id	sid	tid	token	lemma	pos
ejpam-5021	1	1	european	european	PROPN
ejpam-5021	1	2	journal	journal	PROPN
ejpam-5021	1	3	of	of	ADP
ejpam-5021	1	4	pure	pure	ADJ
ejpam-5021	1	5	and	and	CCONJ
ejpam-5021	1	6	applied	apply	VERB
ejpam-5021	1	7	mathematics	mathematic	NOUN
ejpam-5021	1	8	vol	vol	NOUN
ejpam-5021	1	9	.	.	PROPN
ejpam-5021	2	1	17	17	NUM
ejpam-5021	2	2	,	,	PUNCT
ejpam-5021	2	3	no	no	INTJ
ejpam-5021	2	4	.	.	NOUN
ejpam-5021	2	5	1	1	NUM
ejpam-5021	2	6	,	,	PUNCT
ejpam-5021	2	7	2024	2024	NUM
ejpam-5021	2	8	,	,	PUNCT
ejpam-5021	2	9	270	270	NUM
ejpam-5021	2	10	-	-	SYM
ejpam-5021	2	11	285	285	NUM
ejpam-5021	2	12	issn	issn	PROPN
ejpam-5021	2	13	1307	1307	NUM
ejpam-5021	2	14	-	-	SYM
ejpam-5021	2	15	5543	5543	NUM
ejpam-5021	2	16	–	–	PUNCT
ejpam-5021	3	1	ejpam.com	ejpam.com	X
ejpam-5021	3	2	published	publish	VERB
ejpam-5021	3	3	by	by	ADP
ejpam-5021	3	4	new	new	PROPN
ejpam-5021	3	5	york	york	PROPN
ejpam-5021	3	6	business	business	PROPN
ejpam-5021	3	7	global	global	PROPN
ejpam-5021	3	8	a	a	DET
ejpam-5021	3	9	fuzzy	fuzzy	ADJ
ejpam-5021	3	10	semibipolar	semibipolar	ADJ
ejpam-5021	3	11	soft	soft	ADJ
ejpam-5021	3	12	filter	filter	NOUN
ejpam-5021	3	13	and	and	CCONJ
ejpam-5021	3	14	its	its	PRON
ejpam-5021	3	15	association	association	NOUN
ejpam-5021	3	16	with	with	ADP
ejpam-5021	3	17	green	green	PROPN
ejpam-5021	3	18	’s	’s	PART
ejpam-5021	3	19	relation	relation	NOUN
ejpam-5021	3	20	n	n	CCONJ
ejpam-5021	3	21	rukchart	rukchart	PROPN
ejpam-5021	3	22	prasertpong1,∗	prasertpong1,∗	NOUN
ejpam-5021	3	23	,	,	PUNCT
ejpam-5021	3	24	pongpun	pongpun	PROPN
ejpam-5021	3	25	julatha2	julatha2	PROPN
ejpam-5021	3	26	,	,	PUNCT
ejpam-5021	3	27	aiyared	aiyare	VERB
ejpam-5021	3	28	iampan3	iampan3	NOUN
ejpam-5021	3	29	1	1	NUM
ejpam-5021	3	30	division	division	NOUN
ejpam-5021	3	31	of	of	ADP
ejpam-5021	3	32	mathematics	mathematic	NOUN
ejpam-5021	3	33	and	and	CCONJ
ejpam-5021	3	34	statistics	statistic	NOUN
ejpam-5021	3	35	,	,	PUNCT
ejpam-5021	3	36	faculty	faculty	NOUN
ejpam-5021	3	37	of	of	ADP
ejpam-5021	3	38	science	science	NOUN
ejpam-5021	3	39	and	and	CCONJ
ejpam-5021	3	40	technology	technology	NOUN
ejpam-5021	3	41	,	,	PUNCT
ejpam-5021	3	42	nakhon	nakhon	PROPN
ejpam-5021	3	43	sawan	sawan	PROPN
ejpam-5021	3	44	rajabhat	rajabhat	PROPN
ejpam-5021	3	45	university	university	PROPN
ejpam-5021	3	46	,	,	PUNCT
ejpam-5021	3	47	nakhon	nakhon	PROPN
ejpam-5021	3	48	sawan	sawan	PROPN
ejpam-5021	3	49	60000	60000	NUM
ejpam-5021	3	50	,	,	PUNCT
ejpam-5021	3	51	thailand	thailand	PROPN
ejpam-5021	3	52	2	2	NUM
ejpam-5021	3	53	department	department	NOUN
ejpam-5021	3	54	of	of	ADP
ejpam-5021	3	55	mathematics	mathematic	NOUN
ejpam-5021	3	56	,	,	PUNCT
ejpam-5021	3	57	faculty	faculty	NOUN
ejpam-5021	3	58	of	of	ADP
ejpam-5021	3	59	science	science	NOUN
ejpam-5021	3	60	and	and	CCONJ
ejpam-5021	3	61	technology	technology	NOUN
ejpam-5021	3	62	,	,	PUNCT
ejpam-5021	3	63	pibulsongkram	pibulsongkram	PROPN
ejpam-5021	3	64	rajabhat	rajabhat	PROPN
ejpam-5021	3	65	university	university	NOUN
ejpam-5021	3	66	,	,	PUNCT
ejpam-5021	3	67	phitsanulok	phitsanulok	NOUN
ejpam-5021	3	68	65000	65000	NUM
ejpam-5021	3	69	,	,	PUNCT
ejpam-5021	3	70	thailand	thailand	PROPN
ejpam-5021	3	71	3	3	NUM
ejpam-5021	3	72	fuzzy	fuzzy	ADJ
ejpam-5021	3	73	algebras	algebra	NOUN
ejpam-5021	3	74	and	and	CCONJ
ejpam-5021	3	75	decision	decision	NOUN
ejpam-5021	3	76	-	-	PUNCT
ejpam-5021	3	77	making	make	VERB
ejpam-5021	3	78	problems	problem	NOUN
ejpam-5021	3	79	research	research	NOUN
ejpam-5021	3	80	unit	unit	NOUN
ejpam-5021	3	81	,	,	PUNCT
ejpam-5021	3	82	department	department	NOUN
ejpam-5021	3	83	of	of	ADP
ejpam-5021	3	84	mathematics	mathematic	NOUN
ejpam-5021	3	85	,	,	PUNCT
ejpam-5021	3	86	school	school	NOUN
ejpam-5021	3	87	of	of	ADP
ejpam-5021	3	88	science	science	NOUN
ejpam-5021	3	89	,	,	PUNCT
ejpam-5021	3	90	mae	mae	PROPN
ejpam-5021	3	91	ka	ka	PROPN
ejpam-5021	3	92	,	,	PUNCT
ejpam-5021	3	93	university	university	NOUN
ejpam-5021	3	94	of	of	ADP
ejpam-5021	3	95	phayao	phayao	NOUN
ejpam-5021	3	96	,	,	PUNCT
ejpam-5021	3	97	phayao	phayao	NOUN
ejpam-5021	3	98	56000	56000	NUM
ejpam-5021	3	99	,	,	PUNCT
ejpam-5021	3	100	thailand	thailand	PROPN
ejpam-5021	3	101	abstract	abstract	NOUN
ejpam-5021	3	102	.	.	PUNCT
ejpam-5021	4	1	this	this	DET
ejpam-5021	4	2	paper	paper	NOUN
ejpam-5021	4	3	introduces	introduce	VERB
ejpam-5021	4	4	the	the	DET
ejpam-5021	4	5	concept	concept	NOUN
ejpam-5021	4	6	of	of	ADP
ejpam-5021	4	7	fuzzy	fuzzy	ADJ
ejpam-5021	4	8	semibipolar	semibipolar	ADJ
ejpam-5021	4	9	soft	soft	ADJ
ejpam-5021	4	10	filters	filter	NOUN
ejpam-5021	4	11	in	in	ADP
ejpam-5021	4	12	ordered	order	VERB
ejpam-5021	4	13	groupoids	groupoid	NOUN
ejpam-5021	4	14	.	.	PUNCT
ejpam-5021	5	1	it	it	PRON
ejpam-5021	5	2	is	be	AUX
ejpam-5021	5	3	defined	define	VERB
ejpam-5021	5	4	in	in	ADP
ejpam-5021	5	5	the	the	DET
ejpam-5021	5	6	form	form	NOUN
ejpam-5021	5	7	of	of	ADP
ejpam-5021	5	8	fuzzy	fuzzy	ADJ
ejpam-5021	5	9	semibipolar	semibipolar	ADJ
ejpam-5021	5	10	soft	soft	ADJ
ejpam-5021	5	11	sets	set	NOUN
ejpam-5021	5	12	over	over	ADP
ejpam-5021	5	13	universal	universal	ADJ
ejpam-5021	5	14	sets	set	NOUN
ejpam-5021	5	15	.	.	PUNCT
ejpam-5021	6	1	then	then	ADV
ejpam-5021	6	2	,	,	PUNCT
ejpam-5021	6	3	a	a	DET
ejpam-5021	6	4	corresponding	corresponding	ADJ
ejpam-5021	6	5	example	example	NOUN
ejpam-5021	6	6	is	be	AUX
ejpam-5021	6	7	proposed	propose	VERB
ejpam-5021	6	8	.	.	PUNCT
ejpam-5021	7	1	at	at	ADP
ejpam-5021	7	2	this	this	DET
ejpam-5021	7	3	point	point	NOUN
ejpam-5021	7	4	,	,	PUNCT
ejpam-5021	7	5	a	a	DET
ejpam-5021	7	6	necessary	necessary	ADJ
ejpam-5021	7	7	and	and	CCONJ
ejpam-5021	7	8	sufficient	sufficient	ADJ
ejpam-5021	7	9	condition	condition	NOUN
ejpam-5021	7	10	for	for	ADP
ejpam-5021	7	11	fuzzy	fuzzy	ADJ
ejpam-5021	7	12	semibipolar	semibipolar	ADJ
ejpam-5021	7	13	soft	soft	ADJ
ejpam-5021	7	14	filters	filter	NOUN
ejpam-5021	7	15	is	be	AUX
ejpam-5021	7	16	provided	provide	VERB
ejpam-5021	7	17	.	.	PUNCT
ejpam-5021	8	1	finally	finally	ADV
ejpam-5021	8	2	,	,	PUNCT
ejpam-5021	8	3	green	green	PROPN
ejpam-5021	8	4	’s	’s	PART
ejpam-5021	8	5	relation	relation	NOUN
ejpam-5021	8	6	n	n	PROPN
ejpam-5021	8	7	on	on	ADP
ejpam-5021	8	8	ordered	order	VERB
ejpam-5021	8	9	groupoids	groupoid	NOUN
ejpam-5021	8	10	is	be	AUX
ejpam-5021	8	11	described	describe	VERB
ejpam-5021	8	12	in	in	ADP
ejpam-5021	8	13	terms	term	NOUN
ejpam-5021	8	14	of	of	ADP
ejpam-5021	8	15	fuzzy	fuzzy	ADJ
ejpam-5021	8	16	semibipolar	semibipolar	ADJ
ejpam-5021	8	17	soft	soft	ADJ
ejpam-5021	8	18	filters	filter	NOUN
ejpam-5021	8	19	.	.	PUNCT
ejpam-5021	9	1	2020	2020	NUM
ejpam-5021	9	2	mathematics	mathematic	NOUN
ejpam-5021	9	3	subject	subject	NOUN
ejpam-5021	9	4	classifications	classification	NOUN
ejpam-5021	9	5	:	:	PUNCT
ejpam-5021	9	6	08a72	08a72	NUM
ejpam-5021	9	7	,	,	PUNCT
ejpam-5021	9	8	03e20	03e20	NUM
ejpam-5021	9	9	,	,	PUNCT
ejpam-5021	9	10	06f99	06f99	X
ejpam-5021	9	11	key	key	ADJ
ejpam-5021	9	12	words	word	NOUN
ejpam-5021	9	13	and	and	CCONJ
ejpam-5021	9	14	phrases	phrase	NOUN
ejpam-5021	9	15	:	:	PUNCT
ejpam-5021	9	16	green	green	PROPN
ejpam-5021	9	17	’s	’s	PART
ejpam-5021	9	18	relation	relation	NOUN
ejpam-5021	9	19	,	,	PUNCT
ejpam-5021	9	20	ordered	order	VERB
ejpam-5021	9	21	groupoid	groupoid	PROPN
ejpam-5021	9	22	,	,	PUNCT
ejpam-5021	9	23	fuzzy	fuzzy	ADJ
ejpam-5021	9	24	filter	filter	NOUN
ejpam-5021	9	25	,	,	PUNCT
ejpam-5021	9	26	soft	soft	ADJ
ejpam-5021	9	27	set	set	NOUN
ejpam-5021	9	28	1	1	NUM
ejpam-5021	9	29	.	.	PUNCT
ejpam-5021	10	1	introduction	introduction	NOUN
ejpam-5021	10	2	and	and	CCONJ
ejpam-5021	10	3	earlier	early	ADV
ejpam-5021	10	4	works	work	VERB
ejpam-5021	10	5	the	the	DET
ejpam-5021	10	6	fuzzy	fuzzy	ADJ
ejpam-5021	10	7	set	set	NOUN
ejpam-5021	10	8	theory	theory	NOUN
ejpam-5021	10	9	was	be	AUX
ejpam-5021	10	10	introduced	introduce	VERB
ejpam-5021	10	11	by	by	ADP
ejpam-5021	10	12	zadeh	zadeh	PROPN
ejpam-5021	11	1	[	[	X
ejpam-5021	11	2	27	27	NUM
ejpam-5021	11	3	]	]	PUNCT
ejpam-5021	11	4	in	in	ADP
ejpam-5021	11	5	1965	1965	NUM
ejpam-5021	11	6	.	.	PUNCT
ejpam-5021	12	1	zadeh	zadeh	PROPN
ejpam-5021	12	2	found	find	VERB
ejpam-5021	12	3	that	that	SCONJ
ejpam-5021	12	4	the	the	DET
ejpam-5021	12	5	traditional	traditional	ADJ
ejpam-5021	12	6	crisp	crisp	ADJ
ejpam-5021	12	7	set	set	NOUN
ejpam-5021	12	8	is	be	AUX
ejpam-5021	12	9	not	not	PART
ejpam-5021	12	10	capable	capable	ADJ
ejpam-5021	12	11	of	of	ADP
ejpam-5021	12	12	explaining	explain	VERB
ejpam-5021	12	13	the	the	DET
ejpam-5021	12	14	whole	whole	ADJ
ejpam-5021	12	15	thing	thing	NOUN
ejpam-5021	12	16	realistically	realistically	ADV
ejpam-5021	12	17	.	.	PUNCT
ejpam-5021	13	1	he	he	PRON
ejpam-5021	13	2	proposed	propose	VERB
ejpam-5021	13	3	fuzzy	fuzzy	ADJ
ejpam-5021	13	4	sets	set	NOUN
ejpam-5021	13	5	to	to	PART
ejpam-5021	13	6	solve	solve	VERB
ejpam-5021	13	7	this	this	DET
ejpam-5021	13	8	problem	problem	NOUN
ejpam-5021	13	9	.	.	PUNCT
ejpam-5021	14	1	thus	thus	ADV
ejpam-5021	14	2	,	,	PUNCT
ejpam-5021	14	3	he	he	PRON
ejpam-5021	14	4	presented	present	VERB
ejpam-5021	14	5	a	a	DET
ejpam-5021	14	6	classical	classical	ADJ
ejpam-5021	14	7	fuzzy	fuzzy	ADJ
ejpam-5021	14	8	set	set	NOUN
ejpam-5021	14	9	as	as	ADP
ejpam-5021	14	10	a	a	DET
ejpam-5021	14	11	function	function	NOUN
ejpam-5021	14	12	from	from	ADP
ejpam-5021	14	13	a	a	DET
ejpam-5021	14	14	universe	universe	NOUN
ejpam-5021	14	15	to	to	ADP
ejpam-5021	14	16	the	the	DET
ejpam-5021	14	17	unit	unit	NOUN
ejpam-5021	14	18	interval	interval	NOUN
ejpam-5021	14	19	.	.	PUNCT
ejpam-5021	15	1	based	base	VERB
ejpam-5021	15	2	on	on	ADP
ejpam-5021	15	3	this	this	DET
ejpam-5021	15	4	point	point	NOUN
ejpam-5021	15	5	,	,	PUNCT
ejpam-5021	15	6	the	the	DET
ejpam-5021	15	7	fuzzy	fuzzy	ADJ
ejpam-5021	15	8	set	set	NOUN
ejpam-5021	15	9	theory	theory	NOUN
ejpam-5021	15	10	is	be	AUX
ejpam-5021	15	11	regarded	regard	VERB
ejpam-5021	15	12	as	as	ADP
ejpam-5021	15	13	an	an	DET
ejpam-5021	15	14	effective	effective	ADJ
ejpam-5021	15	15	mathematical	mathematical	ADJ
ejpam-5021	15	16	approach	approach	NOUN
ejpam-5021	15	17	to	to	ADP
ejpam-5021	15	18	algebraic	algebraic	ADJ
ejpam-5021	15	19	structures	structure	NOUN
ejpam-5021	15	20	.	.	PUNCT
ejpam-5021	16	1	the	the	DET
ejpam-5021	16	2	concept	concept	NOUN
ejpam-5021	16	3	of	of	ADP
ejpam-5021	16	4	fuzzy	fuzzy	ADJ
ejpam-5021	16	5	groups	group	NOUN
ejpam-5021	16	6	was	be	AUX
ejpam-5021	16	7	first	first	ADV
ejpam-5021	16	8	introduced	introduce	VERB
ejpam-5021	16	9	by	by	ADP
ejpam-5021	16	10	rosenfeld	rosenfeld	PROPN
ejpam-5021	17	1	[	[	X
ejpam-5021	17	2	25	25	NUM
ejpam-5021	17	3	]	]	PUNCT
ejpam-5021	17	4	in	in	ADP
ejpam-5021	17	5	1971	1971	NUM
ejpam-5021	17	6	.	.	PUNCT
ejpam-5021	18	1	at	at	ADP
ejpam-5021	18	2	this	this	DET
ejpam-5021	18	3	point	point	NOUN
ejpam-5021	18	4	,	,	PUNCT
ejpam-5021	18	5	the	the	DET
ejpam-5021	18	6	fuzzy	fuzzy	ADJ
ejpam-5021	18	7	sets	set	NOUN
ejpam-5021	18	8	-	-	PUNCT
ejpam-5021	18	9	based	base	VERB
ejpam-5021	18	10	ideal	ideal	ADJ
ejpam-5021	18	11	theory	theory	NOUN
ejpam-5021	18	12	was	be	AUX
ejpam-5021	18	13	also	also	ADV
ejpam-5021	18	14	proposed	propose	VERB
ejpam-5021	18	15	.	.	PUNCT
ejpam-5021	19	1	according	accord	VERB
ejpam-5021	19	2	to	to	ADP
ejpam-5021	19	3	the	the	DET
ejpam-5021	19	4	definition	definition	NOUN
ejpam-5021	19	5	of	of	ADP
ejpam-5021	19	6	zadeh	zadeh	PROPN
ejpam-5021	19	7	’s	’s	PART
ejpam-5021	19	8	fuzzy	fuzzy	ADJ
ejpam-5021	19	9	set	set	NOUN
ejpam-5021	19	10	theory	theory	NOUN
ejpam-5021	19	11	,	,	PUNCT
ejpam-5021	19	12	rosenfeld	rosenfeld	PROPN
ejpam-5021	19	13	was	be	AUX
ejpam-5021	19	14	the	the	DET
ejpam-5021	19	15	first	first	ADJ
ejpam-5021	19	16	who	who	PRON
ejpam-5021	19	17	consider	consider	VERB
ejpam-5021	19	18	the	the	DET
ejpam-5021	19	19	case	case	NOUN
ejpam-5021	19	20	when	when	SCONJ
ejpam-5021	19	21	a	a	DET
ejpam-5021	19	22	domain	domain	NOUN
ejpam-5021	19	23	of	of	ADP
ejpam-5021	19	24	functions	function	NOUN
ejpam-5021	19	25	is	be	AUX
ejpam-5021	19	26	a	a	DET
ejpam-5021	19	27	groupoid	groupoid	NOUN
ejpam-5021	19	28	.	.	PUNCT
ejpam-5021	20	1	moreover	moreover	ADV
ejpam-5021	20	2	,	,	PUNCT
ejpam-5021	20	3	he	he	PRON
ejpam-5021	20	4	introduced	introduce	VERB
ejpam-5021	20	5	the	the	DET
ejpam-5021	20	6	idea	idea	NOUN
ejpam-5021	20	7	of	of	ADP
ejpam-5021	20	8	fuzzy	fuzzy	ADJ
ejpam-5021	20	9	subgroupoids	subgroupoid	NOUN
ejpam-5021	20	10	and	and	CCONJ
ejpam-5021	20	11	fuzzy	fuzzy	ADJ
ejpam-5021	20	12	left	left	NOUN
ejpam-5021	20	13	(	(	PUNCT
ejpam-5021	20	14	resp	resp	NOUN
ejpam-5021	20	15	.	.	PUNCT
ejpam-5021	20	16	,	,	PUNCT
ejpam-5021	21	1	right	right	ADJ
ejpam-5021	21	2	and	and	CCONJ
ejpam-5021	21	3	two	two	NUM
ejpam-5021	21	4	-	-	PUNCT
ejpam-5021	21	5	sided	sided	ADJ
ejpam-5021	21	6	)	)	PUNCT
ejpam-5021	21	7	ideals	ideal	NOUN
ejpam-5021	21	8	.	.	PUNCT
ejpam-5021	22	1	in	in	ADP
ejpam-5021	22	2	1981	1981	NUM
ejpam-5021	22	3	,	,	PUNCT
ejpam-5021	22	4	kuroki	kuroki	X
ejpam-5021	22	5	[	[	X
ejpam-5021	22	6	17	17	NUM
ejpam-5021	22	7	]	]	PUNCT
ejpam-5021	22	8	first	first	ADV
ejpam-5021	22	9	proposed	propose	VERB
ejpam-5021	22	10	the	the	DET
ejpam-5021	22	11	notion	notion	NOUN
ejpam-5021	22	12	of	of	ADP
ejpam-5021	22	13	fuzzy	fuzzy	ADJ
ejpam-5021	22	14	ideals	ideal	NOUN
ejpam-5021	22	15	in	in	ADP
ejpam-5021	22	16	semigroups	semigroup	NOUN
ejpam-5021	22	17	.	.	PUNCT
ejpam-5021	23	1	in	in	ADP
ejpam-5021	23	2	particular	particular	ADJ
ejpam-5021	23	3	,	,	PUNCT
ejpam-5021	23	4	a	a	DET
ejpam-5021	23	5	systematic	systematic	ADJ
ejpam-5021	23	6	exposition	exposition	NOUN
ejpam-5021	23	7	of	of	ADP
ejpam-5021	23	8	fuzzy	fuzzy	ADJ
ejpam-5021	23	9	semigroups	semigroup	NOUN
ejpam-5021	23	10	by	by	ADP
ejpam-5021	23	11	mordeson	mordeson	NOUN
ejpam-5021	23	12	et	et	PROPN
ejpam-5021	23	13	al	al	PROPN
ejpam-5021	23	14	.	.	PROPN
ejpam-5021	23	15	appeared	appear	VERB
ejpam-5021	23	16	in	in	ADP
ejpam-5021	23	17	[	[	X
ejpam-5021	23	18	22	22	NUM
ejpam-5021	23	19	]	]	PUNCT
ejpam-5021	23	20	.	.	PUNCT
ejpam-5021	24	1	in	in	ADP
ejpam-5021	24	2	structural	structural	ADJ
ejpam-5021	24	3	development	development	NOUN
ejpam-5021	24	4	,	,	PUNCT
ejpam-5021	24	5	fuzzy	fuzzy	ADJ
ejpam-5021	24	6	ordered	order	VERB
ejpam-5021	24	7	groupoids	groupoid	NOUN
ejpam-5021	24	8	and	and	CCONJ
ejpam-5021	24	9	ordered	order	VERB
ejpam-5021	24	10	semigroups	semigroup	NOUN
ejpam-5021	24	11	were	be	AUX
ejpam-5021	24	12	proposed	propose	VERB
ejpam-5021	24	13	∗corresponding	∗corresponde	VERB
ejpam-5021	24	14	author	author	NOUN
ejpam-5021	24	15	.	.	PUNCT
ejpam-5021	25	1	doi	doi	NOUN
ejpam-5021	25	2	:	:	PUNCT
ejpam-5021	25	3	https://doi.org/10.29020/nybg.ejpam.v17i1.5021	https://doi.org/10.29020/nybg.ejpam.v17i1.5021	NOUN
ejpam-5021	25	4	email	email	NOUN
ejpam-5021	25	5	addresses	address	VERB
ejpam-5021	25	6	:	:	PUNCT
ejpam-5021	25	7	rukchart.p@nsru.ac.th	rukchart.p@nsru.ac.th	PROPN
ejpam-5021	25	8	(	(	PUNCT
ejpam-5021	25	9	r.	r.	PROPN
ejpam-5021	25	10	prasertpong	prasertpong	PROPN
ejpam-5021	25	11	)	)	PUNCT
ejpam-5021	25	12	,	,	PUNCT
ejpam-5021	25	13	pongpun.j@psru.ac.th	pongpun.j@psru.ac.th	PROPN
ejpam-5021	25	14	(	(	PUNCT
ejpam-5021	25	15	p.	p.	NOUN
ejpam-5021	25	16	julatha	julatha	NOUN
ejpam-5021	25	17	)	)	PUNCT
ejpam-5021	25	18	,	,	PUNCT
ejpam-5021	25	19	aiyared.ia@up.ac.th	aiyared.ia@up.ac.th	NOUN
ejpam-5021	25	20	(	(	PUNCT
ejpam-5021	25	21	a.	a.	NOUN
ejpam-5021	25	22	iampan	iampan	PROPN
ejpam-5021	25	23	)	)	PUNCT
ejpam-5021	25	24	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5021	26	1	270	270	NUM
ejpam-5021	26	2	©	©	ADP
ejpam-5021	26	3	2024	2024	NUM
ejpam-5021	26	4	ejpam	ejpam	NOUN
ejpam-5021	26	5	all	all	DET
ejpam-5021	26	6	rights	right	NOUN
ejpam-5021	26	7	reserved	reserve	VERB
ejpam-5021	26	8	.	.	PUNCT
ejpam-5021	27	1	r.	r.	PROPN
ejpam-5021	27	2	prasertpong	prasertpong	PROPN
ejpam-5021	27	3	,	,	PUNCT
ejpam-5021	27	4	p.	p.	PROPN
ejpam-5021	27	5	julatha	julatha	PROPN
ejpam-5021	27	6	,	,	PUNCT
ejpam-5021	27	7	a.	a.	NOUN
ejpam-5021	27	8	iampan	iampan	PROPN
ejpam-5021	27	9	/	/	SYM
ejpam-5021	27	10	eur	eur	PROPN
ejpam-5021	27	11	.	.	PUNCT
ejpam-5021	28	1	j.	j.	PROPN
ejpam-5021	28	2	pure	pure	PROPN
ejpam-5021	28	3	appl	appl	PROPN
ejpam-5021	28	4	.	.	PROPN
ejpam-5021	28	5	math	math	PROPN
ejpam-5021	28	6	,	,	PUNCT
ejpam-5021	28	7	17	17	NUM
ejpam-5021	28	8	(	(	PUNCT
ejpam-5021	28	9	1	1	NUM
ejpam-5021	28	10	)	)	PUNCT
ejpam-5021	28	11	(	(	PUNCT
ejpam-5021	28	12	2024	2024	NUM
ejpam-5021	28	13	)	)	PUNCT
ejpam-5021	28	14	,	,	PUNCT
ejpam-5021	28	15	270	270	NUM
ejpam-5021	28	16	-	-	SYM
ejpam-5021	28	17	285	285	NUM
ejpam-5021	28	18	271	271	NUM
ejpam-5021	28	19	by	by	ADP
ejpam-5021	28	20	kehayopulu	kehayopulu	ADJ
ejpam-5021	28	21	and	and	CCONJ
ejpam-5021	28	22	tsingelis	tsingeli	VERB
ejpam-5021	28	23	[	[	X
ejpam-5021	28	24	11	11	NUM
ejpam-5021	28	25	,	,	PUNCT
ejpam-5021	28	26	12	12	NUM
ejpam-5021	28	27	]	]	PUNCT
ejpam-5021	28	28	.	.	PUNCT
ejpam-5021	29	1	khan	khan	PROPN
ejpam-5021	29	2	et	et	PROPN
ejpam-5021	29	3	al	al	PROPN
ejpam-5021	29	4	.	.	PUNCT
ejpam-5021	30	1	[	[	X
ejpam-5021	30	2	14	14	NUM
ejpam-5021	30	3	]	]	PUNCT
ejpam-5021	30	4	gave	give	VERB
ejpam-5021	30	5	the	the	DET
ejpam-5021	30	6	idea	idea	NOUN
ejpam-5021	30	7	of	of	ADP
ejpam-5021	30	8	fuzzy	fuzzy	ADJ
ejpam-5021	30	9	ideals	ideal	NOUN
ejpam-5021	30	10	in	in	ADP
ejpam-5021	30	11	ordered	order	VERB
ejpam-5021	30	12	semigroups	semigroup	NOUN
ejpam-5021	30	13	.	.	PUNCT
ejpam-5021	31	1	furthermore	furthermore	ADV
ejpam-5021	31	2	,	,	PUNCT
ejpam-5021	31	3	other	other	ADJ
ejpam-5021	31	4	algebraic	algebraic	ADJ
ejpam-5021	31	5	structures	structure	NOUN
ejpam-5021	31	6	are	be	AUX
ejpam-5021	31	7	considered	consider	VERB
ejpam-5021	31	8	under	under	ADP
ejpam-5021	31	9	the	the	DET
ejpam-5021	31	10	concept	concept	NOUN
ejpam-5021	31	11	of	of	ADP
ejpam-5021	31	12	fuzzy	fuzzy	ADJ
ejpam-5021	31	13	sets	set	NOUN
ejpam-5021	31	14	,	,	PUNCT
ejpam-5021	31	15	continuously	continuously	ADV
ejpam-5021	31	16	.	.	PUNCT
ejpam-5021	32	1	when	when	SCONJ
ejpam-5021	32	2	the	the	DET
ejpam-5021	32	3	focus	focus	NOUN
ejpam-5021	32	4	is	be	AUX
ejpam-5021	32	5	on	on	ADP
ejpam-5021	32	6	the	the	DET
ejpam-5021	32	7	context	context	NOUN
ejpam-5021	32	8	of	of	ADP
ejpam-5021	32	9	geen	geen	PROPN
ejpam-5021	32	10	’s	’s	PART
ejpam-5021	32	11	relations	relation	NOUN
ejpam-5021	32	12	,	,	PUNCT
ejpam-5021	32	13	the	the	DET
ejpam-5021	32	14	combination	combination	NOUN
ejpam-5021	32	15	of	of	ADP
ejpam-5021	32	16	fuzzy	fuzzy	ADJ
ejpam-5021	32	17	ideals	ideal	NOUN
ejpam-5021	32	18	and	and	CCONJ
ejpam-5021	32	19	green	green	PROPN
ejpam-5021	32	20	’s	’s	PART
ejpam-5021	32	21	relations	relation	NOUN
ejpam-5021	32	22	in	in	ADP
ejpam-5021	32	23	semigroups	semigroup	NOUN
ejpam-5021	32	24	was	be	AUX
ejpam-5021	32	25	studied	study	VERB
ejpam-5021	32	26	by	by	ADP
ejpam-5021	32	27	mclean	mclean	PROPN
ejpam-5021	32	28	and	and	CCONJ
ejpam-5021	32	29	kummer	kummer	NOUN
ejpam-5021	32	30	[	[	X
ejpam-5021	32	31	20	20	NUM
ejpam-5021	32	32	]	]	PUNCT
ejpam-5021	32	33	in	in	ADP
ejpam-5021	32	34	1992	1992	NUM
ejpam-5021	32	35	.	.	PUNCT
ejpam-5021	33	1	based	base	VERB
ejpam-5021	33	2	on	on	ADP
ejpam-5021	33	3	this	this	DET
ejpam-5021	33	4	interesting	interesting	ADJ
ejpam-5021	33	5	point	point	NOUN
ejpam-5021	33	6	,	,	PUNCT
ejpam-5021	33	7	kehayopulu	kehayopulu	ADJ
ejpam-5021	33	8	and	and	CCONJ
ejpam-5021	33	9	tsingelis	tsingeli	NOUN
ejpam-5021	34	1	[	[	X
ejpam-5021	34	2	12	12	NUM
ejpam-5021	34	3	]	]	PUNCT
ejpam-5021	34	4	presented	present	VERB
ejpam-5021	34	5	the	the	DET
ejpam-5021	34	6	notion	notion	NOUN
ejpam-5021	34	7	of	of	ADP
ejpam-5021	34	8	fuzzy	fuzzy	ADJ
ejpam-5021	34	9	filters	filter	NOUN
ejpam-5021	34	10	in	in	ADP
ejpam-5021	34	11	ordered	order	VERB
ejpam-5021	34	12	semigroups	semigroup	NOUN
ejpam-5021	34	13	.	.	PUNCT
ejpam-5021	35	1	then	then	ADV
ejpam-5021	35	2	,	,	PUNCT
ejpam-5021	35	3	some	some	DET
ejpam-5021	35	4	authors	author	NOUN
ejpam-5021	35	5	used	use	VERB
ejpam-5021	35	6	such	such	DET
ejpam-5021	35	7	a	a	DET
ejpam-5021	35	8	concept	concept	NOUN
ejpam-5021	35	9	to	to	PART
ejpam-5021	35	10	describe	describe	VERB
ejpam-5021	35	11	green	green	PROPN
ejpam-5021	35	12	’s	’s	PART
ejpam-5021	35	13	relations	relation	NOUN
ejpam-5021	35	14	.	.	PUNCT
ejpam-5021	36	1	the	the	DET
ejpam-5021	36	2	concept	concept	NOUN
ejpam-5021	36	3	of	of	ADP
ejpam-5021	36	4	fuzzy	fuzzy	ADJ
ejpam-5021	36	5	filters	filter	NOUN
ejpam-5021	36	6	for	for	ADP
ejpam-5021	36	7	various	various	ADJ
ejpam-5021	36	8	algebraic	algebraic	ADJ
ejpam-5021	36	9	structures	structure	NOUN
ejpam-5021	36	10	has	have	AUX
ejpam-5021	36	11	been	be	AUX
ejpam-5021	36	12	studied	study	VERB
ejpam-5021	36	13	by	by	ADP
ejpam-5021	36	14	many	many	ADJ
ejpam-5021	36	15	authors	author	NOUN
ejpam-5021	36	16	.	.	PUNCT
ejpam-5021	37	1	in	in	ADP
ejpam-5021	37	2	2007	2007	NUM
ejpam-5021	37	3	,	,	PUNCT
ejpam-5021	37	4	green	green	PROPN
ejpam-5021	37	5	’s	’s	PART
ejpam-5021	37	6	relation	relation	NOUN
ejpam-5021	37	7	n	n	PART
ejpam-5021	37	8	was	be	AUX
ejpam-5021	37	9	characterized	characterize	VERB
ejpam-5021	37	10	in	in	ADP
ejpam-5021	37	11	terms	term	NOUN
ejpam-5021	37	12	of	of	ADP
ejpam-5021	37	13	fuzzy	fuzzy	ADJ
ejpam-5021	37	14	filters	filter	NOUN
ejpam-5021	37	15	of	of	ADP
ejpam-5021	37	16	ordered	order	VERB
ejpam-5021	37	17	groupoids	groupoid	NOUN
ejpam-5021	37	18	by	by	ADP
ejpam-5021	37	19	kehayopulu	kehayopulu	PROPN
ejpam-5021	37	20	[	[	X
ejpam-5021	37	21	13	13	NUM
ejpam-5021	37	22	]	]	PUNCT
ejpam-5021	37	23	.	.	PUNCT
ejpam-5021	38	1	in	in	ADP
ejpam-5021	38	2	2012	2012	NUM
ejpam-5021	38	3	,	,	PUNCT
ejpam-5021	38	4	green	green	PROPN
ejpam-5021	38	5	’s	’s	PART
ejpam-5021	38	6	relationn	relationn	PROPN
ejpam-5021	38	7	was	be	AUX
ejpam-5021	38	8	characterized	characterize	VERB
ejpam-5021	38	9	in	in	ADP
ejpam-5021	38	10	terms	term	NOUN
ejpam-5021	38	11	of	of	ADP
ejpam-5021	38	12	fuzzy	fuzzy	ADJ
ejpam-5021	38	13	filters	filter	NOUN
ejpam-5021	38	14	of	of	ADP
ejpam-5021	38	15	ordered	order	VERB
ejpam-5021	38	16	gamma	gamma	NOUN
ejpam-5021	38	17	-	-	PUNCT
ejpam-5021	38	18	semigroups	semigroup	NOUN
ejpam-5021	38	19	by	by	ADP
ejpam-5021	38	20	iampan	iampan	NOUN
ejpam-5021	38	21	and	and	CCONJ
ejpam-5021	38	22	siripitukdet	siripitukdet	NOUN
ejpam-5021	39	1	[	[	X
ejpam-5021	39	2	7	7	NUM
ejpam-5021	39	3	]	]	PUNCT
ejpam-5021	39	4	.	.	PUNCT
ejpam-5021	40	1	in	in	ADP
ejpam-5021	40	2	2013	2013	NUM
ejpam-5021	40	3	,	,	PUNCT
ejpam-5021	40	4	green	green	PROPN
ejpam-5021	40	5	’s	’s	PART
ejpam-5021	40	6	relation	relation	NOUN
ejpam-5021	40	7	n	n	PART
ejpam-5021	40	8	was	be	AUX
ejpam-5021	40	9	characterized	characterize	VERB
ejpam-5021	40	10	in	in	ADP
ejpam-5021	40	11	terms	term	NOUN
ejpam-5021	40	12	of	of	ADP
ejpam-5021	40	13	fuzzy	fuzzy	ADJ
ejpam-5021	40	14	filters	filter	NOUN
ejpam-5021	40	15	of	of	ADP
ejpam-5021	40	16	ordered	order	VERB
ejpam-5021	40	17	gamma	gamma	NOUN
ejpam-5021	40	18	-	-	PUNCT
ejpam-5021	40	19	groupoids	groupoid	NOUN
ejpam-5021	40	20	by	by	ADP
ejpam-5021	40	21	iampan	iampan	NOUN
ejpam-5021	40	22	and	and	CCONJ
ejpam-5021	40	23	siripitukdet	siripitukdet	NOUN
ejpam-5021	41	1	[	[	X
ejpam-5021	41	2	8	8	NUM
ejpam-5021	41	3	]	]	PUNCT
ejpam-5021	41	4	.	.	PUNCT
ejpam-5021	42	1	as	as	SCONJ
ejpam-5021	42	2	reviewed	review	VERB
ejpam-5021	42	3	above	above	ADV
ejpam-5021	42	4	,	,	PUNCT
ejpam-5021	42	5	the	the	DET
ejpam-5021	42	6	concept	concept	NOUN
ejpam-5021	42	7	of	of	ADP
ejpam-5021	42	8	green	green	PROPN
ejpam-5021	42	9	’s	’s	PART
ejpam-5021	42	10	relations	relation	NOUN
ejpam-5021	42	11	plays	play	VERB
ejpam-5021	42	12	an	an	DET
ejpam-5021	42	13	important	important	ADJ
ejpam-5021	42	14	role	role	NOUN
ejpam-5021	42	15	in	in	ADP
ejpam-5021	42	16	studying	study	VERB
ejpam-5021	42	17	the	the	DET
ejpam-5021	42	18	structure	structure	NOUN
ejpam-5021	42	19	of	of	ADP
ejpam-5021	42	20	semigroups	semigroup	NOUN
ejpam-5021	42	21	.	.	PUNCT
ejpam-5021	43	1	based	base	VERB
ejpam-5021	43	2	on	on	ADP
ejpam-5021	43	3	this	this	DET
ejpam-5021	43	4	point	point	NOUN
ejpam-5021	43	5	,	,	PUNCT
ejpam-5021	43	6	it	it	PRON
ejpam-5021	43	7	is	be	AUX
ejpam-5021	43	8	considered	consider	VERB
ejpam-5021	43	9	in	in	ADP
ejpam-5021	43	10	the	the	DET
ejpam-5021	43	11	sense	sense	NOUN
ejpam-5021	43	12	of	of	ADP
ejpam-5021	43	13	computer	computer	NOUN
ejpam-5021	43	14	science	science	NOUN
ejpam-5021	43	15	.	.	PUNCT
ejpam-5021	44	1	in	in	ADP
ejpam-5021	44	2	2011	2011	NUM
ejpam-5021	44	3	,	,	PUNCT
ejpam-5021	44	4	the	the	DET
ejpam-5021	44	5	notion	notion	NOUN
ejpam-5021	44	6	of	of	ADP
ejpam-5021	44	7	green	green	PROPN
ejpam-5021	44	8	’s	’s	PART
ejpam-5021	44	9	relations	relation	NOUN
ejpam-5021	44	10	and	and	CCONJ
ejpam-5021	44	11	their	their	PRON
ejpam-5021	44	12	use	use	NOUN
ejpam-5021	44	13	in	in	ADP
ejpam-5021	44	14	automata	automata	NOUN
ejpam-5021	44	15	theory	theory	NOUN
ejpam-5021	44	16	was	be	AUX
ejpam-5021	44	17	introduced	introduce	VERB
ejpam-5021	44	18	by	by	ADP
ejpam-5021	44	19	colcombet	colcombet	NOUN
ejpam-5021	44	20	[	[	X
ejpam-5021	44	21	2	2	NUM
ejpam-5021	44	22	]	]	PUNCT
ejpam-5021	44	23	.	.	PUNCT
ejpam-5021	45	1	in	in	ADP
ejpam-5021	45	2	2019	2019	NUM
ejpam-5021	45	3	,	,	PUNCT
ejpam-5021	45	4	the	the	DET
ejpam-5021	45	5	concept	concept	NOUN
ejpam-5021	45	6	of	of	ADP
ejpam-5021	45	7	green	green	PROPN
ejpam-5021	45	8	’s	’s	PART
ejpam-5021	45	9	relations	relation	NOUN
ejpam-5021	45	10	in	in	ADP
ejpam-5021	45	11	deterministic	deterministic	ADJ
ejpam-5021	45	12	finite	finite	NOUN
ejpam-5021	45	13	automata	automata	NOUN
ejpam-5021	45	14	was	be	AUX
ejpam-5021	45	15	proposed	propose	VERB
ejpam-5021	45	16	by	by	ADP
ejpam-5021	45	17	fleischer	fleischer	NOUN
ejpam-5021	45	18	and	and	CCONJ
ejpam-5021	45	19	kufleitner	kufleitner	NOUN
ejpam-5021	45	20	[	[	X
ejpam-5021	45	21	5	5	NUM
ejpam-5021	45	22	]	]	PUNCT
ejpam-5021	45	23	.	.	PUNCT
ejpam-5021	46	1	in	in	ADP
ejpam-5021	46	2	2022	2022	NUM
ejpam-5021	46	3	,	,	PUNCT
ejpam-5021	46	4	the	the	DET
ejpam-5021	46	5	notion	notion	NOUN
ejpam-5021	46	6	of	of	ADP
ejpam-5021	46	7	green	green	PROPN
ejpam-5021	46	8	’s	’s	PART
ejpam-5021	46	9	relations	relation	NOUN
ejpam-5021	46	10	in	in	ADP
ejpam-5021	46	11	l	l	NOUN
ejpam-5021	46	12	-	-	PUNCT
ejpam-5021	46	13	e	e	ADJ
ejpam-5021	46	14	-	-	ADJ
ejpam-5021	46	15	fuzzy	fuzzy	ADJ
ejpam-5021	46	16	skew	skew	NOUN
ejpam-5021	46	17	lattices	lattice	NOUN
ejpam-5021	46	18	was	be	AUX
ejpam-5021	46	19	presented	present	VERB
ejpam-5021	46	20	by	by	ADP
ejpam-5021	46	21	zhi	zhi	PROPN
ejpam-5021	46	22	et	et	PROPN
ejpam-5021	46	23	al	al	PROPN
ejpam-5021	46	24	.	.	PUNCT
ejpam-5021	47	1	[	[	X
ejpam-5021	47	2	28	28	NUM
ejpam-5021	47	3	]	]	PUNCT
ejpam-5021	47	4	.	.	PUNCT
ejpam-5021	48	1	in	in	ADP
ejpam-5021	48	2	1999	1999	NUM
ejpam-5021	48	3	,	,	PUNCT
ejpam-5021	48	4	molodtsov	molodtsov	NOUN
ejpam-5021	48	5	[	[	X
ejpam-5021	48	6	21	21	NUM
ejpam-5021	48	7	]	]	PUNCT
ejpam-5021	48	8	initiated	initiate	VERB
ejpam-5021	48	9	the	the	DET
ejpam-5021	48	10	concept	concept	NOUN
ejpam-5021	48	11	of	of	ADP
ejpam-5021	48	12	soft	soft	ADJ
ejpam-5021	48	13	set	set	NOUN
ejpam-5021	48	14	theory	theory	NOUN
ejpam-5021	48	15	as	as	ADP
ejpam-5021	48	16	a	a	DET
ejpam-5021	48	17	tuple	tuple	NOUN
ejpam-5021	48	18	that	that	PRON
ejpam-5021	48	19	is	be	AUX
ejpam-5021	48	20	associated	associate	VERB
ejpam-5021	48	21	with	with	ADP
ejpam-5021	48	22	a	a	DET
ejpam-5021	48	23	set	set	NOUN
ejpam-5021	48	24	of	of	ADP
ejpam-5021	48	25	parameters	parameter	NOUN
ejpam-5021	48	26	and	and	CCONJ
ejpam-5021	48	27	a	a	DET
ejpam-5021	48	28	function	function	NOUN
ejpam-5021	48	29	from	from	ADP
ejpam-5021	48	30	a	a	DET
ejpam-5021	48	31	parameter	parameter	NOUN
ejpam-5021	48	32	set	set	VERB
ejpam-5021	48	33	to	to	ADP
ejpam-5021	48	34	the	the	DET
ejpam-5021	48	35	power	power	NOUN
ejpam-5021	48	36	set	set	NOUN
ejpam-5021	48	37	of	of	ADP
ejpam-5021	48	38	a	a	DET
ejpam-5021	48	39	universal	universal	ADJ
ejpam-5021	48	40	set	set	NOUN
ejpam-5021	48	41	.	.	PUNCT
ejpam-5021	49	1	the	the	DET
ejpam-5021	49	2	major	major	ADJ
ejpam-5021	49	3	advantage	advantage	NOUN
ejpam-5021	49	4	of	of	ADP
ejpam-5021	49	5	soft	soft	ADJ
ejpam-5021	49	6	set	set	NOUN
ejpam-5021	49	7	theory	theory	NOUN
ejpam-5021	49	8	is	be	AUX
ejpam-5021	49	9	that	that	SCONJ
ejpam-5021	49	10	it	it	PRON
ejpam-5021	49	11	does	do	AUX
ejpam-5021	49	12	need	need	VERB
ejpam-5021	49	13	not	not	PART
ejpam-5021	49	14	to	to	PART
ejpam-5021	49	15	bother	bother	VERB
ejpam-5021	49	16	with	with	ADP
ejpam-5021	49	17	any	any	DET
ejpam-5021	49	18	additional	additional	ADJ
ejpam-5021	49	19	information	information	NOUN
ejpam-5021	49	20	about	about	ADP
ejpam-5021	49	21	the	the	DET
ejpam-5021	49	22	data	datum	NOUN
ejpam-5021	49	23	such	such	ADJ
ejpam-5021	49	24	as	as	ADP
ejpam-5021	49	25	probability	probability	NOUN
ejpam-5021	49	26	in	in	ADP
ejpam-5021	49	27	statistics	statistic	NOUN
ejpam-5021	49	28	or	or	CCONJ
ejpam-5021	49	29	possibility	possibility	NOUN
ejpam-5021	49	30	value	value	NOUN
ejpam-5021	49	31	in	in	ADP
ejpam-5021	49	32	fuzzy	fuzzy	ADJ
ejpam-5021	49	33	set	set	NOUN
ejpam-5021	49	34	theory	theory	NOUN
ejpam-5021	49	35	.	.	PUNCT
ejpam-5021	50	1	in	in	ADP
ejpam-5021	50	2	other	other	ADJ
ejpam-5021	50	3	words	word	NOUN
ejpam-5021	50	4	,	,	PUNCT
ejpam-5021	50	5	the	the	DET
ejpam-5021	50	6	soft	soft	ADJ
ejpam-5021	50	7	set	set	NOUN
ejpam-5021	50	8	theory	theory	NOUN
ejpam-5021	50	9	can	can	AUX
ejpam-5021	50	10	be	be	AUX
ejpam-5021	50	11	considered	consider	VERB
ejpam-5021	50	12	as	as	ADP
ejpam-5021	50	13	an	an	DET
ejpam-5021	50	14	extended	extended	ADJ
ejpam-5021	50	15	notion	notion	NOUN
ejpam-5021	50	16	of	of	ADP
ejpam-5021	50	17	fuzzy	fuzzy	ADJ
ejpam-5021	50	18	set	set	NOUN
ejpam-5021	50	19	theory	theory	NOUN
ejpam-5021	50	20	.	.	PUNCT
ejpam-5021	51	1	the	the	DET
ejpam-5021	51	2	research	research	NOUN
ejpam-5021	51	3	of	of	ADP
ejpam-5021	51	4	the	the	DET
ejpam-5021	51	5	theory	theory	NOUN
ejpam-5021	51	6	for	for	ADP
ejpam-5021	51	7	combining	combine	VERB
ejpam-5021	51	8	the	the	DET
ejpam-5021	51	9	soft	soft	ADJ
ejpam-5021	51	10	set	set	NOUN
ejpam-5021	51	11	with	with	ADP
ejpam-5021	51	12	other	other	ADJ
ejpam-5021	51	13	mathematical	mathematical	ADJ
ejpam-5021	51	14	theories	theory	NOUN
ejpam-5021	51	15	has	have	AUX
ejpam-5021	51	16	been	be	AUX
ejpam-5021	51	17	developed	develop	VERB
ejpam-5021	51	18	by	by	ADP
ejpam-5021	51	19	many	many	ADJ
ejpam-5021	51	20	authors	author	NOUN
ejpam-5021	51	21	.	.	PUNCT
ejpam-5021	52	1	this	this	DET
ejpam-5021	52	2	literature	literature	NOUN
ejpam-5021	52	3	is	be	AUX
ejpam-5021	52	4	contained	contain	VERB
ejpam-5021	52	5	in	in	ADP
ejpam-5021	52	6	the	the	DET
ejpam-5021	52	7	review	review	NOUN
ejpam-5021	52	8	on	on	ADP
ejpam-5021	52	9	soft	soft	ADJ
ejpam-5021	52	10	set	set	NOUN
ejpam-5021	52	11	-	-	PUNCT
ejpam-5021	52	12	based	base	VERB
ejpam-5021	52	13	parameter	parameter	NOUN
ejpam-5021	52	14	reduction	reduction	NOUN
ejpam-5021	52	15	and	and	CCONJ
ejpam-5021	52	16	decisionmaking	decisionmake	VERB
ejpam-5021	52	17	[	[	X
ejpam-5021	52	18	3	3	NUM
ejpam-5021	52	19	]	]	PUNCT
ejpam-5021	52	20	.	.	PUNCT
ejpam-5021	53	1	in	in	ADP
ejpam-5021	53	2	2001	2001	NUM
ejpam-5021	53	3	,	,	PUNCT
ejpam-5021	53	4	maji	maji	PROPN
ejpam-5021	53	5	et	et	PROPN
ejpam-5021	53	6	al	al	PROPN
ejpam-5021	53	7	.	.	PUNCT
ejpam-5021	54	1	[	[	X
ejpam-5021	54	2	19	19	NUM
ejpam-5021	54	3	]	]	PUNCT
ejpam-5021	54	4	proposed	propose	VERB
ejpam-5021	54	5	the	the	DET
ejpam-5021	54	6	notion	notion	NOUN
ejpam-5021	54	7	of	of	ADP
ejpam-5021	54	8	fuzzy	fuzzy	ADJ
ejpam-5021	54	9	soft	soft	ADJ
ejpam-5021	54	10	set	set	NOUN
ejpam-5021	54	11	theory	theory	NOUN
ejpam-5021	54	12	in	in	ADP
ejpam-5021	54	13	terms	term	NOUN
ejpam-5021	54	14	of	of	ADP
ejpam-5021	54	15	soft	soft	ADJ
ejpam-5021	54	16	set	set	NOUN
ejpam-5021	54	17	theory	theory	NOUN
ejpam-5021	54	18	.	.	PUNCT
ejpam-5021	55	1	in	in	ADP
ejpam-5021	55	2	this	this	DET
ejpam-5021	55	3	way	way	NOUN
ejpam-5021	55	4	,	,	PUNCT
ejpam-5021	55	5	a	a	DET
ejpam-5021	55	6	power	power	NOUN
ejpam-5021	55	7	set	set	NOUN
ejpam-5021	55	8	of	of	ADP
ejpam-5021	55	9	a	a	DET
ejpam-5021	55	10	universe	universe	NOUN
ejpam-5021	55	11	is	be	AUX
ejpam-5021	55	12	replaced	replace	VERB
ejpam-5021	55	13	by	by	ADP
ejpam-5021	55	14	a	a	DET
ejpam-5021	55	15	set	set	NOUN
ejpam-5021	55	16	of	of	ADP
ejpam-5021	55	17	all	all	DET
ejpam-5021	55	18	fuzzy	fuzzy	ADJ
ejpam-5021	55	19	subsets	subset	NOUN
ejpam-5021	55	20	of	of	ADP
ejpam-5021	55	21	a	a	DET
ejpam-5021	55	22	universe	universe	NOUN
ejpam-5021	55	23	.	.	PUNCT
ejpam-5021	56	1	the	the	DET
ejpam-5021	56	2	application	application	NOUN
ejpam-5021	56	3	area	area	NOUN
ejpam-5021	56	4	of	of	ADP
ejpam-5021	56	5	this	this	PRON
ejpam-5021	56	6	such	such	ADJ
ejpam-5021	56	7	as	as	ADP
ejpam-5021	56	8	the	the	DET
ejpam-5021	56	9	decision	decision	NOUN
ejpam-5021	56	10	support	support	NOUN
ejpam-5021	56	11	system	system	NOUN
ejpam-5021	56	12	[	[	X
ejpam-5021	56	13	15	15	NUM
ejpam-5021	56	14	]	]	PUNCT
ejpam-5021	56	15	and	and	CCONJ
ejpam-5021	56	16	the	the	DET
ejpam-5021	56	17	real	real	ADJ
ejpam-5021	56	18	-	-	PUNCT
ejpam-5021	56	19	life	life	NOUN
ejpam-5021	56	20	problem	problem	NOUN
ejpam-5021	56	21	:	:	PUNCT
ejpam-5021	56	22	classification	classification	NOUN
ejpam-5021	56	23	of	of	ADP
ejpam-5021	56	24	wood	wood	NOUN
ejpam-5021	56	25	materials	material	NOUN
ejpam-5021	56	26	to	to	PART
ejpam-5021	56	27	prevent	prevent	VERB
ejpam-5021	56	28	fire	fire	NOUN
ejpam-5021	56	29	-	-	PUNCT
ejpam-5021	56	30	related	relate	VERB
ejpam-5021	56	31	injuries	injury	NOUN
ejpam-5021	56	32	and	and	CCONJ
ejpam-5021	56	33	deaths	death	NOUN
ejpam-5021	56	34	[	[	X
ejpam-5021	56	35	16	16	NUM
ejpam-5021	56	36	]	]	PUNCT
ejpam-5021	56	37	.	.	PUNCT
ejpam-5021	57	1	as	as	SCONJ
ejpam-5021	57	2	mentioned	mention	VERB
ejpam-5021	57	3	before	before	ADV
ejpam-5021	57	4	,	,	PUNCT
ejpam-5021	57	5	up	up	ADP
ejpam-5021	57	6	to	to	ADP
ejpam-5021	57	7	the	the	DET
ejpam-5021	57	8	present	present	NOUN
ejpam-5021	57	9	,	,	PUNCT
ejpam-5021	57	10	there	there	PRON
ejpam-5021	57	11	has	have	AUX
ejpam-5021	57	12	been	be	AUX
ejpam-5021	57	13	much	much	ADV
ejpam-5021	57	14	practical	practical	ADJ
ejpam-5021	57	15	application	application	NOUN
ejpam-5021	57	16	of	of	ADP
ejpam-5021	57	17	fuzzy	fuzzy	ADJ
ejpam-5021	57	18	soft	soft	ADJ
ejpam-5021	57	19	set	set	NOUN
ejpam-5021	57	20	theory	theory	NOUN
ejpam-5021	57	21	,	,	PUNCT
ejpam-5021	57	22	especially	especially	ADV
ejpam-5021	57	23	the	the	DET
ejpam-5021	57	24	use	use	NOUN
ejpam-5021	57	25	of	of	ADP
ejpam-5021	57	26	the	the	DET
ejpam-5021	57	27	fuzzy	fuzzy	ADJ
ejpam-5021	57	28	soft	soft	ADJ
ejpam-5021	57	29	set	set	NOUN
ejpam-5021	57	30	to	to	PART
ejpam-5021	57	31	solve	solve	VERB
ejpam-5021	57	32	the	the	DET
ejpam-5021	57	33	decision	decision	NOUN
ejpam-5021	57	34	-	-	PUNCT
ejpam-5021	57	35	making	making	NOUN
ejpam-5021	57	36	problem	problem	NOUN
ejpam-5021	57	37	.	.	PUNCT
ejpam-5021	58	1	then	then	ADV
ejpam-5021	58	2	,	,	PUNCT
ejpam-5021	58	3	the	the	DET
ejpam-5021	58	4	context	context	NOUN
ejpam-5021	58	5	of	of	ADP
ejpam-5021	58	6	bipolarity	bipolarity	NOUN
ejpam-5021	58	7	attracts	attract	VERB
ejpam-5021	58	8	some	some	DET
ejpam-5021	58	9	researchers	researcher	NOUN
ejpam-5021	58	10	for	for	ADP
ejpam-5021	58	11	continuous	continuous	ADJ
ejpam-5021	58	12	development	development	NOUN
ejpam-5021	58	13	.	.	PUNCT
ejpam-5021	59	1	shabir	shabir	PROPN
ejpam-5021	59	2	and	and	CCONJ
ejpam-5021	59	3	naz	naz	PROPN
ejpam-5021	59	4	[	[	X
ejpam-5021	59	5	26	26	NUM
ejpam-5021	59	6	]	]	PUNCT
ejpam-5021	59	7	proposed	propose	VERB
ejpam-5021	59	8	the	the	DET
ejpam-5021	59	9	notion	notion	NOUN
ejpam-5021	59	10	of	of	ADP
ejpam-5021	59	11	bipolar	bipolar	ADJ
ejpam-5021	59	12	soft	soft	ADJ
ejpam-5021	59	13	set	set	NOUN
ejpam-5021	59	14	theory	theory	NOUN
ejpam-5021	59	15	.	.	PUNCT
ejpam-5021	60	1	this	this	DET
ejpam-5021	60	2	notion	notion	NOUN
ejpam-5021	60	3	is	be	AUX
ejpam-5021	60	4	generated	generate	VERB
ejpam-5021	60	5	by	by	ADP
ejpam-5021	60	6	the	the	DET
ejpam-5021	60	7	hybridization	hybridization	NOUN
ejpam-5021	60	8	of	of	ADP
ejpam-5021	60	9	the	the	DET
ejpam-5021	60	10	bipolarity	bipolarity	NOUN
ejpam-5021	60	11	concept	concept	NOUN
ejpam-5021	60	12	of	of	ADP
ejpam-5021	60	13	dubois	dubois	PROPN
ejpam-5021	60	14	and	and	CCONJ
ejpam-5021	60	15	prade	prade	NOUN
ejpam-5021	60	16	[	[	X
ejpam-5021	60	17	4	4	NUM
ejpam-5021	60	18	]	]	PUNCT
ejpam-5021	60	19	and	and	CCONJ
ejpam-5021	60	20	soft	soft	ADJ
ejpam-5021	60	21	set	set	NOUN
ejpam-5021	60	22	theory	theory	NOUN
ejpam-5021	60	23	.	.	PUNCT
ejpam-5021	61	1	they	they	PRON
ejpam-5021	61	2	have	have	AUX
ejpam-5021	61	3	studied	study	VERB
ejpam-5021	61	4	the	the	DET
ejpam-5021	61	5	notion	notion	NOUN
ejpam-5021	61	6	of	of	ADP
ejpam-5021	61	7	the	the	DET
ejpam-5021	61	8	bipolarity	bipolarity	NOUN
ejpam-5021	61	9	of	of	ADP
ejpam-5021	61	10	information	information	NOUN
ejpam-5021	61	11	in	in	ADP
ejpam-5021	61	12	terms	term	NOUN
ejpam-5021	61	13	of	of	ADP
ejpam-5021	61	14	soft	soft	ADJ
ejpam-5021	61	15	sets	set	NOUN
ejpam-5021	61	16	.	.	PUNCT
ejpam-5021	62	1	bipolar	bipolar	ADJ
ejpam-5021	62	2	soft	soft	ADJ
ejpam-5021	62	3	set	set	NOUN
ejpam-5021	62	4	theory	theory	NOUN
ejpam-5021	62	5	is	be	AUX
ejpam-5021	62	6	described	describe	VERB
ejpam-5021	62	7	by	by	ADP
ejpam-5021	62	8	two	two	NUM
ejpam-5021	62	9	soft	soft	ADJ
ejpam-5021	62	10	sets	set	NOUN
ejpam-5021	62	11	,	,	PUNCT
ejpam-5021	62	12	one	one	NUM
ejpam-5021	62	13	of	of	ADP
ejpam-5021	62	14	which	which	PRON
ejpam-5021	62	15	provides	provide	VERB
ejpam-5021	62	16	positive	positive	ADJ
ejpam-5021	62	17	information	information	NOUN
ejpam-5021	62	18	and	and	CCONJ
ejpam-5021	62	19	the	the	DET
ejpam-5021	62	20	other	other	ADJ
ejpam-5021	62	21	provides	provide	VERB
ejpam-5021	62	22	negative	negative	ADJ
ejpam-5021	62	23	information	information	NOUN
ejpam-5021	62	24	.	.	PUNCT
ejpam-5021	63	1	therefore	therefore	ADV
ejpam-5021	63	2	,	,	PUNCT
ejpam-5021	63	3	in	in	ADP
ejpam-5021	63	4	2014	2014	NUM
ejpam-5021	63	5	,	,	PUNCT
ejpam-5021	63	6	naz	naz	PROPN
ejpam-5021	63	7	and	and	CCONJ
ejpam-5021	63	8	shabir	shabir	PROPN
ejpam-5021	63	9	[	[	X
ejpam-5021	63	10	23	23	NUM
ejpam-5021	63	11	]	]	PUNCT
ejpam-5021	63	12	proposed	propose	VERB
ejpam-5021	63	13	the	the	DET
ejpam-5021	63	14	notion	notion	NOUN
ejpam-5021	63	15	of	of	ADP
ejpam-5021	63	16	fuzzy	fuzzy	ADJ
ejpam-5021	63	17	bipolar	bipolar	ADJ
ejpam-5021	63	18	soft	soft	ADJ
ejpam-5021	63	19	sets	set	NOUN
ejpam-5021	63	20	based	base	VERB
ejpam-5021	63	21	on	on	ADP
ejpam-5021	63	22	fuzzy	fuzzy	ADJ
ejpam-5021	63	23	soft	soft	ADJ
ejpam-5021	63	24	set	set	NOUN
ejpam-5021	63	25	theory	theory	NOUN
ejpam-5021	63	26	and	and	CCONJ
ejpam-5021	63	27	bipolar	bipolar	ADJ
ejpam-5021	63	28	soft	soft	ADJ
ejpam-5021	63	29	set	set	NOUN
ejpam-5021	63	30	theory	theory	NOUN
ejpam-5021	63	31	.	.	PUNCT
ejpam-5021	64	1	fuzzy	fuzzy	ADJ
ejpam-5021	64	2	bipolar	bipolar	ADJ
ejpam-5021	64	3	soft	soft	ADJ
ejpam-5021	64	4	set	set	NOUN
ejpam-5021	64	5	theory	theory	NOUN
ejpam-5021	64	6	has	have	VERB
ejpam-5021	64	7	the	the	DET
ejpam-5021	64	8	potential	potential	NOUN
ejpam-5021	64	9	to	to	PART
ejpam-5021	64	10	handle	handle	VERB
ejpam-5021	64	11	the	the	DET
ejpam-5021	64	12	bipolarity	bipolarity	NOUN
ejpam-5021	64	13	of	of	ADP
ejpam-5021	64	14	the	the	DET
ejpam-5021	64	15	information	information	NOUN
ejpam-5021	64	16	about	about	ADP
ejpam-5021	64	17	some	some	DET
ejpam-5021	64	18	objects	object	NOUN
ejpam-5021	64	19	with	with	ADP
ejpam-5021	64	20	the	the	DET
ejpam-5021	64	21	help	help	NOUN
ejpam-5021	64	22	of	of	ADP
ejpam-5021	64	23	two	two	NUM
ejpam-5021	64	24	functions	function	NOUN
ejpam-5021	64	25	.	.	PUNCT
ejpam-5021	65	1	one	one	NUM
ejpam-5021	65	2	function	function	NOUN
ejpam-5021	65	3	handles	handle	VERB
ejpam-5021	65	4	the	the	DET
ejpam-5021	65	5	positivity	positivity	NOUN
ejpam-5021	65	6	of	of	ADP
ejpam-5021	65	7	the	the	DET
ejpam-5021	65	8	information	information	NOUN
ejpam-5021	65	9	,	,	PUNCT
ejpam-5021	65	10	while	while	SCONJ
ejpam-5021	65	11	the	the	DET
ejpam-5021	65	12	other	other	ADJ
ejpam-5021	65	13	function	function	NOUN
ejpam-5021	65	14	measures	measure	VERB
ejpam-5021	65	15	the	the	DET
ejpam-5021	65	16	negativity	negativity	NOUN
ejpam-5021	65	17	.	.	PUNCT
ejpam-5021	66	1	to	to	PART
ejpam-5021	66	2	support	support	VERB
ejpam-5021	66	3	solving	solve	VERB
ejpam-5021	66	4	covid-19	covid-19	PROPN
ejpam-5021	66	5	,	,	PUNCT
ejpam-5021	66	6	ali	ali	PROPN
ejpam-5021	66	7	et	et	PROPN
ejpam-5021	66	8	al	al	PROPN
ejpam-5021	66	9	.	.	PUNCT
ejpam-5021	67	1	[	[	X
ejpam-5021	67	2	1	1	X
ejpam-5021	67	3	]	]	PUNCT
ejpam-5021	67	4	r.	r.	PROPN
ejpam-5021	67	5	prasertpong	prasertpong	PROPN
ejpam-5021	67	6	,	,	PUNCT
ejpam-5021	67	7	p.	p.	PROPN
ejpam-5021	67	8	julatha	julatha	PROPN
ejpam-5021	67	9	,	,	PUNCT
ejpam-5021	67	10	a.	a.	NOUN
ejpam-5021	67	11	iampan	iampan	PROPN
ejpam-5021	67	12	/	/	SYM
ejpam-5021	67	13	eur	eur	PROPN
ejpam-5021	67	14	.	.	PUNCT
ejpam-5021	68	1	j.	j.	PROPN
ejpam-5021	68	2	pure	pure	PROPN
ejpam-5021	68	3	appl	appl	PROPN
ejpam-5021	68	4	.	.	PROPN
ejpam-5021	68	5	math	math	PROPN
ejpam-5021	68	6	,	,	PUNCT
ejpam-5021	68	7	17	17	NUM
ejpam-5021	68	8	(	(	PUNCT
ejpam-5021	68	9	1	1	NUM
ejpam-5021	68	10	)	)	PUNCT
ejpam-5021	68	11	(	(	PUNCT
ejpam-5021	68	12	2024	2024	NUM
ejpam-5021	68	13	)	)	PUNCT
ejpam-5021	68	14	,	,	PUNCT
ejpam-5021	68	15	270	270	NUM
ejpam-5021	68	16	-	-	SYM
ejpam-5021	68	17	285	285	NUM
ejpam-5021	68	18	272	272	NUM
ejpam-5021	68	19	presented	present	VERB
ejpam-5021	68	20	the	the	DET
ejpam-5021	68	21	issue	issue	NOUN
ejpam-5021	68	22	of	of	ADP
ejpam-5021	68	23	ranking	rank	VERB
ejpam-5021	68	24	the	the	DET
ejpam-5021	68	25	effectiveness	effectiveness	NOUN
ejpam-5021	68	26	of	of	ADP
ejpam-5021	68	27	covid-19	covid-19	PROPN
ejpam-5021	68	28	tests	test	NOUN
ejpam-5021	68	29	via	via	ADP
ejpam-5021	68	30	fuzzy	fuzzy	ADJ
ejpam-5021	68	31	bipolar	bipolar	ADJ
ejpam-5021	68	32	soft	soft	ADJ
ejpam-5021	68	33	expert	expert	NOUN
ejpam-5021	68	34	sets	set	NOUN
ejpam-5021	68	35	.	.	PUNCT
ejpam-5021	69	1	furthermore	furthermore	ADV
ejpam-5021	69	2	,	,	PUNCT
ejpam-5021	69	3	they	they	PRON
ejpam-5021	69	4	verified	verify	VERB
ejpam-5021	69	5	a	a	DET
ejpam-5021	69	6	comparative	comparative	ADJ
ejpam-5021	69	7	analysis	analysis	NOUN
ejpam-5021	69	8	of	of	ADP
ejpam-5021	69	9	fuzzy	fuzzy	ADJ
ejpam-5021	69	10	soft	soft	ADJ
ejpam-5021	69	11	expert	expert	NOUN
ejpam-5021	69	12	sets	set	NOUN
ejpam-5021	69	13	and	and	CCONJ
ejpam-5021	69	14	fuzzy	fuzzy	ADJ
ejpam-5021	69	15	bipolar	bipolar	ADJ
ejpam-5021	69	16	soft	soft	ADJ
ejpam-5021	69	17	sets	set	NOUN
ejpam-5021	69	18	.	.	PUNCT
ejpam-5021	70	1	to	to	PART
ejpam-5021	70	2	solve	solve	VERB
ejpam-5021	70	3	uncertainty	uncertainty	NOUN
ejpam-5021	70	4	in	in	ADP
ejpam-5021	70	5	algebraic	algebraic	ADJ
ejpam-5021	70	6	structures	structure	NOUN
ejpam-5021	70	7	,	,	PUNCT
ejpam-5021	70	8	hakim	hakim	PROPN
ejpam-5021	70	9	et	et	PROPN
ejpam-5021	70	10	al	al	PROPN
ejpam-5021	70	11	.	.	PUNCT
ejpam-5021	71	1	[	[	X
ejpam-5021	71	2	6	6	NUM
ejpam-5021	71	3	]	]	PUNCT
ejpam-5021	71	4	introduced	introduce	VERB
ejpam-5021	71	5	the	the	DET
ejpam-5021	71	6	notion	notion	NOUN
ejpam-5021	71	7	of	of	ADP
ejpam-5021	71	8	fuzzy	fuzzy	ADJ
ejpam-5021	71	9	bipolar	bipolar	ADJ
ejpam-5021	71	10	soft	soft	ADJ
ejpam-5021	71	11	prime	prime	ADJ
ejpam-5021	71	12	ideal	ideal	NOUN
ejpam-5021	71	13	theory	theory	NOUN
ejpam-5021	71	14	in	in	ADP
ejpam-5021	71	15	ordered	order	VERB
ejpam-5021	71	16	semigroups	semigroup	NOUN
ejpam-5021	71	17	.	.	PUNCT
ejpam-5021	72	1	recently	recently	ADV
ejpam-5021	72	2	,	,	PUNCT
ejpam-5021	72	3	the	the	DET
ejpam-5021	72	4	concept	concept	NOUN
ejpam-5021	72	5	of	of	ADP
ejpam-5021	72	6	fuzzy	fuzzy	ADJ
ejpam-5021	72	7	semibipolar	semibipolar	ADJ
ejpam-5021	72	8	soft	soft	ADJ
ejpam-5021	72	9	sets	set	NOUN
ejpam-5021	72	10	was	be	AUX
ejpam-5021	72	11	developed	develop	VERB
ejpam-5021	72	12	as	as	ADP
ejpam-5021	72	13	one	one	NUM
ejpam-5021	72	14	of	of	ADP
ejpam-5021	72	15	the	the	DET
ejpam-5021	72	16	important	important	ADJ
ejpam-5021	72	17	dimensions	dimension	NOUN
ejpam-5021	72	18	of	of	ADP
ejpam-5021	72	19	fuzzy	fuzzy	ADJ
ejpam-5021	72	20	bipolar	bipolar	ADJ
ejpam-5021	72	21	soft	soft	ADJ
ejpam-5021	72	22	sets	set	NOUN
ejpam-5021	72	23	.	.	PUNCT
ejpam-5021	73	1	such	such	DET
ejpam-5021	73	2	an	an	DET
ejpam-5021	73	3	idea	idea	NOUN
ejpam-5021	73	4	was	be	AUX
ejpam-5021	73	5	proposed	propose	VERB
ejpam-5021	73	6	by	by	ADP
ejpam-5021	73	7	prasertpong	prasertpong	PROPN
ejpam-5021	73	8	[	[	X
ejpam-5021	73	9	24	24	NUM
ejpam-5021	73	10	]	]	PUNCT
ejpam-5021	73	11	.	.	PUNCT
ejpam-5021	74	1	in	in	ADP
ejpam-5021	74	2	this	this	DET
ejpam-5021	74	3	way	way	NOUN
ejpam-5021	74	4	,	,	PUNCT
ejpam-5021	74	5	a	a	DET
ejpam-5021	74	6	fuzzy	fuzzy	ADJ
ejpam-5021	74	7	semibipolar	semibipolar	ADJ
ejpam-5021	74	8	soft	soft	ADJ
ejpam-5021	74	9	set	set	NOUN
ejpam-5021	74	10	is	be	AUX
ejpam-5021	74	11	generated	generate	VERB
ejpam-5021	74	12	by	by	ADP
ejpam-5021	74	13	two	two	NUM
ejpam-5021	74	14	fuzzy	fuzzy	ADJ
ejpam-5021	74	15	soft	soft	ADJ
ejpam-5021	74	16	sets	set	NOUN
ejpam-5021	74	17	induced	induce	VERB
ejpam-5021	74	18	by	by	ADP
ejpam-5021	74	19	the	the	DET
ejpam-5021	74	20	same	same	ADJ
ejpam-5021	74	21	parameter	parameter	NOUN
ejpam-5021	74	22	set	set	NOUN
ejpam-5021	74	23	.	.	PUNCT
ejpam-5021	75	1	then	then	ADV
ejpam-5021	75	2	,	,	PUNCT
ejpam-5021	75	3	for	for	ADP
ejpam-5021	75	4	each	each	DET
ejpam-5021	75	5	parameter	parameter	NOUN
ejpam-5021	75	6	element	element	NOUN
ejpam-5021	75	7	of	of	ADP
ejpam-5021	75	8	a	a	DET
ejpam-5021	75	9	fuzzy	fuzzy	ADJ
ejpam-5021	75	10	semibipolar	semibipolar	ADJ
ejpam-5021	75	11	soft	soft	ADJ
ejpam-5021	75	12	set	set	NOUN
ejpam-5021	75	13	,	,	PUNCT
ejpam-5021	75	14	there	there	PRON
ejpam-5021	75	15	is	be	VERB
ejpam-5021	75	16	both	both	PRON
ejpam-5021	75	17	positive	positive	ADJ
ejpam-5021	75	18	and	and	CCONJ
ejpam-5021	75	19	negative	negative	ADJ
ejpam-5021	75	20	information	information	NOUN
ejpam-5021	75	21	.	.	PUNCT
ejpam-5021	76	1	a	a	DET
ejpam-5021	76	2	single	single	ADJ
ejpam-5021	76	3	parameter	parameter	NOUN
ejpam-5021	76	4	related	relate	VERB
ejpam-5021	76	5	to	to	ADP
ejpam-5021	76	6	two	two	NUM
ejpam-5021	76	7	-	-	PUNCT
ejpam-5021	76	8	way	way	NOUN
ejpam-5021	76	9	information	information	NOUN
ejpam-5021	76	10	is	be	AUX
ejpam-5021	76	11	a	a	DET
ejpam-5021	76	12	prominent	prominent	ADJ
ejpam-5021	76	13	point	point	NOUN
ejpam-5021	76	14	of	of	ADP
ejpam-5021	76	15	this	this	DET
ejpam-5021	76	16	concept	concept	NOUN
ejpam-5021	76	17	in	in	ADP
ejpam-5021	76	18	which	which	PRON
ejpam-5021	76	19	the	the	DET
ejpam-5021	76	20	notion	notion	NOUN
ejpam-5021	76	21	of	of	ADP
ejpam-5021	76	22	fuzzy	fuzzy	ADJ
ejpam-5021	76	23	bipolar	bipolar	ADJ
ejpam-5021	76	24	soft	soft	ADJ
ejpam-5021	76	25	sets	set	NOUN
ejpam-5021	76	26	has	have	VERB
ejpam-5021	76	27	no	no	DET
ejpam-5021	76	28	such	such	ADJ
ejpam-5021	76	29	rule	rule	NOUN
ejpam-5021	76	30	.	.	PUNCT
ejpam-5021	77	1	at	at	ADP
ejpam-5021	77	2	this	this	DET
ejpam-5021	77	3	point	point	NOUN
ejpam-5021	77	4	,	,	PUNCT
ejpam-5021	77	5	prasertpong	prasertpong	PROPN
ejpam-5021	77	6	proposed	propose	VERB
ejpam-5021	77	7	green	green	PROPN
ejpam-5021	77	8	’s	’s	PART
ejpam-5021	77	9	relations	relation	NOUN
ejpam-5021	77	10	l	l	PROPN
ejpam-5021	77	11	and	and	CCONJ
ejpam-5021	77	12	r	r	NOUN
ejpam-5021	77	13	defined	define	VERB
ejpam-5021	77	14	by	by	ADP
ejpam-5021	77	15	fuzzy	fuzzy	ADJ
ejpam-5021	77	16	semibipolar	semibipolar	ADJ
ejpam-5021	77	17	soft	soft	ADJ
ejpam-5021	77	18	left	left	ADJ
ejpam-5021	77	19	ideals	ideal	NOUN
ejpam-5021	77	20	and	and	CCONJ
ejpam-5021	77	21	fuzzy	fuzzy	ADJ
ejpam-5021	77	22	semibipolar	semibipolar	ADJ
ejpam-5021	77	23	soft	soft	ADJ
ejpam-5021	77	24	right	right	ADJ
ejpam-5021	77	25	ideals	ideal	NOUN
ejpam-5021	77	26	,	,	PUNCT
ejpam-5021	77	27	respectively	respectively	ADV
ejpam-5021	77	28	.	.	PUNCT
ejpam-5021	78	1	as	as	ADP
ejpam-5021	78	2	a	a	DET
ejpam-5021	78	3	developing	develop	VERB
ejpam-5021	78	4	point	point	NOUN
ejpam-5021	78	5	of	of	ADP
ejpam-5021	78	6	filters	filter	NOUN
ejpam-5021	78	7	based	base	VERB
ejpam-5021	78	8	on	on	ADP
ejpam-5021	78	9	bipolarity	bipolarity	NOUN
ejpam-5021	78	10	contexts	contexts	NOUN
ejpam-5021	78	11	,	,	PUNCT
ejpam-5021	78	12	in	in	ADP
ejpam-5021	78	13	this	this	DET
ejpam-5021	78	14	paper	paper	NOUN
ejpam-5021	78	15	,	,	PUNCT
ejpam-5021	78	16	we	we	PRON
ejpam-5021	78	17	shall	shall	AUX
ejpam-5021	78	18	introduce	introduce	VERB
ejpam-5021	78	19	the	the	DET
ejpam-5021	78	20	concept	concept	NOUN
ejpam-5021	78	21	of	of	ADP
ejpam-5021	78	22	filters	filter	NOUN
ejpam-5021	78	23	in	in	ADP
ejpam-5021	78	24	terms	term	NOUN
ejpam-5021	78	25	of	of	ADP
ejpam-5021	78	26	fuzzy	fuzzy	ADJ
ejpam-5021	78	27	semibipolar	semibipolar	ADJ
ejpam-5021	78	28	soft	soft	ADJ
ejpam-5021	78	29	sets	set	NOUN
ejpam-5021	78	30	,	,	PUNCT
ejpam-5021	78	31	namely	namely	ADV
ejpam-5021	78	32	,	,	PUNCT
ejpam-5021	78	33	fuzzy	fuzzy	ADJ
ejpam-5021	78	34	semibipolar	semibipolar	ADJ
ejpam-5021	78	35	soft	soft	ADJ
ejpam-5021	78	36	filters	filter	NOUN
ejpam-5021	78	37	.	.	PUNCT
ejpam-5021	79	1	afterward	afterward	ADV
ejpam-5021	79	2	,	,	PUNCT
ejpam-5021	79	3	green	green	PROPN
ejpam-5021	79	4	’s	’s	PART
ejpam-5021	79	5	relation	relation	NOUN
ejpam-5021	79	6	n	n	PRON
ejpam-5021	79	7	will	will	AUX
ejpam-5021	79	8	be	be	AUX
ejpam-5021	79	9	considered	consider	VERB
ejpam-5021	79	10	via	via	ADP
ejpam-5021	79	11	fuzzy	fuzzy	ADJ
ejpam-5021	79	12	semibipolar	semibipolar	ADJ
ejpam-5021	79	13	soft	soft	ADJ
ejpam-5021	79	14	filters	filter	NOUN
ejpam-5021	79	15	.	.	PUNCT
ejpam-5021	80	1	in	in	ADP
ejpam-5021	80	2	other	other	ADJ
ejpam-5021	80	3	words	word	NOUN
ejpam-5021	80	4	,	,	PUNCT
ejpam-5021	80	5	green	green	PROPN
ejpam-5021	80	6	’s	’s	PART
ejpam-5021	80	7	relation	relation	NOUN
ejpam-5021	80	8	n	n	PRON
ejpam-5021	80	9	will	will	AUX
ejpam-5021	80	10	be	be	AUX
ejpam-5021	80	11	described	describe	VERB
ejpam-5021	80	12	by	by	ADP
ejpam-5021	80	13	the	the	DET
ejpam-5021	80	14	rule	rule	NOUN
ejpam-5021	80	15	of	of	ADP
ejpam-5021	80	16	fuzzy	fuzzy	ADJ
ejpam-5021	80	17	semibipolar	semibipolar	ADJ
ejpam-5021	80	18	soft	soft	ADJ
ejpam-5021	80	19	filters	filter	NOUN
ejpam-5021	80	20	.	.	PUNCT
ejpam-5021	81	1	to	to	PART
ejpam-5021	81	2	achieve	achieve	VERB
ejpam-5021	81	3	this	this	PRON
ejpam-5021	81	4	,	,	PUNCT
ejpam-5021	81	5	we	we	PRON
ejpam-5021	81	6	shall	shall	AUX
ejpam-5021	81	7	recall	recall	VERB
ejpam-5021	81	8	the	the	DET
ejpam-5021	81	9	connection	connection	NOUN
ejpam-5021	81	10	between	between	ADP
ejpam-5021	81	11	filter	filter	NOUN
ejpam-5021	81	12	classes	class	NOUN
ejpam-5021	81	13	and	and	CCONJ
ejpam-5021	81	14	green	green	PROPN
ejpam-5021	81	15	’s	’s	PART
ejpam-5021	81	16	relation	relation	NOUN
ejpam-5021	81	17	n	n	CCONJ
ejpam-5021	81	18	together	together	ADV
ejpam-5021	81	19	with	with	ADP
ejpam-5021	81	20	mathematical	mathematical	ADJ
ejpam-5021	81	21	tools	tool	NOUN
ejpam-5021	81	22	for	for	ADP
ejpam-5021	81	23	the	the	DET
ejpam-5021	81	24	fuzzy	fuzzy	ADJ
ejpam-5021	81	25	set	set	VERB
ejpam-5021	81	26	theory	theory	NOUN
ejpam-5021	81	27	-	-	PUNCT
ejpam-5021	81	28	based	base	VERB
ejpam-5021	81	29	descriptions	description	NOUN
ejpam-5021	81	30	of	of	ADP
ejpam-5021	81	31	these	these	PRON
ejpam-5021	81	32	.	.	PUNCT
ejpam-5021	82	1	throughout	throughout	ADP
ejpam-5021	82	2	this	this	DET
ejpam-5021	82	3	paper	paper	NOUN
ejpam-5021	82	4	,	,	PUNCT
ejpam-5021	82	5	u	u	PROPN
ejpam-5021	82	6	denotes	denote	VERB
ejpam-5021	82	7	a	a	DET
ejpam-5021	82	8	non	non	ADJ
ejpam-5021	82	9	-	-	ADJ
ejpam-5021	82	10	empty	empty	ADJ
ejpam-5021	82	11	universal	universal	ADJ
ejpam-5021	82	12	set	set	NOUN
ejpam-5021	82	13	.	.	PUNCT
ejpam-5021	83	1	f	f	PROPN
ejpam-5021	83	2	is	be	AUX
ejpam-5021	83	3	said	say	VERB
ejpam-5021	83	4	to	to	PART
ejpam-5021	83	5	be	be	AUX
ejpam-5021	83	6	a	a	DET
ejpam-5021	83	7	fuzzy	fuzzy	ADJ
ejpam-5021	83	8	subset	subset	NOUN
ejpam-5021	83	9	of	of	ADP
ejpam-5021	83	10	u	u	PRON
ejpam-5021	83	11	if	if	SCONJ
ejpam-5021	83	12	it	it	PRON
ejpam-5021	83	13	is	be	AUX
ejpam-5021	83	14	a	a	DET
ejpam-5021	83	15	function	function	NOUN
ejpam-5021	83	16	from	from	ADP
ejpam-5021	83	17	u	u	PRON
ejpam-5021	83	18	to	to	ADP
ejpam-5021	83	19	the	the	DET
ejpam-5021	83	20	closed	closed	ADJ
ejpam-5021	83	21	unit	unit	NOUN
ejpam-5021	83	22	interval	interval	NOUN
ejpam-5021	83	23	[	[	X
ejpam-5021	83	24	0	0	NUM
ejpam-5021	83	25	,	,	PUNCT
ejpam-5021	83	26	1	1	NUM
ejpam-5021	83	27	]	]	PUNCT
ejpam-5021	84	1	[	[	X
ejpam-5021	84	2	27	27	NUM
ejpam-5021	84	3	]	]	PUNCT
ejpam-5021	84	4	.	.	PUNCT
ejpam-5021	85	1	throughout	throughout	ADP
ejpam-5021	85	2	this	this	DET
ejpam-5021	85	3	paper	paper	NOUN
ejpam-5021	85	4	,	,	PUNCT
ejpam-5021	85	5	f(u	f(u	PROPN
ejpam-5021	85	6	)	)	PUNCT
ejpam-5021	85	7	denotes	denote	VERB
ejpam-5021	85	8	a	a	DET
ejpam-5021	85	9	collection	collection	NOUN
ejpam-5021	85	10	of	of	ADP
ejpam-5021	85	11	all	all	DET
ejpam-5021	85	12	fuzzy	fuzzy	ADJ
ejpam-5021	85	13	subsets	subset	NOUN
ejpam-5021	85	14	of	of	ADP
ejpam-5021	85	15	u.	u.	NOUN
ejpam-5021	85	16	in	in	ADP
ejpam-5021	85	17	this	this	DET
ejpam-5021	85	18	way	way	NOUN
ejpam-5021	85	19	,	,	PUNCT
ejpam-5021	85	20	1u	1u	NUM
ejpam-5021	85	21	is	be	AUX
ejpam-5021	85	22	denoted	denote	VERB
ejpam-5021	85	23	as	as	ADP
ejpam-5021	85	24	a	a	DET
ejpam-5021	85	25	fuzzy	fuzzy	ADJ
ejpam-5021	85	26	subset	subset	NOUN
ejpam-5021	85	27	of	of	ADP
ejpam-5021	85	28	u	u	PRON
ejpam-5021	85	29	defined	define	VERB
ejpam-5021	85	30	by	by	ADP
ejpam-5021	85	31	1u	1u	NUM
ejpam-5021	85	32	(	(	PUNCT
ejpam-5021	85	33	u	u	NOUN
ejpam-5021	85	34	)	)	PUNCT
ejpam-5021	85	35	=	=	SYM
ejpam-5021	85	36	1	1	NUM
ejpam-5021	85	37	for	for	ADP
ejpam-5021	85	38	all	all	PRON
ejpam-5021	85	39	u	u	PROPN
ejpam-5021	85	40	∈	∈	PROPN
ejpam-5021	85	41	u	u	NOUN
ejpam-5021	85	42	,	,	PUNCT
ejpam-5021	85	43	and	and	CCONJ
ejpam-5021	85	44	0u	0u	ADJ
ejpam-5021	85	45	is	be	AUX
ejpam-5021	85	46	denoted	denote	VERB
ejpam-5021	85	47	as	as	ADP
ejpam-5021	85	48	a	a	DET
ejpam-5021	85	49	fuzzy	fuzzy	ADJ
ejpam-5021	85	50	subset	subset	NOUN
ejpam-5021	85	51	of	of	ADP
ejpam-5021	85	52	u	u	NOUN
ejpam-5021	85	53	defined	define	VERB
ejpam-5021	85	54	by	by	ADP
ejpam-5021	85	55	0u	0u	ADJ
ejpam-5021	85	56	(	(	PUNCT
ejpam-5021	85	57	u	u	NOUN
ejpam-5021	85	58	)	)	PUNCT
ejpam-5021	85	59	=	=	SYM
ejpam-5021	85	60	0	0	NUM
ejpam-5021	85	61	for	for	ADP
ejpam-5021	85	62	all	all	DET
ejpam-5021	85	63	u	u	NOUN
ejpam-5021	85	64	∈	∈	PROPN
ejpam-5021	85	65	u	u	NOUN
ejpam-5021	86	1	[	[	X
ejpam-5021	86	2	27	27	NUM
ejpam-5021	86	3	]	]	PUNCT
ejpam-5021	86	4	.	.	PUNCT
ejpam-5021	87	1	obviously	obviously	ADV
ejpam-5021	87	2	,	,	PUNCT
ejpam-5021	87	3	1u	1u	NUM
ejpam-5021	87	4	is	be	AUX
ejpam-5021	87	5	the	the	DET
ejpam-5021	87	6	greatest	great	ADJ
ejpam-5021	87	7	element	element	NOUN
ejpam-5021	87	8	of	of	ADP
ejpam-5021	87	9	f(u	f(u	PROPN
ejpam-5021	87	10	)	)	PUNCT
ejpam-5021	87	11	,	,	PUNCT
ejpam-5021	87	12	and	and	CCONJ
ejpam-5021	87	13	0u	0u	ADJ
ejpam-5021	87	14	is	be	AUX
ejpam-5021	87	15	the	the	DET
ejpam-5021	87	16	least	least	ADJ
ejpam-5021	87	17	element	element	NOUN
ejpam-5021	87	18	of	of	ADP
ejpam-5021	87	19	f(u	f(u	PROPN
ejpam-5021	87	20	)	)	PUNCT
ejpam-5021	88	1	[	[	X
ejpam-5021	88	2	27	27	NUM
ejpam-5021	88	3	]	]	PUNCT
ejpam-5021	88	4	.	.	PUNCT
ejpam-5021	89	1	for	for	ADP
ejpam-5021	89	2	f	f	PROPN
ejpam-5021	89	3	,	,	PUNCT
ejpam-5021	89	4	g	g	PROPN
ejpam-5021	89	5	∈	∈	PROPN
ejpam-5021	89	6	f(u	f(u	PROPN
ejpam-5021	89	7	)	)	PUNCT
ejpam-5021	89	8	,	,	PUNCT
ejpam-5021	89	9	the	the	DET
ejpam-5021	89	10	notation	notation	NOUN
ejpam-5021	89	11	f	f	PROPN
ejpam-5021	89	12	∧̃g	∧̃g	PROPN
ejpam-5021	89	13	(	(	PUNCT
ejpam-5021	89	14	resp	resp	PROPN
ejpam-5021	89	15	.	.	PUNCT
ejpam-5021	89	16	,	,	PUNCT
ejpam-5021	89	17	f	f	PROPN
ejpam-5021	89	18	∨̃g	∨̃g	PROPN
ejpam-5021	89	19	and	and	CCONJ
ejpam-5021	89	20	f+̃g	f+̃g	NOUN
ejpam-5021	89	21	)	)	PUNCT
ejpam-5021	89	22	is	be	AUX
ejpam-5021	89	23	denoted	denote	VERB
ejpam-5021	89	24	as	as	ADP
ejpam-5021	89	25	the	the	DET
ejpam-5021	89	26	fuzzy	fuzzy	ADJ
ejpam-5021	89	27	subset	subset	NOUN
ejpam-5021	89	28	of	of	ADP
ejpam-5021	89	29	u	u	PRON
ejpam-5021	89	30	given	give	VERB
ejpam-5021	89	31	by	by	ADP
ejpam-5021	89	32	(	(	PUNCT
ejpam-5021	89	33	f	f	PROPN
ejpam-5021	89	34	∧̃g)(u	∧̃g)(u	PROPN
ejpam-5021	89	35	)	)	PUNCT
ejpam-5021	89	36	=	=	SYM
ejpam-5021	89	37	min{f(u	min{f(u	PROPN
ejpam-5021	89	38	)	)	PUNCT
ejpam-5021	89	39	,	,	PUNCT
ejpam-5021	89	40	g(u	g(u	PROPN
ejpam-5021	89	41	)	)	PUNCT
ejpam-5021	89	42	}	}	PUNCT
ejpam-5021	89	43	(	(	PUNCT
ejpam-5021	89	44	resp	resp	NOUN
ejpam-5021	89	45	.	.	PUNCT
ejpam-5021	89	46	,	,	PUNCT
ejpam-5021	89	47	(	(	PUNCT
ejpam-5021	89	48	f	f	PROPN
ejpam-5021	89	49	∨̃g)(u	∨̃g)(u	PROPN
ejpam-5021	89	50	)	)	PUNCT
ejpam-5021	89	51	=	=	SYM
ejpam-5021	89	52	max{f(u	max{f(u	PROPN
ejpam-5021	89	53	)	)	PUNCT
ejpam-5021	89	54	,	,	PUNCT
ejpam-5021	89	55	g(u	g(u	PROPN
ejpam-5021	89	56	)	)	PUNCT
ejpam-5021	89	57	}	}	PUNCT
ejpam-5021	89	58	and	and	CCONJ
ejpam-5021	89	59	(	(	PUNCT
ejpam-5021	89	60	f+̃g)(u	f+̃g)(u	ADJ
ejpam-5021	89	61	)	)	PUNCT
ejpam-5021	89	62	=	=	SYM
ejpam-5021	89	63	f(u	f(u	PROPN
ejpam-5021	89	64	)	)	PUNCT
ejpam-5021	90	1	+	+	CCONJ
ejpam-5021	91	1	g(u	g(u	PROPN
ejpam-5021	91	2	)	)	PUNCT
ejpam-5021	91	3	)	)	PUNCT
ejpam-5021	91	4	for	for	ADP
ejpam-5021	91	5	all	all	DET
ejpam-5021	91	6	u	u	PROPN
ejpam-5021	91	7	∈	∈	PROPN
ejpam-5021	91	8	u.	u.	NOUN
ejpam-5021	91	9	for	for	ADP
ejpam-5021	91	10	f	f	PROPN
ejpam-5021	91	11	,	,	PUNCT
ejpam-5021	91	12	g	g	PROPN
ejpam-5021	91	13	∈	∈	PROPN
ejpam-5021	91	14	f(u	f(u	PROPN
ejpam-5021	91	15	)	)	PUNCT
ejpam-5021	91	16	,	,	PUNCT
ejpam-5021	91	17	f≤̃g	f≤̃g	PROPN
ejpam-5021	91	18	is	be	AUX
ejpam-5021	91	19	denoted	denote	VERB
ejpam-5021	91	20	by	by	ADP
ejpam-5021	91	21	meaning	mean	VERB
ejpam-5021	91	22	f(u	f(u	PROPN
ejpam-5021	91	23	)	)	PUNCT
ejpam-5021	91	24	≤	≤	NOUN
ejpam-5021	91	25	g(u	g(u	PROPN
ejpam-5021	91	26	)	)	PUNCT
ejpam-5021	91	27	for	for	ADP
ejpam-5021	91	28	all	all	DET
ejpam-5021	91	29	u	u	NOUN
ejpam-5021	91	30	∈	∈	PROPN
ejpam-5021	91	31	u	u	NOUN
ejpam-5021	91	32	[	[	X
ejpam-5021	91	33	27	27	NUM
ejpam-5021	91	34	]	]	PUNCT
ejpam-5021	91	35	.	.	PUNCT
ejpam-5021	92	1	at	at	ADP
ejpam-5021	92	2	this	this	DET
ejpam-5021	92	3	point	point	NOUN
ejpam-5021	92	4	,	,	PUNCT
ejpam-5021	92	5	the	the	DET
ejpam-5021	92	6	statement	statement	NOUN
ejpam-5021	92	7	f≥̃g	f≥̃g	PROPN
ejpam-5021	92	8	means	mean	VERB
ejpam-5021	92	9	g≤̃f	g≤̃f	PROPN
ejpam-5021	92	10	.	.	PUNCT
ejpam-5021	93	1	let	let	VERB
ejpam-5021	93	2	{	{	PUNCT
ejpam-5021	93	3	fi	fi	NOUN
ejpam-5021	93	4	:	:	PUNCT
ejpam-5021	93	5	i	i	PRON
ejpam-5021	93	6	∈	∈	VERB
ejpam-5021	94	1	i	i	PRON
ejpam-5021	94	2	}	}	PUNCT
ejpam-5021	94	3	be	be	VERB
ejpam-5021	94	4	a	a	DET
ejpam-5021	94	5	non	non	ADJ
ejpam-5021	94	6	-	-	ADJ
ejpam-5021	94	7	empty	empty	ADJ
ejpam-5021	94	8	collection	collection	NOUN
ejpam-5021	94	9	of	of	ADP
ejpam-5021	94	10	all	all	DET
ejpam-5021	94	11	fuzzy	fuzzy	ADJ
ejpam-5021	94	12	subsets	subset	NOUN
ejpam-5021	94	13	of	of	ADP
ejpam-5021	94	14	u.	u.	NOUN
ejpam-5021	94	15	define∧̃	define∧̃	PROPN
ejpam-5021	94	16	i∈i	i∈i	ADJ
ejpam-5021	94	17	fi	fi	NOUN
ejpam-5021	94	18	:	:	PUNCT
ejpam-5021	94	19	u	u	X
ejpam-5021	94	20	→	→	SYM
ejpam-5021	94	21	[	[	X
ejpam-5021	94	22	0	0	NUM
ejpam-5021	94	23	,	,	PUNCT
ejpam-5021	94	24	1]|u	1]|u	NUM
ejpam-5021	94	25	7→	7→	NUM
ejpam-5021	94	26	(	(	PUNCT
ejpam-5021	94	27	∧̃	∧̃	PROPN
ejpam-5021	94	28	i∈i	i∈i	ADJ
ejpam-5021	94	29	fi)(u	fi)(u	PROPN
ejpam-5021	94	30	)	)	PUNCT
ejpam-5021	94	31	:	:	PUNCT
ejpam-5021	94	32	=	=	SYM
ejpam-5021	94	33	inf{fi(u	inf{fi(u	PROPN
ejpam-5021	94	34	)	)	PUNCT
ejpam-5021	94	35	:	:	PUNCT
ejpam-5021	95	1	i	i	PRON
ejpam-5021	95	2	∈	∈	VERB
ejpam-5021	95	3	i	i	X
ejpam-5021	95	4	}	}	PUNCT
ejpam-5021	95	5	and	and	CCONJ
ejpam-5021	95	6	∨̃	∨̃	PROPN
ejpam-5021	95	7	i∈i	i∈i	ADJ
ejpam-5021	95	8	fi	fi	NOUN
ejpam-5021	95	9	:	:	PUNCT
ejpam-5021	95	10	u	u	X
ejpam-5021	95	11	→	→	SYM
ejpam-5021	95	12	[	[	X
ejpam-5021	95	13	0	0	NUM
ejpam-5021	95	14	,	,	PUNCT
ejpam-5021	95	15	1]|u	1]|u	NUM
ejpam-5021	95	16	7→	7→	NUM
ejpam-5021	95	17	(	(	PUNCT
ejpam-5021	95	18	∨̃	∨̃	PROPN
ejpam-5021	95	19	i∈i	i∈i	ADJ
ejpam-5021	95	20	fi)(u	fi)(u	PROPN
ejpam-5021	95	21	)	)	PUNCT
ejpam-5021	95	22	:	:	PUNCT
ejpam-5021	95	23	=	=	SYM
ejpam-5021	95	24	sup{fi(u	sup{fi(u	NOUN
ejpam-5021	95	25	)	)	PUNCT
ejpam-5021	95	26	:	:	PUNCT
ejpam-5021	96	1	i	i	PRON
ejpam-5021	96	2	∈	∈	VERB
ejpam-5021	96	3	i	i	PRON
ejpam-5021	96	4	}	}	PUNCT
ejpam-5021	96	5	.	.	PUNCT
ejpam-5021	97	1	then	then	ADV
ejpam-5021	97	2	∧̃	∧̃	PROPN
ejpam-5021	97	3	i∈ifi	i∈ifi	PROPN
ejpam-5021	97	4	,	,	PUNCT
ejpam-5021	97	5	∨̃	∨̃	PROPN
ejpam-5021	97	6	i∈ifi	i∈ifi	PROPN
ejpam-5021	97	7	∈	∈	PROPN
ejpam-5021	97	8	f(u	f(u	PROPN
ejpam-5021	97	9	)	)	PUNCT
ejpam-5021	98	1	[	[	X
ejpam-5021	98	2	13	13	NUM
ejpam-5021	98	3	]	]	PUNCT
ejpam-5021	98	4	.	.	PUNCT
ejpam-5021	99	1	in	in	ADP
ejpam-5021	99	2	addition	addition	NOUN
ejpam-5021	99	3	,	,	PUNCT
ejpam-5021	99	4	it	it	PRON
ejpam-5021	99	5	is	be	AUX
ejpam-5021	99	6	true	true	ADJ
ejpam-5021	99	7	that∧̃	that∧̃	ADJ
ejpam-5021	99	8	i∈i	i∈i	ADJ
ejpam-5021	99	9	fi	fi	NOUN
ejpam-5021	99	10	=	=	PUNCT
ejpam-5021	99	11	inf{fi	inf{fi	NOUN
ejpam-5021	99	12	:	:	PUNCT
ejpam-5021	100	1	i	i	PRON
ejpam-5021	100	2	∈	∈	VERB
ejpam-5021	100	3	i	i	X
ejpam-5021	100	4	}	}	PUNCT
ejpam-5021	100	5	and	and	CCONJ
ejpam-5021	100	6	∨̃	∨̃	PROPN
ejpam-5021	100	7	i∈i	i∈i	ADJ
ejpam-5021	100	8	fi	fi	NOUN
ejpam-5021	100	9	=	=	NOUN
ejpam-5021	100	10	sup{fi	sup{fi	PRON
ejpam-5021	100	11	:	:	PUNCT
ejpam-5021	101	1	i	i	PRON
ejpam-5021	101	2	∈	∈	VERB
ejpam-5021	101	3	i}[13	i}[13	PROPN
ejpam-5021	101	4	]	]	X
ejpam-5021	101	5	.	.	PUNCT
ejpam-5021	102	1	r.	r.	PROPN
ejpam-5021	102	2	prasertpong	prasertpong	PROPN
ejpam-5021	102	3	,	,	PUNCT
ejpam-5021	102	4	p.	p.	PROPN
ejpam-5021	102	5	julatha	julatha	PROPN
ejpam-5021	102	6	,	,	PUNCT
ejpam-5021	102	7	a.	a.	NOUN
ejpam-5021	102	8	iampan	iampan	PROPN
ejpam-5021	102	9	/	/	SYM
ejpam-5021	102	10	eur	eur	PROPN
ejpam-5021	102	11	.	.	PUNCT
ejpam-5021	103	1	j.	j.	PROPN
ejpam-5021	103	2	pure	pure	PROPN
ejpam-5021	103	3	appl	appl	PROPN
ejpam-5021	103	4	.	.	PROPN
ejpam-5021	103	5	math	math	PROPN
ejpam-5021	103	6	,	,	PUNCT
ejpam-5021	103	7	17	17	NUM
ejpam-5021	103	8	(	(	PUNCT
ejpam-5021	103	9	1	1	NUM
ejpam-5021	103	10	)	)	PUNCT
ejpam-5021	103	11	(	(	PUNCT
ejpam-5021	103	12	2024	2024	NUM
ejpam-5021	103	13	)	)	PUNCT
ejpam-5021	103	14	,	,	PUNCT
ejpam-5021	103	15	270	270	NUM
ejpam-5021	103	16	-	-	SYM
ejpam-5021	103	17	285	285	NUM
ejpam-5021	103	18	273	273	NUM
ejpam-5021	103	19	in	in	ADP
ejpam-5021	103	20	the	the	DET
ejpam-5021	103	21	following	following	NOUN
ejpam-5021	103	22	,	,	PUNCT
ejpam-5021	103	23	p(u	p(u	ADJ
ejpam-5021	103	24	)	)	PUNCT
ejpam-5021	103	25	denotes	denote	VERB
ejpam-5021	103	26	a	a	DET
ejpam-5021	103	27	collection	collection	NOUN
ejpam-5021	103	28	of	of	ADP
ejpam-5021	103	29	subsets	subset	NOUN
ejpam-5021	103	30	of	of	ADP
ejpam-5021	103	31	u.	u.	PROPN
ejpam-5021	103	32	v	v	PROPN
ejpam-5021	103	33	denotes	denote	VERB
ejpam-5021	103	34	a	a	DET
ejpam-5021	103	35	non	non	ADJ
ejpam-5021	103	36	-	-	ADJ
ejpam-5021	103	37	empty	empty	ADJ
ejpam-5021	103	38	universal	universal	ADJ
ejpam-5021	103	39	set	set	NOUN
ejpam-5021	103	40	.	.	PUNCT
ejpam-5021	104	1	let	let	VERB
ejpam-5021	104	2	x	x	PRON
ejpam-5021	104	3	be	be	AUX
ejpam-5021	104	4	a	a	DET
ejpam-5021	104	5	non	non	ADJ
ejpam-5021	104	6	-	-	ADJ
ejpam-5021	104	7	empty	empty	ADJ
ejpam-5021	104	8	subset	subset	NOUN
ejpam-5021	104	9	of	of	ADP
ejpam-5021	104	10	v.	v.	ADV
ejpam-5021	104	11	if	if	SCONJ
ejpam-5021	104	12	f	f	PROPN
ejpam-5021	104	13	is	be	AUX
ejpam-5021	104	14	a	a	DET
ejpam-5021	104	15	function	function	NOUN
ejpam-5021	104	16	from	from	ADP
ejpam-5021	104	17	x	x	PRON
ejpam-5021	104	18	to	to	ADP
ejpam-5021	104	19	p(u	p(u	PROPN
ejpam-5021	104	20	)	)	PUNCT
ejpam-5021	104	21	,	,	PUNCT
ejpam-5021	104	22	then	then	ADV
ejpam-5021	104	23	(	(	PUNCT
ejpam-5021	104	24	f	f	X
ejpam-5021	104	25	,	,	PUNCT
ejpam-5021	104	26	x	x	X
ejpam-5021	104	27	)	)	PUNCT
ejpam-5021	104	28	is	be	AUX
ejpam-5021	104	29	said	say	VERB
ejpam-5021	104	30	to	to	PART
ejpam-5021	104	31	be	be	AUX
ejpam-5021	104	32	a	a	DET
ejpam-5021	104	33	soft	soft	ADJ
ejpam-5021	104	34	set	set	NOUN
ejpam-5021	104	35	over	over	ADP
ejpam-5021	104	36	u	u	NOUN
ejpam-5021	104	37	with	with	ADP
ejpam-5021	104	38	respect	respect	NOUN
ejpam-5021	104	39	to	to	ADP
ejpam-5021	104	40	x.	x.	NOUN
ejpam-5021	104	41	as	as	ADP
ejpam-5021	104	42	the	the	DET
ejpam-5021	104	43	understanding	understanding	NOUN
ejpam-5021	104	44	of	of	ADP
ejpam-5021	104	45	the	the	DET
ejpam-5021	104	46	soft	soft	ADJ
ejpam-5021	104	47	set	set	NOUN
ejpam-5021	104	48	,	,	PUNCT
ejpam-5021	104	49	u	u	NOUN
ejpam-5021	104	50	is	be	AUX
ejpam-5021	104	51	said	say	VERB
ejpam-5021	104	52	to	to	PART
ejpam-5021	104	53	be	be	AUX
ejpam-5021	104	54	a	a	DET
ejpam-5021	104	55	universe	universe	NOUN
ejpam-5021	104	56	of	of	ADP
ejpam-5021	104	57	all	all	DET
ejpam-5021	104	58	alternative	alternative	ADJ
ejpam-5021	104	59	objects	object	NOUN
ejpam-5021	104	60	of	of	ADP
ejpam-5021	104	61	(	(	PUNCT
ejpam-5021	104	62	f	f	X
ejpam-5021	104	63	,	,	PUNCT
ejpam-5021	104	64	x	x	NOUN
ejpam-5021	104	65	)	)	PUNCT
ejpam-5021	104	66	,	,	PUNCT
ejpam-5021	104	67	and	and	CCONJ
ejpam-5021	104	68	v	v	NOUN
ejpam-5021	104	69	is	be	AUX
ejpam-5021	104	70	said	say	VERB
ejpam-5021	104	71	to	to	PART
ejpam-5021	104	72	be	be	AUX
ejpam-5021	104	73	a	a	DET
ejpam-5021	104	74	set	set	NOUN
ejpam-5021	104	75	of	of	ADP
ejpam-5021	104	76	all	all	DET
ejpam-5021	104	77	parameters	parameter	NOUN
ejpam-5021	104	78	of	of	ADP
ejpam-5021	104	79	(	(	PUNCT
ejpam-5021	104	80	f	f	X
ejpam-5021	104	81	,	,	PUNCT
ejpam-5021	104	82	x	x	NOUN
ejpam-5021	104	83	)	)	PUNCT
ejpam-5021	104	84	,	,	PUNCT
ejpam-5021	104	85	where	where	SCONJ
ejpam-5021	104	86	parameters	parameter	NOUN
ejpam-5021	104	87	are	be	AUX
ejpam-5021	104	88	attributes	attribute	NOUN
ejpam-5021	104	89	,	,	PUNCT
ejpam-5021	104	90	characteristics	characteristic	NOUN
ejpam-5021	104	91	or	or	CCONJ
ejpam-5021	104	92	statements	statement	NOUN
ejpam-5021	104	93	of	of	ADP
ejpam-5021	104	94	alternative	alternative	ADJ
ejpam-5021	104	95	objects	object	NOUN
ejpam-5021	104	96	in	in	ADP
ejpam-5021	104	97	u.	u.	NOUN
ejpam-5021	104	98	for	for	ADP
ejpam-5021	104	99	any	any	DET
ejpam-5021	104	100	element	element	NOUN
ejpam-5021	104	101	x	x	SYM
ejpam-5021	104	102	∈	∈	PROPN
ejpam-5021	104	103	x	x	X
ejpam-5021	104	104	,	,	PUNCT
ejpam-5021	104	105	f	f	PROPN
ejpam-5021	104	106	(	(	PUNCT
ejpam-5021	104	107	x	x	X
ejpam-5021	104	108	)	)	PUNCT
ejpam-5021	104	109	is	be	AUX
ejpam-5021	104	110	considered	consider	VERB
ejpam-5021	104	111	as	as	ADP
ejpam-5021	104	112	a	a	DET
ejpam-5021	104	113	set	set	NOUN
ejpam-5021	104	114	of	of	ADP
ejpam-5021	104	115	x	x	ADJ
ejpam-5021	104	116	-	-	ADJ
ejpam-5021	104	117	approximate	approximate	ADJ
ejpam-5021	104	118	elements	element	NOUN
ejpam-5021	104	119	(	(	PUNCT
ejpam-5021	104	120	or	or	CCONJ
ejpam-5021	104	121	x	x	ADJ
ejpam-5021	104	122	-	-	ADJ
ejpam-5021	104	123	alternative	alternative	ADJ
ejpam-5021	104	124	objects	object	NOUN
ejpam-5021	104	125	)	)	PUNCT
ejpam-5021	104	126	of	of	ADP
ejpam-5021	104	127	(	(	PUNCT
ejpam-5021	104	128	f	f	X
ejpam-5021	104	129	,	,	PUNCT
ejpam-5021	104	130	x	x	X
ejpam-5021	104	131	)	)	PUNCT
ejpam-5021	105	1	[	[	X
ejpam-5021	105	2	21	21	NUM
ejpam-5021	105	3	]	]	PUNCT
ejpam-5021	105	4	.	.	PUNCT
ejpam-5021	106	1	throughout	throughout	ADP
ejpam-5021	106	2	this	this	DET
ejpam-5021	106	3	work	work	NOUN
ejpam-5021	106	4	,	,	PUNCT
ejpam-5021	106	5	x	x	PUNCT
ejpam-5021	106	6	and	and	CCONJ
ejpam-5021	106	7	y	y	PROPN
ejpam-5021	106	8	are	be	AUX
ejpam-5021	106	9	denoted	denote	VERB
ejpam-5021	106	10	as	as	ADP
ejpam-5021	106	11	two	two	NUM
ejpam-5021	106	12	non	non	ADJ
ejpam-5021	106	13	-	-	ADJ
ejpam-5021	106	14	empty	empty	ADJ
ejpam-5021	106	15	subsets	subset	NOUN
ejpam-5021	106	16	of	of	ADP
ejpam-5021	106	17	v.	v.	ADP
ejpam-5021	106	18	definition	definition	NOUN
ejpam-5021	106	19	1	1	NUM
ejpam-5021	106	20	.	.	PUNCT
ejpam-5021	107	1	[	[	X
ejpam-5021	107	2	24	24	NUM
ejpam-5021	107	3	]	]	X
ejpam-5021	107	4	the	the	DET
ejpam-5021	107	5	triple	triple	ADJ
ejpam-5021	107	6	notation	notation	NOUN
ejpam-5021	107	7	(	(	PUNCT
ejpam-5021	107	8	f,¬f	f,¬f	PROPN
ejpam-5021	107	9	,	,	PUNCT
ejpam-5021	107	10	x	x	PRON
ejpam-5021	107	11	)	)	PUNCT
ejpam-5021	107	12	is	be	AUX
ejpam-5021	107	13	called	call	VERB
ejpam-5021	107	14	a	a	DET
ejpam-5021	107	15	fuzzy	fuzzy	ADJ
ejpam-5021	107	16	semibipolar	semibipolar	ADJ
ejpam-5021	107	17	soft	soft	ADJ
ejpam-5021	107	18	set	set	NOUN
ejpam-5021	107	19	(	(	PUNCT
ejpam-5021	107	20	briefly	briefly	ADV
ejpam-5021	107	21	,	,	PUNCT
ejpam-5021	107	22	fsss	fsss	PROPN
ejpam-5021	107	23	)	)	PUNCT
ejpam-5021	107	24	over	over	ADP
ejpam-5021	107	25	u	u	NOUN
ejpam-5021	107	26	with	with	ADP
ejpam-5021	107	27	respect	respect	NOUN
ejpam-5021	107	28	to	to	ADP
ejpam-5021	107	29	x	x	PRON
ejpam-5021	107	30	if	if	SCONJ
ejpam-5021	107	31	f	f	X
ejpam-5021	107	32	:	:	PUNCT
ejpam-5021	107	33	x	x	X
ejpam-5021	107	34	→	→	SYM
ejpam-5021	107	35	f(u	f(u	PROPN
ejpam-5021	107	36	)	)	PUNCT
ejpam-5021	107	37	and	and	CCONJ
ejpam-5021	107	38	¬f	¬f	NUM
ejpam-5021	107	39	:	:	PUNCT
ejpam-5021	107	40	x	x	SYM
ejpam-5021	107	41	→	→	SYM
ejpam-5021	107	42	f(u	f(u	PROPN
ejpam-5021	107	43	)	)	PUNCT
ejpam-5021	107	44	are	be	AUX
ejpam-5021	107	45	disjoint	disjoint	NOUN
ejpam-5021	107	46	functions	function	NOUN
ejpam-5021	107	47	such	such	ADJ
ejpam-5021	107	48	that	that	SCONJ
ejpam-5021	107	49	f(x)+̃¬f(x	f(x)+̃¬f(x	NOUN
ejpam-5021	107	50	)	)	PUNCT
ejpam-5021	108	1	=	=	NOUN
ejpam-5021	108	2	1u	1u	NUM
ejpam-5021	108	3	for	for	ADP
ejpam-5021	108	4	all	all	DET
ejpam-5021	108	5	x	x	SYM
ejpam-5021	108	6	∈	∈	NOUN
ejpam-5021	108	7	x.	x.	NOUN
ejpam-5021	108	8	definition	definition	NOUN
ejpam-5021	108	9	2	2	NUM
ejpam-5021	108	10	.	.	PUNCT
ejpam-5021	109	1	[	[	X
ejpam-5021	109	2	24	24	NUM
ejpam-5021	109	3	]	]	PUNCT
ejpam-5021	109	4	let	let	VERB
ejpam-5021	109	5	f	f	NOUN
ejpam-5021	109	6	:	:	PUNCT
ejpam-5021	109	7	=	=	SYM
ejpam-5021	109	8	(	(	PUNCT
ejpam-5021	109	9	f,¬f	f,¬f	NOUN
ejpam-5021	109	10	,	,	PUNCT
ejpam-5021	109	11	x	x	NOUN
ejpam-5021	109	12	)	)	PUNCT
ejpam-5021	109	13	and	and	CCONJ
ejpam-5021	109	14	g	g	NOUN
ejpam-5021	109	15	:	:	PUNCT
ejpam-5021	109	16	=	=	SYM
ejpam-5021	109	17	(	(	PUNCT
ejpam-5021	109	18	g,¬g	g,¬g	PROPN
ejpam-5021	109	19	,	,	PUNCT
ejpam-5021	109	20	y	y	PROPN
ejpam-5021	109	21	)	)	PUNCT
ejpam-5021	109	22	be	be	AUX
ejpam-5021	109	23	fssss	fssss	NOUN
ejpam-5021	109	24	over	over	ADP
ejpam-5021	109	25	u	u	NOUN
ejpam-5021	109	26	with	with	ADP
ejpam-5021	109	27	respect	respect	NOUN
ejpam-5021	109	28	to	to	ADP
ejpam-5021	109	29	x	x	PUNCT
ejpam-5021	109	30	and	and	CCONJ
ejpam-5021	109	31	y	y	PROPN
ejpam-5021	109	32	,	,	PUNCT
ejpam-5021	109	33	respectively	respectively	ADV
ejpam-5021	109	34	.	.	PUNCT
ejpam-5021	110	1	f	f	PROPN
ejpam-5021	110	2	is	be	AUX
ejpam-5021	110	3	a	a	DET
ejpam-5021	110	4	fuzzy	fuzzy	ADJ
ejpam-5021	110	5	semibipolar	semibipolar	ADJ
ejpam-5021	110	6	soft	soft	ADJ
ejpam-5021	110	7	subset	subset	NOUN
ejpam-5021	110	8	of	of	ADP
ejpam-5021	110	9	g	g	NOUN
ejpam-5021	110	10	,	,	PUNCT
ejpam-5021	110	11	denoted	denote	VERB
ejpam-5021	110	12	by	by	ADP
ejpam-5021	110	13	f⊆̃g	f⊆̃g	PROPN
ejpam-5021	110	14	,	,	PUNCT
ejpam-5021	110	15	if	if	SCONJ
ejpam-5021	110	16	x	x	PROPN
ejpam-5021	110	17	⊆	⊆	NUM
ejpam-5021	110	18	y	y	NOUN
ejpam-5021	110	19	and	and	CCONJ
ejpam-5021	110	20	f(x)≤̃g(x	f(x)≤̃g(x	NUM
ejpam-5021	110	21	)	)	PUNCT
ejpam-5021	110	22	and	and	CCONJ
ejpam-5021	110	23	¬f(x)≥̃¬g(x	¬f(x)≥̃¬g(x	NOUN
ejpam-5021	110	24	)	)	PUNCT
ejpam-5021	110	25	for	for	ADP
ejpam-5021	110	26	all	all	PRON
ejpam-5021	110	27	x	x	SYM
ejpam-5021	110	28	∈	∈	NOUN
ejpam-5021	110	29	x.	x.	NOUN
ejpam-5021	110	30	at	at	ADP
ejpam-5021	110	31	this	this	DET
ejpam-5021	110	32	point	point	NOUN
ejpam-5021	110	33	,	,	PUNCT
ejpam-5021	110	34	we	we	PRON
ejpam-5021	110	35	say	say	VERB
ejpam-5021	110	36	that	that	SCONJ
ejpam-5021	110	37	g	g	PROPN
ejpam-5021	110	38	is	be	AUX
ejpam-5021	110	39	a	a	DET
ejpam-5021	110	40	fuzzy	fuzzy	ADJ
ejpam-5021	110	41	semibipolar	semibipolar	ADJ
ejpam-5021	110	42	soft	soft	ADJ
ejpam-5021	110	43	superset	superset	NOUN
ejpam-5021	110	44	of	of	ADP
ejpam-5021	110	45	f.	f.	PROPN
ejpam-5021	110	46	we	we	PRON
ejpam-5021	110	47	write	write	VERB
ejpam-5021	110	48	g⊇̃f	g⊇̃f	PROPN
ejpam-5021	110	49	.	.	PUNCT
ejpam-5021	111	1	furthermore	furthermore	ADV
ejpam-5021	111	2	,	,	PUNCT
ejpam-5021	111	3	f	f	PROPN
ejpam-5021	111	4	is	be	AUX
ejpam-5021	111	5	equal	equal	ADJ
ejpam-5021	111	6	to	to	ADP
ejpam-5021	111	7	g	g	PROPN
ejpam-5021	111	8	if	if	SCONJ
ejpam-5021	111	9	f⊆̃g	f⊆̃g	PROPN
ejpam-5021	111	10	and	and	CCONJ
ejpam-5021	111	11	f⊇̃g	f⊇̃g	ADJ
ejpam-5021	111	12	.	.	PUNCT
ejpam-5021	112	1	definition	definition	NOUN
ejpam-5021	112	2	3	3	NUM
ejpam-5021	112	3	.	.	PUNCT
ejpam-5021	113	1	[	[	X
ejpam-5021	113	2	24	24	NUM
ejpam-5021	113	3	]	]	X
ejpam-5021	113	4	if	if	SCONJ
ejpam-5021	113	5	(	(	PUNCT
ejpam-5021	113	6	fa,¬fa	fa,¬fa	NOUN
ejpam-5021	113	7	,	,	PUNCT
ejpam-5021	113	8	x	x	PRON
ejpam-5021	113	9	)	)	PUNCT
ejpam-5021	113	10	is	be	AUX
ejpam-5021	113	11	a	a	DET
ejpam-5021	113	12	given	give	VERB
ejpam-5021	113	13	fsss	fsss	NOUN
ejpam-5021	113	14	over	over	ADP
ejpam-5021	113	15	u	u	NOUN
ejpam-5021	113	16	with	with	ADP
ejpam-5021	113	17	respect	respect	NOUN
ejpam-5021	113	18	to	to	ADP
ejpam-5021	113	19	x	x	SYM
ejpam-5021	113	20	defined	define	VERB
ejpam-5021	113	21	by	by	ADP
ejpam-5021	113	22	f(x	f(x	PROPN
ejpam-5021	113	23	)	)	PUNCT
ejpam-5021	114	1	=	=	NOUN
ejpam-5021	114	2	1u	1u	NUM
ejpam-5021	114	3	and	and	CCONJ
ejpam-5021	114	4	¬f(x	¬f(x	NOUN
ejpam-5021	114	5	)	)	PUNCT
ejpam-5021	115	1	=	=	VERB
ejpam-5021	115	2	0u	0u	ADJ
ejpam-5021	115	3	for	for	ADP
ejpam-5021	115	4	all	all	DET
ejpam-5021	115	5	x	x	SYM
ejpam-5021	115	6	∈	∈	NOUN
ejpam-5021	115	7	x	x	NOUN
ejpam-5021	115	8	,	,	PUNCT
ejpam-5021	115	9	then	then	ADV
ejpam-5021	115	10	it	it	PRON
ejpam-5021	115	11	is	be	AUX
ejpam-5021	115	12	called	call	VERB
ejpam-5021	115	13	a	a	DET
ejpam-5021	115	14	relative	relative	ADJ
ejpam-5021	115	15	whole	whole	ADJ
ejpam-5021	115	16	fsss	fsss	NOUN
ejpam-5021	115	17	over	over	ADP
ejpam-5021	115	18	u	u	NOUN
ejpam-5021	115	19	with	with	ADP
ejpam-5021	115	20	respect	respect	NOUN
ejpam-5021	115	21	to	to	ADP
ejpam-5021	115	22	x.	x.	NOUN
ejpam-5021	115	23	in	in	ADP
ejpam-5021	115	24	the	the	DET
ejpam-5021	115	25	following	following	NOUN
ejpam-5021	115	26	,	,	PUNCT
ejpam-5021	115	27	we	we	PRON
ejpam-5021	115	28	use	use	VERB
ejpam-5021	115	29	the	the	DET
ejpam-5021	115	30	notation	notation	NOUN
ejpam-5021	115	31	wx	wx	NOUN
ejpam-5021	115	32	:	:	PUNCT
ejpam-5021	115	33	=	=	SYM
ejpam-5021	115	34	(	(	PUNCT
ejpam-5021	115	35	wx	wx	PROPN
ejpam-5021	115	36	,	,	PUNCT
ejpam-5021	115	37	¬wx	¬wx	PROPN
ejpam-5021	115	38	,	,	PUNCT
ejpam-5021	115	39	x	x	NOUN
ejpam-5021	115	40	)	)	PUNCT
ejpam-5021	115	41	instead	instead	ADV
ejpam-5021	115	42	of	of	ADP
ejpam-5021	115	43	a	a	DET
ejpam-5021	115	44	relative	relative	ADJ
ejpam-5021	115	45	whole	whole	ADJ
ejpam-5021	115	46	fsss	fsss	NOUN
ejpam-5021	115	47	over	over	ADP
ejpam-5021	115	48	u	u	NOUN
ejpam-5021	115	49	with	with	ADP
ejpam-5021	115	50	respect	respect	NOUN
ejpam-5021	115	51	to	to	ADP
ejpam-5021	115	52	x.	x.	NOUN
ejpam-5021	115	53	proposition	proposition	NOUN
ejpam-5021	115	54	1	1	NUM
ejpam-5021	115	55	.	.	PUNCT
ejpam-5021	116	1	[	[	X
ejpam-5021	116	2	24	24	NUM
ejpam-5021	116	3	]	]	X
ejpam-5021	116	4	let	let	VERB
ejpam-5021	116	5	{	{	PUNCT
ejpam-5021	116	6	(	(	PUNCT
ejpam-5021	116	7	fi,¬fi	fi,¬fi	PROPN
ejpam-5021	116	8	,	,	PUNCT
ejpam-5021	116	9	x	x	NOUN
ejpam-5021	116	10	)	)	PUNCT
ejpam-5021	116	11	:	:	PUNCT
ejpam-5021	117	1	i	i	PRON
ejpam-5021	117	2	∈	∈	VERB
ejpam-5021	117	3	i	i	PRON
ejpam-5021	117	4	}	}	PUNCT
ejpam-5021	117	5	be	be	VERB
ejpam-5021	117	6	a	a	DET
ejpam-5021	117	7	non	non	ADJ
ejpam-5021	117	8	-	-	ADJ
ejpam-5021	117	9	empty	empty	ADJ
ejpam-5021	117	10	set	set	NOUN
ejpam-5021	117	11	of	of	ADP
ejpam-5021	117	12	all	all	DET
ejpam-5021	117	13	fssss	fssss	NOUN
ejpam-5021	117	14	over	over	ADP
ejpam-5021	117	15	u	u	NOUN
ejpam-5021	117	16	with	with	ADP
ejpam-5021	117	17	respect	respect	NOUN
ejpam-5021	117	18	to	to	ADP
ejpam-5021	117	19	x.	x.	NOUN
ejpam-5021	117	20	define⋂̃	define⋂̃	PROPN
ejpam-5021	117	21	i∈i	i∈i	ADJ
ejpam-5021	117	22	fi	fi	NOUN
ejpam-5021	117	23	:	:	PUNCT
ejpam-5021	117	24	x	x	X
ejpam-5021	117	25	→	→	SYM
ejpam-5021	117	26	f(u)|x	f(u)|x	PROPN
ejpam-5021	117	27	7→	7→	PROPN
ejpam-5021	117	28	(	(	PUNCT
ejpam-5021	117	29	⋂̃	⋂̃	NOUN
ejpam-5021	117	30	i∈i	i∈i	ADJ
ejpam-5021	117	31	fi)(x	fi)(x	PROPN
ejpam-5021	117	32	)	)	PUNCT
ejpam-5021	117	33	:	:	PUNCT
ejpam-5021	118	1	=	=	SYM
ejpam-5021	118	2	∧̃	∧̃	PROPN
ejpam-5021	118	3	i∈i	i∈i	ADJ
ejpam-5021	118	4	fi(x	fi(x	PROPN
ejpam-5021	118	5	)	)	PUNCT
ejpam-5021	118	6	and	and	CCONJ
ejpam-5021	118	7	⋃̃	⋃̃	PROPN
ejpam-5021	118	8	i∈i	i∈i	NOUN
ejpam-5021	118	9	¬fi	¬fi	PROPN
ejpam-5021	118	10	:	:	PUNCT
ejpam-5021	118	11	x	x	X
ejpam-5021	118	12	→	→	SYM
ejpam-5021	118	13	f(u)|x	f(u)|x	PROPN
ejpam-5021	118	14	7→	7→	PROPN
ejpam-5021	118	15	(	(	PUNCT
ejpam-5021	118	16	⋃̃	⋃̃	PROPN
ejpam-5021	118	17	i∈i	i∈i	ADJ
ejpam-5021	118	18	¬fi)(x	¬fi)(x	PROPN
ejpam-5021	118	19	)	)	PUNCT
ejpam-5021	118	20	:	:	PUNCT
ejpam-5021	119	1	=	=	PUNCT
ejpam-5021	119	2	∨̃	∨̃	PROPN
ejpam-5021	119	3	i∈i	i∈i	ADJ
ejpam-5021	119	4	¬fi(x	¬fi(x	PROPN
ejpam-5021	119	5	)	)	PUNCT
ejpam-5021	119	6	.	.	PUNCT
ejpam-5021	120	1	then	then	ADV
ejpam-5021	120	2	(	(	PUNCT
ejpam-5021	120	3	⋂̃	⋂̃	PROPN
ejpam-5021	120	4	i∈ifi	i∈ifi	PROPN
ejpam-5021	120	5	,	,	PUNCT
ejpam-5021	120	6	⋃̃	⋃̃	PROPN
ejpam-5021	120	7	i∈i¬fi	i∈i¬fi	PROPN
ejpam-5021	120	8	,	,	PUNCT
ejpam-5021	120	9	x	x	X
ejpam-5021	120	10	)	)	PUNCT
ejpam-5021	120	11	belongs	belong	VERB
ejpam-5021	120	12	to	to	ADP
ejpam-5021	120	13	the	the	DET
ejpam-5021	120	14	collection	collection	NOUN
ejpam-5021	120	15	of	of	ADP
ejpam-5021	120	16	all	all	DET
ejpam-5021	120	17	fssss	fssss	NOUN
ejpam-5021	120	18	over	over	ADP
ejpam-5021	120	19	u.	u.	PROPN
ejpam-5021	120	20	remark	remark	PROPN
ejpam-5021	120	21	1	1	NUM
ejpam-5021	120	22	.	.	PUNCT
ejpam-5021	121	1	[	[	X
ejpam-5021	121	2	24	24	NUM
ejpam-5021	121	3	]	]	PUNCT
ejpam-5021	121	4	according	accord	VERB
ejpam-5021	121	5	to	to	ADP
ejpam-5021	121	6	proposition	proposition	NOUN
ejpam-5021	121	7	1	1	NUM
ejpam-5021	121	8	,	,	PUNCT
ejpam-5021	121	9	it	it	PRON
ejpam-5021	121	10	is	be	AUX
ejpam-5021	121	11	true	true	ADJ
ejpam-5021	121	12	that	that	SCONJ
ejpam-5021	121	13	(	(	PUNCT
ejpam-5021	121	14	⋂̃	⋂̃	X
ejpam-5021	121	15	i∈i	i∈i	ADJ
ejpam-5021	121	16	fi	fi	NOUN
ejpam-5021	121	17	,	,	PUNCT
ejpam-5021	121	18	⋃̃	⋃̃	PROPN
ejpam-5021	121	19	i∈i	i∈i	ADJ
ejpam-5021	121	20	¬fi	¬fi	PROPN
ejpam-5021	121	21	,	,	PUNCT
ejpam-5021	121	22	x)⊆̃(fj	x)⊆̃(fj	NOUN
ejpam-5021	121	23	,	,	PUNCT
ejpam-5021	121	24	¬fj	¬fj	NOUN
ejpam-5021	121	25	,	,	PUNCT
ejpam-5021	121	26	x	x	X
ejpam-5021	121	27	)	)	PUNCT
ejpam-5021	121	28	for	for	ADP
ejpam-5021	121	29	every	every	DET
ejpam-5021	121	30	j	j	PROPN
ejpam-5021	121	31	∈	∈	PROPN
ejpam-5021	121	32	i.	i.	PROPN
ejpam-5021	121	33	r.	r.	PROPN
ejpam-5021	121	34	prasertpong	prasertpong	PROPN
ejpam-5021	121	35	,	,	PUNCT
ejpam-5021	121	36	p.	p.	PROPN
ejpam-5021	121	37	julatha	julatha	PROPN
ejpam-5021	121	38	,	,	PUNCT
ejpam-5021	121	39	a.	a.	NOUN
ejpam-5021	121	40	iampan	iampan	PROPN
ejpam-5021	121	41	/	/	SYM
ejpam-5021	121	42	eur	eur	PROPN
ejpam-5021	121	43	.	.	PUNCT
ejpam-5021	122	1	j.	j.	PROPN
ejpam-5021	122	2	pure	pure	PROPN
ejpam-5021	122	3	appl	appl	PROPN
ejpam-5021	122	4	.	.	PROPN
ejpam-5021	122	5	math	math	PROPN
ejpam-5021	122	6	,	,	PUNCT
ejpam-5021	122	7	17	17	NUM
ejpam-5021	122	8	(	(	PUNCT
ejpam-5021	122	9	1	1	NUM
ejpam-5021	122	10	)	)	PUNCT
ejpam-5021	122	11	(	(	PUNCT
ejpam-5021	122	12	2024	2024	NUM
ejpam-5021	122	13	)	)	PUNCT
ejpam-5021	122	14	,	,	PUNCT
ejpam-5021	122	15	270	270	NUM
ejpam-5021	122	16	-	-	SYM
ejpam-5021	122	17	285	285	NUM
ejpam-5021	122	18	274	274	NUM
ejpam-5021	122	19	proposition	proposition	NOUN
ejpam-5021	122	20	2	2	NUM
ejpam-5021	122	21	.	.	PUNCT
ejpam-5021	123	1	[	[	X
ejpam-5021	123	2	24	24	NUM
ejpam-5021	123	3	]	]	X
ejpam-5021	123	4	let	let	VERB
ejpam-5021	123	5	{	{	PUNCT
ejpam-5021	123	6	(	(	PUNCT
ejpam-5021	123	7	fi,¬fi	fi,¬fi	PROPN
ejpam-5021	123	8	,	,	PUNCT
ejpam-5021	123	9	x	x	NOUN
ejpam-5021	123	10	)	)	PUNCT
ejpam-5021	123	11	:	:	PUNCT
ejpam-5021	124	1	i	i	PRON
ejpam-5021	124	2	∈	∈	VERB
ejpam-5021	124	3	i	i	PRON
ejpam-5021	124	4	}	}	PUNCT
ejpam-5021	124	5	be	be	VERB
ejpam-5021	124	6	a	a	DET
ejpam-5021	124	7	non	non	ADJ
ejpam-5021	124	8	-	-	ADJ
ejpam-5021	124	9	empty	empty	ADJ
ejpam-5021	124	10	set	set	NOUN
ejpam-5021	124	11	of	of	ADP
ejpam-5021	124	12	all	all	DET
ejpam-5021	124	13	fssss	fssss	NOUN
ejpam-5021	124	14	over	over	ADP
ejpam-5021	124	15	u	u	NOUN
ejpam-5021	124	16	with	with	ADP
ejpam-5021	124	17	respect	respect	NOUN
ejpam-5021	124	18	to	to	ADP
ejpam-5021	124	19	x.	x.	NOUN
ejpam-5021	124	20	then	then	ADV
ejpam-5021	124	21	(	(	PUNCT
ejpam-5021	124	22	⋂̃	⋂̃	X
ejpam-5021	124	23	i∈i	i∈i	ADJ
ejpam-5021	124	24	fi	fi	NOUN
ejpam-5021	124	25	,	,	PUNCT
ejpam-5021	124	26	⋃̃	⋃̃	PROPN
ejpam-5021	124	27	i∈i	i∈i	ADJ
ejpam-5021	124	28	¬fi	¬fi	PROPN
ejpam-5021	124	29	,	,	PUNCT
ejpam-5021	124	30	x	x	NOUN
ejpam-5021	124	31	)	)	PUNCT
ejpam-5021	124	32	=	=	SYM
ejpam-5021	124	33	(	(	PUNCT
ejpam-5021	124	34	inf	inf	NOUN
ejpam-5021	124	35	x	x	X
ejpam-5021	124	36	{	{	PUNCT
ejpam-5021	124	37	fi	fi	NOUN
ejpam-5021	124	38	:	:	PUNCT
ejpam-5021	124	39	i	i	PRON
ejpam-5021	124	40	∈	∈	VERB
ejpam-5021	124	41	i	i	X
ejpam-5021	124	42	}	}	PUNCT
ejpam-5021	124	43	,	,	PUNCT
ejpam-5021	124	44	sup	sup	PROPN
ejpam-5021	124	45	x	x	PUNCT
ejpam-5021	124	46	{	{	PUNCT
ejpam-5021	124	47	¬fi	¬fi	PROPN
ejpam-5021	124	48	:	:	PUNCT
ejpam-5021	124	49	i	i	PRON
ejpam-5021	124	50	∈	∈	VERB
ejpam-5021	124	51	i	i	X
ejpam-5021	124	52	}	}	PUNCT
ejpam-5021	124	53	,	,	PUNCT
ejpam-5021	124	54	x	x	NOUN
ejpam-5021	124	55	)	)	PUNCT
ejpam-5021	124	56	.	.	PUNCT
ejpam-5021	125	1	definition	definition	NOUN
ejpam-5021	125	2	4	4	NUM
ejpam-5021	125	3	.	.	PUNCT
ejpam-5021	126	1	[	[	X
ejpam-5021	126	2	24	24	NUM
ejpam-5021	126	3	]	]	PUNCT
ejpam-5021	126	4	let	let	VERB
ejpam-5021	126	5	a	a	DET
ejpam-5021	126	6	⊆	⊆	NUM
ejpam-5021	126	7	x	x	AUX
ejpam-5021	126	8	be	be	AUX
ejpam-5021	126	9	given	give	VERB
ejpam-5021	126	10	.	.	PUNCT
ejpam-5021	127	1	if	if	SCONJ
ejpam-5021	127	2	(	(	PUNCT
ejpam-5021	127	3	fa,¬fa	fa,¬fa	NOUN
ejpam-5021	127	4	,	,	PUNCT
ejpam-5021	127	5	x	x	PRON
ejpam-5021	127	6	)	)	PUNCT
ejpam-5021	127	7	is	be	AUX
ejpam-5021	127	8	a	a	DET
ejpam-5021	127	9	fsss	fsss	NOUN
ejpam-5021	127	10	over	over	ADP
ejpam-5021	127	11	u	u	NOUN
ejpam-5021	127	12	with	with	ADP
ejpam-5021	127	13	respect	respect	NOUN
ejpam-5021	127	14	to	to	ADP
ejpam-5021	127	15	x	x	SYM
ejpam-5021	127	16	defined	define	VERB
ejpam-5021	127	17	by	by	ADP
ejpam-5021	127	18	fa(x	fa(x	NOUN
ejpam-5021	127	19	)	)	PUNCT
ejpam-5021	127	20	=	=	NOUN
ejpam-5021	127	21	{	{	PUNCT
ejpam-5021	127	22	1u	1u	NUM
ejpam-5021	127	23	if	if	SCONJ
ejpam-5021	127	24	x	x	PROPN
ejpam-5021	127	25	∈	∈	PROPN
ejpam-5021	127	26	a	a	X
ejpam-5021	127	27	,	,	PUNCT
ejpam-5021	127	28	0u	0u	ADJ
ejpam-5021	127	29	if	if	SCONJ
ejpam-5021	127	30	x	x	X
ejpam-5021	127	31	/∈	/∈	NOUN
ejpam-5021	127	32	a	a	X
ejpam-5021	127	33	,	,	PUNCT
ejpam-5021	127	34	and	and	CCONJ
ejpam-5021	127	35	¬fa(x	¬fa(x	NOUN
ejpam-5021	127	36	)	)	PUNCT
ejpam-5021	127	37	=	=	NOUN
ejpam-5021	127	38	{	{	PUNCT
ejpam-5021	127	39	0u	0u	ADJ
ejpam-5021	127	40	if	if	SCONJ
ejpam-5021	127	41	x	x	PROPN
ejpam-5021	127	42	∈	∈	PROPN
ejpam-5021	127	43	a	a	X
ejpam-5021	127	44	,	,	PUNCT
ejpam-5021	127	45	1u	1u	NUM
ejpam-5021	127	46	if	if	SCONJ
ejpam-5021	127	47	x	x	PROPN
ejpam-5021	127	48	/∈	/∈	PUNCT
ejpam-5021	127	49	a	a	X
ejpam-5021	127	50	for	for	ADP
ejpam-5021	127	51	all	all	DET
ejpam-5021	127	52	x	x	SYM
ejpam-5021	127	53	∈	∈	NOUN
ejpam-5021	127	54	x	x	NOUN
ejpam-5021	127	55	,	,	PUNCT
ejpam-5021	127	56	then	then	ADV
ejpam-5021	127	57	it	it	PRON
ejpam-5021	127	58	is	be	AUX
ejpam-5021	127	59	called	call	VERB
ejpam-5021	127	60	a	a	DET
ejpam-5021	127	61	fsss	fsss	NOUN
ejpam-5021	127	62	over	over	ADP
ejpam-5021	127	63	u	u	NOUN
ejpam-5021	127	64	concerning	concern	VERB
ejpam-5021	127	65	a.	a.	NOUN
ejpam-5021	127	66	in	in	ADP
ejpam-5021	127	67	the	the	DET
ejpam-5021	127	68	specificity	specificity	NOUN
ejpam-5021	127	69	,	,	PUNCT
ejpam-5021	127	70	if	if	SCONJ
ejpam-5021	127	71	f	f	X
ejpam-5021	127	72	:	:	PUNCT
ejpam-5021	127	73	=	=	SYM
ejpam-5021	127	74	(	(	PUNCT
ejpam-5021	127	75	f,¬f	f,¬f	NOUN
ejpam-5021	127	76	,	,	PUNCT
ejpam-5021	127	77	x	x	X
ejpam-5021	127	78	)	)	PUNCT
ejpam-5021	127	79	is	be	AUX
ejpam-5021	127	80	any	any	DET
ejpam-5021	127	81	fsss	fsss	NOUN
ejpam-5021	127	82	over	over	ADP
ejpam-5021	127	83	u	u	NOUN
ejpam-5021	127	84	with	with	ADP
ejpam-5021	127	85	respect	respect	NOUN
ejpam-5021	127	86	to	to	ADP
ejpam-5021	127	87	x	x	PUNCT
ejpam-5021	127	88	and	and	CCONJ
ejpam-5021	127	89	a	a	DET
ejpam-5021	127	90	fixed	fix	VERB
ejpam-5021	127	91	element	element	NOUN
ejpam-5021	127	92	x	x	SYM
ejpam-5021	127	93	∈	∈	PROPN
ejpam-5021	127	94	x	x	PUNCT
ejpam-5021	127	95	such	such	ADJ
ejpam-5021	127	96	that	that	SCONJ
ejpam-5021	127	97	f(x	f(x	NOUN
ejpam-5021	127	98	)	)	PUNCT
ejpam-5021	128	1	=	=	NOUN
ejpam-5021	128	2	1u	1u	NUM
ejpam-5021	128	3	and	and	CCONJ
ejpam-5021	128	4	¬f(x	¬f(x	NOUN
ejpam-5021	128	5	)	)	PUNCT
ejpam-5021	129	1	=	=	VERB
ejpam-5021	130	1	0u	0u	ADJ
ejpam-5021	130	2	,	,	PUNCT
ejpam-5021	130	3	then	then	ADV
ejpam-5021	130	4	we	we	PRON
ejpam-5021	130	5	say	say	VERB
ejpam-5021	130	6	that	that	SCONJ
ejpam-5021	130	7	f	f	PROPN
ejpam-5021	130	8	contains	contain	VERB
ejpam-5021	130	9	x.	x.	NOUN
ejpam-5021	130	10	remark	remark	PROPN
ejpam-5021	130	11	2	2	NUM
ejpam-5021	130	12	.	.	PUNCT
ejpam-5021	131	1	[	[	X
ejpam-5021	131	2	24	24	NUM
ejpam-5021	131	3	]	]	PUNCT
ejpam-5021	131	4	according	accord	VERB
ejpam-5021	131	5	to	to	ADP
ejpam-5021	131	6	definition	definition	NOUN
ejpam-5021	131	7	4	4	NUM
ejpam-5021	131	8	,	,	PUNCT
ejpam-5021	131	9	it	it	PRON
ejpam-5021	131	10	is	be	AUX
ejpam-5021	131	11	true	true	ADJ
ejpam-5021	131	12	that	that	SCONJ
ejpam-5021	131	13	for	for	ADP
ejpam-5021	131	14	any	any	DET
ejpam-5021	131	15	subsets	subset	NOUN
ejpam-5021	131	16	a	a	PRON
ejpam-5021	131	17	and	and	CCONJ
ejpam-5021	131	18	b	b	NOUN
ejpam-5021	131	19	of	of	ADP
ejpam-5021	131	20	x	x	PRON
ejpam-5021	131	21	,	,	PUNCT
ejpam-5021	131	22	a	a	DET
ejpam-5021	131	23	⊆	⊆	NUM
ejpam-5021	131	24	b	b	NOUN
ejpam-5021	131	25	if	if	SCONJ
ejpam-5021	131	26	and	and	CCONJ
ejpam-5021	131	27	only	only	ADV
ejpam-5021	131	28	if	if	SCONJ
ejpam-5021	131	29	(	(	PUNCT
ejpam-5021	131	30	fa,¬fa	fa,¬fa	NOUN
ejpam-5021	131	31	,	,	PUNCT
ejpam-5021	131	32	x)⊆̃(fb,¬fb	x)⊆̃(fb,¬fb	PROPN
ejpam-5021	131	33	,	,	PUNCT
ejpam-5021	131	34	x	x	NOUN
ejpam-5021	131	35	)	)	PUNCT
ejpam-5021	131	36	.	.	PUNCT
ejpam-5021	132	1	in	in	ADP
ejpam-5021	132	2	addition	addition	NOUN
ejpam-5021	132	3	,	,	PUNCT
ejpam-5021	132	4	an	an	DET
ejpam-5021	132	5	equality	equality	NOUN
ejpam-5021	132	6	case	case	NOUN
ejpam-5021	132	7	is	be	AUX
ejpam-5021	132	8	also	also	ADV
ejpam-5021	132	9	true	true	ADJ
ejpam-5021	132	10	.	.	PUNCT
ejpam-5021	133	1	recall	recall	VERB
ejpam-5021	133	2	that	that	SCONJ
ejpam-5021	133	3	a	a	DET
ejpam-5021	133	4	groupoid	groupoid	NOUN
ejpam-5021	133	5	is	be	AUX
ejpam-5021	133	6	a	a	DET
ejpam-5021	133	7	non	non	ADJ
ejpam-5021	133	8	-	-	ADJ
ejpam-5021	133	9	empty	empty	ADJ
ejpam-5021	133	10	set	set	NOUN
ejpam-5021	133	11	v	v	NOUN
ejpam-5021	133	12	together	together	ADV
ejpam-5021	133	13	with	with	ADP
ejpam-5021	133	14	a	a	DET
ejpam-5021	133	15	binary	binary	ADJ
ejpam-5021	133	16	operation	operation	NOUN
ejpam-5021	133	17	∗	∗	NOUN
ejpam-5021	133	18	on	on	ADP
ejpam-5021	133	19	v	v	NOUN
ejpam-5021	133	20	,	,	PUNCT
ejpam-5021	133	21	denoted	denote	VERB
ejpam-5021	133	22	by	by	ADP
ejpam-5021	133	23	(	(	PUNCT
ejpam-5021	133	24	v	v	NOUN
ejpam-5021	133	25	,	,	PUNCT
ejpam-5021	133	26	∗	∗	NOUN
ejpam-5021	133	27	)	)	PUNCT
ejpam-5021	133	28	.	.	PUNCT
ejpam-5021	134	1	generally	generally	ADV
ejpam-5021	134	2	,	,	PUNCT
ejpam-5021	134	3	if	if	SCONJ
ejpam-5021	134	4	(	(	PUNCT
ejpam-5021	134	5	v	v	NOUN
ejpam-5021	134	6	,	,	PUNCT
ejpam-5021	134	7	∗	∗	NOUN
ejpam-5021	134	8	)	)	PUNCT
ejpam-5021	134	9	is	be	AUX
ejpam-5021	134	10	a	a	DET
ejpam-5021	134	11	groupoid	groupoid	NOUN
ejpam-5021	134	12	,	,	PUNCT
ejpam-5021	134	13	then	then	ADV
ejpam-5021	134	14	x	x	X
ejpam-5021	134	15	∗	∗	PROPN
ejpam-5021	134	16	y	y	PROPN
ejpam-5021	134	17	is	be	AUX
ejpam-5021	134	18	denoted	denote	VERB
ejpam-5021	134	19	by	by	ADP
ejpam-5021	134	20	xy	xy	PROPN
ejpam-5021	134	21	for	for	ADP
ejpam-5021	134	22	all	all	DET
ejpam-5021	134	23	x	x	NOUN
ejpam-5021	134	24	,	,	PUNCT
ejpam-5021	134	25	y	y	PROPN
ejpam-5021	134	26	∈	∈	PROPN
ejpam-5021	134	27	v.	v.	CCONJ
ejpam-5021	134	28	given	give	VERB
ejpam-5021	134	29	two	two	NUM
ejpam-5021	134	30	non	non	ADJ
ejpam-5021	134	31	-	-	ADJ
ejpam-5021	134	32	empty	empty	ADJ
ejpam-5021	134	33	subsets	subset	NOUN
ejpam-5021	134	34	x	x	PUNCT
ejpam-5021	134	35	and	and	CCONJ
ejpam-5021	134	36	y	y	PROPN
ejpam-5021	134	37	of	of	ADP
ejpam-5021	134	38	a	a	DET
ejpam-5021	134	39	groupoid	groupoid	NOUN
ejpam-5021	134	40	(	(	PUNCT
ejpam-5021	134	41	v	v	NOUN
ejpam-5021	134	42	,	,	PUNCT
ejpam-5021	134	43	∗	∗	NOUN
ejpam-5021	134	44	)	)	PUNCT
ejpam-5021	134	45	,	,	PUNCT
ejpam-5021	134	46	the	the	DET
ejpam-5021	134	47	product	product	NOUN
ejpam-5021	134	48	x	x	PUNCT
ejpam-5021	134	49	∗	∗	NOUN
ejpam-5021	134	50	y	y	PROPN
ejpam-5021	134	51	(	(	PUNCT
ejpam-5021	134	52	simply	simply	ADV
ejpam-5021	134	53	xy	xy	PROPN
ejpam-5021	134	54	)	)	PUNCT
ejpam-5021	134	55	is	be	AUX
ejpam-5021	134	56	defined	define	VERB
ejpam-5021	134	57	by	by	ADP
ejpam-5021	134	58	xy	xy	PROPN
ejpam-5021	134	59	=	=	PUNCT
ejpam-5021	134	60	{	{	PUNCT
ejpam-5021	134	61	xy	xy	NOUN
ejpam-5021	134	62	:	:	PUNCT
ejpam-5021	135	1	x	x	SYM
ejpam-5021	135	2	∈	∈	PROPN
ejpam-5021	135	3	x	x	X
ejpam-5021	135	4	and	and	CCONJ
ejpam-5021	135	5	y	y	PROPN
ejpam-5021	135	6	∈	∈	PROPN
ejpam-5021	135	7	y	y	PROPN
ejpam-5021	135	8	}	}	PUNCT
ejpam-5021	135	9	.	.	PUNCT
ejpam-5021	136	1	let	let	VERB
ejpam-5021	136	2	≤v	≤v	PRON
ejpam-5021	136	3	be	be	AUX
ejpam-5021	136	4	a	a	DET
ejpam-5021	136	5	given	give	VERB
ejpam-5021	136	6	binary	binary	ADJ
ejpam-5021	136	7	relation	relation	NOUN
ejpam-5021	136	8	on	on	ADP
ejpam-5021	136	9	v.	v.	ADP
ejpam-5021	136	10	an	an	DET
ejpam-5021	136	11	ordered	order	VERB
ejpam-5021	136	12	groupoid	groupoid	NOUN
ejpam-5021	136	13	,	,	PUNCT
ejpam-5021	136	14	denoted	denote	VERB
ejpam-5021	136	15	by	by	ADP
ejpam-5021	136	16	(	(	PUNCT
ejpam-5021	136	17	v	v	NOUN
ejpam-5021	136	18	,	,	PUNCT
ejpam-5021	136	19	∗,≤v	∗,≤v	NOUN
ejpam-5021	136	20	)	)	PUNCT
ejpam-5021	136	21	,	,	PUNCT
ejpam-5021	136	22	is	be	AUX
ejpam-5021	136	23	a	a	DET
ejpam-5021	136	24	groupoid	groupoid	NOUN
ejpam-5021	136	25	(	(	PUNCT
ejpam-5021	136	26	v	v	NOUN
ejpam-5021	136	27	,	,	PUNCT
ejpam-5021	136	28	∗	∗	NOUN
ejpam-5021	136	29	)	)	PUNCT
ejpam-5021	136	30	whose	whose	DET
ejpam-5021	136	31	elements	element	NOUN
ejpam-5021	136	32	of	of	ADP
ejpam-5021	136	33	v	v	NOUN
ejpam-5021	136	34	are	be	AUX
ejpam-5021	136	35	partially	partially	ADV
ejpam-5021	136	36	ordered	order	VERB
ejpam-5021	136	37	by	by	ADP
ejpam-5021	136	38	≤v	≤v	NOUN
ejpam-5021	136	39	satisfying	satisfying	NOUN
ejpam-5021	136	40	with	with	ADP
ejpam-5021	136	41	the	the	DET
ejpam-5021	136	42	property	property	NOUN
ejpam-5021	136	43	that	that	PRON
ejpam-5021	136	44	for	for	ADP
ejpam-5021	136	45	all	all	DET
ejpam-5021	136	46	x	x	NOUN
ejpam-5021	136	47	,	,	PUNCT
ejpam-5021	136	48	y	y	PROPN
ejpam-5021	136	49	,	,	PUNCT
ejpam-5021	136	50	z	z	PROPN
ejpam-5021	136	51	∈	∈	PROPN
ejpam-5021	136	52	v	v	NOUN
ejpam-5021	136	53	,	,	PUNCT
ejpam-5021	136	54	x	x	PROPN
ejpam-5021	136	55	≤v	≤v	PROPN
ejpam-5021	136	56	y	y	PROPN
ejpam-5021	136	57	implies	imply	VERB
ejpam-5021	136	58	xz	xz	PROPN
ejpam-5021	136	59	≤v	≤v	PROPN
ejpam-5021	136	60	yz	yz	PROPN
ejpam-5021	136	61	and	and	CCONJ
ejpam-5021	136	62	zx	zx	NUM
ejpam-5021	137	1	≤v	≤v	INTJ
ejpam-5021	137	2	zy	zy	PROPN
ejpam-5021	137	3	.	.	PUNCT
ejpam-5021	138	1	we	we	PRON
ejpam-5021	138	2	usually	usually	ADV
ejpam-5021	138	3	write	write	VERB
ejpam-5021	138	4	simply	simply	ADV
ejpam-5021	138	5	v	v	ADV
ejpam-5021	138	6	instead	instead	ADV
ejpam-5021	138	7	of	of	ADP
ejpam-5021	138	8	(	(	PUNCT
ejpam-5021	138	9	v	v	NOUN
ejpam-5021	138	10	,	,	PUNCT
ejpam-5021	138	11	∗,≤v	∗,≤v	NOUN
ejpam-5021	138	12	)	)	PUNCT
ejpam-5021	138	13	.	.	PUNCT
ejpam-5021	139	1	recall	recall	VERB
ejpam-5021	139	2	that	that	SCONJ
ejpam-5021	139	3	an	an	DET
ejpam-5021	139	4	ordered	order	VERB
ejpam-5021	139	5	semigroup	semigroup	NOUN
ejpam-5021	139	6	is	be	AUX
ejpam-5021	139	7	defined	define	VERB
ejpam-5021	139	8	as	as	ADP
ejpam-5021	139	9	an	an	DET
ejpam-5021	139	10	ordered	ordered	ADJ
ejpam-5021	139	11	associative	associative	ADJ
ejpam-5021	139	12	groupoid	groupoid	NOUN
ejpam-5021	139	13	.	.	PUNCT
ejpam-5021	140	1	to	to	PART
ejpam-5021	140	2	benefit	benefit	VERB
ejpam-5021	140	3	for	for	ADP
ejpam-5021	140	4	the	the	DET
ejpam-5021	140	5	characterization	characterization	NOUN
ejpam-5021	140	6	of	of	ADP
ejpam-5021	140	7	green	green	PROPN
ejpam-5021	140	8	’s	’s	PART
ejpam-5021	140	9	relations	relation	NOUN
ejpam-5021	140	10	,	,	PUNCT
ejpam-5021	140	11	we	we	PRON
ejpam-5021	140	12	shall	shall	AUX
ejpam-5021	140	13	review	review	VERB
ejpam-5021	140	14	some	some	DET
ejpam-5021	140	15	concepts	concept	NOUN
ejpam-5021	140	16	in	in	ADP
ejpam-5021	140	17	an	an	DET
ejpam-5021	140	18	ordered	order	VERB
ejpam-5021	140	19	groupoid	groupoid	PROPN
ejpam-5021	140	20	v	v	NOUN
ejpam-5021	140	21	as	as	SCONJ
ejpam-5021	140	22	follows	follow	VERB
ejpam-5021	140	23	.	.	PUNCT
ejpam-5021	141	1	in	in	ADP
ejpam-5021	141	2	1987	1987	NUM
ejpam-5021	141	3	,	,	PUNCT
ejpam-5021	141	4	kehayopulu	kehayopulu	VERB
ejpam-5021	141	5	[	[	X
ejpam-5021	141	6	9	9	NUM
ejpam-5021	141	7	]	]	PUNCT
ejpam-5021	141	8	was	be	AUX
ejpam-5021	141	9	the	the	DET
ejpam-5021	141	10	first	first	ADJ
ejpam-5021	141	11	to	to	PART
ejpam-5021	141	12	verify	verify	VERB
ejpam-5021	141	13	filters	filter	NOUN
ejpam-5021	141	14	.	.	PUNCT
ejpam-5021	142	1	a	a	DET
ejpam-5021	142	2	non	non	ADJ
ejpam-5021	142	3	-	-	ADJ
ejpam-5021	142	4	empty	empty	ADJ
ejpam-5021	142	5	subset	subset	NOUN
ejpam-5021	142	6	x	x	X
ejpam-5021	142	7	of	of	ADP
ejpam-5021	142	8	v	v	NOUN
ejpam-5021	142	9	is	be	AUX
ejpam-5021	142	10	called	call	VERB
ejpam-5021	142	11	a	a	DET
ejpam-5021	142	12	filter	filter	NOUN
ejpam-5021	142	13	of	of	ADP
ejpam-5021	142	14	v	v	NOUN
ejpam-5021	142	15	if	if	SCONJ
ejpam-5021	142	16	(	(	PUNCT
ejpam-5021	142	17	i	i	NOUN
ejpam-5021	142	18	)	)	PUNCT
ejpam-5021	142	19	for	for	ADP
ejpam-5021	142	20	all	all	DET
ejpam-5021	142	21	x	x	NOUN
ejpam-5021	142	22	,	,	PUNCT
ejpam-5021	142	23	y	y	PROPN
ejpam-5021	142	24	∈	∈	PROPN
ejpam-5021	142	25	v	v	NOUN
ejpam-5021	142	26	,	,	PUNCT
ejpam-5021	142	27	xy	xy	PROPN
ejpam-5021	142	28	∈	∈	PROPN
ejpam-5021	142	29	x	x	PUNCT
ejpam-5021	142	30	implies	imply	VERB
ejpam-5021	142	31	x	x	PUNCT
ejpam-5021	142	32	∈	∈	PROPN
ejpam-5021	142	33	v	v	NOUN
ejpam-5021	142	34	and	and	CCONJ
ejpam-5021	142	35	y	y	PROPN
ejpam-5021	142	36	∈	∈	PROPN
ejpam-5021	142	37	v	v	NOUN
ejpam-5021	142	38	;	;	PUNCT
ejpam-5021	142	39	(	(	PUNCT
ejpam-5021	142	40	ii	ii	NOUN
ejpam-5021	142	41	)	)	PUNCT
ejpam-5021	142	42	for	for	ADP
ejpam-5021	142	43	all	all	DET
ejpam-5021	142	44	x	x	NOUN
ejpam-5021	142	45	,	,	PUNCT
ejpam-5021	142	46	y	y	PROPN
ejpam-5021	142	47	∈	∈	PROPN
ejpam-5021	142	48	v	v	NOUN
ejpam-5021	142	49	,	,	PUNCT
ejpam-5021	142	50	x	x	SYM
ejpam-5021	142	51	∈	∈	NOUN
ejpam-5021	142	52	x	x	X
ejpam-5021	142	53	and	and	CCONJ
ejpam-5021	142	54	x	x	SYM
ejpam-5021	142	55	≤v	≤v	PROPN
ejpam-5021	142	56	y	y	PROPN
ejpam-5021	142	57	∈	∈	PROPN
ejpam-5021	142	58	v	v	AUX
ejpam-5021	142	59	imply	imply	VERB
ejpam-5021	142	60	y	y	PROPN
ejpam-5021	142	61	∈	∈	PROPN
ejpam-5021	142	62	x.	x.	NOUN
ejpam-5021	142	63	for	for	ADP
ejpam-5021	142	64	each	each	DET
ejpam-5021	142	65	x	x	SYM
ejpam-5021	142	66	∈	∈	PROPN
ejpam-5021	142	67	v	v	NOUN
ejpam-5021	142	68	,	,	PUNCT
ejpam-5021	142	69	n(x	n(x	PROPN
ejpam-5021	142	70	)	)	PUNCT
ejpam-5021	142	71	is	be	AUX
ejpam-5021	142	72	denoted	denote	VERB
ejpam-5021	142	73	as	as	ADP
ejpam-5021	142	74	a	a	DET
ejpam-5021	142	75	filter	filter	NOUN
ejpam-5021	142	76	of	of	ADP
ejpam-5021	142	77	v	v	NUM
ejpam-5021	142	78	generated	generate	VERB
ejpam-5021	142	79	by	by	ADP
ejpam-5021	142	80	x.	x.	NOUN
ejpam-5021	142	81	the	the	DET
ejpam-5021	142	82	green	green	PROPN
ejpam-5021	142	83	’s	’s	PART
ejpam-5021	142	84	relation	relation	NOUN
ejpam-5021	142	85	n	n	PROPN
ejpam-5021	142	86	on	on	ADP
ejpam-5021	142	87	u	u	NOUN
ejpam-5021	142	88	in	in	ADP
ejpam-5021	142	89	[	[	X
ejpam-5021	142	90	10	10	NUM
ejpam-5021	142	91	]	]	PUNCT
ejpam-5021	142	92	is	be	AUX
ejpam-5021	142	93	defined	define	VERB
ejpam-5021	142	94	as	as	ADP
ejpam-5021	142	95	n	n	NOUN
ejpam-5021	142	96	:	:	PUNCT
ejpam-5021	142	97	=	=	SYM
ejpam-5021	142	98	{	{	PUNCT
ejpam-5021	142	99	(	(	PUNCT
ejpam-5021	142	100	x	x	NOUN
ejpam-5021	142	101	,	,	PUNCT
ejpam-5021	142	102	y	y	NOUN
ejpam-5021	142	103	)	)	PUNCT
ejpam-5021	142	104	∈	∈	PROPN
ejpam-5021	142	105	v	v	ADP
ejpam-5021	142	106	×	×	NOUN
ejpam-5021	142	107	v	v	NOUN
ejpam-5021	142	108	:	:	PUNCT
ejpam-5021	142	109	n(x	n(x	X
ejpam-5021	142	110	)	)	PUNCT
ejpam-5021	142	111	=	=	SYM
ejpam-5021	142	112	n(y	n(y	PROPN
ejpam-5021	142	113	)	)	PUNCT
ejpam-5021	142	114	}	}	PUNCT
ejpam-5021	142	115	.	.	PUNCT
ejpam-5021	143	1	as	as	ADP
ejpam-5021	143	2	an	an	DET
ejpam-5021	143	3	existential	existential	ADJ
ejpam-5021	143	4	classical	classical	ADJ
ejpam-5021	143	5	relation	relation	NOUN
ejpam-5021	143	6	of	of	ADP
ejpam-5021	143	7	green	green	PROPN
ejpam-5021	143	8	’s	’s	PART
ejpam-5021	143	9	relation	relation	NOUN
ejpam-5021	143	10	n	n	X
ejpam-5021	143	11	above	above	ADV
ejpam-5021	143	12	,	,	PUNCT
ejpam-5021	143	13	this	this	DET
ejpam-5021	143	14	paper	paper	NOUN
ejpam-5021	143	15	contains	contain	VERB
ejpam-5021	143	16	novel	novel	ADJ
ejpam-5021	143	17	knowledge	knowledge	NOUN
ejpam-5021	143	18	based	base	VERB
ejpam-5021	143	19	on	on	ADP
ejpam-5021	143	20	fuzzy	fuzzy	ADJ
ejpam-5021	143	21	semibipolar	semibipolar	ADJ
ejpam-5021	143	22	soft	soft	ADJ
ejpam-5021	143	23	set	set	NOUN
ejpam-5021	143	24	theory	theory	NOUN
ejpam-5021	143	25	as	as	SCONJ
ejpam-5021	143	26	follows	follow	VERB
ejpam-5021	143	27	.	.	PUNCT
ejpam-5021	144	1	•	•	NOUN
ejpam-5021	144	2	the	the	DET
ejpam-5021	144	3	concept	concept	NOUN
ejpam-5021	144	4	of	of	ADP
ejpam-5021	144	5	fuzzy	fuzzy	ADJ
ejpam-5021	144	6	semibipolar	semibipolar	ADJ
ejpam-5021	144	7	soft	soft	ADJ
ejpam-5021	144	8	filters	filter	NOUN
ejpam-5021	144	9	in	in	ADP
ejpam-5021	144	10	ordered	order	VERB
ejpam-5021	144	11	groupoids	groupoid	NOUN
ejpam-5021	144	12	is	be	AUX
ejpam-5021	144	13	introduced	introduce	VERB
ejpam-5021	144	14	.	.	PUNCT
ejpam-5021	145	1	a	a	DET
ejpam-5021	145	2	corresponding	corresponding	ADJ
ejpam-5021	145	3	example	example	NOUN
ejpam-5021	145	4	is	be	AUX
ejpam-5021	145	5	proposed	propose	VERB
ejpam-5021	145	6	.	.	PUNCT
ejpam-5021	146	1	a	a	DET
ejpam-5021	146	2	necessary	necessary	ADJ
ejpam-5021	146	3	and	and	CCONJ
ejpam-5021	146	4	sufficient	sufficient	ADJ
ejpam-5021	146	5	condition	condition	NOUN
ejpam-5021	146	6	for	for	ADP
ejpam-5021	146	7	fuzzy	fuzzy	ADJ
ejpam-5021	146	8	semibipolar	semibipolar	ADJ
ejpam-5021	146	9	soft	soft	ADJ
ejpam-5021	146	10	filters	filter	NOUN
ejpam-5021	146	11	is	be	AUX
ejpam-5021	146	12	examined	examine	VERB
ejpam-5021	146	13	.	.	PUNCT
ejpam-5021	147	1	•	•	NUM
ejpam-5021	147	2	green	green	PROPN
ejpam-5021	147	3	’s	’s	PART
ejpam-5021	147	4	relation	relation	NOUN
ejpam-5021	147	5	n	n	PROPN
ejpam-5021	147	6	on	on	ADP
ejpam-5021	147	7	ordered	order	VERB
ejpam-5021	147	8	groupoids	groupoid	NOUN
ejpam-5021	147	9	is	be	AUX
ejpam-5021	147	10	described	describe	VERB
ejpam-5021	147	11	in	in	ADP
ejpam-5021	147	12	terms	term	NOUN
ejpam-5021	147	13	of	of	ADP
ejpam-5021	147	14	fuzzy	fuzzy	ADJ
ejpam-5021	147	15	semibipolar	semibipolar	ADJ
ejpam-5021	147	16	soft	soft	ADJ
ejpam-5021	147	17	filters	filter	NOUN
ejpam-5021	147	18	.	.	PUNCT
ejpam-5021	148	1	finally	finally	ADV
ejpam-5021	148	2	,	,	PUNCT
ejpam-5021	148	3	the	the	DET
ejpam-5021	148	4	work	work	NOUN
ejpam-5021	148	5	is	be	AUX
ejpam-5021	148	6	summarized	summarize	VERB
ejpam-5021	148	7	.	.	PUNCT
ejpam-5021	149	1	r.	r.	PROPN
ejpam-5021	149	2	prasertpong	prasertpong	PROPN
ejpam-5021	149	3	,	,	PUNCT
ejpam-5021	149	4	p.	p.	PROPN
ejpam-5021	149	5	julatha	julatha	PROPN
ejpam-5021	149	6	,	,	PUNCT
ejpam-5021	149	7	a.	a.	NOUN
ejpam-5021	149	8	iampan	iampan	PROPN
ejpam-5021	149	9	/	/	SYM
ejpam-5021	149	10	eur	eur	PROPN
ejpam-5021	149	11	.	.	PUNCT
ejpam-5021	150	1	j.	j.	PROPN
ejpam-5021	150	2	pure	pure	PROPN
ejpam-5021	150	3	appl	appl	PROPN
ejpam-5021	150	4	.	.	PROPN
ejpam-5021	150	5	math	math	PROPN
ejpam-5021	150	6	,	,	PUNCT
ejpam-5021	150	7	17	17	NUM
ejpam-5021	150	8	(	(	PUNCT
ejpam-5021	150	9	1	1	NUM
ejpam-5021	150	10	)	)	PUNCT
ejpam-5021	150	11	(	(	PUNCT
ejpam-5021	150	12	2024	2024	NUM
ejpam-5021	150	13	)	)	PUNCT
ejpam-5021	150	14	,	,	PUNCT
ejpam-5021	150	15	270	270	NUM
ejpam-5021	150	16	-	-	SYM
ejpam-5021	150	17	285	285	NUM
ejpam-5021	150	18	275	275	NUM
ejpam-5021	150	19	2	2	NUM
ejpam-5021	150	20	.	.	PUNCT
ejpam-5021	150	21	main	main	ADJ
ejpam-5021	150	22	results	result	NOUN
ejpam-5021	150	23	in	in	ADP
ejpam-5021	150	24	this	this	DET
ejpam-5021	150	25	section	section	NOUN
ejpam-5021	150	26	,	,	PUNCT
ejpam-5021	150	27	we	we	PRON
ejpam-5021	150	28	use	use	VERB
ejpam-5021	150	29	the	the	DET
ejpam-5021	150	30	previous	previous	ADJ
ejpam-5021	150	31	fundamental	fundamental	ADJ
ejpam-5021	150	32	notion	notion	NOUN
ejpam-5021	150	33	to	to	PART
ejpam-5021	150	34	study	study	VERB
ejpam-5021	150	35	the	the	DET
ejpam-5021	150	36	characterization	characterization	NOUN
ejpam-5021	150	37	of	of	ADP
ejpam-5021	150	38	a	a	DET
ejpam-5021	150	39	novel	novel	ADJ
ejpam-5021	150	40	filters	filter	NOUN
ejpam-5021	150	41	-	-	PUNCT
ejpam-5021	150	42	based	base	VERB
ejpam-5021	150	43	green	green	NOUN
ejpam-5021	150	44	’s	’s	PART
ejpam-5021	150	45	relation	relation	NOUN
ejpam-5021	150	46	n	n	PRON
ejpam-5021	150	47	on	on	ADP
ejpam-5021	150	48	ordered	order	VERB
ejpam-5021	150	49	groupoids	groupoid	NOUN
ejpam-5021	150	50	.	.	PUNCT
ejpam-5021	151	1	to	to	PART
ejpam-5021	151	2	achieve	achieve	VERB
ejpam-5021	151	3	the	the	DET
ejpam-5021	151	4	goal	goal	NOUN
ejpam-5021	151	5	,	,	PUNCT
ejpam-5021	151	6	in	in	ADP
ejpam-5021	151	7	the	the	DET
ejpam-5021	151	8	starting	starting	NOUN
ejpam-5021	151	9	point	point	NOUN
ejpam-5021	151	10	,	,	PUNCT
ejpam-5021	151	11	we	we	PRON
ejpam-5021	151	12	construct	construct	VERB
ejpam-5021	151	13	the	the	DET
ejpam-5021	151	14	concept	concept	NOUN
ejpam-5021	151	15	of	of	ADP
ejpam-5021	151	16	filters	filter	NOUN
ejpam-5021	151	17	in	in	ADP
ejpam-5021	151	18	terms	term	NOUN
ejpam-5021	151	19	of	of	ADP
ejpam-5021	151	20	fuzzy	fuzzy	ADJ
ejpam-5021	151	21	semibipolar	semibipolar	ADJ
ejpam-5021	151	22	soft	soft	ADJ
ejpam-5021	151	23	sets	set	NOUN
ejpam-5021	151	24	as	as	SCONJ
ejpam-5021	151	25	follows	follow	VERB
ejpam-5021	151	26	.	.	PUNCT
ejpam-5021	152	1	definition	definition	NOUN
ejpam-5021	152	2	5	5	NUM
ejpam-5021	152	3	.	.	PUNCT
ejpam-5021	153	1	let	let	VERB
ejpam-5021	153	2	(	(	PUNCT
ejpam-5021	153	3	x	x	X
ejpam-5021	153	4	,	,	PUNCT
ejpam-5021	153	5	∗,≤x	∗,≤x	NUM
ejpam-5021	153	6	)	)	PUNCT
ejpam-5021	153	7	be	be	AUX
ejpam-5021	153	8	an	an	DET
ejpam-5021	153	9	ordered	order	VERB
ejpam-5021	153	10	groupoid	groupoid	NOUN
ejpam-5021	153	11	and	and	CCONJ
ejpam-5021	153	12	f	f	NOUN
ejpam-5021	153	13	:	:	PUNCT
ejpam-5021	154	1	=	=	SYM
ejpam-5021	154	2	(	(	PUNCT
ejpam-5021	154	3	f,¬f	f,¬f	NOUN
ejpam-5021	154	4	,	,	PUNCT
ejpam-5021	154	5	x	x	X
ejpam-5021	154	6	)	)	PUNCT
ejpam-5021	154	7	a	a	DET
ejpam-5021	154	8	fsss	fsss	NOUN
ejpam-5021	154	9	over	over	ADP
ejpam-5021	154	10	u	u	NOUN
ejpam-5021	154	11	with	with	ADP
ejpam-5021	154	12	respect	respect	NOUN
ejpam-5021	154	13	to	to	ADP
ejpam-5021	154	14	x.	x.	PROPN
ejpam-5021	154	15	(	(	PUNCT
ejpam-5021	154	16	i	i	NOUN
ejpam-5021	154	17	)	)	PUNCT
ejpam-5021	154	18	f	f	PROPN
ejpam-5021	154	19	is	be	AUX
ejpam-5021	154	20	called	call	VERB
ejpam-5021	154	21	a	a	DET
ejpam-5021	154	22	fuzzy	fuzzy	ADJ
ejpam-5021	154	23	semibipolar	semibipolar	ADJ
ejpam-5021	154	24	soft	soft	ADJ
ejpam-5021	154	25	subgroupoid	subgroupoid	NOUN
ejpam-5021	154	26	if	if	SCONJ
ejpam-5021	154	27	it	it	PRON
ejpam-5021	154	28	satisfies	satisfy	VERB
ejpam-5021	154	29	•	•	NUM
ejpam-5021	154	30	f(xy)≥̃f(x)∧̃f(y	f(xy)≥̃f(x)∧̃f(y	NUM
ejpam-5021	154	31	)	)	PUNCT
ejpam-5021	154	32	and	and	CCONJ
ejpam-5021	154	33	¬f(xy)≤̃¬f(x)∨̃¬f(y	¬f(xy)≤̃¬f(x)∨̃¬f(y	NUM
ejpam-5021	154	34	)	)	PUNCT
ejpam-5021	154	35	for	for	ADP
ejpam-5021	154	36	all	all	DET
ejpam-5021	154	37	x	x	NOUN
ejpam-5021	154	38	,	,	PUNCT
ejpam-5021	154	39	y	y	PROPN
ejpam-5021	154	40	∈	∈	PROPN
ejpam-5021	154	41	x.	x.	NOUN
ejpam-5021	154	42	(	(	PUNCT
ejpam-5021	154	43	ii	ii	PROPN
ejpam-5021	154	44	)	)	PUNCT
ejpam-5021	154	45	f	f	PROPN
ejpam-5021	154	46	is	be	AUX
ejpam-5021	154	47	called	call	VERB
ejpam-5021	154	48	a	a	DET
ejpam-5021	154	49	fuzzy	fuzzy	ADJ
ejpam-5021	154	50	semibipolar	semibipolar	ADJ
ejpam-5021	154	51	soft	soft	ADJ
ejpam-5021	154	52	filter	filter	NOUN
ejpam-5021	154	53	(	(	PUNCT
ejpam-5021	154	54	briefly	briefly	ADV
ejpam-5021	154	55	,	,	PUNCT
ejpam-5021	154	56	fssf	fssf	NOUN
ejpam-5021	154	57	)	)	PUNCT
ejpam-5021	154	58	if	if	SCONJ
ejpam-5021	154	59	it	it	PRON
ejpam-5021	154	60	satisfies	satisfy	VERB
ejpam-5021	154	61	two	two	NUM
ejpam-5021	154	62	conditions	condition	NOUN
ejpam-5021	154	63	below	below	ADV
ejpam-5021	154	64	.	.	PUNCT
ejpam-5021	155	1	•	•	NUM
ejpam-5021	155	2	f(xy	f(xy	NUM
ejpam-5021	155	3	)	)	PUNCT
ejpam-5021	155	4	=	=	SYM
ejpam-5021	155	5	f(x)∧̃f(y	f(x)∧̃f(y	NOUN
ejpam-5021	155	6	)	)	PUNCT
ejpam-5021	155	7	and	and	CCONJ
ejpam-5021	155	8	¬f(xy	¬f(xy	NUM
ejpam-5021	155	9	)	)	PUNCT
ejpam-5021	155	10	=	=	SYM
ejpam-5021	155	11	¬f(x)∨̃¬f(y	¬f(x)∨̃¬f(y	NOUN
ejpam-5021	155	12	)	)	PUNCT
ejpam-5021	155	13	for	for	ADP
ejpam-5021	155	14	all	all	DET
ejpam-5021	155	15	x	x	NOUN
ejpam-5021	155	16	,	,	PUNCT
ejpam-5021	155	17	y	y	PROPN
ejpam-5021	155	18	∈	∈	PROPN
ejpam-5021	155	19	x.	x.	NOUN
ejpam-5021	155	20	•	•	NOUN
ejpam-5021	155	21	for	for	ADP
ejpam-5021	155	22	any	any	DET
ejpam-5021	155	23	x	x	NOUN
ejpam-5021	155	24	,	,	PUNCT
ejpam-5021	155	25	y	y	PROPN
ejpam-5021	155	26	∈	∈	PROPN
ejpam-5021	155	27	x	x	X
ejpam-5021	155	28	,	,	PUNCT
ejpam-5021	155	29	x	x	SYM
ejpam-5021	155	30	≤x	≤x	AUX
ejpam-5021	155	31	y	y	PROPN
ejpam-5021	155	32	implies	imply	VERB
ejpam-5021	155	33	f(x)≤̃f(y	f(x)≤̃f(y	PROPN
ejpam-5021	155	34	)	)	PUNCT
ejpam-5021	155	35	and	and	CCONJ
ejpam-5021	155	36	¬f(x)≥̃¬f(y	¬f(x)≥̃¬f(y	NOUN
ejpam-5021	155	37	)	)	PUNCT
ejpam-5021	155	38	.	.	PUNCT
ejpam-5021	156	1	example	example	NOUN
ejpam-5021	157	1	1	1	X
ejpam-5021	157	2	.	.	PUNCT
ejpam-5021	157	3	let	let	VERB
ejpam-5021	157	4	u	u	PRON
ejpam-5021	157	5	:	:	PUNCT
ejpam-5021	157	6	=	=	SYM
ejpam-5021	157	7	{	{	PUNCT
ejpam-5021	157	8	u	u	NOUN
ejpam-5021	157	9	:	:	PUNCT
ejpam-5021	157	10	u	u	NOUN
ejpam-5021	157	11	is	be	AUX
ejpam-5021	157	12	a	a	DET
ejpam-5021	157	13	natural	natural	ADJ
ejpam-5021	157	14	number	number	NOUN
ejpam-5021	157	15	and	and	CCONJ
ejpam-5021	157	16	2024	2024	NUM
ejpam-5021	157	17	≤	≤	NUM
ejpam-5021	157	18	u	u	NOUN
ejpam-5021	157	19	≤	≤	NOUN
ejpam-5021	157	20	2033	2033	NUM
ejpam-5021	157	21	}	}	PUNCT
ejpam-5021	157	22	be	be	AUX
ejpam-5021	157	23	given	give	VERB
ejpam-5021	157	24	,	,	PUNCT
ejpam-5021	157	25	and	and	CCONJ
ejpam-5021	157	26	let	let	VERB
ejpam-5021	157	27	f	f	PRON
ejpam-5021	157	28	be	be	AUX
ejpam-5021	157	29	a	a	DET
ejpam-5021	157	30	family	family	NOUN
ejpam-5021	157	31	of	of	ADP
ejpam-5021	157	32	subsets	subset	NOUN
ejpam-5021	157	33	of	of	ADP
ejpam-5021	157	34	u	u	NOUN
ejpam-5021	157	35	defined	define	VERB
ejpam-5021	157	36	by	by	ADP
ejpam-5021	157	37	the	the	DET
ejpam-5021	157	38	set	set	NOUN
ejpam-5021	157	39	{	{	PUNCT
ejpam-5021	157	40	p	p	X
ejpam-5021	157	41	:	:	PUNCT
ejpam-5021	157	42	=	=	SYM
ejpam-5021	157	43	{	{	PUNCT
ejpam-5021	157	44	u	u	NOUN
ejpam-5021	157	45	∈	∈	PROPN
ejpam-5021	157	46	u	u	NOUN
ejpam-5021	157	47	:	:	PUNCT
ejpam-5021	157	48	u	u	NOUN
ejpam-5021	157	49	is	be	AUX
ejpam-5021	157	50	a	a	DET
ejpam-5021	157	51	prime	prime	ADJ
ejpam-5021	157	52	number	number	NOUN
ejpam-5021	157	53	}	}	PUNCT
ejpam-5021	157	54	,	,	PUNCT
ejpam-5021	157	55	c	c	NOUN
ejpam-5021	157	56	:	:	PUNCT
ejpam-5021	157	57	=	=	SYM
ejpam-5021	157	58	{	{	PUNCT
ejpam-5021	157	59	u	u	NOUN
ejpam-5021	157	60	∈	∈	PROPN
ejpam-5021	157	61	u	u	NOUN
ejpam-5021	157	62	:	:	PUNCT
ejpam-5021	157	63	u	u	NOUN
ejpam-5021	157	64	is	be	AUX
ejpam-5021	157	65	a	a	DET
ejpam-5021	157	66	composite	composite	ADJ
ejpam-5021	157	67	number	number	NOUN
ejpam-5021	157	68	}	}	PUNCT
ejpam-5021	157	69	}	}	PUNCT
ejpam-5021	157	70	.	.	PUNCT
ejpam-5021	158	1	then	then	ADV
ejpam-5021	158	2	,	,	PUNCT
ejpam-5021	158	3	it	it	PRON
ejpam-5021	158	4	is	be	AUX
ejpam-5021	158	5	clear	clear	ADJ
ejpam-5021	158	6	that	that	SCONJ
ejpam-5021	158	7	f	f	PROPN
ejpam-5021	158	8	is	be	AUX
ejpam-5021	158	9	a	a	DET
ejpam-5021	158	10	partition	partition	NOUN
ejpam-5021	158	11	of	of	ADP
ejpam-5021	158	12	u.	u.	NOUN
ejpam-5021	158	13	define	define	VERB
ejpam-5021	158	14	two	two	NUM
ejpam-5021	158	15	fuzzy	fuzzy	ADJ
ejpam-5021	158	16	subsets	subset	NOUN
ejpam-5021	158	17	α	α	NOUN
ejpam-5021	158	18	and	and	CCONJ
ejpam-5021	158	19	¬α	¬α	NOUN
ejpam-5021	158	20	of	of	ADP
ejpam-5021	158	21	u	u	NOUN
ejpam-5021	158	22	by	by	ADP
ejpam-5021	158	23	α(u	α(u	NOUN
ejpam-5021	158	24	)	)	PUNCT
ejpam-5021	158	25	=	=	NOUN
ejpam-5021	158	26	{	{	PUNCT
ejpam-5021	158	27	0.8	0.8	NUM
ejpam-5021	158	28	if	if	SCONJ
ejpam-5021	158	29	u	u	PROPN
ejpam-5021	158	30	∈	∈	PROPN
ejpam-5021	158	31	c	c	PROPN
ejpam-5021	158	32	,	,	PUNCT
ejpam-5021	158	33	0.2	0.2	NUM
ejpam-5021	158	34	if	if	SCONJ
ejpam-5021	158	35	u	u	PROPN
ejpam-5021	158	36	∈	∈	PROPN
ejpam-5021	158	37	p	p	X
ejpam-5021	158	38	,	,	PUNCT
ejpam-5021	158	39	and	and	CCONJ
ejpam-5021	158	40	¬α(u	¬α(u	VERB
ejpam-5021	158	41	)	)	PUNCT
ejpam-5021	158	42	=	=	PRON
ejpam-5021	158	43	{	{	PUNCT
ejpam-5021	158	44	0.2	0.2	NUM
ejpam-5021	158	45	if	if	SCONJ
ejpam-5021	158	46	u	u	PROPN
ejpam-5021	158	47	∈	∈	PROPN
ejpam-5021	158	48	c	c	PROPN
ejpam-5021	158	49	,	,	PUNCT
ejpam-5021	158	50	0.8	0.8	NUM
ejpam-5021	158	51	if	if	SCONJ
ejpam-5021	158	52	u	u	PROPN
ejpam-5021	158	53	∈	∈	PROPN
ejpam-5021	158	54	p	p	NOUN
ejpam-5021	158	55	for	for	ADP
ejpam-5021	158	56	all	all	PRON
ejpam-5021	158	57	u	u	PROPN
ejpam-5021	158	58	∈	∈	NOUN
ejpam-5021	158	59	u.	u.	NOUN
ejpam-5021	158	60	let	let	VERB
ejpam-5021	158	61	v	v	X
ejpam-5021	158	62	:	:	PUNCT
ejpam-5021	158	63	=	=	SYM
ejpam-5021	158	64	{	{	PUNCT
ejpam-5021	158	65	xi	xi	X
ejpam-5021	158	66	:	:	PUNCT
ejpam-5021	158	67	i	i	PRON
ejpam-5021	158	68	is	be	AUX
ejpam-5021	158	69	a	a	DET
ejpam-5021	158	70	natural	natural	ADJ
ejpam-5021	158	71	number	number	NOUN
ejpam-5021	158	72	}	}	PUNCT
ejpam-5021	158	73	,	,	PUNCT
ejpam-5021	158	74	and	and	CCONJ
ejpam-5021	158	75	let	let	VERB
ejpam-5021	158	76	x	x	PRON
ejpam-5021	158	77	:	:	PUNCT
ejpam-5021	158	78	=	=	SYM
ejpam-5021	158	79	{	{	PUNCT
ejpam-5021	158	80	x1	x1	PROPN
ejpam-5021	158	81	,	,	PUNCT
ejpam-5021	158	82	x2	x2	PROPN
ejpam-5021	158	83	,	,	PUNCT
ejpam-5021	158	84	x3	x3	ADJ
ejpam-5021	158	85	,	,	PUNCT
ejpam-5021	158	86	x4	x4	PROPN
ejpam-5021	158	87	}	}	PUNCT
ejpam-5021	158	88	⊆	⊆	NUM
ejpam-5021	158	89	v	v	NOUN
ejpam-5021	158	90	be	be	AUX
ejpam-5021	158	91	a	a	DET
ejpam-5021	158	92	set	set	NOUN
ejpam-5021	158	93	whose	whose	DET
ejpam-5021	158	94	elements	element	NOUN
ejpam-5021	158	95	of	of	ADP
ejpam-5021	158	96	x	x	SYM
ejpam-5021	158	97	are	be	AUX
ejpam-5021	158	98	partially	partially	ADV
ejpam-5021	158	99	ordered	order	VERB
ejpam-5021	158	100	by	by	ADP
ejpam-5021	158	101	≤x	≤x	PROPN
ejpam-5021	158	102	satisfying	satisfy	VERB
ejpam-5021	158	103	≤x	≤x	NOUN
ejpam-5021	158	104	:	:	PUNCT
ejpam-5021	158	105	=	=	SYM
ejpam-5021	158	106	{	{	PUNCT
ejpam-5021	158	107	(	(	PUNCT
ejpam-5021	158	108	x1	x1	PROPN
ejpam-5021	158	109	,	,	PUNCT
ejpam-5021	158	110	x1	x1	PROPN
ejpam-5021	158	111	)	)	PUNCT
ejpam-5021	158	112	,	,	PUNCT
ejpam-5021	158	113	(	(	PUNCT
ejpam-5021	158	114	x2	x2	INTJ
ejpam-5021	158	115	,	,	PUNCT
ejpam-5021	158	116	x2	x2	PROPN
ejpam-5021	158	117	)	)	PUNCT
ejpam-5021	158	118	,	,	PUNCT
ejpam-5021	158	119	(	(	PUNCT
ejpam-5021	158	120	x3	x3	ADJ
ejpam-5021	158	121	,	,	PUNCT
ejpam-5021	158	122	x3	x3	ADJ
ejpam-5021	158	123	)	)	PUNCT
ejpam-5021	158	124	,	,	PUNCT
ejpam-5021	158	125	(	(	PUNCT
ejpam-5021	158	126	x4	x4	PROPN
ejpam-5021	158	127	,	,	PUNCT
ejpam-5021	158	128	x4	x4	PROPN
ejpam-5021	158	129	)	)	PUNCT
ejpam-5021	158	130	,	,	PUNCT
ejpam-5021	158	131	(	(	PUNCT
ejpam-5021	158	132	x1	x1	X
ejpam-5021	158	133	,	,	PUNCT
ejpam-5021	158	134	x2	x2	PROPN
ejpam-5021	158	135	)	)	PUNCT
ejpam-5021	158	136	,	,	PUNCT
ejpam-5021	158	137	(	(	PUNCT
ejpam-5021	158	138	x3	x3	ADJ
ejpam-5021	158	139	,	,	PUNCT
ejpam-5021	158	140	x4	x4	PROPN
ejpam-5021	158	141	)	)	PUNCT
ejpam-5021	158	142	,	,	PUNCT
ejpam-5021	158	143	(	(	PUNCT
ejpam-5021	158	144	x4	x4	PROPN
ejpam-5021	158	145	,	,	PUNCT
ejpam-5021	158	146	x3	x3	ADJ
ejpam-5021	158	147	)	)	PUNCT
ejpam-5021	158	148	}	}	PUNCT
ejpam-5021	158	149	.	.	PUNCT
ejpam-5021	159	1	define	define	VERB
ejpam-5021	159	2	a	a	DET
ejpam-5021	159	3	binary	binary	ADJ
ejpam-5021	159	4	operation	operation	NOUN
ejpam-5021	159	5	∗	∗	NOUN
ejpam-5021	159	6	on	on	ADP
ejpam-5021	159	7	x	x	PUNCT
ejpam-5021	159	8	by	by	ADP
ejpam-5021	159	9	multiplication	multiplication	NOUN
ejpam-5021	159	10	rules	rule	NOUN
ejpam-5021	159	11	as	as	ADP
ejpam-5021	159	12	table	table	NOUN
ejpam-5021	159	13	1	1	NUM
ejpam-5021	159	14	below	below	ADV
ejpam-5021	159	15	.	.	PUNCT
ejpam-5021	160	1	table	table	NOUN
ejpam-5021	160	2	1	1	NUM
ejpam-5021	160	3	:	:	PUNCT
ejpam-5021	160	4	the	the	DET
ejpam-5021	160	5	table	table	NOUN
ejpam-5021	160	6	of	of	ADP
ejpam-5021	160	7	multiplication	multiplication	NOUN
ejpam-5021	160	8	rules	rule	NOUN
ejpam-5021	160	9	on	on	ADP
ejpam-5021	160	10	x	x	X
ejpam-5021	160	11	∗	∗	NOUN
ejpam-5021	161	1	x1	x1	NOUN
ejpam-5021	162	1	x2	x2	NOUN
ejpam-5021	162	2	x3	x3	PROPN
ejpam-5021	163	1	x4	x4	PROPN
ejpam-5021	163	2	x1	x1	PROPN
ejpam-5021	164	1	x1	x1	NUM
ejpam-5021	165	1	x1	x1	NUM
ejpam-5021	165	2	x3	x3	PROPN
ejpam-5021	166	1	x4	x4	PROPN
ejpam-5021	167	1	x2	x2	PROPN
ejpam-5021	168	1	x1	x1	NUM
ejpam-5021	169	1	x2	x2	PROPN
ejpam-5021	169	2	x3	x3	PROPN
ejpam-5021	169	3	x4	x4	PROPN
ejpam-5021	169	4	x3	x3	PROPN
ejpam-5021	169	5	x3	x3	PROPN
ejpam-5021	170	1	x4	x4	PROPN
ejpam-5021	170	2	x3	x3	PROPN
ejpam-5021	170	3	x4	x4	PROPN
ejpam-5021	170	4	x4	x4	PROPN
ejpam-5021	170	5	x3	x3	PROPN
ejpam-5021	170	6	x4	x4	PROPN
ejpam-5021	171	1	x4	x4	PROPN
ejpam-5021	171	2	x3	x3	PROPN
ejpam-5021	171	3	r.	r.	PROPN
ejpam-5021	171	4	prasertpong	prasertpong	PROPN
ejpam-5021	171	5	,	,	PUNCT
ejpam-5021	171	6	p.	p.	PROPN
ejpam-5021	171	7	julatha	julatha	PROPN
ejpam-5021	171	8	,	,	PUNCT
ejpam-5021	171	9	a.	a.	NOUN
ejpam-5021	171	10	iampan	iampan	PROPN
ejpam-5021	171	11	/	/	SYM
ejpam-5021	171	12	eur	eur	PROPN
ejpam-5021	171	13	.	.	PUNCT
ejpam-5021	172	1	j.	j.	PROPN
ejpam-5021	172	2	pure	pure	PROPN
ejpam-5021	172	3	appl	appl	PROPN
ejpam-5021	172	4	.	.	PROPN
ejpam-5021	172	5	math	math	PROPN
ejpam-5021	172	6	,	,	PUNCT
ejpam-5021	172	7	17	17	NUM
ejpam-5021	172	8	(	(	PUNCT
ejpam-5021	172	9	1	1	NUM
ejpam-5021	172	10	)	)	PUNCT
ejpam-5021	172	11	(	(	PUNCT
ejpam-5021	172	12	2024	2024	NUM
ejpam-5021	172	13	)	)	PUNCT
ejpam-5021	172	14	,	,	PUNCT
ejpam-5021	172	15	270	270	NUM
ejpam-5021	172	16	-	-	SYM
ejpam-5021	172	17	285	285	NUM
ejpam-5021	172	18	276	276	NUM
ejpam-5021	172	19	then	then	ADV
ejpam-5021	172	20	,	,	PUNCT
ejpam-5021	172	21	it	it	PRON
ejpam-5021	172	22	is	be	AUX
ejpam-5021	172	23	routine	routine	ADJ
ejpam-5021	172	24	to	to	PART
ejpam-5021	172	25	verify	verify	VERB
ejpam-5021	172	26	that	that	SCONJ
ejpam-5021	172	27	(	(	PUNCT
ejpam-5021	172	28	x	x	X
ejpam-5021	172	29	,	,	PUNCT
ejpam-5021	172	30	∗,≤x	∗,≤x	NUM
ejpam-5021	172	31	)	)	PUNCT
ejpam-5021	172	32	is	be	AUX
ejpam-5021	172	33	an	an	DET
ejpam-5021	172	34	ordered	ordered	ADJ
ejpam-5021	172	35	groupoid	groupoid	NOUN
ejpam-5021	172	36	.	.	PUNCT
ejpam-5021	173	1	define	define	VERB
ejpam-5021	173	2	a	a	DET
ejpam-5021	173	3	function	function	NOUN
ejpam-5021	173	4	f	f	NOUN
ejpam-5021	173	5	:	:	PUNCT
ejpam-5021	173	6	x	x	X
ejpam-5021	173	7	→	→	SYM
ejpam-5021	173	8	f(u	f(u	PROPN
ejpam-5021	173	9	)	)	PUNCT
ejpam-5021	173	10	by	by	ADP
ejpam-5021	173	11	f(x	f(x	PROPN
ejpam-5021	173	12	)	)	PUNCT
ejpam-5021	174	1	=	=	SYM
ejpam-5021	174	2	α	α	PROPN
ejpam-5021	174	3	and	and	CCONJ
ejpam-5021	174	4	f(y	f(y	NOUN
ejpam-5021	174	5	)	)	PUNCT
ejpam-5021	174	6	=	=	PUNCT
ejpam-5021	174	7	¬α	¬α	NOUN
ejpam-5021	174	8	for	for	ADP
ejpam-5021	174	9	all	all	DET
ejpam-5021	174	10	x	x	SYM
ejpam-5021	174	11	∈	∈	PROPN
ejpam-5021	174	12	{	{	PUNCT
ejpam-5021	174	13	x1	x1	PROPN
ejpam-5021	174	14	,	,	PUNCT
ejpam-5021	174	15	x2	x2	PROPN
ejpam-5021	174	16	}	}	PUNCT
ejpam-5021	174	17	,	,	PUNCT
ejpam-5021	174	18	y	y	PROPN
ejpam-5021	174	19	∈	∈	PROPN
ejpam-5021	174	20	{	{	PUNCT
ejpam-5021	174	21	x3	x3	PROPN
ejpam-5021	174	22	,	,	PUNCT
ejpam-5021	174	23	x4	x4	PROPN
ejpam-5021	174	24	}	}	PUNCT
ejpam-5021	174	25	.	.	PUNCT
ejpam-5021	175	1	define	define	VERB
ejpam-5021	175	2	a	a	DET
ejpam-5021	175	3	function	function	NOUN
ejpam-5021	175	4	¬f	¬f	PROPN
ejpam-5021	175	5	:	:	PUNCT
ejpam-5021	175	6	x	x	SYM
ejpam-5021	175	7	→	→	SYM
ejpam-5021	175	8	f(u	f(u	PROPN
ejpam-5021	175	9	)	)	PUNCT
ejpam-5021	175	10	by	by	ADP
ejpam-5021	175	11	¬f(x	¬f(x	NOUN
ejpam-5021	175	12	)	)	PUNCT
ejpam-5021	175	13	=	=	SYM
ejpam-5021	175	14	¬α	¬α	NOUN
ejpam-5021	175	15	and	and	CCONJ
ejpam-5021	175	16	¬f(y	¬f(y	NOUN
ejpam-5021	175	17	)	)	PUNCT
ejpam-5021	176	1	=	=	SYM
ejpam-5021	176	2	α	α	PROPN
ejpam-5021	176	3	for	for	ADP
ejpam-5021	176	4	all	all	DET
ejpam-5021	176	5	x	x	SYM
ejpam-5021	176	6	∈	∈	PROPN
ejpam-5021	176	7	{	{	PUNCT
ejpam-5021	176	8	x1	x1	PROPN
ejpam-5021	176	9	,	,	PUNCT
ejpam-5021	176	10	x2	x2	PROPN
ejpam-5021	176	11	}	}	PUNCT
ejpam-5021	176	12	,	,	PUNCT
ejpam-5021	176	13	y	y	PROPN
ejpam-5021	176	14	∈	∈	PROPN
ejpam-5021	176	15	{	{	PUNCT
ejpam-5021	176	16	x3	x3	PROPN
ejpam-5021	176	17	,	,	PUNCT
ejpam-5021	176	18	x4	x4	PROPN
ejpam-5021	176	19	}	}	PUNCT
ejpam-5021	176	20	.	.	PUNCT
ejpam-5021	177	1	then	then	ADV
ejpam-5021	177	2	,	,	PUNCT
ejpam-5021	177	3	we	we	PRON
ejpam-5021	177	4	compute	compute	VERB
ejpam-5021	177	5	that	that	SCONJ
ejpam-5021	177	6	f(x)+̃¬f(x	f(x)+̃¬f(x	NOUN
ejpam-5021	177	7	)	)	PUNCT
ejpam-5021	177	8	=	=	NOUN
ejpam-5021	177	9	1u	1u	NUM
ejpam-5021	177	10	for	for	ADP
ejpam-5021	177	11	all	all	DET
ejpam-5021	177	12	x	x	SYM
ejpam-5021	177	13	∈	∈	ADJ
ejpam-5021	177	14	x.	x.	NOUN
ejpam-5021	177	15	hence	hence	ADV
ejpam-5021	177	16	(	(	PUNCT
ejpam-5021	177	17	f,¬f	f,¬f	NOUN
ejpam-5021	177	18	,	,	PUNCT
ejpam-5021	177	19	x	x	X
ejpam-5021	177	20	)	)	PUNCT
ejpam-5021	177	21	is	be	AUX
ejpam-5021	177	22	a	a	DET
ejpam-5021	177	23	fsss	fsss	NOUN
ejpam-5021	177	24	over	over	ADP
ejpam-5021	177	25	u.	u.	NOUN
ejpam-5021	177	26	we	we	PRON
ejpam-5021	177	27	verify	verify	VERB
ejpam-5021	177	28	that	that	PRON
ejpam-5021	177	29	f(xy	f(xy	NOUN
ejpam-5021	177	30	)	)	PUNCT
ejpam-5021	177	31	=	=	SYM
ejpam-5021	177	32	f(x)∧̃f(y	f(x)∧̃f(y	NOUN
ejpam-5021	177	33	)	)	PUNCT
ejpam-5021	177	34	and	and	CCONJ
ejpam-5021	177	35	¬f(xy	¬f(xy	NUM
ejpam-5021	177	36	)	)	PUNCT
ejpam-5021	177	37	=	=	SYM
ejpam-5021	177	38	¬f(x)∨̃¬f(y	¬f(x)∨̃¬f(y	NOUN
ejpam-5021	177	39	)	)	PUNCT
ejpam-5021	177	40	for	for	ADP
ejpam-5021	177	41	all	all	DET
ejpam-5021	177	42	x	x	NOUN
ejpam-5021	177	43	,	,	PUNCT
ejpam-5021	177	44	y	y	PROPN
ejpam-5021	177	45	∈	∈	PROPN
ejpam-5021	177	46	x.	x.	NOUN
ejpam-5021	177	47	in	in	ADP
ejpam-5021	177	48	addition	addition	NOUN
ejpam-5021	177	49	,	,	PUNCT
ejpam-5021	177	50	for	for	ADP
ejpam-5021	177	51	any	any	DET
ejpam-5021	177	52	x	x	NOUN
ejpam-5021	177	53	,	,	PUNCT
ejpam-5021	177	54	y	y	PROPN
ejpam-5021	177	55	∈	∈	PROPN
ejpam-5021	177	56	x	x	X
ejpam-5021	177	57	,	,	PUNCT
ejpam-5021	177	58	x	x	SYM
ejpam-5021	177	59	≤x	≤x	AUX
ejpam-5021	177	60	y	y	PROPN
ejpam-5021	177	61	implies	imply	VERB
ejpam-5021	177	62	f(x)≤̃f(y	f(x)≤̃f(y	PROPN
ejpam-5021	177	63	)	)	PUNCT
ejpam-5021	177	64	and	and	CCONJ
ejpam-5021	177	65	¬f(x)≥̃¬f(y	¬f(x)≥̃¬f(y	NOUN
ejpam-5021	177	66	)	)	PUNCT
ejpam-5021	177	67	.	.	PUNCT
ejpam-5021	178	1	therefore	therefore	ADV
ejpam-5021	178	2	(	(	PUNCT
ejpam-5021	178	3	f,¬f	f,¬f	NOUN
ejpam-5021	178	4	,	,	PUNCT
ejpam-5021	178	5	x	x	X
ejpam-5021	178	6	)	)	PUNCT
ejpam-5021	178	7	is	be	AUX
ejpam-5021	178	8	a	a	DET
ejpam-5021	178	9	fssf	fssf	NOUN
ejpam-5021	178	10	.	.	PUNCT
ejpam-5021	179	1	this	this	PRON
ejpam-5021	179	2	is	be	AUX
ejpam-5021	179	3	provided	provide	VERB
ejpam-5021	179	4	according	accord	VERB
ejpam-5021	179	5	to	to	ADP
ejpam-5021	179	6	definition	definition	NOUN
ejpam-5021	179	7	5	5	NUM
ejpam-5021	179	8	above	above	ADV
ejpam-5021	179	9	.	.	PUNCT
ejpam-5021	180	1	proposition	proposition	NOUN
ejpam-5021	180	2	3	3	X
ejpam-5021	180	3	.	.	PUNCT
ejpam-5021	181	1	let	let	VERB
ejpam-5021	181	2	(	(	PUNCT
ejpam-5021	181	3	x	x	X
ejpam-5021	181	4	,	,	PUNCT
ejpam-5021	181	5	∗,≤x	∗,≤x	NUM
ejpam-5021	181	6	)	)	PUNCT
ejpam-5021	181	7	be	be	AUX
ejpam-5021	181	8	an	an	DET
ejpam-5021	181	9	ordered	ordered	ADJ
ejpam-5021	181	10	groupoid	groupoid	NOUN
ejpam-5021	181	11	,	,	PUNCT
ejpam-5021	181	12	and	and	CCONJ
ejpam-5021	181	13	let	let	VERB
ejpam-5021	181	14	{	{	PUNCT
ejpam-5021	181	15	(	(	PUNCT
ejpam-5021	181	16	fi,¬fi	fi,¬fi	PROPN
ejpam-5021	181	17	,	,	PUNCT
ejpam-5021	181	18	x	x	NOUN
ejpam-5021	181	19	)	)	PUNCT
ejpam-5021	181	20	:	:	PUNCT
ejpam-5021	182	1	i	i	PRON
ejpam-5021	182	2	∈	∈	VERB
ejpam-5021	182	3	i	i	PRON
ejpam-5021	182	4	}	}	PUNCT
ejpam-5021	182	5	be	be	VERB
ejpam-5021	182	6	a	a	DET
ejpam-5021	182	7	non	non	ADJ
ejpam-5021	182	8	-	-	ADJ
ejpam-5021	182	9	empty	empty	ADJ
ejpam-5021	182	10	collection	collection	NOUN
ejpam-5021	182	11	of	of	ADP
ejpam-5021	182	12	all	all	DET
ejpam-5021	182	13	fssss	fssss	NOUN
ejpam-5021	182	14	over	over	ADP
ejpam-5021	182	15	u	u	NOUN
ejpam-5021	182	16	with	with	ADP
ejpam-5021	182	17	respect	respect	NOUN
ejpam-5021	182	18	to	to	ADP
ejpam-5021	182	19	x.	x.	NOUN
ejpam-5021	182	20	if	if	SCONJ
ejpam-5021	182	21	(	(	PUNCT
ejpam-5021	182	22	fi,¬fi	fi,¬fi	PROPN
ejpam-5021	182	23	,	,	PUNCT
ejpam-5021	182	24	x	x	PRON
ejpam-5021	182	25	)	)	PUNCT
ejpam-5021	182	26	is	be	AUX
ejpam-5021	182	27	a	a	DET
ejpam-5021	182	28	fuzzy	fuzzy	ADJ
ejpam-5021	182	29	semibipolar	semibipolar	ADJ
ejpam-5021	182	30	soft	soft	ADJ
ejpam-5021	182	31	subgroupoid	subgroupoid	NOUN
ejpam-5021	182	32	(	(	PUNCT
ejpam-5021	182	33	resp	resp	NOUN
ejpam-5021	182	34	.	.	PROPN
ejpam-5021	182	35	,	,	PUNCT
ejpam-5021	182	36	a	a	DET
ejpam-5021	182	37	fssf	fssf	NOUN
ejpam-5021	182	38	)	)	PUNCT
ejpam-5021	182	39	for	for	ADP
ejpam-5021	182	40	all	all	PRON
ejpam-5021	182	41	i	i	PRON
ejpam-5021	182	42	∈	∈	PROPN
ejpam-5021	183	1	i	i	PRON
ejpam-5021	183	2	,	,	PUNCT
ejpam-5021	183	3	then	then	ADV
ejpam-5021	183	4	(	(	PUNCT
ejpam-5021	183	5	⋂̃	⋂̃	PROPN
ejpam-5021	183	6	i∈ifi	i∈ifi	PROPN
ejpam-5021	183	7	,	,	PUNCT
ejpam-5021	183	8	⋃̃	⋃̃	PROPN
ejpam-5021	183	9	i∈i¬fi	i∈i¬fi	PROPN
ejpam-5021	183	10	,	,	PUNCT
ejpam-5021	183	11	x	x	X
ejpam-5021	183	12	)	)	PUNCT
ejpam-5021	183	13	is	be	AUX
ejpam-5021	183	14	a	a	DET
ejpam-5021	183	15	fuzzy	fuzzy	ADJ
ejpam-5021	183	16	semibipolar	semibipolar	ADJ
ejpam-5021	183	17	soft	soft	ADJ
ejpam-5021	183	18	subgroupoid	subgroupoid	NOUN
ejpam-5021	183	19	(	(	PUNCT
ejpam-5021	183	20	resp	resp	NOUN
ejpam-5021	183	21	.	.	PROPN
ejpam-5021	183	22	,	,	PUNCT
ejpam-5021	183	23	a	a	DET
ejpam-5021	183	24	fssf	fssf	NOUN
ejpam-5021	183	25	)	)	PUNCT
ejpam-5021	183	26	.	.	PUNCT
ejpam-5021	184	1	proof	proof	NOUN
ejpam-5021	184	2	.	.	PUNCT
ejpam-5021	185	1	assume	assume	VERB
ejpam-5021	185	2	that	that	SCONJ
ejpam-5021	185	3	(	(	PUNCT
ejpam-5021	185	4	fi,¬fi	fi,¬fi	PROPN
ejpam-5021	185	5	,	,	PUNCT
ejpam-5021	185	6	x	x	PRON
ejpam-5021	185	7	)	)	PUNCT
ejpam-5021	185	8	is	be	AUX
ejpam-5021	185	9	a	a	DET
ejpam-5021	185	10	fuzzy	fuzzy	ADJ
ejpam-5021	185	11	semibipolar	semibipolar	ADJ
ejpam-5021	185	12	soft	soft	ADJ
ejpam-5021	185	13	subgroupoid	subgroupoid	NOUN
ejpam-5021	185	14	for	for	ADP
ejpam-5021	185	15	all	all	PRON
ejpam-5021	185	16	i	i	PRON
ejpam-5021	185	17	∈	∈	PROPN
ejpam-5021	185	18	i.	i.	NOUN
ejpam-5021	185	19	let	let	VERB
ejpam-5021	185	20	x	x	PRON
ejpam-5021	185	21	,	,	PUNCT
ejpam-5021	185	22	y	y	PROPN
ejpam-5021	185	23	∈	∈	PROPN
ejpam-5021	185	24	x.	x.	NOUN
ejpam-5021	185	25	then	then	ADV
ejpam-5021	185	26	fi(xy)≥̃fi(x)∧̃fi(y	fi(xy)≥̃fi(x)∧̃fi(y	PUNCT
ejpam-5021	185	27	)	)	PUNCT
ejpam-5021	185	28	and	and	CCONJ
ejpam-5021	185	29	¬fi(xy)≤̃¬fi(x)∨̃¬fi(y	¬fi(xy)≤̃¬fi(x)∨̃¬fi(y	NOUN
ejpam-5021	185	30	)	)	PUNCT
ejpam-5021	185	31	for	for	ADP
ejpam-5021	185	32	all	all	PRON
ejpam-5021	185	33	i	i	PRON
ejpam-5021	185	34	∈	∈	PROPN
ejpam-5021	185	35	i.	i.	NOUN
ejpam-5021	185	36	thus	thus	ADV
ejpam-5021	185	37	fi(xy)≥̃fi(x)≥̃	fi(xy)≥̃fi(x)≥̃	PROPN
ejpam-5021	185	38	inf{fi(x	inf{fi(x	PROPN
ejpam-5021	185	39	)	)	PUNCT
ejpam-5021	185	40	:	:	PUNCT
ejpam-5021	186	1	i	i	PRON
ejpam-5021	186	2	∈	∈	VERB
ejpam-5021	186	3	i	i	PRON
ejpam-5021	186	4	}	}	PUNCT
ejpam-5021	186	5	=	=	NOUN
ejpam-5021	186	6	:	:	PUNCT
ejpam-5021	186	7	(	(	PUNCT
ejpam-5021	186	8	⋂̃	⋂̃	X
ejpam-5021	186	9	i∈i	i∈i	ADJ
ejpam-5021	186	10	fi)(x	fi)(x	PROPN
ejpam-5021	186	11	)	)	PUNCT
ejpam-5021	186	12	or	or	CCONJ
ejpam-5021	186	13	fi(xy)≥̃fi(y)≥̃	fi(xy)≥̃fi(y)≥̃	PROPN
ejpam-5021	186	14	inf{fi(y	inf{fi(y	PROPN
ejpam-5021	186	15	)	)	PUNCT
ejpam-5021	186	16	:	:	PUNCT
ejpam-5021	187	1	i	i	PRON
ejpam-5021	187	2	∈	∈	VERB
ejpam-5021	187	3	i	i	PRON
ejpam-5021	187	4	}	}	PUNCT
ejpam-5021	187	5	=	=	NOUN
ejpam-5021	187	6	:	:	PUNCT
ejpam-5021	187	7	(	(	PUNCT
ejpam-5021	187	8	⋂̃	⋂̃	X
ejpam-5021	187	9	i∈i	i∈i	ADJ
ejpam-5021	187	10	fi)(y	fi)(y	PROPN
ejpam-5021	187	11	)	)	PUNCT
ejpam-5021	187	12	and	and	CCONJ
ejpam-5021	187	13	¬fi(xy)≤̃¬fi(x)≤̃	¬fi(xy)≤̃¬fi(x)≤̃	PROPN
ejpam-5021	187	14	sup{¬fi(x	sup{¬fi(x	NOUN
ejpam-5021	187	15	)	)	PUNCT
ejpam-5021	187	16	:	:	PUNCT
ejpam-5021	188	1	i	i	PRON
ejpam-5021	188	2	∈	∈	VERB
ejpam-5021	188	3	i	i	PRON
ejpam-5021	188	4	}	}	PUNCT
ejpam-5021	188	5	=	=	NOUN
ejpam-5021	188	6	:	:	PUNCT
ejpam-5021	188	7	(	(	PUNCT
ejpam-5021	188	8	⋃̃	⋃̃	PROPN
ejpam-5021	188	9	i∈i	i∈i	ADJ
ejpam-5021	188	10	¬fi)(x	¬fi)(x	PROPN
ejpam-5021	188	11	)	)	PUNCT
ejpam-5021	188	12	or	or	CCONJ
ejpam-5021	188	13	¬fi(xy)≤̃¬fi(y)≤̃	¬fi(xy)≤̃¬fi(y)≤̃	PROPN
ejpam-5021	188	14	sup{¬fi(y	sup{¬fi(y	VERB
ejpam-5021	188	15	)	)	PUNCT
ejpam-5021	188	16	:	:	PUNCT
ejpam-5021	189	1	i	i	PRON
ejpam-5021	189	2	∈	∈	VERB
ejpam-5021	189	3	i	i	PRON
ejpam-5021	189	4	}	}	PUNCT
ejpam-5021	189	5	=	=	NOUN
ejpam-5021	189	6	:	:	PUNCT
ejpam-5021	189	7	(	(	PUNCT
ejpam-5021	189	8	⋃̃	⋃̃	PROPN
ejpam-5021	189	9	i∈i	i∈i	NOUN
ejpam-5021	189	10	¬fi)(y	¬fi)(y	PROPN
ejpam-5021	189	11	)	)	PUNCT
ejpam-5021	189	12	for	for	ADP
ejpam-5021	189	13	all	all	PRON
ejpam-5021	189	14	i	i	PRON
ejpam-5021	189	15	∈	∈	PROPN
ejpam-5021	189	16	i.	i.	NOUN
ejpam-5021	189	17	for	for	ADP
ejpam-5021	189	18	each	each	DET
ejpam-5021	189	19	i	i	PRON
ejpam-5021	189	20	∈	∈	PROPN
ejpam-5021	190	1	i	i	PRON
ejpam-5021	190	2	,	,	PUNCT
ejpam-5021	190	3	fi(xy)≥̃	fi(xy)≥̃	PROPN
ejpam-5021	190	4	(	(	PUNCT
ejpam-5021	190	5	⋂̃	⋂̃	ADJ
ejpam-5021	190	6	i∈i	i∈i	ADJ
ejpam-5021	190	7	fi)(x)∧̃	fi)(x)∧̃	NOUN
ejpam-5021	190	8	(	(	PUNCT
ejpam-5021	190	9	⋂̃	⋂̃	X
ejpam-5021	190	10	i∈i	i∈i	ADJ
ejpam-5021	190	11	fi)(y	fi)(y	PROPN
ejpam-5021	190	12	)	)	PUNCT
ejpam-5021	190	13	and	and	CCONJ
ejpam-5021	190	14	¬fi(xy)≤̃	¬fi(xy)≤̃	PROPN
ejpam-5021	190	15	(	(	PUNCT
ejpam-5021	190	16	⋃̃	⋃̃	PROPN
ejpam-5021	190	17	i∈i	i∈i	ADJ
ejpam-5021	190	18	¬fi)(x)∨̃	¬fi)(x)∨̃	PROPN
ejpam-5021	190	19	(	(	PUNCT
ejpam-5021	190	20	⋃̃	⋃̃	PROPN
ejpam-5021	190	21	i∈i	i∈i	ADJ
ejpam-5021	190	22	¬fi)(y	¬fi)(y	PROPN
ejpam-5021	190	23	)	)	PUNCT
ejpam-5021	190	24	.	.	PUNCT
ejpam-5021	191	1	r.	r.	PROPN
ejpam-5021	191	2	prasertpong	prasertpong	PROPN
ejpam-5021	191	3	,	,	PUNCT
ejpam-5021	191	4	p.	p.	PROPN
ejpam-5021	191	5	julatha	julatha	PROPN
ejpam-5021	191	6	,	,	PUNCT
ejpam-5021	191	7	a.	a.	NOUN
ejpam-5021	191	8	iampan	iampan	PROPN
ejpam-5021	191	9	/	/	SYM
ejpam-5021	191	10	eur	eur	PROPN
ejpam-5021	191	11	.	.	PUNCT
ejpam-5021	192	1	j.	j.	PROPN
ejpam-5021	192	2	pure	pure	PROPN
ejpam-5021	192	3	appl	appl	PROPN
ejpam-5021	192	4	.	.	PROPN
ejpam-5021	192	5	math	math	PROPN
ejpam-5021	192	6	,	,	PUNCT
ejpam-5021	192	7	17	17	NUM
ejpam-5021	192	8	(	(	PUNCT
ejpam-5021	192	9	1	1	NUM
ejpam-5021	192	10	)	)	PUNCT
ejpam-5021	192	11	(	(	PUNCT
ejpam-5021	192	12	2024	2024	NUM
ejpam-5021	192	13	)	)	PUNCT
ejpam-5021	192	14	,	,	PUNCT
ejpam-5021	192	15	270	270	NUM
ejpam-5021	192	16	-	-	SYM
ejpam-5021	192	17	285	285	NUM
ejpam-5021	192	18	277	277	NUM
ejpam-5021	192	19	hence	hence	ADV
ejpam-5021	192	20	(	(	PUNCT
ejpam-5021	192	21	⋂̃	⋂̃	X
ejpam-5021	192	22	i∈i	i∈i	ADJ
ejpam-5021	192	23	fi)(xy	fi)(xy	PROPN
ejpam-5021	192	24	)	)	PUNCT
ejpam-5021	192	25	:	:	PUNCT
ejpam-5021	192	26	=	=	PUNCT
ejpam-5021	192	27	inf{fi(xy	inf{fi(xy	PROPN
ejpam-5021	192	28	)	)	PUNCT
ejpam-5021	192	29	:	:	PUNCT
ejpam-5021	193	1	i	i	PRON
ejpam-5021	193	2	∈	∈	VERB
ejpam-5021	193	3	i}≥̃	i}≥̃	NOUN
ejpam-5021	193	4	(	(	PUNCT
ejpam-5021	193	5	⋂̃	⋂̃	ADJ
ejpam-5021	193	6	i∈i	i∈i	ADJ
ejpam-5021	193	7	fi)(x)∧̃	fi)(x)∧̃	NOUN
ejpam-5021	193	8	(	(	PUNCT
ejpam-5021	193	9	⋂̃	⋂̃	X
ejpam-5021	193	10	i∈i	i∈i	ADJ
ejpam-5021	193	11	fi)(y	fi)(y	PROPN
ejpam-5021	193	12	)	)	PUNCT
ejpam-5021	193	13	and	and	CCONJ
ejpam-5021	193	14	(	(	PUNCT
ejpam-5021	193	15	⋃̃	⋃̃	PROPN
ejpam-5021	193	16	i∈i	i∈i	ADJ
ejpam-5021	193	17	¬fi)(xy	¬fi)(xy	PROPN
ejpam-5021	193	18	)	)	PUNCT
ejpam-5021	193	19	:	:	PUNCT
ejpam-5021	193	20	=	=	PUNCT
ejpam-5021	193	21	sup{¬fi(xy	sup{¬fi(xy	PROPN
ejpam-5021	193	22	)	)	PUNCT
ejpam-5021	193	23	:	:	PUNCT
ejpam-5021	194	1	i	i	PRON
ejpam-5021	194	2	∈	∈	PROPN
ejpam-5021	194	3	i}≤̃	i}≤̃	PROPN
ejpam-5021	194	4	(	(	PUNCT
ejpam-5021	194	5	⋃̃	⋃̃	PROPN
ejpam-5021	194	6	i∈i	i∈i	ADJ
ejpam-5021	194	7	¬fi)(x)∨̃	¬fi)(x)∨̃	PROPN
ejpam-5021	194	8	(	(	PUNCT
ejpam-5021	194	9	⋃̃	⋃̃	PROPN
ejpam-5021	194	10	i∈i	i∈i	ADJ
ejpam-5021	194	11	¬fi)(y	¬fi)(y	PROPN
ejpam-5021	194	12	)	)	PUNCT
ejpam-5021	194	13	.	.	PUNCT
ejpam-5021	195	1	this	this	PRON
ejpam-5021	195	2	implies	imply	VERB
ejpam-5021	195	3	that	that	SCONJ
ejpam-5021	195	4	(	(	PUNCT
ejpam-5021	195	5	⋂̃	⋂̃	ADJ
ejpam-5021	195	6	i∈ifi	i∈ifi	PROPN
ejpam-5021	195	7	,	,	PUNCT
ejpam-5021	195	8	⋃̃	⋃̃	PROPN
ejpam-5021	195	9	i∈i¬fi	i∈i¬fi	PROPN
ejpam-5021	195	10	,	,	PUNCT
ejpam-5021	195	11	x	x	X
ejpam-5021	195	12	)	)	PUNCT
ejpam-5021	195	13	is	be	AUX
ejpam-5021	195	14	a	a	DET
ejpam-5021	195	15	fuzzy	fuzzy	ADJ
ejpam-5021	195	16	semibipolar	semibipolar	ADJ
ejpam-5021	195	17	soft	soft	ADJ
ejpam-5021	195	18	subgroupoid	subgroupoid	NOUN
ejpam-5021	195	19	.	.	PUNCT
ejpam-5021	196	1	assume	assume	VERB
ejpam-5021	196	2	(	(	PUNCT
ejpam-5021	196	3	fi,¬fi	fi,¬fi	PROPN
ejpam-5021	196	4	,	,	PUNCT
ejpam-5021	196	5	x	x	PRON
ejpam-5021	196	6	)	)	PUNCT
ejpam-5021	196	7	is	be	AUX
ejpam-5021	196	8	a	a	DET
ejpam-5021	196	9	fssf	fssf	NOUN
ejpam-5021	196	10	for	for	ADP
ejpam-5021	196	11	all	all	PRON
ejpam-5021	196	12	i	i	PRON
ejpam-5021	196	13	∈	∈	PROPN
ejpam-5021	196	14	i.	i.	NOUN
ejpam-5021	196	15	let	let	VERB
ejpam-5021	196	16	x	x	PRON
ejpam-5021	196	17	,	,	PUNCT
ejpam-5021	196	18	y	y	PROPN
ejpam-5021	196	19	∈	∈	PROPN
ejpam-5021	196	20	x.	x.	NOUN
ejpam-5021	196	21	then	then	ADV
ejpam-5021	196	22	fi(xy	fi(xy	PROPN
ejpam-5021	196	23	)	)	PUNCT
ejpam-5021	196	24	=	=	PRON
ejpam-5021	196	25	fi(x)∧̃fi(y	fi(x)∧̃fi(y	X
ejpam-5021	196	26	)	)	PUNCT
ejpam-5021	196	27	and	and	CCONJ
ejpam-5021	196	28	¬fi(xy	¬fi(xy	PROPN
ejpam-5021	196	29	)	)	PUNCT
ejpam-5021	196	30	=	=	PUNCT
ejpam-5021	196	31	¬fi(x)∨̃¬fi(y	¬fi(x)∨̃¬fi(y	PROPN
ejpam-5021	196	32	)	)	PUNCT
ejpam-5021	196	33	for	for	ADP
ejpam-5021	196	34	all	all	DET
ejpam-5021	196	35	i	i	PRON
ejpam-5021	196	36	∈	∈	PROPN
ejpam-5021	196	37	i.	i.	NOUN
ejpam-5021	196	38	hence	hence	ADV
ejpam-5021	196	39	fi(xy)≤̃fi(x),fi(xy)≤̃fi(y),¬fi(xy)≥̃¬fi(x	fi(xy)≤̃fi(x),fi(xy)≤̃fi(y),¬fi(xy)≥̃¬fi(x	NUM
ejpam-5021	196	40	)	)	PUNCT
ejpam-5021	196	41	,	,	PUNCT
ejpam-5021	196	42	and	and	CCONJ
ejpam-5021	196	43	¬fi(xy)≥̃¬fi(y	¬fi(xy)≥̃¬fi(y	NOUN
ejpam-5021	196	44	)	)	PUNCT
ejpam-5021	196	45	for	for	ADP
ejpam-5021	196	46	all	all	DET
ejpam-5021	196	47	i	i	PRON
ejpam-5021	196	48	∈	∈	PROPN
ejpam-5021	196	49	i.	i.	NOUN
ejpam-5021	196	50	whence	whence	PROPN
ejpam-5021	196	51	(	(	PUNCT
ejpam-5021	196	52	⋂̃	⋂̃	X
ejpam-5021	196	53	i∈i	i∈i	ADJ
ejpam-5021	196	54	fi)(xy	fi)(xy	PROPN
ejpam-5021	196	55	)	)	PUNCT
ejpam-5021	196	56	:	:	PUNCT
ejpam-5021	197	1	=	=	SYM
ejpam-5021	197	2	⋂̃	⋂̃	X
ejpam-5021	197	3	{	{	PUNCT
ejpam-5021	197	4	fi(xy)|i	fi(xy)|i	NOUN
ejpam-5021	197	5	∈	∈	PROPN
ejpam-5021	197	6	i}≤̃	i}≤̃	PROPN
ejpam-5021	197	7	⋂̃	⋂̃	PROPN
ejpam-5021	197	8	{	{	PUNCT
ejpam-5021	197	9	fi(x)|i	fi(x)|i	NOUN
ejpam-5021	197	10	∈	∈	NOUN
ejpam-5021	197	11	i	i	NOUN
ejpam-5021	197	12	}	}	PUNCT
ejpam-5021	197	13	=	=	NOUN
ejpam-5021	197	14	:	:	PUNCT
ejpam-5021	197	15	(	(	PUNCT
ejpam-5021	197	16	⋂̃	⋂̃	X
ejpam-5021	197	17	i∈i	i∈i	ADJ
ejpam-5021	197	18	fi)(x	fi)(x	PROPN
ejpam-5021	197	19	)	)	PUNCT
ejpam-5021	197	20	,	,	PUNCT
ejpam-5021	197	21	(	(	PUNCT
ejpam-5021	197	22	⋂̃	⋂̃	X
ejpam-5021	197	23	i∈i	i∈i	ADJ
ejpam-5021	197	24	fi)(xy	fi)(xy	PROPN
ejpam-5021	197	25	)	)	PUNCT
ejpam-5021	197	26	:	:	PUNCT
ejpam-5021	198	1	=	=	SYM
ejpam-5021	198	2	⋂̃	⋂̃	X
ejpam-5021	198	3	{	{	PUNCT
ejpam-5021	198	4	fi(xy)|i	fi(xy)|i	NOUN
ejpam-5021	198	5	∈	∈	PROPN
ejpam-5021	198	6	i}≤̃	i}≤̃	PROPN
ejpam-5021	198	7	⋂̃	⋂̃	PROPN
ejpam-5021	198	8	{	{	PUNCT
ejpam-5021	198	9	fi(y)|i	fi(y)|i	PROPN
ejpam-5021	198	10	∈	∈	PROPN
ejpam-5021	198	11	i	i	PRON
ejpam-5021	198	12	}	}	PUNCT
ejpam-5021	198	13	=	=	NOUN
ejpam-5021	198	14	:	:	PUNCT
ejpam-5021	198	15	(	(	PUNCT
ejpam-5021	198	16	⋂̃	⋂̃	X
ejpam-5021	198	17	i∈i	i∈i	ADJ
ejpam-5021	198	18	fi)(y	fi)(y	PROPN
ejpam-5021	198	19	)	)	PUNCT
ejpam-5021	198	20	,	,	PUNCT
ejpam-5021	198	21	(	(	PUNCT
ejpam-5021	198	22	⋃̃	⋃̃	PROPN
ejpam-5021	198	23	i∈i	i∈i	ADJ
ejpam-5021	198	24	¬fi)(xy	¬fi)(xy	PROPN
ejpam-5021	198	25	)	)	PUNCT
ejpam-5021	198	26	:	:	PUNCT
ejpam-5021	198	27	=	=	SYM
ejpam-5021	198	28	⋃̃	⋃̃	PROPN
ejpam-5021	198	29	{	{	PUNCT
ejpam-5021	198	30	¬fi(xy)|i	¬fi(xy)|i	PROPN
ejpam-5021	198	31	∈	∈	PROPN
ejpam-5021	198	32	i}≥̃	i}≥̃	NOUN
ejpam-5021	198	33	⋃̃	⋃̃	PROPN
ejpam-5021	198	34	{	{	PUNCT
ejpam-5021	198	35	¬fi(x)|i	¬fi(x)|i	NUM
ejpam-5021	198	36	∈	∈	NOUN
ejpam-5021	198	37	i	i	NOUN
ejpam-5021	198	38	}	}	PUNCT
ejpam-5021	198	39	=	=	NOUN
ejpam-5021	198	40	:	:	PUNCT
ejpam-5021	198	41	(	(	PUNCT
ejpam-5021	198	42	⋃̃	⋃̃	PROPN
ejpam-5021	198	43	i∈i	i∈i	ADJ
ejpam-5021	198	44	¬fi)(x	¬fi)(x	NUM
ejpam-5021	198	45	)	)	PUNCT
ejpam-5021	198	46	,	,	PUNCT
ejpam-5021	198	47	(	(	PUNCT
ejpam-5021	198	48	⋃̃	⋃̃	PROPN
ejpam-5021	198	49	i∈i	i∈i	ADJ
ejpam-5021	198	50	¬fi)(xy	¬fi)(xy	PROPN
ejpam-5021	198	51	)	)	PUNCT
ejpam-5021	198	52	:	:	PUNCT
ejpam-5021	198	53	=	=	SYM
ejpam-5021	198	54	⋃̃	⋃̃	PROPN
ejpam-5021	198	55	{	{	PUNCT
ejpam-5021	198	56	¬fi(xy)|i	¬fi(xy)|i	PROPN
ejpam-5021	198	57	∈	∈	PROPN
ejpam-5021	198	58	i}≥̃	i}≥̃	NOUN
ejpam-5021	198	59	⋃̃	⋃̃	PROPN
ejpam-5021	198	60	{	{	PUNCT
ejpam-5021	198	61	¬fi(y)|i	¬fi(y)|i	PUNCT
ejpam-5021	198	62	∈	∈	PROPN
ejpam-5021	198	63	i	i	NOUN
ejpam-5021	198	64	}	}	PUNCT
ejpam-5021	198	65	=	=	NOUN
ejpam-5021	198	66	:	:	PUNCT
ejpam-5021	198	67	(	(	PUNCT
ejpam-5021	198	68	⋃̃	⋃̃	PROPN
ejpam-5021	198	69	i∈i	i∈i	NOUN
ejpam-5021	198	70	¬fi)(y	¬fi)(y	PROPN
ejpam-5021	198	71	)	)	PUNCT
ejpam-5021	198	72	.	.	PUNCT
ejpam-5021	199	1	therefore	therefore	ADV
ejpam-5021	199	2	(	(	PUNCT
ejpam-5021	199	3	⋂̃	⋂̃	ADJ
ejpam-5021	199	4	i∈i	i∈i	ADJ
ejpam-5021	199	5	fi)(xy)≤̃	fi)(xy)≤̃	PROPN
ejpam-5021	199	6	(	(	PUNCT
ejpam-5021	199	7	⋂̃	⋂̃	ADJ
ejpam-5021	199	8	i∈i	i∈i	ADJ
ejpam-5021	199	9	fi)(x)∧̃	fi)(x)∧̃	NOUN
ejpam-5021	199	10	(	(	PUNCT
ejpam-5021	199	11	⋂̃	⋂̃	X
ejpam-5021	199	12	i∈i	i∈i	ADJ
ejpam-5021	199	13	fi)(y	fi)(y	PROPN
ejpam-5021	199	14	)	)	PUNCT
ejpam-5021	199	15	and	and	CCONJ
ejpam-5021	199	16	(	(	PUNCT
ejpam-5021	199	17	⋃̃	⋃̃	PROPN
ejpam-5021	199	18	i∈i	i∈i	ADJ
ejpam-5021	199	19	¬fi)(xy)≥̃	¬fi)(xy)≥̃	PROPN
ejpam-5021	199	20	(	(	PUNCT
ejpam-5021	199	21	⋃̃	⋃̃	PROPN
ejpam-5021	199	22	i∈i	i∈i	ADJ
ejpam-5021	199	23	¬fi)(x)∨̃	¬fi)(x)∨̃	PROPN
ejpam-5021	199	24	(	(	PUNCT
ejpam-5021	199	25	⋃̃	⋃̃	PROPN
ejpam-5021	199	26	i∈i	i∈i	ADJ
ejpam-5021	199	27	¬fi)(y	¬fi)(y	PROPN
ejpam-5021	199	28	)	)	PUNCT
ejpam-5021	199	29	.	.	PUNCT
ejpam-5021	200	1	it	it	PRON
ejpam-5021	200	2	is	be	AUX
ejpam-5021	200	3	easy	easy	ADJ
ejpam-5021	200	4	to	to	PART
ejpam-5021	200	5	verify	verify	VERB
ejpam-5021	200	6	that	that	SCONJ
ejpam-5021	200	7	(	(	PUNCT
ejpam-5021	200	8	⋂̃	⋂̃	ADJ
ejpam-5021	200	9	i∈ifi	i∈ifi	PROPN
ejpam-5021	200	10	,	,	PUNCT
ejpam-5021	200	11	⋃̃	⋃̃	PROPN
ejpam-5021	200	12	i∈i¬fi	i∈i¬fi	PROPN
ejpam-5021	200	13	,	,	PUNCT
ejpam-5021	200	14	x	x	X
ejpam-5021	200	15	)	)	PUNCT
ejpam-5021	200	16	is	be	AUX
ejpam-5021	200	17	a	a	DET
ejpam-5021	200	18	fuzzy	fuzzy	ADJ
ejpam-5021	200	19	semibipolar	semibipolar	ADJ
ejpam-5021	200	20	soft	soft	ADJ
ejpam-5021	200	21	subgroupoid	subgroupoid	NOUN
ejpam-5021	200	22	.	.	PUNCT
ejpam-5021	201	1	thus	thus	ADV
ejpam-5021	201	2	(	(	PUNCT
ejpam-5021	201	3	⋂̃	⋂̃	X
ejpam-5021	201	4	i∈i	i∈i	NOUN
ejpam-5021	201	5	fi)(xy)≥̃	fi)(xy)≥̃	VERB
ejpam-5021	201	6	(	(	PUNCT
ejpam-5021	201	7	⋂̃	⋂̃	ADJ
ejpam-5021	201	8	i∈i	i∈i	ADJ
ejpam-5021	201	9	fi)(x)∧̃	fi)(x)∧̃	NOUN
ejpam-5021	201	10	(	(	PUNCT
ejpam-5021	201	11	⋂̃	⋂̃	X
ejpam-5021	201	12	i∈i	i∈i	ADJ
ejpam-5021	201	13	fi)(y	fi)(y	PROPN
ejpam-5021	201	14	)	)	PUNCT
ejpam-5021	201	15	and	and	CCONJ
ejpam-5021	201	16	(	(	PUNCT
ejpam-5021	201	17	⋃̃	⋃̃	PROPN
ejpam-5021	201	18	i∈i	i∈i	ADJ
ejpam-5021	201	19	¬fi)(xy)≤̃	¬fi)(xy)≤̃	PROPN
ejpam-5021	201	20	(	(	PUNCT
ejpam-5021	201	21	⋃̃	⋃̃	PROPN
ejpam-5021	201	22	i∈i	i∈i	ADJ
ejpam-5021	201	23	¬fi)(x)∨̃	¬fi)(x)∨̃	PROPN
ejpam-5021	201	24	(	(	PUNCT
ejpam-5021	201	25	⋃̃	⋃̃	PROPN
ejpam-5021	201	26	i∈i	i∈i	ADJ
ejpam-5021	201	27	¬fi)(y	¬fi)(y	PROPN
ejpam-5021	201	28	)	)	PUNCT
ejpam-5021	201	29	.	.	PUNCT
ejpam-5021	202	1	r.	r.	PROPN
ejpam-5021	202	2	prasertpong	prasertpong	PROPN
ejpam-5021	202	3	,	,	PUNCT
ejpam-5021	202	4	p.	p.	PROPN
ejpam-5021	202	5	julatha	julatha	PROPN
ejpam-5021	202	6	,	,	PUNCT
ejpam-5021	202	7	a.	a.	NOUN
ejpam-5021	202	8	iampan	iampan	PROPN
ejpam-5021	202	9	/	/	SYM
ejpam-5021	202	10	eur	eur	PROPN
ejpam-5021	202	11	.	.	PUNCT
ejpam-5021	203	1	j.	j.	PROPN
ejpam-5021	203	2	pure	pure	PROPN
ejpam-5021	203	3	appl	appl	PROPN
ejpam-5021	203	4	.	.	PROPN
ejpam-5021	203	5	math	math	PROPN
ejpam-5021	203	6	,	,	PUNCT
ejpam-5021	203	7	17	17	NUM
ejpam-5021	203	8	(	(	PUNCT
ejpam-5021	203	9	1	1	NUM
ejpam-5021	203	10	)	)	PUNCT
ejpam-5021	203	11	(	(	PUNCT
ejpam-5021	203	12	2024	2024	NUM
ejpam-5021	203	13	)	)	PUNCT
ejpam-5021	203	14	,	,	PUNCT
ejpam-5021	203	15	270	270	NUM
ejpam-5021	203	16	-	-	SYM
ejpam-5021	203	17	285	285	NUM
ejpam-5021	203	18	278	278	NUM
ejpam-5021	203	19	it	it	PRON
ejpam-5021	203	20	follows	follow	VERB
ejpam-5021	203	21	that	that	SCONJ
ejpam-5021	203	22	(	(	PUNCT
ejpam-5021	203	23	⋂̃	⋂̃	X
ejpam-5021	203	24	i∈i	i∈i	ADJ
ejpam-5021	203	25	fi)(xy	fi)(xy	PUNCT
ejpam-5021	203	26	)	)	PUNCT
ejpam-5021	203	27	=	=	SYM
ejpam-5021	203	28	(	(	PUNCT
ejpam-5021	203	29	⋂̃	⋂̃	X
ejpam-5021	203	30	i∈i	i∈i	ADJ
ejpam-5021	203	31	fi)(x)∧̃	fi)(x)∧̃	NOUN
ejpam-5021	203	32	(	(	PUNCT
ejpam-5021	203	33	⋂̃	⋂̃	X
ejpam-5021	203	34	i∈i	i∈i	ADJ
ejpam-5021	203	35	fi)(y	fi)(y	PROPN
ejpam-5021	203	36	)	)	PUNCT
ejpam-5021	203	37	and	and	CCONJ
ejpam-5021	203	38	(	(	PUNCT
ejpam-5021	203	39	⋃̃	⋃̃	PROPN
ejpam-5021	203	40	i∈i	i∈i	ADJ
ejpam-5021	203	41	¬fi)(xy	¬fi)(xy	PROPN
ejpam-5021	203	42	)	)	PUNCT
ejpam-5021	203	43	=	=	PRON
ejpam-5021	204	1	(	(	PUNCT
ejpam-5021	204	2	⋃̃	⋃̃	PROPN
ejpam-5021	204	3	i∈i	i∈i	ADJ
ejpam-5021	204	4	¬fi)(x)∨̃	¬fi)(x)∨̃	PROPN
ejpam-5021	204	5	(	(	PUNCT
ejpam-5021	204	6	⋃̃	⋃̃	PROPN
ejpam-5021	204	7	i∈i	i∈i	ADJ
ejpam-5021	204	8	¬fi)(y	¬fi)(y	PROPN
ejpam-5021	204	9	)	)	PUNCT
ejpam-5021	204	10	.	.	PUNCT
ejpam-5021	205	1	assume	assume	VERB
ejpam-5021	205	2	that	that	SCONJ
ejpam-5021	205	3	x	x	PUNCT
ejpam-5021	205	4	≤x	≤x	PROPN
ejpam-5021	205	5	y.	y.	PROPN
ejpam-5021	205	6	then	then	ADV
ejpam-5021	205	7	fi(x)≤̃fi(y	fi(x)≤̃fi(y	VERB
ejpam-5021	205	8	)	)	PUNCT
ejpam-5021	205	9	and	and	CCONJ
ejpam-5021	205	10	¬fi(x)≥̃¬fi(y	¬fi(x)≥̃¬fi(y	VERB
ejpam-5021	205	11	)	)	PUNCT
ejpam-5021	205	12	for	for	ADP
ejpam-5021	205	13	all	all	DET
ejpam-5021	205	14	i	i	PRON
ejpam-5021	205	15	∈	∈	PROPN
ejpam-5021	205	16	i.	i.	NOUN
ejpam-5021	205	17	thus	thus	ADV
ejpam-5021	205	18	(	(	PUNCT
ejpam-5021	205	19	⋂̃	⋂̃	X
ejpam-5021	205	20	i∈i	i∈i	ADJ
ejpam-5021	205	21	fi)(x	fi)(x	PROPN
ejpam-5021	205	22	)	)	PUNCT
ejpam-5021	205	23	:	:	PUNCT
ejpam-5021	206	1	=	=	SYM
ejpam-5021	206	2	⋂̃	⋂̃	ADJ
ejpam-5021	206	3	{	{	PUNCT
ejpam-5021	206	4	fi(x)|i	fi(x)|i	NOUN
ejpam-5021	206	5	∈	∈	PROPN
ejpam-5021	206	6	i}≤̃	i}≤̃	PROPN
ejpam-5021	206	7	⋂̃	⋂̃	PROPN
ejpam-5021	206	8	{	{	PUNCT
ejpam-5021	206	9	fi(y)|i	fi(y)|i	PROPN
ejpam-5021	206	10	∈	∈	PROPN
ejpam-5021	206	11	i	i	PRON
ejpam-5021	206	12	}	}	PUNCT
ejpam-5021	206	13	=	=	NOUN
ejpam-5021	206	14	:	:	PUNCT
ejpam-5021	206	15	(	(	PUNCT
ejpam-5021	206	16	⋂̃	⋂̃	X
ejpam-5021	206	17	i∈i	i∈i	ADJ
ejpam-5021	206	18	fi)(y	fi)(y	PROPN
ejpam-5021	206	19	)	)	PUNCT
ejpam-5021	206	20	and	and	CCONJ
ejpam-5021	206	21	(	(	PUNCT
ejpam-5021	206	22	⋃̃	⋃̃	PROPN
ejpam-5021	206	23	i∈i	i∈i	ADJ
ejpam-5021	206	24	¬fi)(x	¬fi)(x	PROPN
ejpam-5021	206	25	)	)	PUNCT
ejpam-5021	206	26	:	:	PUNCT
ejpam-5021	206	27	=	=	SYM
ejpam-5021	206	28	⋃̃	⋃̃	PROPN
ejpam-5021	206	29	{	{	PUNCT
ejpam-5021	206	30	¬fi(x)|i	¬fi(x)|i	NUM
ejpam-5021	206	31	∈	∈	PROPN
ejpam-5021	206	32	i}≥̃	i}≥̃	NOUN
ejpam-5021	206	33	⋃̃	⋃̃	PROPN
ejpam-5021	206	34	{	{	PUNCT
ejpam-5021	206	35	¬fi(y)|i	¬fi(y)|i	PUNCT
ejpam-5021	206	36	∈	∈	PROPN
ejpam-5021	206	37	i	i	NOUN
ejpam-5021	206	38	}	}	PUNCT
ejpam-5021	206	39	=	=	NOUN
ejpam-5021	206	40	:	:	PUNCT
ejpam-5021	206	41	(	(	PUNCT
ejpam-5021	206	42	⋃̃	⋃̃	PROPN
ejpam-5021	206	43	i∈i	i∈i	NOUN
ejpam-5021	206	44	¬fi)(y	¬fi)(y	PROPN
ejpam-5021	206	45	)	)	PUNCT
ejpam-5021	206	46	.	.	PUNCT
ejpam-5021	207	1	as	as	ADP
ejpam-5021	207	2	a	a	DET
ejpam-5021	207	3	consequence	consequence	NOUN
ejpam-5021	207	4	,	,	PUNCT
ejpam-5021	207	5	(	(	PUNCT
ejpam-5021	207	6	⋂̃	⋂̃	PROPN
ejpam-5021	207	7	i∈ifi	i∈ifi	PROPN
ejpam-5021	207	8	,	,	PUNCT
ejpam-5021	207	9	⋃̃	⋃̃	PROPN
ejpam-5021	207	10	i∈i¬fi	i∈i¬fi	PROPN
ejpam-5021	207	11	,	,	PUNCT
ejpam-5021	207	12	x	x	X
ejpam-5021	207	13	)	)	PUNCT
ejpam-5021	207	14	is	be	AUX
ejpam-5021	207	15	a	a	DET
ejpam-5021	207	16	fssf	fssf	NOUN
ejpam-5021	207	17	.	.	PUNCT
ejpam-5021	208	1	notation	notation	NOUN
ejpam-5021	208	2	1	1	NUM
ejpam-5021	208	3	.	.	PUNCT
ejpam-5021	209	1	for	for	ADP
ejpam-5021	209	2	an	an	DET
ejpam-5021	209	3	ordered	order	VERB
ejpam-5021	209	4	groupoid	groupoid	NOUN
ejpam-5021	209	5	(	(	PUNCT
ejpam-5021	209	6	x	x	X
ejpam-5021	209	7	,	,	PUNCT
ejpam-5021	209	8	∗,≤x	∗,≤x	NUM
ejpam-5021	209	9	)	)	PUNCT
ejpam-5021	209	10	and	and	CCONJ
ejpam-5021	209	11	a	a	DET
ejpam-5021	209	12	fsss	fsss	NOUN
ejpam-5021	209	13	f	f	NOUN
ejpam-5021	209	14	:	:	PUNCT
ejpam-5021	209	15	=	=	SYM
ejpam-5021	209	16	(	(	PUNCT
ejpam-5021	209	17	f,¬f	f,¬f	NOUN
ejpam-5021	209	18	,	,	PUNCT
ejpam-5021	209	19	x	x	NOUN
ejpam-5021	209	20	)	)	PUNCT
ejpam-5021	209	21	over	over	ADP
ejpam-5021	209	22	u	u	NOUN
ejpam-5021	209	23	,	,	PUNCT
ejpam-5021	209	24	we	we	PRON
ejpam-5021	209	25	denote	denote	VERB
ejpam-5021	209	26	the	the	DET
ejpam-5021	209	27	notation	notation	NOUN
ejpam-5021	209	28	nf	nf	NOUN
ejpam-5021	209	29	:	:	PUNCT
ejpam-5021	209	30	=	=	SYM
ejpam-5021	209	31	{	{	PUNCT
ejpam-5021	209	32	g	g	NOUN
ejpam-5021	209	33	:	:	PUNCT
ejpam-5021	209	34	=	=	SYM
ejpam-5021	209	35	(	(	PUNCT
ejpam-5021	209	36	g,¬g	g,¬g	PROPN
ejpam-5021	209	37	,	,	PUNCT
ejpam-5021	209	38	x	x	NOUN
ejpam-5021	209	39	)	)	PUNCT
ejpam-5021	209	40	:	:	PUNCT
ejpam-5021	209	41	g	g	PROPN
ejpam-5021	209	42	is	be	AUX
ejpam-5021	209	43	a	a	DET
ejpam-5021	209	44	fssf	fssf	NOUN
ejpam-5021	209	45	over	over	ADP
ejpam-5021	209	46	u	u	NOUN
ejpam-5021	209	47	and	and	CCONJ
ejpam-5021	209	48	f⊆̃g	f⊆̃g	NUM
ejpam-5021	209	49	}	}	PUNCT
ejpam-5021	209	50	.	.	PUNCT
ejpam-5021	210	1	remark	remark	NOUN
ejpam-5021	210	2	3	3	NUM
ejpam-5021	210	3	.	.	PUNCT
ejpam-5021	210	4	as	as	ADP
ejpam-5021	210	5	notation	notation	NOUN
ejpam-5021	210	6	1	1	NUM
ejpam-5021	210	7	above	above	ADV
ejpam-5021	210	8	,	,	PUNCT
ejpam-5021	210	9	we	we	PRON
ejpam-5021	210	10	observe	observe	VERB
ejpam-5021	210	11	that	that	SCONJ
ejpam-5021	210	12	(	(	PUNCT
ejpam-5021	210	13	wx	wx	PROPN
ejpam-5021	210	14	,	,	PUNCT
ejpam-5021	210	15	¬wx	¬wx	PROPN
ejpam-5021	210	16	,	,	PUNCT
ejpam-5021	210	17	x	x	X
ejpam-5021	210	18	)	)	PUNCT
ejpam-5021	210	19	belongs	belong	VERB
ejpam-5021	210	20	to	to	PART
ejpam-5021	210	21	nf	nf	VERB
ejpam-5021	210	22	.	.	PUNCT
ejpam-5021	211	1	then	then	ADV
ejpam-5021	211	2	nf	nf	PROPN
ejpam-5021	211	3	is	be	AUX
ejpam-5021	211	4	a	a	DET
ejpam-5021	211	5	non	non	ADJ
ejpam-5021	211	6	-	-	ADJ
ejpam-5021	211	7	empty	empty	ADJ
ejpam-5021	211	8	subset	subset	NOUN
ejpam-5021	211	9	of	of	ADP
ejpam-5021	211	10	a	a	DET
ejpam-5021	211	11	non	non	ADJ
ejpam-5021	211	12	-	-	ADJ
ejpam-5021	211	13	empty	empty	ADJ
ejpam-5021	211	14	collection	collection	NOUN
ejpam-5021	211	15	of	of	ADP
ejpam-5021	211	16	all	all	DET
ejpam-5021	211	17	fssss	fssss	NOUN
ejpam-5021	211	18	over	over	ADP
ejpam-5021	211	19	u.	u.	NOUN
ejpam-5021	211	20	by	by	ADP
ejpam-5021	211	21	proposition	proposition	NOUN
ejpam-5021	211	22	1	1	NUM
ejpam-5021	211	23	,	,	PUNCT
ejpam-5021	211	24	we	we	PRON
ejpam-5021	211	25	see	see	VERB
ejpam-5021	211	26	that	that	SCONJ
ejpam-5021	211	27	a	a	DET
ejpam-5021	211	28	fsss	fsss	NOUN
ejpam-5021	211	29	(	(	PUNCT
ejpam-5021	211	30	⋂̃	⋂̃	NOUN
ejpam-5021	211	31	g	g	NOUN
ejpam-5021	211	32	,	,	PUNCT
ejpam-5021	211	33	⋃̃	⋃̃	PROPN
ejpam-5021	211	34	¬g	¬g	PROPN
ejpam-5021	211	35	,	,	PUNCT
ejpam-5021	211	36	x	x	NOUN
ejpam-5021	211	37	)	)	PUNCT
ejpam-5021	211	38	over	over	ADP
ejpam-5021	211	39	u	u	NOUN
ejpam-5021	211	40	in	in	ADP
ejpam-5021	211	41	which	which	PRON
ejpam-5021	211	42	(	(	PUNCT
ejpam-5021	211	43	g,¬g	g,¬g	PROPN
ejpam-5021	211	44	,	,	PUNCT
ejpam-5021	211	45	x	x	X
ejpam-5021	211	46	)	)	PUNCT
ejpam-5021	211	47	belongs	belong	VERB
ejpam-5021	211	48	to	to	PART
ejpam-5021	211	49	nf	nf	ADJ
ejpam-5021	211	50	exists	exist	NOUN
ejpam-5021	211	51	in	in	ADP
ejpam-5021	211	52	such	such	ADJ
ejpam-5021	211	53	non	non	ADJ
ejpam-5021	211	54	-	-	ADJ
ejpam-5021	211	55	empty	empty	ADJ
ejpam-5021	211	56	collection	collection	NOUN
ejpam-5021	211	57	of	of	ADP
ejpam-5021	211	58	all	all	DET
ejpam-5021	211	59	fssss	fssss	NOUN
ejpam-5021	211	60	over	over	ADP
ejpam-5021	211	61	u.	u.	NOUN
ejpam-5021	211	62	using	use	VERB
ejpam-5021	211	63	proposition	proposition	NOUN
ejpam-5021	211	64	3	3	NUM
ejpam-5021	211	65	,	,	PUNCT
ejpam-5021	211	66	we	we	PRON
ejpam-5021	211	67	obtain	obtain	VERB
ejpam-5021	211	68	that	that	SCONJ
ejpam-5021	211	69	the	the	DET
ejpam-5021	211	70	fsss	fsss	NOUN
ejpam-5021	211	71	(	(	PUNCT
ejpam-5021	211	72	⋂̃	⋂̃	NOUN
ejpam-5021	211	73	g	g	NOUN
ejpam-5021	211	74	,	,	PUNCT
ejpam-5021	211	75	⋃̃	⋃̃	PROPN
ejpam-5021	211	76	¬g	¬g	PROPN
ejpam-5021	211	77	,	,	PUNCT
ejpam-5021	211	78	x	x	NOUN
ejpam-5021	211	79	)	)	PUNCT
ejpam-5021	211	80	over	over	ADP
ejpam-5021	211	81	u	u	NOUN
ejpam-5021	211	82	in	in	ADP
ejpam-5021	211	83	which	which	PRON
ejpam-5021	211	84	(	(	PUNCT
ejpam-5021	211	85	g,¬g	g,¬g	PROPN
ejpam-5021	211	86	,	,	PUNCT
ejpam-5021	211	87	x	x	X
ejpam-5021	211	88	)	)	PUNCT
ejpam-5021	211	89	belongs	belong	VERB
ejpam-5021	211	90	to	to	PART
ejpam-5021	211	91	nf	nf	PROPN
ejpam-5021	211	92	is	be	AUX
ejpam-5021	211	93	a	a	DET
ejpam-5021	211	94	fssf	fssf	NOUN
ejpam-5021	211	95	.	.	PUNCT
ejpam-5021	212	1	proposition	proposition	NOUN
ejpam-5021	212	2	4	4	NUM
ejpam-5021	212	3	.	.	PUNCT
ejpam-5021	213	1	let	let	VERB
ejpam-5021	213	2	(	(	PUNCT
ejpam-5021	213	3	x	x	X
ejpam-5021	213	4	,	,	PUNCT
ejpam-5021	213	5	∗,≤x	∗,≤x	NUM
ejpam-5021	213	6	)	)	PUNCT
ejpam-5021	213	7	be	be	AUX
ejpam-5021	213	8	a	a	DET
ejpam-5021	213	9	given	give	VERB
ejpam-5021	213	10	ordered	order	VERB
ejpam-5021	213	11	groupoid	groupoid	PROPN
ejpam-5021	213	12	.	.	PUNCT
ejpam-5021	214	1	let	let	VERB
ejpam-5021	214	2	f	f	NOUN
ejpam-5021	214	3	:	:	PUNCT
ejpam-5021	214	4	=	=	SYM
ejpam-5021	214	5	(	(	PUNCT
ejpam-5021	214	6	f,¬f	f,¬f	NOUN
ejpam-5021	214	7	,	,	PUNCT
ejpam-5021	214	8	x	x	PRON
ejpam-5021	214	9	)	)	PUNCT
ejpam-5021	214	10	be	be	VERB
ejpam-5021	214	11	a	a	DET
ejpam-5021	214	12	given	give	VERB
ejpam-5021	214	13	fsss	fsss	NOUN
ejpam-5021	214	14	over	over	ADP
ejpam-5021	214	15	u.	u.	PROPN
ejpam-5021	214	16	then	then	ADV
ejpam-5021	214	17	,	,	PUNCT
ejpam-5021	214	18	a	a	DET
ejpam-5021	214	19	fsss	fsss	NOUN
ejpam-5021	214	20	(	(	PUNCT
ejpam-5021	214	21	⋂̃	⋂̃	NOUN
ejpam-5021	214	22	g	g	NOUN
ejpam-5021	214	23	,	,	PUNCT
ejpam-5021	214	24	⋃̃	⋃̃	PROPN
ejpam-5021	214	25	¬g	¬g	PROPN
ejpam-5021	214	26	,	,	PUNCT
ejpam-5021	214	27	x	x	NOUN
ejpam-5021	214	28	)	)	PUNCT
ejpam-5021	214	29	over	over	ADP
ejpam-5021	214	30	u	u	NOUN
ejpam-5021	214	31	in	in	ADP
ejpam-5021	214	32	which	which	PRON
ejpam-5021	214	33	(	(	PUNCT
ejpam-5021	214	34	g,¬g	g,¬g	PROPN
ejpam-5021	214	35	,	,	PUNCT
ejpam-5021	214	36	x	x	X
ejpam-5021	214	37	)	)	PUNCT
ejpam-5021	214	38	belongs	belong	VERB
ejpam-5021	214	39	to	to	PART
ejpam-5021	214	40	nf	nf	PROPN
ejpam-5021	214	41	is	be	AUX
ejpam-5021	214	42	an	an	DET
ejpam-5021	214	43	element	element	NOUN
ejpam-5021	214	44	of	of	ADP
ejpam-5021	214	45	nf	nf	NOUN
ejpam-5021	214	46	.	.	PUNCT
ejpam-5021	215	1	proof	proof	NOUN
ejpam-5021	215	2	.	.	PUNCT
ejpam-5021	216	1	by	by	ADP
ejpam-5021	216	2	remark	remark	NOUN
ejpam-5021	216	3	3	3	NUM
ejpam-5021	216	4	,	,	PUNCT
ejpam-5021	216	5	we	we	PRON
ejpam-5021	216	6	have	have	VERB
ejpam-5021	216	7	a	a	DET
ejpam-5021	216	8	fsss	fsss	NOUN
ejpam-5021	216	9	(	(	PUNCT
ejpam-5021	216	10	⋂̃	⋂̃	NOUN
ejpam-5021	216	11	g	g	NOUN
ejpam-5021	216	12	,	,	PUNCT
ejpam-5021	216	13	⋃̃	⋃̃	PROPN
ejpam-5021	216	14	¬g	¬g	PROPN
ejpam-5021	216	15	,	,	PUNCT
ejpam-5021	216	16	x	x	NOUN
ejpam-5021	216	17	)	)	PUNCT
ejpam-5021	216	18	over	over	ADP
ejpam-5021	216	19	u	u	NOUN
ejpam-5021	216	20	in	in	ADP
ejpam-5021	216	21	which	which	PRON
ejpam-5021	216	22	(	(	PUNCT
ejpam-5021	216	23	g,¬g	g,¬g	PROPN
ejpam-5021	216	24	,	,	PUNCT
ejpam-5021	216	25	x	x	X
ejpam-5021	216	26	)	)	PUNCT
ejpam-5021	216	27	belongs	belong	VERB
ejpam-5021	216	28	to	to	PART
ejpam-5021	216	29	nf	nf	PROPN
ejpam-5021	216	30	is	be	AUX
ejpam-5021	216	31	a	a	DET
ejpam-5021	216	32	fssf	fssf	NOUN
ejpam-5021	216	33	.	.	PUNCT
ejpam-5021	217	1	suppose	suppose	VERB
ejpam-5021	217	2	(	(	PUNCT
ejpam-5021	217	3	g,¬g	g,¬g	PROPN
ejpam-5021	217	4	,	,	PUNCT
ejpam-5021	217	5	x	x	X
ejpam-5021	217	6	)	)	PUNCT
ejpam-5021	217	7	∈	∈	PROPN
ejpam-5021	217	8	nf	nf	NOUN
ejpam-5021	217	9	.	.	PUNCT
ejpam-5021	218	1	then	then	ADV
ejpam-5021	218	2	f⊆̃(g,¬g	f⊆̃(g,¬g	PROPN
ejpam-5021	218	3	,	,	PUNCT
ejpam-5021	218	4	x	x	NOUN
ejpam-5021	218	5	)	)	PUNCT
ejpam-5021	218	6	.	.	PUNCT
ejpam-5021	219	1	let	let	VERB
ejpam-5021	219	2	x	x	SYM
ejpam-5021	219	3	∈	∈	PROPN
ejpam-5021	219	4	x.	x.	NOUN
ejpam-5021	219	5	then	then	ADV
ejpam-5021	219	6	f(x)≤̃g(x	f(x)≤̃g(x	ADV
ejpam-5021	219	7	)	)	PUNCT
ejpam-5021	219	8	and	and	CCONJ
ejpam-5021	219	9	¬f(x)≥̃¬g(x	¬f(x)≥̃¬g(x	NOUN
ejpam-5021	219	10	)	)	PUNCT
ejpam-5021	219	11	.	.	PUNCT
ejpam-5021	220	1	hence	hence	ADV
ejpam-5021	220	2	f(x)≤̃	f(x)≤̃	PROPN
ejpam-5021	220	3	inf{g(x	inf{g(x	PROPN
ejpam-5021	220	4	)	)	PUNCT
ejpam-5021	220	5	}	}	PUNCT
ejpam-5021	221	1	=	=	NOUN
ejpam-5021	221	2	:	:	PUNCT
ejpam-5021	221	3	(	(	PUNCT
ejpam-5021	221	4	⋂̃	⋂̃	NOUN
ejpam-5021	221	5	g)(x	g)(x	PROPN
ejpam-5021	221	6	)	)	PUNCT
ejpam-5021	221	7	and	and	CCONJ
ejpam-5021	221	8	¬f(x)≥̃	¬f(x)≥̃	VERB
ejpam-5021	221	9	sup{¬g(x	sup{¬g(x	ADV
ejpam-5021	221	10	)	)	PUNCT
ejpam-5021	221	11	}	}	PUNCT
ejpam-5021	222	1	=	=	NOUN
ejpam-5021	222	2	:	:	PUNCT
ejpam-5021	222	3	(	(	PUNCT
ejpam-5021	222	4	⋃̃	⋃̃	PROPN
ejpam-5021	222	5	¬g)(x	¬g)(x	PROPN
ejpam-5021	222	6	)	)	PUNCT
ejpam-5021	222	7	.	.	PUNCT
ejpam-5021	223	1	it	it	PRON
ejpam-5021	223	2	follows	follow	VERB
ejpam-5021	223	3	that	that	SCONJ
ejpam-5021	223	4	f⊆̃	f⊆̃	PROPN
ejpam-5021	223	5	(	(	PUNCT
ejpam-5021	223	6	⋂̃	⋂̃	NOUN
ejpam-5021	223	7	g	g	NOUN
ejpam-5021	223	8	,	,	PUNCT
ejpam-5021	223	9	⋃̃	⋃̃	PROPN
ejpam-5021	223	10	¬g	¬g	PROPN
ejpam-5021	223	11	,	,	PUNCT
ejpam-5021	223	12	x	x	NOUN
ejpam-5021	223	13	)	)	PUNCT
ejpam-5021	223	14	.	.	PUNCT
ejpam-5021	224	1	this	this	PRON
ejpam-5021	224	2	means	mean	VERB
ejpam-5021	224	3	that	that	SCONJ
ejpam-5021	224	4	(	(	PUNCT
ejpam-5021	224	5	⋂̃	⋂̃	NOUN
ejpam-5021	224	6	g	g	NOUN
ejpam-5021	224	7	,	,	PUNCT
ejpam-5021	224	8	⋃̃	⋃̃	PROPN
ejpam-5021	224	9	¬g	¬g	PROPN
ejpam-5021	224	10	,	,	PUNCT
ejpam-5021	224	11	x	x	X
ejpam-5021	224	12	)	)	PUNCT
ejpam-5021	224	13	∈	∈	PROPN
ejpam-5021	224	14	nf	nf	PROPN
ejpam-5021	224	15	.	.	PUNCT
ejpam-5021	224	16	r.	r.	PROPN
ejpam-5021	224	17	prasertpong	prasertpong	PROPN
ejpam-5021	224	18	,	,	PUNCT
ejpam-5021	224	19	p.	p.	PROPN
ejpam-5021	224	20	julatha	julatha	PROPN
ejpam-5021	224	21	,	,	PUNCT
ejpam-5021	224	22	a.	a.	NOUN
ejpam-5021	224	23	iampan	iampan	PROPN
ejpam-5021	224	24	/	/	SYM
ejpam-5021	224	25	eur	eur	PROPN
ejpam-5021	224	26	.	.	PUNCT
ejpam-5021	225	1	j.	j.	PROPN
ejpam-5021	225	2	pure	pure	PROPN
ejpam-5021	225	3	appl	appl	PROPN
ejpam-5021	225	4	.	.	PROPN
ejpam-5021	225	5	math	math	PROPN
ejpam-5021	225	6	,	,	PUNCT
ejpam-5021	225	7	17	17	NUM
ejpam-5021	225	8	(	(	PUNCT
ejpam-5021	225	9	1	1	NUM
ejpam-5021	225	10	)	)	PUNCT
ejpam-5021	225	11	(	(	PUNCT
ejpam-5021	225	12	2024	2024	NUM
ejpam-5021	225	13	)	)	PUNCT
ejpam-5021	225	14	,	,	PUNCT
ejpam-5021	225	15	270	270	NUM
ejpam-5021	225	16	-	-	SYM
ejpam-5021	225	17	285	285	NUM
ejpam-5021	225	18	279	279	NUM
ejpam-5021	225	19	proposition	proposition	NOUN
ejpam-5021	225	20	5	5	NUM
ejpam-5021	225	21	.	.	PUNCT
ejpam-5021	226	1	let	let	VERB
ejpam-5021	226	2	(	(	PUNCT
ejpam-5021	226	3	x	x	X
ejpam-5021	226	4	,	,	PUNCT
ejpam-5021	226	5	∗,≤x	∗,≤x	NUM
ejpam-5021	226	6	)	)	PUNCT
ejpam-5021	226	7	be	be	AUX
ejpam-5021	226	8	a	a	DET
ejpam-5021	226	9	given	give	VERB
ejpam-5021	226	10	ordered	order	VERB
ejpam-5021	226	11	groupoid	groupoid	PROPN
ejpam-5021	226	12	.	.	PUNCT
ejpam-5021	227	1	let	let	VERB
ejpam-5021	227	2	f	f	NOUN
ejpam-5021	227	3	:	:	PUNCT
ejpam-5021	227	4	=	=	SYM
ejpam-5021	227	5	(	(	PUNCT
ejpam-5021	227	6	f,¬f	f,¬f	NOUN
ejpam-5021	227	7	,	,	PUNCT
ejpam-5021	227	8	x	x	PRON
ejpam-5021	227	9	)	)	PUNCT
ejpam-5021	227	10	be	be	VERB
ejpam-5021	227	11	a	a	DET
ejpam-5021	227	12	given	give	VERB
ejpam-5021	227	13	fsss	fsss	NOUN
ejpam-5021	227	14	over	over	ADP
ejpam-5021	227	15	u.	u.	PROPN
ejpam-5021	227	16	then	then	ADV
ejpam-5021	227	17	,	,	PUNCT
ejpam-5021	227	18	a	a	DET
ejpam-5021	227	19	fsss	fsss	NOUN
ejpam-5021	227	20	(	(	PUNCT
ejpam-5021	227	21	⋂̃	⋂̃	NOUN
ejpam-5021	227	22	g	g	NOUN
ejpam-5021	227	23	,	,	PUNCT
ejpam-5021	227	24	⋃̃	⋃̃	PROPN
ejpam-5021	227	25	¬g	¬g	PROPN
ejpam-5021	227	26	,	,	PUNCT
ejpam-5021	227	27	x	x	NOUN
ejpam-5021	227	28	)	)	PUNCT
ejpam-5021	227	29	over	over	ADP
ejpam-5021	227	30	u	u	NOUN
ejpam-5021	227	31	in	in	ADP
ejpam-5021	227	32	which	which	PRON
ejpam-5021	227	33	(	(	PUNCT
ejpam-5021	227	34	g,¬g	g,¬g	PROPN
ejpam-5021	227	35	,	,	PUNCT
ejpam-5021	227	36	x	x	X
ejpam-5021	227	37	)	)	PUNCT
ejpam-5021	227	38	belongs	belong	VERB
ejpam-5021	227	39	to	to	PART
ejpam-5021	227	40	nf	nf	PROPN
ejpam-5021	227	41	is	be	AUX
ejpam-5021	227	42	a	a	DET
ejpam-5021	227	43	fuzzy	fuzzy	ADJ
ejpam-5021	227	44	semibipolar	semibipolar	ADJ
ejpam-5021	227	45	soft	soft	ADJ
ejpam-5021	227	46	subset	subset	NOUN
ejpam-5021	227	47	of	of	ADP
ejpam-5021	227	48	(	(	PUNCT
ejpam-5021	227	49	h,¬h	h,¬h	INTJ
ejpam-5021	227	50	,	,	PUNCT
ejpam-5021	227	51	x	x	NOUN
ejpam-5021	227	52	)	)	PUNCT
ejpam-5021	227	53	for	for	ADP
ejpam-5021	227	54	every	every	DET
ejpam-5021	227	55	(	(	PUNCT
ejpam-5021	227	56	h,¬h	h,¬h	PROPN
ejpam-5021	227	57	,	,	PUNCT
ejpam-5021	227	58	x	x	X
ejpam-5021	227	59	)	)	PUNCT
ejpam-5021	227	60	∈	∈	PROPN
ejpam-5021	227	61	nf	nf	NOUN
ejpam-5021	227	62	.	.	PUNCT
ejpam-5021	228	1	proof	proof	NOUN
ejpam-5021	228	2	.	.	PUNCT
ejpam-5021	229	1	from	from	ADP
ejpam-5021	229	2	remark	remark	NOUN
ejpam-5021	229	3	1	1	NUM
ejpam-5021	229	4	,	,	PUNCT
ejpam-5021	229	5	it	it	PRON
ejpam-5021	229	6	follows	follow	VERB
ejpam-5021	229	7	that	that	SCONJ
ejpam-5021	229	8	the	the	DET
ejpam-5021	229	9	statement	statement	NOUN
ejpam-5021	229	10	holds	hold	VERB
ejpam-5021	229	11	.	.	PUNCT
ejpam-5021	230	1	definition	definition	NOUN
ejpam-5021	230	2	6	6	NUM
ejpam-5021	230	3	.	.	PUNCT
ejpam-5021	231	1	let	let	VERB
ejpam-5021	231	2	(	(	PUNCT
ejpam-5021	231	3	x	x	X
ejpam-5021	231	4	,	,	PUNCT
ejpam-5021	231	5	∗,≤x	∗,≤x	NUM
ejpam-5021	231	6	)	)	PUNCT
ejpam-5021	231	7	be	be	AUX
ejpam-5021	231	8	an	an	DET
ejpam-5021	231	9	ordered	order	VERB
ejpam-5021	231	10	groupoid	groupoid	NOUN
ejpam-5021	231	11	and	and	CCONJ
ejpam-5021	231	12	f	f	NOUN
ejpam-5021	231	13	:	:	PUNCT
ejpam-5021	232	1	=	=	SYM
ejpam-5021	232	2	(	(	PUNCT
ejpam-5021	232	3	f,¬f	f,¬f	NOUN
ejpam-5021	232	4	,	,	PUNCT
ejpam-5021	232	5	x	x	X
ejpam-5021	232	6	)	)	PUNCT
ejpam-5021	232	7	a	a	DET
ejpam-5021	232	8	fsss	fsss	NOUN
ejpam-5021	232	9	over	over	ADP
ejpam-5021	232	10	u.	u.	PROPN
ejpam-5021	232	11	a	a	DET
ejpam-5021	232	12	fsss	fsss	NOUN
ejpam-5021	232	13	(	(	PUNCT
ejpam-5021	232	14	g,¬g	g,¬g	PROPN
ejpam-5021	232	15	,	,	PUNCT
ejpam-5021	232	16	x	x	NOUN
ejpam-5021	232	17	)	)	PUNCT
ejpam-5021	232	18	over	over	ADP
ejpam-5021	232	19	u	u	NOUN
ejpam-5021	232	20	is	be	AUX
ejpam-5021	232	21	called	call	VERB
ejpam-5021	232	22	a	a	DET
ejpam-5021	232	23	fssf	fssf	NOUN
ejpam-5021	232	24	generated	generate	VERB
ejpam-5021	232	25	by	by	ADP
ejpam-5021	232	26	f	f	PROPN
ejpam-5021	232	27	if	if	SCONJ
ejpam-5021	232	28	(	(	PUNCT
ejpam-5021	232	29	g,¬g	g,¬g	PROPN
ejpam-5021	232	30	,	,	PUNCT
ejpam-5021	232	31	x	x	X
ejpam-5021	232	32	)	)	PUNCT
ejpam-5021	232	33	∈	∈	NOUN
ejpam-5021	232	34	nf	nf	NOUN
ejpam-5021	232	35	and	and	CCONJ
ejpam-5021	232	36	(	(	PUNCT
ejpam-5021	232	37	g,¬g	g,¬g	PROPN
ejpam-5021	232	38	,	,	PUNCT
ejpam-5021	232	39	x)⊆̃(h,¬h	x)⊆̃(h,¬h	PROPN
ejpam-5021	232	40	,	,	PUNCT
ejpam-5021	232	41	x	x	NOUN
ejpam-5021	232	42	)	)	PUNCT
ejpam-5021	232	43	for	for	ADP
ejpam-5021	232	44	all	all	DET
ejpam-5021	232	45	(	(	PUNCT
ejpam-5021	232	46	h,¬h	h,¬h	PROPN
ejpam-5021	232	47	,	,	PUNCT
ejpam-5021	232	48	x	x	X
ejpam-5021	232	49	)	)	PUNCT
ejpam-5021	232	50	∈	∈	PROPN
ejpam-5021	232	51	nf	nf	PROPN
ejpam-5021	232	52	.	.	PUNCT
ejpam-5021	232	53	remark	remark	PROPN
ejpam-5021	232	54	4	4	NUM
ejpam-5021	232	55	.	.	PUNCT
ejpam-5021	233	1	according	accord	VERB
ejpam-5021	233	2	to	to	ADP
ejpam-5021	233	3	propositions	proposition	NOUN
ejpam-5021	233	4	4	4	NUM
ejpam-5021	233	5	and	and	CCONJ
ejpam-5021	233	6	5	5	NUM
ejpam-5021	233	7	,	,	PUNCT
ejpam-5021	233	8	it	it	PRON
ejpam-5021	233	9	is	be	AUX
ejpam-5021	233	10	easy	easy	ADJ
ejpam-5021	233	11	to	to	PART
ejpam-5021	233	12	see	see	VERB
ejpam-5021	233	13	that	that	SCONJ
ejpam-5021	233	14	a	a	DET
ejpam-5021	233	15	fsss	fsss	NOUN
ejpam-5021	233	16	(	(	PUNCT
ejpam-5021	233	17	⋂̃	⋂̃	NOUN
ejpam-5021	233	18	g	g	NOUN
ejpam-5021	233	19	,	,	PUNCT
ejpam-5021	233	20	⋃̃	⋃̃	PROPN
ejpam-5021	233	21	¬g	¬g	PROPN
ejpam-5021	233	22	,	,	PUNCT
ejpam-5021	233	23	x	x	NOUN
ejpam-5021	233	24	)	)	PUNCT
ejpam-5021	233	25	over	over	ADP
ejpam-5021	233	26	u	u	NOUN
ejpam-5021	233	27	in	in	ADP
ejpam-5021	233	28	which	which	PRON
ejpam-5021	233	29	(	(	PUNCT
ejpam-5021	233	30	g,¬g	g,¬g	PROPN
ejpam-5021	233	31	,	,	PUNCT
ejpam-5021	233	32	x	x	X
ejpam-5021	233	33	)	)	PUNCT
ejpam-5021	233	34	belongs	belong	VERB
ejpam-5021	233	35	to	to	PART
ejpam-5021	233	36	nf	nf	PROPN
ejpam-5021	233	37	is	be	AUX
ejpam-5021	233	38	a	a	DET
ejpam-5021	233	39	fssf	fssf	NOUN
ejpam-5021	233	40	generated	generate	VERB
ejpam-5021	233	41	by	by	ADP
ejpam-5021	233	42	f.	f.	PROPN
ejpam-5021	233	43	proposition	proposition	PROPN
ejpam-5021	233	44	6	6	NUM
ejpam-5021	233	45	.	.	PUNCT
ejpam-5021	234	1	let	let	VERB
ejpam-5021	234	2	(	(	PUNCT
ejpam-5021	234	3	x	x	X
ejpam-5021	234	4	,	,	PUNCT
ejpam-5021	234	5	∗,≤x	∗,≤x	NUM
ejpam-5021	234	6	)	)	PUNCT
ejpam-5021	234	7	be	be	AUX
ejpam-5021	234	8	an	an	DET
ejpam-5021	234	9	ordered	order	VERB
ejpam-5021	234	10	groupoid	groupoid	NOUN
ejpam-5021	234	11	and	and	CCONJ
ejpam-5021	234	12	f	f	NOUN
ejpam-5021	234	13	:	:	PUNCT
ejpam-5021	235	1	=	=	SYM
ejpam-5021	235	2	(	(	PUNCT
ejpam-5021	235	3	f,¬f	f,¬f	NOUN
ejpam-5021	235	4	,	,	PUNCT
ejpam-5021	235	5	x	x	X
ejpam-5021	235	6	)	)	PUNCT
ejpam-5021	235	7	a	a	DET
ejpam-5021	235	8	fsss	fsss	NOUN
ejpam-5021	235	9	over	over	ADP
ejpam-5021	235	10	u.	u.	NOUN
ejpam-5021	235	11	if	if	SCONJ
ejpam-5021	235	12	(	(	PUNCT
ejpam-5021	235	13	g,¬g	g,¬g	PROPN
ejpam-5021	235	14	,	,	PUNCT
ejpam-5021	235	15	x	x	X
ejpam-5021	235	16	)	)	PUNCT
ejpam-5021	235	17	is	be	AUX
ejpam-5021	235	18	a	a	DET
ejpam-5021	235	19	fssf	fssf	NOUN
ejpam-5021	235	20	over	over	ADP
ejpam-5021	235	21	u	u	NOUN
ejpam-5021	235	22	generated	generate	VERB
ejpam-5021	235	23	by	by	ADP
ejpam-5021	235	24	f	f	PROPN
ejpam-5021	235	25	,	,	PUNCT
ejpam-5021	235	26	then	then	ADV
ejpam-5021	235	27	a	a	DET
ejpam-5021	235	28	fsss	fsss	NOUN
ejpam-5021	235	29	(	(	PUNCT
ejpam-5021	235	30	⋂̃	⋂̃	ADJ
ejpam-5021	235	31	h	h	NOUN
ejpam-5021	235	32	,	,	PUNCT
ejpam-5021	235	33	⋃̃	⋃̃	PROPN
ejpam-5021	235	34	¬h	¬h	PROPN
ejpam-5021	235	35	,	,	PUNCT
ejpam-5021	235	36	x	x	NOUN
ejpam-5021	235	37	)	)	PUNCT
ejpam-5021	235	38	over	over	ADP
ejpam-5021	235	39	u	u	NOUN
ejpam-5021	235	40	in	in	ADP
ejpam-5021	235	41	which	which	PRON
ejpam-5021	235	42	(	(	PUNCT
ejpam-5021	235	43	h,¬h	h,¬h	INTJ
ejpam-5021	235	44	,	,	PUNCT
ejpam-5021	235	45	x	x	X
ejpam-5021	235	46	)	)	PUNCT
ejpam-5021	235	47	belongs	belong	VERB
ejpam-5021	235	48	to	to	PART
ejpam-5021	235	49	nf	nf	PROPN
ejpam-5021	235	50	is	be	AUX
ejpam-5021	235	51	equal	equal	ADJ
ejpam-5021	235	52	to	to	ADP
ejpam-5021	235	53	(	(	PUNCT
ejpam-5021	235	54	g,¬g	g,¬g	PROPN
ejpam-5021	235	55	,	,	PUNCT
ejpam-5021	235	56	x	x	NOUN
ejpam-5021	235	57	)	)	PUNCT
ejpam-5021	235	58	.	.	PUNCT
ejpam-5021	236	1	proof	proof	NOUN
ejpam-5021	236	2	.	.	PUNCT
ejpam-5021	237	1	suppose	suppose	VERB
ejpam-5021	237	2	(	(	PUNCT
ejpam-5021	237	3	g,¬g	g,¬g	PROPN
ejpam-5021	237	4	,	,	PUNCT
ejpam-5021	237	5	x	x	X
ejpam-5021	237	6	)	)	PUNCT
ejpam-5021	237	7	is	be	AUX
ejpam-5021	237	8	a	a	DET
ejpam-5021	237	9	fssf	fssf	NOUN
ejpam-5021	237	10	over	over	ADP
ejpam-5021	237	11	u	u	NOUN
ejpam-5021	237	12	generated	generate	VERB
ejpam-5021	237	13	by	by	ADP
ejpam-5021	237	14	f.	f.	PROPN
ejpam-5021	237	15	then	then	ADV
ejpam-5021	237	16	(	(	PUNCT
ejpam-5021	237	17	g,¬g	g,¬g	PROPN
ejpam-5021	237	18	,	,	PUNCT
ejpam-5021	237	19	x	x	X
ejpam-5021	237	20	)	)	PUNCT
ejpam-5021	237	21	∈	∈	PROPN
ejpam-5021	237	22	nf	nf	NOUN
ejpam-5021	237	23	.	.	PUNCT
ejpam-5021	238	1	by	by	ADP
ejpam-5021	238	2	remark	remark	NOUN
ejpam-5021	238	3	1	1	NUM
ejpam-5021	238	4	,	,	PUNCT
ejpam-5021	238	5	we	we	PRON
ejpam-5021	238	6	get	get	VERB
ejpam-5021	238	7	that	that	SCONJ
ejpam-5021	238	8	a	a	DET
ejpam-5021	238	9	fsss	fsss	NOUN
ejpam-5021	238	10	(	(	PUNCT
ejpam-5021	238	11	⋂̃	⋂̃	ADJ
ejpam-5021	238	12	h	h	NOUN
ejpam-5021	238	13	,	,	PUNCT
ejpam-5021	238	14	⋃̃	⋃̃	PROPN
ejpam-5021	238	15	¬h	¬h	PROPN
ejpam-5021	238	16	,	,	PUNCT
ejpam-5021	238	17	x	x	NOUN
ejpam-5021	238	18	)	)	PUNCT
ejpam-5021	238	19	over	over	ADP
ejpam-5021	238	20	u	u	NOUN
ejpam-5021	238	21	in	in	ADP
ejpam-5021	238	22	which	which	PRON
ejpam-5021	238	23	(	(	PUNCT
ejpam-5021	238	24	h,¬h	h,¬h	INTJ
ejpam-5021	238	25	,	,	PUNCT
ejpam-5021	238	26	x	x	X
ejpam-5021	238	27	)	)	PUNCT
ejpam-5021	238	28	belongs	belong	VERB
ejpam-5021	238	29	to	to	PART
ejpam-5021	238	30	nf	nf	PROPN
ejpam-5021	238	31	is	be	AUX
ejpam-5021	238	32	a	a	DET
ejpam-5021	238	33	fuzzy	fuzzy	ADJ
ejpam-5021	238	34	semibipolar	semibipolar	ADJ
ejpam-5021	238	35	soft	soft	ADJ
ejpam-5021	238	36	subset	subset	NOUN
ejpam-5021	238	37	of	of	ADP
ejpam-5021	238	38	(	(	PUNCT
ejpam-5021	238	39	g,¬g	g,¬g	PROPN
ejpam-5021	238	40	,	,	PUNCT
ejpam-5021	238	41	x	x	NOUN
ejpam-5021	238	42	)	)	PUNCT
ejpam-5021	238	43	.	.	PUNCT
ejpam-5021	239	1	from	from	ADP
ejpam-5021	239	2	proposition	proposition	NOUN
ejpam-5021	239	3	4	4	NUM
ejpam-5021	239	4	,	,	PUNCT
ejpam-5021	239	5	it	it	PRON
ejpam-5021	239	6	follows	follow	VERB
ejpam-5021	239	7	that	that	SCONJ
ejpam-5021	239	8	the	the	DET
ejpam-5021	239	9	fsss	fsss	NOUN
ejpam-5021	239	10	(	(	PUNCT
ejpam-5021	239	11	⋂̃	⋂̃	ADJ
ejpam-5021	239	12	h	h	NOUN
ejpam-5021	239	13	,	,	PUNCT
ejpam-5021	239	14	⋃̃	⋃̃	PROPN
ejpam-5021	239	15	¬h	¬h	PROPN
ejpam-5021	239	16	,	,	PUNCT
ejpam-5021	239	17	x	x	NOUN
ejpam-5021	239	18	)	)	PUNCT
ejpam-5021	239	19	over	over	ADP
ejpam-5021	239	20	u	u	NOUN
ejpam-5021	239	21	in	in	ADP
ejpam-5021	239	22	which	which	PRON
ejpam-5021	239	23	(	(	PUNCT
ejpam-5021	239	24	h,¬h	h,¬h	INTJ
ejpam-5021	239	25	,	,	PUNCT
ejpam-5021	239	26	x	x	X
ejpam-5021	239	27	)	)	PUNCT
ejpam-5021	239	28	belongs	belong	VERB
ejpam-5021	239	29	to	to	PART
ejpam-5021	239	30	nf	nf	PROPN
ejpam-5021	239	31	is	be	AUX
ejpam-5021	239	32	an	an	DET
ejpam-5021	239	33	element	element	NOUN
ejpam-5021	239	34	of	of	ADP
ejpam-5021	239	35	nf	nf	NOUN
ejpam-5021	239	36	.	.	PUNCT
ejpam-5021	240	1	by	by	ADP
ejpam-5021	240	2	the	the	DET
ejpam-5021	240	3	assumption	assumption	NOUN
ejpam-5021	240	4	,	,	PUNCT
ejpam-5021	240	5	we	we	PRON
ejpam-5021	240	6	obtain	obtain	VERB
ejpam-5021	240	7	that	that	SCONJ
ejpam-5021	240	8	the	the	DET
ejpam-5021	240	9	fsss	fsss	NOUN
ejpam-5021	240	10	(	(	PUNCT
ejpam-5021	240	11	⋂̃	⋂̃	ADJ
ejpam-5021	240	12	h	h	NOUN
ejpam-5021	240	13	,	,	PUNCT
ejpam-5021	240	14	⋃̃	⋃̃	PROPN
ejpam-5021	240	15	¬h	¬h	PROPN
ejpam-5021	240	16	,	,	PUNCT
ejpam-5021	240	17	x	x	NOUN
ejpam-5021	240	18	)	)	PUNCT
ejpam-5021	240	19	over	over	ADP
ejpam-5021	240	20	u	u	NOUN
ejpam-5021	240	21	in	in	ADP
ejpam-5021	240	22	which	which	PRON
ejpam-5021	240	23	(	(	PUNCT
ejpam-5021	240	24	h,¬h	h,¬h	INTJ
ejpam-5021	240	25	,	,	PUNCT
ejpam-5021	240	26	x	x	X
ejpam-5021	240	27	)	)	PUNCT
ejpam-5021	240	28	belongs	belong	VERB
ejpam-5021	240	29	to	to	PART
ejpam-5021	240	30	nf	nf	PROPN
ejpam-5021	240	31	is	be	AUX
ejpam-5021	240	32	a	a	DET
ejpam-5021	240	33	fuzzy	fuzzy	ADJ
ejpam-5021	240	34	semibipolar	semibipolar	ADJ
ejpam-5021	240	35	soft	soft	ADJ
ejpam-5021	240	36	superset	superset	NOUN
ejpam-5021	240	37	of	of	ADP
ejpam-5021	240	38	(	(	PUNCT
ejpam-5021	240	39	g,¬g	g,¬g	PROPN
ejpam-5021	240	40	,	,	PUNCT
ejpam-5021	240	41	x	x	NOUN
ejpam-5021	240	42	)	)	PUNCT
ejpam-5021	240	43	.	.	PUNCT
ejpam-5021	241	1	the	the	DET
ejpam-5021	241	2	proof	proof	NOUN
ejpam-5021	241	3	is	be	AUX
ejpam-5021	241	4	complete	complete	ADJ
ejpam-5021	241	5	.	.	PUNCT
ejpam-5021	242	1	notation	notation	NOUN
ejpam-5021	242	2	2	2	NUM
ejpam-5021	242	3	.	.	PUNCT
ejpam-5021	243	1	for	for	ADP
ejpam-5021	243	2	an	an	DET
ejpam-5021	243	3	ordered	order	VERB
ejpam-5021	243	4	groupoid	groupoid	NOUN
ejpam-5021	243	5	(	(	PUNCT
ejpam-5021	243	6	x	x	X
ejpam-5021	243	7	,	,	PUNCT
ejpam-5021	243	8	∗,≤x	∗,≤x	NUM
ejpam-5021	243	9	)	)	PUNCT
ejpam-5021	243	10	and	and	CCONJ
ejpam-5021	243	11	a	a	DET
ejpam-5021	243	12	fsss	fsss	NOUN
ejpam-5021	243	13	f	f	NOUN
ejpam-5021	243	14	:	:	PUNCT
ejpam-5021	243	15	=	=	SYM
ejpam-5021	243	16	(	(	PUNCT
ejpam-5021	243	17	f,¬f	f,¬f	NOUN
ejpam-5021	243	18	,	,	PUNCT
ejpam-5021	243	19	x	x	NOUN
ejpam-5021	243	20	)	)	PUNCT
ejpam-5021	243	21	over	over	ADP
ejpam-5021	243	22	u	u	NOUN
ejpam-5021	243	23	,	,	PUNCT
ejpam-5021	243	24	we	we	PRON
ejpam-5021	243	25	denote	denote	VERB
ejpam-5021	243	26	by	by	ADP
ejpam-5021	243	27	n(f	n(f	PROPN
ejpam-5021	243	28	)	)	PUNCT
ejpam-5021	243	29	a	a	DET
ejpam-5021	243	30	fssf	fssf	NOUN
ejpam-5021	243	31	over	over	ADP
ejpam-5021	243	32	u	u	NOUN
ejpam-5021	243	33	generated	generate	VERB
ejpam-5021	243	34	by	by	ADP
ejpam-5021	243	35	f.	f.	PROPN
ejpam-5021	243	36	that	that	PRON
ejpam-5021	243	37	is	be	AUX
ejpam-5021	243	38	,	,	PUNCT
ejpam-5021	243	39	a	a	DET
ejpam-5021	243	40	fsss	fsss	NOUN
ejpam-5021	243	41	(	(	PUNCT
ejpam-5021	243	42	⋂̃	⋂̃	NOUN
ejpam-5021	243	43	g	g	NOUN
ejpam-5021	243	44	,	,	PUNCT
ejpam-5021	243	45	⋃̃	⋃̃	PROPN
ejpam-5021	243	46	¬g	¬g	PROPN
ejpam-5021	243	47	,	,	PUNCT
ejpam-5021	243	48	x	x	NOUN
ejpam-5021	243	49	)	)	PUNCT
ejpam-5021	243	50	over	over	ADP
ejpam-5021	243	51	u	u	NOUN
ejpam-5021	243	52	in	in	ADP
ejpam-5021	243	53	which	which	PRON
ejpam-5021	243	54	(	(	PUNCT
ejpam-5021	243	55	g,¬g	g,¬g	PROPN
ejpam-5021	243	56	,	,	PUNCT
ejpam-5021	243	57	x	x	X
ejpam-5021	243	58	)	)	PUNCT
ejpam-5021	243	59	belongs	belong	VERB
ejpam-5021	243	60	to	to	PART
ejpam-5021	243	61	nf	nf	PROPN
ejpam-5021	243	62	is	be	AUX
ejpam-5021	243	63	denoted	denote	VERB
ejpam-5021	243	64	as	as	ADP
ejpam-5021	243	65	n(f	n(f	PROPN
ejpam-5021	243	66	)	)	PUNCT
ejpam-5021	243	67	.	.	PUNCT
ejpam-5021	244	1	notation	notation	NOUN
ejpam-5021	244	2	3	3	NUM
ejpam-5021	244	3	.	.	PUNCT
ejpam-5021	245	1	for	for	ADP
ejpam-5021	245	2	an	an	DET
ejpam-5021	245	3	ordered	order	VERB
ejpam-5021	245	4	groupoid	groupoid	NOUN
ejpam-5021	245	5	(	(	PUNCT
ejpam-5021	245	6	x	x	X
ejpam-5021	245	7	,	,	PUNCT
ejpam-5021	245	8	∗,≤x	∗,≤x	NUM
ejpam-5021	245	9	)	)	PUNCT
ejpam-5021	245	10	and	and	CCONJ
ejpam-5021	245	11	x	x	PUNCT
ejpam-5021	245	12	∈	∈	NOUN
ejpam-5021	245	13	x	x	X
ejpam-5021	245	14	,	,	PUNCT
ejpam-5021	245	15	we	we	PRON
ejpam-5021	245	16	denote	denote	VERB
ejpam-5021	245	17	the	the	DET
ejpam-5021	245	18	notation	notation	NOUN
ejpam-5021	245	19	nx	nx	NOUN
ejpam-5021	246	1	:	:	PUNCT
ejpam-5021	246	2	=	=	X
ejpam-5021	246	3	{	{	PUNCT
ejpam-5021	246	4	f	f	NOUN
ejpam-5021	246	5	:	:	PUNCT
ejpam-5021	246	6	=	=	SYM
ejpam-5021	246	7	(	(	PUNCT
ejpam-5021	246	8	f,¬f	f,¬f	NOUN
ejpam-5021	246	9	,	,	PUNCT
ejpam-5021	246	10	x	x	NOUN
ejpam-5021	246	11	)	)	PUNCT
ejpam-5021	246	12	:	:	PUNCT
ejpam-5021	246	13	f	f	PROPN
ejpam-5021	246	14	is	be	AUX
ejpam-5021	246	15	a	a	DET
ejpam-5021	246	16	fssf	fssf	NOUN
ejpam-5021	246	17	over	over	ADP
ejpam-5021	246	18	u	u	PROPN
ejpam-5021	246	19	,	,	PUNCT
ejpam-5021	246	20	f(x	f(x	PROPN
ejpam-5021	246	21	)	)	PUNCT
ejpam-5021	247	1	=	=	NOUN
ejpam-5021	247	2	1u	1u	NUM
ejpam-5021	247	3	,	,	PUNCT
ejpam-5021	247	4	and	and	CCONJ
ejpam-5021	247	5	¬f(x	¬f(x	NOUN
ejpam-5021	247	6	)	)	PUNCT
ejpam-5021	247	7	=	=	SYM
ejpam-5021	248	1	0u	0u	ADJ
ejpam-5021	248	2	}	}	PUNCT
ejpam-5021	248	3	.	.	PUNCT
ejpam-5021	249	1	remark	remark	NOUN
ejpam-5021	249	2	5	5	NUM
ejpam-5021	249	3	.	.	PUNCT
ejpam-5021	250	1	in	in	ADP
ejpam-5021	250	2	notation	notation	NOUN
ejpam-5021	250	3	3	3	NUM
ejpam-5021	250	4	,	,	PUNCT
ejpam-5021	250	5	we	we	PRON
ejpam-5021	250	6	observe	observe	VERB
ejpam-5021	250	7	that	that	SCONJ
ejpam-5021	250	8	(	(	PUNCT
ejpam-5021	250	9	wx	wx	PROPN
ejpam-5021	250	10	,	,	PUNCT
ejpam-5021	250	11	¬wx	¬wx	PROPN
ejpam-5021	250	12	,	,	PUNCT
ejpam-5021	250	13	x	x	X
ejpam-5021	250	14	)	)	PUNCT
ejpam-5021	250	15	belongs	belong	VERB
ejpam-5021	250	16	to	to	ADP
ejpam-5021	250	17	nx	nx	PROPN
ejpam-5021	250	18	.	.	PUNCT
ejpam-5021	251	1	then	then	ADV
ejpam-5021	251	2	nx	nx	PROPN
ejpam-5021	251	3	is	be	AUX
ejpam-5021	251	4	a	a	DET
ejpam-5021	251	5	non	non	ADJ
ejpam-5021	251	6	-	-	ADJ
ejpam-5021	251	7	empty	empty	ADJ
ejpam-5021	251	8	subset	subset	NOUN
ejpam-5021	251	9	of	of	ADP
ejpam-5021	251	10	a	a	DET
ejpam-5021	251	11	non	non	ADJ
ejpam-5021	251	12	-	-	ADJ
ejpam-5021	251	13	empty	empty	ADJ
ejpam-5021	251	14	collection	collection	NOUN
ejpam-5021	251	15	of	of	ADP
ejpam-5021	251	16	all	all	DET
ejpam-5021	251	17	fssss	fssss	NOUN
ejpam-5021	251	18	over	over	ADP
ejpam-5021	251	19	u.	u.	NOUN
ejpam-5021	251	20	by	by	ADP
ejpam-5021	251	21	proposition	proposition	NOUN
ejpam-5021	251	22	1	1	NUM
ejpam-5021	251	23	,	,	PUNCT
ejpam-5021	251	24	we	we	PRON
ejpam-5021	251	25	see	see	VERB
ejpam-5021	251	26	that	that	SCONJ
ejpam-5021	251	27	a	a	DET
ejpam-5021	251	28	fsss	fsss	NOUN
ejpam-5021	251	29	(	(	PUNCT
ejpam-5021	251	30	⋂̃	⋂̃	NOUN
ejpam-5021	251	31	g	g	NOUN
ejpam-5021	251	32	,	,	PUNCT
ejpam-5021	251	33	⋃̃	⋃̃	PROPN
ejpam-5021	251	34	¬g	¬g	PROPN
ejpam-5021	251	35	,	,	PUNCT
ejpam-5021	251	36	x	x	NOUN
ejpam-5021	251	37	)	)	PUNCT
ejpam-5021	251	38	over	over	ADP
ejpam-5021	251	39	u	u	NOUN
ejpam-5021	251	40	in	in	ADP
ejpam-5021	251	41	which	which	PRON
ejpam-5021	251	42	(	(	PUNCT
ejpam-5021	251	43	g,¬g	g,¬g	PROPN
ejpam-5021	251	44	,	,	PUNCT
ejpam-5021	251	45	x	x	X
ejpam-5021	251	46	)	)	PUNCT
ejpam-5021	251	47	belongs	belong	VERB
ejpam-5021	251	48	to	to	ADP
ejpam-5021	251	49	nx	nx	PROPN
ejpam-5021	251	50	exists	exist	NOUN
ejpam-5021	251	51	in	in	ADP
ejpam-5021	251	52	the	the	DET
ejpam-5021	251	53	non	non	ADJ
ejpam-5021	251	54	-	-	ADJ
ejpam-5021	251	55	empty	empty	ADJ
ejpam-5021	251	56	collection	collection	NOUN
ejpam-5021	251	57	of	of	ADP
ejpam-5021	251	58	all	all	DET
ejpam-5021	251	59	fssss	fssss	NOUN
ejpam-5021	251	60	over	over	ADP
ejpam-5021	251	61	u.	u.	NOUN
ejpam-5021	251	62	by	by	ADP
ejpam-5021	251	63	proposition	proposition	NOUN
ejpam-5021	251	64	3	3	NUM
ejpam-5021	251	65	,	,	PUNCT
ejpam-5021	251	66	it	it	PRON
ejpam-5021	251	67	follows	follow	VERB
ejpam-5021	251	68	that	that	SCONJ
ejpam-5021	251	69	the	the	DET
ejpam-5021	251	70	fsss	fsss	NOUN
ejpam-5021	251	71	(	(	PUNCT
ejpam-5021	251	72	⋂̃	⋂̃	NOUN
ejpam-5021	251	73	g	g	NOUN
ejpam-5021	251	74	,	,	PUNCT
ejpam-5021	251	75	⋃̃	⋃̃	PROPN
ejpam-5021	251	76	¬g	¬g	PROPN
ejpam-5021	251	77	,	,	PUNCT
ejpam-5021	251	78	x	x	NOUN
ejpam-5021	251	79	)	)	PUNCT
ejpam-5021	251	80	over	over	ADP
ejpam-5021	251	81	u	u	NOUN
ejpam-5021	251	82	in	in	ADP
ejpam-5021	251	83	which	which	PRON
ejpam-5021	251	84	(	(	PUNCT
ejpam-5021	251	85	g,¬g	g,¬g	PROPN
ejpam-5021	251	86	,	,	PUNCT
ejpam-5021	251	87	x	x	X
ejpam-5021	251	88	)	)	PUNCT
ejpam-5021	251	89	belongs	belong	VERB
ejpam-5021	251	90	to	to	ADP
ejpam-5021	251	91	nx	nx	PROPN
ejpam-5021	251	92	is	be	AUX
ejpam-5021	251	93	a	a	DET
ejpam-5021	251	94	fssf	fssf	NOUN
ejpam-5021	251	95	.	.	PUNCT
ejpam-5021	252	1	theorem	theorem	NOUN
ejpam-5021	252	2	1	1	NUM
ejpam-5021	252	3	.	.	PUNCT
ejpam-5021	253	1	if	if	SCONJ
ejpam-5021	253	2	(	(	PUNCT
ejpam-5021	253	3	x	x	X
ejpam-5021	253	4	,	,	PUNCT
ejpam-5021	253	5	∗,≤x	∗,≤x	NUM
ejpam-5021	253	6	)	)	PUNCT
ejpam-5021	253	7	is	be	AUX
ejpam-5021	253	8	an	an	DET
ejpam-5021	253	9	ordered	order	VERB
ejpam-5021	253	10	groupoid	groupoid	NOUN
ejpam-5021	253	11	and	and	CCONJ
ejpam-5021	253	12	x	x	SYM
ejpam-5021	253	13	∈	∈	PROPN
ejpam-5021	253	14	x	x	NOUN
ejpam-5021	253	15	,	,	PUNCT
ejpam-5021	253	16	then	then	ADV
ejpam-5021	253	17	nx	nx	X
ejpam-5021	253	18	=	=	PUNCT
ejpam-5021	253	19	nf{x}:=(f{x},¬f{x},x	nf{x}:=(f{x},¬f{x},x	PROPN
ejpam-5021	253	20	)	)	PUNCT
ejpam-5021	253	21	.	.	PUNCT
ejpam-5021	254	1	proof	proof	NOUN
ejpam-5021	254	2	.	.	PUNCT
ejpam-5021	255	1	let	let	VERB
ejpam-5021	255	2	f	f	NOUN
ejpam-5021	255	3	:	:	PUNCT
ejpam-5021	255	4	=	=	SYM
ejpam-5021	255	5	(	(	PUNCT
ejpam-5021	255	6	f,¬f	f,¬f	NOUN
ejpam-5021	255	7	,	,	PUNCT
ejpam-5021	255	8	x	x	X
ejpam-5021	255	9	)	)	PUNCT
ejpam-5021	255	10	∈	∈	PROPN
ejpam-5021	256	1	nx	nx	X
ejpam-5021	256	2	.	.	PUNCT
ejpam-5021	257	1	then	then	ADV
ejpam-5021	257	2	,	,	PUNCT
ejpam-5021	257	3	we	we	PRON
ejpam-5021	257	4	get	get	VERB
ejpam-5021	257	5	that	that	SCONJ
ejpam-5021	257	6	f	f	PROPN
ejpam-5021	257	7	is	be	AUX
ejpam-5021	257	8	a	a	DET
ejpam-5021	257	9	fssf	fssf	NOUN
ejpam-5021	257	10	over	over	ADP
ejpam-5021	257	11	u.	u.	PROPN
ejpam-5021	257	12	moreover	moreover	ADV
ejpam-5021	257	13	,	,	PUNCT
ejpam-5021	257	14	f(x	f(x	PROPN
ejpam-5021	257	15	)	)	PUNCT
ejpam-5021	258	1	=	=	SYM
ejpam-5021	258	2	1u	1u	NUM
ejpam-5021	258	3	and	and	CCONJ
ejpam-5021	258	4	¬f(x	¬f(x	NOUN
ejpam-5021	258	5	)	)	PUNCT
ejpam-5021	259	1	=	=	VERB
ejpam-5021	259	2	0u	0u	ADJ
ejpam-5021	259	3	.	.	PUNCT
ejpam-5021	260	1	thus	thus	ADV
ejpam-5021	260	2	f	f	PROPN
ejpam-5021	260	3	∈	∈	PROPN
ejpam-5021	260	4	nf{x	nf{x	PROPN
ejpam-5021	260	5	}	}	PUNCT
ejpam-5021	260	6	.	.	PUNCT
ejpam-5021	261	1	indeed	indeed	ADV
ejpam-5021	261	2	,	,	PUNCT
ejpam-5021	261	3	let	let	VERB
ejpam-5021	261	4	y	y	PROPN
ejpam-5021	261	5	∈	∈	PROPN
ejpam-5021	261	6	x	x	PART
ejpam-5021	261	7	be	be	AUX
ejpam-5021	261	8	given	give	VERB
ejpam-5021	261	9	.	.	PUNCT
ejpam-5021	262	1	r.	r.	PROPN
ejpam-5021	262	2	prasertpong	prasertpong	PROPN
ejpam-5021	262	3	,	,	PUNCT
ejpam-5021	262	4	p.	p.	PROPN
ejpam-5021	262	5	julatha	julatha	PROPN
ejpam-5021	262	6	,	,	PUNCT
ejpam-5021	262	7	a.	a.	NOUN
ejpam-5021	262	8	iampan	iampan	PROPN
ejpam-5021	262	9	/	/	SYM
ejpam-5021	262	10	eur	eur	PROPN
ejpam-5021	262	11	.	.	PUNCT
ejpam-5021	263	1	j.	j.	PROPN
ejpam-5021	263	2	pure	pure	PROPN
ejpam-5021	263	3	appl	appl	PROPN
ejpam-5021	263	4	.	.	PROPN
ejpam-5021	263	5	math	math	PROPN
ejpam-5021	263	6	,	,	PUNCT
ejpam-5021	263	7	17	17	NUM
ejpam-5021	263	8	(	(	PUNCT
ejpam-5021	263	9	1	1	NUM
ejpam-5021	263	10	)	)	PUNCT
ejpam-5021	263	11	(	(	PUNCT
ejpam-5021	263	12	2024	2024	NUM
ejpam-5021	263	13	)	)	PUNCT
ejpam-5021	263	14	,	,	PUNCT
ejpam-5021	263	15	270	270	NUM
ejpam-5021	263	16	-	-	SYM
ejpam-5021	263	17	285	285	NUM
ejpam-5021	263	18	280	280	NUM
ejpam-5021	263	19	case	case	NOUN
ejpam-5021	263	20	1	1	NUM
ejpam-5021	263	21	.	.	X
ejpam-5021	263	22	assume	assume	VERB
ejpam-5021	263	23	x	x	X
ejpam-5021	263	24	=	=	PUNCT
ejpam-5021	263	25	y.	y.	NOUN
ejpam-5021	263	26	then	then	ADV
ejpam-5021	263	27	f(y	f(y	NOUN
ejpam-5021	263	28	)	)	PUNCT
ejpam-5021	263	29	=	=	SYM
ejpam-5021	263	30	f(x	f(x	PROPN
ejpam-5021	263	31	)	)	PUNCT
ejpam-5021	264	1	=	=	SYM
ejpam-5021	264	2	1u	1u	NOUN
ejpam-5021	264	3	and	and	CCONJ
ejpam-5021	264	4	¬f(y	¬f(y	NUM
ejpam-5021	264	5	)	)	PUNCT
ejpam-5021	264	6	=	=	SYM
ejpam-5021	264	7	¬f(x	¬f(x	NOUN
ejpam-5021	264	8	)	)	PUNCT
ejpam-5021	264	9	=	=	SYM
ejpam-5021	265	1	0u	0u	ADJ
ejpam-5021	265	2	.	.	PUNCT
ejpam-5021	266	1	furthermore	furthermore	ADV
ejpam-5021	266	2	,	,	PUNCT
ejpam-5021	266	3	observe	observe	VERB
ejpam-5021	266	4	that	that	SCONJ
ejpam-5021	266	5	f{x}(y	f{x}(y	NOUN
ejpam-5021	266	6	)	)	PUNCT
ejpam-5021	266	7	=	=	SYM
ejpam-5021	266	8	1u	1u	NOUN
ejpam-5021	266	9	and	and	CCONJ
ejpam-5021	266	10	¬f{x}(y	¬f{x}(y	PROPN
ejpam-5021	266	11	)	)	PUNCT
ejpam-5021	266	12	=	=	VERB
ejpam-5021	267	1	0u	0u	ADJ
ejpam-5021	267	2	.	.	PUNCT
ejpam-5021	268	1	it	it	PRON
ejpam-5021	268	2	follows	follow	VERB
ejpam-5021	268	3	that	that	SCONJ
ejpam-5021	268	4	f{x}(y	f{x}(y	PROPN
ejpam-5021	268	5	)	)	PUNCT
ejpam-5021	268	6	=	=	SYM
ejpam-5021	268	7	f(y	f(y	NOUN
ejpam-5021	268	8	)	)	PUNCT
ejpam-5021	268	9	and	and	CCONJ
ejpam-5021	268	10	¬f{x}(y	¬f{x}(y	PROPN
ejpam-5021	268	11	)	)	PUNCT
ejpam-5021	268	12	=	=	SYM
ejpam-5021	268	13	¬f(y	¬f(y	NOUN
ejpam-5021	268	14	)	)	PUNCT
ejpam-5021	268	15	.	.	PUNCT
ejpam-5021	269	1	thus	thus	ADV
ejpam-5021	269	2	f⊇̃f{x	f⊇̃f{x	ADJ
ejpam-5021	269	3	}	}	PUNCT
ejpam-5021	269	4	.	.	PUNCT
ejpam-5021	270	1	case	case	NOUN
ejpam-5021	270	2	2	2	X
ejpam-5021	270	3	.	.	X
ejpam-5021	270	4	assume	assume	VERB
ejpam-5021	270	5	x	x	PUNCT
ejpam-5021	270	6	̸=	̸=	PROPN
ejpam-5021	270	7	y.	y.	PROPN
ejpam-5021	270	8	then	then	ADV
ejpam-5021	270	9	f{x}(y	f{x}(y	NUM
ejpam-5021	270	10	)	)	PUNCT
ejpam-5021	271	1	=	=	VERB
ejpam-5021	271	2	0u	0u	ADJ
ejpam-5021	271	3	≤̃f(y	≤̃f(y	NOUN
ejpam-5021	271	4	)	)	PUNCT
ejpam-5021	271	5	and	and	CCONJ
ejpam-5021	271	6	¬f{x}(y	¬f{x}(y	PROPN
ejpam-5021	271	7	)	)	PUNCT
ejpam-5021	272	1	=	=	NOUN
ejpam-5021	272	2	1u	1u	NUM
ejpam-5021	272	3	≥̃f(y	≥̃f(y	NUM
ejpam-5021	272	4	)	)	PUNCT
ejpam-5021	272	5	.	.	PUNCT
ejpam-5021	273	1	whence	whence	PROPN
ejpam-5021	273	2	f⊇̃f{x	f⊇̃f{x	PROPN
ejpam-5021	273	3	}	}	PUNCT
ejpam-5021	273	4	.	.	PUNCT
ejpam-5021	274	1	conversely	conversely	ADV
ejpam-5021	274	2	,	,	PUNCT
ejpam-5021	274	3	let	let	VERB
ejpam-5021	274	4	g	g	NOUN
ejpam-5021	274	5	:	:	PUNCT
ejpam-5021	274	6	=	=	SYM
ejpam-5021	274	7	(	(	PUNCT
ejpam-5021	274	8	g,¬g	g,¬g	PROPN
ejpam-5021	274	9	,	,	PUNCT
ejpam-5021	274	10	x	x	X
ejpam-5021	274	11	)	)	PUNCT
ejpam-5021	274	12	∈	∈	PROPN
ejpam-5021	274	13	nf{x	nf{x	PROPN
ejpam-5021	274	14	}	}	PUNCT
ejpam-5021	274	15	.	.	PUNCT
ejpam-5021	275	1	then	then	ADV
ejpam-5021	275	2	g	g	PROPN
ejpam-5021	275	3	is	be	AUX
ejpam-5021	275	4	a	a	DET
ejpam-5021	275	5	fssf	fssf	NOUN
ejpam-5021	275	6	over	over	ADP
ejpam-5021	275	7	u	u	NOUN
ejpam-5021	275	8	and	and	CCONJ
ejpam-5021	275	9	g⊇̃f{x	g⊇̃f{x	NOUN
ejpam-5021	275	10	}	}	PUNCT
ejpam-5021	275	11	.	.	PUNCT
ejpam-5021	276	1	it	it	PRON
ejpam-5021	276	2	is	be	AUX
ejpam-5021	276	3	true	true	ADJ
ejpam-5021	276	4	that	that	SCONJ
ejpam-5021	276	5	1u	1u	NUM
ejpam-5021	276	6	=	=	SYM
ejpam-5021	276	7	f{x}(x)≤̃g(x	f{x}(x)≤̃g(x	X
ejpam-5021	276	8	)	)	PUNCT
ejpam-5021	276	9	and	and	CCONJ
ejpam-5021	276	10	0u	0u	ADJ
ejpam-5021	276	11	=	=	SYM
ejpam-5021	276	12	¬f{x}(x)≥̃¬g(x	¬f{x}(x)≥̃¬g(x	NOUN
ejpam-5021	276	13	)	)	PUNCT
ejpam-5021	276	14	.	.	PUNCT
ejpam-5021	277	1	observe	observe	VERB
ejpam-5021	277	2	that	that	SCONJ
ejpam-5021	277	3	g(x	g(x	NOUN
ejpam-5021	277	4	)	)	PUNCT
ejpam-5021	278	1	=	=	SYM
ejpam-5021	278	2	1u	1u	NOUN
ejpam-5021	278	3	and	and	CCONJ
ejpam-5021	278	4	¬g(x	¬g(x	NOUN
ejpam-5021	278	5	)	)	PUNCT
ejpam-5021	279	1	=	=	VERB
ejpam-5021	280	1	0u	0u	ADJ
ejpam-5021	280	2	,	,	PUNCT
ejpam-5021	280	3	which	which	PRON
ejpam-5021	280	4	yields	yield	VERB
ejpam-5021	280	5	g	g	PROPN
ejpam-5021	280	6	∈	∈	PROPN
ejpam-5021	280	7	nx	nx	PROPN
ejpam-5021	280	8	.	.	PUNCT
ejpam-5021	281	1	therefore	therefore	ADV
ejpam-5021	281	2	nx	nx	PROPN
ejpam-5021	281	3	=	=	SYM
ejpam-5021	281	4	nf{x	nf{x	PROPN
ejpam-5021	281	5	}	}	PUNCT
ejpam-5021	281	6	.	.	PUNCT
ejpam-5021	282	1	in	in	ADP
ejpam-5021	282	2	propositions	proposition	NOUN
ejpam-5021	282	3	7	7	NUM
ejpam-5021	282	4	and	and	CCONJ
ejpam-5021	282	5	8	8	NUM
ejpam-5021	282	6	below	below	ADV
ejpam-5021	282	7	,	,	PUNCT
ejpam-5021	282	8	it	it	PRON
ejpam-5021	282	9	is	be	AUX
ejpam-5021	282	10	not	not	PART
ejpam-5021	282	11	hard	hard	ADJ
ejpam-5021	282	12	to	to	PART
ejpam-5021	282	13	verify	verify	VERB
ejpam-5021	282	14	that	that	SCONJ
ejpam-5021	282	15	two	two	NUM
ejpam-5021	282	16	arguments	argument	NOUN
ejpam-5021	282	17	are	be	AUX
ejpam-5021	282	18	true	true	ADJ
ejpam-5021	282	19	.	.	PUNCT
ejpam-5021	283	1	proposition	proposition	NOUN
ejpam-5021	283	2	7	7	NUM
ejpam-5021	283	3	.	.	PUNCT
ejpam-5021	284	1	let	let	VERB
ejpam-5021	284	2	(	(	PUNCT
ejpam-5021	284	3	x	x	X
ejpam-5021	284	4	,	,	PUNCT
ejpam-5021	284	5	∗,≤x	∗,≤x	NUM
ejpam-5021	284	6	)	)	PUNCT
ejpam-5021	284	7	be	be	AUX
ejpam-5021	284	8	an	an	DET
ejpam-5021	284	9	ordered	order	VERB
ejpam-5021	284	10	groupoid	groupoid	NOUN
ejpam-5021	284	11	and	and	CCONJ
ejpam-5021	284	12	f	f	NOUN
ejpam-5021	284	13	:	:	PUNCT
ejpam-5021	285	1	=	=	SYM
ejpam-5021	285	2	(	(	PUNCT
ejpam-5021	285	3	f,¬f	f,¬f	NOUN
ejpam-5021	285	4	,	,	PUNCT
ejpam-5021	285	5	x	x	X
ejpam-5021	285	6	)	)	PUNCT
ejpam-5021	285	7	a	a	DET
ejpam-5021	285	8	fsss	fsss	NOUN
ejpam-5021	285	9	over	over	ADP
ejpam-5021	285	10	u.	u.	PROPN
ejpam-5021	285	11	if	if	SCONJ
ejpam-5021	285	12	f	f	PROPN
ejpam-5021	285	13	is	be	AUX
ejpam-5021	285	14	a	a	DET
ejpam-5021	285	15	fssf	fssf	NOUN
ejpam-5021	285	16	,	,	PUNCT
ejpam-5021	285	17	then	then	ADV
ejpam-5021	285	18	f−1(1u	f−1(1u	NOUN
ejpam-5021	285	19	)	)	PUNCT
ejpam-5021	286	1	=	=	PUNCT
ejpam-5021	286	2	∅	∅	NOUN
ejpam-5021	286	3	(	(	PUNCT
ejpam-5021	286	4	resp	resp	NOUN
ejpam-5021	286	5	.	.	PUNCT
ejpam-5021	286	6	,¬f−1(0u	,¬f−1(0u	PUNCT
ejpam-5021	286	7	)	)	PUNCT
ejpam-5021	287	1	=	=	SYM
ejpam-5021	287	2	∅	∅	NOUN
ejpam-5021	287	3	)	)	PUNCT
ejpam-5021	287	4	or	or	CCONJ
ejpam-5021	287	5	f−1(1u	f−1(1u	NOUN
ejpam-5021	287	6	)	)	PUNCT
ejpam-5021	287	7	(	(	PUNCT
ejpam-5021	287	8	resp	resp	NOUN
ejpam-5021	287	9	.	.	PUNCT
ejpam-5021	287	10	,¬f−1(0u	,¬f−1(0u	PUNCT
ejpam-5021	287	11	)	)	PUNCT
ejpam-5021	287	12	)	)	PUNCT
ejpam-5021	287	13	is	be	AUX
ejpam-5021	287	14	a	a	DET
ejpam-5021	287	15	filter	filter	NOUN
ejpam-5021	287	16	of	of	ADP
ejpam-5021	287	17	x.	x.	NOUN
ejpam-5021	287	18	proposition	proposition	PROPN
ejpam-5021	287	19	8	8	NUM
ejpam-5021	287	20	.	.	PUNCT
ejpam-5021	288	1	let	let	VERB
ejpam-5021	288	2	(	(	PUNCT
ejpam-5021	288	3	x	x	X
ejpam-5021	288	4	,	,	PUNCT
ejpam-5021	288	5	∗,≤x	∗,≤x	NUM
ejpam-5021	288	6	)	)	PUNCT
ejpam-5021	288	7	be	be	AUX
ejpam-5021	288	8	an	an	DET
ejpam-5021	288	9	ordered	order	VERB
ejpam-5021	288	10	groupoid	groupoid	NOUN
ejpam-5021	288	11	and	and	CCONJ
ejpam-5021	288	12	x	x	SYM
ejpam-5021	288	13	∈	∈	PROPN
ejpam-5021	288	14	x.	x.	NOUN
ejpam-5021	288	15	then	then	ADV
ejpam-5021	288	16	(	(	PUNCT
ejpam-5021	288	17	fg−1(1u	fg−1(1u	PROPN
ejpam-5021	288	18	)	)	PUNCT
ejpam-5021	288	19	,	,	PUNCT
ejpam-5021	288	20	¬f¬g−1(0u	¬f¬g−1(0u	PUNCT
ejpam-5021	288	21	)	)	PUNCT
ejpam-5021	288	22	,	,	PUNCT
ejpam-5021	288	23	x)⊆̃(g,¬g	x)⊆̃(g,¬g	PROPN
ejpam-5021	288	24	,	,	PUNCT
ejpam-5021	288	25	x	x	NOUN
ejpam-5021	288	26	)	)	PUNCT
ejpam-5021	288	27	for	for	ADP
ejpam-5021	288	28	all	all	DET
ejpam-5021	288	29	(	(	PUNCT
ejpam-5021	288	30	g,¬g	g,¬g	PROPN
ejpam-5021	288	31	,	,	PUNCT
ejpam-5021	288	32	x	x	X
ejpam-5021	288	33	)	)	PUNCT
ejpam-5021	288	34	∈	∈	PROPN
ejpam-5021	288	35	nx	nx	PROPN
ejpam-5021	288	36	.	.	PROPN
ejpam-5021	288	37	in	in	ADP
ejpam-5021	288	38	the	the	DET
ejpam-5021	288	39	following	following	NOUN
ejpam-5021	288	40	,	,	PUNCT
ejpam-5021	288	41	a	a	DET
ejpam-5021	288	42	necessary	necessary	ADJ
ejpam-5021	288	43	and	and	CCONJ
ejpam-5021	288	44	sufficient	sufficient	ADJ
ejpam-5021	288	45	condition	condition	NOUN
ejpam-5021	288	46	for	for	ADP
ejpam-5021	288	47	fssfs	fssfs	ADJ
ejpam-5021	288	48	is	be	AUX
ejpam-5021	288	49	introduced	introduce	VERB
ejpam-5021	288	50	.	.	PUNCT
ejpam-5021	289	1	lemma	lemma	PROPN
ejpam-5021	289	2	1	1	X
ejpam-5021	289	3	.	.	PUNCT
ejpam-5021	290	1	let	let	VERB
ejpam-5021	290	2	(	(	PUNCT
ejpam-5021	290	3	x	x	X
ejpam-5021	290	4	,	,	PUNCT
ejpam-5021	290	5	∗,≤x	∗,≤x	NUM
ejpam-5021	290	6	)	)	PUNCT
ejpam-5021	290	7	be	be	AUX
ejpam-5021	290	8	an	an	DET
ejpam-5021	290	9	ordered	ordered	ADJ
ejpam-5021	290	10	groupoid	groupoid	NOUN
ejpam-5021	290	11	,	,	PUNCT
ejpam-5021	290	12	and	and	CCONJ
ejpam-5021	290	13	let	let	VERB
ejpam-5021	290	14	a	a	PRON
ejpam-5021	290	15	be	be	AUX
ejpam-5021	290	16	a	a	DET
ejpam-5021	290	17	non	non	ADJ
ejpam-5021	290	18	-	-	ADJ
ejpam-5021	290	19	empty	empty	ADJ
ejpam-5021	290	20	subset	subset	NOUN
ejpam-5021	290	21	of	of	ADP
ejpam-5021	290	22	x.	x.	NOUN
ejpam-5021	290	23	then	then	ADV
ejpam-5021	290	24	a	a	PRON
ejpam-5021	290	25	is	be	AUX
ejpam-5021	290	26	a	a	DET
ejpam-5021	290	27	filter	filter	NOUN
ejpam-5021	290	28	of	of	ADP
ejpam-5021	290	29	x	x	SYM
ejpam-5021	290	30	if	if	SCONJ
ejpam-5021	291	1	and	and	CCONJ
ejpam-5021	291	2	only	only	ADV
ejpam-5021	291	3	if	if	SCONJ
ejpam-5021	291	4	the	the	DET
ejpam-5021	291	5	fsss	fsss	NOUN
ejpam-5021	291	6	(	(	PUNCT
ejpam-5021	291	7	fa,¬fa	fa,¬fa	NOUN
ejpam-5021	291	8	,	,	PUNCT
ejpam-5021	291	9	x	x	NOUN
ejpam-5021	291	10	)	)	PUNCT
ejpam-5021	291	11	over	over	ADP
ejpam-5021	291	12	u	u	NOUN
ejpam-5021	291	13	concerning	concern	VERB
ejpam-5021	291	14	a	a	PRON
ejpam-5021	291	15	is	be	AUX
ejpam-5021	291	16	a	a	DET
ejpam-5021	291	17	fssf	fssf	NOUN
ejpam-5021	291	18	.	.	PUNCT
ejpam-5021	292	1	proof	proof	NOUN
ejpam-5021	292	2	.	.	PUNCT
ejpam-5021	293	1	suppose	suppose	VERB
ejpam-5021	293	2	that	that	SCONJ
ejpam-5021	293	3	a	a	PRON
ejpam-5021	293	4	is	be	AUX
ejpam-5021	293	5	a	a	DET
ejpam-5021	293	6	filter	filter	NOUN
ejpam-5021	293	7	of	of	ADP
ejpam-5021	293	8	x	x	PUNCT
ejpam-5021	293	9	and	and	CCONJ
ejpam-5021	293	10	let	let	VERB
ejpam-5021	293	11	x	x	PRON
ejpam-5021	293	12	,	,	PUNCT
ejpam-5021	293	13	y	y	PROPN
ejpam-5021	293	14	∈	∈	PROPN
ejpam-5021	293	15	x.	x.	NOUN
ejpam-5021	293	16	then	then	ADV
ejpam-5021	293	17	,	,	PUNCT
ejpam-5021	293	18	we	we	PRON
ejpam-5021	293	19	consider	consider	VERB
ejpam-5021	293	20	the	the	DET
ejpam-5021	293	21	following	follow	VERB
ejpam-5021	293	22	two	two	NUM
ejpam-5021	293	23	cases	case	NOUN
ejpam-5021	293	24	.	.	PUNCT
ejpam-5021	294	1	case	case	NOUN
ejpam-5021	294	2	1	1	X
ejpam-5021	294	3	.	.	X
ejpam-5021	294	4	assume	assume	VERB
ejpam-5021	294	5	xy	xy	PROPN
ejpam-5021	294	6	∈	∈	PROPN
ejpam-5021	294	7	a.	a.	NOUN
ejpam-5021	294	8	then	then	ADV
ejpam-5021	294	9	fa(xy	fa(xy	NOUN
ejpam-5021	294	10	)	)	PUNCT
ejpam-5021	295	1	=	=	NOUN
ejpam-5021	295	2	1u	1u	NOUN
ejpam-5021	295	3	and	and	CCONJ
ejpam-5021	295	4	¬fa(xy	¬fa(xy	PROPN
ejpam-5021	295	5	)	)	PUNCT
ejpam-5021	296	1	=	=	NOUN
ejpam-5021	296	2	0u	0u	ADJ
ejpam-5021	296	3	.	.	PUNCT
ejpam-5021	297	1	furthermore	furthermore	ADV
ejpam-5021	297	2	,	,	PUNCT
ejpam-5021	297	3	we	we	PRON
ejpam-5021	297	4	obtain	obtain	VERB
ejpam-5021	297	5	that	that	SCONJ
ejpam-5021	297	6	x	x	SYM
ejpam-5021	297	7	∈	∈	PROPN
ejpam-5021	297	8	a	a	PRON
ejpam-5021	297	9	and	and	CCONJ
ejpam-5021	297	10	y	y	PROPN
ejpam-5021	297	11	∈	∈	PROPN
ejpam-5021	297	12	a.	a.	NOUN
ejpam-5021	297	13	hence	hence	ADV
ejpam-5021	297	14	fa(x	fa(x	VERB
ejpam-5021	297	15	)	)	PUNCT
ejpam-5021	297	16	=	=	SYM
ejpam-5021	297	17	1u	1u	NUM
ejpam-5021	297	18	=	=	SYM
ejpam-5021	297	19	f(y	f(y	NOUN
ejpam-5021	297	20	)	)	PUNCT
ejpam-5021	297	21	and	and	CCONJ
ejpam-5021	297	22	¬fa(x	¬fa(x	NOUN
ejpam-5021	297	23	)	)	PUNCT
ejpam-5021	297	24	=	=	SYM
ejpam-5021	297	25	0u	0u	ADJ
ejpam-5021	297	26	=	=	SYM
ejpam-5021	297	27	¬f(y	¬f(y	NOUN
ejpam-5021	297	28	)	)	PUNCT
ejpam-5021	297	29	.	.	PUNCT
ejpam-5021	298	1	r.	r.	PROPN
ejpam-5021	298	2	prasertpong	prasertpong	PROPN
ejpam-5021	298	3	,	,	PUNCT
ejpam-5021	298	4	p.	p.	PROPN
ejpam-5021	298	5	julatha	julatha	PROPN
ejpam-5021	298	6	,	,	PUNCT
ejpam-5021	298	7	a.	a.	NOUN
ejpam-5021	298	8	iampan	iampan	PROPN
ejpam-5021	298	9	/	/	SYM
ejpam-5021	298	10	eur	eur	PROPN
ejpam-5021	298	11	.	.	PUNCT
ejpam-5021	299	1	j.	j.	PROPN
ejpam-5021	299	2	pure	pure	PROPN
ejpam-5021	299	3	appl	appl	PROPN
ejpam-5021	299	4	.	.	PROPN
ejpam-5021	299	5	math	math	PROPN
ejpam-5021	299	6	,	,	PUNCT
ejpam-5021	299	7	17	17	NUM
ejpam-5021	299	8	(	(	PUNCT
ejpam-5021	299	9	1	1	NUM
ejpam-5021	299	10	)	)	PUNCT
ejpam-5021	299	11	(	(	PUNCT
ejpam-5021	299	12	2024	2024	NUM
ejpam-5021	299	13	)	)	PUNCT
ejpam-5021	299	14	,	,	PUNCT
ejpam-5021	299	15	270	270	NUM
ejpam-5021	299	16	-	-	SYM
ejpam-5021	299	17	285	285	NUM
ejpam-5021	299	18	281	281	NUM
ejpam-5021	299	19	thus	thus	ADV
ejpam-5021	299	20	fa(xy	fa(xy	NOUN
ejpam-5021	299	21	)	)	PUNCT
ejpam-5021	299	22	=	=	SYM
ejpam-5021	299	23	1u	1u	NUM
ejpam-5021	299	24	=	=	SYM
ejpam-5021	299	25	fa(x)∧̃f(y	fa(x)∧̃f(y	PROPN
ejpam-5021	299	26	)	)	PUNCT
ejpam-5021	299	27	and	and	CCONJ
ejpam-5021	299	28	¬fa(xy	¬fa(xy	PROPN
ejpam-5021	299	29	)	)	PUNCT
ejpam-5021	299	30	=	=	SYM
ejpam-5021	300	1	0u	0u	ADJ
ejpam-5021	300	2	=	=	SYM
ejpam-5021	300	3	fa(x)∨̃fa(y	fa(x)∨̃fa(y	PROPN
ejpam-5021	300	4	)	)	PUNCT
ejpam-5021	300	5	.	.	PUNCT
ejpam-5021	301	1	case	case	NOUN
ejpam-5021	301	2	2	2	X
ejpam-5021	301	3	.	.	X
ejpam-5021	301	4	assume	assume	VERB
ejpam-5021	301	5	xy	xy	PROPN
ejpam-5021	301	6	/∈	/∈	PUNCT
ejpam-5021	302	1	a.	a.	NOUN
ejpam-5021	302	2	then	then	ADV
ejpam-5021	302	3	fa(xy	fa(xy	NOUN
ejpam-5021	302	4	)	)	PUNCT
ejpam-5021	303	1	=	=	NOUN
ejpam-5021	303	2	∅	∅	NOUN
ejpam-5021	303	3	and	and	CCONJ
ejpam-5021	303	4	¬fa(xy	¬fa(xy	PROPN
ejpam-5021	303	5	)	)	PUNCT
ejpam-5021	304	1	=	=	NOUN
ejpam-5021	304	2	1u	1u	NOUN
ejpam-5021	304	3	.	.	PUNCT
ejpam-5021	305	1	moreover	moreover	ADV
ejpam-5021	305	2	,	,	PUNCT
ejpam-5021	305	3	we	we	PRON
ejpam-5021	305	4	obtain	obtain	VERB
ejpam-5021	305	5	that	that	PRON
ejpam-5021	305	6	x	x	PROPN
ejpam-5021	305	7	/∈	/∈	PUNCT
ejpam-5021	306	1	a	a	DET
ejpam-5021	306	2	or	or	CCONJ
ejpam-5021	306	3	y	y	PROPN
ejpam-5021	306	4	/∈	/∈	PUNCT
ejpam-5021	306	5	a.	a.	NOUN
ejpam-5021	307	1	thus	thus	ADV
ejpam-5021	307	2	(	(	PUNCT
ejpam-5021	307	3	fa(x	fa(x	NOUN
ejpam-5021	307	4	)	)	PUNCT
ejpam-5021	307	5	=	=	SYM
ejpam-5021	307	6	0u	0u	ADJ
ejpam-5021	307	7	and	and	CCONJ
ejpam-5021	307	8	¬fa(x	¬fa(x	NOUN
ejpam-5021	307	9	)	)	PUNCT
ejpam-5021	307	10	=	=	SYM
ejpam-5021	307	11	1u	1u	NOUN
ejpam-5021	307	12	)	)	PUNCT
ejpam-5021	307	13	or	or	CCONJ
ejpam-5021	307	14	(	(	PUNCT
ejpam-5021	307	15	fa(y	fa(y	PROPN
ejpam-5021	307	16	)	)	PUNCT
ejpam-5021	307	17	=	=	SYM
ejpam-5021	308	1	0u	0u	ADJ
ejpam-5021	308	2	and	and	CCONJ
ejpam-5021	308	3	¬fa(y	¬fa(y	ADJ
ejpam-5021	308	4	)	)	PUNCT
ejpam-5021	309	1	=	=	NOUN
ejpam-5021	309	2	1u	1u	NUM
ejpam-5021	309	3	)	)	PUNCT
ejpam-5021	309	4	.	.	PUNCT
ejpam-5021	310	1	hence	hence	ADV
ejpam-5021	310	2	fa(xy	fa(xy	NOUN
ejpam-5021	310	3	)	)	PUNCT
ejpam-5021	311	1	=	=	SYM
ejpam-5021	311	2	0u	0u	ADJ
ejpam-5021	311	3	=	=	NOUN
ejpam-5021	311	4	fa(x)∧̃fa(y	fa(x)∧̃fa(y	NOUN
ejpam-5021	311	5	)	)	PUNCT
ejpam-5021	311	6	and	and	CCONJ
ejpam-5021	311	7	¬fa(xy	¬fa(xy	PROPN
ejpam-5021	311	8	)	)	PUNCT
ejpam-5021	312	1	=	=	SYM
ejpam-5021	312	2	1u	1u	NUM
ejpam-5021	312	3	=	=	SYM
ejpam-5021	312	4	¬fa(x)∨̃¬fa(y	¬fa(x)∨̃¬fa(y	PROPN
ejpam-5021	312	5	)	)	PUNCT
ejpam-5021	312	6	.	.	PUNCT
ejpam-5021	313	1	next	next	ADV
ejpam-5021	313	2	,	,	PUNCT
ejpam-5021	313	3	assume	assume	VERB
ejpam-5021	313	4	that	that	SCONJ
ejpam-5021	313	5	x	x	PUNCT
ejpam-5021	313	6	≤x	≤x	VERB
ejpam-5021	313	7	y.	y.	PROPN
ejpam-5021	313	8	then	then	ADV
ejpam-5021	313	9	,	,	PUNCT
ejpam-5021	313	10	we	we	PRON
ejpam-5021	313	11	consider	consider	VERB
ejpam-5021	313	12	the	the	DET
ejpam-5021	313	13	following	follow	VERB
ejpam-5021	313	14	two	two	NUM
ejpam-5021	313	15	cases	case	NOUN
ejpam-5021	313	16	.	.	PUNCT
ejpam-5021	314	1	case	case	NOUN
ejpam-5021	314	2	1	1	X
ejpam-5021	314	3	.	.	X
ejpam-5021	314	4	assume	assume	VERB
ejpam-5021	314	5	x	x	SYM
ejpam-5021	314	6	∈	∈	PROPN
ejpam-5021	314	7	a.	a.	NOUN
ejpam-5021	314	8	then	then	ADV
ejpam-5021	314	9	fa(x	fa(x	NOUN
ejpam-5021	314	10	)	)	PUNCT
ejpam-5021	314	11	=	=	SYM
ejpam-5021	314	12	1u	1u	NOUN
ejpam-5021	314	13	and	and	CCONJ
ejpam-5021	314	14	¬fa(x	¬fa(x	NOUN
ejpam-5021	314	15	)	)	PUNCT
ejpam-5021	314	16	=	=	VERB
ejpam-5021	315	1	0u	0u	ADJ
ejpam-5021	315	2	.	.	PUNCT
ejpam-5021	316	1	by	by	ADP
ejpam-5021	316	2	the	the	DET
ejpam-5021	316	3	hypothesis	hypothesis	NOUN
ejpam-5021	316	4	,	,	PUNCT
ejpam-5021	316	5	we	we	PRON
ejpam-5021	316	6	have	have	VERB
ejpam-5021	316	7	y	y	PROPN
ejpam-5021	316	8	∈	∈	PROPN
ejpam-5021	316	9	a.	a.	NOUN
ejpam-5021	316	10	hence	hence	ADV
ejpam-5021	316	11	fa(y	fa(y	PROPN
ejpam-5021	316	12	)	)	PUNCT
ejpam-5021	317	1	=	=	SYM
ejpam-5021	317	2	1u	1u	NOUN
ejpam-5021	317	3	and	and	CCONJ
ejpam-5021	317	4	¬fa(y	¬fa(y	PROPN
ejpam-5021	317	5	)	)	PUNCT
ejpam-5021	318	1	=	=	VERB
ejpam-5021	318	2	0u	0u	ADJ
ejpam-5021	318	3	.	.	PUNCT
ejpam-5021	319	1	whence	whence	NOUN
ejpam-5021	319	2	fa(x	fa(x	PROPN
ejpam-5021	319	3	)	)	PUNCT
ejpam-5021	319	4	=	=	SYM
ejpam-5021	319	5	1u	1u	NUM
ejpam-5021	319	6	=	=	SYM
ejpam-5021	319	7	fa(y	fa(y	PROPN
ejpam-5021	319	8	)	)	PUNCT
ejpam-5021	319	9	and	and	CCONJ
ejpam-5021	319	10	¬fa(x	¬fa(x	NOUN
ejpam-5021	319	11	)	)	PUNCT
ejpam-5021	319	12	=	=	SYM
ejpam-5021	319	13	0u	0u	ADJ
ejpam-5021	319	14	=	=	SYM
ejpam-5021	319	15	¬fa(y	¬fa(y	PROPN
ejpam-5021	319	16	)	)	PUNCT
ejpam-5021	319	17	.	.	PUNCT
ejpam-5021	320	1	case	case	NOUN
ejpam-5021	320	2	2	2	X
ejpam-5021	320	3	.	.	PUNCT
ejpam-5021	320	4	suppose	suppose	VERB
ejpam-5021	320	5	x	x	X
ejpam-5021	320	6	/∈	/∈	PUNCT
ejpam-5021	320	7	a.	a.	NOUN
ejpam-5021	320	8	then	then	ADV
ejpam-5021	320	9	fa(x	fa(x	NOUN
ejpam-5021	320	10	)	)	PUNCT
ejpam-5021	320	11	=	=	VERB
ejpam-5021	320	12	0u	0u	ADJ
ejpam-5021	320	13	≤̃fa(y	≤̃fa(y	PRON
ejpam-5021	320	14	)	)	PUNCT
ejpam-5021	320	15	and	and	CCONJ
ejpam-5021	320	16	¬fa(x	¬fa(x	NOUN
ejpam-5021	320	17	)	)	PUNCT
ejpam-5021	320	18	=	=	NUM
ejpam-5021	320	19	1u	1u	NUM
ejpam-5021	320	20	≥̃¬fa(y	≥̃¬fa(y	PROPN
ejpam-5021	320	21	)	)	PUNCT
ejpam-5021	320	22	.	.	PUNCT
ejpam-5021	321	1	this	this	PRON
ejpam-5021	321	2	implies	imply	VERB
ejpam-5021	321	3	that	that	SCONJ
ejpam-5021	321	4	(	(	PUNCT
ejpam-5021	321	5	fa,¬fa	fa,¬fa	NOUN
ejpam-5021	321	6	,	,	PUNCT
ejpam-5021	321	7	x	x	PRON
ejpam-5021	321	8	)	)	PUNCT
ejpam-5021	321	9	is	be	AUX
ejpam-5021	321	10	a	a	DET
ejpam-5021	321	11	fssf	fssf	NOUN
ejpam-5021	321	12	over	over	ADP
ejpam-5021	321	13	u.	u.	NOUN
ejpam-5021	321	14	conversely	conversely	ADV
ejpam-5021	321	15	,	,	PUNCT
ejpam-5021	321	16	suppose	suppose	VERB
ejpam-5021	321	17	(	(	PUNCT
ejpam-5021	321	18	fa,¬fa	fa,¬fa	NOUN
ejpam-5021	321	19	,	,	PUNCT
ejpam-5021	321	20	x	x	PRON
ejpam-5021	321	21	)	)	PUNCT
ejpam-5021	321	22	is	be	AUX
ejpam-5021	321	23	a	a	DET
ejpam-5021	321	24	fssf	fssf	NOUN
ejpam-5021	321	25	over	over	ADP
ejpam-5021	321	26	u.	u.	PROPN
ejpam-5021	321	27	then	then	ADV
ejpam-5021	321	28	,	,	PUNCT
ejpam-5021	321	29	it	it	PRON
ejpam-5021	321	30	is	be	AUX
ejpam-5021	321	31	easy	easy	ADJ
ejpam-5021	321	32	to	to	PART
ejpam-5021	321	33	verify	verify	VERB
ejpam-5021	321	34	that	that	SCONJ
ejpam-5021	321	35	a	a	PRON
ejpam-5021	321	36	is	be	AUX
ejpam-5021	321	37	a	a	DET
ejpam-5021	321	38	subgroupoid	subgroupoid	NOUN
ejpam-5021	321	39	of	of	ADP
ejpam-5021	321	40	x.	x.	NOUN
ejpam-5021	321	41	let	let	VERB
ejpam-5021	321	42	x	x	PRON
ejpam-5021	321	43	,	,	PUNCT
ejpam-5021	321	44	y	y	PROPN
ejpam-5021	321	45	∈	∈	PROPN
ejpam-5021	321	46	x	x	X
ejpam-5021	321	47	and	and	CCONJ
ejpam-5021	321	48	xy	xy	PROPN
ejpam-5021	321	49	∈	∈	PROPN
ejpam-5021	321	50	a.	a.	NOUN
ejpam-5021	321	51	then	then	ADV
ejpam-5021	321	52	1u	1u	NUM
ejpam-5021	321	53	=	=	SYM
ejpam-5021	321	54	fa(xy	fa(xy	NOUN
ejpam-5021	321	55	)	)	PUNCT
ejpam-5021	321	56	=	=	SYM
ejpam-5021	321	57	fa(x)∧̃fa(y	fa(x)∧̃fa(y	NOUN
ejpam-5021	321	58	)	)	PUNCT
ejpam-5021	321	59	and	and	CCONJ
ejpam-5021	321	60	0u	0u	ADJ
ejpam-5021	321	61	=	=	SYM
ejpam-5021	321	62	¬fa(xy	¬fa(xy	PROPN
ejpam-5021	321	63	)	)	PUNCT
ejpam-5021	321	64	=	=	SYM
ejpam-5021	321	65	¬fa(x)∨̃¬fa(y	¬fa(x)∨̃¬fa(y	PROPN
ejpam-5021	321	66	)	)	PUNCT
ejpam-5021	321	67	.	.	PUNCT
ejpam-5021	322	1	we	we	PRON
ejpam-5021	322	2	observe	observe	VERB
ejpam-5021	322	3	that	that	SCONJ
ejpam-5021	322	4	fa(x	fa(x	NOUN
ejpam-5021	322	5	)	)	PUNCT
ejpam-5021	322	6	=	=	SYM
ejpam-5021	322	7	fa(y	fa(y	NOUN
ejpam-5021	322	8	)	)	PUNCT
ejpam-5021	322	9	=	=	SYM
ejpam-5021	322	10	1u	1u	NOUN
ejpam-5021	322	11	and	and	CCONJ
ejpam-5021	322	12	¬fa(x	¬fa(x	NOUN
ejpam-5021	322	13	)	)	PUNCT
ejpam-5021	322	14	=	=	SYM
ejpam-5021	322	15	¬fa(y	¬fa(y	PROPN
ejpam-5021	322	16	)	)	PUNCT
ejpam-5021	322	17	=	=	NOUN
ejpam-5021	323	1	0u	0u	ADJ
ejpam-5021	323	2	.	.	PUNCT
ejpam-5021	324	1	it	it	PRON
ejpam-5021	324	2	follows	follow	VERB
ejpam-5021	324	3	that	that	SCONJ
ejpam-5021	324	4	x	x	SYM
ejpam-5021	324	5	,	,	PUNCT
ejpam-5021	324	6	y	y	PROPN
ejpam-5021	324	7	∈	∈	PROPN
ejpam-5021	324	8	a.	a.	NOUN
ejpam-5021	324	9	next	next	ADV
ejpam-5021	324	10	,	,	PUNCT
ejpam-5021	324	11	assume	assume	VERB
ejpam-5021	324	12	that	that	SCONJ
ejpam-5021	324	13	x	x	PUNCT
ejpam-5021	324	14	≤x	≤x	VERB
ejpam-5021	324	15	y	y	PROPN
ejpam-5021	324	16	and	and	CCONJ
ejpam-5021	324	17	x	x	SYM
ejpam-5021	324	18	∈	∈	PROPN
ejpam-5021	324	19	a.	a.	NOUN
ejpam-5021	324	20	then	then	ADV
ejpam-5021	324	21	1u	1u	NUM
ejpam-5021	324	22	=	=	SYM
ejpam-5021	324	23	fa(x)≤̃fa(y	fa(x)≤̃fa(y	PROPN
ejpam-5021	324	24	)	)	PUNCT
ejpam-5021	324	25	and	and	CCONJ
ejpam-5021	324	26	0u	0u	ADJ
ejpam-5021	324	27	=	=	SYM
ejpam-5021	324	28	¬fa(x)≥̃¬fa(y	¬fa(x)≥̃¬fa(y	PROPN
ejpam-5021	324	29	)	)	PUNCT
ejpam-5021	324	30	.	.	PUNCT
ejpam-5021	325	1	we	we	PRON
ejpam-5021	325	2	obtain	obtain	VERB
ejpam-5021	325	3	that	that	DET
ejpam-5021	325	4	fa(y	fa(y	NOUN
ejpam-5021	325	5	)	)	PUNCT
ejpam-5021	326	1	=	=	SYM
ejpam-5021	326	2	1u	1u	NOUN
ejpam-5021	326	3	and	and	CCONJ
ejpam-5021	326	4	¬fa(y	¬fa(y	PROPN
ejpam-5021	326	5	)	)	PUNCT
ejpam-5021	327	1	=	=	SYM
ejpam-5021	327	2	0u	0u	ADJ
ejpam-5021	327	3	,	,	PUNCT
ejpam-5021	327	4	which	which	PRON
ejpam-5021	327	5	yields	yield	VERB
ejpam-5021	327	6	y	y	PROPN
ejpam-5021	327	7	∈	∈	PROPN
ejpam-5021	327	8	a.	a.	NOUN
ejpam-5021	328	1	this	this	PRON
ejpam-5021	328	2	implies	imply	VERB
ejpam-5021	328	3	that	that	SCONJ
ejpam-5021	328	4	a	a	PRON
ejpam-5021	328	5	is	be	AUX
ejpam-5021	328	6	a	a	DET
ejpam-5021	328	7	filter	filter	NOUN
ejpam-5021	328	8	of	of	ADP
ejpam-5021	328	9	x.	x.	PROPN
ejpam-5021	328	10	r.	r.	PROPN
ejpam-5021	328	11	prasertpong	prasertpong	PROPN
ejpam-5021	328	12	,	,	PUNCT
ejpam-5021	328	13	p.	p.	PROPN
ejpam-5021	328	14	julatha	julatha	PROPN
ejpam-5021	328	15	,	,	PUNCT
ejpam-5021	328	16	a.	a.	NOUN
ejpam-5021	328	17	iampan	iampan	PROPN
ejpam-5021	328	18	/	/	SYM
ejpam-5021	328	19	eur	eur	PROPN
ejpam-5021	328	20	.	.	PUNCT
ejpam-5021	329	1	j.	j.	PROPN
ejpam-5021	329	2	pure	pure	PROPN
ejpam-5021	329	3	appl	appl	PROPN
ejpam-5021	329	4	.	.	PROPN
ejpam-5021	329	5	math	math	PROPN
ejpam-5021	329	6	,	,	PUNCT
ejpam-5021	329	7	17	17	NUM
ejpam-5021	329	8	(	(	PUNCT
ejpam-5021	329	9	1	1	NUM
ejpam-5021	329	10	)	)	PUNCT
ejpam-5021	329	11	(	(	PUNCT
ejpam-5021	329	12	2024	2024	NUM
ejpam-5021	329	13	)	)	PUNCT
ejpam-5021	329	14	,	,	PUNCT
ejpam-5021	329	15	270	270	NUM
ejpam-5021	329	16	-	-	SYM
ejpam-5021	329	17	285	285	NUM
ejpam-5021	329	18	282	282	NUM
ejpam-5021	329	19	theorem	theorem	NOUN
ejpam-5021	329	20	2	2	NUM
ejpam-5021	329	21	.	.	PUNCT
ejpam-5021	330	1	if	if	SCONJ
ejpam-5021	330	2	(	(	PUNCT
ejpam-5021	330	3	x	x	X
ejpam-5021	330	4	,	,	PUNCT
ejpam-5021	330	5	∗,≤x	∗,≤x	NUM
ejpam-5021	330	6	)	)	PUNCT
ejpam-5021	330	7	is	be	AUX
ejpam-5021	330	8	an	an	DET
ejpam-5021	330	9	ordered	order	VERB
ejpam-5021	330	10	groupoid	groupoid	NOUN
ejpam-5021	330	11	and	and	CCONJ
ejpam-5021	330	12	x	x	SYM
ejpam-5021	330	13	∈	∈	PROPN
ejpam-5021	330	14	x	x	NOUN
ejpam-5021	330	15	,	,	PUNCT
ejpam-5021	330	16	then	then	ADV
ejpam-5021	330	17	n(f{x},¬f{x	n(f{x},¬f{x	ADJ
ejpam-5021	330	18	}	}	PUNCT
ejpam-5021	330	19	,	,	PUNCT
ejpam-5021	330	20	x	x	X
ejpam-5021	330	21	)	)	PUNCT
ejpam-5021	330	22	=	=	SYM
ejpam-5021	330	23	(	(	PUNCT
ejpam-5021	330	24	fn(x),¬fn(x	fn(x),¬fn(x	X
ejpam-5021	330	25	)	)	PUNCT
ejpam-5021	330	26	,	,	PUNCT
ejpam-5021	330	27	x	x	X
ejpam-5021	330	28	)	)	PUNCT
ejpam-5021	330	29	.	.	PUNCT
ejpam-5021	331	1	proof	proof	NOUN
ejpam-5021	331	2	.	.	PUNCT
ejpam-5021	332	1	by	by	ADP
ejpam-5021	332	2	notation	notation	NOUN
ejpam-5021	332	3	2	2	NUM
ejpam-5021	332	4	and	and	CCONJ
ejpam-5021	332	5	theorem	theorem	VERB
ejpam-5021	332	6	1	1	NUM
ejpam-5021	332	7	,	,	PUNCT
ejpam-5021	332	8	we	we	PRON
ejpam-5021	332	9	observe	observe	VERB
ejpam-5021	332	10	that	that	SCONJ
ejpam-5021	332	11	a	a	DET
ejpam-5021	332	12	fsss	fsss	NOUN
ejpam-5021	332	13	(	(	PUNCT
ejpam-5021	332	14	⋂̃	⋂̃	NOUN
ejpam-5021	332	15	g	g	NOUN
ejpam-5021	332	16	,	,	PUNCT
ejpam-5021	332	17	⋃̃	⋃̃	PROPN
ejpam-5021	332	18	¬g	¬g	PROPN
ejpam-5021	332	19	,	,	PUNCT
ejpam-5021	332	20	x	x	NOUN
ejpam-5021	332	21	)	)	PUNCT
ejpam-5021	332	22	over	over	ADP
ejpam-5021	332	23	u	u	NOUN
ejpam-5021	332	24	in	in	ADP
ejpam-5021	332	25	which	which	PRON
ejpam-5021	332	26	(	(	PUNCT
ejpam-5021	332	27	g,¬g	g,¬g	PROPN
ejpam-5021	332	28	,	,	PUNCT
ejpam-5021	332	29	x	x	X
ejpam-5021	332	30	)	)	PUNCT
ejpam-5021	332	31	belongs	belong	VERB
ejpam-5021	332	32	to	to	ADP
ejpam-5021	332	33	nx	nx	PROPN
ejpam-5021	332	34	is	be	AUX
ejpam-5021	332	35	equal	equal	ADJ
ejpam-5021	332	36	to	to	ADP
ejpam-5021	332	37	the	the	DET
ejpam-5021	332	38	fsss	fsss	NOUN
ejpam-5021	332	39	n(f{x},¬f{x	n(f{x},¬f{x	PROPN
ejpam-5021	332	40	}	}	PUNCT
ejpam-5021	332	41	,	,	PUNCT
ejpam-5021	332	42	x	x	X
ejpam-5021	332	43	)	)	PUNCT
ejpam-5021	332	44	over	over	ADP
ejpam-5021	332	45	u.	u.	NOUN
ejpam-5021	332	46	by	by	ADP
ejpam-5021	332	47	remark	remark	NOUN
ejpam-5021	332	48	1	1	NUM
ejpam-5021	332	49	,	,	PUNCT
ejpam-5021	332	50	we	we	PRON
ejpam-5021	332	51	have	have	VERB
ejpam-5021	332	52	the	the	DET
ejpam-5021	332	53	fsss	fsss	NOUN
ejpam-5021	332	54	(	(	PUNCT
ejpam-5021	332	55	⋂̃	⋂̃	NOUN
ejpam-5021	332	56	g	g	NOUN
ejpam-5021	332	57	,	,	PUNCT
ejpam-5021	332	58	⋃̃	⋃̃	PROPN
ejpam-5021	332	59	¬g	¬g	PROPN
ejpam-5021	332	60	,	,	PUNCT
ejpam-5021	332	61	x	x	NOUN
ejpam-5021	332	62	)	)	PUNCT
ejpam-5021	332	63	over	over	ADP
ejpam-5021	332	64	u	u	NOUN
ejpam-5021	332	65	in	in	ADP
ejpam-5021	332	66	which	which	PRON
ejpam-5021	332	67	(	(	PUNCT
ejpam-5021	332	68	g,¬g	g,¬g	PROPN
ejpam-5021	332	69	,	,	PUNCT
ejpam-5021	332	70	x	x	X
ejpam-5021	332	71	)	)	PUNCT
ejpam-5021	332	72	belongs	belong	VERB
ejpam-5021	332	73	to	to	ADP
ejpam-5021	332	74	nx	nx	PROPN
ejpam-5021	332	75	is	be	AUX
ejpam-5021	332	76	a	a	DET
ejpam-5021	332	77	fuzzy	fuzzy	ADJ
ejpam-5021	332	78	semibipolar	semibipolar	ADJ
ejpam-5021	332	79	soft	soft	ADJ
ejpam-5021	332	80	subset	subset	NOUN
ejpam-5021	332	81	of	of	ADP
ejpam-5021	332	82	(	(	PUNCT
ejpam-5021	332	83	g,¬g	g,¬g	PROPN
ejpam-5021	332	84	,	,	PUNCT
ejpam-5021	332	85	x	x	NOUN
ejpam-5021	332	86	)	)	PUNCT
ejpam-5021	332	87	for	for	ADP
ejpam-5021	332	88	all	all	DET
ejpam-5021	332	89	(	(	PUNCT
ejpam-5021	332	90	g,¬g	g,¬g	PROPN
ejpam-5021	332	91	,	,	PUNCT
ejpam-5021	332	92	x	x	X
ejpam-5021	332	93	)	)	PUNCT
ejpam-5021	332	94	∈	∈	PROPN
ejpam-5021	332	95	nx	nx	NOUN
ejpam-5021	332	96	.	.	PUNCT
ejpam-5021	332	97	thus	thus	ADV
ejpam-5021	332	98	n(f{x},¬f{x	n(f{x},¬f{x	VERB
ejpam-5021	332	99	}	}	PUNCT
ejpam-5021	332	100	,	,	PUNCT
ejpam-5021	332	101	x)⊆̃(g,¬g	x)⊆̃(g,¬g	PROPN
ejpam-5021	332	102	,	,	PUNCT
ejpam-5021	332	103	x	x	NOUN
ejpam-5021	332	104	)	)	PUNCT
ejpam-5021	332	105	for	for	ADP
ejpam-5021	332	106	all	all	DET
ejpam-5021	332	107	(	(	PUNCT
ejpam-5021	332	108	g,¬g	g,¬g	PROPN
ejpam-5021	332	109	,	,	PUNCT
ejpam-5021	332	110	x	x	X
ejpam-5021	332	111	)	)	PUNCT
ejpam-5021	332	112	∈	∈	PROPN
ejpam-5021	332	113	nx	nx	NOUN
ejpam-5021	332	114	.	.	PUNCT
ejpam-5021	332	115	since	since	SCONJ
ejpam-5021	332	116	n(x	n(x	PROPN
ejpam-5021	332	117	)	)	PUNCT
ejpam-5021	332	118	is	be	AUX
ejpam-5021	332	119	a	a	DET
ejpam-5021	332	120	filter	filter	NOUN
ejpam-5021	332	121	of	of	ADP
ejpam-5021	332	122	x	x	PRON
ejpam-5021	332	123	,	,	PUNCT
ejpam-5021	332	124	we	we	PRON
ejpam-5021	332	125	have	have	AUX
ejpam-5021	332	126	(	(	PUNCT
ejpam-5021	332	127	fn(x),¬fn(x	fn(x),¬fn(x	X
ejpam-5021	332	128	)	)	PUNCT
ejpam-5021	332	129	,	,	PUNCT
ejpam-5021	332	130	x	x	X
ejpam-5021	332	131	)	)	PUNCT
ejpam-5021	332	132	is	be	AUX
ejpam-5021	332	133	a	a	DET
ejpam-5021	332	134	fssf	fssf	NOUN
ejpam-5021	332	135	over	over	ADP
ejpam-5021	332	136	u	u	NOUN
ejpam-5021	332	137	due	due	ADP
ejpam-5021	332	138	to	to	ADP
ejpam-5021	332	139	lemma	lemma	PROPN
ejpam-5021	332	140	1	1	NUM
ejpam-5021	332	141	.	.	PUNCT
ejpam-5021	332	142	note	note	VERB
ejpam-5021	332	143	that	that	SCONJ
ejpam-5021	332	144	fn(x)(x	fn(x)(x	NOUN
ejpam-5021	332	145	)	)	PUNCT
ejpam-5021	333	1	=	=	SYM
ejpam-5021	333	2	1u	1u	NUM
ejpam-5021	333	3	and	and	CCONJ
ejpam-5021	333	4	(	(	PUNCT
ejpam-5021	333	5	¬fn(x))(x	¬fn(x))(x	PROPN
ejpam-5021	333	6	)	)	PUNCT
ejpam-5021	333	7	=	=	VERB
ejpam-5021	334	1	0u	0u	ADJ
ejpam-5021	334	2	.	.	PUNCT
ejpam-5021	335	1	then	then	ADV
ejpam-5021	335	2	(	(	PUNCT
ejpam-5021	335	3	fn(x),¬fn(x	fn(x),¬fn(x	X
ejpam-5021	335	4	)	)	PUNCT
ejpam-5021	335	5	,	,	PUNCT
ejpam-5021	335	6	x	x	X
ejpam-5021	335	7	)	)	PUNCT
ejpam-5021	335	8	∈	∈	PROPN
ejpam-5021	335	9	nx	nx	X
ejpam-5021	335	10	.	.	PUNCT
ejpam-5021	336	1	this	this	PRON
ejpam-5021	336	2	means	mean	VERB
ejpam-5021	336	3	that	that	SCONJ
ejpam-5021	336	4	n(f{x},¬f{x	n(f{x},¬f{x	ADJ
ejpam-5021	336	5	}	}	PUNCT
ejpam-5021	336	6	,	,	PUNCT
ejpam-5021	336	7	x)⊆̃(fn(x),¬fn(x	x)⊆̃(fn(x),¬fn(x	PROPN
ejpam-5021	336	8	)	)	PUNCT
ejpam-5021	336	9	,	,	PUNCT
ejpam-5021	336	10	x	x	NOUN
ejpam-5021	336	11	)	)	PUNCT
ejpam-5021	336	12	.	.	PUNCT
ejpam-5021	337	1	on	on	ADP
ejpam-5021	337	2	the	the	DET
ejpam-5021	337	3	other	other	ADJ
ejpam-5021	337	4	hand	hand	NOUN
ejpam-5021	337	5	,	,	PUNCT
ejpam-5021	337	6	we	we	PRON
ejpam-5021	337	7	shall	shall	AUX
ejpam-5021	337	8	prove	prove	VERB
ejpam-5021	337	9	that	that	SCONJ
ejpam-5021	337	10	(	(	PUNCT
ejpam-5021	337	11	fn(x),¬fn(x	fn(x),¬fn(x	X
ejpam-5021	337	12	)	)	PUNCT
ejpam-5021	337	13	,	,	PUNCT
ejpam-5021	337	14	x	x	X
ejpam-5021	337	15	)	)	PUNCT
ejpam-5021	337	16	is	be	AUX
ejpam-5021	337	17	a	a	DET
ejpam-5021	337	18	fuzzy	fuzzy	ADJ
ejpam-5021	337	19	semibipolar	semibipolar	ADJ
ejpam-5021	337	20	soft	soft	ADJ
ejpam-5021	337	21	subset	subset	NOUN
ejpam-5021	337	22	of	of	ADP
ejpam-5021	337	23	(	(	PUNCT
ejpam-5021	337	24	h,¬h	h,¬h	INTJ
ejpam-5021	337	25	,	,	PUNCT
ejpam-5021	337	26	x	x	NOUN
ejpam-5021	337	27	)	)	PUNCT
ejpam-5021	337	28	for	for	ADP
ejpam-5021	337	29	all	all	DET
ejpam-5021	337	30	(	(	PUNCT
ejpam-5021	337	31	h,¬h	h,¬h	PROPN
ejpam-5021	337	32	,	,	PUNCT
ejpam-5021	337	33	x	x	X
ejpam-5021	337	34	)	)	PUNCT
ejpam-5021	337	35	∈	∈	PROPN
ejpam-5021	337	36	nx	nx	X
ejpam-5021	337	37	.	.	PUNCT
ejpam-5021	337	38	suppose	suppose	VERB
ejpam-5021	337	39	(	(	PUNCT
ejpam-5021	337	40	h,¬h	h,¬h	INTJ
ejpam-5021	337	41	,	,	PUNCT
ejpam-5021	337	42	x	x	X
ejpam-5021	337	43	)	)	PUNCT
ejpam-5021	337	44	∈	∈	PROPN
ejpam-5021	337	45	nx	nx	X
ejpam-5021	337	46	.	.	PROPN
ejpam-5021	338	1	then	then	ADV
ejpam-5021	338	2	h(x	h(x	PROPN
ejpam-5021	338	3	)	)	PUNCT
ejpam-5021	339	1	=	=	NOUN
ejpam-5021	339	2	1u	1u	NUM
ejpam-5021	339	3	and	and	CCONJ
ejpam-5021	339	4	¬h(x	¬h(x	NOUN
ejpam-5021	339	5	)	)	PUNCT
ejpam-5021	340	1	=	=	VERB
ejpam-5021	341	1	0u	0u	ADJ
ejpam-5021	341	2	.	.	PUNCT
ejpam-5021	342	1	therefore	therefore	ADV
ejpam-5021	342	2	x	x	X
ejpam-5021	342	3	∈	∈	PROPN
ejpam-5021	342	4	h−1(1u	h−1(1u	NOUN
ejpam-5021	342	5	)	)	PUNCT
ejpam-5021	342	6	∩	∩	PROPN
ejpam-5021	342	7	¬h−1(0u	¬h−1(0u	PROPN
ejpam-5021	342	8	)	)	PUNCT
ejpam-5021	342	9	.	.	PUNCT
ejpam-5021	343	1	from	from	ADP
ejpam-5021	343	2	proposition	proposition	NOUN
ejpam-5021	343	3	7	7	NUM
ejpam-5021	343	4	,	,	PUNCT
ejpam-5021	343	5	we	we	PRON
ejpam-5021	343	6	have	have	VERB
ejpam-5021	343	7	h−1(1u	h−1(1u	NOUN
ejpam-5021	343	8	)	)	PUNCT
ejpam-5021	343	9	and	and	CCONJ
ejpam-5021	343	10	¬h−1(0u	¬h−1(0u	PROPN
ejpam-5021	343	11	)	)	PUNCT
ejpam-5021	343	12	are	be	AUX
ejpam-5021	343	13	filters	filter	NOUN
ejpam-5021	343	14	of	of	ADP
ejpam-5021	343	15	x	x	PUNCT
ejpam-5021	343	16	containing	contain	VERB
ejpam-5021	343	17	x.	x.	NOUN
ejpam-5021	343	18	it	it	PRON
ejpam-5021	343	19	follows	follow	VERB
ejpam-5021	343	20	that	that	SCONJ
ejpam-5021	343	21	n(x	n(x	ADJ
ejpam-5021	343	22	)	)	PUNCT
ejpam-5021	343	23	⊆	⊆	NUM
ejpam-5021	343	24	h−1(1u	h−1(1u	NOUN
ejpam-5021	343	25	)	)	PUNCT
ejpam-5021	343	26	and	and	CCONJ
ejpam-5021	343	27	n(x	n(x	NOUN
ejpam-5021	343	28	)	)	PUNCT
ejpam-5021	343	29	⊆	⊆	NUM
ejpam-5021	343	30	¬h−1(0u	¬h−1(0u	NOUN
ejpam-5021	343	31	)	)	PUNCT
ejpam-5021	343	32	.	.	PUNCT
ejpam-5021	344	1	from	from	ADP
ejpam-5021	344	2	remark	remark	NOUN
ejpam-5021	344	3	2	2	NUM
ejpam-5021	344	4	and	and	CCONJ
ejpam-5021	344	5	proposition	proposition	NOUN
ejpam-5021	344	6	8	8	NUM
ejpam-5021	344	7	,	,	PUNCT
ejpam-5021	344	8	it	it	PRON
ejpam-5021	344	9	follows	follow	VERB
ejpam-5021	344	10	that	that	SCONJ
ejpam-5021	344	11	(	(	PUNCT
ejpam-5021	344	12	fn(x),¬fn(x	fn(x),¬fn(x	X
ejpam-5021	344	13	)	)	PUNCT
ejpam-5021	344	14	,	,	PUNCT
ejpam-5021	344	15	x)⊆̃(fh−1(1u	x)⊆̃(fh−1(1u	NOUN
ejpam-5021	344	16	)	)	PUNCT
ejpam-5021	344	17	,	,	PUNCT
ejpam-5021	344	18	¬f¬h−1(0u	¬f¬h−1(0u	NUM
ejpam-5021	344	19	)	)	PUNCT
ejpam-5021	344	20	,	,	PUNCT
ejpam-5021	344	21	x)⊆̃(h,¬h	x)⊆̃(h,¬h	PROPN
ejpam-5021	344	22	,	,	PUNCT
ejpam-5021	344	23	x	x	NOUN
ejpam-5021	344	24	)	)	PUNCT
ejpam-5021	344	25	.	.	PUNCT
ejpam-5021	345	1	observe	observe	VERB
ejpam-5021	345	2	that	that	SCONJ
ejpam-5021	345	3	a	a	DET
ejpam-5021	345	4	fsss	fsss	NOUN
ejpam-5021	345	5	(	(	PUNCT
ejpam-5021	345	6	infx{h	infx{h	PROPN
ejpam-5021	345	7	}	}	PUNCT
ejpam-5021	345	8	,	,	PUNCT
ejpam-5021	345	9	supx{¬h	supx{¬h	ADJ
ejpam-5021	345	10	}	}	PUNCT
ejpam-5021	345	11	,	,	PUNCT
ejpam-5021	345	12	x	x	X
ejpam-5021	345	13	)	)	PUNCT
ejpam-5021	345	14	over	over	ADP
ejpam-5021	345	15	u	u	NOUN
ejpam-5021	345	16	in	in	ADP
ejpam-5021	345	17	which	which	PRON
ejpam-5021	345	18	(	(	PUNCT
ejpam-5021	345	19	h,¬h	h,¬h	INTJ
ejpam-5021	345	20	,	,	PUNCT
ejpam-5021	345	21	x	x	X
ejpam-5021	345	22	)	)	PUNCT
ejpam-5021	345	23	belongs	belong	VERB
ejpam-5021	345	24	to	to	ADP
ejpam-5021	345	25	nx	nx	PROPN
ejpam-5021	345	26	is	be	AUX
ejpam-5021	345	27	a	a	DET
ejpam-5021	345	28	fuzzy	fuzzy	ADJ
ejpam-5021	345	29	semibipolar	semibipolar	ADJ
ejpam-5021	345	30	soft	soft	ADJ
ejpam-5021	345	31	superset	superset	NOUN
ejpam-5021	345	32	of	of	ADP
ejpam-5021	345	33	(	(	PUNCT
ejpam-5021	345	34	fn(x),¬fn(x	fn(x),¬fn(x	X
ejpam-5021	345	35	)	)	PUNCT
ejpam-5021	345	36	,	,	PUNCT
ejpam-5021	345	37	x	x	NOUN
ejpam-5021	345	38	)	)	PUNCT
ejpam-5021	345	39	.	.	PUNCT
ejpam-5021	346	1	by	by	ADP
ejpam-5021	346	2	proposition	proposition	NOUN
ejpam-5021	346	3	2	2	NUM
ejpam-5021	346	4	,	,	PUNCT
ejpam-5021	346	5	we	we	PRON
ejpam-5021	346	6	see	see	VERB
ejpam-5021	346	7	that	that	SCONJ
ejpam-5021	346	8	(	(	PUNCT
ejpam-5021	346	9	⋂̃	⋂̃	ADJ
ejpam-5021	346	10	h	h	NOUN
ejpam-5021	346	11	,	,	PUNCT
ejpam-5021	346	12	⋃̃	⋃̃	PROPN
ejpam-5021	346	13	¬h	¬h	PROPN
ejpam-5021	346	14	,	,	PUNCT
ejpam-5021	346	15	x	x	NOUN
ejpam-5021	346	16	)	)	PUNCT
ejpam-5021	346	17	=	=	SYM
ejpam-5021	346	18	(	(	PUNCT
ejpam-5021	346	19	inf	inf	NOUN
ejpam-5021	346	20	x	x	X
ejpam-5021	346	21	{	{	PUNCT
ejpam-5021	346	22	h	h	NOUN
ejpam-5021	346	23	}	}	PUNCT
ejpam-5021	346	24	,	,	PUNCT
ejpam-5021	346	25	sup	sup	NOUN
ejpam-5021	346	26	x	x	INTJ
ejpam-5021	346	27	{	{	PUNCT
ejpam-5021	346	28	¬h	¬h	X
ejpam-5021	346	29	}	}	PUNCT
ejpam-5021	346	30	,	,	PUNCT
ejpam-5021	346	31	x	x	NOUN
ejpam-5021	346	32	)	)	PUNCT
ejpam-5021	346	33	.	.	PUNCT
ejpam-5021	347	1	that	that	PRON
ejpam-5021	347	2	is	be	AUX
ejpam-5021	347	3	,	,	PUNCT
ejpam-5021	347	4	we	we	PRON
ejpam-5021	347	5	get	get	VERB
ejpam-5021	347	6	that	that	SCONJ
ejpam-5021	347	7	the	the	DET
ejpam-5021	347	8	fsss	fsss	NOUN
ejpam-5021	347	9	(	(	PUNCT
ejpam-5021	347	10	⋂̃	⋂̃	ADJ
ejpam-5021	347	11	h	h	NOUN
ejpam-5021	347	12	,	,	PUNCT
ejpam-5021	347	13	⋃̃	⋃̃	PROPN
ejpam-5021	347	14	¬h	¬h	PROPN
ejpam-5021	347	15	,	,	PUNCT
ejpam-5021	347	16	x	x	NOUN
ejpam-5021	347	17	)	)	PUNCT
ejpam-5021	347	18	over	over	ADP
ejpam-5021	347	19	u	u	NOUN
ejpam-5021	347	20	in	in	ADP
ejpam-5021	347	21	which	which	PRON
ejpam-5021	347	22	(	(	PUNCT
ejpam-5021	347	23	h,¬h	h,¬h	INTJ
ejpam-5021	347	24	,	,	PUNCT
ejpam-5021	347	25	x	x	X
ejpam-5021	347	26	)	)	PUNCT
ejpam-5021	347	27	belongs	belong	VERB
ejpam-5021	347	28	to	to	ADP
ejpam-5021	347	29	nx	nx	PROPN
ejpam-5021	347	30	is	be	AUX
ejpam-5021	347	31	a	a	DET
ejpam-5021	347	32	fuzzy	fuzzy	ADJ
ejpam-5021	347	33	semibipolar	semibipolar	ADJ
ejpam-5021	347	34	soft	soft	ADJ
ejpam-5021	347	35	superset	superset	NOUN
ejpam-5021	347	36	of	of	ADP
ejpam-5021	347	37	(	(	PUNCT
ejpam-5021	347	38	fn(x),¬fn(x	fn(x),¬fn(x	X
ejpam-5021	347	39	)	)	PUNCT
ejpam-5021	347	40	,	,	PUNCT
ejpam-5021	347	41	x	x	NOUN
ejpam-5021	347	42	)	)	PUNCT
ejpam-5021	347	43	.	.	PUNCT
ejpam-5021	348	1	by	by	ADP
ejpam-5021	348	2	notation	notation	NOUN
ejpam-5021	348	3	2	2	NUM
ejpam-5021	348	4	and	and	CCONJ
ejpam-5021	348	5	theorem	theorem	VERB
ejpam-5021	348	6	1	1	NUM
ejpam-5021	348	7	,	,	PUNCT
ejpam-5021	348	8	we	we	PRON
ejpam-5021	348	9	obtain	obtain	VERB
ejpam-5021	348	10	that	that	DET
ejpam-5021	348	11	(	(	PUNCT
ejpam-5021	348	12	fn(x),¬fn(x	fn(x),¬fn(x	X
ejpam-5021	348	13	)	)	PUNCT
ejpam-5021	348	14	,	,	PUNCT
ejpam-5021	348	15	x)⊆̃n(f{x},¬f{x	x)⊆̃n(f{x},¬f{x	PROPN
ejpam-5021	348	16	}	}	PUNCT
ejpam-5021	348	17	,	,	PUNCT
ejpam-5021	348	18	x	x	NOUN
ejpam-5021	348	19	)	)	PUNCT
ejpam-5021	348	20	.	.	PUNCT
ejpam-5021	349	1	this	this	PRON
ejpam-5021	349	2	implies	imply	VERB
ejpam-5021	349	3	that	that	SCONJ
ejpam-5021	349	4	n(f{x},¬f{x	n(f{x},¬f{x	ADJ
ejpam-5021	349	5	}	}	PUNCT
ejpam-5021	349	6	,	,	PUNCT
ejpam-5021	349	7	x	x	X
ejpam-5021	349	8	)	)	PUNCT
ejpam-5021	349	9	=	=	SYM
ejpam-5021	349	10	(	(	PUNCT
ejpam-5021	349	11	fn(x),¬fn(x	fn(x),¬fn(x	X
ejpam-5021	349	12	)	)	PUNCT
ejpam-5021	349	13	,	,	PUNCT
ejpam-5021	349	14	x	x	X
ejpam-5021	349	15	)	)	PUNCT
ejpam-5021	349	16	.	.	PUNCT
ejpam-5021	350	1	notation	notation	NOUN
ejpam-5021	350	2	4	4	NUM
ejpam-5021	350	3	.	.	PUNCT
ejpam-5021	351	1	for	for	ADP
ejpam-5021	351	2	an	an	DET
ejpam-5021	351	3	ordered	order	VERB
ejpam-5021	351	4	groupoid	groupoid	NOUN
ejpam-5021	351	5	(	(	PUNCT
ejpam-5021	351	6	x	x	X
ejpam-5021	351	7	,	,	PUNCT
ejpam-5021	351	8	∗,≤x	∗,≤x	NUM
ejpam-5021	351	9	)	)	PUNCT
ejpam-5021	351	10	and	and	CCONJ
ejpam-5021	351	11	x	x	PUNCT
ejpam-5021	351	12	∈	∈	NOUN
ejpam-5021	351	13	x	x	X
ejpam-5021	351	14	,	,	PUNCT
ejpam-5021	351	15	we	we	PRON
ejpam-5021	351	16	denote	denote	VERB
ejpam-5021	351	17	the	the	DET
ejpam-5021	351	18	notation	notation	NOUN
ejpam-5021	351	19	nb(x	nb(x	PUNCT
ejpam-5021	351	20	)	)	PUNCT
ejpam-5021	351	21	:	:	PUNCT
ejpam-5021	352	1	=	=	PUNCT
ejpam-5021	352	2	n(f{x},¬f{x	n(f{x},¬f{x	PROPN
ejpam-5021	352	3	}	}	PUNCT
ejpam-5021	352	4	,	,	PUNCT
ejpam-5021	352	5	x	x	NOUN
ejpam-5021	352	6	)	)	PUNCT
ejpam-5021	352	7	.	.	PUNCT
ejpam-5021	353	1	remark	remark	PROPN
ejpam-5021	353	2	6	6	NUM
ejpam-5021	353	3	.	.	PUNCT
ejpam-5021	353	4	by	by	ADP
ejpam-5021	353	5	notation	notation	NOUN
ejpam-5021	353	6	2	2	NUM
ejpam-5021	353	7	,	,	PUNCT
ejpam-5021	353	8	notation	notation	NOUN
ejpam-5021	353	9	4	4	NUM
ejpam-5021	353	10	and	and	CCONJ
ejpam-5021	353	11	theorem	theorem	VERB
ejpam-5021	353	12	1	1	NUM
ejpam-5021	353	13	,	,	PUNCT
ejpam-5021	353	14	observe	observe	VERB
ejpam-5021	353	15	that	that	SCONJ
ejpam-5021	353	16	a	a	DET
ejpam-5021	353	17	fsss	fsss	NOUN
ejpam-5021	353	18	(	(	PUNCT
ejpam-5021	353	19	⋂̃	⋂̃	NOUN
ejpam-5021	353	20	f	f	X
ejpam-5021	353	21	,	,	PUNCT
ejpam-5021	353	22	⋃̃	⋃̃	PROPN
ejpam-5021	353	23	¬f	¬f	PROPN
ejpam-5021	353	24	,	,	PUNCT
ejpam-5021	353	25	x	x	NOUN
ejpam-5021	353	26	)	)	PUNCT
ejpam-5021	353	27	over	over	ADP
ejpam-5021	353	28	u	u	NOUN
ejpam-5021	353	29	in	in	ADP
ejpam-5021	353	30	which	which	PRON
ejpam-5021	353	31	(	(	PUNCT
ejpam-5021	353	32	f,¬f	f,¬f	NOUN
ejpam-5021	353	33	,	,	PUNCT
ejpam-5021	353	34	x	x	X
ejpam-5021	353	35	)	)	PUNCT
ejpam-5021	353	36	belongs	belong	VERB
ejpam-5021	353	37	to	to	ADP
ejpam-5021	353	38	nx	nx	PROPN
ejpam-5021	353	39	.	.	PUNCT
ejpam-5021	354	1	then	then	ADV
ejpam-5021	354	2	,	,	PUNCT
ejpam-5021	354	3	by	by	ADP
ejpam-5021	354	4	proposition	proposition	NOUN
ejpam-5021	354	5	3	3	NUM
ejpam-5021	354	6	,	,	PUNCT
ejpam-5021	354	7	we	we	PRON
ejpam-5021	354	8	see	see	VERB
ejpam-5021	354	9	that	that	DET
ejpam-5021	354	10	nb(x	nb(x	PUNCT
ejpam-5021	354	11	)	)	PUNCT
ejpam-5021	354	12	∈	∈	PROPN
ejpam-5021	354	13	nx	nx	NOUN
ejpam-5021	354	14	and	and	CCONJ
ejpam-5021	354	15	nb(x)⊆̃(g,¬g	nb(x)⊆̃(g,¬g	ADV
ejpam-5021	354	16	,	,	PUNCT
ejpam-5021	354	17	x	x	X
ejpam-5021	354	18	)	)	PUNCT
ejpam-5021	354	19	for	for	ADP
ejpam-5021	354	20	all	all	DET
ejpam-5021	354	21	(	(	PUNCT
ejpam-5021	354	22	g,¬g	g,¬g	PROPN
ejpam-5021	354	23	,	,	PUNCT
ejpam-5021	354	24	x	x	X
ejpam-5021	354	25	)	)	PUNCT
ejpam-5021	354	26	∈	∈	PROPN
ejpam-5021	354	27	nx	nx	PROPN
ejpam-5021	354	28	.	.	PROPN
ejpam-5021	354	29	from	from	ADP
ejpam-5021	354	30	definition	definition	NOUN
ejpam-5021	354	31	4	4	NUM
ejpam-5021	354	32	,	,	PUNCT
ejpam-5021	354	33	it	it	PRON
ejpam-5021	354	34	follows	follow	VERB
ejpam-5021	354	35	that	that	SCONJ
ejpam-5021	354	36	nb(x	nb(x	PUNCT
ejpam-5021	354	37	)	)	PUNCT
ejpam-5021	354	38	is	be	AUX
ejpam-5021	354	39	a	a	DET
ejpam-5021	354	40	fssf	fssf	NOUN
ejpam-5021	354	41	over	over	ADP
ejpam-5021	354	42	u	u	NOUN
ejpam-5021	354	43	containing	contain	VERB
ejpam-5021	354	44	x.	x.	NOUN
ejpam-5021	354	45	this	this	DET
ejpam-5021	354	46	remark	remark	NOUN
ejpam-5021	354	47	leads	lead	VERB
ejpam-5021	354	48	to	to	ADP
ejpam-5021	354	49	the	the	DET
ejpam-5021	354	50	following	follow	VERB
ejpam-5021	354	51	definition	definition	NOUN
ejpam-5021	354	52	.	.	PUNCT
ejpam-5021	355	1	r.	r.	PROPN
ejpam-5021	355	2	prasertpong	prasertpong	PROPN
ejpam-5021	355	3	,	,	PUNCT
ejpam-5021	355	4	p.	p.	PROPN
ejpam-5021	355	5	julatha	julatha	PROPN
ejpam-5021	355	6	,	,	PUNCT
ejpam-5021	355	7	a.	a.	NOUN
ejpam-5021	355	8	iampan	iampan	PROPN
ejpam-5021	355	9	/	/	SYM
ejpam-5021	355	10	eur	eur	PROPN
ejpam-5021	355	11	.	.	PUNCT
ejpam-5021	356	1	j.	j.	PROPN
ejpam-5021	356	2	pure	pure	PROPN
ejpam-5021	356	3	appl	appl	PROPN
ejpam-5021	356	4	.	.	PROPN
ejpam-5021	356	5	math	math	PROPN
ejpam-5021	356	6	,	,	PUNCT
ejpam-5021	356	7	17	17	NUM
ejpam-5021	356	8	(	(	PUNCT
ejpam-5021	356	9	1	1	NUM
ejpam-5021	356	10	)	)	PUNCT
ejpam-5021	356	11	(	(	PUNCT
ejpam-5021	356	12	2024	2024	NUM
ejpam-5021	356	13	)	)	PUNCT
ejpam-5021	356	14	,	,	PUNCT
ejpam-5021	356	15	270	270	NUM
ejpam-5021	356	16	-	-	SYM
ejpam-5021	356	17	285	285	NUM
ejpam-5021	356	18	283	283	NUM
ejpam-5021	356	19	definition	definition	NOUN
ejpam-5021	356	20	7	7	NUM
ejpam-5021	356	21	.	.	PUNCT
ejpam-5021	357	1	let	let	VERB
ejpam-5021	357	2	(	(	PUNCT
ejpam-5021	357	3	x	x	X
ejpam-5021	357	4	,	,	PUNCT
ejpam-5021	357	5	∗,≤x	∗,≤x	NUM
ejpam-5021	357	6	)	)	PUNCT
ejpam-5021	357	7	be	be	AUX
ejpam-5021	357	8	an	an	DET
ejpam-5021	357	9	ordered	order	VERB
ejpam-5021	357	10	groupoid	groupoid	NOUN
ejpam-5021	357	11	and	and	CCONJ
ejpam-5021	357	12	x	x	SYM
ejpam-5021	357	13	∈	∈	NOUN
ejpam-5021	357	14	x.	x.	NOUN
ejpam-5021	358	1	we	we	PRON
ejpam-5021	358	2	call	call	VERB
ejpam-5021	358	3	nb(x	nb(x	VERB
ejpam-5021	358	4	)	)	PUNCT
ejpam-5021	358	5	the	the	DET
ejpam-5021	358	6	fssf	fssf	NOUN
ejpam-5021	358	7	over	over	ADP
ejpam-5021	358	8	u	u	NOUN
ejpam-5021	358	9	generated	generate	VERB
ejpam-5021	358	10	by	by	ADP
ejpam-5021	358	11	x.	x.	NOUN
ejpam-5021	358	12	we	we	PRON
ejpam-5021	358	13	are	be	AUX
ejpam-5021	358	14	now	now	ADV
ejpam-5021	358	15	ready	ready	ADJ
ejpam-5021	358	16	for	for	ADP
ejpam-5021	358	17	the	the	DET
ejpam-5021	358	18	presentation	presentation	NOUN
ejpam-5021	358	19	of	of	ADP
ejpam-5021	358	20	a	a	DET
ejpam-5021	358	21	binary	binary	ADJ
ejpam-5021	358	22	relation	relation	NOUN
ejpam-5021	358	23	induced	induce	VERB
ejpam-5021	358	24	by	by	ADP
ejpam-5021	358	25	a	a	DET
ejpam-5021	358	26	fssf	fssf	NOUN
ejpam-5021	358	27	over	over	ADP
ejpam-5021	358	28	u.	u.	ADJ
ejpam-5021	358	29	definition	definition	NOUN
ejpam-5021	358	30	8	8	NUM
ejpam-5021	358	31	.	.	PUNCT
ejpam-5021	359	1	let	let	VERB
ejpam-5021	359	2	(	(	PUNCT
ejpam-5021	359	3	x	x	X
ejpam-5021	359	4	,	,	PUNCT
ejpam-5021	359	5	∗,≤x	∗,≤x	NUM
ejpam-5021	359	6	)	)	PUNCT
ejpam-5021	359	7	be	be	AUX
ejpam-5021	359	8	an	an	DET
ejpam-5021	359	9	ordered	ordered	ADJ
ejpam-5021	359	10	groupoid	groupoid	NOUN
ejpam-5021	359	11	.	.	PUNCT
ejpam-5021	360	1	we	we	PRON
ejpam-5021	360	2	define	define	VERB
ejpam-5021	360	3	relations	relation	NOUN
ejpam-5021	360	4	nb	nb	INTJ
ejpam-5021	360	5	on	on	ADP
ejpam-5021	360	6	x	x	PUNCT
ejpam-5021	360	7	as	as	SCONJ
ejpam-5021	360	8	follows	follow	VERB
ejpam-5021	360	9	:	:	PUNCT
ejpam-5021	360	10	nb	nb	INTJ
ejpam-5021	360	11	:	:	PUNCT
ejpam-5021	360	12	=	=	SYM
ejpam-5021	360	13	{	{	PUNCT
ejpam-5021	360	14	(	(	PUNCT
ejpam-5021	360	15	x	x	NOUN
ejpam-5021	360	16	,	,	PUNCT
ejpam-5021	360	17	y	y	NOUN
ejpam-5021	360	18	)	)	PUNCT
ejpam-5021	360	19	∈	∈	PROPN
ejpam-5021	360	20	x	x	X
ejpam-5021	360	21	×x	×x	X
ejpam-5021	360	22	:	:	PUNCT
ejpam-5021	360	23	nb(x	nb(x	NUM
ejpam-5021	360	24	)	)	PUNCT
ejpam-5021	360	25	=	=	SYM
ejpam-5021	360	26	nb(y	nb(y	NUM
ejpam-5021	360	27	)	)	PUNCT
ejpam-5021	360	28	}	}	PUNCT
ejpam-5021	360	29	.	.	PUNCT
ejpam-5021	361	1	as	as	SCONJ
ejpam-5021	361	2	mentioned	mention	VERB
ejpam-5021	361	3	above	above	ADV
ejpam-5021	361	4	,	,	PUNCT
ejpam-5021	361	5	we	we	PRON
ejpam-5021	361	6	shall	shall	AUX
ejpam-5021	361	7	verify	verify	VERB
ejpam-5021	361	8	the	the	DET
ejpam-5021	361	9	relationship	relationship	NOUN
ejpam-5021	361	10	between	between	ADP
ejpam-5021	361	11	two	two	NUM
ejpam-5021	361	12	binary	binary	ADJ
ejpam-5021	361	13	relations	relation	NOUN
ejpam-5021	361	14	n	n	PROPN
ejpam-5021	361	15	and	and	CCONJ
ejpam-5021	361	16	nb	nb	INTJ
ejpam-5021	361	17	as	as	ADP
ejpam-5021	361	18	the	the	DET
ejpam-5021	361	19	following	follow	VERB
ejpam-5021	361	20	theorem	theorem	NOUN
ejpam-5021	361	21	.	.	PUNCT
ejpam-5021	361	22	theorem	theorem	NOUN
ejpam-5021	361	23	3	3	NUM
ejpam-5021	361	24	.	.	PUNCT
ejpam-5021	362	1	if	if	SCONJ
ejpam-5021	362	2	(	(	PUNCT
ejpam-5021	362	3	x	x	X
ejpam-5021	362	4	,	,	PUNCT
ejpam-5021	362	5	∗,≤x	∗,≤x	NUM
ejpam-5021	362	6	)	)	PUNCT
ejpam-5021	362	7	is	be	AUX
ejpam-5021	362	8	an	an	DET
ejpam-5021	362	9	ordered	ordered	ADJ
ejpam-5021	362	10	groupoid	groupoid	NOUN
ejpam-5021	362	11	,	,	PUNCT
ejpam-5021	362	12	then	then	ADV
ejpam-5021	362	13	n	n	ADV
ejpam-5021	362	14	and	and	CCONJ
ejpam-5021	362	15	nb	nb	PROPN
ejpam-5021	362	16	are	be	AUX
ejpam-5021	362	17	identical	identical	ADJ
ejpam-5021	362	18	.	.	PUNCT
ejpam-5021	363	1	proof	proof	NOUN
ejpam-5021	363	2	.	.	PUNCT
ejpam-5021	364	1	let	let	VERB
ejpam-5021	364	2	x	x	PRON
ejpam-5021	364	3	,	,	PUNCT
ejpam-5021	364	4	y	y	PROPN
ejpam-5021	364	5	∈	∈	PROPN
ejpam-5021	364	6	x	x	AUX
ejpam-5021	364	7	be	be	AUX
ejpam-5021	364	8	given	give	VERB
ejpam-5021	364	9	.	.	PUNCT
ejpam-5021	365	1	then	then	ADV
ejpam-5021	365	2	,	,	PUNCT
ejpam-5021	365	3	we	we	PRON
ejpam-5021	365	4	obtain	obtain	VERB
ejpam-5021	365	5	that	that	PRON
ejpam-5021	365	6	(	(	PUNCT
ejpam-5021	365	7	x	x	X
ejpam-5021	365	8	,	,	PUNCT
ejpam-5021	365	9	y	y	NOUN
ejpam-5021	365	10	)	)	PUNCT
ejpam-5021	365	11	∈	∈	PROPN
ejpam-5021	365	12	nb	nb	ADP
ejpam-5021	365	13	⇐	⇐	PROPN
ejpam-5021	365	14	⇒	⇒	NOUN
ejpam-5021	365	15	nb(x	nb(x	NUM
ejpam-5021	365	16	)	)	PUNCT
ejpam-5021	365	17	=	=	SYM
ejpam-5021	365	18	nb(y	nb(y	NUM
ejpam-5021	365	19	)	)	PUNCT
ejpam-5021	365	20	⇐	⇐	ADJ
ejpam-5021	365	21	⇒	⇒	NOUN
ejpam-5021	365	22	n(f{x},¬f{x	n(f{x},¬f{x	VERB
ejpam-5021	365	23	}	}	PUNCT
ejpam-5021	365	24	,	,	PUNCT
ejpam-5021	365	25	x	x	X
ejpam-5021	365	26	)	)	PUNCT
ejpam-5021	365	27	=	=	SYM
ejpam-5021	365	28	n(f{y},¬f{y	n(f{y},¬f{y	PROPN
ejpam-5021	365	29	}	}	PUNCT
ejpam-5021	365	30	,	,	PUNCT
ejpam-5021	365	31	x	x	X
ejpam-5021	365	32	)	)	PUNCT
ejpam-5021	365	33	⇐	⇐	ADJ
ejpam-5021	365	34	⇒	⇒	NOUN
ejpam-5021	365	35	(	(	PUNCT
ejpam-5021	365	36	fn(x),¬fn(x	fn(x),¬fn(x	X
ejpam-5021	365	37	)	)	PUNCT
ejpam-5021	365	38	,	,	PUNCT
ejpam-5021	365	39	x	x	X
ejpam-5021	365	40	)	)	PUNCT
ejpam-5021	365	41	=	=	SYM
ejpam-5021	365	42	(	(	PUNCT
ejpam-5021	365	43	fn(y),¬fn(y	fn(y),¬fn(y	PROPN
ejpam-5021	365	44	)	)	PUNCT
ejpam-5021	365	45	,	,	PUNCT
ejpam-5021	365	46	x	x	X
ejpam-5021	365	47	)	)	PUNCT
ejpam-5021	365	48	⇐	⇐	ADJ
ejpam-5021	365	49	⇒	⇒	NOUN
ejpam-5021	365	50	n(x	n(x	NUM
ejpam-5021	365	51	)	)	PUNCT
ejpam-5021	365	52	=	=	SYM
ejpam-5021	365	53	n(y	n(y	ADJ
ejpam-5021	365	54	)	)	PUNCT
ejpam-5021	365	55	⇐	⇐	ADJ
ejpam-5021	365	56	⇒	⇒	NOUN
ejpam-5021	365	57	(	(	PUNCT
ejpam-5021	365	58	x	x	X
ejpam-5021	365	59	,	,	PUNCT
ejpam-5021	365	60	y	y	NOUN
ejpam-5021	365	61	)	)	PUNCT
ejpam-5021	365	62	∈	∈	PROPN
ejpam-5021	365	63	n	n	X
ejpam-5021	365	64	due	due	ADJ
ejpam-5021	365	65	to	to	PART
ejpam-5021	365	66	remark	remark	VERB
ejpam-5021	365	67	2	2	NUM
ejpam-5021	365	68	,	,	PUNCT
ejpam-5021	365	69	theorem	theorem	ADJ
ejpam-5021	365	70	2	2	NUM
ejpam-5021	365	71	,	,	PUNCT
ejpam-5021	365	72	notation	notation	NOUN
ejpam-5021	365	73	4	4	NUM
ejpam-5021	365	74	,	,	PUNCT
ejpam-5021	365	75	and	and	CCONJ
ejpam-5021	365	76	definition	definition	NOUN
ejpam-5021	365	77	8	8	NUM
ejpam-5021	365	78	.	.	PUNCT
ejpam-5021	366	1	whence	whence	NOUN
ejpam-5021	366	2	n	n	NOUN
ejpam-5021	366	3	=	=	SYM
ejpam-5021	366	4	nb	nb	PROPN
ejpam-5021	366	5	.	.	PROPN
ejpam-5021	367	1	3	3	X
ejpam-5021	367	2	.	.	X
ejpam-5021	367	3	conclusions	conclusion	NOUN
ejpam-5021	367	4	as	as	SCONJ
ejpam-5021	367	5	studied	study	VERB
ejpam-5021	367	6	before	before	ADV
ejpam-5021	367	7	,	,	PUNCT
ejpam-5021	367	8	there	there	PRON
ejpam-5021	367	9	has	have	AUX
ejpam-5021	367	10	been	be	AUX
ejpam-5021	367	11	much	much	ADV
ejpam-5021	367	12	technical	technical	ADJ
ejpam-5021	367	13	association	association	NOUN
ejpam-5021	367	14	of	of	ADP
ejpam-5021	367	15	fuzzy	fuzzy	ADJ
ejpam-5021	367	16	semibipolar	semibipolar	ADJ
ejpam-5021	367	17	soft	soft	ADJ
ejpam-5021	367	18	set	set	NOUN
ejpam-5021	367	19	theory	theory	NOUN
ejpam-5021	367	20	,	,	PUNCT
ejpam-5021	367	21	especially	especially	ADV
ejpam-5021	367	22	the	the	DET
ejpam-5021	367	23	use	use	NOUN
ejpam-5021	367	24	of	of	ADP
ejpam-5021	367	25	the	the	DET
ejpam-5021	367	26	fssfs	fssfs	NOUN
ejpam-5021	367	27	to	to	PART
ejpam-5021	367	28	describe	describe	VERB
ejpam-5021	367	29	green	green	PROPN
ejpam-5021	367	30	’s	’s	PART
ejpam-5021	367	31	relation	relation	NOUN
ejpam-5021	367	32	n	n	X
ejpam-5021	367	33	.	.	PUNCT
ejpam-5021	368	1	observe	observe	VERB
ejpam-5021	368	2	that	that	SCONJ
ejpam-5021	368	3	green	green	PROPN
ejpam-5021	368	4	’s	’s	PART
ejpam-5021	368	5	relation	relation	NOUN
ejpam-5021	368	6	n	n	CCONJ
ejpam-5021	368	7	on	on	ADP
ejpam-5021	368	8	groupoids	groupoid	NOUN
ejpam-5021	368	9	in	in	ADP
ejpam-5021	368	10	this	this	DET
ejpam-5021	368	11	work	work	NOUN
ejpam-5021	368	12	is	be	AUX
ejpam-5021	368	13	induced	induce	VERB
ejpam-5021	368	14	by	by	ADP
ejpam-5021	368	15	the	the	DET
ejpam-5021	368	16	two	two	NUM
ejpam-5021	368	17	-	-	PUNCT
ejpam-5021	368	18	way	way	NOUN
ejpam-5021	368	19	function	function	NOUN
ejpam-5021	368	20	and	and	CCONJ
ejpam-5021	368	21	that	that	PRON
ejpam-5021	368	22	extends	extend	VERB
ejpam-5021	368	23	the	the	DET
ejpam-5021	368	24	concept	concept	NOUN
ejpam-5021	368	25	of	of	ADP
ejpam-5021	368	26	the	the	DET
ejpam-5021	368	27	one	one	NUM
ejpam-5021	368	28	-	-	PUNCT
ejpam-5021	368	29	way	way	NOUN
ejpam-5021	368	30	function	function	NOUN
ejpam-5021	368	31	in	in	ADP
ejpam-5021	368	32	[	[	X
ejpam-5021	368	33	13	13	NUM
ejpam-5021	368	34	]	]	PUNCT
ejpam-5021	368	35	.	.	PUNCT
ejpam-5021	369	1	in	in	ADP
ejpam-5021	369	2	addition	addition	NOUN
ejpam-5021	369	3	,	,	PUNCT
ejpam-5021	369	4	we	we	PRON
ejpam-5021	369	5	obtained	obtain	VERB
ejpam-5021	369	6	that	that	SCONJ
ejpam-5021	369	7	if	if	SCONJ
ejpam-5021	369	8	a	a	DET
ejpam-5021	369	9	fssfs	fssfs	ADV
ejpam-5021	369	10	-	-	PUNCT
ejpam-5021	369	11	based	base	VERB
ejpam-5021	369	12	binary	binary	ADJ
ejpam-5021	369	13	relation	relation	NOUN
ejpam-5021	369	14	exists	exist	VERB
ejpam-5021	369	15	,	,	PUNCT
ejpam-5021	369	16	then	then	ADV
ejpam-5021	369	17	two	two	NUM
ejpam-5021	369	18	parameters	parameter	NOUN
ejpam-5021	369	19	of	of	ADP
ejpam-5021	369	20	a	a	DET
ejpam-5021	369	21	fuzzy	fuzzy	ADJ
ejpam-5021	369	22	semibipolar	semibipolar	ADJ
ejpam-5021	369	23	soft	soft	ADJ
ejpam-5021	369	24	set	set	NOUN
ejpam-5021	369	25	are	be	AUX
ejpam-5021	369	26	related	relate	VERB
ejpam-5021	369	27	under	under	ADP
ejpam-5021	369	28	green	green	PROPN
ejpam-5021	369	29	’s	’s	PART
ejpam-5021	369	30	relation	relation	NOUN
ejpam-5021	369	31	n	n	PROPN
ejpam-5021	369	32	.	.	PUNCT
ejpam-5021	370	1	for	for	ADP
ejpam-5021	370	2	the	the	DET
ejpam-5021	370	3	context	context	NOUN
ejpam-5021	370	4	of	of	ADP
ejpam-5021	370	5	filters	filter	NOUN
ejpam-5021	370	6	,	,	PUNCT
ejpam-5021	370	7	mahmood	mahmood	PROPN
ejpam-5021	370	8	et	et	PROPN
ejpam-5021	370	9	al.[18	al.[18	PROPN
ejpam-5021	370	10	]	]	PUNCT
ejpam-5021	370	11	proposed	propose	VERB
ejpam-5021	370	12	the	the	DET
ejpam-5021	370	13	fundamentals	fundamental	NOUN
ejpam-5021	370	14	of	of	ADP
ejpam-5021	370	15	fuzzy	fuzzy	ADJ
ejpam-5021	370	16	filters	filter	NOUN
ejpam-5021	370	17	in	in	ADP
ejpam-5021	370	18	terms	term	NOUN
ejpam-5021	370	19	of	of	ADP
ejpam-5021	370	20	rough	rough	ADJ
ejpam-5021	370	21	set	set	NOUN
ejpam-5021	370	22	theory	theory	NOUN
ejpam-5021	370	23	,	,	PUNCT
ejpam-5021	370	24	in	in	ADP
ejpam-5021	370	25	which	which	PRON
ejpam-5021	370	26	rough	rough	ADJ
ejpam-5021	370	27	set	set	NOUN
ejpam-5021	370	28	theory	theory	NOUN
ejpam-5021	370	29	is	be	AUX
ejpam-5021	370	30	an	an	DET
ejpam-5021	370	31	important	important	ADJ
ejpam-5021	370	32	concept	concept	NOUN
ejpam-5021	370	33	for	for	ADP
ejpam-5021	370	34	dealing	deal	VERB
ejpam-5021	370	35	with	with	ADP
ejpam-5021	370	36	vagueness	vagueness	NOUN
ejpam-5021	370	37	problems	problem	NOUN
ejpam-5021	370	38	.	.	PUNCT
ejpam-5021	371	1	in	in	ADP
ejpam-5021	371	2	the	the	DET
ejpam-5021	371	3	future	future	NOUN
ejpam-5021	371	4	,	,	PUNCT
ejpam-5021	371	5	to	to	PART
ejpam-5021	371	6	extend	extend	VERB
ejpam-5021	371	7	such	such	DET
ejpam-5021	371	8	a	a	DET
ejpam-5021	371	9	concept	concept	NOUN
ejpam-5021	371	10	via	via	ADP
ejpam-5021	371	11	a	a	DET
ejpam-5021	371	12	two	two	NUM
ejpam-5021	371	13	-	-	PUNCT
ejpam-5021	371	14	way	way	NOUN
ejpam-5021	371	15	function	function	NOUN
ejpam-5021	371	16	,	,	PUNCT
ejpam-5021	371	17	the	the	DET
ejpam-5021	371	18	notion	notion	NOUN
ejpam-5021	371	19	of	of	ADP
ejpam-5021	371	20	fssfs	fssfs	ADJ
ejpam-5021	371	21	will	will	AUX
ejpam-5021	371	22	be	be	AUX
ejpam-5021	371	23	considered	consider	VERB
ejpam-5021	371	24	under	under	ADP
ejpam-5021	371	25	rough	rough	ADJ
ejpam-5021	371	26	set	set	NOUN
ejpam-5021	371	27	theory	theory	NOUN
ejpam-5021	371	28	in	in	ADP
ejpam-5021	371	29	the	the	DET
ejpam-5021	371	30	next	next	ADJ
ejpam-5021	371	31	step	step	NOUN
ejpam-5021	371	32	.	.	PUNCT
ejpam-5021	372	1	acknowledgements	acknowledgement	NOUN
ejpam-5021	372	2	we	we	PRON
ejpam-5021	372	3	would	would	AUX
ejpam-5021	372	4	like	like	VERB
ejpam-5021	372	5	to	to	PART
ejpam-5021	372	6	thank	thank	VERB
ejpam-5021	372	7	the	the	DET
ejpam-5021	372	8	expert	expert	NOUN
ejpam-5021	372	9	reviewers	reviewer	NOUN
ejpam-5021	372	10	for	for	ADP
ejpam-5021	372	11	their	their	PRON
ejpam-5021	372	12	helpful	helpful	ADJ
ejpam-5021	372	13	suggestions	suggestion	NOUN
ejpam-5021	372	14	.	.	PUNCT
ejpam-5021	373	1	we	we	PRON
ejpam-5021	373	2	would	would	AUX
ejpam-5021	373	3	like	like	VERB
ejpam-5021	373	4	to	to	PART
ejpam-5021	373	5	thank	thank	VERB
ejpam-5021	373	6	supporter	supporter	NOUN
ejpam-5021	373	7	organizations	organization	NOUN
ejpam-5021	373	8	:	:	PUNCT
ejpam-5021	373	9	division	division	NOUN
ejpam-5021	373	10	of	of	ADP
ejpam-5021	373	11	mathematics	mathematic	NOUN
ejpam-5021	373	12	and	and	CCONJ
ejpam-5021	373	13	statistics	statistic	NOUN
ejpam-5021	373	14	,	,	PUNCT
ejpam-5021	373	15	faculty	faculty	NOUN
ejpam-5021	373	16	of	of	ADP
ejpam-5021	373	17	science	science	NOUN
ejpam-5021	373	18	and	and	CCONJ
ejpam-5021	373	19	technology	technology	NOUN
ejpam-5021	373	20	,	,	PUNCT
ejpam-5021	373	21	nakhon	nakhon	PROPN
ejpam-5021	373	22	sawan	sawan	PROPN
ejpam-5021	373	23	rajabhat	rajabhat	PROPN
ejpam-5021	373	24	university	university	PROPN
ejpam-5021	373	25	,	,	PUNCT
ejpam-5021	373	26	thailand	thailand	PROPN
ejpam-5021	373	27	.	.	PUNCT
ejpam-5021	374	1	references	reference	NOUN
ejpam-5021	374	2	284	284	NUM
ejpam-5021	374	3	references	reference	NOUN
ejpam-5021	374	4	[	[	X
ejpam-5021	374	5	1	1	NUM
ejpam-5021	374	6	]	]	X
ejpam-5021	374	7	g	g	PROPN
ejpam-5021	374	8	ali	ali	PROPN
ejpam-5021	374	9	,	,	PUNCT
ejpam-5021	374	10	g	g	PROPN
ejpam-5021	374	11	muhiuddin	muhiuddin	PROPN
ejpam-5021	374	12	,	,	PUNCT
ejpam-5021	374	13	a	a	DET
ejpam-5021	374	14	adeel	adeel	NOUN
ejpam-5021	374	15	,	,	PUNCT
ejpam-5021	374	16	and	and	CCONJ
ejpam-5021	374	17	m	m	PROPN
ejpam-5021	374	18	z	z	NOUN
ejpam-5021	374	19	ul	ul	INTJ
ejpam-5021	374	20	abidin	abidin	VERB
ejpam-5021	374	21	.	.	PUNCT
ejpam-5021	375	1	ranking	rank	VERB
ejpam-5021	375	2	effectiveness	effectiveness	NOUN
ejpam-5021	375	3	of	of	ADP
ejpam-5021	375	4	covid-19	covid-19	PROPN
ejpam-5021	375	5	tests	test	NOUN
ejpam-5021	375	6	using	use	VERB
ejpam-5021	375	7	fuzzy	fuzzy	ADJ
ejpam-5021	375	8	bipolar	bipolar	ADJ
ejpam-5021	375	9	soft	soft	ADJ
ejpam-5021	375	10	expert	expert	NOUN
ejpam-5021	375	11	sets	set	NOUN
ejpam-5021	375	12	.	.	PUNCT
ejpam-5021	376	1	mathematical	mathematical	ADJ
ejpam-5021	376	2	problems	problem	NOUN
ejpam-5021	376	3	in	in	ADP
ejpam-5021	376	4	engineering	engineering	NOUN
ejpam-5021	376	5	,	,	PUNCT
ejpam-5021	376	6	2021:1–19	2021:1–19	NUM
ejpam-5021	376	7	,	,	PUNCT
ejpam-5021	376	8	2021	2021	NUM
ejpam-5021	376	9	.	.	PUNCT
ejpam-5021	377	1	[	[	X
ejpam-5021	377	2	2	2	NUM
ejpam-5021	377	3	]	]	PUNCT
ejpam-5021	377	4	t	t	NOUN
ejpam-5021	377	5	colcombet	colcombet	NOUN
ejpam-5021	377	6	.	.	PUNCT
ejpam-5021	378	1	green	green	PROPN
ejpam-5021	378	2	’s	’s	PART
ejpam-5021	378	3	relations	relation	NOUN
ejpam-5021	378	4	and	and	CCONJ
ejpam-5021	378	5	their	their	PRON
ejpam-5021	378	6	use	use	NOUN
ejpam-5021	378	7	in	in	ADP
ejpam-5021	378	8	automata	automata	NOUN
ejpam-5021	378	9	theory	theory	NOUN
ejpam-5021	378	10	.	.	PUNCT
ejpam-5021	379	1	springer	springer	NOUN
ejpam-5021	379	2	,	,	PUNCT
ejpam-5021	379	3	berlin	berlin	PROPN
ejpam-5021	379	4	,	,	PUNCT
ejpam-5021	379	5	heidelberg	heidelberg	PROPN
ejpam-5021	379	6	,	,	PUNCT
ejpam-5021	379	7	2011	2011	NUM
ejpam-5021	379	8	.	.	PUNCT
ejpam-5021	380	1	[	[	X
ejpam-5021	380	2	3	3	NUM
ejpam-5021	380	3	]	]	X
ejpam-5021	380	4	s	s	PART
ejpam-5021	380	5	danjuma	danjuma	NOUN
ejpam-5021	380	6	,	,	PUNCT
ejpam-5021	380	7	t	t	PROPN
ejpam-5021	380	8	herawan	herawan	PROPN
ejpam-5021	380	9	,	,	PUNCT
ejpam-5021	380	10	m	m	VERB
ejpam-5021	380	11	a	a	DET
ejpam-5021	380	12	ismail	ismail	NOUN
ejpam-5021	380	13	,	,	PUNCT
ejpam-5021	380	14	h	h	PROPN
ejpam-5021	380	15	chiroma	chiroma	PROPN
ejpam-5021	380	16	,	,	PUNCT
ejpam-5021	380	17	a	a	DET
ejpam-5021	380	18	i	i	PROPN
ejpam-5021	380	19	abubakar	abubakar	PROPN
ejpam-5021	380	20	,	,	PUNCT
ejpam-5021	380	21	and	and	CCONJ
ejpam-5021	380	22	a	a	DET
ejpam-5021	380	23	m	m	PROPN
ejpam-5021	380	24	zeki	zeki	PROPN
ejpam-5021	380	25	.	.	PUNCT
ejpam-5021	381	1	a	a	DET
ejpam-5021	381	2	review	review	NOUN
ejpam-5021	381	3	on	on	ADP
ejpam-5021	381	4	soft	soft	ADJ
ejpam-5021	381	5	set	set	NOUN
ejpam-5021	381	6	-	-	PUNCT
ejpam-5021	381	7	based	base	VERB
ejpam-5021	381	8	parameter	parameter	NOUN
ejpam-5021	381	9	reduction	reduction	NOUN
ejpam-5021	381	10	and	and	CCONJ
ejpam-5021	381	11	decision	decision	NOUN
ejpam-5021	381	12	making	making	NOUN
ejpam-5021	381	13	.	.	PUNCT
ejpam-5021	382	1	ieee	ieee	NOUN
ejpam-5021	382	2	access	access	NOUN
ejpam-5021	382	3	,	,	PUNCT
ejpam-5021	382	4	5:4671–4689	5:4671–4689	NUM
ejpam-5021	382	5	,	,	PUNCT
ejpam-5021	382	6	2017	2017	NUM
ejpam-5021	382	7	.	.	PUNCT
ejpam-5021	383	1	[	[	X
ejpam-5021	383	2	4	4	NUM
ejpam-5021	383	3	]	]	X
ejpam-5021	383	4	d	d	X
ejpam-5021	383	5	dubois	dubois	PROPN
ejpam-5021	383	6	and	and	CCONJ
ejpam-5021	383	7	h	h	PROPN
ejpam-5021	383	8	prade	prade	NOUN
ejpam-5021	383	9	.	.	PUNCT
ejpam-5021	384	1	an	an	DET
ejpam-5021	384	2	introduction	introduction	NOUN
ejpam-5021	384	3	to	to	ADP
ejpam-5021	384	4	bipolar	bipolar	ADJ
ejpam-5021	384	5	representations	representation	NOUN
ejpam-5021	384	6	of	of	ADP
ejpam-5021	384	7	information	information	NOUN
ejpam-5021	384	8	and	and	CCONJ
ejpam-5021	384	9	preference	preference	NOUN
ejpam-5021	384	10	.	.	PUNCT
ejpam-5021	385	1	international	international	ADJ
ejpam-5021	385	2	journal	journal	NOUN
ejpam-5021	385	3	of	of	ADP
ejpam-5021	385	4	intelligent	intelligent	ADJ
ejpam-5021	385	5	systems	system	NOUN
ejpam-5021	385	6	,	,	PUNCT
ejpam-5021	385	7	23:866–877	23:866–877	PROPN
ejpam-5021	385	8	,	,	PUNCT
ejpam-5021	385	9	2008	2008	NUM
ejpam-5021	385	10	.	.	PUNCT
ejpam-5021	386	1	[	[	X
ejpam-5021	386	2	5	5	NUM
ejpam-5021	386	3	]	]	PUNCT
ejpam-5021	386	4	l	l	NOUN
ejpam-5021	386	5	fleischer	fleischer	NOUN
ejpam-5021	386	6	and	and	CCONJ
ejpam-5021	386	7	m	m	PROPN
ejpam-5021	386	8	kufleitner	kufleitner	NOUN
ejpam-5021	386	9	.	.	PUNCT
ejpam-5021	387	1	green	green	PROPN
ejpam-5021	387	2	’s	’s	PART
ejpam-5021	387	3	relations	relation	NOUN
ejpam-5021	387	4	in	in	ADP
ejpam-5021	387	5	deterministic	deterministic	ADJ
ejpam-5021	387	6	finite	finite	ADJ
ejpam-5021	387	7	automata	automata	NOUN
ejpam-5021	387	8	.	.	PUNCT
ejpam-5021	388	1	theory	theory	NOUN
ejpam-5021	388	2	of	of	ADP
ejpam-5021	388	3	computing	computing	NOUN
ejpam-5021	388	4	systems	system	NOUN
ejpam-5021	388	5	,	,	PUNCT
ejpam-5021	388	6	63:666–687	63:666–687	PROPN
ejpam-5021	388	7	,	,	PUNCT
ejpam-5021	388	8	2019	2019	NUM
ejpam-5021	388	9	.	.	PUNCT
ejpam-5021	389	1	[	[	X
ejpam-5021	389	2	6	6	NUM
ejpam-5021	389	3	]	]	PUNCT
ejpam-5021	389	4	a	a	DET
ejpam-5021	389	5	u	u	NOUN
ejpam-5021	389	6	hakim	hakim	PROPN
ejpam-5021	389	7	,	,	PUNCT
ejpam-5021	389	8	h	h	PROPN
ejpam-5021	389	9	khan	khan	PROPN
ejpam-5021	389	10	,	,	PUNCT
ejpam-5021	389	11	i	i	PRON
ejpam-5021	389	12	ahmad	ahmad	PROPN
ejpam-5021	389	13	,	,	PUNCT
ejpam-5021	389	14	,	,	PUNCT
ejpam-5021	389	15	and	and	CCONJ
ejpam-5021	389	16	a	a	DET
ejpam-5021	389	17	khan	khan	PROPN
ejpam-5021	389	18	.	.	PUNCT
ejpam-5021	390	1	fuzzy	fuzzy	ADJ
ejpam-5021	390	2	bipolar	bipolar	ADJ
ejpam-5021	390	3	soft	soft	ADJ
ejpam-5021	390	4	semiprime	semiprime	NOUN
ejpam-5021	390	5	ideals	ideal	NOUN
ejpam-5021	390	6	in	in	ADP
ejpam-5021	390	7	ordered	order	VERB
ejpam-5021	390	8	semigroups	semigroup	NOUN
ejpam-5021	390	9	.	.	PUNCT
ejpam-5021	391	1	heliyon	heliyon	NOUN
ejpam-5021	391	2	,	,	PUNCT
ejpam-5021	391	3	7	7	NUM
ejpam-5021	391	4	:	:	SYM
ejpam-5021	391	5	e06618	e06618	NOUN
ejpam-5021	391	6	,	,	PUNCT
ejpam-5021	391	7	2021	2021	NUM
ejpam-5021	391	8	.	.	PUNCT
ejpam-5021	392	1	[	[	X
ejpam-5021	392	2	7	7	X
ejpam-5021	392	3	]	]	X
ejpam-5021	392	4	a	a	DET
ejpam-5021	392	5	iampan	iampan	NOUN
ejpam-5021	392	6	and	and	CCONJ
ejpam-5021	392	7	m	m	PROPN
ejpam-5021	392	8	siripitukdet	siripitukdet	NOUN
ejpam-5021	392	9	.	.	PUNCT
ejpam-5021	393	1	green	green	PROPN
ejpam-5021	393	2	’s	’s	PART
ejpam-5021	393	3	relations	relation	NOUN
ejpam-5021	393	4	in	in	ADP
ejpam-5021	393	5	ordered	order	VERB
ejpam-5021	393	6	gamma	gamma	NOUN
ejpam-5021	393	7	-	-	PUNCT
ejpam-5021	393	8	semigroups	semigroup	NOUN
ejpam-5021	393	9	in	in	ADP
ejpam-5021	393	10	terms	term	NOUN
ejpam-5021	393	11	of	of	ADP
ejpam-5021	393	12	fuzzy	fuzzy	ADJ
ejpam-5021	393	13	subsets	subset	NOUN
ejpam-5021	393	14	.	.	PUNCT
ejpam-5021	394	1	iaeng	iaeng	PROPN
ejpam-5021	394	2	international	international	PROPN
ejpam-5021	394	3	journal	journal	PROPN
ejpam-5021	394	4	of	of	ADP
ejpam-5021	394	5	applied	apply	VERB
ejpam-5021	394	6	mathematics	mathematic	NOUN
ejpam-5021	394	7	,	,	PUNCT
ejpam-5021	394	8	42(2):74–79	42(2):74–79	NUM
ejpam-5021	394	9	,	,	PUNCT
ejpam-5021	394	10	2012	2012	NUM
ejpam-5021	394	11	.	.	PUNCT
ejpam-5021	395	1	[	[	X
ejpam-5021	395	2	8	8	NUM
ejpam-5021	395	3	]	]	X
ejpam-5021	395	4	a	a	DET
ejpam-5021	395	5	iampan	iampan	NOUN
ejpam-5021	395	6	and	and	CCONJ
ejpam-5021	395	7	m	m	PROPN
ejpam-5021	395	8	siripitukdet	siripitukdet	NOUN
ejpam-5021	395	9	.	.	PUNCT
ejpam-5021	396	1	describing	describe	VERB
ejpam-5021	396	2	green	green	PROPN
ejpam-5021	396	3	’s	’s	PART
ejpam-5021	396	4	relations	relation	NOUN
ejpam-5021	396	5	in	in	ADP
ejpam-5021	396	6	ordered	order	VERB
ejpam-5021	396	7	gammagroupoids	gammagroupoid	NOUN
ejpam-5021	396	8	using	use	VERB
ejpam-5021	396	9	a	a	DET
ejpam-5021	396	10	new	new	ADJ
ejpam-5021	396	11	concept	concept	NOUN
ejpam-5021	396	12	:	:	PUNCT
ejpam-5021	396	13	fuzzy	fuzzy	ADJ
ejpam-5021	396	14	subsets	subset	NOUN
ejpam-5021	396	15	.	.	PUNCT
ejpam-5021	397	1	italian	italian	ADJ
ejpam-5021	397	2	journal	journal	NOUN
ejpam-5021	397	3	of	of	ADP
ejpam-5021	397	4	pure	pure	ADJ
ejpam-5021	397	5	and	and	CCONJ
ejpam-5021	397	6	applied	applied	ADJ
ejpam-5021	397	7	mathematics	mathematic	NOUN
ejpam-5021	397	8	,	,	PUNCT
ejpam-5021	397	9	31:125–140	31:125–140	PROPN
ejpam-5021	397	10	,	,	PUNCT
ejpam-5021	397	11	2013	2013	NUM
ejpam-5021	397	12	.	.	PUNCT
ejpam-5021	398	1	[	[	X
ejpam-5021	398	2	9	9	NUM
ejpam-5021	398	3	]	]	PUNCT
ejpam-5021	398	4	n	n	PRON
ejpam-5021	398	5	kehayopulu	kehayopulu	VERB
ejpam-5021	398	6	.	.	PUNCT
ejpam-5021	399	1	on	on	ADP
ejpam-5021	399	2	weakly	weakly	ADJ
ejpam-5021	399	3	commutative	commutative	ADJ
ejpam-5021	399	4	poe	poe	PROPN
ejpam-5021	399	5	-	-	PUNCT
ejpam-5021	399	6	semigroups	semigroup	NOUN
ejpam-5021	399	7	.	.	PUNCT
ejpam-5021	400	1	semigroup	semigroup	PROPN
ejpam-5021	400	2	forum	forum	PROPN
ejpam-5021	400	3	,	,	PUNCT
ejpam-5021	400	4	34:367	34:367	NUM
ejpam-5021	400	5	–	–	PUNCT
ejpam-5021	400	6	370	370	NUM
ejpam-5021	400	7	,	,	PUNCT
ejpam-5021	400	8	1987	1987	NUM
ejpam-5021	400	9	.	.	PUNCT
ejpam-5021	401	1	[	[	X
ejpam-5021	401	2	10	10	NUM
ejpam-5021	401	3	]	]	PUNCT
ejpam-5021	401	4	n	n	PRON
ejpam-5021	401	5	kehayopulu	kehayopulu	ADJ
ejpam-5021	401	6	.	.	PUNCT
ejpam-5021	402	1	note	note	NOUN
ejpam-5021	402	2	on	on	ADP
ejpam-5021	402	3	green	green	PROPN
ejpam-5021	402	4	’s	’s	PART
ejpam-5021	402	5	relations	relation	NOUN
ejpam-5021	402	6	in	in	ADP
ejpam-5021	402	7	ordered	order	VERB
ejpam-5021	402	8	semigroups	semigroup	NOUN
ejpam-5021	402	9	.	.	PUNCT
ejpam-5021	403	1	mathematica	mathematica	PROPN
ejpam-5021	403	2	japonica	japonica	PROPN
ejpam-5021	403	3	,	,	PUNCT
ejpam-5021	403	4	36:211–214	36:211–214	PROPN
ejpam-5021	403	5	,	,	PUNCT
ejpam-5021	403	6	1991	1991	NUM
ejpam-5021	403	7	.	.	PUNCT
ejpam-5021	404	1	[	[	X
ejpam-5021	404	2	11	11	NUM
ejpam-5021	404	3	]	]	PUNCT
ejpam-5021	404	4	n	n	CCONJ
ejpam-5021	404	5	kehayopulu	kehayopulu	ADJ
ejpam-5021	404	6	and	and	CCONJ
ejpam-5021	404	7	m	m	PROPN
ejpam-5021	404	8	tsingelis	tsingelis	PROPN
ejpam-5021	404	9	.	.	PUNCT
ejpam-5021	405	1	a	a	DET
ejpam-5021	405	2	note	note	NOUN
ejpam-5021	405	3	on	on	ADP
ejpam-5021	405	4	fuzzy	fuzzy	ADJ
ejpam-5021	405	5	sets	set	NOUN
ejpam-5021	405	6	in	in	ADP
ejpam-5021	405	7	semigroups	semigroup	NOUN
ejpam-5021	405	8	.	.	PUNCT
ejpam-5021	406	1	scientiae	scientiae	PROPN
ejpam-5021	406	2	mathematicae	mathematicae	PROPN
ejpam-5021	406	3	,	,	PUNCT
ejpam-5021	406	4	2(3):411–413	2(3):411–413	NUM
ejpam-5021	406	5	,	,	PUNCT
ejpam-5021	406	6	1999	1999	NUM
ejpam-5021	406	7	.	.	PUNCT
ejpam-5021	407	1	[	[	X
ejpam-5021	407	2	12	12	NUM
ejpam-5021	407	3	]	]	PUNCT
ejpam-5021	407	4	n	n	CCONJ
ejpam-5021	407	5	kehayopulu	kehayopulu	ADJ
ejpam-5021	407	6	and	and	CCONJ
ejpam-5021	407	7	m	m	PROPN
ejpam-5021	407	8	tsingelis	tsingelis	PROPN
ejpam-5021	407	9	.	.	PUNCT
ejpam-5021	408	1	fuzzy	fuzzy	ADJ
ejpam-5021	408	2	sets	set	NOUN
ejpam-5021	408	3	in	in	ADP
ejpam-5021	408	4	ordered	order	VERB
ejpam-5021	408	5	groupoids	groupoid	NOUN
ejpam-5021	408	6	.	.	PUNCT
ejpam-5021	409	1	semigroup	semigroup	PROPN
ejpam-5021	409	2	forum	forum	PROPN
ejpam-5021	409	3	,	,	PUNCT
ejpam-5021	409	4	65:128–132	65:128–132	PROPN
ejpam-5021	409	5	,	,	PUNCT
ejpam-5021	409	6	2002	2002	NUM
ejpam-5021	409	7	.	.	PUNCT
ejpam-5021	410	1	[	[	X
ejpam-5021	410	2	13	13	NUM
ejpam-5021	410	3	]	]	PUNCT
ejpam-5021	410	4	n	n	CCONJ
ejpam-5021	410	5	kehayopulu	kehayopulu	ADJ
ejpam-5021	410	6	and	and	CCONJ
ejpam-5021	410	7	m	m	PROPN
ejpam-5021	410	8	tsingelis	tsingelis	PROPN
ejpam-5021	410	9	.	.	PUNCT
ejpam-5021	411	1	green	green	PROPN
ejpam-5021	411	2	’s	’s	PART
ejpam-5021	411	3	relations	relation	NOUN
ejpam-5021	411	4	in	in	ADP
ejpam-5021	411	5	ordered	order	VERB
ejpam-5021	411	6	groupoids	groupoid	NOUN
ejpam-5021	411	7	in	in	ADP
ejpam-5021	411	8	terms	term	NOUN
ejpam-5021	411	9	of	of	ADP
ejpam-5021	411	10	fuzzy	fuzzy	ADJ
ejpam-5021	411	11	subsets	subset	NOUN
ejpam-5021	411	12	.	.	PUNCT
ejpam-5021	412	1	soochow	soochow	PROPN
ejpam-5021	412	2	journal	journal	PROPN
ejpam-5021	412	3	of	of	ADP
ejpam-5021	412	4	mathematics	mathematic	NOUN
ejpam-5021	412	5	,	,	PUNCT
ejpam-5021	412	6	33(3):383–397	33(3):383–397	NUM
ejpam-5021	412	7	,	,	PUNCT
ejpam-5021	412	8	2007	2007	NUM
ejpam-5021	412	9	.	.	PUNCT
ejpam-5021	413	1	[	[	X
ejpam-5021	413	2	14	14	NUM
ejpam-5021	413	3	]	]	X
ejpam-5021	413	4	a	a	DET
ejpam-5021	413	5	khan	khan	PROPN
ejpam-5021	413	6	,	,	PUNCT
ejpam-5021	413	7	y	y	PROPN
ejpam-5021	413	8	b	b	PROPN
ejpam-5021	413	9	jun	jun	PROPN
ejpam-5021	413	10	,	,	PUNCT
ejpam-5021	413	11	and	and	CCONJ
ejpam-5021	413	12	m	m	PROPN
ejpam-5021	413	13	shabir	shabir	PROPN
ejpam-5021	413	14	.	.	PUNCT
ejpam-5021	414	1	fuzzy	fuzzy	ADJ
ejpam-5021	414	2	ideals	ideal	NOUN
ejpam-5021	414	3	in	in	ADP
ejpam-5021	414	4	ordered	order	VERB
ejpam-5021	414	5	semigroups	semigroups	PROPN
ejpam-5021	414	6	i.	i.	PROPN
ejpam-5021	414	7	quasigroups	quasigroups	PROPN
ejpam-5021	414	8	and	and	CCONJ
ejpam-5021	414	9	related	related	ADJ
ejpam-5021	414	10	systems	system	NOUN
ejpam-5021	414	11	,	,	PUNCT
ejpam-5021	414	12	16:207–220	16:207–220	NUM
ejpam-5021	414	13	,	,	PUNCT
ejpam-5021	414	14	2008	2008	NUM
ejpam-5021	414	15	.	.	PUNCT
ejpam-5021	415	1	references	reference	NOUN
ejpam-5021	415	2	285	285	NUM
ejpam-5021	416	1	[	[	X
ejpam-5021	416	2	15	15	NUM
ejpam-5021	416	3	]	]	X
ejpam-5021	416	4	m	m	PROPN
ejpam-5021	416	5	j	j	PROPN
ejpam-5021	416	6	khan	khan	PROPN
ejpam-5021	416	7	,	,	PUNCT
ejpam-5021	416	8	p	p	NOUN
ejpam-5021	416	9	kumam	kumam	NOUN
ejpam-5021	416	10	,	,	PUNCT
ejpam-5021	416	11	p	p	PROPN
ejpam-5021	416	12	liu	liu	PROPN
ejpam-5021	416	13	,	,	PUNCT
ejpam-5021	416	14	w	w	PROPN
ejpam-5021	416	15	kumam	kumam	PROPN
ejpam-5021	416	16	,	,	PUNCT
ejpam-5021	416	17	and	and	CCONJ
ejpam-5021	416	18	s	s	VERB
ejpam-5021	416	19	ashraf	ashraf	NOUN
ejpam-5021	416	20	.	.	PUNCT
ejpam-5021	417	1	a	a	DET
ejpam-5021	417	2	novel	novel	ADJ
ejpam-5021	417	3	approach	approach	NOUN
ejpam-5021	417	4	to	to	ADP
ejpam-5021	417	5	generalized	generalize	VERB
ejpam-5021	417	6	intuitionistic	intuitionistic	ADJ
ejpam-5021	417	7	fuzzy	fuzzy	ADJ
ejpam-5021	417	8	soft	soft	ADJ
ejpam-5021	417	9	sets	set	NOUN
ejpam-5021	417	10	and	and	CCONJ
ejpam-5021	417	11	its	its	PRON
ejpam-5021	417	12	application	application	NOUN
ejpam-5021	417	13	in	in	ADP
ejpam-5021	417	14	decision	decision	NOUN
ejpam-5021	417	15	support	support	NOUN
ejpam-5021	417	16	system	system	NOUN
ejpam-5021	417	17	.	.	PUNCT
ejpam-5021	418	1	mathematics	mathematic	NOUN
ejpam-5021	418	2	,	,	PUNCT
ejpam-5021	418	3	7:742	7:742	NUM
ejpam-5021	418	4	,	,	PUNCT
ejpam-5021	418	5	2019	2019	NUM
ejpam-5021	418	6	.	.	PUNCT
ejpam-5021	419	1	[	[	X
ejpam-5021	419	2	16	16	NUM
ejpam-5021	419	3	]	]	X
ejpam-5021	419	4	e	e	X
ejpam-5021	419	5	korkmaz	korkmaz	PROPN
ejpam-5021	419	6	,	,	PUNCT
ejpam-5021	419	7	c	c	PROPN
ejpam-5021	419	8	özcan	özcan	PROPN
ejpam-5021	419	9	,	,	PUNCT
ejpam-5021	419	10	and	and	CCONJ
ejpam-5021	419	11	m	m	PROPN
ejpam-5021	419	12	korkmaz	korkmaz	PROPN
ejpam-5021	419	13	.	.	PUNCT
ejpam-5021	420	1	an	an	DET
ejpam-5021	420	2	application	application	NOUN
ejpam-5021	420	3	of	of	ADP
ejpam-5021	420	4	fuzzy	fuzzy	ADJ
ejpam-5021	420	5	soft	soft	ADJ
ejpam-5021	420	6	sets	set	NOUN
ejpam-5021	420	7	to	to	ADP
ejpam-5021	420	8	a	a	DET
ejpam-5021	420	9	real	real	ADJ
ejpam-5021	420	10	-	-	PUNCT
ejpam-5021	420	11	life	life	NOUN
ejpam-5021	420	12	problem	problem	NOUN
ejpam-5021	420	13	:	:	PUNCT
ejpam-5021	420	14	classification	classification	NOUN
ejpam-5021	420	15	of	of	ADP
ejpam-5021	420	16	wood	wood	NOUN
ejpam-5021	420	17	materials	material	NOUN
ejpam-5021	420	18	to	to	PART
ejpam-5021	420	19	prevent	prevent	VERB
ejpam-5021	420	20	fire	fire	NOUN
ejpam-5021	420	21	-	-	PUNCT
ejpam-5021	420	22	related	relate	VERB
ejpam-5021	420	23	injuries	injury	NOUN
ejpam-5021	420	24	and	and	CCONJ
ejpam-5021	420	25	deaths	death	NOUN
ejpam-5021	420	26	.	.	PUNCT
ejpam-5021	421	1	applied	apply	VERB
ejpam-5021	421	2	soft	soft	ADJ
ejpam-5021	421	3	computing	computing	NOUN
ejpam-5021	421	4	,	,	PUNCT
ejpam-5021	421	5	132:109875	132:109875	NUM
ejpam-5021	421	6	,	,	PUNCT
ejpam-5021	421	7	2023	2023	NUM
ejpam-5021	421	8	.	.	PUNCT
ejpam-5021	422	1	[	[	X
ejpam-5021	422	2	17	17	NUM
ejpam-5021	422	3	]	]	PUNCT
ejpam-5021	422	4	n	n	PRON
ejpam-5021	422	5	kuroki	kuroki	NOUN
ejpam-5021	422	6	.	.	PUNCT
ejpam-5021	423	1	on	on	ADP
ejpam-5021	423	2	fuzzy	fuzzy	ADJ
ejpam-5021	423	3	ideals	ideal	NOUN
ejpam-5021	423	4	and	and	CCONJ
ejpam-5021	423	5	fuzzy	fuzzy	ADJ
ejpam-5021	423	6	bi	bi	NOUN
ejpam-5021	423	7	-	-	NOUN
ejpam-5021	423	8	ideals	ideal	NOUN
ejpam-5021	423	9	in	in	ADP
ejpam-5021	423	10	semigroups	semigroup	NOUN
ejpam-5021	423	11	.	.	PUNCT
ejpam-5021	424	1	fuzzy	fuzzy	ADJ
ejpam-5021	424	2	sets	set	NOUN
ejpam-5021	424	3	and	and	CCONJ
ejpam-5021	424	4	systems	system	NOUN
ejpam-5021	424	5	,	,	PUNCT
ejpam-5021	424	6	5:203–215	5:203–215	NUM
ejpam-5021	424	7	,	,	PUNCT
ejpam-5021	424	8	1981	1981	NUM
ejpam-5021	424	9	.	.	PUNCT
ejpam-5021	425	1	[	[	X
ejpam-5021	425	2	18	18	NUM
ejpam-5021	425	3	]	]	PUNCT
ejpam-5021	425	4	t	t	PROPN
ejpam-5021	425	5	mahmood	mahmood	PROPN
ejpam-5021	425	6	,	,	PUNCT
ejpam-5021	425	7	m	m	VERB
ejpam-5021	425	8	i	i	NOUN
ejpam-5021	425	9	ali	ali	VERB
ejpam-5021	425	10	,	,	PUNCT
ejpam-5021	425	11	,	,	PUNCT
ejpam-5021	425	12	and	and	CCONJ
ejpam-5021	425	13	a	a	DET
ejpam-5021	425	14	hussain	hussain	NOUN
ejpam-5021	425	15	.	.	PUNCT
ejpam-5021	426	1	generalized	generalized	ADJ
ejpam-5021	426	2	roughness	roughness	NOUN
ejpam-5021	426	3	in	in	ADP
ejpam-5021	426	4	fuzzy	fuzzy	ADJ
ejpam-5021	426	5	filters	filter	NOUN
ejpam-5021	426	6	and	and	CCONJ
ejpam-5021	426	7	fuzzy	fuzzy	ADJ
ejpam-5021	426	8	ideals	ideal	NOUN
ejpam-5021	426	9	with	with	ADP
ejpam-5021	426	10	thresholds	threshold	NOUN
ejpam-5021	426	11	in	in	ADP
ejpam-5021	426	12	ordered	order	VERB
ejpam-5021	426	13	semigroups	semigroup	NOUN
ejpam-5021	426	14	.	.	PUNCT
ejpam-5021	427	1	computational	computational	ADJ
ejpam-5021	427	2	and	and	CCONJ
ejpam-5021	427	3	applied	applied	ADJ
ejpam-5021	427	4	mathematics	mathematic	NOUN
ejpam-5021	427	5	,	,	PUNCT
ejpam-5021	427	6	37:5013–5033	37:5013–5033	NUM
ejpam-5021	427	7	,	,	PUNCT
ejpam-5021	427	8	2018	2018	NUM
ejpam-5021	427	9	.	.	PUNCT
ejpam-5021	428	1	[	[	X
ejpam-5021	428	2	19	19	NUM
ejpam-5021	428	3	]	]	X
ejpam-5021	428	4	p	p	X
ejpam-5021	428	5	k	k	PROPN
ejpam-5021	428	6	maji	maji	PROPN
ejpam-5021	428	7	,	,	PUNCT
ejpam-5021	428	8	r	r	NOUN
ejpam-5021	428	9	biswas	biswas	PROPN
ejpam-5021	428	10	,	,	PUNCT
ejpam-5021	428	11	and	and	CCONJ
ejpam-5021	428	12	a	a	DET
ejpam-5021	428	13	r	r	NOUN
ejpam-5021	428	14	roy	roy	PROPN
ejpam-5021	428	15	.	.	PROPN
ejpam-5021	428	16	fuzzy	fuzzy	ADJ
ejpam-5021	428	17	soft	soft	ADJ
ejpam-5021	428	18	sets	set	NOUN
ejpam-5021	428	19	.	.	PUNCT
ejpam-5021	429	1	journal	journal	NOUN
ejpam-5021	429	2	of	of	ADP
ejpam-5021	429	3	fuzzy	fuzzy	ADJ
ejpam-5021	429	4	mathematics	mathematic	NOUN
ejpam-5021	429	5	,	,	PUNCT
ejpam-5021	429	6	9:589–602	9:589–602	NUM
ejpam-5021	429	7	,	,	PUNCT
ejpam-5021	429	8	2001	2001	NUM
ejpam-5021	429	9	.	.	PUNCT
ejpam-5021	430	1	[	[	X
ejpam-5021	430	2	20	20	NUM
ejpam-5021	430	3	]	]	SYM
ejpam-5021	430	4	r	r	NOUN
ejpam-5021	430	5	g	g	PROPN
ejpam-5021	430	6	mclean	mclean	PROPN
ejpam-5021	430	7	and	and	CCONJ
ejpam-5021	430	8	h	h	PROPN
ejpam-5021	430	9	kummer	kummer	NOUN
ejpam-5021	430	10	.	.	PUNCT
ejpam-5021	431	1	fuzzy	fuzzy	ADJ
ejpam-5021	431	2	ideals	ideal	NOUN
ejpam-5021	431	3	in	in	ADP
ejpam-5021	431	4	semigroups	semigroup	NOUN
ejpam-5021	431	5	.	.	PUNCT
ejpam-5021	432	1	fuzzy	fuzzy	ADJ
ejpam-5021	432	2	sets	set	NOUN
ejpam-5021	432	3	and	and	CCONJ
ejpam-5021	432	4	systems	system	NOUN
ejpam-5021	432	5	,	,	PUNCT
ejpam-5021	432	6	48:137–140	48:137–140	NUM
ejpam-5021	432	7	,	,	PUNCT
ejpam-5021	432	8	1992	1992	NUM
ejpam-5021	432	9	.	.	PUNCT
ejpam-5021	433	1	[	[	X
ejpam-5021	433	2	21	21	NUM
ejpam-5021	433	3	]	]	X
ejpam-5021	433	4	d	d	X
ejpam-5021	433	5	molodtsov	molodtsov	PROPN
ejpam-5021	433	6	.	.	PUNCT
ejpam-5021	434	1	soft	soft	ADJ
ejpam-5021	434	2	set	set	NOUN
ejpam-5021	434	3	theory	theory	NOUN
ejpam-5021	434	4	-	-	PUNCT
ejpam-5021	434	5	first	first	ADJ
ejpam-5021	434	6	results	result	NOUN
ejpam-5021	434	7	.	.	PUNCT
ejpam-5021	435	1	computers	computer	NOUN
ejpam-5021	435	2	and	and	CCONJ
ejpam-5021	435	3	mathematics	mathematic	NOUN
ejpam-5021	435	4	with	with	ADP
ejpam-5021	435	5	applications	application	NOUN
ejpam-5021	435	6	,	,	PUNCT
ejpam-5021	435	7	37:19–31	37:19–31	NUM
ejpam-5021	435	8	,	,	PUNCT
ejpam-5021	435	9	1999	1999	NUM
ejpam-5021	435	10	.	.	PUNCT
ejpam-5021	436	1	[	[	X
ejpam-5021	436	2	22	22	NUM
ejpam-5021	436	3	]	]	X
ejpam-5021	436	4	j	j	PROPN
ejpam-5021	436	5	n	n	PRON
ejpam-5021	436	6	mordeson	mordeson	NOUN
ejpam-5021	436	7	,	,	PUNCT
ejpam-5021	437	1	d	d	PROPN
ejpam-5021	437	2	s	s	PROPN
ejpam-5021	437	3	malik	malik	PROPN
ejpam-5021	437	4	,	,	PUNCT
ejpam-5021	437	5	and	and	CCONJ
ejpam-5021	437	6	n	n	PRON
ejpam-5021	437	7	kuroki	kuroki	NOUN
ejpam-5021	437	8	.	.	PUNCT
ejpam-5021	438	1	fuzzy	fuzzy	ADJ
ejpam-5021	438	2	semigroups	semigroup	NOUN
ejpam-5021	438	3	.	.	PUNCT
ejpam-5021	439	1	springer	springer	NOUN
ejpam-5021	439	2	,	,	PUNCT
ejpam-5021	439	3	berlin	berlin	PROPN
ejpam-5021	439	4	,	,	PUNCT
ejpam-5021	439	5	heidelberg	heidelberg	PROPN
ejpam-5021	439	6	,	,	PUNCT
ejpam-5021	439	7	2003	2003	NUM
ejpam-5021	439	8	.	.	PUNCT
ejpam-5021	440	1	[	[	X
ejpam-5021	440	2	23	23	NUM
ejpam-5021	440	3	]	]	X
ejpam-5021	440	4	m	m	VERB
ejpam-5021	440	5	naz	naz	PROPN
ejpam-5021	440	6	and	and	CCONJ
ejpam-5021	440	7	m	m	PROPN
ejpam-5021	440	8	shabir	shabir	PROPN
ejpam-5021	440	9	.	.	PUNCT
ejpam-5021	441	1	on	on	ADP
ejpam-5021	441	2	fuzzy	fuzzy	ADJ
ejpam-5021	441	3	bipolar	bipolar	ADJ
ejpam-5021	441	4	soft	soft	ADJ
ejpam-5021	441	5	sets	set	NOUN
ejpam-5021	441	6	,	,	PUNCT
ejpam-5021	441	7	their	their	PRON
ejpam-5021	441	8	algebraic	algebraic	ADJ
ejpam-5021	441	9	structures	structure	NOUN
ejpam-5021	441	10	and	and	CCONJ
ejpam-5021	441	11	applications	application	NOUN
ejpam-5021	441	12	.	.	PUNCT
ejpam-5021	442	1	journal	journal	NOUN
ejpam-5021	442	2	of	of	ADP
ejpam-5021	442	3	intelligent	intelligent	ADJ
ejpam-5021	442	4	&	&	CCONJ
ejpam-5021	442	5	fuzzy	fuzzy	ADJ
ejpam-5021	442	6	systems	system	NOUN
ejpam-5021	442	7	,	,	PUNCT
ejpam-5021	442	8	26:1645–1656	26:1645–1656	NUM
ejpam-5021	442	9	,	,	PUNCT
ejpam-5021	442	10	2014	2014	NUM
ejpam-5021	442	11	.	.	PUNCT
ejpam-5021	443	1	[	[	X
ejpam-5021	443	2	24	24	NUM
ejpam-5021	443	3	]	]	X
ejpam-5021	443	4	r	r	NOUN
ejpam-5021	443	5	prasertpong	prasertpong	NOUN
ejpam-5021	443	6	.	.	PUNCT
ejpam-5021	444	1	green	green	PROPN
ejpam-5021	444	2	’s	’s	PART
ejpam-5021	444	3	relations	relation	NOUN
ejpam-5021	444	4	on	on	ADP
ejpam-5021	444	5	ordered	order	VERB
ejpam-5021	444	6	groupoids	groupoid	NOUN
ejpam-5021	444	7	in	in	ADP
ejpam-5021	444	8	terms	term	NOUN
ejpam-5021	444	9	of	of	ADP
ejpam-5021	444	10	fuzzy	fuzzy	ADJ
ejpam-5021	444	11	semibipolar	semibipolar	ADJ
ejpam-5021	444	12	soft	soft	ADJ
ejpam-5021	444	13	sets	set	NOUN
ejpam-5021	444	14	.	.	PUNCT
ejpam-5021	445	1	international	international	ADJ
ejpam-5021	445	2	journal	journal	NOUN
ejpam-5021	445	3	of	of	ADP
ejpam-5021	445	4	mathematics	mathematic	NOUN
ejpam-5021	445	5	and	and	CCONJ
ejpam-5021	445	6	computer	computer	NOUN
ejpam-5021	445	7	science	science	NOUN
ejpam-5021	445	8	,	,	PUNCT
ejpam-5021	445	9	17:1113–1132	17:1113–1132	NUM
ejpam-5021	445	10	,	,	PUNCT
ejpam-5021	445	11	2022	2022	NUM
ejpam-5021	445	12	.	.	PUNCT
ejpam-5021	446	1	[	[	X
ejpam-5021	446	2	25	25	NUM
ejpam-5021	446	3	]	]	PUNCT
ejpam-5021	446	4	a	a	DET
ejpam-5021	446	5	rosenfeld	rosenfeld	PROPN
ejpam-5021	446	6	.	.	PUNCT
ejpam-5021	447	1	fuzzy	fuzzy	ADJ
ejpam-5021	447	2	groups	group	NOUN
ejpam-5021	447	3	.	.	PUNCT
ejpam-5021	448	1	journal	journal	PROPN
ejpam-5021	448	2	of	of	ADP
ejpam-5021	448	3	mathematical	mathematical	ADJ
ejpam-5021	448	4	analysis	analysis	NOUN
ejpam-5021	448	5	and	and	CCONJ
ejpam-5021	448	6	applications	application	NOUN
ejpam-5021	448	7	,	,	PUNCT
ejpam-5021	448	8	35:512–517	35:512–517	PROPN
ejpam-5021	448	9	,	,	PUNCT
ejpam-5021	448	10	1971	1971	NUM
ejpam-5021	448	11	.	.	PUNCT
ejpam-5021	449	1	[	[	X
ejpam-5021	449	2	26	26	NUM
ejpam-5021	449	3	]	]	X
ejpam-5021	449	4	m	m	VERB
ejpam-5021	449	5	shabir	shabir	NOUN
ejpam-5021	449	6	and	and	CCONJ
ejpam-5021	449	7	m	m	PROPN
ejpam-5021	449	8	naz	naz	PROPN
ejpam-5021	449	9	.	.	PUNCT
ejpam-5021	450	1	on	on	ADP
ejpam-5021	450	2	bipolar	bipolar	ADJ
ejpam-5021	450	3	soft	soft	ADJ
ejpam-5021	450	4	sets	set	NOUN
ejpam-5021	450	5	.	.	PUNCT
ejpam-5021	451	1	arxiv:1303.1344	arxiv:1303.1344	NOUN
ejpam-5021	451	2	,	,	PUNCT
ejpam-5021	451	3	2013	2013	NUM
ejpam-5021	451	4	.	.	PUNCT
ejpam-5021	452	1	[	[	X
ejpam-5021	452	2	27	27	NUM
ejpam-5021	452	3	]	]	X
ejpam-5021	452	4	l	l	NOUN
ejpam-5021	452	5	a	a	DET
ejpam-5021	452	6	zadeh	zadeh	PROPN
ejpam-5021	452	7	.	.	PUNCT
ejpam-5021	452	8	fuzzy	fuzzy	ADJ
ejpam-5021	452	9	sets	set	NOUN
ejpam-5021	452	10	.	.	PUNCT
ejpam-5021	453	1	information	information	NOUN
ejpam-5021	453	2	control	control	NOUN
ejpam-5021	453	3	,	,	PUNCT
ejpam-5021	453	4	8:338–353	8:338–353	NUM
ejpam-5021	453	5	,	,	PUNCT
ejpam-5021	453	6	1965	1965	NUM
ejpam-5021	453	7	.	.	PUNCT
ejpam-5021	454	1	[	[	X
ejpam-5021	454	2	28	28	NUM
ejpam-5021	454	3	]	]	X
ejpam-5021	454	4	y	y	PROPN
ejpam-5021	454	5	zhi	zhi	PROPN
ejpam-5021	454	6	,	,	PUNCT
ejpam-5021	454	7	x	x	PROPN
ejpam-5021	454	8	zhou	zhou	PROPN
ejpam-5021	454	9	,	,	PUNCT
ejpam-5021	454	10	and	and	CCONJ
ejpam-5021	454	11	q	q	PROPN
ejpam-5021	454	12	li	li	PROPN
ejpam-5021	454	13	.	.	PROPN
ejpam-5021	454	14	green	green	PROPN
ejpam-5021	454	15	’s	’s	PART
ejpam-5021	454	16	relations	relation	NOUN
ejpam-5021	454	17	in	in	ADP
ejpam-5021	454	18	l	l	NOUN
ejpam-5021	454	19	-	-	PUNCT
ejpam-5021	454	20	e	e	ADJ
ejpam-5021	454	21	-	-	ADJ
ejpam-5021	454	22	fuzzy	fuzzy	ADJ
ejpam-5021	454	23	skew	skew	ADJ
ejpam-5021	454	24	lattices	lattice	NOUN
ejpam-5021	454	25	.	.	PUNCT
ejpam-5021	454	26	soft	soft	ADJ
ejpam-5021	454	27	computing	computing	NOUN
ejpam-5021	454	28	,	,	PUNCT
ejpam-5021	454	29	26:6481–6494	26:6481–6494	NUM
ejpam-5021	454	30	,	,	PUNCT
ejpam-5021	454	31	2022	2022	NUM
ejpam-5021	454	32	.	.	PUNCT