id	sid	tid	token	lemma	pos
easat-3708	1	1	edelweiss	edelweiss	PROPN
easat-3708	1	2	applied	apply	VERB
easat-3708	1	3	science	science	NOUN
easat-3708	1	4	and	and	CCONJ
easat-3708	1	5	technology	technology	NOUN
easat-3708	1	6	issn	issn	PROPN
easat-3708	1	7	:	:	PUNCT
easat-3708	1	8	2576	2576	NUM
easat-3708	1	9	-	-	SYM
easat-3708	1	10	8484	8484	NUM
easat-3708	1	11	vol	vol	NOUN
easat-3708	1	12	.	.	PROPN
easat-3708	1	13	8	8	NUM
easat-3708	1	14	,	,	PUNCT
easat-3708	1	15	no	no	INTJ
easat-3708	1	16	.	.	NOUN
easat-3708	1	17	6	6	NUM
easat-3708	1	18	,	,	PUNCT
easat-3708	1	19	7802	7802	NUM
easat-3708	1	20	-	-	SYM
easat-3708	1	21	7812	7812	NUM
easat-3708	1	22	2024	2024	NUM
easat-3708	1	23	publisher	publisher	NOUN
easat-3708	1	24	:	:	PUNCT
easat-3708	1	25	learning	learn	VERB
easat-3708	1	26	gate	gate	NOUN
easat-3708	1	27	doi	doi	PROPN
easat-3708	1	28	:	:	PUNCT
easat-3708	1	29	10.55214/25768484.v8i6.3708	10.55214/25768484.v8i6.3708	NUM
easat-3708	1	30	©	©	PROPN
easat-3708	1	31	2024	2024	NUM
easat-3708	1	32	by	by	ADP
easat-3708	1	33	the	the	DET
easat-3708	1	34	authors	author	NOUN
easat-3708	1	35	;	;	PUNCT
easat-3708	1	36	licensee	licensee	PROPN
easat-3708	1	37	learning	learning	NOUN
easat-3708	1	38	gate	gate	NOUN
easat-3708	1	39	©	©	PROPN
easat-3708	1	40	2024	2024	NUM
easat-3708	1	41	by	by	ADP
easat-3708	1	42	the	the	DET
easat-3708	1	43	authors	author	NOUN
easat-3708	1	44	;	;	PUNCT
easat-3708	1	45	licensee	licensee	PROPN
easat-3708	1	46	learning	learn	VERB
easat-3708	1	47	gate	gate	NOUN
easat-3708	1	48	*	*	PUNCT
easat-3708	1	49	correspondence	correspondence	NOUN
easat-3708	1	50	:	:	PUNCT
easat-3708	1	51	a-foroughi@qom.ac.ir	a-foroughi@qom.ac.ir	ADP
easat-3708	1	52	solving	solve	VERB
easat-3708	1	53	fuzzy	fuzzy	ADJ
easat-3708	1	54	fractional	fractional	ADJ
easat-3708	1	55	programming	programming	NOUN
easat-3708	1	56	problems	problem	NOUN
easat-3708	1	57	by	by	ADP
easat-3708	1	58	vns	vns	PROPN
easat-3708	1	59	algorithm	algorithm	NOUN
easat-3708	1	60	using	use	VERB
easat-3708	1	61	modified	modify	VERB
easat-3708	1	62	kerre	kerre	PROPN
easat-3708	1	63	's	's	PART
easat-3708	1	64	inequality	inequality	NOUN
easat-3708	1	65	dhurgam	dhurgam	NOUN
easat-3708	1	66	kalel	kalel	PROPN
easat-3708	1	67	ibrahim	ibrahim	PROPN
easat-3708	1	68	alsaad1	alsaad1	PROPN
easat-3708	1	69	,	,	PUNCT
easat-3708	1	70	aliasghar	aliasghar	VERB
easat-3708	1	71	foroughi1	foroughi1	PROPN
easat-3708	1	72	*	*	PUNCT
easat-3708	1	73	,	,	PUNCT
easat-3708	1	74	khatere	khatere	PROPN
easat-3708	1	75	ghorbani	ghorbani	PROPN
easat-3708	1	76	-	-	PUNCT
easat-3708	1	77	moghadam2	moghadam2	PROPN
easat-3708	1	78	,	,	PUNCT
easat-3708	1	79	reza	reza	PROPN
easat-3708	1	80	ghanbari3	ghanbari3	PROPN
easat-3708	2	1	1department	1department	NUM
easat-3708	2	2	of	of	ADP
easat-3708	2	3	mathematics	mathematic	NOUN
easat-3708	2	4	,	,	PUNCT
easat-3708	2	5	university	university	PROPN
easat-3708	2	6	of	of	ADP
easat-3708	2	7	qom	qom	PROPN
easat-3708	2	8	,	,	PUNCT
easat-3708	2	9	qom	qom	PROPN
easat-3708	2	10	,	,	PUNCT
easat-3708	2	11	iran	iran	PROPN
easat-3708	2	12	;	;	PUNCT
easat-3708	2	13	aalimath2018@gmail.com	aalimath2018@gmail.com	X
easat-3708	2	14	(	(	PUNCT
easat-3708	2	15	d.k.i.a	d.k.i.a	PROPN
easat-3708	2	16	.	.	PUNCT
easat-3708	2	17	)	)	PUNCT
easat-3708	3	1	a-foroughi@qom.ac.ir	a-foroughi@qom.ac.ir	ADP
easat-3708	3	2	(	(	PUNCT
easat-3708	3	3	a.f	a.f	PROPN
easat-3708	3	4	.	.	PROPN
easat-3708	3	5	)	)	PUNCT
easat-3708	3	6	.	.	PUNCT
easat-3708	4	1	2mosaheb	2mosaheb	NUM
easat-3708	4	2	institute	institute	NOUN
easat-3708	4	3	of	of	ADP
easat-3708	4	4	mathematics	mathematics	PROPN
easat-3708	4	5	,	,	PUNCT
easat-3708	4	6	kharazmi	kharazmi	PROPN
easat-3708	4	7	university	university	PROPN
easat-3708	4	8	,	,	PUNCT
easat-3708	4	9	tehran	tehran	PROPN
easat-3708	4	10	,	,	PUNCT
easat-3708	4	11	iran	iran	PROPN
easat-3708	4	12	;	;	PUNCT
easat-3708	4	13	k.ghorbani@khu.ac.ir	k.ghorbani@khu.ac.ir	X
easat-3708	4	14	(	(	PUNCT
easat-3708	4	15	k.g.m	k.g.m	NOUN
easat-3708	4	16	.	.	PUNCT
easat-3708	4	17	)	)	PUNCT
easat-3708	4	18	.	.	PUNCT
easat-3708	5	1	3faculty	3faculty	NUM
easat-3708	5	2	of	of	ADP
easat-3708	5	3	mathematical	mathematical	ADJ
easat-3708	5	4	sciences	science	NOUN
easat-3708	5	5	,	,	PUNCT
easat-3708	5	6	department	department	NOUN
easat-3708	5	7	of	of	ADP
easat-3708	5	8	applied	apply	VERB
easat-3708	5	9	mathematics	mathematic	NOUN
easat-3708	5	10	,	,	PUNCT
easat-3708	5	11	ferdowsi	ferdowsi	NOUN
easat-3708	5	12	university	university	PROPN
easat-3708	5	13	of	of	ADP
easat-3708	5	14	mashhad	mashhad	PROPN
easat-3708	5	15	,	,	PUNCT
easat-3708	5	16	mashhad	mashhad	PROPN
easat-3708	5	17	,	,	PUNCT
easat-3708	5	18	iran	iran	PROPN
easat-3708	5	19	;	;	PUNCT
easat-3708	5	20	rghanbari@um.ac.ir	rghanbari@um.ac.ir	PROPN
easat-3708	5	21	(	(	PUNCT
easat-3708	5	22	r.z	r.z	PROPN
easat-3708	5	23	.	.	PUNCT
easat-3708	5	24	)	)	PUNCT
easat-3708	5	25	.	.	PUNCT
easat-3708	6	1	abstract	abstract	ADV
easat-3708	6	2	:	:	PUNCT
easat-3708	6	3	here	here	ADV
easat-3708	6	4	,	,	PUNCT
easat-3708	6	5	we	we	PRON
easat-3708	6	6	propose	propose	VERB
easat-3708	6	7	a	a	DET
easat-3708	6	8	new	new	ADJ
easat-3708	6	9	variable	variable	ADJ
easat-3708	6	10	neighbourhood	neighbourhood	NOUN
easat-3708	6	11	search	search	NOUN
easat-3708	6	12	(	(	PUNCT
easat-3708	6	13	vns	vns	NOUN
easat-3708	6	14	)	)	PUNCT
easat-3708	6	15	algorithm	algorithm	NOUN
easat-3708	6	16	for	for	ADP
easat-3708	6	17	solving	solve	VERB
easat-3708	6	18	fractional	fractional	ADJ
easat-3708	6	19	fuzzy	fuzzy	ADJ
easat-3708	6	20	number	number	NOUN
easat-3708	6	21	linear	linear	NOUN
easat-3708	6	22	programming	programming	NOUN
easat-3708	6	23	problems	problem	NOUN
easat-3708	6	24	(	(	PUNCT
easat-3708	6	25	ffnlpps	ffnlpps	INTJ
easat-3708	6	26	)	)	PUNCT
easat-3708	6	27	.	.	PUNCT
easat-3708	7	1	we	we	PRON
easat-3708	7	2	make	make	VERB
easat-3708	7	3	use	use	NOUN
easat-3708	7	4	of	of	ADP
easat-3708	7	5	modified	modify	VERB
easat-3708	7	6	kerre	kerre	PROPN
easat-3708	7	7	’s	’s	PART
easat-3708	7	8	inequality	inequality	NOUN
easat-3708	7	9	for	for	ADP
easat-3708	7	10	comparison	comparison	NOUN
easat-3708	7	11	of	of	ADP
easat-3708	7	12	lr	lr	PRON
easat-3708	7	13	fuzzy	fuzzy	ADJ
easat-3708	7	14	numbers	number	NOUN
easat-3708	7	15	.	.	PUNCT
easat-3708	8	1	in	in	ADP
easat-3708	8	2	our	our	PRON
easat-3708	8	3	proposed	propose	VERB
easat-3708	8	4	algorithm	algorithm	NOUN
easat-3708	8	5	,	,	PUNCT
easat-3708	8	6	we	we	PRON
easat-3708	8	7	introduced	introduce	VERB
easat-3708	8	8	a	a	DET
easat-3708	8	9	new	new	ADJ
easat-3708	8	10	local	local	ADJ
easat-3708	8	11	search	search	NOUN
easat-3708	8	12	defined	define	VERB
easat-3708	8	13	based	base	VERB
easat-3708	8	14	on	on	ADP
easat-3708	8	15	descent	descent	NOUN
easat-3708	8	16	directions	direction	NOUN
easat-3708	8	17	,	,	PUNCT
easat-3708	8	18	which	which	PRON
easat-3708	8	19	are	be	AUX
easat-3708	8	20	found	find	VERB
easat-3708	8	21	by	by	ADP
easat-3708	8	22	solving	solve	VERB
easat-3708	8	23	four	four	NUM
easat-3708	8	24	crisp	crisp	ADJ
easat-3708	8	25	mathematical	mathematical	ADJ
easat-3708	8	26	programming	programming	NOUN
easat-3708	8	27	problems	problem	NOUN
easat-3708	8	28	.	.	PUNCT
easat-3708	9	1	in	in	ADP
easat-3708	9	2	several	several	ADJ
easat-3708	9	3	methods	method	NOUN
easat-3708	9	4	,	,	PUNCT
easat-3708	9	5	a	a	DET
easat-3708	9	6	fuzzy	fuzzy	ADJ
easat-3708	9	7	fractional	fractional	ADJ
easat-3708	9	8	optimization	optimization	NOUN
easat-3708	9	9	problem	problem	NOUN
easat-3708	9	10	is	be	AUX
easat-3708	9	11	converted	convert	VERB
easat-3708	9	12	to	to	ADP
easat-3708	9	13	a	a	DET
easat-3708	9	14	crisp	crisp	ADJ
easat-3708	9	15	problem	problem	NOUN
easat-3708	9	16	.	.	PUNCT
easat-3708	10	1	still	still	ADV
easat-3708	10	2	,	,	PUNCT
easat-3708	10	3	in	in	ADP
easat-3708	10	4	our	our	PRON
easat-3708	10	5	proposed	propose	VERB
easat-3708	10	6	method	method	NOUN
easat-3708	10	7	,	,	PUNCT
easat-3708	10	8	using	use	VERB
easat-3708	10	9	modified	modify	VERB
easat-3708	10	10	kerre	kerre	PROPN
easat-3708	10	11	’s	’s	PART
easat-3708	10	12	inequality	inequality	NOUN
easat-3708	10	13	,	,	PUNCT
easat-3708	10	14	the	the	DET
easat-3708	10	15	fuzzy	fuzzy	ADJ
easat-3708	10	16	optimization	optimization	NOUN
easat-3708	10	17	problem	problem	NOUN
easat-3708	10	18	is	be	AUX
easat-3708	10	19	solved	solve	VERB
easat-3708	10	20	directly	directly	ADV
easat-3708	10	21	,	,	PUNCT
easat-3708	10	22	without	without	ADP
easat-3708	10	23	changing	change	VERB
easat-3708	10	24	it	it	PRON
easat-3708	10	25	to	to	ADP
easat-3708	10	26	a	a	DET
easat-3708	10	27	crisp	crisp	ADJ
easat-3708	10	28	program	program	NOUN
easat-3708	10	29	.	.	PUNCT
easat-3708	11	1	to	to	PART
easat-3708	11	2	show	show	VERB
easat-3708	11	3	the	the	DET
easat-3708	11	4	effectiveness	effectiveness	NOUN
easat-3708	11	5	of	of	ADP
easat-3708	11	6	our	our	PRON
easat-3708	11	7	method	method	NOUN
easat-3708	11	8	,	,	PUNCT
easat-3708	11	9	we	we	PRON
easat-3708	11	10	compare	compare	VERB
easat-3708	11	11	our	our	PRON
easat-3708	11	12	proposed	propose	VERB
easat-3708	11	13	algorithm	algorithm	NOUN
easat-3708	11	14	with	with	ADP
easat-3708	11	15	other	other	ADJ
easat-3708	11	16	available	available	ADJ
easat-3708	11	17	methods	method	NOUN
easat-3708	11	18	.	.	PUNCT
easat-3708	12	1	keywords	keyword	NOUN
easat-3708	12	2	:	:	PUNCT
easat-3708	12	3	fractional	fractional	ADJ
easat-3708	12	4	linear	linear	PROPN
easat-3708	12	5	optimization	optimization	NOUN
easat-3708	12	6	,	,	PUNCT
easat-3708	12	7	modified	modify	VERB
easat-3708	12	8	kerre	kerre	PROPN
easat-3708	12	9	’s	’s	PART
easat-3708	12	10	inequality	inequality	NOUN
easat-3708	12	11	,	,	PUNCT
easat-3708	12	12	vns	vns	PROPN
easat-3708	12	13	algorithm	algorithm	NOUN
easat-3708	12	14	.	.	PUNCT
easat-3708	13	1	1	1	X
easat-3708	13	2	.	.	X
easat-3708	13	3	introduction	introduction	NOUN
easat-3708	13	4	charnes	charne	NOUN
easat-3708	13	5	and	and	CCONJ
easat-3708	13	6	cooper	cooper	NOUN
easat-3708	14	1	[	[	X
easat-3708	14	2	4	4	NUM
easat-3708	14	3	]	]	PUNCT
easat-3708	14	4	first	first	ADV
easat-3708	14	5	formulated	formulate	VERB
easat-3708	14	6	a	a	DET
easat-3708	14	7	linear	linear	ADJ
easat-3708	14	8	fractional	fractional	ADJ
easat-3708	14	9	programming	programming	NOUN
easat-3708	14	10	problem	problem	NOUN
easat-3708	14	11	as	as	ADP
easat-3708	14	12	an	an	DET
easat-3708	14	13	optimization	optimization	NOUN
easat-3708	14	14	problem	problem	NOUN
easat-3708	14	15	of	of	ADP
easat-3708	14	16	a	a	DET
easat-3708	14	17	ratio	ratio	NOUN
easat-3708	14	18	of	of	ADP
easat-3708	14	19	linear	linear	ADJ
easat-3708	14	20	functions	function	NOUN
easat-3708	14	21	subject	subject	ADJ
easat-3708	14	22	to	to	ADP
easat-3708	14	23	linear	linear	ADJ
easat-3708	14	24	constraints	constraint	NOUN
easat-3708	14	25	.	.	PUNCT
easat-3708	15	1	such	such	ADJ
easat-3708	15	2	linear	linear	ADJ
easat-3708	15	3	fractional	fractional	ADJ
easat-3708	15	4	objectives	objective	NOUN
easat-3708	15	5	(	(	PUNCT
easat-3708	15	6	i.e.	i.e.	X
easat-3708	15	7	,	,	PUNCT
easat-3708	15	8	ratio	ratio	NOUN
easat-3708	15	9	objectives	objective	NOUN
easat-3708	15	10	that	that	PRON
easat-3708	15	11	have	have	VERB
easat-3708	15	12	a	a	DET
easat-3708	15	13	linear	linear	ADJ
easat-3708	15	14	numerator	numerator	NOUN
easat-3708	15	15	and	and	CCONJ
easat-3708	15	16	denominator	denominator	NOUN
easat-3708	15	17	)	)	PUNCT
easat-3708	15	18	are	be	AUX
easat-3708	15	19	helpful	helpful	ADJ
easat-3708	15	20	in	in	ADP
easat-3708	15	21	production	production	NOUN
easat-3708	15	22	planning	planning	NOUN
easat-3708	15	23	,	,	PUNCT
easat-3708	15	24	financial	financial	ADJ
easat-3708	15	25	and	and	CCONJ
easat-3708	15	26	corporate	corporate	ADJ
easat-3708	15	27	planning	planning	NOUN
easat-3708	15	28	,	,	PUNCT
easat-3708	15	29	health	health	NOUN
easat-3708	15	30	care	care	NOUN
easat-3708	15	31	,	,	PUNCT
easat-3708	15	32	hospital	hospital	NOUN
easat-3708	15	33	planning	planning	NOUN
easat-3708	15	34	,	,	PUNCT
easat-3708	15	35	and	and	CCONJ
easat-3708	15	36	so	so	ADV
easat-3708	15	37	forth	forth	ADV
easat-3708	15	38	.	.	PUNCT
easat-3708	16	1	examples	example	NOUN
easat-3708	16	2	of	of	ADP
easat-3708	16	3	fractional	fractional	ADJ
easat-3708	16	4	objectives	objective	NOUN
easat-3708	16	5	in	in	ADP
easat-3708	16	6	production	production	NOUN
easat-3708	16	7	planning	planning	NOUN
easat-3708	16	8	include	include	VERB
easat-3708	16	9	inventory	inventory	NOUN
easat-3708	16	10	/	/	SYM
easat-3708	16	11	sales	sale	NOUN
easat-3708	16	12	,	,	PUNCT
easat-3708	16	13	output	output	NOUN
easat-3708	16	14	/	/	SYM
easat-3708	16	15	employee	employee	NOUN
easat-3708	16	16	,	,	PUNCT
easat-3708	16	17	etc	etc	X
easat-3708	16	18	.	.	X
easat-3708	16	19	for	for	ADP
easat-3708	16	20	single	single	ADJ
easat-3708	16	21	objective	objective	NOUN
easat-3708	16	22	,	,	PUNCT
easat-3708	16	23	linear	linear	ADJ
easat-3708	16	24	fractional	fractional	ADJ
easat-3708	16	25	programming	programming	NOUN
easat-3708	16	26	,	,	PUNCT
easat-3708	16	27	the	the	DET
easat-3708	16	28	charnes	charne	NOUN
easat-3708	16	29	and	and	CCONJ
easat-3708	16	30	cooper	cooper	NOUN
easat-3708	16	31	[	[	X
easat-3708	16	32	4	4	NUM
easat-3708	16	33	]	]	PUNCT
easat-3708	16	34	transformation	transformation	NOUN
easat-3708	16	35	can	can	AUX
easat-3708	16	36	transform	transform	VERB
easat-3708	16	37	the	the	DET
easat-3708	16	38	problem	problem	NOUN
easat-3708	16	39	into	into	ADP
easat-3708	16	40	a	a	DET
easat-3708	16	41	linear	linear	ADJ
easat-3708	16	42	programming	programming	NOUN
easat-3708	16	43	problem	problem	NOUN
easat-3708	16	44	.	.	PUNCT
easat-3708	17	1	in	in	ADP
easat-3708	17	2	many	many	ADJ
easat-3708	17	3	real	real	ADJ
easat-3708	17	4	-	-	PUNCT
easat-3708	17	5	world	world	NOUN
easat-3708	17	6	situations	situation	NOUN
easat-3708	17	7	,	,	PUNCT
easat-3708	17	8	some	some	DET
easat-3708	17	9	parameters	parameter	NOUN
easat-3708	17	10	of	of	ADP
easat-3708	17	11	a	a	DET
easat-3708	17	12	linear	linear	ADJ
easat-3708	17	13	program	program	NOUN
easat-3708	17	14	are	be	AUX
easat-3708	17	15	given	give	VERB
easat-3708	17	16	by	by	ADP
easat-3708	17	17	experts	expert	NOUN
easat-3708	17	18	.	.	PUNCT
easat-3708	18	1	however	however	ADV
easat-3708	18	2	,	,	PUNCT
easat-3708	18	3	experts	expert	NOUN
easat-3708	18	4	and	and	CCONJ
easat-3708	18	5	decision	decision	NOUN
easat-3708	18	6	-	-	PUNCT
easat-3708	18	7	makers	maker	NOUN
easat-3708	18	8	frequently	frequently	ADV
easat-3708	18	9	are	be	AUX
easat-3708	18	10	not	not	PART
easat-3708	18	11	aware	aware	ADJ
easat-3708	18	12	of	of	ADP
easat-3708	18	13	the	the	DET
easat-3708	18	14	precise	precise	ADJ
easat-3708	18	15	values	value	NOUN
easat-3708	18	16	of	of	ADP
easat-3708	18	17	the	the	DET
easat-3708	18	18	parameters	parameter	NOUN
easat-3708	18	19	.	.	PUNCT
easat-3708	19	1	since	since	SCONJ
easat-3708	19	2	some	some	DET
easat-3708	19	3	optimization	optimization	NOUN
easat-3708	19	4	problems	problem	NOUN
easat-3708	19	5	contain	contain	VERB
easat-3708	19	6	parameters	parameter	NOUN
easat-3708	19	7	with	with	ADP
easat-3708	19	8	imprecise	imprecise	ADJ
easat-3708	19	9	values	value	NOUN
easat-3708	19	10	(	(	PUNCT
easat-3708	19	11	see	see	VERB
easat-3708	19	12	[	[	X
easat-3708	19	13	3	3	NUM
easat-3708	19	14	]	]	NUM
easat-3708	19	15	)	)	PUNCT
easat-3708	19	16	,	,	PUNCT
easat-3708	19	17	fuzzy	fuzzy	ADJ
easat-3708	19	18	number	number	NOUN
easat-3708	19	19	linear	linear	NOUN
easat-3708	19	20	programs	program	NOUN
easat-3708	19	21	(	(	PUNCT
easat-3708	19	22	fnlps	fnlps	VERB
easat-3708	19	23	)	)	PUNCT
easat-3708	19	24	are	be	AUX
easat-3708	19	25	handy	handy	ADJ
easat-3708	19	26	tools	tool	NOUN
easat-3708	19	27	for	for	ADP
easat-3708	19	28	modelling	modelling	NOUN
easat-3708	19	29	and	and	CCONJ
easat-3708	19	30	solving	solve	VERB
easat-3708	19	31	real	real	ADJ
easat-3708	19	32	-	-	PUNCT
easat-3708	19	33	world	world	NOUN
easat-3708	19	34	problems	problem	NOUN
easat-3708	19	35	.	.	PUNCT
easat-3708	20	1	arya	arya	PROPN
easat-3708	20	2	et	et	PROPN
easat-3708	20	3	al	al	PROPN
easat-3708	20	4	.	.	PUNCT
easat-3708	21	1	[	[	X
easat-3708	21	2	1	1	X
easat-3708	21	3	]	]	PUNCT
easat-3708	21	4	presented	present	VERB
easat-3708	21	5	a	a	DET
easat-3708	21	6	fuzzy	fuzzy	ADJ
easat-3708	21	7	based	base	VERB
easat-3708	21	8	branch	branch	NOUN
easat-3708	21	9	-	-	PUNCT
easat-3708	21	10	bound	bind	VERB
easat-3708	21	11	approach	approach	NOUN
easat-3708	21	12	is	be	AUX
easat-3708	21	13	attempted	attempt	VERB
easat-3708	21	14	for	for	ADP
easat-3708	21	15	solving	solve	VERB
easat-3708	21	16	multiobjective	multiobjective	ADJ
easat-3708	21	17	linear	linear	ADJ
easat-3708	21	18	fractional	fractional	ADJ
easat-3708	21	19	(	(	PUNCT
easat-3708	21	20	molf	molf	NOUN
easat-3708	21	21	)	)	PUNCT
easat-3708	21	22	optimization	optimization	NOUN
easat-3708	21	23	problems	problem	NOUN
easat-3708	21	24	.	.	PUNCT
easat-3708	22	1	the	the	DET
easat-3708	22	2	original	original	ADJ
easat-3708	22	3	molf	molf	NOUN
easat-3708	22	4	optimization	optimization	NOUN
easat-3708	22	5	problem	problem	NOUN
easat-3708	22	6	is	be	AUX
easat-3708	22	7	converted	convert	VERB
easat-3708	22	8	into	into	ADP
easat-3708	22	9	an	an	DET
easat-3708	22	10	equivalent	equivalent	ADJ
easat-3708	22	11	fuzzy	fuzzy	ADJ
easat-3708	22	12	multi	multi	ADJ
easat-3708	22	13	-	-	ADJ
easat-3708	22	14	objective	objective	ADJ
easat-3708	22	15	linear	linear	ADJ
easat-3708	22	16	fractional	fractional	ADJ
easat-3708	22	17	(	(	PUNCT
easat-3708	22	18	fmolf	fmolf	ADJ
easat-3708	22	19	)	)	PUNCT
easat-3708	22	20	optimization	optimization	NOUN
easat-3708	22	21	problem	problem	NOUN
easat-3708	22	22	.	.	PUNCT
easat-3708	23	1	then	then	ADV
easat-3708	23	2	,	,	PUNCT
easat-3708	23	3	branch	branch	NOUN
easat-3708	23	4	and	and	CCONJ
easat-3708	23	5	bound	bound	ADJ
easat-3708	23	6	techniques	technique	NOUN
easat-3708	23	7	were	be	AUX
easat-3708	23	8	applied	apply	VERB
easat-3708	23	9	to	to	ADP
easat-3708	23	10	the	the	DET
easat-3708	23	11	fmolf	fmolf	PROPN
easat-3708	23	12	optimization	optimization	NOUN
easat-3708	23	13	problem	problem	NOUN
easat-3708	23	14	.	.	PUNCT
easat-3708	24	1	the	the	DET
easat-3708	24	2	feasible	feasible	ADJ
easat-3708	24	3	space	space	NOUN
easat-3708	24	4	of	of	ADP
easat-3708	24	5	fmolf	fmolf	ADJ
easat-3708	24	6	optimization	optimization	NOUN
easat-3708	24	7	problem	problem	NOUN
easat-3708	24	8	was	be	AUX
easat-3708	24	9	bounded	bound	VERB
easat-3708	24	10	by	by	ADP
easat-3708	24	11	triangular	triangular	NOUN
easat-3708	24	12	simplex	simplex	NOUN
easat-3708	24	13	space	space	NOUN
easat-3708	24	14	.	.	PUNCT
easat-3708	25	1	the	the	DET
easat-3708	25	2	weak	weak	ADJ
easat-3708	25	3	duality	duality	NOUN
easat-3708	25	4	theorem	theorem	NOUN
easat-3708	25	5	was	be	AUX
easat-3708	25	6	used	use	VERB
easat-3708	25	7	to	to	PART
easat-3708	25	8	generate	generate	VERB
easat-3708	25	9	the	the	DET
easat-3708	25	10	bound	bind	VERB
easat-3708	25	11	for	for	ADP
easat-3708	25	12	each	each	DET
easat-3708	25	13	partition	partition	NOUN
easat-3708	25	14	and	and	CCONJ
easat-3708	25	15	feasibility	feasibility	NOUN
easat-3708	25	16	conditions	condition	NOUN
easat-3708	25	17	were	be	AUX
easat-3708	25	18	applied	apply	VERB
easat-3708	25	19	to	to	AUX
easat-3708	25	20	neglect	neglect	VERB
easat-3708	25	21	one	one	NUM
easat-3708	25	22	partition	partition	NOUN
easat-3708	25	23	in	in	ADP
easat-3708	25	24	each	each	DET
easat-3708	25	25	step	step	NOUN
easat-3708	25	26	.	.	PUNCT
easat-3708	26	1	after	after	ADP
easat-3708	26	2	finite	finite	ADJ
easat-3708	26	3	number	number	NOUN
easat-3708	26	4	of	of	ADP
easat-3708	26	5	steps	step	NOUN
easat-3708	26	6	,	,	PUNCT
easat-3708	26	7	a	a	DET
easat-3708	26	8	fuzzy	fuzzy	ADJ
easat-3708	26	9	efficient	efficient	ADJ
easat-3708	26	10	(	(	PUNCT
easat-3708	26	11	pareto	pareto	VERB
easat-3708	26	12	-	-	PUNCT
easat-3708	26	13	optimal	optimal	ADJ
easat-3708	26	14	)	)	PUNCT
easat-3708	26	15	solution	solution	NOUN
easat-3708	26	16	was	be	AUX
easat-3708	26	17	obtained	obtain	VERB
easat-3708	26	18	for	for	ADP
easat-3708	26	19	fmolf	fmolf	NOUN
easat-3708	26	20	optimization	optimization	NOUN
easat-3708	26	21	problem	problem	NOUN
easat-3708	26	22	which	which	PRON
easat-3708	26	23	was	be	AUX
easat-3708	26	24	also	also	ADV
easat-3708	26	25	efficient	efficient	ADJ
easat-3708	26	26	(	(	PUNCT
easat-3708	26	27	pareto	pareto	VERB
easat-3708	26	28	-	-	PUNCT
easat-3708	26	29	optimal	optimal	ADJ
easat-3708	26	30	)	)	PUNCT
easat-3708	26	31	solution	solution	NOUN
easat-3708	26	32	of	of	ADP
easat-3708	26	33	the	the	DET
easat-3708	26	34	original	original	ADJ
easat-3708	26	35	molf	molf	NOUN
easat-3708	26	36	optimization	optimization	NOUN
easat-3708	26	37	problem	problem	NOUN
easat-3708	26	38	.	.	PUNCT
easat-3708	27	1	some	some	DET
easat-3708	27	2	theoretical	theoretical	ADJ
easat-3708	27	3	validations	validation	NOUN
easat-3708	27	4	were	be	AUX
easat-3708	27	5	also	also	ADV
easat-3708	27	6	established	establish	VERB
easat-3708	27	7	for	for	ADP
easat-3708	27	8	the	the	DET
easat-3708	27	9	proposed	propose	VERB
easat-3708	27	10	approach	approach	NOUN
easat-3708	27	11	on	on	ADP
easat-3708	27	12	fmolf	fmolf	ADJ
easat-3708	27	13	optimization	optimization	NOUN
easat-3708	27	14	problem	problem	NOUN
easat-3708	27	15	.	.	PUNCT
easat-3708	28	1	chinnadurai	chinnadurai	PROPN
easat-3708	28	2	and	and	CCONJ
easat-3708	28	3	muthukumar	muthukumar	PROPN
easat-3708	29	1	[	[	X
easat-3708	29	2	5	5	NUM
easat-3708	29	3	]	]	PUNCT
easat-3708	29	4	proposed	propose	VERB
easat-3708	29	5	using	use	VERB
easat-3708	29	6	the	the	DET
easat-3708	29	7	(	(	PUNCT
easat-3708	29	8	α	α	NOUN
easat-3708	29	9	,	,	PUNCT
easat-3708	29	10	r	r	NOUN
easat-3708	29	11	)	)	PUNCT
easat-3708	29	12	acceptable	acceptable	ADJ
easat-3708	29	13	optimal	optimal	ADJ
easat-3708	29	14	value	value	NOUN
easat-3708	29	15	for	for	ADP
easat-3708	29	16	a	a	DET
easat-3708	29	17	linear	linear	ADJ
easat-3708	29	18	fractional	fractional	ADJ
easat-3708	29	19	programming	programming	NOUN
easat-3708	29	20	problem	problem	NOUN
easat-3708	29	21	with	with	ADP
easat-3708	29	22	fuzzy	fuzzy	ADJ
easat-3708	29	23	coefficients	coefficient	NOUN
easat-3708	29	24	and	and	CCONJ
easat-3708	29	25	fuzzy	fuzzy	ADJ
easat-3708	29	26	decision	decision	NOUN
easat-3708	29	27	variables	variable	NOUN
easat-3708	29	28	,	,	PUNCT
easat-3708	29	29	as	as	ADV
easat-3708	29	30	well	well	ADV
easat-3708	29	31	as	as	ADP
easat-3708	29	32	developing	develop	VERB
easat-3708	29	33	a	a	DET
easat-3708	29	34	method	method	NOUN
easat-3708	29	35	for	for	ADP
easat-3708	29	36	computing	compute	VERB
easat-3708	29	37	them	they	PRON
easat-3708	29	38	.	.	PUNCT
easat-3708	30	1	to	to	PART
easat-3708	30	2	obtain	obtain	VERB
easat-3708	30	3	acceptable	acceptable	ADJ
easat-3708	30	4	(	(	PUNCT
easat-3708	30	5	α	α	NOUN
easat-3708	30	6	,	,	PUNCT
easat-3708	30	7	r	r	NOUN
easat-3708	30	8	)	)	PUNCT
easat-3708	30	9	optimal	optimal	ADJ
easat-3708	30	10	values	value	NOUN
easat-3708	30	11	,	,	PUNCT
easat-3708	30	12	they	they	PRON
easat-3708	30	13	take	take	VERB
easat-3708	30	14	an	an	DET
easat-3708	30	15	α	α	NOUN
easat-3708	30	16	-	-	NOUN
easat-3708	30	17	cut	cut	NOUN
easat-3708	30	18	on	on	ADP
easat-3708	30	19	the	the	DET
easat-3708	30	20	objective	objective	ADJ
easat-3708	30	21	function	function	NOUN
easat-3708	30	22	and	and	CCONJ
easat-3708	30	23	r	r	NOUN
easat-3708	30	24	-	-	PUNCT
easat-3708	30	25	cut	cut	NOUN
easat-3708	30	26	on	on	ADP
easat-3708	30	27	the	the	DET
easat-3708	30	28	7803	7803	NUM
easat-3708	30	29	edelweiss	edelweiss	PROPN
easat-3708	30	30	applied	apply	VERB
easat-3708	30	31	science	science	NOUN
easat-3708	30	32	and	and	CCONJ
easat-3708	30	33	technology	technology	NOUN
easat-3708	30	34	issn	issn	PROPN
easat-3708	30	35	:	:	PUNCT
easat-3708	30	36	2576	2576	NUM
easat-3708	30	37	-	-	SYM
easat-3708	30	38	8484	8484	NUM
easat-3708	30	39	vol	vol	NOUN
easat-3708	30	40	.	.	PROPN
easat-3708	31	1	8	8	NUM
easat-3708	31	2	,	,	PUNCT
easat-3708	31	3	no	no	INTJ
easat-3708	31	4	.	.	NOUN
easat-3708	31	5	6	6	NUM
easat-3708	31	6	:	:	SYM
easat-3708	31	7	7802	7802	NUM
easat-3708	31	8	-	-	SYM
easat-3708	31	9	7812	7812	NUM
easat-3708	31	10	,	,	PUNCT
easat-3708	31	11	2024	2024	NUM
easat-3708	31	12	doi	doi	NOUN
easat-3708	31	13	:	:	PUNCT
easat-3708	31	14	10.55214/25768484.v8i6.3708	10.55214/25768484.v8i6.3708	NUM
easat-3708	31	15	©	©	PROPN
easat-3708	31	16	2024	2024	NUM
easat-3708	31	17	by	by	ADP
easat-3708	31	18	the	the	DET
easat-3708	31	19	authors	author	NOUN
easat-3708	31	20	;	;	PUNCT
easat-3708	32	1	licensee	licensee	PROPN
easat-3708	32	2	learning	learn	VERB
easat-3708	32	3	gate	gate	NOUN
easat-3708	32	4	constraints	constraint	NOUN
easat-3708	32	5	.	.	PUNCT
easat-3708	33	1	they	they	PRON
easat-3708	33	2	then	then	ADV
easat-3708	33	3	formulated	formulate	VERB
easat-3708	33	4	an	an	DET
easat-3708	33	5	equivalent	equivalent	ADJ
easat-3708	33	6	bi	bi	ADJ
easat-3708	33	7	-	-	ADJ
easat-3708	33	8	objective	objective	ADJ
easat-3708	33	9	linear	linear	ADJ
easat-3708	33	10	fractional	fractional	ADJ
easat-3708	33	11	programming	programming	NOUN
easat-3708	33	12	problem	problem	NOUN
easat-3708	33	13	to	to	PART
easat-3708	33	14	calculate	calculate	VERB
easat-3708	33	15	the	the	DET
easat-3708	33	16	upper	upper	ADJ
easat-3708	33	17	and	and	CCONJ
easat-3708	33	18	lower	low	ADJ
easat-3708	33	19	bounds	bound	NOUN
easat-3708	33	20	of	of	ADP
easat-3708	33	21	the	the	DET
easat-3708	33	22	fully	fully	ADV
easat-3708	33	23	fuzzy	fuzzy	ADJ
easat-3708	33	24	linear	linear	ADJ
easat-3708	33	25	fractional	fractional	ADJ
easat-3708	33	26	programming	programming	NOUN
easat-3708	33	27	(	(	PUNCT
easat-3708	33	28	lfp	lfp	PROPN
easat-3708	33	29	)	)	PUNCT
easat-3708	33	30	problem	problem	NOUN
easat-3708	33	31	.	.	PUNCT
easat-3708	34	1	using	use	VERB
easat-3708	34	2	the	the	DET
easat-3708	34	3	upper	upper	ADJ
easat-3708	34	4	and	and	CCONJ
easat-3708	34	5	lower	low	ADJ
easat-3708	34	6	bounds	bound	NOUN
easat-3708	34	7	obtained	obtain	VERB
easat-3708	34	8	,	,	PUNCT
easat-3708	34	9	they	they	PRON
easat-3708	34	10	constructed	construct	VERB
easat-3708	34	11	the	the	DET
easat-3708	34	12	membership	membership	NOUN
easat-3708	34	13	functions	function	NOUN
easat-3708	34	14	of	of	ADP
easat-3708	34	15	the	the	DET
easat-3708	34	16	optimal	optimal	ADJ
easat-3708	34	17	values	value	NOUN
easat-3708	34	18	numerically	numerically	ADV
easat-3708	34	19	.	.	PUNCT
easat-3708	35	1	wang	wang	PROPN
easat-3708	35	2	et	et	PROPN
easat-3708	35	3	al	al	PROPN
easat-3708	35	4	.	.	PUNCT
easat-3708	36	1	[	[	X
easat-3708	36	2	33	33	NUM
easat-3708	36	3	]	]	PUNCT
easat-3708	36	4	obtained	obtain	VERB
easat-3708	36	5	the	the	DET
easat-3708	36	6	solution	solution	NOUN
easat-3708	36	7	to	to	ADP
easat-3708	36	8	bi	bi	ADJ
easat-3708	36	9	-	-	ADJ
easat-3708	36	10	level	level	ADJ
easat-3708	36	11	linear	linear	ADJ
easat-3708	36	12	fractional	fractional	ADJ
easat-3708	36	13	programming	programming	NOUN
easat-3708	36	14	problem	problem	NOUN
easat-3708	36	15	(	(	PUNCT
easat-3708	36	16	blfp	blfp	NOUN
easat-3708	36	17	)	)	PUNCT
easat-3708	36	18	using	use	VERB
easat-3708	36	19	an	an	DET
easat-3708	36	20	optimization	optimization	NOUN
easat-3708	36	21	algorithm	algorithm	NOUN
easat-3708	36	22	based	base	VERB
easat-3708	36	23	on	on	ADP
easat-3708	36	24	the	the	DET
easat-3708	36	25	duality	duality	NOUN
easat-3708	36	26	gap	gap	NOUN
easat-3708	36	27	of	of	ADP
easat-3708	36	28	the	the	DET
easat-3708	36	29	lower	low	ADJ
easat-3708	36	30	level	level	NOUN
easat-3708	36	31	problem	problem	NOUN
easat-3708	36	32	.	.	PUNCT
easat-3708	37	1	in	in	ADP
easat-3708	37	2	their	their	PRON
easat-3708	37	3	algorithm	algorithm	NOUN
easat-3708	37	4	,	,	PUNCT
easat-3708	37	5	the	the	DET
easat-3708	37	6	bi	bi	ADJ
easat-3708	37	7	-	-	ADJ
easat-3708	37	8	level	level	ADJ
easat-3708	37	9	linear	linear	ADJ
easat-3708	37	10	fractional	fractional	ADJ
easat-3708	37	11	programming	programming	NOUN
easat-3708	37	12	problem	problem	NOUN
easat-3708	37	13	was	be	AUX
easat-3708	37	14	transformed	transform	VERB
easat-3708	37	15	into	into	ADP
easat-3708	37	16	an	an	DET
easat-3708	37	17	equivalent	equivalent	ADJ
easat-3708	37	18	single	single	ADJ
easat-3708	37	19	-	-	PUNCT
easat-3708	37	20	level	level	NOUN
easat-3708	37	21	programming	programming	NOUN
easat-3708	37	22	problem	problem	NOUN
easat-3708	37	23	by	by	ADP
easat-3708	37	24	forcing	force	VERB
easat-3708	37	25	the	the	DET
easat-3708	37	26	dual	dual	ADJ
easat-3708	37	27	gap	gap	NOUN
easat-3708	37	28	of	of	ADP
easat-3708	37	29	the	the	DET
easat-3708	37	30	lower	low	ADJ
easat-3708	37	31	level	level	NOUN
easat-3708	37	32	problem	problem	NOUN
easat-3708	37	33	to	to	ADP
easat-3708	37	34	zero	zero	NUM
easat-3708	37	35	.	.	PUNCT
easat-3708	38	1	then	then	ADV
easat-3708	38	2	,	,	PUNCT
easat-3708	38	3	by	by	ADP
easat-3708	38	4	obtaining	obtain	VERB
easat-3708	38	5	all	all	DET
easat-3708	38	6	vertices	vertex	NOUN
easat-3708	38	7	of	of	ADP
easat-3708	38	8	a	a	DET
easat-3708	38	9	polyhedron	polyhedron	NOUN
easat-3708	38	10	,	,	PUNCT
easat-3708	38	11	the	the	DET
easat-3708	38	12	single	single	ADJ
easat-3708	38	13	-	-	PUNCT
easat-3708	38	14	level	level	NOUN
easat-3708	38	15	programming	programming	NOUN
easat-3708	38	16	problem	problem	NOUN
easat-3708	38	17	could	could	AUX
easat-3708	38	18	be	be	AUX
easat-3708	38	19	converted	convert	VERB
easat-3708	38	20	into	into	ADP
easat-3708	38	21	a	a	DET
easat-3708	38	22	series	series	NOUN
easat-3708	38	23	of	of	ADP
easat-3708	38	24	linear	linear	ADJ
easat-3708	38	25	fractional	fractional	ADJ
easat-3708	38	26	programming	programming	NOUN
easat-3708	38	27	problems	problem	NOUN
easat-3708	38	28	.	.	PUNCT
easat-3708	39	1	pal	pal	PROPN
easat-3708	39	2	et	et	PROPN
easat-3708	39	3	al	al	PROPN
easat-3708	39	4	.	.	PUNCT
easat-3708	40	1	[	[	X
easat-3708	40	2	17	17	NUM
easat-3708	40	3	]	]	PUNCT
easat-3708	40	4	,	,	PUNCT
easat-3708	40	5	presented	present	VERB
easat-3708	40	6	a	a	DET
easat-3708	40	7	goal	goal	NOUN
easat-3708	40	8	programming	programming	NOUN
easat-3708	40	9	(	(	PUNCT
easat-3708	40	10	gp	gp	NOUN
easat-3708	40	11	)	)	PUNCT
easat-3708	40	12	procedure	procedure	NOUN
easat-3708	40	13	for	for	ADP
easat-3708	40	14	fuzzy	fuzzy	ADJ
easat-3708	40	15	multi	multi	ADJ
easat-3708	40	16	-	-	ADJ
easat-3708	40	17	objective	objective	ADJ
easat-3708	40	18	linear	linear	ADJ
easat-3708	40	19	fractional	fractional	ADJ
easat-3708	40	20	programming	programming	NOUN
easat-3708	40	21	(	(	PUNCT
easat-3708	40	22	fmolfp	fmolfp	NOUN
easat-3708	40	23	)	)	PUNCT
easat-3708	40	24	problems	problem	NOUN
easat-3708	40	25	.	.	PUNCT
easat-3708	41	1	in	in	ADP
easat-3708	41	2	the	the	DET
easat-3708	41	3	proposed	propose	VERB
easat-3708	41	4	approach	approach	NOUN
easat-3708	41	5	,	,	PUNCT
easat-3708	41	6	which	which	PRON
easat-3708	41	7	is	be	AUX
easat-3708	41	8	motivated	motivate	VERB
easat-3708	41	9	by	by	ADP
easat-3708	41	10	mohamed	mohamed	PROPN
easat-3708	41	11	(	(	PUNCT
easat-3708	41	12	fuzzy	fuzzy	ADJ
easat-3708	41	13	sets	set	NOUN
easat-3708	41	14	and	and	CCONJ
easat-3708	41	15	systems	system	NOUN
easat-3708	41	16	89	89	NUM
easat-3708	41	17	(	(	PUNCT
easat-3708	41	18	1997	1997	NUM
easat-3708	41	19	)	)	PUNCT
easat-3708	41	20	215	215	NUM
easat-3708	41	21	)	)	PUNCT
easat-3708	41	22	,	,	PUNCT
easat-3708	41	23	gp	gp	NOUN
easat-3708	41	24	model	model	NOUN
easat-3708	41	25	for	for	ADP
easat-3708	41	26	achievement	achievement	NOUN
easat-3708	41	27	of	of	ADP
easat-3708	41	28	the	the	DET
easat-3708	41	29	highest	high	ADJ
easat-3708	41	30	membership	membership	NOUN
easat-3708	41	31	value	value	NOUN
easat-3708	41	32	of	of	ADP
easat-3708	41	33	each	each	PRON
easat-3708	41	34	of	of	ADP
easat-3708	41	35	fuzzy	fuzzy	ADJ
easat-3708	41	36	goals	goal	NOUN
easat-3708	41	37	defined	define	VERB
easat-3708	41	38	for	for	ADP
easat-3708	41	39	the	the	DET
easat-3708	41	40	fractional	fractional	ADJ
easat-3708	41	41	objectives	objective	NOUN
easat-3708	41	42	is	be	AUX
easat-3708	41	43	formulated	formulate	VERB
easat-3708	41	44	.	.	PUNCT
easat-3708	42	1	in	in	ADP
easat-3708	42	2	the	the	DET
easat-3708	42	3	solution	solution	NOUN
easat-3708	42	4	process	process	NOUN
easat-3708	42	5	,	,	PUNCT
easat-3708	42	6	the	the	DET
easat-3708	42	7	method	method	NOUN
easat-3708	42	8	of	of	ADP
easat-3708	42	9	variable	variable	ADJ
easat-3708	42	10	change	change	NOUN
easat-3708	42	11	on	on	ADP
easat-3708	42	12	the	the	DET
easat-3708	42	13	underand	underand	NOUN
easat-3708	42	14	overdeviational	overdeviational	ADJ
easat-3708	42	15	variables	variable	NOUN
easat-3708	42	16	of	of	ADP
easat-3708	42	17	the	the	DET
easat-3708	42	18	membership	membership	NOUN
easat-3708	42	19	goals	goal	NOUN
easat-3708	42	20	associated	associate	VERB
easat-3708	42	21	with	with	ADP
easat-3708	42	22	the	the	DET
easat-3708	42	23	fuzzy	fuzzy	ADJ
easat-3708	42	24	goals	goal	NOUN
easat-3708	42	25	of	of	ADP
easat-3708	42	26	the	the	DET
easat-3708	42	27	model	model	NOUN
easat-3708	42	28	is	be	AUX
easat-3708	42	29	introduced	introduce	VERB
easat-3708	42	30	to	to	PART
easat-3708	42	31	solve	solve	VERB
easat-3708	42	32	the	the	DET
easat-3708	42	33	problem	problem	NOUN
easat-3708	42	34	efficiently	efficiently	ADV
easat-3708	42	35	using	use	VERB
easat-3708	42	36	linear	linear	ADJ
easat-3708	42	37	goal	goal	NOUN
easat-3708	42	38	programming	programming	NOUN
easat-3708	42	39	(	(	PUNCT
easat-3708	42	40	lgp	lgp	NOUN
easat-3708	42	41	)	)	PUNCT
easat-3708	42	42	methodology	methodology	NOUN
easat-3708	42	43	.	.	PUNCT
easat-3708	43	1	yang	yang	PROPN
easat-3708	43	2	et	et	PROPN
easat-3708	43	3	al	al	PROPN
easat-3708	43	4	.	.	PUNCT
easat-3708	44	1	[	[	X
easat-3708	44	2	34	34	NUM
easat-3708	44	3	]	]	PUNCT
easat-3708	44	4	,	,	PUNCT
easat-3708	44	5	presented	present	VERB
easat-3708	44	6	to	to	PART
easat-3708	44	7	solve	solve	VERB
easat-3708	44	8	fuzzy	fuzzy	ADJ
easat-3708	44	9	multi	multi	ADJ
easat-3708	44	10	-	-	ADJ
easat-3708	44	11	objective	objective	ADJ
easat-3708	44	12	linear	linear	ADJ
easat-3708	44	13	fractional	fractional	ADJ
easat-3708	44	14	programming	programming	NOUN
easat-3708	44	15	(	(	PUNCT
easat-3708	44	16	fmolfp	fmolfp	NOUN
easat-3708	44	17	)	)	PUNCT
easat-3708	44	18	problems	problem	NOUN
easat-3708	44	19	through	through	ADP
easat-3708	44	20	an	an	DET
easat-3708	44	21	approach	approach	NOUN
easat-3708	44	22	based	base	VERB
easat-3708	44	23	on	on	ADP
easat-3708	44	24	superiority	superiority	NOUN
easat-3708	44	25	and	and	CCONJ
easat-3708	44	26	inferiority	inferiority	NOUN
easat-3708	44	27	measures	measure	NOUN
easat-3708	44	28	method	method	NOUN
easat-3708	44	29	(	(	PUNCT
easat-3708	44	30	simm	simm	PROPN
easat-3708	44	31	)	)	PUNCT
easat-3708	44	32	.	.	PUNCT
easat-3708	45	1	in	in	ADP
easat-3708	45	2	the	the	DET
easat-3708	45	3	model	model	NOUN
easat-3708	45	4	for	for	ADP
easat-3708	45	5	the	the	DET
easat-3708	45	6	proposed	propose	VERB
easat-3708	45	7	approach	approach	NOUN
easat-3708	45	8	,	,	PUNCT
easat-3708	45	9	each	each	PRON
easat-3708	45	10	of	of	ADP
easat-3708	45	11	fuzzy	fuzzy	ADJ
easat-3708	45	12	goals	goal	NOUN
easat-3708	45	13	defined	define	VERB
easat-3708	45	14	for	for	ADP
easat-3708	45	15	the	the	DET
easat-3708	45	16	fractional	fractional	ADJ
easat-3708	45	17	objectives	objective	NOUN
easat-3708	45	18	and	and	CCONJ
easat-3708	45	19	some	some	DET
easat-3708	45	20	constraints	constraint	NOUN
easat-3708	45	21	have	have	VERB
easat-3708	45	22	fuzzy	fuzzy	ADJ
easat-3708	45	23	numbers	number	NOUN
easat-3708	45	24	.	.	PUNCT
easat-3708	46	1	to	to	PART
easat-3708	46	2	achieve	achieve	VERB
easat-3708	46	3	the	the	DET
easat-3708	46	4	highest	high	ADJ
easat-3708	46	5	membership	membership	NOUN
easat-3708	46	6	value	value	NOUN
easat-3708	46	7	,	,	PUNCT
easat-3708	46	8	simm	simm	PROPN
easat-3708	46	9	was	be	AUX
easat-3708	46	10	adopted	adopt	VERB
easat-3708	46	11	to	to	PART
easat-3708	46	12	deal	deal	VERB
easat-3708	46	13	with	with	ADP
easat-3708	46	14	fuzzy	fuzzy	ADJ
easat-3708	46	15	number	number	NOUN
easat-3708	46	16	in	in	ADP
easat-3708	46	17	constraints	constraint	NOUN
easat-3708	46	18	,	,	PUNCT
easat-3708	46	19	then	then	ADV
easat-3708	46	20	a	a	DET
easat-3708	46	21	linear	linear	ADJ
easat-3708	46	22	goal	goal	NOUN
easat-3708	46	23	programming	programming	NOUN
easat-3708	46	24	methodology	methodology	NOUN
easat-3708	46	25	was	be	AUX
easat-3708	46	26	introduced	introduce	VERB
easat-3708	46	27	to	to	PART
easat-3708	46	28	solve	solve	VERB
easat-3708	46	29	the	the	DET
easat-3708	46	30	problem	problem	NOUN
easat-3708	46	31	in	in	ADP
easat-3708	46	32	which	which	PRON
easat-3708	46	33	the	the	DET
easat-3708	46	34	fractional	fractional	ADJ
easat-3708	46	35	objectives	objective	NOUN
easat-3708	46	36	was	be	AUX
easat-3708	46	37	fuzzy	fuzzy	ADJ
easat-3708	46	38	goals	goal	NOUN
easat-3708	46	39	.	.	PUNCT
easat-3708	47	1	a	a	DET
easat-3708	47	2	case	case	NOUN
easat-3708	47	3	of	of	ADP
easat-3708	47	4	agricultural	agricultural	ADJ
easat-3708	47	5	planting	planting	NOUN
easat-3708	47	6	structures	structure	NOUN
easat-3708	47	7	optimization	optimization	NOUN
easat-3708	47	8	problem	problem	NOUN
easat-3708	47	9	was	be	AUX
easat-3708	47	10	solved	solve	VERB
easat-3708	47	11	to	to	PART
easat-3708	47	12	illustrate	illustrate	VERB
easat-3708	47	13	the	the	DET
easat-3708	47	14	application	application	NOUN
easat-3708	47	15	of	of	ADP
easat-3708	47	16	the	the	DET
easat-3708	47	17	algorithm	algorithm	NOUN
easat-3708	47	18	.	.	PUNCT
easat-3708	48	1	sakawa	sakawa	PROPN
easat-3708	48	2	and	and	CCONJ
easat-3708	48	3	kato	kato	PROPN
easat-3708	49	1	[	[	X
easat-3708	49	2	24	24	NUM
easat-3708	49	3	]	]	PUNCT
easat-3708	49	4	,	,	PUNCT
easat-3708	49	5	by	by	ADP
easat-3708	49	6	considering	consider	VERB
easat-3708	49	7	the	the	DET
easat-3708	49	8	experts	expert	NOUN
easat-3708	49	9	’	’	PART
easat-3708	49	10	vague	vague	ADJ
easat-3708	49	11	or	or	CCONJ
easat-3708	49	12	fuzzy	fuzzy	ADJ
easat-3708	49	13	understanding	understanding	NOUN
easat-3708	49	14	of	of	ADP
easat-3708	49	15	the	the	DET
easat-3708	49	16	nature	nature	NOUN
easat-3708	49	17	of	of	ADP
easat-3708	49	18	the	the	DET
easat-3708	49	19	parameters	parameter	NOUN
easat-3708	49	20	in	in	ADP
easat-3708	49	21	the	the	DET
easat-3708	49	22	problem	problem	NOUN
easat-3708	49	23	formulation	formulation	NOUN
easat-3708	49	24	process	process	NOUN
easat-3708	49	25	,	,	PUNCT
easat-3708	49	26	multi	multi	ADJ
easat-3708	49	27	-	-	ADJ
easat-3708	49	28	objective	objective	ADJ
easat-3708	49	29	linear	linear	ADJ
easat-3708	49	30	fractional	fractional	ADJ
easat-3708	49	31	programming	programming	NOUN
easat-3708	49	32	problems	problem	NOUN
easat-3708	49	33	with	with	ADP
easat-3708	49	34	block	block	NOUN
easat-3708	49	35	angular	angular	ADJ
easat-3708	49	36	structure	structure	NOUN
easat-3708	49	37	involving	involve	VERB
easat-3708	49	38	fuzzy	fuzzy	ADJ
easat-3708	49	39	numbers	number	NOUN
easat-3708	49	40	are	be	AUX
easat-3708	49	41	formulated	formulate	VERB
easat-3708	49	42	.	.	PUNCT
easat-3708	50	1	sakawa	sakawa	PROPN
easat-3708	50	2	and	and	CCONJ
easat-3708	50	3	kato	kato	PROPN
easat-3708	50	4	[	[	X
easat-3708	50	5	24	24	NUM
easat-3708	50	6	]	]	PUNCT
easat-3708	50	7	proposed	propose	VERB
easat-3708	50	8	the	the	DET
easat-3708	50	9	following	following	ADJ
easat-3708	50	10	model	model	NOUN
easat-3708	50	11	:	:	PUNCT
easat-3708	50	12	min	min	PROPN
easat-3708	50	13	𝑧1(𝑥	𝑧1(𝑥	PROPN
easat-3708	50	14	,	,	PUNCT
easat-3708	50	15	�	�	PROPN
easat-3708	50	16	̃	̃	PROPN
easat-3708	50	17	�	�	NOUN
easat-3708	50	18	1	1	NUM
easat-3708	50	19	,	,	PUNCT
easat-3708	50	20	�	�	PROPN
easat-3708	50	21	̃	̃	NOUN
easat-3708	50	22	�	�	NOUN
easat-3708	50	23	1	1	NUM
easat-3708	50	24	)	)	PUNCT
easat-3708	50	25	.	.	PUNCT
easat-3708	50	26	.	.	PUNCT
easat-3708	50	27	.	.	PUNCT
easat-3708	51	1	min	min	PROPN
easat-3708	51	2	𝑧𝑘(𝑥	𝑧𝑘(𝑥	PROPN
easat-3708	51	3	,	,	PUNCT
easat-3708	51	4	�	�	PROPN
easat-3708	51	5	̃	̃	PROPN
easat-3708	51	6	�	�	PROPN
easat-3708	51	7	𝑘	𝑘	PRON
easat-3708	51	8	,	,	PUNCT
easat-3708	51	9	�	�	PROPN
easat-3708	51	10	̃	̃	PROPN
easat-3708	51	11	�	�	PROPN
easat-3708	51	12	𝑘)𝑠.	𝑘)𝑠.	ADJ
easat-3708	51	13	𝑡.	𝑡.	NOUN
easat-3708	51	14	(	(	PUNCT
easat-3708	51	15	1	1	X
easat-3708	51	16	)	)	PUNCT
easat-3708	51	17	�	�	PROPN
easat-3708	51	18	̃	̃	PROPN
easat-3708	51	19	�	�	PROPN
easat-3708	51	20	1𝑥1	1𝑥1	NUM
easat-3708	51	21	+	+	SYM
easat-3708	51	22	⋯	⋯	PROPN
easat-3708	51	23	+	+	SYM
easat-3708	51	24	�	�	PROPN
easat-3708	51	25	̃	̃	PROPN
easat-3708	51	26	�	�	NOUN
easat-3708	51	27	𝑝𝑥𝑝	𝑝𝑥𝑝	NOUN
easat-3708	51	28	≤	≤	NUM
easat-3708	51	29	�	�	PROPN
easat-3708	51	30	̃	̃	PROPN
easat-3708	51	31	�	�	NOUN
easat-3708	51	32	0	0	NUM
easat-3708	51	33	,	,	PUNCT
easat-3708	51	34	�	�	PROPN
easat-3708	51	35	̃	̃	PROPN
easat-3708	51	36	�	�	PROPN
easat-3708	51	37	1𝑥1	1𝑥1	NUM
easat-3708	51	38	≤	≤	NUM
easat-3708	51	39	�	�	PROPN
easat-3708	51	40	̃	̃	PROPN
easat-3708	51	41	�	�	NOUN
easat-3708	51	42	1	1	NUM
easat-3708	51	43	,	,	PUNCT
easat-3708	51	44	.	.	PUNCT
easat-3708	51	45	.	.	PUNCT
easat-3708	51	46	.	.	PUNCT
easat-3708	52	1	�	�	PROPN
easat-3708	52	2	̃	̃	PROPN
easat-3708	52	3	�	�	PROPN
easat-3708	52	4	𝑝𝑥𝑝	𝑝𝑥𝑝	NOUN
easat-3708	52	5	≤	≤	NUM
easat-3708	52	6	�	�	PROPN
easat-3708	52	7	̃	̃	PROPN
easat-3708	52	8	�	�	PROPN
easat-3708	52	9	𝑝	𝑝	PROPN
easat-3708	52	10	,	,	PUNCT
easat-3708	52	11	𝑥𝑗	𝑥𝑗	PROPN
easat-3708	52	12	≥	≥	NOUN
easat-3708	52	13	0	0	NUM
easat-3708	52	14	,	,	PUNCT
easat-3708	52	15	𝑗	𝑗	NOUN
easat-3708	52	16	=	=	SYM
easat-3708	52	17	0	0	NUM
easat-3708	52	18	,	,	PUNCT
easat-3708	52	19	⋯	⋯	PROPN
easat-3708	52	20	,	,	PUNCT
easat-3708	52	21	𝑝.	𝑝.	VERB
easat-3708	52	22	where	where	SCONJ
easat-3708	52	23	,	,	PUNCT
easat-3708	52	24	𝑥𝑗	𝑥𝑗	PROPN
easat-3708	52	25	,	,	PUNCT
easat-3708	52	26	𝑗	𝑗	NOUN
easat-3708	52	27	=	=	SYM
easat-3708	52	28	1	1	NUM
easat-3708	52	29	,	,	PUNCT
easat-3708	52	30	⋯	⋯	PROPN
easat-3708	52	31	,	,	PUNCT
easat-3708	52	32	𝑝	𝑝	PROPN
easat-3708	52	33	,	,	PUNCT
easat-3708	52	34	are	be	AUX
easat-3708	52	35	𝑛𝑗	𝑛𝑗	ADP
easat-3708	52	36	dimensional	dimensional	ADJ
easat-3708	52	37	column	column	NOUN
easat-3708	52	38	vectors	vector	NOUN
easat-3708	52	39	of	of	ADP
easat-3708	52	40	decision	decision	NOUN
easat-3708	52	41	variables	variable	NOUN
easat-3708	52	42	,	,	PUNCT
easat-3708	52	43	�	�	PROPN
easat-3708	52	44	̃	̃	PROPN
easat-3708	52	45	�	�	PROPN
easat-3708	52	46	1𝑥1	1𝑥1	NUM
easat-3708	52	47	+	+	SYM
easat-3708	52	48	⋯	⋯	PROPN
easat-3708	52	49	+	+	SYM
easat-3708	52	50	�	�	PROPN
easat-3708	52	51	̃	̃	PROPN
easat-3708	52	52	�	�	NOUN
easat-3708	52	53	𝑝𝑥𝑝	𝑝𝑥𝑝	NOUN
easat-3708	52	54	≤	≤	NUM
easat-3708	52	55	�	�	PROPN
easat-3708	52	56	̃	̃	PROPN
easat-3708	52	57	�	�	NOUN
easat-3708	52	58	0	0	NUM
easat-3708	52	59	are	be	AUX
easat-3708	52	60	𝑚0	𝑚0	NOUN
easat-3708	52	61	-	-	PUNCT
easat-3708	52	62	dimensional	dimensional	ADJ
easat-3708	52	63	coupling	coupling	NOUN
easat-3708	52	64	constraints	constraint	NOUN
easat-3708	52	65	,	,	PUNCT
easat-3708	52	66	and	and	CCONJ
easat-3708	52	67	�	�	PROPN
easat-3708	52	68	̃	̃	PROPN
easat-3708	52	69	�	�	NOUN
easat-3708	52	70	𝑗	𝑗	NOUN
easat-3708	52	71	,	,	PUNCT
easat-3708	52	72	𝑗	𝑗	NOUN
easat-3708	52	73	=	=	SYM
easat-3708	52	74	1	1	NUM
easat-3708	52	75	,	,	PUNCT
easat-3708	52	76	⋯	⋯	PROPN
easat-3708	52	77	,	,	PUNCT
easat-3708	52	78	𝑝	𝑝	PROPN
easat-3708	52	79	are	be	AUX
easat-3708	52	80	𝑚0	𝑚0	NOUN
easat-3708	52	81	×	×	NOUN
easat-3708	52	82	𝑛	𝑛	PRON
easat-3708	52	83	fuzzy	fuzzy	ADJ
easat-3708	52	84	coefficient	coefficient	NOUN
easat-3708	52	85	matrices	matrix	NOUN
easat-3708	52	86	.	.	PUNCT
easat-3708	53	1	�	�	PROPN
easat-3708	53	2	̃	̃	PROPN
easat-3708	53	3	�	�	PROPN
easat-3708	53	4	𝑗𝑥𝑗	𝑗𝑥𝑗	NOUN
easat-3708	53	5	≤	≤	NUM
easat-3708	53	6	�	�	PROPN
easat-3708	53	7	̃	̃	PROPN
easat-3708	53	8	�	�	NOUN
easat-3708	53	9	𝑗	𝑗	NOUN
easat-3708	53	10	are	be	AUX
easat-3708	53	11	𝑚𝑗-dimensional	𝑚𝑗-dimensional	ADJ
easat-3708	53	12	block	block	NOUN
easat-3708	53	13	constraints	constraint	NOUN
easat-3708	53	14	with	with	ADP
easat-3708	53	15	respect	respect	NOUN
easat-3708	53	16	to	to	ADP
easat-3708	53	17	𝑥𝑗	𝑥𝑗	PROPN
easat-3708	53	18	,	,	PUNCT
easat-3708	53	19	�	�	PROPN
easat-3708	53	20	̃	̃	PROPN
easat-3708	53	21	�	�	NOUN
easat-3708	53	22	𝑗	𝑗	NOUN
easat-3708	53	23	,	,	PUNCT
easat-3708	53	24	𝑗	𝑗	NOUN
easat-3708	53	25	=	=	SYM
easat-3708	53	26	1	1	NUM
easat-3708	53	27	,	,	PUNCT
easat-3708	53	28	⋯	⋯	PROPN
easat-3708	53	29	,	,	PUNCT
easat-3708	53	30	𝑝	𝑝	PROPN
easat-3708	53	31	are	be	AUX
easat-3708	53	32	𝑚𝑗	𝑚𝑗	ADJ
easat-3708	53	33	×	×	NOUN
easat-3708	53	34	𝑛𝑗	𝑛𝑗	ADP
easat-3708	53	35	fuzzy	fuzzy	ADJ
easat-3708	53	36	coefficient	coefficient	NOUN
easat-3708	53	37	matrices	matrix	NOUN
easat-3708	53	38	and	and	CCONJ
easat-3708	53	39	�	�	PROPN
easat-3708	53	40	̃	̃	PROPN
easat-3708	53	41	�	�	NOUN
easat-3708	53	42	𝑗	𝑗	NOUN
easat-3708	53	43	,	,	PUNCT
easat-3708	53	44	𝑗	𝑗	NOUN
easat-3708	53	45	=	=	SYM
easat-3708	53	46	1	1	NUM
easat-3708	53	47	,	,	PUNCT
easat-3708	53	48	⋯	⋯	PROPN
easat-3708	53	49	,	,	PUNCT
easat-3708	53	50	𝑝	𝑝	PROPN
easat-3708	53	51	,	,	PUNCT
easat-3708	53	52	are	be	AUX
easat-3708	53	53	𝑚𝑗-dimensional	𝑚𝑗-dimensional	ADJ
easat-3708	53	54	column	column	NOUN
easat-3708	53	55	fuzzy	fuzzy	ADJ
easat-3708	53	56	vectors	vector	NOUN
easat-3708	53	57	.	.	PUNCT
easat-3708	54	1	furthermore	furthermore	ADV
easat-3708	54	2	,	,	PUNCT
easat-3708	54	3	𝑧1(𝑥	𝑧1(𝑥	NOUN
easat-3708	54	4	,	,	PUNCT
easat-3708	54	5	�	�	PROPN
easat-3708	54	6	̃	̃	PROPN
easat-3708	54	7	�	�	NOUN
easat-3708	54	8	1	1	NUM
easat-3708	54	9	,	,	PUNCT
easat-3708	54	10	�	�	PROPN
easat-3708	54	11	̃	̃	NOUN
easat-3708	54	12	�	�	NOUN
easat-3708	54	13	1	1	NUM
easat-3708	54	14	)	)	PUNCT
easat-3708	54	15	,	,	PUNCT
easat-3708	54	16	⋯	⋯	PROPN
easat-3708	54	17	,	,	PUNCT
easat-3708	54	18	𝑧𝑘(𝑥	𝑧𝑘(𝑥	NUM
easat-3708	54	19	,	,	PUNCT
easat-3708	54	20	�	�	PROPN
easat-3708	54	21	̃	̃	PROPN
easat-3708	54	22	�	�	PROPN
easat-3708	54	23	𝑘	𝑘	PRON
easat-3708	54	24	,	,	PUNCT
easat-3708	54	25	�	�	PROPN
easat-3708	54	26	̃	̃	PROPN
easat-3708	54	27	�	�	NOUN
easat-3708	54	28	𝑘	𝑘	PRON
easat-3708	54	29	)	)	PUNCT
easat-3708	54	30	are	be	AUX
easat-3708	54	31	𝑘	𝑘	DET
easat-3708	54	32	distinct	distinct	ADJ
easat-3708	54	33	fuzzy	fuzzy	ADJ
easat-3708	54	34	linear	linear	ADJ
easat-3708	54	35	fractional	fractional	ADJ
easat-3708	54	36	objective	objective	ADJ
easat-3708	54	37	functions	function	NOUN
easat-3708	54	38	defined	define	VERB
easat-3708	54	39	by	by	ADP
easat-3708	54	40	:	:	PUNCT
easat-3708	54	41	𝑧𝑖(𝑥	𝑧𝑖(𝑥	NUM
easat-3708	54	42	,	,	PUNCT
easat-3708	54	43	�	�	PROPN
easat-3708	54	44	̃	̃	NOUN
easat-3708	54	45	�	�	NOUN
easat-3708	54	46	𝑖	𝑖	SYM
easat-3708	54	47	,	,	PUNCT
easat-3708	54	48	�	�	PROPN
easat-3708	54	49	̃	̃	PROPN
easat-3708	54	50	�	�	NOUN
easat-3708	54	51	𝑖	𝑖	NUM
easat-3708	54	52	)	)	PUNCT
easat-3708	54	53	=	=	SYM
easat-3708	54	54	𝑝𝑖(𝑥,𝑐̃𝑖	𝑝𝑖(𝑥,𝑐̃𝑖	NUM
easat-3708	54	55	)	)	PUNCT
easat-3708	55	1	𝑞𝑖(𝑥,	𝑞𝑖(𝑥,	PROPN
easat-3708	55	2	�	�	PROPN
easat-3708	55	3	̃	̃	NOUN
easat-3708	55	4	�	�	NOUN
easat-3708	55	5	𝑖	𝑖	NUM
easat-3708	55	6	)	)	PUNCT
easat-3708	56	1	=	=	PRON
easat-3708	56	2	𝑐̃𝑖1𝑥1+⋯+𝑐̃𝑖𝑝𝑥𝑝+𝑐̃𝑖,𝑝+1	𝑐̃𝑖1𝑥1+⋯+𝑐̃𝑖𝑝𝑥𝑝+𝑐̃𝑖,𝑝+1	NOUN
easat-3708	56	3	�	�	PROPN
easat-3708	56	4	̃	̃	PROPN
easat-3708	56	5	�	�	PROPN
easat-3708	56	6	𝑖1𝑥1+⋯+	𝑖1𝑥1+⋯+	NOUN
easat-3708	56	7	�	�	PROPN
easat-3708	56	8	̃	̃	PROPN
easat-3708	56	9	�	�	PROPN
easat-3708	56	10	𝑖𝑝𝑥𝑝+	𝑖𝑝𝑥𝑝+	SYM
easat-3708	56	11	�	�	PROPN
easat-3708	56	12	̃	̃	NOUN
easat-3708	56	13	�	�	NOUN
easat-3708	56	14	𝑖,𝑝+1	𝑖,𝑝+1	PROPN
easat-3708	56	15	.	.	PUNCT
easat-3708	57	1	using	use	VERB
easat-3708	57	2	the	the	DET
easat-3708	57	3	a	a	DET
easat-3708	57	4	-	-	PUNCT
easat-3708	57	5	level	level	NOUN
easat-3708	57	6	sets	set	NOUN
easat-3708	57	7	of	of	ADP
easat-3708	57	8	fuzzy	fuzzy	ADJ
easat-3708	57	9	numbers	number	NOUN
easat-3708	57	10	,	,	PUNCT
easat-3708	57	11	the	the	DET
easat-3708	57	12	corresponding	corresponding	ADJ
easat-3708	57	13	non	non	ADJ
easat-3708	57	14	-	-	ADJ
easat-3708	57	15	fuzzy	fuzzy	ADJ
easat-3708	57	16	α	α	NOUN
easat-3708	57	17	-	-	ADJ
easat-3708	57	18	multi	multi	ADJ
easat-3708	57	19	-	-	ADJ
easat-3708	57	20	objective	objective	ADJ
easat-3708	57	21	linear	linear	ADJ
easat-3708	57	22	fractional	fractional	ADJ
easat-3708	57	23	programming	programming	NOUN
easat-3708	57	24	problem	problem	NOUN
easat-3708	57	25	is	be	AUX
easat-3708	57	26	introduced	introduce	VERB
easat-3708	57	27	.	.	PUNCT
easat-3708	58	1	the	the	DET
easat-3708	58	2	fuzzy	fuzzy	ADJ
easat-3708	58	3	goals	goal	NOUN
easat-3708	58	4	of	of	ADP
easat-3708	58	5	the	the	DET
easat-3708	58	6	decision	decision	NOUN
easat-3708	58	7	maker	maker	NOUN
easat-3708	58	8	for	for	ADP
easat-3708	58	9	the	the	DET
easat-3708	58	10	objective	objective	ADJ
easat-3708	58	11	functions	function	NOUN
easat-3708	58	12	are	be	AUX
easat-3708	58	13	quantified	quantify	VERB
easat-3708	58	14	by	by	ADP
easat-3708	58	15	eliciting	elicit	VERB
easat-3708	58	16	the	the	DET
easat-3708	58	17	corresponding	correspond	VERB
easat-3708	58	18	membership	membership	NOUN
easat-3708	58	19	functions	function	NOUN
easat-3708	58	20	,	,	PUNCT
easat-3708	58	21	including	include	VERB
easat-3708	58	22	nonlinear	nonlinear	ADJ
easat-3708	58	23	ones	one	NOUN
easat-3708	58	24	.	.	PUNCT
easat-3708	59	1	through	through	ADP
easat-3708	59	2	the	the	DET
easat-3708	59	3	introduction	introduction	NOUN
easat-3708	59	4	of	of	ADP
easat-3708	59	5	extended	extended	ADJ
easat-3708	59	6	pareto	pareto	ADJ
easat-3708	59	7	optimality	optimality	NOUN
easat-3708	59	8	concepts	concept	NOUN
easat-3708	59	9	,	,	PUNCT
easat-3708	59	10	if	if	SCONJ
easat-3708	59	11	the	the	DET
easat-3708	59	12	decision	decision	NOUN
easat-3708	59	13	maker	maker	NOUN
easat-3708	59	14	specifies	specify	VERB
easat-3708	59	15	the	the	DET
easat-3708	59	16	degree	degree	NOUN
easat-3708	59	17	α	α	NOUN
easat-3708	59	18	and	and	CCONJ
easat-3708	59	19	the	the	DET
easat-3708	59	20	reference	reference	NOUN
easat-3708	59	21	membership	membership	NOUN
easat-3708	59	22	values	value	NOUN
easat-3708	59	23	,	,	PUNCT
easat-3708	59	24	the	the	DET
easat-3708	59	25	corresponding	corresponding	ADJ
easat-3708	59	26	extended	extend	VERB
easat-3708	59	27	pareto	pareto	ADJ
easat-3708	59	28	optimal	optimal	ADJ
easat-3708	59	29	solution	solution	NOUN
easat-3708	59	30	can	can	AUX
easat-3708	59	31	be	be	AUX
easat-3708	59	32	obtained	obtain	VERB
easat-3708	59	33	by	by	ADP
easat-3708	59	34	solving	solve	VERB
easat-3708	59	35	the	the	DET
easat-3708	59	36	minimax	minimax	NOUN
easat-3708	59	37	problems	problem	NOUN
easat-3708	59	38	for	for	ADP
easat-3708	59	39	which	which	PRON
easat-3708	59	40	the	the	DET
easat-3708	59	41	dantzig	dantzig	PROPN
easat-3708	59	42	-	-	PUNCT
easat-3708	59	43	wolfe	wolfe	PROPN
easat-3708	59	44	decomposition	decomposition	NOUN
easat-3708	59	45	method	method	NOUN
easat-3708	59	46	and	and	CCONJ
easat-3708	59	47	ritter	ritter	NOUN
easat-3708	59	48	’s	’s	PART
easat-3708	59	49	partitioning	partition	VERB
easat-3708	59	50	procedure	procedure	NOUN
easat-3708	59	51	are	be	AUX
easat-3708	59	52	applicable	applicable	ADJ
easat-3708	59	53	.	.	PUNCT
easat-3708	60	1	jiao	jiao	PROPN
easat-3708	60	2	et	et	PROPN
easat-3708	60	3	al	al	PROPN
easat-3708	60	4	.	.	PUNCT
easat-3708	61	1	[	[	X
easat-3708	61	2	14	14	NUM
easat-3708	61	3	]	]	PUNCT
easat-3708	61	4	,	,	PUNCT
easat-3708	61	5	presented	present	VERB
easat-3708	61	6	a	a	DET
easat-3708	61	7	branch	branch	NOUN
easat-3708	61	8	-	-	PUNCT
easat-3708	61	9	and	and	CCONJ
easat-3708	61	10	-	-	PUNCT
easat-3708	61	11	bound	bind	VERB
easat-3708	61	12	algorithm	algorithm	NOUN
easat-3708	61	13	for	for	ADP
easat-3708	61	14	globally	globally	ADV
easat-3708	61	15	solving	solve	VERB
easat-3708	61	16	a	a	DET
easat-3708	61	17	wide	wide	ADJ
easat-3708	61	18	class	class	NOUN
easat-3708	61	19	of	of	ADP
easat-3708	61	20	generalized	generalized	ADJ
easat-3708	61	21	linear	linear	ADJ
easat-3708	61	22	fractional	fractional	ADJ
easat-3708	61	23	programming	programming	NOUN
easat-3708	61	24	problems	problem	NOUN
easat-3708	61	25	(	(	PUNCT
easat-3708	61	26	glfp	glfp	NOUN
easat-3708	61	27	)	)	PUNCT
easat-3708	61	28	.	.	PUNCT
easat-3708	62	1	this	this	DET
easat-3708	62	2	class	class	NOUN
easat-3708	62	3	included	include	VERB
easat-3708	62	4	such	such	ADJ
easat-3708	62	5	problems	problem	NOUN
easat-3708	62	6	as	as	ADP
easat-3708	62	7	:	:	PUNCT
easat-3708	62	8	minimizing	minimize	VERB
easat-3708	62	9	a	a	DET
easat-3708	62	10	sum	sum	NOUN
easat-3708	62	11	,	,	PUNCT
easat-3708	62	12	or	or	CCONJ
easat-3708	62	13	error	error	NOUN
easat-3708	62	14	for	for	ADP
easat-3708	62	15	product	product	NOUN
easat-3708	62	16	of	of	ADP
easat-3708	62	17	a	a	DET
easat-3708	62	18	finite	finite	ADJ
easat-3708	62	19	number	number	NOUN
easat-3708	62	20	of	of	ADP
easat-3708	62	21	ratios	ratio	NOUN
easat-3708	62	22	of	of	ADP
easat-3708	62	23	linear	linear	PROPN
easat-3708	62	24	functions	function	NOUN
easat-3708	62	25	,	,	PUNCT
easat-3708	62	26	linear	linear	PROPN
easat-3708	62	27	multiplicative	multiplicative	ADJ
easat-3708	62	28	programming	programming	NOUN
easat-3708	62	29	,	,	PUNCT
easat-3708	62	30	polynomial	polynomial	ADJ
easat-3708	62	31	programming	programming	NOUN
easat-3708	62	32	,	,	PUNCT
easat-3708	62	33	etc	etc	X
easat-3708	62	34	.	.	X
easat-3708	62	35	over	over	ADP
easat-3708	62	36	nonconvex	nonconvex	NOUN
easat-3708	62	37	feasible	feasible	ADJ
easat-3708	62	38	region	region	NOUN
easat-3708	62	39	.	.	PUNCT
easat-3708	63	1	first	first	ADV
easat-3708	63	2	a	a	DET
easat-3708	63	3	problem	problem	NOUN
easat-3708	63	4	(	(	PUNCT
easat-3708	63	5	q	q	X
easat-3708	63	6	)	)	PUNCT
easat-3708	63	7	was	be	AUX
easat-3708	63	8	derived	derive	VERB
easat-3708	63	9	equivalent	equivalent	ADJ
easat-3708	63	10	to	to	ADP
easat-3708	63	11	problem	problem	NOUN
easat-3708	63	12	(	(	PUNCT
easat-3708	63	13	glfp	glfp	NOUN
easat-3708	63	14	)	)	PUNCT
easat-3708	63	15	.	.	PUNCT
easat-3708	64	1	in	in	ADP
easat-3708	64	2	the	the	DET
easat-3708	64	3	algorithm	algorithm	NOUN
easat-3708	64	4	,	,	PUNCT
easat-3708	64	5	lower	low	ADJ
easat-3708	64	6	bounds	bound	NOUN
easat-3708	64	7	were	be	AUX
easat-3708	64	8	derived	derive	VERB
easat-3708	64	9	by	by	ADP
easat-3708	64	10	solving	solve	VERB
easat-3708	64	11	a	a	DET
easat-3708	64	12	sequence	sequence	NOUN
easat-3708	64	13	of	of	ADP
easat-3708	64	14	linear	linear	ADJ
easat-3708	64	15	relaxation	relaxation	NOUN
easat-3708	64	16	programming	programming	NOUN
easat-3708	64	17	problems	problem	NOUN
easat-3708	64	18	,	,	PUNCT
easat-3708	64	19	which	which	PRON
easat-3708	64	20	was	be	AUX
easat-3708	64	21	7804	7804	NUM
easat-3708	64	22	edelweiss	edelweiss	PROPN
easat-3708	64	23	applied	apply	VERB
easat-3708	64	24	science	science	NOUN
easat-3708	64	25	and	and	CCONJ
easat-3708	64	26	technology	technology	NOUN
easat-3708	64	27	issn	issn	PROPN
easat-3708	64	28	:	:	PUNCT
easat-3708	64	29	2576	2576	NUM
easat-3708	64	30	-	-	SYM
easat-3708	64	31	8484	8484	NUM
easat-3708	64	32	vol	vol	NOUN
easat-3708	64	33	.	.	PROPN
easat-3708	65	1	8	8	NUM
easat-3708	65	2	,	,	PUNCT
easat-3708	65	3	no	no	INTJ
easat-3708	65	4	.	.	NOUN
easat-3708	65	5	6	6	NUM
easat-3708	65	6	:	:	SYM
easat-3708	65	7	7802	7802	NUM
easat-3708	65	8	-	-	SYM
easat-3708	65	9	7812	7812	NUM
easat-3708	65	10	,	,	PUNCT
easat-3708	65	11	2024	2024	NUM
easat-3708	65	12	doi	doi	NOUN
easat-3708	65	13	:	:	PUNCT
easat-3708	65	14	10.55214/25768484.v8i6.3708	10.55214/25768484.v8i6.3708	NUM
easat-3708	65	15	©	©	PROPN
easat-3708	65	16	2024	2024	NUM
easat-3708	65	17	by	by	ADP
easat-3708	65	18	the	the	DET
easat-3708	65	19	authors	author	NOUN
easat-3708	65	20	;	;	PUNCT
easat-3708	65	21	licensee	licensee	PROPN
easat-3708	65	22	learning	learning	NOUN
easat-3708	65	23	gate	gate	NOUN
easat-3708	65	24	based	base	VERB
easat-3708	65	25	on	on	ADP
easat-3708	65	26	the	the	DET
easat-3708	65	27	construction	construction	NOUN
easat-3708	65	28	of	of	ADP
easat-3708	65	29	the	the	DET
easat-3708	65	30	linear	linear	NOUN
easat-3708	65	31	lower	low	ADJ
easat-3708	65	32	bounding	bounding	NOUN
easat-3708	65	33	functions	function	NOUN
easat-3708	65	34	for	for	ADP
easat-3708	65	35	the	the	DET
easat-3708	65	36	objective	objective	ADJ
easat-3708	65	37	function	function	NOUN
easat-3708	65	38	and	and	CCONJ
easat-3708	65	39	constraint	constraint	NOUN
easat-3708	65	40	functions	function	NOUN
easat-3708	65	41	of	of	ADP
easat-3708	65	42	the	the	DET
easat-3708	65	43	problem	problem	NOUN
easat-3708	65	44	(	(	PUNCT
easat-3708	65	45	q	q	X
easat-3708	65	46	)	)	PUNCT
easat-3708	65	47	over	over	ADP
easat-3708	65	48	the	the	DET
easat-3708	65	49	feasible	feasible	ADJ
easat-3708	65	50	region	region	NOUN
easat-3708	65	51	.	.	PUNCT
easat-3708	66	1	shen	shen	PROPN
easat-3708	66	2	et	et	PROPN
easat-3708	66	3	al	al	PROPN
easat-3708	66	4	.	.	PUNCT
easat-3708	67	1	[	[	X
easat-3708	67	2	26	26	NUM
easat-3708	67	3	]	]	PUNCT
easat-3708	67	4	,	,	PUNCT
easat-3708	67	5	proposed	propose	VERB
easat-3708	67	6	an	an	DET
easat-3708	67	7	interactive	interactive	ADJ
easat-3708	67	8	fuzzy	fuzzy	ADJ
easat-3708	67	9	programming	programming	NOUN
easat-3708	67	10	method	method	NOUN
easat-3708	67	11	for	for	ADP
easat-3708	67	12	seeking	seek	VERB
easat-3708	67	13	a	a	DET
easat-3708	67	14	satisfactory	satisfactory	ADJ
easat-3708	67	15	solution	solution	NOUN
easat-3708	67	16	for	for	ADP
easat-3708	67	17	multi	multi	ADJ
easat-3708	67	18	-	-	ADJ
easat-3708	67	19	objective	objective	ADJ
easat-3708	67	20	two	two	NUM
easat-3708	67	21	-	-	PUNCT
easat-3708	67	22	level	level	NOUN
easat-3708	67	23	linear	linear	ADJ
easat-3708	67	24	fractional	fractional	ADJ
easat-3708	67	25	programming	programming	NOUN
easat-3708	67	26	problems	problem	NOUN
easat-3708	67	27	in	in	ADP
easat-3708	67	28	which	which	PRON
easat-3708	67	29	the	the	DET
easat-3708	67	30	decision	decision	NOUN
easat-3708	67	31	makers	maker	NOUN
easat-3708	67	32	in	in	ADP
easat-3708	67	33	the	the	DET
easat-3708	67	34	upper	upper	ADJ
easat-3708	67	35	and	and	CCONJ
easat-3708	67	36	lower	low	ADJ
easat-3708	67	37	levels	level	NOUN
easat-3708	67	38	have	have	VERB
easat-3708	67	39	several	several	ADJ
easat-3708	67	40	objectives	objective	NOUN
easat-3708	67	41	,	,	PUNCT
easat-3708	67	42	by	by	ADP
easat-3708	67	43	first	first	ADV
easat-3708	67	44	setting	set	VERB
easat-3708	67	45	up	up	ADP
easat-3708	67	46	the	the	DET
easat-3708	67	47	fuzzy	fuzzy	ADJ
easat-3708	67	48	goals	goal	NOUN
easat-3708	67	49	for	for	ADP
easat-3708	67	50	several	several	ADJ
easat-3708	67	51	objectives	objective	NOUN
easat-3708	67	52	of	of	ADP
easat-3708	67	53	each	each	DET
easat-3708	67	54	decision	decision	NOUN
easat-3708	67	55	maker	maker	NOUN
easat-3708	67	56	and	and	CCONJ
easat-3708	67	57	seeking	seek	VERB
easat-3708	67	58	a	a	DET
easat-3708	67	59	satisfactory	satisfactory	ADJ
easat-3708	67	60	solution	solution	NOUN
easat-3708	67	61	for	for	ADP
easat-3708	67	62	the	the	DET
easat-3708	67	63	degree	degree	NOUN
easat-3708	67	64	of	of	ADP
easat-3708	67	65	satisfaction	satisfaction	NOUN
easat-3708	67	66	of	of	ADP
easat-3708	67	67	two	two	NUM
easat-3708	67	68	decision	decision	NOUN
easat-3708	67	69	makers	maker	NOUN
easat-3708	67	70	in	in	ADP
easat-3708	67	71	a	a	DET
easat-3708	67	72	cooperative	cooperative	ADJ
easat-3708	67	73	manner	manner	NOUN
easat-3708	67	74	.	.	PUNCT
easat-3708	68	1	in	in	ADP
easat-3708	68	2	the	the	DET
easat-3708	68	3	proposed	propose	VERB
easat-3708	68	4	method	method	NOUN
easat-3708	68	5	,	,	PUNCT
easat-3708	68	6	the	the	DET
easat-3708	68	7	decision	decision	NOUN
easat-3708	68	8	maker	maker	NOUN
easat-3708	68	9	at	at	ADP
easat-3708	68	10	the	the	DET
easat-3708	68	11	upper	upper	ADJ
easat-3708	68	12	level	level	NOUN
easat-3708	68	13	sets	set	VERB
easat-3708	68	14	the	the	DET
easat-3708	68	15	minimal	minimal	ADJ
easat-3708	68	16	satisfactory	satisfactory	ADJ
easat-3708	68	17	levels	level	NOUN
easat-3708	68	18	for	for	ADP
easat-3708	68	19	each	each	DET
easat-3708	68	20	fuzzy	fuzzy	ADJ
easat-3708	68	21	goal	goal	NOUN
easat-3708	68	22	.	.	PUNCT
easat-3708	69	1	the	the	DET
easat-3708	69	2	decision	decision	NOUN
easat-3708	69	3	-	-	PUNCT
easat-3708	69	4	maker	maker	NOUN
easat-3708	69	5	at	at	ADP
easat-3708	69	6	the	the	DET
easat-3708	69	7	lower	low	ADJ
easat-3708	69	8	level	level	NOUN
easat-3708	69	9	determines	determine	VERB
easat-3708	69	10	the	the	DET
easat-3708	69	11	aspiration	aspiration	NOUN
easat-3708	69	12	levels	level	NOUN
easat-3708	69	13	.	.	PUNCT
easat-3708	70	1	the	the	DET
easat-3708	70	2	minimal	minimal	ADJ
easat-3708	70	3	satisfactory	satisfactory	ADJ
easat-3708	70	4	levels	level	NOUN
easat-3708	70	5	were	be	AUX
easat-3708	70	6	treated	treat	VERB
easat-3708	70	7	as	as	ADP
easat-3708	70	8	a	a	DET
easat-3708	70	9	constraint	constraint	NOUN
easat-3708	70	10	and	and	CCONJ
easat-3708	70	11	the	the	DET
easat-3708	70	12	solution	solution	NOUN
easat-3708	70	13	closest	close	ADJ
easat-3708	70	14	to	to	ADP
easat-3708	70	15	the	the	DET
easat-3708	70	16	aspiration	aspiration	NOUN
easat-3708	70	17	levels	level	NOUN
easat-3708	70	18	of	of	ADP
easat-3708	70	19	the	the	DET
easat-3708	70	20	decision	decision	NOUN
easat-3708	70	21	maker	maker	NOUN
easat-3708	70	22	at	at	ADP
easat-3708	70	23	the	the	DET
easat-3708	70	24	lower	low	ADJ
easat-3708	70	25	level	level	NOUN
easat-3708	70	26	is	be	AUX
easat-3708	70	27	computed	compute	VERB
easat-3708	70	28	.	.	PUNCT
easat-3708	71	1	the	the	DET
easat-3708	71	2	ratio	ratio	NOUN
easat-3708	71	3	of	of	ADP
easat-3708	71	4	the	the	DET
easat-3708	71	5	aggregative	aggregative	ADJ
easat-3708	71	6	degrees	degree	NOUN
easat-3708	71	7	of	of	ADP
easat-3708	71	8	satisfaction	satisfaction	NOUN
easat-3708	71	9	of	of	ADP
easat-3708	71	10	the	the	DET
easat-3708	71	11	decision	decision	NOUN
easat-3708	71	12	makers	maker	NOUN
easat-3708	71	13	in	in	ADP
easat-3708	71	14	the	the	DET
easat-3708	71	15	upper	upper	ADJ
easat-3708	71	16	and	and	CCONJ
easat-3708	71	17	lower	low	ADJ
easat-3708	71	18	levels	level	NOUN
easat-3708	71	19	with	with	ADP
easat-3708	71	20	the	the	DET
easat-3708	71	21	obtained	obtain	VERB
easat-3708	71	22	solution	solution	NOUN
easat-3708	71	23	is	be	AUX
easat-3708	71	24	evaluated	evaluate	VERB
easat-3708	71	25	by	by	ADP
easat-3708	71	26	using	use	VERB
easat-3708	71	27	partial	partial	ADJ
easat-3708	71	28	information	information	NOUN
easat-3708	71	29	on	on	ADP
easat-3708	71	30	the	the	DET
easat-3708	71	31	preference	preference	NOUN
easat-3708	71	32	of	of	ADP
easat-3708	71	33	the	the	DET
easat-3708	71	34	decision	decision	NOUN
easat-3708	71	35	makers	maker	NOUN
easat-3708	71	36	.	.	PUNCT
easat-3708	72	1	chun	chun	PROPN
easat-3708	72	2	-	-	PUNCT
easat-3708	72	3	feng	feng	PROPN
easat-3708	72	4	and	and	CCONJ
easat-3708	72	5	pei	pei	PROPN
easat-3708	72	6	-	-	PUNCT
easat-3708	72	7	ping	ping	NOUN
easat-3708	73	1	[	[	X
easat-3708	73	2	6	6	NUM
easat-3708	73	3	]	]	PUNCT
easat-3708	73	4	,	,	PUNCT
easat-3708	73	5	presented	present	VERB
easat-3708	73	6	an	an	DET
easat-3708	73	7	efficient	efficient	ADJ
easat-3708	73	8	branch	branch	NOUN
easat-3708	73	9	and	and	CCONJ
easat-3708	73	10	bound	bind	VERB
easat-3708	73	11	method	method	NOUN
easat-3708	73	12	for	for	ADP
easat-3708	73	13	general	general	ADJ
easat-3708	73	14	linear	linear	ADJ
easat-3708	73	15	fractional	fractional	ADJ
easat-3708	73	16	problem	problem	NOUN
easat-3708	73	17	(	(	PUNCT
easat-3708	73	18	gfp	gfp	PROPN
easat-3708	73	19	)	)	PUNCT
easat-3708	73	20	.	.	PUNCT
easat-3708	74	1	first	first	ADV
easat-3708	74	2	,	,	PUNCT
easat-3708	74	3	using	use	VERB
easat-3708	74	4	a	a	DET
easat-3708	74	5	transformation	transformation	NOUN
easat-3708	74	6	technique	technique	NOUN
easat-3708	74	7	,	,	PUNCT
easat-3708	74	8	an	an	DET
easat-3708	74	9	equivalent	equivalent	ADJ
easat-3708	74	10	problem	problem	NOUN
easat-3708	74	11	(	(	PUNCT
easat-3708	74	12	ep	ep	PROPN
easat-3708	74	13	)	)	PUNCT
easat-3708	74	14	of	of	ADP
easat-3708	74	15	gfp	gfp	PROPN
easat-3708	74	16	was	be	AUX
easat-3708	74	17	derived	derive	VERB
easat-3708	74	18	,	,	PUNCT
easat-3708	74	19	then	then	ADV
easat-3708	74	20	by	by	ADP
easat-3708	74	21	exploiting	exploit	VERB
easat-3708	74	22	structure	structure	NOUN
easat-3708	74	23	of	of	ADP
easat-3708	74	24	ep	ep	PROPN
easat-3708	74	25	,	,	PUNCT
easat-3708	74	26	a	a	DET
easat-3708	74	27	linear	linear	ADJ
easat-3708	74	28	relaxation	relaxation	NOUN
easat-3708	74	29	programming	programming	NOUN
easat-3708	74	30	(	(	PUNCT
easat-3708	74	31	lrp	lrp	PROPN
easat-3708	74	32	)	)	PUNCT
easat-3708	74	33	of	of	ADP
easat-3708	74	34	ep	ep	PROPN
easat-3708	74	35	was	be	AUX
easat-3708	74	36	obtained	obtain	VERB
easat-3708	74	37	.	.	PUNCT
easat-3708	75	1	to	to	PART
easat-3708	75	2	implement	implement	VERB
easat-3708	75	3	the	the	DET
easat-3708	75	4	algorithm	algorithm	NOUN
easat-3708	75	5	,	,	PUNCT
easat-3708	75	6	primary	primary	ADJ
easat-3708	75	7	computation	computation	NOUN
easat-3708	75	8	involve	involve	VERB
easat-3708	75	9	solving	solve	VERB
easat-3708	75	10	a	a	DET
easat-3708	75	11	sequence	sequence	NOUN
easat-3708	75	12	of	of	ADP
easat-3708	75	13	linear	linear	ADJ
easat-3708	75	14	programming	programming	NOUN
easat-3708	75	15	problem	problem	NOUN
easat-3708	75	16	,	,	PUNCT
easat-3708	75	17	which	which	PRON
easat-3708	75	18	could	could	AUX
easat-3708	75	19	be	be	AUX
easat-3708	75	20	solved	solve	VERB
easat-3708	75	21	efficiently	efficiently	ADV
easat-3708	75	22	.	.	PUNCT
easat-3708	76	1	the	the	DET
easat-3708	76	2	proposed	propose	VERB
easat-3708	76	3	algorithm	algorithm	NOUN
easat-3708	76	4	converged	converge	VERB
easat-3708	76	5	to	to	ADP
easat-3708	76	6	the	the	DET
easat-3708	76	7	global	global	ADJ
easat-3708	76	8	maximum	maximum	NOUN
easat-3708	76	9	through	through	ADP
easat-3708	76	10	the	the	DET
easat-3708	76	11	successive	successive	ADJ
easat-3708	76	12	refinement	refinement	NOUN
easat-3708	76	13	of	of	ADP
easat-3708	76	14	the	the	DET
easat-3708	76	15	solutions	solution	NOUN
easat-3708	76	16	of	of	ADP
easat-3708	76	17	a	a	DET
easat-3708	76	18	series	series	NOUN
easat-3708	76	19	of	of	ADP
easat-3708	76	20	linear	linear	PROPN
easat-3708	76	21	programming	programming	NOUN
easat-3708	76	22	problems	problem	NOUN
easat-3708	76	23	.	.	PUNCT
easat-3708	77	1	d’amato	d’amato	NOUN
easat-3708	77	2	and	and	CCONJ
easat-3708	77	3	bernstein	bernstein	PROPN
easat-3708	78	1	[	[	X
easat-3708	78	2	8	8	NUM
easat-3708	78	3	]	]	PUNCT
easat-3708	78	4	,	,	PUNCT
easat-3708	78	5	used	use	VERB
easat-3708	78	6	retrospective	retrospective	ADJ
easat-3708	78	7	cost	cost	NOUN
easat-3708	78	8	optimization	optimization	NOUN
easat-3708	78	9	to	to	PART
easat-3708	78	10	determine	determine	VERB
easat-3708	78	11	linear	linear	ADJ
easat-3708	78	12	fractional	fractional	ADJ
easat-3708	78	13	transformations	transformation	NOUN
easat-3708	78	14	(	(	PUNCT
easat-3708	78	15	lfts	lft	NOUN
easat-3708	78	16	)	)	PUNCT
easat-3708	78	17	.	.	PUNCT
easat-3708	79	1	this	this	DET
easat-3708	79	2	method	method	NOUN
easat-3708	79	3	used	use	VERB
easat-3708	79	4	an	an	DET
easat-3708	79	5	adaptive	adaptive	ADJ
easat-3708	79	6	controller	controller	NOUN
easat-3708	79	7	in	in	ADP
easat-3708	79	8	feedback	feedback	NOUN
easat-3708	79	9	with	with	ADP
easat-3708	79	10	a	a	DET
easat-3708	79	11	known	know	VERB
easat-3708	79	12	system	system	NOUN
easat-3708	79	13	model	model	NOUN
easat-3708	79	14	.	.	PUNCT
easat-3708	80	1	the	the	DET
easat-3708	80	2	goal	goal	NOUN
easat-3708	80	3	was	be	AUX
easat-3708	80	4	to	to	PART
easat-3708	80	5	identify	identify	VERB
easat-3708	80	6	the	the	DET
easat-3708	80	7	feedback	feedback	NOUN
easat-3708	80	8	portion	portion	NOUN
easat-3708	80	9	of	of	ADP
easat-3708	80	10	the	the	DET
easat-3708	80	11	lft	lft	NOUN
easat-3708	80	12	by	by	ADP
easat-3708	80	13	adapting	adapt	VERB
easat-3708	80	14	the	the	DET
easat-3708	80	15	controller	controller	NOUN
easat-3708	80	16	with	with	ADP
easat-3708	80	17	a	a	DET
easat-3708	80	18	retrospective	retrospective	ADJ
easat-3708	80	19	cost	cost	NOUN
easat-3708	80	20	.	.	PUNCT
easat-3708	81	1	d’amato	d’amato	NOUN
easat-3708	81	2	and	and	CCONJ
easat-3708	81	3	bernstein	bernstein	PROPN
easat-3708	82	1	[	[	X
easat-3708	82	2	8	8	NUM
easat-3708	82	3	]	]	PUNCT
easat-3708	82	4	demonstrated	demonstrate	VERB
easat-3708	82	5	this	this	DET
easat-3708	82	6	method	method	NOUN
easat-3708	82	7	on	on	ADP
easat-3708	82	8	numerical	numerical	ADJ
easat-3708	82	9	examples	example	NOUN
easat-3708	82	10	of	of	ADP
easat-3708	82	11	increasing	increase	VERB
easat-3708	82	12	complexity	complexity	NOUN
easat-3708	82	13	,	,	PUNCT
easat-3708	82	14	ranging	range	VERB
easat-3708	82	15	from	from	ADP
easat-3708	82	16	linear	linear	ADJ
easat-3708	82	17	examples	example	NOUN
easat-3708	82	18	with	with	ADP
easat-3708	82	19	unknown	unknown	ADJ
easat-3708	82	20	feedback	feedback	NOUN
easat-3708	82	21	terms	term	NOUN
easat-3708	82	22	to	to	ADP
easat-3708	82	23	nonlinear	nonlinear	ADJ
easat-3708	82	24	examples	example	NOUN
easat-3708	82	25	.	.	PUNCT
easat-3708	83	1	sheikhi	sheikhi	PROPN
easat-3708	83	2	and	and	CCONJ
easat-3708	83	3	ebadi	ebadi	VERB
easat-3708	83	4	[	[	X
easat-3708	83	5	27	27	NUM
easat-3708	83	6	]	]	PUNCT
easat-3708	83	7	presented	present	VERB
easat-3708	83	8	a	a	DET
easat-3708	83	9	novel	novel	ADJ
easat-3708	83	10	method	method	NOUN
easat-3708	83	11	for	for	ADP
easat-3708	83	12	solving	solve	VERB
easat-3708	83	13	fractional	fractional	ADJ
easat-3708	83	14	transportation	transportation	NOUN
easat-3708	83	15	problems	problem	NOUN
easat-3708	83	16	(	(	PUNCT
easat-3708	83	17	ftps	ftps	PROPN
easat-3708	83	18	)	)	PUNCT
easat-3708	83	19	with	with	ADP
easat-3708	83	20	fuzzy	fuzzy	ADJ
easat-3708	83	21	numbers	number	NOUN
easat-3708	83	22	using	use	VERB
easat-3708	83	23	a	a	DET
easat-3708	83	24	ranking	rank	VERB
easat-3708	83	25	function	function	NOUN
easat-3708	83	26	.	.	PUNCT
easat-3708	84	1	the	the	DET
easat-3708	84	2	proposed	propose	VERB
easat-3708	84	3	method	method	NOUN
easat-3708	84	4	introduces	introduce	VERB
easat-3708	84	5	a	a	DET
easat-3708	84	6	transformation	transformation	NOUN
easat-3708	84	7	technique	technique	NOUN
easat-3708	84	8	that	that	PRON
easat-3708	84	9	converts	convert	VERB
easat-3708	84	10	an	an	DET
easat-3708	84	11	ftp	ftp	NOUN
easat-3708	84	12	with	with	ADP
easat-3708	84	13	fuzzy	fuzzy	ADJ
easat-3708	84	14	numbers	number	NOUN
easat-3708	84	15	into	into	ADP
easat-3708	84	16	an	an	DET
easat-3708	84	17	ftp	ftp	NOUN
easat-3708	84	18	with	with	ADP
easat-3708	84	19	crisp	crisp	ADJ
easat-3708	84	20	numbers	number	NOUN
easat-3708	84	21	by	by	ADP
easat-3708	84	22	employing	employ	VERB
easat-3708	84	23	the	the	DET
easat-3708	84	24	robust	robust	ADJ
easat-3708	84	25	ranking	ranking	ADJ
easat-3708	84	26	technique	technique	NOUN
easat-3708	84	27	.	.	PUNCT
easat-3708	85	1	then	then	ADV
easat-3708	85	2	,	,	PUNCT
easat-3708	85	3	they	they	PRON
easat-3708	85	4	formulated	formulate	VERB
easat-3708	85	5	two	two	NUM
easat-3708	85	6	transportation	transportation	NOUN
easat-3708	85	7	problems	problem	NOUN
easat-3708	85	8	,	,	PUNCT
easat-3708	85	9	one	one	NUM
easat-3708	85	10	for	for	ADP
easat-3708	85	11	maximization	maximization	NOUN
easat-3708	85	12	and	and	CCONJ
easat-3708	85	13	another	another	PRON
easat-3708	85	14	for	for	ADP
easat-3708	85	15	depreciation	depreciation	NOUN
easat-3708	85	16	,	,	PUNCT
easat-3708	85	17	based	base	VERB
easat-3708	85	18	on	on	ADP
easat-3708	85	19	the	the	DET
easat-3708	85	20	given	give	VERB
easat-3708	85	21	ftp	ftp	PROPN
easat-3708	85	22	.	.	PROPN
easat-3708	85	23	see	see	VERB
easat-3708	85	24	other	other	ADJ
easat-3708	85	25	works	work	NOUN
easat-3708	85	26	in	in	ADP
easat-3708	85	27	fuzzy	fuzzy	ADJ
easat-3708	85	28	in	in	ADP
easat-3708	85	29	[	[	X
easat-3708	85	30	2	2	NUM
easat-3708	85	31	,	,	PUNCT
easat-3708	85	32	11	11	NUM
easat-3708	85	33	,	,	PUNCT
easat-3708	85	34	12	12	NUM
easat-3708	85	35	,	,	PUNCT
easat-3708	85	36	19	19	NUM
easat-3708	85	37	,	,	PUNCT
easat-3708	85	38	20	20	NUM
easat-3708	85	39	,	,	PUNCT
easat-3708	85	40	22	22	NUM
easat-3708	85	41	,	,	PUNCT
easat-3708	85	42	21	21	NUM
easat-3708	85	43	,	,	PUNCT
easat-3708	85	44	25	25	NUM
easat-3708	85	45	]	]	PUNCT
easat-3708	85	46	.	.	PUNCT
easat-3708	86	1	a	a	DET
easat-3708	86	2	type	type	NOUN
easat-3708	86	3	of	of	ADP
easat-3708	86	4	fractional	fractional	ADJ
easat-3708	86	5	fuzzy	fuzzy	ADJ
easat-3708	86	6	number	number	NOUN
easat-3708	86	7	linear	linear	NOUN
easat-3708	86	8	programming	programming	NOUN
easat-3708	86	9	problem	problem	NOUN
easat-3708	86	10	(	(	PUNCT
easat-3708	86	11	ffnlpp	ffnlpp	NOUN
easat-3708	86	12	)	)	PUNCT
easat-3708	86	13	can	can	AUX
easat-3708	86	14	be	be	AUX
easat-3708	86	15	described	describe	VERB
easat-3708	86	16	as	as	SCONJ
easat-3708	86	17	follows	follow	VERB
easat-3708	86	18	:	:	PUNCT
easat-3708	86	19	max	max	PROPN
easat-3708	86	20	�	�	PROPN
easat-3708	86	21	̃	̃	PROPN
easat-3708	86	22	�	�	PROPN
easat-3708	86	23	𝑥+	𝑥+	SYM
easat-3708	86	24	�	�	PROPN
easat-3708	86	25	̃	̃	PROPN
easat-3708	86	26	�	�	PROPN
easat-3708	86	27	𝑐̃𝑥+	𝑐̃𝑥+	PROPN
easat-3708	86	28	�	�	PROPN
easat-3708	86	29	̃	̃	PROPN
easat-3708	86	30	�	�	PROPN
easat-3708	86	31	𝑠.	𝑠.	NOUN
easat-3708	86	32	𝑡.	𝑡.	NOUN
easat-3708	86	33	(	(	PUNCT
easat-3708	86	34	2	2	X
easat-3708	86	35	)	)	PUNCT
easat-3708	86	36	𝐴𝑥	𝐴𝑥	NOUN
easat-3708	86	37	≤	≤	NUM
easat-3708	86	38	ℎ	ℎ	PROPN
easat-3708	86	39	,	,	PUNCT
easat-3708	86	40	𝑥	𝑥	PRON
easat-3708	86	41	≥	≥	NOUN
easat-3708	86	42	0	0	NUM
easat-3708	86	43	,	,	PUNCT
easat-3708	86	44	where	where	SCONJ
easat-3708	86	45	,	,	PUNCT
easat-3708	86	46	�	�	PROPN
easat-3708	86	47	̃	̃	PROPN
easat-3708	86	48	�	�	PROPN
easat-3708	86	49	∈	∈	PROPN
easat-3708	86	50	𝐹(ℝ𝑛	𝐹(ℝ𝑛	NUM
easat-3708	86	51	)	)	PUNCT
easat-3708	86	52	,	,	PUNCT
easat-3708	86	53	�	�	PROPN
easat-3708	86	54	̃	̃	PROPN
easat-3708	86	55	�	�	PROPN
easat-3708	86	56	∈	∈	PROPN
easat-3708	86	57	𝐹(ℝ𝑛	𝐹(ℝ𝑛	NUM
easat-3708	86	58	)	)	PUNCT
easat-3708	86	59	,	,	PUNCT
easat-3708	86	60	�	�	PROPN
easat-3708	86	61	̃	̃	PROPN
easat-3708	86	62	�	�	PROPN
easat-3708	86	63	∈	∈	PROPN
easat-3708	86	64	𝐹(ℝ	𝐹(ℝ	NOUN
easat-3708	86	65	)	)	PUNCT
easat-3708	86	66	,	,	PUNCT
easat-3708	86	67	�	�	PROPN
easat-3708	86	68	̃	̃	PROPN
easat-3708	86	69	�	�	PROPN
easat-3708	86	70	∈	∈	PROPN
easat-3708	86	71	𝐹(ℝ	𝐹(ℝ	NOUN
easat-3708	86	72	)	)	PUNCT
easat-3708	86	73	,	,	PUNCT
easat-3708	86	74	𝑥	𝑥	PRON
easat-3708	86	75	∈	∈	PROPN
easat-3708	87	1	ℝ𝑛	ℝ𝑛	PROPN
easat-3708	87	2	,	,	PUNCT
easat-3708	87	3	𝐴	𝐴	PROPN
easat-3708	87	4	∈	∈	PROPN
easat-3708	87	5	ℝ𝑚×𝑛	ℝ𝑚×𝑛	NOUN
easat-3708	87	6	and	and	CCONJ
easat-3708	87	7	ℎ	ℎ	PART
easat-3708	87	8	∈	∈	PROPN
easat-3708	87	9	ℝ𝑚	ℝ𝑚	PROPN
easat-3708	87	10	,	,	PUNCT
easat-3708	87	11	with	with	ADP
easat-3708	87	12	𝐹(ℝ	𝐹(ℝ	NOUN
easat-3708	87	13	)	)	PUNCT
easat-3708	87	14	being	be	AUX
easat-3708	87	15	the	the	DET
easat-3708	87	16	set	set	NOUN
easat-3708	87	17	of	of	ADP
easat-3708	87	18	all	all	DET
easat-3708	87	19	fuzzy	fuzzy	ADJ
easat-3708	87	20	numbers	number	NOUN
easat-3708	87	21	.	.	PUNCT
easat-3708	88	1	for	for	ADP
easat-3708	88	2	solving	solve	VERB
easat-3708	88	3	(	(	PUNCT
easat-3708	88	4	2	2	NUM
easat-3708	88	5	)	)	PUNCT
easat-3708	88	6	,	,	PUNCT
easat-3708	88	7	we	we	PRON
easat-3708	88	8	propose	propose	VERB
easat-3708	88	9	a	a	DET
easat-3708	88	10	new	new	ADJ
easat-3708	88	11	fuzzy	fuzzy	ADJ
easat-3708	88	12	vns	vns	NOUN
easat-3708	88	13	algorithm	algorithm	NOUN
easat-3708	88	14	with	with	ADP
easat-3708	88	15	its	its	PRON
easat-3708	88	16	local	local	ADJ
easat-3708	88	17	search	search	NOUN
easat-3708	88	18	intended	intend	VERB
easat-3708	88	19	to	to	PART
easat-3708	88	20	find	find	VERB
easat-3708	88	21	a	a	DET
easat-3708	88	22	feasible	feasible	ADJ
easat-3708	88	23	solution	solution	NOUN
easat-3708	88	24	by	by	ADP
easat-3708	88	25	using	use	VERB
easat-3708	88	26	increasing	increase	VERB
easat-3708	88	27	directions	direction	NOUN
easat-3708	88	28	,	,	PUNCT
easat-3708	88	29	leading	lead	VERB
easat-3708	88	30	to	to	ADP
easat-3708	88	31	the	the	DET
easat-3708	88	32	value	value	NOUN
easat-3708	88	33	of	of	ADP
easat-3708	88	34	the	the	DET
easat-3708	88	35	objective	objective	ADJ
easat-3708	88	36	function	function	NOUN
easat-3708	88	37	being	be	AUX
easat-3708	88	38	more	more	ADV
easat-3708	88	39	significant	significant	ADJ
easat-3708	88	40	than	than	ADP
easat-3708	88	41	the	the	DET
easat-3708	88	42	current	current	ADJ
easat-3708	88	43	solution	solution	NOUN
easat-3708	88	44	.	.	PUNCT
easat-3708	89	1	in	in	ADP
easat-3708	89	2	our	our	PRON
easat-3708	89	3	proposed	propose	VERB
easat-3708	89	4	algorithm	algorithm	NOUN
easat-3708	89	5	,	,	PUNCT
easat-3708	89	6	we	we	PRON
easat-3708	89	7	compare	compare	VERB
easat-3708	89	8	the	the	DET
easat-3708	89	9	fuzzy	fuzzy	ADJ
easat-3708	89	10	value	value	NOUN
easat-3708	89	11	of	of	ADP
easat-3708	89	12	the	the	DET
easat-3708	89	13	objective	objective	ADJ
easat-3708	89	14	function	function	NOUN
easat-3708	89	15	using	use	VERB
easat-3708	89	16	the	the	DET
easat-3708	89	17	modified	modify	VERB
easat-3708	89	18	kerre	kerre	PROPN
easat-3708	89	19	’s	’s	PART
easat-3708	89	20	inequality	inequality	NOUN
easat-3708	89	21	.	.	PUNCT
easat-3708	90	1	using	use	VERB
easat-3708	90	2	kerre	kerre	PROPN
easat-3708	90	3	’s	’s	PART
easat-3708	90	4	inequality	inequality	NOUN
easat-3708	90	5	,	,	PUNCT
easat-3708	90	6	we	we	PRON
easat-3708	90	7	can	can	AUX
easat-3708	90	8	solve	solve	VERB
easat-3708	90	9	the	the	DET
easat-3708	90	10	problem	problem	NOUN
easat-3708	90	11	(	(	PUNCT
easat-3708	90	12	2	2	X
easat-3708	90	13	)	)	PUNCT
easat-3708	90	14	directly	directly	ADV
easat-3708	90	15	without	without	ADP
easat-3708	90	16	changing	change	VERB
easat-3708	90	17	it	it	PRON
easat-3708	90	18	to	to	ADP
easat-3708	90	19	the	the	DET
easat-3708	90	20	crisp	crisp	ADJ
easat-3708	90	21	problem	problem	NOUN
easat-3708	90	22	[	[	X
easat-3708	90	23	10	10	NUM
easat-3708	90	24	]	]	PUNCT
easat-3708	90	25	.	.	PUNCT
easat-3708	91	1	the	the	DET
easat-3708	91	2	rest	rest	NOUN
easat-3708	91	3	of	of	ADP
easat-3708	91	4	our	our	PRON
easat-3708	91	5	research	research	NOUN
easat-3708	91	6	is	be	AUX
easat-3708	91	7	structured	structure	VERB
easat-3708	91	8	in	in	ADP
easat-3708	91	9	the	the	DET
easat-3708	91	10	following	following	ADJ
easat-3708	91	11	manner	manner	NOUN
easat-3708	91	12	.	.	PUNCT
easat-3708	92	1	in	in	ADP
easat-3708	92	2	section	section	NOUN
easat-3708	92	3	2	2	NUM
easat-3708	92	4	,	,	PUNCT
easat-3708	92	5	we	we	PRON
easat-3708	92	6	provide	provide	VERB
easat-3708	92	7	some	some	DET
easat-3708	92	8	necessary	necessary	ADJ
easat-3708	92	9	definitions	definition	NOUN
easat-3708	92	10	,	,	PUNCT
easat-3708	92	11	properties	property	NOUN
easat-3708	92	12	of	of	ADP
easat-3708	92	13	fuzzy	fuzzy	ADJ
easat-3708	92	14	ordering	ordering	NOUN
easat-3708	92	15	and	and	CCONJ
easat-3708	92	16	fundamental	fundamental	ADJ
easat-3708	92	17	aspects	aspect	NOUN
easat-3708	92	18	of	of	ADP
easat-3708	92	19	modified	modify	VERB
easat-3708	92	20	kerre	kerre	PROPN
easat-3708	92	21	’s	’s	PART
easat-3708	92	22	method	method	NOUN
easat-3708	92	23	.	.	PUNCT
easat-3708	93	1	we	we	PRON
easat-3708	93	2	present	present	VERB
easat-3708	93	3	our	our	PRON
easat-3708	93	4	model	model	NOUN
easat-3708	93	5	in	in	ADP
easat-3708	93	6	section	section	NOUN
easat-3708	93	7	3	3	NUM
easat-3708	93	8	.	.	PUNCT
easat-3708	94	1	in	in	ADP
easat-3708	94	2	section	section	NOUN
easat-3708	94	3	4	4	NUM
easat-3708	94	4	,	,	PUNCT
easat-3708	94	5	we	we	PRON
easat-3708	94	6	first	first	ADV
easat-3708	94	7	talk	talk	VERB
easat-3708	94	8	about	about	ADP
easat-3708	94	9	our	our	PRON
easat-3708	94	10	vns	vns	NOUN
easat-3708	94	11	algorithm	algorithm	NOUN
easat-3708	94	12	for	for	ADP
easat-3708	94	13	solving	solve	VERB
easat-3708	94	14	our	our	PRON
easat-3708	94	15	proposed	propose	VERB
easat-3708	94	16	model	model	NOUN
easat-3708	94	17	,	,	PUNCT
easat-3708	94	18	then	then	ADV
easat-3708	94	19	to	to	PART
easat-3708	94	20	make	make	VERB
easat-3708	94	21	the	the	DET
easat-3708	94	22	algorithm	algorithm	NOUN
easat-3708	94	23	more	more	ADV
easat-3708	94	24	clear	clear	ADJ
easat-3708	94	25	we	we	PRON
easat-3708	94	26	implement	implement	VERB
easat-3708	94	27	our	our	PRON
easat-3708	94	28	proposed	propose	VERB
easat-3708	94	29	algorithm	algorithm	NOUN
easat-3708	94	30	on	on	ADP
easat-3708	94	31	an	an	DET
easat-3708	94	32	example	example	NOUN
easat-3708	94	33	.	.	PUNCT
easat-3708	95	1	we	we	PRON
easat-3708	95	2	test	test	VERB
easat-3708	95	3	our	our	PRON
easat-3708	95	4	algorithm	algorithm	NOUN
easat-3708	95	5	on	on	ADP
easat-3708	95	6	several	several	ADJ
easat-3708	95	7	examples	example	NOUN
easat-3708	95	8	in	in	ADP
easat-3708	95	9	section	section	NOUN
easat-3708	95	10	5	5	NUM
easat-3708	95	11	,	,	PUNCT
easat-3708	95	12	and	and	CCONJ
easat-3708	95	13	conclude	conclude	VERB
easat-3708	95	14	in	in	ADP
easat-3708	95	15	section	section	NOUN
easat-3708	95	16	6	6	NUM
easat-3708	95	17	.	.	NOUN
easat-3708	95	18	2	2	NUM
easat-3708	95	19	.	.	PUNCT
easat-3708	95	20	preliminaries	preliminary	NOUN
easat-3708	95	21	here	here	ADV
easat-3708	95	22	,	,	PUNCT
easat-3708	95	23	we	we	PRON
easat-3708	95	24	provide	provide	VERB
easat-3708	95	25	an	an	DET
easat-3708	95	26	overview	overview	NOUN
easat-3708	95	27	of	of	ADP
easat-3708	95	28	the	the	DET
easat-3708	95	29	basic	basic	ADJ
easat-3708	95	30	principles	principle	NOUN
easat-3708	95	31	of	of	ADP
easat-3708	95	32	fuzzy	fuzzy	ADJ
easat-3708	95	33	set	set	NOUN
easat-3708	95	34	theory	theory	NOUN
easat-3708	95	35	.	.	PUNCT
easat-3708	96	1	2.1	2.1	NUM
easat-3708	96	2	.	.	PUNCT
easat-3708	96	3	definitions	definition	NOUN
easat-3708	96	4	and	and	CCONJ
easat-3708	96	5	notation	notation	NOUN
easat-3708	96	6	definition	definition	NOUN
easat-3708	96	7	1	1	NUM
easat-3708	96	8	[	[	SYM
easat-3708	96	9	35	35	NUM
easat-3708	96	10	]	]	PUNCT
easat-3708	96	11	let	let	VERB
easat-3708	96	12	ℝ	ℝ	PRON
easat-3708	96	13	be	be	AUX
easat-3708	96	14	a	a	DET
easat-3708	96	15	collection	collection	NOUN
easat-3708	96	16	of	of	ADP
easat-3708	96	17	objects	object	NOUN
easat-3708	96	18	denoted	denote	VERB
easat-3708	96	19	by	by	ADP
easat-3708	96	20	𝑥.	𝑥.	NOUN
easat-3708	96	21	then	then	ADV
easat-3708	96	22	�	�	PROPN
easat-3708	96	23	̃	̃	PROPN
easat-3708	96	24	�	�	PROPN
easat-3708	96	25	is	be	AUX
easat-3708	96	26	called	call	VERB
easat-3708	96	27	a	a	DET
easat-3708	96	28	fuzzy	fuzzy	ADJ
easat-3708	96	29	set	set	NOUN
easat-3708	96	30	in	in	ADP
easat-3708	96	31	ℝ	ℝ	PROPN
easat-3708	96	32	,	,	PUNCT
easat-3708	96	33	if	if	SCONJ
easat-3708	96	34	�	�	PROPN
easat-3708	96	35	̃	̃	PROPN
easat-3708	96	36	�	�	PROPN
easat-3708	96	37	is	be	AUX
easat-3708	96	38	a	a	DET
easat-3708	96	39	set	set	NOUN
easat-3708	96	40	of	of	ADP
easat-3708	96	41	ordered	order	VERB
easat-3708	96	42	pairs	pair	NOUN
easat-3708	96	43	,	,	PUNCT
easat-3708	96	44	7805	7805	NUM
easat-3708	96	45	edelweiss	edelweiss	PROPN
easat-3708	96	46	applied	apply	VERB
easat-3708	96	47	science	science	NOUN
easat-3708	96	48	and	and	CCONJ
easat-3708	96	49	technology	technology	NOUN
easat-3708	96	50	issn	issn	PROPN
easat-3708	96	51	:	:	PUNCT
easat-3708	96	52	2576	2576	NUM
easat-3708	96	53	-	-	SYM
easat-3708	96	54	8484	8484	NUM
easat-3708	96	55	vol	vol	NOUN
easat-3708	96	56	.	.	PROPN
easat-3708	96	57	8	8	NUM
easat-3708	96	58	,	,	PUNCT
easat-3708	96	59	no	no	INTJ
easat-3708	96	60	.	.	NOUN
easat-3708	96	61	6	6	NUM
easat-3708	96	62	:	:	SYM
easat-3708	96	63	7802	7802	NUM
easat-3708	96	64	-	-	SYM
easat-3708	96	65	7812	7812	NUM
easat-3708	96	66	,	,	PUNCT
easat-3708	96	67	2024	2024	NUM
easat-3708	96	68	doi	doi	NOUN
easat-3708	96	69	:	:	PUNCT
easat-3708	96	70	10.55214/25768484.v8i6.3708	10.55214/25768484.v8i6.3708	NUM
easat-3708	96	71	©	©	PROPN
easat-3708	96	72	2024	2024	NUM
easat-3708	96	73	by	by	ADP
easat-3708	96	74	the	the	DET
easat-3708	96	75	authors	author	NOUN
easat-3708	96	76	;	;	PUNCT
easat-3708	96	77	licensee	licensee	PROPN
easat-3708	96	78	learning	learning	PROPN
easat-3708	96	79	gate	gate	PROPN
easat-3708	96	80	�	�	PROPN
easat-3708	96	81	̃	̃	PROPN
easat-3708	96	82	�	�	NOUN
easat-3708	96	83	=	=	SYM
easat-3708	96	84	{	{	PUNCT
easat-3708	96	85	(	(	PUNCT
easat-3708	96	86	𝑥	𝑥	NOUN
easat-3708	96	87	,	,	PUNCT
easat-3708	96	88	𝜇	𝜇	ADP
easat-3708	96	89	�	�	PROPN
easat-3708	96	90	̃	̃	NOUN
easat-3708	96	91	�	�	NOUN
easat-3708	96	92	(𝑥	(𝑥	NOUN
easat-3708	96	93	)	)	PUNCT
easat-3708	96	94	)	)	PUNCT
easat-3708	97	1	|	|	ADV
easat-3708	97	2	𝑥	𝑥	PRON
easat-3708	97	3	∈	∈	NOUN
easat-3708	97	4	ℝ	ℝ	PROPN
easat-3708	97	5	}	}	PUNCT
easat-3708	97	6	,	,	PUNCT
easat-3708	97	7	where	where	SCONJ
easat-3708	97	8	𝜇	𝜇	ADP
easat-3708	97	9	�	�	PROPN
easat-3708	97	10	̃	̃	NOUN
easat-3708	97	11	�	�	NOUN
easat-3708	97	12	(𝑥	(𝑥	NOUN
easat-3708	97	13	)	)	PUNCT
easat-3708	97	14	∈	∈	PROPN
easat-3708	98	1	[	[	X
easat-3708	98	2	0,1	0,1	NUM
easat-3708	98	3	]	]	PUNCT
easat-3708	98	4	is	be	AUX
easat-3708	98	5	called	call	VERB
easat-3708	98	6	the	the	DET
easat-3708	98	7	membership	membership	NOUN
easat-3708	98	8	function	function	NOUN
easat-3708	98	9	or	or	CCONJ
easat-3708	98	10	grade	grade	NOUN
easat-3708	98	11	of	of	ADP
easat-3708	98	12	membership	membership	NOUN
easat-3708	98	13	of	of	ADP
easat-3708	98	14	𝑥	𝑥	PROPN
easat-3708	98	15	in	in	ADP
easat-3708	98	16	�	�	PROPN
easat-3708	98	17	̃	̃	PROPN
easat-3708	98	18	�	�	PROPN
easat-3708	98	19	.	.	PUNCT
easat-3708	99	1	definition	definition	NOUN
easat-3708	99	2	2	2	NUM
easat-3708	99	3	[	[	X
easat-3708	99	4	29	29	NUM
easat-3708	99	5	]	]	X
easat-3708	99	6	a	a	DET
easat-3708	99	7	fuzzy	fuzzy	ADJ
easat-3708	99	8	number	number	NOUN
easat-3708	99	9	is	be	AUX
easat-3708	99	10	a	a	DET
easat-3708	99	11	fuzzy	fuzzy	ADJ
easat-3708	99	12	quantity	quantity	NOUN
easat-3708	99	13	�	�	PROPN
easat-3708	99	14	̃	̃	NOUN
easat-3708	99	15	�	�	NOUN
easat-3708	99	16	satisfying	satisfy	VERB
easat-3708	99	17	the	the	DET
easat-3708	99	18	following	follow	VERB
easat-3708	99	19	conditions	condition	NOUN
easat-3708	99	20	:	:	PUNCT
easat-3708	100	1	1	1	X
easat-3708	100	2	.	.	PUNCT
easat-3708	100	3	𝜇	𝜇	ADP
easat-3708	100	4	�	�	PROPN
easat-3708	100	5	̃	̃	PROPN
easat-3708	100	6	�	�	NOUN
easat-3708	100	7	(𝑥	(𝑥	NOUN
easat-3708	100	8	)	)	PUNCT
easat-3708	100	9	=	=	SYM
easat-3708	100	10	1	1	NUM
easat-3708	100	11	,	,	PUNCT
easat-3708	100	12	for	for	ADP
easat-3708	100	13	exactly	exactly	ADV
easat-3708	100	14	one	one	NUM
easat-3708	100	15	𝑥	𝑥	NOUN
easat-3708	100	16	.	.	PUNCT
easat-3708	101	1	2	2	X
easat-3708	101	2	.	.	PUNCT
easat-3708	102	1	the	the	DET
easat-3708	102	2	support	support	NOUN
easat-3708	102	3	{	{	PUNCT
easat-3708	102	4	𝑥	𝑥	NOUN
easat-3708	102	5	:	:	PUNCT
easat-3708	102	6	𝜇	𝜇	PART
easat-3708	102	7	�	�	PROPN
easat-3708	102	8	̃	̃	PROPN
easat-3708	102	9	�	�	NOUN
easat-3708	102	10	(𝑥	(𝑥	NOUN
easat-3708	102	11	)	)	PUNCT
easat-3708	102	12	>	>	X
easat-3708	102	13	0	0	NUM
easat-3708	102	14	}	}	PUNCT
easat-3708	102	15	of	of	ADP
easat-3708	102	16	�	�	PROPN
easat-3708	102	17	̃	̃	PROPN
easat-3708	102	18	�	�	PROPN
easat-3708	102	19	is	be	AUX
easat-3708	102	20	bounded	bound	VERB
easat-3708	102	21	.	.	PUNCT
easat-3708	103	1	3	3	X
easat-3708	103	2	.	.	PUNCT
easat-3708	104	1	the	the	DET
easat-3708	104	2	𝛼-cuts	𝛼-cut	NOUN
easat-3708	104	3	of	of	ADP
easat-3708	104	4	�	�	PROPN
easat-3708	104	5	̃	̃	PROPN
easat-3708	104	6	�	�	PROPN
easat-3708	104	7	are	be	AUX
easat-3708	104	8	closed	close	VERB
easat-3708	104	9	intervals	interval	NOUN
easat-3708	104	10	.	.	PUNCT
easat-3708	105	1	definition	definition	NOUN
easat-3708	105	2	3	3	NUM
easat-3708	105	3	[	[	X
easat-3708	105	4	35	35	NUM
easat-3708	105	5	]	]	X
easat-3708	105	6	a	a	DET
easat-3708	105	7	fuzzy	fuzzy	ADJ
easat-3708	105	8	number	number	NOUN
easat-3708	105	9	�	�	PROPN
easat-3708	105	10	̃	̃	PROPN
easat-3708	105	11	�	�	PROPN
easat-3708	105	12	is	be	AUX
easat-3708	105	13	of	of	ADP
easat-3708	105	14	lr	lr	NOUN
easat-3708	105	15	-	-	PUNCT
easat-3708	105	16	type	type	NOUN
easat-3708	105	17	if	if	SCONJ
easat-3708	105	18	there	there	PRON
easat-3708	105	19	exist	exist	VERB
easat-3708	105	20	shape	shape	NOUN
easat-3708	105	21	functions	function	NOUN
easat-3708	105	22	𝐿	𝐿	PROPN
easat-3708	105	23	(	(	PUNCT
easat-3708	105	24	for	for	ADP
easat-3708	105	25	left	left	ADJ
easat-3708	105	26	)	)	PUNCT
easat-3708	105	27	,	,	PUNCT
easat-3708	105	28	𝑅	𝑅	PROPN
easat-3708	105	29	(	(	PUNCT
easat-3708	105	30	for	for	ADP
easat-3708	105	31	right	right	NOUN
easat-3708	105	32	)	)	PUNCT
easat-3708	105	33	,	,	PUNCT
easat-3708	105	34	and	and	CCONJ
easat-3708	105	35	scalars	scalar	VERB
easat-3708	105	36	𝛼	𝛼	INTJ
easat-3708	105	37	>	>	X
easat-3708	105	38	0	0	PUNCT
easat-3708	105	39	and	and	CCONJ
easat-3708	105	40	𝛽	𝛽	NOUN
easat-3708	105	41	>	>	X
easat-3708	105	42	0	0	NUM
easat-3708	106	1	such	such	ADJ
easat-3708	106	2	that	that	SCONJ
easat-3708	106	3	𝜇	𝜇	ADP
easat-3708	106	4	�	�	PROPN
easat-3708	106	5	̃	̃	NOUN
easat-3708	106	6	�	�	NOUN
easat-3708	106	7	(𝑥	(𝑥	NOUN
easat-3708	106	8	)	)	PUNCT
easat-3708	106	9	=	=	SYM
easat-3708	106	10	{	{	PUNCT
easat-3708	106	11	𝐿	𝐿	PROPN
easat-3708	106	12	(	(	PUNCT
easat-3708	106	13	𝑎−𝑥	𝑎−𝑥	PROPN
easat-3708	106	14	𝛼	𝛼	X
easat-3708	106	15	)	)	PUNCT
easat-3708	106	16	,	,	PUNCT
easat-3708	106	17	𝑥	𝑥	PROPN
easat-3708	106	18	≤	≤	NUM
easat-3708	106	19	𝑎	𝑎	ADJ
easat-3708	106	20	,	,	PUNCT
easat-3708	106	21	𝑅	𝑅	PROPN
easat-3708	106	22	(	(	PUNCT
easat-3708	106	23	𝑥−𝑎	𝑥−𝑎	PROPN
easat-3708	106	24	𝛽	𝛽	PROPN
easat-3708	106	25	)	)	PUNCT
easat-3708	106	26	,	,	PUNCT
easat-3708	106	27	𝑥	𝑥	PROPN
easat-3708	106	28	≥	≥	NOUN
easat-3708	106	29	𝑎.	𝑎.	VERB
easat-3708	106	30	the	the	DET
easat-3708	106	31	mean	mean	ADJ
easat-3708	106	32	value	value	NOUN
easat-3708	106	33	of	of	ADP
easat-3708	106	34	�	�	PROPN
easat-3708	106	35	̃	̃	PROPN
easat-3708	106	36	�	�	PROPN
easat-3708	106	37	,	,	PUNCT
easat-3708	106	38	𝑎	𝑎	PROPN
easat-3708	106	39	,	,	PUNCT
easat-3708	106	40	is	be	AUX
easat-3708	106	41	a	a	DET
easat-3708	106	42	real	real	ADJ
easat-3708	106	43	number	number	NOUN
easat-3708	106	44	,	,	PUNCT
easat-3708	106	45	and	and	CCONJ
easat-3708	106	46	𝛼	𝛼	X
easat-3708	106	47	and	and	CCONJ
easat-3708	106	48	𝛽	𝛽	PROPN
easat-3708	106	49	are	be	AUX
easat-3708	106	50	called	call	VERB
easat-3708	106	51	the	the	DET
easat-3708	106	52	left	left	ADJ
easat-3708	106	53	and	and	CCONJ
easat-3708	106	54	right	right	ADJ
easat-3708	106	55	spreads	spread	NOUN
easat-3708	106	56	,	,	PUNCT
easat-3708	106	57	respectively	respectively	ADV
easat-3708	106	58	.	.	PUNCT
easat-3708	107	1	here	here	ADV
easat-3708	107	2	,	,	PUNCT
easat-3708	107	3	�	�	PROPN
easat-3708	107	4	̃	̃	PROPN
easat-3708	107	5	�	�	PROPN
easat-3708	107	6	is	be	AUX
easat-3708	107	7	denoted	denote	VERB
easat-3708	107	8	by	by	ADP
easat-3708	107	9	(	(	PUNCT
easat-3708	107	10	𝑎	𝑎	X
easat-3708	107	11	−	−	NOUN
easat-3708	107	12	𝛼/𝑎/𝑎	𝛼/𝑎/𝑎	NUM
easat-3708	107	13	+	+	X
easat-3708	107	14	𝛽)𝐿𝑅	𝛽)𝐿𝑅	X
easat-3708	107	15	.	.	PUNCT
easat-3708	108	1	remark	remark	NOUN
easat-3708	108	2	1	1	NUM
easat-3708	108	3	based	base	VERB
easat-3708	108	4	on	on	ADP
easat-3708	108	5	definition	definition	NOUN
easat-3708	108	6	3	3	NUM
easat-3708	108	7	,	,	PUNCT
easat-3708	108	8	another	another	DET
easat-3708	108	9	representation	representation	NOUN
easat-3708	108	10	of	of	ADP
easat-3708	108	11	an	an	DET
easat-3708	108	12	lr	lr	NOUN
easat-3708	108	13	fuzzy	fuzzy	ADJ
easat-3708	108	14	number	number	NOUN
easat-3708	108	15	�	�	PROPN
easat-3708	108	16	̃	̃	PROPN
easat-3708	108	17	�	�	PROPN
easat-3708	108	18	is	be	AUX
easat-3708	108	19	�	�	PROPN
easat-3708	108	20	̃	̃	NOUN
easat-3708	108	21	�	�	NOUN
easat-3708	108	22	=	=	SYM
easat-3708	108	23	(	(	PUNCT
easat-3708	108	24	𝐴𝐿	𝐴𝐿	PROPN
easat-3708	108	25	,	,	PUNCT
easat-3708	108	26	𝐴𝑅	𝐴𝑅	PROPN
easat-3708	108	27	)	)	PUNCT
easat-3708	108	28	,	,	PUNCT
easat-3708	108	29	where	where	SCONJ
easat-3708	108	30	𝐴𝐿	𝐴𝐿	PROPN
easat-3708	108	31	is	be	AUX
easat-3708	108	32	a	a	DET
easat-3708	108	33	shape	shape	NOUN
easat-3708	108	34	function	function	NOUN
easat-3708	108	35	for	for	ADP
easat-3708	108	36	the	the	DET
easat-3708	108	37	left	left	ADJ
easat-3708	108	38	arm	arm	NOUN
easat-3708	108	39	and	and	CCONJ
easat-3708	108	40	𝐴𝑅	𝐴𝑅	PROPN
easat-3708	108	41	is	be	AUX
easat-3708	108	42	a	a	DET
easat-3708	108	43	shape	shape	NOUN
easat-3708	108	44	function	function	NOUN
easat-3708	108	45	for	for	ADP
easat-3708	108	46	the	the	DET
easat-3708	108	47	right	right	ADJ
easat-3708	108	48	arm	arm	NOUN
easat-3708	108	49	.	.	PUNCT
easat-3708	109	1	definition	definition	NOUN
easat-3708	109	2	4	4	NUM
easat-3708	109	3	[	[	X
easat-3708	109	4	3	3	X
easat-3708	109	5	]	]	PUNCT
easat-3708	109	6	a	a	DET
easat-3708	109	7	triangular	triangular	NOUN
easat-3708	109	8	fuzzy	fuzzy	ADJ
easat-3708	109	9	number	number	NOUN
easat-3708	109	10	�	�	PROPN
easat-3708	109	11	̃	̃	PROPN
easat-3708	109	12	�	�	PROPN
easat-3708	109	13	is	be	AUX
easat-3708	109	14	defined	define	VERB
easat-3708	109	15	by	by	ADP
easat-3708	109	16	three	three	NUM
easat-3708	109	17	real	real	ADJ
easat-3708	109	18	numbers	number	NOUN
easat-3708	109	19	𝑎	𝑎	X
easat-3708	109	20	<	<	X
easat-3708	109	21	𝑏	𝑏	X
easat-3708	109	22	<	<	X
easat-3708	109	23	𝑐	𝑐	PROPN
easat-3708	109	24	,	,	PUNCT
easat-3708	109	25	where	where	SCONJ
easat-3708	109	26	the	the	DET
easat-3708	109	27	base	base	NOUN
easat-3708	109	28	of	of	ADP
easat-3708	109	29	the	the	DET
easat-3708	109	30	triangle	triangle	NOUN
easat-3708	109	31	is	be	AUX
easat-3708	109	32	the	the	DET
easat-3708	109	33	interval	interval	NOUN
easat-3708	110	1	[	[	X
easat-3708	110	2	𝑎	𝑎	X
easat-3708	110	3	,	,	PUNCT
easat-3708	110	4	𝑐	𝑐	NOUN
easat-3708	110	5	]	]	X
easat-3708	110	6	and	and	CCONJ
easat-3708	110	7	its	its	PRON
easat-3708	110	8	vertex	vertex	NOUN
easat-3708	110	9	is	be	AUX
easat-3708	110	10	at	at	ADP
easat-3708	110	11	𝑥	𝑥	NOUN
easat-3708	110	12	=	=	SYM
easat-3708	110	13	𝑏	𝑏	PROPN
easat-3708	110	14	.	.	PUNCT
easat-3708	111	1	remark	remark	NOUN
easat-3708	111	2	2	2	NUM
easat-3708	111	3	another	another	DET
easat-3708	111	4	representation	representation	NOUN
easat-3708	111	5	of	of	ADP
easat-3708	111	6	a	a	DET
easat-3708	111	7	triangular	triangular	NOUN
easat-3708	111	8	fuzzy	fuzzy	ADJ
easat-3708	111	9	number	number	NOUN
easat-3708	111	10	�	�	PROPN
easat-3708	111	11	̃	̃	PROPN
easat-3708	111	12	�	�	PROPN
easat-3708	111	13	is	be	AUX
easat-3708	111	14	�	�	PROPN
easat-3708	111	15	̃	̃	NOUN
easat-3708	111	16	�	�	NOUN
easat-3708	111	17	=	=	SYM
easat-3708	111	18	(	(	PUNCT
easat-3708	111	19	𝑀𝐿	𝑀𝐿	PROPN
easat-3708	111	20	,	,	PUNCT
easat-3708	111	21	𝑀𝑅	𝑀𝑅	PROPN
easat-3708	111	22	)	)	PUNCT
easat-3708	111	23	,	,	PUNCT
easat-3708	111	24	where	where	SCONJ
easat-3708	111	25	𝑀𝐿	𝑀𝐿	PROPN
easat-3708	111	26	and	and	CCONJ
easat-3708	111	27	𝑀𝑅	𝑀𝑅	PROPN
easat-3708	111	28	are	be	AUX
easat-3708	111	29	the	the	DET
easat-3708	111	30	functions	function	NOUN
easat-3708	111	31	for	for	ADP
easat-3708	111	32	the	the	DET
easat-3708	111	33	left	left	ADJ
easat-3708	111	34	arm	arm	NOUN
easat-3708	111	35	and	and	CCONJ
easat-3708	111	36	the	the	DET
easat-3708	111	37	right	right	ADJ
easat-3708	111	38	arm	arm	NOUN
easat-3708	111	39	of	of	ADP
easat-3708	111	40	triangular	triangular	NOUN
easat-3708	111	41	fuzzy	fuzzy	ADJ
easat-3708	111	42	number	number	NOUN
easat-3708	111	43	�	�	PROPN
easat-3708	111	44	̃	̃	PROPN
easat-3708	111	45	�	�	NOUN
easat-3708	111	46	=	=	SYM
easat-3708	111	47	(	(	PUNCT
easat-3708	111	48	𝑎/𝑏/𝑐	𝑎/𝑏/𝑐	PROPN
easat-3708	111	49	)	)	PUNCT
easat-3708	111	50	,	,	PUNCT
easat-3708	111	51	respectively	respectively	ADV
easat-3708	111	52	.	.	PUNCT
easat-3708	112	1	note	note	VERB
easat-3708	112	2	1	1	NUM
easat-3708	112	3	in	in	ADP
easat-3708	112	4	the	the	DET
easat-3708	112	5	rest	rest	NOUN
easat-3708	112	6	of	of	ADP
easat-3708	112	7	our	our	PRON
easat-3708	112	8	work	work	NOUN
easat-3708	112	9	,	,	PUNCT
easat-3708	112	10	triangular	triangular	ADJ
easat-3708	112	11	fuzzy	fuzzy	ADJ
easat-3708	112	12	numbers	number	NOUN
easat-3708	112	13	will	will	AUX
easat-3708	112	14	be	be	AUX
easat-3708	112	15	represented	represent	VERB
easat-3708	112	16	as	as	ADP
easat-3708	112	17	�	�	PROPN
easat-3708	112	18	̃	̃	PROPN
easat-3708	112	19	�	�	NOUN
easat-3708	112	20	=	=	SYM
easat-3708	112	21	(	(	PUNCT
easat-3708	112	22	𝑎/𝑏/𝑐	𝑎/𝑏/𝑐	ADJ
easat-3708	112	23	)	)	PUNCT
easat-3708	112	24	.	.	PUNCT
easat-3708	113	1	we	we	PRON
easat-3708	113	2	also	also	ADV
easat-3708	113	3	denote	denote	VERB
easat-3708	113	4	a	a	DET
easat-3708	113	5	real	real	ADJ
easat-3708	113	6	number	number	NOUN
easat-3708	113	7	a	a	PRON
easat-3708	113	8	by	by	ADP
easat-3708	113	9	�	�	PROPN
easat-3708	113	10	̃	̃	PROPN
easat-3708	113	11	�	�	NOUN
easat-3708	113	12	=	=	SYM
easat-3708	113	13	(	(	PUNCT
easat-3708	113	14	𝑎/𝑎/𝑎	𝑎/𝑎/𝑎	NOUN
easat-3708	113	15	)	)	PUNCT
easat-3708	113	16	.	.	PUNCT
easat-3708	114	1	theorem	theorem	VERB
easat-3708	114	2	1	1	NUM
easat-3708	115	1	[	[	SYM
easat-3708	115	2	35	35	NUM
easat-3708	115	3	]	]	PUNCT
easat-3708	115	4	let	let	VERB
easat-3708	115	5	�	�	PROPN
easat-3708	115	6	̃	̃	PROPN
easat-3708	115	7	�	�	NOUN
easat-3708	115	8	=	=	SYM
easat-3708	115	9	(	(	PUNCT
easat-3708	115	10	𝑚𝐿/𝑚/𝑚𝑅)𝐿𝑅	𝑚𝐿/𝑚/𝑚𝑅)𝐿𝑅	PROPN
easat-3708	115	11	,	,	PUNCT
easat-3708	115	12	let	let	VERB
easat-3708	115	13	�	�	PROPN
easat-3708	115	14	̃	̃	NOUN
easat-3708	115	15	�	�	NOUN
easat-3708	115	16	=	=	SYM
easat-3708	115	17	(	(	PUNCT
easat-3708	115	18	𝑛𝐿/𝑛/𝑛𝑅)𝐿𝑅	𝑛𝐿/𝑛/𝑛𝑅)𝐿𝑅	NUM
easat-3708	115	19	,	,	PUNCT
easat-3708	115	20	and	and	CCONJ
easat-3708	115	21	let	let	VERB
easat-3708	115	22	𝜆	𝜆	DET
easat-3708	115	23	∈	∈	PROPN
easat-3708	115	24	ℝ+	ℝ+	PROPN
easat-3708	115	25	.	.	PUNCT
easat-3708	116	1	then	then	ADV
easat-3708	116	2	,	,	PUNCT
easat-3708	116	3	1	1	X
easat-3708	116	4	.	.	PUNCT
easat-3708	117	1	𝜆	𝜆	DET
easat-3708	117	2	�	�	PROPN
easat-3708	117	3	̃	̃	NOUN
easat-3708	117	4	�	�	NOUN
easat-3708	117	5	=	=	SYM
easat-3708	117	6	(	(	PUNCT
easat-3708	117	7	𝜆𝑚𝐿/𝜆𝑚/𝜆𝑚𝑅)𝐿𝑅	𝜆𝑚𝐿/𝜆𝑚/𝜆𝑚𝑅)𝐿𝑅	X
easat-3708	117	8	.	.	PUNCT
easat-3708	117	9	2	2	NUM
easat-3708	117	10	.	.	PUNCT
easat-3708	118	1	−	−	NOUN
easat-3708	118	2	�	�	PROPN
easat-3708	118	3	̃	̃	NOUN
easat-3708	118	4	�	�	NOUN
easat-3708	118	5	=	=	SYM
easat-3708	118	6	(	(	PUNCT
easat-3708	118	7	−𝑚𝑅/−𝑚/−𝑚𝐿)𝐿𝑅	−𝑚𝑅/−𝑚/−𝑚𝐿)𝐿𝑅	PROPN
easat-3708	118	8	.	.	PUNCT
easat-3708	118	9	3	3	NUM
easat-3708	118	10	.	.	PUNCT
easat-3708	118	11	�	�	PROPN
easat-3708	118	12	̃	̃	PROPN
easat-3708	118	13	�	�	PROPN
easat-3708	118	14	⊕	⊕	PROPN
easat-3708	118	15	�	�	PROPN
easat-3708	118	16	̃	̃	PROPN
easat-3708	118	17	�	�	PROPN
easat-3708	118	18	=	=	SYM
easat-3708	118	19	(	(	PUNCT
easat-3708	118	20	𝑚𝐿	𝑚𝐿	VERB
easat-3708	118	21	+	+	NOUN
easat-3708	118	22	𝑛𝐿/𝑚	𝑛𝐿/𝑚	ADJ
easat-3708	118	23	+	+	CCONJ
easat-3708	118	24	𝑛/𝑚𝑅	𝑛/𝑚𝑅	NOUN
easat-3708	118	25	+	+	CCONJ
easat-3708	118	26	𝑛𝑅)𝐿𝑅	𝑛𝑅)𝐿𝑅	ADJ
easat-3708	118	27	.	.	PUNCT
easat-3708	119	1	2.1.1	2.1.1	X
easat-3708	119	2	.	.	PUNCT
easat-3708	119	3	modified	modify	VERB
easat-3708	119	4	kerre	kerre	PROPN
easat-3708	119	5	’s	’s	PART
easat-3708	119	6	inequality	inequality	PROPN
easat-3708	119	7	kerre	kerre	PROPN
easat-3708	119	8	’s	’s	PART
easat-3708	119	9	inequality	inequality	NOUN
easat-3708	119	10	is	be	AUX
easat-3708	119	11	recognized	recognize	VERB
easat-3708	119	12	as	as	ADP
easat-3708	119	13	a	a	DET
easat-3708	119	14	highly	highly	ADV
easat-3708	119	15	efficient	efficient	ADJ
easat-3708	119	16	method	method	NOUN
easat-3708	119	17	for	for	ADP
easat-3708	119	18	assessing	assess	VERB
easat-3708	119	19	fuzzy	fuzzy	ADJ
easat-3708	119	20	number	number	NOUN
easat-3708	119	21	comparisons	comparison	NOUN
easat-3708	119	22	[	[	X
easat-3708	119	23	32	32	NUM
easat-3708	119	24	]	]	PUNCT
easat-3708	119	25	.	.	PUNCT
easat-3708	120	1	ghanbari	ghanbari	PROPN
easat-3708	120	2	et	et	PROPN
easat-3708	120	3	al	al	PROPN
easat-3708	120	4	.	.	PUNCT
easat-3708	121	1	[	[	X
easat-3708	121	2	10	10	NUM
easat-3708	121	3	]	]	PUNCT
easat-3708	121	4	introduced	introduce	VERB
easat-3708	121	5	a	a	DET
easat-3708	121	6	modified	modify	VERB
easat-3708	121	7	version	version	NOUN
easat-3708	121	8	of	of	ADP
easat-3708	121	9	kerre	kerre	PROPN
easat-3708	121	10	’s	’s	PART
easat-3708	121	11	inequality	inequality	NOUN
easat-3708	121	12	and	and	CCONJ
easat-3708	121	13	established	establish	VERB
easat-3708	121	14	straightforward	straightforward	ADJ
easat-3708	121	15	formulas	formula	NOUN
easat-3708	121	16	for	for	ADP
easat-3708	121	17	comparing	compare	VERB
easat-3708	121	18	fuzzy	fuzzy	ADJ
easat-3708	121	19	triangular	triangular	NOUN
easat-3708	121	20	numbers	number	NOUN
easat-3708	121	21	,	,	PUNCT
easat-3708	121	22	as	as	SCONJ
easat-3708	121	23	stated	state	VERB
easat-3708	121	24	in	in	ADP
easat-3708	121	25	the	the	DET
easat-3708	121	26	following	follow	VERB
easat-3708	121	27	theorem	theorem	PROPN
easat-3708	121	28	.	.	PUNCT
easat-3708	121	29	theorem	theorem	ADJ
easat-3708	121	30	2	2	NUM
easat-3708	122	1	[	[	SYM
easat-3708	122	2	10	10	NUM
easat-3708	122	3	]	]	PUNCT
easat-3708	122	4	consider	consider	VERB
easat-3708	122	5	�	�	PROPN
easat-3708	122	6	̃	̃	NOUN
easat-3708	122	7	�	�	NOUN
easat-3708	122	8	=	=	SYM
easat-3708	122	9	(	(	PUNCT
easat-3708	122	10	𝑎/𝑏/𝑐	𝑎/𝑏/𝑐	ADJ
easat-3708	122	11	)	)	PUNCT
easat-3708	122	12	and	and	CCONJ
easat-3708	122	13	�	�	PROPN
easat-3708	122	14	̃	̃	PROPN
easat-3708	122	15	�	�	NOUN
easat-3708	122	16	=	=	SYM
easat-3708	122	17	(	(	PUNCT
easat-3708	122	18	𝑎′/𝑏′/𝑐′	𝑎′/𝑏′/𝑐′	NOUN
easat-3708	122	19	)	)	PUNCT
easat-3708	122	20	as	as	ADP
easat-3708	122	21	two	two	NUM
easat-3708	122	22	triangular	triangular	ADJ
easat-3708	122	23	fuzzy	fuzzy	ADJ
easat-3708	122	24	numbers	number	NOUN
easat-3708	122	25	with	with	ADP
easat-3708	122	26	𝑏	𝑏	NOUN
easat-3708	122	27	≤	≤	PROPN
easat-3708	122	28	𝑏′.	𝑏′.	ADV
easat-3708	122	29	then	then	ADV
easat-3708	122	30	the	the	DET
easat-3708	122	31	following	follow	VERB
easat-3708	122	32	assertions	assertion	NOUN
easat-3708	122	33	hold	hold	VERB
easat-3708	122	34	:	:	PUNCT
easat-3708	123	1	1	1	X
easat-3708	123	2	.	.	PUNCT
easat-3708	124	1	if	if	SCONJ
easat-3708	124	2	𝑐	𝑐	PROPN
easat-3708	124	3	≤	≤	X
easat-3708	124	4	𝑎′	𝑎′	NUM
easat-3708	124	5	,	,	PUNCT
easat-3708	124	6	then	then	ADV
easat-3708	124	7	𝑟(	𝑟(	NUM
easat-3708	124	8	�	�	PROPN
easat-3708	124	9	̃	̃	PROPN
easat-3708	124	10	�	�	PROPN
easat-3708	124	11	,	,	PUNCT
easat-3708	124	12	�	�	PROPN
easat-3708	124	13	̃	̃	PROPN
easat-3708	124	14	�	�	PROPN
easat-3708	124	15	)	)	PUNCT
easat-3708	124	16	=	=	SYM
easat-3708	124	17	𝑐′−𝑎′	𝑐′−𝑎′	NOUN
easat-3708	124	18	2	2	NUM
easat-3708	124	19	+	+	NUM
easat-3708	124	20	𝑐−𝑎	𝑐−𝑎	NOUN
easat-3708	124	21	2	2	NUM
easat-3708	124	22	.	.	PUNCT
easat-3708	125	1	(	(	PUNCT
easat-3708	125	2	3	3	X
easat-3708	125	3	)	)	PUNCT
easat-3708	125	4	2	2	NUM
easat-3708	125	5	.	.	PUNCT
easat-3708	126	1	if	if	SCONJ
easat-3708	126	2	𝑏	𝑏	PROPN
easat-3708	126	3	=	=	SYM
easat-3708	126	4	𝑏′	𝑏′	PROPN
easat-3708	126	5	,	,	PUNCT
easat-3708	126	6	then	then	ADV
easat-3708	126	7	𝑟(	𝑟(	NUM
easat-3708	126	8	�	�	PROPN
easat-3708	126	9	̃	̃	PROPN
easat-3708	126	10	�	�	PROPN
easat-3708	126	11	,	,	PUNCT
easat-3708	126	12	�	�	PROPN
easat-3708	126	13	̃	̃	NOUN
easat-3708	126	14	�	�	PROPN
easat-3708	126	15	)	)	PUNCT
easat-3708	126	16	=	=	PUNCT
easat-3708	126	17	𝑐′+𝑎′	𝑐′+𝑎′	PUNCT
easat-3708	126	18	2	2	NUM
easat-3708	126	19	−	−	NOUN
easat-3708	126	20	𝑐+𝑎	𝑐+𝑎	PROPN
easat-3708	126	21	2	2	NUM
easat-3708	126	22	.	.	PUNCT
easat-3708	126	23	(	(	PUNCT
easat-3708	126	24	4	4	NUM
easat-3708	126	25	)	)	PUNCT
easat-3708	126	26	7806	7806	NUM
easat-3708	126	27	edelweiss	edelweiss	PROPN
easat-3708	126	28	applied	apply	VERB
easat-3708	126	29	science	science	NOUN
easat-3708	126	30	and	and	CCONJ
easat-3708	126	31	technology	technology	NOUN
easat-3708	126	32	issn	issn	PROPN
easat-3708	126	33	:	:	PUNCT
easat-3708	126	34	2576	2576	NUM
easat-3708	126	35	-	-	SYM
easat-3708	126	36	8484	8484	NUM
easat-3708	126	37	vol	vol	NOUN
easat-3708	126	38	.	.	PROPN
easat-3708	126	39	8	8	NUM
easat-3708	126	40	,	,	PUNCT
easat-3708	126	41	no	no	INTJ
easat-3708	126	42	.	.	NOUN
easat-3708	126	43	6	6	NUM
easat-3708	126	44	:	:	SYM
easat-3708	126	45	7802	7802	NUM
easat-3708	126	46	-	-	SYM
easat-3708	126	47	7812	7812	NUM
easat-3708	126	48	,	,	PUNCT
easat-3708	126	49	2024	2024	NUM
easat-3708	126	50	doi	doi	NOUN
easat-3708	126	51	:	:	PUNCT
easat-3708	126	52	10.55214/25768484.v8i6.3708	10.55214/25768484.v8i6.3708	NUM
easat-3708	126	53	©	©	PROPN
easat-3708	126	54	2024	2024	NUM
easat-3708	126	55	by	by	ADP
easat-3708	126	56	the	the	DET
easat-3708	126	57	authors	author	NOUN
easat-3708	126	58	;	;	PUNCT
easat-3708	126	59	licensee	licensee	PROPN
easat-3708	126	60	learning	learning	NOUN
easat-3708	126	61	gate	gate	NOUN
easat-3708	126	62	3	3	NUM
easat-3708	126	63	.	.	PUNCT
easat-3708	127	1	if	if	SCONJ
easat-3708	127	2	𝑏	𝑏	DET
easat-3708	127	3	<	<	X
easat-3708	127	4	𝑏′	𝑏′	PROPN
easat-3708	127	5	and	and	CCONJ
easat-3708	127	6	𝑎′	𝑎′	PRON
easat-3708	127	7	<	<	X
easat-3708	127	8	𝑐	𝑐	PROPN
easat-3708	127	9	then	then	ADV
easat-3708	127	10	𝑟(	𝑟(	NUM
easat-3708	127	11	�	�	PROPN
easat-3708	127	12	̃	̃	PROPN
easat-3708	127	13	�	�	PROPN
easat-3708	127	14	,	,	PUNCT
easat-3708	127	15	�	�	PROPN
easat-3708	127	16	̃	̃	PROPN
easat-3708	127	17	�	�	PROPN
easat-3708	127	18	)	)	PUNCT
easat-3708	127	19	=	=	SYM
easat-3708	127	20	𝑐′−𝑎′	𝑐′−𝑎′	NOUN
easat-3708	127	21	2	2	NUM
easat-3708	127	22	+	+	NUM
easat-3708	127	23	𝑐−𝑎	𝑐−𝑎	NOUN
easat-3708	127	24	2	2	NUM
easat-3708	127	25	−	−	NOUN
easat-3708	127	26	�	�	NOUN
easat-3708	127	27	̅	̅	NOUN
easat-3708	127	28	�	�	NOUN
easat-3708	127	29	(𝑐	(𝑐	NOUN
easat-3708	127	30	−	−	NOUN
easat-3708	127	31	𝑎′	𝑎′	NUM
easat-3708	127	32	)	)	PUNCT
easat-3708	127	33	,	,	PUNCT
easat-3708	127	34	(	(	PUNCT
easat-3708	127	35	5	5	X
easat-3708	127	36	)	)	PUNCT
easat-3708	127	37	where	where	SCONJ
easat-3708	127	38	�	�	NOUN
easat-3708	127	39	̅	̅	NOUN
easat-3708	127	40	�	�	NOUN
easat-3708	127	41	=	=	SYM
easat-3708	127	42	𝑀𝑅(	𝑀𝑅(	PROPN
easat-3708	127	43	�	�	PROPN
easat-3708	127	44	̅	̅	NOUN
easat-3708	127	45	�	�	NOUN
easat-3708	127	46	)	)	PUNCT
easat-3708	127	47	=	=	SYM
easat-3708	127	48	𝑁𝐿(	𝑁𝐿(	PROPN
easat-3708	127	49	�	�	PROPN
easat-3708	127	50	̅	̅	NOUN
easat-3708	127	51	�	�	NOUN
easat-3708	127	52	)	)	PUNCT
easat-3708	127	53	in	in	ADP
easat-3708	127	54	which	which	PRON
easat-3708	127	55	�	�	NOUN
easat-3708	127	56	̅	̅	NOUN
easat-3708	127	57	�	�	NOUN
easat-3708	127	58	is	be	AUX
easat-3708	127	59	the	the	DET
easat-3708	127	60	length	length	NOUN
easat-3708	127	61	of	of	ADP
easat-3708	127	62	the	the	DET
easat-3708	127	63	intersection	intersection	NOUN
easat-3708	127	64	point	point	NOUN
easat-3708	127	65	of	of	ADP
easat-3708	127	66	𝑀𝑅	𝑀𝑅	PROPN
easat-3708	127	67	and	and	CCONJ
easat-3708	127	68	𝑁𝐿	𝑁𝐿	PROPN
easat-3708	127	69	and	and	CCONJ
easat-3708	127	70	defined	define	VERB
easat-3708	127	71	as	as	ADP
easat-3708	127	72	follows	follow	VERB
easat-3708	127	73	:	:	PUNCT
easat-3708	127	74	�	�	NOUN
easat-3708	127	75	̅	̅	NOUN
easat-3708	127	76	�	�	PROPN
easat-3708	127	77	=	=	SYM
easat-3708	127	78	𝑏′𝑐−𝑏𝑎′	𝑏′𝑐−𝑏𝑎′	PROPN
easat-3708	127	79	(	(	PUNCT
easat-3708	127	80	𝑏′−𝑎′)+(𝑐−𝑏	𝑏′−𝑎′)+(𝑐−𝑏	PROPN
easat-3708	127	81	)	)	PUNCT
easat-3708	127	82	.	.	PUNCT
easat-3708	128	1	so	so	ADV
easat-3708	128	2	,	,	PUNCT
easat-3708	128	3	�	�	PROPN
easat-3708	128	4	̅	̅	NOUN
easat-3708	128	5	�	�	NOUN
easat-3708	128	6	in	in	ADP
easat-3708	128	7	(	(	PUNCT
easat-3708	128	8	5	5	NUM
easat-3708	128	9	)	)	PUNCT
easat-3708	128	10	is	be	AUX
easat-3708	128	11	defined	define	VERB
easat-3708	128	12	as	as	SCONJ
easat-3708	128	13	follows	follow	VERB
easat-3708	128	14	:	:	PUNCT
easat-3708	128	15	�	�	NOUN
easat-3708	128	16	̅	̅	NOUN
easat-3708	128	17	�	�	NOUN
easat-3708	128	18	=	=	SYM
easat-3708	128	19	(	(	PUNCT
easat-3708	128	20	𝑐−𝑎′	𝑐−𝑎′	NOUN
easat-3708	128	21	)	)	PUNCT
easat-3708	128	22	(	(	PUNCT
easat-3708	128	23	𝑏′−𝑎′)+(𝑐−𝑏	𝑏′−𝑎′)+(𝑐−𝑏	PROPN
easat-3708	128	24	)	)	PUNCT
easat-3708	128	25	.	.	PUNCT
easat-3708	129	1	(	(	PUNCT
easat-3708	129	2	6	6	X
easat-3708	129	3	)	)	PUNCT
easat-3708	129	4	note	note	NOUN
easat-3708	129	5	2	2	NUM
easat-3708	129	6	if	if	SCONJ
easat-3708	129	7	𝑟(	𝑟(	NUM
easat-3708	129	8	�	�	PROPN
easat-3708	129	9	̃	̃	PROPN
easat-3708	129	10	�	�	PROPN
easat-3708	129	11	,	,	PUNCT
easat-3708	129	12	�	�	PROPN
easat-3708	129	13	̃	̃	PROPN
easat-3708	129	14	�	�	PROPN
easat-3708	129	15	)	)	PUNCT
easat-3708	129	16	≥	≥	NOUN
easat-3708	129	17	0	0	PUNCT
easat-3708	129	18	then	then	ADV
easat-3708	129	19	�	�	PROPN
easat-3708	129	20	̃	̃	PROPN
easat-3708	129	21	�	�	PROPN
easat-3708	129	22	≤	≤	NUM
easat-3708	129	23	�	�	PROPN
easat-3708	129	24	̃	̃	PROPN
easat-3708	129	25	�	�	PROPN
easat-3708	129	26	,	,	PUNCT
easat-3708	129	27	otherwise	otherwise	ADV
easat-3708	129	28	�	�	PROPN
easat-3708	129	29	̃	̃	PROPN
easat-3708	129	30	�	�	PROPN
easat-3708	129	31	≥	≥	NUM
easat-3708	129	32	�	�	PROPN
easat-3708	129	33	̃	̃	PROPN
easat-3708	129	34	�	�	PROPN
easat-3708	130	1	[	[	X
easat-3708	130	2	10	10	NUM
easat-3708	130	3	.	.	PUNCT
easat-3708	130	4	]	]	PUNCT
easat-3708	131	1	note	note	VERB
easat-3708	131	2	3	3	NUM
easat-3708	131	3	throughout	throughout	ADP
easat-3708	131	4	our	our	PRON
easat-3708	131	5	work	work	NOUN
easat-3708	131	6	,	,	PUNCT
easat-3708	131	7	<	<	X
easat-3708	131	8	,	,	PUNCT
easat-3708	131	9	>	>	PUNCT
easat-3708	131	10	,	,	PUNCT
easat-3708	131	11	and	and	CCONJ
easat-3708	131	12	=	=	X
easat-3708	131	13	on	on	ADP
easat-3708	131	14	fuzzy	fuzzy	ADJ
easat-3708	131	15	numbers	number	NOUN
easat-3708	131	16	are	be	AUX
easat-3708	131	17	defined	define	VERB
easat-3708	131	18	based	base	VERB
easat-3708	131	19	on	on	ADP
easat-3708	131	20	our	our	PRON
easat-3708	131	21	modified	modify	VERB
easat-3708	131	22	kerre	kerre	PROPN
easat-3708	131	23	’s	’s	PART
easat-3708	131	24	inequality	inequality	NOUN
easat-3708	131	25	,	,	PUNCT
easat-3708	131	26	and	and	CCONJ
easat-3708	131	27	so	so	ADV
easat-3708	131	28	we	we	PRON
easat-3708	131	29	show	show	VERB
easat-3708	131	30	them	they	PRON
easat-3708	131	31	by	by	ADP
easat-3708	131	32	<	<	X
easat-3708	131	33	𝐾	𝐾	PROPN
easat-3708	131	34	,	,	PUNCT
easat-3708	131	35	>	>	PUNCT
easat-3708	131	36	𝐾	𝐾	PROPN
easat-3708	131	37	,	,	PUNCT
easat-3708	131	38	and	and	CCONJ
easat-3708	131	39	=	=	PROPN
easat-3708	131	40	𝐾	𝐾	PROPN
easat-3708	131	41	,	,	PUNCT
easat-3708	131	42	respectively	respectively	ADV
easat-3708	131	43	[	[	X
easat-3708	131	44	10	10	NUM
easat-3708	131	45	]	]	PUNCT
easat-3708	131	46	.	.	PUNCT
easat-3708	132	1	3	3	X
easat-3708	132	2	.	.	X
easat-3708	132	3	the	the	DET
easat-3708	132	4	proposed	propose	VERB
easat-3708	132	5	model	model	NOUN
easat-3708	132	6	we	we	PRON
easat-3708	132	7	consider	consider	VERB
easat-3708	132	8	the	the	DET
easat-3708	132	9	following	follow	VERB
easat-3708	132	10	fractional	fractional	ADJ
easat-3708	132	11	programming	programming	NOUN
easat-3708	132	12	problem	problem	NOUN
easat-3708	132	13	:	:	PUNCT
easat-3708	132	14	max	max	PROPN
easat-3708	132	15	�	�	PROPN
easat-3708	132	16	̃	̃	PROPN
easat-3708	132	17	�	�	PROPN
easat-3708	132	18	𝑇𝑥+	𝑇𝑥+	VERB
easat-3708	132	19	�	�	PROPN
easat-3708	132	20	̃	̃	PROPN
easat-3708	132	21	�	�	PROPN
easat-3708	132	22	𝑐𝑇𝑥+𝛽	𝑐𝑇𝑥+𝛽	PROPN
easat-3708	132	23	(	(	PUNCT
easat-3708	132	24	𝐹𝐹𝑁𝐿𝑃𝑃	𝐹𝐹𝑁𝐿𝑃𝑃	PROPN
easat-3708	132	25	)	)	PUNCT
easat-3708	132	26	𝑠.	𝑠.	PROPN
easat-3708	132	27	𝑡.	𝑡.	NOUN
easat-3708	132	28	(	(	PUNCT
easat-3708	132	29	7	7	X
easat-3708	132	30	)	)	PUNCT
easat-3708	132	31	𝐴𝑥	𝐴𝑥	NOUN
easat-3708	132	32	≤	≤	ADJ
easat-3708	132	33	𝑏	𝑏	NOUN
easat-3708	132	34	,	,	PUNCT
easat-3708	132	35	𝑥	𝑥	PRON
easat-3708	132	36	≥	≥	NOUN
easat-3708	132	37	0	0	NUM
easat-3708	132	38	,	,	PUNCT
easat-3708	132	39	where	where	SCONJ
easat-3708	132	40	,	,	PUNCT
easat-3708	132	41	�	�	PROPN
easat-3708	132	42	̃	̃	PROPN
easat-3708	132	43	�	�	PROPN
easat-3708	132	44	∈	∈	PROPN
easat-3708	132	45	𝐹(ℝ𝑛	𝐹(ℝ𝑛	NUM
easat-3708	132	46	)	)	PUNCT
easat-3708	132	47	,	,	PUNCT
easat-3708	132	48	�	�	PROPN
easat-3708	132	49	̃	̃	PROPN
easat-3708	132	50	�	�	PROPN
easat-3708	132	51	∈	∈	PROPN
easat-3708	132	52	𝐹(ℝ	𝐹(ℝ	NOUN
easat-3708	132	53	)	)	PUNCT
easat-3708	132	54	,	,	PUNCT
easat-3708	132	55	𝑐	𝑐	PROPN
easat-3708	132	56	∈	∈	PROPN
easat-3708	133	1	ℝ𝑛	ℝ𝑛	NOUN
easat-3708	133	2	,	,	PUNCT
easat-3708	133	3	𝛽	𝛽	PROPN
easat-3708	133	4	∈	∈	PROPN
easat-3708	133	5	ℝ	ℝ	PROPN
easat-3708	133	6	,	,	PUNCT
easat-3708	133	7	�	�	PROPN
easat-3708	133	8	̃	̃	PROPN
easat-3708	133	9	�	�	PROPN
easat-3708	133	10	and	and	CCONJ
easat-3708	133	11	�	�	PROPN
easat-3708	133	12	̃	̃	PROPN
easat-3708	133	13	�	�	PROPN
easat-3708	133	14	are	be	AUX
easat-3708	133	15	𝐿𝑅	𝐿𝑅	NUM
easat-3708	133	16	fuzzy	fuzzy	ADJ
easat-3708	133	17	numbers	number	NOUN
easat-3708	133	18	and	and	CCONJ
easat-3708	133	19	𝑐𝑇𝑥	𝑐𝑇𝑥	PRON
easat-3708	133	20	+	+	NOUN
easat-3708	133	21	𝛽	𝛽	NOUN
easat-3708	133	22	>	>	X
easat-3708	133	23	0	0	PUNCT
easat-3708	133	24	for	for	ADP
easat-3708	133	25	any	any	DET
easat-3708	133	26	feasible	feasible	ADJ
easat-3708	133	27	solution	solution	NOUN
easat-3708	133	28	𝑥.	𝑥.	ADV
easat-3708	133	29	let	let	VERB
easat-3708	133	30	𝑧	𝑧	VERB
easat-3708	133	31	=	=	SYM
easat-3708	133	32	1	1	NUM
easat-3708	133	33	𝑐𝑇𝑥+𝛽	𝑐𝑇𝑥+𝛽	NOUN
easat-3708	133	34	and	and	CCONJ
easat-3708	133	35	𝑦	𝑦	NOUN
easat-3708	133	36	=	=	X
easat-3708	133	37	𝑧𝑇𝑥.	𝑧𝑇𝑥.	ADV
easat-3708	133	38	by	by	ADP
easat-3708	133	39	getting	get	VERB
easat-3708	133	40	the	the	DET
easat-3708	133	41	ideas	idea	NOUN
easat-3708	133	42	from	from	ADP
easat-3708	133	43	[	[	X
easat-3708	133	44	4	4	NUM
easat-3708	133	45	]	]	PUNCT
easat-3708	133	46	,	,	PUNCT
easat-3708	133	47	the	the	DET
easat-3708	133	48	problem	problem	NOUN
easat-3708	133	49	(	(	PUNCT
easat-3708	133	50	7	7	X
easat-3708	133	51	)	)	PUNCT
easat-3708	133	52	can	can	AUX
easat-3708	133	53	be	be	AUX
easat-3708	133	54	converted	convert	VERB
easat-3708	133	55	to	to	ADP
easat-3708	133	56	the	the	DET
easat-3708	133	57	following	following	ADJ
easat-3708	133	58	problem	problem	NOUN
easat-3708	133	59	:	:	PUNCT
easat-3708	133	60	max	max	PROPN
easat-3708	133	61	�	�	PROPN
easat-3708	133	62	̃	̃	PROPN
easat-3708	133	63	�	�	PROPN
easat-3708	133	64	𝑇𝑦	𝑇𝑦	PROPN
easat-3708	133	65	+	+	SYM
easat-3708	133	66	�	�	PROPN
easat-3708	133	67	̃	̃	PROPN
easat-3708	133	68	�	�	PROPN
easat-3708	133	69	𝑧	𝑧	PART
easat-3708	133	70	,	,	PUNCT
easat-3708	133	71	𝑠.	𝑠.	NOUN
easat-3708	133	72	𝑡.	𝑡.	NOUN
easat-3708	133	73	(	(	PUNCT
easat-3708	133	74	8	8	X
easat-3708	133	75	)	)	PUNCT
easat-3708	134	1	𝐴𝑦	𝐴𝑦	PROPN
easat-3708	134	2	−	−	NOUN
easat-3708	134	3	𝑏𝑧	𝑏𝑧	VERB
easat-3708	134	4	≤	≤	NOUN
easat-3708	134	5	0	0	NUM
easat-3708	134	6	,	,	PUNCT
easat-3708	134	7	𝑐𝑇𝑦	𝑐𝑇𝑦	X
easat-3708	134	8	+	+	CCONJ
easat-3708	134	9	𝛽𝑧	𝛽𝑧	NOUN
easat-3708	134	10	=	=	SYM
easat-3708	134	11	1	1	NUM
easat-3708	134	12	,	,	PUNCT
easat-3708	134	13	𝑦	𝑦	NOUN
easat-3708	134	14	,	,	PUNCT
easat-3708	134	15	𝑧	𝑧	PRON
easat-3708	134	16	≥	≥	NOUN
easat-3708	134	17	0	0	NUM
easat-3708	134	18	,	,	PUNCT
easat-3708	134	19	we	we	PRON
easat-3708	134	20	can	can	AUX
easat-3708	134	21	rewrite	rewrite	VERB
easat-3708	134	22	the	the	DET
easat-3708	134	23	problem	problem	NOUN
easat-3708	134	24	(	(	PUNCT
easat-3708	134	25	8)	8)	NUM
easat-3708	134	26	to	to	ADP
easat-3708	134	27	the	the	DET
easat-3708	134	28	vector	vector	NOUN
easat-3708	134	29	form	form	NOUN
easat-3708	134	30	as	as	SCONJ
easat-3708	134	31	follows	follow	VERB
easat-3708	134	32	:	:	PUNCT
easat-3708	134	33	max	max	PROPN
easat-3708	134	34	[	[	X
easat-3708	134	35	�	�	PROPN
easat-3708	134	36	̃	̃	PROPN
easat-3708	134	37	�	�	PROPN
easat-3708	134	38	,	,	PUNCT
easat-3708	134	39	�	�	PROPN
easat-3708	134	40	̃	̃	PROPN
easat-3708	134	41	�	�	NOUN
easat-3708	134	42	]	]	X
easat-3708	134	43	[	[	PUNCT
easat-3708	134	44	𝑦	𝑦	X
easat-3708	134	45	𝑧	𝑧	X
easat-3708	134	46	]	]	PUNCT
easat-3708	134	47	,	,	PUNCT
easat-3708	134	48	𝑠.	𝑠.	PROPN
easat-3708	134	49	𝑡.	𝑡.	PROPN
easat-3708	134	50	,	,	PUNCT
easat-3708	134	51	(	(	PUNCT
easat-3708	134	52	9	9	NUM
easat-3708	134	53	)	)	PUNCT
easat-3708	134	54	[	[	X
easat-3708	134	55	𝐴	𝐴	PROPN
easat-3708	134	56	,	,	PUNCT
easat-3708	134	57	−𝑏𝑇	−𝑏𝑇	NOUN
easat-3708	134	58	]	]	X
easat-3708	134	59	[	[	PUNCT
easat-3708	134	60	𝑦	𝑦	X
easat-3708	134	61	𝑧	𝑧	X
easat-3708	134	62	]	]	PUNCT
easat-3708	134	63	≤	≤	NUM
easat-3708	134	64	0	0	NUM
easat-3708	134	65	,	,	PUNCT
easat-3708	134	66	[	[	X
easat-3708	134	67	𝑐𝑇	𝑐𝑇	NOUN
easat-3708	134	68	,	,	PUNCT
easat-3708	134	69	𝛽	𝛽	NOUN
easat-3708	134	70	]	]	X
easat-3708	134	71	[	[	PUNCT
easat-3708	134	72	𝑦	𝑦	X
easat-3708	134	73	𝑧	𝑧	X
easat-3708	134	74	]	]	PUNCT
easat-3708	134	75	=	=	SYM
easat-3708	134	76	1[𝑦	1[𝑦	NUM
easat-3708	134	77	,	,	PUNCT
easat-3708	134	78	𝑧	𝑧	X
easat-3708	134	79	]	]	X
easat-3708	134	80	≥	≥	NOUN
easat-3708	134	81	0	0	NUM
easat-3708	134	82	,	,	PUNCT
easat-3708	134	83	if	if	SCONJ
easat-3708	134	84	we	we	PRON
easat-3708	134	85	suppose	suppose	VERB
easat-3708	134	86	𝑋	𝑋	PROPN
easat-3708	134	87	=	=	PUNCT
easat-3708	134	88	[	[	PUNCT
easat-3708	134	89	𝑦	𝑦	X
easat-3708	134	90	𝑧	𝑧	X
easat-3708	134	91	]	]	X
easat-3708	134	92	,	,	PUNCT
easat-3708	134	93	�	�	PROPN
easat-3708	134	94	̃	̃	NOUN
easat-3708	134	95	�	�	NOUN
easat-3708	134	96	=	=	PUNCT
easat-3708	135	1	[	[	X
easat-3708	135	2	�	�	PROPN
easat-3708	135	3	̃	̃	PROPN
easat-3708	135	4	�	�	PROPN
easat-3708	135	5	,	,	PUNCT
easat-3708	135	6	�	�	PROPN
easat-3708	135	7	̃	̃	PROPN
easat-3708	135	8	�	�	PROPN
easat-3708	135	9	]	]	PUNCT
easat-3708	135	10	,	,	PUNCT
easat-3708	135	11	𝐵	𝐵	NOUN
easat-3708	135	12	=	=	PUNCT
easat-3708	135	13	[	[	X
easat-3708	135	14	𝐴	𝐴	PROPN
easat-3708	135	15	,	,	PUNCT
easat-3708	135	16	−𝑏𝑇	−𝑏𝑇	NOUN
easat-3708	135	17	]	]	PUNCT
easat-3708	135	18	and	and	CCONJ
easat-3708	135	19	𝐻	𝐻	PROPN
easat-3708	135	20	=	=	PUNCT
easat-3708	136	1	[	[	X
easat-3708	136	2	𝑐𝑇	𝑐𝑇	NOUN
easat-3708	136	3	,	,	PUNCT
easat-3708	136	4	𝛽	𝛽	NOUN
easat-3708	136	5	]	]	PUNCT
easat-3708	136	6	then	then	ADV
easat-3708	136	7	we	we	PRON
easat-3708	136	8	have	have	VERB
easat-3708	136	9	,	,	PUNCT
easat-3708	136	10	max	max	PROPN
easat-3708	136	11	𝑓(𝑋	𝑓(𝑋	PROPN
easat-3708	136	12	)	)	PUNCT
easat-3708	136	13	=	=	SYM
easat-3708	136	14	�	�	PROPN
easat-3708	136	15	̃	̃	PROPN
easat-3708	136	16	�	�	PROPN
easat-3708	136	17	𝑋	𝑋	NOUN
easat-3708	136	18	,	,	PUNCT
easat-3708	136	19	𝑠.	𝑠.	NOUN
easat-3708	136	20	𝑡.	𝑡.	NOUN
easat-3708	136	21	(	(	PUNCT
easat-3708	136	22	10	10	NUM
easat-3708	136	23	)	)	PUNCT
easat-3708	136	24	𝐵𝑋	𝐵𝑋	PROPN
easat-3708	136	25	≤	≤	NUM
easat-3708	136	26	0	0	NUM
easat-3708	136	27	,	,	PUNCT
easat-3708	136	28	𝐻𝑋	𝐻𝑋	PROPN
easat-3708	136	29	=	=	SYM
easat-3708	136	30	1𝑋	1𝑋	PROPN
easat-3708	136	31	≥	≥	NOUN
easat-3708	136	32	0	0	NUM
easat-3708	136	33	.	.	PUNCT
easat-3708	137	1	by	by	ADP
easat-3708	137	2	solving	solve	VERB
easat-3708	137	3	the	the	DET
easat-3708	137	4	problem	problem	NOUN
easat-3708	137	5	(	(	PUNCT
easat-3708	137	6	10	10	NUM
easat-3708	137	7	)	)	PUNCT
easat-3708	137	8	,	,	PUNCT
easat-3708	137	9	we	we	PRON
easat-3708	137	10	can	can	AUX
easat-3708	137	11	find	find	VERB
easat-3708	137	12	the	the	DET
easat-3708	137	13	so	so	ADV
easat-3708	137	14	lution	lution	PROPN
easat-3708	137	15	of	of	ADP
easat-3708	137	16	the	the	DET
easat-3708	137	17	problem	problem	NOUN
easat-3708	137	18	(	(	PUNCT
easat-3708	137	19	7	7	NUM
easat-3708	137	20	)	)	PUNCT
easat-3708	137	21	.	.	PUNCT
easat-3708	138	1	example	example	NOUN
easat-3708	139	1	1	1	NUM
easat-3708	139	2	consider	consider	VERB
easat-3708	139	3	the	the	DET
easat-3708	139	4	following	follow	VERB
easat-3708	139	5	programming	programming	NOUN
easat-3708	139	6	problem	problem	NOUN
easat-3708	139	7	:	:	PUNCT
easat-3708	139	8	max	max	PROPN
easat-3708	139	9	(	(	PUNCT
easat-3708	139	10	−43/−3/0)𝑥1+(−76/−48/45)𝑥2+(−22/15/41	−43/−3/0)𝑥1+(−76/−48/45)𝑥2+(−22/15/41	PROPN
easat-3708	139	11	)	)	PUNCT
easat-3708	139	12	14𝑥1	14𝑥1	NUM
easat-3708	140	1	+	+	PROPN
easat-3708	140	2	55𝑥2	55𝑥2	NUM
easat-3708	140	3	+	+	SYM
easat-3708	140	4	9	9	NUM
easat-3708	141	1	,	,	PUNCT
easat-3708	141	2	𝑠.	𝑠.	NOUN
easat-3708	141	3	𝑡.	𝑡.	PROPN
easat-3708	141	4	,	,	PUNCT
easat-3708	141	5	(	(	PUNCT
easat-3708	141	6	11	11	NUM
easat-3708	141	7	)	)	PUNCT
easat-3708	141	8	100𝑥1	100𝑥1	NUM
easat-3708	141	9	+	+	CCONJ
easat-3708	141	10	59𝑥2	59𝑥2	NUM
easat-3708	141	11	≤	≤	NOUN
easat-3708	141	12	359,24𝑥1	359,24𝑥1	NUM
easat-3708	141	13	+	+	CCONJ
easat-3708	141	14	41𝑥2	41𝑥2	NUM
easat-3708	141	15	≤	≤	NUM
easat-3708	141	16	229	229	NUM
easat-3708	141	17	,	,	PUNCT
easat-3708	141	18	𝑥1	𝑥1	NOUN
easat-3708	141	19	,	,	PUNCT
easat-3708	141	20	𝑥2	𝑥2	NOUN
easat-3708	141	21	≥	≥	NOUN
easat-3708	141	22	0	0	NUM
easat-3708	141	23	.	.	PUNCT
easat-3708	142	1	let	let	VERB
easat-3708	142	2	,	,	PUNCT
easat-3708	142	3	𝑧	𝑧	NOUN
easat-3708	142	4	=	=	VERB
easat-3708	142	5	1	1	NUM
easat-3708	142	6	14𝑥1	14𝑥1	NUM
easat-3708	142	7	+	+	SYM
easat-3708	142	8	55𝑥2	55𝑥2	NUM
easat-3708	142	9	+	+	SYM
easat-3708	142	10	9	9	NUM
easat-3708	142	11	and	and	CCONJ
easat-3708	142	12	𝑦	𝑦	NOUN
easat-3708	142	13	=	=	SYM
easat-3708	142	14	𝑧𝑥.	𝑧𝑥.	NOUN
easat-3708	143	1	so	so	ADV
easat-3708	143	2	the	the	DET
easat-3708	143	3	problem	problem	NOUN
easat-3708	143	4	(	(	PUNCT
easat-3708	143	5	11	11	NUM
easat-3708	143	6	)	)	PUNCT
easat-3708	143	7	convert	convert	NOUN
easat-3708	143	8	to	to	ADP
easat-3708	143	9	the	the	DET
easat-3708	143	10	following	following	ADJ
easat-3708	143	11	problem	problem	NOUN
easat-3708	143	12	:	:	PUNCT
easat-3708	143	13	max	max	PROPN
easat-3708	143	14	(	(	PUNCT
easat-3708	143	15	−43/−3/0)𝑦1	−43/−3/0)𝑦1	PROPN
easat-3708	143	16	+	+	CCONJ
easat-3708	143	17	(	(	PUNCT
easat-3708	143	18	−76/−48/45)𝑦2	−76/−48/45)𝑦2	NOUN
easat-3708	143	19	+	+	CCONJ
easat-3708	143	20	(	(	PUNCT
easat-3708	143	21	−22/15/41)𝑧	−22/15/41)𝑧	PROPN
easat-3708	143	22	,	,	PUNCT
easat-3708	143	23	𝑠.	𝑠.	NOUN
easat-3708	143	24	𝑡.	𝑡.	PROPN
easat-3708	143	25	,	,	PUNCT
easat-3708	143	26	(	(	PUNCT
easat-3708	143	27	12	12	NUM
easat-3708	143	28	)	)	PUNCT
easat-3708	143	29	100𝑦1	100𝑦1	NUM
easat-3708	143	30	+	+	CCONJ
easat-3708	144	1	59𝑦2	59𝑦2	NUM
easat-3708	144	2	−	−	PROPN
easat-3708	144	3	359𝑧	359𝑧	PROPN
easat-3708	144	4	≤	≤	NOUN
easat-3708	144	5	0,24𝑦1	0,24𝑦1	X
easat-3708	145	1	+	+	CCONJ
easat-3708	145	2	41𝑦2	41𝑦2	NUM
easat-3708	145	3	−	−	PROPN
easat-3708	145	4	229𝑧	229𝑧	NOUN
easat-3708	145	5	≤	≤	NOUN
easat-3708	145	6	0,14𝑦1	0,14𝑦1	PRON
easat-3708	146	1	+	+	CCONJ
easat-3708	147	1	55𝑦2	55𝑦2	NUM
easat-3708	147	2	+	+	NOUN
easat-3708	147	3	9𝑧	9𝑧	NOUN
easat-3708	147	4	=	=	SYM
easat-3708	147	5	1	1	NUM
easat-3708	147	6	,	,	PUNCT
easat-3708	147	7	𝑦1	𝑦1	PROPN
easat-3708	147	8	,	,	PUNCT
easat-3708	147	9	𝑦2	𝑦2	PROPN
easat-3708	147	10	,	,	PUNCT
easat-3708	147	11	𝑧	𝑧	PRON
easat-3708	147	12	≥	≥	NOUN
easat-3708	147	13	0	0	NUM
easat-3708	147	14	.	.	NOUN
easat-3708	147	15	7807	7807	NUM
easat-3708	147	16	edelweiss	edelweiss	PROPN
easat-3708	147	17	applied	apply	VERB
easat-3708	147	18	science	science	NOUN
easat-3708	147	19	and	and	CCONJ
easat-3708	147	20	technology	technology	NOUN
easat-3708	147	21	issn	issn	PROPN
easat-3708	147	22	:	:	PUNCT
easat-3708	147	23	2576	2576	NUM
easat-3708	147	24	-	-	SYM
easat-3708	147	25	8484	8484	NUM
easat-3708	147	26	vol	vol	NOUN
easat-3708	147	27	.	.	PROPN
easat-3708	147	28	8	8	NUM
easat-3708	147	29	,	,	PUNCT
easat-3708	147	30	no	no	INTJ
easat-3708	147	31	.	.	NOUN
easat-3708	147	32	6	6	NUM
easat-3708	147	33	:	:	SYM
easat-3708	147	34	7802	7802	NUM
easat-3708	147	35	-	-	SYM
easat-3708	147	36	7812	7812	NUM
easat-3708	147	37	,	,	PUNCT
easat-3708	147	38	2024	2024	NUM
easat-3708	147	39	doi	doi	NOUN
easat-3708	147	40	:	:	PUNCT
easat-3708	147	41	10.55214/25768484.v8i6.3708	10.55214/25768484.v8i6.3708	NUM
easat-3708	147	42	©	©	PROPN
easat-3708	147	43	2024	2024	NUM
easat-3708	147	44	by	by	ADP
easat-3708	147	45	the	the	DET
easat-3708	147	46	authors	author	NOUN
easat-3708	147	47	;	;	PUNCT
easat-3708	147	48	licensee	licensee	PROPN
easat-3708	147	49	learning	learning	NOUN
easat-3708	147	50	gate	gate	NOUN
easat-3708	147	51	finally	finally	ADV
easat-3708	147	52	,	,	PUNCT
easat-3708	147	53	we	we	PRON
easat-3708	147	54	can	can	AUX
easat-3708	147	55	rewrite	rewrite	VERB
easat-3708	147	56	the	the	DET
easat-3708	147	57	problem	problem	NOUN
easat-3708	147	58	(	(	PUNCT
easat-3708	147	59	12	12	NUM
easat-3708	147	60	)	)	PUNCT
easat-3708	147	61	to	to	ADP
easat-3708	147	62	the	the	DET
easat-3708	147	63	following	following	ADJ
easat-3708	147	64	problem	problem	NOUN
easat-3708	147	65	:	:	PUNCT
easat-3708	147	66	max	max	PROPN
easat-3708	147	67	(	(	PUNCT
easat-3708	147	68	(	(	PUNCT
easat-3708	147	69	−43	−43	NOUN
easat-3708	147	70	,	,	PUNCT
easat-3708	147	71	−3,0	−3,0	PRON
easat-3708	147	72	)	)	PUNCT
easat-3708	147	73	,	,	PUNCT
easat-3708	147	74	(	(	PUNCT
easat-3708	147	75	−76	−76	ADV
easat-3708	147	76	,	,	PUNCT
easat-3708	147	77	−48,45	−48,45	NUM
easat-3708	147	78	)	)	PUNCT
easat-3708	147	79	,	,	PUNCT
easat-3708	147	80	(	(	PUNCT
easat-3708	147	81	−22,15,41	−22,15,41	ADV
easat-3708	147	82	)	)	PUNCT
easat-3708	147	83	)	)	PUNCT
easat-3708	148	1	(	(	PUNCT
easat-3708	148	2	𝑦1	𝑦1	NOUN
easat-3708	148	3	𝑦2	𝑦2	PROPN
easat-3708	148	4	𝑧	𝑧	PART
easat-3708	148	5	)	)	PUNCT
easat-3708	148	6	,	,	PUNCT
easat-3708	148	7	𝑠.	𝑠.	PROPN
easat-3708	148	8	𝑡.	𝑡.	PROPN
easat-3708	148	9	,	,	PUNCT
easat-3708	148	10	(	(	PUNCT
easat-3708	148	11	13	13	NUM
easat-3708	148	12	)	)	PUNCT
easat-3708	149	1	[	[	X
easat-3708	149	2	14,55,9	14,55,9	NUM
easat-3708	149	3	]	]	X
easat-3708	149	4	(	(	PUNCT
easat-3708	149	5	𝑦1	𝑦1	PROPN
easat-3708	149	6	𝑦2	𝑦2	PROPN
easat-3708	149	7	𝑧	𝑧	PART
easat-3708	149	8	)	)	PUNCT
easat-3708	150	1	=	=	SYM
easat-3708	150	2	1	1	NUM
easat-3708	150	3	(	(	PUNCT
easat-3708	150	4	100	100	NUM
easat-3708	150	5	59	59	NUM
easat-3708	150	6	−395	−395	NOUN
easat-3708	150	7	24	24	NUM
easat-3708	150	8	41	41	NUM
easat-3708	150	9	−229	−229	NOUN
easat-3708	150	10	)	)	PUNCT
easat-3708	150	11	(	(	PUNCT
easat-3708	150	12	𝑦1	𝑦1	PROPN
easat-3708	150	13	𝑦2	𝑦2	PROPN
easat-3708	150	14	𝑧	𝑧	PART
easat-3708	150	15	)	)	PUNCT
easat-3708	150	16	≤	≤	NOUN
easat-3708	150	17	0	0	NUM
easat-3708	150	18	,	,	PUNCT
easat-3708	150	19	𝑦1	𝑦1	PROPN
easat-3708	150	20	,	,	PUNCT
easat-3708	150	21	𝑦2	𝑦2	PROPN
easat-3708	150	22	,	,	PUNCT
easat-3708	150	23	𝑧	𝑧	PRON
easat-3708	150	24	≥	≥	NOUN
easat-3708	150	25	0	0	NUM
easat-3708	150	26	.	.	PUNCT
easat-3708	151	1	in	in	ADP
easat-3708	151	2	the	the	DET
easat-3708	151	3	next	next	ADJ
easat-3708	151	4	section	section	NOUN
easat-3708	151	5	we	we	PRON
easat-3708	151	6	propose	propose	VERB
easat-3708	151	7	vns	vns	NOUN
easat-3708	151	8	algorithm	algorithm	NOUN
easat-3708	151	9	for	for	ADP
easat-3708	151	10	solving	solve	VERB
easat-3708	151	11	the	the	DET
easat-3708	151	12	problem	problem	NOUN
easat-3708	151	13	(	(	PUNCT
easat-3708	151	14	10	10	NUM
easat-3708	151	15	)	)	PUNCT
easat-3708	151	16	.	.	PUNCT
easat-3708	152	1	4	4	X
easat-3708	152	2	.	.	X
easat-3708	152	3	vns	vns	PROPN
easat-3708	152	4	algorithm	algorithm	NOUN
easat-3708	152	5	for	for	ADP
easat-3708	152	6	solving	solve	VERB
easat-3708	152	7	fuzzy	fuzzy	ADJ
easat-3708	152	8	fractional	fractional	ADJ
easat-3708	152	9	programming	programming	NOUN
easat-3708	152	10	problem	problem	NOUN
easat-3708	152	11	with	with	ADP
easat-3708	152	12	fuzzy	fuzzy	ADJ
easat-3708	152	13	objective	objective	ADJ
easat-3708	152	14	parameter	parameter	NOUN
easat-3708	152	15	the	the	DET
easat-3708	152	16	vns	vns	PROPN
easat-3708	152	17	algorithm	algorithm	NOUN
easat-3708	152	18	was	be	AUX
easat-3708	152	19	initially	initially	ADV
easat-3708	152	20	introduced	introduce	VERB
easat-3708	152	21	by	by	ADP
easat-3708	152	22	mladenovic	mladenovic	PROPN
easat-3708	152	23	and	and	CCONJ
easat-3708	152	24	hansen	hansen	NOUN
easat-3708	153	1	[	[	X
easat-3708	153	2	18	18	NUM
easat-3708	153	3	]	]	PUNCT
easat-3708	153	4	.	.	PUNCT
easat-3708	154	1	it	it	PRON
easat-3708	154	2	is	be	AUX
easat-3708	154	3	a	a	DET
easat-3708	154	4	local	local	ADJ
easat-3708	154	5	search	search	NOUN
easat-3708	154	6	approach	approach	NOUN
easat-3708	154	7	that	that	PRON
easat-3708	154	8	systematically	systematically	ADV
easat-3708	154	9	explores	explore	VERB
easat-3708	154	10	the	the	DET
easat-3708	154	11	search	search	NOUN
easat-3708	154	12	space	space	NOUN
easat-3708	154	13	by	by	ADP
easat-3708	154	14	introducing	introduce	VERB
easat-3708	154	15	deliberate	deliberate	ADJ
easat-3708	154	16	modifications	modification	NOUN
easat-3708	154	17	to	to	ADP
easat-3708	154	18	neighbourhood	neighbourhood	NOUN
easat-3708	154	19	structures	structure	NOUN
easat-3708	154	20	.	.	PUNCT
easat-3708	155	1	considering	consider	VERB
easat-3708	155	2	the	the	DET
easat-3708	155	3	demonstrated	demonstrate	VERB
easat-3708	155	4	effectiveness	effectiveness	NOUN
easat-3708	155	5	of	of	ADP
easat-3708	155	6	vns	vns	NOUN
easat-3708	155	7	and	and	CCONJ
easat-3708	155	8	its	its	PRON
easat-3708	155	9	extensions	extension	NOUN
easat-3708	155	10	in	in	ADP
easat-3708	155	11	addressing	address	VERB
easat-3708	155	12	combinatorial	combinatorial	ADJ
easat-3708	155	13	and	and	CCONJ
easat-3708	155	14	continuous	continuous	ADJ
easat-3708	155	15	optimization	optimization	NOUN
easat-3708	155	16	problems	problem	NOUN
easat-3708	155	17	[	[	X
easat-3708	155	18	18	18	NUM
easat-3708	155	19	]	]	PUNCT
easat-3708	155	20	,	,	PUNCT
easat-3708	155	21	we	we	PRON
easat-3708	155	22	propose	propose	VERB
easat-3708	155	23	the	the	DET
easat-3708	155	24	utilization	utilization	NOUN
easat-3708	155	25	of	of	ADP
easat-3708	155	26	vns	vns	PROPN
easat-3708	155	27	.	.	PUNCT
easat-3708	156	1	in	in	ADP
easat-3708	156	2	each	each	DET
easat-3708	156	3	iteration	iteration	NOUN
easat-3708	156	4	,	,	PUNCT
easat-3708	156	5	a	a	DET
easat-3708	156	6	specific	specific	ADJ
easat-3708	156	7	neighborhood	neighborhood	NOUN
easat-3708	156	8	structure	structure	NOUN
easat-3708	156	9	,	,	PUNCT
easat-3708	156	10	denoted	denote	VERB
easat-3708	156	11	as	as	ADP
easat-3708	156	12	k	k	PROPN
easat-3708	156	13	,	,	PUNCT
easat-3708	156	14	is	be	AUX
easat-3708	156	15	chosen	choose	VERB
easat-3708	156	16	following	follow	VERB
easat-3708	156	17	the	the	DET
easat-3708	156	18	sequence	sequence	NOUN
easat-3708	156	19	outlined	outline	VERB
easat-3708	156	20	in	in	ADP
easat-3708	156	21	[	[	X
easat-3708	156	22	10	10	NUM
easat-3708	156	23	]	]	PUNCT
easat-3708	156	24	.	.	PUNCT
easat-3708	157	1	a	a	DET
easat-3708	157	2	random	random	ADJ
easat-3708	157	3	neighbor	neighbor	NOUN
easat-3708	157	4	s^	s^	NOUN
easat-3708	157	5	'	'	PUNCT
easat-3708	157	6	is	be	AUX
easat-3708	157	7	generated	generate	VERB
easat-3708	157	8	in	in	ADP
easat-3708	157	9	this	this	DET
easat-3708	157	10	neighborhood	neighborhood	NOUN
easat-3708	157	11	.	.	PUNCT
easat-3708	158	1	afterwards	afterwards	ADV
easat-3708	158	2	,	,	PUNCT
easat-3708	158	3	a	a	DET
easat-3708	158	4	descent	descent	NOUN
easat-3708	158	5	method	method	NOUN
easat-3708	158	6	is	be	AUX
easat-3708	158	7	applied	apply	VERB
easat-3708	158	8	to	to	ADP
easat-3708	158	9	s^	s^	NOUN
easat-3708	158	10	'	'	PUNCT
easat-3708	158	11	.	.	PUNCT
easat-3708	159	1	if	if	SCONJ
easat-3708	159	2	the	the	DET
easat-3708	159	3	best	good	ADJ
easat-3708	159	4	solution	solution	NOUN
easat-3708	159	5	found	find	VERB
easat-3708	159	6	by	by	ADP
easat-3708	159	7	descent	descent	NOUN
easat-3708	159	8	method	method	NOUN
easat-3708	159	9	,	,	PUNCT
easat-3708	159	10	s^	s^	PROPN
easat-3708	159	11	"	"	PUNCT
easat-3708	159	12	,	,	PUNCT
easat-3708	159	13	is	be	AUX
easat-3708	159	14	better	well	ADJ
easat-3708	159	15	than	than	ADP
easat-3708	159	16	the	the	DET
easat-3708	159	17	best	well	ADV
easat-3708	159	18	known	know	VERB
easat-3708	159	19	solution	solution	NOUN
easat-3708	159	20	,	,	PUNCT
easat-3708	159	21	it	it	PRON
easat-3708	159	22	is	be	AUX
easat-3708	159	23	updated	update	VERB
easat-3708	159	24	and	and	CCONJ
easat-3708	159	25	the	the	DET
easat-3708	159	26	neighborhood	neighborhood	NOUN
easat-3708	159	27	structure	structure	NOUN
easat-3708	159	28	is	be	AUX
easat-3708	159	29	set	set	VERB
easat-3708	159	30	to	to	ADP
easat-3708	159	31	the	the	DET
easat-3708	159	32	first	first	ADJ
easat-3708	159	33	one	one	NUM
easat-3708	159	34	.	.	PUNCT
easat-3708	160	1	otherwise	otherwise	ADV
easat-3708	160	2	,	,	PUNCT
easat-3708	160	3	the	the	DET
easat-3708	160	4	search	search	NOUN
easat-3708	160	5	continues	continue	VERB
easat-3708	160	6	in	in	ADP
easat-3708	160	7	the	the	DET
easat-3708	160	8	following	follow	VERB
easat-3708	160	9	neighborhood	neighborhood	NOUN
easat-3708	160	10	structure	structure	NOUN
easat-3708	160	11	.	.	PUNCT
easat-3708	161	1	when	when	SCONJ
easat-3708	161	2	we	we	PRON
easat-3708	161	3	explore	explore	VERB
easat-3708	161	4	the	the	DET
easat-3708	161	5	last	last	ADJ
easat-3708	161	6	neighborhood	neighborhood	NOUN
easat-3708	161	7	structure	structure	NOUN
easat-3708	161	8	kmax	kmax	PROPN
easat-3708	161	9	,	,	PUNCT
easat-3708	161	10	the	the	DET
easat-3708	161	11	search	search	NOUN
easat-3708	161	12	return	return	NOUN
easat-3708	161	13	to	to	ADP
easat-3708	161	14	the	the	DET
easat-3708	161	15	first	first	ADJ
easat-3708	161	16	neighborhood	neighborhood	NOUN
easat-3708	161	17	.	.	PUNCT
easat-3708	162	1	this	this	DET
easat-3708	162	2	process	process	NOUN
easat-3708	162	3	continues	continue	VERB
easat-3708	162	4	until	until	SCONJ
easat-3708	162	5	a	a	DET
easat-3708	162	6	stop	stop	NOUN
easat-3708	162	7	condition	condition	NOUN
easat-3708	162	8	is	be	AUX
easat-3708	162	9	reached	reach	VERB
easat-3708	162	10	.	.	PUNCT
easat-3708	163	1	some	some	DET
easat-3708	163	2	successful	successful	ADJ
easat-3708	163	3	examples	example	NOUN
easat-3708	163	4	of	of	ADP
easat-3708	163	5	application	application	NOUN
easat-3708	163	6	of	of	ADP
easat-3708	163	7	vns	vns	PROPN
easat-3708	163	8	can	can	AUX
easat-3708	163	9	also	also	ADV
easat-3708	163	10	be	be	AUX
easat-3708	163	11	found	find	VERB
easat-3708	163	12	in	in	ADP
easat-3708	163	13	[	[	X
easat-3708	163	14	7	7	NUM
easat-3708	163	15	,	,	PUNCT
easat-3708	163	16	30	30	NUM
easat-3708	163	17	,	,	PUNCT
easat-3708	163	18	31	31	NUM
easat-3708	163	19	]	]	PUNCT
easat-3708	163	20	.	.	PUNCT
easat-3708	164	1	based	base	VERB
easat-3708	164	2	on	on	ADP
easat-3708	164	3	the	the	DET
easat-3708	164	4	definition	definition	NOUN
easat-3708	164	5	of	of	ADP
easat-3708	164	6	the	the	DET
easat-3708	164	7	objective	objective	ADJ
easat-3708	164	8	function	function	NOUN
easat-3708	164	9	in	in	ADP
easat-3708	164	10	the	the	DET
easat-3708	164	11	(	(	PUNCT
easat-3708	164	12	𝐹𝐹𝑁𝐿𝑃𝑃	𝐹𝐹𝑁𝐿𝑃𝑃	PROPN
easat-3708	164	13	)	)	PUNCT
easat-3708	164	14	,	,	PUNCT
easat-3708	164	15	the	the	DET
easat-3708	164	16	value	value	NOUN
easat-3708	164	17	of	of	ADP
easat-3708	164	18	the	the	DET
easat-3708	164	19	objective	objective	ADJ
easat-3708	164	20	function	function	NOUN
easat-3708	164	21	for	for	ADP
easat-3708	164	22	each	each	DET
easat-3708	164	23	feasible	feasible	ADJ
easat-3708	164	24	solution	solution	NOUN
easat-3708	164	25	is	be	AUX
easat-3708	164	26	a	a	DET
easat-3708	164	27	fuzzy	fuzzy	ADJ
easat-3708	164	28	number	number	NOUN
easat-3708	164	29	.	.	PUNCT
easat-3708	165	1	thus	thus	ADV
easat-3708	165	2	,	,	PUNCT
easat-3708	165	3	to	to	PART
easat-3708	165	4	compare	compare	VERB
easat-3708	165	5	the	the	DET
easat-3708	165	6	solutions	solution	NOUN
easat-3708	165	7	in	in	ADP
easat-3708	165	8	the	the	DET
easat-3708	165	9	proposed	propose	VERB
easat-3708	165	10	algorithm	algorithm	NOUN
easat-3708	165	11	(	(	PUNCT
easat-3708	165	12	e.g.	e.g.	ADV
easat-3708	165	13	,	,	PUNCT
easat-3708	165	14	step	step	NOUN
easat-3708	165	15	1	1	NUM
easat-3708	165	16	-	-	SYM
easat-3708	165	17	2	2	NUM
easat-3708	165	18	-	-	PUNCT
easat-3708	165	19	3	3	NUM
easat-3708	165	20	)	)	PUNCT
easat-3708	165	21	,	,	PUNCT
easat-3708	165	22	we	we	PRON
easat-3708	165	23	use	use	VERB
easat-3708	165	24	modified	modified	ADJ
easat-3708	165	25	kerre	kerre	PROPN
easat-3708	165	26	’s	’s	PART
easat-3708	165	27	inequality	inequality	NOUN
easat-3708	165	28	in	in	ADP
easat-3708	165	29	theorem	theorem	NOUN
easat-3708	165	30	2	2	NUM
easat-3708	165	31	.	.	PUNCT
easat-3708	165	32	using	use	VERB
easat-3708	165	33	our	our	PRON
easat-3708	165	34	modified	modify	VERB
easat-3708	165	35	kerre	kerre	PROPN
easat-3708	165	36	’s	’s	PART
easat-3708	165	37	inequality	inequality	NOUN
easat-3708	165	38	,	,	PUNCT
easat-3708	165	39	the	the	DET
easat-3708	165	40	fuzzy	fuzzy	ADJ
easat-3708	165	41	optimization	optimization	NOUN
easat-3708	165	42	problem	problem	NOUN
easat-3708	165	43	is	be	AUX
easat-3708	165	44	solved	solve	VERB
easat-3708	165	45	directly	directly	ADV
easat-3708	165	46	without	without	ADP
easat-3708	165	47	changing	change	VERB
easat-3708	165	48	it	it	PRON
easat-3708	165	49	to	to	ADP
easat-3708	165	50	a	a	DET
easat-3708	165	51	crisp	crisp	ADJ
easat-3708	165	52	problem	problem	NOUN
easat-3708	165	53	.	.	PUNCT
easat-3708	166	1	algorithm	algorithm	NOUN
easat-3708	166	2	1	1	NUM
easat-3708	166	3	fvns	fvns	NOUN
easat-3708	166	4	for	for	ADP
easat-3708	166	5	solving	solve	VERB
easat-3708	166	6	𝑭𝑭𝑵𝑳𝑷𝑷	𝑭𝑭𝑵𝑳𝑷𝑷	NOUN
easat-3708	166	7	inputs	input	NOUN
easat-3708	166	8	:	:	PUNCT
easat-3708	166	9	neighboring	neighboring	NOUN
easat-3708	166	10	structures	structure	NOUN
easat-3708	166	11	𝑵𝒕	𝑵𝒕	NOUN
easat-3708	166	12	(	(	PUNCT
easat-3708	166	13	𝒕	𝒕	NOUN
easat-3708	166	14	=	=	SYM
easat-3708	166	15	𝟏	𝟏	PROPN
easat-3708	166	16	,	,	PUNCT
easat-3708	166	17	𝟐	𝟐	NUM
easat-3708	166	18	,	,	PUNCT
easat-3708	166	19	⋯	⋯	PROPN
easat-3708	166	20	,	,	PUNCT
easat-3708	166	21	𝒕𝐦𝐚𝐱	𝒕𝐦𝐚𝐱	PROPN
easat-3708	166	22	)	)	PUNCT
easat-3708	166	23	,	,	PUNCT
easat-3708	166	24	an	an	DET
easat-3708	166	25	initial	initial	ADJ
easat-3708	166	26	feasible	feasible	ADJ
easat-3708	166	27	solution	solution	NOUN
easat-3708	166	28	𝒙𝟎	𝒙𝟎	ADJ
easat-3708	166	29	and	and	CCONJ
easat-3708	166	30	𝒎𝒂𝒙𝒊𝒕𝒆𝒓	𝒎𝒂𝒙𝒊𝒕𝒆𝒓	ADJ
easat-3708	166	31	(	(	PUNCT
easat-3708	166	32	maximum	maximum	ADJ
easat-3708	166	33	number	number	NOUN
easat-3708	166	34	of	of	ADP
easat-3708	166	35	iterations	iteration	NOUN
easat-3708	166	36	)	)	PUNCT
easat-3708	166	37	.	.	PUNCT
easat-3708	167	1	[	[	X
easat-3708	167	2	output	output	NOUN
easat-3708	167	3	:	:	PUNCT
easat-3708	167	4	]	]	PUNCT
easat-3708	167	5	return	return	NOUN
easat-3708	167	6	𝒙∗.	𝒙∗.	NOUN
easat-3708	167	7	[	[	X
easat-3708	167	8	1	1	X
easat-3708	167	9	.	.	PUNCT
easat-3708	167	10	]	]	PUNCT
easat-3708	167	11	while	while	SCONJ
easat-3708	167	12	𝒌	𝒌	ADP
easat-3708	167	13	<	<	X
easat-3708	167	14	𝒎𝒂𝒙𝒊𝒕𝒆𝒓	𝒎𝒂𝒙𝒊𝒕𝒆𝒓	NOUN
easat-3708	167	15	do	do	AUX
easat-3708	167	16	:	:	PUNCT
easat-3708	167	17	1	1	X
easat-3708	167	18	.	.	PUNCT
easat-3708	168	1	𝒕	𝒕	NOUN
easat-3708	168	2	=	=	PUNCT
easat-3708	168	3	𝟏	𝟏	X
easat-3708	168	4	.	.	PUNCT
easat-3708	169	1	2	2	NUM
easat-3708	169	2	.	.	PUNCT
easat-3708	170	1	if	if	SCONJ
easat-3708	170	2	𝒕	𝒕	PRON
easat-3708	170	3	<	<	X
easat-3708	170	4	𝒕𝐦𝐚𝐱	𝒕𝐦𝐚𝐱	NOUN
easat-3708	170	5	then	then	ADV
easat-3708	170	6	:	:	PUNCT
easat-3708	170	7	(	(	PUNCT
easat-3708	170	8	a	a	X
easat-3708	170	9	)	)	PUNCT
easat-3708	170	10	select	select	ADJ
easat-3708	170	11	one	one	NUM
easat-3708	170	12	point	point	NOUN
easat-3708	170	13	in	in	ADP
easat-3708	170	14	the	the	DET
easat-3708	170	15	neighborhood	neighborhood	NOUN
easat-3708	170	16	of	of	ADP
easat-3708	170	17	𝒙𝟎	𝒙𝟎	NOUN
easat-3708	170	18	and	and	CCONJ
easat-3708	170	19	name	name	VERB
easat-3708	170	20	it	it	PRON
easat-3708	170	21	to	to	PART
easat-3708	170	22	be	be	AUX
easat-3708	170	23	𝒙𝟏	𝒙𝟏	NOUN
easat-3708	170	24	(	(	PUNCT
easat-3708	170	25	𝒙𝟏	𝒙𝟏	NOUN
easat-3708	170	26	∈	∈	PROPN
easat-3708	170	27	𝑵𝒕(𝒙𝟎	𝑵𝒕(𝒙𝟎	NOUN
easat-3708	170	28	)	)	PUNCT
easat-3708	170	29	)	)	PUNCT
easat-3708	170	30	.	.	PUNCT
easat-3708	171	1	(	(	PUNCT
easat-3708	171	2	b	b	X
easat-3708	171	3	)	)	PUNCT
easat-3708	171	4	apply	apply	VERB
easat-3708	171	5	local	local	ADJ
easat-3708	171	6	search	search	NOUN
easat-3708	171	7	on	on	ADP
easat-3708	171	8	𝒙𝟏	𝒙𝟏	NOUN
easat-3708	171	9	and	and	CCONJ
easat-3708	171	10	name	name	VERB
easat-3708	171	11	the	the	DET
easat-3708	171	12	new	new	ADJ
easat-3708	171	13	point	point	NOUN
easat-3708	171	14	as	as	ADP
easat-3708	171	15	𝒙𝟐	𝒙𝟐	NOUN
easat-3708	171	16	.	.	PUNCT
easat-3708	172	1	(	(	PUNCT
easat-3708	172	2	c	c	X
easat-3708	172	3	)	)	PUNCT
easat-3708	172	4	if	if	SCONJ
easat-3708	172	5	�	�	PROPN
easat-3708	172	6	̃	̃	PROPN
easat-3708	172	7	�	�	PROPN
easat-3708	172	8	(𝒙𝟐	(𝒙𝟐	PUNCT
easat-3708	172	9	)	)	PUNCT
easat-3708	172	10	≤𝑲	≤𝑲	PROPN
easat-3708	172	11	�	�	PROPN
easat-3708	172	12	̃	̃	PROPN
easat-3708	172	13	�	�	PROPN
easat-3708	172	14	(𝒙𝟎	(𝒙𝟎	PUNCT
easat-3708	172	15	)	)	PUNCT
easat-3708	172	16	then	then	ADV
easat-3708	172	17	let	let	VERB
easat-3708	172	18	𝒕	𝒕	NOUN
easat-3708	172	19	=	=	SYM
easat-3708	172	20	𝒕	𝒕	PROPN
easat-3708	173	1	+	+	CCONJ
easat-3708	173	2	𝟏	𝟏	NUM
easat-3708	173	3	and	and	CCONJ
easat-3708	173	4	go	go	VERB
easat-3708	173	5	to	to	ADP
easat-3708	173	6	1	1	NUM
easat-3708	173	7	-	-	SYM
easat-3708	173	8	2	2	NUM
easat-3708	173	9	,	,	PUNCT
easat-3708	173	10	else	else	ADV
easat-3708	173	11	go	go	VERB
easat-3708	173	12	to	to	ADP
easat-3708	173	13	1	1	NUM
easat-3708	173	14	-	-	SYM
easat-3708	173	15	3	3	NUM
easat-3708	173	16	.	.	NOUN
easat-3708	174	1	3	3	NUM
easat-3708	174	2	.	.	PUNCT
easat-3708	175	1	𝒙𝟎	𝒙𝟎	ADJ
easat-3708	175	2	=	=	NOUN
easat-3708	175	3	𝒙𝟐	𝒙𝟐	NOUN
easat-3708	175	4	.	.	PUNCT
easat-3708	176	1	4	4	X
easat-3708	176	2	.	.	PUNCT
easat-3708	177	1	𝒌	𝒌	PUNCT
easat-3708	177	2	=	=	PUNCT
easat-3708	178	1	𝒌	𝒌	PROPN
easat-3708	179	1	+	+	ADJ
easat-3708	179	2	𝟏	𝟏	X
easat-3708	179	3	.	.	PUNCT
easat-3708	180	1	details	detail	NOUN
easat-3708	180	2	of	of	ADP
easat-3708	180	3	the	the	DET
easat-3708	180	4	steps	step	NOUN
easat-3708	180	5	involved	involve	VERB
easat-3708	180	6	in	in	ADP
easat-3708	180	7	algorithm	algorithm	NOUN
easat-3708	180	8	1	1	NUM
easat-3708	180	9	are	be	AUX
easat-3708	180	10	described	describe	VERB
easat-3708	180	11	below	below	ADV
easat-3708	180	12	.	.	PUNCT
easat-3708	181	1	1	1	X
easat-3708	181	2	.	.	PUNCT
easat-3708	182	1	neighboring	neighboring	NOUN
easat-3708	182	2	structure	structure	NOUN
easat-3708	183	1	[	[	X
easat-3708	183	2	10	10	NUM
easat-3708	183	3	]	]	PUNCT
easat-3708	183	4	:	:	PUNCT
easat-3708	183	5	we	we	PRON
easat-3708	183	6	define	define	VERB
easat-3708	183	7	neighboring	neighboring	NOUN
easat-3708	183	8	structure	structure	NOUN
easat-3708	183	9	as	as	SCONJ
easat-3708	183	10	follows	follow	VERB
easat-3708	183	11	:	:	PUNCT
easat-3708	183	12	||𝑥′	||𝑥′	VERB
easat-3708	183	13	−	−	PROPN
easat-3708	183	14	𝑥0||	𝑥0||	PROPN
easat-3708	183	15	<	<	X
easat-3708	183	16	𝑡𝜖	𝑡𝜖	PROPN
easat-3708	183	17	,	,	PUNCT
easat-3708	183	18	(	(	PUNCT
easat-3708	183	19	14	14	NUM
easat-3708	183	20	)	)	PUNCT
easat-3708	183	21	7808	7808	NUM
easat-3708	183	22	edelweiss	edelweiss	PROPN
easat-3708	183	23	applied	apply	VERB
easat-3708	183	24	science	science	NOUN
easat-3708	183	25	and	and	CCONJ
easat-3708	183	26	technology	technology	NOUN
easat-3708	183	27	issn	issn	PROPN
easat-3708	183	28	:	:	PUNCT
easat-3708	183	29	2576	2576	NUM
easat-3708	183	30	-	-	SYM
easat-3708	183	31	8484	8484	NUM
easat-3708	183	32	vol	vol	NOUN
easat-3708	183	33	.	.	PROPN
easat-3708	183	34	8	8	NUM
easat-3708	183	35	,	,	PUNCT
easat-3708	183	36	no	no	INTJ
easat-3708	183	37	.	.	NOUN
easat-3708	184	1	6	6	NUM
easat-3708	184	2	:	:	SYM
easat-3708	184	3	7802	7802	NUM
easat-3708	184	4	-	-	SYM
easat-3708	184	5	7812	7812	NUM
easat-3708	184	6	,	,	PUNCT
easat-3708	184	7	2024	2024	NUM
easat-3708	184	8	doi	doi	NOUN
easat-3708	184	9	:	:	PUNCT
easat-3708	184	10	10.55214/25768484.v8i6.3708	10.55214/25768484.v8i6.3708	NUM
easat-3708	184	11	©	©	PROPN
easat-3708	184	12	2024	2024	NUM
easat-3708	184	13	by	by	ADP
easat-3708	184	14	the	the	DET
easat-3708	184	15	authors	author	NOUN
easat-3708	184	16	;	;	PUNCT
easat-3708	184	17	licensee	licensee	NOUN
easat-3708	184	18	learning	learning	NOUN
easat-3708	184	19	gate	gate	NOUN
easat-3708	184	20	for	for	ADP
easat-3708	184	21	𝑡	𝑡	PROPN
easat-3708	184	22	=	=	SYM
easat-3708	184	23	1	1	NUM
easat-3708	184	24	,	,	PUNCT
easat-3708	184	25	⋯	⋯	NOUN
easat-3708	184	26	,	,	PUNCT
easat-3708	184	27	𝑡max	𝑡max	PROPN
easat-3708	184	28	,	,	PUNCT
easat-3708	184	29	where	where	SCONJ
easat-3708	184	30	𝑥′	𝑥′	PUNCT
easat-3708	184	31	is	be	AUX
easat-3708	184	32	in	in	ADP
easat-3708	184	33	the	the	DET
easat-3708	184	34	𝑡-th	𝑡-th	PROPN
easat-3708	184	35	neighborhood	neighborhood	NOUN
easat-3708	184	36	of	of	ADP
easat-3708	184	37	𝑥0	𝑥0	NOUN
easat-3708	184	38	and	and	CCONJ
easat-3708	184	39	𝜖	𝜖	PROPN
easat-3708	184	40	is	be	AUX
easat-3708	184	41	an	an	DET
easat-3708	184	42	arbitrary	arbitrary	ADJ
easat-3708	184	43	parameter	parameter	NOUN
easat-3708	184	44	.	.	PUNCT
easat-3708	185	1	2	2	X
easat-3708	185	2	.	.	PUNCT
easat-3708	185	3	selection	selection	NOUN
easat-3708	185	4	of	of	ADP
easat-3708	185	5	a	a	DET
easat-3708	185	6	point	point	NOUN
easat-3708	185	7	in	in	ADP
easat-3708	185	8	the	the	DET
easat-3708	185	9	neighborhood	neighborhood	NOUN
easat-3708	185	10	of	of	ADP
easat-3708	185	11	𝑥0	𝑥0	NOUN
easat-3708	185	12	:	:	PUNCT
easat-3708	185	13	let	let	VERB
easat-3708	185	14	𝑥′	𝑥′	PART
easat-3708	185	15	be	be	AUX
easat-3708	185	16	a	a	DET
easat-3708	185	17	point	point	NOUN
easat-3708	185	18	in	in	ADP
easat-3708	185	19	the	the	DET
easat-3708	185	20	neighborhood	neighborhood	NOUN
easat-3708	185	21	of	of	ADP
easat-3708	185	22	𝑥0	𝑥0	NOUN
easat-3708	185	23	.	.	PUNCT
easat-3708	186	1	then	then	ADV
easat-3708	186	2	,	,	PUNCT
easat-3708	186	3	𝑥′	𝑥′	NUM
easat-3708	186	4	is	be	AUX
easat-3708	186	5	to	to	PART
easat-3708	186	6	satisfy	satisfy	VERB
easat-3708	186	7	in	in	ADP
easat-3708	186	8	the	the	DET
easat-3708	186	9	following	follow	VERB
easat-3708	186	10	conditions	condition	NOUN
easat-3708	186	11	:	:	PUNCT
easat-3708	186	12	(	(	PUNCT
easat-3708	186	13	a	a	X
easat-3708	186	14	)	)	PUNCT
easat-3708	186	15	(	(	PUNCT
easat-3708	186	16	𝑡	𝑡	NOUN
easat-3708	186	17	−	−	PROPN
easat-3708	186	18	1)𝜖	1)𝜖	NOUN
easat-3708	186	19	<	<	X
easat-3708	186	20	||𝑥′	||𝑥′	VERB
easat-3708	186	21	−	−	PROPN
easat-3708	186	22	𝑥0||	𝑥0||	PROPN
easat-3708	186	23	≤	≤	NOUN
easat-3708	186	24	𝑡𝜖	𝑡𝜖	PROPN
easat-3708	186	25	.	.	PUNCT
easat-3708	187	1	(	(	PUNCT
easat-3708	187	2	b	b	X
easat-3708	187	3	)	)	PUNCT
easat-3708	187	4	𝐵𝑥′	𝐵𝑥′	NOUN
easat-3708	187	5	≤	≤	NOUN
easat-3708	187	6	0	0	NUM
easat-3708	187	7	.	.	PUNCT
easat-3708	188	1	(	(	PUNCT
easat-3708	188	2	c	c	X
easat-3708	188	3	)	)	PUNCT
easat-3708	188	4	𝐻𝑥′	𝐻𝑥′	ADV
easat-3708	188	5	=	=	SYM
easat-3708	188	6	1	1	X
easat-3708	188	7	.	.	PUNCT
easat-3708	189	1	(	(	PUNCT
easat-3708	189	2	d	d	X
easat-3708	189	3	)	)	PUNCT
easat-3708	189	4	𝑥′	𝑥′	X
easat-3708	189	5	≥	≥	NOUN
easat-3708	189	6	0	0	NUM
easat-3708	189	7	.	.	PUNCT
easat-3708	190	1	see	see	VERB
easat-3708	190	2	details	detail	NOUN
easat-3708	190	3	in	in	ADP
easat-3708	190	4	[	[	X
easat-3708	190	5	10	10	NUM
easat-3708	190	6	.	.	PUNCT
easat-3708	190	7	]	]	X
easat-3708	191	1	3	3	X
easat-3708	191	2	.	.	PUNCT
easat-3708	191	3	local	local	ADJ
easat-3708	191	4	search[10	search[10	ADV
easat-3708	191	5	]	]	PUNCT
easat-3708	191	6	:	:	PUNCT
easat-3708	191	7	let	let	VERB
easat-3708	191	8	𝑥𝑘	𝑥𝑘	PRON
easat-3708	191	9	represent	represent	VERB
easat-3708	191	10	a	a	DET
easat-3708	191	11	feasible	feasible	ADJ
easat-3708	191	12	solution	solution	NOUN
easat-3708	191	13	during	during	ADP
easat-3708	191	14	iteration	iteration	NOUN
easat-3708	191	15	𝑘	𝑘	NOUN
easat-3708	191	16	,	,	PUNCT
easat-3708	191	17	we	we	PRON
easat-3708	191	18	want	want	VERB
easat-3708	191	19	to	to	PART
easat-3708	191	20	find	find	VERB
easat-3708	191	21	a	a	DET
easat-3708	191	22	feasible	feasible	ADJ
easat-3708	191	23	solution	solution	NOUN
easat-3708	191	24	with	with	ADP
easat-3708	191	25	larger	large	ADJ
easat-3708	191	26	value	value	NOUN
easat-3708	191	27	of	of	ADP
easat-3708	191	28	the	the	DET
easat-3708	191	29	objective	objective	ADJ
easat-3708	191	30	function	function	NOUN
easat-3708	191	31	with	with	ADP
easat-3708	191	32	respect	respect	NOUN
easat-3708	191	33	to	to	ADP
easat-3708	191	34	𝑥𝑘.	𝑥𝑘.	NOUN
easat-3708	191	35	in	in	ADP
easat-3708	191	36	other	other	ADJ
easat-3708	191	37	words	word	NOUN
easat-3708	191	38	,	,	PUNCT
easat-3708	191	39	we	we	PRON
easat-3708	191	40	must	must	AUX
easat-3708	191	41	find	find	VERB
easat-3708	191	42	𝑠𝑘	𝑠𝑘	NOUN
easat-3708	191	43	such	such	ADJ
easat-3708	191	44	that	that	DET
easat-3708	191	45	�	�	PROPN
easat-3708	191	46	̃	̃	PROPN
easat-3708	191	47	�	�	PROPN
easat-3708	191	48	𝑇(𝑥𝑘	𝑇(𝑥𝑘	ADJ
easat-3708	191	49	+	+	ADJ
easat-3708	191	50	𝑠𝑘	𝑠𝑘	NOUN
easat-3708	191	51	)	)	PUNCT
easat-3708	191	52	≥𝑘	≥𝑘	PROPN
easat-3708	191	53	�	�	PROPN
easat-3708	191	54	̃	̃	PROPN
easat-3708	191	55	�	�	PROPN
easat-3708	191	56	𝑇𝑥𝑘	𝑇𝑥𝑘	PROPN
easat-3708	191	57	,	,	PUNCT
easat-3708	191	58	where	where	SCONJ
easat-3708	191	59	,	,	PUNCT
easat-3708	191	60	{	{	PUNCT
easat-3708	191	61	�	�	PROPN
easat-3708	191	62	̃	̃	NOUN
easat-3708	191	63	�	�	PROPN
easat-3708	191	64	𝑇(𝑥𝑘	𝑇(𝑥𝑘	ADJ
easat-3708	191	65	+	+	ADJ
easat-3708	191	66	𝑠𝑘	𝑠𝑘	NOUN
easat-3708	191	67	)	)	PUNCT
easat-3708	191	68	=	=	SYM
easat-3708	191	69	(	(	PUNCT
easat-3708	191	70	𝐷𝐿𝑇	𝐷𝐿𝑇	PROPN
easat-3708	191	71	(	(	PUNCT
easat-3708	191	72	𝑥𝑘	𝑥𝑘	NOUN
easat-3708	191	73	+	+	CCONJ
easat-3708	191	74	𝑠𝑘)/𝐷𝑇(𝑥𝑘	𝑠𝑘)/𝐷𝑇(𝑥𝑘	PROPN
easat-3708	191	75	+	+	CCONJ
easat-3708	191	76	𝑠𝑘)/𝐷𝑅𝑇	𝑠𝑘)/𝐷𝑅𝑇	NOUN
easat-3708	191	77	(	(	PUNCT
easat-3708	191	78	𝑥𝑘	𝑥𝑘	NOUN
easat-3708	191	79	+	+	CCONJ
easat-3708	191	80	𝑠𝑘	𝑠𝑘	NOUN
easat-3708	191	81	)	)	PUNCT
easat-3708	191	82	)	)	PUNCT
easat-3708	191	83	,	,	PUNCT
easat-3708	191	84	�	�	PROPN
easat-3708	191	85	̃	̃	PROPN
easat-3708	191	86	�	�	PROPN
easat-3708	191	87	𝑇𝑥𝑘	𝑇𝑥𝑘	PROPN
easat-3708	191	88	=	=	PUNCT
easat-3708	191	89	(	(	PUNCT
easat-3708	191	90	𝐷𝐿𝑇	𝐷𝐿𝑇	PROPN
easat-3708	191	91	𝑥𝑘/𝐷𝑇𝑥𝑘/𝐷𝑅𝑇	𝑥𝑘/𝐷𝑇𝑥𝑘/𝐷𝑅𝑇	ADJ
easat-3708	191	92	𝑥𝑘	𝑥𝑘	NOUN
easat-3708	191	93	)	)	PUNCT
easat-3708	191	94	.	.	PUNCT
easat-3708	192	1	since	since	SCONJ
easat-3708	192	2	the	the	DET
easat-3708	192	3	given	give	VERB
easat-3708	192	4	results	result	NOUN
easat-3708	192	5	for	for	ADP
easat-3708	192	6	the	the	DET
easat-3708	192	7	modified	modify	VERB
easat-3708	192	8	kerre	kerre	PROPN
easat-3708	192	9	’s	’s	PART
easat-3708	192	10	method	method	NOUN
easat-3708	192	11	depend	depend	VERB
easat-3708	192	12	on	on	ADP
easat-3708	192	13	the	the	DET
easat-3708	192	14	mean	mean	ADJ
easat-3708	192	15	value	value	NOUN
easat-3708	192	16	of	of	ADP
easat-3708	192	17	the	the	DET
easat-3708	192	18	fuzzy	fuzzy	ADJ
easat-3708	192	19	numbers	number	NOUN
easat-3708	192	20	,	,	PUNCT
easat-3708	192	21	to	to	PART
easat-3708	192	22	find	find	VERB
easat-3708	192	23	𝑠𝑘	𝑠𝑘	NOUN
easat-3708	192	24	we	we	PRON
easat-3708	192	25	consider	consider	VERB
easat-3708	192	26	the	the	DET
easat-3708	192	27	following	follow	VERB
easat-3708	192	28	three	three	NUM
easat-3708	192	29	cases	case	NOUN
easat-3708	192	30	:	:	PUNCT
easat-3708	192	31	case	case	NOUN
easat-3708	192	32	1	1	NUM
easat-3708	192	33	:	:	PUNCT
easat-3708	192	34	𝐷𝑇𝑥𝑘	𝐷𝑇𝑥𝑘	PROPN
easat-3708	192	35	<	<	X
easat-3708	192	36	𝐷𝑇(𝑥𝑘	𝐷𝑇(𝑥𝑘	PROPN
easat-3708	192	37	+	+	CCONJ
easat-3708	192	38	𝑠𝑘	𝑠𝑘	NOUN
easat-3708	192	39	)	)	PUNCT
easat-3708	192	40	,	,	PUNCT
easat-3708	192	41	case	case	NOUN
easat-3708	192	42	2	2	NUM
easat-3708	192	43	:	:	PUNCT
easat-3708	192	44	𝐷𝑇(𝑥𝑘	𝐷𝑇(𝑥𝑘	PROPN
easat-3708	192	45	+	+	CCONJ
easat-3708	192	46	𝑠𝑘	𝑠𝑘	NOUN
easat-3708	192	47	)	)	PUNCT
easat-3708	192	48	<	<	X
easat-3708	192	49	𝐷𝑇𝑥𝑘	𝐷𝑇𝑥𝑘	PROPN
easat-3708	192	50	,	,	PUNCT
easat-3708	192	51	case	case	NOUN
easat-3708	192	52	3	3	NUM
easat-3708	192	53	:	:	PUNCT
easat-3708	192	54	𝐷𝑇(𝑥𝑘	𝐷𝑇(𝑥𝑘	PROPN
easat-3708	192	55	+	+	CCONJ
easat-3708	192	56	𝑠𝑘	𝑠𝑘	NOUN
easat-3708	192	57	)	)	PUNCT
easat-3708	192	58	=	=	SYM
easat-3708	192	59	𝐷𝑇𝑥𝑘	𝐷𝑇𝑥𝑘	PROPN
easat-3708	192	60	.	.	PUNCT
easat-3708	193	1	(	(	PUNCT
easat-3708	193	2	a	a	X
easat-3708	193	3	)	)	PUNCT
easat-3708	193	4	let	let	VERB
easat-3708	193	5	𝐷𝑇𝑥𝑘	𝐷𝑇𝑥𝑘	PROPN
easat-3708	193	6	<	<	X
easat-3708	193	7	𝐷𝑇(𝑥𝑘	𝐷𝑇(𝑥𝑘	PROPN
easat-3708	193	8	+	+	CCONJ
easat-3708	193	9	𝑠𝑘	𝑠𝑘	NOUN
easat-3708	193	10	)	)	PUNCT
easat-3708	193	11	,	,	PUNCT
easat-3708	193	12	based	base	VERB
easat-3708	193	13	on	on	ADP
easat-3708	193	14	note	note	NOUN
easat-3708	193	15	2	2	NUM
easat-3708	193	16	,	,	PUNCT
easat-3708	193	17	we	we	PRON
easat-3708	193	18	must	must	AUX
easat-3708	193	19	have	have	VERB
easat-3708	193	20	𝑟(	𝑟(	NUM
easat-3708	193	21	�	�	PROPN
easat-3708	193	22	̃	̃	PROPN
easat-3708	193	23	�	�	PROPN
easat-3708	193	24	𝑇𝑥𝑘	𝑇𝑥𝑘	PROPN
easat-3708	193	25	,	,	PUNCT
easat-3708	193	26	�	�	PROPN
easat-3708	193	27	̃	̃	PROPN
easat-3708	193	28	�	�	PROPN
easat-3708	193	29	𝑇(𝑥𝑘	𝑇(𝑥𝑘	ADJ
easat-3708	193	30	+	+	ADJ
easat-3708	193	31	𝑠𝑘	𝑠𝑘	NOUN
easat-3708	193	32	)	)	PUNCT
easat-3708	193	33	)	)	PUNCT
easat-3708	193	34	≥	≥	NOUN
easat-3708	193	35	0	0	NUM
easat-3708	193	36	,	,	PUNCT
easat-3708	193	37	and	and	CCONJ
easat-3708	193	38	thus	thus	ADV
easat-3708	193	39	we	we	PRON
easat-3708	193	40	propose	propose	VERB
easat-3708	193	41	problem	problem	NOUN
easat-3708	193	42	(	(	PUNCT
easat-3708	193	43	𝑃1	𝑃1	NOUN
easat-3708	193	44	)	)	PUNCT
easat-3708	193	45	as	as	SCONJ
easat-3708	193	46	follows	follow	VERB
easat-3708	193	47	:	:	PUNCT
easat-3708	193	48	max	max	PROPN
easat-3708	193	49	𝑟(	𝑟(	NUM
easat-3708	193	50	�	�	PROPN
easat-3708	193	51	̃	̃	PROPN
easat-3708	193	52	�	�	NOUN
easat-3708	193	53	𝑇(𝑥𝑘	𝑇(𝑥𝑘	NUM
easat-3708	193	54	)	)	PUNCT
easat-3708	193	55	,	,	PUNCT
easat-3708	193	56	�	�	PROPN
easat-3708	193	57	̃	̃	PROPN
easat-3708	193	58	�	�	PROPN
easat-3708	193	59	𝑇(𝑥𝑘	𝑇(𝑥𝑘	ADJ
easat-3708	193	60	+	+	ADJ
easat-3708	193	61	𝑠𝑘	𝑠𝑘	NOUN
easat-3708	193	62	)	)	PUNCT
easat-3708	193	63	)	)	PUNCT
easat-3708	193	64	,	,	PUNCT
easat-3708	193	65	𝑠.	𝑠.	NOUN
easat-3708	193	66	𝑡.	𝑡.	NOUN
easat-3708	193	67	(	(	PUNCT
easat-3708	193	68	15	15	NUM
easat-3708	193	69	)	)	PUNCT
easat-3708	193	70	(	(	PUNCT
easat-3708	193	71	𝑃1	𝑃1	NOUN
easat-3708	193	72	)	)	PUNCT
easat-3708	193	73	𝐷𝑇𝑠𝑘	𝐷𝑇𝑠𝑘	ADJ
easat-3708	193	74	≥	≥	NOUN
easat-3708	193	75	0	0	NUM
easat-3708	193	76	,	,	PUNCT
easat-3708	193	77	𝐵𝑠𝑘	𝐵𝑠𝑘	PROPN
easat-3708	193	78	≤	≤	X
easat-3708	193	79	−𝐵𝑥𝑘	−𝐵𝑥𝑘	NOUN
easat-3708	193	80	,	,	PUNCT
easat-3708	194	1	𝐻𝑠𝑘	𝐻𝑠𝑘	PROPN
easat-3708	194	2	=	=	SYM
easat-3708	194	3	1	1	NUM
easat-3708	194	4	−	−	PROPN
easat-3708	194	5	𝐻𝑥𝑘	𝐻𝑥𝑘	PROPN
easat-3708	194	6	,	,	PUNCT
easat-3708	194	7	−𝑠𝑘	−𝑠𝑘	NOUN
easat-3708	194	8	≤	≤	NOUN
easat-3708	194	9	𝑥𝑘	𝑥𝑘	X
easat-3708	194	10	.	.	PUNCT
easat-3708	195	1	note	note	VERB
easat-3708	195	2	that	that	SCONJ
easat-3708	195	3	replacing	replace	VERB
easat-3708	195	4	the	the	DET
easat-3708	195	5	constraint	constraint	NOUN
easat-3708	195	6	𝐷𝑇𝑠𝑘	𝐷𝑇𝑠𝑘	PUNCT
easat-3708	195	7	>	>	X
easat-3708	195	8	0	0	PUNCT
easat-3708	195	9	with	with	ADP
easat-3708	195	10	𝐷𝑇𝑠𝑘	𝐷𝑇𝑠𝑘	PROPN
easat-3708	195	11	≥	≥	X
easat-3708	195	12	0	0	NUM
easat-3708	195	13	has	have	VERB
easat-3708	195	14	no	no	DET
easat-3708	195	15	impact	impact	NOUN
easat-3708	195	16	on	on	ADP
easat-3708	195	17	the	the	DET
easat-3708	195	18	solution	solution	NOUN
easat-3708	195	19	of	of	ADP
easat-3708	195	20	(	(	PUNCT
easat-3708	195	21	𝑃1	𝑃1	NOUN
easat-3708	195	22	)	)	PUNCT
easat-3708	195	23	.	.	PUNCT
easat-3708	196	1	i.	i.	PROPN
easat-3708	196	2	let	let	VERB
easat-3708	196	3	(	(	PUNCT
easat-3708	196	4	�	�	PROPN
easat-3708	196	5	̃	̃	NOUN
easat-3708	196	6	�	�	NOUN
easat-3708	196	7	𝑇𝑥𝑘)𝑅	𝑇𝑥𝑘)𝑅	PART
easat-3708	196	8	and	and	CCONJ
easat-3708	196	9	(	(	PUNCT
easat-3708	196	10	�	�	PROPN
easat-3708	196	11	̃	̃	NOUN
easat-3708	196	12	�	�	PROPN
easat-3708	196	13	𝑇(𝑥𝑘	𝑇(𝑥𝑘	ADJ
easat-3708	196	14	+	+	PUNCT
easat-3708	196	15	𝑠𝑘))𝐿	𝑠𝑘))𝐿	NOUN
easat-3708	196	16	have	have	VERB
easat-3708	196	17	an	an	DET
easat-3708	196	18	intersection	intersection	NOUN
easat-3708	196	19	point	point	NOUN
easat-3708	196	20	.	.	PUNCT
easat-3708	197	1	in	in	ADP
easat-3708	197	2	this	this	DET
easat-3708	197	3	case	case	NOUN
easat-3708	197	4	,	,	PUNCT
easat-3708	197	5	we	we	PRON
easat-3708	197	6	have	have	VERB
easat-3708	197	7	𝐷𝑇𝑥𝑘	𝐷𝑇𝑥𝑘	PROPN
easat-3708	197	8	≤	≤	PROPN
easat-3708	197	9	𝐷𝑇(𝑥𝑘	𝐷𝑇(𝑥𝑘	PROPN
easat-3708	197	10	+	+	CCONJ
easat-3708	197	11	𝑠𝑘	𝑠𝑘	NOUN
easat-3708	197	12	)	)	PUNCT
easat-3708	197	13	and	and	CCONJ
easat-3708	197	14	𝐷𝐿𝑇	𝐷𝐿𝑇	PROPN
easat-3708	197	15	(	(	PUNCT
easat-3708	197	16	𝑥𝑘	𝑥𝑘	NOUN
easat-3708	197	17	+	+	CCONJ
easat-3708	197	18	𝑠𝑘	𝑠𝑘	NOUN
easat-3708	197	19	)	)	PUNCT
easat-3708	197	20	≤	≤	NOUN
easat-3708	197	21	𝐷𝑅𝑇	𝐷𝑅𝑇	PROPN
easat-3708	197	22	𝑥𝑘	𝑥𝑘	PROPN
easat-3708	197	23	,	,	PUNCT
easat-3708	197	24	and	and	CCONJ
easat-3708	197	25	(	(	PUNCT
easat-3708	197	26	15	15	X
easat-3708	197	27	)	)	PUNCT
easat-3708	197	28	turns	turn	VERB
easat-3708	197	29	into	into	ADP
easat-3708	197	30	(	(	PUNCT
easat-3708	197	31	𝑃1	𝑃1	NOUN
easat-3708	197	32	′	′	NUM
easat-3708	197	33	)	)	PUNCT
easat-3708	197	34	as	as	SCONJ
easat-3708	197	35	follows	follow	VERB
easat-3708	197	36	:	:	PUNCT
easat-3708	197	37	max	max	PROPN
easat-3708	197	38	(	(	PUNCT
easat-3708	197	39	𝐷𝑅	𝐷𝑅	PROPN
easat-3708	197	40	−	−	PROPN
easat-3708	197	41	𝐷𝐿)𝑇𝑥𝑘	𝐷𝐿)𝑇𝑥𝑘	PROPN
easat-3708	197	42	+	+	CCONJ
easat-3708	197	43	(	(	PUNCT
easat-3708	197	44	𝐷𝑅−𝐷𝐿)𝑇	𝐷𝑅−𝐷𝐿)𝑇	PROPN
easat-3708	197	45	2	2	NUM
easat-3708	197	46	𝑠𝑘	𝑠𝑘	NOUN
easat-3708	197	47	−	−	PROPN
easat-3708	197	48	(	(	PUNCT
easat-3708	197	49	(	(	PUNCT
easat-3708	197	50	𝐷𝑅−𝐷𝐿)𝑇𝑥𝑘−𝐷𝐿𝑇	𝐷𝑅−𝐷𝐿)𝑇𝑥𝑘−𝐷𝐿𝑇	PROPN
easat-3708	197	51	𝑠𝑘)2	𝑠𝑘)2	PROPN
easat-3708	197	52	(	(	PUNCT
easat-3708	197	53	𝐷𝑅−𝐷𝐿)𝑇𝑥𝑘+(𝐷−𝐷𝐿)𝑇𝑠𝑘	𝐷𝑅−𝐷𝐿)𝑇𝑥𝑘+(𝐷−𝐷𝐿)𝑇𝑠𝑘	PROPN
easat-3708	197	54	,	,	PUNCT
easat-3708	197	55	𝑠.	𝑠.	PROPN
easat-3708	197	56	𝑡.	𝑡.	PROPN
easat-3708	197	57	,	,	PUNCT
easat-3708	197	58	(	(	PUNCT
easat-3708	197	59	16	16	NUM
easat-3708	197	60	)	)	PUNCT
easat-3708	197	61	(	(	PUNCT
easat-3708	197	62	𝑃1	𝑃1	NOUN
easat-3708	197	63	′	′	NUM
easat-3708	197	64	)	)	PUNCT
easat-3708	198	1	−	−	PROPN
easat-3708	198	2	𝐷𝑇𝑠𝑘	𝐷𝑇𝑠𝑘	ADJ
easat-3708	198	3	≤	≤	NOUN
easat-3708	198	4	0	0	NUM
easat-3708	198	5	,	,	PUNCT
easat-3708	198	6	𝐷𝐿𝑇	𝐷𝐿𝑇	PROPN
easat-3708	198	7	𝑠𝑘	𝑠𝑘	NOUN
easat-3708	198	8	≤	≤	NOUN
easat-3708	198	9	(	(	PUNCT
easat-3708	198	10	𝐷𝑅	𝐷𝑅	PROPN
easat-3708	198	11	−	−	PROPN
easat-3708	198	12	𝐷𝐿)𝑇𝑥𝑘	𝐷𝐿)𝑇𝑥𝑘	PROPN
easat-3708	198	13	,	,	PUNCT
easat-3708	198	14	𝐵𝑠𝑘	𝐵𝑠𝑘	PROPN
easat-3708	198	15	≤	≤	X
easat-3708	198	16	−𝐵𝑥𝑘	−𝐵𝑥𝑘	NOUN
easat-3708	198	17	,	,	PUNCT
easat-3708	198	18	𝐻𝑠𝑘	𝐻𝑠𝑘	PROPN
easat-3708	198	19	=	=	SYM
easat-3708	198	20	1	1	NUM
easat-3708	198	21	−	−	PROPN
easat-3708	198	22	𝐻𝑥𝑘	𝐻𝑥𝑘	PROPN
easat-3708	198	23	,	,	PUNCT
easat-3708	198	24	−𝑠𝑘	−𝑠𝑘	NOUN
easat-3708	198	25	≤	≤	NOUN
easat-3708	198	26	𝑥𝑘	𝑥𝑘	X
easat-3708	198	27	.	.	PUNCT
easat-3708	199	1	note	note	VERB
easat-3708	199	2	that	that	SCONJ
easat-3708	199	3	(	(	PUNCT
easat-3708	199	4	𝑃1	𝑃1	NOUN
easat-3708	199	5	′	′	NOUN
easat-3708	199	6	)	)	PUNCT
easat-3708	199	7	is	be	AUX
easat-3708	199	8	a	a	DET
easat-3708	199	9	quadratic	quadratic	ADJ
easat-3708	199	10	fractional	fractional	ADJ
easat-3708	199	11	programming	programming	NOUN
easat-3708	199	12	problem	problem	NOUN
easat-3708	199	13	.	.	PUNCT
easat-3708	200	1	by	by	ADP
easat-3708	200	2	using	use	VERB
easat-3708	200	3	a	a	DET
easat-3708	200	4	method	method	NOUN
easat-3708	200	5	that	that	PRON
easat-3708	200	6	is	be	AUX
easat-3708	200	7	proposed	propose	VERB
easat-3708	200	8	in	in	ADP
easat-3708	200	9	[	[	X
easat-3708	200	10	9	9	NUM
easat-3708	200	11	]	]	PUNCT
easat-3708	200	12	(	(	PUNCT
easat-3708	200	13	theorem	theorem	NOUN
easat-3708	200	14	and	and	CCONJ
easat-3708	200	15	section	section	NOUN
easat-3708	200	16	3	3	NUM
easat-3708	200	17	)	)	PUNCT
easat-3708	200	18	we	we	PRON
easat-3708	200	19	solve	solve	VERB
easat-3708	200	20	problem	problem	NOUN
easat-3708	200	21	(	(	PUNCT
easat-3708	200	22	𝑃1	𝑃1	NOUN
easat-3708	200	23	′	′	NUM
easat-3708	200	24	)	)	PUNCT
easat-3708	200	25	.	.	PUNCT
easat-3708	201	1	ii	ii	X
easat-3708	201	2	.	.	PUNCT
easat-3708	202	1	𝐷𝑅𝑇	𝐷𝑅𝑇	PROPN
easat-3708	202	2	𝑥𝑘	𝑥𝑘	X
easat-3708	202	3	≤	≤	NUM
easat-3708	202	4	𝐷𝐿𝑇	𝐷𝐿𝑇	PROPN
easat-3708	202	5	(	(	PUNCT
easat-3708	202	6	𝑥𝑘	𝑥𝑘	NOUN
easat-3708	202	7	+	+	CCONJ
easat-3708	202	8	𝑠𝑘	𝑠𝑘	NOUN
easat-3708	202	9	)	)	PUNCT
easat-3708	202	10	,	,	PUNCT
easat-3708	202	11	that	that	PRON
easat-3708	202	12	means	mean	VERB
easat-3708	202	13	two	two	NUM
easat-3708	202	14	numbers	number	NOUN
easat-3708	202	15	do	do	AUX
easat-3708	202	16	not	not	PART
easat-3708	202	17	have	have	VERB
easat-3708	202	18	any	any	DET
easat-3708	202	19	intersection	intersection	NOUN
easat-3708	202	20	point	point	NOUN
easat-3708	202	21	(	(	PUNCT
easat-3708	202	22	see	see	VERB
easat-3708	202	23	(	(	PUNCT
easat-3708	202	24	3	3	NUM
easat-3708	202	25	)	)	PUNCT
easat-3708	202	26	)	)	PUNCT
easat-3708	202	27	.	.	PUNCT
easat-3708	203	1	by	by	ADP
easat-3708	203	2	using	use	VERB
easat-3708	203	3	(	(	PUNCT
easat-3708	203	4	3	3	NUM
easat-3708	203	5	)	)	PUNCT
easat-3708	203	6	we	we	PRON
easat-3708	203	7	have	have	VERB
easat-3708	203	8	the	the	DET
easat-3708	203	9	following	follow	VERB
easat-3708	203	10	program	program	NOUN
easat-3708	203	11	:	:	PUNCT
easat-3708	203	12	max	max	PROPN
easat-3708	203	13	(	(	PUNCT
easat-3708	203	14	𝐷𝑅	𝐷𝑅	PROPN
easat-3708	203	15	−	−	PROPN
easat-3708	204	1	𝐷𝐿)𝑇𝑥𝑘	𝐷𝐿)𝑇𝑥𝑘	PROPN
easat-3708	204	2	+	+	CCONJ
easat-3708	204	3	(	(	PUNCT
easat-3708	204	4	𝐷𝑅−𝐷𝐿)𝑇	𝐷𝑅−𝐷𝐿)𝑇	PROPN
easat-3708	204	5	2	2	NUM
easat-3708	204	6	𝑠𝑘	𝑠𝑘	NOUN
easat-3708	204	7	,	,	PUNCT
easat-3708	204	8	𝑠.	𝑠.	PROPN
easat-3708	204	9	𝑡.	𝑡.	PROPN
easat-3708	204	10	,	,	PUNCT
easat-3708	204	11	(	(	PUNCT
easat-3708	204	12	17	17	NUM
easat-3708	204	13	)	)	PUNCT
easat-3708	204	14	(	(	PUNCT
easat-3708	204	15	𝑃2	𝑃2	PROPN
easat-3708	204	16	)	)	PUNCT
easat-3708	204	17	−	−	PROPN
easat-3708	204	18	𝐷𝑇𝑠𝑘	𝐷𝑇𝑠𝑘	ADJ
easat-3708	204	19	≤	≤	NOUN
easat-3708	204	20	0	0	NUM
easat-3708	204	21	,	,	PUNCT
easat-3708	204	22	−𝐷𝐿𝑇	−𝐷𝐿𝑇	NOUN
easat-3708	204	23	𝑠𝑘	𝑠𝑘	NOUN
easat-3708	204	24	≤	≤	NOUN
easat-3708	205	1	(	(	PUNCT
easat-3708	205	2	𝐷𝐿	𝐷𝐿	PROPN
easat-3708	205	3	−	−	PROPN
easat-3708	205	4	𝐷𝑅)𝑇𝑥𝑘	𝐷𝑅)𝑇𝑥𝑘	PROPN
easat-3708	205	5	,	,	PUNCT
easat-3708	205	6	𝐵𝑠𝑘	𝐵𝑠𝑘	PROPN
easat-3708	205	7	≤	≤	X
easat-3708	205	8	−𝐵𝑥𝑘	−𝐵𝑥𝑘	NOUN
easat-3708	205	9	,	,	PUNCT
easat-3708	206	1	𝐻𝑠𝑘	𝐻𝑠𝑘	PROPN
easat-3708	206	2	=	=	SYM
easat-3708	206	3	1	1	NUM
easat-3708	206	4	−	−	PROPN
easat-3708	206	5	𝐻𝑥𝑘	𝐻𝑥𝑘	PROPN
easat-3708	206	6	,	,	PUNCT
easat-3708	206	7	−𝑠𝑘	−𝑠𝑘	NOUN
easat-3708	206	8	≤	≤	NOUN
easat-3708	206	9	𝑥𝑘	𝑥𝑘	X
easat-3708	206	10	.	.	PUNCT
easat-3708	207	1	after	after	ADP
easat-3708	207	2	removing	remove	VERB
easat-3708	207	3	the	the	DET
easat-3708	207	4	constant	constant	ADJ
easat-3708	207	5	terms	term	NOUN
easat-3708	207	6	,	,	PUNCT
easat-3708	207	7	we	we	PRON
easat-3708	207	8	have	have	VERB
easat-3708	207	9	:	:	PUNCT
easat-3708	208	1	max	max	PROPN
easat-3708	208	2	(	(	PUNCT
easat-3708	208	3	𝐷𝑅−𝐷𝐿)𝑇	𝐷𝑅−𝐷𝐿)𝑇	PROPN
easat-3708	208	4	2	2	NUM
easat-3708	208	5	𝑠𝑘	𝑠𝑘	NOUN
easat-3708	208	6	,	,	PUNCT
easat-3708	208	7	𝑠.	𝑠.	PROPN
easat-3708	208	8	𝑡.	𝑡.	PROPN
easat-3708	208	9	,	,	PUNCT
easat-3708	208	10	(	(	PUNCT
easat-3708	208	11	18	18	NUM
easat-3708	208	12	)	)	PUNCT
easat-3708	208	13	(	(	PUNCT
easat-3708	208	14	𝑃2	𝑃2	PROPN
easat-3708	208	15	′	′	NOUN
easat-3708	208	16	)	)	PUNCT
easat-3708	208	17	−	−	PROPN
easat-3708	208	18	𝐷𝑇𝑠𝑘	𝐷𝑇𝑠𝑘	ADJ
easat-3708	208	19	≤	≤	NOUN
easat-3708	208	20	0	0	NUM
easat-3708	208	21	,	,	PUNCT
easat-3708	208	22	−𝐷𝐿𝑇	−𝐷𝐿𝑇	NOUN
easat-3708	208	23	𝑠𝑘	𝑠𝑘	NOUN
easat-3708	208	24	≤	≤	NOUN
easat-3708	208	25	(	(	PUNCT
easat-3708	208	26	𝐷𝐿	𝐷𝐿	PROPN
easat-3708	208	27	−	−	PROPN
easat-3708	208	28	𝐷𝑅)𝑇𝑥𝑘	𝐷𝑅)𝑇𝑥𝑘	PROPN
easat-3708	208	29	,	,	PUNCT
easat-3708	208	30	𝐵𝑠𝑘	𝐵𝑠𝑘	PROPN
easat-3708	208	31	≤	≤	X
easat-3708	208	32	−𝐵𝑥𝑘	−𝐵𝑥𝑘	NOUN
easat-3708	208	33	,	,	PUNCT
easat-3708	208	34	𝐻𝑠𝑘	𝐻𝑠𝑘	PROPN
easat-3708	208	35	=	=	SYM
easat-3708	208	36	1	1	NUM
easat-3708	208	37	−	−	PROPN
easat-3708	208	38	𝐻𝑥𝑘	𝐻𝑥𝑘	PROPN
easat-3708	208	39	,	,	PUNCT
easat-3708	208	40	−𝑠𝑘	−𝑠𝑘	NOUN
easat-3708	208	41	≤	≤	NOUN
easat-3708	208	42	𝑥𝑘	𝑥𝑘	X
easat-3708	208	43	.	.	PUNCT
easat-3708	209	1	7809	7809	NUM
easat-3708	209	2	edelweiss	edelweiss	PROPN
easat-3708	209	3	applied	apply	VERB
easat-3708	209	4	science	science	NOUN
easat-3708	209	5	and	and	CCONJ
easat-3708	209	6	technology	technology	NOUN
easat-3708	209	7	issn	issn	PROPN
easat-3708	209	8	:	:	PUNCT
easat-3708	209	9	2576	2576	NUM
easat-3708	209	10	-	-	SYM
easat-3708	209	11	8484	8484	NUM
easat-3708	209	12	vol	vol	NOUN
easat-3708	209	13	.	.	PROPN
easat-3708	209	14	8	8	NUM
easat-3708	209	15	,	,	PUNCT
easat-3708	209	16	no	no	INTJ
easat-3708	209	17	.	.	NOUN
easat-3708	209	18	6	6	NUM
easat-3708	209	19	:	:	SYM
easat-3708	209	20	7802	7802	NUM
easat-3708	209	21	-	-	SYM
easat-3708	209	22	7812	7812	NUM
easat-3708	209	23	,	,	PUNCT
easat-3708	209	24	2024	2024	NUM
easat-3708	209	25	doi	doi	NOUN
easat-3708	209	26	:	:	PUNCT
easat-3708	209	27	10.55214/25768484.v8i6.3708	10.55214/25768484.v8i6.3708	NUM
easat-3708	209	28	©	©	PROPN
easat-3708	209	29	2024	2024	NUM
easat-3708	209	30	by	by	ADP
easat-3708	209	31	the	the	DET
easat-3708	209	32	authors	author	NOUN
easat-3708	209	33	;	;	PUNCT
easat-3708	209	34	licensee	licensee	PROPN
easat-3708	209	35	learning	learning	NOUN
easat-3708	209	36	gate	gate	NOUN
easat-3708	209	37	(	(	PUNCT
easat-3708	209	38	b	b	X
easat-3708	209	39	)	)	PUNCT
easat-3708	209	40	let	let	VERB
easat-3708	209	41	𝐷𝑇𝑥𝑘	𝐷𝑇𝑥𝑘	PROPN
easat-3708	209	42	>	>	X
easat-3708	209	43	𝐷𝑇(𝑥𝑘	𝐷𝑇(𝑥𝑘	PROPN
easat-3708	209	44	+	+	CCONJ
easat-3708	209	45	𝑠𝑘	𝑠𝑘	NOUN
easat-3708	209	46	)	)	PUNCT
easat-3708	209	47	.	.	PUNCT
easat-3708	210	1	in	in	ADP
easat-3708	210	2	this	this	DET
easat-3708	210	3	case	case	NOUN
easat-3708	210	4	if	if	SCONJ
easat-3708	210	5	𝑟(	𝑟(	NUM
easat-3708	210	6	�	�	PROPN
easat-3708	210	7	̃	̃	PROPN
easat-3708	210	8	�	�	PROPN
easat-3708	210	9	𝑇(𝑥𝑘	𝑇(𝑥𝑘	ADJ
easat-3708	210	10	+	+	ADJ
easat-3708	210	11	𝑠𝑘	𝑠𝑘	NOUN
easat-3708	210	12	)	)	PUNCT
easat-3708	210	13	,	,	PUNCT
easat-3708	210	14	�	�	PROPN
easat-3708	210	15	̃	̃	PROPN
easat-3708	210	16	�	�	PROPN
easat-3708	210	17	𝑇𝑥𝑘	𝑇𝑥𝑘	ADJ
easat-3708	210	18	)	)	PUNCT
easat-3708	210	19	≤	≤	NOUN
easat-3708	210	20	0	0	PUNCT
easat-3708	210	21	then	then	ADV
easat-3708	210	22	�	�	PROPN
easat-3708	210	23	̃	̃	PROPN
easat-3708	210	24	�	�	PROPN
easat-3708	210	25	𝑇(𝑥𝑘	𝑇(𝑥𝑘	ADJ
easat-3708	210	26	+	+	ADJ
easat-3708	210	27	𝑠𝑘	𝑠𝑘	NOUN
easat-3708	210	28	)	)	PUNCT
easat-3708	210	29	>	>	X
easat-3708	210	30	𝑘	𝑘	DET
easat-3708	210	31	�	�	PROPN
easat-3708	210	32	̃	̃	PROPN
easat-3708	210	33	�	�	PROPN
easat-3708	210	34	𝑇𝑥𝑘.	𝑇𝑥𝑘.	PROPN
easat-3708	210	35	so	so	ADV
easat-3708	210	36	,	,	PUNCT
easat-3708	210	37	we	we	PRON
easat-3708	210	38	propose	propose	VERB
easat-3708	210	39	the	the	DET
easat-3708	210	40	following	following	ADJ
easat-3708	210	41	problem	problem	NOUN
easat-3708	210	42	:	:	PUNCT
easat-3708	210	43	min	min	PROPN
easat-3708	210	44	𝑟(	𝑟(	PROPN
easat-3708	210	45	�	�	PROPN
easat-3708	210	46	̃	̃	PROPN
easat-3708	210	47	�	�	PROPN
easat-3708	210	48	𝑇(𝑥𝑘	𝑇(𝑥𝑘	ADJ
easat-3708	210	49	+	+	ADJ
easat-3708	210	50	𝑠𝑘	𝑠𝑘	NOUN
easat-3708	210	51	)	)	PUNCT
easat-3708	210	52	,	,	PUNCT
easat-3708	210	53	�	�	PROPN
easat-3708	210	54	̃	̃	PROPN
easat-3708	210	55	�	�	PROPN
easat-3708	210	56	𝑇𝑥𝑘	𝑇𝑥𝑘	ADJ
easat-3708	210	57	)	)	PUNCT
easat-3708	210	58	,	,	PUNCT
easat-3708	210	59	𝑠.	𝑠.	PROPN
easat-3708	210	60	𝑡.	𝑡.	PROPN
easat-3708	210	61	,	,	PUNCT
easat-3708	210	62	(	(	PUNCT
easat-3708	210	63	19	19	NUM
easat-3708	210	64	)	)	PUNCT
easat-3708	210	65	(	(	PUNCT
easat-3708	210	66	𝑃3	𝑃3	NOUN
easat-3708	210	67	)	)	PUNCT
easat-3708	210	68	𝐷𝑇𝑠𝑘	𝐷𝑇𝑠𝑘	ADJ
easat-3708	210	69	≤	≤	NOUN
easat-3708	210	70	0	0	NUM
easat-3708	210	71	,	,	PUNCT
easat-3708	210	72	𝐵𝑠𝑘	𝐵𝑠𝑘	PROPN
easat-3708	210	73	≤	≤	X
easat-3708	210	74	−𝐵𝑥𝑘	−𝐵𝑥𝑘	NOUN
easat-3708	210	75	,	,	PUNCT
easat-3708	211	1	𝐻𝑠𝑘	𝐻𝑠𝑘	PROPN
easat-3708	211	2	=	=	SYM
easat-3708	211	3	1	1	NUM
easat-3708	211	4	−	−	PROPN
easat-3708	211	5	𝐻𝑥𝑘	𝐻𝑥𝑘	PROPN
easat-3708	211	6	,	,	PUNCT
easat-3708	211	7	−𝑠𝑘	−𝑠𝑘	NOUN
easat-3708	211	8	≤	≤	NOUN
easat-3708	211	9	𝑥𝑘	𝑥𝑘	X
easat-3708	211	10	.	.	PUNCT
easat-3708	212	1	note	note	VERB
easat-3708	212	2	that	that	SCONJ
easat-3708	212	3	replacing	replace	VERB
easat-3708	212	4	the	the	DET
easat-3708	212	5	constraint	constraint	NOUN
easat-3708	212	6	𝐷𝑇𝑠𝑘	𝐷𝑇𝑠𝑘	PUNCT
easat-3708	212	7	<	<	X
easat-3708	212	8	0	0	NUM
easat-3708	212	9	with	with	ADP
easat-3708	212	10	𝐷𝑇𝑠𝑘	𝐷𝑇𝑠𝑘	ADJ
easat-3708	212	11	≤	≤	NOUN
easat-3708	212	12	0	0	PUNCT
easat-3708	212	13	has	have	VERB
easat-3708	212	14	no	no	DET
easat-3708	212	15	impact	impact	NOUN
easat-3708	212	16	on	on	ADP
easat-3708	212	17	the	the	DET
easat-3708	212	18	solution	solution	NOUN
easat-3708	212	19	of	of	ADP
easat-3708	212	20	(	(	PUNCT
easat-3708	212	21	𝑃3	𝑃3	NOUN
easat-3708	212	22	)	)	PUNCT
easat-3708	212	23	.	.	PUNCT
easat-3708	213	1	i.	i.	PROPN
easat-3708	213	2	let	let	VERB
easat-3708	213	3	(	(	PUNCT
easat-3708	213	4	�	�	PROPN
easat-3708	213	5	̃	̃	NOUN
easat-3708	213	6	�	�	NOUN
easat-3708	213	7	𝑇(𝑥𝑘	𝑇(𝑥𝑘	ADJ
easat-3708	213	8	+	+	NUM
easat-3708	213	9	𝑠𝑘))𝑅	𝑠𝑘))𝑅	PROPN
easat-3708	213	10	and	and	CCONJ
easat-3708	213	11	(	(	PUNCT
easat-3708	213	12	�	�	PROPN
easat-3708	213	13	̃	̃	PROPN
easat-3708	213	14	�	�	PROPN
easat-3708	213	15	𝑇𝑥𝑘)𝐿	𝑇𝑥𝑘)𝐿	NOUN
easat-3708	213	16	have	have	VERB
easat-3708	213	17	an	an	DET
easat-3708	213	18	intersection	intersection	NOUN
easat-3708	213	19	point	point	NOUN
easat-3708	213	20	.	.	PUNCT
easat-3708	214	1	in	in	ADP
easat-3708	214	2	this	this	DET
easat-3708	214	3	case	case	NOUN
easat-3708	214	4	,	,	PUNCT
easat-3708	214	5	we	we	PRON
easat-3708	214	6	have	have	VERB
easat-3708	214	7	𝐷𝑇𝑥𝑘	𝐷𝑇𝑥𝑘	PROPN
easat-3708	214	8	≥	≥	PRON
easat-3708	214	9	𝐷𝑇(𝑥𝑘	𝐷𝑇(𝑥𝑘	NOUN
easat-3708	214	10	+	+	CCONJ
easat-3708	214	11	𝑠𝑘	𝑠𝑘	NOUN
easat-3708	214	12	)	)	PUNCT
easat-3708	214	13	and	and	CCONJ
easat-3708	214	14	𝐷𝐿𝑇	𝐷𝐿𝑇	PROPN
easat-3708	214	15	𝑥𝑘	𝑥𝑘	X
easat-3708	214	16	≤	≤	ADJ
easat-3708	214	17	𝐷𝑅𝑇	𝐷𝑅𝑇	PROPN
easat-3708	214	18	(	(	PUNCT
easat-3708	214	19	𝑥𝑘	𝑥𝑘	X
easat-3708	214	20	+	+	CCONJ
easat-3708	214	21	𝑠𝑘	𝑠𝑘	NOUN
easat-3708	214	22	)	)	PUNCT
easat-3708	214	23	,	,	PUNCT
easat-3708	214	24	the	the	DET
easat-3708	214	25	problem	problem	NOUN
easat-3708	214	26	(	(	PUNCT
easat-3708	214	27	19	19	NUM
easat-3708	214	28	)	)	PUNCT
easat-3708	214	29	turns	turn	VERB
easat-3708	214	30	into	into	ADP
easat-3708	214	31	(	(	PUNCT
easat-3708	214	32	𝑃3	𝑃3	NOUN
easat-3708	214	33	′	′	NOUN
easat-3708	214	34	)	)	PUNCT
easat-3708	214	35	as	as	SCONJ
easat-3708	214	36	follows	follow	VERB
easat-3708	214	37	:	:	PUNCT
easat-3708	214	38	min	min	NOUN
easat-3708	214	39	(	(	PUNCT
easat-3708	214	40	𝐷𝑅	𝐷𝑅	PROPN
easat-3708	214	41	−	−	PROPN
easat-3708	215	1	𝐷𝐿)𝑇𝑥𝑘	𝐷𝐿)𝑇𝑥𝑘	PROPN
easat-3708	215	2	+	+	CCONJ
easat-3708	215	3	(	(	PUNCT
easat-3708	215	4	𝐷𝑅−𝐷𝐿)𝑇	𝐷𝑅−𝐷𝐿)𝑇	PROPN
easat-3708	215	5	2	2	NUM
easat-3708	215	6	𝑠𝑘	𝑠𝑘	NOUN
easat-3708	215	7	−	−	PROPN
easat-3708	215	8	(	(	PUNCT
easat-3708	215	9	(	(	PUNCT
easat-3708	215	10	𝐷𝑅−𝐷𝐿)𝑇𝑥𝑘+𝐷𝑅𝑇	𝐷𝑅−𝐷𝐿)𝑇𝑥𝑘+𝐷𝑅𝑇	PROPN
easat-3708	215	11	𝑠𝑘)2	𝑠𝑘)2	PROPN
easat-3708	215	12	(	(	PUNCT
easat-3708	215	13	𝐷𝑅−𝐷𝐿)𝑇𝑥𝑘+(𝐷𝑅−𝐷)𝑇𝑠𝑘	𝐷𝑅−𝐷𝐿)𝑇𝑥𝑘+(𝐷𝑅−𝐷)𝑇𝑠𝑘	PROPN
easat-3708	215	14	,	,	PUNCT
easat-3708	215	15	𝑠.	𝑠.	PROPN
easat-3708	215	16	𝑡.	𝑡.	PROPN
easat-3708	215	17	,	,	PUNCT
easat-3708	215	18	(	(	PUNCT
easat-3708	215	19	20	20	NUM
easat-3708	215	20	)	)	PUNCT
easat-3708	215	21	(	(	PUNCT
easat-3708	215	22	𝑃3	𝑃3	NOUN
easat-3708	215	23	′	′	NOUN
easat-3708	215	24	)	)	PUNCT
easat-3708	215	25	𝐷𝑇𝑠𝑘	𝐷𝑇𝑠𝑘	PROPN
easat-3708	216	1	≤	≤	ADV
easat-3708	216	2	0	0	NUM
easat-3708	216	3	,	,	PUNCT
easat-3708	216	4	−𝐷𝑅𝑇	−𝐷𝑅𝑇	NOUN
easat-3708	216	5	𝑠𝑘	𝑠𝑘	NOUN
easat-3708	216	6	≤	≤	NOUN
easat-3708	216	7	(	(	PUNCT
easat-3708	216	8	𝐷𝑅	𝐷𝑅	PROPN
easat-3708	216	9	−	−	PROPN
easat-3708	216	10	𝐷𝐿)𝑇𝑥𝑘𝐵𝑠𝑘	𝐷𝐿)𝑇𝑥𝑘𝐵𝑠𝑘	PROPN
easat-3708	216	11	≤	≤	PUNCT
easat-3708	216	12	−𝐵𝑥𝑘	−𝐵𝑥𝑘	NOUN
easat-3708	216	13	,	,	PUNCT
easat-3708	216	14	𝐻𝑠𝑘	𝐻𝑠𝑘	PROPN
easat-3708	216	15	=	=	SYM
easat-3708	216	16	1	1	NUM
easat-3708	216	17	−	−	PROPN
easat-3708	216	18	𝐻𝑥𝑘	𝐻𝑥𝑘	PROPN
easat-3708	216	19	,	,	PUNCT
easat-3708	216	20	−𝑠𝑘	−𝑠𝑘	NOUN
easat-3708	216	21	≤	≤	NOUN
easat-3708	216	22	𝑥𝑘	𝑥𝑘	X
easat-3708	216	23	.	.	PUNCT
easat-3708	217	1	by	by	ADP
easat-3708	217	2	using	use	VERB
easat-3708	217	3	a	a	DET
easat-3708	217	4	method	method	NOUN
easat-3708	217	5	that	that	PRON
easat-3708	217	6	is	be	AUX
easat-3708	217	7	proposed	propose	VERB
easat-3708	217	8	in	in	ADP
easat-3708	217	9	[	[	X
easat-3708	217	10	9	9	NUM
easat-3708	217	11	]	]	PUNCT
easat-3708	217	12	(	(	PUNCT
easat-3708	217	13	theorem	theorem	NOUN
easat-3708	217	14	and	and	CCONJ
easat-3708	217	15	section	section	NOUN
easat-3708	217	16	3	3	NUM
easat-3708	217	17	)	)	PUNCT
easat-3708	217	18	we	we	PRON
easat-3708	217	19	solve	solve	VERB
easat-3708	217	20	problem	problem	NOUN
easat-3708	217	21	(	(	PUNCT
easat-3708	217	22	𝑃3	𝑃3	NOUN
easat-3708	217	23	′	′	NOUN
easat-3708	217	24	)	)	PUNCT
easat-3708	217	25	.	.	PUNCT
easat-3708	218	1	ii	ii	X
easat-3708	218	2	.	.	PUNCT
easat-3708	219	1	𝐷𝑅𝑇	𝐷𝑅𝑇	PROPN
easat-3708	219	2	(	(	PUNCT
easat-3708	219	3	𝑥𝑘	𝑥𝑘	X
easat-3708	219	4	+	+	CCONJ
easat-3708	219	5	𝑠𝑘	𝑠𝑘	NOUN
easat-3708	219	6	)	)	PUNCT
easat-3708	219	7	<	<	X
easat-3708	219	8	𝐷𝐿𝑇	𝐷𝐿𝑇	PROPN
easat-3708	219	9	𝑥𝑘	𝑥𝑘	PROPN
easat-3708	219	10	,	,	PUNCT
easat-3708	219	11	that	that	PRON
easat-3708	219	12	means	mean	VERB
easat-3708	219	13	two	two	NUM
easat-3708	219	14	numbers	number	NOUN
easat-3708	219	15	do	do	AUX
easat-3708	219	16	not	not	PART
easat-3708	219	17	have	have	VERB
easat-3708	219	18	any	any	DET
easat-3708	219	19	intersection	intersection	NOUN
easat-3708	219	20	point	point	NOUN
easat-3708	219	21	(	(	PUNCT
easat-3708	219	22	see	see	VERB
easat-3708	219	23	(	(	PUNCT
easat-3708	219	24	3	3	NUM
easat-3708	219	25	)	)	PUNCT
easat-3708	219	26	)	)	PUNCT
easat-3708	219	27	.	.	PUNCT
easat-3708	220	1	since	since	SCONJ
easat-3708	220	2	𝐷𝑅𝑇	𝐷𝑅𝑇	PROPN
easat-3708	220	3	(	(	PUNCT
easat-3708	220	4	𝑥𝑘	𝑥𝑘	X
easat-3708	220	5	+	+	CCONJ
easat-3708	220	6	𝑠𝑘	𝑠𝑘	NOUN
easat-3708	220	7	)	)	PUNCT
easat-3708	220	8	<	<	X
easat-3708	220	9	𝐷𝐿𝑇	𝐷𝐿𝑇	PROPN
easat-3708	220	10	𝑥𝑘	𝑥𝑘	X
easat-3708	220	11	and	and	CCONJ
easat-3708	220	12	�	�	PROPN
easat-3708	220	13	̃	̃	PROPN
easat-3708	220	14	�	�	PROPN
easat-3708	220	15	𝑇(𝑥𝑘	𝑇(𝑥𝑘	ADJ
easat-3708	220	16	+	+	ADJ
easat-3708	220	17	𝑠𝑘	𝑠𝑘	NOUN
easat-3708	220	18	)	)	PUNCT
easat-3708	220	19	is	be	AUX
easat-3708	220	20	located	locate	VERB
easat-3708	220	21	completely	completely	ADV
easat-3708	220	22	on	on	ADP
easat-3708	220	23	the	the	DET
easat-3708	220	24	left	left	ADJ
easat-3708	220	25	side	side	NOUN
easat-3708	220	26	of	of	ADP
easat-3708	220	27	�	�	PROPN
easat-3708	220	28	̃	̃	PROPN
easat-3708	220	29	�	�	PROPN
easat-3708	220	30	𝑇𝑥𝑘	𝑇𝑥𝑘	PROPN
easat-3708	220	31	and	and	CCONJ
easat-3708	220	32	according	accord	VERB
easat-3708	220	33	to	to	ADP
easat-3708	220	34	(	(	PUNCT
easat-3708	220	35	5	5	NUM
easat-3708	220	36	)	)	PUNCT
easat-3708	220	37	𝑟(	𝑟(	NUM
easat-3708	220	38	�	�	PROPN
easat-3708	220	39	̃	̃	PROPN
easat-3708	220	40	�	�	PROPN
easat-3708	220	41	𝑇(𝑥𝑘	𝑇(𝑥𝑘	ADJ
easat-3708	220	42	+	+	ADJ
easat-3708	220	43	𝑠𝑘	𝑠𝑘	NOUN
easat-3708	220	44	)	)	PUNCT
easat-3708	220	45	,	,	PUNCT
easat-3708	220	46	�	�	PROPN
easat-3708	220	47	̃	̃	PROPN
easat-3708	220	48	�	�	NOUN
easat-3708	220	49	𝑇(𝑥𝑘	𝑇(𝑥𝑘	NUM
easat-3708	220	50	)	)	PUNCT
easat-3708	220	51	)	)	PUNCT
easat-3708	221	1	>	>	X
easat-3708	221	2	0	0	NUM
easat-3708	221	3	,	,	PUNCT
easat-3708	221	4	so	so	SCONJ
easat-3708	221	5	there	there	PRON
easat-3708	221	6	is	be	VERB
easat-3708	221	7	no	no	DET
easat-3708	221	8	increasing	increase	VERB
easat-3708	221	9	direction	direction	NOUN
easat-3708	221	10	.	.	PUNCT
easat-3708	222	1	(	(	PUNCT
easat-3708	222	2	c	c	X
easat-3708	222	3	)	)	PUNCT
easat-3708	222	4	let	let	VERB
easat-3708	222	5	𝐷𝑇𝑥𝑘	𝐷𝑇𝑥𝑘	PROPN
easat-3708	222	6	=	=	SYM
easat-3708	223	1	𝐷𝑇(𝑥𝑘	𝐷𝑇(𝑥𝑘	PROPN
easat-3708	223	2	+	+	CCONJ
easat-3708	223	3	𝑠𝑘	𝑠𝑘	NOUN
easat-3708	223	4	)	)	PUNCT
easat-3708	223	5	.	.	PUNCT
easat-3708	224	1	so	so	ADV
easat-3708	224	2	,	,	PUNCT
easat-3708	224	3	according	accord	VERB
easat-3708	224	4	to	to	ADP
easat-3708	224	5	(	(	PUNCT
easat-3708	224	6	4	4	NUM
easat-3708	224	7	)	)	PUNCT
easat-3708	224	8	,	,	PUNCT
easat-3708	224	9	this	this	DET
easat-3708	224	10	case	case	NOUN
easat-3708	224	11	is	be	AUX
easat-3708	224	12	divided	divide	VERB
easat-3708	224	13	into	into	ADP
easat-3708	224	14	two	two	NUM
easat-3708	224	15	cases	case	NOUN
easat-3708	224	16	:	:	PUNCT
easat-3708	224	17	i.	i.	NOUN
easat-3708	224	18	suppose	suppose	VERB
easat-3708	224	19	𝑎	𝑎	PRON
easat-3708	224	20	=	=	ADJ
easat-3708	224	21	𝐷𝐿𝑇	𝐷𝐿𝑇	PROPN
easat-3708	224	22	𝑥𝑘	𝑥𝑘	NOUN
easat-3708	224	23	,	,	PUNCT
easat-3708	224	24	𝑐	𝑐	PROPN
easat-3708	224	25	=	=	SYM
easat-3708	224	26	𝐷𝑅𝑇	𝐷𝑅𝑇	PROPN
easat-3708	224	27	𝑥𝑘	𝑥𝑘	PROPN
easat-3708	224	28	,	,	PUNCT
easat-3708	224	29	𝑎′	𝑎′	X
easat-3708	224	30	=	=	SYM
easat-3708	224	31	𝐷𝐿𝑇	𝐷𝐿𝑇	NOUN
easat-3708	224	32	(	(	PUNCT
easat-3708	224	33	𝑥𝑘	𝑥𝑘	NOUN
easat-3708	224	34	+	+	CCONJ
easat-3708	224	35	𝑠𝑘	𝑠𝑘	NOUN
easat-3708	224	36	)	)	PUNCT
easat-3708	224	37	and	and	CCONJ
easat-3708	224	38	𝑐′	𝑐′	X
easat-3708	224	39	=	=	SYM
easat-3708	224	40	𝐷𝑅𝑇	𝐷𝑅𝑇	PROPN
easat-3708	224	41	(	(	PUNCT
easat-3708	224	42	𝑥𝑘	𝑥𝑘	X
easat-3708	224	43	+	+	CCONJ
easat-3708	224	44	𝑠𝑘	𝑠𝑘	NOUN
easat-3708	224	45	)	)	PUNCT
easat-3708	224	46	in	in	ADP
easat-3708	224	47	(	(	PUNCT
easat-3708	224	48	4	4	NUM
easat-3708	224	49	:)	:)	INTJ
easat-3708	224	50	max	max	PROPN
easat-3708	224	51	(	(	PUNCT
easat-3708	224	52	𝐷𝑅+𝐷𝐿)𝑇	𝐷𝑅+𝐷𝐿)𝑇	NOUN
easat-3708	224	53	2	2	NUM
easat-3708	224	54	𝑠𝑘	𝑠𝑘	NOUN
easat-3708	224	55	,	,	PUNCT
easat-3708	224	56	𝑠.	𝑠.	PROPN
easat-3708	224	57	𝑡.	𝑡.	PROPN
easat-3708	224	58	,	,	PUNCT
easat-3708	224	59	(	(	PUNCT
easat-3708	224	60	21	21	NUM
easat-3708	224	61	)	)	PUNCT
easat-3708	224	62	(	(	PUNCT
easat-3708	224	63	𝑃4	𝑃4	NOUN
easat-3708	224	64	)	)	PUNCT
easat-3708	224	65	𝐷𝑇𝑠𝑘	𝐷𝑇𝑠𝑘	PUNCT
easat-3708	224	66	=	=	SYM
easat-3708	225	1	0	0	NUM
easat-3708	225	2	,	,	PUNCT
easat-3708	225	3	𝐵𝑠𝑘	𝐵𝑠𝑘	PROPN
easat-3708	225	4	≤	≤	X
easat-3708	225	5	−𝐵𝑥𝑘	−𝐵𝑥𝑘	NOUN
easat-3708	225	6	,	,	PUNCT
easat-3708	225	7	𝐻𝑠𝑘	𝐻𝑠𝑘	PROPN
easat-3708	225	8	=	=	SYM
easat-3708	225	9	1	1	NUM
easat-3708	225	10	−	−	PROPN
easat-3708	225	11	𝐻𝑥𝑘	𝐻𝑥𝑘	PROPN
easat-3708	225	12	,	,	PUNCT
easat-3708	225	13	−𝑠𝑘	−𝑠𝑘	NOUN
easat-3708	225	14	≤	≤	NOUN
easat-3708	225	15	𝑥𝑘	𝑥𝑘	X
easat-3708	225	16	.	.	PUNCT
easat-3708	226	1	ii	ii	PROPN
easat-3708	226	2	.	.	PUNCT
easat-3708	226	3	suppose	suppose	VERB
easat-3708	226	4	𝑎	𝑎	PRON
easat-3708	226	5	=	=	SYM
easat-3708	226	6	𝐷𝐿𝑇	𝐷𝐿𝑇	NOUN
easat-3708	226	7	(	(	PUNCT
easat-3708	226	8	𝑥𝑘	𝑥𝑘	NOUN
easat-3708	226	9	+	+	CCONJ
easat-3708	226	10	𝑠𝑘	𝑠𝑘	NOUN
easat-3708	226	11	)	)	PUNCT
easat-3708	226	12	,	,	PUNCT
easat-3708	226	13	𝑐	𝑐	NOUN
easat-3708	226	14	=	=	PUNCT
easat-3708	226	15	𝐷𝐿𝑇	𝐷𝐿𝑇	PROPN
easat-3708	226	16	(	(	PUNCT
easat-3708	226	17	𝑥𝑘	𝑥𝑘	NOUN
easat-3708	226	18	+	+	CCONJ
easat-3708	226	19	𝑠𝑘	𝑠𝑘	NOUN
easat-3708	226	20	)	)	PUNCT
easat-3708	226	21	,	,	PUNCT
easat-3708	226	22	𝑎′	𝑎′	X
easat-3708	226	23	=	=	SYM
easat-3708	226	24	𝐷𝐿𝑇	𝐷𝐿𝑇	NOUN
easat-3708	226	25	𝑥𝑘	𝑥𝑘	NOUN
easat-3708	226	26	,	,	PUNCT
easat-3708	226	27	𝑐′	𝑐′	PUNCT
easat-3708	226	28	=	=	SYM
easat-3708	226	29	𝐷𝑅𝑇	𝐷𝑅𝑇	PROPN
easat-3708	226	30	𝑥𝑘	𝑥𝑘	NOUN
easat-3708	226	31	,	,	PUNCT
easat-3708	226	32	in	in	ADP
easat-3708	226	33	(	(	PUNCT
easat-3708	226	34	4	4	NUM
easat-3708	226	35	:)	:)	INTJ
easat-3708	226	36	min	min	NOUN
easat-3708	226	37	−	−	PROPN
easat-3708	226	38	(	(	PUNCT
easat-3708	226	39	𝐷𝑅+𝐷𝐿)𝑇	𝐷𝑅+𝐷𝐿)𝑇	NOUN
easat-3708	226	40	2	2	NUM
easat-3708	226	41	𝑠𝑘	𝑠𝑘	NOUN
easat-3708	226	42	,	,	PUNCT
easat-3708	226	43	𝑠.	𝑠.	PROPN
easat-3708	226	44	𝑡.	𝑡.	PROPN
easat-3708	226	45	,	,	PUNCT
easat-3708	226	46	(	(	PUNCT
easat-3708	226	47	22	22	NUM
easat-3708	226	48	)	)	PUNCT
easat-3708	226	49	(	(	PUNCT
easat-3708	226	50	𝑃5	𝑃5	NOUN
easat-3708	226	51	)	)	PUNCT
easat-3708	226	52	𝐷𝑇𝑠𝑘	𝐷𝑇𝑠𝑘	PUNCT
easat-3708	226	53	=	=	SYM
easat-3708	226	54	0	0	NUM
easat-3708	226	55	,	,	PUNCT
easat-3708	226	56	𝐵𝑠𝑘	𝐵𝑠𝑘	PROPN
easat-3708	226	57	≤	≤	X
easat-3708	226	58	−𝐵𝑥𝑘	−𝐵𝑥𝑘	NOUN
easat-3708	226	59	,	,	PUNCT
easat-3708	227	1	𝐻𝑠𝑘	𝐻𝑠𝑘	PROPN
easat-3708	227	2	=	=	SYM
easat-3708	227	3	1	1	NUM
easat-3708	227	4	−	−	PROPN
easat-3708	227	5	𝐻𝑥𝑘	𝐻𝑥𝑘	PROPN
easat-3708	227	6	,	,	PUNCT
easat-3708	227	7	−𝑠𝑘	−𝑠𝑘	NOUN
easat-3708	227	8	≤	≤	NOUN
easat-3708	227	9	𝑥𝑘	𝑥𝑘	X
easat-3708	227	10	.	.	PUNCT
easat-3708	228	1	4	4	X
easat-3708	228	2	.	.	X
easat-3708	228	3	stopping	stop	VERB
easat-3708	228	4	condition[10	condition[10	NOUN
easat-3708	228	5	]	]	PUNCT
easat-3708	228	6	:	:	PUNCT
easat-3708	228	7	we	we	PRON
easat-3708	228	8	stop	stop	VERB
easat-3708	228	9	the	the	DET
easat-3708	228	10	proposed	propose	VERB
easat-3708	228	11	fvns	fvns	NOUN
easat-3708	228	12	algorithm	algorithm	NOUN
easat-3708	228	13	when	when	SCONJ
easat-3708	228	14	reach	reach	VERB
easat-3708	228	15	maxiter	maxit	ADJ
easat-3708	228	16	successive	successive	ADJ
easat-3708	228	17	iterati	iterati	PROPN
easat-3708	228	18	ons	ons	PROPN
easat-3708	228	19	without	without	ADP
easat-3708	228	20	improvement	improvement	NOUN
easat-3708	228	21	.	.	PUNCT
easat-3708	229	1	note	note	VERB
easat-3708	229	2	4	4	NUM
easat-3708	229	3	the	the	DET
easat-3708	229	4	(	(	PUNCT
easat-3708	229	5	21	21	NUM
easat-3708	229	6	)	)	PUNCT
easat-3708	229	7	and	and	CCONJ
easat-3708	229	8	(	(	PUNCT
easat-3708	229	9	22	22	NUM
easat-3708	229	10	)	)	PUNCT
easat-3708	229	11	problems	problem	NOUN
easat-3708	229	12	have	have	VERB
easat-3708	229	13	the	the	DET
easat-3708	229	14	same	same	ADJ
easat-3708	229	15	solution	solution	NOUN
easat-3708	229	16	,	,	PUNCT
easat-3708	229	17	so	so	SCONJ
easat-3708	229	18	you	you	PRON
easat-3708	229	19	can	can	AUX
easat-3708	229	20	find	find	VERB
easat-3708	229	21	the	the	DET
easat-3708	229	22	increasing	increase	VERB
easat-3708	229	23	direction	direction	NOUN
easat-3708	229	24	by	by	ADP
easat-3708	229	25	solving	solve	VERB
easat-3708	229	26	either	either	CCONJ
easat-3708	229	27	one	one	NUM
easat-3708	229	28	.	.	PUNCT
easat-3708	230	1	finally	finally	ADV
easat-3708	230	2	,	,	PUNCT
easat-3708	230	3	to	to	PART
easat-3708	230	4	find	find	VERB
easat-3708	230	5	s_k	s_k	NUM
easat-3708	230	6	,	,	PUNCT
easat-3708	230	7	we	we	PRON
easat-3708	230	8	need	need	VERB
easat-3708	230	9	to	to	PART
easat-3708	230	10	solve	solve	VERB
easat-3708	230	11	for	for	ADP
easat-3708	230	12	p_1^	p_1^	NOUN
easat-3708	230	13	'	'	PUNCT
easat-3708	230	14	,	,	PUNCT
easat-3708	230	15	p_2	p_2	PROPN
easat-3708	230	16	,	,	PUNCT
easat-3708	230	17	p_3^	p_3^	NOUN
easat-3708	230	18	'	'	PUNCT
easat-3708	230	19	,	,	PUNCT
easat-3708	230	20	and	and	CCONJ
easat-3708	230	21	p_4	p_4	NOUN
easat-3708	230	22	.	.	PUNCT
easat-3708	231	1	it	it	PRON
easat-3708	231	2	is	be	AUX
easat-3708	231	3	clear	clear	ADJ
easat-3708	231	4	that	that	SCONJ
easat-3708	231	5	p_1^	p_1^	PROPN
easat-3708	231	6	'	'	PUNCT
easat-3708	231	7	,	,	PUNCT
easat-3708	231	8	p_2	p_2	PROPN
easat-3708	231	9	,	,	PUNCT
easat-3708	231	10	p_3^	p_3^	NOUN
easat-3708	231	11	'	'	PUNCT
easat-3708	231	12	and	and	CCONJ
easat-3708	231	13	p_4	p_4	NOUN
easat-3708	231	14	can	can	AUX
easat-3708	231	15	be	be	AUX
easat-3708	231	16	solved	solve	VERB
easat-3708	231	17	in	in	ADP
easat-3708	231	18	parallel	parallel	NOUN
easat-3708	231	19	.	.	PUNCT
easat-3708	232	1	after	after	ADP
easat-3708	232	2	solving	solve	VERB
easat-3708	232	3	these	these	DET
easat-3708	232	4	problems	problem	NOUN
easat-3708	232	5	,	,	PUNCT
easat-3708	232	6	choose	choose	VERB
easat-3708	232	7	the	the	DET
easat-3708	232	8	best	good	ADJ
easat-3708	232	9	s_k	s_k	NOUN
easat-3708	232	10	.	.	PUNCT
easat-3708	233	1	that	that	PRON
easat-3708	233	2	is	be	AUX
easat-3708	233	3	,	,	PUNCT
easat-3708	233	4	the	the	DET
easat-3708	233	5	one	one	NOUN
easat-3708	233	6	given	give	VERB
easat-3708	233	7	by	by	ADP
easat-3708	233	8	p_1^	p_1^	NOUN
easat-3708	233	9	'	'	PUNCT
easat-3708	233	10	,	,	PUNCT
easat-3708	233	11	p_2	p_2	PROPN
easat-3708	233	12	,	,	PUNCT
easat-3708	233	13	p_3^	p_3^	NOUN
easat-3708	233	14	'	'	PUNCT
easat-3708	233	15	and	and	CCONJ
easat-3708	233	16	p_4	p_4	NOUN
easat-3708	233	17	that	that	PRON
easat-3708	233	18	causes	cause	VERB
easat-3708	233	19	the	the	DET
easat-3708	233	20	largest	large	ADJ
easat-3708	233	21	increase	increase	NOUN
easat-3708	233	22	in	in	ADP
easat-3708	233	23	the	the	DET
easat-3708	233	24	objective	objective	ADJ
easat-3708	233	25	function	function	NOUN
easat-3708	233	26	.	.	PUNCT
easat-3708	234	1	example	example	NOUN
easat-3708	235	1	2	2	NUM
easat-3708	235	2	suppose	suppose	VERB
easat-3708	235	3	the	the	DET
easat-3708	235	4	fuzzy	fuzzy	ADJ
easat-3708	235	5	fractional	fractional	ADJ
easat-3708	235	6	linear	linear	ADJ
easat-3708	235	7	programming	programming	NOUN
easat-3708	235	8	problem	problem	NOUN
easat-3708	235	9	as	as	SCONJ
easat-3708	235	10	follows	follow	VERB
easat-3708	235	11	:	:	PUNCT
easat-3708	235	12	max	max	PROPN
easat-3708	235	13	𝑓(𝑥	𝑓(𝑥	NOUN
easat-3708	235	14	)	)	PUNCT
easat-3708	235	15	=	=	SYM
easat-3708	235	16	(	(	PUNCT
easat-3708	235	17	−97,−73,−31)𝑥1+(−37,−27,9)𝑥2+(−99,−27,42)𝑥3+(−77,−53,14	−97,−73,−31)𝑥1+(−37,−27,9)𝑥2+(−99,−27,42)𝑥3+(−77,−53,14	PROPN
easat-3708	235	18	)	)	PUNCT
easat-3708	236	1	64𝑥1	64𝑥1	NUM
easat-3708	237	1	+	+	NOUN
easat-3708	237	2	3𝑥2	3𝑥2	NUM
easat-3708	237	3	+	+	NOUN
easat-3708	237	4	12𝑥3	12𝑥3	NUM
easat-3708	237	5	+	+	SYM
easat-3708	237	6	82	82	NUM
easat-3708	237	7	,	,	PUNCT
easat-3708	237	8	𝑠.	𝑠.	NOUN
easat-3708	237	9	𝑡.	𝑡.	NOUN
easat-3708	237	10	(	(	PUNCT
easat-3708	237	11	23	23	NUM
easat-3708	237	12	)	)	PUNCT
easat-3708	237	13	86𝑥1	86𝑥1	NUM
easat-3708	238	1	+	+	CCONJ
easat-3708	238	2	11𝑥2	11𝑥2	NUM
easat-3708	238	3	+	+	SYM
easat-3708	238	4	86𝑥3	86𝑥3	NUM
easat-3708	238	5	≤	≤	NOUN
easat-3708	238	6	280,73𝑥1	280,73𝑥1	NUM
easat-3708	239	1	+	+	SYM
easat-3708	239	2	90𝑥2	90𝑥2	NUM
easat-3708	239	3	+	+	NUM
easat-3708	239	4	17𝑥3	17𝑥3	NUM
easat-3708	239	5	≤	≤	NUM
easat-3708	239	6	343	343	NUM
easat-3708	239	7	,	,	PUNCT
easat-3708	239	8	𝑥1	𝑥1	NOUN
easat-3708	239	9	,	,	PUNCT
easat-3708	239	10	𝑥2	𝑥2	NOUN
easat-3708	239	11	,	,	PUNCT
easat-3708	239	12	𝑥3	𝑥3	NOUN
easat-3708	239	13	≥	≥	NOUN
easat-3708	239	14	0	0	NUM
easat-3708	239	15	.	.	PUNCT
easat-3708	240	1	with	with	ADP
easat-3708	240	2	x_0	x_0	PROPN
easat-3708	240	3	as	as	ADP
easat-3708	240	4	the	the	DET
easat-3708	240	5	starting	starting	NOUN
easat-3708	240	6	point	point	NOUN
easat-3708	240	7	(	(	PUNCT
easat-3708	240	8	which	which	PRON
easat-3708	240	9	can	can	AUX
easat-3708	240	10	be	be	AUX
easat-3708	240	11	generated	generate	VERB
easat-3708	240	12	randomly	randomly	ADV
easat-3708	240	13	in	in	ADP
easat-3708	240	14	the	the	DET
easat-3708	240	15	interval	interval	NOUN
easat-3708	240	16	[	[	X
easat-3708	240	17	1,5	1,5	NUM
easat-3708	240	18	]	]	PUNCT
easat-3708	240	19	)	)	PUNCT
easat-3708	240	20	,	,	PUNCT
easat-3708	240	21	using	use	VERB
easat-3708	240	22	algorithm	algorithm	NOUN
easat-3708	240	23	4	4	NUM
easat-3708	240	24	,	,	PUNCT
easat-3708	240	25	after	after	ADP
easat-3708	240	26	one	one	NUM
easat-3708	240	27	iteration	iteration	NOUN
easat-3708	240	28	we	we	PRON
easat-3708	240	29	obtain	obtain	VERB
easat-3708	240	30	:	:	PUNCT
easat-3708	240	31	𝑥0	𝑥0	NOUN
easat-3708	240	32	=	=	PUNCT
easat-3708	241	1	[	[	X
easat-3708	241	2	2,2,1	2,2,1	NUM
easat-3708	241	3	]	]	X
easat-3708	241	4	,	,	PUNCT
easat-3708	241	5	𝑓(𝑥0	𝑓(𝑥0	NUM
easat-3708	241	6	)	)	PUNCT
easat-3708	241	7	=	=	PUNCT
easat-3708	242	1	[	[	X
easat-3708	242	2	−3.6680	−3.6680	NOUN
easat-3708	242	3	,	,	PUNCT
easat-3708	242	4	−2.3028,0.0987	−2.3028,0.0987	NOUN
easat-3708	242	5	]	]	PUNCT
easat-3708	242	6	,	,	PUNCT
easat-3708	242	7	𝑥∗	𝑥∗	PROPN
easat-3708	242	8	=	=	PUNCT
easat-3708	243	1	[	[	X
easat-3708	243	2	0,0.3575,3.2101	0,0.3575,3.2101	PROPN
easat-3708	243	3	]	]	X
easat-3708	243	4	,	,	PUNCT
easat-3708	243	5	𝑓(𝑥∗	𝑓(𝑥∗	NUM
easat-3708	243	6	)	)	PUNCT
easat-3708	243	7	=	=	PUNCT
easat-3708	244	1	[	[	X
easat-3708	244	2	−3.3557	−3.3557	X
easat-3708	244	3	,	,	PUNCT
easat-3708	244	4	−1.2281,1.2504	−1.2281,1.2504	PROPN
easat-3708	244	5	]	]	PUNCT
easat-3708	244	6	,	,	PUNCT
easat-3708	244	7	𝑟(𝑓(𝑥0	𝑟(𝑓(𝑥0	PROPN
easat-3708	244	8	)	)	PUNCT
easat-3708	244	9	,	,	PUNCT
easat-3708	244	10	𝑓(𝑥∗	𝑓(𝑥∗	NUM
easat-3708	244	11	)	)	PUNCT
easat-3708	244	12	)	)	PUNCT
easat-3708	245	1	=	=	PUNCT
easat-3708	245	2	1.5517	1.5517	NUM
easat-3708	245	3	.	.	PUNCT
easat-3708	246	1	(	(	PUNCT
easat-3708	246	2	24	24	NUM
easat-3708	246	3	)	)	PUNCT
easat-3708	246	4	according	accord	VERB
easat-3708	246	5	to	to	PART
easat-3708	246	6	note	note	NOUN
easat-3708	246	7	2	2	NUM
easat-3708	246	8	,	,	PUNCT
easat-3708	246	9	we	we	PRON
easat-3708	246	10	can	can	AUX
easat-3708	246	11	conclude	conclude	VERB
easat-3708	246	12	that	that	SCONJ
easat-3708	246	13	𝑓(𝑥∗	𝑓(𝑥∗	PROPN
easat-3708	246	14	)	)	PUNCT
easat-3708	246	15	>	>	X
easat-3708	246	16	𝑘	𝑘	PROPN
easat-3708	246	17	𝑓(𝑥0	𝑓(𝑥0	NOUN
easat-3708	246	18	)	)	PUNCT
easat-3708	246	19	.	.	PUNCT
easat-3708	247	1	7810	7810	NUM
easat-3708	247	2	edelweiss	edelweiss	PROPN
easat-3708	247	3	applied	apply	VERB
easat-3708	247	4	science	science	NOUN
easat-3708	247	5	and	and	CCONJ
easat-3708	247	6	technology	technology	NOUN
easat-3708	247	7	issn	issn	PROPN
easat-3708	247	8	:	:	PUNCT
easat-3708	247	9	2576	2576	NUM
easat-3708	247	10	-	-	SYM
easat-3708	247	11	8484	8484	NUM
easat-3708	247	12	vol	vol	NOUN
easat-3708	247	13	.	.	PROPN
easat-3708	247	14	8	8	NUM
easat-3708	247	15	,	,	PUNCT
easat-3708	247	16	no	no	INTJ
easat-3708	247	17	.	.	NOUN
easat-3708	247	18	6	6	NUM
easat-3708	247	19	:	:	SYM
easat-3708	247	20	7802	7802	NUM
easat-3708	247	21	-	-	SYM
easat-3708	247	22	7812	7812	NUM
easat-3708	247	23	,	,	PUNCT
easat-3708	247	24	2024	2024	NUM
easat-3708	247	25	doi	doi	NOUN
easat-3708	247	26	:	:	PUNCT
easat-3708	247	27	10.55214/25768484.v8i6.3708	10.55214/25768484.v8i6.3708	NUM
easat-3708	247	28	©	©	PROPN
easat-3708	247	29	2024	2024	NUM
easat-3708	247	30	by	by	ADP
easat-3708	247	31	the	the	DET
easat-3708	247	32	authors	author	NOUN
easat-3708	247	33	;	;	PUNCT
easat-3708	247	34	licensee	licensee	PROPN
easat-3708	247	35	learning	learning	NOUN
easat-3708	247	36	gate	gate	NOUN
easat-3708	247	37	5	5	NUM
easat-3708	247	38	.	.	PUNCT
easat-3708	248	1	numerical	numerical	ADJ
easat-3708	248	2	results	result	NOUN
easat-3708	248	3	in	in	ADP
easat-3708	248	4	this	this	DET
easat-3708	248	5	section	section	NOUN
easat-3708	248	6	,	,	PUNCT
easat-3708	248	7	we	we	PRON
easat-3708	248	8	demonstrate	demonstrate	VERB
easat-3708	248	9	the	the	DET
easat-3708	248	10	effectiveness	effectiveness	NOUN
easat-3708	248	11	of	of	ADP
easat-3708	248	12	the	the	DET
easat-3708	248	13	algorithm	algorithm	NOUN
easat-3708	248	14	4	4	NUM
easat-3708	248	15	we	we	PRON
easat-3708	248	16	have	have	AUX
easat-3708	248	17	developed	develop	VERB
easat-3708	248	18	.	.	PUNCT
easat-3708	249	1	to	to	PART
easat-3708	249	2	evaluate	evaluate	VERB
easat-3708	249	3	its	its	PRON
easat-3708	249	4	performance	performance	NOUN
easat-3708	249	5	,	,	PUNCT
easat-3708	249	6	we	we	PRON
easat-3708	249	7	generated	generate	VERB
easat-3708	249	8	numerous	numerous	ADJ
easat-3708	249	9	test	test	NOUN
easat-3708	249	10	problems	problem	NOUN
easat-3708	249	11	for	for	ADP
easat-3708	249	12	the	the	DET
easat-3708	249	13	fflpp	fflpp	NOUN
easat-3708	249	14	.	.	PUNCT
easat-3708	250	1	these	these	DET
easat-3708	250	2	test	test	NOUN
easat-3708	250	3	problems	problem	NOUN
easat-3708	250	4	were	be	AUX
easat-3708	250	5	created	create	VERB
easat-3708	250	6	using	use	VERB
easat-3708	250	7	a	a	DET
easat-3708	250	8	random	random	ADJ
easat-3708	250	9	generation	generation	NOUN
easat-3708	250	10	process	process	NOUN
easat-3708	250	11	in	in	ADP
easat-3708	250	12	the	the	DET
easat-3708	250	13	matlab	matlab	PROPN
easat-3708	250	14	7.0	7.0	NUM
easat-3708	250	15	programming	programming	NOUN
easat-3708	250	16	environment	environment	NOUN
easat-3708	250	17	,	,	PUNCT
easat-3708	250	18	executed	execute	VERB
easat-3708	250	19	on	on	ADP
easat-3708	250	20	a	a	DET
easat-3708	250	21	notebook	notebook	NOUN
easat-3708	250	22	equipped	equip	VERB
easat-3708	250	23	with	with	ADP
easat-3708	250	24	an	an	DET
easat-3708	250	25	intel(r	intel(r	NOUN
easat-3708	250	26	)	)	PUNCT
easat-3708	250	27	core(tm	core(tm	NOUN
easat-3708	250	28	)	)	PUNCT
easat-3708	250	29	i5	i5	PROPN
easat-3708	250	30	-	-	PUNCT
easat-3708	250	31	3210	3210	NUM
easat-3708	250	32	m	m	PROPN
easat-3708	250	33	cpu	cpu	NOUN
easat-3708	250	34	running	run	VERB
easat-3708	250	35	at	at	ADP
easat-3708	250	36	2.5	2.5	NUM
easat-3708	250	37	ghz	ghz	NOUN
easat-3708	250	38	,	,	PUNCT
easat-3708	250	39	with	with	ADP
easat-3708	250	40	4.00	4.00	NUM
easat-3708	250	41	gb	gb	NOUN
easat-3708	250	42	of	of	ADP
easat-3708	250	43	ram	ram	NOUN
easat-3708	250	44	.	.	PUNCT
easat-3708	251	1	to	to	PART
easat-3708	251	2	introduce	introduce	VERB
easat-3708	251	3	fuzzy	fuzzy	ADJ
easat-3708	251	4	random	random	ADJ
easat-3708	251	5	coefficients	coefficient	NOUN
easat-3708	251	6	into	into	ADP
easat-3708	251	7	the	the	DET
easat-3708	251	8	objective	objective	ADJ
easat-3708	251	9	function	function	NOUN
easat-3708	251	10	,	,	PUNCT
easat-3708	251	11	we	we	PRON
easat-3708	251	12	initiated	initiate	VERB
easat-3708	251	13	the	the	DET
easat-3708	251	14	process	process	NOUN
easat-3708	251	15	by	by	ADP
easat-3708	251	16	generating	generate	VERB
easat-3708	251	17	three	three	NUM
easat-3708	251	18	numbers	number	NOUN
easat-3708	251	19	within	within	ADP
easat-3708	251	20	the	the	DET
easat-3708	251	21	range	range	NOUN
easat-3708	251	22	of	of	ADP
easat-3708	251	23	[	[	X
easat-3708	251	24	100,100	100,100	NUM
easat-3708	251	25	]	]	X
easat-3708	251	26	.	.	PUNCT
easat-3708	252	1	subsequently	subsequently	ADV
easat-3708	252	2	,	,	PUNCT
easat-3708	252	3	these	these	DET
easat-3708	252	4	numbers	number	NOUN
easat-3708	252	5	were	be	AUX
easat-3708	252	6	sorted	sort	VERB
easat-3708	252	7	in	in	ADP
easat-3708	252	8	ascending	ascend	VERB
easat-3708	252	9	order	order	NOUN
easat-3708	252	10	and	and	CCONJ
easat-3708	252	11	employed	employ	VERB
easat-3708	252	12	as	as	ADP
easat-3708	252	13	the	the	DET
easat-3708	252	14	components	component	NOUN
easat-3708	252	15	of	of	ADP
easat-3708	252	16	the	the	DET
easat-3708	252	17	fuzzy	fuzzy	ADJ
easat-3708	252	18	number	number	NOUN
easat-3708	252	19	.	.	PUNCT
easat-3708	253	1	table	table	NOUN
easat-3708	253	2	1	1	NUM
easat-3708	253	3	.	.	X
easat-3708	253	4	objective	objective	ADJ
easat-3708	253	5	function	function	NOUN
easat-3708	253	6	values	value	NOUN
easat-3708	253	7	obtained	obtain	VERB
easat-3708	253	8	by	by	ADP
easat-3708	253	9	various	various	ADJ
easat-3708	253	10	methods	method	NOUN
easat-3708	253	11	on	on	ADP
easat-3708	253	12	the	the	DET
easat-3708	253	13	examples	example	NOUN
easat-3708	253	14	.	.	PUNCT
easat-3708	254	1	𝐝𝐢𝐦	𝐝𝐢𝐦	PROPN
easat-3708	254	2	obj(init	obj(init	PROPN
easat-3708	254	3	)	)	PUNCT
easat-3708	254	4	obj	obj	PROPN
easat-3708	254	5	(	(	PUNCT
easat-3708	254	6	a	a	NOUN
easat-3708	254	7	)	)	PUNCT
easat-3708	254	8	1	1	NUM
easat-3708	254	9	]	]	SYM
easat-3708	254	10	𝐫(𝐀𝐥𝟏	𝐫(𝐀𝐥𝟏	NOUN
easat-3708	254	11	)	)	PUNCT
easat-3708	254	12	,	,	PUNCT
easat-3708	254	13	10	10	NUM
easat-3708	254	14	×	×	NOUN
easat-3708	254	15	20	20	NUM
easat-3708	255	1	[	[	X
easat-3708	255	2	−12.5611/−6.5882/0.5839	−12.5611/−6.5882/0.5839	NOUN
easat-3708	255	3	]	]	PUNCT
easat-3708	255	4	[	[	X
easat-3708	255	5	−4.7204/−3.8596/−2.6984	−4.7204/−3.8596/−2.6984	X
easat-3708	255	6	]	]	X
easat-3708	255	7	4.081016	4.081016	NUM
easat-3708	255	8	15	15	NUM
easat-3708	255	9	×	×	NOUN
easat-3708	255	10	45	45	NUM
easat-3708	255	11	[	[	X
easat-3708	255	12	−13.3151/−4.8021/3.0413	−13.3151/−4.8021/3.0413	X
easat-3708	255	13	]	]	X
easat-3708	255	14	[	[	X
easat-3708	255	15	−5.7192/−5.0795/−0.4860	−5.7192/−5.0795/−0.4860	X
easat-3708	255	16	]	]	X
easat-3708	255	17	-1.7628	-1.7628	X
easat-3708	256	1	20	20	NUM
easat-3708	256	2	×	×	NOUN
easat-3708	256	3	50	50	NUM
easat-3708	257	1	[	[	X
easat-3708	257	2	−83.3284/−29.3203/19.0412	−83.3284/−29.3203/19.0412	X
easat-3708	257	3	]	]	X
easat-3708	258	1	[	[	X
easat-3708	258	2	−24.2866/−10.7058/1.1153	−24.2866/−10.7058/1.1153	X
easat-3708	258	3	]	]	SYM
easat-3708	258	4	33.5785	33.5785	NUM
easat-3708	258	5	25	25	NUM
easat-3708	258	6	×	×	NOUN
easat-3708	258	7	75	75	NUM
easat-3708	259	1	[	[	X
easat-3708	259	2	−37.0272/−18.1645/5.1532	−37.0272/−18.1645/5.1532	NOUN
easat-3708	259	3	]	]	X
easat-3708	259	4	[	[	X
easat-3708	259	5	−14.7937/−5.1766/−2.6203	−14.7937/−5.1766/−2.6203	X
easat-3708	259	6	]	]	PUNCT
easat-3708	259	7	15.0961	15.0961	NUM
easat-3708	259	8	60	60	NUM
easat-3708	259	9	×	×	NOUN
easat-3708	259	10	100	100	NUM
easat-3708	260	1	[	[	X
easat-3708	260	2	−117.8211/−42.6375/32.4857	−117.8211/−42.6375/32.4857	X
easat-3708	260	3	]	]	X
easat-3708	260	4	[	[	X
easat-3708	260	5	−40.4461/−36.0957/−25.3402	−40.4461/−36.0957/−25.3402	X
easat-3708	260	6	]	]	X
easat-3708	260	7	15.7779	15.7779	NUM
easat-3708	260	8	25	25	NUM
easat-3708	260	9	×	×	NOUN
easat-3708	260	10	200	200	NUM
easat-3708	261	1	[	[	X
easat-3708	261	2	−76.6690/−72.7284/−29.6852	−76.6690/−72.7284/−29.6852	X
easat-3708	261	3	]	]	X
easat-3708	262	1	[	[	X
easat-3708	262	2	−187.8614/−74.2193/41.3462	−187.8614/−74.2193/41.3462	X
easat-3708	262	3	]	]	X
easat-3708	262	4	21.5528	21.5528	NUM
easat-3708	262	5	40	40	NUM
easat-3708	262	6	×	×	NOUN
easat-3708	262	7	300	300	NUM
easat-3708	262	8	[	[	X
easat-3708	262	9	−56.8188/−21.7506/13.0071	−56.8188/−21.7506/13.0071	X
easat-3708	262	10	]	]	X
easat-3708	262	11	[	[	X
easat-3708	262	12	−23.6253/−19.7209/−0.8734	−23.6253/−19.7209/−0.8734	NUM
easat-3708	262	13	]	]	PUNCT
easat-3708	262	14	11.5796	11.5796	NUM
easat-3708	262	15	300	300	NUM
easat-3708	262	16	×	×	NOUN
easat-3708	262	17	600	600	NUM
easat-3708	263	1	[	[	X
easat-3708	263	2	−222.6613/−88.4877/48.5212	−222.6613/−88.4877/48.5212	X
easat-3708	263	3	]	]	X
easat-3708	264	1	[	[	X
easat-3708	264	2	−86.3218/−81.8225/−77.2927	−86.3218/−81.8225/−77.2927	X
easat-3708	264	3	]	]	X
easat-3708	264	4	11.6141	11.6141	NUM
easat-3708	264	5	in	in	ADP
easat-3708	264	6	table	table	NOUN
easat-3708	264	7	1	1	NUM
easat-3708	264	8	,	,	PUNCT
easat-3708	264	9	the	the	DET
easat-3708	264	10	dim	dim	ADJ
easat-3708	264	11	column	column	NOUN
easat-3708	264	12	shows	show	VERB
easat-3708	264	13	the	the	DET
easat-3708	264	14	dimensions	dimension	NOUN
easat-3708	264	15	of	of	ADP
easat-3708	264	16	the	the	DET
easat-3708	264	17	test	test	NOUN
easat-3708	264	18	problems	problem	NOUN
easat-3708	264	19	,	,	PUNCT
easat-3708	264	20	the	the	DET
easat-3708	264	21	column	column	NOUN
easat-3708	264	22	entitled	entitle	VERB
easat-3708	264	23	obj	obj	PROPN
easat-3708	264	24	(	(	PUNCT
easat-3708	264	25	init	init	PROPN
easat-3708	264	26	)	)	PUNCT
easat-3708	264	27	shows	show	VERB
easat-3708	264	28	the	the	DET
easat-3708	264	29	value	value	NOUN
easat-3708	264	30	of	of	ADP
easat-3708	264	31	the	the	DET
easat-3708	264	32	objective	objective	ADJ
easat-3708	264	33	function	function	NOUN
easat-3708	264	34	corresponding	correspond	VERB
easat-3708	264	35	to	to	ADP
easat-3708	264	36	the	the	DET
easat-3708	264	37	initial	initial	ADJ
easat-3708	264	38	solution	solution	NOUN
easat-3708	264	39	of	of	ADP
easat-3708	264	40	algorithm	algorithm	NOUN
easat-3708	264	41	1	1	NUM
easat-3708	264	42	,	,	PUNCT
easat-3708	264	43	the	the	DET
easat-3708	264	44	column	column	NOUN
easat-3708	264	45	entitled	entitle	VERB
easat-3708	264	46	obj	obj	PROPN
easat-3708	264	47	(	(	PUNCT
easat-3708	264	48	al4	al4	PROPN
easat-3708	264	49	)	)	PUNCT
easat-3708	264	50	shows	show	VERB
easat-3708	264	51	the	the	DET
easat-3708	264	52	values	value	NOUN
easat-3708	264	53	of	of	ADP
easat-3708	264	54	the	the	DET
easat-3708	264	55	objective	objective	ADJ
easat-3708	264	56	functions	function	NOUN
easat-3708	264	57	obtained	obtain	VERB
easat-3708	264	58	by	by	ADP
easat-3708	264	59	algorithm	algorithm	NOUN
easat-3708	264	60	1	1	NUM
easat-3708	264	61	and	and	CCONJ
easat-3708	264	62	the	the	DET
easat-3708	264	63	column	column	NOUN
easat-3708	264	64	entitled	entitle	VERB
easat-3708	264	65	r(al1	r(al1	PROPN
easat-3708	264	66	,	,	PUNCT
easat-3708	264	67	)	)	PUNCT
easat-3708	264	68	shows	show	VERB
easat-3708	264	69	the	the	DET
easat-3708	264	70	comparison	comparison	NOUN
easat-3708	264	71	of	of	ADP
easat-3708	264	72	the	the	DET
easat-3708	264	73	value	value	NOUN
easat-3708	264	74	of	of	ADP
easat-3708	264	75	objective	objective	ADJ
easat-3708	264	76	function	function	NOUN
easat-3708	264	77	of	of	ADP
easat-3708	264	78	initial	initial	ADJ
easat-3708	264	79	solution	solution	NOUN
easat-3708	264	80	corresponding	correspond	VERB
easat-3708	264	81	to	to	ADP
easat-3708	264	82	algorithm	algorithm	NOUN
easat-3708	264	83	1	1	NUM
easat-3708	264	84	with	with	ADP
easat-3708	264	85	the	the	DET
easat-3708	264	86	ones	one	NOUN
easat-3708	264	87	obtained	obtain	VERB
easat-3708	264	88	by	by	ADP
easat-3708	264	89	algorithm4	algorithm4	NOUN
easat-3708	264	90	using	use	VERB
easat-3708	264	91	(	(	PUNCT
easat-3708	264	92	5	5	NUM
easat-3708	264	93	)	)	PUNCT
easat-3708	264	94	.	.	PUNCT
easat-3708	265	1	according	accord	VERB
easat-3708	265	2	to	to	ADP
easat-3708	265	3	the	the	DET
easat-3708	265	4	obtained	obtain	VERB
easat-3708	265	5	results	result	NOUN
easat-3708	265	6	shown	show	VERB
easat-3708	265	7	in	in	ADP
easat-3708	265	8	column	column	NOUN
easat-3708	265	9	labeled	label	VERB
easat-3708	265	10	as	as	ADP
easat-3708	265	11	r(al1	r(al1	PROPN
easat-3708	265	12	,	,	PUNCT
easat-3708	265	13	)	)	PUNCT
easat-3708	265	14	,	,	PUNCT
easat-3708	265	15	it	it	PRON
easat-3708	265	16	is	be	AUX
easat-3708	265	17	observed	observe	VERB
easat-3708	265	18	(	(	PUNCT
easat-3708	265	19	based	base	VERB
easat-3708	265	20	on	on	ADP
easat-3708	265	21	note	note	NOUN
easat-3708	265	22	(	(	PUNCT
easat-3708	265	23	2	2	NUM
easat-3708	265	24	)	)	PUNCT
easat-3708	265	25	)	)	PUNCT
easat-3708	265	26	that	that	SCONJ
easat-3708	265	27	the	the	DET
easat-3708	265	28	algorithm	algorithm	NOUN
easat-3708	265	29	4	4	NUM
easat-3708	265	30	can	can	AUX
easat-3708	265	31	improve	improve	VERB
easat-3708	265	32	the	the	DET
easat-3708	265	33	initial	initial	ADJ
easat-3708	265	34	solution	solution	NOUN
easat-3708	265	35	.	.	PUNCT
easat-3708	266	1	all	all	DET
easat-3708	266	2	problems	problem	NOUN
easat-3708	266	3	were	be	AUX
easat-3708	266	4	also	also	ADV
easat-3708	266	5	solved	solve	VERB
easat-3708	266	6	by	by	ADP
easat-3708	266	7	the	the	DET
easat-3708	266	8	methods	method	NOUN
easat-3708	266	9	due	due	ADJ
easat-3708	266	10	to	to	ADP
easat-3708	266	11	[	[	X
easat-3708	266	12	27	27	NUM
easat-3708	266	13	]	]	PUNCT
easat-3708	266	14	.	.	PUNCT
easat-3708	267	1	sheikhi	sheikhi	PROPN
easat-3708	267	2	and	and	CCONJ
easat-3708	267	3	ebadi	ebadi	VERB
easat-3708	267	4	in	in	ADP
easat-3708	267	5	[	[	X
easat-3708	267	6	27	27	NUM
easat-3708	267	7	]	]	PUNCT
easat-3708	267	8	proposed	propose	VERB
easat-3708	267	9	method	method	NOUN
easat-3708	267	10	introduces	introduce	VERB
easat-3708	267	11	a	a	DET
easat-3708	267	12	transformation	transformation	NOUN
easat-3708	267	13	technique	technique	NOUN
easat-3708	267	14	that	that	PRON
easat-3708	267	15	converts	convert	VERB
easat-3708	267	16	an	an	DET
easat-3708	267	17	ftp	ftp	NOUN
easat-3708	267	18	with	with	ADP
easat-3708	267	19	fuzzy	fuzzy	ADJ
easat-3708	267	20	numbers	number	NOUN
easat-3708	267	21	into	into	ADP
easat-3708	267	22	an	an	DET
easat-3708	267	23	ffnlpp	ffnlpp	NOUN
easat-3708	267	24	with	with	ADP
easat-3708	267	25	crisp	crisp	ADJ
easat-3708	267	26	numbers	number	NOUN
easat-3708	267	27	by	by	ADP
easat-3708	267	28	employing	employ	VERB
easat-3708	267	29	the	the	DET
easat-3708	267	30	robust	robust	ADJ
easat-3708	267	31	ranking	ranking	ADJ
easat-3708	267	32	technique	technique	NOUN
easat-3708	267	33	.	.	PUNCT
easat-3708	268	1	details	detail	NOUN
easat-3708	269	1	o	o	NOUN
easat-3708	269	2	the	the	DET
easat-3708	269	3	results	result	NOUN
easat-3708	269	4	are	be	AUX
easat-3708	269	5	shown	show	VERB
easat-3708	269	6	in	in	ADP
easat-3708	269	7	table	table	NOUN
easat-3708	269	8	2	2	NUM
easat-3708	269	9	.	.	PUNCT
easat-3708	269	10	table	table	NOUN
easat-3708	269	11	2	2	NUM
easat-3708	269	12	.	.	X
easat-3708	269	13	objective	objective	ADJ
easat-3708	269	14	function	function	NOUN
easat-3708	269	15	values	value	NOUN
easat-3708	269	16	obtained	obtain	VERB
easat-3708	269	17	by	by	ADP
easat-3708	269	18	sheikhi	sheikhi	NOUN
easat-3708	269	19	and	and	CCONJ
easat-3708	269	20	ebadi	ebadi	VERB
easat-3708	269	21	[	[	X
easat-3708	269	22	27	27	NUM
easat-3708	269	23	]	]	PUNCT
easat-3708	269	24	on	on	ADP
easat-3708	269	25	the	the	DET
easat-3708	269	26	examples	example	NOUN
easat-3708	269	27	.	.	PUNCT
easat-3708	270	1	dim	dim	ADJ
easat-3708	270	2	obj(al[27	obj(al[27	NOUN
easat-3708	270	3	]	]	PUNCT
easat-3708	270	4	)	)	PUNCT
easat-3708	270	5	r(obj(al	r(obj(al	NOUN
easat-3708	270	6	]	]	PUNCT
easat-3708	270	7	)	)	PUNCT
easat-3708	270	8	,	,	PUNCT
easat-3708	270	9	obj(al[27	obj(al[27	NUM
easat-3708	270	10	]	]	PUNCT
easat-3708	270	11	)	)	PUNCT
easat-3708	270	12	)	)	PUNCT
easat-3708	271	1	10	10	NUM
easat-3708	271	2	×	×	NOUN
easat-3708	271	3	20	20	NUM
easat-3708	272	1	[	[	X
easat-3708	272	2	−10.7321/−4.1001/1.2150	−10.7321/−4.1001/1.2150	NOUN
easat-3708	272	3	]	]	X
easat-3708	272	4	3.2697	3.2697	NUM
easat-3708	272	5	15	15	NUM
easat-3708	272	6	×	×	NOUN
easat-3708	272	7	45	45	NUM
easat-3708	273	1	[	[	X
easat-3708	273	2	−14.8912/−6.1221/1.7841	−14.8912/−6.1221/1.7841	X
easat-3708	273	3	]	]	X
easat-3708	274	1	2.6305	2.6305	NUM
easat-3708	274	2	20	20	NUM
easat-3708	274	3	×	×	NOUN
easat-3708	274	4	50	50	NUM
easat-3708	274	5	[	[	X
easat-3708	274	6	−80.1432/−35.5698/16.1201	−80.1432/−35.5698/16.1201	X
easat-3708	274	7	]	]	X
easat-3708	274	8	5.7479	5.7479	NUM
easat-3708	274	9	25	25	NUM
easat-3708	274	10	×	×	NOUN
easat-3708	274	11	75	75	NUM
easat-3708	275	1	[	[	X
easat-3708	275	2	−30.8531/−20.1345/−10.5200	−30.8531/−20.1345/−10.5200	X
easat-3708	275	3	]	]	PUNCT
easat-3708	275	4	6.5833	6.5833	NUM
easat-3708	275	5	60	60	NUM
easat-3708	275	6	×	×	NOUN
easat-3708	275	7	100	100	NUM
easat-3708	276	1	[	[	X
easat-3708	276	2	−120.2510/−50.3217/25.1432	−120.2510/−50.3217/25.1432	X
easat-3708	276	3	]	]	X
easat-3708	276	4	12.1784	12.1784	NUM
easat-3708	276	5	25	25	NUM
easat-3708	276	6	×	×	NOUN
easat-3708	276	7	200	200	NUM
easat-3708	277	1	[	[	X
easat-3708	277	2	−110.2002/−80.1214/−10.4879	−110.2002/−80.1214/−10.4879	X
easat-3708	277	3	]	]	X
easat-3708	277	4	13.8171	13.8171	NUM
easat-3708	277	5	40	40	NUM
easat-3708	277	6	×	×	NOUN
easat-3708	277	7	300	300	NUM
easat-3708	278	1	[	[	X
easat-3708	278	2	−60.1901/−30.3114/20.5417	−60.1901/−30.3114/20.5417	X
easat-3708	278	3	]	]	X
easat-3708	278	4	5.6262	5.6262	NUM
easat-3708	278	5	300	300	NUM
easat-3708	278	6	×	×	NOUN
easat-3708	278	7	600	600	NUM
easat-3708	279	1	[	[	X
easat-3708	279	2	−150.1122/−90.3333/−20.5417	−150.1122/−90.3333/−20.5417	X
easat-3708	279	3	]	]	X
easat-3708	279	4	0.0858	0.0858	NUM
easat-3708	279	5	in	in	ADP
easat-3708	279	6	table	table	NOUN
easat-3708	279	7	2	2	NUM
easat-3708	279	8	,	,	PUNCT
easat-3708	279	9	the	the	DET
easat-3708	279	10	dim	dim	ADJ
easat-3708	279	11	column	column	NOUN
easat-3708	279	12	shows	show	VERB
easat-3708	279	13	the	the	DET
easat-3708	279	14	dimension	dimension	NOUN
easat-3708	279	15	of	of	ADP
easat-3708	279	16	problems	problem	NOUN
easat-3708	279	17	,	,	PUNCT
easat-3708	279	18	the	the	DET
easat-3708	279	19	column	column	NOUN
easat-3708	279	20	entitled	entitle	VERB
easat-3708	279	21	obj(al	obj(al	NOUN
easat-3708	279	22	[	[	X
easat-3708	279	23	27	27	NUM
easat-3708	279	24	]	]	PUNCT
easat-3708	279	25	)	)	PUNCT
easat-3708	279	26	shows	show	VERB
easat-3708	279	27	the	the	DET
easat-3708	279	28	value	value	NOUN
easat-3708	279	29	of	of	ADP
easat-3708	279	30	the	the	DET
easat-3708	279	31	objective	objective	ADJ
easat-3708	279	32	function	function	NOUN
easat-3708	279	33	corresponding	correspond	VERB
easat-3708	279	34	to	to	ADP
easat-3708	279	35	the	the	DET
easat-3708	279	36	solution	solution	NOUN
easat-3708	279	37	obtained	obtain	VERB
easat-3708	279	38	by	by	ADP
easat-3708	279	39	algorithm	algorithm	NOUN
easat-3708	279	40	proposed	propose	VERB
easat-3708	279	41	in	in	ADP
easat-3708	279	42	[	[	X
easat-3708	279	43	27	27	NUM
easat-3708	279	44	]	]	PUNCT
easat-3708	279	45	,	,	PUNCT
easat-3708	279	46	and	and	CCONJ
easat-3708	279	47	the	the	DET
easat-3708	279	48	column	column	NOUN
easat-3708	279	49	entitled	entitle	VERB
easat-3708	279	50	r(al1	r(al1	PROPN
easat-3708	279	51	,	,	PUNCT
easat-3708	279	52	al([27	al([27	PROPN
easat-3708	279	53	]	]	NOUN
easat-3708	279	54	)	)	PUNCT
easat-3708	279	55	)	)	PUNCT
easat-3708	279	56	shows	show	VERB
easat-3708	279	57	the	the	DET
easat-3708	279	58	comparison	comparison	NOUN
easat-3708	279	59	of	of	ADP
easat-3708	279	60	the	the	DET
easat-3708	279	61	value	value	NOUN
easat-3708	279	62	of	of	ADP
easat-3708	279	63	objective	objective	ADJ
easat-3708	279	64	function	function	NOUN
easat-3708	279	65	corresponding	correspond	VERB
easat-3708	279	66	to	to	ADP
easat-3708	279	67	algorithm	algorithm	NOUN
easat-3708	279	68	4	4	NUM
easat-3708	279	69	with	with	ADP
easat-3708	279	70	the	the	DET
easat-3708	279	71	ones	one	NOUN
easat-3708	279	72	obtained	obtain	VERB
easat-3708	279	73	by	by	ADP
easat-3708	279	74	the	the	DET
easat-3708	279	75	methods	method	NOUN
easat-3708	279	76	using	use	VERB
easat-3708	279	77	in	in	ADP
easat-3708	279	78	[	[	X
easat-3708	279	79	27	27	NUM
easat-3708	279	80	]	]	PUNCT
easat-3708	279	81	.	.	PUNCT
easat-3708	280	1	according	accord	VERB
easat-3708	280	2	to	to	ADP
easat-3708	280	3	the	the	DET
easat-3708	280	4	7811	7811	NUM
easat-3708	280	5	edelweiss	edelweiss	PROPN
easat-3708	280	6	applied	apply	VERB
easat-3708	280	7	science	science	NOUN
easat-3708	280	8	and	and	CCONJ
easat-3708	280	9	technology	technology	NOUN
easat-3708	280	10	issn	issn	PROPN
easat-3708	280	11	:	:	PUNCT
easat-3708	280	12	2576	2576	NUM
easat-3708	280	13	-	-	SYM
easat-3708	280	14	8484	8484	NUM
easat-3708	280	15	vol	vol	NOUN
easat-3708	280	16	.	.	PROPN
easat-3708	280	17	8	8	NUM
easat-3708	280	18	,	,	PUNCT
easat-3708	280	19	no	no	INTJ
easat-3708	280	20	.	.	NOUN
easat-3708	280	21	6	6	NUM
easat-3708	280	22	:	:	SYM
easat-3708	280	23	7802	7802	NUM
easat-3708	280	24	-	-	SYM
easat-3708	280	25	7812	7812	NUM
easat-3708	280	26	,	,	PUNCT
easat-3708	280	27	2024	2024	NUM
easat-3708	280	28	doi	doi	NOUN
easat-3708	280	29	:	:	PUNCT
easat-3708	280	30	10.55214/25768484.v8i6.3708	10.55214/25768484.v8i6.3708	NUM
easat-3708	280	31	©	©	PROPN
easat-3708	280	32	2024	2024	NUM
easat-3708	280	33	by	by	ADP
easat-3708	280	34	the	the	DET
easat-3708	280	35	authors	author	NOUN
easat-3708	280	36	;	;	PUNCT
easat-3708	280	37	licensee	licensee	PROPN
easat-3708	280	38	learning	learning	PROPN
easat-3708	280	39	gate	gate	NOUN
easat-3708	280	40	obtained	obtain	VERB
easat-3708	280	41	results	result	NOUN
easat-3708	280	42	shown	show	VERB
easat-3708	280	43	in	in	ADP
easat-3708	280	44	column	column	NOUN
easat-3708	280	45	labeled	label	VERB
easat-3708	280	46	as	as	ADP
easat-3708	280	47	r(al1	r(al1	PROPN
easat-3708	280	48	,	,	PUNCT
easat-3708	280	49	al([27	al([27	PROPN
easat-3708	280	50	]	]	NOUN
easat-3708	280	51	)	)	PUNCT
easat-3708	280	52	)	)	PUNCT
easat-3708	280	53	,	,	PUNCT
easat-3708	280	54	it	it	PRON
easat-3708	280	55	is	be	AUX
easat-3708	280	56	observed	observe	VERB
easat-3708	280	57	that	that	SCONJ
easat-3708	280	58	the	the	DET
easat-3708	280	59	objective	objective	ADJ
easat-3708	280	60	function	function	NOUN
easat-3708	280	61	values	value	NOUN
easat-3708	280	62	obtained	obtain	VERB
easat-3708	280	63	by	by	ADP
easat-3708	280	64	algorithm	algorithm	NOUN
easat-3708	280	65	1	1	NUM
easat-3708	280	66	are	be	AUX
easat-3708	280	67	more	more	ADV
easat-3708	280	68	significant	significant	ADJ
easat-3708	280	69	than	than	ADP
easat-3708	280	70	the	the	DET
easat-3708	280	71	ones	one	NOUN
easat-3708	280	72	due	due	ADJ
easat-3708	280	73	to	to	ADP
easat-3708	280	74	other	other	ADJ
easat-3708	280	75	methods	method	NOUN
easat-3708	280	76	on	on	ADP
easat-3708	280	77	all	all	DET
easat-3708	280	78	the	the	DET
easat-3708	280	79	test	test	NOUN
easat-3708	280	80	problems	problem	NOUN
easat-3708	280	81	.	.	PUNCT
easat-3708	281	1	the	the	DET
easat-3708	281	2	obtained	obtain	VERB
easat-3708	281	3	results	result	NOUN
easat-3708	281	4	showed	show	VERB
easat-3708	281	5	that	that	SCONJ
easat-3708	281	6	the	the	DET
easat-3708	281	7	objective	objective	ADJ
easat-3708	281	8	function	function	NOUN
easat-3708	281	9	values	value	NOUN
easat-3708	281	10	obtained	obtain	VERB
easat-3708	281	11	by	by	ADP
easat-3708	281	12	the	the	DET
easat-3708	281	13	proposed	propose	VERB
easat-3708	281	14	algorithm	algorithm	NOUN
easat-3708	281	15	were	be	AUX
easat-3708	281	16	significant	significant	ADJ
easat-3708	281	17	than	than	ADP
easat-3708	281	18	the	the	DET
easat-3708	281	19	ones	one	NOUN
easat-3708	281	20	obtained	obtain	VERB
easat-3708	281	21	by	by	ADP
easat-3708	281	22	the	the	DET
easat-3708	281	23	algorithms	algorithm	NOUN
easat-3708	281	24	due	due	ADP
easat-3708	281	25	to	to	ADP
easat-3708	281	26	sheikhi	sheikhi	NOUN
easat-3708	281	27	and	and	CCONJ
easat-3708	281	28	ebadi	ebadi	VERB
easat-3708	281	29	in	in	ADP
easat-3708	281	30	[	[	X
easat-3708	281	31	27	27	NUM
easat-3708	281	32	]	]	SYM
easat-3708	281	33	6	6	NUM
easat-3708	281	34	.	.	PUNCT
easat-3708	281	35	conclusions	conclusion	NOUN
easat-3708	281	36	and	and	CCONJ
easat-3708	281	37	future	future	ADJ
easat-3708	281	38	work	work	NOUN
easat-3708	281	39	in	in	ADP
easat-3708	281	40	this	this	DET
easat-3708	281	41	paper	paper	NOUN
easat-3708	281	42	,	,	PUNCT
easat-3708	281	43	we	we	PRON
easat-3708	281	44	considered	consider	VERB
easat-3708	281	45	a	a	DET
easat-3708	281	46	fractional	fractional	ADJ
easat-3708	281	47	fuzzy	fuzzy	ADJ
easat-3708	281	48	linear	linear	ADJ
easat-3708	281	49	programming	programming	NOUN
easat-3708	281	50	problem	problem	NOUN
easat-3708	281	51	,	,	PUNCT
easat-3708	281	52	with	with	ADP
easat-3708	281	53	the	the	DET
easat-3708	281	54	assumption	assumption	NOUN
easat-3708	281	55	that	that	SCONJ
easat-3708	281	56	the	the	DET
easat-3708	281	57	parameters	parameter	NOUN
easat-3708	281	58	of	of	ADP
easat-3708	281	59	the	the	DET
easat-3708	281	60	objective	objective	ADJ
easat-3708	281	61	function	function	NOUN
easat-3708	281	62	are	be	AUX
easat-3708	281	63	fuzzy	fuzzy	ADJ
easat-3708	281	64	numbers	number	NOUN
easat-3708	281	65	,	,	PUNCT
easat-3708	281	66	and	and	CCONJ
easat-3708	281	67	we	we	PRON
easat-3708	281	68	presented	present	VERB
easat-3708	281	69	a	a	DET
easat-3708	281	70	new	new	ADJ
easat-3708	281	71	model	model	NOUN
easat-3708	281	72	with	with	ADP
easat-3708	281	73	the	the	DET
easat-3708	281	74	name	name	NOUN
easat-3708	281	75	ffnlpp	ffnlpp	NOUN
easat-3708	281	76	.	.	PUNCT
easat-3708	282	1	we	we	PRON
easat-3708	282	2	proposed	propose	VERB
easat-3708	282	3	an	an	DET
easat-3708	282	4	fvns	fvns	ADJ
easat-3708	282	5	algorithm	algorithm	NOUN
easat-3708	282	6	based	base	VERB
easat-3708	282	7	on	on	ADP
easat-3708	282	8	modified	modify	VERB
easat-3708	282	9	kerre	kerre	PROPN
easat-3708	282	10	’s	’s	PART
easat-3708	282	11	inequality	inequality	NOUN
easat-3708	282	12	for	for	ADP
easat-3708	282	13	solving	solve	VERB
easat-3708	282	14	ffnlpp	ffnlpp	NOUN
easat-3708	282	15	.	.	PUNCT
easat-3708	283	1	we	we	PRON
easat-3708	283	2	generated	generate	VERB
easat-3708	283	3	and	and	CCONJ
easat-3708	283	4	solved	solve	VERB
easat-3708	283	5	some	some	DET
easat-3708	283	6	randomly	randomly	ADV
easat-3708	283	7	tested	test	VERB
easat-3708	283	8	examples	example	NOUN
easat-3708	283	9	with	with	ADP
easat-3708	283	10	triangular	triangular	ADJ
easat-3708	283	11	fuzzy	fuzzy	ADJ
easat-3708	283	12	coefficients	coefficient	NOUN
easat-3708	283	13	,	,	PUNCT
easat-3708	283	14	and	and	CCONJ
easat-3708	283	15	we	we	PRON
easat-3708	283	16	concluded	conclude	VERB
easat-3708	283	17	that	that	SCONJ
easat-3708	283	18	our	our	PRON
easat-3708	283	19	proposed	propose	VERB
easat-3708	283	20	algorithm	algorithm	NOUN
easat-3708	283	21	could	could	AUX
easat-3708	283	22	improve	improve	VERB
easat-3708	283	23	the	the	DET
easat-3708	283	24	initial	initial	ADJ
easat-3708	283	25	solution	solution	NOUN
easat-3708	283	26	by	by	ADP
easat-3708	283	27	increasing	increase	VERB
easat-3708	283	28	the	the	DET
easat-3708	283	29	direction	direction	NOUN
easat-3708	283	30	we	we	PRON
easat-3708	283	31	introduced	introduce	VERB
easat-3708	283	32	through	through	ADP
easat-3708	283	33	kerre	kerre	PROPN
easat-3708	283	34	’s	’s	PART
easat-3708	283	35	inequality	inequality	NOUN
easat-3708	283	36	.	.	PUNCT
easat-3708	284	1	also	also	ADV
easat-3708	284	2	,	,	PUNCT
easat-3708	284	3	we	we	PRON
easat-3708	284	4	compare	compare	VERB
easat-3708	284	5	our	our	PRON
easat-3708	284	6	proposed	propose	VERB
easat-3708	284	7	algorithm	algorithm	NOUN
easat-3708	284	8	with	with	ADP
easat-3708	284	9	another	another	DET
easat-3708	284	10	method	method	NOUN
easat-3708	284	11	.	.	PUNCT
easat-3708	285	1	similar	similar	ADJ
easat-3708	285	2	to	to	ADP
easat-3708	285	3	technique	technique	NOUN
easat-3708	285	4	that	that	PRON
easat-3708	285	5	is	be	AUX
easat-3708	285	6	introduced	introduce	VERB
easat-3708	285	7	in	in	ADP
easat-3708	285	8	[	[	X
easat-3708	285	9	13	13	NUM
easat-3708	285	10	]	]	PUNCT
easat-3708	285	11	,	,	PUNCT
easat-3708	285	12	by	by	ADP
easat-3708	285	13	using	use	VERB
easat-3708	285	14	abs	ab	NOUN
easat-3708	285	15	algorithm	algorithm	NOUN
easat-3708	285	16	the	the	DET
easat-3708	285	17	fractional	fractional	ADJ
easat-3708	285	18	fuzzy	fuzzy	ADJ
easat-3708	285	19	linear	linear	NOUN
easat-3708	285	20	programming	programming	NOUN
easat-3708	285	21	can	can	AUX
easat-3708	285	22	be	be	AUX
easat-3708	285	23	simplified	simplify	VERB
easat-3708	285	24	and	and	CCONJ
easat-3708	285	25	by	by	ADP
easat-3708	285	26	using	use	VERB
easat-3708	285	27	of	of	ADP
easat-3708	285	28	this	this	DET
easat-3708	285	29	method	method	NOUN
easat-3708	285	30	we	we	PRON
easat-3708	285	31	can	can	AUX
easat-3708	285	32	decrease	decrease	VERB
easat-3708	285	33	the	the	DET
easat-3708	285	34	number	number	NOUN
easat-3708	285	35	of	of	ADP
easat-3708	285	36	variables	variable	NOUN
easat-3708	285	37	.	.	PUNCT
easat-3708	286	1	copyright	copyright	NOUN
easat-3708	286	2	:	:	PUNCT
easat-3708	286	3	©	©	PROPN
easat-3708	286	4	2024	2024	NUM
easat-3708	286	5	by	by	ADP
easat-3708	286	6	the	the	DET
easat-3708	286	7	authors	author	NOUN
easat-3708	286	8	.	.	PUNCT
easat-3708	287	1	this	this	DET
easat-3708	287	2	article	article	NOUN
easat-3708	287	3	is	be	AUX
easat-3708	287	4	an	an	DET
easat-3708	287	5	open	open	ADJ
easat-3708	287	6	access	access	NOUN
easat-3708	287	7	article	article	NOUN
easat-3708	287	8	distributed	distribute	VERB
easat-3708	287	9	under	under	ADP
easat-3708	287	10	the	the	DET
easat-3708	287	11	terms	term	NOUN
easat-3708	287	12	and	and	CCONJ
easat-3708	287	13	conditions	condition	NOUN
easat-3708	287	14	of	of	ADP
easat-3708	287	15	the	the	DET
easat-3708	287	16	creative	creative	ADJ
easat-3708	287	17	commons	common	NOUN
easat-3708	287	18	attribution	attribution	NOUN
easat-3708	287	19	(	(	PUNCT
easat-3708	287	20	cc	cc	NOUN
easat-3708	287	21	by	by	ADP
easat-3708	287	22	)	)	PUNCT
easat-3708	287	23	license	license	NOUN
easat-3708	287	24	(	(	PUNCT
easat-3708	287	25	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
easat-3708	287	26	)	)	PUNCT
easat-3708	287	27	.	.	PUNCT
easat-3708	288	1	references	reference	NOUN
easat-3708	288	2	[	[	X
easat-3708	288	3	1	1	NUM
easat-3708	288	4	]	]	PUNCT
easat-3708	288	5	r.	r.	PROPN
easat-3708	288	6	arya	arya	PROPN
easat-3708	288	7	,	,	PUNCT
easat-3708	288	8	p.	p.	PROPN
easat-3708	288	9	singh	singh	PROPN
easat-3708	288	10	and	and	CCONJ
easat-3708	288	11	d.	d.	PROPN
easat-3708	288	12	bhati	bhati	PROPN
easat-3708	288	13	,	,	PUNCT
easat-3708	288	14	a	a	DET
easat-3708	288	15	fuzzy	fuzzy	ADJ
easat-3708	288	16	based	base	VERB
easat-3708	288	17	branch	branch	NOUN
easat-3708	288	18	and	and	CCONJ
easat-3708	288	19	bound	bind	VERB
easat-3708	288	20	approach	approach	NOUN
easat-3708	288	21	for	for	ADP
easat-3708	288	22	multi	multi	ADJ
easat-3708	288	23	-	-	ADJ
easat-3708	288	24	objective	objective	ADJ
easat-3708	288	25	linear	linear	ADJ
easat-3708	288	26	fractional	fractional	NOUN
easat-3708	288	27	(	(	PUNCT
easat-3708	288	28	molf	molf	NOUN
easat-3708	288	29	)	)	PUNCT
easat-3708	288	30	optimization	optimization	NOUN
easat-3708	288	31	problems	problem	NOUN
easat-3708	288	32	,	,	PUNCT
easat-3708	288	33	journal	journal	NOUN
easat-3708	288	34	of	of	ADP
easat-3708	288	35	computational	computational	ADJ
easat-3708	288	36	science	science	NOUN
easat-3708	288	37	24	24	NUM
easat-3708	288	38	(	(	PUNCT
easat-3708	288	39	2018	2018	NUM
easat-3708	288	40	)	)	PUNCT
easat-3708	288	41	54	54	NUM
easat-3708	288	42	-	-	SYM
easat-3708	288	43	64	64	NUM
easat-3708	288	44	.	.	PUNCT
easat-3708	289	1	[	[	X
easat-3708	289	2	2	2	X
easat-3708	289	3	]	]	PUNCT
easat-3708	289	4	s.	s.	PROPN
easat-3708	289	5	m.	m.	PROPN
easat-3708	289	6	azimi	azimi	PROPN
easat-3708	289	7	,	,	PUNCT
easat-3708	289	8	h.	h.	PROPN
easat-3708	289	9	chun	chun	PROPN
easat-3708	289	10	,	,	PUNCT
easat-3708	289	11	c.	c.	PROPN
easat-3708	289	12	zhihong	zhihong	PROPN
easat-3708	289	13	and	and	CCONJ
easat-3708	289	14	a.	a.	NOUN
easat-3708	289	15	nafei	nafei	PROPN
easat-3708	289	16	,	,	PUNCT
easat-3708	289	17	a	a	DET
easat-3708	289	18	new	new	ADJ
easat-3708	289	19	approach	approach	NOUN
easat-3708	289	20	for	for	ADP
easat-3708	289	21	solving	solve	VERB
easat-3708	289	22	interval	interval	NOUN
easat-3708	289	23	neutrosophic	neutrosophic	ADJ
easat-3708	289	24	integer	integer	NOUN
easat-3708	289	25	programming	programming	NOUN
easat-3708	289	26	problems	problem	NOUN
easat-3708	289	27	,	,	PUNCT
easat-3708	289	28	fuzzy	fuzzy	ADJ
easat-3708	289	29	optimization	optimization	NOUN
easat-3708	289	30	and	and	CCONJ
easat-3708	289	31	modeling	modeling	NOUN
easat-3708	289	32	journal	journal	NOUN
easat-3708	289	33	2	2	NUM
easat-3708	289	34	(	(	PUNCT
easat-3708	289	35	2021	2021	NUM
easat-3708	289	36	)	)	PUNCT
easat-3708	289	37	1	1	NUM
easat-3708	289	38	-	-	SYM
easat-3708	289	39	11	11	NUM
easat-3708	289	40	.	.	PUNCT
easat-3708	290	1	[	[	X
easat-3708	290	2	3	3	X
easat-3708	290	3	]	]	X
easat-3708	290	4	j.	j.	PROPN
easat-3708	290	5	j.	j.	PROPN
easat-3708	290	6	buckely	buckely	ADV
easat-3708	290	7	and	and	CCONJ
easat-3708	290	8	l.	l.	PROPN
easat-3708	290	9	j.	j.	PROPN
easat-3708	290	10	jowers	jowers	PROPN
easat-3708	290	11	,	,	PUNCT
easat-3708	290	12	monte	monte	PROPN
easat-3708	290	13	carlo	carlo	PROPN
easat-3708	290	14	method	method	NOUN
easat-3708	290	15	in	in	ADP
easat-3708	290	16	fuzzy	fuzzy	ADJ
easat-3708	290	17	optimization	optimization	NOUN
easat-3708	290	18	,	,	PUNCT
easat-3708	290	19	springer	springer	NOUN
easat-3708	290	20	,	,	PUNCT
easat-3708	290	21	2007	2007	NUM
easat-3708	290	22	.	.	PUNCT
easat-3708	291	1	[	[	X
easat-3708	291	2	4	4	NUM
easat-3708	291	3	]	]	PUNCT
easat-3708	291	4	a.	a.	NOUN
easat-3708	291	5	charnes	charne	NOUN
easat-3708	291	6	and	and	CCONJ
easat-3708	291	7	w.	w.	PROPN
easat-3708	291	8	w.	w.	PROPN
easat-3708	291	9	cooper	cooper	PROPN
easat-3708	291	10	,	,	PUNCT
easat-3708	291	11	programming	program	VERB
easat-3708	291	12	with	with	ADP
easat-3708	291	13	linear	linear	ADJ
easat-3708	291	14	fractional	fractional	ADJ
easat-3708	291	15	functions	function	NOUN
easat-3708	291	16	,	,	PUNCT
easat-3708	291	17	naval	naval	ADJ
easat-3708	291	18	research	research	NOUN
easat-3708	291	19	logistics	logistic	NOUN
easat-3708	291	20	quarterly	quarterly	ADJ
easat-3708	291	21	9	9	NUM
easat-3708	291	22	(	(	PUNCT
easat-3708	291	23	1962	1962	NUM
easat-3708	291	24	)	)	PUNCT
easat-3708	291	25	181	181	NUM
easat-3708	291	26	-	-	SYM
easat-3708	291	27	186	186	NUM
easat-3708	291	28	.	.	PUNCT
easat-3708	292	1	[	[	X
easat-3708	292	2	5	5	NUM
easat-3708	292	3	]	]	PUNCT
easat-3708	292	4	v.	v.	ADP
easat-3708	292	5	chinnadurai	chinnadurai	PROPN
easat-3708	292	6	and	and	CCONJ
easat-3708	292	7	s.	s.	PROPN
easat-3708	292	8	muthukumar	muthukumar	PROPN
easat-3708	292	9	,	,	PUNCT
easat-3708	292	10	solving	solve	VERB
easat-3708	292	11	the	the	DET
easat-3708	292	12	linear	linear	ADJ
easat-3708	292	13	fractional	fractional	ADJ
easat-3708	292	14	programming	programming	NOUN
easat-3708	292	15	problem	problem	NOUN
easat-3708	292	16	in	in	ADP
easat-3708	292	17	a	a	DET
easat-3708	292	18	fuzzy	fuzzy	ADJ
easat-3708	292	19	environment	environment	NOUN
easat-3708	292	20	:	:	PUNCT
easat-3708	292	21	numerical	numerical	ADJ
easat-3708	292	22	approach	approach	NOUN
easat-3708	292	23	,	,	PUNCT
easat-3708	292	24	applied	apply	VERB
easat-3708	292	25	mathematical	mathematical	ADJ
easat-3708	292	26	modelling	model	VERB
easat-3708	292	27	40	40	NUM
easat-3708	292	28	(	(	PUNCT
easat-3708	292	29	2016	2016	NUM
easat-3708	292	30	)	)	PUNCT
easat-3708	292	31	6148–6164	6148–6164	NOUN
easat-3708	292	32	.	.	PUNCT
easat-3708	293	1	[	[	X
easat-3708	293	2	6	6	NUM
easat-3708	293	3	]	]	PUNCT
easat-3708	293	4	w.	w.	PROPN
easat-3708	293	5	chun	chun	PROPN
easat-3708	293	6	-	-	PUNCT
easat-3708	293	7	feng	feng	PROPN
easat-3708	293	8	and	and	CCONJ
easat-3708	293	9	sh	sh	PROPN
easat-3708	293	10	.	.	PROPN
easat-3708	293	11	pei	pei	PROPN
easat-3708	293	12	-	-	PUNCT
easat-3708	293	13	ping	ping	PROPN
easat-3708	293	14	,	,	PUNCT
easat-3708	293	15	a	a	DET
easat-3708	293	16	global	global	ADJ
easat-3708	293	17	optimization	optimization	NOUN
easat-3708	293	18	algorithm	algorithm	NOUN
easat-3708	293	19	for	for	ADP
easat-3708	293	20	linear	linear	ADJ
easat-3708	293	21	fractional	fractional	ADJ
easat-3708	293	22	programming	programming	NOUN
easat-3708	293	23	,	,	PUNCT
easat-3708	293	24	applied	apply	VERB
easat-3708	293	25	mathematics	mathematic	NOUN
easat-3708	293	26	and	and	CCONJ
easat-3708	293	27	computation	computation	NOUN
easat-3708	293	28	204	204	NUM
easat-3708	293	29	(	(	PUNCT
easat-3708	293	30	2008	2008	NUM
easat-3708	293	31	)	)	PUNCT
easat-3708	293	32	281	281	NUM
easat-3708	293	33	-	-	SYM
easat-3708	293	34	287	287	NUM
easat-3708	293	35	.	.	PUNCT
easat-3708	294	1	[	[	X
easat-3708	294	2	7	7	X
easat-3708	294	3	]	]	X
easat-3708	294	4	w.	w.	PROPN
easat-3708	294	5	e.	e.	PROPN
easat-3708	294	6	costa	costa	PROPN
easat-3708	294	7	,	,	PUNCT
easat-3708	294	8	m.	m.	PROPN
easat-3708	294	9	c.	c.	PROPN
easat-3708	294	10	goldbarg	goldbarg	PROPN
easat-3708	294	11	,	,	PUNCT
easat-3708	294	12	e.	e.	PROPN
easat-3708	294	13	f.	f.	PROPN
easat-3708	294	14	g.	g.	PROPN
easat-3708	294	15	goldbarg	goldbarg	PROPN
easat-3708	294	16	,	,	PUNCT
easat-3708	294	17	new	new	ADJ
easat-3708	294	18	vns	vns	PROPN
easat-3708	294	19	heuristic	heuristic	NOUN
easat-3708	294	20	for	for	ADP
easat-3708	294	21	total	total	ADJ
easat-3708	294	22	flowtime	flowtime	ADJ
easat-3708	294	23	flowshop	flowshop	ADJ
easat-3708	294	24	scheduling	scheduling	NOUN
easat-3708	294	25	problem	problem	NOUN
easat-3708	294	26	.	.	PUNCT
easat-3708	294	27	,	,	PUNCT
easat-3708	294	28	expert	expert	NOUN
easat-3708	294	29	systems	system	NOUN
easat-3708	294	30	with	with	ADP
easat-3708	294	31	applications	application	NOUN
easat-3708	294	32	39	39	NUM
easat-3708	294	33	(	(	PUNCT
easat-3708	294	34	2012	2012	NUM
easat-3708	294	35	)	)	PUNCT
easat-3708	294	36	8149–8161	8149–8161	NUM
easat-3708	294	37	.	.	PUNCT
easat-3708	295	1	[	[	X
easat-3708	295	2	8	8	NUM
easat-3708	295	3	]	]	PUNCT
easat-3708	295	4	a.	a.	NOUN
easat-3708	295	5	m.	m.	NOUN
easat-3708	295	6	d’amato	d’amato	PROPN
easat-3708	295	7	and	and	CCONJ
easat-3708	295	8	d.	d.	PROPN
easat-3708	295	9	s.	s.	PROPN
easat-3708	295	10	bernstein	bernstein	PROPN
easat-3708	295	11	,	,	PUNCT
easat-3708	295	12	linear	linear	ADJ
easat-3708	295	13	fractional	fractional	ADJ
easat-3708	295	14	transformation	transformation	NOUN
easat-3708	295	15	identification	identification	NOUN
easat-3708	295	16	using	use	VERB
easat-3708	295	17	retrospective	retrospective	ADJ
easat-3708	295	18	cost	cost	NOUN
easat-3708	295	19	optimization	optimization	NOUN
easat-3708	295	20	,	,	PUNCT
easat-3708	295	21	ifac	ifac	NOUN
easat-3708	295	22	proceedings	proceeding	NOUN
easat-3708	295	23	volumes	volume	NOUN
easat-3708	295	24	42	42	NUM
easat-3708	295	25	(	(	PUNCT
easat-3708	295	26	2009	2009	NUM
easat-3708	295	27	)	)	PUNCT
easat-3708	295	28	450	450	NUM
easat-3708	295	29	-	-	SYM
easat-3708	295	30	455	455	NUM
easat-3708	295	31	.	.	PUNCT
easat-3708	296	1	[	[	X
easat-3708	296	2	9	9	NUM
easat-3708	296	3	]	]	PUNCT
easat-3708	296	4	w.	w.	PROPN
easat-3708	296	5	dinkelbach	dinkelbach	PROPN
easat-3708	296	6	,	,	PUNCT
easat-3708	296	7	on	on	ADP
easat-3708	296	8	non	non	ADJ
easat-3708	296	9	-	-	ADJ
easat-3708	296	10	linear	linear	ADJ
easat-3708	296	11	fractional	fractional	ADJ
easat-3708	296	12	programming	programming	NOUN
easat-3708	296	13	,	,	PUNCT
easat-3708	296	14	management	management	NOUN
easat-3708	296	15	sciences	science	NOUN
easat-3708	296	16	13	13	NUM
easat-3708	296	17	(	(	PUNCT
easat-3708	296	18	1967	1967	NUM
easat-3708	296	19	)	)	PUNCT
easat-3708	296	20	492	492	NUM
easat-3708	296	21	-	-	SYM
easat-3708	296	22	498	498	NUM
easat-3708	296	23	.	.	PUNCT
easat-3708	297	1	[	[	X
easat-3708	297	2	10	10	NUM
easat-3708	297	3	]	]	X
easat-3708	297	4	r.	r.	PROPN
easat-3708	297	5	ghanbari	ghanbari	PROPN
easat-3708	297	6	,	,	PUNCT
easat-3708	297	7	kh	kh	PROPN
easat-3708	297	8	.	.	PUNCT
easat-3708	297	9	ghorbani	ghorbani	PROPN
easat-3708	297	10	-	-	PUNCT
easat-3708	297	11	moghadam	moghadam	PROPN
easat-3708	297	12	and	and	CCONJ
easat-3708	297	13	n.	n.	NOUN
easat-3708	297	14	mahdavi	mahdavi	PROPN
easat-3708	297	15	-	-	PUNCT
easat-3708	297	16	amir	amir	NOUN
easat-3708	297	17	,	,	PUNCT
easat-3708	297	18	vns	vns	PROPN
easat-3708	297	19	algorithm	algorithm	NOUN
easat-3708	297	20	for	for	ADP
easat-3708	297	21	solving	solve	VERB
easat-3708	297	22	fuzzy	fuzzy	ADJ
easat-3708	297	23	number	number	NOUN
easat-3708	297	24	linear	linear	NOUN
easat-3708	297	25	programming	programming	NOUN
easat-3708	297	26	problems	problem	NOUN
easat-3708	297	27	using	use	VERB
easat-3708	297	28	modified	modified	ADJ
easat-3708	297	29	kerre	kerre	PROPN
easat-3708	297	30	’s	’s	PART
easat-3708	297	31	method	method	NOUN
easat-3708	297	32	,	,	PUNCT
easat-3708	297	33	ieee	ieee	NOUN
easat-3708	297	34	transaction	transaction	NOUN
easat-3708	297	35	on	on	ADP
easat-3708	297	36	fuzzy	fuzzy	ADJ
easat-3708	297	37	systems	system	NOUN
easat-3708	297	38	27	27	NUM
easat-3708	297	39	(	(	PUNCT
easat-3708	297	40	2019	2019	NUM
easat-3708	297	41	)	)	PUNCT
easat-3708	297	42	1286–1294	1286–1294	NUM
easat-3708	297	43	.	.	PUNCT
easat-3708	298	1	[	[	X
easat-3708	298	2	11	11	NUM
easat-3708	298	3	]	]	X
easat-3708	298	4	r.	r.	PROPN
easat-3708	298	5	ghanbari	ghanbari	PROPN
easat-3708	298	6	,	,	PUNCT
easat-3708	298	7	kh	kh	PROPN
easat-3708	298	8	.	.	PUNCT
easat-3708	298	9	ghorbani	ghorbani	PROPN
easat-3708	298	10	-	-	PUNCT
easat-3708	298	11	moghadam	moghadam	PROPN
easat-3708	298	12	and	and	CCONJ
easat-3708	298	13	n.	n.	NOUN
easat-3708	298	14	mahdavi	mahdavi	PROPN
easat-3708	298	15	-	-	PUNCT
easat-3708	298	16	amir	amir	NOUN
easat-3708	298	17	,	,	PUNCT
easat-3708	298	18	vns	vns	PROPN
easat-3708	298	19	algorithm	algorithm	NOUN
easat-3708	298	20	for	for	ADP
easat-3708	298	21	solving	solve	VERB
easat-3708	298	22	fuzzy	fuzzy	ADJ
easat-3708	298	23	number	number	NOUN
easat-3708	298	24	quadratic	quadratic	ADJ
easat-3708	298	25	programming	programming	NOUN
easat-3708	298	26	problems	problem	NOUN
easat-3708	298	27	using	use	VERB
easat-3708	298	28	modified	modified	ADJ
easat-3708	298	29	kerre	kerre	PROPN
easat-3708	298	30	’s	’s	PART
easat-3708	298	31	method	method	NOUN
easat-3708	298	32	,	,	PUNCT
easat-3708	298	33	soft	soft	ADJ
easat-3708	298	34	computing	computing	NOUN
easat-3708	298	35	23	23	NUM
easat-3708	298	36	,	,	PUNCT
easat-3708	298	37	12305	12305	NUM
easat-3708	298	38	-	-	SYM
easat-3708	298	39	12315	12315	NUM
easat-3708	298	40	(	(	PUNCT
easat-3708	298	41	2019	2019	NUM
easat-3708	298	42	)	)	PUNCT
easat-3708	298	43	.	.	PUNCT
easat-3708	299	1	[	[	X
easat-3708	299	2	12	12	NUM
easat-3708	299	3	]	]	PUNCT
easat-3708	299	4	r.	r.	PROPN
easat-3708	299	5	ghanbari	ghanbari	PROPN
easat-3708	299	6	,	,	PUNCT
easat-3708	299	7	kh	kh	PROPN
easat-3708	299	8	.	.	PUNCT
easat-3708	299	9	ghorbani	ghorbani	PROPN
easat-3708	299	10	-	-	PUNCT
easat-3708	299	11	moghadam	moghadam	PROPN
easat-3708	299	12	and	and	CCONJ
easat-3708	299	13	n.	n.	NOUN
easat-3708	299	14	mahdavi	mahdavi	PROPN
easat-3708	299	15	-	-	PUNCT
easat-3708	299	16	amir	amir	PROPN
easat-3708	299	17	and	and	CCONJ
easat-3708	299	18	b.	b.	PROPN
easat-3708	299	19	de	de	PROPN
easat-3708	299	20	beats	beat	NOUN
easat-3708	299	21	,	,	PUNCT
easat-3708	299	22	fuzzy	fuzzy	ADJ
easat-3708	299	23	linear	linear	ADJ
easat-3708	299	24	programming	programming	NOUN
easat-3708	299	25	problems	problem	NOUN
easat-3708	299	26	:	:	PUNCT
easat-3708	299	27	models	model	NOUN
easat-3708	299	28	and	and	CCONJ
easat-3708	299	29	solutions	solution	NOUN
easat-3708	299	30	,	,	PUNCT
easat-3708	299	31	soft	soft	ADJ
easat-3708	299	32	computing	computing	NOUN
easat-3708	299	33	24	24	NUM
easat-3708	299	34	,	,	PUNCT
easat-3708	299	35	10043–10073	10043–10073	NUM
easat-3708	299	36	(	(	PUNCT
easat-3708	299	37	2020	2020	NUM
easat-3708	299	38	)	)	PUNCT
easat-3708	299	39	.	.	PUNCT
easat-3708	300	1	[	[	X
easat-3708	300	2	13	13	NUM
easat-3708	300	3	]	]	PUNCT
easat-3708	300	4	r.	r.	PROPN
easat-3708	300	5	ghanbari	ghanbari	PROPN
easat-3708	300	6	and	and	CCONJ
easat-3708	300	7	n.	n.	NOUN
easat-3708	300	8	mahdavi	mahdavi	PROPN
easat-3708	300	9	-	-	PUNCT
easat-3708	300	10	amir	amir	ADJ
easat-3708	300	11	,	,	PUNCT
easat-3708	300	12	new	new	ADJ
easat-3708	300	13	solutions	solution	NOUN
easat-3708	300	14	of	of	ADP
easat-3708	300	15	lr	lr	PRON
easat-3708	300	16	fuzzy	fuzzy	ADJ
easat-3708	300	17	linear	linear	PROPN
easat-3708	300	18	systems	system	NOUN
easat-3708	300	19	using	use	VERB
easat-3708	300	20	ranking	ranking	NOUN
easat-3708	300	21	functions	function	NOUN
easat-3708	300	22	and	and	CCONJ
easat-3708	300	23	abs	ab	NOUN
easat-3708	300	24	algorithms	algorithm	NOUN
easat-3708	300	25	,	,	PUNCT
easat-3708	300	26	applied	apply	VERB
easat-3708	300	27	mathematical	mathematical	ADJ
easat-3708	300	28	modelling	model	VERB
easat-3708	300	29	34	34	NUM
easat-3708	300	30	,	,	PUNCT
easat-3708	300	31	3363–3375	3363–3375	NUM
easat-3708	300	32	(	(	PUNCT
easat-3708	300	33	2010	2010	NUM
easat-3708	300	34	)	)	PUNCT
easat-3708	300	35	.	.	PUNCT
easat-3708	301	1	[	[	X
easat-3708	301	2	14	14	NUM
easat-3708	301	3	]	]	X
easat-3708	301	4	h.	h.	PROPN
easat-3708	301	5	jiao	jiao	PROPN
easat-3708	301	6	,	,	PUNCT
easat-3708	301	7	y.	y.	PROPN
easat-3708	301	8	guo	guo	PROPN
easat-3708	301	9	and	and	CCONJ
easat-3708	301	10	p.	p.	PROPN
easat-3708	301	11	shen	shen	PROPN
easat-3708	301	12	,	,	PUNCT
easat-3708	301	13	global	global	ADJ
easat-3708	301	14	optimization	optimization	NOUN
easat-3708	301	15	of	of	ADP
easat-3708	301	16	generalized	generalized	ADJ
easat-3708	301	17	linear	linear	ADJ
easat-3708	301	18	fractional	fractional	ADJ
easat-3708	301	19	programming	programming	NOUN
easat-3708	301	20	with	with	ADP
easat-3708	301	21	nonlinear	nonlinear	ADJ
easat-3708	301	22	constraints	constraint	NOUN
easat-3708	301	23	,	,	PUNCT
easat-3708	301	24	applied	apply	VERB
easat-3708	301	25	mathematics	mathematic	NOUN
easat-3708	301	26	and	and	CCONJ
easat-3708	301	27	computation	computation	NOUN
easat-3708	301	28	183	183	NUM
easat-3708	301	29	(	(	PUNCT
easat-3708	301	30	2008	2008	NUM
easat-3708	301	31	)	)	PUNCT
easat-3708	301	32	717	717	NUM
easat-3708	301	33	-	-	SYM
easat-3708	301	34	728	728	NUM
easat-3708	301	35	.	.	PUNCT
easat-3708	302	1	[	[	X
easat-3708	302	2	15	15	NUM
easat-3708	302	3	]	]	X
easat-3708	302	4	e.	e.	PROPN
easat-3708	302	5	khorram	khorram	PROPN
easat-3708	302	6	,	,	PUNCT
easat-3708	302	7	r.ezzati	r.ezzati	NOUN
easat-3708	302	8	and	and	CCONJ
easat-3708	302	9	z.valizadeh	z.valizadeh	NUM
easat-3708	302	10	,	,	PUNCT
easat-3708	302	11	linear	linear	ADJ
easat-3708	302	12	fractional	fractional	ADJ
easat-3708	302	13	multi	multi	ADJ
easat-3708	302	14	-	-	ADJ
easat-3708	302	15	objective	objective	ADJ
easat-3708	302	16	optimization	optimization	NOUN
easat-3708	302	17	problems	problem	NOUN
easat-3708	302	18	subject	subject	ADJ
easat-3708	302	19	to	to	ADP
easat-3708	302	20	fuzzy	fuzzy	ADJ
easat-3708	302	21	relational	relational	ADJ
easat-3708	302	22	equations	equation	NOUN
easat-3708	302	23	with	with	ADP
easat-3708	302	24	a	a	DET
easat-3708	302	25	continuous	continuous	ADJ
easat-3708	302	26	archimedean	archimedean	ADJ
easat-3708	302	27	triangular	triangular	NOUN
easat-3708	302	28	norm	norm	NOUN
easat-3708	302	29	,	,	PUNCT
easat-3708	302	30	information	information	NOUN
easat-3708	302	31	sciences	science	NOUN
easat-3708	302	32	267	267	NUM
easat-3708	302	33	(	(	PUNCT
easat-3708	302	34	2014	2014	NUM
easat-3708	302	35	)	)	PUNCT
easat-3708	302	36	225	225	NUM
easat-3708	302	37	-	-	SYM
easat-3708	302	38	239	239	NUM
easat-3708	302	39	.	.	PUNCT
easat-3708	303	1	[	[	X
easat-3708	303	2	16	16	NUM
easat-3708	303	3	]	]	X
easat-3708	303	4	e.	e.	PROPN
easat-3708	303	5	khorram	khorram	PROPN
easat-3708	303	6	,	,	PUNCT
easat-3708	303	7	r.ezzati	r.ezzati	NOUN
easat-3708	303	8	and	and	CCONJ
easat-3708	303	9	z.valizadeh	z.valizadeh	NUM
easat-3708	303	10	,	,	PUNCT
easat-3708	303	11	linear	linear	ADJ
easat-3708	303	12	fractional	fractional	ADJ
easat-3708	303	13	multi	multi	ADJ
easat-3708	303	14	-	-	ADJ
easat-3708	303	15	objective	objective	ADJ
easat-3708	303	16	optimization	optimization	NOUN
easat-3708	303	17	problems	problem	NOUN
easat-3708	303	18	subject	subject	ADJ
easat-3708	303	19	to	to	ADP
easat-3708	303	20	fuzzy	fuzzy	ADJ
easat-3708	303	21	relational	relational	ADJ
easat-3708	303	22	equations	equation	NOUN
easat-3708	303	23	with	with	ADP
easat-3708	303	24	a	a	DET
easat-3708	303	25	continuous	continuous	ADJ
easat-3708	303	26	archimedean	archimedean	ADJ
easat-3708	303	27	triangular	triangular	NOUN
easat-3708	303	28	norm	norm	NOUN
easat-3708	303	29	,	,	PUNCT
easat-3708	303	30	information	information	NOUN
easat-3708	303	31	sciences	science	NOUN
easat-3708	303	32	267	267	NUM
easat-3708	303	33	(	(	PUNCT
easat-3708	303	34	2014	2014	NUM
easat-3708	303	35	)	)	PUNCT
easat-3708	303	36	225	225	NUM
easat-3708	303	37	-	-	SYM
easat-3708	303	38	239	239	NUM
easat-3708	303	39	.	.	PUNCT
easat-3708	304	1	[	[	X
easat-3708	304	2	17	17	NUM
easat-3708	304	3	]	]	X
easat-3708	304	4	b.	b.	PROPN
easat-3708	304	5	b.	b.	PROPN
easat-3708	304	6	pal	pal	PROPN
easat-3708	304	7	,	,	PUNCT
easat-3708	304	8	b.	b.	PROPN
easat-3708	304	9	n.	n.	PROPN
easat-3708	304	10	moitra	moitra	PROPN
easat-3708	304	11	and	and	CCONJ
easat-3708	304	12	u.	u.	PROPN
easat-3708	304	13	maulik	maulik	PROPN
easat-3708	304	14	,	,	PUNCT
easat-3708	304	15	a	a	DET
easat-3708	304	16	goal	goal	NOUN
easat-3708	304	17	programming	programming	NOUN
easat-3708	304	18	procedure	procedure	NOUN
easat-3708	304	19	for	for	ADP
easat-3708	304	20	fuzzy	fuzzy	ADJ
easat-3708	304	21	multiobjective	multiobjective	ADJ
easat-3708	304	22	linear	linear	ADJ
easat-3708	304	23	fractional	fractional	ADJ
easat-3708	304	24	programming	programming	NOUN
easat-3708	304	25	problem	problem	NOUN
easat-3708	304	26	,	,	PUNCT
easat-3708	304	27	fuzzy	fuzzy	ADJ
easat-3708	304	28	sets	set	NOUN
easat-3708	304	29	and	and	CCONJ
easat-3708	304	30	systems	system	NOUN
easat-3708	304	31	139	139	NUM
easat-3708	304	32	(	(	PUNCT
easat-3708	304	33	2003	2003	NUM
easat-3708	304	34	)	)	PUNCT
easat-3708	304	35	395	395	NUM
easat-3708	304	36	-	-	SYM
easat-3708	304	37	405	405	NUM
easat-3708	304	38	.	.	PUNCT
easat-3708	305	1	[	[	X
easat-3708	305	2	18	18	NUM
easat-3708	305	3	]	]	X
easat-3708	305	4	n.	n.	NOUN
easat-3708	305	5	mladenovic	mladenovic	PROPN
easat-3708	305	6	and	and	CCONJ
easat-3708	305	7	p.	p.	PROPN
easat-3708	305	8	hansen	hansen	PROPN
easat-3708	305	9	,	,	PUNCT
easat-3708	305	10	variable	variable	ADJ
easat-3708	305	11	neighborhood	neighborhood	NOUN
easat-3708	305	12	search	search	NOUN
easat-3708	305	13	,	,	PUNCT
easat-3708	305	14	in	in	ADP
easat-3708	305	15	:	:	PUNCT
easat-3708	305	16	computers	computer	NOUN
easat-3708	305	17	and	and	CCONJ
easat-3708	305	18	operations	operation	NOUN
easat-3708	305	19	research	research	NOUN
easat-3708	305	20	,	,	PUNCT
easat-3708	305	21	1997	1997	NUM
easat-3708	305	22	,	,	PUNCT
easat-3708	305	23	pp	pp	ADJ
easat-3708	305	24	.	.	PUNCT
easat-3708	305	25	24	24	NUM
easat-3708	305	26	,	,	PUNCT
easat-3708	305	27	1097–1100	1097–1100	NUM
easat-3708	305	28	.	.	PUNCT
easat-3708	306	1	[	[	X
easat-3708	306	2	19	19	NUM
easat-3708	306	3	]	]	PUNCT
easat-3708	306	4	a.	a.	NOUN
easat-3708	306	5	h.	h.	PROPN
easat-3708	306	6	nafei	nafei	PROPN
easat-3708	306	7	and	and	CCONJ
easat-3708	306	8	s.	s.	PROPN
easat-3708	306	9	h.	h.	PROPN
easat-3708	306	10	nasseri	nasseri	PROPN
easat-3708	306	11	,	,	PUNCT
easat-3708	306	12	a	a	DET
easat-3708	306	13	new	new	ADJ
easat-3708	306	14	approach	approach	NOUN
easat-3708	306	15	for	for	ADP
easat-3708	306	16	solving	solve	VERB
easat-3708	306	17	neutrosophic	neutrosophic	ADJ
easat-3708	306	18	integer	integer	NOUN
easat-3708	306	19	programming	programming	NOUN
easat-3708	306	20	problems	problem	NOUN
easat-3708	306	21	.	.	PUNCT
easat-3708	307	1	international	international	ADJ
easat-3708	307	2	journal	journal	PROPN
easat-3708	307	3	of	of	ADP
easat-3708	307	4	applied	apply	VERB
easat-3708	307	5	9	9	NUM
easat-3708	307	6	(	(	PUNCT
easat-3708	307	7	2019	2019	NUM
easat-3708	307	8	)	)	PUNCT
easat-3708	307	9	1	1	NUM
easat-3708	307	10	-	-	SYM
easat-3708	307	11	9	9	NUM
easat-3708	307	12	.	.	PUNCT
easat-3708	308	1	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
easat-3708	308	2	7812	7812	NUM
easat-3708	308	3	edelweiss	edelweiss	PROPN
easat-3708	308	4	applied	apply	VERB
easat-3708	308	5	science	science	NOUN
easat-3708	308	6	and	and	CCONJ
easat-3708	308	7	technology	technology	NOUN
easat-3708	308	8	issn	issn	PROPN
easat-3708	308	9	:	:	PUNCT
easat-3708	308	10	2576	2576	NUM
easat-3708	308	11	-	-	SYM
easat-3708	308	12	8484	8484	NUM
easat-3708	308	13	vol	vol	NOUN
easat-3708	308	14	.	.	PROPN
easat-3708	308	15	8	8	NUM
easat-3708	308	16	,	,	PUNCT
easat-3708	308	17	no	no	INTJ
easat-3708	308	18	.	.	NOUN
easat-3708	308	19	6	6	NUM
easat-3708	308	20	:	:	SYM
easat-3708	308	21	7802	7802	NUM
easat-3708	308	22	-	-	SYM
easat-3708	308	23	7812	7812	NUM
easat-3708	308	24	,	,	PUNCT
easat-3708	308	25	2024	2024	NUM
easat-3708	308	26	doi	doi	NOUN
easat-3708	308	27	:	:	PUNCT
easat-3708	308	28	10.55214/25768484.v8i6.3708	10.55214/25768484.v8i6.3708	NUM
easat-3708	308	29	©	©	PROPN
easat-3708	308	30	2024	2024	NUM
easat-3708	308	31	by	by	ADP
easat-3708	308	32	the	the	DET
easat-3708	308	33	authors	author	NOUN
easat-3708	308	34	;	;	PUNCT
easat-3708	308	35	licensee	licensee	PROPN
easat-3708	308	36	learning	learning	NOUN
easat-3708	308	37	gate	gate	NOUN
easat-3708	309	1	[	[	X
easat-3708	309	2	20	20	NUM
easat-3708	309	3	]	]	PUNCT
easat-3708	309	4	m.	m.	NOUN
easat-3708	309	5	nezhadkian	nezhadkian	PROPN
easat-3708	309	6	,	,	PUNCT
easat-3708	309	7	,	,	PUNCT
easat-3708	309	8	s.	s.	PROPN
easat-3708	309	9	m.	m.	PROPN
easat-3708	309	10	azimi	azimi	PROPN
easat-3708	309	11	,	,	PUNCT
easat-3708	309	12	a.	a.	NOUN
easat-3708	309	13	ferro	ferro	PROPN
easat-3708	309	14	and	and	CCONJ
easat-3708	309	15	a.	a.	PROPN
easat-3708	309	16	h.	h.	PROPN
easat-3708	309	17	nafei	nafei	PROPN
easat-3708	309	18	,	,	PUNCT
easat-3708	309	19	a	a	DET
easat-3708	309	20	model	model	NOUN
easat-3708	309	21	for	for	ADP
easat-3708	309	22	new	new	ADJ
easat-3708	309	23	product	product	NOUN
easat-3708	309	24	development	development	NOUN
easat-3708	309	25	in	in	ADP
easat-3708	309	26	business	business	NOUN
easat-3708	309	27	companies	company	NOUN
easat-3708	309	28	based	base	VERB
easat-3708	309	29	on	on	ADP
easat-3708	309	30	grounded	ground	VERB
easat-3708	309	31	theory	theory	NOUN
easat-3708	309	32	approach	approach	NOUN
easat-3708	309	33	and	and	CCONJ
easat-3708	309	34	fuzzy	fuzzy	ADJ
easat-3708	309	35	method	method	NOUN
easat-3708	309	36	,	,	PUNCT
easat-3708	309	37	journal	journal	NOUN
easat-3708	309	38	of	of	ADP
easat-3708	309	39	computational	computational	ADJ
easat-3708	309	40	and	and	CCONJ
easat-3708	309	41	cognitive	cognitive	ADJ
easat-3708	309	42	engineering	engineering	NOUN
easat-3708	309	43	2	2	NUM
easat-3708	309	44	(	(	PUNCT
easat-3708	309	45	2023	2023	NUM
easat-3708	309	46	)	)	PUNCT
easat-3708	309	47	124	124	NUM
easat-3708	309	48	-	-	SYM
easat-3708	309	49	132	132	NUM
easat-3708	309	50	.	.	PUNCT
easat-3708	310	1	[	[	X
easat-3708	310	2	21	21	NUM
easat-3708	310	3	]	]	X
easat-3708	310	4	m.	m.	NOUN
easat-3708	310	5	pourrafiee	pourrafiee	PROPN
easat-3708	310	6	,	,	PUNCT
easat-3708	310	7	a.	a.	NOUN
easat-3708	310	8	nafei	nafei	PROPN
easat-3708	310	9	,	,	PUNCT
easat-3708	310	10	s.	s.	PROPN
easat-3708	310	11	banihashemi	banihashemi	PROPN
easat-3708	310	12	and	and	CCONJ
easat-3708	310	13	s.	s.	PROPN
easat-3708	310	14	pourmohammad	pourmohammad	PROPN
easat-3708	310	15	azizi	azizi	PROPN
easat-3708	310	16	,	,	PUNCT
easat-3708	310	17	comparing	compare	VERB
easat-3708	310	18	entropies	entropy	NOUN
easat-3708	310	19	in	in	ADP
easat-3708	310	20	portfolio	portfolio	NOUN
easat-3708	310	21	diversification	diversification	NOUN
easat-3708	310	22	with	with	ADP
easat-3708	310	23	fuzzy	fuzzy	ADJ
easat-3708	310	24	value	value	NOUN
easat-3708	310	25	at	at	ADP
easat-3708	310	26	risk	risk	NOUN
easat-3708	310	27	and	and	CCONJ
easat-3708	310	28	higher	high	ADJ
easat-3708	310	29	-	-	PUNCT
easat-3708	310	30	order	order	NOUN
easat-3708	310	31	moment	moment	NOUN
easat-3708	310	32	.	.	PUNCT
easat-3708	311	1	fuzzy	fuzzy	ADJ
easat-3708	311	2	information	information	NOUN
easat-3708	311	3	and	and	CCONJ
easat-3708	311	4	engineering	engineering	NOUN
easat-3708	311	5	12	12	NUM
easat-3708	311	6	(	(	PUNCT
easat-3708	311	7	2020	2020	NUM
easat-3708	311	8	)	)	PUNCT
easat-3708	311	9	123138	123138	NUM
easat-3708	311	10	.	.	PUNCT
easat-3708	312	1	[	[	X
easat-3708	312	2	22	22	NUM
easat-3708	312	3	]	]	X
easat-3708	312	4	g.	g.	PROPN
easat-3708	312	5	shakouri	shakouri	PROPN
easat-3708	312	6	,	,	PUNCT
easat-3708	312	7	s.	s.	PROPN
easat-3708	312	8	h.	h.	PROPN
easat-3708	312	9	nasseri	nasseri	PROPN
easat-3708	312	10	and	and	CCONJ
easat-3708	312	11	m.	m.	PROPN
easat-3708	312	12	m.	m.	PROPN
easat-3708	312	13	paydar	paydar	PROPN
easat-3708	312	14	,	,	PUNCT
easat-3708	312	15	fuzzy	fuzzy	ADJ
easat-3708	312	16	mathematical	mathematical	ADJ
easat-3708	312	17	programming	programming	NOUN
easat-3708	312	18	approach	approach	NOUN
easat-3708	312	19	for	for	ADP
easat-3708	312	20	transportation	transportation	NOUN
easat-3708	312	21	problem	problem	NOUN
easat-3708	312	22	with	with	ADP
easat-3708	312	23	flexible	flexible	ADJ
easat-3708	312	24	constraints	constraint	NOUN
easat-3708	312	25	,	,	PUNCT
easat-3708	312	26	journal	journal	NOUN
easat-3708	312	27	of	of	ADP
easat-3708	312	28	operational	operational	ADJ
easat-3708	312	29	research	research	NOUN
easat-3708	312	30	in	in	ADP
easat-3708	312	31	its	its	PRON
easat-3708	312	32	applications	application	NOUN
easat-3708	312	33	(	(	PUNCT
easat-3708	312	34	applied	apply	VERB
easat-3708	312	35	mathematics)lahijan	mathematics)lahijan	PROPN
easat-3708	312	36	azad	azad	PROPN
easat-3708	312	37	university	university	PROPN
easat-3708	312	38	19	19	NUM
easat-3708	312	39	(	(	PUNCT
easat-3708	312	40	2022	2022	NUM
easat-3708	312	41	)	)	PUNCT
easat-3708	312	42	29	29	NUM
easat-3708	312	43	-	-	SYM
easat-3708	312	44	44	44	NUM
easat-3708	312	45	.	.	PUNCT
easat-3708	313	1	[	[	X
easat-3708	313	2	23	23	NUM
easat-3708	313	3	]	]	PUNCT
easat-3708	313	4	m.	m.	NOUN
easat-3708	313	5	sakawa	sakawa	PROPN
easat-3708	313	6	,	,	PUNCT
easat-3708	313	7	i.	i.	PROPN
easat-3708	313	8	nishizaki	nishizaki	PROPN
easat-3708	313	9	and	and	CCONJ
easat-3708	313	10	s.	s.	PROPN
easat-3708	313	11	yongxin	yongxin	PROPN
easat-3708	313	12	,	,	PUNCT
easat-3708	313	13	interactive	interactive	ADJ
easat-3708	313	14	fuzzy	fuzzy	ADJ
easat-3708	313	15	programming	programming	NOUN
easat-3708	313	16	for	for	ADP
easat-3708	313	17	multiobjective	multiobjective	ADJ
easat-3708	313	18	two	two	NUM
easat-3708	313	19	-	-	PUNCT
easat-3708	313	20	level	level	NOUN
easat-3708	313	21	linear	linear	ADJ
easat-3708	313	22	fractional	fractional	ADJ
easat-3708	313	23	programming	programming	NOUN
easat-3708	313	24	problems	problem	NOUN
easat-3708	313	25	with	with	ADP
easat-3708	313	26	partial	partial	ADJ
easat-3708	313	27	information	information	NOUN
easat-3708	313	28	of	of	ADP
easat-3708	313	29	preference	preference	NOUN
easat-3708	313	30	,	,	PUNCT
easat-3708	313	31	international	international	ADJ
easat-3708	313	32	journal	journal	NOUN
easat-3708	313	33	of	of	ADP
easat-3708	313	34	fuzzy	fuzzy	ADJ
easat-3708	313	35	systems	system	NOUN
easat-3708	313	36	,	,	PUNCT
easat-3708	313	37	3	3	NUM
easat-3708	313	38	(	(	PUNCT
easat-3708	313	39	2001	2001	NUM
easat-3708	313	40	)	)	PUNCT
easat-3708	313	41	452	452	NUM
easat-3708	313	42	–	–	PUNCT
easat-3708	313	43	61	61	NUM
easat-3708	313	44	.	.	PUNCT
easat-3708	314	1	[	[	X
easat-3708	314	2	24	24	NUM
easat-3708	314	3	]	]	PUNCT
easat-3708	314	4	m.	m.	NOUN
easat-3708	314	5	sakawa	sakawa	PROPN
easat-3708	314	6	and	and	CCONJ
easat-3708	314	7	k.	k.	PROPN
easat-3708	314	8	kato	kato	PROPN
easat-3708	314	9	,	,	PUNCT
easat-3708	314	10	an	an	DET
easat-3708	314	11	interactive	interactive	ADJ
easat-3708	314	12	fuzzy	fuzzy	ADJ
easat-3708	314	13	satisficing	satisficing	NOUN
easat-3708	314	14	method	method	NOUN
easat-3708	314	15	for	for	ADP
easat-3708	314	16	structured	structured	ADJ
easat-3708	314	17	multiobjective	multiobjective	ADJ
easat-3708	314	18	linear	linear	ADJ
easat-3708	314	19	fractional	fractional	ADJ
easat-3708	314	20	programs	program	NOUN
easat-3708	314	21	with	with	ADP
easat-3708	314	22	fuzzy	fuzzy	ADJ
easat-3708	314	23	numbers	number	NOUN
easat-3708	314	24	,	,	PUNCT
easat-3708	314	25	european	european	ADJ
easat-3708	314	26	journal	journal	PROPN
easat-3708	314	27	of	of	ADP
easat-3708	314	28	operational	operational	ADJ
easat-3708	314	29	research	research	NOUN
easat-3708	314	30	,	,	PUNCT
easat-3708	314	31	107	107	NUM
easat-3708	314	32	(	(	PUNCT
easat-3708	314	33	1998	1998	NUM
easat-3708	314	34	)	)	PUNCT
easat-3708	314	35	575	575	NUM
easat-3708	314	36	-	-	SYM
easat-3708	314	37	589	589	NUM
easat-3708	314	38	.	.	PUNCT
easat-3708	315	1	[	[	X
easat-3708	315	2	25	25	NUM
easat-3708	315	3	]	]	PUNCT
easat-3708	315	4	b.	b.	PROPN
easat-3708	315	5	stanojević	stanojević	PROPN
easat-3708	315	6	,	,	PUNCT
easat-3708	315	7	s.	s.	PROPN
easat-3708	315	8	dzitac	dzitac	PROPN
easat-3708	315	9	and	and	CCONJ
easat-3708	315	10	i.	i.	PROPN
easat-3708	315	11	dzitac	dzitac	PROPN
easat-3708	315	12	,	,	PUNCT
easat-3708	315	13	fuzzy	fuzzy	ADJ
easat-3708	315	14	numbers	number	NOUN
easat-3708	315	15	and	and	CCONJ
easat-3708	315	16	fractional	fractional	ADJ
easat-3708	315	17	programming	programming	NOUN
easat-3708	315	18	in	in	ADP
easat-3708	315	19	making	make	VERB
easat-3708	315	20	decisions	decision	NOUN
easat-3708	315	21	.	.	PUNCT
easat-3708	316	1	international	international	ADJ
easat-3708	316	2	journal	journal	PROPN
easat-3708	316	3	of	of	ADP
easat-3708	316	4	information	information	NOUN
easat-3708	316	5	technology	technology	NOUN
easat-3708	316	6	and	and	CCONJ
easat-3708	316	7	decision	decision	NOUN
easat-3708	316	8	making	make	VERB
easat-3708	316	9	19	19	NUM
easat-3708	316	10	(	(	PUNCT
easat-3708	316	11	2020	2020	NUM
easat-3708	316	12	)	)	PUNCT
easat-3708	316	13	1123	1123	NUM
easat-3708	316	14	-	-	SYM
easat-3708	316	15	1147	1147	NUM
easat-3708	316	16	.	.	PUNCT
easat-3708	317	1	[	[	X
easat-3708	317	2	26	26	NUM
easat-3708	317	3	]	]	X
easat-3708	317	4	y.	y.	PROPN
easat-3708	317	5	shen	shen	PROPN
easat-3708	317	6	,	,	PUNCT
easat-3708	317	7	m.	m.	NOUN
easat-3708	317	8	sakawa	sakawa	PROPN
easat-3708	317	9	and	and	CCONJ
easat-3708	317	10	i.	i.	PROPN
easat-3708	317	11	nishizaki	nishizaki	PROPN
easat-3708	317	12	,	,	PUNCT
easat-3708	317	13	interactive	interactive	ADJ
easat-3708	317	14	fuzzy	fuzzy	ADJ
easat-3708	317	15	programming	programming	NOUN
easat-3708	317	16	using	use	VERB
easat-3708	317	17	partial	partial	ADJ
easat-3708	317	18	information	information	NOUN
easat-3708	317	19	about	about	ADP
easat-3708	317	20	preference	preference	NOUN
easat-3708	317	21	for	for	ADP
easat-3708	317	22	multiobjective	multiobjective	ADJ
easat-3708	317	23	two	two	NUM
easat-3708	317	24	-	-	PUNCT
easat-3708	317	25	level	level	NOUN
easat-3708	317	26	linear	linear	ADJ
easat-3708	317	27	fractional	fractional	ADJ
easat-3708	317	28	programming	programming	NOUN
easat-3708	317	29	problems	problem	NOUN
easat-3708	317	30	,	,	PUNCT
easat-3708	317	31	electronics	electronic	NOUN
easat-3708	317	32	and	and	CCONJ
easat-3708	317	33	communications	communication	NOUN
easat-3708	317	34	in	in	ADP
easat-3708	317	35	japan	japan	PROPN
easat-3708	317	36	86	86	NUM
easat-3708	317	37	(	(	PUNCT
easat-3708	317	38	2002	2002	NUM
easat-3708	317	39	)	)	PUNCT
easat-3708	318	1	298–305	298–305	NUM
easat-3708	318	2	.	.	PUNCT
easat-3708	319	1	[	[	X
easat-3708	319	2	27	27	NUM
easat-3708	319	3	]	]	PUNCT
easat-3708	319	4	a.	a.	NOUN
easat-3708	319	5	sheikhi	sheikhi	PROPN
easat-3708	319	6	and	and	CCONJ
easat-3708	319	7	m.	m.	PROPN
easat-3708	319	8	j.	j.	PROPN
easat-3708	319	9	ebadi	ebadi	PROPN
easat-3708	319	10	,	,	PUNCT
easat-3708	319	11	on	on	ADP
easat-3708	319	12	solving	solve	VERB
easat-3708	319	13	linear	linear	ADJ
easat-3708	319	14	fractional	fractional	ADJ
easat-3708	319	15	programming	programming	NOUN
easat-3708	319	16	transportation	transportation	NOUN
easat-3708	319	17	problems	problem	NOUN
easat-3708	319	18	with	with	ADP
easat-3708	319	19	fuzzy	fuzzy	ADJ
easat-3708	319	20	numbers	number	NOUN
easat-3708	319	21	,	,	PUNCT
easat-3708	319	22	journal	journal	NOUN
easat-3708	319	23	of	of	ADP
easat-3708	319	24	fuzzy	fuzzy	ADJ
easat-3708	319	25	extension	extension	NOUN
easat-3708	319	26	and	and	CCONJ
easat-3708	319	27	applications	application	NOUN
easat-3708	319	28	4	4	NUM
easat-3708	319	29	(	(	PUNCT
easat-3708	319	30	2023	2023	NUM
easat-3708	319	31	)	)	PUNCT
easat-3708	319	32	327	327	NUM
easat-3708	319	33	-	-	SYM
easat-3708	319	34	339	339	NUM
easat-3708	319	35	.	.	PUNCT
easat-3708	320	1	[	[	X
easat-3708	320	2	28	28	NUM
easat-3708	320	3	]	]	X
easat-3708	320	4	zanina	zanina	PROPN
easat-3708	320	5	,	,	PUNCT
easat-3708	320	6	y.	y.	PROPN
easat-3708	320	7	lazarev	lazarev	PROPN
easat-3708	320	8	and	and	CCONJ
easat-3708	320	9	a.	a.	NOUN
easat-3708	320	10	radaev	radaev	PROPN
easat-3708	320	11	,	,	PUNCT
easat-3708	320	12	determination	determination	NOUN
easat-3708	320	13	of	of	ADP
easat-3708	320	14	the	the	DET
easat-3708	320	15	structure	structure	NOUN
easat-3708	320	16	for	for	ADP
easat-3708	320	17	the	the	DET
easat-3708	320	18	road	road	NOUN
easat-3708	320	19	construction	construction	NOUN
easat-3708	320	20	machinery	machinery	NOUN
easat-3708	320	21	fleet	fleet	NOUN
easat-3708	320	22	on	on	ADP
easat-3708	320	23	the	the	DET
easat-3708	320	24	basis	basis	NOUN
easat-3708	320	25	of	of	ADP
easat-3708	320	26	fractional	fractional	ADJ
easat-3708	320	27	linear	linear	PROPN
easat-3708	320	28	optimization	optimization	NOUN
easat-3708	320	29	,	,	PUNCT
easat-3708	320	30	transportation	transportation	NOUN
easat-3708	320	31	research	research	NOUN
easat-3708	320	32	procedia	procedia	NOUN
easat-3708	320	33	,	,	PUNCT
easat-3708	320	34	63	63	NUM
easat-3708	320	35	(	(	PUNCT
easat-3708	320	36	2022	2022	NUM
easat-3708	320	37	)	)	PUNCT
easat-3708	320	38	27	27	NUM
easat-3708	320	39	-	-	SYM
easat-3708	320	40	40	40	NUM
easat-3708	320	41	.	.	PUNCT
easat-3708	321	1	[	[	X
easat-3708	321	2	29	29	NUM
easat-3708	321	3	]	]	X
easat-3708	321	4	h.	h.	PROPN
easat-3708	321	5	t.	t.	PROPN
easat-3708	321	6	nguyen	nguyen	PROPN
easat-3708	321	7	and	and	CCONJ
easat-3708	321	8	e.	e.	PROPN
easat-3708	321	9	a.	a.	PROPN
easat-3708	321	10	walker	walker	PROPN
easat-3708	321	11	,	,	PUNCT
easat-3708	321	12	a	a	DET
easat-3708	321	13	first	first	ADJ
easat-3708	321	14	course	course	NOUN
easat-3708	321	15	in	in	ADP
easat-3708	321	16	fuzzy	fuzzy	ADJ
easat-3708	321	17	logic	logic	NOUN
easat-3708	321	18	,	,	PUNCT
easat-3708	321	19	chapman	chapman	NOUN
easat-3708	321	20	and	and	CCONJ
easat-3708	321	21	hall	hall	PROPN
easat-3708	321	22	,	,	PUNCT
easat-3708	321	23	2000	2000	NUM
easat-3708	321	24	.	.	PUNCT
easat-3708	322	1	[	[	X
easat-3708	322	2	30	30	NUM
easat-3708	322	3	]	]	X
easat-3708	322	4	s.	s.	PROPN
easat-3708	322	5	vlah	vlah	PROPN
easat-3708	322	6	,	,	PUNCT
easat-3708	322	7	z.	z.	PROPN
easat-3708	322	8	lukac	lukac	PROPN
easat-3708	322	9	,	,	PUNCT
easat-3708	322	10	j.	j.	PROPN
easat-3708	322	11	pacheco	pacheco	PROPN
easat-3708	322	12	,	,	PUNCT
easat-3708	322	13	use	use	NOUN
easat-3708	322	14	of	of	ADP
easat-3708	322	15	vns	vns	NOUN
easat-3708	322	16	heuristics	heuristic	NOUN
easat-3708	322	17	for	for	ADP
easat-3708	322	18	scheduling	scheduling	NOUN
easat-3708	322	19	of	of	ADP
easat-3708	322	20	patients	patient	NOUN
easat-3708	322	21	in	in	ADP
easat-3708	322	22	hospital	hospital	NOUN
easat-3708	322	23	,	,	PUNCT
easat-3708	322	24	jors	jor	NOUN
easat-3708	322	25	62	62	NUM
easat-3708	322	26	(	(	PUNCT
easat-3708	322	27	2011	2011	NUM
easat-3708	322	28	)	)	PUNCT
easat-3708	322	29	1227–1238	1227–1238	NUM
easat-3708	322	30	.	.	PUNCT
easat-3708	323	1	[	[	X
easat-3708	323	2	31	31	NUM
easat-3708	323	3	]	]	PUNCT
easat-3708	323	4	x.	x.	PROPN
easat-3708	323	5	wang	wang	PROPN
easat-3708	323	6	,	,	PUNCT
easat-3708	323	7	l.	l.	PROPN
easat-3708	323	8	tang	tang	PROPN
easat-3708	323	9	,	,	PUNCT
easat-3708	323	10	a	a	DET
easat-3708	323	11	hybrid	hybrid	ADJ
easat-3708	323	12	vns	vns	NOUN
easat-3708	323	13	with	with	ADP
easat-3708	323	14	ts	t	NOUN
easat-3708	323	15	for	for	ADP
easat-3708	323	16	the	the	DET
easat-3708	323	17	single	single	ADJ
easat-3708	323	18	machine	machine	NOUN
easat-3708	323	19	scheduling	scheduling	NOUN
easat-3708	323	20	problem	problem	NOUN
easat-3708	323	21	to	to	PART
easat-3708	323	22	minimize	minimize	VERB
easat-3708	323	23	the	the	DET
easat-3708	323	24	sum	sum	NOUN
easat-3708	323	25	of	of	ADP
easat-3708	323	26	weighted	weight	VERB
easat-3708	323	27	tardiness	tardiness	NOUN
easat-3708	323	28	of	of	ADP
easat-3708	323	29	jobs	job	NOUN
easat-3708	323	30	,	,	PUNCT
easat-3708	323	31	proceedings	proceeding	NOUN
easat-3708	323	32	of	of	ADP
easat-3708	323	33	the	the	DET
easat-3708	323	34	4th	4th	ADJ
easat-3708	323	35	international	international	ADJ
easat-3708	323	36	conference	conference	NOUN
easat-3708	323	37	on	on	ADP
easat-3708	323	38	intelligent	intelligent	ADJ
easat-3708	323	39	computing	computing	NOUN
easat-3708	323	40	:	:	PUNCT
easat-3708	323	41	advanced	advanced	ADJ
easat-3708	323	42	intelligent	intelligent	ADJ
easat-3708	323	43	computing	computing	NOUN
easat-3708	323	44	theories	theory	NOUN
easat-3708	323	45	and	and	CCONJ
easat-3708	323	46	applications	application	NOUN
easat-3708	323	47	with	with	ADP
easat-3708	323	48	aspects	aspect	NOUN
easat-3708	323	49	of	of	ADP
easat-3708	323	50	artificial	artificial	ADJ
easat-3708	323	51	intelligence	intelligence	NOUN
easat-3708	323	52	,	,	PUNCT
easat-3708	323	53	springer	springer	NOUN
easat-3708	323	54	-	-	PUNCT
easat-3708	323	55	verlag	verlag	PROPN
easat-3708	323	56	,	,	PUNCT
easat-3708	323	57	berlin	berlin	PROPN
easat-3708	323	58	,	,	PUNCT
easat-3708	323	59	heidelberg	heidelberg	PROPN
easat-3708	323	60	(	(	PUNCT
easat-3708	323	61	2008	2008	NUM
easat-3708	323	62	)	)	PUNCT
easat-3708	323	63	727–733	727–733	NUM
easat-3708	323	64	.	.	PUNCT
easat-3708	324	1	[	[	X
easat-3708	324	2	32	32	NUM
easat-3708	324	3	]	]	X
easat-3708	324	4	y.	y.	PROPN
easat-3708	324	5	wang	wang	PROPN
easat-3708	324	6	,	,	PUNCT
easat-3708	324	7	l.	l.	PROPN
easat-3708	324	8	liu	liu	PROPN
easat-3708	324	9	,	,	PUNCT
easat-3708	324	10	sh	sh	PROPN
easat-3708	324	11	.	.	PUNCT
easat-3708	324	12	guo	guo	PROPN
easat-3708	324	13	,	,	PUNCT
easat-3708	324	14	q.	q.	PROPN
easat-3708	324	15	yue	yue	PROPN
easat-3708	324	16	and	and	CCONJ
easat-3708	324	17	p.	p.	PROPN
easat-3708	324	18	guo	guo	PROPN
easat-3708	324	19	,	,	PUNCT
easat-3708	324	20	a	a	DET
easat-3708	324	21	bi	bi	ADJ
easat-3708	324	22	-	-	ADJ
easat-3708	324	23	level	level	ADJ
easat-3708	324	24	multi	multi	ADJ
easat-3708	324	25	-	-	ADJ
easat-3708	324	26	objective	objective	ADJ
easat-3708	324	27	linear	linear	ADJ
easat-3708	324	28	fractional	fractional	ADJ
easat-3708	324	29	programming	programming	NOUN
easat-3708	324	30	for	for	ADP
easat-3708	324	31	water	water	NOUN
easat-3708	324	32	consumption	consumption	NOUN
easat-3708	324	33	structure	structure	NOUN
easat-3708	324	34	optimization	optimization	NOUN
easat-3708	324	35	based	base	VERB
easat-3708	324	36	on	on	ADP
easat-3708	324	37	water	water	NOUN
easat-3708	324	38	shortage	shortage	NOUN
easat-3708	324	39	risk	risk	NOUN
easat-3708	324	40	,	,	PUNCT
easat-3708	324	41	journal	journal	NOUN
easat-3708	324	42	of	of	ADP
easat-3708	324	43	cleaner	clean	ADJ
easat-3708	324	44	production	production	NOUN
easat-3708	324	45	237	237	NUM
easat-3708	324	46	(	(	PUNCT
easat-3708	324	47	2019	2019	NUM
easat-3708	324	48	)	)	PUNCT
easat-3708	324	49	1	1	NUM
easat-3708	324	50	-	-	SYM
easat-3708	324	51	13	13	NUM
easat-3708	324	52	.	.	PUNCT
easat-3708	325	1	[	[	X
easat-3708	325	2	33	33	NUM
easat-3708	325	3	]	]	PUNCT
easat-3708	325	4	g.	g.	PROPN
easat-3708	325	5	wang	wang	PROPN
easat-3708	325	6	,	,	PUNCT
easat-3708	325	7	g.	g.	PROPN
easat-3708	325	8	ziyou	ziyou	PROPN
easat-3708	325	9	and	and	CCONJ
easat-3708	325	10	w.	w.	PROPN
easat-3708	325	11	zhongping	zhongping	PROPN
easat-3708	325	12	,	,	PUNCT
easat-3708	325	13	a	a	DET
easat-3708	325	14	global	global	ADJ
easat-3708	325	15	optimization	optimization	NOUN
easat-3708	325	16	algorithm	algorithm	NOUN
easat-3708	325	17	for	for	ADP
easat-3708	325	18	solving	solve	VERB
easat-3708	325	19	the	the	DET
easat-3708	325	20	bi	bi	ADJ
easat-3708	325	21	-	-	ADJ
easat-3708	325	22	level	level	ADJ
easat-3708	325	23	linear	linear	ADJ
easat-3708	325	24	fractional	fractional	ADJ
easat-3708	325	25	programming	programming	NOUN
easat-3708	325	26	problem	problem	NOUN
easat-3708	325	27	,	,	PUNCT
easat-3708	325	28	computers	computer	NOUN
easat-3708	325	29	and	and	CCONJ
easat-3708	325	30	industrial	industrial	ADJ
easat-3708	325	31	engineering	engineering	NOUN
easat-3708	325	32	63	63	NUM
easat-3708	325	33	(	(	PUNCT
easat-3708	325	34	2012	2012	NUM
easat-3708	325	35	)	)	PUNCT
easat-3708	325	36	428	428	NUM
easat-3708	325	37	-	-	SYM
easat-3708	325	38	432	432	NUM
easat-3708	325	39	.	.	PUNCT
easat-3708	326	1	[	[	X
easat-3708	326	2	34	34	NUM
easat-3708	326	3	]	]	X
easat-3708	326	4	g.	g.	PROPN
easat-3708	326	5	yang	yang	PROPN
easat-3708	326	6	,	,	PUNCT
easat-3708	326	7	x.	x.	PROPN
easat-3708	326	8	li	li	PROPN
easat-3708	326	9	,	,	PUNCT
easat-3708	326	10	l.	l.	PROPN
easat-3708	326	11	huo	huo	PROPN
easat-3708	326	12	and	and	CCONJ
easat-3708	326	13	q.	q.	PROPN
easat-3708	326	14	liu	liu	PROPN
easat-3708	326	15	,	,	PUNCT
easat-3708	326	16	a	a	DET
easat-3708	326	17	solving	solving	NOUN
easat-3708	326	18	approach	approach	NOUN
easat-3708	326	19	for	for	ADP
easat-3708	326	20	fuzzy	fuzzy	ADJ
easat-3708	326	21	multi	multi	ADJ
easat-3708	326	22	-	-	ADJ
easat-3708	326	23	objective	objective	ADJ
easat-3708	326	24	linear	linear	ADJ
easat-3708	326	25	fractional	fractional	ADJ
easat-3708	326	26	programming	programming	NOUN
easat-3708	326	27	and	and	CCONJ
easat-3708	326	28	application	application	NOUN
easat-3708	326	29	to	to	ADP
easat-3708	326	30	an	an	DET
easat-3708	326	31	agricultural	agricultural	ADJ
easat-3708	326	32	planting	planting	NOUN
easat-3708	326	33	structure	structure	NOUN
easat-3708	326	34	optimization	optimization	NOUN
easat-3708	326	35	problem	problem	NOUN
easat-3708	326	36	,	,	PUNCT
easat-3708	326	37	chaos	chaos	NOUN
easat-3708	326	38	,	,	PUNCT
easat-3708	326	39	solitons	soliton	NOUN
easat-3708	326	40	&	&	CCONJ
easat-3708	326	41	fractals	fractal	NOUN
easat-3708	326	42	,	,	PUNCT
easat-3708	326	43	141	141	NUM
easat-3708	326	44	(	(	PUNCT
easat-3708	326	45	2020	2020	NUM
easat-3708	326	46	)	)	PUNCT
easat-3708	326	47	.	.	PUNCT
easat-3708	327	1	[	[	X
easat-3708	327	2	35	35	NUM
easat-3708	327	3	]	]	X
easat-3708	327	4	h.	h.	PROPN
easat-3708	327	5	j.	j.	PROPN
easat-3708	327	6	zimmermann	zimmermann	PROPN
easat-3708	327	7	,	,	PUNCT
easat-3708	327	8	fuzzy	fuzzy	ADJ
easat-3708	327	9	set	set	NOUN
easat-3708	327	10	theory	theory	NOUN
easat-3708	327	11	and	and	CCONJ
easat-3708	327	12	its	its	PRON
easat-3708	327	13	applications	application	NOUN
easat-3708	327	14	,	,	PUNCT
easat-3708	327	15	kluwer	kluwer	NOUN
easat-3708	327	16	academic	academic	ADJ
easat-3708	327	17	publishers	publisher	NOUN
easat-3708	327	18	,	,	PUNCT
easat-3708	327	19	2001	2001	NUM
easat-3708	327	20	.	.	PUNCT