id	sid	tid	token	lemma	pos
cana-3106	1	1	communications	communication	NOUN
cana-3106	1	2	on	on	ADP
cana-3106	1	3	applied	apply	VERB
cana-3106	1	4	nonlinear	nonlinear	ADJ
cana-3106	1	5	analysis	analysis	NOUN
cana-3106	1	6	issn	issn	NOUN
cana-3106	1	7	:	:	PUNCT
cana-3106	1	8	1074	1074	NUM
cana-3106	1	9	-	-	PUNCT
cana-3106	1	10	133x	133x	NUM
cana-3106	1	11	vol	vol	NOUN
cana-3106	1	12	32	32	NUM
cana-3106	1	13	no	no	NOUN
cana-3106	1	14	.	.	PUNCT
cana-3106	2	1	5s	5s	NUM
cana-3106	2	2	(	(	PUNCT
cana-3106	2	3	2024	2024	NUM
cana-3106	2	4	)	)	PUNCT
cana-3106	2	5	353	353	NUM
cana-3106	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3106	2	7	an	an	DET
cana-3106	2	8	interval	interval	NOUN
cana-3106	2	9	approach	approach	NOUN
cana-3106	2	10	to	to	PART
cana-3106	2	11	solve	solve	VERB
cana-3106	2	12	fuzzy	fuzzy	ADJ
cana-3106	2	13	fractional	fractional	ADJ
cana-3106	2	14	programming	programming	NOUN
cana-3106	2	15	problem	problem	NOUN
cana-3106	2	16	as	as	ADP
cana-3106	2	17	a	a	DET
cana-3106	2	18	fuzzy	fuzzy	ADJ
cana-3106	2	19	linear	linear	ADJ
cana-3106	2	20	complementarity	complementarity	NOUN
cana-3106	2	21	problem	problem	NOUN
cana-3106	2	22	jenifer	jenifer	PROPN
cana-3106	2	23	d	d	PROPN
cana-3106	2	24	h1	h1	PROPN
cana-3106	2	25	,	,	PUNCT
cana-3106	2	26	r.	r.	PROPN
cana-3106	2	27	irene	irene	PROPN
cana-3106	2	28	hepzibah	hepzibah	PROPN
cana-3106	2	29	2	2	NUM
cana-3106	2	30	1	1	NUM
cana-3106	2	31	&	&	CCONJ
cana-3106	2	32	2	2	NUM
cana-3106	2	33	pg	pg	PROPN
cana-3106	2	34	&	&	CCONJ
cana-3106	2	35	research	research	PROPN
cana-3106	2	36	department	department	PROPN
cana-3106	2	37	of	of	ADP
cana-3106	2	38	mathematics	mathematics	PROPN
cana-3106	2	39	,	,	PUNCT
cana-3106	2	40	t.b.m.l	t.b.m.l	PROPN
cana-3106	2	41	.	.	PUNCT
cana-3106	3	1	college	college	PROPN
cana-3106	3	2	,	,	PUNCT
cana-3106	3	3	porayar	porayar	PROPN
cana-3106	3	4	,	,	PUNCT
cana-3106	3	5	affiliated	affiliate	VERB
cana-3106	3	6	to	to	ADP
cana-3106	3	7	annamalai	annamalai	PROPN
cana-3106	3	8	university	university	PROPN
cana-3106	3	9	tamil	tamil	PROPN
cana-3106	3	10	nadu	nadu	PROPN
cana-3106	3	11	,	,	PUNCT
cana-3106	3	12	india	india	PROPN
cana-3106	3	13	.	.	PUNCT
cana-3106	4	1	e-mail:1jenifer808282@gmail.com	e-mail:1jenifer808282@gmail.com	ADP
cana-3106	4	2	,	,	PUNCT
cana-3106	4	3	2ireneraj74@gmail.com	2ireneraj74@gmail.com	NUM
cana-3106	4	4	orcid	orcid	NOUN
cana-3106	4	5	id:10009	id:10009	NOUN
cana-3106	4	6	-	-	PUNCT
cana-3106	4	7	0009	0009	NUM
cana-3106	4	8	-	-	PUNCT
cana-3106	4	9	5196	5196	NUM
cana-3106	4	10	-	-	PUNCT
cana-3106	4	11	7733	7733	NUM
cana-3106	4	12	,	,	PUNCT
cana-3106	4	13	20000	20000	NUM
cana-3106	4	14	-	-	SYM
cana-3106	4	15	0003	0003	NUM
cana-3106	4	16	-	-	PUNCT
cana-3106	4	17	1019	1019	NUM
cana-3106	4	18	-	-	PUNCT
cana-3106	4	19	573x	573x	NUM
cana-3106	4	20	article	article	NOUN
cana-3106	4	21	history	history	NOUN
cana-3106	4	22	:	:	PUNCT
cana-3106	4	23	received	receive	VERB
cana-3106	4	24	:	:	PUNCT
cana-3106	4	25	09	09	NUM
cana-3106	4	26	-	-	SYM
cana-3106	4	27	10	10	NUM
cana-3106	4	28	-	-	PUNCT
cana-3106	4	29	2024	2024	NUM
cana-3106	4	30	revised	revise	VERB
cana-3106	4	31	:	:	PUNCT
cana-3106	4	32	27	27	NUM
cana-3106	4	33	-	-	SYM
cana-3106	4	34	11	11	NUM
cana-3106	4	35	-	-	PUNCT
cana-3106	4	36	2024	2024	NUM
cana-3106	4	37	accepted	accept	VERB
cana-3106	4	38	:	:	PUNCT
cana-3106	4	39	07	07	NUM
cana-3106	4	40	-	-	SYM
cana-3106	4	41	12	12	NUM
cana-3106	4	42	-	-	PUNCT
cana-3106	4	43	2024	2024	NUM
cana-3106	4	44	abstract	abstract	NOUN
cana-3106	4	45	:	:	PUNCT
cana-3106	4	46	an	an	DET
cana-3106	4	47	optimization	optimization	NOUN
cana-3106	4	48	problem	problem	NOUN
cana-3106	4	49	where	where	SCONJ
cana-3106	4	50	the	the	DET
cana-3106	4	51	goal	goal	NOUN
cana-3106	4	52	function	function	NOUN
cana-3106	4	53	is	be	AUX
cana-3106	4	54	a	a	DET
cana-3106	4	55	proportion	proportion	NOUN
cana-3106	4	56	between	between	ADP
cana-3106	4	57	two	two	NUM
cana-3106	4	58	functions	function	NOUN
cana-3106	4	59	is	be	AUX
cana-3106	4	60	known	know	VERB
cana-3106	4	61	as	as	ADP
cana-3106	4	62	fractional	fractional	ADJ
cana-3106	4	63	programming	programming	NOUN
cana-3106	4	64	,	,	PUNCT
cana-3106	4	65	and	and	CCONJ
cana-3106	4	66	the	the	DET
cana-3106	4	67	goal	goal	NOUN
cana-3106	4	68	is	be	AUX
cana-3106	4	69	to	to	PART
cana-3106	4	70	maximize	maximize	VERB
cana-3106	4	71	or	or	CCONJ
cana-3106	4	72	minimize	minimize	VERB
cana-3106	4	73	the	the	DET
cana-3106	4	74	ratio	ratio	NOUN
cana-3106	4	75	.	.	PUNCT
cana-3106	5	1	this	this	DET
cana-3106	5	2	paper	paper	NOUN
cana-3106	5	3	discusses	discuss	VERB
cana-3106	5	4	a	a	DET
cana-3106	5	5	methodology	methodology	NOUN
cana-3106	5	6	to	to	PART
cana-3106	5	7	resolve	resolve	VERB
cana-3106	5	8	fuzzy	fuzzy	ADJ
cana-3106	5	9	fractional	fractional	ADJ
cana-3106	5	10	programming	programming	NOUN
cana-3106	5	11	problem	problem	NOUN
cana-3106	5	12	as	as	ADP
cana-3106	5	13	a	a	DET
cana-3106	5	14	fuzzy	fuzzy	ADJ
cana-3106	5	15	linear	linear	ADJ
cana-3106	5	16	complementarity	complementarity	NOUN
cana-3106	5	17	problem	problem	NOUN
cana-3106	5	18	.	.	PUNCT
cana-3106	6	1	the	the	DET
cana-3106	6	2	study	study	NOUN
cana-3106	6	3	seeks	seek	VERB
cana-3106	6	4	to	to	PART
cana-3106	6	5	emphasize	emphasize	VERB
cana-3106	6	6	the	the	DET
cana-3106	6	7	key	key	ADJ
cana-3106	6	8	characteristics	characteristic	NOUN
cana-3106	6	9	,	,	PUNCT
cana-3106	6	10	make	make	VERB
cana-3106	6	11	some	some	DET
cana-3106	6	12	new	new	ADJ
cana-3106	6	13	observation	observation	NOUN
cana-3106	6	14	and	and	CCONJ
cana-3106	6	15	motivate	motivate	VERB
cana-3106	6	16	further	further	ADJ
cana-3106	6	17	application	application	NOUN
cana-3106	6	18	in	in	ADP
cana-3106	6	19	linear	linear	ADJ
cana-3106	6	20	complementarity	complementarity	NOUN
cana-3106	6	21	problem	problem	NOUN
cana-3106	6	22	.	.	PUNCT
cana-3106	7	1	the	the	DET
cana-3106	7	2	constraints	constraint	NOUN
cana-3106	7	3	of	of	ADP
cana-3106	7	4	the	the	DET
cana-3106	7	5	fractional	fractional	ADJ
cana-3106	7	6	programming	programming	NOUN
cana-3106	7	7	problem	problem	NOUN
cana-3106	7	8	is	be	AUX
cana-3106	7	9	taken	take	VERB
cana-3106	7	10	as	as	ADP
cana-3106	7	11	a	a	DET
cana-3106	7	12	fuzzy	fuzzy	ADJ
cana-3106	7	13	linear	linear	ADJ
cana-3106	7	14	programming	programming	NOUN
cana-3106	7	15	problem	problem	NOUN
cana-3106	7	16	and	and	CCONJ
cana-3106	7	17	further	far	ADV
cana-3106	7	18	it	it	PRON
cana-3106	7	19	transformed	transform	VERB
cana-3106	7	20	in	in	ADP
cana-3106	7	21	to	to	ADP
cana-3106	7	22	fuzzy	fuzzy	ADJ
cana-3106	7	23	linear	linear	ADJ
cana-3106	7	24	complementarity	complementarity	NOUN
cana-3106	7	25	problem	problem	NOUN
cana-3106	7	26	by	by	ADP
cana-3106	7	27	taking	take	VERB
cana-3106	7	28	various	various	ADJ
cana-3106	7	29	𝛼	𝛼	ADJ
cana-3106	7	30	–	–	PUNCT
cana-3106	7	31	cut	cut	NOUN
cana-3106	7	32	levels	level	NOUN
cana-3106	7	33	.	.	PUNCT
cana-3106	8	1	utilizing	utilize	VERB
cana-3106	8	2	interval	interval	NOUN
cana-3106	8	3	numbers	number	NOUN
cana-3106	8	4	operations	operation	VERB
cana-3106	8	5	the	the	DET
cana-3106	8	6	given	give	VERB
cana-3106	8	7	problem	problem	NOUN
cana-3106	8	8	is	be	AUX
cana-3106	8	9	resolved	resolve	VERB
cana-3106	8	10	.	.	PUNCT
cana-3106	9	1	a	a	DET
cana-3106	9	2	numerical	numerical	ADJ
cana-3106	9	3	instance	instance	NOUN
cana-3106	9	4	is	be	AUX
cana-3106	9	5	provided	provide	VERB
cana-3106	9	6	to	to	PART
cana-3106	9	7	show	show	VERB
cana-3106	9	8	how	how	SCONJ
cana-3106	9	9	the	the	DET
cana-3106	9	10	suggested	suggest	VERB
cana-3106	9	11	strategy	strategy	NOUN
cana-3106	9	12	works	work	VERB
cana-3106	9	13	.	.	PUNCT
cana-3106	10	1	keywords	keyword	NOUN
cana-3106	10	2	:	:	PUNCT
cana-3106	10	3	fuzzy	fuzzy	ADJ
cana-3106	10	4	fractional	fractional	ADJ
cana-3106	10	5	programming	programming	NOUN
cana-3106	10	6	problem	problem	NOUN
cana-3106	10	7	(	(	PUNCT
cana-3106	10	8	ffpp	ffpp	ADJ
cana-3106	10	9	)	)	PUNCT
cana-3106	10	10	,	,	PUNCT
cana-3106	10	11	linear	linear	ADJ
cana-3106	10	12	programming	programming	NOUN
cana-3106	10	13	problem	problem	NOUN
cana-3106	10	14	(	(	PUNCT
cana-3106	10	15	lpp	lpp	PROPN
cana-3106	10	16	)	)	PUNCT
cana-3106	10	17	,	,	PUNCT
cana-3106	10	18	fuzzy	fuzzy	ADJ
cana-3106	10	19	linear	linear	ADJ
cana-3106	10	20	complementarity	complementarity	NOUN
cana-3106	10	21	problem	problem	NOUN
cana-3106	10	22	(	(	PUNCT
cana-3106	10	23	flcp	flcp	NOUN
cana-3106	10	24	)	)	PUNCT
cana-3106	10	25	,	,	PUNCT
cana-3106	10	26	fuzzy	fuzzy	ADJ
cana-3106	10	27	number	number	NOUN
cana-3106	10	28	(	(	PUNCT
cana-3106	10	29	fn	fn	NOUN
cana-3106	10	30	)	)	PUNCT
cana-3106	10	31	,	,	PUNCT
cana-3106	10	32	triangular	triangular	NOUN
cana-3106	10	33	fuzzy	fuzzy	ADJ
cana-3106	10	34	number	number	NOUN
cana-3106	10	35	(	(	PUNCT
cana-3106	10	36	tfn	tfn	NOUN
cana-3106	10	37	)	)	PUNCT
cana-3106	10	38	,	,	PUNCT
cana-3106	10	39	interval	interval	NOUN
cana-3106	10	40	number	number	NOUN
cana-3106	10	41	(	(	PUNCT
cana-3106	10	42	in	in	ADP
cana-3106	10	43	)	)	PUNCT
cana-3106	10	44	.	.	PUNCT
cana-3106	11	1	2020	2020	NUM
cana-3106	11	2	ams	am	NOUN
cana-3106	11	3	subject	subject	ADJ
cana-3106	11	4	classification	classification	NOUN
cana-3106	11	5	:	:	PUNCT
cana-3106	11	6	90c32	90c32	NUM
cana-3106	11	7	:	:	PUNCT
cana-3106	11	8	90c70	90c70	NUM
cana-3106	11	9	:	:	PUNCT
cana-3106	11	10	90c90	90c90	NUM
cana-3106	12	1	1	1	NUM
cana-3106	12	2	.	.	PUNCT
cana-3106	12	3	introduction	introduction	NOUN
cana-3106	12	4	a	a	DET
cana-3106	12	5	particular	particular	ADJ
cana-3106	12	6	type	type	NOUN
cana-3106	12	7	of	of	ADP
cana-3106	12	8	optimization	optimization	NOUN
cana-3106	12	9	problem	problem	NOUN
cana-3106	12	10	known	know	VERB
cana-3106	12	11	as	as	ADP
cana-3106	12	12	fractional	fractional	ADJ
cana-3106	12	13	programming	programming	NOUN
cana-3106	12	14	[	[	X
cana-3106	12	15	1	1	NUM
cana-3106	12	16	,	,	PUNCT
cana-3106	12	17	4	4	NUM
cana-3106	12	18	,	,	PUNCT
cana-3106	12	19	27	27	NUM
cana-3106	12	20	]	]	PUNCT
cana-3106	12	21	,	,	PUNCT
cana-3106	12	22	aims	aim	VERB
cana-3106	12	23	to	to	PART
cana-3106	12	24	maximize	maximize	VERB
cana-3106	12	25	or	or	CCONJ
cana-3106	12	26	minimize	minimize	VERB
cana-3106	12	27	a	a	DET
cana-3106	12	28	ratio	ratio	NOUN
cana-3106	12	29	between	between	ADP
cana-3106	12	30	two	two	NUM
cana-3106	12	31	functions	function	NOUN
cana-3106	12	32	,	,	PUNCT
cana-3106	12	33	which	which	PRON
cana-3106	12	34	is	be	AUX
cana-3106	12	35	the	the	DET
cana-3106	12	36	objective	objective	ADJ
cana-3106	12	37	function	function	NOUN
cana-3106	12	38	.	.	PUNCT
cana-3106	13	1	it	it	PRON
cana-3106	13	2	is	be	AUX
cana-3106	13	3	an	an	DET
cana-3106	13	4	extension	extension	NOUN
cana-3106	13	5	of	of	ADP
cana-3106	13	6	lpp	lpp	PROPN
cana-3106	13	7	.	.	PUNCT
cana-3106	14	1	in	in	ADP
cana-3106	14	2	this	this	DET
cana-3106	14	3	case	case	NOUN
cana-3106	14	4	,	,	PUNCT
cana-3106	14	5	the	the	DET
cana-3106	14	6	objective	objective	ADJ
cana-3106	14	7	function	function	NOUN
cana-3106	14	8	is	be	AUX
cana-3106	14	9	a	a	DET
cana-3106	14	10	linear	linear	ADJ
cana-3106	14	11	function	function	NOUN
cana-3106	14	12	,	,	PUNCT
cana-3106	14	13	this	this	DET
cana-3106	14	14	formulation	formulation	NOUN
cana-3106	14	15	allows	allow	VERB
cana-3106	14	16	for	for	ADP
cana-3106	14	17	modelling	model	VERB
cana-3106	14	18	a	a	DET
cana-3106	14	19	wide	wide	ADJ
cana-3106	14	20	range	range	NOUN
cana-3106	14	21	of	of	ADP
cana-3106	14	22	real	real	ADJ
cana-3106	14	23	-	-	PUNCT
cana-3106	14	24	world	world	NOUN
cana-3106	14	25	problems	problem	NOUN
cana-3106	14	26	where	where	SCONJ
cana-3106	14	27	optimizing	optimize	VERB
cana-3106	14	28	a	a	DET
cana-3106	14	29	ratio	ratio	NOUN
cana-3106	14	30	or	or	CCONJ
cana-3106	14	31	a	a	DET
cana-3106	14	32	proportion	proportion	NOUN
cana-3106	14	33	is	be	AUX
cana-3106	14	34	the	the	DET
cana-3106	14	35	primary	primary	ADJ
cana-3106	14	36	goal	goal	NOUN
cana-3106	14	37	.	.	PUNCT
cana-3106	15	1	unlike	unlike	ADP
cana-3106	15	2	conventional	conventional	ADJ
cana-3106	15	3	optimization	optimization	NOUN
cana-3106	15	4	problems	problem	NOUN
cana-3106	15	5	where	where	SCONJ
cana-3106	15	6	the	the	DET
cana-3106	15	7	primary	primary	ADJ
cana-3106	15	8	goal	goal	NOUN
cana-3106	15	9	is	be	AUX
cana-3106	15	10	to	to	PART
cana-3106	15	11	maximize	maximize	VERB
cana-3106	15	12	or	or	CCONJ
cana-3106	15	13	reduce	reduce	VERB
cana-3106	15	14	a	a	DET
cana-3106	15	15	single	single	ADJ
cana-3106	15	16	objective	objective	ADJ
cana-3106	15	17	function	function	NOUN
cana-3106	15	18	.	.	PUNCT
cana-3106	16	1	the	the	DET
cana-3106	16	2	goal	goal	NOUN
cana-3106	16	3	of	of	ADP
cana-3106	16	4	fractional	fractional	ADJ
cana-3106	16	5	programming	programming	NOUN
cana-3106	16	6	problems	problem	NOUN
cana-3106	16	7	[	[	X
cana-3106	16	8	9	9	NUM
cana-3106	16	9	]	]	PUNCT
cana-3106	16	10	is	be	AUX
cana-3106	16	11	to	to	PART
cana-3106	16	12	maximize	maximize	VERB
cana-3106	16	13	a	a	DET
cana-3106	16	14	relative	relative	ADJ
cana-3106	16	15	measure	measure	NOUN
cana-3106	16	16	,	,	PUNCT
cana-3106	16	17	like	like	ADP
cana-3106	16	18	a	a	DET
cana-3106	16	19	utility	utility	NOUN
cana-3106	16	20	function	function	NOUN
cana-3106	16	21	,	,	PUNCT
cana-3106	16	22	efficiency	efficiency	NOUN
cana-3106	16	23	meter	meter	NOUN
cana-3106	16	24	,	,	PUNCT
cana-3106	16	25	or	or	CCONJ
cana-3106	16	26	performance	performance	NOUN
cana-3106	16	27	metric	metric	ADJ
cana-3106	16	28	.	.	PUNCT
cana-3106	17	1	these	these	DET
cana-3106	17	2	problems	problem	NOUN
cana-3106	17	3	present	present	VERB
cana-3106	17	4	unique	unique	ADJ
cana-3106	17	5	hurdles	hurdle	NOUN
cana-3106	17	6	because	because	SCONJ
cana-3106	17	7	of	of	ADP
cana-3106	17	8	this	this	DET
cana-3106	17	9	particular	particular	ADJ
cana-3106	17	10	structure	structure	NOUN
cana-3106	17	11	,	,	PUNCT
cana-3106	17	12	necessitating	necessitate	VERB
cana-3106	17	13	the	the	DET
cana-3106	17	14	use	use	NOUN
cana-3106	17	15	of	of	ADP
cana-3106	17	16	specialist	specialist	ADJ
cana-3106	17	17	methodologies	methodology	NOUN
cana-3106	17	18	and	and	CCONJ
cana-3106	17	19	strategies	strategy	NOUN
cana-3106	17	20	.	.	PUNCT
cana-3106	18	1	numerous	numerous	ADJ
cana-3106	18	2	practical	practical	ADJ
cana-3106	18	3	situations	situation	NOUN
cana-3106	18	4	,	,	PUNCT
cana-3106	18	5	including	include	VERB
cana-3106	18	6	resource	resource	NOUN
cana-3106	18	7	allocation	allocation	NOUN
cana-3106	18	8	,	,	PUNCT
cana-3106	18	9	portfolio	portfolio	NOUN
cana-3106	18	10	optimization	optimization	NOUN
cana-3106	18	11	,	,	PUNCT
cana-3106	18	12	performance	performance	NOUN
cana-3106	18	13	optimization	optimization	NOUN
cana-3106	18	14	,	,	PUNCT
cana-3106	18	15	and	and	CCONJ
cana-3106	18	16	network	network	NOUN
cana-3106	18	17	optimization	optimization	NOUN
cana-3106	18	18	,	,	PUNCT
cana-3106	18	19	are	be	AUX
cana-3106	18	20	modelled	model	VERB
cana-3106	18	21	by	by	ADP
cana-3106	18	22	fractional	fractional	ADJ
cana-3106	18	23	programming	programming	NOUN
cana-3106	18	24	problems	problem	NOUN
cana-3106	18	25	.	.	PUNCT
cana-3106	19	1	charnes	charne	NOUN
cana-3106	19	2	and	and	CCONJ
cana-3106	19	3	cooper	cooper	NOUN
cana-3106	19	4	(	(	PUNCT
cana-3106	19	5	1962	1962	NUM
cana-3106	19	6	)	)	PUNCT
cana-3106	20	1	[	[	X
cana-3106	20	2	6	6	NUM
cana-3106	20	3	]	]	PUNCT
cana-3106	20	4	demonstrated	demonstrate	VERB
cana-3106	20	5	that	that	SCONJ
cana-3106	20	6	an	an	DET
cana-3106	20	7	lpp	lpp	PROPN
cana-3106	20	8	can	can	AUX
cana-3106	20	9	be	be	AUX
cana-3106	20	10	solved	solve	VERB
cana-3106	20	11	to	to	PART
cana-3106	20	12	optimize	optimize	VERB
cana-3106	20	13	the	the	DET
cana-3106	20	14	linear	linear	ADJ
cana-3106	20	15	fractional	fractional	ADJ
cana-3106	20	16	programming	programming	NOUN
cana-3106	20	17	problem	problem	NOUN
cana-3106	20	18	(	(	PUNCT
cana-3106	20	19	lfpp	lfpp	PROPN
cana-3106	20	20	)	)	PUNCT
cana-3106	20	21	.	.	PUNCT
cana-3106	21	1	in	in	ADP
cana-3106	21	2	1967	1967	NUM
cana-3106	21	3	,	,	PUNCT
cana-3106	21	4	r.	r.	PROPN
cana-3106	21	5	l.	l.	PROPN
cana-3106	21	6	graves	graves	PROPN
cana-3106	21	7	[	[	X
cana-3106	21	8	24	24	NUM
cana-3106	21	9	]	]	PUNCT
cana-3106	21	10	put	put	VERB
cana-3106	21	11	forth	forth	ADP
cana-3106	21	12	a	a	DET
cana-3106	21	13	principle	principle	NOUN
cana-3106	21	14	pivoting	pivot	VERB
cana-3106	21	15	method	method	NOUN
cana-3106	21	16	for	for	ADP
cana-3106	21	17	complementarity	complementarity	NOUN
cana-3106	21	18	problems	problem	NOUN
cana-3106	21	19	.	.	PUNCT
cana-3106	22	1	bimatrix	bimatrix	NOUN
cana-3106	22	2	games	games	PROPN
cana-3106	22	3	,	,	PUNCT
cana-3106	22	4	linear	linear	ADJ
cana-3106	22	5	and	and	CCONJ
cana-3106	22	6	quadratic	quadratic	ADJ
cana-3106	22	7	programs	program	NOUN
cana-3106	22	8	were	be	AUX
cana-3106	22	9	developed	develop	VERB
cana-3106	22	10	together	together	ADV
cana-3106	22	11	by	by	ADP
cana-3106	22	12	cottle	cottle	PROPN
cana-3106	22	13	and	and	CCONJ
cana-3106	22	14	danzig	danzig	PROPN
cana-3106	23	1	[	[	X
cana-3106	23	2	8	8	NUM
cana-3106	23	3	]	]	PUNCT
cana-3106	23	4	.	.	PUNCT
cana-3106	24	1	bellman	bellman	PROPN
cana-3106	24	2	and	and	CCONJ
cana-3106	24	3	zadeh	zadeh	PROPN
cana-3106	24	4	(	(	PUNCT
cana-3106	24	5	1970	1970	NUM
cana-3106	24	6	)	)	PUNCT
cana-3106	25	1	[	[	X
cana-3106	25	2	3	3	NUM
cana-3106	25	3	,	,	PUNCT
cana-3106	25	4	29	29	NUM
cana-3106	25	5	,	,	PUNCT
cana-3106	25	6	30	30	NUM
cana-3106	25	7	]	]	PUNCT
cana-3106	25	8	proposed	propose	VERB
cana-3106	25	9	a	a	DET
cana-3106	25	10	concept	concept	NOUN
cana-3106	25	11	for	for	ADP
cana-3106	25	12	making	make	VERB
cana-3106	25	13	decisions	decision	NOUN
cana-3106	25	14	in	in	ADP
cana-3106	25	15	fuzzy	fuzzy	ADJ
cana-3106	25	16	environments	environment	NOUN
cana-3106	25	17	.	.	PUNCT
cana-3106	26	1	communications	communication	NOUN
cana-3106	26	2	on	on	ADP
cana-3106	26	3	applied	apply	VERB
cana-3106	26	4	nonlinear	nonlinear	ADJ
cana-3106	26	5	analysis	analysis	NOUN
cana-3106	26	6	issn	issn	NOUN
cana-3106	26	7	:	:	PUNCT
cana-3106	26	8	1074	1074	NUM
cana-3106	26	9	-	-	PUNCT
cana-3106	26	10	133x	133x	NUM
cana-3106	26	11	vol	vol	NOUN
cana-3106	26	12	32	32	NUM
cana-3106	26	13	no	no	NOUN
cana-3106	26	14	.	.	PUNCT
cana-3106	27	1	5s	5s	NUM
cana-3106	27	2	(	(	PUNCT
cana-3106	27	3	2024	2024	NUM
cana-3106	27	4	)	)	PUNCT
cana-3106	27	5	354	354	NUM
cana-3106	27	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3106	28	1	it	it	PRON
cana-3106	28	2	can	can	AUX
cana-3106	28	3	be	be	AUX
cana-3106	28	4	difficult	difficult	ADJ
cana-3106	28	5	to	to	PART
cana-3106	28	6	solve	solve	VERB
cana-3106	28	7	fpp	fpp	PROPN
cana-3106	28	8	[	[	X
cana-3106	28	9	25	25	NUM
cana-3106	28	10	]	]	PUNCT
cana-3106	28	11	,	,	PUNCT
cana-3106	28	12	although	although	SCONJ
cana-3106	28	13	several	several	ADJ
cana-3106	28	14	approaches	approach	NOUN
cana-3106	28	15	have	have	AUX
cana-3106	28	16	been	be	AUX
cana-3106	28	17	devised	devise	VERB
cana-3106	28	18	such	such	ADJ
cana-3106	28	19	as	as	ADP
cana-3106	28	20	branch	branch	NOUN
cana-3106	28	21	and	and	CCONJ
cana-3106	28	22	bound	bound	ADJ
cana-3106	28	23	algorithms	algorithm	NOUN
cana-3106	28	24	,	,	PUNCT
cana-3106	28	25	dinkelbach	dinkelbach	PROPN
cana-3106	28	26	's	's	PART
cana-3106	28	27	method	method	NOUN
cana-3106	28	28	,	,	PUNCT
cana-3106	28	29	linearization	linearization	NOUN
cana-3106	28	30	techniques	technique	NOUN
cana-3106	28	31	,	,	PUNCT
cana-3106	28	32	heuristics	heuristic	NOUN
cana-3106	28	33	,	,	PUNCT
cana-3106	28	34	and	and	CCONJ
cana-3106	28	35	approximations	approximation	NOUN
cana-3106	28	36	.	.	PUNCT
cana-3106	29	1	numerous	numerous	ADJ
cana-3106	29	2	disciplines	discipline	NOUN
cana-3106	29	3	,	,	PUNCT
cana-3106	29	4	including	include	VERB
cana-3106	29	5	computer	computer	NOUN
cana-3106	29	6	science	science	NOUN
cana-3106	29	7	,	,	PUNCT
cana-3106	29	8	engineering	engineering	NOUN
cana-3106	29	9	,	,	PUNCT
cana-3106	29	10	economics	economic	NOUN
cana-3106	29	11	,	,	PUNCT
cana-3106	29	12	management	management	NOUN
cana-3106	29	13	,	,	PUNCT
cana-3106	29	14	and	and	CCONJ
cana-3106	29	15	finance	finance	NOUN
cana-3106	29	16	,	,	PUNCT
cana-3106	29	17	have	have	AUX
cana-3106	29	18	used	use	VERB
cana-3106	29	19	fractional	fractional	ADJ
cana-3106	29	20	programming	programming	NOUN
cana-3106	29	21	.	.	PUNCT
cana-3106	30	1	the	the	DET
cana-3106	30	2	lcp	lcp	NOUN
cana-3106	31	1	[	[	X
cana-3106	31	2	10	10	NUM
cana-3106	31	3	,	,	PUNCT
cana-3106	31	4	23	23	NUM
cana-3106	31	5	,	,	PUNCT
cana-3106	31	6	28	28	NUM
cana-3106	31	7	]	]	PUNCT
cana-3106	31	8	is	be	AUX
cana-3106	31	9	a	a	DET
cana-3106	31	10	fundamental	fundamental	ADJ
cana-3106	31	11	problem	problem	NOUN
cana-3106	31	12	in	in	ADP
cana-3106	31	13	mathematics	mathematics	NOUN
cana-3106	31	14	and	and	CCONJ
cana-3106	31	15	computer	computer	NOUN
cana-3106	31	16	science	science	NOUN
cana-3106	31	17	that	that	PRON
cana-3106	31	18	combines	combine	VERB
cana-3106	31	19	elements	element	NOUN
cana-3106	31	20	of	of	ADP
cana-3106	31	21	linear	linear	ADJ
cana-3106	31	22	algebra	algebra	NOUN
cana-3106	31	23	and	and	CCONJ
cana-3106	31	24	complementarity	complementarity	NOUN
cana-3106	31	25	constraints	constraint	NOUN
cana-3106	31	26	.	.	PUNCT
cana-3106	32	1	it	it	PRON
cana-3106	32	2	is	be	AUX
cana-3106	32	3	an	an	DET
cana-3106	32	4	effective	effective	ADJ
cana-3106	32	5	framework	framework	NOUN
cana-3106	32	6	for	for	ADP
cana-3106	32	7	modelling	modelling	NOUN
cana-3106	32	8	and	and	CCONJ
cana-3106	32	9	resolving	resolve	VERB
cana-3106	32	10	a	a	DET
cana-3106	32	11	wide	wide	ADJ
cana-3106	32	12	range	range	NOUN
cana-3106	32	13	of	of	ADP
cana-3106	32	14	equilibrium	equilibrium	NOUN
cana-3106	32	15	issues	issue	NOUN
cana-3106	32	16	,	,	PUNCT
cana-3106	32	17	game	game	NOUN
cana-3106	32	18	-	-	PUNCT
cana-3106	32	19	theoretic	theoretic	NOUN
cana-3106	32	20	models	model	NOUN
cana-3106	32	21	,	,	PUNCT
cana-3106	32	22	and	and	CCONJ
cana-3106	32	23	optimization	optimization	NOUN
cana-3106	32	24	problems	problem	NOUN
cana-3106	32	25	[	[	X
cana-3106	32	26	12	12	NUM
cana-3106	32	27	]	]	PUNCT
cana-3106	32	28	.	.	PUNCT
cana-3106	33	1	the	the	DET
cana-3106	33	2	lcp	lcp	NOUN
cana-3106	33	3	is	be	AUX
cana-3106	33	4	useful	useful	ADJ
cana-3106	33	5	in	in	ADP
cana-3106	33	6	a	a	DET
cana-3106	33	7	wide	wide	ADJ
cana-3106	33	8	range	range	NOUN
cana-3106	33	9	of	of	ADP
cana-3106	33	10	applications	application	NOUN
cana-3106	33	11	:	:	PUNCT
cana-3106	33	12	optimization	optimization	NOUN
cana-3106	33	13	:	:	PUNCT
cana-3106	33	14	linear	linear	ADJ
cana-3106	33	15	and	and	CCONJ
cana-3106	33	16	quadratic	quadratic	ADJ
cana-3106	33	17	programs	program	NOUN
cana-3106	33	18	,	,	PUNCT
cana-3106	33	19	convex	convex	NOUN
cana-3106	33	20	optimization	optimization	NOUN
cana-3106	33	21	,	,	PUNCT
cana-3106	33	22	game	game	NOUN
cana-3106	33	23	theory	theory	NOUN
cana-3106	33	24	,	,	PUNCT
cana-3106	33	25	economics	economic	NOUN
cana-3106	33	26	,	,	PUNCT
cana-3106	33	27	physics	physics	NOUN
cana-3106	33	28	,	,	PUNCT
cana-3106	33	29	and	and	CCONJ
cana-3106	33	30	engineering	engineering	NOUN
cana-3106	33	31	:	:	PUNCT
cana-3106	33	32	structural	structural	ADJ
cana-3106	33	33	analysis	analysis	NOUN
cana-3106	33	34	,	,	PUNCT
cana-3106	33	35	mechanical	mechanical	ADJ
cana-3106	33	36	systems	system	NOUN
cana-3106	33	37	.	.	PUNCT
cana-3106	34	1	a	a	DET
cana-3106	34	2	complementarity	complementarity	NOUN
cana-3106	34	3	pivoting	pivot	VERB
cana-3106	34	4	algorithm	algorithm	NOUN
cana-3106	34	5	was	be	AUX
cana-3106	34	6	suggested	suggest	VERB
cana-3106	34	7	by	by	ADP
cana-3106	34	8	lemke	lemke	PROPN
cana-3106	34	9	et	et	PROPN
cana-3106	34	10	al	al	PROPN
cana-3106	34	11	.	.	PUNCT
cana-3106	35	1	[	[	X
cana-3106	35	2	2	2	NUM
cana-3106	35	3	,	,	PUNCT
cana-3106	35	4	22	22	NUM
cana-3106	35	5	]	]	PUNCT
cana-3106	35	6	in	in	ADP
cana-3106	35	7	1968	1968	NUM
cana-3106	35	8	to	to	PART
cana-3106	35	9	solve	solve	VERB
cana-3106	35	10	linear	linear	ADJ
cana-3106	35	11	complementarity	complementarity	NOUN
cana-3106	35	12	problems	problem	NOUN
cana-3106	35	13	.	.	PUNCT
cana-3106	36	1	k.g	k.g	PROPN
cana-3106	36	2	.	.	PROPN
cana-3106	36	3	murthy	murthy	PROPN
cana-3106	36	4	et	et	PROPN
cana-3106	36	5	al	al	PROPN
cana-3106	36	6	.	.	PROPN
cana-3106	36	7	suggested	suggest	VERB
cana-3106	36	8	a	a	DET
cana-3106	36	9	solution	solution	NOUN
cana-3106	36	10	to	to	PART
cana-3106	36	11	parametric	parametric	VERB
cana-3106	36	12	lcps	lcp	NOUN
cana-3106	36	13	in	in	ADP
cana-3106	36	14	1997	1997	NUM
cana-3106	36	15	[	[	X
cana-3106	36	16	21	21	NUM
cana-3106	36	17	]	]	PUNCT
cana-3106	36	18	.	.	PUNCT
cana-3106	37	1	subsequently	subsequently	ADV
cana-3106	37	2	,	,	PUNCT
cana-3106	37	3	a	a	DET
cana-3106	37	4	vast	vast	ADJ
cana-3106	37	5	amount	amount	NOUN
cana-3106	37	6	of	of	ADP
cana-3106	37	7	research	research	NOUN
cana-3106	37	8	has	have	AUX
cana-3106	37	9	been	be	AUX
cana-3106	37	10	done	do	VERB
cana-3106	37	11	on	on	ADP
cana-3106	37	12	complementarity	complementarity	NOUN
cana-3106	37	13	difficulties	difficulty	NOUN
cana-3106	37	14	.	.	PUNCT
cana-3106	38	1	because	because	SCONJ
cana-3106	38	2	of	of	ADP
cana-3106	38	3	their	their	PRON
cana-3106	38	4	complexity	complexity	NOUN
cana-3106	38	5	and	and	CCONJ
cana-3106	38	6	the	the	DET
cana-3106	38	7	ensuing	ensue	VERB
cana-3106	38	8	numerical	numerical	ADJ
cana-3106	38	9	challenges	challenge	NOUN
cana-3106	38	10	,	,	PUNCT
cana-3106	38	11	enormous	enormous	ADJ
cana-3106	38	12	sized	sized	ADJ
cana-3106	38	13	lp	lp	NOUN
cana-3106	38	14	can	can	AUX
cana-3106	38	15	not	not	PART
cana-3106	38	16	be	be	AUX
cana-3106	38	17	solved	solve	VERB
cana-3106	38	18	using	use	VERB
cana-3106	38	19	the	the	DET
cana-3106	38	20	well	well	ADV
cana-3106	38	21	-	-	PUNCT
cana-3106	38	22	known	know	VERB
cana-3106	38	23	simplex	simplex	NOUN
cana-3106	38	24	method	method	NOUN
cana-3106	38	25	.	.	PUNCT
cana-3106	39	1	as	as	ADP
cana-3106	39	2	a	a	DET
cana-3106	39	3	result	result	NOUN
cana-3106	39	4	,	,	PUNCT
cana-3106	39	5	iterative	iterative	ADJ
cana-3106	39	6	methods	method	NOUN
cana-3106	39	7	designed	design	VERB
cana-3106	39	8	for	for	ADP
cana-3106	39	9	tackling	tackle	VERB
cana-3106	39	10	lcps	lcp	NOUN
cana-3106	39	11	hold	hold	VERB
cana-3106	39	12	considerable	considerable	ADJ
cana-3106	39	13	potential	potential	NOUN
cana-3106	39	14	for	for	ADP
cana-3106	39	15	handling	handle	VERB
cana-3106	39	16	these	these	DET
cana-3106	39	17	programs	program	NOUN
cana-3106	39	18	.	.	PUNCT
cana-3106	40	1	let	let	VERB
cana-3106	40	2	m	m	PRON
cana-3106	40	3	be	be	AUX
cana-3106	40	4	a	a	DET
cana-3106	40	5	given	give	VERB
cana-3106	40	6	a	a	DET
cana-3106	40	7	real	real	ADJ
cana-3106	40	8	nxn	nxn	PROPN
cana-3106	40	9	square	square	ADJ
cana-3106	40	10	matrix	matrix	NOUN
cana-3106	40	11	and	and	CCONJ
cana-3106	40	12	let	let	VERB
cana-3106	40	13	q	q	PUNCT
cana-3106	40	14	be	be	AUX
cana-3106	40	15	a	a	DET
cana-3106	40	16	nx1	nx1	NOUN
cana-3106	40	17	real	real	ADJ
cana-3106	40	18	vector	vector	NOUN
cana-3106	40	19	,	,	PUNCT
cana-3106	40	20	then	then	ADV
cana-3106	40	21	the	the	DET
cana-3106	40	22	lcp	lcp	NOUN
cana-3106	40	23	(	(	PUNCT
cana-3106	40	24	q	q	NOUN
cana-3106	40	25	,	,	PUNCT
cana-3106	40	26	m	m	VERB
cana-3106	40	27	)	)	PUNCT
cana-3106	40	28	is	be	AUX
cana-3106	40	29	to	to	PART
cana-3106	40	30	find	find	VERB
cana-3106	40	31	real	real	ADJ
cana-3106	40	32	nx1	nx1	NOUN
cana-3106	40	33	vector	vector	PROPN
cana-3106	40	34	w	w	PROPN
cana-3106	40	35	,	,	PUNCT
cana-3106	40	36	z	z	VERB
cana-3106	40	37	such	such	ADJ
cana-3106	40	38	that	that	SCONJ
cana-3106	40	39	w	w	PROPN
cana-3106	40	40	-	-	PUNCT
cana-3106	40	41	mz	mz	NOUN
cana-3106	40	42	=	=	NOUN
cana-3106	40	43	q	q	PROPN
cana-3106	40	44	(	(	PUNCT
cana-3106	40	45	1.1	1.1	NUM
cana-3106	40	46	)	)	PUNCT
cana-3106	40	47	𝑊𝑗	𝑊𝑗	PROPN
cana-3106	40	48	≥	≥	NOUN
cana-3106	40	49	0	0	NUM
cana-3106	40	50	,	,	PUNCT
cana-3106	40	51	𝑍𝑗	𝑍𝑗	PROPN
cana-3106	40	52	≥	≥	NOUN
cana-3106	40	53	0	0	NUM
cana-3106	40	54	,	,	PUNCT
cana-3106	40	55	𝑍0	𝑍0	PROPN
cana-3106	40	56	≥	≥	NOUN
cana-3106	40	57	0	0	NUM
cana-3106	40	58	,	,	PUNCT
cana-3106	40	59	𝑗	𝑗	NOUN
cana-3106	40	60	=	=	SYM
cana-3106	40	61	1	1	NUM
cana-3106	40	62	,	,	PUNCT
cana-3106	40	63	…	…	PUNCT
cana-3106	40	64	,	,	PUNCT
cana-3106	40	65	𝑛	𝑛	X
cana-3106	40	66	(	(	PUNCT
cana-3106	40	67	1.2	1.2	NUM
cana-3106	40	68	)	)	PUNCT
cana-3106	40	69	𝑊𝑗𝑍𝑗	𝑊𝑗𝑍𝑗	PROPN
cana-3106	40	70	=	=	SYM
cana-3106	40	71	0	0	NUM
cana-3106	40	72	,	,	PUNCT
cana-3106	40	73	𝑗	𝑗	NOUN
cana-3106	40	74	=	=	SYM
cana-3106	40	75	1	1	NUM
cana-3106	40	76	,	,	PUNCT
cana-3106	40	77	…	…	PUNCT
cana-3106	40	78	,	,	PUNCT
cana-3106	40	79	𝑛	𝑛	X
cana-3106	40	80	(	(	PUNCT
cana-3106	40	81	1.3	1.3	NUM
cana-3106	40	82	)	)	PUNCT
cana-3106	40	83	the	the	DET
cana-3106	40	84	pair	pair	NOUN
cana-3106	40	85	(	(	PUNCT
cana-3106	40	86	wj	wj	PROPN
cana-3106	40	87	,	,	PUNCT
cana-3106	40	88	zj	zj	PROPN
cana-3106	40	89	)	)	PUNCT
cana-3106	40	90	is	be	AUX
cana-3106	40	91	a	a	DET
cana-3106	40	92	complementary	complementary	ADJ
cana-3106	40	93	variables	variable	NOUN
cana-3106	40	94	.	.	PUNCT
cana-3106	41	1	two	two	NUM
cana-3106	41	2	variables	variable	NOUN
cana-3106	41	3	in	in	ADP
cana-3106	41	4	an	an	DET
cana-3106	41	5	lcp	lcp	NOUN
cana-3106	41	6	;	;	PUNCT
cana-3106	41	7	one	one	NUM
cana-3106	41	8	of	of	ADP
cana-3106	41	9	the	the	DET
cana-3106	41	10	variables	variable	NOUN
cana-3106	41	11	must	must	AUX
cana-3106	41	12	always	always	ADV
cana-3106	41	13	be	be	AUX
cana-3106	41	14	zero	zero	NUM
cana-3106	41	15	.	.	PUNCT
cana-3106	42	1	it	it	PRON
cana-3106	42	2	is	be	AUX
cana-3106	42	3	argued	argue	VERB
cana-3106	42	4	that	that	SCONJ
cana-3106	42	5	each	each	DET
cana-3106	42	6	variable	variable	NOUN
cana-3106	42	7	in	in	ADP
cana-3106	42	8	a	a	DET
cana-3106	42	9	pair	pair	NOUN
cana-3106	42	10	is	be	AUX
cana-3106	42	11	complementary	complementary	ADJ
cana-3106	42	12	to	to	ADP
cana-3106	42	13	the	the	DET
cana-3106	42	14	other	other	ADJ
cana-3106	42	15	.	.	PUNCT
cana-3106	43	1	from	from	ADP
cana-3106	43	2	the	the	DET
cana-3106	43	3	reference	reference	NOUN
cana-3106	43	4	of	of	ADP
cana-3106	43	5	jenifer	jenifer	PROPN
cana-3106	43	6	d	d	PROPN
cana-3106	43	7	h	h	PROPN
cana-3106	43	8	and	and	CCONJ
cana-3106	43	9	r.	r.	PROPN
cana-3106	43	10	irene	irene	PROPN
cana-3106	43	11	hepzibah	hepzibah	PROPN
cana-3106	43	12	[	[	X
cana-3106	43	13	13	13	NUM
cana-3106	43	14	,	,	PUNCT
cana-3106	43	15	14	14	NUM
cana-3106	43	16	,	,	PUNCT
cana-3106	43	17	15	15	NUM
cana-3106	43	18	]	]	PUNCT
cana-3106	43	19	discussed	discuss	VERB
cana-3106	43	20	the	the	DET
cana-3106	43	21	conversion	conversion	NOUN
cana-3106	43	22	of	of	ADP
cana-3106	43	23	solving	solve	VERB
cana-3106	43	24	fuzzy	fuzzy	ADJ
cana-3106	43	25	linear	linear	ADJ
cana-3106	43	26	programming	programming	NOUN
cana-3106	43	27	problem	problem	NOUN
cana-3106	43	28	as	as	ADP
cana-3106	43	29	a	a	DET
cana-3106	43	30	fuzzy	fuzzy	ADJ
cana-3106	43	31	linear	linear	ADJ
cana-3106	43	32	complementarity	complementarity	NOUN
cana-3106	43	33	problem	problem	NOUN
cana-3106	43	34	by	by	ADP
cana-3106	43	35	maximum	maximum	ADJ
cana-3106	43	36	index	index	NOUN
cana-3106	43	37	method	method	NOUN
cana-3106	43	38	and	and	CCONJ
cana-3106	43	39	also	also	ADV
cana-3106	43	40	the	the	DET
cana-3106	43	41	inverse	inverse	NOUN
cana-3106	43	42	of	of	ADP
cana-3106	43	43	the	the	DET
cana-3106	43	44	basis	basis	NOUN
cana-3106	43	45	method	method	NOUN
cana-3106	43	46	.	.	PUNCT
cana-3106	44	1	moumita	moumita	PROPN
cana-3106	44	2	and	and	CCONJ
cana-3106	44	3	p.k	p.k	PROPN
cana-3106	44	4	.	.	PROPN
cana-3106	44	5	de	de	PROPN
cana-3106	45	1	[	[	X
cana-3106	45	2	20	20	NUM
cana-3106	45	3	]	]	SYM
cana-3106	45	4	2015	2015	NUM
cana-3106	45	5	discussed	discuss	VERB
cana-3106	45	6	fuzzy	fuzzy	ADJ
cana-3106	45	7	linear	linear	ADJ
cana-3106	45	8	fractional	fractional	ADJ
cana-3106	45	9	programming	programming	NOUN
cana-3106	45	10	problem	problem	NOUN
cana-3106	45	11	with	with	ADP
cana-3106	45	12	triangular	triangular	NOUN
cana-3106	45	13	and	and	CCONJ
cana-3106	45	14	trapezoidal	trapezoidal	ADJ
cana-3106	45	15	fuzzy	fuzzy	ADJ
cana-3106	45	16	numbers	number	NOUN
cana-3106	45	17	.	.	PUNCT
cana-3106	46	1	chen	chen	PROPN
cana-3106	46	2	s.h	s.h	PROPN
cana-3106	46	3	.	.	PROPN
cana-3106	46	4	,	,	PUNCT
cana-3106	46	5	hsieh	hsieh	PROPN
cana-3106	46	6	c.h	c.h	PROPN
cana-3106	46	7	.	.	PROPN
cana-3106	46	8	,	,	PUNCT
cana-3106	46	9	(	(	PUNCT
cana-3106	46	10	1999	1999	NUM
cana-3106	46	11	)	)	PUNCT
cana-3106	47	1	[	[	X
cana-3106	47	2	7	7	X
cana-3106	47	3	]	]	PUNCT
cana-3106	47	4	proposed	propose	VERB
cana-3106	47	5	graded	grade	VERB
cana-3106	47	6	mean	mean	NOUN
cana-3106	47	7	integration	integration	NOUN
cana-3106	47	8	representation	representation	NOUN
cana-3106	47	9	of	of	ADP
cana-3106	47	10	generalized	generalized	ADJ
cana-3106	47	11	fuzzy	fuzzy	ADJ
cana-3106	47	12	number	number	NOUN
cana-3106	47	13	,	,	PUNCT
cana-3106	47	14	this	this	DET
cana-3106	47	15	paper	paper	NOUN
cana-3106	47	16	is	be	AUX
cana-3106	47	17	extended	extend	VERB
cana-3106	47	18	to	to	ADP
cana-3106	47	19	fuzzy	fuzzy	ADJ
cana-3106	47	20	fractional	fractional	ADJ
cana-3106	47	21	programming	programming	NOUN
cana-3106	47	22	problem	problem	NOUN
cana-3106	47	23	.	.	PUNCT
cana-3106	48	1	on	on	ADP
cana-3106	48	2	account	account	NOUN
cana-3106	48	3	of	of	ADP
cana-3106	48	4	,	,	PUNCT
cana-3106	48	5	this	this	DET
cana-3106	48	6	method	method	NOUN
cana-3106	48	7	can	can	AUX
cana-3106	48	8	be	be	AUX
cana-3106	48	9	used	use	VERB
cana-3106	48	10	in	in	ADP
cana-3106	48	11	various	various	ADJ
cana-3106	48	12	types	type	NOUN
cana-3106	48	13	of	of	ADP
cana-3106	48	14	fns	fns	PROPN
cana-3106	48	15	.	.	PUNCT
cana-3106	49	1	this	this	DET
cana-3106	49	2	work	work	NOUN
cana-3106	49	3	aims	aim	VERB
cana-3106	49	4	to	to	PART
cana-3106	49	5	address	address	VERB
cana-3106	49	6	a	a	DET
cana-3106	49	7	certain	certain	ADJ
cana-3106	49	8	kind	kind	NOUN
cana-3106	49	9	of	of	ADP
cana-3106	49	10	ffpp	ffpp	NOUN
cana-3106	49	11	,	,	PUNCT
cana-3106	49	12	in	in	ADP
cana-3106	49	13	which	which	PRON
cana-3106	49	14	all	all	DET
cana-3106	49	15	parameters	parameter	NOUN
cana-3106	49	16	as	as	ADV
cana-3106	49	17	well	well	ADV
cana-3106	49	18	as	as	ADP
cana-3106	49	19	variables	variable	NOUN
cana-3106	49	20	are	be	AUX
cana-3106	49	21	tfn	tfn	NOUN
cana-3106	49	22	[	[	X
cana-3106	49	23	11	11	NUM
cana-3106	49	24	]	]	PUNCT
cana-3106	49	25	and	and	CCONJ
cana-3106	49	26	it	it	PRON
cana-3106	49	27	can	can	AUX
cana-3106	49	28	be	be	AUX
cana-3106	49	29	solved	solve	VERB
cana-3106	49	30	with	with	ADP
cana-3106	49	31	the	the	DET
cana-3106	49	32	proposed	propose	VERB
cana-3106	49	33	algorithm	algorithm	NOUN
cana-3106	49	34	by	by	ADP
cana-3106	49	35	taking	take	VERB
cana-3106	49	36	levels	level	NOUN
cana-3106	49	37	of	of	ADP
cana-3106	49	38	alpha	alpha	NOUN
cana-3106	49	39	-	-	PUNCT
cana-3106	49	40	cuts	cut	NOUN
cana-3106	49	41	[	[	X
cana-3106	49	42	5	5	NUM
cana-3106	49	43	]	]	PUNCT
cana-3106	49	44	.	.	PUNCT
cana-3106	50	1	an	an	DET
cana-3106	50	2	endeavour	endeavour	NOUN
cana-3106	50	3	has	have	AUX
cana-3106	50	4	been	be	AUX
cana-3106	50	5	undertaken	undertake	VERB
cana-3106	50	6	in	in	ADP
cana-3106	50	7	this	this	DET
cana-3106	50	8	research	research	NOUN
cana-3106	50	9	to	to	PART
cana-3106	50	10	create	create	VERB
cana-3106	50	11	an	an	DET
cana-3106	50	12	algorithm	algorithm	NOUN
cana-3106	50	13	to	to	PART
cana-3106	50	14	execute	execute	VERB
cana-3106	50	15	ffpp	ffpp	ADJ
cana-3106	50	16	as	as	ADP
cana-3106	50	17	an	an	DET
cana-3106	50	18	flcp	flcp	NOUN
cana-3106	50	19	in	in	ADP
cana-3106	50	20	interval	interval	NOUN
cana-3106	50	21	numbers	number	NOUN
cana-3106	50	22	[	[	X
cana-3106	50	23	26	26	NUM
cana-3106	50	24	,	,	PUNCT
cana-3106	50	25	19	19	NUM
cana-3106	50	26	]	]	PUNCT
cana-3106	50	27	.	.	PUNCT
cana-3106	51	1	the	the	DET
cana-3106	51	2	given	give	VERB
cana-3106	51	3	problem	problem	NOUN
cana-3106	51	4	can	can	AUX
cana-3106	51	5	be	be	AUX
cana-3106	51	6	first	first	ADV
cana-3106	51	7	converted	convert	VERB
cana-3106	51	8	into	into	ADP
cana-3106	51	9	flpp	flpp	NOUN
cana-3106	51	10	further	far	ADV
cana-3106	51	11	it	it	PRON
cana-3106	51	12	transformed	transform	VERB
cana-3106	51	13	into	into	ADP
cana-3106	51	14	flcp	flcp	NOUN
cana-3106	51	15	.	.	PUNCT
cana-3106	52	1	the	the	DET
cana-3106	52	2	aim	aim	NOUN
cana-3106	52	3	is	be	AUX
cana-3106	52	4	to	to	PART
cana-3106	52	5	explore	explore	VERB
cana-3106	52	6	the	the	DET
cana-3106	52	7	theoretical	theoretical	ADJ
cana-3106	52	8	and	and	CCONJ
cana-3106	52	9	computational	computational	ADJ
cana-3106	52	10	aspects	aspect	NOUN
cana-3106	52	11	of	of	ADP
cana-3106	52	12	fractional	fractional	ADJ
cana-3106	52	13	programming	programming	NOUN
cana-3106	52	14	problems	problem	NOUN
cana-3106	52	15	and	and	CCONJ
cana-3106	52	16	develop	develop	VERB
cana-3106	52	17	a	a	DET
cana-3106	52	18	new	new	ADJ
cana-3106	52	19	algorithm	algorithm	NOUN
cana-3106	52	20	for	for	ADP
cana-3106	52	21	solving	solve	VERB
cana-3106	52	22	in	in	ADP
cana-3106	52	23	terms	term	NOUN
cana-3106	52	24	of	of	ADP
cana-3106	52	25	complementarity	complementarity	NOUN
cana-3106	52	26	side	side	NOUN
cana-3106	52	27	.	.	PUNCT
cana-3106	53	1	the	the	DET
cana-3106	53	2	structure	structure	NOUN
cana-3106	53	3	of	of	ADP
cana-3106	53	4	the	the	DET
cana-3106	53	5	paper	paper	NOUN
cana-3106	53	6	is	be	AUX
cana-3106	53	7	as	as	SCONJ
cana-3106	53	8	follows	follow	VERB
cana-3106	53	9	:	:	PUNCT
cana-3106	53	10	the	the	DET
cana-3106	53	11	definitions	definition	NOUN
cana-3106	53	12	,	,	PUNCT
cana-3106	53	13	arithmetic	arithmetic	ADJ
cana-3106	53	14	operations	operation	NOUN
cana-3106	53	15	of	of	ADP
cana-3106	53	16	in	in	ADP
cana-3106	53	17	and	and	CCONJ
cana-3106	53	18	fuzzy	fuzzy	ADJ
cana-3106	53	19	linear	linear	ADJ
cana-3106	53	20	complementarity	complementarity	NOUN
cana-3106	53	21	problem	problem	NOUN
cana-3106	53	22	are	be	AUX
cana-3106	53	23	covered	cover	VERB
cana-3106	53	24	in	in	ADP
cana-3106	53	25	section	section	NOUN
cana-3106	53	26	2	2	NUM
cana-3106	53	27	.	.	PUNCT
cana-3106	54	1	an	an	DET
cana-3106	54	2	algorithm	algorithm	NOUN
cana-3106	54	3	that	that	PRON
cana-3106	54	4	provides	provide	VERB
cana-3106	54	5	the	the	DET
cana-3106	54	6	computing	computing	NOUN
cana-3106	54	7	process	process	NOUN
cana-3106	54	8	for	for	ADP
cana-3106	54	9	the	the	DET
cana-3106	54	10	best	good	ADJ
cana-3106	54	11	result	result	NOUN
cana-3106	54	12	is	be	AUX
cana-3106	54	13	developed	develop	VERB
cana-3106	54	14	in	in	ADP
cana-3106	54	15	section	section	NOUN
cana-3106	54	16	3	3	NUM
cana-3106	54	17	.	.	PUNCT
cana-3106	54	18	section	section	NOUN
cana-3106	54	19	4	4	NUM
cana-3106	54	20	provides	provide	VERB
cana-3106	54	21	a	a	DET
cana-3106	54	22	numerical	numerical	ADJ
cana-3106	54	23	illustration	illustration	NOUN
cana-3106	54	24	to	to	PART
cana-3106	54	25	clarify	clarify	VERB
cana-3106	54	26	the	the	DET
cana-3106	54	27	preceding	precede	VERB
cana-3106	54	28	method	method	NOUN
cana-3106	54	29	with	with	ADP
cana-3106	54	30	different	different	ADJ
cana-3106	54	31	levels	level	NOUN
cana-3106	54	32	of	of	ADP
cana-3106	54	33	𝛼	𝛼	PRON
cana-3106	54	34	−	−	NOUN
cana-3106	54	35	𝑐𝑢𝑡.	𝑐𝑢𝑡.	NOUN
cana-3106	54	36	section	section	NOUN
cana-3106	54	37	5	5	NUM
cana-3106	54	38	concludes	conclude	VERB
cana-3106	54	39	with	with	ADP
cana-3106	54	40	main	main	ADJ
cana-3106	54	41	results	result	NOUN
cana-3106	54	42	.	.	PUNCT
cana-3106	55	1	communications	communication	NOUN
cana-3106	55	2	on	on	ADP
cana-3106	55	3	applied	apply	VERB
cana-3106	55	4	nonlinear	nonlinear	ADJ
cana-3106	55	5	analysis	analysis	NOUN
cana-3106	55	6	issn	issn	NOUN
cana-3106	55	7	:	:	PUNCT
cana-3106	55	8	1074	1074	NUM
cana-3106	55	9	-	-	PUNCT
cana-3106	55	10	133x	133x	NUM
cana-3106	55	11	vol	vol	NOUN
cana-3106	55	12	32	32	NUM
cana-3106	55	13	no	no	NOUN
cana-3106	55	14	.	.	PUNCT
cana-3106	56	1	5s	5s	NUM
cana-3106	56	2	(	(	PUNCT
cana-3106	56	3	2024	2024	NUM
cana-3106	56	4	)	)	PUNCT
cana-3106	56	5	355	355	NUM
cana-3106	56	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3106	56	7	2	2	NUM
cana-3106	56	8	.	.	PUNCT
cana-3106	56	9	preliminaries	preliminary	NOUN
cana-3106	56	10	2.1	2.1	NUM
cana-3106	56	11	triangular	triangular	NOUN
cana-3106	56	12	fuzzy	fuzzy	ADJ
cana-3106	56	13	number	number	NOUN
cana-3106	56	14	a	a	DET
cana-3106	56	15	tfn	tfn	NOUN
cana-3106	56	16	ã	ã	X
cana-3106	56	17	=	=	SYM
cana-3106	56	18	(	(	PUNCT
cana-3106	56	19	a1	a1	PROPN
cana-3106	56	20	,	,	PUNCT
cana-3106	56	21	a2	a2	PROPN
cana-3106	56	22	,	,	PUNCT
cana-3106	56	23	a3	a3	NOUN
cana-3106	56	24	)	)	PUNCT
cana-3106	56	25	such	such	ADJ
cana-3106	56	26	that	that	DET
cana-3106	56	27	a1	a1	NOUN
cana-3106	56	28			PROPN
cana-3106	56	29	a2	a2	PROPN
cana-3106	56	30			PROPN
cana-3106	56	31	a3	a3	NOUN
cana-3106	56	32	,	,	PUNCT
cana-3106	56	33	with	with	ADP
cana-3106	56	34	membership	membership	NOUN
cana-3106	56	35	function	function	NOUN
cana-3106	56	36	defined	define	VERB
cana-3106	56	37	as	as	ADP
cana-3106	56	38	𝑥−𝑎1	𝑥−𝑎1	ADV
cana-3106	56	39	𝑎2−𝑎1	𝑎2−𝑎1	ADV
cana-3106	56	40	,	,	PUNCT
cana-3106	56	41	𝑎1	𝑎1	ADP
cana-3106	56	42	≤	≤	NUM
cana-3106	56	43	𝑥	𝑥	DET
cana-3106	56	44	≤	≤	PROPN
cana-3106	56	45	𝑎2	𝑎2	PROPN
cana-3106	56	46	𝜇	𝜇	ADP
cana-3106	56	47	�	�	PROPN
cana-3106	56	48	̃	̃	PROPN
cana-3106	56	49	�	�	NOUN
cana-3106	56	50	(𝑥	(𝑥	NOUN
cana-3106	56	51	)	)	PUNCT
cana-3106	56	52	=	=	PUNCT
cana-3106	56	53	(	(	PUNCT
cana-3106	56	54	𝑎3−𝑥	𝑎3−𝑥	PROPN
cana-3106	56	55	)	)	PUNCT
cana-3106	56	56	(	(	PUNCT
cana-3106	56	57	𝑎3−𝑎2	𝑎3−𝑎2	X
cana-3106	56	58	)	)	PUNCT
cana-3106	56	59	,	,	PUNCT
cana-3106	57	1	𝑎2	𝑎2	NOUN
cana-3106	57	2	≤	≤	NUM
cana-3106	57	3	𝑥	𝑥	PROPN
cana-3106	57	4	≤	≤	NUM
cana-3106	57	5	𝑎3	𝑎3	PROPN
cana-3106	57	6	0	0	NUM
cana-3106	57	7	,	,	PUNCT
cana-3106	57	8	otherwise	otherwise	ADV
cana-3106	57	9	2.2	2.2	NUM
cana-3106	57	10	fractional	fractional	ADJ
cana-3106	57	11	programming	programming	NOUN
cana-3106	57	12	problem	problem	NOUN
cana-3106	57	13	a	a	DET
cana-3106	57	14	flp	flp	NOUN
cana-3106	57	15	problem	problem	NOUN
cana-3106	57	16	is	be	AUX
cana-3106	57	17	defined	define	VERB
cana-3106	57	18	as	as	ADP
cana-3106	57	19	max	max	PROPN
cana-3106	57	20	z	z	PROPN
cana-3106	57	21	=	=	SYM
cana-3106	57	22	𝑒𝑥	𝑒𝑥	PROPN
cana-3106	58	1	+	+	NOUN
cana-3106	58	2	𝑟	𝑟	X
cana-3106	58	3	𝑓𝑥	𝑓𝑥	ADP
cana-3106	58	4	+	+	NOUN
cana-3106	58	5	𝑠	𝑠	PROPN
cana-3106	58	6	subject	subject	NOUN
cana-3106	58	7	to	to	ADP
cana-3106	58	8	𝐴𝑋	𝐴𝑋	PROPN
cana-3106	58	9	≤	≤	NOUN
cana-3106	58	10	𝐵	𝐵	PROPN
cana-3106	58	11	,	,	PUNCT
cana-3106	58	12	𝑋	𝑋	NOUN
cana-3106	58	13	≥	≥	NOUN
cana-3106	58	14	0	0	NUM
cana-3106	58	15	where	where	SCONJ
cana-3106	58	16	e	e	NOUN
cana-3106	58	17	=	=	SYM
cana-3106	58	18	(	(	PUNCT
cana-3106	58	19	𝑒1	𝑒1	NOUN
cana-3106	58	20	,	,	PUNCT
cana-3106	58	21	𝑒2	𝑒2	PROPN
cana-3106	58	22	,	,	PUNCT
cana-3106	58	23	…	…	PUNCT
cana-3106	58	24	,	,	PUNCT
cana-3106	58	25	𝑒𝑛	𝑒𝑛	PROPN
cana-3106	58	26	)	)	PUNCT
cana-3106	58	27	,	,	PUNCT
cana-3106	58	28	f	f	X
cana-3106	59	1	=	=	PRON
cana-3106	59	2	(	(	PUNCT
cana-3106	59	3	𝑓1	𝑓1	ADJ
cana-3106	59	4	,	,	PUNCT
cana-3106	59	5	𝑓2	𝑓2	NOUN
cana-3106	59	6	,	,	PUNCT
cana-3106	59	7	…	…	PUNCT
cana-3106	59	8	,	,	PUNCT
cana-3106	59	9	𝑓𝑛	𝑓𝑛	NOUN
cana-3106	59	10	)	)	PUNCT
cana-3106	59	11	,	,	PUNCT
cana-3106	59	12	b	b	X
cana-3106	59	13	=	=	PUNCT
cana-3106	59	14	(	(	PUNCT
cana-3106	59	15	𝑏1	𝑏1	NOUN
cana-3106	59	16	,	,	PUNCT
cana-3106	59	17	𝑏2	𝑏2	PROPN
cana-3106	59	18	,	,	PUNCT
cana-3106	59	19	…	…	PUNCT
cana-3106	59	20	,	,	PUNCT
cana-3106	59	21	𝑏𝑚)𝑇	𝑏𝑚)𝑇	PROPN
cana-3106	59	22	,	,	PUNCT
cana-3106	59	23	𝑋𝜖ℝ𝑛	𝑋𝜖ℝ𝑛	PROPN
cana-3106	59	24	,	,	PUNCT
cana-3106	59	25	𝑥	𝑥	PROPN
cana-3106	59	26	𝜖	𝜖	PROPN
cana-3106	59	27	𝑋	𝑋	PROPN
cana-3106	59	28	,	,	PUNCT
cana-3106	59	29	r	r	NOUN
cana-3106	59	30	and	and	CCONJ
cana-3106	59	31	s	s	NOUN
cana-3106	59	32	are	be	AUX
cana-3106	59	33	scalar	scalar	ADJ
cana-3106	59	34	and	and	CCONJ
cana-3106	59	35	a=(𝑎𝑖𝑗)𝑛xm	a=(𝑎𝑖𝑗)𝑛xm	PROPN
cana-3106	59	36	.	.	PUNCT
cana-3106	60	1	2.3	2.3	NUM
cana-3106	60	2	interval	interval	NOUN
cana-3106	60	3	number	number	NOUN
cana-3106	60	4	if	if	SCONJ
cana-3106	60	5	�	�	PROPN
cana-3106	60	6	̃	̃	PROPN
cana-3106	60	7	�	�	PROPN
cana-3106	60	8	𝐹	𝐹	PROPN
cana-3106	60	9	is	be	AUX
cana-3106	60	10	a	a	DET
cana-3106	60	11	tfn	tfn	NOUN
cana-3106	60	12	,	,	PUNCT
cana-3106	60	13	let	let	VERB
cana-3106	60	14	�	�	PROPN
cana-3106	60	15	̃	̃	PROPN
cana-3106	60	16	�	�	PROPN
cana-3106	60	17	𝐹	𝐹	NOUN
cana-3106	60	18	𝛼	𝛼	NOUN
cana-3106	60	19	=	=	PUNCT
cana-3106	61	1	[	[	X
cana-3106	61	2	𝑇−	𝑇−	NUM
cana-3106	61	3	𝛼	𝛼	NOUN
cana-3106	61	4	,	,	PUNCT
cana-3106	61	5	𝑇+	𝑇+	PUNCT
cana-3106	61	6	𝛼	𝛼	X
cana-3106	61	7	]	]	X
cana-3106	61	8	be	be	VERB
cana-3106	61	9	the	the	DET
cana-3106	61	10	closed	closed	ADJ
cana-3106	61	11	interval	interval	NOUN
cana-3106	61	12	,	,	PUNCT
cana-3106	61	13	this	this	PRON
cana-3106	61	14	represents	represent	VERB
cana-3106	61	15	an	an	DET
cana-3106	61	16			NOUN
cana-3106	61	17	cut	cut	VERB
cana-3106	61	18	for	for	ADP
cana-3106	61	19	�	�	PROPN
cana-3106	61	20	̃	̃	PROPN
cana-3106	61	21	�	�	PROPN
cana-3106	61	22	𝐹	𝐹	PROPN
cana-3106	61	23	with	with	ADP
cana-3106	61	24	its	its	PRON
cana-3106	61	25	left	left	NOUN
cana-3106	61	26	and	and	CCONJ
cana-3106	61	27	right	right	ADJ
cana-3106	61	28	end	end	NOUN
cana-3106	61	29	points	point	NOUN
cana-3106	61	30	of	of	ADP
cana-3106	61	31	𝑇−	𝑇−	PROPN
cana-3106	61	32	𝛼	𝛼	NOUN
cana-3106	61	33	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-3106	61	34	𝑇+	𝑇+	PUNCT
cana-3106	61	35	𝛼	𝛼	X
cana-3106	61	36	respectively	respectively	ADV
cana-3106	61	37	.	.	PUNCT
cana-3106	62	1	let	let	VERB
cana-3106	62	2	s	s	PRON
cana-3106	62	3	and	and	CCONJ
cana-3106	62	4	r	r	NOUN
cana-3106	62	5	are	be	AUX
cana-3106	62	6	specified	specify	VERB
cana-3106	62	7	by	by	ADP
cana-3106	62	8	ordered	order	VERB
cana-3106	62	9	pairs	pair	NOUN
cana-3106	62	10	of	of	ADP
cana-3106	62	11	real	real	ADJ
cana-3106	62	12	numbers	number	NOUN
cana-3106	62	13	.	.	PUNCT
cana-3106	63	1	s	s	PART
cana-3106	63	2	=	=	PUNCT
cana-3106	64	1	[	[	X
cana-3106	64	2	a	a	PRON
cana-3106	64	3	,	,	PUNCT
cana-3106	64	4	b	b	NOUN
cana-3106	64	5	]	]	X
cana-3106	64	6	,	,	PUNCT
cana-3106	64	7	where	where	SCONJ
cana-3106	64	8	a	a	DET
cana-3106	64	9			PROPN
cana-3106	64	10	b	b	NOUN
cana-3106	64	11	,	,	PUNCT
cana-3106	64	12	r	r	NOUN
cana-3106	64	13	=	=	PUNCT
cana-3106	65	1	[	[	X
cana-3106	65	2	c	c	X
cana-3106	65	3	,	,	PUNCT
cana-3106	65	4	d	d	X
cana-3106	65	5	]	]	X
cana-3106	65	6	,	,	PUNCT
cana-3106	65	7	where	where	SCONJ
cana-3106	65	8	c	c	X
cana-3106	65	9			NUM
cana-3106	65	10	d	d	NOUN
cana-3106	65	11	,	,	PUNCT
cana-3106	65	12	when	when	SCONJ
cana-3106	65	13	a	a	DET
cana-3106	65	14	=	=	SYM
cana-3106	65	15	b	b	NOUN
cana-3106	65	16	and	and	CCONJ
cana-3106	65	17	c	c	NOUN
cana-3106	65	18	=	=	SYM
cana-3106	65	19	d	d	PROPN
cana-3106	65	20	,	,	PUNCT
cana-3106	65	21	these	these	DET
cana-3106	65	22	interval	interval	NOUN
cana-3106	65	23	numbers	number	NOUN
cana-3106	65	24	degenerate	degenerate	VERB
cana-3106	65	25	to	to	ADP
cana-3106	65	26	a	a	DET
cana-3106	65	27	scalar	scalar	ADJ
cana-3106	65	28	real	real	ADJ
cana-3106	65	29	number	number	NOUN
cana-3106	65	30	.	.	PUNCT
cana-3106	66	1	2.4	2.4	NUM
cana-3106	66	2	modified	modify	VERB
cana-3106	66	3	arithmetic	arithmetic	ADJ
cana-3106	66	4	operations	operation	NOUN
cana-3106	66	5	on	on	ADP
cana-3106	66	6	interval	interval	NOUN
cana-3106	66	7	numbers	number	NOUN
cana-3106	66	8	any	any	DET
cana-3106	66	9	interval	interval	NOUN
cana-3106	66	10	number	number	NOUN
cana-3106	66	11	�	�	PROPN
cana-3106	66	12	̃	̃	PROPN
cana-3106	66	13	�	�	NOUN
cana-3106	66	14	=	=	PUNCT
cana-3106	67	1	[	[	X
cana-3106	67	2	𝜌1	𝜌1	NOUN
cana-3106	67	3	,	,	PUNCT
cana-3106	67	4	𝜌2	𝜌2	ADJ
cana-3106	67	5	]	]	PUNCT
cana-3106	67	6	is	be	AUX
cana-3106	67	7	alternatively	alternatively	ADV
cana-3106	67	8	represented	represent	VERB
cana-3106	67	9	as	as	ADP
cana-3106	67	10	�	�	PROPN
cana-3106	67	11	̃	̃	PROPN
cana-3106	67	12	�	�	PROPN
cana-3106	67	13	=	=	SYM
cana-3106	67	14	〈	〈	PROPN
cana-3106	67	15	𝑡(	𝑡(	PROPN
cana-3106	67	16	�	�	PROPN
cana-3106	67	17	̃	̃	PROPN
cana-3106	67	18	�	�	PROPN
cana-3106	67	19	)	)	PUNCT
cana-3106	67	20	,	,	PUNCT
cana-3106	67	21	𝑠(	𝑠(	PROPN
cana-3106	67	22	�	�	PROPN
cana-3106	67	23	̃	̃	PROPN
cana-3106	67	24	�	�	NOUN
cana-3106	67	25	)	)	PUNCT
cana-3106	67	26	〉	〉	NOUN
cana-3106	67	27	,	,	PUNCT
cana-3106	67	28	where	where	SCONJ
cana-3106	67	29	𝑡(	𝑡(	PROPN
cana-3106	67	30	�	�	PROPN
cana-3106	67	31	̃	̃	NOUN
cana-3106	67	32	�	�	PROPN
cana-3106	67	33	)	)	PUNCT
cana-3106	67	34	=	=	SYM
cana-3106	68	1	𝜌1+𝜌2	𝜌1+𝜌2	PROPN
cana-3106	68	2	2	2	NUM
cana-3106	68	3	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-3106	68	4	𝑠(	𝑠(	PROPN
cana-3106	68	5	�	�	PROPN
cana-3106	68	6	̃	̃	PROPN
cana-3106	68	7	�	�	PROPN
cana-3106	68	8	)	)	PUNCT
cana-3106	68	9	=	=	PUNCT
cana-3106	69	1	𝜌1−𝜌2	𝜌1−𝜌2	NUM
cana-3106	69	2	2	2	NUM
cana-3106	69	3	are	be	AUX
cana-3106	69	4	the	the	DET
cana-3106	69	5	mid	mid	ADJ
cana-3106	69	6	-	-	NOUN
cana-3106	69	7	point	point	NOUN
cana-3106	69	8	and	and	CCONJ
cana-3106	69	9	half	half	ADJ
cana-3106	69	10	-	-	PUNCT
cana-3106	69	11	width	width	NOUN
cana-3106	69	12	of	of	ADP
cana-3106	69	13	the	the	DET
cana-3106	69	14	interval	interval	NOUN
cana-3106	69	15	number	number	NOUN
cana-3106	69	16	�	�	PROPN
cana-3106	69	17	̃	̃	PROPN
cana-3106	69	18	�	�	PROPN
cana-3106	69	19	.	.	PUNCT
cana-3106	70	1	let	let	VERB
cana-3106	70	2	�	�	PROPN
cana-3106	70	3	̃	̃	PROPN
cana-3106	70	4	�	�	NOUN
cana-3106	70	5	=	=	PUNCT
cana-3106	71	1	[	[	X
cana-3106	71	2	𝑡	𝑡	X
cana-3106	71	3	,	,	PUNCT
cana-3106	71	4	𝑠	𝑠	X
cana-3106	71	5	]	]	PUNCT
cana-3106	71	6	has	have	VERB
cana-3106	71	7	the	the	DET
cana-3106	71	8	canonical	canonical	ADJ
cana-3106	71	9	expression	expression	NOUN
cana-3106	71	10	�	�	PROPN
cana-3106	71	11	̃	̃	NOUN
cana-3106	71	12	�	�	NOUN
cana-3106	71	13	=	=	PUNCT
cana-3106	72	1	[	[	X
cana-3106	72	2	𝑡	𝑡	X
cana-3106	72	3	−	−	NOUN
cana-3106	72	4	𝑠	𝑠	PROPN
cana-3106	72	5	,	,	PUNCT
cana-3106	72	6	𝑡	𝑡	PROPN
cana-3106	72	7	+	+	PROPN
cana-3106	72	8	𝑠	𝑠	X
cana-3106	72	9	]	]	PUNCT
cana-3106	72	10	.	.	PUNCT
cana-3106	73	1	�	�	PROPN
cana-3106	73	2	̃	̃	PROPN
cana-3106	73	3	�	�	NOUN
cana-3106	73	4	=	=	PUNCT
cana-3106	74	1	[	[	X
cana-3106	74	2	𝑟1	𝑟1	NOUN
cana-3106	74	3	,	,	PUNCT
cana-3106	74	4	𝑟2]𝑎𝑛𝑑	𝑟2]𝑎𝑛𝑑	NUM
cana-3106	74	5	�	�	SYM
cana-3106	74	6	̃	̃	NOUN
cana-3106	74	7	�	�	NOUN
cana-3106	74	8	=	=	PUNCT
cana-3106	75	1	[	[	X
cana-3106	75	2	𝑠1	𝑠1	PROPN
cana-3106	75	3	,	,	PUNCT
cana-3106	75	4	𝑠2	𝑠2	PROPN
cana-3106	75	5	]	]	PUNCT
cana-3106	75	6	are	be	AUX
cana-3106	75	7	two	two	NUM
cana-3106	75	8	ins	in	NOUN
cana-3106	75	9	,	,	PUNCT
cana-3106	75	10	addition	addition	NOUN
cana-3106	75	11	:	:	PUNCT
cana-3106	76	1	�	�	PROPN
cana-3106	76	2	̃	̃	PROPN
cana-3106	76	3	�	�	PROPN
cana-3106	76	4	+	+	SYM
cana-3106	76	5	�	�	PROPN
cana-3106	76	6	̃	̃	NOUN
cana-3106	76	7	�	�	NOUN
cana-3106	76	8	=	=	PUNCT
cana-3106	77	1	[	[	X
cana-3106	77	2	𝑟1	𝑟1	NOUN
cana-3106	77	3	,	,	PUNCT
cana-3106	77	4	𝑟2	𝑟2	NOUN
cana-3106	77	5	]	]	PUNCT
cana-3106	77	6	+	+	CCONJ
cana-3106	77	7	[	[	PUNCT
cana-3106	77	8	𝑠1	𝑠1	NOUN
cana-3106	77	9	,	,	PUNCT
cana-3106	77	10	𝑠2	𝑠2	NOUN
cana-3106	77	11	]	]	PUNCT
cana-3106	77	12	=	=	SYM
cana-3106	78	1	[	[	X
cana-3106	78	2	(	(	PUNCT
cana-3106	78	3	m(	m(	PROPN
cana-3106	78	4	�	�	PROPN
cana-3106	78	5	̃	̃	PROPN
cana-3106	78	6	�	�	PROPN
cana-3106	78	7	)	)	PUNCT
cana-3106	78	8	+	+	CCONJ
cana-3106	78	9	m(	m(	PROPN
cana-3106	78	10	�	�	PROPN
cana-3106	78	11	̃	̃	PROPN
cana-3106	78	12	�	�	PROPN
cana-3106	78	13	)	)	PUNCT
cana-3106	78	14	)	)	PUNCT
cana-3106	79	1	k	k	NOUN
cana-3106	79	2	,	,	PUNCT
cana-3106	79	3	(	(	PUNCT
cana-3106	79	4	m(	m(	PROPN
cana-3106	79	5	�	�	PROPN
cana-3106	79	6	̃	̃	PROPN
cana-3106	79	7	�	�	PROPN
cana-3106	79	8	)	)	PUNCT
cana-3106	79	9	+	+	CCONJ
cana-3106	79	10	m(	m(	PROPN
cana-3106	79	11	�	�	PROPN
cana-3106	79	12	̃	̃	PROPN
cana-3106	79	13	�	�	PROPN
cana-3106	79	14	)	)	PUNCT
cana-3106	79	15	)	)	PUNCT
cana-3106	80	1	+	+	CCONJ
cana-3106	81	1	k	k	X
cana-3106	81	2	]	]	X
cana-3106	81	3	,	,	PUNCT
cana-3106	81	4	where	where	SCONJ
cana-3106	81	5	k	k	PROPN
cana-3106	81	6	=	=	PRON
cana-3106	81	7	{	{	PUNCT
cana-3106	81	8	(	(	PUNCT
cana-3106	81	9	𝑠2+𝑟2)−(𝑠1+𝑟1	𝑠2+𝑟2)−(𝑠1+𝑟1	PROPN
cana-3106	81	10	)	)	PUNCT
cana-3106	81	11	2	2	NUM
cana-3106	81	12	}	}	PUNCT
cana-3106	81	13	.	.	PUNCT
cana-3106	82	1	subtraction	subtraction	NOUN
cana-3106	82	2	:	:	PUNCT
cana-3106	82	3	�	�	PROPN
cana-3106	82	4	̃	̃	PROPN
cana-3106	82	5	�	�	PROPN
cana-3106	82	6	−	−	PROPN
cana-3106	82	7	�	�	PROPN
cana-3106	82	8	̃	̃	NOUN
cana-3106	82	9	�	�	NOUN
cana-3106	82	10	=	=	PUNCT
cana-3106	83	1	[	[	X
cana-3106	83	2	𝑟1	𝑟1	NOUN
cana-3106	83	3	,	,	PUNCT
cana-3106	83	4	𝑟2	𝑟2	NOUN
cana-3106	83	5	]	]	PUNCT
cana-3106	83	6	[	[	PUNCT
cana-3106	83	7	𝑠1	𝑠1	NOUN
cana-3106	83	8	,	,	PUNCT
cana-3106	83	9	𝑠2	𝑠2	NOUN
cana-3106	83	10	]	]	PUNCT
cana-3106	83	11	=	=	SYM
cana-3106	84	1	[	[	X
cana-3106	84	2	(	(	PUNCT
cana-3106	84	3	m(	m(	PROPN
cana-3106	84	4	�	�	PROPN
cana-3106	84	5	̃	̃	PROPN
cana-3106	84	6	�	�	PROPN
cana-3106	84	7	)	)	PUNCT
cana-3106	84	8	m(	m(	PROPN
cana-3106	84	9	�	�	PROPN
cana-3106	84	10	̃	̃	PROPN
cana-3106	84	11	�	�	PROPN
cana-3106	84	12	)	)	PUNCT
cana-3106	84	13	)	)	PUNCT
cana-3106	85	1	k	k	NOUN
cana-3106	85	2	,	,	PUNCT
cana-3106	85	3	(	(	PUNCT
cana-3106	85	4	m(	m(	PROPN
cana-3106	85	5	�	�	PROPN
cana-3106	85	6	̃	̃	PROPN
cana-3106	85	7	�	�	PROPN
cana-3106	85	8	)	)	PUNCT
cana-3106	85	9	m(	m(	PROPN
cana-3106	85	10	�	�	PROPN
cana-3106	85	11	̃	̃	PROPN
cana-3106	85	12	�	�	PROPN
cana-3106	85	13	))+	))+	PROPN
cana-3106	85	14	k	k	X
cana-3106	86	1	]	]	X
cana-3106	86	2	,	,	PUNCT
cana-3106	86	3	where	where	SCONJ
cana-3106	86	4	k	k	PROPN
cana-3106	86	5	=	=	PRON
cana-3106	86	6	{	{	PUNCT
cana-3106	86	7	(	(	PUNCT
cana-3106	86	8	𝑠2+𝑟2)−(𝑠1+𝑟1	𝑠2+𝑟2)−(𝑠1+𝑟1	PROPN
cana-3106	86	9	)	)	PUNCT
cana-3106	86	10	2	2	NUM
cana-3106	86	11	}	}	PUNCT
cana-3106	86	12	.	.	PUNCT
cana-3106	87	1	scalar	scalar	ADJ
cana-3106	87	2	multiplication	multiplication	NOUN
cana-3106	87	3	:	:	PUNCT
cana-3106	87	4	let	let	VERB
cana-3106	87	5	𝜆	𝜆	PRON
cana-3106	87	6	∈	∈	PROPN
cana-3106	87	7	ℝ	ℝ	PROPN
cana-3106	87	8	then	then	ADV
cana-3106	87	9	𝜆	𝜆	PROPN
cana-3106	87	10	�	�	PROPN
cana-3106	87	11	̃	̃	NOUN
cana-3106	87	12	�	�	NOUN
cana-3106	87	13	=	=	PUNCT
cana-3106	88	1	[	[	X
cana-3106	88	2	𝜆𝑟1	𝜆𝑟1	X
cana-3106	88	3	,	,	PUNCT
cana-3106	88	4	𝜆𝑟2	𝜆𝑟2	PROPN
cana-3106	88	5	]	]	PUNCT
cana-3106	88	6	for	for	ADP
cana-3106	88	7	𝜆	𝜆	DET
cana-3106	88	8	≥	≥	NOUN
cana-3106	88	9	0	0	NUM
cana-3106	88	10	,	,	PUNCT
cana-3106	88	11	[	[	X
cana-3106	88	12	𝜆𝑟2	𝜆𝑟2	NOUN
cana-3106	88	13	,	,	PUNCT
cana-3106	88	14	𝜆𝑟1	𝜆𝑟1	PROPN
cana-3106	88	15	]	]	PUNCT
cana-3106	88	16	for	for	ADP
cana-3106	88	17	𝜆	𝜆	PRON
cana-3106	88	18	<	<	X
cana-3106	88	19	0	0	NUM
cana-3106	88	20	.	.	PUNCT
cana-3106	88	21	multiplication	multiplication	NOUN
cana-3106	88	22	:	:	PUNCT
cana-3106	88	23	�	�	PROPN
cana-3106	88	24	̃	̃	PROPN
cana-3106	88	25	�	�	PROPN
cana-3106	88	26	�	�	PROPN
cana-3106	88	27	̃	̃	PROPN
cana-3106	88	28	�	�	NOUN
cana-3106	88	29	=	=	PUNCT
cana-3106	88	30	[	[	X
cana-3106	88	31	𝑟1	𝑟1	NOUN
cana-3106	88	32	,	,	PUNCT
cana-3106	88	33	𝑟2	𝑟2	NOUN
cana-3106	88	34	]	]	PUNCT
cana-3106	88	35	[	[	PUNCT
cana-3106	88	36	𝑠1	𝑠1	NOUN
cana-3106	88	37	,	,	PUNCT
cana-3106	88	38	𝑠2	𝑠2	NOUN
cana-3106	88	39	]	]	PUNCT
cana-3106	88	40	=	=	SYM
cana-3106	89	1	[	[	X
cana-3106	89	2	(	(	PUNCT
cana-3106	89	3	m(	m(	PROPN
cana-3106	89	4	�	�	PROPN
cana-3106	89	5	̃	̃	PROPN
cana-3106	89	6	�	�	PROPN
cana-3106	89	7	)	)	PUNCT
cana-3106	89	8	m(	m(	PROPN
cana-3106	89	9	�	�	PROPN
cana-3106	89	10	̃	̃	PROPN
cana-3106	89	11	�	�	PROPN
cana-3106	89	12	)	)	PUNCT
cana-3106	89	13	)	)	PUNCT
cana-3106	90	1	k	k	NOUN
cana-3106	90	2	,	,	PUNCT
cana-3106	90	3	(	(	PUNCT
cana-3106	90	4	m(	m(	PROPN
cana-3106	90	5	�	�	PROPN
cana-3106	90	6	̃	̃	PROPN
cana-3106	90	7	�	�	PROPN
cana-3106	90	8	)	)	PUNCT
cana-3106	90	9	m(	m(	PROPN
cana-3106	90	10	�	�	PROPN
cana-3106	90	11	̃	̃	PROPN
cana-3106	90	12	�	�	PROPN
cana-3106	90	13	)	)	PUNCT
cana-3106	90	14	)	)	PUNCT
cana-3106	91	1	+	+	CCONJ
cana-3106	91	2	k	k	X
cana-3106	91	3	]	]	X
cana-3106	91	4	,	,	PUNCT
cana-3106	91	5	communications	communication	NOUN
cana-3106	91	6	on	on	ADP
cana-3106	91	7	applied	apply	VERB
cana-3106	91	8	nonlinear	nonlinear	ADJ
cana-3106	91	9	analysis	analysis	NOUN
cana-3106	91	10	issn	issn	NOUN
cana-3106	91	11	:	:	PUNCT
cana-3106	91	12	1074	1074	NUM
cana-3106	91	13	-	-	PUNCT
cana-3106	91	14	133x	133x	NUM
cana-3106	91	15	vol	vol	NOUN
cana-3106	91	16	32	32	NUM
cana-3106	91	17	no	no	NOUN
cana-3106	91	18	.	.	PUNCT
cana-3106	92	1	5s	5s	NUM
cana-3106	92	2	(	(	PUNCT
cana-3106	92	3	2024	2024	NUM
cana-3106	92	4	)	)	PUNCT
cana-3106	92	5	356	356	NUM
cana-3106	92	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3106	92	7	where	where	SCONJ
cana-3106	92	8	k	k	PROPN
cana-3106	92	9	=	=	SYM
cana-3106	92	10	min{(m(	min{(m(	PROPN
cana-3106	92	11	�	�	PROPN
cana-3106	92	12	̃	̃	PROPN
cana-3106	92	13	�	�	PROPN
cana-3106	92	14	)m(	)m(	SYM
cana-3106	92	15	�	�	PROPN
cana-3106	92	16	̃	̃	PROPN
cana-3106	92	17	�	�	PROPN
cana-3106	92	18	)	)	PUNCT
cana-3106	92	19	)	)	PUNCT
cana-3106	93	1	−	−	PROPN
cana-3106	93	2	α	α	X
cana-3106	93	3	,	,	PUNCT
cana-3106	93	4	β	β	X
cana-3106	93	5	−	−	PROPN
cana-3106	93	6	(	(	PUNCT
cana-3106	93	7	m(	m(	PROPN
cana-3106	93	8	�	�	PROPN
cana-3106	93	9	̃	̃	PROPN
cana-3106	93	10	�	�	PROPN
cana-3106	93	11	)m(	)m(	SYM
cana-3106	93	12	�	�	PROPN
cana-3106	93	13	̃	̃	PROPN
cana-3106	93	14	�	�	PROPN
cana-3106	93	15	)	)	PUNCT
cana-3106	93	16	)	)	PUNCT
cana-3106	93	17	}	}	PUNCT
cana-3106	93	18	,	,	PUNCT
cana-3106	93	19	α	α	PROPN
cana-3106	93	20	=	=	SYM
cana-3106	93	21	min	min	PROPN
cana-3106	93	22	(	(	PUNCT
cana-3106	93	23	𝑟1𝑠1	𝑟1𝑠1	NOUN
cana-3106	93	24	,	,	PUNCT
cana-3106	93	25	𝑟1𝑠2	𝑟1𝑠2	NOUN
cana-3106	93	26	,	,	PUNCT
cana-3106	93	27	𝑠2𝑟1	𝑠2𝑟1	PROPN
cana-3106	93	28	,	,	PUNCT
cana-3106	93	29	𝑟2𝑠2	𝑟2𝑠2	NUM
cana-3106	93	30	)	)	PUNCT
cana-3106	93	31	and	and	CCONJ
cana-3106	93	32	β	β	X
cana-3106	93	33	=	=	SYM
cana-3106	93	34	max(𝑟1𝑠1	max(𝑟1𝑠1	PROPN
cana-3106	93	35	,	,	PUNCT
cana-3106	93	36	𝑟1𝑠2	𝑟1𝑠2	NOUN
cana-3106	93	37	,	,	PUNCT
cana-3106	93	38	𝑠2𝑟1	𝑠2𝑟1	PROPN
cana-3106	93	39	,	,	PUNCT
cana-3106	93	40	𝑟2𝑠2	𝑟2𝑠2	NOUN
cana-3106	93	41	)	)	PUNCT
cana-3106	93	42	.	.	PUNCT
cana-3106	94	1	inverse	inverse	NOUN
cana-3106	94	2	:	:	PUNCT
cana-3106	94	3	𝑟−1̃	𝑟−1̃	PUNCT
cana-3106	94	4	=	=	PUNCT
cana-3106	95	1	[	[	X
cana-3106	95	2	𝑟1	𝑟1	NOUN
cana-3106	95	3	,	,	PUNCT
cana-3106	95	4	𝑟2	𝑟2	NOUN
cana-3106	95	5	]	]	PUNCT
cana-3106	95	6	−1	−1	NOUN
cana-3106	95	7	=	=	SYM
cana-3106	95	8	1	1	NUM
cana-3106	96	1	[	[	X
cana-3106	96	2	𝑟1,𝑟2	𝑟1,𝑟2	NOUN
cana-3106	96	3	]	]	X
cana-3106	96	4	=	=	PUNCT
cana-3106	96	5	[	[	PUNCT
cana-3106	96	6	1	1	NUM
cana-3106	96	7	[	[	X
cana-3106	96	8	𝑟1,𝑟2	𝑟1,𝑟2	NOUN
cana-3106	96	9	]	]	X
cana-3106	96	10	−	−	PROPN
cana-3106	96	11	𝑘	𝑘	ADP
cana-3106	96	12	,	,	PUNCT
cana-3106	96	13	1	1	NUM
cana-3106	96	14	[	[	X
cana-3106	96	15	𝑟1,𝑟2	𝑟1,𝑟2	NOUN
cana-3106	96	16	]	]	X
cana-3106	97	1	+	+	X
cana-3106	97	2	k	k	X
cana-3106	97	3	]	]	X
cana-3106	97	4	,	,	PUNCT
cana-3106	97	5	where	where	SCONJ
cana-3106	97	6	k	k	PROPN
cana-3106	97	7	=	=	SYM
cana-3106	97	8	min	min	PROPN
cana-3106	97	9	{	{	PUNCT
cana-3106	97	10	1	1	NUM
cana-3106	97	11	𝑟2	𝑟2	NOUN
cana-3106	97	12	(	(	PUNCT
cana-3106	97	13	𝑟2−𝑟1	𝑟2−𝑟1	NUM
cana-3106	97	14	𝑟1+𝑟2	𝑟1+𝑟2	NOUN
cana-3106	97	15	)	)	PUNCT
cana-3106	97	16	,	,	PUNCT
cana-3106	97	17	1	1	NUM
cana-3106	97	18	𝑟1	𝑟1	NOUN
cana-3106	97	19	(	(	PUNCT
cana-3106	97	20	𝑟2−𝑟1	𝑟2−𝑟1	NUM
cana-3106	97	21	𝑟1+𝑟2	𝑟1+𝑟2	NOUN
cana-3106	97	22	)	)	PUNCT
cana-3106	97	23	}	}	PUNCT
cana-3106	97	24	,	,	PUNCT
cana-3106	97	25	0∈	0∈	NOUN
cana-3106	98	1	[	[	X
cana-3106	98	2	𝑟1	𝑟1	NOUN
cana-3106	98	3	,	,	PUNCT
cana-3106	98	4	𝑟2	𝑟2	NOUN
cana-3106	98	5	]	]	PUNCT
cana-3106	98	6	.	.	PUNCT
cana-3106	99	1	2.5	2.5	NUM
cana-3106	99	2	graded	grade	VERB
cana-3106	99	3	mean	mean	NOUN
cana-3106	99	4	integration	integration	NOUN
cana-3106	99	5	method	method	NOUN
cana-3106	99	6	[	[	X
cana-3106	99	7	3	3	X
cana-3106	99	8	]	]	PUNCT
cana-3106	99	9	a	a	DET
cana-3106	99	10	triangular	triangular	NOUN
cana-3106	99	11	fuzzy	fuzzy	ADJ
cana-3106	99	12	number	number	NOUN
cana-3106	99	13	a	a	PRON
cana-3106	99	14	~	~	PUNCT
cana-3106	99	15	=	=	SYM
cana-3106	99	16	(	(	PUNCT
cana-3106	99	17	g1	g1	PROPN
cana-3106	99	18	,	,	PUNCT
cana-3106	99	19	g2	g2	PROPN
cana-3106	99	20	,	,	PUNCT
cana-3106	99	21	g3	g3	PROPN
cana-3106	99	22	)	)	PUNCT
cana-3106	99	23	,	,	PUNCT
cana-3106	99	24	then	then	ADV
cana-3106	99	25	the	the	DET
cana-3106	99	26	defuzzification	defuzzification	NOUN
cana-3106	99	27	of	of	ADP
cana-3106	99	28	the	the	DET
cana-3106	99	29	fn	fn	NOUN
cana-3106	99	30	is	be	AUX
cana-3106	99	31	p	p	X
cana-3106	99	32	(	(	PUNCT
cana-3106	99	33	a	a	PRON
cana-3106	99	34	~	~	PUNCT
cana-3106	99	35	)	)	PUNCT
cana-3106	99	36	=(	=(	NOUN
cana-3106	99	37	g1	g1	PROPN
cana-3106	99	38	+	+	NUM
cana-3106	99	39	2g2	2g2	NUM
cana-3106	99	40	+	+	CCONJ
cana-3106	99	41	g3	g3	NOUN
cana-3106	99	42	)	)	PUNCT
cana-3106	99	43	/	/	SYM
cana-3106	99	44	4	4	NUM
cana-3106	99	45	.	.	SYM
cana-3106	99	46	2.6	2.6	NUM
cana-3106	99	47	fuzzy	fuzzy	ADJ
cana-3106	99	48	linear	linear	ADJ
cana-3106	99	49	complementarity	complementarity	NOUN
cana-3106	99	50	problem	problem	NOUN
cana-3106	99	51	the	the	DET
cana-3106	99	52	parameters	parameter	NOUN
cana-3106	99	53	in	in	ADP
cana-3106	99	54	(	(	PUNCT
cana-3106	99	55	1.1	1.1	NUM
cana-3106	99	56	)	)	PUNCT
cana-3106	99	57	(	(	PUNCT
cana-3106	99	58	1.3	1.3	NUM
cana-3106	99	59	)	)	PUNCT
cana-3106	99	60	are	be	AUX
cana-3106	99	61	fuzzy	fuzzy	ADJ
cana-3106	99	62	numbers	number	NOUN
cana-3106	99	63	.	.	PUNCT
cana-3106	100	1	then	then	ADV
cana-3106	100	2	,	,	PUNCT
cana-3106	100	3	by	by	ADP
cana-3106	100	4	substituting	substitute	VERB
cana-3106	100	5	fuzzy	fuzzy	ADJ
cana-3106	100	6	numbers	number	NOUN
cana-3106	100	7	for	for	ADP
cana-3106	100	8	crisp	crisp	ADJ
cana-3106	100	9	parameters	parameter	NOUN
cana-3106	100	10	,	,	PUNCT
cana-3106	100	11	the	the	DET
cana-3106	100	12	ensuing	ensue	VERB
cana-3106	100	13	flcp	flcp	NOUN
cana-3106	100	14	can	can	AUX
cana-3106	100	15	be	be	AUX
cana-3106	100	16	identified	identify	VERB
cana-3106	100	17	.	.	PUNCT
cana-3106	101	1	�	�	PROPN
cana-3106	101	2	̃	̃	PROPN
cana-3106	101	3	�	�	PROPN
cana-3106	101	4	-	-	PUNCT
cana-3106	101	5	�	�	PROPN
cana-3106	101	6	̃	̃	PROPN
cana-3106	101	7	�	�	PROPN
cana-3106	101	8	�	�	PROPN
cana-3106	101	9	̃	̃	PROPN
cana-3106	101	10	�	�	PROPN
cana-3106	101	11	=	=	SYM
cana-3106	101	12	�	�	PROPN
cana-3106	101	13	̃	̃	PROPN
cana-3106	101	14	�	�	PROPN
cana-3106	101	15	(	(	PUNCT
cana-3106	101	16	2.6.1	2.6.1	NUM
cana-3106	101	17	)	)	PUNCT
cana-3106	101	18	�	�	PROPN
cana-3106	101	19	̃	̃	PROPN
cana-3106	101	20	�	�	PROPN
cana-3106	101	21	𝑗	𝑗	PROPN
cana-3106	101	22	≥	≥	NUM
cana-3106	101	23	0	0	NUM
cana-3106	101	24	,	,	PUNCT
cana-3106	101	25	�	�	PROPN
cana-3106	101	26	̃	̃	PROPN
cana-3106	101	27	�	�	PROPN
cana-3106	101	28	𝑗	𝑗	PROPN
cana-3106	101	29	≥	≥	NUM
cana-3106	101	30	0	0	NUM
cana-3106	101	31	,	,	PUNCT
cana-3106	101	32	�	�	PROPN
cana-3106	101	33	̃	̃	PROPN
cana-3106	101	34	�	�	PROPN
cana-3106	101	35	0	0	NUM
cana-3106	101	36	≥	≥	NOUN
cana-3106	101	37	0	0	NUM
cana-3106	101	38	,	,	PUNCT
cana-3106	101	39	𝑗	𝑗	NOUN
cana-3106	101	40	=	=	SYM
cana-3106	101	41	1	1	NUM
cana-3106	101	42	,	,	PUNCT
cana-3106	101	43	…	…	PUNCT
cana-3106	101	44	,	,	PUNCT
cana-3106	101	45	𝑛	𝑛	X
cana-3106	101	46	(	(	PUNCT
cana-3106	101	47	2.6.2	2.6.2	NUM
cana-3106	101	48	)	)	PUNCT
cana-3106	101	49	�	�	PROPN
cana-3106	101	50	̃	̃	PROPN
cana-3106	101	51	�	�	PROPN
cana-3106	101	52	𝑗	𝑗	PROPN
cana-3106	101	53	�	�	PROPN
cana-3106	101	54	̃	̃	PROPN
cana-3106	101	55	�	�	NOUN
cana-3106	101	56	𝑗	𝑗	NOUN
cana-3106	101	57	=	=	SYM
cana-3106	101	58	0	0	NUM
cana-3106	101	59	,	,	PUNCT
cana-3106	101	60	𝑗	𝑗	NOUN
cana-3106	101	61	=	=	SYM
cana-3106	101	62	1	1	NUM
cana-3106	101	63	,	,	PUNCT
cana-3106	101	64	…	…	PUNCT
cana-3106	101	65	,	,	PUNCT
cana-3106	101	66	𝑛	𝑛	X
cana-3106	101	67	(	(	PUNCT
cana-3106	101	68	2.6.3	2.6.3	NUM
cana-3106	101	69	)	)	PUNCT
cana-3106	101	70	the	the	DET
cana-3106	101	71	pair	pair	NOUN
cana-3106	101	72	(	(	PUNCT
cana-3106	101	73	�	�	PROPN
cana-3106	101	74	̃	̃	NOUN
cana-3106	101	75	�	�	NOUN
cana-3106	101	76	𝑗	𝑗	PROPN
cana-3106	101	77	,	,	PUNCT
cana-3106	101	78	�	�	PROPN
cana-3106	101	79	̃	̃	PROPN
cana-3106	101	80	�	�	NOUN
cana-3106	101	81	𝑗	𝑗	NOUN
cana-3106	101	82	)	)	PUNCT
cana-3106	101	83	is	be	AUX
cana-3106	101	84	said	say	VERB
cana-3106	101	85	to	to	PART
cana-3106	101	86	be	be	AUX
cana-3106	101	87	a	a	DET
cana-3106	101	88	pair	pair	NOUN
cana-3106	101	89	of	of	ADP
cana-3106	101	90	fuzzy	fuzzy	ADJ
cana-3106	101	91	complementary	complementary	ADJ
cana-3106	101	92	variables	variable	NOUN
cana-3106	101	93	.	.	PUNCT
cana-3106	102	1	3	3	X
cana-3106	102	2	.	.	X
cana-3106	102	3	algorithm	algorithm	NOUN
cana-3106	102	4	for	for	ADP
cana-3106	102	5	the	the	DET
cana-3106	102	6	fuzzy	fuzzy	ADJ
cana-3106	102	7	fractional	fractional	ADJ
cana-3106	102	8	linear	linear	ADJ
cana-3106	102	9	complementarity	complementarity	NOUN
cana-3106	102	10	problem	problem	NOUN
cana-3106	102	11	step	step	NOUN
cana-3106	102	12	1	1	NUM
cana-3106	102	13	:	:	PUNCT
cana-3106	102	14	consider	consider	VERB
cana-3106	102	15	the	the	DET
cana-3106	102	16	constraints	constraint	NOUN
cana-3106	102	17	of	of	ADP
cana-3106	102	18	the	the	DET
cana-3106	102	19	fpp	fpp	PROPN
cana-3106	102	20	as	as	ADP
cana-3106	102	21	a	a	DET
cana-3106	102	22	triangular	triangular	NOUN
cana-3106	102	23	fuzzy	fuzzy	ADJ
cana-3106	102	24	number	number	NOUN
cana-3106	102	25	.	.	PUNCT
cana-3106	103	1	step	step	NOUN
cana-3106	103	2	2	2	NUM
cana-3106	103	3	:	:	PUNCT
cana-3106	103	4	rewrite	rewrite	VERB
cana-3106	103	5	the	the	DET
cana-3106	103	6	constraints	constraint	NOUN
cana-3106	103	7	in	in	ADP
cana-3106	103	8	terms	term	NOUN
cana-3106	103	9	of	of	ADP
cana-3106	103	10	linear	linear	ADJ
cana-3106	103	11	programming	programming	NOUN
cana-3106	103	12	problem	problem	NOUN
cana-3106	103	13	.	.	PUNCT
cana-3106	104	1	step	step	NOUN
cana-3106	104	2	3	3	NUM
cana-3106	104	3	:	:	PUNCT
cana-3106	104	4	using	use	VERB
cana-3106	104	5	the	the	DET
cana-3106	104	6	conversion	conversion	NOUN
cana-3106	104	7	algorithm	algorithm	NOUN
cana-3106	104	8	of	of	ADP
cana-3106	104	9	lpp	lpp	PROPN
cana-3106	104	10	in	in	ADP
cana-3106	104	11	to	to	ADP
cana-3106	104	12	lcp	lcp	PROPN
cana-3106	104	13	[	[	X
cana-3106	104	14	17	17	NUM
cana-3106	104	15	]	]	PUNCT
cana-3106	104	16	,	,	PUNCT
cana-3106	104	17	the	the	DET
cana-3106	104	18	given	give	VERB
cana-3106	104	19	values	value	NOUN
cana-3106	104	20	can	can	AUX
cana-3106	104	21	be	be	AUX
cana-3106	104	22	converted	convert	VERB
cana-3106	104	23	into	into	ADP
cana-3106	104	24	complementarity	complementarity	NOUN
cana-3106	104	25	values	value	NOUN
cana-3106	104	26	.	.	PUNCT
cana-3106	105	1	step	step	NOUN
cana-3106	105	2	4	4	NUM
cana-3106	105	3	:	:	PUNCT
cana-3106	105	4	convert	convert	VERB
cana-3106	105	5	the	the	DET
cana-3106	105	6	parameters	parameter	NOUN
cana-3106	105	7	and	and	CCONJ
cana-3106	105	8	variables	variable	NOUN
cana-3106	105	9	in	in	ADP
cana-3106	105	10	interval	interval	NOUN
cana-3106	105	11	number	number	NOUN
cana-3106	105	12	by	by	ADP
cana-3106	105	13	taking	take	VERB
cana-3106	105	14	different	different	ADJ
cana-3106	105	15	levels	level	NOUN
cana-3106	105	16	of	of	ADP
cana-3106	105	17	𝛼	𝛼	NOUN
cana-3106	105	18	–	–	PUNCT
cana-3106	105	19	cut	cut	NOUN
cana-3106	105	20	.	.	PUNCT
cana-3106	106	1	step	step	NOUN
cana-3106	106	2	5	5	NUM
cana-3106	106	3	:	:	PUNCT
cana-3106	106	4	the	the	DET
cana-3106	106	5	converted	converted	ADJ
cana-3106	106	6	systems	system	NOUN
cana-3106	106	7	can	can	AUX
cana-3106	106	8	be	be	AUX
cana-3106	106	9	solved	solve	VERB
cana-3106	106	10	according	accord	VERB
cana-3106	106	11	to	to	ADP
cana-3106	106	12	the	the	DET
cana-3106	106	13	lemke	lemke	NOUN
cana-3106	106	14	’s	’s	PART
cana-3106	106	15	algorithm	algorithm	NOUN
cana-3106	107	1	[	[	X
cana-3106	107	2	18	18	NUM
cana-3106	107	3	]	]	PUNCT
cana-3106	107	4	.	.	PUNCT
cana-3106	108	1	step	step	NOUN
cana-3106	108	2	6	6	NUM
cana-3106	108	3	:	:	PUNCT
cana-3106	108	4	consider	consider	VERB
cana-3106	108	5	the	the	DET
cana-3106	108	6	flcp	flcp	NOUN
cana-3106	108	7	(	(	PUNCT
cana-3106	108	8	�	�	PROPN
cana-3106	108	9	̃	̃	PROPN
cana-3106	108	10	�	�	PROPN
cana-3106	108	11	,	,	PUNCT
cana-3106	108	12	�	�	PROPN
cana-3106	108	13	̃	̃	PROPN
cana-3106	108	14	�	�	PROPN
cana-3106	108	15	)	)	PUNCT
cana-3106	108	16	of	of	ADP
cana-3106	108	17	order	order	NOUN
cana-3106	108	18	n	n	CCONJ
cana-3106	108	19	,	,	PUNCT
cana-3106	108	20	and	and	CCONJ
cana-3106	108	21	𝑞	𝑞	X
cana-3106	108	22	𝜖	𝜖	X
cana-3106	108	23	ℝ𝑛	ℝ𝑛	PROPN
cana-3106	108	24	satisfies	satisfy	VERB
cana-3106	108	25	the	the	DET
cana-3106	108	26	condition	condition	NOUN
cana-3106	108	27	�	�	PROPN
cana-3106	108	28	̃	̃	PROPN
cana-3106	108	29	�	�	PROPN
cana-3106	108	30	�	�	PROPN
cana-3106	108	31	̃	̃	PROPN
cana-3106	108	32	�	�	PROPN
cana-3106	108	33	𝐼	𝐼	PROPN
cana-3106	108	34	�	�	PROPN
cana-3106	108	35	̃	̃	PROPN
cana-3106	108	36	�	�	PROPN
cana-3106	108	37	�	�	PROPN
cana-3106	108	38	̃	̃	PROPN
cana-3106	108	39	�	�	PROPN
cana-3106	108	40	step	step	NOUN
cana-3106	108	41	7	7	NUM
cana-3106	108	42	:	:	PUNCT
cana-3106	108	43	identify	identify	VERB
cana-3106	108	44	t	t	PROPN
cana-3106	108	45	=	=	SYM
cana-3106	108	46	�	�	PROPN
cana-3106	108	47	̃	̃	PROPN
cana-3106	108	48	�	�	PROPN
cana-3106	108	49	𝑡	𝑡	PROPN
cana-3106	108	50	�	�	PROPN
cana-3106	108	51	̃	̃	NOUN
cana-3106	108	52	�	�	PROPN
cana-3106	108	53	𝑡𝑠	𝑡𝑠	ADJ
cana-3106	108	54	=	=	ADJ
cana-3106	108	55	𝑚𝑖𝑛𝑖𝑚𝑢𝑚	𝑚𝑖𝑛𝑖𝑚𝑢𝑚	NOUN
cana-3106	108	56	{	{	PUNCT
cana-3106	108	57	�	�	PROPN
cana-3106	108	58	̃	̃	NOUN
cana-3106	108	59	�	�	PROPN
cana-3106	108	60	𝑡	𝑡	PROPN
cana-3106	108	61	�	�	PROPN
cana-3106	108	62	̃	̃	NOUN
cana-3106	108	63	�	�	PROPN
cana-3106	108	64	𝑡𝑠	𝑡𝑠	NOUN
cana-3106	108	65	𝑖	𝑖	NOUN
cana-3106	108	66	=	=	SYM
cana-3106	108	67	1	1	NUM
cana-3106	108	68	𝑡𝑜	𝑡𝑜	NOUN
cana-3106	108	69	𝑛	𝑛	ADP
cana-3106	108	70	}	}	PUNCT
cana-3106	108	71	the	the	DET
cana-3106	108	72	column	column	NOUN
cana-3106	108	73	vector	vector	NOUN
cana-3106	108	74	on	on	ADP
cana-3106	108	75	the	the	DET
cana-3106	108	76	right	right	ADJ
cana-3106	108	77	side	side	NOUN
cana-3106	108	78	,	,	PUNCT
cana-3106	108	79	pivots	pivot	NOUN
cana-3106	108	80	and	and	CCONJ
cana-3106	108	81	becomes	become	VERB
cana-3106	108	82	nonnegative	nonnegative	ADJ
cana-3106	108	83	.	.	PUNCT
cana-3106	109	1	step	step	NOUN
cana-3106	109	2	8	8	NUM
cana-3106	109	3	:	:	PUNCT
cana-3106	109	4	the	the	DET
cana-3106	109	5	flcp	flcp	ADJ
cana-3106	109	6	solution	solution	NOUN
cana-3106	109	7	ends	end	VERB
cana-3106	109	8	if	if	SCONJ
cana-3106	109	9	s	s	NOUN
cana-3106	109	10	=	=	NOUN
cana-3106	109	11	t.	t.	NOUN
cana-3106	109	12	if	if	SCONJ
cana-3106	109	13	s	s	PROPN
cana-3106	109	14	≠	≠	PROPN
cana-3106	109	15	t	t	PROPN
cana-3106	109	16	,	,	PUNCT
cana-3106	109	17	then	then	ADV
cana-3106	109	18	there	there	PRON
cana-3106	109	19	is	be	VERB
cana-3106	109	20	precisely	precisely	ADV
cana-3106	109	21	one	one	NUM
cana-3106	109	22	fuzzy	fuzzy	ADJ
cana-3106	109	23	complementarity	complementarity	NOUN
cana-3106	109	24	pair	pair	NOUN
cana-3106	109	25	in	in	ADP
cana-3106	109	26	which	which	PRON
cana-3106	109	27	both	both	DET
cana-3106	109	28	variables	variable	NOUN
cana-3106	109	29	are	be	AUX
cana-3106	109	30	contained	contain	VERB
cana-3106	109	31	,	,	PUNCT
cana-3106	109	32	as	as	ADV
cana-3106	109	33	well	well	ADV
cana-3106	109	34	as	as	ADP
cana-3106	109	35	exactly	exactly	ADV
cana-3106	109	36	one	one	NUM
cana-3106	109	37	basic	basic	ADJ
cana-3106	109	38	variable	variable	NOUN
cana-3106	109	39	and	and	CCONJ
cana-3106	109	40	that	that	PRON
cana-3106	109	41	contains	contain	VERB
cana-3106	109	42	both	both	DET
cana-3106	109	43	variables	variable	NOUN
cana-3106	109	44	.	.	PUNCT
cana-3106	110	1	step	step	NOUN
cana-3106	110	2	9	9	NUM
cana-3106	110	3	:	:	PUNCT
cana-3106	110	4	choose	choose	VERB
cana-3106	110	5	�	�	PROPN
cana-3106	110	6	̃	̃	PROPN
cana-3106	110	7	�	�	NOUN
cana-3106	110	8	𝑠	𝑠	PROPN
cana-3106	110	9	as	as	ADP
cana-3106	110	10	entering	enter	VERB
cana-3106	110	11	variable	variable	NOUN
cana-3106	110	12	and	and	CCONJ
cana-3106	110	13	it	it	PRON
cana-3106	110	14	is	be	AUX
cana-3106	110	15	ascertained	ascertain	VERB
cana-3106	110	16	by	by	ADP
cana-3106	110	17	the	the	DET
cana-3106	110	18	complementary	complementary	ADJ
cana-3106	110	19	pivot	pivot	NOUN
cana-3106	110	20	rule	rule	NOUN
cana-3106	110	21	.	.	PUNCT
cana-3106	111	1	communications	communication	NOUN
cana-3106	111	2	on	on	ADP
cana-3106	111	3	applied	apply	VERB
cana-3106	111	4	nonlinear	nonlinear	ADJ
cana-3106	111	5	analysis	analysis	NOUN
cana-3106	111	6	issn	issn	NOUN
cana-3106	111	7	:	:	PUNCT
cana-3106	111	8	1074	1074	NUM
cana-3106	111	9	-	-	PUNCT
cana-3106	111	10	133x	133x	NUM
cana-3106	111	11	vol	vol	NOUN
cana-3106	111	12	32	32	NUM
cana-3106	111	13	no	no	NOUN
cana-3106	111	14	.	.	PUNCT
cana-3106	112	1	5s	5s	NUM
cana-3106	112	2	(	(	PUNCT
cana-3106	112	3	2024	2024	NUM
cana-3106	112	4	)	)	PUNCT
cana-3106	112	5	357	357	NUM
cana-3106	112	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3106	112	7	step	step	NOUN
cana-3106	112	8	10	10	NUM
cana-3106	112	9	:	:	PUNCT
cana-3106	112	10	finally	finally	ADV
cana-3106	112	11	,	,	PUNCT
cana-3106	112	12	one	one	NUM
cana-3106	112	13	variable	variable	NOUN
cana-3106	112	14	from	from	ADP
cana-3106	112	15	the	the	DET
cana-3106	112	16	complementary	complementary	ADJ
cana-3106	112	17	pair	pair	NOUN
cana-3106	112	18	either	either	CCONJ
cana-3106	112	19	drops	drop	VERB
cana-3106	112	20	out	out	ADP
cana-3106	112	21	from	from	ADP
cana-3106	112	22	the	the	DET
cana-3106	112	23	basic	basic	ADJ
cana-3106	112	24	vector	vector	NOUN
cana-3106	112	25	,	,	PUNCT
cana-3106	112	26	equals	equal	VERB
cana-3106	112	27	zero	zero	NUM
cana-3106	112	28	,	,	PUNCT
cana-3106	112	29	or	or	CCONJ
cana-3106	112	30	,	,	PUNCT
cana-3106	112	31	in	in	ADP
cana-3106	112	32	the	the	DET
cana-3106	112	33	case	case	NOUN
cana-3106	112	34	of	of	ADP
cana-3106	112	35	strictly	strictly	ADV
cana-3106	112	36	positive	positive	ADJ
cana-3106	112	37	in	in	ADP
cana-3106	112	38	basic	basic	ADJ
cana-3106	112	39	feasible	feasible	ADJ
cana-3106	112	40	solution	solution	NOUN
cana-3106	112	41	.	.	PUNCT
cana-3106	113	1	4	4	X
cana-3106	113	2	.	.	X
cana-3106	113	3	numerical	numerical	ADJ
cana-3106	113	4	illustration	illustration	NOUN
cana-3106	113	5	consider	consider	VERB
cana-3106	113	6	the	the	DET
cana-3106	113	7	following	follow	VERB
cana-3106	113	8	linear	linear	ADJ
cana-3106	113	9	fractional	fractional	ADJ
cana-3106	113	10	programming	programming	NOUN
cana-3106	113	11	problem	problem	NOUN
cana-3106	113	12	:	:	PUNCT
cana-3106	113	13	max	max	PROPN
cana-3106	113	14	z	z	PROPN
cana-3106	113	15	=	=	SYM
cana-3106	113	16	5𝑥1	5𝑥1	NUM
cana-3106	113	17	+	+	NOUN
cana-3106	113	18	6𝑥2	6𝑥2	NUM
cana-3106	113	19	2𝑥2	2𝑥2	NUM
cana-3106	113	20	+7	+7	NOUN
cana-3106	113	21	subject	subject	ADJ
cana-3106	113	22	to	to	ADP
cana-3106	113	23	the	the	DET
cana-3106	113	24	constraints	constraint	NOUN
cana-3106	113	25	:	:	PUNCT
cana-3106	113	26	2𝑥1	2𝑥1	NUM
cana-3106	113	27	+	+	CCONJ
cana-3106	113	28	3𝑥2	3𝑥2	NUM
cana-3106	113	29	≤	≤	NUM
cana-3106	113	30	6	6	NUM
cana-3106	113	31	2𝑥1	2𝑥1	NUM
cana-3106	113	32	+	+	CCONJ
cana-3106	113	33	𝑥2	𝑥2	NOUN
cana-3106	113	34	≤	≤	NUM
cana-3106	113	35	3	3	NUM
cana-3106	113	36	𝑥1	𝑥1	NOUN
cana-3106	113	37	,	,	PUNCT
cana-3106	113	38	𝑥2	𝑥2	NOUN
cana-3106	113	39	≥	≥	NOUN
cana-3106	113	40	0	0	NUM
cana-3106	113	41	.	.	PUNCT
cana-3106	114	1	the	the	DET
cana-3106	114	2	given	give	VERB
cana-3106	114	3	problem	problem	NOUN
cana-3106	114	4	can	can	AUX
cana-3106	114	5	be	be	AUX
cana-3106	114	6	developed	develop	VERB
cana-3106	114	7	by	by	ADP
cana-3106	114	8	the	the	DET
cana-3106	114	9	above	above	ADJ
cana-3106	114	10	proposed	propose	VERB
cana-3106	114	11	algorithm	algorithm	NOUN
cana-3106	114	12	and	and	CCONJ
cana-3106	114	13	it	it	PRON
cana-3106	114	14	is	be	AUX
cana-3106	114	15	converted	convert	VERB
cana-3106	114	16	by	by	ADP
cana-3106	114	17	means	mean	NOUN
cana-3106	114	18	of	of	ADP
cana-3106	114	19	conversion	conversion	NOUN
cana-3106	114	20	algorithm	algorithm	NOUN
cana-3106	114	21	of	of	ADP
cana-3106	114	22	linear	linear	PROPN
cana-3106	114	23	programming	programming	NOUN
cana-3106	114	24	problem	problem	NOUN
cana-3106	115	1	[	[	X
cana-3106	115	2	16	16	NUM
cana-3106	115	3	]	]	PUNCT
cana-3106	115	4	.	.	PUNCT
cana-3106	116	1	so	so	ADV
cana-3106	116	2	the	the	DET
cana-3106	116	3	following	follow	VERB
cana-3106	116	4	steps	step	NOUN
cana-3106	116	5	will	will	AUX
cana-3106	116	6	be	be	AUX
cana-3106	116	7	:	:	PUNCT
cana-3106	116	8	m	m	VERB
cana-3106	116	9	=	=	PUNCT
cana-3106	116	10	[	[	PUNCT
cana-3106	116	11	(	(	PUNCT
cana-3106	116	12	−1,0,1	−1,0,1	NOUN
cana-3106	116	13	)	)	PUNCT
cana-3106	116	14	(	(	PUNCT
cana-3106	116	15	0,0,0	0,0,0	NOUN
cana-3106	116	16	)	)	PUNCT
cana-3106	116	17	(	(	PUNCT
cana-3106	116	18	1,2,3	1,2,3	NOUN
cana-3106	116	19	)	)	PUNCT
cana-3106	116	20	(	(	PUNCT
cana-3106	116	21	0,2,4	0,2,4	NOUN
cana-3106	116	22	)	)	PUNCT
cana-3106	116	23	(	(	PUNCT
cana-3106	116	24	0,0,0	0,0,0	NOUN
cana-3106	116	25	)	)	PUNCT
cana-3106	116	26	(	(	PUNCT
cana-3106	116	27	−1,0,1	−1,0,1	NOUN
cana-3106	116	28	)	)	PUNCT
cana-3106	116	29	(	(	PUNCT
cana-3106	116	30	2,3,4	2,3,4	NUM
cana-3106	116	31	)	)	PUNCT
cana-3106	116	32	(	(	PUNCT
cana-3106	116	33	0,1,2	0,1,2	X
cana-3106	116	34	)	)	PUNCT
cana-3106	116	35	(	(	PUNCT
cana-3106	116	36	−3,−2,−1	−3,−2,−1	NOUN
cana-3106	116	37	)	)	PUNCT
cana-3106	116	38	(	(	PUNCT
cana-3106	116	39	−4,−3,−2	−4,−3,−2	NUM
cana-3106	116	40	)	)	PUNCT
cana-3106	116	41	(	(	PUNCT
cana-3106	116	42	−2,0,2	−2,0,2	NOUN
cana-3106	116	43	)	)	PUNCT
cana-3106	116	44	(	(	PUNCT
cana-3106	116	45	0,0,0	0,0,0	NOUN
cana-3106	116	46	)	)	PUNCT
cana-3106	116	47	(	(	PUNCT
cana-3106	116	48	−3,−2,−1	−3,−2,−1	NOUN
cana-3106	116	49	)	)	PUNCT
cana-3106	116	50	(	(	PUNCT
cana-3106	116	51	−2,−1,0	−2,−1,0	ADV
cana-3106	116	52	)	)	PUNCT
cana-3106	116	53	(	(	PUNCT
cana-3106	116	54	0,0,0	0,0,0	NOUN
cana-3106	116	55	)	)	PUNCT
cana-3106	116	56	(	(	PUNCT
cana-3106	116	57	−1,0,1	−1,0,1	NOUN
cana-3106	116	58	)	)	PUNCT
cana-3106	116	59	]	]	PUNCT
cana-3106	116	60	,	,	PUNCT
cana-3106	116	61	q	q	X
cana-3106	117	1	=	=	PUNCT
cana-3106	117	2	[	[	PUNCT
cana-3106	117	3	(	(	PUNCT
cana-3106	117	4	3,5,7	3,5,7	NUM
cana-3106	117	5	)	)	PUNCT
cana-3106	117	6	(	(	PUNCT
cana-3106	117	7	5,6,7	5,6,7	NOUN
cana-3106	117	8	)	)	PUNCT
cana-3106	117	9	(	(	PUNCT
cana-3106	117	10	−8,−6,−4	−8,−6,−4	NOUN
cana-3106	117	11	)	)	PUNCT
cana-3106	117	12	(	(	PUNCT
cana-3106	117	13	−5,−3,−1	−5,−3,−1	NUM
cana-3106	117	14	)	)	PUNCT
cana-3106	117	15	]	]	PUNCT
cana-3106	118	1	therefore	therefore	ADV
cana-3106	118	2	x1	x1	PROPN
cana-3106	118	3	=	=	SYM
cana-3106	118	4	z1	z1	PROPN
cana-3106	118	5	and	and	CCONJ
cana-3106	118	6	x2	x2	NOUN
cana-3106	118	7	=	=	SYM
cana-3106	118	8	z2	z2	PROPN
cana-3106	118	9	will	will	AUX
cana-3106	118	10	be	be	AUX
cana-3106	118	11	an	an	DET
cana-3106	118	12	optimal	optimal	ADJ
cana-3106	118	13	solution	solution	NOUN
cana-3106	118	14	to	to	ADP
cana-3106	118	15	the	the	DET
cana-3106	118	16	given	give	VERB
cana-3106	118	17	lpp	lpp	PROPN
cana-3106	118	18	.	.	PUNCT
cana-3106	119	1	the	the	DET
cana-3106	119	2	constraints	constraint	NOUN
cana-3106	119	3	of	of	ADP
cana-3106	119	4	the	the	DET
cana-3106	119	5	fractional	fractional	ADJ
cana-3106	119	6	programming	programming	NOUN
cana-3106	119	7	problem	problem	NOUN
cana-3106	119	8	is	be	AUX
cana-3106	119	9	taken	take	VERB
cana-3106	119	10	as	as	ADP
cana-3106	119	11	an	an	DET
cana-3106	119	12	interval	interval	NOUN
cana-3106	119	13	number	number	NOUN
cana-3106	119	14	with	with	ADP
cana-3106	119	15	different	different	ADJ
cana-3106	119	16	levels	level	NOUN
cana-3106	119	17	of	of	ADP
cana-3106	119	18	𝛼	𝛼	PROPN
cana-3106	119	19	cut	cut	NOUN
cana-3106	119	20	.	.	PUNCT
cana-3106	120	1	after	after	ADP
cana-3106	120	2	attempting	attempt	VERB
cana-3106	120	3	these	these	DET
cana-3106	120	4	steps	step	NOUN
cana-3106	120	5	the	the	DET
cana-3106	120	6	following	follow	VERB
cana-3106	120	7	equations	equation	NOUN
cana-3106	120	8	are	be	AUX
cana-3106	120	9	given	give	VERB
cana-3106	120	10	below	below	ADP
cana-3106	120	11	,	,	PUNCT
cana-3106	120	12	when	when	SCONJ
cana-3106	120	13	𝛼	𝛼	X
cana-3106	120	14	=	=	SYM
cana-3106	120	15	1	1	NUM
cana-3106	120	16	,	,	PUNCT
cana-3106	120	17	w	w	PROPN
cana-3106	120	18	mz	mz	PROPN
cana-3106	120	19	=	=	SYM
cana-3106	120	20	q	q	PROPN
cana-3106	120	21	,	,	PUNCT
cana-3106	120	22	gives	give	VERB
cana-3106	120	23	[	[	PUNCT
cana-3106	120	24	𝑤1	𝑤1	VERB
cana-3106	120	25	𝑤2	𝑤2	NOUN
cana-3106	120	26	𝑤3	𝑤3	NOUN
cana-3106	120	27	𝑤4	𝑤4	NOUN
cana-3106	120	28	]	]	PUNCT
cana-3106	120	29	[	[	PUNCT
cana-3106	120	30	[	[	X
cana-3106	120	31	0,0	0,0	NOUN
cana-3106	120	32	]	]	PUNCT
cana-3106	120	33	[	[	X
cana-3106	120	34	0,0	0,0	NOUN
cana-3106	120	35	]	]	X
cana-3106	121	1	[	[	X
cana-3106	121	2	2,2	2,2	NUM
cana-3106	121	3	]	]	X
cana-3106	121	4	[	[	X
cana-3106	121	5	2,2	2,2	NUM
cana-3106	121	6	]	]	X
cana-3106	122	1	[	[	X
cana-3106	122	2	0,0	0,0	NOUN
cana-3106	122	3	]	]	PUNCT
cana-3106	123	1	[	[	X
cana-3106	123	2	0,0	0,0	NOUN
cana-3106	123	3	]	]	X
cana-3106	124	1	[	[	X
cana-3106	124	2	3,3	3,3	X
cana-3106	124	3	]	]	X
cana-3106	124	4	[	[	X
cana-3106	124	5	1,1	1,1	NUM
cana-3106	124	6	]	]	X
cana-3106	125	1	[	[	X
cana-3106	125	2	−2,−2	−2,−2	VERB
cana-3106	125	3	]	]	X
cana-3106	125	4	[	[	X
cana-3106	125	5	−3,−3	−3,−3	X
cana-3106	125	6	]	]	X
cana-3106	125	7	[	[	X
cana-3106	125	8	0,0	0,0	NOUN
cana-3106	125	9	]	]	PUNCT
cana-3106	125	10	[	[	X
cana-3106	125	11	0,0	0,0	NOUN
cana-3106	125	12	]	]	X
cana-3106	125	13	[	[	X
cana-3106	125	14	−2,−2	−2,−2	VERB
cana-3106	125	15	]	]	X
cana-3106	126	1	[	[	X
cana-3106	126	2	−1,−1	−1,−1	X
cana-3106	126	3	]	]	X
cana-3106	126	4	[	[	X
cana-3106	126	5	0,0	0,0	NOUN
cana-3106	126	6	]	]	PUNCT
cana-3106	126	7	[	[	X
cana-3106	126	8	0,0	0,0	NOUN
cana-3106	126	9	]	]	X
cana-3106	126	10	]	]	X
cana-3106	126	11	[	[	PUNCT
cana-3106	126	12	𝑧1	𝑧1	PROPN
cana-3106	126	13	𝑧2	𝑧2	PROPN
cana-3106	126	14	𝑧3	𝑧3	PROPN
cana-3106	126	15	𝑧4	𝑧4	PROPN
cana-3106	126	16	]	]	PUNCT
cana-3106	126	17	=	=	PUNCT
cana-3106	127	1	[	[	PUNCT
cana-3106	127	2	[	[	X
cana-3106	127	3	5,5	5,5	NUM
cana-3106	127	4	]	]	PUNCT
cana-3106	128	1	[	[	X
cana-3106	128	2	6,6	6,6	NUM
cana-3106	128	3	]	]	X
cana-3106	129	1	[	[	X
cana-3106	129	2	−6,−6	−6,−6	X
cana-3106	129	3	]	]	X
cana-3106	129	4	[	[	X
cana-3106	129	5	−3,−3	−3,−3	X
cana-3106	129	6	]	]	X
cana-3106	129	7	]	]	X
cana-3106	129	8	the	the	DET
cana-3106	129	9	results	result	NOUN
cana-3106	129	10	are	be	AUX
cana-3106	129	11	tabulated	tabulate	VERB
cana-3106	129	12	below	below	ADV
cana-3106	129	13	,	,	PUNCT
cana-3106	129	14	table	table	NOUN
cana-3106	129	15	4.1	4.1	NUM
cana-3106	129	16	values	value	NOUN
cana-3106	129	17	are	be	AUX
cana-3106	129	18	taken	take	VERB
cana-3106	129	19	as	as	ADP
cana-3106	129	20	an	an	DET
cana-3106	129	21	interval	interval	NOUN
cana-3106	129	22	numbers	number	NOUN
cana-3106	129	23	,	,	PUNCT
cana-3106	129	24	the	the	DET
cana-3106	129	25	following	follow	VERB
cana-3106	129	26	iterations	iteration	NOUN
cana-3106	129	27	are	be	AUX
cana-3106	129	28	performed	perform	VERB
cana-3106	129	29	by	by	ADP
cana-3106	129	30	lemke	lemke	PROPN
cana-3106	129	31	’s	’s	PART
cana-3106	129	32	algorithm	algorithm	NOUN
cana-3106	129	33	.	.	PUNCT
cana-3106	130	1	bv	bv	PROPN
cana-3106	130	2	w1	w1	PROPN
cana-3106	130	3	w2	w2	PROPN
cana-3106	130	4	w3	w3	PROPN
cana-3106	130	5	w4	w4	PROPN
cana-3106	130	6	z1	z1	PROPN
cana-3106	130	7	z2	z2	PROPN
cana-3106	130	8	z3	z3	PROPN
cana-3106	130	9	z4	z4	PROPN
cana-3106	130	10	q	q	PROPN
cana-3106	130	11	w1	w1	PROPN
cana-3106	131	1	[	[	X
cana-3106	131	2	1,1	1,1	NUM
cana-3106	131	3	]	]	X
cana-3106	132	1	[	[	X
cana-3106	132	2	0,0	0,0	NOUN
cana-3106	132	3	]	]	PUNCT
cana-3106	133	1	[	[	X
cana-3106	133	2	0,0	0,0	NOUN
cana-3106	133	3	]	]	PUNCT
cana-3106	134	1	[	[	X
cana-3106	134	2	0,0	0,0	NOUN
cana-3106	134	3	]	]	PUNCT
cana-3106	135	1	[	[	X
cana-3106	135	2	0,0	0,0	NOUN
cana-3106	135	3	]	]	PUNCT
cana-3106	136	1	[	[	X
cana-3106	136	2	0,0	0,0	NOUN
cana-3106	136	3	]	]	X
cana-3106	137	1	[	[	X
cana-3106	137	2	2,2	2,2	NUM
cana-3106	137	3	]	]	X
cana-3106	137	4	[	[	X
cana-3106	137	5	2,2	2,2	X
cana-3106	137	6	]	]	X
cana-3106	137	7	[	[	X
cana-3106	137	8	5,5	5,5	NUM
cana-3106	137	9	]	]	X
cana-3106	137	10	w2	w2	NOUN
cana-3106	137	11	[	[	X
cana-3106	137	12	0,0	0,0	NOUN
cana-3106	137	13	]	]	PUNCT
cana-3106	138	1	[	[	X
cana-3106	138	2	1,1	1,1	NUM
cana-3106	138	3	]	]	X
cana-3106	138	4	[	[	X
cana-3106	138	5	0,0	0,0	NOUN
cana-3106	138	6	]	]	PUNCT
cana-3106	139	1	[	[	X
cana-3106	139	2	0,0	0,0	NOUN
cana-3106	139	3	]	]	PUNCT
cana-3106	140	1	[	[	X
cana-3106	140	2	0,0	0,0	NOUN
cana-3106	140	3	]	]	PUNCT
cana-3106	141	1	[	[	X
cana-3106	141	2	0,0	0,0	NOUN
cana-3106	141	3	]	]	X
cana-3106	142	1	[	[	X
cana-3106	142	2	3,3	3,3	X
cana-3106	142	3	]	]	X
cana-3106	142	4	[	[	X
cana-3106	142	5	1,1	1,1	X
cana-3106	142	6	]	]	X
cana-3106	142	7	[	[	X
cana-3106	142	8	6,6	6,6	NUM
cana-3106	142	9	]	]	X
cana-3106	142	10	w3	w3	NOUN
cana-3106	143	1	[	[	X
cana-3106	143	2	0,0	0,0	NOUN
cana-3106	143	3	]	]	PUNCT
cana-3106	144	1	[	[	X
cana-3106	144	2	0,0	0,0	NOUN
cana-3106	144	3	]	]	X
cana-3106	145	1	[	[	X
cana-3106	145	2	1,1	1,1	NUM
cana-3106	145	3	]	]	X
cana-3106	145	4	[	[	X
cana-3106	145	5	0,0	0,0	NOUN
cana-3106	145	6	]	]	X
cana-3106	146	1	[	[	X
cana-3106	146	2	-2,-2	-2,-2	X
cana-3106	146	3	]	]	X
cana-3106	147	1	[	[	X
cana-3106	147	2	-3,-3	-3,-3	X
cana-3106	147	3	]	]	X
cana-3106	148	1	[	[	X
cana-3106	148	2	0,0	0,0	NOUN
cana-3106	148	3	]	]	PUNCT
cana-3106	149	1	[	[	X
cana-3106	149	2	0,0	0,0	NOUN
cana-3106	149	3	]	]	PUNCT
cana-3106	149	4	[	[	X
cana-3106	149	5	-6,-6	-6,-6	X
cana-3106	149	6	]	]	X
cana-3106	149	7	w4	w4	NOUN
cana-3106	149	8	[	[	X
cana-3106	149	9	0,0	0,0	NOUN
cana-3106	149	10	]	]	PUNCT
cana-3106	150	1	[	[	X
cana-3106	150	2	0,0	0,0	NOUN
cana-3106	150	3	]	]	PUNCT
cana-3106	151	1	[	[	X
cana-3106	151	2	0,0	0,0	NOUN
cana-3106	151	3	]	]	X
cana-3106	152	1	[	[	X
cana-3106	152	2	1,1	1,1	X
cana-3106	152	3	]	]	X
cana-3106	153	1	[	[	X
cana-3106	153	2	-2,-2	-2,-2	X
cana-3106	153	3	]	]	X
cana-3106	154	1	[	[	X
cana-3106	154	2	-1,-1	-1,-1	X
cana-3106	154	3	]	]	X
cana-3106	155	1	[	[	X
cana-3106	155	2	0,0	0,0	NOUN
cana-3106	155	3	]	]	PUNCT
cana-3106	156	1	[	[	X
cana-3106	156	2	0,0	0,0	NOUN
cana-3106	156	3	]	]	X
cana-3106	156	4	[	[	X
cana-3106	156	5	-3,-3	-3,-3	X
cana-3106	156	6	]	]	X
cana-3106	156	7	w1	w1	NOUN
cana-3106	157	1	[	[	X
cana-3106	157	2	1,1	1,1	NUM
cana-3106	157	3	]	]	X
cana-3106	157	4	[	[	X
cana-3106	157	5	0,0	0,0	NOUN
cana-3106	157	6	]	]	PUNCT
cana-3106	158	1	[	[	X
cana-3106	158	2	0,0	0,0	NOUN
cana-3106	158	3	]	]	PUNCT
cana-3106	159	1	[	[	X
cana-3106	159	2	0,0	0,0	NOUN
cana-3106	159	3	]	]	PUNCT
cana-3106	160	1	[	[	X
cana-3106	160	2	0,0	0,0	NOUN
cana-3106	160	3	]	]	PUNCT
cana-3106	161	1	[	[	X
cana-3106	161	2	0,0	0,0	NOUN
cana-3106	161	3	]	]	X
cana-3106	162	1	[	[	X
cana-3106	162	2	2,2	2,2	NUM
cana-3106	162	3	]	]	X
cana-3106	162	4	[	[	X
cana-3106	162	5	2,2	2,2	X
cana-3106	162	6	]	]	X
cana-3106	162	7	[	[	X
cana-3106	162	8	5,5	5,5	NUM
cana-3106	162	9	]	]	X
cana-3106	162	10	w2	w2	NOUN
cana-3106	162	11	[	[	X
cana-3106	162	12	0,0	0,0	NOUN
cana-3106	162	13	]	]	PUNCT
cana-3106	163	1	[	[	X
cana-3106	163	2	1,1	1,1	NUM
cana-3106	163	3	]	]	X
cana-3106	163	4	[	[	X
cana-3106	163	5	0,0	0,0	NOUN
cana-3106	163	6	]	]	PUNCT
cana-3106	164	1	[	[	X
cana-3106	164	2	0,0	0,0	NOUN
cana-3106	164	3	]	]	PUNCT
cana-3106	165	1	[	[	X
cana-3106	165	2	0,0	0,0	NOUN
cana-3106	165	3	]	]	PUNCT
cana-3106	166	1	[	[	X
cana-3106	166	2	0,0	0,0	NOUN
cana-3106	166	3	]	]	X
cana-3106	167	1	[	[	X
cana-3106	167	2	3,3	3,3	X
cana-3106	167	3	]	]	X
cana-3106	167	4	[	[	X
cana-3106	167	5	1,1	1,1	X
cana-3106	167	6	]	]	X
cana-3106	167	7	[	[	X
cana-3106	167	8	6,6	6,6	NUM
cana-3106	167	9	]	]	X
cana-3106	167	10	z2	z2	NOUN
cana-3106	167	11	[	[	X
cana-3106	167	12	0,0	0,0	NOUN
cana-3106	167	13	]	]	PUNCT
cana-3106	167	14	[	[	X
cana-3106	167	15	0,0	0,0	NOUN
cana-3106	167	16	]	]	X
cana-3106	168	1	[	[	X
cana-3106	168	2	-0.33,-0.33	-0.33,-0.33	X
cana-3106	168	3	]	]	X
cana-3106	168	4	[	[	X
cana-3106	168	5	0,0	0,0	NOUN
cana-3106	168	6	]	]	X
cana-3106	169	1	[	[	X
cana-3106	169	2	0.666,0.666	0.666,0.666	X
cana-3106	169	3	]	]	X
cana-3106	170	1	[	[	X
cana-3106	170	2	1,1	1,1	NUM
cana-3106	170	3	]	]	X
cana-3106	171	1	[	[	X
cana-3106	171	2	0,0	0,0	NOUN
cana-3106	171	3	]	]	PUNCT
cana-3106	172	1	[	[	X
cana-3106	172	2	0,0	0,0	NOUN
cana-3106	172	3	]	]	X
cana-3106	172	4	[	[	X
cana-3106	172	5	2,2	2,2	NUM
cana-3106	172	6	]	]	X
cana-3106	172	7	w4	w4	NOUN
cana-3106	172	8	[	[	X
cana-3106	172	9	0,0	0,0	NOUN
cana-3106	172	10	]	]	PUNCT
cana-3106	173	1	[	[	X
cana-3106	173	2	0,0	0,0	NOUN
cana-3106	173	3	]	]	X
cana-3106	174	1	[	[	X
cana-3106	174	2	-0.33,-0.33	-0.33,-0.33	X
cana-3106	174	3	]	]	X
cana-3106	174	4	[	[	X
cana-3106	174	5	1,1	1,1	X
cana-3106	174	6	]	]	X
cana-3106	174	7	[	[	X
cana-3106	174	8	1.333,1.333	1.333,1.333	X
cana-3106	174	9	]	]	X
cana-3106	175	1	[	[	X
cana-3106	175	2	0,0	0,0	NOUN
cana-3106	175	3	]	]	PUNCT
cana-3106	176	1	[	[	X
cana-3106	176	2	0,0	0,0	NOUN
cana-3106	176	3	]	]	PUNCT
cana-3106	177	1	[	[	X
cana-3106	177	2	0,0	0,0	NOUN
cana-3106	177	3	]	]	X
cana-3106	177	4	[	[	X
cana-3106	177	5	-1,-1	-1,-1	X
cana-3106	177	6	]	]	X
cana-3106	177	7	w1	w1	NOUN
cana-3106	178	1	[	[	X
cana-3106	178	2	1,1	1,1	X
cana-3106	178	3	]	]	X
cana-3106	178	4	[	[	X
cana-3106	178	5	0,0	0,0	NOUN
cana-3106	178	6	]	]	PUNCT
cana-3106	179	1	[	[	X
cana-3106	179	2	0,0	0,0	NOUN
cana-3106	179	3	]	]	PUNCT
cana-3106	180	1	[	[	X
cana-3106	180	2	0,0	0,0	NOUN
cana-3106	180	3	]	]	PUNCT
cana-3106	181	1	[	[	X
cana-3106	181	2	0,0	0,0	NOUN
cana-3106	181	3	]	]	PUNCT
cana-3106	182	1	[	[	X
cana-3106	182	2	0,0	0,0	NOUN
cana-3106	182	3	]	]	X
cana-3106	183	1	[	[	X
cana-3106	183	2	2,2	2,2	NUM
cana-3106	183	3	]	]	X
cana-3106	183	4	[	[	X
cana-3106	183	5	2,2	2,2	X
cana-3106	183	6	]	]	X
cana-3106	183	7	[	[	X
cana-3106	183	8	5,5	5,5	NUM
cana-3106	183	9	]	]	X
cana-3106	183	10	w2	w2	NOUN
cana-3106	183	11	[	[	X
cana-3106	183	12	0,0	0,0	NOUN
cana-3106	183	13	]	]	PUNCT
cana-3106	184	1	[	[	X
cana-3106	184	2	1,1	1,1	NUM
cana-3106	184	3	]	]	X
cana-3106	184	4	[	[	X
cana-3106	184	5	0,0	0,0	NOUN
cana-3106	184	6	]	]	PUNCT
cana-3106	185	1	[	[	X
cana-3106	185	2	0,0	0,0	NOUN
cana-3106	185	3	]	]	PUNCT
cana-3106	186	1	[	[	X
cana-3106	186	2	0,0	0,0	NOUN
cana-3106	186	3	]	]	PUNCT
cana-3106	187	1	[	[	X
cana-3106	187	2	0,0	0,0	NOUN
cana-3106	187	3	]	]	X
cana-3106	188	1	[	[	X
cana-3106	188	2	3,3	3,3	X
cana-3106	188	3	]	]	X
cana-3106	188	4	[	[	X
cana-3106	188	5	1,1	1,1	X
cana-3106	188	6	]	]	X
cana-3106	188	7	[	[	X
cana-3106	188	8	6,6	6,6	NUM
cana-3106	188	9	]	]	X
cana-3106	188	10	z2	z2	NOUN
cana-3106	188	11	[	[	X
cana-3106	188	12	0,0	0,0	NOUN
cana-3106	188	13	]	]	PUNCT
cana-3106	188	14	[	[	X
cana-3106	188	15	0,0	0,0	NOUN
cana-3106	188	16	]	]	X
cana-3106	189	1	[	[	X
cana-3106	189	2	-0.5,-0.5	-0.5,-0.5	X
cana-3106	189	3	]	]	X
cana-3106	189	4	[	[	X
cana-3106	189	5	0.5,0.5	0.5,0.5	X
cana-3106	189	6	]	]	X
cana-3106	189	7	[	[	X
cana-3106	189	8	0,0	0,0	NOUN
cana-3106	189	9	]	]	X
cana-3106	190	1	[	[	X
cana-3106	190	2	1,1	1,1	NUM
cana-3106	190	3	]	]	X
cana-3106	190	4	[	[	X
cana-3106	190	5	0,0	0,0	NOUN
cana-3106	190	6	]	]	PUNCT
cana-3106	191	1	[	[	X
cana-3106	191	2	0,0	0,0	NOUN
cana-3106	191	3	]	]	X
cana-3106	191	4	[	[	X
cana-3106	191	5	1.5,1.5	1.5,1.5	X
cana-3106	191	6	]	]	X
cana-3106	191	7	z1	z1	NOUN
cana-3106	191	8	[	[	X
cana-3106	191	9	0,0	0,0	NOUN
cana-3106	191	10	]	]	PUNCT
cana-3106	192	1	[	[	X
cana-3106	192	2	0,0	0,0	NOUN
cana-3106	192	3	]	]	X
cana-3106	193	1	[	[	X
cana-3106	193	2	0.25,0.25	0.25,0.25	X
cana-3106	193	3	]	]	X
cana-3106	194	1	[	[	X
cana-3106	194	2	0.75,0.75	0.75,0.75	X
cana-3106	194	3	]	]	X
cana-3106	195	1	[	[	X
cana-3106	195	2	1,1	1,1	X
cana-3106	195	3	]	]	X
cana-3106	195	4	[	[	X
cana-3106	195	5	0,0	0,0	NOUN
cana-3106	195	6	]	]	PUNCT
cana-3106	196	1	[	[	X
cana-3106	196	2	0,0	0,0	NOUN
cana-3106	196	3	]	]	PUNCT
cana-3106	197	1	[	[	X
cana-3106	197	2	0,0	0,0	NOUN
cana-3106	197	3	]	]	X
cana-3106	197	4	[	[	X
cana-3106	197	5	0.75,0.75	0.75,0.75	X
cana-3106	197	6	]	]	X
cana-3106	197	7	values	value	NOUN
cana-3106	197	8	are	be	AUX
cana-3106	197	9	expressed	express	VERB
cana-3106	197	10	by	by	ADP
cana-3106	197	11	taking	take	VERB
cana-3106	197	12	𝛼	𝛼	PRON
cana-3106	197	13	=	=	NOUN
cana-3106	197	14	1	1	NUM
cana-3106	197	15	to	to	ADP
cana-3106	197	16	tfns	tfns	PROPN
cana-3106	197	17	,	,	PUNCT
cana-3106	197	18	w	w	PROPN
cana-3106	197	19	and	and	CCONJ
cana-3106	197	20	z	z	NOUN
cana-3106	197	21	are	be	AUX
cana-3106	197	22	complementary	complementary	ADJ
cana-3106	197	23	pair	pair	NOUN
cana-3106	197	24	,	,	PUNCT
cana-3106	197	25	q	q	PUNCT
cana-3106	197	26	is	be	AUX
cana-3106	197	27	a	a	DET
cana-3106	197	28	vector	vector	NOUN
cana-3106	197	29	.	.	PUNCT
cana-3106	198	1	communications	communication	NOUN
cana-3106	198	2	on	on	ADP
cana-3106	198	3	applied	apply	VERB
cana-3106	198	4	nonlinear	nonlinear	ADJ
cana-3106	198	5	analysis	analysis	NOUN
cana-3106	198	6	issn	issn	NOUN
cana-3106	198	7	:	:	PUNCT
cana-3106	198	8	1074	1074	NUM
cana-3106	198	9	-	-	PUNCT
cana-3106	198	10	133x	133x	NUM
cana-3106	198	11	vol	vol	NOUN
cana-3106	198	12	32	32	NUM
cana-3106	198	13	no	no	NOUN
cana-3106	198	14	.	.	PUNCT
cana-3106	199	1	5s	5s	NUM
cana-3106	199	2	(	(	PUNCT
cana-3106	199	3	2024	2024	NUM
cana-3106	199	4	)	)	PUNCT
cana-3106	199	5	358	358	NUM
cana-3106	199	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3106	200	1	the	the	DET
cana-3106	200	2	optimal	optimal	ADJ
cana-3106	200	3	solution	solution	NOUN
cana-3106	200	4	for	for	ADP
cana-3106	200	5	𝛼	𝛼	NOUN
cana-3106	200	6	=	=	SYM
cana-3106	200	7	1	1	NUM
cana-3106	200	8	(	(	PUNCT
cana-3106	200	9	table	table	NOUN
cana-3106	200	10	4.1	4.1	NUM
cana-3106	200	11	)	)	PUNCT
cana-3106	200	12	is	be	AUX
cana-3106	200	13	[	[	X
cana-3106	200	14	w1	w1	NOUN
cana-3106	200	15	,	,	PUNCT
cana-3106	200	16	w2	w2	NOUN
cana-3106	200	17	,	,	PUNCT
cana-3106	200	18	w3	w3	PROPN
cana-3106	200	19	,	,	PUNCT
cana-3106	200	20	w4	w4	NOUN
cana-3106	200	21	:	:	PUNCT
cana-3106	200	22	z1	z1	PROPN
cana-3106	200	23	,	,	PUNCT
cana-3106	200	24	z2	z2	PROPN
cana-3106	200	25	,	,	PUNCT
cana-3106	200	26	z3	z3	PROPN
cana-3106	200	27	,	,	PUNCT
cana-3106	200	28	z4	z4	X
cana-3106	200	29	]	]	X
cana-3106	200	30	=	=	PUNCT
cana-3106	201	1	[	[	PUNCT
cana-3106	201	2	[	[	X
cana-3106	201	3	5,5	5,5	NUM
cana-3106	201	4	]	]	PUNCT
cana-3106	201	5	,	,	PUNCT
cana-3106	201	6	[	[	X
cana-3106	201	7	6,6	6,6	NUM
cana-3106	201	8	]	]	PUNCT
cana-3106	201	9	,	,	PUNCT
cana-3106	201	10	[	[	X
cana-3106	201	11	0,0],[0,0	0,0],[0,0	NOUN
cana-3106	201	12	]	]	X
cana-3106	201	13	:	:	PUNCT
cana-3106	202	1	[	[	X
cana-3106	202	2	0.75,0.75	0.75,0.75	X
cana-3106	202	3	]	]	X
cana-3106	202	4	,	,	PUNCT
cana-3106	202	5	[	[	X
cana-3106	202	6	1.5,1.5	1.5,1.5	X
cana-3106	202	7	]	]	PUNCT
cana-3106	202	8	,	,	PUNCT
cana-3106	202	9	[	[	X
cana-3106	202	10	0,0],[0,0	0,0],[0,0	NOUN
cana-3106	202	11	]	]	X
cana-3106	202	12	]	]	PUNCT
cana-3106	202	13	when	when	SCONJ
cana-3106	202	14	𝛼	𝛼	X
cana-3106	202	15	=	=	SYM
cana-3106	202	16	0	0	NUM
cana-3106	202	17	,	,	PUNCT
cana-3106	202	18	w	w	PROPN
cana-3106	202	19	mz	mz	PROPN
cana-3106	202	20	=	=	SYM
cana-3106	202	21	q	q	PROPN
cana-3106	202	22	,	,	PUNCT
cana-3106	202	23	gives	give	VERB
cana-3106	202	24	[	[	PUNCT
cana-3106	202	25	𝑤1	𝑤1	VERB
cana-3106	202	26	𝑤2	𝑤2	NOUN
cana-3106	202	27	𝑤3	𝑤3	NOUN
cana-3106	202	28	𝑤4	𝑤4	NOUN
cana-3106	202	29	]	]	PUNCT
cana-3106	202	30	[	[	PUNCT
cana-3106	202	31	[	[	X
cana-3106	202	32	−1,1	−1,1	X
cana-3106	202	33	]	]	X
cana-3106	203	1	[	[	X
cana-3106	203	2	0,0	0,0	NOUN
cana-3106	203	3	]	]	X
cana-3106	204	1	[	[	X
cana-3106	204	2	1,3	1,3	X
cana-3106	204	3	]	]	X
cana-3106	205	1	[	[	X
cana-3106	205	2	0,4	0,4	NOUN
cana-3106	205	3	]	]	PUNCT
cana-3106	205	4	[	[	X
cana-3106	205	5	0,0	0,0	NOUN
cana-3106	205	6	]	]	X
cana-3106	206	1	[	[	X
cana-3106	206	2	−1,1	−1,1	X
cana-3106	206	3	]	]	X
cana-3106	207	1	[	[	X
cana-3106	207	2	2,4	2,4	X
cana-3106	207	3	]	]	X
cana-3106	208	1	[	[	X
cana-3106	208	2	0,2	0,2	X
cana-3106	208	3	]	]	X
cana-3106	208	4	[	[	X
cana-3106	208	5	−3,−1	−3,−1	X
cana-3106	208	6	]	]	X
cana-3106	208	7	[	[	X
cana-3106	208	8	−4,−2	−4,−2	X
cana-3106	208	9	]	]	X
cana-3106	209	1	[	[	X
cana-3106	209	2	−2,2	−2,2	X
cana-3106	209	3	]	]	X
cana-3106	210	1	[	[	X
cana-3106	210	2	0,0	0,0	NOUN
cana-3106	210	3	]	]	PUNCT
cana-3106	211	1	[	[	X
cana-3106	211	2	−3,−1	−3,−1	X
cana-3106	211	3	]	]	X
cana-3106	212	1	[	[	X
cana-3106	212	2	−2,0	−2,0	X
cana-3106	212	3	]	]	X
cana-3106	213	1	[	[	X
cana-3106	213	2	0,0	0,0	NOUN
cana-3106	213	3	]	]	X
cana-3106	214	1	[	[	X
cana-3106	214	2	−1,1	−1,1	NOUN
cana-3106	214	3	]	]	X
cana-3106	214	4	]	]	X
cana-3106	214	5	[	[	PUNCT
cana-3106	214	6	𝑧1	𝑧1	PROPN
cana-3106	214	7	𝑧2	𝑧2	PROPN
cana-3106	214	8	𝑧3	𝑧3	PROPN
cana-3106	214	9	𝑧4	𝑧4	PROPN
cana-3106	214	10	]	]	PUNCT
cana-3106	214	11	=	=	PUNCT
cana-3106	215	1	[	[	PUNCT
cana-3106	215	2	[	[	X
cana-3106	215	3	3,7	3,7	NUM
cana-3106	215	4	]	]	PUNCT
cana-3106	215	5	[	[	X
cana-3106	215	6	5,7	5,7	NUM
cana-3106	215	7	]	]	PUNCT
cana-3106	215	8	[	[	X
cana-3106	215	9	−8,−4	−8,−4	X
cana-3106	215	10	]	]	X
cana-3106	215	11	[	[	X
cana-3106	215	12	−5,−1	−5,−1	ADP
cana-3106	215	13	]	]	X
cana-3106	215	14	]	]	X
cana-3106	215	15	the	the	DET
cana-3106	215	16	results	result	NOUN
cana-3106	215	17	are	be	AUX
cana-3106	215	18	tabulated	tabulate	VERB
cana-3106	215	19	below	below	ADP
cana-3106	215	20	table	table	NOUN
cana-3106	215	21	4.2	4.2	NUM
cana-3106	215	22	the	the	DET
cana-3106	215	23	same	same	ADJ
cana-3106	215	24	procedure	procedure	NOUN
cana-3106	215	25	is	be	AUX
cana-3106	215	26	followed	follow	VERB
cana-3106	215	27	in	in	ADP
cana-3106	215	28	table	table	NOUN
cana-3106	215	29	4.2	4.2	NUM
cana-3106	215	30	,	,	PUNCT
cana-3106	215	31	where	where	SCONJ
cana-3106	215	32	the	the	DET
cana-3106	215	33	following	follow	VERB
cana-3106	215	34	values	value	NOUN
cana-3106	215	35	are	be	AUX
cana-3106	215	36	operated	operate	VERB
cana-3106	215	37	by	by	ADP
cana-3106	215	38	the	the	DET
cana-3106	215	39	arithmetic	arithmetic	ADJ
cana-3106	215	40	operations	operation	NOUN
cana-3106	215	41	of	of	ADP
cana-3106	215	42	interval	interval	NOUN
cana-3106	215	43	numbers	number	NOUN
cana-3106	215	44	.	.	PUNCT
cana-3106	216	1	bv	bv	PROPN
cana-3106	216	2	w1	w1	PROPN
cana-3106	216	3	w2	w2	PROPN
cana-3106	216	4	w3	w3	PROPN
cana-3106	216	5	w4	w4	PROPN
cana-3106	216	6	z1	z1	PROPN
cana-3106	216	7	z2	z2	PROPN
cana-3106	216	8	z3	z3	PROPN
cana-3106	216	9	z4	z4	PROPN
cana-3106	216	10	q	q	PROPN
cana-3106	216	11	w1	w1	PROPN
cana-3106	217	1	[	[	X
cana-3106	217	2	1,1	1,1	NUM
cana-3106	217	3	]	]	X
cana-3106	218	1	[	[	X
cana-3106	218	2	0,0	0,0	NOUN
cana-3106	218	3	]	]	PUNCT
cana-3106	219	1	[	[	X
cana-3106	219	2	0,0	0,0	NOUN
cana-3106	219	3	]	]	PUNCT
cana-3106	220	1	[	[	X
cana-3106	220	2	0,0	0,0	NOUN
cana-3106	220	3	]	]	X
cana-3106	221	1	[	[	X
cana-3106	221	2	-1,1	-1,1	X
cana-3106	221	3	]	]	X
cana-3106	222	1	[	[	X
cana-3106	222	2	0,0	0,0	NOUN
cana-3106	222	3	]	]	X
cana-3106	223	1	[	[	X
cana-3106	223	2	1,3	1,3	X
cana-3106	223	3	]	]	X
cana-3106	224	1	[	[	X
cana-3106	224	2	0,4	0,4	NOUN
cana-3106	224	3	]	]	PUNCT
cana-3106	224	4	[	[	X
cana-3106	224	5	3,7	3,7	NUM
cana-3106	224	6	]	]	X
cana-3106	224	7	w2	w2	NOUN
cana-3106	224	8	[	[	X
cana-3106	224	9	0,0	0,0	NOUN
cana-3106	224	10	]	]	PUNCT
cana-3106	225	1	[	[	X
cana-3106	225	2	1,1	1,1	NUM
cana-3106	225	3	]	]	X
cana-3106	225	4	[	[	X
cana-3106	225	5	0,0	0,0	NOUN
cana-3106	225	6	]	]	PUNCT
cana-3106	226	1	[	[	X
cana-3106	226	2	0,0	0,0	NOUN
cana-3106	226	3	]	]	PUNCT
cana-3106	227	1	[	[	X
cana-3106	227	2	0,0	0,0	NOUN
cana-3106	227	3	]	]	X
cana-3106	228	1	[	[	X
cana-3106	228	2	-1,1	-1,1	X
cana-3106	228	3	]	]	X
cana-3106	229	1	[	[	X
cana-3106	229	2	2,4	2,4	X
cana-3106	229	3	]	]	X
cana-3106	230	1	[	[	X
cana-3106	230	2	0,2	0,2	X
cana-3106	230	3	]	]	X
cana-3106	231	1	[	[	X
cana-3106	231	2	5,7	5,7	NUM
cana-3106	231	3	]	]	X
cana-3106	231	4	w3	w3	NOUN
cana-3106	231	5	[	[	X
cana-3106	231	6	0,0	0,0	NOUN
cana-3106	231	7	]	]	PUNCT
cana-3106	231	8	[	[	X
cana-3106	231	9	0,0	0,0	NOUN
cana-3106	231	10	]	]	X
cana-3106	232	1	[	[	X
cana-3106	232	2	1,1	1,1	NUM
cana-3106	232	3	]	]	X
cana-3106	232	4	[	[	X
cana-3106	232	5	0,0	0,0	NOUN
cana-3106	232	6	]	]	PUNCT
cana-3106	233	1	[	[	X
cana-3106	233	2	-3,-1	-3,-1	X
cana-3106	233	3	]	]	X
cana-3106	234	1	[	[	X
cana-3106	234	2	-4,-2	-4,-2	X
cana-3106	234	3	]	]	X
cana-3106	235	1	[	[	X
cana-3106	235	2	-2,2	-2,2	X
cana-3106	235	3	]	]	X
cana-3106	235	4	[	[	X
cana-3106	235	5	0,0	0,0	NOUN
cana-3106	235	6	]	]	X
cana-3106	235	7	[	[	X
cana-3106	235	8	-8,-4	-8,-4	X
cana-3106	235	9	]	]	X
cana-3106	235	10	w4	w4	NOUN
cana-3106	235	11	[	[	X
cana-3106	235	12	0,0	0,0	NOUN
cana-3106	235	13	]	]	PUNCT
cana-3106	235	14	[	[	X
cana-3106	235	15	0,0	0,0	NOUN
cana-3106	235	16	]	]	PUNCT
cana-3106	235	17	[	[	X
cana-3106	235	18	0,0	0,0	NOUN
cana-3106	235	19	]	]	X
cana-3106	236	1	[	[	X
cana-3106	236	2	1,1	1,1	NUM
cana-3106	236	3	]	]	X
cana-3106	237	1	[	[	X
cana-3106	237	2	-3,-1	-3,-1	X
cana-3106	237	3	]	]	X
cana-3106	238	1	[	[	X
cana-3106	238	2	-2,0	-2,0	X
cana-3106	238	3	]	]	X
cana-3106	239	1	[	[	X
cana-3106	239	2	0,0	0,0	NOUN
cana-3106	239	3	]	]	X
cana-3106	240	1	[	[	X
cana-3106	240	2	-1,1	-1,1	X
cana-3106	240	3	]	]	X
cana-3106	240	4	[	[	X
cana-3106	240	5	-5,-1	-5,-1	X
cana-3106	240	6	]	]	X
cana-3106	240	7	w1	w1	NOUN
cana-3106	241	1	[	[	X
cana-3106	241	2	1,1	1,1	NUM
cana-3106	241	3	]	]	X
cana-3106	241	4	[	[	X
cana-3106	241	5	0,0	0,0	NOUN
cana-3106	241	6	]	]	PUNCT
cana-3106	242	1	[	[	X
cana-3106	242	2	0,0	0,0	NOUN
cana-3106	242	3	]	]	PUNCT
cana-3106	243	1	[	[	X
cana-3106	243	2	0,0	0,0	NOUN
cana-3106	243	3	]	]	X
cana-3106	244	1	[	[	X
cana-3106	244	2	-1,1	-1,1	X
cana-3106	244	3	]	]	X
cana-3106	245	1	[	[	X
cana-3106	245	2	0,0	0,0	NOUN
cana-3106	245	3	]	]	X
cana-3106	246	1	[	[	X
cana-3106	246	2	1,3	1,3	X
cana-3106	246	3	]	]	X
cana-3106	247	1	[	[	X
cana-3106	247	2	0,4	0,4	NOUN
cana-3106	247	3	]	]	PUNCT
cana-3106	247	4	[	[	X
cana-3106	247	5	3,7	3,7	NUM
cana-3106	247	6	]	]	X
cana-3106	247	7	w2	w2	NOUN
cana-3106	247	8	[	[	X
cana-3106	247	9	0,0	0,0	NOUN
cana-3106	247	10	]	]	PUNCT
cana-3106	248	1	[	[	X
cana-3106	248	2	1,1	1,1	NUM
cana-3106	248	3	]	]	X
cana-3106	248	4	[	[	X
cana-3106	248	5	0,0	0,0	NOUN
cana-3106	248	6	]	]	PUNCT
cana-3106	249	1	[	[	X
cana-3106	249	2	0,0	0,0	NOUN
cana-3106	249	3	]	]	PUNCT
cana-3106	250	1	[	[	X
cana-3106	250	2	-1.25,1.25	-1.25,1.25	X
cana-3106	250	3	]	]	X
cana-3106	251	1	[	[	X
cana-3106	251	2	-2.66,2.66	-2.66,2.66	X
cana-3106	251	3	]	]	X
cana-3106	251	4	[	[	X
cana-3106	251	5	1.2,4.8	1.2,4.8	X
cana-3106	251	6	]	]	X
cana-3106	252	1	[	[	X
cana-3106	252	2	0,2	0,2	X
cana-3106	252	3	]	]	X
cana-3106	253	1	[	[	X
cana-3106	253	2	1.7,0.3	1.7,0.3	NUM
cana-3106	253	3	]	]	X
cana-3106	253	4	z2	z2	NOUN
cana-3106	253	5	[	[	X
cana-3106	253	6	0,0	0,0	NOUN
cana-3106	253	7	]	]	PUNCT
cana-3106	253	8	[	[	X
cana-3106	253	9	0,0	0,0	NOUN
cana-3106	253	10	]	]	X
cana-3106	254	1	[	[	X
cana-3106	254	2	0.4167,0.2500	0.4167,0.2500	X
cana-3106	254	3	]	]	X
cana-3106	254	4	[	[	X
cana-3106	254	5	0,0	0,0	NOUN
cana-3106	254	6	]	]	X
cana-3106	255	1	[	[	X
cana-3106	255	2	0.25,1.08	0.25,1.08	X
cana-3106	255	3	]	]	X
cana-3106	256	1	[	[	X
cana-3106	256	2	0.50,1.50	0.50,1.50	X
cana-3106	256	3	]	]	X
cana-3106	256	4	[	[	X
cana-3106	256	5	-0.83,0.83	-0.83,0.83	X
cana-3106	256	6	]	]	X
cana-3106	256	7	[	[	X
cana-3106	256	8	0,0	0,0	NOUN
cana-3106	256	9	]	]	X
cana-3106	256	10	[	[	X
cana-3106	256	11	1,2.996	1,2.996	X
cana-3106	256	12	]	]	X
cana-3106	256	13	w4	w4	NOUN
cana-3106	256	14	[	[	X
cana-3106	256	15	0,0	0,0	NOUN
cana-3106	256	16	]	]	PUNCT
cana-3106	257	1	[	[	X
cana-3106	257	2	0,0	0,0	NOUN
cana-3106	257	3	]	]	X
cana-3106	258	1	[	[	X
cana-3106	258	2	-0.6667,0	-0.6667,0	X
cana-3106	258	3	]	]	X
cana-3106	258	4	[	[	X
cana-3106	258	5	1,1	1,1	X
cana-3106	258	6	]	]	X
cana-3106	259	1	[	[	X
cana-3106	259	2	-3.0,0.33	-3.0,0.33	X
cana-3106	259	3	]	]	X
cana-3106	260	1	[	[	X
cana-3106	260	2	-2,2	-2,2	X
cana-3106	260	3	]	]	X
cana-3106	261	1	[	[	X
cana-3106	261	2	1.333,1.333	1.333,1.333	X
cana-3106	261	3	]	]	X
cana-3106	261	4	[	[	X
cana-3106	261	5	-1,1	-1,1	X
cana-3106	261	6	]	]	X
cana-3106	261	7	[	[	X
cana-3106	261	8	-5,3	-5,3	X
cana-3106	261	9	]	]	X
cana-3106	261	10	w1	w1	NOUN
cana-3106	262	1	[	[	X
cana-3106	262	2	1,1	1,1	X
cana-3106	262	3	]	]	X
cana-3106	262	4	[	[	X
cana-3106	262	5	0,0	0,0	NOUN
cana-3106	262	6	]	]	PUNCT
cana-3106	263	1	[	[	X
cana-3106	263	2	-3.02,3.02	-3.02,3.02	X
cana-3106	263	3	]	]	X
cana-3106	264	1	[	[	X
cana-3106	264	2	4.53,4.53	4.53,4.53	NUM
cana-3106	264	3	]	]	X
cana-3106	265	1	[	[	X
cana-3106	265	2	14.58,14.58	14.58,14.58	X
cana-3106	265	3	]	]	X
cana-3106	266	1	[	[	X
cana-3106	266	2	-9.06,9.06	-9.06,9.06	X
cana-3106	266	3	]	]	X
cana-3106	267	1	[	[	X
cana-3106	267	2	-5.02,9.02	-5.02,9.02	X
cana-3106	267	3	]	]	X
cana-3106	268	1	[	[	X
cana-3106	268	2	4.53,8.53	4.53,8.53	X
cana-3106	268	3	]	]	X
cana-3106	268	4	[	[	X
cana-3106	268	5	19.64,29.64	19.64,29.64	X
cana-3106	268	6	]	]	X
cana-3106	268	7	w2	w2	NOUN
cana-3106	268	8	[	[	X
cana-3106	268	9	0,0	0,0	NOUN
cana-3106	268	10	]	]	PUNCT
cana-3106	269	1	[	[	X
cana-3106	269	2	1,1	1,1	X
cana-3106	269	3	]	]	X
cana-3106	270	1	[	[	X
cana-3106	270	2	-3.77,3.77	-3.77,3.77	X
cana-3106	270	3	]	]	X
cana-3106	271	1	[	[	X
cana-3106	271	2	5.66,5.66	5.66,5.66	X
cana-3106	271	3	]	]	X
cana-3106	271	4	[	[	X
cana-3106	271	5	18.23,18.23	18.23,18.23	X
cana-3106	271	6	]	]	X
cana-3106	272	1	[	[	X
cana-3106	272	2	13.98,13.98	13.98,13.98	X
cana-3106	272	3	]	]	X
cana-3106	273	1	[	[	X
cana-3106	273	2	-6.33,12.33	-6.33,12.33	X
cana-3106	273	3	]	]	X
cana-3106	273	4	[	[	X
cana-3106	273	5	5.66,7.66	5.66,7.66	X
cana-3106	273	6	]	]	X
cana-3106	273	7	[	[	X
cana-3106	273	8	-26.6,38.6	-26.6,38.6	X
cana-3106	273	9	]	]	X
cana-3106	273	10	z2	z2	PROPN
cana-3106	273	11	[	[	X
cana-3106	273	12	0,0	0,0	NOUN
cana-3106	273	13	]	]	PUNCT
cana-3106	273	14	[	[	X
cana-3106	273	15	0,0	0,0	NOUN
cana-3106	273	16	]	]	PUNCT
cana-3106	274	1	[	[	X
cana-3106	274	2	-2.96,1.96	-2.96,1.96	X
cana-3106	274	3	]	]	X
cana-3106	275	1	[	[	X
cana-3106	275	2	-3.3,4.3	-3.3,4.3	X
cana-3106	275	3	]	]	X
cana-3106	276	1	[	[	X
cana-3106	276	2	-10.9,10.9	-10.9,10.9	X
cana-3106	276	3	]	]	X
cana-3106	277	1	[	[	X
cana-3106	277	2	-8.11,10.11	-8.11,10.11	X
cana-3106	277	3	]	]	X
cana-3106	278	1	[	[	X
cana-3106	278	2	-6.6,6.6	-6.6,6.6	X
cana-3106	278	3	]	]	X
cana-3106	278	4	[	[	X
cana-3106	278	5	-4.3,4.3	-4.3,4.3	X
cana-3106	278	6	]	]	X
cana-3106	278	7	[	[	X
cana-3106	278	8	16.52,19.52	16.52,19.52	X
cana-3106	278	9	]	]	X
cana-3106	278	10	z1	z1	NOUN
cana-3106	278	11	[	[	X
cana-3106	278	12	0,0	0,0	NOUN
cana-3106	278	13	]	]	PUNCT
cana-3106	279	1	[	[	X
cana-3106	279	2	0,0	0,0	NOUN
cana-3106	279	3	]	]	PUNCT
cana-3106	280	1	[	[	X
cana-3106	280	2	-2.02,2.70	-2.02,2.70	X
cana-3106	280	3	]	]	X
cana-3106	281	1	[	[	X
cana-3106	281	2	-4.8,3.3	-4.8,3.3	X
cana-3106	281	3	]	]	X
cana-3106	282	1	[	[	X
cana-3106	282	2	-9.9,11.09	-9.9,11.09	X
cana-3106	282	3	]	]	X
cana-3106	283	1	[	[	X
cana-3106	283	2	-9.6,9.6	-9.6,9.6	X
cana-3106	283	3	]	]	X
cana-3106	284	1	[	[	X
cana-3106	284	2	-6.38,6.38	-6.38,6.38	X
cana-3106	284	3	]	]	X
cana-3106	284	4	[	[	X
cana-3106	284	5	-4.8,4.8	-4.8,4.8	X
cana-3106	284	6	]	]	X
cana-3106	284	7	[	[	X
cana-3106	284	8	-15.0,16.50	-15.0,16.50	X
cana-3106	284	9	]	]	X
cana-3106	284	10	value	value	NOUN
cana-3106	284	11	of	of	ADP
cana-3106	284	12	𝛼	𝛼	NOUN
cana-3106	284	13	=	=	NOUN
cana-3106	284	14	0	0	PROPN
cana-3106	284	15	.	.	PUNCT
cana-3106	285	1	the	the	DET
cana-3106	285	2	optimal	optimal	ADJ
cana-3106	285	3	solutions	solution	NOUN
cana-3106	285	4	are	be	AUX
cana-3106	285	5	obtained	obtain	VERB
cana-3106	285	6	when	when	SCONJ
cana-3106	285	7	the	the	DET
cana-3106	285	8	component	component	NOUN
cana-3106	285	9	of	of	ADP
cana-3106	285	10	q	q	PROPN
cana-3106	285	11	vector	vector	NOUN
cana-3106	285	12	is	be	AUX
cana-3106	285	13	positive	positive	ADJ
cana-3106	285	14	.	.	PUNCT
cana-3106	286	1	the	the	DET
cana-3106	286	2	optimal	optimal	ADJ
cana-3106	286	3	solution	solution	NOUN
cana-3106	286	4	for	for	ADP
cana-3106	286	5	𝛼	𝛼	NOUN
cana-3106	286	6	=	=	SYM
cana-3106	286	7	0	0	PUNCT
cana-3106	286	8	(	(	PUNCT
cana-3106	286	9	table	table	NOUN
cana-3106	286	10	4.2	4.2	NUM
cana-3106	286	11	)	)	PUNCT
cana-3106	286	12	is	be	AUX
cana-3106	286	13	[	[	X
cana-3106	286	14	w1	w1	NOUN
cana-3106	286	15	,	,	PUNCT
cana-3106	286	16	w2	w2	NOUN
cana-3106	286	17	,	,	PUNCT
cana-3106	286	18	w3	w3	PROPN
cana-3106	286	19	,	,	PUNCT
cana-3106	286	20	w4	w4	NOUN
cana-3106	286	21	:	:	PUNCT
cana-3106	286	22	z1	z1	PROPN
cana-3106	286	23	,	,	PUNCT
cana-3106	286	24	z2	z2	PROPN
cana-3106	286	25	,	,	PUNCT
cana-3106	286	26	z3	z3	PROPN
cana-3106	286	27	,	,	PUNCT
cana-3106	286	28	z4	z4	X
cana-3106	286	29	]	]	X
cana-3106	286	30	=	=	PUNCT
cana-3106	287	1	[	[	PUNCT
cana-3106	287	2	[	[	X
cana-3106	287	3	-19.64,29.64	-19.64,29.64	X
cana-3106	287	4	]	]	X
cana-3106	287	5	,	,	PUNCT
cana-3106	287	6	[	[	X
cana-3106	287	7	-26.6,38.6	-26.6,38.6	X
cana-3106	287	8	]	]	X
cana-3106	287	9	,	,	PUNCT
cana-3106	287	10	[	[	X
cana-3106	287	11	0,0],[0,0	0,0],[0,0	NOUN
cana-3106	287	12	]	]	X
cana-3106	287	13	:	:	PUNCT
cana-3106	288	1	[	[	X
cana-3106	288	2	-15.00,16.50	-15.00,16.50	X
cana-3106	288	3	]	]	X
cana-3106	288	4	,	,	PUNCT
cana-3106	288	5	[	[	X
cana-3106	288	6	-16.52,19.52	-16.52,19.52	NOUN
cana-3106	288	7	]	]	X
cana-3106	288	8	,	,	PUNCT
cana-3106	288	9	[	[	X
cana-3106	288	10	0,0],[0,0	0,0],[0,0	NOUN
cana-3106	288	11	]	]	X
cana-3106	288	12	]	]	PUNCT
cana-3106	288	13	the	the	DET
cana-3106	288	14	other	other	ADJ
cana-3106	288	15	values	value	NOUN
cana-3106	288	16	are	be	AUX
cana-3106	288	17	tabulated	tabulate	VERB
cana-3106	288	18	below	below	ADV
cana-3106	288	19	,	,	PUNCT
cana-3106	288	20	𝜶	𝜶	ADP
cana-3106	288	21	−	−	NOUN
cana-3106	288	22	𝒗𝒂𝒍𝒖𝒆𝒔	𝒗𝒂𝒍𝒖𝒆𝒔	VERB
cana-3106	288	23	optimal	optimal	ADJ
cana-3106	288	24	values	value	NOUN
cana-3106	288	25	od	od	INTJ
cana-3106	288	26	z	z	NOUN
cana-3106	288	27	𝛼	𝛼	NOUN
cana-3106	288	28	=	=	SYM
cana-3106	288	29	1	1	NUM
cana-3106	289	1	[	[	PUNCT
cana-3106	289	2	1.3	1.3	NUM
cana-3106	289	3	1.3	1.3	NUM
cana-3106	289	4	]	]	PUNCT
cana-3106	289	5	𝛼	𝛼	NOUN
cana-3106	289	6	=	=	NUM
cana-3106	289	7	0.8	0.8	NUM
cana-3106	290	1	[	[	X
cana-3106	290	2	-11.3	-11.3	ADJ
cana-3106	290	3	,	,	PUNCT
cana-3106	290	4	12.4	12.4	NUM
cana-3106	290	5	]	]	PUNCT
cana-3106	290	6	𝛼	𝛼	X
cana-3106	290	7	=	=	SYM
cana-3106	290	8	0.6	0.6	NUM
cana-3106	291	1	[	[	X
cana-3106	291	2	-20.2	-20.2	PROPN
cana-3106	291	3	23.3	23.3	NUM
cana-3106	291	4	]	]	PUNCT
cana-3106	291	5	𝛼	𝛼	NOUN
cana-3106	291	6	=	=	SYM
cana-3106	291	7	0.4	0.4	NUM
cana-3106	292	1	[	[	X
cana-3106	292	2	-30.1	-30.1	ADJ
cana-3106	292	3	,	,	PUNCT
cana-3106	292	4	33.2	33.2	NUM
cana-3106	292	5	]	]	PUNCT
cana-3106	292	6	𝛼	𝛼	NOUN
cana-3106	292	7	=	=	NOUN
cana-3106	292	8	0.2	0.2	NUM
cana-3106	293	1	[	[	X
cana-3106	293	2	-39	-39	PROPN
cana-3106	293	3	,	,	PUNCT
cana-3106	293	4	42	42	NUM
cana-3106	293	5	]	]	X
cana-3106	293	6	𝛼	𝛼	X
cana-3106	293	7	=	=	SYM
cana-3106	293	8	0	0	PUNCT
cana-3106	294	1	[	[	X
cana-3106	294	2	-49	-49	X
cana-3106	294	3	,	,	PUNCT
cana-3106	294	4	51	51	NUM
cana-3106	294	5	]	]	PUNCT
cana-3106	294	6	the	the	DET
cana-3106	294	7	matlab	matlab	PROPN
cana-3106	294	8	output	output	NOUN
cana-3106	294	9	for	for	ADP
cana-3106	294	10	the	the	DET
cana-3106	294	11	above	above	ADJ
cana-3106	294	12	example	example	NOUN
cana-3106	294	13	is	be	AUX
cana-3106	294	14	:	:	PUNCT
cana-3106	294	15	figure	figure	VERB
cana-3106	294	16	4.1	4.1	NUM
cana-3106	294	17	denotes	denote	NOUN
cana-3106	294	18	the	the	DET
cana-3106	294	19	different	different	ADJ
cana-3106	294	20	levels	level	NOUN
cana-3106	294	21	of	of	ADP
cana-3106	294	22	𝜶	𝜶	NOUN
cana-3106	294	23	−	−	NOUN
cana-3106	294	24	𝒄𝒖𝒕𝒔	𝒄𝒖𝒕𝒔	ADV
cana-3106	294	25	,	,	PUNCT
cana-3106	294	26	the	the	DET
cana-3106	294	27	values	value	NOUN
cana-3106	294	28	are	be	AUX
cana-3106	294	29	taken	take	VERB
cana-3106	294	30	in	in	ADP
cana-3106	294	31	the	the	DET
cana-3106	294	32	interval	interval	NOUN
cana-3106	294	33	numbers	number	NOUN
cana-3106	294	34	and	and	CCONJ
cana-3106	294	35	obtained	obtain	VERB
cana-3106	294	36	from	from	ADP
cana-3106	294	37	the	the	DET
cana-3106	294	38	matlab	matlab	PROPN
cana-3106	294	39	output	output	NOUN
cana-3106	294	40	.	.	PUNCT
cana-3106	295	1	communications	communication	NOUN
cana-3106	295	2	on	on	ADP
cana-3106	295	3	applied	apply	VERB
cana-3106	295	4	nonlinear	nonlinear	ADJ
cana-3106	295	5	analysis	analysis	NOUN
cana-3106	295	6	issn	issn	NOUN
cana-3106	295	7	:	:	PUNCT
cana-3106	295	8	1074	1074	NUM
cana-3106	295	9	-	-	PUNCT
cana-3106	295	10	133x	133x	NUM
cana-3106	295	11	vol	vol	NOUN
cana-3106	295	12	32	32	NUM
cana-3106	295	13	no	no	NOUN
cana-3106	295	14	.	.	PUNCT
cana-3106	296	1	5s	5s	NUM
cana-3106	296	2	(	(	PUNCT
cana-3106	296	3	2024	2024	NUM
cana-3106	296	4	)	)	PUNCT
cana-3106	296	5	359	359	NUM
cana-3106	297	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-3106	297	2	fig	fig	NOUN
cana-3106	297	3	4.1	4.1	NUM
cana-3106	297	4	5	5	NUM
cana-3106	297	5	.	.	PUNCT
cana-3106	298	1	conclusion	conclusion	NOUN
cana-3106	298	2	this	this	DET
cana-3106	298	3	study	study	NOUN
cana-3106	298	4	discusses	discuss	VERB
cana-3106	298	5	an	an	DET
cana-3106	298	6	algorithm	algorithm	NOUN
cana-3106	298	7	for	for	ADP
cana-3106	298	8	solving	solve	VERB
cana-3106	298	9	fuzzy	fuzzy	ADJ
cana-3106	298	10	fractional	fractional	ADJ
cana-3106	298	11	programming	programming	NOUN
cana-3106	298	12	problem	problem	NOUN
cana-3106	298	13	in	in	ADP
cana-3106	298	14	a	a	DET
cana-3106	298	15	complementarity	complementarity	NOUN
cana-3106	298	16	terms	term	NOUN
cana-3106	298	17	.	.	PUNCT
cana-3106	299	1	in	in	ADP
cana-3106	299	2	the	the	DET
cana-3106	299	3	proposed	propose	VERB
cana-3106	299	4	algorithm	algorithm	NOUN
cana-3106	299	5	,	,	PUNCT
cana-3106	299	6	firstly	firstly	ADV
cana-3106	299	7	the	the	DET
cana-3106	299	8	ffpp	ffpp	NOUN
cana-3106	299	9	is	be	AUX
cana-3106	299	10	transformed	transform	VERB
cana-3106	299	11	into	into	ADP
cana-3106	299	12	flpp	flpp	NOUN
cana-3106	299	13	and	and	CCONJ
cana-3106	299	14	then	then	ADV
cana-3106	299	15	the	the	DET
cana-3106	299	16	resultant	resultant	NOUN
cana-3106	299	17	flpp	flpp	NOUN
cana-3106	299	18	is	be	AUX
cana-3106	299	19	converted	convert	VERB
cana-3106	299	20	in	in	ADP
cana-3106	299	21	to	to	PART
cana-3106	299	22	flcp	flcp	VERB
cana-3106	299	23	under	under	ADP
cana-3106	299	24	the	the	DET
cana-3106	299	25	interval	interval	NOUN
cana-3106	299	26	numbers	number	NOUN
cana-3106	299	27	.	.	PUNCT
cana-3106	300	1	using	use	VERB
cana-3106	300	2	this	this	DET
cana-3106	300	3	method	method	NOUN
cana-3106	300	4	,	,	PUNCT
cana-3106	300	5	the	the	DET
cana-3106	300	6	output	output	NOUN
cana-3106	300	7	is	be	AUX
cana-3106	300	8	easy	easy	ADJ
cana-3106	300	9	and	and	CCONJ
cana-3106	300	10	unmistakable	unmistakable	ADJ
cana-3106	300	11	.	.	PUNCT
cana-3106	301	1	the	the	DET
cana-3106	301	2	design	design	NOUN
cana-3106	301	3	of	of	ADP
cana-3106	301	4	this	this	DET
cana-3106	301	5	problem	problem	NOUN
cana-3106	301	6	ensures	ensure	VERB
cana-3106	301	7	that	that	SCONJ
cana-3106	301	8	every	every	DET
cana-3106	301	9	α	α	NOUN
cana-3106	301	10	-	-	NOUN
cana-3106	301	11	cut	cut	NOUN
cana-3106	301	12	of	of	ADP
cana-3106	301	13	the	the	DET
cana-3106	301	14	interval	interval	NOUN
cana-3106	301	15	is	be	AUX
cana-3106	301	16	examined	examine	VERB
cana-3106	301	17	in	in	ADP
cana-3106	301	18	order	order	NOUN
cana-3106	301	19	to	to	PART
cana-3106	301	20	get	get	VERB
cana-3106	301	21	the	the	DET
cana-3106	301	22	best	good	ADJ
cana-3106	301	23	possible	possible	ADJ
cana-3106	301	24	optimal	optimal	ADJ
cana-3106	301	25	solution	solution	NOUN
cana-3106	301	26	.	.	PUNCT
cana-3106	302	1	these	these	DET
cana-3106	302	2	methods	method	NOUN
cana-3106	302	3	provide	provide	VERB
cana-3106	302	4	additional	additional	ADJ
cana-3106	302	5	concepts	concept	NOUN
cana-3106	302	6	for	for	ADP
cana-3106	302	7	creating	create	VERB
cana-3106	302	8	new	new	ADJ
cana-3106	302	9	flcp	flcp	NOUN
cana-3106	302	10	implementations	implementation	NOUN
cana-3106	302	11	.	.	PUNCT
cana-3106	303	1	funding	funding	NOUN
cana-3106	303	2	:	:	PUNCT
cana-3106	303	3	this	this	DET
cana-3106	303	4	research	research	NOUN
cana-3106	303	5	received	receive	VERB
cana-3106	303	6	no	no	DET
cana-3106	303	7	external	external	ADJ
cana-3106	303	8	funding	funding	NOUN
cana-3106	303	9	.	.	PUNCT
cana-3106	304	1	conflicts	conflict	NOUN
cana-3106	304	2	of	of	ADP
cana-3106	304	3	interest	interest	NOUN
cana-3106	304	4	:	:	PUNCT
cana-3106	304	5	the	the	DET
cana-3106	304	6	authors	author	NOUN
cana-3106	304	7	declare	declare	VERB
cana-3106	304	8	no	no	DET
cana-3106	304	9	conflict	conflict	NOUN
cana-3106	304	10	of	of	ADP
cana-3106	304	11	interest	interest	NOUN
cana-3106	304	12	.	.	PUNCT
cana-3106	305	1	acknowledgement	acknowledgement	NOUN
cana-3106	305	2	the	the	DET
cana-3106	305	3	authors	author	NOUN
cana-3106	305	4	wish	wish	VERB
cana-3106	305	5	to	to	PART
cana-3106	305	6	thank	thank	VERB
cana-3106	305	7	unanimous	unanimous	ADJ
cana-3106	305	8	referees	referee	NOUN
cana-3106	305	9	for	for	ADP
cana-3106	305	10	their	their	PRON
cana-3106	305	11	guidance	guidance	NOUN
cana-3106	305	12	and	and	CCONJ
cana-3106	305	13	expertise	expertise	NOUN
cana-3106	305	14	throughout	throughout	ADP
cana-3106	305	15	this	this	DET
cana-3106	305	16	research	research	NOUN
cana-3106	305	17	work	work	NOUN
cana-3106	305	18	.	.	PUNCT
cana-3106	306	1	references	reference	NOUN
cana-3106	306	2	[	[	X
cana-3106	306	3	1	1	NUM
cana-3106	306	4	]	]	PUNCT
cana-3106	306	5	bajalinov	bajalinov	PROPN
cana-3106	306	6	e.b	e.b	PROPN
cana-3106	306	7	,	,	PUNCT
cana-3106	306	8	(	(	PUNCT
cana-3106	306	9	2003	2003	NUM
cana-3106	306	10	)	)	PUNCT
cana-3106	306	11	“	"	PUNCT
cana-3106	306	12	linear	linear	ADJ
cana-3106	306	13	-	-	PUNCT
cana-3106	306	14	fractional	fractional	ADJ
cana-3106	306	15	programming	programming	NOUN
cana-3106	306	16	theory	theory	NOUN
cana-3106	306	17	,	,	PUNCT
cana-3106	306	18	methods	method	NOUN
cana-3106	306	19	,	,	PUNCT
cana-3106	306	20	applications	application	NOUN
cana-3106	306	21	and	and	CCONJ
cana-3106	306	22	software	software	NOUN
cana-3106	306	23	”	"	PUNCT
cana-3106	306	24	,	,	PUNCT
cana-3106	306	25	springer	springer	NOUN
cana-3106	306	26	science	science	NOUN
cana-3106	306	27	and	and	CCONJ
cana-3106	306	28	business	business	NOUN
cana-3106	306	29	media	medium	NOUN
cana-3106	306	30	,	,	PUNCT
cana-3106	306	31	vol.84	vol.84	NOUN
cana-3106	306	32	.	.	PUNCT
cana-3106	307	1	[	[	X
cana-3106	307	2	2	2	NUM
cana-3106	307	3	]	]	PUNCT
cana-3106	307	4	bazaraa	bazaraa	NOUN
cana-3106	307	5	,	,	PUNCT
cana-3106	307	6	m.s	m.s	PROPN
cana-3106	307	7	.	.	PROPN
cana-3106	307	8	,	,	PUNCT
cana-3106	307	9	sherali	sherali	PROPN
cana-3106	307	10	,	,	PUNCT
cana-3106	307	11	h.d	h.d	PROPN
cana-3106	307	12	,	,	PUNCT
cana-3106	307	13	and	and	CCONJ
cana-3106	307	14	shetty	shetty	PROPN
cana-3106	307	15	.	.	PUNCT
cana-3106	308	1	c.m	c.m	PROPN
cana-3106	308	2	.	.	PROPN
cana-3106	308	3	,	,	PUNCT
cana-3106	308	4	(	(	PUNCT
cana-3106	308	5	1979	1979	NUM
cana-3106	308	6	)	)	PUNCT
cana-3106	308	7	,	,	PUNCT
cana-3106	308	8	nonlinear	nonlinear	ADJ
cana-3106	308	9	programming	programming	NOUN
cana-3106	308	10	:	:	PUNCT
cana-3106	308	11	theory	theory	NOUN
cana-3106	308	12	and	and	CCONJ
cana-3106	308	13	algorithms	algorithm	NOUN
cana-3106	308	14	,	,	PUNCT
cana-3106	308	15	john	john	PROPN
cana-3106	308	16	wiley	wiley	PROPN
cana-3106	308	17	and	and	CCONJ
cana-3106	308	18	sons	son	NOUN
cana-3106	308	19	,	,	PUNCT
cana-3106	308	20	newyork	newyork	NOUN
cana-3106	308	21	.	.	PUNCT
cana-3106	309	1	[	[	X
cana-3106	309	2	3	3	NUM
cana-3106	309	3	]	]	X
cana-3106	309	4	bellman	bellman	NOUN
cana-3106	309	5	,	,	PUNCT
cana-3106	309	6	r.e	r.e	PROPN
cana-3106	309	7	.	.	PROPN
cana-3106	309	8	,	,	PUNCT
cana-3106	309	9	zadeh	zadeh	PROPN
cana-3106	309	10	,	,	PUNCT
cana-3106	309	11	l.a	l.a	PROPN
cana-3106	309	12	.	.	PROPN
cana-3106	309	13	,	,	PUNCT
cana-3106	309	14	(	(	PUNCT
cana-3106	309	15	1970	1970	NUM
cana-3106	309	16	)	)	PUNCT
cana-3106	309	17	decision	decision	NOUN
cana-3106	309	18	making	making	NOUN
cana-3106	309	19	in	in	ADP
cana-3106	309	20	a	a	DET
cana-3106	309	21	fuzzy	fuzzy	ADJ
cana-3106	309	22	environment	environment	NOUN
cana-3106	309	23	,	,	PUNCT
cana-3106	309	24	management	management	NOUN
cana-3106	309	25	science	science	NOUN
cana-3106	309	26	17,141	17,141	NUM
cana-3106	309	27	-	-	SYM
cana-3106	309	28	164	164	NUM
cana-3106	309	29	.	.	PUNCT
cana-3106	310	1	[	[	X
cana-3106	310	2	4	4	X
cana-3106	310	3	]	]	PUNCT
cana-3106	310	4	bitran	bitran	NOUN
cana-3106	310	5	g.r	g.r	PROPN
cana-3106	310	6	.	.	PROPN
cana-3106	311	1	and	and	CCONJ
cana-3106	311	2	novaes	novaes	PROPN
cana-3106	311	3	a.g	a.g	PROPN
cana-3106	311	4	,	,	PUNCT
cana-3106	311	5	(	(	PUNCT
cana-3106	311	6	1973	1973	NUM
cana-3106	311	7	)	)	PUNCT
cana-3106	311	8	“	"	PUNCT
cana-3106	311	9	linear	linear	ADJ
cana-3106	311	10	programming	programming	NOUN
cana-3106	311	11	with	with	ADP
cana-3106	311	12	a	a	DET
cana-3106	311	13	fractional	fractional	ADJ
cana-3106	311	14	function	function	NOUN
cana-3106	311	15	”	"	PUNCT
cana-3106	311	16	,	,	PUNCT
cana-3106	311	17	operations	operation	NOUN
cana-3106	311	18	research	research	NOUN
cana-3106	311	19	,	,	PUNCT
cana-3106	311	20	vol.21	vol.21	NOUN
cana-3106	311	21	,	,	PUNCT
cana-3106	311	22	no	no	INTJ
cana-3106	311	23	.	.	NOUN
cana-3106	311	24	1	1	NUM
cana-3106	311	25	,	,	PUNCT
cana-3106	311	26	pp	pp	ADJ
cana-3106	311	27	.	.	PUNCT
cana-3106	312	1	22	22	NUM
cana-3106	312	2	-	-	SYM
cana-3106	312	3	29	29	NUM
cana-3106	312	4	.	.	PUNCT
cana-3106	313	1	doi:10.1287	doi:10.1287	PROPN
cana-3106	313	2	/	/	SYM
cana-3106	313	3	opre.21.1/22	opre.21.1/22	PROPN
cana-3106	313	4	.	.	PUNCT
cana-3106	314	1	[	[	X
cana-3106	314	2	5	5	NUM
cana-3106	314	3	]	]	X
cana-3106	314	4	borza	borza	NOUN
cana-3106	314	5	.	.	PUNCT
cana-3106	315	1	m	m	VERB
cana-3106	315	2	and	and	CCONJ
cana-3106	315	3	rambely	rambely	ADV
cana-3106	315	4	.	.	PUNCT
cana-3106	316	1	a.s,(2022	a.s,(2022	NOUN
cana-3106	316	2	)	)	PUNCT
cana-3106	316	3	“	"	PUNCT
cana-3106	316	4	an	an	DET
cana-3106	316	5	approach	approach	NOUN
cana-3106	316	6	based	base	VERB
cana-3106	316	7	on	on	ADP
cana-3106	316	8	alpha	alpha	NOUN
cana-3106	316	9	-	-	PUNCT
cana-3106	316	10	cuts	cut	NOUN
cana-3106	316	11	and	and	CCONJ
cana-3106	316	12	max	max	PROPN
cana-3106	316	13	-	-	PUNCT
cana-3106	316	14	min	min	NOUN
cana-3106	316	15	technique	technique	NOUN
cana-3106	316	16	to	to	PART
cana-3106	316	17	linear	linear	VERB
cana-3106	316	18	fractional	fractional	ADJ
cana-3106	316	19	programming	programming	NOUN
cana-3106	316	20	with	with	ADP
cana-3106	316	21	fuzzy	fuzzy	ADJ
cana-3106	316	22	coefficients	coefficient	NOUN
cana-3106	316	23	,	,	PUNCT
cana-3106	316	24	”	"	PUNCT
cana-3106	316	25	iranian	iranian	ADJ
cana-3106	316	26	journal	journal	NOUN
cana-3106	316	27	of	of	ADP
cana-3106	316	28	fuzzysystems	fuzzysystem	NOUN
cana-3106	316	29	,	,	PUNCT
cana-3106	316	30	vol	vol	NOUN
cana-3106	316	31	.	.	PROPN
cana-3106	316	32	19	19	NUM
cana-3106	316	33	,	,	PUNCT
cana-3106	316	34	no	no	INTJ
cana-3106	316	35	.	.	NOUN
cana-3106	316	36	1	1	NUM
cana-3106	316	37	,	,	PUNCT
cana-3106	316	38	pp	pp	ADJ
cana-3106	316	39	.	.	PUNCT
cana-3106	317	1	153	153	NUM
cana-3106	317	2	-	-	SYM
cana-3106	317	3	169	169	NUM
cana-3106	317	4	.	.	PUNCT
cana-3106	318	1	communications	communication	NOUN
cana-3106	318	2	on	on	ADP
cana-3106	318	3	applied	apply	VERB
cana-3106	318	4	nonlinear	nonlinear	ADJ
cana-3106	318	5	analysis	analysis	NOUN
cana-3106	318	6	issn	issn	NOUN
cana-3106	318	7	:	:	PUNCT
cana-3106	318	8	1074	1074	NUM
cana-3106	318	9	-	-	PUNCT
cana-3106	318	10	133x	133x	NUM
cana-3106	318	11	vol	vol	NOUN
cana-3106	318	12	32	32	NUM
cana-3106	318	13	no	no	NOUN
cana-3106	318	14	.	.	PUNCT
cana-3106	319	1	5s	5s	NUM
cana-3106	319	2	(	(	PUNCT
cana-3106	319	3	2024	2024	NUM
cana-3106	319	4	)	)	PUNCT
cana-3106	319	5	360	360	NUM
cana-3106	319	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3106	320	1	[	[	X
cana-3106	320	2	6	6	NUM
cana-3106	320	3	]	]	SYM
cana-3106	320	4	charnes	charne	NOUN
cana-3106	320	5	.a	.a	NOUN
cana-3106	320	6	and	and	CCONJ
cana-3106	320	7	w.w	w.w	PROPN
cana-3106	320	8	.	.	PROPN
cana-3106	320	9	cooper,(1962	cooper,(1962	PROPN
cana-3106	320	10	)	)	PUNCT
cana-3106	320	11	“	"	PUNCT
cana-3106	320	12	programs	program	NOUN
cana-3106	320	13	with	with	ADP
cana-3106	320	14	linear	linear	ADJ
cana-3106	320	15	fractional	fractional	ADJ
cana-3106	320	16	functions	function	NOUN
cana-3106	320	17	”	"	PUNCT
cana-3106	320	18	,	,	PUNCT
cana-3106	320	19	naval	naval	ADJ
cana-3106	320	20	research	research	NOUN
cana-3106	320	21	logistic	logistic	ADJ
cana-3106	320	22	quarterly	quarterly	ADV
cana-3106	320	23	,	,	PUNCT
cana-3106	320	24	vol.9	vol.9	PROPN
cana-3106	320	25	,	,	PUNCT
cana-3106	320	26	no	no	INTJ
cana-3106	320	27	.	.	NOUN
cana-3106	321	1	3	3	NUM
cana-3106	321	2	-	-	SYM
cana-3106	321	3	4	4	NUM
cana-3106	321	4	,	,	PUNCT
cana-3106	321	5	pp	pp	ADJ
cana-3106	321	6	.	.	PUNCT
cana-3106	322	1	181	181	NUM
cana-3106	322	2	-	-	SYM
cana-3106	322	3	196	196	NUM
cana-3106	322	4	,	,	PUNCT
cana-3106	322	5	doi:10.1002	doi:10.1002	NOUN
cana-3106	322	6	/	/	SYM
cana-3106	322	7	nav.3800090303	nav.3800090303	PRON
cana-3106	322	8	[	[	X
cana-3106	322	9	7	7	NUM
cana-3106	322	10	]	]	X
cana-3106	322	11	chen	chen	PROPN
cana-3106	322	12	,	,	PUNCT
cana-3106	322	13	s.h	s.h	PROPN
cana-3106	322	14	.	.	PROPN
cana-3106	322	15	,	,	PUNCT
cana-3106	322	16	hsieh	hsieh	PROPN
cana-3106	322	17	,	,	PUNCT
cana-3106	322	18	c.h	c.h	PROPN
cana-3106	322	19	.	.	PROPN
cana-3106	322	20	,	,	PUNCT
cana-3106	322	21	(	(	PUNCT
cana-3106	322	22	1999	1999	NUM
cana-3106	322	23	)	)	PUNCT
cana-3106	322	24	graded	grade	VERB
cana-3106	322	25	mean	mean	NOUN
cana-3106	322	26	integration	integration	NOUN
cana-3106	322	27	representation	representation	NOUN
cana-3106	322	28	of	of	ADP
cana-3106	322	29	generalized	generalized	ADJ
cana-3106	322	30	fuzzy	fuzzy	ADJ
cana-3106	322	31	number	number	NOUN
cana-3106	322	32	,	,	PUNCT
cana-3106	322	33	journal	journal	NOUN
cana-3106	322	34	of	of	ADP
cana-3106	322	35	chinese	chinese	ADJ
cana-3106	322	36	fuzzy	fuzzy	ADJ
cana-3106	322	37	systems	system	NOUN
cana-3106	322	38	5(2	5(2	NUM
cana-3106	322	39	)	)	PUNCT
cana-3106	322	40	,	,	PUNCT
cana-3106	322	41	1	1	NUM
cana-3106	322	42	-	-	SYM
cana-3106	322	43	7	7	NUM
cana-3106	322	44	.	.	PUNCT
cana-3106	323	1	[	[	X
cana-3106	323	2	8	8	NUM
cana-3106	323	3	]	]	X
cana-3106	323	4	cottle	cottle	NOUN
cana-3106	323	5	,	,	PUNCT
cana-3106	323	6	r.w	r.w	PROPN
cana-3106	323	7	.	.	PROPN
cana-3106	323	8	,	,	PUNCT
cana-3106	323	9	dantzig	dantzig	PROPN
cana-3106	323	10	,	,	PUNCT
cana-3106	323	11	g.b	g.b	PROPN
cana-3106	323	12	.	.	PROPN
cana-3106	323	13	,	,	PUNCT
cana-3106	323	14	(	(	PUNCT
cana-3106	323	15	1968	1968	NUM
cana-3106	323	16	)	)	PUNCT
cana-3106	323	17	complementarity	complementarity	NOUN
cana-3106	323	18	pivot	pivot	NOUN
cana-3106	323	19	theory	theory	NOUN
cana-3106	323	20	of	of	ADP
cana-3106	323	21	mathematical	mathematical	ADJ
cana-3106	323	22	programming	programming	NOUN
cana-3106	323	23	,	,	PUNCT
cana-3106	323	24	linear	linear	ADJ
cana-3106	323	25	algebra	algebra	NOUN
cana-3106	323	26	and	and	CCONJ
cana-3106	323	27	its	its	PRON
cana-3106	323	28	applications	application	NOUN
cana-3106	323	29	1	1	NUM
cana-3106	323	30	,	,	PUNCT
cana-3106	323	31	103	103	NUM
cana-3106	323	32	-	-	SYM
cana-3106	323	33	125	125	NUM
cana-3106	323	34	.	.	PUNCT
cana-3106	324	1	[	[	X
cana-3106	324	2	9	9	NUM
cana-3106	324	3	]	]	PUNCT
cana-3106	324	4	craven	craven	NOUN
cana-3106	324	5	,	,	PUNCT
cana-3106	324	6	b.	b.	PROPN
cana-3106	324	7	d.	d.	PROPN
cana-3106	324	8	(	(	PUNCT
cana-3106	324	9	1988	1988	NUM
cana-3106	324	10	)	)	PUNCT
cana-3106	324	11	fractional	fractional	ADJ
cana-3106	324	12	programming	programming	NOUN
cana-3106	324	13	,	,	PUNCT
cana-3106	324	14	(	(	PUNCT
cana-3106	324	15	sigma	sigma	PROPN
cana-3106	324	16	series	series	PROPN
cana-3106	324	17	in	in	ADP
cana-3106	324	18	applied	applied	ADJ
cana-3106	324	19	mathematics	mathematic	NOUN
cana-3106	324	20	)	)	PUNCT
cana-3106	324	21	heldermann	heldermann	PROPN
cana-3106	324	22	verlag	verlag	PROPN
cana-3106	324	23	,	,	PUNCT
cana-3106	324	24	berlin	berlin	PROPN
cana-3106	324	25	,	,	PUNCT
cana-3106	324	26	dm-48	dm-48	X
cana-3106	324	27	,	,	PUNCT
cana-3106	324	28	4	4	NUM
cana-3106	324	29	,	,	PUNCT
cana-3106	324	30	145pp	145pp	NOUN
cana-3106	324	31	.	.	PUNCT
cana-3106	325	1	[	[	X
cana-3106	325	2	10	10	NUM
cana-3106	325	3	]	]	X
cana-3106	325	4	de	de	X
cana-3106	325	5	schutter.b	schutter.b	NOUN
cana-3106	325	6	,	,	PUNCT
cana-3106	325	7	heemels	heemel	NOUN
cana-3106	325	8	.	.	PUNCT
cana-3106	326	1	w.p.m.h	w.p.m.h	PROPN
cana-3106	326	2	,	,	PUNCT
cana-3106	326	3	bemporad	bemporad	PROPN
cana-3106	326	4	,	,	PUNCT
cana-3106	326	5	a.	a.	NOUN
cana-3106	326	6	,(2002	,(2002	PROPN
cana-3106	326	7	)	)	PUNCT
cana-3106	326	8	on	on	ADP
cana-3106	326	9	the	the	DET
cana-3106	326	10	equivalence	equivalence	NOUN
cana-3106	326	11	of	of	ADP
cana-3106	326	12	linear	linear	ADJ
cana-3106	326	13	complementarity	complementarity	NOUN
cana-3106	326	14	problems	problem	NOUN
cana-3106	326	15	,	,	PUNCT
cana-3106	326	16	operations	operation	NOUN
cana-3106	326	17	research	research	NOUN
cana-3106	326	18	letters	letter	NOUN
cana-3106	326	19	,	,	PUNCT
cana-3106	326	20	elsevier	elsevier	NOUN
cana-3106	326	21	,	,	PUNCT
cana-3106	326	22	30	30	NUM
cana-3106	326	23	,	,	PUNCT
cana-3106	326	24	211	211	NUM
cana-3106	326	25	-	-	SYM
cana-3106	326	26	222	222	NUM
cana-3106	326	27	.	.	PUNCT
cana-3106	327	1	[	[	X
cana-3106	327	2	11	11	NUM
cana-3106	327	3	]	]	X
cana-3106	327	4	dubois	dubois	PROPN
cana-3106	327	5	,	,	PUNCT
cana-3106	327	6	d.	d.	PROPN
cana-3106	327	7	,	,	PUNCT
cana-3106	327	8	and	and	CCONJ
cana-3106	327	9	prade	prade	NOUN
cana-3106	327	10	,	,	PUNCT
cana-3106	327	11	h.	h.	PROPN
cana-3106	327	12	,	,	PUNCT
cana-3106	327	13	(	(	PUNCT
cana-3106	327	14	1978	1978	NUM
cana-3106	327	15	)	)	PUNCT
cana-3106	327	16	operation	operation	NOUN
cana-3106	327	17	of	of	ADP
cana-3106	327	18	fuzzy	fuzzy	ADJ
cana-3106	327	19	numbers	number	NOUN
cana-3106	327	20	,	,	PUNCT
cana-3106	327	21	internat	internat	NOUN
cana-3106	327	22	.	.	PUNCT
cana-3106	328	1	j.systems	j.systems	PROPN
cana-3106	328	2	sci	sci	PROPN
cana-3106	328	3	.	.	PROPN
cana-3106	328	4	9(6	9(6	NUM
cana-3106	328	5	)	)	PUNCT
cana-3106	328	6	,	,	PUNCT
cana-3106	328	7	613	613	NUM
cana-3106	328	8	-	-	SYM
cana-3106	328	9	626	626	NUM
cana-3106	328	10	.	.	PUNCT
cana-3106	329	1	[	[	X
cana-3106	329	2	12	12	NUM
cana-3106	329	3	]	]	PUNCT
cana-3106	329	4	hamdy	hamdy	PROPN
cana-3106	329	5	.	.	PUNCT
cana-3106	329	6	a.	a.	PROPN
cana-3106	329	7	taha	taha	PROPN
cana-3106	329	8	,	,	PUNCT
cana-3106	329	9	(	(	PUNCT
cana-3106	329	10	2006	2006	NUM
cana-3106	329	11	)	)	PUNCT
cana-3106	329	12	operations	operation	NOUN
cana-3106	329	13	research	research	NOUN
cana-3106	329	14	:	:	PUNCT
cana-3106	329	15	an	an	DET
cana-3106	329	16	introduction	introduction	NOUN
cana-3106	329	17	,	,	PUNCT
cana-3106	329	18	eighth	eighth	ADJ
cana-3106	329	19	edition	edition	NOUN
cana-3106	329	20	,	,	PUNCT
cana-3106	329	21	prentice	prentice	NOUN
cana-3106	329	22	–	–	PUNCT
cana-3106	329	23	hall	hall	NOUN
cana-3106	329	24	of	of	ADP
cana-3106	329	25	india	india	PROPN
cana-3106	329	26	private	private	PROPN
cana-3106	329	27	ltd	ltd	PROPN
cana-3106	329	28	,	,	PUNCT
cana-3106	329	29	delhi	delhi	PROPN
cana-3106	329	30	.	.	PUNCT
cana-3106	330	1	[	[	X
cana-3106	330	2	13	13	NUM
cana-3106	330	3	]	]	PUNCT
cana-3106	330	4	irene	irene	NOUN
cana-3106	330	5	hepzibah.r	hepzibah.r	PROPN
cana-3106	330	6	.	.	PUNCT
cana-3106	331	1	,	,	PUNCT
cana-3106	331	2	(	(	PUNCT
cana-3106	331	3	2021	2021	NUM
cana-3106	331	4	)	)	PUNCT
cana-3106	331	5	an	an	DET
cana-3106	331	6	algorithmic	algorithmic	ADJ
cana-3106	331	7	approach	approach	NOUN
cana-3106	331	8	to	to	ADP
cana-3106	331	9	fuzzy	fuzzy	ADJ
cana-3106	331	10	linear	linear	ADJ
cana-3106	331	11	complementarity	complementarity	NOUN
cana-3106	331	12	problems	problem	NOUN
cana-3106	331	13	,	,	PUNCT
cana-3106	331	14	lambert	lambert	PROPN
cana-3106	331	15	academic	academic	ADJ
cana-3106	331	16	publishing	publishing	NOUN
cana-3106	331	17	,	,	PUNCT
cana-3106	331	18	germany	germany	PROPN
cana-3106	331	19	.	.	PUNCT
cana-3106	332	1	[	[	X
cana-3106	332	2	14	14	NUM
cana-3106	332	3	]	]	PUNCT
cana-3106	332	4	jenifer	jenifer	NOUN
cana-3106	332	5	.	.	PUNCT
cana-3106	333	1	d	d	X
cana-3106	333	2	h	h	NOUN
cana-3106	333	3	,	,	PUNCT
cana-3106	333	4	irene	irene	PROPN
cana-3106	333	5	hebzibah	hebzibah	NOUN
cana-3106	333	6	.	.	PUNCT
cana-3106	334	1	r	r	NOUN
cana-3106	334	2	,	,	PUNCT
cana-3106	334	3	(	(	PUNCT
cana-3106	334	4	2023	2023	NUM
cana-3106	334	5	)	)	PUNCT
cana-3106	334	6	on	on	ADP
cana-3106	334	7	solving	solve	VERB
cana-3106	334	8	fuzzy	fuzzy	ADJ
cana-3106	334	9	linear	linear	ADJ
cana-3106	334	10	complementarity	complementarity	NOUN
cana-3106	334	11	problem	problem	NOUN
cana-3106	334	12	via	via	ADP
cana-3106	334	13	maximum	maximum	ADJ
cana-3106	334	14	index	index	NOUN
cana-3106	334	15	method	method	NOUN
cana-3106	334	16	,	,	PUNCT
cana-3106	334	17	referred	refer	VERB
cana-3106	334	18	proceedings	proceeding	NOUN
cana-3106	334	19	of	of	ADP
cana-3106	334	20	2nd	2nd	ADJ
cana-3106	334	21	international	international	ADJ
cana-3106	334	22	conference	conference	NOUN
cana-3106	334	23	on	on	ADP
cana-3106	334	24	emerging	emerge	VERB
cana-3106	334	25	trends	trend	NOUN
cana-3106	334	26	in	in	ADP
cana-3106	334	27	science	science	NOUN
cana-3106	334	28	and	and	CCONJ
cana-3106	334	29	social	social	ADJ
cana-3106	334	30	science	science	NOUN
cana-3106	334	31	in	in	ADP
cana-3106	334	32	pattaya	pattaya	PROPN
cana-3106	334	33	,	,	PUNCT
cana-3106	334	34	thailand	thailand	PROPN
cana-3106	334	35	.	.	PUNCT
cana-3106	335	1	[	[	X
cana-3106	335	2	15	15	NUM
cana-3106	335	3	]	]	PUNCT
cana-3106	335	4	jenifer	jenifer	NOUN
cana-3106	335	5	.	.	PUNCT
cana-3106	336	1	d	d	X
cana-3106	336	2	h	h	NOUN
cana-3106	336	3	,	,	PUNCT
cana-3106	336	4	irene	irene	PROPN
cana-3106	336	5	hebzibah	hebzibah	NOUN
cana-3106	336	6	.	.	PUNCT
cana-3106	337	1	r	r	NOUN
cana-3106	337	2	,	,	PUNCT
cana-3106	337	3	(	(	PUNCT
cana-3106	337	4	2024	2024	NUM
cana-3106	337	5	)	)	PUNCT
cana-3106	337	6	solving	solve	VERB
cana-3106	337	7	neutrosophic	neutrosophic	ADJ
cana-3106	337	8	linear	linear	ADJ
cana-3106	337	9	complementarity	complementarity	NOUN
cana-3106	337	10	problem	problem	NOUN
cana-3106	337	11	using	use	VERB
cana-3106	337	12	the	the	DET
cana-3106	337	13	inverse	inverse	NOUN
cana-3106	337	14	of	of	ADP
cana-3106	337	15	the	the	DET
cana-3106	337	16	basis	basis	NOUN
cana-3106	337	17	,	,	PUNCT
cana-3106	337	18	journal	journal	NOUN
cana-3106	337	19	of	of	ADP
cana-3106	337	20	nonlinear	nonlinear	ADJ
cana-3106	337	21	analysis	analysis	NOUN
cana-3106	337	22	and	and	CCONJ
cana-3106	337	23	optimization	optimization	NOUN
cana-3106	337	24	,	,	PUNCT
cana-3106	337	25	vol	vol	NOUN
cana-3106	337	26	.	.	PROPN
cana-3106	337	27	15	15	NUM
cana-3106	337	28	,	,	PUNCT
cana-3106	337	29	issue	issue	NOUN
cana-3106	337	30	.	.	PUNCT
cana-3106	338	1	1	1	NUM
cana-3106	338	2	,	,	PUNCT
cana-3106	338	3	no	no	INTJ
cana-3106	338	4	.	.	NOUN
cana-3106	338	5	10	10	NUM
cana-3106	338	6	,	,	PUNCT
cana-3106	338	7	89	89	NUM
cana-3106	338	8	-	-	SYM
cana-3106	338	9	95	95	NUM
cana-3106	338	10	.	.	PUNCT
cana-3106	339	1	[	[	X
cana-3106	339	2	16	16	NUM
cana-3106	339	3	]	]	PUNCT
cana-3106	339	4	jenifer	jenifer	NOUN
cana-3106	339	5	.	.	PUNCT
cana-3106	340	1	d	d	PROPN
cana-3106	340	2	h	h	NOUN
cana-3106	340	3	,	,	PUNCT
cana-3106	340	4	irene	irene	PROPN
cana-3106	340	5	hebzibah	hebzibah	NOUN
cana-3106	340	6	.	.	PUNCT
cana-3106	341	1	r	r	NOUN
cana-3106	341	2	,	,	PUNCT
cana-3106	341	3	(	(	PUNCT
cana-3106	341	4	2024	2024	NUM
cana-3106	341	5	)	)	PUNCT
cana-3106	341	6	a	a	DET
cana-3106	341	7	methodology	methodology	NOUN
cana-3106	341	8	for	for	ADP
cana-3106	341	9	solving	solve	VERB
cana-3106	341	10	fuzzy	fuzzy	ADJ
cana-3106	341	11	linear	linear	ADJ
cana-3106	341	12	programming	programming	NOUN
cana-3106	341	13	problem	problem	NOUN
cana-3106	341	14	as	as	ADP
cana-3106	341	15	a	a	DET
cana-3106	341	16	fuzzy	fuzzy	ADJ
cana-3106	341	17	linear	linear	ADJ
cana-3106	341	18	complementarity	complementarity	NOUN
cana-3106	341	19	problem	problem	NOUN
cana-3106	341	20	,	,	PUNCT
cana-3106	341	21	communications	communication	NOUN
cana-3106	341	22	on	on	ADP
cana-3106	341	23	applied	apply	VERB
cana-3106	341	24	nonlinear	nonlinear	ADJ
cana-3106	341	25	analysis	analysis	NOUN
cana-3106	341	26	,	,	PUNCT
cana-3106	341	27	vol	vol	NOUN
cana-3106	341	28	.	.	PUNCT
cana-3106	342	1	31,no	31,no	NUM
cana-3106	342	2	,	,	PUNCT
cana-3106	342	3	2s,1	2s,1	NUM
cana-3106	342	4	-	-	SYM
cana-3106	342	5	8	8	NUM
cana-3106	342	6	.	.	PUNCT
cana-3106	343	1	[	[	X
cana-3106	343	2	17	17	NUM
cana-3106	343	3	]	]	X
cana-3106	343	4	laisin	laisin	PROPN
cana-3106	343	5	,	,	PUNCT
cana-3106	343	6	m.	m.	NOUN
cana-3106	343	7	,	,	PUNCT
cana-3106	343	8	okeke	okeke	ADJ
cana-3106	343	9	,	,	PUNCT
cana-3106	343	10	j.e	j.e	PROPN
cana-3106	343	11	.	.	PROPN
cana-3106	343	12	,	,	PUNCT
cana-3106	343	13	(	(	PUNCT
cana-3106	343	14	2017	2017	NUM
cana-3106	343	15	)	)	PUNCT
cana-3106	343	16	“	"	PUNCT
cana-3106	343	17	linear	linear	ADJ
cana-3106	343	18	complementarity	complementarity	NOUN
cana-3106	343	19	problems	problem	NOUN
cana-3106	343	20	applications	application	NOUN
cana-3106	343	21	to	to	ADP
cana-3106	343	22	other	other	ADJ
cana-3106	343	23	programming	programming	NOUN
cana-3106	343	24	problems	problem	NOUN
cana-3106	343	25	”	"	PUNCT
cana-3106	343	26	,	,	PUNCT
cana-3106	343	27	coou	coou	NOUN
cana-3106	343	28	journal	journal	PROPN
cana-3106	343	29	of	of	ADP
cana-3106	343	30	physical	physical	ADJ
cana-3106	343	31	science	science	NOUN
cana-3106	343	32	1(2	1(2	NUM
cana-3106	343	33	)	)	PUNCT
cana-3106	343	34	,	,	PUNCT
cana-3106	343	35	147	147	NUM
cana-3106	343	36	-	-	SYM
cana-3106	343	37	156	156	NUM
cana-3106	343	38	.	.	PUNCT
cana-3106	344	1	[	[	X
cana-3106	344	2	18	18	NUM
cana-3106	344	3	]	]	SYM
cana-3106	344	4	lemke	lemke	PROPN
cana-3106	344	5	,	,	PUNCT
cana-3106	344	6	c.e	c.e	PROPN
cana-3106	344	7	.	.	PROPN
cana-3106	344	8	,	,	PUNCT
cana-3106	344	9	(	(	PUNCT
cana-3106	344	10	1968	1968	NUM
cana-3106	344	11	)	)	PUNCT
cana-3106	344	12	“	"	PUNCT
cana-3106	344	13	on	on	ADP
cana-3106	344	14	complementary	complementary	ADJ
cana-3106	344	15	pivot	pivot	NOUN
cana-3106	344	16	theory	theory	NOUN
cana-3106	344	17	”	"	PUNCT
cana-3106	344	18	,	,	PUNCT
cana-3106	344	19	mathematics	mathematic	NOUN
cana-3106	344	20	of	of	ADP
cana-3106	344	21	the	the	DET
cana-3106	344	22	decision	decision	NOUN
cana-3106	344	23	sciences	science	NOUN
cana-3106	344	24	,	,	PUNCT
cana-3106	344	25	g.b.danting	g.b.dante	VERB
cana-3106	344	26	and	and	CCONJ
cana-3106	344	27	a.f.veioff	a.f.veioff	NOUN
cana-3106	344	28	,	,	PUNCT
cana-3106	344	29	eds	eds	PROPN
cana-3106	344	30	.	.	PUNCT
cana-3106	345	1	[	[	X
cana-3106	345	2	19	19	NUM
cana-3106	345	3	]	]	X
cana-3106	345	4	moore	moore	PROPN
cana-3106	345	5	r.e	r.e	PROPN
cana-3106	345	6	and	and	CCONJ
cana-3106	345	7	kearfott	kearfott	VERB
cana-3106	345	8	r.b	r.b	PROPN
cana-3106	345	9	,	,	PUNCT
cana-3106	345	10	m.j	m.j	PROPN
cana-3106	345	11	.	.	PROPN
cana-3106	345	12	cloud	cloud	PROPN
cana-3106	345	13	,	,	PUNCT
cana-3106	345	14	(	(	PUNCT
cana-3106	345	15	2009	2009	NUM
cana-3106	345	16	)	)	PUNCT
cana-3106	345	17	introduction	introduction	NOUN
cana-3106	345	18	to	to	ADP
cana-3106	345	19	interval	interval	NOUN
cana-3106	345	20	analysis	analysis	NOUN
cana-3106	345	21	,	,	PUNCT
cana-3106	345	22	philadelphia	philadelphia	PROPN
cana-3106	345	23	.	.	PUNCT
cana-3106	346	1	[	[	X
cana-3106	346	2	20	20	NUM
cana-3106	346	3	]	]	PUNCT
cana-3106	346	4	moumita	moumita	PROPN
cana-3106	346	5	deb	deb	PROPN
cana-3106	346	6	and	and	CCONJ
cana-3106	346	7	p.	p.	PROPN
cana-3106	346	8	k.	k.	PROPN
cana-3106	347	1	de	de	PROPN
cana-3106	347	2	,	,	PUNCT
cana-3106	347	3	(	(	PUNCT
cana-3106	347	4	2015	2015	NUM
cana-3106	347	5	)	)	PUNCT
cana-3106	347	6	optimal	optimal	ADJ
cana-3106	347	7	solution	solution	NOUN
cana-3106	347	8	of	of	ADP
cana-3106	347	9	a	a	DET
cana-3106	347	10	fully	fully	ADV
cana-3106	347	11	fuzzy	fuzzy	ADJ
cana-3106	347	12	linear	linear	ADJ
cana-3106	347	13	fractional	fractional	ADJ
cana-3106	347	14	programming	programming	NOUN
cana-3106	347	15	problem	problem	NOUN
cana-3106	347	16	by	by	ADP
cana-3106	347	17	using	use	VERB
cana-3106	347	18	graded	grade	VERB
cana-3106	347	19	mean	mean	PROPN
cana-3106	347	20	intergration	intergration	NOUN
cana-3106	347	21	representation	representation	NOUN
cana-3106	347	22	method	method	NOUN
cana-3106	347	23	,	,	PUNCT
cana-3106	347	24	applications	application	NOUN
cana-3106	347	25	and	and	CCONJ
cana-3106	347	26	applied	apply	VERB
cana-3106	347	27	mathematics	mathematic	NOUN
cana-3106	347	28	:	:	PUNCT
cana-3106	347	29	an	an	DET
cana-3106	347	30	international	international	ADJ
cana-3106	347	31	journal	journal	NOUN
cana-3106	347	32	,	,	PUNCT
cana-3106	347	33	vol	vol	NOUN
cana-3106	347	34	.	.	PROPN
cana-3106	347	35	10	10	NUM
cana-3106	347	36	,	,	PUNCT
cana-3106	347	37	issue	issue	NOUN
cana-3106	347	38	.	.	PUNCT
cana-3106	348	1	1	1	NUM
cana-3106	348	2	,	,	PUNCT
cana-3106	348	3	pp	pp	ADJ
cana-3106	348	4	.	.	PUNCT
cana-3106	349	1	571	571	NUM
cana-3106	349	2	-	-	SYM
cana-3106	349	3	587	587	NUM
cana-3106	349	4	.	.	PUNCT
cana-3106	350	1	[	[	X
cana-3106	350	2	21	21	NUM
cana-3106	350	3	]	]	X
cana-3106	350	4	murthy	murthy	PROPN
cana-3106	350	5	.	.	PUNCT
cana-3106	351	1	k.g	k.g	PROPN
cana-3106	351	2	.	.	PROPN
cana-3106	351	3	,	,	PUNCT
cana-3106	351	4	(	(	PUNCT
cana-3106	351	5	1997	1997	NUM
cana-3106	351	6	)	)	PUNCT
cana-3106	351	7	“	"	PUNCT
cana-3106	351	8	linear	linear	ADJ
cana-3106	351	9	complementarity	complementarity	NOUN
cana-3106	351	10	,	,	PUNCT
cana-3106	351	11	linear	linear	ADJ
cana-3106	351	12	and	and	CCONJ
cana-3106	351	13	nonlinear	nonlinear	ADJ
cana-3106	351	14	programming	programming	NOUN
cana-3106	351	15	”	"	PUNCT
cana-3106	351	16	,	,	PUNCT
cana-3106	351	17	internet	internet	NOUN
cana-3106	351	18	edition	edition	NOUN
cana-3106	351	19	,	,	PUNCT
cana-3106	351	20	http://www.personal.engin.umich.edu/~murty	http://www.personal.engin.umich.edu/~murty	NOUN
cana-3106	351	21	,	,	PUNCT
cana-3106	351	22	254	254	NUM
cana-3106	351	23	-	-	SYM
cana-3106	351	24	273	273	NUM
cana-3106	351	25	.	.	PUNCT
cana-3106	352	1	[	[	X
cana-3106	352	2	22	22	NUM
cana-3106	352	3	]	]	X
cana-3106	352	4	premkumar	premkumar	PROPN
cana-3106	352	5	gupta	gupta	PROPN
cana-3106	352	6	.	.	PROPN
cana-3106	352	7	,	,	PUNCT
cana-3106	352	8	hira	hira	PROPN
cana-3106	352	9	,	,	PUNCT
cana-3106	352	10	d.s	d.s	PROPN
cana-3106	352	11	.	.	PROPN
cana-3106	352	12	,	,	PUNCT
cana-3106	352	13	(	(	PUNCT
cana-3106	352	14	2004	2004	NUM
cana-3106	352	15	)	)	PUNCT
cana-3106	352	16	operations	operation	NOUN
cana-3106	352	17	research	research	NOUN
cana-3106	352	18	,	,	PUNCT
cana-3106	352	19	s.	s.	PROPN
cana-3106	352	20	chand	chand	PROPN
cana-3106	352	21	&	&	CCONJ
cana-3106	352	22	company	company	PROPN
cana-3106	352	23	ltd	ltd	PROPN
cana-3106	352	24	.	.	PUNCT
cana-3106	353	1	[	[	X
cana-3106	353	2	23	23	NUM
cana-3106	353	3	]	]	X
cana-3106	353	4	richard	richard	PROPN
cana-3106	353	5	w.cottle	w.cottle	PROPN
cana-3106	353	6	,	,	PUNCT
cana-3106	353	7	jong	jong	PROPN
cana-3106	353	8	-	-	PUNCT
cana-3106	353	9	shi	shi	PROPN
cana-3106	353	10	pang	pang	PROPN
cana-3106	353	11	,	,	PUNCT
cana-3106	353	12	richard	richard	PROPN
cana-3106	353	13	e.stone	e.stone	PROPN
cana-3106	353	14	.	.	PUNCT
cana-3106	353	15	,	,	PUNCT
cana-3106	353	16	(	(	PUNCT
cana-3106	353	17	2009	2009	NUM
cana-3106	353	18	)	)	PUNCT
cana-3106	353	19	the	the	DET
cana-3106	353	20	linear	linear	ADJ
cana-3106	353	21	complementarity	complementarity	NOUN
cana-3106	353	22	problem	problem	NOUN
cana-3106	353	23	,	,	PUNCT
cana-3106	353	24	siam	siam	NOUN
cana-3106	353	25	.	.	PUNCT
cana-3106	354	1	[	[	X
cana-3106	354	2	24	24	NUM
cana-3106	354	3	]	]	X
cana-3106	354	4	robert	robert	PROPN
cana-3106	354	5	.	.	PROPN
cana-3106	354	6	l.	l.	PROPN
cana-3106	354	7	graves	graves	PROPN
cana-3106	354	8	,	,	PUNCT
cana-3106	354	9	(	(	PUNCT
cana-3106	354	10	1967	1967	NUM
cana-3106	354	11	)	)	PUNCT
cana-3106	354	12	a	a	DET
cana-3106	354	13	principal	principal	ADJ
cana-3106	354	14	pivoting	pivot	VERB
cana-3106	354	15	simplex	simplex	NOUN
cana-3106	354	16	algorithm	algorithm	NOUN
cana-3106	354	17	for	for	ADP
cana-3106	354	18	linear	linear	ADJ
cana-3106	354	19	and	and	CCONJ
cana-3106	354	20	quadratic	quadratic	ADJ
cana-3106	354	21	programming	programming	NOUN
cana-3106	354	22	,	,	PUNCT
cana-3106	354	23	operations	operation	NOUN
cana-3106	354	24	research	research	NOUN
cana-3106	354	25	,	,	PUNCT
cana-3106	354	26	482	482	NUM
cana-3106	354	27	-	-	SYM
cana-3106	354	28	494	494	NUM
cana-3106	354	29	.	.	PUNCT
cana-3106	355	1	[	[	X
cana-3106	355	2	25	25	NUM
cana-3106	355	3	]	]	X
cana-3106	355	4	singh	singh	PROPN
cana-3106	355	5	.	.	PUNCT
cana-3106	356	1	c	c	X
cana-3106	356	2	,	,	PUNCT
cana-3106	356	3	(	(	PUNCT
cana-3106	356	4	1990	1990	NUM
cana-3106	356	5	)	)	PUNCT
cana-3106	356	6	“	"	PUNCT
cana-3106	356	7	optimality	optimality	NOUN
cana-3106	356	8	conditions	condition	NOUN
cana-3106	356	9	in	in	ADP
cana-3106	356	10	fractional	fractional	ADJ
cana-3106	356	11	programming	programming	NOUN
cana-3106	356	12	,	,	PUNCT
cana-3106	356	13	”	"	PUNCT
cana-3106	356	14	journal	journal	NOUN
cana-3106	356	15	of	of	ADP
cana-3106	356	16	optimization	optimization	NOUN
cana-3106	356	17	theory	theory	NOUN
cana-3106	356	18	and	and	CCONJ
cana-3106	356	19	applications	application	NOUN
cana-3106	356	20	,	,	PUNCT
cana-3106	356	21	vol	vol	NOUN
cana-3106	356	22	.	.	PROPN
cana-3106	357	1	33	33	NUM
cana-3106	357	2	,	,	PUNCT
cana-3106	357	3	no	no	INTJ
cana-3106	357	4	.	.	NOUN
cana-3106	357	5	2	2	NUM
cana-3106	357	6	,	,	PUNCT
cana-3106	357	7	pp	pp	ADJ
cana-3106	357	8	.	.	PUNCT
cana-3106	358	1	287	287	NUM
cana-3106	358	2	-	-	SYM
cana-3106	358	3	294	294	NUM
cana-3106	358	4	.	.	PUNCT
cana-3106	359	1	[	[	X
cana-3106	359	2	26	26	NUM
cana-3106	359	3	]	]	X
cana-3106	359	4	sohrab	sohrab	NOUN
cana-3106	359	5	effati	effati	PROPN
cana-3106	359	6	and	and	CCONJ
cana-3106	359	7	morteza	morteza	PROPN
cana-3106	359	8	pakdaman	pakdaman	NOUN
cana-3106	359	9	,	,	PUNCT
cana-3106	359	10	(	(	PUNCT
cana-3106	359	11	2012	2012	NUM
cana-3106	359	12	)	)	PUNCT
cana-3106	359	13	solving	solve	VERB
cana-3106	359	14	the	the	DET
cana-3106	359	15	interval	interval	NOUN
cana-3106	359	16	–	–	PUNCT
cana-3106	359	17	valued	value	VERB
cana-3106	359	18	fractional	fractional	ADJ
cana-3106	359	19	programming	programming	NOUN
cana-3106	359	20	problem	problem	NOUN
cana-3106	359	21	,	,	PUNCT
cana-3106	359	22	american	american	ADJ
cana-3106	359	23	journal	journal	NOUN
cana-3106	359	24	of	of	ADP
cana-3106	359	25	computational	computational	ADJ
cana-3106	359	26	mathematics	mathematic	NOUN
cana-3106	359	27	,	,	PUNCT
cana-3106	359	28	vol	vol	NOUN
cana-3106	359	29	.	.	PROPN
cana-3106	359	30	2	2	NUM
cana-3106	359	31	,	,	PUNCT
cana-3106	359	32	51	51	NUM
cana-3106	359	33	-	-	SYM
cana-3106	359	34	55	55	NUM
cana-3106	359	35	.	.	PUNCT
cana-3106	360	1	[	[	X
cana-3106	360	2	27	27	NUM
cana-3106	360	3	]	]	X
cana-3106	360	4	swarup	swarup	NOUN
cana-3106	360	5	.	.	PUNCT
cana-3106	361	1	k	k	X
cana-3106	361	2	,	,	PUNCT
cana-3106	361	3	(	(	PUNCT
cana-3106	361	4	1965	1965	NUM
cana-3106	361	5	)	)	PUNCT
cana-3106	361	6	“	"	PUNCT
cana-3106	361	7	linear	linear	ADJ
cana-3106	361	8	fractional	fractional	ADJ
cana-3106	361	9	functionals	functional	NOUN
cana-3106	361	10	programming	programming	NOUN
cana-3106	361	11	”	"	PUNCT
cana-3106	361	12	,	,	PUNCT
cana-3106	361	13	operations	operation	NOUN
cana-3106	361	14	research	research	NOUN
cana-3106	361	15	,	,	PUNCT
cana-3106	361	16	vol	vol	NOUN
cana-3106	361	17	.	.	PROPN
cana-3106	361	18	13	13	NUM
cana-3106	361	19	,	,	PUNCT
cana-3106	361	20	no	no	INTJ
cana-3106	361	21	.	.	NOUN
cana-3106	361	22	6	6	NUM
cana-3106	361	23	,	,	PUNCT
cana-3106	361	24	pp	pp	ADJ
cana-3106	361	25	.	.	PUNCT
cana-3106	361	26	10291036	10291036	NUM
cana-3106	361	27	.	.	PUNCT
cana-3106	362	1	[	[	X
cana-3106	362	2	28	28	NUM
cana-3106	362	3	]	]	X
cana-3106	362	4	youssef	youssef	PROPN
cana-3106	362	5	elfoutayeni	elfoutayeni	PROPN
cana-3106	362	6	,	,	PUNCT
cana-3106	362	7	mohamed	mohamed	PROPN
cana-3106	362	8	khaladi	khaladi	PROPN
cana-3106	362	9	,	,	PUNCT
cana-3106	362	10	(	(	PUNCT
cana-3106	362	11	2012	2012	NUM
cana-3106	362	12	)	)	PUNCT
cana-3106	362	13	using	use	VERB
cana-3106	362	14	vector	vector	NOUN
cana-3106	362	15	divisions	division	NOUN
cana-3106	362	16	in	in	ADP
cana-3106	362	17	solving	solve	VERB
cana-3106	362	18	the	the	DET
cana-3106	362	19	linear	linear	ADJ
cana-3106	362	20	complementarity	complementarity	NOUN
cana-3106	362	21	problem	problem	NOUN
cana-3106	362	22	,	,	PUNCT
cana-3106	362	23	journal	journal	NOUN
cana-3106	362	24	of	of	ADP
cana-3106	362	25	computational	computational	ADJ
cana-3106	362	26	and	and	CCONJ
cana-3106	362	27	applied	applied	ADJ
cana-3106	362	28	mathematics	mathematic	NOUN
cana-3106	362	29	,	,	PUNCT
cana-3106	362	30	elsevier	elsevier	NOUN
cana-3106	362	31	,	,	PUNCT
cana-3106	362	32	236	236	NUM
cana-3106	362	33	,	,	PUNCT
cana-3106	362	34	1919	1919	NUM
cana-3106	362	35	-	-	SYM
cana-3106	362	36	1925	1925	NUM
cana-3106	362	37	.	.	PUNCT
cana-3106	363	1	[	[	X
cana-3106	363	2	29	29	NUM
cana-3106	363	3	]	]	X
cana-3106	363	4	zadeh	zadeh	PROPN
cana-3106	363	5	,	,	PUNCT
cana-3106	363	6	l.a	l.a	PROPN
cana-3106	363	7	,	,	PUNCT
cana-3106	363	8	(	(	PUNCT
cana-3106	363	9	1965	1965	NUM
cana-3106	363	10	)	)	PUNCT
cana-3106	363	11	“	"	PUNCT
cana-3106	363	12	fuzzy	fuzzy	ADJ
cana-3106	363	13	stes	ste	NOUN
cana-3106	363	14	”	"	PUNCT
cana-3106	363	15	information	information	NOUN
cana-3106	363	16	and	and	CCONJ
cana-3106	363	17	control	control	NOUN
cana-3106	363	18	8	8	NUM
cana-3106	363	19	,	,	PUNCT
cana-3106	363	20	pp	pp	ADJ
cana-3106	363	21	.	.	PUNCT
cana-3106	363	22	338	338	NUM
cana-3106	363	23	-	-	SYM
cana-3106	363	24	353	353	NUM
cana-3106	363	25	.	.	PUNCT
cana-3106	364	1	[	[	X
cana-3106	364	2	30	30	NUM
cana-3106	364	3	]	]	X
cana-3106	364	4	zimmermann	zimmermann	PROPN
cana-3106	364	5	.	.	PUNCT
cana-3106	365	1	h.j	h.j	PROPN
cana-3106	365	2	,	,	PUNCT
cana-3106	365	3	(	(	PUNCT
cana-3106	365	4	1991	1991	NUM
cana-3106	365	5	)	)	PUNCT
cana-3106	365	6	“	"	PUNCT
cana-3106	365	7	fuzzy	fuzzy	ADJ
cana-3106	365	8	set	set	NOUN
cana-3106	365	9	theory	theory	NOUN
cana-3106	365	10	and	and	CCONJ
cana-3106	365	11	its	its	PRON
cana-3106	365	12	applications	application	NOUN
cana-3106	365	13	”	"	PUNCT
cana-3106	365	14	,	,	PUNCT
cana-3106	365	15	second	second	ADJ
cana-3106	365	16	edition	edition	NOUN
cana-3106	365	17	,	,	PUNCT
cana-3106	365	18	kluwer	kluwer	PROPN
cana-3106	365	19	academic	academic	PROPN
cana-3106	365	20	publishers	publishers	PROPN
cana-3106	365	21	germany	germany	PROPN
cana-3106	365	22	.	.	PUNCT