras	PROPN
ejpam-3412	4	29	,	,	PUNCT
ejpam-3412	4	30	fuzzy	fuzzy	ADJ
ejpam-3412	4	31	soft	soft	ADJ
ejpam-3412	4	32	near	near	ADP
ejpam-3412	4	33	ups	up	NOUN
ejpam-3412	4	34	-	-	PUNCT
ejpam-3412	4	35	filters	filter	NOUN
ejpam-3412	4	36	,	,	PUNCT
ejpam-3412	4	37	fuzzy	fuzzy	ADJ
ejpam-3412	4	38	soft	soft	ADJ
ejpam-3412	4	39	near	near	ADP
ejpam-3412	4	40	upi	upi	NOUN
ejpam-3412	4	41	-	-	PUNCT
ejpam-3412	4	42	filters	filter	NOUN
ejpam-3412	4	43	,	,	PUNCT
ejpam-3412	4	44	fuzzy	fuzzy	ADJ
ejpam-3412	4	45	soft	soft	ADJ
ejpam-3412	4	46	ups	up	NOUN
ejpam-3412	4	47	-	-	PUNCT
ejpam-3412	4	48	filters	filter	NOUN
ejpam-3412	4	49	,	,	PUNCT
ejpam-3412	4	50	fuzzy	fuzzy	ADJ
ejpam-3412	4	51	soft	soft	ADJ
ejpam-3412	4	52	upi	upi	NOUN
ejpam-3412	4	53	-	-	PUNCT
ejpam-3412	4	54	filters	filter	NOUN
ejpam-3412	4	55	,	,	PUNCT
ejpam-3412	4	56	fuzzy	fuzzy	ADJ
ejpam-3412	4	57	soft	soft	ADJ
ejpam-3412	4	58	ups	up	NOUN
ejpam-3412	4	59	-	-	PUNCT
ejpam-3412	4	60	ideals	ideal	NOUN
ejpam-3412	4	61	,	,	PUNCT
ejpam-3412	4	62	fuzzy	fuzzy	ADJ
ejpam-3412	4	63	soft	soft	ADJ
ejpam-3412	4	64	upi	upi	NOUN
ejpam-3412	4	65	-	-	PUNCT
ejpam-3412	4	66	ideals	ideal	NOUN
ejpam-3412	4	67	,	,	PUNCT
ejpam-3412	4	68	fuzzy	fuzzy	ADJ
ejpam-3412	4	69	soft	soft	ADJ
ejpam-3412	4	70	strongly	strongly	ADV
ejpam-3412	4	71	ups	up	NOUN
ejpam-3412	4	72	-	-	PUNCT
ejpam-3412	4	73	ideals	ideal	NOUN
ejpam-3412	4	74	,	,	PUNCT
ejpam-3412	4	75	fuzzy	fuzzy	ADJ
ejpam-3412	4	76	soft	soft	ADJ
ejpam-3412	4	77	strongly	strongly	ADV
ejpam-3412	4	78	upi	upi	NOUN
ejpam-3412	4	79	-	-	PUNCT
ejpam-3412	4	80	ideals	ideal	NOUN
ejpam-3412	4	81	)	)	PUNCT
ejpam-3412	4	82	of	of	ADP
ejpam-3412	4	83	fully	fully	ADV
ejpam-3412	4	84	up	up	ADP
ejpam-3412	4	85	-	-	PUNCT
ejpam-3412	4	86	semigroups	semigroup	NOUN
ejpam-3412	4	87	.	.	PUNCT
ejpam-3412	5	1	2010	2010	NUM
ejpam-3412	5	2	mathematics	mathematic	NOUN
ejpam-3412	5	3	subject	subject	NOUN
ejpam-3412	5	4	classifications	classification	NOUN
ejpam-3412	5	5	:	:	PUNCT
ejpam-3412	5	6	03g25	03g25	NUM
ejpam-3412	5	7	,	,	PUNCT
ejpam-3412	5	8	08a72	08a72	NOUN
ejpam-3412	5	9	key	key	ADJ
ejpam-3412	5	10	words	word	NOUN
ejpam-3412	5	11	and	and	CCONJ
ejpam-3412	5	12	phrases	phrase	NOUN
ejpam-3412	5	13	:	:	PUNCT
ejpam-3412	5	14	up	up	ADP
ejpam-3412	5	15	-	-	PUNCT
ejpam-3412	5	16	algebra	algebra	NOUN
ejpam-3412	5	17	,	,	PUNCT
ejpam-3412	5	18	fully	fully	ADV
ejpam-3412	5	19	up	up	ADP
ejpam-3412	5	20	-	-	PUNCT
ejpam-3412	5	21	semigroup	semigroup	NOUN
ejpam-3412	5	22	,	,	PUNCT
ejpam-3412	5	23	fuzzy	fuzzy	ADJ
ejpam-3412	5	24	soft	soft	ADJ
ejpam-3412	5	25	set	set	NOUN
ejpam-3412	5	26	.	.	PUNCT
ejpam-3412	6	1	1	1	X
ejpam-3412	6	2	.	.	X
ejpam-3412	6	3	introduction	introduction	NOUN
ejpam-3412	6	4	and	and	CCONJ
ejpam-3412	6	5	preliminaries	preliminary	NOUN
ejpam-3412	6	6	several	several	ADJ
ejpam-3412	6	7	researches	research	NOUN
ejpam-3412	6	8	introduced	introduce	VERB
ejpam-3412	6	9	a	a	DET
ejpam-3412	6	10	new	new	ADJ
ejpam-3412	6	11	class	class	NOUN
ejpam-3412	6	12	of	of	ADP
ejpam-3412	6	13	algebras	algebras	PROPN
ejpam-3412	6	14	related	relate	VERB
ejpam-3412	6	15	to	to	ADP
ejpam-3412	6	16	logical	logical	ADJ
ejpam-3412	6	17	algebras	algebra	NOUN
ejpam-3412	6	18	and	and	CCONJ
ejpam-3412	6	19	semigroups	semigroup	NOUN
ejpam-3412	6	20	such	such	ADJ
ejpam-3412	6	21	as	as	ADP
ejpam-3412	6	22	:	:	PUNCT
ejpam-3412	6	23	in	in	ADP
ejpam-3412	6	24	1993	1993	NUM
ejpam-3412	6	25	,	,	PUNCT
ejpam-3412	6	26	jun	jun	PROPN
ejpam-3412	6	27	et	et	PROPN
ejpam-3412	6	28	al	al	PROPN
ejpam-3412	6	29	.	.	PUNCT
ejpam-3412	7	1	[	[	X
ejpam-3412	7	2	10	10	NUM
ejpam-3412	7	3	]	]	PUNCT
ejpam-3412	7	4	introduced	introduce	VERB
ejpam-3412	7	5	the	the	DET
ejpam-3412	7	6	notion	notion	NOUN
ejpam-3412	7	7	of	of	ADP
ejpam-3412	7	8	bci	bci	NOUN
ejpam-3412	7	9	-	-	PUNCT
ejpam-3412	7	10	semigroups	semigroup	NOUN
ejpam-3412	7	11	.	.	PUNCT
ejpam-3412	8	1	in	in	ADP
ejpam-3412	8	2	1998	1998	NUM
ejpam-3412	8	3	,	,	PUNCT
ejpam-3412	8	4	jun	jun	PROPN
ejpam-3412	8	5	et	et	PROPN
ejpam-3412	8	6	al	al	PROPN
ejpam-3412	8	7	.	.	PUNCT
ejpam-3412	9	1	[	[	X
ejpam-3412	9	2	13	13	NUM
ejpam-3412	9	3	]	]	PUNCT
ejpam-3412	9	4	renamed	rename	VERB
ejpam-3412	9	5	the	the	DET
ejpam-3412	9	6	bci	bci	PROPN
ejpam-3412	9	7	-	-	PUNCT
ejpam-3412	9	8	semigroup	semigroup	NOUN
ejpam-3412	9	9	as	as	ADP
ejpam-3412	9	10	the	the	DET
ejpam-3412	9	11	is	is	NOUN
ejpam-3412	9	12	-	-	PUNCT
ejpam-3412	9	13	algebra	algebra	NOUN
ejpam-3412	9	14	.	.	PUNCT
ejpam-3412	10	1	in	in	ADP
ejpam-3412	10	2	2006	2006	NUM
ejpam-3412	10	3	,	,	PUNCT
ejpam-3412	10	4	kim	kim	PROPN
ejpam-3412	10	5	[	[	X
ejpam-3412	10	6	14	14	NUM
ejpam-3412	10	7	]	]	PUNCT
ejpam-3412	10	8	introduced	introduce	VERB
ejpam-3412	10	9	the	the	DET
ejpam-3412	10	10	notion	notion	NOUN
ejpam-3412	10	11	of	of	ADP
ejpam-3412	10	12	ks	ks	NOUN
ejpam-3412	10	13	-	-	PUNCT
ejpam-3412	10	14	semigroups	semigroup	NOUN
ejpam-3412	10	15	.	.	PUNCT
ejpam-3412	11	1	in	in	ADP
ejpam-3412	11	2	2015	2015	NUM
ejpam-3412	11	3	,	,	PUNCT
ejpam-3412	11	4	endam	endam	NOUN
ejpam-3412	11	5	and	and	CCONJ
ejpam-3412	11	6	vilela	vilela	NOUN
ejpam-3412	11	7	[	[	X
ejpam-3412	11	8	3	3	X
ejpam-3412	11	9	]	]	PUNCT
ejpam-3412	11	10	introduced	introduce	VERB
ejpam-3412	11	11	the	the	DET
ejpam-3412	11	12	notion	notion	NOUN
ejpam-3412	11	13	of	of	ADP
ejpam-3412	11	14	jb	jb	PROPN
ejpam-3412	11	15	-	-	PUNCT
ejpam-3412	11	16	semigroups	semigroup	NOUN
ejpam-3412	11	17	.	.	PUNCT
ejpam-3412	12	1	in	in	ADP
ejpam-3412	12	2	2018	2018	NUM
ejpam-3412	12	3	,	,	PUNCT
ejpam-3412	12	4	iampan	iampan	NOUN
ejpam-3412	12	5	[	[	X
ejpam-3412	12	6	6	6	NUM
ejpam-3412	12	7	]	]	PUNCT
ejpam-3412	12	8	introduced	introduce	VERB
ejpam-3412	12	9	the	the	DET
ejpam-3412	12	10	notion	notion	NOUN
ejpam-3412	12	11	of	of	ADP
ejpam-3412	12	12	fully	fully	ADV
ejpam-3412	12	13	upsemigroups	upsemigroup	NOUN
ejpam-3412	12	14	.	.	PUNCT
ejpam-3412	13	1	a	a	DET
ejpam-3412	13	2	fuzzy	fuzzy	ADJ
ejpam-3412	13	3	subset	subset	NOUN
ejpam-3412	13	4	f	f	PROPN
ejpam-3412	13	5	of	of	ADP
ejpam-3412	13	6	a	a	DET
ejpam-3412	13	7	set	set	NOUN
ejpam-3412	13	8	x	x	PUNCT
ejpam-3412	13	9	is	be	AUX
ejpam-3412	13	10	a	a	DET
ejpam-3412	13	11	function	function	NOUN
ejpam-3412	13	12	from	from	ADP
ejpam-3412	13	13	x	x	PRON
ejpam-3412	13	14	to	to	ADP
ejpam-3412	13	15	a	a	DET
ejpam-3412	13	16	closed	closed	ADJ
ejpam-3412	13	17	interval	interval	NOUN
ejpam-3412	13	18	[	[	X
ejpam-3412	13	19	0,1	0,1	NUM
ejpam-3412	13	20	]	]	PUNCT
ejpam-3412	13	21	.	.	PUNCT
ejpam-3412	14	1	the	the	DET
ejpam-3412	14	2	concept	concept	NOUN
ejpam-3412	14	3	of	of	ADP
ejpam-3412	14	4	a	a	DET
ejpam-3412	14	5	fuzzy	fuzzy	ADJ
ejpam-3412	14	6	subset	subset	NOUN
ejpam-3412	14	7	of	of	ADP
ejpam-3412	14	8	a	a	DET
ejpam-3412	14	9	set	set	NOUN
ejpam-3412	14	10	was	be	AUX
ejpam-3412	14	11	first	first	ADV
ejpam-3412	14	12	considered	consider	VERB
ejpam-3412	14	13	by	by	ADP
ejpam-3412	14	14	zadeh	zadeh	PROPN
ejpam-3412	15	1	[	[	X
ejpam-3412	15	2	27	27	NUM
ejpam-3412	15	3	]	]	PUNCT
ejpam-3412	15	4	in	in	ADP
ejpam-3412	15	5	1965	1965	NUM
ejpam-3412	15	6	.	.	PUNCT
ejpam-3412	16	1	the	the	DET
ejpam-3412	16	2	fuzzy	fuzzy	ADJ
ejpam-3412	16	3	set	set	NOUN
ejpam-3412	16	4	theories	theory	NOUN
ejpam-3412	16	5	developed	develop	VERB
ejpam-3412	16	6	by	by	ADP
ejpam-3412	16	7	zadeh	zadeh	NOUN
ejpam-3412	16	8	and	and	CCONJ
ejpam-3412	16	9	others	other	NOUN
ejpam-3412	16	10	have	have	AUX
ejpam-3412	16	11	found	find	VERB
ejpam-3412	16	12	many	many	ADJ
ejpam-3412	16	13	applications	application	NOUN
ejpam-3412	16	14	in	in	ADP
ejpam-3412	16	15	the	the	DET
ejpam-3412	16	16	domain	domain	NOUN
ejpam-3412	16	17	of	of	ADP
ejpam-3412	16	18	mathematics	mathematic	NOUN
ejpam-3412	16	19	and	and	CCONJ
ejpam-3412	16	20	elsewhere	elsewhere	ADV
ejpam-3412	16	21	.	.	PUNCT
ejpam-3412	17	1	after	after	ADP
ejpam-3412	17	2	the	the	DET
ejpam-3412	17	3	introduction	introduction	NOUN
ejpam-3412	17	4	of	of	ADP
ejpam-3412	17	5	the	the	DET
ejpam-3412	17	6	concept	concept	NOUN
ejpam-3412	17	7	of	of	ADP
ejpam-3412	17	8	fuzzy	fuzzy	ADJ
ejpam-3412	17	9	sets	set	NOUN
ejpam-3412	17	10	by	by	ADP
ejpam-3412	17	11	zadeh	zadeh	PROPN
ejpam-3412	17	12	[	[	X
ejpam-3412	17	13	27	27	NUM
ejpam-3412	17	14	]	]	PUNCT
ejpam-3412	17	15	,	,	PUNCT
ejpam-3412	17	16	several	several	ADJ
ejpam-3412	17	17	researches	research	NOUN
ejpam-3412	17	18	were	be	AUX
ejpam-3412	17	19	conducted	conduct	VERB
ejpam-3412	17	20	on	on	ADP
ejpam-3412	17	21	the	the	DET
ejpam-3412	17	22	generalizations	generalization	NOUN
ejpam-3412	17	23	of	of	ADP
ejpam-3412	17	24	the	the	DET
ejpam-3412	17	25	notion	notion	NOUN
ejpam-3412	17	26	of	of	ADP
ejpam-3412	17	27	fuzzy	fuzzy	ADJ
ejpam-3412	17	28	set	set	NOUN
ejpam-3412	17	29	and	and	CCONJ
ejpam-3412	17	30	application	application	NOUN
ejpam-3412	17	31	to	to	ADP
ejpam-3412	17	32	many	many	ADJ
ejpam-3412	17	33	logical	logical	ADJ
ejpam-3412	17	34	algebras	algebra	NOUN
ejpam-3412	17	35	such	such	ADJ
ejpam-3412	17	36	as	as	ADP
ejpam-3412	17	37	:	:	PUNCT
ejpam-3412	17	38	in	in	ADP
ejpam-3412	17	39	1998	1998	NUM
ejpam-3412	17	40	,	,	PUNCT
ejpam-3412	17	41	jun	jun	PROPN
ejpam-3412	17	42	et	et	PROPN
ejpam-3412	17	43	al	al	PROPN
ejpam-3412	17	44	.	.	PUNCT
ejpam-3412	18	1	[	[	X
ejpam-3412	18	2	9	9	NUM
ejpam-3412	18	3	]	]	PUNCT
ejpam-3412	18	4	applied	apply	VERB
ejpam-3412	18	5	the	the	DET
ejpam-3412	18	6	notion	notion	NOUN
ejpam-3412	18	7	of	of	ADP
ejpam-3412	18	8	fuzzy	fuzzy	ADJ
ejpam-3412	18	9	sets	set	NOUN
ejpam-3412	18	10	to	to	ADP
ejpam-3412	18	11	bci	bci	NOUN
ejpam-3412	18	12	-	-	PUNCT
ejpam-3412	18	13	semigroups	semigroup	NOUN
ejpam-3412	18	14	(	(	PUNCT
ejpam-3412	18	15	it	it	PRON
ejpam-3412	18	16	was	be	AUX
ejpam-3412	18	17	renamed	rename	VERB
ejpam-3412	18	18	as	as	ADP
ejpam-3412	18	19	an	an	DET
ejpam-3412	18	20	is	is	NOUN
ejpam-3412	18	21	-	-	PUNCT
ejpam-3412	18	22	algebra	algebra	NOUN
ejpam-3412	18	23	for	for	ADP
ejpam-3412	18	24	the	the	DET
ejpam-3412	18	25	convenience	convenience	NOUN
ejpam-3412	18	26	of	of	ADP
ejpam-3412	18	27	study	study	NOUN
ejpam-3412	18	28	)	)	PUNCT
ejpam-3412	18	29	,	,	PUNCT
ejpam-3412	18	30	and	and	CCONJ
ejpam-3412	18	31	introduced	introduce	VERB
ejpam-3412	18	32	the	the	DET
ejpam-3412	18	33	concept	concept	NOUN
ejpam-3412	18	34	of	of	ADP
ejpam-3412	18	35	fuzzy	fuzzy	ADJ
ejpam-3412	18	36	i	i	NOUN
ejpam-3412	18	37	-	-	NOUN
ejpam-3412	18	38	ideals	ideal	NOUN
ejpam-3412	18	39	.	.	PUNCT
ejpam-3412	19	1	in	in	ADP
ejpam-3412	19	2	2000	2000	NUM
ejpam-3412	19	3	,	,	PUNCT
ejpam-3412	19	4	roh	roh	PROPN
ejpam-3412	19	5	et	et	PROPN
ejpam-3412	19	6	al	al	PROPN
ejpam-3412	19	7	.	.	PUNCT
ejpam-3412	20	1	[	[	X
ejpam-3412	20	2	21	21	NUM
ejpam-3412	20	3	]	]	PUNCT
ejpam-3412	20	4	considered	consider	VERB
ejpam-3412	20	5	the	the	DET
ejpam-3412	20	6	fuzzification	fuzzification	NOUN
ejpam-3412	20	7	of	of	ADP
ejpam-3412	20	8	an	an	DET
ejpam-3412	20	9	associative	associative	ADJ
ejpam-3412	20	10	i	i	NOUN
ejpam-3412	20	11	-	-	PUNCT
ejpam-3412	20	12	ideal	ideal	NOUN
ejpam-3412	20	13	of	of	ADP
ejpam-3412	20	14	an	an	DET
ejpam-3412	20	15	is	is	NOUN
ejpam-3412	20	16	-	-	PUNCT
ejpam-3412	20	17	algebra	algebra	NOUN
ejpam-3412	20	18	.	.	PUNCT
ejpam-3412	21	1	they	they	PRON
ejpam-3412	21	2	proved	prove	VERB
ejpam-3412	21	3	that	that	SCONJ
ejpam-3412	21	4	every	every	DET
ejpam-3412	21	5	fuzzy	fuzzy	ADJ
ejpam-3412	21	6	associative	associative	NOUN
ejpam-3412	21	7	i	i	NOUN
ejpam-3412	21	8	-	-	PUNCT
ejpam-3412	21	9	ideal	ideal	NOUN
ejpam-3412	21	10	is	be	AUX
ejpam-3412	21	11	a	a	DET
ejpam-3412	21	12	fuzzy	fuzzy	ADJ
ejpam-3412	21	13	i	i	NOUN
ejpam-3412	21	14	-	-	PUNCT
ejpam-3412	21	15	ideal	ideal	ADJ
ejpam-3412	21	16	.	.	PUNCT
ejpam-3412	22	1	by	by	ADP
ejpam-3412	22	2	giving	give	VERB
ejpam-3412	22	3	an	an	DET
ejpam-3412	22	4	appropriate	appropriate	ADJ
ejpam-3412	22	5	example	example	NOUN
ejpam-3412	22	6	,	,	PUNCT
ejpam-3412	22	7	they	they	PRON
ejpam-3412	22	8	verified	verify	VERB
ejpam-3412	22	9	that	that	SCONJ
ejpam-3412	22	10	∗this	∗this	NUM
ejpam-3412	22	11	work	work	NOUN
ejpam-3412	22	12	was	be	AUX
ejpam-3412	22	13	financially	financially	ADV
ejpam-3412	22	14	supported	support	VERB
ejpam-3412	22	15	by	by	ADP
ejpam-3412	22	16	the	the	DET
ejpam-3412	22	17	university	university	NOUN
ejpam-3412	22	18	of	of	ADP
ejpam-3412	22	19	phayao	phayao	NOUN
ejpam-3412	22	20	.	.	PUNCT
ejpam-3412	23	1	†corresponding	†corresponde	VERB
ejpam-3412	23	2	author	author	NOUN
ejpam-3412	23	3	.	.	PUNCT
ejpam-3412	24	1	doi	doi	NOUN
ejpam-3412	24	2	:	:	PUNCT
ejpam-3412	24	3	https://doi.org/10.29020/nybg.ejpam.v12i2.3412	https://doi.org/10.29020/nybg.ejpam.v12i2.3412	ADJ
ejpam-3412	24	4	email	email	NOUN
ejpam-3412	24	5	addresses	address	NOUN
ejpam-3412	24	6	:	:	PUNCT
ejpam-3412	24	7	akarachai.sa@gmail.com	akarachai.sa@gmail.com	PROPN
ejpam-3412	24	8	(	(	PUNCT
ejpam-3412	24	9	a.	a.	PROPN
ejpam-3412	24	10	satirad	satirad	PROPN
ejpam-3412	24	11	)	)	PUNCT
ejpam-3412	24	12	,	,	PUNCT
ejpam-3412	24	13	aiyared.ia@up.ac.th	aiyared.ia@up.ac.th	NOUN
ejpam-3412	24	14	(	(	PUNCT
ejpam-3412	24	15	a.	a.	NOUN
ejpam-3412	24	16	iampan	iampan	PROPN
ejpam-3412	24	17	)	)	PUNCT
ejpam-3412	24	18	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3412	25	1	294	294	NUM
ejpam-3412	25	2	c	c	X
ejpam-3412	25	3	©	©	PROPN
ejpam-3412	25	4	2019	2019	NUM
ejpam-3412	25	5	ejpam	ejpam	NOUN
ejpam-3412	25	6	all	all	DET
ejpam-3412	25	7	rights	right	NOUN
ejpam-3412	25	8	reserved	reserve	VERB
ejpam-3412	25	9	.	.	PUNCT
ejpam-3412	26	1	a.	a.	PROPN
ejpam-3412	26	2	satirad	satirad	PROPN
ejpam-3412	26	3	,	,	PUNCT
ejpam-3412	26	4	a.	a.	NOUN
ejpam-3412	26	5	iampan	iampan	PROPN
ejpam-3412	26	6	/	/	SYM
ejpam-3412	26	7	eur	eur	PROPN
ejpam-3412	26	8	.	.	PUNCT
ejpam-3412	27	1	j.	j.	PROPN
ejpam-3412	27	2	pure	pure	PROPN
ejpam-3412	27	3	appl	appl	PROPN
ejpam-3412	27	4	.	.	PROPN
ejpam-3412	27	5	math	math	PROPN
ejpam-3412	27	6	,	,	PUNCT
ejpam-3412	27	7	12	12	NUM
ejpam-3412	27	8	(	(	PUNCT
ejpam-3412	27	9	2	2	NUM
ejpam-3412	27	10	)	)	PUNCT
ejpam-3412	27	11	(	(	PUNCT
ejpam-3412	27	12	2019	2019	NUM
ejpam-3412	27	13	)	)	PUNCT
ejpam-3412	27	14	,	,	PUNCT
ejpam-3412	27	15	294	294	NUM
ejpam-3412	27	16	-	-	SYM
ejpam-3412	27	17	331	331	NUM
ejpam-3412	27	18	295	295	NUM
ejpam-3412	27	19	a	a	DET
ejpam-3412	27	20	fuzzy	fuzzy	ADJ
ejpam-3412	27	21	i	i	PRON
ejpam-3412	27	22	-	-	PUNCT
ejpam-3412	27	23	ideal	ideal	NOUN
ejpam-3412	27	24	may	may	AUX
ejpam-3412	27	25	not	not	PART
ejpam-3412	27	26	be	be	AUX
ejpam-3412	27	27	a	a	DET
ejpam-3412	27	28	fuzzy	fuzzy	ADJ
ejpam-3412	27	29	associative	associative	NOUN
ejpam-3412	27	30	i	i	NOUN
ejpam-3412	27	31	-	-	PUNCT
ejpam-3412	27	32	ideal	ideal	ADJ
ejpam-3412	27	33	.	.	PUNCT
ejpam-3412	28	1	they	they	PRON
ejpam-3412	28	2	gave	give	VERB
ejpam-3412	28	3	a	a	DET
ejpam-3412	28	4	condition	condition	NOUN
ejpam-3412	28	5	for	for	ADP
ejpam-3412	28	6	a	a	DET
ejpam-3412	28	7	fuzzy	fuzzy	ADJ
ejpam-3412	28	8	i	i	NOUN
ejpam-3412	28	9	-	-	PUNCT
ejpam-3412	28	10	ideal	ideal	NOUN
ejpam-3412	28	11	to	to	PART
ejpam-3412	28	12	be	be	AUX
ejpam-3412	28	13	a	a	DET
ejpam-3412	28	14	fuzzy	fuzzy	ADJ
ejpam-3412	28	15	associative	associative	NOUN
ejpam-3412	28	16	i	i	NOUN
ejpam-3412	28	17	-	-	PUNCT
ejpam-3412	28	18	ideal	ideal	ADJ
ejpam-3412	28	19	,	,	PUNCT
ejpam-3412	28	20	and	and	CCONJ
ejpam-3412	28	21	they	they	PRON
ejpam-3412	28	22	investigated	investigate	VERB
ejpam-3412	28	23	some	some	DET
ejpam-3412	28	24	related	related	ADJ
ejpam-3412	28	25	properties	property	NOUN
ejpam-3412	28	26	.	.	PUNCT
ejpam-3412	29	1	in	in	ADP
ejpam-3412	29	2	2003	2003	NUM
ejpam-3412	29	3	,	,	PUNCT
ejpam-3412	29	4	jun	jun	PROPN
ejpam-3412	29	5	and	and	CCONJ
ejpam-3412	29	6	kondo	kondo	PROPN
ejpam-3412	29	7	[	[	X
ejpam-3412	29	8	11	11	NUM
ejpam-3412	29	9	]	]	PUNCT
ejpam-3412	29	10	proved	prove	VERB
ejpam-3412	29	11	that	that	SCONJ
ejpam-3412	29	12	some	some	DET
ejpam-3412	29	13	concepts	concept	NOUN
ejpam-3412	29	14	of	of	ADP
ejpam-3412	29	15	bck	bck	PROPN
ejpam-3412	29	16	/	/	SYM
ejpam-3412	29	17	bci	bci	NOUN
ejpam-3412	29	18	-	-	PUNCT
ejpam-3412	29	19	algebras	algebras	PROPN
ejpam-3412	29	20	expressed	express	VERB
ejpam-3412	29	21	by	by	ADP
ejpam-3412	29	22	a	a	DET
ejpam-3412	29	23	certain	certain	ADJ
ejpam-3412	29	24	formula	formula	NOUN
ejpam-3412	29	25	can	can	AUX
ejpam-3412	29	26	be	be	AUX
ejpam-3412	29	27	naturally	naturally	ADV
ejpam-3412	29	28	extended	extend	VERB
ejpam-3412	29	29	to	to	ADP
ejpam-3412	29	30	the	the	DET
ejpam-3412	29	31	fuzzy	fuzzy	ADJ
ejpam-3412	29	32	setting	setting	NOUN
ejpam-3412	29	33	and	and	CCONJ
ejpam-3412	29	34	that	that	SCONJ
ejpam-3412	29	35	many	many	ADJ
ejpam-3412	29	36	results	result	NOUN
ejpam-3412	29	37	are	be	AUX
ejpam-3412	29	38	obtained	obtain	VERB
ejpam-3412	29	39	immediately	immediately	ADV
ejpam-3412	29	40	with	with	ADP
ejpam-3412	29	41	the	the	DET
ejpam-3412	29	42	use	use	NOUN
ejpam-3412	29	43	of	of	ADP
ejpam-3412	29	44	our	our	PRON
ejpam-3412	29	45	method	method	NOUN
ejpam-3412	29	46	.	.	PUNCT
ejpam-3412	30	1	moreover	moreover	ADV
ejpam-3412	30	2	,	,	PUNCT
ejpam-3412	30	3	they	they	PRON
ejpam-3412	30	4	proved	prove	VERB
ejpam-3412	30	5	that	that	SCONJ
ejpam-3412	30	6	these	these	DET
ejpam-3412	30	7	results	result	NOUN
ejpam-3412	30	8	can	can	AUX
ejpam-3412	30	9	be	be	AUX
ejpam-3412	30	10	extended	extend	VERB
ejpam-3412	30	11	to	to	ADP
ejpam-3412	30	12	fuzzy	fuzzy	ADJ
ejpam-3412	30	13	is	be	AUX
ejpam-3412	30	14	-	-	PUNCT
ejpam-3412	30	15	algebras	algebra	NOUN
ejpam-3412	30	16	.	.	PUNCT
ejpam-3412	31	1	in	in	ADP
ejpam-3412	31	2	2003	2003	NUM
ejpam-3412	31	3	,	,	PUNCT
ejpam-3412	31	4	jianming	jianming	NOUN
ejpam-3412	31	5	and	and	CCONJ
ejpam-3412	31	6	dajing	daje	VERB
ejpam-3412	31	7	[	[	X
ejpam-3412	31	8	8	8	NUM
ejpam-3412	31	9	]	]	PUNCT
ejpam-3412	31	10	introduced	introduce	VERB
ejpam-3412	31	11	the	the	DET
ejpam-3412	31	12	concept	concept	NOUN
ejpam-3412	31	13	of	of	ADP
ejpam-3412	31	14	intuitionistic	intuitionistic	ADJ
ejpam-3412	31	15	fuzzy	fuzzy	ADJ
ejpam-3412	31	16	associative	associative	NOUN
ejpam-3412	31	17	i	i	NOUN
ejpam-3412	31	18	-	-	PUNCT
ejpam-3412	31	19	ideals	ideal	NOUN
ejpam-3412	31	20	of	of	ADP
ejpam-3412	31	21	is	be	AUX
ejpam-3412	31	22	-	-	PUNCT
ejpam-3412	31	23	algebras	algebra	NOUN
ejpam-3412	31	24	and	and	CCONJ
ejpam-3412	31	25	they	they	PRON
ejpam-3412	31	26	investigated	investigate	VERB
ejpam-3412	31	27	some	some	DET
ejpam-3412	31	28	related	related	ADJ
ejpam-3412	31	29	properties	property	NOUN
ejpam-3412	31	30	.	.	PUNCT
ejpam-3412	32	1	in	in	ADP
ejpam-3412	32	2	2007	2007	NUM
ejpam-3412	32	3	,	,	PUNCT
ejpam-3412	32	4	prince	prince	PROPN
ejpam-3412	32	5	williams	williams	PROPN
ejpam-3412	32	6	and	and	CCONJ
ejpam-3412	32	7	husain	husain	PROPN
ejpam-3412	33	1	[	[	X
ejpam-3412	33	2	26	26	NUM
ejpam-3412	33	3	]	]	PUNCT
ejpam-3412	33	4	studied	study	VERB
ejpam-3412	33	5	fuzzy	fuzzy	ADJ
ejpam-3412	33	6	ks	ks	NOUN
ejpam-3412	33	7	-	-	PUNCT
ejpam-3412	33	8	semigroups	semigroup	NOUN
ejpam-3412	33	9	.	.	PUNCT
ejpam-3412	34	1	in	in	ADP
ejpam-3412	34	2	2016	2016	NUM
ejpam-3412	34	3	,	,	PUNCT
ejpam-3412	34	4	endam	endam	NOUN
ejpam-3412	34	5	and	and	CCONJ
ejpam-3412	34	6	manahon	manahon	NOUN
ejpam-3412	34	7	[	[	X
ejpam-3412	34	8	2	2	NUM
ejpam-3412	34	9	]	]	PUNCT
ejpam-3412	34	10	introduced	introduce	VERB
ejpam-3412	34	11	the	the	DET
ejpam-3412	34	12	notion	notion	NOUN
ejpam-3412	34	13	of	of	ADP
ejpam-3412	34	14	fuzzy	fuzzy	ADJ
ejpam-3412	34	15	jb	jb	NOUN
ejpam-3412	34	16	-	-	PUNCT
ejpam-3412	34	17	semigroups	semigroup	NOUN
ejpam-3412	34	18	and	and	CCONJ
ejpam-3412	34	19	they	they	PRON
ejpam-3412	34	20	investigated	investigate	VERB
ejpam-3412	34	21	some	some	PRON
ejpam-3412	34	22	of	of	ADP
ejpam-3412	34	23	its	its	PRON
ejpam-3412	34	24	properties	property	NOUN
ejpam-3412	34	25	.	.	PUNCT
ejpam-3412	35	1	in	in	ADP
ejpam-3412	35	2	2018	2018	NUM
ejpam-3412	35	3	,	,	PUNCT
ejpam-3412	35	4	satirad	satirad	PROPN
ejpam-3412	35	5	and	and	CCONJ
ejpam-3412	35	6	iampan	iampan	PROPN
ejpam-3412	35	7	[	[	X
ejpam-3412	35	8	23	23	NUM
ejpam-3412	35	9	]	]	PUNCT
ejpam-3412	35	10	introduced	introduce	VERB
ejpam-3412	35	11	the	the	DET
ejpam-3412	35	12	notion	notion	NOUN
ejpam-3412	35	13	of	of	ADP
ejpam-3412	35	14	fuzzy	fuzzy	ADJ
ejpam-3412	35	15	sets	set	NOUN
ejpam-3412	35	16	in	in	ADP
ejpam-3412	35	17	fully	fully	ADV
ejpam-3412	35	18	up	up	ADP
ejpam-3412	35	19	-	-	PUNCT
ejpam-3412	35	20	semigroups	semigroup	NOUN
ejpam-3412	35	21	and	and	CCONJ
ejpam-3412	35	22	they	they	PRON
ejpam-3412	35	23	investigated	investigate	VERB
ejpam-3412	35	24	some	some	PRON
ejpam-3412	35	25	of	of	ADP
ejpam-3412	35	26	its	its	PRON
ejpam-3412	35	27	properties	property	NOUN
ejpam-3412	35	28	.	.	PUNCT
ejpam-3412	36	1	in	in	ADP
ejpam-3412	36	2	1999	1999	NUM
ejpam-3412	36	3	,	,	PUNCT
ejpam-3412	36	4	to	to	PART
ejpam-3412	36	5	solve	solve	VERB
ejpam-3412	36	6	complicated	complicated	ADJ
ejpam-3412	36	7	problems	problem	NOUN
ejpam-3412	36	8	in	in	ADP
ejpam-3412	36	9	economics	economic	NOUN
ejpam-3412	36	10	,	,	PUNCT
ejpam-3412	36	11	engineering	engineering	NOUN
ejpam-3412	36	12	,	,	PUNCT
ejpam-3412	36	13	and	and	CCONJ
ejpam-3412	36	14	environment	environment	NOUN
ejpam-3412	36	15	,	,	PUNCT
ejpam-3412	36	16	we	we	PRON
ejpam-3412	36	17	can	can	AUX
ejpam-3412	36	18	not	not	PART
ejpam-3412	36	19	successfully	successfully	ADV
ejpam-3412	36	20	use	use	VERB
ejpam-3412	36	21	classical	classical	ADJ
ejpam-3412	36	22	methods	method	NOUN
ejpam-3412	36	23	because	because	SCONJ
ejpam-3412	36	24	of	of	ADP
ejpam-3412	36	25	various	various	ADJ
ejpam-3412	36	26	uncertainties	uncertainty	NOUN
ejpam-3412	36	27	typical	typical	ADJ
ejpam-3412	36	28	for	for	ADP
ejpam-3412	36	29	those	those	DET
ejpam-3412	36	30	problems	problem	NOUN
ejpam-3412	36	31	.	.	PUNCT
ejpam-3412	37	1	uncertainties	uncertainty	NOUN
ejpam-3412	37	2	can	can	AUX
ejpam-3412	37	3	not	not	PART
ejpam-3412	37	4	be	be	AUX
ejpam-3412	37	5	handled	handle	VERB
ejpam-3412	37	6	using	use	VERB
ejpam-3412	37	7	traditional	traditional	ADJ
ejpam-3412	37	8	mathematical	mathematical	ADJ
ejpam-3412	37	9	tools	tool	NOUN
ejpam-3412	37	10	but	but	CCONJ
ejpam-3412	37	11	may	may	AUX
ejpam-3412	37	12	be	be	AUX
ejpam-3412	37	13	dealt	deal	VERB
ejpam-3412	37	14	with	with	ADP
ejpam-3412	37	15	using	use	VERB
ejpam-3412	37	16	a	a	DET
ejpam-3412	37	17	wide	wide	ADJ
ejpam-3412	37	18	range	range	NOUN
ejpam-3412	37	19	of	of	ADP
ejpam-3412	37	20	existing	exist	VERB
ejpam-3412	37	21	theories	theory	NOUN
ejpam-3412	37	22	such	such	ADJ
ejpam-3412	37	23	as	as	ADP
ejpam-3412	37	24	the	the	DET
ejpam-3412	37	25	probability	probability	NOUN
ejpam-3412	37	26	theory	theory	NOUN
ejpam-3412	37	27	,	,	PUNCT
ejpam-3412	37	28	the	the	DET
ejpam-3412	37	29	theory	theory	NOUN
ejpam-3412	37	30	of	of	ADP
ejpam-3412	37	31	(	(	PUNCT
ejpam-3412	37	32	intuitionistic	intuitionistic	ADJ
ejpam-3412	37	33	)	)	PUNCT
ejpam-3412	37	34	fuzzy	fuzzy	ADJ
ejpam-3412	37	35	sets	set	NOUN
ejpam-3412	37	36	,	,	PUNCT
ejpam-3412	37	37	the	the	DET
ejpam-3412	37	38	theory	theory	NOUN
ejpam-3412	37	39	of	of	ADP
ejpam-3412	37	40	vague	vague	ADJ
ejpam-3412	37	41	sets	set	NOUN
ejpam-3412	37	42	,	,	PUNCT
ejpam-3412	37	43	the	the	DET
ejpam-3412	37	44	theory	theory	NOUN
ejpam-3412	37	45	of	of	ADP
ejpam-3412	37	46	interval	interval	NOUN
ejpam-3412	37	47	mathematics	mathematic	NOUN
ejpam-3412	37	48	,	,	PUNCT
ejpam-3412	37	49	and	and	CCONJ
ejpam-3412	37	50	the	the	DET
ejpam-3412	37	51	theory	theory	NOUN
ejpam-3412	37	52	of	of	ADP
ejpam-3412	37	53	rough	rough	ADJ
ejpam-3412	37	54	sets	set	NOUN
ejpam-3412	37	55	.	.	PUNCT
ejpam-3412	38	1	however	however	ADV
ejpam-3412	38	2	,	,	PUNCT
ejpam-3412	38	3	all	all	PRON
ejpam-3412	38	4	of	of	ADP
ejpam-3412	38	5	these	these	DET
ejpam-3412	38	6	theories	theory	NOUN
ejpam-3412	38	7	have	have	VERB
ejpam-3412	38	8	their	their	PRON
ejpam-3412	38	9	own	own	ADJ
ejpam-3412	38	10	difficulties	difficulty	NOUN
ejpam-3412	38	11	which	which	PRON
ejpam-3412	38	12	are	be	AUX
ejpam-3412	38	13	pointed	point	VERB
ejpam-3412	38	14	out	out	ADP
ejpam-3412	38	15	in	in	ADP
ejpam-3412	38	16	[	[	X
ejpam-3412	38	17	18	18	NUM
ejpam-3412	38	18	]	]	PUNCT
ejpam-3412	38	19	.	.	PUNCT
ejpam-3412	39	1	in	in	ADP
ejpam-3412	39	2	2001	2001	NUM
ejpam-3412	39	3	,	,	PUNCT
ejpam-3412	39	4	maji	maji	PROPN
ejpam-3412	39	5	et	et	PROPN
ejpam-3412	39	6	al	al	PROPN
ejpam-3412	39	7	.	.	PUNCT
ejpam-3412	40	1	[	[	X
ejpam-3412	40	2	17	17	NUM
ejpam-3412	40	3	]	]	PUNCT
ejpam-3412	40	4	introduced	introduce	VERB
ejpam-3412	40	5	the	the	DET
ejpam-3412	40	6	concept	concept	NOUN
ejpam-3412	40	7	of	of	ADP
ejpam-3412	40	8	fuzzy	fuzzy	ADJ
ejpam-3412	40	9	soft	soft	ADJ
ejpam-3412	40	10	sets	set	NOUN
ejpam-3412	40	11	as	as	ADP
ejpam-3412	40	12	a	a	DET
ejpam-3412	40	13	generalization	generalization	NOUN
ejpam-3412	40	14	of	of	ADP
ejpam-3412	40	15	the	the	DET
ejpam-3412	40	16	standard	standard	ADJ
ejpam-3412	40	17	soft	soft	ADJ
ejpam-3412	40	18	sets	set	NOUN
ejpam-3412	40	19	,	,	PUNCT
ejpam-3412	40	20	and	and	CCONJ
ejpam-3412	40	21	presented	present	VERB
ejpam-3412	40	22	an	an	DET
ejpam-3412	40	23	application	application	NOUN
ejpam-3412	40	24	of	of	ADP
ejpam-3412	40	25	fuzzy	fuzzy	ADJ
ejpam-3412	40	26	soft	soft	ADJ
ejpam-3412	40	27	sets	set	NOUN
ejpam-3412	40	28	in	in	ADP
ejpam-3412	40	29	a	a	DET
ejpam-3412	40	30	decision	decision	NOUN
ejpam-3412	40	31	making	make	VERB
ejpam-3412	40	32	problem	problem	NOUN
ejpam-3412	40	33	.	.	PUNCT
ejpam-3412	41	1	in	in	ADP
ejpam-3412	41	2	2010	2010	NUM
ejpam-3412	41	3	,	,	PUNCT
ejpam-3412	41	4	jun	jun	PROPN
ejpam-3412	41	5	et	et	PROPN
ejpam-3412	41	6	al	al	PROPN
ejpam-3412	41	7	.	.	PUNCT
ejpam-3412	42	1	[	[	X
ejpam-3412	42	2	12	12	NUM
ejpam-3412	42	3	]	]	PUNCT
ejpam-3412	42	4	applied	apply	VERB
ejpam-3412	42	5	fuzzy	fuzzy	ADJ
ejpam-3412	42	6	soft	soft	ADJ
ejpam-3412	42	7	set	set	NOUN
ejpam-3412	42	8	for	for	ADP
ejpam-3412	42	9	dealing	deal	VERB
ejpam-3412	42	10	with	with	ADP
ejpam-3412	42	11	several	several	ADJ
ejpam-3412	42	12	kinds	kind	NOUN
ejpam-3412	42	13	of	of	ADP
ejpam-3412	42	14	theories	theory	NOUN
ejpam-3412	42	15	in	in	ADP
ejpam-3412	42	16	bck	bck	PROPN
ejpam-3412	42	17	/	/	SYM
ejpam-3412	42	18	bci	bci	NOUN
ejpam-3412	42	19	-	-	PUNCT
ejpam-3412	42	20	algebras	algebras	X
ejpam-3412	42	21	.	.	PUNCT
ejpam-3412	43	1	the	the	DET
ejpam-3412	43	2	notions	notion	NOUN
ejpam-3412	43	3	of	of	ADP
ejpam-3412	43	4	fuzzy	fuzzy	ADJ
ejpam-3412	43	5	soft	soft	ADJ
ejpam-3412	43	6	bck	bck	NOUN
ejpam-3412	43	7	/	/	SYM
ejpam-3412	43	8	bci	bci	NOUN
ejpam-3412	43	9	-	-	PUNCT
ejpam-3412	43	10	algebras	algebra	NOUN
ejpam-3412	43	11	,	,	PUNCT
ejpam-3412	43	12	(	(	PUNCT
ejpam-3412	43	13	closed	closed	ADJ
ejpam-3412	43	14	)	)	PUNCT
ejpam-3412	43	15	fuzzy	fuzzy	ADJ
ejpam-3412	43	16	soft	soft	ADJ
ejpam-3412	43	17	ideals	ideal	NOUN
ejpam-3412	43	18	and	and	CCONJ
ejpam-3412	43	19	fuzzy	fuzzy	ADJ
ejpam-3412	43	20	soft	soft	ADJ
ejpam-3412	43	21	p	p	NOUN
ejpam-3412	43	22	-	-	PUNCT
ejpam-3412	43	23	ideals	ideal	NOUN
ejpam-3412	43	24	are	be	AUX
ejpam-3412	43	25	introduced	introduce	VERB
ejpam-3412	43	26	,	,	PUNCT
ejpam-3412	43	27	and	and	CCONJ
ejpam-3412	43	28	related	related	ADJ
ejpam-3412	43	29	properties	property	NOUN
ejpam-3412	43	30	are	be	AUX
ejpam-3412	43	31	investigated	investigate	VERB
ejpam-3412	43	32	.	.	PUNCT
ejpam-3412	44	1	before	before	SCONJ
ejpam-3412	44	2	we	we	PRON
ejpam-3412	44	3	begin	begin	VERB
ejpam-3412	44	4	our	our	PRON
ejpam-3412	44	5	study	study	NOUN
ejpam-3412	44	6	,	,	PUNCT
ejpam-3412	44	7	we	we	PRON
ejpam-3412	44	8	will	will	AUX
ejpam-3412	44	9	introduce	introduce	VERB
ejpam-3412	44	10	the	the	DET
ejpam-3412	44	11	definition	definition	NOUN
ejpam-3412	44	12	of	of	ADP
ejpam-3412	44	13	a	a	DET
ejpam-3412	44	14	up	up	NOUN
ejpam-3412	44	15	-	-	PUNCT
ejpam-3412	44	16	algebra	algebra	NOUN
ejpam-3412	44	17	.	.	PUNCT
ejpam-3412	45	1	definition	definition	NOUN
ejpam-3412	45	2	1	1	NUM
ejpam-3412	45	3	.	.	PUNCT
ejpam-3412	46	1	[	[	X
ejpam-3412	46	2	5	5	X
ejpam-3412	46	3	]	]	PUNCT
ejpam-3412	46	4	an	an	DET
ejpam-3412	46	5	algebra	algebra	NOUN
ejpam-3412	46	6	a	a	X
ejpam-3412	46	7	=	=	X
ejpam-3412	46	8	(	(	PUNCT
ejpam-3412	46	9	a	a	PRON
ejpam-3412	46	10	,	,	PUNCT
ejpam-3412	46	11	·	·	PUNCT
ejpam-3412	46	12	,	,	PUNCT
ejpam-3412	46	13	0	0	NUM
ejpam-3412	46	14	)	)	PUNCT
ejpam-3412	46	15	of	of	ADP
ejpam-3412	46	16	type	type	NOUN
ejpam-3412	46	17	(	(	PUNCT
ejpam-3412	46	18	2	2	NUM
ejpam-3412	46	19	,	,	PUNCT
ejpam-3412	46	20	0	0	NUM
ejpam-3412	46	21	)	)	PUNCT
ejpam-3412	46	22	is	be	AUX
ejpam-3412	46	23	called	call	VERB
ejpam-3412	46	24	a	a	DET
ejpam-3412	46	25	up	up	NOUN
ejpam-3412	46	26	-	-	PUNCT
ejpam-3412	46	27	algebra	algebra	NOUN
ejpam-3412	46	28	where	where	SCONJ
ejpam-3412	46	29	a	a	PRON
ejpam-3412	46	30	is	be	AUX
ejpam-3412	46	31	a	a	DET
ejpam-3412	46	32	nonempty	nonempty	ADJ
ejpam-3412	46	33	set	set	VERB
ejpam-3412	46	34	,	,	PUNCT
ejpam-3412	46	35	·	·	PUNCT
ejpam-3412	46	36	is	be	AUX
ejpam-3412	46	37	a	a	DET
ejpam-3412	46	38	binary	binary	ADJ
ejpam-3412	46	39	operation	operation	NOUN
ejpam-3412	46	40	on	on	ADP
ejpam-3412	46	41	a	a	PRON
ejpam-3412	46	42	,	,	PUNCT
ejpam-3412	46	43	and	and	CCONJ
ejpam-3412	46	44	0	0	NUM
ejpam-3412	46	45	is	be	AUX
ejpam-3412	46	46	a	a	DET
ejpam-3412	46	47	fixed	fix	VERB
ejpam-3412	46	48	element	element	NOUN
ejpam-3412	46	49	of	of	ADP
ejpam-3412	46	50	a	a	DET
ejpam-3412	46	51	(	(	PUNCT
ejpam-3412	46	52	i.e.	i.e.	X
ejpam-3412	46	53	,	,	PUNCT
ejpam-3412	46	54	a	a	DET
ejpam-3412	46	55	nullary	nullary	ADJ
ejpam-3412	46	56	operation	operation	NOUN
ejpam-3412	46	57	)	)	PUNCT
ejpam-3412	46	58	if	if	SCONJ
ejpam-3412	46	59	it	it	PRON
ejpam-3412	46	60	satisfies	satisfy	VERB
ejpam-3412	46	61	the	the	DET
ejpam-3412	46	62	following	follow	VERB
ejpam-3412	46	63	axioms	axiom	NOUN
ejpam-3412	46	64	:	:	PUNCT
ejpam-3412	46	65	(	(	PUNCT
ejpam-3412	46	66	up-1	up-1	NOUN
ejpam-3412	46	67	)	)	PUNCT
ejpam-3412	46	68	(	(	PUNCT
ejpam-3412	46	69	∀x	∀x	X
ejpam-3412	46	70	,	,	PUNCT
ejpam-3412	46	71	y	y	PROPN
ejpam-3412	46	72	,	,	PUNCT
ejpam-3412	46	73	z	z	NOUN
ejpam-3412	46	74	∈	∈	PROPN
ejpam-3412	46	75	a)((y	a)((y	NOUN
ejpam-3412	46	76	·	·	PUNCT
ejpam-3412	47	1	z	z	X
ejpam-3412	47	2	)	)	PUNCT
ejpam-3412	47	3	·	·	PUNCT
ejpam-3412	47	4	(	(	PUNCT
ejpam-3412	47	5	(	(	PUNCT
ejpam-3412	47	6	x	x	SYM
ejpam-3412	47	7	·	·	PUNCT
ejpam-3412	47	8	y	y	X
ejpam-3412	47	9	)	)	PUNCT
ejpam-3412	47	10	·	·	PUNCT
ejpam-3412	48	1	(	(	PUNCT
ejpam-3412	48	2	x	x	X
ejpam-3412	48	3	·	·	PUNCT
ejpam-3412	48	4	z	z	NOUN
ejpam-3412	48	5	)	)	PUNCT
ejpam-3412	48	6	)	)	PUNCT
ejpam-3412	49	1	=	=	PUNCT
ejpam-3412	49	2	0	0	NUM
ejpam-3412	49	3	)	)	PUNCT
ejpam-3412	49	4	,	,	PUNCT
ejpam-3412	49	5	(	(	PUNCT
ejpam-3412	49	6	up-2	up-2	NUM
ejpam-3412	49	7	)	)	PUNCT
ejpam-3412	49	8	(	(	PUNCT
ejpam-3412	49	9	∀x	∀x	X
ejpam-3412	49	10	∈	∈	PROPN
ejpam-3412	49	11	a)(0	a)(0	PROPN
ejpam-3412	49	12	·	·	PUNCT
ejpam-3412	49	13	x	x	PUNCT
ejpam-3412	50	1	=	=	PUNCT
ejpam-3412	50	2	x	x	NOUN
ejpam-3412	50	3	)	)	PUNCT
ejpam-3412	50	4	,	,	PUNCT
ejpam-3412	50	5	(	(	PUNCT
ejpam-3412	50	6	up-3	up-3	NOUN
ejpam-3412	50	7	)	)	PUNCT
ejpam-3412	50	8	(	(	PUNCT
ejpam-3412	50	9	∀x	∀x	X
ejpam-3412	50	10	∈	∈	PROPN
ejpam-3412	50	11	a)(x	a)(x	NOUN
ejpam-3412	50	12	·	·	PUNCT
ejpam-3412	50	13	0	0	PUNCT
ejpam-3412	51	1	=	=	SYM
ejpam-3412	51	2	0	0	NUM
ejpam-3412	51	3	)	)	PUNCT
ejpam-3412	51	4	,	,	PUNCT
ejpam-3412	51	5	and	and	CCONJ
ejpam-3412	51	6	(	(	PUNCT
ejpam-3412	51	7	up-4	up-4	ADV
ejpam-3412	51	8	)	)	PUNCT
ejpam-3412	51	9	(	(	PUNCT
ejpam-3412	51	10	∀x	∀x	X
ejpam-3412	51	11	,	,	PUNCT
ejpam-3412	51	12	y	y	PROPN
ejpam-3412	51	13	∈	∈	PROPN
ejpam-3412	51	14	a)(x	a)(x	X
ejpam-3412	51	15	·	·	PUNCT
ejpam-3412	51	16	y	y	X
ejpam-3412	51	17	=	=	SYM
ejpam-3412	51	18	0	0	PROPN
ejpam-3412	51	19	,	,	PUNCT
ejpam-3412	51	20	y	y	PROPN
ejpam-3412	51	21	·	·	PUNCT
ejpam-3412	51	22	x	x	PUNCT
ejpam-3412	52	1	=	=	PUNCT
ejpam-3412	52	2	0⇒	0⇒	NUM
ejpam-3412	52	3	x	x	X
ejpam-3412	52	4	=	=	SYM
ejpam-3412	52	5	y	y	PROPN
ejpam-3412	52	6	)	)	PUNCT
ejpam-3412	52	7	,	,	PUNCT
ejpam-3412	52	8	from	from	ADP
ejpam-3412	52	9	[	[	X
ejpam-3412	52	10	5	5	NUM
ejpam-3412	52	11	]	]	PUNCT
ejpam-3412	52	12	,	,	PUNCT
ejpam-3412	52	13	we	we	PRON
ejpam-3412	52	14	know	know	VERB
ejpam-3412	52	15	that	that	SCONJ
ejpam-3412	52	16	the	the	DET
ejpam-3412	52	17	notion	notion	NOUN
ejpam-3412	52	18	of	of	ADP
ejpam-3412	52	19	up	up	ADV
ejpam-3412	52	20	-	-	PUNCT
ejpam-3412	52	21	algebras	algebras	PROPN
ejpam-3412	52	22	is	be	AUX
ejpam-3412	52	23	a	a	DET
ejpam-3412	52	24	generalization	generalization	NOUN
ejpam-3412	52	25	of	of	ADP
ejpam-3412	52	26	ku	ku	PROPN
ejpam-3412	52	27	-	-	PUNCT
ejpam-3412	52	28	algebras	algebras	PROPN
ejpam-3412	52	29	(	(	PUNCT
ejpam-3412	52	30	see	see	VERB
ejpam-3412	52	31	[	[	X
ejpam-3412	52	32	19	19	NUM
ejpam-3412	52	33	]	]	NUM
ejpam-3412	52	34	)	)	PUNCT
ejpam-3412	52	35	.	.	PUNCT
ejpam-3412	53	1	on	on	ADP
ejpam-3412	53	2	a	a	DET
ejpam-3412	53	3	up	up	NOUN
ejpam-3412	53	4	-	-	PUNCT
ejpam-3412	53	5	algebra	algebra	NOUN
ejpam-3412	53	6	a	a	PRON
ejpam-3412	53	7	=	=	X
ejpam-3412	53	8	(	(	PUNCT
ejpam-3412	53	9	a	a	PRON
ejpam-3412	53	10	,	,	PUNCT
ejpam-3412	53	11	·	·	PUNCT
ejpam-3412	53	12	,	,	PUNCT
ejpam-3412	53	13	0	0	NUM
ejpam-3412	53	14	)	)	PUNCT
ejpam-3412	53	15	,	,	PUNCT
ejpam-3412	53	16	we	we	PRON
ejpam-3412	53	17	define	define	VERB
ejpam-3412	53	18	a	a	DET
ejpam-3412	53	19	binary	binary	ADJ
ejpam-3412	53	20	relation	relation	NOUN
ejpam-3412	53	21	≤	≤	NUM
ejpam-3412	53	22	on	on	ADP
ejpam-3412	53	23	a	a	DET
ejpam-3412	53	24	[	[	X
ejpam-3412	53	25	5	5	NUM
ejpam-3412	53	26	]	]	PUNCT
ejpam-3412	53	27	as	as	SCONJ
ejpam-3412	53	28	follows	follow	VERB
ejpam-3412	53	29	:	:	PUNCT
ejpam-3412	53	30	(	(	PUNCT
ejpam-3412	53	31	∀x	∀x	X
ejpam-3412	53	32	,	,	PUNCT
ejpam-3412	53	33	y	y	PROPN
ejpam-3412	53	34	∈	∈	PROPN
ejpam-3412	53	35	a)(x	a)(x	PROPN
ejpam-3412	53	36	≤	≤	PUNCT
ejpam-3412	53	37	y	y	PROPN
ejpam-3412	53	38	⇔	⇔	PROPN
ejpam-3412	53	39	x	x	PROPN
ejpam-3412	53	40	·	·	PUNCT
ejpam-3412	53	41	y	y	SYM
ejpam-3412	53	42	=	=	NOUN
ejpam-3412	53	43	0	0	NUM
ejpam-3412	53	44	)	)	PUNCT
ejpam-3412	53	45	.	.	PUNCT
ejpam-3412	54	1	example	example	NOUN
ejpam-3412	55	1	1	1	NUM
ejpam-3412	55	2	.	.	PUNCT
ejpam-3412	56	1	[	[	X
ejpam-3412	56	2	24	24	NUM
ejpam-3412	56	3	]	]	PUNCT
ejpam-3412	56	4	let	let	VERB
ejpam-3412	56	5	x	x	PRON
ejpam-3412	56	6	be	be	AUX
ejpam-3412	56	7	a	a	DET
ejpam-3412	56	8	universal	universal	ADJ
ejpam-3412	56	9	set	set	NOUN
ejpam-3412	56	10	and	and	CCONJ
ejpam-3412	56	11	let	let	VERB
ejpam-3412	56	12	ω	ω	NUM
ejpam-3412	56	13	∈	∈	PROPN
ejpam-3412	56	14	p(x	p(x	PROPN
ejpam-3412	56	15	)	)	PUNCT
ejpam-3412	56	16	.	.	PUNCT
ejpam-3412	57	1	let	let	VERB
ejpam-3412	57	2	pω(x	pω(x	X
ejpam-3412	57	3	)	)	PUNCT
ejpam-3412	57	4	=	=	SYM
ejpam-3412	57	5	{	{	PUNCT
ejpam-3412	57	6	a	a	DET
ejpam-3412	57	7	∈	∈	PROPN
ejpam-3412	57	8	p(x	p(x	NOUN
ejpam-3412	57	9	)	)	PUNCT
ejpam-3412	57	10	|	|	ADV
ejpam-3412	57	11	ω	ω	NUM
ejpam-3412	57	12	⊆	⊆	NUM
ejpam-3412	57	13	a	a	PRON
ejpam-3412	57	14	}	}	PUNCT
ejpam-3412	57	15	.	.	PUNCT
ejpam-3412	58	1	define	define	VERB
ejpam-3412	58	2	a	a	DET
ejpam-3412	58	3	binary	binary	ADJ
ejpam-3412	58	4	operation	operation	NOUN
ejpam-3412	58	5	·	·	PUNCT
ejpam-3412	58	6	on	on	ADP
ejpam-3412	58	7	pω(x	pω(x	NOUN
ejpam-3412	58	8	)	)	PUNCT
ejpam-3412	58	9	by	by	ADP
ejpam-3412	58	10	putting	put	VERB
ejpam-3412	58	11	a	a	DET
ejpam-3412	58	12	·	·	PUNCT
ejpam-3412	58	13	b	b	X
ejpam-3412	58	14	=	=	SYM
ejpam-3412	58	15	b	b	PROPN
ejpam-3412	58	16	∩	∩	NOUN
ejpam-3412	58	17	(	(	PUNCT
ejpam-3412	58	18	a′	a′	PROPN
ejpam-3412	58	19	∪	∪	X
ejpam-3412	58	20	ω	ω	NOUN
ejpam-3412	58	21	)	)	PUNCT
ejpam-3412	58	22	for	for	ADP
ejpam-3412	58	23	all	all	DET
ejpam-3412	58	24	a	a	DET
ejpam-3412	58	25	,	,	PUNCT
ejpam-3412	58	26	b	b	NOUN
ejpam-3412	58	27	∈	∈	NOUN
ejpam-3412	58	28	pω(x	pω(x	NOUN
ejpam-3412	58	29	)	)	PUNCT
ejpam-3412	58	30	.	.	PUNCT
ejpam-3412	59	1	then	then	ADV
ejpam-3412	59	2	(	(	PUNCT
ejpam-3412	59	3	pω(x	pω(x	NOUN
ejpam-3412	59	4	)	)	PUNCT
ejpam-3412	59	5	,	,	PUNCT
ejpam-3412	59	6	·	·	PUNCT
ejpam-3412	59	7	,	,	PUNCT
ejpam-3412	59	8	ω	ω	NUM
ejpam-3412	59	9	)	)	PUNCT
ejpam-3412	59	10	is	be	AUX
ejpam-3412	59	11	a	a	DET
ejpam-3412	59	12	up	up	NOUN
ejpam-3412	59	13	-	-	PUNCT
ejpam-3412	59	14	algebra	algebra	NOUN
ejpam-3412	59	15	and	and	CCONJ
ejpam-3412	59	16	we	we	PRON
ejpam-3412	59	17	shall	shall	AUX
ejpam-3412	59	18	call	call	VERB
ejpam-3412	59	19	it	it	PRON
ejpam-3412	59	20	the	the	DET
ejpam-3412	59	21	generalized	generalized	ADJ
ejpam-3412	59	22	power	power	NOUN
ejpam-3412	59	23	up	up	ADP
ejpam-3412	59	24	-	-	PUNCT
ejpam-3412	59	25	algebra	algebra	NOUN
ejpam-3412	59	26	of	of	ADP
ejpam-3412	59	27	type	type	NOUN
ejpam-3412	59	28	1	1	NUM
ejpam-3412	59	29	with	with	ADP
ejpam-3412	59	30	respect	respect	NOUN
ejpam-3412	59	31	to	to	ADP
ejpam-3412	59	32	ω	ω	NUM
ejpam-3412	59	33	.	.	PUNCT
ejpam-3412	59	34	a.	a.	PROPN
ejpam-3412	59	35	satirad	satirad	PROPN
ejpam-3412	59	36	,	,	PUNCT
ejpam-3412	59	37	a.	a.	NOUN
ejpam-3412	59	38	iampan	iampan	PROPN
ejpam-3412	59	39	/	/	SYM
ejpam-3412	59	40	eur	eur	PROPN
ejpam-3412	59	41	.	.	PUNCT
ejpam-3412	60	1	j.	j.	PROPN
ejpam-3412	60	2	pure	pure	PROPN
ejpam-3412	60	3	appl	appl	PROPN
ejpam-3412	60	4	.	.	PROPN
ejpam-3412	60	5	math	math	PROPN
ejpam-3412	60	6	,	,	PUNCT
ejpam-3412	60	7	12	12	NUM
ejpam-3412	60	8	(	(	PUNCT
ejpam-3412	60	9	2	2	NUM
ejpam-3412	60	10	)	)	PUNCT
ejpam-3412	60	11	(	(	PUNCT
ejpam-3412	60	12	2019	2019	NUM
ejpam-3412	60	13	)	)	PUNCT
ejpam-3412	60	14	,	,	PUNCT
ejpam-3412	60	15	294	294	NUM
ejpam-3412	60	16	-	-	SYM
ejpam-3412	60	17	331	331	NUM
ejpam-3412	60	18	296	296	NUM
ejpam-3412	60	19	example	example	NOUN
ejpam-3412	60	20	2	2	NUM
ejpam-3412	60	21	.	.	PUNCT
ejpam-3412	61	1	[	[	X
ejpam-3412	61	2	24	24	NUM
ejpam-3412	61	3	]	]	PUNCT
ejpam-3412	61	4	let	let	VERB
ejpam-3412	61	5	x	x	PRON
ejpam-3412	61	6	be	be	AUX
ejpam-3412	61	7	a	a	DET
ejpam-3412	61	8	universal	universal	ADJ
ejpam-3412	61	9	set	set	NOUN
ejpam-3412	61	10	and	and	CCONJ
ejpam-3412	61	11	let	let	VERB
ejpam-3412	61	12	ω	ω	NUM
ejpam-3412	61	13	∈	∈	PROPN
ejpam-3412	61	14	p(x	p(x	PROPN
ejpam-3412	61	15	)	)	PUNCT
ejpam-3412	61	16	.	.	PUNCT
ejpam-3412	62	1	let	let	VERB
ejpam-3412	62	2	pω(x	pω(x	X
ejpam-3412	62	3	)	)	PUNCT
ejpam-3412	62	4	=	=	SYM
ejpam-3412	62	5	{	{	PUNCT
ejpam-3412	62	6	a	a	DET
ejpam-3412	62	7	∈	∈	PROPN
ejpam-3412	62	8	p(x	p(x	NOUN
ejpam-3412	62	9	)	)	PUNCT
ejpam-3412	62	10	|	|	ADV
ejpam-3412	62	11	a	a	DET
ejpam-3412	62	12	⊆	⊆	NUM
ejpam-3412	62	13	ω	ω	NUM
ejpam-3412	62	14	}	}	PUNCT
ejpam-3412	62	15	.	.	PUNCT
ejpam-3412	63	1	define	define	VERB
ejpam-3412	63	2	a	a	DET
ejpam-3412	63	3	binary	binary	ADJ
ejpam-3412	63	4	operation	operation	NOUN
ejpam-3412	63	5	∗	∗	NOUN
ejpam-3412	63	6	on	on	ADP
ejpam-3412	63	7	pω(x	pω(x	NOUN
ejpam-3412	63	8	)	)	PUNCT
ejpam-3412	63	9	by	by	ADP
ejpam-3412	63	10	putting	put	VERB
ejpam-3412	63	11	a	a	DET
ejpam-3412	63	12	∗	∗	NOUN
ejpam-3412	63	13	b	b	NOUN
ejpam-3412	63	14	=	=	SYM
ejpam-3412	63	15	b	b	X
ejpam-3412	63	16	∪	∪	X
ejpam-3412	63	17	(	(	PUNCT
ejpam-3412	63	18	a′	a′	PROPN
ejpam-3412	63	19	∩	∩	ADJ
ejpam-3412	63	20	ω	ω	NOUN
ejpam-3412	63	21	)	)	PUNCT
ejpam-3412	63	22	for	for	ADP
ejpam-3412	63	23	all	all	DET
ejpam-3412	63	24	a	a	DET
ejpam-3412	63	25	,	,	PUNCT
ejpam-3412	63	26	b	b	NOUN
ejpam-3412	63	27	∈	∈	NOUN
ejpam-3412	63	28	pω(x	pω(x	NOUN
ejpam-3412	63	29	)	)	PUNCT
ejpam-3412	63	30	.	.	PUNCT
ejpam-3412	64	1	then	then	ADV
ejpam-3412	64	2	(	(	PUNCT
ejpam-3412	64	3	pω(x	pω(x	NOUN
ejpam-3412	64	4	)	)	PUNCT
ejpam-3412	64	5	,	,	PUNCT
ejpam-3412	64	6	∗,ω	∗,ω	PROPN
ejpam-3412	64	7	)	)	PUNCT
ejpam-3412	64	8	is	be	AUX
ejpam-3412	64	9	a	a	DET
ejpam-3412	64	10	up	up	NOUN
ejpam-3412	64	11	-	-	PUNCT
ejpam-3412	64	12	algebra	algebra	NOUN
ejpam-3412	64	13	and	and	CCONJ
ejpam-3412	64	14	we	we	PRON
ejpam-3412	64	15	shall	shall	AUX
ejpam-3412	64	16	call	call	VERB
ejpam-3412	64	17	it	it	PRON
ejpam-3412	64	18	the	the	DET
ejpam-3412	64	19	generalized	generalized	ADJ
ejpam-3412	64	20	power	power	NOUN
ejpam-3412	64	21	up	up	ADP
ejpam-3412	64	22	-	-	PUNCT
ejpam-3412	64	23	algebra	algebra	NOUN
ejpam-3412	64	24	of	of	ADP
ejpam-3412	64	25	type	type	NOUN
ejpam-3412	64	26	2	2	NUM
ejpam-3412	64	27	with	with	ADP
ejpam-3412	64	28	respect	respect	NOUN
ejpam-3412	64	29	to	to	ADP
ejpam-3412	64	30	ω	ω	NUM
ejpam-3412	64	31	.	.	PUNCT
ejpam-3412	65	1	in	in	ADP
ejpam-3412	65	2	particular	particular	ADJ
ejpam-3412	65	3	,	,	PUNCT
ejpam-3412	65	4	(	(	PUNCT
ejpam-3412	65	5	p(x	p(x	PROPN
ejpam-3412	65	6	)	)	PUNCT
ejpam-3412	65	7	,	,	PUNCT
ejpam-3412	65	8	·	·	PUNCT
ejpam-3412	65	9	,	,	PUNCT
ejpam-3412	65	10	∅	∅	NOUN
ejpam-3412	65	11	)	)	PUNCT
ejpam-3412	65	12	is	be	AUX
ejpam-3412	65	13	the	the	DET
ejpam-3412	65	14	power	power	NOUN
ejpam-3412	65	15	up	up	ADP
ejpam-3412	65	16	-	-	PUNCT
ejpam-3412	65	17	algebra	algebra	NOUN
ejpam-3412	65	18	of	of	ADP
ejpam-3412	65	19	type	type	NOUN
ejpam-3412	65	20	1	1	NUM
ejpam-3412	65	21	and	and	CCONJ
ejpam-3412	65	22	(	(	PUNCT
ejpam-3412	65	23	p(x	p(x	PROPN
ejpam-3412	65	24	)	)	PUNCT
ejpam-3412	65	25	,	,	PUNCT
ejpam-3412	65	26	∗	∗	NOUN
ejpam-3412	65	27	,	,	PUNCT
ejpam-3412	65	28	x	x	X
ejpam-3412	65	29	)	)	PUNCT
ejpam-3412	65	30	is	be	AUX
ejpam-3412	65	31	the	the	DET
ejpam-3412	65	32	power	power	NOUN
ejpam-3412	65	33	up	up	ADP
ejpam-3412	65	34	-	-	PUNCT
ejpam-3412	65	35	algebra	algebra	NOUN
ejpam-3412	65	36	of	of	ADP
ejpam-3412	65	37	type	type	NOUN
ejpam-3412	65	38	2	2	NUM
ejpam-3412	65	39	.	.	PUNCT
ejpam-3412	66	1	in	in	ADP
ejpam-3412	66	2	a	a	DET
ejpam-3412	66	3	up	up	NOUN
ejpam-3412	66	4	-	-	PUNCT
ejpam-3412	66	5	algebra	algebra	NOUN
ejpam-3412	66	6	a	a	PRON
ejpam-3412	66	7	=	=	X
ejpam-3412	66	8	(	(	PUNCT
ejpam-3412	66	9	a	a	PRON
ejpam-3412	66	10	,	,	PUNCT
ejpam-3412	66	11	·	·	PUNCT
ejpam-3412	66	12	,	,	PUNCT
ejpam-3412	66	13	0	0	NUM
ejpam-3412	66	14	)	)	PUNCT
ejpam-3412	66	15	,	,	PUNCT
ejpam-3412	66	16	the	the	DET
ejpam-3412	66	17	following	follow	VERB
ejpam-3412	66	18	assertions	assertion	NOUN
ejpam-3412	66	19	are	be	AUX
ejpam-3412	66	20	valid	valid	ADJ
ejpam-3412	66	21	(	(	PUNCT
ejpam-3412	66	22	see	see	VERB
ejpam-3412	66	23	[	[	X
ejpam-3412	66	24	5	5	NUM
ejpam-3412	66	25	,	,	PUNCT
ejpam-3412	66	26	6	6	NUM
ejpam-3412	66	27	]	]	NUM
ejpam-3412	66	28	)	)	PUNCT
ejpam-3412	66	29	.	.	PUNCT
ejpam-3412	67	1	(	(	PUNCT
ejpam-3412	67	2	∀x	∀x	X
ejpam-3412	67	3	∈	∈	NOUN
ejpam-3412	67	4	a)(x	a)(x	NOUN
ejpam-3412	67	5	·	·	PUNCT
ejpam-3412	67	6	x	x	SYM
ejpam-3412	68	1	=	=	PUNCT
ejpam-3412	68	2	0	0	NUM
ejpam-3412	68	3	)	)	PUNCT
ejpam-3412	68	4	,	,	PUNCT
ejpam-3412	68	5	(	(	PUNCT
ejpam-3412	68	6	1.1	1.1	NUM
ejpam-3412	68	7	)	)	PUNCT
ejpam-3412	68	8	(	(	PUNCT
ejpam-3412	68	9	∀x	∀x	X
ejpam-3412	68	10	,	,	PUNCT
ejpam-3412	68	11	y	y	PROPN
ejpam-3412	68	12	,	,	PUNCT
ejpam-3412	68	13	z	z	NOUN
ejpam-3412	68	14	∈	∈	NOUN
ejpam-3412	68	15	a)(x	a)(x	NOUN
ejpam-3412	68	16	·	·	PUNCT
ejpam-3412	68	17	y	y	X
ejpam-3412	68	18	=	=	SYM
ejpam-3412	68	19	0	0	PROPN
ejpam-3412	68	20	,	,	PUNCT
ejpam-3412	68	21	y	y	PROPN
ejpam-3412	68	22	·	·	PUNCT
ejpam-3412	68	23	z	z	X
ejpam-3412	68	24	=	=	SYM
ejpam-3412	68	25	0⇒	0⇒	NUM
ejpam-3412	68	26	x	x	SYM
ejpam-3412	69	1	·	·	PUNCT
ejpam-3412	69	2	z	z	X
ejpam-3412	69	3	=	=	SYM
ejpam-3412	69	4	0	0	NUM
ejpam-3412	69	5	)	)	PUNCT
ejpam-3412	69	6	,	,	PUNCT
ejpam-3412	69	7	(	(	PUNCT
ejpam-3412	69	8	1.2	1.2	NUM
ejpam-3412	69	9	)	)	PUNCT
ejpam-3412	69	10	(	(	PUNCT
ejpam-3412	69	11	∀x	∀x	X
ejpam-3412	69	12	,	,	PUNCT
ejpam-3412	69	13	y	y	PROPN
ejpam-3412	69	14	,	,	PUNCT
ejpam-3412	69	15	z	z	NOUN
ejpam-3412	69	16	∈	∈	NOUN
ejpam-3412	69	17	a)(x	a)(x	NOUN
ejpam-3412	69	18	·	·	PUNCT
ejpam-3412	69	19	y	y	X
ejpam-3412	69	20	=	=	SYM
ejpam-3412	69	21	0⇒	0⇒	PROPN
ejpam-3412	69	22	(	(	PUNCT
ejpam-3412	69	23	z	z	NOUN
ejpam-3412	69	24	·	·	PUNCT
ejpam-3412	69	25	x	x	X
ejpam-3412	69	26	)	)	PUNCT
ejpam-3412	69	27	·	·	PUNCT
ejpam-3412	69	28	(	(	PUNCT
ejpam-3412	69	29	z	z	X
ejpam-3412	69	30	·	·	PUNCT
ejpam-3412	69	31	y	y	X
ejpam-3412	69	32	)	)	PUNCT
ejpam-3412	70	1	=	=	NOUN
ejpam-3412	70	2	0	0	NUM
ejpam-3412	70	3	)	)	PUNCT
ejpam-3412	70	4	,	,	PUNCT
ejpam-3412	70	5	(	(	PUNCT
ejpam-3412	70	6	1.3	1.3	NUM
ejpam-3412	70	7	)	)	PUNCT
ejpam-3412	70	8	(	(	PUNCT
ejpam-3412	70	9	∀x	∀x	X
ejpam-3412	70	10	,	,	PUNCT
ejpam-3412	70	11	y	y	PROPN
ejpam-3412	70	12	,	,	PUNCT
ejpam-3412	70	13	z	z	NOUN
ejpam-3412	70	14	∈	∈	NOUN
ejpam-3412	70	15	a)(x	a)(x	NOUN
ejpam-3412	70	16	·	·	PUNCT
ejpam-3412	71	1	y	y	X
ejpam-3412	71	2	=	=	SYM
ejpam-3412	71	3	0⇒	0⇒	PROPN
ejpam-3412	71	4	(	(	PUNCT
ejpam-3412	71	5	y	y	PROPN
ejpam-3412	71	6	·	·	PUNCT
ejpam-3412	71	7	z	z	X
ejpam-3412	71	8	)	)	PUNCT
ejpam-3412	71	9	·	·	PUNCT
ejpam-3412	71	10	(	(	PUNCT
ejpam-3412	71	11	x	x	X
ejpam-3412	71	12	·	·	PUNCT
ejpam-3412	72	1	z	z	X
ejpam-3412	72	2	)	)	PUNCT
ejpam-3412	72	3	=	=	SYM
ejpam-3412	72	4	0	0	NUM
ejpam-3412	72	5	)	)	PUNCT
ejpam-3412	72	6	,	,	PUNCT
ejpam-3412	72	7	(	(	PUNCT
ejpam-3412	72	8	1.4	1.4	NUM
ejpam-3412	72	9	)	)	PUNCT
ejpam-3412	72	10	(	(	PUNCT
ejpam-3412	72	11	∀x	∀x	X
ejpam-3412	72	12	,	,	PUNCT
ejpam-3412	72	13	y	y	PROPN
ejpam-3412	72	14	∈	∈	PROPN
ejpam-3412	72	15	a)(x	a)(x	PROPN
ejpam-3412	72	16	·	·	PUNCT
ejpam-3412	72	17	(	(	PUNCT
ejpam-3412	72	18	y	y	NOUN
ejpam-3412	72	19	·	·	PUNCT
ejpam-3412	72	20	x	x	X
ejpam-3412	72	21	)	)	PUNCT
ejpam-3412	72	22	=	=	SYM
ejpam-3412	72	23	0	0	NUM
ejpam-3412	72	24	)	)	PUNCT
ejpam-3412	72	25	,	,	PUNCT
ejpam-3412	72	26	(	(	PUNCT
ejpam-3412	72	27	1.5	1.5	NUM
ejpam-3412	72	28	)	)	PUNCT
ejpam-3412	72	29	(	(	PUNCT
ejpam-3412	72	30	∀x	∀x	X
ejpam-3412	72	31	,	,	PUNCT
ejpam-3412	72	32	y	y	PROPN
ejpam-3412	72	33	∈	∈	PROPN
ejpam-3412	72	34	a)((y	a)((y	NOUN
ejpam-3412	72	35	·	·	PUNCT
ejpam-3412	72	36	x	x	X
ejpam-3412	72	37	)	)	PUNCT
ejpam-3412	72	38	·	·	PUNCT
ejpam-3412	72	39	x	x	PUNCT
ejpam-3412	73	1	=	=	PUNCT
ejpam-3412	73	2	0⇔	0⇔	NOUN
ejpam-3412	73	3	x	x	X
ejpam-3412	74	1	=	=	PUNCT
ejpam-3412	74	2	y	y	PROPN
ejpam-3412	74	3	·	·	PUNCT
ejpam-3412	74	4	x	x	X
ejpam-3412	74	5	)	)	PUNCT
ejpam-3412	74	6	,	,	PUNCT
ejpam-3412	74	7	(	(	PUNCT
ejpam-3412	74	8	1.6	1.6	NUM
ejpam-3412	74	9	)	)	PUNCT
ejpam-3412	74	10	(	(	PUNCT
ejpam-3412	74	11	∀x	∀x	X
ejpam-3412	74	12	,	,	PUNCT
ejpam-3412	74	13	y	y	PROPN
ejpam-3412	74	14	∈	∈	PROPN
ejpam-3412	74	15	a)(x	a)(x	PROPN
ejpam-3412	74	16	·	·	PUNCT
ejpam-3412	74	17	(	(	PUNCT
ejpam-3412	74	18	y	y	PROPN
ejpam-3412	74	19	·	·	PUNCT
ejpam-3412	74	20	y	y	X
ejpam-3412	74	21	)	)	PUNCT
ejpam-3412	74	22	=	=	SYM
ejpam-3412	74	23	0	0	NUM
ejpam-3412	74	24	)	)	PUNCT
ejpam-3412	74	25	,	,	PUNCT
ejpam-3412	74	26	(	(	PUNCT
ejpam-3412	74	27	1.7	1.7	NUM
ejpam-3412	74	28	)	)	PUNCT
ejpam-3412	74	29	(	(	PUNCT
ejpam-3412	74	30	∀a	∀a	X
ejpam-3412	74	31	,	,	PUNCT
ejpam-3412	74	32	x	x	X
ejpam-3412	74	33	,	,	PUNCT
ejpam-3412	74	34	y	y	PROPN
ejpam-3412	74	35	,	,	PUNCT
ejpam-3412	74	36	z	z	PROPN
ejpam-3412	74	37	∈	∈	PROPN
ejpam-3412	74	38	a)((x	a)((x	NOUN
ejpam-3412	74	39	·	·	PUNCT
ejpam-3412	74	40	(	(	PUNCT
ejpam-3412	74	41	y	y	PROPN
ejpam-3412	74	42	·	·	PUNCT
ejpam-3412	74	43	z	z	NOUN
ejpam-3412	74	44	)	)	PUNCT
ejpam-3412	74	45	)	)	PUNCT
ejpam-3412	74	46	·	·	PUNCT
ejpam-3412	75	1	(	(	PUNCT
ejpam-3412	75	2	x	x	X
ejpam-3412	75	3	·	·	PUNCT
ejpam-3412	75	4	(	(	PUNCT
ejpam-3412	75	5	(	(	PUNCT
ejpam-3412	75	6	a	a	DET
ejpam-3412	75	7	·	·	PUNCT
ejpam-3412	75	8	y	y	NOUN
ejpam-3412	75	9	)	)	PUNCT
ejpam-3412	75	10	·	·	PUNCT
ejpam-3412	75	11	(	(	PUNCT
ejpam-3412	75	12	a	a	DET
ejpam-3412	75	13	·	·	PUNCT
ejpam-3412	75	14	z	z	NOUN
ejpam-3412	75	15	)	)	PUNCT
ejpam-3412	75	16	)	)	PUNCT
ejpam-3412	75	17	)	)	PUNCT
ejpam-3412	76	1	=	=	PUNCT
ejpam-3412	76	2	0	0	NUM
ejpam-3412	76	3	)	)	PUNCT
ejpam-3412	76	4	,	,	PUNCT
ejpam-3412	76	5	(	(	PUNCT
ejpam-3412	76	6	1.8	1.8	NUM
ejpam-3412	76	7	)	)	PUNCT
ejpam-3412	76	8	(	(	PUNCT
ejpam-3412	76	9	∀a	∀a	X
ejpam-3412	76	10	,	,	PUNCT
ejpam-3412	76	11	x	x	X
ejpam-3412	76	12	,	,	PUNCT
ejpam-3412	76	13	y	y	PROPN
ejpam-3412	76	14	,	,	PUNCT
ejpam-3412	76	15	z	z	PROPN
ejpam-3412	76	16	∈	∈	PROPN
ejpam-3412	76	17	a)((((a	a)((((a	NOUN
ejpam-3412	76	18	·	·	PUNCT
ejpam-3412	76	19	x	x	X
ejpam-3412	76	20	)	)	PUNCT
ejpam-3412	76	21	·	·	PUNCT
ejpam-3412	76	22	(	(	PUNCT
ejpam-3412	76	23	a	a	DET
ejpam-3412	76	24	·	·	PUNCT
ejpam-3412	76	25	y	y	NOUN
ejpam-3412	76	26	)	)	PUNCT
ejpam-3412	76	27	)	)	PUNCT
ejpam-3412	76	28	·	·	PUNCT
ejpam-3412	77	1	z	z	X
ejpam-3412	77	2	)	)	PUNCT
ejpam-3412	77	3	·	·	PUNCT
ejpam-3412	77	4	(	(	PUNCT
ejpam-3412	77	5	(	(	PUNCT
ejpam-3412	77	6	x	x	SYM
ejpam-3412	77	7	·	·	PUNCT
ejpam-3412	77	8	y	y	X
ejpam-3412	77	9	)	)	PUNCT
ejpam-3412	77	10	·	·	PUNCT
ejpam-3412	78	1	z	z	X
ejpam-3412	78	2	)	)	PUNCT
ejpam-3412	78	3	=	=	SYM
ejpam-3412	78	4	0	0	NUM
ejpam-3412	78	5	)	)	PUNCT
ejpam-3412	78	6	,	,	PUNCT
ejpam-3412	78	7	(	(	PUNCT
ejpam-3412	78	8	1.9	1.9	NUM
ejpam-3412	78	9	)	)	PUNCT
ejpam-3412	78	10	(	(	PUNCT
ejpam-3412	78	11	∀x	∀x	X
ejpam-3412	78	12	,	,	PUNCT
ejpam-3412	78	13	y	y	PROPN
ejpam-3412	78	14	,	,	PUNCT
ejpam-3412	78	15	z	z	NOUN
ejpam-3412	78	16	∈	∈	PROPN
ejpam-3412	78	17	a)(((x	a)(((x	NOUN
ejpam-3412	78	18	·	·	SYM
ejpam-3412	78	19	y	y	X
ejpam-3412	78	20	)	)	PUNCT
ejpam-3412	78	21	·	·	PUNCT
ejpam-3412	79	1	z	z	X
ejpam-3412	79	2	)	)	PUNCT
ejpam-3412	79	3	·	·	PUNCT
ejpam-3412	79	4	(	(	PUNCT
ejpam-3412	79	5	y	y	PROPN
ejpam-3412	79	6	·	·	PUNCT
ejpam-3412	79	7	z	z	X
ejpam-3412	79	8	)	)	PUNCT
ejpam-3412	79	9	=	=	SYM
ejpam-3412	79	10	0	0	NUM
ejpam-3412	79	11	)	)	PUNCT
ejpam-3412	79	12	,	,	PUNCT
ejpam-3412	79	13	(	(	PUNCT
ejpam-3412	79	14	1.10	1.10	NUM
ejpam-3412	79	15	)	)	PUNCT
ejpam-3412	79	16	(	(	PUNCT
ejpam-3412	79	17	∀x	∀x	X
ejpam-3412	79	18	,	,	PUNCT
ejpam-3412	79	19	y	y	PROPN
ejpam-3412	79	20	,	,	PUNCT
ejpam-3412	79	21	z	z	NOUN
ejpam-3412	79	22	∈	∈	NOUN
ejpam-3412	79	23	a)(x	a)(x	NOUN
ejpam-3412	79	24	·	·	PUNCT
ejpam-3412	79	25	y	y	X
ejpam-3412	79	26	=	=	SYM
ejpam-3412	79	27	0⇒	0⇒	PROPN
ejpam-3412	79	28	x	x	SYM
ejpam-3412	79	29	·	·	PUNCT
ejpam-3412	79	30	(	(	PUNCT
ejpam-3412	79	31	z	z	NOUN
ejpam-3412	79	32	·	·	PUNCT
ejpam-3412	79	33	y	y	X
ejpam-3412	79	34	)	)	PUNCT
ejpam-3412	79	35	=	=	NOUN
ejpam-3412	79	36	0	0	NUM
ejpam-3412	79	37	)	)	PUNCT
ejpam-3412	79	38	,	,	PUNCT
ejpam-3412	79	39	(	(	PUNCT
ejpam-3412	79	40	1.11	1.11	NUM
ejpam-3412	79	41	)	)	PUNCT
ejpam-3412	79	42	(	(	PUNCT
ejpam-3412	79	43	∀x	∀x	X
ejpam-3412	79	44	,	,	PUNCT
ejpam-3412	79	45	y	y	PROPN
ejpam-3412	79	46	,	,	PUNCT
ejpam-3412	79	47	z	z	NOUN
ejpam-3412	79	48	∈	∈	PROPN
ejpam-3412	79	49	a)(((x	a)(((x	NOUN
ejpam-3412	79	50	·	·	SYM
ejpam-3412	79	51	y	y	X
ejpam-3412	79	52	)	)	PUNCT
ejpam-3412	79	53	·	·	PUNCT
ejpam-3412	80	1	z	z	X
ejpam-3412	80	2	)	)	PUNCT
ejpam-3412	80	3	·	·	PUNCT
ejpam-3412	80	4	(	(	PUNCT
ejpam-3412	80	5	x	x	X
ejpam-3412	80	6	·	·	PUNCT
ejpam-3412	80	7	(	(	PUNCT
ejpam-3412	80	8	y	y	PROPN
ejpam-3412	80	9	·	·	PUNCT
ejpam-3412	80	10	z	z	NOUN
ejpam-3412	80	11	)	)	PUNCT
ejpam-3412	80	12	)	)	PUNCT
ejpam-3412	81	1	=	=	PUNCT
ejpam-3412	81	2	0	0	NUM
ejpam-3412	81	3	)	)	PUNCT
ejpam-3412	81	4	,	,	PUNCT
ejpam-3412	81	5	and	and	CCONJ
ejpam-3412	81	6	(	(	PUNCT
ejpam-3412	81	7	1.12	1.12	NUM
ejpam-3412	81	8	)	)	PUNCT
ejpam-3412	81	9	(	(	PUNCT
ejpam-3412	81	10	∀a	∀a	X
ejpam-3412	81	11	,	,	PUNCT
ejpam-3412	81	12	x	x	X
ejpam-3412	81	13	,	,	PUNCT
ejpam-3412	81	14	y	y	PROPN
ejpam-3412	81	15	,	,	PUNCT
ejpam-3412	81	16	z	z	NOUN
ejpam-3412	81	17	∈	∈	PROPN
ejpam-3412	81	18	a)(((x	a)(((x	NOUN
ejpam-3412	81	19	·	·	SYM
ejpam-3412	81	20	y	y	X
ejpam-3412	81	21	)	)	PUNCT
ejpam-3412	81	22	·	·	PUNCT
ejpam-3412	82	1	z	z	X
ejpam-3412	82	2	)	)	PUNCT
ejpam-3412	82	3	·	·	PUNCT
ejpam-3412	82	4	(	(	PUNCT
ejpam-3412	82	5	y	y	PROPN
ejpam-3412	82	6	·	·	PUNCT
ejpam-3412	82	7	(	(	PUNCT
ejpam-3412	82	8	a	a	DET
ejpam-3412	82	9	·	·	PUNCT
ejpam-3412	82	10	z	z	NOUN
ejpam-3412	82	11	)	)	PUNCT
ejpam-3412	82	12	)	)	PUNCT
ejpam-3412	83	1	=	=	PUNCT
ejpam-3412	83	2	0	0	NUM
ejpam-3412	83	3	)	)	PUNCT
ejpam-3412	83	4	.	.	PUNCT
ejpam-3412	84	1	(	(	PUNCT
ejpam-3412	84	2	1.13	1.13	NUM
ejpam-3412	84	3	)	)	PUNCT
ejpam-3412	84	4	definition	definition	NOUN
ejpam-3412	84	5	2	2	NUM
ejpam-3412	84	6	.	.	PUNCT
ejpam-3412	85	1	[	[	X
ejpam-3412	85	2	4	4	NUM
ejpam-3412	85	3	,	,	PUNCT
ejpam-3412	85	4	5	5	NUM
ejpam-3412	85	5	,	,	PUNCT
ejpam-3412	85	6	7	7	NUM
ejpam-3412	85	7	,	,	PUNCT
ejpam-3412	85	8	25	25	NUM
ejpam-3412	85	9	]	]	PUNCT
ejpam-3412	85	10	a	a	DET
ejpam-3412	85	11	nonempty	nonempty	NOUN
ejpam-3412	85	12	subset	subset	VERB
ejpam-3412	85	13	s	s	NOUN
ejpam-3412	85	14	of	of	ADP
ejpam-3412	85	15	a	a	DET
ejpam-3412	85	16	up	up	NOUN
ejpam-3412	85	17	-	-	PUNCT
ejpam-3412	85	18	algebra	algebra	NOUN
ejpam-3412	85	19	(	(	PUNCT
ejpam-3412	85	20	a	a	PRON
ejpam-3412	85	21	,	,	PUNCT
ejpam-3412	85	22	·	·	PUNCT
ejpam-3412	85	23	,	,	PUNCT
ejpam-3412	85	24	0	0	NUM
ejpam-3412	85	25	)	)	PUNCT
ejpam-3412	85	26	is	be	AUX
ejpam-3412	85	27	called	call	VERB
ejpam-3412	85	28	(	(	PUNCT
ejpam-3412	85	29	1	1	NUM
ejpam-3412	85	30	)	)	PUNCT
ejpam-3412	85	31	a	a	DET
ejpam-3412	85	32	up	up	ADJ
ejpam-3412	85	33	-	-	PUNCT
ejpam-3412	85	34	subalgebra	subalgebra	NOUN
ejpam-3412	85	35	of	of	ADP
ejpam-3412	85	36	a	a	DET
ejpam-3412	85	37	if	if	NOUN
ejpam-3412	85	38	(	(	PUNCT
ejpam-3412	85	39	∀x	∀x	X
ejpam-3412	85	40	,	,	PUNCT
ejpam-3412	85	41	y	y	PROPN
ejpam-3412	85	42	∈	∈	PROPN
ejpam-3412	85	43	s)(x	s)(x	PROPN
ejpam-3412	85	44	·	·	PUNCT
ejpam-3412	86	1	y	y	PROPN
ejpam-3412	86	2	∈	∈	PROPN
ejpam-3412	86	3	s	s	PART
ejpam-3412	86	4	)	)	PUNCT
ejpam-3412	86	5	.	.	PUNCT
ejpam-3412	87	1	(	(	PUNCT
ejpam-3412	87	2	2	2	X
ejpam-3412	87	3	)	)	PUNCT
ejpam-3412	87	4	a	a	DET
ejpam-3412	87	5	near	near	ADJ
ejpam-3412	87	6	up	up	NOUN
ejpam-3412	87	7	-	-	PUNCT
ejpam-3412	87	8	filter	filter	NOUN
ejpam-3412	87	9	of	of	ADP
ejpam-3412	87	10	a	a	PRON
ejpam-3412	87	11	if	if	SCONJ
ejpam-3412	87	12	it	it	PRON
ejpam-3412	87	13	satisfies	satisfy	VERB
ejpam-3412	87	14	the	the	DET
ejpam-3412	87	15	following	follow	VERB
ejpam-3412	87	16	properties	property	NOUN
ejpam-3412	87	17	:	:	PUNCT
ejpam-3412	87	18	(	(	PUNCT
ejpam-3412	87	19	i	i	NOUN
ejpam-3412	87	20	)	)	PUNCT
ejpam-3412	87	21	the	the	DET
ejpam-3412	87	22	constant	constant	ADJ
ejpam-3412	87	23	0	0	NUM
ejpam-3412	87	24	of	of	ADP
ejpam-3412	87	25	a	a	PRON
ejpam-3412	87	26	is	be	AUX
ejpam-3412	87	27	in	in	ADP
ejpam-3412	87	28	s	s	PROPN
ejpam-3412	87	29	,	,	PUNCT
ejpam-3412	87	30	and	and	CCONJ
ejpam-3412	87	31	(	(	PUNCT
ejpam-3412	87	32	ii	ii	NOUN
ejpam-3412	87	33	)	)	PUNCT
ejpam-3412	87	34	(	(	PUNCT
ejpam-3412	87	35	∀x	∀x	X
ejpam-3412	87	36	,	,	PUNCT
ejpam-3412	87	37	y	y	PROPN
ejpam-3412	87	38	∈	∈	PROPN
ejpam-3412	87	39	a)(x	a)(x	PROPN
ejpam-3412	87	40	∈	∈	PROPN
ejpam-3412	87	41	a	a	PRON
ejpam-3412	87	42	,	,	PUNCT
ejpam-3412	87	43	y	y	PROPN
ejpam-3412	87	44	∈	∈	PROPN
ejpam-3412	87	45	s	s	PART
ejpam-3412	87	46	⇒	⇒	NOUN
ejpam-3412	87	47	x	x	X
ejpam-3412	87	48	·	·	PUNCT
ejpam-3412	87	49	y	y	X
ejpam-3412	87	50	∈	∈	PROPN
ejpam-3412	87	51	s	s	PART
ejpam-3412	87	52	)	)	PUNCT
ejpam-3412	87	53	.	.	PUNCT
ejpam-3412	88	1	(	(	PUNCT
ejpam-3412	88	2	3	3	X
ejpam-3412	88	3	)	)	PUNCT
ejpam-3412	88	4	a	a	DET
ejpam-3412	88	5	up	up	ADJ
ejpam-3412	88	6	-	-	PUNCT
ejpam-3412	88	7	filter	filter	NOUN
ejpam-3412	88	8	of	of	ADP
ejpam-3412	88	9	a	a	PRON
ejpam-3412	88	10	if	if	SCONJ
ejpam-3412	88	11	it	it	PRON
ejpam-3412	88	12	satisfies	satisfy	VERB
ejpam-3412	88	13	the	the	DET
ejpam-3412	88	14	following	follow	VERB
ejpam-3412	88	15	properties	property	NOUN
ejpam-3412	88	16	:	:	PUNCT
ejpam-3412	88	17	(	(	PUNCT
ejpam-3412	88	18	i	i	NOUN
ejpam-3412	88	19	)	)	PUNCT
ejpam-3412	88	20	the	the	DET
ejpam-3412	88	21	constant	constant	ADJ
ejpam-3412	88	22	0	0	NUM
ejpam-3412	88	23	of	of	ADP
ejpam-3412	88	24	a	a	PRON
ejpam-3412	88	25	is	be	AUX
ejpam-3412	88	26	in	in	ADP
ejpam-3412	88	27	s	s	PROPN
ejpam-3412	88	28	,	,	PUNCT
ejpam-3412	88	29	and	and	CCONJ
ejpam-3412	88	30	(	(	PUNCT
ejpam-3412	88	31	ii	ii	NOUN
ejpam-3412	88	32	)	)	PUNCT
ejpam-3412	88	33	(	(	PUNCT
ejpam-3412	88	34	∀x	∀x	X
ejpam-3412	88	35	,	,	PUNCT
ejpam-3412	88	36	y	y	PROPN
ejpam-3412	88	37	∈	∈	PROPN
ejpam-3412	88	38	a)(x	a)(x	NOUN
ejpam-3412	88	39	·	·	PUNCT
ejpam-3412	89	1	y	y	X
ejpam-3412	89	2	∈	∈	PROPN
ejpam-3412	89	3	s	s	PROPN
ejpam-3412	89	4	,	,	PUNCT
ejpam-3412	89	5	x	x	SYM
ejpam-3412	89	6	∈	∈	PROPN
ejpam-3412	89	7	s	s	PART
ejpam-3412	89	8	⇒	⇒	NOUN
ejpam-3412	89	9	y	y	PROPN
ejpam-3412	89	10	∈	∈	PROPN
ejpam-3412	89	11	s	s	PART
ejpam-3412	89	12	)	)	PUNCT
ejpam-3412	89	13	.	.	PUNCT
ejpam-3412	90	1	(	(	PUNCT
ejpam-3412	90	2	4	4	X
ejpam-3412	90	3	)	)	PUNCT
ejpam-3412	90	4	a	a	DET
ejpam-3412	90	5	up	up	ADJ
ejpam-3412	90	6	-	-	PUNCT
ejpam-3412	90	7	ideal	ideal	NOUN
ejpam-3412	90	8	of	of	ADP
ejpam-3412	90	9	a	a	PRON
ejpam-3412	90	10	if	if	SCONJ
ejpam-3412	90	11	it	it	PRON
ejpam-3412	90	12	satisfies	satisfy	VERB
ejpam-3412	90	13	the	the	DET
ejpam-3412	90	14	following	follow	VERB
ejpam-3412	90	15	properties	property	NOUN
ejpam-3412	90	16	:	:	PUNCT
ejpam-3412	90	17	(	(	PUNCT
ejpam-3412	90	18	i	i	NOUN
ejpam-3412	90	19	)	)	PUNCT
ejpam-3412	90	20	the	the	DET
ejpam-3412	90	21	constant	constant	ADJ
ejpam-3412	90	22	0	0	NUM
ejpam-3412	90	23	of	of	ADP
ejpam-3412	90	24	a	a	PRON
ejpam-3412	90	25	is	be	AUX
ejpam-3412	90	26	in	in	ADP
ejpam-3412	90	27	s	s	PROPN
ejpam-3412	90	28	,	,	PUNCT
ejpam-3412	90	29	and	and	CCONJ
ejpam-3412	90	30	(	(	PUNCT
ejpam-3412	90	31	ii	ii	NOUN
ejpam-3412	90	32	)	)	PUNCT
ejpam-3412	90	33	(	(	PUNCT
ejpam-3412	90	34	∀x	∀x	X
ejpam-3412	90	35	,	,	PUNCT
ejpam-3412	90	36	y	y	PROPN
ejpam-3412	90	37	,	,	PUNCT
ejpam-3412	90	38	z	z	NOUN
ejpam-3412	90	39	∈	∈	NOUN
ejpam-3412	90	40	a)(x	a)(x	PROPN
ejpam-3412	90	41	·	·	PUNCT
ejpam-3412	91	1	(	(	PUNCT
ejpam-3412	91	2	y	y	PROPN
ejpam-3412	91	3	·	·	PUNCT
ejpam-3412	91	4	z	z	X
ejpam-3412	91	5	)	)	PUNCT
ejpam-3412	91	6	∈	∈	PROPN
ejpam-3412	91	7	s	s	PROPN
ejpam-3412	91	8	,	,	PUNCT
ejpam-3412	91	9	y	y	PROPN
ejpam-3412	91	10	∈	∈	PROPN
ejpam-3412	91	11	s	s	PART
ejpam-3412	91	12	⇒	⇒	NOUN
ejpam-3412	91	13	x	x	PUNCT
ejpam-3412	91	14	·	·	PUNCT
ejpam-3412	91	15	z	z	PUNCT
ejpam-3412	91	16	∈	∈	PROPN
ejpam-3412	91	17	s	s	NOUN
ejpam-3412	91	18	)	)	PUNCT
ejpam-3412	91	19	.	.	PUNCT
ejpam-3412	92	1	(	(	PUNCT
ejpam-3412	92	2	5	5	X
ejpam-3412	92	3	)	)	PUNCT
ejpam-3412	92	4	a	a	DET
ejpam-3412	92	5	strongly	strongly	ADV
ejpam-3412	92	6	up	up	ADJ
ejpam-3412	92	7	-	-	PUNCT
ejpam-3412	92	8	ideal	ideal	NOUN
ejpam-3412	92	9	of	of	ADP
ejpam-3412	92	10	a	a	PRON
ejpam-3412	92	11	if	if	SCONJ
ejpam-3412	92	12	it	it	PRON
ejpam-3412	92	13	satisfies	satisfy	VERB
ejpam-3412	92	14	the	the	DET
ejpam-3412	92	15	following	follow	VERB
ejpam-3412	92	16	properties	property	NOUN
ejpam-3412	92	17	:	:	PUNCT
ejpam-3412	92	18	a.	a.	PROPN
ejpam-3412	92	19	satirad	satirad	PROPN
ejpam-3412	92	20	,	,	PUNCT
ejpam-3412	92	21	a.	a.	NOUN
ejpam-3412	92	22	iampan	iampan	PROPN
ejpam-3412	92	23	/	/	SYM
ejpam-3412	92	24	eur	eur	PROPN
ejpam-3412	92	25	.	.	PUNCT
ejpam-3412	93	1	j.	j.	PROPN
ejpam-3412	93	2	pure	pure	PROPN
ejpam-3412	93	3	appl	appl	PROPN
ejpam-3412	93	4	.	.	PROPN
ejpam-3412	93	5	math	math	PROPN
ejpam-3412	93	6	,	,	PUNCT
ejpam-3412	93	7	12	12	NUM
ejpam-3412	93	8	(	(	PUNCT
ejpam-3412	93	9	2	2	NUM
ejpam-3412	93	10	)	)	PUNCT
ejpam-3412	93	11	(	(	PUNCT
ejpam-3412	93	12	2019	2019	NUM
ejpam-3412	93	13	)	)	PUNCT
ejpam-3412	93	14	,	,	PUNCT
ejpam-3412	93	15	294	294	NUM
ejpam-3412	93	16	-	-	SYM
ejpam-3412	93	17	331	331	NUM
ejpam-3412	93	18	297	297	NUM
ejpam-3412	93	19	(	(	PUNCT
ejpam-3412	93	20	i	i	NOUN
ejpam-3412	93	21	)	)	PUNCT
ejpam-3412	93	22	the	the	DET
ejpam-3412	93	23	constant	constant	ADJ
ejpam-3412	93	24	0	0	NUM
ejpam-3412	93	25	of	of	ADP
ejpam-3412	93	26	a	a	PRON
ejpam-3412	93	27	is	be	AUX
ejpam-3412	93	28	in	in	ADP
ejpam-3412	93	29	s	s	PROPN
ejpam-3412	93	30	,	,	PUNCT
ejpam-3412	93	31	and	and	CCONJ
ejpam-3412	93	32	(	(	PUNCT
ejpam-3412	93	33	ii	ii	NOUN
ejpam-3412	93	34	)	)	PUNCT
ejpam-3412	93	35	(	(	PUNCT
ejpam-3412	93	36	∀x	∀x	X
ejpam-3412	93	37	,	,	PUNCT
ejpam-3412	93	38	y	y	PROPN
ejpam-3412	93	39	,	,	PUNCT
ejpam-3412	93	40	z	z	PROPN
ejpam-3412	93	41	∈	∈	PROPN
ejpam-3412	93	42	a)((z	a)((z	X
ejpam-3412	93	43	·	·	PUNCT
ejpam-3412	93	44	y	y	X
ejpam-3412	93	45	)	)	PUNCT
ejpam-3412	93	46	·	·	PUNCT
ejpam-3412	94	1	(	(	PUNCT
ejpam-3412	94	2	z	z	NOUN
ejpam-3412	94	3	·	·	PUNCT
ejpam-3412	94	4	x	x	X
ejpam-3412	94	5	)	)	PUNCT
ejpam-3412	94	6	∈	∈	PROPN
ejpam-3412	94	7	s	s	PROPN
ejpam-3412	94	8	,	,	PUNCT
ejpam-3412	94	9	y	y	PROPN
ejpam-3412	94	10	∈	∈	PROPN
ejpam-3412	94	11	s	s	PART
ejpam-3412	94	12	⇒	⇒	NOUN
ejpam-3412	94	13	x	x	PUNCT
ejpam-3412	94	14	∈	∈	PROPN
ejpam-3412	94	15	s	s	PART
ejpam-3412	94	16	)	)	PUNCT
ejpam-3412	94	17	.	.	PUNCT
ejpam-3412	95	1	we	we	PRON
ejpam-3412	95	2	know	know	VERB
ejpam-3412	95	3	that	that	SCONJ
ejpam-3412	95	4	the	the	DET
ejpam-3412	95	5	notion	notion	NOUN
ejpam-3412	95	6	of	of	ADP
ejpam-3412	95	7	up	up	ADV
ejpam-3412	95	8	-	-	PUNCT
ejpam-3412	95	9	subalgebras	subalgebras	PROPN
ejpam-3412	95	10	is	be	AUX
ejpam-3412	95	11	a	a	DET
ejpam-3412	95	12	generalization	generalization	NOUN
ejpam-3412	95	13	of	of	ADP
ejpam-3412	95	14	near	near	ADP
ejpam-3412	95	15	up	up	NOUN
ejpam-3412	95	16	-	-	PUNCT
ejpam-3412	95	17	filters	filter	NOUN
ejpam-3412	95	18	,	,	PUNCT
ejpam-3412	95	19	the	the	DET
ejpam-3412	95	20	notion	notion	NOUN
ejpam-3412	95	21	of	of	ADP
ejpam-3412	95	22	near	near	ADP
ejpam-3412	95	23	up	up	ADP
ejpam-3412	95	24	-	-	PUNCT
ejpam-3412	95	25	filters	filter	NOUN
ejpam-3412	95	26	is	be	AUX
ejpam-3412	95	27	a	a	DET
ejpam-3412	95	28	generalization	generalization	NOUN
ejpam-3412	95	29	of	of	ADP
ejpam-3412	95	30	up	up	ADJ
ejpam-3412	95	31	-	-	PUNCT
ejpam-3412	95	32	filters	filter	NOUN
ejpam-3412	95	33	,	,	PUNCT
ejpam-3412	95	34	the	the	DET
ejpam-3412	95	35	notion	notion	NOUN
ejpam-3412	95	36	of	of	ADP
ejpam-3412	95	37	up	up	ADP
ejpam-3412	95	38	-	-	PUNCT
ejpam-3412	95	39	filters	filter	NOUN
ejpam-3412	95	40	is	be	AUX
ejpam-3412	95	41	a	a	DET
ejpam-3412	95	42	generalization	generalization	NOUN
ejpam-3412	95	43	of	of	ADP
ejpam-3412	95	44	up	up	ADJ
ejpam-3412	95	45	-	-	PUNCT
ejpam-3412	95	46	ideals	ideal	NOUN
ejpam-3412	95	47	,	,	PUNCT
ejpam-3412	95	48	and	and	CCONJ
ejpam-3412	95	49	the	the	DET
ejpam-3412	95	50	notion	notion	NOUN
ejpam-3412	95	51	of	of	ADP
ejpam-3412	95	52	up	up	ADJ
ejpam-3412	95	53	-	-	PUNCT
ejpam-3412	95	54	ideals	ideal	NOUN
ejpam-3412	95	55	is	be	AUX
ejpam-3412	95	56	a	a	DET
ejpam-3412	95	57	generalization	generalization	NOUN
ejpam-3412	95	58	of	of	ADP
ejpam-3412	95	59	strongly	strongly	ADV
ejpam-3412	95	60	upideals	upideal	NOUN
ejpam-3412	95	61	.	.	PUNCT
ejpam-3412	96	1	moreover	moreover	ADV
ejpam-3412	96	2	,	,	PUNCT
ejpam-3412	96	3	they	they	PRON
ejpam-3412	96	4	also	also	ADV
ejpam-3412	96	5	proved	prove	VERB
ejpam-3412	96	6	that	that	SCONJ
ejpam-3412	96	7	a	a	DET
ejpam-3412	96	8	up	up	NOUN
ejpam-3412	96	9	-	-	PUNCT
ejpam-3412	96	10	algebra	algebra	NOUN
ejpam-3412	96	11	a	a	PRON
ejpam-3412	96	12	is	be	AUX
ejpam-3412	96	13	the	the	DET
ejpam-3412	96	14	only	only	ADJ
ejpam-3412	96	15	one	one	NUM
ejpam-3412	96	16	strongly	strongly	ADV
ejpam-3412	96	17	up	up	ADP
ejpam-3412	96	18	-	-	PUNCT
ejpam-3412	96	19	ideal	ideal	NOUN
ejpam-3412	96	20	of	of	ADP
ejpam-3412	96	21	itself	itself	PRON
ejpam-3412	96	22	.	.	PUNCT
ejpam-3412	97	1	definition	definition	NOUN
ejpam-3412	97	2	3	3	NUM
ejpam-3412	97	3	.	.	PUNCT
ejpam-3412	98	1	[	[	X
ejpam-3412	98	2	15	15	NUM
ejpam-3412	98	3	]	]	X
ejpam-3412	98	4	a	a	DET
ejpam-3412	98	5	nonempty	nonempty	NOUN
ejpam-3412	98	6	subset	subset	VERB
ejpam-3412	98	7	s	s	NOUN
ejpam-3412	98	8	of	of	ADP
ejpam-3412	98	9	a	a	DET
ejpam-3412	98	10	semigroup	semigroup	NOUN
ejpam-3412	98	11	(	(	PUNCT
ejpam-3412	98	12	a	a	PRON
ejpam-3412	98	13	,	,	PUNCT
ejpam-3412	98	14	∗	∗	NOUN
ejpam-3412	98	15	)	)	PUNCT
ejpam-3412	98	16	is	be	AUX
ejpam-3412	98	17	called	call	VERB
ejpam-3412	98	18	(	(	PUNCT
ejpam-3412	98	19	1	1	NUM
ejpam-3412	98	20	)	)	PUNCT
ejpam-3412	98	21	a	a	DET
ejpam-3412	98	22	subsemigroup	subsemigroup	NOUN
ejpam-3412	98	23	of	of	ADP
ejpam-3412	98	24	a	a	DET
ejpam-3412	98	25	if	if	NOUN
ejpam-3412	98	26	(	(	PUNCT
ejpam-3412	98	27	∀x	∀x	X
ejpam-3412	98	28	,	,	PUNCT
ejpam-3412	98	29	y	y	PROPN
ejpam-3412	98	30	∈	∈	PROPN
ejpam-3412	98	31	s)(x	s)(x	PROPN
ejpam-3412	98	32	∗	∗	VERB
ejpam-3412	98	33	y	y	PROPN
ejpam-3412	98	34	∈	∈	PROPN
ejpam-3412	98	35	s	s	PART
ejpam-3412	98	36	)	)	PUNCT
ejpam-3412	98	37	.	.	PUNCT
ejpam-3412	99	1	(	(	PUNCT
ejpam-3412	99	2	2	2	X
ejpam-3412	99	3	)	)	PUNCT
ejpam-3412	99	4	an	an	DET
ejpam-3412	99	5	ideal	ideal	NOUN
ejpam-3412	99	6	of	of	ADP
ejpam-3412	99	7	a	a	DET
ejpam-3412	99	8	if	if	NOUN
ejpam-3412	99	9	(	(	PUNCT
ejpam-3412	99	10	∀x	∀x	X
ejpam-3412	99	11	,	,	PUNCT
ejpam-3412	99	12	y	y	PROPN
ejpam-3412	99	13	∈	∈	PROPN
ejpam-3412	99	14	a)(x	a)(x	PROPN
ejpam-3412	99	15	∈	∈	PROPN
ejpam-3412	99	16	a	a	PRON
ejpam-3412	99	17	,	,	PUNCT
ejpam-3412	99	18	y	y	PROPN
ejpam-3412	99	19	∈	∈	PROPN
ejpam-3412	99	20	s	s	PART
ejpam-3412	99	21	⇒	⇒	NOUN
ejpam-3412	99	22	x	x	PROPN
ejpam-3412	99	23	∗	∗	PROPN
ejpam-3412	99	24	y	y	PROPN
ejpam-3412	99	25	,	,	PUNCT
ejpam-3412	99	26	y	y	PROPN
ejpam-3412	99	27	∗	∗	NOUN
ejpam-3412	99	28	x	x	PUNCT
ejpam-3412	99	29	∈	∈	NOUN
ejpam-3412	99	30	s	s	NOUN
ejpam-3412	99	31	)	)	PUNCT
ejpam-3412	99	32	.	.	PUNCT
ejpam-3412	100	1	clearly	clearly	ADV
ejpam-3412	100	2	,	,	PUNCT
ejpam-3412	100	3	an	an	DET
ejpam-3412	100	4	ideal	ideal	NOUN
ejpam-3412	100	5	is	be	AUX
ejpam-3412	100	6	a	a	DET
ejpam-3412	100	7	subsemigroup	subsemigroup	NOUN
ejpam-3412	100	8	.	.	PUNCT
ejpam-3412	101	1	definition	definition	NOUN
ejpam-3412	101	2	4	4	NUM
ejpam-3412	101	3	.	.	PUNCT
ejpam-3412	102	1	[	[	X
ejpam-3412	102	2	6	6	NUM
ejpam-3412	102	3	]	]	PUNCT
ejpam-3412	102	4	let	let	VERB
ejpam-3412	102	5	a	a	PRON
ejpam-3412	102	6	be	be	AUX
ejpam-3412	102	7	a	a	DET
ejpam-3412	102	8	nonempty	nonempty	ADJ
ejpam-3412	102	9	set	set	VERB
ejpam-3412	102	10	,	,	PUNCT
ejpam-3412	102	11	·	·	PUNCT
ejpam-3412	102	12	and	and	CCONJ
ejpam-3412	102	13	∗	∗	NOUN
ejpam-3412	102	14	are	be	AUX
ejpam-3412	102	15	binary	binary	ADJ
ejpam-3412	102	16	operations	operation	NOUN
ejpam-3412	102	17	on	on	ADP
ejpam-3412	102	18	a	a	PRON
ejpam-3412	102	19	,	,	PUNCT
ejpam-3412	102	20	and	and	CCONJ
ejpam-3412	102	21	0	0	NUM
ejpam-3412	102	22	is	be	AUX
ejpam-3412	102	23	a	a	DET
ejpam-3412	102	24	fixed	fix	VERB
ejpam-3412	102	25	element	element	NOUN
ejpam-3412	102	26	of	of	ADP
ejpam-3412	102	27	a	a	DET
ejpam-3412	102	28	(	(	PUNCT
ejpam-3412	102	29	i.e.	i.e.	X
ejpam-3412	102	30	,	,	PUNCT
ejpam-3412	102	31	a	a	DET
ejpam-3412	102	32	nullary	nullary	ADJ
ejpam-3412	102	33	operation	operation	NOUN
ejpam-3412	102	34	)	)	PUNCT
ejpam-3412	102	35	.	.	PUNCT
ejpam-3412	103	1	an	an	DET
ejpam-3412	103	2	algebra	algebra	NOUN
ejpam-3412	103	3	a	a	X
ejpam-3412	103	4	=	=	X
ejpam-3412	103	5	(	(	PUNCT
ejpam-3412	103	6	a	a	PRON
ejpam-3412	103	7	,	,	PUNCT
ejpam-3412	103	8	·	·	PUNCT
ejpam-3412	103	9	,	,	PUNCT
ejpam-3412	103	10	∗	∗	NOUN
ejpam-3412	103	11	,	,	PUNCT
ejpam-3412	103	12	0	0	NUM
ejpam-3412	103	13	)	)	PUNCT
ejpam-3412	103	14	of	of	ADP
ejpam-3412	103	15	type	type	NOUN
ejpam-3412	103	16	(	(	PUNCT
ejpam-3412	103	17	2	2	NUM
ejpam-3412	103	18	,	,	PUNCT
ejpam-3412	103	19	2	2	NUM
ejpam-3412	103	20	,	,	PUNCT
ejpam-3412	103	21	0	0	NUM
ejpam-3412	103	22	)	)	PUNCT
ejpam-3412	103	23	in	in	ADP
ejpam-3412	103	24	which	which	PRON
ejpam-3412	103	25	(	(	PUNCT
ejpam-3412	103	26	a	a	PRON
ejpam-3412	103	27	,	,	PUNCT
ejpam-3412	103	28	·	·	PUNCT
ejpam-3412	103	29	,	,	PUNCT
ejpam-3412	103	30	0	0	NUM
ejpam-3412	103	31	)	)	PUNCT
ejpam-3412	103	32	is	be	AUX
ejpam-3412	103	33	a	a	DET
ejpam-3412	103	34	up	up	NOUN
ejpam-3412	103	35	-	-	PUNCT
ejpam-3412	103	36	algebra	algebra	NOUN
ejpam-3412	103	37	and	and	CCONJ
ejpam-3412	103	38	(	(	PUNCT
ejpam-3412	103	39	a	a	PRON
ejpam-3412	103	40	,	,	PUNCT
ejpam-3412	103	41	∗	∗	NOUN
ejpam-3412	103	42	)	)	PUNCT
ejpam-3412	103	43	is	be	AUX
ejpam-3412	103	44	a	a	DET
ejpam-3412	103	45	semigroup	semigroup	NOUN
ejpam-3412	103	46	is	be	AUX
ejpam-3412	103	47	called	call	VERB
ejpam-3412	103	48	a	a	DET
ejpam-3412	103	49	fully	fully	ADV
ejpam-3412	103	50	up	up	ADJ
ejpam-3412	103	51	-	-	PUNCT
ejpam-3412	103	52	semigroup	semigroup	NOUN
ejpam-3412	103	53	(	(	PUNCT
ejpam-3412	103	54	in	in	ADP
ejpam-3412	103	55	short	short	ADJ
ejpam-3412	103	56	,	,	PUNCT
ejpam-3412	104	1	an	an	DET
ejpam-3412	104	2	f	f	PROPN
ejpam-3412	104	3	-up	-up	NOUN
ejpam-3412	104	4	-	-	PUNCT
ejpam-3412	104	5	semigroup	semigroup	NOUN
ejpam-3412	104	6	)	)	PUNCT
ejpam-3412	104	7	if	if	SCONJ
ejpam-3412	104	8	the	the	DET
ejpam-3412	104	9	operation	operation	NOUN
ejpam-3412	104	10	“	"	PUNCT
ejpam-3412	104	11	∗	∗	NOUN
ejpam-3412	104	12	”	"	PUNCT
ejpam-3412	104	13	is	be	AUX
ejpam-3412	104	14	distributive	distributive	ADJ
ejpam-3412	104	15	(	(	PUNCT
ejpam-3412	104	16	on	on	ADP
ejpam-3412	104	17	both	both	DET
ejpam-3412	104	18	sides	side	NOUN
ejpam-3412	104	19	)	)	PUNCT
ejpam-3412	104	20	over	over	ADP
ejpam-3412	104	21	the	the	DET
ejpam-3412	104	22	operation	operation	NOUN
ejpam-3412	104	23	“	"	PUNCT
ejpam-3412	104	24	·	·	PUNCT
ejpam-3412	104	25	”	"	PUNCT
ejpam-3412	105	1	.	.	PUNCT
ejpam-3412	106	1	definition	definition	NOUN
ejpam-3412	106	2	5	5	NUM
ejpam-3412	106	3	.	.	PUNCT
ejpam-3412	107	1	[	[	X
ejpam-3412	107	2	27	27	NUM
ejpam-3412	107	3	]	]	X
ejpam-3412	107	4	a	a	DET
ejpam-3412	107	5	fuzzy	fuzzy	ADJ
ejpam-3412	107	6	set	set	VERB
ejpam-3412	107	7	f	f	PROPN
ejpam-3412	107	8	in	in	ADP
ejpam-3412	107	9	a	a	DET
ejpam-3412	107	10	nonempty	nonempty	ADV
ejpam-3412	107	11	set	set	VERB
ejpam-3412	107	12	u	u	NOUN
ejpam-3412	107	13	(	(	PUNCT
ejpam-3412	107	14	or	or	CCONJ
ejpam-3412	107	15	a	a	DET
ejpam-3412	107	16	fuzzy	fuzzy	ADJ
ejpam-3412	107	17	subset	subset	NOUN
ejpam-3412	107	18	of	of	ADP
ejpam-3412	107	19	u	u	NOUN
ejpam-3412	107	20	)	)	PUNCT
ejpam-3412	107	21	is	be	AUX
ejpam-3412	107	22	described	describe	VERB
ejpam-3412	107	23	by	by	ADP
ejpam-3412	107	24	its	its	PRON
ejpam-3412	107	25	membership	membership	NOUN
ejpam-3412	107	26	function	function	NOUN
ejpam-3412	107	27	ff	ff	NOUN
ejpam-3412	107	28	.	.	PUNCT
ejpam-3412	108	1	to	to	ADP
ejpam-3412	108	2	every	every	DET
ejpam-3412	108	3	point	point	NOUN
ejpam-3412	108	4	x	x	X
ejpam-3412	108	5	∈	∈	PROPN
ejpam-3412	108	6	u	u	NOUN
ejpam-3412	108	7	,	,	PUNCT
ejpam-3412	108	8	this	this	DET
ejpam-3412	108	9	function	function	NOUN
ejpam-3412	108	10	associates	associate	VERB
ejpam-3412	108	11	a	a	DET
ejpam-3412	108	12	real	real	ADJ
ejpam-3412	108	13	number	number	NOUN
ejpam-3412	108	14	ff(x	ff(x	NOUN
ejpam-3412	108	15	)	)	PUNCT
ejpam-3412	108	16	in	in	ADP
ejpam-3412	108	17	the	the	DET
ejpam-3412	108	18	interval	interval	NOUN
ejpam-3412	108	19	[	[	X
ejpam-3412	108	20	0	0	NUM
ejpam-3412	108	21	,	,	PUNCT
ejpam-3412	108	22	1	1	NUM
ejpam-3412	108	23	]	]	PUNCT
ejpam-3412	108	24	.	.	PUNCT
ejpam-3412	109	1	the	the	DET
ejpam-3412	109	2	number	number	NOUN
ejpam-3412	109	3	ff(x	ff(x	NOUN
ejpam-3412	109	4	)	)	PUNCT
ejpam-3412	109	5	is	be	AUX
ejpam-3412	109	6	interpreted	interpret	VERB
ejpam-3412	109	7	for	for	ADP
ejpam-3412	109	8	the	the	DET
ejpam-3412	109	9	point	point	NOUN
ejpam-3412	109	10	as	as	ADP
ejpam-3412	109	11	a	a	DET
ejpam-3412	109	12	degree	degree	NOUN
ejpam-3412	109	13	of	of	ADP
ejpam-3412	109	14	belonging	belong	VERB
ejpam-3412	109	15	x	x	PUNCT
ejpam-3412	109	16	to	to	ADP
ejpam-3412	109	17	the	the	DET
ejpam-3412	109	18	fuzzy	fuzzy	ADJ
ejpam-3412	109	19	set	set	NOUN
ejpam-3412	109	20	f	f	NOUN
ejpam-3412	109	21	,	,	PUNCT
ejpam-3412	109	22	that	that	ADV
ejpam-3412	109	23	is	is	ADV
ejpam-3412	109	24	,	,	PUNCT
ejpam-3412	109	25	f	f	X
ejpam-3412	109	26	:	:	PUNCT
ejpam-3412	109	27	=	=	SYM
ejpam-3412	109	28	{	{	PUNCT
ejpam-3412	109	29	(	(	PUNCT
ejpam-3412	109	30	x	x	NOUN
ejpam-3412	109	31	,	,	PUNCT
ejpam-3412	109	32	ff(x	ff(x	NOUN
ejpam-3412	109	33	)	)	PUNCT
ejpam-3412	109	34	)	)	PUNCT
ejpam-3412	110	1	|	|	ADV
ejpam-3412	110	2	x	x	SYM
ejpam-3412	110	3	∈	∈	NOUN
ejpam-3412	110	4	u	u	NOUN
ejpam-3412	110	5	}	}	PUNCT
ejpam-3412	110	6	.	.	PUNCT
ejpam-3412	111	1	we	we	PRON
ejpam-3412	111	2	say	say	VERB
ejpam-3412	111	3	that	that	SCONJ
ejpam-3412	111	4	a	a	DET
ejpam-3412	111	5	fuzzy	fuzzy	ADJ
ejpam-3412	111	6	set	set	NOUN
ejpam-3412	111	7	f	f	PROPN
ejpam-3412	111	8	in	in	ADP
ejpam-3412	111	9	u	u	NOUN
ejpam-3412	111	10	is	be	AUX
ejpam-3412	111	11	constant	constant	ADJ
ejpam-3412	111	12	if	if	SCONJ
ejpam-3412	111	13	its	its	PRON
ejpam-3412	111	14	membership	membership	NOUN
ejpam-3412	111	15	function	function	NOUN
ejpam-3412	111	16	ff	ff	NOUN
ejpam-3412	111	17	is	be	AUX
ejpam-3412	111	18	constant	constant	ADJ
ejpam-3412	111	19	.	.	PUNCT
ejpam-3412	112	1	definition	definition	NOUN
ejpam-3412	112	2	6	6	NUM
ejpam-3412	112	3	.	.	PUNCT
ejpam-3412	113	1	[	[	X
ejpam-3412	113	2	16	16	NUM
ejpam-3412	113	3	]	]	PUNCT
ejpam-3412	113	4	let	let	VERB
ejpam-3412	113	5	f	f	PROPN
ejpam-3412	113	6	and	and	CCONJ
ejpam-3412	113	7	g	g	PROPN
ejpam-3412	113	8	be	be	VERB
ejpam-3412	113	9	fuzzy	fuzzy	ADJ
ejpam-3412	113	10	sets	set	NOUN
ejpam-3412	113	11	in	in	ADP
ejpam-3412	113	12	a	a	DET
ejpam-3412	113	13	nonempty	nonempty	ADV
ejpam-3412	113	14	set	set	VERB
ejpam-3412	113	15	u	u	NOUN
ejpam-3412	113	16	.	.	PUNCT
ejpam-3412	114	1	then	then	ADV
ejpam-3412	114	2	f	f	PROPN
ejpam-3412	114	3	≤	≤	PROPN
ejpam-3412	114	4	g	g	NOUN
ejpam-3412	114	5	is	be	AUX
ejpam-3412	114	6	defined	define	VERB
ejpam-3412	114	7	by	by	ADP
ejpam-3412	114	8	ff(x	ff(x	NOUN
ejpam-3412	114	9	)	)	PUNCT
ejpam-3412	114	10	≤	≤	NUM
ejpam-3412	114	11	fg(x	fg(x	PUNCT
ejpam-3412	114	12	)	)	PUNCT
ejpam-3412	114	13	for	for	ADP
ejpam-3412	114	14	all	all	DET
ejpam-3412	114	15	x	x	SYM
ejpam-3412	114	16	∈	∈	PROPN
ejpam-3412	114	17	u	u	NOUN
ejpam-3412	114	18	.	.	PUNCT
ejpam-3412	115	1	definition	definition	NOUN
ejpam-3412	115	2	7	7	NUM
ejpam-3412	115	3	.	.	PUNCT
ejpam-3412	116	1	[	[	X
ejpam-3412	116	2	15	15	NUM
ejpam-3412	116	3	]	]	X
ejpam-3412	116	4	let	let	VERB
ejpam-3412	116	5	f	f	PROPN
ejpam-3412	116	6	and	and	CCONJ
ejpam-3412	116	7	g	g	PROPN
ejpam-3412	116	8	be	be	VERB
ejpam-3412	116	9	fuzzy	fuzzy	ADJ
ejpam-3412	116	10	sets	set	NOUN
ejpam-3412	116	11	in	in	ADP
ejpam-3412	116	12	a	a	DET
ejpam-3412	116	13	semigroup	semigroup	NOUN
ejpam-3412	116	14	a	a	PRON
ejpam-3412	116	15	=	=	X
ejpam-3412	116	16	(	(	PUNCT
ejpam-3412	116	17	a	a	PRON
ejpam-3412	116	18	,	,	PUNCT
ejpam-3412	116	19	∗	∗	NOUN
ejpam-3412	116	20	)	)	PUNCT
ejpam-3412	116	21	.	.	PUNCT
ejpam-3412	117	1	then	then	ADV
ejpam-3412	117	2	the	the	DET
ejpam-3412	117	3	product	product	NOUN
ejpam-3412	117	4	of	of	ADP
ejpam-3412	117	5	f	f	PROPN
ejpam-3412	117	6	and	and	CCONJ
ejpam-3412	117	7	g	g	PROPN
ejpam-3412	117	8	,	,	PUNCT
ejpam-3412	117	9	denoted	denote	VERB
ejpam-3412	117	10	by	by	ADP
ejpam-3412	117	11	f	f	PROPN
ejpam-3412	117	12	◦	◦	NOUN
ejpam-3412	117	13	g	g	NOUN
ejpam-3412	117	14	,	,	PUNCT
ejpam-3412	117	15	is	be	AUX
ejpam-3412	117	16	described	describe	VERB
ejpam-3412	117	17	by	by	ADP
ejpam-3412	117	18	their	their	PRON
ejpam-3412	117	19	membership	membership	NOUN
ejpam-3412	117	20	function	function	NOUN
ejpam-3412	117	21	ff	ff	NOUN
ejpam-3412	117	22	and	and	CCONJ
ejpam-3412	117	23	fg	fg	PROPN
ejpam-3412	117	24	,	,	PUNCT
ejpam-3412	117	25	respectively	respectively	ADV
ejpam-3412	117	26	which	which	PRON
ejpam-3412	117	27	defined	define	VERB
ejpam-3412	117	28	as	as	SCONJ
ejpam-3412	117	29	follows	follow	VERB
ejpam-3412	117	30	:	:	PUNCT
ejpam-3412	117	31	(	(	PUNCT
ejpam-3412	117	32	∀x	∀x	X
ejpam-3412	117	33	∈	∈	PROPN
ejpam-3412	117	34	a	a	NOUN
ejpam-3412	117	35	)	)	PUNCT
ejpam-3412	117	36	(	(	PUNCT
ejpam-3412	117	37	(	(	PUNCT
ejpam-3412	117	38	ff	ff	NOUN
ejpam-3412	117	39	◦	◦	NOUN
ejpam-3412	117	40	fg)(x	fg)(x	NOUN
ejpam-3412	117	41	)	)	PUNCT
ejpam-3412	118	1	=	=	PRON
ejpam-3412	118	2	{	{	PUNCT
ejpam-3412	118	3	sup{min{ff(y	sup{min{ff(y	ADP
ejpam-3412	118	4	)	)	PUNCT
ejpam-3412	118	5	,	,	PUNCT
ejpam-3412	118	6	fg(z)}}x	fg(z)}}x	PUNCT
ejpam-3412	118	7	=	=	NOUN
ejpam-3412	118	8	y∗z	y∗z	X
ejpam-3412	118	9	if	if	SCONJ
ejpam-3412	118	10	∃y	∃y	PROPN
ejpam-3412	118	11	,	,	PUNCT
ejpam-3412	118	12	z	z	PROPN
ejpam-3412	118	13	∈	∈	PROPN
ejpam-3412	118	14	a	a	DET
ejpam-3412	118	15	such	such	ADJ
ejpam-3412	118	16	that	that	PRON
ejpam-3412	118	17	x	x	X
ejpam-3412	118	18	=	=	SYM
ejpam-3412	118	19	y	y	PROPN
ejpam-3412	118	20	∗	∗	PROPN
ejpam-3412	118	21	z	z	PROPN
ejpam-3412	118	22	,	,	PUNCT
ejpam-3412	118	23	0	0	NUM
ejpam-3412	118	24	otherwise	otherwise	ADV
ejpam-3412	118	25	.	.	PUNCT
ejpam-3412	118	26	)	)	PUNCT
ejpam-3412	119	1	rosenfeld	rosenfeld	PROPN
ejpam-3412	120	1	[	[	X
ejpam-3412	120	2	22	22	NUM
ejpam-3412	120	3	]	]	PUNCT
ejpam-3412	120	4	introduced	introduce	VERB
ejpam-3412	120	5	the	the	DET
ejpam-3412	120	6	notion	notion	NOUN
ejpam-3412	120	7	of	of	ADP
ejpam-3412	120	8	fuzzy	fuzzy	ADJ
ejpam-3412	120	9	subsemigroups	subsemigroup	NOUN
ejpam-3412	120	10	(	(	PUNCT
ejpam-3412	120	11	resp	resp	NOUN
ejpam-3412	120	12	.	.	PUNCT
ejpam-3412	120	13	,	,	PUNCT
ejpam-3412	120	14	fuzzy	fuzzy	ADJ
ejpam-3412	120	15	ideals	ideal	NOUN
ejpam-3412	120	16	)	)	PUNCT
ejpam-3412	120	17	of	of	ADP
ejpam-3412	120	18	semigroups	semigroup	NOUN
ejpam-3412	120	19	as	as	SCONJ
ejpam-3412	120	20	follows	follow	VERB
ejpam-3412	120	21	:	:	PUNCT
ejpam-3412	120	22	definition	definition	NOUN
ejpam-3412	120	23	8	8	NUM
ejpam-3412	120	24	.	.	PUNCT
ejpam-3412	121	1	a	a	DET
ejpam-3412	121	2	fuzzy	fuzzy	ADJ
ejpam-3412	121	3	set	set	VERB
ejpam-3412	121	4	f	f	PROPN
ejpam-3412	121	5	in	in	ADP
ejpam-3412	121	6	a	a	DET
ejpam-3412	121	7	semigroup	semigroup	NOUN
ejpam-3412	121	8	a	a	PRON
ejpam-3412	121	9	=	=	X
ejpam-3412	121	10	(	(	PUNCT
ejpam-3412	121	11	a	a	PRON
ejpam-3412	121	12	,	,	PUNCT
ejpam-3412	121	13	∗	∗	NOUN
ejpam-3412	121	14	)	)	PUNCT
ejpam-3412	121	15	is	be	AUX
ejpam-3412	121	16	called	call	VERB
ejpam-3412	121	17	(	(	PUNCT
ejpam-3412	121	18	1	1	NUM
ejpam-3412	121	19	)	)	PUNCT
ejpam-3412	121	20	a	a	DET
ejpam-3412	121	21	fuzzy	fuzzy	ADJ
ejpam-3412	121	22	subsemigroup	subsemigroup	NOUN
ejpam-3412	121	23	of	of	ADP
ejpam-3412	121	24	a	a	DET
ejpam-3412	121	25	if	if	NOUN
ejpam-3412	121	26	(	(	PUNCT
ejpam-3412	121	27	∀x	∀x	X
ejpam-3412	121	28	,	,	PUNCT
ejpam-3412	121	29	y	y	PROPN
ejpam-3412	121	30	∈	∈	PROPN
ejpam-3412	121	31	a)(ff(x	a)(ff(x	PROPN
ejpam-3412	121	32	∗	∗	PROPN
ejpam-3412	121	33	y	y	PROPN
ejpam-3412	121	34	)	)	PUNCT
ejpam-3412	121	35	≥	≥	PROPN
ejpam-3412	121	36	min{ff(x	min{ff(x	PROPN
ejpam-3412	121	37	)	)	PUNCT
ejpam-3412	121	38	,	,	PUNCT
ejpam-3412	121	39	ff(y	ff(y	NUM
ejpam-3412	121	40	)	)	PUNCT
ejpam-3412	121	41	}	}	PUNCT
ejpam-3412	121	42	)	)	PUNCT
ejpam-3412	121	43	.	.	PUNCT
ejpam-3412	122	1	(	(	PUNCT
ejpam-3412	122	2	2	2	X
ejpam-3412	122	3	)	)	PUNCT
ejpam-3412	122	4	a	a	DET
ejpam-3412	122	5	fuzzy	fuzzy	ADJ
ejpam-3412	122	6	ideal	ideal	NOUN
ejpam-3412	122	7	of	of	ADP
ejpam-3412	122	8	a	a	DET
ejpam-3412	122	9	if	if	NOUN
ejpam-3412	122	10	(	(	PUNCT
ejpam-3412	122	11	∀x	∀x	X
ejpam-3412	122	12	,	,	PUNCT
ejpam-3412	122	13	y	y	PROPN
ejpam-3412	122	14	∈	∈	PROPN
ejpam-3412	122	15	a)(ff(x	a)(ff(x	PROPN
ejpam-3412	122	16	∗	∗	PROPN
ejpam-3412	122	17	y	y	PROPN
ejpam-3412	122	18	)	)	PUNCT
ejpam-3412	122	19	≥	≥	PROPN
ejpam-3412	122	20	max{ff(x	max{ff(x	PROPN
ejpam-3412	122	21	)	)	PUNCT
ejpam-3412	122	22	,	,	PUNCT
ejpam-3412	122	23	ff(y	ff(y	NUM
ejpam-3412	122	24	)	)	PUNCT
ejpam-3412	122	25	}	}	PUNCT
ejpam-3412	122	26	)	)	PUNCT
ejpam-3412	122	27	.	.	PUNCT
ejpam-3412	123	1	a.	a.	PROPN
ejpam-3412	123	2	satirad	satirad	PROPN
ejpam-3412	123	3	,	,	PUNCT
ejpam-3412	123	4	a.	a.	NOUN
ejpam-3412	123	5	iampan	iampan	PROPN
ejpam-3412	123	6	/	/	SYM
ejpam-3412	123	7	eur	eur	PROPN
ejpam-3412	123	8	.	.	PUNCT
ejpam-3412	124	1	j.	j.	PROPN
ejpam-3412	124	2	pure	pure	PROPN
ejpam-3412	124	3	appl	appl	PROPN
ejpam-3412	124	4	.	.	PROPN
ejpam-3412	124	5	math	math	PROPN
ejpam-3412	124	6	,	,	PUNCT
ejpam-3412	124	7	12	12	NUM
ejpam-3412	124	8	(	(	PUNCT
ejpam-3412	124	9	2	2	NUM
ejpam-3412	124	10	)	)	PUNCT
ejpam-3412	124	11	(	(	PUNCT
ejpam-3412	124	12	2019	2019	NUM
ejpam-3412	124	13	)	)	PUNCT
ejpam-3412	124	14	,	,	PUNCT
ejpam-3412	124	15	294	294	NUM
ejpam-3412	124	16	-	-	SYM
ejpam-3412	124	17	331	331	NUM
ejpam-3412	124	18	298	298	NUM
ejpam-3412	124	19	clearly	clearly	ADV
ejpam-3412	124	20	,	,	PUNCT
ejpam-3412	124	21	a	a	DET
ejpam-3412	124	22	fuzzy	fuzzy	ADJ
ejpam-3412	124	23	ideal	ideal	NOUN
ejpam-3412	124	24	is	be	AUX
ejpam-3412	124	25	a	a	DET
ejpam-3412	124	26	fuzzy	fuzzy	ADJ
ejpam-3412	124	27	subsemigroup	subsemigroup	NOUN
ejpam-3412	124	28	.	.	PUNCT
ejpam-3412	125	1	definition	definition	NOUN
ejpam-3412	125	2	9	9	NUM
ejpam-3412	125	3	.	.	PUNCT
ejpam-3412	126	1	[	[	X
ejpam-3412	126	2	15	15	NUM
ejpam-3412	126	3	]	]	X
ejpam-3412	126	4	the	the	DET
ejpam-3412	126	5	semigroup	semigroup	NOUN
ejpam-3412	126	6	a	a	DET
ejpam-3412	126	7	itself	itself	PRON
ejpam-3412	126	8	is	be	AUX
ejpam-3412	126	9	a	a	DET
ejpam-3412	126	10	fuzzy	fuzzy	ADJ
ejpam-3412	126	11	set	set	NOUN
ejpam-3412	126	12	of	of	ADP
ejpam-3412	126	13	a	a	PRON
ejpam-3412	126	14	,	,	PUNCT
ejpam-3412	126	15	denoted	denote	VERB
ejpam-3412	126	16	by	by	ADP
ejpam-3412	126	17	a	a	DET
ejpam-3412	126	18	such	such	ADJ
ejpam-3412	126	19	that	that	PRON
ejpam-3412	126	20	fa(x	fa(x	NOUN
ejpam-3412	126	21	)	)	PUNCT
ejpam-3412	126	22	=	=	SYM
ejpam-3412	126	23	1	1	NUM
ejpam-3412	126	24	for	for	ADP
ejpam-3412	126	25	all	all	DET
ejpam-3412	126	26	x	x	SYM
ejpam-3412	126	27	∈	∈	PROPN
ejpam-3412	126	28	a.	a.	NOUN
ejpam-3412	126	29	lemma	lemma	PROPN
ejpam-3412	126	30	1	1	NUM
ejpam-3412	126	31	.	.	PUNCT
ejpam-3412	127	1	[	[	X
ejpam-3412	127	2	15	15	NUM
ejpam-3412	127	3	]	]	PUNCT
ejpam-3412	127	4	let	let	VERB
ejpam-3412	127	5	f	f	PRON
ejpam-3412	127	6	be	be	AUX
ejpam-3412	127	7	a	a	DET
ejpam-3412	127	8	fuzzy	fuzzy	ADJ
ejpam-3412	127	9	set	set	NOUN
ejpam-3412	127	10	in	in	ADP
ejpam-3412	127	11	a	a	DET
ejpam-3412	127	12	semigroup	semigroup	NOUN
ejpam-3412	127	13	a	a	PRON
ejpam-3412	127	14	=	=	X
ejpam-3412	127	15	(	(	PUNCT
ejpam-3412	127	16	a	a	PRON
ejpam-3412	127	17	,	,	PUNCT
ejpam-3412	127	18	∗	∗	NOUN
ejpam-3412	127	19	)	)	PUNCT
ejpam-3412	127	20	.	.	PUNCT
ejpam-3412	128	1	then	then	ADV
ejpam-3412	128	2	(	(	PUNCT
ejpam-3412	128	3	1	1	X
ejpam-3412	128	4	)	)	PUNCT
ejpam-3412	128	5	f	f	PROPN
ejpam-3412	128	6	is	be	AUX
ejpam-3412	128	7	a	a	DET
ejpam-3412	128	8	fuzzy	fuzzy	ADJ
ejpam-3412	128	9	subsemigroup	subsemigroup	NOUN
ejpam-3412	128	10	of	of	ADP
ejpam-3412	128	11	a	a	DET
ejpam-3412	128	12	if	if	NOUN
ejpam-3412	128	13	and	and	CCONJ
ejpam-3412	128	14	only	only	ADV
ejpam-3412	128	15	if	if	SCONJ
ejpam-3412	128	16	it	it	PRON
ejpam-3412	128	17	satisfies	satisfy	VERB
ejpam-3412	128	18	the	the	DET
ejpam-3412	128	19	condition	condition	NOUN
ejpam-3412	128	20	f	f	PROPN
ejpam-3412	128	21	◦	◦	NOUN
ejpam-3412	128	22	f	f	PROPN
ejpam-3412	128	23	≤	≤	PROPN
ejpam-3412	128	24	f.	f.	PROPN
ejpam-3412	128	25	(	(	PUNCT
ejpam-3412	128	26	1.14	1.14	NUM
ejpam-3412	128	27	)	)	PUNCT
ejpam-3412	128	28	(	(	PUNCT
ejpam-3412	128	29	2	2	X
ejpam-3412	128	30	)	)	PUNCT
ejpam-3412	128	31	f	f	PROPN
ejpam-3412	128	32	is	be	AUX
ejpam-3412	128	33	a	a	DET
ejpam-3412	128	34	fuzzy	fuzzy	ADJ
ejpam-3412	128	35	ideal	ideal	NOUN
ejpam-3412	128	36	of	of	ADP
ejpam-3412	128	37	a	a	DET
ejpam-3412	128	38	if	if	NOUN
ejpam-3412	128	39	and	and	CCONJ
ejpam-3412	128	40	only	only	ADV
ejpam-3412	128	41	if	if	SCONJ
ejpam-3412	128	42	it	it	PRON
ejpam-3412	128	43	satisfies	satisfy	VERB
ejpam-3412	128	44	the	the	DET
ejpam-3412	128	45	condition	condition	NOUN
ejpam-3412	128	46	a	a	DET
ejpam-3412	128	47	◦	◦	NOUN
ejpam-3412	128	48	f	f	NOUN
ejpam-3412	128	49	≤	≤	ADJ
ejpam-3412	128	50	f	f	PROPN
ejpam-3412	128	51	and	and	CCONJ
ejpam-3412	128	52	f	f	PROPN
ejpam-3412	128	53	◦	◦	NOUN
ejpam-3412	128	54	a	a	DET
ejpam-3412	128	55	≤	≤	ADJ
ejpam-3412	128	56	f.	f.	NOUN
ejpam-3412	128	57	(	(	PUNCT
ejpam-3412	128	58	1.15	1.15	NUM
ejpam-3412	128	59	)	)	PUNCT
ejpam-3412	128	60	definition	definition	NOUN
ejpam-3412	128	61	10	10	NUM
ejpam-3412	128	62	.	.	PUNCT
ejpam-3412	129	1	[	[	X
ejpam-3412	129	2	16	16	NUM
ejpam-3412	129	3	]	]	X
ejpam-3412	129	4	let	let	AUX
ejpam-3412	129	5	{	{	PUNCT
ejpam-3412	129	6	fi}i∈i	fi}i∈i	VERB
ejpam-3412	129	7	be	be	AUX
ejpam-3412	129	8	a	a	DET
ejpam-3412	129	9	nonempty	nonempty	ADJ
ejpam-3412	129	10	family	family	NOUN
ejpam-3412	129	11	of	of	ADP
ejpam-3412	129	12	fuzzy	fuzzy	ADJ
ejpam-3412	129	13	sets	set	NOUN
ejpam-3412	129	14	in	in	ADP
ejpam-3412	129	15	a	a	DET
ejpam-3412	129	16	nonempty	nonempty	ADV
ejpam-3412	129	17	set	set	VERB
ejpam-3412	129	18	u	u	NOUN
ejpam-3412	129	19	where	where	SCONJ
ejpam-3412	129	20	i	i	PRON
ejpam-3412	129	21	is	be	AUX
ejpam-3412	129	22	an	an	DET
ejpam-3412	129	23	arbitrary	arbitrary	ADJ
ejpam-3412	129	24	index	index	NOUN
ejpam-3412	129	25	set	set	NOUN
ejpam-3412	129	26	.	.	PUNCT
ejpam-3412	130	1	the	the	DET
ejpam-3412	130	2	intersection	intersection	NOUN
ejpam-3412	130	3	of	of	ADP
ejpam-3412	130	4	fi	fi	NOUN
ejpam-3412	130	5	,	,	PUNCT
ejpam-3412	130	6	denoted	denote	VERB
ejpam-3412	130	7	by	by	ADP
ejpam-3412	130	8	⋂	⋂	PROPN
ejpam-3412	130	9	i∈i	i∈i	ADJ
ejpam-3412	130	10	fi	fi	NOUN
ejpam-3412	130	11	,	,	PUNCT
ejpam-3412	130	12	is	be	AUX
ejpam-3412	130	13	described	describe	VERB
ejpam-3412	130	14	by	by	ADP
ejpam-3412	130	15	its	its	PRON
ejpam-3412	130	16	membership	membership	NOUN
ejpam-3412	130	17	function	function	NOUN
ejpam-3412	130	18	f⋂	f⋂	ADP
ejpam-3412	130	19	i∈i	i∈i	ADJ
ejpam-3412	130	20	fi	fi	NOUN
ejpam-3412	130	21	which	which	PRON
ejpam-3412	130	22	defined	define	VERB
ejpam-3412	130	23	as	as	ADP
ejpam-3412	130	24	follows	follow	VERB
ejpam-3412	130	25	:	:	PUNCT
ejpam-3412	130	26	(	(	PUNCT
ejpam-3412	130	27	∀x	∀x	X
ejpam-3412	130	28	∈	∈	PROPN
ejpam-3412	130	29	u)(f⋂	u)(f⋂	NOUN
ejpam-3412	130	30	i∈i	i∈i	ADJ
ejpam-3412	130	31	fi	fi	NOUN
ejpam-3412	130	32	(	(	PUNCT
ejpam-3412	130	33	x	x	NOUN
ejpam-3412	130	34	)	)	PUNCT
ejpam-3412	130	35	=	=	SYM
ejpam-3412	130	36	inf{ffi(x)}i∈i	inf{ffi(x)}i∈i	NOUN
ejpam-3412	130	37	)	)	PUNCT
ejpam-3412	130	38	.	.	PUNCT
ejpam-3412	131	1	the	the	DET
ejpam-3412	131	2	union	union	NOUN
ejpam-3412	131	3	of	of	ADP
ejpam-3412	131	4	fi	fi	PROPN
ejpam-3412	131	5	,	,	PUNCT
ejpam-3412	131	6	denoted	denote	VERB
ejpam-3412	131	7	by	by	ADP
ejpam-3412	131	8	⋃	⋃	PROPN
ejpam-3412	131	9	i∈i	i∈i	ADJ
ejpam-3412	131	10	fi	fi	NOUN
ejpam-3412	131	11	,	,	PUNCT
ejpam-3412	131	12	is	be	AUX
ejpam-3412	131	13	described	describe	VERB
ejpam-3412	131	14	by	by	ADP
ejpam-3412	131	15	its	its	PRON
ejpam-3412	131	16	membership	membership	NOUN
ejpam-3412	131	17	function	function	NOUN
ejpam-3412	131	18	f⋃	f⋃	NOUN
ejpam-3412	131	19	i∈i	i∈i	ADJ
ejpam-3412	131	20	fi	fi	NOUN
ejpam-3412	131	21	which	which	PRON
ejpam-3412	131	22	defined	define	VERB
ejpam-3412	131	23	as	as	ADP
ejpam-3412	131	24	follows	follow	VERB
ejpam-3412	131	25	:	:	PUNCT
ejpam-3412	131	26	(	(	PUNCT
ejpam-3412	131	27	∀x	∀x	X
ejpam-3412	131	28	∈	∈	PROPN
ejpam-3412	131	29	u)(f⋃	u)(f⋃	NOUN
ejpam-3412	131	30	i∈i	i∈i	ADJ
ejpam-3412	131	31	fi	fi	NOUN
ejpam-3412	131	32	(	(	PUNCT
ejpam-3412	131	33	x	x	NOUN
ejpam-3412	131	34	)	)	PUNCT
ejpam-3412	131	35	=	=	SYM
ejpam-3412	131	36	sup{ffi(x)}i∈i	sup{ffi(x)}i∈i	PROPN
ejpam-3412	131	37	)	)	PUNCT
ejpam-3412	131	38	somjanta	somjanta	NOUN
ejpam-3412	131	39	et	et	PROPN
ejpam-3412	131	40	al	al	PROPN
ejpam-3412	131	41	.	.	PUNCT
ejpam-3412	132	1	[	[	X
ejpam-3412	132	2	25	25	NUM
ejpam-3412	132	3	]	]	PUNCT
ejpam-3412	132	4	and	and	CCONJ
ejpam-3412	132	5	guntasow	guntasow	VERB
ejpam-3412	132	6	et	et	PROPN
ejpam-3412	132	7	al	al	PROPN
ejpam-3412	132	8	.	.	PUNCT
ejpam-3412	133	1	[	[	X
ejpam-3412	133	2	4	4	X
ejpam-3412	133	3	]	]	PUNCT
ejpam-3412	133	4	introduced	introduce	VERB
ejpam-3412	133	5	the	the	DET
ejpam-3412	133	6	notion	notion	NOUN
ejpam-3412	133	7	of	of	ADP
ejpam-3412	133	8	fuzzy	fuzzy	ADJ
ejpam-3412	133	9	upsubalgebras	upsubalgebra	NOUN
ejpam-3412	133	10	(	(	PUNCT
ejpam-3412	133	11	resp	resp	NOUN
ejpam-3412	133	12	.	.	PUNCT
ejpam-3412	133	13	,	,	PUNCT
ejpam-3412	133	14	fuzzy	fuzzy	ADJ
ejpam-3412	133	15	up	up	ADP
ejpam-3412	133	16	-	-	PUNCT
ejpam-3412	133	17	filters	filter	NOUN
ejpam-3412	133	18	,	,	PUNCT
ejpam-3412	133	19	fuzzy	fuzzy	ADJ
ejpam-3412	133	20	up	up	NOUN
ejpam-3412	133	21	-	-	PUNCT
ejpam-3412	133	22	ideals	ideal	NOUN
ejpam-3412	133	23	,	,	PUNCT
ejpam-3412	133	24	fuzzy	fuzzy	ADJ
ejpam-3412	133	25	strongly	strongly	ADV
ejpam-3412	133	26	up	up	ADP
ejpam-3412	133	27	-	-	PUNCT
ejpam-3412	133	28	ideals	ideal	NOUN
ejpam-3412	133	29	)	)	PUNCT
ejpam-3412	133	30	of	of	ADP
ejpam-3412	133	31	upalgebras	upalgebra	NOUN
ejpam-3412	133	32	as	as	SCONJ
ejpam-3412	133	33	follows	follow	VERB
ejpam-3412	133	34	:	:	PUNCT
ejpam-3412	133	35	definition	definition	NOUN
ejpam-3412	133	36	11	11	NUM
ejpam-3412	133	37	.	.	PUNCT
ejpam-3412	134	1	a	a	DET
ejpam-3412	134	2	fuzzy	fuzzy	ADJ
ejpam-3412	134	3	set	set	NOUN
ejpam-3412	134	4	f	f	PROPN
ejpam-3412	134	5	in	in	ADP
ejpam-3412	134	6	a	a	PRON
ejpam-3412	134	7	up	up	NOUN
ejpam-3412	134	8	-	-	PUNCT
ejpam-3412	134	9	algebra	algebra	NOUN
ejpam-3412	134	10	a	a	PRON
ejpam-3412	134	11	=	=	X
ejpam-3412	134	12	(	(	PUNCT
ejpam-3412	134	13	a	a	PRON
ejpam-3412	134	14	,	,	PUNCT
ejpam-3412	134	15	·	·	PUNCT
ejpam-3412	134	16	,	,	PUNCT
ejpam-3412	134	17	0	0	NUM
ejpam-3412	134	18	)	)	PUNCT
ejpam-3412	134	19	is	be	AUX
ejpam-3412	134	20	called	call	VERB
ejpam-3412	134	21	(	(	PUNCT
ejpam-3412	134	22	1	1	NUM
ejpam-3412	134	23	)	)	PUNCT
ejpam-3412	134	24	a	a	DET
ejpam-3412	134	25	fuzzy	fuzzy	ADJ
ejpam-3412	134	26	up	up	NOUN
ejpam-3412	134	27	-	-	PUNCT
ejpam-3412	134	28	subalgebra	subalgebra	NOUN
ejpam-3412	134	29	of	of	ADP
ejpam-3412	134	30	a	a	DET
ejpam-3412	134	31	if	if	NOUN
ejpam-3412	134	32	(	(	PUNCT
ejpam-3412	134	33	∀x	∀x	X
ejpam-3412	134	34	,	,	PUNCT
ejpam-3412	134	35	y	y	PROPN
ejpam-3412	134	36	∈	∈	PROPN
ejpam-3412	134	37	a)(ff(x	a)(ff(x	PUNCT
ejpam-3412	134	38	·	·	PUNCT
ejpam-3412	134	39	y	y	X
ejpam-3412	134	40	)	)	PUNCT
ejpam-3412	134	41	≥	≥	PROPN
ejpam-3412	134	42	min{ff(x	min{ff(x	PROPN
ejpam-3412	134	43	)	)	PUNCT
ejpam-3412	134	44	,	,	PUNCT
ejpam-3412	134	45	ff(y	ff(y	NUM
ejpam-3412	134	46	)	)	PUNCT
ejpam-3412	134	47	}	}	PUNCT
ejpam-3412	134	48	)	)	PUNCT
ejpam-3412	134	49	.	.	PUNCT
ejpam-3412	135	1	(	(	PUNCT
ejpam-3412	135	2	2	2	X
ejpam-3412	135	3	)	)	PUNCT
ejpam-3412	135	4	a	a	DET
ejpam-3412	135	5	fuzzy	fuzzy	ADJ
ejpam-3412	135	6	up	up	NOUN
ejpam-3412	135	7	-	-	PUNCT
ejpam-3412	135	8	filter	filter	NOUN
ejpam-3412	135	9	of	of	ADP
ejpam-3412	135	10	a	a	DET
ejpam-3412	135	11	if	if	NOUN
ejpam-3412	135	12	(	(	PUNCT
ejpam-3412	135	13	i	i	NOUN
ejpam-3412	135	14	)	)	PUNCT
ejpam-3412	135	15	(	(	PUNCT
ejpam-3412	135	16	∀x	∀x	X
ejpam-3412	135	17	∈	∈	PROPN
ejpam-3412	135	18	a)(ff(0	a)(ff(0	NOUN
ejpam-3412	135	19	)	)	PUNCT
ejpam-3412	135	20	≥	≥	NOUN
ejpam-3412	135	21	ff(x	ff(x	NOUN
ejpam-3412	135	22	)	)	PUNCT
ejpam-3412	135	23	)	)	PUNCT
ejpam-3412	135	24	,	,	PUNCT
ejpam-3412	135	25	and	and	CCONJ
ejpam-3412	135	26	(	(	PUNCT
ejpam-3412	135	27	ii	ii	NOUN
ejpam-3412	135	28	)	)	PUNCT
ejpam-3412	135	29	(	(	PUNCT
ejpam-3412	135	30	∀x	∀x	X
ejpam-3412	135	31	,	,	PUNCT
ejpam-3412	135	32	y	y	PROPN
ejpam-3412	135	33	∈	∈	PROPN
ejpam-3412	135	34	a)(ff(y	a)(ff(y	NOUN
ejpam-3412	135	35	)	)	PUNCT
ejpam-3412	135	36	≥	≥	PROPN
ejpam-3412	135	37	min{ff(x	min{ff(x	X
ejpam-3412	135	38	·	·	PUNCT
ejpam-3412	135	39	y	y	PROPN
ejpam-3412	135	40	)	)	PUNCT
ejpam-3412	135	41	,	,	PUNCT
ejpam-3412	135	42	ff(x	ff(x	NOUN
ejpam-3412	135	43	)	)	PUNCT
ejpam-3412	135	44	}	}	PUNCT
ejpam-3412	135	45	)	)	PUNCT
ejpam-3412	135	46	.	.	PUNCT
ejpam-3412	136	1	(	(	PUNCT
ejpam-3412	136	2	3	3	X
ejpam-3412	136	3	)	)	PUNCT
ejpam-3412	136	4	a	a	DET
ejpam-3412	136	5	fuzzy	fuzzy	ADJ
ejpam-3412	136	6	up	up	NOUN
ejpam-3412	136	7	-	-	PUNCT
ejpam-3412	136	8	ideal	ideal	NOUN
ejpam-3412	136	9	of	of	ADP
ejpam-3412	136	10	a	a	DET
ejpam-3412	136	11	if	if	NOUN
ejpam-3412	136	12	(	(	PUNCT
ejpam-3412	136	13	i	i	NOUN
ejpam-3412	136	14	)	)	PUNCT
ejpam-3412	136	15	(	(	PUNCT
ejpam-3412	136	16	∀x	∀x	X
ejpam-3412	136	17	∈	∈	PROPN
ejpam-3412	136	18	a)(ff(0	a)(ff(0	NOUN
ejpam-3412	136	19	)	)	PUNCT
ejpam-3412	136	20	≥	≥	NOUN
ejpam-3412	136	21	ff(x	ff(x	NOUN
ejpam-3412	136	22	)	)	PUNCT
ejpam-3412	136	23	)	)	PUNCT
ejpam-3412	136	24	,	,	PUNCT
ejpam-3412	136	25	and	and	CCONJ
ejpam-3412	136	26	(	(	PUNCT
ejpam-3412	136	27	ii	ii	NOUN
ejpam-3412	136	28	)	)	PUNCT
ejpam-3412	136	29	(	(	PUNCT
ejpam-3412	136	30	∀x	∀x	X
ejpam-3412	136	31	,	,	PUNCT
ejpam-3412	136	32	y	y	PROPN
ejpam-3412	136	33	,	,	PUNCT
ejpam-3412	136	34	z	z	NOUN
ejpam-3412	136	35	∈	∈	PROPN
ejpam-3412	136	36	a)(ff(x	a)(ff(x	PUNCT
ejpam-3412	136	37	·	·	PUNCT
ejpam-3412	136	38	z	z	X
ejpam-3412	136	39	)	)	PUNCT
ejpam-3412	136	40	≥	≥	PROPN
ejpam-3412	136	41	min{ff(x	min{ff(x	PROPN
ejpam-3412	136	42	·	·	PUNCT
ejpam-3412	136	43	(	(	PUNCT
ejpam-3412	136	44	y	y	PROPN
ejpam-3412	136	45	·	·	PUNCT
ejpam-3412	136	46	z	z	NOUN
ejpam-3412	136	47	)	)	PUNCT
ejpam-3412	136	48	)	)	PUNCT
ejpam-3412	136	49	,	,	PUNCT
ejpam-3412	136	50	ff(y	ff(y	NUM
ejpam-3412	136	51	)	)	PUNCT
ejpam-3412	136	52	}	}	PUNCT
ejpam-3412	136	53	)	)	PUNCT
ejpam-3412	136	54	.	.	PUNCT
ejpam-3412	137	1	(	(	PUNCT
ejpam-3412	137	2	4	4	X
ejpam-3412	137	3	)	)	PUNCT
ejpam-3412	137	4	a	a	DET
ejpam-3412	137	5	fuzzy	fuzzy	ADJ
ejpam-3412	137	6	strongly	strongly	ADV
ejpam-3412	137	7	up	up	ADP
ejpam-3412	137	8	-	-	PUNCT
ejpam-3412	137	9	ideal	ideal	NOUN
ejpam-3412	137	10	of	of	ADP
ejpam-3412	137	11	a	a	DET
ejpam-3412	137	12	if	if	NOUN
ejpam-3412	137	13	(	(	PUNCT
ejpam-3412	137	14	i	i	NOUN
ejpam-3412	137	15	)	)	PUNCT
ejpam-3412	137	16	(	(	PUNCT
ejpam-3412	137	17	∀x	∀x	X
ejpam-3412	137	18	∈	∈	PROPN
ejpam-3412	137	19	a)(ff(0	a)(ff(0	NOUN
ejpam-3412	137	20	)	)	PUNCT
ejpam-3412	137	21	≥	≥	NOUN
ejpam-3412	137	22	ff(x	ff(x	NOUN
ejpam-3412	137	23	)	)	PUNCT
ejpam-3412	137	24	)	)	PUNCT
ejpam-3412	137	25	,	,	PUNCT
ejpam-3412	137	26	and	and	CCONJ
ejpam-3412	137	27	(	(	PUNCT
ejpam-3412	137	28	ii	ii	NOUN
ejpam-3412	137	29	)	)	PUNCT
ejpam-3412	137	30	(	(	PUNCT
ejpam-3412	137	31	∀x	∀x	X
ejpam-3412	137	32	,	,	PUNCT
ejpam-3412	137	33	y	y	PROPN
ejpam-3412	137	34	,	,	PUNCT
ejpam-3412	137	35	z	z	PROPN
ejpam-3412	137	36	∈	∈	PROPN
ejpam-3412	137	37	a)(ff(x	a)(ff(x	NOUN
ejpam-3412	137	38	)	)	PUNCT
ejpam-3412	137	39	≥	≥	NOUN
ejpam-3412	138	1	min{ff((z	min{ff((z	NOUN
ejpam-3412	138	2	·	·	PUNCT
ejpam-3412	138	3	y	y	X
ejpam-3412	138	4	)	)	PUNCT
ejpam-3412	138	5	·	·	PUNCT
ejpam-3412	139	1	(	(	PUNCT
ejpam-3412	139	2	z	z	NOUN
ejpam-3412	139	3	·	·	PUNCT
ejpam-3412	139	4	x	x	X
ejpam-3412	139	5	)	)	PUNCT
ejpam-3412	139	6	)	)	PUNCT
ejpam-3412	139	7	,	,	PUNCT
ejpam-3412	139	8	ff(y	ff(y	NUM
ejpam-3412	139	9	)	)	PUNCT
ejpam-3412	139	10	}	}	PUNCT
ejpam-3412	139	11	)	)	PUNCT
ejpam-3412	139	12	.	.	PUNCT
ejpam-3412	140	1	a.	a.	PROPN
ejpam-3412	140	2	satirad	satirad	PROPN
ejpam-3412	140	3	,	,	PUNCT
ejpam-3412	140	4	a.	a.	NOUN
ejpam-3412	140	5	iampan	iampan	PROPN
ejpam-3412	140	6	/	/	SYM
ejpam-3412	140	7	eur	eur	PROPN
ejpam-3412	140	8	.	.	PUNCT
ejpam-3412	141	1	j.	j.	PROPN
ejpam-3412	141	2	pure	pure	PROPN
ejpam-3412	141	3	appl	appl	PROPN
ejpam-3412	141	4	.	.	PROPN
ejpam-3412	141	5	math	math	PROPN
ejpam-3412	141	6	,	,	PUNCT
ejpam-3412	141	7	12	12	NUM
ejpam-3412	141	8	(	(	PUNCT
ejpam-3412	141	9	2	2	NUM
ejpam-3412	141	10	)	)	PUNCT
ejpam-3412	141	11	(	(	PUNCT
ejpam-3412	141	12	2019	2019	NUM
ejpam-3412	141	13	)	)	PUNCT
ejpam-3412	141	14	,	,	PUNCT
ejpam-3412	141	15	294	294	NUM
ejpam-3412	141	16	-	-	SYM
ejpam-3412	141	17	331	331	NUM
ejpam-3412	141	18	299	299	NUM
ejpam-3412	141	19	now	now	ADV
ejpam-3412	141	20	,	,	PUNCT
ejpam-3412	141	21	we	we	PRON
ejpam-3412	141	22	introduce	introduce	VERB
ejpam-3412	141	23	the	the	DET
ejpam-3412	141	24	notion	notion	NOUN
ejpam-3412	141	25	of	of	ADP
ejpam-3412	141	26	fuzzy	fuzzy	ADJ
ejpam-3412	141	27	near	near	ADP
ejpam-3412	141	28	up	up	ADP
ejpam-3412	141	29	-	-	PUNCT
ejpam-3412	141	30	filters	filter	NOUN
ejpam-3412	141	31	of	of	ADP
ejpam-3412	141	32	up	up	ADV
ejpam-3412	141	33	-	-	PUNCT
ejpam-3412	141	34	algebras	algebra	NOUN
ejpam-3412	141	35	as	as	SCONJ
ejpam-3412	141	36	follows	follow	VERB
ejpam-3412	141	37	:	:	PUNCT
ejpam-3412	141	38	definition	definition	NOUN
ejpam-3412	141	39	12	12	NUM
ejpam-3412	141	40	.	.	PUNCT
ejpam-3412	142	1	a	a	DET
ejpam-3412	142	2	fuzzy	fuzzy	ADJ
ejpam-3412	142	3	set	set	NOUN
ejpam-3412	142	4	f	f	PROPN
ejpam-3412	142	5	in	in	ADP
ejpam-3412	142	6	a	a	DET
ejpam-3412	142	7	up	up	NOUN
ejpam-3412	142	8	-	-	PUNCT
ejpam-3412	142	9	algebra	algebra	NOUN
ejpam-3412	142	10	a	a	PRON
ejpam-3412	142	11	=	=	X
ejpam-3412	142	12	(	(	PUNCT
ejpam-3412	142	13	a	a	PRON
ejpam-3412	142	14	,	,	PUNCT
ejpam-3412	142	15	·	·	PUNCT
ejpam-3412	142	16	,	,	PUNCT
ejpam-3412	142	17	0	0	NUM
ejpam-3412	142	18	)	)	PUNCT
ejpam-3412	142	19	is	be	AUX
ejpam-3412	142	20	called	call	VERB
ejpam-3412	142	21	a	a	DET
ejpam-3412	142	22	fuzzy	fuzzy	ADJ
ejpam-3412	142	23	near	near	ADP
ejpam-3412	142	24	up	up	ADJ
ejpam-3412	142	25	-	-	PUNCT
ejpam-3412	142	26	filter	filter	NOUN
ejpam-3412	142	27	of	of	ADP
ejpam-3412	142	28	a	a	DET
ejpam-3412	142	29	if	if	NOUN
ejpam-3412	142	30	(	(	PUNCT
ejpam-3412	142	31	i	i	NOUN
ejpam-3412	142	32	)	)	PUNCT
ejpam-3412	142	33	(	(	PUNCT
ejpam-3412	142	34	∀x	∀x	X
ejpam-3412	142	35	∈	∈	PROPN
ejpam-3412	142	36	a)(ff(0	a)(ff(0	NOUN
ejpam-3412	142	37	)	)	PUNCT
ejpam-3412	142	38	≥	≥	NOUN
ejpam-3412	142	39	ff(x	ff(x	NOUN
ejpam-3412	142	40	)	)	PUNCT
ejpam-3412	142	41	)	)	PUNCT
ejpam-3412	142	42	,	,	PUNCT
ejpam-3412	142	43	and	and	CCONJ
ejpam-3412	142	44	(	(	PUNCT
ejpam-3412	142	45	ii	ii	NOUN
ejpam-3412	142	46	)	)	PUNCT
ejpam-3412	142	47	(	(	PUNCT
ejpam-3412	142	48	∀x	∀x	X
ejpam-3412	142	49	,	,	PUNCT
ejpam-3412	142	50	y	y	PROPN
ejpam-3412	142	51	∈	∈	PROPN
ejpam-3412	142	52	a)(ff(x	a)(ff(x	PUNCT
ejpam-3412	142	53	·	·	PUNCT
ejpam-3412	142	54	y	y	X
ejpam-3412	142	55	)	)	PUNCT
ejpam-3412	142	56	≥	≥	NOUN
ejpam-3412	142	57	ff(y	ff(y	NUM
ejpam-3412	142	58	)	)	PUNCT
ejpam-3412	142	59	)	)	PUNCT
ejpam-3412	142	60	.	.	PUNCT
ejpam-3412	143	1	we	we	PRON
ejpam-3412	143	2	know	know	VERB
ejpam-3412	143	3	that	that	SCONJ
ejpam-3412	143	4	the	the	DET
ejpam-3412	143	5	notion	notion	NOUN
ejpam-3412	143	6	of	of	ADP
ejpam-3412	143	7	fuzzy	fuzzy	ADJ
ejpam-3412	143	8	up	up	ADP
ejpam-3412	143	9	-	-	PUNCT
ejpam-3412	143	10	subalgebras	subalgebras	PROPN
ejpam-3412	143	11	is	be	AUX
ejpam-3412	143	12	a	a	DET
ejpam-3412	143	13	generalization	generalization	NOUN
ejpam-3412	143	14	of	of	ADP
ejpam-3412	143	15	fuzzy	fuzzy	ADJ
ejpam-3412	143	16	near	near	ADP
ejpam-3412	143	17	upfilters	upfilter	NOUN
ejpam-3412	143	18	,	,	PUNCT
ejpam-3412	143	19	the	the	DET
ejpam-3412	143	20	notion	notion	NOUN
ejpam-3412	143	21	of	of	ADP
ejpam-3412	143	22	fuzzy	fuzzy	ADJ
ejpam-3412	143	23	near	near	ADP
ejpam-3412	143	24	up	up	ADP
ejpam-3412	143	25	-	-	PUNCT
ejpam-3412	143	26	filters	filter	NOUN
ejpam-3412	143	27	is	be	AUX
ejpam-3412	143	28	a	a	DET
ejpam-3412	143	29	generalization	generalization	NOUN
ejpam-3412	143	30	of	of	ADP
ejpam-3412	143	31	fuzzy	fuzzy	ADJ
ejpam-3412	143	32	up	up	NOUN
ejpam-3412	143	33	-	-	PUNCT
ejpam-3412	143	34	filters	filter	NOUN
ejpam-3412	143	35	,	,	PUNCT
ejpam-3412	143	36	the	the	DET
ejpam-3412	143	37	notion	notion	NOUN
ejpam-3412	143	38	of	of	ADP
ejpam-3412	143	39	fuzzy	fuzzy	ADJ
ejpam-3412	143	40	up	up	NOUN
ejpam-3412	143	41	-	-	PUNCT
ejpam-3412	143	42	filters	filter	NOUN
ejpam-3412	143	43	is	be	AUX
ejpam-3412	143	44	a	a	DET
ejpam-3412	143	45	generalization	generalization	NOUN
ejpam-3412	143	46	of	of	ADP
ejpam-3412	143	47	fuzzy	fuzzy	ADJ
ejpam-3412	143	48	up	up	NOUN
ejpam-3412	143	49	-	-	PUNCT
ejpam-3412	143	50	ideals	ideal	NOUN
ejpam-3412	143	51	,	,	PUNCT
ejpam-3412	143	52	and	and	CCONJ
ejpam-3412	143	53	the	the	DET
ejpam-3412	143	54	notion	notion	NOUN
ejpam-3412	143	55	of	of	ADP
ejpam-3412	143	56	fuzzy	fuzzy	ADJ
ejpam-3412	143	57	up	up	NOUN
ejpam-3412	143	58	-	-	PUNCT
ejpam-3412	143	59	ideals	ideal	NOUN
ejpam-3412	143	60	is	be	AUX
ejpam-3412	143	61	a	a	DET
ejpam-3412	143	62	generalization	generalization	NOUN
ejpam-3412	143	63	of	of	ADP
ejpam-3412	143	64	fuzzy	fuzzy	ADJ
ejpam-3412	143	65	strongly	strongly	ADV
ejpam-3412	143	66	up	up	ADP
ejpam-3412	143	67	-	-	PUNCT
ejpam-3412	143	68	ideals	ideal	NOUN
ejpam-3412	143	69	.	.	PUNCT
ejpam-3412	144	1	moreover	moreover	ADV
ejpam-3412	144	2	,	,	PUNCT
ejpam-3412	144	3	fuzzy	fuzzy	ADJ
ejpam-3412	144	4	strongly	strongly	ADV
ejpam-3412	144	5	up	up	ADJ
ejpam-3412	144	6	-	-	PUNCT
ejpam-3412	144	7	ideals	ideal	NOUN
ejpam-3412	144	8	and	and	CCONJ
ejpam-3412	144	9	constant	constant	ADJ
ejpam-3412	144	10	fuzzy	fuzzy	ADJ
ejpam-3412	144	11	sets	set	NOUN
ejpam-3412	144	12	coincide	coincide	VERB
ejpam-3412	144	13	in	in	ADP
ejpam-3412	144	14	up	up	ADP
ejpam-3412	144	15	-	-	PUNCT
ejpam-3412	144	16	algebras	algebras	X
ejpam-3412	144	17	.	.	PUNCT
ejpam-3412	145	1	satirad	satirad	PROPN
ejpam-3412	145	2	and	and	CCONJ
ejpam-3412	145	3	iampan	iampan	PROPN
ejpam-3412	145	4	[	[	X
ejpam-3412	145	5	23	23	NUM
ejpam-3412	145	6	]	]	PUNCT
ejpam-3412	145	7	introduced	introduce	VERB
ejpam-3412	145	8	the	the	DET
ejpam-3412	145	9	notion	notion	NOUN
ejpam-3412	145	10	of	of	ADP
ejpam-3412	145	11	fuzzy	fuzzy	ADJ
ejpam-3412	145	12	ups	up	NOUN
ejpam-3412	145	13	-	-	PUNCT
ejpam-3412	145	14	subalgebras	subalgebras	PROPN
ejpam-3412	145	15	(	(	PUNCT
ejpam-3412	145	16	resp	resp	PROPN
ejpam-3412	145	17	.	.	PUNCT
ejpam-3412	145	18	,	,	PUNCT
ejpam-3412	145	19	fuzzy	fuzzy	ADJ
ejpam-3412	145	20	upi	upi	PROPN
ejpam-3412	145	21	-	-	PUNCT
ejpam-3412	145	22	subalgebras	subalgebras	PROPN
ejpam-3412	145	23	,	,	PUNCT
ejpam-3412	145	24	fuzzy	fuzzy	ADJ
ejpam-3412	145	25	ups	up	NOUN
ejpam-3412	145	26	-	-	PUNCT
ejpam-3412	145	27	filters	filter	NOUN
ejpam-3412	145	28	,	,	PUNCT
ejpam-3412	145	29	fuzzy	fuzzy	ADJ
ejpam-3412	145	30	upi	upi	NOUN
ejpam-3412	145	31	-	-	PUNCT
ejpam-3412	145	32	filters	filter	NOUN
ejpam-3412	145	33	,	,	PUNCT
ejpam-3412	145	34	fuzzy	fuzzy	ADJ
ejpam-3412	145	35	ups	up	NOUN
ejpam-3412	145	36	-	-	PUNCT
ejpam-3412	145	37	ideals	ideal	NOUN
ejpam-3412	145	38	,	,	PUNCT
ejpam-3412	145	39	fuzzy	fuzzy	ADJ
ejpam-3412	145	40	upi	upi	NOUN
ejpam-3412	145	41	-	-	PUNCT
ejpam-3412	145	42	ideals	ideal	NOUN
ejpam-3412	145	43	,	,	PUNCT
ejpam-3412	145	44	fuzzy	fuzzy	ADJ
ejpam-3412	145	45	strongly	strongly	ADV
ejpam-3412	145	46	ups	up	NOUN
ejpam-3412	145	47	-	-	PUNCT
ejpam-3412	145	48	ideals	ideal	NOUN
ejpam-3412	145	49	,	,	PUNCT
ejpam-3412	145	50	fuzzy	fuzzy	ADJ
ejpam-3412	145	51	strongly	strongly	ADV
ejpam-3412	145	52	upi	upi	NOUN
ejpam-3412	145	53	-	-	PUNCT
ejpam-3412	145	54	ideals	ideal	NOUN
ejpam-3412	145	55	)	)	PUNCT
ejpam-3412	145	56	of	of	ADP
ejpam-3412	145	57	f	f	PROPN
ejpam-3412	145	58	-up	-up	NOUN
ejpam-3412	145	59	-	-	PUNCT
ejpam-3412	145	60	semigroups	semigroup	NOUN
ejpam-3412	145	61	as	as	SCONJ
ejpam-3412	145	62	follows	follow	VERB
ejpam-3412	145	63	:	:	PUNCT
ejpam-3412	145	64	definition	definition	NOUN
ejpam-3412	145	65	13	13	NUM
ejpam-3412	145	66	.	.	PUNCT
ejpam-3412	146	1	[	[	X
ejpam-3412	146	2	23	23	NUM
ejpam-3412	146	3	]	]	PUNCT
ejpam-3412	146	4	a	a	DET
ejpam-3412	146	5	fuzzy	fuzzy	ADJ
ejpam-3412	146	6	set	set	VERB
ejpam-3412	146	7	f	f	PROPN
ejpam-3412	146	8	in	in	ADP
ejpam-3412	146	9	an	an	DET
ejpam-3412	146	10	f	f	PROPN
ejpam-3412	146	11	-up	-up	NOUN
ejpam-3412	146	12	-	-	NOUN
ejpam-3412	146	13	semigroup	semigroup	NOUN
ejpam-3412	146	14	a	a	X
ejpam-3412	146	15	=	=	X
ejpam-3412	146	16	(	(	PUNCT
ejpam-3412	146	17	a	a	PRON
ejpam-3412	146	18	,	,	PUNCT
ejpam-3412	146	19	·	·	PUNCT
ejpam-3412	146	20	,	,	PUNCT
ejpam-3412	146	21	∗	∗	NOUN
ejpam-3412	146	22	,	,	PUNCT
ejpam-3412	146	23	0	0	NUM
ejpam-3412	146	24	)	)	PUNCT
ejpam-3412	146	25	is	be	AUX
ejpam-3412	146	26	called	call	VERB
ejpam-3412	146	27	(	(	PUNCT
ejpam-3412	146	28	1	1	NUM
ejpam-3412	146	29	)	)	PUNCT
ejpam-3412	146	30	a	a	DET
ejpam-3412	146	31	fuzzy	fuzzy	ADJ
ejpam-3412	146	32	ups	up	NOUN
ejpam-3412	146	33	-	-	PUNCT
ejpam-3412	146	34	subalgebra	subalgebra	NOUN
ejpam-3412	146	35	of	of	ADP
ejpam-3412	146	36	a	a	PRON
ejpam-3412	146	37	if	if	SCONJ
ejpam-3412	146	38	f	f	PROPN
ejpam-3412	146	39	is	be	AUX
ejpam-3412	146	40	a	a	DET
ejpam-3412	146	41	fuzzy	fuzzy	ADJ
ejpam-3412	146	42	up	up	NOUN
ejpam-3412	146	43	-	-	PUNCT
ejpam-3412	146	44	subalgebra	subalgebra	NOUN
ejpam-3412	146	45	of	of	ADP
ejpam-3412	146	46	(	(	PUNCT
ejpam-3412	146	47	a	a	PRON
ejpam-3412	146	48	,	,	PUNCT
ejpam-3412	146	49	·	·	PUNCT
ejpam-3412	146	50	,	,	PUNCT
ejpam-3412	146	51	0	0	NUM
ejpam-3412	146	52	)	)	PUNCT
ejpam-3412	146	53	and	and	CCONJ
ejpam-3412	146	54	a	a	DET
ejpam-3412	146	55	fuzzy	fuzzy	ADJ
ejpam-3412	146	56	subsemigroup	subsemigroup	NOUN
ejpam-3412	146	57	of	of	ADP
ejpam-3412	146	58	(	(	PUNCT
ejpam-3412	146	59	a	a	PRON
ejpam-3412	146	60	,	,	PUNCT
ejpam-3412	146	61	∗	∗	NOUN
ejpam-3412	146	62	)	)	PUNCT
ejpam-3412	146	63	.	.	PUNCT
ejpam-3412	147	1	(	(	PUNCT
ejpam-3412	147	2	2	2	X
ejpam-3412	147	3	)	)	PUNCT
ejpam-3412	147	4	a	a	DET
ejpam-3412	147	5	fuzzy	fuzzy	ADJ
ejpam-3412	147	6	upi	upi	NOUN
ejpam-3412	147	7	-	-	PUNCT
ejpam-3412	147	8	subalgebra	subalgebra	NOUN
ejpam-3412	147	9	of	of	ADP
ejpam-3412	147	10	a	a	PRON
ejpam-3412	147	11	if	if	SCONJ
ejpam-3412	147	12	f	f	PROPN
ejpam-3412	147	13	is	be	AUX
ejpam-3412	147	14	a	a	DET
ejpam-3412	147	15	fuzzy	fuzzy	ADJ
ejpam-3412	147	16	up	up	NOUN
ejpam-3412	147	17	-	-	PUNCT
ejpam-3412	147	18	subalgebra	subalgebra	NOUN
ejpam-3412	147	19	of	of	ADP
ejpam-3412	147	20	(	(	PUNCT
ejpam-3412	147	21	a	a	PRON
ejpam-3412	147	22	,	,	PUNCT
ejpam-3412	147	23	·	·	PUNCT
ejpam-3412	147	24	,	,	PUNCT
ejpam-3412	147	25	0	0	NUM
ejpam-3412	147	26	)	)	PUNCT
ejpam-3412	147	27	and	and	CCONJ
ejpam-3412	147	28	a	a	DET
ejpam-3412	147	29	fuzzy	fuzzy	ADJ
ejpam-3412	147	30	ideal	ideal	NOUN
ejpam-3412	147	31	of	of	ADP
ejpam-3412	147	32	(	(	PUNCT
ejpam-3412	147	33	a	a	PRON
ejpam-3412	147	34	,	,	PUNCT
ejpam-3412	147	35	∗	∗	NOUN
ejpam-3412	147	36	)	)	PUNCT
ejpam-3412	147	37	.	.	PUNCT
ejpam-3412	148	1	(	(	PUNCT
ejpam-3412	148	2	3	3	X
ejpam-3412	148	3	)	)	PUNCT
ejpam-3412	148	4	a	a	DET
ejpam-3412	148	5	fuzzy	fuzzy	ADJ
ejpam-3412	148	6	ups	up	NOUN
ejpam-3412	148	7	-	-	PUNCT
ejpam-3412	148	8	filter	filter	NOUN
ejpam-3412	148	9	of	of	ADP
ejpam-3412	148	10	a	a	PRON
ejpam-3412	148	11	if	if	SCONJ
ejpam-3412	148	12	f	f	PROPN
ejpam-3412	148	13	is	be	AUX
ejpam-3412	148	14	a	a	DET
ejpam-3412	148	15	fuzzy	fuzzy	ADJ
ejpam-3412	148	16	up	up	NOUN
ejpam-3412	148	17	-	-	PUNCT
ejpam-3412	148	18	filter	filter	NOUN
ejpam-3412	148	19	of	of	ADP
ejpam-3412	148	20	(	(	PUNCT
ejpam-3412	148	21	a	a	PRON
ejpam-3412	148	22	,	,	PUNCT
ejpam-3412	148	23	·	·	PUNCT
ejpam-3412	148	24	,	,	PUNCT
ejpam-3412	148	25	0	0	NUM
ejpam-3412	148	26	)	)	PUNCT
ejpam-3412	148	27	and	and	CCONJ
ejpam-3412	148	28	a	a	DET
ejpam-3412	148	29	fuzzy	fuzzy	ADJ
ejpam-3412	148	30	subsemigroup	subsemigroup	NOUN
ejpam-3412	148	31	of	of	ADP
ejpam-3412	148	32	(	(	PUNCT
ejpam-3412	148	33	a	a	PRON
ejpam-3412	148	34	,	,	PUNCT
ejpam-3412	148	35	∗	∗	NOUN
ejpam-3412	148	36	)	)	PUNCT
ejpam-3412	148	37	.	.	PUNCT
ejpam-3412	149	1	(	(	PUNCT
ejpam-3412	149	2	4	4	X
ejpam-3412	149	3	)	)	PUNCT
ejpam-3412	149	4	a	a	DET
ejpam-3412	149	5	fuzzy	fuzzy	ADJ
ejpam-3412	149	6	upi	upi	NOUN
ejpam-3412	149	7	-	-	PUNCT
ejpam-3412	149	8	filter	filter	NOUN
ejpam-3412	149	9	of	of	ADP
ejpam-3412	149	10	a	a	PRON
ejpam-3412	149	11	if	if	SCONJ
ejpam-3412	149	12	f	f	PROPN
ejpam-3412	149	13	is	be	AUX
ejpam-3412	149	14	a	a	DET
ejpam-3412	149	15	fuzzy	fuzzy	ADJ
ejpam-3412	149	16	up	up	NOUN
ejpam-3412	149	17	-	-	PUNCT
ejpam-3412	149	18	filter	filter	NOUN
ejpam-3412	149	19	of	of	ADP
ejpam-3412	149	20	(	(	PUNCT
ejpam-3412	149	21	a	a	PRON
ejpam-3412	149	22	,	,	PUNCT
ejpam-3412	149	23	·	·	PUNCT
ejpam-3412	149	24	,	,	PUNCT
ejpam-3412	149	25	0	0	NUM
ejpam-3412	149	26	)	)	PUNCT
ejpam-3412	149	27	and	and	CCONJ
ejpam-3412	149	28	a	a	DET
ejpam-3412	149	29	fuzzy	fuzzy	ADJ
ejpam-3412	149	30	ideal	ideal	NOUN
ejpam-3412	149	31	of	of	ADP
ejpam-3412	149	32	(	(	PUNCT
ejpam-3412	149	33	a	a	PRON
ejpam-3412	149	34	,	,	PUNCT
ejpam-3412	149	35	∗	∗	NOUN
ejpam-3412	149	36	)	)	PUNCT
ejpam-3412	149	37	.	.	PUNCT
ejpam-3412	150	1	(	(	PUNCT
ejpam-3412	150	2	5	5	X
ejpam-3412	150	3	)	)	PUNCT
ejpam-3412	150	4	a	a	DET
ejpam-3412	150	5	fuzzy	fuzzy	ADJ
ejpam-3412	150	6	ups	up	NOUN
ejpam-3412	150	7	-	-	PUNCT
ejpam-3412	150	8	ideal	ideal	NOUN
ejpam-3412	150	9	of	of	ADP
ejpam-3412	150	10	a	a	PRON
ejpam-3412	150	11	if	if	SCONJ
ejpam-3412	150	12	f	f	PROPN
ejpam-3412	150	13	is	be	AUX
ejpam-3412	150	14	a	a	DET
ejpam-3412	150	15	fuzzy	fuzzy	ADJ
ejpam-3412	150	16	up	up	ADJ
ejpam-3412	150	17	-	-	PUNCT
ejpam-3412	150	18	ideal	ideal	NOUN
ejpam-3412	150	19	of	of	ADP
ejpam-3412	150	20	(	(	PUNCT
ejpam-3412	150	21	a	a	PRON
ejpam-3412	150	22	,	,	PUNCT
ejpam-3412	150	23	·	·	PUNCT
ejpam-3412	150	24	,	,	PUNCT
ejpam-3412	150	25	0	0	NUM
ejpam-3412	150	26	)	)	PUNCT
ejpam-3412	150	27	and	and	CCONJ
ejpam-3412	150	28	a	a	DET
ejpam-3412	150	29	fuzzy	fuzzy	ADJ
ejpam-3412	150	30	subsemigroup	subsemigroup	NOUN
ejpam-3412	150	31	of	of	ADP
ejpam-3412	150	32	(	(	PUNCT
ejpam-3412	150	33	a	a	PRON
ejpam-3412	150	34	,	,	PUNCT
ejpam-3412	150	35	∗	∗	NOUN
ejpam-3412	150	36	)	)	PUNCT
ejpam-3412	150	37	.	.	PUNCT
ejpam-3412	151	1	(	(	PUNCT
ejpam-3412	151	2	6	6	X
ejpam-3412	151	3	)	)	PUNCT
ejpam-3412	151	4	a	a	DET
ejpam-3412	151	5	fuzzy	fuzzy	ADJ
ejpam-3412	151	6	upi	upi	NOUN
ejpam-3412	151	7	-	-	PUNCT
ejpam-3412	151	8	ideal	ideal	NOUN
ejpam-3412	151	9	of	of	ADP
ejpam-3412	151	10	a	a	PRON
ejpam-3412	151	11	if	if	SCONJ
ejpam-3412	151	12	f	f	PROPN
ejpam-3412	151	13	is	be	AUX
ejpam-3412	151	14	a	a	DET
ejpam-3412	151	15	fuzzy	fuzzy	ADJ
ejpam-3412	151	16	up	up	ADJ
ejpam-3412	151	17	-	-	PUNCT
ejpam-3412	151	18	ideal	ideal	NOUN
ejpam-3412	151	19	of	of	ADP
ejpam-3412	151	20	(	(	PUNCT
ejpam-3412	151	21	a	a	PRON
ejpam-3412	151	22	,	,	PUNCT
ejpam-3412	151	23	·	·	PUNCT
ejpam-3412	151	24	,	,	PUNCT
ejpam-3412	151	25	0	0	NUM
ejpam-3412	151	26	)	)	PUNCT
ejpam-3412	151	27	and	and	CCONJ
ejpam-3412	151	28	a	a	DET
ejpam-3412	151	29	fuzzy	fuzzy	ADJ
ejpam-3412	151	30	ideal	ideal	NOUN
ejpam-3412	151	31	of	of	ADP
ejpam-3412	151	32	(	(	PUNCT
ejpam-3412	151	33	a	a	PRON
ejpam-3412	151	34	,	,	PUNCT
ejpam-3412	151	35	∗	∗	NOUN
ejpam-3412	151	36	)	)	PUNCT
ejpam-3412	151	37	.	.	PUNCT
ejpam-3412	152	1	(	(	PUNCT
ejpam-3412	152	2	7	7	X
ejpam-3412	152	3	)	)	PUNCT
ejpam-3412	152	4	a	a	DET
ejpam-3412	152	5	fuzzy	fuzzy	ADJ
ejpam-3412	152	6	strongly	strongly	ADV
ejpam-3412	152	7	ups	up	NOUN
ejpam-3412	152	8	-	-	PUNCT
ejpam-3412	152	9	ideal	ideal	NOUN
ejpam-3412	152	10	of	of	ADP
ejpam-3412	152	11	a	a	PRON
ejpam-3412	152	12	if	if	SCONJ
ejpam-3412	152	13	f	f	PROPN
ejpam-3412	152	14	is	be	AUX
ejpam-3412	152	15	a	a	DET
ejpam-3412	152	16	fuzzy	fuzzy	ADJ
ejpam-3412	152	17	strongly	strongly	ADV
ejpam-3412	152	18	up	up	ADP
ejpam-3412	152	19	-	-	PUNCT
ejpam-3412	152	20	ideal	ideal	NOUN
ejpam-3412	152	21	of	of	ADP
ejpam-3412	152	22	(	(	PUNCT
ejpam-3412	152	23	a	a	PRON
ejpam-3412	152	24	,	,	PUNCT
ejpam-3412	152	25	·	·	PUNCT
ejpam-3412	152	26	,	,	PUNCT
ejpam-3412	152	27	0	0	NUM
ejpam-3412	152	28	)	)	PUNCT
ejpam-3412	152	29	and	and	CCONJ
ejpam-3412	152	30	a	a	DET
ejpam-3412	152	31	fuzzy	fuzzy	ADJ
ejpam-3412	152	32	subsemigroup	subsemigroup	NOUN
ejpam-3412	152	33	of	of	ADP
ejpam-3412	152	34	(	(	PUNCT
ejpam-3412	152	35	a	a	PRON
ejpam-3412	152	36	,	,	PUNCT
ejpam-3412	152	37	∗	∗	NOUN
ejpam-3412	152	38	)	)	PUNCT
ejpam-3412	152	39	.	.	PUNCT
ejpam-3412	153	1	(	(	PUNCT
ejpam-3412	153	2	8)	8)	X
ejpam-3412	153	3	a	a	DET
ejpam-3412	153	4	fuzzy	fuzzy	ADJ
ejpam-3412	153	5	strongly	strongly	ADV
ejpam-3412	153	6	upi	upi	NOUN
ejpam-3412	153	7	-	-	PUNCT
ejpam-3412	153	8	ideal	ideal	NOUN
ejpam-3412	153	9	of	of	ADP
ejpam-3412	153	10	a	a	PRON
ejpam-3412	153	11	if	if	SCONJ
ejpam-3412	153	12	f	f	PROPN
ejpam-3412	153	13	is	be	AUX
ejpam-3412	153	14	a	a	DET
ejpam-3412	153	15	fuzzy	fuzzy	ADJ
ejpam-3412	153	16	strongly	strongly	ADV
ejpam-3412	153	17	up	up	ADP
ejpam-3412	153	18	-	-	PUNCT
ejpam-3412	153	19	ideal	ideal	NOUN
ejpam-3412	153	20	of	of	ADP
ejpam-3412	153	21	(	(	PUNCT
ejpam-3412	153	22	a	a	PRON
ejpam-3412	153	23	,	,	PUNCT
ejpam-3412	153	24	·	·	PUNCT
ejpam-3412	153	25	,	,	PUNCT
ejpam-3412	153	26	0	0	NUM
ejpam-3412	153	27	)	)	PUNCT
ejpam-3412	153	28	and	and	CCONJ
ejpam-3412	153	29	a	a	DET
ejpam-3412	153	30	fuzzy	fuzzy	ADJ
ejpam-3412	153	31	ideal	ideal	NOUN
ejpam-3412	153	32	of	of	ADP
ejpam-3412	153	33	(	(	PUNCT
ejpam-3412	153	34	a	a	PRON
ejpam-3412	153	35	,	,	PUNCT
ejpam-3412	153	36	∗	∗	NOUN
ejpam-3412	153	37	)	)	PUNCT
ejpam-3412	153	38	.	.	PUNCT
ejpam-3412	154	1	now	now	ADV
ejpam-3412	154	2	,	,	PUNCT
ejpam-3412	154	3	we	we	PRON
ejpam-3412	154	4	introduce	introduce	VERB
ejpam-3412	154	5	the	the	DET
ejpam-3412	154	6	notion	notion	NOUN
ejpam-3412	154	7	fuzzy	fuzzy	ADJ
ejpam-3412	154	8	near	near	ADP
ejpam-3412	154	9	ups	up	NOUN
ejpam-3412	154	10	-	-	PUNCT
ejpam-3412	154	11	filters	filter	NOUN
ejpam-3412	154	12	of	of	ADP
ejpam-3412	154	13	f	f	PROPN
ejpam-3412	154	14	-up	-up	NOUN
ejpam-3412	154	15	-	-	PUNCT
ejpam-3412	154	16	semigroups	semigroups	X
ejpam-3412	154	17	(	(	PUNCT
ejpam-3412	154	18	resp	resp	NOUN
ejpam-3412	154	19	.	.	PUNCT
ejpam-3412	154	20	,	,	PUNCT
ejpam-3412	154	21	fuzzy	fuzzy	ADJ
ejpam-3412	154	22	near	near	ADP
ejpam-3412	154	23	upi	upi	NOUN
ejpam-3412	154	24	-	-	PUNCT
ejpam-3412	154	25	filters	filter	NOUN
ejpam-3412	154	26	)	)	PUNCT
ejpam-3412	154	27	as	as	SCONJ
ejpam-3412	154	28	follows	follow	VERB
ejpam-3412	154	29	:	:	PUNCT
ejpam-3412	154	30	definition	definition	NOUN
ejpam-3412	154	31	14	14	NUM
ejpam-3412	154	32	.	.	PUNCT
ejpam-3412	155	1	a	a	DET
ejpam-3412	155	2	fuzzy	fuzzy	ADJ
ejpam-3412	155	3	set	set	VERB
ejpam-3412	155	4	f	f	PROPN
ejpam-3412	155	5	in	in	ADP
ejpam-3412	155	6	an	an	DET
ejpam-3412	155	7	f	f	PROPN
ejpam-3412	155	8	-up	-up	NOUN
ejpam-3412	155	9	-	-	NOUN
ejpam-3412	155	10	semigroup	semigroup	NOUN
ejpam-3412	155	11	a	a	X
ejpam-3412	155	12	=	=	X
ejpam-3412	155	13	(	(	PUNCT
ejpam-3412	155	14	a	a	PRON
ejpam-3412	155	15	,	,	PUNCT
ejpam-3412	155	16	·	·	PUNCT
ejpam-3412	155	17	,	,	PUNCT
ejpam-3412	155	18	∗	∗	NOUN
ejpam-3412	155	19	,	,	PUNCT
ejpam-3412	155	20	0	0	NUM
ejpam-3412	155	21	)	)	PUNCT
ejpam-3412	155	22	is	be	AUX
ejpam-3412	155	23	called	call	VERB
ejpam-3412	155	24	(	(	PUNCT
ejpam-3412	155	25	1	1	NUM
ejpam-3412	155	26	)	)	PUNCT
ejpam-3412	155	27	a	a	DET
ejpam-3412	155	28	fuzzy	fuzzy	ADJ
ejpam-3412	155	29	near	near	ADP
ejpam-3412	155	30	ups	up	NOUN
ejpam-3412	155	31	-	-	PUNCT
ejpam-3412	155	32	filter	filter	NOUN
ejpam-3412	155	33	of	of	ADP
ejpam-3412	155	34	a	a	PRON
ejpam-3412	155	35	if	if	SCONJ
ejpam-3412	155	36	f	f	PROPN
ejpam-3412	155	37	is	be	AUX
ejpam-3412	155	38	a	a	DET
ejpam-3412	155	39	fuzzy	fuzzy	ADJ
ejpam-3412	155	40	near	near	ADP
ejpam-3412	155	41	up	up	ADJ
ejpam-3412	155	42	-	-	PUNCT
ejpam-3412	155	43	filter	filter	NOUN
ejpam-3412	155	44	of	of	ADP
ejpam-3412	155	45	(	(	PUNCT
ejpam-3412	155	46	a	a	PRON
ejpam-3412	155	47	,	,	PUNCT
ejpam-3412	155	48	·	·	PUNCT
ejpam-3412	155	49	,	,	PUNCT
ejpam-3412	155	50	0	0	NUM
ejpam-3412	155	51	)	)	PUNCT
ejpam-3412	155	52	and	and	CCONJ
ejpam-3412	155	53	a	a	DET
ejpam-3412	155	54	fuzzy	fuzzy	ADJ
ejpam-3412	155	55	subsemigroup	subsemigroup	NOUN
ejpam-3412	155	56	of	of	ADP
ejpam-3412	155	57	(	(	PUNCT
ejpam-3412	155	58	a	a	PRON
ejpam-3412	155	59	,	,	PUNCT
ejpam-3412	155	60	∗	∗	NOUN
ejpam-3412	155	61	)	)	PUNCT
ejpam-3412	155	62	.	.	PUNCT
ejpam-3412	156	1	a.	a.	PROPN
ejpam-3412	156	2	satirad	satirad	PROPN
ejpam-3412	156	3	,	,	PUNCT
ejpam-3412	156	4	a.	a.	NOUN
ejpam-3412	156	5	iampan	iampan	PROPN
ejpam-3412	156	6	/	/	SYM
ejpam-3412	156	7	eur	eur	PROPN
ejpam-3412	156	8	.	.	PUNCT
ejpam-3412	157	1	j.	j.	PROPN
ejpam-3412	157	2	pure	pure	PROPN
ejpam-3412	157	3	appl	appl	PROPN
ejpam-3412	157	4	.	.	PROPN
ejpam-3412	157	5	math	math	PROPN
ejpam-3412	157	6	,	,	PUNCT
ejpam-3412	157	7	12	12	NUM
ejpam-3412	157	8	(	(	PUNCT
ejpam-3412	157	9	2	2	NUM
ejpam-3412	157	10	)	)	PUNCT
ejpam-3412	157	11	(	(	PUNCT
ejpam-3412	157	12	2019	2019	NUM
ejpam-3412	157	13	)	)	PUNCT
ejpam-3412	157	14	,	,	PUNCT
ejpam-3412	157	15	294	294	NUM
ejpam-3412	157	16	-	-	SYM
ejpam-3412	157	17	331	331	NUM
ejpam-3412	157	18	300	300	NUM
ejpam-3412	157	19	(	(	PUNCT
ejpam-3412	157	20	2	2	NUM
ejpam-3412	157	21	)	)	PUNCT
ejpam-3412	157	22	a	a	DET
ejpam-3412	157	23	fuzzy	fuzzy	ADJ
ejpam-3412	157	24	near	near	ADP
ejpam-3412	157	25	upi	upi	NOUN
ejpam-3412	157	26	-	-	PUNCT
ejpam-3412	157	27	filter	filter	NOUN
ejpam-3412	157	28	of	of	ADP
ejpam-3412	157	29	a	a	PRON
ejpam-3412	157	30	if	if	SCONJ
ejpam-3412	157	31	f	f	PROPN
ejpam-3412	157	32	is	be	AUX
ejpam-3412	157	33	a	a	DET
ejpam-3412	157	34	fuzzy	fuzzy	ADJ
ejpam-3412	157	35	near	near	ADP
ejpam-3412	157	36	up	up	ADJ
ejpam-3412	157	37	-	-	PUNCT
ejpam-3412	157	38	filter	filter	NOUN
ejpam-3412	157	39	of	of	ADP
ejpam-3412	157	40	(	(	PUNCT
ejpam-3412	157	41	a	a	PRON
ejpam-3412	157	42	,	,	PUNCT
ejpam-3412	157	43	·	·	PUNCT
ejpam-3412	157	44	,	,	PUNCT
ejpam-3412	157	45	0	0	NUM
ejpam-3412	157	46	)	)	PUNCT
ejpam-3412	157	47	and	and	CCONJ
ejpam-3412	157	48	a	a	DET
ejpam-3412	157	49	fuzzy	fuzzy	ADJ
ejpam-3412	157	50	ideal	ideal	NOUN
ejpam-3412	157	51	of	of	ADP
ejpam-3412	157	52	(	(	PUNCT
ejpam-3412	157	53	a	a	PRON
ejpam-3412	157	54	,	,	PUNCT
ejpam-3412	157	55	∗	∗	NOUN
ejpam-3412	157	56	)	)	PUNCT
ejpam-3412	157	57	.	.	PUNCT
ejpam-3412	158	1	clearly	clearly	ADV
ejpam-3412	158	2	,	,	PUNCT
ejpam-3412	158	3	a	a	DET
ejpam-3412	158	4	fuzzy	fuzzy	ADJ
ejpam-3412	158	5	near	near	ADP
ejpam-3412	158	6	upi	upi	PROPN
ejpam-3412	158	7	-	-	PUNCT
ejpam-3412	158	8	filter	filter	NOUN
ejpam-3412	158	9	is	be	AUX
ejpam-3412	158	10	a	a	DET
ejpam-3412	158	11	fuzzy	fuzzy	ADJ
ejpam-3412	158	12	near	near	ADP
ejpam-3412	158	13	ups	up	NOUN
ejpam-3412	158	14	-	-	PUNCT
ejpam-3412	158	15	filter	filter	NOUN
ejpam-3412	158	16	.	.	PUNCT
ejpam-3412	158	17	example	example	NOUN
ejpam-3412	159	1	3	3	X
ejpam-3412	159	2	.	.	PUNCT
ejpam-3412	159	3	let	let	VERB
ejpam-3412	159	4	a	a	PRON
ejpam-3412	159	5	=	=	PUNCT
ejpam-3412	159	6	{	{	PUNCT
ejpam-3412	159	7	0	0	NUM
ejpam-3412	159	8	,	,	PUNCT
ejpam-3412	159	9	1	1	NUM
ejpam-3412	159	10	,	,	PUNCT
ejpam-3412	159	11	2	2	NUM
ejpam-3412	159	12	,	,	PUNCT
ejpam-3412	159	13	3	3	NUM
ejpam-3412	159	14	}	}	PUNCT
ejpam-3412	159	15	be	be	AUX
ejpam-3412	159	16	a	a	DET
ejpam-3412	159	17	set	set	NOUN
ejpam-3412	159	18	with	with	ADP
ejpam-3412	159	19	two	two	NUM
ejpam-3412	159	20	binary	binary	ADJ
ejpam-3412	159	21	operations	operation	NOUN
ejpam-3412	159	22	·	·	PUNCT
ejpam-3412	159	23	and	and	CCONJ
ejpam-3412	159	24	∗	∗	NOUN
ejpam-3412	159	25	defined	define	VERB
ejpam-3412	159	26	by	by	ADP
ejpam-3412	159	27	the	the	DET
ejpam-3412	159	28	following	following	ADJ
ejpam-3412	159	29	cayley	cayley	ADJ
ejpam-3412	159	30	tables	table	NOUN
ejpam-3412	159	31	:	:	PUNCT
ejpam-3412	159	32	·	·	SYM
ejpam-3412	159	33	0	0	NUM
ejpam-3412	159	34	1	1	NUM
ejpam-3412	159	35	2	2	NUM
ejpam-3412	159	36	3	3	NUM
ejpam-3412	159	37	0	0	NUM
ejpam-3412	159	38	0	0	NUM
ejpam-3412	159	39	1	1	NUM
ejpam-3412	159	40	2	2	NUM
ejpam-3412	159	41	3	3	NUM
ejpam-3412	159	42	1	1	NUM
ejpam-3412	159	43	0	0	NUM
ejpam-3412	159	44	0	0	NUM
ejpam-3412	159	45	2	2	NUM
ejpam-3412	159	46	3	3	NUM
ejpam-3412	159	47	2	2	NUM
ejpam-3412	159	48	0	0	NUM
ejpam-3412	159	49	1	1	NUM
ejpam-3412	159	50	0	0	NUM
ejpam-3412	159	51	3	3	NUM
ejpam-3412	159	52	3	3	NUM
ejpam-3412	159	53	0	0	NUM
ejpam-3412	159	54	1	1	NUM
ejpam-3412	159	55	2	2	NUM
ejpam-3412	159	56	0	0	NUM
ejpam-3412	159	57	∗	∗	NOUN
ejpam-3412	159	58	0	0	NUM
ejpam-3412	159	59	1	1	NUM
ejpam-3412	159	60	2	2	NUM
ejpam-3412	159	61	3	3	NUM
ejpam-3412	159	62	0	0	NUM
ejpam-3412	159	63	0	0	NUM
ejpam-3412	159	64	0	0	NUM
ejpam-3412	159	65	0	0	NUM
ejpam-3412	159	66	0	0	NUM
ejpam-3412	159	67	1	1	NUM
ejpam-3412	159	68	0	0	NUM
ejpam-3412	159	69	0	0	NUM
ejpam-3412	159	70	0	0	NUM
ejpam-3412	159	71	0	0	NUM
ejpam-3412	159	72	2	2	NUM
ejpam-3412	159	73	0	0	NUM
ejpam-3412	159	74	0	0	NUM
ejpam-3412	159	75	0	0	NUM
ejpam-3412	159	76	1	1	NUM
ejpam-3412	159	77	3	3	NUM
ejpam-3412	159	78	0	0	NUM
ejpam-3412	159	79	0	0	NUM
ejpam-3412	159	80	1	1	NUM
ejpam-3412	159	81	0	0	NUM
ejpam-3412	159	82	then	then	ADV
ejpam-3412	159	83	a	a	DET
ejpam-3412	159	84	=	=	X
ejpam-3412	159	85	(	(	PUNCT
ejpam-3412	159	86	a	a	PRON
ejpam-3412	159	87	,	,	PUNCT
ejpam-3412	159	88	·	·	PUNCT
ejpam-3412	159	89	,	,	PUNCT
ejpam-3412	159	90	∗	∗	NOUN
ejpam-3412	159	91	,	,	PUNCT
ejpam-3412	159	92	0	0	NUM
ejpam-3412	159	93	)	)	PUNCT
ejpam-3412	159	94	is	be	AUX
ejpam-3412	159	95	an	an	DET
ejpam-3412	159	96	f	f	PROPN
ejpam-3412	159	97	-up	-up	NOUN
ejpam-3412	159	98	-	-	PUNCT
ejpam-3412	159	99	semigroup	semigroup	NOUN
ejpam-3412	159	100	.	.	PUNCT
ejpam-3412	160	1	we	we	PRON
ejpam-3412	160	2	define	define	VERB
ejpam-3412	160	3	a	a	DET
ejpam-3412	160	4	membership	membership	NOUN
ejpam-3412	160	5	function	function	NOUN
ejpam-3412	160	6	ff	ff	NOUN
ejpam-3412	160	7	as	as	SCONJ
ejpam-3412	160	8	follows	follow	VERB
ejpam-3412	160	9	:	:	PUNCT
ejpam-3412	160	10	ff(0	ff(0	NOUN
ejpam-3412	160	11	)	)	PUNCT
ejpam-3412	160	12	=	=	SYM
ejpam-3412	160	13	1	1	NUM
ejpam-3412	160	14	,	,	PUNCT
ejpam-3412	160	15	ff(1	ff(1	PROPN
ejpam-3412	160	16	)	)	PUNCT
ejpam-3412	160	17	=	=	SYM
ejpam-3412	160	18	0.4	0.4	NUM
ejpam-3412	160	19	,	,	PUNCT
ejpam-3412	160	20	ff(2	ff(2	PROPN
ejpam-3412	160	21	)	)	PUNCT
ejpam-3412	160	22	=	=	NUM
ejpam-3412	160	23	0.5	0.5	NUM
ejpam-3412	160	24	,	,	PUNCT
ejpam-3412	160	25	and	and	CCONJ
ejpam-3412	160	26	ff(3	ff(3	NOUN
ejpam-3412	160	27	)	)	PUNCT
ejpam-3412	160	28	=	=	NOUN
ejpam-3412	160	29	0.2	0.2	NUM
ejpam-3412	160	30	.	.	PUNCT
ejpam-3412	161	1	then	then	ADV
ejpam-3412	161	2	f	f	PROPN
ejpam-3412	161	3	is	be	AUX
ejpam-3412	161	4	a	a	DET
ejpam-3412	161	5	fuzzy	fuzzy	ADJ
ejpam-3412	161	6	near	near	ADP
ejpam-3412	161	7	ups	up	NOUN
ejpam-3412	161	8	-	-	PUNCT
ejpam-3412	161	9	filter	filter	NOUN
ejpam-3412	161	10	of	of	ADP
ejpam-3412	161	11	a.	a.	NOUN
ejpam-3412	161	12	since	since	SCONJ
ejpam-3412	161	13	ff(2∗3	ff(2∗3	PROPN
ejpam-3412	161	14	)	)	PUNCT
ejpam-3412	161	15	=	=	SYM
ejpam-3412	161	16	ff(1	ff(1	PROPN
ejpam-3412	161	17	)	)	PUNCT
ejpam-3412	161	18	=	=	SYM
ejpam-3412	161	19	0.4	0.4	NUM
ejpam-3412	161	20	�	�	PROPN
ejpam-3412	161	21	0.5	0.5	NUM
ejpam-3412	161	22	=	=	SYM
ejpam-3412	161	23	max{0.5	max{0.5	PROPN
ejpam-3412	161	24	,	,	PUNCT
ejpam-3412	161	25	0.2	0.2	NUM
ejpam-3412	161	26	}	}	PUNCT
ejpam-3412	161	27	=	=	SYM
ejpam-3412	161	28	max{ff(2	max{ff(2	PROPN
ejpam-3412	161	29	)	)	PUNCT
ejpam-3412	161	30	,	,	PUNCT
ejpam-3412	161	31	ff(3	ff(3	NOUN
ejpam-3412	161	32	)	)	PUNCT
ejpam-3412	161	33	}	}	PUNCT
ejpam-3412	161	34	,	,	PUNCT
ejpam-3412	161	35	we	we	PRON
ejpam-3412	161	36	have	have	VERB
ejpam-3412	161	37	f	f	PROPN
ejpam-3412	161	38	is	be	AUX
ejpam-3412	161	39	not	not	PART
ejpam-3412	161	40	a	a	DET
ejpam-3412	161	41	fuzzy	fuzzy	ADJ
ejpam-3412	161	42	near	near	ADP
ejpam-3412	161	43	upi	upi	NOUN
ejpam-3412	161	44	-	-	PUNCT
ejpam-3412	161	45	filter	filter	NOUN
ejpam-3412	161	46	of	of	ADP
ejpam-3412	161	47	a.	a.	NOUN
ejpam-3412	161	48	from	from	ADP
ejpam-3412	161	49	[	[	X
ejpam-3412	161	50	7	7	NUM
ejpam-3412	161	51	]	]	PUNCT
ejpam-3412	161	52	,	,	PUNCT
ejpam-3412	161	53	we	we	PRON
ejpam-3412	161	54	can	can	AUX
ejpam-3412	161	55	easily	easily	ADV
ejpam-3412	161	56	prove	prove	VERB
ejpam-3412	161	57	theorems	theorem	NOUN
ejpam-3412	161	58	1	1	NUM
ejpam-3412	161	59	,	,	PUNCT
ejpam-3412	161	60	2	2	NUM
ejpam-3412	161	61	,	,	PUNCT
ejpam-3412	161	62	3	3	NUM
ejpam-3412	161	63	,	,	PUNCT
ejpam-3412	161	64	and	and	CCONJ
ejpam-3412	161	65	4	4	NUM
ejpam-3412	161	66	.	.	X
ejpam-3412	161	67	theorem	theorem	NOUN
ejpam-3412	161	68	1	1	NUM
ejpam-3412	161	69	.	.	PUNCT
ejpam-3412	162	1	every	every	DET
ejpam-3412	162	2	fuzzy	fuzzy	ADJ
ejpam-3412	162	3	near	near	ADP
ejpam-3412	162	4	ups	up	NOUN
ejpam-3412	162	5	-	-	PUNCT
ejpam-3412	162	6	filter	filter	NOUN
ejpam-3412	162	7	of	of	ADP
ejpam-3412	162	8	an	an	DET
ejpam-3412	162	9	f	f	PROPN
ejpam-3412	162	10	-up	-up	NOUN
ejpam-3412	162	11	-	-	PUNCT
ejpam-3412	162	12	semigroup	semigroup	PROPN
ejpam-3412	162	13	is	be	AUX
ejpam-3412	162	14	a	a	DET
ejpam-3412	162	15	fuzzy	fuzzy	ADJ
ejpam-3412	162	16	ups	up	NOUN
ejpam-3412	162	17	-	-	PUNCT
ejpam-3412	162	18	subalgebra	subalgebra	NOUN
ejpam-3412	162	19	.	.	PUNCT
ejpam-3412	163	1	the	the	DET
ejpam-3412	163	2	following	follow	VERB
ejpam-3412	163	3	example	example	NOUN
ejpam-3412	163	4	shows	show	VERB
ejpam-3412	163	5	that	that	SCONJ
ejpam-3412	163	6	the	the	DET
ejpam-3412	163	7	converse	converse	NOUN
ejpam-3412	163	8	of	of	ADP
ejpam-3412	163	9	theorem	theorem	NOUN
ejpam-3412	163	10	1	1	NUM
ejpam-3412	163	11	is	be	AUX
ejpam-3412	163	12	not	not	PART
ejpam-3412	163	13	true	true	ADJ
ejpam-3412	163	14	.	.	PUNCT
ejpam-3412	164	1	example	example	NOUN
ejpam-3412	165	1	4	4	NUM
ejpam-3412	165	2	.	.	PUNCT
ejpam-3412	165	3	let	let	VERB
ejpam-3412	165	4	a	a	PRON
ejpam-3412	165	5	=	=	PUNCT
ejpam-3412	165	6	{	{	PUNCT
ejpam-3412	165	7	0	0	NUM
ejpam-3412	165	8	,	,	PUNCT
ejpam-3412	165	9	1	1	NUM
ejpam-3412	165	10	,	,	PUNCT
ejpam-3412	165	11	2	2	NUM
ejpam-3412	165	12	,	,	PUNCT
ejpam-3412	165	13	3	3	NUM
ejpam-3412	165	14	}	}	PUNCT
ejpam-3412	165	15	be	be	AUX
ejpam-3412	165	16	a	a	DET
ejpam-3412	165	17	set	set	NOUN
ejpam-3412	165	18	with	with	ADP
ejpam-3412	165	19	two	two	NUM
ejpam-3412	165	20	binary	binary	ADJ
ejpam-3412	165	21	operations	operation	NOUN
ejpam-3412	165	22	·	·	PUNCT
ejpam-3412	165	23	and	and	CCONJ
ejpam-3412	165	24	∗	∗	NOUN
ejpam-3412	165	25	defined	define	VERB
ejpam-3412	165	26	by	by	ADP
ejpam-3412	165	27	the	the	DET
ejpam-3412	165	28	following	following	ADJ
ejpam-3412	165	29	cayley	cayley	ADJ
ejpam-3412	165	30	tables	table	NOUN
ejpam-3412	165	31	:	:	PUNCT
ejpam-3412	165	32	·	·	SYM
ejpam-3412	165	33	0	0	NUM
ejpam-3412	165	34	1	1	NUM
ejpam-3412	165	35	2	2	NUM
ejpam-3412	165	36	3	3	NUM
ejpam-3412	165	37	0	0	NUM
ejpam-3412	165	38	0	0	NUM
ejpam-3412	165	39	1	1	NUM
ejpam-3412	165	40	2	2	NUM
ejpam-3412	165	41	3	3	NUM
ejpam-3412	165	42	1	1	NUM
ejpam-3412	165	43	0	0	NUM
ejpam-3412	165	44	0	0	NUM
ejpam-3412	165	45	1	1	NUM
ejpam-3412	165	46	3	3	NUM
ejpam-3412	165	47	2	2	NUM
ejpam-3412	165	48	0	0	NUM
ejpam-3412	165	49	0	0	NUM
ejpam-3412	165	50	0	0	NUM
ejpam-3412	165	51	3	3	NUM
ejpam-3412	165	52	3	3	NUM
ejpam-3412	165	53	0	0	NUM
ejpam-3412	165	54	1	1	NUM
ejpam-3412	165	55	1	1	NUM
ejpam-3412	165	56	0	0	NUM
ejpam-3412	165	57	∗	∗	NOUN
ejpam-3412	165	58	0	0	NUM
ejpam-3412	165	59	1	1	NUM
ejpam-3412	165	60	2	2	NUM
ejpam-3412	165	61	3	3	NUM
ejpam-3412	165	62	0	0	NUM
ejpam-3412	165	63	0	0	NUM
ejpam-3412	165	64	0	0	NUM
ejpam-3412	165	65	0	0	NUM
ejpam-3412	165	66	0	0	NUM
ejpam-3412	165	67	1	1	NUM
ejpam-3412	165	68	0	0	NUM
ejpam-3412	165	69	0	0	NUM
ejpam-3412	165	70	0	0	NUM
ejpam-3412	165	71	0	0	NUM
ejpam-3412	165	72	2	2	NUM
ejpam-3412	165	73	0	0	NUM
ejpam-3412	165	74	0	0	NUM
ejpam-3412	165	75	0	0	NUM
ejpam-3412	165	76	0	0	NUM
ejpam-3412	165	77	3	3	NUM
ejpam-3412	165	78	0	0	NUM
ejpam-3412	165	79	0	0	NUM
ejpam-3412	165	80	0	0	NUM
ejpam-3412	165	81	1	1	NUM
ejpam-3412	165	82	then	then	ADV
ejpam-3412	165	83	a	a	DET
ejpam-3412	165	84	=	=	X
ejpam-3412	165	85	(	(	PUNCT
ejpam-3412	165	86	a	a	PRON
ejpam-3412	165	87	,	,	PUNCT
ejpam-3412	165	88	·	·	PUNCT
ejpam-3412	165	89	,	,	PUNCT
ejpam-3412	165	90	∗	∗	NOUN
ejpam-3412	165	91	,	,	PUNCT
ejpam-3412	165	92	0	0	NUM
ejpam-3412	165	93	)	)	PUNCT
ejpam-3412	165	94	is	be	AUX
ejpam-3412	165	95	an	an	DET
ejpam-3412	165	96	f	f	PROPN
ejpam-3412	165	97	-up	-up	NOUN
ejpam-3412	165	98	-	-	PUNCT
ejpam-3412	165	99	semigroup	semigroup	NOUN
ejpam-3412	165	100	.	.	PUNCT
ejpam-3412	166	1	we	we	PRON
ejpam-3412	166	2	define	define	VERB
ejpam-3412	166	3	a	a	DET
ejpam-3412	166	4	membership	membership	NOUN
ejpam-3412	166	5	function	function	NOUN
ejpam-3412	166	6	ff	ff	NOUN
ejpam-3412	166	7	as	as	SCONJ
ejpam-3412	166	8	follows	follow	VERB
ejpam-3412	166	9	:	:	PUNCT
ejpam-3412	166	10	ff(0	ff(0	NOUN
ejpam-3412	166	11	)	)	PUNCT
ejpam-3412	166	12	=	=	SYM
ejpam-3412	166	13	1	1	NUM
ejpam-3412	166	14	,	,	PUNCT
ejpam-3412	166	15	ff(1	ff(1	PROPN
ejpam-3412	166	16	)	)	PUNCT
ejpam-3412	166	17	=	=	SYM
ejpam-3412	166	18	0.8	0.8	NUM
ejpam-3412	166	19	,	,	PUNCT
ejpam-3412	166	20	ff(2	ff(2	PROPN
ejpam-3412	166	21	)	)	PUNCT
ejpam-3412	166	22	=	=	NUM
ejpam-3412	166	23	0.9	0.9	NUM
ejpam-3412	166	24	,	,	PUNCT
ejpam-3412	166	25	and	and	CCONJ
ejpam-3412	166	26	ff(3	ff(3	NOUN
ejpam-3412	166	27	)	)	PUNCT
ejpam-3412	166	28	=	=	NOUN
ejpam-3412	167	1	0.7	0.7	NUM
ejpam-3412	167	2	.	.	PUNCT
ejpam-3412	168	1	then	then	ADV
ejpam-3412	168	2	f	f	PROPN
ejpam-3412	168	3	is	be	AUX
ejpam-3412	168	4	a	a	DET
ejpam-3412	168	5	fuzzy	fuzzy	ADJ
ejpam-3412	168	6	ups	up	NOUN
ejpam-3412	168	7	-	-	PUNCT
ejpam-3412	168	8	subalgebra	subalgebra	NOUN
ejpam-3412	168	9	of	of	ADP
ejpam-3412	168	10	a.	a.	NOUN
ejpam-3412	168	11	since	since	SCONJ
ejpam-3412	168	12	ff(1	ff(1	PROPN
ejpam-3412	168	13	·	·	PUNCT
ejpam-3412	168	14	2	2	X
ejpam-3412	168	15	)	)	PUNCT
ejpam-3412	168	16	=	=	SYM
ejpam-3412	168	17	ff(1	ff(1	PROPN
ejpam-3412	168	18	)	)	PUNCT
ejpam-3412	168	19	=	=	SYM
ejpam-3412	168	20	0.8	0.8	NUM
ejpam-3412	168	21	�	�	PROPN
ejpam-3412	168	22	0.9	0.9	NUM
ejpam-3412	168	23	=	=	SYM
ejpam-3412	168	24	ff(2	ff(2	NUM
ejpam-3412	168	25	)	)	PUNCT
ejpam-3412	168	26	,	,	PUNCT
ejpam-3412	168	27	we	we	PRON
ejpam-3412	168	28	have	have	VERB
ejpam-3412	168	29	f	f	PROPN
ejpam-3412	168	30	is	be	AUX
ejpam-3412	168	31	not	not	PART
ejpam-3412	168	32	a	a	DET
ejpam-3412	168	33	fuzzy	fuzzy	ADJ
ejpam-3412	168	34	near	near	ADP
ejpam-3412	168	35	ups	up	NOUN
ejpam-3412	168	36	-	-	PUNCT
ejpam-3412	168	37	filter	filter	NOUN
ejpam-3412	168	38	of	of	ADP
ejpam-3412	168	39	a.	a.	NOUN
ejpam-3412	168	40	theorem	theorem	NOUN
ejpam-3412	168	41	2	2	NUM
ejpam-3412	168	42	.	.	PUNCT
ejpam-3412	169	1	every	every	DET
ejpam-3412	169	2	fuzzy	fuzzy	NOUN
ejpam-3412	169	3	near	near	ADP
ejpam-3412	169	4	upi	upi	PROPN
ejpam-3412	169	5	-	-	PUNCT
ejpam-3412	169	6	filter	filter	NOUN
ejpam-3412	169	7	of	of	ADP
ejpam-3412	169	8	an	an	DET
ejpam-3412	169	9	f	f	PROPN
ejpam-3412	169	10	-up	-up	NOUN
ejpam-3412	169	11	-	-	PUNCT
ejpam-3412	169	12	semigroup	semigroup	PROPN
ejpam-3412	169	13	is	be	AUX
ejpam-3412	169	14	a	a	DET
ejpam-3412	169	15	fuzzy	fuzzy	ADJ
ejpam-3412	169	16	upi	upi	NOUN
ejpam-3412	169	17	-	-	PUNCT
ejpam-3412	169	18	subalgebra	subalgebra	PROPN
ejpam-3412	169	19	.	.	PUNCT
ejpam-3412	170	1	in	in	ADP
ejpam-3412	170	2	example	example	NOUN
ejpam-3412	170	3	4	4	NUM
ejpam-3412	170	4	,	,	PUNCT
ejpam-3412	170	5	we	we	PRON
ejpam-3412	170	6	have	have	VERB
ejpam-3412	170	7	f	f	PROPN
ejpam-3412	170	8	is	be	AUX
ejpam-3412	170	9	a	a	DET
ejpam-3412	170	10	fuzzy	fuzzy	ADJ
ejpam-3412	170	11	upi	upi	NOUN
ejpam-3412	170	12	-	-	PUNCT
ejpam-3412	170	13	subalgebra	subalgebra	NOUN
ejpam-3412	170	14	of	of	ADP
ejpam-3412	170	15	a	a	PRON
ejpam-3412	171	1	but	but	CCONJ
ejpam-3412	171	2	f	f	PROPN
ejpam-3412	171	3	is	be	AUX
ejpam-3412	171	4	not	not	PART
ejpam-3412	171	5	a	a	DET
ejpam-3412	171	6	fuzzy	fuzzy	ADJ
ejpam-3412	171	7	near	near	ADP
ejpam-3412	171	8	upi	upi	NOUN
ejpam-3412	171	9	-	-	PUNCT
ejpam-3412	171	10	filter	filter	NOUN
ejpam-3412	171	11	of	of	ADP
ejpam-3412	171	12	a.	a.	NOUN
ejpam-3412	171	13	theorem	theorem	NOUN
ejpam-3412	171	14	3	3	X
ejpam-3412	171	15	.	.	PUNCT
ejpam-3412	172	1	every	every	DET
ejpam-3412	172	2	fuzzy	fuzzy	ADJ
ejpam-3412	172	3	ups	up	NOUN
ejpam-3412	172	4	-	-	PUNCT
ejpam-3412	172	5	filter	filter	NOUN
ejpam-3412	172	6	of	of	ADP
ejpam-3412	172	7	an	an	DET
ejpam-3412	172	8	f	f	PROPN
ejpam-3412	172	9	-up	-up	NOUN
ejpam-3412	172	10	-	-	PUNCT
ejpam-3412	172	11	semigroup	semigroup	PROPN
ejpam-3412	172	12	is	be	AUX
ejpam-3412	172	13	a	a	DET
ejpam-3412	172	14	fuzzy	fuzzy	ADJ
ejpam-3412	172	15	near	near	ADP
ejpam-3412	172	16	ups	up	NOUN
ejpam-3412	172	17	-	-	PUNCT
ejpam-3412	172	18	filter	filter	NOUN
ejpam-3412	172	19	.	.	PUNCT
ejpam-3412	173	1	a.	a.	PROPN
ejpam-3412	173	2	satirad	satirad	PROPN
ejpam-3412	173	3	,	,	PUNCT
ejpam-3412	173	4	a.	a.	NOUN
ejpam-3412	173	5	iampan	iampan	PROPN
ejpam-3412	173	6	/	/	SYM
ejpam-3412	173	7	eur	eur	PROPN
ejpam-3412	173	8	.	.	PUNCT
ejpam-3412	174	1	j.	j.	PROPN
ejpam-3412	174	2	pure	pure	PROPN
ejpam-3412	174	3	appl	appl	PROPN
ejpam-3412	174	4	.	.	PROPN
ejpam-3412	174	5	math	math	PROPN
ejpam-3412	174	6	,	,	PUNCT
ejpam-3412	174	7	12	12	NUM
ejpam-3412	174	8	(	(	PUNCT
ejpam-3412	174	9	2	2	NUM
ejpam-3412	174	10	)	)	PUNCT
ejpam-3412	174	11	(	(	PUNCT
ejpam-3412	174	12	2019	2019	NUM
ejpam-3412	174	13	)	)	PUNCT
ejpam-3412	174	14	,	,	PUNCT
ejpam-3412	174	15	294	294	NUM
ejpam-3412	174	16	-	-	SYM
ejpam-3412	174	17	331	331	NUM
ejpam-3412	174	18	301	301	NUM
ejpam-3412	174	19	the	the	DET
ejpam-3412	174	20	following	follow	VERB
ejpam-3412	174	21	example	example	NOUN
ejpam-3412	174	22	shows	show	VERB
ejpam-3412	174	23	that	that	SCONJ
ejpam-3412	174	24	the	the	DET
ejpam-3412	174	25	converse	converse	NOUN
ejpam-3412	174	26	of	of	ADP
ejpam-3412	174	27	theorem	theorem	NOUN
ejpam-3412	174	28	3	3	NUM
ejpam-3412	174	29	is	be	AUX
ejpam-3412	174	30	not	not	PART
ejpam-3412	174	31	true	true	ADJ
ejpam-3412	174	32	.	.	PUNCT
ejpam-3412	175	1	example	example	NOUN
ejpam-3412	175	2	5	5	NUM
ejpam-3412	175	3	.	.	PUNCT
ejpam-3412	176	1	let	let	VERB
ejpam-3412	176	2	a	a	PRON
ejpam-3412	176	3	=	=	PUNCT
ejpam-3412	176	4	{	{	PUNCT
ejpam-3412	176	5	0	0	NUM
ejpam-3412	176	6	,	,	PUNCT
ejpam-3412	176	7	1	1	NUM
ejpam-3412	176	8	,	,	PUNCT
ejpam-3412	176	9	2	2	NUM
ejpam-3412	176	10	,	,	PUNCT
ejpam-3412	176	11	3	3	NUM
ejpam-3412	176	12	}	}	PUNCT
ejpam-3412	176	13	be	be	AUX
ejpam-3412	176	14	a	a	DET
ejpam-3412	176	15	set	set	NOUN
ejpam-3412	176	16	with	with	ADP
ejpam-3412	176	17	two	two	NUM
ejpam-3412	176	18	binary	binary	ADJ
ejpam-3412	176	19	operations	operation	NOUN
ejpam-3412	176	20	·	·	PUNCT
ejpam-3412	176	21	and	and	CCONJ
ejpam-3412	177	1	∗	∗	NOUN
ejpam-3412	177	2	defined	define	VERB
ejpam-3412	177	3	by	by	ADP
ejpam-3412	177	4	the	the	DET
ejpam-3412	177	5	following	following	ADJ
ejpam-3412	177	6	cayley	cayley	ADJ
ejpam-3412	177	7	tables	table	NOUN
ejpam-3412	177	8	:	:	PUNCT
ejpam-3412	177	9	·	·	SYM
ejpam-3412	177	10	0	0	NUM
ejpam-3412	177	11	1	1	NUM
ejpam-3412	177	12	2	2	NUM
ejpam-3412	177	13	3	3	NUM
ejpam-3412	177	14	0	0	NUM
ejpam-3412	177	15	0	0	NUM
ejpam-3412	177	16	1	1	NUM
ejpam-3412	177	17	2	2	NUM
ejpam-3412	177	18	3	3	NUM
ejpam-3412	177	19	1	1	NUM
ejpam-3412	177	20	0	0	NUM
ejpam-3412	177	21	0	0	NUM
ejpam-3412	177	22	2	2	NUM
ejpam-3412	177	23	3	3	NUM
ejpam-3412	177	24	2	2	NUM
ejpam-3412	177	25	0	0	NUM
ejpam-3412	177	26	0	0	NUM
ejpam-3412	177	27	0	0	NUM
ejpam-3412	177	28	3	3	NUM
ejpam-3412	177	29	3	3	NUM
ejpam-3412	177	30	0	0	NUM
ejpam-3412	177	31	0	0	NUM
ejpam-3412	177	32	0	0	NUM
ejpam-3412	177	33	0	0	NUM
ejpam-3412	177	34	∗	∗	NOUN
ejpam-3412	177	35	0	0	NUM
ejpam-3412	177	36	1	1	NUM
ejpam-3412	177	37	2	2	NUM
ejpam-3412	177	38	3	3	NUM
ejpam-3412	177	39	0	0	NUM
ejpam-3412	177	40	0	0	NUM
ejpam-3412	177	41	0	0	NUM
ejpam-3412	177	42	0	0	NUM
ejpam-3412	177	43	0	0	NUM
ejpam-3412	177	44	1	1	NUM
ejpam-3412	177	45	0	0	NUM
ejpam-3412	177	46	0	0	NUM
ejpam-3412	177	47	0	0	NUM
ejpam-3412	177	48	0	0	NUM
ejpam-3412	177	49	2	2	NUM
ejpam-3412	177	50	0	0	NUM
ejpam-3412	177	51	0	0	NUM
ejpam-3412	177	52	0	0	NUM
ejpam-3412	177	53	0	0	NUM
ejpam-3412	177	54	3	3	NUM
ejpam-3412	177	55	0	0	NUM
ejpam-3412	177	56	0	0	NUM
ejpam-3412	177	57	0	0	NUM
ejpam-3412	177	58	2	2	NUM
ejpam-3412	177	59	then	then	ADV
ejpam-3412	177	60	a	a	PRON
ejpam-3412	177	61	=	=	X
ejpam-3412	177	62	(	(	PUNCT
ejpam-3412	177	63	a	a	PRON
ejpam-3412	177	64	,	,	PUNCT
ejpam-3412	177	65	·	·	PUNCT
ejpam-3412	177	66	,	,	PUNCT
ejpam-3412	177	67	∗	∗	NOUN
ejpam-3412	177	68	,	,	PUNCT
ejpam-3412	177	69	0	0	NUM
ejpam-3412	177	70	)	)	PUNCT
ejpam-3412	177	71	is	be	AUX
ejpam-3412	177	72	an	an	DET
ejpam-3412	177	73	f	f	PROPN
ejpam-3412	177	74	-up	-up	NOUN
ejpam-3412	177	75	-	-	PUNCT
ejpam-3412	177	76	semigroup	semigroup	NOUN
ejpam-3412	177	77	.	.	PUNCT
ejpam-3412	178	1	we	we	PRON
ejpam-3412	178	2	define	define	VERB
ejpam-3412	178	3	a	a	DET
ejpam-3412	178	4	membership	membership	NOUN
ejpam-3412	178	5	function	function	NOUN
ejpam-3412	178	6	ff	ff	NOUN
ejpam-3412	178	7	as	as	SCONJ
ejpam-3412	178	8	follows	follow	VERB
ejpam-3412	178	9	:	:	PUNCT
ejpam-3412	178	10	ff(0	ff(0	NOUN
ejpam-3412	178	11	)	)	PUNCT
ejpam-3412	178	12	=	=	SYM
ejpam-3412	178	13	1	1	NUM
ejpam-3412	178	14	,	,	PUNCT
ejpam-3412	178	15	ff(1	ff(1	PROPN
ejpam-3412	178	16	)	)	PUNCT
ejpam-3412	178	17	=	=	SYM
ejpam-3412	178	18	0.7	0.7	NUM
ejpam-3412	178	19	,	,	PUNCT
ejpam-3412	178	20	ff(2	ff(2	PROPN
ejpam-3412	178	21	)	)	PUNCT
ejpam-3412	178	22	=	=	NUM
ejpam-3412	178	23	0.9	0.9	NUM
ejpam-3412	178	24	,	,	PUNCT
ejpam-3412	178	25	and	and	CCONJ
ejpam-3412	178	26	ff(3	ff(3	NOUN
ejpam-3412	178	27	)	)	PUNCT
ejpam-3412	178	28	=	=	PUNCT
ejpam-3412	178	29	0.8	0.8	NUM
ejpam-3412	178	30	.	.	PUNCT
ejpam-3412	179	1	then	then	ADV
ejpam-3412	179	2	f	f	PROPN
ejpam-3412	179	3	is	be	AUX
ejpam-3412	179	4	a	a	DET
ejpam-3412	179	5	fuzzy	fuzzy	ADJ
ejpam-3412	179	6	near	near	ADP
ejpam-3412	179	7	ups	up	NOUN
ejpam-3412	179	8	-	-	PUNCT
ejpam-3412	179	9	filter	filter	NOUN
ejpam-3412	179	10	of	of	ADP
ejpam-3412	179	11	a.	a.	NOUN
ejpam-3412	179	12	since	since	SCONJ
ejpam-3412	179	13	ff(1	ff(1	PROPN
ejpam-3412	179	14	)	)	PUNCT
ejpam-3412	179	15	=	=	SYM
ejpam-3412	179	16	0.7	0.7	NUM
ejpam-3412	179	17	�	�	PROPN
ejpam-3412	179	18	0.8	0.8	NUM
ejpam-3412	179	19	=	=	SYM
ejpam-3412	179	20	min{1	min{1	PROPN
ejpam-3412	179	21	,	,	PUNCT
ejpam-3412	179	22	0.8	0.8	NUM
ejpam-3412	179	23	}	}	PUNCT
ejpam-3412	179	24	=	=	SYM
ejpam-3412	179	25	min{ff(0	min{ff(0	PROPN
ejpam-3412	179	26	)	)	PUNCT
ejpam-3412	179	27	,	,	PUNCT
ejpam-3412	179	28	ff(3	ff(3	NOUN
ejpam-3412	179	29	)	)	PUNCT
ejpam-3412	179	30	}	}	PUNCT
ejpam-3412	179	31	=	=	PUNCT
ejpam-3412	179	32	min{ff(3	min{ff(3	NOUN
ejpam-3412	179	33	·	·	PUNCT
ejpam-3412	179	34	1	1	NUM
ejpam-3412	179	35	)	)	PUNCT
ejpam-3412	179	36	,	,	PUNCT
ejpam-3412	179	37	ff(3	ff(3	NOUN
ejpam-3412	179	38	)	)	PUNCT
ejpam-3412	179	39	}	}	PUNCT
ejpam-3412	179	40	,	,	PUNCT
ejpam-3412	179	41	we	we	PRON
ejpam-3412	179	42	have	have	VERB
ejpam-3412	179	43	f	f	PROPN
ejpam-3412	179	44	is	be	AUX
ejpam-3412	179	45	not	not	PART
ejpam-3412	179	46	a	a	DET
ejpam-3412	179	47	fuzzy	fuzzy	ADJ
ejpam-3412	179	48	ups	up	NOUN
ejpam-3412	179	49	-	-	PUNCT
ejpam-3412	179	50	filter	filter	NOUN
ejpam-3412	179	51	of	of	ADP
ejpam-3412	179	52	a.	a.	NOUN
ejpam-3412	179	53	theorem	theorem	NOUN
ejpam-3412	179	54	4	4	NUM
ejpam-3412	179	55	.	.	PUNCT
ejpam-3412	180	1	every	every	DET
ejpam-3412	180	2	fuzzy	fuzzy	ADJ
ejpam-3412	180	3	upi	upi	NOUN
ejpam-3412	180	4	-	-	PUNCT
ejpam-3412	180	5	filter	filter	NOUN
ejpam-3412	180	6	of	of	ADP
ejpam-3412	180	7	an	an	DET
ejpam-3412	180	8	f	f	PROPN
ejpam-3412	180	9	-up	-up	NOUN
ejpam-3412	180	10	-	-	PUNCT
ejpam-3412	180	11	semigroup	semigroup	PROPN
ejpam-3412	180	12	is	be	AUX
ejpam-3412	180	13	a	a	DET
ejpam-3412	180	14	fuzzy	fuzzy	ADJ
ejpam-3412	180	15	near	near	ADP
ejpam-3412	180	16	upi	upi	NOUN
ejpam-3412	180	17	-	-	PUNCT
ejpam-3412	180	18	filter	filter	NOUN
ejpam-3412	180	19	.	.	PUNCT
ejpam-3412	181	1	in	in	ADP
ejpam-3412	181	2	example	example	NOUN
ejpam-3412	181	3	5	5	NUM
ejpam-3412	181	4	,	,	PUNCT
ejpam-3412	181	5	we	we	PRON
ejpam-3412	181	6	have	have	VERB
ejpam-3412	181	7	f	f	PROPN
ejpam-3412	181	8	is	be	AUX
ejpam-3412	181	9	a	a	DET
ejpam-3412	181	10	fuzzy	fuzzy	ADJ
ejpam-3412	181	11	near	near	ADP
ejpam-3412	181	12	upi	upi	NOUN
ejpam-3412	181	13	-	-	PUNCT
ejpam-3412	181	14	filter	filter	NOUN
ejpam-3412	181	15	of	of	ADP
ejpam-3412	181	16	a	a	PRON
ejpam-3412	182	1	but	but	CCONJ
ejpam-3412	182	2	it	it	PRON
ejpam-3412	182	3	is	be	AUX
ejpam-3412	182	4	not	not	PART
ejpam-3412	182	5	a	a	DET
ejpam-3412	182	6	fuzzy	fuzzy	ADJ
ejpam-3412	182	7	upi	upi	NOUN
ejpam-3412	182	8	-	-	PUNCT
ejpam-3412	182	9	filter	filter	NOUN
ejpam-3412	182	10	of	of	ADP
ejpam-3412	182	11	a.	a.	NOUN
ejpam-3412	182	12	hence	hence	ADV
ejpam-3412	182	13	,	,	PUNCT
ejpam-3412	182	14	we	we	PRON
ejpam-3412	182	15	get	get	VERB
ejpam-3412	182	16	the	the	DET
ejpam-3412	182	17	diagram	diagram	NOUN
ejpam-3412	182	18	of	of	ADP
ejpam-3412	182	19	generalization	generalization	NOUN
ejpam-3412	182	20	of	of	ADP
ejpam-3412	182	21	fuzzy	fuzzy	ADJ
ejpam-3412	182	22	sets	set	NOUN
ejpam-3412	182	23	in	in	ADP
ejpam-3412	182	24	fully	fully	ADV
ejpam-3412	182	25	up	up	ADP
ejpam-3412	182	26	-	-	PUNCT
ejpam-3412	182	27	semigroups	semigroup	NOUN
ejpam-3412	182	28	as	as	SCONJ
ejpam-3412	182	29	shown	show	VERB
ejpam-3412	182	30	in	in	ADP
ejpam-3412	182	31	figure	figure	NOUN
ejpam-3412	182	32	1	1	NUM
ejpam-3412	182	33	.	.	PUNCT
ejpam-3412	182	34	figure	figure	NOUN
ejpam-3412	182	35	1	1	NUM
ejpam-3412	182	36	:	:	PUNCT
ejpam-3412	182	37	fuzzy	fuzzy	ADJ
ejpam-3412	182	38	sets	set	NOUN
ejpam-3412	182	39	in	in	ADP
ejpam-3412	182	40	fully	fully	ADV
ejpam-3412	182	41	up	up	ADP
ejpam-3412	182	42	-	-	PUNCT
ejpam-3412	182	43	semigroups	semigroup	NOUN
ejpam-3412	182	44	theorem	theorem	VERB
ejpam-3412	182	45	5	5	NUM
ejpam-3412	182	46	.	.	PUNCT
ejpam-3412	183	1	[	[	X
ejpam-3412	183	2	23	23	NUM
ejpam-3412	183	3	]	]	PUNCT
ejpam-3412	183	4	the	the	DET
ejpam-3412	183	5	intersection	intersection	NOUN
ejpam-3412	183	6	of	of	ADP
ejpam-3412	183	7	any	any	DET
ejpam-3412	183	8	nonempty	nonempty	ADJ
ejpam-3412	183	9	family	family	NOUN
ejpam-3412	183	10	of	of	ADP
ejpam-3412	183	11	fuzzy	fuzzy	ADJ
ejpam-3412	183	12	ups	up	NOUN
ejpam-3412	183	13	-	-	PUNCT
ejpam-3412	183	14	subalgebras	subalgebras	PROPN
ejpam-3412	183	15	(	(	PUNCT
ejpam-3412	183	16	resp	resp	PROPN
ejpam-3412	183	17	.	.	PUNCT
ejpam-3412	183	18	,	,	PUNCT
ejpam-3412	183	19	fuzzy	fuzzy	ADJ
ejpam-3412	183	20	upi	upi	PROPN
ejpam-3412	183	21	-	-	PUNCT
ejpam-3412	183	22	subalgebras	subalgebras	PROPN
ejpam-3412	183	23	,	,	PUNCT
ejpam-3412	183	24	fuzzy	fuzzy	ADJ
ejpam-3412	183	25	ups	up	NOUN
ejpam-3412	183	26	-	-	PUNCT
ejpam-3412	183	27	filters	filter	NOUN
ejpam-3412	183	28	,	,	PUNCT
ejpam-3412	183	29	fuzzy	fuzzy	ADJ
ejpam-3412	183	30	upi	upi	NOUN
ejpam-3412	183	31	-	-	PUNCT
ejpam-3412	183	32	filters	filter	NOUN
ejpam-3412	183	33	,	,	PUNCT
ejpam-3412	183	34	fuzzy	fuzzy	ADJ
ejpam-3412	183	35	ups	up	NOUN
ejpam-3412	183	36	-	-	PUNCT
ejpam-3412	183	37	ideals	ideal	NOUN
ejpam-3412	183	38	,	,	PUNCT
ejpam-3412	183	39	fuzzy	fuzzy	ADJ
ejpam-3412	183	40	upiideals	upiideal	NOUN
ejpam-3412	183	41	,	,	PUNCT
ejpam-3412	183	42	fuzzy	fuzzy	ADJ
ejpam-3412	183	43	strongly	strongly	ADV
ejpam-3412	183	44	ups	up	NOUN
ejpam-3412	183	45	-	-	PUNCT
ejpam-3412	183	46	ideals	ideal	NOUN
ejpam-3412	183	47	,	,	PUNCT
ejpam-3412	183	48	fuzzy	fuzzy	ADJ
ejpam-3412	183	49	strongly	strongly	ADV
ejpam-3412	183	50	upi	upi	NOUN
ejpam-3412	183	51	-	-	PUNCT
ejpam-3412	183	52	ideals	ideal	NOUN
ejpam-3412	183	53	)	)	PUNCT
ejpam-3412	183	54	of	of	ADP
ejpam-3412	183	55	an	an	DET
ejpam-3412	183	56	f	f	PROPN
ejpam-3412	183	57	-up	-up	NOUN
ejpam-3412	183	58	-	-	PUNCT
ejpam-3412	183	59	semigroup	semigroup	PROPN
ejpam-3412	183	60	is	be	AUX
ejpam-3412	183	61	also	also	ADV
ejpam-3412	183	62	a	a	DET
ejpam-3412	183	63	fuzzy	fuzzy	ADJ
ejpam-3412	183	64	ups	up	NOUN
ejpam-3412	183	65	-	-	PUNCT
ejpam-3412	183	66	subalgebra	subalgebra	NOUN
ejpam-3412	183	67	(	(	PUNCT
ejpam-3412	183	68	resp	resp	NOUN
ejpam-3412	183	69	.	.	PUNCT
ejpam-3412	183	70	,	,	PUNCT
ejpam-3412	183	71	fuzzy	fuzzy	ADJ
ejpam-3412	183	72	upi	upi	NOUN
ejpam-3412	183	73	-	-	PUNCT
ejpam-3412	183	74	subalgebra	subalgebra	PROPN
ejpam-3412	183	75	,	,	PUNCT
ejpam-3412	183	76	fuzzy	fuzzy	ADJ
ejpam-3412	183	77	ups	up	NOUN
ejpam-3412	183	78	-	-	PUNCT
ejpam-3412	183	79	filter	filter	NOUN
ejpam-3412	183	80	,	,	PUNCT
ejpam-3412	183	81	fuzzy	fuzzy	ADJ
ejpam-3412	183	82	upi	upi	NOUN
ejpam-3412	183	83	-	-	PUNCT
ejpam-3412	183	84	filter	filter	NOUN
ejpam-3412	183	85	,	,	PUNCT
ejpam-3412	183	86	fuzzy	fuzzy	ADJ
ejpam-3412	183	87	ups	up	NOUN
ejpam-3412	183	88	-	-	PUNCT
ejpam-3412	183	89	ideal	ideal	ADJ
ejpam-3412	183	90	,	,	PUNCT
ejpam-3412	183	91	fuzzy	fuzzy	ADJ
ejpam-3412	183	92	upi	upi	NOUN
ejpam-3412	183	93	-	-	PUNCT
ejpam-3412	183	94	ideal	ideal	ADJ
ejpam-3412	183	95	,	,	PUNCT
ejpam-3412	183	96	fuzzy	fuzzy	ADJ
ejpam-3412	183	97	strongly	strongly	ADV
ejpam-3412	183	98	ups	up	NOUN
ejpam-3412	183	99	-	-	PUNCT
ejpam-3412	183	100	ideal	ideal	ADJ
ejpam-3412	183	101	,	,	PUNCT
ejpam-3412	183	102	fuzzy	fuzzy	ADJ
ejpam-3412	183	103	strongly	strongly	ADV
ejpam-3412	183	104	upi	upi	NOUN
ejpam-3412	183	105	-	-	PUNCT
ejpam-3412	183	106	ideal	ideal	NOUN
ejpam-3412	183	107	)	)	PUNCT
ejpam-3412	183	108	.	.	PUNCT
ejpam-3412	184	1	a.	a.	PROPN
ejpam-3412	184	2	satirad	satirad	PROPN
ejpam-3412	184	3	,	,	PUNCT
ejpam-3412	184	4	a.	a.	NOUN
ejpam-3412	184	5	iampan	iampan	PROPN
ejpam-3412	184	6	/	/	SYM
ejpam-3412	184	7	eur	eur	PROPN
ejpam-3412	184	8	.	.	PUNCT
ejpam-3412	185	1	j.	j.	PROPN
ejpam-3412	185	2	pure	pure	PROPN
ejpam-3412	185	3	appl	appl	PROPN
ejpam-3412	185	4	.	.	PROPN
ejpam-3412	185	5	math	math	PROPN
ejpam-3412	185	6	,	,	PUNCT
ejpam-3412	185	7	12	12	NUM
ejpam-3412	185	8	(	(	PUNCT
ejpam-3412	185	9	2	2	NUM
ejpam-3412	185	10	)	)	PUNCT
ejpam-3412	185	11	(	(	PUNCT
ejpam-3412	185	12	2019	2019	NUM
ejpam-3412	185	13	)	)	PUNCT
ejpam-3412	185	14	,	,	PUNCT
ejpam-3412	185	15	294	294	NUM
ejpam-3412	185	16	-	-	SYM
ejpam-3412	185	17	331	331	NUM
ejpam-3412	185	18	302	302	NUM
ejpam-3412	185	19	theorem	theorem	NOUN
ejpam-3412	185	20	6	6	NUM
ejpam-3412	185	21	.	.	PUNCT
ejpam-3412	186	1	[	[	X
ejpam-3412	186	2	23	23	NUM
ejpam-3412	186	3	]	]	PUNCT
ejpam-3412	186	4	the	the	DET
ejpam-3412	186	5	union	union	NOUN
ejpam-3412	186	6	of	of	ADP
ejpam-3412	186	7	any	any	DET
ejpam-3412	186	8	nonempty	nonempty	ADJ
ejpam-3412	186	9	family	family	NOUN
ejpam-3412	186	10	of	of	ADP
ejpam-3412	186	11	fuzzy	fuzzy	ADJ
ejpam-3412	186	12	strongly	strongly	ADV
ejpam-3412	186	13	ups	up	NOUN
ejpam-3412	186	14	-	-	PUNCT
ejpam-3412	186	15	ideals	ideal	NOUN
ejpam-3412	186	16	(	(	PUNCT
ejpam-3412	186	17	resp	resp	NOUN
ejpam-3412	186	18	.	.	PUNCT
ejpam-3412	186	19	,	,	PUNCT
ejpam-3412	186	20	fuzzy	fuzzy	ADJ
ejpam-3412	186	21	strongly	strongly	ADV
ejpam-3412	186	22	upi	upi	NOUN
ejpam-3412	186	23	-	-	PUNCT
ejpam-3412	186	24	ideals	ideal	NOUN
ejpam-3412	186	25	)	)	PUNCT
ejpam-3412	186	26	of	of	ADP
ejpam-3412	186	27	an	an	DET
ejpam-3412	186	28	f	f	PROPN
ejpam-3412	186	29	-up	-up	NOUN
ejpam-3412	186	30	-	-	PUNCT
ejpam-3412	186	31	semigroup	semigroup	PROPN
ejpam-3412	186	32	is	be	AUX
ejpam-3412	186	33	also	also	ADV
ejpam-3412	186	34	a	a	DET
ejpam-3412	186	35	fuzzy	fuzzy	ADJ
ejpam-3412	186	36	strongly	strongly	ADV
ejpam-3412	186	37	ups	up	NOUN
ejpam-3412	186	38	-	-	PUNCT
ejpam-3412	186	39	ideal	ideal	NOUN
ejpam-3412	186	40	(	(	PUNCT
ejpam-3412	186	41	resp	resp	NOUN
ejpam-3412	186	42	.	.	PUNCT
ejpam-3412	186	43	,	,	PUNCT
ejpam-3412	186	44	fuzzy	fuzzy	ADJ
ejpam-3412	186	45	strongly	strongly	ADV
ejpam-3412	186	46	upi	upi	NOUN
ejpam-3412	186	47	-	-	PUNCT
ejpam-3412	186	48	ideal	ideal	NOUN
ejpam-3412	186	49	)	)	PUNCT
ejpam-3412	186	50	.	.	PUNCT
ejpam-3412	187	1	theorem	theorem	VERB
ejpam-3412	187	2	7	7	NUM
ejpam-3412	187	3	.	.	PUNCT
ejpam-3412	188	1	the	the	DET
ejpam-3412	188	2	intersection	intersection	NOUN
ejpam-3412	188	3	of	of	ADP
ejpam-3412	188	4	any	any	DET
ejpam-3412	188	5	nonempty	nonempty	ADJ
ejpam-3412	188	6	family	family	NOUN
ejpam-3412	188	7	of	of	ADP
ejpam-3412	188	8	fuzzy	fuzzy	ADJ
ejpam-3412	188	9	near	near	ADP
ejpam-3412	188	10	ups	up	NOUN
ejpam-3412	188	11	-	-	PUNCT
ejpam-3412	188	12	filters	filter	NOUN
ejpam-3412	188	13	of	of	ADP
ejpam-3412	188	14	an	an	DET
ejpam-3412	188	15	f	f	PROPN
ejpam-3412	188	16	-up	-up	NOUN
ejpam-3412	188	17	-	-	NOUN
ejpam-3412	188	18	semigroup	semigroup	NOUN
ejpam-3412	188	19	a	a	X
ejpam-3412	188	20	=	=	X
ejpam-3412	188	21	(	(	PUNCT
ejpam-3412	188	22	a	a	PRON
ejpam-3412	188	23	,	,	PUNCT
ejpam-3412	188	24	·	·	PUNCT
ejpam-3412	188	25	,	,	PUNCT
ejpam-3412	188	26	∗	∗	NOUN
ejpam-3412	188	27	,	,	PUNCT
ejpam-3412	188	28	0	0	NUM
ejpam-3412	188	29	)	)	PUNCT
ejpam-3412	188	30	is	be	AUX
ejpam-3412	188	31	also	also	ADV
ejpam-3412	188	32	a	a	DET
ejpam-3412	188	33	fuzzy	fuzzy	ADJ
ejpam-3412	188	34	near	near	ADP
ejpam-3412	188	35	ups	up	NOUN
ejpam-3412	188	36	-	-	PUNCT
ejpam-3412	188	37	filter	filter	NOUN
ejpam-3412	188	38	.	.	PUNCT
ejpam-3412	189	1	proof	proof	NOUN
ejpam-3412	189	2	.	.	PUNCT
ejpam-3412	190	1	let	let	VERB
ejpam-3412	190	2	fi	fi	NOUN
ejpam-3412	190	3	be	be	AUX
ejpam-3412	190	4	a	a	DET
ejpam-3412	190	5	fuzzy	fuzzy	ADJ
ejpam-3412	190	6	near	near	ADP
ejpam-3412	190	7	ups	up	NOUN
ejpam-3412	190	8	-	-	PUNCT
ejpam-3412	190	9	filter	filter	NOUN
ejpam-3412	190	10	of	of	ADP
ejpam-3412	190	11	an	an	DET
ejpam-3412	190	12	f	f	PROPN
ejpam-3412	190	13	-up	-up	NOUN
ejpam-3412	190	14	-	-	NOUN
ejpam-3412	190	15	semigroup	semigroup	NOUN
ejpam-3412	191	1	a	a	X
ejpam-3412	191	2	=	=	X
ejpam-3412	191	3	(	(	PUNCT
ejpam-3412	191	4	a	a	PRON
ejpam-3412	191	5	,	,	PUNCT
ejpam-3412	191	6	·	·	PUNCT
ejpam-3412	191	7	,	,	PUNCT
ejpam-3412	191	8	∗	∗	NOUN
ejpam-3412	191	9	,	,	PUNCT
ejpam-3412	191	10	0	0	NUM
ejpam-3412	191	11	)	)	PUNCT
ejpam-3412	191	12	for	for	ADP
ejpam-3412	191	13	all	all	PRON
ejpam-3412	191	14	i	i	PRON
ejpam-3412	191	15	∈	∈	PROPN
ejpam-3412	191	16	i.	i.	NOUN
ejpam-3412	191	17	then	then	ADV
ejpam-3412	191	18	f⋂	f⋂	ADP
ejpam-3412	191	19	i∈i	i∈i	ADJ
ejpam-3412	191	20	fi	fi	NOUN
ejpam-3412	191	21	(	(	PUNCT
ejpam-3412	191	22	0	0	NUM
ejpam-3412	191	23	)	)	PUNCT
ejpam-3412	191	24	=	=	PUNCT
ejpam-3412	192	1	inf{ffi(0)}i∈i	inf{ffi(0)}i∈i	X
ejpam-3412	192	2	≥	≥	NOUN
ejpam-3412	192	3	inf{ffi(x)}i∈i	inf{ffi(x)}i∈i	NOUN
ejpam-3412	192	4	=	=	SYM
ejpam-3412	192	5	f⋂	f⋂	NOUN
ejpam-3412	192	6	i∈i	i∈i	ADJ
ejpam-3412	192	7	fi	fi	NOUN
ejpam-3412	192	8	(	(	PUNCT
ejpam-3412	192	9	x	x	NOUN
ejpam-3412	192	10	)	)	PUNCT
ejpam-3412	192	11	,	,	PUNCT
ejpam-3412	192	12	f⋂	f⋂	ADP
ejpam-3412	192	13	i∈i	i∈i	ADJ
ejpam-3412	192	14	fi	fi	NOUN
ejpam-3412	192	15	(	(	PUNCT
ejpam-3412	192	16	x	x	PROPN
ejpam-3412	192	17	·	·	PUNCT
ejpam-3412	192	18	y	y	X
ejpam-3412	192	19	)	)	PUNCT
ejpam-3412	193	1	=	=	SYM
ejpam-3412	193	2	inf{ffi(x	inf{ffi(x	PROPN
ejpam-3412	193	3	·	·	PUNCT
ejpam-3412	193	4	y)}i∈i	y)}i∈i	NOUN
ejpam-3412	193	5	≥	≥	X
ejpam-3412	193	6	inf{ffi(y)}i∈i	inf{ffi(y)}i∈i	ADJ
ejpam-3412	193	7	=	=	SYM
ejpam-3412	193	8	f⋂	f⋂	NOUN
ejpam-3412	193	9	i∈i	i∈i	ADJ
ejpam-3412	193	10	fi	fi	NOUN
ejpam-3412	193	11	(	(	PUNCT
ejpam-3412	193	12	y	y	NOUN
ejpam-3412	193	13	)	)	PUNCT
ejpam-3412	193	14	,	,	PUNCT
ejpam-3412	193	15	and	and	CCONJ
ejpam-3412	193	16	f⋂	f⋂	ADP
ejpam-3412	193	17	i∈i	i∈i	ADJ
ejpam-3412	193	18	fi	fi	NOUN
ejpam-3412	193	19	(	(	PUNCT
ejpam-3412	193	20	x	x	PROPN
ejpam-3412	193	21	∗	∗	NOUN
ejpam-3412	193	22	y	y	NOUN
ejpam-3412	193	23	)	)	PUNCT
ejpam-3412	194	1	=	=	SYM
ejpam-3412	194	2	inf{ffi(x	inf{ffi(x	PROPN
ejpam-3412	194	3	∗	∗	NOUN
ejpam-3412	194	4	y)}i∈i	y)}i∈i	PROPN
ejpam-3412	194	5	≥	≥	NOUN
ejpam-3412	194	6	inf{min{ffi(x	inf{min{ffi(x	PROPN
ejpam-3412	194	7	)	)	PUNCT
ejpam-3412	194	8	,	,	PUNCT
ejpam-3412	194	9	ffi(y)}}i∈i	ffi(y)}}i∈i	NOUN
ejpam-3412	194	10	=	=	SYM
ejpam-3412	194	11	min{inf{ffi(x)}i∈i	min{inf{ffi(x)}i∈i	NUM
ejpam-3412	194	12	,	,	PUNCT
ejpam-3412	194	13	inf{ffi(y)}i∈i	inf{ffi(y)}i∈i	ADJ
ejpam-3412	194	14	}	}	PUNCT
ejpam-3412	194	15	=	=	SYM
ejpam-3412	194	16	min{f⋂	min{f⋂	PROPN
ejpam-3412	194	17	i∈i	i∈i	ADJ
ejpam-3412	194	18	fi	fi	NOUN
ejpam-3412	194	19	(	(	PUNCT
ejpam-3412	194	20	x	x	NOUN
ejpam-3412	194	21	)	)	PUNCT
ejpam-3412	194	22	,	,	PUNCT
ejpam-3412	194	23	f⋂	f⋂	ADP
ejpam-3412	194	24	i∈i	i∈i	ADJ
ejpam-3412	194	25	fi	fi	NOUN
ejpam-3412	194	26	(	(	PUNCT
ejpam-3412	194	27	y	y	NOUN
ejpam-3412	194	28	)	)	PUNCT
ejpam-3412	194	29	}	}	PUNCT
ejpam-3412	194	30	.	.	PUNCT
ejpam-3412	195	1	hence	hence	ADV
ejpam-3412	195	2	,	,	PUNCT
ejpam-3412	195	3	⋂	⋂	PROPN
ejpam-3412	195	4	i∈i	i∈i	ADJ
ejpam-3412	195	5	fi	fi	NOUN
ejpam-3412	195	6	is	be	AUX
ejpam-3412	195	7	a	a	DET
ejpam-3412	195	8	fuzzy	fuzzy	ADJ
ejpam-3412	195	9	near	near	ADP
ejpam-3412	195	10	ups	up	NOUN
ejpam-3412	195	11	-	-	PUNCT
ejpam-3412	195	12	filter	filter	NOUN
ejpam-3412	195	13	of	of	ADP
ejpam-3412	195	14	a.	a.	NOUN
ejpam-3412	195	15	the	the	DET
ejpam-3412	195	16	following	follow	VERB
ejpam-3412	195	17	example	example	NOUN
ejpam-3412	195	18	shows	show	VERB
ejpam-3412	195	19	that	that	SCONJ
ejpam-3412	195	20	the	the	DET
ejpam-3412	195	21	union	union	NOUN
ejpam-3412	195	22	of	of	ADP
ejpam-3412	195	23	two	two	NUM
ejpam-3412	195	24	fuzzy	fuzzy	ADJ
ejpam-3412	195	25	near	near	ADP
ejpam-3412	195	26	ups	up	NOUN
ejpam-3412	195	27	-	-	PUNCT
ejpam-3412	195	28	filters	filter	NOUN
ejpam-3412	195	29	of	of	ADP
ejpam-3412	195	30	an	an	DET
ejpam-3412	195	31	f	f	PROPN
ejpam-3412	195	32	-upsemigroup	-upsemigroup	NOUN
ejpam-3412	195	33	is	be	AUX
ejpam-3412	195	34	not	not	PART
ejpam-3412	195	35	a	a	DET
ejpam-3412	195	36	fuzzy	fuzzy	ADJ
ejpam-3412	195	37	near	near	ADP
ejpam-3412	195	38	ups	up	NOUN
ejpam-3412	195	39	-	-	PUNCT
ejpam-3412	195	40	filter	filter	NOUN
ejpam-3412	195	41	.	.	PUNCT
ejpam-3412	195	42	example	example	NOUN
ejpam-3412	196	1	6	6	NUM
ejpam-3412	196	2	.	.	PUNCT
ejpam-3412	197	1	by	by	ADP
ejpam-3412	197	2	cayley	cayley	ADJ
ejpam-3412	197	3	tables	table	NOUN
ejpam-3412	197	4	in	in	ADP
ejpam-3412	197	5	example	example	NOUN
ejpam-3412	197	6	3	3	NUM
ejpam-3412	197	7	,	,	PUNCT
ejpam-3412	197	8	we	we	PRON
ejpam-3412	197	9	know	know	VERB
ejpam-3412	197	10	that	that	SCONJ
ejpam-3412	197	11	a	a	DET
ejpam-3412	197	12	=	=	X
ejpam-3412	197	13	(	(	PUNCT
ejpam-3412	197	14	a	a	PRON
ejpam-3412	197	15	,	,	PUNCT
ejpam-3412	197	16	·	·	PUNCT
ejpam-3412	197	17	,	,	PUNCT
ejpam-3412	197	18	∗	∗	NOUN
ejpam-3412	197	19	,	,	PUNCT
ejpam-3412	197	20	0	0	NUM
ejpam-3412	197	21	)	)	PUNCT
ejpam-3412	197	22	is	be	AUX
ejpam-3412	197	23	an	an	DET
ejpam-3412	197	24	f	f	PROPN
ejpam-3412	197	25	-upsemigroup	-upsemigroup	NOUN
ejpam-3412	197	26	.	.	PUNCT
ejpam-3412	198	1	we	we	PRON
ejpam-3412	198	2	define	define	VERB
ejpam-3412	198	3	two	two	NUM
ejpam-3412	198	4	membership	membership	NOUN
ejpam-3412	198	5	functions	function	NOUN
ejpam-3412	198	6	ff1	ff1	NOUN
ejpam-3412	198	7	and	and	CCONJ
ejpam-3412	198	8	ff2	ff2	PROPN
ejpam-3412	198	9	as	as	SCONJ
ejpam-3412	198	10	follows	follow	VERB
ejpam-3412	198	11	:	:	PUNCT
ejpam-3412	198	12	a	a	DET
ejpam-3412	198	13	0	0	NUM
ejpam-3412	198	14	1	1	NUM
ejpam-3412	198	15	2	2	NUM
ejpam-3412	198	16	3	3	NUM
ejpam-3412	198	17	ff1	ff1	NOUN
ejpam-3412	198	18	1	1	NUM
ejpam-3412	198	19	0.7	0.7	NUM
ejpam-3412	198	20	1	1	NUM
ejpam-3412	198	21	0.5	0.5	NUM
ejpam-3412	198	22	ff2	ff2	NOUN
ejpam-3412	198	23	1	1	NUM
ejpam-3412	198	24	0.5	0.5	NUM
ejpam-3412	198	25	0.3	0.3	NUM
ejpam-3412	198	26	0.8	0.8	NUM
ejpam-3412	198	27	then	then	ADV
ejpam-3412	198	28	f1	f1	PROPN
ejpam-3412	198	29	and	and	CCONJ
ejpam-3412	198	30	f2	f2	PROPN
ejpam-3412	198	31	are	be	AUX
ejpam-3412	198	32	fuzzy	fuzzy	ADJ
ejpam-3412	198	33	near	near	ADP
ejpam-3412	198	34	ups	up	NOUN
ejpam-3412	198	35	-	-	PUNCT
ejpam-3412	198	36	filters	filter	NOUN
ejpam-3412	198	37	of	of	ADP
ejpam-3412	198	38	a	a	PRON
ejpam-3412	198	39	but	but	CCONJ
ejpam-3412	198	40	f1∪f2	f1∪f2	NOUN
ejpam-3412	198	41	is	be	AUX
ejpam-3412	198	42	not	not	PART
ejpam-3412	198	43	a	a	DET
ejpam-3412	198	44	fuzzy	fuzzy	ADJ
ejpam-3412	198	45	near	near	ADP
ejpam-3412	198	46	ups	up	NOUN
ejpam-3412	198	47	-	-	PUNCT
ejpam-3412	198	48	filter	filter	NOUN
ejpam-3412	198	49	of	of	ADP
ejpam-3412	198	50	a.	a.	NOUN
ejpam-3412	198	51	indeed	indeed	ADV
ejpam-3412	198	52	,	,	PUNCT
ejpam-3412	198	53	ff1∪f2(3∗2	ff1∪f2(3∗2	ADJ
ejpam-3412	198	54	)	)	PUNCT
ejpam-3412	198	55	=	=	SYM
ejpam-3412	198	56	ff1∪f2(1	ff1∪f2(1	PROPN
ejpam-3412	198	57	)	)	PUNCT
ejpam-3412	198	58	=	=	NOUN
ejpam-3412	198	59	0.7	0.7	NUM
ejpam-3412	198	60	�	�	PROPN
ejpam-3412	198	61	0.8	0.8	NUM
ejpam-3412	198	62	=	=	SYM
ejpam-3412	198	63	min{0.8	min{0.8	PROPN
ejpam-3412	198	64	,	,	PUNCT
ejpam-3412	198	65	1	1	NUM
ejpam-3412	198	66	}	}	PUNCT
ejpam-3412	198	67	=	=	SYM
ejpam-3412	198	68	min{ff1∪f2(3	min{ff1∪f2(3	NOUN
ejpam-3412	198	69	)	)	PUNCT
ejpam-3412	198	70	,	,	PUNCT
ejpam-3412	198	71	ff1∪f2(2	ff1∪f2(2	PROPN
ejpam-3412	198	72	)	)	PUNCT
ejpam-3412	198	73	}	}	PUNCT
ejpam-3412	198	74	.	.	PUNCT
ejpam-3412	199	1	theorem	theorem	VERB
ejpam-3412	199	2	8	8	NUM
ejpam-3412	199	3	.	.	PUNCT
ejpam-3412	200	1	the	the	DET
ejpam-3412	200	2	intersection	intersection	NOUN
ejpam-3412	200	3	of	of	ADP
ejpam-3412	200	4	any	any	DET
ejpam-3412	200	5	nonempty	nonempty	ADJ
ejpam-3412	200	6	family	family	NOUN
ejpam-3412	200	7	of	of	ADP
ejpam-3412	200	8	fuzzy	fuzzy	ADJ
ejpam-3412	200	9	near	near	ADP
ejpam-3412	200	10	upi	upi	PROPN
ejpam-3412	200	11	-	-	PUNCT
ejpam-3412	200	12	filters	filter	NOUN
ejpam-3412	200	13	of	of	ADP
ejpam-3412	200	14	an	an	DET
ejpam-3412	200	15	f	f	PROPN
ejpam-3412	200	16	-up	-up	NOUN
ejpam-3412	200	17	-	-	NOUN
ejpam-3412	200	18	semigroup	semigroup	NOUN
ejpam-3412	200	19	a	a	X
ejpam-3412	200	20	=	=	X
ejpam-3412	200	21	(	(	PUNCT
ejpam-3412	200	22	a	a	PRON
ejpam-3412	200	23	,	,	PUNCT
ejpam-3412	200	24	·	·	PUNCT
ejpam-3412	200	25	,	,	PUNCT
ejpam-3412	200	26	∗	∗	NOUN
ejpam-3412	200	27	,	,	PUNCT
ejpam-3412	200	28	0	0	NUM
ejpam-3412	200	29	)	)	PUNCT
ejpam-3412	200	30	is	be	AUX
ejpam-3412	200	31	also	also	ADV
ejpam-3412	200	32	a	a	DET
ejpam-3412	200	33	fuzzy	fuzzy	ADJ
ejpam-3412	200	34	near	near	ADP
ejpam-3412	200	35	upi	upi	NOUN
ejpam-3412	200	36	-	-	PUNCT
ejpam-3412	200	37	filter	filter	NOUN
ejpam-3412	200	38	.	.	PUNCT
ejpam-3412	201	1	proof	proof	NOUN
ejpam-3412	201	2	.	.	PUNCT
ejpam-3412	202	1	let	let	VERB
ejpam-3412	202	2	fi	fi	NOUN
ejpam-3412	202	3	be	be	AUX
ejpam-3412	202	4	a	a	DET
ejpam-3412	202	5	fuzzy	fuzzy	ADJ
ejpam-3412	202	6	near	near	ADP
ejpam-3412	202	7	upi	upi	NOUN
ejpam-3412	202	8	-	-	PUNCT
ejpam-3412	202	9	filter	filter	NOUN
ejpam-3412	202	10	of	of	ADP
ejpam-3412	202	11	an	an	DET
ejpam-3412	202	12	f	f	PROPN
ejpam-3412	202	13	-up	-up	NOUN
ejpam-3412	202	14	-	-	NOUN
ejpam-3412	202	15	semigroup	semigroup	NOUN
ejpam-3412	203	1	a	a	X
ejpam-3412	203	2	=	=	X
ejpam-3412	203	3	(	(	PUNCT
ejpam-3412	203	4	a	a	PRON
ejpam-3412	203	5	,	,	PUNCT
ejpam-3412	203	6	·	·	PUNCT
ejpam-3412	203	7	,	,	PUNCT
ejpam-3412	203	8	∗	∗	NOUN
ejpam-3412	203	9	,	,	PUNCT
ejpam-3412	203	10	0	0	NUM
ejpam-3412	203	11	)	)	PUNCT
ejpam-3412	203	12	for	for	ADP
ejpam-3412	203	13	all	all	PRON
ejpam-3412	203	14	i	i	PRON
ejpam-3412	203	15	∈	∈	PROPN
ejpam-3412	203	16	i.	i.	NOUN
ejpam-3412	203	17	then	then	ADV
ejpam-3412	203	18	,	,	PUNCT
ejpam-3412	203	19	by	by	ADP
ejpam-3412	203	20	the	the	DET
ejpam-3412	203	21	proof	proof	NOUN
ejpam-3412	203	22	of	of	ADP
ejpam-3412	203	23	theorem	theorem	NOUN
ejpam-3412	203	24	7	7	NUM
ejpam-3412	203	25	,	,	PUNCT
ejpam-3412	203	26	we	we	PRON
ejpam-3412	203	27	have	have	VERB
ejpam-3412	203	28	f⋂	f⋂	NOUN
ejpam-3412	203	29	i∈i	i∈i	ADJ
ejpam-3412	203	30	fi	fi	NOUN
ejpam-3412	203	31	(	(	PUNCT
ejpam-3412	203	32	0	0	NUM
ejpam-3412	203	33	)	)	PUNCT
ejpam-3412	203	34	≥	≥	NOUN
ejpam-3412	203	35	f⋂	f⋂	ADP
ejpam-3412	203	36	i∈i	i∈i	ADJ
ejpam-3412	203	37	fi	fi	NOUN
ejpam-3412	203	38	(	(	PUNCT
ejpam-3412	203	39	x	x	NOUN
ejpam-3412	203	40	)	)	PUNCT
ejpam-3412	203	41	and	and	CCONJ
ejpam-3412	203	42	f⋂	f⋂	ADP
ejpam-3412	203	43	i∈i	i∈i	ADJ
ejpam-3412	203	44	fi	fi	NOUN
ejpam-3412	203	45	(	(	PUNCT
ejpam-3412	203	46	x·y	x·y	PROPN
ejpam-3412	203	47	)	)	PUNCT
ejpam-3412	203	48	≥	≥	PROPN
ejpam-3412	203	49	f⋂	f⋂	ADP
ejpam-3412	203	50	i∈i	i∈i	ADJ
ejpam-3412	203	51	fi	fi	NOUN
ejpam-3412	203	52	(	(	PUNCT
ejpam-3412	203	53	y	y	NOUN
ejpam-3412	203	54	)	)	PUNCT
ejpam-3412	203	55	.	.	PUNCT
ejpam-3412	204	1	thus	thus	ADV
ejpam-3412	204	2	f⋂	f⋂	ADP
ejpam-3412	204	3	i∈i	i∈i	ADJ
ejpam-3412	204	4	fi	fi	NOUN
ejpam-3412	204	5	(	(	PUNCT
ejpam-3412	204	6	x	x	PROPN
ejpam-3412	204	7	∗	∗	NOUN
ejpam-3412	204	8	y	y	NOUN
ejpam-3412	204	9	)	)	PUNCT
ejpam-3412	204	10	=	=	SYM
ejpam-3412	204	11	inf{ffi(x	inf{ffi(x	PROPN
ejpam-3412	204	12	∗	∗	NOUN
ejpam-3412	204	13	y)}i∈i	y)}i∈i	PROPN
ejpam-3412	204	14	≥	≥	NOUN
ejpam-3412	204	15	inf{max{ffi(x	inf{max{ffi(x	PROPN
ejpam-3412	204	16	)	)	PUNCT
ejpam-3412	204	17	,	,	PUNCT
ejpam-3412	204	18	ffi(y)}}i∈i	ffi(y)}}i∈i	X
ejpam-3412	204	19	≥	≥	X
ejpam-3412	204	20	max{inf{ffi(x)}i∈i	max{inf{ffi(x)}i∈i	NUM
ejpam-3412	204	21	,	,	PUNCT
ejpam-3412	204	22	inf{ffi(y)}i∈i	inf{ffi(y)}i∈i	ADJ
ejpam-3412	204	23	}	}	PUNCT
ejpam-3412	204	24	=	=	SYM
ejpam-3412	204	25	max{f⋂	max{f⋂	NOUN
ejpam-3412	204	26	i∈i	i∈i	ADJ
ejpam-3412	204	27	fi	fi	NOUN
ejpam-3412	204	28	(	(	PUNCT
ejpam-3412	204	29	x	x	NOUN
ejpam-3412	204	30	)	)	PUNCT
ejpam-3412	204	31	,	,	PUNCT
ejpam-3412	204	32	f⋂	f⋂	ADP
ejpam-3412	204	33	i∈i	i∈i	ADJ
ejpam-3412	204	34	fi	fi	NOUN
ejpam-3412	204	35	(	(	PUNCT
ejpam-3412	204	36	y	y	NOUN
ejpam-3412	204	37	)	)	PUNCT
ejpam-3412	204	38	}	}	PUNCT
ejpam-3412	204	39	.	.	PUNCT
ejpam-3412	205	1	hence	hence	ADV
ejpam-3412	205	2	,	,	PUNCT
ejpam-3412	205	3	⋂	⋂	PROPN
ejpam-3412	205	4	i∈i	i∈i	ADJ
ejpam-3412	205	5	fi	fi	NOUN
ejpam-3412	205	6	is	be	AUX
ejpam-3412	205	7	a	a	DET
ejpam-3412	205	8	fuzzy	fuzzy	ADJ
ejpam-3412	205	9	near	near	ADP
ejpam-3412	205	10	upi	upi	NOUN
ejpam-3412	205	11	-	-	PUNCT
ejpam-3412	205	12	filter	filter	NOUN
ejpam-3412	205	13	of	of	ADP
ejpam-3412	205	14	a.	a.	PROPN
ejpam-3412	205	15	a.	a.	PROPN
ejpam-3412	205	16	satirad	satirad	PROPN
ejpam-3412	205	17	,	,	PUNCT
ejpam-3412	205	18	a.	a.	NOUN
ejpam-3412	205	19	iampan	iampan	PROPN
ejpam-3412	205	20	/	/	SYM
ejpam-3412	205	21	eur	eur	PROPN
ejpam-3412	205	22	.	.	PUNCT
ejpam-3412	206	1	j.	j.	PROPN
ejpam-3412	206	2	pure	pure	PROPN
ejpam-3412	206	3	appl	appl	PROPN
ejpam-3412	206	4	.	.	PROPN
ejpam-3412	206	5	math	math	PROPN
ejpam-3412	206	6	,	,	PUNCT
ejpam-3412	206	7	12	12	NUM
ejpam-3412	206	8	(	(	PUNCT
ejpam-3412	206	9	2	2	NUM
ejpam-3412	206	10	)	)	PUNCT
ejpam-3412	206	11	(	(	PUNCT
ejpam-3412	206	12	2019	2019	NUM
ejpam-3412	206	13	)	)	PUNCT
ejpam-3412	206	14	,	,	PUNCT
ejpam-3412	206	15	294	294	NUM
ejpam-3412	206	16	-	-	SYM
ejpam-3412	206	17	331	331	NUM
ejpam-3412	206	18	303	303	NUM
ejpam-3412	206	19	theorem	theorem	NOUN
ejpam-3412	206	20	9	9	NUM
ejpam-3412	206	21	.	.	PUNCT
ejpam-3412	207	1	the	the	DET
ejpam-3412	207	2	union	union	NOUN
ejpam-3412	207	3	of	of	ADP
ejpam-3412	207	4	any	any	DET
ejpam-3412	207	5	nonempty	nonempty	ADJ
ejpam-3412	207	6	family	family	NOUN
ejpam-3412	207	7	of	of	ADP
ejpam-3412	207	8	fuzzy	fuzzy	ADJ
ejpam-3412	207	9	near	near	ADP
ejpam-3412	207	10	upi	upi	PROPN
ejpam-3412	207	11	-	-	PUNCT
ejpam-3412	207	12	filters	filter	NOUN
ejpam-3412	207	13	of	of	ADP
ejpam-3412	207	14	an	an	DET
ejpam-3412	207	15	f	f	PROPN
ejpam-3412	207	16	-upsemigroup	-upsemigroup	PROPN
ejpam-3412	207	17	a	a	X
ejpam-3412	207	18	=	=	X
ejpam-3412	207	19	(	(	PUNCT
ejpam-3412	207	20	a	a	PRON
ejpam-3412	207	21	,	,	PUNCT
ejpam-3412	207	22	·	·	PUNCT
ejpam-3412	207	23	,	,	PUNCT
ejpam-3412	207	24	∗	∗	NOUN
ejpam-3412	207	25	,	,	PUNCT
ejpam-3412	207	26	0	0	NUM
ejpam-3412	207	27	)	)	PUNCT
ejpam-3412	207	28	is	be	AUX
ejpam-3412	207	29	also	also	ADV
ejpam-3412	207	30	a	a	DET
ejpam-3412	207	31	fuzzy	fuzzy	ADJ
ejpam-3412	207	32	near	near	ADP
ejpam-3412	207	33	upi	upi	NOUN
ejpam-3412	207	34	-	-	PUNCT
ejpam-3412	207	35	filter	filter	NOUN
ejpam-3412	207	36	.	.	PUNCT
ejpam-3412	208	1	proof	proof	NOUN
ejpam-3412	208	2	.	.	PUNCT
ejpam-3412	209	1	let	let	VERB
ejpam-3412	209	2	fi	fi	NOUN
ejpam-3412	209	3	be	be	AUX
ejpam-3412	209	4	a	a	DET
ejpam-3412	209	5	fuzzy	fuzzy	ADJ
ejpam-3412	209	6	near	near	ADP
ejpam-3412	209	7	upi	upi	NOUN
ejpam-3412	209	8	-	-	PUNCT
ejpam-3412	209	9	filter	filter	NOUN
ejpam-3412	209	10	of	of	ADP
ejpam-3412	209	11	an	an	DET
ejpam-3412	209	12	f	f	PROPN
ejpam-3412	209	13	-up	-up	NOUN
ejpam-3412	209	14	-	-	NOUN
ejpam-3412	209	15	semigroup	semigroup	NOUN
ejpam-3412	210	1	a	a	X
ejpam-3412	210	2	=	=	X
ejpam-3412	210	3	(	(	PUNCT
ejpam-3412	210	4	a	a	PRON
ejpam-3412	210	5	,	,	PUNCT
ejpam-3412	210	6	·	·	PUNCT
ejpam-3412	210	7	,	,	PUNCT
ejpam-3412	210	8	∗	∗	NOUN
ejpam-3412	210	9	,	,	PUNCT
ejpam-3412	210	10	0	0	NUM
ejpam-3412	210	11	)	)	PUNCT
ejpam-3412	210	12	for	for	ADP
ejpam-3412	210	13	all	all	PRON
ejpam-3412	210	14	i	i	PRON
ejpam-3412	210	15	∈	∈	PROPN
ejpam-3412	210	16	i.	i.	NOUN
ejpam-3412	210	17	then	then	ADV
ejpam-3412	210	18	f⋃	f⋃	AUX
ejpam-3412	210	19	i∈i	i∈i	ADJ
ejpam-3412	210	20	fi	fi	NOUN
ejpam-3412	210	21	(	(	PUNCT
ejpam-3412	210	22	0	0	NUM
ejpam-3412	210	23	)	)	PUNCT
ejpam-3412	210	24	=	=	PUNCT
ejpam-3412	211	1	sup{ffi(0)}i∈i	sup{ffi(0)}i∈i	ADJ
ejpam-3412	211	2	≥	≥	NOUN
ejpam-3412	211	3	sup{ffi(x)}i∈i	sup{ffi(x)}i∈i	NOUN
ejpam-3412	211	4	=	=	SYM
ejpam-3412	211	5	f⋃	f⋃	NOUN
ejpam-3412	211	6	i∈i	i∈i	ADJ
ejpam-3412	211	7	fi	fi	NOUN
ejpam-3412	211	8	(	(	PUNCT
ejpam-3412	211	9	x	x	NOUN
ejpam-3412	211	10	)	)	PUNCT
ejpam-3412	211	11	,	,	PUNCT
ejpam-3412	211	12	f⋃	f⋃	X
ejpam-3412	211	13	i∈i	i∈i	ADJ
ejpam-3412	211	14	fi	fi	NOUN
ejpam-3412	211	15	(	(	PUNCT
ejpam-3412	211	16	x	x	PROPN
ejpam-3412	211	17	·	·	PUNCT
ejpam-3412	211	18	y	y	X
ejpam-3412	211	19	)	)	PUNCT
ejpam-3412	212	1	=	=	SYM
ejpam-3412	212	2	sup{ffi(x	sup{ffi(x	NOUN
ejpam-3412	212	3	·	·	PUNCT
ejpam-3412	212	4	y)}i∈i	y)}i∈i	NOUN
ejpam-3412	212	5	≥	≥	NOUN
ejpam-3412	212	6	sup{ffi(y)}i∈i	sup{ffi(y)}i∈i	NOUN
ejpam-3412	212	7	=	=	SYM
ejpam-3412	212	8	f⋃	f⋃	NOUN
ejpam-3412	212	9	i∈i	i∈i	ADJ
ejpam-3412	212	10	fi	fi	NOUN
ejpam-3412	212	11	(	(	PUNCT
ejpam-3412	212	12	y	y	NOUN
ejpam-3412	212	13	)	)	PUNCT
ejpam-3412	212	14	,	,	PUNCT
ejpam-3412	212	15	and	and	CCONJ
ejpam-3412	212	16	f⋃	f⋃	AUX
ejpam-3412	212	17	i∈i	i∈i	ADJ
ejpam-3412	212	18	fi	fi	NOUN
ejpam-3412	212	19	(	(	PUNCT
ejpam-3412	212	20	x	x	PROPN
ejpam-3412	212	21	∗	∗	NOUN
ejpam-3412	212	22	y	y	NOUN
ejpam-3412	212	23	)	)	PUNCT
ejpam-3412	213	1	=	=	SYM
ejpam-3412	213	2	sup{ffi(x	sup{ffi(x	NOUN
ejpam-3412	213	3	∗	∗	NOUN
ejpam-3412	213	4	y)}i∈i	y)}i∈i	PROPN
ejpam-3412	213	5	≥	≥	NOUN
ejpam-3412	213	6	sup{max{ffi(x	sup{max{ffi(x	PROPN
ejpam-3412	213	7	)	)	PUNCT
ejpam-3412	213	8	,	,	PUNCT
ejpam-3412	213	9	ffi(y)}}i∈i	ffi(y)}}i∈i	NOUN
ejpam-3412	213	10	=	=	SYM
ejpam-3412	213	11	max{sup{ffi(x)}i∈i	max{sup{ffi(x)}i∈i	NOUN
ejpam-3412	213	12	,	,	PUNCT
ejpam-3412	213	13	sup{ffi(y)}i∈i	sup{ffi(y)}i∈i	VERB
ejpam-3412	213	14	}	}	PUNCT
ejpam-3412	213	15	=	=	SYM
ejpam-3412	213	16	max{f⋃	max{f⋃	NOUN
ejpam-3412	213	17	i∈i	i∈i	ADJ
ejpam-3412	213	18	fi	fi	NOUN
ejpam-3412	213	19	(	(	PUNCT
ejpam-3412	213	20	x	x	NOUN
ejpam-3412	213	21	)	)	PUNCT
ejpam-3412	213	22	,	,	PUNCT
ejpam-3412	213	23	f⋃	f⋃	X
ejpam-3412	213	24	i∈i	i∈i	ADJ
ejpam-3412	213	25	fi	fi	NOUN
ejpam-3412	213	26	(	(	PUNCT
ejpam-3412	213	27	y	y	NOUN
ejpam-3412	213	28	)	)	PUNCT
ejpam-3412	213	29	}	}	PUNCT
ejpam-3412	213	30	.	.	PUNCT
ejpam-3412	214	1	hence	hence	ADV
ejpam-3412	214	2	,	,	PUNCT
ejpam-3412	214	3	⋃	⋃	ADP
ejpam-3412	214	4	i∈i	i∈i	ADJ
ejpam-3412	214	5	fi	fi	NOUN
ejpam-3412	214	6	is	be	AUX
ejpam-3412	214	7	a	a	DET
ejpam-3412	214	8	fuzzy	fuzzy	ADJ
ejpam-3412	214	9	near	near	ADP
ejpam-3412	214	10	upi	upi	NOUN
ejpam-3412	214	11	-	-	PUNCT
ejpam-3412	214	12	filter	filter	NOUN
ejpam-3412	214	13	of	of	ADP
ejpam-3412	214	14	a.	a.	NOUN
ejpam-3412	214	15	2	2	NUM
ejpam-3412	214	16	.	.	PUNCT
ejpam-3412	215	1	properties	property	NOUN
ejpam-3412	215	2	of	of	ADP
ejpam-3412	215	3	fuzzy	fuzzy	ADJ
ejpam-3412	215	4	sets	set	NOUN
ejpam-3412	215	5	in	in	ADP
ejpam-3412	215	6	up	up	ADV
ejpam-3412	215	7	-	-	PUNCT
ejpam-3412	215	8	algebras	algebras	NOUN
ejpam-3412	215	9	in	in	ADP
ejpam-3412	215	10	this	this	DET
ejpam-3412	215	11	section	section	NOUN
ejpam-3412	215	12	,	,	PUNCT
ejpam-3412	215	13	we	we	PRON
ejpam-3412	215	14	shall	shall	AUX
ejpam-3412	215	15	let	let	VERB
ejpam-3412	215	16	a	a	PRON
ejpam-3412	215	17	be	be	AUX
ejpam-3412	215	18	a	a	DET
ejpam-3412	215	19	up	up	NOUN
ejpam-3412	215	20	-	-	PUNCT
ejpam-3412	215	21	algebra	algebra	NOUN
ejpam-3412	215	22	a	a	PRON
ejpam-3412	215	23	=	=	X
ejpam-3412	215	24	(	(	PUNCT
ejpam-3412	215	25	a	a	PRON
ejpam-3412	215	26	,	,	PUNCT
ejpam-3412	215	27	·	·	PUNCT
ejpam-3412	215	28	,	,	PUNCT
ejpam-3412	215	29	0	0	NUM
ejpam-3412	215	30	)	)	PUNCT
ejpam-3412	215	31	and	and	CCONJ
ejpam-3412	215	32	find	find	VERB
ejpam-3412	215	33	some	some	DET
ejpam-3412	215	34	properties	property	NOUN
ejpam-3412	215	35	of	of	ADP
ejpam-3412	215	36	fuzzy	fuzzy	ADJ
ejpam-3412	215	37	sets	set	NOUN
ejpam-3412	215	38	in	in	ADP
ejpam-3412	215	39	up	up	ADP
ejpam-3412	215	40	-	-	PUNCT
ejpam-3412	215	41	algebras	algebras	X
ejpam-3412	215	42	.	.	PUNCT
ejpam-3412	216	1	proposition	proposition	NOUN
ejpam-3412	216	2	1	1	NUM
ejpam-3412	216	3	.	.	PUNCT
ejpam-3412	217	1	[	[	X
ejpam-3412	217	2	25	25	NUM
ejpam-3412	217	3	]	]	X
ejpam-3412	217	4	if	if	SCONJ
ejpam-3412	217	5	f	f	PROPN
ejpam-3412	217	6	is	be	AUX
ejpam-3412	217	7	a	a	DET
ejpam-3412	217	8	fuzzy	fuzzy	ADJ
ejpam-3412	217	9	up	up	NOUN
ejpam-3412	217	10	-	-	PUNCT
ejpam-3412	217	11	subalgebra	subalgebra	NOUN
ejpam-3412	217	12	of	of	ADP
ejpam-3412	217	13	a	a	PRON
ejpam-3412	217	14	,	,	PUNCT
ejpam-3412	217	15	then	then	ADV
ejpam-3412	217	16	(	(	PUNCT
ejpam-3412	217	17	∀x	∀x	X
ejpam-3412	217	18	∈	∈	PROPN
ejpam-3412	217	19	a)(ff(0	a)(ff(0	NOUN
ejpam-3412	217	20	)	)	PUNCT
ejpam-3412	217	21	≥	≥	NOUN
ejpam-3412	217	22	ff(x	ff(x	NOUN
ejpam-3412	217	23	)	)	PUNCT
ejpam-3412	217	24	)	)	PUNCT
ejpam-3412	217	25	.	.	PUNCT
ejpam-3412	218	1	(	(	PUNCT
ejpam-3412	218	2	2.1	2.1	NUM
ejpam-3412	218	3	)	)	PUNCT
ejpam-3412	218	4	proposition	proposition	NOUN
ejpam-3412	218	5	2	2	NUM
ejpam-3412	218	6	.	.	PUNCT
ejpam-3412	219	1	[	[	X
ejpam-3412	219	2	23	23	NUM
ejpam-3412	219	3	]	]	X
ejpam-3412	219	4	if	if	SCONJ
ejpam-3412	219	5	f	f	PROPN
ejpam-3412	219	6	is	be	AUX
ejpam-3412	219	7	a	a	DET
ejpam-3412	219	8	fuzzy	fuzzy	ADJ
ejpam-3412	219	9	up	up	NOUN
ejpam-3412	219	10	-	-	PUNCT
ejpam-3412	219	11	filter	filter	NOUN
ejpam-3412	219	12	of	of	ADP
ejpam-3412	219	13	a	a	PRON
ejpam-3412	219	14	,	,	PUNCT
ejpam-3412	219	15	then	then	ADV
ejpam-3412	219	16	(	(	PUNCT
ejpam-3412	219	17	∀x	∀x	X
ejpam-3412	219	18	,	,	PUNCT
ejpam-3412	219	19	y	y	PROPN
ejpam-3412	219	20	∈	∈	PROPN
ejpam-3412	219	21	a)(x	a)(x	NOUN
ejpam-3412	219	22	≤	≤	NUM
ejpam-3412	219	23	y	y	PROPN
ejpam-3412	219	24	⇒	⇒	NOUN
ejpam-3412	219	25	ff(x	ff(x	NOUN
ejpam-3412	219	26	)	)	PUNCT
ejpam-3412	219	27	≤	≤	NOUN
ejpam-3412	219	28	ff(y	ff(y	NOUN
ejpam-3412	219	29	)	)	PUNCT
ejpam-3412	219	30	)	)	PUNCT
ejpam-3412	219	31	.	.	PUNCT
ejpam-3412	220	1	(	(	PUNCT
ejpam-3412	220	2	2.2	2.2	NUM
ejpam-3412	220	3	)	)	PUNCT
ejpam-3412	220	4	proposition	proposition	NOUN
ejpam-3412	220	5	3	3	NUM
ejpam-3412	220	6	.	.	PUNCT
ejpam-3412	221	1	if	if	SCONJ
ejpam-3412	221	2	f	f	PROPN
ejpam-3412	221	3	is	be	AUX
ejpam-3412	221	4	a	a	DET
ejpam-3412	221	5	fuzzy	fuzzy	ADJ
ejpam-3412	221	6	set	set	NOUN
ejpam-3412	221	7	in	in	ADP
ejpam-3412	221	8	a	a	DET
ejpam-3412	221	9	satisfying	satisfying	NOUN
ejpam-3412	221	10	the	the	DET
ejpam-3412	221	11	condition	condition	NOUN
ejpam-3412	221	12	(	(	PUNCT
ejpam-3412	221	13	∀x	∀x	X
ejpam-3412	221	14	,	,	PUNCT
ejpam-3412	221	15	y	y	PROPN
ejpam-3412	221	16	,	,	PUNCT
ejpam-3412	221	17	z	z	PROPN
ejpam-3412	221	18	∈	∈	PROPN
ejpam-3412	221	19	a)(z	a)(z	PROPN
ejpam-3412	221	20	≤	≤	NUM
ejpam-3412	221	21	x⇒	x⇒	PUNCT
ejpam-3412	221	22	ff(x	ff(x	PRON
ejpam-3412	221	23	·	·	PUNCT
ejpam-3412	221	24	y	y	X
ejpam-3412	221	25	)	)	PUNCT
ejpam-3412	221	26	≥	≥	NOUN
ejpam-3412	221	27	min{ff(z	min{ff(z	NOUN
ejpam-3412	221	28	)	)	PUNCT
ejpam-3412	221	29	,	,	PUNCT
ejpam-3412	221	30	ff(y	ff(y	NUM
ejpam-3412	221	31	)	)	PUNCT
ejpam-3412	221	32	}	}	PUNCT
ejpam-3412	221	33	)	)	PUNCT
ejpam-3412	221	34	,	,	PUNCT
ejpam-3412	221	35	(	(	PUNCT
ejpam-3412	221	36	2.3	2.3	NUM
ejpam-3412	221	37	)	)	PUNCT
ejpam-3412	221	38	then	then	ADV
ejpam-3412	221	39	f	f	PROPN
ejpam-3412	221	40	is	be	AUX
ejpam-3412	221	41	a	a	DET
ejpam-3412	221	42	fuzzy	fuzzy	ADJ
ejpam-3412	221	43	up	up	NOUN
ejpam-3412	221	44	-	-	PUNCT
ejpam-3412	221	45	subalgebra	subalgebra	NOUN
ejpam-3412	221	46	of	of	ADP
ejpam-3412	221	47	a.	a.	NOUN
ejpam-3412	221	48	proof	proof	NOUN
ejpam-3412	221	49	.	.	PUNCT
ejpam-3412	222	1	let	let	VERB
ejpam-3412	222	2	x	x	PRON
ejpam-3412	222	3	,	,	PUNCT
ejpam-3412	222	4	y	y	PROPN
ejpam-3412	222	5	∈	∈	PROPN
ejpam-3412	222	6	a.	a.	NOUN
ejpam-3412	222	7	by	by	ADP
ejpam-3412	222	8	(	(	PUNCT
ejpam-3412	222	9	1.1	1.1	NUM
ejpam-3412	222	10	)	)	PUNCT
ejpam-3412	222	11	,	,	PUNCT
ejpam-3412	222	12	we	we	PRON
ejpam-3412	222	13	have	have	VERB
ejpam-3412	222	14	x	x	NOUN
ejpam-3412	222	15	≤	≤	NUM
ejpam-3412	222	16	x.	x.	NOUN
ejpam-3412	223	1	it	it	PRON
ejpam-3412	223	2	follows	follow	VERB
ejpam-3412	223	3	from	from	ADP
ejpam-3412	223	4	(	(	PUNCT
ejpam-3412	223	5	2.3	2.3	NUM
ejpam-3412	223	6	)	)	PUNCT
ejpam-3412	223	7	that	that	PRON
ejpam-3412	223	8	ff(x	ff(x	VERB
ejpam-3412	223	9	·	·	PUNCT
ejpam-3412	223	10	y	y	X
ejpam-3412	223	11	)	)	PUNCT
ejpam-3412	223	12	≥	≥	PROPN
ejpam-3412	223	13	min{ff(x	min{ff(x	PROPN
ejpam-3412	223	14	)	)	PUNCT
ejpam-3412	223	15	,	,	PUNCT
ejpam-3412	223	16	ff(y	ff(y	NUM
ejpam-3412	223	17	)	)	PUNCT
ejpam-3412	223	18	}	}	PUNCT
ejpam-3412	223	19	.	.	PUNCT
ejpam-3412	224	1	hence	hence	ADV
ejpam-3412	224	2	,	,	PUNCT
ejpam-3412	224	3	f	f	PROPN
ejpam-3412	224	4	is	be	AUX
ejpam-3412	224	5	a	a	DET
ejpam-3412	224	6	fuzzy	fuzzy	ADJ
ejpam-3412	224	7	up	up	NOUN
ejpam-3412	224	8	-	-	PUNCT
ejpam-3412	224	9	subalgebra	subalgebra	NOUN
ejpam-3412	224	10	of	of	ADP
ejpam-3412	224	11	a.	a.	NOUN
ejpam-3412	224	12	theorem	theorem	NOUN
ejpam-3412	224	13	10	10	NUM
ejpam-3412	224	14	.	.	PUNCT
ejpam-3412	225	1	if	if	SCONJ
ejpam-3412	225	2	f	f	PROPN
ejpam-3412	225	3	is	be	AUX
ejpam-3412	225	4	a	a	DET
ejpam-3412	225	5	fuzzy	fuzzy	ADJ
ejpam-3412	225	6	set	set	NOUN
ejpam-3412	225	7	in	in	ADP
ejpam-3412	225	8	a	a	DET
ejpam-3412	225	9	satisfying	satisfying	NOUN
ejpam-3412	225	10	the	the	DET
ejpam-3412	225	11	condition	condition	NOUN
ejpam-3412	225	12	(	(	PUNCT
ejpam-3412	225	13	2.3	2.3	NUM
ejpam-3412	225	14	)	)	PUNCT
ejpam-3412	225	15	,	,	PUNCT
ejpam-3412	225	16	then	then	ADV
ejpam-3412	225	17	f	f	PROPN
ejpam-3412	225	18	satisfies	satisfy	VERB
ejpam-3412	225	19	the	the	DET
ejpam-3412	225	20	condition	condition	NOUN
ejpam-3412	225	21	(	(	PUNCT
ejpam-3412	225	22	2.1	2.1	NUM
ejpam-3412	225	23	)	)	PUNCT
ejpam-3412	225	24	.	.	PUNCT
ejpam-3412	226	1	proof	proof	NOUN
ejpam-3412	226	2	.	.	PUNCT
ejpam-3412	227	1	it	it	PRON
ejpam-3412	227	2	is	be	AUX
ejpam-3412	227	3	straightforward	straightforward	ADJ
ejpam-3412	227	4	by	by	ADP
ejpam-3412	227	5	proposition	proposition	NOUN
ejpam-3412	227	6	3	3	NUM
ejpam-3412	227	7	.	.	PUNCT
ejpam-3412	228	1	the	the	DET
ejpam-3412	228	2	following	follow	VERB
ejpam-3412	228	3	example	example	NOUN
ejpam-3412	228	4	shows	show	VERB
ejpam-3412	228	5	that	that	SCONJ
ejpam-3412	228	6	the	the	DET
ejpam-3412	228	7	converse	converse	NOUN
ejpam-3412	228	8	of	of	ADP
ejpam-3412	228	9	theorem	theorem	NOUN
ejpam-3412	228	10	10	10	NUM
ejpam-3412	228	11	is	be	AUX
ejpam-3412	228	12	not	not	PART
ejpam-3412	228	13	true	true	ADJ
ejpam-3412	228	14	.	.	PUNCT
ejpam-3412	229	1	a.	a.	PROPN
ejpam-3412	229	2	satirad	satirad	PROPN
ejpam-3412	229	3	,	,	PUNCT
ejpam-3412	229	4	a.	a.	NOUN
ejpam-3412	229	5	iampan	iampan	PROPN
ejpam-3412	229	6	/	/	SYM
ejpam-3412	229	7	eur	eur	PROPN
ejpam-3412	229	8	.	.	PUNCT
ejpam-3412	230	1	j.	j.	PROPN
ejpam-3412	230	2	pure	pure	PROPN
ejpam-3412	230	3	appl	appl	PROPN
ejpam-3412	230	4	.	.	PROPN
ejpam-3412	230	5	math	math	PROPN
ejpam-3412	230	6	,	,	PUNCT
ejpam-3412	230	7	12	12	NUM
ejpam-3412	230	8	(	(	PUNCT
ejpam-3412	230	9	2	2	NUM
ejpam-3412	230	10	)	)	PUNCT
ejpam-3412	230	11	(	(	PUNCT
ejpam-3412	230	12	2019	2019	NUM
ejpam-3412	230	13	)	)	PUNCT
ejpam-3412	230	14	,	,	PUNCT
ejpam-3412	230	15	294	294	NUM
ejpam-3412	230	16	-	-	SYM
ejpam-3412	230	17	331	331	NUM
ejpam-3412	230	18	304	304	NUM
ejpam-3412	230	19	example	example	NOUN
ejpam-3412	230	20	7	7	NUM
ejpam-3412	230	21	.	.	PUNCT
ejpam-3412	231	1	let	let	VERB
ejpam-3412	231	2	a	a	PRON
ejpam-3412	231	3	=	=	PUNCT
ejpam-3412	231	4	{	{	PUNCT
ejpam-3412	231	5	0	0	NUM
ejpam-3412	231	6	,	,	PUNCT
ejpam-3412	231	7	1	1	NUM
ejpam-3412	231	8	,	,	PUNCT
ejpam-3412	231	9	2	2	NUM
ejpam-3412	231	10	,	,	PUNCT
ejpam-3412	231	11	3	3	NUM
ejpam-3412	231	12	}	}	PUNCT
ejpam-3412	231	13	be	be	AUX
ejpam-3412	231	14	a	a	DET
ejpam-3412	231	15	set	set	NOUN
ejpam-3412	231	16	with	with	ADP
ejpam-3412	231	17	a	a	DET
ejpam-3412	231	18	binary	binary	ADJ
ejpam-3412	231	19	operation	operation	NOUN
ejpam-3412	231	20	·	·	PUNCT
ejpam-3412	231	21	defined	define	VERB
ejpam-3412	231	22	by	by	ADP
ejpam-3412	231	23	the	the	DET
ejpam-3412	231	24	following	following	ADJ
ejpam-3412	231	25	cayley	cayley	ADJ
ejpam-3412	231	26	table	table	NOUN
ejpam-3412	231	27	:	:	PUNCT
ejpam-3412	231	28	·	·	PUNCT
ejpam-3412	231	29	0	0	NUM
ejpam-3412	232	1	1	1	NUM
ejpam-3412	232	2	2	2	NUM
ejpam-3412	232	3	3	3	NUM
ejpam-3412	232	4	0	0	NUM
ejpam-3412	232	5	0	0	NUM
ejpam-3412	232	6	1	1	NUM
ejpam-3412	232	7	2	2	NUM
ejpam-3412	232	8	3	3	NUM
ejpam-3412	232	9	1	1	NUM
ejpam-3412	232	10	0	0	NUM
ejpam-3412	232	11	0	0	NUM
ejpam-3412	232	12	2	2	NUM
ejpam-3412	232	13	2	2	NUM
ejpam-3412	232	14	2	2	NUM
ejpam-3412	232	15	0	0	NUM
ejpam-3412	232	16	1	1	NUM
ejpam-3412	232	17	0	0	NUM
ejpam-3412	232	18	2	2	NUM
ejpam-3412	232	19	3	3	NUM
ejpam-3412	232	20	0	0	NUM
ejpam-3412	232	21	1	1	NUM
ejpam-3412	232	22	0	0	NUM
ejpam-3412	232	23	0	0	NUM
ejpam-3412	232	24	then	then	ADV
ejpam-3412	232	25	a	a	PRON
ejpam-3412	232	26	=	=	X
ejpam-3412	232	27	(	(	PUNCT
ejpam-3412	232	28	a	a	PRON
ejpam-3412	232	29	,	,	PUNCT
ejpam-3412	232	30	·	·	PUNCT
ejpam-3412	232	31	,	,	PUNCT
ejpam-3412	232	32	0	0	NUM
ejpam-3412	232	33	)	)	PUNCT
ejpam-3412	232	34	is	be	AUX
ejpam-3412	232	35	a	a	DET
ejpam-3412	232	36	up	up	NOUN
ejpam-3412	232	37	-	-	PUNCT
ejpam-3412	232	38	algebra	algebra	NOUN
ejpam-3412	232	39	.	.	PUNCT
ejpam-3412	233	1	we	we	PRON
ejpam-3412	233	2	define	define	VERB
ejpam-3412	233	3	a	a	DET
ejpam-3412	233	4	membership	membership	NOUN
ejpam-3412	233	5	function	function	NOUN
ejpam-3412	233	6	ff	ff	NOUN
ejpam-3412	233	7	as	as	SCONJ
ejpam-3412	233	8	follows	follow	VERB
ejpam-3412	233	9	:	:	PUNCT
ejpam-3412	233	10	ff(0	ff(0	NOUN
ejpam-3412	233	11	)	)	PUNCT
ejpam-3412	233	12	=	=	SYM
ejpam-3412	233	13	1	1	NUM
ejpam-3412	233	14	,	,	PUNCT
ejpam-3412	233	15	ff(1	ff(1	PROPN
ejpam-3412	233	16	)	)	PUNCT
ejpam-3412	233	17	=	=	SYM
ejpam-3412	233	18	0.6	0.6	NUM
ejpam-3412	233	19	,	,	PUNCT
ejpam-3412	233	20	ff(2	ff(2	PROPN
ejpam-3412	233	21	)	)	PUNCT
ejpam-3412	233	22	=	=	NUM
ejpam-3412	233	23	0.2	0.2	NUM
ejpam-3412	233	24	,	,	PUNCT
ejpam-3412	233	25	and	and	CCONJ
ejpam-3412	233	26	ff(3	ff(3	NOUN
ejpam-3412	233	27	)	)	PUNCT
ejpam-3412	233	28	=	=	NOUN
ejpam-3412	233	29	0.9	0.9	NUM
ejpam-3412	233	30	.	.	PUNCT
ejpam-3412	234	1	then	then	ADV
ejpam-3412	234	2	f	f	PROPN
ejpam-3412	234	3	satisfies	satisfy	VERB
ejpam-3412	234	4	the	the	DET
ejpam-3412	234	5	condition	condition	NOUN
ejpam-3412	234	6	(	(	PUNCT
ejpam-3412	234	7	2.1	2.1	NUM
ejpam-3412	234	8	)	)	PUNCT
ejpam-3412	234	9	but	but	CCONJ
ejpam-3412	234	10	it	it	PRON
ejpam-3412	234	11	does	do	AUX
ejpam-3412	234	12	not	not	PART
ejpam-3412	234	13	satisfy	satisfy	VERB
ejpam-3412	234	14	the	the	DET
ejpam-3412	234	15	condition	condition	NOUN
ejpam-3412	234	16	(	(	PUNCT
ejpam-3412	234	17	2.3	2.3	NUM
ejpam-3412	234	18	)	)	PUNCT
ejpam-3412	234	19	.	.	PUNCT
ejpam-3412	235	1	indeed	indeed	ADV
ejpam-3412	235	2	,	,	PUNCT
ejpam-3412	235	3	1	1	NUM
ejpam-3412	235	4	≤	≤	NUM
ejpam-3412	235	5	1	1	NUM
ejpam-3412	235	6	but	but	CCONJ
ejpam-3412	235	7	ff(1	ff(1	X
ejpam-3412	235	8	·	·	PUNCT
ejpam-3412	235	9	3	3	X
ejpam-3412	235	10	)	)	PUNCT
ejpam-3412	235	11	=	=	SYM
ejpam-3412	235	12	ff(2	ff(2	NUM
ejpam-3412	235	13	)	)	PUNCT
ejpam-3412	235	14	=	=	NUM
ejpam-3412	235	15	0.2	0.2	NUM
ejpam-3412	235	16	�	�	PROPN
ejpam-3412	235	17	0.6	0.6	NUM
ejpam-3412	235	18	=	=	SYM
ejpam-3412	235	19	min{0.6	min{0.6	PROPN
ejpam-3412	235	20	,	,	PUNCT
ejpam-3412	235	21	0.9	0.9	NUM
ejpam-3412	235	22	}	}	PUNCT
ejpam-3412	235	23	=	=	SYM
ejpam-3412	235	24	min{ff(1	min{ff(1	PROPN
ejpam-3412	235	25	)	)	PUNCT
ejpam-3412	235	26	,	,	PUNCT
ejpam-3412	235	27	ff(3	ff(3	NOUN
ejpam-3412	235	28	)	)	PUNCT
ejpam-3412	235	29	}	}	PUNCT
ejpam-3412	235	30	.	.	PUNCT
ejpam-3412	236	1	it	it	PRON
ejpam-3412	236	2	is	be	AUX
ejpam-3412	236	3	clear	clear	ADJ
ejpam-3412	236	4	that	that	SCONJ
ejpam-3412	236	5	we	we	PRON
ejpam-3412	236	6	have	have	VERB
ejpam-3412	236	7	the	the	DET
ejpam-3412	236	8	following	follow	VERB
ejpam-3412	236	9	proposition	proposition	NOUN
ejpam-3412	236	10	.	.	PUNCT
ejpam-3412	237	1	proposition	proposition	NOUN
ejpam-3412	237	2	4	4	NUM
ejpam-3412	237	3	.	.	PUNCT
ejpam-3412	238	1	if	if	SCONJ
ejpam-3412	238	2	f	f	PROPN
ejpam-3412	238	3	is	be	AUX
ejpam-3412	238	4	a	a	DET
ejpam-3412	238	5	fuzzy	fuzzy	ADJ
ejpam-3412	238	6	set	set	NOUN
ejpam-3412	238	7	in	in	ADP
ejpam-3412	238	8	a	a	DET
ejpam-3412	238	9	satisfying	satisfying	NOUN
ejpam-3412	238	10	the	the	DET
ejpam-3412	238	11	condition	condition	NOUN
ejpam-3412	238	12	(	(	PUNCT
ejpam-3412	238	13	∀x	∀x	X
ejpam-3412	238	14	,	,	PUNCT
ejpam-3412	238	15	y	y	PROPN
ejpam-3412	238	16	,	,	PUNCT
ejpam-3412	238	17	z	z	NOUN
ejpam-3412	238	18	∈	∈	PROPN
ejpam-3412	238	19	a)(ff(x	a)(ff(x	PUNCT
ejpam-3412	238	20	·	·	PUNCT
ejpam-3412	238	21	y	y	X
ejpam-3412	238	22	)	)	PUNCT
ejpam-3412	238	23	≥	≥	NOUN
ejpam-3412	238	24	min{ff(z	min{ff(z	NOUN
ejpam-3412	238	25	)	)	PUNCT
ejpam-3412	238	26	,	,	PUNCT
ejpam-3412	238	27	ff(y	ff(y	NUM
ejpam-3412	238	28	)	)	PUNCT
ejpam-3412	238	29	}	}	PUNCT
ejpam-3412	238	30	)	)	PUNCT
ejpam-3412	238	31	,	,	PUNCT
ejpam-3412	238	32	(	(	PUNCT
ejpam-3412	238	33	2.4	2.4	NUM
ejpam-3412	238	34	)	)	PUNCT
ejpam-3412	238	35	then	then	ADV
ejpam-3412	238	36	f	f	PROPN
ejpam-3412	238	37	satisfies	satisfy	VERB
ejpam-3412	238	38	the	the	DET
ejpam-3412	238	39	condition	condition	NOUN
ejpam-3412	238	40	(	(	PUNCT
ejpam-3412	238	41	2.3	2.3	NUM
ejpam-3412	238	42	)	)	PUNCT
ejpam-3412	238	43	.	.	PUNCT
ejpam-3412	239	1	the	the	DET
ejpam-3412	239	2	following	follow	VERB
ejpam-3412	239	3	example	example	NOUN
ejpam-3412	239	4	shows	show	VERB
ejpam-3412	239	5	that	that	SCONJ
ejpam-3412	239	6	the	the	DET
ejpam-3412	239	7	converse	converse	NOUN
ejpam-3412	239	8	of	of	ADP
ejpam-3412	239	9	proposition	proposition	NOUN
ejpam-3412	239	10	4	4	NUM
ejpam-3412	239	11	is	be	AUX
ejpam-3412	239	12	not	not	PART
ejpam-3412	239	13	true	true	ADJ
ejpam-3412	239	14	.	.	PUNCT
ejpam-3412	240	1	example	example	NOUN
ejpam-3412	240	2	8	8	NUM
ejpam-3412	240	3	.	.	PUNCT
ejpam-3412	241	1	let	let	VERB
ejpam-3412	241	2	a	a	PRON
ejpam-3412	241	3	=	=	PUNCT
ejpam-3412	241	4	{	{	PUNCT
ejpam-3412	241	5	0	0	NUM
ejpam-3412	241	6	,	,	PUNCT
ejpam-3412	241	7	1	1	NUM
ejpam-3412	241	8	,	,	PUNCT
ejpam-3412	241	9	2	2	NUM
ejpam-3412	241	10	,	,	PUNCT
ejpam-3412	241	11	3	3	NUM
ejpam-3412	241	12	}	}	PUNCT
ejpam-3412	241	13	be	be	AUX
ejpam-3412	241	14	a	a	DET
ejpam-3412	241	15	set	set	NOUN
ejpam-3412	241	16	with	with	ADP
ejpam-3412	241	17	a	a	DET
ejpam-3412	241	18	binary	binary	ADJ
ejpam-3412	241	19	operation	operation	NOUN
ejpam-3412	241	20	·	·	PUNCT
ejpam-3412	241	21	defined	define	VERB
ejpam-3412	241	22	by	by	ADP
ejpam-3412	241	23	the	the	DET
ejpam-3412	241	24	following	following	ADJ
ejpam-3412	241	25	cayley	cayley	ADJ
ejpam-3412	241	26	table	table	NOUN
ejpam-3412	241	27	:	:	PUNCT
ejpam-3412	241	28	·	·	PUNCT
ejpam-3412	241	29	0	0	NUM
ejpam-3412	242	1	1	1	NUM
ejpam-3412	242	2	2	2	NUM
ejpam-3412	242	3	3	3	NUM
ejpam-3412	242	4	0	0	NUM
ejpam-3412	242	5	0	0	NUM
ejpam-3412	242	6	1	1	NUM
ejpam-3412	242	7	2	2	NUM
ejpam-3412	242	8	3	3	NUM
ejpam-3412	242	9	1	1	NUM
ejpam-3412	242	10	0	0	NUM
ejpam-3412	242	11	0	0	NUM
ejpam-3412	242	12	3	3	NUM
ejpam-3412	242	13	3	3	NUM
ejpam-3412	242	14	2	2	NUM
ejpam-3412	242	15	0	0	NUM
ejpam-3412	242	16	1	1	NUM
ejpam-3412	242	17	0	0	NUM
ejpam-3412	242	18	0	0	NUM
ejpam-3412	242	19	3	3	NUM
ejpam-3412	242	20	0	0	NUM
ejpam-3412	242	21	1	1	NUM
ejpam-3412	242	22	2	2	NUM
ejpam-3412	242	23	0	0	NUM
ejpam-3412	242	24	then	then	ADV
ejpam-3412	242	25	a	a	PRON
ejpam-3412	242	26	=	=	X
ejpam-3412	242	27	(	(	PUNCT
ejpam-3412	242	28	a	a	PRON
ejpam-3412	242	29	,	,	PUNCT
ejpam-3412	242	30	·	·	PUNCT
ejpam-3412	242	31	,	,	PUNCT
ejpam-3412	242	32	0	0	NUM
ejpam-3412	242	33	)	)	PUNCT
ejpam-3412	242	34	is	be	AUX
ejpam-3412	242	35	a	a	DET
ejpam-3412	242	36	up	up	NOUN
ejpam-3412	242	37	-	-	PUNCT
ejpam-3412	242	38	algebra	algebra	NOUN
ejpam-3412	242	39	.	.	PUNCT
ejpam-3412	243	1	we	we	PRON
ejpam-3412	243	2	define	define	VERB
ejpam-3412	243	3	a	a	DET
ejpam-3412	243	4	membership	membership	NOUN
ejpam-3412	243	5	function	function	NOUN
ejpam-3412	243	6	ff	ff	NOUN
ejpam-3412	243	7	as	as	SCONJ
ejpam-3412	243	8	follows	follow	VERB
ejpam-3412	243	9	:	:	PUNCT
ejpam-3412	243	10	ff(0	ff(0	NOUN
ejpam-3412	243	11	)	)	PUNCT
ejpam-3412	243	12	=	=	SYM
ejpam-3412	243	13	1	1	NUM
ejpam-3412	243	14	,	,	PUNCT
ejpam-3412	243	15	ff(1	ff(1	NOUN
ejpam-3412	243	16	)	)	PUNCT
ejpam-3412	243	17	=	=	NOUN
ejpam-3412	243	18	0.1	0.1	NUM
ejpam-3412	243	19	,	,	PUNCT
ejpam-3412	243	20	ff(2	ff(2	NOUN
ejpam-3412	243	21	)	)	PUNCT
ejpam-3412	243	22	=	=	NUM
ejpam-3412	243	23	0.8	0.8	NUM
ejpam-3412	243	24	,	,	PUNCT
ejpam-3412	243	25	and	and	CCONJ
ejpam-3412	243	26	ff(3	ff(3	NOUN
ejpam-3412	243	27	)	)	PUNCT
ejpam-3412	243	28	=	=	NOUN
ejpam-3412	243	29	0.2	0.2	NUM
ejpam-3412	243	30	.	.	PUNCT
ejpam-3412	244	1	then	then	ADV
ejpam-3412	244	2	f	f	PROPN
ejpam-3412	244	3	satisfies	satisfy	VERB
ejpam-3412	244	4	the	the	DET
ejpam-3412	244	5	condition	condition	NOUN
ejpam-3412	244	6	(	(	PUNCT
ejpam-3412	244	7	2.3	2.3	NUM
ejpam-3412	244	8	)	)	PUNCT
ejpam-3412	244	9	but	but	CCONJ
ejpam-3412	244	10	it	it	PRON
ejpam-3412	244	11	does	do	AUX
ejpam-3412	244	12	not	not	PART
ejpam-3412	244	13	satisfy	satisfy	VERB
ejpam-3412	244	14	the	the	DET
ejpam-3412	244	15	condition	condition	NOUN
ejpam-3412	244	16	(	(	PUNCT
ejpam-3412	244	17	2.4	2.4	NUM
ejpam-3412	244	18	)	)	PUNCT
ejpam-3412	244	19	.	.	PUNCT
ejpam-3412	245	1	indeed	indeed	ADV
ejpam-3412	245	2	,	,	PUNCT
ejpam-3412	245	3	ff(1	ff(1	X
ejpam-3412	245	4	·	·	PUNCT
ejpam-3412	245	5	2	2	X
ejpam-3412	245	6	)	)	PUNCT
ejpam-3412	245	7	=	=	SYM
ejpam-3412	245	8	ff(3	ff(3	NOUN
ejpam-3412	245	9	)	)	PUNCT
ejpam-3412	245	10	=	=	SYM
ejpam-3412	245	11	0.2	0.2	NUM
ejpam-3412	245	12	�	�	PROPN
ejpam-3412	245	13	0.8	0.8	NUM
ejpam-3412	245	14	=	=	SYM
ejpam-3412	245	15	min{1	min{1	PROPN
ejpam-3412	245	16	,	,	PUNCT
ejpam-3412	245	17	0.8	0.8	NUM
ejpam-3412	245	18	}	}	PUNCT
ejpam-3412	245	19	=	=	SYM
ejpam-3412	245	20	min{ff(0	min{ff(0	PROPN
ejpam-3412	245	21	)	)	PUNCT
ejpam-3412	245	22	,	,	PUNCT
ejpam-3412	245	23	ff(2	ff(2	NOUN
ejpam-3412	245	24	)	)	PUNCT
ejpam-3412	245	25	}	}	PUNCT
ejpam-3412	245	26	.	.	PUNCT
ejpam-3412	246	1	proposition	proposition	NOUN
ejpam-3412	246	2	5	5	NUM
ejpam-3412	246	3	.	.	PUNCT
ejpam-3412	247	1	if	if	SCONJ
ejpam-3412	247	2	f	f	PROPN
ejpam-3412	247	3	is	be	AUX
ejpam-3412	247	4	a	a	DET
ejpam-3412	247	5	fuzzy	fuzzy	ADJ
ejpam-3412	247	6	set	set	NOUN
ejpam-3412	247	7	in	in	ADP
ejpam-3412	247	8	a	a	DET
ejpam-3412	247	9	satisfying	satisfying	NOUN
ejpam-3412	247	10	the	the	DET
ejpam-3412	247	11	condition	condition	NOUN
ejpam-3412	247	12	(	(	PUNCT
ejpam-3412	247	13	2.2	2.2	NUM
ejpam-3412	247	14	)	)	PUNCT
ejpam-3412	247	15	,	,	PUNCT
ejpam-3412	247	16	then	then	ADV
ejpam-3412	247	17	f	f	PROPN
ejpam-3412	247	18	is	be	AUX
ejpam-3412	247	19	a	a	DET
ejpam-3412	247	20	fuzzy	fuzzy	ADJ
ejpam-3412	247	21	near	near	ADP
ejpam-3412	247	22	up	up	ADJ
ejpam-3412	247	23	-	-	PUNCT
ejpam-3412	247	24	filter	filter	NOUN
ejpam-3412	247	25	of	of	ADP
ejpam-3412	247	26	a.	a.	NOUN
ejpam-3412	247	27	proof	proof	NOUN
ejpam-3412	247	28	.	.	PUNCT
ejpam-3412	248	1	let	let	VERB
ejpam-3412	248	2	x	x	PRON
ejpam-3412	248	3	,	,	PUNCT
ejpam-3412	248	4	y	y	PROPN
ejpam-3412	248	5	∈	∈	PROPN
ejpam-3412	248	6	a.	a.	NOUN
ejpam-3412	248	7	by	by	ADP
ejpam-3412	248	8	(	(	PUNCT
ejpam-3412	248	9	up-3	up-3	NOUN
ejpam-3412	248	10	)	)	PUNCT
ejpam-3412	248	11	,	,	PUNCT
ejpam-3412	248	12	we	we	PRON
ejpam-3412	248	13	have	have	VERB
ejpam-3412	248	14	x	x	NOUN
ejpam-3412	248	15	≤	≤	NUM
ejpam-3412	248	16	0	0	NUM
ejpam-3412	248	17	.	.	PUNCT
ejpam-3412	249	1	it	it	PRON
ejpam-3412	249	2	follows	follow	VERB
ejpam-3412	249	3	from	from	ADP
ejpam-3412	249	4	(	(	PUNCT
ejpam-3412	249	5	2.2	2.2	NUM
ejpam-3412	249	6	)	)	PUNCT
ejpam-3412	249	7	that	that	DET
ejpam-3412	249	8	ff(0	ff(0	NOUN
ejpam-3412	249	9	)	)	PUNCT
ejpam-3412	249	10	≥	≥	NOUN
ejpam-3412	249	11	ff(x	ff(x	NOUN
ejpam-3412	249	12	)	)	PUNCT
ejpam-3412	249	13	.	.	PUNCT
ejpam-3412	250	1	by	by	ADP
ejpam-3412	250	2	(	(	PUNCT
ejpam-3412	250	3	1.5	1.5	NUM
ejpam-3412	250	4	)	)	PUNCT
ejpam-3412	250	5	,	,	PUNCT
ejpam-3412	250	6	we	we	PRON
ejpam-3412	250	7	have	have	VERB
ejpam-3412	250	8	y	y	NOUN
ejpam-3412	250	9	≤	≤	NUM
ejpam-3412	250	10	x	x	X
ejpam-3412	250	11	·	·	PUNCT
ejpam-3412	251	1	y.	y.	NOUN
ejpam-3412	251	2	it	it	PRON
ejpam-3412	251	3	follows	follow	VERB
ejpam-3412	251	4	from	from	ADP
ejpam-3412	251	5	(	(	PUNCT
ejpam-3412	251	6	2.2	2.2	NUM
ejpam-3412	251	7	)	)	PUNCT
ejpam-3412	251	8	that	that	PRON
ejpam-3412	251	9	ff(x	ff(x	VERB
ejpam-3412	251	10	·	·	PUNCT
ejpam-3412	251	11	y	y	X
ejpam-3412	251	12	)	)	PUNCT
ejpam-3412	251	13	≥	≥	NOUN
ejpam-3412	251	14	ff(y	ff(y	NUM
ejpam-3412	251	15	)	)	PUNCT
ejpam-3412	251	16	.	.	PUNCT
ejpam-3412	252	1	hence	hence	ADV
ejpam-3412	252	2	,	,	PUNCT
ejpam-3412	252	3	f	f	PROPN
ejpam-3412	252	4	is	be	AUX
ejpam-3412	252	5	a	a	DET
ejpam-3412	252	6	fuzzy	fuzzy	ADJ
ejpam-3412	252	7	near	near	ADP
ejpam-3412	252	8	up	up	ADJ
ejpam-3412	252	9	-	-	PUNCT
ejpam-3412	252	10	filter	filter	NOUN
ejpam-3412	252	11	of	of	ADP
ejpam-3412	252	12	a.	a.	NOUN
ejpam-3412	252	13	theorem	theorem	NOUN
ejpam-3412	252	14	11	11	NUM
ejpam-3412	252	15	.	.	PUNCT
ejpam-3412	253	1	if	if	SCONJ
ejpam-3412	253	2	f	f	PROPN
ejpam-3412	253	3	is	be	AUX
ejpam-3412	253	4	a	a	DET
ejpam-3412	253	5	fuzzy	fuzzy	ADJ
ejpam-3412	253	6	set	set	NOUN
ejpam-3412	253	7	in	in	ADP
ejpam-3412	253	8	a	a	DET
ejpam-3412	253	9	satisfying	satisfying	NOUN
ejpam-3412	253	10	the	the	DET
ejpam-3412	253	11	condition	condition	NOUN
ejpam-3412	253	12	(	(	PUNCT
ejpam-3412	253	13	2.2	2.2	NUM
ejpam-3412	253	14	)	)	PUNCT
ejpam-3412	253	15	,	,	PUNCT
ejpam-3412	253	16	then	then	ADV
ejpam-3412	253	17	f	f	PROPN
ejpam-3412	253	18	satisfies	satisfy	VERB
ejpam-3412	253	19	the	the	DET
ejpam-3412	253	20	condition	condition	NOUN
ejpam-3412	253	21	(	(	PUNCT
ejpam-3412	253	22	2.4	2.4	NUM
ejpam-3412	253	23	)	)	PUNCT
ejpam-3412	253	24	.	.	PUNCT
ejpam-3412	254	1	a.	a.	PROPN
ejpam-3412	254	2	satirad	satirad	PROPN
ejpam-3412	254	3	,	,	PUNCT
ejpam-3412	254	4	a.	a.	NOUN
ejpam-3412	254	5	iampan	iampan	PROPN
ejpam-3412	254	6	/	/	SYM
ejpam-3412	254	7	eur	eur	PROPN
ejpam-3412	254	8	.	.	PUNCT
ejpam-3412	255	1	j.	j.	PROPN
ejpam-3412	255	2	pure	pure	PROPN
ejpam-3412	255	3	appl	appl	PROPN
ejpam-3412	255	4	.	.	PROPN
ejpam-3412	255	5	math	math	PROPN
ejpam-3412	255	6	,	,	PUNCT
ejpam-3412	255	7	12	12	NUM
ejpam-3412	255	8	(	(	PUNCT
ejpam-3412	255	9	2	2	NUM
ejpam-3412	255	10	)	)	PUNCT
ejpam-3412	255	11	(	(	PUNCT
ejpam-3412	255	12	2019	2019	NUM
ejpam-3412	255	13	)	)	PUNCT
ejpam-3412	255	14	,	,	PUNCT
ejpam-3412	255	15	294	294	NUM
ejpam-3412	255	16	-	-	SYM
ejpam-3412	255	17	331	331	NUM
ejpam-3412	255	18	305	305	NUM
ejpam-3412	255	19	proof	proof	NOUN
ejpam-3412	255	20	.	.	PUNCT
ejpam-3412	256	1	let	let	VERB
ejpam-3412	256	2	x	x	PRON
ejpam-3412	256	3	,	,	PUNCT
ejpam-3412	256	4	y	y	PROPN
ejpam-3412	256	5	,	,	PUNCT
ejpam-3412	256	6	z	z	PROPN
ejpam-3412	256	7	∈	∈	NOUN
ejpam-3412	256	8	a.	a.	NOUN
ejpam-3412	256	9	by	by	ADP
ejpam-3412	256	10	(	(	PUNCT
ejpam-3412	256	11	1.5	1.5	NUM
ejpam-3412	256	12	)	)	PUNCT
ejpam-3412	256	13	,	,	PUNCT
ejpam-3412	256	14	we	we	PRON
ejpam-3412	256	15	have	have	VERB
ejpam-3412	256	16	y	y	NOUN
ejpam-3412	256	17	≤	≤	NUM
ejpam-3412	256	18	x	x	X
ejpam-3412	256	19	·	·	PUNCT
ejpam-3412	257	1	y.	y.	NOUN
ejpam-3412	257	2	it	it	PRON
ejpam-3412	257	3	follows	follow	VERB
ejpam-3412	257	4	from	from	ADP
ejpam-3412	257	5	(	(	PUNCT
ejpam-3412	257	6	2.2	2.2	NUM
ejpam-3412	257	7	)	)	PUNCT
ejpam-3412	257	8	that	that	PRON
ejpam-3412	257	9	ff(x	ff(x	VERB
ejpam-3412	257	10	·	·	PUNCT
ejpam-3412	257	11	y	y	X
ejpam-3412	257	12	)	)	PUNCT
ejpam-3412	257	13	≥	≥	NOUN
ejpam-3412	257	14	ff(y	ff(y	NUM
ejpam-3412	257	15	)	)	PUNCT
ejpam-3412	257	16	≥	≥	NOUN
ejpam-3412	257	17	min{ff(z	min{ff(z	NOUN
ejpam-3412	257	18	)	)	PUNCT
ejpam-3412	257	19	,	,	PUNCT
ejpam-3412	257	20	ff(y	ff(y	NUM
ejpam-3412	257	21	)	)	PUNCT
ejpam-3412	257	22	}	}	PUNCT
ejpam-3412	257	23	.	.	PUNCT
ejpam-3412	258	1	hence	hence	ADV
ejpam-3412	258	2	,	,	PUNCT
ejpam-3412	258	3	f	f	PROPN
ejpam-3412	258	4	satisfies	satisfie	NOUN
ejpam-3412	258	5	(	(	PUNCT
ejpam-3412	258	6	2.4	2.4	NUM
ejpam-3412	258	7	)	)	PUNCT
ejpam-3412	258	8	.	.	PUNCT
ejpam-3412	259	1	the	the	DET
ejpam-3412	259	2	following	follow	VERB
ejpam-3412	259	3	example	example	NOUN
ejpam-3412	259	4	shows	show	VERB
ejpam-3412	259	5	that	that	SCONJ
ejpam-3412	259	6	the	the	DET
ejpam-3412	259	7	converse	converse	NOUN
ejpam-3412	259	8	of	of	ADP
ejpam-3412	259	9	theorem	theorem	NOUN
ejpam-3412	259	10	11	11	NUM
ejpam-3412	259	11	is	be	AUX
ejpam-3412	259	12	not	not	PART
ejpam-3412	259	13	true	true	ADJ
ejpam-3412	259	14	.	.	PUNCT
ejpam-3412	260	1	example	example	NOUN
ejpam-3412	261	1	9	9	NUM
ejpam-3412	261	2	.	.	PUNCT
ejpam-3412	261	3	let	let	VERB
ejpam-3412	261	4	a	a	PRON
ejpam-3412	261	5	=	=	PUNCT
ejpam-3412	261	6	{	{	PUNCT
ejpam-3412	261	7	0	0	NUM
ejpam-3412	261	8	,	,	PUNCT
ejpam-3412	261	9	1	1	NUM
ejpam-3412	261	10	,	,	PUNCT
ejpam-3412	261	11	2	2	NUM
ejpam-3412	261	12	,	,	PUNCT
ejpam-3412	261	13	3	3	NUM
ejpam-3412	261	14	}	}	PUNCT
ejpam-3412	261	15	be	be	AUX
ejpam-3412	261	16	a	a	DET
ejpam-3412	261	17	set	set	NOUN
ejpam-3412	261	18	with	with	ADP
ejpam-3412	261	19	a	a	DET
ejpam-3412	261	20	binary	binary	ADJ
ejpam-3412	261	21	operation	operation	NOUN
ejpam-3412	261	22	·	·	PUNCT
ejpam-3412	261	23	defined	define	VERB
ejpam-3412	261	24	by	by	ADP
ejpam-3412	261	25	the	the	DET
ejpam-3412	261	26	following	following	ADJ
ejpam-3412	261	27	cayley	cayley	ADJ
ejpam-3412	261	28	table	table	NOUN
ejpam-3412	261	29	:	:	PUNCT
ejpam-3412	261	30	·	·	PUNCT
ejpam-3412	261	31	0	0	NUM
ejpam-3412	262	1	1	1	NUM
ejpam-3412	262	2	2	2	NUM
ejpam-3412	262	3	3	3	NUM
ejpam-3412	262	4	0	0	NUM
ejpam-3412	262	5	0	0	NUM
ejpam-3412	262	6	1	1	NUM
ejpam-3412	262	7	2	2	NUM
ejpam-3412	262	8	3	3	NUM
ejpam-3412	262	9	1	1	NUM
ejpam-3412	262	10	0	0	NUM
ejpam-3412	262	11	0	0	NUM
ejpam-3412	262	12	2	2	NUM
ejpam-3412	262	13	3	3	NUM
ejpam-3412	262	14	2	2	NUM
ejpam-3412	262	15	0	0	NUM
ejpam-3412	262	16	0	0	NUM
ejpam-3412	262	17	0	0	NUM
ejpam-3412	262	18	3	3	NUM
ejpam-3412	262	19	3	3	NUM
ejpam-3412	262	20	0	0	NUM
ejpam-3412	262	21	0	0	NUM
ejpam-3412	262	22	0	0	NUM
ejpam-3412	262	23	0	0	NUM
ejpam-3412	262	24	then	then	ADV
ejpam-3412	262	25	a	a	PRON
ejpam-3412	262	26	=	=	X
ejpam-3412	262	27	(	(	PUNCT
ejpam-3412	262	28	a	a	PRON
ejpam-3412	262	29	,	,	PUNCT
ejpam-3412	262	30	·	·	PUNCT
ejpam-3412	262	31	,	,	PUNCT
ejpam-3412	262	32	0	0	NUM
ejpam-3412	262	33	)	)	PUNCT
ejpam-3412	262	34	is	be	AUX
ejpam-3412	262	35	a	a	DET
ejpam-3412	262	36	up	up	NOUN
ejpam-3412	262	37	-	-	PUNCT
ejpam-3412	262	38	algebra	algebra	NOUN
ejpam-3412	262	39	.	.	PUNCT
ejpam-3412	263	1	we	we	PRON
ejpam-3412	263	2	define	define	VERB
ejpam-3412	263	3	a	a	DET
ejpam-3412	263	4	membership	membership	NOUN
ejpam-3412	263	5	function	function	NOUN
ejpam-3412	263	6	ff	ff	NOUN
ejpam-3412	263	7	as	as	SCONJ
ejpam-3412	263	8	follows	follow	VERB
ejpam-3412	263	9	:	:	PUNCT
ejpam-3412	263	10	ff(0	ff(0	NOUN
ejpam-3412	263	11	)	)	PUNCT
ejpam-3412	263	12	=	=	SYM
ejpam-3412	263	13	1	1	NUM
ejpam-3412	263	14	,	,	PUNCT
ejpam-3412	263	15	ff(1	ff(1	NOUN
ejpam-3412	263	16	)	)	PUNCT
ejpam-3412	263	17	=	=	NOUN
ejpam-3412	263	18	0.1	0.1	NUM
ejpam-3412	263	19	,	,	PUNCT
ejpam-3412	263	20	ff(2	ff(2	NOUN
ejpam-3412	263	21	)	)	PUNCT
ejpam-3412	263	22	=	=	NOUN
ejpam-3412	263	23	0.7	0.7	NUM
ejpam-3412	263	24	,	,	PUNCT
ejpam-3412	263	25	and	and	CCONJ
ejpam-3412	263	26	ff(3	ff(3	NOUN
ejpam-3412	263	27	)	)	PUNCT
ejpam-3412	263	28	=	=	PUNCT
ejpam-3412	263	29	0.8	0.8	NUM
ejpam-3412	263	30	.	.	PUNCT
ejpam-3412	264	1	then	then	ADV
ejpam-3412	264	2	f	f	PROPN
ejpam-3412	264	3	satisfies	satisfy	VERB
ejpam-3412	264	4	the	the	DET
ejpam-3412	264	5	condition	condition	NOUN
ejpam-3412	264	6	(	(	PUNCT
ejpam-3412	264	7	2.4	2.4	NUM
ejpam-3412	264	8	)	)	PUNCT
ejpam-3412	264	9	but	but	CCONJ
ejpam-3412	264	10	it	it	PRON
ejpam-3412	264	11	does	do	AUX
ejpam-3412	264	12	not	not	PART
ejpam-3412	264	13	satisfy	satisfy	VERB
ejpam-3412	264	14	the	the	DET
ejpam-3412	264	15	condition	condition	NOUN
ejpam-3412	264	16	(	(	PUNCT
ejpam-3412	264	17	2.2	2.2	NUM
ejpam-3412	264	18	)	)	PUNCT
ejpam-3412	264	19	.	.	PUNCT
ejpam-3412	265	1	indeed	indeed	ADV
ejpam-3412	265	2	,	,	PUNCT
ejpam-3412	265	3	3	3	NUM
ejpam-3412	265	4	≤	≤	NUM
ejpam-3412	265	5	2	2	NUM
ejpam-3412	265	6	but	but	CCONJ
ejpam-3412	265	7	ff(2	ff(2	PROPN
ejpam-3412	265	8	)	)	PUNCT
ejpam-3412	265	9	=	=	SYM
ejpam-3412	265	10	ff(1	ff(1	PROPN
ejpam-3412	265	11	)	)	PUNCT
ejpam-3412	265	12	=	=	NOUN
ejpam-3412	265	13	0.7	0.7	NUM
ejpam-3412	265	14	�	�	PROPN
ejpam-3412	265	15	0.8	0.8	NUM
ejpam-3412	265	16	=	=	SYM
ejpam-3412	265	17	ff(3	ff(3	PROPN
ejpam-3412	265	18	)	)	PUNCT
ejpam-3412	265	19	.	.	PUNCT
ejpam-3412	266	1	theorem	theorem	NOUN
ejpam-3412	266	2	12	12	NUM
ejpam-3412	266	3	.	.	PUNCT
ejpam-3412	267	1	if	if	SCONJ
ejpam-3412	267	2	f	f	PROPN
ejpam-3412	267	3	is	be	AUX
ejpam-3412	267	4	a	a	DET
ejpam-3412	267	5	fuzzy	fuzzy	ADJ
ejpam-3412	267	6	up	up	NOUN
ejpam-3412	267	7	-	-	PUNCT
ejpam-3412	267	8	subalgebra	subalgebra	NOUN
ejpam-3412	267	9	of	of	ADP
ejpam-3412	267	10	a	a	DET
ejpam-3412	267	11	satisfying	satisfying	NOUN
ejpam-3412	267	12	the	the	DET
ejpam-3412	267	13	condition	condition	NOUN
ejpam-3412	267	14	(	(	PUNCT
ejpam-3412	267	15	∀x	∀x	NUM
ejpam-3412	267	16	,	,	PUNCT
ejpam-3412	267	17	y	y	PROPN
ejpam-3412	267	18	∈	∈	PROPN
ejpam-3412	267	19	a)(x	a)(x	X
ejpam-3412	267	20	·	·	PUNCT
ejpam-3412	267	21	y	y	PROPN
ejpam-3412	267	22	6=	6=	NUM
ejpam-3412	267	23	0⇒	0⇒	PROPN
ejpam-3412	267	24	ff(x	ff(x	NOUN
ejpam-3412	267	25	)	)	PUNCT
ejpam-3412	267	26	≥	≥	NOUN
ejpam-3412	267	27	ff(y	ff(y	NUM
ejpam-3412	267	28	)	)	PUNCT
ejpam-3412	267	29	)	)	PUNCT
ejpam-3412	267	30	,	,	PUNCT
ejpam-3412	267	31	(	(	PUNCT
ejpam-3412	267	32	2.5	2.5	NUM
ejpam-3412	267	33	)	)	PUNCT
ejpam-3412	267	34	then	then	ADV
ejpam-3412	267	35	f	f	PROPN
ejpam-3412	267	36	is	be	AUX
ejpam-3412	267	37	a	a	DET
ejpam-3412	267	38	fuzzy	fuzzy	ADJ
ejpam-3412	267	39	near	near	ADP
ejpam-3412	267	40	up	up	ADJ
ejpam-3412	267	41	-	-	PUNCT
ejpam-3412	267	42	filter	filter	NOUN
ejpam-3412	267	43	of	of	ADP
ejpam-3412	267	44	a.	a.	NOUN
ejpam-3412	267	45	proof	proof	NOUN
ejpam-3412	267	46	.	.	PUNCT
ejpam-3412	268	1	let	let	VERB
ejpam-3412	268	2	x	x	PRON
ejpam-3412	268	3	,	,	PUNCT
ejpam-3412	268	4	y	y	PROPN
ejpam-3412	268	5	∈	∈	PROPN
ejpam-3412	268	6	a.	a.	NOUN
ejpam-3412	268	7	if	if	SCONJ
ejpam-3412	268	8	x	x	X
ejpam-3412	268	9	·	·	PUNCT
ejpam-3412	268	10	y	y	SYM
ejpam-3412	268	11	=	=	SYM
ejpam-3412	268	12	0	0	PROPN
ejpam-3412	268	13	,	,	PUNCT
ejpam-3412	268	14	then	then	ADV
ejpam-3412	268	15	by	by	ADP
ejpam-3412	268	16	(	(	PUNCT
ejpam-3412	268	17	2.1	2.1	NUM
ejpam-3412	268	18	)	)	PUNCT
ejpam-3412	268	19	,	,	PUNCT
ejpam-3412	268	20	we	we	PRON
ejpam-3412	268	21	have	have	VERB
ejpam-3412	268	22	ff(x	ff(x	PRON
ejpam-3412	268	23	·	·	PUNCT
ejpam-3412	268	24	y	y	X
ejpam-3412	268	25	)	)	PUNCT
ejpam-3412	268	26	=	=	SYM
ejpam-3412	268	27	ff(0	ff(0	PROPN
ejpam-3412	268	28	)	)	PUNCT
ejpam-3412	268	29	≥	≥	NOUN
ejpam-3412	268	30	ff(y	ff(y	NUM
ejpam-3412	268	31	)	)	PUNCT
ejpam-3412	268	32	.	.	PUNCT
ejpam-3412	269	1	if	if	SCONJ
ejpam-3412	269	2	x	x	X
ejpam-3412	269	3	·	·	PUNCT
ejpam-3412	269	4	y	y	PROPN
ejpam-3412	269	5	6=	6=	PROPN
ejpam-3412	269	6	0	0	NUM
ejpam-3412	269	7	,	,	PUNCT
ejpam-3412	269	8	then	then	ADV
ejpam-3412	269	9	by	by	ADP
ejpam-3412	269	10	(	(	PUNCT
ejpam-3412	269	11	2.5	2.5	NUM
ejpam-3412	269	12	)	)	PUNCT
ejpam-3412	269	13	,	,	PUNCT
ejpam-3412	269	14	we	we	PRON
ejpam-3412	269	15	have	have	VERB
ejpam-3412	269	16	ff(x	ff(x	PRON
ejpam-3412	269	17	·	·	PUNCT
ejpam-3412	269	18	y	y	X
ejpam-3412	269	19	)	)	PUNCT
ejpam-3412	269	20	≥	≥	PROPN
ejpam-3412	269	21	min{ff(x	min{ff(x	PROPN
ejpam-3412	269	22	)	)	PUNCT
ejpam-3412	269	23	,	,	PUNCT
ejpam-3412	269	24	ff(y	ff(y	NUM
ejpam-3412	269	25	)	)	PUNCT
ejpam-3412	269	26	}	}	PUNCT
ejpam-3412	270	1	=	=	SYM
ejpam-3412	270	2	ff(y	ff(y	NUM
ejpam-3412	270	3	)	)	PUNCT
ejpam-3412	270	4	.	.	PUNCT
ejpam-3412	271	1	hence	hence	ADV
ejpam-3412	271	2	,	,	PUNCT
ejpam-3412	271	3	f	f	PROPN
ejpam-3412	271	4	is	be	AUX
ejpam-3412	271	5	a	a	DET
ejpam-3412	271	6	fuzzy	fuzzy	ADJ
ejpam-3412	271	7	near	near	ADP
ejpam-3412	271	8	up	up	ADJ
ejpam-3412	271	9	-	-	PUNCT
ejpam-3412	271	10	filter	filter	NOUN
ejpam-3412	271	11	of	of	ADP
ejpam-3412	271	12	a.	a.	NOUN
ejpam-3412	271	13	proposition	proposition	NOUN
ejpam-3412	271	14	6	6	NUM
ejpam-3412	271	15	.	.	PUNCT
ejpam-3412	272	1	a	a	DET
ejpam-3412	272	2	fuzzy	fuzzy	ADJ
ejpam-3412	272	3	set	set	VERB
ejpam-3412	272	4	f	f	PROPN
ejpam-3412	272	5	in	in	ADP
ejpam-3412	272	6	a	a	DET
ejpam-3412	272	7	satisfies	satisfie	NOUN
ejpam-3412	272	8	the	the	DET
ejpam-3412	272	9	condition	condition	NOUN
ejpam-3412	272	10	(	(	PUNCT
ejpam-3412	272	11	∀x	∀x	X
ejpam-3412	272	12	,	,	PUNCT
ejpam-3412	272	13	y	y	PROPN
ejpam-3412	272	14	,	,	PUNCT
ejpam-3412	272	15	z	z	PROPN
ejpam-3412	272	16	∈	∈	PROPN
ejpam-3412	272	17	a)(z	a)(z	PUNCT
ejpam-3412	272	18	≤	≤	NUM
ejpam-3412	272	19	x	x	SYM
ejpam-3412	272	20	·	·	PUNCT
ejpam-3412	272	21	y	y	PROPN
ejpam-3412	272	22	⇒	⇒	PROPN
ejpam-3412	272	23	ff(y	ff(y	NUM
ejpam-3412	272	24	)	)	PUNCT
ejpam-3412	272	25	≥	≥	NOUN
ejpam-3412	272	26	min{ff(z	min{ff(z	NOUN
ejpam-3412	272	27	)	)	PUNCT
ejpam-3412	272	28	,	,	PUNCT
ejpam-3412	272	29	ff(x	ff(x	NOUN
ejpam-3412	272	30	)	)	PUNCT
ejpam-3412	272	31	}	}	PUNCT
ejpam-3412	272	32	)	)	PUNCT
ejpam-3412	273	1	(	(	PUNCT
ejpam-3412	273	2	2.6	2.6	NUM
ejpam-3412	273	3	)	)	PUNCT
ejpam-3412	273	4	if	if	SCONJ
ejpam-3412	273	5	and	and	CCONJ
ejpam-3412	273	6	only	only	ADV
ejpam-3412	273	7	if	if	SCONJ
ejpam-3412	273	8	f	f	PROPN
ejpam-3412	273	9	is	be	AUX
ejpam-3412	273	10	a	a	DET
ejpam-3412	273	11	fuzzy	fuzzy	ADJ
ejpam-3412	273	12	up	up	ADJ
ejpam-3412	273	13	-	-	PUNCT
ejpam-3412	273	14	filter	filter	NOUN
ejpam-3412	273	15	of	of	ADP
ejpam-3412	273	16	a.	a.	NOUN
ejpam-3412	273	17	proof	proof	NOUN
ejpam-3412	273	18	.	.	PUNCT
ejpam-3412	274	1	let	let	VERB
ejpam-3412	274	2	x	x	PUNCT
ejpam-3412	274	3	∈	∈	VERB
ejpam-3412	274	4	a.	a.	NOUN
ejpam-3412	274	5	by	by	ADP
ejpam-3412	274	6	(	(	PUNCT
ejpam-3412	274	7	up-3	up-3	NOUN
ejpam-3412	274	8	)	)	PUNCT
ejpam-3412	274	9	,	,	PUNCT
ejpam-3412	274	10	we	we	PRON
ejpam-3412	274	11	have	have	VERB
ejpam-3412	274	12	x	x	NOUN
ejpam-3412	274	13	≤	≤	NUM
ejpam-3412	274	14	x	x	SYM
ejpam-3412	274	15	·	·	PUNCT
ejpam-3412	274	16	0	0	X
ejpam-3412	274	17	.	.	PUNCT
ejpam-3412	275	1	it	it	PRON
ejpam-3412	275	2	follows	follow	VERB
ejpam-3412	275	3	from	from	ADP
ejpam-3412	275	4	(	(	PUNCT
ejpam-3412	275	5	2.6	2.6	NUM
ejpam-3412	275	6	)	)	PUNCT
ejpam-3412	275	7	that	that	DET
ejpam-3412	275	8	ff(0	ff(0	NOUN
ejpam-3412	275	9	)	)	PUNCT
ejpam-3412	275	10	≥	≥	PROPN
ejpam-3412	275	11	min{ff(x	min{ff(x	PROPN
ejpam-3412	275	12	)	)	PUNCT
ejpam-3412	275	13	,	,	PUNCT
ejpam-3412	275	14	ff(x	ff(x	NOUN
ejpam-3412	275	15	)	)	PUNCT
ejpam-3412	275	16	}	}	PUNCT
ejpam-3412	275	17	=	=	SYM
ejpam-3412	275	18	ff(x	ff(x	NOUN
ejpam-3412	275	19	)	)	PUNCT
ejpam-3412	275	20	.	.	PUNCT
ejpam-3412	276	1	let	let	VERB
ejpam-3412	276	2	x	x	PRON
ejpam-3412	276	3	,	,	PUNCT
ejpam-3412	276	4	y	y	PROPN
ejpam-3412	276	5	∈	∈	PROPN
ejpam-3412	276	6	a.	a.	NOUN
ejpam-3412	276	7	by	by	ADP
ejpam-3412	276	8	(	(	PUNCT
ejpam-3412	276	9	1.1	1.1	NUM
ejpam-3412	276	10	)	)	PUNCT
ejpam-3412	276	11	,	,	PUNCT
ejpam-3412	276	12	we	we	PRON
ejpam-3412	276	13	have	have	VERB
ejpam-3412	276	14	x	x	X
ejpam-3412	276	15	·	·	PUNCT
ejpam-3412	276	16	y	y	X
ejpam-3412	276	17	≤	≤	NUM
ejpam-3412	276	18	x	x	X
ejpam-3412	276	19	·	·	PUNCT
ejpam-3412	277	1	y.	y.	NOUN
ejpam-3412	277	2	it	it	PRON
ejpam-3412	277	3	follows	follow	VERB
ejpam-3412	277	4	from	from	ADP
ejpam-3412	277	5	(	(	PUNCT
ejpam-3412	277	6	2.6	2.6	NUM
ejpam-3412	277	7	)	)	PUNCT
ejpam-3412	278	1	that	that	PRON
ejpam-3412	278	2	ff(y	ff(y	NUM
ejpam-3412	278	3	)	)	PUNCT
ejpam-3412	278	4	≥	≥	PROPN
ejpam-3412	278	5	min{ff(x	min{ff(x	PROPN
ejpam-3412	278	6	·	·	PUNCT
ejpam-3412	278	7	y	y	PROPN
ejpam-3412	278	8	)	)	PUNCT
ejpam-3412	278	9	,	,	PUNCT
ejpam-3412	278	10	ff(x	ff(x	NOUN
ejpam-3412	278	11	)	)	PUNCT
ejpam-3412	278	12	}	}	PUNCT
ejpam-3412	279	1	.	.	PUNCT
ejpam-3412	280	1	hence	hence	ADV
ejpam-3412	280	2	,	,	PUNCT
ejpam-3412	280	3	f	f	PROPN
ejpam-3412	280	4	is	be	AUX
ejpam-3412	280	5	a	a	DET
ejpam-3412	280	6	fuzzy	fuzzy	ADJ
ejpam-3412	280	7	up	up	ADJ
ejpam-3412	280	8	-	-	PUNCT
ejpam-3412	280	9	filter	filter	NOUN
ejpam-3412	280	10	of	of	ADP
ejpam-3412	280	11	a.	a.	NOUN
ejpam-3412	280	12	conversely	conversely	ADV
ejpam-3412	280	13	,	,	PUNCT
ejpam-3412	280	14	let	let	VERB
ejpam-3412	280	15	x	x	PRON
ejpam-3412	280	16	,	,	PUNCT
ejpam-3412	280	17	y	y	PROPN
ejpam-3412	280	18	,	,	PUNCT
ejpam-3412	280	19	z	z	PROPN
ejpam-3412	280	20	∈	∈	PROPN
ejpam-3412	280	21	a	a	DET
ejpam-3412	280	22	be	be	AUX
ejpam-3412	280	23	such	such	ADJ
ejpam-3412	280	24	that	that	SCONJ
ejpam-3412	280	25	z	z	NOUN
ejpam-3412	280	26	≤	≤	NUM
ejpam-3412	280	27	x	x	X
ejpam-3412	280	28	·	·	PUNCT
ejpam-3412	280	29	y.	y.	NOUN
ejpam-3412	280	30	then	then	ADV
ejpam-3412	280	31	z	z	NOUN
ejpam-3412	280	32	·	·	PUNCT
ejpam-3412	280	33	(	(	PUNCT
ejpam-3412	280	34	x	x	X
ejpam-3412	280	35	·	·	PUNCT
ejpam-3412	280	36	y	y	X
ejpam-3412	280	37	)	)	PUNCT
ejpam-3412	281	1	=	=	SYM
ejpam-3412	281	2	0	0	NUM
ejpam-3412	281	3	,	,	PUNCT
ejpam-3412	281	4	so	so	SCONJ
ejpam-3412	281	5	ff(x	ff(x	ADP
ejpam-3412	281	6	·	·	PUNCT
ejpam-3412	281	7	y	y	X
ejpam-3412	281	8	)	)	PUNCT
ejpam-3412	281	9	≥	≥	NOUN
ejpam-3412	281	10	min{ff(z	min{ff(z	X
ejpam-3412	281	11	·	·	PUNCT
ejpam-3412	281	12	(	(	PUNCT
ejpam-3412	281	13	x	x	X
ejpam-3412	281	14	·	·	PUNCT
ejpam-3412	281	15	y	y	NOUN
ejpam-3412	281	16	)	)	PUNCT
ejpam-3412	281	17	)	)	PUNCT
ejpam-3412	281	18	,	,	PUNCT
ejpam-3412	281	19	ff(z	ff(z	X
ejpam-3412	281	20	)	)	PUNCT
ejpam-3412	281	21	}	}	PUNCT
ejpam-3412	281	22	=	=	SYM
ejpam-3412	281	23	min{ff(0	min{ff(0	PROPN
ejpam-3412	281	24	)	)	PUNCT
ejpam-3412	281	25	,	,	PUNCT
ejpam-3412	281	26	ff(z	ff(z	X
ejpam-3412	281	27	)	)	PUNCT
ejpam-3412	281	28	}	}	PUNCT
ejpam-3412	281	29	=	=	PUNCT
ejpam-3412	281	30	ff(z	ff(z	X
ejpam-3412	281	31	)	)	PUNCT
ejpam-3412	281	32	.	.	PUNCT
ejpam-3412	282	1	thus	thus	ADV
ejpam-3412	282	2	ff(y	ff(y	NUM
ejpam-3412	282	3	)	)	PUNCT
ejpam-3412	282	4	≥	≥	PROPN
ejpam-3412	282	5	min{ff(x	min{ff(x	PROPN
ejpam-3412	282	6	·	·	PUNCT
ejpam-3412	282	7	y	y	PROPN
ejpam-3412	282	8	)	)	PUNCT
ejpam-3412	282	9	,	,	PUNCT
ejpam-3412	282	10	ff(x	ff(x	NOUN
ejpam-3412	282	11	)	)	PUNCT
ejpam-3412	282	12	}	}	PUNCT
ejpam-3412	282	13	≥	≥	NUM
ejpam-3412	282	14	min{ff(z	min{ff(z	NOUN
ejpam-3412	282	15	)	)	PUNCT
ejpam-3412	282	16	,	,	PUNCT
ejpam-3412	282	17	ff(x	ff(x	NOUN
ejpam-3412	282	18	)	)	PUNCT
ejpam-3412	282	19	}	}	PUNCT
ejpam-3412	282	20	.	.	PUNCT
ejpam-3412	283	1	hence	hence	ADV
ejpam-3412	283	2	,	,	PUNCT
ejpam-3412	283	3	f	f	PROPN
ejpam-3412	283	4	satisfies	satisfie	NOUN
ejpam-3412	283	5	(	(	PUNCT
ejpam-3412	283	6	2.6	2.6	NUM
ejpam-3412	283	7	)	)	PUNCT
ejpam-3412	283	8	.	.	PUNCT
ejpam-3412	284	1	theorem	theorem	VERB
ejpam-3412	284	2	13	13	NUM
ejpam-3412	284	3	.	.	PUNCT
ejpam-3412	285	1	if	if	SCONJ
ejpam-3412	285	2	f	f	PROPN
ejpam-3412	285	3	is	be	AUX
ejpam-3412	285	4	a	a	DET
ejpam-3412	285	5	fuzzy	fuzzy	ADJ
ejpam-3412	285	6	set	set	NOUN
ejpam-3412	285	7	in	in	ADP
ejpam-3412	285	8	a	a	DET
ejpam-3412	285	9	satisfying	satisfying	NOUN
ejpam-3412	285	10	the	the	DET
ejpam-3412	285	11	condition	condition	NOUN
ejpam-3412	285	12	(	(	PUNCT
ejpam-3412	285	13	2.6	2.6	NUM
ejpam-3412	285	14	)	)	PUNCT
ejpam-3412	285	15	,	,	PUNCT
ejpam-3412	285	16	then	then	ADV
ejpam-3412	285	17	f	f	PROPN
ejpam-3412	285	18	satisfies	satisfy	VERB
ejpam-3412	285	19	the	the	DET
ejpam-3412	285	20	condition	condition	NOUN
ejpam-3412	285	21	(	(	PUNCT
ejpam-3412	285	22	2.2	2.2	NUM
ejpam-3412	285	23	)	)	PUNCT
ejpam-3412	285	24	.	.	PUNCT
ejpam-3412	286	1	a.	a.	PROPN
ejpam-3412	286	2	satirad	satirad	PROPN
ejpam-3412	286	3	,	,	PUNCT
ejpam-3412	286	4	a.	a.	NOUN
ejpam-3412	286	5	iampan	iampan	PROPN
ejpam-3412	286	6	/	/	SYM
ejpam-3412	286	7	eur	eur	PROPN
ejpam-3412	286	8	.	.	PUNCT
ejpam-3412	287	1	j.	j.	PROPN
ejpam-3412	287	2	pure	pure	PROPN
ejpam-3412	287	3	appl	appl	PROPN
ejpam-3412	287	4	.	.	PROPN
ejpam-3412	287	5	math	math	PROPN
ejpam-3412	287	6	,	,	PUNCT
ejpam-3412	287	7	12	12	NUM
ejpam-3412	287	8	(	(	PUNCT
ejpam-3412	287	9	2	2	NUM
ejpam-3412	287	10	)	)	PUNCT
ejpam-3412	287	11	(	(	PUNCT
ejpam-3412	287	12	2019	2019	NUM
ejpam-3412	287	13	)	)	PUNCT
ejpam-3412	287	14	,	,	PUNCT
ejpam-3412	287	15	294	294	NUM
ejpam-3412	287	16	-	-	SYM
ejpam-3412	287	17	331	331	NUM
ejpam-3412	287	18	306	306	NUM
ejpam-3412	287	19	proof	proof	NOUN
ejpam-3412	287	20	.	.	PUNCT
ejpam-3412	288	1	let	let	VERB
ejpam-3412	288	2	x	x	PRON
ejpam-3412	288	3	,	,	PUNCT
ejpam-3412	288	4	y	y	PROPN
ejpam-3412	288	5	∈	∈	PROPN
ejpam-3412	288	6	a	a	DET
ejpam-3412	288	7	such	such	ADJ
ejpam-3412	288	8	that	that	SCONJ
ejpam-3412	288	9	x	x	X
ejpam-3412	288	10	≤	≤	X
ejpam-3412	288	11	y.	y.	NOUN
ejpam-3412	288	12	by	by	ADP
ejpam-3412	288	13	(	(	PUNCT
ejpam-3412	288	14	1.11	1.11	NUM
ejpam-3412	288	15	)	)	PUNCT
ejpam-3412	288	16	,	,	PUNCT
ejpam-3412	288	17	we	we	PRON
ejpam-3412	288	18	have	have	VERB
ejpam-3412	288	19	x	x	NOUN
ejpam-3412	288	20	≤	≤	NUM
ejpam-3412	288	21	x	x	X
ejpam-3412	288	22	·	·	PUNCT
ejpam-3412	288	23	y.	y.	NOUN
ejpam-3412	288	24	it	it	PRON
ejpam-3412	288	25	follows	follow	VERB
ejpam-3412	288	26	from	from	ADP
ejpam-3412	288	27	(	(	PUNCT
ejpam-3412	288	28	2.6	2.6	NUM
ejpam-3412	288	29	)	)	PUNCT
ejpam-3412	289	1	that	that	PRON
ejpam-3412	289	2	ff(y	ff(y	NUM
ejpam-3412	289	3	)	)	PUNCT
ejpam-3412	289	4	≥	≥	PROPN
ejpam-3412	289	5	min{ff(x	min{ff(x	PROPN
ejpam-3412	289	6	)	)	PUNCT
ejpam-3412	289	7	,	,	PUNCT
ejpam-3412	289	8	ff(x	ff(x	NOUN
ejpam-3412	289	9	)	)	PUNCT
ejpam-3412	289	10	}	}	PUNCT
ejpam-3412	289	11	=	=	SYM
ejpam-3412	289	12	ff(x	ff(x	NOUN
ejpam-3412	289	13	)	)	PUNCT
ejpam-3412	290	1	.	.	PUNCT
ejpam-3412	291	1	hence	hence	ADV
ejpam-3412	291	2	,	,	PUNCT
ejpam-3412	291	3	f	f	PROPN
ejpam-3412	291	4	satisfies	satisfie	NOUN
ejpam-3412	291	5	(	(	PUNCT
ejpam-3412	291	6	2.2	2.2	NUM
ejpam-3412	291	7	)	)	PUNCT
ejpam-3412	291	8	.	.	PUNCT
ejpam-3412	292	1	the	the	DET
ejpam-3412	292	2	following	follow	VERB
ejpam-3412	292	3	example	example	NOUN
ejpam-3412	292	4	shows	show	VERB
ejpam-3412	292	5	that	that	SCONJ
ejpam-3412	292	6	the	the	DET
ejpam-3412	292	7	converse	converse	NOUN
ejpam-3412	292	8	of	of	ADP
ejpam-3412	292	9	theorem	theorem	NOUN
ejpam-3412	292	10	13	13	NUM
ejpam-3412	292	11	is	be	AUX
ejpam-3412	292	12	not	not	PART
ejpam-3412	292	13	true	true	ADJ
ejpam-3412	292	14	.	.	PUNCT
ejpam-3412	293	1	example	example	NOUN
ejpam-3412	293	2	10	10	NUM
ejpam-3412	293	3	.	.	PUNCT
ejpam-3412	294	1	let	let	VERB
ejpam-3412	294	2	a	a	PRON
ejpam-3412	294	3	=	=	PUNCT
ejpam-3412	294	4	{	{	PUNCT
ejpam-3412	294	5	0	0	NUM
ejpam-3412	294	6	,	,	PUNCT
ejpam-3412	294	7	1	1	NUM
ejpam-3412	294	8	,	,	PUNCT
ejpam-3412	294	9	2	2	NUM
ejpam-3412	294	10	,	,	PUNCT
ejpam-3412	294	11	3	3	NUM
ejpam-3412	294	12	}	}	PUNCT
ejpam-3412	294	13	be	be	AUX
ejpam-3412	294	14	a	a	DET
ejpam-3412	294	15	set	set	NOUN
ejpam-3412	294	16	with	with	ADP
ejpam-3412	294	17	a	a	DET
ejpam-3412	294	18	binary	binary	ADJ
ejpam-3412	294	19	operation	operation	NOUN
ejpam-3412	294	20	·	·	PUNCT
ejpam-3412	294	21	defined	define	VERB
ejpam-3412	294	22	by	by	ADP
ejpam-3412	294	23	the	the	DET
ejpam-3412	294	24	following	following	ADJ
ejpam-3412	294	25	cayley	cayley	ADJ
ejpam-3412	294	26	table	table	NOUN
ejpam-3412	294	27	:	:	PUNCT
ejpam-3412	294	28	·	·	PUNCT
ejpam-3412	294	29	0	0	NUM
ejpam-3412	295	1	1	1	NUM
ejpam-3412	295	2	2	2	NUM
ejpam-3412	295	3	3	3	NUM
ejpam-3412	295	4	0	0	NUM
ejpam-3412	295	5	0	0	NUM
ejpam-3412	295	6	1	1	NUM
ejpam-3412	295	7	2	2	NUM
ejpam-3412	295	8	3	3	NUM
ejpam-3412	295	9	1	1	NUM
ejpam-3412	295	10	0	0	NUM
ejpam-3412	295	11	0	0	NUM
ejpam-3412	295	12	2	2	NUM
ejpam-3412	295	13	2	2	NUM
ejpam-3412	295	14	2	2	NUM
ejpam-3412	295	15	0	0	NUM
ejpam-3412	295	16	1	1	NUM
ejpam-3412	295	17	0	0	NUM
ejpam-3412	295	18	1	1	NUM
ejpam-3412	295	19	3	3	NUM
ejpam-3412	295	20	0	0	NUM
ejpam-3412	295	21	0	0	NUM
ejpam-3412	295	22	0	0	NUM
ejpam-3412	295	23	0	0	NUM
ejpam-3412	295	24	then	then	ADV
ejpam-3412	295	25	a	a	PRON
ejpam-3412	295	26	=	=	X
ejpam-3412	295	27	(	(	PUNCT
ejpam-3412	295	28	a	a	PRON
ejpam-3412	295	29	,	,	PUNCT
ejpam-3412	295	30	·	·	PUNCT
ejpam-3412	295	31	,	,	PUNCT
ejpam-3412	295	32	0	0	NUM
ejpam-3412	295	33	)	)	PUNCT
ejpam-3412	295	34	is	be	AUX
ejpam-3412	295	35	a	a	DET
ejpam-3412	295	36	up	up	NOUN
ejpam-3412	295	37	-	-	PUNCT
ejpam-3412	295	38	algebra	algebra	NOUN
ejpam-3412	295	39	.	.	PUNCT
ejpam-3412	296	1	we	we	PRON
ejpam-3412	296	2	define	define	VERB
ejpam-3412	296	3	a	a	DET
ejpam-3412	296	4	membership	membership	NOUN
ejpam-3412	296	5	function	function	NOUN
ejpam-3412	296	6	ff	ff	NOUN
ejpam-3412	296	7	as	as	SCONJ
ejpam-3412	296	8	follows	follow	VERB
ejpam-3412	296	9	:	:	PUNCT
ejpam-3412	296	10	ff(0	ff(0	NOUN
ejpam-3412	296	11	)	)	PUNCT
ejpam-3412	296	12	=	=	SYM
ejpam-3412	296	13	0.9	0.9	NUM
ejpam-3412	296	14	,	,	PUNCT
ejpam-3412	296	15	ff(1	ff(1	PROPN
ejpam-3412	296	16	)	)	PUNCT
ejpam-3412	296	17	=	=	SYM
ejpam-3412	296	18	0.3	0.3	NUM
ejpam-3412	296	19	,	,	PUNCT
ejpam-3412	296	20	ff(2	ff(2	PROPN
ejpam-3412	296	21	)	)	PUNCT
ejpam-3412	296	22	=	=	SYM
ejpam-3412	296	23	0.6	0.6	NUM
ejpam-3412	296	24	,	,	PUNCT
ejpam-3412	296	25	and	and	CCONJ
ejpam-3412	296	26	ff(3	ff(3	NOUN
ejpam-3412	296	27	)	)	PUNCT
ejpam-3412	296	28	=	=	NOUN
ejpam-3412	296	29	0.2	0.2	NUM
ejpam-3412	296	30	.	.	PUNCT
ejpam-3412	297	1	then	then	ADV
ejpam-3412	297	2	f	f	PROPN
ejpam-3412	297	3	satisfies	satisfy	VERB
ejpam-3412	297	4	the	the	DET
ejpam-3412	297	5	condition	condition	NOUN
ejpam-3412	297	6	(	(	PUNCT
ejpam-3412	297	7	2.2	2.2	NUM
ejpam-3412	297	8	)	)	PUNCT
ejpam-3412	297	9	but	but	CCONJ
ejpam-3412	297	10	it	it	PRON
ejpam-3412	297	11	does	do	AUX
ejpam-3412	297	12	not	not	PART
ejpam-3412	297	13	satisfy	satisfy	VERB
ejpam-3412	297	14	the	the	DET
ejpam-3412	297	15	condition	condition	NOUN
ejpam-3412	297	16	(	(	PUNCT
ejpam-3412	297	17	2.6	2.6	NUM
ejpam-3412	297	18	)	)	PUNCT
ejpam-3412	297	19	.	.	PUNCT
ejpam-3412	298	1	indeed	indeed	ADV
ejpam-3412	298	2	,	,	PUNCT
ejpam-3412	298	3	1	1	NUM
ejpam-3412	298	4	≤	≤	NUM
ejpam-3412	298	5	2	2	NUM
ejpam-3412	298	6	·	·	SYM
ejpam-3412	298	7	3	3	NUM
ejpam-3412	298	8	but	but	CCONJ
ejpam-3412	298	9	ff(3	ff(3	NOUN
ejpam-3412	298	10	)	)	PUNCT
ejpam-3412	298	11	=	=	SYM
ejpam-3412	298	12	0.2	0.2	NUM
ejpam-3412	298	13	�	�	PROPN
ejpam-3412	298	14	0.3	0.3	NUM
ejpam-3412	298	15	=	=	SYM
ejpam-3412	298	16	min{0.3	min{0.3	PROPN
ejpam-3412	298	17	,	,	PUNCT
ejpam-3412	298	18	0.6	0.6	NUM
ejpam-3412	298	19	}	}	PUNCT
ejpam-3412	298	20	=	=	SYM
ejpam-3412	298	21	min{ff(1	min{ff(1	PROPN
ejpam-3412	298	22	)	)	PUNCT
ejpam-3412	298	23	,	,	PUNCT
ejpam-3412	298	24	ff(2	ff(2	NOUN
ejpam-3412	298	25	)	)	PUNCT
ejpam-3412	298	26	}	}	PUNCT
ejpam-3412	298	27	.	.	PUNCT
ejpam-3412	299	1	theorem	theorem	VERB
ejpam-3412	299	2	14	14	NUM
ejpam-3412	299	3	.	.	PUNCT
ejpam-3412	300	1	if	if	SCONJ
ejpam-3412	300	2	f	f	PROPN
ejpam-3412	300	3	is	be	AUX
ejpam-3412	300	4	a	a	DET
ejpam-3412	300	5	fuzzy	fuzzy	ADJ
ejpam-3412	300	6	near	near	ADP
ejpam-3412	300	7	up	up	ADJ
ejpam-3412	300	8	-	-	PUNCT
ejpam-3412	300	9	filter	filter	NOUN
ejpam-3412	300	10	of	of	ADP
ejpam-3412	300	11	a	a	DET
ejpam-3412	300	12	satisfying	satisfying	NOUN
ejpam-3412	300	13	the	the	DET
ejpam-3412	300	14	condition	condition	NOUN
ejpam-3412	300	15	(	(	PUNCT
ejpam-3412	300	16	∀x	∀x	NUM
ejpam-3412	300	17	,	,	PUNCT
ejpam-3412	300	18	y	y	PROPN
ejpam-3412	300	19	∈	∈	PROPN
ejpam-3412	300	20	a)(ff(x	a)(ff(x	PUNCT
ejpam-3412	300	21	·	·	PUNCT
ejpam-3412	300	22	y	y	X
ejpam-3412	300	23	)	)	PUNCT
ejpam-3412	300	24	=	=	SYM
ejpam-3412	300	25	ff(y	ff(y	NUM
ejpam-3412	300	26	)	)	PUNCT
ejpam-3412	300	27	)	)	PUNCT
ejpam-3412	300	28	,	,	PUNCT
ejpam-3412	300	29	(	(	PUNCT
ejpam-3412	300	30	2.7	2.7	NUM
ejpam-3412	300	31	)	)	PUNCT
ejpam-3412	300	32	then	then	ADV
ejpam-3412	300	33	f	f	PROPN
ejpam-3412	300	34	is	be	AUX
ejpam-3412	300	35	a	a	DET
ejpam-3412	300	36	fuzzy	fuzzy	ADJ
ejpam-3412	300	37	up	up	ADJ
ejpam-3412	300	38	-	-	PUNCT
ejpam-3412	300	39	filter	filter	NOUN
ejpam-3412	300	40	of	of	ADP
ejpam-3412	300	41	a.	a.	NOUN
ejpam-3412	300	42	proof	proof	NOUN
ejpam-3412	300	43	.	.	PUNCT
ejpam-3412	301	1	let	let	VERB
ejpam-3412	301	2	x	x	PRON
ejpam-3412	301	3	,	,	PUNCT
ejpam-3412	301	4	y	y	PROPN
ejpam-3412	301	5	∈	∈	PROPN
ejpam-3412	301	6	a.	a.	NOUN
ejpam-3412	301	7	by	by	ADP
ejpam-3412	301	8	(	(	PUNCT
ejpam-3412	301	9	2.7	2.7	NUM
ejpam-3412	301	10	)	)	PUNCT
ejpam-3412	301	11	,	,	PUNCT
ejpam-3412	301	12	we	we	PRON
ejpam-3412	301	13	have	have	VERB
ejpam-3412	301	14	ff(y	ff(y	NUM
ejpam-3412	301	15	)	)	PUNCT
ejpam-3412	301	16	≥	≥	NOUN
ejpam-3412	301	17	min{ff(y	min{ff(y	NOUN
ejpam-3412	301	18	)	)	PUNCT
ejpam-3412	301	19	,	,	PUNCT
ejpam-3412	301	20	ff(x	ff(x	NOUN
ejpam-3412	301	21	)	)	PUNCT
ejpam-3412	301	22	}	}	PUNCT
ejpam-3412	301	23	=	=	SYM
ejpam-3412	301	24	min{ff(x	min{ff(x	X
ejpam-3412	301	25	·	·	PUNCT
ejpam-3412	301	26	y	y	PROPN
ejpam-3412	301	27	)	)	PUNCT
ejpam-3412	301	28	,	,	PUNCT
ejpam-3412	301	29	ff(x	ff(x	NOUN
ejpam-3412	301	30	)	)	PUNCT
ejpam-3412	301	31	}	}	PUNCT
ejpam-3412	301	32	.	.	PUNCT
ejpam-3412	302	1	hence	hence	ADV
ejpam-3412	302	2	,	,	PUNCT
ejpam-3412	302	3	f	f	PROPN
ejpam-3412	302	4	is	be	AUX
ejpam-3412	302	5	a	a	DET
ejpam-3412	302	6	fuzzy	fuzzy	ADJ
ejpam-3412	302	7	up	up	ADJ
ejpam-3412	302	8	-	-	PUNCT
ejpam-3412	302	9	filter	filter	NOUN
ejpam-3412	302	10	of	of	ADP
ejpam-3412	302	11	a.	a.	NOUN
ejpam-3412	302	12	proposition	proposition	NOUN
ejpam-3412	302	13	7	7	NUM
ejpam-3412	302	14	.	.	PUNCT
ejpam-3412	303	1	a	a	DET
ejpam-3412	303	2	fuzzy	fuzzy	ADJ
ejpam-3412	303	3	set	set	NOUN
ejpam-3412	303	4	f	f	PROPN
ejpam-3412	303	5	in	in	ADP
ejpam-3412	303	6	a	a	DET
ejpam-3412	303	7	satisfies	satisfie	NOUN
ejpam-3412	303	8	the	the	DET
ejpam-3412	303	9	condition	condition	NOUN
ejpam-3412	303	10	(	(	PUNCT
ejpam-3412	303	11	∀a	∀a	X
ejpam-3412	303	12	,	,	PUNCT
ejpam-3412	303	13	x	x	X
ejpam-3412	303	14	,	,	PUNCT
ejpam-3412	303	15	y	y	PROPN
ejpam-3412	303	16	,	,	PUNCT
ejpam-3412	303	17	z	z	NOUN
ejpam-3412	303	18	∈	∈	PROPN
ejpam-3412	303	19	a)(a	a)(a	PUNCT
ejpam-3412	303	20	≤	≤	NUM
ejpam-3412	303	21	x	x	SYM
ejpam-3412	303	22	·	·	PUNCT
ejpam-3412	303	23	(	(	PUNCT
ejpam-3412	303	24	y	y	PROPN
ejpam-3412	303	25	·	·	PUNCT
ejpam-3412	303	26	z)⇒	z)⇒	NOUN
ejpam-3412	303	27	ff(x	ff(x	NOUN
ejpam-3412	303	28	·	·	PUNCT
ejpam-3412	303	29	z	z	X
ejpam-3412	303	30	)	)	PUNCT
ejpam-3412	303	31	≥	≥	NOUN
ejpam-3412	303	32	min{ff(a	min{ff(a	NOUN
ejpam-3412	303	33	)	)	PUNCT
ejpam-3412	303	34	,	,	PUNCT
ejpam-3412	303	35	ff(y	ff(y	NUM
ejpam-3412	303	36	)	)	PUNCT
ejpam-3412	303	37	}	}	PUNCT
ejpam-3412	303	38	)	)	PUNCT
ejpam-3412	303	39	(	(	PUNCT
ejpam-3412	303	40	2.8	2.8	NUM
ejpam-3412	303	41	)	)	PUNCT
ejpam-3412	303	42	if	if	SCONJ
ejpam-3412	303	43	and	and	CCONJ
ejpam-3412	303	44	only	only	ADV
ejpam-3412	303	45	if	if	SCONJ
ejpam-3412	303	46	f	f	PROPN
ejpam-3412	303	47	is	be	AUX
ejpam-3412	303	48	a	a	DET
ejpam-3412	303	49	fuzzy	fuzzy	ADJ
ejpam-3412	303	50	up	up	ADJ
ejpam-3412	303	51	-	-	PUNCT
ejpam-3412	303	52	ideal	ideal	NOUN
ejpam-3412	303	53	of	of	ADP
ejpam-3412	303	54	a.	a.	NOUN
ejpam-3412	303	55	proof	proof	NOUN
ejpam-3412	303	56	.	.	PUNCT
ejpam-3412	304	1	let	let	VERB
ejpam-3412	304	2	x	x	PUNCT
ejpam-3412	304	3	∈	∈	VERB
ejpam-3412	304	4	a.	a.	NOUN
ejpam-3412	304	5	by	by	ADP
ejpam-3412	304	6	(	(	PUNCT
ejpam-3412	304	7	up-3	up-3	NOUN
ejpam-3412	304	8	)	)	PUNCT
ejpam-3412	304	9	,	,	PUNCT
ejpam-3412	304	10	we	we	PRON
ejpam-3412	304	11	have	have	VERB
ejpam-3412	304	12	x	x	NOUN
ejpam-3412	304	13	≤	≤	NUM
ejpam-3412	304	14	x	x	SYM
ejpam-3412	304	15	·	·	PUNCT
ejpam-3412	304	16	(	(	PUNCT
ejpam-3412	304	17	x	x	X
ejpam-3412	304	18	·	·	PUNCT
ejpam-3412	304	19	0	0	NUM
ejpam-3412	304	20	)	)	PUNCT
ejpam-3412	304	21	.	.	PUNCT
ejpam-3412	305	1	by	by	ADP
ejpam-3412	305	2	(	(	PUNCT
ejpam-3412	305	3	up-3	up-3	NOUN
ejpam-3412	305	4	)	)	PUNCT
ejpam-3412	305	5	and	and	CCONJ
ejpam-3412	305	6	(	(	PUNCT
ejpam-3412	305	7	2.8	2.8	NUM
ejpam-3412	305	8	)	)	PUNCT
ejpam-3412	305	9	,	,	PUNCT
ejpam-3412	305	10	we	we	PRON
ejpam-3412	305	11	have	have	VERB
ejpam-3412	305	12	ff(0	ff(0	NOUN
ejpam-3412	305	13	)	)	PUNCT
ejpam-3412	305	14	=	=	NOUN
ejpam-3412	305	15	ff(x	ff(x	X
ejpam-3412	305	16	·	·	PUNCT
ejpam-3412	305	17	0	0	NUM
ejpam-3412	305	18	)	)	PUNCT
ejpam-3412	305	19	≥	≥	PROPN
ejpam-3412	305	20	min{ff(x	min{ff(x	PROPN
ejpam-3412	305	21	)	)	PUNCT
ejpam-3412	305	22	,	,	PUNCT
ejpam-3412	305	23	ff(x	ff(x	NOUN
ejpam-3412	305	24	)	)	PUNCT
ejpam-3412	305	25	}	}	PUNCT
ejpam-3412	305	26	=	=	SYM
ejpam-3412	305	27	ff(x	ff(x	NOUN
ejpam-3412	305	28	)	)	PUNCT
ejpam-3412	305	29	.	.	PUNCT
ejpam-3412	306	1	let	let	VERB
ejpam-3412	306	2	x	x	PRON
ejpam-3412	306	3	,	,	PUNCT
ejpam-3412	306	4	y	y	PROPN
ejpam-3412	306	5	,	,	PUNCT
ejpam-3412	306	6	z	z	PROPN
ejpam-3412	306	7	∈	∈	NOUN
ejpam-3412	306	8	a.	a.	NOUN
ejpam-3412	306	9	by	by	ADP
ejpam-3412	306	10	(	(	PUNCT
ejpam-3412	306	11	1.1	1.1	NUM
ejpam-3412	306	12	)	)	PUNCT
ejpam-3412	306	13	,	,	PUNCT
ejpam-3412	306	14	we	we	PRON
ejpam-3412	306	15	have	have	VERB
ejpam-3412	306	16	x	x	X
ejpam-3412	306	17	·	·	PUNCT
ejpam-3412	306	18	(	(	PUNCT
ejpam-3412	306	19	y	y	PROPN
ejpam-3412	306	20	·	·	PUNCT
ejpam-3412	306	21	z	z	X
ejpam-3412	306	22	)	)	PUNCT
ejpam-3412	306	23	≤	≤	NUM
ejpam-3412	306	24	x	x	X
ejpam-3412	306	25	·	·	PUNCT
ejpam-3412	306	26	(	(	PUNCT
ejpam-3412	306	27	y	y	PROPN
ejpam-3412	306	28	·	·	PUNCT
ejpam-3412	307	1	z	z	X
ejpam-3412	307	2	)	)	PUNCT
ejpam-3412	307	3	.	.	PUNCT
ejpam-3412	308	1	it	it	PRON
ejpam-3412	308	2	follows	follow	VERB
ejpam-3412	308	3	from	from	ADP
ejpam-3412	308	4	(	(	PUNCT
ejpam-3412	308	5	2.8	2.8	NUM
ejpam-3412	308	6	)	)	PUNCT
ejpam-3412	308	7	that	that	PRON
ejpam-3412	308	8	ff(x	ff(x	VERB
ejpam-3412	308	9	·	·	PUNCT
ejpam-3412	308	10	z	z	X
ejpam-3412	308	11	)	)	PUNCT
ejpam-3412	308	12	≥	≥	PROPN
ejpam-3412	308	13	min{ff(x	min{ff(x	PROPN
ejpam-3412	308	14	·	·	PUNCT
ejpam-3412	308	15	(	(	PUNCT
ejpam-3412	308	16	y	y	PROPN
ejpam-3412	308	17	·	·	PUNCT
ejpam-3412	308	18	z	z	NOUN
ejpam-3412	308	19	)	)	PUNCT
ejpam-3412	308	20	)	)	PUNCT
ejpam-3412	308	21	,	,	PUNCT
ejpam-3412	308	22	ff(y	ff(y	NUM
ejpam-3412	308	23	)	)	PUNCT
ejpam-3412	308	24	}	}	PUNCT
ejpam-3412	308	25	.	.	PUNCT
ejpam-3412	309	1	hence	hence	ADV
ejpam-3412	309	2	,	,	PUNCT
ejpam-3412	309	3	f	f	PROPN
ejpam-3412	309	4	is	be	AUX
ejpam-3412	309	5	a	a	DET
ejpam-3412	309	6	fuzzy	fuzzy	ADJ
ejpam-3412	309	7	up	up	ADJ
ejpam-3412	309	8	-	-	PUNCT
ejpam-3412	309	9	ideal	ideal	NOUN
ejpam-3412	309	10	of	of	ADP
ejpam-3412	309	11	a.	a.	NOUN
ejpam-3412	309	12	conversely	conversely	ADV
ejpam-3412	309	13	,	,	PUNCT
ejpam-3412	309	14	let	let	VERB
ejpam-3412	309	15	a	a	DET
ejpam-3412	309	16	,	,	PUNCT
ejpam-3412	309	17	x	x	NOUN
ejpam-3412	309	18	,	,	PUNCT
ejpam-3412	309	19	y	y	PROPN
ejpam-3412	309	20	,	,	PUNCT
ejpam-3412	309	21	z	z	PROPN
ejpam-3412	309	22	∈	∈	PROPN
ejpam-3412	309	23	a	a	DET
ejpam-3412	309	24	be	be	AUX
ejpam-3412	309	25	such	such	ADJ
ejpam-3412	309	26	that	that	SCONJ
ejpam-3412	309	27	a	a	DET
ejpam-3412	309	28	≤	≤	NOUN
ejpam-3412	309	29	x	x	SYM
ejpam-3412	309	30	·	·	PUNCT
ejpam-3412	309	31	(	(	PUNCT
ejpam-3412	309	32	y	y	PROPN
ejpam-3412	309	33	·	·	PUNCT
ejpam-3412	309	34	z	z	NOUN
ejpam-3412	309	35	)	)	PUNCT
ejpam-3412	309	36	.	.	PUNCT
ejpam-3412	310	1	by	by	ADP
ejpam-3412	310	2	proposition	proposition	NOUN
ejpam-3412	310	3	2	2	NUM
ejpam-3412	310	4	,	,	PUNCT
ejpam-3412	310	5	we	we	PRON
ejpam-3412	310	6	have	have	AUX
ejpam-3412	310	7	ff(a	ff(a	VERB
ejpam-3412	310	8	)	)	PUNCT
ejpam-3412	310	9	≤	≤	NOUN
ejpam-3412	310	10	ff(x	ff(x	X
ejpam-3412	310	11	·	·	PUNCT
ejpam-3412	310	12	(	(	PUNCT
ejpam-3412	310	13	y	y	PROPN
ejpam-3412	310	14	·	·	PUNCT
ejpam-3412	310	15	z	z	NOUN
ejpam-3412	310	16	)	)	PUNCT
ejpam-3412	310	17	)	)	PUNCT
ejpam-3412	310	18	.	.	PUNCT
ejpam-3412	311	1	thus	thus	ADV
ejpam-3412	311	2	ff(x	ff(x	X
ejpam-3412	311	3	·	·	PUNCT
ejpam-3412	311	4	z	z	X
ejpam-3412	311	5	)	)	PUNCT
ejpam-3412	311	6	≥	≥	PROPN
ejpam-3412	311	7	min{ff(x	min{ff(x	PROPN
ejpam-3412	311	8	·	·	PUNCT
ejpam-3412	311	9	(	(	PUNCT
ejpam-3412	311	10	y	y	PROPN
ejpam-3412	311	11	·	·	PUNCT
ejpam-3412	311	12	z	z	NOUN
ejpam-3412	311	13	)	)	PUNCT
ejpam-3412	311	14	)	)	PUNCT
ejpam-3412	311	15	,	,	PUNCT
ejpam-3412	311	16	ff(y	ff(y	NUM
ejpam-3412	311	17	)	)	PUNCT
ejpam-3412	311	18	}	}	PUNCT
ejpam-3412	311	19	≥	≥	X
ejpam-3412	311	20	min{ff(a	min{ff(a	NOUN
ejpam-3412	311	21	)	)	PUNCT
ejpam-3412	311	22	,	,	PUNCT
ejpam-3412	311	23	ff(y	ff(y	NUM
ejpam-3412	311	24	)	)	PUNCT
ejpam-3412	311	25	}	}	PUNCT
ejpam-3412	311	26	.	.	PUNCT
ejpam-3412	312	1	hence	hence	ADV
ejpam-3412	312	2	,	,	PUNCT
ejpam-3412	312	3	f	f	PROPN
ejpam-3412	312	4	satisfies	satisfie	NOUN
ejpam-3412	312	5	(	(	PUNCT
ejpam-3412	312	6	2.8	2.8	NUM
ejpam-3412	312	7	)	)	PUNCT
ejpam-3412	312	8	.	.	PUNCT
ejpam-3412	313	1	a.	a.	PROPN
ejpam-3412	313	2	satirad	satirad	PROPN
ejpam-3412	313	3	,	,	PUNCT
ejpam-3412	313	4	a.	a.	NOUN
ejpam-3412	313	5	iampan	iampan	PROPN
ejpam-3412	313	6	/	/	SYM
ejpam-3412	313	7	eur	eur	PROPN
ejpam-3412	313	8	.	.	PUNCT
ejpam-3412	314	1	j.	j.	PROPN
ejpam-3412	314	2	pure	pure	PROPN
ejpam-3412	314	3	appl	appl	PROPN
ejpam-3412	314	4	.	.	PROPN
ejpam-3412	314	5	math	math	PROPN
ejpam-3412	314	6	,	,	PUNCT
ejpam-3412	314	7	12	12	NUM
ejpam-3412	314	8	(	(	PUNCT
ejpam-3412	314	9	2	2	NUM
ejpam-3412	314	10	)	)	PUNCT
ejpam-3412	314	11	(	(	PUNCT
ejpam-3412	314	12	2019	2019	NUM
ejpam-3412	314	13	)	)	PUNCT
ejpam-3412	314	14	,	,	PUNCT
ejpam-3412	314	15	294	294	NUM
ejpam-3412	314	16	-	-	SYM
ejpam-3412	314	17	331	331	NUM
ejpam-3412	314	18	307	307	NUM
ejpam-3412	314	19	proposition	proposition	NOUN
ejpam-3412	314	20	8	8	NUM
ejpam-3412	314	21	.	.	PUNCT
ejpam-3412	315	1	if	if	SCONJ
ejpam-3412	315	2	f	f	PROPN
ejpam-3412	315	3	is	be	AUX
ejpam-3412	315	4	a	a	DET
ejpam-3412	315	5	fuzzy	fuzzy	ADJ
ejpam-3412	315	6	up	up	ADJ
ejpam-3412	315	7	-	-	PUNCT
ejpam-3412	315	8	ideal	ideal	NOUN
ejpam-3412	315	9	of	of	ADP
ejpam-3412	315	10	a	a	PRON
ejpam-3412	315	11	,	,	PUNCT
ejpam-3412	315	12	then	then	ADV
ejpam-3412	315	13	(	(	PUNCT
ejpam-3412	315	14	∀a	∀a	NOUN
ejpam-3412	315	15	,	,	PUNCT
ejpam-3412	315	16	x	x	X
ejpam-3412	315	17	,	,	PUNCT
ejpam-3412	315	18	y	y	PROPN
ejpam-3412	315	19	,	,	PUNCT
ejpam-3412	315	20	z	z	NOUN
ejpam-3412	315	21	∈	∈	PROPN
ejpam-3412	315	22	a)(a	a)(a	PUNCT
ejpam-3412	315	23	≤	≤	NUM
ejpam-3412	315	24	x	x	SYM
ejpam-3412	315	25	·	·	PUNCT
ejpam-3412	315	26	(	(	PUNCT
ejpam-3412	315	27	y	y	PROPN
ejpam-3412	315	28	·	·	PUNCT
ejpam-3412	315	29	z)⇒	z)⇒	NOUN
ejpam-3412	315	30	ff(a	ff(a	NUM
ejpam-3412	316	1	·	·	PUNCT
ejpam-3412	316	2	z	z	X
ejpam-3412	316	3	)	)	PUNCT
ejpam-3412	316	4	≥	≥	PROPN
ejpam-3412	316	5	min{ff(x	min{ff(x	PROPN
ejpam-3412	316	6	)	)	PUNCT
ejpam-3412	316	7	,	,	PUNCT
ejpam-3412	316	8	ff(y	ff(y	NUM
ejpam-3412	316	9	)	)	PUNCT
ejpam-3412	316	10	}	}	PUNCT
ejpam-3412	316	11	)	)	PUNCT
ejpam-3412	316	12	.	.	PUNCT
ejpam-3412	317	1	(	(	PUNCT
ejpam-3412	317	2	2.9	2.9	NUM
ejpam-3412	317	3	)	)	PUNCT
ejpam-3412	317	4	proof	proof	NOUN
ejpam-3412	317	5	.	.	PUNCT
ejpam-3412	318	1	let	let	VERB
ejpam-3412	318	2	a	a	DET
ejpam-3412	318	3	,	,	PUNCT
ejpam-3412	318	4	x	x	NOUN
ejpam-3412	318	5	,	,	PUNCT
ejpam-3412	318	6	y	y	PROPN
ejpam-3412	318	7	,	,	PUNCT
ejpam-3412	318	8	z	z	PROPN
ejpam-3412	318	9	∈	∈	PROPN
ejpam-3412	318	10	a	a	DET
ejpam-3412	318	11	be	be	AUX
ejpam-3412	318	12	such	such	ADJ
ejpam-3412	318	13	that	that	SCONJ
ejpam-3412	318	14	a	a	DET
ejpam-3412	318	15	≤	≤	NOUN
ejpam-3412	318	16	x	x	SYM
ejpam-3412	318	17	·	·	PUNCT
ejpam-3412	318	18	(	(	PUNCT
ejpam-3412	318	19	y	y	PROPN
ejpam-3412	318	20	·	·	PUNCT
ejpam-3412	318	21	z	z	X
ejpam-3412	318	22	)	)	PUNCT
ejpam-3412	318	23	.	.	PUNCT
ejpam-3412	319	1	then	then	ADV
ejpam-3412	319	2	a	a	DET
ejpam-3412	319	3	·	·	PUNCT
ejpam-3412	319	4	(	(	PUNCT
ejpam-3412	319	5	x	x	PART
ejpam-3412	319	6	·	·	PUNCT
ejpam-3412	319	7	(	(	PUNCT
ejpam-3412	319	8	y	y	PROPN
ejpam-3412	319	9	·	·	PUNCT
ejpam-3412	319	10	z	z	NOUN
ejpam-3412	319	11	)	)	PUNCT
ejpam-3412	319	12	)	)	PUNCT
ejpam-3412	320	1	=	=	PUNCT
ejpam-3412	320	2	0	0	NUM
ejpam-3412	320	3	,	,	PUNCT
ejpam-3412	320	4	so	so	ADV
ejpam-3412	320	5	ff(a	ff(a	ADP
ejpam-3412	320	6	·	·	PUNCT
ejpam-3412	320	7	(	(	PUNCT
ejpam-3412	320	8	y	y	PROPN
ejpam-3412	320	9	·	·	PUNCT
ejpam-3412	320	10	z	z	NOUN
ejpam-3412	320	11	)	)	PUNCT
ejpam-3412	320	12	)	)	PUNCT
ejpam-3412	320	13	≥	≥	AUX
ejpam-3412	320	14	min{ff(a	min{ff(a	X
ejpam-3412	320	15	·	·	PUNCT
ejpam-3412	320	16	(	(	PUNCT
ejpam-3412	320	17	x	x	X
ejpam-3412	320	18	·	·	PUNCT
ejpam-3412	320	19	(	(	PUNCT
ejpam-3412	320	20	y	y	PROPN
ejpam-3412	320	21	·	·	PUNCT
ejpam-3412	320	22	z	z	NOUN
ejpam-3412	320	23	)	)	PUNCT
ejpam-3412	320	24	)	)	PUNCT
ejpam-3412	320	25	)	)	PUNCT
ejpam-3412	320	26	,	,	PUNCT
ejpam-3412	320	27	ff(x	ff(x	NOUN
ejpam-3412	320	28	)	)	PUNCT
ejpam-3412	320	29	}	}	PUNCT
ejpam-3412	320	30	=	=	SYM
ejpam-3412	320	31	min{ff(0	min{ff(0	PROPN
ejpam-3412	320	32	)	)	PUNCT
ejpam-3412	320	33	,	,	PUNCT
ejpam-3412	320	34	ff(x	ff(x	NOUN
ejpam-3412	320	35	)	)	PUNCT
ejpam-3412	320	36	}	}	PUNCT
ejpam-3412	320	37	=	=	SYM
ejpam-3412	320	38	ff(x	ff(x	NOUN
ejpam-3412	320	39	)	)	PUNCT
ejpam-3412	320	40	.	.	PUNCT
ejpam-3412	321	1	thus	thus	ADV
ejpam-3412	321	2	ff(a	ff(a	X
ejpam-3412	321	3	·	·	PUNCT
ejpam-3412	322	1	z	z	X
ejpam-3412	322	2	)	)	PUNCT
ejpam-3412	322	3	≥	≥	NOUN
ejpam-3412	322	4	min{ff(a	min{ff(a	X
ejpam-3412	322	5	·	·	PUNCT
ejpam-3412	322	6	(	(	PUNCT
ejpam-3412	322	7	y	y	PROPN
ejpam-3412	322	8	·	·	PUNCT
ejpam-3412	322	9	z	z	NOUN
ejpam-3412	322	10	)	)	PUNCT
ejpam-3412	322	11	)	)	PUNCT
ejpam-3412	322	12	,	,	PUNCT
ejpam-3412	322	13	ff(y	ff(y	NUM
ejpam-3412	322	14	)	)	PUNCT
ejpam-3412	322	15	}	}	PUNCT
ejpam-3412	322	16	≥	≥	PROPN
ejpam-3412	322	17	min{ff(x	min{ff(x	PROPN
ejpam-3412	322	18	)	)	PUNCT
ejpam-3412	322	19	,	,	PUNCT
ejpam-3412	322	20	ff(y	ff(y	NUM
ejpam-3412	322	21	)	)	PUNCT
ejpam-3412	322	22	}	}	PUNCT
ejpam-3412	322	23	.	.	PUNCT
ejpam-3412	323	1	corollary	corollary	ADJ
ejpam-3412	323	2	1	1	NUM
ejpam-3412	323	3	.	.	PUNCT
ejpam-3412	324	1	if	if	SCONJ
ejpam-3412	324	2	f	f	PROPN
ejpam-3412	324	3	is	be	AUX
ejpam-3412	324	4	a	a	DET
ejpam-3412	324	5	fuzzy	fuzzy	ADJ
ejpam-3412	324	6	set	set	NOUN
ejpam-3412	324	7	in	in	ADP
ejpam-3412	324	8	a	a	DET
ejpam-3412	324	9	satisfying	satisfying	NOUN
ejpam-3412	324	10	the	the	DET
ejpam-3412	324	11	condition	condition	NOUN
ejpam-3412	324	12	(	(	PUNCT
ejpam-3412	324	13	2.8	2.8	NUM
ejpam-3412	324	14	)	)	PUNCT
ejpam-3412	324	15	,	,	PUNCT
ejpam-3412	324	16	then	then	ADV
ejpam-3412	324	17	f	f	PROPN
ejpam-3412	324	18	satisfies	satisfy	VERB
ejpam-3412	324	19	the	the	DET
ejpam-3412	324	20	condition	condition	NOUN
ejpam-3412	324	21	(	(	PUNCT
ejpam-3412	324	22	2.9	2.9	NUM
ejpam-3412	324	23	)	)	PUNCT
ejpam-3412	324	24	.	.	PUNCT
ejpam-3412	325	1	proof	proof	NOUN
ejpam-3412	325	2	.	.	PUNCT
ejpam-3412	326	1	it	it	PRON
ejpam-3412	326	2	is	be	AUX
ejpam-3412	326	3	straightforward	straightforward	ADJ
ejpam-3412	326	4	by	by	ADP
ejpam-3412	326	5	propositions	proposition	NOUN
ejpam-3412	326	6	7	7	NUM
ejpam-3412	326	7	and	and	CCONJ
ejpam-3412	326	8	8	8	NUM
ejpam-3412	326	9	.	.	PUNCT
ejpam-3412	327	1	theorem	theorem	NOUN
ejpam-3412	327	2	15	15	NUM
ejpam-3412	327	3	.	.	PUNCT
ejpam-3412	328	1	let	let	VERB
ejpam-3412	328	2	a	a	PRON
ejpam-3412	328	3	be	be	AUX
ejpam-3412	328	4	a	a	DET
ejpam-3412	328	5	up	up	ADJ
ejpam-3412	328	6	-	-	PUNCT
ejpam-3412	328	7	algebra	algebra	NOUN
ejpam-3412	328	8	satisfying	satisfy	VERB
ejpam-3412	328	9	the	the	DET
ejpam-3412	328	10	condition	condition	NOUN
ejpam-3412	328	11	(	(	PUNCT
ejpam-3412	328	12	∀x	∀x	X
ejpam-3412	328	13	,	,	PUNCT
ejpam-3412	328	14	y	y	PROPN
ejpam-3412	328	15	,	,	PUNCT
ejpam-3412	328	16	z	z	PROPN
ejpam-3412	328	17	∈	∈	PROPN
ejpam-3412	328	18	a)(z	a)(z	PUNCT
ejpam-3412	328	19	·	·	PUNCT
ejpam-3412	329	1	(	(	PUNCT
ejpam-3412	329	2	y	y	PROPN
ejpam-3412	329	3	·	·	PUNCT
ejpam-3412	329	4	x	x	X
ejpam-3412	329	5	)	)	PUNCT
ejpam-3412	329	6	=	=	SYM
ejpam-3412	329	7	y	y	PROPN
ejpam-3412	329	8	·	·	PUNCT
ejpam-3412	329	9	(	(	PUNCT
ejpam-3412	329	10	z	z	NOUN
ejpam-3412	329	11	·	·	PUNCT
ejpam-3412	329	12	x	x	X
ejpam-3412	329	13	)	)	PUNCT
ejpam-3412	329	14	)	)	PUNCT
ejpam-3412	329	15	.	.	PUNCT
ejpam-3412	330	1	(	(	PUNCT
ejpam-3412	330	2	2.10	2.10	NUM
ejpam-3412	330	3	)	)	PUNCT
ejpam-3412	330	4	if	if	SCONJ
ejpam-3412	330	5	f	f	PROPN
ejpam-3412	330	6	is	be	AUX
ejpam-3412	330	7	a	a	DET
ejpam-3412	330	8	fuzzy	fuzzy	ADJ
ejpam-3412	330	9	set	set	NOUN
ejpam-3412	330	10	in	in	ADP
ejpam-3412	330	11	a	a	DET
ejpam-3412	330	12	satisfying	satisfying	NOUN
ejpam-3412	330	13	the	the	DET
ejpam-3412	330	14	condition	condition	NOUN
ejpam-3412	330	15	(	(	PUNCT
ejpam-3412	330	16	2.9	2.9	NUM
ejpam-3412	330	17	)	)	PUNCT
ejpam-3412	330	18	,	,	PUNCT
ejpam-3412	330	19	then	then	ADV
ejpam-3412	330	20	f	f	PROPN
ejpam-3412	330	21	satisfies	satisfy	VERB
ejpam-3412	330	22	the	the	DET
ejpam-3412	330	23	condition	condition	NOUN
ejpam-3412	330	24	(	(	PUNCT
ejpam-3412	330	25	2.8	2.8	NUM
ejpam-3412	330	26	)	)	PUNCT
ejpam-3412	330	27	.	.	PUNCT
ejpam-3412	331	1	proof	proof	NOUN
ejpam-3412	331	2	.	.	PUNCT
ejpam-3412	332	1	let	let	VERB
ejpam-3412	332	2	a	a	DET
ejpam-3412	332	3	,	,	PUNCT
ejpam-3412	332	4	x	x	NOUN
ejpam-3412	332	5	,	,	PUNCT
ejpam-3412	332	6	y	y	PROPN
ejpam-3412	332	7	,	,	PUNCT
ejpam-3412	332	8	z	z	PROPN
ejpam-3412	332	9	∈	∈	PROPN
ejpam-3412	332	10	a	a	DET
ejpam-3412	332	11	such	such	ADJ
ejpam-3412	332	12	that	that	SCONJ
ejpam-3412	332	13	a	a	DET
ejpam-3412	332	14	≤	≤	NOUN
ejpam-3412	332	15	x	x	SYM
ejpam-3412	332	16	·	·	PUNCT
ejpam-3412	332	17	(	(	PUNCT
ejpam-3412	332	18	y	y	PROPN
ejpam-3412	332	19	·	·	PROPN
ejpam-3412	332	20	z	z	NOUN
ejpam-3412	332	21	)	)	PUNCT
ejpam-3412	332	22	.	.	PUNCT
ejpam-3412	333	1	by	by	ADP
ejpam-3412	333	2	(	(	PUNCT
ejpam-3412	333	3	2.10	2.10	NUM
ejpam-3412	333	4	)	)	PUNCT
ejpam-3412	333	5	,	,	PUNCT
ejpam-3412	333	6	we	we	PRON
ejpam-3412	333	7	have	have	VERB
ejpam-3412	333	8	0	0	NUM
ejpam-3412	333	9	=	=	SYM
ejpam-3412	333	10	a	a	DET
ejpam-3412	333	11	·	·	PUNCT
ejpam-3412	333	12	(	(	PUNCT
ejpam-3412	333	13	x	x	SYM
ejpam-3412	333	14	·	·	PUNCT
ejpam-3412	333	15	(	(	PUNCT
ejpam-3412	333	16	y	y	PROPN
ejpam-3412	333	17	·	·	PROPN
ejpam-3412	333	18	z	z	NOUN
ejpam-3412	333	19	)	)	PUNCT
ejpam-3412	333	20	)	)	PUNCT
ejpam-3412	334	1	=	=	PUNCT
ejpam-3412	334	2	x	x	SYM
ejpam-3412	334	3	·	·	PUNCT
ejpam-3412	334	4	(	(	PUNCT
ejpam-3412	334	5	a	a	DET
ejpam-3412	334	6	·	·	PUNCT
ejpam-3412	334	7	(	(	PUNCT
ejpam-3412	334	8	y	y	PROPN
ejpam-3412	334	9	·	·	PUNCT
ejpam-3412	334	10	z	z	NOUN
ejpam-3412	334	11	)	)	PUNCT
ejpam-3412	334	12	)	)	PUNCT
ejpam-3412	334	13	,	,	PUNCT
ejpam-3412	334	14	that	that	ADV
ejpam-3412	334	15	is	is	ADV
ejpam-3412	334	16	,	,	PUNCT
ejpam-3412	334	17	x	x	SYM
ejpam-3412	334	18	≤	≤	ADV
ejpam-3412	334	19	a	a	PRON
ejpam-3412	334	20	·	·	PUNCT
ejpam-3412	334	21	(	(	PUNCT
ejpam-3412	334	22	y	y	PROPN
ejpam-3412	334	23	·	·	PUNCT
ejpam-3412	335	1	z	z	X
ejpam-3412	335	2	)	)	PUNCT
ejpam-3412	335	3	.	.	PUNCT
ejpam-3412	336	1	it	it	PRON
ejpam-3412	336	2	follows	follow	VERB
ejpam-3412	336	3	from	from	ADP
ejpam-3412	336	4	(	(	PUNCT
ejpam-3412	336	5	2.9	2.9	NUM
ejpam-3412	336	6	)	)	PUNCT
ejpam-3412	336	7	that	that	PRON
ejpam-3412	336	8	ff(x	ff(x	VERB
ejpam-3412	336	9	·	·	PUNCT
ejpam-3412	336	10	z	z	X
ejpam-3412	336	11	)	)	PUNCT
ejpam-3412	336	12	≥	≥	NOUN
ejpam-3412	336	13	min{ff(a	min{ff(a	NOUN
ejpam-3412	336	14	)	)	PUNCT
ejpam-3412	336	15	,	,	PUNCT
ejpam-3412	336	16	ff(y	ff(y	NUM
ejpam-3412	336	17	)	)	PUNCT
ejpam-3412	336	18	}	}	PUNCT
ejpam-3412	336	19	.	.	PUNCT
ejpam-3412	337	1	hence	hence	ADV
ejpam-3412	337	2	,	,	PUNCT
ejpam-3412	337	3	f	f	PROPN
ejpam-3412	337	4	satisfies	satisfie	NOUN
ejpam-3412	337	5	(	(	PUNCT
ejpam-3412	337	6	2.8	2.8	NUM
ejpam-3412	337	7	)	)	PUNCT
ejpam-3412	337	8	.	.	PUNCT
ejpam-3412	338	1	theorem	theorem	VERB
ejpam-3412	338	2	16	16	NUM
ejpam-3412	338	3	.	.	PUNCT
ejpam-3412	339	1	if	if	SCONJ
ejpam-3412	339	2	f	f	PROPN
ejpam-3412	339	3	is	be	AUX
ejpam-3412	339	4	a	a	DET
ejpam-3412	339	5	fuzzy	fuzzy	ADJ
ejpam-3412	339	6	set	set	NOUN
ejpam-3412	339	7	in	in	ADP
ejpam-3412	339	8	a	a	DET
ejpam-3412	339	9	satisfying	satisfying	NOUN
ejpam-3412	339	10	the	the	DET
ejpam-3412	339	11	condition	condition	NOUN
ejpam-3412	339	12	(	(	PUNCT
ejpam-3412	339	13	2.9	2.9	NUM
ejpam-3412	339	14	)	)	PUNCT
ejpam-3412	339	15	,	,	PUNCT
ejpam-3412	339	16	then	then	ADV
ejpam-3412	339	17	f	f	PROPN
ejpam-3412	339	18	satisfies	satisfy	VERB
ejpam-3412	339	19	the	the	DET
ejpam-3412	339	20	condition	condition	NOUN
ejpam-3412	339	21	(	(	PUNCT
ejpam-3412	339	22	2.6	2.6	NUM
ejpam-3412	339	23	)	)	PUNCT
ejpam-3412	339	24	.	.	PUNCT
ejpam-3412	340	1	proof	proof	NOUN
ejpam-3412	340	2	.	.	PUNCT
ejpam-3412	341	1	let	let	VERB
ejpam-3412	341	2	x	x	PRON
ejpam-3412	341	3	,	,	PUNCT
ejpam-3412	341	4	y	y	PROPN
ejpam-3412	341	5	,	,	PUNCT
ejpam-3412	341	6	z	z	PROPN
ejpam-3412	341	7	∈	∈	PROPN
ejpam-3412	341	8	a	a	DET
ejpam-3412	341	9	be	be	AUX
ejpam-3412	341	10	such	such	ADJ
ejpam-3412	341	11	that	that	SCONJ
ejpam-3412	341	12	z	z	NOUN
ejpam-3412	341	13	≤	≤	NUM
ejpam-3412	341	14	x	x	X
ejpam-3412	341	15	·	·	PUNCT
ejpam-3412	341	16	y.	y.	NOUN
ejpam-3412	341	17	by	by	ADP
ejpam-3412	341	18	(	(	PUNCT
ejpam-3412	341	19	1.1	1.1	NUM
ejpam-3412	341	20	)	)	PUNCT
ejpam-3412	341	21	and	and	CCONJ
ejpam-3412	341	22	(	(	PUNCT
ejpam-3412	341	23	1.3	1.3	NUM
ejpam-3412	341	24	)	)	PUNCT
ejpam-3412	341	25	,	,	PUNCT
ejpam-3412	341	26	we	we	PRON
ejpam-3412	341	27	have	have	VERB
ejpam-3412	341	28	0	0	NUM
ejpam-3412	342	1	=	=	SYM
ejpam-3412	342	2	z	z	X
ejpam-3412	342	3	·	·	PUNCT
ejpam-3412	342	4	z	z	NOUN
ejpam-3412	342	5	≤	≤	NUM
ejpam-3412	342	6	z	z	NOUN
ejpam-3412	342	7	·	·	PUNCT
ejpam-3412	342	8	(	(	PUNCT
ejpam-3412	342	9	x	x	X
ejpam-3412	342	10	·	·	PUNCT
ejpam-3412	342	11	y	y	X
ejpam-3412	342	12	)	)	PUNCT
ejpam-3412	342	13	.	.	PUNCT
ejpam-3412	343	1	by	by	ADP
ejpam-3412	343	2	(	(	PUNCT
ejpam-3412	343	3	up-2	up-2	NUM
ejpam-3412	343	4	)	)	PUNCT
ejpam-3412	343	5	and	and	CCONJ
ejpam-3412	343	6	(	(	PUNCT
ejpam-3412	343	7	2.9	2.9	NUM
ejpam-3412	343	8	)	)	PUNCT
ejpam-3412	343	9	,	,	PUNCT
ejpam-3412	343	10	we	we	PRON
ejpam-3412	343	11	have	have	VERB
ejpam-3412	343	12	ff(y	ff(y	NUM
ejpam-3412	343	13	)	)	PUNCT
ejpam-3412	343	14	=	=	SYM
ejpam-3412	343	15	ff(0	ff(0	PROPN
ejpam-3412	343	16	·	·	SYM
ejpam-3412	343	17	y	y	X
ejpam-3412	343	18	)	)	PUNCT
ejpam-3412	343	19	≥	≥	NOUN
ejpam-3412	343	20	min{ff(z	min{ff(z	NOUN
ejpam-3412	343	21	)	)	PUNCT
ejpam-3412	343	22	,	,	PUNCT
ejpam-3412	343	23	ff(x	ff(x	NOUN
ejpam-3412	343	24	)	)	PUNCT
ejpam-3412	343	25	}	}	PUNCT
ejpam-3412	343	26	.	.	PUNCT
ejpam-3412	344	1	hence	hence	ADV
ejpam-3412	344	2	,	,	PUNCT
ejpam-3412	344	3	f	f	PROPN
ejpam-3412	344	4	satisfies	satisfie	NOUN
ejpam-3412	344	5	(	(	PUNCT
ejpam-3412	344	6	2.6	2.6	NUM
ejpam-3412	344	7	)	)	PUNCT
ejpam-3412	344	8	.	.	PUNCT
ejpam-3412	345	1	corollary	corollary	ADJ
ejpam-3412	345	2	2	2	NUM
ejpam-3412	345	3	.	.	PUNCT
ejpam-3412	346	1	if	if	SCONJ
ejpam-3412	346	2	f	f	PROPN
ejpam-3412	346	3	is	be	AUX
ejpam-3412	346	4	a	a	DET
ejpam-3412	346	5	fuzzy	fuzzy	ADJ
ejpam-3412	346	6	set	set	NOUN
ejpam-3412	346	7	in	in	ADP
ejpam-3412	346	8	a	a	DET
ejpam-3412	346	9	satisfying	satisfying	NOUN
ejpam-3412	346	10	the	the	DET
ejpam-3412	346	11	condition	condition	NOUN
ejpam-3412	346	12	(	(	PUNCT
ejpam-3412	346	13	2.8	2.8	NUM
ejpam-3412	346	14	)	)	PUNCT
ejpam-3412	346	15	,	,	PUNCT
ejpam-3412	346	16	then	then	ADV
ejpam-3412	346	17	f	f	PROPN
ejpam-3412	346	18	satisfies	satisfy	VERB
ejpam-3412	346	19	the	the	DET
ejpam-3412	346	20	condition	condition	NOUN
ejpam-3412	346	21	(	(	PUNCT
ejpam-3412	346	22	2.6	2.6	NUM
ejpam-3412	346	23	)	)	PUNCT
ejpam-3412	346	24	.	.	PUNCT
ejpam-3412	347	1	proof	proof	NOUN
ejpam-3412	347	2	.	.	PUNCT
ejpam-3412	348	1	it	it	PRON
ejpam-3412	348	2	is	be	AUX
ejpam-3412	348	3	straightforward	straightforward	ADJ
ejpam-3412	348	4	by	by	ADP
ejpam-3412	348	5	corollary	corollary	ADJ
ejpam-3412	348	6	1	1	NUM
ejpam-3412	348	7	and	and	CCONJ
ejpam-3412	348	8	theorem	theorem	VERB
ejpam-3412	348	9	16	16	NUM
ejpam-3412	348	10	.	.	PUNCT
ejpam-3412	349	1	the	the	DET
ejpam-3412	349	2	following	follow	VERB
ejpam-3412	349	3	example	example	NOUN
ejpam-3412	349	4	shows	show	VERB
ejpam-3412	349	5	that	that	SCONJ
ejpam-3412	349	6	the	the	DET
ejpam-3412	349	7	converse	converse	NOUN
ejpam-3412	349	8	of	of	ADP
ejpam-3412	349	9	theorem	theorem	NOUN
ejpam-3412	349	10	16	16	NUM
ejpam-3412	349	11	is	be	AUX
ejpam-3412	349	12	not	not	PART
ejpam-3412	349	13	true	true	ADJ
ejpam-3412	349	14	.	.	PUNCT
ejpam-3412	350	1	example	example	NOUN
ejpam-3412	351	1	11	11	NUM
ejpam-3412	351	2	.	.	PUNCT
ejpam-3412	352	1	let	let	VERB
ejpam-3412	352	2	a	a	PRON
ejpam-3412	352	3	=	=	PUNCT
ejpam-3412	352	4	{	{	PUNCT
ejpam-3412	352	5	0	0	NUM
ejpam-3412	352	6	,	,	PUNCT
ejpam-3412	352	7	1	1	NUM
ejpam-3412	352	8	,	,	PUNCT
ejpam-3412	352	9	2	2	NUM
ejpam-3412	352	10	,	,	PUNCT
ejpam-3412	352	11	3	3	NUM
ejpam-3412	352	12	}	}	PUNCT
ejpam-3412	352	13	be	be	AUX
ejpam-3412	352	14	a	a	DET
ejpam-3412	352	15	set	set	NOUN
ejpam-3412	352	16	with	with	ADP
ejpam-3412	352	17	a	a	DET
ejpam-3412	352	18	binary	binary	ADJ
ejpam-3412	352	19	operation	operation	NOUN
ejpam-3412	352	20	·	·	PUNCT
ejpam-3412	352	21	defined	define	VERB
ejpam-3412	352	22	by	by	ADP
ejpam-3412	352	23	the	the	DET
ejpam-3412	352	24	following	following	ADJ
ejpam-3412	352	25	cayley	cayley	ADJ
ejpam-3412	352	26	table	table	NOUN
ejpam-3412	352	27	:	:	PUNCT
ejpam-3412	352	28	·	·	PUNCT
ejpam-3412	352	29	0	0	NUM
ejpam-3412	352	30	1	1	NUM
ejpam-3412	352	31	2	2	NUM
ejpam-3412	352	32	3	3	NUM
ejpam-3412	352	33	0	0	NUM
ejpam-3412	352	34	0	0	NUM
ejpam-3412	352	35	1	1	NUM
ejpam-3412	352	36	2	2	NUM
ejpam-3412	352	37	3	3	NUM
ejpam-3412	352	38	1	1	NUM
ejpam-3412	352	39	0	0	NUM
ejpam-3412	352	40	0	0	NUM
ejpam-3412	352	41	3	3	NUM
ejpam-3412	352	42	3	3	NUM
ejpam-3412	352	43	2	2	NUM
ejpam-3412	352	44	0	0	NUM
ejpam-3412	352	45	1	1	NUM
ejpam-3412	352	46	0	0	NUM
ejpam-3412	352	47	0	0	NUM
ejpam-3412	352	48	3	3	NUM
ejpam-3412	352	49	0	0	NUM
ejpam-3412	352	50	1	1	NUM
ejpam-3412	352	51	2	2	NUM
ejpam-3412	352	52	0	0	NUM
ejpam-3412	352	53	a.	a.	NOUN
ejpam-3412	352	54	satirad	satirad	PROPN
ejpam-3412	352	55	,	,	PUNCT
ejpam-3412	352	56	a.	a.	NOUN
ejpam-3412	352	57	iampan	iampan	PROPN
ejpam-3412	352	58	/	/	SYM
ejpam-3412	352	59	eur	eur	PROPN
ejpam-3412	352	60	.	.	PUNCT
ejpam-3412	353	1	j.	j.	PROPN
ejpam-3412	353	2	pure	pure	PROPN
ejpam-3412	353	3	appl	appl	PROPN
ejpam-3412	353	4	.	.	PROPN
ejpam-3412	353	5	math	math	PROPN
ejpam-3412	353	6	,	,	PUNCT
ejpam-3412	353	7	12	12	NUM
ejpam-3412	353	8	(	(	PUNCT
ejpam-3412	353	9	2	2	NUM
ejpam-3412	353	10	)	)	PUNCT
ejpam-3412	353	11	(	(	PUNCT
ejpam-3412	353	12	2019	2019	NUM
ejpam-3412	353	13	)	)	PUNCT
ejpam-3412	353	14	,	,	PUNCT
ejpam-3412	353	15	294	294	NUM
ejpam-3412	353	16	-	-	SYM
ejpam-3412	353	17	331	331	NUM
ejpam-3412	353	18	308	308	NUM
ejpam-3412	353	19	then	then	ADV
ejpam-3412	353	20	a	a	PRON
ejpam-3412	353	21	=	=	X
ejpam-3412	353	22	(	(	PUNCT
ejpam-3412	353	23	a	a	PRON
ejpam-3412	353	24	,	,	PUNCT
ejpam-3412	353	25	·	·	PUNCT
ejpam-3412	353	26	,	,	PUNCT
ejpam-3412	353	27	0	0	NUM
ejpam-3412	353	28	)	)	PUNCT
ejpam-3412	353	29	is	be	AUX
ejpam-3412	353	30	a	a	DET
ejpam-3412	353	31	up	up	NOUN
ejpam-3412	353	32	-	-	PUNCT
ejpam-3412	353	33	algebra	algebra	NOUN
ejpam-3412	353	34	.	.	PUNCT
ejpam-3412	354	1	we	we	PRON
ejpam-3412	354	2	define	define	VERB
ejpam-3412	354	3	a	a	DET
ejpam-3412	354	4	membership	membership	NOUN
ejpam-3412	354	5	function	function	NOUN
ejpam-3412	354	6	ff	ff	NOUN
ejpam-3412	354	7	as	as	SCONJ
ejpam-3412	354	8	follows	follow	VERB
ejpam-3412	354	9	:	:	PUNCT
ejpam-3412	354	10	ff(0	ff(0	NOUN
ejpam-3412	354	11	)	)	PUNCT
ejpam-3412	354	12	=	=	SYM
ejpam-3412	354	13	1	1	NUM
ejpam-3412	354	14	,	,	PUNCT
ejpam-3412	354	15	ff(1	ff(1	PROPN
ejpam-3412	354	16	)	)	PUNCT
ejpam-3412	354	17	=	=	SYM
ejpam-3412	354	18	0.9	0.9	NUM
ejpam-3412	354	19	,	,	PUNCT
ejpam-3412	354	20	ff(2	ff(2	PROPN
ejpam-3412	354	21	)	)	PUNCT
ejpam-3412	354	22	=	=	NOUN
ejpam-3412	354	23	0.1	0.1	NUM
ejpam-3412	354	24	,	,	PUNCT
ejpam-3412	354	25	and	and	CCONJ
ejpam-3412	354	26	ff(3	ff(3	NOUN
ejpam-3412	354	27	)	)	PUNCT
ejpam-3412	354	28	=	=	NOUN
ejpam-3412	354	29	0.1	0.1	NUM
ejpam-3412	354	30	.	.	PUNCT
ejpam-3412	355	1	then	then	ADV
ejpam-3412	355	2	f	f	PROPN
ejpam-3412	355	3	satisfies	satisfy	VERB
ejpam-3412	355	4	the	the	DET
ejpam-3412	355	5	condition	condition	NOUN
ejpam-3412	355	6	(	(	PUNCT
ejpam-3412	355	7	2.6	2.6	NUM
ejpam-3412	355	8	)	)	PUNCT
ejpam-3412	355	9	but	but	CCONJ
ejpam-3412	355	10	it	it	PRON
ejpam-3412	355	11	does	do	AUX
ejpam-3412	355	12	not	not	PART
ejpam-3412	355	13	satisfy	satisfy	VERB
ejpam-3412	355	14	the	the	DET
ejpam-3412	355	15	condition	condition	NOUN
ejpam-3412	355	16	(	(	PUNCT
ejpam-3412	355	17	2.9	2.9	NUM
ejpam-3412	355	18	)	)	PUNCT
ejpam-3412	355	19	.	.	PUNCT
ejpam-3412	356	1	indeed	indeed	ADV
ejpam-3412	356	2	,	,	PUNCT
ejpam-3412	356	3	3	3	NUM
ejpam-3412	356	4	≤	≤	NUM
ejpam-3412	356	5	1	1	NUM
ejpam-3412	356	6	·	·	PUNCT
ejpam-3412	356	7	(	(	PUNCT
ejpam-3412	356	8	1	1	NUM
ejpam-3412	356	9	·	·	SYM
ejpam-3412	356	10	2	2	NUM
ejpam-3412	356	11	)	)	PUNCT
ejpam-3412	356	12	but	but	CCONJ
ejpam-3412	356	13	ff(3	ff(3	PROPN
ejpam-3412	356	14	·	·	PUNCT
ejpam-3412	356	15	2	2	NUM
ejpam-3412	356	16	)	)	PUNCT
ejpam-3412	356	17	=	=	SYM
ejpam-3412	356	18	ff(2	ff(2	NUM
ejpam-3412	356	19	)	)	PUNCT
ejpam-3412	356	20	=	=	SYM
ejpam-3412	356	21	0.1	0.1	NUM
ejpam-3412	356	22	�	�	PROPN
ejpam-3412	356	23	0.9	0.9	NUM
ejpam-3412	356	24	=	=	SYM
ejpam-3412	356	25	ff(1	ff(1	PROPN
ejpam-3412	356	26	)	)	PUNCT
ejpam-3412	356	27	=	=	SYM
ejpam-3412	356	28	min{ff(1	min{ff(1	PROPN
ejpam-3412	356	29	)	)	PUNCT
ejpam-3412	356	30	,	,	PUNCT
ejpam-3412	356	31	ff(1	ff(1	PROPN
ejpam-3412	356	32	)	)	PUNCT
ejpam-3412	356	33	}	}	PUNCT
ejpam-3412	356	34	.	.	PUNCT
ejpam-3412	357	1	the	the	DET
ejpam-3412	357	2	following	follow	VERB
ejpam-3412	357	3	example	example	NOUN
ejpam-3412	357	4	shows	show	VERB
ejpam-3412	357	5	that	that	SCONJ
ejpam-3412	357	6	fuzzy	fuzzy	ADJ
ejpam-3412	357	7	set	set	NOUN
ejpam-3412	357	8	in	in	ADP
ejpam-3412	357	9	a	a	DET
ejpam-3412	357	10	up	up	NOUN
ejpam-3412	357	11	-	-	PUNCT
ejpam-3412	357	12	algebra	algebra	NOUN
ejpam-3412	357	13	which	which	PRON
ejpam-3412	357	14	satisfies	satisfy	VERB
ejpam-3412	357	15	the	the	DET
ejpam-3412	357	16	condition	condition	NOUN
ejpam-3412	357	17	(	(	PUNCT
ejpam-3412	357	18	2.8	2.8	NUM
ejpam-3412	357	19	)	)	PUNCT
ejpam-3412	357	20	is	be	AUX
ejpam-3412	357	21	not	not	PART
ejpam-3412	357	22	constant	constant	ADJ
ejpam-3412	357	23	.	.	PUNCT
ejpam-3412	357	24	example	example	NOUN
ejpam-3412	358	1	12	12	NUM
ejpam-3412	358	2	.	.	PUNCT
ejpam-3412	359	1	let	let	VERB
ejpam-3412	359	2	a	a	PRON
ejpam-3412	359	3	=	=	PUNCT
ejpam-3412	359	4	{	{	PUNCT
ejpam-3412	359	5	0	0	NUM
ejpam-3412	359	6	,	,	PUNCT
ejpam-3412	359	7	1	1	NUM
ejpam-3412	359	8	,	,	PUNCT
ejpam-3412	359	9	2	2	NUM
ejpam-3412	359	10	,	,	PUNCT
ejpam-3412	359	11	3	3	NUM
ejpam-3412	359	12	}	}	PUNCT
ejpam-3412	359	13	be	be	AUX
ejpam-3412	359	14	a	a	DET
ejpam-3412	359	15	set	set	NOUN
ejpam-3412	359	16	with	with	ADP
ejpam-3412	359	17	a	a	DET
ejpam-3412	359	18	binary	binary	ADJ
ejpam-3412	359	19	operation	operation	NOUN
ejpam-3412	359	20	·	·	PUNCT
ejpam-3412	359	21	defined	define	VERB
ejpam-3412	359	22	by	by	ADP
ejpam-3412	359	23	the	the	DET
ejpam-3412	359	24	following	following	ADJ
ejpam-3412	359	25	cayley	cayley	ADJ
ejpam-3412	359	26	table	table	NOUN
ejpam-3412	359	27	:	:	PUNCT
ejpam-3412	359	28	·	·	PUNCT
ejpam-3412	359	29	0	0	NUM
ejpam-3412	360	1	1	1	NUM
ejpam-3412	360	2	2	2	NUM
ejpam-3412	360	3	3	3	NUM
ejpam-3412	360	4	0	0	NUM
ejpam-3412	360	5	0	0	NUM
ejpam-3412	360	6	1	1	NUM
ejpam-3412	360	7	2	2	NUM
ejpam-3412	360	8	3	3	NUM
ejpam-3412	360	9	1	1	NUM
ejpam-3412	360	10	0	0	NUM
ejpam-3412	360	11	0	0	NUM
ejpam-3412	360	12	2	2	NUM
ejpam-3412	360	13	3	3	NUM
ejpam-3412	360	14	2	2	NUM
ejpam-3412	360	15	0	0	NUM
ejpam-3412	360	16	1	1	NUM
ejpam-3412	360	17	0	0	NUM
ejpam-3412	360	18	3	3	NUM
ejpam-3412	360	19	3	3	NUM
ejpam-3412	360	20	0	0	NUM
ejpam-3412	360	21	1	1	NUM
ejpam-3412	360	22	2	2	NUM
ejpam-3412	360	23	0	0	NUM
ejpam-3412	360	24	then	then	ADV
ejpam-3412	360	25	a	a	PRON
ejpam-3412	360	26	=	=	X
ejpam-3412	360	27	(	(	PUNCT
ejpam-3412	360	28	a	a	PRON
ejpam-3412	360	29	,	,	PUNCT
ejpam-3412	360	30	·	·	PUNCT
ejpam-3412	360	31	,	,	PUNCT
ejpam-3412	360	32	0	0	NUM
ejpam-3412	360	33	)	)	PUNCT
ejpam-3412	360	34	is	be	AUX
ejpam-3412	360	35	a	a	DET
ejpam-3412	360	36	up	up	NOUN
ejpam-3412	360	37	-	-	PUNCT
ejpam-3412	360	38	algebra	algebra	NOUN
ejpam-3412	360	39	.	.	PUNCT
ejpam-3412	361	1	we	we	PRON
ejpam-3412	361	2	define	define	VERB
ejpam-3412	361	3	a	a	DET
ejpam-3412	361	4	membership	membership	NOUN
ejpam-3412	361	5	function	function	NOUN
ejpam-3412	361	6	ff	ff	NOUN
ejpam-3412	361	7	as	as	SCONJ
ejpam-3412	361	8	follows	follow	VERB
ejpam-3412	361	9	:	:	PUNCT
ejpam-3412	361	10	ff(0	ff(0	NOUN
ejpam-3412	361	11	)	)	PUNCT
ejpam-3412	361	12	=	=	SYM
ejpam-3412	361	13	0.7	0.7	NUM
ejpam-3412	361	14	,	,	PUNCT
ejpam-3412	361	15	ff(1	ff(1	NOUN
ejpam-3412	361	16	)	)	PUNCT
ejpam-3412	361	17	=	=	NOUN
ejpam-3412	361	18	0.5	0.5	NUM
ejpam-3412	361	19	,	,	PUNCT
ejpam-3412	361	20	ff(2	ff(2	PROPN
ejpam-3412	361	21	)	)	PUNCT
ejpam-3412	361	22	=	=	NUM
ejpam-3412	361	23	0.4	0.4	NUM
ejpam-3412	361	24	,	,	PUNCT
ejpam-3412	361	25	and	and	CCONJ
ejpam-3412	361	26	ff(3	ff(3	NOUN
ejpam-3412	361	27	)	)	PUNCT
ejpam-3412	361	28	=	=	PUNCT
ejpam-3412	361	29	0.4	0.4	NUM
ejpam-3412	361	30	.	.	PUNCT
ejpam-3412	362	1	then	then	ADV
ejpam-3412	362	2	f	f	PROPN
ejpam-3412	362	3	satisfies	satisfy	VERB
ejpam-3412	362	4	the	the	DET
ejpam-3412	362	5	condition	condition	NOUN
ejpam-3412	362	6	(	(	PUNCT
ejpam-3412	362	7	2.8	2.8	NUM
ejpam-3412	362	8	)	)	PUNCT
ejpam-3412	362	9	but	but	CCONJ
ejpam-3412	362	10	it	it	PRON
ejpam-3412	362	11	is	be	AUX
ejpam-3412	362	12	not	not	PART
ejpam-3412	362	13	constant	constant	ADJ
ejpam-3412	362	14	.	.	PUNCT
ejpam-3412	363	1	theorem	theorem	NOUN
ejpam-3412	363	2	17	17	NUM
ejpam-3412	363	3	.	.	PUNCT
ejpam-3412	364	1	if	if	SCONJ
ejpam-3412	364	2	f	f	PROPN
ejpam-3412	364	3	is	be	AUX
ejpam-3412	364	4	a	a	DET
ejpam-3412	364	5	fuzzy	fuzzy	ADJ
ejpam-3412	364	6	up	up	NOUN
ejpam-3412	364	7	-	-	PUNCT
ejpam-3412	364	8	filter	filter	NOUN
ejpam-3412	364	9	of	of	ADP
ejpam-3412	364	10	a	a	DET
ejpam-3412	364	11	satisfying	satisfying	NOUN
ejpam-3412	364	12	the	the	DET
ejpam-3412	364	13	condition	condition	NOUN
ejpam-3412	364	14	(	(	PUNCT
ejpam-3412	364	15	∀x	∀x	X
ejpam-3412	364	16	,	,	PUNCT
ejpam-3412	364	17	y	y	PROPN
ejpam-3412	364	18	,	,	PUNCT
ejpam-3412	364	19	z	z	PROPN
ejpam-3412	364	20	∈	∈	PROPN
ejpam-3412	364	21	a)(ff(y	a)(ff(y	PUNCT
ejpam-3412	364	22	·	·	PUNCT
ejpam-3412	364	23	(	(	PUNCT
ejpam-3412	364	24	x	x	X
ejpam-3412	364	25	·	·	PUNCT
ejpam-3412	364	26	z	z	NOUN
ejpam-3412	364	27	)	)	PUNCT
ejpam-3412	364	28	)	)	PUNCT
ejpam-3412	365	1	=	=	SYM
ejpam-3412	365	2	ff(x	ff(x	NOUN
ejpam-3412	365	3	·	·	PUNCT
ejpam-3412	365	4	(	(	PUNCT
ejpam-3412	365	5	y	y	PROPN
ejpam-3412	365	6	·	·	PUNCT
ejpam-3412	365	7	z	z	NOUN
ejpam-3412	365	8	)	)	PUNCT
ejpam-3412	365	9	)	)	PUNCT
ejpam-3412	365	10	)	)	PUNCT
ejpam-3412	365	11	,	,	PUNCT
ejpam-3412	365	12	(	(	PUNCT
ejpam-3412	365	13	2.11	2.11	NUM
ejpam-3412	365	14	)	)	PUNCT
ejpam-3412	365	15	then	then	ADV
ejpam-3412	365	16	f	f	PROPN
ejpam-3412	365	17	is	be	AUX
ejpam-3412	365	18	a	a	DET
ejpam-3412	365	19	fuzzy	fuzzy	ADJ
ejpam-3412	365	20	up	up	ADJ
ejpam-3412	365	21	-	-	PUNCT
ejpam-3412	365	22	ideal	ideal	NOUN
ejpam-3412	365	23	of	of	ADP
ejpam-3412	365	24	a.	a.	NOUN
ejpam-3412	365	25	proof	proof	NOUN
ejpam-3412	365	26	.	.	PUNCT
ejpam-3412	366	1	let	let	VERB
ejpam-3412	366	2	x	x	PRON
ejpam-3412	366	3	,	,	PUNCT
ejpam-3412	366	4	y	y	PROPN
ejpam-3412	366	5	,	,	PUNCT
ejpam-3412	366	6	z	z	PROPN
ejpam-3412	366	7	∈	∈	NOUN
ejpam-3412	366	8	a.	a.	NOUN
ejpam-3412	366	9	by	by	ADP
ejpam-3412	366	10	(	(	PUNCT
ejpam-3412	366	11	2.11	2.11	NUM
ejpam-3412	366	12	)	)	PUNCT
ejpam-3412	366	13	,	,	PUNCT
ejpam-3412	366	14	we	we	PRON
ejpam-3412	366	15	have	have	VERB
ejpam-3412	366	16	ff(x	ff(x	PRON
ejpam-3412	366	17	·	·	PUNCT
ejpam-3412	366	18	z	z	X
ejpam-3412	366	19	)	)	PUNCT
ejpam-3412	366	20	≥	≥	X
ejpam-3412	366	21	min{ff(y	min{ff(y	ADJ
ejpam-3412	366	22	·	·	PUNCT
ejpam-3412	366	23	(	(	PUNCT
ejpam-3412	366	24	x	x	X
ejpam-3412	366	25	·	·	PUNCT
ejpam-3412	366	26	z	z	NOUN
ejpam-3412	366	27	)	)	PUNCT
ejpam-3412	366	28	)	)	PUNCT
ejpam-3412	366	29	,	,	PUNCT
ejpam-3412	366	30	ff(y	ff(y	NUM
ejpam-3412	366	31	)	)	PUNCT
ejpam-3412	366	32	}	}	PUNCT
ejpam-3412	366	33	=	=	SYM
ejpam-3412	366	34	min{ff(x	min{ff(x	NOUN
ejpam-3412	366	35	·	·	PUNCT
ejpam-3412	366	36	(	(	PUNCT
ejpam-3412	366	37	y	y	PROPN
ejpam-3412	366	38	·	·	PUNCT
ejpam-3412	366	39	z	z	NOUN
ejpam-3412	366	40	)	)	PUNCT
ejpam-3412	366	41	)	)	PUNCT
ejpam-3412	366	42	,	,	PUNCT
ejpam-3412	366	43	ff(y	ff(y	NUM
ejpam-3412	366	44	)	)	PUNCT
ejpam-3412	366	45	}	}	PUNCT
ejpam-3412	366	46	.	.	PUNCT
ejpam-3412	367	1	hence	hence	ADV
ejpam-3412	367	2	,	,	PUNCT
ejpam-3412	367	3	f	f	PROPN
ejpam-3412	367	4	is	be	AUX
ejpam-3412	367	5	a	a	DET
ejpam-3412	367	6	fuzzy	fuzzy	ADJ
ejpam-3412	367	7	up	up	ADJ
ejpam-3412	367	8	-	-	PUNCT
ejpam-3412	367	9	ideal	ideal	NOUN
ejpam-3412	367	10	of	of	ADP
ejpam-3412	367	11	a.	a.	NOUN
ejpam-3412	367	12	proposition	proposition	NOUN
ejpam-3412	367	13	9	9	NUM
ejpam-3412	367	14	.	.	PUNCT
ejpam-3412	368	1	a	a	DET
ejpam-3412	368	2	fuzzy	fuzzy	ADJ
ejpam-3412	368	3	set	set	VERB
ejpam-3412	368	4	f	f	PROPN
ejpam-3412	368	5	in	in	ADP
ejpam-3412	368	6	a	a	DET
ejpam-3412	368	7	satisfies	satisfie	NOUN
ejpam-3412	368	8	the	the	DET
ejpam-3412	368	9	condition	condition	NOUN
ejpam-3412	368	10	(	(	PUNCT
ejpam-3412	368	11	∀a	∀a	X
ejpam-3412	368	12	,	,	PUNCT
ejpam-3412	368	13	x	x	X
ejpam-3412	368	14	,	,	PUNCT
ejpam-3412	368	15	y	y	PROPN
ejpam-3412	368	16	,	,	PUNCT
ejpam-3412	368	17	z	z	NOUN
ejpam-3412	368	18	∈	∈	PROPN
ejpam-3412	368	19	a)(a	a)(a	PUNCT
ejpam-3412	368	20	≤	≤	PROPN
ejpam-3412	368	21	(	(	PUNCT
ejpam-3412	368	22	z	z	NOUN
ejpam-3412	368	23	·	·	PUNCT
ejpam-3412	368	24	y	y	X
ejpam-3412	368	25	)	)	PUNCT
ejpam-3412	368	26	·	·	PUNCT
ejpam-3412	369	1	(	(	PUNCT
ejpam-3412	369	2	z	z	X
ejpam-3412	369	3	·	·	PUNCT
ejpam-3412	369	4	x)⇒	x)⇒	NOUN
ejpam-3412	369	5	ff(x	ff(x	NOUN
ejpam-3412	369	6	)	)	PUNCT
ejpam-3412	369	7	≥	≥	NOUN
ejpam-3412	369	8	min{ff(a	min{ff(a	NOUN
ejpam-3412	369	9	)	)	PUNCT
ejpam-3412	369	10	,	,	PUNCT
ejpam-3412	369	11	ff(y	ff(y	NUM
ejpam-3412	369	12	)	)	PUNCT
ejpam-3412	369	13	}	}	PUNCT
ejpam-3412	369	14	)	)	PUNCT
ejpam-3412	370	1	(	(	PUNCT
ejpam-3412	370	2	2.12	2.12	NUM
ejpam-3412	370	3	)	)	PUNCT
ejpam-3412	370	4	if	if	SCONJ
ejpam-3412	370	5	and	and	CCONJ
ejpam-3412	370	6	only	only	ADV
ejpam-3412	370	7	if	if	SCONJ
ejpam-3412	370	8	f	f	PROPN
ejpam-3412	370	9	is	be	AUX
ejpam-3412	370	10	a	a	DET
ejpam-3412	370	11	fuzzy	fuzzy	ADJ
ejpam-3412	370	12	strongly	strongly	ADV
ejpam-3412	370	13	up	up	ADP
ejpam-3412	370	14	-	-	PUNCT
ejpam-3412	370	15	ideal	ideal	NOUN
ejpam-3412	370	16	of	of	ADP
ejpam-3412	370	17	a.	a.	NOUN
ejpam-3412	370	18	proof	proof	NOUN
ejpam-3412	370	19	.	.	PUNCT
ejpam-3412	371	1	let	let	VERB
ejpam-3412	371	2	x	x	PUNCT
ejpam-3412	371	3	∈	∈	VERB
ejpam-3412	371	4	a.	a.	NOUN
ejpam-3412	371	5	by	by	ADP
ejpam-3412	371	6	(	(	PUNCT
ejpam-3412	371	7	up-3	up-3	NOUN
ejpam-3412	371	8	)	)	PUNCT
ejpam-3412	371	9	,	,	PUNCT
ejpam-3412	371	10	we	we	PRON
ejpam-3412	371	11	have	have	VERB
ejpam-3412	371	12	x	x	NOUN
ejpam-3412	371	13	≤	≤	X
ejpam-3412	371	14	0	0	NUM
ejpam-3412	372	1	=	=	PUNCT
ejpam-3412	372	2	x	x	SYM
ejpam-3412	372	3	·	·	PUNCT
ejpam-3412	372	4	0	0	PUNCT
ejpam-3412	373	1	=	=	SYM
ejpam-3412	373	2	(	(	PUNCT
ejpam-3412	373	3	0	0	NUM
ejpam-3412	373	4	·	·	PUNCT
ejpam-3412	373	5	x	x	X
ejpam-3412	373	6	)	)	PUNCT
ejpam-3412	373	7	·	·	PUNCT
ejpam-3412	373	8	(	(	PUNCT
ejpam-3412	373	9	0	0	NUM
ejpam-3412	373	10	·	·	PUNCT
ejpam-3412	373	11	0	0	NUM
ejpam-3412	373	12	)	)	PUNCT
ejpam-3412	373	13	.	.	PUNCT
ejpam-3412	374	1	by	by	ADP
ejpam-3412	374	2	(	(	PUNCT
ejpam-3412	374	3	2.12	2.12	NUM
ejpam-3412	374	4	)	)	PUNCT
ejpam-3412	374	5	,	,	PUNCT
ejpam-3412	374	6	we	we	PRON
ejpam-3412	374	7	have	have	VERB
ejpam-3412	374	8	ff(0	ff(0	NOUN
ejpam-3412	374	9	)	)	PUNCT
ejpam-3412	374	10	≥	≥	PROPN
ejpam-3412	374	11	min{ff(x	min{ff(x	PROPN
ejpam-3412	374	12	)	)	PUNCT
ejpam-3412	374	13	,	,	PUNCT
ejpam-3412	374	14	ff(x	ff(x	NOUN
ejpam-3412	374	15	)	)	PUNCT
ejpam-3412	374	16	}	}	PUNCT
ejpam-3412	374	17	=	=	SYM
ejpam-3412	374	18	ff(x	ff(x	NOUN
ejpam-3412	374	19	)	)	PUNCT
ejpam-3412	374	20	.	.	PUNCT
ejpam-3412	375	1	let	let	VERB
ejpam-3412	375	2	x	x	PRON
ejpam-3412	375	3	,	,	PUNCT
ejpam-3412	375	4	y	y	PROPN
ejpam-3412	375	5	,	,	PUNCT
ejpam-3412	375	6	z	z	PROPN
ejpam-3412	375	7	∈	∈	NOUN
ejpam-3412	375	8	a.	a.	NOUN
ejpam-3412	375	9	by	by	ADP
ejpam-3412	375	10	(	(	PUNCT
ejpam-3412	375	11	1.1	1.1	NUM
ejpam-3412	375	12	)	)	PUNCT
ejpam-3412	375	13	,	,	PUNCT
ejpam-3412	375	14	we	we	PRON
ejpam-3412	375	15	have	have	VERB
ejpam-3412	375	16	(	(	PUNCT
ejpam-3412	375	17	z	z	NOUN
ejpam-3412	375	18	·	·	PUNCT
ejpam-3412	375	19	y	y	X
ejpam-3412	375	20	)	)	PUNCT
ejpam-3412	375	21	·	·	PUNCT
ejpam-3412	376	1	(	(	PUNCT
ejpam-3412	376	2	z	z	NOUN
ejpam-3412	376	3	·	·	SYM
ejpam-3412	376	4	x	x	X
ejpam-3412	376	5	)	)	PUNCT
ejpam-3412	376	6	≤	≤	NOUN
ejpam-3412	376	7	(	(	PUNCT
ejpam-3412	376	8	z	z	NOUN
ejpam-3412	376	9	·	·	PUNCT
ejpam-3412	376	10	y	y	X
ejpam-3412	376	11	)	)	PUNCT
ejpam-3412	376	12	·	·	PUNCT
ejpam-3412	377	1	(	(	PUNCT
ejpam-3412	377	2	z	z	X
ejpam-3412	377	3	·	·	PUNCT
ejpam-3412	377	4	x	x	X
ejpam-3412	377	5	)	)	PUNCT
ejpam-3412	377	6	.	.	PUNCT
ejpam-3412	378	1	by	by	ADP
ejpam-3412	378	2	(	(	PUNCT
ejpam-3412	378	3	2.12	2.12	NUM
ejpam-3412	378	4	)	)	PUNCT
ejpam-3412	378	5	,	,	PUNCT
ejpam-3412	378	6	we	we	PRON
ejpam-3412	378	7	have	have	VERB
ejpam-3412	378	8	ff(x	ff(x	NOUN
ejpam-3412	378	9	)	)	PUNCT
ejpam-3412	378	10	≥	≥	NOUN
ejpam-3412	378	11	min{ff((z	min{ff((z	NOUN
ejpam-3412	378	12	·	·	PUNCT
ejpam-3412	378	13	y	y	X
ejpam-3412	378	14	)	)	PUNCT
ejpam-3412	378	15	·	·	PUNCT
ejpam-3412	379	1	(	(	PUNCT
ejpam-3412	379	2	z	z	NOUN
ejpam-3412	379	3	·	·	PUNCT
ejpam-3412	379	4	x	x	X
ejpam-3412	379	5	)	)	PUNCT
ejpam-3412	379	6	)	)	PUNCT
ejpam-3412	379	7	,	,	PUNCT
ejpam-3412	379	8	ff(y	ff(y	NUM
ejpam-3412	379	9	)	)	PUNCT
ejpam-3412	379	10	}	}	PUNCT
ejpam-3412	379	11	.	.	PUNCT
ejpam-3412	380	1	hence	hence	ADV
ejpam-3412	380	2	,	,	PUNCT
ejpam-3412	380	3	f	f	PROPN
ejpam-3412	380	4	is	be	AUX
ejpam-3412	380	5	a	a	DET
ejpam-3412	380	6	fuzzy	fuzzy	ADJ
ejpam-3412	380	7	strongly	strongly	ADV
ejpam-3412	380	8	up	up	ADP
ejpam-3412	380	9	-	-	PUNCT
ejpam-3412	380	10	ideal	ideal	NOUN
ejpam-3412	380	11	of	of	ADP
ejpam-3412	380	12	a.	a.	NOUN
ejpam-3412	380	13	the	the	DET
ejpam-3412	380	14	converse	converse	NOUN
ejpam-3412	380	15	is	be	AUX
ejpam-3412	380	16	obvious	obvious	ADJ
ejpam-3412	380	17	because	because	SCONJ
ejpam-3412	380	18	f	f	PROPN
ejpam-3412	380	19	is	be	AUX
ejpam-3412	380	20	constant	constant	ADJ
ejpam-3412	380	21	.	.	PUNCT
ejpam-3412	381	1	a.	a.	PROPN
ejpam-3412	381	2	satirad	satirad	PROPN
ejpam-3412	381	3	,	,	PUNCT
ejpam-3412	381	4	a.	a.	NOUN
ejpam-3412	381	5	iampan	iampan	PROPN
ejpam-3412	381	6	/	/	SYM
ejpam-3412	381	7	eur	eur	PROPN
ejpam-3412	381	8	.	.	PUNCT
ejpam-3412	382	1	j.	j.	PROPN
ejpam-3412	382	2	pure	pure	PROPN
ejpam-3412	382	3	appl	appl	PROPN
ejpam-3412	382	4	.	.	PROPN
ejpam-3412	382	5	math	math	PROPN
ejpam-3412	382	6	,	,	PUNCT
ejpam-3412	382	7	12	12	NUM
ejpam-3412	382	8	(	(	PUNCT
ejpam-3412	382	9	2	2	NUM
ejpam-3412	382	10	)	)	PUNCT
ejpam-3412	382	11	(	(	PUNCT
ejpam-3412	382	12	2019	2019	NUM
ejpam-3412	382	13	)	)	PUNCT
ejpam-3412	382	14	,	,	PUNCT
ejpam-3412	382	15	294	294	NUM
ejpam-3412	382	16	-	-	SYM
ejpam-3412	382	17	331	331	NUM
ejpam-3412	382	18	309	309	NUM
ejpam-3412	382	19	theorem	theorem	VERB
ejpam-3412	382	20	18	18	NUM
ejpam-3412	382	21	.	.	PUNCT
ejpam-3412	383	1	if	if	SCONJ
ejpam-3412	383	2	f	f	PROPN
ejpam-3412	383	3	is	be	AUX
ejpam-3412	383	4	a	a	DET
ejpam-3412	383	5	fuzzy	fuzzy	ADJ
ejpam-3412	383	6	set	set	NOUN
ejpam-3412	383	7	in	in	ADP
ejpam-3412	383	8	a	a	DET
ejpam-3412	383	9	satisfying	satisfying	NOUN
ejpam-3412	383	10	the	the	DET
ejpam-3412	383	11	condition	condition	NOUN
ejpam-3412	383	12	(	(	PUNCT
ejpam-3412	383	13	∀x	∀x	X
ejpam-3412	383	14	,	,	PUNCT
ejpam-3412	383	15	y	y	PROPN
ejpam-3412	383	16	,	,	PUNCT
ejpam-3412	383	17	z	z	PROPN
ejpam-3412	383	18	∈	∈	PROPN
ejpam-3412	383	19	a)(z	a)(z	PUNCT
ejpam-3412	383	20	≤	≤	NUM
ejpam-3412	383	21	x	x	SYM
ejpam-3412	383	22	·	·	PUNCT
ejpam-3412	383	23	y	y	PROPN
ejpam-3412	383	24	⇒	⇒	PROPN
ejpam-3412	383	25	ff(z	ff(z	PUNCT
ejpam-3412	383	26	)	)	PUNCT
ejpam-3412	383	27	≥	≥	PROPN
ejpam-3412	383	28	min{ff(x	min{ff(x	PROPN
ejpam-3412	383	29	)	)	PUNCT
ejpam-3412	383	30	,	,	PUNCT
ejpam-3412	383	31	ff(y	ff(y	NUM
ejpam-3412	383	32	)	)	PUNCT
ejpam-3412	383	33	}	}	PUNCT
ejpam-3412	383	34	)	)	PUNCT
ejpam-3412	383	35	,	,	PUNCT
ejpam-3412	383	36	(	(	PUNCT
ejpam-3412	383	37	2.13	2.13	NUM
ejpam-3412	383	38	)	)	PUNCT
ejpam-3412	383	39	then	then	ADV
ejpam-3412	383	40	f	f	PROPN
ejpam-3412	383	41	satisfies	satisfy	VERB
ejpam-3412	383	42	the	the	DET
ejpam-3412	383	43	condition	condition	NOUN
ejpam-3412	383	44	(	(	PUNCT
ejpam-3412	383	45	2.3	2.3	NUM
ejpam-3412	383	46	)	)	PUNCT
ejpam-3412	383	47	.	.	PUNCT
ejpam-3412	384	1	proof	proof	NOUN
ejpam-3412	384	2	.	.	PUNCT
ejpam-3412	385	1	let	let	VERB
ejpam-3412	385	2	x	x	PRON
ejpam-3412	385	3	,	,	PUNCT
ejpam-3412	385	4	y	y	PROPN
ejpam-3412	385	5	,	,	PUNCT
ejpam-3412	385	6	z	z	PROPN
ejpam-3412	385	7	∈	∈	PROPN
ejpam-3412	385	8	a	a	DET
ejpam-3412	385	9	be	be	AUX
ejpam-3412	385	10	such	such	ADJ
ejpam-3412	385	11	that	that	SCONJ
ejpam-3412	385	12	z	z	NOUN
ejpam-3412	385	13	≤	≤	NOUN
ejpam-3412	385	14	x.	x.	PUNCT
ejpam-3412	385	15	by	by	ADP
ejpam-3412	385	16	(	(	PUNCT
ejpam-3412	385	17	1.4	1.4	NUM
ejpam-3412	385	18	)	)	PUNCT
ejpam-3412	385	19	,	,	PUNCT
ejpam-3412	385	20	we	we	PRON
ejpam-3412	385	21	have	have	VERB
ejpam-3412	385	22	x	x	X
ejpam-3412	385	23	·	·	PUNCT
ejpam-3412	385	24	y	y	SYM
ejpam-3412	385	25	≤	≤	PROPN
ejpam-3412	386	1	z	z	NOUN
ejpam-3412	386	2	·	·	PUNCT
ejpam-3412	386	3	y.	y.	NOUN
ejpam-3412	386	4	by	by	ADP
ejpam-3412	386	5	(	(	PUNCT
ejpam-3412	386	6	2.13	2.13	NUM
ejpam-3412	386	7	)	)	PUNCT
ejpam-3412	386	8	,	,	PUNCT
ejpam-3412	386	9	we	we	PRON
ejpam-3412	386	10	have	have	VERB
ejpam-3412	386	11	ff(x	ff(x	PRON
ejpam-3412	386	12	·	·	PUNCT
ejpam-3412	386	13	y	y	X
ejpam-3412	386	14	)	)	PUNCT
ejpam-3412	386	15	≥	≥	NOUN
ejpam-3412	386	16	min{ff(z	min{ff(z	NOUN
ejpam-3412	386	17	)	)	PUNCT
ejpam-3412	386	18	,	,	PUNCT
ejpam-3412	386	19	ff(y	ff(y	NUM
ejpam-3412	386	20	)	)	PUNCT
ejpam-3412	386	21	}	}	PUNCT
ejpam-3412	386	22	.	.	PUNCT
ejpam-3412	387	1	hence	hence	ADV
ejpam-3412	387	2	,	,	PUNCT
ejpam-3412	387	3	f	f	PROPN
ejpam-3412	387	4	satisfies	satisfie	NOUN
ejpam-3412	387	5	(	(	PUNCT
ejpam-3412	387	6	2.3	2.3	NUM
ejpam-3412	387	7	)	)	PUNCT
ejpam-3412	387	8	.	.	PUNCT
ejpam-3412	388	1	proposition	proposition	NOUN
ejpam-3412	388	2	10	10	NUM
ejpam-3412	388	3	.	.	PUNCT
ejpam-3412	389	1	a	a	DET
ejpam-3412	389	2	fuzzy	fuzzy	ADJ
ejpam-3412	389	3	set	set	NOUN
ejpam-3412	389	4	f	f	PROPN
ejpam-3412	389	5	in	in	ADP
ejpam-3412	389	6	a	a	DET
ejpam-3412	389	7	satisfies	satisfie	NOUN
ejpam-3412	389	8	the	the	DET
ejpam-3412	389	9	condition	condition	NOUN
ejpam-3412	389	10	(	(	PUNCT
ejpam-3412	389	11	2.13	2.13	NUM
ejpam-3412	389	12	)	)	PUNCT
ejpam-3412	389	13	if	if	SCONJ
ejpam-3412	389	14	and	and	CCONJ
ejpam-3412	389	15	only	only	ADV
ejpam-3412	389	16	if	if	SCONJ
ejpam-3412	389	17	f	f	PROPN
ejpam-3412	389	18	is	be	AUX
ejpam-3412	389	19	a	a	DET
ejpam-3412	389	20	fuzzy	fuzzy	ADJ
ejpam-3412	389	21	strongly	strongly	ADV
ejpam-3412	389	22	up	up	ADP
ejpam-3412	389	23	-	-	PUNCT
ejpam-3412	389	24	ideal	ideal	NOUN
ejpam-3412	389	25	of	of	ADP
ejpam-3412	389	26	a.	a.	NOUN
ejpam-3412	389	27	proof	proof	NOUN
ejpam-3412	389	28	.	.	PUNCT
ejpam-3412	390	1	let	let	VERB
ejpam-3412	390	2	x	x	PUNCT
ejpam-3412	390	3	∈	∈	VERB
ejpam-3412	390	4	a.	a.	NOUN
ejpam-3412	390	5	by	by	ADP
ejpam-3412	390	6	(	(	PUNCT
ejpam-3412	390	7	up-3	up-3	NOUN
ejpam-3412	390	8	)	)	PUNCT
ejpam-3412	390	9	,	,	PUNCT
ejpam-3412	390	10	we	we	PRON
ejpam-3412	390	11	have	have	VERB
ejpam-3412	390	12	x	x	NOUN
ejpam-3412	390	13	≤	≤	X
ejpam-3412	390	14	0	0	NUM
ejpam-3412	391	1	=	=	SYM
ejpam-3412	391	2	0	0	NUM
ejpam-3412	391	3	·	·	PUNCT
ejpam-3412	391	4	0	0	X
ejpam-3412	391	5	.	.	PUNCT
ejpam-3412	392	1	by	by	ADP
ejpam-3412	392	2	(	(	PUNCT
ejpam-3412	392	3	2.13	2.13	NUM
ejpam-3412	392	4	)	)	PUNCT
ejpam-3412	392	5	,	,	PUNCT
ejpam-3412	392	6	we	we	PRON
ejpam-3412	392	7	have	have	VERB
ejpam-3412	392	8	ff(x	ff(x	NOUN
ejpam-3412	392	9	)	)	PUNCT
ejpam-3412	392	10	≥	≥	PROPN
ejpam-3412	392	11	min{ff(0	min{ff(0	PROPN
ejpam-3412	392	12	)	)	PUNCT
ejpam-3412	392	13	,	,	PUNCT
ejpam-3412	392	14	ff(0	ff(0	NOUN
ejpam-3412	392	15	)	)	PUNCT
ejpam-3412	392	16	}	}	PUNCT
ejpam-3412	392	17	=	=	SYM
ejpam-3412	392	18	ff(0	ff(0	NOUN
ejpam-3412	392	19	)	)	PUNCT
ejpam-3412	392	20	.	.	PUNCT
ejpam-3412	393	1	by	by	ADP
ejpam-3412	393	2	theorem	theorem	NOUN
ejpam-3412	393	3	18	18	NUM
ejpam-3412	393	4	and	and	CCONJ
ejpam-3412	393	5	proposition	proposition	NOUN
ejpam-3412	393	6	3	3	NUM
ejpam-3412	393	7	,	,	PUNCT
ejpam-3412	393	8	we	we	PRON
ejpam-3412	393	9	have	have	VERB
ejpam-3412	393	10	ff(0	ff(0	NOUN
ejpam-3412	393	11	)	)	PUNCT
ejpam-3412	393	12	≥	≥	NUM
ejpam-3412	393	13	ff(x	ff(x	NOUN
ejpam-3412	393	14	)	)	PUNCT
ejpam-3412	393	15	.	.	PUNCT
ejpam-3412	394	1	thus	thus	ADV
ejpam-3412	394	2	ff(x	ff(x	NOUN
ejpam-3412	394	3	)	)	PUNCT
ejpam-3412	394	4	=	=	SYM
ejpam-3412	394	5	ff(0	ff(0	NOUN
ejpam-3412	394	6	)	)	PUNCT
ejpam-3412	394	7	for	for	ADP
ejpam-3412	394	8	all	all	PRON
ejpam-3412	394	9	x	x	SYM
ejpam-3412	394	10	∈	∈	PROPN
ejpam-3412	394	11	a	a	PRON
ejpam-3412	394	12	,	,	PUNCT
ejpam-3412	394	13	so	so	CCONJ
ejpam-3412	394	14	f	f	PROPN
ejpam-3412	394	15	is	be	AUX
ejpam-3412	394	16	constant	constant	ADJ
ejpam-3412	394	17	.	.	PUNCT
ejpam-3412	395	1	hence	hence	ADV
ejpam-3412	395	2	,	,	PUNCT
ejpam-3412	395	3	f	f	PROPN
ejpam-3412	395	4	a	a	DET
ejpam-3412	395	5	fuzzy	fuzzy	ADJ
ejpam-3412	395	6	strongly	strongly	ADV
ejpam-3412	395	7	up	up	ADP
ejpam-3412	395	8	-	-	PUNCT
ejpam-3412	395	9	ideal	ideal	NOUN
ejpam-3412	395	10	of	of	ADP
ejpam-3412	395	11	a.	a.	NOUN
ejpam-3412	395	12	the	the	DET
ejpam-3412	395	13	converse	converse	NOUN
ejpam-3412	395	14	is	be	AUX
ejpam-3412	395	15	obvious	obvious	ADJ
ejpam-3412	395	16	because	because	SCONJ
ejpam-3412	395	17	f	f	PROPN
ejpam-3412	395	18	is	be	AUX
ejpam-3412	395	19	constant	constant	ADJ
ejpam-3412	395	20	.	.	PUNCT
ejpam-3412	396	1	theorem	theorem	NOUN
ejpam-3412	396	2	19	19	NUM
ejpam-3412	396	3	.	.	PUNCT
ejpam-3412	397	1	if	if	SCONJ
ejpam-3412	397	2	f	f	PROPN
ejpam-3412	397	3	is	be	AUX
ejpam-3412	397	4	a	a	DET
ejpam-3412	397	5	fuzzy	fuzzy	ADJ
ejpam-3412	397	6	set	set	NOUN
ejpam-3412	397	7	in	in	ADP
ejpam-3412	397	8	a	a	DET
ejpam-3412	397	9	satisfying	satisfying	NOUN
ejpam-3412	397	10	the	the	DET
ejpam-3412	397	11	condition	condition	NOUN
ejpam-3412	397	12	(	(	PUNCT
ejpam-3412	397	13	∀x	∀x	X
ejpam-3412	397	14	,	,	PUNCT
ejpam-3412	397	15	y	y	PROPN
ejpam-3412	397	16	,	,	PUNCT
ejpam-3412	397	17	z	z	PROPN
ejpam-3412	397	18	∈	∈	PROPN
ejpam-3412	397	19	a)(z	a)(z	PUNCT
ejpam-3412	397	20	≤	≤	NUM
ejpam-3412	397	21	x	x	SYM
ejpam-3412	397	22	·	·	PUNCT
ejpam-3412	397	23	y	y	PROPN
ejpam-3412	397	24	⇒	⇒	PROPN
ejpam-3412	397	25	ff(z	ff(z	PUNCT
ejpam-3412	397	26	)	)	PUNCT
ejpam-3412	397	27	≥	≥	NOUN
ejpam-3412	397	28	ff(y	ff(y	NUM
ejpam-3412	397	29	)	)	PUNCT
ejpam-3412	397	30	)	)	PUNCT
ejpam-3412	397	31	,	,	PUNCT
ejpam-3412	397	32	(	(	PUNCT
ejpam-3412	397	33	2.14	2.14	NUM
ejpam-3412	397	34	)	)	PUNCT
ejpam-3412	397	35	then	then	ADV
ejpam-3412	397	36	f	f	PROPN
ejpam-3412	397	37	satisfies	satisfy	VERB
ejpam-3412	397	38	the	the	DET
ejpam-3412	397	39	condition	condition	NOUN
ejpam-3412	397	40	(	(	PUNCT
ejpam-3412	397	41	2.3	2.3	NUM
ejpam-3412	397	42	)	)	PUNCT
ejpam-3412	397	43	.	.	PUNCT
ejpam-3412	398	1	proof	proof	NOUN
ejpam-3412	398	2	.	.	PUNCT
ejpam-3412	399	1	let	let	VERB
ejpam-3412	399	2	x	x	PRON
ejpam-3412	399	3	,	,	PUNCT
ejpam-3412	399	4	y	y	PROPN
ejpam-3412	399	5	,	,	PUNCT
ejpam-3412	399	6	z	z	PROPN
ejpam-3412	399	7	∈	∈	PROPN
ejpam-3412	399	8	a	a	DET
ejpam-3412	399	9	be	be	AUX
ejpam-3412	399	10	such	such	ADJ
ejpam-3412	399	11	that	that	SCONJ
ejpam-3412	399	12	z	z	NOUN
ejpam-3412	399	13	≤	≤	NOUN
ejpam-3412	399	14	x.	x.	PUNCT
ejpam-3412	399	15	by	by	ADP
ejpam-3412	399	16	(	(	PUNCT
ejpam-3412	399	17	1.4	1.4	NUM
ejpam-3412	399	18	)	)	PUNCT
ejpam-3412	399	19	,	,	PUNCT
ejpam-3412	399	20	we	we	PRON
ejpam-3412	399	21	have	have	VERB
ejpam-3412	399	22	x	x	X
ejpam-3412	399	23	·	·	PUNCT
ejpam-3412	399	24	y	y	SYM
ejpam-3412	399	25	≤	≤	PROPN
ejpam-3412	400	1	z	z	NOUN
ejpam-3412	400	2	·	·	PUNCT
ejpam-3412	400	3	y.	y.	NOUN
ejpam-3412	400	4	it	it	PRON
ejpam-3412	400	5	follows	follow	VERB
ejpam-3412	400	6	from	from	ADP
ejpam-3412	400	7	(	(	PUNCT
ejpam-3412	400	8	2.14	2.14	NUM
ejpam-3412	400	9	)	)	PUNCT
ejpam-3412	400	10	that	that	PRON
ejpam-3412	400	11	ff(x	ff(x	X
ejpam-3412	400	12	·	·	PUNCT
ejpam-3412	400	13	y	y	X
ejpam-3412	400	14	)	)	PUNCT
ejpam-3412	400	15	≥	≥	NOUN
ejpam-3412	400	16	ff(y	ff(y	NUM
ejpam-3412	400	17	)	)	PUNCT
ejpam-3412	400	18	≥	≥	NOUN
ejpam-3412	400	19	min{ff(z	min{ff(z	NOUN
ejpam-3412	400	20	)	)	PUNCT
ejpam-3412	400	21	,	,	PUNCT
ejpam-3412	400	22	ff(y	ff(y	NUM
ejpam-3412	400	23	)	)	PUNCT
ejpam-3412	400	24	}	}	PUNCT
ejpam-3412	400	25	.	.	PUNCT
ejpam-3412	401	1	hence	hence	ADV
ejpam-3412	401	2	,	,	PUNCT
ejpam-3412	401	3	f	f	PROPN
ejpam-3412	401	4	satisfies	satisfie	NOUN
ejpam-3412	401	5	(	(	PUNCT
ejpam-3412	401	6	2.3	2.3	NUM
ejpam-3412	401	7	)	)	PUNCT
ejpam-3412	401	8	.	.	PUNCT
ejpam-3412	402	1	proposition	proposition	NOUN
ejpam-3412	402	2	11	11	NUM
ejpam-3412	402	3	.	.	PUNCT
ejpam-3412	403	1	a	a	DET
ejpam-3412	403	2	fuzzy	fuzzy	ADJ
ejpam-3412	403	3	set	set	NOUN
ejpam-3412	403	4	f	f	PROPN
ejpam-3412	403	5	in	in	ADP
ejpam-3412	403	6	a	a	DET
ejpam-3412	403	7	satisfies	satisfie	NOUN
ejpam-3412	403	8	the	the	DET
ejpam-3412	403	9	condition	condition	NOUN
ejpam-3412	403	10	(	(	PUNCT
ejpam-3412	403	11	2.14	2.14	NUM
ejpam-3412	403	12	)	)	PUNCT
ejpam-3412	403	13	if	if	SCONJ
ejpam-3412	403	14	and	and	CCONJ
ejpam-3412	403	15	only	only	ADV
ejpam-3412	403	16	if	if	SCONJ
ejpam-3412	403	17	f	f	PROPN
ejpam-3412	403	18	is	be	AUX
ejpam-3412	403	19	a	a	DET
ejpam-3412	403	20	fuzzy	fuzzy	ADJ
ejpam-3412	403	21	strongly	strongly	ADV
ejpam-3412	403	22	up	up	ADP
ejpam-3412	403	23	-	-	PUNCT
ejpam-3412	403	24	ideal	ideal	NOUN
ejpam-3412	403	25	of	of	ADP
ejpam-3412	403	26	a.	a.	NOUN
ejpam-3412	403	27	proof	proof	NOUN
ejpam-3412	403	28	.	.	PUNCT
ejpam-3412	404	1	let	let	VERB
ejpam-3412	404	2	x	x	PUNCT
ejpam-3412	404	3	∈	∈	VERB
ejpam-3412	404	4	a.	a.	NOUN
ejpam-3412	404	5	by	by	ADP
ejpam-3412	404	6	(	(	PUNCT
ejpam-3412	404	7	up-3	up-3	NOUN
ejpam-3412	404	8	)	)	PUNCT
ejpam-3412	404	9	,	,	PUNCT
ejpam-3412	404	10	we	we	PRON
ejpam-3412	404	11	have	have	VERB
ejpam-3412	404	12	x	x	NOUN
ejpam-3412	404	13	≤	≤	X
ejpam-3412	404	14	0	0	NUM
ejpam-3412	405	1	=	=	SYM
ejpam-3412	405	2	0	0	NUM
ejpam-3412	405	3	·	·	PUNCT
ejpam-3412	405	4	0	0	X
ejpam-3412	405	5	.	.	PUNCT
ejpam-3412	406	1	by	by	ADP
ejpam-3412	406	2	(	(	PUNCT
ejpam-3412	406	3	2.14	2.14	NUM
ejpam-3412	406	4	)	)	PUNCT
ejpam-3412	406	5	,	,	PUNCT
ejpam-3412	406	6	we	we	PRON
ejpam-3412	406	7	have	have	VERB
ejpam-3412	406	8	ff(x	ff(x	NOUN
ejpam-3412	406	9	)	)	PUNCT
ejpam-3412	406	10	≥	≥	NOUN
ejpam-3412	406	11	ff(0	ff(0	NOUN
ejpam-3412	406	12	)	)	PUNCT
ejpam-3412	406	13	.	.	PUNCT
ejpam-3412	407	1	by	by	ADP
ejpam-3412	407	2	theorem	theorem	NOUN
ejpam-3412	407	3	19	19	NUM
ejpam-3412	407	4	and	and	CCONJ
ejpam-3412	407	5	proposition	proposition	NOUN
ejpam-3412	407	6	3	3	NUM
ejpam-3412	407	7	,	,	PUNCT
ejpam-3412	407	8	we	we	PRON
ejpam-3412	407	9	have	have	VERB
ejpam-3412	407	10	ff(0	ff(0	NOUN
ejpam-3412	407	11	)	)	PUNCT
ejpam-3412	407	12	≥	≥	NUM
ejpam-3412	407	13	ff(x	ff(x	NOUN
ejpam-3412	407	14	)	)	PUNCT
ejpam-3412	407	15	.	.	PUNCT
ejpam-3412	408	1	thus	thus	ADV
ejpam-3412	408	2	ff(x	ff(x	NOUN
ejpam-3412	408	3	)	)	PUNCT
ejpam-3412	408	4	=	=	SYM
ejpam-3412	408	5	ff(0	ff(0	NOUN
ejpam-3412	408	6	)	)	PUNCT
ejpam-3412	408	7	for	for	ADP
ejpam-3412	408	8	all	all	PRON
ejpam-3412	408	9	x	x	SYM
ejpam-3412	408	10	∈	∈	PROPN
ejpam-3412	408	11	a	a	PRON
ejpam-3412	408	12	,	,	PUNCT
ejpam-3412	408	13	so	so	CCONJ
ejpam-3412	408	14	f	f	PROPN
ejpam-3412	408	15	is	be	AUX
ejpam-3412	408	16	constant	constant	ADJ
ejpam-3412	408	17	.	.	PUNCT
ejpam-3412	409	1	hence	hence	ADV
ejpam-3412	409	2	,	,	PUNCT
ejpam-3412	409	3	f	f	PROPN
ejpam-3412	409	4	is	be	AUX
ejpam-3412	409	5	a	a	DET
ejpam-3412	409	6	fuzzy	fuzzy	ADJ
ejpam-3412	409	7	strongly	strongly	ADV
ejpam-3412	409	8	up	up	ADP
ejpam-3412	409	9	-	-	PUNCT
ejpam-3412	409	10	ideal	ideal	NOUN
ejpam-3412	409	11	of	of	ADP
ejpam-3412	409	12	a.	a.	NOUN
ejpam-3412	409	13	the	the	DET
ejpam-3412	409	14	converse	converse	NOUN
ejpam-3412	409	15	is	be	AUX
ejpam-3412	409	16	obvious	obvious	ADJ
ejpam-3412	409	17	because	because	SCONJ
ejpam-3412	409	18	f	f	PROPN
ejpam-3412	409	19	is	be	AUX
ejpam-3412	409	20	constant	constant	ADJ
ejpam-3412	409	21	.	.	PUNCT
ejpam-3412	410	1	we	we	PRON
ejpam-3412	410	2	have	have	AUX
ejpam-3412	410	3	provided	provide	VERB
ejpam-3412	410	4	various	various	ADJ
ejpam-3412	410	5	important	important	ADJ
ejpam-3412	410	6	properties	property	NOUN
ejpam-3412	410	7	of	of	ADP
ejpam-3412	410	8	fuzzy	fuzzy	ADJ
ejpam-3412	410	9	sets	set	NOUN
ejpam-3412	410	10	in	in	ADP
ejpam-3412	410	11	various	various	ADJ
ejpam-3412	410	12	types	type	NOUN
ejpam-3412	410	13	in	in	ADP
ejpam-3412	410	14	upalgebras	upalgebra	NOUN
ejpam-3412	410	15	which	which	PRON
ejpam-3412	410	16	will	will	AUX
ejpam-3412	410	17	be	be	AUX
ejpam-3412	410	18	used	use	VERB
ejpam-3412	410	19	in	in	ADP
ejpam-3412	410	20	the	the	DET
ejpam-3412	410	21	next	next	ADJ
ejpam-3412	410	22	section	section	NOUN
ejpam-3412	410	23	.	.	PUNCT
ejpam-3412	411	1	we	we	PRON
ejpam-3412	411	2	get	get	VERB
ejpam-3412	411	3	the	the	DET
ejpam-3412	411	4	diagram	diagram	NOUN
ejpam-3412	411	5	of	of	ADP
ejpam-3412	411	6	the	the	DET
ejpam-3412	411	7	properties	property	NOUN
ejpam-3412	411	8	of	of	ADP
ejpam-3412	411	9	fuzzy	fuzzy	ADJ
ejpam-3412	411	10	sets	set	NOUN
ejpam-3412	411	11	in	in	ADP
ejpam-3412	411	12	up	up	ADV
ejpam-3412	411	13	-	-	PUNCT
ejpam-3412	411	14	algebras	algebra	NOUN
ejpam-3412	411	15	as	as	SCONJ
ejpam-3412	411	16	shown	show	VERB
ejpam-3412	411	17	in	in	ADP
ejpam-3412	411	18	figure	figure	NOUN
ejpam-3412	411	19	2	2	NUM
ejpam-3412	411	20	.	.	NOUN
ejpam-3412	411	21	3	3	NUM
ejpam-3412	411	22	.	.	NOUN
ejpam-3412	411	23	fuzzy	fuzzy	ADJ
ejpam-3412	411	24	soft	soft	ADJ
ejpam-3412	411	25	sets	set	NOUN
ejpam-3412	411	26	over	over	ADP
ejpam-3412	411	27	fully	fully	ADV
ejpam-3412	411	28	up	up	ADP
ejpam-3412	411	29	-	-	PUNCT
ejpam-3412	411	30	semigroups	semigroup	NOUN
ejpam-3412	411	31	from	from	ADP
ejpam-3412	411	32	now	now	ADV
ejpam-3412	411	33	on	on	ADV
ejpam-3412	411	34	,	,	PUNCT
ejpam-3412	411	35	we	we	PRON
ejpam-3412	411	36	shall	shall	AUX
ejpam-3412	411	37	let	let	VERB
ejpam-3412	411	38	a	a	DET
ejpam-3412	411	39	be	be	AUX
ejpam-3412	411	40	an	an	DET
ejpam-3412	411	41	f	f	PROPN
ejpam-3412	411	42	-up	-up	NOUN
ejpam-3412	411	43	-	-	NOUN
ejpam-3412	411	44	semigroup	semigroup	NOUN
ejpam-3412	411	45	a	a	X
ejpam-3412	411	46	=	=	X
ejpam-3412	411	47	(	(	PUNCT
ejpam-3412	411	48	a	a	PRON
ejpam-3412	411	49	,	,	PUNCT
ejpam-3412	411	50	·	·	PUNCT
ejpam-3412	411	51	,	,	PUNCT
ejpam-3412	411	52	∗	∗	NOUN
ejpam-3412	411	53	,	,	PUNCT
ejpam-3412	411	54	0	0	NUM
ejpam-3412	411	55	)	)	PUNCT
ejpam-3412	411	56	and	and	CCONJ
ejpam-3412	411	57	p	p	NOUN
ejpam-3412	411	58	be	be	AUX
ejpam-3412	411	59	a	a	DET
ejpam-3412	411	60	set	set	NOUN
ejpam-3412	411	61	of	of	ADP
ejpam-3412	411	62	parameters	parameter	NOUN
ejpam-3412	411	63	.	.	PUNCT
ejpam-3412	412	1	let	let	AUX
ejpam-3412	412	2	f(a	f(a	NOUN
ejpam-3412	412	3	)	)	PUNCT
ejpam-3412	412	4	denotes	denote	VERB
ejpam-3412	412	5	the	the	DET
ejpam-3412	412	6	set	set	NOUN
ejpam-3412	412	7	of	of	ADP
ejpam-3412	412	8	all	all	DET
ejpam-3412	412	9	fuzzy	fuzzy	ADJ
ejpam-3412	412	10	sets	set	NOUN
ejpam-3412	412	11	in	in	ADP
ejpam-3412	412	12	a.	a.	NOUN
ejpam-3412	412	13	a	a	DET
ejpam-3412	412	14	subset	subset	NOUN
ejpam-3412	412	15	e	e	NOUN
ejpam-3412	412	16	of	of	ADP
ejpam-3412	412	17	p	p	PROPN
ejpam-3412	412	18	is	be	AUX
ejpam-3412	412	19	called	call	VERB
ejpam-3412	412	20	a	a	DET
ejpam-3412	412	21	set	set	NOUN
ejpam-3412	412	22	of	of	ADP
ejpam-3412	412	23	statistics	statistic	NOUN
ejpam-3412	412	24	.	.	PUNCT
ejpam-3412	413	1	a.	a.	PROPN
ejpam-3412	413	2	satirad	satirad	PROPN
ejpam-3412	413	3	,	,	PUNCT
ejpam-3412	413	4	a.	a.	NOUN
ejpam-3412	413	5	iampan	iampan	PROPN
ejpam-3412	413	6	/	/	SYM
ejpam-3412	413	7	eur	eur	PROPN
ejpam-3412	413	8	.	.	PUNCT
ejpam-3412	414	1	j.	j.	PROPN
ejpam-3412	414	2	pure	pure	PROPN
ejpam-3412	414	3	appl	appl	PROPN
ejpam-3412	414	4	.	.	PROPN
ejpam-3412	414	5	math	math	PROPN
ejpam-3412	414	6	,	,	PUNCT
ejpam-3412	414	7	12	12	NUM
ejpam-3412	414	8	(	(	PUNCT
ejpam-3412	414	9	2	2	NUM
ejpam-3412	414	10	)	)	PUNCT
ejpam-3412	414	11	(	(	PUNCT
ejpam-3412	414	12	2019	2019	NUM
ejpam-3412	414	13	)	)	PUNCT
ejpam-3412	414	14	,	,	PUNCT
ejpam-3412	414	15	294	294	NUM
ejpam-3412	414	16	-	-	SYM
ejpam-3412	414	17	331	331	NUM
ejpam-3412	414	18	310	310	NUM
ejpam-3412	414	19	figure	figure	NOUN
ejpam-3412	414	20	2	2	NUM
ejpam-3412	414	21	:	:	PUNCT
ejpam-3412	414	22	properties	property	NOUN
ejpam-3412	414	23	of	of	ADP
ejpam-3412	414	24	fuzzy	fuzzy	ADJ
ejpam-3412	414	25	sets	set	NOUN
ejpam-3412	414	26	in	in	ADP
ejpam-3412	414	27	up	up	ADV
ejpam-3412	414	28	-	-	PUNCT
ejpam-3412	414	29	algebras	algebras	NOUN
ejpam-3412	414	30	definition	definition	NOUN
ejpam-3412	414	31	15	15	NUM
ejpam-3412	414	32	.	.	PUNCT
ejpam-3412	415	1	let	let	VERB
ejpam-3412	415	2	e	e	NOUN
ejpam-3412	415	3	⊆	⊆	NUM
ejpam-3412	415	4	p	p	NOUN
ejpam-3412	415	5	.	.	PUNCT
ejpam-3412	416	1	a	a	DET
ejpam-3412	416	2	pair	pair	NOUN
ejpam-3412	416	3	(	(	PUNCT
ejpam-3412	416	4	f̃	f̃	PROPN
ejpam-3412	416	5	,	,	PUNCT
ejpam-3412	416	6	e	e	NOUN
ejpam-3412	416	7	)	)	PUNCT
ejpam-3412	416	8	is	be	AUX
ejpam-3412	416	9	called	call	VERB
ejpam-3412	416	10	a	a	DET
ejpam-3412	416	11	fuzzy	fuzzy	ADJ
ejpam-3412	416	12	soft	soft	ADJ
ejpam-3412	416	13	set	set	NOUN
ejpam-3412	416	14	over	over	ADP
ejpam-3412	416	15	a	a	PRON
ejpam-3412	416	16	if	if	SCONJ
ejpam-3412	416	17	f̃	f̃	PROPN
ejpam-3412	416	18	is	be	AUX
ejpam-3412	416	19	a	a	DET
ejpam-3412	416	20	mapping	mapping	NOUN
ejpam-3412	416	21	given	give	VERB
ejpam-3412	416	22	by	by	ADP
ejpam-3412	416	23	f̃	f̃	PROPN
ejpam-3412	416	24	:	:	PUNCT
ejpam-3412	416	25	e	e	X
ejpam-3412	416	26	→	→	SYM
ejpam-3412	416	27	f(a	f(a	PROPN
ejpam-3412	416	28	)	)	PUNCT
ejpam-3412	416	29	,	,	PUNCT
ejpam-3412	416	30	that	that	ADV
ejpam-3412	416	31	is	is	ADV
ejpam-3412	416	32	,	,	PUNCT
ejpam-3412	416	33	a	a	DET
ejpam-3412	416	34	fuzzy	fuzzy	ADJ
ejpam-3412	416	35	soft	soft	ADJ
ejpam-3412	416	36	set	set	NOUN
ejpam-3412	416	37	is	be	AUX
ejpam-3412	416	38	a	a	DET
ejpam-3412	416	39	statistic	statistic	ADJ
ejpam-3412	416	40	family	family	NOUN
ejpam-3412	416	41	of	of	ADP
ejpam-3412	416	42	fuzzy	fuzzy	ADJ
ejpam-3412	416	43	sets	set	NOUN
ejpam-3412	416	44	in	in	ADP
ejpam-3412	416	45	a.	a.	NOUN
ejpam-3412	416	46	in	in	ADP
ejpam-3412	416	47	general	general	ADJ
ejpam-3412	416	48	,	,	PUNCT
ejpam-3412	416	49	for	for	ADP
ejpam-3412	416	50	every	every	DET
ejpam-3412	416	51	e	e	PROPN
ejpam-3412	416	52	∈	∈	PROPN
ejpam-3412	416	53	e	e	NOUN
ejpam-3412	416	54	,	,	PUNCT
ejpam-3412	416	55	f̃[e	f̃[e	PROPN
ejpam-3412	416	56	]	]	X
ejpam-3412	416	57	:	:	PUNCT
ejpam-3412	416	58	=	=	SYM
ejpam-3412	416	59	{	{	PUNCT
ejpam-3412	416	60	(	(	PUNCT
ejpam-3412	416	61	x	x	X
ejpam-3412	416	62	,	,	PUNCT
ejpam-3412	416	63	f	f	PROPN
ejpam-3412	416	64	f̃[e	f̃[e	NOUN
ejpam-3412	416	65	]	]	X
ejpam-3412	416	66	(	(	PUNCT
ejpam-3412	416	67	x	x	NOUN
ejpam-3412	416	68	)	)	PUNCT
ejpam-3412	416	69	)	)	PUNCT
ejpam-3412	417	1	|	|	ADV
ejpam-3412	417	2	x	x	SYM
ejpam-3412	417	3	∈	∈	PROPN
ejpam-3412	417	4	a	a	PRON
ejpam-3412	417	5	}	}	PUNCT
ejpam-3412	417	6	is	be	AUX
ejpam-3412	417	7	a	a	DET
ejpam-3412	417	8	fuzzy	fuzzy	ADJ
ejpam-3412	417	9	set	set	NOUN
ejpam-3412	417	10	in	in	ADP
ejpam-3412	417	11	a	a	PRON
ejpam-3412	417	12	and	and	CCONJ
ejpam-3412	417	13	it	it	PRON
ejpam-3412	417	14	is	be	AUX
ejpam-3412	417	15	called	call	VERB
ejpam-3412	417	16	a	a	DET
ejpam-3412	417	17	fuzzy	fuzzy	ADJ
ejpam-3412	417	18	value	value	NOUN
ejpam-3412	417	19	set	set	NOUN
ejpam-3412	417	20	of	of	ADP
ejpam-3412	417	21	statistic	statistic	ADJ
ejpam-3412	417	22	e.	e.	PROPN
ejpam-3412	417	23	definition	definition	NOUN
ejpam-3412	417	24	16	16	NUM
ejpam-3412	417	25	.	.	PUNCT
ejpam-3412	418	1	let	let	AUX
ejpam-3412	418	2	(	(	PUNCT
ejpam-3412	418	3	f̃	f̃	PROPN
ejpam-3412	418	4	,	,	PUNCT
ejpam-3412	418	5	e1	e1	PROPN
ejpam-3412	418	6	)	)	PUNCT
ejpam-3412	418	7	and	and	CCONJ
ejpam-3412	418	8	(	(	PUNCT
ejpam-3412	418	9	g̃	g̃	PROPN
ejpam-3412	418	10	,	,	PUNCT
ejpam-3412	418	11	e2	e2	PROPN
ejpam-3412	418	12	)	)	PUNCT
ejpam-3412	418	13	be	be	VERB
ejpam-3412	418	14	two	two	NUM
ejpam-3412	418	15	fuzzy	fuzzy	ADJ
ejpam-3412	418	16	soft	soft	ADJ
ejpam-3412	418	17	sets	set	NOUN
ejpam-3412	418	18	over	over	ADP
ejpam-3412	418	19	a	a	DET
ejpam-3412	418	20	common	common	ADJ
ejpam-3412	418	21	universe	universe	NOUN
ejpam-3412	418	22	u	u	NOUN
ejpam-3412	418	23	.	.	PUNCT
ejpam-3412	419	1	the	the	DET
ejpam-3412	419	2	union	union	NOUN
ejpam-3412	419	3	[	[	X
ejpam-3412	419	4	17	17	NUM
ejpam-3412	419	5	]	]	PUNCT
ejpam-3412	419	6	of	of	ADP
ejpam-3412	419	7	(	(	PUNCT
ejpam-3412	419	8	f̃	f̃	PROPN
ejpam-3412	419	9	,	,	PUNCT
ejpam-3412	419	10	e1	e1	PROPN
ejpam-3412	419	11	)	)	PUNCT
ejpam-3412	419	12	and	and	CCONJ
ejpam-3412	419	13	(	(	PUNCT
ejpam-3412	419	14	g̃	g̃	PROPN
ejpam-3412	419	15	,	,	PUNCT
ejpam-3412	419	16	e2	e2	PROPN
ejpam-3412	419	17	)	)	PUNCT
ejpam-3412	419	18	is	be	AUX
ejpam-3412	419	19	defined	define	VERB
ejpam-3412	419	20	to	to	PART
ejpam-3412	419	21	be	be	AUX
ejpam-3412	419	22	the	the	DET
ejpam-3412	419	23	fuzzy	fuzzy	ADJ
ejpam-3412	419	24	soft	soft	ADJ
ejpam-3412	419	25	set	set	NOUN
ejpam-3412	419	26	(	(	PUNCT
ejpam-3412	419	27	f̃	f̃	PROPN
ejpam-3412	419	28	,	,	PUNCT
ejpam-3412	419	29	e1)∪	e1)∪	NOUN
ejpam-3412	419	30	(	(	PUNCT
ejpam-3412	419	31	g̃	g̃	PROPN
ejpam-3412	419	32	,	,	PUNCT
ejpam-3412	419	33	e2	e2	PROPN
ejpam-3412	419	34	)	)	PUNCT
ejpam-3412	419	35	=	=	SYM
ejpam-3412	419	36	(	(	PUNCT
ejpam-3412	419	37	h̃	h̃	PROPN
ejpam-3412	419	38	,	,	PUNCT
ejpam-3412	419	39	e	e	NOUN
ejpam-3412	419	40	)	)	PUNCT
ejpam-3412	419	41	satisfying	satisfy	VERB
ejpam-3412	419	42	the	the	DET
ejpam-3412	419	43	following	follow	VERB
ejpam-3412	419	44	conditions	condition	NOUN
ejpam-3412	419	45	:	:	PUNCT
ejpam-3412	419	46	(	(	PUNCT
ejpam-3412	419	47	i	i	NOUN
ejpam-3412	419	48	)	)	PUNCT
ejpam-3412	419	49	e	e	X
ejpam-3412	419	50	=	=	NOUN
ejpam-3412	419	51	e1	e1	PROPN
ejpam-3412	419	52	∪	∪	PROPN
ejpam-3412	419	53	e2	e2	PROPN
ejpam-3412	419	54	and	and	CCONJ
ejpam-3412	419	55	(	(	PUNCT
ejpam-3412	419	56	ii	ii	NOUN
ejpam-3412	419	57	)	)	PUNCT
ejpam-3412	419	58	for	for	ADP
ejpam-3412	419	59	all	all	DET
ejpam-3412	419	60	e	e	PROPN
ejpam-3412	419	61	∈	∈	PROPN
ejpam-3412	419	62	e	e	NOUN
ejpam-3412	419	63	,	,	PUNCT
ejpam-3412	419	64	h̃[e	h̃[e	PROPN
ejpam-3412	419	65	]	]	X
ejpam-3412	420	1	=	=	PUNCT
ejpam-3412	420	2			PRON
ejpam-3412	420	3	f̃[e	f̃[e	INTJ
ejpam-3412	420	4	]	]	X
ejpam-3412	420	5	if	if	SCONJ
ejpam-3412	420	6	e	e	PROPN
ejpam-3412	420	7	∈	∈	PROPN
ejpam-3412	420	8	e1	e1	PROPN
ejpam-3412	420	9	\	\	PROPN
ejpam-3412	420	10	e2	e2	PROPN
ejpam-3412	420	11	g̃[e	g̃[e	PROPN
ejpam-3412	420	12	]	]	PUNCT
ejpam-3412	420	13	if	if	SCONJ
ejpam-3412	420	14	e	e	PROPN
ejpam-3412	420	15	∈	∈	PROPN
ejpam-3412	420	16	e2	e2	PROPN
ejpam-3412	420	17	\	\	PROPN
ejpam-3412	420	18	e1	e1	PROPN
ejpam-3412	420	19	f̃[e	f̃[e	NOUN
ejpam-3412	420	20	]	]	X
ejpam-3412	420	21	∪	∪	ADP
ejpam-3412	420	22	g̃[e	g̃[e	NOUN
ejpam-3412	420	23	]	]	PUNCT
ejpam-3412	420	24	if	if	SCONJ
ejpam-3412	420	25	e	e	PROPN
ejpam-3412	420	26	∈	∈	PROPN
ejpam-3412	420	27	e1	e1	NOUN
ejpam-3412	420	28	∩	∩	ADJ
ejpam-3412	420	29	e2	e2	PROPN
ejpam-3412	420	30	.	.	PUNCT
ejpam-3412	421	1	the	the	DET
ejpam-3412	421	2	restricted	restricted	ADJ
ejpam-3412	421	3	union	union	NOUN
ejpam-3412	421	4	[	[	X
ejpam-3412	421	5	20	20	NUM
ejpam-3412	421	6	]	]	PUNCT
ejpam-3412	421	7	of	of	ADP
ejpam-3412	421	8	(	(	PUNCT
ejpam-3412	421	9	f̃	f̃	PROPN
ejpam-3412	421	10	,	,	PUNCT
ejpam-3412	421	11	e1	e1	PROPN
ejpam-3412	421	12	)	)	PUNCT
ejpam-3412	421	13	and	and	CCONJ
ejpam-3412	421	14	(	(	PUNCT
ejpam-3412	421	15	g̃	g̃	PROPN
ejpam-3412	421	16	,	,	PUNCT
ejpam-3412	421	17	e2	e2	PROPN
ejpam-3412	421	18	)	)	PUNCT
ejpam-3412	421	19	is	be	AUX
ejpam-3412	421	20	defined	define	VERB
ejpam-3412	421	21	to	to	PART
ejpam-3412	421	22	be	be	AUX
ejpam-3412	421	23	the	the	DET
ejpam-3412	421	24	fuzzy	fuzzy	ADJ
ejpam-3412	421	25	soft	soft	ADJ
ejpam-3412	421	26	set	set	NOUN
ejpam-3412	421	27	(	(	PUNCT
ejpam-3412	421	28	f̃	f̃	PROPN
ejpam-3412	421	29	,	,	PUNCT
ejpam-3412	421	30	e1)d	e1)d	NOUN
ejpam-3412	421	31	(	(	PUNCT
ejpam-3412	421	32	g̃	g̃	PROPN
ejpam-3412	421	33	,	,	PUNCT
ejpam-3412	421	34	e2	e2	PROPN
ejpam-3412	421	35	)	)	PUNCT
ejpam-3412	422	1	=	=	SYM
ejpam-3412	422	2	(	(	PUNCT
ejpam-3412	422	3	h̃	h̃	PROPN
ejpam-3412	422	4	,	,	PUNCT
ejpam-3412	422	5	e	e	NOUN
ejpam-3412	422	6	)	)	PUNCT
ejpam-3412	422	7	satisfying	satisfy	VERB
ejpam-3412	422	8	the	the	DET
ejpam-3412	422	9	following	follow	VERB
ejpam-3412	422	10	conditions	condition	NOUN
ejpam-3412	422	11	:	:	PUNCT
ejpam-3412	422	12	(	(	PUNCT
ejpam-3412	422	13	i	i	NOUN
ejpam-3412	422	14	)	)	PUNCT
ejpam-3412	422	15	e	e	X
ejpam-3412	423	1	=	=	SYM
ejpam-3412	423	2	e1	e1	PROPN
ejpam-3412	423	3	∩	∩	ADJ
ejpam-3412	423	4	e2	e2	PROPN
ejpam-3412	423	5	6=	6=	NUM
ejpam-3412	423	6	∅	∅	NOUN
ejpam-3412	423	7	and	and	CCONJ
ejpam-3412	423	8	(	(	PUNCT
ejpam-3412	423	9	ii	ii	NOUN
ejpam-3412	423	10	)	)	PUNCT
ejpam-3412	423	11	h̃[e	h̃[e	PROPN
ejpam-3412	423	12	]	]	X
ejpam-3412	424	1	=	=	PUNCT
ejpam-3412	424	2	f̃[e	f̃[e	X
ejpam-3412	424	3	]	]	X
ejpam-3412	424	4	∪	∪	ADP
ejpam-3412	424	5	g̃[e	g̃[e	NOUN
ejpam-3412	424	6	]	]	PUNCT
ejpam-3412	424	7	for	for	ADP
ejpam-3412	424	8	all	all	DET
ejpam-3412	424	9	e	e	PROPN
ejpam-3412	424	10	∈	∈	PROPN
ejpam-3412	424	11	e.	e.	PROPN
ejpam-3412	424	12	definition	definition	NOUN
ejpam-3412	424	13	17	17	NUM
ejpam-3412	424	14	.	.	PUNCT
ejpam-3412	425	1	[	[	X
ejpam-3412	425	2	20	20	NUM
ejpam-3412	425	3	]	]	X
ejpam-3412	425	4	let	let	ADJ
ejpam-3412	425	5	(	(	PUNCT
ejpam-3412	425	6	f̃	f̃	PROPN
ejpam-3412	425	7	,	,	PUNCT
ejpam-3412	425	8	e1	e1	PROPN
ejpam-3412	425	9	)	)	PUNCT
ejpam-3412	425	10	and	and	CCONJ
ejpam-3412	425	11	(	(	PUNCT
ejpam-3412	425	12	g̃	g̃	PROPN
ejpam-3412	425	13	,	,	PUNCT
ejpam-3412	425	14	e2	e2	PROPN
ejpam-3412	425	15	)	)	PUNCT
ejpam-3412	425	16	be	be	VERB
ejpam-3412	425	17	two	two	NUM
ejpam-3412	425	18	fuzzy	fuzzy	ADJ
ejpam-3412	425	19	soft	soft	ADJ
ejpam-3412	425	20	sets	set	NOUN
ejpam-3412	425	21	over	over	ADP
ejpam-3412	425	22	a	a	DET
ejpam-3412	425	23	common	common	ADJ
ejpam-3412	425	24	universe	universe	NOUN
ejpam-3412	425	25	u	u	NOUN
ejpam-3412	425	26	.	.	PUNCT
ejpam-3412	426	1	the	the	DET
ejpam-3412	426	2	extended	extended	ADJ
ejpam-3412	426	3	intersection	intersection	NOUN
ejpam-3412	426	4	of	of	ADP
ejpam-3412	426	5	(	(	PUNCT
ejpam-3412	426	6	f̃	f̃	PROPN
ejpam-3412	426	7	,	,	PUNCT
ejpam-3412	426	8	e1	e1	PROPN
ejpam-3412	426	9	)	)	PUNCT
ejpam-3412	426	10	and	and	CCONJ
ejpam-3412	426	11	(	(	PUNCT
ejpam-3412	426	12	g̃	g̃	PROPN
ejpam-3412	426	13	,	,	PUNCT
ejpam-3412	426	14	e2	e2	PROPN
ejpam-3412	426	15	)	)	PUNCT
ejpam-3412	426	16	is	be	AUX
ejpam-3412	426	17	defined	define	VERB
ejpam-3412	426	18	to	to	PART
ejpam-3412	426	19	be	be	AUX
ejpam-3412	426	20	the	the	DET
ejpam-3412	426	21	fuzzy	fuzzy	ADJ
ejpam-3412	426	22	soft	soft	ADJ
ejpam-3412	426	23	set	set	NOUN
ejpam-3412	426	24	(	(	PUNCT
ejpam-3412	426	25	f̃	f̃	PROPN
ejpam-3412	426	26	,	,	PUNCT
ejpam-3412	426	27	e1	e1	NOUN
ejpam-3412	426	28	)	)	PUNCT
ejpam-3412	426	29	∩	∩	NOUN
ejpam-3412	426	30	(	(	PUNCT
ejpam-3412	426	31	g̃	g̃	PROPN
ejpam-3412	426	32	,	,	PUNCT
ejpam-3412	426	33	e2	e2	PROPN
ejpam-3412	426	34	)	)	PUNCT
ejpam-3412	426	35	=	=	SYM
ejpam-3412	426	36	(	(	PUNCT
ejpam-3412	426	37	h̃	h̃	PROPN
ejpam-3412	426	38	,	,	PUNCT
ejpam-3412	426	39	e	e	NOUN
ejpam-3412	426	40	)	)	PUNCT
ejpam-3412	426	41	satisfying	satisfy	VERB
ejpam-3412	426	42	the	the	DET
ejpam-3412	426	43	following	follow	VERB
ejpam-3412	426	44	conditions	condition	NOUN
ejpam-3412	426	45	:	:	PUNCT
ejpam-3412	426	46	(	(	PUNCT
ejpam-3412	426	47	i	i	NOUN
ejpam-3412	426	48	)	)	PUNCT
ejpam-3412	426	49	e	e	X
ejpam-3412	426	50	=	=	NOUN
ejpam-3412	426	51	e1	e1	PROPN
ejpam-3412	426	52	∪	∪	PROPN
ejpam-3412	426	53	e2	e2	PROPN
ejpam-3412	426	54	and	and	CCONJ
ejpam-3412	426	55	a.	a.	NOUN
ejpam-3412	426	56	satirad	satirad	PROPN
ejpam-3412	426	57	,	,	PUNCT
ejpam-3412	426	58	a.	a.	NOUN
ejpam-3412	426	59	iampan	iampan	PROPN
ejpam-3412	426	60	/	/	SYM
ejpam-3412	426	61	eur	eur	PROPN
ejpam-3412	426	62	.	.	PUNCT
ejpam-3412	427	1	j.	j.	PROPN
ejpam-3412	427	2	pure	pure	PROPN
ejpam-3412	427	3	appl	appl	PROPN
ejpam-3412	427	4	.	.	PROPN
ejpam-3412	427	5	math	math	PROPN
ejpam-3412	427	6	,	,	PUNCT
ejpam-3412	427	7	12	12	NUM
ejpam-3412	427	8	(	(	PUNCT
ejpam-3412	427	9	2	2	NUM
ejpam-3412	427	10	)	)	PUNCT
ejpam-3412	427	11	(	(	PUNCT
ejpam-3412	427	12	2019	2019	NUM
ejpam-3412	427	13	)	)	PUNCT
ejpam-3412	427	14	,	,	PUNCT
ejpam-3412	427	15	294	294	NUM
ejpam-3412	427	16	-	-	SYM
ejpam-3412	427	17	331	331	NUM
ejpam-3412	427	18	311	311	NUM
ejpam-3412	427	19	(	(	PUNCT
ejpam-3412	427	20	ii	ii	NOUN
ejpam-3412	427	21	)	)	PUNCT
ejpam-3412	427	22	for	for	ADP
ejpam-3412	427	23	all	all	DET
ejpam-3412	427	24	e	e	PROPN
ejpam-3412	427	25	∈	∈	PROPN
ejpam-3412	427	26	e	e	NOUN
ejpam-3412	427	27	,	,	PUNCT
ejpam-3412	427	28	h̃[e	h̃[e	PROPN
ejpam-3412	427	29	]	]	X
ejpam-3412	428	1	=	=	PUNCT
ejpam-3412	428	2			PRON
ejpam-3412	428	3	f̃[e	f̃[e	INTJ
ejpam-3412	428	4	]	]	X
ejpam-3412	428	5	if	if	SCONJ
ejpam-3412	428	6	e	e	PROPN
ejpam-3412	428	7	∈	∈	PROPN
ejpam-3412	428	8	e1	e1	PROPN
ejpam-3412	428	9	\	\	PROPN
ejpam-3412	428	10	e2	e2	PROPN
ejpam-3412	428	11	g̃[e	g̃[e	PROPN
ejpam-3412	428	12	]	]	PUNCT
ejpam-3412	428	13	if	if	SCONJ
ejpam-3412	428	14	e	e	PROPN
ejpam-3412	428	15	∈	∈	PROPN
ejpam-3412	428	16	e2	e2	PROPN
ejpam-3412	428	17	\	\	PROPN
ejpam-3412	428	18	e1	e1	PROPN
ejpam-3412	428	19	f̃[e	f̃[e	NOUN
ejpam-3412	428	20	]	]	X
ejpam-3412	428	21	∩	∩	ADJ
ejpam-3412	428	22	g̃[e	g̃[e	NOUN
ejpam-3412	428	23	]	]	X
ejpam-3412	428	24	if	if	SCONJ
ejpam-3412	428	25	e	e	PROPN
ejpam-3412	428	26	∈	∈	PROPN
ejpam-3412	428	27	e1	e1	NOUN
ejpam-3412	428	28	∩	∩	ADJ
ejpam-3412	428	29	e2	e2	PROPN
ejpam-3412	428	30	.	.	PUNCT
ejpam-3412	429	1	the	the	DET
ejpam-3412	429	2	intersection	intersection	NOUN
ejpam-3412	429	3	[	[	X
ejpam-3412	429	4	1	1	X
ejpam-3412	429	5	]	]	PUNCT
ejpam-3412	429	6	of	of	ADP
ejpam-3412	429	7	(	(	PUNCT
ejpam-3412	429	8	f̃	f̃	PROPN
ejpam-3412	429	9	,	,	PUNCT
ejpam-3412	429	10	e1	e1	PROPN
ejpam-3412	429	11	)	)	PUNCT
ejpam-3412	429	12	and	and	CCONJ
ejpam-3412	429	13	(	(	PUNCT
ejpam-3412	429	14	g̃	g̃	PROPN
ejpam-3412	429	15	,	,	PUNCT
ejpam-3412	429	16	e2	e2	PROPN
ejpam-3412	429	17	)	)	PUNCT
ejpam-3412	429	18	is	be	AUX
ejpam-3412	429	19	defined	define	VERB
ejpam-3412	429	20	to	to	PART
ejpam-3412	429	21	be	be	AUX
ejpam-3412	429	22	the	the	DET
ejpam-3412	429	23	fuzzy	fuzzy	ADJ
ejpam-3412	429	24	soft	soft	ADJ
ejpam-3412	429	25	set	set	NOUN
ejpam-3412	429	26	(	(	PUNCT
ejpam-3412	429	27	f̃	f̃	PROPN
ejpam-3412	429	28	,	,	PUNCT
ejpam-3412	429	29	e1	e1	PROPN
ejpam-3412	429	30	)	)	PUNCT
ejpam-3412	429	31	e	e	NOUN
ejpam-3412	429	32	(	(	PUNCT
ejpam-3412	429	33	g̃	g̃	PROPN
ejpam-3412	429	34	,	,	PUNCT
ejpam-3412	429	35	e2	e2	PROPN
ejpam-3412	429	36	)	)	PUNCT
ejpam-3412	429	37	=	=	SYM
ejpam-3412	429	38	(	(	PUNCT
ejpam-3412	429	39	h̃	h̃	PROPN
ejpam-3412	429	40	,	,	PUNCT
ejpam-3412	429	41	e	e	NOUN
ejpam-3412	429	42	)	)	PUNCT
ejpam-3412	429	43	satisfying	satisfy	VERB
ejpam-3412	429	44	the	the	DET
ejpam-3412	429	45	following	follow	VERB
ejpam-3412	429	46	conditions	condition	NOUN
ejpam-3412	429	47	:	:	PUNCT
ejpam-3412	429	48	(	(	PUNCT
ejpam-3412	429	49	i	i	NOUN
ejpam-3412	429	50	)	)	PUNCT
ejpam-3412	430	1	e	e	X
ejpam-3412	431	1	=	=	SYM
ejpam-3412	431	2	e1	e1	PROPN
ejpam-3412	431	3	∩	∩	ADJ
ejpam-3412	431	4	e2	e2	PROPN
ejpam-3412	431	5	6=	6=	NUM
ejpam-3412	431	6	∅	∅	NOUN
ejpam-3412	431	7	and	and	CCONJ
ejpam-3412	431	8	(	(	PUNCT
ejpam-3412	431	9	ii	ii	NOUN
ejpam-3412	431	10	)	)	PUNCT
ejpam-3412	431	11	h̃[e	h̃[e	PROPN
ejpam-3412	431	12	]	]	X
ejpam-3412	432	1	=	=	PUNCT
ejpam-3412	432	2	f̃[e	f̃[e	NOUN
ejpam-3412	432	3	]	]	X
ejpam-3412	432	4	∩	∩	ADJ
ejpam-3412	432	5	g̃[e	g̃[e	NOUN
ejpam-3412	432	6	]	]	PUNCT
ejpam-3412	432	7	for	for	ADP
ejpam-3412	432	8	all	all	DET
ejpam-3412	432	9	e	e	PROPN
ejpam-3412	432	10	∈	∈	PROPN
ejpam-3412	432	11	e.	e.	PROPN
ejpam-3412	432	12	3.1	3.1	NUM
ejpam-3412	432	13	.	.	PUNCT
ejpam-3412	433	1	fuzzy	fuzzy	ADJ
ejpam-3412	433	2	soft	soft	ADJ
ejpam-3412	433	3	ups	up	NOUN
ejpam-3412	433	4	-	-	PUNCT
ejpam-3412	433	5	subalgebras	subalgebras	PROPN
ejpam-3412	433	6	definition	definition	NOUN
ejpam-3412	433	7	18	18	NUM
ejpam-3412	433	8	.	.	PUNCT
ejpam-3412	434	1	a	a	DET
ejpam-3412	434	2	fuzzy	fuzzy	ADJ
ejpam-3412	434	3	soft	soft	ADJ
ejpam-3412	434	4	set	set	NOUN
ejpam-3412	434	5	(	(	PUNCT
ejpam-3412	434	6	f̃	f̃	PROPN
ejpam-3412	434	7	,	,	PUNCT
ejpam-3412	434	8	e	e	NOUN
ejpam-3412	434	9	)	)	PUNCT
ejpam-3412	434	10	over	over	ADP
ejpam-3412	434	11	a	a	PRON
ejpam-3412	434	12	is	be	AUX
ejpam-3412	434	13	called	call	VERB
ejpam-3412	434	14	a	a	DET
ejpam-3412	434	15	fuzzy	fuzzy	ADJ
ejpam-3412	434	16	soft	soft	ADJ
ejpam-3412	434	17	ups	up	NOUN
ejpam-3412	434	18	-	-	PUNCT
ejpam-3412	434	19	subalgebra	subalgebra	NOUN
ejpam-3412	434	20	based	base	VERB
ejpam-3412	434	21	on	on	ADP
ejpam-3412	434	22	e	e	PROPN
ejpam-3412	434	23	∈	∈	PROPN
ejpam-3412	434	24	e	e	X
ejpam-3412	434	25	(	(	PUNCT
ejpam-3412	434	26	we	we	PRON
ejpam-3412	434	27	shortly	shortly	ADV
ejpam-3412	434	28	call	call	VERB
ejpam-3412	434	29	an	an	DET
ejpam-3412	434	30	e	e	ADJ
ejpam-3412	434	31	-	-	ADJ
ejpam-3412	434	32	fuzzy	fuzzy	ADJ
ejpam-3412	434	33	soft	soft	ADJ
ejpam-3412	434	34	ups	up	NOUN
ejpam-3412	434	35	-	-	PUNCT
ejpam-3412	434	36	subalgebra	subalgebra	NOUN
ejpam-3412	434	37	)	)	PUNCT
ejpam-3412	434	38	of	of	ADP
ejpam-3412	434	39	a	a	DET
ejpam-3412	434	40	if	if	SCONJ
ejpam-3412	434	41	a	a	DET
ejpam-3412	434	42	fuzzy	fuzzy	ADJ
ejpam-3412	434	43	set	set	NOUN
ejpam-3412	434	44	f̃[e	f̃[e	X
ejpam-3412	434	45	]	]	X
ejpam-3412	434	46	in	in	ADP
ejpam-3412	434	47	a	a	PRON
ejpam-3412	434	48	is	be	AUX
ejpam-3412	434	49	a	a	DET
ejpam-3412	434	50	fuzzy	fuzzy	ADJ
ejpam-3412	434	51	ups	up	NOUN
ejpam-3412	434	52	-	-	PUNCT
ejpam-3412	434	53	subalgebra	subalgebra	NOUN
ejpam-3412	434	54	of	of	ADP
ejpam-3412	434	55	a.	a.	NOUN
ejpam-3412	434	56	if	if	SCONJ
ejpam-3412	434	57	(	(	PUNCT
ejpam-3412	434	58	f̃	f̃	PROPN
ejpam-3412	434	59	,	,	PUNCT
ejpam-3412	434	60	e	e	NOUN
ejpam-3412	434	61	)	)	PUNCT
ejpam-3412	434	62	is	be	AUX
ejpam-3412	434	63	an	an	DET
ejpam-3412	434	64	e	e	ADJ
ejpam-3412	434	65	-	-	ADJ
ejpam-3412	434	66	fuzzy	fuzzy	ADJ
ejpam-3412	434	67	soft	soft	ADJ
ejpam-3412	434	68	ups	up	NOUN
ejpam-3412	434	69	-	-	PUNCT
ejpam-3412	434	70	subalgebra	subalgebra	NOUN
ejpam-3412	434	71	of	of	ADP
ejpam-3412	434	72	a	a	PRON
ejpam-3412	434	73	for	for	ADP
ejpam-3412	434	74	all	all	DET
ejpam-3412	434	75	e	e	NOUN
ejpam-3412	434	76	∈	∈	PROPN
ejpam-3412	434	77	e	e	NOUN
ejpam-3412	434	78	,	,	PUNCT
ejpam-3412	434	79	we	we	PRON
ejpam-3412	434	80	say	say	VERB
ejpam-3412	434	81	that	that	SCONJ
ejpam-3412	434	82	(	(	PUNCT
ejpam-3412	434	83	f̃	f̃	PROPN
ejpam-3412	434	84	,	,	PUNCT
ejpam-3412	434	85	e	e	NOUN
ejpam-3412	434	86	)	)	PUNCT
ejpam-3412	434	87	is	be	AUX
ejpam-3412	434	88	a	a	DET
ejpam-3412	434	89	fuzzy	fuzzy	ADJ
ejpam-3412	434	90	soft	soft	ADJ
ejpam-3412	434	91	ups	up	NOUN
ejpam-3412	434	92	-	-	PUNCT
ejpam-3412	434	93	subalgebra	subalgebra	NOUN
ejpam-3412	434	94	of	of	ADP
ejpam-3412	434	95	a.	a.	NOUN
ejpam-3412	434	96	in	in	ADP
ejpam-3412	434	97	the	the	DET
ejpam-3412	434	98	next	next	ADJ
ejpam-3412	434	99	theorem	theorem	NOUN
ejpam-3412	434	100	,	,	PUNCT
ejpam-3412	434	101	we	we	PRON
ejpam-3412	434	102	give	give	VERB
ejpam-3412	434	103	necessary	necessary	ADJ
ejpam-3412	434	104	condition	condition	NOUN
ejpam-3412	434	105	for	for	ADP
ejpam-3412	434	106	fuzzy	fuzzy	ADJ
ejpam-3412	434	107	soft	soft	ADJ
ejpam-3412	434	108	ups	up	NOUN
ejpam-3412	434	109	-	-	PUNCT
ejpam-3412	434	110	subalgebras	subalgebras	PROPN
ejpam-3412	434	111	of	of	ADP
ejpam-3412	434	112	f	f	PROPN
ejpam-3412	434	113	-up	-up	NOUN
ejpam-3412	434	114	-	-	PUNCT
ejpam-3412	434	115	semigroups	semigroup	NOUN
ejpam-3412	434	116	.	.	PUNCT
ejpam-3412	435	1	theorem	theorem	NOUN
ejpam-3412	435	2	20	20	NUM
ejpam-3412	435	3	.	.	PUNCT
ejpam-3412	436	1	if	if	SCONJ
ejpam-3412	436	2	(	(	PUNCT
ejpam-3412	436	3	f̃	f̃	PROPN
ejpam-3412	436	4	,	,	PUNCT
ejpam-3412	436	5	e	e	NOUN
ejpam-3412	436	6	)	)	PUNCT
ejpam-3412	436	7	is	be	AUX
ejpam-3412	436	8	a	a	DET
ejpam-3412	436	9	fuzzy	fuzzy	ADJ
ejpam-3412	436	10	soft	soft	ADJ
ejpam-3412	436	11	set	set	NOUN
ejpam-3412	436	12	over	over	ADP
ejpam-3412	436	13	a	a	DET
ejpam-3412	436	14	such	such	ADJ
ejpam-3412	436	15	that	that	PRON
ejpam-3412	436	16	for	for	ADP
ejpam-3412	436	17	all	all	DET
ejpam-3412	436	18	e	e	NOUN
ejpam-3412	436	19	∈	∈	PROPN
ejpam-3412	436	20	e	e	NOUN
ejpam-3412	436	21	,	,	PUNCT
ejpam-3412	436	22	a	a	DET
ejpam-3412	436	23	fuzzy	fuzzy	ADJ
ejpam-3412	436	24	set	set	NOUN
ejpam-3412	436	25	f̃[e	f̃[e	NOUN
ejpam-3412	436	26	]	]	X
ejpam-3412	436	27	in	in	ADP
ejpam-3412	436	28	a	a	DET
ejpam-3412	436	29	satisfies	satisfie	NOUN
ejpam-3412	436	30	the	the	DET
ejpam-3412	436	31	conditions	condition	NOUN
ejpam-3412	436	32	(	(	PUNCT
ejpam-3412	436	33	2.3	2.3	NUM
ejpam-3412	436	34	)	)	PUNCT
ejpam-3412	436	35	and	and	CCONJ
ejpam-3412	436	36	(	(	PUNCT
ejpam-3412	436	37	1.14	1.14	NUM
ejpam-3412	436	38	)	)	PUNCT
ejpam-3412	436	39	,	,	PUNCT
ejpam-3412	436	40	then	then	ADV
ejpam-3412	436	41	(	(	PUNCT
ejpam-3412	436	42	f̃	f̃	PROPN
ejpam-3412	436	43	,	,	PUNCT
ejpam-3412	436	44	e	e	NOUN
ejpam-3412	436	45	)	)	PUNCT
ejpam-3412	436	46	is	be	AUX
ejpam-3412	436	47	a	a	DET
ejpam-3412	436	48	fuzzy	fuzzy	ADJ
ejpam-3412	436	49	soft	soft	ADJ
ejpam-3412	436	50	ups	up	NOUN
ejpam-3412	436	51	-	-	PUNCT
ejpam-3412	436	52	subalgebra	subalgebra	NOUN
ejpam-3412	436	53	of	of	ADP
ejpam-3412	436	54	a.	a.	NOUN
ejpam-3412	436	55	proof	proof	NOUN
ejpam-3412	436	56	.	.	PUNCT
ejpam-3412	437	1	it	it	PRON
ejpam-3412	437	2	is	be	AUX
ejpam-3412	437	3	straightforward	straightforward	ADJ
ejpam-3412	437	4	by	by	ADP
ejpam-3412	437	5	proposition	proposition	NOUN
ejpam-3412	437	6	3	3	NUM
ejpam-3412	437	7	and	and	CCONJ
ejpam-3412	437	8	lemma	lemma	PROPN
ejpam-3412	437	9	1	1	NUM
ejpam-3412	437	10	(	(	PUNCT
ejpam-3412	437	11	1	1	NUM
ejpam-3412	437	12	)	)	PUNCT
ejpam-3412	437	13	.	.	PUNCT
ejpam-3412	438	1	the	the	DET
ejpam-3412	438	2	proof	proof	NOUN
ejpam-3412	438	3	of	of	ADP
ejpam-3412	438	4	the	the	DET
ejpam-3412	438	5	following	follow	VERB
ejpam-3412	438	6	theorem	theorem	NOUN
ejpam-3412	438	7	can	can	AUX
ejpam-3412	438	8	be	be	AUX
ejpam-3412	438	9	verified	verify	VERB
ejpam-3412	438	10	easily	easily	ADV
ejpam-3412	438	11	.	.	PUNCT
ejpam-3412	439	1	theorem	theorem	NOUN
ejpam-3412	439	2	21	21	NUM
ejpam-3412	439	3	.	.	PUNCT
ejpam-3412	440	1	if	if	SCONJ
ejpam-3412	440	2	(	(	PUNCT
ejpam-3412	440	3	f̃	f̃	PROPN
ejpam-3412	440	4	,	,	PUNCT
ejpam-3412	440	5	e	e	NOUN
ejpam-3412	440	6	)	)	PUNCT
ejpam-3412	440	7	is	be	AUX
ejpam-3412	440	8	a	a	DET
ejpam-3412	440	9	fuzzy	fuzzy	ADJ
ejpam-3412	440	10	soft	soft	ADJ
ejpam-3412	440	11	ups	up	NOUN
ejpam-3412	440	12	-	-	PUNCT
ejpam-3412	440	13	subalgebra	subalgebra	NOUN
ejpam-3412	440	14	of	of	ADP
ejpam-3412	440	15	a	a	PRON
ejpam-3412	440	16	and	and	CCONJ
ejpam-3412	440	17	∅	∅	NOUN
ejpam-3412	440	18	6=	6=	ADP
ejpam-3412	440	19	e∗	e∗	PROPN
ejpam-3412	440	20	⊆	⊆	NUM
ejpam-3412	440	21	e	e	NOUN
ejpam-3412	440	22	,	,	PUNCT
ejpam-3412	440	23	then	then	ADV
ejpam-3412	440	24	(	(	PUNCT
ejpam-3412	440	25	f̃|e∗	f̃|e∗	PROPN
ejpam-3412	440	26	,	,	PUNCT
ejpam-3412	440	27	e∗	e∗	PROPN
ejpam-3412	440	28	)	)	PUNCT
ejpam-3412	440	29	is	be	AUX
ejpam-3412	440	30	a	a	DET
ejpam-3412	440	31	fuzzy	fuzzy	ADJ
ejpam-3412	440	32	soft	soft	ADJ
ejpam-3412	440	33	ups	up	NOUN
ejpam-3412	440	34	-	-	PUNCT
ejpam-3412	440	35	subalgebra	subalgebra	NOUN
ejpam-3412	440	36	of	of	ADP
ejpam-3412	440	37	a.	a.	NOUN
ejpam-3412	440	38	the	the	DET
ejpam-3412	440	39	following	follow	VERB
ejpam-3412	440	40	example	example	NOUN
ejpam-3412	440	41	shows	show	VERB
ejpam-3412	440	42	that	that	SCONJ
ejpam-3412	440	43	there	there	PRON
ejpam-3412	440	44	exists	exist	VERB
ejpam-3412	440	45	a	a	DET
ejpam-3412	440	46	nonempty	nonempty	NOUN
ejpam-3412	440	47	subset	subset	VERB
ejpam-3412	440	48	e∗	e∗	NOUN
ejpam-3412	440	49	of	of	ADP
ejpam-3412	440	50	e	e	PRON
ejpam-3412	440	51	such	such	ADJ
ejpam-3412	440	52	that	that	SCONJ
ejpam-3412	440	53	(	(	PUNCT
ejpam-3412	440	54	f̃|e∗	f̃|e∗	PROPN
ejpam-3412	440	55	,	,	PUNCT
ejpam-3412	440	56	e∗	e∗	PROPN
ejpam-3412	440	57	)	)	PUNCT
ejpam-3412	440	58	is	be	AUX
ejpam-3412	440	59	a	a	DET
ejpam-3412	440	60	fuzzy	fuzzy	ADJ
ejpam-3412	440	61	soft	soft	ADJ
ejpam-3412	440	62	ups	up	NOUN
ejpam-3412	440	63	-	-	PUNCT
ejpam-3412	440	64	subalgebra	subalgebra	NOUN
ejpam-3412	440	65	of	of	ADP
ejpam-3412	440	66	a	a	PRON
ejpam-3412	440	67	,	,	PUNCT
ejpam-3412	440	68	but	but	CCONJ
ejpam-3412	440	69	(	(	PUNCT
ejpam-3412	440	70	f̃	f̃	PROPN
ejpam-3412	440	71	,	,	PUNCT
ejpam-3412	440	72	e	e	NOUN
ejpam-3412	440	73	)	)	PUNCT
ejpam-3412	440	74	is	be	AUX
ejpam-3412	440	75	not	not	PART
ejpam-3412	440	76	a	a	DET
ejpam-3412	440	77	fuzzy	fuzzy	ADJ
ejpam-3412	440	78	soft	soft	ADJ
ejpam-3412	440	79	ups	up	NOUN
ejpam-3412	440	80	-	-	PUNCT
ejpam-3412	440	81	subalgebra	subalgebra	NOUN
ejpam-3412	440	82	of	of	ADP
ejpam-3412	440	83	a.	a.	NOUN
ejpam-3412	440	84	example	example	NOUN
ejpam-3412	440	85	13	13	NUM
ejpam-3412	440	86	.	.	PUNCT
ejpam-3412	441	1	let	let	VERB
ejpam-3412	441	2	a	a	DET
ejpam-3412	441	3	be	be	AUX
ejpam-3412	441	4	the	the	DET
ejpam-3412	441	5	set	set	NOUN
ejpam-3412	441	6	of	of	ADP
ejpam-3412	441	7	four	four	NUM
ejpam-3412	441	8	series	series	NOUN
ejpam-3412	441	9	of	of	ADP
ejpam-3412	441	10	the	the	DET
ejpam-3412	441	11	iphone	iphone	NOUN
ejpam-3412	441	12	,	,	PUNCT
ejpam-3412	441	13	that	that	ADV
ejpam-3412	441	14	is	is	ADV
ejpam-3412	441	15	,	,	PUNCT
ejpam-3412	441	16	a	a	PRON
ejpam-3412	441	17	=	=	X
ejpam-3412	441	18	{	{	PUNCT
ejpam-3412	441	19	5	5	NUM
ejpam-3412	441	20	,	,	PUNCT
ejpam-3412	441	21	6	6	NUM
ejpam-3412	441	22	,	,	PUNCT
ejpam-3412	441	23	7	7	NUM
ejpam-3412	441	24	,	,	PUNCT
ejpam-3412	441	25	x	x	NOUN
ejpam-3412	441	26	}	}	PUNCT
ejpam-3412	441	27	.	.	PUNCT
ejpam-3412	442	1	define	define	VERB
ejpam-3412	442	2	two	two	NUM
ejpam-3412	442	3	binary	binary	ADJ
ejpam-3412	442	4	operations	operation	NOUN
ejpam-3412	442	5	·	·	PUNCT
ejpam-3412	442	6	and	and	CCONJ
ejpam-3412	442	7	∗	∗	NOUN
ejpam-3412	442	8	on	on	ADP
ejpam-3412	442	9	a	a	PRON
ejpam-3412	442	10	as	as	ADP
ejpam-3412	442	11	the	the	DET
ejpam-3412	442	12	following	follow	VERB
ejpam-3412	442	13	cayley	cayley	ADJ
ejpam-3412	442	14	tables	table	NOUN
ejpam-3412	442	15	:	:	PUNCT
ejpam-3412	442	16	·	·	PUNCT
ejpam-3412	442	17	x	x	SYM
ejpam-3412	442	18	7	7	NUM
ejpam-3412	442	19	6	6	NUM
ejpam-3412	442	20	5	5	NUM
ejpam-3412	442	21	x	x	SYM
ejpam-3412	442	22	x	x	SYM
ejpam-3412	442	23	7	7	NUM
ejpam-3412	442	24	6	6	NUM
ejpam-3412	442	25	5	5	NUM
ejpam-3412	442	26	7	7	NUM
ejpam-3412	442	27	x	x	SYM
ejpam-3412	442	28	x	x	SYM
ejpam-3412	442	29	6	6	NUM
ejpam-3412	442	30	5	5	NUM
ejpam-3412	442	31	6	6	NUM
ejpam-3412	442	32	x	x	SYM
ejpam-3412	442	33	7	7	NUM
ejpam-3412	442	34	x	x	SYM
ejpam-3412	442	35	5	5	NUM
ejpam-3412	442	36	5	5	NUM
ejpam-3412	442	37	x	x	SYM
ejpam-3412	442	38	7	7	NUM
ejpam-3412	442	39	6	6	NUM
ejpam-3412	442	40	x	x	SYM
ejpam-3412	442	41	∗	∗	NOUN
ejpam-3412	442	42	x	x	NOUN
ejpam-3412	442	43	7	7	NUM
ejpam-3412	442	44	6	6	NUM
ejpam-3412	442	45	5	5	NUM
ejpam-3412	442	46	x	x	SYM
ejpam-3412	442	47	x	x	PUNCT
ejpam-3412	442	48	x	x	PUNCT
ejpam-3412	442	49	x	x	PUNCT
ejpam-3412	442	50	x	x	X
ejpam-3412	442	51	7	7	NUM
ejpam-3412	442	52	x	x	SYM
ejpam-3412	442	53	x	x	PUNCT
ejpam-3412	442	54	x	x	SYM
ejpam-3412	442	55	x	x	SYM
ejpam-3412	442	56	6	6	NUM
ejpam-3412	442	57	x	x	SYM
ejpam-3412	442	58	x	x	SYM
ejpam-3412	442	59	x	x	SYM
ejpam-3412	442	60	7	7	NUM
ejpam-3412	442	61	5	5	NUM
ejpam-3412	442	62	x	x	SYM
ejpam-3412	442	63	x	x	SYM
ejpam-3412	442	64	7	7	NUM
ejpam-3412	442	65	x	x	SYM
ejpam-3412	442	66	a.	a.	NOUN
ejpam-3412	442	67	satirad	satirad	PROPN
ejpam-3412	442	68	,	,	PUNCT
ejpam-3412	442	69	a.	a.	NOUN
ejpam-3412	442	70	iampan	iampan	PROPN
ejpam-3412	442	71	/	/	SYM
ejpam-3412	442	72	eur	eur	PROPN
ejpam-3412	442	73	.	.	PUNCT
ejpam-3412	443	1	j.	j.	PROPN
ejpam-3412	443	2	pure	pure	PROPN
ejpam-3412	443	3	appl	appl	PROPN
ejpam-3412	443	4	.	.	PROPN
ejpam-3412	443	5	math	math	PROPN
ejpam-3412	443	6	,	,	PUNCT
ejpam-3412	443	7	12	12	NUM
ejpam-3412	443	8	(	(	PUNCT
ejpam-3412	443	9	2	2	NUM
ejpam-3412	443	10	)	)	PUNCT
ejpam-3412	443	11	(	(	PUNCT
ejpam-3412	443	12	2019	2019	NUM
ejpam-3412	443	13	)	)	PUNCT
ejpam-3412	443	14	,	,	PUNCT
ejpam-3412	443	15	294	294	NUM
ejpam-3412	443	16	-	-	SYM
ejpam-3412	443	17	331	331	NUM
ejpam-3412	443	18	312	312	NUM
ejpam-3412	443	19	then	then	ADV
ejpam-3412	443	20	a	a	PRON
ejpam-3412	443	21	=	=	X
ejpam-3412	443	22	(	(	PUNCT
ejpam-3412	443	23	a	a	PRON
ejpam-3412	443	24	,	,	PUNCT
ejpam-3412	443	25	·	·	PUNCT
ejpam-3412	443	26	,	,	PUNCT
ejpam-3412	443	27	∗,x	∗,x	NUM
ejpam-3412	443	28	)	)	PUNCT
ejpam-3412	443	29	is	be	AUX
ejpam-3412	443	30	an	an	DET
ejpam-3412	443	31	f	f	PROPN
ejpam-3412	443	32	-up	-up	NOUN
ejpam-3412	443	33	-	-	PUNCT
ejpam-3412	443	34	semigroup	semigroup	NOUN
ejpam-3412	443	35	.	.	PUNCT
ejpam-3412	444	1	let	let	AUX
ejpam-3412	444	2	(	(	PUNCT
ejpam-3412	444	3	f̃	f̃	PROPN
ejpam-3412	444	4	,	,	PUNCT
ejpam-3412	444	5	e	e	NOUN
ejpam-3412	444	6	)	)	PUNCT
ejpam-3412	444	7	be	be	AUX
ejpam-3412	444	8	a	a	DET
ejpam-3412	444	9	fuzzy	fuzzy	ADJ
ejpam-3412	444	10	soft	soft	ADJ
ejpam-3412	444	11	set	set	NOUN
ejpam-3412	444	12	over	over	ADP
ejpam-3412	444	13	a	a	DET
ejpam-3412	444	14	where	where	SCONJ
ejpam-3412	444	15	e	e	NOUN
ejpam-3412	444	16	:	:	PUNCT
ejpam-3412	444	17	=	=	SYM
ejpam-3412	444	18	{	{	PUNCT
ejpam-3412	444	19	price	price	NOUN
ejpam-3412	444	20	,	,	PUNCT
ejpam-3412	444	21	beauty	beauty	NOUN
ejpam-3412	444	22	,	,	PUNCT
ejpam-3412	444	23	specifications	specification	NOUN
ejpam-3412	444	24	,	,	PUNCT
ejpam-3412	444	25	stability	stability	NOUN
ejpam-3412	444	26	}	}	PUNCT
ejpam-3412	444	27	with	with	ADP
ejpam-3412	444	28	f̃[price	f̃[price	NOUN
ejpam-3412	444	29	]	]	PUNCT
ejpam-3412	444	30	,	,	PUNCT
ejpam-3412	444	31	f̃[beauty	f̃[beauty	PROPN
ejpam-3412	444	32	]	]	PUNCT
ejpam-3412	444	33	,	,	PUNCT
ejpam-3412	444	34	f̃[specifications	f̃[specification	NOUN
ejpam-3412	444	35	]	]	PUNCT
ejpam-3412	444	36	,	,	PUNCT
ejpam-3412	444	37	and	and	CCONJ
ejpam-3412	444	38	f̃[stability	f̃[stability	NOUN
ejpam-3412	444	39	]	]	PUNCT
ejpam-3412	444	40	are	be	AUX
ejpam-3412	444	41	fuzzy	fuzzy	ADJ
ejpam-3412	444	42	sets	set	NOUN
ejpam-3412	444	43	in	in	ADP
ejpam-3412	444	44	a	a	DET
ejpam-3412	444	45	defined	define	VERB
ejpam-3412	444	46	as	as	SCONJ
ejpam-3412	444	47	follows	follow	VERB
ejpam-3412	444	48	:	:	PUNCT
ejpam-3412	444	49	f̃	f̃	PROPN
ejpam-3412	444	50	x	x	SYM
ejpam-3412	444	51	7	7	NUM
ejpam-3412	444	52	6	6	NUM
ejpam-3412	444	53	5	5	NUM
ejpam-3412	444	54	price	price	NOUN
ejpam-3412	444	55	0.8	0.8	NUM
ejpam-3412	444	56	0.3	0.3	NUM
ejpam-3412	444	57	0.7	0.7	NUM
ejpam-3412	444	58	0.1	0.1	NUM
ejpam-3412	444	59	beauty	beauty	NOUN
ejpam-3412	444	60	0.5	0.5	NUM
ejpam-3412	444	61	0.3	0.3	NUM
ejpam-3412	444	62	0.2	0.2	NUM
ejpam-3412	444	63	0.4	0.4	NUM
ejpam-3412	444	64	specifications	specification	NOUN
ejpam-3412	444	65	0.9	0.9	NUM
ejpam-3412	444	66	0.8	0.8	NUM
ejpam-3412	444	67	0.5	0.5	NUM
ejpam-3412	444	68	0.6	0.6	NUM
ejpam-3412	444	69	stability	stability	NOUN
ejpam-3412	444	70	1	1	NUM
ejpam-3412	444	71	0.4	0.4	NUM
ejpam-3412	444	72	0.7	0.7	NUM
ejpam-3412	444	73	0.6	0.6	NUM
ejpam-3412	444	74	then	then	ADV
ejpam-3412	444	75	f̃[stability	f̃[stability	NOUN
ejpam-3412	444	76	]	]	PUNCT
ejpam-3412	444	77	is	be	AUX
ejpam-3412	444	78	not	not	PART
ejpam-3412	444	79	a	a	DET
ejpam-3412	444	80	fuzzy	fuzzy	ADJ
ejpam-3412	444	81	ups	up	NOUN
ejpam-3412	444	82	-	-	PUNCT
ejpam-3412	444	83	subalgebra	subalgebra	NOUN
ejpam-3412	444	84	of	of	ADP
ejpam-3412	444	85	a.	a.	NOUN
ejpam-3412	444	86	indeed	indeed	ADV
ejpam-3412	444	87	,	,	PUNCT
ejpam-3412	444	88	f	f	PROPN
ejpam-3412	444	89	f̃[stability	f̃[stability	NOUN
ejpam-3412	444	90	]	]	X
ejpam-3412	444	91	(	(	PUNCT
ejpam-3412	444	92	5	5	NUM
ejpam-3412	444	93	∗	∗	NOUN
ejpam-3412	444	94	6	6	NUM
ejpam-3412	444	95	)	)	PUNCT
ejpam-3412	444	96	=	=	SYM
ejpam-3412	444	97	f	f	X
ejpam-3412	444	98	f̃[stability	f̃[stability	NOUN
ejpam-3412	444	99	]	]	X
ejpam-3412	444	100	(	(	PUNCT
ejpam-3412	444	101	7	7	X
ejpam-3412	444	102	)	)	PUNCT
ejpam-3412	444	103	=	=	SYM
ejpam-3412	444	104	0.4	0.4	NUM
ejpam-3412	444	105	�	�	PROPN
ejpam-3412	444	106	0.6	0.6	NUM
ejpam-3412	444	107	=	=	SYM
ejpam-3412	444	108	min{0.6	min{0.6	PROPN
ejpam-3412	444	109	,	,	PUNCT
ejpam-3412	444	110	0.7	0.7	NUM
ejpam-3412	444	111	}	}	PUNCT
ejpam-3412	444	112	=	=	SYM
ejpam-3412	444	113	min{f	min{f	ADJ
ejpam-3412	444	114	f̃[stability	f̃[stability	NOUN
ejpam-3412	444	115	]	]	X
ejpam-3412	444	116	(	(	PUNCT
ejpam-3412	444	117	5	5	NUM
ejpam-3412	444	118	)	)	PUNCT
ejpam-3412	444	119	,	,	PUNCT
ejpam-3412	444	120	f	f	PROPN
ejpam-3412	444	121	f̃[stability	f̃[stability	NOUN
ejpam-3412	444	122	]	]	X
ejpam-3412	444	123	(	(	PUNCT
ejpam-3412	444	124	6	6	NUM
ejpam-3412	444	125	)	)	PUNCT
ejpam-3412	444	126	}	}	PUNCT
ejpam-3412	444	127	.	.	PUNCT
ejpam-3412	445	1	hence	hence	ADV
ejpam-3412	445	2	,	,	PUNCT
ejpam-3412	445	3	(	(	PUNCT
ejpam-3412	445	4	f̃	f̃	PROPN
ejpam-3412	445	5	,	,	PUNCT
ejpam-3412	445	6	e	e	NOUN
ejpam-3412	445	7	)	)	PUNCT
ejpam-3412	445	8	is	be	AUX
ejpam-3412	445	9	not	not	PART
ejpam-3412	445	10	a	a	DET
ejpam-3412	445	11	fuzzy	fuzzy	ADJ
ejpam-3412	445	12	soft	soft	ADJ
ejpam-3412	445	13	ups	up	NOUN
ejpam-3412	445	14	-	-	PUNCT
ejpam-3412	445	15	subalgebra	subalgebra	NOUN
ejpam-3412	445	16	of	of	ADP
ejpam-3412	445	17	a.	a.	NOUN
ejpam-3412	445	18	we	we	PRON
ejpam-3412	445	19	take	take	VERB
ejpam-3412	445	20	e∗	e∗	NOUN
ejpam-3412	445	21	:	:	PUNCT
ejpam-3412	445	22	=	=	SYM
ejpam-3412	445	23	{	{	PUNCT
ejpam-3412	445	24	price	price	NOUN
ejpam-3412	445	25	,	,	PUNCT
ejpam-3412	445	26	beauty	beauty	NOUN
ejpam-3412	445	27	,	,	PUNCT
ejpam-3412	445	28	specifications	specification	NOUN
ejpam-3412	445	29	}	}	PUNCT
ejpam-3412	445	30	.	.	PUNCT
ejpam-3412	446	1	thus	thus	ADV
ejpam-3412	446	2	(	(	PUNCT
ejpam-3412	446	3	f̃|e∗	f̃|e∗	PROPN
ejpam-3412	446	4	,	,	PUNCT
ejpam-3412	446	5	e∗	e∗	PROPN
ejpam-3412	446	6	)	)	PUNCT
ejpam-3412	446	7	is	be	AUX
ejpam-3412	446	8	a	a	DET
ejpam-3412	446	9	fuzzy	fuzzy	ADJ
ejpam-3412	446	10	soft	soft	ADJ
ejpam-3412	446	11	ups	up	NOUN
ejpam-3412	446	12	-	-	PUNCT
ejpam-3412	446	13	subalgebra	subalgebra	NOUN
ejpam-3412	446	14	of	of	ADP
ejpam-3412	446	15	a.	a.	NOUN
ejpam-3412	446	16	theorem	theorem	NOUN
ejpam-3412	446	17	22	22	NUM
ejpam-3412	446	18	.	.	PUNCT
ejpam-3412	447	1	the	the	DET
ejpam-3412	447	2	extended	extended	ADJ
ejpam-3412	447	3	intersection	intersection	NOUN
ejpam-3412	447	4	of	of	ADP
ejpam-3412	447	5	two	two	NUM
ejpam-3412	447	6	fuzzy	fuzzy	ADJ
ejpam-3412	447	7	soft	soft	ADJ
ejpam-3412	447	8	ups	up	NOUN
ejpam-3412	447	9	-	-	PUNCT
ejpam-3412	447	10	subalgebras	subalgebras	PROPN
ejpam-3412	447	11	of	of	ADP
ejpam-3412	447	12	a	a	PRON
ejpam-3412	447	13	is	be	AUX
ejpam-3412	447	14	also	also	ADV
ejpam-3412	447	15	a	a	DET
ejpam-3412	447	16	fuzzy	fuzzy	ADJ
ejpam-3412	447	17	soft	soft	ADJ
ejpam-3412	447	18	ups	up	NOUN
ejpam-3412	447	19	-	-	PUNCT
ejpam-3412	447	20	subalgebra	subalgebra	NOUN
ejpam-3412	447	21	.	.	PUNCT
ejpam-3412	448	1	moreover	moreover	ADV
ejpam-3412	448	2	,	,	PUNCT
ejpam-3412	448	3	the	the	DET
ejpam-3412	448	4	intersection	intersection	NOUN
ejpam-3412	448	5	of	of	ADP
ejpam-3412	448	6	two	two	NUM
ejpam-3412	448	7	fuzzy	fuzzy	ADJ
ejpam-3412	448	8	soft	soft	ADJ
ejpam-3412	448	9	ups	up	NOUN
ejpam-3412	448	10	-	-	PUNCT
ejpam-3412	448	11	subalgebras	subalgebras	PROPN
ejpam-3412	448	12	of	of	ADP
ejpam-3412	448	13	a	a	PRON
ejpam-3412	448	14	is	be	AUX
ejpam-3412	448	15	also	also	ADV
ejpam-3412	448	16	a	a	DET
ejpam-3412	448	17	fuzzy	fuzzy	ADJ
ejpam-3412	448	18	soft	soft	ADJ
ejpam-3412	448	19	ups	up	NOUN
ejpam-3412	448	20	-	-	PUNCT
ejpam-3412	448	21	subalgebra	subalgebra	NOUN
ejpam-3412	448	22	.	.	PUNCT
ejpam-3412	449	1	proof	proof	NOUN
ejpam-3412	449	2	.	.	PUNCT
ejpam-3412	450	1	let	let	AUX
ejpam-3412	450	2	(	(	PUNCT
ejpam-3412	450	3	f̃	f̃	PROPN
ejpam-3412	450	4	,	,	PUNCT
ejpam-3412	450	5	e1	e1	PROPN
ejpam-3412	450	6	)	)	PUNCT
ejpam-3412	450	7	and	and	CCONJ
ejpam-3412	450	8	(	(	PUNCT
ejpam-3412	450	9	g̃	g̃	PROPN
ejpam-3412	450	10	,	,	PUNCT
ejpam-3412	450	11	e2	e2	PROPN
ejpam-3412	450	12	)	)	PUNCT
ejpam-3412	450	13	be	be	VERB
ejpam-3412	450	14	two	two	NUM
ejpam-3412	450	15	fuzzy	fuzzy	ADJ
ejpam-3412	450	16	soft	soft	ADJ
ejpam-3412	450	17	ups	up	NOUN
ejpam-3412	450	18	-	-	PUNCT
ejpam-3412	450	19	subalgebras	subalgebras	PROPN
ejpam-3412	450	20	of	of	ADP
ejpam-3412	450	21	a.	a.	NOUN
ejpam-3412	450	22	assume	assume	VERB
ejpam-3412	450	23	that	that	SCONJ
ejpam-3412	450	24	(	(	PUNCT
ejpam-3412	450	25	f̃	f̃	PROPN
ejpam-3412	450	26	,	,	PUNCT
ejpam-3412	450	27	e1	e1	NOUN
ejpam-3412	450	28	)	)	PUNCT
ejpam-3412	450	29	∩	∩	NOUN
ejpam-3412	450	30	(	(	PUNCT
ejpam-3412	450	31	g̃	g̃	PROPN
ejpam-3412	450	32	,	,	PUNCT
ejpam-3412	450	33	e2	e2	PROPN
ejpam-3412	450	34	)	)	PUNCT
ejpam-3412	450	35	=	=	SYM
ejpam-3412	450	36	(	(	PUNCT
ejpam-3412	450	37	h̃	h̃	PROPN
ejpam-3412	450	38	,	,	PUNCT
ejpam-3412	450	39	e	e	NOUN
ejpam-3412	450	40	)	)	PUNCT
ejpam-3412	450	41	with	with	ADP
ejpam-3412	450	42	e	e	NOUN
ejpam-3412	450	43	=	=	NOUN
ejpam-3412	450	44	e1	e1	PROPN
ejpam-3412	450	45	∪	∪	PROPN
ejpam-3412	450	46	e2	e2	PROPN
ejpam-3412	450	47	.	.	PUNCT
ejpam-3412	451	1	let	let	VERB
ejpam-3412	451	2	e	e	PRON
ejpam-3412	451	3	∈	∈	PROPN
ejpam-3412	451	4	e.	e.	PROPN
ejpam-3412	451	5	case	case	NOUN
ejpam-3412	451	6	1	1	NUM
ejpam-3412	451	7	:	:	PUNCT
ejpam-3412	451	8	e	e	PROPN
ejpam-3412	451	9	∈	∈	PROPN
ejpam-3412	451	10	e1	e1	PROPN
ejpam-3412	451	11	\	\	PROPN
ejpam-3412	451	12	e2	e2	PROPN
ejpam-3412	451	13	(	(	PUNCT
ejpam-3412	451	14	resp	resp	NOUN
ejpam-3412	451	15	.	.	PUNCT
ejpam-3412	451	16	,	,	PUNCT
ejpam-3412	451	17	e	e	PROPN
ejpam-3412	451	18	∈	∈	PROPN
ejpam-3412	451	19	e2	e2	PROPN
ejpam-3412	451	20	\	\	PROPN
ejpam-3412	451	21	e1	e1	PROPN
ejpam-3412	451	22	)	)	PUNCT
ejpam-3412	451	23	.	.	PUNCT
ejpam-3412	452	1	then	then	ADV
ejpam-3412	452	2	h̃[e	h̃[e	X
ejpam-3412	452	3	]	]	X
ejpam-3412	452	4	=	=	PUNCT
ejpam-3412	452	5	f̃[e	f̃[e	NOUN
ejpam-3412	452	6	]	]	X
ejpam-3412	452	7	(	(	PUNCT
ejpam-3412	452	8	resp	resp	NOUN
ejpam-3412	452	9	.	.	PUNCT
ejpam-3412	452	10	,	,	PUNCT
ejpam-3412	452	11	h̃[e	h̃[e	PROPN
ejpam-3412	452	12	]	]	X
ejpam-3412	452	13	=	=	SYM
ejpam-3412	452	14	g̃[e	g̃[e	NOUN
ejpam-3412	452	15	]	]	PUNCT
ejpam-3412	452	16	)	)	PUNCT
ejpam-3412	452	17	is	be	AUX
ejpam-3412	452	18	a	a	DET
ejpam-3412	452	19	fuzzy	fuzzy	ADJ
ejpam-3412	452	20	soft	soft	ADJ
ejpam-3412	452	21	ups	up	NOUN
ejpam-3412	452	22	-	-	PUNCT
ejpam-3412	452	23	subalgebra	subalgebra	NOUN
ejpam-3412	452	24	of	of	ADP
ejpam-3412	452	25	a.	a.	NOUN
ejpam-3412	452	26	case	case	NOUN
ejpam-3412	452	27	2	2	NUM
ejpam-3412	452	28	:	:	PUNCT
ejpam-3412	452	29	e	e	PROPN
ejpam-3412	452	30	∈	∈	PROPN
ejpam-3412	452	31	e1	e1	PROPN
ejpam-3412	452	32	∩	∩	ADJ
ejpam-3412	452	33	e2	e2	PROPN
ejpam-3412	452	34	.	.	PUNCT
ejpam-3412	453	1	by	by	ADP
ejpam-3412	453	2	theorem	theorem	NOUN
ejpam-3412	453	3	5	5	NUM
ejpam-3412	453	4	,	,	PUNCT
ejpam-3412	453	5	we	we	PRON
ejpam-3412	453	6	have	have	VERB
ejpam-3412	453	7	h̃[e	h̃[e	NOUN
ejpam-3412	453	8	]	]	X
ejpam-3412	454	1	=	=	SYM
ejpam-3412	454	2	f̃[e	f̃[e	PROPN
ejpam-3412	454	3	]	]	X
ejpam-3412	454	4	∩	∩	ADJ
ejpam-3412	454	5	g̃[e	g̃[e	PROPN
ejpam-3412	454	6	]	]	X
ejpam-3412	454	7	is	be	AUX
ejpam-3412	454	8	a	a	DET
ejpam-3412	454	9	fuzzy	fuzzy	ADJ
ejpam-3412	454	10	soft	soft	ADJ
ejpam-3412	454	11	ups	up	NOUN
ejpam-3412	454	12	-	-	PUNCT
ejpam-3412	454	13	subalgebra	subalgebra	NOUN
ejpam-3412	454	14	.	.	PUNCT
ejpam-3412	455	1	thus	thus	ADV
ejpam-3412	455	2	(	(	PUNCT
ejpam-3412	455	3	h̃	h̃	PROPN
ejpam-3412	455	4	,	,	PUNCT
ejpam-3412	455	5	e	e	NOUN
ejpam-3412	455	6	)	)	PUNCT
ejpam-3412	455	7	is	be	AUX
ejpam-3412	455	8	an	an	DET
ejpam-3412	455	9	e	e	ADJ
ejpam-3412	455	10	-	-	ADJ
ejpam-3412	455	11	fuzzy	fuzzy	ADJ
ejpam-3412	455	12	soft	soft	ADJ
ejpam-3412	455	13	ups	up	NOUN
ejpam-3412	455	14	-	-	PUNCT
ejpam-3412	455	15	subalgebra	subalgebra	NOUN
ejpam-3412	455	16	of	of	ADP
ejpam-3412	455	17	a	a	PRON
ejpam-3412	455	18	for	for	ADP
ejpam-3412	455	19	all	all	DET
ejpam-3412	455	20	e	e	PROPN
ejpam-3412	455	21	∈	∈	PROPN
ejpam-3412	455	22	e.	e.	PROPN
ejpam-3412	455	23	hence	hence	PROPN
ejpam-3412	455	24	,	,	PUNCT
ejpam-3412	455	25	(	(	PUNCT
ejpam-3412	455	26	h̃	h̃	PROPN
ejpam-3412	455	27	,	,	PUNCT
ejpam-3412	455	28	e	e	NOUN
ejpam-3412	455	29	)	)	PUNCT
ejpam-3412	455	30	is	be	AUX
ejpam-3412	455	31	a	a	DET
ejpam-3412	455	32	fuzzy	fuzzy	ADJ
ejpam-3412	455	33	soft	soft	ADJ
ejpam-3412	455	34	ups	up	NOUN
ejpam-3412	455	35	-	-	PUNCT
ejpam-3412	455	36	subalgebra	subalgebra	NOUN
ejpam-3412	455	37	of	of	ADP
ejpam-3412	455	38	a.	a.	NOUN
ejpam-3412	455	39	theorem	theorem	NOUN
ejpam-3412	455	40	23	23	NUM
ejpam-3412	455	41	.	.	PUNCT
ejpam-3412	456	1	the	the	DET
ejpam-3412	456	2	union	union	NOUN
ejpam-3412	456	3	of	of	ADP
ejpam-3412	456	4	two	two	NUM
ejpam-3412	456	5	fuzzy	fuzzy	ADJ
ejpam-3412	456	6	soft	soft	ADJ
ejpam-3412	456	7	ups	up	NOUN
ejpam-3412	456	8	-	-	PUNCT
ejpam-3412	456	9	subalgebras	subalgebras	PROPN
ejpam-3412	456	10	of	of	ADP
ejpam-3412	456	11	a	a	PRON
ejpam-3412	456	12	is	be	AUX
ejpam-3412	456	13	also	also	ADV
ejpam-3412	456	14	a	a	DET
ejpam-3412	456	15	fuzzy	fuzzy	ADJ
ejpam-3412	456	16	soft	soft	ADJ
ejpam-3412	456	17	upssubalgebra	upssubalgebra	NOUN
ejpam-3412	456	18	if	if	SCONJ
ejpam-3412	456	19	sets	set	NOUN
ejpam-3412	456	20	of	of	ADP
ejpam-3412	456	21	statistics	statistic	NOUN
ejpam-3412	456	22	of	of	ADP
ejpam-3412	456	23	two	two	NUM
ejpam-3412	456	24	fuzzy	fuzzy	ADJ
ejpam-3412	456	25	soft	soft	ADJ
ejpam-3412	456	26	ups	up	NOUN
ejpam-3412	456	27	-	-	PUNCT
ejpam-3412	456	28	subalgebras	subalgebra	NOUN
ejpam-3412	456	29	are	be	AUX
ejpam-3412	456	30	disjoint	disjoint	ADJ
ejpam-3412	456	31	.	.	PUNCT
ejpam-3412	457	1	proof	proof	NOUN
ejpam-3412	457	2	.	.	PUNCT
ejpam-3412	458	1	let	let	AUX
ejpam-3412	458	2	(	(	PUNCT
ejpam-3412	458	3	f̃	f̃	PROPN
ejpam-3412	458	4	,	,	PUNCT
ejpam-3412	458	5	e1	e1	PROPN
ejpam-3412	458	6	)	)	PUNCT
ejpam-3412	458	7	and	and	CCONJ
ejpam-3412	458	8	(	(	PUNCT
ejpam-3412	458	9	g̃	g̃	PROPN
ejpam-3412	458	10	,	,	PUNCT
ejpam-3412	458	11	e2	e2	PROPN
ejpam-3412	458	12	)	)	PUNCT
ejpam-3412	458	13	be	be	VERB
ejpam-3412	458	14	two	two	NUM
ejpam-3412	458	15	fuzzy	fuzzy	ADJ
ejpam-3412	458	16	soft	soft	ADJ
ejpam-3412	458	17	ups	up	NOUN
ejpam-3412	458	18	-	-	PUNCT
ejpam-3412	458	19	subalgebras	subalgebras	PROPN
ejpam-3412	458	20	of	of	ADP
ejpam-3412	458	21	a	a	DET
ejpam-3412	458	22	such	such	ADJ
ejpam-3412	458	23	that	that	DET
ejpam-3412	458	24	e1	e1	NOUN
ejpam-3412	458	25	∩e2	∩e2	NOUN
ejpam-3412	459	1	=	=	PRON
ejpam-3412	459	2	∅.	∅.	AUX
ejpam-3412	459	3	assume	assume	VERB
ejpam-3412	459	4	that	that	SCONJ
ejpam-3412	459	5	(	(	PUNCT
ejpam-3412	459	6	f̃	f̃	PROPN
ejpam-3412	459	7	,	,	PUNCT
ejpam-3412	459	8	e1)∪	e1)∪	NOUN
ejpam-3412	459	9	(	(	PUNCT
ejpam-3412	459	10	g̃	g̃	PROPN
ejpam-3412	459	11	,	,	PUNCT
ejpam-3412	459	12	e2	e2	PROPN
ejpam-3412	459	13	)	)	PUNCT
ejpam-3412	459	14	=	=	SYM
ejpam-3412	459	15	(	(	PUNCT
ejpam-3412	459	16	h̃	h̃	PROPN
ejpam-3412	459	17	,	,	PUNCT
ejpam-3412	459	18	e	e	NOUN
ejpam-3412	459	19	)	)	PUNCT
ejpam-3412	459	20	with	with	ADP
ejpam-3412	459	21	e	e	NOUN
ejpam-3412	459	22	=	=	NOUN
ejpam-3412	459	23	e1	e1	VERB
ejpam-3412	459	24	∪e2	∪e2	NOUN
ejpam-3412	459	25	.	.	PUNCT
ejpam-3412	460	1	let	let	VERB
ejpam-3412	460	2	e	e	PROPN
ejpam-3412	460	3	∈	∈	PROPN
ejpam-3412	460	4	e.	e.	PROPN
ejpam-3412	460	5	since	since	SCONJ
ejpam-3412	460	6	e1	e1	PROPN
ejpam-3412	460	7	∩	∩	ADJ
ejpam-3412	460	8	e2	e2	NOUN
ejpam-3412	460	9	=	=	VERB
ejpam-3412	460	10	∅	∅	NOUN
ejpam-3412	460	11	,	,	PUNCT
ejpam-3412	460	12	we	we	PRON
ejpam-3412	460	13	have	have	VERB
ejpam-3412	460	14	e	e	PROPN
ejpam-3412	460	15	∈	∈	PROPN
ejpam-3412	460	16	e1	e1	PROPN
ejpam-3412	460	17	\	\	PROPN
ejpam-3412	460	18	e2	e2	PROPN
ejpam-3412	460	19	or	or	CCONJ
ejpam-3412	460	20	e	e	NOUN
ejpam-3412	460	21	∈	∈	PROPN
ejpam-3412	460	22	e2	e2	PROPN
ejpam-3412	460	23	\	\	PROPN
ejpam-3412	460	24	e1	e1	PROPN
ejpam-3412	460	25	.	.	PUNCT
ejpam-3412	460	26	case	case	NOUN
ejpam-3412	460	27	1	1	NUM
ejpam-3412	460	28	:	:	PUNCT
ejpam-3412	460	29	e	e	PROPN
ejpam-3412	460	30	∈	∈	PROPN
ejpam-3412	460	31	e1	e1	PROPN
ejpam-3412	460	32	\	\	PROPN
ejpam-3412	460	33	e2	e2	PROPN
ejpam-3412	460	34	.	.	PUNCT
ejpam-3412	461	1	then	then	ADV
ejpam-3412	461	2	h̃[e	h̃[e	X
ejpam-3412	461	3	]	]	X
ejpam-3412	461	4	=	=	PUNCT
ejpam-3412	461	5	f̃[e	f̃[e	PROPN
ejpam-3412	461	6	]	]	X
ejpam-3412	461	7	is	be	AUX
ejpam-3412	461	8	a	a	DET
ejpam-3412	461	9	fuzzy	fuzzy	ADJ
ejpam-3412	461	10	soft	soft	ADJ
ejpam-3412	461	11	ups	up	NOUN
ejpam-3412	461	12	-	-	PUNCT
ejpam-3412	461	13	subalgebra	subalgebra	NOUN
ejpam-3412	461	14	of	of	ADP
ejpam-3412	461	15	a.	a.	NOUN
ejpam-3412	461	16	case	case	NOUN
ejpam-3412	461	17	2	2	NUM
ejpam-3412	461	18	:	:	PUNCT
ejpam-3412	461	19	e	e	PROPN
ejpam-3412	461	20	∈	∈	PROPN
ejpam-3412	461	21	e2	e2	PROPN
ejpam-3412	461	22	\	\	PROPN
ejpam-3412	461	23	e1	e1	PROPN
ejpam-3412	461	24	.	.	PUNCT
ejpam-3412	462	1	then	then	ADV
ejpam-3412	462	2	h̃[e	h̃[e	X
ejpam-3412	462	3	]	]	X
ejpam-3412	462	4	=	=	SYM
ejpam-3412	462	5	g̃[e	g̃[e	X
ejpam-3412	462	6	]	]	X
ejpam-3412	462	7	is	be	AUX
ejpam-3412	462	8	a	a	DET
ejpam-3412	462	9	fuzzy	fuzzy	ADJ
ejpam-3412	462	10	soft	soft	ADJ
ejpam-3412	462	11	ups	up	NOUN
ejpam-3412	462	12	-	-	PUNCT
ejpam-3412	462	13	subalgebra	subalgebra	NOUN
ejpam-3412	462	14	of	of	ADP
ejpam-3412	462	15	a.	a.	NOUN
ejpam-3412	462	16	thus	thus	ADV
ejpam-3412	462	17	(	(	PUNCT
ejpam-3412	462	18	h̃	h̃	PROPN
ejpam-3412	462	19	,	,	PUNCT
ejpam-3412	462	20	e	e	NOUN
ejpam-3412	462	21	)	)	PUNCT
ejpam-3412	462	22	is	be	AUX
ejpam-3412	462	23	an	an	DET
ejpam-3412	462	24	e	e	ADJ
ejpam-3412	462	25	-	-	ADJ
ejpam-3412	462	26	fuzzy	fuzzy	ADJ
ejpam-3412	462	27	soft	soft	ADJ
ejpam-3412	462	28	ups	up	NOUN
ejpam-3412	462	29	-	-	PUNCT
ejpam-3412	462	30	subalgebra	subalgebra	NOUN
ejpam-3412	462	31	of	of	ADP
ejpam-3412	462	32	a	a	PRON
ejpam-3412	462	33	for	for	ADP
ejpam-3412	462	34	all	all	DET
ejpam-3412	462	35	e	e	PROPN
ejpam-3412	462	36	∈	∈	PROPN
ejpam-3412	462	37	e.	e.	PROPN
ejpam-3412	462	38	hence	hence	PROPN
ejpam-3412	462	39	,	,	PUNCT
ejpam-3412	462	40	(	(	PUNCT
ejpam-3412	462	41	h̃	h̃	PROPN
ejpam-3412	462	42	,	,	PUNCT
ejpam-3412	462	43	e	e	NOUN
ejpam-3412	462	44	)	)	PUNCT
ejpam-3412	462	45	is	be	AUX
ejpam-3412	462	46	a	a	DET
ejpam-3412	462	47	fuzzy	fuzzy	ADJ
ejpam-3412	462	48	soft	soft	ADJ
ejpam-3412	462	49	ups	up	NOUN
ejpam-3412	462	50	-	-	PUNCT
ejpam-3412	462	51	subalgebra	subalgebra	NOUN
ejpam-3412	462	52	of	of	ADP
ejpam-3412	462	53	a.	a.	NOUN
ejpam-3412	462	54	the	the	DET
ejpam-3412	462	55	following	follow	VERB
ejpam-3412	462	56	example	example	NOUN
ejpam-3412	462	57	shows	show	VERB
ejpam-3412	462	58	that	that	SCONJ
ejpam-3412	462	59	theorem	theorem	VERB
ejpam-3412	462	60	23	23	NUM
ejpam-3412	462	61	is	be	AUX
ejpam-3412	462	62	not	not	PART
ejpam-3412	462	63	valid	valid	ADJ
ejpam-3412	462	64	if	if	SCONJ
ejpam-3412	462	65	sets	set	NOUN
ejpam-3412	462	66	of	of	ADP
ejpam-3412	462	67	statistics	statistic	NOUN
ejpam-3412	462	68	of	of	ADP
ejpam-3412	462	69	two	two	NUM
ejpam-3412	462	70	fuzzy	fuzzy	ADJ
ejpam-3412	462	71	soft	soft	ADJ
ejpam-3412	462	72	ups	up	NOUN
ejpam-3412	462	73	-	-	PUNCT
ejpam-3412	462	74	subalgebras	subalgebra	NOUN
ejpam-3412	462	75	are	be	AUX
ejpam-3412	462	76	not	not	PART
ejpam-3412	462	77	disjoint	disjoint	ADJ
ejpam-3412	462	78	.	.	PUNCT
ejpam-3412	463	1	a.	a.	PROPN
ejpam-3412	463	2	satirad	satirad	PROPN
ejpam-3412	463	3	,	,	PUNCT
ejpam-3412	463	4	a.	a.	NOUN
ejpam-3412	463	5	iampan	iampan	PROPN
ejpam-3412	463	6	/	/	SYM
ejpam-3412	463	7	eur	eur	PROPN
ejpam-3412	463	8	.	.	PUNCT
ejpam-3412	464	1	j.	j.	PROPN
ejpam-3412	464	2	pure	pure	PROPN
ejpam-3412	464	3	appl	appl	PROPN
ejpam-3412	464	4	.	.	PROPN
ejpam-3412	464	5	math	math	PROPN
ejpam-3412	464	6	,	,	PUNCT
ejpam-3412	464	7	12	12	NUM
ejpam-3412	464	8	(	(	PUNCT
ejpam-3412	464	9	2	2	NUM
ejpam-3412	464	10	)	)	PUNCT
ejpam-3412	464	11	(	(	PUNCT
ejpam-3412	464	12	2019	2019	NUM
ejpam-3412	464	13	)	)	PUNCT
ejpam-3412	464	14	,	,	PUNCT
ejpam-3412	464	15	294	294	NUM
ejpam-3412	464	16	-	-	SYM
ejpam-3412	464	17	331	331	NUM
ejpam-3412	464	18	313	313	NUM
ejpam-3412	464	19	example	example	NOUN
ejpam-3412	464	20	14	14	NUM
ejpam-3412	464	21	.	.	PUNCT
ejpam-3412	465	1	by	by	ADP
ejpam-3412	465	2	cayley	cayley	ADJ
ejpam-3412	465	3	tables	table	NOUN
ejpam-3412	465	4	in	in	ADP
ejpam-3412	465	5	example	example	NOUN
ejpam-3412	465	6	13	13	NUM
ejpam-3412	465	7	,	,	PUNCT
ejpam-3412	465	8	we	we	PRON
ejpam-3412	465	9	know	know	VERB
ejpam-3412	465	10	that	that	SCONJ
ejpam-3412	465	11	a	a	PRON
ejpam-3412	465	12	=	=	X
ejpam-3412	465	13	(	(	PUNCT
ejpam-3412	465	14	a	a	PRON
ejpam-3412	465	15	,	,	PUNCT
ejpam-3412	465	16	·	·	PUNCT
ejpam-3412	465	17	,	,	PUNCT
ejpam-3412	465	18	∗,x	∗,x	NUM
ejpam-3412	465	19	)	)	PUNCT
ejpam-3412	465	20	is	be	AUX
ejpam-3412	465	21	an	an	DET
ejpam-3412	465	22	f	f	PROPN
ejpam-3412	465	23	-upsemigroup	-upsemigroup	PROPN
ejpam-3412	465	24	.	.	PUNCT
ejpam-3412	466	1	let	let	AUX
ejpam-3412	466	2	(	(	PUNCT
ejpam-3412	466	3	g̃1	g̃1	NOUN
ejpam-3412	466	4	,	,	PUNCT
ejpam-3412	466	5	e1	e1	PROPN
ejpam-3412	466	6	)	)	PUNCT
ejpam-3412	466	7	and	and	CCONJ
ejpam-3412	466	8	(	(	PUNCT
ejpam-3412	466	9	g̃2	g̃2	PROPN
ejpam-3412	466	10	,	,	PUNCT
ejpam-3412	466	11	e2	e2	PROPN
ejpam-3412	466	12	)	)	PUNCT
ejpam-3412	466	13	be	be	VERB
ejpam-3412	466	14	two	two	NUM
ejpam-3412	466	15	fuzzy	fuzzy	ADJ
ejpam-3412	466	16	soft	soft	ADJ
ejpam-3412	466	17	sets	set	NOUN
ejpam-3412	466	18	over	over	ADP
ejpam-3412	466	19	a	a	DET
ejpam-3412	466	20	where	where	SCONJ
ejpam-3412	466	21	e1	e1	NOUN
ejpam-3412	466	22	:	:	PUNCT
ejpam-3412	466	23	=	=	NUM
ejpam-3412	466	24	{	{	PUNCT
ejpam-3412	466	25	price	price	NOUN
ejpam-3412	466	26	,	,	PUNCT
ejpam-3412	466	27	beauty	beauty	NOUN
ejpam-3412	466	28	,	,	PUNCT
ejpam-3412	466	29	specifications	specification	NOUN
ejpam-3412	466	30	}	}	PUNCT
ejpam-3412	466	31	and	and	CCONJ
ejpam-3412	466	32	e2	e2	PROPN
ejpam-3412	466	33	:	:	PUNCT
ejpam-3412	466	34	=	=	SYM
ejpam-3412	466	35	{	{	PUNCT
ejpam-3412	466	36	price	price	NOUN
ejpam-3412	466	37	,	,	PUNCT
ejpam-3412	466	38	stability	stability	NOUN
ejpam-3412	466	39	}	}	PUNCT
ejpam-3412	466	40	with	with	ADP
ejpam-3412	466	41	g̃1[price	g̃1[price	PROPN
ejpam-3412	466	42	]	]	PUNCT
ejpam-3412	466	43	,	,	PUNCT
ejpam-3412	466	44	g̃1[beauty	g̃1[beauty	PROPN
ejpam-3412	466	45	]	]	X
ejpam-3412	466	46	,	,	PUNCT
ejpam-3412	466	47	g̃1[specifications	g̃1[specification	NOUN
ejpam-3412	466	48	]	]	PUNCT
ejpam-3412	466	49	,	,	PUNCT
ejpam-3412	466	50	g̃2[price	g̃2[price	PROPN
ejpam-3412	466	51	]	]	X
ejpam-3412	466	52	,	,	PUNCT
ejpam-3412	466	53	and	and	CCONJ
ejpam-3412	466	54	g̃2[stability	g̃2[stability	PROPN
ejpam-3412	466	55	]	]	PUNCT
ejpam-3412	466	56	are	be	AUX
ejpam-3412	466	57	fuzzy	fuzzy	ADJ
ejpam-3412	466	58	sets	set	NOUN
ejpam-3412	466	59	in	in	ADP
ejpam-3412	466	60	a	a	DET
ejpam-3412	466	61	defined	define	VERB
ejpam-3412	466	62	as	as	SCONJ
ejpam-3412	466	63	follows	follow	VERB
ejpam-3412	466	64	:	:	PUNCT
ejpam-3412	467	1	g̃1	g̃1	NOUN
ejpam-3412	467	2	x	x	SYM
ejpam-3412	467	3	7	7	NUM
ejpam-3412	467	4	6	6	NUM
ejpam-3412	467	5	5	5	NUM
ejpam-3412	467	6	price	price	NOUN
ejpam-3412	467	7	0.9	0.9	NUM
ejpam-3412	467	8	0.7	0.7	NUM
ejpam-3412	467	9	0.9	0.9	NUM
ejpam-3412	467	10	0.2	0.2	NUM
ejpam-3412	467	11	beauty	beauty	NOUN
ejpam-3412	467	12	1	1	NUM
ejpam-3412	467	13	0.8	0.8	NUM
ejpam-3412	467	14	0.3	0.3	NUM
ejpam-3412	467	15	0.2	0.2	NUM
ejpam-3412	467	16	specifications	specification	NOUN
ejpam-3412	467	17	0.6	0.6	NUM
ejpam-3412	467	18	0.5	0.5	NUM
ejpam-3412	467	19	0.3	0.3	NUM
ejpam-3412	467	20	0.4	0.4	NUM
ejpam-3412	467	21	g̃2	g̃2	NOUN
ejpam-3412	467	22	x	x	SYM
ejpam-3412	467	23	7	7	NUM
ejpam-3412	467	24	6	6	NUM
ejpam-3412	467	25	5	5	NUM
ejpam-3412	467	26	price	price	NOUN
ejpam-3412	467	27	0.9	0.9	NUM
ejpam-3412	467	28	0.3	0.3	NUM
ejpam-3412	467	29	0.2	0.2	NUM
ejpam-3412	467	30	0.8	0.8	NUM
ejpam-3412	467	31	stability	stability	NOUN
ejpam-3412	467	32	0.7	0.7	NUM
ejpam-3412	467	33	0.2	0.2	NUM
ejpam-3412	467	34	0.5	0.5	NUM
ejpam-3412	467	35	0.2	0.2	NUM
ejpam-3412	467	36	then	then	ADV
ejpam-3412	467	37	(	(	PUNCT
ejpam-3412	467	38	g̃1	g̃1	NOUN
ejpam-3412	467	39	,	,	PUNCT
ejpam-3412	467	40	e1	e1	PROPN
ejpam-3412	467	41	)	)	PUNCT
ejpam-3412	467	42	and	and	CCONJ
ejpam-3412	467	43	(	(	PUNCT
ejpam-3412	467	44	g̃2	g̃2	PROPN
ejpam-3412	467	45	,	,	PUNCT
ejpam-3412	467	46	e2	e2	PROPN
ejpam-3412	467	47	)	)	PUNCT
ejpam-3412	467	48	are	be	AUX
ejpam-3412	467	49	two	two	NUM
ejpam-3412	467	50	fuzzy	fuzzy	ADJ
ejpam-3412	467	51	soft	soft	ADJ
ejpam-3412	467	52	ups	up	NOUN
ejpam-3412	467	53	-	-	PUNCT
ejpam-3412	467	54	subalgebras	subalgebras	PROPN
ejpam-3412	467	55	of	of	ADP
ejpam-3412	467	56	a.	a.	NOUN
ejpam-3412	467	57	since	since	SCONJ
ejpam-3412	467	58	price	price	NOUN
ejpam-3412	467	59	∈	∈	PROPN
ejpam-3412	467	60	e1∩e2	e1∩e2	PROPN
ejpam-3412	467	61	,	,	PUNCT
ejpam-3412	467	62	we	we	PRON
ejpam-3412	467	63	have	have	VERB
ejpam-3412	467	64	(	(	PUNCT
ejpam-3412	467	65	f	f	PROPN
ejpam-3412	467	66	g̃1[price]∪g̃2[price	g̃1[price]∪g̃2[price	X
ejpam-3412	467	67	]	]	X
ejpam-3412	467	68	)	)	PUNCT
ejpam-3412	467	69	(	(	PUNCT
ejpam-3412	467	70	6	6	NUM
ejpam-3412	467	71	∗	∗	NOUN
ejpam-3412	467	72	5	5	NUM
ejpam-3412	467	73	)	)	PUNCT
ejpam-3412	467	74	=	=	PUNCT
ejpam-3412	468	1	(	(	PUNCT
ejpam-3412	468	2	f	f	X
ejpam-3412	468	3	g̃1[price]∪g̃2[price	g̃1[price]∪g̃2[price	X
ejpam-3412	468	4	]	]	X
ejpam-3412	468	5	)	)	PUNCT
ejpam-3412	468	6	(	(	PUNCT
ejpam-3412	468	7	7	7	X
ejpam-3412	468	8	)	)	PUNCT
ejpam-3412	468	9	=	=	SYM
ejpam-3412	468	10	0.7	0.7	NUM
ejpam-3412	468	11	�	�	PROPN
ejpam-3412	468	12	0.8	0.8	NUM
ejpam-3412	468	13	=	=	SYM
ejpam-3412	468	14	min{0.9	min{0.9	PROPN
ejpam-3412	468	15	,	,	PUNCT
ejpam-3412	468	16	0.8	0.8	NUM
ejpam-3412	468	17	}	}	PUNCT
ejpam-3412	468	18	=	=	SYM
ejpam-3412	468	19	min{(f	min{(f	SYM
ejpam-3412	468	20	g̃1[price]∪g̃2[price	g̃1[price]∪g̃2[price	X
ejpam-3412	468	21	]	]	X
ejpam-3412	468	22	)	)	PUNCT
ejpam-3412	468	23	(	(	PUNCT
ejpam-3412	468	24	6	6	NUM
ejpam-3412	468	25	)	)	PUNCT
ejpam-3412	468	26	,	,	PUNCT
ejpam-3412	468	27	(	(	PUNCT
ejpam-3412	468	28	f	f	PROPN
ejpam-3412	468	29	g̃1[price]∪g̃2[price	g̃1[price]∪g̃2[price	X
ejpam-3412	468	30	]	]	X
ejpam-3412	468	31	)	)	PUNCT
ejpam-3412	468	32	(	(	PUNCT
ejpam-3412	468	33	5	5	NUM
ejpam-3412	468	34	)	)	PUNCT
ejpam-3412	468	35	}	}	PUNCT
ejpam-3412	468	36	.	.	PUNCT
ejpam-3412	469	1	thus	thus	ADV
ejpam-3412	469	2	g̃1[price]∪	g̃1[price]∪	NOUN
ejpam-3412	469	3	g̃2[price	g̃2[price	PROPN
ejpam-3412	469	4	]	]	PUNCT
ejpam-3412	469	5	is	be	AUX
ejpam-3412	469	6	not	not	PART
ejpam-3412	469	7	a	a	DET
ejpam-3412	469	8	fuzzy	fuzzy	ADJ
ejpam-3412	469	9	ups	up	NOUN
ejpam-3412	469	10	-	-	PUNCT
ejpam-3412	469	11	subalgebra	subalgebra	NOUN
ejpam-3412	469	12	of	of	ADP
ejpam-3412	469	13	a	a	DET
ejpam-3412	469	14	,	,	PUNCT
ejpam-3412	469	15	that	that	ADV
ejpam-3412	469	16	is	is	ADV
ejpam-3412	469	17	,	,	PUNCT
ejpam-3412	469	18	(	(	PUNCT
ejpam-3412	469	19	g̃1	g̃1	NOUN
ejpam-3412	469	20	,	,	PUNCT
ejpam-3412	469	21	e1)∪	e1)∪	PROPN
ejpam-3412	469	22	(	(	PUNCT
ejpam-3412	469	23	g̃2	g̃2	PROPN
ejpam-3412	469	24	,	,	PUNCT
ejpam-3412	469	25	e2	e2	PROPN
ejpam-3412	469	26	)	)	PUNCT
ejpam-3412	469	27	is	be	AUX
ejpam-3412	469	28	not	not	PART
ejpam-3412	469	29	a	a	DET
ejpam-3412	469	30	price	price	NOUN
ejpam-3412	469	31	-	-	PUNCT
ejpam-3412	469	32	fuzzy	fuzzy	ADJ
ejpam-3412	469	33	soft	soft	ADJ
ejpam-3412	469	34	ups	up	NOUN
ejpam-3412	469	35	-	-	PUNCT
ejpam-3412	469	36	subalgebra	subalgebra	NOUN
ejpam-3412	469	37	of	of	ADP
ejpam-3412	469	38	a.	a.	NOUN
ejpam-3412	469	39	hence	hence	ADV
ejpam-3412	469	40	,	,	PUNCT
ejpam-3412	469	41	(	(	PUNCT
ejpam-3412	469	42	g̃1	g̃1	NOUN
ejpam-3412	469	43	,	,	PUNCT
ejpam-3412	469	44	e1	e1	NOUN
ejpam-3412	469	45	)	)	PUNCT
ejpam-3412	469	46	∪	∪	NOUN
ejpam-3412	469	47	(	(	PUNCT
ejpam-3412	469	48	g̃2	g̃2	PROPN
ejpam-3412	469	49	,	,	PUNCT
ejpam-3412	469	50	e2	e2	PROPN
ejpam-3412	469	51	)	)	PUNCT
ejpam-3412	469	52	is	be	AUX
ejpam-3412	469	53	not	not	PART
ejpam-3412	469	54	a	a	DET
ejpam-3412	469	55	fuzzy	fuzzy	ADJ
ejpam-3412	469	56	soft	soft	ADJ
ejpam-3412	469	57	ups	up	NOUN
ejpam-3412	469	58	-	-	PUNCT
ejpam-3412	469	59	subalgebra	subalgebra	NOUN
ejpam-3412	469	60	of	of	ADP
ejpam-3412	469	61	a.	a.	NOUN
ejpam-3412	469	62	moreover	moreover	ADV
ejpam-3412	469	63	,	,	PUNCT
ejpam-3412	469	64	(	(	PUNCT
ejpam-3412	469	65	g̃1	g̃1	NOUN
ejpam-3412	469	66	,	,	PUNCT
ejpam-3412	469	67	e1)d	e1)d	NOUN
ejpam-3412	469	68	(	(	PUNCT
ejpam-3412	469	69	g̃2	g̃2	PROPN
ejpam-3412	469	70	,	,	PUNCT
ejpam-3412	469	71	e2	e2	PROPN
ejpam-3412	469	72	)	)	PUNCT
ejpam-3412	469	73	is	be	AUX
ejpam-3412	469	74	not	not	PART
ejpam-3412	469	75	a	a	DET
ejpam-3412	469	76	fuzzy	fuzzy	ADJ
ejpam-3412	469	77	soft	soft	ADJ
ejpam-3412	469	78	ups	up	NOUN
ejpam-3412	469	79	-	-	PUNCT
ejpam-3412	469	80	subalgebra	subalgebra	NOUN
ejpam-3412	469	81	of	of	ADP
ejpam-3412	469	82	a.	a.	NOUN
ejpam-3412	469	83	3.2	3.2	NUM
ejpam-3412	469	84	.	.	PUNCT
ejpam-3412	470	1	fuzzy	fuzzy	ADJ
ejpam-3412	470	2	soft	soft	ADJ
ejpam-3412	470	3	upi	upi	NOUN
ejpam-3412	470	4	-	-	PUNCT
ejpam-3412	470	5	subalgebras	subalgebras	PROPN
ejpam-3412	470	6	definition	definition	NOUN
ejpam-3412	470	7	19	19	NUM
ejpam-3412	470	8	.	.	PUNCT
ejpam-3412	471	1	a	a	DET
ejpam-3412	471	2	fuzzy	fuzzy	ADJ
ejpam-3412	471	3	soft	soft	ADJ
ejpam-3412	471	4	set	set	NOUN
ejpam-3412	471	5	(	(	PUNCT
ejpam-3412	471	6	f̃	f̃	PROPN
ejpam-3412	471	7	,	,	PUNCT
ejpam-3412	471	8	e	e	NOUN
ejpam-3412	471	9	)	)	PUNCT
ejpam-3412	471	10	over	over	ADP
ejpam-3412	471	11	a	a	PRON
ejpam-3412	471	12	is	be	AUX
ejpam-3412	471	13	called	call	VERB
ejpam-3412	471	14	a	a	DET
ejpam-3412	471	15	fuzzy	fuzzy	ADJ
ejpam-3412	471	16	soft	soft	ADJ
ejpam-3412	471	17	upi	upi	NOUN
ejpam-3412	471	18	-	-	PUNCT
ejpam-3412	471	19	subalgebra	subalgebra	NOUN
ejpam-3412	471	20	based	base	VERB
ejpam-3412	471	21	on	on	ADP
ejpam-3412	471	22	e	e	PROPN
ejpam-3412	471	23	∈	∈	PROPN
ejpam-3412	471	24	e	e	X
ejpam-3412	471	25	(	(	PUNCT
ejpam-3412	471	26	we	we	PRON
ejpam-3412	471	27	shortly	shortly	ADV
ejpam-3412	471	28	call	call	VERB
ejpam-3412	471	29	an	an	DET
ejpam-3412	471	30	e	e	ADJ
ejpam-3412	471	31	-	-	ADJ
ejpam-3412	471	32	fuzzy	fuzzy	ADJ
ejpam-3412	471	33	soft	soft	ADJ
ejpam-3412	471	34	upi	upi	NOUN
ejpam-3412	471	35	-	-	PUNCT
ejpam-3412	471	36	subalgebra	subalgebra	NOUN
ejpam-3412	471	37	)	)	PUNCT
ejpam-3412	471	38	of	of	ADP
ejpam-3412	471	39	a	a	DET
ejpam-3412	471	40	if	if	SCONJ
ejpam-3412	471	41	a	a	DET
ejpam-3412	471	42	fuzzy	fuzzy	ADJ
ejpam-3412	471	43	set	set	NOUN
ejpam-3412	471	44	f̃[e	f̃[e	X
ejpam-3412	471	45	]	]	X
ejpam-3412	471	46	in	in	ADP
ejpam-3412	471	47	a	a	PRON
ejpam-3412	471	48	is	be	AUX
ejpam-3412	471	49	a	a	DET
ejpam-3412	471	50	fuzzy	fuzzy	ADJ
ejpam-3412	471	51	upi	upi	NOUN
ejpam-3412	471	52	-	-	PUNCT
ejpam-3412	471	53	subalgebra	subalgebra	NOUN
ejpam-3412	471	54	of	of	ADP
ejpam-3412	471	55	a.	a.	NOUN
ejpam-3412	471	56	if	if	SCONJ
ejpam-3412	471	57	(	(	PUNCT
ejpam-3412	471	58	f̃	f̃	PROPN
ejpam-3412	471	59	,	,	PUNCT
ejpam-3412	471	60	e	e	NOUN
ejpam-3412	471	61	)	)	PUNCT
ejpam-3412	471	62	is	be	AUX
ejpam-3412	471	63	an	an	DET
ejpam-3412	471	64	e	e	ADJ
ejpam-3412	471	65	-	-	ADJ
ejpam-3412	471	66	fuzzy	fuzzy	ADJ
ejpam-3412	471	67	soft	soft	ADJ
ejpam-3412	471	68	upi	upi	NOUN
ejpam-3412	471	69	-	-	PUNCT
ejpam-3412	471	70	subalgebra	subalgebra	NOUN
ejpam-3412	471	71	of	of	ADP
ejpam-3412	471	72	a	a	PRON
ejpam-3412	471	73	for	for	ADP
ejpam-3412	471	74	all	all	DET
ejpam-3412	471	75	e	e	NOUN
ejpam-3412	471	76	∈	∈	PROPN
ejpam-3412	471	77	e	e	NOUN
ejpam-3412	471	78	,	,	PUNCT
ejpam-3412	471	79	we	we	PRON
ejpam-3412	471	80	say	say	VERB
ejpam-3412	471	81	that	that	SCONJ
ejpam-3412	471	82	(	(	PUNCT
ejpam-3412	471	83	f̃	f̃	PROPN
ejpam-3412	471	84	,	,	PUNCT
ejpam-3412	471	85	e	e	NOUN
ejpam-3412	471	86	)	)	PUNCT
ejpam-3412	471	87	is	be	AUX
ejpam-3412	471	88	a	a	DET
ejpam-3412	471	89	fuzzy	fuzzy	ADJ
ejpam-3412	471	90	soft	soft	ADJ
ejpam-3412	471	91	upi	upi	NOUN
ejpam-3412	471	92	-	-	PUNCT
ejpam-3412	471	93	subalgebra	subalgebra	NOUN
ejpam-3412	471	94	of	of	ADP
ejpam-3412	471	95	a.	a.	NOUN
ejpam-3412	471	96	in	in	ADP
ejpam-3412	471	97	the	the	DET
ejpam-3412	471	98	next	next	ADJ
ejpam-3412	471	99	theorem	theorem	NOUN
ejpam-3412	471	100	,	,	PUNCT
ejpam-3412	471	101	we	we	PRON
ejpam-3412	471	102	give	give	VERB
ejpam-3412	471	103	necessary	necessary	ADJ
ejpam-3412	471	104	condition	condition	NOUN
ejpam-3412	471	105	for	for	ADP
ejpam-3412	471	106	fuzzy	fuzzy	ADJ
ejpam-3412	471	107	soft	soft	ADJ
ejpam-3412	471	108	upi	upi	NOUN
ejpam-3412	471	109	-	-	PUNCT
ejpam-3412	471	110	subalgebras	subalgebras	PROPN
ejpam-3412	471	111	of	of	ADP
ejpam-3412	471	112	f	f	PROPN
ejpam-3412	471	113	-up	-up	NOUN
ejpam-3412	471	114	-	-	PUNCT
ejpam-3412	471	115	semigroups	semigroup	NOUN
ejpam-3412	471	116	.	.	PUNCT
ejpam-3412	472	1	theorem	theorem	NOUN
ejpam-3412	472	2	24	24	NUM
ejpam-3412	472	3	.	.	PUNCT
ejpam-3412	473	1	if	if	SCONJ
ejpam-3412	473	2	(	(	PUNCT
ejpam-3412	473	3	f̃	f̃	PROPN
ejpam-3412	473	4	,	,	PUNCT
ejpam-3412	473	5	e	e	NOUN
ejpam-3412	473	6	)	)	PUNCT
ejpam-3412	473	7	is	be	AUX
ejpam-3412	473	8	a	a	DET
ejpam-3412	473	9	fuzzy	fuzzy	ADJ
ejpam-3412	473	10	soft	soft	ADJ
ejpam-3412	473	11	set	set	NOUN
ejpam-3412	473	12	over	over	ADP
ejpam-3412	473	13	a	a	DET
ejpam-3412	473	14	such	such	ADJ
ejpam-3412	473	15	that	that	PRON
ejpam-3412	473	16	for	for	ADP
ejpam-3412	473	17	all	all	DET
ejpam-3412	473	18	e	e	NOUN
ejpam-3412	473	19	∈	∈	PROPN
ejpam-3412	473	20	e	e	NOUN
ejpam-3412	473	21	,	,	PUNCT
ejpam-3412	473	22	a	a	DET
ejpam-3412	473	23	fuzzy	fuzzy	ADJ
ejpam-3412	473	24	set	set	NOUN
ejpam-3412	473	25	f̃[e	f̃[e	NOUN
ejpam-3412	473	26	]	]	X
ejpam-3412	473	27	in	in	ADP
ejpam-3412	473	28	a	a	DET
ejpam-3412	473	29	satisfies	satisfie	NOUN
ejpam-3412	473	30	the	the	DET
ejpam-3412	473	31	conditions	condition	NOUN
ejpam-3412	473	32	(	(	PUNCT
ejpam-3412	473	33	2.3	2.3	NUM
ejpam-3412	473	34	)	)	PUNCT
ejpam-3412	473	35	and	and	CCONJ
ejpam-3412	473	36	(	(	PUNCT
ejpam-3412	473	37	1.15	1.15	NUM
ejpam-3412	473	38	)	)	PUNCT
ejpam-3412	473	39	,	,	PUNCT
ejpam-3412	473	40	then	then	ADV
ejpam-3412	473	41	(	(	PUNCT
ejpam-3412	473	42	f̃	f̃	PROPN
ejpam-3412	473	43	,	,	PUNCT
ejpam-3412	473	44	e	e	NOUN
ejpam-3412	473	45	)	)	PUNCT
ejpam-3412	473	46	is	be	AUX
ejpam-3412	473	47	a	a	DET
ejpam-3412	473	48	fuzzy	fuzzy	ADJ
ejpam-3412	473	49	soft	soft	ADJ
ejpam-3412	473	50	upi	upi	NOUN
ejpam-3412	473	51	-	-	PUNCT
ejpam-3412	473	52	subalgebra	subalgebra	NOUN
ejpam-3412	473	53	of	of	ADP
ejpam-3412	473	54	a.	a.	NOUN
ejpam-3412	473	55	proof	proof	NOUN
ejpam-3412	473	56	.	.	PUNCT
ejpam-3412	474	1	it	it	PRON
ejpam-3412	474	2	is	be	AUX
ejpam-3412	474	3	straightforward	straightforward	ADJ
ejpam-3412	474	4	by	by	ADP
ejpam-3412	474	5	proposition	proposition	NOUN
ejpam-3412	474	6	3	3	NUM
ejpam-3412	474	7	and	and	CCONJ
ejpam-3412	474	8	lemma	lemma	PROPN
ejpam-3412	474	9	1	1	NUM
ejpam-3412	474	10	(	(	PUNCT
ejpam-3412	474	11	2	2	NUM
ejpam-3412	474	12	)	)	PUNCT
ejpam-3412	474	13	.	.	PUNCT
ejpam-3412	475	1	from	from	ADP
ejpam-3412	475	2	figure	figure	NOUN
ejpam-3412	475	3	1	1	NUM
ejpam-3412	475	4	,	,	PUNCT
ejpam-3412	475	5	we	we	PRON
ejpam-3412	475	6	have	have	VERB
ejpam-3412	475	7	the	the	DET
ejpam-3412	475	8	following	follow	VERB
ejpam-3412	475	9	theorem	theorem	PROPN
ejpam-3412	475	10	.	.	PUNCT
ejpam-3412	475	11	a.	a.	PROPN
ejpam-3412	475	12	satirad	satirad	PROPN
ejpam-3412	475	13	,	,	PUNCT
ejpam-3412	475	14	a.	a.	NOUN
ejpam-3412	475	15	iampan	iampan	PROPN
ejpam-3412	475	16	/	/	SYM
ejpam-3412	475	17	eur	eur	PROPN
ejpam-3412	475	18	.	.	PUNCT
ejpam-3412	476	1	j.	j.	PROPN
ejpam-3412	476	2	pure	pure	PROPN
ejpam-3412	476	3	appl	appl	PROPN
ejpam-3412	476	4	.	.	PROPN
ejpam-3412	476	5	math	math	PROPN
ejpam-3412	476	6	,	,	PUNCT
ejpam-3412	476	7	12	12	NUM
ejpam-3412	476	8	(	(	PUNCT
ejpam-3412	476	9	2	2	NUM
ejpam-3412	476	10	)	)	PUNCT
ejpam-3412	476	11	(	(	PUNCT
ejpam-3412	476	12	2019	2019	NUM
ejpam-3412	476	13	)	)	PUNCT
ejpam-3412	476	14	,	,	PUNCT
ejpam-3412	476	15	294	294	NUM
ejpam-3412	476	16	-	-	SYM
ejpam-3412	476	17	331	331	NUM
ejpam-3412	476	18	314	314	NUM
ejpam-3412	476	19	theorem	theorem	NOUN
ejpam-3412	476	20	25	25	NUM
ejpam-3412	476	21	.	.	PUNCT
ejpam-3412	477	1	every	every	DET
ejpam-3412	477	2	e	e	ADJ
ejpam-3412	477	3	-	-	ADJ
ejpam-3412	477	4	fuzzy	fuzzy	ADJ
ejpam-3412	477	5	soft	soft	ADJ
ejpam-3412	477	6	upi	upi	NOUN
ejpam-3412	477	7	-	-	PUNCT
ejpam-3412	477	8	subalgebra	subalgebra	NOUN
ejpam-3412	477	9	of	of	ADP
ejpam-3412	477	10	a	a	PRON
ejpam-3412	477	11	is	be	AUX
ejpam-3412	477	12	an	an	DET
ejpam-3412	477	13	e	e	ADJ
ejpam-3412	477	14	-	-	ADJ
ejpam-3412	477	15	fuzzy	fuzzy	ADJ
ejpam-3412	477	16	soft	soft	ADJ
ejpam-3412	477	17	ups	up	NOUN
ejpam-3412	477	18	-	-	PUNCT
ejpam-3412	477	19	subalgebra	subalgebra	NOUN
ejpam-3412	477	20	.	.	PUNCT
ejpam-3412	478	1	moreover	moreover	ADV
ejpam-3412	478	2	,	,	PUNCT
ejpam-3412	478	3	every	every	DET
ejpam-3412	478	4	fuzzy	fuzzy	ADJ
ejpam-3412	478	5	soft	soft	ADJ
ejpam-3412	478	6	upi	upi	NOUN
ejpam-3412	478	7	-	-	PUNCT
ejpam-3412	478	8	subalgebra	subalgebra	NOUN
ejpam-3412	478	9	of	of	ADP
ejpam-3412	478	10	a	a	PRON
ejpam-3412	478	11	is	be	AUX
ejpam-3412	478	12	a	a	DET
ejpam-3412	478	13	fuzzy	fuzzy	ADJ
ejpam-3412	478	14	soft	soft	ADJ
ejpam-3412	478	15	ups	up	NOUN
ejpam-3412	478	16	-	-	PUNCT
ejpam-3412	478	17	subalgebra	subalgebra	NOUN
ejpam-3412	478	18	.	.	PUNCT
ejpam-3412	479	1	the	the	DET
ejpam-3412	479	2	following	follow	VERB
ejpam-3412	479	3	example	example	NOUN
ejpam-3412	479	4	shows	show	VERB
ejpam-3412	479	5	that	that	SCONJ
ejpam-3412	479	6	the	the	DET
ejpam-3412	479	7	converse	converse	NOUN
ejpam-3412	479	8	of	of	ADP
ejpam-3412	479	9	theorem	theorem	NOUN
ejpam-3412	479	10	25	25	NUM
ejpam-3412	479	11	is	be	AUX
ejpam-3412	479	12	not	not	PART
ejpam-3412	479	13	true	true	ADJ
ejpam-3412	479	14	.	.	PUNCT
ejpam-3412	480	1	example	example	NOUN
ejpam-3412	481	1	15	15	NUM
ejpam-3412	481	2	.	.	PUNCT
ejpam-3412	482	1	in	in	ADP
ejpam-3412	482	2	example	example	NOUN
ejpam-3412	482	3	13	13	NUM
ejpam-3412	482	4	,	,	PUNCT
ejpam-3412	482	5	we	we	PRON
ejpam-3412	482	6	know	know	VERB
ejpam-3412	482	7	that	that	SCONJ
ejpam-3412	482	8	(	(	PUNCT
ejpam-3412	482	9	f̃	f̃	PROPN
ejpam-3412	482	10	,	,	PUNCT
ejpam-3412	482	11	e	e	NOUN
ejpam-3412	482	12	)	)	PUNCT
ejpam-3412	482	13	is	be	AUX
ejpam-3412	482	14	a	a	DET
ejpam-3412	482	15	price	price	NOUN
ejpam-3412	482	16	-	-	PUNCT
ejpam-3412	482	17	fuzzy	fuzzy	ADJ
ejpam-3412	482	18	soft	soft	ADJ
ejpam-3412	482	19	ups	up	NOUN
ejpam-3412	482	20	-	-	PUNCT
ejpam-3412	482	21	subalgebra	subalgebra	NOUN
ejpam-3412	482	22	of	of	ADP
ejpam-3412	482	23	a	a	DET
ejpam-3412	482	24	but	but	CCONJ
ejpam-3412	482	25	f̃[price	f̃[price	NOUN
ejpam-3412	482	26	]	]	PUNCT
ejpam-3412	482	27	is	be	AUX
ejpam-3412	482	28	not	not	PART
ejpam-3412	482	29	a	a	DET
ejpam-3412	482	30	fuzzy	fuzzy	ADJ
ejpam-3412	482	31	upi	upi	NOUN
ejpam-3412	482	32	-	-	PUNCT
ejpam-3412	482	33	subalgebra	subalgebra	NOUN
ejpam-3412	482	34	of	of	ADP
ejpam-3412	482	35	a.	a.	NOUN
ejpam-3412	482	36	indeed	indeed	ADV
ejpam-3412	482	37	,	,	PUNCT
ejpam-3412	482	38	f	f	PROPN
ejpam-3412	482	39	f̃[price	f̃[price	PROPN
ejpam-3412	482	40	]	]	X
ejpam-3412	482	41	(	(	PUNCT
ejpam-3412	482	42	6	6	NUM
ejpam-3412	482	43	∗	∗	NOUN
ejpam-3412	482	44	5	5	NUM
ejpam-3412	482	45	)	)	PUNCT
ejpam-3412	482	46	=	=	SYM
ejpam-3412	482	47	f	f	X
ejpam-3412	482	48	f̃[price	f̃[price	PROPN
ejpam-3412	482	49	]	]	X
ejpam-3412	482	50	(	(	PUNCT
ejpam-3412	482	51	7	7	X
ejpam-3412	482	52	)	)	PUNCT
ejpam-3412	482	53	=	=	SYM
ejpam-3412	482	54	0.3	0.3	NUM
ejpam-3412	482	55	�	�	PROPN
ejpam-3412	482	56	0.7	0.7	NUM
ejpam-3412	482	57	=	=	SYM
ejpam-3412	482	58	max{0.7	max{0.7	PROPN
ejpam-3412	482	59	,	,	PUNCT
ejpam-3412	482	60	0.1	0.1	NUM
ejpam-3412	482	61	}	}	PUNCT
ejpam-3412	482	62	=	=	SYM
ejpam-3412	482	63	max{f	max{f	PROPN
ejpam-3412	482	64	f̃[price	f̃[price	PROPN
ejpam-3412	482	65	]	]	PUNCT
ejpam-3412	482	66	(	(	PUNCT
ejpam-3412	482	67	6	6	NUM
ejpam-3412	482	68	)	)	PUNCT
ejpam-3412	482	69	,	,	PUNCT
ejpam-3412	482	70	f	f	PROPN
ejpam-3412	482	71	f̃[price	f̃[price	PROPN
ejpam-3412	482	72	]	]	X
ejpam-3412	482	73	(	(	PUNCT
ejpam-3412	482	74	5	5	NUM
ejpam-3412	482	75	)	)	PUNCT
ejpam-3412	482	76	}	}	PUNCT
ejpam-3412	482	77	.	.	PUNCT
ejpam-3412	483	1	hence	hence	ADV
ejpam-3412	483	2	,	,	PUNCT
ejpam-3412	483	3	(	(	PUNCT
ejpam-3412	483	4	f̃	f̃	PROPN
ejpam-3412	483	5	,	,	PUNCT
ejpam-3412	483	6	e	e	NOUN
ejpam-3412	483	7	)	)	PUNCT
ejpam-3412	483	8	is	be	AUX
ejpam-3412	483	9	not	not	PART
ejpam-3412	483	10	a	a	DET
ejpam-3412	483	11	price	price	NOUN
ejpam-3412	483	12	-	-	PUNCT
ejpam-3412	483	13	fuzzy	fuzzy	ADJ
ejpam-3412	483	14	soft	soft	ADJ
ejpam-3412	483	15	upi	upi	NOUN
ejpam-3412	483	16	-	-	PUNCT
ejpam-3412	483	17	subalgebra	subalgebra	NOUN
ejpam-3412	483	18	of	of	ADP
ejpam-3412	483	19	a.	a.	NOUN
ejpam-3412	483	20	the	the	DET
ejpam-3412	483	21	proof	proof	NOUN
ejpam-3412	483	22	of	of	ADP
ejpam-3412	483	23	the	the	DET
ejpam-3412	483	24	following	follow	VERB
ejpam-3412	483	25	theorem	theorem	NOUN
ejpam-3412	483	26	can	can	AUX
ejpam-3412	483	27	be	be	AUX
ejpam-3412	483	28	verified	verify	VERB
ejpam-3412	483	29	easily	easily	ADV
ejpam-3412	483	30	.	.	PUNCT
ejpam-3412	484	1	theorem	theorem	VERB
ejpam-3412	484	2	26	26	NUM
ejpam-3412	484	3	.	.	PUNCT
ejpam-3412	485	1	if	if	SCONJ
ejpam-3412	485	2	(	(	PUNCT
ejpam-3412	485	3	f̃	f̃	PROPN
ejpam-3412	485	4	,	,	PUNCT
ejpam-3412	485	5	e	e	NOUN
ejpam-3412	485	6	)	)	PUNCT
ejpam-3412	485	7	is	be	AUX
ejpam-3412	485	8	a	a	DET
ejpam-3412	485	9	fuzzy	fuzzy	ADJ
ejpam-3412	485	10	soft	soft	ADJ
ejpam-3412	485	11	upi	upi	NOUN
ejpam-3412	485	12	-	-	PUNCT
ejpam-3412	485	13	subalgebra	subalgebra	NOUN
ejpam-3412	485	14	of	of	ADP
ejpam-3412	485	15	a	a	PRON
ejpam-3412	485	16	and	and	CCONJ
ejpam-3412	485	17	∅	∅	NOUN
ejpam-3412	485	18	6=	6=	ADP
ejpam-3412	485	19	e∗	e∗	PROPN
ejpam-3412	485	20	⊆	⊆	NUM
ejpam-3412	485	21	e	e	NOUN
ejpam-3412	485	22	,	,	PUNCT
ejpam-3412	485	23	then	then	ADV
ejpam-3412	485	24	(	(	PUNCT
ejpam-3412	485	25	f̃|e∗	f̃|e∗	PROPN
ejpam-3412	485	26	,	,	PUNCT
ejpam-3412	485	27	e∗	e∗	PROPN
ejpam-3412	485	28	)	)	PUNCT
ejpam-3412	485	29	is	be	AUX
ejpam-3412	485	30	a	a	DET
ejpam-3412	485	31	fuzzy	fuzzy	ADJ
ejpam-3412	485	32	soft	soft	ADJ
ejpam-3412	485	33	upi	upi	NOUN
ejpam-3412	485	34	-	-	PUNCT
ejpam-3412	485	35	subalgebra	subalgebra	NOUN
ejpam-3412	485	36	of	of	ADP
ejpam-3412	485	37	a.	a.	NOUN
ejpam-3412	485	38	the	the	DET
ejpam-3412	485	39	following	follow	VERB
ejpam-3412	485	40	two	two	NUM
ejpam-3412	485	41	theorems	theorem	NOUN
ejpam-3412	485	42	can	can	AUX
ejpam-3412	485	43	be	be	AUX
ejpam-3412	485	44	deduced	deduce	VERB
ejpam-3412	485	45	in	in	ADP
ejpam-3412	485	46	the	the	DET
ejpam-3412	485	47	same	same	ADJ
ejpam-3412	485	48	way	way	NOUN
ejpam-3412	485	49	as	as	ADP
ejpam-3412	485	50	theorems	theorem	NOUN
ejpam-3412	485	51	22	22	NUM
ejpam-3412	485	52	and	and	CCONJ
ejpam-3412	485	53	23	23	NUM
ejpam-3412	485	54	.	.	PUNCT
ejpam-3412	486	1	theorem	theorem	VERB
ejpam-3412	486	2	27	27	NUM
ejpam-3412	486	3	.	.	PUNCT
ejpam-3412	487	1	the	the	DET
ejpam-3412	487	2	extended	extended	ADJ
ejpam-3412	487	3	intersection	intersection	NOUN
ejpam-3412	487	4	of	of	ADP
ejpam-3412	487	5	two	two	NUM
ejpam-3412	487	6	fuzzy	fuzzy	ADJ
ejpam-3412	487	7	soft	soft	ADJ
ejpam-3412	487	8	upi	upi	NOUN
ejpam-3412	487	9	-	-	PUNCT
ejpam-3412	487	10	subalgebras	subalgebras	PROPN
ejpam-3412	487	11	of	of	ADP
ejpam-3412	487	12	a	a	PRON
ejpam-3412	487	13	is	be	AUX
ejpam-3412	487	14	also	also	ADV
ejpam-3412	487	15	a	a	DET
ejpam-3412	487	16	fuzzy	fuzzy	ADJ
ejpam-3412	487	17	soft	soft	ADJ
ejpam-3412	487	18	upi	upi	NOUN
ejpam-3412	487	19	-	-	PUNCT
ejpam-3412	487	20	subalgebra	subalgebra	NOUN
ejpam-3412	487	21	.	.	PUNCT
ejpam-3412	488	1	moreover	moreover	ADV
ejpam-3412	488	2	,	,	PUNCT
ejpam-3412	488	3	the	the	DET
ejpam-3412	488	4	intersection	intersection	NOUN
ejpam-3412	488	5	of	of	ADP
ejpam-3412	488	6	two	two	NUM
ejpam-3412	488	7	fuzzy	fuzzy	ADJ
ejpam-3412	488	8	soft	soft	ADJ
ejpam-3412	488	9	upi	upi	NOUN
ejpam-3412	488	10	-	-	PUNCT
ejpam-3412	488	11	subalgebras	subalgebras	PROPN
ejpam-3412	488	12	of	of	ADP
ejpam-3412	488	13	a	a	PRON
ejpam-3412	488	14	is	be	AUX
ejpam-3412	488	15	also	also	ADV
ejpam-3412	488	16	a	a	DET
ejpam-3412	488	17	fuzzy	fuzzy	ADJ
ejpam-3412	488	18	soft	soft	ADJ
ejpam-3412	488	19	upi	upi	NOUN
ejpam-3412	488	20	-	-	PUNCT
ejpam-3412	488	21	subalgebra	subalgebra	NOUN
ejpam-3412	488	22	.	.	PUNCT
ejpam-3412	489	1	theorem	theorem	NOUN
ejpam-3412	489	2	28	28	NUM
ejpam-3412	489	3	.	.	PUNCT
ejpam-3412	490	1	the	the	DET
ejpam-3412	490	2	union	union	NOUN
ejpam-3412	490	3	of	of	ADP
ejpam-3412	490	4	two	two	NUM
ejpam-3412	490	5	fuzzy	fuzzy	ADJ
ejpam-3412	490	6	soft	soft	ADJ
ejpam-3412	490	7	upi	upi	NOUN
ejpam-3412	490	8	-	-	PUNCT
ejpam-3412	490	9	subalgebras	subalgebras	PROPN
ejpam-3412	490	10	of	of	ADP
ejpam-3412	490	11	a	a	PRON
ejpam-3412	490	12	is	be	AUX
ejpam-3412	490	13	also	also	ADV
ejpam-3412	490	14	a	a	DET
ejpam-3412	490	15	fuzzy	fuzzy	ADJ
ejpam-3412	490	16	soft	soft	ADJ
ejpam-3412	490	17	upisubalgebra	upisubalgebra	NOUN
ejpam-3412	490	18	if	if	SCONJ
ejpam-3412	490	19	sets	set	NOUN
ejpam-3412	490	20	of	of	ADP
ejpam-3412	490	21	statistics	statistic	NOUN
ejpam-3412	490	22	of	of	ADP
ejpam-3412	490	23	two	two	NUM
ejpam-3412	490	24	fuzzy	fuzzy	ADJ
ejpam-3412	490	25	soft	soft	ADJ
ejpam-3412	490	26	upi	upi	NOUN
ejpam-3412	490	27	-	-	PUNCT
ejpam-3412	490	28	subalgebras	subalgebras	PROPN
ejpam-3412	490	29	are	be	AUX
ejpam-3412	490	30	disjoint	disjoint	ADJ
ejpam-3412	490	31	.	.	PUNCT
ejpam-3412	491	1	the	the	DET
ejpam-3412	491	2	following	follow	VERB
ejpam-3412	491	3	example	example	NOUN
ejpam-3412	491	4	shows	show	VERB
ejpam-3412	491	5	that	that	SCONJ
ejpam-3412	491	6	theorem	theorem	VERB
ejpam-3412	491	7	28	28	NUM
ejpam-3412	491	8	is	be	AUX
ejpam-3412	491	9	not	not	PART
ejpam-3412	491	10	valid	valid	ADJ
ejpam-3412	491	11	if	if	SCONJ
ejpam-3412	491	12	sets	set	NOUN
ejpam-3412	491	13	of	of	ADP
ejpam-3412	491	14	statistics	statistic	NOUN
ejpam-3412	491	15	of	of	ADP
ejpam-3412	491	16	two	two	NUM
ejpam-3412	491	17	fuzzy	fuzzy	ADJ
ejpam-3412	491	18	soft	soft	ADJ
ejpam-3412	491	19	upi	upi	NOUN
ejpam-3412	491	20	-	-	PUNCT
ejpam-3412	491	21	subalgebras	subalgebras	PROPN
ejpam-3412	491	22	are	be	AUX
ejpam-3412	491	23	not	not	PART
ejpam-3412	491	24	disjoint	disjoint	ADJ
ejpam-3412	491	25	.	.	PUNCT
ejpam-3412	491	26	example	example	NOUN
ejpam-3412	492	1	16	16	NUM
ejpam-3412	492	2	.	.	PUNCT
ejpam-3412	493	1	let	let	VERB
ejpam-3412	493	2	a	a	DET
ejpam-3412	493	3	be	be	AUX
ejpam-3412	493	4	the	the	DET
ejpam-3412	493	5	set	set	NOUN
ejpam-3412	493	6	of	of	ADP
ejpam-3412	493	7	four	four	NUM
ejpam-3412	493	8	types	type	NOUN
ejpam-3412	493	9	of	of	ADP
ejpam-3412	493	10	a	a	DET
ejpam-3412	493	11	music	music	NOUN
ejpam-3412	493	12	,	,	PUNCT
ejpam-3412	493	13	that	that	ADV
ejpam-3412	493	14	is	is	ADV
ejpam-3412	493	15	,	,	PUNCT
ejpam-3412	493	16	a	a	DET
ejpam-3412	493	17	=	=	X
ejpam-3412	493	18	{	{	PUNCT
ejpam-3412	493	19	pop	pop	NOUN
ejpam-3412	493	20	,	,	PUNCT
ejpam-3412	493	21	rock	rock	NOUN
ejpam-3412	493	22	,	,	PUNCT
ejpam-3412	493	23	classic	classic	ADJ
ejpam-3412	493	24	,	,	PUNCT
ejpam-3412	493	25	disco	disco	NOUN
ejpam-3412	493	26	}	}	PUNCT
ejpam-3412	493	27	.	.	PUNCT
ejpam-3412	494	1	define	define	VERB
ejpam-3412	494	2	two	two	NUM
ejpam-3412	494	3	binary	binary	ADJ
ejpam-3412	494	4	operations	operation	NOUN
ejpam-3412	494	5	·	·	PUNCT
ejpam-3412	494	6	and	and	CCONJ
ejpam-3412	494	7	∗	∗	NOUN
ejpam-3412	494	8	on	on	ADP
ejpam-3412	494	9	a	a	PRON
ejpam-3412	494	10	as	as	ADP
ejpam-3412	494	11	the	the	DET
ejpam-3412	494	12	following	follow	VERB
ejpam-3412	494	13	cayley	cayley	ADJ
ejpam-3412	494	14	tables	table	NOUN
ejpam-3412	494	15	:	:	PUNCT
ejpam-3412	494	16	·	·	PUNCT
ejpam-3412	494	17	pop	pop	VERB
ejpam-3412	494	18	rock	rock	NOUN
ejpam-3412	494	19	disco	disco	PROPN
ejpam-3412	494	20	classic	classic	ADJ
ejpam-3412	494	21	pop	pop	NOUN
ejpam-3412	494	22	pop	pop	NOUN
ejpam-3412	494	23	rock	rock	NOUN
ejpam-3412	494	24	disco	disco	PROPN
ejpam-3412	494	25	classic	classic	ADJ
ejpam-3412	494	26	rock	rock	NOUN
ejpam-3412	494	27	pop	pop	NOUN
ejpam-3412	494	28	pop	pop	NOUN
ejpam-3412	494	29	disco	disco	PROPN
ejpam-3412	494	30	disco	disco	PROPN
ejpam-3412	494	31	disco	disco	PROPN
ejpam-3412	494	32	pop	pop	PROPN
ejpam-3412	494	33	rock	rock	NOUN
ejpam-3412	494	34	pop	pop	NOUN
ejpam-3412	494	35	disco	disco	PROPN
ejpam-3412	494	36	classic	classic	ADJ
ejpam-3412	494	37	pop	pop	NOUN
ejpam-3412	494	38	rock	rock	NOUN
ejpam-3412	494	39	pop	pop	NOUN
ejpam-3412	494	40	pop	pop	NOUN
ejpam-3412	494	41	∗	∗	NOUN
ejpam-3412	494	42	pop	pop	NOUN
ejpam-3412	494	43	rock	rock	PROPN
ejpam-3412	494	44	disco	disco	PROPN
ejpam-3412	494	45	classic	classic	ADJ
ejpam-3412	494	46	pop	pop	NOUN
ejpam-3412	494	47	pop	pop	NOUN
ejpam-3412	494	48	pop	pop	NOUN
ejpam-3412	494	49	pop	pop	NOUN
ejpam-3412	494	50	pop	pop	NOUN
ejpam-3412	494	51	rock	rock	NOUN
ejpam-3412	494	52	pop	pop	NOUN
ejpam-3412	494	53	pop	pop	NOUN
ejpam-3412	494	54	pop	pop	NOUN
ejpam-3412	494	55	pop	pop	NOUN
ejpam-3412	494	56	disco	disco	NOUN
ejpam-3412	494	57	pop	pop	NOUN
ejpam-3412	494	58	pop	pop	NOUN
ejpam-3412	494	59	pop	pop	NOUN
ejpam-3412	494	60	pop	pop	NOUN
ejpam-3412	494	61	classic	classic	ADJ
ejpam-3412	494	62	pop	pop	NOUN
ejpam-3412	494	63	pop	pop	NOUN
ejpam-3412	494	64	pop	pop	NOUN
ejpam-3412	494	65	pop	pop	NOUN
ejpam-3412	494	66	then	then	ADV
ejpam-3412	494	67	a	a	PRON
ejpam-3412	494	68	=	=	X
ejpam-3412	494	69	(	(	PUNCT
ejpam-3412	494	70	a	a	PRON
ejpam-3412	494	71	,	,	PUNCT
ejpam-3412	494	72	·	·	PUNCT
ejpam-3412	494	73	,	,	PUNCT
ejpam-3412	494	74	∗	∗	NOUN
ejpam-3412	494	75	,	,	PUNCT
ejpam-3412	494	76	pop	pop	NOUN
ejpam-3412	494	77	)	)	PUNCT
ejpam-3412	494	78	is	be	AUX
ejpam-3412	494	79	an	an	DET
ejpam-3412	494	80	f	f	PROPN
ejpam-3412	494	81	-up	-up	NOUN
ejpam-3412	494	82	-	-	PUNCT
ejpam-3412	494	83	semigroup	semigroup	NOUN
ejpam-3412	494	84	.	.	PUNCT
ejpam-3412	495	1	let	let	AUX
ejpam-3412	495	2	(	(	PUNCT
ejpam-3412	495	3	g̃1	g̃1	NOUN
ejpam-3412	495	4	,	,	PUNCT
ejpam-3412	495	5	e1	e1	PROPN
ejpam-3412	495	6	)	)	PUNCT
ejpam-3412	495	7	and	and	CCONJ
ejpam-3412	495	8	(	(	PUNCT
ejpam-3412	495	9	g̃2	g̃2	PROPN
ejpam-3412	495	10	,	,	PUNCT
ejpam-3412	495	11	e2	e2	PROPN
ejpam-3412	495	12	)	)	PUNCT
ejpam-3412	495	13	be	be	VERB
ejpam-3412	495	14	two	two	NUM
ejpam-3412	495	15	fuzzy	fuzzy	ADJ
ejpam-3412	495	16	soft	soft	ADJ
ejpam-3412	495	17	sets	set	NOUN
ejpam-3412	495	18	over	over	ADP
ejpam-3412	495	19	a	a	DET
ejpam-3412	495	20	where	where	SCONJ
ejpam-3412	495	21	e1	e1	NOUN
ejpam-3412	495	22	:	:	PUNCT
ejpam-3412	495	23	=	=	PRON
ejpam-3412	495	24	{	{	PUNCT
ejpam-3412	495	25	sorrow	sorrow	NOUN
ejpam-3412	495	26	,	,	PUNCT
ejpam-3412	495	27	modernity	modernity	NOUN
ejpam-3412	495	28	}	}	PUNCT
ejpam-3412	495	29	and	and	CCONJ
ejpam-3412	495	30	e2	e2	PROPN
ejpam-3412	495	31	:	:	PUNCT
ejpam-3412	495	32	=	=	SYM
ejpam-3412	495	33	{	{	PUNCT
ejpam-3412	495	34	modernity	modernity	NOUN
ejpam-3412	495	35	,	,	PUNCT
ejpam-3412	495	36	enjoyment	enjoyment	NOUN
ejpam-3412	495	37	}	}	PUNCT
ejpam-3412	495	38	a.	a.	NOUN
ejpam-3412	495	39	satirad	satirad	PROPN
ejpam-3412	495	40	,	,	PUNCT
ejpam-3412	495	41	a.	a.	NOUN
ejpam-3412	495	42	iampan	iampan	PROPN
ejpam-3412	495	43	/	/	SYM
ejpam-3412	495	44	eur	eur	PROPN
ejpam-3412	495	45	.	.	PUNCT
ejpam-3412	496	1	j.	j.	PROPN
ejpam-3412	496	2	pure	pure	PROPN
ejpam-3412	496	3	appl	appl	PROPN
ejpam-3412	496	4	.	.	PROPN
ejpam-3412	496	5	math	math	PROPN
ejpam-3412	496	6	,	,	PUNCT
ejpam-3412	496	7	12	12	NUM
ejpam-3412	496	8	(	(	PUNCT
ejpam-3412	496	9	2	2	NUM
ejpam-3412	496	10	)	)	PUNCT
ejpam-3412	496	11	(	(	PUNCT
ejpam-3412	496	12	2019	2019	NUM
ejpam-3412	496	13	)	)	PUNCT
ejpam-3412	496	14	,	,	PUNCT
ejpam-3412	496	15	294	294	NUM
ejpam-3412	496	16	-	-	SYM
ejpam-3412	496	17	331	331	NUM
ejpam-3412	496	18	315	315	NUM
ejpam-3412	496	19	with	with	ADP
ejpam-3412	496	20	g̃1[sorrow	g̃1[sorrow	PROPN
ejpam-3412	496	21	]	]	NOUN
ejpam-3412	496	22	,	,	PUNCT
ejpam-3412	496	23	g̃1[modernity	g̃1[modernity	NOUN
ejpam-3412	496	24	]	]	X
ejpam-3412	496	25	,	,	PUNCT
ejpam-3412	496	26	g̃2[modernity	g̃2[modernity	NOUN
ejpam-3412	496	27	]	]	PUNCT
ejpam-3412	496	28	,	,	PUNCT
ejpam-3412	496	29	and	and	CCONJ
ejpam-3412	496	30	g̃2[enjoyment	g̃2[enjoyment	NOUN
ejpam-3412	496	31	]	]	X
ejpam-3412	496	32	are	be	AUX
ejpam-3412	496	33	fuzzy	fuzzy	ADJ
ejpam-3412	496	34	sets	set	NOUN
ejpam-3412	496	35	in	in	ADP
ejpam-3412	496	36	a	a	DET
ejpam-3412	496	37	defined	define	VERB
ejpam-3412	496	38	as	as	SCONJ
ejpam-3412	496	39	follows	follow	VERB
ejpam-3412	496	40	:	:	PUNCT
ejpam-3412	496	41	g̃1	g̃1	NOUN
ejpam-3412	496	42	pop	pop	NOUN
ejpam-3412	496	43	rock	rock	NOUN
ejpam-3412	496	44	disco	disco	PROPN
ejpam-3412	496	45	classic	classic	ADJ
ejpam-3412	496	46	sorrow	sorrow	NOUN
ejpam-3412	496	47	0.7	0.7	NUM
ejpam-3412	496	48	0.7	0.7	NUM
ejpam-3412	496	49	0.5	0.5	NUM
ejpam-3412	496	50	0.5	0.5	NUM
ejpam-3412	496	51	modernity	modernity	NOUN
ejpam-3412	496	52	0.9	0.9	NUM
ejpam-3412	496	53	0.8	0.8	NUM
ejpam-3412	496	54	0.3	0.3	NUM
ejpam-3412	496	55	0.3	0.3	NUM
ejpam-3412	496	56	g̃2	g̃2	PROPN
ejpam-3412	496	57	pop	pop	NOUN
ejpam-3412	496	58	rock	rock	NOUN
ejpam-3412	496	59	disco	disco	NOUN
ejpam-3412	496	60	classic	classic	ADJ
ejpam-3412	496	61	modernity	modernity	NOUN
ejpam-3412	496	62	0.8	0.8	NUM
ejpam-3412	496	63	0.3	0.3	NUM
ejpam-3412	496	64	0.4	0.4	NUM
ejpam-3412	496	65	0.5	0.5	NUM
ejpam-3412	496	66	enjoyment	enjoyment	NOUN
ejpam-3412	496	67	1	1	NUM
ejpam-3412	496	68	0.9	0.9	NUM
ejpam-3412	496	69	0.1	0.1	NUM
ejpam-3412	496	70	0.1	0.1	NUM
ejpam-3412	496	71	then	then	ADV
ejpam-3412	496	72	(	(	PUNCT
ejpam-3412	496	73	g̃1	g̃1	NOUN
ejpam-3412	496	74	,	,	PUNCT
ejpam-3412	496	75	e1	e1	PROPN
ejpam-3412	496	76	)	)	PUNCT
ejpam-3412	496	77	and	and	CCONJ
ejpam-3412	496	78	(	(	PUNCT
ejpam-3412	496	79	g̃2	g̃2	PROPN
ejpam-3412	496	80	,	,	PUNCT
ejpam-3412	496	81	e2	e2	PROPN
ejpam-3412	496	82	)	)	PUNCT
ejpam-3412	496	83	are	be	AUX
ejpam-3412	496	84	two	two	NUM
ejpam-3412	496	85	fuzzy	fuzzy	ADJ
ejpam-3412	496	86	soft	soft	ADJ
ejpam-3412	496	87	upi	upi	NOUN
ejpam-3412	496	88	-	-	PUNCT
ejpam-3412	496	89	subalgebras	subalgebras	PROPN
ejpam-3412	496	90	of	of	ADP
ejpam-3412	496	91	a.	a.	NOUN
ejpam-3412	496	92	since	since	SCONJ
ejpam-3412	496	93	modernity	modernity	NOUN
ejpam-3412	496	94	∈	∈	NOUN
ejpam-3412	496	95	e1	e1	NOUN
ejpam-3412	496	96	∩	∩	PROPN
ejpam-3412	496	97	e2	e2	PROPN
ejpam-3412	496	98	,	,	PUNCT
ejpam-3412	496	99	we	we	PRON
ejpam-3412	496	100	have	have	VERB
ejpam-3412	496	101	(	(	PUNCT
ejpam-3412	496	102	f	f	NOUN
ejpam-3412	496	103	g̃1[modernity]∪g̃2[modernity	g̃1[modernity]∪g̃2[modernity	PROPN
ejpam-3412	496	104	]	]	PUNCT
ejpam-3412	496	105	)	)	PUNCT
ejpam-3412	496	106	(	(	PUNCT
ejpam-3412	496	107	rock	rock	NOUN
ejpam-3412	496	108	·	·	SYM
ejpam-3412	496	109	classic	classic	NOUN
ejpam-3412	496	110	)	)	PUNCT
ejpam-3412	496	111	=	=	PUNCT
ejpam-3412	497	1	(	(	PUNCT
ejpam-3412	497	2	f	f	NOUN
ejpam-3412	497	3	g̃1[modernity]∪g̃2[modernity	g̃1[modernity]∪g̃2[modernity	NOUN
ejpam-3412	497	4	]	]	PUNCT
ejpam-3412	497	5	)	)	PUNCT
ejpam-3412	497	6	(	(	PUNCT
ejpam-3412	497	7	disco	disco	NOUN
ejpam-3412	497	8	)	)	PUNCT
ejpam-3412	497	9	=	=	SYM
ejpam-3412	497	10	0.4	0.4	NUM
ejpam-3412	497	11	�	�	PROPN
ejpam-3412	497	12	0.5	0.5	NUM
ejpam-3412	497	13	=	=	SYM
ejpam-3412	497	14	min{0.8	min{0.8	PROPN
ejpam-3412	497	15	,	,	PUNCT
ejpam-3412	497	16	0.5	0.5	NUM
ejpam-3412	497	17	}	}	PUNCT
ejpam-3412	497	18	=	=	SYM
ejpam-3412	497	19	min{(f	min{(f	NOUN
ejpam-3412	497	20	g̃1[modernity]∪g̃2[modernity	g̃1[modernity]∪g̃2[modernity	NOUN
ejpam-3412	497	21	]	]	PUNCT
ejpam-3412	497	22	)	)	PUNCT
ejpam-3412	497	23	(	(	PUNCT
ejpam-3412	497	24	rock	rock	NOUN
ejpam-3412	497	25	)	)	PUNCT
ejpam-3412	497	26	,	,	PUNCT
ejpam-3412	497	27	(	(	PUNCT
ejpam-3412	497	28	f	f	PROPN
ejpam-3412	497	29	g̃1[modernity]∪g̃2[modernity	g̃1[modernity]∪g̃2[modernity	NOUN
ejpam-3412	497	30	]	]	PUNCT
ejpam-3412	497	31	)	)	PUNCT
ejpam-3412	497	32	(	(	PUNCT
ejpam-3412	497	33	classic	classic	NOUN
ejpam-3412	497	34	)	)	PUNCT
ejpam-3412	497	35	}	}	PUNCT
ejpam-3412	497	36	.	.	PUNCT
ejpam-3412	498	1	thus	thus	ADV
ejpam-3412	498	2	g̃1[modernity]∪	g̃1[modernity]∪	VERB
ejpam-3412	498	3	g̃2[modernity	g̃2[modernity	NOUN
ejpam-3412	498	4	]	]	PUNCT
ejpam-3412	498	5	is	be	AUX
ejpam-3412	498	6	not	not	PART
ejpam-3412	498	7	a	a	DET
ejpam-3412	498	8	fuzzy	fuzzy	ADJ
ejpam-3412	498	9	upi	upi	NOUN
ejpam-3412	498	10	-	-	PUNCT
ejpam-3412	498	11	subalgebra	subalgebra	NOUN
ejpam-3412	498	12	of	of	ADP
ejpam-3412	498	13	a	a	DET
ejpam-3412	498	14	,	,	PUNCT
ejpam-3412	498	15	that	that	ADV
ejpam-3412	498	16	is	is	ADV
ejpam-3412	498	17	,	,	PUNCT
ejpam-3412	498	18	(	(	PUNCT
ejpam-3412	498	19	g̃1	g̃1	NOUN
ejpam-3412	498	20	,	,	PUNCT
ejpam-3412	498	21	e1)∪	e1)∪	PROPN
ejpam-3412	498	22	(	(	PUNCT
ejpam-3412	498	23	g̃2	g̃2	PROPN
ejpam-3412	498	24	,	,	PUNCT
ejpam-3412	498	25	e2	e2	PROPN
ejpam-3412	498	26	)	)	PUNCT
ejpam-3412	498	27	is	be	AUX
ejpam-3412	498	28	not	not	PART
ejpam-3412	498	29	a	a	DET
ejpam-3412	498	30	modernity	modernity	NOUN
ejpam-3412	498	31	-	-	PUNCT
ejpam-3412	498	32	fuzzy	fuzzy	ADJ
ejpam-3412	498	33	soft	soft	ADJ
ejpam-3412	498	34	upi	upi	NOUN
ejpam-3412	498	35	-	-	PUNCT
ejpam-3412	498	36	subalgebra	subalgebra	NOUN
ejpam-3412	498	37	of	of	ADP
ejpam-3412	498	38	a.	a.	NOUN
ejpam-3412	498	39	hence	hence	ADV
ejpam-3412	498	40	,	,	PUNCT
ejpam-3412	498	41	(	(	PUNCT
ejpam-3412	498	42	g̃1	g̃1	NOUN
ejpam-3412	498	43	,	,	PUNCT
ejpam-3412	498	44	e1	e1	NOUN
ejpam-3412	498	45	)	)	PUNCT
ejpam-3412	498	46	∪	∪	NOUN
ejpam-3412	498	47	(	(	PUNCT
ejpam-3412	498	48	g̃2	g̃2	PROPN
ejpam-3412	498	49	,	,	PUNCT
ejpam-3412	498	50	e2	e2	PROPN
ejpam-3412	498	51	)	)	PUNCT
ejpam-3412	498	52	is	be	AUX
ejpam-3412	498	53	not	not	PART
ejpam-3412	498	54	a	a	DET
ejpam-3412	498	55	fuzzy	fuzzy	ADJ
ejpam-3412	498	56	soft	soft	ADJ
ejpam-3412	498	57	upi	upi	NOUN
ejpam-3412	498	58	-	-	PUNCT
ejpam-3412	498	59	subalgebra	subalgebra	NOUN
ejpam-3412	498	60	of	of	ADP
ejpam-3412	498	61	a.	a.	NOUN
ejpam-3412	498	62	moreover	moreover	ADV
ejpam-3412	498	63	,	,	PUNCT
ejpam-3412	498	64	(	(	PUNCT
ejpam-3412	498	65	g̃1	g̃1	NOUN
ejpam-3412	498	66	,	,	PUNCT
ejpam-3412	498	67	e1	e1	NOUN
ejpam-3412	498	68	)	)	PUNCT
ejpam-3412	498	69	d	d	NOUN
ejpam-3412	498	70	(	(	PUNCT
ejpam-3412	498	71	g̃2	g̃2	PROPN
ejpam-3412	498	72	,	,	PUNCT
ejpam-3412	498	73	e2	e2	PROPN
ejpam-3412	498	74	)	)	PUNCT
ejpam-3412	498	75	is	be	AUX
ejpam-3412	498	76	not	not	PART
ejpam-3412	498	77	a	a	DET
ejpam-3412	498	78	fuzzy	fuzzy	ADJ
ejpam-3412	498	79	soft	soft	ADJ
ejpam-3412	498	80	upi	upi	NOUN
ejpam-3412	498	81	-	-	PUNCT
ejpam-3412	498	82	subalgebra	subalgebra	NOUN
ejpam-3412	498	83	of	of	ADP
ejpam-3412	498	84	a.	a.	NOUN
ejpam-3412	498	85	3.3	3.3	NUM
ejpam-3412	498	86	.	.	PUNCT
ejpam-3412	499	1	fuzzy	fuzzy	ADJ
ejpam-3412	499	2	soft	soft	ADJ
ejpam-3412	499	3	near	near	ADP
ejpam-3412	499	4	ups	up	NOUN
ejpam-3412	499	5	-	-	PUNCT
ejpam-3412	499	6	filters	filter	NOUN
ejpam-3412	499	7	definition	definition	NOUN
ejpam-3412	499	8	20	20	NUM
ejpam-3412	499	9	.	.	PUNCT
ejpam-3412	500	1	a	a	DET
ejpam-3412	500	2	fuzzy	fuzzy	ADJ
ejpam-3412	500	3	soft	soft	ADJ
ejpam-3412	500	4	set	set	NOUN
ejpam-3412	500	5	(	(	PUNCT
ejpam-3412	500	6	f̃	f̃	PROPN
ejpam-3412	500	7	,	,	PUNCT
ejpam-3412	500	8	e	e	NOUN
ejpam-3412	500	9	)	)	PUNCT
ejpam-3412	500	10	over	over	ADP
ejpam-3412	500	11	a	a	PRON
ejpam-3412	500	12	is	be	AUX
ejpam-3412	500	13	called	call	VERB
ejpam-3412	500	14	a	a	DET
ejpam-3412	500	15	fuzzy	fuzzy	ADJ
ejpam-3412	500	16	soft	soft	ADJ
ejpam-3412	500	17	near	near	ADP
ejpam-3412	500	18	ups	up	NOUN
ejpam-3412	500	19	-	-	PUNCT
ejpam-3412	500	20	filter	filter	NOUN
ejpam-3412	500	21	based	base	VERB
ejpam-3412	500	22	on	on	ADP
ejpam-3412	500	23	e	e	PROPN
ejpam-3412	500	24	∈	∈	PROPN
ejpam-3412	500	25	e	e	X
ejpam-3412	500	26	(	(	PUNCT
ejpam-3412	500	27	we	we	PRON
ejpam-3412	500	28	shortly	shortly	ADV
ejpam-3412	500	29	call	call	VERB
ejpam-3412	500	30	an	an	DET
ejpam-3412	500	31	e	e	NOUN
ejpam-3412	500	32	-	-	ADJ
ejpam-3412	500	33	fuzzy	fuzzy	ADJ
ejpam-3412	500	34	soft	soft	ADJ
ejpam-3412	500	35	near	near	ADP
ejpam-3412	500	36	ups	up	NOUN
ejpam-3412	500	37	-	-	PUNCT
ejpam-3412	500	38	filter	filter	NOUN
ejpam-3412	500	39	)	)	PUNCT
ejpam-3412	500	40	of	of	ADP
ejpam-3412	500	41	a	a	DET
ejpam-3412	500	42	if	if	SCONJ
ejpam-3412	500	43	a	a	DET
ejpam-3412	500	44	fuzzy	fuzzy	ADJ
ejpam-3412	500	45	set	set	NOUN
ejpam-3412	500	46	f̃[e	f̃[e	X
ejpam-3412	500	47	]	]	X
ejpam-3412	500	48	in	in	ADP
ejpam-3412	500	49	a	a	PRON
ejpam-3412	500	50	is	be	AUX
ejpam-3412	500	51	a	a	DET
ejpam-3412	500	52	fuzzy	fuzzy	ADJ
ejpam-3412	500	53	near	near	ADP
ejpam-3412	500	54	ups	up	NOUN
ejpam-3412	500	55	-	-	PUNCT
ejpam-3412	500	56	filter	filter	NOUN
ejpam-3412	500	57	of	of	ADP
ejpam-3412	500	58	a.	a.	NOUN
ejpam-3412	500	59	if	if	SCONJ
ejpam-3412	500	60	(	(	PUNCT
ejpam-3412	500	61	f̃	f̃	PROPN
ejpam-3412	500	62	,	,	PUNCT
ejpam-3412	500	63	e	e	NOUN
ejpam-3412	500	64	)	)	PUNCT
ejpam-3412	500	65	is	be	AUX
ejpam-3412	500	66	an	an	DET
ejpam-3412	500	67	e	e	ADJ
ejpam-3412	500	68	-	-	ADJ
ejpam-3412	500	69	fuzzy	fuzzy	ADJ
ejpam-3412	500	70	soft	soft	ADJ
ejpam-3412	500	71	near	near	ADP
ejpam-3412	500	72	ups	up	NOUN
ejpam-3412	500	73	-	-	PUNCT
ejpam-3412	500	74	filter	filter	NOUN
ejpam-3412	500	75	of	of	ADP
ejpam-3412	500	76	a	a	PRON
ejpam-3412	500	77	for	for	ADP
ejpam-3412	500	78	all	all	DET
ejpam-3412	500	79	e	e	NOUN
ejpam-3412	500	80	∈	∈	PROPN
ejpam-3412	500	81	e	e	NOUN
ejpam-3412	500	82	,	,	PUNCT
ejpam-3412	500	83	we	we	PRON
ejpam-3412	500	84	say	say	VERB
ejpam-3412	500	85	that	that	SCONJ
ejpam-3412	500	86	(	(	PUNCT
ejpam-3412	500	87	f̃	f̃	PROPN
ejpam-3412	500	88	,	,	PUNCT
ejpam-3412	500	89	e	e	NOUN
ejpam-3412	500	90	)	)	PUNCT
ejpam-3412	500	91	is	be	AUX
ejpam-3412	500	92	a	a	DET
ejpam-3412	500	93	fuzzy	fuzzy	ADJ
ejpam-3412	500	94	soft	soft	ADJ
ejpam-3412	500	95	near	near	ADP
ejpam-3412	500	96	ups	up	NOUN
ejpam-3412	500	97	-	-	PUNCT
ejpam-3412	500	98	filter	filter	NOUN
ejpam-3412	500	99	of	of	ADP
ejpam-3412	500	100	a.	a.	NOUN
ejpam-3412	500	101	in	in	ADP
ejpam-3412	500	102	the	the	DET
ejpam-3412	500	103	next	next	ADJ
ejpam-3412	500	104	theorem	theorem	NOUN
ejpam-3412	500	105	,	,	PUNCT
ejpam-3412	500	106	we	we	PRON
ejpam-3412	500	107	give	give	VERB
ejpam-3412	500	108	necessary	necessary	ADJ
ejpam-3412	500	109	condition	condition	NOUN
ejpam-3412	500	110	for	for	ADP
ejpam-3412	500	111	fuzzy	fuzzy	ADJ
ejpam-3412	500	112	soft	soft	ADJ
ejpam-3412	500	113	near	near	ADP
ejpam-3412	500	114	ups	up	NOUN
ejpam-3412	500	115	-	-	PUNCT
ejpam-3412	500	116	filters	filter	NOUN
ejpam-3412	500	117	of	of	ADP
ejpam-3412	500	118	f	f	PROPN
ejpam-3412	500	119	-up	-up	NOUN
ejpam-3412	500	120	-	-	PUNCT
ejpam-3412	500	121	semigroups	semigroup	NOUN
ejpam-3412	500	122	.	.	PUNCT
ejpam-3412	501	1	theorem	theorem	NOUN
ejpam-3412	501	2	29	29	NUM
ejpam-3412	501	3	.	.	PUNCT
ejpam-3412	502	1	if	if	SCONJ
ejpam-3412	502	2	(	(	PUNCT
ejpam-3412	502	3	f̃	f̃	PROPN
ejpam-3412	502	4	,	,	PUNCT
ejpam-3412	502	5	e	e	NOUN
ejpam-3412	502	6	)	)	PUNCT
ejpam-3412	502	7	is	be	AUX
ejpam-3412	502	8	a	a	DET
ejpam-3412	502	9	fuzzy	fuzzy	ADJ
ejpam-3412	502	10	soft	soft	ADJ
ejpam-3412	502	11	set	set	NOUN
ejpam-3412	502	12	over	over	ADP
ejpam-3412	502	13	a	a	DET
ejpam-3412	502	14	such	such	ADJ
ejpam-3412	502	15	that	that	PRON
ejpam-3412	502	16	for	for	ADP
ejpam-3412	502	17	all	all	DET
ejpam-3412	502	18	e	e	NOUN
ejpam-3412	502	19	∈	∈	PROPN
ejpam-3412	502	20	e	e	NOUN
ejpam-3412	502	21	,	,	PUNCT
ejpam-3412	502	22	a	a	DET
ejpam-3412	502	23	fuzzy	fuzzy	ADJ
ejpam-3412	502	24	set	set	NOUN
ejpam-3412	502	25	f̃[e	f̃[e	NOUN
ejpam-3412	502	26	]	]	X
ejpam-3412	502	27	in	in	ADP
ejpam-3412	502	28	a	a	DET
ejpam-3412	502	29	satisfies	satisfie	NOUN
ejpam-3412	502	30	the	the	DET
ejpam-3412	502	31	conditions	condition	NOUN
ejpam-3412	502	32	(	(	PUNCT
ejpam-3412	502	33	2.2	2.2	NUM
ejpam-3412	502	34	)	)	PUNCT
ejpam-3412	502	35	and	and	CCONJ
ejpam-3412	502	36	(	(	PUNCT
ejpam-3412	502	37	1.14	1.14	NUM
ejpam-3412	502	38	)	)	PUNCT
ejpam-3412	502	39	,	,	PUNCT
ejpam-3412	502	40	then	then	ADV
ejpam-3412	502	41	(	(	PUNCT
ejpam-3412	502	42	f̃	f̃	PROPN
ejpam-3412	502	43	,	,	PUNCT
ejpam-3412	502	44	e	e	NOUN
ejpam-3412	502	45	)	)	PUNCT
ejpam-3412	502	46	is	be	AUX
ejpam-3412	502	47	a	a	DET
ejpam-3412	502	48	fuzzy	fuzzy	ADJ
ejpam-3412	502	49	soft	soft	ADJ
ejpam-3412	502	50	near	near	ADP
ejpam-3412	502	51	ups	up	NOUN
ejpam-3412	502	52	-	-	PUNCT
ejpam-3412	502	53	filter	filter	NOUN
ejpam-3412	502	54	of	of	ADP
ejpam-3412	502	55	a.	a.	NOUN
ejpam-3412	502	56	proof	proof	NOUN
ejpam-3412	502	57	.	.	PUNCT
ejpam-3412	503	1	it	it	PRON
ejpam-3412	503	2	is	be	AUX
ejpam-3412	503	3	straightforward	straightforward	ADJ
ejpam-3412	503	4	by	by	ADP
ejpam-3412	503	5	proposition	proposition	NOUN
ejpam-3412	503	6	5	5	NUM
ejpam-3412	503	7	and	and	CCONJ
ejpam-3412	503	8	lemma	lemma	PROPN
ejpam-3412	503	9	1	1	NUM
ejpam-3412	503	10	(	(	PUNCT
ejpam-3412	503	11	1	1	NUM
ejpam-3412	503	12	)	)	PUNCT
ejpam-3412	503	13	.	.	PUNCT
ejpam-3412	504	1	from	from	ADP
ejpam-3412	504	2	figure	figure	NOUN
ejpam-3412	504	3	1	1	NUM
ejpam-3412	504	4	,	,	PUNCT
ejpam-3412	504	5	we	we	PRON
ejpam-3412	504	6	have	have	VERB
ejpam-3412	504	7	the	the	DET
ejpam-3412	504	8	following	follow	VERB
ejpam-3412	504	9	theorem	theorem	VERB
ejpam-3412	504	10	.	.	PUNCT
ejpam-3412	504	11	theorem	theorem	NOUN
ejpam-3412	504	12	30	30	NUM
ejpam-3412	504	13	.	.	PUNCT
ejpam-3412	505	1	every	every	DET
ejpam-3412	505	2	e	e	ADJ
ejpam-3412	505	3	-	-	ADJ
ejpam-3412	505	4	fuzzy	fuzzy	ADJ
ejpam-3412	505	5	soft	soft	ADJ
ejpam-3412	505	6	near	near	ADP
ejpam-3412	505	7	ups	up	NOUN
ejpam-3412	505	8	-	-	PUNCT
ejpam-3412	505	9	filter	filter	NOUN
ejpam-3412	505	10	of	of	ADP
ejpam-3412	505	11	a	a	PRON
ejpam-3412	505	12	is	be	AUX
ejpam-3412	505	13	an	an	DET
ejpam-3412	505	14	e	e	ADJ
ejpam-3412	505	15	-	-	ADJ
ejpam-3412	505	16	fuzzy	fuzzy	ADJ
ejpam-3412	505	17	soft	soft	ADJ
ejpam-3412	505	18	ups	up	NOUN
ejpam-3412	505	19	-	-	PUNCT
ejpam-3412	505	20	subalgebra	subalgebra	NOUN
ejpam-3412	505	21	.	.	PUNCT
ejpam-3412	506	1	moreover	moreover	ADV
ejpam-3412	506	2	,	,	PUNCT
ejpam-3412	506	3	every	every	DET
ejpam-3412	506	4	fuzzy	fuzzy	ADJ
ejpam-3412	506	5	soft	soft	ADJ
ejpam-3412	506	6	near	near	ADP
ejpam-3412	506	7	ups	up	NOUN
ejpam-3412	506	8	-	-	PUNCT
ejpam-3412	506	9	filter	filter	NOUN
ejpam-3412	506	10	of	of	ADP
ejpam-3412	506	11	a	a	PRON
ejpam-3412	506	12	is	be	AUX
ejpam-3412	506	13	a	a	DET
ejpam-3412	506	14	fuzzy	fuzzy	ADJ
ejpam-3412	506	15	soft	soft	ADJ
ejpam-3412	506	16	ups	up	NOUN
ejpam-3412	506	17	-	-	PUNCT
ejpam-3412	506	18	subalgebra	subalgebra	NOUN
ejpam-3412	506	19	.	.	PUNCT
ejpam-3412	507	1	the	the	DET
ejpam-3412	507	2	following	follow	VERB
ejpam-3412	507	3	example	example	NOUN
ejpam-3412	507	4	shows	show	VERB
ejpam-3412	507	5	that	that	SCONJ
ejpam-3412	507	6	the	the	DET
ejpam-3412	507	7	converse	converse	NOUN
ejpam-3412	507	8	of	of	ADP
ejpam-3412	507	9	theorem	theorem	ADJ
ejpam-3412	507	10	30	30	NUM
ejpam-3412	507	11	is	be	AUX
ejpam-3412	507	12	not	not	PART
ejpam-3412	507	13	true	true	ADJ
ejpam-3412	507	14	.	.	PUNCT
ejpam-3412	508	1	a.	a.	PROPN
ejpam-3412	508	2	satirad	satirad	PROPN
ejpam-3412	508	3	,	,	PUNCT
ejpam-3412	508	4	a.	a.	NOUN
ejpam-3412	508	5	iampan	iampan	PROPN
ejpam-3412	508	6	/	/	SYM
ejpam-3412	508	7	eur	eur	PROPN
ejpam-3412	508	8	.	.	PUNCT
ejpam-3412	509	1	j.	j.	PROPN
ejpam-3412	509	2	pure	pure	PROPN
ejpam-3412	509	3	appl	appl	PROPN
ejpam-3412	509	4	.	.	PROPN
ejpam-3412	509	5	math	math	PROPN
ejpam-3412	509	6	,	,	PUNCT
ejpam-3412	509	7	12	12	NUM
ejpam-3412	509	8	(	(	PUNCT
ejpam-3412	509	9	2	2	NUM
ejpam-3412	509	10	)	)	PUNCT
ejpam-3412	509	11	(	(	PUNCT
ejpam-3412	509	12	2019	2019	NUM
ejpam-3412	509	13	)	)	PUNCT
ejpam-3412	509	14	,	,	PUNCT
ejpam-3412	509	15	294	294	NUM
ejpam-3412	509	16	-	-	SYM
ejpam-3412	509	17	331	331	NUM
ejpam-3412	509	18	316	316	NUM
ejpam-3412	509	19	example	example	NOUN
ejpam-3412	509	20	17	17	NUM
ejpam-3412	509	21	.	.	PUNCT
ejpam-3412	510	1	let	let	VERB
ejpam-3412	510	2	a	a	DET
ejpam-3412	510	3	be	be	AUX
ejpam-3412	510	4	a	a	DET
ejpam-3412	510	5	set	set	NOUN
ejpam-3412	510	6	of	of	ADP
ejpam-3412	510	7	four	four	NUM
ejpam-3412	510	8	foods	food	NOUN
ejpam-3412	510	9	,	,	PUNCT
ejpam-3412	510	10	that	that	ADV
ejpam-3412	510	11	is	is	ADV
ejpam-3412	510	12	,	,	PUNCT
ejpam-3412	510	13	a	a	DET
ejpam-3412	510	14	=	=	X
ejpam-3412	510	15	{	{	PUNCT
ejpam-3412	510	16	apple	apple	NOUN
ejpam-3412	510	17	,	,	PUNCT
ejpam-3412	510	18	banana	banana	NOUN
ejpam-3412	510	19	,	,	PUNCT
ejpam-3412	510	20	meat	meat	NOUN
ejpam-3412	510	21	,	,	PUNCT
ejpam-3412	510	22	rice	rice	NOUN
ejpam-3412	510	23	}	}	PUNCT
ejpam-3412	510	24	.	.	PUNCT
ejpam-3412	511	1	define	define	VERB
ejpam-3412	511	2	two	two	NUM
ejpam-3412	511	3	binary	binary	ADJ
ejpam-3412	511	4	operations	operation	NOUN
ejpam-3412	511	5	·	·	PUNCT
ejpam-3412	511	6	and	and	CCONJ
ejpam-3412	511	7	∗	∗	NOUN
ejpam-3412	511	8	on	on	ADP
ejpam-3412	511	9	a	a	PRON
ejpam-3412	511	10	as	as	ADP
ejpam-3412	511	11	the	the	DET
ejpam-3412	511	12	following	follow	VERB
ejpam-3412	511	13	cayley	cayley	ADJ
ejpam-3412	511	14	tables	table	NOUN
ejpam-3412	511	15	:	:	PUNCT
ejpam-3412	511	16	·	·	PUNCT
ejpam-3412	511	17	rice	rice	NOUN
ejpam-3412	511	18	apple	apple	NOUN
ejpam-3412	511	19	banana	banana	NOUN
ejpam-3412	511	20	meat	meat	NOUN
ejpam-3412	511	21	rice	rice	NOUN
ejpam-3412	511	22	rice	rice	NOUN
ejpam-3412	511	23	apple	apple	NOUN
ejpam-3412	511	24	banana	banana	NOUN
ejpam-3412	511	25	meat	meat	NOUN
ejpam-3412	511	26	apple	apple	NOUN
ejpam-3412	511	27	rice	rice	NOUN
ejpam-3412	511	28	rice	rice	NOUN
ejpam-3412	511	29	apple	apple	NOUN
ejpam-3412	511	30	meat	meat	NOUN
ejpam-3412	511	31	banana	banana	NOUN
ejpam-3412	511	32	rice	rice	PROPN
ejpam-3412	511	33	rice	rice	NOUN
ejpam-3412	511	34	rice	rice	NOUN
ejpam-3412	511	35	meat	meat	NOUN
ejpam-3412	511	36	meat	meat	NOUN
ejpam-3412	511	37	rice	rice	NOUN
ejpam-3412	511	38	apple	apple	NOUN
ejpam-3412	511	39	apple	apple	NOUN
ejpam-3412	511	40	rice	rice	NOUN
ejpam-3412	511	41	∗	∗	NOUN
ejpam-3412	511	42	rice	rice	NOUN
ejpam-3412	511	43	apple	apple	NOUN
ejpam-3412	511	44	banana	banana	NOUN
ejpam-3412	511	45	meat	meat	NOUN
ejpam-3412	511	46	rice	rice	NOUN
ejpam-3412	511	47	rice	rice	PROPN
ejpam-3412	511	48	rice	rice	PROPN
ejpam-3412	511	49	rice	rice	PROPN
ejpam-3412	511	50	rice	rice	PROPN
ejpam-3412	511	51	apple	apple	PROPN
ejpam-3412	511	52	rice	rice	PROPN
ejpam-3412	511	53	rice	rice	PROPN
ejpam-3412	511	54	rice	rice	PROPN
ejpam-3412	511	55	rice	rice	PROPN
ejpam-3412	511	56	banana	banana	PROPN
ejpam-3412	511	57	rice	rice	PROPN
ejpam-3412	511	58	rice	rice	PROPN
ejpam-3412	511	59	rice	rice	PROPN
ejpam-3412	511	60	rice	rice	NOUN
ejpam-3412	511	61	meat	meat	NOUN
ejpam-3412	511	62	rice	rice	NOUN
ejpam-3412	511	63	rice	rice	NOUN
ejpam-3412	511	64	rice	rice	NOUN
ejpam-3412	511	65	apple	apple	NOUN
ejpam-3412	511	66	then	then	ADV
ejpam-3412	511	67	a	a	DET
ejpam-3412	511	68	=	=	X
ejpam-3412	511	69	(	(	PUNCT
ejpam-3412	511	70	a	a	PRON
ejpam-3412	511	71	,	,	PUNCT
ejpam-3412	511	72	·	·	PUNCT
ejpam-3412	511	73	,	,	PUNCT
ejpam-3412	511	74	∗	∗	NOUN
ejpam-3412	511	75	,	,	PUNCT
ejpam-3412	511	76	rice	rice	NOUN
ejpam-3412	511	77	)	)	PUNCT
ejpam-3412	511	78	is	be	AUX
ejpam-3412	511	79	an	an	DET
ejpam-3412	511	80	f	f	PROPN
ejpam-3412	511	81	-up	-up	NOUN
ejpam-3412	511	82	-	-	PUNCT
ejpam-3412	511	83	semigroup	semigroup	NOUN
ejpam-3412	511	84	.	.	PUNCT
ejpam-3412	512	1	let	let	AUX
ejpam-3412	512	2	(	(	PUNCT
ejpam-3412	512	3	f̃	f̃	PROPN
ejpam-3412	512	4	,	,	PUNCT
ejpam-3412	512	5	e	e	NOUN
ejpam-3412	512	6	)	)	PUNCT
ejpam-3412	512	7	be	be	AUX
ejpam-3412	512	8	a	a	DET
ejpam-3412	512	9	fuzzy	fuzzy	ADJ
ejpam-3412	512	10	soft	soft	ADJ
ejpam-3412	512	11	set	set	NOUN
ejpam-3412	512	12	over	over	ADP
ejpam-3412	512	13	a	a	DET
ejpam-3412	512	14	where	where	SCONJ
ejpam-3412	512	15	e	e	NOUN
ejpam-3412	512	16	:	:	PUNCT
ejpam-3412	512	17	=	=	SYM
ejpam-3412	512	18	{	{	PUNCT
ejpam-3412	512	19	pig	pig	NOUN
ejpam-3412	512	20	,	,	PUNCT
ejpam-3412	512	21	monkey	monkey	NOUN
ejpam-3412	512	22	,	,	PUNCT
ejpam-3412	512	23	chicken	chicken	PROPN
ejpam-3412	512	24	}	}	PUNCT
ejpam-3412	512	25	with	with	ADP
ejpam-3412	512	26	f̃[pig	f̃[pig	PROPN
ejpam-3412	512	27	]	]	PUNCT
ejpam-3412	512	28	,	,	PUNCT
ejpam-3412	512	29	f̃[monkey	f̃[monkey	PROPN
ejpam-3412	512	30	]	]	PUNCT
ejpam-3412	512	31	,	,	PUNCT
ejpam-3412	512	32	and	and	CCONJ
ejpam-3412	512	33	f̃[chicken	f̃[chicken	PROPN
ejpam-3412	512	34	]	]	PUNCT
ejpam-3412	512	35	are	be	AUX
ejpam-3412	512	36	fuzzy	fuzzy	ADJ
ejpam-3412	512	37	sets	set	NOUN
ejpam-3412	512	38	in	in	ADP
ejpam-3412	512	39	a	a	DET
ejpam-3412	512	40	defined	define	VERB
ejpam-3412	512	41	as	as	SCONJ
ejpam-3412	512	42	follows	follow	VERB
ejpam-3412	512	43	:	:	PUNCT
ejpam-3412	512	44	f̃	f̃	PROPN
ejpam-3412	512	45	rice	rice	NOUN
ejpam-3412	512	46	apple	apple	NOUN
ejpam-3412	512	47	banana	banana	NOUN
ejpam-3412	512	48	meat	meat	NOUN
ejpam-3412	512	49	pig	pig	NOUN
ejpam-3412	512	50	1	1	NUM
ejpam-3412	512	51	0.8	0.8	NUM
ejpam-3412	512	52	0.9	0.9	NUM
ejpam-3412	512	53	0.3	0.3	NUM
ejpam-3412	512	54	monkey	monkey	NOUN
ejpam-3412	512	55	0.8	0.8	NUM
ejpam-3412	512	56	0.4	0.4	NUM
ejpam-3412	512	57	0.8	0.8	NUM
ejpam-3412	512	58	0.3	0.3	NUM
ejpam-3412	512	59	chicken	chicken	NOUN
ejpam-3412	512	60	0.7	0.7	NUM
ejpam-3412	512	61	0.4	0.4	NUM
ejpam-3412	512	62	0.3	0.3	NUM
ejpam-3412	512	63	0.2	0.2	NUM
ejpam-3412	512	64	then	then	ADV
ejpam-3412	512	65	(	(	PUNCT
ejpam-3412	512	66	f̃	f̃	PROPN
ejpam-3412	512	67	,	,	PUNCT
ejpam-3412	512	68	e	e	NOUN
ejpam-3412	512	69	)	)	PUNCT
ejpam-3412	512	70	is	be	AUX
ejpam-3412	512	71	a	a	DET
ejpam-3412	512	72	pig	pig	NOUN
ejpam-3412	512	73	-	-	PUNCT
ejpam-3412	512	74	fuzzy	fuzzy	ADJ
ejpam-3412	512	75	soft	soft	ADJ
ejpam-3412	512	76	ups	up	NOUN
ejpam-3412	512	77	-	-	PUNCT
ejpam-3412	512	78	subalgebra	subalgebra	NOUN
ejpam-3412	512	79	of	of	ADP
ejpam-3412	512	80	a.	a.	NOUN
ejpam-3412	512	81	but	but	CCONJ
ejpam-3412	512	82	(	(	PUNCT
ejpam-3412	512	83	f̃	f̃	PROPN
ejpam-3412	512	84	,	,	PUNCT
ejpam-3412	512	85	e	e	NOUN
ejpam-3412	512	86	)	)	PUNCT
ejpam-3412	512	87	is	be	AUX
ejpam-3412	512	88	not	not	PART
ejpam-3412	512	89	a	a	DET
ejpam-3412	512	90	pig	pig	NOUN
ejpam-3412	512	91	-	-	PUNCT
ejpam-3412	512	92	fuzzy	fuzzy	ADJ
ejpam-3412	512	93	soft	soft	ADJ
ejpam-3412	512	94	near	near	ADP
ejpam-3412	512	95	ups	up	NOUN
ejpam-3412	512	96	-	-	PUNCT
ejpam-3412	512	97	filter	filter	NOUN
ejpam-3412	512	98	of	of	ADP
ejpam-3412	512	99	a	a	DET
ejpam-3412	512	100	since	since	SCONJ
ejpam-3412	512	101	f	f	PROPN
ejpam-3412	512	102	f̃[pig	f̃[pig	PROPN
ejpam-3412	512	103	]	]	X
ejpam-3412	512	104	(	(	PUNCT
ejpam-3412	512	105	meat	meat	NOUN
ejpam-3412	512	106	·	·	PUNCT
ejpam-3412	512	107	banana	banana	NOUN
ejpam-3412	512	108	)	)	PUNCT
ejpam-3412	513	1	=	=	SYM
ejpam-3412	513	2	f	f	PROPN
ejpam-3412	513	3	f̃[pig	f̃[pig	PROPN
ejpam-3412	513	4	]	]	X
ejpam-3412	513	5	(	(	PUNCT
ejpam-3412	513	6	apple	apple	NOUN
ejpam-3412	513	7	)	)	PUNCT
ejpam-3412	513	8	=	=	SYM
ejpam-3412	513	9	0.8	0.8	NUM
ejpam-3412	513	10	�	�	PROPN
ejpam-3412	513	11	0.9	0.9	NUM
ejpam-3412	513	12	=	=	SYM
ejpam-3412	513	13	f	f	PROPN
ejpam-3412	513	14	f̃[pig	f̃[pig	PROPN
ejpam-3412	513	15	]	]	X
ejpam-3412	513	16	(	(	PUNCT
ejpam-3412	513	17	banana	banana	NOUN
ejpam-3412	513	18	)	)	PUNCT
ejpam-3412	513	19	,	,	PUNCT
ejpam-3412	513	20	that	that	ADV
ejpam-3412	513	21	is	is	ADV
ejpam-3412	513	22	,	,	PUNCT
ejpam-3412	513	23	f̃[pig	f̃[pig	PROPN
ejpam-3412	513	24	]	]	PUNCT
ejpam-3412	513	25	is	be	AUX
ejpam-3412	513	26	not	not	PART
ejpam-3412	513	27	a	a	DET
ejpam-3412	513	28	fuzzy	fuzzy	ADJ
ejpam-3412	513	29	near	near	ADP
ejpam-3412	513	30	ups	up	NOUN
ejpam-3412	513	31	-	-	PUNCT
ejpam-3412	513	32	filter	filter	NOUN
ejpam-3412	513	33	of	of	ADP
ejpam-3412	513	34	a.	a.	NOUN
ejpam-3412	513	35	in	in	ADP
ejpam-3412	513	36	the	the	DET
ejpam-3412	513	37	next	next	ADJ
ejpam-3412	513	38	theorem	theorem	NOUN
ejpam-3412	513	39	,	,	PUNCT
ejpam-3412	513	40	we	we	PRON
ejpam-3412	513	41	give	give	VERB
ejpam-3412	513	42	necessary	necessary	ADJ
ejpam-3412	513	43	condition	condition	NOUN
ejpam-3412	513	44	for	for	ADP
ejpam-3412	513	45	fuzzy	fuzzy	ADJ
ejpam-3412	513	46	soft	soft	ADJ
ejpam-3412	513	47	ups	up	NOUN
ejpam-3412	513	48	-	-	PUNCT
ejpam-3412	513	49	subalgebras	subalgebras	PROPN
ejpam-3412	513	50	as	as	ADP
ejpam-3412	513	51	fuzzy	fuzzy	ADJ
ejpam-3412	513	52	soft	soft	ADJ
ejpam-3412	513	53	near	near	ADP
ejpam-3412	513	54	ups	up	NOUN
ejpam-3412	513	55	-	-	PUNCT
ejpam-3412	513	56	filters	filter	NOUN
ejpam-3412	513	57	of	of	ADP
ejpam-3412	513	58	f	f	PROPN
ejpam-3412	513	59	-up	-up	NOUN
ejpam-3412	513	60	-	-	PUNCT
ejpam-3412	513	61	semigroups	semigroup	NOUN
ejpam-3412	513	62	.	.	PUNCT
ejpam-3412	514	1	theorem	theorem	NOUN
ejpam-3412	514	2	31	31	NUM
ejpam-3412	514	3	.	.	PUNCT
ejpam-3412	515	1	if	if	SCONJ
ejpam-3412	515	2	(	(	PUNCT
ejpam-3412	515	3	f̃	f̃	PROPN
ejpam-3412	515	4	,	,	PUNCT
ejpam-3412	515	5	e	e	NOUN
ejpam-3412	515	6	)	)	PUNCT
ejpam-3412	515	7	is	be	AUX
ejpam-3412	515	8	a	a	DET
ejpam-3412	515	9	fuzzy	fuzzy	ADJ
ejpam-3412	515	10	soft	soft	ADJ
ejpam-3412	515	11	ups	up	NOUN
ejpam-3412	515	12	-	-	PUNCT
ejpam-3412	515	13	subalgebra	subalgebra	NOUN
ejpam-3412	515	14	of	of	ADP
ejpam-3412	515	15	a	a	DET
ejpam-3412	515	16	such	such	ADJ
ejpam-3412	515	17	that	that	PRON
ejpam-3412	515	18	for	for	ADP
ejpam-3412	515	19	all	all	DET
ejpam-3412	515	20	e	e	NOUN
ejpam-3412	515	21	∈	∈	PROPN
ejpam-3412	515	22	e	e	NOUN
ejpam-3412	515	23	,	,	PUNCT
ejpam-3412	515	24	a	a	DET
ejpam-3412	515	25	fuzzy	fuzzy	ADJ
ejpam-3412	515	26	set	set	NOUN
ejpam-3412	515	27	f̃[e	f̃[e	NOUN
ejpam-3412	515	28	]	]	X
ejpam-3412	515	29	in	in	ADP
ejpam-3412	515	30	a	a	DET
ejpam-3412	515	31	satisfies	satisfie	NOUN
ejpam-3412	515	32	the	the	DET
ejpam-3412	515	33	condition	condition	NOUN
ejpam-3412	515	34	(	(	PUNCT
ejpam-3412	515	35	2.5	2.5	NUM
ejpam-3412	515	36	)	)	PUNCT
ejpam-3412	515	37	,	,	PUNCT
ejpam-3412	515	38	then	then	ADV
ejpam-3412	515	39	(	(	PUNCT
ejpam-3412	515	40	f̃	f̃	PROPN
ejpam-3412	515	41	,	,	PUNCT
ejpam-3412	515	42	e	e	NOUN
ejpam-3412	515	43	)	)	PUNCT
ejpam-3412	515	44	is	be	AUX
ejpam-3412	515	45	a	a	DET
ejpam-3412	515	46	fuzzy	fuzzy	ADJ
ejpam-3412	515	47	soft	soft	ADJ
ejpam-3412	515	48	near	near	ADP
ejpam-3412	515	49	ups	up	NOUN
ejpam-3412	515	50	-	-	PUNCT
ejpam-3412	515	51	filter	filter	NOUN
ejpam-3412	515	52	of	of	ADP
ejpam-3412	515	53	a.	a.	NOUN
ejpam-3412	515	54	proof	proof	NOUN
ejpam-3412	515	55	.	.	PUNCT
ejpam-3412	516	1	it	it	PRON
ejpam-3412	516	2	is	be	AUX
ejpam-3412	516	3	straightforward	straightforward	ADJ
ejpam-3412	516	4	by	by	ADP
ejpam-3412	516	5	theorem	theorem	NOUN
ejpam-3412	516	6	12	12	NUM
ejpam-3412	516	7	.	.	PUNCT
ejpam-3412	517	1	the	the	DET
ejpam-3412	517	2	proof	proof	NOUN
ejpam-3412	517	3	of	of	ADP
ejpam-3412	517	4	the	the	DET
ejpam-3412	517	5	following	follow	VERB
ejpam-3412	517	6	theorem	theorem	NOUN
ejpam-3412	517	7	can	can	AUX
ejpam-3412	517	8	be	be	AUX
ejpam-3412	517	9	verified	verify	VERB
ejpam-3412	517	10	easily	easily	ADV
ejpam-3412	517	11	.	.	PUNCT
ejpam-3412	518	1	theorem	theorem	VERB
ejpam-3412	518	2	32	32	NUM
ejpam-3412	518	3	.	.	PUNCT
ejpam-3412	519	1	if	if	SCONJ
ejpam-3412	519	2	(	(	PUNCT
ejpam-3412	519	3	f̃	f̃	PROPN
ejpam-3412	519	4	,	,	PUNCT
ejpam-3412	519	5	e	e	NOUN
ejpam-3412	519	6	)	)	PUNCT
ejpam-3412	519	7	is	be	AUX
ejpam-3412	519	8	a	a	DET
ejpam-3412	519	9	fuzzy	fuzzy	ADJ
ejpam-3412	519	10	soft	soft	ADJ
ejpam-3412	519	11	near	near	ADP
ejpam-3412	519	12	ups	up	NOUN
ejpam-3412	519	13	-	-	PUNCT
ejpam-3412	519	14	filter	filter	NOUN
ejpam-3412	519	15	of	of	ADP
ejpam-3412	519	16	a	a	PRON
ejpam-3412	519	17	and	and	CCONJ
ejpam-3412	519	18	∅	∅	NOUN
ejpam-3412	519	19	6=	6=	ADP
ejpam-3412	519	20	e∗	e∗	PROPN
ejpam-3412	519	21	⊆	⊆	NUM
ejpam-3412	519	22	e	e	NOUN
ejpam-3412	519	23	,	,	PUNCT
ejpam-3412	519	24	then	then	ADV
ejpam-3412	519	25	(	(	PUNCT
ejpam-3412	519	26	f̃|e∗	f̃|e∗	PROPN
ejpam-3412	519	27	,	,	PUNCT
ejpam-3412	519	28	e∗	e∗	PROPN
ejpam-3412	519	29	)	)	PUNCT
ejpam-3412	519	30	is	be	AUX
ejpam-3412	519	31	a	a	DET
ejpam-3412	519	32	fuzzy	fuzzy	ADJ
ejpam-3412	519	33	soft	soft	ADJ
ejpam-3412	519	34	near	near	ADP
ejpam-3412	519	35	ups	up	NOUN
ejpam-3412	519	36	-	-	PUNCT
ejpam-3412	519	37	filter	filter	NOUN
ejpam-3412	519	38	of	of	ADP
ejpam-3412	519	39	a.	a.	PROPN
ejpam-3412	519	40	a.	a.	PROPN
ejpam-3412	519	41	satirad	satirad	PROPN
ejpam-3412	519	42	,	,	PUNCT
ejpam-3412	519	43	a.	a.	NOUN
ejpam-3412	519	44	iampan	iampan	PROPN
ejpam-3412	519	45	/	/	SYM
ejpam-3412	519	46	eur	eur	PROPN
ejpam-3412	519	47	.	.	PUNCT
ejpam-3412	520	1	j.	j.	PROPN
ejpam-3412	520	2	pure	pure	PROPN
ejpam-3412	520	3	appl	appl	PROPN
ejpam-3412	520	4	.	.	PROPN
ejpam-3412	520	5	math	math	PROPN
ejpam-3412	520	6	,	,	PUNCT
ejpam-3412	520	7	12	12	NUM
ejpam-3412	520	8	(	(	PUNCT
ejpam-3412	520	9	2	2	NUM
ejpam-3412	520	10	)	)	PUNCT
ejpam-3412	520	11	(	(	PUNCT
ejpam-3412	520	12	2019	2019	NUM
ejpam-3412	520	13	)	)	PUNCT
ejpam-3412	520	14	,	,	PUNCT
ejpam-3412	520	15	294	294	NUM
ejpam-3412	520	16	-	-	SYM
ejpam-3412	520	17	331	331	NUM
ejpam-3412	520	18	317	317	NUM
ejpam-3412	520	19	the	the	DET
ejpam-3412	520	20	following	follow	VERB
ejpam-3412	520	21	two	two	NUM
ejpam-3412	520	22	theorems	theorem	NOUN
ejpam-3412	520	23	can	can	AUX
ejpam-3412	520	24	be	be	AUX
ejpam-3412	520	25	deduced	deduce	VERB
ejpam-3412	520	26	in	in	ADP
ejpam-3412	520	27	the	the	DET
ejpam-3412	520	28	same	same	ADJ
ejpam-3412	520	29	way	way	NOUN
ejpam-3412	520	30	as	as	ADP
ejpam-3412	520	31	theorems	theorem	NOUN
ejpam-3412	520	32	22	22	NUM
ejpam-3412	520	33	and	and	CCONJ
ejpam-3412	520	34	23	23	NUM
ejpam-3412	520	35	.	.	PUNCT
ejpam-3412	521	1	theorem	theorem	VERB
ejpam-3412	521	2	33	33	NUM
ejpam-3412	521	3	.	.	PUNCT
ejpam-3412	522	1	the	the	DET
ejpam-3412	522	2	extended	extended	ADJ
ejpam-3412	522	3	intersection	intersection	NOUN
ejpam-3412	522	4	of	of	ADP
ejpam-3412	522	5	two	two	NUM
ejpam-3412	522	6	fuzzy	fuzzy	ADJ
ejpam-3412	522	7	soft	soft	ADJ
ejpam-3412	522	8	near	near	ADP
ejpam-3412	522	9	ups	up	NOUN
ejpam-3412	522	10	-	-	PUNCT
ejpam-3412	522	11	filters	filter	NOUN
ejpam-3412	522	12	of	of	ADP
ejpam-3412	522	13	a	a	PRON
ejpam-3412	522	14	is	be	AUX
ejpam-3412	522	15	also	also	ADV
ejpam-3412	522	16	a	a	DET
ejpam-3412	522	17	fuzzy	fuzzy	ADJ
ejpam-3412	522	18	soft	soft	ADJ
ejpam-3412	522	19	near	near	ADP
ejpam-3412	522	20	ups	up	NOUN
ejpam-3412	522	21	-	-	PUNCT
ejpam-3412	522	22	filter	filter	NOUN
ejpam-3412	522	23	.	.	PUNCT
ejpam-3412	523	1	moreover	moreover	ADV
ejpam-3412	523	2	,	,	PUNCT
ejpam-3412	523	3	the	the	DET
ejpam-3412	523	4	intersection	intersection	NOUN
ejpam-3412	523	5	of	of	ADP
ejpam-3412	523	6	two	two	NUM
ejpam-3412	523	7	fuzzy	fuzzy	ADJ
ejpam-3412	523	8	soft	soft	ADJ
ejpam-3412	523	9	near	near	ADP
ejpam-3412	523	10	ups	up	NOUN
ejpam-3412	523	11	-	-	PUNCT
ejpam-3412	523	12	filters	filter	NOUN
ejpam-3412	523	13	of	of	ADP
ejpam-3412	523	14	a	a	PRON
ejpam-3412	523	15	is	be	AUX
ejpam-3412	523	16	also	also	ADV
ejpam-3412	523	17	a	a	DET
ejpam-3412	523	18	fuzzy	fuzzy	ADJ
ejpam-3412	523	19	soft	soft	ADJ
ejpam-3412	523	20	near	near	ADP
ejpam-3412	523	21	ups	up	NOUN
ejpam-3412	523	22	-	-	PUNCT
ejpam-3412	523	23	filter	filter	NOUN
ejpam-3412	523	24	.	.	PUNCT
ejpam-3412	524	1	theorem	theorem	VERB
ejpam-3412	524	2	34	34	NUM
ejpam-3412	524	3	.	.	PUNCT
ejpam-3412	525	1	the	the	DET
ejpam-3412	525	2	union	union	NOUN
ejpam-3412	525	3	of	of	ADP
ejpam-3412	525	4	two	two	NUM
ejpam-3412	525	5	fuzzy	fuzzy	ADJ
ejpam-3412	525	6	soft	soft	ADJ
ejpam-3412	525	7	near	near	ADP
ejpam-3412	525	8	ups	up	NOUN
ejpam-3412	525	9	-	-	PUNCT
ejpam-3412	525	10	filters	filter	NOUN
ejpam-3412	525	11	of	of	ADP
ejpam-3412	525	12	a	a	PRON
ejpam-3412	525	13	is	be	AUX
ejpam-3412	525	14	also	also	ADV
ejpam-3412	525	15	a	a	DET
ejpam-3412	525	16	fuzzy	fuzzy	ADJ
ejpam-3412	525	17	soft	soft	ADJ
ejpam-3412	525	18	near	near	ADP
ejpam-3412	525	19	ups	up	NOUN
ejpam-3412	525	20	-	-	PUNCT
ejpam-3412	525	21	filter	filter	NOUN
ejpam-3412	525	22	if	if	SCONJ
ejpam-3412	525	23	sets	set	NOUN
ejpam-3412	525	24	of	of	ADP
ejpam-3412	525	25	statistics	statistic	NOUN
ejpam-3412	525	26	of	of	ADP
ejpam-3412	525	27	two	two	NUM
ejpam-3412	525	28	fuzzy	fuzzy	ADJ
ejpam-3412	525	29	soft	soft	ADJ
ejpam-3412	525	30	near	near	ADP
ejpam-3412	525	31	ups	up	NOUN
ejpam-3412	525	32	-	-	PUNCT
ejpam-3412	525	33	filters	filter	NOUN
ejpam-3412	525	34	are	be	AUX
ejpam-3412	525	35	disjoint	disjoint	ADJ
ejpam-3412	525	36	.	.	PUNCT
ejpam-3412	526	1	the	the	DET
ejpam-3412	526	2	following	follow	VERB
ejpam-3412	526	3	example	example	NOUN
ejpam-3412	526	4	shows	show	VERB
ejpam-3412	526	5	that	that	SCONJ
ejpam-3412	526	6	theorem	theorem	VERB
ejpam-3412	526	7	34	34	NUM
ejpam-3412	526	8	is	be	AUX
ejpam-3412	526	9	not	not	PART
ejpam-3412	526	10	valid	valid	ADJ
ejpam-3412	526	11	if	if	SCONJ
ejpam-3412	526	12	sets	set	NOUN
ejpam-3412	526	13	of	of	ADP
ejpam-3412	526	14	statistics	statistic	NOUN
ejpam-3412	526	15	of	of	ADP
ejpam-3412	526	16	two	two	NUM
ejpam-3412	526	17	fuzzy	fuzzy	ADJ
ejpam-3412	526	18	soft	soft	ADJ
ejpam-3412	526	19	near	near	ADP
ejpam-3412	526	20	ups	up	NOUN
ejpam-3412	526	21	-	-	PUNCT
ejpam-3412	526	22	filters	filter	NOUN
ejpam-3412	526	23	are	be	AUX
ejpam-3412	526	24	not	not	PART
ejpam-3412	526	25	disjoint	disjoint	ADJ
ejpam-3412	526	26	.	.	PUNCT
ejpam-3412	526	27	example	example	NOUN
ejpam-3412	527	1	18	18	NUM
ejpam-3412	527	2	.	.	PUNCT
ejpam-3412	528	1	in	in	ADP
ejpam-3412	528	2	example	example	NOUN
ejpam-3412	528	3	14	14	NUM
ejpam-3412	528	4	,	,	PUNCT
ejpam-3412	528	5	we	we	PRON
ejpam-3412	528	6	have	have	AUX
ejpam-3412	528	7	(	(	PUNCT
ejpam-3412	528	8	g̃1	g̃1	NOUN
ejpam-3412	528	9	,	,	PUNCT
ejpam-3412	528	10	e1	e1	NOUN
ejpam-3412	528	11	)	)	PUNCT
ejpam-3412	528	12	and	and	CCONJ
ejpam-3412	528	13	(	(	PUNCT
ejpam-3412	528	14	g̃2	g̃2	PROPN
ejpam-3412	528	15	,	,	PUNCT
ejpam-3412	528	16	e2	e2	PROPN
ejpam-3412	528	17	)	)	PUNCT
ejpam-3412	528	18	are	be	AUX
ejpam-3412	528	19	two	two	NUM
ejpam-3412	528	20	fuzzy	fuzzy	ADJ
ejpam-3412	528	21	soft	soft	ADJ
ejpam-3412	528	22	near	near	ADP
ejpam-3412	528	23	ups	up	NOUN
ejpam-3412	528	24	-	-	PUNCT
ejpam-3412	528	25	filters	filter	NOUN
ejpam-3412	528	26	of	of	ADP
ejpam-3412	528	27	a.	a.	NOUN
ejpam-3412	528	28	since	since	SCONJ
ejpam-3412	528	29	price	price	NOUN
ejpam-3412	528	30	∈	∈	NOUN
ejpam-3412	528	31	e1	e1	NOUN
ejpam-3412	528	32	∩	∩	ADJ
ejpam-3412	528	33	e2	e2	PROPN
ejpam-3412	528	34	,	,	PUNCT
ejpam-3412	528	35	we	we	PRON
ejpam-3412	528	36	have	have	VERB
ejpam-3412	528	37	(	(	PUNCT
ejpam-3412	528	38	f	f	PROPN
ejpam-3412	528	39	g̃1[price]∪g̃2[price	g̃1[price]∪g̃2[price	X
ejpam-3412	528	40	]	]	X
ejpam-3412	528	41	)	)	PUNCT
ejpam-3412	528	42	(	(	PUNCT
ejpam-3412	528	43	6	6	NUM
ejpam-3412	528	44	∗	∗	NOUN
ejpam-3412	528	45	5	5	NUM
ejpam-3412	528	46	)	)	PUNCT
ejpam-3412	528	47	=	=	PUNCT
ejpam-3412	529	1	(	(	PUNCT
ejpam-3412	529	2	f	f	X
ejpam-3412	529	3	g̃1[price]∪g̃2[price	g̃1[price]∪g̃2[price	X
ejpam-3412	529	4	]	]	X
ejpam-3412	529	5	)	)	PUNCT
ejpam-3412	529	6	(	(	PUNCT
ejpam-3412	529	7	7	7	X
ejpam-3412	529	8	)	)	PUNCT
ejpam-3412	529	9	=	=	SYM
ejpam-3412	529	10	0.7	0.7	NUM
ejpam-3412	529	11	�	�	PROPN
ejpam-3412	529	12	0.8	0.8	NUM
ejpam-3412	529	13	=	=	SYM
ejpam-3412	529	14	min{0.9	min{0.9	PROPN
ejpam-3412	529	15	,	,	PUNCT
ejpam-3412	529	16	0.8	0.8	NUM
ejpam-3412	529	17	}	}	PUNCT
ejpam-3412	529	18	=	=	SYM
ejpam-3412	529	19	min{(f	min{(f	SYM
ejpam-3412	529	20	g̃1[price]∪g̃2[price	g̃1[price]∪g̃2[price	X
ejpam-3412	529	21	]	]	X
ejpam-3412	529	22	)	)	PUNCT
ejpam-3412	529	23	(	(	PUNCT
ejpam-3412	529	24	6	6	NUM
ejpam-3412	529	25	)	)	PUNCT
ejpam-3412	529	26	,	,	PUNCT
ejpam-3412	529	27	(	(	PUNCT
ejpam-3412	529	28	f	f	PROPN
ejpam-3412	529	29	g̃1[price]∪g̃2[price	g̃1[price]∪g̃2[price	X
ejpam-3412	529	30	]	]	X
ejpam-3412	529	31	)	)	PUNCT
ejpam-3412	529	32	(	(	PUNCT
ejpam-3412	529	33	5	5	NUM
ejpam-3412	529	34	)	)	PUNCT
ejpam-3412	529	35	}	}	PUNCT
ejpam-3412	529	36	.	.	PUNCT
ejpam-3412	530	1	thus	thus	ADV
ejpam-3412	530	2	g̃1[price	g̃1[price	X
ejpam-3412	530	3	]	]	PUNCT
ejpam-3412	530	4	∪	∪	X
ejpam-3412	530	5	g̃2[price	g̃2[price	PROPN
ejpam-3412	530	6	]	]	PUNCT
ejpam-3412	530	7	is	be	AUX
ejpam-3412	530	8	not	not	PART
ejpam-3412	530	9	a	a	DET
ejpam-3412	530	10	fuzzy	fuzzy	ADJ
ejpam-3412	530	11	near	near	ADP
ejpam-3412	530	12	ups	up	NOUN
ejpam-3412	530	13	-	-	PUNCT
ejpam-3412	530	14	filter	filter	NOUN
ejpam-3412	530	15	of	of	ADP
ejpam-3412	530	16	a	a	PRON
ejpam-3412	530	17	,	,	PUNCT
ejpam-3412	530	18	that	that	ADV
ejpam-3412	530	19	is	is	ADV
ejpam-3412	530	20	,	,	PUNCT
ejpam-3412	530	21	(	(	PUNCT
ejpam-3412	530	22	g̃1	g̃1	NOUN
ejpam-3412	530	23	,	,	PUNCT
ejpam-3412	530	24	e1	e1	NOUN
ejpam-3412	530	25	)	)	PUNCT
ejpam-3412	530	26	∪	∪	NOUN
ejpam-3412	530	27	(	(	PUNCT
ejpam-3412	530	28	g̃2	g̃2	PROPN
ejpam-3412	530	29	,	,	PUNCT
ejpam-3412	530	30	e2	e2	PROPN
ejpam-3412	530	31	)	)	PUNCT
ejpam-3412	530	32	is	be	AUX
ejpam-3412	530	33	not	not	PART
ejpam-3412	530	34	a	a	DET
ejpam-3412	530	35	price	price	NOUN
ejpam-3412	530	36	-	-	PUNCT
ejpam-3412	530	37	fuzzy	fuzzy	NOUN
ejpam-3412	530	38	soft	soft	ADJ
ejpam-3412	530	39	near	near	ADP
ejpam-3412	530	40	ups	up	NOUN
ejpam-3412	530	41	-	-	PUNCT
ejpam-3412	530	42	filter	filter	NOUN
ejpam-3412	530	43	of	of	ADP
ejpam-3412	530	44	a.	a.	NOUN
ejpam-3412	530	45	hence	hence	ADV
ejpam-3412	530	46	,	,	PUNCT
ejpam-3412	530	47	(	(	PUNCT
ejpam-3412	530	48	g̃1	g̃1	NOUN
ejpam-3412	530	49	,	,	PUNCT
ejpam-3412	530	50	e1	e1	NOUN
ejpam-3412	530	51	)	)	PUNCT
ejpam-3412	530	52	∪	∪	NOUN
ejpam-3412	530	53	(	(	PUNCT
ejpam-3412	530	54	g̃2	g̃2	PROPN
ejpam-3412	530	55	,	,	PUNCT
ejpam-3412	530	56	e2	e2	PROPN
ejpam-3412	530	57	)	)	PUNCT
ejpam-3412	530	58	is	be	AUX
ejpam-3412	530	59	not	not	PART
ejpam-3412	530	60	a	a	DET
ejpam-3412	530	61	fuzzy	fuzzy	ADJ
ejpam-3412	530	62	soft	soft	ADJ
ejpam-3412	530	63	near	near	ADP
ejpam-3412	530	64	ups	up	NOUN
ejpam-3412	530	65	-	-	PUNCT
ejpam-3412	530	66	filter	filter	NOUN
ejpam-3412	530	67	of	of	ADP
ejpam-3412	530	68	a.	a.	NOUN
ejpam-3412	530	69	moreover	moreover	ADV
ejpam-3412	530	70	,	,	PUNCT
ejpam-3412	530	71	(	(	PUNCT
ejpam-3412	530	72	g̃1	g̃1	NOUN
ejpam-3412	530	73	,	,	PUNCT
ejpam-3412	530	74	e1)d	e1)d	NOUN
ejpam-3412	530	75	(	(	PUNCT
ejpam-3412	530	76	g̃2	g̃2	PROPN
ejpam-3412	530	77	,	,	PUNCT
ejpam-3412	530	78	e2	e2	PROPN
ejpam-3412	530	79	)	)	PUNCT
ejpam-3412	530	80	is	be	AUX
ejpam-3412	530	81	not	not	PART
ejpam-3412	530	82	a	a	DET
ejpam-3412	530	83	fuzzy	fuzzy	ADJ
ejpam-3412	530	84	soft	soft	ADJ
ejpam-3412	530	85	near	near	ADP
ejpam-3412	530	86	ups	up	NOUN
ejpam-3412	530	87	-	-	PUNCT
ejpam-3412	530	88	filter	filter	NOUN
ejpam-3412	530	89	of	of	ADP
ejpam-3412	530	90	a.	a.	NOUN
ejpam-3412	530	91	3.4	3.4	NUM
ejpam-3412	530	92	.	.	PUNCT
ejpam-3412	531	1	fuzzy	fuzzy	ADJ
ejpam-3412	531	2	soft	soft	ADJ
ejpam-3412	531	3	near	near	ADP
ejpam-3412	531	4	upi	upi	NOUN
ejpam-3412	531	5	-	-	PUNCT
ejpam-3412	531	6	filters	filter	NOUN
ejpam-3412	531	7	definition	definition	NOUN
ejpam-3412	531	8	21	21	NUM
ejpam-3412	531	9	.	.	PUNCT
ejpam-3412	532	1	a	a	DET
ejpam-3412	532	2	fuzzy	fuzzy	ADJ
ejpam-3412	532	3	soft	soft	ADJ
ejpam-3412	532	4	set	set	NOUN
ejpam-3412	532	5	(	(	PUNCT
ejpam-3412	532	6	f̃	f̃	PROPN
ejpam-3412	532	7	,	,	PUNCT
ejpam-3412	532	8	e	e	NOUN
ejpam-3412	532	9	)	)	PUNCT
ejpam-3412	532	10	over	over	ADP
ejpam-3412	532	11	a	a	PRON
ejpam-3412	532	12	is	be	AUX
ejpam-3412	532	13	called	call	VERB
ejpam-3412	532	14	a	a	DET
ejpam-3412	532	15	fuzzy	fuzzy	ADJ
ejpam-3412	532	16	soft	soft	ADJ
ejpam-3412	532	17	near	near	ADP
ejpam-3412	532	18	upi	upi	NOUN
ejpam-3412	532	19	-	-	PUNCT
ejpam-3412	532	20	filter	filter	NOUN
ejpam-3412	532	21	based	base	VERB
ejpam-3412	532	22	on	on	ADP
ejpam-3412	532	23	e	e	PROPN
ejpam-3412	532	24	∈	∈	PROPN
ejpam-3412	532	25	e	e	X
ejpam-3412	532	26	(	(	PUNCT
ejpam-3412	532	27	we	we	PRON
ejpam-3412	532	28	shortly	shortly	ADV
ejpam-3412	532	29	call	call	VERB
ejpam-3412	532	30	an	an	DET
ejpam-3412	532	31	e	e	NOUN
ejpam-3412	532	32	-	-	ADJ
ejpam-3412	532	33	fuzzy	fuzzy	ADJ
ejpam-3412	532	34	soft	soft	ADJ
ejpam-3412	532	35	near	near	ADP
ejpam-3412	532	36	upi	upi	NOUN
ejpam-3412	532	37	-	-	PUNCT
ejpam-3412	532	38	filter	filter	NOUN
ejpam-3412	532	39	)	)	PUNCT
ejpam-3412	532	40	of	of	ADP
ejpam-3412	532	41	a	a	DET
ejpam-3412	532	42	if	if	SCONJ
ejpam-3412	532	43	a	a	DET
ejpam-3412	532	44	fuzzy	fuzzy	ADJ
ejpam-3412	532	45	set	set	NOUN
ejpam-3412	532	46	f̃[e	f̃[e	X
ejpam-3412	532	47	]	]	X
ejpam-3412	532	48	in	in	ADP
ejpam-3412	532	49	a	a	PRON
ejpam-3412	532	50	is	be	AUX
ejpam-3412	532	51	a	a	DET
ejpam-3412	532	52	fuzzy	fuzzy	ADJ
ejpam-3412	532	53	near	near	ADP
ejpam-3412	532	54	upi	upi	NOUN
ejpam-3412	532	55	-	-	PUNCT
ejpam-3412	532	56	filter	filter	NOUN
ejpam-3412	532	57	of	of	ADP
ejpam-3412	532	58	a.	a.	NOUN
ejpam-3412	532	59	if	if	SCONJ
ejpam-3412	532	60	(	(	PUNCT
ejpam-3412	532	61	f̃	f̃	PROPN
ejpam-3412	532	62	,	,	PUNCT
ejpam-3412	532	63	e	e	NOUN
ejpam-3412	532	64	)	)	PUNCT
ejpam-3412	532	65	is	be	AUX
ejpam-3412	532	66	an	an	DET
ejpam-3412	532	67	e	e	ADJ
ejpam-3412	532	68	-	-	ADJ
ejpam-3412	532	69	fuzzy	fuzzy	ADJ
ejpam-3412	532	70	soft	soft	ADJ
ejpam-3412	532	71	near	near	ADP
ejpam-3412	532	72	upi	upi	NOUN
ejpam-3412	532	73	-	-	PUNCT
ejpam-3412	532	74	filter	filter	NOUN
ejpam-3412	532	75	of	of	ADP
ejpam-3412	532	76	a	a	PRON
ejpam-3412	532	77	for	for	ADP
ejpam-3412	532	78	all	all	DET
ejpam-3412	532	79	e	e	NOUN
ejpam-3412	532	80	∈	∈	PROPN
ejpam-3412	532	81	e	e	NOUN
ejpam-3412	532	82	,	,	PUNCT
ejpam-3412	532	83	we	we	PRON
ejpam-3412	532	84	say	say	VERB
ejpam-3412	532	85	that	that	SCONJ
ejpam-3412	532	86	(	(	PUNCT
ejpam-3412	532	87	f̃	f̃	PROPN
ejpam-3412	532	88	,	,	PUNCT
ejpam-3412	532	89	e	e	NOUN
ejpam-3412	532	90	)	)	PUNCT
ejpam-3412	532	91	is	be	AUX
ejpam-3412	532	92	a	a	DET
ejpam-3412	532	93	fuzzy	fuzzy	ADJ
ejpam-3412	532	94	soft	soft	ADJ
ejpam-3412	532	95	near	near	ADP
ejpam-3412	532	96	upi	upi	NOUN
ejpam-3412	532	97	-	-	PUNCT
ejpam-3412	532	98	filter	filter	NOUN
ejpam-3412	532	99	of	of	ADP
ejpam-3412	532	100	a.	a.	NOUN
ejpam-3412	532	101	in	in	ADP
ejpam-3412	532	102	the	the	DET
ejpam-3412	532	103	next	next	ADJ
ejpam-3412	532	104	theorem	theorem	NOUN
ejpam-3412	532	105	,	,	PUNCT
ejpam-3412	532	106	we	we	PRON
ejpam-3412	532	107	give	give	VERB
ejpam-3412	532	108	necessary	necessary	ADJ
ejpam-3412	532	109	condition	condition	NOUN
ejpam-3412	532	110	for	for	ADP
ejpam-3412	532	111	fuzzy	fuzzy	ADJ
ejpam-3412	532	112	soft	soft	ADJ
ejpam-3412	532	113	near	near	ADP
ejpam-3412	532	114	upi	upi	NOUN
ejpam-3412	532	115	-	-	PUNCT
ejpam-3412	532	116	filters	filter	NOUN
ejpam-3412	532	117	of	of	ADP
ejpam-3412	532	118	f	f	PROPN
ejpam-3412	532	119	-up	-up	NOUN
ejpam-3412	532	120	-	-	PUNCT
ejpam-3412	532	121	semigroups	semigroup	NOUN
ejpam-3412	532	122	.	.	PUNCT
ejpam-3412	533	1	theorem	theorem	NOUN
ejpam-3412	533	2	35	35	NUM
ejpam-3412	533	3	.	.	PUNCT
ejpam-3412	534	1	if	if	SCONJ
ejpam-3412	534	2	(	(	PUNCT
ejpam-3412	534	3	f̃	f̃	PROPN
ejpam-3412	534	4	,	,	PUNCT
ejpam-3412	534	5	e	e	NOUN
ejpam-3412	534	6	)	)	PUNCT
ejpam-3412	534	7	is	be	AUX
ejpam-3412	534	8	a	a	DET
ejpam-3412	534	9	fuzzy	fuzzy	ADJ
ejpam-3412	534	10	soft	soft	ADJ
ejpam-3412	534	11	set	set	NOUN
ejpam-3412	534	12	over	over	ADP
ejpam-3412	534	13	a	a	DET
ejpam-3412	534	14	such	such	ADJ
ejpam-3412	534	15	that	that	PRON
ejpam-3412	534	16	for	for	ADP
ejpam-3412	534	17	all	all	DET
ejpam-3412	534	18	e	e	NOUN
ejpam-3412	534	19	∈	∈	PROPN
ejpam-3412	534	20	e	e	NOUN
ejpam-3412	534	21	,	,	PUNCT
ejpam-3412	534	22	a	a	DET
ejpam-3412	534	23	fuzzy	fuzzy	ADJ
ejpam-3412	534	24	set	set	NOUN
ejpam-3412	534	25	f̃[e	f̃[e	NOUN
ejpam-3412	534	26	]	]	X
ejpam-3412	534	27	in	in	ADP
ejpam-3412	534	28	a	a	DET
ejpam-3412	534	29	satisfies	satisfie	NOUN
ejpam-3412	534	30	the	the	DET
ejpam-3412	534	31	conditions	condition	NOUN
ejpam-3412	534	32	(	(	PUNCT
ejpam-3412	534	33	2.2	2.2	NUM
ejpam-3412	534	34	)	)	PUNCT
ejpam-3412	534	35	and	and	CCONJ
ejpam-3412	534	36	(	(	PUNCT
ejpam-3412	534	37	1.15	1.15	NUM
ejpam-3412	534	38	)	)	PUNCT
ejpam-3412	534	39	,	,	PUNCT
ejpam-3412	534	40	then	then	ADV
ejpam-3412	534	41	(	(	PUNCT
ejpam-3412	534	42	f̃	f̃	PROPN
ejpam-3412	534	43	,	,	PUNCT
ejpam-3412	534	44	e	e	NOUN
ejpam-3412	534	45	)	)	PUNCT
ejpam-3412	534	46	is	be	AUX
ejpam-3412	534	47	a	a	DET
ejpam-3412	534	48	fuzzy	fuzzy	ADJ
ejpam-3412	534	49	soft	soft	ADJ
ejpam-3412	534	50	near	near	ADP
ejpam-3412	534	51	upi	upi	NOUN
ejpam-3412	534	52	-	-	PUNCT
ejpam-3412	534	53	filter	filter	NOUN
ejpam-3412	534	54	of	of	ADP
ejpam-3412	534	55	a.	a.	NOUN
ejpam-3412	534	56	proof	proof	NOUN
ejpam-3412	534	57	.	.	PUNCT
ejpam-3412	535	1	it	it	PRON
ejpam-3412	535	2	is	be	AUX
ejpam-3412	535	3	straightforward	straightforward	ADJ
ejpam-3412	535	4	by	by	ADP
ejpam-3412	535	5	proposition	proposition	NOUN
ejpam-3412	535	6	5	5	NUM
ejpam-3412	535	7	and	and	CCONJ
ejpam-3412	535	8	lemma	lemma	PROPN
ejpam-3412	535	9	1	1	NUM
ejpam-3412	535	10	(	(	PUNCT
ejpam-3412	535	11	2	2	NUM
ejpam-3412	535	12	)	)	PUNCT
ejpam-3412	535	13	.	.	PUNCT
ejpam-3412	536	1	from	from	ADP
ejpam-3412	536	2	figure	figure	NOUN
ejpam-3412	536	3	1	1	NUM
ejpam-3412	536	4	,	,	PUNCT
ejpam-3412	536	5	we	we	PRON
ejpam-3412	536	6	have	have	VERB
ejpam-3412	536	7	the	the	DET
ejpam-3412	536	8	following	follow	VERB
ejpam-3412	536	9	two	two	NUM
ejpam-3412	536	10	theorems	theorem	NOUN
ejpam-3412	536	11	.	.	PUNCT
ejpam-3412	537	1	theorem	theorem	NOUN
ejpam-3412	537	2	36	36	NUM
ejpam-3412	537	3	.	.	PUNCT
ejpam-3412	538	1	every	every	DET
ejpam-3412	538	2	e	e	ADJ
ejpam-3412	538	3	-	-	ADJ
ejpam-3412	538	4	fuzzy	fuzzy	ADJ
ejpam-3412	538	5	soft	soft	ADJ
ejpam-3412	538	6	near	near	ADP
ejpam-3412	538	7	upi	upi	NOUN
ejpam-3412	538	8	-	-	PUNCT
ejpam-3412	538	9	filter	filter	NOUN
ejpam-3412	538	10	of	of	ADP
ejpam-3412	538	11	a	a	PRON
ejpam-3412	538	12	is	be	AUX
ejpam-3412	538	13	an	an	DET
ejpam-3412	538	14	e	e	ADJ
ejpam-3412	538	15	-	-	ADJ
ejpam-3412	538	16	fuzzy	fuzzy	ADJ
ejpam-3412	538	17	soft	soft	ADJ
ejpam-3412	538	18	near	near	ADP
ejpam-3412	538	19	ups	up	NOUN
ejpam-3412	538	20	-	-	PUNCT
ejpam-3412	538	21	filter	filter	NOUN
ejpam-3412	538	22	.	.	PUNCT
ejpam-3412	539	1	moreover	moreover	ADV
ejpam-3412	539	2	,	,	PUNCT
ejpam-3412	539	3	every	every	DET
ejpam-3412	539	4	fuzzy	fuzzy	ADJ
ejpam-3412	539	5	soft	soft	ADJ
ejpam-3412	539	6	near	near	ADP
ejpam-3412	539	7	upi	upi	NOUN
ejpam-3412	539	8	-	-	PUNCT
ejpam-3412	539	9	filter	filter	NOUN
ejpam-3412	539	10	of	of	ADP
ejpam-3412	539	11	a	a	PRON
ejpam-3412	539	12	is	be	AUX
ejpam-3412	539	13	a	a	DET
ejpam-3412	539	14	fuzzy	fuzzy	ADJ
ejpam-3412	539	15	soft	soft	ADJ
ejpam-3412	539	16	near	near	ADP
ejpam-3412	539	17	ups	up	NOUN
ejpam-3412	539	18	-	-	PUNCT
ejpam-3412	539	19	filter	filter	NOUN
ejpam-3412	539	20	.	.	PUNCT
ejpam-3412	540	1	a.	a.	PROPN
ejpam-3412	540	2	satirad	satirad	PROPN
ejpam-3412	540	3	,	,	PUNCT
ejpam-3412	540	4	a.	a.	NOUN
ejpam-3412	540	5	iampan	iampan	PROPN
ejpam-3412	540	6	/	/	SYM
ejpam-3412	540	7	eur	eur	PROPN
ejpam-3412	540	8	.	.	PUNCT
ejpam-3412	541	1	j.	j.	PROPN
ejpam-3412	541	2	pure	pure	PROPN
ejpam-3412	541	3	appl	appl	PROPN
ejpam-3412	541	4	.	.	PROPN
ejpam-3412	541	5	math	math	PROPN
ejpam-3412	541	6	,	,	PUNCT
ejpam-3412	541	7	12	12	NUM
ejpam-3412	541	8	(	(	PUNCT
ejpam-3412	541	9	2	2	NUM
ejpam-3412	541	10	)	)	PUNCT
ejpam-3412	541	11	(	(	PUNCT
ejpam-3412	541	12	2019	2019	NUM
ejpam-3412	541	13	)	)	PUNCT
ejpam-3412	541	14	,	,	PUNCT
ejpam-3412	541	15	294	294	NUM
ejpam-3412	541	16	-	-	SYM
ejpam-3412	541	17	331	331	NUM
ejpam-3412	541	18	318	318	NUM
ejpam-3412	541	19	theorem	theorem	VERB
ejpam-3412	541	20	37	37	NUM
ejpam-3412	541	21	.	.	PUNCT
ejpam-3412	542	1	every	every	DET
ejpam-3412	542	2	e	e	ADJ
ejpam-3412	542	3	-	-	ADJ
ejpam-3412	542	4	fuzzy	fuzzy	ADJ
ejpam-3412	542	5	soft	soft	ADJ
ejpam-3412	542	6	near	near	ADP
ejpam-3412	542	7	upi	upi	NOUN
ejpam-3412	542	8	-	-	PUNCT
ejpam-3412	542	9	filter	filter	NOUN
ejpam-3412	542	10	of	of	ADP
ejpam-3412	542	11	a	a	PRON
ejpam-3412	542	12	is	be	AUX
ejpam-3412	542	13	an	an	DET
ejpam-3412	542	14	e	e	ADJ
ejpam-3412	542	15	-	-	ADJ
ejpam-3412	542	16	fuzzy	fuzzy	ADJ
ejpam-3412	542	17	soft	soft	ADJ
ejpam-3412	542	18	upi	upi	NOUN
ejpam-3412	542	19	-	-	PUNCT
ejpam-3412	542	20	subalgebra	subalgebra	NOUN
ejpam-3412	542	21	.	.	PUNCT
ejpam-3412	543	1	moreover	moreover	ADV
ejpam-3412	543	2	,	,	PUNCT
ejpam-3412	543	3	every	every	DET
ejpam-3412	543	4	fuzzy	fuzzy	ADJ
ejpam-3412	543	5	soft	soft	ADJ
ejpam-3412	543	6	near	near	ADP
ejpam-3412	543	7	upi	upi	NOUN
ejpam-3412	543	8	-	-	PUNCT
ejpam-3412	543	9	filter	filter	NOUN
ejpam-3412	543	10	of	of	ADP
ejpam-3412	543	11	a	a	PRON
ejpam-3412	543	12	is	be	AUX
ejpam-3412	543	13	a	a	DET
ejpam-3412	543	14	fuzzy	fuzzy	ADJ
ejpam-3412	543	15	soft	soft	ADJ
ejpam-3412	543	16	upi	upi	NOUN
ejpam-3412	543	17	-	-	PUNCT
ejpam-3412	543	18	subalgebra	subalgebra	NOUN
ejpam-3412	543	19	.	.	PUNCT
ejpam-3412	544	1	the	the	DET
ejpam-3412	544	2	following	follow	VERB
ejpam-3412	544	3	two	two	NUM
ejpam-3412	544	4	examples	example	NOUN
ejpam-3412	544	5	show	show	VERB
ejpam-3412	544	6	that	that	SCONJ
ejpam-3412	544	7	the	the	DET
ejpam-3412	544	8	converse	converse	NOUN
ejpam-3412	544	9	of	of	ADP
ejpam-3412	544	10	theorems	theorem	NOUN
ejpam-3412	544	11	36	36	NUM
ejpam-3412	544	12	and	and	CCONJ
ejpam-3412	544	13	37	37	NUM
ejpam-3412	544	14	is	be	AUX
ejpam-3412	544	15	not	not	PART
ejpam-3412	544	16	true	true	ADJ
ejpam-3412	544	17	.	.	PUNCT
ejpam-3412	545	1	example	example	NOUN
ejpam-3412	546	1	19	19	NUM
ejpam-3412	546	2	.	.	PUNCT
ejpam-3412	547	1	in	in	ADP
ejpam-3412	547	2	example	example	NOUN
ejpam-3412	547	3	13	13	NUM
ejpam-3412	547	4	,	,	PUNCT
ejpam-3412	547	5	we	we	PRON
ejpam-3412	547	6	know	know	VERB
ejpam-3412	547	7	that	that	SCONJ
ejpam-3412	547	8	(	(	PUNCT
ejpam-3412	547	9	f̃	f̃	PROPN
ejpam-3412	547	10	,	,	PUNCT
ejpam-3412	547	11	e	e	NOUN
ejpam-3412	547	12	)	)	PUNCT
ejpam-3412	547	13	is	be	AUX
ejpam-3412	547	14	a	a	DET
ejpam-3412	547	15	price	price	NOUN
ejpam-3412	547	16	-	-	PUNCT
ejpam-3412	547	17	fuzzy	fuzzy	NOUN
ejpam-3412	547	18	soft	soft	ADJ
ejpam-3412	547	19	near	near	ADP
ejpam-3412	547	20	ups	up	NOUN
ejpam-3412	547	21	-	-	PUNCT
ejpam-3412	547	22	filter	filter	NOUN
ejpam-3412	547	23	of	of	ADP
ejpam-3412	547	24	a	a	DET
ejpam-3412	547	25	but	but	CCONJ
ejpam-3412	547	26	f̃[price	f̃[price	NOUN
ejpam-3412	547	27	]	]	PUNCT
ejpam-3412	547	28	is	be	AUX
ejpam-3412	547	29	not	not	PART
ejpam-3412	547	30	a	a	DET
ejpam-3412	547	31	fuzzy	fuzzy	ADJ
ejpam-3412	547	32	near	near	ADP
ejpam-3412	547	33	upi	upi	NOUN
ejpam-3412	547	34	-	-	PUNCT
ejpam-3412	547	35	filter	filter	NOUN
ejpam-3412	547	36	of	of	ADP
ejpam-3412	547	37	a.	a.	NOUN
ejpam-3412	547	38	indeed	indeed	ADV
ejpam-3412	547	39	,	,	PUNCT
ejpam-3412	547	40	f	f	PROPN
ejpam-3412	547	41	f̃[price	f̃[price	PROPN
ejpam-3412	547	42	]	]	X
ejpam-3412	547	43	(	(	PUNCT
ejpam-3412	547	44	6	6	NUM
ejpam-3412	547	45	∗	∗	NOUN
ejpam-3412	547	46	5	5	NUM
ejpam-3412	547	47	)	)	PUNCT
ejpam-3412	547	48	=	=	SYM
ejpam-3412	547	49	f	f	X
ejpam-3412	547	50	f̃[price	f̃[price	PROPN
ejpam-3412	547	51	]	]	X
ejpam-3412	547	52	(	(	PUNCT
ejpam-3412	547	53	7	7	X
ejpam-3412	547	54	)	)	PUNCT
ejpam-3412	547	55	=	=	SYM
ejpam-3412	547	56	0.3	0.3	NUM
ejpam-3412	547	57	�	�	PROPN
ejpam-3412	547	58	0.7	0.7	NUM
ejpam-3412	547	59	=	=	SYM
ejpam-3412	547	60	max{0.7	max{0.7	PROPN
ejpam-3412	547	61	,	,	PUNCT
ejpam-3412	547	62	0.1	0.1	NUM
ejpam-3412	547	63	}	}	PUNCT
ejpam-3412	547	64	=	=	SYM
ejpam-3412	547	65	max{f	max{f	PROPN
ejpam-3412	547	66	f̃[price	f̃[price	PROPN
ejpam-3412	547	67	]	]	PUNCT
ejpam-3412	547	68	(	(	PUNCT
ejpam-3412	547	69	6	6	NUM
ejpam-3412	547	70	)	)	PUNCT
ejpam-3412	547	71	,	,	PUNCT
ejpam-3412	547	72	f	f	PROPN
ejpam-3412	547	73	f̃[price	f̃[price	PROPN
ejpam-3412	547	74	]	]	X
ejpam-3412	547	75	(	(	PUNCT
ejpam-3412	547	76	5	5	NUM
ejpam-3412	547	77	)	)	PUNCT
ejpam-3412	547	78	}	}	PUNCT
ejpam-3412	547	79	.	.	PUNCT
ejpam-3412	548	1	hence	hence	ADV
ejpam-3412	548	2	,	,	PUNCT
ejpam-3412	548	3	(	(	PUNCT
ejpam-3412	548	4	f̃	f̃	PROPN
ejpam-3412	548	5	,	,	PUNCT
ejpam-3412	548	6	e	e	NOUN
ejpam-3412	548	7	)	)	PUNCT
ejpam-3412	548	8	is	be	AUX
ejpam-3412	548	9	not	not	PART
ejpam-3412	548	10	a	a	DET
ejpam-3412	548	11	price	price	NOUN
ejpam-3412	548	12	-	-	PUNCT
ejpam-3412	548	13	fuzzy	fuzzy	NOUN
ejpam-3412	548	14	soft	soft	ADJ
ejpam-3412	548	15	near	near	ADP
ejpam-3412	548	16	upi	upi	NOUN
ejpam-3412	548	17	-	-	PUNCT
ejpam-3412	548	18	filter	filter	NOUN
ejpam-3412	548	19	of	of	ADP
ejpam-3412	548	20	a.	a.	NOUN
ejpam-3412	548	21	example	example	NOUN
ejpam-3412	548	22	20	20	NUM
ejpam-3412	548	23	.	.	PUNCT
ejpam-3412	549	1	in	in	ADP
ejpam-3412	549	2	example	example	NOUN
ejpam-3412	549	3	17	17	NUM
ejpam-3412	549	4	,	,	PUNCT
ejpam-3412	549	5	we	we	PRON
ejpam-3412	549	6	know	know	VERB
ejpam-3412	549	7	that	that	SCONJ
ejpam-3412	549	8	(	(	PUNCT
ejpam-3412	549	9	f̃	f̃	PROPN
ejpam-3412	549	10	,	,	PUNCT
ejpam-3412	549	11	e	e	NOUN
ejpam-3412	549	12	)	)	PUNCT
ejpam-3412	549	13	is	be	AUX
ejpam-3412	549	14	a	a	DET
ejpam-3412	549	15	monkey	monkey	NOUN
ejpam-3412	549	16	-	-	PUNCT
ejpam-3412	549	17	fuzzy	fuzzy	ADJ
ejpam-3412	549	18	soft	soft	ADJ
ejpam-3412	549	19	upi	upi	NOUN
ejpam-3412	549	20	-	-	PUNCT
ejpam-3412	549	21	subalgebra	subalgebra	NOUN
ejpam-3412	549	22	of	of	ADP
ejpam-3412	549	23	a	a	DET
ejpam-3412	549	24	but	but	CCONJ
ejpam-3412	549	25	f̃[monkey	f̃[monkey	NUM
ejpam-3412	549	26	]	]	PUNCT
ejpam-3412	549	27	is	be	AUX
ejpam-3412	549	28	not	not	PART
ejpam-3412	549	29	a	a	DET
ejpam-3412	549	30	fuzzy	fuzzy	ADJ
ejpam-3412	549	31	near	near	ADP
ejpam-3412	549	32	upi	upi	NOUN
ejpam-3412	549	33	-	-	PUNCT
ejpam-3412	549	34	filter	filter	NOUN
ejpam-3412	549	35	of	of	ADP
ejpam-3412	549	36	a.	a.	NOUN
ejpam-3412	549	37	indeed	indeed	ADV
ejpam-3412	549	38	,	,	PUNCT
ejpam-3412	549	39	f	f	PROPN
ejpam-3412	549	40	f̃[monkey	f̃[monkey	PROPN
ejpam-3412	549	41	]	]	X
ejpam-3412	549	42	(	(	PUNCT
ejpam-3412	549	43	apple	apple	NOUN
ejpam-3412	549	44	·	·	PUNCT
ejpam-3412	549	45	banana	banana	NOUN
ejpam-3412	549	46	)	)	PUNCT
ejpam-3412	550	1	=	=	SYM
ejpam-3412	550	2	f	f	X
ejpam-3412	550	3	f̃[monkey	f̃[monkey	PROPN
ejpam-3412	550	4	]	]	X
ejpam-3412	550	5	(	(	PUNCT
ejpam-3412	550	6	apple	apple	NOUN
ejpam-3412	550	7	)	)	PUNCT
ejpam-3412	550	8	=	=	SYM
ejpam-3412	550	9	0.4	0.4	NUM
ejpam-3412	550	10	�	�	PROPN
ejpam-3412	550	11	0.8	0.8	NUM
ejpam-3412	550	12	=	=	SYM
ejpam-3412	550	13	f	f	SYM
ejpam-3412	550	14	f̃[monkey	f̃[monkey	PROPN
ejpam-3412	550	15	]	]	X
ejpam-3412	550	16	(	(	PUNCT
ejpam-3412	550	17	banana	banana	NOUN
ejpam-3412	550	18	)	)	PUNCT
ejpam-3412	550	19	.	.	PUNCT
ejpam-3412	551	1	hence	hence	ADV
ejpam-3412	551	2	,	,	PUNCT
ejpam-3412	551	3	(	(	PUNCT
ejpam-3412	551	4	f̃	f̃	PROPN
ejpam-3412	551	5	,	,	PUNCT
ejpam-3412	551	6	e	e	NOUN
ejpam-3412	551	7	)	)	PUNCT
ejpam-3412	551	8	is	be	AUX
ejpam-3412	551	9	not	not	PART
ejpam-3412	551	10	a	a	DET
ejpam-3412	551	11	monkey	monkey	NOUN
ejpam-3412	551	12	-	-	PUNCT
ejpam-3412	551	13	fuzzy	fuzzy	ADJ
ejpam-3412	551	14	soft	soft	ADJ
ejpam-3412	551	15	near	near	ADP
ejpam-3412	551	16	upi	upi	NOUN
ejpam-3412	551	17	-	-	PUNCT
ejpam-3412	551	18	filter	filter	NOUN
ejpam-3412	551	19	of	of	ADP
ejpam-3412	551	20	a.	a.	NOUN
ejpam-3412	551	21	in	in	ADP
ejpam-3412	551	22	the	the	DET
ejpam-3412	551	23	next	next	ADJ
ejpam-3412	551	24	theorem	theorem	NOUN
ejpam-3412	551	25	,	,	PUNCT
ejpam-3412	551	26	we	we	PRON
ejpam-3412	551	27	give	give	VERB
ejpam-3412	551	28	necessary	necessary	ADJ
ejpam-3412	551	29	condition	condition	NOUN
ejpam-3412	551	30	for	for	ADP
ejpam-3412	551	31	fuzzy	fuzzy	ADJ
ejpam-3412	551	32	soft	soft	ADJ
ejpam-3412	551	33	upi	upi	NOUN
ejpam-3412	551	34	-	-	PUNCT
ejpam-3412	551	35	subalgebras	subalgebras	PROPN
ejpam-3412	551	36	as	as	ADP
ejpam-3412	551	37	fuzzy	fuzzy	ADJ
ejpam-3412	551	38	soft	soft	ADJ
ejpam-3412	551	39	near	near	ADP
ejpam-3412	551	40	upi	upi	NOUN
ejpam-3412	551	41	-	-	PUNCT
ejpam-3412	551	42	filters	filter	NOUN
ejpam-3412	551	43	of	of	ADP
ejpam-3412	551	44	f	f	PROPN
ejpam-3412	551	45	-up	-up	NOUN
ejpam-3412	551	46	-	-	PUNCT
ejpam-3412	551	47	semigroups	semigroup	NOUN
ejpam-3412	551	48	.	.	PUNCT
ejpam-3412	552	1	theorem	theorem	VERB
ejpam-3412	552	2	38	38	NUM
ejpam-3412	552	3	.	.	PUNCT
ejpam-3412	553	1	if	if	SCONJ
ejpam-3412	553	2	(	(	PUNCT
ejpam-3412	553	3	f̃	f̃	PROPN
ejpam-3412	553	4	,	,	PUNCT
ejpam-3412	553	5	e	e	NOUN
ejpam-3412	553	6	)	)	PUNCT
ejpam-3412	553	7	is	be	AUX
ejpam-3412	553	8	a	a	DET
ejpam-3412	553	9	fuzzy	fuzzy	ADJ
ejpam-3412	553	10	soft	soft	ADJ
ejpam-3412	553	11	upi	upi	NOUN
ejpam-3412	553	12	-	-	PUNCT
ejpam-3412	553	13	subalgebra	subalgebra	NOUN
ejpam-3412	553	14	of	of	ADP
ejpam-3412	553	15	a	a	DET
ejpam-3412	553	16	such	such	ADJ
ejpam-3412	553	17	that	that	PRON
ejpam-3412	553	18	for	for	ADP
ejpam-3412	553	19	all	all	DET
ejpam-3412	553	20	e	e	NOUN
ejpam-3412	553	21	∈	∈	PROPN
ejpam-3412	553	22	e	e	NOUN
ejpam-3412	553	23	,	,	PUNCT
ejpam-3412	553	24	a	a	DET
ejpam-3412	553	25	fuzzy	fuzzy	ADJ
ejpam-3412	553	26	set	set	NOUN
ejpam-3412	553	27	f̃[e	f̃[e	NOUN
ejpam-3412	553	28	]	]	X
ejpam-3412	553	29	in	in	ADP
ejpam-3412	553	30	a	a	DET
ejpam-3412	553	31	satisfies	satisfie	NOUN
ejpam-3412	553	32	the	the	DET
ejpam-3412	553	33	condition	condition	NOUN
ejpam-3412	553	34	(	(	PUNCT
ejpam-3412	553	35	2.5	2.5	NUM
ejpam-3412	553	36	)	)	PUNCT
ejpam-3412	553	37	,	,	PUNCT
ejpam-3412	553	38	then	then	ADV
ejpam-3412	553	39	(	(	PUNCT
ejpam-3412	553	40	f̃	f̃	PROPN
ejpam-3412	553	41	,	,	PUNCT
ejpam-3412	553	42	e	e	NOUN
ejpam-3412	553	43	)	)	PUNCT
ejpam-3412	553	44	is	be	AUX
ejpam-3412	553	45	a	a	DET
ejpam-3412	553	46	fuzzy	fuzzy	ADJ
ejpam-3412	553	47	soft	soft	ADJ
ejpam-3412	553	48	near	near	ADP
ejpam-3412	553	49	upi	upi	NOUN
ejpam-3412	553	50	-	-	PUNCT
ejpam-3412	553	51	filter	filter	NOUN
ejpam-3412	553	52	of	of	ADP
ejpam-3412	553	53	a.	a.	NOUN
ejpam-3412	553	54	proof	proof	NOUN
ejpam-3412	553	55	.	.	PUNCT
ejpam-3412	554	1	it	it	PRON
ejpam-3412	554	2	is	be	AUX
ejpam-3412	554	3	straightforward	straightforward	ADJ
ejpam-3412	554	4	by	by	ADP
ejpam-3412	554	5	theorem	theorem	NOUN
ejpam-3412	554	6	12	12	NUM
ejpam-3412	554	7	.	.	PUNCT
ejpam-3412	555	1	the	the	DET
ejpam-3412	555	2	proof	proof	NOUN
ejpam-3412	555	3	of	of	ADP
ejpam-3412	555	4	the	the	DET
ejpam-3412	555	5	following	follow	VERB
ejpam-3412	555	6	theorem	theorem	NOUN
ejpam-3412	555	7	can	can	AUX
ejpam-3412	555	8	be	be	AUX
ejpam-3412	555	9	verified	verify	VERB
ejpam-3412	555	10	easily	easily	ADV
ejpam-3412	555	11	.	.	PUNCT
ejpam-3412	556	1	theorem	theorem	VERB
ejpam-3412	556	2	39	39	NUM
ejpam-3412	556	3	.	.	PUNCT
ejpam-3412	557	1	if	if	SCONJ
ejpam-3412	557	2	(	(	PUNCT
ejpam-3412	557	3	f̃	f̃	PROPN
ejpam-3412	557	4	,	,	PUNCT
ejpam-3412	557	5	e	e	NOUN
ejpam-3412	557	6	)	)	PUNCT
ejpam-3412	557	7	is	be	AUX
ejpam-3412	557	8	a	a	DET
ejpam-3412	557	9	fuzzy	fuzzy	ADJ
ejpam-3412	557	10	soft	soft	ADJ
ejpam-3412	557	11	near	near	ADP
ejpam-3412	557	12	upi	upi	NOUN
ejpam-3412	557	13	-	-	PUNCT
ejpam-3412	557	14	filter	filter	NOUN
ejpam-3412	557	15	of	of	ADP
ejpam-3412	557	16	a	a	PRON
ejpam-3412	557	17	and	and	CCONJ
ejpam-3412	557	18	∅	∅	NOUN
ejpam-3412	557	19	6=	6=	ADP
ejpam-3412	557	20	e∗	e∗	PROPN
ejpam-3412	557	21	⊆	⊆	NUM
ejpam-3412	557	22	e	e	NOUN
ejpam-3412	557	23	,	,	PUNCT
ejpam-3412	557	24	then	then	ADV
ejpam-3412	557	25	(	(	PUNCT
ejpam-3412	557	26	f̃|e∗	f̃|e∗	PROPN
ejpam-3412	557	27	,	,	PUNCT
ejpam-3412	557	28	e∗	e∗	PROPN
ejpam-3412	557	29	)	)	PUNCT
ejpam-3412	557	30	is	be	AUX
ejpam-3412	557	31	a	a	DET
ejpam-3412	557	32	fuzzy	fuzzy	ADJ
ejpam-3412	557	33	soft	soft	ADJ
ejpam-3412	557	34	near	near	ADP
ejpam-3412	557	35	upi	upi	NOUN
ejpam-3412	557	36	-	-	PUNCT
ejpam-3412	557	37	filter	filter	NOUN
ejpam-3412	557	38	of	of	ADP
ejpam-3412	557	39	a.	a.	NOUN
ejpam-3412	557	40	by	by	ADP
ejpam-3412	557	41	using	use	VERB
ejpam-3412	557	42	theorem	theorem	NOUN
ejpam-3412	557	43	9	9	NUM
ejpam-3412	557	44	,	,	PUNCT
ejpam-3412	557	45	we	we	PRON
ejpam-3412	557	46	can	can	AUX
ejpam-3412	557	47	obtain	obtain	VERB
ejpam-3412	557	48	the	the	DET
ejpam-3412	557	49	following	follow	VERB
ejpam-3412	557	50	two	two	NUM
ejpam-3412	557	51	theorems	theorem	NOUN
ejpam-3412	557	52	in	in	ADP
ejpam-3412	557	53	the	the	DET
ejpam-3412	557	54	same	same	ADJ
ejpam-3412	557	55	way	way	NOUN
ejpam-3412	557	56	as	as	ADP
ejpam-3412	557	57	theorems	theorem	NOUN
ejpam-3412	557	58	22	22	NUM
ejpam-3412	557	59	and	and	CCONJ
ejpam-3412	557	60	23	23	NUM
ejpam-3412	557	61	.	.	PUNCT
ejpam-3412	558	1	theorem	theorem	VERB
ejpam-3412	558	2	40	40	NUM
ejpam-3412	558	3	.	.	PUNCT
ejpam-3412	559	1	the	the	DET
ejpam-3412	559	2	extended	extended	ADJ
ejpam-3412	559	3	intersection	intersection	NOUN
ejpam-3412	559	4	of	of	ADP
ejpam-3412	559	5	two	two	NUM
ejpam-3412	559	6	fuzzy	fuzzy	ADJ
ejpam-3412	559	7	soft	soft	ADJ
ejpam-3412	559	8	near	near	ADP
ejpam-3412	559	9	upi	upi	NOUN
ejpam-3412	559	10	-	-	PUNCT
ejpam-3412	559	11	filters	filter	NOUN
ejpam-3412	559	12	of	of	ADP
ejpam-3412	559	13	a	a	PRON
ejpam-3412	559	14	is	be	AUX
ejpam-3412	559	15	also	also	ADV
ejpam-3412	559	16	a	a	DET
ejpam-3412	559	17	fuzzy	fuzzy	ADJ
ejpam-3412	559	18	soft	soft	ADJ
ejpam-3412	559	19	near	near	ADP
ejpam-3412	559	20	upi	upi	NOUN
ejpam-3412	559	21	-	-	PUNCT
ejpam-3412	559	22	filter	filter	NOUN
ejpam-3412	559	23	.	.	PUNCT
ejpam-3412	560	1	moreover	moreover	ADV
ejpam-3412	560	2	,	,	PUNCT
ejpam-3412	560	3	the	the	DET
ejpam-3412	560	4	intersection	intersection	NOUN
ejpam-3412	560	5	of	of	ADP
ejpam-3412	560	6	two	two	NUM
ejpam-3412	560	7	fuzzy	fuzzy	ADJ
ejpam-3412	560	8	soft	soft	ADJ
ejpam-3412	560	9	near	near	ADP
ejpam-3412	560	10	upi	upi	NOUN
ejpam-3412	560	11	-	-	PUNCT
ejpam-3412	560	12	filters	filter	NOUN
ejpam-3412	560	13	of	of	ADP
ejpam-3412	560	14	a	a	PRON
ejpam-3412	560	15	is	be	AUX
ejpam-3412	560	16	also	also	ADV
ejpam-3412	560	17	a	a	DET
ejpam-3412	560	18	fuzzy	fuzzy	ADJ
ejpam-3412	560	19	soft	soft	ADJ
ejpam-3412	560	20	near	near	ADP
ejpam-3412	560	21	upi	upi	NOUN
ejpam-3412	560	22	-	-	PUNCT
ejpam-3412	560	23	filter	filter	NOUN
ejpam-3412	560	24	.	.	PUNCT
ejpam-3412	561	1	theorem	theorem	VERB
ejpam-3412	561	2	41	41	NUM
ejpam-3412	561	3	.	.	PUNCT
ejpam-3412	562	1	the	the	DET
ejpam-3412	562	2	union	union	NOUN
ejpam-3412	562	3	of	of	ADP
ejpam-3412	562	4	two	two	NUM
ejpam-3412	562	5	fuzzy	fuzzy	ADJ
ejpam-3412	562	6	soft	soft	ADJ
ejpam-3412	562	7	near	near	ADP
ejpam-3412	562	8	upi	upi	NOUN
ejpam-3412	562	9	-	-	PUNCT
ejpam-3412	562	10	filters	filter	NOUN
ejpam-3412	562	11	of	of	ADP
ejpam-3412	562	12	a	a	PRON
ejpam-3412	562	13	is	be	AUX
ejpam-3412	562	14	also	also	ADV
ejpam-3412	562	15	a	a	DET
ejpam-3412	562	16	fuzzy	fuzzy	ADJ
ejpam-3412	562	17	soft	soft	ADJ
ejpam-3412	562	18	near	near	ADP
ejpam-3412	562	19	upi	upi	NOUN
ejpam-3412	562	20	-	-	PUNCT
ejpam-3412	562	21	filter	filter	NOUN
ejpam-3412	562	22	.	.	PUNCT
ejpam-3412	563	1	moreover	moreover	ADV
ejpam-3412	563	2	,	,	PUNCT
ejpam-3412	563	3	the	the	DET
ejpam-3412	563	4	restricted	restricted	ADJ
ejpam-3412	563	5	union	union	NOUN
ejpam-3412	563	6	of	of	ADP
ejpam-3412	563	7	two	two	NUM
ejpam-3412	563	8	fuzzy	fuzzy	ADJ
ejpam-3412	563	9	soft	soft	ADJ
ejpam-3412	563	10	near	near	ADP
ejpam-3412	563	11	upi	upi	NOUN
ejpam-3412	563	12	-	-	PUNCT
ejpam-3412	563	13	filters	filter	NOUN
ejpam-3412	563	14	of	of	ADP
ejpam-3412	563	15	a	a	PRON
ejpam-3412	563	16	is	be	AUX
ejpam-3412	563	17	also	also	ADV
ejpam-3412	563	18	a	a	DET
ejpam-3412	563	19	fuzzy	fuzzy	ADJ
ejpam-3412	563	20	soft	soft	ADJ
ejpam-3412	563	21	near	near	ADP
ejpam-3412	563	22	upi	upi	NOUN
ejpam-3412	563	23	-	-	PUNCT
ejpam-3412	563	24	filter	filter	NOUN
ejpam-3412	563	25	.	.	PUNCT
ejpam-3412	564	1	a.	a.	PROPN
ejpam-3412	564	2	satirad	satirad	PROPN
ejpam-3412	564	3	,	,	PUNCT
ejpam-3412	564	4	a.	a.	NOUN
ejpam-3412	564	5	iampan	iampan	PROPN
ejpam-3412	564	6	/	/	SYM
ejpam-3412	564	7	eur	eur	PROPN
ejpam-3412	564	8	.	.	PUNCT
ejpam-3412	565	1	j.	j.	PROPN
ejpam-3412	565	2	pure	pure	PROPN
ejpam-3412	565	3	appl	appl	PROPN
ejpam-3412	565	4	.	.	PROPN
ejpam-3412	565	5	math	math	PROPN
ejpam-3412	565	6	,	,	PUNCT
ejpam-3412	565	7	12	12	NUM
ejpam-3412	565	8	(	(	PUNCT
ejpam-3412	565	9	2	2	NUM
ejpam-3412	565	10	)	)	PUNCT
ejpam-3412	565	11	(	(	PUNCT
ejpam-3412	565	12	2019	2019	NUM
ejpam-3412	565	13	)	)	PUNCT
ejpam-3412	565	14	,	,	PUNCT
ejpam-3412	565	15	294	294	NUM
ejpam-3412	565	16	-	-	SYM
ejpam-3412	565	17	331	331	NUM
ejpam-3412	565	18	319	319	NUM
ejpam-3412	565	19	3.5	3.5	NUM
ejpam-3412	565	20	.	.	PUNCT
ejpam-3412	566	1	fuzzy	fuzzy	ADJ
ejpam-3412	566	2	soft	soft	ADJ
ejpam-3412	566	3	ups	up	NOUN
ejpam-3412	566	4	-	-	PUNCT
ejpam-3412	566	5	filters	filter	NOUN
ejpam-3412	566	6	definition	definition	NOUN
ejpam-3412	566	7	22	22	NUM
ejpam-3412	566	8	.	.	PUNCT
ejpam-3412	567	1	a	a	DET
ejpam-3412	567	2	fuzzy	fuzzy	ADJ
ejpam-3412	567	3	soft	soft	ADJ
ejpam-3412	567	4	set	set	NOUN
ejpam-3412	567	5	(	(	PUNCT
ejpam-3412	567	6	f̃	f̃	PROPN
ejpam-3412	567	7	,	,	PUNCT
ejpam-3412	567	8	e	e	NOUN
ejpam-3412	567	9	)	)	PUNCT
ejpam-3412	567	10	over	over	ADP
ejpam-3412	567	11	a	a	PRON
ejpam-3412	567	12	is	be	AUX
ejpam-3412	567	13	called	call	VERB
ejpam-3412	567	14	a	a	DET
ejpam-3412	567	15	fuzzy	fuzzy	ADJ
ejpam-3412	567	16	soft	soft	ADJ
ejpam-3412	567	17	ups	up	NOUN
ejpam-3412	567	18	-	-	PUNCT
ejpam-3412	567	19	filter	filter	NOUN
ejpam-3412	567	20	based	base	VERB
ejpam-3412	567	21	on	on	ADP
ejpam-3412	567	22	e	e	PROPN
ejpam-3412	567	23	∈	∈	PROPN
ejpam-3412	567	24	e	e	X
ejpam-3412	567	25	(	(	PUNCT
ejpam-3412	567	26	we	we	PRON
ejpam-3412	567	27	shortly	shortly	ADV
ejpam-3412	567	28	call	call	VERB
ejpam-3412	567	29	an	an	DET
ejpam-3412	567	30	e	e	ADJ
ejpam-3412	567	31	-	-	ADJ
ejpam-3412	567	32	fuzzy	fuzzy	ADJ
ejpam-3412	567	33	soft	soft	ADJ
ejpam-3412	567	34	ups	up	NOUN
ejpam-3412	567	35	-	-	PUNCT
ejpam-3412	567	36	filter	filter	NOUN
ejpam-3412	567	37	)	)	PUNCT
ejpam-3412	567	38	of	of	ADP
ejpam-3412	567	39	a	a	DET
ejpam-3412	567	40	if	if	SCONJ
ejpam-3412	567	41	a	a	DET
ejpam-3412	567	42	fuzzy	fuzzy	ADJ
ejpam-3412	567	43	set	set	NOUN
ejpam-3412	567	44	f̃[e	f̃[e	X
ejpam-3412	567	45	]	]	X
ejpam-3412	567	46	in	in	ADP
ejpam-3412	567	47	a	a	PRON
ejpam-3412	567	48	is	be	AUX
ejpam-3412	567	49	a	a	DET
ejpam-3412	567	50	fuzzy	fuzzy	ADJ
ejpam-3412	567	51	ups	up	NOUN
ejpam-3412	567	52	-	-	PUNCT
ejpam-3412	567	53	filter	filter	NOUN
ejpam-3412	567	54	of	of	ADP
ejpam-3412	567	55	a.	a.	NOUN
ejpam-3412	567	56	if	if	SCONJ
ejpam-3412	567	57	(	(	PUNCT
ejpam-3412	567	58	f̃	f̃	PROPN
ejpam-3412	567	59	,	,	PUNCT
ejpam-3412	567	60	e	e	NOUN
ejpam-3412	567	61	)	)	PUNCT
ejpam-3412	567	62	is	be	AUX
ejpam-3412	567	63	an	an	DET
ejpam-3412	567	64	e	e	ADJ
ejpam-3412	567	65	-	-	ADJ
ejpam-3412	567	66	fuzzy	fuzzy	ADJ
ejpam-3412	567	67	soft	soft	ADJ
ejpam-3412	567	68	ups	up	NOUN
ejpam-3412	567	69	-	-	PUNCT
ejpam-3412	567	70	filter	filter	NOUN
ejpam-3412	567	71	of	of	ADP
ejpam-3412	567	72	a	a	PRON
ejpam-3412	567	73	for	for	ADP
ejpam-3412	567	74	all	all	DET
ejpam-3412	567	75	e	e	NOUN
ejpam-3412	567	76	∈	∈	PROPN
ejpam-3412	567	77	e	e	NOUN
ejpam-3412	567	78	,	,	PUNCT
ejpam-3412	567	79	we	we	PRON
ejpam-3412	567	80	say	say	VERB
ejpam-3412	567	81	that	that	SCONJ
ejpam-3412	567	82	(	(	PUNCT
ejpam-3412	567	83	f̃	f̃	PROPN
ejpam-3412	567	84	,	,	PUNCT
ejpam-3412	567	85	e	e	NOUN
ejpam-3412	567	86	)	)	PUNCT
ejpam-3412	567	87	is	be	AUX
ejpam-3412	567	88	a	a	DET
ejpam-3412	567	89	fuzzy	fuzzy	ADJ
ejpam-3412	567	90	soft	soft	ADJ
ejpam-3412	567	91	ups	up	NOUN
ejpam-3412	567	92	-	-	PUNCT
ejpam-3412	567	93	filter	filter	NOUN
ejpam-3412	567	94	of	of	ADP
ejpam-3412	567	95	a.	a.	NOUN
ejpam-3412	567	96	in	in	ADP
ejpam-3412	567	97	the	the	DET
ejpam-3412	567	98	next	next	ADJ
ejpam-3412	567	99	theorem	theorem	NOUN
ejpam-3412	567	100	,	,	PUNCT
ejpam-3412	567	101	we	we	PRON
ejpam-3412	567	102	give	give	VERB
ejpam-3412	567	103	necessary	necessary	ADJ
ejpam-3412	567	104	condition	condition	NOUN
ejpam-3412	567	105	for	for	ADP
ejpam-3412	567	106	fuzzy	fuzzy	ADJ
ejpam-3412	567	107	soft	soft	ADJ
ejpam-3412	567	108	ups	up	NOUN
ejpam-3412	567	109	-	-	PUNCT
ejpam-3412	567	110	filters	filter	NOUN
ejpam-3412	567	111	of	of	ADP
ejpam-3412	567	112	f	f	PROPN
ejpam-3412	567	113	-upsemigroups	-upsemigroup	NOUN
ejpam-3412	567	114	.	.	PUNCT
ejpam-3412	568	1	theorem	theorem	VERB
ejpam-3412	568	2	42	42	NUM
ejpam-3412	568	3	.	.	PUNCT
ejpam-3412	569	1	if	if	SCONJ
ejpam-3412	569	2	(	(	PUNCT
ejpam-3412	569	3	f̃	f̃	PROPN
ejpam-3412	569	4	,	,	PUNCT
ejpam-3412	569	5	e	e	NOUN
ejpam-3412	569	6	)	)	PUNCT
ejpam-3412	569	7	is	be	AUX
ejpam-3412	569	8	a	a	DET
ejpam-3412	569	9	fuzzy	fuzzy	ADJ
ejpam-3412	569	10	soft	soft	ADJ
ejpam-3412	569	11	set	set	NOUN
ejpam-3412	569	12	over	over	ADP
ejpam-3412	569	13	a	a	DET
ejpam-3412	569	14	such	such	ADJ
ejpam-3412	569	15	that	that	PRON
ejpam-3412	569	16	for	for	ADP
ejpam-3412	569	17	all	all	DET
ejpam-3412	569	18	e	e	NOUN
ejpam-3412	569	19	∈	∈	PROPN
ejpam-3412	569	20	e	e	NOUN
ejpam-3412	569	21	,	,	PUNCT
ejpam-3412	569	22	a	a	DET
ejpam-3412	569	23	fuzzy	fuzzy	ADJ
ejpam-3412	569	24	set	set	NOUN
ejpam-3412	569	25	f̃[e	f̃[e	NOUN
ejpam-3412	569	26	]	]	X
ejpam-3412	569	27	in	in	ADP
ejpam-3412	569	28	a	a	DET
ejpam-3412	569	29	satisfies	satisfie	NOUN
ejpam-3412	569	30	the	the	DET
ejpam-3412	569	31	conditions	condition	NOUN
ejpam-3412	569	32	(	(	PUNCT
ejpam-3412	569	33	2.6	2.6	NUM
ejpam-3412	569	34	)	)	PUNCT
ejpam-3412	569	35	and	and	CCONJ
ejpam-3412	569	36	(	(	PUNCT
ejpam-3412	569	37	1.14	1.14	NUM
ejpam-3412	569	38	)	)	PUNCT
ejpam-3412	569	39	,	,	PUNCT
ejpam-3412	569	40	then	then	ADV
ejpam-3412	569	41	(	(	PUNCT
ejpam-3412	569	42	f̃	f̃	PROPN
ejpam-3412	569	43	,	,	PUNCT
ejpam-3412	569	44	e	e	NOUN
ejpam-3412	569	45	)	)	PUNCT
ejpam-3412	569	46	is	be	AUX
ejpam-3412	569	47	a	a	DET
ejpam-3412	569	48	fuzzy	fuzzy	ADJ
ejpam-3412	569	49	soft	soft	ADJ
ejpam-3412	569	50	ups	up	NOUN
ejpam-3412	569	51	-	-	PUNCT
ejpam-3412	569	52	filter	filter	NOUN
ejpam-3412	569	53	of	of	ADP
ejpam-3412	569	54	a.	a.	NOUN
ejpam-3412	569	55	proof	proof	NOUN
ejpam-3412	569	56	.	.	PUNCT
ejpam-3412	570	1	it	it	PRON
ejpam-3412	570	2	is	be	AUX
ejpam-3412	570	3	straightforward	straightforward	ADJ
ejpam-3412	570	4	by	by	ADP
ejpam-3412	570	5	proposition	proposition	NOUN
ejpam-3412	570	6	6	6	NUM
ejpam-3412	570	7	and	and	CCONJ
ejpam-3412	570	8	lemma	lemma	PROPN
ejpam-3412	570	9	1	1	NUM
ejpam-3412	570	10	(	(	PUNCT
ejpam-3412	570	11	1	1	NUM
ejpam-3412	570	12	)	)	PUNCT
ejpam-3412	570	13	.	.	PUNCT
ejpam-3412	571	1	from	from	ADP
ejpam-3412	571	2	figure	figure	NOUN
ejpam-3412	571	3	1	1	NUM
ejpam-3412	571	4	,	,	PUNCT
ejpam-3412	571	5	we	we	PRON
ejpam-3412	571	6	have	have	VERB
ejpam-3412	571	7	the	the	DET
ejpam-3412	571	8	following	follow	VERB
ejpam-3412	571	9	theorem	theorem	PROPN
ejpam-3412	571	10	.	.	PUNCT
ejpam-3412	571	11	theorem	theorem	PROPN
ejpam-3412	571	12	43	43	NUM
ejpam-3412	571	13	.	.	PUNCT
ejpam-3412	572	1	every	every	DET
ejpam-3412	572	2	e	e	ADJ
ejpam-3412	572	3	-	-	ADJ
ejpam-3412	572	4	fuzzy	fuzzy	ADJ
ejpam-3412	572	5	soft	soft	ADJ
ejpam-3412	572	6	ups	up	NOUN
ejpam-3412	572	7	-	-	PUNCT
ejpam-3412	572	8	filter	filter	NOUN
ejpam-3412	572	9	of	of	ADP
ejpam-3412	572	10	a	a	PRON
ejpam-3412	572	11	is	be	AUX
ejpam-3412	572	12	an	an	DET
ejpam-3412	572	13	e	e	ADJ
ejpam-3412	572	14	-	-	ADJ
ejpam-3412	572	15	fuzzy	fuzzy	ADJ
ejpam-3412	572	16	soft	soft	ADJ
ejpam-3412	572	17	near	near	ADP
ejpam-3412	572	18	ups	up	NOUN
ejpam-3412	572	19	-	-	PUNCT
ejpam-3412	572	20	filter	filter	NOUN
ejpam-3412	572	21	.	.	PUNCT
ejpam-3412	573	1	moreover	moreover	ADV
ejpam-3412	573	2	,	,	PUNCT
ejpam-3412	573	3	every	every	DET
ejpam-3412	573	4	fuzzy	fuzzy	ADJ
ejpam-3412	573	5	soft	soft	ADJ
ejpam-3412	573	6	ups	up	NOUN
ejpam-3412	573	7	-	-	PUNCT
ejpam-3412	573	8	filter	filter	NOUN
ejpam-3412	573	9	of	of	ADP
ejpam-3412	573	10	a	a	PRON
ejpam-3412	573	11	is	be	AUX
ejpam-3412	573	12	a	a	DET
ejpam-3412	573	13	fuzzy	fuzzy	ADJ
ejpam-3412	573	14	soft	soft	ADJ
ejpam-3412	573	15	near	near	ADP
ejpam-3412	573	16	ups	up	NOUN
ejpam-3412	573	17	-	-	PUNCT
ejpam-3412	573	18	filter	filter	NOUN
ejpam-3412	573	19	.	.	PUNCT
ejpam-3412	574	1	the	the	DET
ejpam-3412	574	2	following	follow	VERB
ejpam-3412	574	3	example	example	NOUN
ejpam-3412	574	4	shows	show	VERB
ejpam-3412	574	5	that	that	SCONJ
ejpam-3412	574	6	the	the	DET
ejpam-3412	574	7	converse	converse	NOUN
ejpam-3412	574	8	of	of	ADP
ejpam-3412	574	9	theorem	theorem	NOUN
ejpam-3412	574	10	43	43	NUM
ejpam-3412	574	11	is	be	AUX
ejpam-3412	574	12	not	not	PART
ejpam-3412	574	13	true	true	ADJ
ejpam-3412	574	14	.	.	PUNCT
ejpam-3412	575	1	example	example	NOUN
ejpam-3412	576	1	21	21	NUM
ejpam-3412	576	2	.	.	PUNCT
ejpam-3412	577	1	let	let	VERB
ejpam-3412	577	2	a	a	DET
ejpam-3412	577	3	be	be	AUX
ejpam-3412	577	4	a	a	DET
ejpam-3412	577	5	set	set	NOUN
ejpam-3412	577	6	of	of	ADP
ejpam-3412	577	7	four	four	NUM
ejpam-3412	577	8	coffees	coffee	NOUN
ejpam-3412	577	9	,	,	PUNCT
ejpam-3412	577	10	that	that	ADV
ejpam-3412	577	11	is	is	ADV
ejpam-3412	577	12	,	,	PUNCT
ejpam-3412	577	13	a	a	PRON
ejpam-3412	577	14	=	=	X
ejpam-3412	577	15	{	{	PUNCT
ejpam-3412	577	16	mocha(m	mocha(m	NOUN
ejpam-3412	577	17	)	)	PUNCT
ejpam-3412	577	18	,	,	PUNCT
ejpam-3412	577	19	americano(a	americano(a	PROPN
ejpam-3412	577	20	)	)	PUNCT
ejpam-3412	577	21	,	,	PUNCT
ejpam-3412	577	22	cappuccino(c	cappuccino(c	NOUN
ejpam-3412	577	23	)	)	PUNCT
ejpam-3412	577	24	,	,	PUNCT
ejpam-3412	577	25	latte(l	latte(l	PROPN
ejpam-3412	577	26	)	)	PUNCT
ejpam-3412	577	27	}	}	PUNCT
ejpam-3412	577	28	.	.	PUNCT
ejpam-3412	578	1	define	define	VERB
ejpam-3412	578	2	two	two	NUM
ejpam-3412	578	3	binary	binary	ADJ
ejpam-3412	578	4	operations	operation	NOUN
ejpam-3412	578	5	·	·	PUNCT
ejpam-3412	578	6	and	and	CCONJ
ejpam-3412	578	7	∗	∗	NOUN
ejpam-3412	578	8	on	on	ADP
ejpam-3412	578	9	a	a	PRON
ejpam-3412	578	10	as	as	ADP
ejpam-3412	578	11	the	the	DET
ejpam-3412	578	12	following	follow	VERB
ejpam-3412	578	13	cayley	cayley	ADJ
ejpam-3412	578	14	tables	table	NOUN
ejpam-3412	578	15	:	:	PUNCT
ejpam-3412	578	16	·	·	PUNCT
ejpam-3412	578	17	l	l	NOUN
ejpam-3412	578	18	a	a	DET
ejpam-3412	578	19	m	m	NOUN
ejpam-3412	578	20	c	c	NOUN
ejpam-3412	578	21	l	l	NOUN
ejpam-3412	578	22	l	l	NOUN
ejpam-3412	578	23	a	a	DET
ejpam-3412	578	24	m	m	NOUN
ejpam-3412	578	25	c	c	NOUN
ejpam-3412	578	26	a	a	DET
ejpam-3412	578	27	l	l	NOUN
ejpam-3412	578	28	l	l	NOUN
ejpam-3412	578	29	m	m	NOUN
ejpam-3412	578	30	c	c	NOUN
ejpam-3412	578	31	m	m	NOUN
ejpam-3412	578	32	l	l	NOUN
ejpam-3412	578	33	l	l	NOUN
ejpam-3412	578	34	l	l	NOUN
ejpam-3412	579	1	c	c	NOUN
ejpam-3412	579	2	c	c	NOUN
ejpam-3412	579	3	l	l	NOUN
ejpam-3412	579	4	l	l	X
ejpam-3412	579	5	l	l	X
ejpam-3412	579	6	l	l	NOUN
ejpam-3412	579	7	·	·	PUNCT
ejpam-3412	579	8	l	l	NOUN
ejpam-3412	579	9	a	a	DET
ejpam-3412	579	10	m	m	NOUN
ejpam-3412	579	11	c	c	NOUN
ejpam-3412	579	12	l	l	NOUN
ejpam-3412	579	13	l	l	NOUN
ejpam-3412	579	14	l	l	X
ejpam-3412	579	15	l	l	X
ejpam-3412	579	16	l	l	NOUN
ejpam-3412	579	17	a	a	DET
ejpam-3412	579	18	l	l	NOUN
ejpam-3412	579	19	l	l	NOUN
ejpam-3412	579	20	l	l	X
ejpam-3412	579	21	l	l	NOUN
ejpam-3412	579	22	m	m	NOUN
ejpam-3412	579	23	l	l	NOUN
ejpam-3412	579	24	l	l	NOUN
ejpam-3412	579	25	l	l	X
ejpam-3412	579	26	l	l	NOUN
ejpam-3412	579	27	c	c	NOUN
ejpam-3412	579	28	l	l	NOUN
ejpam-3412	579	29	l	l	X
ejpam-3412	579	30	l	l	NOUN
ejpam-3412	579	31	m	m	VERB
ejpam-3412	579	32	then	then	ADV
ejpam-3412	579	33	a	a	PRON
ejpam-3412	579	34	=	=	X
ejpam-3412	579	35	(	(	PUNCT
ejpam-3412	579	36	a	a	PRON
ejpam-3412	579	37	,	,	PUNCT
ejpam-3412	579	38	·	·	PUNCT
ejpam-3412	579	39	,	,	PUNCT
ejpam-3412	579	40	∗,latte	∗,latte	PROPN
ejpam-3412	579	41	)	)	PUNCT
ejpam-3412	579	42	is	be	AUX
ejpam-3412	579	43	an	an	DET
ejpam-3412	579	44	f	f	PROPN
ejpam-3412	579	45	-up	-up	NOUN
ejpam-3412	579	46	-	-	PUNCT
ejpam-3412	579	47	semigroup	semigroup	NOUN
ejpam-3412	579	48	.	.	PUNCT
ejpam-3412	580	1	let	let	AUX
ejpam-3412	580	2	(	(	PUNCT
ejpam-3412	580	3	f̃	f̃	PROPN
ejpam-3412	580	4	,	,	PUNCT
ejpam-3412	580	5	e	e	NOUN
ejpam-3412	580	6	)	)	PUNCT
ejpam-3412	580	7	be	be	AUX
ejpam-3412	580	8	a	a	DET
ejpam-3412	580	9	fuzzy	fuzzy	ADJ
ejpam-3412	580	10	soft	soft	ADJ
ejpam-3412	580	11	set	set	NOUN
ejpam-3412	580	12	over	over	ADP
ejpam-3412	580	13	a	a	DET
ejpam-3412	580	14	where	where	SCONJ
ejpam-3412	580	15	e	e	NOUN
ejpam-3412	580	16	:	:	PUNCT
ejpam-3412	580	17	=	=	SYM
ejpam-3412	580	18	{	{	PUNCT
ejpam-3412	580	19	sweetness	sweetness	NOUN
ejpam-3412	580	20	,	,	PUNCT
ejpam-3412	580	21	strong	strong	ADJ
ejpam-3412	580	22	,	,	PUNCT
ejpam-3412	580	23	aroma	aroma	NOUN
ejpam-3412	580	24	}	}	PUNCT
ejpam-3412	580	25	with	with	ADP
ejpam-3412	580	26	f̃[sweetness	f̃[sweetness	NUM
ejpam-3412	580	27	]	]	PUNCT
ejpam-3412	580	28	,	,	PUNCT
ejpam-3412	580	29	f̃[strong	f̃[strong	PROPN
ejpam-3412	580	30	]	]	X
ejpam-3412	580	31	,	,	PUNCT
ejpam-3412	580	32	and	and	CCONJ
ejpam-3412	580	33	f̃[aroma	f̃[aroma	PROPN
ejpam-3412	580	34	]	]	PUNCT
ejpam-3412	580	35	are	be	AUX
ejpam-3412	580	36	fuzzy	fuzzy	ADJ
ejpam-3412	580	37	sets	set	NOUN
ejpam-3412	580	38	in	in	ADP
ejpam-3412	580	39	a	a	DET
ejpam-3412	580	40	defined	define	VERB
ejpam-3412	580	41	as	as	SCONJ
ejpam-3412	580	42	follows	follow	VERB
ejpam-3412	580	43	:	:	PUNCT
ejpam-3412	580	44	f̃	f̃	PROPN
ejpam-3412	580	45	l	l	PROPN
ejpam-3412	580	46	a	a	DET
ejpam-3412	580	47	m	m	NOUN
ejpam-3412	580	48	c	c	NOUN
ejpam-3412	580	49	sweetness	sweetness	NOUN
ejpam-3412	580	50	0.8	0.8	NUM
ejpam-3412	580	51	0.1	0.1	NUM
ejpam-3412	580	52	0.6	0.6	NUM
ejpam-3412	580	53	0.6	0.6	NUM
ejpam-3412	580	54	strong	strong	ADJ
ejpam-3412	580	55	0.7	0.7	NUM
ejpam-3412	580	56	0.7	0.7	NUM
ejpam-3412	580	57	0.6	0.6	NUM
ejpam-3412	580	58	0.5	0.5	NUM
ejpam-3412	580	59	aroma	aroma	NOUN
ejpam-3412	580	60	0.5	0.5	NUM
ejpam-3412	580	61	0.3	0.3	NUM
ejpam-3412	580	62	0.4	0.4	NUM
ejpam-3412	580	63	0.1	0.1	NUM
ejpam-3412	580	64	then	then	ADV
ejpam-3412	580	65	(	(	PUNCT
ejpam-3412	580	66	f̃	f̃	PROPN
ejpam-3412	580	67	,	,	PUNCT
ejpam-3412	580	68	e	e	NOUN
ejpam-3412	580	69	)	)	PUNCT
ejpam-3412	580	70	is	be	AUX
ejpam-3412	580	71	a	a	DET
ejpam-3412	580	72	sweetness	sweetness	NOUN
ejpam-3412	580	73	-	-	PUNCT
ejpam-3412	580	74	fuzzy	fuzzy	ADJ
ejpam-3412	580	75	soft	soft	ADJ
ejpam-3412	580	76	near	near	ADP
ejpam-3412	580	77	ups	up	NOUN
ejpam-3412	580	78	-	-	PUNCT
ejpam-3412	580	79	filter	filter	NOUN
ejpam-3412	580	80	of	of	ADP
ejpam-3412	580	81	a	a	DET
ejpam-3412	580	82	but	but	CCONJ
ejpam-3412	580	83	f̃[sweetness	f̃[sweetness	NUM
ejpam-3412	580	84	]	]	PUNCT
ejpam-3412	580	85	is	be	AUX
ejpam-3412	580	86	not	not	PART
ejpam-3412	580	87	a	a	DET
ejpam-3412	580	88	fuzzy	fuzzy	ADJ
ejpam-3412	580	89	ups	up	NOUN
ejpam-3412	580	90	-	-	PUNCT
ejpam-3412	580	91	filter	filter	NOUN
ejpam-3412	580	92	of	of	ADP
ejpam-3412	580	93	a.	a.	NOUN
ejpam-3412	580	94	indeed	indeed	ADV
ejpam-3412	580	95	,	,	PUNCT
ejpam-3412	580	96	a.	a.	PROPN
ejpam-3412	580	97	satirad	satirad	PROPN
ejpam-3412	580	98	,	,	PUNCT
ejpam-3412	580	99	a.	a.	NOUN
ejpam-3412	580	100	iampan	iampan	PROPN
ejpam-3412	580	101	/	/	SYM
ejpam-3412	580	102	eur	eur	PROPN
ejpam-3412	580	103	.	.	PUNCT
ejpam-3412	581	1	j.	j.	PROPN
ejpam-3412	581	2	pure	pure	PROPN
ejpam-3412	581	3	appl	appl	PROPN
ejpam-3412	581	4	.	.	PROPN
ejpam-3412	581	5	math	math	PROPN
ejpam-3412	581	6	,	,	PUNCT
ejpam-3412	581	7	12	12	NUM
ejpam-3412	581	8	(	(	PUNCT
ejpam-3412	581	9	2	2	NUM
ejpam-3412	581	10	)	)	PUNCT
ejpam-3412	581	11	(	(	PUNCT
ejpam-3412	581	12	2019	2019	NUM
ejpam-3412	581	13	)	)	PUNCT
ejpam-3412	581	14	,	,	PUNCT
ejpam-3412	581	15	294	294	NUM
ejpam-3412	581	16	-	-	SYM
ejpam-3412	581	17	331	331	NUM
ejpam-3412	581	18	320	320	NUM
ejpam-3412	581	19	f	f	NOUN
ejpam-3412	581	20	f̃[sweetness	f̃[sweetness	PROPN
ejpam-3412	581	21	]	]	X
ejpam-3412	581	22	(	(	PUNCT
ejpam-3412	581	23	a	a	X
ejpam-3412	581	24	)	)	PUNCT
ejpam-3412	581	25	=	=	SYM
ejpam-3412	581	26	0.1	0.1	NUM
ejpam-3412	581	27	�	�	NOUN
ejpam-3412	581	28	0.6	0.6	NUM
ejpam-3412	581	29	=	=	SYM
ejpam-3412	581	30	min{0.8	min{0.8	PROPN
ejpam-3412	581	31	,	,	PUNCT
ejpam-3412	581	32	0.6	0.6	NUM
ejpam-3412	581	33	}	}	PUNCT
ejpam-3412	581	34	=	=	SYM
ejpam-3412	581	35	min{f	min{f	ADJ
ejpam-3412	581	36	f̃[sweetness	f̃[sweetness	NUM
ejpam-3412	581	37	]	]	X
ejpam-3412	581	38	(	(	PUNCT
ejpam-3412	581	39	l	l	NOUN
ejpam-3412	581	40	)	)	PUNCT
ejpam-3412	581	41	,	,	PUNCT
ejpam-3412	581	42	f	f	PROPN
ejpam-3412	581	43	f̃[sweetness	f̃[sweetness	PROPN
ejpam-3412	581	44	]	]	X
ejpam-3412	581	45	(	(	PUNCT
ejpam-3412	581	46	m	m	NOUN
ejpam-3412	581	47	)	)	PUNCT
ejpam-3412	581	48	}	}	PUNCT
ejpam-3412	581	49	=	=	SYM
ejpam-3412	581	50	min{f	min{f	ADJ
ejpam-3412	581	51	f̃[sweetness	f̃[sweetness	NUM
ejpam-3412	581	52	]	]	X
ejpam-3412	581	53	(	(	PUNCT
ejpam-3412	581	54	m	m	PROPN
ejpam-3412	581	55	·	·	SYM
ejpam-3412	581	56	a	a	NOUN
ejpam-3412	581	57	)	)	PUNCT
ejpam-3412	581	58	,	,	PUNCT
ejpam-3412	581	59	f	f	PROPN
ejpam-3412	581	60	f̃[sweetness	f̃[sweetness	PROPN
ejpam-3412	581	61	]	]	X
ejpam-3412	581	62	(	(	PUNCT
ejpam-3412	581	63	m	m	NOUN
ejpam-3412	581	64	)	)	PUNCT
ejpam-3412	581	65	}	}	PUNCT
ejpam-3412	581	66	hence	hence	ADV
ejpam-3412	581	67	,	,	PUNCT
ejpam-3412	581	68	(	(	PUNCT
ejpam-3412	581	69	f̃	f̃	PROPN
ejpam-3412	581	70	,	,	PUNCT
ejpam-3412	581	71	e	e	NOUN
ejpam-3412	581	72	)	)	PUNCT
ejpam-3412	581	73	is	be	AUX
ejpam-3412	581	74	not	not	PART
ejpam-3412	581	75	a	a	DET
ejpam-3412	581	76	sweetness	sweetness	NOUN
ejpam-3412	581	77	-	-	PUNCT
ejpam-3412	581	78	fuzzy	fuzzy	ADJ
ejpam-3412	581	79	soft	soft	ADJ
ejpam-3412	581	80	ups	up	NOUN
ejpam-3412	581	81	-	-	PUNCT
ejpam-3412	581	82	filter	filter	NOUN
ejpam-3412	581	83	of	of	ADP
ejpam-3412	581	84	a.	a.	NOUN
ejpam-3412	581	85	in	in	ADP
ejpam-3412	581	86	the	the	DET
ejpam-3412	581	87	next	next	ADJ
ejpam-3412	581	88	theorem	theorem	NOUN
ejpam-3412	581	89	,	,	PUNCT
ejpam-3412	581	90	we	we	PRON
ejpam-3412	581	91	give	give	VERB
ejpam-3412	581	92	necessary	necessary	ADJ
ejpam-3412	581	93	condition	condition	NOUN
ejpam-3412	581	94	for	for	ADP
ejpam-3412	581	95	fuzzy	fuzzy	ADJ
ejpam-3412	581	96	soft	soft	ADJ
ejpam-3412	581	97	near	near	ADP
ejpam-3412	581	98	ups	up	NOUN
ejpam-3412	581	99	-	-	PUNCT
ejpam-3412	581	100	filters	filter	NOUN
ejpam-3412	581	101	as	as	ADP
ejpam-3412	581	102	fuzzy	fuzzy	ADJ
ejpam-3412	581	103	soft	soft	ADJ
ejpam-3412	581	104	ups	up	NOUN
ejpam-3412	581	105	-	-	PUNCT
ejpam-3412	581	106	filters	filter	NOUN
ejpam-3412	581	107	of	of	ADP
ejpam-3412	581	108	f	f	PROPN
ejpam-3412	581	109	-up	-up	NOUN
ejpam-3412	581	110	-	-	PUNCT
ejpam-3412	581	111	semigroups	semigroup	NOUN
ejpam-3412	581	112	.	.	PUNCT
ejpam-3412	582	1	theorem	theorem	NOUN
ejpam-3412	582	2	44	44	NUM
ejpam-3412	582	3	.	.	PUNCT
ejpam-3412	583	1	if	if	SCONJ
ejpam-3412	583	2	(	(	PUNCT
ejpam-3412	583	3	f̃	f̃	PROPN
ejpam-3412	583	4	,	,	PUNCT
ejpam-3412	583	5	e	e	NOUN
ejpam-3412	583	6	)	)	PUNCT
ejpam-3412	583	7	is	be	AUX
ejpam-3412	583	8	a	a	DET
ejpam-3412	583	9	fuzzy	fuzzy	ADJ
ejpam-3412	583	10	soft	soft	ADJ
ejpam-3412	583	11	near	near	ADP
ejpam-3412	583	12	ups	up	NOUN
ejpam-3412	583	13	-	-	PUNCT
ejpam-3412	583	14	filter	filter	NOUN
ejpam-3412	583	15	of	of	ADP
ejpam-3412	583	16	a	a	DET
ejpam-3412	583	17	such	such	ADJ
ejpam-3412	583	18	that	that	PRON
ejpam-3412	583	19	for	for	ADP
ejpam-3412	583	20	all	all	DET
ejpam-3412	583	21	e	e	NOUN
ejpam-3412	583	22	∈	∈	PROPN
ejpam-3412	583	23	e	e	NOUN
ejpam-3412	583	24	,	,	PUNCT
ejpam-3412	583	25	a	a	DET
ejpam-3412	583	26	fuzzy	fuzzy	ADJ
ejpam-3412	583	27	set	set	NOUN
ejpam-3412	583	28	f̃[e	f̃[e	NOUN
ejpam-3412	583	29	]	]	X
ejpam-3412	583	30	in	in	ADP
ejpam-3412	583	31	a	a	DET
ejpam-3412	583	32	satisfies	satisfie	NOUN
ejpam-3412	583	33	the	the	DET
ejpam-3412	583	34	condition	condition	NOUN
ejpam-3412	583	35	(	(	PUNCT
ejpam-3412	583	36	2.7	2.7	NUM
ejpam-3412	583	37	)	)	PUNCT
ejpam-3412	583	38	,	,	PUNCT
ejpam-3412	583	39	then	then	ADV
ejpam-3412	583	40	(	(	PUNCT
ejpam-3412	583	41	f̃	f̃	PROPN
ejpam-3412	583	42	,	,	PUNCT
ejpam-3412	583	43	e	e	NOUN
ejpam-3412	583	44	)	)	PUNCT
ejpam-3412	583	45	is	be	AUX
ejpam-3412	583	46	a	a	DET
ejpam-3412	583	47	fuzzy	fuzzy	ADJ
ejpam-3412	583	48	soft	soft	ADJ
ejpam-3412	583	49	ups	up	NOUN
ejpam-3412	583	50	-	-	PUNCT
ejpam-3412	583	51	filter	filter	NOUN
ejpam-3412	583	52	of	of	ADP
ejpam-3412	583	53	a.	a.	NOUN
ejpam-3412	583	54	proof	proof	NOUN
ejpam-3412	583	55	.	.	PUNCT
ejpam-3412	584	1	it	it	PRON
ejpam-3412	584	2	is	be	AUX
ejpam-3412	584	3	straightforward	straightforward	ADJ
ejpam-3412	584	4	by	by	ADP
ejpam-3412	584	5	theorem	theorem	NOUN
ejpam-3412	584	6	14	14	NUM
ejpam-3412	584	7	.	.	PUNCT
ejpam-3412	585	1	the	the	DET
ejpam-3412	585	2	proof	proof	NOUN
ejpam-3412	585	3	of	of	ADP
ejpam-3412	585	4	the	the	DET
ejpam-3412	585	5	following	follow	VERB
ejpam-3412	585	6	theorem	theorem	NOUN
ejpam-3412	585	7	can	can	AUX
ejpam-3412	585	8	be	be	AUX
ejpam-3412	585	9	verified	verify	VERB
ejpam-3412	585	10	easily	easily	ADV
ejpam-3412	585	11	.	.	PUNCT
ejpam-3412	586	1	theorem	theorem	VERB
ejpam-3412	586	2	45	45	NUM
ejpam-3412	586	3	.	.	PUNCT
ejpam-3412	587	1	if	if	SCONJ
ejpam-3412	587	2	(	(	PUNCT
ejpam-3412	587	3	f̃	f̃	PROPN
ejpam-3412	587	4	,	,	PUNCT
ejpam-3412	587	5	e	e	NOUN
ejpam-3412	587	6	)	)	PUNCT
ejpam-3412	587	7	is	be	AUX
ejpam-3412	587	8	a	a	DET
ejpam-3412	587	9	fuzzy	fuzzy	ADJ
ejpam-3412	587	10	soft	soft	ADJ
ejpam-3412	587	11	ups	up	NOUN
ejpam-3412	587	12	-	-	PUNCT
ejpam-3412	587	13	filter	filter	NOUN
ejpam-3412	587	14	of	of	ADP
ejpam-3412	587	15	a	a	PRON
ejpam-3412	587	16	and	and	CCONJ
ejpam-3412	587	17	∅	∅	NOUN
ejpam-3412	587	18	6=	6=	ADP
ejpam-3412	587	19	e∗	e∗	PROPN
ejpam-3412	587	20	⊆	⊆	NUM
ejpam-3412	587	21	e	e	NOUN
ejpam-3412	587	22	,	,	PUNCT
ejpam-3412	587	23	then	then	ADV
ejpam-3412	587	24	(	(	PUNCT
ejpam-3412	587	25	f̃|e∗	f̃|e∗	PROPN
ejpam-3412	587	26	,	,	PUNCT
ejpam-3412	587	27	e∗	e∗	PROPN
ejpam-3412	587	28	)	)	PUNCT
ejpam-3412	587	29	is	be	AUX
ejpam-3412	587	30	a	a	DET
ejpam-3412	587	31	fuzzy	fuzzy	ADJ
ejpam-3412	587	32	soft	soft	ADJ
ejpam-3412	587	33	ups	up	NOUN
ejpam-3412	587	34	-	-	PUNCT
ejpam-3412	587	35	filter	filter	NOUN
ejpam-3412	587	36	of	of	ADP
ejpam-3412	587	37	a.	a.	NOUN
ejpam-3412	587	38	the	the	DET
ejpam-3412	587	39	following	follow	VERB
ejpam-3412	587	40	two	two	NUM
ejpam-3412	587	41	theorems	theorem	NOUN
ejpam-3412	587	42	can	can	AUX
ejpam-3412	587	43	be	be	AUX
ejpam-3412	587	44	deduced	deduce	VERB
ejpam-3412	587	45	in	in	ADP
ejpam-3412	587	46	the	the	DET
ejpam-3412	587	47	same	same	ADJ
ejpam-3412	587	48	way	way	NOUN
ejpam-3412	587	49	as	as	ADP
ejpam-3412	587	50	theorems	theorem	NOUN
ejpam-3412	587	51	22	22	NUM
ejpam-3412	587	52	and	and	CCONJ
ejpam-3412	587	53	23	23	NUM
ejpam-3412	587	54	.	.	PUNCT
ejpam-3412	588	1	theorem	theorem	VERB
ejpam-3412	588	2	46	46	NUM
ejpam-3412	588	3	.	.	PUNCT
ejpam-3412	589	1	the	the	DET
ejpam-3412	589	2	extended	extended	ADJ
ejpam-3412	589	3	intersection	intersection	NOUN
ejpam-3412	589	4	of	of	ADP
ejpam-3412	589	5	two	two	NUM
ejpam-3412	589	6	fuzzy	fuzzy	ADJ
ejpam-3412	589	7	soft	soft	ADJ
ejpam-3412	589	8	ups	up	NOUN
ejpam-3412	589	9	-	-	PUNCT
ejpam-3412	589	10	filters	filter	NOUN
ejpam-3412	589	11	of	of	ADP
ejpam-3412	589	12	a	a	PRON
ejpam-3412	589	13	is	be	AUX
ejpam-3412	589	14	also	also	ADV
ejpam-3412	589	15	a	a	DET
ejpam-3412	589	16	fuzzy	fuzzy	ADJ
ejpam-3412	589	17	soft	soft	ADJ
ejpam-3412	589	18	ups	up	NOUN
ejpam-3412	589	19	-	-	PUNCT
ejpam-3412	589	20	filter	filter	NOUN
ejpam-3412	589	21	.	.	PUNCT
ejpam-3412	590	1	moreover	moreover	ADV
ejpam-3412	590	2	,	,	PUNCT
ejpam-3412	590	3	the	the	DET
ejpam-3412	590	4	intersection	intersection	NOUN
ejpam-3412	590	5	of	of	ADP
ejpam-3412	590	6	two	two	NUM
ejpam-3412	590	7	fuzzy	fuzzy	ADJ
ejpam-3412	590	8	soft	soft	ADJ
ejpam-3412	590	9	ups	up	NOUN
ejpam-3412	590	10	-	-	PUNCT
ejpam-3412	590	11	filters	filter	NOUN
ejpam-3412	590	12	of	of	ADP
ejpam-3412	590	13	a	a	PRON
ejpam-3412	590	14	is	be	AUX
ejpam-3412	590	15	also	also	ADV
ejpam-3412	590	16	a	a	DET
ejpam-3412	590	17	fuzzy	fuzzy	ADJ
ejpam-3412	590	18	soft	soft	ADJ
ejpam-3412	590	19	ups	up	NOUN
ejpam-3412	590	20	-	-	PUNCT
ejpam-3412	590	21	filter	filter	NOUN
ejpam-3412	590	22	.	.	PUNCT
ejpam-3412	591	1	theorem	theorem	VERB
ejpam-3412	591	2	47	47	NUM
ejpam-3412	591	3	.	.	PUNCT
ejpam-3412	592	1	the	the	DET
ejpam-3412	592	2	union	union	NOUN
ejpam-3412	592	3	of	of	ADP
ejpam-3412	592	4	two	two	NUM
ejpam-3412	592	5	fuzzy	fuzzy	ADJ
ejpam-3412	592	6	soft	soft	ADJ
ejpam-3412	592	7	ups	up	NOUN
ejpam-3412	592	8	-	-	PUNCT
ejpam-3412	592	9	filters	filter	NOUN
ejpam-3412	592	10	of	of	ADP
ejpam-3412	592	11	a	a	PRON
ejpam-3412	592	12	is	be	AUX
ejpam-3412	592	13	also	also	ADV
ejpam-3412	592	14	a	a	DET
ejpam-3412	592	15	fuzzy	fuzzy	ADJ
ejpam-3412	592	16	soft	soft	ADJ
ejpam-3412	592	17	ups	up	NOUN
ejpam-3412	592	18	-	-	PUNCT
ejpam-3412	592	19	filter	filter	NOUN
ejpam-3412	592	20	if	if	SCONJ
ejpam-3412	592	21	sets	set	NOUN
ejpam-3412	592	22	of	of	ADP
ejpam-3412	592	23	statistics	statistic	NOUN
ejpam-3412	592	24	of	of	ADP
ejpam-3412	592	25	two	two	NUM
ejpam-3412	592	26	fuzzy	fuzzy	ADJ
ejpam-3412	592	27	soft	soft	ADJ
ejpam-3412	592	28	ups	up	NOUN
ejpam-3412	592	29	-	-	PUNCT
ejpam-3412	592	30	filters	filter	NOUN
ejpam-3412	592	31	are	be	AUX
ejpam-3412	592	32	disjoint	disjoint	ADJ
ejpam-3412	592	33	.	.	PUNCT
ejpam-3412	593	1	the	the	DET
ejpam-3412	593	2	following	follow	VERB
ejpam-3412	593	3	example	example	NOUN
ejpam-3412	593	4	shows	show	VERB
ejpam-3412	593	5	that	that	SCONJ
ejpam-3412	593	6	theorem	theorem	VERB
ejpam-3412	593	7	47	47	NUM
ejpam-3412	593	8	is	be	AUX
ejpam-3412	593	9	not	not	PART
ejpam-3412	593	10	valid	valid	ADJ
ejpam-3412	593	11	if	if	SCONJ
ejpam-3412	593	12	sets	set	NOUN
ejpam-3412	593	13	of	of	ADP
ejpam-3412	593	14	statistics	statistic	NOUN
ejpam-3412	593	15	of	of	ADP
ejpam-3412	593	16	two	two	NUM
ejpam-3412	593	17	fuzzy	fuzzy	ADJ
ejpam-3412	593	18	soft	soft	ADJ
ejpam-3412	593	19	ups	up	NOUN
ejpam-3412	593	20	-	-	PUNCT
ejpam-3412	593	21	filters	filter	NOUN
ejpam-3412	593	22	are	be	AUX
ejpam-3412	593	23	not	not	PART
ejpam-3412	593	24	disjoint	disjoint	ADJ
ejpam-3412	593	25	.	.	PUNCT
ejpam-3412	593	26	example	example	NOUN
ejpam-3412	594	1	22	22	NUM
ejpam-3412	594	2	.	.	PUNCT
ejpam-3412	595	1	in	in	ADP
ejpam-3412	595	2	example	example	NOUN
ejpam-3412	595	3	14	14	NUM
ejpam-3412	595	4	,	,	PUNCT
ejpam-3412	595	5	we	we	PRON
ejpam-3412	595	6	have	have	AUX
ejpam-3412	595	7	(	(	PUNCT
ejpam-3412	595	8	g̃1	g̃1	NOUN
ejpam-3412	595	9	,	,	PUNCT
ejpam-3412	595	10	e1	e1	NOUN
ejpam-3412	595	11	)	)	PUNCT
ejpam-3412	595	12	and	and	CCONJ
ejpam-3412	595	13	(	(	PUNCT
ejpam-3412	595	14	g̃2	g̃2	PROPN
ejpam-3412	595	15	,	,	PUNCT
ejpam-3412	595	16	e2	e2	PROPN
ejpam-3412	595	17	)	)	PUNCT
ejpam-3412	595	18	are	be	AUX
ejpam-3412	595	19	two	two	NUM
ejpam-3412	595	20	fuzzy	fuzzy	ADJ
ejpam-3412	595	21	soft	soft	ADJ
ejpam-3412	595	22	ups	up	NOUN
ejpam-3412	595	23	-	-	PUNCT
ejpam-3412	595	24	filters	filter	NOUN
ejpam-3412	595	25	of	of	ADP
ejpam-3412	595	26	a.	a.	NOUN
ejpam-3412	595	27	since	since	SCONJ
ejpam-3412	595	28	price	price	NOUN
ejpam-3412	595	29	∈	∈	NOUN
ejpam-3412	595	30	e1	e1	NOUN
ejpam-3412	595	31	∩	∩	ADJ
ejpam-3412	595	32	e2	e2	PROPN
ejpam-3412	595	33	,	,	PUNCT
ejpam-3412	595	34	we	we	PRON
ejpam-3412	595	35	have	have	VERB
ejpam-3412	595	36	(	(	PUNCT
ejpam-3412	595	37	f	f	PROPN
ejpam-3412	595	38	g̃1[price]∪g̃2[price	g̃1[price]∪g̃2[price	X
ejpam-3412	595	39	]	]	X
ejpam-3412	595	40	)	)	PUNCT
ejpam-3412	595	41	(	(	PUNCT
ejpam-3412	595	42	6	6	NUM
ejpam-3412	595	43	∗	∗	NOUN
ejpam-3412	595	44	5	5	NUM
ejpam-3412	595	45	)	)	PUNCT
ejpam-3412	595	46	=	=	PUNCT
ejpam-3412	596	1	(	(	PUNCT
ejpam-3412	596	2	f	f	X
ejpam-3412	596	3	g̃1[price]∪g̃2[price	g̃1[price]∪g̃2[price	X
ejpam-3412	596	4	]	]	X
ejpam-3412	596	5	)	)	PUNCT
ejpam-3412	596	6	(	(	PUNCT
ejpam-3412	596	7	7	7	X
ejpam-3412	596	8	)	)	PUNCT
ejpam-3412	596	9	=	=	SYM
ejpam-3412	596	10	0.7	0.7	NUM
ejpam-3412	596	11	�	�	PROPN
ejpam-3412	596	12	0.8	0.8	NUM
ejpam-3412	596	13	=	=	SYM
ejpam-3412	596	14	min{0.9	min{0.9	PROPN
ejpam-3412	596	15	,	,	PUNCT
ejpam-3412	596	16	0.8	0.8	NUM
ejpam-3412	596	17	}	}	PUNCT
ejpam-3412	596	18	=	=	SYM
ejpam-3412	596	19	min{(f	min{(f	SYM
ejpam-3412	596	20	g̃1[price]∪g̃2[price	g̃1[price]∪g̃2[price	X
ejpam-3412	596	21	]	]	X
ejpam-3412	596	22	)	)	PUNCT
ejpam-3412	596	23	(	(	PUNCT
ejpam-3412	596	24	6	6	NUM
ejpam-3412	596	25	)	)	PUNCT
ejpam-3412	596	26	,	,	PUNCT
ejpam-3412	596	27	(	(	PUNCT
ejpam-3412	596	28	f	f	PROPN
ejpam-3412	596	29	g̃1[price]∪g̃2[price	g̃1[price]∪g̃2[price	X
ejpam-3412	596	30	]	]	X
ejpam-3412	596	31	)	)	PUNCT
ejpam-3412	596	32	(	(	PUNCT
ejpam-3412	596	33	5	5	NUM
ejpam-3412	596	34	)	)	PUNCT
ejpam-3412	596	35	}	}	PUNCT
ejpam-3412	596	36	.	.	PUNCT
ejpam-3412	597	1	thus	thus	ADV
ejpam-3412	597	2	g̃1[price]∪	g̃1[price]∪	NOUN
ejpam-3412	597	3	g̃2[price	g̃2[price	PROPN
ejpam-3412	597	4	]	]	PUNCT
ejpam-3412	597	5	is	be	AUX
ejpam-3412	597	6	not	not	PART
ejpam-3412	597	7	a	a	DET
ejpam-3412	597	8	fuzzy	fuzzy	ADJ
ejpam-3412	597	9	ups	up	NOUN
ejpam-3412	597	10	-	-	PUNCT
ejpam-3412	597	11	filter	filter	NOUN
ejpam-3412	597	12	of	of	ADP
ejpam-3412	597	13	a	a	DET
ejpam-3412	597	14	,	,	PUNCT
ejpam-3412	597	15	that	that	ADV
ejpam-3412	597	16	is	is	ADV
ejpam-3412	597	17	,	,	PUNCT
ejpam-3412	597	18	(	(	PUNCT
ejpam-3412	597	19	g̃1	g̃1	NOUN
ejpam-3412	597	20	,	,	PUNCT
ejpam-3412	597	21	e1)∪	e1)∪	PROPN
ejpam-3412	597	22	(	(	PUNCT
ejpam-3412	597	23	g̃2	g̃2	PROPN
ejpam-3412	597	24	,	,	PUNCT
ejpam-3412	597	25	e2	e2	PROPN
ejpam-3412	597	26	)	)	PUNCT
ejpam-3412	597	27	is	be	AUX
ejpam-3412	597	28	not	not	PART
ejpam-3412	597	29	a	a	DET
ejpam-3412	597	30	price	price	NOUN
ejpam-3412	597	31	-	-	PUNCT
ejpam-3412	597	32	fuzzy	fuzzy	ADJ
ejpam-3412	597	33	soft	soft	ADJ
ejpam-3412	597	34	ups	up	NOUN
ejpam-3412	597	35	-	-	PUNCT
ejpam-3412	597	36	filter	filter	NOUN
ejpam-3412	597	37	of	of	ADP
ejpam-3412	597	38	a.	a.	NOUN
ejpam-3412	597	39	hence	hence	ADV
ejpam-3412	597	40	,	,	PUNCT
ejpam-3412	597	41	(	(	PUNCT
ejpam-3412	597	42	g̃1	g̃1	NOUN
ejpam-3412	597	43	,	,	PUNCT
ejpam-3412	597	44	e1)∪	e1)∪	PROPN
ejpam-3412	597	45	(	(	PUNCT
ejpam-3412	597	46	g̃2	g̃2	PROPN
ejpam-3412	597	47	,	,	PUNCT
ejpam-3412	597	48	e2	e2	PROPN
ejpam-3412	597	49	)	)	PUNCT
ejpam-3412	597	50	is	be	AUX
ejpam-3412	597	51	not	not	PART
ejpam-3412	597	52	a	a	DET
ejpam-3412	597	53	fuzzy	fuzzy	ADJ
ejpam-3412	597	54	soft	soft	ADJ
ejpam-3412	597	55	ups	up	NOUN
ejpam-3412	597	56	-	-	PUNCT
ejpam-3412	597	57	filter	filter	NOUN
ejpam-3412	597	58	of	of	ADP
ejpam-3412	597	59	a.	a.	NOUN
ejpam-3412	597	60	moreover	moreover	ADV
ejpam-3412	597	61	,	,	PUNCT
ejpam-3412	597	62	(	(	PUNCT
ejpam-3412	597	63	g̃1	g̃1	NOUN
ejpam-3412	597	64	,	,	PUNCT
ejpam-3412	597	65	e1	e1	NOUN
ejpam-3412	597	66	)	)	PUNCT
ejpam-3412	597	67	d	d	NOUN
ejpam-3412	597	68	(	(	PUNCT
ejpam-3412	597	69	g̃2	g̃2	PROPN
ejpam-3412	597	70	,	,	PUNCT
ejpam-3412	597	71	e2	e2	PROPN
ejpam-3412	597	72	)	)	PUNCT
ejpam-3412	597	73	is	be	AUX
ejpam-3412	597	74	not	not	PART
ejpam-3412	597	75	a	a	DET
ejpam-3412	597	76	fuzzy	fuzzy	ADJ
ejpam-3412	597	77	soft	soft	ADJ
ejpam-3412	597	78	ups	up	NOUN
ejpam-3412	597	79	-	-	PUNCT
ejpam-3412	597	80	filter	filter	NOUN
ejpam-3412	597	81	of	of	ADP
ejpam-3412	597	82	a.	a.	NOUN
ejpam-3412	597	83	3.6	3.6	NUM
ejpam-3412	597	84	.	.	PUNCT
ejpam-3412	598	1	fuzzy	fuzzy	ADJ
ejpam-3412	598	2	soft	soft	ADJ
ejpam-3412	598	3	upi	upi	NOUN
ejpam-3412	598	4	-	-	PUNCT
ejpam-3412	598	5	filters	filter	NOUN
ejpam-3412	598	6	definition	definition	NOUN
ejpam-3412	598	7	23	23	NUM
ejpam-3412	598	8	.	.	PUNCT
ejpam-3412	599	1	a	a	DET
ejpam-3412	599	2	fuzzy	fuzzy	ADJ
ejpam-3412	599	3	soft	soft	ADJ
ejpam-3412	599	4	set	set	NOUN
ejpam-3412	599	5	(	(	PUNCT
ejpam-3412	599	6	f̃	f̃	PROPN
ejpam-3412	599	7	,	,	PUNCT
ejpam-3412	599	8	e	e	NOUN
ejpam-3412	599	9	)	)	PUNCT
ejpam-3412	599	10	over	over	ADP
ejpam-3412	599	11	a	a	PRON
ejpam-3412	599	12	is	be	AUX
ejpam-3412	599	13	called	call	VERB
ejpam-3412	599	14	a	a	DET
ejpam-3412	599	15	fuzzy	fuzzy	ADJ
ejpam-3412	599	16	soft	soft	ADJ
ejpam-3412	599	17	upi	upi	NOUN
ejpam-3412	599	18	-	-	PUNCT
ejpam-3412	599	19	filter	filter	NOUN
ejpam-3412	599	20	based	base	VERB
ejpam-3412	599	21	on	on	ADP
ejpam-3412	599	22	e	e	PROPN
ejpam-3412	599	23	∈	∈	PROPN
ejpam-3412	599	24	e	e	X
ejpam-3412	599	25	(	(	PUNCT
ejpam-3412	599	26	we	we	PRON
ejpam-3412	599	27	shortly	shortly	ADV
ejpam-3412	599	28	call	call	VERB
ejpam-3412	599	29	an	an	DET
ejpam-3412	599	30	e	e	ADJ
ejpam-3412	599	31	-	-	ADJ
ejpam-3412	599	32	fuzzy	fuzzy	ADJ
ejpam-3412	599	33	soft	soft	ADJ
ejpam-3412	599	34	upi	upi	NOUN
ejpam-3412	599	35	-	-	PUNCT
ejpam-3412	599	36	filter	filter	NOUN
ejpam-3412	599	37	)	)	PUNCT
ejpam-3412	599	38	of	of	ADP
ejpam-3412	599	39	a	a	DET
ejpam-3412	599	40	if	if	SCONJ
ejpam-3412	599	41	a	a	DET
ejpam-3412	599	42	fuzzy	fuzzy	ADJ
ejpam-3412	599	43	set	set	NOUN
ejpam-3412	599	44	f̃[e	f̃[e	X
ejpam-3412	599	45	]	]	X
ejpam-3412	599	46	in	in	ADP
ejpam-3412	599	47	a	a	PRON
ejpam-3412	599	48	is	be	AUX
ejpam-3412	599	49	a	a	DET
ejpam-3412	599	50	fuzzy	fuzzy	ADJ
ejpam-3412	599	51	upi	upi	NOUN
ejpam-3412	599	52	-	-	PUNCT
ejpam-3412	599	53	filter	filter	NOUN
ejpam-3412	599	54	of	of	ADP
ejpam-3412	599	55	a.	a.	NOUN
ejpam-3412	599	56	if	if	SCONJ
ejpam-3412	599	57	(	(	PUNCT
ejpam-3412	599	58	f̃	f̃	PROPN
ejpam-3412	599	59	,	,	PUNCT
ejpam-3412	599	60	e	e	NOUN
ejpam-3412	599	61	)	)	PUNCT
ejpam-3412	599	62	is	be	AUX
ejpam-3412	599	63	an	an	DET
ejpam-3412	599	64	e	e	ADJ
ejpam-3412	599	65	-	-	ADJ
ejpam-3412	599	66	fuzzy	fuzzy	ADJ
ejpam-3412	599	67	soft	soft	ADJ
ejpam-3412	599	68	upi	upi	NOUN
ejpam-3412	599	69	-	-	PUNCT
ejpam-3412	599	70	filter	filter	NOUN
ejpam-3412	599	71	of	of	ADP
ejpam-3412	599	72	a	a	PRON
ejpam-3412	599	73	for	for	ADP
ejpam-3412	599	74	all	all	DET
ejpam-3412	599	75	e	e	NOUN
ejpam-3412	599	76	∈	∈	PROPN
ejpam-3412	599	77	e	e	NOUN
ejpam-3412	599	78	,	,	PUNCT
ejpam-3412	599	79	we	we	PRON
ejpam-3412	599	80	say	say	VERB
ejpam-3412	599	81	that	that	SCONJ
ejpam-3412	599	82	(	(	PUNCT
ejpam-3412	599	83	f̃	f̃	PROPN
ejpam-3412	599	84	,	,	PUNCT
ejpam-3412	599	85	e	e	NOUN
ejpam-3412	599	86	)	)	PUNCT
ejpam-3412	599	87	is	be	AUX
ejpam-3412	599	88	a	a	DET
ejpam-3412	599	89	fuzzy	fuzzy	ADJ
ejpam-3412	599	90	soft	soft	ADJ
ejpam-3412	599	91	upi	upi	NOUN
ejpam-3412	599	92	-	-	PUNCT
ejpam-3412	599	93	filter	filter	NOUN
ejpam-3412	599	94	of	of	ADP
ejpam-3412	599	95	a.	a.	NOUN
ejpam-3412	599	96	in	in	ADP
ejpam-3412	599	97	the	the	DET
ejpam-3412	599	98	next	next	ADJ
ejpam-3412	599	99	theorem	theorem	NOUN
ejpam-3412	599	100	,	,	PUNCT
ejpam-3412	599	101	we	we	PRON
ejpam-3412	599	102	give	give	VERB
ejpam-3412	599	103	necessary	necessary	ADJ
ejpam-3412	599	104	condition	condition	NOUN
ejpam-3412	599	105	for	for	ADP
ejpam-3412	599	106	fuzzy	fuzzy	ADJ
ejpam-3412	599	107	soft	soft	ADJ
ejpam-3412	599	108	upi	upi	NOUN
ejpam-3412	599	109	-	-	PUNCT
ejpam-3412	599	110	filters	filter	NOUN
ejpam-3412	599	111	of	of	ADP
ejpam-3412	599	112	f	f	PROPN
ejpam-3412	599	113	-upsemigroups	-upsemigroup	NOUN
ejpam-3412	599	114	.	.	PUNCT
ejpam-3412	600	1	a.	a.	PROPN
ejpam-3412	600	2	satirad	satirad	PROPN
ejpam-3412	600	3	,	,	PUNCT
ejpam-3412	600	4	a.	a.	NOUN
ejpam-3412	600	5	iampan	iampan	PROPN
ejpam-3412	600	6	/	/	SYM
ejpam-3412	600	7	eur	eur	PROPN
ejpam-3412	600	8	.	.	PUNCT
ejpam-3412	601	1	j.	j.	PROPN
ejpam-3412	601	2	pure	pure	PROPN
ejpam-3412	601	3	appl	appl	PROPN
ejpam-3412	601	4	.	.	PROPN
ejpam-3412	601	5	math	math	PROPN
ejpam-3412	601	6	,	,	PUNCT
ejpam-3412	601	7	12	12	NUM
ejpam-3412	601	8	(	(	PUNCT
ejpam-3412	601	9	2	2	NUM
ejpam-3412	601	10	)	)	PUNCT
ejpam-3412	601	11	(	(	PUNCT
ejpam-3412	601	12	2019	2019	NUM
ejpam-3412	601	13	)	)	PUNCT
ejpam-3412	601	14	,	,	PUNCT
ejpam-3412	601	15	294	294	NUM
ejpam-3412	601	16	-	-	SYM
ejpam-3412	601	17	331	331	NUM
ejpam-3412	601	18	321	321	NUM
ejpam-3412	601	19	theorem	theorem	NOUN
ejpam-3412	601	20	48	48	NUM
ejpam-3412	601	21	.	.	PUNCT
ejpam-3412	602	1	if	if	SCONJ
ejpam-3412	602	2	(	(	PUNCT
ejpam-3412	602	3	f̃	f̃	PROPN
ejpam-3412	602	4	,	,	PUNCT
ejpam-3412	602	5	e	e	NOUN
ejpam-3412	602	6	)	)	PUNCT
ejpam-3412	602	7	is	be	AUX
ejpam-3412	602	8	a	a	DET
ejpam-3412	602	9	fuzzy	fuzzy	ADJ
ejpam-3412	602	10	soft	soft	ADJ
ejpam-3412	602	11	set	set	NOUN
ejpam-3412	602	12	over	over	ADP
ejpam-3412	602	13	a	a	DET
ejpam-3412	602	14	such	such	ADJ
ejpam-3412	602	15	that	that	PRON
ejpam-3412	602	16	for	for	ADP
ejpam-3412	602	17	all	all	DET
ejpam-3412	602	18	e	e	NOUN
ejpam-3412	602	19	∈	∈	PROPN
ejpam-3412	602	20	e	e	NOUN
ejpam-3412	602	21	,	,	PUNCT
ejpam-3412	602	22	a	a	DET
ejpam-3412	602	23	fuzzy	fuzzy	ADJ
ejpam-3412	602	24	set	set	NOUN
ejpam-3412	602	25	f̃[e	f̃[e	NOUN
ejpam-3412	602	26	]	]	X
ejpam-3412	602	27	in	in	ADP
ejpam-3412	602	28	a	a	DET
ejpam-3412	602	29	satisfies	satisfie	NOUN
ejpam-3412	602	30	the	the	DET
ejpam-3412	602	31	conditions	condition	NOUN
ejpam-3412	602	32	(	(	PUNCT
ejpam-3412	602	33	2.6	2.6	NUM
ejpam-3412	602	34	)	)	PUNCT
ejpam-3412	602	35	and	and	CCONJ
ejpam-3412	602	36	(	(	PUNCT
ejpam-3412	602	37	1.15	1.15	NUM
ejpam-3412	602	38	)	)	PUNCT
ejpam-3412	602	39	,	,	PUNCT
ejpam-3412	602	40	then	then	ADV
ejpam-3412	602	41	(	(	PUNCT
ejpam-3412	602	42	f̃	f̃	PROPN
ejpam-3412	602	43	,	,	PUNCT
ejpam-3412	602	44	e	e	NOUN
ejpam-3412	602	45	)	)	PUNCT
ejpam-3412	602	46	is	be	AUX
ejpam-3412	602	47	a	a	DET
ejpam-3412	602	48	fuzzy	fuzzy	ADJ
ejpam-3412	602	49	soft	soft	ADJ
ejpam-3412	602	50	upi	upi	NOUN
ejpam-3412	602	51	-	-	PUNCT
ejpam-3412	602	52	filter	filter	NOUN
ejpam-3412	602	53	of	of	ADP
ejpam-3412	602	54	a.	a.	NOUN
ejpam-3412	602	55	proof	proof	NOUN
ejpam-3412	602	56	.	.	PUNCT
ejpam-3412	603	1	it	it	PRON
ejpam-3412	603	2	is	be	AUX
ejpam-3412	603	3	straightforward	straightforward	ADJ
ejpam-3412	603	4	by	by	ADP
ejpam-3412	603	5	proposition	proposition	NOUN
ejpam-3412	603	6	6	6	NUM
ejpam-3412	603	7	and	and	CCONJ
ejpam-3412	603	8	lemma	lemma	PROPN
ejpam-3412	603	9	1	1	NUM
ejpam-3412	603	10	(	(	PUNCT
ejpam-3412	603	11	2	2	NUM
ejpam-3412	603	12	)	)	PUNCT
ejpam-3412	603	13	.	.	PUNCT
ejpam-3412	604	1	from	from	ADP
ejpam-3412	604	2	figure	figure	NOUN
ejpam-3412	604	3	1	1	NUM
ejpam-3412	604	4	,	,	PUNCT
ejpam-3412	604	5	we	we	PRON
ejpam-3412	604	6	have	have	VERB
ejpam-3412	604	7	the	the	DET
ejpam-3412	604	8	following	follow	VERB
ejpam-3412	604	9	two	two	NUM
ejpam-3412	604	10	theorems	theorem	NOUN
ejpam-3412	604	11	.	.	PUNCT
ejpam-3412	605	1	theorem	theorem	VERB
ejpam-3412	605	2	49	49	NUM
ejpam-3412	605	3	.	.	PUNCT
ejpam-3412	606	1	every	every	DET
ejpam-3412	606	2	e	e	ADJ
ejpam-3412	606	3	-	-	ADJ
ejpam-3412	606	4	fuzzy	fuzzy	ADJ
ejpam-3412	606	5	soft	soft	ADJ
ejpam-3412	606	6	upi	upi	NOUN
ejpam-3412	606	7	-	-	PUNCT
ejpam-3412	606	8	filter	filter	NOUN
ejpam-3412	606	9	of	of	ADP
ejpam-3412	606	10	a	a	PRON
ejpam-3412	606	11	is	be	AUX
ejpam-3412	606	12	an	an	DET
ejpam-3412	606	13	e	e	ADJ
ejpam-3412	606	14	-	-	ADJ
ejpam-3412	606	15	fuzzy	fuzzy	ADJ
ejpam-3412	606	16	soft	soft	ADJ
ejpam-3412	606	17	ups	up	NOUN
ejpam-3412	606	18	-	-	PUNCT
ejpam-3412	606	19	filter	filter	NOUN
ejpam-3412	606	20	.	.	PUNCT
ejpam-3412	607	1	moreover	moreover	ADV
ejpam-3412	607	2	,	,	PUNCT
ejpam-3412	607	3	every	every	DET
ejpam-3412	607	4	fuzzy	fuzzy	ADJ
ejpam-3412	607	5	soft	soft	ADJ
ejpam-3412	607	6	upi	upi	NOUN
ejpam-3412	607	7	-	-	PUNCT
ejpam-3412	607	8	filter	filter	NOUN
ejpam-3412	607	9	of	of	ADP
ejpam-3412	607	10	a	a	PRON
ejpam-3412	607	11	is	be	AUX
ejpam-3412	607	12	a	a	DET
ejpam-3412	607	13	fuzzy	fuzzy	ADJ
ejpam-3412	607	14	soft	soft	ADJ
ejpam-3412	607	15	ups	up	NOUN
ejpam-3412	607	16	-	-	PUNCT
ejpam-3412	607	17	filter	filter	NOUN
ejpam-3412	607	18	.	.	PUNCT
ejpam-3412	608	1	theorem	theorem	VERB
ejpam-3412	608	2	50	50	NUM
ejpam-3412	608	3	.	.	PUNCT
ejpam-3412	609	1	every	every	DET
ejpam-3412	609	2	e	e	ADJ
ejpam-3412	609	3	-	-	ADJ
ejpam-3412	609	4	fuzzy	fuzzy	ADJ
ejpam-3412	609	5	soft	soft	ADJ
ejpam-3412	609	6	upi	upi	NOUN
ejpam-3412	609	7	-	-	PUNCT
ejpam-3412	609	8	filter	filter	NOUN
ejpam-3412	609	9	of	of	ADP
ejpam-3412	609	10	a	a	PRON
ejpam-3412	609	11	is	be	AUX
ejpam-3412	609	12	an	an	DET
ejpam-3412	609	13	e	e	ADJ
ejpam-3412	609	14	-	-	ADJ
ejpam-3412	609	15	fuzzy	fuzzy	ADJ
ejpam-3412	609	16	soft	soft	ADJ
ejpam-3412	609	17	near	near	ADP
ejpam-3412	609	18	upi	upi	NOUN
ejpam-3412	609	19	-	-	PUNCT
ejpam-3412	609	20	filter	filter	NOUN
ejpam-3412	609	21	.	.	PUNCT
ejpam-3412	610	1	moreover	moreover	ADV
ejpam-3412	610	2	,	,	PUNCT
ejpam-3412	610	3	every	every	DET
ejpam-3412	610	4	fuzzy	fuzzy	ADJ
ejpam-3412	610	5	soft	soft	ADJ
ejpam-3412	610	6	upi	upi	NOUN
ejpam-3412	610	7	-	-	PUNCT
ejpam-3412	610	8	filter	filter	NOUN
ejpam-3412	610	9	of	of	ADP
ejpam-3412	610	10	a	a	PRON
ejpam-3412	610	11	is	be	AUX
ejpam-3412	610	12	a	a	DET
ejpam-3412	610	13	fuzzy	fuzzy	ADJ
ejpam-3412	610	14	soft	soft	ADJ
ejpam-3412	610	15	near	near	ADP
ejpam-3412	610	16	upi	upi	NOUN
ejpam-3412	610	17	-	-	PUNCT
ejpam-3412	610	18	filter	filter	NOUN
ejpam-3412	610	19	.	.	PUNCT
ejpam-3412	611	1	the	the	DET
ejpam-3412	611	2	following	follow	VERB
ejpam-3412	611	3	two	two	NUM
ejpam-3412	611	4	examples	example	NOUN
ejpam-3412	611	5	show	show	VERB
ejpam-3412	611	6	that	that	SCONJ
ejpam-3412	611	7	the	the	DET
ejpam-3412	611	8	converse	converse	NOUN
ejpam-3412	611	9	of	of	ADP
ejpam-3412	611	10	theorems	theorem	NOUN
ejpam-3412	611	11	49	49	NUM
ejpam-3412	611	12	and	and	CCONJ
ejpam-3412	611	13	50	50	NUM
ejpam-3412	611	14	is	be	AUX
ejpam-3412	611	15	not	not	PART
ejpam-3412	611	16	true	true	ADJ
ejpam-3412	611	17	.	.	PUNCT
ejpam-3412	612	1	example	example	NOUN
ejpam-3412	612	2	23	23	NUM
ejpam-3412	612	3	.	.	PUNCT
ejpam-3412	613	1	in	in	ADP
ejpam-3412	613	2	example	example	NOUN
ejpam-3412	613	3	13	13	NUM
ejpam-3412	613	4	,	,	PUNCT
ejpam-3412	613	5	we	we	PRON
ejpam-3412	613	6	know	know	VERB
ejpam-3412	613	7	that	that	SCONJ
ejpam-3412	613	8	(	(	PUNCT
ejpam-3412	613	9	f̃	f̃	PROPN
ejpam-3412	613	10	,	,	PUNCT
ejpam-3412	613	11	e	e	NOUN
ejpam-3412	613	12	)	)	PUNCT
ejpam-3412	613	13	is	be	AUX
ejpam-3412	613	14	a	a	DET
ejpam-3412	613	15	beauty	beauty	NOUN
ejpam-3412	613	16	-	-	PUNCT
ejpam-3412	613	17	fuzzy	fuzzy	ADJ
ejpam-3412	613	18	soft	soft	ADJ
ejpam-3412	613	19	ups	up	NOUN
ejpam-3412	613	20	-	-	PUNCT
ejpam-3412	613	21	filter	filter	NOUN
ejpam-3412	613	22	of	of	ADP
ejpam-3412	613	23	a	a	PRON
ejpam-3412	613	24	but	but	CCONJ
ejpam-3412	613	25	f̃[beauty	f̃[beauty	NOUN
ejpam-3412	613	26	]	]	PUNCT
ejpam-3412	613	27	is	be	AUX
ejpam-3412	613	28	not	not	PART
ejpam-3412	613	29	a	a	DET
ejpam-3412	613	30	fuzzy	fuzzy	ADJ
ejpam-3412	613	31	upi	upi	NOUN
ejpam-3412	613	32	-	-	PUNCT
ejpam-3412	613	33	filter	filter	NOUN
ejpam-3412	613	34	of	of	ADP
ejpam-3412	613	35	a.	a.	NOUN
ejpam-3412	613	36	indeed	indeed	ADV
ejpam-3412	613	37	,	,	PUNCT
ejpam-3412	613	38	f	f	PROPN
ejpam-3412	613	39	f̃[beauty	f̃[beauty	PROPN
ejpam-3412	613	40	]	]	PUNCT
ejpam-3412	613	41	(	(	PUNCT
ejpam-3412	613	42	6	6	NUM
ejpam-3412	613	43	∗	∗	NOUN
ejpam-3412	613	44	5	5	NUM
ejpam-3412	613	45	)	)	PUNCT
ejpam-3412	613	46	=	=	SYM
ejpam-3412	613	47	f	f	X
ejpam-3412	613	48	f̃[beauty	f̃[beauty	PROPN
ejpam-3412	613	49	]	]	PUNCT
ejpam-3412	613	50	(	(	PUNCT
ejpam-3412	613	51	7	7	X
ejpam-3412	613	52	)	)	PUNCT
ejpam-3412	613	53	=	=	SYM
ejpam-3412	613	54	0.3	0.3	NUM
ejpam-3412	613	55	�	�	NOUN
ejpam-3412	613	56	0.4	0.4	NUM
ejpam-3412	613	57	=	=	SYM
ejpam-3412	613	58	max{0.2	max{0.2	PROPN
ejpam-3412	613	59	,	,	PUNCT
ejpam-3412	613	60	0.4	0.4	NUM
ejpam-3412	613	61	}	}	PUNCT
ejpam-3412	613	62	=	=	SYM
ejpam-3412	613	63	max{f	max{f	PROPN
ejpam-3412	613	64	f̃[beauty	f̃[beauty	PROPN
ejpam-3412	613	65	]	]	PUNCT
ejpam-3412	613	66	(	(	PUNCT
ejpam-3412	613	67	6	6	NUM
ejpam-3412	613	68	)	)	PUNCT
ejpam-3412	613	69	,	,	PUNCT
ejpam-3412	613	70	f	f	PROPN
ejpam-3412	613	71	f̃[beauty	f̃[beauty	PROPN
ejpam-3412	613	72	]	]	PUNCT
ejpam-3412	613	73	(	(	PUNCT
ejpam-3412	613	74	5	5	NUM
ejpam-3412	613	75	)	)	PUNCT
ejpam-3412	613	76	}	}	PUNCT
ejpam-3412	613	77	.	.	PUNCT
ejpam-3412	614	1	hence	hence	ADV
ejpam-3412	614	2	,	,	PUNCT
ejpam-3412	614	3	(	(	PUNCT
ejpam-3412	614	4	f̃	f̃	PROPN
ejpam-3412	614	5	,	,	PUNCT
ejpam-3412	614	6	e	e	NOUN
ejpam-3412	614	7	)	)	PUNCT
ejpam-3412	614	8	is	be	AUX
ejpam-3412	614	9	not	not	PART
ejpam-3412	614	10	a	a	DET
ejpam-3412	614	11	beauty	beauty	NOUN
ejpam-3412	614	12	-	-	PUNCT
ejpam-3412	614	13	fuzzy	fuzzy	ADJ
ejpam-3412	614	14	soft	soft	ADJ
ejpam-3412	614	15	upi	upi	NOUN
ejpam-3412	614	16	-	-	PUNCT
ejpam-3412	614	17	filter	filter	NOUN
ejpam-3412	614	18	of	of	ADP
ejpam-3412	614	19	a.	a.	NOUN
ejpam-3412	614	20	example	example	NOUN
ejpam-3412	614	21	24	24	NUM
ejpam-3412	614	22	.	.	PUNCT
ejpam-3412	615	1	in	in	ADP
ejpam-3412	615	2	example	example	NOUN
ejpam-3412	615	3	21	21	NUM
ejpam-3412	615	4	,	,	PUNCT
ejpam-3412	615	5	we	we	PRON
ejpam-3412	615	6	know	know	VERB
ejpam-3412	615	7	that	that	SCONJ
ejpam-3412	615	8	(	(	PUNCT
ejpam-3412	615	9	f̃	f̃	PROPN
ejpam-3412	615	10	,	,	PUNCT
ejpam-3412	615	11	e	e	NOUN
ejpam-3412	615	12	)	)	PUNCT
ejpam-3412	615	13	is	be	AUX
ejpam-3412	615	14	a	a	DET
ejpam-3412	615	15	aroma	aroma	NOUN
ejpam-3412	615	16	-	-	PUNCT
ejpam-3412	615	17	fuzzy	fuzzy	NOUN
ejpam-3412	615	18	soft	soft	ADJ
ejpam-3412	615	19	near	near	ADP
ejpam-3412	615	20	upi	upi	NOUN
ejpam-3412	615	21	-	-	PUNCT
ejpam-3412	615	22	filter	filter	NOUN
ejpam-3412	615	23	of	of	ADP
ejpam-3412	615	24	a	a	PRON
ejpam-3412	615	25	but	but	CCONJ
ejpam-3412	615	26	f̃[aroma	f̃[aroma	PROPN
ejpam-3412	615	27	]	]	PUNCT
ejpam-3412	615	28	is	be	AUX
ejpam-3412	615	29	not	not	PART
ejpam-3412	615	30	a	a	DET
ejpam-3412	615	31	fuzzy	fuzzy	ADJ
ejpam-3412	615	32	upi	upi	NOUN
ejpam-3412	615	33	-	-	PUNCT
ejpam-3412	615	34	filter	filter	NOUN
ejpam-3412	615	35	of	of	ADP
ejpam-3412	615	36	a.	a.	NOUN
ejpam-3412	615	37	indeed	indeed	ADV
ejpam-3412	615	38	,	,	PUNCT
ejpam-3412	615	39	f	f	PROPN
ejpam-3412	615	40	f̃[aroma	f̃[aroma	PROPN
ejpam-3412	615	41	]	]	X
ejpam-3412	615	42	(	(	PUNCT
ejpam-3412	615	43	a	a	X
ejpam-3412	615	44	)	)	PUNCT
ejpam-3412	615	45	=	=	SYM
ejpam-3412	615	46	0.3	0.3	NUM
ejpam-3412	615	47	�	�	PROPN
ejpam-3412	615	48	0.4	0.4	NUM
ejpam-3412	615	49	=	=	SYM
ejpam-3412	615	50	min{0.5	min{0.5	PROPN
ejpam-3412	615	51	,	,	PUNCT
ejpam-3412	615	52	0.4	0.4	NUM
ejpam-3412	615	53	}	}	PUNCT
ejpam-3412	615	54	=	=	SYM
ejpam-3412	615	55	min{f	min{f	NUM
ejpam-3412	615	56	f̃[aroma	f̃[aroma	NOUN
ejpam-3412	615	57	]	]	X
ejpam-3412	615	58	(	(	PUNCT
ejpam-3412	615	59	l	l	NOUN
ejpam-3412	615	60	)	)	PUNCT
ejpam-3412	615	61	,	,	PUNCT
ejpam-3412	615	62	f	f	PROPN
ejpam-3412	615	63	f̃[aroma	f̃[aroma	PROPN
ejpam-3412	615	64	]	]	X
ejpam-3412	615	65	(	(	PUNCT
ejpam-3412	615	66	m	m	NOUN
ejpam-3412	615	67	)	)	PUNCT
ejpam-3412	615	68	}	}	PUNCT
ejpam-3412	615	69	=	=	SYM
ejpam-3412	615	70	min{f	min{f	NUM
ejpam-3412	615	71	f̃[aroma	f̃[aroma	NOUN
ejpam-3412	615	72	]	]	X
ejpam-3412	615	73	(	(	PUNCT
ejpam-3412	615	74	m	m	PROPN
ejpam-3412	615	75	·	·	SYM
ejpam-3412	615	76	a	a	NOUN
ejpam-3412	615	77	)	)	PUNCT
ejpam-3412	615	78	,	,	PUNCT
ejpam-3412	615	79	f	f	PROPN
ejpam-3412	615	80	f̃[aroma	f̃[aroma	PROPN
ejpam-3412	615	81	]	]	X
ejpam-3412	615	82	(	(	PUNCT
ejpam-3412	615	83	m	m	NOUN
ejpam-3412	615	84	)	)	PUNCT
ejpam-3412	615	85	}	}	PUNCT
ejpam-3412	615	86	.	.	PUNCT
ejpam-3412	616	1	hence	hence	ADV
ejpam-3412	616	2	,	,	PUNCT
ejpam-3412	616	3	(	(	PUNCT
ejpam-3412	616	4	f̃	f̃	PROPN
ejpam-3412	616	5	,	,	PUNCT
ejpam-3412	616	6	e	e	NOUN
ejpam-3412	616	7	)	)	PUNCT
ejpam-3412	616	8	is	be	AUX
ejpam-3412	616	9	not	not	PART
ejpam-3412	616	10	a	a	DET
ejpam-3412	616	11	aroma	aroma	NOUN
ejpam-3412	616	12	-	-	PUNCT
ejpam-3412	616	13	fuzzy	fuzzy	ADJ
ejpam-3412	616	14	soft	soft	ADJ
ejpam-3412	616	15	upi	upi	NOUN
ejpam-3412	616	16	-	-	PUNCT
ejpam-3412	616	17	filter	filter	NOUN
ejpam-3412	616	18	of	of	ADP
ejpam-3412	616	19	a.	a.	NOUN
ejpam-3412	616	20	in	in	ADP
ejpam-3412	616	21	the	the	DET
ejpam-3412	616	22	next	next	ADJ
ejpam-3412	616	23	theorem	theorem	NOUN
ejpam-3412	616	24	,	,	PUNCT
ejpam-3412	616	25	we	we	PRON
ejpam-3412	616	26	give	give	VERB
ejpam-3412	616	27	necessary	necessary	ADJ
ejpam-3412	616	28	condition	condition	NOUN
ejpam-3412	616	29	for	for	ADP
ejpam-3412	616	30	fuzzy	fuzzy	ADJ
ejpam-3412	616	31	soft	soft	ADJ
ejpam-3412	616	32	near	near	ADP
ejpam-3412	616	33	upi	upi	NOUN
ejpam-3412	616	34	-	-	PUNCT
ejpam-3412	616	35	filters	filter	NOUN
ejpam-3412	616	36	as	as	ADP
ejpam-3412	616	37	fuzzy	fuzzy	ADJ
ejpam-3412	616	38	soft	soft	ADJ
ejpam-3412	616	39	upi	upi	NOUN
ejpam-3412	616	40	-	-	PUNCT
ejpam-3412	616	41	filters	filter	NOUN
ejpam-3412	616	42	of	of	ADP
ejpam-3412	616	43	f	f	PROPN
ejpam-3412	616	44	-up	-up	NOUN
ejpam-3412	616	45	-	-	PUNCT
ejpam-3412	616	46	semigroups	semigroup	NOUN
ejpam-3412	616	47	.	.	PUNCT
ejpam-3412	617	1	theorem	theorem	VERB
ejpam-3412	617	2	51	51	NUM
ejpam-3412	617	3	.	.	PUNCT
ejpam-3412	618	1	if	if	SCONJ
ejpam-3412	618	2	(	(	PUNCT
ejpam-3412	618	3	f̃	f̃	PROPN
ejpam-3412	618	4	,	,	PUNCT
ejpam-3412	618	5	e	e	NOUN
ejpam-3412	618	6	)	)	PUNCT
ejpam-3412	618	7	is	be	AUX
ejpam-3412	618	8	a	a	DET
ejpam-3412	618	9	fuzzy	fuzzy	ADJ
ejpam-3412	618	10	soft	soft	ADJ
ejpam-3412	618	11	near	near	ADP
ejpam-3412	618	12	upi	upi	NOUN
ejpam-3412	618	13	-	-	PUNCT
ejpam-3412	618	14	filter	filter	NOUN
ejpam-3412	618	15	of	of	ADP
ejpam-3412	618	16	a	a	DET
ejpam-3412	618	17	such	such	ADJ
ejpam-3412	618	18	that	that	PRON
ejpam-3412	618	19	for	for	ADP
ejpam-3412	618	20	all	all	DET
ejpam-3412	618	21	e	e	NOUN
ejpam-3412	618	22	∈	∈	PROPN
ejpam-3412	618	23	e	e	NOUN
ejpam-3412	618	24	,	,	PUNCT
ejpam-3412	618	25	a	a	DET
ejpam-3412	618	26	fuzzy	fuzzy	ADJ
ejpam-3412	618	27	set	set	NOUN
ejpam-3412	618	28	f̃[e	f̃[e	NOUN
ejpam-3412	618	29	]	]	X
ejpam-3412	618	30	in	in	ADP
ejpam-3412	618	31	a	a	DET
ejpam-3412	618	32	satisfies	satisfie	NOUN
ejpam-3412	618	33	the	the	DET
ejpam-3412	618	34	condition	condition	NOUN
ejpam-3412	618	35	(	(	PUNCT
ejpam-3412	618	36	2.7	2.7	NUM
ejpam-3412	618	37	)	)	PUNCT
ejpam-3412	618	38	,	,	PUNCT
ejpam-3412	618	39	then	then	ADV
ejpam-3412	618	40	(	(	PUNCT
ejpam-3412	618	41	f̃	f̃	PROPN
ejpam-3412	618	42	,	,	PUNCT
ejpam-3412	618	43	e	e	NOUN
ejpam-3412	618	44	)	)	PUNCT
ejpam-3412	618	45	is	be	AUX
ejpam-3412	618	46	a	a	DET
ejpam-3412	618	47	fuzzy	fuzzy	ADJ
ejpam-3412	618	48	soft	soft	ADJ
ejpam-3412	618	49	upi	upi	NOUN
ejpam-3412	618	50	-	-	PUNCT
ejpam-3412	618	51	filter	filter	NOUN
ejpam-3412	618	52	of	of	ADP
ejpam-3412	618	53	a.	a.	NOUN
ejpam-3412	618	54	proof	proof	NOUN
ejpam-3412	618	55	.	.	PUNCT
ejpam-3412	619	1	it	it	PRON
ejpam-3412	619	2	is	be	AUX
ejpam-3412	619	3	straightforward	straightforward	ADJ
ejpam-3412	619	4	by	by	ADP
ejpam-3412	619	5	theorem	theorem	NOUN
ejpam-3412	619	6	14	14	NUM
ejpam-3412	619	7	.	.	PUNCT
ejpam-3412	620	1	the	the	DET
ejpam-3412	620	2	proof	proof	NOUN
ejpam-3412	620	3	of	of	ADP
ejpam-3412	620	4	the	the	DET
ejpam-3412	620	5	following	follow	VERB
ejpam-3412	620	6	theorem	theorem	NOUN
ejpam-3412	620	7	can	can	AUX
ejpam-3412	620	8	be	be	AUX
ejpam-3412	620	9	verified	verify	VERB
ejpam-3412	620	10	easily	easily	ADV
ejpam-3412	620	11	.	.	PUNCT
ejpam-3412	621	1	theorem	theorem	VERB
ejpam-3412	621	2	52	52	NUM
ejpam-3412	621	3	.	.	PUNCT
ejpam-3412	622	1	if	if	SCONJ
ejpam-3412	622	2	(	(	PUNCT
ejpam-3412	622	3	f̃	f̃	PROPN
ejpam-3412	622	4	,	,	PUNCT
ejpam-3412	622	5	e	e	NOUN
ejpam-3412	622	6	)	)	PUNCT
ejpam-3412	622	7	is	be	AUX
ejpam-3412	622	8	a	a	DET
ejpam-3412	622	9	fuzzy	fuzzy	ADJ
ejpam-3412	622	10	soft	soft	ADJ
ejpam-3412	622	11	upi	upi	NOUN
ejpam-3412	622	12	-	-	PUNCT
ejpam-3412	622	13	filter	filter	NOUN
ejpam-3412	622	14	of	of	ADP
ejpam-3412	622	15	a	a	PRON
ejpam-3412	622	16	and	and	CCONJ
ejpam-3412	622	17	∅	∅	NOUN
ejpam-3412	622	18	6=	6=	ADP
ejpam-3412	622	19	e∗	e∗	PROPN
ejpam-3412	622	20	⊆	⊆	NUM
ejpam-3412	622	21	e	e	NOUN
ejpam-3412	622	22	,	,	PUNCT
ejpam-3412	622	23	then	then	ADV
ejpam-3412	622	24	(	(	PUNCT
ejpam-3412	622	25	f̃|e∗	f̃|e∗	PROPN
ejpam-3412	622	26	,	,	PUNCT
ejpam-3412	622	27	e∗	e∗	PROPN
ejpam-3412	622	28	)	)	PUNCT
ejpam-3412	622	29	is	be	AUX
ejpam-3412	622	30	a	a	DET
ejpam-3412	622	31	fuzzy	fuzzy	ADJ
ejpam-3412	622	32	soft	soft	ADJ
ejpam-3412	622	33	upi	upi	NOUN
ejpam-3412	622	34	-	-	PUNCT
ejpam-3412	622	35	filter	filter	NOUN
ejpam-3412	622	36	of	of	ADP
ejpam-3412	622	37	a.	a.	NOUN
ejpam-3412	622	38	the	the	DET
ejpam-3412	622	39	following	follow	VERB
ejpam-3412	622	40	two	two	NUM
ejpam-3412	622	41	theorems	theorem	NOUN
ejpam-3412	622	42	can	can	AUX
ejpam-3412	622	43	be	be	AUX
ejpam-3412	622	44	deduced	deduce	VERB
ejpam-3412	622	45	in	in	ADP
ejpam-3412	622	46	the	the	DET
ejpam-3412	622	47	same	same	ADJ
ejpam-3412	622	48	way	way	NOUN
ejpam-3412	622	49	as	as	ADP
ejpam-3412	622	50	theorems	theorem	NOUN
ejpam-3412	622	51	22	22	NUM
ejpam-3412	622	52	and	and	CCONJ
ejpam-3412	622	53	23	23	NUM
ejpam-3412	622	54	.	.	PUNCT
ejpam-3412	623	1	theorem	theorem	VERB
ejpam-3412	623	2	53	53	NUM
ejpam-3412	623	3	.	.	PUNCT
ejpam-3412	624	1	the	the	DET
ejpam-3412	624	2	extended	extended	ADJ
ejpam-3412	624	3	intersection	intersection	NOUN
ejpam-3412	624	4	of	of	ADP
ejpam-3412	624	5	two	two	NUM
ejpam-3412	624	6	fuzzy	fuzzy	ADJ
ejpam-3412	624	7	soft	soft	ADJ
ejpam-3412	624	8	upi	upi	NOUN
ejpam-3412	624	9	-	-	PUNCT
ejpam-3412	624	10	filters	filter	NOUN
ejpam-3412	624	11	of	of	ADP
ejpam-3412	624	12	a	a	PRON
ejpam-3412	624	13	is	be	AUX
ejpam-3412	624	14	also	also	ADV
ejpam-3412	624	15	a	a	DET
ejpam-3412	624	16	fuzzy	fuzzy	ADJ
ejpam-3412	624	17	soft	soft	ADJ
ejpam-3412	624	18	upi	upi	NOUN
ejpam-3412	624	19	-	-	PUNCT
ejpam-3412	624	20	filter	filter	NOUN
ejpam-3412	624	21	.	.	PUNCT
ejpam-3412	625	1	moreover	moreover	ADV
ejpam-3412	625	2	,	,	PUNCT
ejpam-3412	625	3	the	the	DET
ejpam-3412	625	4	intersection	intersection	NOUN
ejpam-3412	625	5	of	of	ADP
ejpam-3412	625	6	two	two	NUM
ejpam-3412	625	7	fuzzy	fuzzy	ADJ
ejpam-3412	625	8	soft	soft	ADJ
ejpam-3412	625	9	upi	upi	NOUN
ejpam-3412	625	10	-	-	PUNCT
ejpam-3412	625	11	filters	filter	NOUN
ejpam-3412	625	12	of	of	ADP
ejpam-3412	625	13	a	a	PRON
ejpam-3412	625	14	is	be	AUX
ejpam-3412	625	15	also	also	ADV
ejpam-3412	625	16	a	a	DET
ejpam-3412	625	17	fuzzy	fuzzy	ADJ
ejpam-3412	625	18	soft	soft	ADJ
ejpam-3412	625	19	upi	upi	NOUN
ejpam-3412	625	20	-	-	PUNCT
ejpam-3412	625	21	filter	filter	NOUN
ejpam-3412	625	22	.	.	PUNCT
ejpam-3412	626	1	a.	a.	PROPN
ejpam-3412	626	2	satirad	satirad	PROPN
ejpam-3412	626	3	,	,	PUNCT
ejpam-3412	626	4	a.	a.	NOUN
ejpam-3412	626	5	iampan	iampan	PROPN
ejpam-3412	626	6	/	/	SYM
ejpam-3412	626	7	eur	eur	PROPN
ejpam-3412	626	8	.	.	PUNCT
ejpam-3412	627	1	j.	j.	PROPN
ejpam-3412	627	2	pure	pure	PROPN
ejpam-3412	627	3	appl	appl	PROPN
ejpam-3412	627	4	.	.	PROPN
ejpam-3412	627	5	math	math	PROPN
ejpam-3412	627	6	,	,	PUNCT
ejpam-3412	627	7	12	12	NUM
ejpam-3412	627	8	(	(	PUNCT
ejpam-3412	627	9	2	2	NUM
ejpam-3412	627	10	)	)	PUNCT
ejpam-3412	627	11	(	(	PUNCT
ejpam-3412	627	12	2019	2019	NUM
ejpam-3412	627	13	)	)	PUNCT
ejpam-3412	627	14	,	,	PUNCT
ejpam-3412	627	15	294	294	NUM
ejpam-3412	627	16	-	-	SYM
ejpam-3412	627	17	331	331	NUM
ejpam-3412	627	18	322	322	NUM
ejpam-3412	627	19	theorem	theorem	VERB
ejpam-3412	627	20	54	54	NUM
ejpam-3412	627	21	.	.	PUNCT
ejpam-3412	628	1	the	the	DET
ejpam-3412	628	2	union	union	NOUN
ejpam-3412	628	3	of	of	ADP
ejpam-3412	628	4	two	two	NUM
ejpam-3412	628	5	fuzzy	fuzzy	ADJ
ejpam-3412	628	6	soft	soft	ADJ
ejpam-3412	628	7	upi	upi	NOUN
ejpam-3412	628	8	-	-	PUNCT
ejpam-3412	628	9	filters	filter	NOUN
ejpam-3412	628	10	of	of	ADP
ejpam-3412	628	11	a	a	PRON
ejpam-3412	628	12	is	be	AUX
ejpam-3412	628	13	also	also	ADV
ejpam-3412	628	14	a	a	DET
ejpam-3412	628	15	fuzzy	fuzzy	ADJ
ejpam-3412	628	16	soft	soft	ADJ
ejpam-3412	628	17	upi	upi	NOUN
ejpam-3412	628	18	-	-	PUNCT
ejpam-3412	628	19	filter	filter	NOUN
ejpam-3412	628	20	if	if	SCONJ
ejpam-3412	628	21	sets	set	NOUN
ejpam-3412	628	22	of	of	ADP
ejpam-3412	628	23	statistics	statistic	NOUN
ejpam-3412	628	24	of	of	ADP
ejpam-3412	628	25	two	two	NUM
ejpam-3412	628	26	fuzzy	fuzzy	ADJ
ejpam-3412	628	27	soft	soft	ADJ
ejpam-3412	628	28	upi	upi	NOUN
ejpam-3412	628	29	-	-	PUNCT
ejpam-3412	628	30	filters	filter	NOUN
ejpam-3412	628	31	are	be	AUX
ejpam-3412	628	32	disjoint	disjoint	ADJ
ejpam-3412	628	33	.	.	PUNCT
ejpam-3412	629	1	the	the	DET
ejpam-3412	629	2	following	follow	VERB
ejpam-3412	629	3	example	example	NOUN
ejpam-3412	629	4	shows	show	VERB
ejpam-3412	629	5	that	that	SCONJ
ejpam-3412	629	6	theorem	theorem	VERB
ejpam-3412	629	7	54	54	NUM
ejpam-3412	629	8	is	be	AUX
ejpam-3412	629	9	not	not	PART
ejpam-3412	629	10	valid	valid	ADJ
ejpam-3412	629	11	if	if	SCONJ
ejpam-3412	629	12	sets	set	NOUN
ejpam-3412	629	13	of	of	ADP
ejpam-3412	629	14	statistics	statistic	NOUN
ejpam-3412	629	15	of	of	ADP
ejpam-3412	629	16	two	two	NUM
ejpam-3412	629	17	fuzzy	fuzzy	ADJ
ejpam-3412	629	18	soft	soft	ADJ
ejpam-3412	629	19	upi	upi	NOUN
ejpam-3412	629	20	-	-	PUNCT
ejpam-3412	629	21	filters	filter	NOUN
ejpam-3412	629	22	are	be	AUX
ejpam-3412	629	23	not	not	PART
ejpam-3412	629	24	disjoint	disjoint	ADJ
ejpam-3412	629	25	.	.	PUNCT
ejpam-3412	630	1	example	example	NOUN
ejpam-3412	631	1	25	25	NUM
ejpam-3412	631	2	.	.	PUNCT
ejpam-3412	632	1	let	let	VERB
ejpam-3412	632	2	a	a	DET
ejpam-3412	632	3	be	be	AUX
ejpam-3412	632	4	a	a	DET
ejpam-3412	632	5	set	set	NOUN
ejpam-3412	632	6	of	of	ADP
ejpam-3412	632	7	four	four	NUM
ejpam-3412	632	8	colors	color	NOUN
ejpam-3412	632	9	,	,	PUNCT
ejpam-3412	632	10	that	that	ADV
ejpam-3412	632	11	is	is	ADV
ejpam-3412	632	12	,	,	PUNCT
ejpam-3412	632	13	a	a	PRON
ejpam-3412	632	14	=	=	X
ejpam-3412	632	15	{	{	PUNCT
ejpam-3412	632	16	blue	blue	ADJ
ejpam-3412	632	17	,	,	PUNCT
ejpam-3412	632	18	green	green	ADJ
ejpam-3412	632	19	,	,	PUNCT
ejpam-3412	632	20	cyan	cyan	ADJ
ejpam-3412	632	21	,	,	PUNCT
ejpam-3412	632	22	black	black	NOUN
ejpam-3412	632	23	}	}	PUNCT
ejpam-3412	632	24	.	.	PUNCT
ejpam-3412	633	1	define	define	VERB
ejpam-3412	633	2	two	two	NUM
ejpam-3412	633	3	binary	binary	ADJ
ejpam-3412	633	4	operations	operation	NOUN
ejpam-3412	633	5	·	·	PUNCT
ejpam-3412	633	6	and	and	CCONJ
ejpam-3412	633	7	∗	∗	NOUN
ejpam-3412	633	8	on	on	ADP
ejpam-3412	633	9	a	a	PRON
ejpam-3412	633	10	as	as	ADP
ejpam-3412	633	11	the	the	DET
ejpam-3412	633	12	following	follow	VERB
ejpam-3412	633	13	cayley	cayley	ADJ
ejpam-3412	633	14	tables	table	NOUN
ejpam-3412	633	15	:	:	PUNCT
ejpam-3412	633	16	·	·	PUNCT
ejpam-3412	633	17	black	black	ADJ
ejpam-3412	633	18	cyan	cyan	NOUN
ejpam-3412	633	19	blue	blue	ADJ
ejpam-3412	633	20	green	green	ADJ
ejpam-3412	633	21	black	black	ADJ
ejpam-3412	633	22	black	black	ADJ
ejpam-3412	633	23	cyan	cyan	NOUN
ejpam-3412	633	24	blue	blue	ADJ
ejpam-3412	633	25	green	green	PROPN
ejpam-3412	633	26	cyan	cyan	PROPN
ejpam-3412	633	27	black	black	ADJ
ejpam-3412	633	28	black	black	ADJ
ejpam-3412	633	29	blue	blue	ADJ
ejpam-3412	633	30	blue	blue	ADJ
ejpam-3412	633	31	blue	blue	ADJ
ejpam-3412	633	32	black	black	ADJ
ejpam-3412	633	33	cyan	cyan	NOUN
ejpam-3412	633	34	black	black	ADJ
ejpam-3412	633	35	cyan	cyan	NOUN
ejpam-3412	633	36	green	green	PROPN
ejpam-3412	633	37	black	black	ADJ
ejpam-3412	633	38	black	black	ADJ
ejpam-3412	633	39	black	black	ADJ
ejpam-3412	633	40	black	black	ADJ
ejpam-3412	633	41	∗	∗	NOUN
ejpam-3412	633	42	black	black	ADJ
ejpam-3412	633	43	cyan	cyan	NOUN
ejpam-3412	633	44	blue	blue	ADJ
ejpam-3412	633	45	green	green	ADJ
ejpam-3412	633	46	black	black	ADJ
ejpam-3412	633	47	black	black	ADJ
ejpam-3412	633	48	black	black	ADJ
ejpam-3412	633	49	black	black	ADJ
ejpam-3412	633	50	black	black	ADJ
ejpam-3412	633	51	cyan	cyan	NOUN
ejpam-3412	633	52	black	black	ADJ
ejpam-3412	633	53	black	black	ADJ
ejpam-3412	633	54	black	black	ADJ
ejpam-3412	633	55	black	black	ADJ
ejpam-3412	633	56	blue	blue	ADJ
ejpam-3412	633	57	black	black	ADJ
ejpam-3412	633	58	black	black	ADJ
ejpam-3412	633	59	black	black	ADJ
ejpam-3412	633	60	black	black	ADJ
ejpam-3412	633	61	green	green	ADJ
ejpam-3412	633	62	black	black	ADJ
ejpam-3412	633	63	black	black	ADJ
ejpam-3412	633	64	black	black	ADJ
ejpam-3412	633	65	black	black	NOUN
ejpam-3412	633	66	then	then	ADV
ejpam-3412	633	67	a	a	PRON
ejpam-3412	633	68	=	=	X
ejpam-3412	633	69	(	(	PUNCT
ejpam-3412	633	70	a	a	PRON
ejpam-3412	633	71	,	,	PUNCT
ejpam-3412	633	72	·	·	PUNCT
ejpam-3412	633	73	,	,	PUNCT
ejpam-3412	633	74	∗	∗	NOUN
ejpam-3412	633	75	,	,	PUNCT
ejpam-3412	633	76	black	black	NOUN
ejpam-3412	633	77	)	)	PUNCT
ejpam-3412	633	78	is	be	AUX
ejpam-3412	633	79	an	an	DET
ejpam-3412	633	80	f	f	PROPN
ejpam-3412	633	81	-up	-up	NOUN
ejpam-3412	633	82	-	-	PUNCT
ejpam-3412	633	83	semigroup	semigroup	NOUN
ejpam-3412	633	84	.	.	PUNCT
ejpam-3412	634	1	let	let	AUX
ejpam-3412	634	2	(	(	PUNCT
ejpam-3412	634	3	g̃1	g̃1	NOUN
ejpam-3412	634	4	,	,	PUNCT
ejpam-3412	634	5	e1	e1	PROPN
ejpam-3412	634	6	)	)	PUNCT
ejpam-3412	634	7	and	and	CCONJ
ejpam-3412	634	8	(	(	PUNCT
ejpam-3412	634	9	g̃2	g̃2	PROPN
ejpam-3412	634	10	,	,	PUNCT
ejpam-3412	634	11	e2	e2	PROPN
ejpam-3412	634	12	)	)	PUNCT
ejpam-3412	634	13	be	be	VERB
ejpam-3412	634	14	two	two	NUM
ejpam-3412	634	15	fuzzy	fuzzy	ADJ
ejpam-3412	634	16	soft	soft	ADJ
ejpam-3412	634	17	sets	set	NOUN
ejpam-3412	634	18	over	over	ADP
ejpam-3412	634	19	a	a	DET
ejpam-3412	634	20	where	where	SCONJ
ejpam-3412	634	21	e1	e1	NOUN
ejpam-3412	634	22	:	:	PUNCT
ejpam-3412	634	23	=	=	SYM
ejpam-3412	634	24	{	{	PUNCT
ejpam-3412	634	25	endurance	endurance	NOUN
ejpam-3412	634	26	,	,	PUNCT
ejpam-3412	634	27	beauty	beauty	NOUN
ejpam-3412	634	28	}	}	PUNCT
ejpam-3412	634	29	and	and	CCONJ
ejpam-3412	634	30	e2	e2	PROPN
ejpam-3412	634	31	:	:	PUNCT
ejpam-3412	635	1	=	=	SYM
ejpam-3412	635	2	{	{	PUNCT
ejpam-3412	635	3	endurance	endurance	NOUN
ejpam-3412	635	4	,	,	PUNCT
ejpam-3412	635	5	warmth	warmth	NOUN
ejpam-3412	635	6	}	}	PUNCT
ejpam-3412	635	7	with	with	ADP
ejpam-3412	635	8	g̃1[endurance	g̃1[endurance	NOUN
ejpam-3412	635	9	]	]	PUNCT
ejpam-3412	635	10	,	,	PUNCT
ejpam-3412	635	11	g̃1[beauty	g̃1[beauty	PROPN
ejpam-3412	635	12	]	]	X
ejpam-3412	635	13	,	,	PUNCT
ejpam-3412	635	14	g̃2[endurance	g̃2[endurance	PROPN
ejpam-3412	635	15	]	]	PUNCT
ejpam-3412	635	16	,	,	PUNCT
ejpam-3412	635	17	and	and	CCONJ
ejpam-3412	635	18	g̃2[warmth	g̃2[warmth	PROPN
ejpam-3412	635	19	]	]	PUNCT
ejpam-3412	635	20	are	be	AUX
ejpam-3412	635	21	fuzzy	fuzzy	ADJ
ejpam-3412	635	22	sets	set	NOUN
ejpam-3412	635	23	in	in	ADP
ejpam-3412	635	24	a	a	DET
ejpam-3412	635	25	defined	define	VERB
ejpam-3412	635	26	as	as	SCONJ
ejpam-3412	635	27	follows	follow	VERB
ejpam-3412	635	28	:	:	PUNCT
ejpam-3412	635	29	g̃1	g̃1	NOUN
ejpam-3412	635	30	black	black	ADJ
ejpam-3412	635	31	cyan	cyan	NOUN
ejpam-3412	635	32	blue	blue	ADJ
ejpam-3412	635	33	green	green	ADJ
ejpam-3412	635	34	endurance	endurance	NOUN
ejpam-3412	635	35	1	1	NUM
ejpam-3412	635	36	0.5	0.5	NUM
ejpam-3412	635	37	0.7	0.7	NUM
ejpam-3412	635	38	0.5	0.5	NUM
ejpam-3412	635	39	beauty	beauty	NOUN
ejpam-3412	635	40	0.4	0.4	NUM
ejpam-3412	635	41	0.3	0.3	NUM
ejpam-3412	635	42	0.2	0.2	NUM
ejpam-3412	635	43	0.2	0.2	NUM
ejpam-3412	635	44	g̃2	g̃2	PROPN
ejpam-3412	635	45	black	black	ADJ
ejpam-3412	635	46	cyan	cyan	NOUN
ejpam-3412	635	47	blue	blue	ADJ
ejpam-3412	635	48	green	green	ADJ
ejpam-3412	635	49	endurance	endurance	NOUN
ejpam-3412	635	50	1	1	NUM
ejpam-3412	635	51	0.6	0.6	NUM
ejpam-3412	635	52	0.5	0.5	NUM
ejpam-3412	635	53	0.5	0.5	NUM
ejpam-3412	635	54	warmth	warmth	NOUN
ejpam-3412	635	55	0.9	0.9	NUM
ejpam-3412	635	56	0.4	0.4	NUM
ejpam-3412	635	57	0.5	0.5	NUM
ejpam-3412	635	58	0.4	0.4	NUM
ejpam-3412	635	59	then	then	ADV
ejpam-3412	635	60	(	(	PUNCT
ejpam-3412	635	61	g̃1	g̃1	NOUN
ejpam-3412	635	62	,	,	PUNCT
ejpam-3412	635	63	e1	e1	PROPN
ejpam-3412	635	64	)	)	PUNCT
ejpam-3412	635	65	and	and	CCONJ
ejpam-3412	635	66	(	(	PUNCT
ejpam-3412	635	67	g̃2	g̃2	PROPN
ejpam-3412	635	68	,	,	PUNCT
ejpam-3412	635	69	e2	e2	PROPN
ejpam-3412	635	70	)	)	PUNCT
ejpam-3412	635	71	are	be	AUX
ejpam-3412	635	72	two	two	NUM
ejpam-3412	635	73	fuzzy	fuzzy	ADJ
ejpam-3412	635	74	soft	soft	ADJ
ejpam-3412	635	75	upi	upi	NOUN
ejpam-3412	635	76	-	-	PUNCT
ejpam-3412	635	77	filters	filter	NOUN
ejpam-3412	635	78	of	of	ADP
ejpam-3412	635	79	a.	a.	NOUN
ejpam-3412	635	80	since	since	SCONJ
ejpam-3412	635	81	endurance	endurance	PROPN
ejpam-3412	635	82	∈	∈	PROPN
ejpam-3412	635	83	e1∩e2	e1∩e2	PROPN
ejpam-3412	635	84	,	,	PUNCT
ejpam-3412	635	85	we	we	PRON
ejpam-3412	635	86	have	have	VERB
ejpam-3412	635	87	(	(	PUNCT
ejpam-3412	635	88	f	f	PROPN
ejpam-3412	635	89	g̃1[endurance]∪g̃2[endurance	g̃1[endurance]∪g̃2[endurance	PROPN
ejpam-3412	635	90	]	]	X
ejpam-3412	635	91	)	)	PUNCT
ejpam-3412	635	92	(	(	PUNCT
ejpam-3412	635	93	green	green	ADJ
ejpam-3412	635	94	)	)	PUNCT
ejpam-3412	635	95	=	=	SYM
ejpam-3412	635	96	0.5	0.5	NUM
ejpam-3412	635	97	�	�	PROPN
ejpam-3412	635	98	0.6	0.6	NUM
ejpam-3412	635	99	=	=	SYM
ejpam-3412	635	100	min{0.6	min{0.6	PROPN
ejpam-3412	635	101	,	,	PUNCT
ejpam-3412	635	102	0.7	0.7	NUM
ejpam-3412	635	103	}	}	PUNCT
ejpam-3412	635	104	=	=	SYM
ejpam-3412	635	105	min{(f	min{(f	NOUN
ejpam-3412	635	106	g̃1[endurance]∪g̃2[endurance	g̃1[endurance]∪g̃2[endurance	NOUN
ejpam-3412	635	107	]	]	PUNCT
ejpam-3412	635	108	)	)	PUNCT
ejpam-3412	635	109	(	(	PUNCT
ejpam-3412	635	110	cyan	cyan	NOUN
ejpam-3412	635	111	)	)	PUNCT
ejpam-3412	635	112	,	,	PUNCT
ejpam-3412	635	113	(	(	PUNCT
ejpam-3412	635	114	f	f	PROPN
ejpam-3412	635	115	g̃1[endurance]∪g̃2[endurance	g̃1[endurance]∪g̃2[endurance	PROPN
ejpam-3412	635	116	]	]	X
ejpam-3412	635	117	)	)	PUNCT
ejpam-3412	635	118	(	(	PUNCT
ejpam-3412	635	119	blue	blue	ADJ
ejpam-3412	635	120	)	)	PUNCT
ejpam-3412	635	121	}	}	PUNCT
ejpam-3412	635	122	=	=	SYM
ejpam-3412	635	123	min{(f	min{(f	NOUN
ejpam-3412	635	124	g̃1[endurance]∪g̃2[endurance	g̃1[endurance]∪g̃2[endurance	NOUN
ejpam-3412	635	125	]	]	PUNCT
ejpam-3412	635	126	)	)	PUNCT
ejpam-3412	635	127	(	(	PUNCT
ejpam-3412	635	128	blue	blue	ADJ
ejpam-3412	635	129	·	·	SYM
ejpam-3412	635	130	green	green	ADJ
ejpam-3412	635	131	)	)	PUNCT
ejpam-3412	635	132	,	,	PUNCT
ejpam-3412	635	133	(	(	PUNCT
ejpam-3412	635	134	f	f	PROPN
ejpam-3412	635	135	g̃1[endurance]∪g̃2[endurance	g̃1[endurance]∪g̃2[endurance	PROPN
ejpam-3412	635	136	]	]	X
ejpam-3412	635	137	)	)	PUNCT
ejpam-3412	635	138	(	(	PUNCT
ejpam-3412	635	139	blue	blue	ADJ
ejpam-3412	635	140	)	)	PUNCT
ejpam-3412	635	141	}	}	PUNCT
ejpam-3412	635	142	.	.	PUNCT
ejpam-3412	636	1	thus	thus	ADV
ejpam-3412	636	2	g̃1[endurance	g̃1[endurance	NOUN
ejpam-3412	636	3	]	]	PUNCT
ejpam-3412	636	4	∪	∪	ADP
ejpam-3412	636	5	g̃2[endurance	g̃2[endurance	PROPN
ejpam-3412	636	6	]	]	PUNCT
ejpam-3412	636	7	is	be	AUX
ejpam-3412	636	8	not	not	PART
ejpam-3412	636	9	a	a	DET
ejpam-3412	636	10	fuzzy	fuzzy	ADJ
ejpam-3412	636	11	upi	upi	NOUN
ejpam-3412	636	12	-	-	PUNCT
ejpam-3412	636	13	filter	filter	NOUN
ejpam-3412	636	14	of	of	ADP
ejpam-3412	636	15	a	a	PRON
ejpam-3412	636	16	,	,	PUNCT
ejpam-3412	636	17	that	that	ADV
ejpam-3412	636	18	is	is	ADV
ejpam-3412	636	19	,	,	PUNCT
ejpam-3412	636	20	(	(	PUNCT
ejpam-3412	636	21	g̃1	g̃1	NOUN
ejpam-3412	636	22	,	,	PUNCT
ejpam-3412	636	23	e1	e1	NOUN
ejpam-3412	636	24	)	)	PUNCT
ejpam-3412	636	25	∪	∪	NOUN
ejpam-3412	636	26	(	(	PUNCT
ejpam-3412	636	27	g̃2	g̃2	PROPN
ejpam-3412	636	28	,	,	PUNCT
ejpam-3412	636	29	e2	e2	PROPN
ejpam-3412	636	30	)	)	PUNCT
ejpam-3412	636	31	is	be	AUX
ejpam-3412	636	32	not	not	PART
ejpam-3412	636	33	a	a	DET
ejpam-3412	636	34	endurance	endurance	NOUN
ejpam-3412	636	35	-	-	PUNCT
ejpam-3412	636	36	fuzzy	fuzzy	ADJ
ejpam-3412	636	37	soft	soft	ADJ
ejpam-3412	636	38	upi	upi	NOUN
ejpam-3412	636	39	-	-	PUNCT
ejpam-3412	636	40	filter	filter	NOUN
ejpam-3412	636	41	of	of	ADP
ejpam-3412	636	42	a.	a.	NOUN
ejpam-3412	636	43	hence	hence	ADV
ejpam-3412	636	44	,	,	PUNCT
ejpam-3412	636	45	(	(	PUNCT
ejpam-3412	636	46	g̃1	g̃1	NOUN
ejpam-3412	636	47	,	,	PUNCT
ejpam-3412	636	48	e1	e1	NOUN
ejpam-3412	636	49	)	)	PUNCT
ejpam-3412	636	50	∪	∪	NOUN
ejpam-3412	636	51	(	(	PUNCT
ejpam-3412	636	52	g̃2	g̃2	PROPN
ejpam-3412	636	53	,	,	PUNCT
ejpam-3412	636	54	e2	e2	PROPN
ejpam-3412	636	55	)	)	PUNCT
ejpam-3412	636	56	is	be	AUX
ejpam-3412	636	57	not	not	PART
ejpam-3412	636	58	a	a	DET
ejpam-3412	636	59	fuzzy	fuzzy	ADJ
ejpam-3412	636	60	soft	soft	ADJ
ejpam-3412	636	61	upi	upi	NOUN
ejpam-3412	636	62	-	-	PUNCT
ejpam-3412	636	63	filter	filter	NOUN
ejpam-3412	636	64	of	of	ADP
ejpam-3412	636	65	a.	a.	NOUN
ejpam-3412	636	66	moreover	moreover	ADV
ejpam-3412	636	67	,	,	PUNCT
ejpam-3412	636	68	(	(	PUNCT
ejpam-3412	636	69	g̃1	g̃1	NOUN
ejpam-3412	636	70	,	,	PUNCT
ejpam-3412	636	71	e1	e1	NOUN
ejpam-3412	636	72	)	)	PUNCT
ejpam-3412	636	73	d	d	NOUN
ejpam-3412	636	74	(	(	PUNCT
ejpam-3412	636	75	g̃2	g̃2	PROPN
ejpam-3412	636	76	,	,	PUNCT
ejpam-3412	636	77	e2	e2	PROPN
ejpam-3412	636	78	)	)	PUNCT
ejpam-3412	636	79	is	be	AUX
ejpam-3412	636	80	not	not	PART
ejpam-3412	636	81	a	a	DET
ejpam-3412	636	82	fuzzy	fuzzy	ADJ
ejpam-3412	636	83	soft	soft	ADJ
ejpam-3412	636	84	upi	upi	NOUN
ejpam-3412	636	85	-	-	PUNCT
ejpam-3412	636	86	filter	filter	NOUN
ejpam-3412	636	87	of	of	ADP
ejpam-3412	636	88	a.	a.	PROPN
ejpam-3412	636	89	a.	a.	PROPN
ejpam-3412	636	90	satirad	satirad	PROPN
ejpam-3412	636	91	,	,	PUNCT
ejpam-3412	636	92	a.	a.	NOUN
ejpam-3412	636	93	iampan	iampan	PROPN
ejpam-3412	636	94	/	/	SYM
ejpam-3412	636	95	eur	eur	PROPN
ejpam-3412	636	96	.	.	PUNCT
ejpam-3412	637	1	j.	j.	PROPN
ejpam-3412	637	2	pure	pure	PROPN
ejpam-3412	637	3	appl	appl	PROPN
ejpam-3412	637	4	.	.	PROPN
ejpam-3412	637	5	math	math	PROPN
ejpam-3412	637	6	,	,	PUNCT
ejpam-3412	637	7	12	12	NUM
ejpam-3412	637	8	(	(	PUNCT
ejpam-3412	637	9	2	2	NUM
ejpam-3412	637	10	)	)	PUNCT
ejpam-3412	637	11	(	(	PUNCT
ejpam-3412	637	12	2019	2019	NUM
ejpam-3412	637	13	)	)	PUNCT
ejpam-3412	637	14	,	,	PUNCT
ejpam-3412	637	15	294	294	NUM
ejpam-3412	637	16	-	-	SYM
ejpam-3412	637	17	331	331	NUM
ejpam-3412	637	18	323	323	NUM
ejpam-3412	637	19	3.7	3.7	NUM
ejpam-3412	637	20	.	.	PUNCT
ejpam-3412	638	1	fuzzy	fuzzy	ADJ
ejpam-3412	638	2	soft	soft	ADJ
ejpam-3412	638	3	ups	up	NOUN
ejpam-3412	638	4	-	-	PUNCT
ejpam-3412	638	5	ideals	ideal	NOUN
ejpam-3412	638	6	definition	definition	NOUN
ejpam-3412	638	7	24	24	NUM
ejpam-3412	638	8	.	.	PUNCT
ejpam-3412	639	1	a	a	DET
ejpam-3412	639	2	fuzzy	fuzzy	ADJ
ejpam-3412	639	3	soft	soft	ADJ
ejpam-3412	639	4	set	set	NOUN
ejpam-3412	639	5	(	(	PUNCT
ejpam-3412	639	6	f̃	f̃	PROPN
ejpam-3412	639	7	,	,	PUNCT
ejpam-3412	639	8	e	e	NOUN
ejpam-3412	639	9	)	)	PUNCT
ejpam-3412	639	10	over	over	ADP
ejpam-3412	639	11	a	a	PRON
ejpam-3412	639	12	is	be	AUX
ejpam-3412	639	13	called	call	VERB
ejpam-3412	639	14	a	a	DET
ejpam-3412	639	15	fuzzy	fuzzy	ADJ
ejpam-3412	639	16	soft	soft	ADJ
ejpam-3412	639	17	ups	up	NOUN
ejpam-3412	639	18	-	-	PUNCT
ejpam-3412	639	19	ideal	ideal	NOUN
ejpam-3412	639	20	based	base	VERB
ejpam-3412	639	21	on	on	ADP
ejpam-3412	639	22	e	e	PROPN
ejpam-3412	639	23	∈	∈	PROPN
ejpam-3412	639	24	e	e	X
ejpam-3412	639	25	(	(	PUNCT
ejpam-3412	639	26	we	we	PRON
ejpam-3412	639	27	shortly	shortly	ADV
ejpam-3412	639	28	call	call	VERB
ejpam-3412	639	29	an	an	DET
ejpam-3412	639	30	e	e	ADJ
ejpam-3412	639	31	-	-	ADJ
ejpam-3412	639	32	fuzzy	fuzzy	ADJ
ejpam-3412	639	33	soft	soft	ADJ
ejpam-3412	639	34	ups	up	NOUN
ejpam-3412	639	35	-	-	PUNCT
ejpam-3412	639	36	ideal	ideal	NOUN
ejpam-3412	639	37	)	)	PUNCT
ejpam-3412	639	38	of	of	ADP
ejpam-3412	639	39	a	a	DET
ejpam-3412	639	40	if	if	SCONJ
ejpam-3412	639	41	a	a	DET
ejpam-3412	639	42	fuzzy	fuzzy	ADJ
ejpam-3412	639	43	set	set	NOUN
ejpam-3412	639	44	f̃[e	f̃[e	X
ejpam-3412	639	45	]	]	X
ejpam-3412	639	46	in	in	ADP
ejpam-3412	639	47	a	a	PRON
ejpam-3412	639	48	is	be	AUX
ejpam-3412	639	49	a	a	DET
ejpam-3412	639	50	fuzzy	fuzzy	ADJ
ejpam-3412	639	51	ups	up	NOUN
ejpam-3412	639	52	-	-	PUNCT
ejpam-3412	639	53	ideal	ideal	NOUN
ejpam-3412	639	54	of	of	ADP
ejpam-3412	639	55	a.	a.	NOUN
ejpam-3412	639	56	if	if	SCONJ
ejpam-3412	639	57	(	(	PUNCT
ejpam-3412	639	58	f̃	f̃	PROPN
ejpam-3412	639	59	,	,	PUNCT
ejpam-3412	639	60	e	e	NOUN
ejpam-3412	639	61	)	)	PUNCT
ejpam-3412	639	62	is	be	AUX
ejpam-3412	639	63	an	an	DET
ejpam-3412	639	64	e	e	ADJ
ejpam-3412	639	65	-	-	ADJ
ejpam-3412	639	66	fuzzy	fuzzy	ADJ
ejpam-3412	639	67	soft	soft	ADJ
ejpam-3412	639	68	ups	up	NOUN
ejpam-3412	639	69	-	-	PUNCT
ejpam-3412	639	70	ideal	ideal	NOUN
ejpam-3412	639	71	of	of	ADP
ejpam-3412	639	72	a	a	PRON
ejpam-3412	639	73	for	for	ADP
ejpam-3412	639	74	all	all	DET
ejpam-3412	639	75	e	e	NOUN
ejpam-3412	639	76	∈	∈	PROPN
ejpam-3412	639	77	e	e	NOUN
ejpam-3412	639	78	,	,	PUNCT
ejpam-3412	639	79	we	we	PRON
ejpam-3412	639	80	say	say	VERB
ejpam-3412	639	81	that	that	SCONJ
ejpam-3412	639	82	(	(	PUNCT
ejpam-3412	639	83	f̃	f̃	PROPN
ejpam-3412	639	84	,	,	PUNCT
ejpam-3412	639	85	e	e	NOUN
ejpam-3412	639	86	)	)	PUNCT
ejpam-3412	639	87	is	be	AUX
ejpam-3412	639	88	a	a	DET
ejpam-3412	639	89	fuzzy	fuzzy	ADJ
ejpam-3412	639	90	soft	soft	ADJ
ejpam-3412	639	91	ups	up	NOUN
ejpam-3412	639	92	-	-	PUNCT
ejpam-3412	639	93	ideal	ideal	NOUN
ejpam-3412	639	94	of	of	ADP
ejpam-3412	639	95	a.	a.	NOUN
ejpam-3412	639	96	in	in	ADP
ejpam-3412	639	97	the	the	DET
ejpam-3412	639	98	next	next	ADJ
ejpam-3412	639	99	theorem	theorem	NOUN
ejpam-3412	639	100	and	and	CCONJ
ejpam-3412	639	101	corollary	corollary	ADJ
ejpam-3412	639	102	,	,	PUNCT
ejpam-3412	639	103	we	we	PRON
ejpam-3412	639	104	give	give	VERB
ejpam-3412	639	105	necessary	necessary	ADJ
ejpam-3412	639	106	condition	condition	NOUN
ejpam-3412	639	107	for	for	ADP
ejpam-3412	639	108	fuzzy	fuzzy	ADJ
ejpam-3412	639	109	soft	soft	ADJ
ejpam-3412	639	110	ups	up	NOUN
ejpam-3412	639	111	-	-	PUNCT
ejpam-3412	639	112	ideals	ideal	NOUN
ejpam-3412	639	113	of	of	ADP
ejpam-3412	639	114	f	f	PROPN
ejpam-3412	639	115	-up	-up	NOUN
ejpam-3412	639	116	-	-	PUNCT
ejpam-3412	639	117	semigroups	semigroup	NOUN
ejpam-3412	639	118	.	.	PUNCT
ejpam-3412	640	1	theorem	theorem	VERB
ejpam-3412	640	2	55	55	NUM
ejpam-3412	640	3	.	.	PUNCT
ejpam-3412	641	1	if	if	SCONJ
ejpam-3412	641	2	(	(	PUNCT
ejpam-3412	641	3	f̃	f̃	PROPN
ejpam-3412	641	4	,	,	PUNCT
ejpam-3412	641	5	e	e	NOUN
ejpam-3412	641	6	)	)	PUNCT
ejpam-3412	641	7	is	be	AUX
ejpam-3412	641	8	a	a	DET
ejpam-3412	641	9	fuzzy	fuzzy	ADJ
ejpam-3412	641	10	soft	soft	ADJ
ejpam-3412	641	11	set	set	NOUN
ejpam-3412	641	12	over	over	ADP
ejpam-3412	641	13	a	a	DET
ejpam-3412	641	14	such	such	ADJ
ejpam-3412	641	15	that	that	PRON
ejpam-3412	641	16	for	for	ADP
ejpam-3412	641	17	all	all	DET
ejpam-3412	641	18	e	e	NOUN
ejpam-3412	641	19	∈	∈	PROPN
ejpam-3412	641	20	e	e	NOUN
ejpam-3412	641	21	,	,	PUNCT
ejpam-3412	641	22	a	a	DET
ejpam-3412	641	23	fuzzy	fuzzy	ADJ
ejpam-3412	641	24	set	set	NOUN
ejpam-3412	641	25	f̃[e	f̃[e	NOUN
ejpam-3412	641	26	]	]	X
ejpam-3412	641	27	in	in	ADP
ejpam-3412	641	28	a	a	DET
ejpam-3412	641	29	satisfies	satisfie	NOUN
ejpam-3412	641	30	the	the	DET
ejpam-3412	641	31	conditions	condition	NOUN
ejpam-3412	641	32	(	(	PUNCT
ejpam-3412	641	33	2.8	2.8	NUM
ejpam-3412	641	34	)	)	PUNCT
ejpam-3412	641	35	and	and	CCONJ
ejpam-3412	641	36	(	(	PUNCT
ejpam-3412	641	37	1.14	1.14	NUM
ejpam-3412	641	38	)	)	PUNCT
ejpam-3412	641	39	,	,	PUNCT
ejpam-3412	641	40	then	then	ADV
ejpam-3412	641	41	(	(	PUNCT
ejpam-3412	641	42	f̃	f̃	PROPN
ejpam-3412	641	43	,	,	PUNCT
ejpam-3412	641	44	e	e	NOUN
ejpam-3412	641	45	)	)	PUNCT
ejpam-3412	641	46	is	be	AUX
ejpam-3412	641	47	a	a	DET
ejpam-3412	641	48	fuzzy	fuzzy	ADJ
ejpam-3412	641	49	soft	soft	ADJ
ejpam-3412	641	50	ups	up	NOUN
ejpam-3412	641	51	-	-	PUNCT
ejpam-3412	641	52	ideal	ideal	NOUN
ejpam-3412	641	53	of	of	ADP
ejpam-3412	641	54	a.	a.	NOUN
ejpam-3412	641	55	proof	proof	NOUN
ejpam-3412	641	56	.	.	PUNCT
ejpam-3412	642	1	it	it	PRON
ejpam-3412	642	2	is	be	AUX
ejpam-3412	642	3	straightforward	straightforward	ADJ
ejpam-3412	642	4	by	by	ADP
ejpam-3412	642	5	proposition	proposition	NOUN
ejpam-3412	642	6	7	7	NUM
ejpam-3412	642	7	and	and	CCONJ
ejpam-3412	642	8	lemma	lemma	PROPN
ejpam-3412	642	9	1	1	NUM
ejpam-3412	642	10	(	(	PUNCT
ejpam-3412	642	11	1	1	NUM
ejpam-3412	642	12	)	)	PUNCT
ejpam-3412	642	13	.	.	PUNCT
ejpam-3412	643	1	corollary	corollary	ADJ
ejpam-3412	643	2	3	3	X
ejpam-3412	643	3	.	.	PUNCT
ejpam-3412	644	1	let	let	VERB
ejpam-3412	644	2	a	a	DET
ejpam-3412	644	3	be	be	AUX
ejpam-3412	644	4	an	an	DET
ejpam-3412	644	5	f	f	PROPN
ejpam-3412	644	6	-up	-up	NOUN
ejpam-3412	644	7	-	-	PUNCT
ejpam-3412	644	8	semigroup	semigroup	NOUN
ejpam-3412	644	9	satisfying	satisfy	VERB
ejpam-3412	644	10	the	the	DET
ejpam-3412	644	11	condition	condition	NOUN
ejpam-3412	644	12	(	(	PUNCT
ejpam-3412	644	13	2.10	2.10	NUM
ejpam-3412	644	14	)	)	PUNCT
ejpam-3412	644	15	.	.	PUNCT
ejpam-3412	645	1	if	if	SCONJ
ejpam-3412	645	2	(	(	PUNCT
ejpam-3412	645	3	f̃	f̃	PROPN
ejpam-3412	645	4	,	,	PUNCT
ejpam-3412	645	5	e	e	NOUN
ejpam-3412	645	6	)	)	PUNCT
ejpam-3412	645	7	is	be	AUX
ejpam-3412	645	8	a	a	DET
ejpam-3412	645	9	fuzzy	fuzzy	ADJ
ejpam-3412	645	10	soft	soft	ADJ
ejpam-3412	645	11	set	set	NOUN
ejpam-3412	645	12	over	over	ADP
ejpam-3412	645	13	a	a	DET
ejpam-3412	645	14	such	such	ADJ
ejpam-3412	645	15	that	that	PRON
ejpam-3412	645	16	for	for	ADP
ejpam-3412	645	17	all	all	DET
ejpam-3412	645	18	e	e	NOUN
ejpam-3412	645	19	∈	∈	PROPN
ejpam-3412	645	20	e	e	NOUN
ejpam-3412	645	21	,	,	PUNCT
ejpam-3412	645	22	a	a	DET
ejpam-3412	645	23	fuzzy	fuzzy	ADJ
ejpam-3412	645	24	set	set	NOUN
ejpam-3412	645	25	f̃[e	f̃[e	NOUN
ejpam-3412	645	26	]	]	X
ejpam-3412	645	27	in	in	ADP
ejpam-3412	645	28	a	a	DET
ejpam-3412	645	29	satisfies	satisfie	NOUN
ejpam-3412	645	30	the	the	DET
ejpam-3412	645	31	conditions	condition	NOUN
ejpam-3412	645	32	(	(	PUNCT
ejpam-3412	645	33	2.9	2.9	NUM
ejpam-3412	645	34	)	)	PUNCT
ejpam-3412	645	35	and	and	CCONJ
ejpam-3412	645	36	(	(	PUNCT
ejpam-3412	645	37	1.14	1.14	NUM
ejpam-3412	645	38	)	)	PUNCT
ejpam-3412	645	39	,	,	PUNCT
ejpam-3412	645	40	then	then	ADV
ejpam-3412	645	41	(	(	PUNCT
ejpam-3412	645	42	f̃	f̃	PROPN
ejpam-3412	645	43	,	,	PUNCT
ejpam-3412	645	44	e	e	NOUN
ejpam-3412	645	45	)	)	PUNCT
ejpam-3412	645	46	is	be	AUX
ejpam-3412	645	47	a	a	DET
ejpam-3412	645	48	fuzzy	fuzzy	ADJ
ejpam-3412	645	49	soft	soft	ADJ
ejpam-3412	645	50	ups	up	NOUN
ejpam-3412	645	51	-	-	PUNCT
ejpam-3412	645	52	ideal	ideal	NOUN
ejpam-3412	645	53	of	of	ADP
ejpam-3412	645	54	a.	a.	NOUN
ejpam-3412	645	55	proof	proof	NOUN
ejpam-3412	645	56	.	.	PUNCT
ejpam-3412	646	1	it	it	PRON
ejpam-3412	646	2	is	be	AUX
ejpam-3412	646	3	straightforward	straightforward	ADJ
ejpam-3412	646	4	by	by	ADP
ejpam-3412	646	5	theorems	theorem	NOUN
ejpam-3412	646	6	55	55	NUM
ejpam-3412	646	7	and	and	CCONJ
ejpam-3412	646	8	15	15	NUM
ejpam-3412	646	9	.	.	PUNCT
ejpam-3412	647	1	from	from	ADP
ejpam-3412	647	2	figure	figure	NOUN
ejpam-3412	647	3	1	1	NUM
ejpam-3412	647	4	,	,	PUNCT
ejpam-3412	647	5	we	we	PRON
ejpam-3412	647	6	have	have	VERB
ejpam-3412	647	7	the	the	DET
ejpam-3412	647	8	following	follow	VERB
ejpam-3412	647	9	theorem	theorem	VERB
ejpam-3412	647	10	.	.	PUNCT
ejpam-3412	647	11	theorem	theorem	VERB
ejpam-3412	647	12	56	56	NUM
ejpam-3412	647	13	.	.	PUNCT
ejpam-3412	648	1	every	every	DET
ejpam-3412	648	2	e	e	ADJ
ejpam-3412	648	3	-	-	ADJ
ejpam-3412	648	4	fuzzy	fuzzy	ADJ
ejpam-3412	648	5	soft	soft	ADJ
ejpam-3412	648	6	ups	up	NOUN
ejpam-3412	648	7	-	-	PUNCT
ejpam-3412	648	8	ideal	ideal	NOUN
ejpam-3412	648	9	of	of	ADP
ejpam-3412	648	10	a	a	PRON
ejpam-3412	648	11	is	be	AUX
ejpam-3412	648	12	an	an	DET
ejpam-3412	648	13	e	e	ADJ
ejpam-3412	648	14	-	-	ADJ
ejpam-3412	648	15	fuzzy	fuzzy	ADJ
ejpam-3412	648	16	soft	soft	ADJ
ejpam-3412	648	17	ups	up	NOUN
ejpam-3412	648	18	-	-	PUNCT
ejpam-3412	648	19	filter	filter	NOUN
ejpam-3412	648	20	.	.	PUNCT
ejpam-3412	649	1	moreover	moreover	ADV
ejpam-3412	649	2	,	,	PUNCT
ejpam-3412	649	3	every	every	DET
ejpam-3412	649	4	fuzzy	fuzzy	ADJ
ejpam-3412	649	5	soft	soft	ADJ
ejpam-3412	649	6	ups	up	NOUN
ejpam-3412	649	7	-	-	PUNCT
ejpam-3412	649	8	ideal	ideal	NOUN
ejpam-3412	649	9	of	of	ADP
ejpam-3412	649	10	a	a	PRON
ejpam-3412	649	11	is	be	AUX
ejpam-3412	649	12	a	a	DET
ejpam-3412	649	13	fuzzy	fuzzy	ADJ
ejpam-3412	649	14	soft	soft	ADJ
ejpam-3412	649	15	ups	up	NOUN
ejpam-3412	649	16	-	-	PUNCT
ejpam-3412	649	17	filter	filter	NOUN
ejpam-3412	649	18	.	.	PUNCT
ejpam-3412	650	1	the	the	DET
ejpam-3412	650	2	following	follow	VERB
ejpam-3412	650	3	example	example	NOUN
ejpam-3412	650	4	shows	show	VERB
ejpam-3412	650	5	that	that	SCONJ
ejpam-3412	650	6	the	the	DET
ejpam-3412	650	7	converse	converse	NOUN
ejpam-3412	650	8	of	of	ADP
ejpam-3412	650	9	theorem	theorem	NOUN
ejpam-3412	650	10	56	56	NUM
ejpam-3412	650	11	is	be	AUX
ejpam-3412	650	12	not	not	PART
ejpam-3412	650	13	true	true	ADJ
ejpam-3412	650	14	.	.	PUNCT
ejpam-3412	651	1	example	example	NOUN
ejpam-3412	651	2	26	26	NUM
ejpam-3412	651	3	.	.	PUNCT
ejpam-3412	652	1	by	by	ADP
ejpam-3412	652	2	cayley	cayley	ADJ
ejpam-3412	652	3	tables	table	NOUN
ejpam-3412	652	4	in	in	ADP
ejpam-3412	652	5	example	example	NOUN
ejpam-3412	652	6	16	16	NUM
ejpam-3412	652	7	,	,	PUNCT
ejpam-3412	652	8	we	we	PRON
ejpam-3412	652	9	know	know	VERB
ejpam-3412	652	10	that	that	SCONJ
ejpam-3412	652	11	a	a	PRON
ejpam-3412	652	12	=	=	X
ejpam-3412	652	13	(	(	PUNCT
ejpam-3412	652	14	a	a	PRON
ejpam-3412	652	15	,	,	PUNCT
ejpam-3412	652	16	·	·	PUNCT
ejpam-3412	652	17	,	,	PUNCT
ejpam-3412	652	18	∗	∗	NOUN
ejpam-3412	652	19	,	,	PUNCT
ejpam-3412	652	20	pop	pop	NOUN
ejpam-3412	652	21	)	)	PUNCT
ejpam-3412	652	22	is	be	AUX
ejpam-3412	652	23	an	an	DET
ejpam-3412	652	24	f	f	PROPN
ejpam-3412	652	25	-up	-up	NOUN
ejpam-3412	652	26	-	-	PUNCT
ejpam-3412	652	27	semigroup	semigroup	NOUN
ejpam-3412	652	28	.	.	PUNCT
ejpam-3412	653	1	let	let	AUX
ejpam-3412	653	2	(	(	PUNCT
ejpam-3412	653	3	f̃	f̃	PROPN
ejpam-3412	653	4	,	,	PUNCT
ejpam-3412	653	5	e	e	NOUN
ejpam-3412	653	6	)	)	PUNCT
ejpam-3412	653	7	be	be	AUX
ejpam-3412	653	8	a	a	DET
ejpam-3412	653	9	fuzzy	fuzzy	ADJ
ejpam-3412	653	10	soft	soft	ADJ
ejpam-3412	653	11	set	set	NOUN
ejpam-3412	653	12	over	over	ADP
ejpam-3412	653	13	a	a	DET
ejpam-3412	653	14	where	where	SCONJ
ejpam-3412	653	15	e	e	NOUN
ejpam-3412	653	16	:	:	PUNCT
ejpam-3412	653	17	=	=	SYM
ejpam-3412	653	18	{	{	PUNCT
ejpam-3412	653	19	sorrow	sorrow	NOUN
ejpam-3412	653	20	,	,	PUNCT
ejpam-3412	653	21	relaxation	relaxation	NOUN
ejpam-3412	653	22	,	,	PUNCT
ejpam-3412	653	23	enjoyment	enjoyment	NOUN
ejpam-3412	653	24	}	}	PUNCT
ejpam-3412	653	25	with	with	ADP
ejpam-3412	653	26	f̃[sorrow	f̃[sorrow	NOUN
ejpam-3412	653	27	]	]	PUNCT
ejpam-3412	653	28	,	,	PUNCT
ejpam-3412	653	29	f̃[modernity	f̃[modernity	NOUN
ejpam-3412	653	30	]	]	PUNCT
ejpam-3412	653	31	,	,	PUNCT
ejpam-3412	653	32	and	and	CCONJ
ejpam-3412	653	33	f̃[enjoyment	f̃[enjoyment	NOUN
ejpam-3412	653	34	]	]	PUNCT
ejpam-3412	653	35	are	be	AUX
ejpam-3412	653	36	fuzzy	fuzzy	ADJ
ejpam-3412	653	37	sets	set	NOUN
ejpam-3412	653	38	in	in	ADP
ejpam-3412	653	39	a	a	DET
ejpam-3412	653	40	defined	define	VERB
ejpam-3412	653	41	as	as	SCONJ
ejpam-3412	653	42	follows	follow	VERB
ejpam-3412	653	43	:	:	PUNCT
ejpam-3412	653	44	f̃	f̃	PROPN
ejpam-3412	653	45	pop	pop	NOUN
ejpam-3412	653	46	rock	rock	PROPN
ejpam-3412	653	47	disco	disco	PROPN
ejpam-3412	653	48	classic	classic	ADJ
ejpam-3412	653	49	sorrow	sorrow	NOUN
ejpam-3412	653	50	0.6	0.6	NUM
ejpam-3412	653	51	0.2	0.2	NUM
ejpam-3412	653	52	0.1	0.1	NUM
ejpam-3412	653	53	0.1	0.1	NUM
ejpam-3412	653	54	modernity	modernity	NOUN
ejpam-3412	653	55	1	1	NUM
ejpam-3412	653	56	0.5	0.5	NUM
ejpam-3412	653	57	0.5	0.5	NUM
ejpam-3412	653	58	0.5	0.5	NUM
ejpam-3412	653	59	enjoyment	enjoyment	NOUN
ejpam-3412	653	60	0.7	0.7	NUM
ejpam-3412	653	61	0.5	0.5	NUM
ejpam-3412	653	62	0.2	0.2	NUM
ejpam-3412	653	63	0.2	0.2	NUM
ejpam-3412	653	64	then	then	ADV
ejpam-3412	653	65	(	(	PUNCT
ejpam-3412	653	66	f̃	f̃	PROPN
ejpam-3412	653	67	,	,	PUNCT
ejpam-3412	653	68	e	e	NOUN
ejpam-3412	653	69	)	)	PUNCT
ejpam-3412	653	70	is	be	AUX
ejpam-3412	653	71	a	a	DET
ejpam-3412	653	72	sorrow	sorrow	ADJ
ejpam-3412	653	73	-	-	PUNCT
ejpam-3412	653	74	fuzzy	fuzzy	ADJ
ejpam-3412	653	75	soft	soft	ADJ
ejpam-3412	653	76	ups	up	NOUN
ejpam-3412	653	77	-	-	PUNCT
ejpam-3412	653	78	filter	filter	NOUN
ejpam-3412	653	79	of	of	ADP
ejpam-3412	653	80	a	a	PRON
ejpam-3412	653	81	but	but	CCONJ
ejpam-3412	653	82	f̃[sorrow	f̃[sorrow	NOUN
ejpam-3412	653	83	]	]	X
ejpam-3412	653	84	is	be	AUX
ejpam-3412	653	85	not	not	PART
ejpam-3412	653	86	a	a	DET
ejpam-3412	653	87	fuzzy	fuzzy	ADJ
ejpam-3412	653	88	ups	up	NOUN
ejpam-3412	653	89	-	-	PUNCT
ejpam-3412	653	90	ideal	ideal	NOUN
ejpam-3412	653	91	of	of	ADP
ejpam-3412	653	92	a.	a.	NOUN
ejpam-3412	653	93	indeed	indeed	ADV
ejpam-3412	653	94	,	,	PUNCT
ejpam-3412	653	95	f	f	PROPN
ejpam-3412	653	96	f̃[sorrow	f̃[sorrow	PROPN
ejpam-3412	653	97	]	]	X
ejpam-3412	653	98	(	(	PUNCT
ejpam-3412	653	99	disco	disco	NOUN
ejpam-3412	653	100	·	·	SYM
ejpam-3412	653	101	classic	classic	ADJ
ejpam-3412	653	102	)	)	PUNCT
ejpam-3412	654	1	=	=	SYM
ejpam-3412	654	2	f	f	X
ejpam-3412	654	3	f̃[sorrow	f̃[sorrow	NOUN
ejpam-3412	654	4	]	]	X
ejpam-3412	654	5	(	(	PUNCT
ejpam-3412	654	6	disco	disco	NOUN
ejpam-3412	654	7	)	)	PUNCT
ejpam-3412	654	8	=	=	SYM
ejpam-3412	654	9	0.1	0.1	NUM
ejpam-3412	654	10	�	�	PROPN
ejpam-3412	654	11	0.2	0.2	NUM
ejpam-3412	654	12	=	=	SYM
ejpam-3412	654	13	min{0.6	min{0.6	PROPN
ejpam-3412	654	14	,	,	PUNCT
ejpam-3412	654	15	0.2	0.2	NUM
ejpam-3412	654	16	}	}	PUNCT
ejpam-3412	654	17	=	=	NOUN
ejpam-3412	654	18	min{f	min{f	ADJ
ejpam-3412	654	19	f̃[sorrow	f̃[sorrow	NOUN
ejpam-3412	654	20	]	]	X
ejpam-3412	654	21	(	(	PUNCT
ejpam-3412	654	22	pop	pop	NOUN
ejpam-3412	654	23	)	)	PUNCT
ejpam-3412	654	24	,	,	PUNCT
ejpam-3412	654	25	f	f	PROPN
ejpam-3412	654	26	f̃[sorrow	f̃[sorrow	PROPN
ejpam-3412	654	27	]	]	X
ejpam-3412	654	28	(	(	PUNCT
ejpam-3412	654	29	rock	rock	NOUN
ejpam-3412	654	30	)	)	PUNCT
ejpam-3412	654	31	}	}	PUNCT
ejpam-3412	654	32	=	=	PUNCT
ejpam-3412	654	33	min{f	min{f	ADJ
ejpam-3412	654	34	f̃[sorrow	f̃[sorrow	NOUN
ejpam-3412	654	35	]	]	X
ejpam-3412	654	36	(	(	PUNCT
ejpam-3412	654	37	disco	disco	NOUN
ejpam-3412	654	38	·	·	PUNCT
ejpam-3412	654	39	(	(	PUNCT
ejpam-3412	654	40	rock	rock	NOUN
ejpam-3412	654	41	·	·	SYM
ejpam-3412	654	42	classic	classic	NOUN
ejpam-3412	654	43	)	)	PUNCT
ejpam-3412	654	44	)	)	PUNCT
ejpam-3412	654	45	,	,	PUNCT
ejpam-3412	654	46	f	f	PROPN
ejpam-3412	654	47	f̃[sorrow	f̃[sorrow	PROPN
ejpam-3412	654	48	]	]	X
ejpam-3412	654	49	(	(	PUNCT
ejpam-3412	654	50	rock	rock	NOUN
ejpam-3412	654	51	)	)	PUNCT
ejpam-3412	654	52	}	}	PUNCT
ejpam-3412	654	53	.	.	PUNCT
ejpam-3412	655	1	hence	hence	ADV
ejpam-3412	655	2	,	,	PUNCT
ejpam-3412	655	3	(	(	PUNCT
ejpam-3412	655	4	f̃	f̃	PROPN
ejpam-3412	655	5	,	,	PUNCT
ejpam-3412	655	6	e	e	NOUN
ejpam-3412	655	7	)	)	PUNCT
ejpam-3412	655	8	is	be	AUX
ejpam-3412	655	9	not	not	PART
ejpam-3412	655	10	a	a	DET
ejpam-3412	655	11	sorrow	sorrow	ADJ
ejpam-3412	655	12	-	-	PUNCT
ejpam-3412	655	13	fuzzy	fuzzy	ADJ
ejpam-3412	655	14	soft	soft	ADJ
ejpam-3412	655	15	ups	up	NOUN
ejpam-3412	655	16	-	-	PUNCT
ejpam-3412	655	17	ideal	ideal	NOUN
ejpam-3412	655	18	of	of	ADP
ejpam-3412	655	19	a.	a.	PROPN
ejpam-3412	655	20	a.	a.	PROPN
ejpam-3412	655	21	satirad	satirad	PROPN
ejpam-3412	655	22	,	,	PUNCT
ejpam-3412	655	23	a.	a.	NOUN
ejpam-3412	655	24	iampan	iampan	PROPN
ejpam-3412	655	25	/	/	SYM
ejpam-3412	655	26	eur	eur	PROPN
ejpam-3412	655	27	.	.	PUNCT
ejpam-3412	656	1	j.	j.	PROPN
ejpam-3412	656	2	pure	pure	PROPN
ejpam-3412	656	3	appl	appl	PROPN
ejpam-3412	656	4	.	.	PROPN
ejpam-3412	656	5	math	math	PROPN
ejpam-3412	656	6	,	,	PUNCT
ejpam-3412	656	7	12	12	NUM
ejpam-3412	656	8	(	(	PUNCT
ejpam-3412	656	9	2	2	NUM
ejpam-3412	656	10	)	)	PUNCT
ejpam-3412	656	11	(	(	PUNCT
ejpam-3412	656	12	2019	2019	NUM
ejpam-3412	656	13	)	)	PUNCT
ejpam-3412	656	14	,	,	PUNCT
ejpam-3412	656	15	294	294	NUM
ejpam-3412	656	16	-	-	SYM
ejpam-3412	656	17	331	331	NUM
ejpam-3412	656	18	324	324	NUM
ejpam-3412	656	19	in	in	ADP
ejpam-3412	656	20	the	the	DET
ejpam-3412	656	21	next	next	ADJ
ejpam-3412	656	22	theorem	theorem	NOUN
ejpam-3412	657	1	,	,	PUNCT
ejpam-3412	657	2	we	we	PRON
ejpam-3412	657	3	give	give	VERB
ejpam-3412	657	4	necessary	necessary	ADJ
ejpam-3412	657	5	condition	condition	NOUN
ejpam-3412	657	6	for	for	ADP
ejpam-3412	657	7	fuzzy	fuzzy	ADJ
ejpam-3412	657	8	soft	soft	ADJ
ejpam-3412	657	9	ups	up	NOUN
ejpam-3412	657	10	-	-	PUNCT
ejpam-3412	657	11	filters	filter	NOUN
ejpam-3412	657	12	as	as	ADP
ejpam-3412	657	13	fuzzy	fuzzy	ADJ
ejpam-3412	657	14	soft	soft	ADJ
ejpam-3412	657	15	ups	up	NOUN
ejpam-3412	657	16	-	-	PUNCT
ejpam-3412	657	17	ideals	ideal	NOUN
ejpam-3412	657	18	of	of	ADP
ejpam-3412	657	19	f	f	PROPN
ejpam-3412	657	20	-up	-up	NOUN
ejpam-3412	657	21	-	-	PUNCT
ejpam-3412	657	22	semigroups	semigroup	NOUN
ejpam-3412	657	23	.	.	PUNCT
ejpam-3412	658	1	theorem	theorem	VERB
ejpam-3412	658	2	57	57	NUM
ejpam-3412	658	3	.	.	PUNCT
ejpam-3412	659	1	if	if	SCONJ
ejpam-3412	659	2	(	(	PUNCT
ejpam-3412	659	3	f̃	f̃	PROPN
ejpam-3412	659	4	,	,	PUNCT
ejpam-3412	659	5	e	e	NOUN
ejpam-3412	659	6	)	)	PUNCT
ejpam-3412	659	7	is	be	AUX
ejpam-3412	659	8	a	a	DET
ejpam-3412	659	9	fuzzy	fuzzy	ADJ
ejpam-3412	659	10	soft	soft	ADJ
ejpam-3412	659	11	ups	up	NOUN
ejpam-3412	659	12	-	-	PUNCT
ejpam-3412	659	13	filter	filter	NOUN
ejpam-3412	659	14	of	of	ADP
ejpam-3412	659	15	a	a	DET
ejpam-3412	659	16	such	such	ADJ
ejpam-3412	659	17	that	that	PRON
ejpam-3412	659	18	for	for	ADP
ejpam-3412	659	19	all	all	DET
ejpam-3412	659	20	e	e	NOUN
ejpam-3412	659	21	∈	∈	PROPN
ejpam-3412	659	22	e	e	NOUN
ejpam-3412	659	23	,	,	PUNCT
ejpam-3412	659	24	a	a	DET
ejpam-3412	659	25	fuzzy	fuzzy	ADJ
ejpam-3412	659	26	set	set	NOUN
ejpam-3412	659	27	f̃[e	f̃[e	NOUN
ejpam-3412	659	28	]	]	X
ejpam-3412	659	29	in	in	ADP
ejpam-3412	659	30	a	a	DET
ejpam-3412	659	31	satisfies	satisfie	NOUN
ejpam-3412	659	32	the	the	DET
ejpam-3412	659	33	condition	condition	NOUN
ejpam-3412	659	34	(	(	PUNCT
ejpam-3412	659	35	2.11	2.11	NUM
ejpam-3412	659	36	)	)	PUNCT
ejpam-3412	659	37	,	,	PUNCT
ejpam-3412	659	38	then	then	ADV
ejpam-3412	659	39	(	(	PUNCT
ejpam-3412	659	40	f̃	f̃	PROPN
ejpam-3412	659	41	,	,	PUNCT
ejpam-3412	659	42	e	e	NOUN
ejpam-3412	659	43	)	)	PUNCT
ejpam-3412	659	44	is	be	AUX
ejpam-3412	659	45	a	a	DET
ejpam-3412	659	46	fuzzy	fuzzy	ADJ
ejpam-3412	659	47	soft	soft	ADJ
ejpam-3412	659	48	ups	up	NOUN
ejpam-3412	659	49	-	-	PUNCT
ejpam-3412	659	50	ideal	ideal	NOUN
ejpam-3412	659	51	of	of	ADP
ejpam-3412	659	52	a.	a.	NOUN
ejpam-3412	659	53	proof	proof	NOUN
ejpam-3412	659	54	.	.	PUNCT
ejpam-3412	660	1	it	it	PRON
ejpam-3412	660	2	is	be	AUX
ejpam-3412	660	3	straightforward	straightforward	ADJ
ejpam-3412	660	4	by	by	ADP
ejpam-3412	660	5	theorem	theorem	NOUN
ejpam-3412	660	6	17	17	NUM
ejpam-3412	660	7	.	.	PUNCT
ejpam-3412	661	1	the	the	DET
ejpam-3412	661	2	proof	proof	NOUN
ejpam-3412	661	3	of	of	ADP
ejpam-3412	661	4	the	the	DET
ejpam-3412	661	5	following	follow	VERB
ejpam-3412	661	6	theorem	theorem	NOUN
ejpam-3412	661	7	can	can	AUX
ejpam-3412	661	8	be	be	AUX
ejpam-3412	661	9	verified	verify	VERB
ejpam-3412	661	10	easily	easily	ADV
ejpam-3412	661	11	.	.	PUNCT
ejpam-3412	662	1	theorem	theorem	VERB
ejpam-3412	662	2	58	58	NUM
ejpam-3412	662	3	.	.	PUNCT
ejpam-3412	663	1	if	if	SCONJ
ejpam-3412	663	2	(	(	PUNCT
ejpam-3412	663	3	f̃	f̃	PROPN
ejpam-3412	663	4	,	,	PUNCT
ejpam-3412	663	5	e	e	NOUN
ejpam-3412	663	6	)	)	PUNCT
ejpam-3412	663	7	is	be	AUX
ejpam-3412	663	8	a	a	DET
ejpam-3412	663	9	fuzzy	fuzzy	ADJ
ejpam-3412	663	10	soft	soft	ADJ
ejpam-3412	663	11	ups	up	NOUN
ejpam-3412	663	12	-	-	PUNCT
ejpam-3412	663	13	ideal	ideal	NOUN
ejpam-3412	663	14	of	of	ADP
ejpam-3412	663	15	a	a	PRON
ejpam-3412	663	16	and	and	CCONJ
ejpam-3412	663	17	∅	∅	NOUN
ejpam-3412	663	18	6=	6=	ADP
ejpam-3412	663	19	e∗	e∗	PROPN
ejpam-3412	663	20	⊆	⊆	NUM
ejpam-3412	663	21	e	e	NOUN
ejpam-3412	663	22	,	,	PUNCT
ejpam-3412	663	23	then	then	ADV
ejpam-3412	663	24	(	(	PUNCT
ejpam-3412	663	25	f̃|e∗	f̃|e∗	PROPN
ejpam-3412	663	26	,	,	PUNCT
ejpam-3412	663	27	e∗	e∗	PROPN
ejpam-3412	663	28	)	)	PUNCT
ejpam-3412	663	29	is	be	AUX
ejpam-3412	663	30	a	a	DET
ejpam-3412	663	31	fuzzy	fuzzy	ADJ
ejpam-3412	663	32	soft	soft	ADJ
ejpam-3412	663	33	ups	up	NOUN
ejpam-3412	663	34	-	-	PUNCT
ejpam-3412	663	35	ideal	ideal	NOUN
ejpam-3412	663	36	of	of	ADP
ejpam-3412	663	37	a.	a.	NOUN
ejpam-3412	663	38	the	the	DET
ejpam-3412	663	39	following	follow	VERB
ejpam-3412	663	40	two	two	NUM
ejpam-3412	663	41	theorems	theorem	NOUN
ejpam-3412	663	42	can	can	AUX
ejpam-3412	663	43	be	be	AUX
ejpam-3412	663	44	deduced	deduce	VERB
ejpam-3412	663	45	in	in	ADP
ejpam-3412	663	46	the	the	DET
ejpam-3412	663	47	same	same	ADJ
ejpam-3412	663	48	way	way	NOUN
ejpam-3412	663	49	as	as	ADP
ejpam-3412	663	50	theorems	theorem	NOUN
ejpam-3412	663	51	22	22	NUM
ejpam-3412	663	52	and	and	CCONJ
ejpam-3412	663	53	23	23	NUM
ejpam-3412	663	54	.	.	PUNCT
ejpam-3412	664	1	theorem	theorem	VERB
ejpam-3412	664	2	59	59	NUM
ejpam-3412	664	3	.	.	PUNCT
ejpam-3412	665	1	the	the	DET
ejpam-3412	665	2	extended	extended	ADJ
ejpam-3412	665	3	intersection	intersection	NOUN
ejpam-3412	665	4	of	of	ADP
ejpam-3412	665	5	two	two	NUM
ejpam-3412	665	6	fuzzy	fuzzy	ADJ
ejpam-3412	665	7	soft	soft	ADJ
ejpam-3412	665	8	ups	up	NOUN
ejpam-3412	665	9	-	-	PUNCT
ejpam-3412	665	10	ideals	ideal	NOUN
ejpam-3412	665	11	of	of	ADP
ejpam-3412	665	12	a	a	PRON
ejpam-3412	665	13	is	be	AUX
ejpam-3412	665	14	also	also	ADV
ejpam-3412	665	15	a	a	DET
ejpam-3412	665	16	fuzzy	fuzzy	ADJ
ejpam-3412	665	17	soft	soft	ADJ
ejpam-3412	665	18	ups	up	NOUN
ejpam-3412	665	19	-	-	PUNCT
ejpam-3412	665	20	ideal	ideal	NOUN
ejpam-3412	665	21	.	.	PUNCT
ejpam-3412	666	1	moreover	moreover	ADV
ejpam-3412	666	2	,	,	PUNCT
ejpam-3412	666	3	the	the	DET
ejpam-3412	666	4	intersection	intersection	NOUN
ejpam-3412	666	5	of	of	ADP
ejpam-3412	666	6	two	two	NUM
ejpam-3412	666	7	fuzzy	fuzzy	ADJ
ejpam-3412	666	8	soft	soft	ADJ
ejpam-3412	666	9	ups	up	NOUN
ejpam-3412	666	10	-	-	PUNCT
ejpam-3412	666	11	ideals	ideal	NOUN
ejpam-3412	666	12	of	of	ADP
ejpam-3412	666	13	a	a	PRON
ejpam-3412	666	14	is	be	AUX
ejpam-3412	666	15	also	also	ADV
ejpam-3412	666	16	a	a	DET
ejpam-3412	666	17	fuzzy	fuzzy	ADJ
ejpam-3412	666	18	soft	soft	ADJ
ejpam-3412	666	19	ups	up	NOUN
ejpam-3412	666	20	-	-	PUNCT
ejpam-3412	666	21	ideal	ideal	NOUN
ejpam-3412	666	22	.	.	PUNCT
ejpam-3412	667	1	theorem	theorem	ADJ
ejpam-3412	667	2	60	60	NUM
ejpam-3412	667	3	.	.	PUNCT
ejpam-3412	668	1	the	the	DET
ejpam-3412	668	2	union	union	NOUN
ejpam-3412	668	3	of	of	ADP
ejpam-3412	668	4	two	two	NUM
ejpam-3412	668	5	fuzzy	fuzzy	ADJ
ejpam-3412	668	6	soft	soft	ADJ
ejpam-3412	668	7	ups	up	NOUN
ejpam-3412	668	8	-	-	PUNCT
ejpam-3412	668	9	ideals	ideal	NOUN
ejpam-3412	668	10	of	of	ADP
ejpam-3412	668	11	a	a	PRON
ejpam-3412	668	12	is	be	AUX
ejpam-3412	668	13	also	also	ADV
ejpam-3412	668	14	a	a	DET
ejpam-3412	668	15	fuzzy	fuzzy	ADJ
ejpam-3412	668	16	soft	soft	ADJ
ejpam-3412	668	17	ups	up	NOUN
ejpam-3412	668	18	-	-	PUNCT
ejpam-3412	668	19	ideal	ideal	NOUN
ejpam-3412	668	20	if	if	SCONJ
ejpam-3412	668	21	sets	set	NOUN
ejpam-3412	668	22	of	of	ADP
ejpam-3412	668	23	statistics	statistic	NOUN
ejpam-3412	668	24	of	of	ADP
ejpam-3412	668	25	two	two	NUM
ejpam-3412	668	26	fuzzy	fuzzy	ADJ
ejpam-3412	668	27	soft	soft	ADJ
ejpam-3412	668	28	ups	up	NOUN
ejpam-3412	668	29	-	-	PUNCT
ejpam-3412	668	30	ideals	ideal	NOUN
ejpam-3412	668	31	are	be	AUX
ejpam-3412	668	32	disjoint	disjoint	ADJ
ejpam-3412	668	33	.	.	PUNCT
ejpam-3412	669	1	the	the	DET
ejpam-3412	669	2	following	follow	VERB
ejpam-3412	669	3	example	example	NOUN
ejpam-3412	669	4	shows	show	VERB
ejpam-3412	669	5	that	that	SCONJ
ejpam-3412	669	6	theorem	theorem	VERB
ejpam-3412	669	7	60	60	NUM
ejpam-3412	669	8	is	be	AUX
ejpam-3412	669	9	not	not	PART
ejpam-3412	669	10	valid	valid	ADJ
ejpam-3412	669	11	if	if	SCONJ
ejpam-3412	669	12	sets	set	NOUN
ejpam-3412	669	13	of	of	ADP
ejpam-3412	669	14	statistics	statistic	NOUN
ejpam-3412	669	15	of	of	ADP
ejpam-3412	669	16	two	two	NUM
ejpam-3412	669	17	fuzzy	fuzzy	ADJ
ejpam-3412	669	18	soft	soft	ADJ
ejpam-3412	669	19	ups	up	NOUN
ejpam-3412	669	20	-	-	PUNCT
ejpam-3412	669	21	ideals	ideal	NOUN
ejpam-3412	669	22	are	be	AUX
ejpam-3412	669	23	not	not	PART
ejpam-3412	669	24	disjoint	disjoint	ADJ
ejpam-3412	669	25	.	.	PUNCT
ejpam-3412	669	26	example	example	NOUN
ejpam-3412	670	1	27	27	NUM
ejpam-3412	670	2	.	.	PUNCT
ejpam-3412	671	1	in	in	ADP
ejpam-3412	671	2	example	example	NOUN
ejpam-3412	671	3	14	14	NUM
ejpam-3412	671	4	,	,	PUNCT
ejpam-3412	671	5	we	we	PRON
ejpam-3412	671	6	have	have	AUX
ejpam-3412	671	7	(	(	PUNCT
ejpam-3412	671	8	g̃1	g̃1	NOUN
ejpam-3412	671	9	,	,	PUNCT
ejpam-3412	671	10	e1	e1	NOUN
ejpam-3412	671	11	)	)	PUNCT
ejpam-3412	671	12	and	and	CCONJ
ejpam-3412	671	13	(	(	PUNCT
ejpam-3412	671	14	g̃2	g̃2	PROPN
ejpam-3412	671	15	,	,	PUNCT
ejpam-3412	671	16	e2	e2	PROPN
ejpam-3412	671	17	)	)	PUNCT
ejpam-3412	671	18	are	be	AUX
ejpam-3412	671	19	two	two	NUM
ejpam-3412	671	20	fuzzy	fuzzy	ADJ
ejpam-3412	671	21	soft	soft	ADJ
ejpam-3412	671	22	ups	up	NOUN
ejpam-3412	671	23	-	-	PUNCT
ejpam-3412	671	24	ideals	ideal	NOUN
ejpam-3412	671	25	of	of	ADP
ejpam-3412	671	26	a.	a.	NOUN
ejpam-3412	671	27	since	since	SCONJ
ejpam-3412	671	28	price	price	NOUN
ejpam-3412	671	29	∈	∈	NOUN
ejpam-3412	671	30	e1	e1	NOUN
ejpam-3412	671	31	∩	∩	ADJ
ejpam-3412	671	32	e2	e2	PROPN
ejpam-3412	671	33	,	,	PUNCT
ejpam-3412	671	34	we	we	PRON
ejpam-3412	671	35	have	have	VERB
ejpam-3412	671	36	(	(	PUNCT
ejpam-3412	671	37	f	f	PROPN
ejpam-3412	671	38	g̃1[price]∪g̃2[price	g̃1[price]∪g̃2[price	X
ejpam-3412	671	39	]	]	X
ejpam-3412	671	40	)	)	PUNCT
ejpam-3412	671	41	(	(	PUNCT
ejpam-3412	671	42	6	6	NUM
ejpam-3412	671	43	∗	∗	NOUN
ejpam-3412	671	44	5	5	NUM
ejpam-3412	671	45	)	)	PUNCT
ejpam-3412	671	46	=	=	PUNCT
ejpam-3412	672	1	(	(	PUNCT
ejpam-3412	672	2	f	f	X
ejpam-3412	672	3	g̃1[price]∪g̃2[price	g̃1[price]∪g̃2[price	X
ejpam-3412	672	4	]	]	X
ejpam-3412	672	5	)	)	PUNCT
ejpam-3412	672	6	(	(	PUNCT
ejpam-3412	672	7	7	7	X
ejpam-3412	672	8	)	)	PUNCT
ejpam-3412	672	9	=	=	SYM
ejpam-3412	672	10	0.7	0.7	NUM
ejpam-3412	672	11	�	�	PROPN
ejpam-3412	672	12	0.8	0.8	NUM
ejpam-3412	672	13	=	=	SYM
ejpam-3412	672	14	min{0.9	min{0.9	PROPN
ejpam-3412	672	15	,	,	PUNCT
ejpam-3412	672	16	0.8	0.8	NUM
ejpam-3412	672	17	}	}	PUNCT
ejpam-3412	672	18	=	=	SYM
ejpam-3412	672	19	min{(f	min{(f	SYM
ejpam-3412	672	20	g̃1[price]∪g̃2[price	g̃1[price]∪g̃2[price	X
ejpam-3412	672	21	]	]	X
ejpam-3412	672	22	)	)	PUNCT
ejpam-3412	672	23	(	(	PUNCT
ejpam-3412	672	24	6	6	NUM
ejpam-3412	672	25	)	)	PUNCT
ejpam-3412	672	26	,	,	PUNCT
ejpam-3412	672	27	(	(	PUNCT
ejpam-3412	672	28	f	f	PROPN
ejpam-3412	672	29	g̃1[price]∪g̃2[price	g̃1[price]∪g̃2[price	X
ejpam-3412	672	30	]	]	X
ejpam-3412	672	31	)	)	PUNCT
ejpam-3412	672	32	(	(	PUNCT
ejpam-3412	672	33	5	5	NUM
ejpam-3412	672	34	)	)	PUNCT
ejpam-3412	672	35	}	}	PUNCT
ejpam-3412	672	36	.	.	PUNCT
ejpam-3412	673	1	thus	thus	ADV
ejpam-3412	673	2	g̃1[price]∪	g̃1[price]∪	NOUN
ejpam-3412	673	3	g̃2[price	g̃2[price	PROPN
ejpam-3412	673	4	]	]	PUNCT
ejpam-3412	673	5	is	be	AUX
ejpam-3412	673	6	not	not	PART
ejpam-3412	673	7	a	a	DET
ejpam-3412	673	8	fuzzy	fuzzy	ADJ
ejpam-3412	673	9	ups	up	NOUN
ejpam-3412	673	10	-	-	PUNCT
ejpam-3412	673	11	ideal	ideal	NOUN
ejpam-3412	673	12	of	of	ADP
ejpam-3412	673	13	a	a	DET
ejpam-3412	673	14	,	,	PUNCT
ejpam-3412	673	15	that	that	ADV
ejpam-3412	673	16	is	is	ADV
ejpam-3412	673	17	,	,	PUNCT
ejpam-3412	673	18	(	(	PUNCT
ejpam-3412	673	19	g̃1	g̃1	NOUN
ejpam-3412	673	20	,	,	PUNCT
ejpam-3412	673	21	e1)∪	e1)∪	PROPN
ejpam-3412	673	22	(	(	PUNCT
ejpam-3412	673	23	g̃2	g̃2	PROPN
ejpam-3412	673	24	,	,	PUNCT
ejpam-3412	673	25	e2	e2	PROPN
ejpam-3412	673	26	)	)	PUNCT
ejpam-3412	673	27	is	be	AUX
ejpam-3412	673	28	not	not	PART
ejpam-3412	673	29	a	a	DET
ejpam-3412	673	30	price	price	NOUN
ejpam-3412	673	31	-	-	PUNCT
ejpam-3412	673	32	fuzzy	fuzzy	ADJ
ejpam-3412	673	33	soft	soft	ADJ
ejpam-3412	673	34	ups	up	NOUN
ejpam-3412	673	35	-	-	PUNCT
ejpam-3412	673	36	ideal	ideal	NOUN
ejpam-3412	673	37	of	of	ADP
ejpam-3412	673	38	a.	a.	NOUN
ejpam-3412	673	39	hence	hence	ADV
ejpam-3412	673	40	,	,	PUNCT
ejpam-3412	673	41	(	(	PUNCT
ejpam-3412	673	42	g̃1	g̃1	NOUN
ejpam-3412	673	43	,	,	PUNCT
ejpam-3412	673	44	e1)∪	e1)∪	PROPN
ejpam-3412	673	45	(	(	PUNCT
ejpam-3412	673	46	g̃2	g̃2	PROPN
ejpam-3412	673	47	,	,	PUNCT
ejpam-3412	673	48	e2	e2	PROPN
ejpam-3412	673	49	)	)	PUNCT
ejpam-3412	673	50	is	be	AUX
ejpam-3412	673	51	not	not	PART
ejpam-3412	673	52	a	a	DET
ejpam-3412	673	53	fuzzy	fuzzy	ADJ
ejpam-3412	673	54	soft	soft	ADJ
ejpam-3412	673	55	ups	up	NOUN
ejpam-3412	673	56	-	-	PUNCT
ejpam-3412	673	57	ideal	ideal	NOUN
ejpam-3412	673	58	of	of	ADP
ejpam-3412	673	59	a.	a.	NOUN
ejpam-3412	673	60	moreover	moreover	ADV
ejpam-3412	673	61	,	,	PUNCT
ejpam-3412	673	62	(	(	PUNCT
ejpam-3412	673	63	g̃1	g̃1	NOUN
ejpam-3412	673	64	,	,	PUNCT
ejpam-3412	673	65	e1	e1	NOUN
ejpam-3412	673	66	)	)	PUNCT
ejpam-3412	673	67	d	d	NOUN
ejpam-3412	673	68	(	(	PUNCT
ejpam-3412	673	69	g̃2	g̃2	PROPN
ejpam-3412	673	70	,	,	PUNCT
ejpam-3412	673	71	e2	e2	PROPN
ejpam-3412	673	72	)	)	PUNCT
ejpam-3412	673	73	is	be	AUX
ejpam-3412	673	74	not	not	PART
ejpam-3412	673	75	a	a	DET
ejpam-3412	673	76	fuzzy	fuzzy	ADJ
ejpam-3412	673	77	soft	soft	ADJ
ejpam-3412	673	78	ups	up	NOUN
ejpam-3412	673	79	-	-	PUNCT
ejpam-3412	673	80	ideal	ideal	NOUN
ejpam-3412	673	81	of	of	ADP
ejpam-3412	673	82	a.	a.	NOUN
ejpam-3412	673	83	3.8	3.8	NUM
ejpam-3412	673	84	.	.	PUNCT
ejpam-3412	674	1	fuzzy	fuzzy	ADJ
ejpam-3412	674	2	soft	soft	ADJ
ejpam-3412	674	3	upi	upi	NOUN
ejpam-3412	674	4	-	-	PUNCT
ejpam-3412	674	5	ideals	ideal	NOUN
ejpam-3412	674	6	definition	definition	NOUN
ejpam-3412	674	7	25	25	NUM
ejpam-3412	674	8	.	.	PUNCT
ejpam-3412	675	1	a	a	DET
ejpam-3412	675	2	fuzzy	fuzzy	ADJ
ejpam-3412	675	3	soft	soft	ADJ
ejpam-3412	675	4	set	set	NOUN
ejpam-3412	675	5	(	(	PUNCT
ejpam-3412	675	6	f̃	f̃	PROPN
ejpam-3412	675	7	,	,	PUNCT
ejpam-3412	675	8	e	e	NOUN
ejpam-3412	675	9	)	)	PUNCT
ejpam-3412	675	10	over	over	ADP
ejpam-3412	675	11	a	a	PRON
ejpam-3412	675	12	is	be	AUX
ejpam-3412	675	13	called	call	VERB
ejpam-3412	675	14	a	a	DET
ejpam-3412	675	15	fuzzy	fuzzy	ADJ
ejpam-3412	675	16	soft	soft	ADJ
ejpam-3412	675	17	upi	upi	NOUN
ejpam-3412	675	18	-	-	PUNCT
ejpam-3412	675	19	ideal	ideal	NOUN
ejpam-3412	675	20	based	base	VERB
ejpam-3412	675	21	on	on	ADP
ejpam-3412	675	22	e	e	PROPN
ejpam-3412	675	23	∈	∈	PROPN
ejpam-3412	675	24	e	e	X
ejpam-3412	675	25	(	(	PUNCT
ejpam-3412	675	26	we	we	PRON
ejpam-3412	675	27	shortly	shortly	ADV
ejpam-3412	675	28	call	call	VERB
ejpam-3412	675	29	an	an	DET
ejpam-3412	675	30	e	e	ADJ
ejpam-3412	675	31	-	-	ADJ
ejpam-3412	675	32	fuzzy	fuzzy	ADJ
ejpam-3412	675	33	soft	soft	ADJ
ejpam-3412	675	34	upi	upi	NOUN
ejpam-3412	675	35	-	-	PUNCT
ejpam-3412	675	36	ideal	ideal	NOUN
ejpam-3412	675	37	)	)	PUNCT
ejpam-3412	675	38	of	of	ADP
ejpam-3412	675	39	a	a	DET
ejpam-3412	675	40	if	if	SCONJ
ejpam-3412	675	41	a	a	DET
ejpam-3412	675	42	fuzzy	fuzzy	ADJ
ejpam-3412	675	43	set	set	NOUN
ejpam-3412	675	44	f̃[e	f̃[e	X
ejpam-3412	675	45	]	]	X
ejpam-3412	675	46	in	in	ADP
ejpam-3412	675	47	a	a	PRON
ejpam-3412	675	48	is	be	AUX
ejpam-3412	675	49	a	a	DET
ejpam-3412	675	50	fuzzy	fuzzy	ADJ
ejpam-3412	675	51	upi	upi	NOUN
ejpam-3412	675	52	-	-	PUNCT
ejpam-3412	675	53	ideal	ideal	NOUN
ejpam-3412	675	54	of	of	ADP
ejpam-3412	675	55	a.	a.	NOUN
ejpam-3412	675	56	if	if	SCONJ
ejpam-3412	675	57	(	(	PUNCT
ejpam-3412	675	58	f̃	f̃	PROPN
ejpam-3412	675	59	,	,	PUNCT
ejpam-3412	675	60	e	e	NOUN
ejpam-3412	675	61	)	)	PUNCT
ejpam-3412	675	62	is	be	AUX
ejpam-3412	675	63	an	an	DET
ejpam-3412	675	64	e	e	ADJ
ejpam-3412	675	65	-	-	ADJ
ejpam-3412	675	66	fuzzy	fuzzy	ADJ
ejpam-3412	675	67	soft	soft	ADJ
ejpam-3412	675	68	upi	upi	NOUN
ejpam-3412	675	69	-	-	PUNCT
ejpam-3412	675	70	ideal	ideal	NOUN
ejpam-3412	675	71	of	of	ADP
ejpam-3412	675	72	a	a	PRON
ejpam-3412	675	73	for	for	ADP
ejpam-3412	675	74	all	all	DET
ejpam-3412	675	75	e	e	NOUN
ejpam-3412	675	76	∈	∈	PROPN
ejpam-3412	675	77	e	e	NOUN
ejpam-3412	675	78	,	,	PUNCT
ejpam-3412	675	79	we	we	PRON
ejpam-3412	675	80	say	say	VERB
ejpam-3412	675	81	that	that	SCONJ
ejpam-3412	675	82	(	(	PUNCT
ejpam-3412	675	83	f̃	f̃	PROPN
ejpam-3412	675	84	,	,	PUNCT
ejpam-3412	675	85	e	e	NOUN
ejpam-3412	675	86	)	)	PUNCT
ejpam-3412	675	87	is	be	AUX
ejpam-3412	675	88	a	a	DET
ejpam-3412	675	89	fuzzy	fuzzy	ADJ
ejpam-3412	675	90	soft	soft	ADJ
ejpam-3412	675	91	upi	upi	NOUN
ejpam-3412	675	92	-	-	PUNCT
ejpam-3412	675	93	ideal	ideal	NOUN
ejpam-3412	675	94	of	of	ADP
ejpam-3412	675	95	a.	a.	NOUN
ejpam-3412	675	96	in	in	ADP
ejpam-3412	675	97	the	the	DET
ejpam-3412	675	98	next	next	ADJ
ejpam-3412	675	99	theorem	theorem	NOUN
ejpam-3412	675	100	and	and	CCONJ
ejpam-3412	675	101	corollary	corollary	ADJ
ejpam-3412	675	102	,	,	PUNCT
ejpam-3412	675	103	we	we	PRON
ejpam-3412	675	104	give	give	VERB
ejpam-3412	675	105	necessary	necessary	ADJ
ejpam-3412	675	106	condition	condition	NOUN
ejpam-3412	675	107	for	for	ADP
ejpam-3412	675	108	fuzzy	fuzzy	ADJ
ejpam-3412	675	109	soft	soft	ADJ
ejpam-3412	675	110	upi	upi	NOUN
ejpam-3412	675	111	-	-	PUNCT
ejpam-3412	675	112	ideals	ideal	NOUN
ejpam-3412	675	113	of	of	ADP
ejpam-3412	675	114	f	f	PROPN
ejpam-3412	675	115	-up	-up	NOUN
ejpam-3412	675	116	-	-	PUNCT
ejpam-3412	675	117	semigroups	semigroup	NOUN
ejpam-3412	675	118	.	.	PUNCT
ejpam-3412	676	1	theorem	theorem	VERB
ejpam-3412	676	2	61	61	NUM
ejpam-3412	676	3	.	.	PUNCT
ejpam-3412	677	1	if	if	SCONJ
ejpam-3412	677	2	(	(	PUNCT
ejpam-3412	677	3	f̃	f̃	PROPN
ejpam-3412	677	4	,	,	PUNCT
ejpam-3412	677	5	e	e	NOUN
ejpam-3412	677	6	)	)	PUNCT
ejpam-3412	677	7	is	be	AUX
ejpam-3412	677	8	a	a	DET
ejpam-3412	677	9	fuzzy	fuzzy	ADJ
ejpam-3412	677	10	soft	soft	ADJ
ejpam-3412	677	11	set	set	NOUN
ejpam-3412	677	12	over	over	ADP
ejpam-3412	677	13	a	a	DET
ejpam-3412	677	14	such	such	ADJ
ejpam-3412	677	15	that	that	PRON
ejpam-3412	677	16	for	for	ADP
ejpam-3412	677	17	all	all	DET
ejpam-3412	677	18	e	e	NOUN
ejpam-3412	677	19	∈	∈	PROPN
ejpam-3412	677	20	e	e	NOUN
ejpam-3412	677	21	,	,	PUNCT
ejpam-3412	677	22	a	a	DET
ejpam-3412	677	23	fuzzy	fuzzy	ADJ
ejpam-3412	677	24	set	set	NOUN
ejpam-3412	677	25	f̃[e	f̃[e	NOUN
ejpam-3412	677	26	]	]	X
ejpam-3412	677	27	in	in	ADP
ejpam-3412	677	28	a	a	DET
ejpam-3412	677	29	satisfies	satisfie	NOUN
ejpam-3412	677	30	the	the	DET
ejpam-3412	677	31	conditions	condition	NOUN
ejpam-3412	677	32	(	(	PUNCT
ejpam-3412	677	33	2.8	2.8	NUM
ejpam-3412	677	34	)	)	PUNCT
ejpam-3412	677	35	and	and	CCONJ
ejpam-3412	677	36	(	(	PUNCT
ejpam-3412	677	37	1.15	1.15	NUM
ejpam-3412	677	38	)	)	PUNCT
ejpam-3412	677	39	,	,	PUNCT
ejpam-3412	677	40	then	then	ADV
ejpam-3412	677	41	(	(	PUNCT
ejpam-3412	677	42	f̃	f̃	PROPN
ejpam-3412	677	43	,	,	PUNCT
ejpam-3412	677	44	e	e	NOUN
ejpam-3412	677	45	)	)	PUNCT
ejpam-3412	677	46	is	be	AUX
ejpam-3412	677	47	a	a	DET
ejpam-3412	677	48	fuzzy	fuzzy	ADJ
ejpam-3412	677	49	soft	soft	ADJ
ejpam-3412	677	50	upi	upi	NOUN
ejpam-3412	677	51	-	-	PUNCT
ejpam-3412	677	52	ideal	ideal	NOUN
ejpam-3412	677	53	of	of	ADP
ejpam-3412	677	54	a.	a.	PROPN
ejpam-3412	677	55	a.	a.	PROPN
ejpam-3412	677	56	satirad	satirad	PROPN
ejpam-3412	677	57	,	,	PUNCT
ejpam-3412	677	58	a.	a.	NOUN
ejpam-3412	677	59	iampan	iampan	PROPN
ejpam-3412	677	60	/	/	SYM
ejpam-3412	677	61	eur	eur	PROPN
ejpam-3412	677	62	.	.	PUNCT
ejpam-3412	678	1	j.	j.	PROPN
ejpam-3412	678	2	pure	pure	PROPN
ejpam-3412	678	3	appl	appl	PROPN
ejpam-3412	678	4	.	.	PROPN
ejpam-3412	678	5	math	math	PROPN
ejpam-3412	678	6	,	,	PUNCT
ejpam-3412	678	7	12	12	NUM
ejpam-3412	678	8	(	(	PUNCT
ejpam-3412	678	9	2	2	NUM
ejpam-3412	678	10	)	)	PUNCT
ejpam-3412	678	11	(	(	PUNCT
ejpam-3412	678	12	2019	2019	NUM
ejpam-3412	678	13	)	)	PUNCT
ejpam-3412	678	14	,	,	PUNCT
ejpam-3412	678	15	294	294	NUM
ejpam-3412	678	16	-	-	SYM
ejpam-3412	678	17	331	331	NUM
ejpam-3412	678	18	325	325	NUM
ejpam-3412	678	19	proof	proof	NOUN
ejpam-3412	678	20	.	.	PUNCT
ejpam-3412	679	1	it	it	PRON
ejpam-3412	679	2	is	be	AUX
ejpam-3412	679	3	straightforward	straightforward	ADJ
ejpam-3412	679	4	by	by	ADP
ejpam-3412	679	5	proposition	proposition	NOUN
ejpam-3412	679	6	7	7	NUM
ejpam-3412	679	7	and	and	CCONJ
ejpam-3412	679	8	lemma	lemma	PROPN
ejpam-3412	679	9	1	1	NUM
ejpam-3412	679	10	(	(	PUNCT
ejpam-3412	679	11	2	2	NUM
ejpam-3412	679	12	)	)	PUNCT
ejpam-3412	679	13	.	.	PUNCT
ejpam-3412	680	1	corollary	corollary	ADJ
ejpam-3412	680	2	4	4	NUM
ejpam-3412	680	3	.	.	PUNCT
ejpam-3412	680	4	let	let	VERB
ejpam-3412	680	5	a	a	DET
ejpam-3412	680	6	be	be	AUX
ejpam-3412	680	7	an	an	DET
ejpam-3412	680	8	f	f	PROPN
ejpam-3412	680	9	-up	-up	NOUN
ejpam-3412	680	10	-	-	PUNCT
ejpam-3412	680	11	semigroup	semigroup	NOUN
ejpam-3412	680	12	satisfying	satisfy	VERB
ejpam-3412	680	13	the	the	DET
ejpam-3412	680	14	condition	condition	NOUN
ejpam-3412	680	15	(	(	PUNCT
ejpam-3412	680	16	2.10	2.10	NUM
ejpam-3412	680	17	)	)	PUNCT
ejpam-3412	680	18	.	.	PUNCT
ejpam-3412	681	1	if	if	SCONJ
ejpam-3412	681	2	(	(	PUNCT
ejpam-3412	681	3	f̃	f̃	PROPN
ejpam-3412	681	4	,	,	PUNCT
ejpam-3412	681	5	e	e	NOUN
ejpam-3412	681	6	)	)	PUNCT
ejpam-3412	681	7	is	be	AUX
ejpam-3412	681	8	a	a	DET
ejpam-3412	681	9	fuzzy	fuzzy	ADJ
ejpam-3412	681	10	soft	soft	ADJ
ejpam-3412	681	11	set	set	NOUN
ejpam-3412	681	12	over	over	ADP
ejpam-3412	681	13	a	a	DET
ejpam-3412	681	14	such	such	ADJ
ejpam-3412	681	15	that	that	PRON
ejpam-3412	681	16	for	for	ADP
ejpam-3412	681	17	all	all	DET
ejpam-3412	681	18	e	e	NOUN
ejpam-3412	681	19	∈	∈	PROPN
ejpam-3412	681	20	e	e	NOUN
ejpam-3412	681	21	,	,	PUNCT
ejpam-3412	681	22	a	a	DET
ejpam-3412	681	23	fuzzy	fuzzy	ADJ
ejpam-3412	681	24	set	set	NOUN
ejpam-3412	681	25	f̃[e	f̃[e	NOUN
ejpam-3412	681	26	]	]	X
ejpam-3412	681	27	in	in	ADP
ejpam-3412	681	28	a	a	DET
ejpam-3412	681	29	satisfies	satisfie	NOUN
ejpam-3412	681	30	the	the	DET
ejpam-3412	681	31	conditions	condition	NOUN
ejpam-3412	681	32	(	(	PUNCT
ejpam-3412	681	33	2.9	2.9	NUM
ejpam-3412	681	34	)	)	PUNCT
ejpam-3412	681	35	and	and	CCONJ
ejpam-3412	681	36	(	(	PUNCT
ejpam-3412	681	37	1.15	1.15	NUM
ejpam-3412	681	38	)	)	PUNCT
ejpam-3412	681	39	,	,	PUNCT
ejpam-3412	681	40	then	then	ADV
ejpam-3412	681	41	(	(	PUNCT
ejpam-3412	681	42	f̃	f̃	PROPN
ejpam-3412	681	43	,	,	PUNCT
ejpam-3412	681	44	e	e	NOUN
ejpam-3412	681	45	)	)	PUNCT
ejpam-3412	681	46	is	be	AUX
ejpam-3412	681	47	a	a	DET
ejpam-3412	681	48	fuzzy	fuzzy	ADJ
ejpam-3412	681	49	soft	soft	ADJ
ejpam-3412	681	50	upi	upi	NOUN
ejpam-3412	681	51	-	-	PUNCT
ejpam-3412	681	52	ideal	ideal	NOUN
ejpam-3412	681	53	of	of	ADP
ejpam-3412	681	54	a.	a.	NOUN
ejpam-3412	681	55	proof	proof	NOUN
ejpam-3412	681	56	.	.	PUNCT
ejpam-3412	682	1	it	it	PRON
ejpam-3412	682	2	is	be	AUX
ejpam-3412	682	3	straightforward	straightforward	ADJ
ejpam-3412	682	4	by	by	ADP
ejpam-3412	682	5	theorems	theorem	NOUN
ejpam-3412	682	6	61	61	NUM
ejpam-3412	682	7	and	and	CCONJ
ejpam-3412	682	8	15	15	NUM
ejpam-3412	682	9	.	.	PUNCT
ejpam-3412	683	1	from	from	ADP
ejpam-3412	683	2	figure	figure	NOUN
ejpam-3412	683	3	1	1	NUM
ejpam-3412	683	4	,	,	PUNCT
ejpam-3412	683	5	we	we	PRON
ejpam-3412	683	6	have	have	VERB
ejpam-3412	683	7	the	the	DET
ejpam-3412	683	8	following	follow	VERB
ejpam-3412	683	9	two	two	NUM
ejpam-3412	683	10	theorems	theorem	NOUN
ejpam-3412	683	11	.	.	PUNCT
ejpam-3412	684	1	theorem	theorem	VERB
ejpam-3412	684	2	62	62	NUM
ejpam-3412	684	3	.	.	PUNCT
ejpam-3412	685	1	every	every	DET
ejpam-3412	685	2	e	e	ADJ
ejpam-3412	685	3	-	-	ADJ
ejpam-3412	685	4	fuzzy	fuzzy	ADJ
ejpam-3412	685	5	soft	soft	ADJ
ejpam-3412	685	6	upi	upi	NOUN
ejpam-3412	685	7	-	-	PUNCT
ejpam-3412	685	8	ideal	ideal	NOUN
ejpam-3412	685	9	of	of	ADP
ejpam-3412	685	10	a	a	PRON
ejpam-3412	685	11	is	be	AUX
ejpam-3412	685	12	an	an	DET
ejpam-3412	685	13	e	e	ADJ
ejpam-3412	685	14	-	-	ADJ
ejpam-3412	685	15	fuzzy	fuzzy	ADJ
ejpam-3412	685	16	soft	soft	ADJ
ejpam-3412	685	17	ups	up	NOUN
ejpam-3412	685	18	-	-	PUNCT
ejpam-3412	685	19	ideal	ideal	NOUN
ejpam-3412	685	20	.	.	PUNCT
ejpam-3412	686	1	moreover	moreover	ADV
ejpam-3412	686	2	,	,	PUNCT
ejpam-3412	686	3	every	every	DET
ejpam-3412	686	4	fuzzy	fuzzy	ADJ
ejpam-3412	686	5	soft	soft	ADJ
ejpam-3412	686	6	upi	upi	NOUN
ejpam-3412	686	7	-	-	PUNCT
ejpam-3412	686	8	ideal	ideal	NOUN
ejpam-3412	686	9	of	of	ADP
ejpam-3412	686	10	a	a	PRON
ejpam-3412	686	11	is	be	AUX
ejpam-3412	686	12	a	a	DET
ejpam-3412	686	13	fuzzy	fuzzy	ADJ
ejpam-3412	686	14	soft	soft	ADJ
ejpam-3412	686	15	ups	up	NOUN
ejpam-3412	686	16	-	-	PUNCT
ejpam-3412	686	17	ideal	ideal	NOUN
ejpam-3412	686	18	.	.	PUNCT
ejpam-3412	687	1	theorem	theorem	VERB
ejpam-3412	687	2	63	63	NUM
ejpam-3412	687	3	.	.	PUNCT
ejpam-3412	688	1	every	every	DET
ejpam-3412	688	2	e	e	ADJ
ejpam-3412	688	3	-	-	ADJ
ejpam-3412	688	4	fuzzy	fuzzy	ADJ
ejpam-3412	688	5	soft	soft	ADJ
ejpam-3412	688	6	upi	upi	NOUN
ejpam-3412	688	7	-	-	PUNCT
ejpam-3412	688	8	ideal	ideal	NOUN
ejpam-3412	688	9	of	of	ADP
ejpam-3412	688	10	a	a	PRON
ejpam-3412	688	11	is	be	AUX
ejpam-3412	688	12	an	an	DET
ejpam-3412	688	13	e	e	ADJ
ejpam-3412	688	14	-	-	ADJ
ejpam-3412	688	15	fuzzy	fuzzy	ADJ
ejpam-3412	688	16	soft	soft	ADJ
ejpam-3412	688	17	upi	upi	NOUN
ejpam-3412	688	18	-	-	PUNCT
ejpam-3412	688	19	filter	filter	NOUN
ejpam-3412	688	20	.	.	PUNCT
ejpam-3412	689	1	moreover	moreover	ADV
ejpam-3412	689	2	,	,	PUNCT
ejpam-3412	689	3	every	every	DET
ejpam-3412	689	4	fuzzy	fuzzy	ADJ
ejpam-3412	689	5	soft	soft	ADJ
ejpam-3412	689	6	upi	upi	NOUN
ejpam-3412	689	7	-	-	PUNCT
ejpam-3412	689	8	ideal	ideal	NOUN
ejpam-3412	689	9	of	of	ADP
ejpam-3412	689	10	a	a	PRON
ejpam-3412	689	11	is	be	AUX
ejpam-3412	689	12	a	a	DET
ejpam-3412	689	13	fuzzy	fuzzy	ADJ
ejpam-3412	689	14	soft	soft	ADJ
ejpam-3412	689	15	upi	upi	NOUN
ejpam-3412	689	16	-	-	PUNCT
ejpam-3412	689	17	filter	filter	NOUN
ejpam-3412	689	18	.	.	PUNCT
ejpam-3412	690	1	the	the	DET
ejpam-3412	690	2	following	follow	VERB
ejpam-3412	690	3	two	two	NUM
ejpam-3412	690	4	examples	example	NOUN
ejpam-3412	690	5	show	show	VERB
ejpam-3412	690	6	that	that	SCONJ
ejpam-3412	690	7	the	the	DET
ejpam-3412	690	8	converse	converse	NOUN
ejpam-3412	690	9	of	of	ADP
ejpam-3412	690	10	theorems	theorem	NOUN
ejpam-3412	690	11	62	62	NUM
ejpam-3412	690	12	and	and	CCONJ
ejpam-3412	690	13	63	63	NUM
ejpam-3412	690	14	is	be	AUX
ejpam-3412	690	15	not	not	PART
ejpam-3412	690	16	true	true	ADJ
ejpam-3412	690	17	.	.	PUNCT
ejpam-3412	691	1	example	example	NOUN
ejpam-3412	692	1	28	28	NUM
ejpam-3412	692	2	.	.	PUNCT
ejpam-3412	693	1	in	in	ADP
ejpam-3412	693	2	example	example	NOUN
ejpam-3412	693	3	13	13	NUM
ejpam-3412	693	4	,	,	PUNCT
ejpam-3412	693	5	we	we	PRON
ejpam-3412	693	6	know	know	VERB
ejpam-3412	693	7	that	that	SCONJ
ejpam-3412	693	8	(	(	PUNCT
ejpam-3412	693	9	f̃	f̃	PROPN
ejpam-3412	693	10	,	,	PUNCT
ejpam-3412	693	11	e	e	NOUN
ejpam-3412	693	12	)	)	PUNCT
ejpam-3412	693	13	is	be	AUX
ejpam-3412	693	14	a	a	DET
ejpam-3412	693	15	price	price	NOUN
ejpam-3412	693	16	-	-	PUNCT
ejpam-3412	693	17	fuzzy	fuzzy	ADJ
ejpam-3412	693	18	soft	soft	ADJ
ejpam-3412	693	19	ups	up	NOUN
ejpam-3412	693	20	-	-	PUNCT
ejpam-3412	693	21	ideal	ideal	NOUN
ejpam-3412	693	22	of	of	ADP
ejpam-3412	693	23	a	a	DET
ejpam-3412	693	24	but	but	CCONJ
ejpam-3412	693	25	f̃[price	f̃[price	NOUN
ejpam-3412	693	26	]	]	PUNCT
ejpam-3412	693	27	is	be	AUX
ejpam-3412	693	28	not	not	PART
ejpam-3412	693	29	a	a	DET
ejpam-3412	693	30	fuzzy	fuzzy	ADJ
ejpam-3412	693	31	upi	upi	NOUN
ejpam-3412	693	32	-	-	PUNCT
ejpam-3412	693	33	ideal	ideal	NOUN
ejpam-3412	693	34	of	of	ADP
ejpam-3412	693	35	a.	a.	NOUN
ejpam-3412	693	36	indeed	indeed	ADV
ejpam-3412	693	37	,	,	PUNCT
ejpam-3412	693	38	f	f	PROPN
ejpam-3412	693	39	f̃[price	f̃[price	PROPN
ejpam-3412	693	40	]	]	X
ejpam-3412	693	41	(	(	PUNCT
ejpam-3412	693	42	5	5	NUM
ejpam-3412	693	43	∗	∗	NOUN
ejpam-3412	693	44	6	6	NUM
ejpam-3412	693	45	)	)	PUNCT
ejpam-3412	693	46	=	=	SYM
ejpam-3412	693	47	f	f	X
ejpam-3412	693	48	f̃[price	f̃[price	PROPN
ejpam-3412	693	49	]	]	X
ejpam-3412	693	50	(	(	PUNCT
ejpam-3412	693	51	7	7	X
ejpam-3412	693	52	)	)	PUNCT
ejpam-3412	693	53	=	=	SYM
ejpam-3412	693	54	0.3	0.3	NUM
ejpam-3412	693	55	�	�	NOUN
ejpam-3412	693	56	0.7	0.7	NUM
ejpam-3412	693	57	=	=	SYM
ejpam-3412	693	58	max{0.1	max{0.1	PROPN
ejpam-3412	693	59	,	,	PUNCT
ejpam-3412	693	60	0.7	0.7	NUM
ejpam-3412	693	61	}	}	PUNCT
ejpam-3412	693	62	=	=	SYM
ejpam-3412	693	63	max{f	max{f	PROPN
ejpam-3412	693	64	f̃[price	f̃[price	PROPN
ejpam-3412	693	65	]	]	PUNCT
ejpam-3412	693	66	(	(	PUNCT
ejpam-3412	693	67	5	5	NUM
ejpam-3412	693	68	)	)	PUNCT
ejpam-3412	693	69	,	,	PUNCT
ejpam-3412	693	70	f	f	PROPN
ejpam-3412	693	71	f̃[price	f̃[price	PROPN
ejpam-3412	693	72	]	]	X
ejpam-3412	693	73	(	(	PUNCT
ejpam-3412	693	74	6	6	NUM
ejpam-3412	693	75	)	)	PUNCT
ejpam-3412	693	76	}	}	PUNCT
ejpam-3412	693	77	.	.	PUNCT
ejpam-3412	694	1	hence	hence	ADV
ejpam-3412	694	2	,	,	PUNCT
ejpam-3412	694	3	(	(	PUNCT
ejpam-3412	694	4	f̃	f̃	PROPN
ejpam-3412	694	5	,	,	PUNCT
ejpam-3412	694	6	e	e	NOUN
ejpam-3412	694	7	)	)	PUNCT
ejpam-3412	694	8	is	be	AUX
ejpam-3412	694	9	not	not	PART
ejpam-3412	694	10	a	a	DET
ejpam-3412	694	11	price	price	NOUN
ejpam-3412	694	12	-	-	PUNCT
ejpam-3412	694	13	fuzzy	fuzzy	ADJ
ejpam-3412	694	14	soft	soft	ADJ
ejpam-3412	694	15	upi	upi	NOUN
ejpam-3412	694	16	-	-	PUNCT
ejpam-3412	694	17	ideal	ideal	NOUN
ejpam-3412	694	18	of	of	ADP
ejpam-3412	694	19	a.	a.	NOUN
ejpam-3412	694	20	example	example	NOUN
ejpam-3412	694	21	29	29	NUM
ejpam-3412	694	22	.	.	PUNCT
ejpam-3412	695	1	in	in	ADP
ejpam-3412	695	2	example	example	NOUN
ejpam-3412	695	3	26	26	NUM
ejpam-3412	695	4	,	,	PUNCT
ejpam-3412	695	5	we	we	PRON
ejpam-3412	695	6	know	know	VERB
ejpam-3412	695	7	that	that	SCONJ
ejpam-3412	695	8	(	(	PUNCT
ejpam-3412	695	9	f̃	f̃	PROPN
ejpam-3412	695	10	,	,	PUNCT
ejpam-3412	695	11	e	e	NOUN
ejpam-3412	695	12	)	)	PUNCT
ejpam-3412	695	13	is	be	AUX
ejpam-3412	695	14	a	a	DET
ejpam-3412	695	15	enjoyment	enjoyment	NOUN
ejpam-3412	695	16	-	-	PUNCT
ejpam-3412	695	17	fuzzy	fuzzy	ADJ
ejpam-3412	695	18	soft	soft	ADJ
ejpam-3412	695	19	upi	upi	NOUN
ejpam-3412	695	20	-	-	PUNCT
ejpam-3412	695	21	filter	filter	NOUN
ejpam-3412	695	22	of	of	ADP
ejpam-3412	695	23	a	a	PRON
ejpam-3412	695	24	but	but	CCONJ
ejpam-3412	695	25	f̃[enjoyment	f̃[enjoyment	NOUN
ejpam-3412	695	26	]	]	PUNCT
ejpam-3412	695	27	is	be	AUX
ejpam-3412	695	28	not	not	PART
ejpam-3412	695	29	a	a	DET
ejpam-3412	695	30	fuzzy	fuzzy	ADJ
ejpam-3412	695	31	upi	upi	NOUN
ejpam-3412	695	32	-	-	PUNCT
ejpam-3412	695	33	ideal	ideal	NOUN
ejpam-3412	695	34	of	of	ADP
ejpam-3412	695	35	a.	a.	NOUN
ejpam-3412	695	36	indeed	indeed	ADV
ejpam-3412	695	37	,	,	PUNCT
ejpam-3412	695	38	f	f	PROPN
ejpam-3412	695	39	f̃[enjoyment	f̃[enjoyment	PROPN
ejpam-3412	695	40	]	]	X
ejpam-3412	695	41	(	(	PUNCT
ejpam-3412	695	42	disco	disco	NOUN
ejpam-3412	695	43	·	·	SYM
ejpam-3412	695	44	classic	classic	ADJ
ejpam-3412	695	45	)	)	PUNCT
ejpam-3412	696	1	=	=	SYM
ejpam-3412	696	2	f	f	X
ejpam-3412	697	1	f̃[enjoyment	f̃[enjoyment	PROPN
ejpam-3412	697	2	]	]	X
ejpam-3412	697	3	(	(	PUNCT
ejpam-3412	697	4	disco	disco	NOUN
ejpam-3412	697	5	)	)	PUNCT
ejpam-3412	697	6	=	=	SYM
ejpam-3412	697	7	0.2	0.2	NUM
ejpam-3412	697	8	�	�	PROPN
ejpam-3412	697	9	0.5	0.5	NUM
ejpam-3412	697	10	=	=	SYM
ejpam-3412	697	11	min{0.7	min{0.7	PROPN
ejpam-3412	697	12	,	,	PUNCT
ejpam-3412	697	13	0.5	0.5	NUM
ejpam-3412	697	14	}	}	PUNCT
ejpam-3412	697	15	=	=	SYM
ejpam-3412	697	16	min{f	min{f	ADJ
ejpam-3412	697	17	f̃[enjoyment	f̃[enjoyment	NOUN
ejpam-3412	697	18	]	]	X
ejpam-3412	697	19	(	(	PUNCT
ejpam-3412	697	20	pop	pop	NOUN
ejpam-3412	697	21	)	)	PUNCT
ejpam-3412	697	22	,	,	PUNCT
ejpam-3412	697	23	f	f	PROPN
ejpam-3412	697	24	f̃[enjoyment	f̃[enjoyment	PROPN
ejpam-3412	697	25	]	]	X
ejpam-3412	697	26	(	(	PUNCT
ejpam-3412	697	27	rock	rock	NOUN
ejpam-3412	697	28	)	)	PUNCT
ejpam-3412	697	29	}	}	PUNCT
ejpam-3412	697	30	=	=	SYM
ejpam-3412	697	31	min{f	min{f	ADJ
ejpam-3412	697	32	f̃[enjoyment	f̃[enjoyment	NOUN
ejpam-3412	697	33	]	]	X
ejpam-3412	697	34	(	(	PUNCT
ejpam-3412	697	35	disco	disco	NOUN
ejpam-3412	697	36	·	·	PUNCT
ejpam-3412	697	37	(	(	PUNCT
ejpam-3412	697	38	rock	rock	NOUN
ejpam-3412	697	39	·	·	SYM
ejpam-3412	697	40	classic	classic	NOUN
ejpam-3412	697	41	)	)	PUNCT
ejpam-3412	697	42	)	)	PUNCT
ejpam-3412	697	43	,	,	PUNCT
ejpam-3412	697	44	f	f	PROPN
ejpam-3412	697	45	f̃[enjoyment	f̃[enjoyment	PROPN
ejpam-3412	697	46	]	]	X
ejpam-3412	697	47	(	(	PUNCT
ejpam-3412	697	48	rock	rock	NOUN
ejpam-3412	697	49	)	)	PUNCT
ejpam-3412	697	50	}	}	PUNCT
ejpam-3412	697	51	.	.	PUNCT
ejpam-3412	698	1	hence	hence	ADV
ejpam-3412	698	2	,	,	PUNCT
ejpam-3412	698	3	(	(	PUNCT
ejpam-3412	698	4	f̃	f̃	PROPN
ejpam-3412	698	5	,	,	PUNCT
ejpam-3412	698	6	e	e	NOUN
ejpam-3412	698	7	)	)	PUNCT
ejpam-3412	698	8	is	be	AUX
ejpam-3412	698	9	not	not	PART
ejpam-3412	698	10	a	a	DET
ejpam-3412	698	11	enjoyment	enjoyment	NOUN
ejpam-3412	698	12	-	-	PUNCT
ejpam-3412	698	13	fuzzy	fuzzy	ADJ
ejpam-3412	698	14	soft	soft	ADJ
ejpam-3412	698	15	upi	upi	NOUN
ejpam-3412	698	16	-	-	PUNCT
ejpam-3412	698	17	ideal	ideal	NOUN
ejpam-3412	698	18	of	of	ADP
ejpam-3412	698	19	a.	a.	NOUN
ejpam-3412	698	20	in	in	ADP
ejpam-3412	698	21	the	the	DET
ejpam-3412	698	22	next	next	ADJ
ejpam-3412	698	23	theorem	theorem	NOUN
ejpam-3412	698	24	,	,	PUNCT
ejpam-3412	698	25	we	we	PRON
ejpam-3412	698	26	give	give	VERB
ejpam-3412	698	27	necessary	necessary	ADJ
ejpam-3412	698	28	condition	condition	NOUN
ejpam-3412	698	29	for	for	ADP
ejpam-3412	698	30	fuzzy	fuzzy	ADJ
ejpam-3412	698	31	soft	soft	ADJ
ejpam-3412	698	32	upi	upi	NOUN
ejpam-3412	698	33	-	-	PUNCT
ejpam-3412	698	34	filters	filter	NOUN
ejpam-3412	698	35	as	as	ADP
ejpam-3412	698	36	fuzzy	fuzzy	ADJ
ejpam-3412	698	37	soft	soft	ADJ
ejpam-3412	698	38	upi	upi	NOUN
ejpam-3412	698	39	-	-	PUNCT
ejpam-3412	698	40	ideals	ideal	NOUN
ejpam-3412	698	41	of	of	ADP
ejpam-3412	698	42	f	f	PROPN
ejpam-3412	698	43	-up	-up	NOUN
ejpam-3412	698	44	-	-	PUNCT
ejpam-3412	698	45	semigroups	semigroup	NOUN
ejpam-3412	698	46	.	.	PUNCT
ejpam-3412	699	1	theorem	theorem	VERB
ejpam-3412	699	2	64	64	NUM
ejpam-3412	699	3	.	.	PUNCT
ejpam-3412	700	1	if	if	SCONJ
ejpam-3412	700	2	(	(	PUNCT
ejpam-3412	700	3	f̃	f̃	PROPN
ejpam-3412	700	4	,	,	PUNCT
ejpam-3412	700	5	e	e	NOUN
ejpam-3412	700	6	)	)	PUNCT
ejpam-3412	700	7	is	be	AUX
ejpam-3412	700	8	a	a	DET
ejpam-3412	700	9	fuzzy	fuzzy	ADJ
ejpam-3412	700	10	soft	soft	ADJ
ejpam-3412	700	11	upi	upi	NOUN
ejpam-3412	700	12	-	-	PUNCT
ejpam-3412	700	13	filter	filter	NOUN
ejpam-3412	700	14	of	of	ADP
ejpam-3412	700	15	a	a	DET
ejpam-3412	700	16	such	such	ADJ
ejpam-3412	700	17	that	that	PRON
ejpam-3412	700	18	for	for	ADP
ejpam-3412	700	19	all	all	DET
ejpam-3412	700	20	e	e	NOUN
ejpam-3412	700	21	∈	∈	PROPN
ejpam-3412	700	22	e	e	NOUN
ejpam-3412	700	23	,	,	PUNCT
ejpam-3412	700	24	a	a	DET
ejpam-3412	700	25	fuzzy	fuzzy	ADJ
ejpam-3412	700	26	set	set	NOUN
ejpam-3412	700	27	f̃[e	f̃[e	NOUN
ejpam-3412	700	28	]	]	X
ejpam-3412	700	29	in	in	ADP
ejpam-3412	700	30	a	a	DET
ejpam-3412	700	31	satisfies	satisfie	NOUN
ejpam-3412	700	32	the	the	DET
ejpam-3412	700	33	condition	condition	NOUN
ejpam-3412	700	34	(	(	PUNCT
ejpam-3412	700	35	2.11	2.11	NUM
ejpam-3412	700	36	)	)	PUNCT
ejpam-3412	700	37	,	,	PUNCT
ejpam-3412	700	38	then	then	ADV
ejpam-3412	700	39	(	(	PUNCT
ejpam-3412	700	40	f̃	f̃	PROPN
ejpam-3412	700	41	,	,	PUNCT
ejpam-3412	700	42	e	e	NOUN
ejpam-3412	700	43	)	)	PUNCT
ejpam-3412	700	44	is	be	AUX
ejpam-3412	700	45	a	a	DET
ejpam-3412	700	46	fuzzy	fuzzy	ADJ
ejpam-3412	700	47	soft	soft	ADJ
ejpam-3412	700	48	upi	upi	NOUN
ejpam-3412	700	49	-	-	PUNCT
ejpam-3412	700	50	ideal	ideal	NOUN
ejpam-3412	700	51	of	of	ADP
ejpam-3412	700	52	a.	a.	NOUN
ejpam-3412	700	53	proof	proof	NOUN
ejpam-3412	700	54	.	.	PUNCT
ejpam-3412	701	1	it	it	PRON
ejpam-3412	701	2	is	be	AUX
ejpam-3412	701	3	straightforward	straightforward	ADJ
ejpam-3412	701	4	by	by	ADP
ejpam-3412	701	5	theorem	theorem	NOUN
ejpam-3412	701	6	17	17	NUM
ejpam-3412	701	7	.	.	PUNCT
ejpam-3412	702	1	the	the	DET
ejpam-3412	702	2	proof	proof	NOUN
ejpam-3412	702	3	of	of	ADP
ejpam-3412	702	4	the	the	DET
ejpam-3412	702	5	following	follow	VERB
ejpam-3412	702	6	theorem	theorem	NOUN
ejpam-3412	702	7	can	can	AUX
ejpam-3412	702	8	be	be	AUX
ejpam-3412	702	9	verified	verify	VERB
ejpam-3412	702	10	easily	easily	ADV
ejpam-3412	702	11	.	.	PUNCT
ejpam-3412	703	1	theorem	theorem	VERB
ejpam-3412	703	2	65	65	NUM
ejpam-3412	703	3	.	.	PUNCT
ejpam-3412	704	1	if	if	SCONJ
ejpam-3412	704	2	(	(	PUNCT
ejpam-3412	704	3	f̃	f̃	PROPN
ejpam-3412	704	4	,	,	PUNCT
ejpam-3412	704	5	e	e	NOUN
ejpam-3412	704	6	)	)	PUNCT
ejpam-3412	704	7	is	be	AUX
ejpam-3412	704	8	a	a	DET
ejpam-3412	704	9	fuzzy	fuzzy	ADJ
ejpam-3412	704	10	soft	soft	ADJ
ejpam-3412	704	11	upi	upi	NOUN
ejpam-3412	704	12	-	-	PUNCT
ejpam-3412	704	13	ideal	ideal	NOUN
ejpam-3412	704	14	of	of	ADP
ejpam-3412	704	15	a	a	PRON
ejpam-3412	704	16	and	and	CCONJ
ejpam-3412	704	17	∅	∅	NOUN
ejpam-3412	704	18	6=	6=	ADP
ejpam-3412	704	19	e∗	e∗	PROPN
ejpam-3412	704	20	⊆	⊆	NUM
ejpam-3412	704	21	e	e	NOUN
ejpam-3412	704	22	,	,	PUNCT
ejpam-3412	704	23	then	then	ADV
ejpam-3412	704	24	(	(	PUNCT
ejpam-3412	704	25	f̃|e∗	f̃|e∗	PROPN
ejpam-3412	704	26	,	,	PUNCT
ejpam-3412	704	27	e∗	e∗	PROPN
ejpam-3412	704	28	)	)	PUNCT
ejpam-3412	704	29	is	be	AUX
ejpam-3412	704	30	a	a	DET
ejpam-3412	704	31	fuzzy	fuzzy	ADJ
ejpam-3412	704	32	soft	soft	ADJ
ejpam-3412	704	33	upi	upi	NOUN
ejpam-3412	704	34	-	-	PUNCT
ejpam-3412	704	35	ideal	ideal	NOUN
ejpam-3412	704	36	of	of	ADP
ejpam-3412	704	37	a.	a.	NOUN
ejpam-3412	704	38	the	the	DET
ejpam-3412	704	39	following	follow	VERB
ejpam-3412	704	40	two	two	NUM
ejpam-3412	704	41	theorems	theorem	NOUN
ejpam-3412	704	42	can	can	AUX
ejpam-3412	704	43	be	be	AUX
ejpam-3412	704	44	deduced	deduce	VERB
ejpam-3412	704	45	in	in	ADP
ejpam-3412	704	46	the	the	DET
ejpam-3412	704	47	same	same	ADJ
ejpam-3412	704	48	way	way	NOUN
ejpam-3412	704	49	as	as	ADP
ejpam-3412	704	50	theorems	theorem	NOUN
ejpam-3412	704	51	22	22	NUM
ejpam-3412	704	52	and	and	CCONJ
ejpam-3412	704	53	23	23	NUM
ejpam-3412	704	54	.	.	PUNCT
ejpam-3412	705	1	a.	a.	PROPN
ejpam-3412	705	2	satirad	satirad	PROPN
ejpam-3412	705	3	,	,	PUNCT
ejpam-3412	705	4	a.	a.	NOUN
ejpam-3412	705	5	iampan	iampan	PROPN
ejpam-3412	705	6	/	/	SYM
ejpam-3412	705	7	eur	eur	PROPN
ejpam-3412	705	8	.	.	PUNCT
ejpam-3412	706	1	j.	j.	PROPN
ejpam-3412	706	2	pure	pure	PROPN
ejpam-3412	706	3	appl	appl	PROPN
ejpam-3412	706	4	.	.	PROPN
ejpam-3412	706	5	math	math	PROPN
ejpam-3412	706	6	,	,	PUNCT
ejpam-3412	706	7	12	12	NUM
ejpam-3412	706	8	(	(	PUNCT
ejpam-3412	706	9	2	2	NUM
ejpam-3412	706	10	)	)	PUNCT
ejpam-3412	706	11	(	(	PUNCT
ejpam-3412	706	12	2019	2019	NUM
ejpam-3412	706	13	)	)	PUNCT
ejpam-3412	706	14	,	,	PUNCT
ejpam-3412	706	15	294	294	NUM
ejpam-3412	706	16	-	-	SYM
ejpam-3412	706	17	331	331	NUM
ejpam-3412	706	18	326	326	NUM
ejpam-3412	706	19	theorem	theorem	VERB
ejpam-3412	706	20	66	66	NUM
ejpam-3412	706	21	.	.	PUNCT
ejpam-3412	707	1	the	the	DET
ejpam-3412	707	2	extended	extended	ADJ
ejpam-3412	707	3	intersection	intersection	NOUN
ejpam-3412	707	4	of	of	ADP
ejpam-3412	707	5	two	two	NUM
ejpam-3412	707	6	fuzzy	fuzzy	ADJ
ejpam-3412	707	7	soft	soft	ADJ
ejpam-3412	707	8	upi	upi	NOUN
ejpam-3412	707	9	-	-	PUNCT
ejpam-3412	707	10	ideals	ideal	NOUN
ejpam-3412	707	11	of	of	ADP
ejpam-3412	707	12	a	a	PRON
ejpam-3412	707	13	is	be	AUX
ejpam-3412	707	14	also	also	ADV
ejpam-3412	707	15	a	a	DET
ejpam-3412	707	16	fuzzy	fuzzy	ADJ
ejpam-3412	707	17	soft	soft	ADJ
ejpam-3412	707	18	upi	upi	NOUN
ejpam-3412	707	19	-	-	PUNCT
ejpam-3412	707	20	ideal	ideal	NOUN
ejpam-3412	707	21	.	.	PUNCT
ejpam-3412	708	1	moreover	moreover	ADV
ejpam-3412	708	2	,	,	PUNCT
ejpam-3412	708	3	the	the	DET
ejpam-3412	708	4	intersection	intersection	NOUN
ejpam-3412	708	5	of	of	ADP
ejpam-3412	708	6	two	two	NUM
ejpam-3412	708	7	fuzzy	fuzzy	ADJ
ejpam-3412	708	8	soft	soft	ADJ
ejpam-3412	708	9	upi	upi	NOUN
ejpam-3412	708	10	-	-	PUNCT
ejpam-3412	708	11	ideals	ideal	NOUN
ejpam-3412	708	12	of	of	ADP
ejpam-3412	708	13	a	a	PRON
ejpam-3412	708	14	is	be	AUX
ejpam-3412	708	15	also	also	ADV
ejpam-3412	708	16	a	a	DET
ejpam-3412	708	17	fuzzy	fuzzy	ADJ
ejpam-3412	708	18	soft	soft	ADJ
ejpam-3412	708	19	upi	upi	NOUN
ejpam-3412	708	20	-	-	PUNCT
ejpam-3412	708	21	ideal	ideal	NOUN
ejpam-3412	708	22	.	.	PUNCT
ejpam-3412	709	1	theorem	theorem	VERB
ejpam-3412	709	2	67	67	NUM
ejpam-3412	709	3	.	.	PUNCT
ejpam-3412	710	1	the	the	DET
ejpam-3412	710	2	union	union	NOUN
ejpam-3412	710	3	of	of	ADP
ejpam-3412	710	4	two	two	NUM
ejpam-3412	710	5	fuzzy	fuzzy	ADJ
ejpam-3412	710	6	soft	soft	ADJ
ejpam-3412	710	7	upi	upi	NOUN
ejpam-3412	710	8	-	-	PUNCT
ejpam-3412	710	9	ideals	ideal	NOUN
ejpam-3412	710	10	of	of	ADP
ejpam-3412	710	11	a	a	PRON
ejpam-3412	710	12	is	be	AUX
ejpam-3412	710	13	also	also	ADV
ejpam-3412	710	14	a	a	DET
ejpam-3412	710	15	fuzzy	fuzzy	ADJ
ejpam-3412	710	16	soft	soft	ADJ
ejpam-3412	710	17	upi	upi	NOUN
ejpam-3412	710	18	-	-	PUNCT
ejpam-3412	710	19	ideal	ideal	NOUN
ejpam-3412	710	20	if	if	SCONJ
ejpam-3412	710	21	sets	set	NOUN
ejpam-3412	710	22	of	of	ADP
ejpam-3412	710	23	statistics	statistic	NOUN
ejpam-3412	710	24	of	of	ADP
ejpam-3412	710	25	two	two	NUM
ejpam-3412	710	26	fuzzy	fuzzy	ADJ
ejpam-3412	710	27	soft	soft	ADJ
ejpam-3412	710	28	upi	upi	NOUN
ejpam-3412	710	29	-	-	PUNCT
ejpam-3412	710	30	ideals	ideal	NOUN
ejpam-3412	710	31	are	be	AUX
ejpam-3412	710	32	disjoint	disjoint	ADJ
ejpam-3412	710	33	.	.	PUNCT
ejpam-3412	711	1	the	the	DET
ejpam-3412	711	2	following	follow	VERB
ejpam-3412	711	3	example	example	NOUN
ejpam-3412	711	4	shows	show	VERB
ejpam-3412	711	5	that	that	SCONJ
ejpam-3412	711	6	the	the	DET
ejpam-3412	711	7	converse	converse	NOUN
ejpam-3412	711	8	of	of	ADP
ejpam-3412	711	9	theorem	theorem	NOUN
ejpam-3412	711	10	67	67	NUM
ejpam-3412	711	11	is	be	AUX
ejpam-3412	711	12	not	not	PART
ejpam-3412	711	13	true	true	ADJ
ejpam-3412	711	14	.	.	PUNCT
ejpam-3412	712	1	example	example	NOUN
ejpam-3412	712	2	30	30	NUM
ejpam-3412	712	3	.	.	PUNCT
ejpam-3412	713	1	in	in	ADP
ejpam-3412	713	2	example	example	NOUN
ejpam-3412	713	3	25	25	NUM
ejpam-3412	713	4	,	,	PUNCT
ejpam-3412	713	5	we	we	PRON
ejpam-3412	713	6	have	have	AUX
ejpam-3412	713	7	(	(	PUNCT
ejpam-3412	713	8	g̃1	g̃1	NOUN
ejpam-3412	713	9	,	,	PUNCT
ejpam-3412	713	10	e1	e1	NOUN
ejpam-3412	713	11	)	)	PUNCT
ejpam-3412	713	12	and	and	CCONJ
ejpam-3412	713	13	(	(	PUNCT
ejpam-3412	713	14	g̃2	g̃2	PROPN
ejpam-3412	713	15	,	,	PUNCT
ejpam-3412	713	16	e2	e2	PROPN
ejpam-3412	713	17	)	)	PUNCT
ejpam-3412	713	18	are	be	AUX
ejpam-3412	713	19	two	two	NUM
ejpam-3412	713	20	fuzzy	fuzzy	ADJ
ejpam-3412	713	21	soft	soft	ADJ
ejpam-3412	713	22	upi	upi	NOUN
ejpam-3412	713	23	-	-	PUNCT
ejpam-3412	713	24	ideals	ideal	NOUN
ejpam-3412	713	25	of	of	ADP
ejpam-3412	713	26	a.	a.	NOUN
ejpam-3412	713	27	since	since	SCONJ
ejpam-3412	713	28	endurance	endurance	NOUN
ejpam-3412	713	29	∈	∈	PROPN
ejpam-3412	713	30	e1	e1	PROPN
ejpam-3412	713	31	∩	∩	PROPN
ejpam-3412	713	32	e2	e2	PROPN
ejpam-3412	713	33	,	,	PUNCT
ejpam-3412	713	34	we	we	PRON
ejpam-3412	713	35	have	have	VERB
ejpam-3412	713	36	(	(	PUNCT
ejpam-3412	713	37	f	f	PROPN
ejpam-3412	713	38	g̃1[endurance]∪g̃2[endurance	g̃1[endurance]∪g̃2[endurance	PROPN
ejpam-3412	713	39	]	]	X
ejpam-3412	713	40	)	)	PUNCT
ejpam-3412	713	41	(	(	PUNCT
ejpam-3412	713	42	black	black	ADJ
ejpam-3412	713	43	·	·	SYM
ejpam-3412	713	44	green	green	NOUN
ejpam-3412	713	45	)	)	PUNCT
ejpam-3412	713	46	=	=	PUNCT
ejpam-3412	714	1	(	(	PUNCT
ejpam-3412	714	2	f	f	PROPN
ejpam-3412	714	3	g̃1[endurance]∪g̃2[endurance	g̃1[endurance]∪g̃2[endurance	PROPN
ejpam-3412	714	4	]	]	X
ejpam-3412	714	5	)	)	PUNCT
ejpam-3412	714	6	(	(	PUNCT
ejpam-3412	714	7	green	green	ADJ
ejpam-3412	714	8	)	)	PUNCT
ejpam-3412	714	9	=	=	SYM
ejpam-3412	714	10	0.5	0.5	NUM
ejpam-3412	714	11	�	�	PROPN
ejpam-3412	714	12	0.6	0.6	NUM
ejpam-3412	714	13	=	=	SYM
ejpam-3412	714	14	min{0.6	min{0.6	PROPN
ejpam-3412	714	15	,	,	PUNCT
ejpam-3412	714	16	0.7	0.7	NUM
ejpam-3412	714	17	}	}	PUNCT
ejpam-3412	714	18	=	=	SYM
ejpam-3412	714	19	min{(f	min{(f	NOUN
ejpam-3412	714	20	g̃1[endurance]∪g̃2[endurance	g̃1[endurance]∪g̃2[endurance	NOUN
ejpam-3412	714	21	]	]	PUNCT
ejpam-3412	714	22	)	)	PUNCT
ejpam-3412	714	23	(	(	PUNCT
ejpam-3412	714	24	cyan	cyan	NOUN
ejpam-3412	714	25	)	)	PUNCT
ejpam-3412	714	26	,	,	PUNCT
ejpam-3412	714	27	(	(	PUNCT
ejpam-3412	714	28	f	f	PROPN
ejpam-3412	714	29	g̃1[endurance]∪g̃2[endurance	g̃1[endurance]∪g̃2[endurance	PROPN
ejpam-3412	714	30	]	]	X
ejpam-3412	714	31	)	)	PUNCT
ejpam-3412	714	32	(	(	PUNCT
ejpam-3412	714	33	blue	blue	ADJ
ejpam-3412	714	34	)	)	PUNCT
ejpam-3412	714	35	}	}	PUNCT
ejpam-3412	714	36	=	=	SYM
ejpam-3412	714	37	min{(f	min{(f	NOUN
ejpam-3412	714	38	g̃1[endurance]∪g̃2[endurance	g̃1[endurance]∪g̃2[endurance	NOUN
ejpam-3412	714	39	]	]	PUNCT
ejpam-3412	714	40	)	)	PUNCT
ejpam-3412	714	41	(	(	PUNCT
ejpam-3412	714	42	black	black	NOUN
ejpam-3412	714	43	·	·	PUNCT
ejpam-3412	714	44	(	(	PUNCT
ejpam-3412	714	45	blue	blue	ADJ
ejpam-3412	714	46	·	·	SYM
ejpam-3412	714	47	green	green	ADJ
ejpam-3412	714	48	)	)	PUNCT
ejpam-3412	714	49	)	)	PUNCT
ejpam-3412	714	50	,	,	PUNCT
ejpam-3412	714	51	(	(	PUNCT
ejpam-3412	714	52	f	f	PROPN
ejpam-3412	714	53	g̃1[endurance]∪g̃2[endurance	g̃1[endurance]∪g̃2[endurance	PROPN
ejpam-3412	714	54	]	]	X
ejpam-3412	714	55	)	)	PUNCT
ejpam-3412	714	56	(	(	PUNCT
ejpam-3412	714	57	blue	blue	ADJ
ejpam-3412	714	58	)	)	PUNCT
ejpam-3412	714	59	}	}	PUNCT
ejpam-3412	714	60	.	.	PUNCT
ejpam-3412	715	1	thus	thus	ADV
ejpam-3412	715	2	g̃1[endurance	g̃1[endurance	NOUN
ejpam-3412	715	3	]	]	PUNCT
ejpam-3412	715	4	∪	∪	ADP
ejpam-3412	715	5	g̃2[endurance	g̃2[endurance	PROPN
ejpam-3412	715	6	]	]	PUNCT
ejpam-3412	715	7	is	be	AUX
ejpam-3412	715	8	not	not	PART
ejpam-3412	715	9	a	a	DET
ejpam-3412	715	10	fuzzy	fuzzy	ADJ
ejpam-3412	715	11	upi	upi	NOUN
ejpam-3412	715	12	-	-	PUNCT
ejpam-3412	715	13	ideal	ideal	NOUN
ejpam-3412	715	14	of	of	ADP
ejpam-3412	715	15	a	a	PRON
ejpam-3412	715	16	,	,	PUNCT
ejpam-3412	715	17	that	that	ADV
ejpam-3412	715	18	is	is	ADV
ejpam-3412	715	19	,	,	PUNCT
ejpam-3412	715	20	(	(	PUNCT
ejpam-3412	715	21	g̃1	g̃1	NOUN
ejpam-3412	715	22	,	,	PUNCT
ejpam-3412	715	23	e1	e1	NOUN
ejpam-3412	715	24	)	)	PUNCT
ejpam-3412	715	25	∪	∪	NOUN
ejpam-3412	715	26	(	(	PUNCT
ejpam-3412	715	27	g̃2	g̃2	PROPN
ejpam-3412	715	28	,	,	PUNCT
ejpam-3412	715	29	e2	e2	PROPN
ejpam-3412	715	30	)	)	PUNCT
ejpam-3412	715	31	is	be	AUX
ejpam-3412	715	32	not	not	PART
ejpam-3412	715	33	a	a	DET
ejpam-3412	715	34	endurance	endurance	NOUN
ejpam-3412	715	35	-	-	PUNCT
ejpam-3412	715	36	fuzzy	fuzzy	ADJ
ejpam-3412	715	37	soft	soft	ADJ
ejpam-3412	715	38	upi	upi	NOUN
ejpam-3412	715	39	-	-	PUNCT
ejpam-3412	715	40	ideal	ideal	NOUN
ejpam-3412	715	41	of	of	ADP
ejpam-3412	715	42	a.	a.	NOUN
ejpam-3412	715	43	hence	hence	ADV
ejpam-3412	715	44	,	,	PUNCT
ejpam-3412	715	45	(	(	PUNCT
ejpam-3412	715	46	g̃1	g̃1	NOUN
ejpam-3412	715	47	,	,	PUNCT
ejpam-3412	715	48	e1	e1	NOUN
ejpam-3412	715	49	)	)	PUNCT
ejpam-3412	715	50	∪	∪	NOUN
ejpam-3412	715	51	(	(	PUNCT
ejpam-3412	715	52	g̃2	g̃2	PROPN
ejpam-3412	715	53	,	,	PUNCT
ejpam-3412	715	54	e2	e2	PROPN
ejpam-3412	715	55	)	)	PUNCT
ejpam-3412	715	56	is	be	AUX
ejpam-3412	715	57	not	not	PART
ejpam-3412	715	58	a	a	DET
ejpam-3412	715	59	fuzzy	fuzzy	ADJ
ejpam-3412	715	60	soft	soft	ADJ
ejpam-3412	715	61	upi	upi	NOUN
ejpam-3412	715	62	-	-	PUNCT
ejpam-3412	715	63	ideal	ideal	NOUN
ejpam-3412	715	64	of	of	ADP
ejpam-3412	715	65	a.	a.	NOUN
ejpam-3412	715	66	moreover	moreover	ADV
ejpam-3412	715	67	,	,	PUNCT
ejpam-3412	715	68	(	(	PUNCT
ejpam-3412	715	69	g̃1	g̃1	NOUN
ejpam-3412	715	70	,	,	PUNCT
ejpam-3412	715	71	e1	e1	NOUN
ejpam-3412	715	72	)	)	PUNCT
ejpam-3412	715	73	d	d	NOUN
ejpam-3412	715	74	(	(	PUNCT
ejpam-3412	715	75	g̃2	g̃2	PROPN
ejpam-3412	715	76	,	,	PUNCT
ejpam-3412	715	77	e2	e2	PROPN
ejpam-3412	715	78	)	)	PUNCT
ejpam-3412	715	79	is	be	AUX
ejpam-3412	715	80	not	not	PART
ejpam-3412	715	81	a	a	DET
ejpam-3412	715	82	fuzzy	fuzzy	ADJ
ejpam-3412	715	83	soft	soft	ADJ
ejpam-3412	715	84	upi	upi	NOUN
ejpam-3412	715	85	-	-	PUNCT
ejpam-3412	715	86	ideal	ideal	NOUN
ejpam-3412	715	87	of	of	ADP
ejpam-3412	715	88	a.	a.	NOUN
ejpam-3412	715	89	3.9	3.9	NUM
ejpam-3412	715	90	.	.	PUNCT
ejpam-3412	716	1	fuzzy	fuzzy	ADJ
ejpam-3412	716	2	soft	soft	ADJ
ejpam-3412	716	3	strongly	strongly	ADV
ejpam-3412	716	4	ups	up	NOUN
ejpam-3412	716	5	-	-	PUNCT
ejpam-3412	716	6	ideals	ideal	NOUN
ejpam-3412	716	7	definition	definition	NOUN
ejpam-3412	716	8	26	26	NUM
ejpam-3412	716	9	.	.	PUNCT
ejpam-3412	717	1	a	a	DET
ejpam-3412	717	2	fuzzy	fuzzy	ADJ
ejpam-3412	717	3	soft	soft	ADJ
ejpam-3412	717	4	set	set	NOUN
ejpam-3412	717	5	(	(	PUNCT
ejpam-3412	717	6	f̃	f̃	PROPN
ejpam-3412	717	7	,	,	PUNCT
ejpam-3412	717	8	e	e	NOUN
ejpam-3412	717	9	)	)	PUNCT
ejpam-3412	717	10	over	over	ADP
ejpam-3412	717	11	a	a	PRON
ejpam-3412	717	12	is	be	AUX
ejpam-3412	717	13	called	call	VERB
ejpam-3412	717	14	a	a	DET
ejpam-3412	717	15	fuzzy	fuzzy	ADJ
ejpam-3412	717	16	soft	soft	ADJ
ejpam-3412	717	17	strongly	strongly	ADV
ejpam-3412	717	18	ups	up	NOUN
ejpam-3412	717	19	-	-	PUNCT
ejpam-3412	717	20	ideal	ideal	NOUN
ejpam-3412	717	21	based	base	VERB
ejpam-3412	717	22	on	on	ADP
ejpam-3412	717	23	e	e	PROPN
ejpam-3412	717	24	∈	∈	PROPN
ejpam-3412	717	25	e	e	X
ejpam-3412	717	26	(	(	PUNCT
ejpam-3412	717	27	we	we	PRON
ejpam-3412	717	28	shortly	shortly	ADV
ejpam-3412	717	29	call	call	VERB
ejpam-3412	717	30	an	an	DET
ejpam-3412	717	31	e	e	ADJ
ejpam-3412	717	32	-	-	ADJ
ejpam-3412	717	33	fuzzy	fuzzy	ADJ
ejpam-3412	717	34	soft	soft	ADJ
ejpam-3412	717	35	strongly	strongly	ADV
ejpam-3412	717	36	ups	up	NOUN
ejpam-3412	717	37	-	-	PUNCT
ejpam-3412	717	38	ideal	ideal	NOUN
ejpam-3412	717	39	)	)	PUNCT
ejpam-3412	717	40	of	of	ADP
ejpam-3412	717	41	a	a	DET
ejpam-3412	717	42	if	if	SCONJ
ejpam-3412	717	43	a	a	DET
ejpam-3412	717	44	fuzzy	fuzzy	ADJ
ejpam-3412	717	45	set	set	NOUN
ejpam-3412	717	46	f̃[e	f̃[e	X
ejpam-3412	717	47	]	]	X
ejpam-3412	717	48	in	in	ADP
ejpam-3412	717	49	a	a	PRON
ejpam-3412	717	50	is	be	AUX
ejpam-3412	717	51	a	a	DET
ejpam-3412	717	52	fuzzy	fuzzy	ADJ
ejpam-3412	717	53	strongly	strongly	ADV
ejpam-3412	717	54	ups	up	NOUN
ejpam-3412	717	55	-	-	PUNCT
ejpam-3412	717	56	ideal	ideal	NOUN
ejpam-3412	717	57	of	of	ADP
ejpam-3412	717	58	a.	a.	NOUN
ejpam-3412	717	59	if	if	SCONJ
ejpam-3412	717	60	(	(	PUNCT
ejpam-3412	717	61	f̃	f̃	PROPN
ejpam-3412	717	62	,	,	PUNCT
ejpam-3412	717	63	e	e	NOUN
ejpam-3412	717	64	)	)	PUNCT
ejpam-3412	717	65	is	be	AUX
ejpam-3412	717	66	an	an	DET
ejpam-3412	717	67	e	e	ADJ
ejpam-3412	717	68	-	-	ADJ
ejpam-3412	717	69	fuzzy	fuzzy	ADJ
ejpam-3412	717	70	soft	soft	ADJ
ejpam-3412	717	71	strongly	strongly	ADV
ejpam-3412	717	72	ups	up	NOUN
ejpam-3412	717	73	-	-	PUNCT
ejpam-3412	717	74	ideal	ideal	NOUN
ejpam-3412	717	75	of	of	ADP
ejpam-3412	717	76	a	a	PRON
ejpam-3412	717	77	for	for	ADP
ejpam-3412	717	78	all	all	DET
ejpam-3412	717	79	e	e	NOUN
ejpam-3412	717	80	∈	∈	PROPN
ejpam-3412	717	81	e	e	NOUN
ejpam-3412	717	82	,	,	PUNCT
ejpam-3412	717	83	we	we	PRON
ejpam-3412	717	84	say	say	VERB
ejpam-3412	717	85	that	that	SCONJ
ejpam-3412	717	86	(	(	PUNCT
ejpam-3412	717	87	f̃	f̃	PROPN
ejpam-3412	717	88	,	,	PUNCT
ejpam-3412	717	89	e	e	NOUN
ejpam-3412	717	90	)	)	PUNCT
ejpam-3412	717	91	is	be	AUX
ejpam-3412	717	92	a	a	DET
ejpam-3412	717	93	fuzzy	fuzzy	ADJ
ejpam-3412	717	94	soft	soft	ADJ
ejpam-3412	717	95	strongly	strongly	ADV
ejpam-3412	717	96	ups	up	NOUN
ejpam-3412	717	97	-	-	PUNCT
ejpam-3412	717	98	ideal	ideal	NOUN
ejpam-3412	717	99	of	of	ADP
ejpam-3412	717	100	a.	a.	NOUN
ejpam-3412	717	101	definition	definition	NOUN
ejpam-3412	717	102	27	27	NUM
ejpam-3412	717	103	.	.	PUNCT
ejpam-3412	718	1	a	a	DET
ejpam-3412	718	2	fuzzy	fuzzy	ADJ
ejpam-3412	718	3	soft	soft	ADJ
ejpam-3412	718	4	set	set	NOUN
ejpam-3412	718	5	(	(	PUNCT
ejpam-3412	718	6	f̃	f̃	PROPN
ejpam-3412	718	7	,	,	PUNCT
ejpam-3412	718	8	e	e	NOUN
ejpam-3412	718	9	)	)	PUNCT
ejpam-3412	718	10	over	over	ADP
ejpam-3412	718	11	a	a	PRON
ejpam-3412	718	12	is	be	AUX
ejpam-3412	718	13	called	call	VERB
ejpam-3412	718	14	a	a	DET
ejpam-3412	718	15	constant	constant	ADJ
ejpam-3412	718	16	fuzzy	fuzzy	ADJ
ejpam-3412	718	17	soft	soft	ADJ
ejpam-3412	718	18	set	set	NOUN
ejpam-3412	718	19	based	base	VERB
ejpam-3412	718	20	on	on	ADP
ejpam-3412	718	21	e	e	PROPN
ejpam-3412	718	22	∈	∈	PROPN
ejpam-3412	718	23	e	e	X
ejpam-3412	718	24	(	(	PUNCT
ejpam-3412	718	25	we	we	PRON
ejpam-3412	718	26	shortly	shortly	ADV
ejpam-3412	718	27	call	call	VERB
ejpam-3412	718	28	an	an	DET
ejpam-3412	718	29	e	e	NOUN
ejpam-3412	718	30	-	-	ADJ
ejpam-3412	718	31	constant	constant	ADJ
ejpam-3412	718	32	fuzzy	fuzzy	ADJ
ejpam-3412	718	33	soft	soft	ADJ
ejpam-3412	718	34	set	set	NOUN
ejpam-3412	718	35	)	)	PUNCT
ejpam-3412	718	36	of	of	ADP
ejpam-3412	718	37	a	a	DET
ejpam-3412	718	38	if	if	SCONJ
ejpam-3412	718	39	a	a	DET
ejpam-3412	718	40	fuzzy	fuzzy	ADJ
ejpam-3412	718	41	set	set	NOUN
ejpam-3412	718	42	f̃[e	f̃[e	X
ejpam-3412	718	43	]	]	X
ejpam-3412	718	44	in	in	SCONJ
ejpam-3412	718	45	a	a	PRON
ejpam-3412	718	46	is	be	AUX
ejpam-3412	718	47	constant	constant	ADJ
ejpam-3412	718	48	.	.	PUNCT
ejpam-3412	719	1	if	if	SCONJ
ejpam-3412	719	2	(	(	PUNCT
ejpam-3412	719	3	f̃	f̃	PROPN
ejpam-3412	719	4	,	,	PUNCT
ejpam-3412	719	5	e	e	NOUN
ejpam-3412	719	6	)	)	PUNCT
ejpam-3412	719	7	is	be	AUX
ejpam-3412	719	8	an	an	DET
ejpam-3412	719	9	e	e	ADJ
ejpam-3412	719	10	-	-	ADJ
ejpam-3412	719	11	constant	constant	ADJ
ejpam-3412	719	12	fuzzy	fuzzy	ADJ
ejpam-3412	719	13	soft	soft	ADJ
ejpam-3412	719	14	set	set	NOUN
ejpam-3412	719	15	over	over	ADP
ejpam-3412	719	16	a	a	PRON
ejpam-3412	719	17	for	for	ADP
ejpam-3412	719	18	all	all	DET
ejpam-3412	719	19	e	e	NOUN
ejpam-3412	719	20	∈	∈	PROPN
ejpam-3412	719	21	e	e	NOUN
ejpam-3412	719	22	,	,	PUNCT
ejpam-3412	719	23	we	we	PRON
ejpam-3412	719	24	say	say	VERB
ejpam-3412	719	25	that	that	SCONJ
ejpam-3412	719	26	(	(	PUNCT
ejpam-3412	719	27	f̃	f̃	PROPN
ejpam-3412	719	28	,	,	PUNCT
ejpam-3412	719	29	e	e	NOUN
ejpam-3412	719	30	)	)	PUNCT
ejpam-3412	719	31	is	be	AUX
ejpam-3412	719	32	a	a	DET
ejpam-3412	719	33	constant	constant	ADJ
ejpam-3412	719	34	fuzzy	fuzzy	ADJ
ejpam-3412	719	35	soft	soft	ADJ
ejpam-3412	719	36	set	set	NOUN
ejpam-3412	719	37	over	over	ADP
ejpam-3412	719	38	a.	a.	NOUN
ejpam-3412	719	39	from	from	ADP
ejpam-3412	719	40	figure	figure	NOUN
ejpam-3412	719	41	1	1	NUM
ejpam-3412	719	42	,	,	PUNCT
ejpam-3412	719	43	we	we	PRON
ejpam-3412	719	44	have	have	VERB
ejpam-3412	719	45	the	the	DET
ejpam-3412	719	46	following	follow	VERB
ejpam-3412	719	47	two	two	NUM
ejpam-3412	719	48	theorem	theorem	ADJ
ejpam-3412	719	49	.	.	PUNCT
ejpam-3412	720	1	theorem	theorem	PROPN
ejpam-3412	720	2	68	68	NUM
ejpam-3412	720	3	.	.	PUNCT
ejpam-3412	721	1	every	every	DET
ejpam-3412	721	2	e	e	ADJ
ejpam-3412	721	3	-	-	ADJ
ejpam-3412	721	4	fuzzy	fuzzy	ADJ
ejpam-3412	721	5	soft	soft	ADJ
ejpam-3412	721	6	strongly	strongly	ADV
ejpam-3412	721	7	ups	up	NOUN
ejpam-3412	721	8	-	-	PUNCT
ejpam-3412	721	9	ideal	ideal	NOUN
ejpam-3412	721	10	of	of	ADP
ejpam-3412	721	11	a	a	PRON
ejpam-3412	721	12	is	be	AUX
ejpam-3412	721	13	an	an	DET
ejpam-3412	721	14	e	e	ADJ
ejpam-3412	721	15	-	-	ADJ
ejpam-3412	721	16	fuzzy	fuzzy	ADJ
ejpam-3412	721	17	soft	soft	ADJ
ejpam-3412	721	18	ups	up	NOUN
ejpam-3412	721	19	-	-	PUNCT
ejpam-3412	721	20	ideal	ideal	NOUN
ejpam-3412	721	21	.	.	PUNCT
ejpam-3412	722	1	moreover	moreover	ADV
ejpam-3412	722	2	,	,	PUNCT
ejpam-3412	722	3	every	every	DET
ejpam-3412	722	4	fuzzy	fuzzy	ADJ
ejpam-3412	722	5	soft	soft	ADJ
ejpam-3412	722	6	strongly	strongly	ADV
ejpam-3412	722	7	ups	up	NOUN
ejpam-3412	722	8	-	-	PUNCT
ejpam-3412	722	9	ideal	ideal	NOUN
ejpam-3412	722	10	of	of	ADP
ejpam-3412	722	11	a	a	PRON
ejpam-3412	722	12	is	be	AUX
ejpam-3412	722	13	a	a	DET
ejpam-3412	722	14	fuzzy	fuzzy	ADJ
ejpam-3412	722	15	soft	soft	ADJ
ejpam-3412	722	16	ups	up	NOUN
ejpam-3412	722	17	-	-	PUNCT
ejpam-3412	722	18	ideal	ideal	NOUN
ejpam-3412	722	19	.	.	PUNCT
ejpam-3412	723	1	theorem	theorem	VERB
ejpam-3412	723	2	69	69	NUM
ejpam-3412	723	3	.	.	PUNCT
ejpam-3412	724	1	e	e	X
ejpam-3412	724	2	-	-	ADJ
ejpam-3412	724	3	fuzzy	fuzzy	ADJ
ejpam-3412	724	4	soft	soft	ADJ
ejpam-3412	724	5	strongly	strongly	ADV
ejpam-3412	724	6	ups	up	NOUN
ejpam-3412	724	7	-	-	PUNCT
ejpam-3412	724	8	ideals	ideal	NOUN
ejpam-3412	724	9	and	and	CCONJ
ejpam-3412	724	10	e	e	NOUN
ejpam-3412	724	11	-	-	ADJ
ejpam-3412	724	12	constant	constant	ADJ
ejpam-3412	724	13	fuzzy	fuzzy	ADJ
ejpam-3412	724	14	soft	soft	ADJ
ejpam-3412	724	15	sets	set	NOUN
ejpam-3412	724	16	coincide	coincide	NOUN
ejpam-3412	724	17	in	in	ADP
ejpam-3412	724	18	a.	a.	NOUN
ejpam-3412	724	19	moreover	moreover	ADV
ejpam-3412	724	20	,	,	PUNCT
ejpam-3412	724	21	fuzzy	fuzzy	ADJ
ejpam-3412	724	22	soft	soft	ADJ
ejpam-3412	724	23	strongly	strongly	ADV
ejpam-3412	724	24	ups	up	NOUN
ejpam-3412	724	25	-	-	PUNCT
ejpam-3412	724	26	ideals	ideal	NOUN
ejpam-3412	724	27	and	and	CCONJ
ejpam-3412	724	28	constant	constant	ADJ
ejpam-3412	724	29	fuzzy	fuzzy	ADJ
ejpam-3412	724	30	soft	soft	ADJ
ejpam-3412	724	31	sets	set	NOUN
ejpam-3412	724	32	coincide	coincide	NOUN
ejpam-3412	724	33	in	in	ADP
ejpam-3412	724	34	a.	a.	NOUN
ejpam-3412	724	35	in	in	ADP
ejpam-3412	724	36	the	the	DET
ejpam-3412	724	37	next	next	ADJ
ejpam-3412	724	38	theorem	theorem	NOUN
ejpam-3412	724	39	,	,	PUNCT
ejpam-3412	724	40	we	we	PRON
ejpam-3412	724	41	give	give	VERB
ejpam-3412	724	42	necessary	necessary	ADJ
ejpam-3412	724	43	condition	condition	NOUN
ejpam-3412	724	44	for	for	ADP
ejpam-3412	724	45	fuzzy	fuzzy	ADJ
ejpam-3412	724	46	soft	soft	ADJ
ejpam-3412	724	47	strongly	strongly	ADV
ejpam-3412	724	48	ups	up	NOUN
ejpam-3412	724	49	-	-	PUNCT
ejpam-3412	724	50	ideals	ideal	NOUN
ejpam-3412	724	51	of	of	ADP
ejpam-3412	724	52	f	f	PROPN
ejpam-3412	724	53	-up	-up	NOUN
ejpam-3412	724	54	-	-	PUNCT
ejpam-3412	724	55	semigroups	semigroup	NOUN
ejpam-3412	724	56	.	.	PUNCT
ejpam-3412	725	1	theorem	theorem	NOUN
ejpam-3412	725	2	70	70	NUM
ejpam-3412	725	3	.	.	PUNCT
ejpam-3412	726	1	if	if	SCONJ
ejpam-3412	726	2	(	(	PUNCT
ejpam-3412	726	3	f̃	f̃	PROPN
ejpam-3412	726	4	,	,	PUNCT
ejpam-3412	726	5	e	e	NOUN
ejpam-3412	726	6	)	)	PUNCT
ejpam-3412	726	7	is	be	AUX
ejpam-3412	726	8	a	a	DET
ejpam-3412	726	9	fuzzy	fuzzy	ADJ
ejpam-3412	726	10	soft	soft	ADJ
ejpam-3412	726	11	set	set	NOUN
ejpam-3412	726	12	over	over	ADP
ejpam-3412	726	13	a	a	DET
ejpam-3412	726	14	such	such	ADJ
ejpam-3412	726	15	that	that	PRON
ejpam-3412	726	16	for	for	ADP
ejpam-3412	726	17	all	all	DET
ejpam-3412	726	18	e	e	NOUN
ejpam-3412	726	19	∈	∈	PROPN
ejpam-3412	726	20	e	e	NOUN
ejpam-3412	726	21	,	,	PUNCT
ejpam-3412	726	22	a	a	DET
ejpam-3412	726	23	fuzzy	fuzzy	ADJ
ejpam-3412	726	24	set	set	NOUN
ejpam-3412	726	25	f̃[e	f̃[e	NOUN
ejpam-3412	726	26	]	]	X
ejpam-3412	726	27	in	in	ADP
ejpam-3412	726	28	a	a	DET
ejpam-3412	726	29	satisfies	satisfie	NOUN
ejpam-3412	726	30	the	the	DET
ejpam-3412	726	31	conditions	condition	NOUN
ejpam-3412	726	32	(	(	PUNCT
ejpam-3412	726	33	2.12	2.12	NUM
ejpam-3412	726	34	)	)	PUNCT
ejpam-3412	726	35	(	(	PUNCT
ejpam-3412	726	36	or	or	CCONJ
ejpam-3412	726	37	(	(	PUNCT
ejpam-3412	726	38	2.13	2.13	NUM
ejpam-3412	726	39	)	)	PUNCT
ejpam-3412	726	40	or	or	CCONJ
ejpam-3412	726	41	(	(	PUNCT
ejpam-3412	726	42	2.14	2.14	NUM
ejpam-3412	726	43	)	)	PUNCT
ejpam-3412	726	44	)	)	PUNCT
ejpam-3412	727	1	and	and	CCONJ
ejpam-3412	727	2	(	(	PUNCT
ejpam-3412	727	3	1.14	1.14	NUM
ejpam-3412	727	4	)	)	PUNCT
ejpam-3412	727	5	,	,	PUNCT
ejpam-3412	727	6	then	then	ADV
ejpam-3412	727	7	(	(	PUNCT
ejpam-3412	727	8	f̃	f̃	PROPN
ejpam-3412	727	9	,	,	PUNCT
ejpam-3412	727	10	e	e	NOUN
ejpam-3412	727	11	)	)	PUNCT
ejpam-3412	727	12	is	be	AUX
ejpam-3412	727	13	a	a	DET
ejpam-3412	727	14	fuzzy	fuzzy	ADJ
ejpam-3412	727	15	soft	soft	ADJ
ejpam-3412	727	16	strongly	strongly	ADV
ejpam-3412	727	17	ups	up	NOUN
ejpam-3412	727	18	-	-	PUNCT
ejpam-3412	727	19	ideal	ideal	NOUN
ejpam-3412	727	20	of	of	ADP
ejpam-3412	727	21	a.	a.	PROPN
ejpam-3412	727	22	a.	a.	PROPN
ejpam-3412	727	23	satirad	satirad	PROPN
ejpam-3412	727	24	,	,	PUNCT
ejpam-3412	727	25	a.	a.	NOUN
ejpam-3412	727	26	iampan	iampan	PROPN
ejpam-3412	727	27	/	/	SYM
ejpam-3412	727	28	eur	eur	PROPN
ejpam-3412	727	29	.	.	PUNCT
ejpam-3412	728	1	j.	j.	PROPN
ejpam-3412	728	2	pure	pure	PROPN
ejpam-3412	728	3	appl	appl	PROPN
ejpam-3412	728	4	.	.	PROPN
ejpam-3412	728	5	math	math	PROPN
ejpam-3412	728	6	,	,	PUNCT
ejpam-3412	728	7	12	12	NUM
ejpam-3412	728	8	(	(	PUNCT
ejpam-3412	728	9	2	2	NUM
ejpam-3412	728	10	)	)	PUNCT
ejpam-3412	728	11	(	(	PUNCT
ejpam-3412	728	12	2019	2019	NUM
ejpam-3412	728	13	)	)	PUNCT
ejpam-3412	728	14	,	,	PUNCT
ejpam-3412	728	15	294	294	NUM
ejpam-3412	728	16	-	-	SYM
ejpam-3412	728	17	331	331	NUM
ejpam-3412	728	18	327	327	NUM
ejpam-3412	728	19	proof	proof	NOUN
ejpam-3412	728	20	.	.	PUNCT
ejpam-3412	729	1	it	it	PRON
ejpam-3412	729	2	is	be	AUX
ejpam-3412	729	3	straightforward	straightforward	ADJ
ejpam-3412	729	4	by	by	ADP
ejpam-3412	729	5	propositions	proposition	NOUN
ejpam-3412	729	6	9	9	NUM
ejpam-3412	729	7	(	(	PUNCT
ejpam-3412	729	8	or	or	CCONJ
ejpam-3412	729	9	10	10	NUM
ejpam-3412	729	10	or	or	CCONJ
ejpam-3412	729	11	11	11	NUM
ejpam-3412	729	12	)	)	PUNCT
ejpam-3412	729	13	and	and	CCONJ
ejpam-3412	729	14	lemma	lemma	PROPN
ejpam-3412	729	15	1	1	NUM
ejpam-3412	729	16	(	(	PUNCT
ejpam-3412	729	17	1	1	NUM
ejpam-3412	729	18	)	)	PUNCT
ejpam-3412	729	19	.	.	PUNCT
ejpam-3412	730	1	the	the	DET
ejpam-3412	730	2	following	follow	VERB
ejpam-3412	730	3	example	example	NOUN
ejpam-3412	730	4	shows	show	VERB
ejpam-3412	730	5	that	that	SCONJ
ejpam-3412	730	6	the	the	DET
ejpam-3412	730	7	converse	converse	NOUN
ejpam-3412	730	8	of	of	ADP
ejpam-3412	730	9	theorem	theorem	NOUN
ejpam-3412	730	10	68	68	NUM
ejpam-3412	730	11	is	be	AUX
ejpam-3412	730	12	not	not	PART
ejpam-3412	730	13	true	true	ADJ
ejpam-3412	730	14	.	.	PUNCT
ejpam-3412	731	1	example	example	NOUN
ejpam-3412	731	2	31	31	NUM
ejpam-3412	731	3	.	.	PUNCT
ejpam-3412	732	1	let	let	VERB
ejpam-3412	732	2	a	a	DET
ejpam-3412	732	3	be	be	AUX
ejpam-3412	732	4	a	a	DET
ejpam-3412	732	5	set	set	NOUN
ejpam-3412	732	6	of	of	ADP
ejpam-3412	732	7	four	four	NUM
ejpam-3412	732	8	brands	brand	NOUN
ejpam-3412	732	9	of	of	ADP
ejpam-3412	732	10	a	a	DET
ejpam-3412	732	11	pick	pick	VERB
ejpam-3412	732	12	-	-	PUNCT
ejpam-3412	732	13	up	up	ADP
ejpam-3412	732	14	truck	truck	NOUN
ejpam-3412	732	15	,	,	PUNCT
ejpam-3412	732	16	that	that	ADV
ejpam-3412	732	17	is	is	ADV
ejpam-3412	732	18	,	,	PUNCT
ejpam-3412	732	19	a	a	DET
ejpam-3412	732	20	=	=	X
ejpam-3412	732	21	{	{	PUNCT
ejpam-3412	732	22	toyota	toyota	PROPN
ejpam-3412	732	23	hilux	hilux	PROPN
ejpam-3412	732	24	(	(	PUNCT
ejpam-3412	732	25	th	th	INTJ
ejpam-3412	732	26	)	)	PUNCT
ejpam-3412	732	27	,	,	PUNCT
ejpam-3412	732	28	mitsubishi	mitsubishi	PROPN
ejpam-3412	732	29	triton(mt	triton(mt	PROPN
ejpam-3412	732	30	)	)	PUNCT
ejpam-3412	732	31	,	,	PUNCT
ejpam-3412	732	32	ford	ford	PROPN
ejpam-3412	732	33	ranger(fr	ranger(fr	PROPN
ejpam-3412	732	34	)	)	PUNCT
ejpam-3412	732	35	,	,	PUNCT
ejpam-3412	732	36	isuzu	isuzu	PROPN
ejpam-3412	732	37	d	d	PROPN
ejpam-3412	732	38	-	-	PUNCT
ejpam-3412	732	39	max	max	PROPN
ejpam-3412	732	40	(	(	PUNCT
ejpam-3412	732	41	i	i	NOUN
ejpam-3412	732	42	d	d	PROPN
ejpam-3412	732	43	)	)	PUNCT
ejpam-3412	732	44	}	}	PUNCT
ejpam-3412	732	45	.	.	PUNCT
ejpam-3412	733	1	define	define	VERB
ejpam-3412	733	2	two	two	NUM
ejpam-3412	733	3	binary	binary	ADJ
ejpam-3412	733	4	operations	operation	NOUN
ejpam-3412	733	5	·	·	PUNCT
ejpam-3412	733	6	and	and	CCONJ
ejpam-3412	733	7	∗	∗	NOUN
ejpam-3412	733	8	on	on	ADP
ejpam-3412	733	9	a	a	PRON
ejpam-3412	733	10	as	as	ADP
ejpam-3412	733	11	the	the	DET
ejpam-3412	733	12	following	follow	VERB
ejpam-3412	733	13	cayley	cayley	ADJ
ejpam-3412	733	14	tables	table	NOUN
ejpam-3412	733	15	:	:	PUNCT
ejpam-3412	734	1	·	·	PUNCT
ejpam-3412	734	2	mt	mt	INTJ
ejpam-3412	735	1	fr	fr	INTJ
ejpam-3412	736	1	i	i	PROPN
ejpam-3412	736	2	d	d	PROPN
ejpam-3412	736	3	th	th	PROPN
ejpam-3412	736	4	mt	mt	PROPN
ejpam-3412	736	5	mt	mt	PROPN
ejpam-3412	737	1	fr	fr	PROPN
ejpam-3412	738	1	i	i	PROPN
ejpam-3412	738	2	d	d	PROPN
ejpam-3412	739	1	th	th	X
ejpam-3412	740	1	fr	fr	PROPN
ejpam-3412	741	1	mt	mt	PROPN
ejpam-3412	742	1	mt	mt	PROPN
ejpam-3412	743	1	i	i	PROPN
ejpam-3412	743	2	d	d	PROPN
ejpam-3412	743	3	th	th	X
ejpam-3412	743	4	i	i	PROPN
ejpam-3412	743	5	d	d	PROPN
ejpam-3412	743	6	mt	mt	PROPN
ejpam-3412	744	1	fr	fr	PROPN
ejpam-3412	744	2	mt	mt	PROPN
ejpam-3412	744	3	th	th	X
ejpam-3412	744	4	th	th	X
ejpam-3412	744	5	mt	mt	PROPN
ejpam-3412	745	1	fr	fr	INTJ
ejpam-3412	745	2	i	i	PROPN
ejpam-3412	745	3	d	d	PROPN
ejpam-3412	745	4	mt	mt	PROPN
ejpam-3412	745	5	∗	∗	PROPN
ejpam-3412	745	6	mt	mt	PROPN
ejpam-3412	746	1	fr	fr	INTJ
ejpam-3412	746	2	i	i	PROPN
ejpam-3412	746	3	d	d	PROPN
ejpam-3412	746	4	th	th	PROPN
ejpam-3412	746	5	mt	mt	PROPN
ejpam-3412	746	6	mt	mt	PROPN
ejpam-3412	746	7	mt	mt	PROPN
ejpam-3412	746	8	mt	mt	PROPN
ejpam-3412	746	9	mt	mt	PROPN
ejpam-3412	746	10	fr	fr	PROPN
ejpam-3412	746	11	mt	mt	PROPN
ejpam-3412	747	1	fr	fr	PROPN
ejpam-3412	747	2	mt	mt	PROPN
ejpam-3412	747	3	mt	mt	PROPN
ejpam-3412	748	1	i	i	PROPN
ejpam-3412	748	2	d	d	PROPN
ejpam-3412	748	3	mt	mt	PROPN
ejpam-3412	749	1	mt	mt	PROPN
ejpam-3412	750	1	i	i	PROPN
ejpam-3412	750	2	d	d	PROPN
ejpam-3412	750	3	mt	mt	PROPN
ejpam-3412	750	4	th	th	PROPN
ejpam-3412	750	5	mt	mt	PROPN
ejpam-3412	750	6	th	th	PROPN
ejpam-3412	750	7	mt	mt	PROPN
ejpam-3412	750	8	mt	mt	PROPN
ejpam-3412	750	9	then	then	ADV
ejpam-3412	750	10	a	a	PRON
ejpam-3412	750	11	=	=	X
ejpam-3412	750	12	(	(	PUNCT
ejpam-3412	750	13	a	a	PRON
ejpam-3412	750	14	,	,	PUNCT
ejpam-3412	750	15	·	·	PUNCT
ejpam-3412	750	16	,	,	PUNCT
ejpam-3412	750	17	∗,mitsubishi	∗,mitsubishi	PROPN
ejpam-3412	750	18	triton	triton	PROPN
ejpam-3412	750	19	)	)	PUNCT
ejpam-3412	750	20	is	be	AUX
ejpam-3412	750	21	an	an	DET
ejpam-3412	750	22	f	f	PROPN
ejpam-3412	750	23	-up	-up	NOUN
ejpam-3412	750	24	-	-	PUNCT
ejpam-3412	750	25	semigroup	semigroup	NOUN
ejpam-3412	750	26	.	.	PUNCT
ejpam-3412	751	1	let	let	AUX
ejpam-3412	751	2	(	(	PUNCT
ejpam-3412	751	3	f̃	f̃	PROPN
ejpam-3412	751	4	,	,	PUNCT
ejpam-3412	751	5	e	e	NOUN
ejpam-3412	751	6	)	)	PUNCT
ejpam-3412	751	7	be	be	AUX
ejpam-3412	751	8	a	a	DET
ejpam-3412	751	9	fuzzy	fuzzy	ADJ
ejpam-3412	751	10	soft	soft	ADJ
ejpam-3412	751	11	set	set	NOUN
ejpam-3412	751	12	over	over	ADP
ejpam-3412	751	13	a	a	DET
ejpam-3412	751	14	where	where	SCONJ
ejpam-3412	751	15	e	e	NOUN
ejpam-3412	751	16	:	:	PUNCT
ejpam-3412	751	17	=	=	SYM
ejpam-3412	751	18	{	{	PUNCT
ejpam-3412	751	19	displacement	displacement	NOUN
ejpam-3412	751	20	,	,	PUNCT
ejpam-3412	751	21	horse	horse	NOUN
ejpam-3412	751	22	power	power	NOUN
ejpam-3412	751	23	,	,	PUNCT
ejpam-3412	751	24	torque	torque	NOUN
ejpam-3412	751	25	}	}	PUNCT
ejpam-3412	751	26	with	with	ADP
ejpam-3412	751	27	f̃[displacement	f̃[displacement	PROPN
ejpam-3412	751	28	]	]	PUNCT
ejpam-3412	751	29	,	,	PUNCT
ejpam-3412	751	30	f̃[horse	f̃[horse	NOUN
ejpam-3412	751	31	power	power	NOUN
ejpam-3412	751	32	]	]	PUNCT
ejpam-3412	751	33	,	,	PUNCT
ejpam-3412	751	34	and	and	CCONJ
ejpam-3412	751	35	f̃[torque	f̃[torque	NOUN
ejpam-3412	751	36	]	]	PUNCT
ejpam-3412	751	37	are	be	AUX
ejpam-3412	751	38	fuzzy	fuzzy	ADJ
ejpam-3412	751	39	sets	set	NOUN
ejpam-3412	751	40	in	in	ADP
ejpam-3412	751	41	a	a	DET
ejpam-3412	751	42	defined	define	VERB
ejpam-3412	751	43	as	as	SCONJ
ejpam-3412	751	44	follows	follow	VERB
ejpam-3412	751	45	:	:	PUNCT
ejpam-3412	752	1	f̃	f̃	PROPN
ejpam-3412	752	2	mt	mt	PROPN
ejpam-3412	753	1	fr	fr	INTJ
ejpam-3412	753	2	i	i	PROPN
ejpam-3412	753	3	d	d	PROPN
ejpam-3412	753	4	th	th	X
ejpam-3412	753	5	displacement	displacement	NOUN
ejpam-3412	753	6	1	1	NUM
ejpam-3412	753	7	0.6	0.6	NUM
ejpam-3412	753	8	0.4	0.4	NUM
ejpam-3412	753	9	0.7	0.7	NUM
ejpam-3412	753	10	horse	horse	NOUN
ejpam-3412	753	11	power	power	NOUN
ejpam-3412	753	12	0.9	0.9	NUM
ejpam-3412	753	13	0.6	0.6	NUM
ejpam-3412	753	14	0.5	0.5	NUM
ejpam-3412	753	15	0.5	0.5	NUM
ejpam-3412	753	16	torque	torque	NOUN
ejpam-3412	753	17	0.9	0.9	NUM
ejpam-3412	753	18	0.7	0.7	NUM
ejpam-3412	753	19	0.6	0.6	NUM
ejpam-3412	753	20	0.5	0.5	NUM
ejpam-3412	753	21	then	then	ADV
ejpam-3412	753	22	(	(	PUNCT
ejpam-3412	753	23	f̃	f̃	PROPN
ejpam-3412	753	24	,	,	PUNCT
ejpam-3412	753	25	e	e	NOUN
ejpam-3412	753	26	)	)	PUNCT
ejpam-3412	753	27	is	be	AUX
ejpam-3412	753	28	a	a	DET
ejpam-3412	753	29	torque	torque	NOUN
ejpam-3412	753	30	-	-	PUNCT
ejpam-3412	753	31	fuzzy	fuzzy	ADJ
ejpam-3412	753	32	soft	soft	ADJ
ejpam-3412	753	33	ups	up	NOUN
ejpam-3412	753	34	-	-	PUNCT
ejpam-3412	753	35	ideal	ideal	NOUN
ejpam-3412	753	36	of	of	ADP
ejpam-3412	753	37	a	a	PRON
ejpam-3412	753	38	but	but	CCONJ
ejpam-3412	753	39	f̃[torque	f̃[torque	NOUN
ejpam-3412	753	40	]	]	PUNCT
ejpam-3412	753	41	is	be	AUX
ejpam-3412	753	42	not	not	PART
ejpam-3412	753	43	a	a	DET
ejpam-3412	753	44	fuzzy	fuzzy	ADJ
ejpam-3412	753	45	strongly	strongly	ADV
ejpam-3412	753	46	ups	up	NOUN
ejpam-3412	753	47	-	-	PUNCT
ejpam-3412	753	48	ideal	ideal	NOUN
ejpam-3412	753	49	of	of	ADP
ejpam-3412	753	50	a.	a.	NOUN
ejpam-3412	753	51	indeed	indeed	ADV
ejpam-3412	753	52	,	,	PUNCT
ejpam-3412	753	53	f	f	PROPN
ejpam-3412	753	54	f̃[torque	f̃[torque	PROPN
ejpam-3412	753	55	]	]	PUNCT
ejpam-3412	753	56	(	(	PUNCT
ejpam-3412	753	57	i	i	NOUN
ejpam-3412	753	58	d	d	PROPN
ejpam-3412	753	59	)	)	PUNCT
ejpam-3412	754	1	=	=	SYM
ejpam-3412	754	2	0.6	0.6	NUM
ejpam-3412	754	3	�	�	PROPN
ejpam-3412	754	4	0.7	0.7	NUM
ejpam-3412	754	5	=	=	SYM
ejpam-3412	754	6	min{0.9	min{0.9	PROPN
ejpam-3412	754	7	,	,	PUNCT
ejpam-3412	754	8	0.7	0.7	NUM
ejpam-3412	754	9	}	}	PUNCT
ejpam-3412	754	10	=	=	SYM
ejpam-3412	754	11	min{f	min{f	ADJ
ejpam-3412	754	12	f̃[torque	f̃[torque	NOUN
ejpam-3412	754	13	]	]	PUNCT
ejpam-3412	754	14	(	(	PUNCT
ejpam-3412	754	15	mt	mt	PROPN
ejpam-3412	754	16	)	)	PUNCT
ejpam-3412	754	17	,	,	PUNCT
ejpam-3412	754	18	f	f	PROPN
ejpam-3412	754	19	f̃[torque	f̃[torque	PROPN
ejpam-3412	754	20	]	]	PUNCT
ejpam-3412	754	21	(	(	PUNCT
ejpam-3412	754	22	fr	fr	NOUN
ejpam-3412	754	23	)	)	PUNCT
ejpam-3412	754	24	}	}	PUNCT
ejpam-3412	754	25	=	=	SYM
ejpam-3412	754	26	min{f	min{f	ADJ
ejpam-3412	754	27	f̃[torque	f̃[torque	NOUN
ejpam-3412	754	28	]	]	PUNCT
ejpam-3412	754	29	(	(	PUNCT
ejpam-3412	754	30	(	(	PUNCT
ejpam-3412	754	31	i	i	NOUN
ejpam-3412	754	32	d	d	PROPN
ejpam-3412	754	33	·	·	PUNCT
ejpam-3412	754	34	fr	fr	PROPN
ejpam-3412	754	35	)	)	PUNCT
ejpam-3412	754	36	·	·	PUNCT
ejpam-3412	755	1	(	(	PUNCT
ejpam-3412	755	2	i	i	NOUN
ejpam-3412	755	3	d	d	PROPN
ejpam-3412	755	4	·	·	PUNCT
ejpam-3412	755	5	i	i	PROPN
ejpam-3412	755	6	d	d	PROPN
ejpam-3412	755	7	)	)	PUNCT
ejpam-3412	755	8	)	)	PUNCT
ejpam-3412	755	9	,	,	PUNCT
ejpam-3412	755	10	f	f	PROPN
ejpam-3412	755	11	f̃[torque	f̃[torque	PROPN
ejpam-3412	755	12	]	]	PUNCT
ejpam-3412	755	13	(	(	PUNCT
ejpam-3412	755	14	fr	fr	NOUN
ejpam-3412	755	15	)	)	PUNCT
ejpam-3412	755	16	}	}	PUNCT
ejpam-3412	755	17	.	.	PUNCT
ejpam-3412	756	1	hence	hence	ADV
ejpam-3412	756	2	,	,	PUNCT
ejpam-3412	756	3	(	(	PUNCT
ejpam-3412	756	4	f̃	f̃	PROPN
ejpam-3412	756	5	,	,	PUNCT
ejpam-3412	756	6	e	e	NOUN
ejpam-3412	756	7	)	)	PUNCT
ejpam-3412	756	8	is	be	AUX
ejpam-3412	756	9	not	not	PART
ejpam-3412	756	10	a	a	DET
ejpam-3412	756	11	torque	torque	NOUN
ejpam-3412	756	12	-	-	PUNCT
ejpam-3412	756	13	fuzzy	fuzzy	ADJ
ejpam-3412	756	14	soft	soft	ADJ
ejpam-3412	756	15	strongly	strongly	ADV
ejpam-3412	756	16	ups	up	NOUN
ejpam-3412	756	17	-	-	PUNCT
ejpam-3412	756	18	ideal	ideal	NOUN
ejpam-3412	756	19	of	of	ADP
ejpam-3412	756	20	a.	a.	NOUN
ejpam-3412	756	21	the	the	DET
ejpam-3412	756	22	proof	proof	NOUN
ejpam-3412	756	23	of	of	ADP
ejpam-3412	756	24	the	the	DET
ejpam-3412	756	25	following	follow	VERB
ejpam-3412	756	26	theorem	theorem	NOUN
ejpam-3412	756	27	can	can	AUX
ejpam-3412	756	28	be	be	AUX
ejpam-3412	756	29	verified	verify	VERB
ejpam-3412	756	30	easily	easily	ADV
ejpam-3412	756	31	.	.	PUNCT
ejpam-3412	757	1	theorem	theorem	VERB
ejpam-3412	757	2	71	71	NUM
ejpam-3412	757	3	.	.	PUNCT
ejpam-3412	758	1	if	if	SCONJ
ejpam-3412	758	2	(	(	PUNCT
ejpam-3412	758	3	f̃	f̃	PROPN
ejpam-3412	758	4	,	,	PUNCT
ejpam-3412	758	5	e	e	NOUN
ejpam-3412	758	6	)	)	PUNCT
ejpam-3412	758	7	is	be	AUX
ejpam-3412	758	8	a	a	DET
ejpam-3412	758	9	fuzzy	fuzzy	ADJ
ejpam-3412	758	10	soft	soft	ADJ
ejpam-3412	758	11	strongly	strongly	ADV
ejpam-3412	758	12	ups	up	NOUN
ejpam-3412	758	13	-	-	PUNCT
ejpam-3412	758	14	ideal	ideal	NOUN
ejpam-3412	758	15	of	of	ADP
ejpam-3412	758	16	a	a	PRON
ejpam-3412	758	17	and	and	CCONJ
ejpam-3412	758	18	∅	∅	NOUN
ejpam-3412	758	19	6=	6=	ADP
ejpam-3412	758	20	e∗	e∗	PROPN
ejpam-3412	758	21	⊆	⊆	NUM
ejpam-3412	758	22	e	e	NOUN
ejpam-3412	758	23	,	,	PUNCT
ejpam-3412	758	24	then	then	ADV
ejpam-3412	758	25	(	(	PUNCT
ejpam-3412	758	26	f̃|e∗	f̃|e∗	PROPN
ejpam-3412	758	27	,	,	PUNCT
ejpam-3412	758	28	e∗	e∗	PROPN
ejpam-3412	758	29	)	)	PUNCT
ejpam-3412	758	30	is	be	AUX
ejpam-3412	758	31	a	a	DET
ejpam-3412	758	32	fuzzy	fuzzy	ADJ
ejpam-3412	758	33	soft	soft	ADJ
ejpam-3412	758	34	strongly	strongly	ADV
ejpam-3412	758	35	ups	up	NOUN
ejpam-3412	758	36	-	-	PUNCT
ejpam-3412	758	37	ideal	ideal	NOUN
ejpam-3412	758	38	of	of	ADP
ejpam-3412	758	39	a.	a.	NOUN
ejpam-3412	758	40	by	by	ADP
ejpam-3412	758	41	using	use	VERB
ejpam-3412	758	42	theorem	theorem	NOUN
ejpam-3412	758	43	6	6	NUM
ejpam-3412	758	44	,	,	PUNCT
ejpam-3412	758	45	we	we	PRON
ejpam-3412	758	46	can	can	AUX
ejpam-3412	758	47	obtain	obtain	VERB
ejpam-3412	758	48	the	the	DET
ejpam-3412	758	49	following	follow	VERB
ejpam-3412	758	50	two	two	NUM
ejpam-3412	758	51	theorems	theorem	NOUN
ejpam-3412	758	52	in	in	ADP
ejpam-3412	758	53	the	the	DET
ejpam-3412	758	54	same	same	ADJ
ejpam-3412	758	55	way	way	NOUN
ejpam-3412	758	56	as	as	ADP
ejpam-3412	758	57	theorems	theorem	NOUN
ejpam-3412	758	58	22	22	NUM
ejpam-3412	758	59	and	and	CCONJ
ejpam-3412	758	60	23	23	NUM
ejpam-3412	758	61	.	.	PUNCT
ejpam-3412	759	1	theorem	theorem	VERB
ejpam-3412	759	2	72	72	NUM
ejpam-3412	759	3	.	.	PUNCT
ejpam-3412	760	1	the	the	DET
ejpam-3412	760	2	extended	extended	ADJ
ejpam-3412	760	3	intersection	intersection	NOUN
ejpam-3412	760	4	of	of	ADP
ejpam-3412	760	5	two	two	NUM
ejpam-3412	760	6	fuzzy	fuzzy	ADJ
ejpam-3412	760	7	soft	soft	ADJ
ejpam-3412	760	8	strongly	strongly	ADV
ejpam-3412	760	9	ups	up	NOUN
ejpam-3412	760	10	-	-	PUNCT
ejpam-3412	760	11	ideals	ideal	NOUN
ejpam-3412	760	12	of	of	ADP
ejpam-3412	760	13	a	a	PRON
ejpam-3412	760	14	is	be	AUX
ejpam-3412	760	15	also	also	ADV
ejpam-3412	760	16	a	a	DET
ejpam-3412	760	17	fuzzy	fuzzy	ADJ
ejpam-3412	760	18	soft	soft	ADJ
ejpam-3412	760	19	strongly	strongly	ADV
ejpam-3412	760	20	ups	up	NOUN
ejpam-3412	760	21	-	-	PUNCT
ejpam-3412	760	22	ideal	ideal	NOUN
ejpam-3412	760	23	.	.	PUNCT
ejpam-3412	761	1	moreover	moreover	ADV
ejpam-3412	761	2	,	,	PUNCT
ejpam-3412	761	3	the	the	DET
ejpam-3412	761	4	intersection	intersection	NOUN
ejpam-3412	761	5	of	of	ADP
ejpam-3412	761	6	two	two	NUM
ejpam-3412	761	7	fuzzy	fuzzy	ADJ
ejpam-3412	761	8	soft	soft	ADJ
ejpam-3412	761	9	strongly	strongly	ADV
ejpam-3412	761	10	ups	up	NOUN
ejpam-3412	761	11	-	-	PUNCT
ejpam-3412	761	12	ideals	ideal	NOUN
ejpam-3412	761	13	of	of	ADP
ejpam-3412	761	14	a	a	PRON
ejpam-3412	761	15	is	be	AUX
ejpam-3412	761	16	also	also	ADV
ejpam-3412	761	17	a	a	DET
ejpam-3412	761	18	fuzzy	fuzzy	ADJ
ejpam-3412	761	19	soft	soft	ADJ
ejpam-3412	761	20	strongly	strongly	ADV
ejpam-3412	761	21	ups	up	NOUN
ejpam-3412	761	22	-	-	PUNCT
ejpam-3412	761	23	ideal	ideal	NOUN
ejpam-3412	761	24	.	.	PUNCT
ejpam-3412	762	1	theorem	theorem	VERB
ejpam-3412	762	2	73	73	NUM
ejpam-3412	762	3	.	.	PUNCT
ejpam-3412	763	1	the	the	DET
ejpam-3412	763	2	union	union	NOUN
ejpam-3412	763	3	of	of	ADP
ejpam-3412	763	4	two	two	NUM
ejpam-3412	763	5	fuzzy	fuzzy	ADJ
ejpam-3412	763	6	soft	soft	ADJ
ejpam-3412	763	7	strongly	strongly	ADV
ejpam-3412	763	8	ups	up	NOUN
ejpam-3412	763	9	-	-	PUNCT
ejpam-3412	763	10	ideals	ideal	NOUN
ejpam-3412	763	11	is	be	AUX
ejpam-3412	763	12	also	also	ADV
ejpam-3412	763	13	a	a	DET
ejpam-3412	763	14	fuzzy	fuzzy	ADJ
ejpam-3412	763	15	soft	soft	ADJ
ejpam-3412	763	16	strongly	strongly	ADV
ejpam-3412	763	17	ups	up	NOUN
ejpam-3412	763	18	-	-	PUNCT
ejpam-3412	763	19	ideal	ideal	NOUN
ejpam-3412	763	20	.	.	PUNCT
ejpam-3412	764	1	moreover	moreover	ADV
ejpam-3412	764	2	,	,	PUNCT
ejpam-3412	764	3	the	the	DET
ejpam-3412	764	4	restricted	restricted	ADJ
ejpam-3412	764	5	union	union	NOUN
ejpam-3412	764	6	of	of	ADP
ejpam-3412	764	7	two	two	NUM
ejpam-3412	764	8	fuzzy	fuzzy	ADJ
ejpam-3412	764	9	soft	soft	ADJ
ejpam-3412	764	10	strongly	strongly	ADV
ejpam-3412	764	11	ups	up	NOUN
ejpam-3412	764	12	-	-	PUNCT
ejpam-3412	764	13	ideals	ideal	NOUN
ejpam-3412	764	14	of	of	ADP
ejpam-3412	764	15	a	a	PRON
ejpam-3412	764	16	is	be	AUX
ejpam-3412	764	17	also	also	ADV
ejpam-3412	764	18	a	a	DET
ejpam-3412	764	19	fuzzy	fuzzy	ADJ
ejpam-3412	764	20	soft	soft	ADJ
ejpam-3412	764	21	strongly	strongly	ADV
ejpam-3412	764	22	ups	up	NOUN
ejpam-3412	764	23	-	-	PUNCT
ejpam-3412	764	24	ideal	ideal	NOUN
ejpam-3412	764	25	.	.	PUNCT
ejpam-3412	765	1	a.	a.	PROPN
ejpam-3412	765	2	satirad	satirad	PROPN
ejpam-3412	765	3	,	,	PUNCT
ejpam-3412	765	4	a.	a.	NOUN
ejpam-3412	765	5	iampan	iampan	PROPN
ejpam-3412	765	6	/	/	SYM
ejpam-3412	765	7	eur	eur	PROPN
ejpam-3412	765	8	.	.	PUNCT
ejpam-3412	766	1	j.	j.	PROPN
ejpam-3412	766	2	pure	pure	PROPN
ejpam-3412	766	3	appl	appl	PROPN
ejpam-3412	766	4	.	.	PROPN
ejpam-3412	766	5	math	math	PROPN
ejpam-3412	766	6	,	,	PUNCT
ejpam-3412	766	7	12	12	NUM
ejpam-3412	766	8	(	(	PUNCT
ejpam-3412	766	9	2	2	NUM
ejpam-3412	766	10	)	)	PUNCT
ejpam-3412	766	11	(	(	PUNCT
ejpam-3412	766	12	2019	2019	NUM
ejpam-3412	766	13	)	)	PUNCT
ejpam-3412	766	14	,	,	PUNCT
ejpam-3412	766	15	294	294	NUM
ejpam-3412	766	16	-	-	SYM
ejpam-3412	766	17	331	331	NUM
ejpam-3412	766	18	328	328	NUM
ejpam-3412	766	19	3.10	3.10	NUM
ejpam-3412	766	20	.	.	PUNCT
ejpam-3412	767	1	fuzzy	fuzzy	ADJ
ejpam-3412	767	2	soft	soft	ADJ
ejpam-3412	767	3	strongly	strongly	ADV
ejpam-3412	767	4	upi	upi	NOUN
ejpam-3412	767	5	-	-	PUNCT
ejpam-3412	767	6	ideals	ideal	NOUN
ejpam-3412	767	7	definition	definition	NOUN
ejpam-3412	767	8	28	28	NUM
ejpam-3412	767	9	.	.	PUNCT
ejpam-3412	768	1	a	a	DET
ejpam-3412	768	2	fuzzy	fuzzy	ADJ
ejpam-3412	768	3	soft	soft	ADJ
ejpam-3412	768	4	set	set	NOUN
ejpam-3412	768	5	(	(	PUNCT
ejpam-3412	768	6	f̃	f̃	PROPN
ejpam-3412	768	7	,	,	PUNCT
ejpam-3412	768	8	e	e	NOUN
ejpam-3412	768	9	)	)	PUNCT
ejpam-3412	768	10	over	over	ADP
ejpam-3412	768	11	a	a	PRON
ejpam-3412	768	12	is	be	AUX
ejpam-3412	768	13	called	call	VERB
ejpam-3412	768	14	a	a	DET
ejpam-3412	768	15	fuzzy	fuzzy	ADJ
ejpam-3412	768	16	soft	soft	ADJ
ejpam-3412	768	17	strongly	strongly	ADV
ejpam-3412	768	18	upi	upi	NOUN
ejpam-3412	768	19	-	-	PUNCT
ejpam-3412	768	20	ideal	ideal	NOUN
ejpam-3412	768	21	based	base	VERB
ejpam-3412	768	22	on	on	ADP
ejpam-3412	768	23	e	e	PROPN
ejpam-3412	768	24	∈	∈	PROPN
ejpam-3412	768	25	e	e	X
ejpam-3412	768	26	(	(	PUNCT
ejpam-3412	768	27	we	we	PRON
ejpam-3412	768	28	shortly	shortly	ADV
ejpam-3412	768	29	call	call	VERB
ejpam-3412	768	30	an	an	DET
ejpam-3412	768	31	e	e	ADJ
ejpam-3412	768	32	-	-	ADJ
ejpam-3412	768	33	fuzzy	fuzzy	ADJ
ejpam-3412	768	34	soft	soft	ADJ
ejpam-3412	768	35	strongly	strongly	ADV
ejpam-3412	768	36	upi	upi	NOUN
ejpam-3412	768	37	-	-	PUNCT
ejpam-3412	768	38	ideal	ideal	NOUN
ejpam-3412	768	39	)	)	PUNCT
ejpam-3412	768	40	of	of	ADP
ejpam-3412	768	41	a	a	DET
ejpam-3412	768	42	if	if	SCONJ
ejpam-3412	768	43	a	a	DET
ejpam-3412	768	44	fuzzy	fuzzy	ADJ
ejpam-3412	768	45	set	set	NOUN
ejpam-3412	768	46	f̃[e	f̃[e	X
ejpam-3412	768	47	]	]	X
ejpam-3412	768	48	in	in	ADP
ejpam-3412	768	49	a	a	PRON
ejpam-3412	768	50	is	be	AUX
ejpam-3412	768	51	a	a	DET
ejpam-3412	768	52	fuzzy	fuzzy	ADJ
ejpam-3412	768	53	strongly	strongly	ADV
ejpam-3412	768	54	upi	upi	NOUN
ejpam-3412	768	55	-	-	PUNCT
ejpam-3412	768	56	ideal	ideal	NOUN
ejpam-3412	768	57	of	of	ADP
ejpam-3412	768	58	a.	a.	NOUN
ejpam-3412	768	59	if	if	SCONJ
ejpam-3412	768	60	(	(	PUNCT
ejpam-3412	768	61	f̃	f̃	PROPN
ejpam-3412	768	62	,	,	PUNCT
ejpam-3412	768	63	e	e	NOUN
ejpam-3412	768	64	)	)	PUNCT
ejpam-3412	768	65	is	be	AUX
ejpam-3412	768	66	an	an	DET
ejpam-3412	768	67	e	e	ADJ
ejpam-3412	768	68	-	-	ADJ
ejpam-3412	768	69	fuzzy	fuzzy	ADJ
ejpam-3412	768	70	soft	soft	ADJ
ejpam-3412	768	71	strongly	strongly	ADV
ejpam-3412	768	72	upi	upi	NOUN
ejpam-3412	768	73	-	-	PUNCT
ejpam-3412	768	74	ideal	ideal	NOUN
ejpam-3412	768	75	of	of	ADP
ejpam-3412	768	76	a	a	PRON
ejpam-3412	768	77	for	for	ADP
ejpam-3412	768	78	all	all	DET
ejpam-3412	768	79	e	e	NOUN
ejpam-3412	768	80	∈	∈	PROPN
ejpam-3412	768	81	e	e	NOUN
ejpam-3412	768	82	,	,	PUNCT
ejpam-3412	768	83	we	we	PRON
ejpam-3412	768	84	say	say	VERB
ejpam-3412	768	85	that	that	SCONJ
ejpam-3412	768	86	(	(	PUNCT
ejpam-3412	768	87	f̃	f̃	PROPN
ejpam-3412	768	88	,	,	PUNCT
ejpam-3412	768	89	e	e	NOUN
ejpam-3412	768	90	)	)	PUNCT
ejpam-3412	768	91	is	be	AUX
ejpam-3412	768	92	a	a	DET
ejpam-3412	768	93	fuzzy	fuzzy	ADJ
ejpam-3412	768	94	soft	soft	ADJ
ejpam-3412	768	95	strongly	strongly	ADV
ejpam-3412	768	96	upi	upi	NOUN
ejpam-3412	768	97	-	-	PUNCT
ejpam-3412	768	98	ideal	ideal	NOUN
ejpam-3412	768	99	of	of	ADP
ejpam-3412	768	100	a.	a.	NOUN
ejpam-3412	768	101	from	from	ADP
ejpam-3412	768	102	figure	figure	NOUN
ejpam-3412	768	103	1	1	NUM
ejpam-3412	768	104	,	,	PUNCT
ejpam-3412	768	105	we	we	PRON
ejpam-3412	768	106	have	have	VERB
ejpam-3412	768	107	the	the	DET
ejpam-3412	768	108	following	follow	VERB
ejpam-3412	768	109	two	two	NUM
ejpam-3412	768	110	theorem	theorem	ADJ
ejpam-3412	768	111	.	.	PUNCT
ejpam-3412	769	1	theorem	theorem	NOUN
ejpam-3412	769	2	74	74	NUM
ejpam-3412	769	3	.	.	PUNCT
ejpam-3412	770	1	every	every	DET
ejpam-3412	770	2	e	e	ADJ
ejpam-3412	770	3	-	-	ADJ
ejpam-3412	770	4	fuzzy	fuzzy	ADJ
ejpam-3412	770	5	soft	soft	ADJ
ejpam-3412	770	6	strongly	strongly	ADV
ejpam-3412	770	7	upi	upi	NOUN
ejpam-3412	770	8	-	-	PUNCT
ejpam-3412	770	9	ideal	ideal	NOUN
ejpam-3412	770	10	of	of	ADP
ejpam-3412	770	11	a	a	PRON
ejpam-3412	770	12	is	be	AUX
ejpam-3412	770	13	an	an	DET
ejpam-3412	770	14	e	e	ADJ
ejpam-3412	770	15	-	-	ADJ
ejpam-3412	770	16	fuzzy	fuzzy	ADJ
ejpam-3412	770	17	soft	soft	ADJ
ejpam-3412	770	18	upi	upi	NOUN
ejpam-3412	770	19	-	-	PUNCT
ejpam-3412	770	20	ideal	ideal	NOUN
ejpam-3412	770	21	.	.	PUNCT
ejpam-3412	771	1	moreover	moreover	ADV
ejpam-3412	771	2	,	,	PUNCT
ejpam-3412	771	3	every	every	DET
ejpam-3412	771	4	fuzzy	fuzzy	ADJ
ejpam-3412	771	5	soft	soft	ADJ
ejpam-3412	771	6	strongly	strongly	ADV
ejpam-3412	771	7	upi	upi	NOUN
ejpam-3412	771	8	-	-	PUNCT
ejpam-3412	771	9	ideal	ideal	NOUN
ejpam-3412	771	10	of	of	ADP
ejpam-3412	771	11	a	a	PRON
ejpam-3412	771	12	is	be	AUX
ejpam-3412	771	13	a	a	DET
ejpam-3412	771	14	fuzzy	fuzzy	ADJ
ejpam-3412	771	15	soft	soft	ADJ
ejpam-3412	771	16	upi	upi	NOUN
ejpam-3412	771	17	-	-	PUNCT
ejpam-3412	771	18	ideal	ideal	NOUN
ejpam-3412	771	19	.	.	PUNCT
ejpam-3412	772	1	theorem	theorem	NOUN
ejpam-3412	772	2	75	75	NUM
ejpam-3412	772	3	.	.	PUNCT
ejpam-3412	773	1	e	e	X
ejpam-3412	773	2	-	-	ADJ
ejpam-3412	773	3	fuzzy	fuzzy	ADJ
ejpam-3412	773	4	soft	soft	ADJ
ejpam-3412	773	5	strongly	strongly	ADV
ejpam-3412	773	6	upi	upi	NOUN
ejpam-3412	773	7	-	-	PUNCT
ejpam-3412	773	8	ideals	ideal	NOUN
ejpam-3412	773	9	and	and	CCONJ
ejpam-3412	773	10	e	e	NOUN
ejpam-3412	773	11	-	-	ADJ
ejpam-3412	773	12	constant	constant	ADJ
ejpam-3412	773	13	fuzzy	fuzzy	ADJ
ejpam-3412	773	14	soft	soft	ADJ
ejpam-3412	773	15	sets	set	NOUN
ejpam-3412	773	16	coincide	coincide	NOUN
ejpam-3412	773	17	in	in	ADP
ejpam-3412	773	18	a.	a.	NOUN
ejpam-3412	773	19	moreover	moreover	ADV
ejpam-3412	773	20	,	,	PUNCT
ejpam-3412	773	21	fuzzy	fuzzy	ADJ
ejpam-3412	773	22	soft	soft	ADJ
ejpam-3412	773	23	strongly	strongly	ADV
ejpam-3412	773	24	upi	upi	NOUN
ejpam-3412	773	25	-	-	PUNCT
ejpam-3412	773	26	ideals	ideal	NOUN
ejpam-3412	773	27	and	and	CCONJ
ejpam-3412	773	28	constant	constant	ADJ
ejpam-3412	773	29	fuzzy	fuzzy	ADJ
ejpam-3412	773	30	soft	soft	ADJ
ejpam-3412	773	31	sets	set	NOUN
ejpam-3412	773	32	coincide	coincide	NOUN
ejpam-3412	773	33	in	in	ADP
ejpam-3412	773	34	a.	a.	NOUN
ejpam-3412	773	35	corollary	corollary	NOUN
ejpam-3412	773	36	5	5	NUM
ejpam-3412	773	37	.	.	PUNCT
ejpam-3412	774	1	e	e	X
ejpam-3412	774	2	-	-	ADJ
ejpam-3412	774	3	fuzzy	fuzzy	ADJ
ejpam-3412	774	4	soft	soft	ADJ
ejpam-3412	774	5	strongly	strongly	ADV
ejpam-3412	774	6	ups	up	NOUN
ejpam-3412	774	7	-	-	PUNCT
ejpam-3412	774	8	ideals	ideal	NOUN
ejpam-3412	774	9	,	,	PUNCT
ejpam-3412	774	10	e	e	NOUN
ejpam-3412	774	11	-	-	ADJ
ejpam-3412	774	12	fuzzy	fuzzy	ADJ
ejpam-3412	774	13	soft	soft	ADJ
ejpam-3412	774	14	strongly	strongly	ADV
ejpam-3412	774	15	upi	upi	NOUN
ejpam-3412	774	16	-	-	PUNCT
ejpam-3412	774	17	ideals	ideal	NOUN
ejpam-3412	774	18	,	,	PUNCT
ejpam-3412	774	19	and	and	CCONJ
ejpam-3412	774	20	econstant	econstant	ADJ
ejpam-3412	774	21	fuzzy	fuzzy	ADJ
ejpam-3412	774	22	soft	soft	ADJ
ejpam-3412	774	23	sets	set	NOUN
ejpam-3412	774	24	coincide	coincide	NOUN
ejpam-3412	774	25	in	in	ADP
ejpam-3412	774	26	a.	a.	NOUN
ejpam-3412	774	27	moreover	moreover	ADV
ejpam-3412	774	28	,	,	PUNCT
ejpam-3412	774	29	fuzzy	fuzzy	ADJ
ejpam-3412	774	30	soft	soft	ADJ
ejpam-3412	774	31	strongly	strongly	ADV
ejpam-3412	774	32	ups	up	NOUN
ejpam-3412	774	33	-	-	PUNCT
ejpam-3412	774	34	ideals	ideal	NOUN
ejpam-3412	774	35	,	,	PUNCT
ejpam-3412	774	36	fuzzy	fuzzy	ADJ
ejpam-3412	774	37	soft	soft	ADJ
ejpam-3412	774	38	strongly	strongly	ADV
ejpam-3412	774	39	upi	upi	NOUN
ejpam-3412	774	40	-	-	PUNCT
ejpam-3412	774	41	ideals	ideal	NOUN
ejpam-3412	774	42	and	and	CCONJ
ejpam-3412	774	43	constant	constant	ADJ
ejpam-3412	774	44	fuzzy	fuzzy	ADJ
ejpam-3412	774	45	soft	soft	ADJ
ejpam-3412	774	46	sets	set	NOUN
ejpam-3412	774	47	coincide	coincide	NOUN
ejpam-3412	774	48	in	in	ADP
ejpam-3412	774	49	a.	a.	NOUN
ejpam-3412	774	50	proof	proof	NOUN
ejpam-3412	774	51	.	.	PUNCT
ejpam-3412	775	1	it	it	PRON
ejpam-3412	775	2	is	be	AUX
ejpam-3412	775	3	straightforward	straightforward	ADJ
ejpam-3412	775	4	by	by	ADP
ejpam-3412	775	5	theorems	theorem	NOUN
ejpam-3412	775	6	69	69	NUM
ejpam-3412	775	7	and	and	CCONJ
ejpam-3412	775	8	75	75	NUM
ejpam-3412	775	9	.	.	PUNCT
ejpam-3412	776	1	in	in	ADP
ejpam-3412	776	2	the	the	DET
ejpam-3412	776	3	next	next	ADJ
ejpam-3412	776	4	theorem	theorem	NOUN
ejpam-3412	776	5	,	,	PUNCT
ejpam-3412	776	6	we	we	PRON
ejpam-3412	776	7	give	give	VERB
ejpam-3412	776	8	necessary	necessary	ADJ
ejpam-3412	776	9	condition	condition	NOUN
ejpam-3412	776	10	for	for	ADP
ejpam-3412	776	11	fuzzy	fuzzy	ADJ
ejpam-3412	776	12	soft	soft	ADJ
ejpam-3412	776	13	strongly	strongly	ADV
ejpam-3412	776	14	upi	upi	NOUN
ejpam-3412	776	15	-	-	PUNCT
ejpam-3412	776	16	ideals	ideal	NOUN
ejpam-3412	776	17	of	of	ADP
ejpam-3412	776	18	f	f	PROPN
ejpam-3412	776	19	-up	-up	NOUN
ejpam-3412	776	20	-	-	PUNCT
ejpam-3412	776	21	semigroups	semigroup	NOUN
ejpam-3412	776	22	.	.	PUNCT
ejpam-3412	777	1	theorem	theorem	NOUN
ejpam-3412	777	2	76	76	NUM
ejpam-3412	777	3	.	.	PUNCT
ejpam-3412	778	1	if	if	SCONJ
ejpam-3412	778	2	(	(	PUNCT
ejpam-3412	778	3	f̃	f̃	PROPN
ejpam-3412	778	4	,	,	PUNCT
ejpam-3412	778	5	e	e	NOUN
ejpam-3412	778	6	)	)	PUNCT
ejpam-3412	778	7	is	be	AUX
ejpam-3412	778	8	a	a	DET
ejpam-3412	778	9	fuzzy	fuzzy	ADJ
ejpam-3412	778	10	soft	soft	ADJ
ejpam-3412	778	11	set	set	NOUN
ejpam-3412	778	12	over	over	ADP
ejpam-3412	778	13	a	a	DET
ejpam-3412	778	14	such	such	ADJ
ejpam-3412	778	15	that	that	PRON
ejpam-3412	778	16	for	for	ADP
ejpam-3412	778	17	all	all	DET
ejpam-3412	778	18	e	e	NOUN
ejpam-3412	778	19	∈	∈	PROPN
ejpam-3412	778	20	e	e	NOUN
ejpam-3412	778	21	,	,	PUNCT
ejpam-3412	778	22	a	a	DET
ejpam-3412	778	23	fuzzy	fuzzy	ADJ
ejpam-3412	778	24	set	set	NOUN
ejpam-3412	778	25	f̃[e	f̃[e	NOUN
ejpam-3412	778	26	]	]	X
ejpam-3412	778	27	in	in	ADP
ejpam-3412	778	28	a	a	DET
ejpam-3412	778	29	satisfies	satisfie	NOUN
ejpam-3412	778	30	the	the	DET
ejpam-3412	778	31	conditions	condition	NOUN
ejpam-3412	778	32	(	(	PUNCT
ejpam-3412	778	33	2.12	2.12	NUM
ejpam-3412	778	34	)	)	PUNCT
ejpam-3412	778	35	(	(	PUNCT
ejpam-3412	778	36	or	or	CCONJ
ejpam-3412	778	37	(	(	PUNCT
ejpam-3412	778	38	2.13	2.13	NUM
ejpam-3412	778	39	)	)	PUNCT
ejpam-3412	778	40	or	or	CCONJ
ejpam-3412	778	41	(	(	PUNCT
ejpam-3412	778	42	2.14	2.14	NUM
ejpam-3412	778	43	)	)	PUNCT
ejpam-3412	778	44	)	)	PUNCT
ejpam-3412	779	1	and	and	CCONJ
ejpam-3412	779	2	(	(	PUNCT
ejpam-3412	779	3	1.15	1.15	NUM
ejpam-3412	779	4	)	)	PUNCT
ejpam-3412	779	5	,	,	PUNCT
ejpam-3412	779	6	then	then	ADV
ejpam-3412	779	7	(	(	PUNCT
ejpam-3412	779	8	f̃	f̃	PROPN
ejpam-3412	779	9	,	,	PUNCT
ejpam-3412	779	10	e	e	NOUN
ejpam-3412	779	11	)	)	PUNCT
ejpam-3412	779	12	is	be	AUX
ejpam-3412	779	13	a	a	DET
ejpam-3412	779	14	fuzzy	fuzzy	ADJ
ejpam-3412	779	15	soft	soft	ADJ
ejpam-3412	779	16	strongly	strongly	ADV
ejpam-3412	779	17	upi	upi	NOUN
ejpam-3412	779	18	-	-	PUNCT
ejpam-3412	779	19	ideal	ideal	NOUN
ejpam-3412	779	20	of	of	ADP
ejpam-3412	779	21	a.	a.	NOUN
ejpam-3412	779	22	proof	proof	NOUN
ejpam-3412	779	23	.	.	PUNCT
ejpam-3412	780	1	it	it	PRON
ejpam-3412	780	2	is	be	AUX
ejpam-3412	780	3	straightforward	straightforward	ADJ
ejpam-3412	780	4	by	by	ADP
ejpam-3412	780	5	proposition	proposition	NOUN
ejpam-3412	780	6	9	9	NUM
ejpam-3412	780	7	(	(	PUNCT
ejpam-3412	780	8	or	or	CCONJ
ejpam-3412	780	9	10	10	NUM
ejpam-3412	780	10	or	or	CCONJ
ejpam-3412	780	11	11	11	NUM
ejpam-3412	780	12	)	)	PUNCT
ejpam-3412	780	13	and	and	CCONJ
ejpam-3412	780	14	lemma	lemma	PROPN
ejpam-3412	780	15	1	1	NUM
ejpam-3412	780	16	(	(	PUNCT
ejpam-3412	780	17	2	2	NUM
ejpam-3412	780	18	)	)	PUNCT
ejpam-3412	780	19	.	.	PUNCT
ejpam-3412	781	1	the	the	DET
ejpam-3412	781	2	following	follow	VERB
ejpam-3412	781	3	example	example	NOUN
ejpam-3412	781	4	shows	show	VERB
ejpam-3412	781	5	that	that	SCONJ
ejpam-3412	781	6	the	the	DET
ejpam-3412	781	7	converse	converse	NOUN
ejpam-3412	781	8	of	of	ADP
ejpam-3412	781	9	theorem	theorem	NOUN
ejpam-3412	781	10	74	74	NUM
ejpam-3412	781	11	is	be	AUX
ejpam-3412	781	12	not	not	PART
ejpam-3412	781	13	true	true	ADJ
ejpam-3412	781	14	.	.	PUNCT
ejpam-3412	782	1	example	example	NOUN
ejpam-3412	782	2	32	32	NUM
ejpam-3412	782	3	.	.	PUNCT
ejpam-3412	783	1	in	in	ADP
ejpam-3412	783	2	example	example	NOUN
ejpam-3412	783	3	31	31	NUM
ejpam-3412	783	4	,	,	PUNCT
ejpam-3412	783	5	we	we	PRON
ejpam-3412	783	6	know	know	VERB
ejpam-3412	783	7	that	that	SCONJ
ejpam-3412	783	8	(	(	PUNCT
ejpam-3412	783	9	f̃	f̃	PROPN
ejpam-3412	783	10	,	,	PUNCT
ejpam-3412	783	11	e	e	NOUN
ejpam-3412	783	12	)	)	PUNCT
ejpam-3412	783	13	is	be	AUX
ejpam-3412	783	14	a	a	DET
ejpam-3412	783	15	displacement	displacement	NOUN
ejpam-3412	783	16	-	-	PUNCT
ejpam-3412	783	17	fuzzy	fuzzy	ADJ
ejpam-3412	783	18	soft	soft	ADJ
ejpam-3412	783	19	upi	upi	NOUN
ejpam-3412	783	20	-	-	PUNCT
ejpam-3412	783	21	ideal	ideal	NOUN
ejpam-3412	783	22	of	of	ADP
ejpam-3412	783	23	a	a	PRON
ejpam-3412	783	24	but	but	CCONJ
ejpam-3412	783	25	f̃[displacement	f̃[displacement	NOUN
ejpam-3412	783	26	]	]	PUNCT
ejpam-3412	783	27	is	be	AUX
ejpam-3412	783	28	not	not	PART
ejpam-3412	783	29	a	a	DET
ejpam-3412	783	30	fuzzy	fuzzy	ADJ
ejpam-3412	783	31	strongly	strongly	ADV
ejpam-3412	783	32	upi	upi	NOUN
ejpam-3412	783	33	-	-	PUNCT
ejpam-3412	783	34	ideal	ideal	NOUN
ejpam-3412	783	35	of	of	ADP
ejpam-3412	783	36	a.	a.	NOUN
ejpam-3412	783	37	indeed	indeed	ADV
ejpam-3412	783	38	,	,	PUNCT
ejpam-3412	783	39	f	f	PROPN
ejpam-3412	783	40	f̃[displacement	f̃[displacement	PROPN
ejpam-3412	783	41	]	]	X
ejpam-3412	783	42	(	(	PUNCT
ejpam-3412	783	43	i	i	NOUN
ejpam-3412	783	44	d	d	PROPN
ejpam-3412	783	45	)	)	PUNCT
ejpam-3412	784	1	=	=	SYM
ejpam-3412	784	2	0.4	0.4	NUM
ejpam-3412	784	3	�	�	PROPN
ejpam-3412	784	4	0.6	0.6	NUM
ejpam-3412	784	5	=	=	SYM
ejpam-3412	784	6	min{1	min{1	PROPN
ejpam-3412	784	7	,	,	PUNCT
ejpam-3412	784	8	0.6	0.6	NUM
ejpam-3412	784	9	}	}	PUNCT
ejpam-3412	784	10	=	=	SYM
ejpam-3412	784	11	min{f	min{f	ADJ
ejpam-3412	784	12	f̃[displacement	f̃[displacement	NOUN
ejpam-3412	784	13	]	]	X
ejpam-3412	784	14	(	(	PUNCT
ejpam-3412	784	15	mt	mt	PROPN
ejpam-3412	784	16	)	)	PUNCT
ejpam-3412	784	17	,	,	PUNCT
ejpam-3412	784	18	f	f	PROPN
ejpam-3412	784	19	f̃[displacement	f̃[displacement	PROPN
ejpam-3412	784	20	]	]	X
ejpam-3412	784	21	(	(	PUNCT
ejpam-3412	784	22	fr	fr	NOUN
ejpam-3412	784	23	)	)	PUNCT
ejpam-3412	784	24	}	}	PUNCT
ejpam-3412	784	25	=	=	PUNCT
ejpam-3412	784	26	min{f	min{f	ADJ
ejpam-3412	784	27	f̃[displacement	f̃[displacement	NOUN
ejpam-3412	784	28	]	]	X
ejpam-3412	784	29	(	(	PUNCT
ejpam-3412	784	30	(	(	PUNCT
ejpam-3412	784	31	i	i	NOUN
ejpam-3412	784	32	d	d	PROPN
ejpam-3412	784	33	·	·	PUNCT
ejpam-3412	784	34	fr	fr	PROPN
ejpam-3412	784	35	)	)	PUNCT
ejpam-3412	784	36	·	·	PUNCT
ejpam-3412	785	1	(	(	PUNCT
ejpam-3412	785	2	i	i	NOUN
ejpam-3412	785	3	d	d	PROPN
ejpam-3412	785	4	·	·	PUNCT
ejpam-3412	785	5	i	i	PROPN
ejpam-3412	785	6	d	d	PROPN
ejpam-3412	785	7	)	)	PUNCT
ejpam-3412	785	8	)	)	PUNCT
ejpam-3412	785	9	,	,	PUNCT
ejpam-3412	785	10	f	f	PROPN
ejpam-3412	785	11	f̃[displacement	f̃[displacement	PROPN
ejpam-3412	785	12	]	]	X
ejpam-3412	785	13	(	(	PUNCT
ejpam-3412	785	14	fr	fr	NOUN
ejpam-3412	785	15	)	)	PUNCT
ejpam-3412	785	16	}	}	PUNCT
ejpam-3412	785	17	.	.	PUNCT
ejpam-3412	786	1	hence	hence	ADV
ejpam-3412	786	2	,	,	PUNCT
ejpam-3412	786	3	(	(	PUNCT
ejpam-3412	786	4	f̃	f̃	PROPN
ejpam-3412	786	5	,	,	PUNCT
ejpam-3412	786	6	e	e	NOUN
ejpam-3412	786	7	)	)	PUNCT
ejpam-3412	786	8	is	be	AUX
ejpam-3412	786	9	not	not	PART
ejpam-3412	786	10	a	a	DET
ejpam-3412	786	11	displacement	displacement	NOUN
ejpam-3412	786	12	-	-	PUNCT
ejpam-3412	786	13	fuzzy	fuzzy	NOUN
ejpam-3412	786	14	soft	soft	ADJ
ejpam-3412	786	15	strongly	strongly	ADV
ejpam-3412	786	16	upi	upi	NOUN
ejpam-3412	786	17	-	-	PUNCT
ejpam-3412	786	18	ideal	ideal	NOUN
ejpam-3412	786	19	of	of	ADP
ejpam-3412	786	20	a.	a.	NOUN
ejpam-3412	786	21	the	the	DET
ejpam-3412	786	22	proof	proof	NOUN
ejpam-3412	786	23	of	of	ADP
ejpam-3412	786	24	the	the	DET
ejpam-3412	786	25	following	follow	VERB
ejpam-3412	786	26	theorem	theorem	NOUN
ejpam-3412	786	27	can	can	AUX
ejpam-3412	786	28	be	be	AUX
ejpam-3412	786	29	verified	verify	VERB
ejpam-3412	786	30	easily	easily	ADV
ejpam-3412	786	31	.	.	PUNCT
ejpam-3412	787	1	theorem	theorem	VERB
ejpam-3412	787	2	77	77	NUM
ejpam-3412	787	3	.	.	PUNCT
ejpam-3412	788	1	if	if	SCONJ
ejpam-3412	788	2	(	(	PUNCT
ejpam-3412	788	3	f̃	f̃	PROPN
ejpam-3412	788	4	,	,	PUNCT
ejpam-3412	788	5	e	e	NOUN
ejpam-3412	788	6	)	)	PUNCT
ejpam-3412	788	7	is	be	AUX
ejpam-3412	788	8	a	a	DET
ejpam-3412	788	9	fuzzy	fuzzy	ADJ
ejpam-3412	788	10	soft	soft	ADJ
ejpam-3412	788	11	strongly	strongly	ADV
ejpam-3412	788	12	upi	upi	NOUN
ejpam-3412	788	13	-	-	PUNCT
ejpam-3412	788	14	ideal	ideal	NOUN
ejpam-3412	788	15	of	of	ADP
ejpam-3412	788	16	a	a	PRON
ejpam-3412	788	17	and	and	CCONJ
ejpam-3412	788	18	∅	∅	NOUN
ejpam-3412	788	19	6=	6=	ADP
ejpam-3412	788	20	e∗	e∗	PROPN
ejpam-3412	788	21	⊆	⊆	NUM
ejpam-3412	788	22	e	e	NOUN
ejpam-3412	788	23	,	,	PUNCT
ejpam-3412	788	24	then	then	ADV
ejpam-3412	788	25	(	(	PUNCT
ejpam-3412	788	26	f̃|e∗	f̃|e∗	PROPN
ejpam-3412	788	27	,	,	PUNCT
ejpam-3412	788	28	e∗	e∗	PROPN
ejpam-3412	788	29	)	)	PUNCT
ejpam-3412	788	30	is	be	AUX
ejpam-3412	788	31	a	a	DET
ejpam-3412	788	32	fuzzy	fuzzy	ADJ
ejpam-3412	788	33	soft	soft	ADJ
ejpam-3412	788	34	strongly	strongly	ADV
ejpam-3412	788	35	upi	upi	NOUN
ejpam-3412	788	36	-	-	PUNCT
ejpam-3412	788	37	ideal	ideal	NOUN
ejpam-3412	788	38	of	of	ADP
ejpam-3412	788	39	a.	a.	NOUN
ejpam-3412	788	40	by	by	ADP
ejpam-3412	788	41	using	use	VERB
ejpam-3412	788	42	theorem	theorem	NOUN
ejpam-3412	788	43	6	6	NUM
ejpam-3412	788	44	,	,	PUNCT
ejpam-3412	788	45	we	we	PRON
ejpam-3412	788	46	can	can	AUX
ejpam-3412	788	47	obtain	obtain	VERB
ejpam-3412	788	48	the	the	DET
ejpam-3412	788	49	following	follow	VERB
ejpam-3412	788	50	two	two	NUM
ejpam-3412	788	51	theorems	theorem	NOUN
ejpam-3412	788	52	in	in	ADP
ejpam-3412	788	53	the	the	DET
ejpam-3412	788	54	same	same	ADJ
ejpam-3412	788	55	way	way	NOUN
ejpam-3412	788	56	as	as	ADP
ejpam-3412	788	57	theorems	theorem	NOUN
ejpam-3412	788	58	22	22	NUM
ejpam-3412	788	59	and	and	CCONJ
ejpam-3412	788	60	23	23	NUM
ejpam-3412	788	61	.	.	PUNCT
ejpam-3412	789	1	references	reference	NOUN
ejpam-3412	789	2	329	329	NUM
ejpam-3412	789	3	theorem	theorem	VERB
ejpam-3412	789	4	78	78	NUM
ejpam-3412	789	5	.	.	PUNCT
ejpam-3412	790	1	the	the	DET
ejpam-3412	790	2	extended	extended	ADJ
ejpam-3412	790	3	intersection	intersection	NOUN
ejpam-3412	790	4	of	of	ADP
ejpam-3412	790	5	two	two	NUM
ejpam-3412	790	6	fuzzy	fuzzy	ADJ
ejpam-3412	790	7	soft	soft	ADJ
ejpam-3412	790	8	strongly	strongly	ADV
ejpam-3412	790	9	upi	upi	NOUN
ejpam-3412	790	10	-	-	PUNCT
ejpam-3412	790	11	ideals	ideal	NOUN
ejpam-3412	790	12	of	of	ADP
ejpam-3412	790	13	a	a	PRON
ejpam-3412	790	14	is	be	AUX
ejpam-3412	790	15	also	also	ADV
ejpam-3412	790	16	a	a	DET
ejpam-3412	790	17	fuzzy	fuzzy	ADJ
ejpam-3412	790	18	soft	soft	ADJ
ejpam-3412	790	19	strongly	strongly	ADV
ejpam-3412	790	20	upi	upi	NOUN
ejpam-3412	790	21	-	-	PUNCT
ejpam-3412	790	22	ideal	ideal	NOUN
ejpam-3412	790	23	.	.	PUNCT
ejpam-3412	791	1	moreover	moreover	ADV
ejpam-3412	791	2	,	,	PUNCT
ejpam-3412	791	3	the	the	DET
ejpam-3412	791	4	intersection	intersection	NOUN
ejpam-3412	791	5	of	of	ADP
ejpam-3412	791	6	two	two	NUM
ejpam-3412	791	7	fuzzy	fuzzy	ADJ
ejpam-3412	791	8	soft	soft	ADJ
ejpam-3412	791	9	strongly	strongly	ADV
ejpam-3412	791	10	upi	upi	NOUN
ejpam-3412	791	11	-	-	PUNCT
ejpam-3412	791	12	ideals	ideal	NOUN
ejpam-3412	791	13	of	of	ADP
ejpam-3412	791	14	a	a	PRON
ejpam-3412	791	15	is	be	AUX
ejpam-3412	791	16	also	also	ADV
ejpam-3412	791	17	a	a	DET
ejpam-3412	791	18	fuzzy	fuzzy	ADJ
ejpam-3412	791	19	soft	soft	ADJ
ejpam-3412	791	20	strongly	strongly	ADV
ejpam-3412	791	21	upi	upi	NOUN
ejpam-3412	791	22	-	-	PUNCT
ejpam-3412	791	23	ideal	ideal	NOUN
ejpam-3412	791	24	.	.	PUNCT
ejpam-3412	792	1	theorem	theorem	VERB
ejpam-3412	792	2	79	79	NUM
ejpam-3412	792	3	.	.	PUNCT
ejpam-3412	793	1	the	the	DET
ejpam-3412	793	2	union	union	NOUN
ejpam-3412	793	3	of	of	ADP
ejpam-3412	793	4	two	two	NUM
ejpam-3412	793	5	fuzzy	fuzzy	ADJ
ejpam-3412	793	6	soft	soft	ADJ
ejpam-3412	793	7	strongly	strongly	ADV
ejpam-3412	793	8	upi	upi	NOUN
ejpam-3412	793	9	-	-	PUNCT
ejpam-3412	793	10	ideals	ideal	NOUN
ejpam-3412	793	11	of	of	ADP
ejpam-3412	793	12	a	a	PRON
ejpam-3412	793	13	is	be	AUX
ejpam-3412	793	14	also	also	ADV
ejpam-3412	793	15	a	a	DET
ejpam-3412	793	16	fuzzy	fuzzy	ADJ
ejpam-3412	793	17	soft	soft	ADJ
ejpam-3412	793	18	strongly	strongly	ADV
ejpam-3412	793	19	ups	up	NOUN
ejpam-3412	793	20	-	-	PUNCT
ejpam-3412	793	21	ideal	ideal	NOUN
ejpam-3412	793	22	.	.	PUNCT
ejpam-3412	794	1	moreover	moreover	ADV
ejpam-3412	794	2	,	,	PUNCT
ejpam-3412	794	3	the	the	DET
ejpam-3412	794	4	restricted	restricted	ADJ
ejpam-3412	794	5	union	union	NOUN
ejpam-3412	794	6	of	of	ADP
ejpam-3412	794	7	two	two	NUM
ejpam-3412	794	8	fuzzy	fuzzy	ADJ
ejpam-3412	794	9	soft	soft	ADJ
ejpam-3412	794	10	strongly	strongly	ADV
ejpam-3412	794	11	upi	upi	NOUN
ejpam-3412	794	12	-	-	PUNCT
ejpam-3412	794	13	ideals	ideal	NOUN
ejpam-3412	794	14	of	of	ADP
ejpam-3412	794	15	a	a	PRON
ejpam-3412	794	16	is	be	AUX
ejpam-3412	794	17	also	also	ADV
ejpam-3412	794	18	a	a	DET
ejpam-3412	794	19	fuzzy	fuzzy	ADJ
ejpam-3412	794	20	soft	soft	ADJ
ejpam-3412	794	21	strongly	strongly	ADV
ejpam-3412	794	22	upi	upi	NOUN
ejpam-3412	794	23	-	-	PUNCT
ejpam-3412	794	24	ideal	ideal	NOUN
ejpam-3412	794	25	.	.	PUNCT
ejpam-3412	795	1	4	4	X
ejpam-3412	795	2	.	.	X
ejpam-3412	795	3	conclusions	conclusion	NOUN
ejpam-3412	795	4	in	in	ADP
ejpam-3412	795	5	this	this	DET
ejpam-3412	795	6	paper	paper	NOUN
ejpam-3412	795	7	,	,	PUNCT
ejpam-3412	795	8	we	we	PRON
ejpam-3412	795	9	have	have	AUX
ejpam-3412	795	10	introduced	introduce	VERB
ejpam-3412	795	11	the	the	DET
ejpam-3412	795	12	notions	notion	NOUN
ejpam-3412	795	13	of	of	ADP
ejpam-3412	795	14	fuzzy	fuzzy	ADJ
ejpam-3412	795	15	soft	soft	ADJ
ejpam-3412	795	16	ups	up	NOUN
ejpam-3412	795	17	-	-	PUNCT
ejpam-3412	795	18	subalgebras	subalgebras	X
ejpam-3412	795	19	,	,	PUNCT
ejpam-3412	795	20	fuzzy	fuzzy	ADJ
ejpam-3412	795	21	soft	soft	ADJ
ejpam-3412	795	22	upi	upi	PROPN
ejpam-3412	795	23	-	-	PUNCT
ejpam-3412	795	24	subalgebras	subalgebras	PROPN
ejpam-3412	795	25	,	,	PUNCT
ejpam-3412	795	26	fuzzy	fuzzy	ADJ
ejpam-3412	795	27	soft	soft	ADJ
ejpam-3412	795	28	near	near	ADP
ejpam-3412	795	29	ups	up	NOUN
ejpam-3412	795	30	-	-	PUNCT
ejpam-3412	795	31	filters	filter	NOUN
ejpam-3412	795	32	,	,	PUNCT
ejpam-3412	795	33	fuzzy	fuzzy	ADJ
ejpam-3412	795	34	soft	soft	ADJ
ejpam-3412	795	35	near	near	ADP
ejpam-3412	795	36	upi	upi	NOUN
ejpam-3412	795	37	-	-	PUNCT
ejpam-3412	795	38	filters	filter	NOUN
ejpam-3412	795	39	,	,	PUNCT
ejpam-3412	795	40	fuzzy	fuzzy	ADJ
ejpam-3412	795	41	soft	soft	ADJ
ejpam-3412	795	42	ups	up	NOUN
ejpam-3412	795	43	-	-	PUNCT
ejpam-3412	795	44	filters	filter	NOUN
ejpam-3412	795	45	,	,	PUNCT
ejpam-3412	795	46	fuzzy	fuzzy	ADJ
ejpam-3412	795	47	soft	soft	ADJ
ejpam-3412	795	48	upi	upi	NOUN
ejpam-3412	795	49	-	-	PUNCT
ejpam-3412	795	50	filters	filter	NOUN
ejpam-3412	795	51	,	,	PUNCT
ejpam-3412	795	52	fuzzy	fuzzy	ADJ
ejpam-3412	795	53	soft	soft	ADJ
ejpam-3412	795	54	ups	up	NOUN
ejpam-3412	795	55	-	-	PUNCT
ejpam-3412	795	56	ideals	ideal	NOUN
ejpam-3412	795	57	,	,	PUNCT
ejpam-3412	795	58	fuzzy	fuzzy	ADJ
ejpam-3412	795	59	soft	soft	ADJ
ejpam-3412	795	60	upi	upi	NOUN
ejpam-3412	795	61	-	-	PUNCT
ejpam-3412	795	62	ideals	ideal	NOUN
ejpam-3412	795	63	,	,	PUNCT
ejpam-3412	795	64	fuzzy	fuzzy	ADJ
ejpam-3412	795	65	soft	soft	ADJ
ejpam-3412	795	66	strongly	strongly	ADV
ejpam-3412	795	67	ups	up	NOUN
ejpam-3412	795	68	-	-	PUNCT
ejpam-3412	795	69	ideals	ideal	NOUN
ejpam-3412	795	70	,	,	PUNCT
ejpam-3412	795	71	and	and	CCONJ
ejpam-3412	795	72	fuzzy	fuzzy	ADJ
ejpam-3412	795	73	soft	soft	ADJ
ejpam-3412	795	74	strongly	strongly	ADV
ejpam-3412	795	75	upi	upi	NOUN
ejpam-3412	795	76	-	-	PUNCT
ejpam-3412	795	77	ideals	ideal	NOUN
ejpam-3412	795	78	of	of	ADP
ejpam-3412	795	79	fully	fully	ADV
ejpam-3412	795	80	up	up	ADP
ejpam-3412	795	81	-	-	PUNCT
ejpam-3412	795	82	semigroups	semigroup	NOUN
ejpam-3412	795	83	and	and	CCONJ
ejpam-3412	795	84	the	the	DET
ejpam-3412	795	85	conditions	condition	NOUN
ejpam-3412	795	86	for	for	ADP
ejpam-3412	795	87	fuzzy	fuzzy	ADJ
ejpam-3412	795	88	soft	soft	ADJ
ejpam-3412	795	89	sets	set	NOUN
ejpam-3412	795	90	over	over	ADP
ejpam-3412	795	91	fully	fully	ADV
ejpam-3412	795	92	up	up	ADP
ejpam-3412	795	93	-	-	PUNCT
ejpam-3412	795	94	semigroups	semigroup	NOUN
ejpam-3412	795	95	,	,	PUNCT
ejpam-3412	795	96	proved	prove	VERB
ejpam-3412	795	97	its	its	PRON
ejpam-3412	795	98	generalizations	generalization	NOUN
ejpam-3412	795	99	and	and	CCONJ
ejpam-3412	795	100	investigated	investigate	VERB
ejpam-3412	795	101	some	some	PRON
ejpam-3412	795	102	of	of	ADP
ejpam-3412	795	103	its	its	PRON
ejpam-3412	795	104	important	important	ADJ
ejpam-3412	795	105	properties	property	NOUN
ejpam-3412	795	106	.	.	PUNCT
ejpam-3412	796	1	then	then	ADV
ejpam-3412	796	2	,	,	PUNCT
ejpam-3412	796	3	we	we	PRON
ejpam-3412	796	4	get	get	VERB
ejpam-3412	796	5	the	the	DET
ejpam-3412	796	6	diagram	diagram	NOUN
ejpam-3412	796	7	of	of	ADP
ejpam-3412	796	8	generalization	generalization	NOUN
ejpam-3412	796	9	of	of	ADP
ejpam-3412	796	10	fuzzy	fuzzy	ADJ
ejpam-3412	796	11	soft	soft	ADJ
ejpam-3412	796	12	sets	set	NOUN
ejpam-3412	796	13	over	over	ADP
ejpam-3412	796	14	fully	fully	ADV
ejpam-3412	796	15	up	up	ADP
ejpam-3412	796	16	-	-	PUNCT
ejpam-3412	796	17	semigroups	semigroup	NOUN
ejpam-3412	796	18	as	as	SCONJ
ejpam-3412	796	19	shown	show	VERB
ejpam-3412	796	20	in	in	ADP
ejpam-3412	796	21	figure	figure	NOUN
ejpam-3412	796	22	3	3	NUM
ejpam-3412	796	23	.	.	PUNCT
ejpam-3412	796	24	figure	figure	VERB
ejpam-3412	796	25	3	3	NUM
ejpam-3412	796	26	:	:	PUNCT
ejpam-3412	796	27	fuzzy	fuzzy	ADJ
ejpam-3412	796	28	soft	soft	ADJ
ejpam-3412	796	29	sets	set	NOUN
ejpam-3412	796	30	over	over	ADP
ejpam-3412	796	31	fully	fully	ADV
ejpam-3412	796	32	up	up	ADP
ejpam-3412	796	33	-	-	PUNCT
ejpam-3412	796	34	semigroups	semigroup	NOUN
ejpam-3412	796	35	acknowledgements	acknowledgement	NOUN
ejpam-3412	796	36	the	the	DET
ejpam-3412	796	37	authors	author	NOUN
ejpam-3412	796	38	wish	wish	VERB
ejpam-3412	796	39	to	to	PART
ejpam-3412	796	40	express	express	VERB
ejpam-3412	796	41	their	their	PRON
ejpam-3412	796	42	sincere	sincere	ADJ
ejpam-3412	796	43	thanks	thank	NOUN
ejpam-3412	796	44	to	to	ADP
ejpam-3412	796	45	the	the	DET
ejpam-3412	796	46	referees	referee	NOUN
ejpam-3412	796	47	for	for	ADP
ejpam-3412	796	48	the	the	DET
ejpam-3412	796	49	valuable	valuable	ADJ
ejpam-3412	796	50	suggestions	suggestion	NOUN
ejpam-3412	796	51	which	which	PRON
ejpam-3412	796	52	lead	lead	VERB
ejpam-3412	796	53	to	to	ADP
ejpam-3412	796	54	an	an	DET
ejpam-3412	796	55	improvement	improvement	NOUN
ejpam-3412	796	56	of	of	ADP
ejpam-3412	796	57	this	this	DET
ejpam-3412	796	58	paper	paper	NOUN
ejpam-3412	796	59	.	.	PUNCT
ejpam-3412	797	1	references	reference	NOUN
ejpam-3412	797	2	[	[	X
ejpam-3412	797	3	1	1	NUM
ejpam-3412	797	4	]	]	PUNCT
ejpam-3412	797	5	b.	b.	PROPN
ejpam-3412	797	6	ahmad	ahmad	PROPN
ejpam-3412	797	7	and	and	CCONJ
ejpam-3412	797	8	a.	a.	PROPN
ejpam-3412	797	9	kharal	kharal	PROPN
ejpam-3412	797	10	.	.	PUNCT
ejpam-3412	798	1	on	on	ADP
ejpam-3412	798	2	fuzzy	fuzzy	ADJ
ejpam-3412	798	3	soft	soft	ADJ
ejpam-3412	798	4	sets	set	NOUN
ejpam-3412	798	5	.	.	PUNCT
ejpam-3412	799	1	advances	advance	NOUN
ejpam-3412	799	2	in	in	ADP
ejpam-3412	799	3	fuzzy	fuzzy	ADJ
ejpam-3412	799	4	systems	system	NOUN
ejpam-3412	799	5	,	,	PUNCT
ejpam-3412	799	6	2009	2009	NUM
ejpam-3412	799	7	:	:	PUNCT
ejpam-3412	799	8	article	article	NOUN
ejpam-3412	799	9	i	i	PROPN
ejpam-3412	799	10	d	d	PROPN
ejpam-3412	799	11	586507	586507	NUM
ejpam-3412	799	12	,	,	PUNCT
ejpam-3412	799	13	2009	2009	NUM
ejpam-3412	799	14	.	.	PUNCT
ejpam-3412	800	1	references	reference	NOUN
ejpam-3412	800	2	330	330	NUM
ejpam-3412	800	3	[	[	X
ejpam-3412	800	4	2	2	NUM
ejpam-3412	800	5	]	]	PUNCT
ejpam-3412	800	6	j.	j.	PROPN
ejpam-3412	800	7	c.	c.	PROPN
ejpam-3412	800	8	endam	endam	PROPN
ejpam-3412	800	9	and	and	CCONJ
ejpam-3412	800	10	m.	m.	PROPN
ejpam-3412	800	11	d.	d.	PROPN
ejpam-3412	800	12	manahon	manahon	PROPN
ejpam-3412	800	13	.	.	PUNCT
ejpam-3412	801	1	on	on	ADP
ejpam-3412	801	2	fuzzy	fuzzy	ADJ
ejpam-3412	801	3	jb	jb	PROPN
ejpam-3412	801	4	-	-	PUNCT
ejpam-3412	801	5	semigroups	semigroup	NOUN
ejpam-3412	801	6	.	.	PUNCT
ejpam-3412	802	1	int	int	NOUN
ejpam-3412	802	2	.	.	PUNCT
ejpam-3412	803	1	math	math	NOUN
ejpam-3412	803	2	.	.	PUNCT
ejpam-3412	804	1	forum	forum	PROPN
ejpam-3412	804	2	,	,	PUNCT
ejpam-3412	804	3	11(8):379–386	11(8):379–386	PROPN
ejpam-3412	804	4	,	,	PUNCT
ejpam-3412	804	5	2016	2016	NUM
ejpam-3412	804	6	.	.	PUNCT
ejpam-3412	805	1	[	[	X
ejpam-3412	805	2	3	3	X
ejpam-3412	805	3	]	]	X
ejpam-3412	805	4	j.	j.	PROPN
ejpam-3412	805	5	c.	c.	PROPN
ejpam-3412	805	6	endam	endam	PROPN
ejpam-3412	805	7	and	and	CCONJ
ejpam-3412	805	8	j.	j.	PROPN
ejpam-3412	805	9	p.	p.	PROPN
ejpam-3412	805	10	vilela	vilela	PROPN
ejpam-3412	805	11	.	.	PUNCT
ejpam-3412	806	1	on	on	ADP
ejpam-3412	806	2	jb	jb	PROPN
ejpam-3412	806	3	-	-	PUNCT
ejpam-3412	806	4	semigroups	semigroup	NOUN
ejpam-3412	806	5	.	.	PUNCT
ejpam-3412	807	1	appl	appl	PROPN
ejpam-3412	807	2	.	.	PROPN
ejpam-3412	807	3	math	math	PROPN
ejpam-3412	807	4	.	.	PUNCT
ejpam-3412	808	1	sci	sci	PROPN
ejpam-3412	808	2	.	.	PROPN
ejpam-3412	808	3	,	,	PUNCT
ejpam-3412	808	4	9(59):2901–2911	9(59):2901–2911	NUM
ejpam-3412	808	5	,	,	PUNCT
ejpam-3412	808	6	2015	2015	NUM
ejpam-3412	808	7	.	.	PUNCT
ejpam-3412	809	1	[	[	X
ejpam-3412	809	2	4	4	X
ejpam-3412	809	3	]	]	X
ejpam-3412	809	4	t.	t.	NOUN
ejpam-3412	809	5	guntasow	guntasow	NOUN
ejpam-3412	809	6	,	,	PUNCT
ejpam-3412	809	7	s.	s.	PROPN
ejpam-3412	809	8	sajak	sajak	PROPN
ejpam-3412	809	9	,	,	PUNCT
ejpam-3412	809	10	a.	a.	PROPN
ejpam-3412	809	11	jomkham	jomkham	PROPN
ejpam-3412	809	12	,	,	PUNCT
ejpam-3412	809	13	and	and	CCONJ
ejpam-3412	809	14	a.	a.	NOUN
ejpam-3412	809	15	iampan	iampan	PROPN
ejpam-3412	809	16	.	.	PUNCT
ejpam-3412	810	1	fuzzy	fuzzy	ADJ
ejpam-3412	810	2	translations	translation	NOUN
ejpam-3412	810	3	of	of	ADP
ejpam-3412	810	4	a	a	DET
ejpam-3412	810	5	fuzzy	fuzzy	ADJ
ejpam-3412	810	6	set	set	NOUN
ejpam-3412	810	7	in	in	ADP
ejpam-3412	810	8	up	up	ADP
ejpam-3412	810	9	-	-	PUNCT
ejpam-3412	810	10	algebras	algebras	X
ejpam-3412	810	11	.	.	PUNCT
ejpam-3412	811	1	j.	j.	PROPN
ejpam-3412	811	2	indones	indones	PROPN
ejpam-3412	811	3	.	.	PUNCT
ejpam-3412	812	1	math	math	NOUN
ejpam-3412	812	2	.	.	PUNCT
ejpam-3412	813	1	soc	soc	PROPN
ejpam-3412	813	2	.	.	PROPN
ejpam-3412	813	3	,	,	PUNCT
ejpam-3412	813	4	23(2):1–19	23(2):1–19	NUM
ejpam-3412	813	5	,	,	PUNCT
ejpam-3412	813	6	2017	2017	NUM
ejpam-3412	813	7	.	.	PUNCT
ejpam-3412	814	1	[	[	X
ejpam-3412	814	2	5	5	NUM
ejpam-3412	814	3	]	]	PUNCT
ejpam-3412	814	4	a.	a.	NOUN
ejpam-3412	814	5	iampan	iampan	PROPN
ejpam-3412	814	6	.	.	PUNCT
ejpam-3412	815	1	a	a	DET
ejpam-3412	815	2	new	new	ADJ
ejpam-3412	815	3	branch	branch	NOUN
ejpam-3412	815	4	of	of	ADP
ejpam-3412	815	5	the	the	DET
ejpam-3412	815	6	logical	logical	ADJ
ejpam-3412	815	7	algebra	algebra	NOUN
ejpam-3412	815	8	:	:	PUNCT
ejpam-3412	815	9	up	up	ADP
ejpam-3412	815	10	-	-	PUNCT
ejpam-3412	815	11	algebras	algebras	X
ejpam-3412	815	12	.	.	PUNCT
ejpam-3412	816	1	j.	j.	PROPN
ejpam-3412	816	2	algebra	algebra	PROPN
ejpam-3412	816	3	relat	relat	PROPN
ejpam-3412	816	4	.	.	PUNCT
ejpam-3412	817	1	top	top	PROPN
ejpam-3412	817	2	.	.	PROPN
ejpam-3412	817	3	,	,	PUNCT
ejpam-3412	817	4	5(1):35–54	5(1):35–54	NUM
ejpam-3412	817	5	,	,	PUNCT
ejpam-3412	817	6	2017	2017	NUM
ejpam-3412	817	7	.	.	PUNCT
ejpam-3412	818	1	[	[	X
ejpam-3412	818	2	6	6	NUM
ejpam-3412	818	3	]	]	PUNCT
ejpam-3412	818	4	a.	a.	NOUN
ejpam-3412	818	5	iampan	iampan	PROPN
ejpam-3412	818	6	.	.	PUNCT
ejpam-3412	819	1	introducing	introduce	VERB
ejpam-3412	819	2	fully	fully	ADV
ejpam-3412	819	3	up	up	ADP
ejpam-3412	819	4	-	-	PUNCT
ejpam-3412	819	5	semigroups	semigroup	NOUN
ejpam-3412	819	6	.	.	PUNCT
ejpam-3412	820	1	discuss	discuss	PROPN
ejpam-3412	820	2	.	.	PUNCT
ejpam-3412	820	3	math	math	PROPN
ejpam-3412	820	4	.	.	PUNCT
ejpam-3412	820	5	,	,	PUNCT
ejpam-3412	821	1	gen	gen	PROPN
ejpam-3412	821	2	.	.	PROPN
ejpam-3412	821	3	algebra	algebra	PROPN
ejpam-3412	821	4	appl	appl	PROPN
ejpam-3412	821	5	.	.	PROPN
ejpam-3412	821	6	,	,	PUNCT
ejpam-3412	821	7	38(2):297–306	38(2):297–306	NUM
ejpam-3412	821	8	,	,	PUNCT
ejpam-3412	821	9	2018	2018	NUM
ejpam-3412	821	10	.	.	PUNCT
ejpam-3412	822	1	[	[	X
ejpam-3412	822	2	7	7	NUM
ejpam-3412	822	3	]	]	PUNCT
ejpam-3412	822	4	a.	a.	NOUN
ejpam-3412	822	5	iampan	iampan	PROPN
ejpam-3412	822	6	.	.	PUNCT
ejpam-3412	823	1	multipliers	multiplier	NOUN
ejpam-3412	823	2	and	and	CCONJ
ejpam-3412	823	3	near	near	ADP
ejpam-3412	823	4	up	up	ADP
ejpam-3412	823	5	-	-	PUNCT
ejpam-3412	823	6	filters	filter	NOUN
ejpam-3412	823	7	of	of	ADP
ejpam-3412	823	8	up	up	ADP
ejpam-3412	823	9	-	-	PUNCT
ejpam-3412	823	10	algebras	algebras	X
ejpam-3412	823	11	.	.	PUNCT
ejpam-3412	824	1	manuscript	manuscript	NOUN
ejpam-3412	824	2	submitted	submit	VERB
ejpam-3412	824	3	for	for	ADP
ejpam-3412	824	4	publication	publication	NOUN
ejpam-3412	824	5	,	,	PUNCT
ejpam-3412	824	6	september	september	PROPN
ejpam-3412	824	7	2018	2018	NUM
ejpam-3412	824	8	.	.	PUNCT
ejpam-3412	825	1	[	[	X
ejpam-3412	825	2	8	8	NUM
ejpam-3412	825	3	]	]	X
ejpam-3412	825	4	z.	z.	PROPN
ejpam-3412	825	5	jianming	jianming	PROPN
ejpam-3412	825	6	and	and	CCONJ
ejpam-3412	825	7	x.	x.	NOUN
ejpam-3412	825	8	dajing	dajing	PROPN
ejpam-3412	825	9	.	.	PUNCT
ejpam-3412	826	1	intuitionistic	intuitionistic	ADJ
ejpam-3412	826	2	fuzzy	fuzzy	ADJ
ejpam-3412	826	3	associative	associative	NOUN
ejpam-3412	826	4	i	i	NOUN
ejpam-3412	826	5	-	-	PUNCT
ejpam-3412	826	6	ideals	ideal	NOUN
ejpam-3412	826	7	of	of	ADP
ejpam-3412	826	8	is	is	NOUN
ejpam-3412	826	9	-	-	PUNCT
ejpam-3412	826	10	algebras	algebra	NOUN
ejpam-3412	826	11	.	.	PUNCT
ejpam-3412	827	1	sci	sci	PROPN
ejpam-3412	827	2	.	.	PROPN
ejpam-3412	827	3	math	math	PROPN
ejpam-3412	827	4	.	.	PUNCT
ejpam-3412	828	1	jpn	jpn	PROPN
ejpam-3412	828	2	.	.	PROPN
ejpam-3412	829	1	online	online	PROPN
ejpam-3412	829	2	,	,	PUNCT
ejpam-3412	829	3	10:93–98	10:93–98	NUM
ejpam-3412	829	4	,	,	PUNCT
ejpam-3412	829	5	2004	2004	NUM
ejpam-3412	829	6	.	.	PUNCT
ejpam-3412	830	1	[	[	X
ejpam-3412	830	2	9	9	NUM
ejpam-3412	830	3	]	]	X
ejpam-3412	830	4	y.	y.	PROPN
ejpam-3412	830	5	b.	b.	PROPN
ejpam-3412	830	6	jun	jun	PROPN
ejpam-3412	830	7	,	,	PUNCT
ejpam-3412	830	8	s.	s.	PROPN
ejpam-3412	830	9	s.	s.	PROPN
ejpam-3412	830	10	ahn	ahn	PROPN
ejpam-3412	830	11	,	,	PUNCT
ejpam-3412	830	12	j.	j.	PROPN
ejpam-3412	830	13	y.	y.	PROPN
ejpam-3412	830	14	kim	kim	PROPN
ejpam-3412	830	15	,	,	PUNCT
ejpam-3412	830	16	and	and	CCONJ
ejpam-3412	830	17	h.	h.	PROPN
ejpam-3412	830	18	s.	s.	PROPN
ejpam-3412	830	19	kim	kim	PROPN
ejpam-3412	830	20	.	.	PUNCT
ejpam-3412	831	1	fuzzy	fuzzy	PROPN
ejpam-3412	832	1	i	i	PRON
ejpam-3412	832	2	-	-	PUNCT
ejpam-3412	832	3	ideals	ideal	NOUN
ejpam-3412	832	4	in	in	ADP
ejpam-3412	832	5	bci	bci	NOUN
ejpam-3412	832	6	-	-	PUNCT
ejpam-3412	832	7	semigroups	semigroup	NOUN
ejpam-3412	832	8	.	.	PUNCT
ejpam-3412	833	1	southeast	southeast	ADJ
ejpam-3412	833	2	asian	asian	ADJ
ejpam-3412	833	3	bull	bull	PROPN
ejpam-3412	833	4	.	.	PUNCT
ejpam-3412	834	1	math	math	NOUN
ejpam-3412	834	2	.	.	PUNCT
ejpam-3412	834	3	,	,	PUNCT
ejpam-3412	834	4	2:147–153	2:147–153	NUM
ejpam-3412	834	5	,	,	PUNCT
ejpam-3412	834	6	1998	1998	NUM
ejpam-3412	834	7	.	.	PUNCT
ejpam-3412	835	1	[	[	X
ejpam-3412	835	2	10	10	NUM
ejpam-3412	835	3	]	]	X
ejpam-3412	835	4	y.	y.	PROPN
ejpam-3412	835	5	b.	b.	PROPN
ejpam-3412	835	6	jun	jun	PROPN
ejpam-3412	835	7	,	,	PUNCT
ejpam-3412	835	8	s.	s.	PROPN
ejpam-3412	835	9	m.	m.	PROPN
ejpam-3412	835	10	hong	hong	PROPN
ejpam-3412	835	11	,	,	PUNCT
ejpam-3412	835	12	and	and	CCONJ
ejpam-3412	835	13	e.	e.	PROPN
ejpam-3412	835	14	h.	h.	PROPN
ejpam-3412	835	15	roh	roh	PROPN
ejpam-3412	835	16	.	.	PUNCT
ejpam-3412	836	1	bci	bci	NOUN
ejpam-3412	836	2	-	-	PUNCT
ejpam-3412	836	3	semigroups	semigroup	NOUN
ejpam-3412	836	4	.	.	PUNCT
ejpam-3412	837	1	honam	honam	PROPN
ejpam-3412	837	2	math	math	PROPN
ejpam-3412	837	3	.	.	PUNCT
ejpam-3412	838	1	j.	j.	PROPN
ejpam-3412	838	2	,	,	PUNCT
ejpam-3412	838	3	15(1):59	15(1):59	NUM
ejpam-3412	838	4	–	–	PUNCT
ejpam-3412	838	5	64	64	NUM
ejpam-3412	838	6	,	,	PUNCT
ejpam-3412	838	7	1993	1993	NUM
ejpam-3412	838	8	.	.	PUNCT
ejpam-3412	839	1	[	[	X
ejpam-3412	839	2	11	11	NUM
ejpam-3412	839	3	]	]	X
ejpam-3412	839	4	y.	y.	PROPN
ejpam-3412	839	5	b.	b.	PROPN
ejpam-3412	839	6	jun	jun	PROPN
ejpam-3412	839	7	and	and	CCONJ
ejpam-3412	839	8	m.	m.	PROPN
ejpam-3412	839	9	kondo	kondo	PROPN
ejpam-3412	839	10	.	.	PUNCT
ejpam-3412	840	1	on	on	ADP
ejpam-3412	840	2	transfer	transfer	NOUN
ejpam-3412	840	3	principle	principle	NOUN
ejpam-3412	840	4	of	of	ADP
ejpam-3412	840	5	fuzzy	fuzzy	ADJ
ejpam-3412	840	6	bck	bck	PROPN
ejpam-3412	840	7	/	/	SYM
ejpam-3412	840	8	bci	bci	NOUN
ejpam-3412	840	9	-	-	PUNCT
ejpam-3412	840	10	algebras	algebra	NOUN
ejpam-3412	840	11	.	.	PUNCT
ejpam-3412	841	1	sci	sci	PROPN
ejpam-3412	841	2	.	.	PROPN
ejpam-3412	841	3	math	math	PROPN
ejpam-3412	841	4	.	.	PUNCT
ejpam-3412	842	1	jpn	jpn	PROPN
ejpam-3412	842	2	.	.	PROPN
ejpam-3412	843	1	online	online	PROPN
ejpam-3412	843	2	,	,	PUNCT
ejpam-3412	843	3	9:95–100	9:95–100	NUM
ejpam-3412	843	4	,	,	PUNCT
ejpam-3412	843	5	2003	2003	NUM
ejpam-3412	843	6	.	.	PUNCT
ejpam-3412	844	1	[	[	X
ejpam-3412	844	2	12	12	NUM
ejpam-3412	844	3	]	]	X
ejpam-3412	844	4	y.	y.	PROPN
ejpam-3412	844	5	b.	b.	PROPN
ejpam-3412	844	6	jun	jun	PROPN
ejpam-3412	844	7	,	,	PUNCT
ejpam-3412	844	8	k.	k.	PROPN
ejpam-3412	844	9	j.	j.	PROPN
ejpam-3412	844	10	lee	lee	PROPN
ejpam-3412	844	11	,	,	PUNCT
ejpam-3412	844	12	and	and	CCONJ
ejpam-3412	844	13	c.	c.	PROPN
ejpam-3412	844	14	h.	h.	PROPN
ejpam-3412	844	15	park	park	PROPN
ejpam-3412	844	16	.	.	PUNCT
ejpam-3412	845	1	fuzzy	fuzzy	ADJ
ejpam-3412	845	2	soft	soft	ADJ
ejpam-3412	845	3	set	set	NOUN
ejpam-3412	845	4	theory	theory	NOUN
ejpam-3412	845	5	applied	apply	VERB
ejpam-3412	845	6	to	to	PART
ejpam-3412	845	7	bck	bck	VERB
ejpam-3412	845	8	/	/	SYM
ejpam-3412	845	9	bcialgebras	bcialgebra	NOUN
ejpam-3412	845	10	.	.	PUNCT
ejpam-3412	846	1	comput	comput	NOUN
ejpam-3412	846	2	.	.	PUNCT
ejpam-3412	847	1	math	math	NOUN
ejpam-3412	847	2	.	.	PUNCT
ejpam-3412	848	1	appl	appl	PROPN
ejpam-3412	848	2	.	.	PROPN
ejpam-3412	848	3	,	,	PUNCT
ejpam-3412	848	4	59:3180–3192	59:3180–3192	NUM
ejpam-3412	848	5	,	,	PUNCT
ejpam-3412	848	6	2010	2010	NUM
ejpam-3412	848	7	.	.	PUNCT
ejpam-3412	849	1	[	[	X
ejpam-3412	849	2	13	13	NUM
ejpam-3412	849	3	]	]	X
ejpam-3412	849	4	y.	y.	PROPN
ejpam-3412	849	5	b.	b.	PROPN
ejpam-3412	849	6	jun	jun	PROPN
ejpam-3412	849	7	,	,	PUNCT
ejpam-3412	849	8	x.	x.	PROPN
ejpam-3412	849	9	l.	l.	PROPN
ejpam-3412	849	10	xin	xin	PROPN
ejpam-3412	849	11	,	,	PUNCT
ejpam-3412	849	12	and	and	CCONJ
ejpam-3412	849	13	e.	e.	PROPN
ejpam-3412	849	14	h.	h.	PROPN
ejpam-3412	849	15	roh	roh	PROPN
ejpam-3412	849	16	.	.	PUNCT
ejpam-3412	850	1	a	a	DET
ejpam-3412	850	2	class	class	NOUN
ejpam-3412	850	3	of	of	ADP
ejpam-3412	850	4	algebras	algebras	PROPN
ejpam-3412	850	5	related	relate	VERB
ejpam-3412	850	6	to	to	ADP
ejpam-3412	850	7	bci	bci	NOUN
ejpam-3412	850	8	-	-	PUNCT
ejpam-3412	850	9	algebras	algebra	NOUN
ejpam-3412	850	10	and	and	CCONJ
ejpam-3412	850	11	semigroups	semigroup	NOUN
ejpam-3412	850	12	.	.	PUNCT
ejpam-3412	851	1	soochow	soochow	PROPN
ejpam-3412	851	2	j.	j.	PROPN
ejpam-3412	851	3	math	math	PROPN
ejpam-3412	851	4	.	.	PUNCT
ejpam-3412	852	1	,	,	PUNCT
ejpam-3412	852	2	24(4):309–321	24(4):309–321	NUM
ejpam-3412	852	3	,	,	PUNCT
ejpam-3412	852	4	1998	1998	NUM
ejpam-3412	852	5	.	.	PUNCT
ejpam-3412	853	1	[	[	X
ejpam-3412	853	2	14	14	NUM
ejpam-3412	853	3	]	]	PUNCT
ejpam-3412	853	4	k.	k.	PROPN
ejpam-3412	853	5	h.	h.	PROPN
ejpam-3412	853	6	kim	kim	PROPN
ejpam-3412	853	7	.	.	PUNCT
ejpam-3412	854	1	on	on	ADP
ejpam-3412	854	2	structure	structure	NOUN
ejpam-3412	854	3	of	of	ADP
ejpam-3412	854	4	ks	ks	NOUN
ejpam-3412	854	5	-	-	PUNCT
ejpam-3412	854	6	semigroups	semigroup	NOUN
ejpam-3412	854	7	.	.	PUNCT
ejpam-3412	855	1	int	int	NOUN
ejpam-3412	855	2	.	.	PUNCT
ejpam-3412	856	1	math	math	NOUN
ejpam-3412	856	2	.	.	PUNCT
ejpam-3412	857	1	forum	forum	PROPN
ejpam-3412	857	2	,	,	PUNCT
ejpam-3412	857	3	1(2):67–76	1(2):67–76	NUM
ejpam-3412	857	4	,	,	PUNCT
ejpam-3412	857	5	2006	2006	NUM
ejpam-3412	857	6	.	.	PUNCT
ejpam-3412	858	1	[	[	X
ejpam-3412	858	2	15	15	NUM
ejpam-3412	858	3	]	]	X
ejpam-3412	858	4	n.	n.	PROPN
ejpam-3412	858	5	kuroki	kuroki	PROPN
ejpam-3412	858	6	.	.	PUNCT
ejpam-3412	859	1	on	on	ADP
ejpam-3412	859	2	fuzzy	fuzzy	ADJ
ejpam-3412	859	3	semigroups	semigroup	NOUN
ejpam-3412	859	4	.	.	PUNCT
ejpam-3412	859	5	inf	inf	PROPN
ejpam-3412	859	6	.	.	PUNCT
ejpam-3412	860	1	sci	sci	PROPN
ejpam-3412	860	2	.	.	PROPN
ejpam-3412	860	3	,	,	PUNCT
ejpam-3412	860	4	53:203–236	53:203–236	NUM
ejpam-3412	860	5	,	,	PUNCT
ejpam-3412	860	6	1991	1991	NUM
ejpam-3412	860	7	.	.	PUNCT
ejpam-3412	861	1	[	[	X
ejpam-3412	861	2	16	16	NUM
ejpam-3412	861	3	]	]	PUNCT
ejpam-3412	861	4	k.	k.	PROPN
ejpam-3412	861	5	h.	h.	PROPN
ejpam-3412	861	6	lee	lee	PROPN
ejpam-3412	861	7	.	.	PUNCT
ejpam-3412	862	1	first	first	ADJ
ejpam-3412	862	2	course	course	NOUN
ejpam-3412	862	3	on	on	ADP
ejpam-3412	862	4	fuzzy	fuzzy	ADJ
ejpam-3412	862	5	theory	theory	NOUN
ejpam-3412	862	6	and	and	CCONJ
ejpam-3412	862	7	applications	application	NOUN
ejpam-3412	862	8	.	.	PUNCT
ejpam-3412	863	1	springer	springer	NOUN
ejpam-3412	863	2	-	-	PUNCT
ejpam-3412	863	3	verlag	verlag	PROPN
ejpam-3412	863	4	berlin	berlin	PROPN
ejpam-3412	863	5	heidelberg	heidelberg	PROPN
ejpam-3412	863	6	,	,	PUNCT
ejpam-3412	863	7	republic	republic	NOUN
ejpam-3412	863	8	of	of	ADP
ejpam-3412	863	9	south	south	PROPN
ejpam-3412	863	10	korea	korea	PROPN
ejpam-3412	863	11	,	,	PUNCT
ejpam-3412	863	12	2005	2005	NUM
ejpam-3412	863	13	.	.	PUNCT
ejpam-3412	864	1	[	[	X
ejpam-3412	864	2	17	17	NUM
ejpam-3412	864	3	]	]	PUNCT
ejpam-3412	864	4	p.	p.	PROPN
ejpam-3412	864	5	k.	k.	PROPN
ejpam-3412	865	1	maji	maji	PROPN
ejpam-3412	865	2	,	,	PUNCT
ejpam-3412	865	3	r.	r.	PROPN
ejpam-3412	865	4	biswas	biswas	PROPN
ejpam-3412	865	5	,	,	PUNCT
ejpam-3412	865	6	and	and	CCONJ
ejpam-3412	866	1	a.	a.	PROPN
ejpam-3412	866	2	r.	r.	PROPN
ejpam-3412	866	3	roy	roy	PROPN
ejpam-3412	866	4	.	.	PROPN
ejpam-3412	866	5	fuzzy	fuzzy	ADJ
ejpam-3412	866	6	soft	soft	ADJ
ejpam-3412	866	7	sets	set	NOUN
ejpam-3412	866	8	.	.	PUNCT
ejpam-3412	867	1	j.	j.	PROPN
ejpam-3412	867	2	fuzzy	fuzzy	PROPN
ejpam-3412	867	3	math	math	PROPN
ejpam-3412	867	4	.	.	PUNCT
ejpam-3412	867	5	,	,	PUNCT
ejpam-3412	867	6	9(3):589–602	9(3):589–602	NOUN
ejpam-3412	867	7	,	,	PUNCT
ejpam-3412	867	8	2001	2001	NUM
ejpam-3412	867	9	.	.	PUNCT
ejpam-3412	868	1	[	[	X
ejpam-3412	868	2	18	18	NUM
ejpam-3412	868	3	]	]	X
ejpam-3412	868	4	d.	d.	PROPN
ejpam-3412	868	5	molodtsov	molodtsov	PROPN
ejpam-3412	868	6	.	.	PUNCT
ejpam-3412	869	1	soft	soft	ADJ
ejpam-3412	869	2	set	set	NOUN
ejpam-3412	869	3	theory	theory	NOUN
ejpam-3412	869	4	-	-	PUNCT
ejpam-3412	869	5	first	first	ADJ
ejpam-3412	869	6	results	result	NOUN
ejpam-3412	869	7	.	.	PUNCT
ejpam-3412	870	1	comput	comput	NOUN
ejpam-3412	870	2	.	.	PUNCT
ejpam-3412	871	1	math	math	NOUN
ejpam-3412	871	2	.	.	PUNCT
ejpam-3412	872	1	appl	appl	PROPN
ejpam-3412	872	2	.	.	PROPN
ejpam-3412	872	3	,	,	PUNCT
ejpam-3412	872	4	37:19–31	37:19–31	PROPN
ejpam-3412	872	5	,	,	PUNCT
ejpam-3412	872	6	1999	1999	NUM
ejpam-3412	872	7	.	.	PUNCT
ejpam-3412	873	1	references	reference	NOUN
ejpam-3412	873	2	331	331	NUM
ejpam-3412	874	1	[	[	X
ejpam-3412	874	2	19	19	NUM
ejpam-3412	874	3	]	]	PUNCT
ejpam-3412	874	4	c.	c.	NOUN
ejpam-3412	874	5	prabpayak	prabpayak	NOUN
ejpam-3412	874	6	and	and	CCONJ
ejpam-3412	874	7	u.	u.	NOUN
ejpam-3412	874	8	leerawat	leerawat	PROPN
ejpam-3412	874	9	.	.	PUNCT
ejpam-3412	875	1	on	on	ADP
ejpam-3412	875	2	ideals	ideal	NOUN
ejpam-3412	875	3	and	and	CCONJ
ejpam-3412	875	4	congruences	congruence	NOUN
ejpam-3412	875	5	in	in	ADP
ejpam-3412	875	6	ku	ku	PROPN
ejpam-3412	875	7	-	-	PUNCT
ejpam-3412	875	8	algebras	algebras	PROPN
ejpam-3412	875	9	.	.	PUNCT
ejpam-3412	876	1	sci	sci	PROPN
ejpam-3412	876	2	.	.	PROPN
ejpam-3412	876	3	magna	magna	PROPN
ejpam-3412	876	4	,	,	PUNCT
ejpam-3412	876	5	5(1):54–57	5(1):54–57	NUM
ejpam-3412	876	6	,	,	PUNCT
ejpam-3412	876	7	2009	2009	NUM
ejpam-3412	876	8	.	.	PUNCT
ejpam-3412	877	1	[	[	X
ejpam-3412	877	2	20	20	NUM
ejpam-3412	877	3	]	]	PUNCT
ejpam-3412	877	4	a.	a.	NOUN
ejpam-3412	877	5	rehman	rehman	PROPN
ejpam-3412	877	6	,	,	PUNCT
ejpam-3412	877	7	s.	s.	PROPN
ejpam-3412	877	8	abdullah	abdullah	PROPN
ejpam-3412	877	9	,	,	PUNCT
ejpam-3412	877	10	m.	m.	NOUN
ejpam-3412	877	11	aslam	aslam	PROPN
ejpam-3412	877	12	,	,	PUNCT
ejpam-3412	877	13	and	and	CCONJ
ejpam-3412	877	14	m.	m.	PROPN
ejpam-3412	877	15	s.	s.	PROPN
ejpam-3412	877	16	kamran	kamran	PROPN
ejpam-3412	877	17	.	.	PUNCT
ejpam-3412	878	1	a	a	DET
ejpam-3412	878	2	study	study	NOUN
ejpam-3412	878	3	on	on	ADP
ejpam-3412	878	4	fuzzy	fuzzy	ADJ
ejpam-3412	878	5	soft	soft	ADJ
ejpam-3412	878	6	set	set	NOUN
ejpam-3412	878	7	and	and	CCONJ
ejpam-3412	878	8	its	its	PRON
ejpam-3412	878	9	operations	operation	NOUN
ejpam-3412	878	10	.	.	PUNCT
ejpam-3412	879	1	ann	ann	PROPN
ejpam-3412	879	2	.	.	PUNCT
ejpam-3412	879	3	fuzzy	fuzzy	ADJ
ejpam-3412	879	4	math	math	NOUN
ejpam-3412	879	5	.	.	PUNCT
ejpam-3412	880	1	inform	inform	NOUN
ejpam-3412	880	2	.	.	PUNCT
ejpam-3412	880	3	,	,	PUNCT
ejpam-3412	880	4	6(2):339–362	6(2):339–362	NUM
ejpam-3412	880	5	,	,	PUNCT
ejpam-3412	880	6	2013	2013	NUM
ejpam-3412	880	7	.	.	PUNCT
ejpam-3412	881	1	[	[	X
ejpam-3412	881	2	21	21	NUM
ejpam-3412	881	3	]	]	X
ejpam-3412	881	4	e.	e.	PROPN
ejpam-3412	881	5	h.	h.	PROPN
ejpam-3412	881	6	roh	roh	PROPN
ejpam-3412	881	7	,	,	PUNCT
ejpam-3412	881	8	y.	y.	PROPN
ejpam-3412	881	9	b.	b.	PROPN
ejpam-3412	881	10	jun	jun	PROPN
ejpam-3412	881	11	,	,	PUNCT
ejpam-3412	881	12	and	and	CCONJ
ejpam-3412	881	13	w.	w.	PROPN
ejpam-3412	881	14	h.	h.	PROPN
ejpam-3412	881	15	shim	shim	PROPN
ejpam-3412	881	16	.	.	PUNCT
ejpam-3412	882	1	fuzzy	fuzzy	ADJ
ejpam-3412	882	2	associative	associative	NOUN
ejpam-3412	882	3	i	i	PRON
ejpam-3412	882	4	-	-	PUNCT
ejpam-3412	882	5	ideals	ideal	NOUN
ejpam-3412	882	6	of	of	ADP
ejpam-3412	882	7	is	is	NOUN
ejpam-3412	882	8	-	-	PUNCT
ejpam-3412	882	9	algebras	algebras	X
ejpam-3412	882	10	.	.	PUNCT
ejpam-3412	883	1	int	int	NOUN
ejpam-3412	883	2	.	.	PUNCT
ejpam-3412	884	1	j.	j.	PROPN
ejpam-3412	884	2	math	math	PROPN
ejpam-3412	884	3	.	.	PUNCT
ejpam-3412	885	1	math	math	NOUN
ejpam-3412	885	2	.	.	PUNCT
ejpam-3412	886	1	sci	sci	PROPN
ejpam-3412	886	2	.	.	PROPN
ejpam-3412	886	3	,	,	PUNCT
ejpam-3412	886	4	24(11):729–735	24(11):729–735	NUM
ejpam-3412	886	5	,	,	PUNCT
ejpam-3412	886	6	2000	2000	NUM
ejpam-3412	886	7	.	.	PUNCT
ejpam-3412	887	1	[	[	X
ejpam-3412	887	2	22	22	NUM
ejpam-3412	887	3	]	]	PUNCT
ejpam-3412	887	4	a.	a.	PROPN
ejpam-3412	887	5	rosenfeld	rosenfeld	PROPN
ejpam-3412	887	6	.	.	PUNCT
ejpam-3412	888	1	fuuzy	fuuzy	VERB
ejpam-3412	888	2	groups	group	NOUN
ejpam-3412	888	3	.	.	PUNCT
ejpam-3412	889	1	j.	j.	PROPN
ejpam-3412	889	2	math	math	PROPN
ejpam-3412	889	3	,	,	PUNCT
ejpam-3412	889	4	anal	anal	PROPN
ejpam-3412	889	5	.	.	PUNCT
ejpam-3412	890	1	appl	appl	PROPN
ejpam-3412	890	2	.	.	PROPN
ejpam-3412	890	3	,	,	PUNCT
ejpam-3412	890	4	35:512–517	35:512–517	PROPN
ejpam-3412	890	5	,	,	PUNCT
ejpam-3412	890	6	1971	1971	NUM
ejpam-3412	890	7	.	.	PUNCT
ejpam-3412	891	1	[	[	X
ejpam-3412	891	2	23	23	NUM
ejpam-3412	891	3	]	]	PUNCT
ejpam-3412	891	4	a.	a.	NOUN
ejpam-3412	891	5	satirad	satirad	PROPN
ejpam-3412	891	6	and	and	CCONJ
ejpam-3412	891	7	a.	a.	NOUN
ejpam-3412	891	8	iampan	iampan	PROPN
ejpam-3412	891	9	.	.	PUNCT
ejpam-3412	892	1	fuzzy	fuzzy	ADJ
ejpam-3412	892	2	sets	set	NOUN
ejpam-3412	892	3	in	in	ADP
ejpam-3412	892	4	fully	fully	ADV
ejpam-3412	892	5	up	up	ADP
ejpam-3412	892	6	-	-	PUNCT
ejpam-3412	892	7	semigroups	semigroup	NOUN
ejpam-3412	892	8	.	.	PUNCT
ejpam-3412	893	1	manuscript	manuscript	NOUN
ejpam-3412	893	2	accepted	accept	VERB
ejpam-3412	893	3	for	for	ADP
ejpam-3412	893	4	publication	publication	NOUN
ejpam-3412	893	5	in	in	ADP
ejpam-3412	893	6	ital	ital	PROPN
ejpam-3412	893	7	.	.	PUNCT
ejpam-3412	894	1	j.	j.	PROPN
ejpam-3412	894	2	pure	pure	PROPN
ejpam-3412	894	3	appl	appl	PROPN
ejpam-3412	894	4	.	.	PUNCT
ejpam-3412	894	5	math	math	PROPN
ejpam-3412	894	6	.	.	PUNCT
ejpam-3412	894	7	,	,	PUNCT
ejpam-3412	894	8	july	july	PROPN
ejpam-3412	894	9	2018	2018	NUM
ejpam-3412	894	10	.	.	PUNCT
ejpam-3412	895	1	[	[	X
ejpam-3412	895	2	24	24	NUM
ejpam-3412	895	3	]	]	PUNCT
ejpam-3412	895	4	a.	a.	NOUN
ejpam-3412	895	5	satirad	satirad	PROPN
ejpam-3412	895	6	,	,	PUNCT
ejpam-3412	895	7	p.	p.	PROPN
ejpam-3412	895	8	mosrijai	mosrijai	PROPN
ejpam-3412	895	9	,	,	PUNCT
ejpam-3412	895	10	and	and	CCONJ
ejpam-3412	895	11	a.	a.	NOUN
ejpam-3412	895	12	iampan	iampan	PROPN
ejpam-3412	895	13	.	.	PUNCT
ejpam-3412	896	1	generalized	generalized	ADJ
ejpam-3412	896	2	power	power	NOUN
ejpam-3412	896	3	up	up	ADP
ejpam-3412	896	4	-	-	PUNCT
ejpam-3412	896	5	algebras	algebras	PROPN
ejpam-3412	896	6	.	.	PUNCT
ejpam-3412	897	1	int	int	NOUN
ejpam-3412	897	2	.	.	PUNCT
ejpam-3412	898	1	j.	j.	PROPN
ejpam-3412	898	2	math	math	PROPN
ejpam-3412	898	3	.	.	PUNCT
ejpam-3412	899	1	comput	comput	NOUN
ejpam-3412	899	2	.	.	PUNCT
ejpam-3412	900	1	sci	sci	PROPN
ejpam-3412	900	2	.	.	PROPN
ejpam-3412	900	3	,	,	PUNCT
ejpam-3412	900	4	14(1):17–25	14(1):17–25	NUM
ejpam-3412	900	5	,	,	PUNCT
ejpam-3412	900	6	2019	2019	NUM
ejpam-3412	900	7	.	.	PUNCT
ejpam-3412	901	1	[	[	X
ejpam-3412	901	2	25	25	NUM
ejpam-3412	901	3	]	]	PUNCT
ejpam-3412	901	4	j.	j.	PROPN
ejpam-3412	901	5	somjanta	somjanta	PROPN
ejpam-3412	901	6	,	,	PUNCT
ejpam-3412	901	7	n.	n.	PROPN
ejpam-3412	901	8	thuekaew	thuekaew	PROPN
ejpam-3412	901	9	,	,	PUNCT
ejpam-3412	901	10	p.	p.	NOUN
ejpam-3412	901	11	kumpeangkeaw	kumpeangkeaw	PROPN
ejpam-3412	901	12	,	,	PUNCT
ejpam-3412	901	13	and	and	CCONJ
ejpam-3412	901	14	a.	a.	NOUN
ejpam-3412	901	15	iampan	iampan	PROPN
ejpam-3412	901	16	.	.	PUNCT
ejpam-3412	902	1	fuzzy	fuzzy	ADJ
ejpam-3412	902	2	sets	set	NOUN
ejpam-3412	902	3	in	in	ADP
ejpam-3412	902	4	upalgebras	upalgebra	NOUN
ejpam-3412	902	5	.	.	PUNCT
ejpam-3412	903	1	ann	ann	PROPN
ejpam-3412	903	2	.	.	PUNCT
ejpam-3412	903	3	fuzzy	fuzzy	ADJ
ejpam-3412	903	4	math	math	NOUN
ejpam-3412	903	5	.	.	PUNCT
ejpam-3412	904	1	inform	inform	NOUN
ejpam-3412	904	2	.	.	PUNCT
ejpam-3412	904	3	,	,	PUNCT
ejpam-3412	904	4	12(6):739–756	12(6):739–756	PROPN
ejpam-3412	904	5	,	,	PUNCT
ejpam-3412	904	6	2016	2016	NUM
ejpam-3412	904	7	.	.	PUNCT
ejpam-3412	905	1	[	[	X
ejpam-3412	905	2	26	26	NUM
ejpam-3412	905	3	]	]	X
ejpam-3412	905	4	d.	d.	PROPN
ejpam-3412	905	5	r.	r.	PROPN
ejpam-3412	905	6	prince	prince	PROPN
ejpam-3412	905	7	williams	williams	PROPN
ejpam-3412	905	8	and	and	CCONJ
ejpam-3412	905	9	s.	s.	PROPN
ejpam-3412	905	10	husain	husain	PROPN
ejpam-3412	905	11	.	.	PUNCT
ejpam-3412	906	1	on	on	ADP
ejpam-3412	906	2	fuzzy	fuzzy	ADJ
ejpam-3412	906	3	ks	ks	NOUN
ejpam-3412	906	4	-	-	PUNCT
ejpam-3412	906	5	semigroups	semigroup	NOUN
ejpam-3412	906	6	.	.	PUNCT
ejpam-3412	907	1	int	int	NOUN
ejpam-3412	907	2	.	.	PUNCT
ejpam-3412	908	1	math	math	NOUN
ejpam-3412	908	2	.	.	PUNCT
ejpam-3412	909	1	forum	forum	PROPN
ejpam-3412	909	2	,	,	PUNCT
ejpam-3412	909	3	2(32):1577–1586	2(32):1577–1586	NUM
ejpam-3412	909	4	,	,	PUNCT
ejpam-3412	909	5	2007	2007	NUM
ejpam-3412	909	6	.	.	PUNCT
ejpam-3412	910	1	[	[	X
ejpam-3412	910	2	27	27	NUM
ejpam-3412	910	3	]	]	X
ejpam-3412	910	4	l.	l.	PROPN
ejpam-3412	910	5	a.	a.	PROPN
ejpam-3412	910	6	zadeh	zadeh	PROPN
ejpam-3412	910	7	.	.	PUNCT
ejpam-3412	910	8	fuzzy	fuzzy	ADJ
ejpam-3412	910	9	sets	set	NOUN
ejpam-3412	910	10	.	.	PUNCT
ejpam-3412	911	1	inf	inf	PROPN
ejpam-3412	911	2	.	.	PUNCT
ejpam-3412	911	3	cont	cont	PROPN
ejpam-3412	911	4	.	.	PROPN
ejpam-3412	911	5	,	,	PUNCT
ejpam-3412	911	6	8:338–353	8:338–353	NUM
ejpam-3412	911	7	,	,	PUNCT
ejpam-3412	911	8	1965	1965	NUM
ejpam-3412	911	9	.	.	PUNCT