id	sid	tid	token	lemma	pos
cana-587	1	1	communications	communication	NOUN
cana-587	1	2	on	on	ADP
cana-587	1	3	applied	apply	VERB
cana-587	1	4	nonlinear	nonlinear	ADJ
cana-587	1	5	analysis	analysis	NOUN
cana-587	1	6	issn	issn	NOUN
cana-587	1	7	:	:	PUNCT
cana-587	1	8	1074	1074	NUM
cana-587	1	9	-	-	PUNCT
cana-587	1	10	133x	133x	NUM
cana-587	1	11	vol	vol	NOUN
cana-587	1	12	31	31	NUM
cana-587	1	13	no	no	NOUN
cana-587	1	14	.	.	PUNCT
cana-587	2	1	2s	2s	NUM
cana-587	2	2	(	(	PUNCT
cana-587	2	3	2024	2024	NUM
cana-587	2	4	)	)	PUNCT
cana-587	2	5	1	1	NUM
cana-587	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-587	2	7	a	a	DET
cana-587	2	8	methodology	methodology	NOUN
cana-587	2	9	for	for	ADP
cana-587	2	10	solving	solve	VERB
cana-587	2	11	fuzzy	fuzzy	ADJ
cana-587	2	12	linear	linear	ADJ
cana-587	2	13	programming	programming	NOUN
cana-587	2	14	problem	problem	NOUN
cana-587	2	15	as	as	ADP
cana-587	2	16	a	a	DET
cana-587	2	17	fuzzy	fuzzy	ADJ
cana-587	2	18	linear	linear	ADJ
cana-587	2	19	complementarity	complementarity	NOUN
cana-587	2	20	problem	problem	NOUN
cana-587	2	21	jenifer	jenifer	PROPN
cana-587	2	22	d	d	PROPN
cana-587	2	23	h1	h1	PROPN
cana-587	2	24	,	,	PUNCT
cana-587	2	25	r.	r.	PROPN
cana-587	2	26	irene	irene	PROPN
cana-587	2	27	hepzibah	hepzibah	PROPN
cana-587	2	28	2	2	NUM
cana-587	2	29	1	1	NUM
cana-587	2	30	&	&	CCONJ
cana-587	2	31	2	2	NUM
cana-587	2	32	pg	pg	PROPN
cana-587	2	33	&	&	CCONJ
cana-587	2	34	research	research	PROPN
cana-587	2	35	department	department	PROPN
cana-587	2	36	of	of	ADP
cana-587	2	37	mathematics	mathematics	PROPN
cana-587	2	38	,	,	PUNCT
cana-587	2	39	t.b.m.l	t.b.m.l	PROPN
cana-587	2	40	.	.	PUNCT
cana-587	3	1	college	college	PROPN
cana-587	3	2	,	,	PUNCT
cana-587	3	3	porayar	porayar	PROPN
cana-587	3	4	,	,	PUNCT
cana-587	3	5	affiliated	affiliate	VERB
cana-587	3	6	to	to	ADP
cana-587	3	7	annamalai	annamalai	PROPN
cana-587	3	8	university	university	PROPN
cana-587	3	9	tamil	tamil	PROPN
cana-587	3	10	nadu	nadu	PROPN
cana-587	3	11	,	,	PUNCT
cana-587	3	12	india	india	PROPN
cana-587	3	13	.	.	PUNCT
cana-587	4	1	e-mail:1jenifer808282@gmail.com	e-mail:1jenifer808282@gmail.com	ADP
cana-587	4	2	,	,	PUNCT
cana-587	4	3	2ireneraj74@gmail.com	2ireneraj74@gmail.com	NUM
cana-587	4	4	article	article	NOUN
cana-587	4	5	history	history	NOUN
cana-587	4	6	:	:	PUNCT
cana-587	4	7	received	receive	VERB
cana-587	4	8	:	:	PUNCT
cana-587	4	9	20	20	NUM
cana-587	4	10	-	-	PUNCT
cana-587	4	11	02	02	NUM
cana-587	4	12	-	-	PUNCT
cana-587	4	13	2024	2024	NUM
cana-587	4	14	revised	revise	VERB
cana-587	4	15	:	:	PUNCT
cana-587	4	16	22	22	NUM
cana-587	4	17	-	-	PUNCT
cana-587	4	18	04	04	NUM
cana-587	4	19	-	-	PUNCT
cana-587	4	20	2024	2024	NUM
cana-587	4	21	accepted	accept	VERB
cana-587	4	22	:	:	PUNCT
cana-587	4	23	05	05	NUM
cana-587	4	24	-	-	PUNCT
cana-587	4	25	05	05	NUM
cana-587	4	26	-	-	PUNCT
cana-587	4	27	2024	2024	NUM
cana-587	4	28	abstract	abstract	NOUN
cana-587	4	29	:	:	PUNCT
cana-587	4	30	in	in	ADP
cana-587	4	31	this	this	DET
cana-587	4	32	paper	paper	NOUN
cana-587	4	33	,	,	PUNCT
cana-587	4	34	the	the	DET
cana-587	4	35	linear	linear	ADJ
cana-587	4	36	complementarity	complementarity	NOUN
cana-587	4	37	problem	problem	NOUN
cana-587	4	38	with	with	ADP
cana-587	4	39	fuzzy	fuzzy	ADJ
cana-587	4	40	parameters	parameter	NOUN
cana-587	4	41	is	be	AUX
cana-587	4	42	discussed	discuss	VERB
cana-587	4	43	.	.	PUNCT
cana-587	5	1	the	the	DET
cana-587	5	2	linear	linear	ADJ
cana-587	5	3	programming	programming	NOUN
cana-587	5	4	problem	problem	NOUN
cana-587	5	5	can	can	AUX
cana-587	5	6	be	be	AUX
cana-587	5	7	transformed	transform	VERB
cana-587	5	8	into	into	ADP
cana-587	5	9	a	a	DET
cana-587	5	10	linear	linear	ADJ
cana-587	5	11	complementarity	complementarity	NOUN
cana-587	5	12	problem	problem	NOUN
cana-587	5	13	.	.	PUNCT
cana-587	6	1	the	the	DET
cana-587	6	2	maximum	maximum	ADJ
cana-587	6	3	index	index	NOUN
cana-587	6	4	method	method	NOUN
cana-587	6	5	is	be	AUX
cana-587	6	6	used	use	VERB
cana-587	6	7	to	to	PART
cana-587	6	8	solve	solve	VERB
cana-587	6	9	the	the	DET
cana-587	6	10	converted	convert	VERB
cana-587	6	11	linear	linear	ADJ
cana-587	6	12	programming	programming	NOUN
cana-587	6	13	problem	problem	NOUN
cana-587	6	14	.	.	PUNCT
cana-587	7	1	the	the	DET
cana-587	7	2	maximum	maximum	ADJ
cana-587	7	3	index	index	NOUN
cana-587	7	4	method	method	NOUN
cana-587	7	5	has	have	AUX
cana-587	7	6	been	be	AUX
cana-587	7	7	introduced	introduce	VERB
cana-587	7	8	as	as	ADP
cana-587	7	9	a	a	DET
cana-587	7	10	potential	potential	ADJ
cana-587	7	11	approach	approach	NOUN
cana-587	7	12	for	for	ADP
cana-587	7	13	identifying	identify	VERB
cana-587	7	14	a	a	DET
cana-587	7	15	complementarity	complementarity	NOUN
cana-587	7	16	feasible	feasible	ADJ
cana-587	7	17	solution	solution	NOUN
cana-587	7	18	to	to	ADP
cana-587	7	19	the	the	DET
cana-587	7	20	linear	linear	ADJ
cana-587	7	21	complementarity	complementarity	NOUN
cana-587	7	22	problem	problem	NOUN
cana-587	7	23	.	.	PUNCT
cana-587	8	1	the	the	DET
cana-587	8	2	fuzzy	fuzzy	ADJ
cana-587	8	3	arithmetic	arithmetic	ADJ
cana-587	8	4	operations	operation	NOUN
cana-587	8	5	are	be	AUX
cana-587	8	6	utilized	utilize	VERB
cana-587	8	7	for	for	ADP
cana-587	8	8	the	the	DET
cana-587	8	9	triangular	triangular	ADJ
cana-587	8	10	fuzzy	fuzzy	ADJ
cana-587	8	11	numbers	number	NOUN
cana-587	8	12	.	.	PUNCT
cana-587	9	1	a	a	DET
cana-587	9	2	real	real	ADJ
cana-587	9	3	-	-	PUNCT
cana-587	9	4	life	life	NOUN
cana-587	9	5	example	example	NOUN
cana-587	9	6	has	have	AUX
cana-587	9	7	been	be	AUX
cana-587	9	8	provided	provide	VERB
cana-587	9	9	to	to	PART
cana-587	9	10	demonstrate	demonstrate	VERB
cana-587	9	11	the	the	DET
cana-587	9	12	suggested	suggest	VERB
cana-587	9	13	approach	approach	NOUN
cana-587	9	14	.	.	PUNCT
cana-587	10	1	keywords	keyword	NOUN
cana-587	10	2	:	:	PUNCT
cana-587	10	3	linear	linear	ADJ
cana-587	10	4	programming	programming	NOUN
cana-587	10	5	problem	problem	NOUN
cana-587	10	6	;	;	PUNCT
cana-587	10	7	linear	linear	ADJ
cana-587	10	8	complementarity	complementarity	NOUN
cana-587	10	9	problem	problem	NOUN
cana-587	10	10	;	;	PUNCT
cana-587	10	11	fuzzy	fuzzy	ADJ
cana-587	10	12	linear	linear	ADJ
cana-587	10	13	complementarity	complementarity	NOUN
cana-587	10	14	problem	problem	NOUN
cana-587	10	15	;	;	PUNCT
cana-587	10	16	fuzzy	fuzzy	ADJ
cana-587	10	17	sets	set	NOUN
cana-587	10	18	;	;	PUNCT
cana-587	10	19	triangular	triangular	VERB
cana-587	10	20	fuzzy	fuzzy	ADJ
cana-587	10	21	numbers	number	NOUN
cana-587	10	22	;	;	PUNCT
cana-587	10	23	maximum	maximum	ADJ
cana-587	10	24	index	index	NOUN
cana-587	10	25	method	method	NOUN
cana-587	10	26	.	.	PUNCT
cana-587	11	1	1	1	X
cana-587	11	2	.	.	X
cana-587	11	3	introduction	introduction	NOUN
cana-587	11	4	linear	linear	PROPN
cana-587	11	5	programming	programming	NOUN
cana-587	11	6	[	[	X
cana-587	11	7	15	15	NUM
cana-587	11	8	]	]	PUNCT
cana-587	11	9	is	be	AUX
cana-587	11	10	concerned	concern	VERB
cana-587	11	11	with	with	ADP
cana-587	11	12	optimizing	optimize	VERB
cana-587	11	13	a	a	DET
cana-587	11	14	function	function	NOUN
cana-587	11	15	with	with	ADP
cana-587	11	16	a	a	DET
cana-587	11	17	variable	variable	ADJ
cana-587	11	18	objective	objective	NOUN
cana-587	11	19	under	under	ADP
cana-587	11	20	the	the	DET
cana-587	11	21	constraints	constraint	NOUN
cana-587	11	22	of	of	ADP
cana-587	11	23	a	a	DET
cana-587	11	24	set	set	NOUN
cana-587	11	25	of	of	ADP
cana-587	11	26	linear	linear	ADJ
cana-587	11	27	equalities	equality	NOUN
cana-587	11	28	and	and	CCONJ
cana-587	11	29	inequalities	inequality	NOUN
cana-587	11	30	.	.	PUNCT
cana-587	12	1	the	the	DET
cana-587	12	2	objective	objective	ADJ
cana-587	12	3	function	function	NOUN
cana-587	12	4	may	may	AUX
cana-587	12	5	pertain	pertain	VERB
cana-587	12	6	to	to	ADP
cana-587	12	7	earnings	earning	NOUN
cana-587	12	8	,	,	PUNCT
cana-587	12	9	expenses	expense	NOUN
cana-587	12	10	,	,	PUNCT
cana-587	12	11	capacity	capacity	NOUN
cana-587	12	12	for	for	ADP
cana-587	12	13	production	production	NOUN
cana-587	12	14	,	,	PUNCT
cana-587	12	15	or	or	CCONJ
cana-587	12	16	any	any	DET
cana-587	12	17	other	other	ADJ
cana-587	12	18	kind	kind	NOUN
cana-587	12	19	of	of	ADP
cana-587	12	20	effectiveness	effectiveness	NOUN
cana-587	12	21	that	that	PRON
cana-587	12	22	has	have	VERB
cana-587	12	23	to	to	PART
cana-587	12	24	be	be	AUX
cana-587	12	25	obtained	obtain	VERB
cana-587	12	26	in	in	ADP
cana-587	12	27	the	the	DET
cana-587	12	28	most	most	ADV
cana-587	12	29	efficient	efficient	ADJ
cana-587	12	30	or	or	CCONJ
cana-587	12	31	ideal	ideal	ADJ
cana-587	12	32	way	way	NOUN
cana-587	12	33	.	.	PUNCT
cana-587	13	1	demand	demand	NOUN
cana-587	13	2	from	from	ADP
cana-587	13	3	the	the	DET
cana-587	13	4	market	market	NOUN
cana-587	13	5	,	,	PUNCT
cana-587	13	6	manufacturing	manufacturing	NOUN
cana-587	13	7	procedures	procedure	NOUN
cana-587	13	8	and	and	CCONJ
cana-587	13	9	equipment	equipment	NOUN
cana-587	13	10	,	,	PUNCT
cana-587	13	11	space	space	NOUN
cana-587	13	12	for	for	ADP
cana-587	13	13	storage	storage	NOUN
cana-587	13	14	,	,	PUNCT
cana-587	13	15	raw	raw	ADJ
cana-587	13	16	material	material	NOUN
cana-587	13	17	availability	availability	NOUN
cana-587	13	18	,	,	PUNCT
cana-587	13	19	and	and	CCONJ
cana-587	13	20	other	other	ADJ
cana-587	13	21	factors	factor	NOUN
cana-587	13	22	may	may	AUX
cana-587	13	23	all	all	PRON
cana-587	13	24	place	place	VERB
cana-587	13	25	constraints	constraint	NOUN
cana-587	13	26	on	on	ADP
cana-587	13	27	the	the	DET
cana-587	13	28	operation	operation	NOUN
cana-587	13	29	.	.	PUNCT
cana-587	14	1	linear	linear	PROPN
cana-587	14	2	programming	programming	NOUN
cana-587	14	3	is	be	AUX
cana-587	14	4	a	a	DET
cana-587	14	5	mathematical	mathematical	ADJ
cana-587	14	6	modeling	modeling	NOUN
cana-587	14	7	technique	technique	NOUN
cana-587	14	8	that	that	PRON
cana-587	14	9	uses	use	VERB
cana-587	14	10	linear	linear	ADJ
cana-587	14	11	relationships	relationship	NOUN
cana-587	14	12	to	to	PART
cana-587	14	13	define	define	VERB
cana-587	14	14	requirements	requirement	NOUN
cana-587	14	15	and	and	CCONJ
cana-587	14	16	achieve	achieve	VERB
cana-587	14	17	the	the	DET
cana-587	14	18	best	good	ADJ
cana-587	14	19	attainable	attainable	ADJ
cana-587	14	20	result	result	NOUN
cana-587	14	21	.	.	PUNCT
cana-587	15	1	it	it	PRON
cana-587	15	2	is	be	AUX
cana-587	15	3	a	a	DET
cana-587	15	4	powerful	powerful	ADJ
cana-587	15	5	tool	tool	NOUN
cana-587	15	6	for	for	ADP
cana-587	15	7	making	make	VERB
cana-587	15	8	decisions	decision	NOUN
cana-587	15	9	based	base	VERB
cana-587	15	10	on	on	ADP
cana-587	15	11	data	datum	NOUN
cana-587	15	12	that	that	PRON
cana-587	15	13	can	can	AUX
cana-587	15	14	increase	increase	VERB
cana-587	15	15	efficiency	efficiency	NOUN
cana-587	15	16	and	and	CCONJ
cana-587	15	17	reduce	reduce	VERB
cana-587	15	18	costs	cost	NOUN
cana-587	15	19	.	.	PUNCT
cana-587	16	1	bellman	bellman	NOUN
cana-587	16	2	and	and	CCONJ
cana-587	16	3	zadeh	zadeh	PROPN
cana-587	17	1	[	[	X
cana-587	17	2	1	1	X
cana-587	17	3	]	]	PUNCT
cana-587	17	4	proposed	propose	VERB
cana-587	17	5	fuzzy	fuzzy	ADJ
cana-587	17	6	decisionmaking	decisionmaking	NOUN
cana-587	17	7	.	.	PUNCT
cana-587	18	1	the	the	DET
cana-587	18	2	lcp	lcp	NOUN
cana-587	18	3	is	be	AUX
cana-587	18	4	one	one	NUM
cana-587	18	5	of	of	ADP
cana-587	18	6	the	the	DET
cana-587	18	7	most	most	ADV
cana-587	18	8	commonly	commonly	ADV
cana-587	18	9	studied	study	VERB
cana-587	18	10	problems	problem	NOUN
cana-587	18	11	in	in	ADP
cana-587	18	12	mathematical	mathematical	ADJ
cana-587	18	13	programming	programming	NOUN
cana-587	18	14	and	and	CCONJ
cana-587	18	15	quadratic	quadratic	ADJ
cana-587	18	16	programming	programming	NOUN
cana-587	18	17	,	,	PUNCT
cana-587	18	18	and	and	CCONJ
cana-587	18	19	it	it	PRON
cana-587	18	20	has	have	AUX
cana-587	18	21	been	be	AUX
cana-587	18	22	studied	study	VERB
cana-587	18	23	and	and	CCONJ
cana-587	18	24	applied	apply	VERB
cana-587	18	25	in	in	ADP
cana-587	18	26	a	a	DET
cana-587	18	27	wide	wide	ADJ
cana-587	18	28	range	range	NOUN
cana-587	18	29	of	of	ADP
cana-587	18	30	areas	area	NOUN
cana-587	18	31	of	of	ADP
cana-587	18	32	operations	operation	NOUN
cana-587	18	33	research	research	NOUN
cana-587	18	34	.	.	PUNCT
cana-587	19	1	in	in	ADP
cana-587	19	2	1967	1967	NUM
cana-587	19	3	,	,	PUNCT
cana-587	19	4	robert	robert	PROPN
cana-587	19	5	l.	l.	PROPN
cana-587	19	6	graves	graves	PROPN
cana-587	19	7	[	[	X
cana-587	19	8	17	17	NUM
cana-587	19	9	]	]	PUNCT
cana-587	19	10	put	put	VERB
cana-587	19	11	forth	forth	ADP
cana-587	19	12	a	a	DET
cana-587	19	13	principal	principal	ADJ
cana-587	19	14	pivoting	pivot	VERB
cana-587	19	15	method	method	NOUN
cana-587	19	16	for	for	ADP
cana-587	19	17	lcps	lcp	NOUN
cana-587	19	18	.	.	PUNCT
cana-587	20	1	cottle	cottle	PROPN
cana-587	20	2	and	and	CCONJ
cana-587	20	3	danzig	danzig	PROPN
cana-587	20	4	[	[	X
cana-587	20	5	4	4	NUM
cana-587	20	6	]	]	PUNCT
cana-587	20	7	unified	unified	ADJ
cana-587	20	8	linear	linear	ADJ
cana-587	20	9	and	and	CCONJ
cana-587	20	10	quadratic	quadratic	ADJ
cana-587	20	11	programs	program	NOUN
cana-587	20	12	,	,	PUNCT
cana-587	20	13	as	as	ADV
cana-587	20	14	well	well	ADV
cana-587	20	15	as	as	ADP
cana-587	20	16	bimatrix	bimatrix	NOUN
cana-587	20	17	games	game	NOUN
cana-587	20	18	.	.	PUNCT
cana-587	21	1	in	in	ADP
cana-587	21	2	1968	1968	NUM
cana-587	21	3	,	,	PUNCT
cana-587	21	4	lemke	lemke	PROPN
cana-587	21	5	et	et	PROPN
cana-587	21	6	al	al	PROPN
cana-587	21	7	,	,	PUNCT
cana-587	22	1	[	[	X
cana-587	22	2	2,10,16	2,10,16	NUM
cana-587	22	3	]	]	PUNCT
cana-587	22	4	proposed	propose	VERB
cana-587	22	5	a	a	DET
cana-587	22	6	complementarity	complementarity	NOUN
cana-587	22	7	pivoting	pivot	VERB
cana-587	22	8	algorithm	algorithm	NOUN
cana-587	22	9	to	to	PART
cana-587	22	10	solve	solve	VERB
cana-587	22	11	linear	linear	ADJ
cana-587	22	12	complementarity	complementarity	NOUN
cana-587	22	13	problems	problem	NOUN
cana-587	22	14	.	.	PUNCT
cana-587	23	1	“	"	PUNCT
cana-587	23	2	the	the	DET
cana-587	23	3	lcp	lcp	NOUN
cana-587	23	4	(	(	PUNCT
cana-587	23	5	q	q	NOUN
cana-587	23	6	,	,	PUNCT
cana-587	23	7	m	m	VERB
cana-587	23	8	)	)	PUNCT
cana-587	23	9	of	of	ADP
cana-587	23	10	order	order	NOUN
cana-587	23	11	n	n	NOUN
cana-587	23	12	and	and	CCONJ
cana-587	23	13	q	q	ADJ
cana-587	23	14	be	be	AUX
cana-587	23	15	a	a	DET
cana-587	23	16	nx1	nx1	NOUN
cana-587	23	17	real	real	ADJ
cana-587	23	18	vector	vector	NOUN
cana-587	23	19	,	,	PUNCT
cana-587	23	20	then	then	ADV
cana-587	23	21	lcp	lcp	PROPN
cana-587	23	22	is	be	AUX
cana-587	23	23	to	to	PART
cana-587	23	24	find	find	VERB
cana-587	23	25	real	real	ADJ
cana-587	23	26	nx1	nx1	NOUN
cana-587	23	27	vector	vector	PROPN
cana-587	23	28	w	w	PROPN
cana-587	23	29	,	,	PUNCT
cana-587	23	30	z	z	VERB
cana-587	23	31	such	such	ADJ
cana-587	23	32	that	that	SCONJ
cana-587	23	33	communications	communication	NOUN
cana-587	23	34	on	on	ADP
cana-587	23	35	applied	apply	VERB
cana-587	23	36	nonlinear	nonlinear	ADJ
cana-587	23	37	analysis	analysis	NOUN
cana-587	23	38	issn	issn	NOUN
cana-587	23	39	:	:	PUNCT
cana-587	23	40	1074	1074	NUM
cana-587	23	41	-	-	PUNCT
cana-587	23	42	133x	133x	NUM
cana-587	23	43	vol	vol	NOUN
cana-587	23	44	31	31	NUM
cana-587	23	45	no	no	NOUN
cana-587	23	46	.	.	PUNCT
cana-587	24	1	2s	2s	NUM
cana-587	24	2	(	(	PUNCT
cana-587	24	3	2024	2024	NUM
cana-587	24	4	)	)	PUNCT
cana-587	24	5	2	2	NUM
cana-587	24	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-587	24	7	a	a	DET
cana-587	24	8	pair	pair	NOUN
cana-587	24	9	of	of	ADP
cana-587	24	10	variables	variable	NOUN
cana-587	24	11	,	,	PUNCT
cana-587	24	12	one	one	NUM
cana-587	24	13	of	of	ADP
cana-587	24	14	which	which	PRON
cana-587	24	15	must	must	AUX
cana-587	24	16	be	be	AUX
cana-587	24	17	zero	zero	NUM
cana-587	24	18	.	.	PUNCT
cana-587	25	1	each	each	DET
cana-587	25	2	variable	variable	NOUN
cana-587	25	3	in	in	ADP
cana-587	25	4	the	the	DET
cana-587	25	5	pair	pair	NOUN
cana-587	25	6	(	(	PUNCT
cana-587	25	7	wj	wj	PROPN
cana-587	25	8	,	,	PUNCT
cana-587	25	9	zj	zj	PROPN
cana-587	25	10	)	)	PUNCT
cana-587	25	11	is	be	AUX
cana-587	25	12	a	a	DET
cana-587	25	13	complement	complement	NOUN
cana-587	25	14	to	to	ADP
cana-587	25	15	each	each	DET
cana-587	25	16	other	other	ADJ
cana-587	25	17	.	.	PUNCT
cana-587	26	1	this	this	DET
cana-587	26	2	paper	paper	NOUN
cana-587	26	3	provides	provide	VERB
cana-587	26	4	a	a	DET
cana-587	26	5	real	real	ADJ
cana-587	26	6	-	-	PUNCT
cana-587	26	7	life	life	NOUN
cana-587	26	8	lpp	lpp	NOUN
cana-587	26	9	that	that	PRON
cana-587	26	10	can	can	AUX
cana-587	26	11	be	be	AUX
cana-587	26	12	converted	convert	VERB
cana-587	26	13	into	into	ADP
cana-587	26	14	a	a	DET
cana-587	26	15	linear	linear	ADJ
cana-587	26	16	complementarity	complementarity	NOUN
cana-587	26	17	problem	problem	NOUN
cana-587	26	18	with	with	ADP
cana-587	26	19	the	the	DET
cana-587	26	20	help	help	NOUN
cana-587	26	21	of	of	ADP
cana-587	26	22	m.laisin	m.laisin	NOUN
cana-587	26	23	and	and	CCONJ
cana-587	26	24	j.e.okeke	j.e.okeke	ADJ
cana-587	27	1	[	[	X
cana-587	27	2	10	10	NUM
cana-587	27	3	]	]	PUNCT
cana-587	27	4	.	.	PUNCT
cana-587	28	1	k.	k.	PROPN
cana-587	28	2	g.	g.	PROPN
cana-587	28	3	murty	murty	PROPN
cana-587	28	4	first	first	ADV
cana-587	28	5	proposed	propose	VERB
cana-587	28	6	an	an	DET
cana-587	28	7	index	index	NOUN
cana-587	28	8	method	method	NOUN
cana-587	28	9	[	[	X
cana-587	28	10	9	9	NUM
cana-587	28	11	,	,	PUNCT
cana-587	28	12	12	12	NUM
cana-587	28	13	]	]	PUNCT
cana-587	28	14	.	.	PUNCT
cana-587	29	1	with	with	ADP
cana-587	29	2	the	the	DET
cana-587	29	3	reference	reference	NOUN
cana-587	29	4	of	of	ADP
cana-587	29	5	nagoorgani	nagoorgani	PROPN
cana-587	29	6	et	et	PROPN
cana-587	29	7	al	al	PROPN
cana-587	29	8	,	,	PUNCT
cana-587	29	9	[	[	X
cana-587	29	10	13	13	NUM
cana-587	29	11	,	,	PUNCT
cana-587	29	12	14	14	NUM
cana-587	29	13	]	]	PUNCT
cana-587	29	14	a	a	DET
cana-587	29	15	maximum	maximum	ADJ
cana-587	29	16	index	index	NOUN
cana-587	29	17	method	method	NOUN
cana-587	29	18	for	for	ADP
cana-587	29	19	solving	solve	VERB
cana-587	29	20	fuzzy	fuzzy	ADJ
cana-587	29	21	lcp	lcp	NOUN
cana-587	29	22	with	with	ADP
cana-587	29	23	tfns	tfns	NOUN
cana-587	29	24	.	.	PUNCT
cana-587	30	1	the	the	DET
cana-587	30	2	fuzzy	fuzzy	ADJ
cana-587	30	3	complementary	complementary	ADJ
cana-587	30	4	pivot	pivot	NOUN
cana-587	30	5	algorithm	algorithm	NOUN
cana-587	30	6	is	be	AUX
cana-587	30	7	carried	carry	VERB
cana-587	30	8	out	out	ADP
cana-587	30	9	in	in	ADP
cana-587	30	10	this	this	DET
cana-587	30	11	method	method	NOUN
cana-587	30	12	without	without	ADP
cana-587	30	13	the	the	DET
cana-587	30	14	use	use	NOUN
cana-587	30	15	of	of	ADP
cana-587	30	16	artificial	artificial	ADJ
cana-587	30	17	variables	variable	NOUN
cana-587	30	18	.	.	PUNCT
cana-587	31	1	this	this	DET
cana-587	31	2	paper	paper	NOUN
cana-587	31	3	is	be	AUX
cana-587	31	4	structured	structure	VERB
cana-587	31	5	as	as	SCONJ
cana-587	31	6	follows	follow	VERB
cana-587	31	7	:	:	PUNCT
cana-587	31	8	the	the	DET
cana-587	31	9	tfn	tfn	NOUN
cana-587	31	10	and	and	CCONJ
cana-587	31	11	its	its	PRON
cana-587	31	12	associated	associated	ADJ
cana-587	31	13	arithmetic	arithmetic	ADJ
cana-587	31	14	operations	operation	NOUN
cana-587	31	15	are	be	AUX
cana-587	31	16	covered	cover	VERB
cana-587	31	17	in	in	ADP
cana-587	31	18	section	section	NOUN
cana-587	31	19	2	2	NUM
cana-587	31	20	.	.	PUNCT
cana-587	31	21	section	section	NOUN
cana-587	31	22	3	3	NUM
cana-587	31	23	,	,	PUNCT
cana-587	31	24	describes	describe	VERB
cana-587	31	25	the	the	DET
cana-587	31	26	flcp	flcp	NOUN
cana-587	31	27	and	and	CCONJ
cana-587	31	28	its	its	PRON
cana-587	31	29	algorithm	algorithm	NOUN
cana-587	31	30	along	along	ADP
cana-587	31	31	with	with	ADP
cana-587	31	32	the	the	DET
cana-587	31	33	methods	method	NOUN
cana-587	31	34	for	for	ADP
cana-587	31	35	solving	solve	VERB
cana-587	31	36	it	it	PRON
cana-587	31	37	.	.	PUNCT
cana-587	32	1	section	section	NOUN
cana-587	32	2	4	4	NUM
cana-587	32	3	describes	describe	VERB
cana-587	32	4	the	the	DET
cana-587	32	5	conversion	conversion	NOUN
cana-587	32	6	of	of	ADP
cana-587	32	7	an	an	DET
cana-587	32	8	flpp	flpp	NOUN
cana-587	32	9	into	into	ADP
cana-587	32	10	an	an	DET
cana-587	32	11	flcp	flcp	NOUN
cana-587	32	12	.	.	PUNCT
cana-587	33	1	section	section	NOUN
cana-587	33	2	5	5	NUM
cana-587	33	3	,	,	PUNCT
cana-587	33	4	includes	include	VERB
cana-587	33	5	a	a	DET
cana-587	33	6	real	real	ADJ
cana-587	33	7	-	-	PUNCT
cana-587	33	8	life	life	NOUN
cana-587	33	9	application	application	NOUN
cana-587	33	10	that	that	PRON
cana-587	33	11	has	have	AUX
cana-587	33	12	been	be	AUX
cana-587	33	13	designed	design	VERB
cana-587	33	14	and	and	CCONJ
cana-587	33	15	developed	develop	VERB
cana-587	33	16	to	to	PART
cana-587	33	17	demonstrate	demonstrate	VERB
cana-587	33	18	how	how	SCONJ
cana-587	33	19	the	the	DET
cana-587	33	20	proposed	propose	VERB
cana-587	33	21	method	method	NOUN
cana-587	33	22	works	work	VERB
cana-587	33	23	.	.	PUNCT
cana-587	34	1	finally	finally	ADV
cana-587	34	2	,	,	PUNCT
cana-587	34	3	section	section	NOUN
cana-587	34	4	6	6	NUM
cana-587	34	5	concludes	conclude	VERB
cana-587	34	6	with	with	ADP
cana-587	34	7	some	some	DET
cana-587	34	8	closing	closing	NOUN
cana-587	34	9	remarks	remark	NOUN
cana-587	34	10	.	.	PUNCT
cana-587	35	1	2	2	X
cana-587	35	2	.	.	X
cana-587	35	3	preliminaries	preliminary	NOUN
cana-587	35	4	this	this	DET
cana-587	35	5	chapter	chapter	NOUN
cana-587	35	6	presents	present	VERB
cana-587	35	7	some	some	DET
cana-587	35	8	fundamental	fundamental	ADJ
cana-587	35	9	definitions	definition	NOUN
cana-587	35	10	and	and	CCONJ
cana-587	35	11	concepts	concept	NOUN
cana-587	35	12	that	that	PRON
cana-587	35	13	are	be	AUX
cana-587	35	14	extremely	extremely	ADV
cana-587	35	15	valuable	valuable	ADJ
cana-587	35	16	in	in	ADP
cana-587	35	17	our	our	PRON
cana-587	35	18	work	work	NOUN
cana-587	35	19	.	.	PUNCT
cana-587	36	1	2.1	2.1	NUM
cana-587	36	2	triangular	triangular	NOUN
cana-587	36	3	fuzzy	fuzzy	ADJ
cana-587	36	4	number	number	NOUN
cana-587	36	5	(	(	PUNCT
cana-587	36	6	tfn	tfn	NOUN
cana-587	36	7	)	)	PUNCT
cana-587	36	8	a	a	DET
cana-587	36	9	tfn	tfn	NOUN
cana-587	36	10	ã	ã	X
cana-587	36	11	=	=	SYM
cana-587	36	12	(	(	PUNCT
cana-587	36	13	a1	a1	PROPN
cana-587	36	14	,	,	PUNCT
cana-587	36	15	a2	a2	PROPN
cana-587	36	16	,	,	PUNCT
cana-587	36	17	a3	a3	NOUN
cana-587	36	18	)	)	PUNCT
cana-587	36	19	,	,	PUNCT
cana-587	36	20	the	the	DET
cana-587	36	21	membership	membership	NOUN
cana-587	36	22	function	function	NOUN
cana-587	36	23	is	be	AUX
cana-587	36	24	defined	define	VERB
cana-587	36	25	as	as	ADP
cana-587	36	26	2.2	2.2	NUM
cana-587	36	27	arithmetic	arithmetic	ADJ
cana-587	36	28	operation	operation	NOUN
cana-587	36	29	of	of	ADP
cana-587	36	30	triangular	triangular	NOUN
cana-587	36	31	fuzzy	fuzzy	ADJ
cana-587	36	32	number	number	NOUN
cana-587	36	33	using	use	VERB
cana-587	36	34	function	function	NOUN
cana-587	36	35	principle	principle	NOUN
cana-587	36	36	:	:	PUNCT
cana-587	36	37	let	let	VERB
cana-587	36	38	�	�	PROPN
cana-587	36	39	̃	̃	PROPN
cana-587	36	40	�	�	NOUN
cana-587	36	41	=	=	SYM
cana-587	36	42	(	(	PUNCT
cana-587	36	43	𝜌1	𝜌1	NOUN
cana-587	36	44	,	,	PUNCT
cana-587	36	45	𝜌2	𝜌2	ADJ
cana-587	36	46	,	,	PUNCT
cana-587	36	47	𝜌3	𝜌3	PROPN
cana-587	36	48	)	)	PUNCT
cana-587	36	49	and	and	CCONJ
cana-587	36	50	ℭ̃	ℭ̃	NOUN
cana-587	36	51	=	=	SYM
cana-587	36	52	(	(	PUNCT
cana-587	36	53	𝜚1	𝜚1	NOUN
cana-587	36	54	,	,	PUNCT
cana-587	36	55	𝜚2	𝜚2	ADV
cana-587	36	56	,	,	PUNCT
cana-587	36	57	𝜚3	𝜚3	ADJ
cana-587	36	58	)	)	PUNCT
cana-587	36	59	then	then	ADV
cana-587	37	1	[	[	X
cana-587	37	2	14	14	NUM
cana-587	37	3	]	]	PUNCT
cana-587	37	4	,	,	PUNCT
cana-587	37	5	addition	addition	NOUN
cana-587	37	6	:	:	PUNCT
cana-587	37	7	�	�	PROPN
cana-587	37	8	̃	̃	NOUN
cana-587	37	9	�	�	PROPN
cana-587	37	10	+	+	NOUN
cana-587	37	11	ℭ̃	ℭ̃	NOUN
cana-587	37	12	=	=	PUNCT
cana-587	37	13	(	(	PUNCT
cana-587	37	14	𝜌	𝜌	PART
cana-587	37	15	1	1	NUM
cana-587	37	16	+	+	SYM
cana-587	37	17	𝜚	𝜚	NOUN
cana-587	37	18	1	1	NUM
cana-587	37	19	,	,	PUNCT
cana-587	37	20	𝜌	𝜌	ADP
cana-587	37	21	2	2	NUM
cana-587	37	22	+	+	SYM
cana-587	37	23	𝜚	𝜚	NOUN
cana-587	37	24	2	2	NUM
cana-587	37	25	,	,	PUNCT
cana-587	37	26	𝜌	𝜌	ADP
cana-587	37	27	3	3	NUM
cana-587	37	28	+	+	SYM
cana-587	37	29	𝜚	𝜚	NOUN
cana-587	37	30	3	3	NUM
cana-587	37	31	)	)	PUNCT
cana-587	37	32	.	.	PUNCT
cana-587	38	1	subtraction	subtraction	NOUN
cana-587	38	2	:	:	PUNCT
cana-587	38	3	�	�	PROPN
cana-587	38	4	̃	̃	NOUN
cana-587	38	5	�	�	PROPN
cana-587	38	6	ℭ̃	ℭ̃	NOUN
cana-587	38	7	=	=	PUNCT
cana-587	38	8	(	(	PUNCT
cana-587	38	9	𝜌	𝜌	X
cana-587	38	10	1	1	NUM
cana-587	38	11	–	–	PUNCT
cana-587	38	12	𝜚	𝜚	NOUN
cana-587	38	13	1	1	NUM
cana-587	38	14	,	,	PUNCT
cana-587	38	15	𝜌	𝜌	ADP
cana-587	38	16	2	2	NUM
cana-587	38	17	–	–	PUNCT
cana-587	38	18	𝜚	𝜚	NOUN
cana-587	38	19	2	2	NUM
cana-587	38	20	,	,	PUNCT
cana-587	38	21	𝜌	𝜌	ADP
cana-587	38	22	3	3	NUM
cana-587	38	23	–	–	PUNCT
cana-587	38	24	𝜚	𝜚	NOUN
cana-587	38	25	3	3	NUM
cana-587	38	26	)	)	PUNCT
cana-587	38	27	.	.	PUNCT
cana-587	39	1	multiplication	multiplication	NOUN
cana-587	39	2	:	:	PUNCT
cana-587	39	3	�	�	PROPN
cana-587	39	4	̃	̃	PROPN
cana-587	39	5	�	�	PROPN
cana-587	39	6	×	×	NOUN
cana-587	39	7	ℭ̃	ℭ̃	PROPN
cana-587	39	8	=	=	PUNCT
cana-587	39	9	(	(	PUNCT
cana-587	39	10	min	min	PROPN
cana-587	39	11	(	(	PUNCT
cana-587	39	12	𝜌	𝜌	ADP
cana-587	39	13	1	1	NUM
cana-587	39	14	𝜚	𝜚	NOUN
cana-587	39	15	1	1	NUM
cana-587	39	16	,	,	PUNCT
cana-587	39	17	𝜌	𝜌	ADP
cana-587	39	18	1	1	NUM
cana-587	39	19	𝜚	𝜚	NOUN
cana-587	39	20	3	3	NUM
cana-587	39	21	,	,	PUNCT
cana-587	39	22	𝜌3	𝜌3	VERB
cana-587	39	23	𝜚	𝜚	PRON
cana-587	39	24	1	1	NUM
cana-587	39	25	,	,	PUNCT
cana-587	39	26	𝜌	𝜌	ADP
cana-587	39	27	3	3	NUM
cana-587	39	28	𝜚	𝜚	NOUN
cana-587	39	29	3	3	NUM
cana-587	39	30	)	)	PUNCT
cana-587	39	31	,	,	PUNCT
cana-587	39	32	𝜌	𝜌	ADP
cana-587	39	33	2	2	NUM
cana-587	39	34	𝜚	𝜚	NOUN
cana-587	39	35	2	2	NUM
cana-587	39	36	,	,	PUNCT
cana-587	39	37	max	max	X
cana-587	39	38	(	(	PUNCT
cana-587	39	39	𝜌	𝜌	ADP
cana-587	39	40	1	1	NUM
cana-587	39	41	𝜚	𝜚	NOUN
cana-587	39	42	1	1	NUM
cana-587	39	43	,	,	PUNCT
cana-587	39	44	𝜌	𝜌	ADP
cana-587	39	45	1	1	NUM
cana-587	39	46	𝜚	𝜚	NOUN
cana-587	39	47	3	3	NUM
cana-587	39	48	,	,	PUNCT
cana-587	39	49	𝜌3	𝜌3	VERB
cana-587	39	50	𝜚	𝜚	PRON
cana-587	39	51	1	1	NUM
cana-587	39	52	,	,	PUNCT
cana-587	39	53	𝜌	𝜌	ADP
cana-587	39	54	3	3	NUM
cana-587	39	55	𝜚	𝜚	NOUN
cana-587	39	56	3	3	NUM
cana-587	39	57	)	)	PUNCT
cana-587	39	58	)	)	PUNCT
cana-587	39	59	.	.	PUNCT
cana-587	40	1	division	division	NOUN
cana-587	40	2	:	:	PUNCT
cana-587	40	3	�	�	PROPN
cana-587	40	4	̃	̃	PROPN
cana-587	40	5	�	�	PROPN
cana-587	40	6	/	/	SYM
cana-587	40	7	ℭ̃	ℭ̃	NOUN
cana-587	40	8	=	=	PUNCT
cana-587	40	9	(	(	PUNCT
cana-587	40	10	𝜌1	𝜌1	NOUN
cana-587	40	11	𝜚1	𝜚1	NOUN
cana-587	40	12	,	,	PUNCT
cana-587	40	13	𝜌2	𝜌2	ADJ
cana-587	40	14	𝜚2	𝜚2	ADV
cana-587	40	15	,	,	PUNCT
cana-587	40	16	𝜌3	𝜌3	VERB
cana-587	40	17	𝜚3	𝜚3	ADJ
cana-587	40	18	)	)	PUNCT
cana-587	40	19	.	.	PUNCT
cana-587	41	1	communications	communication	NOUN
cana-587	41	2	on	on	ADP
cana-587	41	3	applied	apply	VERB
cana-587	41	4	nonlinear	nonlinear	ADJ
cana-587	41	5	analysis	analysis	NOUN
cana-587	41	6	issn	issn	NOUN
cana-587	41	7	:	:	PUNCT
cana-587	41	8	1074	1074	NUM
cana-587	41	9	-	-	PUNCT
cana-587	41	10	133x	133x	NUM
cana-587	41	11	vol	vol	NOUN
cana-587	41	12	31	31	NUM
cana-587	41	13	no	no	NOUN
cana-587	41	14	.	.	PUNCT
cana-587	42	1	2s	2s	NUM
cana-587	42	2	(	(	PUNCT
cana-587	42	3	2024	2024	NUM
cana-587	42	4	)	)	PUNCT
cana-587	42	5	3	3	NUM
cana-587	42	6	https://internationalpubls.com	https://internationalpubls.com	SYM
cana-587	42	7	2.3	2.3	NUM
cana-587	42	8	defuzzification	defuzzification	NOUN
cana-587	42	9	let	let	VERB
cana-587	42	10	a	a	DET
cana-587	42	11	~	~	PUNCT
cana-587	42	12	=	=	SYM
cana-587	42	13	(	(	PUNCT
cana-587	42	14	d1	d1	PROPN
cana-587	42	15	,	,	PUNCT
cana-587	42	16	d2	d2	PROPN
cana-587	42	17	,	,	PUNCT
cana-587	42	18	d3	d3	PROPN
cana-587	42	19	)	)	PUNCT
cana-587	42	20	be	be	VERB
cana-587	42	21	a	a	DET
cana-587	42	22	tfn	tfn	NOUN
cana-587	42	23	,	,	PUNCT
cana-587	42	24	then	then	ADV
cana-587	42	25	the	the	DET
cana-587	42	26	fuzzy	fuzzy	ADJ
cana-587	42	27	number	number	NOUN
cana-587	42	28	can	can	AUX
cana-587	42	29	be	be	AUX
cana-587	42	30	defuzzified	defuzzifie	VERB
cana-587	42	31	in	in	ADP
cana-587	42	32	the	the	DET
cana-587	42	33	following	follow	VERB
cana-587	42	34	manner	manner	NOUN
cana-587	42	35	p	p	X
cana-587	42	36	(	(	PUNCT
cana-587	42	37	a	a	PRON
cana-587	42	38	~	~	PUNCT
cana-587	42	39	)	)	PUNCT
cana-587	43	1	=	=	SYM
cana-587	43	2	(	(	PUNCT
cana-587	43	3	d1	d1	PROPN
cana-587	43	4	+	+	CCONJ
cana-587	43	5	4d2	4d2	NUM
cana-587	43	6	+	+	CCONJ
cana-587	43	7	d3	d3	PROPN
cana-587	43	8	)	)	PUNCT
cana-587	43	9	/	/	SYM
cana-587	44	1	6	6	NUM
cana-587	44	2	.	.	SYM
cana-587	44	3	3	3	NUM
cana-587	44	4	.	.	NOUN
cana-587	44	5	fuzzy	fuzzy	ADJ
cana-587	44	6	linear	linear	ADJ
cana-587	44	7	complementarity	complementarity	NOUN
cana-587	44	8	problem	problem	NOUN
cana-587	44	9	(	(	PUNCT
cana-587	44	10	flcp	flcp	NOUN
cana-587	44	11	)	)	PUNCT
cana-587	44	12	“	"	PUNCT
cana-587	44	13	the	the	DET
cana-587	44	14	parameters	parameter	NOUN
cana-587	44	15	all	all	DET
cana-587	44	16	the	the	DET
cana-587	44	17	parameters	parameter	NOUN
cana-587	44	18	are	be	AUX
cana-587	44	19	in	in	ADP
cana-587	44	20	fuzzy	fuzzy	ADJ
cana-587	44	21	numbers	number	NOUN
cana-587	44	22	.	.	PUNCT
cana-587	45	1	by	by	ADP
cana-587	45	2	replacing	replace	VERB
cana-587	45	3	crisp	crisp	ADJ
cana-587	45	4	parameters	parameter	NOUN
cana-587	45	5	with	with	ADP
cana-587	45	6	fuzzy	fuzzy	ADJ
cana-587	45	7	numbers	number	NOUN
cana-587	45	8	,	,	PUNCT
cana-587	45	9	[	[	X
cana-587	45	10	8	8	NUM
cana-587	45	11	]	]	PUNCT
cana-587	45	12	the	the	DET
cana-587	45	13	pair	pair	NOUN
cana-587	45	14	(	(	PUNCT
cana-587	45	15	,	,	PUNCT
cana-587	45	16	)	)	PUNCT
cana-587	46	1	j	j	PROPN
cana-587	46	2	jw	jw	PROPN
cana-587	46	3	z	z	PROPN
cana-587	46	4	is	be	AUX
cana-587	46	5	said	say	VERB
cana-587	46	6	to	to	PART
cana-587	46	7	be	be	AUX
cana-587	46	8	a	a	DET
cana-587	46	9	pair	pair	NOUN
cana-587	46	10	of	of	ADP
cana-587	46	11	fuzzy	fuzzy	ADJ
cana-587	46	12	complementary	complementary	ADJ
cana-587	46	13	variables	variable	NOUN
cana-587	46	14	”	"	PUNCT
cana-587	46	15	.	.	PUNCT
cana-587	47	1	3.1	3.1	NUM
cana-587	47	2	algorithm	algorithm	NOUN
cana-587	47	3	:	:	PUNCT
cana-587	47	4	fuzzy	fuzzy	ADJ
cana-587	47	5	linear	linear	ADJ
cana-587	47	6	complementarity	complementarity	NOUN
cana-587	47	7	problem	problem	NOUN
cana-587	47	8	lemke	lemke	NOUN
cana-587	48	1	[	[	X
cana-587	48	2	11	11	NUM
cana-587	48	3	]	]	PUNCT
cana-587	48	4	proposed	propose	VERB
cana-587	48	5	a	a	DET
cana-587	48	6	solution	solution	NOUN
cana-587	48	7	algorithm	algorithm	NOUN
cana-587	48	8	for	for	ADP
cana-587	48	9	linear	linear	ADJ
cana-587	48	10	complementarity	complementarity	NOUN
cana-587	48	11	problems	problem	NOUN
cana-587	48	12	.	.	PUNCT
cana-587	49	1	murty	murty	NOUN
cana-587	50	1	[	[	X
cana-587	50	2	9	9	NUM
cana-587	50	3	,	,	PUNCT
cana-587	50	4	12	12	NUM
cana-587	50	5	]	]	PUNCT
cana-587	50	6	suggested	suggest	VERB
cana-587	50	7	,	,	PUNCT
cana-587	50	8	using	use	VERB
cana-587	50	9	an	an	DET
cana-587	50	10	index	index	NOUN
cana-587	50	11	method	method	NOUN
cana-587	50	12	to	to	PART
cana-587	50	13	solve	solve	VERB
cana-587	50	14	lcps	lcp	NOUN
cana-587	50	15	.	.	PUNCT
cana-587	51	1	based	base	VERB
cana-587	51	2	on	on	ADP
cana-587	51	3	this	this	DET
cana-587	51	4	concept	concept	NOUN
cana-587	51	5	,	,	PUNCT
cana-587	51	6	the	the	DET
cana-587	51	7	maximum	maximum	ADJ
cana-587	51	8	index	index	NOUN
cana-587	51	9	method	method	NOUN
cana-587	51	10	for	for	ADP
cana-587	51	11	solving	solve	VERB
cana-587	51	12	the	the	DET
cana-587	51	13	fuzzy	fuzzy	ADJ
cana-587	51	14	linear	linear	ADJ
cana-587	51	15	complementarity	complementarity	NOUN
cana-587	51	16	problem	problem	NOUN
cana-587	51	17	is	be	AUX
cana-587	51	18	developed	develop	VERB
cana-587	51	19	here	here	ADV
cana-587	51	20	.	.	PUNCT
cana-587	52	1	consider	consider	VERB
cana-587	52	2	the	the	DET
cana-587	52	3	flcp	flcp	NOUN
cana-587	52	4	(	(	PUNCT
cana-587	52	5	q	q	PROPN
cana-587	52	6	̃	̃	PROPN
cana-587	52	7	,	,	PUNCT
cana-587	52	8	m	m	VERB
cana-587	52	9	̃	̃	NOUN
cana-587	52	10	)	)	PUNCT
cana-587	52	11	of	of	ADP
cana-587	52	12	order	order	NOUN
cana-587	52	13	n	n	CCONJ
cana-587	52	14	,	,	PUNCT
cana-587	52	15	suppose	suppose	VERB
cana-587	52	16	the	the	DET
cana-587	52	17	fuzzy	fuzzy	ADJ
cana-587	52	18	matrix	matrix	NOUN
cana-587	52	19	satisfies	satisfy	VERB
cana-587	52	20	the	the	DET
cana-587	52	21	conditions	condition	NOUN
cana-587	52	22	:	:	PUNCT
cana-587	52	23	there	there	PRON
cana-587	52	24	is	be	VERB
cana-587	52	25	a	a	DET
cana-587	52	26	column	column	NOUN
cana-587	52	27	vector	vector	NOUN
cana-587	52	28	with	with	ADP
cana-587	52	29	all	all	DET
cana-587	52	30	strictly	strictly	ADV
cana-587	52	31	positive	positive	ADJ
cana-587	52	32	entries	entry	NOUN
cana-587	52	33	.	.	PUNCT
cana-587	53	1	then	then	ADV
cana-587	53	2	a	a	DET
cana-587	53	3	variant	variant	NOUN
cana-587	53	4	of	of	ADP
cana-587	53	5	the	the	DET
cana-587	53	6	complementary	complementary	ADJ
cana-587	53	7	pivot	pivot	NOUN
cana-587	53	8	algorithm	algorithm	NOUN
cana-587	53	9	that	that	PRON
cana-587	53	10	uses	use	VERB
cana-587	53	11	no	no	DET
cana-587	53	12	artificial	artificial	ADJ
cana-587	53	13	variable	variable	NOUN
cana-587	53	14	can	can	AUX
cana-587	53	15	be	be	AUX
cana-587	53	16	applied	apply	VERB
cana-587	53	17	on	on	ADP
cana-587	53	18	the	the	DET
cana-587	53	19	flcp	flcp	NOUN
cana-587	53	20	(	(	PUNCT
cana-587	53	21	q	q	PROPN
cana-587	53	22	̃	̃	PROPN
cana-587	53	23	,	,	PUNCT
cana-587	53	24	m	m	PROPN
cana-587	53	25	̃	̃	PROPN
cana-587	53	26	)	)	PUNCT
cana-587	53	27	.	.	PUNCT
cana-587	54	1	the	the	DET
cana-587	54	2	original	original	ADJ
cana-587	54	3	tableau	tableau	NOUN
cana-587	54	4	for	for	ADP
cana-587	54	5	this	this	DET
cana-587	54	6	version	version	NOUN
cana-587	54	7	of	of	ADP
cana-587	54	8	the	the	DET
cana-587	54	9	algorithm	algorithm	NOUN
cana-587	54	10	is	be	AUX
cana-587	54	11	:	:	PUNCT
cana-587	54	12	�	�	PROPN
cana-587	54	13	̃	̃	PROPN
cana-587	54	14	�	�	PROPN
cana-587	54	15	�	�	PROPN
cana-587	54	16	̃	̃	PROPN
cana-587	54	17	�	�	PROPN
cana-587	54	18	𝐼	𝐼	PROPN
cana-587	54	19	�	�	PROPN
cana-587	54	20	̃	̃	PROPN
cana-587	54	21	�	�	PROPN
cana-587	54	22	�	�	PROPN
cana-587	54	23	̃	̃	PROPN
cana-587	54	24	�	�	PROPN
cana-587	54	25	initially	initially	ADV
cana-587	54	26	set	set	VERB
cana-587	54	27	n=0	n=0	NUM
cana-587	54	28	,	,	PUNCT
cana-587	54	29	q0	q0	NOUN
cana-587	54	30	,	,	PUNCT
cana-587	54	31	m0	m0	NOUN
cana-587	54	32	=	=	SYM
cana-587	54	33	q	q	NOUN
cana-587	54	34	,	,	PUNCT
cana-587	54	35	m.	m.	NOUN
cana-587	54	36	if	if	SCONJ
cana-587	54	37	qn	qn	PROPN
cana-587	54	38	≥	≥	NOUN
cana-587	54	39	0	0	NUM
cana-587	54	40	then	then	ADV
cana-587	54	41	stop	stop	VERB
cana-587	54	42	zn	zn	PROPN
cana-587	54	43	=	=	SYM
cana-587	54	44	0	0	NUM
cana-587	54	45	solves	solve	NOUN
cana-587	54	46	qn	qn	PROPN
cana-587	54	47	,	,	PUNCT
cana-587	54	48	mn	mn	PROPN
cana-587	54	49	,	,	PUNCT
cana-587	54	50	that	that	PRON
cana-587	54	51	is	be	AUX
cana-587	54	52	w	w	NOUN
cana-587	54	53	,	,	PUNCT
cana-587	54	54	z	z	NOUN
cana-587	54	55	=	=	SYM
cana-587	54	56	(	(	PUNCT
cana-587	54	57	𝑞	𝑞	PROPN
cana-587	54	58	,	,	PUNCT
cana-587	54	59	0	0	NUM
cana-587	54	60	)	)	PUNCT
cana-587	55	1	[	[	X
cana-587	55	2	13	13	NUM
cana-587	55	3	]	]	PUNCT
cana-587	55	4	.	.	PUNCT
cana-587	56	1	we	we	PRON
cana-587	56	2	assume	assume	VERB
cana-587	56	3	that	that	SCONJ
cana-587	56	4	𝑞	𝑞	PROPN
cana-587	56	5	̃	̃	PROPN
cana-587	56	6	≥	≥	NOUN
cana-587	56	7	0	0	NUM
cana-587	56	8	.	.	PUNCT
cana-587	57	1	let	let	VERB
cana-587	57	2	r	r	PRON
cana-587	57	3	be	be	AUX
cana-587	57	4	such	such	ADJ
cana-587	57	5	that	that	SCONJ
cana-587	57	6	𝑀	𝑀	PROPN
cana-587	57	7	�	�	PROPN
cana-587	57	8	̃	̃	PROPN
cana-587	57	9	�	�	PROPN
cana-587	57	10	>	>	X
cana-587	57	11	0	0	NUM
cana-587	57	12	.	.	PUNCT
cana-587	58	1	so	so	ADV
cana-587	58	2	,	,	PUNCT
cana-587	58	3	the	the	DET
cana-587	58	4	column	column	NOUN
cana-587	58	5	vector	vector	NOUN
cana-587	58	6	associated	associate	VERB
cana-587	58	7	with	with	ADP
cana-587	58	8	�	�	PROPN
cana-587	58	9	̃	̃	NOUN
cana-587	58	10	�	�	NOUN
cana-587	58	11	𝑟	𝑟	NOUN
cana-587	58	12	is	be	AUX
cana-587	58	13	strictly	strictly	ADV
cana-587	58	14	negative	negative	ADJ
cana-587	58	15	.	.	PUNCT
cana-587	59	1	the	the	DET
cana-587	59	2	variable	variable	NOUN
cana-587	59	3	can	can	AUX
cana-587	59	4	play	play	VERB
cana-587	59	5	the	the	DET
cana-587	59	6	equivalent	equivalent	ADJ
cana-587	59	7	role	role	NOUN
cana-587	59	8	as	as	ADP
cana-587	59	9	the	the	DET
cana-587	59	10	artificial	artificial	ADJ
cana-587	59	11	variable	variable	NOUN
cana-587	59	12	the	the	DET
cana-587	59	13	fuzzy	fuzzy	ADJ
cana-587	59	14	complementary	complementary	ADJ
cana-587	59	15	pivot	pivot	NOUN
cana-587	59	16	algorithm	algorithm	NOUN
cana-587	59	17	,	,	PUNCT
cana-587	59	18	flcp	flcp	NOUN
cana-587	59	19	satisfies	satisfy	VERB
cana-587	59	20	the	the	DET
cana-587	59	21	condition	condition	NOUN
cana-587	59	22	and	and	CCONJ
cana-587	59	23	is	be	AUX
cana-587	59	24	known	know	VERB
cana-587	59	25	as	as	ADP
cana-587	59	26	an	an	DET
cana-587	59	27	almost	almost	ADV
cana-587	59	28	fuzzy	fuzzy	ADJ
cana-587	59	29	complementary	complementary	ADJ
cana-587	59	30	feasible	feasible	ADJ
cana-587	59	31	basic	basic	ADJ
cana-587	59	32	vector	vector	NOUN
cana-587	59	33	.	.	PUNCT
cana-587	60	1	communications	communication	NOUN
cana-587	60	2	on	on	ADP
cana-587	60	3	applied	apply	VERB
cana-587	60	4	nonlinear	nonlinear	ADJ
cana-587	60	5	analysis	analysis	NOUN
cana-587	60	6	issn	issn	NOUN
cana-587	60	7	:	:	PUNCT
cana-587	60	8	1074	1074	NUM
cana-587	60	9	-	-	PUNCT
cana-587	60	10	133x	133x	NUM
cana-587	60	11	vol	vol	NOUN
cana-587	60	12	31	31	NUM
cana-587	60	13	no	no	NOUN
cana-587	60	14	.	.	PUNCT
cana-587	61	1	2s	2s	NUM
cana-587	61	2	(	(	PUNCT
cana-587	61	3	2024	2024	NUM
cana-587	61	4	)	)	PUNCT
cana-587	61	5	4	4	NUM
cana-587	61	6	https://internationalpubls.com	https://internationalpubls.com	SYM
cana-587	61	7	4	4	NUM
cana-587	61	8	.	.	PUNCT
cana-587	61	9	conversion	conversion	NOUN
cana-587	61	10	of	of	ADP
cana-587	61	11	linear	linear	PROPN
cana-587	61	12	programming	programming	NOUN
cana-587	61	13	problem	problem	NOUN
cana-587	61	14	into	into	ADP
cana-587	61	15	linear	linear	ADJ
cana-587	61	16	complementarity	complementarity	NOUN
cana-587	61	17	problem.[8	problem.[8	NOUN
cana-587	61	18	]	]	PUNCT
cana-587	61	19	a	a	DET
cana-587	61	20	linear	linear	ADJ
cana-587	61	21	programming	programming	NOUN
cana-587	61	22	problem	problem	NOUN
cana-587	61	23	(	(	PUNCT
cana-587	61	24	lpp	lpp	PROPN
cana-587	61	25	)	)	PUNCT
cana-587	61	26	can	can	AUX
cana-587	61	27	be	be	AUX
cana-587	61	28	expressed	express	VERB
cana-587	61	29	in	in	ADP
cana-587	61	30	the	the	DET
cana-587	61	31	symmetric	symmetric	ADJ
cana-587	61	32	form	form	NOUN
cana-587	61	33	(	(	PUNCT
cana-587	61	34	the	the	DET
cana-587	61	35	primal	primal	ADJ
cana-587	61	36	problem	problem	NOUN
cana-587	61	37	,	,	PUNCT
cana-587	61	38	(	(	PUNCT
cana-587	61	39	taha	taha	NOUN
cana-587	61	40	)	)	PUNCT
cana-587	62	1	[	[	X
cana-587	62	2	7	7	NUM
cana-587	62	3	]	]	PUNCT
cana-587	62	4	)	)	PUNCT
cana-587	62	5	as	as	SCONJ
cana-587	62	6	follows	follow	VERB
cana-587	62	7	;	;	PUNCT
cana-587	62	8	let	let	VERB
cana-587	62	9	a	a	PRON
cana-587	62	10	is	be	AUX
cana-587	62	11	a	a	DET
cana-587	62	12	matrix	matrix	NOUN
cana-587	62	13	of	of	ADP
cana-587	62	14	order	order	NOUN
cana-587	62	15	m	m	VERB
cana-587	62	16	x	x	VERB
cana-587	62	17	n.	n.	ADJ
cana-587	62	18	if	if	SCONJ
cana-587	62	19	x/	x/	PROPN
cana-587	62	20	∈	∈	PROPN
cana-587	62	21	ℝ𝑛	ℝ𝑛	PROPN
cana-587	62	22	,	,	PUNCT
cana-587	62	23	then	then	ADV
cana-587	62	24	the	the	DET
cana-587	62	25	dual	dual	ADJ
cana-587	62	26	problem	problem	NOUN
cana-587	62	27	of	of	ADP
cana-587	62	28	(	(	PUNCT
cana-587	62	29	4.1	4.1	NUM
cana-587	62	30	)	)	PUNCT
cana-587	62	31	in	in	ADP
cana-587	62	32	symmetric	symmetric	ADJ
cana-587	62	33	form	form	NOUN
cana-587	62	34	as	as	SCONJ
cana-587	62	35	follows	follow	VERB
cana-587	62	36	;	;	PUNCT
cana-587	62	37	maximize	maximize	VERB
cana-587	62	38	z	z	NOUN
cana-587	62	39	=	=	SYM
cana-587	62	40	bty	bty	PROPN
cana-587	62	41	subject	subject	ADJ
cana-587	62	42	to	to	ADP
cana-587	62	43	aty	aty	PROPN
cana-587	62	44	≥	≥	X
cana-587	62	45	ct	ct	PROPN
cana-587	62	46	(	(	PUNCT
cana-587	62	47	4.2	4.2	NUM
cana-587	62	48	)	)	PUNCT
cana-587	62	49	y	y	PROPN
cana-587	62	50	≥	≥	NOUN
cana-587	62	51	0	0	NUM
cana-587	62	52	by	by	ADP
cana-587	62	53	the	the	DET
cana-587	62	54	well	well	ADV
cana-587	62	55	-	-	PUNCT
cana-587	62	56	known	know	VERB
cana-587	62	57	duality	duality	NOUN
cana-587	62	58	theory	theory	NOUN
cana-587	62	59	of	of	ADP
cana-587	62	60	lpp	lpp	PROPN
cana-587	62	61	,	,	PUNCT
cana-587	62	62	there	there	PRON
cana-587	62	63	exists	exist	VERB
cana-587	62	64	a	a	DET
cana-587	62	65	dual	dual	ADJ
cana-587	62	66	vector	vector	NOUN
cana-587	62	67	y/	y/	NOUN
cana-587	62	68	∈	∈	PROPN
cana-587	63	1	ℝ𝑚	ℝ𝑚	ADP
cana-587	63	2	is	be	AUX
cana-587	63	3	an	an	DET
cana-587	63	4	optimal	optimal	ADJ
cana-587	63	5	solution	solution	NOUN
cana-587	63	6	to	to	ADP
cana-587	63	7	the	the	DET
cana-587	63	8	problem	problem	NOUN
cana-587	63	9	(	(	PUNCT
cana-587	63	10	4.2	4.2	NUM
cana-587	63	11	)	)	PUNCT
cana-587	63	12	.	.	PUNCT
cana-587	64	1	by	by	ADP
cana-587	64	2	introducing	introduce	VERB
cana-587	64	3	slack	slack	NOUN
cana-587	64	4	dual	dual	ADJ
cana-587	64	5	variable	variable	ADJ
cana-587	64	6	u	u	NOUN
cana-587	64	7	∈	∈	PROPN
cana-587	64	8	ℝ𝑚	ℝ𝑚	SCONJ
cana-587	64	9	it	it	PRON
cana-587	64	10	follows	follow	VERB
cana-587	64	11	that	that	SCONJ
cana-587	64	12	the	the	DET
cana-587	64	13	constraint	constraint	NOUN
cana-587	64	14	of	of	ADP
cana-587	64	15	(	(	PUNCT
cana-587	64	16	4.2	4.2	NUM
cana-587	64	17	)	)	PUNCT
cana-587	64	18	becomes	become	VERB
cana-587	64	19	;	;	PUNCT
cana-587	64	20	u	u	X
cana-587	64	21	–	–	PUNCT
cana-587	64	22	(	(	PUNCT
cana-587	64	23	aty	aty	NOUN
cana-587	64	24	)	)	PUNCT
cana-587	64	25	=	=	SYM
cana-587	65	1	ct	ct	PROPN
cana-587	65	2	(	(	PUNCT
cana-587	65	3	4.3	4.3	NUM
cana-587	65	4	)	)	PUNCT
cana-587	65	5	we	we	PRON
cana-587	65	6	introduce	introduce	VERB
cana-587	65	7	the	the	DET
cana-587	65	8	primal	primal	ADJ
cana-587	65	9	surplus	surplus	NOUN
cana-587	65	10	variable	variable	NOUN
cana-587	65	11	v	v	ADP
cana-587	65	12	∈	∈	PROPN
cana-587	66	1	ℝ𝑛	ℝ𝑛	ADV
cana-587	66	2	then	then	ADV
cana-587	66	3	,	,	PUNCT
cana-587	66	4	the	the	DET
cana-587	66	5	constraint	constraint	NOUN
cana-587	66	6	of	of	ADP
cana-587	66	7	the	the	DET
cana-587	66	8	problem	problem	NOUN
cana-587	66	9	(	(	PUNCT
cana-587	66	10	4.1	4.1	NUM
cana-587	66	11	)	)	PUNCT
cana-587	66	12	now	now	ADV
cana-587	66	13	follows	follow	VERB
cana-587	66	14	;	;	PUNCT
cana-587	66	15	communications	communication	NOUN
cana-587	66	16	on	on	ADP
cana-587	66	17	applied	apply	VERB
cana-587	66	18	nonlinear	nonlinear	ADJ
cana-587	66	19	analysis	analysis	NOUN
cana-587	66	20	issn	issn	NOUN
cana-587	66	21	:	:	PUNCT
cana-587	66	22	1074	1074	NUM
cana-587	66	23	-	-	PUNCT
cana-587	66	24	133x	133x	NUM
cana-587	66	25	vol	vol	NOUN
cana-587	66	26	31	31	NUM
cana-587	66	27	no	no	NOUN
cana-587	66	28	.	.	PUNCT
cana-587	67	1	2s	2s	NUM
cana-587	67	2	(	(	PUNCT
cana-587	67	3	2024	2024	NUM
cana-587	67	4	)	)	PUNCT
cana-587	67	5	5	5	NUM
cana-587	67	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-587	67	7	v	v	NOUN
cana-587	67	8	aχ	aχ	NOUN
cana-587	67	9	=	=	SYM
cana-587	67	10	-b	-b	PUNCT
cana-587	67	11	(	(	PUNCT
cana-587	67	12	4.4	4.4	NUM
cana-587	67	13	)	)	PUNCT
cana-587	67	14	we	we	PRON
cana-587	67	15	then	then	ADV
cana-587	67	16	combine	combine	VERB
cana-587	67	17	the	the	DET
cana-587	67	18	constraints	constraint	NOUN
cana-587	67	19	of	of	ADP
cana-587	67	20	(	(	PUNCT
cana-587	67	21	4.3	4.3	NUM
cana-587	67	22	)	)	PUNCT
cana-587	67	23	and	and	CCONJ
cana-587	67	24	(	(	PUNCT
cana-587	67	25	4.4	4.4	NUM
cana-587	67	26	)	)	PUNCT
cana-587	67	27	in	in	ADP
cana-587	67	28	matrix	matrix	NOUN
cana-587	67	29	form	form	NOUN
cana-587	67	30	.	.	PUNCT
cana-587	68	1	(	(	PUNCT
cana-587	68	2	𝑢	𝑢	X
cana-587	68	3	.	.	PUNCT
cana-587	68	4	.	.	PUNCT
cana-587	69	1	𝑣	𝑣	X
cana-587	69	2	)	)	PUNCT
cana-587	69	3	(	(	PUNCT
cana-587	69	4	−𝐴𝑇y	−𝐴𝑇y	NOUN
cana-587	69	5	.	.	PUNCT
cana-587	69	6	.	.	PUNCT
cana-587	70	1	𝐴χ	𝐴χ	ADP
cana-587	70	2	)	)	PUNCT
cana-587	71	1	=	=	PUNCT
cana-587	71	2	(	(	PUNCT
cana-587	71	3	ct	ct	INTJ
cana-587	71	4	.	.	PUNCT
cana-587	71	5	.	.	PUNCT
cana-587	72	1	−𝑏	−𝑏	ADJ
cana-587	73	1	)	)	PUNCT
cana-587	73	2	⇒	⇒	PROPN
cana-587	73	3	(	(	PUNCT
cana-587	73	4	𝑢	𝑢	X
cana-587	73	5	.	.	PUNCT
cana-587	73	6	.	.	PUNCT
cana-587	74	1	𝑣	𝑣	X
cana-587	74	2	)	)	PUNCT
cana-587	74	3	(	(	PUNCT
cana-587	74	4	0𝑋	0𝑋	NOUN
cana-587	74	5	−	−	PROPN
cana-587	74	6	𝐴𝑇𝑌	𝐴𝑇𝑌	PROPN
cana-587	74	7	.	.	PUNCT
cana-587	74	8	.	.	PUNCT
cana-587	74	9	.	.	PUNCT
cana-587	75	1	𝐴𝑋	𝐴𝑋	PROPN
cana-587	75	2	−	−	PROPN
cana-587	75	3	0𝑌	0𝑌	NOUN
cana-587	75	4	)	)	PUNCT
cana-587	75	5	=	=	PUNCT
cana-587	76	1	(	(	PUNCT
cana-587	76	2	ct	ct	INTJ
cana-587	76	3	.	.	PUNCT
cana-587	76	4	.	.	PUNCT
cana-587	77	1	−𝑏	−𝑏	ADV
cana-587	77	2	)	)	PUNCT
cana-587	78	1	(	(	PUNCT
cana-587	78	2	𝑢	𝑢	X
cana-587	78	3	.	.	PUNCT
cana-587	78	4	.	.	PUNCT
cana-587	79	1	𝑣	𝑣	X
cana-587	79	2	)	)	PUNCT
cana-587	79	3	≥	≥	NOUN
cana-587	79	4	0	0	NUM
cana-587	79	5	,	,	PUNCT
cana-587	79	6	(	(	PUNCT
cana-587	79	7	𝑋	𝑋	NOUN
cana-587	79	8	.	.	PUNCT
cana-587	79	9	.	.	PUNCT
cana-587	80	1	𝑌	𝑌	PROPN
cana-587	80	2	)	)	PUNCT
cana-587	80	3	≥	≥	NOUN
cana-587	80	4	0	0	NUM
cana-587	81	1	and	and	CCONJ
cana-587	81	2	(	(	PUNCT
cana-587	81	3	𝑢	𝑢	X
cana-587	81	4	.	.	PUNCT
cana-587	81	5	.	.	PUNCT
cana-587	82	1	𝑣	𝑣	X
cana-587	82	2	)	)	PUNCT
cana-587	82	3	𝑇	𝑇	PROPN
cana-587	82	4	(	(	PUNCT
cana-587	82	5	𝑋	𝑋	PROPN
cana-587	82	6	.	.	PUNCT
cana-587	82	7	.	.	PUNCT
cana-587	83	1	𝑌	𝑌	PROPN
cana-587	83	2	)	)	PUNCT
cana-587	84	1	=	=	SYM
cana-587	84	2	0	0	NUM
cana-587	84	3	⇒	⇒	NOUN
cana-587	84	4	(	(	PUNCT
cana-587	84	5	𝑢	𝑢	X
cana-587	84	6	.	.	PUNCT
cana-587	84	7	.	.	PUNCT
cana-587	85	1	𝑣	𝑣	X
cana-587	85	2	)	)	PUNCT
cana-587	85	3	(	(	PUNCT
cana-587	85	4	0	0	NUM
cana-587	85	5	−	−	PROPN
cana-587	85	6	𝐴𝑇𝑌	𝐴𝑇𝑌	NOUN
cana-587	85	7	.	.	PUNCT
cana-587	85	8	.	.	PUNCT
cana-587	85	9	.	.	PUNCT
cana-587	86	1	𝐴𝑋	𝐴𝑋	PROPN
cana-587	86	2	−	−	NOUN
cana-587	86	3	0	0	NUM
cana-587	86	4	)	)	PUNCT
cana-587	87	1	=	=	PRON
cana-587	87	2	(	(	PUNCT
cana-587	87	3	ct	ct	INTJ
cana-587	87	4	.	.	PUNCT
cana-587	87	5	.	.	PUNCT
cana-587	88	1	−𝑏	−𝑏	ADV
cana-587	88	2	)	)	PUNCT
cana-587	89	1	(	(	PUNCT
cana-587	89	2	4.5	4.5	NUM
cana-587	89	3	)	)	PUNCT
cana-587	89	4	conversely	conversely	ADV
cana-587	89	5	,	,	PUNCT
cana-587	89	6	(	(	PUNCT
cana-587	89	7	𝑢	𝑢	X
cana-587	89	8	.	.	PUNCT
cana-587	89	9	.	.	PUNCT
cana-587	90	1	𝑣	𝑣	X
cana-587	90	2	)	)	PUNCT
cana-587	90	3	𝑇	𝑇	PROPN
cana-587	90	4	(	(	PUNCT
cana-587	90	5	𝑋	𝑋	PROPN
cana-587	90	6	.	.	PUNCT
cana-587	90	7	.	.	PUNCT
cana-587	91	1	𝑌	𝑌	PROPN
cana-587	91	2	)	)	PUNCT
cana-587	92	1	=	=	SYM
cana-587	92	2	0	0	PUNCT
cana-587	92	3	together	together	ADV
cana-587	92	4	satisfy	satisfy	VERB
cana-587	92	5	all	all	DET
cana-587	92	6	the	the	DET
cana-587	92	7	conditions	condition	NOUN
cana-587	92	8	of	of	ADP
cana-587	92	9	(	(	PUNCT
cana-587	92	10	4.5	4.5	NUM
cana-587	92	11	)	)	PUNCT
cana-587	92	12	.	.	PUNCT
cana-587	93	1	now	now	ADV
cana-587	93	2	considering	consider	VERB
cana-587	93	3	all	all	DET
cana-587	93	4	the	the	DET
cana-587	93	5	vectors	vector	NOUN
cana-587	93	6	and	and	CCONJ
cana-587	93	7	matrices	matrix	NOUN
cana-587	93	8	in	in	ADP
cana-587	93	9	(	(	PUNCT
cana-587	93	10	4.5	4.5	NUM
cana-587	93	11	)	)	PUNCT
cana-587	93	12	which	which	PRON
cana-587	93	13	are	be	AUX
cana-587	93	14	written	write	VERB
cana-587	93	15	in	in	ADP
cana-587	93	16	partitioned	partition	VERB
cana-587	93	17	form	form	NOUN
cana-587	93	18	as	as	SCONJ
cana-587	93	19	follows	follow	VERB
cana-587	93	20	:	:	PUNCT
cana-587	93	21	w	w	X
cana-587	93	22	=	=	SYM
cana-587	93	23	(	(	PUNCT
cana-587	93	24	𝑢	𝑢	X
cana-587	93	25	.	.	PUNCT
cana-587	93	26	.	.	PUNCT
cana-587	94	1	𝑣	𝑣	X
cana-587	94	2	)	)	PUNCT
cana-587	94	3	,	,	PUNCT
cana-587	94	4	z	z	NOUN
cana-587	94	5	=	=	PUNCT
cana-587	94	6	(	(	PUNCT
cana-587	94	7	𝑋	𝑋	PROPN
cana-587	94	8	.	.	PUNCT
cana-587	94	9	.	.	PUNCT
cana-587	95	1	𝑌	𝑌	PROPN
cana-587	95	2	)	)	PUNCT
cana-587	95	3	,	,	PUNCT
cana-587	95	4	m	m	VERB
cana-587	95	5	=	=	PUNCT
cana-587	95	6	(	(	PUNCT
cana-587	95	7	0	0	NUM
cana-587	95	8	−	−	NOUN
cana-587	95	9	𝐴𝑇	𝐴𝑇	PROPN
cana-587	95	10	.	.	PUNCT
cana-587	95	11	.	.	PUNCT
cana-587	95	12	.	.	PUNCT
cana-587	96	1	𝐴𝑋	𝐴𝑋	PROPN
cana-587	96	2	−	−	NOUN
cana-587	96	3	0	0	NUM
cana-587	96	4	)	)	PUNCT
cana-587	96	5	,	,	PUNCT
cana-587	96	6	q	q	NOUN
cana-587	97	1	=	=	PUNCT
cana-587	97	2	(	(	PUNCT
cana-587	97	3	𝐶𝑇	𝐶𝑇	PROPN
cana-587	97	4	.	.	PUNCT
cana-587	97	5	.	.	PUNCT
cana-587	98	1	−𝑏	−𝑏	ADV
cana-587	98	2	)	)	PUNCT
cana-587	99	1	(	(	PUNCT
cana-587	99	2	4.6	4.6	NUM
cana-587	99	3	)	)	PUNCT
cana-587	99	4	by	by	ADP
cana-587	99	5	solving	solve	VERB
cana-587	99	6	this	this	PRON
cana-587	99	7	,	,	PUNCT
cana-587	99	8	we	we	PRON
cana-587	99	9	obtain	obtain	VERB
cana-587	99	10	a	a	DET
cana-587	99	11	complementary	complementary	ADJ
cana-587	99	12	feasible	feasible	ADJ
cana-587	99	13	solution	solution	NOUN
cana-587	99	14	to	to	ADP
cana-587	99	15	the	the	DET
cana-587	99	16	lcp	lcp	NOUN
cana-587	99	17	.	.	PUNCT
cana-587	100	1	5	5	NUM
cana-587	100	2	.	.	X
cana-587	100	3	numerical	numerical	PROPN
cana-587	100	4	example	example	PROPN
cana-587	100	5	delta	delta	PROPN
cana-587	100	6	produces	produce	VERB
cana-587	100	7	both	both	CCONJ
cana-587	100	8	indian	indian	ADJ
cana-587	100	9	and	and	CCONJ
cana-587	100	10	western	western	ADJ
cana-587	100	11	toilets	toilet	NOUN
cana-587	100	12	from	from	ADP
cana-587	100	13	two	two	NUM
cana-587	100	14	raw	raw	ADJ
cana-587	100	15	materials	material	NOUN
cana-587	100	16	m1	m1	PROPN
cana-587	100	17	and	and	CCONJ
cana-587	100	18	m2	m2	PROPN
cana-587	101	1	.	.	PROPN
cana-587	101	2	communications	communication	NOUN
cana-587	101	3	on	on	ADP
cana-587	101	4	applied	apply	VERB
cana-587	101	5	nonlinear	nonlinear	ADJ
cana-587	101	6	analysis	analysis	NOUN
cana-587	101	7	issn	issn	NOUN
cana-587	101	8	:	:	PUNCT
cana-587	101	9	1074	1074	NUM
cana-587	101	10	-	-	PUNCT
cana-587	101	11	133x	133x	NUM
cana-587	101	12	vol	vol	NOUN
cana-587	101	13	31	31	NUM
cana-587	101	14	no	no	NOUN
cana-587	101	15	.	.	PUNCT
cana-587	102	1	2s	2s	NUM
cana-587	102	2	(	(	PUNCT
cana-587	102	3	2024	2024	NUM
cana-587	102	4	)	)	PUNCT
cana-587	102	5	6	6	NUM
cana-587	102	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-587	102	7	raw	raw	ADJ
cana-587	102	8	materials	material	NOUN
cana-587	102	9	per	per	ADP
cana-587	102	10	ton	ton	NOUN
cana-587	102	11	of	of	ADP
cana-587	102	12	availability(max	availability(max	ADJ
cana-587	102	13	/	/	SYM
cana-587	102	14	day	day	NOUN
cana-587	102	15	)	)	PUNCT
cana-587	102	16	indian	indian	ADJ
cana-587	102	17	toilets	toilet	NOUN
cana-587	102	18	western	western	ADJ
cana-587	102	19	toilets	toilet	NOUN
cana-587	102	20	(	(	PUNCT
cana-587	102	21	m1	m1	NOUN
cana-587	102	22	)	)	PUNCT
cana-587	102	23	3	3	NUM
cana-587	102	24	2	2	NUM
cana-587	102	25	6	6	NUM
cana-587	102	26	(	(	PUNCT
cana-587	102	27	m2	m2	PROPN
cana-587	102	28	)	)	PUNCT
cana-587	102	29	2	2	NUM
cana-587	102	30	1	1	NUM
cana-587	102	31	2	2	NUM
cana-587	102	32	procurement	procurement	NOUN
cana-587	102	33	cost	cost	NOUN
cana-587	102	34	per	per	ADP
cana-587	102	35	ton	ton	NOUN
cana-587	102	36	(	(	PUNCT
cana-587	102	37	$	$	SYM
cana-587	102	38	1000	1000	NUM
cana-587	102	39	)	)	PUNCT
cana-587	102	40	2	2	NUM
cana-587	102	41	5	5	NUM
cana-587	102	42	according	accord	VERB
cana-587	102	43	to	to	ADP
cana-587	102	44	a	a	DET
cana-587	102	45	market	market	NOUN
cana-587	102	46	survey	survey	NOUN
cana-587	102	47	,	,	PUNCT
cana-587	102	48	the	the	DET
cana-587	102	49	daily	daily	ADJ
cana-587	102	50	demand	demand	NOUN
cana-587	102	51	for	for	ADP
cana-587	102	52	western	western	ADJ
cana-587	102	53	toilets	toilet	NOUN
cana-587	102	54	can	can	AUX
cana-587	102	55	not	not	PART
cana-587	102	56	be	be	AUX
cana-587	102	57	more	more	ADJ
cana-587	102	58	than	than	ADP
cana-587	102	59	one	one	NUM
cana-587	102	60	ton	ton	NOUN
cana-587	102	61	higher	high	ADJ
cana-587	102	62	than	than	ADP
cana-587	102	63	that	that	PRON
cana-587	102	64	for	for	ADP
cana-587	102	65	indian	indian	ADJ
cana-587	102	66	toilets	toilet	NOUN
cana-587	102	67	.	.	PUNCT
cana-587	103	1	delta	delta	PROPN
cana-587	103	2	wants	want	VERB
cana-587	103	3	to	to	PART
cana-587	103	4	determine	determine	VERB
cana-587	103	5	the	the	DET
cana-587	103	6	optimal	optimal	ADJ
cana-587	103	7	(	(	PUNCT
cana-587	103	8	best	good	ADJ
cana-587	103	9	)	)	PUNCT
cana-587	103	10	product	product	NOUN
cana-587	103	11	mix	mix	NOUN
cana-587	103	12	of	of	ADP
cana-587	103	13	their	their	PRON
cana-587	103	14	products	product	NOUN
cana-587	103	15	that	that	PRON
cana-587	103	16	minimizes	minimize	VERB
cana-587	103	17	the	the	DET
cana-587	103	18	raw	raw	ADJ
cana-587	103	19	material	material	NOUN
cana-587	103	20	procurement	procurement	NOUN
cana-587	103	21	costs	cost	NOUN
cana-587	103	22	on	on	ADP
cana-587	103	23	a	a	DET
cana-587	103	24	daily	daily	ADJ
cana-587	103	25	basis	basis	NOUN
cana-587	103	26	.	.	PUNCT
cana-587	104	1	the	the	DET
cana-587	104	2	main	main	ADJ
cana-587	104	3	purpose	purpose	NOUN
cana-587	104	4	of	of	ADP
cana-587	104	5	the	the	DET
cana-587	104	6	present	present	ADJ
cana-587	104	7	research	research	NOUN
cana-587	104	8	work	work	NOUN
cana-587	104	9	was	be	AUX
cana-587	104	10	to	to	PART
cana-587	104	11	apply	apply	VERB
cana-587	104	12	a	a	DET
cana-587	104	13	set	set	NOUN
cana-587	104	14	of	of	ADP
cana-587	104	15	fuzzy	fuzzy	ADJ
cana-587	104	16	coefficients	coefficient	NOUN
cana-587	104	17	to	to	ADP
cana-587	104	18	raw	raw	ADJ
cana-587	104	19	material	material	NOUN
cana-587	104	20	components	component	NOUN
cana-587	104	21	to	to	PART
cana-587	104	22	reduce	reduce	VERB
cana-587	104	23	the	the	DET
cana-587	104	24	error	error	NOUN
cana-587	104	25	caused	cause	VERB
cana-587	104	26	by	by	ADP
cana-587	104	27	the	the	DET
cana-587	104	28	difficulty	difficulty	NOUN
cana-587	104	29	in	in	ADP
cana-587	104	30	accurately	accurately	ADV
cana-587	104	31	calculating	calculate	VERB
cana-587	104	32	each	each	PRON
cana-587	104	33	of	of	ADP
cana-587	104	34	the	the	DET
cana-587	104	35	components	component	NOUN
cana-587	104	36	.	.	PUNCT
cana-587	105	1	the	the	DET
cana-587	105	2	fuzzy	fuzzy	ADJ
cana-587	105	3	coefficients	coefficient	NOUN
cana-587	105	4	show	show	VERB
cana-587	105	5	the	the	DET
cana-587	105	6	uncertainty	uncertainty	NOUN
cana-587	105	7	and	and	CCONJ
cana-587	105	8	imprecision	imprecision	NOUN
cana-587	105	9	involved	involve	VERB
cana-587	105	10	in	in	ADP
cana-587	105	11	evaluating	evaluate	VERB
cana-587	105	12	every	every	DET
cana-587	105	13	component	component	NOUN
cana-587	105	14	while	while	SCONJ
cana-587	105	15	minimizing	minimize	VERB
cana-587	105	16	the	the	DET
cana-587	105	17	overall	overall	ADJ
cana-587	105	18	raw	raw	ADJ
cana-587	105	19	material	material	NOUN
cana-587	105	20	procurement	procurement	NOUN
cana-587	105	21	costs	cost	NOUN
cana-587	105	22	.	.	PUNCT
cana-587	106	1	let	let	VERB
cana-587	106	2	x1	x1	PRON
cana-587	106	3	be	be	AUX
cana-587	106	4	the	the	DET
cana-587	106	5	number	number	NOUN
cana-587	106	6	of	of	ADP
cana-587	106	7	units	unit	NOUN
cana-587	106	8	(	(	PUNCT
cana-587	106	9	tons	ton	NOUN
cana-587	106	10	)	)	PUNCT
cana-587	106	11	produced	produce	VERB
cana-587	106	12	daily	daily	ADV
cana-587	106	13	of	of	ADP
cana-587	106	14	indian	indian	ADJ
cana-587	106	15	toilets	toilet	NOUN
cana-587	106	16	.	.	PUNCT
cana-587	107	1	let	let	VERB
cana-587	107	2	x2	x2	PRON
cana-587	107	3	be	be	AUX
cana-587	107	4	the	the	DET
cana-587	107	5	number	number	NOUN
cana-587	107	6	of	of	ADP
cana-587	107	7	units	unit	NOUN
cana-587	107	8	(	(	PUNCT
cana-587	107	9	tons	ton	NOUN
cana-587	107	10	)	)	PUNCT
cana-587	107	11	produced	produce	VERB
cana-587	107	12	daily	daily	ADV
cana-587	107	13	of	of	ADP
cana-587	107	14	western	western	ADJ
cana-587	107	15	toilets	toilet	NOUN
cana-587	107	16	.	.	PUNCT
cana-587	108	1	let	let	VERB
cana-587	108	2	z	z	NOUN
cana-587	108	3	be	be	AUX
cana-587	108	4	the	the	DET
cana-587	108	5	daily	daily	ADJ
cana-587	108	6	total	total	ADJ
cana-587	108	7	procurement	procurement	NOUN
cana-587	108	8	cost	cost	NOUN
cana-587	108	9	,	,	PUNCT
cana-587	108	10	then	then	ADV
cana-587	108	11	min	min	PROPN
cana-587	108	12	z	z	PROPN
cana-587	108	13	=	=	SYM
cana-587	108	14	(	(	PUNCT
cana-587	108	15	1,2,3)χ1	1,2,3)χ1	NUM
cana-587	108	16	+	+	CCONJ
cana-587	108	17	(	(	PUNCT
cana-587	108	18	4,5,6)χ2	4,5,6)χ2	NUM
cana-587	108	19	subject	subject	NOUN
cana-587	108	20	to	to	ADP
cana-587	108	21	the	the	DET
cana-587	108	22	constraints	constraint	NOUN
cana-587	108	23	(	(	PUNCT
cana-587	108	24	2,3	2,3	NUM
cana-587	108	25	,	,	PUNCT
cana-587	108	26	4)χ1	4)χ1	NUM
cana-587	108	27	+	+	CCONJ
cana-587	108	28	(	(	PUNCT
cana-587	108	29	1,2,3)χ2	1,2,3)χ2	NUM
cana-587	108	30	≥	≥	NOUN
cana-587	108	31	(	(	PUNCT
cana-587	108	32	5,6,7	5,6,7	NOUN
cana-587	108	33	)	)	PUNCT
cana-587	108	34	(	(	PUNCT
cana-587	108	35	0,2,4)χ1	0,2,4)χ1	NUM
cana-587	109	1	+	+	CCONJ
cana-587	109	2	(	(	PUNCT
cana-587	109	3	0,1,2)χ2	0,1,2)χ2	NUM
cana-587	109	4	≥	≥	X
cana-587	109	5	(	(	PUNCT
cana-587	109	6	0,2,4	0,2,4	NOUN
cana-587	109	7	)	)	PUNCT
cana-587	109	8	χ1	χ1	NOUN
cana-587	109	9	,	,	PUNCT
cana-587	109	10	χ2	χ2	PROPN
cana-587	109	11	≥	≥	NUM
cana-587	109	12	0	0	NUM
cana-587	110	1	the	the	DET
cana-587	110	2	constraints	constraint	NOUN
cana-587	110	3	listed	list	VERB
cana-587	110	4	above	above	ADV
cana-587	110	5	could	could	AUX
cana-587	110	6	be	be	AUX
cana-587	110	7	written	write	VERB
cana-587	110	8	in	in	ADP
cana-587	110	9	a	a	DET
cana-587	110	10	matrix	matrix	NOUN
cana-587	110	11	form	form	NOUN
cana-587	110	12	.	.	PUNCT
cana-587	111	1	[	[	PUNCT
cana-587	111	2	(	(	PUNCT
cana-587	111	3	2,3,4	2,3,4	NOUN
cana-587	111	4	)	)	PUNCT
cana-587	111	5	(	(	PUNCT
cana-587	111	6	1,2,3	1,2,3	NOUN
cana-587	111	7	)	)	PUNCT
cana-587	111	8	(	(	PUNCT
cana-587	111	9	0,2,4	0,2,4	NOUN
cana-587	111	10	)	)	PUNCT
cana-587	111	11	(	(	PUNCT
cana-587	111	12	0,1,2	0,1,2	X
cana-587	111	13	)	)	PUNCT
cana-587	111	14	]	]	PUNCT
cana-587	112	1	[	[	PUNCT
cana-587	112	2	𝑥1	𝑥1	NOUN
cana-587	112	3	𝑥2	𝑥2	NOUN
cana-587	112	4	]	]	PUNCT
cana-587	112	5	≥	≥	X
cana-587	112	6	[	[	PUNCT
cana-587	112	7	(	(	PUNCT
cana-587	112	8	5,6,7	5,6,7	NOUN
cana-587	112	9	)	)	PUNCT
cana-587	112	10	(	(	PUNCT
cana-587	112	11	0,2,4	0,2,4	NOUN
cana-587	112	12	)	)	PUNCT
cana-587	112	13	]	]	PUNCT
cana-587	113	1	here	here	ADV
cana-587	113	2	,	,	PUNCT
cana-587	113	3	a	a	PRON
cana-587	113	4	=	=	X
cana-587	113	5	[	[	PUNCT
cana-587	113	6	(	(	PUNCT
cana-587	113	7	2,3,4	2,3,4	NUM
cana-587	113	8	)	)	PUNCT
cana-587	113	9	(	(	PUNCT
cana-587	113	10	1,2,3	1,2,3	NOUN
cana-587	113	11	)	)	PUNCT
cana-587	113	12	(	(	PUNCT
cana-587	113	13	0,2,4	0,2,4	NOUN
cana-587	113	14	)	)	PUNCT
cana-587	113	15	(	(	PUNCT
cana-587	113	16	0,1,2	0,1,2	X
cana-587	113	17	)	)	PUNCT
cana-587	113	18	]	]	PUNCT
cana-587	113	19	,	,	PUNCT
cana-587	113	20	b	b	X
cana-587	113	21	=	=	PRON
cana-587	113	22	[	[	PUNCT
cana-587	113	23	(	(	PUNCT
cana-587	113	24	5,6,7	5,6,7	NOUN
cana-587	113	25	)	)	PUNCT
cana-587	113	26	(	(	PUNCT
cana-587	113	27	0,2,4	0,2,4	NOUN
cana-587	113	28	)	)	PUNCT
cana-587	113	29	]	]	PUNCT
cana-587	114	1	-at	-at	PUNCT
cana-587	114	2	=	=	X
cana-587	114	3	[	[	PUNCT
cana-587	114	4	(	(	PUNCT
cana-587	114	5	−4,−3,−2	−4,−3,−2	NUM
cana-587	114	6	)	)	PUNCT
cana-587	114	7	(	(	PUNCT
cana-587	114	8	−4,−2,0	−4,−2,0	PROPN
cana-587	114	9	)	)	PUNCT
cana-587	114	10	(	(	PUNCT
cana-587	114	11	−3,−2,−1	−3,−2,−1	NOUN
cana-587	114	12	)	)	PUNCT
cana-587	114	13	(	(	PUNCT
cana-587	114	14	−3,−1,1	−3,−1,1	NOUN
cana-587	114	15	)	)	PUNCT
cana-587	114	16	]	]	PUNCT
cana-587	114	17	objective	objective	ADJ
cana-587	114	18	constraints	constraint	NOUN
cana-587	114	19	c	c	NOUN
cana-587	115	1	=	=	SYM
cana-587	116	1	[	[	X
cana-587	116	2	(	(	PUNCT
cana-587	116	3	1,2,3	1,2,3	NOUN
cana-587	116	4	)	)	PUNCT
cana-587	116	5	(	(	PUNCT
cana-587	116	6	4,5,6	4,5,6	NUM
cana-587	116	7	)	)	PUNCT
cana-587	116	8	]	]	PUNCT
cana-587	116	9	,	,	PUNCT
cana-587	116	10	ct	ct	NOUN
cana-587	116	11	=	=	PUNCT
cana-587	116	12	[	[	PUNCT
cana-587	116	13	(	(	PUNCT
cana-587	116	14	1,2,3	1,2,3	NOUN
cana-587	116	15	)	)	PUNCT
cana-587	116	16	(	(	PUNCT
cana-587	116	17	4,5,6	4,5,6	NUM
cana-587	116	18	)	)	PUNCT
cana-587	116	19	]	]	PUNCT
cana-587	116	20	now	now	ADV
cana-587	116	21	,	,	PUNCT
cana-587	116	22	letting	let	VERB
cana-587	116	23	m	m	VERB
cana-587	116	24	=	=	PUNCT
cana-587	117	1	[	[	X
cana-587	117	2	0	0	NUM
cana-587	117	3	−𝐴𝑇	−𝐴𝑇	ADJ
cana-587	117	4	𝐴	𝐴	NOUN
cana-587	117	5	0	0	NUM
cana-587	117	6	]	]	PUNCT
cana-587	117	7	,	,	PUNCT
cana-587	117	8	q	q	X
cana-587	117	9	=	=	PUNCT
cana-587	118	1	[	[	X
cana-587	118	2	𝐶	𝐶	PROPN
cana-587	118	3	𝑇	𝑇	PROPN
cana-587	118	4	−𝑏	−𝑏	X
cana-587	118	5	]	]	PUNCT
cana-587	119	1	communications	communication	NOUN
cana-587	119	2	on	on	ADP
cana-587	119	3	applied	apply	VERB
cana-587	119	4	nonlinear	nonlinear	ADJ
cana-587	119	5	analysis	analysis	NOUN
cana-587	119	6	issn	issn	NOUN
cana-587	119	7	:	:	PUNCT
cana-587	119	8	1074	1074	NUM
cana-587	119	9	-	-	PUNCT
cana-587	119	10	133x	133x	NUM
cana-587	119	11	vol	vol	NOUN
cana-587	119	12	31	31	NUM
cana-587	119	13	no	no	NOUN
cana-587	119	14	.	.	PUNCT
cana-587	120	1	2s	2s	NUM
cana-587	120	2	(	(	PUNCT
cana-587	120	3	2024	2024	NUM
cana-587	120	4	)	)	PUNCT
cana-587	120	5	7	7	NUM
cana-587	120	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-587	120	7	m	m	VERB
cana-587	120	8	=	=	X
cana-587	120	9	[	[	PUNCT
cana-587	120	10	(	(	PUNCT
cana-587	120	11	0,0,0	0,0,0	NOUN
cana-587	120	12	)	)	PUNCT
cana-587	120	13	(	(	PUNCT
cana-587	120	14	0,0,0	0,0,0	NOUN
cana-587	120	15	)	)	PUNCT
cana-587	120	16	(	(	PUNCT
cana-587	120	17	−4,−3,−2	−4,−3,−2	NUM
cana-587	120	18	)	)	PUNCT
cana-587	120	19	(	(	PUNCT
cana-587	120	20	−4,−2,0	−4,−2,0	PROPN
cana-587	120	21	)	)	PUNCT
cana-587	120	22	(	(	PUNCT
cana-587	120	23	0,0,0	0,0,0	NOUN
cana-587	120	24	)	)	PUNCT
cana-587	120	25	(	(	PUNCT
cana-587	120	26	0,0,0	0,0,0	NOUN
cana-587	120	27	)	)	PUNCT
cana-587	120	28	(	(	PUNCT
cana-587	120	29	−3,−2,−1	−3,−2,−1	NOUN
cana-587	120	30	)	)	PUNCT
cana-587	120	31	(	(	PUNCT
cana-587	120	32	−3,−1,1	−3,−1,1	NOUN
cana-587	120	33	)	)	PUNCT
cana-587	120	34	(	(	PUNCT
cana-587	120	35	2,3,4	2,3,4	NUM
cana-587	120	36	)	)	PUNCT
cana-587	120	37	(	(	PUNCT
cana-587	120	38	1,2,3	1,2,3	NOUN
cana-587	120	39	)	)	PUNCT
cana-587	120	40	(	(	PUNCT
cana-587	120	41	0,0,0	0,0,0	NOUN
cana-587	120	42	)	)	PUNCT
cana-587	120	43	(	(	PUNCT
cana-587	120	44	0,0,0	0,0,0	NOUN
cana-587	120	45	)	)	PUNCT
cana-587	120	46	(	(	PUNCT
cana-587	120	47	0,2,4	0,2,4	NOUN
cana-587	120	48	)	)	PUNCT
cana-587	120	49	(	(	PUNCT
cana-587	120	50	0,1,2	0,1,2	X
cana-587	120	51	)	)	PUNCT
cana-587	120	52	(	(	PUNCT
cana-587	120	53	0,0,0	0,0,0	NOUN
cana-587	120	54	)	)	PUNCT
cana-587	120	55	(	(	PUNCT
cana-587	120	56	0,0,0	0,0,0	NOUN
cana-587	120	57	)	)	PUNCT
cana-587	120	58	]	]	PUNCT
cana-587	120	59	,	,	PUNCT
cana-587	120	60	q	q	X
cana-587	120	61	=	=	PUNCT
cana-587	120	62	[	[	PUNCT
cana-587	120	63	(	(	PUNCT
cana-587	120	64	1,2,3	1,2,3	NOUN
cana-587	120	65	)	)	PUNCT
cana-587	120	66	(	(	PUNCT
cana-587	120	67	4,5,6	4,5,6	NUM
cana-587	120	68	)	)	PUNCT
cana-587	120	69	(	(	PUNCT
cana-587	120	70	−7,−6,−5	−7,−6,−5	NUM
cana-587	120	71	)	)	PUNCT
cana-587	120	72	(	(	PUNCT
cana-587	120	73	−4,−2,0	−4,−2,0	PROPN
cana-587	120	74	)	)	PUNCT
cana-587	120	75	]	]	PUNCT
cana-587	121	1	therefore	therefore	ADV
cana-587	121	2	x1	x1	X
cana-587	121	3	=	=	SYM
cana-587	121	4	z1	z1	PROPN
cana-587	121	5	and	and	CCONJ
cana-587	121	6	x2	x2	NOUN
cana-587	121	7	=	=	SYM
cana-587	121	8	z2	z2	PROPN
cana-587	121	9	will	will	AUX
cana-587	121	10	be	be	AUX
cana-587	121	11	an	an	DET
cana-587	121	12	optimal	optimal	ADJ
cana-587	121	13	solution	solution	NOUN
cana-587	121	14	to	to	ADP
cana-587	121	15	the	the	DET
cana-587	121	16	given	give	VERB
cana-587	121	17	lpp	lpp	PROPN
cana-587	121	18	.	.	PUNCT
cana-587	122	1	w	w	PROPN
cana-587	122	2	mz	mz	PROPN
cana-587	122	3	=	=	SYM
cana-587	122	4	q	q	PROPN
cana-587	122	5	,	,	PUNCT
cana-587	122	6	gives	give	VERB
cana-587	122	7	[	[	PUNCT
cana-587	122	8	𝑤1	𝑤1	VERB
cana-587	122	9	𝑤2	𝑤2	NOUN
cana-587	122	10	𝑤3	𝑤3	NOUN
cana-587	122	11	𝑤4	𝑤4	NOUN
cana-587	122	12	]	]	PUNCT
cana-587	122	13	[	[	PUNCT
cana-587	122	14	(	(	PUNCT
cana-587	122	15	0,0,0	0,0,0	NOUN
cana-587	122	16	)	)	PUNCT
cana-587	122	17	(	(	PUNCT
cana-587	122	18	0,0,0	0,0,0	NOUN
cana-587	122	19	)	)	PUNCT
cana-587	122	20	(	(	PUNCT
cana-587	122	21	−4,−3,−2	−4,−3,−2	NUM
cana-587	122	22	)	)	PUNCT
cana-587	122	23	(	(	PUNCT
cana-587	122	24	−4,−2,0	−4,−2,0	PROPN
cana-587	122	25	)	)	PUNCT
cana-587	122	26	(	(	PUNCT
cana-587	122	27	0,0,0	0,0,0	NOUN
cana-587	122	28	)	)	PUNCT
cana-587	122	29	(	(	PUNCT
cana-587	122	30	0,0,0	0,0,0	NOUN
cana-587	122	31	)	)	PUNCT
cana-587	122	32	(	(	PUNCT
cana-587	122	33	−3,−2,−1	−3,−2,−1	NOUN
cana-587	122	34	)	)	PUNCT
cana-587	122	35	(	(	PUNCT
cana-587	122	36	−3,−1,1	−3,−1,1	NOUN
cana-587	122	37	)	)	PUNCT
cana-587	122	38	(	(	PUNCT
cana-587	122	39	2,3,4	2,3,4	NUM
cana-587	122	40	)	)	PUNCT
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cana-587	122	42	1,2,3	1,2,3	NOUN
cana-587	122	43	)	)	PUNCT
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cana-587	122	58	)	)	PUNCT
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cana-587	122	62	]	]	PUNCT
cana-587	123	1	[	[	PUNCT
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cana-587	123	3	𝑧2	𝑧2	PROPN
cana-587	123	4	𝑧3	𝑧3	PROPN
cana-587	123	5	𝑧4	𝑧4	PROPN
cana-587	123	6	]	]	PUNCT
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cana-587	124	10	linear	linear	PROPN
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cana-587	124	13	,	,	PUNCT
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cana-587	125	91	)	)	PUNCT
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cana-587	125	231	)	)	PUNCT
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cana-587	125	241	)	)	PUNCT
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cana-587	125	275	)	)	PUNCT
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cana-587	125	281	)	)	PUNCT
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cana-587	125	291	w4	w4	NOUN
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cana-587	125	294	)	)	PUNCT
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cana-587	125	297	)	)	PUNCT
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cana-587	125	309	)	)	PUNCT
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cana-587	125	335	(	(	PUNCT
cana-587	125	336	0,0.7,0	0,0.7,0	NOUN
cana-587	125	337	)	)	PUNCT
cana-587	125	338	(	(	PUNCT
cana-587	125	339	0,0,0	0,0,0	NOUN
cana-587	125	340	)	)	PUNCT
cana-587	125	341	(	(	PUNCT
cana-587	125	342	0,0,0	0,0,0	NOUN
cana-587	125	343	)	)	PUNCT
cana-587	125	344	(	(	PUNCT
cana-587	125	345	0.8,2,2.5	0.8,2,2.5	NUM
cana-587	125	346	)	)	PUNCT
cana-587	125	347	(	(	PUNCT
cana-587	125	348	table	table	NOUN
cana-587	125	349	5.1	5.1	NUM
cana-587	125	350	)	)	PUNCT
cana-587	125	351	the	the	DET
cana-587	125	352	optimal	optimal	ADJ
cana-587	125	353	solution	solution	NOUN
cana-587	125	354	of	of	ADP
cana-587	125	355	the	the	DET
cana-587	125	356	flcp	flcp	NOUN
cana-587	125	357	in	in	ADP
cana-587	125	358	(	(	PUNCT
cana-587	125	359	table	table	NOUN
cana-587	125	360	5.1	5.1	NUM
cana-587	125	361	)	)	PUNCT
cana-587	125	362	(	(	PUNCT
cana-587	125	363	w1	w1	NOUN
cana-587	125	364	,	,	PUNCT
cana-587	125	365	w2	w2	NOUN
cana-587	125	366	,	,	PUNCT
cana-587	125	367	w3	w3	PROPN
cana-587	125	368	,	,	PUNCT
cana-587	125	369	w4	w4	NOUN
cana-587	125	370	:	:	PUNCT
cana-587	125	371	z1	z1	PROPN
cana-587	125	372	,	,	PUNCT
cana-587	125	373	z2	z2	PROPN
cana-587	125	374	,	,	PUNCT
cana-587	125	375	z3	z3	PROPN
cana-587	125	376	,	,	PUNCT
cana-587	125	377	z4	z4	PROPN
cana-587	125	378	)	)	PUNCT
cana-587	125	379	=	=	SYM
cana-587	125	380	(	(	PUNCT
cana-587	125	381	(	(	PUNCT
cana-587	125	382	1,2,3),(4,5,6	1,2,3),(4,5,6	NUM
cana-587	125	383	)	)	PUNCT
cana-587	125	384	,	,	PUNCT
cana-587	125	385	(	(	PUNCT
cana-587	125	386	-0.7,2,2.5),(0,0,0	-0.7,2,2.5),(0,0,0	NOUN
cana-587	125	387	)	)	PUNCT
cana-587	125	388	:	:	PUNCT
cana-587	125	389	(	(	PUNCT
cana-587	125	390	0.8,2,2.5),(0,0,0),(0,0,0),(0,0,0	0.8,2,2.5),(0,0,0),(0,0,0),(0,0,0	NUM
cana-587	125	391	)	)	PUNCT
cana-587	125	392	)	)	PUNCT
cana-587	125	393	.	.	PUNCT
cana-587	126	1	conclusion	conclusion	NOUN
cana-587	126	2	this	this	DET
cana-587	126	3	study	study	NOUN
cana-587	126	4	proposes	propose	VERB
cana-587	126	5	a	a	DET
cana-587	126	6	maximum	maximum	ADJ
cana-587	126	7	index	index	NOUN
cana-587	126	8	method	method	NOUN
cana-587	126	9	for	for	ADP
cana-587	126	10	addressing	address	VERB
cana-587	126	11	an	an	DET
cana-587	126	12	lcp	lcp	NOUN
cana-587	126	13	using	use	VERB
cana-587	126	14	fuzzy	fuzzy	ADJ
cana-587	126	15	parameters	parameter	NOUN
cana-587	126	16	.	.	PUNCT
cana-587	127	1	by	by	ADP
cana-587	127	2	using	use	VERB
cana-587	127	3	this	this	DET
cana-587	127	4	method	method	NOUN
cana-587	127	5	,	,	PUNCT
cana-587	127	6	the	the	DET
cana-587	127	7	outcome	outcome	NOUN
cana-587	127	8	is	be	AUX
cana-587	127	9	unmistakable	unmistakable	ADJ
cana-587	127	10	,	,	PUNCT
cana-587	127	11	the	the	DET
cana-587	127	12	computation	computation	NOUN
cana-587	127	13	is	be	AUX
cana-587	127	14	easy	easy	ADJ
cana-587	127	15	and	and	CCONJ
cana-587	127	16	fast	fast	ADJ
cana-587	127	17	.	.	PUNCT
cana-587	128	1	at	at	ADP
cana-587	128	2	the	the	DET
cana-587	128	3	same	same	ADJ
cana-587	128	4	time	time	NOUN
cana-587	128	5	,	,	PUNCT
cana-587	128	6	it	it	PRON
cana-587	128	7	obtains	obtain	VERB
cana-587	128	8	the	the	DET
cana-587	128	9	same	same	ADJ
cana-587	128	10	result	result	NOUN
cana-587	128	11	.	.	PUNCT
cana-587	129	1	despite	despite	SCONJ
cana-587	129	2	the	the	DET
cana-587	129	3	fact	fact	NOUN
cana-587	129	4	that	that	SCONJ
cana-587	129	5	we	we	PRON
cana-587	129	6	are	be	AUX
cana-587	129	7	focusing	focus	VERB
cana-587	129	8	on	on	ADP
cana-587	129	9	linear	linear	ADJ
cana-587	129	10	programming	programming	NOUN
cana-587	129	11	,	,	PUNCT
cana-587	129	12	this	this	PRON
cana-587	129	13	can	can	AUX
cana-587	129	14	be	be	AUX
cana-587	129	15	easily	easily	ADV
cana-587	129	16	communications	communication	NOUN
cana-587	129	17	on	on	ADP
cana-587	129	18	applied	apply	VERB
cana-587	129	19	nonlinear	nonlinear	ADJ
cana-587	129	20	analysis	analysis	NOUN
cana-587	129	21	issn	issn	NOUN
cana-587	129	22	:	:	PUNCT
cana-587	129	23	1074	1074	NUM
cana-587	129	24	-	-	PUNCT
cana-587	129	25	133x	133x	NUM
cana-587	129	26	vol	vol	NOUN
cana-587	129	27	31	31	NUM
cana-587	129	28	no	no	NOUN
cana-587	129	29	.	.	PUNCT
cana-587	130	1	2s	2s	NUM
cana-587	130	2	(	(	PUNCT
cana-587	130	3	2024	2024	NUM
cana-587	130	4	)	)	PUNCT
cana-587	130	5	8	8	NUM
cana-587	130	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-587	130	7	adaptable	adaptable	ADJ
cana-587	130	8	to	to	ADP
cana-587	130	9	non	non	ADJ
cana-587	130	10	-	-	ADJ
cana-587	130	11	linear	linear	ADJ
cana-587	130	12	and	and	CCONJ
cana-587	130	13	multi	multi	ADJ
cana-587	130	14	-	-	ADJ
cana-587	130	15	objective	objective	ADJ
cana-587	130	16	programming	programming	NOUN
cana-587	130	17	by	by	ADP
cana-587	130	18	incorporating	incorporate	VERB
cana-587	130	19	fuzzy	fuzzy	ADJ
cana-587	130	20	coefficients	coefficient	NOUN
cana-587	130	21	and	and	CCONJ
cana-587	130	22	interval	interval	NOUN
cana-587	130	23	numbers	number	NOUN
cana-587	130	24	.	.	PUNCT
cana-587	131	1	references	reference	NOUN
cana-587	131	2	[	[	X
cana-587	131	3	1	1	NUM
cana-587	131	4	]	]	X
cana-587	131	5	bellman	bellman	NOUN
cana-587	131	6	,	,	PUNCT
cana-587	131	7	r.e	r.e	PROPN
cana-587	131	8	.	.	PROPN
cana-587	131	9	,	,	PUNCT
cana-587	131	10	zadeh	zadeh	PROPN
cana-587	131	11	,	,	PUNCT
cana-587	131	12	l.a	l.a	PROPN
cana-587	131	13	.	.	PROPN
cana-587	131	14	,	,	PUNCT
cana-587	131	15	decision	decision	NOUN
cana-587	131	16	making	making	NOUN
cana-587	131	17	in	in	ADP
cana-587	131	18	a	a	DET
cana-587	131	19	fuzzy	fuzzy	ADJ
cana-587	131	20	environment	environment	NOUN
cana-587	131	21	,	,	PUNCT
cana-587	131	22	management	management	NOUN
cana-587	131	23	science	science	NOUN
cana-587	131	24	17(1970	17(1970	PRON
cana-587	131	25	)	)	PUNCT
cana-587	131	26	141	141	NUM
cana-587	131	27	-	-	SYM
cana-587	131	28	164	164	NUM
cana-587	131	29	.	.	PUNCT
cana-587	132	1	[	[	X
cana-587	132	2	2	2	NUM
cana-587	132	3	]	]	PUNCT
cana-587	132	4	bazaraa	bazaraa	NOUN
cana-587	132	5	,	,	PUNCT
cana-587	132	6	m.s	m.s	PROPN
cana-587	132	7	.	.	PROPN
cana-587	132	8	,	,	PUNCT
cana-587	132	9	sherali	sherali	PROPN
cana-587	132	10	,	,	PUNCT
cana-587	132	11	h.d	h.d	PROPN
cana-587	132	12	,	,	PUNCT
cana-587	132	13	and	and	CCONJ
cana-587	132	14	shetty	shetty	PROPN
cana-587	132	15	.	.	PUNCT
cana-587	133	1	c.m	c.m	PROPN
cana-587	133	2	.	.	PROPN
cana-587	133	3	,	,	PUNCT
cana-587	133	4	(	(	PUNCT
cana-587	133	5	1979	1979	NUM
cana-587	133	6	)	)	PUNCT
cana-587	133	7	nonlinear	nonlinear	ADJ
cana-587	133	8	programming	programming	NOUN
cana-587	133	9	:	:	PUNCT
cana-587	133	10	theory	theory	NOUN
cana-587	133	11	and	and	CCONJ
cana-587	133	12	algorithms	algorithm	NOUN
cana-587	133	13	,	,	PUNCT
cana-587	133	14	john	john	PROPN
cana-587	133	15	wiley	wiley	PROPN
cana-587	133	16	and	and	CCONJ
cana-587	133	17	sons	son	NOUN
cana-587	133	18	,	,	PUNCT
cana-587	133	19	newyork	newyork	NOUN
cana-587	133	20	.	.	PUNCT
cana-587	134	1	[	[	X
cana-587	134	2	3	3	NUM
cana-587	134	3	]	]	X
cana-587	134	4	chen	chen	PROPN
cana-587	134	5	,	,	PUNCT
cana-587	134	6	s.h	s.h	PROPN
cana-587	134	7	.	.	PROPN
cana-587	134	8	,	,	PUNCT
cana-587	134	9	hsieh	hsieh	PROPN
cana-587	134	10	,	,	PUNCT
cana-587	134	11	c.h	c.h	PROPN
cana-587	134	12	.	.	PROPN
cana-587	134	13	,	,	PUNCT
cana-587	134	14	(	(	PUNCT
cana-587	134	15	1999	1999	NUM
cana-587	134	16	)	)	PUNCT
cana-587	134	17	graded	grade	VERB
cana-587	134	18	mean	mean	NOUN
cana-587	134	19	integration	integration	NOUN
cana-587	134	20	representation	representation	NOUN
cana-587	134	21	of	of	ADP
cana-587	134	22	generalized	generalized	ADJ
cana-587	134	23	fuzzy	fuzzy	ADJ
cana-587	134	24	number	number	NOUN
cana-587	134	25	,	,	PUNCT
cana-587	134	26	journal	journal	NOUN
cana-587	134	27	of	of	ADP
cana-587	134	28	chinese	chinese	ADJ
cana-587	134	29	fuzzy	fuzzy	ADJ
cana-587	134	30	systems	system	NOUN
cana-587	134	31	5(2	5(2	NUM
cana-587	134	32	)	)	PUNCT
cana-587	134	33	,	,	PUNCT
cana-587	134	34	1	1	NUM
cana-587	134	35	-	-	SYM
cana-587	134	36	7	7	NUM
cana-587	134	37	.	.	PUNCT
cana-587	135	1	[	[	X
cana-587	135	2	4	4	NUM
cana-587	135	3	]	]	X
cana-587	135	4	cottle	cottle	NOUN
cana-587	135	5	,	,	PUNCT
cana-587	135	6	r.w	r.w	PROPN
cana-587	135	7	.	.	PROPN
cana-587	135	8	,	,	PUNCT
cana-587	135	9	dantzig	dantzig	PROPN
cana-587	135	10	,	,	PUNCT
cana-587	135	11	g.b	g.b	PROPN
cana-587	135	12	.	.	PROPN
cana-587	135	13	,	,	PUNCT
cana-587	135	14	(	(	PUNCT
cana-587	135	15	1968	1968	NUM
cana-587	135	16	)	)	PUNCT
cana-587	135	17	complementarity	complementarity	NOUN
cana-587	135	18	pivot	pivot	NOUN
cana-587	135	19	theory	theory	NOUN
cana-587	135	20	of	of	ADP
cana-587	135	21	mathematical	mathematical	ADJ
cana-587	135	22	programming	programming	NOUN
cana-587	135	23	,	,	PUNCT
cana-587	135	24	linear	linear	ADJ
cana-587	135	25	algebra	algebra	NOUN
cana-587	135	26	and	and	CCONJ
cana-587	135	27	its	its	PRON
cana-587	135	28	applications	application	NOUN
cana-587	135	29	1	1	NUM
cana-587	135	30	,	,	PUNCT
cana-587	135	31	103	103	NUM
cana-587	135	32	-	-	SYM
cana-587	135	33	125	125	NUM
cana-587	135	34	.	.	PUNCT
cana-587	136	1	[	[	X
cana-587	136	2	5	5	NUM
cana-587	136	3	]	]	X
cana-587	136	4	de	de	X
cana-587	136	5	schutter.b	schutter.b	NOUN
cana-587	136	6	,	,	PUNCT
cana-587	136	7	heemels	heemel	NOUN
cana-587	136	8	.	.	PUNCT
cana-587	137	1	w.p.m.h	w.p.m.h	PROPN
cana-587	137	2	,	,	PUNCT
cana-587	137	3	bemporad	bemporad	PROPN
cana-587	137	4	,	,	PUNCT
cana-587	137	5	a.	a.	NOUN
cana-587	137	6	,	,	PUNCT
cana-587	137	7	(	(	PUNCT
cana-587	137	8	2002	2002	NUM
cana-587	137	9	)	)	PUNCT
cana-587	137	10	on	on	ADP
cana-587	137	11	the	the	DET
cana-587	137	12	equivalence	equivalence	NOUN
cana-587	137	13	of	of	ADP
cana-587	137	14	linear	linear	ADJ
cana-587	137	15	complementarity	complementarity	NOUN
cana-587	137	16	problems	problem	NOUN
cana-587	137	17	,	,	PUNCT
cana-587	137	18	operations	operation	NOUN
cana-587	137	19	research	research	NOUN
cana-587	137	20	letters	letter	NOUN
cana-587	137	21	,	,	PUNCT
cana-587	137	22	elsevier	elsevier	NOUN
cana-587	137	23	,	,	PUNCT
cana-587	137	24	30	30	NUM
cana-587	137	25	,	,	PUNCT
cana-587	137	26	211	211	NUM
cana-587	137	27	-	-	SYM
cana-587	137	28	222	222	NUM
cana-587	137	29	.	.	PUNCT
cana-587	138	1	[	[	X
cana-587	138	2	6	6	NUM
cana-587	138	3	]	]	X
cana-587	138	4	dubois	dubois	PROPN
cana-587	138	5	,	,	PUNCT
cana-587	138	6	d.	d.	PROPN
cana-587	138	7	,	,	PUNCT
cana-587	138	8	and	and	CCONJ
cana-587	138	9	prade	prade	NOUN
cana-587	138	10	,	,	PUNCT
cana-587	138	11	h.	h.	PROPN
cana-587	138	12	,	,	PUNCT
cana-587	138	13	(	(	PUNCT
cana-587	138	14	1978	1978	NUM
cana-587	138	15	)	)	PUNCT
cana-587	138	16	operation	operation	NOUN
cana-587	138	17	of	of	ADP
cana-587	138	18	fuzzy	fuzzy	ADJ
cana-587	138	19	numbers	number	NOUN
cana-587	138	20	,	,	PUNCT
cana-587	138	21	internat	internat	NOUN
cana-587	138	22	.	.	PUNCT
cana-587	139	1	j.systems	j.systems	PROPN
cana-587	139	2	sci	sci	PROPN
cana-587	139	3	.	.	PROPN
cana-587	139	4	9(6	9(6	NUM
cana-587	139	5	)	)	PUNCT
cana-587	139	6	,	,	PUNCT
cana-587	139	7	613	613	NUM
cana-587	139	8	-	-	SYM
cana-587	139	9	626	626	NUM
cana-587	139	10	.	.	PUNCT
cana-587	140	1	[	[	X
cana-587	140	2	7	7	NUM
cana-587	140	3	]	]	X
cana-587	140	4	hamdy	hamdy	NOUN
cana-587	140	5	.	.	PUNCT
cana-587	140	6	a.	a.	PROPN
cana-587	140	7	taha	taha	PROPN
cana-587	140	8	,	,	PUNCT
cana-587	140	9	(	(	PUNCT
cana-587	140	10	2006	2006	NUM
cana-587	140	11	)	)	PUNCT
cana-587	140	12	operations	operation	NOUN
cana-587	140	13	research	research	NOUN
cana-587	140	14	:	:	PUNCT
cana-587	140	15	an	an	DET
cana-587	140	16	introduction	introduction	NOUN
cana-587	140	17	,	,	PUNCT
cana-587	140	18	eighth	eighth	ADJ
cana-587	140	19	edition	edition	NOUN
cana-587	140	20	,	,	PUNCT
cana-587	140	21	prentice	prentice	NOUN
cana-587	140	22	–	–	PUNCT
cana-587	140	23	hall	hall	NOUN
cana-587	140	24	of	of	ADP
cana-587	140	25	india	india	PROPN
cana-587	140	26	private	private	PROPN
cana-587	140	27	ltd	ltd	PROPN
cana-587	140	28	,	,	PUNCT
cana-587	140	29	delhi	delhi	PROPN
cana-587	140	30	.	.	PUNCT
cana-587	141	1	[	[	X
cana-587	141	2	8	8	NUM
cana-587	141	3	]	]	PUNCT
cana-587	141	4	irene	irene	NOUN
cana-587	141	5	hepzibah.r	hepzibah.r	PROPN
cana-587	141	6	.	.	PUNCT
cana-587	142	1	,	,	PUNCT
cana-587	142	2	(	(	PUNCT
cana-587	142	3	2021	2021	NUM
cana-587	142	4	)	)	PUNCT
cana-587	142	5	an	an	DET
cana-587	142	6	algorithmic	algorithmic	ADJ
cana-587	142	7	approach	approach	NOUN
cana-587	142	8	to	to	ADP
cana-587	142	9	fuzzy	fuzzy	ADJ
cana-587	142	10	linear	linear	ADJ
cana-587	142	11	complementarity	complementarity	NOUN
cana-587	142	12	problems	problem	NOUN
cana-587	142	13	,	,	PUNCT
cana-587	142	14	lambert	lambert	PROPN
cana-587	142	15	academic	academic	ADJ
cana-587	142	16	publishing	publishing	NOUN
cana-587	142	17	,	,	PUNCT
cana-587	142	18	germany	germany	PROPN
cana-587	142	19	.	.	PUNCT
cana-587	143	1	[	[	X
cana-587	143	2	9	9	NUM
cana-587	143	3	]	]	SYM
cana-587	143	4	jenifer	jenifer	NOUN
cana-587	143	5	.	.	PUNCT
cana-587	144	1	d.h	d.h	PROPN
cana-587	144	2	,	,	PUNCT
cana-587	144	3	irene	irene	PROPN
cana-587	144	4	hebzibah	hebzibah	PROPN
cana-587	144	5	.	.	PUNCT
cana-587	145	1	r	r	NOUN
cana-587	145	2	,	,	PUNCT
cana-587	145	3	(	(	PUNCT
cana-587	145	4	2023	2023	NUM
cana-587	145	5	)	)	PUNCT
cana-587	145	6	on	on	ADP
cana-587	145	7	solving	solve	VERB
cana-587	145	8	fuzzy	fuzzy	ADJ
cana-587	145	9	linear	linear	ADJ
cana-587	145	10	complementarity	complementarity	NOUN
cana-587	145	11	problem	problem	NOUN
cana-587	145	12	via	via	ADP
cana-587	145	13	maximum	maximum	ADJ
cana-587	145	14	index	index	NOUN
cana-587	145	15	method	method	NOUN
cana-587	145	16	,	,	PUNCT
cana-587	145	17	referred	refer	VERB
cana-587	145	18	proceedings	proceeding	NOUN
cana-587	145	19	of	of	ADP
cana-587	145	20	2nd	2nd	ADJ
cana-587	145	21	international	international	ADJ
cana-587	145	22	conference	conference	NOUN
cana-587	145	23	on	on	ADP
cana-587	145	24	emerging	emerge	VERB
cana-587	145	25	trends	trend	NOUN
cana-587	145	26	in	in	ADP
cana-587	145	27	science	science	NOUN
cana-587	145	28	and	and	CCONJ
cana-587	145	29	social	social	ADJ
cana-587	145	30	science	science	NOUN
cana-587	145	31	in	in	ADP
cana-587	145	32	pattaya	pattaya	PROPN
cana-587	145	33	,	,	PUNCT
cana-587	145	34	thailand	thailand	PROPN
cana-587	145	35	.	.	PUNCT
cana-587	146	1	[	[	X
cana-587	146	2	10	10	NUM
cana-587	146	3	]	]	X
cana-587	146	4	komei	komei	PROPN
cana-587	146	5	fukuda	fukuda	PROPN
cana-587	146	6	,	,	PUNCT
cana-587	146	7	makoto	makoto	PROPN
cana-587	146	8	namiki	namiki	PROPN
cana-587	146	9	.	.	PUNCT
cana-587	146	10	,	,	PUNCT
cana-587	146	11	(	(	PUNCT
cana-587	146	12	1994	1994	NUM
cana-587	146	13	)	)	PUNCT
cana-587	146	14	on	on	ADP
cana-587	146	15	extremal	extremal	ADJ
cana-587	146	16	behaviours	behaviour	NOUN
cana-587	146	17	of	of	ADP
cana-587	146	18	murty	murty	NOUN
cana-587	146	19	’s	’s	PART
cana-587	146	20	least	least	ADJ
cana-587	146	21	index	index	NOUN
cana-587	146	22	method	method	NOUN
cana-587	146	23	,	,	PUNCT
cana-587	146	24	mathematical	mathematical	ADJ
cana-587	146	25	programming	programming	NOUN
cana-587	146	26	,	,	PUNCT
cana-587	146	27	64	64	NUM
cana-587	146	28	,	,	PUNCT
cana-587	146	29	365	365	NUM
cana-587	146	30	–	–	PUNCT
cana-587	146	31	370	370	NUM
cana-587	146	32	.	.	PUNCT
cana-587	147	1	[	[	X
cana-587	147	2	11	11	NUM
cana-587	147	3	]	]	X
cana-587	147	4	laisin	laisin	PROPN
cana-587	147	5	,	,	PUNCT
cana-587	147	6	m.	m.	NOUN
cana-587	147	7	,	,	PUNCT
cana-587	147	8	okeke	okeke	ADJ
cana-587	147	9	,	,	PUNCT
cana-587	147	10	j.e	j.e	PROPN
cana-587	147	11	.	.	PROPN
cana-587	147	12	,	,	PUNCT
cana-587	147	13	(	(	PUNCT
cana-587	147	14	2017)“linear	2017)“linear	NUM
cana-587	147	15	complementarity	complementarity	NOUN
cana-587	147	16	problems	problem	NOUN
cana-587	147	17	applications	application	NOUN
cana-587	147	18	to	to	ADP
cana-587	147	19	other	other	ADJ
cana-587	147	20	programming	programming	NOUN
cana-587	147	21	problems	problem	NOUN
cana-587	147	22	”	"	PUNCT
cana-587	147	23	,	,	PUNCT
cana-587	147	24	coou	coou	NOUN
cana-587	147	25	journal	journal	PROPN
cana-587	147	26	of	of	ADP
cana-587	147	27	physical	physical	ADJ
cana-587	147	28	science	science	NOUN
cana-587	147	29	1(2	1(2	NUM
cana-587	147	30	)	)	PUNCT
cana-587	147	31	,	,	PUNCT
cana-587	147	32	147	147	NUM
cana-587	147	33	-	-	SYM
cana-587	147	34	156	156	NUM
cana-587	147	35	.	.	PUNCT
cana-587	148	1	[	[	X
cana-587	148	2	12	12	NUM
cana-587	148	3	]	]	X
cana-587	148	4	lemke	lemke	PROPN
cana-587	148	5	,	,	PUNCT
cana-587	148	6	c.e	c.e	PROPN
cana-587	148	7	.	.	PROPN
cana-587	148	8	,	,	PUNCT
cana-587	148	9	(	(	PUNCT
cana-587	148	10	1968	1968	NUM
cana-587	148	11	)	)	PUNCT
cana-587	148	12	“	"	PUNCT
cana-587	148	13	on	on	ADP
cana-587	148	14	complementary	complementary	ADJ
cana-587	148	15	pivot	pivot	NOUN
cana-587	148	16	theory	theory	NOUN
cana-587	148	17	”	"	PUNCT
cana-587	148	18	,	,	PUNCT
cana-587	148	19	mathematics	mathematic	NOUN
cana-587	148	20	of	of	ADP
cana-587	148	21	the	the	DET
cana-587	148	22	decision	decision	NOUN
cana-587	148	23	sciences	science	NOUN
cana-587	148	24	,	,	PUNCT
cana-587	148	25	g.b.danting	g.b.dante	VERB
cana-587	148	26	and	and	CCONJ
cana-587	148	27	a.f.veioff	a.f.veioff	NOUN
cana-587	148	28	,	,	PUNCT
cana-587	148	29	eds	eds	PROPN
cana-587	148	30	.	.	PUNCT
cana-587	149	1	[	[	X
cana-587	149	2	13	13	NUM
cana-587	149	3	]	]	SYM
cana-587	149	4	murthy	murthy	PROPN
cana-587	149	5	.	.	PUNCT
cana-587	150	1	k.g	k.g	PROPN
cana-587	150	2	.	.	PROPN
cana-587	150	3	,	,	PUNCT
cana-587	150	4	(	(	PUNCT
cana-587	150	5	1997	1997	NUM
cana-587	150	6	)	)	PUNCT
cana-587	150	7	“	"	PUNCT
cana-587	150	8	linear	linear	ADJ
cana-587	150	9	complementarity	complementarity	NOUN
cana-587	150	10	,	,	PUNCT
cana-587	150	11	linear	linear	ADJ
cana-587	150	12	and	and	CCONJ
cana-587	150	13	nonlinear	nonlinear	ADJ
cana-587	150	14	programming	programming	NOUN
cana-587	150	15	”	"	PUNCT
cana-587	150	16	,	,	PUNCT
cana-587	150	17	internet	internet	NOUN
cana-587	150	18	edition	edition	NOUN
cana-587	150	19	,	,	PUNCT
cana-587	150	20	http://www.personal.engin.umich.edu/~murty	http://www.personal.engin.umich.edu/~murty	NOUN
cana-587	150	21	,	,	PUNCT
cana-587	150	22	254	254	NUM
cana-587	150	23	-	-	SYM
cana-587	150	24	273	273	NUM
cana-587	150	25	.	.	PUNCT
cana-587	151	1	[	[	X
cana-587	151	2	14	14	NUM
cana-587	151	3	]	]	SYM
cana-587	151	4	nagoorgani	nagoorgani	PROPN
cana-587	151	5	,	,	PUNCT
cana-587	151	6	a.	a.	PROPN
cana-587	151	7	,	,	PUNCT
cana-587	151	8	arun	arun	PROPN
cana-587	151	9	kumar	kumar	PROPN
cana-587	151	10	,	,	PUNCT
cana-587	151	11	c.	c.	PROPN
cana-587	151	12	,	,	PUNCT
cana-587	151	13	(	(	PUNCT
cana-587	151	14	2012	2012	NUM
cana-587	151	15	)	)	PUNCT
cana-587	151	16	an	an	DET
cana-587	151	17	index	index	NOUN
cana-587	151	18	method	method	NOUN
cana-587	151	19	for	for	ADP
cana-587	151	20	solving	solve	VERB
cana-587	151	21	the	the	DET
cana-587	151	22	linear	linear	ADJ
cana-587	151	23	complementarity	complementarity	NOUN
cana-587	151	24	problem	problem	NOUN
cana-587	151	25	under	under	ADP
cana-587	151	26	fuzzy	fuzzy	ADJ
cana-587	151	27	environment	environment	NOUN
cana-587	151	28	,	,	PUNCT
cana-587	151	29	appl.math.sci	appl.math.sci	PROPN
cana-587	151	30	.	.	PUNCT
cana-587	151	31	vol	vol	NOUN
cana-587	151	32	6	6	NUM
cana-587	151	33	,	,	PUNCT
cana-587	151	34	no	no	DET
cana-587	151	35	41	41	NUM
cana-587	151	36	-	-	SYM
cana-587	151	37	44	44	NUM
cana-587	151	38	,	,	PUNCT
cana-587	151	39	20812089	20812089	NUM
cana-587	151	40	.	.	PUNCT
cana-587	152	1	[	[	X
cana-587	152	2	15	15	NUM
cana-587	152	3	]	]	X
cana-587	152	4	nagoor	nagoor	NOUN
cana-587	152	5	gani	gani	PROPN
cana-587	152	6	.	.	PUNCT
cana-587	153	1	a	a	DET
cana-587	153	2	,	,	PUNCT
cana-587	153	3	s.n	s.n	PROPN
cana-587	153	4	.	.	PROPN
cana-587	153	5	mohamed	mohamed	PROPN
cana-587	153	6	assarudeen	assarudeen	PROPN
cana-587	153	7	,	,	PUNCT
cana-587	153	8	a	a	DET
cana-587	153	9	new	new	ADJ
cana-587	153	10	operation	operation	NOUN
cana-587	153	11	on	on	ADP
cana-587	153	12	triangular	triangular	NOUN
cana-587	153	13	fuzzy	fuzzy	ADJ
cana-587	153	14	number	number	NOUN
cana-587	153	15	for	for	ADP
cana-587	153	16	solving	solve	VERB
cana-587	153	17	linear	linear	ADJ
cana-587	153	18	programming	programming	NOUN
cana-587	153	19	problem	problem	NOUN
cana-587	153	20	,	,	PUNCT
cana-587	153	21	applied	apply	VERB
cana-587	153	22	mathematical	mathematical	ADJ
cana-587	153	23	sciences	science	NOUN
cana-587	153	24	,	,	PUNCT
cana-587	153	25	vol6	vol6	PROPN
cana-587	153	26	,	,	PUNCT
cana-587	153	27	2012	2012	NUM
cana-587	153	28	,	,	PUNCT
cana-587	153	29	no.11	no.11	NOUN
cana-587	153	30	,	,	PUNCT
cana-587	153	31	525	525	NUM
cana-587	153	32	-	-	SYM
cana-587	153	33	532	532	NUM
cana-587	153	34	.	.	PUNCT
cana-587	154	1	[	[	X
cana-587	154	2	16	16	NUM
cana-587	154	3	]	]	X
cana-587	154	4	premkumar	premkumar	PROPN
cana-587	154	5	gupta	gupta	PROPN
cana-587	154	6	.	.	PROPN
cana-587	154	7	,	,	PUNCT
cana-587	154	8	hira	hira	PROPN
cana-587	154	9	,	,	PUNCT
cana-587	154	10	d.s	d.s	PROPN
cana-587	154	11	.	.	PROPN
cana-587	154	12	,	,	PUNCT
cana-587	154	13	(	(	PUNCT
cana-587	154	14	2004	2004	NUM
cana-587	154	15	)	)	PUNCT
cana-587	154	16	operations	operation	NOUN
cana-587	154	17	research	research	NOUN
cana-587	154	18	,	,	PUNCT
cana-587	154	19	s.	s.	PROPN
cana-587	154	20	chand	chand	PROPN
cana-587	154	21	&	&	CCONJ
cana-587	154	22	company	company	PROPN
cana-587	154	23	ltd	ltd	PROPN
cana-587	154	24	.	.	PUNCT
cana-587	155	1	[	[	X
cana-587	155	2	17	17	NUM
cana-587	155	3	]	]	X
cana-587	155	4	richard	richard	PROPN
cana-587	155	5	w.cottle	w.cottle	PROPN
cana-587	155	6	,	,	PUNCT
cana-587	155	7	jong	jong	PROPN
cana-587	155	8	-	-	PUNCT
cana-587	155	9	shi	shi	PROPN
cana-587	155	10	pang	pang	PROPN
cana-587	155	11	,	,	PUNCT
cana-587	155	12	richard	richard	PROPN
cana-587	155	13	e.stone	e.stone	PROPN
cana-587	155	14	.	.	PUNCT
cana-587	155	15	,	,	PUNCT
cana-587	155	16	(	(	PUNCT
cana-587	155	17	2009	2009	NUM
cana-587	155	18	)	)	PUNCT
cana-587	155	19	the	the	DET
cana-587	155	20	linear	linear	ADJ
cana-587	155	21	complementarity	complementarity	NOUN
cana-587	155	22	problem	problem	NOUN
cana-587	155	23	,	,	PUNCT
cana-587	155	24	siam	siam	NOUN
cana-587	155	25	.	.	PUNCT
cana-587	156	1	[	[	X
cana-587	156	2	18	18	NUM
cana-587	156	3	]	]	X
cana-587	156	4	robert	robert	PROPN
cana-587	156	5	.	.	PROPN
cana-587	156	6	l.	l.	PROPN
cana-587	156	7	graves	graves	PROPN
cana-587	156	8	,	,	PUNCT
cana-587	156	9	(	(	PUNCT
cana-587	156	10	1967	1967	NUM
cana-587	156	11	)	)	PUNCT
cana-587	156	12	a	a	DET
cana-587	156	13	principal	principal	ADJ
cana-587	156	14	pivoting	pivot	VERB
cana-587	156	15	simplex	simplex	NOUN
cana-587	156	16	algorithm	algorithm	NOUN
cana-587	156	17	for	for	ADP
cana-587	156	18	linear	linear	ADJ
cana-587	156	19	and	and	CCONJ
cana-587	156	20	quadratic	quadratic	ADJ
cana-587	156	21	programming	programming	NOUN
cana-587	156	22	,	,	PUNCT
cana-587	156	23	operations	operation	NOUN
cana-587	156	24	research	research	NOUN
cana-587	156	25	,	,	PUNCT
cana-587	156	26	482	482	NUM
cana-587	156	27	-	-	SYM
cana-587	156	28	494	494	NUM
cana-587	156	29	.	.	PUNCT
cana-587	157	1	[	[	X
cana-587	157	2	19	19	NUM
cana-587	157	3	]	]	X
cana-587	157	4	youssef	youssef	PROPN
cana-587	157	5	elfoutayeni	elfoutayeni	PROPN
cana-587	157	6	,	,	PUNCT
cana-587	157	7	mohamed	mohamed	PROPN
cana-587	157	8	khaladi	khaladi	PROPN
cana-587	157	9	,	,	PUNCT
cana-587	157	10	(	(	PUNCT
cana-587	157	11	2012	2012	NUM
cana-587	157	12	)	)	PUNCT
cana-587	157	13	using	use	VERB
cana-587	157	14	vector	vector	NOUN
cana-587	157	15	divisions	division	NOUN
cana-587	157	16	in	in	ADP
cana-587	157	17	solving	solve	VERB
cana-587	157	18	the	the	DET
cana-587	157	19	linear	linear	ADJ
cana-587	157	20	complementarity	complementarity	NOUN
cana-587	157	21	problem	problem	NOUN
cana-587	157	22	,	,	PUNCT
cana-587	157	23	journal	journal	NOUN
cana-587	157	24	of	of	ADP
cana-587	157	25	computational	computational	ADJ
cana-587	157	26	and	and	CCONJ
cana-587	157	27	applied	applied	ADJ
cana-587	157	28	mathematics	mathematic	NOUN
cana-587	157	29	,	,	PUNCT
cana-587	157	30	elsevier	elsevier	NOUN
cana-587	157	31	,	,	PUNCT
cana-587	157	32	236	236	NUM
cana-587	157	33	,	,	PUNCT
cana-587	157	34	1919	1919	NUM
cana-587	157	35	-	-	SYM
cana-587	157	36	1925	1925	NUM
cana-587	157	37	.	.	PUNCT