id	sid	tid	token	lemma	pos
cana-1038	1	1	communications	communication	NOUN
cana-1038	1	2	on	on	ADP
cana-1038	1	3	applied	apply	VERB
cana-1038	1	4	nonlinear	nonlinear	ADJ
cana-1038	1	5	analysis	analysis	NOUN
cana-1038	1	6	issn	issn	NOUN
cana-1038	1	7	:	:	PUNCT
cana-1038	1	8	1074	1074	NUM
cana-1038	1	9	-	-	PUNCT
cana-1038	1	10	133x	133x	NUM
cana-1038	1	11	vol	vol	NOUN
cana-1038	1	12	31	31	NUM
cana-1038	1	13	no	no	NOUN
cana-1038	1	14	.	.	PUNCT
cana-1038	2	1	5s	5s	NUM
cana-1038	2	2	(	(	PUNCT
cana-1038	2	3	2024	2024	NUM
cana-1038	2	4	)	)	PUNCT
cana-1038	2	5	296	296	NUM
cana-1038	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1038	2	7	a	a	DET
cana-1038	2	8	comparison	comparison	NOUN
cana-1038	2	9	of	of	ADP
cana-1038	2	10	proposed	propose	VERB
cana-1038	2	11	ranking	ranking	NOUN
cana-1038	2	12	method	method	NOUN
cana-1038	2	13	for	for	ADP
cana-1038	2	14	fuzzy	fuzzy	ADJ
cana-1038	2	15	transportation	transportation	NOUN
cana-1038	2	16	problem	problem	NOUN
cana-1038	2	17	with	with	ADP
cana-1038	2	18	the	the	DET
cana-1038	2	19	existing	exist	VERB
cana-1038	2	20	method	method	NOUN
cana-1038	2	21	e.	e.	PROPN
cana-1038	2	22	fany	fany	PROPN
cana-1038	2	23	helena	helena	PROPN
cana-1038	2	24	1	1	NUM
cana-1038	2	25	,	,	PUNCT
cana-1038	2	26	d.	d.	PROPN
cana-1038	2	27	stephen	stephen	PROPN
cana-1038	2	28	dinagar	dinagar	PROPN
cana-1038	2	29	2	2	NUM
cana-1038	2	30	1assistant	1assistant	NUM
cana-1038	2	31	professor	professor	NOUN
cana-1038	2	32	in	in	ADP
cana-1038	2	33	pg	pg	PROPN
cana-1038	2	34	and	and	CCONJ
cana-1038	2	35	research	research	PROPN
cana-1038	2	36	department	department	PROPN
cana-1038	2	37	of	of	ADP
cana-1038	2	38	mathematics	mathematics	PROPN
cana-1038	2	39	t.b.m.l	t.b.m.l	PROPN
cana-1038	2	40	.	.	PUNCT
cana-1038	3	1	college	college	PROPN
cana-1038	3	2	(	(	PUNCT
cana-1038	3	3	affiliated	affiliate	VERB
cana-1038	3	4	to	to	ADP
cana-1038	3	5	annamalai	annamalai	PROPN
cana-1038	3	6	university)porayar-609307	university)porayar-609307	PROPN
cana-1038	3	7	,	,	PUNCT
cana-1038	3	8	tamil	tamil	PROPN
cana-1038	3	9	nadu	nadu	PROPN
cana-1038	3	10	,	,	PUNCT
cana-1038	3	11	india	india	PROPN
cana-1038	3	12	.	.	PUNCT
cana-1038	4	1	e	e	X
cana-1038	4	2	-	-	NOUN
cana-1038	4	3	mail	mail	NOUN
cana-1038	4	4	:	:	PUNCT
cana-1038	4	5	fanyhelena3@gmail.com	fanyhelena3@gmail.com	X
cana-1038	5	1	2associate	2associate	NUM
cana-1038	5	2	professor	professor	NOUN
cana-1038	5	3	in	in	ADP
cana-1038	5	4	pg	pg	PROPN
cana-1038	5	5	and	and	CCONJ
cana-1038	5	6	research	research	PROPN
cana-1038	5	7	department	department	PROPN
cana-1038	5	8	of	of	ADP
cana-1038	5	9	mathematics	mathematics	PROPN
cana-1038	5	10	t.b.m.l	t.b.m.l	PROPN
cana-1038	5	11	.	.	PUNCT
cana-1038	6	1	college	college	PROPN
cana-1038	6	2	(	(	PUNCT
cana-1038	6	3	affiliated	affiliate	VERB
cana-1038	6	4	to	to	ADP
cana-1038	6	5	annamalai	annamalai	PROPN
cana-1038	6	6	university)porayar-609307	university)porayar-609307	PROPN
cana-1038	6	7	,	,	PUNCT
cana-1038	6	8	tamil	tamil	PROPN
cana-1038	6	9	nadu	nadu	PROPN
cana-1038	6	10	,	,	PUNCT
cana-1038	6	11	india	india	PROPN
cana-1038	6	12	.	.	PUNCT
cana-1038	7	1	e	e	X
cana-1038	7	2	-	-	NOUN
cana-1038	7	3	mail	mail	NOUN
cana-1038	7	4	:	:	PUNCT
cana-1038	8	1	dsdina@rediffmail.com	dsdina@rediffmail.com	X
cana-1038	8	2	article	article	PROPN
cana-1038	8	3	history	history	NOUN
cana-1038	8	4	:	:	PUNCT
cana-1038	8	5	received	receive	VERB
cana-1038	8	6	:	:	PUNCT
cana-1038	8	7	15	15	NUM
cana-1038	8	8	-	-	SYM
cana-1038	8	9	05	05	NUM
cana-1038	8	10	-	-	PUNCT
cana-1038	8	11	2024	2024	NUM
cana-1038	8	12	revised	revise	VERB
cana-1038	8	13	:	:	PUNCT
cana-1038	8	14	25	25	NUM
cana-1038	8	15	-	-	PUNCT
cana-1038	8	16	06	06	NUM
cana-1038	8	17	-	-	PUNCT
cana-1038	8	18	2024	2024	NUM
cana-1038	8	19	accepted	accept	VERB
cana-1038	8	20	:	:	PUNCT
cana-1038	8	21	09	09	NUM
cana-1038	8	22	-	-	SYM
cana-1038	8	23	07	07	NUM
cana-1038	8	24	-	-	PUNCT
cana-1038	8	25	2024	2024	NUM
cana-1038	8	26	abstract	abstract	NOUN
cana-1038	8	27	:	:	PUNCT
cana-1038	8	28	in	in	ADP
cana-1038	8	29	this	this	DET
cana-1038	8	30	paper	paper	NOUN
cana-1038	8	31	,	,	PUNCT
cana-1038	8	32	we	we	PRON
cana-1038	8	33	proposed	propose	VERB
cana-1038	8	34	two	two	NUM
cana-1038	8	35	ranking	ranking	ADJ
cana-1038	8	36	methods	method	NOUN
cana-1038	8	37	to	to	PART
cana-1038	8	38	solve	solve	VERB
cana-1038	8	39	the	the	DET
cana-1038	8	40	transportation	transportation	NOUN
cana-1038	8	41	problems	problem	NOUN
cana-1038	8	42	.	.	PUNCT
cana-1038	9	1	here	here	ADV
cana-1038	9	2	we	we	PRON
cana-1038	9	3	introduced	introduce	VERB
cana-1038	9	4	new	new	ADJ
cana-1038	9	5	methods	method	NOUN
cana-1038	9	6	for	for	ADP
cana-1038	9	7	problem	problem	NOUN
cana-1038	9	8	solving	solving	NOUN
cana-1038	9	9	.	.	PUNCT
cana-1038	10	1	in	in	ADP
cana-1038	10	2	this	this	DET
cana-1038	10	3	article	article	NOUN
cana-1038	10	4	,	,	PUNCT
cana-1038	10	5	we	we	PRON
cana-1038	10	6	proposed	propose	VERB
cana-1038	10	7	two	two	NUM
cana-1038	10	8	ranking	ranking	NOUN
cana-1038	10	9	functions	function	NOUN
cana-1038	10	10	called	call	VERB
cana-1038	10	11	ῡ_μ	ῡ_μ	PUNCT
cana-1038	10	12	(	(	PUNCT
cana-1038	10	13	value	value	NOUN
cana-1038	10	14	ranking	ranking	NOUN
cana-1038	10	15	)	)	PUNCT
cana-1038	10	16	and	and	CCONJ
cana-1038	10	17	ᾱ_μ(ambiguity	ᾱ_μ(ambiguity	NOUN
cana-1038	10	18	ranking	ranking	NOUN
cana-1038	10	19	)	)	PUNCT
cana-1038	10	20	to	to	PART
cana-1038	10	21	solve	solve	VERB
cana-1038	10	22	the	the	DET
cana-1038	10	23	transportation	transportation	NOUN
cana-1038	10	24	problems	problem	NOUN
cana-1038	10	25	.	.	PUNCT
cana-1038	11	1	this	this	DET
cana-1038	11	2	work	work	NOUN
cana-1038	11	3	's	's	PART
cana-1038	11	4	main	main	ADJ
cana-1038	11	5	aim	aim	NOUN
cana-1038	11	6	is	be	AUX
cana-1038	11	7	to	to	PART
cana-1038	11	8	compare	compare	VERB
cana-1038	11	9	the	the	DET
cana-1038	11	10	suggested	suggest	VERB
cana-1038	11	11	ranking	rank	VERB
cana-1038	11	12	function	function	NOUN
cana-1038	11	13	with	with	ADP
cana-1038	11	14	the	the	DET
cana-1038	11	15	existing	exist	VERB
cana-1038	11	16	ranking	ranking	NOUN
cana-1038	11	17	method	method	NOUN
cana-1038	11	18	(	(	PUNCT
cana-1038	11	19	roubast	roubast	NOUN
cana-1038	11	20	ranking	ranking	NOUN
cana-1038	11	21	)	)	PUNCT
cana-1038	11	22	.	.	PUNCT
cana-1038	12	1	we	we	PRON
cana-1038	12	2	have	have	AUX
cana-1038	12	3	compared	compare	VERB
cana-1038	12	4	it	it	PRON
cana-1038	12	5	with	with	ADP
cana-1038	12	6	an	an	DET
cana-1038	12	7	example	example	NOUN
cana-1038	12	8	and	and	CCONJ
cana-1038	12	9	justified	justify	VERB
cana-1038	12	10	it	it	PRON
cana-1038	12	11	..	..	PUNCT
cana-1038	13	1	keywords	keyword	NOUN
cana-1038	13	2	:	:	PUNCT
cana-1038	13	3	trapezoidal	trapezoidal	ADJ
cana-1038	13	4	fuzzy	fuzzy	ADJ
cana-1038	13	5	numbers	number	NOUN
cana-1038	13	6	,	,	PUNCT
cana-1038	13	7	fuzzy	fuzzy	ADJ
cana-1038	13	8	transportation	transportation	NOUN
cana-1038	13	9	problem	problem	NOUN
cana-1038	13	10	,	,	PUNCT
cana-1038	13	11	roubast	roubast	ADJ
cana-1038	13	12	ranking	ranking	NOUN
cana-1038	13	13	method	method	NOUN
cana-1038	13	14	,	,	PUNCT
cana-1038	13	15	value	value	NOUN
cana-1038	13	16	ranking	ranking	NOUN
cana-1038	13	17	,	,	PUNCT
cana-1038	13	18	ambiguity	ambiguity	NOUN
cana-1038	13	19	ranking	ranking	NOUN
cana-1038	13	20	.	.	PUNCT
cana-1038	14	1	1	1	X
cana-1038	14	2	.	.	X
cana-1038	14	3	introduction	introduction	NOUN
cana-1038	14	4	transportation	transportation	NOUN
cana-1038	14	5	models	model	NOUN
cana-1038	14	6	can	can	AUX
cana-1038	14	7	be	be	AUX
cana-1038	14	8	widely	widely	ADV
cana-1038	14	9	utilized	utilize	VERB
cana-1038	14	10	in	in	ADP
cana-1038	14	11	supply	supply	NOUN
cana-1038	14	12	chain	chain	NOUN
cana-1038	14	13	and	and	CCONJ
cana-1038	14	14	logistics	logistic	NOUN
cana-1038	14	15	to	to	PART
cana-1038	14	16	minimize	minimize	VERB
cana-1038	14	17	costs	cost	NOUN
cana-1038	14	18	when	when	SCONJ
cana-1038	14	19	there	there	PRON
cana-1038	14	20	is	be	VERB
cana-1038	14	21	accurate	accurate	ADJ
cana-1038	14	22	knowledge	knowledge	NOUN
cana-1038	14	23	of	of	ADP
cana-1038	14	24	the	the	DET
cana-1038	14	25	demand	demand	NOUN
cana-1038	14	26	and	and	CCONJ
cana-1038	14	27	supply	supply	NOUN
cana-1038	14	28	quantities	quantity	NOUN
cana-1038	14	29	,	,	PUNCT
cana-1038	14	30	as	as	ADV
cana-1038	14	31	well	well	ADV
cana-1038	14	32	as	as	ADP
cana-1038	14	33	the	the	DET
cana-1038	14	34	cost	cost	NOUN
cana-1038	14	35	coefficients	coefficient	NOUN
cana-1038	14	36	.	.	PUNCT
cana-1038	15	1	in	in	ADP
cana-1038	15	2	these	these	DET
cana-1038	15	3	situations	situation	NOUN
cana-1038	15	4	,	,	PUNCT
cana-1038	15	5	efficient	efficient	ADJ
cana-1038	15	6	algorithms	algorithm	NOUN
cana-1038	15	7	for	for	ADP
cana-1038	15	8	solving	solve	VERB
cana-1038	15	9	the	the	DET
cana-1038	15	10	transportation	transportation	NOUN
cana-1038	15	11	problem	problem	NOUN
cana-1038	15	12	have	have	AUX
cana-1038	15	13	been	be	AUX
cana-1038	15	14	developed	develop	VERB
cana-1038	15	15	.	.	PUNCT
cana-1038	16	1	an	an	DET
cana-1038	16	2	optimal	optimal	ADJ
cana-1038	16	3	algorithm	algorithm	NOUN
cana-1038	16	4	for	for	ADP
cana-1038	16	5	a	a	DET
cana-1038	16	6	ftp	ftp	PROPN
cana-1038	16	7	(	(	PUNCT
cana-1038	16	8	fuzzy	fuzzy	ADJ
cana-1038	16	9	transportation	transportation	NOUN
cana-1038	16	10	problem	problem	NOUN
cana-1038	16	11	)	)	PUNCT
cana-1038	16	12	was	be	AUX
cana-1038	16	13	studied	study	VERB
cana-1038	16	14	in	in	ADP
cana-1038	16	15	[	[	X
cana-1038	16	16	1	1	NUM
cana-1038	16	17	]	]	PUNCT
cana-1038	16	18	.	.	PUNCT
cana-1038	17	1	randomness	randomness	NOUN
cana-1038	17	2	and	and	CCONJ
cana-1038	17	3	imprecision	imprecision	NOUN
cana-1038	17	4	are	be	AUX
cana-1038	17	5	inevitable	inevitable	ADJ
cana-1038	17	6	in	in	ADP
cana-1038	17	7	the	the	DET
cana-1038	17	8	real	real	ADJ
cana-1038	17	9	world	world	NOUN
cana-1038	17	10	due	due	ADP
cana-1038	17	11	to	to	ADP
cana-1038	17	12	unanticipated	unanticipated	ADJ
cana-1038	17	13	events	event	NOUN
cana-1038	17	14	.	.	PUNCT
cana-1038	18	1	they	they	PRON
cana-1038	18	2	put	put	VERB
cana-1038	18	3	forth	forth	ADP
cana-1038	18	4	a	a	DET
cana-1038	18	5	novel	novel	ADJ
cana-1038	18	6	strategy	strategy	NOUN
cana-1038	18	7	in	in	ADP
cana-1038	18	8	[	[	X
cana-1038	18	9	2,3	2,3	NUM
cana-1038	18	10	]	]	PUNCT
cana-1038	18	11	to	to	PART
cana-1038	18	12	address	address	VERB
cana-1038	18	13	the	the	DET
cana-1038	18	14	transportation	transportation	NOUN
cana-1038	18	15	issues	issue	NOUN
cana-1038	18	16	with	with	ADP
cana-1038	18	17	fuzzy	fuzzy	ADJ
cana-1038	18	18	numbers	number	NOUN
cana-1038	18	19	.	.	PUNCT
cana-1038	19	1	in	in	ADP
cana-1038	19	2	certain	certain	ADJ
cana-1038	19	3	situations	situation	NOUN
cana-1038	19	4	,	,	PUNCT
cana-1038	19	5	uncontrollable	uncontrollable	ADJ
cana-1038	19	6	factors	factor	NOUN
cana-1038	19	7	may	may	AUX
cana-1038	19	8	lead	lead	VERB
cana-1038	19	9	to	to	ADP
cana-1038	19	10	uncertainty	uncertainty	NOUN
cana-1038	19	11	in	in	ADP
cana-1038	19	12	the	the	DET
cana-1038	19	13	cost	cost	NOUN
cana-1038	19	14	coefficients	coefficient	NOUN
cana-1038	19	15	and	and	CCONJ
cana-1038	19	16	demand	demand	NOUN
cana-1038	19	17	&	&	CCONJ
cana-1038	19	18	supply	supply	NOUN
cana-1038	19	19	quantities	quantity	NOUN
cana-1038	19	20	of	of	ADP
cana-1038	19	21	a	a	DET
cana-1038	19	22	transportation	transportation	NOUN
cana-1038	19	23	problem	problem	NOUN
cana-1038	19	24	.	.	PUNCT
cana-1038	20	1	finding	find	VERB
cana-1038	20	2	the	the	DET
cana-1038	20	3	schedule	schedule	NOUN
cana-1038	20	4	of	of	ADP
cana-1038	20	5	shipping	shipping	NOUN
cana-1038	20	6	which	which	PRON
cana-1038	20	7	reduces	reduce	VERB
cana-1038	20	8	overall	overall	ADJ
cana-1038	20	9	fuzzy	fuzzy	ADJ
cana-1038	20	10	transportation	transportation	NOUN
cana-1038	20	11	costs	cost	NOUN
cana-1038	20	12	while	while	SCONJ
cana-1038	20	13	meeting	meet	VERB
cana-1038	20	14	demand	demand	NOUN
cana-1038	20	15	limits	limit	NOUN
cana-1038	20	16	&	&	CCONJ
cana-1038	20	17	fuzzy	fuzzy	ADJ
cana-1038	20	18	supply	supply	NOUN
cana-1038	20	19	is	be	AUX
cana-1038	20	20	the	the	DET
cana-1038	20	21	aim	aim	NOUN
cana-1038	20	22	of	of	ADP
cana-1038	20	23	the	the	DET
cana-1038	20	24	fuzzy	fuzzy	ADJ
cana-1038	20	25	transportation	transportation	NOUN
cana-1038	20	26	problem	problem	NOUN
cana-1038	20	27	.	.	PUNCT
cana-1038	21	1	we	we	PRON
cana-1038	21	2	proposed	propose	VERB
cana-1038	21	3	a	a	DET
cana-1038	21	4	similarity	similarity	NOUN
cana-1038	21	5	measure	measure	NOUN
cana-1038	21	6	in	in	ADP
cana-1038	21	7	[	[	X
cana-1038	21	8	4,5,6	4,5,6	NUM
cana-1038	21	9	]	]	PUNCT
cana-1038	21	10	using	use	VERB
cana-1038	21	11	vector	vector	NOUN
cana-1038	21	12	length	length	NOUN
cana-1038	21	13	for	for	ADP
cana-1038	21	14	a	a	DET
cana-1038	21	15	trifns	trifns	NOUN
cana-1038	21	16	,	,	PUNCT
cana-1038	21	17	sign	sign	NOUN
cana-1038	21	18	distance	distance	NOUN
cana-1038	21	19	,	,	PUNCT
cana-1038	21	20	and	and	CCONJ
cana-1038	21	21	value	value	NOUN
cana-1038	21	22	ambiguity	ambiguity	NOUN
cana-1038	21	23	indices	index	NOUN
cana-1038	21	24	.	.	PUNCT
cana-1038	22	1	various	various	ADJ
cana-1038	22	2	ranking	ranking	NOUN
cana-1038	22	3	procedures	procedure	NOUN
cana-1038	22	4	are	be	AUX
cana-1038	22	5	used	use	VERB
cana-1038	22	6	to	to	PART
cana-1038	22	7	propose	propose	VERB
cana-1038	22	8	the	the	DET
cana-1038	22	9	measures	measure	NOUN
cana-1038	22	10	.	.	PUNCT
cana-1038	23	1	in	in	ADP
cana-1038	23	2	this	this	DET
cana-1038	23	3	work	work	NOUN
cana-1038	23	4	,	,	PUNCT
cana-1038	23	5	we	we	PRON
cana-1038	23	6	addressed	address	VERB
cana-1038	23	7	more	more	ADV
cana-1038	23	8	practical	practical	ADJ
cana-1038	23	9	issues	issue	NOUN
cana-1038	23	10	,	,	PUNCT
cana-1038	23	11	such	such	ADJ
cana-1038	23	12	as	as	ADP
cana-1038	23	13	the	the	DET
cana-1038	23	14	fuzzy	fuzzy	ADJ
cana-1038	23	15	cost	cost	NOUN
cana-1038	23	16	ƈ𝑖𝑗	ƈ𝑖𝑗	NOUN
cana-1038	23	17	transportation	transportation	NOUN
cana-1038	23	18	problem	problem	NOUN
cana-1038	23	19	.	.	PUNCT
cana-1038	24	1	the	the	DET
cana-1038	24	2	objective	objective	ADJ
cana-1038	24	3	function	function	NOUN
cana-1038	24	4	is	be	AUX
cana-1038	24	5	also	also	ADV
cana-1038	24	6	regarded	regard	VERB
cana-1038	24	7	as	as	ADP
cana-1038	24	8	a	a	DET
cana-1038	24	9	fn	fn	NOUN
cana-1038	24	10	since	since	SCONJ
cana-1038	24	11	the	the	DET
cana-1038	24	12	goal	goal	NOUN
cana-1038	24	13	is	be	AUX
cana-1038	24	14	to	to	PART
cana-1038	24	15	maximize	maximize	VERB
cana-1038	24	16	total	total	ADJ
cana-1038	24	17	profit	profit	NOUN
cana-1038	24	18	or	or	CCONJ
cana-1038	24	19	minimize	minimize	VERB
cana-1038	24	20	total	total	ADJ
cana-1038	24	21	cost	cost	NOUN
cana-1038	24	22	,	,	PUNCT
cana-1038	24	23	subject	subject	ADJ
cana-1038	24	24	to	to	ADP
cana-1038	24	25	certain	certain	ADJ
cana-1038	24	26	fuzzy	fuzzy	ADJ
cana-1038	24	27	constraints	constraint	NOUN
cana-1038	24	28	.	.	PUNCT
cana-1038	25	1	to	to	PART
cana-1038	25	2	find	find	VERB
cana-1038	25	3	the	the	DET
cana-1038	25	4	best	good	ADJ
cana-1038	25	5	option	option	NOUN
cana-1038	25	6	,	,	PUNCT
cana-1038	25	7	the	the	DET
cana-1038	25	8	objective	objective	ADJ
cana-1038	25	9	function	function	NOUN
cana-1038	25	10	’s	’s	PART
cana-1038	25	11	fuzzy	fuzzy	ADJ
cana-1038	25	12	objective	objective	ADJ
cana-1038	25	13	values	value	NOUN
cana-1038	25	14	are	be	AUX
cana-1038	25	15	ranked	rank	VERB
cana-1038	25	16	according	accord	VERB
cana-1038	25	17	to	to	ADP
cana-1038	25	18	value	value	NOUN
cana-1038	25	19	using	use	VERB
cana-1038	25	20	the	the	DET
cana-1038	25	21	ambiguity	ambiguity	NOUN
cana-1038	25	22	ranking	ranking	NOUN
cana-1038	25	23	approach	approach	NOUN
cana-1038	25	24	for	for	ADP
cana-1038	25	25	numbers	number	NOUN
cana-1038	25	26	.	.	PUNCT
cana-1038	26	1	the	the	DET
cana-1038	26	2	ftp	ftp	PROPN
cana-1038	26	3	has	have	AUX
cana-1038	26	4	been	be	AUX
cana-1038	26	5	transformed	transform	VERB
cana-1038	26	6	using	use	VERB
cana-1038	26	7	the	the	DET
cana-1038	26	8	α	α	NOUN
cana-1038	26	9	cut	cut	NOUN
cana-1038	26	10	solution	solution	NOUN
cana-1038	26	11	.	.	PUNCT
cana-1038	27	1	the	the	DET
cana-1038	27	2	concept	concept	NOUN
cana-1038	27	3	involves	involve	VERB
cana-1038	27	4	converting	convert	VERB
cana-1038	27	5	a	a	DET
cana-1038	27	6	fuzzy	fuzzy	ADJ
cana-1038	27	7	parameter	parameter	NOUN
cana-1038	27	8	problem	problem	NOUN
cana-1038	27	9	into	into	ADP
cana-1038	27	10	an	an	DET
cana-1038	27	11	lpp	lpp	NOUN
cana-1038	27	12	and	and	CCONJ
cana-1038	27	13	using	use	VERB
cana-1038	27	14	the	the	DET
cana-1038	27	15	vogel	vogel	NOUN
cana-1038	27	16	approximation	approximation	NOUN
cana-1038	27	17	method	method	NOUN
cana-1038	27	18	to	to	PART
cana-1038	27	19	solve	solve	VERB
cana-1038	27	20	it	it	PRON
cana-1038	27	21	.	.	PUNCT
cana-1038	28	1	communications	communication	NOUN
cana-1038	28	2	on	on	ADP
cana-1038	28	3	applied	apply	VERB
cana-1038	28	4	nonlinear	nonlinear	ADJ
cana-1038	28	5	analysis	analysis	NOUN
cana-1038	28	6	issn	issn	NOUN
cana-1038	28	7	:	:	PUNCT
cana-1038	28	8	1074	1074	NUM
cana-1038	28	9	-	-	PUNCT
cana-1038	28	10	133x	133x	NUM
cana-1038	28	11	vol	vol	NOUN
cana-1038	28	12	31	31	NUM
cana-1038	28	13	no	no	NOUN
cana-1038	28	14	.	.	PUNCT
cana-1038	29	1	5s	5s	NUM
cana-1038	29	2	(	(	PUNCT
cana-1038	29	3	2024	2024	NUM
cana-1038	29	4	)	)	PUNCT
cana-1038	29	5	297	297	NUM
cana-1038	29	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1038	29	7	2	2	NUM
cana-1038	29	8	.	.	X
cana-1038	29	9	objectives	objective	NOUN
cana-1038	29	10	definition:2.1	definition:2.1	VERB
cana-1038	29	11	a	a	DET
cana-1038	29	12	fn	fn	PROPN
cana-1038	29	13	�	�	PROPN
cana-1038	29	14	̃	̃	PROPN
cana-1038	29	15	�	�	PROPN
cana-1038	29	16	has	have	VERB
cana-1038	29	17	to	to	PART
cana-1038	29	18	be	be	AUX
cana-1038	29	19	generalized	generalize	VERB
cana-1038	29	20	trfns	trfns	NOUN
cana-1038	29	21	(	(	PUNCT
cana-1038	29	22	trapezoidal	trapezoidal	ADJ
cana-1038	29	23	fuzzy	fuzzy	ADJ
cana-1038	29	24	number	number	NOUN
cana-1038	29	25	)	)	PUNCT
cana-1038	29	26	having	have	VERB
cana-1038	29	27	a	a	DET
cana-1038	29	28	parameter	parameter	NOUN
cana-1038	29	29	≤	≤	X
cana-1038	30	1	𝑎1	𝑎1	X
cana-1038	30	2	≤	≤	NUM
cana-1038	30	3	𝑎2	𝑎2	NOUN
cana-1038	30	4	≤	≤	NUM
cana-1038	30	5	𝑎3	𝑎3	PROPN
cana-1038	30	6	≤	≤	PROPN
cana-1038	30	7	𝑎4	𝑎4	PROPN
cana-1038	30	8	and	and	CCONJ
cana-1038	30	9	represented	represent	VERB
cana-1038	30	10	by	by	ADP
cana-1038	30	11	�	�	PROPN
cana-1038	30	12	̃	̃	PROPN
cana-1038	30	13	�	�	NOUN
cana-1038	30	14	=	=	PUNCT
cana-1038	30	15	(	(	PUNCT
cana-1038	30	16	𝑎1	𝑎1	PROPN
cana-1038	30	17	,	,	PUNCT
cana-1038	30	18	𝑎2	𝑎2	PROPN
cana-1038	30	19	,	,	PUNCT
cana-1038	30	20	𝑎3	𝑎3	PROPN
cana-1038	30	21	,	,	PUNCT
cana-1038	30	22	𝑎4	𝑎4	PROPN
cana-1038	30	23	)	)	PUNCT
cana-1038	30	24	and	and	CCONJ
cana-1038	30	25	its	its	PRON
cana-1038	30	26	membership	membership	NOUN
cana-1038	30	27	functions	function	NOUN
cana-1038	30	28	are	be	AUX
cana-1038	30	29	followed	follow	VERB
cana-1038	30	30	below	below	ADV
cana-1038	30	31	.	.	PUNCT
cana-1038	30	32	0	0	PUNCT
cana-1038	31	1	𝑖𝑓	𝑖𝑓	ADP
cana-1038	31	2	𝑥	𝑥	X
cana-1038	31	3	<	<	X
cana-1038	31	4	𝑎1	𝑎1	INTJ
cana-1038	31	5	(	(	PUNCT
cana-1038	31	6	𝑥−𝑎1	𝑥−𝑎1	X
cana-1038	31	7	𝑎2−𝑎1	𝑎2−𝑎1	ADV
cana-1038	31	8	)	)	PUNCT
cana-1038	31	9	𝑖𝑓	𝑖𝑓	VERB
cana-1038	32	1	𝑎1	𝑎1	NOUN
cana-1038	32	2	≤	≤	NUM
cana-1038	32	3	𝑥	𝑥	DET
cana-1038	32	4	≤	≤	PROPN
cana-1038	32	5	𝑎2	𝑎2	PROPN
cana-1038	32	6	𝜇	𝜇	ADP
cana-1038	32	7	�	�	PROPN
cana-1038	32	8	̃	̃	PROPN
cana-1038	32	9	�	�	NOUN
cana-1038	32	10	(𝑥	(𝑥	NOUN
cana-1038	32	11	)	)	PUNCT
cana-1038	32	12	=	=	SYM
cana-1038	33	1	1	1	NUM
cana-1038	33	2	𝑖𝑓	𝑖𝑓	ADP
cana-1038	33	3	𝑎2	𝑎2	NOUN
cana-1038	33	4	≤	≤	NUM
cana-1038	33	5	𝑥	𝑥	DET
cana-1038	33	6	≤	≤	NUM
cana-1038	33	7	𝑎3	𝑎3	NOUN
cana-1038	33	8	(	(	PUNCT
cana-1038	33	9	𝑎4−𝑥	𝑎4−𝑥	PROPN
cana-1038	33	10	𝑎4−𝑎3	𝑎4−𝑎3	PROPN
cana-1038	33	11	)	)	PUNCT
cana-1038	33	12	𝑖𝑓	𝑖𝑓	ADP
cana-1038	33	13	𝑎3	𝑎3	PROPN
cana-1038	33	14	≤	≤	PUNCT
cana-1038	34	1	𝑥	𝑥	DET
cana-1038	34	2	≤	≤	NUM
cana-1038	34	3	𝑎4	𝑎4	PROPN
cana-1038	34	4	0	0	NUM
cana-1038	34	5	𝑖𝑓	𝑖𝑓	ADP
cana-1038	34	6	𝑥	𝑥	DET
cana-1038	34	7	>	>	PUNCT
cana-1038	34	8	𝑎4	𝑎4	PROPN
cana-1038	34	9	definition	definition	NOUN
cana-1038	34	10	:	:	PUNCT
cana-1038	34	11	2.2	2.2	NUM
cana-1038	34	12	tough	tough	ADJ
cana-1038	34	13	ranking	ranking	ADJ
cana-1038	34	14	algorithm	algorithm	NOUN
cana-1038	34	15	that	that	PRON
cana-1038	34	16	yields	yield	NOUN
cana-1038	34	17	results	result	VERB
cana-1038	34	18	consistent	consistent	ADJ
cana-1038	34	19	with	with	ADP
cana-1038	34	20	human	human	ADJ
cana-1038	34	21	intuition	intuition	NOUN
cana-1038	34	22	while	while	SCONJ
cana-1038	34	23	meeting	meet	VERB
cana-1038	34	24	linearity	linearity	NOUN
cana-1038	34	25	,	,	PUNCT
cana-1038	34	26	additivity	additivity	NOUN
cana-1038	34	27	,	,	PUNCT
cana-1038	34	28	and	and	CCONJ
cana-1038	34	29	compensation	compensation	NOUN
cana-1038	34	30	requirements	requirement	NOUN
cana-1038	34	31	.	.	PUNCT
cana-1038	35	1	if	if	SCONJ
cana-1038	35	2	ã	ã	X
cana-1038	35	3	then	then	ADV
cana-1038	35	4	the	the	DET
cana-1038	35	5	robust	robust	ADJ
cana-1038	35	6	ranking	ranking	NOUN
cana-1038	35	7	which	which	PRON
cana-1038	35	8	has	have	AUX
cana-1038	35	9	been	be	AUX
cana-1038	35	10	defined	define	VERB
cana-1038	35	11	by	by	ADP
cana-1038	35	12	r(	r(	PROPN
cana-1038	35	13	�	�	PROPN
cana-1038	35	14	̃	̃	PROPN
cana-1038	35	15	�	�	PROPN
cana-1038	35	16	)	)	PUNCT
cana-1038	35	17	=	=	SYM
cana-1038	35	18	∫	∫	PROPN
cana-1038	35	19	(	(	PUNCT
cana-1038	35	20	0.5)(𝑎𝛼	0.5)(𝑎𝛼	NUM
cana-1038	35	21	𝐿	𝐿	PROPN
cana-1038	35	22	𝑎𝛼	𝑎𝛼	ADP
cana-1038	35	23	𝑈)𝑑𝛼	𝑈)𝑑𝛼	PROPN
cana-1038	35	24	1	1	NUM
cana-1038	35	25	0	0	NUM
cana-1038	35	26	where	where	SCONJ
cana-1038	35	27	(	(	PUNCT
cana-1038	35	28	𝑎𝛼	𝑎𝛼	ADP
cana-1038	35	29	𝐿	𝐿	PROPN
cana-1038	35	30	𝑎𝛼	𝑎𝛼	PROPN
cana-1038	35	31	𝑈	𝑈	PROPN
cana-1038	35	32	)	)	PUNCT
cana-1038	35	33	is	be	AUX
cana-1038	35	34	the	the	DET
cana-1038	35	35	𝛼	𝛼	NOUN
cana-1038	35	36	level	level	NOUN
cana-1038	35	37	cut	cut	NOUN
cana-1038	35	38	of	of	ADP
cana-1038	35	39	the	the	DET
cana-1038	35	40	fn	fn	NOUN
cana-1038	36	1	ã	ã	X
cana-1038	36	2	we	we	PRON
cana-1038	36	3	use	use	VERB
cana-1038	36	4	this	this	DET
cana-1038	36	5	approach	approach	NOUN
cana-1038	36	6	for	for	ADP
cana-1038	36	7	objective	objective	ADJ
cana-1038	36	8	values	value	NOUN
cana-1038	36	9	ranking	rank	VERB
cana-1038	36	10	.	.	PUNCT
cana-1038	37	1	the	the	DET
cana-1038	37	2	r(ã	r(ã	PROPN
cana-1038	37	3	)	)	PUNCT
cana-1038	37	4	provides	provide	VERB
cana-1038	37	5	the	the	DET
cana-1038	37	6	representative	representative	ADJ
cana-1038	37	7	value	value	NOUN
cana-1038	37	8	of	of	ADP
cana-1038	37	9	fn	fn	PROPN
cana-1038	37	10	ã	ã	NOUN
cana-1038	37	11	.	.	PROPN
cana-1038	37	12	2.3	2.3	NUM
cana-1038	37	13	arithmetic	arithmetic	ADJ
cana-1038	37	14	operations	operation	NOUN
cana-1038	37	15	on	on	ADP
cana-1038	37	16	generalized	generalized	ADJ
cana-1038	37	17	trapezoidal	trapezoidal	ADJ
cana-1038	37	18	“	"	PUNCT
cana-1038	37	19	fuzzy	fuzzy	ADJ
cana-1038	37	20	numbers	number	NOUN
cana-1038	37	21	let	let	VERB
cana-1038	37	22	�	�	PROPN
cana-1038	37	23	̃	̃	NOUN
cana-1038	37	24	�	�	NOUN
cana-1038	37	25	=	=	SYM
cana-1038	37	26	(	(	PUNCT
cana-1038	37	27	𝑎1	𝑎1	PROPN
cana-1038	37	28	,	,	PUNCT
cana-1038	37	29	𝑎2	𝑎2	PROPN
cana-1038	37	30	,	,	PUNCT
cana-1038	37	31	𝑎3	𝑎3	PROPN
cana-1038	37	32	,	,	PUNCT
cana-1038	37	33	𝑎4	𝑎4	PROPN
cana-1038	37	34	)	)	PUNCT
cana-1038	37	35	and	and	CCONJ
cana-1038	37	36	�	�	PROPN
cana-1038	37	37	̃	̃	PROPN
cana-1038	37	38	�	�	NOUN
cana-1038	37	39	=	=	PUNCT
cana-1038	37	40	(	(	PUNCT
cana-1038	37	41	𝑏1	𝑏1	NOUN
cana-1038	37	42	,	,	PUNCT
cana-1038	37	43	𝑏2	𝑏2	PROPN
cana-1038	37	44	,	,	PUNCT
cana-1038	37	45	𝑏3	𝑏3	NOUN
cana-1038	37	46	,	,	PUNCT
cana-1038	37	47	𝑏4	𝑏4	PROPN
cana-1038	37	48	)	)	PUNCT
cana-1038	37	49	be	be	VERB
cana-1038	37	50	2	2	NUM
cana-1038	37	51	generalized	generalized	ADJ
cana-1038	37	52	trfns	trfns	NOUN
cana-1038	37	53	&	&	CCONJ
cana-1038	37	54	𝜆	𝜆	PROPN
cana-1038	37	55	be	be	AUX
cana-1038	37	56	a	a	DET
cana-1038	37	57	real	real	ADJ
cana-1038	37	58	number	number	NOUN
cana-1038	37	59	.	.	PUNCT
cana-1038	38	1	then	then	ADV
cana-1038	38	2	1	1	X
cana-1038	38	3	.	.	X
cana-1038	38	4	�	�	PROPN
cana-1038	38	5	̃	̃	PROPN
cana-1038	38	6	�	�	PROPN
cana-1038	38	7	+	+	NOUN
cana-1038	38	8	�	�	PROPN
cana-1038	38	9	̃	̃	NOUN
cana-1038	38	10	�	�	NOUN
cana-1038	38	11	=	=	PUNCT
cana-1038	38	12	(	(	PUNCT
cana-1038	38	13	𝑎1	𝑎1	X
cana-1038	38	14	+	+	CCONJ
cana-1038	38	15	𝑏1	𝑏1	ADJ
cana-1038	38	16	,	,	PUNCT
cana-1038	38	17	𝑎2	𝑎2	PROPN
cana-1038	38	18	+	+	CCONJ
cana-1038	38	19	𝑏2	𝑏2	PROPN
cana-1038	38	20	,	,	PUNCT
cana-1038	38	21	𝑎3	𝑎3	PROPN
cana-1038	38	22	+	+	CCONJ
cana-1038	38	23	𝑏3	𝑏3	NOUN
cana-1038	38	24	,	,	PUNCT
cana-1038	38	25	𝑎4	𝑎4	PROPN
cana-1038	38	26	+	+	CCONJ
cana-1038	38	27	𝑏4	𝑏4	PROPN
cana-1038	38	28	)	)	PUNCT
cana-1038	38	29	2	2	NUM
cana-1038	38	30	.	.	X
cana-1038	38	31	�	�	PROPN
cana-1038	38	32	̃	̃	PROPN
cana-1038	38	33	�	�	PROPN
cana-1038	38	34	-	-	PUNCT
cana-1038	38	35	�	�	PROPN
cana-1038	38	36	̃	̃	NOUN
cana-1038	38	37	�	�	NOUN
cana-1038	38	38	=	=	PUNCT
cana-1038	38	39	(	(	PUNCT
cana-1038	38	40	𝑎1	𝑎1	PROPN
cana-1038	38	41	−	−	PROPN
cana-1038	38	42	𝑏4	𝑏4	PROPN
cana-1038	38	43	,	,	PUNCT
cana-1038	38	44	𝑎2	𝑎2	NOUN
cana-1038	38	45	−	−	PROPN
cana-1038	38	46	𝑏3	𝑏3	NOUN
cana-1038	38	47	,	,	PUNCT
cana-1038	38	48	𝑎3	𝑎3	PROPN
cana-1038	38	49	−	−	PROPN
cana-1038	38	50	𝑏2	𝑏2	PROPN
cana-1038	38	51	,	,	PUNCT
cana-1038	38	52	𝑎4	𝑎4	PROPN
cana-1038	38	53	−	−	PROPN
cana-1038	38	54	𝑏1	𝑏1	NOUN
cana-1038	38	55	)	)	PUNCT
cana-1038	38	56	3	3	NUM
cana-1038	38	57	.	.	X
cana-1038	39	1	𝛌	𝛌	PROPN
cana-1038	39	2	�	�	PROPN
cana-1038	39	3	̃	̃	NOUN
cana-1038	39	4	�	�	NOUN
cana-1038	39	5	=	=	SYM
cana-1038	39	6	(	(	PUNCT
cana-1038	39	7	𝛌𝑎1	𝛌𝑎1	PROPN
cana-1038	39	8	,	,	PUNCT
cana-1038	39	9	𝛌𝑎2	𝛌𝑎2	PROPN
cana-1038	39	10	,	,	PUNCT
cana-1038	39	11	𝛌𝑎3	𝛌𝑎3	NOUN
cana-1038	39	12	,	,	PUNCT
cana-1038	39	13	𝛌𝑎4	𝛌𝑎4	PROPN
cana-1038	39	14	)	)	PUNCT
cana-1038	39	15	;	;	PUNCT
cana-1038	39	16	if	if	SCONJ
cana-1038	39	17	𝛌	𝛌	PROPN
cana-1038	39	18	>	>	X
cana-1038	39	19	0	0	PUNCT
cana-1038	39	20	(	(	PUNCT
cana-1038	39	21	𝛌𝑎4	𝛌𝑎4	NOUN
cana-1038	39	22	,	,	PUNCT
cana-1038	39	23	𝛌𝑎3	𝛌𝑎3	PROPN
cana-1038	39	24	,	,	PUNCT
cana-1038	39	25	𝛌𝑎2	𝛌𝑎2	PROPN
cana-1038	39	26	,	,	PUNCT
cana-1038	39	27	𝛌𝑎1	𝛌𝑎1	PROPN
cana-1038	39	28	)	)	PUNCT
cana-1038	40	1	if	if	SCONJ
cana-1038	40	2	𝛌	𝛌	PROPN
cana-1038	40	3	>	>	X
cana-1038	40	4	0	0	NUM
cana-1038	41	1	4.let	4.let	NUM
cana-1038	41	2	𝑅(	𝑅(	PROPN
cana-1038	41	3	�	�	PROPN
cana-1038	41	4	̃	̃	PROPN
cana-1038	41	5	�	�	PROPN
cana-1038	41	6	)	)	PUNCT
cana-1038	41	7	=	=	PUNCT
cana-1038	41	8	𝑏1+𝑏2+𝑏3+𝑏4	𝑏1+𝑏2+𝑏3+𝑏4	VERB
cana-1038	41	9	4	4	NUM
cana-1038	41	10	�	�	NOUN
cana-1038	41	11	̃	̃	PROPN
cana-1038	41	12	�	�	PROPN
cana-1038	41	13	×	×	PROPN
cana-1038	41	14	�	�	PROPN
cana-1038	41	15	̃	̃	PROPN
cana-1038	41	16	�	�	NOUN
cana-1038	41	17	=	=	SYM
cana-1038	41	18	(	(	PUNCT
cana-1038	41	19	𝑎1𝑅(	𝑎1𝑅(	PROPN
cana-1038	41	20	�	�	PROPN
cana-1038	41	21	̃	̃	PROPN
cana-1038	41	22	�	�	PROPN
cana-1038	41	23	)	)	PUNCT
cana-1038	41	24	,	,	PUNCT
cana-1038	41	25	𝑎2𝑅(	𝑎2𝑅(	NUM
cana-1038	41	26	�	�	SYM
cana-1038	41	27	̃	̃	NOUN
cana-1038	41	28	�	�	PROPN
cana-1038	41	29	)	)	PUNCT
cana-1038	41	30	,	,	PUNCT
cana-1038	41	31	𝑎3𝑅(	𝑎3𝑅(	PROPN
cana-1038	41	32	�	�	PROPN
cana-1038	41	33	̃	̃	PROPN
cana-1038	41	34	�	�	PROPN
cana-1038	41	35	)	)	PUNCT
cana-1038	41	36	,	,	PUNCT
cana-1038	41	37	𝑎4𝑅(	𝑎4𝑅(	NUM
cana-1038	41	38	�	�	PROPN
cana-1038	41	39	̃	̃	NOUN
cana-1038	41	40	�	�	PROPN
cana-1038	41	41	)	)	PUNCT
cana-1038	41	42	)	)	PUNCT
cana-1038	42	1	5	5	X
cana-1038	42	2	.	.	X
cana-1038	42	3	let	let	VERB
cana-1038	42	4	𝑅(	𝑅(	PROPN
cana-1038	42	5	�	�	PROPN
cana-1038	42	6	̃	̃	PROPN
cana-1038	42	7	�	�	PROPN
cana-1038	42	8	)	)	PUNCT
cana-1038	42	9	=	=	PUNCT
cana-1038	42	10	𝑏1+𝑏2+𝑏3+𝑏4	𝑏1+𝑏2+𝑏3+𝑏4	VERB
cana-1038	42	11	4	4	NUM
cana-1038	42	12	�	�	NOUN
cana-1038	42	13	̃	̃	PROPN
cana-1038	42	14	�	�	PROPN
cana-1038	42	15	÷	÷	SYM
cana-1038	42	16	�	�	PROPN
cana-1038	42	17	̃	̃	PROPN
cana-1038	42	18	�	�	NOUN
cana-1038	43	1	=	=	PUNCT
cana-1038	43	2	(	(	PUNCT
cana-1038	43	3	𝑎1	𝑎1	PROPN
cana-1038	43	4	𝑅(	𝑅(	PROPN
cana-1038	43	5	�	�	PROPN
cana-1038	43	6	̃	̃	PROPN
cana-1038	43	7	�	�	PROPN
cana-1038	43	8	)	)	PUNCT
cana-1038	43	9	,	,	PUNCT
cana-1038	43	10	𝑎2	𝑎2	PROPN
cana-1038	43	11	𝑅(	𝑅(	PROPN
cana-1038	43	12	�	�	PROPN
cana-1038	43	13	̃	̃	PROPN
cana-1038	43	14	�	�	PROPN
cana-1038	43	15	)	)	PUNCT
cana-1038	43	16	,	,	PUNCT
cana-1038	43	17	𝑎3	𝑎3	PROPN
cana-1038	43	18	𝑅(	𝑅(	PROPN
cana-1038	43	19	�	�	PROPN
cana-1038	43	20	̃	̃	PROPN
cana-1038	43	21	�	�	PROPN
cana-1038	43	22	)	)	PUNCT
cana-1038	43	23	,	,	PUNCT
cana-1038	43	24	𝑎4	𝑎4	PROPN
cana-1038	43	25	𝑅(	𝑅(	PROPN
cana-1038	43	26	�	�	PROPN
cana-1038	43	27	̃	̃	PROPN
cana-1038	43	28	�	�	PROPN
cana-1038	43	29	)	)	PUNCT
cana-1038	43	30	)	)	PUNCT
cana-1038	43	31	communications	communication	NOUN
cana-1038	43	32	on	on	ADP
cana-1038	43	33	applied	apply	VERB
cana-1038	43	34	nonlinear	nonlinear	ADJ
cana-1038	43	35	analysis	analysis	NOUN
cana-1038	43	36	issn	issn	NOUN
cana-1038	43	37	:	:	PUNCT
cana-1038	43	38	1074	1074	NUM
cana-1038	43	39	-	-	PUNCT
cana-1038	43	40	133x	133x	NUM
cana-1038	43	41	vol	vol	NOUN
cana-1038	43	42	31	31	NUM
cana-1038	43	43	no	no	NOUN
cana-1038	43	44	.	.	PUNCT
cana-1038	44	1	5s	5s	NUM
cana-1038	44	2	(	(	PUNCT
cana-1038	44	3	2024	2024	NUM
cana-1038	44	4	)	)	PUNCT
cana-1038	44	5	298	298	NUM
cana-1038	44	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1038	44	7	3	3	X
cana-1038	44	8	.	.	PUNCT
cana-1038	44	9	methods	method	NOUN
cana-1038	44	10	”	"	PUNCT
cana-1038	44	11	(	(	PUNCT
cana-1038	44	12	i	i	NOUN
cana-1038	44	13	)	)	PUNCT
cana-1038	44	14	vague	vague	ADJ
cana-1038	44	15	ranking	ranking	NOUN
cana-1038	44	16	function	function	NOUN
cana-1038	44	17	ῡ𝑖𝑗(𝑥	ῡ𝑖𝑗(𝑥	PROPN
cana-1038	44	18	)	)	PUNCT
cana-1038	44	19	=	=	SYM
cana-1038	44	20	∫	∫	PROPN
cana-1038	44	21	(	(	PUNCT
cana-1038	44	22	𝐿	𝐿	PROPN
cana-1038	44	23	�	�	PROPN
cana-1038	44	24	̃	̃	PROPN
cana-1038	44	25	�	�	NOUN
cana-1038	44	26	𝑖(𝛼	𝑖(𝛼	NOUN
cana-1038	44	27	)	)	PUNCT
cana-1038	45	1	1	1	NUM
cana-1038	45	2	0	0	NUM
cana-1038	45	3	+	+	CCONJ
cana-1038	45	4	𝑅	𝑅	PROPN
cana-1038	45	5	�	�	PROPN
cana-1038	45	6	̃	̃	PROPN
cana-1038	45	7	�	�	PROPN
cana-1038	45	8	𝑖(𝛼))𝑓(𝛼)𝑑𝛼	𝑖(𝛼))𝑓(𝛼)𝑑𝛼	NUM
cana-1038	45	9	ῡ𝑖𝑗(𝑥	ῡ𝑖𝑗(𝑥	PROPN
cana-1038	45	10	)	)	PUNCT
cana-1038	45	11	=	=	SYM
cana-1038	45	12	∫	∫	PROPN
cana-1038	46	1	[	[	X
cana-1038	46	2	𝑎1	𝑎1	X
cana-1038	46	3	+	+	CCONJ
cana-1038	46	4	𝛼(𝑎2	𝛼(𝑎2	NOUN
cana-1038	46	5	−	−	NOUN
cana-1038	46	6	𝑎1	𝑎1	PROPN
cana-1038	46	7	)	)	PUNCT
cana-1038	46	8	+	+	NUM
cana-1038	46	9	𝑎4	𝑎4	PROPN
cana-1038	46	10	−	−	NOUN
cana-1038	46	11	𝛼(𝑎4	𝛼(𝑎4	NOUN
cana-1038	46	12	−	−	ADP
cana-1038	46	13	𝑎3)]𝛼	𝑎3)]𝛼	PROPN
cana-1038	46	14	𝑑𝛼	𝑑𝛼	ADP
cana-1038	46	15	1	1	NUM
cana-1038	46	16	0	0	NUM
cana-1038	46	17	after	after	ADP
cana-1038	46	18	simplification	simplification	NOUN
cana-1038	46	19	,	,	PUNCT
cana-1038	46	20	we	we	PRON
cana-1038	46	21	get	get	VERB
cana-1038	46	22	ῡ𝑖𝑗(𝑥	ῡ𝑖𝑗(𝑥	PRON
cana-1038	46	23	)	)	PUNCT
cana-1038	46	24	=	=	SYM
cana-1038	47	1	𝑎1	𝑎1	NOUN
cana-1038	47	2	+	+	CCONJ
cana-1038	47	3	2𝑎2	2𝑎2	NUM
cana-1038	47	4	+	+	CCONJ
cana-1038	47	5	2𝑎3	2𝑎3	NUM
cana-1038	48	1	+	+	CCONJ
cana-1038	48	2	𝑎4	𝑎4	PROPN
cana-1038	48	3	6	6	NUM
cana-1038	48	4	the	the	DET
cana-1038	48	5	vague	vague	ADJ
cana-1038	48	6	ranking	ranking	ADJ
cana-1038	48	7	function	function	NOUN
cana-1038	48	8	of	of	ADP
cana-1038	48	9	trfn	trfn	NOUN
cana-1038	48	10	is	be	AUX
cana-1038	48	11	defined	define	VERB
cana-1038	48	12	as	as	ADP
cana-1038	48	13	ῡ𝜇(𝑥	ῡ𝜇(𝑥	NOUN
cana-1038	48	14	)	)	PUNCT
cana-1038	49	1	=	=	VERB
cana-1038	49	2	𝑎1	𝑎1	X
cana-1038	49	3	+	+	NOUN
cana-1038	49	4	2𝑎2	2𝑎2	ADJ
cana-1038	49	5	+	+	ADJ
cana-1038	49	6	2𝑎3+𝑎4	2𝑎3+𝑎4	NUM
cana-1038	49	7	6	6	NUM
cana-1038	49	8	(	(	PUNCT
cana-1038	49	9	ii	ii	NOUN
cana-1038	49	10	)	)	PUNCT
cana-1038	49	11	ambiguity	ambiguity	NOUN
cana-1038	49	12	ranking	rank	VERB
cana-1038	49	13	function	function	NOUN
cana-1038	49	14	ᾱ𝑖𝑗(𝑥	ᾱ𝑖𝑗(𝑥	NOUN
cana-1038	49	15	)	)	PUNCT
cana-1038	49	16	=	=	SYM
cana-1038	50	1	∫	∫	PROPN
cana-1038	50	2	(	(	PUNCT
cana-1038	50	3	1	1	NUM
cana-1038	50	4	0	0	NUM
cana-1038	50	5	𝑅	𝑅	PROPN
cana-1038	50	6	�	�	PROPN
cana-1038	50	7	̃	̃	PROPN
cana-1038	50	8	�	�	NOUN
cana-1038	50	9	𝑖(𝛼	𝑖(𝛼	NOUN
cana-1038	50	10	)	)	PUNCT
cana-1038	50	11	−	−	PROPN
cana-1038	50	12	𝐿	𝐿	PROPN
cana-1038	50	13	�	�	PROPN
cana-1038	50	14	̃	̃	PROPN
cana-1038	50	15	�	�	PROPN
cana-1038	50	16	𝑖(𝛼))𝑓(𝛼)𝑑𝛼	𝑖(𝛼))𝑓(𝛼)𝑑𝛼	NUM
cana-1038	50	17	�	�	PROPN
cana-1038	50	18	̃	̃	PROPN
cana-1038	50	19	�	�	NOUN
cana-1038	50	20	𝑖𝑗(𝑥	𝑖𝑗(𝑥	X
cana-1038	50	21	)	)	PUNCT
cana-1038	50	22	=	=	SYM
cana-1038	50	23	∫	∫	PROPN
cana-1038	51	1	[	[	X
cana-1038	51	2	𝑎4	𝑎4	PROPN
cana-1038	51	3	−	−	PROPN
cana-1038	51	4	𝛼(𝑎4	𝛼(𝑎4	NOUN
cana-1038	51	5	−	−	PROPN
cana-1038	51	6	𝑎3	𝑎3	PROPN
cana-1038	51	7	)	)	PUNCT
cana-1038	51	8	−	−	PROPN
cana-1038	52	1	𝑎1	𝑎1	X
cana-1038	52	2	+	+	CCONJ
cana-1038	52	3	𝛼(𝑎2	𝛼(𝑎2	NOUN
cana-1038	52	4	−	−	ADP
cana-1038	52	5	𝑎1)]𝛼	𝑎1)]𝛼	PUNCT
cana-1038	52	6	𝑑𝛼	𝑑𝛼	ADP
cana-1038	52	7	1	1	NUM
cana-1038	52	8	0	0	NUM
cana-1038	52	9	after	after	ADP
cana-1038	52	10	simplification	simplification	NOUN
cana-1038	52	11	,	,	PUNCT
cana-1038	52	12	we	we	PRON
cana-1038	52	13	get	get	VERB
cana-1038	52	14	ᾱ𝜇(𝑥	ᾱ𝜇(𝑥	NOUN
cana-1038	52	15	)	)	PUNCT
cana-1038	53	1	=	=	PUNCT
cana-1038	53	2	−𝑎1	−𝑎1	NOUN
cana-1038	53	3	−	−	NOUN
cana-1038	53	4	2𝑎2	2𝑎2	NUM
cana-1038	53	5	+	+	CCONJ
cana-1038	53	6	2𝑎3	2𝑎3	NUM
cana-1038	53	7	+	+	CCONJ
cana-1038	53	8	𝑎4	𝑎4	PROPN
cana-1038	53	9	6	6	NUM
cana-1038	53	10	the	the	DET
cana-1038	53	11	ambiguity	ambiguity	NOUN
cana-1038	53	12	ranking	rank	VERB
cana-1038	53	13	function	function	NOUN
cana-1038	53	14	of	of	ADP
cana-1038	53	15	trfn	trfn	NOUN
cana-1038	53	16	is	be	AUX
cana-1038	53	17	defined	define	VERB
cana-1038	53	18	as	as	ADP
cana-1038	53	19	ᾱ𝜇(𝑥	ᾱ𝜇(𝑥	ADJ
cana-1038	53	20	)	)	PUNCT
cana-1038	53	21	=	=	PUNCT
cana-1038	54	1	−𝑎1	−𝑎1	NOUN
cana-1038	54	2	−	−	NOUN
cana-1038	54	3	2𝑎2	2𝑎2	NUM
cana-1038	54	4	+	+	CCONJ
cana-1038	54	5	2𝑎3	2𝑎3	NUM
cana-1038	55	1	+	+	CCONJ
cana-1038	55	2	𝑎4	𝑎4	PROPN
cana-1038	55	3	6	6	NUM
cana-1038	55	4	4	4	NUM
cana-1038	55	5	.	.	PUNCT
cana-1038	55	6	results	result	VERB
cana-1038	55	7	transportation	transportation	NOUN
cana-1038	55	8	problem	problem	NOUN
cana-1038	55	9	using	use	VERB
cana-1038	55	10	proposed	propose	VERB
cana-1038	55	11	ranking	ranking	NOUN
cana-1038	55	12	function	function	NOUN
cana-1038	55	13	the	the	DET
cana-1038	55	14	company	company	NOUN
cana-1038	55	15	has	have	VERB
cana-1038	55	16	four	four	NUM
cana-1038	55	17	sources	source	NOUN
cana-1038	55	18	,	,	PUNCT
cana-1038	55	19	denoted	denote	VERB
cana-1038	55	20	as	as	ADP
cana-1038	55	21	𝑠1	𝑠1	PROPN
cana-1038	55	22	,	,	PUNCT
cana-1038	55	23	𝑠2	𝑠2	PROPN
cana-1038	55	24	,	,	PUNCT
cana-1038	55	25	𝑠3	𝑠3	NOUN
cana-1038	55	26	,	,	PUNCT
cana-1038	55	27	and	and	CCONJ
cana-1038	55	28	𝑠4	𝑠4	PROPN
cana-1038	55	29	,	,	PUNCT
cana-1038	55	30	and	and	CCONJ
cana-1038	55	31	four	four	NUM
cana-1038	55	32	destinations	destination	NOUN
cana-1038	55	33	,	,	PUNCT
cana-1038	55	34	also	also	ADV
cana-1038	55	35	denoted	denote	VERB
cana-1038	55	36	as	as	ADP
cana-1038	55	37	𝑠1	𝑠1	PROPN
cana-1038	55	38	,	,	PUNCT
cana-1038	55	39	𝑠2	𝑠2	PROPN
cana-1038	55	40	,	,	PUNCT
cana-1038	55	41	𝑠3	𝑠3	NOUN
cana-1038	55	42	,	,	PUNCT
cana-1038	55	43	and	and	CCONJ
cana-1038	55	44	𝑠4	𝑠4	PROPN
cana-1038	55	45	.	.	PUNCT
cana-1038	56	1	the	the	DET
cana-1038	56	2	fuzzy	fuzzy	ADJ
cana-1038	56	3	transportation	transportation	NOUN
cana-1038	56	4	cost	cost	NOUN
cana-1038	56	5	for	for	ADP
cana-1038	56	6	transferring	transfer	VERB
cana-1038	56	7	one	one	NUM
cana-1038	56	8	unit	unit	NOUN
cana-1038	56	9	of	of	ADP
cana-1038	56	10	the	the	DET
cana-1038	56	11	product	product	NOUN
cana-1038	56	12	from	from	ADP
cana-1038	56	13	the	the	DET
cana-1038	56	14	ith	ith	PROPN
cana-1038	56	15	source	source	NOUN
cana-1038	56	16	to	to	ADP
cana-1038	56	17	the	the	DET
cana-1038	56	18	jth	jth	PROPN
cana-1038	56	19	destination	destination	NOUN
cana-1038	56	20	is	be	AUX
cana-1038	56	21	determined	determine	VERB
cana-1038	56	22	by	by	ADP
cana-1038	56	23	the	the	DET
cana-1038	56	24	given	give	VERB
cana-1038	56	25	formula	formula	NOUN
cana-1038	56	26	.	.	PUNCT
cana-1038	57	1	cij	cij	PROPN
cana-1038	57	2	=(	=(	PROPN
cana-1038	57	3	(	(	PUNCT
cana-1038	57	4	1,2,3,4)(1,3,5,6)(9,11,12,14)(5,7,8,11	1,2,3,4)(1,3,5,6)(9,11,12,14)(5,7,8,11	PROPN
cana-1038	57	5	)	)	PUNCT
cana-1038	57	6	(	(	PUNCT
cana-1038	57	7	0,1,2,4)(−1,0,1,2)(5,6,7,8)(0,1,2,3	0,1,2,4)(−1,0,1,2)(5,6,7,8)(0,1,2,3	PROPN
cana-1038	57	8	)	)	PUNCT
cana-1038	57	9	(	(	PUNCT
cana-1038	57	10	3,5,6,8)(5,8,9,12)(12,15,16,19)(7,9,10,12	3,5,6,8)(5,8,9,12)(12,15,16,19)(7,9,10,12	PROPN
cana-1038	57	11	)	)	PUNCT
cana-1038	57	12	)	)	PUNCT
cana-1038	58	1	the	the	DET
cana-1038	58	2	availability	availability	NOUN
cana-1038	58	3	of	of	ADP
cana-1038	58	4	the	the	DET
cana-1038	58	5	sources	source	NOUN
cana-1038	58	6	are	be	AUX
cana-1038	58	7	(	(	PUNCT
cana-1038	58	8	(	(	PUNCT
cana-1038	58	9	1,6,7,12	1,6,7,12	NUM
cana-1038	58	10	)	)	PUNCT
cana-1038	58	11	,	,	PUNCT
cana-1038	58	12	(	(	PUNCT
cana-1038	58	13	0,1,2,3	0,1,2,3	NUM
cana-1038	58	14	)	)	PUNCT
cana-1038	58	15	,	,	PUNCT
cana-1038	58	16	(	(	PUNCT
cana-1038	58	17	5,10,12,17	5,10,12,17	NUM
cana-1038	58	18	)	)	PUNCT
cana-1038	58	19	)	)	PUNCT
cana-1038	58	20	and	and	CCONJ
cana-1038	58	21	the	the	DET
cana-1038	58	22	product	product	NOUN
cana-1038	58	23	’s	’s	PART
cana-1038	58	24	fuzzy	fuzzy	ADJ
cana-1038	58	25	demand	demand	NOUN
cana-1038	58	26	at	at	ADP
cana-1038	58	27	destinations	destination	NOUN
cana-1038	58	28	are	be	AUX
cana-1038	58	29	(	(	PUNCT
cana-1038	58	30	(	(	PUNCT
cana-1038	58	31	5,7,8,10	5,7,8,10	NUM
cana-1038	58	32	)	)	PUNCT
cana-1038	58	33	,	,	PUNCT
cana-1038	58	34	(	(	PUNCT
cana-1038	58	35	1,5,6,10	1,5,6,10	NUM
cana-1038	58	36	)	)	PUNCT
cana-1038	58	37	,	,	PUNCT
cana-1038	58	38	(	(	PUNCT
cana-1038	58	39	1,3,4,6	1,3,4,6	NUM
cana-1038	58	40	)	)	PUNCT
cana-1038	58	41	(	(	PUNCT
cana-1038	58	42	1,2,3,4	1,2,3,4	NUM
cana-1038	58	43	)	)	PUNCT
cana-1038	58	44	)	)	PUNCT
cana-1038	58	45	correspondingly	correspondingly	ADV
cana-1038	58	46	.	.	PUNCT
cana-1038	59	1	then	then	ADV
cana-1038	59	2	the	the	DET
cana-1038	59	3	problem	problem	NOUN
cana-1038	59	4	becomes	become	VERB
cana-1038	59	5	as	as	SCONJ
cana-1038	59	6	table:1	table:1	NOUN
cana-1038	59	7	communications	communication	NOUN
cana-1038	59	8	on	on	ADP
cana-1038	59	9	applied	apply	VERB
cana-1038	59	10	nonlinear	nonlinear	ADJ
cana-1038	59	11	analysis	analysis	NOUN
cana-1038	59	12	issn	issn	NOUN
cana-1038	59	13	:	:	PUNCT
cana-1038	59	14	1074	1074	NUM
cana-1038	59	15	-	-	PUNCT
cana-1038	59	16	133x	133x	NUM
cana-1038	59	17	vol	vol	NOUN
cana-1038	59	18	31	31	NUM
cana-1038	59	19	no	no	NOUN
cana-1038	59	20	.	.	PUNCT
cana-1038	60	1	5s	5s	NUM
cana-1038	60	2	(	(	PUNCT
cana-1038	60	3	2024	2024	NUM
cana-1038	60	4	)	)	PUNCT
cana-1038	60	5	299	299	NUM
cana-1038	60	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1038	60	7	solution	solution	NOUN
cana-1038	60	8	:	:	PUNCT
cana-1038	60	9	the	the	DET
cana-1038	60	10	following	follow	VERB
cana-1038	60	11	mathematical	mathematical	ADJ
cana-1038	60	12	programming	programming	NOUN
cana-1038	60	13	form	form	NOUN
cana-1038	60	14	can	can	AUX
cana-1038	60	15	be	be	AUX
cana-1038	60	16	used	use	VERB
cana-1038	60	17	to	to	PART
cana-1038	60	18	formulate	formulate	VERB
cana-1038	60	19	the	the	DET
cana-1038	60	20	fuzzy	fuzzy	ADJ
cana-1038	60	21	transportation	transportation	NOUN
cana-1038	60	22	problem	problem	NOUN
cana-1038	60	23	.	.	PUNCT
cana-1038	61	1	(	(	PUNCT
cana-1038	61	2	i	i	NOUN
cana-1038	61	3	)	)	PUNCT
cana-1038	61	4	vague	vague	ADJ
cana-1038	61	5	ranking	ranking	NOUN
cana-1038	61	6	function	function	NOUN
cana-1038	61	7	ῡ𝑖𝑗(𝑥	ῡ𝑖𝑗(𝑥	PROPN
cana-1038	61	8	)	)	PUNCT
cana-1038	61	9	=	=	SYM
cana-1038	62	1	𝑎1	𝑎1	NOUN
cana-1038	62	2	+	+	CCONJ
cana-1038	62	3	2𝑎2	2𝑎2	NUM
cana-1038	62	4	+	+	CCONJ
cana-1038	62	5	2𝑎3	2𝑎3	NUM
cana-1038	63	1	+	+	CCONJ
cana-1038	63	2	𝑎4	𝑎4	PROPN
cana-1038	63	3	6	6	NUM
cana-1038	63	4	by	by	ADP
cana-1038	63	5	substituting	substitute	VERB
cana-1038	63	6	the	the	DET
cana-1038	63	7	values	value	NOUN
cana-1038	63	8	,	,	PUNCT
cana-1038	63	9	we	we	PRON
cana-1038	63	10	get	get	VERB
cana-1038	63	11	ῡ11(𝑥	ῡ11(𝑥	NOUN
cana-1038	63	12	)	)	PUNCT
cana-1038	63	13	=	=	SYM
cana-1038	63	14	2.5	2.5	NUM
cana-1038	63	15	;	;	PUNCT
cana-1038	63	16	ῡ12(𝑥	ῡ12(𝑥	NOUN
cana-1038	63	17	)	)	PUNCT
cana-1038	63	18	=	=	SYM
cana-1038	63	19	3.5	3.5	NUM
cana-1038	63	20	;	;	PUNCT
cana-1038	63	21	ῡ13(𝑥	ῡ13(𝑥	NOUN
cana-1038	63	22	)	)	PUNCT
cana-1038	64	1	=	=	PUNCT
cana-1038	64	2	11.5	11.5	NUM
cana-1038	64	3	;	;	PUNCT
cana-1038	64	4	ῡ14(𝑥	ῡ14(𝑥	NOUN
cana-1038	64	5	)	)	PUNCT
cana-1038	64	6	=	=	SYM
cana-1038	64	7	7.7	7.7	NUM
cana-1038	64	8	ῡ21(𝑥	ῡ21(𝑥	NOUN
cana-1038	64	9	)	)	PUNCT
cana-1038	64	10	=	=	SYM
cana-1038	64	11	1.7	1.7	NUM
cana-1038	64	12	;	;	PUNCT
cana-1038	64	13	ῡ22(𝑥	ῡ22(𝑥	X
cana-1038	64	14	)	)	PUNCT
cana-1038	64	15	=	=	SYM
cana-1038	64	16	0.5	0.5	NUM
cana-1038	64	17	;	;	PUNCT
cana-1038	64	18	ῡ23(𝑥	ῡ23(𝑥	NUM
cana-1038	64	19	)	)	PUNCT
cana-1038	64	20	=	=	PUNCT
cana-1038	65	1	6.5	6.5	NUM
cana-1038	65	2	;	;	PUNCT
cana-1038	65	3	ῡ24(𝑥	ῡ24(𝑥	X
cana-1038	65	4	)	)	PUNCT
cana-1038	65	5	=	=	SYM
cana-1038	65	6	1.5	1.5	NUM
cana-1038	65	7	ῡ31(𝑥	ῡ31(𝑥	NOUN
cana-1038	65	8	)	)	PUNCT
cana-1038	65	9	=	=	PUNCT
cana-1038	65	10	5.5	5.5	NUM
cana-1038	65	11	;	;	PUNCT
cana-1038	65	12	ῡ32(𝑥	ῡ32(𝑥	NOUN
cana-1038	65	13	)	)	PUNCT
cana-1038	65	14	=	=	SYM
cana-1038	65	15	8.5	8.5	NUM
cana-1038	65	16	;	;	PUNCT
cana-1038	65	17	ῡ33(𝑥	ῡ33(𝑥	NUM
cana-1038	65	18	)	)	PUNCT
cana-1038	65	19	=	=	SYM
cana-1038	65	20	15.5	15.5	NUM
cana-1038	65	21	;	;	PUNCT
cana-1038	65	22	ῡ34(𝑥	ῡ34(𝑥	NUM
cana-1038	65	23	)	)	PUNCT
cana-1038	65	24	=	=	SYM
cana-1038	65	25	9.5	9.5	NUM
cana-1038	65	26	supply	supply	NOUN
cana-1038	65	27	ῡ(𝑓𝑆1	ῡ(𝑓𝑆1	NUM
cana-1038	65	28	)	)	PUNCT
cana-1038	65	29	=	=	PUNCT
cana-1038	65	30	6.5	6.5	NUM
cana-1038	65	31	;	;	PUNCT
cana-1038	65	32	ῡ(𝑓𝑆2	ῡ(𝑓𝑆2	NUM
cana-1038	65	33	)	)	PUNCT
cana-1038	65	34	=	=	SYM
cana-1038	65	35	1.5	1.5	NUM
cana-1038	65	36	;	;	PUNCT
cana-1038	65	37	ῡ(𝑓𝑆3	ῡ(𝑓𝑆3	X
cana-1038	65	38	)	)	PUNCT
cana-1038	65	39	=	=	SYM
cana-1038	65	40	11	11	NUM
cana-1038	65	41	demand	demand	NOUN
cana-1038	65	42	ῡ(𝑓𝐷1	ῡ(𝑓𝐷1	PRON
cana-1038	65	43	)	)	PUNCT
cana-1038	65	44	=	=	PUNCT
cana-1038	65	45	7.5	7.5	NUM
cana-1038	65	46	;	;	PUNCT
cana-1038	65	47	ῡ(𝑓𝐷2	ῡ(𝑓𝐷2	NUM
cana-1038	65	48	)	)	PUNCT
cana-1038	65	49	=	=	SYM
cana-1038	65	50	5.5	5.5	NUM
cana-1038	65	51	;	;	PUNCT
cana-1038	65	52	ῡ(𝑓𝐷3	ῡ(𝑓𝐷3	X
cana-1038	65	53	)	)	PUNCT
cana-1038	65	54	=	=	SYM
cana-1038	65	55	3.5	3.5	NUM
cana-1038	65	56	;	;	PUNCT
cana-1038	65	57	ῡ(𝑓𝐷4	ῡ(𝑓𝐷4	NUM
cana-1038	65	58	)	)	PUNCT
cana-1038	65	59	=	=	SYM
cana-1038	65	60	2.5	2.5	NUM
cana-1038	65	61	after	after	ADP
cana-1038	65	62	using	use	VERB
cana-1038	65	63	the	the	DET
cana-1038	65	64	value	value	NOUN
cana-1038	65	65	ranking	ranking	NOUN
cana-1038	65	66	function	function	NOUN
cana-1038	65	67	the	the	DET
cana-1038	65	68	table	table	NOUN
cana-1038	65	69	is	be	AUX
cana-1038	65	70	table:2	table:2	NOUN
cana-1038	65	71	by	by	ADP
cana-1038	65	72	using	use	VERB
cana-1038	65	73	the	the	DET
cana-1038	65	74	vogel	vogel	NOUN
cana-1038	65	75	approximation	approximation	NOUN
cana-1038	65	76	method	method	NOUN
cana-1038	65	77	we	we	PRON
cana-1038	65	78	get	get	VERB
cana-1038	65	79	table:3	table:3	ADP
cana-1038	65	80	the	the	DET
cana-1038	65	81	transportation	transportation	NOUN
cana-1038	65	82	cost	cost	NOUN
cana-1038	65	83	is	be	AUX
cana-1038	65	84	=	=	PUNCT
cana-1038	65	85	(	(	PUNCT
cana-1038	65	86	2.5)(1.0)+(3.5)(5.5)+(1.5)(1.5)+(5.5)(6.5)+(15.5.5)(3.5)+(9.5)(1.0	2.5)(1.0)+(3.5)(5.5)+(1.5)(1.5)+(5.5)(6.5)+(15.5.5)(3.5)+(9.5)(1.0	NUM
cana-1038	65	87	)	)	PUNCT
cana-1038	66	1	=	=	SYM
cana-1038	66	2	123.5	123.5	NUM
cana-1038	66	3	(	(	PUNCT
cana-1038	66	4	ii	ii	NOUN
cana-1038	66	5	)	)	PUNCT
cana-1038	66	6	ambiguity	ambiguity	NOUN
cana-1038	66	7	ranking	rank	VERB
cana-1038	66	8	function	function	NOUN
cana-1038	66	9	ᾱ𝜇(𝑥	ᾱ𝜇(𝑥	NOUN
cana-1038	66	10	)	)	PUNCT
cana-1038	66	11	=	=	PUNCT
cana-1038	66	12	−𝑎1	−𝑎1	NOUN
cana-1038	66	13	−	−	NOUN
cana-1038	66	14	2𝑎2	2𝑎2	NUM
cana-1038	66	15	+	+	CCONJ
cana-1038	66	16	2𝑎3	2𝑎3	NUM
cana-1038	66	17	+	+	CCONJ
cana-1038	66	18	𝑎4	𝑎4	PROPN
cana-1038	66	19	6	6	NUM
cana-1038	66	20	by	by	ADP
cana-1038	66	21	the	the	DET
cana-1038	66	22	ambiguity	ambiguity	NOUN
cana-1038	66	23	ranking	rank	VERB
cana-1038	66	24	function	function	NOUN
cana-1038	66	25	also	also	ADV
cana-1038	66	26	we	we	PRON
cana-1038	66	27	get	get	VERB
cana-1038	66	28	the	the	DET
cana-1038	66	29	same	same	ADJ
cana-1038	66	30	table	table	NOUN
cana-1038	66	31	value	value	NOUN
cana-1038	66	32	as	as	ADP
cana-1038	66	33	in	in	ADP
cana-1038	66	34	the	the	DET
cana-1038	66	35	value	value	NOUN
cana-1038	66	36	ranking	ranking	NOUN
cana-1038	66	37	function	function	NOUN
cana-1038	66	38	.	.	PUNCT
cana-1038	67	1	communications	communication	NOUN
cana-1038	67	2	on	on	ADP
cana-1038	67	3	applied	apply	VERB
cana-1038	67	4	nonlinear	nonlinear	ADJ
cana-1038	67	5	analysis	analysis	NOUN
cana-1038	67	6	issn	issn	NOUN
cana-1038	67	7	:	:	PUNCT
cana-1038	67	8	1074	1074	NUM
cana-1038	67	9	-	-	PUNCT
cana-1038	67	10	133x	133x	NUM
cana-1038	67	11	vol	vol	NOUN
cana-1038	67	12	31	31	NUM
cana-1038	67	13	no	no	NOUN
cana-1038	67	14	.	.	PUNCT
cana-1038	68	1	5s	5s	NUM
cana-1038	68	2	(	(	PUNCT
cana-1038	68	3	2024	2024	NUM
cana-1038	68	4	)	)	PUNCT
cana-1038	68	5	300	300	NUM
cana-1038	68	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1038	68	7	after	after	ADP
cana-1038	68	8	using	use	VERB
cana-1038	68	9	vam	vam	NOUN
cana-1038	68	10	we	we	PRON
cana-1038	68	11	get	get	VERB
cana-1038	68	12	table:4	table:4	NOUN
cana-1038	68	13	the	the	DET
cana-1038	68	14	transportation	transportation	NOUN
cana-1038	68	15	cost	cost	NOUN
cana-1038	68	16	is	be	AUX
cana-1038	68	17	=	=	NOUN
cana-1038	68	18	123.5	123.5	NUM
cana-1038	68	19	.	.	PUNCT
cana-1038	69	1	5	5	NUM
cana-1038	69	2	.	.	X
cana-1038	69	3	discussion	discussion	NOUN
cana-1038	69	4	and	and	CCONJ
cana-1038	69	5	conclusion	conclusion	NOUN
cana-1038	69	6	in	in	ADP
cana-1038	69	7	[	[	X
cana-1038	69	8	7	7	X
cana-1038	69	9	]	]	PUNCT
cana-1038	69	10	they	they	PRON
cana-1038	69	11	used	use	VERB
cana-1038	69	12	the	the	DET
cana-1038	69	13	“	"	PUNCT
cana-1038	69	14	roubast	roubast	ADJ
cana-1038	69	15	ranking	ranking	NOUN
cana-1038	69	16	”	"	PUNCT
cana-1038	69	17	to	to	PART
cana-1038	69	18	solve	solve	VERB
cana-1038	69	19	the	the	DET
cana-1038	69	20	transportation	transportation	NOUN
cana-1038	69	21	.	.	PUNCT
cana-1038	70	1	then	then	ADV
cana-1038	70	2	we	we	PRON
cana-1038	70	3	proposed	propose	VERB
cana-1038	70	4	two	two	NUM
cana-1038	70	5	ranking	rank	VERB
cana-1038	70	6	functions	function	NOUN
cana-1038	70	7	and	and	CCONJ
cana-1038	70	8	we	we	PRON
cana-1038	70	9	compared	compare	VERB
cana-1038	70	10	them	they	PRON
cana-1038	70	11	in	in	ADP
cana-1038	70	12	the	the	DET
cana-1038	70	13	below	below	ADJ
cana-1038	70	14	table	table	NOUN
cana-1038	70	15	table:5	table:5	NOUN
cana-1038	70	16	in	in	ADP
cana-1038	70	17	this	this	DET
cana-1038	70	18	article	article	NOUN
cana-1038	70	19	,	,	PUNCT
cana-1038	70	20	we	we	PRON
cana-1038	70	21	proposed	propose	VERB
cana-1038	70	22	two	two	NUM
cana-1038	70	23	new	new	ADJ
cana-1038	70	24	ranking	ranking	NOUN
cana-1038	70	25	functions	function	NOUN
cana-1038	70	26	called	call	VERB
cana-1038	70	27	“	"	PUNCT
cana-1038	70	28	value	value	NOUN
cana-1038	70	29	ranking	ranking	NOUN
cana-1038	70	30	and	and	CCONJ
cana-1038	70	31	ambiguity	ambiguity	NOUN
cana-1038	70	32	ranking	ranking	NOUN
cana-1038	70	33	”	"	PUNCT
cana-1038	70	34	in	in	ADP
cana-1038	70	35	an	an	DET
cana-1038	70	36	imprecise	imprecise	ADJ
cana-1038	70	37	,	,	PUNCT
cana-1038	70	38	vague	vague	ADJ
cana-1038	70	39	area	area	NOUN
cana-1038	70	40	.	.	PUNCT
cana-1038	71	1	then	then	ADV
cana-1038	71	2	we	we	PRON
cana-1038	71	3	implemented	implement	VERB
cana-1038	71	4	this	this	PRON
cana-1038	71	5	in	in	ADP
cana-1038	71	6	the	the	DET
cana-1038	71	7	same	same	ADJ
cana-1038	71	8	transportation	transportation	NOUN
cana-1038	71	9	problem	problem	NOUN
cana-1038	71	10	and	and	CCONJ
cana-1038	71	11	we	we	PRON
cana-1038	71	12	got	get	VERB
cana-1038	71	13	the	the	DET
cana-1038	71	14	same	same	ADJ
cana-1038	71	15	cost	cost	NOUN
cana-1038	71	16	as	as	ADP
cana-1038	71	17	in	in	ADP
cana-1038	71	18	robust	robust	ADJ
cana-1038	71	19	ranking	ranking	NOUN
cana-1038	71	20	.	.	PUNCT
cana-1038	72	1	to	to	PART
cana-1038	72	2	overcome	overcome	VERB
cana-1038	72	3	the	the	DET
cana-1038	72	4	drawbacks	drawback	NOUN
cana-1038	72	5	of	of	ADP
cana-1038	72	6	the	the	DET
cana-1038	72	7	existing	exist	VERB
cana-1038	72	8	method	method	NOUN
cana-1038	72	9	we	we	PRON
cana-1038	72	10	newly	newly	ADV
cana-1038	72	11	defined	define	VERB
cana-1038	72	12	the	the	DET
cana-1038	72	13	ranking	rank	VERB
cana-1038	72	14	function	function	NOUN
cana-1038	72	15	and	and	CCONJ
cana-1038	72	16	we	we	PRON
cana-1038	72	17	justified	justify	VERB
cana-1038	72	18	it	it	PRON
cana-1038	72	19	by	by	ADP
cana-1038	72	20	comparing	compare	VERB
cana-1038	72	21	them	they	PRON
cana-1038	72	22	.	.	PUNCT
cana-1038	73	1	references	reference	NOUN
cana-1038	73	2	[	[	X
cana-1038	73	3	1	1	NUM
cana-1038	73	4	]	]	PUNCT
cana-1038	73	5	.	.	PUNCT
cana-1038	74	1	rasha	rasha	PROPN
cana-1038	74	2	jalal	jalal	PROPN
cana-1038	74	3	mitlif	mitlif	PROPN
cana-1038	74	4	,	,	PUNCT
cana-1038	74	5	mohammed	mohammed	PROPN
cana-1038	74	6	rasheed	rasheed	PROPN
cana-1038	74	7	,	,	PUNCT
cana-1038	74	8	suha	suha	PROPN
cana-1038	74	9	shihab	shihab	PROPN
cana-1038	74	10	,	,	PUNCT
cana-1038	74	11	an	an	DET
cana-1038	74	12	optimal	optimal	ADJ
cana-1038	74	13	algorithm	algorithm	NOUN
cana-1038	74	14	for	for	ADP
cana-1038	74	15	a	a	DET
cana-1038	74	16	fuzzy	fuzzy	ADJ
cana-1038	74	17	transportation	transportation	NOUN
cana-1038	74	18	problem	problem	NOUN
cana-1038	74	19	,	,	PUNCT
cana-1038	74	20	journal	journal	NOUN
cana-1038	74	21	of	of	ADP
cana-1038	74	22	southwest	southwest	PROPN
cana-1038	74	23	jiaotong	jiaotong	PROPN
cana-1038	74	24	university	university	PROPN
cana-1038	74	25	,	,	PUNCT
cana-1038	74	26	55:3(2020	55:3(2020	NUM
cana-1038	74	27	)	)	PUNCT
cana-1038	74	28	,	,	PUNCT
cana-1038	74	29	1	1	NUM
cana-1038	74	30	-	-	SYM
cana-1038	74	31	11	11	NUM
cana-1038	74	32	.	.	PUNCT
cana-1038	75	1	[	[	X
cana-1038	75	2	2	2	NUM
cana-1038	75	3	]	]	PUNCT
cana-1038	75	4	.	.	PUNCT
cana-1038	76	1	ali	ali	PROPN
cana-1038	76	2	ebrahimnejad	ebrahimnejad	PROPN
cana-1038	76	3	&	&	CCONJ
cana-1038	76	4	jose	jose	PROPN
cana-1038	76	5	luis	luis	PROPN
cana-1038	76	6	verdegay	verdegay	NOUN
cana-1038	76	7	,	,	PUNCT
cana-1038	76	8	a	a	DET
cana-1038	76	9	new	new	ADJ
cana-1038	76	10	approach	approach	NOUN
cana-1038	76	11	for	for	ADP
cana-1038	76	12	solving	solve	VERB
cana-1038	76	13	fully	fully	ADV
cana-1038	76	14	intuitionistic	intuitionistic	ADJ
cana-1038	76	15	fuzzy	fuzzy	ADJ
cana-1038	76	16	transportation	transportation	NOUN
cana-1038	76	17	problems	problem	NOUN
cana-1038	76	18	,	,	PUNCT
cana-1038	76	19	fuzzy	fuzzy	ADJ
cana-1038	76	20	optimization	optimization	NOUN
cana-1038	76	21	and	and	CCONJ
cana-1038	76	22	decision	decision	NOUN
cana-1038	76	23	making17(2018	making17(2018	NOUN
cana-1038	76	24	)	)	PUNCT
cana-1038	76	25	,	,	PUNCT
cana-1038	76	26	447	447	NUM
cana-1038	76	27	–	–	PUNCT
cana-1038	76	28	474	474	NUM
cana-1038	76	29	.	.	PUNCT
cana-1038	77	1	[	[	X
cana-1038	77	2	3	3	NUM
cana-1038	77	3	]	]	PUNCT
cana-1038	77	4	.	.	PUNCT
cana-1038	78	1	laxminarayan	laxminarayan	PROPN
cana-1038	78	2	sahoo	sahoo	PROPN
cana-1038	78	3	,	,	PUNCT
cana-1038	78	4	a	a	DET
cana-1038	78	5	new	new	ADJ
cana-1038	78	6	score	score	NOUN
cana-1038	78	7	function	function	NOUN
cana-1038	78	8	based	base	VERB
cana-1038	78	9	fermatean	fermatean	PROPN
cana-1038	78	10	fuzzy	fuzzy	ADJ
cana-1038	78	11	transportation	transportation	NOUN
cana-1038	78	12	problem	problem	NOUN
cana-1038	78	13	,	,	PUNCT
cana-1038	78	14	results	result	NOUN
cana-1038	78	15	in	in	ADP
cana-1038	78	16	control	control	NOUN
cana-1038	78	17	and	and	CCONJ
cana-1038	78	18	optimization	optimization	NOUN
cana-1038	78	19	4	4	NUM
cana-1038	78	20	(	(	PUNCT
cana-1038	78	21	2021	2021	NUM
cana-1038	78	22	)	)	PUNCT
cana-1038	78	23	,	,	PUNCT
cana-1038	78	24	10040	10040	NUM
cana-1038	78	25	.	.	PUNCT
cana-1038	79	1	[	[	X
cana-1038	79	2	4	4	NUM
cana-1038	79	3	]	]	PUNCT
cana-1038	79	4	.	.	PUNCT
cana-1038	80	1	d.	d.	PROPN
cana-1038	80	2	stephen	stephen	PROPN
cana-1038	80	3	dinagar	dinagar	PROPN
cana-1038	80	4	,	,	PUNCT
cana-1038	80	5	e.	e.	PROPN
cana-1038	80	6	fany	fany	PROPN
cana-1038	80	7	helena	helena	PROPN
cana-1038	80	8	,	,	PUNCT
cana-1038	80	9	similarity	similarity	NOUN
cana-1038	80	10	measure	measure	NOUN
cana-1038	80	11	using	use	VERB
cana-1038	80	12	sign	sign	NOUN
cana-1038	80	13	distance	distance	NOUN
cana-1038	80	14	,	,	PUNCT
cana-1038	80	15	advances	advance	NOUN
cana-1038	80	16	in	in	ADP
cana-1038	80	17	mathematics	mathematic	NOUN
cana-1038	80	18	:	:	PUNCT
cana-1038	80	19	scientific	scientific	ADJ
cana-1038	80	20	journal	journal	NOUN
cana-1038	80	21	10:1	10:1	NUM
cana-1038	80	22	(	(	PUNCT
cana-1038	80	23	2021	2021	NUM
cana-1038	80	24	)	)	PUNCT
cana-1038	80	25	,	,	PUNCT
cana-1038	80	26	193	193	NUM
cana-1038	80	27	-	-	SYM
cana-1038	80	28	197	197	NUM
cana-1038	80	29	.	.	PUNCT
cana-1038	81	1	[	[	X
cana-1038	81	2	5	5	NUM
cana-1038	81	3	]	]	PUNCT
cana-1038	81	4	.	.	PUNCT
cana-1038	82	1	d.	d.	PROPN
cana-1038	82	2	stephen	stephen	PROPN
cana-1038	82	3	dinagar	dinagar	PROPN
cana-1038	82	4	,	,	PUNCT
cana-1038	82	5	e.	e.	PROPN
cana-1038	82	6	fany	fany	PROPN
cana-1038	82	7	helena	helena	PROPN
cana-1038	82	8	,	,	PUNCT
cana-1038	82	9	similarity	similarity	NOUN
cana-1038	82	10	measures	measure	NOUN
cana-1038	82	11	of	of	ADP
cana-1038	82	12	intuitionistic	intuitionistic	ADJ
cana-1038	82	13	trapezoidal	trapezoidal	ADJ
cana-1038	82	14	fuzzy	fuzzy	ADJ
cana-1038	82	15	number	number	NOUN
cana-1038	82	16	using	use	VERB
cana-1038	82	17	centroids	centroid	NOUN
cana-1038	82	18	of	of	ADP
cana-1038	82	19	horizontal	horizontal	PROPN
cana-1038	82	20	&	&	CCONJ
cana-1038	82	21	vertical	vertical	ADJ
cana-1038	82	22	axes	axis	NOUN
cana-1038	82	23	and	and	CCONJ
cana-1038	82	24	value	value	NOUN
cana-1038	82	25	&	&	CCONJ
cana-1038	82	26	ambiguity	ambiguity	NOUN
cana-1038	82	27	indices	index	NOUN
cana-1038	82	28	,	,	PUNCT
cana-1038	82	29	advances	advance	NOUN
cana-1038	82	30	and	and	CCONJ
cana-1038	82	31	applications	application	NOUN
cana-1038	82	32	in	in	ADP
cana-1038	82	33	mathematical	mathematical	ADJ
cana-1038	82	34	sciences	science	NOUN
cana-1038	82	35	20	20	NUM
cana-1038	82	36	:	:	SYM
cana-1038	82	37	5	5	NUM
cana-1038	82	38	(	(	PUNCT
cana-1038	82	39	2021	2021	NUM
cana-1038	82	40	)	)	PUNCT
cana-1038	82	41	,	,	PUNCT
cana-1038	82	42	875	875	NUM
cana-1038	82	43	-	-	SYM
cana-1038	82	44	885	885	NUM
cana-1038	82	45	.	.	PUNCT
cana-1038	83	1	[	[	X
cana-1038	83	2	6	6	NUM
cana-1038	83	3	]	]	PUNCT
cana-1038	83	4	.	.	PUNCT
cana-1038	84	1	d.	d.	PROPN
cana-1038	84	2	stephen	stephen	PROPN
cana-1038	84	3	dinagar	dinagar	PROPN
cana-1038	84	4	,	,	PUNCT
cana-1038	84	5	e.	e.	PROPN
cana-1038	84	6	fany	fany	PROPN
cana-1038	84	7	helena	helena	PROPN
cana-1038	84	8	,	,	PUNCT
cana-1038	84	9	similarity	similarity	NOUN
cana-1038	84	10	measures	measure	NOUN
cana-1038	84	11	with	with	ADP
cana-1038	84	12	vector	vector	NOUN
cana-1038	84	13	–	–	PUNCT
cana-1038	84	14	length	length	NOUN
cana-1038	84	15	under	under	ADP
cana-1038	84	16	fuzzy	fuzzy	ADJ
cana-1038	84	17	environment	environment	NOUN
cana-1038	84	18	,	,	PUNCT
cana-1038	84	19	advances	advance	NOUN
cana-1038	84	20	and	and	CCONJ
cana-1038	84	21	applications	application	NOUN
cana-1038	84	22	in	in	ADP
cana-1038	84	23	mathematical	mathematical	ADJ
cana-1038	84	24	sciences	science	NOUN
cana-1038	84	25	20:8	20:8	NUM
cana-1038	84	26	(	(	PUNCT
cana-1038	84	27	2021),14251432	2021),14251432	NUM
cana-1038	84	28	.	.	NOUN
cana-1038	84	29	https://link.springer.com/article/10.1007/s10700-017-9280-1#auth-ali-ebrahimnejad-aff1	https://link.springer.com/article/10.1007/s10700-017-9280-1#auth-ali-ebrahimnejad-aff1	ADJ
cana-1038	84	30	https://link.springer.com/article/10.1007/s10700-017-9280-1#auth-jose_luis-verdegay-aff2	https://link.springer.com/article/10.1007/s10700-017-9280-1#auth-jose_luis-verdegay-aff2	NOUN
cana-1038	84	31	https://www.sciencedirect.com/journal/results-in-control-and-optimization	https://www.sciencedirect.com/journal/results-in-control-and-optimization	NOUN
cana-1038	84	32	https://www.sciencedirect.com/journal/results-in-control-and-optimization	https://www.sciencedirect.com/journal/results-in-control-and-optimization	PROPN