id	sid	tid	token	lemma	pos
iajs-2858	1	1	ihjpas	ihjpas	PROPN
iajs-2858	1	2	.	.	PUNCT
iajs-2858	2	1	53	53	NUM
iajs-2858	2	2	(	(	PUNCT
iajs-2858	2	3	4)2022	4)2022	NOUN
iajs-2858	2	4	241	241	NUM
iajs-2858	2	5	this	this	DET
iajs-2858	2	6	work	work	NOUN
iajs-2858	2	7	is	be	AUX
iajs-2858	2	8	licensed	license	VERB
iajs-2858	2	9	under	under	ADP
iajs-2858	2	10	a	a	DET
iajs-2858	2	11	creative	creative	ADJ
iajs-2858	2	12	commons	common	NOUN
iajs-2858	2	13	attribution	attribution	NOUN
iajs-2858	2	14	4.0	4.0	NUM
iajs-2858	2	15	international	international	ADJ
iajs-2858	2	16	license	license	NOUN
iajs-2858	2	17	.	.	PUNCT
iajs-2858	3	1	solving	solve	VERB
iajs-2858	3	2	of	of	ADP
iajs-2858	3	3	the	the	DET
iajs-2858	3	4	quadratic	quadratic	ADJ
iajs-2858	3	5	fractional	fractional	ADJ
iajs-2858	3	6	programming	programming	NOUN
iajs-2858	3	7	problems	problem	NOUN
iajs-2858	3	8	by	by	ADP
iajs-2858	3	9	a	a	DET
iajs-2858	3	10	modified	modify	VERB
iajs-2858	3	11	symmetric	symmetric	ADJ
iajs-2858	3	12	fuzzy	fuzzy	ADJ
iajs-2858	3	13	approach	approach	NOUN
iajs-2858	3	14	abstract	abstract	VERB
iajs-2858	3	15	the	the	DET
iajs-2858	3	16	aims	aim	NOUN
iajs-2858	3	17	of	of	ADP
iajs-2858	3	18	the	the	DET
iajs-2858	3	19	paper	paper	NOUN
iajs-2858	3	20	are	be	AUX
iajs-2858	3	21	to	to	PART
iajs-2858	3	22	present	present	VERB
iajs-2858	3	23	a	a	DET
iajs-2858	3	24	modified	modify	VERB
iajs-2858	3	25	symmetric	symmetric	ADJ
iajs-2858	3	26	fuzzy	fuzzy	ADJ
iajs-2858	3	27	approach	approach	NOUN
iajs-2858	3	28	to	to	PART
iajs-2858	3	29	find	find	VERB
iajs-2858	3	30	the	the	DET
iajs-2858	3	31	best	good	ADJ
iajs-2858	3	32	workable	workable	ADJ
iajs-2858	3	33	compromise	compromise	NOUN
iajs-2858	3	34	solution	solution	NOUN
iajs-2858	3	35	for	for	ADP
iajs-2858	3	36	quadratic	quadratic	ADJ
iajs-2858	3	37	fractional	fractional	ADJ
iajs-2858	3	38	programming	programming	NOUN
iajs-2858	3	39	problems	problem	NOUN
iajs-2858	3	40	(	(	PUNCT
iajs-2858	3	41	qfpp	qfpp	PROPN
iajs-2858	3	42	)	)	PUNCT
iajs-2858	3	43	with	with	ADP
iajs-2858	3	44	fuzzy	fuzzy	ADJ
iajs-2858	3	45	crisp	crisp	ADJ
iajs-2858	3	46	in	in	ADP
iajs-2858	3	47	both	both	CCONJ
iajs-2858	3	48	the	the	DET
iajs-2858	3	49	objective	objective	ADJ
iajs-2858	3	50	functions	function	NOUN
iajs-2858	3	51	and	and	CCONJ
iajs-2858	3	52	the	the	DET
iajs-2858	3	53	constraints	constraint	NOUN
iajs-2858	3	54	.	.	PUNCT
iajs-2858	4	1	we	we	PRON
iajs-2858	4	2	introduced	introduce	VERB
iajs-2858	4	3	a	a	DET
iajs-2858	4	4	modified	modified	ADJ
iajs-2858	4	5	symmetric	symmetric	ADJ
iajs-2858	4	6	fuzzy	fuzzy	ADJ
iajs-2858	4	7	by	by	ADP
iajs-2858	4	8	proposing	propose	VERB
iajs-2858	4	9	a	a	DET
iajs-2858	4	10	procedure	procedure	NOUN
iajs-2858	4	11	,	,	PUNCT
iajs-2858	4	12	that	that	PRON
iajs-2858	4	13	starts	start	VERB
iajs-2858	4	14	first	first	ADV
iajs-2858	4	15	by	by	ADP
iajs-2858	4	16	converting	convert	VERB
iajs-2858	4	17	the	the	DET
iajs-2858	4	18	quadratic	quadratic	ADJ
iajs-2858	4	19	fractional	fractional	ADJ
iajs-2858	4	20	programming	programming	NOUN
iajs-2858	4	21	problems	problem	NOUN
iajs-2858	4	22	that	that	PRON
iajs-2858	4	23	exist	exist	VERB
iajs-2858	4	24	in	in	ADP
iajs-2858	4	25	the	the	DET
iajs-2858	4	26	objective	objective	ADJ
iajs-2858	4	27	functions	function	NOUN
iajs-2858	4	28	to	to	ADP
iajs-2858	4	29	crisp	crisp	ADJ
iajs-2858	4	30	numbers	number	NOUN
iajs-2858	4	31	and	and	CCONJ
iajs-2858	4	32	then	then	ADV
iajs-2858	4	33	converts	convert	VERB
iajs-2858	4	34	the	the	DET
iajs-2858	4	35	linear	linear	ADJ
iajs-2858	4	36	function	function	NOUN
iajs-2858	4	37	that	that	PRON
iajs-2858	4	38	exists	exist	VERB
iajs-2858	4	39	in	in	ADP
iajs-2858	4	40	the	the	DET
iajs-2858	4	41	constraints	constraint	NOUN
iajs-2858	4	42	to	to	ADP
iajs-2858	4	43	crisp	crisp	ADJ
iajs-2858	4	44	numbers	number	NOUN
iajs-2858	4	45	.	.	PUNCT
iajs-2858	5	1	after	after	ADP
iajs-2858	5	2	that	that	PRON
iajs-2858	5	3	,	,	PUNCT
iajs-2858	5	4	we	we	PRON
iajs-2858	5	5	applied	apply	VERB
iajs-2858	5	6	the	the	DET
iajs-2858	5	7	fuzzy	fuzzy	ADJ
iajs-2858	5	8	approach	approach	NOUN
iajs-2858	5	9	to	to	PART
iajs-2858	5	10	determine	determine	VERB
iajs-2858	5	11	the	the	DET
iajs-2858	5	12	optimal	optimal	ADJ
iajs-2858	5	13	solution	solution	NOUN
iajs-2858	5	14	for	for	ADP
iajs-2858	5	15	our	our	PRON
iajs-2858	5	16	quadratic	quadratic	ADJ
iajs-2858	5	17	fractional	fractional	ADJ
iajs-2858	5	18	programming	programming	NOUN
iajs-2858	5	19	problem	problem	NOUN
iajs-2858	5	20	which	which	PRON
iajs-2858	5	21	is	be	AUX
iajs-2858	5	22	supported	support	VERB
iajs-2858	5	23	theoretically	theoretically	ADV
iajs-2858	5	24	and	and	CCONJ
iajs-2858	5	25	practically	practically	ADV
iajs-2858	5	26	.	.	PUNCT
iajs-2858	6	1	the	the	DET
iajs-2858	6	2	computer	computer	NOUN
iajs-2858	6	3	application	application	NOUN
iajs-2858	6	4	for	for	ADP
iajs-2858	6	5	the	the	DET
iajs-2858	6	6	algorithm	algorithm	NOUN
iajs-2858	6	7	was	be	AUX
iajs-2858	6	8	tested	test	VERB
iajs-2858	6	9	,	,	PUNCT
iajs-2858	6	10	and	and	CCONJ
iajs-2858	6	11	finally	finally	ADV
iajs-2858	6	12	compared	compare	VERB
iajs-2858	6	13	modified	modify	VERB
iajs-2858	6	14	symmetric	symmetric	ADJ
iajs-2858	6	15	fuzzy	fuzzy	ADJ
iajs-2858	6	16	approach	approach	NOUN
iajs-2858	6	17	with	with	ADP
iajs-2858	6	18	the	the	DET
iajs-2858	6	19	modified	modify	VERB
iajs-2858	6	20	simplex	simplex	NOUN
iajs-2858	6	21	approach	approach	NOUN
iajs-2858	6	22	which	which	PRON
iajs-2858	6	23	is	be	AUX
iajs-2858	6	24	shown	show	VERB
iajs-2858	6	25	in	in	ADP
iajs-2858	6	26	the	the	DET
iajs-2858	6	27	table	table	NOUN
iajs-2858	6	28	1	1	NUM
iajs-2858	6	29	.	.	PUNCT
iajs-2858	7	1	finally	finally	ADV
iajs-2858	7	2	,	,	PUNCT
iajs-2858	7	3	the	the	DET
iajs-2858	7	4	procedures	procedure	NOUN
iajs-2858	7	5	of	of	ADP
iajs-2858	7	6	numeric	numeric	ADJ
iajs-2858	7	7	results	result	NOUN
iajs-2858	7	8	in	in	ADP
iajs-2858	7	9	the	the	DET
iajs-2858	7	10	paper	paper	NOUN
iajs-2858	7	11	indicate	indicate	VERB
iajs-2858	7	12	that	that	SCONJ
iajs-2858	7	13	modified	modify	VERB
iajs-2858	7	14	symmetric	symmetric	ADJ
iajs-2858	7	15	fuzzy	fuzzy	ADJ
iajs-2858	7	16	approach	approach	NOUN
iajs-2858	7	17	is	be	AUX
iajs-2858	7	18	reliable	reliable	ADJ
iajs-2858	7	19	and	and	CCONJ
iajs-2858	7	20	saves	save	VERB
iajs-2858	7	21	valuable	valuable	ADJ
iajs-2858	7	22	time	time	NOUN
iajs-2858	7	23	.	.	PUNCT
iajs-2858	8	1	keywords	keyword	NOUN
iajs-2858	8	2	:	:	PUNCT
iajs-2858	8	3	fuzzy	fuzzy	ADJ
iajs-2858	8	4	system	system	NOUN
iajs-2858	8	5	,	,	PUNCT
iajs-2858	8	6	modified	modify	VERB
iajs-2858	8	7	simplex	simplex	NOUN
iajs-2858	8	8	approach	approach	NOUN
iajs-2858	8	9	,	,	PUNCT
iajs-2858	8	10	modified	modify	VERB
iajs-2858	8	11	symmetric	symmetric	ADJ
iajs-2858	8	12	fuzzy	fuzzy	ADJ
iajs-2858	8	13	,	,	PUNCT
iajs-2858	8	14	quadratic	quadratic	ADJ
iajs-2858	8	15	fractional	fractional	ADJ
iajs-2858	8	16	programming	programming	NOUN
iajs-2858	8	17	problems	problem	NOUN
iajs-2858	8	18	.	.	PUNCT
iajs-2858	9	1	1	1	X
iajs-2858	9	2	.	.	X
iajs-2858	9	3	introduction	introduction	NOUN
iajs-2858	9	4	mathematical	mathematical	ADJ
iajs-2858	9	5	programming	programming	NOUN
iajs-2858	9	6	finds	find	VERB
iajs-2858	9	7	many	many	ADJ
iajs-2858	9	8	applications	application	NOUN
iajs-2858	9	9	in	in	ADP
iajs-2858	9	10	the	the	DET
iajs-2858	9	11	field	field	NOUN
iajs-2858	9	12	of	of	ADP
iajs-2858	9	13	management	management	NOUN
iajs-2858	9	14	.	.	PUNCT
iajs-2858	10	1	optimization	optimization	NOUN
iajs-2858	10	2	of	of	ADP
iajs-2858	10	3	resources	resource	NOUN
iajs-2858	10	4	in	in	ADP
iajs-2858	10	5	any	any	DET
iajs-2858	10	6	organization	organization	NOUN
iajs-2858	10	7	is	be	AUX
iajs-2858	10	8	mostly	mostly	ADV
iajs-2858	10	9	addressed	address	VERB
iajs-2858	10	10	with	with	ADP
iajs-2858	10	11	the	the	DET
iajs-2858	10	12	use	use	NOUN
iajs-2858	10	13	of	of	ADP
iajs-2858	10	14	mathematical	mathematical	ADJ
iajs-2858	10	15	programming	programming	NOUN
iajs-2858	10	16	.	.	PUNCT
iajs-2858	11	1	qfpp	qfpp	PROPN
iajs-2858	11	2	,	,	PUNCT
iajs-2858	11	3	which	which	PRON
iajs-2858	11	4	deals	deal	VERB
iajs-2858	11	5	with	with	ADP
iajs-2858	11	6	situations	situation	NOUN
iajs-2858	11	7	where	where	SCONJ
iajs-2858	11	8	a	a	DET
iajs-2858	11	9	ratio	ratio	NOUN
iajs-2858	11	10	between	between	ADP
iajs-2858	11	11	two	two	NUM
iajs-2858	11	12	mathematical	mathematical	ADJ
iajs-2858	11	13	doi	doi	NOUN
iajs-2858	11	14	:	:	PUNCT
iajs-2858	11	15	10.30526/35.4.2858	10.30526/35.4.2858	NUM
iajs-2858	11	16	article	article	NOUN
iajs-2858	11	17	history	history	NOUN
iajs-2858	11	18	:	:	PUNCT
iajs-2858	11	19	received	receive	VERB
iajs-2858	11	20	17	17	NUM
iajs-2858	11	21	may	may	PROPN
iajs-2858	11	22	2022	2022	NUM
iajs-2858	11	23	,	,	PUNCT
iajs-2858	11	24	accepted	accept	VERB
iajs-2858	11	25	25	25	NUM
iajs-2858	11	26	july2022	july2022	PROPN
iajs-2858	11	27	,	,	PUNCT
iajs-2858	11	28	published	publish	VERB
iajs-2858	11	29	in	in	ADP
iajs-2858	11	30	october	october	PROPN
iajs-2858	11	31	2022	2022	NUM
iajs-2858	11	32	.	.	PUNCT
iajs-2858	12	1	ibn	ibn	PROPN
iajs-2858	12	2	al	al	PROPN
iajs-2858	12	3	haitham	haitham	PROPN
iajs-2858	12	4	journal	journal	PROPN
iajs-2858	12	5	for	for	ADP
iajs-2858	12	6	pure	pure	ADJ
iajs-2858	12	7	and	and	CCONJ
iajs-2858	12	8	applied	applied	ADJ
iajs-2858	12	9	sciences	sciences	PROPN
iajs-2858	12	10	journal	journal	PROPN
iajs-2858	12	11	homepage	homepage	NOUN
iajs-2858	12	12	:	:	PUNCT
iajs-2858	12	13	http://jih.uobaghdad.edu.iq/index.php/j/index	http://jih.uobaghdad.edu.iq/index.php/j/index	PROPN
iajs-2858	12	14	maher	maher	PROPN
iajs-2858	12	15	a.	a.	PROPN
iajs-2858	12	16	nawkhass	nawkhass	PROPN
iajs-2858	12	17	department	department	PROPN
iajs-2858	12	18	of	of	ADP
iajs-2858	12	19	mathematics	mathematics	PROPN
iajs-2858	12	20	,	,	PUNCT
iajs-2858	12	21	college	college	NOUN
iajs-2858	12	22	of	of	ADP
iajs-2858	12	23	education	education	NOUN
iajs-2858	12	24	salahaddin	salahaddin	VERB
iajs-2858	12	25	university	university	NOUN
iajs-2858	12	26	-	-	PUNCT
iajs-2858	12	27	erbil	erbil	PROPN
iajs-2858	12	28	,	,	PUNCT
iajs-2858	12	29	erbil	erbil	PROPN
iajs-2858	12	30	,	,	PUNCT
iajs-2858	12	31	kurdistan	kurdistan	PROPN
iajs-2858	12	32	region	region	NOUN
iajs-2858	12	33	,	,	PUNCT
iajs-2858	12	34	iraq	iraq	PROPN
iajs-2858	12	35	.	.	PUNCT
iajs-2858	13	1	maher.nawkhass@su.edu.krd	maher.nawkhass@su.edu.krd	NOUN
iajs-2858	13	2	nejmaddin	nejmaddin	NOUN
iajs-2858	13	3	a.	a.	NOUN
iajs-2858	13	4	sulaiman	sulaiman	PROPN
iajs-2858	13	5	department	department	PROPN
iajs-2858	13	6	of	of	ADP
iajs-2858	13	7	mathematics	mathematics	PROPN
iajs-2858	13	8	,	,	PUNCT
iajs-2858	13	9	college	college	NOUN
iajs-2858	13	10	of	of	ADP
iajs-2858	13	11	education	education	NOUN
iajs-2858	13	12	salahaddin	salahaddin	VERB
iajs-2858	13	13	universityerbil	universityerbil	NOUN
iajs-2858	13	14	,	,	PUNCT
iajs-2858	13	15	erbil	erbil	PROPN
iajs-2858	13	16	,	,	PUNCT
iajs-2858	13	17	kurdistan	kurdistan	PROPN
iajs-2858	13	18	region	region	NOUN
iajs-2858	13	19	,	,	PUNCT
iajs-2858	13	20	iraq	iraq	PROPN
iajs-2858	13	21	.	.	PUNCT
iajs-2858	14	1	nejmaddin.sulaiman@su.edu.krd	nejmaddin.sulaiman@su.edu.krd	NUM
iajs-2858	14	2	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
iajs-2858	14	3	mailto:maher.nawkhass@su.edu.krd	mailto:maher.nawkhass@su.edu.krd	NOUN
iajs-2858	14	4	mailto:maher.nawkhass@su.edu.krd	mailto:maher.nawkhass@su.edu.krd	PROPN
iajs-2858	14	5	mailto:nejmaddin.sulaiman@su.edu.krd	mailto:nejmaddin.sulaiman@su.edu.krd	PROPN
iajs-2858	14	6	ihjpas	ihjpas	PROPN
iajs-2858	14	7	.	.	PUNCT
iajs-2858	15	1	53	53	NUM
iajs-2858	15	2	(	(	PUNCT
iajs-2858	15	3	4)2022	4)2022	NOUN
iajs-2858	15	4	242	242	NUM
iajs-2858	15	5	functions	function	NOUN
iajs-2858	15	6	is	be	AUX
iajs-2858	15	7	either	either	CCONJ
iajs-2858	15	8	maximized	maximize	VERB
iajs-2858	15	9	or	or	CCONJ
iajs-2858	15	10	minimized	minimize	VERB
iajs-2858	15	11	,	,	PUNCT
iajs-2858	15	12	is	be	AUX
iajs-2858	15	13	an	an	DET
iajs-2858	15	14	important	important	ADJ
iajs-2858	15	15	class	class	NOUN
iajs-2858	15	16	of	of	ADP
iajs-2858	15	17	mathematical	mathematical	ADJ
iajs-2858	15	18	programming	programming	NOUN
iajs-2858	15	19	problems	problem	NOUN
iajs-2858	15	20	that	that	PRON
iajs-2858	15	21	has	have	AUX
iajs-2858	15	22	attracted	attract	VERB
iajs-2858	15	23	a	a	DET
iajs-2858	15	24	lot	lot	NOUN
iajs-2858	15	25	of	of	ADP
iajs-2858	15	26	research	research	NOUN
iajs-2858	15	27	and	and	CCONJ
iajs-2858	15	28	interest	interest	NOUN
iajs-2858	15	29	because	because	SCONJ
iajs-2858	15	30	it	it	PRON
iajs-2858	15	31	is	be	AUX
iajs-2858	15	32	useful	useful	ADJ
iajs-2858	15	33	in	in	ADP
iajs-2858	15	34	production	production	NOUN
iajs-2858	15	35	planning	planning	NOUN
iajs-2858	15	36	,	,	PUNCT
iajs-2858	15	37	economic	economic	ADJ
iajs-2858	15	38	and	and	CCONJ
iajs-2858	15	39	financial	financial	ADJ
iajs-2858	15	40	planning	planning	NOUN
iajs-2858	15	41	,	,	PUNCT
iajs-2858	15	42	medical	medical	ADJ
iajs-2858	15	43	services	service	NOUN
iajs-2858	15	44	,	,	PUNCT
iajs-2858	15	45	and	and	CCONJ
iajs-2858	15	46	healthcare	healthcare	PROPN
iajs-2858	15	47	planning	planning	NOUN
iajs-2858	15	48	.	.	PUNCT
iajs-2858	16	1	there	there	PRON
iajs-2858	16	2	are	be	VERB
iajs-2858	16	3	many	many	ADJ
iajs-2858	16	4	managerial	managerial	ADJ
iajs-2858	16	5	decision	decision	NOUN
iajs-2858	16	6	-	-	PUNCT
iajs-2858	16	7	making	make	VERB
iajs-2858	16	8	situations	situation	NOUN
iajs-2858	16	9	where	where	SCONJ
iajs-2858	16	10	the	the	DET
iajs-2858	16	11	uncertainties	uncertainty	NOUN
iajs-2858	16	12	in	in	ADP
iajs-2858	16	13	working	work	VERB
iajs-2858	16	14	situations	situation	NOUN
iajs-2858	16	15	are	be	AUX
iajs-2858	16	16	best	well	ADV
iajs-2858	16	17	explained	explain	VERB
iajs-2858	16	18	by	by	ADP
iajs-2858	16	19	use	use	NOUN
iajs-2858	16	20	of	of	ADP
iajs-2858	16	21	fuzzy	fuzzy	ADJ
iajs-2858	16	22	set	set	NOUN
iajs-2858	16	23	theory	theory	NOUN
iajs-2858	16	24	.	.	PUNCT
iajs-2858	17	1	the	the	DET
iajs-2858	17	2	nation	nation	NOUN
iajs-2858	17	3	of	of	ADP
iajs-2858	17	4	fuzzy	fuzzy	ADJ
iajs-2858	17	5	set	set	NOUN
iajs-2858	17	6	theory	theory	NOUN
iajs-2858	17	7	is	be	AUX
iajs-2858	17	8	developed	develop	VERB
iajs-2858	17	9	by	by	ADP
iajs-2858	17	10	[	[	X
iajs-2858	17	11	1	1	NUM
iajs-2858	17	12	]	]	PUNCT
iajs-2858	17	13	,	,	PUNCT
iajs-2858	17	14	since	since	SCONJ
iajs-2858	17	15	then	then	ADV
iajs-2858	17	16	a	a	DET
iajs-2858	17	17	considerable	considerable	ADJ
iajs-2858	17	18	number	number	NOUN
iajs-2858	17	19	of	of	ADP
iajs-2858	17	20	scholars	scholar	NOUN
iajs-2858	17	21	have	have	AUX
iajs-2858	17	22	expressed	express	VERB
iajs-2858	17	23	their	their	PRON
iajs-2858	17	24	interest	interest	NOUN
iajs-2858	17	25	in	in	ADP
iajs-2858	17	26	the	the	DET
iajs-2858	17	27	application	application	NOUN
iajs-2858	17	28	of	of	ADP
iajs-2858	17	29	fuzzy	fuzzy	ADJ
iajs-2858	17	30	set	set	NOUN
iajs-2858	17	31	theory	theory	NOUN
iajs-2858	17	32	.	.	PUNCT
iajs-2858	18	1	[	[	X
iajs-2858	18	2	2	2	X
iajs-2858	18	3	]	]	PUNCT
iajs-2858	18	4	established	establish	VERB
iajs-2858	18	5	the	the	DET
iajs-2858	18	6	notion	notion	NOUN
iajs-2858	18	7	of	of	ADP
iajs-2858	18	8	decision	decision	NOUN
iajs-2858	18	9	making	make	VERB
iajs-2858	18	10	in	in	ADP
iajs-2858	18	11	a	a	DET
iajs-2858	18	12	fuzzy	fuzzy	ADJ
iajs-2858	18	13	environment	environment	NOUN
iajs-2858	18	14	and	and	CCONJ
iajs-2858	18	15	their	their	PRON
iajs-2858	18	16	concept	concept	NOUN
iajs-2858	18	17	of	of	ADP
iajs-2858	18	18	fuzzy	fuzzy	ADJ
iajs-2858	18	19	decision	decision	NOUN
iajs-2858	18	20	making	making	NOUN
iajs-2858	18	21	is	be	AUX
iajs-2858	18	22	used	use	VERB
iajs-2858	18	23	in	in	ADP
iajs-2858	18	24	mathematical	mathematical	ADJ
iajs-2858	18	25	programming	programming	NOUN
iajs-2858	18	26	[	[	X
iajs-2858	18	27	3	3	NUM
iajs-2858	18	28	]	]	PUNCT
iajs-2858	18	29	.	.	PUNCT
iajs-2858	19	1	many	many	ADJ
iajs-2858	19	2	authors	author	NOUN
iajs-2858	19	3	have	have	AUX
iajs-2858	19	4	discussed	discuss	VERB
iajs-2858	19	5	the	the	DET
iajs-2858	19	6	use	use	NOUN
iajs-2858	19	7	of	of	ADP
iajs-2858	19	8	fuzzy	fuzzy	ADJ
iajs-2858	19	9	set	set	NOUN
iajs-2858	19	10	theory	theory	NOUN
iajs-2858	19	11	in	in	ADP
iajs-2858	19	12	qfpp	qfpp	PROPN
iajs-2858	19	13	e.g.	e.g.	ADV
iajs-2858	19	14	,	,	PUNCT
iajs-2858	19	15	[	[	X
iajs-2858	19	16	4	4	NUM
iajs-2858	19	17	,	,	PUNCT
iajs-2858	19	18	5	5	NUM
iajs-2858	19	19	,	,	PUNCT
iajs-2858	19	20	6	6	NUM
iajs-2858	19	21	,	,	PUNCT
iajs-2858	19	22	7	7	NUM
iajs-2858	19	23	]	]	PUNCT
iajs-2858	19	24	.	.	PUNCT
iajs-2858	20	1	the	the	DET
iajs-2858	20	2	fuzzy	fuzzy	ADJ
iajs-2858	20	3	system	system	NOUN
iajs-2858	20	4	plays	play	VERB
iajs-2858	20	5	a	a	DET
iajs-2858	20	6	very	very	ADV
iajs-2858	20	7	significant	significant	ADJ
iajs-2858	20	8	role	role	NOUN
iajs-2858	20	9	in	in	ADP
iajs-2858	20	10	the	the	DET
iajs-2858	20	11	theory	theory	NOUN
iajs-2858	20	12	of	of	ADP
iajs-2858	20	13	linear	linear	PROPN
iajs-2858	20	14	programming	programming	NOUN
iajs-2858	20	15	(	(	PUNCT
iajs-2858	20	16	lp	lp	NOUN
iajs-2858	20	17	)	)	PUNCT
iajs-2858	20	18	.	.	PUNCT
iajs-2858	21	1	thus	thus	ADV
iajs-2858	21	2	,	,	PUNCT
iajs-2858	21	3	researchers	researcher	NOUN
iajs-2858	21	4	have	have	AUX
iajs-2858	21	5	shown	show	VERB
iajs-2858	21	6	their	their	PRON
iajs-2858	21	7	interest	interest	NOUN
iajs-2858	21	8	in	in	ADP
iajs-2858	21	9	the	the	DET
iajs-2858	21	10	concept	concept	NOUN
iajs-2858	21	11	of	of	ADP
iajs-2858	21	12	the	the	DET
iajs-2858	21	13	script	script	NOUN
iajs-2858	21	14	for	for	ADP
iajs-2858	21	15	a	a	DET
iajs-2858	21	16	linear	linear	ADJ
iajs-2858	21	17	program	program	NOUN
iajs-2858	21	18	under	under	ADP
iajs-2858	21	19	a	a	DET
iajs-2858	21	20	fuzzy	fuzzy	ADJ
iajs-2858	21	21	environment	environment	NOUN
iajs-2858	21	22	as	as	ADV
iajs-2858	21	23	well	well	ADV
iajs-2858	21	24	e.g.	e.g.	ADV
iajs-2858	21	25	,	,	PUNCT
iajs-2858	21	26	[	[	X
iajs-2858	21	27	8	8	NUM
iajs-2858	21	28	]	]	PUNCT
iajs-2858	21	29	,	,	PUNCT
iajs-2858	21	30	their	their	PRON
iajs-2858	21	31	works	work	NOUN
iajs-2858	21	32	formulates	formulate	VERB
iajs-2858	21	33	a	a	DET
iajs-2858	21	34	quadratic	quadratic	ADJ
iajs-2858	21	35	fractional	fractional	ADJ
iajs-2858	21	36	bi	bi	NOUN
iajs-2858	21	37	-	-	NOUN
iajs-2858	21	38	level	level	NOUN
iajs-2858	21	39	(	(	PUNCT
iajs-2858	21	40	qfbl	qfbl	NOUN
iajs-2858	21	41	)	)	PUNCT
iajs-2858	21	42	programming	programming	NOUN
iajs-2858	21	43	problem	problem	NOUN
iajs-2858	21	44	with	with	ADP
iajs-2858	21	45	probabilistic	probabilistic	ADJ
iajs-2858	21	46	constraints	constraint	NOUN
iajs-2858	21	47	in	in	ADP
iajs-2858	21	48	both	both	CCONJ
iajs-2858	21	49	the	the	DET
iajs-2858	21	50	first	first	ADJ
iajs-2858	21	51	(	(	PUNCT
iajs-2858	21	52	ruler	ruler	NOUN
iajs-2858	21	53	)	)	PUNCT
iajs-2858	21	54	and	and	CCONJ
iajs-2858	21	55	second	second	ADJ
iajs-2858	21	56	(	(	PUNCT
iajs-2858	21	57	supporter	supporter	NOUN
iajs-2858	21	58	)	)	PUNCT
iajs-2858	21	59	levels	level	NOUN
iajs-2858	21	60	,	,	PUNCT
iajs-2858	21	61	with	with	ADP
iajs-2858	21	62	two	two	NUM
iajs-2858	21	63	-	-	PUNCT
iajs-2858	21	64	parameter	parameter	NOUN
iajs-2858	21	65	exponential	exponential	ADJ
iajs-2858	21	66	random	random	ADJ
iajs-2858	21	67	variables	variable	NOUN
iajs-2858	21	68	with	with	ADP
iajs-2858	21	69	recognized	recognize	VERB
iajs-2858	21	70	probabilistic	probabilistic	ADJ
iajs-2858	21	71	,	,	PUNCT
iajs-2858	21	72	and	and	CCONJ
iajs-2858	21	73	fuzziness	fuzziness	NOUN
iajs-2858	21	74	as	as	ADP
iajs-2858	21	75	a	a	DET
iajs-2858	21	76	triangular	triangular	NOUN
iajs-2858	21	77	and	and	CCONJ
iajs-2858	21	78	trapezoidal	trapezoidal	ADJ
iajs-2858	21	79	fuzzy	fuzzy	ADJ
iajs-2858	21	80	number	number	NOUN
iajs-2858	21	81	.	.	PUNCT
iajs-2858	22	1	using	use	VERB
iajs-2858	22	2	a	a	DET
iajs-2858	22	3	chanceconstrained	chanceconstraine	VERB
iajs-2858	22	4	programming	programming	NOUN
iajs-2858	22	5	approach	approach	NOUN
iajs-2858	22	6	,	,	PUNCT
iajs-2858	22	7	the	the	DET
iajs-2858	22	8	issue	issue	NOUN
iajs-2858	22	9	is	be	AUX
iajs-2858	22	10	first	first	ADV
iajs-2858	22	11	turned	turn	VERB
iajs-2858	22	12	into	into	ADP
iajs-2858	22	13	an	an	DET
iajs-2858	22	14	a	a	PRON
iajs-2858	22	15	like	like	ADJ
iajs-2858	22	16	deterministic	deterministic	ADJ
iajs-2858	22	17	quadratic	quadratic	ADJ
iajs-2858	22	18	fractional	fractional	ADJ
iajs-2858	22	19	fuzzy	fuzzy	ADJ
iajs-2858	22	20	bi	bi	ADJ
iajs-2858	22	21	-	-	ADJ
iajs-2858	22	22	level	level	ADJ
iajs-2858	22	23	programming	programming	NOUN
iajs-2858	22	24	model	model	NOUN
iajs-2858	22	25	in	in	ADP
iajs-2858	22	26	the	the	DET
iajs-2858	22	27	suggested	suggest	VERB
iajs-2858	22	28	model	model	NOUN
iajs-2858	22	29	.	.	PUNCT
iajs-2858	23	1	second	second	ADJ
iajs-2858	23	2	,	,	PUNCT
iajs-2858	23	3	each	each	DET
iajs-2858	23	4	objective	objective	ADJ
iajs-2858	23	5	function	function	NOUN
iajs-2858	23	6	of	of	ADP
iajs-2858	23	7	the	the	DET
iajs-2858	23	8	bi	bi	NOUN
iajs-2858	23	9	-	-	NOUN
iajs-2858	23	10	level	level	NOUN
iajs-2858	23	11	qfp	qfp	ADJ
iajs-2858	23	12	issue	issue	NOUN
iajs-2858	23	13	has	have	VERB
iajs-2858	23	14	its	its	PRON
iajs-2858	23	15	own	own	ADJ
iajs-2858	23	16	nonlinear	nonlinear	ADJ
iajs-2858	23	17	membership	membership	NOUN
iajs-2858	23	18	function	function	NOUN
iajs-2858	23	19	in	in	ADP
iajs-2858	23	20	the	the	DET
iajs-2858	23	21	proposed	propose	VERB
iajs-2858	23	22	model	model	NOUN
iajs-2858	23	23	.	.	PUNCT
iajs-2858	24	1	in	in	ADP
iajs-2858	24	2	[	[	X
iajs-2858	24	3	9	9	NUM
iajs-2858	24	4	]	]	PUNCT
iajs-2858	24	5	,	,	PUNCT
iajs-2858	24	6	the	the	DET
iajs-2858	24	7	fuzzy	fuzzy	ADJ
iajs-2858	24	8	environment	environment	NOUN
iajs-2858	24	9	with	with	ADP
iajs-2858	24	10	parabolic	parabolic	ADJ
iajs-2858	24	11	concave	concave	PROPN
iajs-2858	24	12	membership	membership	NOUN
iajs-2858	24	13	functions	function	NOUN
iajs-2858	24	14	is	be	AUX
iajs-2858	24	15	used	use	VERB
iajs-2858	24	16	to	to	PART
iajs-2858	24	17	investigate	investigate	VERB
iajs-2858	24	18	a	a	DET
iajs-2858	24	19	certain	certain	ADJ
iajs-2858	24	20	form	form	NOUN
iajs-2858	24	21	of	of	ADP
iajs-2858	24	22	convex	convex	ADJ
iajs-2858	24	23	fractional	fractional	ADJ
iajs-2858	24	24	programming	programming	NOUN
iajs-2858	24	25	issue	issue	NOUN
iajs-2858	24	26	and	and	CCONJ
iajs-2858	24	27	its	its	PRON
iajs-2858	24	28	dual	dual	ADJ
iajs-2858	24	29	.	.	PUNCT
iajs-2858	25	1	an	an	DET
iajs-2858	25	2	ambition	ambition	NOUN
iajs-2858	25	3	level	level	NOUN
iajs-2858	25	4	technique	technique	NOUN
iajs-2858	25	5	is	be	AUX
iajs-2858	25	6	used	use	VERB
iajs-2858	25	7	to	to	PART
iajs-2858	25	8	determine	determine	VERB
iajs-2858	25	9	appropriate	appropriate	ADJ
iajs-2858	25	10	duality	duality	NOUN
iajs-2858	25	11	outcomes	outcome	NOUN
iajs-2858	25	12	.	.	PUNCT
iajs-2858	26	1	it	it	PRON
iajs-2858	26	2	differs	differ	VERB
iajs-2858	26	3	from	from	ADP
iajs-2858	26	4	other	other	ADJ
iajs-2858	26	5	research	research	NOUN
iajs-2858	26	6	in	in	ADP
iajs-2858	26	7	that	that	SCONJ
iajs-2858	26	8	it	it	PRON
iajs-2858	26	9	uses	use	VERB
iajs-2858	26	10	parabolic	parabolic	ADJ
iajs-2858	26	11	concave	concave	NOUN
iajs-2858	26	12	membership	membership	NOUN
iajs-2858	26	13	functions	function	NOUN
iajs-2858	26	14	to	to	PART
iajs-2858	26	15	reflect	reflect	VERB
iajs-2858	26	16	the	the	DET
iajs-2858	26	17	decision	decision	NOUN
iajs-2858	26	18	-	-	PUNCT
iajs-2858	26	19	level	level	NOUN
iajs-2858	26	20	maker	maker	NOUN
iajs-2858	26	21	's	's	PART
iajs-2858	26	22	of	of	ADP
iajs-2858	26	23	pleasure	pleasure	NOUN
iajs-2858	26	24	.	.	PUNCT
iajs-2858	27	1	the	the	DET
iajs-2858	27	2	fully	fully	ADV
iajs-2858	27	3	fuzzy	fuzzy	ADJ
iajs-2858	27	4	quadratic	quadratic	ADJ
iajs-2858	27	5	fractional	fractional	ADJ
iajs-2858	27	6	programming	programming	NOUN
iajs-2858	27	7	problem	problem	NOUN
iajs-2858	27	8	(	(	PUNCT
iajs-2858	27	9	ffqfpp	ffqfpp	ADJ
iajs-2858	27	10	)	)	PUNCT
iajs-2858	27	11	is	be	AUX
iajs-2858	27	12	solved	solve	VERB
iajs-2858	27	13	using	use	VERB
iajs-2858	27	14	a	a	DET
iajs-2858	27	15	solution	solution	NOUN
iajs-2858	27	16	process	process	NOUN
iajs-2858	27	17	in	in	ADP
iajs-2858	27	18	which	which	PRON
iajs-2858	27	19	all	all	DET
iajs-2858	27	20	variables	variable	NOUN
iajs-2858	27	21	and	and	CCONJ
iajs-2858	27	22	parameters	parameter	NOUN
iajs-2858	27	23	are	be	AUX
iajs-2858	27	24	triangular	triangular	VERB
iajs-2858	27	25	fuzzy	fuzzy	ADJ
iajs-2858	27	26	integers	integer	NOUN
iajs-2858	27	27	.	.	PUNCT
iajs-2858	28	1	in	in	ADP
iajs-2858	28	2	this	this	DET
iajs-2858	28	3	case	case	NOUN
iajs-2858	28	4	,	,	PUNCT
iajs-2858	28	5	ffqfpp	ffqfpp	PROPN
iajs-2858	28	6	was	be	AUX
iajs-2858	28	7	converted	convert	VERB
iajs-2858	28	8	into	into	ADP
iajs-2858	28	9	a	a	DET
iajs-2858	28	10	multi	multi	ADJ
iajs-2858	28	11	-	-	ADJ
iajs-2858	28	12	objective	objective	ADJ
iajs-2858	28	13	quadratic	quadratic	ADJ
iajs-2858	28	14	fractional	fractional	ADJ
iajs-2858	28	15	programming	programming	NOUN
iajs-2858	28	16	issue	issue	NOUN
iajs-2858	28	17	(	(	PUNCT
iajs-2858	28	18	moqfpp	moqfpp	ADJ
iajs-2858	28	19	)	)	PUNCT
iajs-2858	28	20	.	.	PUNCT
iajs-2858	29	1	using	use	VERB
iajs-2858	29	2	a	a	DET
iajs-2858	29	3	mathematical	mathematical	ADJ
iajs-2858	29	4	programming	programming	NOUN
iajs-2858	29	5	method	method	NOUN
iajs-2858	29	6	,	,	PUNCT
iajs-2858	29	7	moqfpp	moqfpp	PROPN
iajs-2858	29	8	is	be	AUX
iajs-2858	29	9	then	then	ADV
iajs-2858	29	10	turned	turn	VERB
iajs-2858	29	11	into	into	ADP
iajs-2858	29	12	an	an	DET
iajs-2858	29	13	analogous	analogous	ADJ
iajs-2858	29	14	multi	multi	ADJ
iajs-2858	29	15	-	-	ADJ
iajs-2858	29	16	objective	objective	ADJ
iajs-2858	29	17	quadratic	quadratic	ADJ
iajs-2858	29	18	programming	programming	NOUN
iajs-2858	29	19	problem	problem	NOUN
iajs-2858	29	20	.	.	PUNCT
iajs-2858	30	1	a	a	DET
iajs-2858	30	2	fuzzy	fuzzy	ADJ
iajs-2858	30	3	goal	goal	NOUN
iajs-2858	30	4	programming	programming	NOUN
iajs-2858	30	5	paradigm	paradigm	NOUN
iajs-2858	30	6	for	for	ADP
iajs-2858	30	7	handling	handle	VERB
iajs-2858	30	8	bilevel	bilevel	ADJ
iajs-2858	30	9	programming	programming	NOUN
iajs-2858	30	10	issues	issue	NOUN
iajs-2858	30	11	with	with	ADP
iajs-2858	30	12	decision	decision	NOUN
iajs-2858	30	13	-	-	PUNCT
iajs-2858	30	14	makers	maker	NOUN
iajs-2858	30	15	'	'	PART
iajs-2858	30	16	objectives	objective	NOUN
iajs-2858	30	17	in	in	ADP
iajs-2858	30	18	quadratic	quadratic	ADJ
iajs-2858	30	19	fractional	fractional	ADJ
iajs-2858	30	20	form	form	NOUN
iajs-2858	30	21	.	.	PUNCT
iajs-2858	31	1	the	the	DET
iajs-2858	31	2	membership	membership	NOUN
iajs-2858	31	3	functions	function	NOUN
iajs-2858	31	4	for	for	ADP
iajs-2858	31	5	the	the	DET
iajs-2858	31	6	defined	define	VERB
iajs-2858	31	7	fuzzy	fuzzy	ADJ
iajs-2858	31	8	goals	goal	NOUN
iajs-2858	31	9	of	of	ADP
iajs-2858	31	10	the	the	DET
iajs-2858	31	11	decision	decision	NOUN
iajs-2858	31	12	-	-	PUNCT
iajs-2858	31	13	makers	maker	NOUN
iajs-2858	31	14	'	'	PART
iajs-2858	31	15	objectives	objective	NOUN
iajs-2858	31	16	at	at	ADP
iajs-2858	31	17	both	both	DET
iajs-2858	31	18	levels	level	NOUN
iajs-2858	31	19	are	be	AUX
iajs-2858	31	20	established	establish	VERB
iajs-2858	31	21	first	first	ADV
iajs-2858	31	22	in	in	ADP
iajs-2858	31	23	the	the	DET
iajs-2858	31	24	suggested	suggest	VERB
iajs-2858	31	25	approach	approach	NOUN
iajs-2858	31	26	.	.	PUNCT
iajs-2858	32	1	then	then	ADV
iajs-2858	32	2	,	,	PUNCT
iajs-2858	32	3	in	in	ADP
iajs-2858	32	4	order	order	NOUN
iajs-2858	32	5	to	to	PART
iajs-2858	32	6	find	find	VERB
iajs-2858	32	7	the	the	DET
iajs-2858	32	8	most	most	ADV
iajs-2858	32	9	satisfactory	satisfactory	ADJ
iajs-2858	32	10	answer	answer	NOUN
iajs-2858	32	11	in	in	ADP
iajs-2858	32	12	the	the	DET
iajs-2858	32	13	decision	decision	NOUN
iajs-2858	32	14	-	-	PUNCT
iajs-2858	32	15	making	make	VERB
iajs-2858	32	16	environment	environment	NOUN
iajs-2858	32	17	,	,	PUNCT
iajs-2858	32	18	a	a	DET
iajs-2858	32	19	fuzzy	fuzzy	ADJ
iajs-2858	32	20	goal	goal	NOUN
iajs-2858	32	21	programming	programming	NOUN
iajs-2858	32	22	model	model	NOUN
iajs-2858	32	23	is	be	AUX
iajs-2858	32	24	constructed	construct	VERB
iajs-2858	32	25	to	to	PART
iajs-2858	32	26	minimize	minimize	VERB
iajs-2858	32	27	the	the	DET
iajs-2858	32	28	group	group	NOUN
iajs-2858	32	29	regret	regret	NOUN
iajs-2858	32	30	of	of	ADP
iajs-2858	32	31	the	the	DET
iajs-2858	32	32	degree	degree	NOUN
iajs-2858	32	33	of	of	ADP
iajs-2858	32	34	satisfaction	satisfaction	NOUN
iajs-2858	32	35	of	of	ADP
iajs-2858	32	36	both	both	DET
iajs-2858	32	37	decision	decision	NOUN
iajs-2858	32	38	-	-	PUNCT
iajs-2858	32	39	makers	maker	NOUN
iajs-2858	32	40	.	.	PUNCT
iajs-2858	33	1	in	in	ADP
iajs-2858	33	2	[	[	X
iajs-2858	33	3	10	10	NUM
iajs-2858	33	4	]	]	PUNCT
iajs-2858	33	5	,	,	PUNCT
iajs-2858	33	6	the	the	DET
iajs-2858	33	7	linear	linear	ADJ
iajs-2858	33	8	constraints	constraint	NOUN
iajs-2858	33	9	of	of	ADP
iajs-2858	33	10	quadratic	quadratic	ADJ
iajs-2858	33	11	fractional	fractional	ADJ
iajs-2858	33	12	objective	objective	ADJ
iajs-2858	33	13	programming	programming	NOUN
iajs-2858	33	14	problem	problem	NOUN
iajs-2858	33	15	(	(	PUNCT
iajs-2858	33	16	qfopp	qfopp	ADV
iajs-2858	33	17	)	)	PUNCT
iajs-2858	33	18	have	have	AUX
iajs-2858	33	19	been	be	AUX
iajs-2858	33	20	established	establish	VERB
iajs-2858	33	21	and	and	CCONJ
iajs-2858	33	22	developed	develop	VERB
iajs-2858	33	23	.	.	PUNCT
iajs-2858	34	1	the	the	DET
iajs-2858	34	2	wolfe	wolfe	PROPN
iajs-2858	34	3	's	's	PART
iajs-2858	34	4	technique	technique	NOUN
iajs-2858	34	5	and	and	CCONJ
iajs-2858	34	6	a	a	DET
iajs-2858	34	7	modified	modify	VERB
iajs-2858	34	8	simplex	simplex	NOUN
iajs-2858	34	9	approach	approach	NOUN
iajs-2858	34	10	were	be	AUX
iajs-2858	34	11	used	use	VERB
iajs-2858	34	12	to	to	PART
iajs-2858	34	13	solve	solve	VERB
iajs-2858	34	14	the	the	DET
iajs-2858	34	15	specific	specific	ADJ
iajs-2858	34	16	case	case	NOUN
iajs-2858	34	17	for	for	ADP
iajs-2858	34	18	this	this	DET
iajs-2858	34	19	problem	problem	NOUN
iajs-2858	34	20	.	.	PUNCT
iajs-2858	35	1	to	to	PART
iajs-2858	35	2	extend	extend	VERB
iajs-2858	35	3	this	this	DET
iajs-2858	35	4	work	work	NOUN
iajs-2858	35	5	,	,	PUNCT
iajs-2858	35	6	we	we	PRON
iajs-2858	35	7	study	study	VERB
iajs-2858	35	8	and	and	CCONJ
iajs-2858	35	9	introduce	introduce	VERB
iajs-2858	35	10	a	a	DET
iajs-2858	35	11	modified	modify	VERB
iajs-2858	35	12	symmetric	symmetric	ADJ
iajs-2858	35	13	fuzzy	fuzzy	ADJ
iajs-2858	35	14	approach	approach	NOUN
iajs-2858	35	15	to	to	PART
iajs-2858	35	16	solve	solve	VERB
iajs-2858	35	17	qfpp	qfpp	PROPN
iajs-2858	35	18	.	.	PUNCT
iajs-2858	36	1	an	an	DET
iajs-2858	36	2	algorithm	algorithm	NOUN
iajs-2858	36	3	and	and	CCONJ
iajs-2858	36	4	practical	practical	ADJ
iajs-2858	36	5	technique	technique	NOUN
iajs-2858	36	6	with	with	ADP
iajs-2858	36	7	theoretical	theoretical	ADJ
iajs-2858	36	8	support	support	NOUN
iajs-2858	36	9	are	be	AUX
iajs-2858	36	10	suggested	suggest	VERB
iajs-2858	36	11	,	,	PUNCT
iajs-2858	36	12	also	also	ADV
iajs-2858	36	13	solving	solve	VERB
iajs-2858	36	14	such	such	DET
iajs-2858	36	15	a	a	DET
iajs-2858	36	16	problem	problem	NOUN
iajs-2858	36	17	by	by	ADP
iajs-2858	36	18	a	a	DET
iajs-2858	36	19	modified	modify	VERB
iajs-2858	36	20	simplex	simplex	NOUN
iajs-2858	36	21	approach	approach	NOUN
iajs-2858	36	22	,	,	PUNCT
iajs-2858	36	23	and	and	CCONJ
iajs-2858	36	24	test	test	VERB
iajs-2858	36	25	the	the	DET
iajs-2858	36	26	validity	validity	NOUN
iajs-2858	36	27	will	will	AUX
iajs-2858	36	28	be	be	AUX
iajs-2858	36	29	compared	compare	VERB
iajs-2858	36	30	against	against	ADP
iajs-2858	36	31	both	both	DET
iajs-2858	36	32	outcomes	outcome	NOUN
iajs-2858	36	33	.	.	PUNCT
iajs-2858	37	1	2	2	X
iajs-2858	37	2	.	.	X
iajs-2858	37	3	fundamentals	fundamental	NOUN
iajs-2858	37	4	of	of	ADP
iajs-2858	37	5	fuzzy	fuzzy	ADJ
iajs-2858	37	6	set	set	NOUN
iajs-2858	37	7	,	,	PUNCT
iajs-2858	37	8	and	and	CCONJ
iajs-2858	37	9	fuzzy	fuzzy	ADJ
iajs-2858	37	10	algebra	algebra	NOUN
iajs-2858	37	11	operation	operation	NOUN
iajs-2858	37	12	some	some	DET
iajs-2858	37	13	fundamentals	fundamental	NOUN
iajs-2858	37	14	and	and	CCONJ
iajs-2858	37	15	algebra	algebra	NOUN
iajs-2858	37	16	operations	operation	NOUN
iajs-2858	37	17	of	of	ADP
iajs-2858	37	18	the	the	DET
iajs-2858	37	19	fuzzy	fuzzy	ADJ
iajs-2858	37	20	environment	environment	NOUN
iajs-2858	37	21	that	that	PRON
iajs-2858	37	22	are	be	AUX
iajs-2858	37	23	utilized	utilize	VERB
iajs-2858	37	24	in	in	ADP
iajs-2858	37	25	this	this	DET
iajs-2858	37	26	research	research	NOUN
iajs-2858	37	27	are	be	AUX
iajs-2858	37	28	listed	list	VERB
iajs-2858	37	29	[	[	PUNCT
iajs-2858	37	30	11	11	NUM
iajs-2858	37	31	,	,	PUNCT
iajs-2858	37	32	12	12	NUM
iajs-2858	37	33	]	]	PUNCT
iajs-2858	37	34	:	:	PUNCT
iajs-2858	37	35	ihjpas	ihjpas	PROPN
iajs-2858	37	36	.	.	PUNCT
iajs-2858	38	1	53	53	NUM
iajs-2858	38	2	(	(	PUNCT
iajs-2858	38	3	4)2022	4)2022	NOUN
iajs-2858	38	4	243	243	NUM
iajs-2858	38	5	2.1	2.1	NUM
iajs-2858	38	6	.	.	PUNCT
iajs-2858	39	1	fundamentals	fundamental	NOUN
iajs-2858	39	2	of	of	ADP
iajs-2858	39	3	fuzzy	fuzzy	ADJ
iajs-2858	39	4	set	set	VERB
iajs-2858	39	5	fuzzy	fuzzy	ADJ
iajs-2858	39	6	set	set	NOUN
iajs-2858	39	7	:	:	PUNCT
iajs-2858	39	8	a	a	DET
iajs-2858	39	9	fuzzy	fuzzy	ADJ
iajs-2858	39	10	set	set	VERB
iajs-2858	39	11	α̃	α̃	PROPN
iajs-2858	39	12	in	in	ADP
iajs-2858	39	13	χ	χ	PRON
iajs-2858	39	14	is	be	AUX
iajs-2858	39	15	a	a	DET
iajs-2858	39	16	set	set	NOUN
iajs-2858	39	17	of	of	ADP
iajs-2858	39	18	ordered	order	VERB
iajs-2858	39	19	pairs	pair	NOUN
iajs-2858	39	20	:	:	PUNCT
iajs-2858	39	21	α̃	α̃	PROPN
iajs-2858	39	22	=	=	SYM
iajs-2858	39	23	{	{	PUNCT
iajs-2858	39	24	(	(	PUNCT
iajs-2858	39	25	𝓍	𝓍	X
iajs-2858	39	26	,	,	PUNCT
iajs-2858	39	27	𝜇α̃(𝓍))|𝓍	𝜇α̃(𝓍))|𝓍	X
iajs-2858	39	28	∈	∈	PROPN
iajs-2858	39	29	χ	χ	X
iajs-2858	39	30	}	}	PUNCT
iajs-2858	39	31	,	,	PUNCT
iajs-2858	39	32	𝜇α̃(𝓍	𝜇α̃(𝓍	PROPN
iajs-2858	39	33	)	)	PUNCT
iajs-2858	39	34	is	be	AUX
iajs-2858	39	35	titled	title	VERB
iajs-2858	39	36	by	by	ADP
iajs-2858	39	37	the	the	DET
iajs-2858	39	38	membership	membership	NOUN
iajs-2858	39	39	function	function	NOUN
iajs-2858	39	40	of	of	ADP
iajs-2858	39	41	𝓍	𝓍	PRON
iajs-2858	39	42	in	in	ADP
iajs-2858	39	43	α̃.	α̃.	NOUN
iajs-2858	39	44	if	if	SCONJ
iajs-2858	39	45	χ	χ	PRON
iajs-2858	39	46	is	be	AUX
iajs-2858	39	47	a	a	DET
iajs-2858	39	48	assemble	assemble	NOUN
iajs-2858	39	49	of	of	ADP
iajs-2858	39	50	contraption	contraption	NOUN
iajs-2858	39	51	defined	define	VERB
iajs-2858	39	52	generally	generally	ADV
iajs-2858	39	53	by	by	ADP
iajs-2858	39	54	𝓍.	𝓍.	VERB
iajs-2858	39	55	the	the	DET
iajs-2858	39	56	support	support	NOUN
iajs-2858	39	57	:	:	PUNCT
iajs-2858	39	58	𝑆(α̃	𝑆(α̃	NUM
iajs-2858	39	59	)	)	PUNCT
iajs-2858	39	60	is	be	AUX
iajs-2858	39	61	the	the	DET
iajs-2858	39	62	crisp	crisp	ADJ
iajs-2858	39	63	set	set	NOUN
iajs-2858	39	64	of	of	ADP
iajs-2858	39	65	all	all	DET
iajs-2858	39	66	𝓍	𝓍	PRON
iajs-2858	39	67	∈	∈	NOUN
iajs-2858	39	68	χ	χ	X
iajs-2858	39	69	if	if	SCONJ
iajs-2858	39	70	𝜇α̃(𝓍	𝜇α̃(𝓍	NOUN
iajs-2858	39	71	)	)	PUNCT
iajs-2858	39	72	>	>	X
iajs-2858	39	73	0	0	PUNCT
iajs-2858	39	74	is	be	AUX
iajs-2858	39	75	called	call	VERB
iajs-2858	39	76	by	by	ADP
iajs-2858	39	77	the	the	DET
iajs-2858	39	78	support	support	NOUN
iajs-2858	39	79	of	of	ADP
iajs-2858	39	80	fuzzy	fuzzy	ADJ
iajs-2858	39	81	set	set	VERB
iajs-2858	39	82	α̃.	α̃.	PROPN
iajs-2858	39	83	𝛼-level	𝛼-level	NOUN
iajs-2858	39	84	set	set	NOUN
iajs-2858	39	85	:	:	PUNCT
iajs-2858	39	86	the	the	DET
iajs-2858	39	87	fragile	fragile	ADJ
iajs-2858	39	88	set	set	NOUN
iajs-2858	39	89	of	of	ADP
iajs-2858	39	90	elements	element	NOUN
iajs-2858	39	91	that	that	PRON
iajs-2858	39	92	pertinence	pertinence	NOUN
iajs-2858	39	93	to	to	ADP
iajs-2858	39	94	the	the	DET
iajs-2858	39	95	fuzzy	fuzzy	ADJ
iajs-2858	39	96	set	set	VERB
iajs-2858	39	97	α̃	α̃	PRON
iajs-2858	39	98	at	at	ADP
iajs-2858	39	99	the	the	DET
iajs-2858	39	100	lower	low	ADJ
iajs-2858	39	101	to	to	ADP
iajs-2858	39	102	the	the	DET
iajs-2858	39	103	grade	grade	NOUN
iajs-2858	39	104	𝛼	𝛼	NOUN
iajs-2858	39	105	is	be	AUX
iajs-2858	39	106	named	name	VERB
iajs-2858	39	107	by	by	ADP
iajs-2858	39	108	𝛼-level	𝛼-level	NOUN
iajs-2858	39	109	set	set	NOUN
iajs-2858	39	110	:	:	PUNCT
iajs-2858	39	111	α𝛼	α𝛼	PROPN
iajs-2858	39	112	=	=	SYM
iajs-2858	39	113	{	{	PUNCT
iajs-2858	39	114	𝓍	𝓍	X
iajs-2858	39	115	∈	∈	PROPN
iajs-2858	39	116	χ|𝜇α̃(𝓍	χ|𝜇α̃(𝓍	PROPN
iajs-2858	39	117	)	)	PUNCT
iajs-2858	39	118	≥	≥	NOUN
iajs-2858	39	119	𝛼	𝛼	NOUN
iajs-2858	39	120	}	}	PUNCT
iajs-2858	39	121	,	,	PUNCT
iajs-2858	39	122	α𝛼	α𝛼	ADP
iajs-2858	39	123	′	′	NUM
iajs-2858	39	124	=	=	PUNCT
iajs-2858	39	125	{	{	PUNCT
iajs-2858	39	126	𝓍	𝓍	X
iajs-2858	39	127	∈	∈	PROPN
iajs-2858	39	128	χ|𝜇α̃(𝓍	χ|𝜇α̃(𝓍	PROPN
iajs-2858	39	129	)	)	PUNCT
iajs-2858	39	130	>	>	PUNCT
iajs-2858	40	1	𝛼	𝛼	X
iajs-2858	40	2	}	}	PUNCT
iajs-2858	40	3	is	be	AUX
iajs-2858	40	4	defined	define	VERB
iajs-2858	40	5	by	by	ADP
iajs-2858	40	6	"	"	PUNCT
iajs-2858	40	7	strong	strong	ADJ
iajs-2858	40	8	𝛼level	𝛼level	NOUN
iajs-2858	40	9	set	set	NOUN
iajs-2858	40	10	"	"	PUNCT
iajs-2858	40	11	or	or	CCONJ
iajs-2858	40	12	"	"	PUNCT
iajs-2858	40	13	strong	strong	ADJ
iajs-2858	40	14	𝛼-cut	𝛼-cut	NOUN
iajs-2858	40	15	"	"	PUNCT
iajs-2858	40	16	.	.	PUNCT
iajs-2858	41	1	2.2	2.2	NUM
iajs-2858	41	2	.	.	PUNCT
iajs-2858	41	3	fuzzy	fuzzy	ADJ
iajs-2858	41	4	algebra	algebra	PROPN
iajs-2858	41	5	operation	operation	NOUN
iajs-2858	41	6	algebraic	algebraic	ADJ
iajs-2858	41	7	sum	sum	NOUN
iajs-2858	41	8	:	:	PUNCT
iajs-2858	41	9	the	the	DET
iajs-2858	41	10	algebraic	algebraic	ADJ
iajs-2858	41	11	sum	sum	NOUN
iajs-2858	41	12	(	(	PUNCT
iajs-2858	41	13	likelihood	likelihood	NOUN
iajs-2858	41	14	sum	sum	NOUN
iajs-2858	41	15	)	)	PUNCT
iajs-2858	41	16	∁̃=	∁̃=	VERB
iajs-2858	41	17	α̃	α̃	PROPN
iajs-2858	41	18	+	+	CCONJ
iajs-2858	41	19	β̃	β̃	PROPN
iajs-2858	41	20	is	be	AUX
iajs-2858	41	21	illustrated	illustrate	VERB
iajs-2858	41	22	as	as	ADP
iajs-2858	41	23	∁̃=	∁̃=	PROPN
iajs-2858	41	24	{	{	PUNCT
iajs-2858	41	25	(	(	PUNCT
iajs-2858	41	26	𝓍	𝓍	X
iajs-2858	41	27	,	,	PUNCT
iajs-2858	41	28	𝜇α̃+β̃(𝓍))|𝓍	𝜇α̃+β̃(𝓍))|𝓍	X
iajs-2858	41	29	∈	∈	PROPN
iajs-2858	41	30	χ	χ	X
iajs-2858	41	31	}	}	PUNCT
iajs-2858	41	32	,	,	PUNCT
iajs-2858	41	33	where	where	SCONJ
iajs-2858	41	34	𝜇α̃+β̃(𝓍	𝜇α̃+β̃(𝓍	NOUN
iajs-2858	41	35	)	)	PUNCT
iajs-2858	41	36	=	=	SYM
iajs-2858	41	37	𝜇α̃(𝓍	𝜇α̃(𝓍	NOUN
iajs-2858	41	38	)	)	PUNCT
iajs-2858	42	1	+	+	NUM
iajs-2858	42	2	𝜇β̃(𝓍	𝜇β̃(𝓍	NOUN
iajs-2858	42	3	)	)	PUNCT
iajs-2858	43	1	−	−	PROPN
iajs-2858	43	2	𝜇α̃(𝓍	𝜇α̃(𝓍	NOUN
iajs-2858	43	3	)	)	PUNCT
iajs-2858	43	4	.	.	PUNCT
iajs-2858	44	1	𝜇β̃(𝓍	𝜇β̃(𝓍	NUM
iajs-2858	44	2	)	)	PUNCT
iajs-2858	44	3	.	.	PUNCT
iajs-2858	45	1	bounded	bounded	ADJ
iajs-2858	45	2	sum	sum	NOUN
iajs-2858	45	3	:	:	PUNCT
iajs-2858	45	4	the	the	DET
iajs-2858	45	5	bounded	bounded	ADJ
iajs-2858	45	6	sum	sum	NOUN
iajs-2858	45	7	∁̃=	∁̃=	PROPN
iajs-2858	45	8	α̃	α̃	PROPN
iajs-2858	45	9	⨁	⨁	PROPN
iajs-2858	45	10	β̃	β̃	PROPN
iajs-2858	45	11	is	be	AUX
iajs-2858	45	12	defined	define	VERB
iajs-2858	45	13	as	as	ADP
iajs-2858	45	14	∁̃=	∁̃=	X
iajs-2858	45	15	{	{	PUNCT
iajs-2858	45	16	(	(	PUNCT
iajs-2858	45	17	𝓍	𝓍	X
iajs-2858	45	18	,	,	PUNCT
iajs-2858	45	19	𝜇α̃	𝜇α̃	X
iajs-2858	45	20	⨁	⨁	PROPN
iajs-2858	45	21	β̃(𝓍))|𝓍	β̃(𝓍))|𝓍	X
iajs-2858	45	22	∈	∈	PROPN
iajs-2858	45	23	χ	χ	X
iajs-2858	45	24	}	}	PUNCT
iajs-2858	45	25	,	,	PUNCT
iajs-2858	45	26	where	where	SCONJ
iajs-2858	45	27	𝜇α̃	𝜇α̃	NUM
iajs-2858	45	28	⨁	⨁	PROPN
iajs-2858	45	29	β̃(𝓍	β̃(𝓍	PROPN
iajs-2858	45	30	)	)	PUNCT
iajs-2858	45	31	=	=	SYM
iajs-2858	45	32	min	min	NOUN
iajs-2858	45	33	{	{	PUNCT
iajs-2858	45	34	1	1	NUM
iajs-2858	45	35	,	,	PUNCT
iajs-2858	45	36	𝜇α̃(𝓍	𝜇α̃(𝓍	NOUN
iajs-2858	45	37	)	)	PUNCT
iajs-2858	45	38	+	+	NUM
iajs-2858	45	39	𝜇β̃(𝓍	𝜇β̃(𝓍	NOUN
iajs-2858	45	40	)	)	PUNCT
iajs-2858	45	41	}	}	PUNCT
iajs-2858	45	42	.	.	PUNCT
iajs-2858	46	1	bounded	bounded	ADJ
iajs-2858	46	2	difference	difference	NOUN
iajs-2858	46	3	:	:	PUNCT
iajs-2858	46	4	the	the	DET
iajs-2858	46	5	bounded	bounded	ADJ
iajs-2858	46	6	difference	difference	NOUN
iajs-2858	46	7	∁̃=	∁̃=	PROPN
iajs-2858	46	8	α̃	α̃	PROPN
iajs-2858	46	9	⊖	⊖	NUM
iajs-2858	46	10	β̃	β̃	PROPN
iajs-2858	46	11	is	be	AUX
iajs-2858	46	12	defined	define	VERB
iajs-2858	46	13	as	as	ADP
iajs-2858	46	14	∁̃=	∁̃=	X
iajs-2858	46	15	{	{	PUNCT
iajs-2858	46	16	(	(	PUNCT
iajs-2858	46	17	𝓍	𝓍	X
iajs-2858	46	18	,	,	PUNCT
iajs-2858	46	19	𝜇α̃⊖β̃(𝓍))|𝓍	𝜇α̃⊖β̃(𝓍))|𝓍	PRON
iajs-2858	46	20	∈	∈	NOUN
iajs-2858	46	21	χ	χ	NOUN
iajs-2858	46	22	}	}	PUNCT
iajs-2858	46	23	,	,	PUNCT
iajs-2858	46	24	where	where	SCONJ
iajs-2858	46	25	𝜇α̃⊖β̃(𝓍	𝜇α̃⊖β̃(𝓍	NOUN
iajs-2858	46	26	)	)	PUNCT
iajs-2858	46	27	=	=	SYM
iajs-2858	46	28	min	min	NOUN
iajs-2858	46	29	{	{	PUNCT
iajs-2858	46	30	1	1	NUM
iajs-2858	46	31	,	,	PUNCT
iajs-2858	46	32	𝜇α̃(𝓍	𝜇α̃(𝓍	NOUN
iajs-2858	46	33	)	)	PUNCT
iajs-2858	46	34	+	+	NUM
iajs-2858	46	35	𝜇β̃(𝓍	𝜇β̃(𝓍	NOUN
iajs-2858	46	36	)	)	PUNCT
iajs-2858	46	37	}	}	PUNCT
iajs-2858	46	38	.	.	PUNCT
iajs-2858	47	1	3	3	X
iajs-2858	47	2	.	.	X
iajs-2858	47	3	mathematical	mathematical	ADJ
iajs-2858	47	4	model	model	NOUN
iajs-2858	47	5	formula	formula	NOUN
iajs-2858	47	6	3.1	3.1	NUM
iajs-2858	47	7	.	.	PUNCT
iajs-2858	48	1	linear	linear	ADJ
iajs-2858	48	2	programming	programming	NOUN
iajs-2858	48	3	models	model	NOUN
iajs-2858	48	4	a	a	DET
iajs-2858	48	5	special	special	ADJ
iajs-2858	48	6	kind	kind	NOUN
iajs-2858	48	7	of	of	ADP
iajs-2858	48	8	decision	decision	NOUN
iajs-2858	48	9	model	model	NOUN
iajs-2858	48	10	introduced	introduce	VERB
iajs-2858	48	11	by	by	ADP
iajs-2858	48	12	[	[	PUNCT
iajs-2858	48	13	13	13	NUM
iajs-2858	48	14	]	]	PUNCT
iajs-2858	48	15	,	,	PUNCT
iajs-2858	48	16	is	be	AUX
iajs-2858	48	17	considered	consider	VERB
iajs-2858	48	18	as	as	ADP
iajs-2858	48	19	linear	linear	ADJ
iajs-2858	48	20	programming	programming	NOUN
iajs-2858	48	21	models	model	NOUN
iajs-2858	48	22	,	,	PUNCT
iajs-2858	48	23	the	the	DET
iajs-2858	48	24	restrictions	restriction	NOUN
iajs-2858	48	25	define	define	VERB
iajs-2858	48	26	the	the	DET
iajs-2858	48	27	decision	decision	NOUN
iajs-2858	48	28	space	space	NOUN
iajs-2858	48	29	;	;	PUNCT
iajs-2858	48	30	the	the	DET
iajs-2858	48	31	objective	objective	ADJ
iajs-2858	48	32	function	function	NOUN
iajs-2858	48	33	defines	define	VERB
iajs-2858	48	34	the	the	DET
iajs-2858	48	35	"	"	PUNCT
iajs-2858	48	36	target	target	NOUN
iajs-2858	48	37	"	"	PUNCT
iajs-2858	48	38	(	(	PUNCT
iajs-2858	48	39	utility	utility	NOUN
iajs-2858	48	40	function	function	NOUN
iajs-2858	48	41	)	)	PUNCT
iajs-2858	48	42	,	,	PUNCT
iajs-2858	48	43	and	and	CCONJ
iajs-2858	48	44	the	the	DET
iajs-2858	48	45	kind	kind	NOUN
iajs-2858	48	46	of	of	ADP
iajs-2858	48	47	choice	choice	NOUN
iajs-2858	48	48	is	be	AUX
iajs-2858	48	49	decision	decision	NOUN
iajs-2858	48	50	making	make	VERB
iajs-2858	48	51	under	under	ADP
iajs-2858	48	52	conditions	condition	NOUN
iajs-2858	48	53	.	.	PUNCT
iajs-2858	49	1	the	the	DET
iajs-2858	49	2	standard	standard	ADJ
iajs-2858	49	3	linear	linear	ADJ
iajs-2858	49	4	programming	programming	NOUN
iajs-2858	49	5	model	model	NOUN
iajs-2858	49	6	is	be	AUX
iajs-2858	49	7	as	as	SCONJ
iajs-2858	49	8	follows	follow	VERB
iajs-2858	49	9	:	:	PUNCT
iajs-2858	49	10	𝑚𝑎𝑥𝑖𝑚𝑖𝑧𝑒	𝑚𝑎𝑥𝑖𝑚𝑖𝑧𝑒	PROPN
iajs-2858	49	11	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-2858	49	12	)	)	PUNCT
iajs-2858	50	1	=	=	VERB
iajs-2858	50	2	𝑐𝑇𝑥	𝑐𝑇𝑥	VERB
iajs-2858	50	3	such	such	ADJ
iajs-2858	50	4	that	that	SCONJ
iajs-2858	50	5	:	:	PUNCT
iajs-2858	50	6	𝐴𝑥	𝐴𝑥	NOUN
iajs-2858	50	7	≤	≤	PUNCT
iajs-2858	51	1	𝑏	𝑏	PRON
iajs-2858	51	2	𝑥	𝑥	PROPN
iajs-2858	51	3	≥	≥	NOUN
iajs-2858	51	4	0	0	NUM
iajs-2858	51	5	with	with	ADP
iajs-2858	51	6	𝑐	𝑐	PROPN
iajs-2858	51	7	,	,	PUNCT
iajs-2858	51	8	𝑥	𝑥	PRON
iajs-2858	51	9	∈	∈	PROPN
iajs-2858	51	10	𝑅𝑛	𝑅𝑛	PROPN
iajs-2858	51	11	,	,	PUNCT
iajs-2858	51	12	𝑏	𝑏	PRON
iajs-2858	51	13	∈	∈	PROPN
iajs-2858	51	14	𝑅𝑛	𝑅𝑛	PROPN
iajs-2858	51	15	,	,	PUNCT
iajs-2858	51	16	𝐴	𝐴	PROPN
iajs-2858	51	17	∈	∈	PROPN
iajs-2858	51	18	𝑅𝑚×𝑛	𝑅𝑚×𝑛	NOUN
iajs-2858	51	19	3.2	3.2	NUM
iajs-2858	51	20	.	.	PUNCT
iajs-2858	52	1	linear	linear	ADJ
iajs-2858	52	2	fractional	fractional	ADJ
iajs-2858	52	3	programming	programming	NOUN
iajs-2858	52	4	formula	formula	NOUN
iajs-2858	52	5	the	the	DET
iajs-2858	52	6	linear	linear	ADJ
iajs-2858	52	7	fractional	fractional	ADJ
iajs-2858	52	8	programming	programming	NOUN
iajs-2858	52	9	problem	problem	NOUN
iajs-2858	52	10	(	(	PUNCT
iajs-2858	52	11	lfpp	lfpp	PROPN
iajs-2858	52	12	)	)	PUNCT
iajs-2858	52	13	introduced	introduce	VERB
iajs-2858	52	14	by	by	ADP
iajs-2858	52	15	[	[	X
iajs-2858	52	16	14	14	NUM
iajs-2858	52	17	]	]	PUNCT
iajs-2858	52	18	can	can	AUX
iajs-2858	52	19	be	be	AUX
iajs-2858	52	20	stated	state	VERB
iajs-2858	52	21	in	in	ADP
iajs-2858	52	22	the	the	DET
iajs-2858	52	23	following	follow	VERB
iajs-2858	52	24	manner	manner	NOUN
iajs-2858	52	25	:	:	PUNCT
iajs-2858	52	26	𝑀𝑎𝑥.	𝑀𝑎𝑥.	PROPN
iajs-2858	52	27	𝑊	𝑊	PROPN
iajs-2858	52	28	=	=	NOUN
iajs-2858	52	29	𝑐1	𝑐1	NOUN
iajs-2858	52	30	′	′	NUM
iajs-2858	53	1	𝓍	𝓍	DET
iajs-2858	53	2	+	+	NUM
iajs-2858	53	3	𝛽	𝛽	NOUN
iajs-2858	53	4	𝑐2	𝑐2	NOUN
iajs-2858	53	5	′	′	NUM
iajs-2858	54	1	𝓍	𝓍	PRON
iajs-2858	55	1	+	+	CCONJ
iajs-2858	55	2	𝛿	𝛿	ADJ
iajs-2858	55	3	subject	subject	NOUN
iajs-2858	55	4	to	to	ADP
iajs-2858	55	5	:	:	PUNCT
iajs-2858	55	6	𝐴𝓍	𝐴𝓍	PROPN
iajs-2858	55	7	=	=	SYM
iajs-2858	55	8	𝑏	𝑏	PROPN
iajs-2858	55	9	,	,	PUNCT
iajs-2858	55	10	𝓍	𝓍	DET
iajs-2858	55	11	≥	≥	NOUN
iajs-2858	55	12	0	0	NUM
iajs-2858	55	13	.	.	PUNCT
iajs-2858	56	1	(	(	PUNCT
iajs-2858	56	2	2	2	X
iajs-2858	56	3	)	)	PUNCT
iajs-2858	56	4	(	(	PUNCT
iajs-2858	56	5	1	1	X
iajs-2858	56	6	)	)	PUNCT
iajs-2858	56	7	ihjpas	ihjpa	NOUN
iajs-2858	56	8	.	.	PUNCT
iajs-2858	57	1	53	53	NUM
iajs-2858	57	2	(	(	PUNCT
iajs-2858	57	3	4)2022	4)2022	NOUN
iajs-2858	57	4	244	244	NUM
iajs-2858	57	5	where	where	SCONJ
iajs-2858	57	6	(	(	PUNCT
iajs-2858	57	7	i	i	NOUN
iajs-2858	57	8	)	)	PUNCT
iajs-2858	57	9	𝑥	𝑥	NOUN
iajs-2858	57	10	,	,	PUNCT
iajs-2858	57	11	𝑐1	𝑐1	NOUN
iajs-2858	57	12	,	,	PUNCT
iajs-2858	57	13	and	and	CCONJ
iajs-2858	57	14	𝑐2	𝑐2	NOUN
iajs-2858	57	15	are	be	AUX
iajs-2858	57	16	𝑛	𝑛	DET
iajs-2858	57	17	×	×	PROPN
iajs-2858	57	18	1	1	NUM
iajs-2858	57	19	column	column	NOUN
iajs-2858	57	20	vectors	vector	NOUN
iajs-2858	57	21	.	.	PUNCT
iajs-2858	58	1	(	(	PUNCT
iajs-2858	58	2	ii	ii	X
iajs-2858	58	3	)	)	PUNCT
iajs-2858	58	4	𝐴	𝐴	PROPN
iajs-2858	58	5	is	be	AUX
iajs-2858	58	6	𝑛	𝑛	DET
iajs-2858	58	7	×	×	NOUN
iajs-2858	58	8	𝑚	𝑚	NOUN
iajs-2858	58	9	matrix	matrix	NOUN
iajs-2858	58	10	.	.	PUNCT
iajs-2858	59	1	(	(	PUNCT
iajs-2858	59	2	iii	iii	X
iajs-2858	59	3	)	)	PUNCT
iajs-2858	59	4	𝑏	𝑏	NOUN
iajs-2858	59	5	is	be	AUX
iajs-2858	59	6	an	an	DET
iajs-2858	59	7	𝑚	𝑚	PROPN
iajs-2858	59	8	×	×	NOUN
iajs-2858	59	9	1	1	NUM
iajs-2858	59	10	vectors	vector	NOUN
iajs-2858	59	11	.	.	PUNCT
iajs-2858	60	1	(	(	PUNCT
iajs-2858	60	2	iv	iv	X
iajs-2858	60	3	)	)	PUNCT
iajs-2858	60	4	the	the	DET
iajs-2858	60	5	prime	prime	NOUN
iajs-2858	60	6	{	{	PUNCT
iajs-2858	60	7	′	′	NOUN
iajs-2858	60	8	}	}	PUNCT
iajs-2858	60	9	on	on	ADP
iajs-2858	60	10	the	the	DET
iajs-2858	60	11	vectors	vector	NOUN
iajs-2858	60	12	𝑐1	𝑐1	NOUN
iajs-2858	60	13	,	,	PUNCT
iajs-2858	60	14	and	and	CCONJ
iajs-2858	60	15	𝑐2	𝑐2	NOUN
iajs-2858	60	16	indicate	indicate	VERB
iajs-2858	60	17	as	as	ADP
iajs-2858	60	18	a	a	DET
iajs-2858	60	19	transpose	transpose	NOUN
iajs-2858	60	20	of	of	ADP
iajs-2858	60	21	vectors	vector	NOUN
iajs-2858	60	22	and	and	CCONJ
iajs-2858	60	23	(	(	PUNCT
iajs-2858	60	24	v	v	NOUN
iajs-2858	60	25	)	)	PUNCT
iajs-2858	60	26	𝛽	𝛽	NOUN
iajs-2858	60	27	,	,	PUNCT
iajs-2858	60	28	𝛿	𝛿	PRON
iajs-2858	60	29	are	be	AUX
iajs-2858	60	30	comparatively	comparatively	ADV
iajs-2858	60	31	numeric	numeric	ADJ
iajs-2858	60	32	.	.	PUNCT
iajs-2858	61	1	the	the	DET
iajs-2858	61	2	procedure	procedure	NOUN
iajs-2858	61	3	solution	solution	NOUN
iajs-2858	61	4	of	of	ADP
iajs-2858	61	5	such	such	ADJ
iajs-2858	61	6	problems	problem	NOUN
iajs-2858	61	7	solved	solve	VERB
iajs-2858	61	8	by	by	ADP
iajs-2858	61	9	[	[	X
iajs-2858	61	10	15	15	NUM
iajs-2858	61	11	]	]	SYM
iajs-2858	61	12	.	.	PUNCT
iajs-2858	62	1	3.3	3.3	NUM
iajs-2858	62	2	.	.	PUNCT
iajs-2858	62	3	quadratic	quadratic	ADJ
iajs-2858	62	4	programming	programming	NOUN
iajs-2858	62	5	problem	problem	NOUN
iajs-2858	62	6	(	(	PUNCT
iajs-2858	62	7	qpp	qpp	NOUN
iajs-2858	62	8	)	)	PUNCT
iajs-2858	62	9	quadratic	quadratic	ADJ
iajs-2858	62	10	programming	programming	NOUN
iajs-2858	62	11	is	be	AUX
iajs-2858	62	12	a	a	DET
iajs-2858	62	13	particular	particular	ADJ
iajs-2858	62	14	kind	kind	NOUN
iajs-2858	62	15	of	of	ADP
iajs-2858	62	16	mathematical	mathematical	ADJ
iajs-2858	62	17	optimization	optimization	NOUN
iajs-2858	62	18	problem	problem	NOUN
iajs-2858	62	19	it	it	PRON
iajs-2858	62	20	is	be	AUX
iajs-2858	62	21	a	a	DET
iajs-2858	62	22	problem	problem	NOUN
iajs-2858	62	23	of	of	ADP
iajs-2858	62	24	reducing	reduce	VERB
iajs-2858	62	25	or	or	CCONJ
iajs-2858	62	26	maximizing	maximize	VERB
iajs-2858	62	27	a	a	DET
iajs-2858	62	28	quadratic	quadratic	ADJ
iajs-2858	62	29	function	function	NOUN
iajs-2858	62	30	of	of	ADP
iajs-2858	62	31	numerous	numerous	ADJ
iajs-2858	62	32	variables	variable	NOUN
iajs-2858	62	33	under	under	ADP
iajs-2858	62	34	linear	linear	ADJ
iajs-2858	62	35	constraints	constraint	NOUN
iajs-2858	62	36	.	.	PUNCT
iajs-2858	63	1	the	the	DET
iajs-2858	63	2	qpp	qpp	NOUN
iajs-2858	63	3	can	can	AUX
iajs-2858	63	4	be	be	AUX
iajs-2858	63	5	written	write	VERB
iajs-2858	63	6	as	as	SCONJ
iajs-2858	63	7	follows	follow	VERB
iajs-2858	63	8	:	:	PUNCT
iajs-2858	63	9	:	:	PUNCT
iajs-2858	63	10	max	max	PROPN
iajs-2858	63	11	.	.	PUNCT
iajs-2858	64	1	𝑧	𝑧	PROPN
iajs-2858	64	2	(	(	PUNCT
iajs-2858	64	3	or	or	CCONJ
iajs-2858	64	4	min	min	NOUN
iajs-2858	64	5	.	.	PROPN
iajs-2858	64	6	z	z	NOUN
iajs-2858	64	7	)	)	PUNCT
iajs-2858	64	8	=	=	SYM
iajs-2858	64	9	𝑥𝑇𝐺𝑥	𝑥𝑇𝐺𝑥	NOUN
iajs-2858	64	10	+	+	CCONJ
iajs-2858	64	11	𝑐𝑇𝑥	𝑐𝑇𝑥	NOUN
iajs-2858	64	12	+	+	X
iajs-2858	64	13	𝛼	𝛼	NOUN
iajs-2858	64	14	subject	subject	NOUN
iajs-2858	64	15	to	to	ADP
iajs-2858	64	16	:	:	PUNCT
iajs-2858	64	17	𝐴𝑥	𝐴𝑥	NOUN
iajs-2858	64	18	(	(	PUNCT
iajs-2858	64	19	≤	≤	X
iajs-2858	64	20	≥	≥	NOUN
iajs-2858	64	21	=	=	SYM
iajs-2858	64	22	)	)	PUNCT
iajs-2858	64	23	b	b	X
iajs-2858	64	24	𝑥	𝑥	PRON
iajs-2858	64	25	≥	≥	NOUN
iajs-2858	64	26	0	0	NUM
iajs-2858	64	27	where	where	SCONJ
iajs-2858	64	28	𝐴	𝐴	PROPN
iajs-2858	64	29	=	=	PUNCT
iajs-2858	64	30	(	(	PUNCT
iajs-2858	64	31	𝑎𝑖𝑗)𝑚×𝑛	𝑎𝑖𝑗)𝑚×𝑛	NOUN
iajs-2858	64	32	matrix	matrix	NOUN
iajs-2858	64	33	of	of	ADP
iajs-2858	64	34	coefficients	coefficient	NOUN
iajs-2858	64	35	,	,	PUNCT
iajs-2858	64	36	for	for	ADP
iajs-2858	64	37	𝑖	𝑖	PRON
iajs-2858	64	38	=	=	SYM
iajs-2858	64	39	1,2	1,2	NUM
iajs-2858	64	40	,	,	PUNCT
iajs-2858	64	41	…	…	PUNCT
iajs-2858	64	42	,	,	PUNCT
iajs-2858	64	43	𝑚	𝑚	PROPN
iajs-2858	64	44	and	and	CCONJ
iajs-2858	64	45	𝑗	𝑗	NOUN
iajs-2858	64	46	=	=	SYM
iajs-2858	64	47	1,2	1,2	NUM
iajs-2858	64	48	,	,	PUNCT
iajs-2858	64	49	…	…	PUNCT
iajs-2858	64	50	,	,	PUNCT
iajs-2858	64	51	𝑛	𝑛	NOUN
iajs-2858	64	52	,	,	PUNCT
iajs-2858	64	53	𝑏	𝑏	NOUN
iajs-2858	64	54	=	=	PUNCT
iajs-2858	64	55	(	(	PUNCT
iajs-2858	64	56	𝑏1	𝑏1	NOUN
iajs-2858	64	57	,	,	PUNCT
iajs-2858	64	58	𝑏2	𝑏2	PROPN
iajs-2858	64	59	,	,	PUNCT
iajs-2858	64	60	…	…	PUNCT
iajs-2858	64	61	,	,	PUNCT
iajs-2858	64	62	𝑏𝑚)𝑇	𝑏𝑚)𝑇	PROPN
iajs-2858	64	63	,	,	PUNCT
iajs-2858	64	64	𝑥	𝑥	X
iajs-2858	64	65	=	=	SYM
iajs-2858	64	66	(	(	PUNCT
iajs-2858	64	67	𝑥1	𝑥1	NOUN
iajs-2858	64	68	,	,	PUNCT
iajs-2858	64	69	𝑥2	𝑥2	NOUN
iajs-2858	64	70	,	,	PUNCT
iajs-2858	64	71	…	…	PUNCT
iajs-2858	64	72	,	,	PUNCT
iajs-2858	64	73	𝑥𝑛)𝑇,𝑐𝑇	𝑥𝑛)𝑇,𝑐𝑇	NOUN
iajs-2858	64	74	=	=	SYM
iajs-2858	64	75	(	(	PUNCT
iajs-2858	64	76	𝑐1	𝑐1	NOUN
iajs-2858	64	77	,	,	PUNCT
iajs-2858	64	78	𝑐2	𝑐2	NOUN
iajs-2858	64	79	,	,	PUNCT
iajs-2858	64	80	…	…	PUNCT
iajs-2858	64	81	,	,	PUNCT
iajs-2858	64	82	𝑐𝑛	𝑐𝑛	PROPN
iajs-2858	64	83	)	)	PUNCT
iajs-2858	64	84	,	,	PUNCT
iajs-2858	64	85	𝛼	𝛼	PROPN
iajs-2858	64	86	is	be	AUX
iajs-2858	64	87	scalar	scalar	ADJ
iajs-2858	64	88	and	and	CCONJ
iajs-2858	64	89	𝐺	𝐺	NOUN
iajs-2858	64	90	=	=	PUNCT
iajs-2858	64	91	(	(	PUNCT
iajs-2858	64	92	𝑔𝑖𝑗)𝑛×𝑛	𝑔𝑖𝑗)𝑛×𝑛	PROPN
iajs-2858	64	93	is	be	AUX
iajs-2858	64	94	assumed	assume	VERB
iajs-2858	64	95	negative	negative	ADJ
iajs-2858	64	96	definite	definite	ADJ
iajs-2858	64	97	of	of	ADP
iajs-2858	64	98	the	the	DET
iajs-2858	64	99	problem	problem	NOUN
iajs-2858	64	100	in	in	ADP
iajs-2858	64	101	maximization	maximization	NOUN
iajs-2858	64	102	,	,	PUNCT
iajs-2858	64	103	and	and	CCONJ
iajs-2858	64	104	positive	positive	ADJ
iajs-2858	64	105	definite	definite	ADJ
iajs-2858	64	106	of	of	ADP
iajs-2858	64	107	problem	problem	NOUN
iajs-2858	64	108	in	in	ADP
iajs-2858	64	109	minimization	minimization	NOUN
iajs-2858	64	110	,	,	PUNCT
iajs-2858	64	111	the	the	DET
iajs-2858	64	112	objective	objective	ADJ
iajs-2858	64	113	function	function	NOUN
iajs-2858	64	114	is	be	AUX
iajs-2858	64	115	quadratic	quadratic	ADJ
iajs-2858	64	116	,	,	PUNCT
iajs-2858	64	117	whereas	whereas	SCONJ
iajs-2858	64	118	the	the	DET
iajs-2858	64	119	restrictions	restriction	NOUN
iajs-2858	64	120	are	be	AUX
iajs-2858	64	121	linear	linear	ADJ
iajs-2858	64	122	.	.	PUNCT
iajs-2858	65	1	[	[	X
iajs-2858	65	2	16	16	NUM
iajs-2858	65	3	]	]	PUNCT
iajs-2858	65	4	.	.	PUNCT
iajs-2858	66	1	3.4	3.4	NUM
iajs-2858	66	2	.	.	PUNCT
iajs-2858	66	3	quadratic	quadratic	ADJ
iajs-2858	66	4	fractional	fractional	ADJ
iajs-2858	66	5	programming	programming	NOUN
iajs-2858	66	6	problem	problem	NOUN
iajs-2858	66	7	(	(	PUNCT
iajs-2858	66	8	qfpp	qfpp	PROPN
iajs-2858	66	9	)	)	PUNCT
iajs-2858	66	10	this	this	DET
iajs-2858	66	11	section	section	NOUN
iajs-2858	66	12	discusses	discuss	VERB
iajs-2858	66	13	a	a	DET
iajs-2858	66	14	specific	specific	ADJ
iajs-2858	66	15	situation	situation	NOUN
iajs-2858	66	16	of	of	ADP
iajs-2858	66	17	qfpp	qfpp	PROPN
iajs-2858	66	18	's	's	PART
iajs-2858	66	19	mathematical	mathematical	ADJ
iajs-2858	66	20	form	form	NOUN
iajs-2858	66	21	,	,	PUNCT
iajs-2858	66	22	which	which	PRON
iajs-2858	66	23	contains	contain	VERB
iajs-2858	66	24	a	a	DET
iajs-2858	66	25	quadratic	quadratic	ADJ
iajs-2858	66	26	function	function	NOUN
iajs-2858	66	27	in	in	ADP
iajs-2858	66	28	the	the	DET
iajs-2858	66	29	numerator	numerator	NOUN
iajs-2858	66	30	and	and	CCONJ
iajs-2858	66	31	a	a	DET
iajs-2858	66	32	denominator	denominator	NOUN
iajs-2858	66	33	that	that	PRON
iajs-2858	66	34	can	can	AUX
iajs-2858	66	35	be	be	AUX
iajs-2858	66	36	represented	represent	VERB
iajs-2858	66	37	as	as	ADP
iajs-2858	66	38	the	the	DET
iajs-2858	66	39	product	product	NOUN
iajs-2858	66	40	of	of	ADP
iajs-2858	66	41	two	two	NUM
iajs-2858	66	42	linear	linear	ADJ
iajs-2858	66	43	components	component	NOUN
iajs-2858	66	44	,	,	PUNCT
iajs-2858	66	45	as	as	ADP
iajs-2858	66	46	the	the	DET
iajs-2858	66	47	following	following	NOUN
iajs-2858	66	48	:	:	PUNCT
iajs-2858	66	49	𝑀𝑎𝑥.	𝑀𝑎𝑥.	PROPN
iajs-2858	66	50	𝑍	𝑍	PROPN
iajs-2858	66	51	=	=	SYM
iajs-2858	66	52	(	(	PUNCT
iajs-2858	66	53	𝑐1	𝑐1	NOUN
iajs-2858	66	54	𝑇𝑥+𝛼)(𝑐2	𝑇𝑥+𝛼)(𝑐2	PROPN
iajs-2858	66	55	𝑇𝑥+𝛽	𝑇𝑥+𝛽	PROPN
iajs-2858	66	56	)	)	PUNCT
iajs-2858	66	57	(	(	PUNCT
iajs-2858	66	58	𝑒1	𝑒1	NOUN
iajs-2858	66	59	𝑇𝑥+𝛾)(𝑒2	𝑇𝑥+𝛾)(𝑒2	NUM
iajs-2858	66	60	𝑇+𝛿	𝑇+𝛿	NOUN
iajs-2858	66	61	)	)	PUNCT
iajs-2858	66	62	=	=	SYM
iajs-2858	66	63	(	(	PUNCT
iajs-2858	66	64	𝑤1)(𝑤2	𝑤1)(𝑤2	NOUN
iajs-2858	66	65	)	)	PUNCT
iajs-2858	66	66	(	(	PUNCT
iajs-2858	66	67	𝑤3)(𝑤4	𝑤3)(𝑤4	NOUN
iajs-2858	66	68	)	)	PUNCT
iajs-2858	66	69	subject	subject	NOUN
iajs-2858	66	70	to	to	ADP
iajs-2858	66	71	:	:	PUNCT
iajs-2858	66	72	𝐴𝑥	𝐴𝑥	X
iajs-2858	66	73	[	[	PUNCT
iajs-2858	66	74	≥	≥	X
iajs-2858	66	75	≤	≤	PUNCT
iajs-2858	66	76	=	=	PUNCT
iajs-2858	66	77	]	]	X
iajs-2858	66	78	𝑏	𝑏	PROPN
iajs-2858	66	79	𝑥	𝑥	PRON
iajs-2858	66	80	≥	≥	NOUN
iajs-2858	66	81	0	0	NUM
iajs-2858	66	82	𝐴	𝐴	PROPN
iajs-2858	66	83	is	be	AUX
iajs-2858	66	84	𝑚	𝑚	PROPN
iajs-2858	66	85	×	×	NOUN
iajs-2858	66	86	𝑛	𝑛	DET
iajs-2858	66	87	matrix	matrix	NOUN
iajs-2858	66	88	,	,	PUNCT
iajs-2858	66	89	where	where	SCONJ
iajs-2858	66	90	𝑥	𝑥	PROPN
iajs-2858	66	91	is	be	AUX
iajs-2858	66	92	𝑛	𝑛	PRON
iajs-2858	66	93	×	×	PROPN
iajs-2858	66	94	1	1	NUM
iajs-2858	66	95	column	column	NOUN
iajs-2858	66	96	vector𝑠	vector𝑠	NOUN
iajs-2858	66	97	of	of	ADP
iajs-2858	66	98	decision	decision	NOUN
iajs-2858	66	99	variables	variable	NOUN
iajs-2858	66	100	,	,	PUNCT
iajs-2858	66	101	𝑐1	𝑐1	NOUN
iajs-2858	66	102	,	,	PUNCT
iajs-2858	66	103	𝑐2	𝑐2	NOUN
iajs-2858	66	104	,	,	PUNCT
iajs-2858	66	105	𝑒	𝑒	PROPN
iajs-2858	66	106	are	be	AUX
iajs-2858	66	107	𝑛	𝑛	DET
iajs-2858	66	108	×	×	PROPN
iajs-2858	66	109	1	1	NUM
iajs-2858	66	110	column	column	NOUN
iajs-2858	66	111	vectors	vector	NOUN
iajs-2858	66	112	of	of	ADP
iajs-2858	66	113	constants	constant	NOUN
iajs-2858	66	114	,	,	PUNCT
iajs-2858	66	115	𝑏	𝑏	PROPN
iajs-2858	66	116	is	be	AUX
iajs-2858	66	117	𝑚	𝑚	PROPN
iajs-2858	66	118	×	×	PROPN
iajs-2858	66	119	1	1	NUM
iajs-2858	66	120	column	column	NOUN
iajs-2858	66	121	vectors	vector	NOUN
iajs-2858	66	122	of	of	ADP
iajs-2858	66	123	constants	constant	NOUN
iajs-2858	66	124	.	.	PUNCT
iajs-2858	67	1	𝛼	𝛼	X
iajs-2858	67	2	,	,	PUNCT
iajs-2858	67	3	𝛽	𝛽	NOUN
iajs-2858	67	4	,	,	PUNCT
iajs-2858	67	5	𝛾	𝛾	NOUN
iajs-2858	67	6	and	and	CCONJ
iajs-2858	67	7	𝛿	𝛿	PROPN
iajs-2858	67	8	are	be	AUX
iajs-2858	67	9	scalars	scalar	NOUN
iajs-2858	67	10	,	,	PUNCT
iajs-2858	67	11	the	the	DET
iajs-2858	67	12	prime	prime	NOUN
iajs-2858	67	13	(	(	PUNCT
iajs-2858	67	14	𝑇	𝑇	PROPN
iajs-2858	67	15	)	)	PUNCT
iajs-2858	67	16	over	over	ADP
iajs-2858	67	17	the	the	DET
iajs-2858	67	18	vectors	vector	NOUN
iajs-2858	67	19	𝑐1	𝑐1	NOUN
iajs-2858	67	20	,	,	PUNCT
iajs-2858	67	21	𝑐2	𝑐2	NOUN
iajs-2858	67	22	,	,	PUNCT
iajs-2858	67	23	𝑒1	𝑒1	NOUN
iajs-2858	67	24	and	and	CCONJ
iajs-2858	67	25	𝑒2	𝑒2	PROPN
iajs-2858	67	26	denoted	denote	VERB
iajs-2858	67	27	the	the	DET
iajs-2858	67	28	transpose	transpose	NOUN
iajs-2858	67	29	of	of	ADP
iajs-2858	67	30	the	the	DET
iajs-2858	67	31	vectors	vector	NOUN
iajs-2858	67	32	.	.	PUNCT
iajs-2858	68	1	𝑤1𝑤2	𝑤1𝑤2	AUX
iajs-2858	68	2	and	and	CCONJ
iajs-2858	68	3	𝑤3𝑤4	𝑤3𝑤4	ADP
iajs-2858	68	4	are	be	AUX
iajs-2858	68	5	the	the	DET
iajs-2858	68	6	values	value	NOUN
iajs-2858	68	7	of	of	ADP
iajs-2858	68	8	numerator	numerator	NOUN
iajs-2858	68	9	and	and	CCONJ
iajs-2858	68	10	denominator	denominator	NOUN
iajs-2858	68	11	of	of	ADP
iajs-2858	68	12	objective	objective	ADJ
iajs-2858	68	13	function	function	NOUN
iajs-2858	68	14	respectively	respectively	ADV
iajs-2858	68	15	3.5	3.5	NUM
iajs-2858	68	16	.	.	PUNCT
iajs-2858	69	1	symmetric	symmetric	ADJ
iajs-2858	69	2	fuzzy	fuzzy	ADJ
iajs-2858	69	3	linear	linear	PROPN
iajs-2858	69	4	programming	programming	NOUN
iajs-2858	69	5	we	we	PRON
iajs-2858	69	6	will	will	AUX
iajs-2858	69	7	suppose	suppose	VERB
iajs-2858	69	8	that	that	SCONJ
iajs-2858	69	9	the	the	DET
iajs-2858	69	10	decision	decision	NOUN
iajs-2858	69	11	-	-	PUNCT
iajs-2858	69	12	maker	maker	NOUN
iajs-2858	69	13	can	can	AUX
iajs-2858	69	14	select	select	VERB
iajs-2858	69	15	an	an	DET
iajs-2858	69	16	ambition	ambition	NOUN
iajs-2858	69	17	level	level	NOUN
iajs-2858	69	18	,	,	PUNCT
iajs-2858	69	19	z	z	NOUN
iajs-2858	69	20	,	,	PUNCT
iajs-2858	69	21	for	for	ADP
iajs-2858	69	22	the	the	DET
iajs-2858	69	23	value	value	NOUN
iajs-2858	69	24	of	of	ADP
iajs-2858	69	25	the	the	DET
iajs-2858	69	26	objective	objective	ADJ
iajs-2858	69	27	function	function	NOUN
iajs-2858	69	28	he	he	PRON
iajs-2858	69	29	or	or	CCONJ
iajs-2858	69	30	she	she	PRON
iajs-2858	69	31	wishes	wish	VERB
iajs-2858	69	32	to	to	PART
iajs-2858	69	33	reach	reach	VERB
iajs-2858	69	34	,	,	PUNCT
iajs-2858	69	35	and	and	CCONJ
iajs-2858	69	36	that	that	SCONJ
iajs-2858	69	37	each	each	DET
iajs-2858	69	38	restriction	restriction	NOUN
iajs-2858	69	39	is	be	AUX
iajs-2858	69	40	modelled	model	VERB
iajs-2858	69	41	as	as	ADP
iajs-2858	69	42	a	a	DET
iajs-2858	69	43	fuzzy	fuzzy	ADJ
iajs-2858	69	44	set	set	NOUN
iajs-2858	69	45	in	in	ADP
iajs-2858	69	46	model	model	NOUN
iajs-2858	69	47	(	(	PUNCT
iajs-2858	69	48	1	1	NUM
iajs-2858	69	49	)	)	PUNCT
iajs-2858	69	50	.	.	PUNCT
iajs-2858	70	1	our	our	PRON
iajs-2858	70	2	fuzzy	fuzzy	ADJ
iajs-2858	70	3	album	album	NOUN
iajs-2858	70	4	then	then	ADV
iajs-2858	70	5	transforms	transform	VERB
iajs-2858	70	6	into	into	ADP
iajs-2858	70	7	:	:	PUNCT
iajs-2858	70	8	(	(	PUNCT
iajs-2858	70	9	3	3	X
iajs-2858	70	10	)	)	PUNCT
iajs-2858	70	11	(	(	PUNCT
iajs-2858	70	12	4	4	X
iajs-2858	70	13	)	)	PUNCT
iajs-2858	70	14	ihjpas	ihjpa	NOUN
iajs-2858	70	15	.	.	PUNCT
iajs-2858	71	1	53	53	NUM
iajs-2858	71	2	(	(	PUNCT
iajs-2858	71	3	4)2022	4)2022	NOUN
iajs-2858	71	4	245	245	NUM
iajs-2858	71	5	find	find	VERB
iajs-2858	71	6	x	x	PART
iajs-2858	71	7	such	such	ADJ
iajs-2858	71	8	that	that	SCONJ
iajs-2858	71	9	𝑐𝑇𝑥	𝑐𝑇𝑥	PRON
iajs-2858	71	10	≧	≧	NOUN
iajs-2858	71	11	𝑧	𝑧	PUNCT
iajs-2858	72	1	𝐴𝑥	𝐴𝑥	NOUN
iajs-2858	72	2	≦	≦	VERB
iajs-2858	72	3	𝑏	𝑏	PRON
iajs-2858	72	4	𝑥	𝑥	PRON
iajs-2858	72	5	≥	≥	NOUN
iajs-2858	72	6	0	0	NUM
iajs-2858	72	7	here	here	ADV
iajs-2858	72	8	≦	≦	AUX
iajs-2858	72	9	signifies	signify	VERB
iajs-2858	72	10	the	the	DET
iajs-2858	72	11	fuzzified	fuzzified	ADJ
iajs-2858	72	12	form	form	NOUN
iajs-2858	72	13	of	of	ADP
iajs-2858	72	14	≤	≤	NUM
iajs-2858	72	15	and	and	CCONJ
iajs-2858	72	16	has	have	VERB
iajs-2858	72	17	the	the	DET
iajs-2858	72	18	linguistic	linguistic	ADJ
iajs-2858	72	19	interpretation	interpretation	NOUN
iajs-2858	72	20	"	"	PUNCT
iajs-2858	72	21	essentially	essentially	ADV
iajs-2858	72	22	smaller	small	ADJ
iajs-2858	72	23	than	than	ADP
iajs-2858	72	24	or	or	CCONJ
iajs-2858	72	25	equal	equal	ADJ
iajs-2858	72	26	to	to	ADP
iajs-2858	72	27	.	.	PUNCT
iajs-2858	72	28	”	"	PUNCT
iajs-2858	73	1	≧	≧	PRON
iajs-2858	73	2	signifies	signify	VERB
iajs-2858	73	3	the	the	DET
iajs-2858	73	4	fuzzified	fuzzified	ADJ
iajs-2858	73	5	form	form	NOUN
iajs-2858	73	6	of	of	ADP
iajs-2858	73	7	≥	≥	NOUN
iajs-2858	73	8	and	and	CCONJ
iajs-2858	73	9	has	have	VERB
iajs-2858	73	10	the	the	DET
iajs-2858	73	11	linguistic	linguistic	ADJ
iajs-2858	73	12	interpretation	interpretation	NOUN
iajs-2858	73	13	"	"	PUNCT
iajs-2858	73	14	essentially	essentially	ADV
iajs-2858	73	15	greater	great	ADJ
iajs-2858	73	16	than	than	ADP
iajs-2858	73	17	or	or	CCONJ
iajs-2858	73	18	equal	equal	ADJ
iajs-2858	73	19	to	to	ADP
iajs-2858	73	20	.	.	PUNCT
iajs-2858	73	21	"	"	PUNCT
iajs-2858	74	1	the	the	DET
iajs-2858	74	2	objective	objective	ADJ
iajs-2858	74	3	function	function	NOUN
iajs-2858	74	4	of	of	ADP
iajs-2858	74	5	a	a	DET
iajs-2858	74	6	model	model	NOUN
iajs-2858	74	7	(	(	PUNCT
iajs-2858	74	8	1	1	X
iajs-2858	74	9	)	)	PUNCT
iajs-2858	74	10	might	might	AUX
iajs-2858	74	11	have	have	VERB
iajs-2858	74	12	to	to	PART
iajs-2858	74	13	be	be	AUX
iajs-2858	74	14	written	write	VERB
iajs-2858	74	15	as	as	ADP
iajs-2858	74	16	a	a	DET
iajs-2858	74	17	minimizing	minimize	VERB
iajs-2858	74	18	goal	goal	NOUN
iajs-2858	74	19	to	to	PART
iajs-2858	74	20	consider	consider	VERB
iajs-2858	74	21	z	z	NOUN
iajs-2858	74	22	as	as	ADP
iajs-2858	74	23	an	an	DET
iajs-2858	74	24	upper	upper	ADJ
iajs-2858	74	25	bound	bind	VERB
iajs-2858	74	26	founded	found	VERB
iajs-2858	74	27	by	by	ADP
iajs-2858	74	28	[	[	X
iajs-2858	74	29	13	13	NUM
iajs-2858	74	30	]	]	PUNCT
iajs-2858	74	31	.	.	PUNCT
iajs-2858	75	1	3.6	3.6	NUM
iajs-2858	75	2	.	.	PUNCT
iajs-2858	76	1	zimmermann	zimmermann	PROPN
iajs-2858	76	2	’s	’s	PART
iajs-2858	76	3	approach	approach	NOUN
iajs-2858	76	4	:	:	PUNCT
iajs-2858	76	5	a	a	DET
iajs-2858	76	6	symmetric	symmetric	ADJ
iajs-2858	76	7	model	model	NOUN
iajs-2858	76	8	principle	principle	NOUN
iajs-2858	76	9	for	for	ADP
iajs-2858	76	10	determining	determine	VERB
iajs-2858	76	11	the	the	DET
iajs-2858	76	12	fuzzy	fuzzy	ADJ
iajs-2858	76	13	choice	choice	NOUN
iajs-2858	76	14	to	to	PART
iajs-2858	76	15	solve	solve	VERB
iajs-2858	76	16	the	the	DET
iajs-2858	76	17	problem	problem	NOUN
iajs-2858	76	18	's	's	PART
iajs-2858	76	19	fuzzy	fuzzy	ADJ
iajs-2858	76	20	system	system	NOUN
iajs-2858	76	21	of	of	ADP
iajs-2858	76	22	inequalities	inequality	NOUN
iajs-2858	76	23	(	(	PUNCT
iajs-2858	76	24	fsi	fsi	PROPN
iajs-2858	76	25	)	)	PUNCT
iajs-2858	76	26	(	(	PUNCT
iajs-2858	76	27	1	1	NUM
iajs-2858	76	28	)	)	PUNCT
iajs-2858	76	29	.	.	PUNCT
iajs-2858	77	1	as	as	ADP
iajs-2858	77	2	a	a	DET
iajs-2858	77	3	result	result	NOUN
iajs-2858	77	4	,	,	PUNCT
iajs-2858	77	5	the	the	DET
iajs-2858	77	6	following	follow	VERB
iajs-2858	77	7	neat	neat	ADJ
iajs-2858	77	8	linear	linear	ADJ
iajs-2858	77	9	programming	programming	NOUN
iajs-2858	77	10	issue	issue	NOUN
iajs-2858	77	11	arises	arise	VERB
iajs-2858	77	12	.	.	PUNCT
iajs-2858	78	1	𝑀𝑎𝑥	𝑀𝑎𝑥	PROPN
iajs-2858	78	2	𝛼	𝛼	PROPN
iajs-2858	78	3	subject	subject	ADJ
iajs-2858	78	4	to	to	ADP
iajs-2858	78	5	,	,	PUNCT
iajs-2858	78	6	𝜇0(𝑐𝑇𝓍	𝜇0(𝑐𝑇𝓍	ADJ
iajs-2858	78	7	)	)	PUNCT
iajs-2858	78	8	=	=	SYM
iajs-2858	78	9	(	(	PUNCT
iajs-2858	78	10	1	1	NUM
iajs-2858	78	11	−	−	NOUN
iajs-2858	78	12	𝑧−𝑐𝑇	𝑧−𝑐𝑇	NOUN
iajs-2858	78	13	𝑝0	𝑝0	NOUN
iajs-2858	78	14	)	)	PUNCT
iajs-2858	78	15	≥	≥	NOUN
iajs-2858	78	16	𝛼	𝛼	PRON
iajs-2858	78	17	𝜇𝑖(𝐴𝑖𝓍	𝜇𝑖(𝐴𝑖𝓍	NOUN
iajs-2858	78	18	)	)	PUNCT
iajs-2858	78	19	=	=	PUNCT
iajs-2858	79	1	(	(	PUNCT
iajs-2858	79	2	1	1	NUM
iajs-2858	79	3	−	−	NOUN
iajs-2858	79	4	𝐴𝑖𝓍	𝐴𝑖𝓍	PROPN
iajs-2858	79	5	−𝑏𝑖	−𝑏𝑖	PROPN
iajs-2858	79	6	𝑝𝑖	𝑝𝑖	NOUN
iajs-2858	79	7	)	)	PUNCT
iajs-2858	79	8	≥	≥	NOUN
iajs-2858	79	9	𝛼	𝛼	NOUN
iajs-2858	79	10	,	,	PUNCT
iajs-2858	79	11	𝑖	𝑖	X
iajs-2858	79	12	=	=	NOUN
iajs-2858	79	13	1	1	NUM
iajs-2858	79	14	,	,	PUNCT
iajs-2858	79	15	…	…	PUNCT
iajs-2858	79	16	,	,	PUNCT
iajs-2858	79	17	𝑚	𝑚	X
iajs-2858	79	18	𝛼	𝛼	PRON
iajs-2858	79	19	∈	∈	NOUN
iajs-2858	80	1	[	[	X
iajs-2858	80	2	0,1	0,1	NUM
iajs-2858	80	3	]	]	X
iajs-2858	80	4	𝑥	𝑥	X
iajs-2858	80	5	≥	≥	NOUN
iajs-2858	80	6	0	0	NUM
iajs-2858	80	7	or	or	CCONJ
iajs-2858	80	8	𝑀𝑎𝑥	𝑀𝑎𝑥	PROPN
iajs-2858	80	9	𝛼	𝛼	NOUN
iajs-2858	80	10	subject	subject	ADJ
iajs-2858	80	11	to	to	ADP
iajs-2858	80	12	𝑐𝑗	𝑐𝑗	NOUN
iajs-2858	80	13	𝑇𝓍	𝑇𝓍	PROPN
iajs-2858	80	14	≥	≥	NUM
iajs-2858	80	15	𝑧0	𝑧0	NOUN
iajs-2858	80	16	−	−	PROPN
iajs-2858	80	17	(	(	PUNCT
iajs-2858	80	18	1	1	NUM
iajs-2858	80	19	−	−	PROPN
iajs-2858	80	20	𝛼)𝑝0	𝛼)𝑝0	PROPN
iajs-2858	80	21	𝐴𝑖𝓍	𝐴𝑖𝓍	PROPN
iajs-2858	80	22	≥	≥	NOUN
iajs-2858	80	23	𝑏𝑖	𝑏𝑖	ADP
iajs-2858	80	24	+	+	CCONJ
iajs-2858	80	25	(	(	PUNCT
iajs-2858	80	26	1	1	NUM
iajs-2858	80	27	−	−	PROPN
iajs-2858	80	28	𝛼)𝑝𝑖.	𝛼)𝑝𝑖.	NOUN
iajs-2858	80	29	,	,	PUNCT
iajs-2858	80	30	𝑖	𝑖	NOUN
iajs-2858	80	31	=	=	SYM
iajs-2858	80	32	1	1	NUM
iajs-2858	80	33	,	,	PUNCT
iajs-2858	80	34	…	…	PUNCT
iajs-2858	80	35	,	,	PUNCT
iajs-2858	80	36	𝑚	𝑚	X
iajs-2858	80	37	𝑥	𝑥	PRON
iajs-2858	80	38	≥	≥	NUM
iajs-2858	80	39	0	0	NUM
iajs-2858	80	40	,	,	PUNCT
iajs-2858	80	41	𝜆	𝜆	PROPN
iajs-2858	80	42	∈	∈	PROPN
iajs-2858	81	1	[	[	X
iajs-2858	81	2	0,1	0,1	NUM
iajs-2858	81	3	]	]	SYM
iajs-2858	81	4	4	4	NUM
iajs-2858	81	5	.	.	PUNCT
iajs-2858	81	6	modified	modify	VERB
iajs-2858	81	7	simplex	simplex	NOUN
iajs-2858	81	8	approach	approach	NOUN
iajs-2858	81	9	development	development	NOUN
iajs-2858	81	10	dantzig	dantzig	PROPN
iajs-2858	81	11	invented	invent	VERB
iajs-2858	81	12	the	the	DET
iajs-2858	81	13	simplex	simplex	NOUN
iajs-2858	81	14	approach	approach	NOUN
iajs-2858	81	15	in	in	ADP
iajs-2858	81	16	1947	1947	NUM
iajs-2858	81	17	.	.	PUNCT
iajs-2858	82	1	the	the	DET
iajs-2858	82	2	simplex	simplex	NOUN
iajs-2858	82	3	technique	technique	NOUN
iajs-2858	82	4	is	be	AUX
iajs-2858	82	5	a	a	DET
iajs-2858	82	6	systematic	systematic	ADJ
iajs-2858	82	7	approach	approach	NOUN
iajs-2858	82	8	that	that	PRON
iajs-2858	82	9	involves	involve	VERB
iajs-2858	82	10	moving	move	VERB
iajs-2858	82	11	from	from	ADP
iajs-2858	82	12	one	one	NUM
iajs-2858	82	13	basic	basic	ADJ
iajs-2858	82	14	variable	variable	ADJ
iajs-2858	82	15	solution	solution	NOUN
iajs-2858	82	16	(	(	PUNCT
iajs-2858	82	17	on	on	ADP
iajs-2858	82	18	the	the	DET
iajs-2858	82	19	vertex	vertex	NOUN
iajs-2858	82	20	)	)	PUNCT
iajs-2858	82	21	to	to	ADP
iajs-2858	82	22	another	another	PRON
iajs-2858	82	23	in	in	ADP
iajs-2858	82	24	a	a	DET
iajs-2858	82	25	predefined	predefine	VERB
iajs-2858	82	26	order	order	NOUN
iajs-2858	82	27	in	in	ADP
iajs-2858	82	28	order	order	NOUN
iajs-2858	82	29	to	to	PART
iajs-2858	82	30	elicit	elicit	VERB
iajs-2858	82	31	the	the	DET
iajs-2858	82	32	value	value	NOUN
iajs-2858	82	33	of	of	ADP
iajs-2858	82	34	the	the	DET
iajs-2858	82	35	objective	objective	ADJ
iajs-2858	82	36	function	function	NOUN
iajs-2858	82	37	.	.	PUNCT
iajs-2858	83	1	this	this	DET
iajs-2858	83	2	leaping	leap	VERB
iajs-2858	83	3	from	from	ADP
iajs-2858	83	4	vertex	vertex	NOUN
iajs-2858	83	5	to	to	ADP
iajs-2858	83	6	vertex	vertex	NOUN
iajs-2858	83	7	operation	operation	NOUN
iajs-2858	83	8	is	be	AUX
iajs-2858	83	9	repeated	repeat	VERB
iajs-2858	83	10	.	.	PUNCT
iajs-2858	84	1	if	if	SCONJ
iajs-2858	84	2	the	the	DET
iajs-2858	84	3	goal	goal	NOUN
iajs-2858	84	4	function	function	NOUN
iajs-2858	84	5	improves	improve	VERB
iajs-2858	84	6	with	with	ADP
iajs-2858	84	7	each	each	DET
iajs-2858	84	8	leap	leap	NOUN
iajs-2858	84	9	,	,	PUNCT
iajs-2858	84	10	no	no	DET
iajs-2858	84	11	basis	basis	NOUN
iajs-2858	84	12	will	will	AUX
iajs-2858	84	13	ever	ever	ADV
iajs-2858	84	14	be	be	AUX
iajs-2858	84	15	duplicated	duplicate	VERB
iajs-2858	84	16	,	,	PUNCT
iajs-2858	84	17	and	and	CCONJ
iajs-2858	84	18	there	there	PRON
iajs-2858	84	19	will	will	AUX
iajs-2858	84	20	be	be	AUX
iajs-2858	84	21	no	no	DET
iajs-2858	84	22	need	need	NOUN
iajs-2858	84	23	to	to	PART
iajs-2858	84	24	return	return	VERB
iajs-2858	84	25	to	to	ADP
iajs-2858	84	26	the	the	DET
iajs-2858	84	27	vertex	vertex	NOUN
iajs-2858	84	28	because	because	SCONJ
iajs-2858	84	29	it	it	PRON
iajs-2858	84	30	has	have	AUX
iajs-2858	84	31	already	already	ADV
iajs-2858	84	32	been	be	AUX
iajs-2858	84	33	covered	cover	VERB
iajs-2858	84	34	.	.	PUNCT
iajs-2858	85	1	the	the	DET
iajs-2858	85	2	algorithm	algorithm	NOUN
iajs-2858	85	3	must	must	AUX
iajs-2858	85	4	lead	lead	VERB
iajs-2858	85	5	to	to	ADP
iajs-2858	85	6	the	the	DET
iajs-2858	85	7	optimum	optimum	ADJ
iajs-2858	85	8	vertex	vertex	NOUN
iajs-2858	85	9	in	in	ADP
iajs-2858	85	10	a	a	DET
iajs-2858	85	11	finite	finite	ADJ
iajs-2858	85	12	number	number	NOUN
iajs-2858	85	13	of	of	ADP
iajs-2858	85	14	steps	step	NOUN
iajs-2858	85	15	since	since	SCONJ
iajs-2858	85	16	the	the	DET
iajs-2858	85	17	number	number	NOUN
iajs-2858	85	18	of	of	ADP
iajs-2858	85	19	vertices	vertex	NOUN
iajs-2858	85	20	is	be	AUX
iajs-2858	85	21	finite	finite	ADJ
iajs-2858	85	22	.	.	PUNCT
iajs-2858	86	1	(	(	PUNCT
iajs-2858	86	2	6	6	NUM
iajs-2858	86	3	)	)	PUNCT
iajs-2858	86	4	(	(	PUNCT
iajs-2858	86	5	5	5	X
iajs-2858	86	6	)	)	PUNCT
iajs-2858	86	7	ihjpas	ihjpa	NOUN
iajs-2858	86	8	.	.	PUNCT
iajs-2858	87	1	53	53	NUM
iajs-2858	87	2	(	(	PUNCT
iajs-2858	87	3	4)2022	4)2022	NOUN
iajs-2858	87	4	246	246	NUM
iajs-2858	87	5	for	for	ADP
iajs-2858	87	6	addressing	address	VERB
iajs-2858	87	7	linear	linear	ADJ
iajs-2858	87	8	programming	programming	NOUN
iajs-2858	87	9	problems	problem	NOUN
iajs-2858	87	10	,	,	PUNCT
iajs-2858	87	11	the	the	DET
iajs-2858	87	12	simplex	simplex	NOUN
iajs-2858	87	13	method	method	NOUN
iajs-2858	87	14	is	be	AUX
iajs-2858	87	15	an	an	DET
iajs-2858	87	16	iterative	iterative	NOUN
iajs-2858	87	17	(	(	PUNCT
iajs-2858	87	18	step	step	NOUN
iajs-2858	87	19	-	-	PUNCT
iajs-2858	87	20	by	by	ADP
iajs-2858	87	21	-	-	PUNCT
iajs-2858	87	22	step	step	NOUN
iajs-2858	87	23	)	)	PUNCT
iajs-2858	87	24	approach	approach	NOUN
iajs-2858	87	25	.	.	PUNCT
iajs-2858	88	1	it	it	PRON
iajs-2858	88	2	entails	entail	VERB
iajs-2858	88	3	the	the	DET
iajs-2858	88	4	following	following	NOUN
iajs-2858	88	5	:	:	PUNCT
iajs-2858	88	6	having	have	VERB
iajs-2858	88	7	a	a	DET
iajs-2858	88	8	fundamental	fundamental	ADJ
iajs-2858	88	9	workable	workable	ADJ
iajs-2858	88	10	solution	solution	NOUN
iajs-2858	88	11	to	to	ADP
iajs-2858	88	12	constraint	constraint	NOUN
iajs-2858	88	13	equations	equation	NOUN
iajs-2858	88	14	.	.	PUNCT
iajs-2858	89	1	ii	ii	X
iajs-2858	89	2	)	)	PUNCT
iajs-2858	89	3	determine	determine	VERB
iajs-2858	89	4	whether	whether	SCONJ
iajs-2858	89	5	it	it	PRON
iajs-2858	89	6	is	be	AUX
iajs-2858	89	7	the	the	DET
iajs-2858	89	8	best	good	ADJ
iajs-2858	89	9	option	option	NOUN
iajs-2858	89	10	.	.	PUNCT
iajs-2858	90	1	iii	iii	X
iajs-2858	90	2	)	)	PUNCT
iajs-2858	90	3	using	use	VERB
iajs-2858	90	4	a	a	DET
iajs-2858	90	5	set	set	NOUN
iajs-2858	90	6	of	of	ADP
iajs-2858	90	7	criteria	criterion	NOUN
iajs-2858	90	8	to	to	PART
iajs-2858	90	9	improve	improve	VERB
iajs-2858	90	10	the	the	DET
iajs-2858	90	11	initial	initial	ADJ
iajs-2858	90	12	trial	trial	NOUN
iajs-2858	90	13	solution	solution	NOUN
iajs-2858	90	14	and	and	CCONJ
iajs-2858	90	15	continuing	continue	VERB
iajs-2858	90	16	the	the	DET
iajs-2858	90	17	procedure	procedure	NOUN
iajs-2858	90	18	until	until	SCONJ
iajs-2858	90	19	an	an	DET
iajs-2858	90	20	ideal	ideal	ADJ
iajs-2858	90	21	solution	solution	NOUN
iajs-2858	90	22	is	be	AUX
iajs-2858	90	23	found	find	VERB
iajs-2858	90	24	.	.	PUNCT
iajs-2858	91	1	for	for	ADP
iajs-2858	91	2	more	more	ADJ
iajs-2858	91	3	details	detail	NOUN
iajs-2858	91	4	.	.	PUNCT
iajs-2858	92	1	4.1	4.1	NUM
iajs-2858	92	2	.	.	PUNCT
iajs-2858	92	3	modified	modify	VERB
iajs-2858	92	4	simplex	simplex	NOUN
iajs-2858	92	5	approach	approach	NOUN
iajs-2858	92	6	to	to	PART
iajs-2858	92	7	solve	solve	VERB
iajs-2858	92	8	quadratic	quadratic	ADJ
iajs-2858	92	9	fractional	fractional	ADJ
iajs-2858	92	10	programming	programming	NOUN
iajs-2858	92	11	problem	problem	NOUN
iajs-2858	92	12	this	this	DET
iajs-2858	92	13	section	section	NOUN
iajs-2858	92	14	deals	deal	VERB
iajs-2858	92	15	with	with	ADP
iajs-2858	92	16	the	the	DET
iajs-2858	92	17	solution	solution	NOUN
iajs-2858	92	18	of	of	ADP
iajs-2858	92	19	the	the	DET
iajs-2858	92	20	quadratic	quadratic	ADJ
iajs-2858	92	21	fractional	fractional	ADJ
iajs-2858	92	22	programming	programming	NOUN
iajs-2858	92	23	problem	problem	NOUN
iajs-2858	92	24	developed	develop	VERB
iajs-2858	92	25	by	by	ADP
iajs-2858	92	26	[	[	X
iajs-2858	92	27	17	17	NUM
iajs-2858	92	28	]	]	PUNCT
iajs-2858	92	29	,	,	PUNCT
iajs-2858	92	30	which	which	PRON
iajs-2858	92	31	the	the	DET
iajs-2858	92	32	solution	solution	NOUN
iajs-2858	92	33	procedure	procedure	NOUN
iajs-2858	92	34	has	have	VERB
iajs-2858	92	35	some	some	DET
iajs-2858	92	36	similarity	similarity	NOUN
iajs-2858	92	37	.	.	PUNCT
iajs-2858	93	1	this	this	DET
iajs-2858	93	2	technology	technology	NOUN
iajs-2858	93	3	can	can	AUX
iajs-2858	93	4	be	be	AUX
iajs-2858	93	5	used	use	VERB
iajs-2858	93	6	to	to	ADP
iajs-2858	93	7	high	high	ADJ
iajs-2858	93	8	-	-	PUNCT
iajs-2858	93	9	speed	speed	NOUN
iajs-2858	93	10	computing	computing	NOUN
iajs-2858	93	11	with	with	ADP
iajs-2858	93	12	success	success	NOUN
iajs-2858	93	13	.	.	PUNCT
iajs-2858	94	1	this	this	DET
iajs-2858	94	2	strategy	strategy	NOUN
iajs-2858	94	3	can	can	AUX
iajs-2858	94	4	be	be	AUX
iajs-2858	94	5	used	use	VERB
iajs-2858	94	6	if	if	SCONJ
iajs-2858	94	7	the	the	DET
iajs-2858	94	8	problem	problem	NOUN
iajs-2858	94	9	's	's	PART
iajs-2858	94	10	constraints	constraint	NOUN
iajs-2858	94	11	are	be	AUX
iajs-2858	94	12	linear	linear	NOUN
iajs-2858	94	13	functions	function	NOUN
iajs-2858	94	14	.	.	PUNCT
iajs-2858	95	1	i.e.	i.e.	X
iajs-2858	95	2	,	,	PUNCT
iajs-2858	95	3	the	the	DET
iajs-2858	95	4	issue	issue	NOUN
iajs-2858	95	5	is	be	AUX
iajs-2858	95	6	of	of	ADP
iajs-2858	95	7	the	the	DET
iajs-2858	95	8	following	following	ADJ
iajs-2858	95	9	existence	existence	NOUN
iajs-2858	95	10	:	:	PUNCT
iajs-2858	95	11	𝑀𝑎𝑥.	𝑀𝑎𝑥.	PROPN
iajs-2858	95	12	𝑧	𝑧	X
iajs-2858	95	13	(	(	PUNCT
iajs-2858	95	14	𝑜𝑟	𝑜𝑟	ADP
iajs-2858	95	15	𝑀𝑖𝑛.	𝑀𝑖𝑛.	PROPN
iajs-2858	95	16	𝑧	𝑧	PART
iajs-2858	95	17	)	)	PUNCT
iajs-2858	95	18	=	=	SYM
iajs-2858	95	19	(	(	PUNCT
iajs-2858	95	20	𝑐1	𝑐1	NOUN
iajs-2858	95	21	𝑇𝑥	𝑇𝑥	ADP
iajs-2858	95	22	+	+	CCONJ
iajs-2858	95	23	𝛼)(𝑐2	𝛼)(𝑐2	ADV
iajs-2858	95	24	𝑇𝑥	𝑇𝑥	ADP
iajs-2858	95	25	+	+	NUM
iajs-2858	95	26	𝛽	𝛽	NOUN
iajs-2858	95	27	)	)	PUNCT
iajs-2858	95	28	(	(	PUNCT
iajs-2858	95	29	𝑒1	𝑒1	NOUN
iajs-2858	95	30	𝑇𝑥	𝑇𝑥	ADP
iajs-2858	95	31	+	+	NUM
iajs-2858	95	32	𝛾)(𝑒2	𝛾)(𝑒2	PROPN
iajs-2858	95	33	𝑇	𝑇	PROPN
iajs-2858	95	34	+	+	CCONJ
iajs-2858	95	35	𝛿	𝛿	ADJ
iajs-2858	95	36	)	)	PUNCT
iajs-2858	95	37	subject	subject	NOUN
iajs-2858	95	38	to	to	ADP
iajs-2858	95	39	:	:	PUNCT
iajs-2858	95	40	𝐴𝑥	𝐴𝑥	NOUN
iajs-2858	95	41	(	(	PUNCT
iajs-2858	95	42	≤	≤	X
iajs-2858	95	43	≥	≥	NOUN
iajs-2858	95	44	=	=	SYM
iajs-2858	95	45	)	)	PUNCT
iajs-2858	96	1	𝑏	𝑏	PRON
iajs-2858	96	2	𝑥	𝑥	PRON
iajs-2858	96	3	≥	≥	NOUN
iajs-2858	96	4	0	0	NUM
iajs-2858	96	5	𝐴	𝐴	PROPN
iajs-2858	96	6	is	be	AUX
iajs-2858	96	7	𝑚	𝑚	PROPN
iajs-2858	96	8	×	×	NOUN
iajs-2858	96	9	𝑛	𝑛	DET
iajs-2858	96	10	matrix	matrix	NOUN
iajs-2858	96	11	;	;	PUNCT
iajs-2858	96	12	𝑥	𝑥	X
iajs-2858	96	13	,	,	PUNCT
iajs-2858	96	14	𝑐1	𝑐1	NOUN
iajs-2858	96	15	,	,	PUNCT
iajs-2858	96	16	𝑐1	𝑐1	NOUN
iajs-2858	96	17	,	,	PUNCT
iajs-2858	96	18	𝑒1	𝑒1	NOUN
iajs-2858	96	19	and	and	CCONJ
iajs-2858	96	20	𝑒2	𝑒2	NOUN
iajs-2858	96	21	are	be	AUX
iajs-2858	96	22	𝑛	𝑛	DET
iajs-2858	96	23	×	×	PROPN
iajs-2858	96	24	1	1	NUM
iajs-2858	96	25	column	column	NOUN
iajs-2858	96	26	vectors	vector	NOUN
iajs-2858	96	27	;	;	PUNCT
iajs-2858	96	28	𝑏	𝑏	PRON
iajs-2858	96	29	is	be	AUX
iajs-2858	96	30	𝑚	𝑚	PROPN
iajs-2858	96	31	×	×	PROPN
iajs-2858	96	32	1	1	NUM
iajs-2858	96	33	column	column	NOUN
iajs-2858	96	34	vectors	vector	NOUN
iajs-2858	96	35	;	;	PUNCT
iajs-2858	96	36	𝛼	𝛼	X
iajs-2858	96	37	,	,	PUNCT
iajs-2858	96	38	𝛽	𝛽	NOUN
iajs-2858	96	39	,	,	PUNCT
iajs-2858	96	40	𝛿	𝛿	PRON
iajs-2858	96	41	are	be	AUX
iajs-2858	96	42	𝛾	𝛾	ADP
iajs-2858	96	43	scalars	scalar	NOUN
iajs-2858	96	44	and	and	CCONJ
iajs-2858	96	45	prime	prime	ADJ
iajs-2858	96	46	(	(	PUNCT
iajs-2858	96	47	𝑇	𝑇	PROPN
iajs-2858	96	48	)	)	PUNCT
iajs-2858	96	49	denoted	denote	VERB
iajs-2858	96	50	the	the	DET
iajs-2858	96	51	transpose	transpose	NOUN
iajs-2858	96	52	of	of	ADP
iajs-2858	96	53	the	the	DET
iajs-2858	96	54	vector	vector	NOUN
iajs-2858	96	55	.	.	PUNCT
iajs-2858	97	1	where	where	SCONJ
iajs-2858	97	2	𝑧1	𝑧1	NOUN
iajs-2858	97	3	=	=	INTJ
iajs-2858	97	4	(	(	PUNCT
iajs-2858	97	5	𝑐1	𝑐1	NOUN
iajs-2858	97	6	𝑇𝑥	𝑇𝑥	ADP
iajs-2858	97	7	+	+	CCONJ
iajs-2858	97	8	𝛼)(𝑐2	𝛼)(𝑐2	ADV
iajs-2858	97	9	𝑇𝑥	𝑇𝑥	ADP
iajs-2858	97	10	+	+	NOUN
iajs-2858	97	11	𝛽	𝛽	NOUN
iajs-2858	97	12	)	)	PUNCT
iajs-2858	97	13	𝑧2	𝑧2	NOUN
iajs-2858	97	14	=	=	SYM
iajs-2858	97	15	(	(	PUNCT
iajs-2858	97	16	𝑒1	𝑒1	NOUN
iajs-2858	97	17	𝑇𝑥	𝑇𝑥	ADP
iajs-2858	97	18	+	+	NUM
iajs-2858	97	19	𝛾)(𝑒2	𝛾)(𝑒2	PROPN
iajs-2858	97	20	𝑇	𝑇	PROPN
iajs-2858	97	21	+	+	CCONJ
iajs-2858	97	22	𝛿	𝛿	X
iajs-2858	97	23	)	)	PUNCT
iajs-2858	97	24	and	and	CCONJ
iajs-2858	97	25	supposed	suppose	VERB
iajs-2858	97	26	𝑧1	𝑧1	NOUN
iajs-2858	97	27	1	1	NUM
iajs-2858	97	28	=	=	SYM
iajs-2858	97	29	(	(	PUNCT
iajs-2858	97	30	𝑐1	𝑐1	NOUN
iajs-2858	97	31	𝑇𝑥	𝑇𝑥	ADP
iajs-2858	97	32	+	+	CCONJ
iajs-2858	97	33	𝛼	𝛼	X
iajs-2858	97	34	)	)	PUNCT
iajs-2858	97	35	𝑧1	𝑧1	NOUN
iajs-2858	97	36	2	2	NUM
iajs-2858	97	37	=	=	SYM
iajs-2858	97	38	(	(	PUNCT
iajs-2858	97	39	𝑐2	𝑐2	NOUN
iajs-2858	97	40	𝑇𝑥	𝑇𝑥	NOUN
iajs-2858	97	41	+	+	CCONJ
iajs-2858	97	42	𝛽	𝛽	NOUN
iajs-2858	97	43	)	)	PUNCT
iajs-2858	97	44	𝑧2	𝑧2	NOUN
iajs-2858	97	45	1	1	NUM
iajs-2858	97	46	=	=	SYM
iajs-2858	97	47	(	(	PUNCT
iajs-2858	97	48	𝑒1	𝑒1	NOUN
iajs-2858	97	49	𝑇𝑥	𝑇𝑥	ADP
iajs-2858	97	50	+	+	CCONJ
iajs-2858	97	51	𝛾	𝛾	NOUN
iajs-2858	97	52	)	)	PUNCT
iajs-2858	97	53	𝑧2	𝑧2	NOUN
iajs-2858	97	54	2	2	NUM
iajs-2858	97	55	=	=	SYM
iajs-2858	97	56	(	(	PUNCT
iajs-2858	97	57	𝑒2	𝑒2	PROPN
iajs-2858	97	58	𝑇	𝑇	PROPN
iajs-2858	97	59	+	+	CCONJ
iajs-2858	97	60	𝛿	𝛿	X
iajs-2858	97	61	)	)	PUNCT
iajs-2858	97	62	to	to	PART
iajs-2858	97	63	apply	apply	VERB
iajs-2858	97	64	simplex	simplex	NOUN
iajs-2858	97	65	process	process	NOUN
iajs-2858	97	66	,	,	PUNCT
iajs-2858	97	67	first	first	ADJ
iajs-2858	97	68	∆𝑗1	∆𝑗1	PROPN
iajs-2858	97	69	and	and	CCONJ
iajs-2858	97	70	∆𝑗2need	∆𝑗2need	NUM
iajs-2858	97	71	to	to	PART
iajs-2858	97	72	be	be	AUX
iajs-2858	97	73	found	find	VERB
iajs-2858	97	74	from	from	ADP
iajs-2858	97	75	the	the	DET
iajs-2858	97	76	coefficients	coefficient	NOUN
iajs-2858	97	77	of	of	ADP
iajs-2858	97	78	the	the	DET
iajs-2858	97	79	first	first	ADJ
iajs-2858	97	80	linear	linear	PROPN
iajs-2858	97	81	vector	vector	NOUN
iajs-2858	97	82	and	and	CCONJ
iajs-2858	97	83	second	second	ADJ
iajs-2858	97	84	linear	linear	ADJ
iajs-2858	97	85	vector	vector	NOUN
iajs-2858	97	86	of	of	ADP
iajs-2858	97	87	objective	objective	ADJ
iajs-2858	97	88	function	function	NOUN
iajs-2858	97	89	respectively	respectively	ADV
iajs-2858	97	90	,	,	PUNCT
iajs-2858	97	91	by	by	ADP
iajs-2858	97	92	using	use	VERB
iajs-2858	97	93	the	the	DET
iajs-2858	97	94	following	follow	VERB
iajs-2858	97	95	formula	formula	NOUN
iajs-2858	97	96	:	:	PUNCT
iajs-2858	97	97	∆𝑖𝑗=	∆𝑖𝑗=	NOUN
iajs-2858	97	98	𝑐𝑖𝑗	𝑐𝑖𝑗	NOUN
iajs-2858	98	1	−	−	PROPN
iajs-2858	98	2	𝑐𝐵𝑖𝑥𝑖𝑗	𝑐𝐵𝑖𝑥𝑖𝑗	PROPN
iajs-2858	98	3	,	,	PUNCT
iajs-2858	98	4	𝑖	𝑖	SYM
iajs-2858	98	5	=	=	SYM
iajs-2858	98	6	1	1	NUM
iajs-2858	98	7	,	,	PUNCT
iajs-2858	98	8	2	2	NUM
iajs-2858	98	9	.	.	X
iajs-2858	99	1	𝑗	𝑗	NOUN
iajs-2858	99	2	=	=	ADJ
iajs-2858	99	3	1	1	NUM
iajs-2858	99	4	,	,	PUNCT
iajs-2858	99	5	2	2	NUM
iajs-2858	99	6	,	,	PUNCT
iajs-2858	99	7	…	…	PUNCT
iajs-2858	99	8	,	,	PUNCT
iajs-2858	99	9	𝑚	𝑚	X
iajs-2858	99	10	+	+	NOUN
iajs-2858	99	11	𝑛	𝑛	DET
iajs-2858	99	12	𝑧1	𝑧1	NOUN
iajs-2858	99	13	=	=	SYM
iajs-2858	99	14	𝑧1	𝑧1	NOUN
iajs-2858	99	15	(	(	PUNCT
iajs-2858	99	16	1)𝑧1	1)𝑧1	NUM
iajs-2858	99	17	(	(	PUNCT
iajs-2858	99	18	2	2	NUM
iajs-2858	99	19	)	)	PUNCT
iajs-2858	99	20	ihjpas	ihjpa	NOUN
iajs-2858	99	21	.	.	PUNCT
iajs-2858	100	1	53	53	NUM
iajs-2858	100	2	(	(	PUNCT
iajs-2858	100	3	4)2022	4)2022	NOUN
iajs-2858	100	4	247	247	NUM
iajs-2858	100	5	𝑧2	𝑧2	NOUN
iajs-2858	100	6	=	=	PROPN
iajs-2858	100	7	𝑧2	𝑧2	PROPN
iajs-2858	100	8	(	(	PUNCT
iajs-2858	100	9	1)𝑧2	1)𝑧2	NUM
iajs-2858	100	10	(	(	PUNCT
iajs-2858	100	11	2	2	NUM
iajs-2858	100	12	)	)	PUNCT
iajs-2858	100	13	𝑧	𝑧	NOUN
iajs-2858	100	14	=	=	ADJ
iajs-2858	100	15	𝑧1/𝑧2	𝑧1/𝑧2	PROPN
iajs-2858	100	16	the	the	DET
iajs-2858	100	17	values	value	NOUN
iajs-2858	100	18	of	of	ADP
iajs-2858	100	19	objective	objective	ADJ
iajs-2858	100	20	functions	function	NOUN
iajs-2858	100	21	in	in	ADP
iajs-2858	100	22	this	this	DET
iajs-2858	100	23	approach	approach	NOUN
iajs-2858	100	24	the	the	DET
iajs-2858	100	25	formula	formula	NOUN
iajs-2858	100	26	is	be	AUX
iajs-2858	100	27	defined	define	VERB
iajs-2858	100	28	to	to	PART
iajs-2858	100	29	find	find	VERB
iajs-2858	100	30	∆𝑗	∆𝑗	PROPN
iajs-2858	100	31	from	from	ADP
iajs-2858	100	32	∆𝜉1𝑗	∆𝜉1𝑗	PROPN
iajs-2858	100	33	,	,	PUNCT
iajs-2858	100	34	∆𝜉2𝑗	∆𝜉2𝑗	ADJ
iajs-2858	100	35	,	,	PUNCT
iajs-2858	100	36	𝑧1	𝑧1	NOUN
iajs-2858	100	37	,	,	PUNCT
iajs-2858	100	38	𝑧2	𝑧2	NOUN
iajs-2858	100	39	following	following	NOUN
iajs-2858	100	40	:	:	PUNCT
iajs-2858	100	41	∆𝑗=	∆𝑗=	X
iajs-2858	100	42	𝑧1∆𝜉1𝑗	𝑧1∆𝜉1𝑗	NOUN
iajs-2858	100	43	+	+	CCONJ
iajs-2858	100	44	𝑧2∆𝜉2𝑗.	𝑧2∆𝜉2𝑗.	PROPN
iajs-2858	100	45	5	5	NUM
iajs-2858	100	46	.	.	PUNCT
iajs-2858	100	47	modify	modify	VERB
iajs-2858	100	48	symmetric	symmetric	ADJ
iajs-2858	100	49	fuzzy	fuzzy	ADJ
iajs-2858	100	50	approach	approach	NOUN
iajs-2858	100	51	(	(	PUNCT
iajs-2858	100	52	msfa	msfa	NOUN
iajs-2858	100	53	)	)	PUNCT
iajs-2858	100	54	to	to	PART
iajs-2858	100	55	solve	solve	VERB
iajs-2858	100	56	quadratic	quadratic	ADJ
iajs-2858	100	57	fractional	fractional	ADJ
iajs-2858	100	58	programming	programming	NOUN
iajs-2858	100	59	problems	problem	NOUN
iajs-2858	100	60	our	our	PRON
iajs-2858	100	61	modified	modified	ADJ
iajs-2858	100	62	approach	approach	NOUN
iajs-2858	100	63	depends	depend	VERB
iajs-2858	100	64	on	on	ADP
iajs-2858	100	65	the	the	DET
iajs-2858	100	66	adopted	adopt	VERB
iajs-2858	100	67	"	"	PUNCT
iajs-2858	100	68	fuzzy	fuzzy	ADJ
iajs-2858	100	69	"	"	PUNCT
iajs-2858	100	70	version	version	NOUN
iajs-2858	100	71	of	of	ADP
iajs-2858	100	72	formula	formula	NOUN
iajs-2858	100	73	(	(	PUNCT
iajs-2858	100	74	4	4	NUM
iajs-2858	100	75	)	)	PUNCT
iajs-2858	100	76	is	be	AUX
iajs-2858	100	77	:	:	PUNCT
iajs-2858	100	78	find	find	VERB
iajs-2858	100	79	𝑥	𝑥	PRON
iajs-2858	100	80	such	such	ADJ
iajs-2858	100	81	that	that	SCONJ
iajs-2858	100	82	(	(	PUNCT
iajs-2858	100	83	𝑐1	𝑐1	NOUN
iajs-2858	100	84	𝑇𝑥+𝛼)(𝑐2	𝑇𝑥+𝛼)(𝑐2	PROPN
iajs-2858	100	85	𝑇𝑥+𝛽	𝑇𝑥+𝛽	PROPN
iajs-2858	100	86	)	)	PUNCT
iajs-2858	100	87	(	(	PUNCT
iajs-2858	100	88	𝑒1	𝑒1	NOUN
iajs-2858	100	89	𝑇𝑥+𝛾)(𝑒2	𝑇𝑥+𝛾)(𝑒2	NOUN
iajs-2858	100	90	𝑇+𝛿	𝑇+𝛿	NOUN
iajs-2858	100	91	)	)	PUNCT
iajs-2858	100	92	≳	≳	NOUN
iajs-2858	100	93	(	(	PUNCT
iajs-2858	100	94	𝑤1)(𝑤2	𝑤1)(𝑤2	NOUN
iajs-2858	100	95	)	)	PUNCT
iajs-2858	100	96	(	(	PUNCT
iajs-2858	100	97	𝑤3)(𝑤4	𝑤3)(𝑤4	X
iajs-2858	100	98	)	)	PUNCT
iajs-2858	101	1	𝐴𝑥	𝐴𝑥	PRON
iajs-2858	101	2	≲	≲	PROPN
iajs-2858	101	3	𝑏	𝑏	PROPN
iajs-2858	101	4	𝑥	𝑥	PRON
iajs-2858	101	5	≧	≧	NOUN
iajs-2858	101	6	0	0	PUNCT
iajs-2858	101	7	here	here	ADV
iajs-2858	101	8	𝑐1	𝑐1	NOUN
iajs-2858	101	9	,	,	PUNCT
iajs-2858	101	10	𝑐2	𝑐2	NOUN
iajs-2858	101	11	,	,	PUNCT
iajs-2858	101	12	𝑒1and	𝑒1and	PROPN
iajs-2858	101	13	𝑒2	𝑒2	PROPN
iajs-2858	101	14	are	be	AUX
iajs-2858	101	15	the	the	DET
iajs-2858	101	16	vector	vector	NOUN
iajs-2858	101	17	of	of	ADP
iajs-2858	101	18	coefficients	coefficient	NOUN
iajs-2858	101	19	of	of	ADP
iajs-2858	101	20	numerator	numerator	NOUN
iajs-2858	101	21	and	and	CCONJ
iajs-2858	101	22	denominator	denominator	NOUN
iajs-2858	101	23	respectively	respectively	ADV
iajs-2858	101	24	of	of	ADP
iajs-2858	101	25	the	the	DET
iajs-2858	101	26	ratio	ratio	NOUN
iajs-2858	101	27	of	of	ADP
iajs-2858	101	28	the	the	DET
iajs-2858	101	29	goal	goal	NOUN
iajs-2858	101	30	function	function	NOUN
iajs-2858	101	31	,	,	PUNCT
iajs-2858	101	32	𝑏	𝑏	PROPN
iajs-2858	101	33	denoted	denote	VERB
iajs-2858	101	34	as	as	ADP
iajs-2858	101	35	a	a	DET
iajs-2858	101	36	vector	vector	NOUN
iajs-2858	101	37	of	of	ADP
iajs-2858	101	38	constraints	constraint	NOUN
iajs-2858	101	39	,	,	PUNCT
iajs-2858	101	40	and	and	CCONJ
iajs-2858	101	41	𝐴	𝐴	PROPN
iajs-2858	101	42	is	be	AUX
iajs-2858	101	43	the	the	DET
iajs-2858	101	44	factor	factor	NOUN
iajs-2858	101	45	of	of	ADP
iajs-2858	101	46	matrix	matrix	NOUN
iajs-2858	101	47	.	.	PUNCT
iajs-2858	102	1	the	the	DET
iajs-2858	102	2	sign	sign	NOUN
iajs-2858	102	3	"	"	PUNCT
iajs-2858	102	4	≲	≲	PROPN
iajs-2858	102	5	"	"	PUNCT
iajs-2858	102	6	indicate	indicate	VERB
iajs-2858	102	7	the	the	DET
iajs-2858	102	8	fuzzified	fuzzified	ADJ
iajs-2858	102	9	type	type	NOUN
iajs-2858	102	10	of	of	ADP
iajs-2858	102	11	"	"	PUNCT
iajs-2858	102	12	≦	≦	PROPN
iajs-2858	102	13	"	"	PUNCT
iajs-2858	102	14	and	and	CCONJ
iajs-2858	102	15	read	read	VERB
iajs-2858	102	16	out	out	ADP
iajs-2858	102	17	"	"	PUNCT
iajs-2858	102	18	basically	basically	ADV
iajs-2858	102	19	smaller	small	ADJ
iajs-2858	102	20	than	than	ADP
iajs-2858	102	21	or	or	CCONJ
iajs-2858	102	22	commensurate	commensurate	ADJ
iajs-2858	102	23	to	to	ADP
iajs-2858	102	24	"	"	PUNCT
iajs-2858	102	25	.	.	PUNCT
iajs-2858	103	1	note	note	VERB
iajs-2858	103	2	that	that	SCONJ
iajs-2858	103	3	(	(	PUNCT
iajs-2858	103	4	7	7	X
iajs-2858	103	5	)	)	PUNCT
iajs-2858	103	6	is	be	AUX
iajs-2858	103	7	wholly	wholly	ADV
iajs-2858	103	8	symmetric	symmetric	ADJ
iajs-2858	103	9	with	with	ADP
iajs-2858	103	10	observance	observance	NOUN
iajs-2858	103	11	to	to	ADP
iajs-2858	103	12	goal	goal	NOUN
iajs-2858	103	13	function	function	NOUN
iajs-2858	103	14	and	and	CCONJ
iajs-2858	103	15	constraints	constraint	NOUN
iajs-2858	103	16	,	,	PUNCT
iajs-2858	103	17	to	to	PART
iajs-2858	103	18	solve	solve	VERB
iajs-2858	103	19	the	the	DET
iajs-2858	103	20	above	above	ADJ
iajs-2858	103	21	problem	problem	NOUN
iajs-2858	103	22	,	,	PUNCT
iajs-2858	103	23	first	first	ADV
iajs-2858	103	24	choose	choose	VERB
iajs-2858	103	25	an	an	DET
iajs-2858	103	26	appropriate	appropriate	ADJ
iajs-2858	103	27	membership	membership	NOUN
iajs-2858	103	28	function	function	NOUN
iajs-2858	103	29	for	for	ADP
iajs-2858	103	30	each	each	PRON
iajs-2858	103	31	of	of	ADP
iajs-2858	103	32	the	the	DET
iajs-2858	103	33	fuzzy	fuzzy	ADJ
iajs-2858	103	34	inequality	inequality	NOUN
iajs-2858	103	35	of	of	ADP
iajs-2858	103	36	(	(	PUNCT
iajs-2858	103	37	7	7	NUM
iajs-2858	103	38	)	)	PUNCT
iajs-2858	103	39	.	.	PUNCT
iajs-2858	104	1	in	in	ADP
iajs-2858	104	2	particular	particular	ADJ
iajs-2858	104	3	,	,	PUNCT
iajs-2858	104	4	let	let	VERB
iajs-2858	104	5	𝑓0	𝑓0	PROPN
iajs-2858	104	6	denote	denote	VERB
iajs-2858	104	7	the	the	DET
iajs-2858	104	8	membership	membership	NOUN
iajs-2858	104	9	function	function	NOUN
iajs-2858	104	10	for	for	ADP
iajs-2858	104	11	objective	objective	ADJ
iajs-2858	104	12	function	function	NOUN
iajs-2858	104	13	and	and	CCONJ
iajs-2858	104	14	𝑓𝑖	𝑓𝑖	PROPN
iajs-2858	104	15	,	,	PUNCT
iajs-2858	104	16	𝑖	𝑖	PROPN
iajs-2858	104	17	=	=	NOUN
iajs-2858	104	18	1	1	NUM
iajs-2858	104	19	,	,	PUNCT
iajs-2858	104	20	…	…	PUNCT
iajs-2858	104	21	,	,	PUNCT
iajs-2858	104	22	𝑚	𝑚	PROPN
iajs-2858	104	23	denote	denote	VERB
iajs-2858	104	24	the	the	DET
iajs-2858	104	25	membership	membership	NOUN
iajs-2858	104	26	function	function	NOUN
iajs-2858	104	27	for	for	ADP
iajs-2858	104	28	constraint	constraint	NOUN
iajs-2858	104	29	,	,	PUNCT
iajs-2858	104	30	let	let	VERB
iajs-2858	104	31	𝑝0	𝑝0	NOUN
iajs-2858	104	32	and	and	CCONJ
iajs-2858	104	33	𝑝𝑖	𝑝𝑖	VERB
iajs-2858	104	34	,	,	PUNCT
iajs-2858	104	35	𝑖	𝑖	NOUN
iajs-2858	104	36	=	=	NOUN
iajs-2858	104	37	1	1	NUM
iajs-2858	104	38	,	,	PUNCT
iajs-2858	104	39	…	…	PUNCT
iajs-2858	104	40	,	,	PUNCT
iajs-2858	104	41	𝑚	𝑚	X
iajs-2858	104	42	be	be	AUX
iajs-2858	104	43	the	the	DET
iajs-2858	104	44	permissible	permissible	ADJ
iajs-2858	104	45	tolerances	tolerance	NOUN
iajs-2858	104	46	for	for	ADP
iajs-2858	104	47	objective	objective	ADJ
iajs-2858	104	48	function	function	NOUN
iajs-2858	104	49	and	and	CCONJ
iajs-2858	104	50	constraint	constraint	NOUN
iajs-2858	104	51	and	and	CCONJ
iajs-2858	104	52	let	let	VERB
iajs-2858	104	53	𝑓0	𝑓0	NOUN
iajs-2858	104	54	and	and	CCONJ
iajs-2858	104	55	𝑓𝑖	𝑓𝑖	VERB
iajs-2858	104	56	,	,	PUNCT
iajs-2858	104	57	𝑖	𝑖	PROPN
iajs-2858	104	58	=	=	NOUN
iajs-2858	104	59	1	1	NUM
iajs-2858	104	60	,	,	PUNCT
iajs-2858	104	61	…	…	PUNCT
iajs-2858	104	62	,	,	PUNCT
iajs-2858	104	63	𝑚	𝑚	X
iajs-2858	104	64	be	be	AUX
iajs-2858	104	65	a	a	DET
iajs-2858	104	66	continuous	continuous	ADJ
iajs-2858	104	67	and	and	CCONJ
iajs-2858	104	68	nondecreasing	nondecreasing	ADJ
iajs-2858	104	69	linear	linear	ADJ
iajs-2858	104	70	membership	membership	NOUN
iajs-2858	104	71	which	which	PRON
iajs-2858	104	72	is	be	AUX
iajs-2858	104	73	explained	explain	VERB
iajs-2858	104	74	below	below	ADV
iajs-2858	104	75	:	:	PUNCT
iajs-2858	104	76	we	we	PRON
iajs-2858	104	77	have	have	VERB
iajs-2858	104	78	two	two	NUM
iajs-2858	104	79	cases	case	NOUN
iajs-2858	104	80	that	that	PRON
iajs-2858	104	81	include	include	VERB
iajs-2858	104	82	only	only	ADV
iajs-2858	104	83	for	for	ADP
iajs-2858	104	84	𝑓0	𝑓0	PROPN
iajs-2858	104	85	:	:	PUNCT
iajs-2858	104	86	first	first	ADJ
iajs-2858	104	87	case	case	NOUN
iajs-2858	104	88	if	if	SCONJ
iajs-2858	104	89	(	(	PUNCT
iajs-2858	104	90	𝑤3)(𝑤4	𝑤3)(𝑤4	NOUN
iajs-2858	104	91	)	)	PUNCT
iajs-2858	104	92	>	>	X
iajs-2858	104	93	(	(	PUNCT
iajs-2858	104	94	𝑤1)(𝑤2	𝑤1)(𝑤2	NOUN
iajs-2858	104	95	)	)	PUNCT
iajs-2858	104	96	𝑓0(𝑐𝑇𝓍	𝑓0(𝑐𝑇𝓍	PROPN
iajs-2858	104	97	)	)	PUNCT
iajs-2858	104	98	=	=	PRON
iajs-2858	104	99	{	{	PUNCT
iajs-2858	104	100	1	1	NUM
iajs-2858	104	101	1−(((𝑤1)(𝑤2)−(𝑤3)(𝑤4	1−(((𝑤1)(𝑤2)−(𝑤3)(𝑤4	NUM
iajs-2858	104	102	)	)	PUNCT
iajs-2858	104	103	)	)	PUNCT
iajs-2858	104	104	−((𝑐1	−((𝑐1	PROPN
iajs-2858	104	105	𝑇𝑥+𝛼)(𝑐2	𝑇𝑥+𝛼)(𝑐2	PROPN
iajs-2858	104	106	𝑇𝑥+𝛽)−(𝑒1	𝑇𝑥+𝛽)−(𝑒1	PROPN
iajs-2858	104	107	𝑇𝑥+𝛾)(𝑒2	𝑇𝑥+𝛾)(𝑒2	NUM
iajs-2858	104	108	𝑇+𝛿	𝑇+𝛿	NOUN
iajs-2858	104	109	)	)	PUNCT
iajs-2858	104	110	)	)	PUNCT
iajs-2858	104	111	)	)	PUNCT
iajs-2858	105	1	𝑝0	𝑝0	NOUN
iajs-2858	105	2	0	0	NUM
iajs-2858	105	3	𝑓𝑜𝑟	𝑓𝑜𝑟	ADV
iajs-2858	105	4	(	(	PUNCT
iajs-2858	105	5	(	(	PUNCT
iajs-2858	105	6	𝑐1	𝑐1	NOUN
iajs-2858	105	7	𝑇𝑥	𝑇𝑥	ADP
iajs-2858	105	8	+	+	CCONJ
iajs-2858	105	9	𝛼)(𝑐2	𝛼)(𝑐2	ADV
iajs-2858	105	10	𝑇𝑥	𝑇𝑥	ADP
iajs-2858	105	11	+	+	NUM
iajs-2858	105	12	𝛽	𝛽	NOUN
iajs-2858	105	13	)	)	PUNCT
iajs-2858	105	14	−	−	PROPN
iajs-2858	105	15	(	(	PUNCT
iajs-2858	105	16	𝑒1	𝑒1	NOUN
iajs-2858	105	17	𝑇𝑥	𝑇𝑥	ADP
iajs-2858	105	18	+	+	NUM
iajs-2858	105	19	𝛾)(𝑒2	𝛾)(𝑒2	PROPN
iajs-2858	105	20	𝑇	𝑇	PROPN
iajs-2858	105	21	+	+	CCONJ
iajs-2858	105	22	𝛿	𝛿	NOUN
iajs-2858	105	23	)	)	PUNCT
iajs-2858	105	24	)	)	PUNCT
iajs-2858	105	25	>	>	PUNCT
iajs-2858	106	1	(	(	PUNCT
iajs-2858	106	2	(	(	PUNCT
iajs-2858	106	3	𝑤1)(𝑤2	𝑤1)(𝑤2	NOUN
iajs-2858	106	4	)	)	PUNCT
iajs-2858	106	5	−	−	PROPN
iajs-2858	106	6	(	(	PUNCT
iajs-2858	106	7	𝑤3)(𝑤4	𝑤3)(𝑤4	NUM
iajs-2858	106	8	)	)	PUNCT
iajs-2858	106	9	)	)	PUNCT
iajs-2858	107	1	𝑓𝑜𝑟	𝑓𝑜𝑟	ADV
iajs-2858	107	2	(	(	PUNCT
iajs-2858	107	3	(	(	PUNCT
iajs-2858	107	4	𝑤1)(𝑤2	𝑤1)(𝑤2	NOUN
iajs-2858	107	5	)	)	PUNCT
iajs-2858	107	6	−	−	PROPN
iajs-2858	107	7	(	(	PUNCT
iajs-2858	107	8	𝑤3)(𝑤4	𝑤3)(𝑤4	NUM
iajs-2858	107	9	)	)	PUNCT
iajs-2858	107	10	)	)	PUNCT
iajs-2858	108	1	−	−	ADP
iajs-2858	108	2	𝑝0	𝑝0	NOUN
iajs-2858	108	3	≤	≤	NOUN
iajs-2858	108	4	(	(	PUNCT
iajs-2858	108	5	(	(	PUNCT
iajs-2858	108	6	𝑐1	𝑐1	NOUN
iajs-2858	108	7	𝑇𝑥	𝑇𝑥	ADP
iajs-2858	108	8	+	+	CCONJ
iajs-2858	108	9	𝛼)(𝑐2	𝛼)(𝑐2	ADV
iajs-2858	108	10	𝑇𝑥	𝑇𝑥	ADP
iajs-2858	108	11	+	+	NUM
iajs-2858	108	12	𝛽	𝛽	NOUN
iajs-2858	108	13	)	)	PUNCT
iajs-2858	108	14	−	−	PROPN
iajs-2858	108	15	(	(	PUNCT
iajs-2858	108	16	𝑒1	𝑒1	NOUN
iajs-2858	108	17	𝑇𝑥	𝑇𝑥	ADP
iajs-2858	108	18	+	+	NUM
iajs-2858	108	19	𝛾)(𝑒2	𝛾)(𝑒2	PROPN
iajs-2858	108	20	𝑇	𝑇	PROPN
iajs-2858	108	21	+	+	CCONJ
iajs-2858	108	22	𝛿	𝛿	ADJ
iajs-2858	108	23	)	)	PUNCT
iajs-2858	108	24	)	)	PUNCT
iajs-2858	108	25	≤	≤	NOUN
iajs-2858	108	26	(	(	PUNCT
iajs-2858	108	27	(	(	PUNCT
iajs-2858	108	28	𝑤1)(𝑤2	𝑤1)(𝑤2	NOUN
iajs-2858	108	29	)	)	PUNCT
iajs-2858	108	30	−	−	PROPN
iajs-2858	108	31	(	(	PUNCT
iajs-2858	108	32	𝑤3)(𝑤4	𝑤3)(𝑤4	NUM
iajs-2858	108	33	)	)	PUNCT
iajs-2858	108	34	)	)	PUNCT
iajs-2858	109	1	𝑓𝑜𝑟	𝑓𝑜𝑟	ADV
iajs-2858	109	2	(	(	PUNCT
iajs-2858	109	3	(	(	PUNCT
iajs-2858	109	4	𝑐1	𝑐1	NOUN
iajs-2858	109	5	𝑇𝑥	𝑇𝑥	ADP
iajs-2858	109	6	+	+	CCONJ
iajs-2858	109	7	𝛼)(𝑐2	𝛼)(𝑐2	ADV
iajs-2858	109	8	𝑇𝑥	𝑇𝑥	ADP
iajs-2858	109	9	+	+	NUM
iajs-2858	109	10	𝛽	𝛽	NOUN
iajs-2858	109	11	)	)	PUNCT
iajs-2858	109	12	−	−	PROPN
iajs-2858	109	13	(	(	PUNCT
iajs-2858	109	14	𝑒1	𝑒1	NOUN
iajs-2858	109	15	𝑇𝑥	𝑇𝑥	ADP
iajs-2858	109	16	+	+	NUM
iajs-2858	109	17	𝛾)(𝑒2	𝛾)(𝑒2	PROPN
iajs-2858	109	18	𝑇	𝑇	PROPN
iajs-2858	109	19	+	+	CCONJ
iajs-2858	109	20	𝛿	𝛿	NOUN
iajs-2858	109	21	)	)	PUNCT
iajs-2858	109	22	)	)	PUNCT
iajs-2858	109	23	<	<	X
iajs-2858	109	24	(	(	PUNCT
iajs-2858	109	25	(	(	PUNCT
iajs-2858	109	26	𝑤1)(𝑤2	𝑤1)(𝑤2	NOUN
iajs-2858	109	27	)	)	PUNCT
iajs-2858	109	28	−	−	PROPN
iajs-2858	109	29	(	(	PUNCT
iajs-2858	109	30	𝑤3)(𝑤4	𝑤3)(𝑤4	NUM
iajs-2858	109	31	)	)	PUNCT
iajs-2858	109	32	)	)	PUNCT
iajs-2858	110	1	−	−	ADP
iajs-2858	110	2	𝑝0	𝑝0	NOUN
iajs-2858	110	3	with	with	ADP
iajs-2858	110	4	𝑓𝑖(𝐴𝑖𝓍	𝑓𝑖(𝐴𝑖𝓍	ADJ
iajs-2858	110	5	)	)	PUNCT
iajs-2858	110	6	=	=	PRON
iajs-2858	110	7	{	{	PUNCT
iajs-2858	110	8	1	1	NUM
iajs-2858	110	9	1−(𝐴𝑖𝓍	1−(𝐴𝑖𝓍	NUM
iajs-2858	110	10	−𝑏𝑖	−𝑏𝑖	NOUN
iajs-2858	110	11	)	)	PUNCT
iajs-2858	110	12	𝑝𝑖	𝑝𝑖	NOUN
iajs-2858	110	13	0	0	NUM
iajs-2858	111	1	𝑓𝑜𝑟	𝑓𝑜𝑟	NOUN
iajs-2858	112	1	𝐴𝑖𝓍	𝐴𝑖𝓍	PROPN
iajs-2858	112	2	<	<	X
iajs-2858	112	3	𝑏𝑖	𝑏𝑖	ADP
iajs-2858	112	4	𝑓𝑜𝑟	𝑓𝑜𝑟	ADP
iajs-2858	112	5	𝑏𝑖	𝑏𝑖	ADP
iajs-2858	112	6	≤	≤	NUM
iajs-2858	112	7	𝐴𝑖𝓍	𝐴𝑖𝓍	PROPN
iajs-2858	112	8	≤	≤	NOUN
iajs-2858	112	9	𝑏𝑖	𝑏𝑖	ADP
iajs-2858	112	10	𝑓𝑜𝑟	𝑓𝑜𝑟	ADV
iajs-2858	112	11	𝐴𝑖𝓍	𝐴𝑖𝓍	PROPN
iajs-2858	112	12	>	>	X
iajs-2858	112	13	𝑏𝑖	𝑏𝑖	PROPN
iajs-2858	112	14	+	+	NUM
iajs-2858	112	15	𝑝𝑖	𝑝𝑖	NOUN
iajs-2858	112	16	+	+	NOUN
iajs-2858	112	17	𝑝𝑖	𝑝𝑖	NOUN
iajs-2858	112	18	,	,	PUNCT
iajs-2858	112	19	i	i	PRON
iajs-2858	112	20	=	=	NOUN
iajs-2858	112	21	1	1	NUM
iajs-2858	112	22	,	,	PUNCT
iajs-2858	112	23	…	…	PUNCT
iajs-2858	112	24	,	,	PUNCT
iajs-2858	112	25	m	m	VERB
iajs-2858	112	26	now	now	ADV
iajs-2858	112	27	,	,	PUNCT
iajs-2858	112	28	in	in	ADP
iajs-2858	112	29	order	order	NOUN
iajs-2858	112	30	to	to	PART
iajs-2858	112	31	solve	solve	VERB
iajs-2858	112	32	the	the	DET
iajs-2858	112	33	problem	problem	NOUN
iajs-2858	112	34	we	we	PRON
iajs-2858	112	35	dentify	dentify	VERB
iajs-2858	112	36	the	the	DET
iajs-2858	112	37	fuzzy	fuzzy	ADJ
iajs-2858	112	38	decision	decision	NOUN
iajs-2858	112	39	as	as	ADP
iajs-2858	112	40	following	follow	VERB
iajs-2858	112	41	approach	approach	NOUN
iajs-2858	112	42	:	:	PUNCT
iajs-2858	112	43	the	the	DET
iajs-2858	112	44	crisp	crisp	ADJ
iajs-2858	112	45	linear	linear	NOUN
iajs-2858	112	46	programming	programming	NOUN
iajs-2858	112	47	denoted	denote	VERB
iajs-2858	112	48	by	by	ADP
iajs-2858	112	49	(	(	PUNCT
iajs-2858	112	50	𝐿𝑃)(𝑓,𝜆	𝐿𝑃)(𝑓,𝜆	NUM
iajs-2858	112	51	)	)	PUNCT
iajs-2858	112	52	is	be	AUX
iajs-2858	112	53	:	:	PUNCT
iajs-2858	112	54	in	in	ADP
iajs-2858	112	55	case	case	NOUN
iajs-2858	112	56	(	(	PUNCT
iajs-2858	112	57	𝑤3)(𝑤4	𝑤3)(𝑤4	NUM
iajs-2858	112	58	)	)	PUNCT
iajs-2858	112	59	>	>	X
iajs-2858	112	60	(	(	PUNCT
iajs-2858	112	61	𝑤1)(𝑤2	𝑤1)(𝑤2	NOUN
iajs-2858	112	62	)	)	PUNCT
iajs-2858	112	63	we	we	PRON
iajs-2858	112	64	have	have	VERB
iajs-2858	112	65	:	:	PUNCT
iajs-2858	112	66	𝑀𝑎𝑥	𝑀𝑎𝑥	PROPN
iajs-2858	112	67	𝜆	𝜆	ADV
iajs-2858	112	68	subject	subject	NOUN
iajs-2858	112	69	to	to	ADP
iajs-2858	112	70	,	,	PUNCT
iajs-2858	112	71	(	(	PUNCT
iajs-2858	112	72	7	7	NUM
iajs-2858	112	73	)	)	PUNCT
iajs-2858	112	74	(	(	PUNCT
iajs-2858	112	75	9	9	NUM
iajs-2858	112	76	)	)	PUNCT
iajs-2858	112	77	(	(	PUNCT
iajs-2858	112	78	8)	8)	NUM
iajs-2858	112	79	ihjpas	ihjpa	NOUN
iajs-2858	112	80	.	.	PUNCT
iajs-2858	113	1	53	53	NUM
iajs-2858	113	2	(	(	PUNCT
iajs-2858	113	3	4)2022	4)2022	NOUN
iajs-2858	113	4	248	248	NUM
iajs-2858	113	5	𝑓0(𝑐𝑇𝓍	𝑓0(𝑐𝑇𝓍	NOUN
iajs-2858	113	6	)	)	PUNCT
iajs-2858	113	7	=	=	SYM
iajs-2858	113	8	(	(	PUNCT
iajs-2858	113	9	1−(((𝑤1)(𝑤2)−(𝑤3)(𝑤4	1−(((𝑤1)(𝑤2)−(𝑤3)(𝑤4	NUM
iajs-2858	113	10	)	)	PUNCT
iajs-2858	113	11	)	)	PUNCT
iajs-2858	113	12	−((𝑐1	−((𝑐1	PROPN
iajs-2858	113	13	𝑇𝑥+𝛼)(𝑐2	𝑇𝑥+𝛼)(𝑐2	PROPN
iajs-2858	113	14	𝑇𝑥+𝛽)−(𝑒1	𝑇𝑥+𝛽)−(𝑒1	PROPN
iajs-2858	113	15	𝑇𝑥+𝛾)(𝑒2	𝑇𝑥+𝛾)(𝑒2	NUM
iajs-2858	113	16	𝑇+𝛿	𝑇+𝛿	NOUN
iajs-2858	113	17	)	)	PUNCT
iajs-2858	113	18	)	)	PUNCT
iajs-2858	113	19	)	)	PUNCT
iajs-2858	113	20	𝑝0	𝑝0	NOUN
iajs-2858	113	21	)	)	PUNCT
iajs-2858	113	22	≥	≥	PROPN
iajs-2858	113	23	𝜆	𝜆	PROPN
iajs-2858	113	24	𝑓𝑖(𝐴𝑖𝓍	𝑓𝑖(𝐴𝑖𝓍	PROPN
iajs-2858	113	25	)	)	PUNCT
iajs-2858	113	26	=	=	PUNCT
iajs-2858	114	1	(	(	PUNCT
iajs-2858	114	2	1−(𝐴𝑖𝓍	1−(𝐴𝑖𝓍	NUM
iajs-2858	114	3	−𝑏𝑖	−𝑏𝑖	NOUN
iajs-2858	114	4	)	)	PUNCT
iajs-2858	114	5	𝑝𝑖	𝑝𝑖	PROPN
iajs-2858	114	6	)	)	PUNCT
iajs-2858	114	7	≥	≥	PROPN
iajs-2858	114	8	𝜆	𝜆	NOUN
iajs-2858	114	9	,	,	PUNCT
iajs-2858	114	10	𝑖	𝑖	SYM
iajs-2858	114	11	=	=	SYM
iajs-2858	114	12	1	1	NUM
iajs-2858	114	13	,	,	PUNCT
iajs-2858	114	14	…	…	PUNCT
iajs-2858	114	15	,	,	PUNCT
iajs-2858	114	16	𝑚	𝑚	X
iajs-2858	114	17	𝜆	𝜆	PRON
iajs-2858	114	18	∈	∈	PROPN
iajs-2858	115	1	[	[	X
iajs-2858	115	2	0,1	0,1	NUM
iajs-2858	115	3	]	]	X
iajs-2858	115	4	𝑥	𝑥	X
iajs-2858	115	5	≥	≥	NOUN
iajs-2858	115	6	0	0	NUM
iajs-2858	115	7	or	or	CCONJ
iajs-2858	115	8	𝑀𝑎𝑥	𝑀𝑎𝑥	PROPN
iajs-2858	115	9	𝜆	𝜆	ADV
iajs-2858	115	10	subject	subject	NOUN
iajs-2858	115	11	to	to	ADP
iajs-2858	115	12	,	,	PUNCT
iajs-2858	115	13	(	(	PUNCT
iajs-2858	115	14	(	(	PUNCT
iajs-2858	115	15	𝑤1)(𝑤2	𝑤1)(𝑤2	NOUN
iajs-2858	115	16	)	)	PUNCT
iajs-2858	115	17	−	−	PROPN
iajs-2858	115	18	(	(	PUNCT
iajs-2858	115	19	𝑤3)(𝑤4	𝑤3)(𝑤4	NUM
iajs-2858	115	20	)	)	PUNCT
iajs-2858	115	21	)	)	PUNCT
iajs-2858	116	1	≤	≤	ADV
iajs-2858	116	2	1	1	NUM
iajs-2858	116	3	−	−	NOUN
iajs-2858	116	4	𝜆𝑝0	𝜆𝑝0	NOUN
iajs-2858	117	1	−	−	PROPN
iajs-2858	118	1	(	(	PUNCT
iajs-2858	118	2	(	(	PUNCT
iajs-2858	118	3	𝑐1	𝑐1	NOUN
iajs-2858	118	4	𝑇𝑥	𝑇𝑥	ADP
iajs-2858	118	5	+	+	CCONJ
iajs-2858	118	6	𝛼)(𝑐2	𝛼)(𝑐2	ADV
iajs-2858	118	7	𝑇𝑥	𝑇𝑥	ADP
iajs-2858	118	8	+	+	NUM
iajs-2858	118	9	𝛽	𝛽	NOUN
iajs-2858	118	10	)	)	PUNCT
iajs-2858	118	11	−	−	PROPN
iajs-2858	118	12	(	(	PUNCT
iajs-2858	118	13	𝑒1	𝑒1	NOUN
iajs-2858	118	14	𝑇𝑥	𝑇𝑥	ADP
iajs-2858	118	15	+	+	NUM
iajs-2858	118	16	𝛾)(𝑒2	𝛾)(𝑒2	PROPN
iajs-2858	118	17	𝑇	𝑇	PROPN
iajs-2858	118	18	+	+	CCONJ
iajs-2858	118	19	𝛿	𝛿	ADJ
iajs-2858	118	20	)	)	PUNCT
iajs-2858	118	21	)	)	PUNCT
iajs-2858	118	22	∑	∑	PUNCT
iajs-2858	118	23	𝑎𝑖𝑘𝑥𝑘	𝑎𝑖𝑘𝑥𝑘	VERB
iajs-2858	118	24	𝑛	𝑛	PRON
iajs-2858	118	25	𝑖=1	𝑖=1	PUNCT
iajs-2858	118	26	≤	≤	NOUN
iajs-2858	119	1	𝑏𝑘	𝑏𝑘	ADP
iajs-2858	119	2	+	+	CCONJ
iajs-2858	119	3	1	1	NUM
iajs-2858	119	4	−	−	NOUN
iajs-2858	119	5	𝜆(𝑝𝑘	𝜆(𝑝𝑘	PROPN
iajs-2858	119	6	)	)	PUNCT
iajs-2858	119	7	,	,	PUNCT
iajs-2858	119	8	𝑘	𝑘	X
iajs-2858	119	9	=	=	SYM
iajs-2858	119	10	1	1	NUM
iajs-2858	119	11	,	,	PUNCT
iajs-2858	119	12	…	…	PUNCT
iajs-2858	119	13	,	,	PUNCT
iajs-2858	119	14	𝑚	𝑚	X
iajs-2858	119	15	𝜆	𝜆	X
iajs-2858	119	16	,	,	PUNCT
iajs-2858	119	17	𝑥𝑘	𝑥𝑘	X
iajs-2858	119	18	≥	≥	NOUN
iajs-2858	119	19	0	0	NUM
iajs-2858	119	20	,	,	PUNCT
iajs-2858	119	21	𝑘	𝑘	X
iajs-2858	119	22	=	=	NOUN
iajs-2858	119	23	1	1	NUM
iajs-2858	119	24	,	,	PUNCT
iajs-2858	119	25	…	…	PUNCT
iajs-2858	119	26	,	,	PUNCT
iajs-2858	119	27	𝑚.	𝑚.	ADJ
iajs-2858	119	28	second	second	ADJ
iajs-2858	119	29	case	case	NOUN
iajs-2858	119	30	if	if	SCONJ
iajs-2858	119	31	(	(	PUNCT
iajs-2858	119	32	𝑤3)(𝑤4	𝑤3)(𝑤4	NOUN
iajs-2858	119	33	)	)	PUNCT
iajs-2858	119	34	<	<	X
iajs-2858	119	35	(	(	PUNCT
iajs-2858	119	36	𝑤1)(𝑤2	𝑤1)(𝑤2	NOUN
iajs-2858	119	37	)	)	PUNCT
iajs-2858	119	38	𝑓0(𝑐𝑇𝓍	𝑓0(𝑐𝑇𝓍	PROPN
iajs-2858	119	39	)	)	PUNCT
iajs-2858	119	40	=	=	PRON
iajs-2858	119	41	{	{	PUNCT
iajs-2858	119	42	1	1	NUM
iajs-2858	119	43	1−(((𝑤3)(𝑤4)−(𝑤1)(𝑤2	1−(((𝑤3)(𝑤4)−(𝑤1)(𝑤2	NUM
iajs-2858	119	44	)	)	PUNCT
iajs-2858	119	45	)	)	PUNCT
iajs-2858	120	1	−((𝑐1	−((𝑐1	PROPN
iajs-2858	120	2	𝑇𝑥+𝛼)(𝑐2	𝑇𝑥+𝛼)(𝑐2	PROPN
iajs-2858	120	3	𝑇𝑥+𝛽)−(𝑒1	𝑇𝑥+𝛽)−(𝑒1	PROPN
iajs-2858	120	4	𝑇𝑥+𝛾)(𝑒2	𝑇𝑥+𝛾)(𝑒2	NUM
iajs-2858	120	5	𝑇+𝛿	𝑇+𝛿	NOUN
iajs-2858	120	6	)	)	PUNCT
iajs-2858	120	7	)	)	PUNCT
iajs-2858	120	8	)	)	PUNCT
iajs-2858	121	1	𝑝0	𝑝0	NOUN
iajs-2858	121	2	0	0	NUM
iajs-2858	121	3	𝑓𝑜𝑟	𝑓𝑜𝑟	ADV
iajs-2858	121	4	(	(	PUNCT
iajs-2858	121	5	(	(	PUNCT
iajs-2858	121	6	𝑐1	𝑐1	NOUN
iajs-2858	121	7	𝑇𝑥	𝑇𝑥	ADP
iajs-2858	121	8	+	+	CCONJ
iajs-2858	121	9	𝛼)(𝑐2	𝛼)(𝑐2	ADV
iajs-2858	121	10	𝑇𝑥	𝑇𝑥	ADP
iajs-2858	121	11	+	+	NUM
iajs-2858	121	12	𝛽	𝛽	NOUN
iajs-2858	121	13	)	)	PUNCT
iajs-2858	121	14	−	−	PROPN
iajs-2858	121	15	(	(	PUNCT
iajs-2858	121	16	𝑒1	𝑒1	NOUN
iajs-2858	121	17	𝑇𝑥	𝑇𝑥	ADP
iajs-2858	121	18	+	+	NUM
iajs-2858	121	19	𝛾)(𝑒2	𝛾)(𝑒2	PROPN
iajs-2858	121	20	𝑇	𝑇	PROPN
iajs-2858	121	21	+	+	CCONJ
iajs-2858	121	22	𝛿	𝛿	NOUN
iajs-2858	121	23	)	)	PUNCT
iajs-2858	121	24	)	)	PUNCT
iajs-2858	121	25	>	>	PUNCT
iajs-2858	121	26	(	(	PUNCT
iajs-2858	121	27	(	(	PUNCT
iajs-2858	121	28	𝑤3)(𝑤4	𝑤3)(𝑤4	NOUN
iajs-2858	121	29	)	)	PUNCT
iajs-2858	121	30	−	−	PROPN
iajs-2858	121	31	(	(	PUNCT
iajs-2858	121	32	𝑤1)(𝑤2	𝑤1)(𝑤2	NOUN
iajs-2858	121	33	)	)	PUNCT
iajs-2858	121	34	)	)	PUNCT
iajs-2858	122	1	𝑓𝑜𝑟	𝑓𝑜𝑟	ADV
iajs-2858	122	2	(	(	PUNCT
iajs-2858	122	3	(	(	PUNCT
iajs-2858	122	4	𝑤3)(𝑤4	𝑤3)(𝑤4	NOUN
iajs-2858	122	5	)	)	PUNCT
iajs-2858	122	6	−	−	PROPN
iajs-2858	122	7	(	(	PUNCT
iajs-2858	122	8	𝑤1)(𝑤2	𝑤1)(𝑤2	NOUN
iajs-2858	122	9	)	)	PUNCT
iajs-2858	122	10	)	)	PUNCT
iajs-2858	123	1	−𝑝0	−𝑝0	PROPN
iajs-2858	123	2	≤	≤	NOUN
iajs-2858	123	3	(	(	PUNCT
iajs-2858	123	4	(	(	PUNCT
iajs-2858	123	5	𝑐1	𝑐1	NOUN
iajs-2858	123	6	𝑇𝑥	𝑇𝑥	ADP
iajs-2858	123	7	+	+	CCONJ
iajs-2858	123	8	𝛼)(𝑐2	𝛼)(𝑐2	ADV
iajs-2858	123	9	𝑇𝑥	𝑇𝑥	ADP
iajs-2858	123	10	+	+	NUM
iajs-2858	123	11	𝛽	𝛽	NOUN
iajs-2858	123	12	)	)	PUNCT
iajs-2858	123	13	−	−	PROPN
iajs-2858	123	14	(	(	PUNCT
iajs-2858	123	15	𝑒1	𝑒1	NOUN
iajs-2858	123	16	𝑇𝑥	𝑇𝑥	ADP
iajs-2858	123	17	+	+	NUM
iajs-2858	123	18	𝛾)(𝑒2	𝛾)(𝑒2	PROPN
iajs-2858	123	19	𝑇	𝑇	PROPN
iajs-2858	123	20	+	+	CCONJ
iajs-2858	123	21	𝛿	𝛿	ADJ
iajs-2858	123	22	)	)	PUNCT
iajs-2858	123	23	)	)	PUNCT
iajs-2858	123	24	≤	≤	NOUN
iajs-2858	123	25	(	(	PUNCT
iajs-2858	123	26	(	(	PUNCT
iajs-2858	123	27	𝑤3)(𝑤4	𝑤3)(𝑤4	NOUN
iajs-2858	123	28	)	)	PUNCT
iajs-2858	123	29	−	−	PROPN
iajs-2858	123	30	(	(	PUNCT
iajs-2858	123	31	𝑤1)(𝑤2	𝑤1)(𝑤2	NOUN
iajs-2858	123	32	)	)	PUNCT
iajs-2858	123	33	)	)	PUNCT
iajs-2858	124	1	𝑓𝑜𝑟	𝑓𝑜𝑟	ADV
iajs-2858	124	2	(	(	PUNCT
iajs-2858	124	3	(	(	PUNCT
iajs-2858	124	4	𝑐1	𝑐1	NOUN
iajs-2858	124	5	𝑇𝑥	𝑇𝑥	ADP
iajs-2858	124	6	+	+	CCONJ
iajs-2858	124	7	𝛼)(𝑐2	𝛼)(𝑐2	ADV
iajs-2858	124	8	𝑇𝑥	𝑇𝑥	ADP
iajs-2858	124	9	+	+	NUM
iajs-2858	124	10	𝛽	𝛽	NOUN
iajs-2858	124	11	)	)	PUNCT
iajs-2858	124	12	−	−	PROPN
iajs-2858	124	13	(	(	PUNCT
iajs-2858	124	14	𝑒1	𝑒1	NOUN
iajs-2858	124	15	𝑇𝑥	𝑇𝑥	ADP
iajs-2858	124	16	+	+	NUM
iajs-2858	124	17	𝛾)(𝑒2	𝛾)(𝑒2	PROPN
iajs-2858	124	18	𝑇	𝑇	PROPN
iajs-2858	124	19	+	+	CCONJ
iajs-2858	124	20	𝛿	𝛿	NOUN
iajs-2858	124	21	)	)	PUNCT
iajs-2858	124	22	)	)	PUNCT
iajs-2858	124	23	<	<	X
iajs-2858	124	24	(	(	PUNCT
iajs-2858	124	25	(	(	PUNCT
iajs-2858	124	26	𝑤3)(𝑤4	𝑤3)(𝑤4	NOUN
iajs-2858	124	27	)	)	PUNCT
iajs-2858	124	28	−	−	PROPN
iajs-2858	124	29	(	(	PUNCT
iajs-2858	124	30	𝑤1)(𝑤2	𝑤1)(𝑤2	NOUN
iajs-2858	124	31	)	)	PUNCT
iajs-2858	124	32	)	)	PUNCT
iajs-2858	125	1	−	−	ADP
iajs-2858	125	2	𝑝0	𝑝0	NOUN
iajs-2858	125	3	with	with	ADP
iajs-2858	125	4	𝑓𝑖(𝐴𝑖𝓍	𝑓𝑖(𝐴𝑖𝓍	ADJ
iajs-2858	125	5	)	)	PUNCT
iajs-2858	125	6	=	=	PRON
iajs-2858	125	7	{	{	PUNCT
iajs-2858	125	8	1	1	NUM
iajs-2858	125	9	1−(𝐴𝑖𝓍	1−(𝐴𝑖𝓍	NUM
iajs-2858	125	10	−𝑏𝑖	−𝑏𝑖	NOUN
iajs-2858	125	11	)	)	PUNCT
iajs-2858	125	12	𝑝𝑖	𝑝𝑖	NOUN
iajs-2858	125	13	0	0	NUM
iajs-2858	126	1	𝑓𝑜𝑟	𝑓𝑜𝑟	NOUN
iajs-2858	127	1	𝐴𝑖𝓍	𝐴𝑖𝓍	PROPN
iajs-2858	127	2	<	<	X
iajs-2858	127	3	𝑏𝑖	𝑏𝑖	ADP
iajs-2858	127	4	𝑓𝑜𝑟	𝑓𝑜𝑟	ADP
iajs-2858	127	5	𝑏𝑖	𝑏𝑖	ADP
iajs-2858	127	6	≤	≤	NUM
iajs-2858	127	7	𝐴𝑖𝓍	𝐴𝑖𝓍	PROPN
iajs-2858	127	8	≤	≤	NOUN
iajs-2858	127	9	𝑏𝑖	𝑏𝑖	ADP
iajs-2858	127	10	𝑓𝑜𝑟	𝑓𝑜𝑟	ADV
iajs-2858	127	11	𝐴𝑖𝓍	𝐴𝑖𝓍	PROPN
iajs-2858	127	12	>	>	X
iajs-2858	127	13	𝑏𝑖	𝑏𝑖	PROPN
iajs-2858	127	14	+	+	NUM
iajs-2858	127	15	𝑝𝑖	𝑝𝑖	NOUN
iajs-2858	127	16	+	+	NOUN
iajs-2858	127	17	𝑝𝑖	𝑝𝑖	NOUN
iajs-2858	127	18	,	,	PUNCT
iajs-2858	127	19	i	i	PRON
iajs-2858	127	20	=	=	NOUN
iajs-2858	127	21	1	1	NUM
iajs-2858	127	22	,	,	PUNCT
iajs-2858	127	23	…	…	PUNCT
iajs-2858	127	24	,	,	PUNCT
iajs-2858	127	25	m	m	VERB
iajs-2858	127	26	now	now	ADV
iajs-2858	127	27	,	,	PUNCT
iajs-2858	127	28	in	in	ADP
iajs-2858	127	29	order	order	NOUN
iajs-2858	127	30	to	to	PART
iajs-2858	127	31	solve	solve	VERB
iajs-2858	127	32	the	the	DET
iajs-2858	127	33	problem	problem	NOUN
iajs-2858	127	34	we	we	PRON
iajs-2858	127	35	identify	identify	VERB
iajs-2858	127	36	the	the	DET
iajs-2858	127	37	fuzzy	fuzzy	ADJ
iajs-2858	127	38	decision	decision	NOUN
iajs-2858	127	39	as	as	ADP
iajs-2858	127	40	following	follow	VERB
iajs-2858	127	41	approach	approach	NOUN
iajs-2858	127	42	:	:	PUNCT
iajs-2858	127	43	the	the	DET
iajs-2858	127	44	crisp	crisp	ADJ
iajs-2858	127	45	linear	linear	NOUN
iajs-2858	127	46	programming	programming	NOUN
iajs-2858	127	47	denoted	denote	VERB
iajs-2858	127	48	by	by	ADP
iajs-2858	127	49	(	(	PUNCT
iajs-2858	127	50	𝐿𝑃)(𝑓,𝜆	𝐿𝑃)(𝑓,𝜆	NUM
iajs-2858	127	51	)	)	PUNCT
iajs-2858	127	52	is	be	AUX
iajs-2858	127	53	:	:	PUNCT
iajs-2858	127	54	in	in	ADP
iajs-2858	127	55	case	case	NOUN
iajs-2858	127	56	(	(	PUNCT
iajs-2858	127	57	𝑤3)(𝑤4	𝑤3)(𝑤4	NUM
iajs-2858	127	58	)	)	PUNCT
iajs-2858	127	59	<	<	X
iajs-2858	127	60	(	(	PUNCT
iajs-2858	127	61	𝑤1)(𝑤2	𝑤1)(𝑤2	NOUN
iajs-2858	127	62	)	)	PUNCT
iajs-2858	127	63	we	we	PRON
iajs-2858	127	64	have	have	VERB
iajs-2858	127	65	:	:	PUNCT
iajs-2858	127	66	𝑀𝑎𝑥	𝑀𝑎𝑥	PROPN
iajs-2858	127	67	𝜆	𝜆	ADV
iajs-2858	127	68	subject	subject	ADJ
iajs-2858	127	69	to	to	ADP
iajs-2858	127	70	,	,	PUNCT
iajs-2858	127	71	𝑓0(𝑐𝑇𝓍	𝑓0(𝑐𝑇𝓍	PROPN
iajs-2858	127	72	)	)	PUNCT
iajs-2858	127	73	=	=	SYM
iajs-2858	127	74	(	(	PUNCT
iajs-2858	127	75	1−(((𝑤3)(𝑤4)−(𝑤1)(𝑤2))−((𝑐1	1−(((𝑤3)(𝑤4)−(𝑤1)(𝑤2))−((𝑐1	NUM
iajs-2858	127	76	𝑇𝓍+𝛽)−(𝑐2	𝑇𝓍+𝛽)−(𝑐2	PROPN
iajs-2858	127	77	𝑇𝑥+𝛿	𝑇𝑥+𝛿	PROPN
iajs-2858	127	78	)	)	PUNCT
iajs-2858	127	79	)	)	PUNCT
iajs-2858	127	80	)	)	PUNCT
iajs-2858	128	1	𝑝0	𝑝0	NOUN
iajs-2858	128	2	)	)	PUNCT
iajs-2858	128	3	≥	≥	PROPN
iajs-2858	128	4	𝜆	𝜆	PROPN
iajs-2858	128	5	𝑓𝑖(𝐴𝑖𝓍	𝑓𝑖(𝐴𝑖𝓍	PROPN
iajs-2858	128	6	)	)	PUNCT
iajs-2858	128	7	=	=	PUNCT
iajs-2858	129	1	(	(	PUNCT
iajs-2858	129	2	1−(𝐴𝑖𝓍	1−(𝐴𝑖𝓍	NUM
iajs-2858	129	3	−𝑏𝑖	−𝑏𝑖	NOUN
iajs-2858	129	4	)	)	PUNCT
iajs-2858	129	5	𝑝𝑖	𝑝𝑖	PROPN
iajs-2858	129	6	)	)	PUNCT
iajs-2858	129	7	≥	≥	PROPN
iajs-2858	129	8	𝜆	𝜆	NOUN
iajs-2858	129	9	,	,	PUNCT
iajs-2858	129	10	𝑖	𝑖	SYM
iajs-2858	129	11	=	=	SYM
iajs-2858	129	12	1	1	NUM
iajs-2858	129	13	,	,	PUNCT
iajs-2858	129	14	…	…	PUNCT
iajs-2858	129	15	,	,	PUNCT
iajs-2858	129	16	𝑚	𝑚	X
iajs-2858	129	17	𝜆	𝜆	PRON
iajs-2858	129	18	∈	∈	PROPN
iajs-2858	130	1	[	[	X
iajs-2858	130	2	0,1	0,1	NUM
iajs-2858	130	3	]	]	PUNCT
iajs-2858	130	4	,	,	PUNCT
iajs-2858	130	5	𝑥	𝑥	PROPN
iajs-2858	130	6	≥	≥	NOUN
iajs-2858	130	7	0	0	NUM
iajs-2858	130	8	or	or	CCONJ
iajs-2858	130	9	(	(	PUNCT
iajs-2858	130	10	10	10	NUM
iajs-2858	130	11	)	)	PUNCT
iajs-2858	130	12	(	(	PUNCT
iajs-2858	130	13	11	11	NUM
iajs-2858	130	14	)	)	PUNCT
iajs-2858	130	15	(	(	PUNCT
iajs-2858	130	16	12	12	NUM
iajs-2858	130	17	)	)	PUNCT
iajs-2858	130	18	ihjpas	ihjpa	NOUN
iajs-2858	130	19	.	.	PUNCT
iajs-2858	131	1	53	53	NUM
iajs-2858	131	2	(	(	PUNCT
iajs-2858	131	3	4)2022	4)2022	NOUN
iajs-2858	131	4	249	249	NUM
iajs-2858	131	5	𝑀𝑎𝑥	𝑀𝑎𝑥	PROPN
iajs-2858	131	6	𝜆	𝜆	ADV
iajs-2858	131	7	subject	subject	NOUN
iajs-2858	131	8	to	to	ADP
iajs-2858	131	9	,	,	PUNCT
iajs-2858	131	10	(	(	PUNCT
iajs-2858	131	11	(	(	PUNCT
iajs-2858	131	12	𝑤3)(𝑤4	𝑤3)(𝑤4	NOUN
iajs-2858	131	13	)	)	PUNCT
iajs-2858	131	14	−	−	PROPN
iajs-2858	131	15	(	(	PUNCT
iajs-2858	131	16	𝑤1)(𝑤2	𝑤1)(𝑤2	NOUN
iajs-2858	131	17	)	)	PUNCT
iajs-2858	131	18	)	)	PUNCT
iajs-2858	131	19	≤	≤	ADV
iajs-2858	132	1	1	1	NUM
iajs-2858	132	2	−	−	NOUN
iajs-2858	132	3	𝜆𝑝0	𝜆𝑝0	NOUN
iajs-2858	133	1	−	−	PROPN
iajs-2858	133	2	(	(	PUNCT
iajs-2858	133	3	(	(	PUNCT
iajs-2858	133	4	𝑐1	𝑐1	NOUN
iajs-2858	133	5	𝑇𝓍	𝑇𝓍	PROPN
iajs-2858	133	6	+	+	CCONJ
iajs-2858	133	7	𝛽	𝛽	NOUN
iajs-2858	133	8	)	)	PUNCT
iajs-2858	133	9	−	−	PROPN
iajs-2858	134	1	(	(	PUNCT
iajs-2858	134	2	𝑐2	𝑐2	NOUN
iajs-2858	134	3	𝑇𝑥	𝑇𝑥	NOUN
iajs-2858	134	4	+	+	CCONJ
iajs-2858	134	5	𝛿	𝛿	ADJ
iajs-2858	134	6	)	)	PUNCT
iajs-2858	134	7	)	)	PUNCT
iajs-2858	134	8	∑	∑	PUNCT
iajs-2858	134	9	𝑎𝑖𝑘𝑥𝑘	𝑎𝑖𝑘𝑥𝑘	VERB
iajs-2858	134	10	𝑛	𝑛	PRON
iajs-2858	134	11	𝑖=1	𝑖=1	PUNCT
iajs-2858	134	12	≤	≤	NOUN
iajs-2858	134	13	𝑏𝑘	𝑏𝑘	ADP
iajs-2858	135	1	+	+	CCONJ
iajs-2858	135	2	1	1	NUM
iajs-2858	135	3	−	−	NOUN
iajs-2858	135	4	𝜆(𝑝𝑘	𝜆(𝑝𝑘	PROPN
iajs-2858	135	5	)	)	PUNCT
iajs-2858	135	6	,	,	PUNCT
iajs-2858	135	7	𝑘	𝑘	X
iajs-2858	135	8	=	=	SYM
iajs-2858	135	9	1	1	NUM
iajs-2858	135	10	,	,	PUNCT
iajs-2858	135	11	…	…	PUNCT
iajs-2858	135	12	,	,	PUNCT
iajs-2858	135	13	𝑚	𝑚	X
iajs-2858	135	14	𝜆	𝜆	X
iajs-2858	135	15	,	,	PUNCT
iajs-2858	135	16	𝑥𝑘	𝑥𝑘	X
iajs-2858	135	17	≥	≥	NOUN
iajs-2858	135	18	0	0	NUM
iajs-2858	135	19	,	,	PUNCT
iajs-2858	135	20	𝑘	𝑘	X
iajs-2858	135	21	=	=	NOUN
iajs-2858	135	22	1	1	NUM
iajs-2858	135	23	,	,	PUNCT
iajs-2858	135	24	…	…	PUNCT
iajs-2858	135	25	,	,	PUNCT
iajs-2858	135	26	𝑚.	𝑚.	ADJ
iajs-2858	135	27	𝑤1𝑤2	𝑤1𝑤2	AUX
iajs-2858	135	28	and	and	CCONJ
iajs-2858	135	29	𝑤3𝑤4	𝑤3𝑤4	ADP
iajs-2858	135	30	are	be	AUX
iajs-2858	135	31	the	the	DET
iajs-2858	135	32	values	value	NOUN
iajs-2858	135	33	of	of	ADP
iajs-2858	135	34	numerator	numerator	NOUN
iajs-2858	135	35	and	and	CCONJ
iajs-2858	135	36	denominator	denominator	NOUN
iajs-2858	135	37	of	of	ADP
iajs-2858	135	38	objective	objective	ADJ
iajs-2858	135	39	function	function	NOUN
iajs-2858	135	40	respectively	respectively	ADV
iajs-2858	135	41	,	,	PUNCT
iajs-2858	135	42	and	and	CCONJ
iajs-2858	135	43	𝑐𝑗	𝑐𝑗	X
iajs-2858	136	1	𝑇𝓍	𝑇𝓍	PROPN
iajs-2858	136	2	are	be	AUX
iajs-2858	136	3	𝑛	𝑛	DET
iajs-2858	136	4	×	×	ADJ
iajs-2858	136	5	1	1	NUM
iajs-2858	136	6	column	column	NOUN
iajs-2858	136	7	vectors	vector	NOUN
iajs-2858	136	8	for	for	ADP
iajs-2858	136	9	𝑗	𝑗	NOUN
iajs-2858	136	10	=	=	SYM
iajs-2858	136	11	1,2	1,2	NUM
iajs-2858	136	12	by	by	ADP
iajs-2858	136	13	using	use	VERB
iajs-2858	136	14	simplex	simplex	NOUN
iajs-2858	136	15	algorithm	algorithm	NOUN
iajs-2858	136	16	,	,	PUNCT
iajs-2858	136	17	we	we	PRON
iajs-2858	136	18	can	can	AUX
iajs-2858	136	19	solve	solve	VERB
iajs-2858	136	20	problem	problem	NOUN
iajs-2858	136	21	(	(	PUNCT
iajs-2858	136	22	10	10	NUM
iajs-2858	136	23	or	or	CCONJ
iajs-2858	136	24	13	13	NUM
iajs-2858	136	25	)	)	PUNCT
iajs-2858	136	26	,	,	PUNCT
iajs-2858	136	27	the	the	DET
iajs-2858	136	28	optimum	optimum	ADJ
iajs-2858	136	29	result	result	NOUN
iajs-2858	136	30	to	to	ADP
iajs-2858	136	31	(	(	PUNCT
iajs-2858	136	32	10	10	NUM
iajs-2858	136	33	or	or	CCONJ
iajs-2858	136	34	13	13	NUM
iajs-2858	136	35	)	)	PUNCT
iajs-2858	136	36	is	be	AUX
iajs-2858	136	37	the	the	DET
iajs-2858	136	38	optimal	optimal	ADJ
iajs-2858	136	39	solution	solution	NOUN
iajs-2858	136	40	as	as	ADV
iajs-2858	136	41	well	well	ADV
iajs-2858	136	42	to	to	PART
iajs-2858	136	43	(	(	PUNCT
iajs-2858	136	44	7	7	NUM
iajs-2858	136	45	)	)	PUNCT
iajs-2858	136	46	and	and	CCONJ
iajs-2858	136	47	as	as	ADV
iajs-2858	136	48	well	well	ADV
iajs-2858	136	49	to	to	PART
iajs-2858	136	50	(	(	PUNCT
iajs-2858	136	51	4	4	NUM
iajs-2858	136	52	)	)	PUNCT
iajs-2858	136	53	.	.	PUNCT
iajs-2858	137	1	theorem	theorem	VERB
iajs-2858	137	2	5.1	5.1	NUM
iajs-2858	137	3	:	:	PUNCT
iajs-2858	137	4	in	in	ADP
iajs-2858	137	5	problem	problem	NOUN
iajs-2858	137	6	(	(	PUNCT
iajs-2858	137	7	7	7	NUM
iajs-2858	137	8	)	)	PUNCT
iajs-2858	137	9	,	,	PUNCT
iajs-2858	137	10	let	let	VERB
iajs-2858	137	11	the	the	DET
iajs-2858	137	12	membership	membership	NOUN
iajs-2858	137	13	functions	function	NOUN
iajs-2858	137	14	𝑓𝑖	𝑓𝑖	PROPN
iajs-2858	137	15	:	:	PUNCT
iajs-2858	137	16	ℝ	ℝ	PROPN
iajs-2858	137	17	→	→	SYM
iajs-2858	137	18	[	[	X
iajs-2858	137	19	0,1	0,1	NUM
iajs-2858	137	20	]	]	PUNCT
iajs-2858	137	21	,	,	PUNCT
iajs-2858	137	22	(	(	PUNCT
iajs-2858	137	23	𝑖	𝑖	SYM
iajs-2858	137	24	=	=	NOUN
iajs-2858	137	25	0	0	NUM
iajs-2858	137	26	,	,	PUNCT
iajs-2858	137	27	…	…	PUNCT
iajs-2858	137	28	,	,	PUNCT
iajs-2858	137	29	𝑚	𝑚	NOUN
iajs-2858	137	30	)	)	PUNCT
iajs-2858	137	31	,	,	PUNCT
iajs-2858	137	32	be	be	AUX
iajs-2858	137	33	continuous	continuous	ADJ
iajs-2858	137	34	and	and	CCONJ
iajs-2858	137	35	nondecreasing	nondecreasing	ADJ
iajs-2858	137	36	.	.	PUNCT
iajs-2858	138	1	then	then	ADV
iajs-2858	138	2	the	the	DET
iajs-2858	138	3	fuzzy	fuzzy	ADJ
iajs-2858	138	4	solution	solution	NOUN
iajs-2858	138	5	of	of	ADP
iajs-2858	138	6	(	(	PUNCT
iajs-2858	138	7	7	7	NUM
iajs-2858	138	8	)	)	PUNCT
iajs-2858	138	9	is	be	AUX
iajs-2858	138	10	assumed	assume	VERB
iajs-2858	138	11	by	by	ADP
iajs-2858	138	12	the	the	DET
iajs-2858	138	13	parametric	parametric	ADJ
iajs-2858	138	14	solution	solution	NOUN
iajs-2858	138	15	of	of	ADP
iajs-2858	138	16	the	the	DET
iajs-2858	138	17	parametric	parametric	ADJ
iajs-2858	138	18	fractional	fractional	ADJ
iajs-2858	138	19	linear	linear	PROPN
iajs-2858	138	20	programming	programming	NOUN
iajs-2858	138	21	problem	problem	NOUN
iajs-2858	138	22	.	.	PUNCT
iajs-2858	138	23	𝐏𝐫𝐨𝐨𝐟.	𝐏𝐫𝐨𝐨𝐟.	PUNCT
iajs-2858	139	1	we	we	PRON
iajs-2858	139	2	have	have	VERB
iajs-2858	139	3	to	to	PART
iajs-2858	139	4	solve	solve	VERB
iajs-2858	139	5	the	the	DET
iajs-2858	139	6	following	following	ADJ
iajs-2858	139	7	problem	problem	NOUN
iajs-2858	139	8	to	to	PART
iajs-2858	139	9	obtain	obtain	VERB
iajs-2858	139	10	the	the	DET
iajs-2858	139	11	solution	solution	NOUN
iajs-2858	139	12	of	of	ADP
iajs-2858	139	13	(	(	PUNCT
iajs-2858	139	14	7	7	NUM
iajs-2858	139	15	)	)	PUNCT
iajs-2858	139	16	.	.	PUNCT
iajs-2858	140	1	(	(	PUNCT
iajs-2858	140	2	𝐿𝑃)(𝑓,𝜆	𝐿𝑃)(𝑓,𝜆	NOUN
iajs-2858	140	3	)	)	PUNCT
iajs-2858	140	4	𝑀𝑎𝑥	𝑀𝑎𝑥	PROPN
iajs-2858	140	5	𝜆	𝜆	ADV
iajs-2858	140	6	subject	subject	NOUN
iajs-2858	140	7	to	to	ADP
iajs-2858	140	8	𝑓0(𝑐𝑇𝓍	𝑓0(𝑐𝑇𝓍	NOUN
iajs-2858	140	9	)	)	PUNCT
iajs-2858	140	10	≥	≥	PROPN
iajs-2858	140	11	𝜆	𝜆	PROPN
iajs-2858	140	12	𝑓𝑖(𝐴𝑖𝓍	𝑓𝑖(𝐴𝑖𝓍	PROPN
iajs-2858	140	13	)	)	PUNCT
iajs-2858	140	14	≥	≥	NOUN
iajs-2858	140	15	𝜆	𝜆	NOUN
iajs-2858	140	16	,	,	PUNCT
iajs-2858	140	17	𝑖	𝑖	SYM
iajs-2858	140	18	=	=	SYM
iajs-2858	140	19	1	1	NUM
iajs-2858	140	20	,	,	PUNCT
iajs-2858	140	21	…	…	PUNCT
iajs-2858	140	22	,	,	PUNCT
iajs-2858	140	23	𝑚	𝑚	X
iajs-2858	140	24	𝑥	𝑥	PRON
iajs-2858	140	25	≥	≥	NUM
iajs-2858	140	26	0	0	NUM
iajs-2858	140	27	,	,	PUNCT
iajs-2858	140	28	𝜆	𝜆	PROPN
iajs-2858	140	29	∈	∈	PROPN
iajs-2858	141	1	[	[	X
iajs-2858	141	2	0,1	0,1	NUM
iajs-2858	141	3	]	]	PUNCT
iajs-2858	141	4	where	where	SCONJ
iajs-2858	141	5	𝑓0(𝑐𝑇𝓍	𝑓0(𝑐𝑇𝓍	ADJ
iajs-2858	141	6	)	)	PUNCT
iajs-2858	141	7	=	=	SYM
iajs-2858	141	8	inf	inf	NOUN
iajs-2858	141	9	(	(	PUNCT
iajs-2858	141	10	𝑓0𝑗(𝑐𝑗	𝑓0𝑗(𝑐𝑗	ADP
iajs-2858	141	11	𝑇𝓍	𝑇𝓍	PROPN
iajs-2858	141	12	)	)	PUNCT
iajs-2858	141	13	)	)	PUNCT
iajs-2858	141	14	and	and	CCONJ
iajs-2858	141	15	𝑓i(𝐴𝑖𝓍	𝑓i(𝐴𝑖𝓍	ADJ
iajs-2858	141	16	)	)	PUNCT
iajs-2858	141	17	=	=	SYM
iajs-2858	141	18	inf	inf	PROPN
iajs-2858	141	19	(	(	PUNCT
iajs-2858	141	20	𝑓ij(𝐴𝑖𝑗𝓍	𝑓ij(𝐴𝑖𝑗𝓍	NOUN
iajs-2858	141	21	)	)	PUNCT
iajs-2858	141	22	)	)	PUNCT
iajs-2858	141	23	,	,	PUNCT
iajs-2858	141	24	𝑖	𝑖	X
iajs-2858	141	25	=	=	SYM
iajs-2858	141	26	1	1	NUM
iajs-2858	141	27	,	,	PUNCT
iajs-2858	141	28	…	…	PUNCT
iajs-2858	141	29	,	,	PUNCT
iajs-2858	141	30	𝑚.	𝑚.	ADJ
iajs-2858	141	31	but	but	CCONJ
iajs-2858	141	32	𝑓ij	𝑓ij	NOUN
iajs-2858	141	33	is	be	AUX
iajs-2858	141	34	nondecreasing	nondecrease	VERB
iajs-2858	141	35	and	and	CCONJ
iajs-2858	141	36	continuous	continuous	ADJ
iajs-2858	141	37	function	function	NOUN
iajs-2858	141	38	,	,	PUNCT
iajs-2858	141	39	given	give	VERB
iajs-2858	141	40	that	that	PRON
iajs-2858	141	41	𝑓𝑖𝑗	𝑓𝑖𝑗	ADJ
iajs-2858	141	42	−1	−1	NOUN
iajs-2858	141	43	exist	exist	VERB
iajs-2858	141	44	,	,	PUNCT
iajs-2858	141	45	and	and	CCONJ
iajs-2858	141	46	𝑓0𝑗(𝑐𝑗	𝑓0𝑗(𝑐𝑗	ADP
iajs-2858	141	47	𝑇𝓍	𝑇𝓍	NOUN
iajs-2858	141	48	)	)	PUNCT
iajs-2858	141	49	≥	≥	NOUN
iajs-2858	141	50	𝜆	𝜆	DET
iajs-2858	141	51	⇒	⇒	NOUN
iajs-2858	141	52	𝑐𝑗	𝑐𝑗	X
iajs-2858	142	1	𝑇𝓍	𝑇𝓍	PROPN
iajs-2858	142	2	≥	≥	NUM
iajs-2858	142	3	𝑓0𝑗	𝑓0𝑗	NOUN
iajs-2858	142	4	−1(𝜆	−1(𝜆	NOUN
iajs-2858	142	5	)	)	PUNCT
iajs-2858	142	6	with	with	ADP
iajs-2858	142	7	𝑓ij(𝐴𝑖𝑗𝓍	𝑓ij(𝐴𝑖𝑗𝓍	NOUN
iajs-2858	142	8	)	)	PUNCT
iajs-2858	142	9	≥	≥	AUX
iajs-2858	143	1	𝜆	𝜆	PRON
iajs-2858	143	2	⇒	⇒	PROPN
iajs-2858	143	3	𝐴𝑖𝑗𝓍	𝐴𝑖𝑗𝓍	PROPN
iajs-2858	143	4	≥	≥	NUM
iajs-2858	143	5	𝑓𝑖𝑗	𝑓𝑖𝑗	ADJ
iajs-2858	143	6	−1(𝜆	−1(𝜆	NOUN
iajs-2858	143	7	)	)	PUNCT
iajs-2858	143	8	.	.	PUNCT
iajs-2858	144	1	therefore	therefore	ADV
iajs-2858	144	2	,	,	PUNCT
iajs-2858	144	3	the	the	DET
iajs-2858	144	4	problem	problem	NOUN
iajs-2858	144	5	(	(	PUNCT
iajs-2858	144	6	𝐿𝑃)(𝑓,𝜆	𝐿𝑃)(𝑓,𝜆	X
iajs-2858	144	7	)	)	PUNCT
iajs-2858	144	8	can	can	AUX
iajs-2858	144	9	be	be	AUX
iajs-2858	144	10	written	write	VERB
iajs-2858	144	11	as	as	ADP
iajs-2858	144	12	𝑀𝑎𝑥	𝑀𝑎𝑥	PROPN
iajs-2858	144	13	𝜆	𝜆	ADV
iajs-2858	144	14	subject	subject	NOUN
iajs-2858	144	15	to	to	ADP
iajs-2858	144	16	𝑐𝑗	𝑐𝑗	NOUN
iajs-2858	144	17	𝑇𝓍	𝑇𝓍	PROPN
iajs-2858	144	18	≥	≥	NOUN
iajs-2858	144	19	𝑓0𝑗	𝑓0𝑗	NOUN
iajs-2858	144	20	−1(𝜆	−1(𝜆	NOUN
iajs-2858	144	21	)	)	PUNCT
iajs-2858	144	22	𝐴𝑖𝓍	𝐴𝑖𝓍	PROPN
iajs-2858	144	23	≥	≥	NOUN
iajs-2858	144	24	𝑓𝑖𝑗	𝑓𝑖𝑗	ADJ
iajs-2858	144	25	−1(𝜆	−1(𝜆	NOUN
iajs-2858	144	26	)	)	PUNCT
iajs-2858	144	27	.	.	PUNCT
iajs-2858	145	1	,	,	PUNCT
iajs-2858	145	2	𝑖	𝑖	X
iajs-2858	145	3	=	=	SYM
iajs-2858	145	4	1	1	NUM
iajs-2858	145	5	,	,	PUNCT
iajs-2858	145	6	…	…	PUNCT
iajs-2858	145	7	,	,	PUNCT
iajs-2858	145	8	𝑚	𝑚	X
iajs-2858	145	9	𝑥	𝑥	PRON
iajs-2858	145	10	≥	≥	NUM
iajs-2858	145	11	0	0	NUM
iajs-2858	145	12	,	,	PUNCT
iajs-2858	145	13	𝜆	𝜆	PROPN
iajs-2858	145	14	∈	∈	PROPN
iajs-2858	146	1	[	[	X
iajs-2858	146	2	0,1	0,1	NUM
iajs-2858	146	3	]	]	PUNCT
iajs-2858	146	4	which	which	PRON
iajs-2858	146	5	is	be	AUX
iajs-2858	146	6	equivalent	equivalent	ADJ
iajs-2858	146	7	to	to	ADP
iajs-2858	146	8	(	(	PUNCT
iajs-2858	146	9	6	6	NUM
iajs-2858	146	10	)	)	PUNCT
iajs-2858	146	11	𝑀𝑎𝑥	𝑀𝑎𝑥	PROPN
iajs-2858	146	12	𝛼	𝛼	NOUN
iajs-2858	146	13	subject	subject	ADJ
iajs-2858	146	14	to	to	ADP
iajs-2858	146	15	𝑐𝑗	𝑐𝑗	NOUN
iajs-2858	147	1	𝑇𝓍	𝑇𝓍	PROPN
iajs-2858	147	2	≥	≥	NUM
iajs-2858	147	3	𝑧0	𝑧0	NOUN
iajs-2858	147	4	−	−	PROPN
iajs-2858	147	5	(	(	PUNCT
iajs-2858	147	6	1	1	NUM
iajs-2858	147	7	−	−	PROPN
iajs-2858	147	8	𝛼)𝑝0	𝛼)𝑝0	PROPN
iajs-2858	147	9	𝐴𝑖𝓍	𝐴𝑖𝓍	PROPN
iajs-2858	147	10	≥	≥	NOUN
iajs-2858	147	11	𝑏𝑖	𝑏𝑖	ADP
iajs-2858	147	12	+	+	CCONJ
iajs-2858	147	13	(	(	PUNCT
iajs-2858	147	14	1	1	NUM
iajs-2858	147	15	−	−	PROPN
iajs-2858	147	16	𝛼)𝑝𝑖.	𝛼)𝑝𝑖.	NOUN
iajs-2858	147	17	,	,	PUNCT
iajs-2858	147	18	𝑖	𝑖	NOUN
iajs-2858	147	19	=	=	SYM
iajs-2858	147	20	1	1	NUM
iajs-2858	147	21	,	,	PUNCT
iajs-2858	147	22	…	…	PUNCT
iajs-2858	147	23	,	,	PUNCT
iajs-2858	147	24	𝑚	𝑚	X
iajs-2858	147	25	𝑥	𝑥	PRON
iajs-2858	147	26	≥	≥	NUM
iajs-2858	147	27	0	0	NUM
iajs-2858	147	28	,	,	PUNCT
iajs-2858	147	29	𝛼	𝛼	PROPN
iajs-2858	147	30	∈	∈	NOUN
iajs-2858	148	1	[	[	X
iajs-2858	148	2	0,1	0,1	NUM
iajs-2858	148	3	]	]	PUNCT
iajs-2858	148	4	thus	thus	ADV
iajs-2858	148	5	,	,	PUNCT
iajs-2858	148	6	the	the	DET
iajs-2858	148	7	fuzzy	fuzzy	ADJ
iajs-2858	148	8	linear	linear	NOUN
iajs-2858	148	9	programming	programming	NOUN
iajs-2858	148	10	(	(	PUNCT
iajs-2858	148	11	10	10	NUM
iajs-2858	148	12	or	or	CCONJ
iajs-2858	148	13	13	13	NUM
iajs-2858	148	14	)	)	PUNCT
iajs-2858	148	15	can	can	AUX
iajs-2858	148	16	be	be	AUX
iajs-2858	148	17	solved	solve	VERB
iajs-2858	148	18	by	by	ADP
iajs-2858	148	19	the	the	DET
iajs-2858	148	20	(	(	PUNCT
iajs-2858	148	21	crisp	crisp	ADJ
iajs-2858	148	22	)	)	PUNCT
iajs-2858	148	23	linear	linear	NOUN
iajs-2858	148	24	programming	programming	NOUN
iajs-2858	148	25	𝑀𝑎𝑥	𝑀𝑎𝑥	PROPN
iajs-2858	148	26	𝛼	𝛼	NOUN
iajs-2858	148	27	subject	subject	ADJ
iajs-2858	148	28	to	to	ADP
iajs-2858	148	29	(	(	PUNCT
iajs-2858	148	30	13	13	NUM
iajs-2858	148	31	)	)	PUNCT
iajs-2858	148	32	ihjpas	ihjpa	NOUN
iajs-2858	148	33	.	.	PUNCT
iajs-2858	149	1	53	53	NUM
iajs-2858	149	2	(	(	PUNCT
iajs-2858	149	3	4)2022	4)2022	NOUN
iajs-2858	149	4	250	250	NUM
iajs-2858	149	5	𝑐𝑗	𝑐𝑗	X
iajs-2858	149	6	𝑇𝓍	𝑇𝓍	PROPN
iajs-2858	149	7	≥	≥	NUM
iajs-2858	149	8	𝑧0	𝑧0	NOUN
iajs-2858	149	9	−	−	PROPN
iajs-2858	150	1	(	(	PUNCT
iajs-2858	150	2	1	1	NUM
iajs-2858	150	3	−	−	PROPN
iajs-2858	150	4	𝛼)𝑝0	𝛼)𝑝0	PROPN
iajs-2858	150	5	𝐴𝑖𝓍	𝐴𝑖𝓍	PROPN
iajs-2858	150	6	≥	≥	NOUN
iajs-2858	150	7	𝑏𝑖	𝑏𝑖	ADP
iajs-2858	150	8	+	+	CCONJ
iajs-2858	150	9	(	(	PUNCT
iajs-2858	150	10	1	1	NUM
iajs-2858	150	11	−	−	PROPN
iajs-2858	150	12	𝛼)𝑝𝑖.	𝛼)𝑝𝑖.	NOUN
iajs-2858	150	13	,	,	PUNCT
iajs-2858	150	14	𝑖	𝑖	NOUN
iajs-2858	150	15	=	=	SYM
iajs-2858	150	16	1	1	NUM
iajs-2858	150	17	,	,	PUNCT
iajs-2858	150	18	…	…	PUNCT
iajs-2858	150	19	,	,	PUNCT
iajs-2858	150	20	𝑚	𝑚	X
iajs-2858	150	21	𝑥	𝑥	PRON
iajs-2858	150	22	≥	≥	NUM
iajs-2858	150	23	0	0	NUM
iajs-2858	150	24	,	,	PUNCT
iajs-2858	150	25	𝛼	𝛼	PROPN
iajs-2858	150	26	∈	∈	NOUN
iajs-2858	151	1	[	[	X
iajs-2858	151	2	0,1	0,1	NUM
iajs-2858	151	3	]	]	PUNCT
iajs-2858	151	4	which	which	PRON
iajs-2858	151	5	is	be	AUX
iajs-2858	151	6	the	the	DET
iajs-2858	151	7	same	same	ADJ
iajs-2858	151	8	as	as	ADP
iajs-2858	151	9	problem	problem	NOUN
iajs-2858	151	10	(	(	PUNCT
iajs-2858	151	11	6	6	NUM
iajs-2858	151	12	)	)	PUNCT
iajs-2858	151	13	with	with	ADP
iajs-2858	151	14	𝜆	𝜆	PRON
iajs-2858	151	15	=	=	SYM
iajs-2858	151	16	𝛼	𝛼	X
iajs-2858	151	17	.	.	PUNCT
iajs-2858	151	18	remark	remark	VERB
iajs-2858	151	19	5.1	5.1	NUM
iajs-2858	151	20	if	if	SCONJ
iajs-2858	151	21	the	the	DET
iajs-2858	151	22	problem	problem	NOUN
iajs-2858	151	23	(	(	PUNCT
iajs-2858	151	24	7	7	X
iajs-2858	151	25	)	)	PUNCT
iajs-2858	151	26	has	have	AUX
iajs-2858	151	27	fuzzy	fuzzy	ADJ
iajs-2858	151	28	as	as	ADV
iajs-2858	151	29	well	well	ADV
iajs-2858	151	30	as	as	ADP
iajs-2858	151	31	crisp	crisp	ADJ
iajs-2858	151	32	constraints	constraint	NOUN
iajs-2858	151	33	,	,	PUNCT
iajs-2858	151	34	then	then	ADV
iajs-2858	151	35	in	in	ADP
iajs-2858	151	36	the	the	DET
iajs-2858	151	37	alike	alike	ADJ
iajs-2858	151	38	(	(	PUNCT
iajs-2858	151	39	crisp	crisp	ADJ
iajs-2858	151	40	)	)	PUNCT
iajs-2858	151	41	linear	linear	ADJ
iajs-2858	151	42	fractional	fractional	ADJ
iajs-2858	151	43	programming	programming	NOUN
iajs-2858	151	44	problem	problem	NOUN
iajs-2858	151	45	,	,	PUNCT
iajs-2858	151	46	the	the	DET
iajs-2858	151	47	original	original	ADJ
iajs-2858	151	48	crisp	crisp	ADJ
iajs-2858	151	49	constraints	constraint	NOUN
iajs-2858	151	50	will	will	AUX
iajs-2858	151	51	not	not	PART
iajs-2858	151	52	have	have	VERB
iajs-2858	151	53	any	any	DET
iajs-2858	151	54	modification	modification	NOUN
iajs-2858	151	55	as	as	ADP
iajs-2858	151	56	for	for	ADP
iajs-2858	151	57	them	they	PRON
iajs-2858	151	58	the	the	DET
iajs-2858	151	59	tolerances	tolerance	NOUN
iajs-2858	151	60	are	be	AUX
iajs-2858	151	61	nil	nil	ADJ
iajs-2858	151	62	.	.	PROPN
iajs-2858	152	1	6	6	X
iajs-2858	152	2	.	.	X
iajs-2858	152	3	algorithm	algorithm	NOUN
iajs-2858	152	4	to	to	PART
iajs-2858	152	5	solve	solve	VERB
iajs-2858	152	6	qfpp	qfpp	NOUN
iajs-2858	152	7	by	by	ADP
iajs-2858	152	8	using	use	VERB
iajs-2858	152	9	msfa	msfa	NOUN
iajs-2858	152	10	to	to	PART
iajs-2858	152	11	find	find	VERB
iajs-2858	152	12	the	the	DET
iajs-2858	152	13	result	result	NOUN
iajs-2858	152	14	of	of	ADP
iajs-2858	152	15	optimal	optimal	ADJ
iajs-2858	152	16	solution	solution	NOUN
iajs-2858	152	17	for	for	ADP
iajs-2858	152	18	the	the	DET
iajs-2858	152	19	qfpp	qfpp	NOUN
iajs-2858	152	20	of	of	ADP
iajs-2858	152	21	formulation	formulation	NOUN
iajs-2858	152	22	(	(	PUNCT
iajs-2858	152	23	4	4	NUM
iajs-2858	152	24	)	)	PUNCT
iajs-2858	152	25	,	,	PUNCT
iajs-2858	152	26	a	a	DET
iajs-2858	152	27	procedure	procedure	NOUN
iajs-2858	152	28	is	be	AUX
iajs-2858	152	29	given	give	VERB
iajs-2858	152	30	as	as	ADP
iajs-2858	152	31	below	below	ADV
iajs-2858	152	32	:	:	PUNCT
iajs-2858	152	33	step	step	VERB
iajs-2858	152	34	one	one	NUM
iajs-2858	152	35	:	:	PUNCT
iajs-2858	152	36	convert	convert	VERB
iajs-2858	152	37	the	the	DET
iajs-2858	152	38	main	main	ADJ
iajs-2858	152	39	problem	problem	NOUN
iajs-2858	152	40	to	to	ADP
iajs-2858	152	41	the	the	DET
iajs-2858	152	42	fuzzy	fuzzy	ADJ
iajs-2858	152	43	version	version	NOUN
iajs-2858	152	44	as	as	ADP
iajs-2858	152	45	formula	formula	NOUN
iajs-2858	152	46	7	7	NUM
iajs-2858	152	47	step	step	NOUN
iajs-2858	152	48	two	two	NUM
iajs-2858	152	49	:	:	PUNCT
iajs-2858	152	50	find	find	VERB
iajs-2858	152	51	the	the	DET
iajs-2858	152	52	value	value	NOUN
iajs-2858	152	53	of	of	ADP
iajs-2858	152	54	𝑝0	𝑝0	PROPN
iajs-2858	152	55	and	and	CCONJ
iajs-2858	152	56	𝑝𝑖	𝑝𝑖	NOUN
iajs-2858	152	57	,	,	PUNCT
iajs-2858	152	58	𝑖	𝑖	NOUN
iajs-2858	152	59	=	=	NOUN
iajs-2858	152	60	1	1	NUM
iajs-2858	152	61	,	,	PUNCT
iajs-2858	152	62	…	…	PUNCT
iajs-2858	152	63	,	,	PUNCT
iajs-2858	152	64	𝑚	𝑚	X
iajs-2858	152	65	which	which	PRON
iajs-2858	152	66	are	be	AUX
iajs-2858	152	67	the	the	DET
iajs-2858	152	68	permissible	permissible	ADJ
iajs-2858	152	69	tolerances	tolerance	NOUN
iajs-2858	152	70	for	for	ADP
iajs-2858	152	71	objective	objective	ADJ
iajs-2858	152	72	function	function	NOUN
iajs-2858	152	73	and	and	CCONJ
iajs-2858	152	74	constraint	constraint	NOUN
iajs-2858	152	75	by	by	ADP
iajs-2858	152	76	using	use	VERB
iajs-2858	152	77	formula	formula	NOUN
iajs-2858	152	78	(	(	PUNCT
iajs-2858	152	79	8	8	NUM
iajs-2858	152	80	,	,	PUNCT
iajs-2858	152	81	11	11	NUM
iajs-2858	152	82	)	)	PUNCT
iajs-2858	152	83	and	and	CCONJ
iajs-2858	152	84	(	(	PUNCT
iajs-2858	152	85	9	9	NUM
iajs-2858	152	86	,	,	PUNCT
iajs-2858	152	87	12	12	NUM
iajs-2858	152	88	)	)	PUNCT
iajs-2858	152	89	,	,	PUNCT
iajs-2858	152	90	respectively	respectively	ADV
iajs-2858	152	91	.	.	PUNCT
iajs-2858	153	1	step	step	NOUN
iajs-2858	153	2	three	three	NUM
iajs-2858	153	3	:	:	PUNCT
iajs-2858	153	4	construct	construct	VERB
iajs-2858	153	5	the	the	DET
iajs-2858	153	6	crisp	crisp	ADJ
iajs-2858	153	7	linear	linear	NOUN
iajs-2858	153	8	programming	programming	NOUN
iajs-2858	153	9	(	(	PUNCT
iajs-2858	153	10	𝐿𝑃)(𝑓,𝜆	𝐿𝑃)(𝑓,𝜆	NUM
iajs-2858	153	11	)	)	PUNCT
iajs-2858	153	12	by	by	ADP
iajs-2858	153	13	using	use	VERB
iajs-2858	153	14	formula	formula	NOUN
iajs-2858	153	15	(	(	PUNCT
iajs-2858	153	16	10	10	NUM
iajs-2858	153	17	,	,	PUNCT
iajs-2858	153	18	13	13	NUM
iajs-2858	153	19	)	)	PUNCT
iajs-2858	153	20	step	step	NOUN
iajs-2858	153	21	four	four	NUM
iajs-2858	153	22	:	:	PUNCT
iajs-2858	153	23	optimize	optimize	VERB
iajs-2858	153	24	step	step	NOUN
iajs-2858	153	25	3	3	NUM
iajs-2858	153	26	by	by	ADP
iajs-2858	153	27	using	use	VERB
iajs-2858	153	28	simplex	simplex	NOUN
iajs-2858	153	29	algorithm	algorithm	NOUN
iajs-2858	153	30	.	.	PUNCT
iajs-2858	154	1	7	7	X
iajs-2858	154	2	.	.	X
iajs-2858	154	3	an	an	DET
iajs-2858	154	4	illustrative	illustrative	ADJ
iajs-2858	154	5	numerical	numerical	ADJ
iajs-2858	154	6	example	example	NOUN
iajs-2858	154	7	and	and	CCONJ
iajs-2858	154	8	results	result	VERB
iajs-2858	154	9	:	:	PUNCT
iajs-2858	154	10	in	in	ADP
iajs-2858	154	11	this	this	DET
iajs-2858	154	12	section	section	NOUN
iajs-2858	154	13	,	,	PUNCT
iajs-2858	154	14	we	we	PRON
iajs-2858	154	15	solve	solve	VERB
iajs-2858	154	16	an	an	DET
iajs-2858	154	17	example	example	NOUN
iajs-2858	154	18	through	through	ADP
iajs-2858	154	19	msfa	msfa	NOUN
iajs-2858	154	20	and	and	CCONJ
iajs-2858	154	21	compared	compare	VERB
iajs-2858	154	22	with	with	ADP
iajs-2858	154	23	modified	modified	ADJ
iajs-2858	154	24	simplex	simplex	NOUN
iajs-2858	154	25	approach	approach	NOUN
iajs-2858	154	26	.	.	PUNCT
iajs-2858	155	1	example	example	NOUN
iajs-2858	155	2	:	:	PUNCT
iajs-2858	155	3	maximize	maximize	VERB
iajs-2858	155	4	z	z	NOUN
iajs-2858	155	5	=	=	SYM
iajs-2858	155	6	(	(	PUNCT
iajs-2858	155	7	4𝑥1	4𝑥1	X
iajs-2858	155	8	+	+	NOUN
iajs-2858	155	9	6𝑥2−2)(2𝑥1	6𝑥2−2)(2𝑥1	NOUN
iajs-2858	155	10	+	+	NOUN
iajs-2858	155	11	3𝑥2	3𝑥2	NUM
iajs-2858	155	12	+	+	NOUN
iajs-2858	155	13	1	1	NUM
iajs-2858	155	14	)	)	PUNCT
iajs-2858	155	15	(	(	PUNCT
iajs-2858	155	16	6𝑥1	6𝑥1	NUM
iajs-2858	155	17	+	+	NOUN
iajs-2858	155	18	9𝑥2	9𝑥2	NUM
iajs-2858	155	19	+	+	ADJ
iajs-2858	155	20	3)2	3)2	NUM
iajs-2858	155	21	subject	subject	NOUN
iajs-2858	155	22	to	to	ADP
iajs-2858	155	23	:	:	PUNCT
iajs-2858	155	24	𝑥1	𝑥1	NOUN
iajs-2858	155	25	+	+	CCONJ
iajs-2858	155	26	3𝑥2	3𝑥2	NUM
iajs-2858	155	27	≤	≤	NUM
iajs-2858	155	28	5	5	NUM
iajs-2858	155	29	2𝑥1	2𝑥1	NUM
iajs-2858	155	30	+	+	CCONJ
iajs-2858	155	31	𝑥2	𝑥2	NOUN
iajs-2858	155	32	≤	≤	NUM
iajs-2858	155	33	2	2	NUM
iajs-2858	155	34	𝑥1	𝑥1	NOUN
iajs-2858	155	35	,	,	PUNCT
iajs-2858	155	36	𝑥2	𝑥2	PROPN
iajs-2858	155	37	≥	≥	NOUN
iajs-2858	155	38	0	0	NUM
iajs-2858	155	39	step	step	NOUN
iajs-2858	155	40	one	one	NUM
iajs-2858	155	41	:	:	PUNCT
iajs-2858	155	42	the	the	DET
iajs-2858	155	43	fuzzy	fuzzy	ADJ
iajs-2858	155	44	version	version	NOUN
iajs-2858	155	45	of	of	ADP
iajs-2858	155	46	problem	problem	NOUN
iajs-2858	155	47	is	be	AUX
iajs-2858	155	48	:	:	PUNCT
iajs-2858	155	49	find	find	VERB
iajs-2858	155	50	𝑥	𝑥	PRON
iajs-2858	155	51	such	such	ADJ
iajs-2858	155	52	that	that	PRON
iajs-2858	155	53	:	:	PUNCT
iajs-2858	155	54	(	(	PUNCT
iajs-2858	155	55	4𝑥1	4𝑥1	NUM
iajs-2858	155	56	+	+	NOUN
iajs-2858	155	57	6𝑥2−2)(2𝑥1	6𝑥2−2)(2𝑥1	NOUN
iajs-2858	155	58	+	+	NOUN
iajs-2858	155	59	3𝑥2	3𝑥2	NUM
iajs-2858	155	60	+	+	NOUN
iajs-2858	155	61	1	1	NUM
iajs-2858	155	62	)	)	PUNCT
iajs-2858	155	63	(	(	PUNCT
iajs-2858	155	64	6𝑥1	6𝑥1	NUM
iajs-2858	155	65	+	+	NOUN
iajs-2858	155	66	9𝑥2	9𝑥2	NUM
iajs-2858	155	67	+	+	ADJ
iajs-2858	155	68	3)(6𝑥1	3)(6𝑥1	NUM
iajs-2858	155	69	+	+	NOUN
iajs-2858	155	70	9𝑥2	9𝑥2	NUM
iajs-2858	155	71	+	+	NOUN
iajs-2858	155	72	3	3	NUM
iajs-2858	155	73	)	)	PUNCT
iajs-2858	155	74	≳	≳	NOUN
iajs-2858	155	75	(	(	PUNCT
iajs-2858	155	76	𝑤1)(𝑤2	𝑤1)(𝑤2	NOUN
iajs-2858	155	77	)	)	PUNCT
iajs-2858	155	78	(	(	PUNCT
iajs-2858	155	79	𝑤3)(𝑤4	𝑤3)(𝑤4	NOUN
iajs-2858	155	80	)	)	PUNCT
iajs-2858	155	81	𝑥1	𝑥1	NOUN
iajs-2858	155	82	+	+	CCONJ
iajs-2858	155	83	3𝑥2	3𝑥2	NUM
iajs-2858	155	84	≲	≲	PROPN
iajs-2858	155	85	5	5	NUM
iajs-2858	155	86	2𝑥1	2𝑥1	NUM
iajs-2858	155	87	+	+	CCONJ
iajs-2858	155	88	𝑥2	𝑥2	NOUN
iajs-2858	155	89	≲	≲	PROPN
iajs-2858	155	90	5	5	NUM
iajs-2858	155	91	𝑥1	𝑥1	NOUN
iajs-2858	155	92	,	,	PUNCT
iajs-2858	155	93	𝑥2	𝑥2	NOUN
iajs-2858	155	94	≧	≧	NOUN
iajs-2858	155	95	0	0	NUM
iajs-2858	155	96	step	step	NOUN
iajs-2858	155	97	two	two	NUM
iajs-2858	155	98	:	:	PUNCT
iajs-2858	155	99	find	find	VERB
iajs-2858	155	100	the	the	DET
iajs-2858	155	101	value	value	NOUN
iajs-2858	155	102	of	of	ADP
iajs-2858	155	103	𝑝0	𝑝0	PROPN
iajs-2858	155	104	and	and	CCONJ
iajs-2858	155	105	𝑝𝑖	𝑝𝑖	NOUN
iajs-2858	155	106	,	,	PUNCT
iajs-2858	155	107	𝑖	𝑖	NOUN
iajs-2858	155	108	=	=	NOUN
iajs-2858	155	109	1	1	NUM
iajs-2858	155	110	,	,	PUNCT
iajs-2858	155	111	…	…	PUNCT
iajs-2858	155	112	,	,	PUNCT
iajs-2858	155	113	𝑚	𝑚	X
iajs-2858	155	114	which	which	PRON
iajs-2858	155	115	are	be	AUX
iajs-2858	155	116	the	the	DET
iajs-2858	155	117	permissible	permissible	ADJ
iajs-2858	155	118	tolerances	tolerance	NOUN
iajs-2858	155	119	for	for	ADP
iajs-2858	155	120	objective	objective	ADJ
iajs-2858	155	121	function	function	NOUN
iajs-2858	155	122	and	and	CCONJ
iajs-2858	155	123	constraint	constraint	NOUN
iajs-2858	155	124	.	.	PUNCT
iajs-2858	156	1	firstly	firstly	ADV
iajs-2858	156	2	,	,	PUNCT
iajs-2858	156	3	obtain	obtain	VERB
iajs-2858	156	4	the	the	DET
iajs-2858	156	5	value	value	NOUN
iajs-2858	156	6	of	of	ADP
iajs-2858	156	7	(	(	PUNCT
iajs-2858	156	8	𝑤1	𝑤1	PROPN
iajs-2858	156	9	)	)	PUNCT
iajs-2858	156	10	,	,	PUNCT
iajs-2858	156	11	(	(	PUNCT
iajs-2858	156	12	𝑤2	𝑤2	NOUN
iajs-2858	156	13	)	)	PUNCT
iajs-2858	156	14	,	,	PUNCT
iajs-2858	156	15	(	(	PUNCT
iajs-2858	156	16	𝑤3	𝑤3	PROPN
iajs-2858	156	17	)	)	PUNCT
iajs-2858	156	18	and	and	CCONJ
iajs-2858	156	19	(	(	PUNCT
iajs-2858	156	20	𝑤4	𝑤4	NOUN
iajs-2858	156	21	)	)	PUNCT
iajs-2858	156	22	by	by	ADP
iajs-2858	156	23	simplex	simplex	NOUN
iajs-2858	156	24	algorithm	algorithm	NOUN
iajs-2858	156	25	as	as	SCONJ
iajs-2858	156	26	follows	follow	VERB
iajs-2858	156	27	:	:	PUNCT
iajs-2858	156	28	𝑀𝑎𝑥.	𝑀𝑎𝑥.	PROPN
iajs-2858	156	29	𝑤1	𝑤1	NOUN
iajs-2858	156	30	=	=	SYM
iajs-2858	156	31	(	(	PUNCT
iajs-2858	156	32	4𝑥1	4𝑥1	NUM
iajs-2858	156	33	+	+	CCONJ
iajs-2858	156	34	6𝑥2	6𝑥2	NUM
iajs-2858	157	1	−	−	PRON
iajs-2858	157	2	2	2	X
iajs-2858	157	3	)	)	PUNCT
iajs-2858	157	4	subject	subject	NOUN
iajs-2858	157	5	to	to	ADP
iajs-2858	157	6	:	:	PUNCT
iajs-2858	157	7	𝑥1	𝑥1	NOUN
iajs-2858	157	8	+	+	CCONJ
iajs-2858	157	9	3𝑥2	3𝑥2	NUM
iajs-2858	157	10	≤	≤	NUM
iajs-2858	157	11	5	5	NUM
iajs-2858	157	12	2𝑥1	2𝑥1	NUM
iajs-2858	157	13	+	+	CCONJ
iajs-2858	157	14	𝑥2	𝑥2	NOUN
iajs-2858	157	15	≤	≤	NUM
iajs-2858	157	16	2	2	NUM
iajs-2858	157	17	𝑥1	𝑥1	NOUN
iajs-2858	157	18	,	,	PUNCT
iajs-2858	157	19	𝑥2	𝑥2	NOUN
iajs-2858	157	20	≥	≥	NOUN
iajs-2858	157	21	0	0	NUM
iajs-2858	157	22	optimal	optimal	ADJ
iajs-2858	157	23	solution	solution	NOUN
iajs-2858	157	24	:	:	PUNCT
iajs-2858	157	25	𝑥1	𝑥1	NOUN
iajs-2858	157	26	=	=	NOUN
iajs-2858	157	27	0.2	0.2	NUM
iajs-2858	157	28	,	,	PUNCT
iajs-2858	157	29	𝑥2	𝑥2	NOUN
iajs-2858	157	30	=	=	NOUN
iajs-2858	157	31	1.6	1.6	NUM
iajs-2858	157	32	𝑀𝑎𝑥.	𝑀𝑎𝑥.	NOUN
iajs-2858	157	33	𝑤1	𝑤1	NOUN
iajs-2858	157	34	=	=	NOUN
iajs-2858	157	35	8.4	8.4	NUM
iajs-2858	157	36	𝑀𝑎𝑥.	𝑀𝑎𝑥.	NOUN
iajs-2858	157	37	𝑤1	𝑤1	NOUN
iajs-2858	157	38	=	=	SYM
iajs-2858	157	39	(	(	PUNCT
iajs-2858	157	40	2𝑥1	2𝑥1	NUM
iajs-2858	157	41	+	+	CCONJ
iajs-2858	157	42	3𝑥2	3𝑥2	NUM
iajs-2858	157	43	+	+	SYM
iajs-2858	157	44	1	1	X
iajs-2858	157	45	)	)	PUNCT
iajs-2858	157	46	subject	subject	NOUN
iajs-2858	157	47	to	to	ADP
iajs-2858	157	48	:	:	PUNCT
iajs-2858	157	49	𝑥1	𝑥1	NOUN
iajs-2858	157	50	+	+	CCONJ
iajs-2858	157	51	3𝑥2	3𝑥2	NUM
iajs-2858	157	52	≤	≤	NUM
iajs-2858	157	53	5	5	NUM
iajs-2858	157	54	2𝑥1	2𝑥1	NUM
iajs-2858	157	55	+	+	CCONJ
iajs-2858	157	56	𝑥2	𝑥2	NOUN
iajs-2858	157	57	≤	≤	NUM
iajs-2858	157	58	2	2	NUM
iajs-2858	157	59	𝑥1	𝑥1	NOUN
iajs-2858	157	60	,	,	PUNCT
iajs-2858	157	61	𝑥2	𝑥2	NOUN
iajs-2858	157	62	≥	≥	NOUN
iajs-2858	157	63	0	0	NUM
iajs-2858	157	64	optimal	optimal	ADJ
iajs-2858	157	65	solution	solution	NOUN
iajs-2858	157	66	:	:	PUNCT
iajs-2858	157	67	𝑥1	𝑥1	NOUN
iajs-2858	157	68	=	=	NOUN
iajs-2858	157	69	0.2	0.2	NUM
iajs-2858	157	70	,	,	PUNCT
iajs-2858	157	71	𝑥2	𝑥2	NOUN
iajs-2858	157	72	=	=	NOUN
iajs-2858	157	73	1.6	1.6	NUM
iajs-2858	157	74	𝑀𝑎𝑥.	𝑀𝑎𝑥.	NOUN
iajs-2858	157	75	𝑤1	𝑤1	NOUN
iajs-2858	157	76	=	=	SYM
iajs-2858	157	77	6,2	6,2	NUM
iajs-2858	157	78	ihjpas	ihjpa	NOUN
iajs-2858	157	79	.	.	PUNCT
iajs-2858	158	1	53	53	NUM
iajs-2858	158	2	(	(	PUNCT
iajs-2858	158	3	4)2022	4)2022	NOUN
iajs-2858	158	4	251	251	NUM
iajs-2858	158	5	𝑀𝑎𝑥.	𝑀𝑎𝑥.	PROPN
iajs-2858	158	6	𝑤1	𝑤1	NOUN
iajs-2858	158	7	=	=	PUNCT
iajs-2858	158	8	(	(	PUNCT
iajs-2858	158	9	6𝑥1	6𝑥1	NUM
iajs-2858	158	10	+	+	CCONJ
iajs-2858	158	11	9𝑥2	9𝑥2	NUM
iajs-2858	158	12	+	+	NUM
iajs-2858	158	13	3	3	X
iajs-2858	158	14	)	)	PUNCT
iajs-2858	158	15	subject	subject	NOUN
iajs-2858	158	16	to	to	ADP
iajs-2858	158	17	:	:	PUNCT
iajs-2858	158	18	𝑥1	𝑥1	NOUN
iajs-2858	158	19	+	+	CCONJ
iajs-2858	158	20	3𝑥2	3𝑥2	NUM
iajs-2858	158	21	≤	≤	NUM
iajs-2858	158	22	5	5	NUM
iajs-2858	158	23	2𝑥1	2𝑥1	NUM
iajs-2858	158	24	+	+	CCONJ
iajs-2858	158	25	𝑥2	𝑥2	NOUN
iajs-2858	158	26	≤	≤	NUM
iajs-2858	158	27	2	2	NUM
iajs-2858	158	28	𝑥1	𝑥1	NOUN
iajs-2858	158	29	,	,	PUNCT
iajs-2858	158	30	𝑥2	𝑥2	NOUN
iajs-2858	158	31	≥	≥	NOUN
iajs-2858	158	32	0	0	NUM
iajs-2858	158	33	optimal	optimal	ADJ
iajs-2858	158	34	solution	solution	NOUN
iajs-2858	158	35	:	:	PUNCT
iajs-2858	158	36	𝑥1	𝑥1	NOUN
iajs-2858	158	37	=	=	NOUN
iajs-2858	158	38	0.2	0.2	NUM
iajs-2858	158	39	,	,	PUNCT
iajs-2858	158	40	𝑥2	𝑥2	NOUN
iajs-2858	158	41	=	=	NOUN
iajs-2858	158	42	1.6	1.6	NUM
iajs-2858	158	43	𝑀𝑎𝑥.	𝑀𝑎𝑥.	PROPN
iajs-2858	158	44	𝑤1	𝑤1	NOUN
iajs-2858	158	45	=	=	NOUN
iajs-2858	158	46	18.6	18.6	NUM
iajs-2858	158	47	𝑀𝑎𝑥.	𝑀𝑎𝑥.	PROPN
iajs-2858	158	48	𝑤1	𝑤1	NOUN
iajs-2858	158	49	=	=	PUNCT
iajs-2858	158	50	(	(	PUNCT
iajs-2858	158	51	6𝑥1	6𝑥1	NUM
iajs-2858	158	52	+	+	CCONJ
iajs-2858	158	53	9𝑥2	9𝑥2	NUM
iajs-2858	158	54	+	+	NUM
iajs-2858	158	55	3	3	X
iajs-2858	158	56	)	)	PUNCT
iajs-2858	158	57	subject	subject	NOUN
iajs-2858	158	58	to	to	ADP
iajs-2858	158	59	:	:	PUNCT
iajs-2858	158	60	𝑥1	𝑥1	NOUN
iajs-2858	158	61	+	+	CCONJ
iajs-2858	158	62	3𝑥2	3𝑥2	NUM
iajs-2858	158	63	≤	≤	NUM
iajs-2858	158	64	5	5	NUM
iajs-2858	158	65	2𝑥1	2𝑥1	NUM
iajs-2858	158	66	+	+	CCONJ
iajs-2858	158	67	𝑥2	𝑥2	NOUN
iajs-2858	158	68	≤	≤	NUM
iajs-2858	158	69	2	2	NUM
iajs-2858	158	70	𝑥1	𝑥1	NOUN
iajs-2858	158	71	,	,	PUNCT
iajs-2858	158	72	𝑥2	𝑥2	NOUN
iajs-2858	158	73	≥	≥	NOUN
iajs-2858	158	74	0	0	NUM
iajs-2858	158	75	optimal	optimal	ADJ
iajs-2858	158	76	solution	solution	NOUN
iajs-2858	158	77	:	:	PUNCT
iajs-2858	158	78	𝑥1	𝑥1	NOUN
iajs-2858	158	79	=	=	NOUN
iajs-2858	158	80	0.2	0.2	NUM
iajs-2858	158	81	,	,	PUNCT
iajs-2858	158	82	𝑥2	𝑥2	NOUN
iajs-2858	158	83	=	=	NOUN
iajs-2858	158	84	1.6	1.6	NUM
iajs-2858	158	85	𝑀𝑎𝑥.	𝑀𝑎𝑥.	PROPN
iajs-2858	158	86	𝑤1	𝑤1	NOUN
iajs-2858	158	87	=	=	NOUN
iajs-2858	158	88	18.6	18.6	NUM
iajs-2858	158	89	now	now	ADV
iajs-2858	158	90	,	,	PUNCT
iajs-2858	158	91	find	find	VERB
iajs-2858	158	92	𝑝0	𝑝0	NOUN
iajs-2858	158	93	by	by	ADP
iajs-2858	158	94	using	use	VERB
iajs-2858	158	95	case	case	NOUN
iajs-2858	158	96	1	1	NUM
iajs-2858	158	97	at	at	ADP
iajs-2858	158	98	decision	decision	NOUN
iajs-2858	158	99	variable	variable	NOUN
iajs-2858	158	100	𝑥1	𝑥1	NOUN
iajs-2858	158	101	=	=	SYM
iajs-2858	158	102	0.2	0.2	NUM
iajs-2858	158	103	,	,	PUNCT
iajs-2858	158	104	𝑥2	𝑥2	NOUN
iajs-2858	158	105	=	=	SYM
iajs-2858	158	106	1.6	1.6	NUM
iajs-2858	158	107	since	since	SCONJ
iajs-2858	158	108	(	(	PUNCT
iajs-2858	158	109	𝑤3)(𝑤4	𝑤3)(𝑤4	NOUN
iajs-2858	158	110	)	)	PUNCT
iajs-2858	158	111	>	>	X
iajs-2858	158	112	(	(	PUNCT
iajs-2858	158	113	𝑤1)(𝑤2	𝑤1)(𝑤2	NOUN
iajs-2858	158	114	)	)	PUNCT
iajs-2858	158	115	,	,	PUNCT
iajs-2858	158	116	so	so	ADV
iajs-2858	158	117	can	can	AUX
iajs-2858	158	118	get	get	VERB
iajs-2858	158	119	it	it	PRON
iajs-2858	158	120	as	as	ADP
iajs-2858	158	121	follow	follow	VERB
iajs-2858	158	122	:	:	PUNCT
iajs-2858	158	123	(	(	PUNCT
iajs-2858	158	124	1	1	NUM
iajs-2858	158	125	−	−	NOUN
iajs-2858	158	126	(	(	PUNCT
iajs-2858	158	127	(	(	PUNCT
iajs-2858	158	128	18.6)(18.6	18.6)(18.6	NUM
iajs-2858	158	129	)	)	PUNCT
iajs-2858	158	130	)	)	PUNCT
iajs-2858	159	1	−	−	PROPN
iajs-2858	159	2	(	(	PUNCT
iajs-2858	159	3	8.6)(6.2	8.6)(6.2	NUM
iajs-2858	159	4	)	)	PUNCT
iajs-2858	159	5	)	)	PUNCT
iajs-2858	160	1	−	−	PROPN
iajs-2858	160	2	(	(	PUNCT
iajs-2858	160	3	(	(	PUNCT
iajs-2858	160	4	4𝑥1	4𝑥1	NUM
iajs-2858	160	5	+	+	SYM
iajs-2858	160	6	6𝑥2	6𝑥2	NUM
iajs-2858	160	7	−	−	PROPN
iajs-2858	160	8	2)(2𝑥1	2)(2𝑥1	NUM
iajs-2858	160	9	+	+	CCONJ
iajs-2858	160	10	3𝑥2	3𝑥2	NUM
iajs-2858	160	11	+	+	NUM
iajs-2858	160	12	1	1	NUM
iajs-2858	160	13	)	)	PUNCT
iajs-2858	160	14	−	−	PROPN
iajs-2858	160	15	(	(	PUNCT
iajs-2858	160	16	6𝑥1	6𝑥1	NUM
iajs-2858	160	17	+	+	CCONJ
iajs-2858	160	18	9𝑥2	9𝑥2	NUM
iajs-2858	161	1	+	+	NUM
iajs-2858	161	2	3)(6𝑥1	3)(6𝑥1	NUM
iajs-2858	161	3	+	+	SYM
iajs-2858	161	4	9𝑥2	9𝑥2	NUM
iajs-2858	162	1	+	+	NUM
iajs-2858	162	2	3	3	NUM
iajs-2858	162	3	)	)	PUNCT
iajs-2858	162	4	)	)	PUNCT
iajs-2858	162	5	𝑝0	𝑝0	NOUN
iajs-2858	162	6	)	)	PUNCT
iajs-2858	162	7	≥	≥	NOUN
iajs-2858	163	1	𝜆	𝜆	X
iajs-2858	163	2	→	→	SYM
iajs-2858	163	3	𝑝0	𝑝0	NOUN
iajs-2858	163	4	≥	≥	NOUN
iajs-2858	163	5	2	2	NUM
iajs-2858	163	6	now	now	ADV
iajs-2858	163	7	,	,	PUNCT
iajs-2858	163	8	find	find	VERB
iajs-2858	163	9	𝑝1	𝑝1	NOUN
iajs-2858	163	10	by	by	ADP
iajs-2858	163	11	using	use	VERB
iajs-2858	163	12	formula	formula	NOUN
iajs-2858	163	13	(	(	PUNCT
iajs-2858	163	14	9	9	NUM
iajs-2858	163	15	)	)	PUNCT
iajs-2858	163	16	at	at	ADP
iajs-2858	163	17	decision	decision	NOUN
iajs-2858	163	18	variable	variable	NOUN
iajs-2858	163	19	𝑥1	𝑥1	NOUN
iajs-2858	163	20	=	=	SYM
iajs-2858	163	21	0.2	0.2	NUM
iajs-2858	163	22	,	,	PUNCT
iajs-2858	163	23	𝑥2	𝑥2	NOUN
iajs-2858	163	24	=	=	SYM
iajs-2858	163	25	1.6	1.6	NUM
iajs-2858	163	26	as	as	SCONJ
iajs-2858	163	27	follow	follow	VERB
iajs-2858	163	28	:	:	PUNCT
iajs-2858	163	29	(	(	PUNCT
iajs-2858	163	30	1	1	NUM
iajs-2858	163	31	−	−	PROPN
iajs-2858	163	32	(	(	PUNCT
iajs-2858	163	33	(	(	PUNCT
iajs-2858	163	34	𝑥	𝑥	NOUN
iajs-2858	163	35	1	1	NUM
iajs-2858	163	36	+	+	NUM
iajs-2858	163	37	3𝑥2	3𝑥2	NUM
iajs-2858	163	38	)	)	PUNCT
iajs-2858	163	39	−	−	ADP
iajs-2858	163	40	5	5	X
iajs-2858	163	41	)	)	PUNCT
iajs-2858	163	42	𝑝1	𝑝1	NOUN
iajs-2858	163	43	)	)	PUNCT
iajs-2858	163	44	≥	≥	PROPN
iajs-2858	163	45	𝜆	𝜆	X
iajs-2858	163	46	→	→	PUNCT
iajs-2858	163	47	𝑝1	𝑝1	NOUN
iajs-2858	163	48	≥	≥	NOUN
iajs-2858	163	49	2	2	NUM
iajs-2858	163	50	for	for	ADP
iajs-2858	163	51	𝑝2	𝑝2	NOUN
iajs-2858	163	52	by	by	ADP
iajs-2858	163	53	using	use	VERB
iajs-2858	163	54	formula	formula	NOUN
iajs-2858	163	55	(	(	PUNCT
iajs-2858	163	56	9	9	NUM
iajs-2858	163	57	)	)	PUNCT
iajs-2858	163	58	at	at	ADP
iajs-2858	163	59	decision	decision	NOUN
iajs-2858	163	60	variable	variable	NOUN
iajs-2858	163	61	𝑥1	𝑥1	NOUN
iajs-2858	163	62	=	=	SYM
iajs-2858	163	63	0.2	0.2	NUM
iajs-2858	163	64	,	,	PUNCT
iajs-2858	163	65	𝑥2	𝑥2	NOUN
iajs-2858	163	66	=	=	SYM
iajs-2858	163	67	1.6	1.6	NUM
iajs-2858	163	68	as	as	SCONJ
iajs-2858	163	69	follow	follow	VERB
iajs-2858	163	70	:	:	PUNCT
iajs-2858	163	71	(	(	PUNCT
iajs-2858	163	72	1	1	NUM
iajs-2858	163	73	−	−	PROPN
iajs-2858	163	74	(	(	PUNCT
iajs-2858	163	75	2𝑥1	2𝑥1	NUM
iajs-2858	163	76	+	+	CCONJ
iajs-2858	163	77	𝑥2	𝑥2	NOUN
iajs-2858	163	78	)	)	PUNCT
iajs-2858	163	79	−	−	ADP
iajs-2858	163	80	5	5	NUM
iajs-2858	163	81	)	)	PUNCT
iajs-2858	163	82	𝑝2	𝑝2	NOUN
iajs-2858	163	83	)	)	PUNCT
iajs-2858	163	84	≥	≥	PROPN
iajs-2858	163	85	𝜆	𝜆	PRON
iajs-2858	163	86	→	→	SYM
iajs-2858	163	87	𝑝2	𝑝2	NOUN
iajs-2858	163	88	≥	≥	NUM
iajs-2858	163	89	2	2	NUM
iajs-2858	163	90	step	step	NOUN
iajs-2858	163	91	three	three	NUM
iajs-2858	163	92	:	:	PUNCT
iajs-2858	163	93	construct	construct	VERB
iajs-2858	163	94	the	the	DET
iajs-2858	163	95	crisp	crisp	ADJ
iajs-2858	163	96	linear	linear	NOUN
iajs-2858	163	97	programming	programming	NOUN
iajs-2858	163	98	(	(	PUNCT
iajs-2858	163	99	𝐿𝑃)(𝑓,𝜆	𝐿𝑃)(𝑓,𝜆	NUM
iajs-2858	163	100	)	)	PUNCT
iajs-2858	163	101	by	by	ADP
iajs-2858	163	102	using	use	VERB
iajs-2858	163	103	formula	formula	NOUN
iajs-2858	163	104	(	(	PUNCT
iajs-2858	163	105	10,13	10,13	NUM
iajs-2858	163	106	)	)	PUNCT
iajs-2858	164	1	𝑀𝑎𝑥	𝑀𝑎𝑥	PROPN
iajs-2858	164	2	𝜆	𝜆	ADV
iajs-2858	164	3	subject	subject	NOUN
iajs-2858	164	4	to	to	ADP
iajs-2858	164	5	,	,	PUNCT
iajs-2858	164	6	2𝜆	2𝜆	NUM
iajs-2858	164	7	−	−	PROPN
iajs-2858	164	8	6𝑥1	6𝑥1	NUM
iajs-2858	164	9	+	+	CCONJ
iajs-2858	164	10	3𝑥2	3𝑥2	NUM
iajs-2858	164	11	≤	≤	NUM
iajs-2858	164	12	30.6	30.6	NUM
iajs-2858	164	13	2𝜆	2𝜆	NUM
iajs-2858	164	14	+	+	CCONJ
iajs-2858	164	15	𝑥1	𝑥1	NOUN
iajs-2858	164	16	+	+	CCONJ
iajs-2858	164	17	3𝑥2	3𝑥2	NUM
iajs-2858	164	18	≤	≤	NUM
iajs-2858	164	19	6	6	NUM
iajs-2858	164	20	2𝜆	2𝜆	NUM
iajs-2858	164	21	+	+	CCONJ
iajs-2858	164	22	2𝑥1	2𝑥1	NUM
iajs-2858	164	23	+	+	CCONJ
iajs-2858	164	24	𝑥2	𝑥2	NOUN
iajs-2858	164	25	≤	≤	NUM
iajs-2858	164	26	3	3	NUM
iajs-2858	164	27	𝜆	𝜆	NOUN
iajs-2858	164	28	,	,	PUNCT
iajs-2858	164	29	𝑥1	𝑥1	NOUN
iajs-2858	164	30	,	,	PUNCT
iajs-2858	164	31	𝑥2	𝑥2	PROPN
iajs-2858	164	32	≥	≥	NOUN
iajs-2858	164	33	0	0	NUM
iajs-2858	164	34	step	step	NOUN
iajs-2858	164	35	four	four	NUM
iajs-2858	164	36	:	:	PUNCT
iajs-2858	164	37	optimize	optimize	VERB
iajs-2858	164	38	crisp	crisp	ADJ
iajs-2858	164	39	linear	linear	NOUN
iajs-2858	164	40	programming	programming	NOUN
iajs-2858	164	41	(	(	PUNCT
iajs-2858	164	42	𝐿𝑃)(𝑓,𝜆	𝐿𝑃)(𝑓,𝜆	NUM
iajs-2858	164	43	)	)	PUNCT
iajs-2858	164	44	by	by	ADP
iajs-2858	164	45	using	use	VERB
iajs-2858	164	46	simplex	simplex	NOUN
iajs-2858	164	47	algorithm	algorithm	NOUN
iajs-2858	164	48	,	,	PUNCT
iajs-2858	164	49	found	find	VERB
iajs-2858	164	50	that	that	SCONJ
iajs-2858	164	51	the	the	DET
iajs-2858	164	52	decision	decision	NOUN
iajs-2858	164	53	variable	variable	NOUN
iajs-2858	164	54	is	be	AUX
iajs-2858	164	55	𝒙𝟏	𝒙𝟏	NOUN
iajs-2858	164	56	=	=	PUNCT
iajs-2858	164	57	𝟎.	𝟎.	X
iajs-2858	164	58	𝟐	𝟐	NUM
iajs-2858	164	59	,	,	PUNCT
iajs-2858	164	60	𝒙𝟐	𝒙𝟐	NOUN
iajs-2858	164	61	=	=	SYM
iajs-2858	164	62	𝟏.	𝟏.	X
iajs-2858	164	63	𝟔	𝟔	NUM
iajs-2858	164	64	and	and	CCONJ
iajs-2858	164	65	𝑴𝒂𝒙.	𝑴𝒂𝒙.	PROPN
iajs-2858	164	66	𝒁	𝒁	PROPN
iajs-2858	164	67	=	=	PUNCT
iajs-2858	164	68	𝟎.	𝟎.	X
iajs-2858	164	69	𝟏𝟓	𝟏𝟓	NUM
iajs-2858	164	70	in	in	ADP
iajs-2858	164	71	additional	additional	ADJ
iajs-2858	164	72	,	,	PUNCT
iajs-2858	164	73	will	will	AUX
iajs-2858	164	74	solve	solve	VERB
iajs-2858	164	75	the	the	DET
iajs-2858	164	76	such	such	ADJ
iajs-2858	164	77	numerical	numerical	ADJ
iajs-2858	164	78	example	example	NOUN
iajs-2858	164	79	by	by	ADP
iajs-2858	164	80	computational	computational	ADJ
iajs-2858	164	81	procedure	procedure	NOUN
iajs-2858	164	82	of	of	ADP
iajs-2858	164	83	quadratic	quadratic	ADJ
iajs-2858	164	84	fractional	fractional	ADJ
iajs-2858	164	85	algorithm	algorithm	NOUN
iajs-2858	164	86	introduced	introduce	VERB
iajs-2858	164	87	by	by	ADP
iajs-2858	164	88	[	[	X
iajs-2858	164	89	10	10	NUM
iajs-2858	164	90	]	]	PUNCT
iajs-2858	164	91	,	,	PUNCT
iajs-2858	164	92	section	section	NOUN
iajs-2858	164	93	4.1	4.1	NUM
iajs-2858	164	94	to	to	PART
iajs-2858	164	95	compare	compare	VERB
iajs-2858	164	96	between	between	ADP
iajs-2858	164	97	two	two	NUM
iajs-2858	164	98	methods	method	NOUN
iajs-2858	164	99	(	(	PUNCT
iajs-2858	164	100	msfa	msfa	NOUN
iajs-2858	164	101	)	)	PUNCT
iajs-2858	164	102	and	and	CCONJ
iajs-2858	164	103	(	(	PUNCT
iajs-2858	164	104	modified	modify	VERB
iajs-2858	164	105	simplex	simplex	NOUN
iajs-2858	164	106	approach	approach	NOUN
iajs-2858	164	107	)	)	PUNCT
iajs-2858	164	108	.	.	PUNCT
iajs-2858	165	1	now	now	ADV
iajs-2858	165	2	,	,	PUNCT
iajs-2858	165	3	maximize	maximize	VERB
iajs-2858	165	4	z	z	NOUN
iajs-2858	165	5	=	=	SYM
iajs-2858	165	6	(	(	PUNCT
iajs-2858	165	7	4𝑥1	4𝑥1	X
iajs-2858	165	8	+	+	NOUN
iajs-2858	165	9	6𝑥2−2)(2𝑥1	6𝑥2−2)(2𝑥1	NOUN
iajs-2858	165	10	+	+	NOUN
iajs-2858	165	11	3𝑥2	3𝑥2	NUM
iajs-2858	165	12	+	+	NOUN
iajs-2858	165	13	1	1	NUM
iajs-2858	165	14	)	)	PUNCT
iajs-2858	165	15	(	(	PUNCT
iajs-2858	165	16	6𝑥1	6𝑥1	NUM
iajs-2858	165	17	+	+	NOUN
iajs-2858	165	18	9𝑥2	9𝑥2	NUM
iajs-2858	165	19	+	+	ADJ
iajs-2858	165	20	3)2	3)2	NUM
iajs-2858	165	21	subject	subject	NOUN
iajs-2858	165	22	to	to	ADP
iajs-2858	165	23	:	:	PUNCT
iajs-2858	165	24	𝑥1	𝑥1	NOUN
iajs-2858	165	25	+	+	CCONJ
iajs-2858	165	26	3𝑥2	3𝑥2	NUM
iajs-2858	165	27	≤	≤	NUM
iajs-2858	165	28	5	5	NUM
iajs-2858	165	29	2𝑥1	2𝑥1	NUM
iajs-2858	165	30	+	+	CCONJ
iajs-2858	165	31	𝑥2	𝑥2	NOUN
iajs-2858	165	32	≤	≤	NUM
iajs-2858	165	33	2	2	NUM
iajs-2858	165	34	𝑥1	𝑥1	NOUN
iajs-2858	165	35	,	,	PUNCT
iajs-2858	165	36	𝑥2	𝑥2	PROPN
iajs-2858	165	37	≥	≥	NOUN
iajs-2858	165	38	0	0	NUM
iajs-2858	165	39	introduce	introduce	VERB
iajs-2858	165	40	the	the	DET
iajs-2858	165	41	slack	slack	NOUN
iajs-2858	165	42	variables	variable	VERB
iajs-2858	165	43	s1	s1	PROPN
iajs-2858	165	44	≥	≥	X
iajs-2858	165	45	0	0	NUM
iajs-2858	165	46	and	and	CCONJ
iajs-2858	165	47	s2	s2	VERB
iajs-2858	165	48	≥	≥	NOUN
iajs-2858	165	49	0	0	NUM
iajs-2858	166	1	the	the	DET
iajs-2858	166	2	problem	problem	NOUN
iajs-2858	166	3	in	in	ADP
iajs-2858	166	4	the	the	DET
iajs-2858	166	5	standard	standard	ADJ
iajs-2858	166	6	form	form	NOUN
iajs-2858	166	7	becomes	become	VERB
iajs-2858	166	8	:	:	PUNCT
iajs-2858	166	9	𝑀𝑎𝑥.	𝑀𝑎𝑥.	PROPN
iajs-2858	166	10	𝑊	𝑊	PROPN
iajs-2858	166	11	=	=	SYM
iajs-2858	166	12	(	(	PUNCT
iajs-2858	166	13	4𝑥1	4𝑥1	NUM
iajs-2858	166	14	+	+	NOUN
iajs-2858	166	15	6𝑥2−2)(2𝑥1	6𝑥2−2)(2𝑥1	NOUN
iajs-2858	166	16	+	+	NOUN
iajs-2858	166	17	3𝑥2	3𝑥2	NUM
iajs-2858	166	18	+	+	NOUN
iajs-2858	166	19	1	1	NUM
iajs-2858	166	20	)	)	PUNCT
iajs-2858	166	21	(	(	PUNCT
iajs-2858	166	22	6𝑥1	6𝑥1	NUM
iajs-2858	166	23	+	+	NOUN
iajs-2858	166	24	9𝑥2	9𝑥2	NUM
iajs-2858	166	25	+	+	ADJ
iajs-2858	166	26	3)(6𝑥1	3)(6𝑥1	NUM
iajs-2858	166	27	+	+	NOUN
iajs-2858	166	28	9𝑥2	9𝑥2	NUM
iajs-2858	166	29	+	+	NOUN
iajs-2858	166	30	3	3	NUM
iajs-2858	166	31	)	)	PUNCT
iajs-2858	166	32	=	=	SYM
iajs-2858	166	33	𝑧(1)𝑧(2	𝑧(1)𝑧(2	PROPN
iajs-2858	166	34	)	)	PUNCT
iajs-2858	166	35	𝑧(3)𝑧(4	𝑧(3)𝑧(4	NOUN
iajs-2858	166	36	)	)	PUNCT
iajs-2858	166	37	subject	subject	NOUN
iajs-2858	166	38	to	to	ADP
iajs-2858	166	39	:	:	PUNCT
iajs-2858	166	40	ihjpas	ihjpas	PROPN
iajs-2858	166	41	.	.	PUNCT
iajs-2858	167	1	53	53	NUM
iajs-2858	167	2	(	(	PUNCT
iajs-2858	167	3	4)2022	4)2022	NOUN
iajs-2858	167	4	252	252	NUM
iajs-2858	167	5	𝑥1	𝑥1	NOUN
iajs-2858	167	6	+	+	CCONJ
iajs-2858	167	7	3𝑥2	3𝑥2	NUM
iajs-2858	167	8	+	+	NUM
iajs-2858	167	9	s1	s1	NOUN
iajs-2858	167	10	=	=	SYM
iajs-2858	167	11	5	5	NUM
iajs-2858	167	12	2𝑥1	2𝑥1	NUM
iajs-2858	167	13	+	+	CCONJ
iajs-2858	167	14	𝑥2+s2	𝑥2+s2	VERB
iajs-2858	167	15	=	=	SYM
iajs-2858	167	16	2	2	NUM
iajs-2858	167	17	𝑥1	𝑥1	NOUN
iajs-2858	167	18	,	,	PUNCT
iajs-2858	167	19	𝑥2	𝑥2	NOUN
iajs-2858	167	20	,	,	PUNCT
iajs-2858	167	21	s1	s1	NOUN
iajs-2858	167	22	,	,	PUNCT
iajs-2858	167	23	s2	s2	X
iajs-2858	167	24	≥	≥	NOUN
iajs-2858	167	25	0	0	NUM
iajs-2858	167	26	for	for	ADP
iajs-2858	167	27	starting	start	VERB
iajs-2858	167	28	table	table	NOUN
iajs-2858	167	29	,	,	PUNCT
iajs-2858	167	30	we	we	PRON
iajs-2858	167	31	will	will	AUX
iajs-2858	167	32	find	find	VERB
iajs-2858	167	33	∆1	∆1	NOUN
iajs-2858	167	34	=	=	SYM
iajs-2858	167	35	−72	−72	NOUN
iajs-2858	167	36	,	,	PUNCT
iajs-2858	167	37	∆2	∆2	X
iajs-2858	167	38	=	=	SYM
iajs-2858	167	39	−108	−108	PROPN
iajs-2858	167	40	,	,	PUNCT
iajs-2858	167	41	∆3	∆3	NOUN
iajs-2858	167	42	=	=	SYM
iajs-2858	167	43	0	0	NUM
iajs-2858	167	44	,	,	PUNCT
iajs-2858	167	45	∆4	∆4	NOUN
iajs-2858	167	46	=	=	NOUN
iajs-2858	167	47	0	0	PROPN
iajs-2858	167	48	.	.	PUNCT
iajs-2858	168	1	we	we	PRON
iajs-2858	168	2	choose	choose	VERB
iajs-2858	168	3	min	min	PROPN
iajs-2858	168	4	∆𝑗	∆𝑗	PROPN
iajs-2858	168	5	(	(	PUNCT
iajs-2858	168	6	∆2	∆2	PROPN
iajs-2858	168	7	in	in	ADP
iajs-2858	168	8	this	this	DET
iajs-2858	168	9	case	case	NOUN
iajs-2858	168	10	)	)	PUNCT
iajs-2858	168	11	.	.	PUNCT
iajs-2858	169	1	thus	thus	ADV
iajs-2858	169	2	,	,	PUNCT
iajs-2858	169	3	z	z	PROPN
iajs-2858	169	4	can	can	AUX
iajs-2858	169	5	be	be	AUX
iajs-2858	169	6	increased	increase	VERB
iajs-2858	169	7	by	by	ADP
iajs-2858	169	8	taking	take	VERB
iajs-2858	169	9	x2	x2	PROPN
iajs-2858	169	10	in	in	ADP
iajs-2858	169	11	the	the	DET
iajs-2858	169	12	basis	basis	NOUN
iajs-2858	169	13	.	.	PUNCT
iajs-2858	170	1	the	the	DET
iajs-2858	170	2	method	method	NOUN
iajs-2858	170	3	to	to	PART
iajs-2858	170	4	determine	determine	VERB
iajs-2858	170	5	the	the	DET
iajs-2858	170	6	leaving	leaving	NOUN
iajs-2858	170	7	variables	variable	NOUN
iajs-2858	170	8	and	and	CCONJ
iajs-2858	170	9	also	also	ADV
iajs-2858	170	10	the	the	DET
iajs-2858	170	11	new	new	ADJ
iajs-2858	170	12	value	value	NOUN
iajs-2858	170	13	of	of	ADP
iajs-2858	170	14	xij	xij	PROPN
iajs-2858	170	15	,	,	PUNCT
iajs-2858	170	16	xb	xb	PROPN
iajs-2858	170	17	,	,	PUNCT
iajs-2858	170	18	∆1	∆1	PROPN
iajs-2858	170	19	,	,	PUNCT
iajs-2858	170	20	∆2	∆2	X
iajs-2858	170	21	,	,	PUNCT
iajs-2858	170	22	∆3	∆3	NOUN
iajs-2858	170	23	and	and	CCONJ
iajs-2858	170	24	∆4	∆4	NOUN
iajs-2858	170	25	corresponding	correspond	VERB
iajs-2858	170	26	to	to	ADP
iajs-2858	170	27	improved	improved	ADJ
iajs-2858	170	28	solution	solution	NOUN
iajs-2858	170	29	will	will	AUX
iajs-2858	170	30	be	be	AUX
iajs-2858	170	31	the	the	DET
iajs-2858	170	32	same	same	ADJ
iajs-2858	170	33	as	as	ADP
iajs-2858	170	34	for	for	ADP
iajs-2858	170	35	ordinary	ordinary	ADJ
iajs-2858	170	36	simplex	simplex	NOUN
iajs-2858	170	37	method	method	NOUN
iajs-2858	170	38	.	.	PUNCT
iajs-2858	171	1	thus	thus	ADV
iajs-2858	171	2	,	,	PUNCT
iajs-2858	171	3	s1	s1	PROPN
iajs-2858	171	4	will	will	AUX
iajs-2858	171	5	be	be	AUX
iajs-2858	171	6	the	the	DET
iajs-2858	171	7	departing	depart	VERB
iajs-2858	171	8	variable	variable	NOUN
iajs-2858	171	9	.	.	PUNCT
iajs-2858	172	1	starting	start	VERB
iajs-2858	172	2	table	table	NOUN
iajs-2858	172	3	c1b	c1b	PROPN
iajs-2858	172	4	4	4	NUM
iajs-2858	172	5	6	6	NUM
iajs-2858	172	6	0	0	NUM
iajs-2858	172	7	0	0	NUM
iajs-2858	172	8	c2b	c2b	ADP
iajs-2858	172	9	2	2	NUM
iajs-2858	172	10	3	3	NUM
iajs-2858	172	11	0	0	NUM
iajs-2858	172	12	0	0	NUM
iajs-2858	172	13	c1b	c1b	PROPN
iajs-2858	172	14	6	6	NUM
iajs-2858	172	15	9	9	NUM
iajs-2858	172	16	0	0	NUM
iajs-2858	172	17	0	0	NUM
iajs-2858	172	18	c2b	c2b	ADP
iajs-2858	172	19	6	6	NUM
iajs-2858	172	20	9	9	NUM
iajs-2858	172	21	0	0	NUM
iajs-2858	172	22	0	0	NUM
iajs-2858	172	23	b	b	X
iajs-2858	172	24	c1b	c1b	NOUN
iajs-2858	172	25	c2b	c2b	ADP
iajs-2858	172	26	c1b	c1b	PROPN
iajs-2858	172	27	c2b	c2b	ADP
iajs-2858	172	28	xb	xb	PROPN
iajs-2858	172	29	x1	x1	PROPN
iajs-2858	172	30	x2	x2	PROPN
iajs-2858	172	31	s1	s1	PROPN
iajs-2858	172	32	s2	s2	PROPN
iajs-2858	172	33	min	min	PROPN
iajs-2858	172	34	(	(	PUNCT
iajs-2858	172	35	xb	xb	PROPN
iajs-2858	172	36	x1	x1	PROPN
iajs-2858	172	37	)	)	PUNCT
iajs-2858	172	38	s1	s1	NOUN
iajs-2858	172	39	0	0	NUM
iajs-2858	172	40	0	0	NUM
iajs-2858	172	41	0	0	NUM
iajs-2858	172	42	0	0	NUM
iajs-2858	172	43	5	5	NUM
iajs-2858	172	44	1	1	NUM
iajs-2858	172	45	3	3	NUM
iajs-2858	172	46	1	1	NUM
iajs-2858	172	47	0	0	NUM
iajs-2858	172	48	1.6	1.6	NUM
iajs-2858	172	49	s2	s2	NOUN
iajs-2858	172	50	0	0	NUM
iajs-2858	172	51	0	0	NUM
iajs-2858	172	52	0	0	NUM
iajs-2858	172	53	0	0	NUM
iajs-2858	172	54	2	2	NUM
iajs-2858	172	55	2	2	NUM
iajs-2858	172	56	1	1	NUM
iajs-2858	172	57	0	0	NUM
iajs-2858	172	58	1	1	NUM
iajs-2858	172	59	2	2	NUM
iajs-2858	172	60	𝑧1	𝑧1	NOUN
iajs-2858	172	61	(	(	PUNCT
iajs-2858	172	62	1	1	NUM
iajs-2858	172	63	)	)	PUNCT
iajs-2858	172	64	=	=	SYM
iajs-2858	172	65	c1bxb	c1bxb	VERB
iajs-2858	172	66	=	=	SYM
iajs-2858	172	67	−2	−2	PROPN
iajs-2858	172	68	δk1	δk1	PROPN
iajs-2858	172	69	1𝑗	1𝑗	NOUN
iajs-2858	172	70	-4	-4	PUNCT
iajs-2858	173	1	-6	-6	PROPN
iajs-2858	173	2	0	0	NUM
iajs-2858	173	3	0	0	NUM
iajs-2858	173	4	𝑧1	𝑧1	NOUN
iajs-2858	173	5	(	(	PUNCT
iajs-2858	173	6	2	2	NUM
iajs-2858	173	7	)	)	PUNCT
iajs-2858	173	8	=	=	VERB
iajs-2858	174	1	c2bxb	c2bxb	PROPN
iajs-2858	174	2	=	=	SYM
iajs-2858	174	3	1	1	NUM
iajs-2858	174	4	δk1	δk1	NOUN
iajs-2858	174	5	2𝑗	2𝑗	NOUN
iajs-2858	174	6	-2	-2	INTJ
iajs-2858	174	7	-3	-3	INTJ
iajs-2858	174	8	0	0	NUM
iajs-2858	174	9	0	0	NUM
iajs-2858	174	10	𝑧2	𝑧2	NOUN
iajs-2858	174	11	(	(	PUNCT
iajs-2858	174	12	1	1	NUM
iajs-2858	174	13	)	)	PUNCT
iajs-2858	174	14	=	=	SYM
iajs-2858	174	15	𝐶1bxb	𝐶1bxb	VERB
iajs-2858	174	16	=	=	SYM
iajs-2858	174	17	3	3	NUM
iajs-2858	174	18	δk2	δk2	NOUN
iajs-2858	174	19	1𝑗	1𝑗	NUM
iajs-2858	174	20	-6	-6	CCONJ
iajs-2858	174	21	-9	-9	PROPN
iajs-2858	174	22	0	0	NUM
iajs-2858	174	23	0	0	NUM
iajs-2858	174	24	𝑧2	𝑧2	NOUN
iajs-2858	174	25	(	(	PUNCT
iajs-2858	174	26	2	2	NUM
iajs-2858	174	27	)	)	PUNCT
iajs-2858	174	28	=	=	SYM
iajs-2858	174	29	𝐶2bxb	𝐶2bxb	PROPN
iajs-2858	174	30	=	=	SYM
iajs-2858	174	31	3	3	NUM
iajs-2858	174	32	δk2	δk2	NOUN
iajs-2858	174	33	2𝑗	2𝑗	NOUN
iajs-2858	174	34	-6	-6	PROPN
iajs-2858	174	35	-9	-9	PROPN
iajs-2858	174	36	0	0	NUM
iajs-2858	174	37	0	0	NUM
iajs-2858	174	38	𝑧1	𝑧1	NOUN
iajs-2858	174	39	=	=	SYM
iajs-2858	174	40	𝑧1	𝑧1	NOUN
iajs-2858	174	41	(	(	PUNCT
iajs-2858	174	42	1)𝑧1	1)𝑧1	NUM
iajs-2858	174	43	(	(	PUNCT
iajs-2858	174	44	2	2	NUM
iajs-2858	174	45	)	)	PUNCT
iajs-2858	174	46	=	=	SYM
iajs-2858	174	47	−2	−2	PROPN
iajs-2858	174	48	∆𝜉1𝑗	∆𝜉1𝑗	PROPN
iajs-2858	174	49	-8	-8	NOUN
iajs-2858	174	50	-12	-12	NUM
iajs-2858	174	51	0	0	NUM
iajs-2858	174	52	0	0	NUM
iajs-2858	174	53	𝑧2	𝑧2	NOUN
iajs-2858	174	54	=	=	PROPN
iajs-2858	174	55	𝑧2	𝑧2	PROPN
iajs-2858	174	56	(	(	PUNCT
iajs-2858	174	57	1)𝑧2	1)𝑧2	NUM
iajs-2858	174	58	(	(	PUNCT
iajs-2858	174	59	2	2	NUM
iajs-2858	174	60	)	)	PUNCT
iajs-2858	174	61	=	=	SYM
iajs-2858	174	62	9	9	NUM
iajs-2858	174	63	∆𝜉2𝑗	∆𝜉2𝑗	VERB
iajs-2858	174	64	0	0	NUM
iajs-2858	174	65	0	0	NUM
iajs-2858	174	66	0	0	NUM
iajs-2858	174	67	0	0	NUM
iajs-2858	175	1	𝑧	𝑧	NOUN
iajs-2858	175	2	=	=	NOUN
iajs-2858	175	3	𝑧1	𝑧1	PROPN
iajs-2858	175	4	𝑧2	𝑧2	NOUN
iajs-2858	175	5	=	=	PROPN
iajs-2858	175	6	−0.222	−0.222	PROPN
iajs-2858	175	7	∆𝑗	∆𝑗	PROPN
iajs-2858	175	8	-72	-72	PROPN
iajs-2858	176	1	-108	-108	NUM
iajs-2858	176	2	0	0	NUM
iajs-2858	176	3	0	0	NUM
iajs-2858	176	4	first	first	ADJ
iajs-2858	176	5	iteration	iteration	NOUN
iajs-2858	176	6	table	table	NOUN
iajs-2858	176	7	introducing	introduce	VERB
iajs-2858	176	8	x2	x2	PROPN
iajs-2858	176	9	and	and	CCONJ
iajs-2858	176	10	dropping	dropping	NOUN
iajs-2858	176	11	s1	s1	NOUN
iajs-2858	176	12	,	,	PUNCT
iajs-2858	176	13	we	we	PRON
iajs-2858	176	14	get	get	VERB
iajs-2858	176	15	the	the	DET
iajs-2858	176	16	following	follow	VERB
iajs-2858	176	17	table	table	NOUN
iajs-2858	176	18	:	:	PUNCT
iajs-2858	176	19	c1b	c1b	NOUN
iajs-2858	176	20	4	4	NUM
iajs-2858	176	21	6	6	NUM
iajs-2858	176	22	0	0	NUM
iajs-2858	176	23	0	0	NUM
iajs-2858	176	24	c2b	c2b	ADP
iajs-2858	176	25	2	2	NUM
iajs-2858	176	26	3	3	NUM
iajs-2858	176	27	0	0	NUM
iajs-2858	176	28	0	0	NUM
iajs-2858	176	29	c1b	c1b	PROPN
iajs-2858	176	30	6	6	NUM
iajs-2858	176	31	9	9	NUM
iajs-2858	176	32	0	0	NUM
iajs-2858	176	33	0	0	NUM
iajs-2858	176	34	c2b	c2b	ADP
iajs-2858	176	35	6	6	NUM
iajs-2858	177	1	9	9	NUM
iajs-2858	177	2	0	0	NUM
iajs-2858	177	3	0	0	NUM
iajs-2858	177	4	b	b	X
iajs-2858	177	5	c1b	c1b	NOUN
iajs-2858	177	6	c2b	c2b	ADP
iajs-2858	177	7	c1b	c1b	PROPN
iajs-2858	177	8	c2b	c2b	ADP
iajs-2858	177	9	xb	xb	PROPN
iajs-2858	177	10	x1	x1	PROPN
iajs-2858	177	11	x2	x2	PROPN
iajs-2858	177	12	s1	s1	PROPN
iajs-2858	177	13	s2	s2	PROPN
iajs-2858	177	14	min	min	PROPN
iajs-2858	177	15	(	(	PUNCT
iajs-2858	177	16	xb	xb	PROPN
iajs-2858	177	17	x1	x1	PROPN
iajs-2858	177	18	)	)	PUNCT
iajs-2858	178	1	x2	x2	NOUN
iajs-2858	178	2	9	9	NUM
iajs-2858	178	3	9	9	NUM
iajs-2858	178	4	6	6	NUM
iajs-2858	178	5	3	3	NUM
iajs-2858	178	6	5/3	5/3	NUM
iajs-2858	178	7	1/3	1/3	NUM
iajs-2858	178	8	1	1	NUM
iajs-2858	178	9	1/3	1/3	NUM
iajs-2858	178	10	0	0	NUM
iajs-2858	178	11	5	5	NUM
iajs-2858	178	12	s2	s2	NOUN
iajs-2858	178	13	0	0	NUM
iajs-2858	178	14	0	0	NUM
iajs-2858	178	15	0	0	NUM
iajs-2858	178	16	0	0	NUM
iajs-2858	178	17	0.33	0.33	NUM
iajs-2858	178	18	1.66	1.66	NUM
iajs-2858	178	19	0	0	NUM
iajs-2858	179	1	-0.33	-0.33	NUM
iajs-2858	179	2	1	1	NUM
iajs-2858	179	3	1.19	1.19	NUM
iajs-2858	179	4	𝑧1	𝑧1	NOUN
iajs-2858	179	5	(	(	PUNCT
iajs-2858	179	6	1	1	NUM
iajs-2858	179	7	)	)	PUNCT
iajs-2858	179	8	=	=	VERB
iajs-2858	179	9	c1bxb	c1bxb	VERB
iajs-2858	179	10	=	=	SYM
iajs-2858	179	11	8	8	NUM
iajs-2858	179	12	δk1	δk1	PROPN
iajs-2858	179	13	1𝑗	1𝑗	NOUN
iajs-2858	179	14	-2	-2	NOUN
iajs-2858	179	15	0	0	NUM
iajs-2858	179	16	2	2	NUM
iajs-2858	179	17	0	0	NUM
iajs-2858	179	18	𝑧1	𝑧1	NOUN
iajs-2858	179	19	(	(	PUNCT
iajs-2858	179	20	2	2	NUM
iajs-2858	179	21	)	)	PUNCT
iajs-2858	179	22	=	=	VERB
iajs-2858	179	23	c2bxb	c2bxb	PROPN
iajs-2858	179	24	=	=	PUNCT
iajs-2858	179	25	6	6	NUM
iajs-2858	179	26	δk1	δk1	ADJ
iajs-2858	179	27	2𝑗	2𝑗	NOUN
iajs-2858	179	28	-1	-1	SYM
iajs-2858	179	29	0	0	NUM
iajs-2858	179	30	1	1	NUM
iajs-2858	179	31	0	0	NUM
iajs-2858	179	32	𝑧2	𝑧2	NOUN
iajs-2858	179	33	(	(	PUNCT
iajs-2858	179	34	1	1	NUM
iajs-2858	179	35	)	)	PUNCT
iajs-2858	179	36	=	=	PUNCT
iajs-2858	179	37	𝐶1bxb	𝐶1bxb	VERB
iajs-2858	179	38	=	=	SYM
iajs-2858	179	39	18	18	NUM
iajs-2858	179	40	δk2	δk2	NOUN
iajs-2858	179	41	1𝑗	1𝑗	NUM
iajs-2858	179	42	-3	-3	SYM
iajs-2858	179	43	0	0	NUM
iajs-2858	179	44	3	3	NUM
iajs-2858	179	45	0	0	NUM
iajs-2858	179	46	𝑧2	𝑧2	NOUN
iajs-2858	179	47	(	(	PUNCT
iajs-2858	179	48	2	2	NUM
iajs-2858	179	49	)	)	PUNCT
iajs-2858	179	50	=	=	SYM
iajs-2858	180	1	𝐶2bxb	𝐶2bxb	PROPN
iajs-2858	180	2	=	=	SYM
iajs-2858	180	3	18	18	NUM
iajs-2858	180	4	δk2	δk2	NOUN
iajs-2858	180	5	2𝑗	2𝑗	NOUN
iajs-2858	180	6	-3	-3	SYM
iajs-2858	180	7	0	0	NUM
iajs-2858	180	8	3	3	NUM
iajs-2858	180	9	0	0	NUM
iajs-2858	180	10	𝑧1	𝑧1	NOUN
iajs-2858	180	11	=	=	SYM
iajs-2858	180	12	𝑧1	𝑧1	NOUN
iajs-2858	180	13	(	(	PUNCT
iajs-2858	180	14	1)𝑧1	1)𝑧1	NUM
iajs-2858	180	15	(	(	PUNCT
iajs-2858	180	16	2	2	NUM
iajs-2858	180	17	)	)	PUNCT
iajs-2858	180	18	=	=	SYM
iajs-2858	180	19	48	48	NUM
iajs-2858	180	20	∆𝜉1𝑗	∆𝜉1𝑗	PROPN
iajs-2858	180	21	-4	-4	SYM
iajs-2858	180	22	0	0	NUM
iajs-2858	180	23	4	4	NUM
iajs-2858	180	24	0	0	NUM
iajs-2858	180	25	𝑧2	𝑧2	NOUN
iajs-2858	180	26	=	=	PROPN
iajs-2858	180	27	𝑧2	𝑧2	PROPN
iajs-2858	180	28	(	(	PUNCT
iajs-2858	180	29	1)𝑧2	1)𝑧2	NUM
iajs-2858	180	30	(	(	PUNCT
iajs-2858	180	31	2	2	NUM
iajs-2858	180	32	)	)	PUNCT
iajs-2858	180	33	=	=	SYM
iajs-2858	180	34	324	324	NUM
iajs-2858	180	35	∆𝜉2𝑗	∆𝜉2𝑗	VERB
iajs-2858	180	36	0	0	NUM
iajs-2858	180	37	0	0	NUM
iajs-2858	180	38	0	0	SYM
iajs-2858	180	39	0	0	NUM
iajs-2858	181	1	∆𝑗	∆𝑗	ADJ
iajs-2858	181	2	-1296	-1296	NOUN
iajs-2858	181	3	0	0	NUM
iajs-2858	181	4	1296	1296	NUM
iajs-2858	181	5	0	0	NUM
iajs-2858	181	6	second	second	ADJ
iajs-2858	181	7	iteration	iteration	NOUN
iajs-2858	181	8	table	table	NOUN
iajs-2858	181	9	introducing	introduce	VERB
iajs-2858	181	10	x1	x1	PROPN
iajs-2858	181	11	and	and	CCONJ
iajs-2858	181	12	dropping	dropping	PROPN
iajs-2858	181	13	s2	s2	PROPN
iajs-2858	181	14	,	,	PUNCT
iajs-2858	181	15	we	we	PRON
iajs-2858	181	16	get	get	VERB
iajs-2858	181	17	the	the	DET
iajs-2858	181	18	following	follow	VERB
iajs-2858	181	19	table	table	NOUN
iajs-2858	181	20	:	:	PUNCT
iajs-2858	181	21	c1b	c1b	NOUN
iajs-2858	181	22	4	4	NUM
iajs-2858	181	23	6	6	NUM
iajs-2858	181	24	0	0	NUM
iajs-2858	181	25	0	0	NUM
iajs-2858	181	26	ihjpas	ihjpa	NOUN
iajs-2858	181	27	.	.	PUNCT
iajs-2858	182	1	53	53	NUM
iajs-2858	182	2	(	(	PUNCT
iajs-2858	182	3	4)2022	4)2022	NOUN
iajs-2858	182	4	253	253	NUM
iajs-2858	182	5	c2b	c2b	ADP
iajs-2858	182	6	2	2	NUM
iajs-2858	182	7	3	3	NUM
iajs-2858	182	8	0	0	NUM
iajs-2858	182	9	0	0	NUM
iajs-2858	182	10	c1b	c1b	PROPN
iajs-2858	182	11	6	6	NUM
iajs-2858	182	12	9	9	NUM
iajs-2858	182	13	0	0	NUM
iajs-2858	182	14	0	0	NUM
iajs-2858	182	15	c2b	c2b	ADP
iajs-2858	182	16	6	6	NUM
iajs-2858	183	1	9	9	NUM
iajs-2858	183	2	0	0	NUM
iajs-2858	183	3	0	0	NUM
iajs-2858	183	4	b	b	X
iajs-2858	183	5	c1b	c1b	NOUN
iajs-2858	183	6	c2b	c2b	ADP
iajs-2858	183	7	c1b	c1b	PROPN
iajs-2858	183	8	c2b	c2b	ADP
iajs-2858	183	9	xb	xb	PROPN
iajs-2858	183	10	x1	x1	PROPN
iajs-2858	183	11	x2	x2	PROPN
iajs-2858	183	12	s1	s1	PROPN
iajs-2858	183	13	s2	s2	PROPN
iajs-2858	183	14	min	min	PROPN
iajs-2858	183	15	(	(	PUNCT
iajs-2858	183	16	xb	xb	PROPN
iajs-2858	183	17	x1	x1	PROPN
iajs-2858	183	18	)	)	PUNCT
iajs-2858	184	1	x2	x2	NOUN
iajs-2858	184	2	9	9	NUM
iajs-2858	184	3	9	9	NUM
iajs-2858	184	4	6	6	NUM
iajs-2858	184	5	3	3	NUM
iajs-2858	184	6	1.6	1.6	NUM
iajs-2858	184	7	0	0	NUM
iajs-2858	184	8	1	1	NUM
iajs-2858	184	9	0.39	0.39	NUM
iajs-2858	184	10	-0.2	-0.2	NUM
iajs-2858	184	11	x1	x1	NUM
iajs-2858	184	12	6	6	NUM
iajs-2858	184	13	6	6	NUM
iajs-2858	184	14	4	4	NUM
iajs-2858	184	15	2	2	NUM
iajs-2858	184	16	0.2	0.2	NUM
iajs-2858	184	17	1	1	NUM
iajs-2858	184	18	0	0	NUM
iajs-2858	184	19	-1.19	-1.19	ADP
iajs-2858	184	20	0.602	0.602	NUM
iajs-2858	184	21	𝑧1	𝑧1	NOUN
iajs-2858	184	22	(	(	PUNCT
iajs-2858	184	23	1	1	NUM
iajs-2858	184	24	)	)	PUNCT
iajs-2858	184	25	=	=	VERB
iajs-2858	184	26	c1bxb	c1bxb	VERB
iajs-2858	184	27	=	=	SYM
iajs-2858	184	28	8.4	8.4	NUM
iajs-2858	184	29	δk1	δk1	VERB
iajs-2858	184	30	1𝑗	1𝑗	NOUN
iajs-2858	184	31	0	0	NUM
iajs-2858	184	32	0	0	NUM
iajs-2858	184	33	1.34	1.34	NUM
iajs-2858	184	34	2	2	NUM
iajs-2858	184	35	𝑧1	𝑧1	NOUN
iajs-2858	184	36	(	(	PUNCT
iajs-2858	184	37	2	2	NUM
iajs-2858	184	38	)	)	PUNCT
iajs-2858	184	39	=	=	VERB
iajs-2858	185	1	c2bxb	c2bxb	PROPN
iajs-2858	185	2	=	=	PUNCT
iajs-2858	186	1	6.2	6.2	NUM
iajs-2858	186	2	δk1	δk1	NOUN
iajs-2858	186	3	2𝑗	2𝑗	NOUN
iajs-2858	186	4	0	0	NUM
iajs-2858	186	5	0	0	NUM
iajs-2858	186	6	0.67	0.67	NUM
iajs-2858	186	7	0.6	0.6	NUM
iajs-2858	186	8	𝑧2	𝑧2	NOUN
iajs-2858	186	9	(	(	PUNCT
iajs-2858	186	10	1	1	NUM
iajs-2858	186	11	)	)	PUNCT
iajs-2858	186	12	=	=	VERB
iajs-2858	186	13	𝐶1bxb	𝐶1bxb	VERB
iajs-2858	187	1	=	=	NUM
iajs-2858	187	2	18.6	18.6	NUM
iajs-2858	187	3	δk2	δk2	NOUN
iajs-2858	187	4	1𝑗	1𝑗	NOUN
iajs-2858	187	5	0	0	NUM
iajs-2858	187	6	0	0	NUM
iajs-2858	187	7	2.01	2.01	NUM
iajs-2858	187	8	1.8	1.8	NUM
iajs-2858	187	9	𝑧2	𝑧2	NOUN
iajs-2858	187	10	(	(	PUNCT
iajs-2858	187	11	2	2	NUM
iajs-2858	187	12	)	)	PUNCT
iajs-2858	187	13	=	=	SYM
iajs-2858	188	1	𝐶2bxb	𝐶2bxb	PUNCT
iajs-2858	188	2	=	=	SYM
iajs-2858	188	3	18.6	18.6	NUM
iajs-2858	188	4	δk2	δk2	NOUN
iajs-2858	188	5	2𝑗	2𝑗	NOUN
iajs-2858	188	6	0	0	NUM
iajs-2858	188	7	0	0	NUM
iajs-2858	188	8	2.01	2.01	NUM
iajs-2858	188	9	1.8	1.8	NUM
iajs-2858	188	10	𝑧1	𝑧1	NOUN
iajs-2858	188	11	=	=	SYM
iajs-2858	188	12	𝑧1	𝑧1	NOUN
iajs-2858	188	13	(	(	PUNCT
iajs-2858	188	14	1)𝑧1	1)𝑧1	NUM
iajs-2858	188	15	(	(	PUNCT
iajs-2858	188	16	2	2	NUM
iajs-2858	188	17	)	)	PUNCT
iajs-2858	188	18	=	=	SYM
iajs-2858	188	19	52.08	52.08	NUM
iajs-2858	188	20	∆𝜉1𝑗	∆𝜉1𝑗	NOUN
iajs-2858	188	21	0	0	NUM
iajs-2858	188	22	0	0	NUM
iajs-2858	188	23	2.68	2.68	NUM
iajs-2858	188	24	2.4	2.4	NUM
iajs-2858	188	25	𝑧2	𝑧2	NOUN
iajs-2858	188	26	=	=	SYM
iajs-2858	188	27	𝑧2	𝑧2	PROPN
iajs-2858	188	28	(	(	PUNCT
iajs-2858	188	29	1)𝑧2	1)𝑧2	NUM
iajs-2858	188	30	(	(	PUNCT
iajs-2858	188	31	2	2	NUM
iajs-2858	188	32	)	)	PUNCT
iajs-2858	188	33	=	=	SYM
iajs-2858	188	34	345.95	345.95	NUM
iajs-2858	188	35	∆𝜉2𝑗	∆𝜉2𝑗	ADJ
iajs-2858	188	36	0	0	NUM
iajs-2858	188	37	0	0	NUM
iajs-2858	188	38	0	0	NUM
iajs-2858	188	39	0	0	NUM
iajs-2858	189	1	𝑧	𝑧	NOUN
iajs-2858	189	2	=	=	NOUN
iajs-2858	189	3	𝑧1	𝑧1	NOUN
iajs-2858	189	4	𝑧2	𝑧2	NOUN
iajs-2858	190	1	=	=	PROPN
iajs-2858	190	2	0.15	0.15	NUM
iajs-2858	190	3	∆𝑗	∆𝑗	NOUN
iajs-2858	190	4	0	0	NUM
iajs-2858	190	5	0	0	NUM
iajs-2858	190	6	926342	926342	NUM
iajs-2858	190	7	83020	83020	NUM
iajs-2858	190	8	since	since	SCONJ
iajs-2858	190	9	all	all	DET
iajs-2858	190	10	∆𝑗≥	∆𝑗≥	PRON
iajs-2858	190	11	0	0	NUM
iajs-2858	190	12	we	we	PRON
iajs-2858	190	13	have	have	AUX
iajs-2858	190	14	reached	reach	VERB
iajs-2858	190	15	the	the	DET
iajs-2858	190	16	optimal	optimal	ADJ
iajs-2858	190	17	solution	solution	NOUN
iajs-2858	190	18	:	:	PUNCT
iajs-2858	190	19	𝐗𝟏	𝐗𝟏	PROPN
iajs-2858	190	20	=	=	SYM
iajs-2858	190	21	𝟎.	𝟎.	X
iajs-2858	190	22	𝟐	𝟐	NUM
iajs-2858	190	23	,	,	PUNCT
iajs-2858	190	24	𝐗𝟐	𝐗𝟐	NOUN
iajs-2858	190	25	=	=	SYM
iajs-2858	190	26	𝟏.	𝟏.	X
iajs-2858	190	27	𝟔	𝟔	NUM
iajs-2858	190	28	,	,	PUNCT
iajs-2858	190	29	𝐒𝟏	𝐒𝟏	NOUN
iajs-2858	190	30	=	=	SYM
iajs-2858	190	31	𝟎	𝟎	PROPN
iajs-2858	190	32	,	,	PUNCT
iajs-2858	190	33	𝐒𝟐	𝐒𝟐	NOUN
iajs-2858	190	34	=	=	SYM
iajs-2858	190	35	𝟎	𝟎	PROPN
iajs-2858	190	36	,	,	PUNCT
iajs-2858	190	37	𝑴𝒂𝒙.	𝑴𝒂𝒙.	PROPN
iajs-2858	190	38	𝑾	𝑾	PROPN
iajs-2858	190	39	=	=	PUNCT
iajs-2858	190	40	𝟎.	𝟎.	X
iajs-2858	190	41	𝟏𝟓	𝟏𝟓	NUM
iajs-2858	190	42	.	.	PUNCT
iajs-2858	191	1	the	the	DET
iajs-2858	191	2	fuzzy	fuzzy	ADJ
iajs-2858	191	3	and	and	CCONJ
iajs-2858	191	4	unfuzzy	unfuzzy	ADJ
iajs-2858	191	5	results	result	NOUN
iajs-2858	191	6	are	be	AUX
iajs-2858	191	7	shown	show	VERB
iajs-2858	191	8	in	in	ADP
iajs-2858	191	9	the	the	DET
iajs-2858	191	10	following	following	NOUN
iajs-2858	191	11	:	:	PUNCT
iajs-2858	191	12	table	table	VERB
iajs-2858	191	13	1the	1the	PROPN
iajs-2858	191	14	result	result	NOUN
iajs-2858	191	15	of	of	ADP
iajs-2858	191	16	numerical	numerical	ADJ
iajs-2858	191	17	example	example	NOUN
iajs-2858	191	18	solved	solve	VERB
iajs-2858	191	19	in	in	ADP
iajs-2858	191	20	two	two	NUM
iajs-2858	191	21	methods	method	NOUN
iajs-2858	191	22	unfuzzy	unfuzzy	ADJ
iajs-2858	192	1	[	[	PUNCT
iajs-2858	192	2	modified	modify	VERB
iajs-2858	192	3	simplex	simplex	NOUN
iajs-2858	192	4	approach	approach	NOUN
iajs-2858	192	5	]	]	PUNCT
iajs-2858	192	6	and	and	CCONJ
iajs-2858	192	7	fuzzy	fuzzy	ADJ
iajs-2858	192	8	[	[	X
iajs-2858	192	9	msfa	msfa	X
iajs-2858	192	10	]	]	X
iajs-2858	192	11	unfuzzy	unfuzzy	ADJ
iajs-2858	192	12	(	(	PUNCT
iajs-2858	192	13	modified	modified	ADJ
iajs-2858	192	14	simplex	simplex	NOUN
iajs-2858	192	15	approach	approach	NOUN
iajs-2858	192	16	)	)	PUNCT
iajs-2858	192	17	fuzzy	fuzzy	ADJ
iajs-2858	192	18	(	(	PUNCT
iajs-2858	192	19	msfa	msfa	NOUN
iajs-2858	192	20	)	)	PUNCT
iajs-2858	192	21	𝑥1	𝑥1	NOUN
iajs-2858	192	22	=	=	SYM
iajs-2858	192	23	0.2	0.2	NUM
iajs-2858	192	24	𝑥2	𝑥2	NOUN
iajs-2858	192	25	=	=	NUM
iajs-2858	192	26	1.6	1.6	NUM
iajs-2858	192	27	𝑊	𝑊	NOUN
iajs-2858	192	28	=	=	SYM
iajs-2858	192	29	0.15	0.15	NUM
iajs-2858	192	30	𝑥1	𝑥1	NOUN
iajs-2858	192	31	=	=	NOUN
iajs-2858	192	32	0.2	0.2	NUM
iajs-2858	192	33	𝑥2	𝑥2	NOUN
iajs-2858	192	34	=	=	NUM
iajs-2858	192	35	1.6	1.6	NUM
iajs-2858	192	36	𝑊	𝑊	NOUN
iajs-2858	192	37	=	=	NOUN
iajs-2858	192	38	0.15	0.15	NUM
iajs-2858	192	39	constraints	constraint	NOUN
iajs-2858	192	40	:	:	PUNCT
iajs-2858	192	41	1	1	NUM
iajs-2858	192	42	5	5	NUM
iajs-2858	192	43	1	1	NUM
iajs-2858	192	44	6	6	NUM
iajs-2858	192	45	2	2	NUM
iajs-2858	192	46	2	2	NUM
iajs-2858	192	47	2	2	NUM
iajs-2858	192	48	3	3	NUM
iajs-2858	192	49	we	we	PRON
iajs-2858	192	50	conclude	conclude	VERB
iajs-2858	192	51	from	from	ADP
iajs-2858	192	52	the	the	DET
iajs-2858	192	53	solution	solution	NOUN
iajs-2858	192	54	we	we	PRON
iajs-2858	192	55	have	have	VERB
iajs-2858	192	56	same	same	ADJ
iajs-2858	192	57	profit	profit	NOUN
iajs-2858	192	58	under	under	ADP
iajs-2858	192	59	regard	regard	NOUN
iajs-2858	192	60	all	all	DET
iajs-2858	192	61	constraints	constraint	NOUN
iajs-2858	192	62	.	.	PUNCT
iajs-2858	193	1	8	8	X
iajs-2858	193	2	.	.	X
iajs-2858	193	3	conclusion	conclusion	NOUN
iajs-2858	193	4	this	this	DET
iajs-2858	193	5	paper	paper	NOUN
iajs-2858	193	6	used	use	VERB
iajs-2858	193	7	modify	modify	VERB
iajs-2858	193	8	symmetric	symmetric	ADJ
iajs-2858	193	9	fuzzy	fuzzy	ADJ
iajs-2858	193	10	approach	approach	NOUN
iajs-2858	193	11	.	.	PUNCT
iajs-2858	194	1	after	after	ADP
iajs-2858	194	2	converting	convert	VERB
iajs-2858	194	3	to	to	ADP
iajs-2858	194	4	crisp	crisp	ADJ
iajs-2858	194	5	linear	linear	NOUN
iajs-2858	194	6	programming	programming	NOUN
iajs-2858	194	7	,	,	PUNCT
iajs-2858	194	8	the	the	DET
iajs-2858	194	9	maximum	maximum	ADJ
iajs-2858	194	10	value	value	NOUN
iajs-2858	194	11	of	of	ADP
iajs-2858	194	12	qfpp	qfpp	PROPN
iajs-2858	194	13	was	be	AUX
iajs-2858	194	14	discovered	discover	VERB
iajs-2858	194	15	and	and	CCONJ
iajs-2858	194	16	compared	compare	VERB
iajs-2858	194	17	to	to	ADP
iajs-2858	194	18	the	the	DET
iajs-2858	194	19	modified	modify	VERB
iajs-2858	194	20	simplex	simplex	NOUN
iajs-2858	194	21	technique	technique	NOUN
iajs-2858	194	22	.	.	PUNCT
iajs-2858	195	1	the	the	DET
iajs-2858	195	2	values	value	NOUN
iajs-2858	195	3	of	of	ADP
iajs-2858	195	4	the	the	DET
iajs-2858	195	5	objective	objective	ADJ
iajs-2858	195	6	function	function	NOUN
iajs-2858	195	7	are	be	AUX
iajs-2858	195	8	used	use	VERB
iajs-2858	195	9	to	to	PART
iajs-2858	195	10	compare	compare	VERB
iajs-2858	195	11	these	these	DET
iajs-2858	195	12	techniques	technique	NOUN
iajs-2858	195	13	,	,	PUNCT
iajs-2858	195	14	the	the	DET
iajs-2858	195	15	study	study	NOUN
iajs-2858	195	16	found	find	VERB
iajs-2858	195	17	that	that	SCONJ
iajs-2858	195	18	𝑀𝑎𝑥.	𝑀𝑎𝑥.	PROPN
iajs-2858	195	19	𝑧	𝑧	ADP
iajs-2858	195	20	resulted	result	VERB
iajs-2858	195	21	of	of	ADP
iajs-2858	195	22	those	those	DET
iajs-2858	195	23	two	two	NUM
iajs-2858	195	24	methods	method	NOUN
iajs-2858	195	25	are	be	AUX
iajs-2858	195	26	same	same	ADJ
iajs-2858	195	27	but	but	CCONJ
iajs-2858	195	28	modify	modify	VERB
iajs-2858	195	29	symmetric	symmetric	ADJ
iajs-2858	195	30	fuzzy	fuzzy	ADJ
iajs-2858	195	31	solve	solve	VERB
iajs-2858	195	32	the	the	DET
iajs-2858	195	33	problem	problem	NOUN
iajs-2858	195	34	directly	directly	ADV
iajs-2858	195	35	without	without	ADP
iajs-2858	195	36	iteration	iteration	NOUN
iajs-2858	195	37	while	while	SCONJ
iajs-2858	195	38	modified	modified	ADJ
iajs-2858	195	39	simplex	simplex	NOUN
iajs-2858	195	40	approach	approach	NOUN
iajs-2858	195	41	take	take	VERB
iajs-2858	195	42	two	two	NUM
iajs-2858	195	43	iterations	iteration	NOUN
iajs-2858	195	44	.	.	PUNCT
iajs-2858	196	1	therefore	therefore	ADV
iajs-2858	196	2	,	,	PUNCT
iajs-2858	196	3	we	we	PRON
iajs-2858	196	4	can	can	AUX
iajs-2858	196	5	solve	solve	VERB
iajs-2858	196	6	special	special	ADJ
iajs-2858	196	7	case	case	NOUN
iajs-2858	196	8	of	of	ADP
iajs-2858	196	9	qfpp	qfpp	NOUN
iajs-2858	196	10	by	by	ADP
iajs-2858	196	11	these	these	DET
iajs-2858	196	12	two	two	NUM
iajs-2858	196	13	methods	method	NOUN
iajs-2858	196	14	under	under	ADP
iajs-2858	196	15	our	our	PRON
iajs-2858	196	16	approach	approach	NOUN
iajs-2858	196	17	and	and	CCONJ
iajs-2858	196	18	algorithm	algorithm	NOUN
iajs-2858	196	19	.	.	PUNCT
iajs-2858	197	1	consequently	consequently	ADV
iajs-2858	197	2	,	,	PUNCT
iajs-2858	197	3	reliable	reliable	ADJ
iajs-2858	197	4	results	result	NOUN
iajs-2858	197	5	have	have	AUX
iajs-2858	197	6	been	be	AUX
iajs-2858	197	7	found	find	VERB
iajs-2858	197	8	.	.	PUNCT
iajs-2858	198	1	ihjpas	ihjpas	PROPN
iajs-2858	198	2	.	.	PUNCT
iajs-2858	199	1	53	53	NUM
iajs-2858	199	2	(	(	PUNCT
iajs-2858	199	3	4)2022	4)2022	NOUN
iajs-2858	199	4	254	254	NUM
iajs-2858	199	5	references	reference	NOUN
iajs-2858	199	6	1	1	NUM
iajs-2858	199	7	.	.	PUNCT
iajs-2858	199	8	zadeh	zadeh	PROPN
iajs-2858	199	9	,	,	PUNCT
iajs-2858	199	10	l.a	l.a	PROPN
iajs-2858	199	11	.	.	PROPN
iajs-2858	199	12	,	,	PUNCT
iajs-2858	199	13	fuzzy	fuzzy	ADJ
iajs-2858	199	14	sets	set	NOUN
iajs-2858	199	15	,	,	PUNCT
iajs-2858	199	16	in	in	ADP
iajs-2858	199	17	fuzzy	fuzzy	ADJ
iajs-2858	199	18	sets	set	NOUN
iajs-2858	199	19	,	,	PUNCT
iajs-2858	199	20	fuzzy	fuzzy	ADJ
iajs-2858	199	21	logic	logic	NOUN
iajs-2858	199	22	,	,	PUNCT
iajs-2858	199	23	and	and	CCONJ
iajs-2858	199	24	fuzzy	fuzzy	ADJ
iajs-2858	199	25	systems	system	NOUN
iajs-2858	199	26	:	:	PUNCT
iajs-2858	199	27	selected	select	VERB
iajs-2858	199	28	papers	paper	NOUN
iajs-2858	199	29	by	by	ADP
iajs-2858	199	30	lotfi	lotfi	PROPN
iajs-2858	199	31	a	a	DET
iajs-2858	199	32	zadeh	zadeh	PROPN
iajs-2858	199	33	.	.	PUNCT
iajs-2858	200	1	world	world	PROPN
iajs-2858	200	2	scientific	scientific	PROPN
iajs-2858	200	3	,	,	PUNCT
iajs-2858	200	4	1996	1996	NUM
iajs-2858	200	5	,	,	PUNCT
iajs-2858	200	6	394	394	NUM
iajs-2858	200	7	-	-	SYM
iajs-2858	200	8	432	432	NUM
iajs-2858	200	9	.	.	PUNCT
iajs-2858	201	1	2	2	X
iajs-2858	201	2	.	.	X
iajs-2858	201	3	bellman	bellman	PROPN
iajs-2858	201	4	,	,	PUNCT
iajs-2858	201	5	r.e	r.e	PROPN
iajs-2858	201	6	.	.	PROPN
iajs-2858	201	7	;	;	PUNCT
iajs-2858	201	8	l.a	l.a	PROPN
iajs-2858	201	9	.	.	PROPN
iajs-2858	201	10	zadeh	zadeh	PROPN
iajs-2858	201	11	,	,	PUNCT
iajs-2858	201	12	decision	decision	NOUN
iajs-2858	201	13	-	-	PUNCT
iajs-2858	201	14	making	making	NOUN
iajs-2858	201	15	in	in	ADP
iajs-2858	201	16	a	a	DET
iajs-2858	201	17	fuzzy	fuzzy	ADJ
iajs-2858	201	18	environment	environment	NOUN
iajs-2858	201	19	.	.	PUNCT
iajs-2858	202	1	management	management	NOUN
iajs-2858	202	2	science	science	PROPN
iajs-2858	202	3	,	,	PUNCT
iajs-2858	202	4	1970	1970	NUM
iajs-2858	202	5	,	,	PUNCT
iajs-2858	202	6	17	17	NUM
iajs-2858	202	7	,	,	PUNCT
iajs-2858	202	8	4	4	NUM
iajs-2858	202	9	,	,	PUNCT
iajs-2858	202	10	141	141	NUM
iajs-2858	202	11	-	-	SYM
iajs-2858	202	12	164	164	NUM
iajs-2858	202	13	.	.	PUNCT
iajs-2858	203	1	3	3	X
iajs-2858	203	2	.	.	X
iajs-2858	203	3	tanaka	tanaka	PROPN
iajs-2858	203	4	,	,	PUNCT
iajs-2858	203	5	h.	h.	PROPN
iajs-2858	203	6	,	,	PUNCT
iajs-2858	203	7	t.	t.	PROPN
iajs-2858	203	8	okuda	okuda	PROPN
iajs-2858	203	9	,	,	PUNCT
iajs-2858	203	10	;	;	PUNCT
iajs-2858	203	11	k.	k.	PROPN
iajs-2858	203	12	asai	asai	PROPN
iajs-2858	203	13	,	,	PUNCT
iajs-2858	203	14	fuzzy	fuzzy	ADJ
iajs-2858	203	15	mathematical	mathematical	ADJ
iajs-2858	203	16	programming	programming	NOUN
iajs-2858	203	17	.	.	PUNCT
iajs-2858	204	1	transactions	transaction	NOUN
iajs-2858	204	2	of	of	ADP
iajs-2858	204	3	the	the	DET
iajs-2858	204	4	society	society	NOUN
iajs-2858	204	5	of	of	ADP
iajs-2858	204	6	instrument	instrument	NOUN
iajs-2858	204	7	and	and	CCONJ
iajs-2858	204	8	control	control	NOUN
iajs-2858	204	9	engineers	engineer	NOUN
iajs-2858	204	10	,	,	PUNCT
iajs-2858	204	11	1973	1973	NUM
iajs-2858	204	12	,	,	PUNCT
iajs-2858	204	13	9	9	NUM
iajs-2858	204	14	,	,	PUNCT
iajs-2858	204	15	5	5	NUM
iajs-2858	204	16	,	,	PUNCT
iajs-2858	204	17	607	607	NUM
iajs-2858	204	18	-	-	SYM
iajs-2858	204	19	613	613	NUM
iajs-2858	204	20	.	.	NOUN
iajs-2858	204	21	4	4	NUM
iajs-2858	204	22	.	.	X
iajs-2858	204	23	biswas	biswas	PROPN
iajs-2858	204	24	,	,	PUNCT
iajs-2858	204	25	a.	a.	PROPN
iajs-2858	204	26	;	;	PUNCT
iajs-2858	204	27	k.	k.	PROPN
iajs-2858	204	28	bose	bose	PROPN
iajs-2858	204	29	.	.	PUNCT
iajs-2858	205	1	fuzzy	fuzzy	ADJ
iajs-2858	205	2	goal	goal	NOUN
iajs-2858	205	3	programming	programming	NOUN
iajs-2858	205	4	approach	approach	NOUN
iajs-2858	205	5	for	for	ADP
iajs-2858	205	6	quadratic	quadratic	ADJ
iajs-2858	205	7	fractional	fractional	ADJ
iajs-2858	205	8	bilevel	bilevel	ADJ
iajs-2858	205	9	programming	programming	NOUN
iajs-2858	205	10	.	.	PUNCT
iajs-2858	206	1	in	in	ADP
iajs-2858	206	2	proceedings	proceeding	NOUN
iajs-2858	206	3	of	of	ADP
iajs-2858	206	4	the	the	DET
iajs-2858	206	5	international	international	ADJ
iajs-2858	206	6	conference	conference	NOUN
iajs-2858	206	7	on	on	ADP
iajs-2858	206	8	scientific	scientific	ADJ
iajs-2858	206	9	computing	computing	NOUN
iajs-2858	206	10	(	(	PUNCT
iajs-2858	206	11	csc	csc	PROPN
iajs-2858	206	12	)	)	PUNCT
iajs-2858	206	13	.	.	PUNCT
iajs-2858	207	1	2011	2011	NUM
iajs-2858	207	2	.	.	PUNCT
iajs-2858	208	1	citeseer	citeseer	NOUN
iajs-2858	208	2	.	.	PUNCT
iajs-2858	209	1	5	5	X
iajs-2858	209	2	.	.	X
iajs-2858	209	3	kassa	kassa	PROPN
iajs-2858	209	4	,	,	PUNCT
iajs-2858	209	5	s.m	s.m	PROPN
iajs-2858	209	6	.	.	PROPN
iajs-2858	209	7	;	;	PUNCT
iajs-2858	209	8	t.h	t.h	PROPN
iajs-2858	209	9	.	.	PROPN
iajs-2858	209	10	tsegay	tsegay	PROPN
iajs-2858	209	11	,	,	PUNCT
iajs-2858	209	12	an	an	DET
iajs-2858	209	13	iterative	iterative	NOUN
iajs-2858	209	14	method	method	NOUN
iajs-2858	209	15	for	for	ADP
iajs-2858	209	16	tri	tri	ADJ
iajs-2858	209	17	-	-	ADJ
iajs-2858	209	18	level	level	ADJ
iajs-2858	209	19	quadratic	quadratic	ADJ
iajs-2858	209	20	fractional	fractional	ADJ
iajs-2858	209	21	programming	programming	NOUN
iajs-2858	209	22	problems	problem	NOUN
iajs-2858	209	23	using	use	VERB
iajs-2858	209	24	fuzzy	fuzzy	ADJ
iajs-2858	209	25	goal	goal	NOUN
iajs-2858	209	26	programming	programming	NOUN
iajs-2858	209	27	approach	approach	NOUN
iajs-2858	209	28	.	.	PUNCT
iajs-2858	210	1	journal	journal	NOUN
iajs-2858	210	2	of	of	ADP
iajs-2858	210	3	industrial	industrial	ADJ
iajs-2858	210	4	engineering	engineering	PROPN
iajs-2858	210	5	international	international	ADJ
iajs-2858	210	6	,	,	PUNCT
iajs-2858	210	7	2018	2018	NUM
iajs-2858	210	8	,	,	PUNCT
iajs-2858	210	9	14	14	NUM
iajs-2858	210	10	,	,	PUNCT
iajs-2858	210	11	2	2	NUM
iajs-2858	210	12	,	,	PUNCT
iajs-2858	210	13	255	255	NUM
iajs-2858	210	14	-	-	SYM
iajs-2858	210	15	264	264	NUM
iajs-2858	210	16	.	.	NOUN
iajs-2858	211	1	6	6	NUM
iajs-2858	211	2	.	.	X
iajs-2858	211	3	rakshit	rakshit	NOUN
iajs-2858	211	4	,	,	PUNCT
iajs-2858	211	5	m.	m.	NOUN
iajs-2858	211	6	;	;	PUNCT
iajs-2858	212	1	m.s	m.s	PROPN
iajs-2858	212	2	.	.	PROPN
iajs-2858	212	3	kumar	kumar	PROPN
iajs-2858	212	4	,	,	PUNCT
iajs-2858	212	5	a	a	DET
iajs-2858	212	6	bilevel	bilevel	ADJ
iajs-2858	212	7	quadratic	quadratic	ADJ
iajs-2858	212	8	–	–	PUNCT
iajs-2858	212	9	quadratic	quadratic	ADJ
iajs-2858	212	10	fractional	fractional	ADJ
iajs-2858	212	11	programming	programming	NOUN
iajs-2858	212	12	through	through	ADP
iajs-2858	212	13	fuzzy	fuzzy	ADJ
iajs-2858	212	14	goal	goal	NOUN
iajs-2858	212	15	programming	programming	NOUN
iajs-2858	212	16	approach	approach	NOUN
iajs-2858	212	17	.	.	PUNCT
iajs-2858	213	1	international	international	ADJ
iajs-2858	213	2	journal	journal	PROPN
iajs-2858	213	3	of	of	ADP
iajs-2858	213	4	mathematics	mathematics	NOUN
iajs-2858	213	5	trends	trend	NOUN
iajs-2858	213	6	and	and	CCONJ
iajs-2858	213	7	technology	technology	NOUN
iajs-2858	213	8	(	(	PUNCT
iajs-2858	213	9	ijmtt	ijmtt	ADJ
iajs-2858	213	10	)	)	PUNCT
iajs-2858	213	11	,	,	PUNCT
iajs-2858	213	12	2016	2016	NUM
iajs-2858	213	13	,	,	PUNCT
iajs-2858	213	14	38	38	NUM
iajs-2858	213	15	,	,	PUNCT
iajs-2858	213	16	3	3	NUM
iajs-2858	213	17	,	,	PUNCT
iajs-2858	213	18	130	130	NUM
iajs-2858	213	19	-	-	SYM
iajs-2858	213	20	137	137	NUM
iajs-2858	213	21	.	.	PUNCT
iajs-2858	214	1	7	7	X
iajs-2858	214	2	.	.	X
iajs-2858	214	3	abdulrahim	abdulrahim	PROPN
iajs-2858	214	4	,	,	PUNCT
iajs-2858	214	5	b.k	b.k	PROPN
iajs-2858	214	6	.	.	PROPN
iajs-2858	214	7	;	;	PUNCT
iajs-2858	214	8	s.o	s.o	PROPN
iajs-2858	214	9	.	.	PROPN
iajs-2858	214	10	abdulla	abdulla	PROPN
iajs-2858	214	11	,	,	PUNCT
iajs-2858	214	12	a	a	DET
iajs-2858	214	13	moqfpp	moqfpp	NOUN
iajs-2858	214	14	method	method	NOUN
iajs-2858	214	15	for	for	ADP
iajs-2858	214	16	solving	solve	VERB
iajs-2858	214	17	quadratic	quadratic	ADJ
iajs-2858	214	18	fractional	fractional	ADJ
iajs-2858	214	19	programming	programming	NOUN
iajs-2858	214	20	under	under	ADP
iajs-2858	214	21	fuzzy	fuzzy	ADJ
iajs-2858	214	22	environment	environment	NOUN
iajs-2858	214	23	,	,	PUNCT
iajs-2858	214	24	jug	jug	NOUN
iajs-2858	214	25	,	,	PUNCT
iajs-2858	214	26	2019	2019	NUM
iajs-2858	214	27	,	,	PUNCT
iajs-2858	214	28	6	6	NUM
iajs-2858	214	29	,	,	PUNCT
iajs-2858	214	30	1	1	NUM
iajs-2858	214	31	,	,	PUNCT
iajs-2858	214	32	114	114	NUM
iajs-2858	214	33	-	-	SYM
iajs-2858	214	34	122	122	NUM
iajs-2858	214	35	.	.	NOUN
iajs-2858	214	36	8	8	NUM
iajs-2858	214	37	.	.	X
iajs-2858	215	1	kausar	kausar	PROPN
iajs-2858	215	2	,	,	PUNCT
iajs-2858	215	3	h.	h.	PROPN
iajs-2858	215	4	,	,	PUNCT
iajs-2858	215	5	a.y	a.y	PROPN
iajs-2858	215	6	.	.	PROPN
iajs-2858	215	7	adhami	adhami	PROPN
iajs-2858	215	8	,	,	PUNCT
iajs-2858	215	9	;	;	PUNCT
iajs-2858	215	10	a.	a.	NOUN
iajs-2858	215	11	rahman	rahman	PROPN
iajs-2858	215	12	,	,	PUNCT
iajs-2858	215	13	quadratic	quadratic	ADJ
iajs-2858	215	14	fractional	fractional	ADJ
iajs-2858	215	15	bi	bi	ADJ
iajs-2858	215	16	-	-	ADJ
iajs-2858	215	17	level	level	ADJ
iajs-2858	215	18	fuzzy	fuzzy	ADJ
iajs-2858	215	19	probabilistic	probabilistic	ADJ
iajs-2858	215	20	programming	programming	NOUN
iajs-2858	215	21	problem	problem	NOUN
iajs-2858	215	22	when	when	SCONJ
iajs-2858	215	23	bi	bi	NOUN
iajs-2858	215	24	follows	follow	VERB
iajs-2858	215	25	exponential	exponential	ADJ
iajs-2858	215	26	distribution	distribution	NOUN
iajs-2858	215	27	.	.	PUNCT
iajs-2858	216	1	reliability	reliability	NOUN
iajs-2858	216	2	:	:	PUNCT
iajs-2858	216	3	theory	theory	NOUN
iajs-2858	216	4	&	&	CCONJ
iajs-2858	216	5	applications	application	NOUN
iajs-2858	216	6	,	,	PUNCT
iajs-2858	216	7	2021	2021	NUM
iajs-2858	216	8	,	,	PUNCT
iajs-2858	216	9	16	16	NUM
iajs-2858	216	10	,	,	PUNCT
iajs-2858	216	11	2	2	NUM
iajs-2858	216	12	,	,	PUNCT
iajs-2858	216	13	289	289	NUM
iajs-2858	216	14	-	-	SYM
iajs-2858	216	15	300	300	NUM
iajs-2858	216	16	9	9	NUM
iajs-2858	216	17	.	.	PUNCT
iajs-2858	217	1	saxena	saxena	PROPN
iajs-2858	217	2	,	,	PUNCT
iajs-2858	217	3	p.	p.	PROPN
iajs-2858	217	4	;	;	PUNCT
iajs-2858	217	5	r.	r.	PROPN
iajs-2858	217	6	jain	jain	PROPN
iajs-2858	217	7	,	,	PUNCT
iajs-2858	217	8	duality	duality	NOUN
iajs-2858	217	9	for	for	ADP
iajs-2858	217	10	a	a	DET
iajs-2858	217	11	nonlinear	nonlinear	ADJ
iajs-2858	217	12	fractional	fractional	ADJ
iajs-2858	217	13	programming	programming	NOUN
iajs-2858	217	14	under	under	ADP
iajs-2858	217	15	fuzzy	fuzzy	ADJ
iajs-2858	217	16	environment	environment	NOUN
iajs-2858	217	17	with	with	ADP
iajs-2858	217	18	parabolic	parabolic	ADJ
iajs-2858	217	19	concave	concave	PROPN
iajs-2858	217	20	membership	membership	NOUN
iajs-2858	217	21	functions	function	NOUN
iajs-2858	217	22	.	.	PUNCT
iajs-2858	218	1	international	international	ADJ
iajs-2858	218	2	journal	journal	PROPN
iajs-2858	218	3	of	of	ADP
iajs-2858	218	4	advanced	advanced	ADJ
iajs-2858	218	5	and	and	CCONJ
iajs-2858	218	6	applied	apply	VERB
iajs-2858	218	7	sciences	science	NOUN
iajs-2858	218	8	,	,	PUNCT
iajs-2858	218	9	2017	2017	NUM
iajs-2858	218	10	,	,	PUNCT
iajs-2858	218	11	4	4	NUM
iajs-2858	218	12	,	,	PUNCT
iajs-2858	218	13	1	1	NUM
iajs-2858	218	14	,	,	PUNCT
iajs-2858	218	15	131	131	NUM
iajs-2858	218	16	-	-	SYM
iajs-2858	218	17	136	136	NUM
iajs-2858	218	18	.	.	PUNCT
iajs-2858	219	1	10	10	NUM
iajs-2858	219	2	.	.	X
iajs-2858	220	1	nejmaddin	nejmaddin	VERB
iajs-2858	220	2	a.	a.	NOUN
iajs-2858	220	3	suleiman	suleiman	PROPN
iajs-2858	220	4	;	;	PUNCT
iajs-2858	220	5	maher	maher	PROPN
iajs-2858	220	6	a.	a.	PROPN
iajs-2858	220	7	nawkhass	nawkhass	PROPN
iajs-2858	220	8	,	,	PUNCT
iajs-2858	220	9	solving	solve	VERB
iajs-2858	220	10	quadratic	quadratic	ADJ
iajs-2858	220	11	fractional	fractional	ADJ
iajs-2858	220	12	programming	programming	NOUN
iajs-2858	220	13	problem	problem	NOUN
iajs-2858	220	14	.	.	PUNCT
iajs-2858	221	1	international	international	ADJ
iajs-2858	221	2	journal	journal	NOUN
iajs-2858	221	3	of	of	ADP
iajs-2858	221	4	applied	apply	VERB
iajs-2858	221	5	mathematics	mathematic	NOUN
iajs-2858	221	6	research	research	NOUN
iajs-2858	221	7	,	,	PUNCT
iajs-2858	221	8	2013	2013	NUM
iajs-2858	221	9	,	,	PUNCT
iajs-2858	221	10	2	2	NUM
iajs-2858	221	11	,	,	PUNCT
iajs-2858	221	12	2	2	NUM
iajs-2858	221	13	,	,	PUNCT
iajs-2858	221	14	303	303	NUM
iajs-2858	221	15	-	-	SYM
iajs-2858	221	16	309	309	NUM
iajs-2858	221	17	.	.	PUNCT
iajs-2858	222	1	11	11	NUM
iajs-2858	222	2	.	.	PUNCT
iajs-2858	223	1	hamadameen	hamadameen	PROPN
iajs-2858	223	2	,	,	PUNCT
iajs-2858	223	3	a.	a.	PROPN
iajs-2858	223	4	,	,	PUNCT
iajs-2858	223	5	a	a	DET
iajs-2858	223	6	novel	novel	ADJ
iajs-2858	223	7	technique	technique	NOUN
iajs-2858	223	8	for	for	ADP
iajs-2858	223	9	solving	solve	VERB
iajs-2858	223	10	multiobjective	multiobjective	ADJ
iajs-2858	223	11	fuzzy	fuzzy	ADJ
iajs-2858	223	12	linear	linear	ADJ
iajs-2858	223	13	programming	programming	NOUN
iajs-2858	223	14	problems	problem	NOUN
iajs-2858	223	15	.	.	PUNCT
iajs-2858	224	1	aro	aro	NOUN
iajs-2858	224	2	-	-	PUNCT
iajs-2858	224	3	the	the	DET
iajs-2858	224	4	scientific	scientific	ADJ
iajs-2858	224	5	journal	journal	NOUN
iajs-2858	224	6	of	of	ADP
iajs-2858	224	7	koya	koya	PROPN
iajs-2858	224	8	university	university	PROPN
iajs-2858	224	9	,	,	PUNCT
iajs-2858	224	10	2017	2017	NUM
iajs-2858	224	11	,	,	PUNCT
iajs-2858	224	12	5	5	NUM
iajs-2858	224	13	,	,	PUNCT
iajs-2858	224	14	1	1	NUM
iajs-2858	224	15	,	,	PUNCT
iajs-2858	224	16	1	1	NUM
iajs-2858	224	17	-	-	SYM
iajs-2858	224	18	8	8	NUM
iajs-2858	224	19	.	.	PUNCT
iajs-2858	224	20	12	12	NUM
iajs-2858	224	21	.	.	PUNCT
iajs-2858	225	1	zimmermann	zimmermann	PROPN
iajs-2858	225	2	,	,	PUNCT
iajs-2858	225	3	h.-j	h.-j	PROPN
iajs-2858	225	4	.	.	PROPN
iajs-2858	225	5	,	,	PUNCT
iajs-2858	225	6	description	description	NOUN
iajs-2858	225	7	and	and	CCONJ
iajs-2858	225	8	optimization	optimization	NOUN
iajs-2858	225	9	of	of	ADP
iajs-2858	225	10	fuzzy	fuzzy	ADJ
iajs-2858	225	11	systems	system	NOUN
iajs-2858	225	12	.	.	PUNCT
iajs-2858	226	1	international	international	ADJ
iajs-2858	226	2	journal	journal	PROPN
iajs-2858	226	3	of	of	ADP
iajs-2858	226	4	general	general	ADJ
iajs-2858	226	5	system	system	NOUN
iajs-2858	226	6	,	,	PUNCT
iajs-2858	226	7	1975	1975	NUM
iajs-2858	226	8	,	,	PUNCT
iajs-2858	226	9	2	2	NUM
iajs-2858	226	10	,	,	PUNCT
iajs-2858	226	11	1	1	NUM
iajs-2858	226	12	,	,	PUNCT
iajs-2858	226	13	209	209	NUM
iajs-2858	226	14	-	-	SYM
iajs-2858	226	15	215	215	NUM
iajs-2858	226	16	.	.	NOUN
iajs-2858	226	17	13	13	NUM
iajs-2858	226	18	.	.	PUNCT
iajs-2858	227	1	zimmermann	zimmermann	PROPN
iajs-2858	227	2	,	,	PUNCT
iajs-2858	227	3	h.-j	h.-j	PROPN
iajs-2858	227	4	.	.	PROPN
iajs-2858	227	5	,	,	PUNCT
iajs-2858	227	6	fuzzy	fuzzy	ADJ
iajs-2858	227	7	set	set	NOUN
iajs-2858	227	8	theory	theory	NOUN
iajs-2858	227	9	—	—	PUNCT
iajs-2858	227	10	and	and	CCONJ
iajs-2858	227	11	its	its	PRON
iajs-2858	227	12	applications	application	NOUN
iajs-2858	227	13	.	.	PUNCT
iajs-2858	228	1	2011	2011	NUM
iajs-2858	228	2	:	:	PUNCT
iajs-2858	228	3	springer	springer	NOUN
iajs-2858	228	4	science	science	PROPN
iajs-2858	228	5	&	&	CCONJ
iajs-2858	228	6	business	business	NOUN
iajs-2858	228	7	media	medium	NOUN
iajs-2858	228	8	.	.	PUNCT
iajs-2858	229	1	14	14	NUM
iajs-2858	229	2	.	.	PUNCT
iajs-2858	229	3	sharma	sharma	PROPN
iajs-2858	229	4	,	,	PUNCT
iajs-2858	229	5	s.	s.	PROPN
iajs-2858	229	6	,	,	PUNCT
iajs-2858	229	7	nonlinear	nonlinear	ADJ
iajs-2858	229	8	and	and	CCONJ
iajs-2858	229	9	dynamic	dynamic	ADJ
iajs-2858	229	10	programming	programming	NOUN
iajs-2858	229	11	.	.	PUNCT
iajs-2858	230	1	kedar	kedar	PROPN
iajs-2858	230	2	nath	nath	PROPN
iajs-2858	230	3	ram	ram	PROPN
iajs-2858	230	4	nath	nath	PROPN
iajs-2858	230	5	and	and	CCONJ
iajs-2858	230	6	co.	co.	PROPN
iajs-2858	230	7	,	,	PUNCT
iajs-2858	230	8	meerut	meerut	PROPN
iajs-2858	230	9	,	,	PUNCT
iajs-2858	230	10	india	india	PROPN
iajs-2858	230	11	,	,	PUNCT
iajs-2858	230	12	1980	1980	NUM
iajs-2858	230	13	,	,	PUNCT
iajs-2858	230	14	547	547	NUM
iajs-2858	230	15	.	.	NOUN
iajs-2858	230	16	15	15	NUM
iajs-2858	230	17	.	.	PUNCT
iajs-2858	231	1	nejmaddin	nejmaddin	VERB
iajs-2858	231	2	a.	a.	NOUN
iajs-2858	231	3	suleiman	suleiman	PROPN
iajs-2858	231	4	;	;	PUNCT
iajs-2858	231	5	maher	maher	PROPN
iajs-2858	231	6	a.	a.	PROPN
iajs-2858	231	7	nawkhass	nawkhass	PROPN
iajs-2858	231	8	,	,	PUNCT
iajs-2858	231	9	symmetric	symmetric	ADJ
iajs-2858	231	10	fuzzy	fuzzy	ADJ
iajs-2858	231	11	approach	approach	NOUN
iajs-2858	231	12	to	to	PART
iajs-2858	231	13	solve	solve	VERB
iajs-2858	231	14	complementary	complementary	ADJ
iajs-2858	231	15	multi	multi	ADJ
iajs-2858	231	16	-	-	ADJ
iajs-2858	231	17	objective	objective	ADJ
iajs-2858	231	18	linear	linear	ADJ
iajs-2858	231	19	fractional	fractional	ADJ
iajs-2858	231	20	programming	programming	NOUN
iajs-2858	231	21	problem	problem	NOUN
iajs-2858	231	22	.	.	PUNCT
iajs-2858	232	1	international	international	ADJ
iajs-2858	232	2	journal	journal	PROPN
iajs-2858	232	3	of	of	ADP
iajs-2858	232	4	nonlinear	nonlinear	ADJ
iajs-2858	232	5	analysis	analysis	NOUN
iajs-2858	232	6	and	and	CCONJ
iajs-2858	232	7	applications	application	NOUN
iajs-2858	232	8	,	,	PUNCT
iajs-2858	232	9	2022	2022	NUM
iajs-2858	232	10	:	:	PUNCT
iajs-2858	232	11	1	1	NUM
iajs-2858	232	12	-	-	SYM
iajs-2858	232	13	6	6	NUM
iajs-2858	232	14	.	.	NOUN
iajs-2858	232	15	16	16	NUM
iajs-2858	232	16	.	.	PUNCT
iajs-2858	233	1	antoniou	antoniou	PROPN
iajs-2858	233	2	,	,	PUNCT
iajs-2858	233	3	a.	a.	NOUN
iajs-2858	233	4	and	and	CCONJ
iajs-2858	233	5	w.-s	w.-	NOUN
iajs-2858	233	6	.	.	PUNCT
iajs-2858	234	1	lu	lu	PROPN
iajs-2858	234	2	,	,	PUNCT
iajs-2858	234	3	practical	practical	ADJ
iajs-2858	234	4	optimization	optimization	NOUN
iajs-2858	234	5	.	.	PUNCT
iajs-2858	235	1	2007	2007	NUM
iajs-2858	235	2	:	:	PUNCT
iajs-2858	235	3	springer	springer	NOUN
iajs-2858	235	4	.	.	PUNCT
iajs-2858	236	1	17.maher	17.maher	NUM
iajs-2858	236	2	a.	a.	NOUN
iajs-2858	236	3	nawkhass	nawkhass	NOUN
iajs-2858	236	4	;	;	PUNCT
iajs-2858	236	5	nejmaddin	nejmaddin	VERB
iajs-2858	236	6	a.	a.	NOUN
iajs-2858	236	7	suleiman	suleiman	PROPN
iajs-2858	236	8	;	;	PUNCT
iajs-2858	236	9	a	a	DET
iajs-2858	236	10	new	new	ADJ
iajs-2858	236	11	modified	modify	VERB
iajs-2858	236	12	simplex	simplex	NOUN
iajs-2858	236	13	method	method	NOUN
iajs-2858	236	14	to	to	PART
iajs-2858	236	15	solve	solve	VERB
iajs-2858	236	16	quadratic	quadratic	ADJ
iajs-2858	236	17	fractional	fractional	ADJ
iajs-2858	236	18	programming	programming	NOUN
iajs-2858	236	19	problem	problem	NOUN
iajs-2858	236	20	and	and	CCONJ
iajs-2858	236	21	compared	compare	VERB
iajs-2858	236	22	it	it	PRON
iajs-2858	236	23	to	to	ADP
iajs-2858	236	24	a	a	DET
iajs-2858	236	25	traditional	traditional	ADJ
iajs-2858	236	26	simplex	simplex	NOUN
iajs-2858	236	27	method	method	NOUN
iajs-2858	236	28	by	by	ADP
iajs-2858	236	29	using	use	VERB
iajs-2858	236	30	pseudoaffinity	pseudoaffinity	NOUN
iajs-2858	236	31	of	of	ADP
iajs-2858	236	32	quadratic	quadratic	ADJ
iajs-2858	236	33	fractional	fractional	ADJ
iajs-2858	236	34	functions	function	NOUN
iajs-2858	236	35	.	.	PUNCT
iajs-2858	237	1	applied	apply	VERB
iajs-2858	237	2	mathematical	mathematical	ADJ
iajs-2858	237	3	sciences	science	NOUN
iajs-2858	237	4	,	,	PUNCT
iajs-2858	237	5	2013	2013	NUM
iajs-2858	237	6	,	,	PUNCT
iajs-2858	237	7	7	7	NUM
iajs-2858	237	8	,	,	PUNCT
iajs-2858	237	9	76	76	NUM
iajs-2858	237	10	,	,	PUNCT
iajs-2858	237	11	3749	3749	NUM
iajs-2858	237	12	-	-	SYM
iajs-2858	237	13	3764	3764	NUM
iajs-2858	237	14	.	.	PUNCT