id	sid	tid	token	lemma	pos
cana-2411	1	1	communications	communication	NOUN
cana-2411	1	2	on	on	ADP
cana-2411	1	3	applied	apply	VERB
cana-2411	1	4	nonlinear	nonlinear	ADJ
cana-2411	1	5	analysis	analysis	NOUN
cana-2411	1	6	issn	issn	NOUN
cana-2411	1	7	:	:	PUNCT
cana-2411	1	8	1074	1074	NUM
cana-2411	1	9	-	-	PUNCT
cana-2411	1	10	133x	133x	NUM
cana-2411	1	11	vol	vol	NOUN
cana-2411	1	12	32	32	NUM
cana-2411	1	13	no	no	NOUN
cana-2411	1	14	.	.	PUNCT
cana-2411	2	1	2s	2s	NUM
cana-2411	2	2	(	(	PUNCT
cana-2411	2	3	2025	2025	NUM
cana-2411	2	4	)	)	PUNCT
cana-2411	2	5	366	366	NUM
cana-2411	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2411	2	7	comparison	comparison	NOUN
cana-2411	2	8	between	between	ADP
cana-2411	2	9	cauchy	cauchy	PROPN
cana-2411	2	10	's	's	PART
cana-2411	2	11	steepest	steep	ADJ
cana-2411	2	12	descent	descent	NOUN
cana-2411	2	13	and	and	CCONJ
cana-2411	2	14	fletcher	fletcher	PROPN
cana-2411	2	15	-	-	PUNCT
cana-2411	2	16	reeves	reeves	PROPN
cana-2411	2	17	methods	method	NOUN
cana-2411	2	18	in	in	ADP
cana-2411	2	19	solving	solve	VERB
cana-2411	2	20	unconstrained	unconstraine	VERB
cana-2411	2	21	neutrosophic	neutrosophic	ADJ
cana-2411	2	22	nonlinear	nonlinear	ADJ
cana-2411	2	23	programming	programming	NOUN
cana-2411	2	24	problems	problem	NOUN
cana-2411	2	25	g.	g.	PROPN
cana-2411	2	26	vanaja1	vanaja1	PROPN
cana-2411	2	27	and	and	CCONJ
cana-2411	2	28	k.	k.	PROPN
cana-2411	2	29	ganesan2	ganesan2	PROPN
cana-2411	2	30	*	*	PROPN
cana-2411	2	31	1,2*department	1,2*department	NUM
cana-2411	2	32	of	of	ADP
cana-2411	2	33	mathematics	mathematic	NOUN
cana-2411	2	34	,	,	PUNCT
cana-2411	2	35	college	college	NOUN
cana-2411	2	36	of	of	ADP
cana-2411	2	37	engineering	engineering	NOUN
cana-2411	2	38	and	and	CCONJ
cana-2411	2	39	technology	technology	NOUN
cana-2411	2	40	,	,	PUNCT
cana-2411	2	41	srm	srm	PROPN
cana-2411	2	42	institute	institute	PROPN
cana-2411	2	43	of	of	ADP
cana-2411	2	44	science	science	NOUN
cana-2411	2	45	and	and	CCONJ
cana-2411	2	46	technology	technology	NOUN
cana-2411	2	47	,	,	PUNCT
cana-2411	2	48	srm	srm	NOUN
cana-2411	2	49	nagar	nagar	PROPN
cana-2411	2	50	,	,	PUNCT
cana-2411	2	51	kattankulathur	kattankulathur	ADJ
cana-2411	2	52	,	,	PUNCT
cana-2411	2	53	tamilnadu	tamilnadu	ADJ
cana-2411	2	54	,	,	PUNCT
cana-2411	2	55	india	india	PROPN
cana-2411	2	56	;	;	PUNCT
cana-2411	2	57	vg5308@srmist.edu.in	vg5308@srmist.edu.in	NUM
cana-2411	2	58	.	.	PUNCT
cana-2411	3	1	*	*	PUNCT
cana-2411	3	2	correspondence	correspondence	NOUN
cana-2411	3	3	:	:	PUNCT
cana-2411	3	4	ganesank@srmist.edu.in	ganesank@srmist.edu.in	PROPN
cana-2411	3	5	article	article	NOUN
cana-2411	3	6	history	history	NOUN
cana-2411	3	7	:	:	PUNCT
cana-2411	3	8	received	receive	VERB
cana-2411	3	9	:	:	PUNCT
cana-2411	3	10	17	17	NUM
cana-2411	3	11	-	-	SYM
cana-2411	3	12	09	09	NUM
cana-2411	3	13	-	-	PUNCT
cana-2411	3	14	2024	2024	NUM
cana-2411	3	15	revised	revise	VERB
cana-2411	3	16	:	:	PUNCT
cana-2411	3	17	25	25	NUM
cana-2411	3	18	-	-	SYM
cana-2411	3	19	10	10	NUM
cana-2411	3	20	-	-	PUNCT
cana-2411	3	21	2024	2024	NUM
cana-2411	3	22	accepted	accept	VERB
cana-2411	3	23	:	:	PUNCT
cana-2411	3	24	05	05	NUM
cana-2411	3	25	-	-	SYM
cana-2411	3	26	11	11	NUM
cana-2411	3	27	-	-	PUNCT
cana-2411	3	28	2024	2024	NUM
cana-2411	3	29	abstract	abstract	NOUN
cana-2411	3	30	:	:	PUNCT
cana-2411	3	31	the	the	DET
cana-2411	3	32	main	main	ADJ
cana-2411	3	33	objective	objective	NOUN
cana-2411	3	34	of	of	ADP
cana-2411	3	35	this	this	DET
cana-2411	3	36	study	study	NOUN
cana-2411	3	37	is	be	AUX
cana-2411	3	38	to	to	PART
cana-2411	3	39	solve	solve	VERB
cana-2411	3	40	unconstrained	unconstraine	VERB
cana-2411	3	41	single	single	ADV
cana-2411	3	42	-	-	PUNCT
cana-2411	3	43	valued	value	VERB
cana-2411	3	44	neutrosophic	neutrosophic	ADJ
cana-2411	3	45	nonlinear	nonlinear	ADJ
cana-2411	3	46	programming	programming	NOUN
cana-2411	3	47	problems	problem	NOUN
cana-2411	3	48	using	use	VERB
cana-2411	3	49	cauchy	cauchy	PROPN
cana-2411	3	50	’s	’s	PART
cana-2411	3	51	steepest	steep	ADJ
cana-2411	3	52	descent	descent	NOUN
cana-2411	3	53	method(csdm	method(csdm	PROPN
cana-2411	3	54	)	)	PUNCT
cana-2411	3	55	and	and	CCONJ
cana-2411	3	56	the	the	DET
cana-2411	3	57	fletcher	fletcher	PROPN
cana-2411	3	58	-	-	PUNCT
cana-2411	3	59	reeves	reeves	PROPN
cana-2411	3	60	method(frm	method(frm	PROPN
cana-2411	3	61	)	)	PUNCT
cana-2411	3	62	.	.	PUNCT
cana-2411	4	1	our	our	PRON
cana-2411	4	2	approach	approach	NOUN
cana-2411	4	3	is	be	AUX
cana-2411	4	4	based	base	VERB
cana-2411	4	5	on	on	ADP
cana-2411	4	6	new	new	ADJ
cana-2411	4	7	arithmetic	arithmetic	ADJ
cana-2411	4	8	operations	operation	NOUN
cana-2411	4	9	and	and	CCONJ
cana-2411	4	10	ranking	rank	VERB
cana-2411	4	11	on	on	ADP
cana-2411	4	12	the	the	DET
cana-2411	4	13	parametric	parametric	ADJ
cana-2411	4	14	representations	representation	NOUN
cana-2411	4	15	of	of	ADP
cana-2411	4	16	triangular	triangular	NOUN
cana-2411	4	17	neutrosophic	neutrosophic	ADJ
cana-2411	4	18	numbers(tnn	numbers(tnn	NOUN
cana-2411	4	19	)	)	PUNCT
cana-2411	4	20	.	.	PUNCT
cana-2411	5	1	we	we	PRON
cana-2411	5	2	prove	prove	VERB
cana-2411	5	3	some	some	DET
cana-2411	5	4	important	important	ADJ
cana-2411	5	5	theorems	theorem	NOUN
cana-2411	5	6	for	for	ADP
cana-2411	5	7	cauchy	cauchy	PROPN
cana-2411	5	8	’s	’s	PART
cana-2411	5	9	steepest	steep	ADJ
cana-2411	5	10	descent	descent	NOUN
cana-2411	5	11	method	method	NOUN
cana-2411	5	12	and	and	CCONJ
cana-2411	5	13	the	the	DET
cana-2411	5	14	fletcher	fletcher	PROPN
cana-2411	5	15	-	-	PUNCT
cana-2411	5	16	reeves	reeves	PROPN
cana-2411	5	17	method	method	PROPN
cana-2411	5	18	.	.	PUNCT
cana-2411	6	1	numerical	numerical	ADJ
cana-2411	6	2	examples	example	NOUN
cana-2411	6	3	are	be	AUX
cana-2411	6	4	presented	present	VERB
cana-2411	6	5	to	to	PART
cana-2411	6	6	illustrate	illustrate	VERB
cana-2411	6	7	the	the	DET
cana-2411	6	8	theory	theory	NOUN
cana-2411	6	9	developed	develop	VERB
cana-2411	6	10	in	in	ADP
cana-2411	6	11	this	this	DET
cana-2411	6	12	article	article	NOUN
cana-2411	6	13	.	.	PUNCT
cana-2411	7	1	the	the	DET
cana-2411	7	2	outcomes	outcome	NOUN
cana-2411	7	3	of	of	ADP
cana-2411	7	4	the	the	DET
cana-2411	7	5	proposed	propose	VERB
cana-2411	7	6	methods	method	NOUN
cana-2411	7	7	are	be	AUX
cana-2411	7	8	compared	compare	VERB
cana-2411	7	9	.	.	PUNCT
cana-2411	8	1	keywords	keyword	NOUN
cana-2411	8	2	:	:	PUNCT
cana-2411	8	3	cauchy	cauchy	PROPN
cana-2411	8	4	’s	’s	PART
cana-2411	8	5	steepest	steep	ADJ
cana-2411	8	6	descent	descent	NOUN
cana-2411	8	7	method	method	NOUN
cana-2411	8	8	;	;	PUNCT
cana-2411	8	9	fletcher	fletcher	PROPN
cana-2411	8	10	reeves	reeves	PROPN
cana-2411	8	11	method	method	PROPN
cana-2411	8	12	;	;	PUNCT
cana-2411	8	13	unconstrained	unconstrained	ADJ
cana-2411	8	14	optimization	optimization	NOUN
cana-2411	8	15	;	;	PUNCT
cana-2411	8	16	single	single	ADJ
cana-2411	8	17	-	-	PUNCT
cana-2411	8	18	valued	value	VERB
cana-2411	8	19	neutrosophic	neutrosophic	ADJ
cana-2411	8	20	number	number	NOUN
cana-2411	8	21	;	;	PUNCT
cana-2411	8	22	arithmetic	arithmetic	ADJ
cana-2411	8	23	operations	operation	NOUN
cana-2411	8	24	and	and	CCONJ
cana-2411	8	25	ranking	rank	VERB
cana-2411	8	26	1	1	NUM
cana-2411	8	27	.	.	PUNCT
cana-2411	8	28	introduction	introduction	NOUN
cana-2411	8	29	the	the	DET
cana-2411	8	30	notion	notion	NOUN
cana-2411	8	31	of	of	ADP
cana-2411	8	32	fuzzy	fuzzy	ADJ
cana-2411	8	33	sets	set	NOUN
cana-2411	8	34	,	,	PUNCT
cana-2411	8	35	proposed	propose	VERB
cana-2411	8	36	by	by	ADP
cana-2411	8	37	zadeh	zadeh	PROPN
cana-2411	9	1	[	[	X
cana-2411	9	2	27	27	NUM
cana-2411	9	3	]	]	PUNCT
cana-2411	9	4	,	,	PUNCT
cana-2411	9	5	has	have	AUX
cana-2411	9	6	played	play	VERB
cana-2411	9	7	a	a	DET
cana-2411	9	8	vital	vital	ADJ
cana-2411	9	9	role	role	NOUN
cana-2411	9	10	in	in	ADP
cana-2411	9	11	addressing	address	VERB
cana-2411	9	12	real	real	ADJ
cana-2411	9	13	-	-	PUNCT
cana-2411	9	14	world	world	NOUN
cana-2411	9	15	challenges	challenge	NOUN
cana-2411	9	16	.	.	PUNCT
cana-2411	10	1	smarandache	smarandache	NOUN
cana-2411	11	1	[	[	X
cana-2411	11	2	21	21	NUM
cana-2411	11	3	]	]	PUNCT
cana-2411	11	4	introduced	introduce	VERB
cana-2411	11	5	neutrosophic	neutrosophic	ADJ
cana-2411	11	6	sets	set	NOUN
cana-2411	11	7	to	to	PART
cana-2411	11	8	shade	shade	VERB
cana-2411	11	9	the	the	DET
cana-2411	11	10	problem	problem	NOUN
cana-2411	11	11	of	of	ADP
cana-2411	11	12	fuzzy	fuzzy	ADJ
cana-2411	11	13	sets	set	NOUN
cana-2411	11	14	that	that	PRON
cana-2411	11	15	handles	handle	VERB
cana-2411	11	16	less	less	ADJ
cana-2411	11	17	and	and	CCONJ
cana-2411	11	18	inconsistent	inconsistent	ADJ
cana-2411	11	19	information	information	NOUN
cana-2411	11	20	.	.	PUNCT
cana-2411	12	1	it	it	PRON
cana-2411	12	2	was	be	AUX
cana-2411	12	3	invented	invent	VERB
cana-2411	12	4	as	as	ADP
cana-2411	12	5	an	an	DET
cana-2411	12	6	protracted	protracted	ADJ
cana-2411	12	7	system	system	NOUN
cana-2411	12	8	of	of	ADP
cana-2411	12	9	fuzzy	fuzzy	ADJ
cana-2411	12	10	,	,	PUNCT
cana-2411	12	11	intuitionistic	intuitionistic	ADJ
cana-2411	12	12	and	and	CCONJ
cana-2411	12	13	traditional	traditional	ADJ
cana-2411	12	14	sets	set	NOUN
cana-2411	12	15	.	.	PUNCT
cana-2411	13	1	here	here	ADV
cana-2411	13	2	indeterminacy	indeterminacy	NOUN
cana-2411	13	3	is	be	AUX
cana-2411	13	4	included	include	VERB
cana-2411	13	5	together	together	ADV
cana-2411	13	6	with	with	ADP
cana-2411	13	7	membership	membership	NOUN
cana-2411	13	8	and	and	CCONJ
cana-2411	13	9	nonmembership	nonmembership	NOUN
cana-2411	13	10	.	.	PUNCT
cana-2411	14	1	hence	hence	ADV
cana-2411	14	2	each	each	DET
cana-2411	14	3	element	element	NOUN
cana-2411	14	4	is	be	AUX
cana-2411	14	5	associated	associate	VERB
cana-2411	14	6	with	with	ADP
cana-2411	14	7	three	three	NUM
cana-2411	14	8	parameters	parameter	NOUN
cana-2411	14	9	i.e.	i.e.	X
cana-2411	14	10	,	,	PUNCT
cana-2411	14	11	truth	truth	NOUN
cana-2411	14	12	,	,	PUNCT
cana-2411	14	13	indeterminacy	indeterminacy	NOUN
cana-2411	14	14	,	,	PUNCT
cana-2411	14	15	and	and	CCONJ
cana-2411	14	16	falsity	falsity	NOUN
cana-2411	14	17	.	.	PUNCT
cana-2411	15	1	the	the	DET
cana-2411	15	2	neutrosophic	neutrosophic	ADJ
cana-2411	15	3	sets	set	NOUN
cana-2411	15	4	and	and	CCONJ
cana-2411	15	5	logic	logic	NOUN
cana-2411	15	6	are	be	AUX
cana-2411	15	7	the	the	DET
cana-2411	15	8	utmost	utmost	ADJ
cana-2411	15	9	way	way	NOUN
cana-2411	15	10	of	of	ADP
cana-2411	15	11	handling	handle	VERB
cana-2411	15	12	real	real	ADJ
cana-2411	15	13	-	-	PUNCT
cana-2411	15	14	life	life	NOUN
cana-2411	15	15	problems	problem	NOUN
cana-2411	15	16	,	,	PUNCT
cana-2411	15	17	which	which	PRON
cana-2411	15	18	obliges	oblige	VERB
cana-2411	15	19	a	a	DET
cana-2411	15	20	generalization	generalization	NOUN
cana-2411	15	21	of	of	ADP
cana-2411	15	22	fuzzy	fuzzy	ADJ
cana-2411	15	23	sets	set	NOUN
cana-2411	15	24	.	.	PUNCT
cana-2411	16	1	al	al	PROPN
cana-2411	16	2	-	-	PUNCT
cana-2411	16	3	naemi	naemi	NOUN
cana-2411	16	4	[	[	X
cana-2411	16	5	1	1	X
cana-2411	16	6	]	]	PUNCT
cana-2411	16	7	introduced	introduce	VERB
cana-2411	16	8	a	a	DET
cana-2411	16	9	novel	novel	ADJ
cana-2411	16	10	parameter	parameter	NOUN
cana-2411	16	11	𝛽𝑘	𝛽𝑘	ADP
cana-2411	16	12	𝐺ℎ	𝐺ℎ	PROPN
cana-2411	16	13	derived	derive	VERB
cana-2411	16	14	from	from	ADP
cana-2411	16	15	the	the	DET
cana-2411	16	16	memoryless	memoryless	NOUN
cana-2411	16	17	self	self	NOUN
cana-2411	16	18	-	-	PUNCT
cana-2411	16	19	scaling	scale	VERB
cana-2411	16	20	dfp	dfp	NOUN
cana-2411	16	21	quasi	quasi	PROPN
cana-2411	16	22	-	-	PROPN
cana-2411	16	23	newton	newton	PROPN
cana-2411	16	24	method	method	NOUN
cana-2411	16	25	.	.	PUNCT
cana-2411	17	1	the	the	DET
cana-2411	17	2	author	author	NOUN
cana-2411	17	3	demonstrated	demonstrate	VERB
cana-2411	17	4	that	that	SCONJ
cana-2411	17	5	any	any	DET
cana-2411	17	6	line	line	NOUN
cana-2411	17	7	search	search	NOUN
cana-2411	17	8	technique	technique	NOUN
cana-2411	17	9	ensuring	ensure	VERB
cana-2411	17	10	sufficient	sufficient	ADJ
cana-2411	17	11	descent	descent	NOUN
cana-2411	17	12	property	property	NOUN
cana-2411	17	13	can	can	AUX
cana-2411	17	14	be	be	AUX
cana-2411	17	15	employed	employ	VERB
cana-2411	17	16	,	,	PUNCT
cana-2411	17	17	and	and	CCONJ
cana-2411	17	18	further	far	ADV
cana-2411	17	19	established	establish	VERB
cana-2411	17	20	the	the	DET
cana-2411	17	21	validity	validity	NOUN
cana-2411	17	22	of	of	ADP
cana-2411	17	23	the	the	DET
cana-2411	17	24	zoutendijk	zoutendijk	NOUN
cana-2411	17	25	condition	condition	NOUN
cana-2411	17	26	,	,	PUNCT
cana-2411	17	27	proving	prove	VERB
cana-2411	17	28	the	the	DET
cana-2411	17	29	method	method	NOUN
cana-2411	17	30	’s	’s	PART
cana-2411	17	31	global	global	ADJ
cana-2411	17	32	convergence	convergence	NOUN
cana-2411	17	33	through	through	ADP
cana-2411	17	34	a	a	DET
cana-2411	17	35	specific	specific	ADJ
cana-2411	17	36	step	step	NOUN
cana-2411	17	37	-	-	PUNCT
cana-2411	17	38	length	length	NOUN
cana-2411	17	39	approach	approach	NOUN
cana-2411	17	40	.	.	PUNCT
cana-2411	18	1	using	use	VERB
cana-2411	18	2	imprecise	imprecise	ADJ
cana-2411	18	3	parameters	parameter	NOUN
cana-2411	18	4	to	to	PART
cana-2411	18	5	manage	manage	VERB
cana-2411	18	6	independent	independent	ADJ
cana-2411	18	7	parameters	parameter	NOUN
cana-2411	18	8	.	.	PUNCT
cana-2411	19	1	according	accord	VERB
cana-2411	19	2	to	to	ADP
cana-2411	19	3	andrei	andrei	NOUN
cana-2411	19	4	[	[	X
cana-2411	19	5	2	2	NUM
cana-2411	19	6	]	]	PUNCT
cana-2411	19	7	,	,	PUNCT
cana-2411	19	8	an	an	DET
cana-2411	19	9	iterative	iterative	NOUN
cana-2411	19	10	process	process	NOUN
cana-2411	19	11	comprises	comprise	VERB
cana-2411	19	12	two	two	NUM
cana-2411	19	13	distinct	distinct	ADJ
cana-2411	19	14	components	component	NOUN
cana-2411	19	15	:	:	PUNCT
cana-2411	19	16	determining	determine	VERB
cana-2411	19	17	a	a	DET
cana-2411	19	18	descent	descent	NOUN
cana-2411	19	19	search	search	NOUN
cana-2411	19	20	direction	direction	NOUN
cana-2411	19	21	𝑑𝑘followed	𝑑𝑘followe	VERB
cana-2411	19	22	by	by	ADP
cana-2411	19	23	a	a	DET
cana-2411	19	24	line	line	NOUN
cana-2411	19	25	search	search	NOUN
cana-2411	19	26	to	to	PART
cana-2411	19	27	identify	identify	VERB
cana-2411	19	28	an	an	DET
cana-2411	19	29	appropriate	appropriate	ADJ
cana-2411	19	30	step	step	NOUN
cana-2411	19	31	size	size	NOUN
cana-2411	19	32	𝛼𝑘.	𝛼𝑘.	X
cana-2411	19	33	the	the	DET
cana-2411	19	34	search	search	NOUN
cana-2411	19	35	direction	direction	NOUN
cana-2411	19	36	in	in	ADP
cana-2411	19	37	the	the	DET
cana-2411	19	38	csdm	csdm	NOUN
cana-2411	19	39	is	be	AUX
cana-2411	19	40	precisely	precisely	ADV
cana-2411	19	41	the	the	DET
cana-2411	19	42	negative	negative	ADJ
cana-2411	19	43	gradient	gradient	NOUN
cana-2411	19	44	.	.	PUNCT
cana-2411	20	1	antczak	antczak	PROPN
cana-2411	21	1	[	[	X
cana-2411	21	2	3	3	NUM
cana-2411	21	3	]	]	PUNCT
cana-2411	21	4	discussed	discuss	VERB
cana-2411	21	5	an	an	DET
cana-2411	21	6	optimization	optimization	NOUN
cana-2411	21	7	problem	problem	NOUN
cana-2411	21	8	involving	involve	VERB
cana-2411	21	9	a	a	DET
cana-2411	21	10	fuzzy	fuzzy	ADJ
cana-2411	21	11	objective	objective	ADJ
cana-2411	21	12	function	function	NOUN
cana-2411	21	13	with	with	ADP
cana-2411	21	14	inequality	inequality	NOUN
cana-2411	21	15	and	and	CCONJ
cana-2411	21	16	equality	equality	NOUN
cana-2411	21	17	constraints	constraint	NOUN
cana-2411	21	18	,	,	PUNCT
cana-2411	21	19	all	all	PRON
cana-2411	21	20	of	of	ADP
cana-2411	21	21	which	which	PRON
cana-2411	21	22	had	have	VERB
cana-2411	21	23	locally	locally	ADV
cana-2411	21	24	lipschitz	lipschitz	NOUN
cana-2411	21	25	functions	function	NOUN
cana-2411	21	26	.	.	PUNCT
cana-2411	22	1	they	they	PRON
cana-2411	22	2	successfully	successfully	ADV
cana-2411	22	3	demonstrated	demonstrate	VERB
cana-2411	22	4	that	that	SCONJ
cana-2411	22	5	for	for	ADP
cana-2411	22	6	this	this	DET
cana-2411	22	7	particular	particular	ADJ
cana-2411	22	8	non	non	ADJ
cana-2411	22	9	-	-	ADJ
cana-2411	22	10	differentiable	differentiable	ADJ
cana-2411	22	11	fuzzy	fuzzy	ADJ
cana-2411	22	12	optimization	optimization	NOUN
cana-2411	22	13	problem	problem	NOUN
cana-2411	22	14	,	,	PUNCT
cana-2411	22	15	they	they	PRON
cana-2411	22	16	could	could	AUX
cana-2411	22	17	create	create	VERB
cana-2411	22	18	an	an	DET
cana-2411	22	19	associated	associated	ADJ
cana-2411	22	20	bi	bi	ADJ
cana-2411	22	21	-	-	ADJ
cana-2411	22	22	objective	objective	ADJ
cana-2411	22	23	optimization	optimization	NOUN
cana-2411	22	24	problem	problem	NOUN
cana-2411	22	25	.	.	PUNCT
cana-2411	23	1	they	they	PRON
cana-2411	23	2	also	also	ADV
cana-2411	23	3	established	establish	VERB
cana-2411	23	4	a	a	DET
cana-2411	23	5	relationship	relationship	NOUN
cana-2411	23	6	between	between	ADP
cana-2411	23	7	the	the	DET
cana-2411	23	8	vector	vector	NOUN
cana-2411	23	9	optimization	optimization	NOUN
cana-2411	23	10	problem	problem	NOUN
cana-2411	23	11	of	of	ADP
cana-2411	23	12	pareto	pareto	ADJ
cana-2411	23	13	solutions	solution	NOUN
cana-2411	23	14	and	and	CCONJ
cana-2411	23	15	the	the	DET
cana-2411	23	16	nondominated	nondominated	ADJ
cana-2411	23	17	(	(	PUNCT
cana-2411	23	18	weakly	weakly	ADJ
cana-2411	23	19	)	)	PUNCT
cana-2411	23	20	solutions	solution	NOUN
cana-2411	23	21	of	of	ADP
cana-2411	23	22	the	the	DET
cana-2411	23	23	original	original	ADJ
cana-2411	23	24	non	non	ADJ
cana-2411	23	25	-	-	ADJ
cana-2411	23	26	differentiable	differentiable	ADJ
cana-2411	23	27	fuzzy	fuzzy	ADJ
cana-2411	23	28	optimization	optimization	NOUN
cana-2411	23	29	problem	problem	NOUN
cana-2411	23	30	.	.	PUNCT
cana-2411	24	1	basim	basim	PROPN
cana-2411	24	2	communications	communication	NOUN
cana-2411	24	3	on	on	ADP
cana-2411	24	4	applied	apply	VERB
cana-2411	24	5	nonlinear	nonlinear	ADJ
cana-2411	24	6	analysis	analysis	NOUN
cana-2411	24	7	issn	issn	NOUN
cana-2411	24	8	:	:	PUNCT
cana-2411	24	9	1074	1074	NUM
cana-2411	24	10	-	-	PUNCT
cana-2411	24	11	133x	133x	NUM
cana-2411	24	12	vol	vol	NOUN
cana-2411	24	13	32	32	NUM
cana-2411	24	14	no	no	NOUN
cana-2411	24	15	.	.	PUNCT
cana-2411	25	1	2s	2s	NUM
cana-2411	25	2	(	(	PUNCT
cana-2411	25	3	2025	2025	NUM
cana-2411	25	4	)	)	PUNCT
cana-2411	25	5	367	367	NUM
cana-2411	25	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2411	26	1	[	[	X
cana-2411	26	2	4	4	X
cana-2411	26	3	]	]	PUNCT
cana-2411	26	4	the	the	DET
cana-2411	26	5	aim	aim	NOUN
cana-2411	26	6	of	of	ADP
cana-2411	26	7	this	this	DET
cana-2411	26	8	work	work	NOUN
cana-2411	26	9	has	have	AUX
cana-2411	26	10	been	be	AUX
cana-2411	26	11	to	to	PART
cana-2411	26	12	develop	develop	VERB
cana-2411	26	13	new	new	ADJ
cana-2411	26	14	,	,	PUNCT
cana-2411	26	15	modified	modify	VERB
cana-2411	26	16	conjugate	conjugate	ADJ
cana-2411	26	17	gradient	gradient	NOUN
cana-2411	26	18	formulas	formula	NOUN
cana-2411	26	19	that	that	PRON
cana-2411	26	20	perform	perform	VERB
cana-2411	26	21	better	well	ADV
cana-2411	26	22	than	than	ADP
cana-2411	26	23	the	the	DET
cana-2411	26	24	conventional	conventional	ADJ
cana-2411	26	25	fr	fr	ADJ
cana-2411	26	26	-	-	PUNCT
cana-2411	26	27	cg	cg	NOUN
cana-2411	26	28	method	method	NOUN
cana-2411	26	29	for	for	ADP
cana-2411	26	30	picture	picture	NOUN
cana-2411	26	31	restoration	restoration	NOUN
cana-2411	26	32	.	.	PUNCT
cana-2411	27	1	the	the	DET
cana-2411	27	2	outcomes	outcome	NOUN
cana-2411	27	3	validate	validate	VERB
cana-2411	27	4	the	the	DET
cana-2411	27	5	efficacy	efficacy	NOUN
cana-2411	27	6	of	of	ADP
cana-2411	27	7	the	the	DET
cana-2411	27	8	approach	approach	NOUN
cana-2411	27	9	employed	employ	VERB
cana-2411	27	10	in	in	ADP
cana-2411	27	11	this	this	DET
cana-2411	27	12	study	study	NOUN
cana-2411	27	13	to	to	PART
cana-2411	27	14	generate	generate	VERB
cana-2411	27	15	variations	variation	NOUN
cana-2411	27	16	of	of	ADP
cana-2411	27	17	the	the	DET
cana-2411	27	18	traditional	traditional	ADJ
cana-2411	27	19	cg	cg	NOUN
cana-2411	27	20	procedure	procedure	NOUN
cana-2411	27	21	.	.	PUNCT
cana-2411	28	1	bellman	bellman	NOUN
cana-2411	28	2	et	et	PROPN
cana-2411	28	3	al	al	PROPN
cana-2411	28	4	.	.	PUNCT
cana-2411	29	1	[	[	X
cana-2411	29	2	5	5	NUM
cana-2411	29	3	]	]	PUNCT
cana-2411	29	4	delved	delve	VERB
cana-2411	29	5	into	into	ADP
cana-2411	29	6	the	the	DET
cana-2411	29	7	field	field	NOUN
cana-2411	29	8	of	of	ADP
cana-2411	29	9	decision	decision	NOUN
cana-2411	29	10	-	-	PUNCT
cana-2411	29	11	making	make	VERB
cana-2411	29	12	processes	process	NOUN
cana-2411	29	13	under	under	ADP
cana-2411	29	14	conditions	condition	NOUN
cana-2411	29	15	of	of	ADP
cana-2411	29	16	fuzziness	fuzziness	NOUN
cana-2411	29	17	.	.	PUNCT
cana-2411	30	1	chakraborty	chakraborty	NOUN
cana-2411	31	1	[	[	X
cana-2411	31	2	6	6	NUM
cana-2411	31	3	]	]	PUNCT
cana-2411	31	4	discussed	discuss	VERB
cana-2411	31	5	a	a	DET
cana-2411	31	6	trapezoidal	trapezoidal	ADJ
cana-2411	31	7	neutrosophic	neutrosophic	ADJ
cana-2411	31	8	number	number	NOUN
cana-2411	31	9	is	be	AUX
cana-2411	31	10	a	a	DET
cana-2411	31	11	more	more	ADV
cana-2411	31	12	useful	useful	ADJ
cana-2411	31	13	concept	concept	NOUN
cana-2411	31	14	than	than	ADP
cana-2411	31	15	a	a	DET
cana-2411	31	16	triangular	triangular	NOUN
cana-2411	31	17	one	one	NUM
cana-2411	31	18	.	.	PUNCT
cana-2411	32	1	the	the	DET
cana-2411	32	2	removal	removal	NOUN
cana-2411	32	3	of	of	ADP
cana-2411	32	4	area	area	NOUN
cana-2411	32	5	method	method	NOUN
cana-2411	32	6	(	(	PUNCT
cana-2411	32	7	i	i	NOUN
cana-2411	32	8	)	)	PUNCT
cana-2411	32	9	and	and	CCONJ
cana-2411	32	10	mean	mean	VERB
cana-2411	32	11	of	of	ADP
cana-2411	32	12	interval	interval	NOUN
cana-2411	32	13	method	method	NOUN
cana-2411	32	14	(	(	PUNCT
cana-2411	32	15	ii	ii	NOUN
cana-2411	32	16	)	)	PUNCT
cana-2411	32	17	are	be	AUX
cana-2411	32	18	two	two	NUM
cana-2411	32	19	important	important	ADJ
cana-2411	32	20	de	de	ADJ
cana-2411	32	21	-	-	ADJ
cana-2411	32	22	neutrosophication	neutrosophication	NOUN
cana-2411	32	23	methods	method	NOUN
cana-2411	32	24	that	that	PRON
cana-2411	32	25	are	be	AUX
cana-2411	32	26	effective	effective	ADJ
cana-2411	32	27	in	in	ADP
cana-2411	32	28	de	de	ADJ
cana-2411	32	29	-	-	ADJ
cana-2411	32	30	neutrosophicating	neutrosophicate	VERB
cana-2411	32	31	the	the	DET
cana-2411	32	32	corresponding	corresponding	ADJ
cana-2411	32	33	number	number	NOUN
cana-2411	32	34	.	.	PUNCT
cana-2411	33	1	hanachi	hanachi	PROPN
cana-2411	33	2	et	et	PROPN
cana-2411	33	3	al	al	PROPN
cana-2411	33	4	.	.	PUNCT
cana-2411	34	1	[	[	X
cana-2411	34	2	7	7	X
cana-2411	34	3	]	]	PUNCT
cana-2411	34	4	introduced	introduce	VERB
cana-2411	34	5	a	a	DET
cana-2411	34	6	novel	novel	ADJ
cana-2411	34	7	hybrid	hybrid	NOUN
cana-2411	34	8	approach	approach	NOUN
cana-2411	34	9	in	in	ADP
cana-2411	34	10	which	which	PRON
cana-2411	34	11	the	the	DET
cana-2411	34	12	parameter	parameter	NOUN
cana-2411	34	13	is	be	AUX
cana-2411	34	14	determined	determine	VERB
cana-2411	34	15	as	as	ADP
cana-2411	34	16	a	a	DET
cana-2411	34	17	convex	convex	NOUN
cana-2411	34	18	combination	combination	NOUN
cana-2411	34	19	of	of	ADP
cana-2411	34	20	three	three	NUM
cana-2411	34	21	parameters	parameter	NOUN
cana-2411	34	22	𝛽𝑘	𝛽𝑘	ADP
cana-2411	34	23	𝐷𝑌	𝐷𝑌	PROPN
cana-2411	34	24	,	,	PUNCT
cana-2411	34	25	𝛽𝑘	𝛽𝑘	ADP
cana-2411	34	26	𝑃𝑅𝑃	𝑃𝑅𝑃	PROPN
cana-2411	34	27	,	,	PUNCT
cana-2411	34	28	𝛽𝑘	𝛽𝑘	ADP
cana-2411	34	29	𝑃𝑅	𝑃𝑅	PROPN
cana-2411	34	30	the	the	DET
cana-2411	34	31	adequacy	adequacy	NOUN
cana-2411	34	32	of	of	ADP
cana-2411	34	33	the	the	DET
cana-2411	34	34	descent	descent	NOUN
cana-2411	34	35	and	and	CCONJ
cana-2411	34	36	the	the	DET
cana-2411	34	37	global	global	ADJ
cana-2411	34	38	convergence	convergence	NOUN
cana-2411	34	39	has	have	AUX
cana-2411	34	40	demonstrated	demonstrate	VERB
cana-2411	34	41	.	.	PUNCT
cana-2411	35	1	practical	practical	ADJ
cana-2411	35	2	results	result	NOUN
cana-2411	35	3	indicate	indicate	VERB
cana-2411	35	4	that	that	SCONJ
cana-2411	35	5	the	the	DET
cana-2411	35	6	chosen	choose	VERB
cana-2411	35	7	approach	approach	NOUN
cana-2411	35	8	is	be	AUX
cana-2411	35	9	betterâ	betterâ	ADJ
cana-2411	35	10	and	and	CCONJ
cana-2411	35	11	more	more	ADV
cana-2411	35	12	efficient	efficient	ADJ
cana-2411	35	13	when	when	SCONJ
cana-2411	35	14	compared	compare	VERB
cana-2411	35	15	to	to	ADP
cana-2411	35	16	the	the	DET
cana-2411	35	17	utilized	utilize	VERB
cana-2411	35	18	methods	method	NOUN
cana-2411	35	19	.	.	PUNCT
cana-2411	36	1	hassan	hassan	PROPN
cana-2411	36	2	et	et	PROPN
cana-2411	36	3	al	al	PROPN
cana-2411	36	4	.	.	PUNCT
cana-2411	37	1	[	[	X
cana-2411	37	2	8	8	NUM
cana-2411	37	3	]	]	PUNCT
cana-2411	37	4	discussed	discuss	VERB
cana-2411	37	5	that	that	SCONJ
cana-2411	37	6	the	the	DET
cana-2411	37	7	research	research	NOUN
cana-2411	37	8	focus	focus	NOUN
cana-2411	37	9	has	have	AUX
cana-2411	37	10	centered	center	VERB
cana-2411	37	11	on	on	ADP
cana-2411	37	12	developing	develop	VERB
cana-2411	37	13	novel	novel	NOUN
cana-2411	37	14	,	,	PUNCT
cana-2411	37	15	modified	modify	VERB
cana-2411	37	16	conjugate	conjugate	ADJ
cana-2411	37	17	gradient	gradient	NOUN
cana-2411	37	18	formulations	formulation	NOUN
cana-2411	37	19	that	that	PRON
cana-2411	37	20	outperform	outperform	VERB
cana-2411	37	21	the	the	DET
cana-2411	37	22	traditional	traditional	ADJ
cana-2411	37	23	fr	fr	NOUN
cana-2411	37	24	cg	cg	NOUN
cana-2411	37	25	approach	approach	NOUN
cana-2411	37	26	in	in	ADP
cana-2411	37	27	image	image	NOUN
cana-2411	37	28	restoration	restoration	NOUN
cana-2411	37	29	applications	application	NOUN
cana-2411	37	30	.	.	PUNCT
cana-2411	38	1	the	the	DET
cana-2411	38	2	findings	finding	NOUN
cana-2411	38	3	demonstrate	demonstrate	VERB
cana-2411	38	4	the	the	DET
cana-2411	38	5	efficacy	efficacy	NOUN
cana-2411	38	6	of	of	ADP
cana-2411	38	7	the	the	DET
cana-2411	38	8	strategy	strategy	NOUN
cana-2411	38	9	employed	employ	VERB
cana-2411	38	10	in	in	ADP
cana-2411	38	11	this	this	DET
cana-2411	38	12	research	research	NOUN
cana-2411	38	13	to	to	PART
cana-2411	38	14	derive	derive	VERB
cana-2411	38	15	variations	variation	NOUN
cana-2411	38	16	of	of	ADP
cana-2411	38	17	the	the	DET
cana-2411	38	18	traditional	traditional	ADJ
cana-2411	38	19	cg	cg	NOUN
cana-2411	38	20	technique	technique	NOUN
cana-2411	38	21	.	.	PUNCT
cana-2411	39	1	the	the	DET
cana-2411	39	2	proposed	propose	VERB
cana-2411	39	3	methods	method	NOUN
cana-2411	39	4	have	have	AUX
cana-2411	39	5	demonstrated	demonstrate	VERB
cana-2411	39	6	global	global	ADJ
cana-2411	39	7	convergence	convergence	NOUN
cana-2411	39	8	under	under	ADP
cana-2411	39	9	the	the	DET
cana-2411	39	10	rigorous	rigorous	ADJ
cana-2411	39	11	wolfe	wolfe	PROPN
cana-2411	39	12	line	line	NOUN
cana-2411	39	13	search	search	NOUN
cana-2411	39	14	conditions	condition	NOUN
cana-2411	39	15	.	.	PUNCT
cana-2411	40	1	husin	husin	PROPN
cana-2411	40	2	et	et	PROPN
cana-2411	40	3	al	al	PROPN
cana-2411	40	4	.	.	PUNCT
cana-2411	41	1	[	[	X
cana-2411	41	2	9	9	NUM
cana-2411	41	3	]	]	PUNCT
cana-2411	41	4	presented	present	VERB
cana-2411	41	5	a	a	DET
cana-2411	41	6	new	new	ADJ
cana-2411	41	7	steepest	steep	ADJ
cana-2411	41	8	descent	descent	NOUN
cana-2411	41	9	(	(	PUNCT
cana-2411	41	10	sd	sd	NOUN
cana-2411	41	11	)	)	PUNCT
cana-2411	41	12	method	method	NOUN
cana-2411	41	13	,	,	PUNCT
cana-2411	41	14	with	with	ADP
cana-2411	41	15	the	the	DET
cana-2411	41	16	primary	primary	ADJ
cana-2411	41	17	goal	goal	NOUN
cana-2411	41	18	being	be	AUX
cana-2411	41	19	the	the	DET
cana-2411	41	20	modification	modification	NOUN
cana-2411	41	21	of	of	ADP
cana-2411	41	22	the	the	DET
cana-2411	41	23	direction	direction	NOUN
cana-2411	41	24	that	that	PRON
cana-2411	41	25	has	have	VERB
cana-2411	41	26	sufficient	sufficient	ADJ
cana-2411	41	27	descent	descent	NOUN
cana-2411	41	28	requirements	requirement	NOUN
cana-2411	41	29	and	and	CCONJ
cana-2411	41	30	global	global	ADJ
cana-2411	41	31	convergence	convergence	NOUN
cana-2411	41	32	properties	property	NOUN
cana-2411	41	33	.	.	PUNCT
cana-2411	42	1	the	the	DET
cana-2411	42	2	second	second	ADJ
cana-2411	42	3	strategy	strategy	NOUN
cana-2411	42	4	involves	involve	VERB
cana-2411	42	5	presenting	present	VERB
cana-2411	42	6	regression	regression	NOUN
cana-2411	42	7	analysis	analysis	NOUN
cana-2411	42	8	for	for	ADP
cana-2411	42	9	real	real	ADJ
cana-2411	42	10	-	-	PUNCT
cana-2411	42	11	world	world	NOUN
cana-2411	42	12	issues	issue	NOUN
cana-2411	42	13	using	use	VERB
cana-2411	42	14	the	the	DET
cana-2411	42	15	suggested	suggest	VERB
cana-2411	42	16	modification	modification	NOUN
cana-2411	42	17	of	of	ADP
cana-2411	42	18	the	the	DET
cana-2411	42	19	sd	sd	NOUN
cana-2411	42	20	method	method	NOUN
cana-2411	42	21	.	.	PUNCT
cana-2411	43	1	hepzibah	hepzibah	PROPN
cana-2411	43	2	et	et	PROPN
cana-2411	43	3	al	al	PROPN
cana-2411	43	4	.	.	PUNCT
cana-2411	44	1	[	[	X
cana-2411	44	2	10	10	NUM
cana-2411	44	3	,	,	PUNCT
cana-2411	44	4	11	11	NUM
cana-2411	44	5	]	]	PUNCT
cana-2411	44	6	discussed	discuss	VERB
cana-2411	44	7	how	how	SCONJ
cana-2411	44	8	unconstrained	unconstrained	ADJ
cana-2411	44	9	optimization	optimization	NOUN
cana-2411	44	10	problems	problem	NOUN
cana-2411	44	11	with	with	ADP
cana-2411	44	12	fuzzy	fuzzy	ADJ
cana-2411	44	13	valued	value	VERB
cana-2411	44	14	functions	function	NOUN
cana-2411	44	15	are	be	AUX
cana-2411	44	16	taken	take	VERB
cana-2411	44	17	into	into	ADP
cana-2411	44	18	consideration	consideration	NOUN
cana-2411	44	19	as	as	ADV
cana-2411	44	20	well	well	ADV
cana-2411	44	21	as	as	ADP
cana-2411	44	22	how	how	SCONJ
cana-2411	44	23	to	to	PART
cana-2411	44	24	solve	solve	VERB
cana-2411	44	25	unconstrained	unconstrained	ADJ
cana-2411	44	26	optimization	optimization	NOUN
cana-2411	44	27	problems	problem	NOUN
cana-2411	44	28	using	use	VERB
cana-2411	44	29	newton	newton	PROPN
cana-2411	44	30	’s	’s	PART
cana-2411	44	31	method	method	NOUN
cana-2411	44	32	with	with	ADP
cana-2411	44	33	svntn	svntn	ADJ
cana-2411	44	34	coefficients	coefficient	NOUN
cana-2411	44	35	.	.	PUNCT
cana-2411	45	1	moreover	moreover	ADV
cana-2411	45	2	,	,	PUNCT
cana-2411	45	3	single	single	ADJ
cana-2411	45	4	variable	variable	ADJ
cana-2411	45	5	and	and	CCONJ
cana-2411	45	6	multivariable	multivariable	ADJ
cana-2411	45	7	fuzzy	fuzzy	ADJ
cana-2411	45	8	unconstrained	unconstraine	VERB
cana-2411	45	9	optimization	optimization	NOUN
cana-2411	45	10	problems	problem	NOUN
cana-2411	45	11	using	use	VERB
cana-2411	45	12	interval	interval	PROPN
cana-2411	45	13	newton	newton	PROPN
cana-2411	45	14	’s	’s	PART
cana-2411	45	15	method	method	NOUN
cana-2411	45	16	are	be	AUX
cana-2411	45	17	discussed	discuss	VERB
cana-2411	45	18	with	with	ADP
cana-2411	45	19	illustrations	illustration	NOUN
cana-2411	45	20	.	.	PUNCT
cana-2411	46	1	kaliyaperumal	kaliyaperumal	PROPN
cana-2411	46	2	and	and	CCONJ
cana-2411	46	3	das	das	PROPN
cana-2411	47	1	[	[	X
cana-2411	47	2	12	12	NUM
cana-2411	47	3	]	]	PUNCT
cana-2411	47	4	introduced	introduce	VERB
cana-2411	47	5	a	a	DET
cana-2411	47	6	fuzzy	fuzzy	ADJ
cana-2411	47	7	version	version	NOUN
cana-2411	47	8	of	of	ADP
cana-2411	47	9	the	the	DET
cana-2411	47	10	problem	problem	NOUN
cana-2411	47	11	,	,	PUNCT
cana-2411	47	12	which	which	PRON
cana-2411	47	13	they	they	PRON
cana-2411	47	14	addressed	address	VERB
cana-2411	47	15	using	use	VERB
cana-2411	47	16	the	the	DET
cana-2411	47	17	necessary	necessary	ADJ
cana-2411	47	18	and	and	CCONJ
cana-2411	47	19	sufficient	sufficient	ADJ
cana-2411	47	20	conditions	condition	NOUN
cana-2411	47	21	of	of	ADP
cana-2411	47	22	lagrangian	lagrangian	ADJ
cana-2411	47	23	multipliers	multiplier	NOUN
cana-2411	47	24	with	with	ADP
cana-2411	47	25	a	a	DET
cana-2411	47	26	focus	focus	NOUN
cana-2411	47	27	on	on	ADP
cana-2411	47	28	fuzziness	fuzziness	NOUN
cana-2411	47	29	.	.	PUNCT
cana-2411	48	1	they	they	PRON
cana-2411	48	2	illustrated	illustrate	VERB
cana-2411	48	3	this	this	DET
cana-2411	48	4	approach	approach	NOUN
cana-2411	48	5	with	with	ADP
cana-2411	48	6	a	a	DET
cana-2411	48	7	numerical	numerical	ADJ
cana-2411	48	8	example	example	NOUN
cana-2411	48	9	.	.	PUNCT
cana-2411	49	1	by	by	ADP
cana-2411	49	2	solving	solve	VERB
cana-2411	49	3	two	two	NUM
cana-2411	49	4	numerical	numerical	ADJ
cana-2411	49	5	examples	example	NOUN
cana-2411	49	6	on	on	ADP
cana-2411	49	7	using	use	VERB
cana-2411	49	8	membership	membership	NOUN
cana-2411	49	9	functions	function	NOUN
cana-2411	49	10	(	(	PUNCT
cana-2411	49	11	mfs	mfs	PROPN
cana-2411	49	12	)	)	PUNCT
cana-2411	49	13	and	and	CCONJ
cana-2411	49	14	the	the	DET
cana-2411	49	15	other	other	ADJ
cana-2411	49	16	using	use	VERB
cana-2411	49	17	robust	robust	ADJ
cana-2411	49	18	rankings	ranking	NOUN
cana-2411	49	19	they	they	PRON
cana-2411	49	20	clarified	clarify	VERB
cana-2411	49	21	the	the	DET
cana-2411	49	22	model	model	NOUN
cana-2411	49	23	’s	’s	PART
cana-2411	49	24	effectiveness	effectiveness	NOUN
cana-2411	49	25	.	.	PUNCT
cana-2411	50	1	this	this	DET
cana-2411	50	2	model	model	NOUN
cana-2411	50	3	is	be	AUX
cana-2411	50	4	designed	design	VERB
cana-2411	50	5	to	to	PART
cana-2411	50	6	tackle	tackle	VERB
cana-2411	50	7	uncertainties	uncertainty	NOUN
cana-2411	50	8	and	and	CCONJ
cana-2411	50	9	subjective	subjective	ADJ
cana-2411	50	10	experiences	experience	NOUN
cana-2411	50	11	of	of	ADP
cana-2411	50	12	decisionmakers	decisionmaker	NOUN
cana-2411	50	13	and	and	CCONJ
cana-2411	50	14	can	can	AUX
cana-2411	50	15	assist	assist	VERB
cana-2411	50	16	in	in	ADP
cana-2411	50	17	resolving	resolve	VERB
cana-2411	50	18	challenges	challenge	NOUN
cana-2411	50	19	associated	associate	VERB
cana-2411	50	20	with	with	ADP
cana-2411	50	21	decision	decision	NOUN
cana-2411	50	22	-	-	PUNCT
cana-2411	50	23	making	making	NOUN
cana-2411	50	24	.	.	PUNCT
cana-2411	51	1	kanaya	kanaya	PROPN
cana-2411	52	1	[	[	X
cana-2411	52	2	13	13	NUM
cana-2411	52	3	]	]	PUNCT
cana-2411	52	4	discussed	discuss	VERB
cana-2411	52	5	a	a	DET
cana-2411	52	6	method	method	NOUN
cana-2411	52	7	for	for	ADP
cana-2411	52	8	solving	solve	VERB
cana-2411	52	9	multi	multi	ADJ
cana-2411	52	10	-	-	ADJ
cana-2411	52	11	objective	objective	ADJ
cana-2411	52	12	nonlinear	nonlinear	ADJ
cana-2411	52	13	programming	programming	NOUN
cana-2411	52	14	problems	problem	NOUN
cana-2411	52	15	involving	involve	VERB
cana-2411	52	16	fuzzy	fuzzy	ADJ
cana-2411	52	17	parameters	parameter	NOUN
cana-2411	52	18	in	in	ADP
cana-2411	52	19	the	the	DET
cana-2411	52	20	objective	objective	ADJ
cana-2411	52	21	functions	function	NOUN
cana-2411	52	22	.	.	PUNCT
cana-2411	53	1	utilizing	utilize	VERB
cana-2411	53	2	an	an	DET
cana-2411	53	3	interactive	interactive	ADJ
cana-2411	53	4	cutting	cutting	NOUN
cana-2411	53	5	-	-	PUNCT
cana-2411	53	6	plane	plane	NOUN
cana-2411	53	7	algorithm	algorithm	NOUN
cana-2411	53	8	,	,	PUNCT
cana-2411	53	9	this	this	DET
cana-2411	53	10	method	method	NOUN
cana-2411	53	11	relies	rely	VERB
cana-2411	53	12	on	on	ADP
cana-2411	53	13	the	the	DET
cana-2411	53	14	stability	stability	NOUN
cana-2411	53	15	set	set	VERB
cana-2411	53	16	corresponding	correspond	VERB
cana-2411	53	17	to	to	ADP
cana-2411	53	18	α	α	NOUN
cana-2411	53	19	-	-	PUNCT
cana-2411	53	20	pareto	pareto	ADJ
cana-2411	53	21	optimal	optimal	ADJ
cana-2411	53	22	solutions	solution	NOUN
cana-2411	53	23	obtained	obtain	VERB
cana-2411	53	24	through	through	ADP
cana-2411	53	25	the	the	DET
cana-2411	53	26	same	same	ADJ
cana-2411	53	27	method	method	NOUN
cana-2411	53	28	.	.	PUNCT
cana-2411	54	1	comprehensive	comprehensive	ADJ
cana-2411	54	2	study	study	NOUN
cana-2411	54	3	on	on	ADP
cana-2411	54	4	nlnns	nlnn	NOUN
cana-2411	54	5	and	and	CCONJ
cana-2411	54	6	nln	nln	NOUN
cana-2411	54	7	-	-	PUNCT
cana-2411	54	8	lpps	lpp	NOUN
cana-2411	54	9	was	be	AUX
cana-2411	54	10	presented	present	VERB
cana-2411	54	11	by	by	ADP
cana-2411	54	12	lachhwani	lachhwani	NOUN
cana-2411	54	13	[	[	X
cana-2411	54	14	14	14	NUM
cana-2411	54	15	]	]	PUNCT
cana-2411	54	16	.	.	PUNCT
cana-2411	55	1	based	base	VERB
cana-2411	55	2	on	on	ADP
cana-2411	55	3	the	the	DET
cana-2411	55	4	proposed	propose	VERB
cana-2411	55	5	modified	modify	VERB
cana-2411	55	6	possibility	possibility	NOUN
cana-2411	55	7	score	score	NOUN
cana-2411	55	8	function	function	NOUN
cana-2411	55	9	,	,	PUNCT
cana-2411	55	10	the	the	DET
cana-2411	55	11	author	author	NOUN
cana-2411	55	12	developed	develop	VERB
cana-2411	55	13	a	a	DET
cana-2411	55	14	novel	novel	ADJ
cana-2411	55	15	solution	solution	NOUN
cana-2411	55	16	technique	technique	NOUN
cana-2411	55	17	for	for	ADP
cana-2411	55	18	nln	nln	NOUN
cana-2411	55	19	-	-	PUNCT
cana-2411	55	20	lpps	lpps	NOUN
cana-2411	55	21	.	.	PUNCT
cana-2411	56	1	nearly	nearly	ADV
cana-2411	56	2	the	the	DET
cana-2411	56	3	whole	whole	ADJ
cana-2411	56	4	range	range	NOUN
cana-2411	56	5	of	of	ADP
cana-2411	56	6	nn	nn	PROPN
cana-2411	56	7	values	value	NOUN
cana-2411	56	8	is	be	AUX
cana-2411	56	9	covered	cover	VERB
cana-2411	56	10	by	by	ADP
cana-2411	56	11	the	the	DET
cana-2411	56	12	suggested	suggest	VERB
cana-2411	56	13	modified	modify	VERB
cana-2411	56	14	possibility	possibility	NOUN
cana-2411	56	15	score	score	NOUN
cana-2411	56	16	function	function	NOUN
cana-2411	56	17	.	.	PUNCT
cana-2411	57	1	maissam	maissam	PROPN
cana-2411	57	2	jdid	jdid	VERB
cana-2411	57	3	[	[	X
cana-2411	57	4	15	15	NUM
cana-2411	57	5	]	]	PUNCT
cana-2411	57	6	demonstrated	demonstrate	VERB
cana-2411	57	7	how	how	SCONJ
cana-2411	57	8	binary	binary	ADJ
cana-2411	57	9	integers	integer	NOUN
cana-2411	57	10	can	can	AUX
cana-2411	57	11	be	be	AUX
cana-2411	57	12	used	use	VERB
cana-2411	57	13	to	to	PART
cana-2411	57	14	convert	convert	VERB
cana-2411	57	15	certain	certain	ADJ
cana-2411	57	16	nonlinear	nonlinear	ADJ
cana-2411	57	17	models	model	NOUN
cana-2411	57	18	into	into	ADP
cana-2411	57	19	linear	linear	ADJ
cana-2411	57	20	ones	one	NOUN
cana-2411	57	21	,	,	PUNCT
cana-2411	57	22	resulting	result	VERB
cana-2411	57	23	in	in	ADP
cana-2411	57	24	integer	integer	NOUN
cana-2411	57	25	solutions	solution	NOUN
cana-2411	57	26	that	that	PRON
cana-2411	57	27	are	be	AUX
cana-2411	57	28	consistent	consistent	ADJ
cana-2411	57	29	with	with	ADP
cana-2411	57	30	the	the	DET
cana-2411	57	31	nature	nature	NOUN
cana-2411	57	32	of	of	ADP
cana-2411	57	33	the	the	DET
cana-2411	57	34	problems	problem	NOUN
cana-2411	57	35	being	be	AUX
cana-2411	57	36	studied	study	VERB
cana-2411	57	37	.	.	PUNCT
cana-2411	58	1	ming	ming	PROPN
cana-2411	58	2	ma	ma	PROPN
cana-2411	58	3	et	et	PROPN
cana-2411	58	4	al	al	PROPN
cana-2411	58	5	.	.	PUNCT
cana-2411	59	1	[	[	X
cana-2411	59	2	16	16	NUM
cana-2411	59	3	]	]	PUNCT
cana-2411	59	4	defined	define	VERB
cana-2411	59	5	a	a	DET
cana-2411	59	6	new	new	ADJ
cana-2411	59	7	fuzzy	fuzzy	ADJ
cana-2411	59	8	arithmetic	arithmetic	NOUN
cana-2411	59	9	and	and	CCONJ
cana-2411	59	10	applied	apply	VERB
cana-2411	59	11	to	to	ADP
cana-2411	59	12	fuzzy	fuzzy	ADJ
cana-2411	59	13	linear	linear	ADJ
cana-2411	59	14	equations	equation	NOUN
cana-2411	59	15	.	.	PUNCT
cana-2411	60	1	nagoorgani	nagoorgani	PROPN
cana-2411	60	2	and	and	CCONJ
cana-2411	60	3	sudha	sudha	PROPN
cana-2411	61	1	[	[	X
cana-2411	61	2	17	17	NUM
cana-2411	61	3	]	]	PUNCT
cana-2411	61	4	studied	study	VERB
cana-2411	61	5	the	the	DET
cana-2411	61	6	optimality	optimality	NOUN
cana-2411	61	7	requirements	requirement	NOUN
cana-2411	61	8	of	of	ADP
cana-2411	61	9	fuzzy	fuzzy	ADJ
cana-2411	61	10	nonlinear	nonlinear	ADJ
cana-2411	61	11	unconstrained	unconstrained	ADJ
cana-2411	61	12	minimization	minimization	NOUN
cana-2411	61	13	issues	issue	NOUN
cana-2411	61	14	.	.	PUNCT
cana-2411	62	1	the	the	DET
cana-2411	62	2	cost	cost	NOUN
cana-2411	62	3	coefficients	coefficient	NOUN
cana-2411	62	4	are	be	AUX
cana-2411	62	5	denoted	denote	VERB
cana-2411	62	6	by	by	ADP
cana-2411	62	7	tfns	tfns	NOUN
cana-2411	62	8	and	and	CCONJ
cana-2411	62	9	illustrated	illustrate	VERB
cana-2411	62	10	with	with	ADP
cana-2411	62	11	several	several	ADJ
cana-2411	62	12	numerical	numerical	ADJ
cana-2411	62	13	examples	example	NOUN
cana-2411	62	14	.	.	PUNCT
cana-2411	63	1	an	an	DET
cana-2411	63	2	alternative	alternative	ADJ
cana-2411	63	3	definition	definition	NOUN
cana-2411	63	4	for	for	ADP
cana-2411	63	5	nlnn	nlnn	NOUN
cana-2411	63	6	was	be	AUX
cana-2411	63	7	provided	provide	VERB
cana-2411	63	8	by	by	ADP
cana-2411	63	9	reig	reig	NOUN
cana-2411	63	10	-	-	PUNCT
cana-2411	63	11	mullor	mullor	NOUN
cana-2411	63	12	[	[	X
cana-2411	63	13	18	18	NUM
cana-2411	63	14	]	]	PUNCT
cana-2411	63	15	,	,	PUNCT
cana-2411	63	16	which	which	PRON
cana-2411	63	17	works	work	VERB
cana-2411	63	18	over	over	ADP
cana-2411	63	19	some	some	PRON
cana-2411	63	20	of	of	ADP
cana-2411	63	21	the	the	DET
cana-2411	63	22	limitations	limitation	NOUN
cana-2411	63	23	mentioned	mention	VERB
cana-2411	63	24	in	in	ADP
cana-2411	63	25	the	the	DET
cana-2411	63	26	literature	literature	NOUN
cana-2411	63	27	.	.	PUNCT
cana-2411	64	1	communications	communication	NOUN
cana-2411	64	2	on	on	ADP
cana-2411	64	3	applied	apply	VERB
cana-2411	64	4	nonlinear	nonlinear	ADJ
cana-2411	64	5	analysis	analysis	NOUN
cana-2411	64	6	issn	issn	NOUN
cana-2411	64	7	:	:	PUNCT
cana-2411	64	8	1074	1074	NUM
cana-2411	64	9	-	-	PUNCT
cana-2411	64	10	133x	133x	NUM
cana-2411	64	11	vol	vol	NOUN
cana-2411	64	12	32	32	NUM
cana-2411	64	13	no	no	NOUN
cana-2411	64	14	.	.	PUNCT
cana-2411	65	1	2s	2s	NUM
cana-2411	65	2	(	(	PUNCT
cana-2411	65	3	2025	2025	NUM
cana-2411	65	4	)	)	PUNCT
cana-2411	65	5	368	368	NUM
cana-2411	65	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2411	65	7	also	also	ADV
cana-2411	65	8	,	,	PUNCT
cana-2411	65	9	they	they	PRON
cana-2411	65	10	developed	develop	VERB
cana-2411	65	11	the	the	DET
cana-2411	65	12	notions	notion	NOUN
cana-2411	65	13	of	of	ADP
cana-2411	65	14	𝛼	𝛼	PROPN
cana-2411	65	15	,	,	PUNCT
cana-2411	65	16	𝛽	𝛽	NOUN
cana-2411	65	17	,	,	PUNCT
cana-2411	65	18	𝛾-cuts	𝛾-cut	NOUN
cana-2411	65	19	,	,	PUNCT
cana-2411	65	20	possibilistic	possibilistic	ADJ
cana-2411	65	21	variance	variance	NOUN
cana-2411	65	22	,	,	PUNCT
cana-2411	65	23	possibilistic	possibilistic	ADJ
cana-2411	65	24	mean	mean	NOUN
cana-2411	65	25	,	,	PUNCT
cana-2411	65	26	and	and	CCONJ
cana-2411	65	27	possibilistic	possibilistic	ADJ
cana-2411	65	28	standard	standard	ADJ
cana-2411	65	29	deviation	deviation	NOUN
cana-2411	65	30	,	,	PUNCT
cana-2411	65	31	which	which	PRON
cana-2411	65	32	are	be	AUX
cana-2411	65	33	among	among	ADP
cana-2411	65	34	the	the	DET
cana-2411	65	35	primary	primary	ADJ
cana-2411	65	36	characteristics	characteristic	NOUN
cana-2411	65	37	of	of	ADP
cana-2411	65	38	nlnn	nlnn	NOUN
cana-2411	65	39	.	.	PUNCT
cana-2411	66	1	seikh	seikh	PROPN
cana-2411	66	2	mijanur	mijanur	NOUN
cana-2411	66	3	rahaman	rahaman	NOUN
cana-2411	66	4	[	[	X
cana-2411	66	5	19	19	NUM
cana-2411	66	6	]	]	PUNCT
cana-2411	66	7	proposed	propose	VERB
cana-2411	66	8	solution	solution	NOUN
cana-2411	66	9	methodologies	methodology	NOUN
cana-2411	66	10	for	for	ADP
cana-2411	66	11	solving	solve	VERB
cana-2411	66	12	a	a	DET
cana-2411	66	13	unique	unique	ADJ
cana-2411	66	14	matrix	matrix	NOUN
cana-2411	66	15	game	game	NOUN
cana-2411	66	16	,	,	PUNCT
cana-2411	66	17	whereby	whereby	SCONJ
cana-2411	66	18	the	the	DET
cana-2411	66	19	payoffs	payoff	NOUN
cana-2411	66	20	are	be	AUX
cana-2411	66	21	expressed	express	VERB
cana-2411	66	22	using	use	VERB
cana-2411	66	23	single	single	ADV
cana-2411	66	24	-	-	PUNCT
cana-2411	66	25	valued	value	VERB
cana-2411	66	26	neutrosophic	neutrosophic	ADJ
cana-2411	66	27	numbers	number	NOUN
cana-2411	66	28	(	(	PUNCT
cana-2411	66	29	svnns	svnns	PROPN
cana-2411	66	30	)	)	PUNCT
cana-2411	66	31	.	.	PUNCT
cana-2411	67	1	two	two	NUM
cana-2411	67	2	non	non	ADJ
cana-2411	67	3	-	-	ADJ
cana-2411	67	4	linear	linear	ADJ
cana-2411	67	5	multi	multi	ADJ
cana-2411	67	6	-	-	ADJ
cana-2411	67	7	objective	objective	ADJ
cana-2411	67	8	programming	programming	NOUN
cana-2411	67	9	tasks	task	NOUN
cana-2411	67	10	are	be	AUX
cana-2411	67	11	defined	define	VERB
cana-2411	67	12	to	to	PART
cana-2411	67	13	determine	determine	VERB
cana-2411	67	14	the	the	DET
cana-2411	67	15	ideal	ideal	ADJ
cana-2411	67	16	values	value	NOUN
cana-2411	67	17	and	and	CCONJ
cana-2411	67	18	strategies	strategy	NOUN
cana-2411	67	19	for	for	ADP
cana-2411	67	20	the	the	DET
cana-2411	67	21	participants	participant	NOUN
cana-2411	67	22	.	.	PUNCT
cana-2411	68	1	these	these	DET
cana-2411	68	2	multi	multi	ADJ
cana-2411	68	3	-	-	ADJ
cana-2411	68	4	objective	objective	ADJ
cana-2411	68	5	programming	programming	NOUN
cana-2411	68	6	issues	issue	NOUN
cana-2411	68	7	are	be	AUX
cana-2411	68	8	converted	convert	VERB
cana-2411	68	9	into	into	ADP
cana-2411	68	10	bi	bi	ADJ
cana-2411	68	11	-	-	ADJ
cana-2411	68	12	objective	objective	ADJ
cana-2411	68	13	programming	programming	NOUN
cana-2411	68	14	problems	problem	NOUN
cana-2411	68	15	by	by	ADP
cana-2411	68	16	assigning	assign	VERB
cana-2411	68	17	equal	equal	ADJ
cana-2411	68	18	significance	significance	NOUN
cana-2411	68	19	to	to	ADP
cana-2411	68	20	the	the	DET
cana-2411	68	21	objective	objective	ADJ
cana-2411	68	22	functions	function	NOUN
cana-2411	68	23	.	.	PUNCT
cana-2411	69	1	shilpa	shilpa	PROPN
cana-2411	69	2	ivin	ivin	PROPN
cana-2411	69	3	emimal	emimal	ADJ
cana-2411	69	4	and	and	CCONJ
cana-2411	69	5	irene	irene	PROPN
cana-2411	69	6	hepzibah	hepzibah	PROPN
cana-2411	69	7	[	[	X
cana-2411	69	8	20	20	NUM
cana-2411	69	9	]	]	PUNCT
cana-2411	69	10	introduced	introduce	VERB
cana-2411	69	11	the	the	DET
cana-2411	69	12	optimization	optimization	NOUN
cana-2411	69	13	of	of	ADP
cana-2411	69	14	intuitionistic	intuitionistic	ADJ
cana-2411	69	15	fuzzy	fuzzy	ADJ
cana-2411	69	16	valued	value	VERB
cana-2411	69	17	functions	function	NOUN
cana-2411	69	18	in	in	ADP
cana-2411	69	19	unconstrained	unconstrained	ADJ
cana-2411	69	20	problems	problem	NOUN
cana-2411	69	21	.	.	PUNCT
cana-2411	70	1	the	the	DET
cana-2411	70	2	interval	interval	NOUN
cana-2411	70	3	newton	newton	PROPN
cana-2411	70	4	's	's	PART
cana-2411	70	5	method	method	NOUN
cana-2411	70	6	using	use	VERB
cana-2411	70	7	an	an	DET
cana-2411	70	8	intuitionistic	intuitionistic	ADJ
cana-2411	70	9	approach	approach	NOUN
cana-2411	70	10	addresses	address	NOUN
cana-2411	70	11	both	both	DET
cana-2411	70	12	single	single	ADJ
cana-2411	70	13	and	and	CCONJ
cana-2411	70	14	multivariable	multivariable	ADJ
cana-2411	70	15	optimization	optimization	NOUN
cana-2411	70	16	problems	problem	NOUN
cana-2411	70	17	.	.	PUNCT
cana-2411	71	1	fuzzy	fuzzy	ADJ
cana-2411	71	2	sets	set	NOUN
cana-2411	71	3	(	(	PUNCT
cana-2411	71	4	fs	fs	ADJ
cana-2411	71	5	)	)	PUNCT
cana-2411	71	6	and	and	CCONJ
cana-2411	71	7	neutrosophic	neutrosophic	ADJ
cana-2411	71	8	sets	set	NOUN
cana-2411	71	9	(	(	PUNCT
cana-2411	71	10	ns	ns	NUM
cana-2411	71	11	)	)	PUNCT
cana-2411	71	12	were	be	AUX
cana-2411	71	13	combined	combine	VERB
cana-2411	71	14	by	by	ADP
cana-2411	71	15	sujit	sujit	PROPN
cana-2411	71	16	das	das	PROPN
cana-2411	72	1	[	[	X
cana-2411	72	2	22	22	NUM
cana-2411	72	3	]	]	PUNCT
cana-2411	72	4	to	to	PART
cana-2411	72	5	formulate	formulate	VERB
cana-2411	72	6	neutrosophic	neutrosophic	ADJ
cana-2411	72	7	fuzzy	fuzzy	ADJ
cana-2411	72	8	sets	set	NOUN
cana-2411	72	9	(	(	PUNCT
cana-2411	72	10	nfs	nfs	NOUN
cana-2411	72	11	)	)	PUNCT
cana-2411	72	12	.	.	PUNCT
cana-2411	73	1	the	the	DET
cana-2411	73	2	primary	primary	ADJ
cana-2411	73	3	characteristic	characteristic	NOUN
cana-2411	73	4	of	of	ADP
cana-2411	73	5	nfs	nfs	NOUN
cana-2411	73	6	is	be	AUX
cana-2411	73	7	its	its	PRON
cana-2411	73	8	ability	ability	NOUN
cana-2411	73	9	to	to	PART
cana-2411	73	10	handle	handle	VERB
cana-2411	73	11	inconsistent	inconsistent	ADJ
cana-2411	73	12	and	and	CCONJ
cana-2411	73	13	imprecise	imprecise	ADJ
cana-2411	73	14	data	datum	NOUN
cana-2411	73	15	,	,	PUNCT
cana-2411	73	16	which	which	PRON
cana-2411	73	17	is	be	AUX
cana-2411	73	18	highly	highly	ADV
cana-2411	73	19	useful	useful	ADJ
cana-2411	73	20	when	when	SCONJ
cana-2411	73	21	managing	manage	VERB
cana-2411	73	22	uncertain	uncertain	ADJ
cana-2411	73	23	and	and	CCONJ
cana-2411	73	24	inconsistent	inconsistent	ADJ
cana-2411	73	25	real	real	ADJ
cana-2411	73	26	-	-	PUNCT
cana-2411	73	27	world	world	NOUN
cana-2411	73	28	applications	application	NOUN
cana-2411	73	29	.	.	PUNCT
cana-2411	74	1	uma	uma	PROPN
cana-2411	74	2	maheswari	maheswari	PROPN
cana-2411	74	3	and	and	CCONJ
cana-2411	74	4	ganesan	ganesan	PROPN
cana-2411	74	5	[	[	X
cana-2411	74	6	23	23	NUM
cana-2411	74	7	]	]	PUNCT
cana-2411	74	8	introduced	introduce	VERB
cana-2411	74	9	a	a	DET
cana-2411	74	10	fuzzy	fuzzy	ADJ
cana-2411	74	11	interpretation	interpretation	NOUN
cana-2411	74	12	of	of	ADP
cana-2411	74	13	the	the	DET
cana-2411	74	14	kkt	kkt	PROPN
cana-2411	74	15	condition	condition	NOUN
cana-2411	74	16	,	,	PUNCT
cana-2411	74	17	specifically	specifically	ADV
cana-2411	74	18	for	for	ADP
cana-2411	74	19	ffnlpp	ffnlpp	NOUN
cana-2411	74	20	,	,	PUNCT
cana-2411	74	21	and	and	CCONJ
cana-2411	74	22	successfully	successfully	ADV
cana-2411	74	23	identified	identify	VERB
cana-2411	74	24	their	their	PRON
cana-2411	74	25	optimal	optimal	ADJ
cana-2411	74	26	fuzzy	fuzzy	ADJ
cana-2411	74	27	outcomes	outcome	NOUN
cana-2411	74	28	.	.	PUNCT
cana-2411	75	1	utilizing	utilize	VERB
cana-2411	75	2	the	the	DET
cana-2411	75	3	gradient	gradient	ADJ
cana-2411	75	4	technique	technique	NOUN
cana-2411	75	5	,	,	PUNCT
cana-2411	75	6	also	also	ADV
cana-2411	75	7	recognized	recognize	VERB
cana-2411	75	8	as	as	ADP
cana-2411	75	9	csdm	csdm	NOUN
cana-2411	75	10	,	,	PUNCT
cana-2411	75	11	they	they	PRON
cana-2411	75	12	transformed	transform	VERB
cana-2411	75	13	it	it	PRON
cana-2411	75	14	into	into	ADP
cana-2411	75	15	an	an	DET
cana-2411	75	16	unconstrained	unconstrained	ADJ
cana-2411	75	17	optimization	optimization	NOUN
cana-2411	75	18	problem	problem	NOUN
cana-2411	75	19	involving	involve	VERB
cana-2411	75	20	multiple	multiple	ADJ
cana-2411	75	21	fuzzy	fuzzy	ADJ
cana-2411	75	22	variables	variable	NOUN
cana-2411	75	23	.	.	PUNCT
cana-2411	76	1	vanaja	vanaja	NOUN
cana-2411	76	2	and	and	CCONJ
cana-2411	76	3	ganesan	ganesan	PROPN
cana-2411	77	1	[	[	X
cana-2411	77	2	24,25	24,25	NUM
cana-2411	77	3	]	]	PUNCT
cana-2411	77	4	developed	develop	VERB
cana-2411	77	5	an	an	DET
cana-2411	77	6	interior	interior	ADJ
cana-2411	77	7	fuzzy	fuzzy	ADJ
cana-2411	77	8	penalty	penalty	NOUN
cana-2411	77	9	function	function	NOUN
cana-2411	77	10	method	method	NOUN
cana-2411	77	11	to	to	PART
cana-2411	77	12	solve	solve	VERB
cana-2411	77	13	fuzzy	fuzzy	ADJ
cana-2411	77	14	nonlinear	nonlinear	ADJ
cana-2411	77	15	programming	programming	NOUN
cana-2411	77	16	problems	problem	NOUN
cana-2411	77	17	(	(	PUNCT
cana-2411	77	18	fnlpp	fnlpp	NOUN
cana-2411	77	19	)	)	PUNCT
cana-2411	77	20	.	.	PUNCT
cana-2411	78	1	they	they	PRON
cana-2411	78	2	introduced	introduce	VERB
cana-2411	78	3	innovative	innovative	ADJ
cana-2411	78	4	fuzzy	fuzzy	ADJ
cana-2411	78	5	arithmetic	arithmetic	ADJ
cana-2411	78	6	and	and	CCONJ
cana-2411	78	7	ranking	ranking	ADJ
cana-2411	78	8	techniques	technique	NOUN
cana-2411	78	9	based	base	VERB
cana-2411	78	10	on	on	ADP
cana-2411	78	11	the	the	DET
cana-2411	78	12	parametric	parametric	ADJ
cana-2411	78	13	representation	representation	NOUN
cana-2411	78	14	of	of	ADP
cana-2411	78	15	triangular	triangular	ADJ
cana-2411	78	16	fuzzy	fuzzy	ADJ
cana-2411	78	17	numbers	number	NOUN
cana-2411	78	18	.	.	PUNCT
cana-2411	79	1	additionally	additionally	ADV
cana-2411	79	2	,	,	PUNCT
cana-2411	79	3	they	they	PRON
cana-2411	79	4	applied	apply	VERB
cana-2411	79	5	the	the	DET
cana-2411	79	6	exterior	exterior	ADJ
cana-2411	79	7	penalty	penalty	NOUN
cana-2411	79	8	method	method	NOUN
cana-2411	79	9	using	use	VERB
cana-2411	79	10	fuzzy	fuzzy	ADV
cana-2411	79	11	-	-	PUNCT
cana-2411	79	12	valued	value	VERB
cana-2411	79	13	functions	function	NOUN
cana-2411	79	14	to	to	PART
cana-2411	79	15	solve	solve	VERB
cana-2411	79	16	these	these	DET
cana-2411	79	17	fnlpps	fnlpps	NOUN
cana-2411	79	18	.	.	PUNCT
cana-2411	80	1	ye	ye	PRON
cana-2411	81	1	[	[	X
cana-2411	81	2	26	26	NUM
cana-2411	81	3	]	]	PUNCT
cana-2411	81	4	presented	present	VERB
cana-2411	81	5	the	the	DET
cana-2411	81	6	notions	notion	NOUN
cana-2411	81	7	of	of	ADP
cana-2411	81	8	nn	nn	X
cana-2411	81	9	linear	linear	ADJ
cana-2411	81	10	and	and	CCONJ
cana-2411	81	11	nonlinear	nonlinear	ADJ
cana-2411	81	12	functions	function	NOUN
cana-2411	81	13	,	,	PUNCT
cana-2411	81	14	as	as	ADV
cana-2411	81	15	well	well	ADV
cana-2411	81	16	as	as	ADP
cana-2411	81	17	inequalities	inequality	NOUN
cana-2411	81	18	that	that	PRON
cana-2411	81	19	include	include	VERB
cana-2411	81	20	indeterminacy	indeterminacy	NOUN
cana-2411	81	21	i	i	PRON
cana-2411	81	22	,	,	PUNCT
cana-2411	81	23	along	along	ADP
cana-2411	81	24	with	with	ADP
cana-2411	81	25	some	some	DET
cana-2411	81	26	basic	basic	ADJ
cana-2411	81	27	operations	operation	NOUN
cana-2411	81	28	of	of	ADP
cana-2411	81	29	neutrosophic	neutrosophic	ADJ
cana-2411	81	30	numbers	number	NOUN
cana-2411	81	31	(	(	PUNCT
cana-2411	81	32	nns	nn	NOUN
cana-2411	81	33	)	)	PUNCT
cana-2411	81	34	.	.	PUNCT
cana-2411	82	1	afterwards	afterwards	ADV
cana-2411	82	2	,	,	PUNCT
cana-2411	82	3	the	the	DET
cana-2411	82	4	authors	author	NOUN
cana-2411	82	5	presented	present	VERB
cana-2411	82	6	general	general	ADJ
cana-2411	82	7	solution	solution	NOUN
cana-2411	82	8	techniques	technique	NOUN
cana-2411	82	9	for	for	ADP
cana-2411	82	10	a	a	DET
cana-2411	82	11	variety	variety	NOUN
cana-2411	82	12	of	of	ADP
cana-2411	82	13	optimization	optimization	NOUN
cana-2411	82	14	models	model	NOUN
cana-2411	82	15	for	for	ADP
cana-2411	82	16	nn	nn	PROPN
cana-2411	82	17	nonlinear	nonlinear	ADJ
cana-2411	82	18	programming	programming	NOUN
cana-2411	82	19	(	(	PUNCT
cana-2411	82	20	nn	nn	PROPN
cana-2411	82	21	-	-	PUNCT
cana-2411	82	22	np	np	NOUN
cana-2411	82	23	)	)	PUNCT
cana-2411	82	24	issues	issue	NOUN
cana-2411	82	25	with	with	ADP
cana-2411	82	26	unconstrained	unconstrained	ADJ
cana-2411	82	27	and	and	CCONJ
cana-2411	82	28	restricted	restricted	ADJ
cana-2411	82	29	optimizations	optimization	NOUN
cana-2411	82	30	.	.	PUNCT
cana-2411	83	1	in	in	ADP
cana-2411	83	2	this	this	DET
cana-2411	83	3	paper	paper	NOUN
cana-2411	83	4	,	,	PUNCT
cana-2411	83	5	we	we	PRON
cana-2411	83	6	discuss	discuss	VERB
cana-2411	83	7	single	single	ADV
cana-2411	83	8	-	-	PUNCT
cana-2411	83	9	valued	value	VERB
cana-2411	83	10	neutrosophic	neutrosophic	ADJ
cana-2411	83	11	nonlinear	nonlinear	ADJ
cana-2411	83	12	programming	programming	NOUN
cana-2411	83	13	problem	problem	NOUN
cana-2411	83	14	(	(	PUNCT
cana-2411	83	15	svnnlpp	svnnlpp	NOUN
cana-2411	83	16	)	)	PUNCT
cana-2411	83	17	involving	involve	VERB
cana-2411	83	18	triangular	triangular	ADJ
cana-2411	83	19	neutrosophic	neutrosophic	ADJ
cana-2411	83	20	numbers	number	NOUN
cana-2411	83	21	.	.	PUNCT
cana-2411	84	1	we	we	PRON
cana-2411	84	2	present	present	VERB
cana-2411	84	3	a	a	DET
cana-2411	84	4	neutrosophic	neutrosophic	ADJ
cana-2411	84	5	version	version	NOUN
cana-2411	84	6	of	of	ADP
cana-2411	84	7	the	the	DET
cana-2411	84	8	cauchy	cauchy	NOUN
cana-2411	84	9	’s	’s	PART
cana-2411	84	10	steepest	steep	ADJ
cana-2411	84	11	descent	descent	NOUN
cana-2411	84	12	method	method	NOUN
cana-2411	84	13	(	(	PUNCT
cana-2411	84	14	csdm	csdm	PROPN
cana-2411	84	15	)	)	PUNCT
cana-2411	84	16	and	and	CCONJ
cana-2411	84	17	fletcherreeves	fletcherreeve	NOUN
cana-2411	84	18	method	method	VERB
cana-2411	84	19	(	(	PUNCT
cana-2411	84	20	frm	frm	PROPN
cana-2411	84	21	)	)	PUNCT
cana-2411	84	22	approaches	approach	NOUN
cana-2411	84	23	based	base	VERB
cana-2411	84	24	on	on	ADP
cana-2411	84	25	a	a	DET
cana-2411	84	26	new	new	ADJ
cana-2411	84	27	method	method	NOUN
cana-2411	84	28	of	of	ADP
cana-2411	84	29	neutrosophic	neutrosophic	ADJ
cana-2411	84	30	arithmetic	arithmetic	ADJ
cana-2411	84	31	operations	operation	NOUN
cana-2411	84	32	on	on	ADP
cana-2411	84	33	the	the	DET
cana-2411	84	34	parametric	parametric	ADJ
cana-2411	84	35	representations	representation	NOUN
cana-2411	84	36	of	of	ADP
cana-2411	84	37	neutrosophic	neutrosophic	ADJ
cana-2411	84	38	numbers	number	NOUN
cana-2411	84	39	and	and	CCONJ
cana-2411	84	40	ranking	rank	VERB
cana-2411	84	41	on	on	ADP
cana-2411	84	42	the	the	DET
cana-2411	84	43	neutrosophic	neutrosophic	ADJ
cana-2411	84	44	numbers	number	NOUN
cana-2411	84	45	of	of	ADP
cana-2411	84	46	the	the	DET
cana-2411	84	47	parametric	parametric	ADJ
cana-2411	84	48	forms	form	NOUN
cana-2411	84	49	.	.	PUNCT
cana-2411	85	1	we	we	PRON
cana-2411	85	2	prove	prove	VERB
cana-2411	85	3	theorems	theorem	NOUN
cana-2411	85	4	for	for	ADP
cana-2411	85	5	the	the	DET
cana-2411	85	6	solution	solution	NOUN
cana-2411	85	7	of	of	ADP
cana-2411	85	8	svnnlpp	svnnlpp	NOUN
cana-2411	85	9	without	without	ADP
cana-2411	85	10	converting	convert	VERB
cana-2411	85	11	the	the	DET
cana-2411	85	12	given	give	VERB
cana-2411	85	13	problem	problem	NOUN
cana-2411	85	14	to	to	ADP
cana-2411	85	15	its	its	PRON
cana-2411	85	16	equivalent	equivalent	ADJ
cana-2411	85	17	crisp	crisp	ADJ
cana-2411	85	18	form	form	NOUN
cana-2411	85	19	.	.	PUNCT
cana-2411	86	1	numerical	numerical	ADJ
cana-2411	86	2	examples	example	NOUN
cana-2411	86	3	are	be	AUX
cana-2411	86	4	presented	present	VERB
cana-2411	86	5	to	to	PART
cana-2411	86	6	illustrate	illustrate	VERB
cana-2411	86	7	the	the	DET
cana-2411	86	8	efficacy	efficacy	NOUN
cana-2411	86	9	of	of	ADP
cana-2411	86	10	the	the	DET
cana-2411	86	11	proposed	propose	VERB
cana-2411	86	12	solution	solution	NOUN
cana-2411	86	13	methods	method	NOUN
cana-2411	86	14	.	.	PUNCT
cana-2411	87	1	the	the	DET
cana-2411	87	2	rest	rest	NOUN
cana-2411	87	3	of	of	ADP
cana-2411	87	4	this	this	DET
cana-2411	87	5	article	article	NOUN
cana-2411	87	6	is	be	AUX
cana-2411	87	7	organized	organize	VERB
cana-2411	87	8	as	as	SCONJ
cana-2411	87	9	follows	follow	VERB
cana-2411	87	10	.	.	PUNCT
cana-2411	88	1	section	section	NOUN
cana-2411	88	2	2	2	NUM
cana-2411	88	3	provides	provide	VERB
cana-2411	88	4	some	some	DET
cana-2411	88	5	basic	basic	ADJ
cana-2411	88	6	preliminaries	preliminary	NOUN
cana-2411	88	7	and	and	CCONJ
cana-2411	88	8	results	result	NOUN
cana-2411	88	9	on	on	ADP
cana-2411	88	10	neutrosophic	neutrosophic	ADJ
cana-2411	88	11	numbers	number	NOUN
cana-2411	88	12	.	.	PUNCT
cana-2411	89	1	section	section	NOUN
cana-2411	89	2	3	3	NUM
cana-2411	89	3	provides	provide	VERB
cana-2411	89	4	nnlpp	nnlpp	NOUN
cana-2411	89	5	.	.	PUNCT
cana-2411	90	1	theorems	theorem	NOUN
cana-2411	90	2	on	on	ADP
cana-2411	90	3	csdm	csdm	NOUN
cana-2411	90	4	and	and	CCONJ
cana-2411	90	5	frm	frm	PROPN
cana-2411	90	6	are	be	AUX
cana-2411	90	7	provided	provide	VERB
cana-2411	90	8	in	in	ADP
cana-2411	90	9	section	section	NOUN
cana-2411	90	10	4	4	NUM
cana-2411	90	11	.	.	PUNCT
cana-2411	90	12	section	section	NOUN
cana-2411	90	13	5	5	NUM
cana-2411	90	14	presents	present	VERB
cana-2411	90	15	the	the	DET
cana-2411	90	16	algorithms	algorithm	NOUN
cana-2411	90	17	for	for	ADP
cana-2411	90	18	csdm	csdm	NOUN
cana-2411	90	19	and	and	CCONJ
cana-2411	90	20	frm	frm	PROPN
cana-2411	90	21	.	.	PROPN
cana-2411	91	1	section	section	NOUN
cana-2411	91	2	6	6	NUM
cana-2411	91	3	deals	deal	NOUN
cana-2411	91	4	with	with	ADP
cana-2411	91	5	numerical	numerical	ADJ
cana-2411	91	6	examples	example	NOUN
cana-2411	91	7	.	.	PUNCT
cana-2411	92	1	result	result	NOUN
cana-2411	92	2	and	and	CCONJ
cana-2411	92	3	discussion	discussion	NOUN
cana-2411	92	4	are	be	AUX
cana-2411	92	5	given	give	VERB
cana-2411	92	6	section	section	NOUN
cana-2411	92	7	7	7	NUM
cana-2411	92	8	.	.	PUNCT
cana-2411	93	1	finally	finally	ADV
cana-2411	93	2	,	,	PUNCT
cana-2411	93	3	a	a	DET
cana-2411	93	4	brief	brief	ADJ
cana-2411	93	5	conclusion	conclusion	NOUN
cana-2411	93	6	is	be	AUX
cana-2411	93	7	given	give	VERB
cana-2411	93	8	in	in	ADP
cana-2411	93	9	section	section	NOUN
cana-2411	93	10	8	8	NUM
cana-2411	93	11	.	.	NOUN
cana-2411	94	1	2	2	NUM
cana-2411	94	2	.	.	X
cana-2411	94	3	preliminaries	preliminary	NOUN
cana-2411	94	4	we	we	PRON
cana-2411	94	5	explored	explore	VERB
cana-2411	94	6	neutrosophic	neutrosophic	ADJ
cana-2411	94	7	definitions	definition	NOUN
cana-2411	94	8	,	,	PUNCT
cana-2411	94	9	which	which	PRON
cana-2411	94	10	capture	capture	VERB
cana-2411	94	11	the	the	DET
cana-2411	94	12	core	core	NOUN
cana-2411	94	13	of	of	ADP
cana-2411	94	14	neutrosophy	neutrosophy	NOUN
cana-2411	94	15	by	by	ADP
cana-2411	94	16	presenting	present	VERB
cana-2411	94	17	subtle	subtle	ADJ
cana-2411	94	18	viewpoints	viewpoint	NOUN
cana-2411	94	19	on	on	ADP
cana-2411	94	20	concepts	concept	NOUN
cana-2411	94	21	frequently	frequently	ADV
cana-2411	94	22	experienced	experience	VERB
cana-2411	94	23	in	in	ADP
cana-2411	94	24	situations	situation	NOUN
cana-2411	94	25	of	of	ADP
cana-2411	94	26	uncertainty	uncertainty	NOUN
cana-2411	94	27	.	.	PUNCT
cana-2411	95	1	by	by	ADP
cana-2411	95	2	employing	employ	VERB
cana-2411	95	3	these	these	DET
cana-2411	95	4	definitions	definition	NOUN
cana-2411	95	5	,	,	PUNCT
cana-2411	95	6	our	our	PRON
cana-2411	95	7	objective	objective	NOUN
cana-2411	95	8	is	be	AUX
cana-2411	95	9	to	to	PART
cana-2411	95	10	shed	shed	VERB
cana-2411	95	11	light	light	NOUN
cana-2411	95	12	the	the	DET
cana-2411	95	13	offer	offer	NOUN
cana-2411	95	14	valuable	valuable	ADJ
cana-2411	95	15	perspectives	perspective	NOUN
cana-2411	95	16	on	on	ADP
cana-2411	95	17	its	its	PRON
cana-2411	95	18	impact	impact	NOUN
cana-2411	95	19	on	on	ADP
cana-2411	95	20	theoretical	theoretical	ADJ
cana-2411	95	21	frameworks	framework	NOUN
cana-2411	95	22	.	.	PUNCT
cana-2411	96	1	communications	communication	NOUN
cana-2411	96	2	on	on	ADP
cana-2411	96	3	applied	apply	VERB
cana-2411	96	4	nonlinear	nonlinear	ADJ
cana-2411	96	5	analysis	analysis	NOUN
cana-2411	96	6	issn	issn	NOUN
cana-2411	96	7	:	:	PUNCT
cana-2411	96	8	1074	1074	NUM
cana-2411	96	9	-	-	PUNCT
cana-2411	96	10	133x	133x	NUM
cana-2411	96	11	vol	vol	NOUN
cana-2411	96	12	32	32	NUM
cana-2411	96	13	no	no	NOUN
cana-2411	96	14	.	.	PUNCT
cana-2411	97	1	2s	2s	NUM
cana-2411	97	2	(	(	PUNCT
cana-2411	97	3	2025	2025	NUM
cana-2411	97	4	)	)	PUNCT
cana-2411	97	5	369	369	NUM
cana-2411	97	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2411	97	7	\textcolor{white	\textcolor{white	X
cana-2411	97	8	}	}	PUNCT
cana-2411	97	9	{	{	PUNCT
cana-2411	97	10	`	`	PUNCT
cana-2411	97	11	`	`	PUNCT
cana-2411	97	12	}	}	PUNCT
cana-2411	97	13	definition	definition	NOUN
cana-2411	97	14	2.1	2.1	NUM
cana-2411	97	15	let	let	VERB
cana-2411	97	16	y	y	PRON
cana-2411	97	17	be	be	AUX
cana-2411	97	18	a	a	DET
cana-2411	97	19	universe	universe	NOUN
cana-2411	97	20	of	of	ADP
cana-2411	97	21	discourse	discourse	NOUN
cana-2411	97	22	.	.	PUNCT
cana-2411	98	1	a	a	DET
cana-2411	98	2	neutrosophic	neutrosophic	ADJ
cana-2411	98	3	set	set	VERB
cana-2411	98	4	�	�	PROPN
cana-2411	98	5	̃	̃	PROPN
cana-2411	98	6	�	�	PROPN
cana-2411	98	7	𝔫	𝔫	NOUN
cana-2411	98	8	in	in	ADP
cana-2411	98	9	υ	υ	PROPN
cana-2411	98	10	is	be	AUX
cana-2411	98	11	characterized	characterize	VERB
cana-2411	98	12	by	by	ADP
cana-2411	98	13	a	a	DET
cana-2411	98	14	truth	truth	NOUN
cana-2411	98	15	-	-	PUNCT
cana-2411	98	16	membership	membership	NOUN
cana-2411	98	17	function	function	NOUN
cana-2411	98	18	t	t	PROPN
cana-2411	98	19	�	�	PROPN
cana-2411	98	20	̃	̃	PROPN
cana-2411	98	21	�	�	PROPN
cana-2411	98	22	𝔫	𝔫	NOUN
cana-2411	98	23	a	a	DET
cana-2411	98	24	indeterminacy	indeterminacy	NOUN
cana-2411	98	25	-	-	PUNCT
cana-2411	98	26	membership	membership	NOUN
cana-2411	98	27	function	function	NOUN
cana-2411	98	28	i	i	PROPN
cana-2411	98	29	�	�	PROPN
cana-2411	98	30	̃	̃	PROPN
cana-2411	98	31	�	�	PROPN
cana-2411	98	32	𝔫	𝔫	NOUN
cana-2411	98	33	and	and	CCONJ
cana-2411	98	34	a	a	DET
cana-2411	98	35	falsity	falsity	NOUN
cana-2411	98	36	-	-	PUNCT
cana-2411	98	37	membership	membership	NOUN
cana-2411	98	38	function	function	NOUN
cana-2411	98	39	f	f	PROPN
cana-2411	98	40	�	�	PROPN
cana-2411	98	41	̃	̃	PROPN
cana-2411	98	42	�	�	PROPN
cana-2411	98	43	𝔫.	𝔫.	PROPN
cana-2411	98	44	t	t	PROPN
cana-2411	98	45	�	�	PROPN
cana-2411	98	46	̃	̃	PROPN
cana-2411	98	47	�	�	NOUN
cana-2411	98	48	𝔫(υ	𝔫(υ	PROPN
cana-2411	98	49	)	)	PUNCT
cana-2411	98	50	;	;	PUNCT
cana-2411	98	51	i	i	PROPN
cana-2411	98	52	�	�	PROPN
cana-2411	98	53	̃	̃	PROPN
cana-2411	98	54	�	�	NOUN
cana-2411	98	55	𝔫(υ	𝔫(υ	NOUN
cana-2411	98	56	)	)	PUNCT
cana-2411	98	57	and	and	CCONJ
cana-2411	98	58	f	f	PROPN
cana-2411	98	59	�	�	PROPN
cana-2411	98	60	̃	̃	PROPN
cana-2411	98	61	�	�	NOUN
cana-2411	98	62	𝔫(υ	𝔫(υ	NOUN
cana-2411	98	63	)	)	PUNCT
cana-2411	98	64	are	be	AUX
cana-2411	98	65	are	be	AUX
cana-2411	98	66	real	real	ADJ
cana-2411	98	67	standard	standard	ADJ
cana-2411	98	68	elements	element	NOUN
cana-2411	98	69	of	of	ADP
cana-2411	98	70	[	[	X
cana-2411	98	71	0,1	0,1	NUM
cana-2411	98	72	]	]	PUNCT
cana-2411	98	73	.	.	PUNCT
cana-2411	99	1	it	it	PRON
cana-2411	99	2	can	can	AUX
cana-2411	99	3	be	be	AUX
cana-2411	99	4	written	write	VERB
cana-2411	99	5	as	as	ADP
cana-2411	99	6	�	�	PROPN
cana-2411	99	7	̃	̃	PROPN
cana-2411	99	8	�	�	PROPN
cana-2411	99	9	𝔫	𝔫	NOUN
cana-2411	99	10	=	=	X
cana-2411	99	11	{	{	PUNCT
cana-2411	99	12	<	<	X
cana-2411	99	13	υ	υ	PROPN
cana-2411	99	14	,	,	PUNCT
cana-2411	99	15	(	(	PUNCT
cana-2411	99	16	t	t	PROPN
cana-2411	99	17	�	�	PROPN
cana-2411	99	18	̃	̃	PROPN
cana-2411	99	19	�	�	NOUN
cana-2411	99	20	𝔫(υ	𝔫(υ	NOUN
cana-2411	99	21	)	)	PUNCT
cana-2411	99	22	,	,	PUNCT
cana-2411	99	23	i	i	PROPN
cana-2411	99	24	�	�	PROPN
cana-2411	99	25	̃	̃	PROPN
cana-2411	99	26	�	�	PROPN
cana-2411	99	27	𝔫(υ),f	𝔫(υ),f	NOUN
cana-2411	99	28	�	�	PROPN
cana-2411	99	29	̃	̃	PROPN
cana-2411	99	30	�	�	NOUN
cana-2411	99	31	𝔫(υ	𝔫(υ	NOUN
cana-2411	99	32	)	)	PUNCT
cana-2411	99	33	)	)	PUNCT
cana-2411	100	1	>	>	X
cana-2411	100	2	|υ	|υ	X
cana-2411	100	3	∈	∈	PROPN
cana-2411	100	4	y	y	PROPN
cana-2411	100	5	}	}	PUNCT
cana-2411	100	6	.	.	PUNCT
cana-2411	101	1	the	the	DET
cana-2411	101	2	function	function	NOUN
cana-2411	101	3	t	t	PROPN
cana-2411	101	4	�	�	PROPN
cana-2411	101	5	̃	̃	PROPN
cana-2411	101	6	�	�	NOUN
cana-2411	101	7	𝔫(υ	𝔫(υ	PROPN
cana-2411	101	8	)	)	PUNCT
cana-2411	102	1	;	;	PUNCT
cana-2411	102	2	i	i	PROPN
cana-2411	102	3	�	�	PROPN
cana-2411	102	4	̃	̃	PROPN
cana-2411	102	5	�	�	NOUN
cana-2411	102	6	𝔫(υ	𝔫(υ	NOUN
cana-2411	102	7	)	)	PUNCT
cana-2411	102	8	and	and	CCONJ
cana-2411	102	9	f	f	PROPN
cana-2411	102	10	�	�	PROPN
cana-2411	102	11	̃	̃	PROPN
cana-2411	102	12	�	�	NOUN
cana-2411	102	13	𝔫(υ	𝔫(υ	NOUN
cana-2411	102	14	)	)	PUNCT
cana-2411	102	15	are	be	AUX
cana-2411	102	16	real	real	ADJ
cana-2411	102	17	standard	standard	ADJ
cana-2411	102	18	or	or	CCONJ
cana-2411	102	19	non	non	ADJ
cana-2411	102	20	standard	standard	ADJ
cana-2411	102	21	subsets	subset	NOUN
cana-2411	102	22	of	of	ADP
cana-2411	102	23	]	]	X
cana-2411	102	24	0−	0−	NUM
cana-2411	102	25	,	,	PUNCT
cana-2411	102	26	1	1	NUM
cana-2411	102	27	+	+	NOUN
cana-2411	102	28	[	[	PUNCT
cana-2411	102	29	\textcolor{white	\textcolor{white	NOUN
cana-2411	102	30	}	}	PUNCT
cana-2411	102	31	{	{	PUNCT
cana-2411	102	32	''	''	PUNCT
cana-2411	102	33	}	}	PUNCT
cana-2411	102	34	i.e.	i.e.	X
cana-2411	102	35	,t	,t	PUNCT
cana-2411	102	36	�	�	PROPN
cana-2411	102	37	̃	̃	NOUN
cana-2411	102	38	�	�	NOUN
cana-2411	102	39	𝔫(υ	𝔫(υ	NOUN
cana-2411	102	40	)	)	PUNCT
cana-2411	102	41	,	,	PUNCT
cana-2411	102	42	i	i	PROPN
cana-2411	102	43	�	�	PROPN
cana-2411	102	44	̃	̃	PROPN
cana-2411	102	45	�	�	PROPN
cana-2411	102	46	𝔫(υ),f	𝔫(υ),f	NOUN
cana-2411	102	47	�	�	PROPN
cana-2411	102	48	̃	̃	PROPN
cana-2411	102	49	�	�	NOUN
cana-2411	102	50	𝔫:y	𝔫:y	ADJ
cana-2411	102	51	→]0−	→]0−	NOUN
cana-2411	102	52	,	,	PUNCT
cana-2411	102	53	1	1	NUM
cana-2411	102	54	+	+	NOUN
cana-2411	102	55	[	[	PUNCT
cana-2411	102	56	.	.	PUNCT
cana-2411	103	1	there	there	PRON
cana-2411	103	2	is	be	VERB
cana-2411	103	3	no	no	DET
cana-2411	103	4	restriction	restriction	NOUN
cana-2411	103	5	is	be	AUX
cana-2411	103	6	applied	apply	VERB
cana-2411	103	7	on	on	ADP
cana-2411	103	8	the	the	DET
cana-2411	103	9	sum	sum	NOUN
cana-2411	103	10	of	of	ADP
cana-2411	103	11	t	t	PROPN
cana-2411	103	12	�	�	PROPN
cana-2411	103	13	̃	̃	PROPN
cana-2411	103	14	�	�	NOUN
cana-2411	103	15	𝔫(υ	𝔫(υ	PROPN
cana-2411	103	16	)	)	PUNCT
cana-2411	103	17	;	;	PUNCT
cana-2411	104	1	i	i	PROPN
cana-2411	104	2	�	�	PROPN
cana-2411	104	3	̃	̃	PROPN
cana-2411	104	4	�	�	NOUN
cana-2411	104	5	𝔫(υ	𝔫(υ	NOUN
cana-2411	104	6	)	)	PUNCT
cana-2411	104	7	and	and	CCONJ
cana-2411	104	8	f	f	PROPN
cana-2411	104	9	�	�	PROPN
cana-2411	104	10	̃	̃	PROPN
cana-2411	104	11	�	�	NOUN
cana-2411	104	12	𝔫(υ	𝔫(υ	NOUN
cana-2411	104	13	)	)	PUNCT
cana-2411	104	14	,	,	PUNCT
cana-2411	104	15	so	so	ADV
cana-2411	104	16	0	0	NUM
cana-2411	104	17	−	−	PROPN
cana-2411	104	18	≤	≤	PROPN
cana-2411	104	19	supt	supt	PROPN
cana-2411	104	20	�	�	PROPN
cana-2411	104	21	̃	̃	PROPN
cana-2411	104	22	�	�	PROPN
cana-2411	104	23	𝔫(υ),+supi	𝔫(υ),+supi	NOUN
cana-2411	104	24	�	�	PROPN
cana-2411	104	25	̃	̃	PROPN
cana-2411	104	26	�	�	PROPN
cana-2411	104	27	𝔫(υ),+supf	𝔫(υ),+supf	PROPN
cana-2411	104	28	�	�	PROPN
cana-2411	104	29	̃	̃	PROPN
cana-2411	104	30	�	�	NOUN
cana-2411	104	31	𝔫(υ	𝔫(υ	NOUN
cana-2411	104	32	)	)	PUNCT
cana-2411	104	33	≤	≤	NOUN
cana-2411	104	34	3	3	NUM
cana-2411	104	35	+	+	CCONJ
cana-2411	104	36	.	.	PUNCT
cana-2411	105	1	for	for	ADP
cana-2411	105	2	a	a	DET
cana-2411	105	3	fixed	fixed	ADJ
cana-2411	105	4	υ	υ	NOUN
cana-2411	105	5	=	=	PUNCT
cana-2411	105	6	υ	υ	PROPN
cana-2411	105	7	∈	∈	PROPN
cana-2411	105	8	y	y	PROPN
cana-2411	105	9	,	,	PUNCT
cana-2411	105	10	t	t	PROPN
cana-2411	105	11	�	�	PROPN
cana-2411	105	12	̃	̃	PROPN
cana-2411	105	13	�	�	NOUN
cana-2411	105	14	𝔫(υ	𝔫(υ	NOUN
cana-2411	105	15	)	)	PUNCT
cana-2411	105	16	,	,	PUNCT
cana-2411	105	17	i	i	PROPN
cana-2411	105	18	�	�	PROPN
cana-2411	105	19	̃	̃	PROPN
cana-2411	105	20	�	�	PROPN
cana-2411	105	21	𝔫(υ),f	𝔫(υ),f	NOUN
cana-2411	105	22	�	�	PROPN
cana-2411	105	23	̃	̃	PROPN
cana-2411	105	24	�	�	NOUN
cana-2411	105	25	𝔫(υ	𝔫(υ	NOUN
cana-2411	105	26	)	)	PUNCT
cana-2411	105	27	,	,	PUNCT
cana-2411	105	28	i.e.	i.e.	X
cana-2411	105	29	,	,	PUNCT
cana-2411	105	30	in	in	ADP
cana-2411	105	31	simply	simply	ADV
cana-2411	105	32	,	,	PUNCT
cana-2411	105	33	t	t	PROPN
cana-2411	105	34	�	�	PROPN
cana-2411	105	35	̃	̃	PROPN
cana-2411	105	36	�	�	NOUN
cana-2411	105	37	𝔫(υ	𝔫(υ	NOUN
cana-2411	105	38	)	)	PUNCT
cana-2411	105	39	,	,	PUNCT
cana-2411	105	40	i	i	PROPN
cana-2411	105	41	�	�	PROPN
cana-2411	105	42	̃	̃	PROPN
cana-2411	105	43	�	�	PROPN
cana-2411	105	44	𝔫(υ),f	𝔫(υ),f	NOUN
cana-2411	105	45	�	�	PROPN
cana-2411	105	46	̃	̃	PROPN
cana-2411	105	47	�	�	NOUN
cana-2411	105	48	𝔫(υ	𝔫(υ	NOUN
cana-2411	105	49	)	)	PUNCT
cana-2411	105	50	is	be	AUX
cana-2411	105	51	called	call	VERB
cana-2411	105	52	neutrosophic	neutrosophic	ADJ
cana-2411	105	53	number	number	NOUN
cana-2411	105	54	(	(	PUNCT
cana-2411	105	55	nn	nn	NOUN
cana-2411	105	56	)	)	PUNCT
cana-2411	105	57	.	.	PUNCT
cana-2411	106	1	\textcolor{white	\textcolor{white	X
cana-2411	106	2	}	}	PUNCT
cana-2411	106	3	{	{	PUNCT
cana-2411	106	4	`	`	PUNCT
cana-2411	106	5	`	`	PUNCT
cana-2411	106	6	}	}	PUNCT
cana-2411	106	7	definition	definition	NOUN
cana-2411	106	8	2.2	2.2	NUM
cana-2411	106	9	let	let	VERB
cana-2411	106	10	y	y	PRON
cana-2411	106	11	be	be	AUX
cana-2411	106	12	a	a	DET
cana-2411	106	13	universe	universe	NOUN
cana-2411	106	14	of	of	ADP
cana-2411	106	15	discourse	discourse	NOUN
cana-2411	106	16	.	.	PUNCT
cana-2411	107	1	a	a	DET
cana-2411	107	2	single	single	ADJ
cana-2411	107	3	valued	value	VERB
cana-2411	107	4	neutrosophic	neutrosophic	ADJ
cana-2411	107	5	set	set	NOUN
cana-2411	107	6	(	(	PUNCT
cana-2411	107	7	svns	svns	NOUN
cana-2411	107	8	)	)	PUNCT
cana-2411	107	9	�	�	PROPN
cana-2411	107	10	̃	̃	PROPN
cana-2411	107	11	�	�	PROPN
cana-2411	107	12	𝔫	𝔫	PROPN
cana-2411	107	13	over	over	ADP
cana-2411	107	14	y	y	PROPN
cana-2411	107	15	is	be	AUX
cana-2411	107	16	an	an	DET
cana-2411	107	17	object	object	NOUN
cana-2411	107	18	having	have	VERB
cana-2411	107	19	the	the	DET
cana-2411	107	20	form	form	NOUN
cana-2411	107	21	�	�	PROPN
cana-2411	107	22	̃	̃	PROPN
cana-2411	107	23	�	�	PROPN
cana-2411	107	24	𝔫	𝔫	NOUN
cana-2411	107	25	=	=	X
cana-2411	107	26	{	{	PUNCT
cana-2411	107	27	<	<	X
cana-2411	107	28	υ	υ	PROPN
cana-2411	107	29	,	,	PUNCT
cana-2411	107	30	(	(	PUNCT
cana-2411	107	31	t	t	PROPN
cana-2411	107	32	�	�	PROPN
cana-2411	107	33	̃	̃	PROPN
cana-2411	107	34	�	�	NOUN
cana-2411	107	35	𝔫(υ	𝔫(υ	NOUN
cana-2411	107	36	)	)	PUNCT
cana-2411	107	37	,	,	PUNCT
cana-2411	107	38	i	i	PROPN
cana-2411	107	39	�	�	PROPN
cana-2411	107	40	̃	̃	PROPN
cana-2411	107	41	�	�	PROPN
cana-2411	107	42	𝔫(υ),f	𝔫(υ),f	NOUN
cana-2411	107	43	�	�	PROPN
cana-2411	107	44	̃	̃	PROPN
cana-2411	107	45	�	�	NOUN
cana-2411	107	46	𝔫(υ	𝔫(υ	NOUN
cana-2411	107	47	)	)	PUNCT
cana-2411	107	48	)	)	PUNCT
cana-2411	108	1	>	>	X
cana-2411	108	2	|υ	|υ	X
cana-2411	108	3	∈	∈	PROPN
cana-2411	108	4	y	y	PROPN
cana-2411	108	5	}	}	PUNCT
cana-2411	108	6	where	where	SCONJ
cana-2411	108	7	t	t	PROPN
cana-2411	108	8	�	�	PROPN
cana-2411	108	9	̃	̃	PROPN
cana-2411	108	10	�	�	PROPN
cana-2411	108	11	𝔫(υ):y	𝔫(υ):y	PROPN
cana-2411	108	12	→	→	SYM
cana-2411	108	13	]	]	SYM
cana-2411	108	14	0−	0−	NUM
cana-2411	108	15	,	,	PUNCT
cana-2411	108	16	1	1	NUM
cana-2411	109	1	+	+	NOUN
cana-2411	109	2	[	[	X
cana-2411	109	3	,	,	PUNCT
cana-2411	109	4	i	i	PROPN
cana-2411	109	5	�	�	PROPN
cana-2411	109	6	̃	̃	PROPN
cana-2411	109	7	�	�	PROPN
cana-2411	109	8	𝔫(υ):y	𝔫(υ):y	PROPN
cana-2411	109	9	→]0−	→]0−	PROPN
cana-2411	109	10	,	,	PUNCT
cana-2411	109	11	1+[,f	1+[,f	PROPN
cana-2411	109	12	�	�	PROPN
cana-2411	109	13	̃	̃	PROPN
cana-2411	109	14	�	�	PROPN
cana-2411	109	15	n	n	CCONJ
cana-2411	109	16	:	:	PUNCT
cana-2411	109	17	y	y	PROPN
cana-2411	109	18	→]0−	→]0−	PROPN
cana-2411	109	19	,	,	PUNCT
cana-2411	109	20	1	1	NUM
cana-2411	109	21	+	+	NOUN
cana-2411	109	22	[	[	PUNCT
cana-2411	109	23	are	be	AUX
cana-2411	109	24	truth	truth	NOUN
cana-2411	109	25	,	,	PUNCT
cana-2411	109	26	indeterminacy	indeterminacy	NOUN
cana-2411	109	27	and	and	CCONJ
cana-2411	109	28	falsity	falsity	NOUN
cana-2411	109	29	membership	membership	NOUN
cana-2411	109	30	with	with	ADP
cana-2411	109	31	0	0	NUM
cana-2411	109	32	≤	≤	NUM
cana-2411	109	33	t	t	PROPN
cana-2411	109	34	�	�	PROPN
cana-2411	109	35	̃	̃	PROPN
cana-2411	109	36	�	�	PROPN
cana-2411	109	37	𝔫(υ),+i	𝔫(υ),+i	PROPN
cana-2411	109	38	�	�	PROPN
cana-2411	109	39	̃	̃	PROPN
cana-2411	109	40	�	�	PROPN
cana-2411	109	41	𝔫(υ),+f	𝔫(υ),+f	PROPN
cana-2411	109	42	�	�	PROPN
cana-2411	109	43	̃	̃	PROPN
cana-2411	109	44	�	�	NOUN
cana-2411	109	45	𝔫(υ	𝔫(υ	NOUN
cana-2411	109	46	)	)	PUNCT
cana-2411	109	47	≤	≤	NOUN
cana-2411	109	48	3	3	NUM
cana-2411	109	49	for	for	ADP
cana-2411	109	50	all	all	PRON
cana-2411	109	51	υ	υ	PROPN
cana-2411	109	52	∈	∈	PROPN
cana-2411	109	53	y.	y.	NOUN
cana-2411	109	54	\textcolor{white	\textcolor{white	PROPN
cana-2411	109	55	}	}	PUNCT
cana-2411	109	56	{	{	PUNCT
cana-2411	109	57	''	''	PUNCT
cana-2411	109	58	}	}	PUNCT
cana-2411	109	59	definition	definition	NOUN
cana-2411	109	60	2.3	2.3	NUM
cana-2411	109	61	a	a	DET
cana-2411	109	62	single	single	ADJ
cana-2411	109	63	valued	value	VERB
cana-2411	109	64	neutrosophic	neutrosophic	ADJ
cana-2411	109	65	number	number	NOUN
cana-2411	109	66	(	(	PUNCT
cana-2411	109	67	svnn	svnn	NOUN
cana-2411	109	68	)	)	PUNCT
cana-2411	109	69	�	�	PROPN
cana-2411	109	70	̃	̃	PROPN
cana-2411	109	71	�	�	PROPN
cana-2411	109	72	𝔫	𝔫	NOUN
cana-2411	109	73	=	=	X
cana-2411	109	74	{	{	PUNCT
cana-2411	109	75	<	<	X
cana-2411	109	76	υ	υ	PROPN
cana-2411	109	77	,	,	PUNCT
cana-2411	109	78	(	(	PUNCT
cana-2411	109	79	t	t	PROPN
cana-2411	109	80	�	�	PROPN
cana-2411	109	81	̃	̃	PROPN
cana-2411	109	82	�	�	NOUN
cana-2411	109	83	𝔫(υ	𝔫(υ	NOUN
cana-2411	109	84	)	)	PUNCT
cana-2411	109	85	,	,	PUNCT
cana-2411	109	86	i	i	PROPN
cana-2411	109	87	�	�	PROPN
cana-2411	109	88	̃	̃	PROPN
cana-2411	109	89	�	�	PROPN
cana-2411	109	90	𝔫(υ),f	𝔫(υ),f	NOUN
cana-2411	109	91	�	�	PROPN
cana-2411	109	92	̃	̃	PROPN
cana-2411	109	93	�	�	NOUN
cana-2411	109	94	𝔫(υ	𝔫(υ	NOUN
cana-2411	109	95	)	)	PUNCT
cana-2411	109	96	)	)	PUNCT
cana-2411	110	1	>	>	X
cana-2411	110	2	|υ	|υ	X
cana-2411	110	3	∈	∈	PROPN
cana-2411	110	4	y	y	PROPN
cana-2411	110	5	}	}	PUNCT
cana-2411	110	6	,	,	PUNCT
cana-2411	110	7	subset	subset	NOUN
cana-2411	110	8	of	of	ADP
cana-2411	110	9	a	a	DET
cana-2411	110	10	real	real	ADJ
cana-2411	110	11	line	line	NOUN
cana-2411	110	12	,	,	PUNCT
cana-2411	110	13	is	be	AUX
cana-2411	110	14	called	call	VERB
cana-2411	110	15	generalised	generalise	VERB
cana-2411	110	16	neutrosophic	neutrosophic	ADJ
cana-2411	110	17	number	number	NOUN
cana-2411	110	18	if	if	SCONJ
cana-2411	110	19	\textcolor{white	\textcolor{white	NOUN
cana-2411	110	20	}	}	PUNCT
cana-2411	110	21	{	{	PUNCT
cana-2411	110	22	`	`	PUNCT
cana-2411	110	23	`	`	PUNCT
cana-2411	110	24	}	}	SYM
cana-2411	110	25	1	1	NUM
cana-2411	110	26	.	.	X
cana-2411	110	27	�	�	PROPN
cana-2411	110	28	̃	̃	PROPN
cana-2411	110	29	�	�	PROPN
cana-2411	110	30	𝔫	𝔫	NOUN
cana-2411	110	31	is	be	AUX
cana-2411	110	32	neut	neut	NOUN
cana-2411	110	33	-	-	PUNCT
cana-2411	110	34	normal	normal	ADJ
cana-2411	110	35	.	.	PUNCT
cana-2411	111	1	2	2	X
cana-2411	111	2	.	.	X
cana-2411	111	3	�	�	PROPN
cana-2411	111	4	̃	̃	PROPN
cana-2411	111	5	�	�	PROPN
cana-2411	111	6	𝔫	𝔫	NOUN
cana-2411	111	7	is	be	AUX
cana-2411	111	8	neut	neut	NOUN
cana-2411	111	9	-	-	PUNCT
cana-2411	111	10	convex	convex	NOUN
cana-2411	111	11	.	.	PUNCT
cana-2411	112	1	3	3	NUM
cana-2411	112	2	.	.	X
cana-2411	112	3	t	t	PROPN
cana-2411	112	4	�	�	PROPN
cana-2411	112	5	̃	̃	PROPN
cana-2411	112	6	�	�	NOUN
cana-2411	112	7	𝔫(υ	𝔫(υ	NOUN
cana-2411	112	8	)	)	PUNCT
cana-2411	112	9	is	be	AUX
cana-2411	112	10	upper	upper	ADJ
cana-2411	112	11	semi	semi	ADJ
cana-2411	112	12	-	-	ADJ
cana-2411	112	13	continuous	continuous	ADJ
cana-2411	112	14	,	,	PUNCT
cana-2411	112	15	i	i	PROPN
cana-2411	112	16	�	�	PROPN
cana-2411	112	17	̃	̃	PROPN
cana-2411	112	18	�	�	NOUN
cana-2411	112	19	𝔫(υ	𝔫(υ	NOUN
cana-2411	112	20	)	)	PUNCT
cana-2411	113	1	is	be	AUX
cana-2411	113	2	lower	low	ADJ
cana-2411	113	3	semi	semi	ADV
cana-2411	113	4	continuous	continuous	ADJ
cana-2411	113	5	and	and	CCONJ
cana-2411	113	6	f	f	PROPN
cana-2411	113	7	�	�	PROPN
cana-2411	113	8	̃	̃	PROPN
cana-2411	113	9	�	�	NOUN
cana-2411	113	10	𝔫(υ	𝔫(υ	NOUN
cana-2411	113	11	)	)	PUNCT
cana-2411	114	1	is	be	AUX
cana-2411	114	2	lower	low	ADJ
cana-2411	114	3	semi	semi	ADV
cana-2411	114	4	continuous	continuous	ADJ
cana-2411	114	5	.	.	PUNCT
cana-2411	115	1	4	4	X
cana-2411	115	2	.	.	X
cana-2411	115	3	�	�	PROPN
cana-2411	115	4	̃	̃	PROPN
cana-2411	115	5	�	�	PROPN
cana-2411	115	6	𝔫	𝔫	NOUN
cana-2411	115	7	is	be	AUX
cana-2411	115	8	support	support	NOUN
cana-2411	115	9	,	,	PUNCT
cana-2411	115	10	i.e.	i.e.	X
cana-2411	115	11	s(	s(	X
cana-2411	115	12	�	�	PROPN
cana-2411	115	13	̃	̃	PROPN
cana-2411	115	14	�	�	PROPN
cana-2411	115	15	𝔫	𝔫	NOUN
cana-2411	115	16	)	)	PUNCT
cana-2411	115	17	=	=	PUNCT
cana-2411	115	18	υ	υ	PROPN
cana-2411	115	19	∈	∈	PROPN
cana-2411	115	20	y	y	PROPN
cana-2411	115	21	:	:	PUNCT
cana-2411	115	22	t	t	PROPN
cana-2411	115	23	�	�	PROPN
cana-2411	115	24	̃	̃	PROPN
cana-2411	115	25	�	�	PROPN
cana-2411	115	26	𝔫	𝔫	X
cana-2411	115	27	>	>	X
cana-2411	115	28	0	0	PROPN
cana-2411	115	29	,	,	PUNCT
cana-2411	115	30	i	i	PRON
cana-2411	115	31	�	�	PROPN
cana-2411	115	32	̃	̃	PROPN
cana-2411	115	33	�	�	PROPN
cana-2411	115	34	𝔫	𝔫	X
cana-2411	115	35	<	<	X
cana-2411	115	36	1,f	1,f	NUM
cana-2411	115	37	�	�	PROPN
cana-2411	115	38	̃	̃	PROPN
cana-2411	115	39	�	�	PROPN
cana-2411	115	40	𝔫	𝔫	X
cana-2411	115	41	<	<	X
cana-2411	115	42	1	1	NUM
cana-2411	115	43	is	be	AUX
cana-2411	115	44	bounded	bound	VERB
cana-2411	115	45	.	.	PUNCT
cana-2411	116	1	\textcolor{white	\textcolor{white	PROPN
cana-2411	116	2	}	}	PUNCT
cana-2411	116	3	{	{	PUNCT
cana-2411	116	4	''	''	PUNCT
cana-2411	116	5	}	}	PUNCT
cana-2411	116	6	definition	definition	NOUN
cana-2411	116	7	2.4	2.4	NUM
cana-2411	116	8	a	a	DET
cana-2411	116	9	single	single	ADJ
cana-2411	116	10	valued	value	VERB
cana-2411	116	11	neutrosophic	neutrosophic	ADJ
cana-2411	116	12	number	number	NOUN
cana-2411	116	13	�	�	PROPN
cana-2411	116	14	̃	̃	PROPN
cana-2411	116	15	�	�	PROPN
cana-2411	116	16	𝔫	𝔫	NOUN
cana-2411	116	17	is	be	AUX
cana-2411	116	18	triangular	triangular	ADJ
cana-2411	116	19	neutrosophic	neutrosophic	ADJ
cana-2411	116	20	number	number	NOUN
cana-2411	116	21	(	(	PUNCT
cana-2411	116	22	tnn	tnn	PROPN
cana-2411	116	23	)	)	PUNCT
cana-2411	116	24	and	and	CCONJ
cana-2411	116	25	is	be	AUX
cana-2411	116	26	denoted	denote	VERB
cana-2411	116	27	by	by	ADP
cana-2411	116	28	�	�	PROPN
cana-2411	116	29	̃	̃	PROPN
cana-2411	116	30	�	�	PROPN
cana-2411	116	31	𝔫	𝔫	NOUN
cana-2411	116	32	=	=	PUNCT
cana-2411	116	33	(	(	PUNCT
cana-2411	116	34	〈	〈	PROPN
cana-2411	116	35	𝔞t1	𝔞t1	PROPN
cana-2411	116	36	,	,	PUNCT
cana-2411	116	37	𝔞t2	𝔞t2	PROPN
cana-2411	116	38	,	,	PUNCT
cana-2411	116	39	𝔞t3	𝔞t3	PROPN
cana-2411	116	40	〉	〉	PROPN
cana-2411	116	41	;	;	PUNCT
cana-2411	116	42	〈	〈	PROPN
cana-2411	116	43	𝔞i1	𝔞i1	PROPN
cana-2411	116	44	,	,	PUNCT
cana-2411	116	45	𝔞i2	𝔞i2	PROPN
cana-2411	116	46	,	,	PUNCT
cana-2411	116	47	𝔞i3	𝔞i3	PROPN
cana-2411	116	48	〉	〉	NOUN
cana-2411	116	49	;	;	PUNCT
cana-2411	116	50	〈	〈	PRON
cana-2411	116	51	𝔞f1	𝔞f1	NOUN
cana-2411	116	52	,	,	PUNCT
cana-2411	116	53	𝔞f2	𝔞f2	NOUN
cana-2411	116	54	,	,	PUNCT
cana-2411	116	55	𝔞f3	𝔞f3	NOUN
cana-2411	116	56	〉	〉	NOUN
cana-2411	116	57	)	)	PUNCT
cana-2411	116	58	having	have	VERB
cana-2411	116	59	the	the	DET
cana-2411	116	60	membership	membership	NOUN
cana-2411	116	61	function	function	NOUN
cana-2411	116	62	,	,	PUNCT
cana-2411	116	63	indeterminacy	indeterminacy	NOUN
cana-2411	116	64	function	function	NOUN
cana-2411	116	65	and	and	CCONJ
cana-2411	116	66	non	non	ADJ
cana-2411	116	67	-	-	ADJ
cana-2411	116	68	membership	membership	ADJ
cana-2411	116	69	function	function	NOUN
cana-2411	116	70	as	as	ADP
cana-2411	116	71	follows.𝒶	follows.𝒶	PROPN
cana-2411	116	72	μ	μ	PROPN
cana-2411	116	73	t	t	PROPN
cana-2411	116	74	(	(	PUNCT
cana-2411	116	75	υ	υ	NOUN
cana-2411	116	76	)	)	PUNCT
cana-2411	116	77	=	=	NOUN
cana-2411	116	78	{	{	PUNCT
cana-2411	117	1	υ−𝔞t1	υ−𝔞t1	INTJ
cana-2411	117	2	𝔞t2	𝔞t2	PROPN
cana-2411	117	3	−𝔞t1	−𝔞t1	INTJ
cana-2411	117	4	,	,	PUNCT
cana-2411	117	5	𝔞t1	𝔞t1	NOUN
cana-2411	117	6	≤	≤	NUM
cana-2411	117	7	υ	υ	DET
cana-2411	117	8	≤	≤	NUM
cana-2411	117	9	𝔞t2	𝔞t2	PROPN
cana-2411	117	10	𝔞t3	𝔞t3	PROPN
cana-2411	117	11	−υ	−υ	NOUN
cana-2411	117	12	𝔞t3	𝔞t3	PROPN
cana-2411	117	13	−𝔞t2	−𝔞t2	PROPN
cana-2411	117	14	,	,	PUNCT
cana-2411	117	15	𝔞t2	𝔞t2	PROPN
cana-2411	117	16	≤	≤	NUM
cana-2411	117	17	υ	υ	DET
cana-2411	117	18	≤	≤	NUM
cana-2411	117	19	𝔞t3	𝔞t3	NOUN
cana-2411	117	20	0	0	NUM
cana-2411	117	21	,	,	PUNCT
cana-2411	117	22	elsewhere	elsewhere	ADV
cana-2411	117	23	μ	μ	NUM
cana-2411	117	24	i	i	PROPN
cana-2411	117	25	(	(	PUNCT
cana-2411	117	26	υ	υ	NOUN
cana-2411	117	27	)	)	PUNCT
cana-2411	118	1	=	=	PRON
cana-2411	118	2	{	{	PUNCT
cana-2411	118	3	υ−𝔞i1	υ−𝔞i1	INTJ
cana-2411	118	4	𝔞i2	𝔞i2	PROPN
cana-2411	118	5	−𝔞i1	−𝔞i1	VERB
cana-2411	118	6	,	,	PUNCT
cana-2411	118	7	𝔞i1	𝔞i1	VERB
cana-2411	118	8	≤	≤	NUM
cana-2411	118	9	υ	υ	PRON
cana-2411	118	10	≤	≤	NUM
cana-2411	118	11	𝔞i2	𝔞i2	PROPN
cana-2411	118	12	𝔞i3	𝔞i3	NOUN
cana-2411	118	13	−υ	−υ	NUM
cana-2411	118	14	𝔞i3	𝔞i3	NOUN
cana-2411	118	15	−𝔞i2	−𝔞i2	PROPN
cana-2411	118	16	,	,	PUNCT
cana-2411	118	17	𝔞i2	𝔞i2	PROPN
cana-2411	118	18	≤	≤	NUM
cana-2411	118	19	υ	υ	PRON
cana-2411	118	20	≤	≤	NUM
cana-2411	118	21	𝔞i3	𝔞i3	NOUN
cana-2411	118	22	0	0	NUM
cana-2411	118	23	,	,	PUNCT
cana-2411	118	24	elsewhere	elsewhere	ADV
cana-2411	118	25	communications	communication	NOUN
cana-2411	118	26	on	on	ADP
cana-2411	118	27	applied	apply	VERB
cana-2411	118	28	nonlinear	nonlinear	ADJ
cana-2411	118	29	analysis	analysis	NOUN
cana-2411	118	30	issn	issn	NOUN
cana-2411	118	31	:	:	PUNCT
cana-2411	118	32	1074	1074	NUM
cana-2411	118	33	-	-	PUNCT
cana-2411	118	34	133x	133x	NUM
cana-2411	118	35	vol	vol	NOUN
cana-2411	118	36	32	32	NUM
cana-2411	118	37	no	no	NOUN
cana-2411	118	38	.	.	PUNCT
cana-2411	119	1	2s	2s	NUM
cana-2411	119	2	(	(	PUNCT
cana-2411	119	3	2025	2025	NUM
cana-2411	119	4	)	)	PUNCT
cana-2411	119	5	370	370	NUM
cana-2411	120	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-2411	120	2	μ	μ	NUM
cana-2411	120	3	f	f	PROPN
cana-2411	120	4	(	(	PUNCT
cana-2411	120	5	υ	υ	NOUN
cana-2411	120	6	)	)	PUNCT
cana-2411	120	7	=	=	PRON
cana-2411	120	8	{	{	PUNCT
cana-2411	120	9	υ−𝔞f1	υ−𝔞f1	NOUN
cana-2411	120	10	𝔞f2	𝔞f2	NOUN
cana-2411	120	11	−𝔞f1	−𝔞f1	NOUN
cana-2411	120	12	,	,	PUNCT
cana-2411	120	13	𝔞f1	𝔞f1	NOUN
cana-2411	120	14	≤	≤	NUM
cana-2411	120	15	υ	υ	PRON
cana-2411	120	16	≤	≤	ADJ
cana-2411	120	17	𝔞f2	𝔞f2	NOUN
cana-2411	120	18	𝔞f3	𝔞f3	NOUN
cana-2411	120	19	−υ	−υ	VERB
cana-2411	120	20	𝔞f3	𝔞f3	NOUN
cana-2411	120	21	−𝔞f2	−𝔞f2	NOUN
cana-2411	120	22	,	,	PUNCT
cana-2411	120	23	𝔞f2	𝔞f2	VERB
cana-2411	120	24	≤	≤	NUM
cana-2411	120	25	υ	υ	DET
cana-2411	120	26	≤	≤	NUM
cana-2411	120	27	𝔞f3	𝔞f3	NOUN
cana-2411	120	28	0	0	NUM
cana-2411	120	29	,	,	PUNCT
cana-2411	120	30	elsewhere	elsewhere	ADV
cana-2411	120	31	we	we	PRON
cana-2411	120	32	use	use	VERB
cana-2411	120	33	ℱ(ℛ	ℱ(ℛ	PUNCT
cana-2411	120	34	)	)	PUNCT
cana-2411	120	35	to	to	PART
cana-2411	120	36	represent	represent	VERB
cana-2411	120	37	the	the	DET
cana-2411	120	38	set	set	NOUN
cana-2411	120	39	of	of	ADP
cana-2411	120	40	all	all	DET
cana-2411	120	41	triangular	triangular	ADJ
cana-2411	120	42	neutrosophic	neutrosophic	ADJ
cana-2411	120	43	numbers	number	NOUN
cana-2411	120	44	defined	define	VERB
cana-2411	120	45	on	on	ADP
cana-2411	120	46	ℛ.	ℛ.	PROPN
cana-2411	120	47	definition	definition	NOUN
cana-2411	120	48	2.5	2.5	NUM
cana-2411	120	49	the	the	DET
cana-2411	120	50	(	(	PUNCT
cana-2411	120	51	α	α	NOUN
cana-2411	120	52	,	,	PUNCT
cana-2411	120	53	β	β	X
cana-2411	120	54	,	,	PUNCT
cana-2411	120	55	γ)-cut	γ)-cut	VERB
cana-2411	120	56	of	of	ADP
cana-2411	120	57	neutrosophic	neutrosophic	ADJ
cana-2411	120	58	set	set	NOUN
cana-2411	120	59	is	be	AUX
cana-2411	120	60	denoted	denote	VERB
cana-2411	120	61	by	by	ADP
cana-2411	120	62	ℱ(α	ℱ(α	ADP
cana-2411	120	63	,	,	PUNCT
cana-2411	120	64	β	β	X
cana-2411	120	65	,	,	PUNCT
cana-2411	120	66	γ	γ	NOUN
cana-2411	120	67	)	)	PUNCT
cana-2411	120	68	,	,	PUNCT
cana-2411	120	69	where	where	SCONJ
cana-2411	120	70	(	(	PUNCT
cana-2411	120	71	α	α	NOUN
cana-2411	120	72	,	,	PUNCT
cana-2411	120	73	β	β	X
cana-2411	120	74	,	,	PUNCT
cana-2411	120	75	γ	γ	NOUN
cana-2411	120	76	)	)	PUNCT
cana-2411	120	77	∈	∈	NOUN
cana-2411	121	1	[	[	X
cana-2411	121	2	0,1	0,1	NUM
cana-2411	121	3	]	]	PUNCT
cana-2411	121	4	and	and	CCONJ
cana-2411	121	5	are	be	AUX
cana-2411	121	6	fixed	fix	VERB
cana-2411	121	7	numbers	number	NOUN
cana-2411	121	8	,	,	PUNCT
cana-2411	121	9	such	such	ADJ
cana-2411	121	10	that	that	SCONJ
cana-2411	121	11	α+	α+	X
cana-2411	121	12	β+	β+	PUNCT
cana-2411	121	13	γ	γ	X
cana-2411	121	14	≤	≤	ADJ
cana-2411	121	15	3	3	NUM
cana-2411	121	16	and	and	CCONJ
cana-2411	121	17	is	be	AUX
cana-2411	121	18	defined	define	VERB
cana-2411	121	19	as	as	ADP
cana-2411	121	20	ℱ(α	ℱ(α	NOUN
cana-2411	121	21	,	,	PUNCT
cana-2411	121	22	β	β	X
cana-2411	121	23	,	,	PUNCT
cana-2411	121	24	γ	γ	NOUN
cana-2411	121	25	)	)	PUNCT
cana-2411	121	26	=	=	SYM
cana-2411	121	27	(	(	PUNCT
cana-2411	121	28	μ	μ	PROPN
cana-2411	121	29	t	t	PROPN
cana-2411	121	30	(	(	PUNCT
cana-2411	121	31	υ),μ	υ),μ	PROPN
cana-2411	121	32	i	i	PRON
cana-2411	121	33	(	(	PUNCT
cana-2411	121	34	υ),μ	υ),μ	PROPN
cana-2411	121	35	f	f	PROPN
cana-2411	121	36	(	(	PUNCT
cana-2411	121	37	υ	υ	NOUN
cana-2411	121	38	)	)	PUNCT
cana-2411	121	39	)	)	PUNCT
cana-2411	121	40	,	,	PUNCT
cana-2411	121	41	where	where	SCONJ
cana-2411	121	42	υ	υ	PROPN
cana-2411	121	43	∈	∈	PROPN
cana-2411	121	44	y	y	PROPN
cana-2411	121	45	,	,	PUNCT
cana-2411	121	46	μ	μ	PROPN
cana-2411	121	47	t	t	PROPN
cana-2411	121	48	(	(	PUNCT
cana-2411	121	49	υ	υ	NOUN
cana-2411	121	50	)	)	PUNCT
cana-2411	121	51	≥	≥	NOUN
cana-2411	121	52	α	α	PROPN
cana-2411	121	53	,	,	PUNCT
cana-2411	121	54	μ	μ	PROPN
cana-2411	121	55	i	i	PROPN
cana-2411	121	56	(	(	PUNCT
cana-2411	121	57	υ	υ	NOUN
cana-2411	121	58	)	)	PUNCT
cana-2411	121	59	≤	≤	NOUN
cana-2411	121	60	β	β	X
cana-2411	121	61	,	,	PUNCT
cana-2411	121	62	μ	μ	PROPN
cana-2411	121	63	f	f	PROPN
cana-2411	121	64	(	(	PUNCT
cana-2411	121	65	υ	υ	NOUN
cana-2411	121	66	)	)	PUNCT
cana-2411	121	67	≤	≤	NOUN
cana-2411	121	68	γ	γ	PROPN
cana-2411	121	69	.	.	PROPN
cana-2411	121	70	definition	definition	NOUN
cana-2411	121	71	2.6	2.6	NUM
cana-2411	121	72	a	a	DET
cana-2411	121	73	triangular	triangular	NOUN
cana-2411	121	74	neutrosophic	neutrosophic	ADJ
cana-2411	121	75	number	number	NOUN
cana-2411	121	76	�	�	PROPN
cana-2411	121	77	̃	̃	PROPN
cana-2411	121	78	�	�	PROPN
cana-2411	121	79	𝔫	𝔫	NOUN
cana-2411	121	80	can	can	AUX
cana-2411	121	81	also	also	ADV
cana-2411	121	82	be	be	AUX
cana-2411	121	83	represented	represent	VERB
cana-2411	121	84	as	as	ADP
cana-2411	121	85	a	a	DET
cana-2411	121	86	pair	pair	NOUN
cana-2411	121	87	�	�	PROPN
cana-2411	121	88	̃	̃	PROPN
cana-2411	121	89	�	�	PROPN
cana-2411	121	90	t	t	PROPN
cana-2411	121	91	𝔫	𝔫	X
cana-2411	121	92	=	=	PUNCT
cana-2411	121	93	(	(	PUNCT
cana-2411	121	94	𝔞t	𝔞t	ADJ
cana-2411	121	95	;	;	PUNCT
cana-2411	121	96	𝔞t	𝔞t	NOUN
cana-2411	121	97	)	)	PUNCT
cana-2411	121	98	,	,	PUNCT
cana-2411	121	99	�	�	PROPN
cana-2411	121	100	̃	̃	PROPN
cana-2411	121	101	�	�	PROPN
cana-2411	121	102	i	i	PRON
cana-2411	121	103	𝔫	𝔫	NOUN
cana-2411	121	104	=	=	PUNCT
cana-2411	121	105	(	(	PUNCT
cana-2411	121	106	𝔞i	𝔞i	NOUN
cana-2411	121	107	;	;	PUNCT
cana-2411	121	108	𝔞i	𝔞i	X
cana-2411	121	109	)	)	PUNCT
cana-2411	121	110	,	,	PUNCT
cana-2411	121	111	�	�	PROPN
cana-2411	121	112	̃	̃	PROPN
cana-2411	121	113	�	�	PROPN
cana-2411	121	114	f	f	PROPN
cana-2411	121	115	𝔫	𝔫	X
cana-2411	121	116	=	=	PUNCT
cana-2411	121	117	(	(	PUNCT
cana-2411	121	118	𝔞f	𝔞f	NOUN
cana-2411	121	119	;	;	PUNCT
cana-2411	121	120	𝔞f	𝔞f	X
cana-2411	121	121	)	)	PUNCT
cana-2411	121	122	of	of	ADP
cana-2411	121	123	functions	function	NOUN
cana-2411	121	124	𝔞t(r	𝔞t(r	NUM
cana-2411	121	125	)	)	PUNCT
cana-2411	121	126	,	,	PUNCT
cana-2411	121	127	𝔞t(r	𝔞t(r	NUM
cana-2411	121	128	)	)	PUNCT
cana-2411	121	129	,	,	PUNCT
cana-2411	121	130	𝔞i(r	𝔞i(r	ADV
cana-2411	121	131	)	)	PUNCT
cana-2411	121	132	,	,	PUNCT
cana-2411	121	133	𝔞i(r	𝔞i(r	ADV
cana-2411	121	134	)	)	PUNCT
cana-2411	121	135	,	,	PUNCT
cana-2411	121	136	𝔞f(r	𝔞f(r	NUM
cana-2411	121	137	)	)	PUNCT
cana-2411	121	138	,	,	PUNCT
cana-2411	121	139	𝔞f(r	𝔞f(r	NUM
cana-2411	121	140	)	)	PUNCT
cana-2411	121	141	0	0	NUM
cana-2411	122	1	≤	≤	NUM
cana-2411	122	2	r	r	NOUN
cana-2411	122	3	≤	≤	NUM
cana-2411	122	4	1	1	NUM
cana-2411	122	5	which	which	PRON
cana-2411	122	6	satisfy	satisfy	VERB
cana-2411	122	7	the	the	DET
cana-2411	122	8	following	follow	VERB
cana-2411	122	9	requirements	requirement	NOUN
cana-2411	122	10	:	:	PUNCT
cana-2411	122	11	•	•	NUM
cana-2411	122	12	𝔞t(r	𝔞t(r	NUM
cana-2411	122	13	)	)	PUNCT
cana-2411	122	14	is	be	AUX
cana-2411	122	15	a	a	DET
cana-2411	122	16	bounded	bounded	ADJ
cana-2411	122	17	monotonic	monotonic	ADJ
cana-2411	122	18	increasing	increasing	NOUN
cana-2411	122	19	left	leave	VERB
cana-2411	122	20	continuous	continuous	ADJ
cana-2411	122	21	function	function	NOUN
cana-2411	122	22	for	for	ADP
cana-2411	122	23	membership	membership	NOUN
cana-2411	122	24	function	function	NOUN
cana-2411	122	25	.	.	PUNCT
cana-2411	123	1	•	•	NUM
cana-2411	123	2	𝔞t(r	𝔞t(r	NUM
cana-2411	123	3	)	)	PUNCT
cana-2411	123	4	is	be	AUX
cana-2411	123	5	a	a	DET
cana-2411	123	6	bounded	bounded	ADJ
cana-2411	123	7	monotonic	monotonic	ADJ
cana-2411	123	8	decreasing	decrease	VERB
cana-2411	123	9	left	leave	VERB
cana-2411	123	10	continuous	continuous	ADJ
cana-2411	123	11	function	function	NOUN
cana-2411	123	12	for	for	ADP
cana-2411	123	13	membership	membership	NOUN
cana-2411	123	14	function	function	NOUN
cana-2411	123	15	.	.	PUNCT
cana-2411	124	1	•	•	NUM
cana-2411	124	2	𝔞i(r	𝔞i(r	CCONJ
cana-2411	124	3	)	)	PUNCT
cana-2411	124	4	is	be	AUX
cana-2411	124	5	a	a	DET
cana-2411	124	6	bounded	bounded	ADJ
cana-2411	124	7	monotonic	monotonic	ADJ
cana-2411	124	8	increasing	increasing	NOUN
cana-2411	124	9	left	leave	VERB
cana-2411	124	10	continuous	continuous	ADJ
cana-2411	124	11	function	function	NOUN
cana-2411	124	12	for	for	ADP
cana-2411	124	13	indeterminacy	indeterminacy	NOUN
cana-2411	124	14	function	function	NOUN
cana-2411	124	15	.	.	PUNCT
cana-2411	125	1	•	•	NUM
cana-2411	125	2	𝔞i(r	𝔞i(r	CCONJ
cana-2411	125	3	)	)	PUNCT
cana-2411	125	4	is	be	AUX
cana-2411	125	5	a	a	DET
cana-2411	125	6	bounded	bound	VERB
cana-2411	125	7	monotonic	monotonic	ADJ
cana-2411	125	8	decreasing	decrease	VERB
cana-2411	125	9	left	leave	VERB
cana-2411	125	10	continuous	continuous	ADJ
cana-2411	125	11	function	function	NOUN
cana-2411	125	12	for	for	ADP
cana-2411	125	13	indeterminacy	indeterminacy	NOUN
cana-2411	125	14	function	function	NOUN
cana-2411	125	15	.	.	PUNCT
cana-2411	126	1	•	•	NUM
cana-2411	126	2	𝔞f(r	𝔞f(r	NOUN
cana-2411	126	3	)	)	PUNCT
cana-2411	126	4	is	be	AUX
cana-2411	126	5	a	a	DET
cana-2411	126	6	bounded	bounded	ADJ
cana-2411	126	7	monotonic	monotonic	ADJ
cana-2411	126	8	increasing	increasing	NOUN
cana-2411	126	9	left	leave	VERB
cana-2411	126	10	continuous	continuous	ADJ
cana-2411	126	11	function	function	NOUN
cana-2411	126	12	for	for	ADP
cana-2411	126	13	non	non	ADJ
cana-2411	126	14	-	-	ADJ
cana-2411	126	15	membership	membership	ADJ
cana-2411	126	16	function	function	NOUN
cana-2411	126	17	.	.	PUNCT
cana-2411	127	1	•	•	NUM
cana-2411	127	2	𝔞f(r	𝔞f(r	NOUN
cana-2411	127	3	)	)	PUNCT
cana-2411	127	4	is	be	AUX
cana-2411	127	5	a	a	DET
cana-2411	127	6	bounded	bounded	ADJ
cana-2411	127	7	monotonic	monotonic	ADJ
cana-2411	127	8	decreasing	decrease	VERB
cana-2411	127	9	left	leave	VERB
cana-2411	127	10	continuous	continuous	ADJ
cana-2411	127	11	function	function	NOUN
cana-2411	127	12	for	for	ADP
cana-2411	127	13	non	non	ADJ
cana-2411	127	14	-	-	ADJ
cana-2411	127	15	membership	membership	ADJ
cana-2411	127	16	function	function	NOUN
cana-2411	127	17	.	.	PUNCT
cana-2411	128	1	•	•	NUM
cana-2411	128	2	𝔞t(r	𝔞t(r	NUM
cana-2411	128	3	)	)	PUNCT
cana-2411	128	4	≤	≤	NOUN
cana-2411	128	5	𝔞t(r	𝔞t(r	NUM
cana-2411	128	6	)	)	PUNCT
cana-2411	128	7	,	,	PUNCT
cana-2411	128	8	𝔞i(r	𝔞i(r	NOUN
cana-2411	128	9	)	)	PUNCT
cana-2411	128	10	≤	≤	NOUN
cana-2411	128	11	𝔞i(r	𝔞i(r	PRON
cana-2411	128	12	)	)	PUNCT
cana-2411	128	13	,	,	PUNCT
cana-2411	128	14	𝔞f(r	𝔞f(r	NOUN
cana-2411	128	15	)	)	PUNCT
cana-2411	129	1	≤	≤	NUM
cana-2411	130	1	𝔞f(r),0	𝔞f(r),0	PROPN
cana-2411	130	2	≤	≤	NUM
cana-2411	130	3	r	r	NOUN
cana-2411	130	4	≤	≤	NUM
cana-2411	130	5	1	1	NUM
cana-2411	130	6	.	.	PUNCT
cana-2411	130	7	definition	definition	NOUN
cana-2411	130	8	2.7	2.7	NUM
cana-2411	130	9	(	(	PUNCT
cana-2411	130	10	parametric	parametric	ADJ
cana-2411	130	11	form	form	NOUN
cana-2411	130	12	)	)	PUNCT
cana-2411	130	13	let	let	VERB
cana-2411	130	14	�	�	PROPN
cana-2411	130	15	̃	̃	PROPN
cana-2411	130	16	�	�	PROPN
cana-2411	130	17	𝔫	𝔫	NOUN
cana-2411	130	18	=	=	PUNCT
cana-2411	130	19	(	(	PUNCT
cana-2411	130	20	𝔞t	𝔞t	PROPN
cana-2411	130	21	,	,	PUNCT
cana-2411	130	22	𝔞i	𝔞i	PROPN
cana-2411	130	23	,	,	PUNCT
cana-2411	130	24	𝔞f	𝔞f	AUX
cana-2411	130	25	)	)	PUNCT
cana-2411	130	26	be	be	VERB
cana-2411	130	27	a	a	DET
cana-2411	130	28	triangular	triangular	NOUN
cana-2411	130	29	neutrosophic	neutrosophic	ADJ
cana-2411	130	30	number	number	NOUN
cana-2411	130	31	and	and	CCONJ
cana-2411	130	32	𝔞t(r	𝔞t(r	NUM
cana-2411	130	33	)	)	PUNCT
cana-2411	131	1	=	=	SYM
cana-2411	131	2	𝔞t3	𝔞t3	PROPN
cana-2411	132	1	−	−	PROPN
cana-2411	132	2	(	(	PUNCT
cana-2411	132	3	𝔞t3	𝔞t3	X
cana-2411	132	4	−	−	PROPN
cana-2411	132	5	𝔞t2	𝔞t2	PROPN
cana-2411	132	6	)	)	PUNCT
cana-2411	132	7	r	r	NOUN
cana-2411	132	8	,	,	PUNCT
cana-2411	132	9	𝔞t(r	𝔞t(r	NUM
cana-2411	132	10	)	)	PUNCT
cana-2411	132	11	=	=	SYM
cana-2411	133	1	𝔞t1	𝔞t1	PROPN
cana-2411	134	1	+	+	CCONJ
cana-2411	134	2	(	(	PUNCT
cana-2411	134	3	𝔞t2	𝔞t2	PROPN
cana-2411	134	4	−	−	PROPN
cana-2411	134	5	𝔞t1	𝔞t1	NOUN
cana-2411	134	6	)	)	PUNCT
cana-2411	134	7	r	r	NOUN
cana-2411	134	8	,	,	PUNCT
cana-2411	134	9	𝔞i(r	𝔞i(r	PUNCT
cana-2411	134	10	)	)	PUNCT
cana-2411	134	11	=	=	SYM
cana-2411	135	1	𝔞i3	𝔞i3	NOUN
cana-2411	135	2	−	−	NOUN
cana-2411	136	1	(	(	PUNCT
cana-2411	136	2	𝔞i3	𝔞i3	NOUN
cana-2411	136	3	−	−	PROPN
cana-2411	136	4	𝔞i2	𝔞i2	PROPN
cana-2411	136	5	)	)	PUNCT
cana-2411	136	6	r	r	NOUN
cana-2411	136	7	,	,	PUNCT
cana-2411	136	8	𝔞i(r	𝔞i(r	PUNCT
cana-2411	136	9	)	)	PUNCT
cana-2411	136	10	=	=	PUNCT
cana-2411	136	11	𝔞i1	𝔞i1	NOUN
cana-2411	137	1	+	+	CCONJ
cana-2411	137	2	(	(	PUNCT
cana-2411	137	3	𝔞i2	𝔞i2	PROPN
cana-2411	137	4	−	−	PROPN
cana-2411	137	5	𝔞i1	𝔞i1	NOUN
cana-2411	137	6	)	)	PUNCT
cana-2411	137	7	r	r	NOUN
cana-2411	137	8	,	,	PUNCT
cana-2411	137	9	𝔞f(r	𝔞f(r	NUM
cana-2411	137	10	)	)	PUNCT
cana-2411	137	11	=	=	SYM
cana-2411	137	12	𝔞f3	𝔞f3	NOUN
cana-2411	137	13	−	−	PROPN
cana-2411	137	14	(	(	PUNCT
cana-2411	137	15	𝔞f3	𝔞f3	NOUN
cana-2411	137	16	−	−	NOUN
cana-2411	137	17	𝔞f2	𝔞f2	NOUN
cana-2411	137	18	)	)	PUNCT
cana-2411	137	19	r	r	NOUN
cana-2411	137	20	,	,	PUNCT
cana-2411	137	21	𝔞f(r	𝔞f(r	NUM
cana-2411	137	22	)	)	PUNCT
cana-2411	137	23	=	=	SYM
cana-2411	138	1	𝔞f1	𝔞f1	NOUN
cana-2411	138	2	+	+	CCONJ
cana-2411	138	3	(	(	PUNCT
cana-2411	138	4	𝔞f2	𝔞f2	NOUN
cana-2411	138	5	−	−	NOUN
cana-2411	138	6	𝔞f1	𝔞f1	NOUN
cana-2411	138	7	)	)	PUNCT
cana-2411	139	1	r	r	NOUN
cana-2411	139	2	,	,	PUNCT
cana-2411	139	3	r	r	NOUN
cana-2411	139	4	∈	∈	PROPN
cana-2411	140	1	[	[	X
cana-2411	140	2	0,1	0,1	NUM
cana-2411	140	3	]	]	PUNCT
cana-2411	140	4	.	.	PUNCT
cana-2411	141	1	the	the	DET
cana-2411	141	2	parametric	parametric	ADJ
cana-2411	141	3	form	form	NOUN
cana-2411	141	4	of	of	ADP
cana-2411	141	5	the	the	DET
cana-2411	141	6	tnn	tnn	PROPN
cana-2411	141	7	is	be	AUX
cana-2411	141	8	defined	define	VERB
cana-2411	141	9	as	as	ADP
cana-2411	141	10	�	�	PROPN
cana-2411	141	11	̃	̃	PROPN
cana-2411	141	12	�	�	NOUN
cana-2411	141	13	=	=	SYM
cana-2411	141	14	(	(	PUNCT
cana-2411	141	15	〈	〈	ADP
cana-2411	141	16	𝔞t0	𝔞t0	NOUN
cana-2411	141	17	,	,	PUNCT
cana-2411	141	18	𝔞t∗	𝔞t∗	PROPN
cana-2411	141	19	,	,	PUNCT
cana-2411	141	20	𝔞t∗	𝔞t∗	PROPN
cana-2411	141	21	〉	〉	NOUN
cana-2411	141	22	;	;	PUNCT
cana-2411	141	23	〈	〈	PRON
cana-2411	141	24	𝔞i0	𝔞i0	NOUN
cana-2411	141	25	,	,	PUNCT
cana-2411	141	26	𝔞i∗	𝔞i∗	NOUN
cana-2411	141	27	,	,	PUNCT
cana-2411	141	28	𝔞i∗	𝔞i∗	NOUN
cana-2411	141	29	〉	〉	NOUN
cana-2411	141	30	;	;	PUNCT
cana-2411	141	31	〈	〈	NOUN
cana-2411	141	32	𝔞f0	𝔞f0	NOUN
cana-2411	141	33	,	,	PUNCT
cana-2411	141	34	𝔞f∗	𝔞f∗	ADJ
cana-2411	141	35	,	,	PUNCT
cana-2411	141	36	𝔞f∗	𝔞f∗	ADJ
cana-2411	141	37	〉	〉	NOUN
cana-2411	141	38	)	)	PUNCT
cana-2411	141	39	,	,	PUNCT
cana-2411	141	40	where	where	SCONJ
cana-2411	141	41	𝔞t∗	𝔞t∗	PROPN
cana-2411	141	42	=	=	PRON
cana-2411	142	1	𝔞t0	𝔞t0	PROPN
cana-2411	143	1	−	−	NOUN
cana-2411	143	2	𝔞t	𝔞t	NOUN
cana-2411	143	3	and	and	CCONJ
cana-2411	143	4	𝔞t∗	𝔞t∗	PROPN
cana-2411	143	5	=	=	PUNCT
cana-2411	143	6	𝔞t	𝔞t	ADP
cana-2411	143	7	−	−	NOUN
cana-2411	143	8	𝔞t0	𝔞t0	NOUN
cana-2411	143	9	,	,	PUNCT
cana-2411	143	10	𝔞i∗	𝔞i∗	NOUN
cana-2411	143	11	=	=	SYM
cana-2411	143	12	𝔞i0	𝔞i0	NOUN
cana-2411	143	13	−	−	NOUN
cana-2411	143	14	𝔞i	𝔞i	NOUN
cana-2411	143	15	and	and	CCONJ
cana-2411	143	16	𝔞i∗	𝔞i∗	NOUN
cana-2411	144	1	=	=	SYM
cana-2411	144	2	𝔞i	𝔞i	ADP
cana-2411	144	3	−	−	PROPN
cana-2411	144	4	𝔞i0	𝔞i0	PROPN
cana-2411	144	5	,	,	PUNCT
cana-2411	144	6	𝔞f∗	𝔞f∗	ADJ
cana-2411	144	7	=	=	NOUN
cana-2411	144	8	𝔞f0	𝔞f0	NOUN
cana-2411	144	9	−	−	NOUN
cana-2411	144	10	𝔞f	𝔞f	NOUN
cana-2411	144	11	and	and	CCONJ
cana-2411	144	12	𝔞f∗	𝔞f∗	ADJ
cana-2411	144	13	=	=	SYM
cana-2411	144	14	𝔞f	𝔞f	ADP
cana-2411	144	15	−	−	NOUN
cana-2411	144	16	𝔞f0	𝔞f0	NOUN
cana-2411	144	17	are	be	AUX
cana-2411	144	18	the	the	DET
cana-2411	144	19	left	left	ADJ
cana-2411	144	20	and	and	CCONJ
cana-2411	144	21	right	right	ADJ
cana-2411	144	22	fuzziness	fuzziness	NOUN
cana-2411	144	23	index	index	NOUN
cana-2411	144	24	functions	function	NOUN
cana-2411	144	25	respectively	respectively	ADV
cana-2411	144	26	.	.	PUNCT
cana-2411	145	1	the	the	DET
cana-2411	145	2	number	number	NOUN
cana-2411	145	3	𝔞t0	𝔞t0	NOUN
cana-2411	145	4	=	=	SYM
cana-2411	145	5	(	(	PUNCT
cana-2411	145	6	𝔞t(1)+𝔞t(1	𝔞t(1)+𝔞t(1	NOUN
cana-2411	145	7	)	)	PUNCT
cana-2411	145	8	2	2	NUM
cana-2411	145	9	)	)	PUNCT
cana-2411	145	10	,	,	PUNCT
cana-2411	145	11	𝔞i0	𝔞i0	X
cana-2411	145	12	=	=	SYM
cana-2411	145	13	(	(	PUNCT
cana-2411	145	14	𝔞i(1)+𝔞i(1	𝔞i(1)+𝔞i(1	ADJ
cana-2411	145	15	)	)	PUNCT
cana-2411	145	16	2	2	NUM
cana-2411	145	17	)	)	PUNCT
cana-2411	145	18	,	,	PUNCT
cana-2411	145	19	𝔞f0	𝔞f0	NOUN
cana-2411	145	20	=	=	SYM
cana-2411	145	21	(	(	PUNCT
cana-2411	145	22	𝔞f(1)+𝔞f(1	𝔞f(1)+𝔞f(1	PROPN
cana-2411	145	23	)	)	PUNCT
cana-2411	145	24	2	2	NUM
cana-2411	145	25	)	)	PUNCT
cana-2411	145	26	is	be	AUX
cana-2411	145	27	called	call	VERB
cana-2411	145	28	the	the	DET
cana-2411	145	29	location	location	NOUN
cana-2411	145	30	index	index	NOUN
cana-2411	145	31	number	number	NOUN
cana-2411	145	32	.	.	PUNCT
cana-2411	146	1	when	when	SCONJ
cana-2411	146	2	r	r	NOUN
cana-2411	146	3	=	=	SYM
cana-2411	146	4	1	1	NUM
cana-2411	146	5	,	,	PUNCT
cana-2411	146	6	we	we	PRON
cana-2411	146	7	get	get	VERB
cana-2411	146	8	𝔞t0	𝔞t0	NUM
cana-2411	147	1	=	=	SYM
cana-2411	147	2	𝔞t2	𝔞t2	PROPN
cana-2411	147	3	,	,	PUNCT
cana-2411	147	4	𝔞i0	𝔞i0	X
cana-2411	147	5	=	=	SYM
cana-2411	147	6	𝔞i2	𝔞i2	PROPN
cana-2411	147	7	,	,	PUNCT
cana-2411	147	8	𝔞f0	𝔞f0	NOUN
cana-2411	147	9	=	=	SYM
cana-2411	147	10	𝔞f2	𝔞f2	NOUN
cana-2411	147	11	.	.	PUNCT
cana-2411	148	1	2.1	2.1	NUM
cana-2411	148	2	arithmetic	arithmetic	ADJ
cana-2411	148	3	operations	operation	NOUN
cana-2411	148	4	on	on	ADP
cana-2411	148	5	neutrosophic	neutrosophic	ADJ
cana-2411	148	6	numbers	number	NOUN
cana-2411	148	7	we	we	PRON
cana-2411	148	8	develop	develop	VERB
cana-2411	148	9	a	a	DET
cana-2411	148	10	new	new	ADJ
cana-2411	148	11	fuzzy	fuzzy	ADJ
cana-2411	148	12	arithmetic	arithmetic	NOUN
cana-2411	148	13	using	use	VERB
cana-2411	148	14	the	the	DET
cana-2411	148	15	parametric	parametric	ADJ
cana-2411	148	16	form	form	NOUN
cana-2411	148	17	of	of	ADP
cana-2411	148	18	triangular	triangular	ADJ
cana-2411	148	19	neutrosophic	neutrosophic	ADJ
cana-2411	148	20	numbers	number	NOUN
cana-2411	148	21	.	.	PUNCT
cana-2411	149	1	this	this	PRON
cana-2411	149	2	involves	involve	VERB
cana-2411	149	3	expressing	express	VERB
cana-2411	149	4	the	the	DET
cana-2411	149	5	numbers	number	NOUN
cana-2411	149	6	in	in	ADP
cana-2411	149	7	terms	term	NOUN
cana-2411	149	8	of	of	ADP
cana-2411	149	9	location	location	NOUN
cana-2411	149	10	index	index	NOUN
cana-2411	149	11	and	and	CCONJ
cana-2411	149	12	fuzziness	fuzziness	NOUN
cana-2411	149	13	index	index	NOUN
cana-2411	149	14	functions	function	NOUN
cana-2411	149	15	for	for	ADP
cana-2411	149	16	membership	membership	NOUN
cana-2411	149	17	,	,	PUNCT
cana-2411	149	18	indeterminacy	indeterminacy	NOUN
cana-2411	149	19	,	,	PUNCT
cana-2411	149	20	and	and	CCONJ
cana-2411	149	21	non	non	ADJ
cana-2411	149	22	-	-	ADJ
cana-2411	149	23	membership	membership	ADJ
cana-2411	149	24	functions	function	NOUN
cana-2411	149	25	.	.	PUNCT
cana-2411	150	1	we	we	PRON
cana-2411	150	2	propose	propose	VERB
cana-2411	150	3	a	a	DET
cana-2411	150	4	new	new	ADJ
cana-2411	150	5	neutrosophic	neutrosophic	ADJ
cana-2411	150	6	arithmetic	arithmetic	ADJ
cana-2411	150	7	operation	operation	NOUN
cana-2411	150	8	,	,	PUNCT
cana-2411	150	9	where	where	SCONJ
cana-2411	150	10	the	the	DET
cana-2411	150	11	lattice	lattice	NOUN
cana-2411	150	12	rule	rule	NOUN
cana-2411	150	13	,	,	PUNCT
cana-2411	150	14	which	which	PRON
cana-2411	150	15	involves	involve	VERB
cana-2411	150	16	the	the	DET
cana-2411	150	17	least	least	ADJ
cana-2411	150	18	upper	upper	ADJ
cana-2411	150	19	bound	bind	VERB
cana-2411	150	20	and	and	CCONJ
cana-2411	150	21	greatest	great	ADJ
cana-2411	150	22	lower	lower	ADV
cana-2411	150	23	bound	bind	VERB
cana-2411	150	24	in	in	ADP
cana-2411	150	25	the	the	DET
cana-2411	150	26	lattice	lattice	PROPN
cana-2411	150	27	l	l	PROPN
cana-2411	150	28	,	,	PUNCT
cana-2411	150	29	defines	define	VERB
cana-2411	150	30	the	the	DET
cana-2411	150	31	fuzziness	fuzziness	NOUN
cana-2411	150	32	index	index	NOUN
cana-2411	150	33	functions	function	NOUN
cana-2411	150	34	and	and	CCONJ
cana-2411	150	35	the	the	DET
cana-2411	150	36	location	location	NOUN
cana-2411	150	37	index	index	NOUN
cana-2411	150	38	number	number	NOUN
cana-2411	150	39	corresponds	correspond	VERB
cana-2411	150	40	to	to	ADP
cana-2411	150	41	standard	standard	ADJ
cana-2411	150	42	arithmetic	arithmetic	ADJ
cana-2411	150	43	.	.	PUNCT
cana-2411	151	1	that	that	PRON
cana-2411	151	2	is	be	AUX
cana-2411	151	3	for	for	ADP
cana-2411	151	4	𝔞	𝔞	PROPN
cana-2411	151	5	,	,	PUNCT
cana-2411	151	6	𝔟	𝔟	PROPN
cana-2411	151	7	∈	∈	PROPN
cana-2411	151	8	l	l	NOUN
cana-2411	151	9	,	,	PUNCT
cana-2411	151	10	𝔞	𝔞	PROPN
cana-2411	151	11	∨	∨	NUM
cana-2411	151	12	𝔟	𝔟	X
cana-2411	151	13	=	=	PUNCT
cana-2411	151	14	max{𝔞	max{𝔞	NOUN
cana-2411	151	15	,	,	PUNCT
cana-2411	151	16	𝔟	𝔟	PRON
cana-2411	151	17	}	}	PUNCT
cana-2411	151	18	and	and	CCONJ
cana-2411	151	19	𝔞	𝔞	PROPN
cana-2411	151	20	∧	∧	NOUN
cana-2411	151	21	𝔟	𝔟	X
cana-2411	151	22	=	=	SYM
cana-2411	151	23	min{𝔞	min{𝔞	PROPN
cana-2411	151	24	,	,	PUNCT
cana-2411	151	25	𝔟	𝔟	PRON
cana-2411	151	26	}	}	PUNCT
cana-2411	151	27	.	.	PUNCT
cana-2411	152	1	for	for	SCONJ
cana-2411	152	2	communications	communication	NOUN
cana-2411	152	3	on	on	ADP
cana-2411	152	4	applied	apply	VERB
cana-2411	152	5	nonlinear	nonlinear	ADJ
cana-2411	152	6	analysis	analysis	NOUN
cana-2411	152	7	issn	issn	NOUN
cana-2411	152	8	:	:	PUNCT
cana-2411	152	9	1074	1074	NUM
cana-2411	152	10	-	-	PUNCT
cana-2411	152	11	133x	133x	NUM
cana-2411	152	12	vol	vol	NOUN
cana-2411	152	13	32	32	NUM
cana-2411	152	14	no	no	NOUN
cana-2411	152	15	.	.	PUNCT
cana-2411	153	1	2s	2s	NUM
cana-2411	153	2	(	(	PUNCT
cana-2411	153	3	2025	2025	NUM
cana-2411	153	4	)	)	PUNCT
cana-2411	153	5	371	371	NUM
cana-2411	153	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2411	153	7	any	any	DET
cana-2411	153	8	two	two	NUM
cana-2411	153	9	fuzzy	fuzzy	ADJ
cana-2411	153	10	numbers	number	NOUN
cana-2411	153	11	�	�	PROPN
cana-2411	153	12	̃	̃	PROPN
cana-2411	153	13	�	�	PROPN
cana-2411	153	14	𝔫	𝔫	NOUN
cana-2411	153	15	=	=	PUNCT
cana-2411	153	16	(	(	PUNCT
cana-2411	153	17	〈	〈	NOUN
cana-2411	153	18	𝔞t0	𝔞t0	NOUN
cana-2411	153	19	,	,	PUNCT
cana-2411	153	20	𝔞t∗	𝔞t∗	PROPN
cana-2411	153	21	,	,	PUNCT
cana-2411	153	22	𝔞t∗	𝔞t∗	PROPN
cana-2411	153	23	〉	〉	NOUN
cana-2411	153	24	;	;	PUNCT
cana-2411	153	25	〈	〈	PRON
cana-2411	153	26	𝔞i0	𝔞i0	NOUN
cana-2411	153	27	,	,	PUNCT
cana-2411	153	28	𝔞i∗	𝔞i∗	NOUN
cana-2411	153	29	,	,	PUNCT
cana-2411	153	30	𝔞i∗	𝔞i∗	NOUN
cana-2411	153	31	〉	〉	NOUN
cana-2411	153	32	;	;	PUNCT
cana-2411	153	33	〈	〈	NOUN
cana-2411	153	34	𝔞f0	𝔞f0	NOUN
cana-2411	153	35	,	,	PUNCT
cana-2411	153	36	𝔞f∗	𝔞f∗	ADJ
cana-2411	153	37	,	,	PUNCT
cana-2411	153	38	𝔞f∗	𝔞f∗	ADJ
cana-2411	153	39	〉	〉	NOUN
cana-2411	153	40	)	)	PUNCT
cana-2411	153	41	,	,	PUNCT
cana-2411	153	42	ℬ̃	ℬ̃	NOUN
cana-2411	153	43	𝔫	𝔫	NOUN
cana-2411	153	44	=	=	SYM
cana-2411	153	45	(	(	PUNCT
cana-2411	153	46	〈	〈	ADP
cana-2411	153	47	𝔟t0	𝔟t0	NOUN
cana-2411	153	48	,	,	PUNCT
cana-2411	153	49	𝔟t∗	𝔟t∗	ADJ
cana-2411	153	50	,	,	PUNCT
cana-2411	153	51	𝔟t∗	𝔟t∗	ADJ
cana-2411	153	52	〉	〉	NOUN
cana-2411	153	53	;	;	PUNCT
cana-2411	153	54	〈	〈	NOUN
cana-2411	153	55	𝔟i0	𝔟i0	NOUN
cana-2411	153	56	,	,	PUNCT
cana-2411	153	57	𝔟i∗	𝔟i∗	NOUN
cana-2411	153	58	,	,	PUNCT
cana-2411	153	59	𝔟i∗	𝔟i∗	ADJ
cana-2411	153	60	〉	〉	NOUN
cana-2411	153	61	;	;	PUNCT
cana-2411	153	62	〈	〈	NOUN
cana-2411	153	63	𝔟f0	𝔟f0	NOUN
cana-2411	153	64	,	,	PUNCT
cana-2411	153	65	𝔟f∗	𝔟f∗	ADJ
cana-2411	153	66	,	,	PUNCT
cana-2411	153	67	𝔟f∗	𝔟f∗	ADJ
cana-2411	153	68	〉	〉	NOUN
cana-2411	153	69	)	)	PUNCT
cana-2411	153	70	the	the	DET
cana-2411	153	71	arithmetic	arithmetic	ADJ
cana-2411	153	72	operations	operation	NOUN
cana-2411	153	73	are	be	AUX
cana-2411	153	74	defined	define	VERB
cana-2411	153	75	as	as	ADP
cana-2411	153	76	�	�	PROPN
cana-2411	153	77	̃	̃	PROPN
cana-2411	153	78	�	�	PROPN
cana-2411	153	79	𝔫	𝔫	NOUN
cana-2411	153	80	∗	∗	NOUN
cana-2411	153	81	ℬ̃	ℬ̃	PROPN
cana-2411	153	82	𝔫	𝔫	NOUN
cana-2411	153	83	=	=	SYM
cana-2411	153	84	(	(	PUNCT
cana-2411	153	85	〈	〈	NOUN
cana-2411	153	86	𝔞t0	𝔞t0	NOUN
cana-2411	153	87	,	,	PUNCT
cana-2411	153	88	𝔞t∗	𝔞t∗	PROPN
cana-2411	153	89	,	,	PUNCT
cana-2411	153	90	𝔞t∗	𝔞t∗	PROPN
cana-2411	153	91	〉	〉	NOUN
cana-2411	153	92	;	;	PUNCT
cana-2411	153	93	〈	〈	PRON
cana-2411	153	94	𝔞i0	𝔞i0	NOUN
cana-2411	153	95	,	,	PUNCT
cana-2411	153	96	𝔞i∗	𝔞i∗	NOUN
cana-2411	153	97	,	,	PUNCT
cana-2411	153	98	𝔞i∗	𝔞i∗	NOUN
cana-2411	153	99	〉	〉	NOUN
cana-2411	153	100	;	;	PUNCT
cana-2411	153	101	〈	〈	NOUN
cana-2411	153	102	𝔞f0	𝔞f0	NOUN
cana-2411	153	103	,	,	PUNCT
cana-2411	153	104	𝔞f∗	𝔞f∗	ADJ
cana-2411	153	105	,	,	PUNCT
cana-2411	153	106	𝔞f∗	𝔞f∗	ADJ
cana-2411	153	107	〉	〉	NOUN
cana-2411	153	108	)	)	PUNCT
cana-2411	153	109	∗	∗	NOUN
cana-2411	153	110	(	(	PUNCT
cana-2411	153	111	〈	〈	ADP
cana-2411	153	112	𝔟t0	𝔟t0	NOUN
cana-2411	153	113	,	,	PUNCT
cana-2411	153	114	𝔟t∗	𝔟t∗	ADJ
cana-2411	153	115	,	,	PUNCT
cana-2411	153	116	𝔟t∗	𝔟t∗	ADJ
cana-2411	153	117	〉	〉	NOUN
cana-2411	153	118	;	;	PUNCT
cana-2411	153	119	〈	〈	NOUN
cana-2411	153	120	𝔟i0	𝔟i0	NOUN
cana-2411	153	121	,	,	PUNCT
cana-2411	153	122	𝔟i∗	𝔟i∗	NOUN
cana-2411	153	123	,	,	PUNCT
cana-2411	153	124	𝔟i∗	𝔟i∗	ADJ
cana-2411	153	125	〉	〉	NOUN
cana-2411	153	126	;	;	PUNCT
cana-2411	153	127	〈	〈	NOUN
cana-2411	153	128	𝔟f0	𝔟f0	NOUN
cana-2411	153	129	,	,	PUNCT
cana-2411	153	130	𝔟f∗	𝔟f∗	ADJ
cana-2411	153	131	,	,	PUNCT
cana-2411	153	132	𝔟f∗	𝔟f∗	ADJ
cana-2411	153	133	〉	〉	NOUN
cana-2411	153	134	)	)	PUNCT
cana-2411	153	135	=	=	PRON
cana-2411	153	136	(	(	PUNCT
cana-2411	153	137	〈	〈	NOUN
cana-2411	153	138	𝔞t0	𝔞t0	PROPN
cana-2411	153	139	∗	∗	NOUN
cana-2411	153	140	𝔟t0	𝔟t0	PROPN
cana-2411	153	141	,	,	PUNCT
cana-2411	153	142	𝔞t∗	𝔞t∗	PROPN
cana-2411	153	143	∨	∨	NUM
cana-2411	153	144	𝔟t∗	𝔟t∗	X
cana-2411	153	145	,	,	PUNCT
cana-2411	153	146	𝔞t∗	𝔞t∗	PROPN
cana-2411	153	147	∨	∨	NUM
cana-2411	153	148	𝔟t∗	𝔟t∗	NOUN
cana-2411	153	149	〉	〉	NOUN
cana-2411	153	150	,	,	PUNCT
cana-2411	153	151	〈	〈	ADP
cana-2411	153	152	𝔞i0	𝔞i0	NOUN
cana-2411	153	153	∗	∗	NOUN
cana-2411	153	154	𝔟i0	𝔟i0	NOUN
cana-2411	153	155	,	,	PUNCT
cana-2411	153	156	𝔞i∗	𝔞i∗	NOUN
cana-2411	153	157	∨	∨	NOUN
cana-2411	153	158	𝔟i∗	𝔟i∗	NOUN
cana-2411	153	159	,	,	PUNCT
cana-2411	153	160	𝔞i∗	𝔞i∗	VERB
cana-2411	153	161	∨	∨	NOUN
cana-2411	153	162	𝔟i∗	𝔟i∗	ADJ
cana-2411	153	163	〉	〉	NOUN
cana-2411	153	164	,	,	PUNCT
cana-2411	153	165	〈	〈	NOUN
cana-2411	153	166	𝔞f0	𝔞f0	NOUN
cana-2411	153	167	∗	∗	NOUN
cana-2411	153	168	𝔟f0	𝔟f0	ADV
cana-2411	153	169	,	,	PUNCT
cana-2411	153	170	𝔞f∗	𝔞f∗	ADJ
cana-2411	153	171	∨	∨	NUM
cana-2411	153	172	𝔟f∗	𝔟f∗	NOUN
cana-2411	153	173	,	,	PUNCT
cana-2411	153	174	𝔞f∗	𝔞f∗	ADJ
cana-2411	153	175	∨	∨	NUM
cana-2411	153	176	𝔟f∗	𝔟f∗	ADJ
cana-2411	153	177	〉	〉	NOUN
cana-2411	153	178	)	)	PUNCT
cana-2411	153	179	in	in	ADP
cana-2411	153	180	particular	particular	ADJ
cana-2411	153	181	for	for	ADP
cana-2411	153	182	�	�	PROPN
cana-2411	153	183	̃	̃	PROPN
cana-2411	153	184	�	�	PROPN
cana-2411	153	185	𝔫	𝔫	NOUN
cana-2411	153	186	=	=	PUNCT
cana-2411	153	187	(	(	PUNCT
cana-2411	153	188	〈	〈	NOUN
cana-2411	153	189	𝔞t0	𝔞t0	NOUN
cana-2411	153	190	,	,	PUNCT
cana-2411	153	191	𝔞t∗	𝔞t∗	PROPN
cana-2411	153	192	,	,	PUNCT
cana-2411	153	193	𝔞t∗	𝔞t∗	PROPN
cana-2411	153	194	〉	〉	NOUN
cana-2411	153	195	;	;	PUNCT
cana-2411	153	196	〈	〈	PRON
cana-2411	153	197	𝔞i0	𝔞i0	NOUN
cana-2411	153	198	,	,	PUNCT
cana-2411	153	199	𝔞i∗	𝔞i∗	NOUN
cana-2411	153	200	,	,	PUNCT
cana-2411	153	201	𝔞i∗	𝔞i∗	NOUN
cana-2411	153	202	〉	〉	NOUN
cana-2411	153	203	;	;	PUNCT
cana-2411	153	204	〈	〈	NOUN
cana-2411	153	205	𝔞f0	𝔞f0	NOUN
cana-2411	153	206	,	,	PUNCT
cana-2411	153	207	𝔞f∗	𝔞f∗	ADJ
cana-2411	153	208	,	,	PUNCT
cana-2411	153	209	𝔞f∗	𝔞f∗	ADJ
cana-2411	153	210	〉	〉	NOUN
cana-2411	153	211	)	)	PUNCT
cana-2411	153	212	,	,	PUNCT
cana-2411	153	213	ℬ̃	ℬ̃	NOUN
cana-2411	153	214	𝔫	𝔫	NOUN
cana-2411	153	215	=	=	SYM
cana-2411	153	216	(	(	PUNCT
cana-2411	153	217	〈	〈	ADP
cana-2411	153	218	𝔟t0	𝔟t0	NOUN
cana-2411	153	219	,	,	PUNCT
cana-2411	153	220	𝔟t∗	𝔟t∗	ADJ
cana-2411	153	221	,	,	PUNCT
cana-2411	153	222	𝔟t∗	𝔟t∗	ADJ
cana-2411	153	223	〉	〉	NOUN
cana-2411	153	224	;	;	PUNCT
cana-2411	153	225	〈	〈	NOUN
cana-2411	153	226	𝔟i0	𝔟i0	NOUN
cana-2411	153	227	,	,	PUNCT
cana-2411	153	228	𝔟i∗	𝔟i∗	NOUN
cana-2411	153	229	,	,	PUNCT
cana-2411	153	230	𝔟i∗	𝔟i∗	ADJ
cana-2411	153	231	〉	〉	NOUN
cana-2411	153	232	;	;	PUNCT
cana-2411	153	233	〈	〈	NOUN
cana-2411	153	234	𝔟f0	𝔟f0	NOUN
cana-2411	153	235	,	,	PUNCT
cana-2411	153	236	𝔟f∗	𝔟f∗	ADJ
cana-2411	153	237	,	,	PUNCT
cana-2411	153	238	𝔟f∗	𝔟f∗	ADJ
cana-2411	153	239	〉	〉	NOUN
cana-2411	153	240	)	)	PUNCT
cana-2411	153	241	∈	∈	PROPN
cana-2411	153	242	ℱ(ℛ	ℱ(ℛ	NUM
cana-2411	153	243	)	)	PUNCT
cana-2411	153	244	,	,	PUNCT
cana-2411	153	245	we	we	PRON
cana-2411	153	246	have	have	VERB
cana-2411	153	247	addition	addition	NOUN
cana-2411	153	248	:	:	PUNCT
cana-2411	153	249	�	�	PROPN
cana-2411	153	250	̃	̃	PROPN
cana-2411	153	251	�	�	PROPN
cana-2411	153	252	𝔫	𝔫	NOUN
cana-2411	153	253	∗	∗	NOUN
cana-2411	153	254	ℬ̃	ℬ̃	PROPN
cana-2411	153	255	𝔫	𝔫	NOUN
cana-2411	153	256	=	=	SYM
cana-2411	153	257	(	(	PUNCT
cana-2411	153	258	〈	〈	NOUN
cana-2411	153	259	𝔞t0	𝔞t0	NOUN
cana-2411	153	260	,	,	PUNCT
cana-2411	153	261	𝔞t∗	𝔞t∗	PROPN
cana-2411	153	262	,	,	PUNCT
cana-2411	153	263	𝔞t∗	𝔞t∗	PROPN
cana-2411	153	264	〉	〉	NOUN
cana-2411	153	265	;	;	PUNCT
cana-2411	153	266	〈	〈	PRON
cana-2411	153	267	𝔞i0	𝔞i0	NOUN
cana-2411	153	268	,	,	PUNCT
cana-2411	153	269	𝔞i∗	𝔞i∗	NOUN
cana-2411	153	270	,	,	PUNCT
cana-2411	153	271	𝔞i∗	𝔞i∗	NOUN
cana-2411	153	272	〉	〉	NOUN
cana-2411	153	273	;	;	PUNCT
cana-2411	153	274	〈	〈	NOUN
cana-2411	153	275	𝔞f0	𝔞f0	NOUN
cana-2411	153	276	,	,	PUNCT
cana-2411	153	277	𝔞f∗	𝔞f∗	ADJ
cana-2411	153	278	,	,	PUNCT
cana-2411	153	279	𝔞f∗	𝔞f∗	ADJ
cana-2411	153	280	〉	〉	NOUN
cana-2411	153	281	)	)	PUNCT
cana-2411	153	282	+	+	CCONJ
cana-2411	153	283	(	(	PUNCT
cana-2411	153	284	〈	〈	ADP
cana-2411	153	285	𝔟t0	𝔟t0	NOUN
cana-2411	153	286	,	,	PUNCT
cana-2411	153	287	𝔟t∗	𝔟t∗	ADJ
cana-2411	153	288	,	,	PUNCT
cana-2411	153	289	𝔟t∗	𝔟t∗	ADJ
cana-2411	153	290	〉	〉	NOUN
cana-2411	153	291	;	;	PUNCT
cana-2411	153	292	〈	〈	NOUN
cana-2411	153	293	𝔟i0	𝔟i0	NOUN
cana-2411	153	294	,	,	PUNCT
cana-2411	153	295	𝔟i∗	𝔟i∗	NOUN
cana-2411	153	296	,	,	PUNCT
cana-2411	153	297	𝔟i∗	𝔟i∗	ADJ
cana-2411	153	298	〉	〉	NOUN
cana-2411	153	299	;	;	PUNCT
cana-2411	153	300	〈	〈	NOUN
cana-2411	153	301	𝔟f0	𝔟f0	NOUN
cana-2411	153	302	,	,	PUNCT
cana-2411	153	303	𝔟f∗	𝔟f∗	ADJ
cana-2411	153	304	,	,	PUNCT
cana-2411	153	305	𝔟f∗	𝔟f∗	ADJ
cana-2411	153	306	〉	〉	NOUN
cana-2411	153	307	)	)	PUNCT
cana-2411	153	308	=	=	PRON
cana-2411	153	309	(	(	PUNCT
cana-2411	153	310	〈	〈	NOUN
cana-2411	153	311	𝔞t0	𝔞t0	NOUN
cana-2411	153	312	+	+	CCONJ
cana-2411	153	313	𝔟t0	𝔟t0	VERB
cana-2411	153	314	,	,	PUNCT
cana-2411	153	315	𝔞t∗	𝔞t∗	PROPN
cana-2411	153	316	∨	∨	NUM
cana-2411	153	317	𝔟t∗	𝔟t∗	X
cana-2411	153	318	,	,	PUNCT
cana-2411	153	319	𝔞t∗	𝔞t∗	PROPN
cana-2411	153	320	∨	∨	NUM
cana-2411	153	321	𝔟t∗	𝔟t∗	NOUN
cana-2411	153	322	〉	〉	NOUN
cana-2411	153	323	,	,	PUNCT
cana-2411	153	324	〈	〈	NOUN
cana-2411	153	325	𝔞i0	𝔞i0	NOUN
cana-2411	153	326	+	+	CCONJ
cana-2411	153	327	𝔟i0	𝔟i0	NOUN
cana-2411	153	328	,	,	PUNCT
cana-2411	153	329	𝔞i∗	𝔞i∗	NOUN
cana-2411	153	330	∨	∨	NOUN
cana-2411	153	331	𝔟i∗	𝔟i∗	NOUN
cana-2411	153	332	,	,	PUNCT
cana-2411	153	333	𝔞i∗	𝔞i∗	VERB
cana-2411	153	334	∨	∨	NOUN
cana-2411	153	335	𝔟i∗	𝔟i∗	ADJ
cana-2411	153	336	〉	〉	NOUN
cana-2411	153	337	,	,	PUNCT
cana-2411	153	338	〈	〈	NOUN
cana-2411	153	339	𝔞f0	𝔞f0	NOUN
cana-2411	153	340	+	+	CCONJ
cana-2411	153	341	𝔟f0	𝔟f0	ADV
cana-2411	153	342	,	,	PUNCT
cana-2411	153	343	𝔞f∗	𝔞f∗	ADJ
cana-2411	153	344	∨	∨	NUM
cana-2411	153	345	𝔟f∗	𝔟f∗	NOUN
cana-2411	153	346	,	,	PUNCT
cana-2411	153	347	𝔞f∗	𝔞f∗	ADJ
cana-2411	153	348	∨	∨	NUM
cana-2411	153	349	𝔟f∗	𝔟f∗	ADJ
cana-2411	153	350	〉	〉	NOUN
cana-2411	153	351	)	)	PUNCT
cana-2411	153	352	subtraction	subtraction	NOUN
cana-2411	153	353	:	:	PUNCT
cana-2411	153	354	�	�	PROPN
cana-2411	153	355	̃	̃	PROPN
cana-2411	153	356	�	�	PROPN
cana-2411	153	357	𝔫	𝔫	NOUN
cana-2411	153	358	∗	∗	NOUN
cana-2411	153	359	ℬ̃	ℬ̃	PROPN
cana-2411	153	360	𝔫	𝔫	NOUN
cana-2411	153	361	=	=	SYM
cana-2411	153	362	(	(	PUNCT
cana-2411	153	363	〈	〈	NOUN
cana-2411	153	364	𝔞t0	𝔞t0	NOUN
cana-2411	153	365	,	,	PUNCT
cana-2411	153	366	𝔞t∗	𝔞t∗	PROPN
cana-2411	153	367	,	,	PUNCT
cana-2411	153	368	𝔞t∗	𝔞t∗	PROPN
cana-2411	153	369	〉	〉	NOUN
cana-2411	153	370	;	;	PUNCT
cana-2411	153	371	〈	〈	PRON
cana-2411	153	372	𝔞i0	𝔞i0	NOUN
cana-2411	153	373	,	,	PUNCT
cana-2411	153	374	𝔞i∗	𝔞i∗	NOUN
cana-2411	153	375	,	,	PUNCT
cana-2411	153	376	𝔞i∗	𝔞i∗	NOUN
cana-2411	153	377	〉	〉	NOUN
cana-2411	153	378	;	;	PUNCT
cana-2411	153	379	〈	〈	NOUN
cana-2411	153	380	𝔞f0	𝔞f0	NOUN
cana-2411	153	381	,	,	PUNCT
cana-2411	153	382	𝔞f∗	𝔞f∗	ADJ
cana-2411	153	383	,	,	PUNCT
cana-2411	153	384	𝔞f∗	𝔞f∗	ADJ
cana-2411	153	385	〉	〉	NOUN
cana-2411	153	386	)	)	PUNCT
cana-2411	154	1	−	−	PROPN
cana-2411	154	2	(	(	PUNCT
cana-2411	154	3	〈	〈	ADP
cana-2411	154	4	𝔟t0	𝔟t0	NOUN
cana-2411	154	5	,	,	PUNCT
cana-2411	154	6	𝔟t∗	𝔟t∗	ADJ
cana-2411	154	7	,	,	PUNCT
cana-2411	154	8	𝔟t∗	𝔟t∗	ADJ
cana-2411	154	9	〉	〉	NOUN
cana-2411	154	10	;	;	PUNCT
cana-2411	154	11	〈	〈	NOUN
cana-2411	154	12	𝔟i0	𝔟i0	NOUN
cana-2411	154	13	,	,	PUNCT
cana-2411	154	14	𝔟i∗	𝔟i∗	NOUN
cana-2411	154	15	,	,	PUNCT
cana-2411	154	16	𝔟i∗	𝔟i∗	ADJ
cana-2411	154	17	〉	〉	NOUN
cana-2411	154	18	;	;	PUNCT
cana-2411	154	19	〈	〈	NOUN
cana-2411	154	20	𝔟f0	𝔟f0	NOUN
cana-2411	154	21	,	,	PUNCT
cana-2411	154	22	𝔟f∗	𝔟f∗	ADJ
cana-2411	154	23	,	,	PUNCT
cana-2411	154	24	𝔟f∗	𝔟f∗	ADJ
cana-2411	154	25	〉	〉	NOUN
cana-2411	154	26	)	)	PUNCT
cana-2411	154	27	=	=	PRON
cana-2411	155	1	(	(	PUNCT
cana-2411	155	2	〈	〈	NOUN
cana-2411	155	3	𝔞t0	𝔞t0	NOUN
cana-2411	155	4	−	−	PROPN
cana-2411	156	1	𝔟t0	𝔟t0	PROPN
cana-2411	156	2	,	,	PUNCT
cana-2411	156	3	𝔞t∗	𝔞t∗	PROPN
cana-2411	156	4	∨	∨	NUM
cana-2411	156	5	𝔟t∗	𝔟t∗	X
cana-2411	156	6	,	,	PUNCT
cana-2411	156	7	𝔞t∗	𝔞t∗	PROPN
cana-2411	156	8	∨	∨	NUM
cana-2411	156	9	𝔟t∗	𝔟t∗	NOUN
cana-2411	156	10	〉	〉	NOUN
cana-2411	156	11	,	,	PUNCT
cana-2411	156	12	〈	〈	NOUN
cana-2411	156	13	𝔞i0	𝔞i0	NOUN
cana-2411	156	14	−	−	NOUN
cana-2411	156	15	𝔟i0	𝔟i0	NOUN
cana-2411	156	16	,	,	PUNCT
cana-2411	156	17	𝔞i∗	𝔞i∗	NOUN
cana-2411	156	18	∨	∨	NOUN
cana-2411	156	19	𝔟i∗	𝔟i∗	NOUN
cana-2411	156	20	,	,	PUNCT
cana-2411	156	21	𝔞i∗	𝔞i∗	VERB
cana-2411	156	22	∨	∨	NOUN
cana-2411	156	23	𝔟i∗	𝔟i∗	ADJ
cana-2411	156	24	〉	〉	NOUN
cana-2411	156	25	,	,	PUNCT
cana-2411	156	26	〈	〈	NOUN
cana-2411	156	27	𝔞f0	𝔞f0	NOUN
cana-2411	156	28	−	−	NOUN
cana-2411	156	29	𝔟f0	𝔟f0	ADV
cana-2411	156	30	,	,	PUNCT
cana-2411	156	31	𝔞f∗	𝔞f∗	ADJ
cana-2411	156	32	∨	∨	NUM
cana-2411	156	33	𝔟f∗	𝔟f∗	NOUN
cana-2411	156	34	,	,	PUNCT
cana-2411	156	35	𝔞f∗	𝔞f∗	ADJ
cana-2411	156	36	∨	∨	NUM
cana-2411	156	37	𝔟f∗	𝔟f∗	ADJ
cana-2411	156	38	〉	〉	NOUN
cana-2411	156	39	)	)	PUNCT
cana-2411	156	40	multiplication	multiplication	NOUN
cana-2411	156	41	:	:	PUNCT
cana-2411	156	42	�	�	PROPN
cana-2411	156	43	̃	̃	PROPN
cana-2411	156	44	�	�	PROPN
cana-2411	156	45	𝔫	𝔫	NOUN
cana-2411	156	46	∗	∗	NOUN
cana-2411	156	47	ℬ̃	ℬ̃	PROPN
cana-2411	156	48	𝔫	𝔫	NOUN
cana-2411	156	49	=	=	SYM
cana-2411	156	50	(	(	PUNCT
cana-2411	156	51	〈	〈	NOUN
cana-2411	156	52	𝔞t0	𝔞t0	NOUN
cana-2411	156	53	,	,	PUNCT
cana-2411	156	54	𝔞t∗	𝔞t∗	PROPN
cana-2411	156	55	,	,	PUNCT
cana-2411	156	56	𝔞t∗	𝔞t∗	PROPN
cana-2411	156	57	〉	〉	NOUN
cana-2411	156	58	;	;	PUNCT
cana-2411	156	59	〈	〈	PRON
cana-2411	156	60	𝔞i0	𝔞i0	NOUN
cana-2411	156	61	,	,	PUNCT
cana-2411	156	62	𝔞i∗	𝔞i∗	NOUN
cana-2411	156	63	,	,	PUNCT
cana-2411	156	64	𝔞i∗	𝔞i∗	NOUN
cana-2411	156	65	〉	〉	NOUN
cana-2411	156	66	;	;	PUNCT
cana-2411	156	67	〈	〈	NOUN
cana-2411	156	68	𝔞f0	𝔞f0	NOUN
cana-2411	156	69	,	,	PUNCT
cana-2411	156	70	𝔞f∗	𝔞f∗	ADJ
cana-2411	156	71	,	,	PUNCT
cana-2411	156	72	𝔞f∗	𝔞f∗	ADJ
cana-2411	156	73	〉	〉	NOUN
cana-2411	156	74	)	)	PUNCT
cana-2411	156	75	×	×	NOUN
cana-2411	156	76	(	(	PUNCT
cana-2411	156	77	〈	〈	ADP
cana-2411	156	78	𝔟t0	𝔟t0	NOUN
cana-2411	156	79	,	,	PUNCT
cana-2411	156	80	𝔟t∗	𝔟t∗	ADJ
cana-2411	156	81	,	,	PUNCT
cana-2411	156	82	𝔟t∗	𝔟t∗	ADJ
cana-2411	156	83	〉	〉	NOUN
cana-2411	156	84	;	;	PUNCT
cana-2411	156	85	〈	〈	NOUN
cana-2411	156	86	𝔟i0	𝔟i0	NOUN
cana-2411	156	87	,	,	PUNCT
cana-2411	156	88	𝔟i∗	𝔟i∗	NOUN
cana-2411	156	89	,	,	PUNCT
cana-2411	156	90	𝔟i∗	𝔟i∗	ADJ
cana-2411	156	91	〉	〉	NOUN
cana-2411	156	92	;	;	PUNCT
cana-2411	156	93	〈	〈	NOUN
cana-2411	156	94	𝔟f0	𝔟f0	NOUN
cana-2411	156	95	,	,	PUNCT
cana-2411	156	96	𝔟f∗	𝔟f∗	ADJ
cana-2411	156	97	,	,	PUNCT
cana-2411	156	98	𝔟f∗	𝔟f∗	ADJ
cana-2411	156	99	〉	〉	NOUN
cana-2411	156	100	)	)	PUNCT
cana-2411	156	101	=	=	PRON
cana-2411	156	102	(	(	PUNCT
cana-2411	156	103	〈	〈	NOUN
cana-2411	156	104	𝔞t0	𝔞t0	PROPN
cana-2411	156	105	×	×	NOUN
cana-2411	156	106	𝔟t0	𝔟t0	INTJ
cana-2411	156	107	,	,	PUNCT
cana-2411	156	108	𝔞t∗	𝔞t∗	PROPN
cana-2411	156	109	∨	∨	NUM
cana-2411	156	110	𝔟t∗	𝔟t∗	X
cana-2411	156	111	,	,	PUNCT
cana-2411	156	112	𝔞t∗	𝔞t∗	PROPN
cana-2411	156	113	∨	∨	NUM
cana-2411	156	114	𝔟t∗	𝔟t∗	NOUN
cana-2411	156	115	〉	〉	NOUN
cana-2411	156	116	,	,	PUNCT
cana-2411	156	117	〈	〈	ADP
cana-2411	156	118	𝔞i0	𝔞i0	NOUN
cana-2411	156	119	×	×	NOUN
cana-2411	156	120	𝔟i0	𝔟i0	NOUN
cana-2411	156	121	,	,	PUNCT
cana-2411	156	122	𝔞i∗	𝔞i∗	NOUN
cana-2411	156	123	∨	∨	NOUN
cana-2411	156	124	𝔟i∗	𝔟i∗	NOUN
cana-2411	156	125	,	,	PUNCT
cana-2411	156	126	𝔞i∗	𝔞i∗	VERB
cana-2411	156	127	∨	∨	NOUN
cana-2411	156	128	𝔟i∗	𝔟i∗	ADJ
cana-2411	156	129	〉	〉	NOUN
cana-2411	156	130	,	,	PUNCT
cana-2411	156	131	〈	〈	NOUN
cana-2411	156	132	𝔞f0	𝔞f0	NOUN
cana-2411	156	133	×	×	NOUN
cana-2411	156	134	𝔟f0	𝔟f0	ADV
cana-2411	156	135	,	,	PUNCT
cana-2411	156	136	𝔞f∗	𝔞f∗	ADJ
cana-2411	156	137	∨	∨	NUM
cana-2411	156	138	𝔟f∗	𝔟f∗	NOUN
cana-2411	156	139	,	,	PUNCT
cana-2411	156	140	𝔞f∗	𝔞f∗	ADJ
cana-2411	156	141	∨	∨	NUM
cana-2411	156	142	𝔟f∗	𝔟f∗	ADJ
cana-2411	156	143	〉	〉	NOUN
cana-2411	156	144	)	)	PUNCT
cana-2411	156	145	division	division	NOUN
cana-2411	156	146	:	:	PUNCT
cana-2411	156	147	�	�	PROPN
cana-2411	156	148	̃	̃	PROPN
cana-2411	156	149	�	�	PROPN
cana-2411	156	150	𝔫	𝔫	NOUN
cana-2411	156	151	∗	∗	NOUN
cana-2411	156	152	ℬ̃	ℬ̃	PROPN
cana-2411	156	153	𝔫	𝔫	NOUN
cana-2411	156	154	=	=	SYM
cana-2411	156	155	(	(	PUNCT
cana-2411	156	156	〈	〈	NOUN
cana-2411	156	157	𝔞t0	𝔞t0	NOUN
cana-2411	156	158	,	,	PUNCT
cana-2411	156	159	𝔞t∗	𝔞t∗	PROPN
cana-2411	156	160	,	,	PUNCT
cana-2411	156	161	𝔞t∗	𝔞t∗	PROPN
cana-2411	156	162	〉	〉	NOUN
cana-2411	156	163	;	;	PUNCT
cana-2411	156	164	〈	〈	PRON
cana-2411	156	165	𝔞i0	𝔞i0	NOUN
cana-2411	156	166	,	,	PUNCT
cana-2411	156	167	𝔞i∗	𝔞i∗	NOUN
cana-2411	156	168	,	,	PUNCT
cana-2411	156	169	𝔞i∗	𝔞i∗	NOUN
cana-2411	156	170	〉	〉	NOUN
cana-2411	156	171	;	;	PUNCT
cana-2411	156	172	〈	〈	NOUN
cana-2411	156	173	𝔞f0	𝔞f0	NOUN
cana-2411	156	174	,	,	PUNCT
cana-2411	156	175	𝔞f∗	𝔞f∗	ADJ
cana-2411	156	176	,	,	PUNCT
cana-2411	156	177	𝔞f∗	𝔞f∗	ADJ
cana-2411	156	178	〉	〉	NOUN
cana-2411	156	179	)	)	PUNCT
cana-2411	156	180	÷	÷	NOUN
cana-2411	157	1	(	(	PUNCT
cana-2411	157	2	〈	〈	ADP
cana-2411	157	3	𝔟t0	𝔟t0	NOUN
cana-2411	157	4	,	,	PUNCT
cana-2411	157	5	𝔟t∗	𝔟t∗	ADJ
cana-2411	157	6	,	,	PUNCT
cana-2411	157	7	𝔟t∗	𝔟t∗	ADJ
cana-2411	157	8	〉	〉	NOUN
cana-2411	157	9	;	;	PUNCT
cana-2411	157	10	〈	〈	NOUN
cana-2411	157	11	𝔟i0	𝔟i0	NOUN
cana-2411	157	12	,	,	PUNCT
cana-2411	157	13	𝔟i∗	𝔟i∗	NOUN
cana-2411	157	14	,	,	PUNCT
cana-2411	157	15	𝔟i∗	𝔟i∗	ADJ
cana-2411	157	16	〉	〉	NOUN
cana-2411	157	17	;	;	PUNCT
cana-2411	157	18	〈	〈	NOUN
cana-2411	157	19	𝔟f0	𝔟f0	NOUN
cana-2411	157	20	,	,	PUNCT
cana-2411	157	21	𝔟f∗	𝔟f∗	ADJ
cana-2411	157	22	,	,	PUNCT
cana-2411	157	23	𝔟f∗	𝔟f∗	ADJ
cana-2411	157	24	〉	〉	NOUN
cana-2411	157	25	)	)	PUNCT
cana-2411	157	26	=	=	PRON
cana-2411	157	27	(	(	PUNCT
cana-2411	157	28	〈	〈	NOUN
cana-2411	157	29	𝔞t0	𝔞t0	PROPN
cana-2411	157	30	÷	÷	NUM
cana-2411	157	31	𝔟t0	𝔟t0	PROPN
cana-2411	157	32	,	,	PUNCT
cana-2411	157	33	𝔞t∗	𝔞t∗	PROPN
cana-2411	157	34	∨	∨	NUM
cana-2411	157	35	𝔟t∗	𝔟t∗	X
cana-2411	157	36	,	,	PUNCT
cana-2411	157	37	𝔞t∗	𝔞t∗	PROPN
cana-2411	157	38	∨	∨	NUM
cana-2411	157	39	𝔟t∗	𝔟t∗	NOUN
cana-2411	157	40	〉	〉	NOUN
cana-2411	157	41	,	,	PUNCT
cana-2411	157	42	〈	〈	NOUN
cana-2411	157	43	𝔞i0	𝔞i0	NOUN
cana-2411	157	44	÷	÷	PUNCT
cana-2411	157	45	𝔟i0	𝔟i0	NOUN
cana-2411	157	46	,	,	PUNCT
cana-2411	157	47	𝔞i∗	𝔞i∗	NOUN
cana-2411	157	48	∨	∨	NOUN
cana-2411	157	49	𝔟i∗	𝔟i∗	NOUN
cana-2411	157	50	,	,	PUNCT
cana-2411	157	51	𝔞i∗	𝔞i∗	VERB
cana-2411	157	52	∨	∨	NOUN
cana-2411	157	53	𝔟i∗	𝔟i∗	ADJ
cana-2411	157	54	〉	〉	NOUN
cana-2411	157	55	,	,	PUNCT
cana-2411	157	56	〈	〈	NOUN
cana-2411	157	57	𝔞f0	𝔞f0	NOUN
cana-2411	157	58	÷	÷	SYM
cana-2411	157	59	𝔟f0	𝔟f0	ADV
cana-2411	157	60	,	,	PUNCT
cana-2411	157	61	𝔞f∗	𝔞f∗	ADJ
cana-2411	157	62	∨	∨	NUM
cana-2411	157	63	𝔟f∗	𝔟f∗	NOUN
cana-2411	157	64	,	,	PUNCT
cana-2411	157	65	𝔞f∗	𝔞f∗	ADJ
cana-2411	157	66	∨	∨	NUM
cana-2411	157	67	𝔟f∗	𝔟f∗	ADJ
cana-2411	157	68	〉	〉	NOUN
cana-2411	157	69	)	)	PUNCT
cana-2411	157	70	provided	provide	VERB
cana-2411	157	71	𝔟t0	𝔟t0	NOUN
cana-2411	157	72	,	,	PUNCT
cana-2411	157	73	𝔟i0	𝔟i0	NOUN
cana-2411	157	74	,	,	PUNCT
cana-2411	157	75	𝔟f0	𝔟f0	ADV
cana-2411	157	76	≠	≠	PROPN
cana-2411	157	77	0	0	X
cana-2411	157	78	.	.	PUNCT
cana-2411	157	79	2.2	2.2	NUM
cana-2411	157	80	ranking	ranking	NOUN
cana-2411	157	81	of	of	ADP
cana-2411	157	82	neutrosophic	neutrosophic	ADJ
cana-2411	157	83	numbers	number	NOUN
cana-2411	157	84	the	the	DET
cana-2411	157	85	ranking	ranking	NOUN
cana-2411	157	86	of	of	ADP
cana-2411	157	87	neutrosophic	neutrosophic	ADJ
cana-2411	157	88	numbers	number	NOUN
cana-2411	157	89	plays	play	VERB
cana-2411	157	90	an	an	DET
cana-2411	157	91	essential	essential	ADJ
cana-2411	157	92	role	role	NOUN
cana-2411	157	93	in	in	ADP
cana-2411	157	94	the	the	DET
cana-2411	157	95	decision	decision	NOUN
cana-2411	157	96	-	-	PUNCT
cana-2411	157	97	making	make	VERB
cana-2411	157	98	process	process	NOUN
cana-2411	157	99	within	within	ADP
cana-2411	157	100	a	a	DET
cana-2411	157	101	fuzzy	fuzzy	ADJ
cana-2411	157	102	environment	environment	NOUN
cana-2411	157	103	.	.	PUNCT
cana-2411	158	1	various	various	ADJ
cana-2411	158	2	authors	author	NOUN
cana-2411	158	3	in	in	ADP
cana-2411	158	4	the	the	DET
cana-2411	158	5	literature	literature	NOUN
cana-2411	158	6	have	have	AUX
cana-2411	158	7	proposed	propose	VERB
cana-2411	158	8	different	different	ADJ
cana-2411	158	9	types	type	NOUN
cana-2411	158	10	of	of	ADP
cana-2411	158	11	ranking	ranking	ADJ
cana-2411	158	12	methods	method	NOUN
cana-2411	158	13	.	.	PUNCT
cana-2411	159	1	this	this	DET
cana-2411	159	2	article	article	NOUN
cana-2411	159	3	uses	use	VERB
cana-2411	159	4	a	a	DET
cana-2411	159	5	highly	highly	ADV
cana-2411	159	6	effective	effective	ADJ
cana-2411	159	7	ranking	ranking	NOUN
cana-2411	159	8	technique	technique	NOUN
cana-2411	159	9	based	base	VERB
cana-2411	159	10	on	on	ADP
cana-2411	159	11	the	the	DET
cana-2411	159	12	graded	grade	VERB
cana-2411	159	13	mean	mean	NOUN
cana-2411	159	14	.	.	PUNCT
cana-2411	160	1	for	for	ADP
cana-2411	160	2	�	�	PROPN
cana-2411	160	3	̃	̃	PROPN
cana-2411	160	4	�	�	PROPN
cana-2411	160	5	𝔫	𝔫	NOUN
cana-2411	160	6	=	=	NOUN
cana-2411	160	7	communications	communication	NOUN
cana-2411	160	8	on	on	ADP
cana-2411	160	9	applied	apply	VERB
cana-2411	160	10	nonlinear	nonlinear	ADJ
cana-2411	160	11	analysis	analysis	NOUN
cana-2411	160	12	issn	issn	NOUN
cana-2411	160	13	:	:	PUNCT
cana-2411	160	14	1074	1074	NUM
cana-2411	160	15	-	-	PUNCT
cana-2411	160	16	133x	133x	NUM
cana-2411	160	17	vol	vol	NOUN
cana-2411	160	18	32	32	NUM
cana-2411	160	19	no	no	NOUN
cana-2411	160	20	.	.	PUNCT
cana-2411	161	1	2s	2s	NUM
cana-2411	161	2	(	(	PUNCT
cana-2411	161	3	2025	2025	NUM
cana-2411	161	4	)	)	PUNCT
cana-2411	161	5	372	372	NUM
cana-2411	161	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2411	161	7	(	(	PUNCT
cana-2411	161	8	〈	〈	NOUN
cana-2411	161	9	𝔞t0	𝔞t0	NOUN
cana-2411	161	10	,	,	PUNCT
cana-2411	161	11	𝔞t∗	𝔞t∗	PROPN
cana-2411	161	12	,	,	PUNCT
cana-2411	161	13	𝔞t∗	𝔞t∗	PROPN
cana-2411	161	14	〉	〉	NOUN
cana-2411	161	15	;	;	PUNCT
cana-2411	161	16	〈	〈	PRON
cana-2411	161	17	𝔞i0	𝔞i0	NOUN
cana-2411	161	18	,	,	PUNCT
cana-2411	161	19	𝔞i∗	𝔞i∗	NOUN
cana-2411	161	20	,	,	PUNCT
cana-2411	161	21	𝔞i∗	𝔞i∗	NOUN
cana-2411	161	22	〉	〉	NOUN
cana-2411	161	23	;	;	PUNCT
cana-2411	161	24	〈	〈	NOUN
cana-2411	161	25	𝔞f0	𝔞f0	NOUN
cana-2411	161	26	,	,	PUNCT
cana-2411	161	27	𝔞f∗	𝔞f∗	ADJ
cana-2411	161	28	,	,	PUNCT
cana-2411	161	29	𝔞f∗	𝔞f∗	ADJ
cana-2411	161	30	〉	〉	NOUN
cana-2411	161	31	)	)	PUNCT
cana-2411	161	32	∈	∈	PROPN
cana-2411	161	33	ℱ(ℛ	ℱ(ℛ	NUM
cana-2411	161	34	)	)	PUNCT
cana-2411	161	35	,	,	PUNCT
cana-2411	161	36	define	define	VERB
cana-2411	161	37	ℜ:ℱ(ℛ	ℜ:ℱ(ℛ	NOUN
cana-2411	161	38	)	)	PUNCT
cana-2411	161	39	→	→	SYM
cana-2411	161	40	ℛ	ℛ	PROPN
cana-2411	161	41	by	by	ADP
cana-2411	161	42	ℜ(	ℜ(	PROPN
cana-2411	161	43	�	�	PROPN
cana-2411	161	44	̃	̃	PROPN
cana-2411	161	45	�	�	PROPN
cana-2411	161	46	𝔫	𝔫	NOUN
cana-2411	161	47	)	)	PUNCT
cana-2411	161	48	=	=	PUNCT
cana-2411	161	49	(	(	PUNCT
cana-2411	161	50	〈	〈	ADP
cana-2411	161	51	𝔞t∗+4𝔞t0	𝔞t∗+4𝔞t0	X
cana-2411	162	1	+	+	NUM
cana-2411	162	2	𝔞	𝔞	PROPN
cana-2411	162	3	t∗〉,〈𝔞i∗+4𝔞i0	t∗〉,〈𝔞i∗+4𝔞i0	NOUN
cana-2411	162	4	+	+	PROPN
cana-2411	162	5	𝔞	𝔞	X
cana-2411	162	6	i∗〉,〈𝔞f∗+4𝔞f0	i∗〉,〈𝔞f∗+4𝔞f0	NOUN
cana-2411	162	7	+	+	PROPN
cana-2411	162	8	𝔞	𝔞	PROPN
cana-2411	162	9	f∗	f∗	NOUN
cana-2411	162	10	〉	〉	NOUN
cana-2411	162	11	6	6	NUM
cana-2411	162	12	)	)	PUNCT
cana-2411	162	13	.	.	PUNCT
cana-2411	163	1	for	for	ADP
cana-2411	163	2	any	any	DET
cana-2411	163	3	two	two	NUM
cana-2411	163	4	triangular	triangular	NOUN
cana-2411	163	5	fuzzy	fuzzy	ADJ
cana-2411	163	6	numbers	number	NOUN
cana-2411	163	7	�	�	PROPN
cana-2411	163	8	̃	̃	PROPN
cana-2411	163	9	�	�	PROPN
cana-2411	163	10	𝔫	𝔫	NOUN
cana-2411	163	11	=	=	PUNCT
cana-2411	163	12	(	(	PUNCT
cana-2411	163	13	〈	〈	NOUN
cana-2411	163	14	𝔞t0	𝔞t0	NOUN
cana-2411	163	15	,	,	PUNCT
cana-2411	163	16	𝔞t∗	𝔞t∗	PROPN
cana-2411	163	17	,	,	PUNCT
cana-2411	163	18	𝔞t∗	𝔞t∗	PROPN
cana-2411	163	19	〉	〉	NOUN
cana-2411	163	20	;	;	PUNCT
cana-2411	163	21	〈	〈	PRON
cana-2411	163	22	𝔞i0	𝔞i0	NOUN
cana-2411	163	23	,	,	PUNCT
cana-2411	163	24	𝔞i∗	𝔞i∗	NOUN
cana-2411	163	25	,	,	PUNCT
cana-2411	163	26	𝔞i∗	𝔞i∗	NOUN
cana-2411	163	27	〉	〉	NOUN
cana-2411	163	28	;	;	PUNCT
cana-2411	163	29	〈	〈	NOUN
cana-2411	163	30	𝔞f0	𝔞f0	NOUN
cana-2411	163	31	,	,	PUNCT
cana-2411	163	32	𝔞f∗	𝔞f∗	ADJ
cana-2411	163	33	,	,	PUNCT
cana-2411	163	34	𝔞f∗	𝔞f∗	ADJ
cana-2411	163	35	〉	〉	NOUN
cana-2411	163	36	)	)	PUNCT
cana-2411	163	37	and	and	CCONJ
cana-2411	163	38	ℬ̃	ℬ̃	NOUN
cana-2411	163	39	𝔫	𝔫	NOUN
cana-2411	163	40	=	=	SYM
cana-2411	163	41	(	(	PUNCT
cana-2411	163	42	〈	〈	ADP
cana-2411	163	43	𝔟t0	𝔟t0	NOUN
cana-2411	163	44	,	,	PUNCT
cana-2411	163	45	𝔟t∗	𝔟t∗	ADJ
cana-2411	163	46	,	,	PUNCT
cana-2411	163	47	𝔟t∗	𝔟t∗	ADJ
cana-2411	163	48	〉	〉	NOUN
cana-2411	163	49	;	;	PUNCT
cana-2411	163	50	〈	〈	NOUN
cana-2411	163	51	𝔟i0	𝔟i0	NOUN
cana-2411	163	52	,	,	PUNCT
cana-2411	163	53	𝔟i∗	𝔟i∗	NOUN
cana-2411	163	54	,	,	PUNCT
cana-2411	163	55	𝔟i∗	𝔟i∗	ADJ
cana-2411	163	56	〉	〉	NOUN
cana-2411	163	57	;	;	PUNCT
cana-2411	163	58	〈	〈	NOUN
cana-2411	163	59	𝔟f0	𝔟f0	NOUN
cana-2411	163	60	,	,	PUNCT
cana-2411	163	61	𝔟f∗	𝔟f∗	ADJ
cana-2411	163	62	,	,	PUNCT
cana-2411	163	63	𝔟f∗	𝔟f∗	ADJ
cana-2411	163	64	〉	〉	NOUN
cana-2411	163	65	)	)	PUNCT
cana-2411	163	66	∈	∈	PROPN
cana-2411	163	67	ℱ(ℛ	ℱ(ℛ	NUM
cana-2411	163	68	)	)	PUNCT
cana-2411	163	69	,	,	PUNCT
cana-2411	163	70	we	we	PRON
cana-2411	163	71	have	have	VERB
cana-2411	163	72	the	the	DET
cana-2411	163	73	following	follow	VERB
cana-2411	163	74	comparison	comparison	NOUN
cana-2411	163	75	:	:	PUNCT
cana-2411	163	76	•	•	ADP
cana-2411	163	77	if	if	SCONJ
cana-2411	163	78	ℜ(	ℜ(	X
cana-2411	163	79	�	�	PROPN
cana-2411	163	80	̃	̃	PROPN
cana-2411	163	81	�	�	PROPN
cana-2411	163	82	𝔫	𝔫	NOUN
cana-2411	163	83	)	)	PUNCT
cana-2411	163	84	<	<	X
cana-2411	163	85	ℜ(ℬ̃	ℜ(ℬ̃	PROPN
cana-2411	163	86	𝔫	𝔫	NOUN
cana-2411	163	87	)	)	PUNCT
cana-2411	163	88	,	,	PUNCT
cana-2411	163	89	then	then	ADV
cana-2411	163	90	�	�	PROPN
cana-2411	163	91	̃	̃	PROPN
cana-2411	163	92	�	�	PROPN
cana-2411	163	93	𝔫	𝔫	NOUN
cana-2411	163	94	≺	≺	NOUN
cana-2411	163	95	ℬ̃	ℬ̃	NUM
cana-2411	163	96	𝔫	𝔫	NOUN
cana-2411	163	97	•	•	NOUN
cana-2411	163	98	if	if	SCONJ
cana-2411	163	99	ℜ(	ℜ(	X
cana-2411	163	100	�	�	PROPN
cana-2411	163	101	̃	̃	PROPN
cana-2411	163	102	�	�	PROPN
cana-2411	163	103	𝔫	𝔫	NOUN
cana-2411	163	104	)	)	PUNCT
cana-2411	163	105	>	>	X
cana-2411	164	1	ℜ(ℬ̃	ℜ(ℬ̃	PROPN
cana-2411	164	2	𝔫	𝔫	NOUN
cana-2411	164	3	)	)	PUNCT
cana-2411	164	4	,	,	PUNCT
cana-2411	164	5	then	then	ADV
cana-2411	164	6	�	�	PROPN
cana-2411	164	7	̃	̃	PROPN
cana-2411	164	8	�	�	PROPN
cana-2411	164	9	𝔫	𝔫	NOUN
cana-2411	164	10	≻	≻	PROPN
cana-2411	164	11	ℬ̃	ℬ̃	NUM
cana-2411	164	12	𝔫	𝔫	NOUN
cana-2411	164	13	•	•	NOUN
cana-2411	164	14	if	if	SCONJ
cana-2411	164	15	ℜ(	ℜ(	X
cana-2411	164	16	�	�	PROPN
cana-2411	164	17	̃	̃	PROPN
cana-2411	164	18	�	�	PROPN
cana-2411	164	19	𝔫	𝔫	NOUN
cana-2411	164	20	)	)	PUNCT
cana-2411	164	21	=	=	SYM
cana-2411	165	1	ℜ(ℬ̃	ℜ(ℬ̃	VERB
cana-2411	165	2	𝔫	𝔫	NOUN
cana-2411	165	3	)	)	PUNCT
cana-2411	165	4	,	,	PUNCT
cana-2411	165	5	then	then	ADV
cana-2411	165	6	�	�	PROPN
cana-2411	165	7	̃	̃	PROPN
cana-2411	165	8	�	�	PROPN
cana-2411	165	9	𝔫	𝔫	NOUN
cana-2411	165	10	≈	≈	PROPN
cana-2411	165	11	ℬ̃	ℬ̃	PROPN
cana-2411	165	12	𝔫	𝔫	NOUN
cana-2411	165	13	.	.	PUNCT
cana-2411	166	1	note	note	NOUN
cana-2411	166	2	1	1	NUM
cana-2411	166	3	.	.	X
cana-2411	166	4	ℜ(	ℜ(	PROPN
cana-2411	166	5	�	�	PROPN
cana-2411	166	6	̃	̃	PROPN
cana-2411	166	7	�	�	PROPN
cana-2411	166	8	𝔫	𝔫	NOUN
cana-2411	166	9	+	+	CCONJ
cana-2411	166	10	ℬ̃	ℬ̃	NUM
cana-2411	166	11	𝔫	𝔫	NOUN
cana-2411	166	12	)	)	PUNCT
cana-2411	166	13	=	=	SYM
cana-2411	166	14	ℜ(	ℜ(	X
cana-2411	166	15	�	�	PROPN
cana-2411	166	16	̃	̃	PROPN
cana-2411	166	17	�	�	PROPN
cana-2411	166	18	𝔫	𝔫	NOUN
cana-2411	166	19	)	)	PUNCT
cana-2411	166	20	+	+	PROPN
cana-2411	166	21	ℜ(ℬ̃	ℜ(ℬ̃	ADJ
cana-2411	166	22	𝔫	𝔫	NOUN
cana-2411	166	23	)	)	PUNCT
cana-2411	166	24	note	note	NOUN
cana-2411	166	25	2	2	NUM
cana-2411	166	26	.	.	X
cana-2411	166	27	ℜ(	ℜ(	PROPN
cana-2411	166	28	�	�	PROPN
cana-2411	166	29	̃	̃	PROPN
cana-2411	166	30	�	�	NOUN
cana-2411	166	31	𝔫.	𝔫.	ADJ
cana-2411	166	32	ℬ̃	ℬ̃	NUM
cana-2411	166	33	𝔫	𝔫	NOUN
cana-2411	166	34	)	)	PUNCT
cana-2411	166	35	=	=	SYM
cana-2411	166	36	ℜ(	ℜ(	PROPN
cana-2411	166	37	�	�	PROPN
cana-2411	166	38	̃	̃	PROPN
cana-2411	166	39	�	�	PROPN
cana-2411	166	40	𝔫).ℜ(ℬ̃	𝔫).ℜ(ℬ̃	VERB
cana-2411	166	41	𝔫	𝔫	NOUN
cana-2411	166	42	)	)	PUNCT
cana-2411	166	43	note	note	NOUN
cana-2411	166	44	3	3	NUM
cana-2411	166	45	.	.	X
cana-2411	166	46	ℜ(	ℜ(	PROPN
cana-2411	166	47	�	�	PROPN
cana-2411	166	48	̃	̃	PROPN
cana-2411	166	49	�	�	PROPN
cana-2411	166	50	𝔫/ℬ̃	𝔫/ℬ̃	VERB
cana-2411	166	51	𝔫	𝔫	NOUN
cana-2411	166	52	)	)	PUNCT
cana-2411	166	53	=	=	SYM
cana-2411	166	54	ℜ(	ℜ(	X
cana-2411	166	55	�	�	PROPN
cana-2411	166	56	̃	̃	PROPN
cana-2411	166	57	�	�	PROPN
cana-2411	166	58	𝔫)/ℜ(ℬ̃	𝔫)/ℜ(ℬ̃	PROPN
cana-2411	166	59	𝔫	𝔫	PROPN
cana-2411	166	60	)	)	PUNCT
cana-2411	166	61	,	,	PUNCT
cana-2411	166	62	provided	provide	VERB
cana-2411	166	63	ℜ(ℬ̃	ℜ(ℬ̃	PROPN
cana-2411	166	64	𝔫	𝔫	NOUN
cana-2411	166	65	)	)	PUNCT
cana-2411	166	66	≠	≠	PROPN
cana-2411	166	67	0	0	NUM
cana-2411	166	68	.	.	NOUN
cana-2411	166	69	3	3	NUM
cana-2411	166	70	.	.	X
cana-2411	166	71	neutrosophic	neutrosophic	PROPN
cana-2411	166	72	non	non	ADJ
cana-2411	166	73	linear	linear	ADJ
cana-2411	166	74	programming	programming	NOUN
cana-2411	166	75	problems	problem	NOUN
cana-2411	166	76	(	(	PUNCT
cana-2411	166	77	nnlpp	nnlpp	NOUN
cana-2411	166	78	)	)	PUNCT
cana-2411	166	79	let	let	VERB
cana-2411	166	80	general	general	ADJ
cana-2411	166	81	nnlpp	nnlpp	NOUN
cana-2411	166	82	"	"	PUNCT
cana-2411	166	83	𝓂𝒾𝓃	𝓂𝒾𝓃	PROPN
cana-2411	166	84	𝑓𝒩(	𝑓𝒩(	PROPN
cana-2411	166	85	�	�	PROPN
cana-2411	166	86	̃	̃	PROPN
cana-2411	166	87	�	�	NOUN
cana-2411	166	88	𝑖	𝑖	NOUN
cana-2411	166	89	)	)	PUNCT
cana-2411	166	90	𝑠𝑢𝑏.	𝑠𝑢𝑏.	PUNCT
cana-2411	166	91	𝑡𝑜	𝑡𝑜	PROPN
cana-2411	166	92	ℎ̃𝒾	ℎ̃𝒾	PROPN
cana-2411	166	93	𝒩	𝒩	PROPN
cana-2411	166	94	(	(	PUNCT
cana-2411	166	95	�	�	PROPN
cana-2411	166	96	̃	̃	PROPN
cana-2411	166	97	�	�	NOUN
cana-2411	166	98	𝑖	𝑖	NOUN
cana-2411	166	99	)	)	PUNCT
cana-2411	167	1	≈	≈	PROPN
cana-2411	167	2	0̃	0̃	NOUN
cana-2411	167	3	𝑓𝑜𝑟	𝑓𝑜𝑟	NOUN
cana-2411	167	4	𝒾	𝒾	X
cana-2411	167	5	=	=	SYM
cana-2411	167	6	1,2	1,2	NUM
cana-2411	167	7	,	,	PUNCT
cana-2411	167	8	⋯	⋯	PROPN
cana-2411	167	9	,	,	PUNCT
cana-2411	167	10	ℓ	ℓ	PROPN
cana-2411	167	11	�	�	PROPN
cana-2411	167	12	̃	̃	PROPN
cana-2411	167	13	�	�	PROPN
cana-2411	167	14	𝑗	𝑗	PROPN
cana-2411	167	15	𝒩(	𝒩(	X
cana-2411	167	16	�	�	PROPN
cana-2411	167	17	̃	̃	PROPN
cana-2411	167	18	�	�	NOUN
cana-2411	167	19	𝑖	𝑖	SYM
cana-2411	167	20	)	)	PUNCT
cana-2411	167	21	⪯	⪯	NOUN
cana-2411	167	22	0̃	0̃	NOUN
cana-2411	167	23	𝑓𝑜𝑟	𝑓𝑜𝑟	NOUN
cana-2411	167	24	𝒿	𝒿	NOUN
cana-2411	167	25	=	=	SYM
cana-2411	167	26	1,2	1,2	NUM
cana-2411	167	27	,	,	PUNCT
cana-2411	167	28	⋯	⋯	PROPN
cana-2411	167	29	,	,	PUNCT
cana-2411	167	30	𝓂	𝓂	PROPN
cana-2411	167	31	�	�	PROPN
cana-2411	167	32	̃	̃	PROPN
cana-2411	167	33	�	�	NOUN
cana-2411	167	34	𝑖	𝑖	SYM
cana-2411	167	35	⪰	⪰	NOUN
cana-2411	167	36	0̃	0̃	NOUN
cana-2411	167	37	"	"	PUNCT
cana-2411	167	38	(	(	PUNCT
cana-2411	167	39	1	1	NUM
cana-2411	167	40	)	)	PUNCT
cana-2411	167	41	where	where	SCONJ
cana-2411	167	42	𝑓𝒩	𝑓𝒩	NOUN
cana-2411	167	43	,	,	PUNCT
cana-2411	167	44	ℎ̃1	ℎ̃1	PROPN
cana-2411	167	45	𝒩	𝒩	PROPN
cana-2411	167	46	,	,	PUNCT
cana-2411	167	47	⋯	⋯	PROPN
cana-2411	167	48	,	,	PUNCT
cana-2411	167	49	ℎ̃𝑙	ℎ̃𝑙	PROPN
cana-2411	167	50	𝒩	𝒩	PROPN
cana-2411	167	51	,	,	PUNCT
cana-2411	167	52	�	�	PROPN
cana-2411	167	53	̃	̃	NOUN
cana-2411	167	54	�	�	PROPN
cana-2411	167	55	1	1	NUM
cana-2411	167	56	𝒩	𝒩	PROPN
cana-2411	167	57	,	,	PUNCT
cana-2411	167	58	⋯	⋯	PROPN
cana-2411	167	59	,	,	PUNCT
cana-2411	167	60	�	�	PROPN
cana-2411	167	61	̃	̃	PROPN
cana-2411	167	62	�	�	PROPN
cana-2411	167	63	𝓂	𝓂	NOUN
cana-2411	167	64	𝒩	𝒩	PROPN
cana-2411	167	65	are	be	AUX
cana-2411	167	66	continuous	continuous	ADJ
cana-2411	167	67	neutrosophic	neutrosophic	ADJ
cana-2411	167	68	valued	value	VERB
cana-2411	167	69	functions	function	NOUN
cana-2411	167	70	defined	define	VERB
cana-2411	167	71	on	on	ADP
cana-2411	167	72	𝑅𝓃.	𝑅𝓃.	PROPN
cana-2411	167	73	a	a	DET
cana-2411	167	74	vector	vector	NOUN
cana-2411	167	75	�	�	PROPN
cana-2411	167	76	̃	̃	NOUN
cana-2411	167	77	�	�	NOUN
cana-2411	167	78	𝑖	𝑖	SYM
cana-2411	167	79	=	=	SYM
cana-2411	167	80	(	(	PUNCT
cana-2411	167	81	�	�	PROPN
cana-2411	167	82	̃	̃	NOUN
cana-2411	167	83	�	�	NOUN
cana-2411	167	84	1	1	NUM
cana-2411	167	85	,	,	PUNCT
cana-2411	167	86	�	�	PROPN
cana-2411	167	87	̃	̃	NOUN
cana-2411	167	88	�	�	NOUN
cana-2411	167	89	2	2	NUM
cana-2411	167	90	,	,	PUNCT
cana-2411	167	91	�	�	PROPN
cana-2411	167	92	̃	̃	NOUN
cana-2411	167	93	�	�	NOUN
cana-2411	167	94	3,⋯	3,⋯	NUM
cana-2411	167	95	,	,	PUNCT
cana-2411	167	96	�	�	PROPN
cana-2411	167	97	̃	̃	PROPN
cana-2411	167	98	�	�	NOUN
cana-2411	167	99	𝑛	𝑛	NOUN
cana-2411	167	100	)	)	PUNCT
cana-2411	167	101	is	be	AUX
cana-2411	167	102	considered	consider	VERB
cana-2411	167	103	a	a	DET
cana-2411	167	104	feasible	feasible	ADJ
cana-2411	167	105	solution	solution	NOUN
cana-2411	167	106	to	to	ADP
cana-2411	167	107	the	the	DET
cana-2411	167	108	nnlpp	nnlpp	NOUN
cana-2411	167	109	(	(	PUNCT
cana-2411	167	110	1	1	X
cana-2411	167	111	)	)	PUNCT
cana-2411	167	112	if	if	SCONJ
cana-2411	167	113	it	it	PRON
cana-2411	167	114	meets	meet	VERB
cana-2411	167	115	all	all	DET
cana-2411	167	116	the	the	DET
cana-2411	167	117	constraints	constraint	NOUN
cana-2411	167	118	and	and	CCONJ
cana-2411	167	119	adheres	adhere	NOUN
cana-2411	167	120	to	to	ADP
cana-2411	167	121	the	the	DET
cana-2411	167	122	non	non	ADJ
cana-2411	167	123	-	-	ADJ
cana-2411	167	124	negativity	negativity	ADJ
cana-2411	167	125	condition	condition	NOUN
cana-2411	167	126	of	of	ADP
cana-2411	167	127	the	the	DET
cana-2411	167	128	nnlpp	nnlpp	NOUN
cana-2411	167	129	.	.	PUNCT
cana-2411	168	1	the	the	DET
cana-2411	168	2	collection	collection	NOUN
cana-2411	168	3	of	of	ADP
cana-2411	168	4	all	all	DET
cana-2411	168	5	such	such	ADJ
cana-2411	168	6	feasible	feasible	ADJ
cana-2411	168	7	solutions	solution	NOUN
cana-2411	168	8	is	be	AUX
cana-2411	168	9	known	know	VERB
cana-2411	168	10	as	as	ADP
cana-2411	168	11	the	the	DET
cana-2411	168	12	feasible	feasible	ADJ
cana-2411	168	13	region	region	NOUN
cana-2411	168	14	,	,	PUNCT
cana-2411	168	15	which	which	PRON
cana-2411	168	16	is	be	AUX
cana-2411	168	17	defined	define	VERB
cana-2411	168	18	by	by	ADP
cana-2411	168	19	these	these	DET
cana-2411	168	20	criteria	criterion	NOUN
cana-2411	168	21	.	.	PUNCT
cana-2411	169	1	�	�	PROPN
cana-2411	169	2	̃	̃	PROPN
cana-2411	169	3	�	�	PROPN
cana-2411	169	4	=	=	SYM
cana-2411	169	5	{	{	PUNCT
cana-2411	169	6	�	�	PROPN
cana-2411	169	7	̃	̃	NOUN
cana-2411	169	8	�	�	PROPN
cana-2411	169	9	𝒊	𝒊	NOUN
cana-2411	169	10	∈	∈	NOUN
cana-2411	169	11	r𝓃/ℎ̃𝒾	r𝓃/ℎ̃𝒾	NOUN
cana-2411	169	12	𝒩	𝒩	PROPN
cana-2411	169	13	(	(	PUNCT
cana-2411	169	14	�	�	PROPN
cana-2411	169	15	̃	̃	PROPN
cana-2411	169	16	�	�	PROPN
cana-2411	169	17	)	)	PUNCT
cana-2411	169	18	≈	≈	PROPN
cana-2411	169	19	0̃	0̃	NOUN
cana-2411	169	20	𝑓𝑜𝑟	𝑓𝑜𝑟	NOUN
cana-2411	169	21	𝒾	𝒾	X
cana-2411	169	22	=	=	SYM
cana-2411	169	23	1,2	1,2	NUM
cana-2411	169	24	,	,	PUNCT
cana-2411	169	25	⋯	⋯	PROPN
cana-2411	169	26	,	,	PUNCT
cana-2411	169	27	ℓ	ℓ	PROPN
cana-2411	169	28	,	,	PUNCT
cana-2411	169	29	�	�	PROPN
cana-2411	169	30	̃	̃	PROPN
cana-2411	169	31	�	�	PROPN
cana-2411	169	32	𝒿	𝒿	PROPN
cana-2411	169	33	𝒩(	𝒩(	X
cana-2411	169	34	�	�	PROPN
cana-2411	169	35	̃	̃	PROPN
cana-2411	169	36	�	�	PROPN
cana-2411	169	37	)𝑓𝑜𝑟	)𝑓𝑜𝑟	PROPN
cana-2411	169	38	𝒿	𝒿	PROPN
cana-2411	169	39	=	=	SYM
cana-2411	169	40	1,2,⋯	1,2,⋯	PROPN
cana-2411	169	41	,	,	PUNCT
cana-2411	169	42	𝓂	𝓂	PROPN
cana-2411	169	43	𝑎𝑛𝑑	𝑎𝑛𝑑	PROPN
cana-2411	169	44	�	�	PROPN
cana-2411	169	45	̃	̃	PROPN
cana-2411	169	46	�	�	NOUN
cana-2411	169	47	𝑖	𝑖	SYM
cana-2411	169	48	⪰	⪰	NOUN
cana-2411	169	49	0̃	0̃	NOUN
cana-2411	169	50	}	}	PUNCT
cana-2411	169	51	.	.	PUNCT
cana-2411	170	1	4	4	X
cana-2411	170	2	.	.	X
cana-2411	170	3	solution	solution	NOUN
cana-2411	170	4	methods	method	NOUN
cana-2411	170	5	we	we	PRON
cana-2411	170	6	investigate	investigate	VERB
cana-2411	170	7	two	two	NUM
cana-2411	170	8	neutrosophic	neutrosophic	ADJ
cana-2411	170	9	optimization	optimization	NOUN
cana-2411	170	10	methods	method	NOUN
cana-2411	170	11	namely	namely	ADV
cana-2411	170	12	neutrosophic	neutrosophic	PROPN
cana-2411	170	13	cauchy	cauchy	PROPN
cana-2411	170	14	’s	’s	PART
cana-2411	170	15	steepest	steep	ADJ
cana-2411	170	16	descent	descent	NOUN
cana-2411	170	17	method	method	NOUN
cana-2411	170	18	and	and	CCONJ
cana-2411	170	19	the	the	DET
cana-2411	170	20	fletcher	fletcher	PROPN
cana-2411	170	21	-	-	PUNCT
cana-2411	170	22	reeves	reeves	PROPN
cana-2411	170	23	method	method	NOUN
cana-2411	170	24	(	(	PUNCT
cana-2411	170	25	also	also	ADV
cana-2411	170	26	called	call	VERB
cana-2411	170	27	the	the	DET
cana-2411	170	28	conjugate	conjugate	ADJ
cana-2411	170	29	gradient	gradient	NOUN
cana-2411	170	30	method	method	NOUN
cana-2411	170	31	)	)	PUNCT
cana-2411	170	32	.	.	PUNCT
cana-2411	171	1	these	these	DET
cana-2411	171	2	techniques	technique	NOUN
cana-2411	171	3	give	give	VERB
cana-2411	171	4	strong	strong	ADJ
cana-2411	171	5	frameworks	framework	NOUN
cana-2411	171	6	for	for	ADP
cana-2411	171	7	improving	improve	VERB
cana-2411	171	8	objective	objective	ADJ
cana-2411	171	9	functions	function	NOUN
cana-2411	171	10	when	when	SCONJ
cana-2411	171	11	facing	face	VERB
cana-2411	171	12	uncertainty	uncertainty	NOUN
cana-2411	171	13	,	,	PUNCT
cana-2411	171	14	incompleteness	incompleteness	NOUN
cana-2411	171	15	,	,	PUNCT
cana-2411	171	16	and	and	CCONJ
cana-2411	171	17	inconsistency	inconsistency	NOUN
cana-2411	171	18	.	.	PUNCT
cana-2411	172	1	our	our	PRON
cana-2411	172	2	goal	goal	NOUN
cana-2411	172	3	is	be	AUX
cana-2411	172	4	to	to	PART
cana-2411	172	5	explain	explain	VERB
cana-2411	172	6	the	the	DET
cana-2411	172	7	theoretical	theoretical	ADJ
cana-2411	172	8	basics	basic	NOUN
cana-2411	172	9	and	and	CCONJ
cana-2411	172	10	real	real	ADJ
cana-2411	172	11	-	-	PUNCT
cana-2411	172	12	world	world	NOUN
cana-2411	172	13	impacts	impact	NOUN
cana-2411	172	14	of	of	ADP
cana-2411	172	15	these	these	DET
cana-2411	172	16	neutrosophic	neutrosophic	ADJ
cana-2411	172	17	optimization	optimization	NOUN
cana-2411	172	18	methods	method	NOUN
cana-2411	172	19	using	use	VERB
cana-2411	172	20	a	a	DET
cana-2411	172	21	series	series	NOUN
cana-2411	172	22	of	of	ADP
cana-2411	172	23	theorems	theorem	NOUN
cana-2411	172	24	and	and	CCONJ
cana-2411	172	25	proofs	proof	NOUN
cana-2411	172	26	.	.	PUNCT
cana-2411	173	1	this	this	PRON
cana-2411	173	2	will	will	AUX
cana-2411	173	3	show	show	VERB
cana-2411	173	4	how	how	SCONJ
cana-2411	173	5	effective	effective	ADJ
cana-2411	173	6	they	they	PRON
cana-2411	173	7	are	be	AUX
cana-2411	173	8	in	in	ADP
cana-2411	173	9	handling	handle	VERB
cana-2411	173	10	complicated	complicated	ADJ
cana-2411	173	11	optimization	optimization	NOUN
cana-2411	173	12	problems	problem	NOUN
cana-2411	173	13	.	.	PUNCT
cana-2411	174	1	4.1	4.1	NUM
cana-2411	174	2	neutrosophic	neutrosophic	PROPN
cana-2411	174	3	cauchy	cauchy	PROPN
cana-2411	174	4	’s	’s	PART
cana-2411	174	5	steepest	steep	ADJ
cana-2411	174	6	descent	descent	NOUN
cana-2411	174	7	method	method	NOUN
cana-2411	174	8	consider	consider	VERB
cana-2411	174	9	an	an	DET
cana-2411	174	10	unconstrained	unconstrained	ADJ
cana-2411	174	11	minimization	minimization	NOUN
cana-2411	174	12	problem	problem	NOUN
cana-2411	174	13	min𝑓𝒩(	min𝑓𝒩(	PROPN
cana-2411	174	14	�	�	PROPN
cana-2411	174	15	̃	̃	NOUN
cana-2411	174	16	�	�	NOUN
cana-2411	174	17	1	1	NUM
cana-2411	174	18	,	,	PUNCT
cana-2411	174	19	�	�	PROPN
cana-2411	174	20	̃	̃	NOUN
cana-2411	174	21	�	�	NOUN
cana-2411	174	22	2	2	NUM
cana-2411	174	23	,	,	PUNCT
cana-2411	174	24	…	…	PUNCT
cana-2411	174	25	,	,	PUNCT
cana-2411	174	26	�	�	PROPN
cana-2411	174	27	̃	̃	PROPN
cana-2411	174	28	�	�	PROPN
cana-2411	174	29	𝔫	𝔫	NOUN
cana-2411	174	30	)	)	PUNCT
cana-2411	174	31	.	.	PUNCT
cana-2411	175	1	the	the	DET
cana-2411	175	2	goal	goal	NOUN
cana-2411	175	3	is	be	AUX
cana-2411	175	4	to	to	PART
cana-2411	175	5	discover	discover	VERB
cana-2411	175	6	a	a	DET
cana-2411	175	7	local	local	ADJ
cana-2411	175	8	minimizer	minimizer	NOUN
cana-2411	175	9	,	,	PUNCT
cana-2411	175	10	also	also	ADV
cana-2411	175	11	known	know	VERB
cana-2411	175	12	as	as	ADP
cana-2411	175	13	a	a	DET
cana-2411	175	14	minimizer	minimizer	NOUN
cana-2411	175	15	.	.	PUNCT
cana-2411	176	1	𝑓𝒩(	𝑓𝒩(	ADP
cana-2411	176	2	�	�	PROPN
cana-2411	176	3	̃	̃	PROPN
cana-2411	176	4	�	�	PROPN
cana-2411	176	5	)	)	PUNCT
cana-2411	176	6	represents	represent	VERB
cana-2411	176	7	the	the	DET
cana-2411	176	8	objective	objective	ADJ
cana-2411	176	9	function	function	NOUN
cana-2411	176	10	for	for	ADP
cana-2411	176	11	this	this	DET
cana-2411	176	12	minimization	minimization	NOUN
cana-2411	176	13	job	job	NOUN
cana-2411	176	14	.	.	PUNCT
cana-2411	177	1	gradient	gradient	NOUN
cana-2411	177	2	-	-	PUNCT
cana-2411	177	3	based	base	VERB
cana-2411	177	4	approaches	approach	NOUN
cana-2411	177	5	are	be	AUX
cana-2411	177	6	based	base	VERB
cana-2411	177	7	on	on	ADP
cana-2411	177	8	the	the	DET
cana-2411	177	9	observation	observation	NOUN
cana-2411	177	10	that	that	SCONJ
cana-2411	177	11	𝑓𝒩	𝑓𝒩	NOUN
cana-2411	177	12	decreases	decrease	VERB
cana-2411	177	13	the	the	DET
cana-2411	177	14	communications	communication	NOUN
cana-2411	177	15	on	on	ADP
cana-2411	177	16	applied	apply	VERB
cana-2411	177	17	nonlinear	nonlinear	ADJ
cana-2411	177	18	analysis	analysis	NOUN
cana-2411	177	19	issn	issn	NOUN
cana-2411	177	20	:	:	PUNCT
cana-2411	177	21	1074	1074	NUM
cana-2411	177	22	-	-	PUNCT
cana-2411	177	23	133x	133x	NUM
cana-2411	177	24	vol	vol	NOUN
cana-2411	177	25	32	32	NUM
cana-2411	177	26	no	no	NOUN
cana-2411	177	27	.	.	PUNCT
cana-2411	178	1	2s	2s	NUM
cana-2411	178	2	(	(	PUNCT
cana-2411	178	3	2025	2025	NUM
cana-2411	178	4	)	)	PUNCT
cana-2411	178	5	373	373	NUM
cana-2411	178	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2411	178	7	fastest	fast	ADJ
cana-2411	178	8	at	at	ADP
cana-2411	178	9	a	a	DET
cana-2411	178	10	point	point	NOUN
cana-2411	178	11	𝑝	𝑝	NOUN
cana-2411	178	12	in	in	ADP
cana-2411	178	13	ℛ	ℛ	NOUN
cana-2411	178	14	while	while	SCONJ
cana-2411	178	15	advancing	advance	VERB
cana-2411	178	16	in	in	ADP
cana-2411	178	17	the	the	DET
cana-2411	178	18	direction	direction	NOUN
cana-2411	178	19	of	of	ADP
cana-2411	178	20	−∇𝑓𝒩(𝑃	−∇𝑓𝒩(𝑃	X
cana-2411	178	21	)	)	PUNCT
cana-2411	178	22	.	.	PUNCT
cana-2411	179	1	as	as	ADP
cana-2411	179	2	a	a	DET
cana-2411	179	3	result	result	NOUN
cana-2411	179	4	,	,	PUNCT
cana-2411	179	5	the	the	DET
cana-2411	179	6	iterative	iterative	NOUN
cana-2411	179	7	approach	approach	NOUN
cana-2411	179	8	consists	consist	VERB
cana-2411	179	9	of	of	ADP
cana-2411	179	10	,	,	PUNCT
cana-2411	179	11	�	�	PROPN
cana-2411	179	12	̃	̃	PROPN
cana-2411	179	13	�	�	PROPN
cana-2411	179	14	𝜅+1	𝜅+1	SYM
cana-2411	179	15	=	=	PUNCT
cana-2411	179	16	�	�	PROPN
cana-2411	179	17	̃	̃	PROPN
cana-2411	179	18	�	�	PROPN
cana-2411	179	19	𝜅	𝜅	NUM
cana-2411	179	20	+	+	X
cana-2411	179	21	(	(	PUNCT
cana-2411	179	22	�	�	PROPN
cana-2411	179	23	̃	̃	PROPN
cana-2411	179	24	�	�	PROPN
cana-2411	179	25	𝜅	𝜅	PROPN
cana-2411	179	26	�	�	PROPN
cana-2411	179	27	̃	̃	PROPN
cana-2411	179	28	�	�	PROPN
cana-2411	179	29	(	(	PUNCT
cana-2411	179	30	�	�	PROPN
cana-2411	179	31	̃	̃	NOUN
cana-2411	179	32	�	�	NOUN
cana-2411	179	33	𝜅))𝒩	𝜅))𝒩	NOUN
cana-2411	179	34	(	(	PUNCT
cana-2411	179	35	2	2	NUM
cana-2411	179	36	)	)	PUNCT
cana-2411	179	37	where	where	SCONJ
cana-2411	179	38	as	as	ADP
cana-2411	179	39	�	�	PROPN
cana-2411	179	40	̃	̃	PROPN
cana-2411	179	41	�	�	PROPN
cana-2411	179	42	𝜅	𝜅	NOUN
cana-2411	179	43	is	be	AUX
cana-2411	179	44	the	the	DET
cana-2411	179	45	current	current	ADJ
cana-2411	179	46	estimate	estimate	NOUN
cana-2411	179	47	of	of	ADP
cana-2411	179	48	�	�	PROPN
cana-2411	179	49	̃	̃	PROPN
cana-2411	179	50	�	�	NOUN
cana-2411	179	51	∗	∗	NOUN
cana-2411	179	52	,	,	PUNCT
cana-2411	179	53	(	(	PUNCT
cana-2411	179	54	�	�	PROPN
cana-2411	179	55	̃	̃	NOUN
cana-2411	179	56	�	�	NOUN
cana-2411	179	57	κ)𝒩	κ)𝒩	NOUN
cana-2411	179	58	=	=	SYM
cana-2411	179	59	(	(	PUNCT
cana-2411	179	60	�	�	PROPN
cana-2411	179	61	̃	̃	NOUN
cana-2411	179	62	�	�	PROPN
cana-2411	179	63	(	(	PUNCT
cana-2411	179	64	�	�	PROPN
cana-2411	179	65	̃	̃	NOUN
cana-2411	179	66	�	�	NOUN
cana-2411	179	67	𝜅))𝒩	𝜅))𝒩	X
cana-2411	179	68	is	be	AUX
cana-2411	179	69	the	the	DET
cana-2411	179	70	search	search	NOUN
cana-2411	179	71	direction	direction	NOUN
cana-2411	179	72	and	and	CCONJ
cana-2411	179	73	𝛼(κ	𝛼(κ	NUM
cana-2411	179	74	)	)	PUNCT
cana-2411	179	75	is	be	AUX
cana-2411	179	76	the	the	DET
cana-2411	179	77	step	step	NOUN
cana-2411	179	78	length	length	NOUN
cana-2411	179	79	parameter	parameter	NOUN
cana-2411	179	80	in	in	ADP
cana-2411	179	81	the	the	DET
cana-2411	179	82	space	space	NOUN
cana-2411	179	83	ℛ𝒩	ℛ𝒩	PROPN
cana-2411	179	84	of	of	ADP
cana-2411	179	85	design	design	NOUN
cana-2411	179	86	variables	variable	NOUN
cana-2411	179	87	.	.	PUNCT
cana-2411	180	1	if	if	SCONJ
cana-2411	180	2	we	we	PRON
cana-2411	180	3	take	take	VERB
cana-2411	180	4	(	(	PUNCT
cana-2411	180	5	�	�	NOUN
cana-2411	180	6	̃	̃	NOUN
cana-2411	180	7	�	�	NOUN
cana-2411	180	8	κ)𝒩	κ)𝒩	NOUN
cana-2411	180	9	=	=	PUNCT
cana-2411	180	10	−(	−(	PROPN
cana-2411	180	11	�	�	NOUN
cana-2411	180	12	̃	̃	NOUN
cana-2411	180	13	�	�	NOUN
cana-2411	180	14	κ)𝒩	κ)𝒩	NOUN
cana-2411	180	15	=	=	SYM
cana-2411	180	16	−∇𝑓𝒩(	−∇𝑓𝒩(	PROPN
cana-2411	180	17	�	�	PROPN
cana-2411	180	18	̃	̃	PROPN
cana-2411	180	19	�	�	NOUN
cana-2411	180	20	κ	κ	NOUN
cana-2411	180	21	)	)	PUNCT
cana-2411	180	22	,	,	PUNCT
cana-2411	180	23	we	we	PRON
cana-2411	180	24	get	get	VERB
cana-2411	180	25	the	the	DET
cana-2411	180	26	method	method	NOUN
cana-2411	180	27	of	of	ADP
cana-2411	180	28	steepest	steep	ADJ
cana-2411	180	29	descent	descent	NOUN
cana-2411	180	30	.	.	PUNCT
cana-2411	181	1	we	we	PRON
cana-2411	181	2	have	have	VERB
cana-2411	181	3	�	�	PROPN
cana-2411	181	4	̃	̃	PROPN
cana-2411	181	5	�	�	PROPN
cana-2411	181	6	(κ+1	(κ+1	NOUN
cana-2411	181	7	)	)	PUNCT
cana-2411	181	8	=	=	SYM
cana-2411	181	9	�	�	PROPN
cana-2411	181	10	̃	̃	PROPN
cana-2411	181	11	�	�	PROPN
cana-2411	181	12	𝜅	𝜅	NUM
cana-2411	181	13	−	−	PROPN
cana-2411	181	14	(	(	PUNCT
cana-2411	181	15	𝛼𝜅(	𝛼𝜅(	PROPN
cana-2411	181	16	�	�	PROPN
cana-2411	181	17	̃	̃	PROPN
cana-2411	181	18	�	�	NOUN
cana-2411	181	19	κ))𝒩	κ))𝒩	PROPN
cana-2411	181	20	,	,	PUNCT
cana-2411	181	21	(	(	PUNCT
cana-2411	181	22	�	�	PROPN
cana-2411	181	23	̃	̃	NOUN
cana-2411	181	24	�	�	NOUN
cana-2411	181	25	κ)𝒩	κ)𝒩	NOUN
cana-2411	181	26	=	=	SYM
cana-2411	181	27	∇𝑓𝒩(	∇𝑓𝒩(	NUM
cana-2411	181	28	�	�	PROPN
cana-2411	181	29	̃	̃	NOUN
cana-2411	181	30	�	�	NOUN
cana-2411	181	31	κ	κ	NOUN
cana-2411	181	32	)	)	PUNCT
cana-2411	181	33	,	,	PUNCT
cana-2411	181	34	where	where	SCONJ
cana-2411	181	35	�	�	PROPN
cana-2411	181	36	̃	̃	PROPN
cana-2411	181	37	�	�	PROPN
cana-2411	181	38	(κ	(κ	NOUN
cana-2411	181	39	)	)	PUNCT
cana-2411	181	40	is	be	AUX
cana-2411	181	41	the	the	DET
cana-2411	181	42	minimizer	minimizer	NOUN
cana-2411	181	43	of	of	ADP
cana-2411	181	44	the	the	DET
cana-2411	181	45	function	function	NOUN
cana-2411	181	46	𝜙(	𝜙(	PROPN
cana-2411	181	47	�	�	PROPN
cana-2411	181	48	̃	̃	PROPN
cana-2411	181	49	�	�	PROPN
cana-2411	181	50	)	)	PUNCT
cana-2411	181	51	=	=	SYM
cana-2411	181	52	𝑓𝒩(	𝑓𝒩(	PROPN
cana-2411	181	53	�	�	PROPN
cana-2411	181	54	̃	̃	PROPN
cana-2411	181	55	�	�	PROPN
cana-2411	181	56	κ	κ	PART
cana-2411	181	57	−	−	PROPN
cana-2411	181	58	(	(	PUNCT
cana-2411	181	59	�	�	PROPN
cana-2411	181	60	̃	̃	PROPN
cana-2411	181	61	�	�	PROPN
cana-2411	181	62	�	�	PROPN
cana-2411	181	63	̃	̃	PROPN
cana-2411	181	64	�	�	NOUN
cana-2411	181	65	κ))𝒩.	κ))𝒩.	VERB
cana-2411	181	66	to	to	PART
cana-2411	181	67	get	get	VERB
cana-2411	181	68	the	the	DET
cana-2411	181	69	value	value	NOUN
cana-2411	181	70	of	of	ADP
cana-2411	181	71	𝛼(κ	𝛼(κ	PROPN
cana-2411	181	72	)	)	PUNCT
cana-2411	181	73	,	,	PUNCT
cana-2411	181	74	one	one	PRON
cana-2411	181	75	can	can	AUX
cana-2411	181	76	use	use	VERB
cana-2411	181	77	any	any	PRON
cana-2411	181	78	of	of	ADP
cana-2411	181	79	the	the	DET
cana-2411	181	80	one	one	NUM
cana-2411	181	81	-	-	PUNCT
cana-2411	181	82	dimensional	dimensional	ADJ
cana-2411	181	83	search	search	NOUN
cana-2411	181	84	techniques	technique	NOUN
cana-2411	181	85	.	.	PUNCT
cana-2411	182	1	to	to	PART
cana-2411	182	2	start	start	VERB
cana-2411	182	3	the	the	DET
cana-2411	182	4	iterative	iterative	NOUN
cana-2411	182	5	process	process	NOUN
cana-2411	182	6	effectively	effectively	ADV
cana-2411	182	7	,	,	PUNCT
cana-2411	182	8	the	the	DET
cana-2411	182	9	first	first	ADJ
cana-2411	182	10	approximation	approximation	NOUN
cana-2411	182	11	�	�	PROPN
cana-2411	182	12	̃	̃	PROPN
cana-2411	182	13	�	�	NOUN
cana-2411	182	14	0	0	NUM
cana-2411	182	15	must	must	AUX
cana-2411	182	16	be	be	AUX
cana-2411	182	17	chosen	choose	VERB
cana-2411	182	18	carefully	carefully	ADV
cana-2411	182	19	and	and	CCONJ
cana-2411	182	20	according	accord	VERB
cana-2411	182	21	to	to	ADP
cana-2411	182	22	the	the	DET
cana-2411	182	23	particular	particular	ADJ
cana-2411	182	24	problem	problem	NOUN
cana-2411	182	25	at	at	ADP
cana-2411	182	26	hand	hand	NOUN
cana-2411	182	27	.	.	PUNCT
cana-2411	183	1	4.1.1	4.1.1	NUM
cana-2411	183	2	analyzing	analyze	VERB
cana-2411	183	3	the	the	DET
cana-2411	183	4	convergence	convergence	NOUN
cana-2411	183	5	of	of	ADP
cana-2411	183	6	quadratic	quadratic	ADJ
cana-2411	183	7	functions	function	NOUN
cana-2411	183	8	using	use	VERB
cana-2411	183	9	the	the	DET
cana-2411	183	10	neutrosophic	neutrosophic	ADJ
cana-2411	183	11	steepest	steep	ADJ
cana-2411	183	12	descent	descent	NOUN
cana-2411	183	13	technique	technique	NOUN
cana-2411	183	14	to	to	PART
cana-2411	183	15	demonstrate	demonstrate	VERB
cana-2411	183	16	the	the	DET
cana-2411	183	17	convergence	convergence	NOUN
cana-2411	183	18	properties	property	NOUN
cana-2411	183	19	of	of	ADP
cana-2411	183	20	gradient	gradient	NOUN
cana-2411	183	21	-	-	PUNCT
cana-2411	183	22	based	base	VERB
cana-2411	183	23	techniques	technique	NOUN
cana-2411	183	24	,	,	PUNCT
cana-2411	183	25	we	we	PRON
cana-2411	183	26	will	will	AUX
cana-2411	183	27	use	use	VERB
cana-2411	183	28	a	a	DET
cana-2411	183	29	quadratic	quadratic	ADJ
cana-2411	183	30	function	function	NOUN
cana-2411	183	31	represented	represent	VERB
cana-2411	183	32	as	as	ADP
cana-2411	183	33	𝑓𝒩(	𝑓𝒩(	PROPN
cana-2411	183	34	�	�	PROPN
cana-2411	183	35	̃	̃	PROPN
cana-2411	183	36	�	�	PROPN
cana-2411	183	37	)	)	PUNCT
cana-2411	184	1	≈	≈	PROPN
cana-2411	184	2	1	1	NUM
cana-2411	184	3	2	2	NUM
cana-2411	184	4	�	�	PROPN
cana-2411	184	5	̃	̃	PROPN
cana-2411	184	6	�	�	PROPN
cana-2411	184	7	𝑇	𝑇	PROPN
cana-2411	184	8	�	�	PROPN
cana-2411	184	9	̃	̃	PROPN
cana-2411	184	10	�	�	PROPN
cana-2411	184	11	�	�	PROPN
cana-2411	184	12	̃	̃	PROPN
cana-2411	184	13	�	�	PROPN
cana-2411	185	1	≈	≈	PROPN
cana-2411	185	2	1	1	NUM
cana-2411	185	3	2	2	NUM
cana-2411	185	4	〈	〈	PROPN
cana-2411	185	5	�	�	PROPN
cana-2411	185	6	̃	̃	PROPN
cana-2411	185	7	�	�	PROPN
cana-2411	185	8	�	�	PROPN
cana-2411	185	9	̃	̃	PROPN
cana-2411	185	10	�	�	PROPN
cana-2411	185	11	,	,	PUNCT
cana-2411	185	12	�	�	PROPN
cana-2411	185	13	̃	̃	PROPN
cana-2411	185	14	�	�	NOUN
cana-2411	185	15	〉	〉	NOUN
cana-2411	185	16	(	(	PUNCT
cana-2411	185	17	3	3	NUM
cana-2411	185	18	)	)	PUNCT
cana-2411	185	19	where	where	SCONJ
cana-2411	185	20	�	�	PROPN
cana-2411	185	21	̃	̃	PROPN
cana-2411	185	22	�	�	PROPN
cana-2411	185	23	is	be	AUX
cana-2411	185	24	positive	positive	ADJ
cana-2411	185	25	definite	definite	ADJ
cana-2411	185	26	.	.	PUNCT
cana-2411	186	1	if	if	SCONJ
cana-2411	186	2	f̃	f̃	PROPN
cana-2411	186	3	𝒩	𝒩	PROPN
cana-2411	186	4	has	have	VERB
cana-2411	186	5	a	a	DET
cana-2411	186	6	minimum	minimum	NOUN
cana-2411	186	7	at	at	ADP
cana-2411	186	8	υ̃∗	υ̃∗	PROPN
cana-2411	186	9	≈	≈	PROPN
cana-2411	186	10	0̃	0̃	NOUN
cana-2411	186	11	with	with	ADP
cana-2411	186	12	f̃	f̃	PROPN
cana-2411	186	13	𝒩	𝒩	PROPN
cana-2411	186	14	(	(	PUNCT
cana-2411	186	15	υ̃∗	υ̃∗	PROPN
cana-2411	186	16	)	)	PUNCT
cana-2411	186	17	≈	≈	PROPN
cana-2411	186	18	0̃	0̃	NOUN
cana-2411	186	19	,	,	PUNCT
cana-2411	186	20	�	�	PROPN
cana-2411	186	21	̃	̃	PROPN
cana-2411	186	22	�	�	PROPN
cana-2411	186	23	𝒩	𝒩	PROPN
cana-2411	186	24	≈	≈	PROPN
cana-2411	186	25	∇f̃	∇f̃	PROPN
cana-2411	186	26	𝒩	𝒩	PROPN
cana-2411	186	27	(	(	PUNCT
cana-2411	186	28	υ̃	υ̃	PROPN
cana-2411	186	29	)	)	PUNCT
cana-2411	186	30	≈	≈	PROPN
cana-2411	186	31	�	�	PROPN
cana-2411	186	32	̃	̃	PROPN
cana-2411	186	33	�	�	PROPN
cana-2411	186	34	υ̃	υ̃	PROPN
cana-2411	186	35	and	and	CCONJ
cana-2411	186	36	∇2f̃	∇2f̃	PROPN
cana-2411	186	37	𝒩	𝒩	PROPN
cana-2411	186	38	(	(	PUNCT
cana-2411	186	39	υ̃	υ̃	PROPN
cana-2411	186	40	)	)	PUNCT
cana-2411	187	1	≈	≈	PROPN
cana-2411	187	2	�	�	PROPN
cana-2411	187	3	̃	̃	PROPN
cana-2411	187	4	�	�	PROPN
cana-2411	187	5	.	.	PUNCT
cana-2411	188	1	then	then	ADV
cana-2411	188	2	ℛ(φ(γ̃𝒩	ℛ(φ(γ̃𝒩	PROPN
cana-2411	188	3	)	)	PUNCT
cana-2411	188	4	)	)	PUNCT
cana-2411	189	1	=	=	SYM
cana-2411	189	2	ℛ	ℛ	PROPN
cana-2411	189	3	(	(	PUNCT
cana-2411	189	4	f̃	f̃	PROPN
cana-2411	189	5	𝒩	𝒩	PROPN
cana-2411	189	6	(	(	PUNCT
cana-2411	189	7	υ̃−	υ̃−	ADV
cana-2411	189	8	γ̃	γ̃	PROPN
cana-2411	189	9	�	�	PROPN
cana-2411	189	10	̃	̃	PROPN
cana-2411	189	11	�	�	PROPN
cana-2411	189	12	𝒩	𝒩	NOUN
cana-2411	189	13	)	)	PUNCT
cana-2411	189	14	)	)	PUNCT
cana-2411	189	15	=	=	SYM
cana-2411	189	16	1	1	NUM
cana-2411	189	17	2	2	NUM
cana-2411	189	18	ℛ(〈[	ℛ(〈[	NOUN
cana-2411	189	19	�	�	PROPN
cana-2411	189	20	̃	̃	PROPN
cana-2411	189	21	�	�	PROPN
cana-2411	189	22	−	−	PROPN
cana-2411	189	23	2γ̃	2γ̃	NUM
cana-2411	189	24	�	�	PROPN
cana-2411	189	25	̃	̃	PROPN
cana-2411	189	26	�	�	NOUN
cana-2411	189	27	2	2	NUM
cana-2411	189	28	+	+	CCONJ
cana-2411	189	29	γ̃2	γ̃2	PROPN
cana-2411	189	30	�	�	PROPN
cana-2411	189	31	̃	̃	PROPN
cana-2411	189	32	�	�	NOUN
cana-2411	189	33	3]υ̃	3]υ̃	NUM
cana-2411	189	34	,	,	PUNCT
cana-2411	189	35	υ̃	υ̃	PROPN
cana-2411	189	36	〉	〉	NOUN
cana-2411	189	37	)	)	PUNCT
cana-2411	189	38	this	this	PRON
cana-2411	189	39	gives	give	VERB
cana-2411	189	40	ℛ(γ̃𝒩	ℛ(γ̃𝒩	NOUN
cana-2411	189	41	)	)	PUNCT
cana-2411	189	42	=	=	SYM
cana-2411	189	43	ℛ(〈	ℛ(〈	PROPN
cana-2411	189	44	�	�	PROPN
cana-2411	189	45	̃	̃	PROPN
cana-2411	189	46	�	�	NOUN
cana-2411	189	47	2υ̃,υ̃	2υ̃,υ̃	NOUN
cana-2411	189	48	)	)	PUNCT
cana-2411	189	49	〉	〉	NOUN
cana-2411	189	50	)	)	PUNCT
cana-2411	189	51	ℛ(〈	ℛ(〈	PROPN
cana-2411	189	52	�	�	PROPN
cana-2411	189	53	̃	̃	PROPN
cana-2411	189	54	�	�	NOUN
cana-2411	189	55	3υ̃,υ̃	3υ̃,υ̃	NUM
cana-2411	189	56	)	)	PUNCT
cana-2411	189	57	〉	〉	NOUN
cana-2411	189	58	)	)	PUNCT
cana-2411	189	59	=	=	PUNCT
cana-2411	189	60	ℛ(⟨	ℛ(⟨	NOUN
cana-2411	189	61	�	�	PROPN
cana-2411	189	62	̃	̃	NOUN
cana-2411	189	63	�	�	NOUN
cana-2411	189	64	υ̃,	υ̃,	NOUN
cana-2411	189	65	�	�	NOUN
cana-2411	189	66	̃	̃	NOUN
cana-2411	189	67	�	�	NOUN
cana-2411	189	68	υ̃⟩	υ̃⟩	NOUN
cana-2411	189	69	)	)	PUNCT
cana-2411	189	70	ℛ(⟨	ℛ(⟨	NOUN
cana-2411	189	71	�	�	PROPN
cana-2411	189	72	̃	̃	PROPN
cana-2411	189	73	�	�	PROPN
cana-2411	189	74	(	(	PUNCT
cana-2411	189	75	�	�	PROPN
cana-2411	189	76	̃	̃	NOUN
cana-2411	189	77	�	�	NOUN
cana-2411	189	78	υ̃),	υ̃),	NOUN
cana-2411	189	79	�	�	PROPN
cana-2411	189	80	̃	̃	NOUN
cana-2411	189	81	�	�	NOUN
cana-2411	189	82	υ̃⟩	υ̃⟩	NOUN
cana-2411	189	83	)	)	PUNCT
cana-2411	189	84	=	=	PUNCT
cana-2411	189	85	ℛ(⟨	ℛ(⟨	NOUN
cana-2411	189	86	�	�	PROPN
cana-2411	189	87	̃	̃	PROPN
cana-2411	189	88	�	�	NOUN
cana-2411	189	89	𝒩	𝒩	PROPN
cana-2411	189	90	,	,	PUNCT
cana-2411	189	91	�	�	PROPN
cana-2411	189	92	̃	̃	PROPN
cana-2411	189	93	�	�	NOUN
cana-2411	189	94	𝒩⟩	𝒩⟩	NOUN
cana-2411	189	95	)	)	PUNCT
cana-2411	189	96	ℛ(⟨	ℛ(⟨	NOUN
cana-2411	189	97	�	�	PROPN
cana-2411	189	98	̃	̃	PROPN
cana-2411	189	99	�	�	PROPN
cana-2411	189	100	�	�	PROPN
cana-2411	189	101	̃	̃	PROPN
cana-2411	189	102	�	�	PROPN
cana-2411	189	103	𝒩	𝒩	PROPN
cana-2411	189	104	,	,	PUNCT
cana-2411	189	105	�	�	PROPN
cana-2411	189	106	̃	̃	PROPN
cana-2411	189	107	�	�	NOUN
cana-2411	189	108	𝒩⟩	𝒩⟩	NOUN
cana-2411	189	109	)	)	PUNCT
cana-2411	189	110	therefore	therefore	ADV
cana-2411	189	111	,	,	PUNCT
cana-2411	189	112	the	the	DET
cana-2411	189	113	iteration	iteration	NOUN
cana-2411	189	114	process	process	NOUN
cana-2411	189	115	of	of	ADP
cana-2411	189	116	steepest	steep	ADJ
cana-2411	189	117	descent	descent	NOUN
cana-2411	189	118	for	for	ADP
cana-2411	189	119	the	the	DET
cana-2411	189	120	quadratic	quadratic	ADJ
cana-2411	189	121	function	function	NOUN
cana-2411	189	122	is	be	AUX
cana-2411	189	123	expressed	express	VERB
cana-2411	189	124	as	as	ADP
cana-2411	189	125	ℛ(υ̃κ+1	ℛ(υ̃κ+1	NOUN
cana-2411	189	126	)	)	PUNCT
cana-2411	190	1	=	=	SYM
cana-2411	190	2	ℛ	ℛ	PROPN
cana-2411	190	3	(	(	PUNCT
cana-2411	190	4	υ̃κ	υ̃κ	NOUN
cana-2411	190	5	−	−	ADP
cana-2411	190	6	⟨(	⟨(	NUM
cana-2411	190	7	�	�	SYM
cana-2411	190	8	̃	̃	NOUN
cana-2411	190	9	�	�	NOUN
cana-2411	190	10	κ)𝒩	κ)𝒩	NOUN
cana-2411	190	11	,	,	PUNCT
cana-2411	190	12	(	(	PUNCT
cana-2411	190	13	�	�	PROPN
cana-2411	190	14	̃	̃	NOUN
cana-2411	190	15	�	�	NOUN
cana-2411	190	16	κ)𝒩⟩	κ)𝒩⟩	NOUN
cana-2411	190	17	⟨	⟨	NOUN
cana-2411	190	18	�	�	PROPN
cana-2411	190	19	̃	̃	PROPN
cana-2411	190	20	�	�	PROPN
cana-2411	190	21	(	(	PUNCT
cana-2411	190	22	�	�	PROPN
cana-2411	190	23	̃	̃	NOUN
cana-2411	190	24	�	�	NOUN
cana-2411	190	25	κ)𝒩	κ)𝒩	NOUN
cana-2411	190	26	,	,	PUNCT
cana-2411	190	27	(	(	PUNCT
cana-2411	190	28	�	�	PROPN
cana-2411	190	29	̃	̃	NOUN
cana-2411	190	30	�	�	PROPN
cana-2411	190	31	κ)𝒩⟩	κ)𝒩⟩	PROPN
cana-2411	190	32	(	(	PUNCT
cana-2411	190	33	�	�	PROPN
cana-2411	190	34	̃	̃	NOUN
cana-2411	190	35	�	�	NOUN
cana-2411	190	36	κ)𝒩	κ)𝒩	NOUN
cana-2411	190	37	)	)	PUNCT
cana-2411	190	38	(	(	PUNCT
cana-2411	190	39	4	4	X
cana-2411	190	40	)	)	PUNCT
cana-2411	190	41	using	use	VERB
cana-2411	190	42	the	the	DET
cana-2411	190	43	above	above	ADJ
cana-2411	190	44	formulation	formulation	NOUN
cana-2411	190	45	and	and	CCONJ
cana-2411	190	46	the	the	DET
cana-2411	190	47	fact	fact	NOUN
cana-2411	190	48	that	that	SCONJ
cana-2411	190	49	ℛ	ℛ	PROPN
cana-2411	190	50	(	(	PUNCT
cana-2411	190	51	f̃	f̃	PROPN
cana-2411	190	52	𝒩	𝒩	PROPN
cana-2411	190	53	(	(	PUNCT
cana-2411	190	54	υ̃κ+1	υ̃κ+1	PROPN
cana-2411	190	55	)	)	PUNCT
cana-2411	190	56	)	)	PUNCT
cana-2411	191	1	=	=	SYM
cana-2411	191	2	ℛ	ℛ	PROPN
cana-2411	191	3	(	(	PUNCT
cana-2411	191	4	f̃	f̃	PROPN
cana-2411	191	5	𝒩	𝒩	PROPN
cana-2411	191	6	(	(	PUNCT
cana-2411	191	7	υ̃κ	υ̃κ	NOUN
cana-2411	191	8	)	)	PUNCT
cana-2411	191	9	−	−	NOUN
cana-2411	191	10	1	1	NUM
cana-2411	191	11	2	2	NUM
cana-2411	191	12	[	[	X
cana-2411	191	13	〈	〈	ADJ
cana-2411	191	14	(	(	PUNCT
cana-2411	191	15	�	�	PROPN
cana-2411	191	16	̃	̃	NOUN
cana-2411	191	17	�	�	NOUN
cana-2411	191	18	κ)𝒩	κ)𝒩	NOUN
cana-2411	191	19	,	,	PUNCT
cana-2411	191	20	(	(	PUNCT
cana-2411	191	21	�	�	PROPN
cana-2411	191	22	̃	̃	NOUN
cana-2411	191	23	�	�	PROPN
cana-2411	191	24	κ)𝒩〉]2	κ)𝒩〉]2	PROPN
cana-2411	191	25	〈	〈	PROPN
cana-2411	191	26	�	�	PROPN
cana-2411	191	27	̃	̃	PROPN
cana-2411	191	28	�	�	PROPN
cana-2411	191	29	(	(	PUNCT
cana-2411	191	30	�	�	PROPN
cana-2411	191	31	̃	̃	NOUN
cana-2411	191	32	�	�	NOUN
cana-2411	191	33	κ)𝒩	κ)𝒩	NOUN
cana-2411	191	34	,	,	PUNCT
cana-2411	191	35	(	(	PUNCT
cana-2411	191	36	�	�	PROPN
cana-2411	191	37	̃	̃	NOUN
cana-2411	191	38	�	�	NOUN
cana-2411	191	39	κ)𝒩	κ)𝒩	NOUN
cana-2411	191	40	〉	〉	NOUN
cana-2411	191	41	)	)	PUNCT
cana-2411	191	42	the	the	PRON
cana-2411	191	43	gives	give	VERB
cana-2411	191	44	ℛ	ℛ	PROPN
cana-2411	191	45	(	(	PUNCT
cana-2411	191	46	f̃	f̃	PROPN
cana-2411	191	47	𝒩	𝒩	PROPN
cana-2411	191	48	(	(	PUNCT
cana-2411	191	49	υ̃κ)−f̃	υ̃κ)−f̃	PROPN
cana-2411	191	50	𝒩	𝒩	PROPN
cana-2411	191	51	(	(	PUNCT
cana-2411	191	52	υ̃κ+1	υ̃κ+1	PROPN
cana-2411	191	53	)	)	PUNCT
cana-2411	191	54	f̃	f̃	PROPN
cana-2411	191	55	𝒩	𝒩	PROPN
cana-2411	191	56	(	(	PUNCT
cana-2411	191	57	υ̃κ	υ̃κ	NOUN
cana-2411	191	58	)	)	PUNCT
cana-2411	191	59	)	)	PUNCT
cana-2411	192	1	=	=	SYM
cana-2411	192	2	ℛ	ℛ	PROPN
cana-2411	192	3	(	(	PUNCT
cana-2411	192	4	[	[	X
cana-2411	192	5	〈	〈	ADJ
cana-2411	192	6	(	(	PUNCT
cana-2411	192	7	�	�	PROPN
cana-2411	192	8	̃	̃	NOUN
cana-2411	192	9	�	�	NOUN
cana-2411	192	10	κ)𝒩	κ)𝒩	NOUN
cana-2411	192	11	,	,	PUNCT
cana-2411	192	12	(	(	PUNCT
cana-2411	192	13	�	�	PROPN
cana-2411	192	14	̃	̃	NOUN
cana-2411	192	15	�	�	PROPN
cana-2411	192	16	κ)𝒩〉]2	κ)𝒩〉]2	PROPN
cana-2411	192	17	〈	〈	PROPN
cana-2411	192	18	�	�	PROPN
cana-2411	192	19	̃	̃	PROPN
cana-2411	192	20	�	�	PROPN
cana-2411	192	21	(	(	PUNCT
cana-2411	192	22	�	�	PROPN
cana-2411	192	23	̃	̃	NOUN
cana-2411	192	24	�	�	NOUN
cana-2411	192	25	κ)𝒩	κ)𝒩	NOUN
cana-2411	192	26	,	,	PUNCT
cana-2411	192	27	(	(	PUNCT
cana-2411	192	28	�	�	PROPN
cana-2411	192	29	̃	̃	PROPN
cana-2411	192	30	�	�	NOUN
cana-2411	192	31	κ)𝒩〉〈(	κ)𝒩〉〈(	VERB
cana-2411	192	32	�	�	PROPN
cana-2411	192	33	̃	̃	PROPN
cana-2411	192	34	�	�	NOUN
cana-2411	192	35	κ)𝒩	κ)𝒩	NOUN
cana-2411	192	36	,	,	PUNCT
cana-2411	192	37	�	�	PROPN
cana-2411	192	38	̃	̃	PROPN
cana-2411	192	39	�	�	PROPN
cana-2411	192	40	−1(	−1(	PROPN
cana-2411	192	41	�	�	PROPN
cana-2411	192	42	̃	̃	NOUN
cana-2411	192	43	�	�	NOUN
cana-2411	192	44	κ)𝒩	κ)𝒩	NOUN
cana-2411	192	45	〉	〉	NOUN
cana-2411	192	46	)	)	PUNCT
cana-2411	192	47	and	and	CCONJ
cana-2411	192	48	hence	hence	ADV
cana-2411	192	49	communications	communication	NOUN
cana-2411	192	50	on	on	ADP
cana-2411	192	51	applied	apply	VERB
cana-2411	192	52	nonlinear	nonlinear	ADJ
cana-2411	192	53	analysis	analysis	NOUN
cana-2411	192	54	issn	issn	NOUN
cana-2411	192	55	:	:	PUNCT
cana-2411	192	56	1074	1074	NUM
cana-2411	192	57	-	-	PUNCT
cana-2411	192	58	133x	133x	NUM
cana-2411	192	59	vol	vol	NOUN
cana-2411	192	60	32	32	NUM
cana-2411	192	61	no	no	NOUN
cana-2411	192	62	.	.	PUNCT
cana-2411	193	1	2s	2s	NUM
cana-2411	193	2	(	(	PUNCT
cana-2411	193	3	2025	2025	NUM
cana-2411	193	4	)	)	PUNCT
cana-2411	193	5	374	374	NUM
cana-2411	193	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2411	193	7	ℛ(f̃	ℛ(f̃	PROPN
cana-2411	193	8	𝒩	𝒩	PROPN
cana-2411	193	9	(	(	PUNCT
cana-2411	193	10	υ̃κ+1	υ̃κ+1	PROPN
cana-2411	193	11	)	)	PUNCT
cana-2411	193	12	)	)	PUNCT
cana-2411	194	1	=	=	PUNCT
cana-2411	195	1	ℛ((1−	ℛ((1−	NOUN
cana-2411	195	2	μ	μ	NOUN
cana-2411	195	3	κ	κ	NOUN
cana-2411	195	4	)	)	PUNCT
cana-2411	195	5	f̃	f̃	PROPN
cana-2411	195	6	𝒩	𝒩	PROPN
cana-2411	195	7	(	(	PUNCT
cana-2411	195	8	υ̃κ	υ̃κ	NOUN
cana-2411	195	9	)	)	PUNCT
cana-2411	195	10	)	)	PUNCT
cana-2411	195	11	(	(	PUNCT
cana-2411	195	12	4a	4a	NOUN
cana-2411	195	13	)	)	PUNCT
cana-2411	195	14	where	where	SCONJ
cana-2411	195	15	μ	μ	PROPN
cana-2411	195	16	κ	κ	X
cana-2411	195	17	=	=	X
cana-2411	196	1	[	[	X
cana-2411	196	2	〈	〈	ADJ
cana-2411	196	3	(	(	PUNCT
cana-2411	196	4	�	�	PROPN
cana-2411	196	5	̃	̃	NOUN
cana-2411	196	6	�	�	NOUN
cana-2411	196	7	κ)𝒩	κ)𝒩	NOUN
cana-2411	196	8	,	,	PUNCT
cana-2411	196	9	(	(	PUNCT
cana-2411	196	10	�	�	PROPN
cana-2411	196	11	̃	̃	NOUN
cana-2411	196	12	�	�	PROPN
cana-2411	196	13	κ)𝒩〉]2	κ)𝒩〉]2	PROPN
cana-2411	196	14	〈	〈	PROPN
cana-2411	196	15	�	�	PROPN
cana-2411	196	16	̃	̃	PROPN
cana-2411	196	17	�	�	PROPN
cana-2411	196	18	(	(	PUNCT
cana-2411	196	19	�	�	PROPN
cana-2411	196	20	̃	̃	NOUN
cana-2411	196	21	�	�	NOUN
cana-2411	196	22	κ)𝒩	κ)𝒩	NOUN
cana-2411	196	23	,	,	PUNCT
cana-2411	196	24	(	(	PUNCT
cana-2411	196	25	�	�	PROPN
cana-2411	196	26	̃	̃	PROPN
cana-2411	196	27	�	�	NOUN
cana-2411	196	28	κ)𝒩〉〈(	κ)𝒩〉〈(	VERB
cana-2411	196	29	�	�	PROPN
cana-2411	196	30	̃	̃	PROPN
cana-2411	196	31	�	�	NOUN
cana-2411	196	32	κ)𝒩	κ)𝒩	NOUN
cana-2411	196	33	,	,	PUNCT
cana-2411	196	34	�	�	PROPN
cana-2411	196	35	̃	̃	PROPN
cana-2411	196	36	�	�	PROPN
cana-2411	196	37	−1(	−1(	PROPN
cana-2411	196	38	�	�	PROPN
cana-2411	196	39	̃	̃	NOUN
cana-2411	196	40	�	�	NOUN
cana-2411	196	41	κ)𝒩	κ)𝒩	NOUN
cana-2411	196	42	〉	〉	NOUN
cana-2411	196	43	theorem	theorem	VERB
cana-2411	196	44	4.1	4.1	NUM
cana-2411	196	45	let	let	VERB
cana-2411	196	46	the	the	DET
cana-2411	196	47	neutrosophic	neutrosophic	ADJ
cana-2411	196	48	quadratic	quadratic	ADJ
cana-2411	196	49	function	function	NOUN
cana-2411	196	50	denoted	denote	VERB
cana-2411	196	51	as	as	ADP
cana-2411	196	52	f̃	f̃	PROPN
cana-2411	196	53	𝒩	𝒩	PROPN
cana-2411	196	54	,	,	PUNCT
cana-2411	196	55	defined	define	VERB
cana-2411	196	56	by	by	ADP
cana-2411	196	57	the	the	DET
cana-2411	196	58	expressions	expression	NOUN
cana-2411	196	59	in	in	ADP
cana-2411	196	60	(	(	PUNCT
cana-2411	196	61	3	3	NUM
cana-2411	196	62	)	)	PUNCT
cana-2411	196	63	,	,	PUNCT
cana-2411	196	64	f̃	f̃	PROPN
cana-2411	196	65	𝒩	𝒩	PROPN
cana-2411	196	66	(	(	PUNCT
cana-2411	196	67	υ̃	υ̃	PROPN
cana-2411	196	68	)	)	PUNCT
cana-2411	197	1	≈	≈	PROPN
cana-2411	197	2	1	1	NUM
cana-2411	197	3	2	2	NUM
cana-2411	197	4	υ̃t	υ̃t	PROPN
cana-2411	197	5	�	�	PROPN
cana-2411	197	6	̃	̃	PROPN
cana-2411	197	7	�	�	PROPN
cana-2411	197	8	υ̃	υ̃	PROPN
cana-2411	197	9	≈	≈	PROPN
cana-2411	197	10	1	1	NUM
cana-2411	197	11	2	2	NUM
cana-2411	197	12	〈	〈	PROPN
cana-2411	197	13	�	�	PROPN
cana-2411	197	14	̃	̃	PROPN
cana-2411	197	15	�	�	PROPN
cana-2411	197	16	υ̃	υ̃	PROPN
cana-2411	197	17	,	,	PUNCT
cana-2411	197	18	υ̃	υ̃	PROPN
cana-2411	197	19	〉	〉	PROPN
cana-2411	197	20	and	and	CCONJ
cana-2411	197	21	(	(	PUNCT
cana-2411	197	22	υ̃κ	υ̃κ	X
cana-2411	197	23	)	)	PUNCT
cana-2411	197	24	represent	represent	VERB
cana-2411	197	25	the	the	DET
cana-2411	197	26	iterates	iterate	NOUN
cana-2411	197	27	generated	generate	VERB
cana-2411	197	28	by	by	ADP
cana-2411	197	29	the	the	DET
cana-2411	197	30	process	process	NOUN
cana-2411	198	1	υ̃κ+1	υ̃κ+1	NOUN
cana-2411	198	2	=	=	PUNCT
cana-2411	198	3	υ̃κ	υ̃κ	X
cana-2411	199	1	−	−	PROPN
cana-2411	199	2	〈	〈	PROPN
cana-2411	199	3	(	(	PUNCT
cana-2411	199	4	�	�	PROPN
cana-2411	199	5	̃	̃	NOUN
cana-2411	199	6	�	�	NOUN
cana-2411	199	7	κ)𝒩	κ)𝒩	NOUN
cana-2411	199	8	,	,	PUNCT
cana-2411	199	9	(	(	PUNCT
cana-2411	199	10	�	�	PROPN
cana-2411	199	11	̃	̃	NOUN
cana-2411	199	12	�	�	NOUN
cana-2411	199	13	κ)𝒩	κ)𝒩	NOUN
cana-2411	199	14	〉	〉	NOUN
cana-2411	199	15	〈	〈	PROPN
cana-2411	199	16	�	�	PROPN
cana-2411	199	17	̃	̃	PROPN
cana-2411	199	18	�	�	PROPN
cana-2411	199	19	(	(	PUNCT
cana-2411	199	20	�	�	PROPN
cana-2411	199	21	̃	̃	NOUN
cana-2411	199	22	�	�	NOUN
cana-2411	199	23	κ)𝒩	κ)𝒩	NOUN
cana-2411	199	24	,	,	PUNCT
cana-2411	199	25	(	(	PUNCT
cana-2411	199	26	�	�	PROPN
cana-2411	199	27	̃	̃	NOUN
cana-2411	199	28	�	�	NOUN
cana-2411	199	29	κ)𝒩	κ)𝒩	NOUN
cana-2411	199	30	〉	〉	NOUN
cana-2411	199	31	(	(	PUNCT
cana-2411	199	32	�	�	PROPN
cana-2411	199	33	̃	̃	NOUN
cana-2411	199	34	�	�	NOUN
cana-2411	199	35	κ)𝒩	κ)𝒩	NOUN
cana-2411	199	36	the	the	DET
cana-2411	199	37	sequence	sequence	NOUN
cana-2411	199	38	υ̃κ	υ̃κ	PRON
cana-2411	199	39	converges	converge	VERB
cana-2411	199	40	linearly	linearly	ADV
cana-2411	199	41	towards	towards	ADP
cana-2411	199	42	the	the	DET
cana-2411	199	43	minimizer	minimizer	NOUN
cana-2411	199	44	υ̃∗	υ̃∗	ADP
cana-2411	199	45	,	,	PUNCT
cana-2411	199	46	which	which	PRON
cana-2411	199	47	is	be	AUX
cana-2411	199	48	approximately	approximately	ADV
cana-2411	199	49	identical	identical	ADJ
cana-2411	199	50	to	to	ADP
cana-2411	199	51	0̃	0̃	PROPN
cana-2411	199	52	,	,	PUNCT
cana-2411	199	53	starting	start	VERB
cana-2411	199	54	from	from	ADP
cana-2411	199	55	any	any	DET
cana-2411	199	56	initial	initial	ADJ
cana-2411	199	57	approximation	approximation	NOUN
cana-2411	199	58	υ̃0	υ̃0	NOUN
cana-2411	199	59	.	.	PUNCT
cana-2411	200	1	proof	proof	NOUN
cana-2411	200	2	:	:	PUNCT
cana-2411	200	3	to	to	PART
cana-2411	200	4	prove	prove	VERB
cana-2411	200	5	υ̃κ+1	υ̃κ+1	NOUN
cana-2411	200	6	=	=	PUNCT
cana-2411	200	7	υ̃κ	υ̃κ	PART
cana-2411	201	1	−	−	PROPN
cana-2411	201	2	〈	〈	PROPN
cana-2411	201	3	(	(	PUNCT
cana-2411	201	4	�	�	PROPN
cana-2411	201	5	̃	̃	NOUN
cana-2411	201	6	�	�	NOUN
cana-2411	201	7	κ)𝒩	κ)𝒩	NOUN
cana-2411	201	8	,	,	PUNCT
cana-2411	201	9	(	(	PUNCT
cana-2411	201	10	�	�	PROPN
cana-2411	201	11	̃	̃	NOUN
cana-2411	201	12	�	�	NOUN
cana-2411	201	13	κ)𝒩	κ)𝒩	NOUN
cana-2411	201	14	〉	〉	NOUN
cana-2411	201	15	〈	〈	PROPN
cana-2411	201	16	�	�	PROPN
cana-2411	201	17	̃	̃	PROPN
cana-2411	201	18	�	�	PROPN
cana-2411	201	19	(	(	PUNCT
cana-2411	201	20	�	�	PROPN
cana-2411	201	21	̃	̃	NOUN
cana-2411	201	22	�	�	NOUN
cana-2411	201	23	κ)𝒩	κ)𝒩	NOUN
cana-2411	201	24	,	,	PUNCT
cana-2411	201	25	(	(	PUNCT
cana-2411	201	26	�	�	PROPN
cana-2411	201	27	̃	̃	NOUN
cana-2411	201	28	�	�	NOUN
cana-2411	201	29	κ)𝒩	κ)𝒩	NOUN
cana-2411	201	30	〉	〉	NOUN
cana-2411	201	31	(	(	PUNCT
cana-2411	201	32	�	�	PROPN
cana-2411	201	33	̃	̃	NOUN
cana-2411	201	34	�	�	NOUN
cana-2411	201	35	κ)𝒩	κ)𝒩	NOUN
cana-2411	201	36	,	,	PUNCT
cana-2411	201	37	it	it	PRON
cana-2411	201	38	is	be	AUX
cana-2411	201	39	enough	enough	ADJ
cana-2411	201	40	to	to	PART
cana-2411	201	41	prove	prove	VERB
cana-2411	201	42	ℛ(υ̃κ+1	ℛ(υ̃κ+1	NOUN
cana-2411	201	43	)	)	PUNCT
cana-2411	202	1	=	=	SYM
cana-2411	202	2	ℛ	ℛ	PROPN
cana-2411	202	3	(	(	PUNCT
cana-2411	202	4	υ̃κ	υ̃κ	NOUN
cana-2411	202	5	−	−	ADP
cana-2411	202	6	⟨(	⟨(	NUM
cana-2411	202	7	�	�	SYM
cana-2411	202	8	̃	̃	NOUN
cana-2411	202	9	�	�	NOUN
cana-2411	202	10	κ)𝒩	κ)𝒩	NOUN
cana-2411	202	11	,	,	PUNCT
cana-2411	202	12	(	(	PUNCT
cana-2411	202	13	�	�	PROPN
cana-2411	202	14	̃	̃	NOUN
cana-2411	202	15	�	�	NOUN
cana-2411	202	16	κ)𝒩⟩	κ)𝒩⟩	NOUN
cana-2411	202	17	⟨	⟨	NOUN
cana-2411	202	18	�	�	PROPN
cana-2411	202	19	̃	̃	PROPN
cana-2411	202	20	�	�	PROPN
cana-2411	202	21	(	(	PUNCT
cana-2411	202	22	�	�	PROPN
cana-2411	202	23	̃	̃	NOUN
cana-2411	202	24	�	�	NOUN
cana-2411	202	25	κ)𝒩	κ)𝒩	NOUN
cana-2411	202	26	,	,	PUNCT
cana-2411	202	27	(	(	PUNCT
cana-2411	202	28	�	�	PROPN
cana-2411	202	29	̃	̃	NOUN
cana-2411	202	30	�	�	PROPN
cana-2411	202	31	κ)𝒩⟩	κ)𝒩⟩	PROPN
cana-2411	202	32	(	(	PUNCT
cana-2411	202	33	�	�	PROPN
cana-2411	202	34	̃	̃	NOUN
cana-2411	202	35	�	�	NOUN
cana-2411	202	36	κ)𝒩	κ)𝒩	NOUN
cana-2411	202	37	)	)	PUNCT
cana-2411	202	38	outlined	outline	VERB
cana-2411	202	39	in	in	ADP
cana-2411	202	40	equation	equation	NOUN
cana-2411	202	41	(	(	PUNCT
cana-2411	202	42	4	4	NUM
cana-2411	202	43	)	)	PUNCT
cana-2411	202	44	.	.	PUNCT
cana-2411	203	1	that	that	PRON
cana-2411	203	2	is	be	AUX
cana-2411	203	3	it	it	PRON
cana-2411	203	4	is	be	AUX
cana-2411	203	5	enough	enough	ADJ
cana-2411	203	6	to	to	PART
cana-2411	203	7	prove	prove	VERB
cana-2411	203	8	ℛ	ℛ	PROPN
cana-2411	203	9	(	(	PUNCT
cana-2411	203	10	f̃	f̃	PROPN
cana-2411	203	11	𝒩	𝒩	PROPN
cana-2411	203	12	(	(	PUNCT
cana-2411	203	13	υ̃κ+1	υ̃κ+1	PROPN
cana-2411	203	14	)	)	PUNCT
cana-2411	203	15	)	)	PUNCT
cana-2411	204	1	=	=	PUNCT
cana-2411	205	1	ℛ((1−	ℛ((1−	PROPN
cana-2411	205	2	μ̃	μ̃	PROPN
cana-2411	205	3	κ	κ	NOUN
cana-2411	205	4	)	)	PUNCT
cana-2411	205	5	f̃	f̃	PROPN
cana-2411	205	6	𝒩	𝒩	PROPN
cana-2411	205	7	(	(	PUNCT
cana-2411	205	8	υ̃κ	υ̃κ	NOUN
cana-2411	205	9	)	)	PUNCT
cana-2411	205	10	)	)	PUNCT
cana-2411	205	11	(	(	PUNCT
cana-2411	205	12	5	5	X
cana-2411	205	13	)	)	PUNCT
cana-2411	205	14	this	this	PRON
cana-2411	205	15	gives	give	VERB
cana-2411	205	16	ℛ	ℛ	PROPN
cana-2411	205	17	(	(	PUNCT
cana-2411	205	18	f̃	f̃	PROPN
cana-2411	205	19	𝒩	𝒩	PROPN
cana-2411	205	20	(	(	PUNCT
cana-2411	205	21	υ̃κ	υ̃κ	NOUN
cana-2411	205	22	)	)	PUNCT
cana-2411	205	23	)	)	PUNCT
cana-2411	206	1	=	=	PUNCT
cana-2411	207	1	∏κ−1	∏κ−1	PROPN
cana-2411	207	2	i=0	i=0	PROPN
cana-2411	207	3	ℛ((1−	ℛ((1−	PROPN
cana-2411	207	4	μ̃	μ̃	PROPN
cana-2411	207	5	κ	κ	NOUN
cana-2411	207	6	)	)	PUNCT
cana-2411	207	7	f̃	f̃	PROPN
cana-2411	207	8	𝒩	𝒩	PROPN
cana-2411	207	9	(	(	PUNCT
cana-2411	207	10	υ̃(0	υ̃(0	NOUN
cana-2411	207	11	)	)	PUNCT
cana-2411	207	12	)	)	PUNCT
cana-2411	207	13	)	)	PUNCT
cana-2411	207	14	,	,	PUNCT
cana-2411	207	15	(	(	PUNCT
cana-2411	207	16	υ̃κ	υ̃κ	X
cana-2411	207	17	)	)	PUNCT
cana-2411	207	18	converges	converge	VERB
cana-2411	207	19	to	to	ADP
cana-2411	207	20	ℛ(υ̃∗	ℛ(υ̃∗	NOUN
cana-2411	207	21	)	)	PUNCT
cana-2411	208	1	=	=	SYM
cana-2411	208	2	0	0	PUNCT
cana-2411	209	1	if	if	SCONJ
cana-2411	209	2	and	and	CCONJ
cana-2411	209	3	only	only	ADV
cana-2411	209	4	if	if	SCONJ
cana-2411	209	5	ℛ(f̃	ℛ(f̃	PROPN
cana-2411	209	6	𝒩	𝒩	PROPN
cana-2411	209	7	(	(	PUNCT
cana-2411	209	8	υ̃κ	υ̃κ	NOUN
cana-2411	209	9	)	)	PUNCT
cana-2411	209	10	)	)	PUNCT
cana-2411	209	11	→	→	SYM
cana-2411	209	12	0	0	NUM
cana-2411	209	13	and	and	CCONJ
cana-2411	209	14	in	in	ADP
cana-2411	209	15	the	the	DET
cana-2411	209	16	view	view	NOUN
cana-2411	209	17	the	the	DET
cana-2411	209	18	above	above	ADJ
cana-2411	209	19	equation	equation	NOUN
cana-2411	209	20	,	,	PUNCT
cana-2411	209	21	this	this	PRON
cana-2411	209	22	is	be	AUX
cana-2411	209	23	possible	possible	ADJ
cana-2411	209	24	if	if	SCONJ
cana-2411	209	25	and	and	CCONJ
cana-2411	209	26	only	only	ADV
cana-2411	209	27	if	if	SCONJ
cana-2411	209	28	∏∞	∏∞	ADJ
cana-2411	209	29	i=0	i=0	PROPN
cana-2411	209	30	ℛ(1−	ℛ(1−	X
cana-2411	209	31	μ̃	μ̃	PROPN
cana-2411	209	32	κ	κ	NOUN
cana-2411	209	33	)	)	PUNCT
cana-2411	209	34	=	=	SYM
cana-2411	209	35	0	0	NUM
cana-2411	209	36	,	,	PUNCT
cana-2411	209	37	which	which	PRON
cana-2411	209	38	is	be	AUX
cana-2411	209	39	true	true	ADJ
cana-2411	209	40	,	,	PUNCT
cana-2411	209	41	because	because	SCONJ
cana-2411	209	42	ℛ(1−	ℛ(1−	PROPN
cana-2411	209	43	μ̃	μ̃	PROPN
cana-2411	209	44	κ	κ	PROPN
cana-2411	209	45	)	)	PUNCT
cana-2411	209	46	≤	≤	NOUN
cana-2411	209	47	ℛ	ℛ	PROPN
cana-2411	209	48	(	(	PUNCT
cana-2411	209	49	γ̃	γ̃	PROPN
cana-2411	209	50	max	max	PROPN
cana-2411	209	51	−γ̃	−γ̃	NOUN
cana-2411	209	52	min	min	NOUN
cana-2411	209	53	γ̃	γ̃	PROPN
cana-2411	209	54	max	max	PROPN
cana-2411	209	55	)	)	PUNCT
cana-2411	209	56	≤	≤	NOUN
cana-2411	209	57	1	1	NUM
cana-2411	209	58	.	.	PUNCT
cana-2411	209	59	as	as	ADP
cana-2411	209	60	ℛ(υ̃∗	ℛ(υ̃∗	NOUN
cana-2411	209	61	)	)	PUNCT
cana-2411	209	62	=	=	SYM
cana-2411	209	63	0	0	NUM
cana-2411	209	64	and	and	CCONJ
cana-2411	209	65	ℛ	ℛ	PROPN
cana-2411	209	66	(	(	PUNCT
cana-2411	209	67	f̃	f̃	PROPN
cana-2411	209	68	𝒩	𝒩	PROPN
cana-2411	209	69	(	(	PUNCT
cana-2411	209	70	υ̃	υ̃	PROPN
cana-2411	209	71	)	)	PUNCT
cana-2411	209	72	)	)	PUNCT
cana-2411	210	1	=	=	SYM
cana-2411	210	2	1	1	NUM
cana-2411	210	3	2	2	NUM
cana-2411	210	4	ℛ(	ℛ(	NOUN
cana-2411	210	5	�	�	PROPN
cana-2411	210	6	̃	̃	PROPN
cana-2411	210	7	�	�	PROPN
cana-2411	210	8	υ̃	υ̃	PROPN
cana-2411	210	9	,	,	PUNCT
cana-2411	210	10	υ̃	υ̃	PROPN
cana-2411	210	11	)	)	PUNCT
cana-2411	210	12	,	,	PUNCT
cana-2411	210	13	rayleigh	rayleigh	PROPN
cana-2411	210	14	inequality	inequality	PROPN
cana-2411	210	15	gives	give	VERB
cana-2411	210	16	ℛ	ℛ	PROPN
cana-2411	210	17	(	(	PUNCT
cana-2411	210	18	γ̃min	γ̃min	NOUN
cana-2411	210	19	2	2	NUM
cana-2411	210	20	∥	∥	NUM
cana-2411	210	21	υ̃κ+1	υ̃κ+1	NOUN
cana-2411	210	22	−	−	NOUN
cana-2411	210	23	υ̃κ	υ̃κ	SYM
cana-2411	210	24	∥2	∥2	NOUN
cana-2411	210	25	)	)	PUNCT
cana-2411	210	26	≤	≤	NOUN
cana-2411	210	27	ℛ(f̃	ℛ(f̃	PROPN
cana-2411	210	28	𝒩	𝒩	PROPN
cana-2411	210	29	(	(	PUNCT
cana-2411	210	30	υ̃κ+1	υ̃κ+1	PROPN
cana-2411	210	31	−	−	PROPN
cana-2411	210	32	υ̃(∗	υ̃(∗	NOUN
cana-2411	210	33	)	)	PUNCT
cana-2411	210	34	)	)	PUNCT
cana-2411	210	35	)	)	PUNCT
cana-2411	211	1	=	=	SYM
cana-2411	211	2	ℛ(f̃	ℛ(f̃	PROPN
cana-2411	211	3	𝒩	𝒩	PROPN
cana-2411	211	4	(	(	PUNCT
cana-2411	211	5	υ̃κ+1	υ̃κ+1	PROPN
cana-2411	211	6	)	)	PUNCT
cana-2411	211	7	)	)	PUNCT
cana-2411	211	8	.	.	PUNCT
cana-2411	212	1	(	(	PUNCT
cana-2411	212	2	6	6	NUM
cana-2411	212	3	)	)	PUNCT
cana-2411	212	4	similarly	similarly	ADV
cana-2411	212	5	,	,	PUNCT
cana-2411	212	6	ℛ	ℛ	PROPN
cana-2411	212	7	(	(	PUNCT
cana-2411	212	8	γ̃	γ̃	PROPN
cana-2411	212	9	max	max	NOUN
cana-2411	212	10	2	2	NUM
cana-2411	212	11	∥	∥	PUNCT
cana-2411	212	12	υ̃κ	υ̃κ	NOUN
cana-2411	213	1	−	−	NOUN
cana-2411	213	2	υ̃(∗	υ̃(∗	NOUN
cana-2411	213	3	)	)	PUNCT
cana-2411	213	4	∥2	∥2	NUM
cana-2411	213	5	)	)	PUNCT
cana-2411	213	6	≥	≥	NOUN
cana-2411	213	7	ℛ(f̃	ℛ(f̃	PROPN
cana-2411	213	8	𝒩	𝒩	PROPN
cana-2411	213	9	(	(	PUNCT
cana-2411	213	10	υ̃κ	υ̃κ	NOUN
cana-2411	213	11	)	)	PUNCT
cana-2411	213	12	−	−	NOUN
cana-2411	213	13	υ̃(∗	υ̃(∗	NOUN
cana-2411	213	14	)	)	PUNCT
cana-2411	213	15	)	)	PUNCT
cana-2411	214	1	=	=	SYM
cana-2411	214	2	ℛ(f̃	ℛ(f̃	PROPN
cana-2411	214	3	𝒩	𝒩	PROPN
cana-2411	214	4	(	(	PUNCT
cana-2411	214	5	υ̃κ	υ̃κ	NOUN
cana-2411	214	6	)	)	PUNCT
cana-2411	214	7	)	)	PUNCT
cana-2411	214	8	(	(	PUNCT
cana-2411	214	9	7	7	X
cana-2411	214	10	)	)	PUNCT
cana-2411	214	11	consequently	consequently	ADV
cana-2411	214	12	(	(	PUNCT
cana-2411	214	13	6	6	NUM
cana-2411	214	14	)	)	PUNCT
cana-2411	214	15	and	and	CCONJ
cana-2411	214	16	(	(	PUNCT
cana-2411	214	17	7	7	NUM
cana-2411	214	18	)	)	PUNCT
cana-2411	214	19	,	,	PUNCT
cana-2411	214	20	we	we	PRON
cana-2411	214	21	get	get	VERB
cana-2411	214	22	ℛ	ℛ	PROPN
cana-2411	214	23	(	(	PUNCT
cana-2411	214	24	γ̃	γ̃	PROPN
cana-2411	214	25	min	min	NOUN
cana-2411	214	26	2	2	NUM
cana-2411	214	27	∥	∥	NUM
cana-2411	214	28	υ̃κ+1	υ̃κ+1	NOUN
cana-2411	214	29	−	−	NOUN
cana-2411	214	30	υ̃κ	υ̃κ	SYM
cana-2411	214	31	∥2	∥2	NOUN
cana-2411	214	32	)	)	PUNCT
cana-2411	214	33	≤	≤	NOUN
cana-2411	214	34	ℛ(f̃	ℛ(f̃	PRON
cana-2411	214	35	𝒩	𝒩	PROPN
cana-2411	214	36	(	(	PUNCT
cana-2411	214	37	υ̃κ+1	υ̃κ+1	PROPN
cana-2411	214	38	)	)	PUNCT
cana-2411	214	39	)	)	PUNCT
cana-2411	215	1	=	=	PUNCT
cana-2411	216	1	ℛ((1−	ℛ((1−	PROPN
cana-2411	216	2	μ̃	μ̃	PROPN
cana-2411	216	3	κ	κ	NOUN
cana-2411	216	4	)	)	PUNCT
cana-2411	216	5	f̃	f̃	PROPN
cana-2411	216	6	𝒩	𝒩	PROPN
cana-2411	216	7	(	(	PUNCT
cana-2411	216	8	υ̃κ	υ̃κ	NOUN
cana-2411	216	9	)	)	PUNCT
cana-2411	216	10	)	)	PUNCT
cana-2411	216	11	≤	≤	NUM
cana-2411	216	12	ℛ	ℛ	PROPN
cana-2411	216	13	(	(	PUNCT
cana-2411	216	14	γ̃	γ̃	PROPN
cana-2411	216	15	max	max	PROPN
cana-2411	216	16	−γ̃	−γ̃	NOUN
cana-2411	216	17	min	min	NOUN
cana-2411	216	18	2	2	NUM
cana-2411	216	19	∥	∥	PUNCT
cana-2411	216	20	υ̃κ	υ̃κ	NOUN
cana-2411	217	1	−	−	ADP
cana-2411	217	2	υ̃∗	υ̃∗	ADV
cana-2411	217	3	∥2	∥2	NUM
cana-2411	217	4	)	)	PUNCT
cana-2411	217	5	communications	communication	NOUN
cana-2411	217	6	on	on	ADP
cana-2411	217	7	applied	apply	VERB
cana-2411	217	8	nonlinear	nonlinear	ADJ
cana-2411	217	9	analysis	analysis	NOUN
cana-2411	217	10	issn	issn	NOUN
cana-2411	217	11	:	:	PUNCT
cana-2411	217	12	1074	1074	NUM
cana-2411	217	13	-	-	PUNCT
cana-2411	217	14	133x	133x	NUM
cana-2411	217	15	vol	vol	NOUN
cana-2411	217	16	32	32	NUM
cana-2411	217	17	no	no	NOUN
cana-2411	217	18	.	.	PUNCT
cana-2411	218	1	2s	2s	NUM
cana-2411	218	2	(	(	PUNCT
cana-2411	218	3	2025	2025	NUM
cana-2411	218	4	)	)	PUNCT
cana-2411	218	5	375	375	NUM
cana-2411	218	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2411	218	7	which	which	PRON
cana-2411	218	8	implies	imply	VERB
cana-2411	218	9	ℛ	ℛ	PROPN
cana-2411	218	10	(	(	PUNCT
cana-2411	218	11	∥υ̃κ+1−υ̃∗∥	∥υ̃κ+1−υ̃∗∥	PROPN
cana-2411	218	12	∥υ̃κ−υ̃∗∥	∥υ̃κ−υ̃∗∥	NOUN
cana-2411	218	13	)	)	PUNCT
cana-2411	218	14	≤	≤	NUM
cana-2411	218	15	ℛ	ℛ	PROPN
cana-2411	218	16	(	(	PUNCT
cana-2411	218	17	√	√	PROPN
cana-2411	218	18	γ̃	γ̃	PROPN
cana-2411	218	19	max	max	PROPN
cana-2411	218	20	−γ̃	−γ̃	NOUN
cana-2411	218	21	min	min	NOUN
cana-2411	218	22	γ̃	γ̃	PROPN
cana-2411	218	23	max	max	PROPN
cana-2411	218	24	)	)	PUNCT
cana-2411	218	25	as	as	ADP
cana-2411	218	26	ℛ	ℛ	PROPN
cana-2411	218	27	(	(	PUNCT
cana-2411	218	28	√	√	PROPN
cana-2411	218	29	γ̃	γ̃	PROPN
cana-2411	218	30	max	max	PROPN
cana-2411	218	31	−γ̃	−γ̃	NOUN
cana-2411	218	32	min	min	NOUN
cana-2411	218	33	γ̃	γ̃	PROPN
cana-2411	218	34	max	max	PROPN
cana-2411	218	35	)	)	PUNCT
cana-2411	218	36	>	>	PUNCT
cana-2411	218	37	0	0	PUNCT
cana-2411	219	1	hence	hence	ADV
cana-2411	219	2	∥υ̃κ+1−υ̃∗∥	∥υ̃κ+1−υ̃∗∥	PROPN
cana-2411	219	3	∥υ̃κ−υ̃∗∥	∥υ̃κ−υ̃∗∥	NOUN
cana-2411	219	4	⪯	⪯	VERB
cana-2411	219	5	√	√	PUNCT
cana-2411	219	6	γ̃	γ̃	PROPN
cana-2411	219	7	max	max	PROPN
cana-2411	219	8	−γ̃	−γ̃	NOUN
cana-2411	219	9	min	min	NOUN
cana-2411	219	10	γ̃	γ̃	PROPN
cana-2411	219	11	max	max	PROPN
cana-2411	219	12	.	.	PUNCT
cana-2411	220	1	it	it	PRON
cana-2411	220	2	implies	imply	VERB
cana-2411	220	3	that	that	SCONJ
cana-2411	220	4	the	the	DET
cana-2411	220	5	convergence	convergence	NOUN
cana-2411	220	6	of	of	ADP
cana-2411	220	7	υ̃κ	υ̃κ	NOUN
cana-2411	220	8	to	to	PART
cana-2411	220	9	υ̃∗	υ̃∗	VERB
cana-2411	220	10	is	be	AUX
cana-2411	220	11	linear	linear	ADJ
cana-2411	220	12	.	.	PUNCT
cana-2411	221	1	4.2	4.2	NUM
cana-2411	221	2	exploring	explore	VERB
cana-2411	221	3	the	the	DET
cana-2411	221	4	neutrosophic	neutrosophic	ADJ
cana-2411	221	5	fletcher	fletcher	PROPN
cana-2411	221	6	-	-	PUNCT
cana-2411	221	7	reeves	reeves	PROPN
cana-2411	221	8	technique	technique	NOUN
cana-2411	221	9	(	(	PUNCT
cana-2411	221	10	neutrosophic	neutrosophic	ADJ
cana-2411	221	11	conjugate	conjugate	ADJ
cana-2411	221	12	gradient	gradient	NOUN
cana-2411	221	13	method	method	NOUN
cana-2411	221	14	)	)	PUNCT
cana-2411	221	15	in	in	ADP
cana-2411	221	16	the	the	DET
cana-2411	221	17	cauchy	cauchy	NOUN
cana-2411	221	18	’s	’s	PART
cana-2411	221	19	steepest	steep	ADJ
cana-2411	221	20	descent	descent	NOUN
cana-2411	221	21	method	method	NOUN
cana-2411	221	22	,	,	PUNCT
cana-2411	221	23	the	the	DET
cana-2411	221	24	determination	determination	NOUN
cana-2411	221	25	of	of	ADP
cana-2411	221	26	(	(	PUNCT
cana-2411	221	27	d̃	d̃	PROPN
cana-2411	221	28	κ	κ	PROPN
cana-2411	221	29	)	)	PUNCT
cana-2411	221	30	𝒩	𝒩	PROPN
cana-2411	221	31	as	as	ADP
cana-2411	221	32	−(	−(	NOUN
cana-2411	221	33	�	�	PROPN
cana-2411	221	34	̃	̃	PROPN
cana-2411	221	35	�	�	NOUN
cana-2411	221	36	κ)𝒩	κ)𝒩	NOUN
cana-2411	221	37	leads	lead	VERB
cana-2411	221	38	the	the	DET
cana-2411	221	39	iterative	iterative	NOUN
cana-2411	221	40	process	process	NOUN
cana-2411	221	41	of	of	ADP
cana-2411	221	42	υ̃κ	υ̃κ	PRON
cana-2411	221	43	towards	towards	ADP
cana-2411	221	44	the	the	DET
cana-2411	221	45	minimizer	minimizer	NOUN
cana-2411	221	46	υ̃∗	υ̃∗	ADP
cana-2411	221	47	in	in	ADP
cana-2411	221	48	a	a	DET
cana-2411	221	49	zigzagging	zigzagging	NOUN
cana-2411	221	50	manner	manner	NOUN
cana-2411	221	51	.	.	PUNCT
cana-2411	222	1	therefore	therefore	ADV
cana-2411	222	2	,	,	PUNCT
cana-2411	222	3	there	there	PRON
cana-2411	222	4	is	be	VERB
cana-2411	222	5	a	a	DET
cana-2411	222	6	necessity	necessity	NOUN
cana-2411	222	7	to	to	PART
cana-2411	222	8	generate	generate	VERB
cana-2411	222	9	a	a	DET
cana-2411	222	10	new	new	ADJ
cana-2411	222	11	search	search	NOUN
cana-2411	222	12	direction	direction	NOUN
cana-2411	222	13	function	function	NOUN
cana-2411	222	14	(	(	PUNCT
cana-2411	222	15	d̃	d̃	PROPN
cana-2411	222	16	κ	κ	PROPN
cana-2411	222	17	)	)	PUNCT
cana-2411	222	18	𝒩	𝒩	PROPN
cana-2411	222	19	that	that	PRON
cana-2411	222	20	will	will	AUX
cana-2411	222	21	accelerate	accelerate	VERB
cana-2411	222	22	the	the	DET
cana-2411	222	23	convergence	convergence	NOUN
cana-2411	222	24	of	of	ADP
cana-2411	222	25	the	the	DET
cana-2411	222	26	iterates	iterate	NOUN
cana-2411	222	27	{	{	PUNCT
cana-2411	222	28	υ̃κ	υ̃κ	NOUN
cana-2411	222	29	}	}	PUNCT
cana-2411	222	30	towards	towards	ADP
cana-2411	222	31	υ̃∗.	υ̃∗.	NOUN
cana-2411	222	32	consider	consider	VERB
cana-2411	222	33	the	the	DET
cana-2411	222	34	quadratic	quadratic	ADJ
cana-2411	222	35	function	function	NOUN
cana-2411	222	36	given	give	VERB
cana-2411	222	37	in	in	ADP
cana-2411	222	38	(	(	PUNCT
cana-2411	222	39	3	3	NUM
cana-2411	222	40	)	)	PUNCT
cana-2411	222	41	,	,	PUNCT
cana-2411	222	42	f̃	f̃	PROPN
cana-2411	222	43	𝒩	𝒩	PROPN
cana-2411	222	44	(	(	PUNCT
cana-2411	222	45	υ̃	υ̃	PROPN
cana-2411	222	46	)	)	PUNCT
cana-2411	223	1	≈	≈	PROPN
cana-2411	223	2	1	1	NUM
cana-2411	223	3	2	2	NUM
cana-2411	223	4	υ̃t	υ̃t	PROPN
cana-2411	223	5	�	�	PROPN
cana-2411	223	6	̃	̃	PROPN
cana-2411	223	7	�	�	PROPN
cana-2411	223	8	υ̃	υ̃	PROPN
cana-2411	223	9	≈	≈	PROPN
cana-2411	223	10	1	1	NUM
cana-2411	223	11	2	2	NUM
cana-2411	223	12	〈	〈	PROPN
cana-2411	223	13	�	�	PROPN
cana-2411	223	14	̃	̃	PROPN
cana-2411	223	15	�	�	PROPN
cana-2411	223	16	υ̃	υ̃	PROPN
cana-2411	223	17	,	,	PUNCT
cana-2411	223	18	υ̃	υ̃	PROPN
cana-2411	223	19	〉	〉	PROPN
cana-2411	223	20	with	with	ADP
cana-2411	223	21	�	�	PROPN
cana-2411	223	22	̃	̃	PROPN
cana-2411	223	23	�	�	NOUN
cana-2411	223	24	positive	positive	ADJ
cana-2411	223	25	definite	definite	NOUN
cana-2411	223	26	.	.	PUNCT
cana-2411	224	1	we	we	PRON
cana-2411	224	2	shall	shall	AUX
cana-2411	224	3	generate	generate	VERB
cana-2411	224	4	ℛ((d̃	ℛ((d̃	PROPN
cana-2411	224	5	κ	κ	NOUN
cana-2411	224	6	)	)	PUNCT
cana-2411	224	7	𝒩	𝒩	PROPN
cana-2411	224	8	)	)	PUNCT
cana-2411	224	9	as	as	ADV
cana-2411	224	10	manually	manually	ADV
cana-2411	224	11	conjugate	conjugate	ADJ
cana-2411	224	12	direction	direction	NOUN
cana-2411	224	13	with	with	ADP
cana-2411	224	14	respect	respect	NOUN
cana-2411	224	15	to	to	ADP
cana-2411	224	16	ℛ(	ℛ(	NOUN
cana-2411	224	17	�	�	PROPN
cana-2411	224	18	̃	̃	PROPN
cana-2411	224	19	�	�	PROPN
cana-2411	224	20	),ℛ(〈	),ℛ(〈	NOUN
cana-2411	224	21	�	�	PROPN
cana-2411	224	22	̃	̃	PROPN
cana-2411	224	23	�	�	PROPN
cana-2411	224	24	(	(	PUNCT
cana-2411	224	25	d̃	d̃	PROPN
cana-2411	224	26	j	j	PROPN
cana-2411	224	27	)	)	PUNCT
cana-2411	224	28	𝒩	𝒩	PROPN
cana-2411	224	29	,	,	PUNCT
cana-2411	224	30	(	(	PUNCT
cana-2411	224	31	d̃	d̃	PROPN
cana-2411	224	32	j	j	PROPN
cana-2411	224	33	)	)	PUNCT
cana-2411	224	34	𝒩	𝒩	PROPN
cana-2411	224	35	〉	〉	NOUN
cana-2411	224	36	)	)	PUNCT
cana-2411	224	37	=	=	SYM
cana-2411	225	1	0	0	NUM
cana-2411	225	2	,	,	PUNCT
cana-2411	225	3	i	i	PRON
cana-2411	225	4	≠	≠	VERB
cana-2411	225	5	j.	j.	NOUN
cana-2411	225	6	the	the	DET
cana-2411	225	7	procedure	procedure	NOUN
cana-2411	225	8	for	for	ADP
cana-2411	225	9	conjugate	conjugate	ADJ
cana-2411	225	10	direction	direction	NOUN
cana-2411	225	11	generation	generation	NOUN
cana-2411	225	12	is	be	AUX
cana-2411	225	13	ℛ	ℛ	ADJ
cana-2411	225	14	(	(	PUNCT
cana-2411	225	15	(	(	PUNCT
cana-2411	225	16	d̃	d̃	PROPN
cana-2411	225	17	0	0	NUM
cana-2411	225	18	)	)	PUNCT
cana-2411	225	19	𝒩	𝒩	PROPN
cana-2411	225	20	)	)	PUNCT
cana-2411	225	21	=	=	SYM
cana-2411	226	1	−ℛ((	−ℛ((	PROPN
cana-2411	226	2	�	�	PROPN
cana-2411	226	3	̃	̃	PROPN
cana-2411	226	4	�	�	NOUN
cana-2411	226	5	0)𝒩	0)𝒩	X
cana-2411	226	6	)	)	PUNCT
cana-2411	227	1	=	=	NOUN
cana-2411	227	2	−ℛ	−ℛ	NOUN
cana-2411	227	3	(	(	PUNCT
cana-2411	227	4	∇f̃	∇f̃	PROPN
cana-2411	227	5	𝒩	𝒩	PROPN
cana-2411	227	6	(	(	PUNCT
cana-2411	227	7	υ̃0	υ̃0	PROPN
cana-2411	227	8	)	)	PUNCT
cana-2411	227	9	)	)	PUNCT
cana-2411	228	1	=	=	PUNCT
cana-2411	228	2	−ℛ(	−ℛ(	PUNCT
cana-2411	228	3	�	�	PROPN
cana-2411	228	4	̃	̃	NOUN
cana-2411	228	5	�	�	NOUN
cana-2411	228	6	𝒩(υ̃0	𝒩(υ̃0	NOUN
cana-2411	228	7	)	)	PUNCT
cana-2411	228	8	)	)	PUNCT
cana-2411	228	9	with	with	ADP
cana-2411	228	10	ℛ(υ̃0	ℛ(υ̃0	ADJ
cana-2411	228	11	)	)	PUNCT
cana-2411	228	12	being	be	AUX
cana-2411	228	13	initial	initial	ADJ
cana-2411	228	14	guess	guess	NOUN
cana-2411	228	15	.	.	PUNCT
cana-2411	229	1	then	then	ADV
cana-2411	229	2	ℛ(υ̃κ+1	ℛ(υ̃κ+1	NUM
cana-2411	229	3	)	)	PUNCT
cana-2411	230	1	=	=	PUNCT
cana-2411	230	2	ℛ(υ̃κ	ℛ(υ̃κ	PUNCT
cana-2411	231	1	−	−	ADP
cana-2411	231	2	α̃κ(d̃	α̃κ(d̃	NOUN
cana-2411	231	3	κ	κ	NOUN
cana-2411	231	4	)	)	PUNCT
cana-2411	231	5	𝒩	𝒩	PROPN
cana-2411	231	6	)	)	PUNCT
cana-2411	231	7	,	,	PUNCT
cana-2411	231	8	we	we	PRON
cana-2411	231	9	get	get	VERB
cana-2411	231	10	ℛ(α̃κ	ℛ(α̃κ	PROPN
cana-2411	231	11	)	)	PUNCT
cana-2411	232	1	=	=	NOUN
cana-2411	232	2	−ℛ	−ℛ	NOUN
cana-2411	232	3	(	(	PUNCT
cana-2411	232	4	〈	〈	PROPN
cana-2411	232	5	(	(	PUNCT
cana-2411	232	6	d̃	d̃	PROPN
cana-2411	232	7	κ	κ	PROPN
cana-2411	232	8	)	)	PUNCT
cana-2411	232	9	𝒩	𝒩	PROPN
cana-2411	232	10	,	,	PUNCT
cana-2411	232	11	(	(	PUNCT
cana-2411	232	12	d̃	d̃	PROPN
cana-2411	232	13	κ	κ	PROPN
cana-2411	232	14	)	)	PUNCT
cana-2411	232	15	𝒩	𝒩	PROPN
cana-2411	232	16	〉	〉	NOUN
cana-2411	232	17	〈	〈	PROPN
cana-2411	232	18	(	(	PUNCT
cana-2411	232	19	�	�	PROPN
cana-2411	232	20	̃	̃	PROPN
cana-2411	232	21	�	�	PROPN
cana-2411	232	22	(d̃	(d̃	SYM
cana-2411	232	23	κ	κ	NOUN
cana-2411	232	24	)	)	PUNCT
cana-2411	232	25	)	)	PUNCT
cana-2411	232	26	𝒩	𝒩	PROPN
cana-2411	232	27	,	,	PUNCT
cana-2411	232	28	(	(	PUNCT
cana-2411	232	29	d̃	d̃	PROPN
cana-2411	232	30	κ	κ	PROPN
cana-2411	232	31	)	)	PUNCT
cana-2411	232	32	𝒩	𝒩	NOUN
cana-2411	232	33	〉	〉	NOUN
cana-2411	232	34	)	)	PUNCT
cana-2411	232	35	.	.	PUNCT
cana-2411	233	1	this	this	DET
cana-2411	233	2	ℛ(α̃κ	ℛ(α̃κ	PROPN
cana-2411	233	3	)	)	PUNCT
cana-2411	233	4	minimize	minimize	VERB
cana-2411	233	5	the	the	DET
cana-2411	233	6	function	function	NOUN
cana-2411	233	7	ℛ(φ̃(α̃	ℛ(φ̃(α̃	NOUN
cana-2411	233	8	)	)	PUNCT
cana-2411	233	9	)	)	PUNCT
cana-2411	234	1	=	=	SYM
cana-2411	234	2	ℛ	ℛ	PROPN
cana-2411	234	3	(	(	PUNCT
cana-2411	234	4	f̃(υ̃	f̃(υ̃	VERB
cana-2411	234	5	−	−	PROPN
cana-2411	234	6	α̃d̃	α̃d̃	PROPN
cana-2411	234	7	κ	κ	PROPN
cana-2411	234	8	)	)	PUNCT
cana-2411	234	9	)	)	PUNCT
cana-2411	234	10	and	and	CCONJ
cana-2411	234	11	hence	hence	ADV
cana-2411	234	12	ℛ(	ℛ(	NOUN
cana-2411	234	13	�	�	PROPN
cana-2411	234	14	̃	̃	PROPN
cana-2411	234	15	�	�	NOUN
cana-2411	234	16	κ+1	κ+1	NUM
cana-2411	234	17	)	)	PUNCT
cana-2411	234	18	is	be	AUX
cana-2411	234	19	orthognal	orthognal	ADJ
cana-2411	234	20	to	to	ADP
cana-2411	234	21	ℛ(d̃	ℛ(d̃	NUM
cana-2411	234	22	κ	κ	NOUN
cana-2411	234	23	)	)	PUNCT
cana-2411	234	24	,	,	PUNCT
cana-2411	234	25	for	for	ADP
cana-2411	234	26	ℛ(α̃	ℛ(α̃	NOUN
cana-2411	234	27	)	)	PUNCT
cana-2411	234	28	that	that	PRON
cana-2411	234	29	minimizes	minimize	VERB
cana-2411	234	30	the	the	DET
cana-2411	234	31	equation	equation	NOUN
cana-2411	234	32	is	be	AUX
cana-2411	234	33	given	give	VERB
cana-2411	234	34	by	by	ADP
cana-2411	234	35	ℛ(ϕ̃	ℛ(ϕ̃	NUM
cana-2411	234	36	′	′	NUM
cana-2411	234	37	(	(	PUNCT
cana-2411	234	38	α̃	α̃	PROPN
cana-2411	234	39	)	)	PUNCT
cana-2411	234	40	)	)	PUNCT
cana-2411	235	1	=	=	SYM
cana-2411	235	2	ℛ	ℛ	PROPN
cana-2411	235	3	(	(	PUNCT
cana-2411	235	4	〈	〈	NOUN
cana-2411	235	5	∇f̃	∇f̃	PROPN
cana-2411	235	6	𝒩	𝒩	PROPN
cana-2411	235	7	(	(	PUNCT
cana-2411	235	8	υ̃−	υ̃−	ADV
cana-2411	235	9	α̃(d̃	α̃(d̃	PROPN
cana-2411	235	10	κ	κ	NOUN
cana-2411	235	11	)	)	PUNCT
cana-2411	235	12	)	)	PUNCT
cana-2411	235	13	𝒩	𝒩	PROPN
cana-2411	235	14	,	,	PUNCT
cana-2411	235	15	(	(	PUNCT
cana-2411	235	16	d̃	d̃	PROPN
cana-2411	235	17	κ	κ	PROPN
cana-2411	235	18	)	)	PUNCT
cana-2411	235	19	𝒩	𝒩	NOUN
cana-2411	235	20	〉	〉	NOUN
cana-2411	235	21	)	)	PUNCT
cana-2411	235	22	=	=	SYM
cana-2411	235	23	0	0	NUM
cana-2411	235	24	which	which	PRON
cana-2411	235	25	is	be	AUX
cana-2411	235	26	same	same	ADJ
cana-2411	235	27	as	as	ADP
cana-2411	235	28	ℛ(〈(	ℛ(〈(	PROPN
cana-2411	235	29	�	�	PROPN
cana-2411	235	30	̃	̃	PROPN
cana-2411	235	31	�	�	NOUN
cana-2411	235	32	κ+1)𝒩	κ+1)𝒩	NOUN
cana-2411	235	33	,	,	PUNCT
cana-2411	235	34	(	(	PUNCT
cana-2411	235	35	d̃	d̃	PROPN
cana-2411	235	36	κ	κ	PROPN
cana-2411	235	37	)	)	PUNCT
cana-2411	235	38	𝒩	𝒩	NOUN
cana-2411	235	39	〉	〉	NOUN
cana-2411	235	40	)	)	PUNCT
cana-2411	235	41	=	=	SYM
cana-2411	235	42	0	0	X
cana-2411	235	43	.	.	PUNCT
cana-2411	236	1	the	the	DET
cana-2411	236	2	nextconjugate	nextconjugate	ADJ
cana-2411	236	3	direction	direction	NOUN
cana-2411	236	4	ℛ(d̃	ℛ(d̃	ADP
cana-2411	236	5	κ+1	κ+1	NUM
cana-2411	236	6	)	)	PUNCT
cana-2411	236	7	𝒩	𝒩	PROPN
cana-2411	236	8	is	be	AUX
cana-2411	236	9	given	give	VERB
cana-2411	236	10	by	by	ADP
cana-2411	236	11	ℛ(d̃	ℛ(d̃	NUM
cana-2411	236	12	κ+1	κ+1	NUM
cana-2411	236	13	)	)	PUNCT
cana-2411	236	14	𝒩	𝒩	PROPN
cana-2411	236	15	+	+	PROPN
cana-2411	236	16	ℛ(β̃	ℛ(β̃	NUM
cana-2411	236	17	κ	κ	X
cana-2411	236	18	(	(	PUNCT
cana-2411	236	19	d̃	d̃	PROPN
cana-2411	236	20	κ	κ	PROPN
cana-2411	236	21	)	)	PUNCT
cana-2411	236	22	𝒩	𝒩	PROPN
cana-2411	236	23	)	)	PUNCT
cana-2411	236	24	where	where	SCONJ
cana-2411	236	25	ℛ((d̃	ℛ((d̃	PROPN
cana-2411	236	26	κ	κ	NOUN
cana-2411	236	27	)	)	PUNCT
cana-2411	236	28	𝒩	𝒩	PROPN
cana-2411	236	29	)	)	PUNCT
cana-2411	236	30	is	be	AUX
cana-2411	236	31	so	so	ADV
cana-2411	236	32	chosen	choose	VERB
cana-2411	236	33	that	that	SCONJ
cana-2411	236	34	ℛ((d̃	ℛ((d̃	PROPN
cana-2411	236	35	κ	κ	NOUN
cana-2411	236	36	)	)	PUNCT
cana-2411	236	37	𝒩	𝒩	PROPN
cana-2411	236	38	)	)	PUNCT
cana-2411	236	39	is	be	AUX
cana-2411	236	40	conjugate	conjugate	ADJ
cana-2411	236	41	to	to	ADP
cana-2411	236	42	ℛ	ℛ	PROPN
cana-2411	236	43	(	(	PUNCT
cana-2411	236	44	(	(	PUNCT
cana-2411	236	45	d̃	d̃	PROPN
cana-2411	236	46	κ+1	κ+1	NUM
cana-2411	236	47	)	)	PUNCT
cana-2411	236	48	𝒩	𝒩	PROPN
cana-2411	236	49	)	)	PUNCT
cana-2411	236	50	with	with	ADP
cana-2411	236	51	respect	respect	NOUN
cana-2411	236	52	to	to	ADP
cana-2411	236	53	ℛ(	ℛ(	NOUN
cana-2411	236	54	�	�	PROPN
cana-2411	236	55	̃	̃	PROPN
cana-2411	236	56	�	�	PROPN
cana-2411	236	57	)	)	PUNCT
cana-2411	236	58	.	.	PUNCT
cana-2411	237	1	this	this	PRON
cana-2411	237	2	gives	give	VERB
cana-2411	237	3	ℛ(β̃	ℛ(β̃	NUM
cana-2411	237	4	κ	κ	NOUN
cana-2411	237	5	)	)	PUNCT
cana-2411	237	6	=	=	SYM
cana-2411	237	7	ℛ	ℛ	PROPN
cana-2411	237	8	(	(	PUNCT
cana-2411	237	9	(	(	PUNCT
cana-2411	237	10	�	�	PROPN
cana-2411	237	11	̃	̃	NOUN
cana-2411	237	12	�	�	NOUN
cana-2411	237	13	κ+1)𝒩	κ+1)𝒩	PROPN
cana-2411	237	14	,	,	PUNCT
cana-2411	237	15	�	�	PROPN
cana-2411	237	16	̃	̃	NOUN
cana-2411	237	17	�	�	PROPN
cana-2411	237	18	(d̃	(d̃	SYM
cana-2411	237	19	κ	κ	NOUN
cana-2411	237	20	)	)	PUNCT
cana-2411	237	21	𝒩	𝒩	PROPN
cana-2411	237	22	(	(	PUNCT
cana-2411	237	23	d̃	d̃	PROPN
cana-2411	237	24	κ	κ	PROPN
cana-2411	237	25	)	)	PUNCT
cana-2411	237	26	𝒩	𝒩	PROPN
cana-2411	237	27	,	,	PUNCT
cana-2411	237	28	�	�	PROPN
cana-2411	237	29	̃	̃	PROPN
cana-2411	237	30	�	�	PROPN
cana-2411	237	31	(d̃	(d̃	SYM
cana-2411	237	32	κ	κ	NOUN
cana-2411	237	33	)	)	PUNCT
cana-2411	237	34	𝒩	𝒩	PROPN
cana-2411	237	35	)	)	PUNCT
cana-2411	237	36	.	.	PUNCT
cana-2411	238	1	to	to	PART
cana-2411	238	2	evaluate	evaluate	VERB
cana-2411	238	3	ℛ(〈(d̃	ℛ(〈(d̃	NOUN
cana-2411	238	4	κ	κ	NOUN
cana-2411	238	5	)	)	PUNCT
cana-2411	238	6	𝒩	𝒩	PROPN
cana-2411	238	7	,	,	PUNCT
cana-2411	238	8	(	(	PUNCT
cana-2411	238	9	�	�	PROPN
cana-2411	238	10	̃	̃	NOUN
cana-2411	238	11	�	�	NOUN
cana-2411	238	12	κ)𝒩	κ)𝒩	NOUN
cana-2411	238	13	〉	〉	NOUN
cana-2411	238	14	)	)	PUNCT
cana-2411	238	15	ℛ(⟨(d̃	ℛ(⟨(d̃	PROPN
cana-2411	238	16	κ	κ	NOUN
cana-2411	238	17	)	)	PUNCT
cana-2411	238	18	𝒩	𝒩	PROPN
cana-2411	238	19	,	,	PUNCT
cana-2411	238	20	(	(	PUNCT
cana-2411	238	21	�	�	PROPN
cana-2411	238	22	̃	̃	NOUN
cana-2411	238	23	�	�	NOUN
cana-2411	238	24	κ)𝒩⟩	κ)𝒩⟩	NOUN
cana-2411	238	25	)	)	PUNCT
cana-2411	238	26	=	=	PUNCT
cana-2411	238	27	−ℛ(⟨(	−ℛ(⟨(	PROPN
cana-2411	238	28	�	�	PROPN
cana-2411	238	29	̃	̃	NOUN
cana-2411	238	30	�	�	NOUN
cana-2411	238	31	κ)𝒩	κ)𝒩	NOUN
cana-2411	238	32	,	,	PUNCT
cana-2411	238	33	(	(	PUNCT
cana-2411	238	34	�	�	PROPN
cana-2411	238	35	̃	̃	NOUN
cana-2411	238	36	�	�	NOUN
cana-2411	238	37	κ)𝒩⟩	κ)𝒩⟩	NOUN
cana-2411	238	38	)	)	PUNCT
cana-2411	239	1	+	+	VERB
cana-2411	239	2	ℛ	ℛ	PROPN
cana-2411	239	3	(	(	PUNCT
cana-2411	239	4	β̃	β̃	PROPN
cana-2411	239	5	κ−1	κ−1	PROPN
cana-2411	239	6	⟨(d̃	⟨(d̃	VERB
cana-2411	239	7	κ−1	κ−1	PROPN
cana-2411	239	8	)	)	PUNCT
cana-2411	239	9	𝒩	𝒩	PROPN
cana-2411	239	10	,	,	PUNCT
cana-2411	239	11	(	(	PUNCT
cana-2411	239	12	�	�	PROPN
cana-2411	239	13	̃	̃	NOUN
cana-2411	239	14	�	�	NOUN
cana-2411	239	15	κ)𝒩⟩	κ)𝒩⟩	NOUN
cana-2411	239	16	)	)	PUNCT
cana-2411	239	17	=	=	SYM
cana-2411	239	18	−ℛ(〈(	−ℛ(〈(	PROPN
cana-2411	239	19	�	�	PROPN
cana-2411	239	20	̃	̃	NOUN
cana-2411	239	21	�	�	NOUN
cana-2411	239	22	κ)𝒩	κ)𝒩	NOUN
cana-2411	239	23	,	,	PUNCT
cana-2411	239	24	(	(	PUNCT
cana-2411	239	25	�	�	PROPN
cana-2411	239	26	̃	̃	NOUN
cana-2411	239	27	�	�	NOUN
cana-2411	239	28	κ)𝒩	κ)𝒩	NOUN
cana-2411	239	29	〉	〉	NOUN
cana-2411	239	30	)	)	PUNCT
cana-2411	239	31	as	as	ADP
cana-2411	239	32	ℛ((	ℛ((	ADJ
cana-2411	239	33	�	�	PROPN
cana-2411	239	34	̃	̃	NOUN
cana-2411	239	35	�	�	NOUN
cana-2411	239	36	κ)𝒩	κ)𝒩	NOUN
cana-2411	239	37	)	)	PUNCT
cana-2411	240	1	⊥	⊥	NOUN
cana-2411	240	2	ℛ((d̃	ℛ((d̃	PROPN
cana-2411	240	3	κ−1	κ−1	PROPN
cana-2411	240	4	)	)	PUNCT
cana-2411	240	5	𝒩	𝒩	PROPN
cana-2411	240	6	)	)	PUNCT
cana-2411	240	7	and	and	CCONJ
cana-2411	240	8	hence	hence	ADV
cana-2411	240	9	ℛ(α̃κ	ℛ(α̃κ	PROPN
cana-2411	240	10	)	)	PUNCT
cana-2411	241	1	=	=	NOUN
cana-2411	241	2	−ℛ	−ℛ	NOUN
cana-2411	241	3	(	(	PUNCT
cana-2411	241	4	〈	〈	PROPN
cana-2411	241	5	(	(	PUNCT
cana-2411	241	6	d̃	d̃	PROPN
cana-2411	241	7	κ	κ	PROPN
cana-2411	241	8	)	)	PUNCT
cana-2411	241	9	𝒩	𝒩	PROPN
cana-2411	241	10	,	,	PUNCT
cana-2411	241	11	(	(	PUNCT
cana-2411	241	12	�	�	PROPN
cana-2411	241	13	̃	̃	NOUN
cana-2411	241	14	�	�	NOUN
cana-2411	241	15	κ)𝒩	κ)𝒩	NOUN
cana-2411	241	16	〉	〉	NOUN
cana-2411	242	1	〈	〈	PROPN
cana-2411	242	2	�	�	PROPN
cana-2411	242	3	̃	̃	PROPN
cana-2411	242	4	�	�	PROPN
cana-2411	242	5	(d̃	(d̃	SYM
cana-2411	242	6	κ	κ	NOUN
cana-2411	242	7	)	)	PUNCT
cana-2411	242	8	𝒩	𝒩	PROPN
cana-2411	242	9	,	,	PUNCT
cana-2411	242	10	(	(	PUNCT
cana-2411	242	11	d̃	d̃	PROPN
cana-2411	242	12	κ	κ	PROPN
cana-2411	242	13	)	)	PUNCT
cana-2411	242	14	𝒩	𝒩	NOUN
cana-2411	242	15	〉	〉	NOUN
cana-2411	242	16	)	)	PUNCT
cana-2411	242	17	.	.	PUNCT
cana-2411	243	1	theorem	theorem	VERB
cana-2411	243	2	4.2	4.2	NUM
cana-2411	243	3	the	the	DET
cana-2411	243	4	neutrosophic	neutrosophic	ADJ
cana-2411	243	5	gradient	gradient	NOUN
cana-2411	243	6	vectors	vector	NOUN
cana-2411	243	7	(	(	PUNCT
cana-2411	243	8	�	�	PROPN
cana-2411	243	9	̃	̃	NOUN
cana-2411	243	10	�	�	NOUN
cana-2411	243	11	κ)𝒩	κ)𝒩	NOUN
cana-2411	243	12	are	be	AUX
cana-2411	243	13	mutually	mutually	ADV
cana-2411	243	14	orthogonal	orthogonal	ADJ
cana-2411	243	15	and	and	CCONJ
cana-2411	243	16	the	the	DET
cana-2411	243	17	direction	direction	NOUN
cana-2411	243	18	search	search	NOUN
cana-2411	243	19	neutrosophic	neutrosophic	ADJ
cana-2411	243	20	vectors	vector	NOUN
cana-2411	243	21	(	(	PUNCT
cana-2411	243	22	d̃	d̃	PROPN
cana-2411	243	23	κ	κ	PROPN
cana-2411	243	24	)	)	PUNCT
cana-2411	243	25	𝒩	𝒩	PROPN
cana-2411	243	26	are	be	AUX
cana-2411	243	27	mutually	mutually	ADV
cana-2411	243	28	𝒬-conjugate	𝒬-conjugate	PROPN
cana-2411	243	29	.	.	PUNCT
cana-2411	243	30	communications	communication	NOUN
cana-2411	243	31	on	on	ADP
cana-2411	243	32	applied	apply	VERB
cana-2411	243	33	nonlinear	nonlinear	ADJ
cana-2411	243	34	analysis	analysis	NOUN
cana-2411	243	35	issn	issn	NOUN
cana-2411	243	36	:	:	PUNCT
cana-2411	243	37	1074	1074	NUM
cana-2411	243	38	-	-	PUNCT
cana-2411	243	39	133x	133x	NUM
cana-2411	243	40	vol	vol	NOUN
cana-2411	243	41	32	32	NUM
cana-2411	243	42	no	no	NOUN
cana-2411	243	43	.	.	PUNCT
cana-2411	244	1	2s	2s	NUM
cana-2411	244	2	(	(	PUNCT
cana-2411	244	3	2025	2025	NUM
cana-2411	244	4	)	)	PUNCT
cana-2411	244	5	376	376	NUM
cana-2411	244	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2411	244	7	proof	proof	NOUN
cana-2411	244	8	:	:	PUNCT
cana-2411	244	9	to	to	PART
cana-2411	244	10	prove	prove	VERB
cana-2411	244	11	the	the	DET
cana-2411	244	12	neutrosophic	neutrosophic	ADJ
cana-2411	244	13	gradient	gradient	NOUN
cana-2411	244	14	vectors	vector	NOUN
cana-2411	244	15	(	(	PUNCT
cana-2411	244	16	�	�	PROPN
cana-2411	244	17	̃	̃	NOUN
cana-2411	244	18	�	�	NOUN
cana-2411	244	19	κ)𝒩	κ)𝒩	NOUN
cana-2411	244	20	are	be	AUX
cana-2411	244	21	mutually	mutually	ADV
cana-2411	244	22	orthogonal	orthogonal	ADJ
cana-2411	244	23	and	and	CCONJ
cana-2411	244	24	the	the	DET
cana-2411	244	25	direction	direction	NOUN
cana-2411	244	26	search	search	NOUN
cana-2411	244	27	neutrosophic	neutrosophic	ADJ
cana-2411	244	28	vectors	vector	NOUN
cana-2411	244	29	(	(	PUNCT
cana-2411	244	30	d̃	d̃	PROPN
cana-2411	244	31	κ	κ	PROPN
cana-2411	244	32	)	)	PUNCT
cana-2411	244	33	𝒩	𝒩	PROPN
cana-2411	244	34	are	be	AUX
cana-2411	244	35	mutually	mutually	ADV
cana-2411	244	36	𝒬-conjugate	𝒬-conjugate	PROPN
cana-2411	244	37	,	,	PUNCT
cana-2411	244	38	it	it	PRON
cana-2411	244	39	is	be	AUX
cana-2411	244	40	enough	enough	ADJ
cana-2411	244	41	to	to	PART
cana-2411	244	42	prove	prove	VERB
cana-2411	244	43	the	the	DET
cana-2411	244	44	neutrosophic	neutrosophic	ADJ
cana-2411	244	45	gradient	gradient	NOUN
cana-2411	244	46	vectors	vector	NOUN
cana-2411	244	47	ℛ((	ℛ((	VERB
cana-2411	244	48	�	�	PROPN
cana-2411	244	49	̃	̃	NOUN
cana-2411	244	50	�	�	NOUN
cana-2411	244	51	κ)𝒩	κ)𝒩	NOUN
cana-2411	244	52	)	)	PUNCT
cana-2411	244	53	are	be	AUX
cana-2411	244	54	mutually	mutually	ADV
cana-2411	244	55	orthogonal	orthogonal	ADJ
cana-2411	244	56	and	and	CCONJ
cana-2411	244	57	the	the	DET
cana-2411	244	58	direction	direction	NOUN
cana-2411	244	59	search	search	NOUN
cana-2411	244	60	neutrosophic	neutrosophic	ADJ
cana-2411	244	61	vectors	vector	NOUN
cana-2411	244	62	ℛ((d̃	ℛ((d̃	NOUN
cana-2411	244	63	κ	κ	NOUN
cana-2411	244	64	)	)	PUNCT
cana-2411	244	65	𝒩	𝒩	PROPN
cana-2411	244	66	)	)	PUNCT
cana-2411	244	67	are	be	AUX
cana-2411	244	68	mutually	mutually	ADV
cana-2411	244	69	𝒬-conjugate	𝒬-conjugate	PROPN
cana-2411	244	70	.	.	PUNCT
cana-2411	245	1	let	let	VERB
cana-2411	245	2	as	as	PART
cana-2411	245	3	prove	prove	VERB
cana-2411	245	4	the	the	DET
cana-2411	245	5	theorem	theorem	NOUN
cana-2411	245	6	by	by	ADP
cana-2411	245	7	mathematical	mathematical	ADJ
cana-2411	245	8	induction	induction	NOUN
cana-2411	245	9	.	.	PUNCT
cana-2411	246	1	the	the	DET
cana-2411	246	2	result	result	NOUN
cana-2411	246	3	is	be	AUX
cana-2411	246	4	true	true	ADJ
cana-2411	246	5	for	for	ADP
cana-2411	246	6	κ	κ	NOUN
cana-2411	246	7	=	=	SYM
cana-2411	246	8	1	1	NUM
cana-2411	246	9	,	,	PUNCT
cana-2411	246	10	since	since	SCONJ
cana-2411	246	11	ℛ((d̃	ℛ((d̃	PROPN
cana-2411	246	12	0	0	NUM
cana-2411	246	13	)	)	PUNCT
cana-2411	246	14	𝒩	𝒩	PROPN
cana-2411	246	15	)	)	PUNCT
cana-2411	246	16	and	and	CCONJ
cana-2411	246	17	ℛ((d̃	ℛ((d̃	PROPN
cana-2411	246	18	1	1	NUM
cana-2411	246	19	)	)	PUNCT
cana-2411	246	20	𝒩	𝒩	PROPN
cana-2411	246	21	)	)	PUNCT
cana-2411	246	22	are	be	AUX
cana-2411	246	23	𝒬-conjugate	𝒬-conjugate	PROPN
cana-2411	246	24	by	by	ADP
cana-2411	246	25	the	the	DET
cana-2411	246	26	choice	choice	NOUN
cana-2411	246	27	of	of	ADP
cana-2411	246	28	ℛ(β̃	ℛ(β̃	NUM
cana-2411	246	29	0	0	NUM
cana-2411	246	30	)	)	PUNCT
cana-2411	246	31	.	.	PUNCT
cana-2411	247	1	also	also	ADV
cana-2411	247	2	ℛ((	ℛ((	VERB
cana-2411	247	3	�	�	PROPN
cana-2411	247	4	̃	̃	NOUN
cana-2411	247	5	�	�	NOUN
cana-2411	247	6	0)𝒩	0)𝒩	X
cana-2411	247	7	)	)	PUNCT
cana-2411	248	1	=	=	PUNCT
cana-2411	248	2	ℛ((−d̃	ℛ((−d̃	NOUN
cana-2411	248	3	0	0	X
cana-2411	248	4	)	)	PUNCT
cana-2411	248	5	𝒩	𝒩	PROPN
cana-2411	248	6	)	)	PUNCT
cana-2411	248	7	is	be	AUX
cana-2411	248	8	orthogonal	orthogonal	ADJ
cana-2411	248	9	to	to	ADP
cana-2411	248	10	ℛ((	ℛ((	ADJ
cana-2411	248	11	�	�	PROPN
cana-2411	248	12	̃	̃	NOUN
cana-2411	248	13	�	�	NOUN
cana-2411	248	14	1)𝒩	1)𝒩	NUM
cana-2411	248	15	)	)	PUNCT
cana-2411	248	16	.	.	PUNCT
cana-2411	249	1	assume	assume	VERB
cana-2411	249	2	that	that	SCONJ
cana-2411	249	3	ℛ((d̃	ℛ((d̃	PRON
cana-2411	249	4	0	0	NUM
cana-2411	249	5	)	)	PUNCT
cana-2411	249	6	𝒩),ℛ((d̃	𝒩),ℛ((d̃	NOUN
cana-2411	249	7	1	1	NUM
cana-2411	249	8	)	)	PUNCT
cana-2411	249	9	𝒩	𝒩	PROPN
cana-2411	249	10	)	)	PUNCT
cana-2411	249	11	,	,	PUNCT
cana-2411	249	12	.	.	PUNCT
cana-2411	249	13	.	.	PUNCT
cana-2411	249	14	.	.	PUNCT
cana-2411	250	1	.	.	PUNCT
cana-2411	251	1	,	,	PUNCT
cana-2411	251	2	ℛ((d̃	ℛ((d̃	PROPN
cana-2411	251	3	m	m	NOUN
cana-2411	251	4	)	)	PUNCT
cana-2411	251	5	𝒩	𝒩	PROPN
cana-2411	251	6	)	)	PUNCT
cana-2411	251	7	are	be	AUX
cana-2411	251	8	mutually	mutually	ADV
cana-2411	251	9	𝒬conjugate	𝒬conjugate	NOUN
cana-2411	251	10	and	and	CCONJ
cana-2411	251	11	ℛ((	ℛ((	ADJ
cana-2411	251	12	�	�	PROPN
cana-2411	251	13	̃	̃	PROPN
cana-2411	251	14	�	�	PROPN
cana-2411	251	15	0)𝒩),ℛ((	0)𝒩),ℛ((	VERB
cana-2411	251	16	�	�	PROPN
cana-2411	251	17	̃	̃	PROPN
cana-2411	251	18	�	�	NOUN
cana-2411	251	19	1)𝒩	1)𝒩	NUM
cana-2411	251	20	)	)	PUNCT
cana-2411	251	21	,	,	PUNCT
cana-2411	251	22	.	.	PUNCT
cana-2411	251	23	.	.	PUNCT
cana-2411	251	24	.	.	PUNCT
cana-2411	252	1	.	.	PUNCT
cana-2411	253	1	,	,	PUNCT
cana-2411	253	2	ℛ((	ℛ((	ADJ
cana-2411	253	3	�	�	PROPN
cana-2411	253	4	̃	̃	PROPN
cana-2411	253	5	�	�	NOUN
cana-2411	253	6	m)𝒩	m)𝒩	NOUN
cana-2411	253	7	)	)	PUNCT
cana-2411	253	8	are	be	AUX
cana-2411	253	9	mutually	mutually	ADV
cana-2411	253	10	orthogonal	orthogonal	ADJ
cana-2411	253	11	.	.	PUNCT
cana-2411	254	1	that	that	PRON
cana-2411	254	2	is	be	AUX
cana-2411	254	3	the	the	DET
cana-2411	254	4	result	result	NOUN
cana-2411	254	5	is	be	AUX
cana-2411	254	6	true	true	ADJ
cana-2411	254	7	for	for	ADP
cana-2411	254	8	κ	κ	NOUN
cana-2411	254	9	=	=	PUNCT
cana-2411	254	10	m.	m.	NOUN
cana-2411	254	11	we	we	PRON
cana-2411	254	12	shall	shall	AUX
cana-2411	254	13	prove	prove	VERB
cana-2411	254	14	the	the	DET
cana-2411	254	15	result	result	NOUN
cana-2411	254	16	for	for	ADP
cana-2411	254	17	κ	κ	NOUN
cana-2411	254	18	=	=	SYM
cana-2411	254	19	m+	m+	NUM
cana-2411	254	20	1	1	NUM
cana-2411	254	21	.	.	PUNCT
cana-2411	255	1	then	then	ADV
cana-2411	255	2	ℛ((	ℛ((	VERB
cana-2411	255	3	�	�	PROPN
cana-2411	255	4	̃	̃	NOUN
cana-2411	255	5	�	�	NOUN
cana-2411	255	6	m+1)𝒩	m+1)𝒩	NOUN
cana-2411	255	7	)	)	PUNCT
cana-2411	255	8	=	=	SYM
cana-2411	255	9	ℛ((	ℛ((	X
cana-2411	255	10	�	�	PROPN
cana-2411	255	11	̃	̃	PROPN
cana-2411	255	12	�	�	NOUN
cana-2411	255	13	m)𝒩	m)𝒩	NOUN
cana-2411	255	14	)	)	PUNCT
cana-2411	255	15	+	+	PROPN
cana-2411	255	16	ℛ(α̃m	ℛ(α̃m	PROPN
cana-2411	255	17	�	�	PROPN
cana-2411	255	18	̃	̃	PROPN
cana-2411	255	19	�	�	PROPN
cana-2411	255	20	(d̃	(d̃	PUNCT
cana-2411	255	21	𝑚	𝑚	NOUN
cana-2411	255	22	)	)	PUNCT
cana-2411	255	23	𝒩	𝒩	PROPN
cana-2411	255	24	)	)	PUNCT
cana-2411	255	25	,	,	PUNCT
cana-2411	255	26	where	where	SCONJ
cana-2411	255	27	ℛ(α̃m	ℛ(α̃m	PUNCT
cana-2411	255	28	)	)	PUNCT
cana-2411	256	1	=	=	NOUN
cana-2411	256	2	−ℛ	−ℛ	NOUN
cana-2411	256	3	(	(	PUNCT
cana-2411	256	4	〈	〈	PROPN
cana-2411	256	5	(	(	PUNCT
cana-2411	256	6	d̃	d̃	PROPN
cana-2411	256	7	m	m	PROPN
cana-2411	256	8	)	)	PUNCT
cana-2411	256	9	𝒩	𝒩	PROPN
cana-2411	256	10	,	,	PUNCT
cana-2411	256	11	(	(	PUNCT
cana-2411	256	12	�	�	PROPN
cana-2411	256	13	̃	̃	PROPN
cana-2411	256	14	�	�	NOUN
cana-2411	256	15	m)𝒩	m)𝒩	NOUN
cana-2411	256	16	〉	〉	NOUN
cana-2411	256	17	〈	〈	PROPN
cana-2411	256	18	(	(	PUNCT
cana-2411	256	19	�	�	PROPN
cana-2411	256	20	̃	̃	PROPN
cana-2411	256	21	�	�	PROPN
cana-2411	256	22	(d̃	(d̃	NOUN
cana-2411	256	23	m	m	NOUN
cana-2411	256	24	)	)	PUNCT
cana-2411	256	25	)	)	PUNCT
cana-2411	256	26	𝒩	𝒩	PROPN
cana-2411	256	27	,	,	PUNCT
cana-2411	256	28	(	(	PUNCT
cana-2411	256	29	d̃	d̃	PROPN
cana-2411	256	30	m	m	PROPN
cana-2411	256	31	)	)	PUNCT
cana-2411	256	32	𝒩	𝒩	NOUN
cana-2411	256	33	〉	〉	NOUN
cana-2411	256	34	)	)	PUNCT
cana-2411	256	35	and	and	CCONJ
cana-2411	256	36	hence	hence	ADV
cana-2411	256	37	ℛ(〈(	ℛ(〈(	PROPN
cana-2411	256	38	�	�	PROPN
cana-2411	256	39	̃	̃	PROPN
cana-2411	256	40	�	�	NOUN
cana-2411	256	41	(m+1))𝒩	(m+1))𝒩	X
cana-2411	256	42	,	,	PUNCT
cana-2411	256	43	(	(	PUNCT
cana-2411	256	44	�	�	PROPN
cana-2411	256	45	̃	̃	NOUN
cana-2411	256	46	�	�	NOUN
cana-2411	256	47	i)𝒩	i)𝒩	NOUN
cana-2411	256	48	〉	〉	NOUN
cana-2411	256	49	)	)	PUNCT
cana-2411	256	50	=	=	SYM
cana-2411	256	51	ℛ(⟨(	ℛ(⟨(	PROPN
cana-2411	256	52	�	�	PROPN
cana-2411	256	53	̃	̃	PROPN
cana-2411	256	54	�	�	NOUN
cana-2411	256	55	m)𝒩	m)𝒩	NUM
cana-2411	256	56	,	,	PUNCT
cana-2411	256	57	(	(	PUNCT
cana-2411	256	58	�	�	PROPN
cana-2411	256	59	̃	̃	NOUN
cana-2411	256	60	�	�	PROPN
cana-2411	256	61	i)𝒩⟩	i)𝒩⟩	ADJ
cana-2411	256	62	+	+	NUM
cana-2411	256	63	⟨α̃m⟩⟨	⟨α̃m⟩⟨	PROPN
cana-2411	256	64	�	�	PROPN
cana-2411	256	65	̃	̃	PROPN
cana-2411	256	66	�	�	PROPN
cana-2411	256	67	(	(	PUNCT
cana-2411	256	68	�	�	PROPN
cana-2411	256	69	̃	̃	PROPN
cana-2411	256	70	�	�	NOUN
cana-2411	256	71	m)𝒩	m)𝒩	NUM
cana-2411	256	72	,	,	PUNCT
cana-2411	256	73	(	(	PUNCT
cana-2411	256	74	�	�	PROPN
cana-2411	256	75	̃	̃	NOUN
cana-2411	256	76	�	�	NOUN
cana-2411	256	77	i)𝒩	i)𝒩	NOUN
cana-2411	256	78	〉	〉	NOUN
cana-2411	256	79	)	)	PUNCT
cana-2411	256	80	=	=	SYM
cana-2411	256	81	ℛ(⟨(	ℛ(⟨(	PROPN
cana-2411	256	82	�	�	PROPN
cana-2411	256	83	̃	̃	PROPN
cana-2411	256	84	�	�	NOUN
cana-2411	256	85	m)𝒩	m)𝒩	NUM
cana-2411	256	86	,	,	PUNCT
cana-2411	256	87	(	(	PUNCT
cana-2411	256	88	�	�	PROPN
cana-2411	256	89	̃	̃	PROPN
cana-2411	256	90	�	�	NOUN
cana-2411	256	91	i)𝒩⟩	i)𝒩⟩	NOUN
cana-2411	256	92	)	)	PUNCT
cana-2411	256	93	+	+	ADP
cana-2411	256	94	ℛ(⟨α̃m⟩⟨	ℛ(⟨α̃m⟩⟨	NOUN
cana-2411	256	95	�	�	PROPN
cana-2411	256	96	̃	̃	PROPN
cana-2411	256	97	�	�	PROPN
cana-2411	256	98	(	(	PUNCT
cana-2411	256	99	�	�	PROPN
cana-2411	256	100	̃	̃	PROPN
cana-2411	256	101	�	�	NOUN
cana-2411	256	102	m)𝒩	m)𝒩	NUM
cana-2411	256	103	,	,	PUNCT
cana-2411	256	104	(	(	PUNCT
cana-2411	256	105	�	�	PROPN
cana-2411	256	106	̃	̃	NOUN
cana-2411	256	107	�	�	NOUN
cana-2411	256	108	i)𝒩	i)𝒩	NOUN
cana-2411	256	109	〉	〉	NOUN
cana-2411	256	110	)	)	PUNCT
cana-2411	256	111	=	=	SYM
cana-2411	256	112	ℛ(⟨(	ℛ(⟨(	PROPN
cana-2411	256	113	�	�	PROPN
cana-2411	256	114	̃	̃	PROPN
cana-2411	256	115	�	�	NOUN
cana-2411	256	116	m)𝒩	m)𝒩	NUM
cana-2411	256	117	,	,	PUNCT
cana-2411	256	118	(	(	PUNCT
cana-2411	256	119	�	�	PROPN
cana-2411	256	120	̃	̃	PROPN
cana-2411	256	121	�	�	PROPN
cana-2411	256	122	i)𝒩⟩	i)𝒩⟩	NOUN
cana-2411	256	123	)	)	PUNCT
cana-2411	256	124	−ℛ(⟨(	−ℛ(⟨(	ADP
cana-2411	256	125	�	�	PROPN
cana-2411	256	126	̃	̃	PROPN
cana-2411	256	127	�	�	NOUN
cana-2411	256	128	m)𝒩	m)𝒩	NUM
cana-2411	256	129	,	,	PUNCT
cana-2411	256	130	(	(	PUNCT
cana-2411	256	131	�	�	PROPN
cana-2411	256	132	̃	̃	PROPN
cana-2411	256	133	�	�	NOUN
cana-2411	256	134	i)𝒩⟩	i)𝒩⟩	NOUN
cana-2411	256	135	)	)	PUNCT
cana-2411	256	136	=	=	SYM
cana-2411	256	137	0	0	NUM
cana-2411	256	138	also	also	ADV
cana-2411	256	139	ℛ((	ℛ((	ADJ
cana-2411	256	140	�	�	PROPN
cana-2411	256	141	̃	̃	NOUN
cana-2411	256	142	�	�	NOUN
cana-2411	256	143	m+1)𝒩	m+1)𝒩	NOUN
cana-2411	256	144	)	)	PUNCT
cana-2411	256	145	=	=	VERB
cana-2411	256	146	−ℛ((	−ℛ((	PROPN
cana-2411	256	147	�	�	PROPN
cana-2411	256	148	̃	̃	PROPN
cana-2411	256	149	�	�	NOUN
cana-2411	256	150	m+1)𝒩	m+1)𝒩	NOUN
cana-2411	256	151	)	)	PUNCT
cana-2411	257	1	+	+	NOUN
cana-2411	257	2	ℛ(β̃	ℛ(β̃	NUM
cana-2411	257	3	m	m	VERB
cana-2411	257	4	(	(	PUNCT
cana-2411	257	5	d̃	d̃	PROPN
cana-2411	257	6	𝑚	𝑚	PROPN
cana-2411	257	7	)	)	PUNCT
cana-2411	257	8	𝒩	𝒩	PROPN
cana-2411	257	9	)	)	PUNCT
cana-2411	257	10	,	,	PUNCT
cana-2411	257	11	where	where	SCONJ
cana-2411	257	12	ℛ(β̃	ℛ(β̃	NUM
cana-2411	257	13	m	m	VERB
cana-2411	257	14	)	)	PUNCT
cana-2411	257	15	=	=	SYM
cana-2411	257	16	ℛ	ℛ	PROPN
cana-2411	257	17	(	(	PUNCT
cana-2411	257	18	〈	〈	PROPN
cana-2411	257	19	(	(	PUNCT
cana-2411	257	20	g̃m+1)𝒩	g̃m+1)𝒩	PROPN
cana-2411	257	21	,	,	PUNCT
cana-2411	257	22	�	�	PROPN
cana-2411	257	23	̃	̃	PROPN
cana-2411	257	24	�	�	PROPN
cana-2411	257	25	(d̃	(d̃	SYM
cana-2411	257	26	m	m	NOUN
cana-2411	257	27	)	)	PUNCT
cana-2411	257	28	𝒩	𝒩	NOUN
cana-2411	257	29	〉	〉	NOUN
cana-2411	257	30	〈	〈	PROPN
cana-2411	257	31	(	(	PUNCT
cana-2411	257	32	d̃	d̃	PROPN
cana-2411	257	33	m	m	PROPN
cana-2411	257	34	)	)	PUNCT
cana-2411	257	35	𝒩	𝒩	PROPN
cana-2411	257	36	,	,	PUNCT
cana-2411	257	37	�	�	PROPN
cana-2411	257	38	̃	̃	PROPN
cana-2411	257	39	�	�	PROPN
cana-2411	257	40	(d̃	(d̃	SYM
cana-2411	257	41	m	m	NOUN
cana-2411	257	42	)	)	PUNCT
cana-2411	257	43	𝒩	𝒩	NOUN
cana-2411	257	44	〉	〉	NOUN
cana-2411	257	45	)	)	PUNCT
cana-2411	257	46	as	as	ADP
cana-2411	257	47	ℛ(d̃	ℛ(d̃	NUM
cana-2411	257	48	0	0	NUM
cana-2411	257	49	)	)	PUNCT
cana-2411	257	50	𝒩	𝒩	PROPN
cana-2411	257	51	,	,	PUNCT
cana-2411	257	52	ℛ(d̃	ℛ(d̃	NUM
cana-2411	257	53	1	1	NUM
cana-2411	257	54	)	)	PUNCT
cana-2411	257	55	𝒩	𝒩	PROPN
cana-2411	257	56	,	,	PUNCT
cana-2411	257	57	.	.	PUNCT
cana-2411	257	58	.	.	PUNCT
cana-2411	257	59	.	.	PUNCT
cana-2411	257	60	.	.	PUNCT
cana-2411	258	1	,	,	PUNCT
cana-2411	258	2	ℛ(d̃	ℛ(d̃	PROPN
cana-2411	258	3	m	m	NOUN
cana-2411	258	4	)	)	PUNCT
cana-2411	258	5	𝒩	𝒩	PROPN
cana-2411	258	6	are	be	AUX
cana-2411	258	7	𝒬-conjugate	𝒬-conjugate	PROPN
cana-2411	258	8	.	.	PUNCT
cana-2411	259	1	taking	take	VERB
cana-2411	259	2	inner	inner	ADJ
cana-2411	259	3	product	product	NOUN
cana-2411	259	4	with	with	ADP
cana-2411	259	5	ℛ(	ℛ(	NOUN
cana-2411	259	6	�	�	PROPN
cana-2411	259	7	̃	̃	PROPN
cana-2411	259	8	�	�	PROPN
cana-2411	259	9	(d̃	(d̃	SYM
cana-2411	259	10	m	m	NOUN
cana-2411	259	11	)	)	PUNCT
cana-2411	259	12	𝒩	𝒩	PROPN
cana-2411	259	13	)	)	PUNCT
cana-2411	259	14	,	,	PUNCT
cana-2411	259	15	we	we	PRON
cana-2411	259	16	have	have	VERB
cana-2411	259	17	〈	〈	SYM
cana-2411	259	18	ℛ(d̃	ℛ(d̃	NUM
cana-2411	259	19	𝑚+1	𝑚+1	NUM
cana-2411	259	20	)	)	PUNCT
cana-2411	259	21	𝒩	𝒩	PROPN
cana-2411	259	22	,	,	PUNCT
cana-2411	259	23	ℛ(	ℛ(	NOUN
cana-2411	259	24	�	�	PROPN
cana-2411	259	25	̃	̃	PROPN
cana-2411	259	26	�	�	PROPN
cana-2411	259	27	(d̃	(d̃	SYM
cana-2411	259	28	m	m	NOUN
cana-2411	259	29	)	)	PUNCT
cana-2411	259	30	𝒩	𝒩	NOUN
cana-2411	259	31	)	)	PUNCT
cana-2411	259	32	〉	〉	NOUN
cana-2411	259	33	=	=	SYM
cana-2411	259	34	−ℛ(〈(	−ℛ(〈(	PROPN
cana-2411	259	35	�	�	PROPN
cana-2411	259	36	̃	̃	PROPN
cana-2411	259	37	�	�	NOUN
cana-2411	259	38	m+1)𝒩	m+1)𝒩	X
cana-2411	259	39	,	,	PUNCT
cana-2411	259	40	�	�	PROPN
cana-2411	259	41	̃	̃	PROPN
cana-2411	259	42	�	�	PROPN
cana-2411	259	43	(d̃	(d̃	SYM
cana-2411	259	44	m	m	NOUN
cana-2411	259	45	)	)	PUNCT
cana-2411	259	46	𝒩	𝒩	NOUN
cana-2411	259	47	〉	〉	NOUN
cana-2411	259	48	)	)	PUNCT
cana-2411	260	1	+	+	ADJ
cana-2411	260	2	ℛ(〈β̃	ℛ(〈β̃	NUM
cana-2411	260	3	m	m	VERB
cana-2411	260	4	〉	〉	NOUN
cana-2411	260	5	〈	〈	PROPN
cana-2411	260	6	(	(	PUNCT
cana-2411	260	7	d̃	d̃	PROPN
cana-2411	260	8	m	m	PROPN
cana-2411	260	9	)	)	PUNCT
cana-2411	260	10	𝒩	𝒩	PROPN
cana-2411	260	11	,	,	PUNCT
cana-2411	260	12	�	�	PROPN
cana-2411	260	13	̃	̃	PROPN
cana-2411	260	14	�	�	PROPN
cana-2411	260	15	(d̃	(d̃	SYM
cana-2411	260	16	m	m	NOUN
cana-2411	260	17	)	)	PUNCT
cana-2411	260	18	𝒩	𝒩	NOUN
cana-2411	260	19	〉	〉	NOUN
cana-2411	260	20	)	)	PUNCT
cana-2411	260	21	=	=	SYM
cana-2411	260	22	−ℛ(〈(	−ℛ(〈(	PROPN
cana-2411	260	23	�	�	PROPN
cana-2411	260	24	̃	̃	PROPN
cana-2411	260	25	�	�	NOUN
cana-2411	260	26	m+1)𝒩	m+1)𝒩	X
cana-2411	260	27	,	,	PUNCT
cana-2411	260	28	�	�	PROPN
cana-2411	260	29	̃	̃	PROPN
cana-2411	260	30	�	�	PROPN
cana-2411	260	31	(d̃	(d̃	SYM
cana-2411	260	32	m	m	NOUN
cana-2411	260	33	)	)	PUNCT
cana-2411	260	34	𝒩	𝒩	NOUN
cana-2411	260	35	〉	〉	NOUN
cana-2411	260	36	)	)	PUNCT
cana-2411	260	37	+	+	SYM
cana-2411	260	38	ℛ(〈(	ℛ(〈(	PROPN
cana-2411	260	39	�	�	PROPN
cana-2411	260	40	̃	̃	NOUN
cana-2411	260	41	�	�	NOUN
cana-2411	260	42	m+1)𝒩	m+1)𝒩	X
cana-2411	260	43	,	,	PUNCT
cana-2411	260	44	�	�	PROPN
cana-2411	260	45	̃	̃	PROPN
cana-2411	260	46	�	�	PROPN
cana-2411	260	47	(d̃	(d̃	SYM
cana-2411	260	48	m	m	NOUN
cana-2411	260	49	)	)	PUNCT
cana-2411	260	50	𝒩	𝒩	NOUN
cana-2411	260	51	〉	〉	NOUN
cana-2411	260	52	)	)	PUNCT
cana-2411	260	53	=	=	SYM
cana-2411	260	54	0	0	PUNCT
cana-2411	261	1	then	then	ADV
cana-2411	261	2	,	,	PUNCT
cana-2411	261	3	ℛ(	ℛ(	PROPN
cana-2411	261	4	�	�	PROPN
cana-2411	261	5	̃	̃	PROPN
cana-2411	261	6	�	�	PROPN
cana-2411	261	7	(d̃	(d̃	PUNCT
cana-2411	261	8	𝑚	𝑚	NOUN
cana-2411	261	9	)	)	PUNCT
cana-2411	261	10	𝒩	𝒩	PROPN
cana-2411	261	11	)	)	PUNCT
cana-2411	261	12	=	=	SYM
cana-2411	261	13	ℛ	ℛ	PROPN
cana-2411	261	14	(	(	PUNCT
cana-2411	261	15	(	(	PUNCT
cana-2411	261	16	�	�	PROPN
cana-2411	261	17	̃	̃	NOUN
cana-2411	261	18	�	�	PROPN
cana-2411	261	19	m+1)𝒩−(	m+1)𝒩−(	NOUN
cana-2411	261	20	�	�	PROPN
cana-2411	261	21	̃	̃	PROPN
cana-2411	261	22	�	�	NOUN
cana-2411	261	23	m)𝒩	m)𝒩	NUM
cana-2411	261	24	α̃m	α̃m	PROPN
cana-2411	261	25	)	)	PUNCT
cana-2411	261	26	.	.	PUNCT
cana-2411	262	1	and	and	CCONJ
cana-2411	262	2	hence	hence	ADV
cana-2411	262	3	we	we	PRON
cana-2411	262	4	have	have	VERB
cana-2411	262	5	ℛ	ℛ	PROPN
cana-2411	262	6	(	(	PUNCT
cana-2411	262	7	〈	〈	PROPN
cana-2411	262	8	(	(	PUNCT
cana-2411	262	9	d̃	d̃	PROPN
cana-2411	262	10	κ	κ	PROPN
cana-2411	262	11	)	)	PUNCT
cana-2411	262	12	𝒩	𝒩	PROPN
cana-2411	262	13	,	,	PUNCT
cana-2411	262	14	�	�	PROPN
cana-2411	262	15	̃	̃	PROPN
cana-2411	262	16	�	�	NOUN
cana-2411	262	17	(d̃	(d̃	PUNCT
cana-2411	262	18	𝑖	𝑖	SYM
cana-2411	262	19	)	)	PUNCT
cana-2411	262	20	𝒩	𝒩	NOUN
cana-2411	262	21	〉	〉	NOUN
cana-2411	262	22	)	)	PUNCT
cana-2411	262	23	=	=	SYM
cana-2411	262	24	ℛ	ℛ	PROPN
cana-2411	262	25	(	(	PUNCT
cana-2411	262	26	〈	〈	PROPN
cana-2411	262	27	(	(	PUNCT
cana-2411	262	28	�	�	PROPN
cana-2411	262	29	̃	̃	NOUN
cana-2411	262	30	�	�	NOUN
cana-2411	262	31	κ)𝒩	κ)𝒩	NOUN
cana-2411	262	32	,	,	PUNCT
cana-2411	262	33	(	(	PUNCT
cana-2411	262	34	�	�	PROPN
cana-2411	262	35	̃	̃	NOUN
cana-2411	262	36	�	�	NOUN
cana-2411	262	37	i+1)𝒩−(	i+1)𝒩−(	ADV
cana-2411	262	38	�	�	PROPN
cana-2411	262	39	̃	̃	NOUN
cana-2411	262	40	�	�	NOUN
cana-2411	262	41	i)𝒩	i)𝒩	NOUN
cana-2411	262	42	〉	〉	NOUN
cana-2411	262	43	α̃i	α̃i	X
cana-2411	262	44	)	)	PUNCT
cana-2411	263	1	(	(	PUNCT
cana-2411	263	2	8)	8)	NUM
cana-2411	263	3	combining	combine	VERB
cana-2411	263	4	the	the	DET
cana-2411	263	5	result	result	NOUN
cana-2411	263	6	we	we	PRON
cana-2411	263	7	have	have	VERB
cana-2411	263	8	ℛ(〈(	ℛ(〈(	PROPN
cana-2411	263	9	�	�	PROPN
cana-2411	263	10	̃	̃	PROPN
cana-2411	263	11	�	�	NOUN
cana-2411	263	12	κ)𝒩	κ)𝒩	NOUN
cana-2411	263	13	,	,	PUNCT
cana-2411	263	14	(	(	PUNCT
cana-2411	263	15	�	�	PROPN
cana-2411	263	16	̃	̃	NOUN
cana-2411	263	17	�	�	NOUN
cana-2411	263	18	i)𝒩	i)𝒩	NOUN
cana-2411	263	19	〉	〉	NOUN
cana-2411	263	20	)	)	PUNCT
cana-2411	263	21	=	=	SYM
cana-2411	263	22	0	0	PUNCT
cana-2411	263	23	=	=	SYM
cana-2411	263	24	ℛ(〈(d̃	ℛ(〈(d̃	PROPN
cana-2411	263	25	κ	κ	NOUN
cana-2411	263	26	)	)	PUNCT
cana-2411	263	27	𝒩	𝒩	PROPN
cana-2411	263	28	,	,	PUNCT
cana-2411	263	29	�	�	PROPN
cana-2411	263	30	̃	̃	PROPN
cana-2411	263	31	�	�	PROPN
cana-2411	263	32	(d̃	(d̃	SYM
cana-2411	263	33	κ	κ	NOUN
cana-2411	263	34	)	)	PUNCT
cana-2411	263	35	𝒩	𝒩	NOUN
cana-2411	263	36	〉	〉	NOUN
cana-2411	263	37	)	)	PUNCT
cana-2411	263	38	,	,	PUNCT
cana-2411	263	39	for	for	ADP
cana-2411	263	40	all	all	DET
cana-2411	263	41	κ	κ	NOUN
cana-2411	263	42	.	.	NOUN
cana-2411	263	43	5	5	NUM
cana-2411	263	44	.	.	X
cana-2411	263	45	algorithms	algorithm	NOUN
cana-2411	263	46	this	this	DET
cana-2411	263	47	section	section	NOUN
cana-2411	263	48	provides	provide	VERB
cana-2411	263	49	the	the	DET
cana-2411	263	50	step	step	NOUN
cana-2411	263	51	-	-	PUNCT
cana-2411	263	52	by	by	ADP
cana-2411	263	53	-	-	PUNCT
cana-2411	263	54	step	step	NOUN
cana-2411	263	55	procedures	procedure	NOUN
cana-2411	263	56	for	for	ADP
cana-2411	263	57	the	the	DET
cana-2411	263	58	neutrosophic	neutrosophic	ADJ
cana-2411	263	59	steepest	steep	ADJ
cana-2411	263	60	descent	descent	NOUN
cana-2411	263	61	and	and	CCONJ
cana-2411	263	62	the	the	DET
cana-2411	263	63	fletcher	fletcher	PROPN
cana-2411	263	64	-	-	PUNCT
cana-2411	263	65	reeves	reeves	PROPN
cana-2411	263	66	methods	method	NOUN
cana-2411	263	67	.	.	PUNCT
cana-2411	264	1	these	these	DET
cana-2411	264	2	algorithms	algorithm	NOUN
cana-2411	264	3	are	be	AUX
cana-2411	264	4	developed	develop	VERB
cana-2411	264	5	to	to	PART
cana-2411	264	6	iteratively	iteratively	ADV
cana-2411	264	7	improve	improve	VERB
cana-2411	264	8	solutions	solution	NOUN
cana-2411	264	9	by	by	ADP
cana-2411	264	10	considering	consider	VERB
cana-2411	264	11	uncertainties	uncertainty	NOUN
cana-2411	264	12	and	and	CCONJ
cana-2411	264	13	inconsistencies	inconsistency	NOUN
cana-2411	264	14	during	during	ADP
cana-2411	264	15	the	the	DET
cana-2411	264	16	process	process	NOUN
cana-2411	264	17	.	.	PUNCT
cana-2411	265	1	they	they	PRON
cana-2411	265	2	represent	represent	VERB
cana-2411	265	3	the	the	DET
cana-2411	265	4	principles	principle	NOUN
cana-2411	265	5	of	of	ADP
cana-2411	265	6	neutrosophy	neutrosophy	NOUN
cana-2411	265	7	and	and	CCONJ
cana-2411	265	8	provide	provide	VERB
cana-2411	265	9	valuable	valuable	ADJ
cana-2411	265	10	insights	insight	NOUN
cana-2411	265	11	into	into	ADP
cana-2411	265	12	managing	manage	VERB
cana-2411	265	13	uncertainty	uncertainty	NOUN
cana-2411	265	14	during	during	ADP
cana-2411	265	15	optimization	optimization	NOUN
cana-2411	265	16	.	.	PUNCT
cana-2411	266	1	communications	communication	NOUN
cana-2411	266	2	on	on	ADP
cana-2411	266	3	applied	apply	VERB
cana-2411	266	4	nonlinear	nonlinear	ADJ
cana-2411	266	5	analysis	analysis	NOUN
cana-2411	266	6	issn	issn	NOUN
cana-2411	266	7	:	:	PUNCT
cana-2411	266	8	1074	1074	NUM
cana-2411	266	9	-	-	PUNCT
cana-2411	266	10	133x	133x	NUM
cana-2411	266	11	vol	vol	NOUN
cana-2411	266	12	32	32	NUM
cana-2411	266	13	no	no	NOUN
cana-2411	266	14	.	.	PUNCT
cana-2411	267	1	2s	2s	NUM
cana-2411	267	2	(	(	PUNCT
cana-2411	267	3	2025	2025	NUM
cana-2411	267	4	)	)	PUNCT
cana-2411	267	5	377	377	NUM
cana-2411	267	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2411	267	7	5.1	5.1	NUM
cana-2411	267	8	algorithm	algorithm	NOUN
cana-2411	267	9	for	for	ADP
cana-2411	267	10	neutrosophic	neutrosophic	PROPN
cana-2411	267	11	cauchy	cauchy	PROPN
cana-2411	267	12	’s	’s	PART
cana-2411	267	13	steepest	steep	ADJ
cana-2411	267	14	descent	descent	NOUN
cana-2411	267	15	method	method	NOUN
cana-2411	267	16	step	step	NOUN
cana-2411	267	17	1	1	NUM
cana-2411	267	18	.	.	PUNCT
cana-2411	268	1	let	let	VERB
cana-2411	268	2	us	we	PRON
cana-2411	268	3	take	take	VERB
cana-2411	268	4	the	the	DET
cana-2411	268	5	svnnlpp	svnnlpp	NOUN
cana-2411	268	6	with	with	ADP
cana-2411	268	7	unconstrained	unconstrained	ADJ
cana-2411	268	8	optimization	optimization	NOUN
cana-2411	268	9	problem	problem	NOUN
cana-2411	268	10	incorporate	incorporate	VERB
cana-2411	268	11	the	the	DET
cana-2411	268	12	neutrosophic	neutrosophic	ADJ
cana-2411	268	13	triangular	triangular	NOUN
cana-2411	268	14	coefficient	coefficient	NOUN
cana-2411	268	15	�	�	PROPN
cana-2411	268	16	̃	̃	PROPN
cana-2411	268	17	�	�	PROPN
cana-2411	268	18	𝒩(υ̃(κ	𝒩(υ̃(κ	NOUN
cana-2411	268	19	)	)	PUNCT
cana-2411	268	20	𝒩	𝒩	PROPN
cana-2411	268	21	)	)	PUNCT
cana-2411	268	22	.	.	PUNCT
cana-2411	269	1	step	step	NOUN
cana-2411	269	2	2	2	NUM
cana-2411	269	3	.	.	PUNCT
cana-2411	269	4	convert	convert	VERB
cana-2411	269	5	the	the	DET
cana-2411	269	6	triangular	triangular	NOUN
cana-2411	269	7	neutrosophic	neutrosophic	ADJ
cana-2411	269	8	number	number	NOUN
cana-2411	269	9	coeffecients	coeffecient	NOUN
cana-2411	269	10	into	into	ADP
cana-2411	269	11	arithmetic	arithmetic	ADJ
cana-2411	269	12	neutrosophic	neutrosophic	ADJ
cana-2411	269	13	number	number	NOUN
cana-2411	269	14	and	and	CCONJ
cana-2411	269	15	then	then	ADV
cana-2411	269	16	covert	covert	ADJ
cana-2411	269	17	to	to	ADP
cana-2411	269	18	parametric	parametric	ADJ
cana-2411	269	19	form	form	NOUN
cana-2411	269	20	.	.	PUNCT
cana-2411	270	1	step	step	NOUN
cana-2411	270	2	3	3	NUM
cana-2411	270	3	.	.	PUNCT
cana-2411	270	4	compute	compute	PROPN
cana-2411	270	5	first	first	ADJ
cana-2411	270	6	and	and	CCONJ
cana-2411	270	7	second	second	ADJ
cana-2411	270	8	derivative	derivative	NOUN
cana-2411	270	9	for	for	ADP
cana-2411	270	10	the	the	DET
cana-2411	270	11	given	give	VERB
cana-2411	270	12	function	function	NOUN
cana-2411	270	13	,	,	PUNCT
cana-2411	270	14	and	and	CCONJ
cana-2411	270	15	choose	choose	VERB
cana-2411	270	16	any	any	DET
cana-2411	270	17	initial	initial	ADJ
cana-2411	270	18	points	point	NOUN
cana-2411	270	19	.	.	PUNCT
cana-2411	271	1	step	step	NOUN
cana-2411	271	2	4	4	NUM
cana-2411	271	3	.	.	PUNCT
cana-2411	272	1	input	input	NOUN
cana-2411	272	2	υ̃(0	υ̃(0	NOUN
cana-2411	272	3	)	)	PUNCT
cana-2411	272	4	𝒩	𝒩	PROPN
cana-2411	272	5	,	,	PUNCT
cana-2411	272	6	let	let	VERB
cana-2411	272	7	κ	κ	PROPN
cana-2411	272	8	←	←	PROPN
cana-2411	272	9	0	0	NUM
cana-2411	272	10	step	step	NOUN
cana-2411	272	11	5	5	NUM
cana-2411	272	12	.	.	PUNCT
cana-2411	272	13	calculate	calculate	VERB
cana-2411	272	14	s̃i	s̃i	PROPN
cana-2411	272	15	𝒩	𝒩	PROPN
cana-2411	272	16	,	,	PUNCT
cana-2411	272	17	s̃i	s̃i	PRON
cana-2411	272	18	𝒩	𝒩	PROPN
cana-2411	272	19	=	=	PUNCT
cana-2411	272	20	−∇	−∇	PROPN
cana-2411	272	21	�	�	PROPN
cana-2411	272	22	̃	̃	PROPN
cana-2411	272	23	�	�	PROPN
cana-2411	272	24	i	i	PRON
cana-2411	272	25	𝒩	𝒩	PROPN
cana-2411	272	26	,	,	PUNCT
cana-2411	272	27	where	where	SCONJ
cana-2411	272	28	�	�	PROPN
cana-2411	272	29	̃	̃	PROPN
cana-2411	272	30	�	�	PROPN
cana-2411	272	31	i	i	NOUN
cana-2411	272	32	𝒩	𝒩	PROPN
cana-2411	272	33	=	=	SYM
cana-2411	272	34	f̃	f̃	PROPN
cana-2411	272	35	𝒩	𝒩	PROPN
cana-2411	272	36	(	(	PUNCT
cana-2411	272	37	υ̃	υ̃	PROPN
cana-2411	272	38	)	)	PUNCT
cana-2411	272	39	,	,	PUNCT
cana-2411	272	40	∇	∇	PROPN
cana-2411	272	41	�	�	PROPN
cana-2411	272	42	̃	̃	PROPN
cana-2411	272	43	�	�	PROPN
cana-2411	272	44	i	i	NOUN
cana-2411	272	45	𝒩	𝒩	PROPN
cana-2411	272	46	=	=	PUNCT
cana-2411	272	47	∇f̃	∇f̃	PROPN
cana-2411	272	48	𝒩	𝒩	PROPN
cana-2411	272	49	(	(	PUNCT
cana-2411	272	50	υ̃κ	υ̃κ	NOUN
cana-2411	272	51	)	)	PUNCT
cana-2411	272	52	.	.	PUNCT
cana-2411	273	1	step	step	NOUN
cana-2411	273	2	6	6	NUM
cana-2411	273	3	.	.	PUNCT
cana-2411	274	1	find	find	VERB
cana-2411	274	2	hessian	hessian	NOUN
cana-2411	274	3	for	for	ADP
cana-2411	274	4	�	�	PROPN
cana-2411	274	5	̃	̃	PROPN
cana-2411	274	6	�	�	PROPN
cana-2411	274	7	i	i	NOUN
cana-2411	274	8	𝒩(x	𝒩(x	NOUN
cana-2411	274	9	)	)	PUNCT
cana-2411	274	10	step	step	NOUN
cana-2411	274	11	7	7	NUM
cana-2411	274	12	.	.	PUNCT
cana-2411	275	1	find	find	VERB
cana-2411	275	2	the	the	DET
cana-2411	275	3	(	(	PUNCT
cana-2411	275	4	υ̃κ+1)𝒩	υ̃κ+1)𝒩	NOUN
cana-2411	275	5	=	=	SYM
cana-2411	275	6	(	(	PUNCT
cana-2411	275	7	υ̃κ)𝒩	υ̃κ)𝒩	NOUN
cana-2411	275	8	−	−	X
cana-2411	275	9	(	(	PUNCT
cana-2411	275	10	γ̃	γ̃	PROPN
cana-2411	275	11	i	i	PRON
cana-2411	275	12	�	�	PROPN
cana-2411	275	13	̃	̃	PROPN
cana-2411	275	14	�	�	NOUN
cana-2411	275	15	κ)𝒩	κ)𝒩	NOUN
cana-2411	275	16	then	then	ADV
cana-2411	275	17	κ	κ	PROPN
cana-2411	275	18	←	←	PROPN
cana-2411	275	19	κ	κ	PROPN
cana-2411	276	1	+	+	PROPN
cana-2411	276	2	1	1	X
cana-2411	276	3	.	.	PUNCT
cana-2411	276	4	where	where	SCONJ
cana-2411	276	5	γ̃	γ̃	PROPN
cana-2411	276	6	=	=	SYM
cana-2411	276	7	−(∇	−(∇	X
cana-2411	276	8	�	�	PROPN
cana-2411	276	9	̃	̃	NOUN
cana-2411	276	10	�	�	NOUN
cana-2411	276	11	i	i	PRON
cana-2411	276	12	𝒩(x))ts̃i	𝒩(x))ts̃i	PROPN
cana-2411	276	13	𝒩	𝒩	PROPN
cana-2411	276	14	(	(	PUNCT
cana-2411	276	15	s̃i	s̃i	PRON
cana-2411	276	16	𝒩	𝒩	PROPN
cana-2411	276	17	)	)	PUNCT
cana-2411	276	18	thi	thi	AUX
cana-2411	276	19	𝒩	𝒩	PROPN
cana-2411	276	20	s̃i	s̃i	DET
cana-2411	276	21	𝒩	𝒩	PROPN
cana-2411	276	22	step	step	NOUN
cana-2411	276	23	8	8	NUM
cana-2411	276	24	.	.	PUNCT
cana-2411	277	1	repeat	repeat	VERB
cana-2411	277	2	the	the	DET
cana-2411	277	3	process	process	NOUN
cana-2411	277	4	until	until	SCONJ
cana-2411	277	5	∥	∥	PROPN
cana-2411	277	6	∇	∇	X
cana-2411	277	7	�	�	PROPN
cana-2411	277	8	̃	̃	PROPN
cana-2411	277	9	�	�	PROPN
cana-2411	277	10	i	i	PRON
cana-2411	277	11	𝒩(υ̃κ	𝒩(υ̃κ	AUX
cana-2411	277	12	)	)	PUNCT
cana-2411	277	13	∥	∥	PUNCT
cana-2411	277	14	<	<	X
cana-2411	277	15	ε	ε	PROPN
cana-2411	277	16	(	(	PUNCT
cana-2411	277	17	or	or	CCONJ
cana-2411	277	18	)	)	PUNCT
cana-2411	277	19	∥	∥	NOUN
cana-2411	277	20	(	(	PUNCT
cana-2411	277	21	υ̃κ)𝒩	υ̃κ)𝒩	NOUN
cana-2411	277	22	−	−	PROPN
cana-2411	277	23	(	(	PUNCT
cana-2411	277	24	υ̃κ+1)𝒩	υ̃κ+1)𝒩	NOUN
cana-2411	277	25	∥	∥	PRON
cana-2411	277	26	<	<	X
cana-2411	277	27	ε	ε	PROPN
cana-2411	277	28	.	.	PUNCT
cana-2411	278	1	then	then	ADV
cana-2411	278	2	halt	halt	VERB
cana-2411	278	3	the	the	DET
cana-2411	278	4	process	process	NOUN
cana-2411	278	5	if	if	SCONJ
cana-2411	278	6	we	we	PRON
cana-2411	278	7	get	get	VERB
cana-2411	278	8	an	an	DET
cana-2411	278	9	optimal	optimal	ADJ
cana-2411	278	10	solution	solution	NOUN
cana-2411	278	11	;	;	PUNCT
cana-2411	278	12	otherwise	otherwise	ADV
cana-2411	278	13	,	,	PUNCT
cana-2411	278	14	go	go	VERB
cana-2411	278	15	to	to	PART
cana-2411	278	16	step	step	VERB
cana-2411	278	17	5	5	NUM
cana-2411	278	18	.	.	PUNCT
cana-2411	279	1	step	step	NOUN
cana-2411	279	2	9	9	NUM
cana-2411	279	3	.	.	PUNCT
cana-2411	279	4	verify	verify	VERB
cana-2411	279	5	the	the	DET
cana-2411	279	6	optimum	optimum	NOUN
cana-2411	279	7	.	.	PUNCT
cana-2411	280	1	5.2	5.2	NUM
cana-2411	280	2	algorithm	algorithm	NOUN
cana-2411	280	3	for	for	ADP
cana-2411	280	4	neutrosophic	neutrosophic	PROPN
cana-2411	280	5	fletcher	fletcher	PROPN
cana-2411	280	6	reeves	reeves	PROPN
cana-2411	280	7	method	method	PROPN
cana-2411	280	8	step	step	NOUN
cana-2411	280	9	1	1	NUM
cana-2411	280	10	.	.	PUNCT
cana-2411	281	1	let	let	VERB
cana-2411	281	2	us	we	PRON
cana-2411	281	3	take	take	VERB
cana-2411	281	4	the	the	DET
cana-2411	281	5	svnnlpp	svnnlpp	NOUN
cana-2411	281	6	with	with	ADP
cana-2411	281	7	an	an	DET
cana-2411	281	8	unconstrained	unconstrained	ADJ
cana-2411	281	9	optimization	optimization	NOUN
cana-2411	281	10	problem	problem	NOUN
cana-2411	281	11	and	and	CCONJ
cana-2411	281	12	incorporate	incorporate	VERB
cana-2411	281	13	the	the	DET
cana-2411	281	14	neutrosophic	neutrosophic	ADJ
cana-2411	281	15	triangular	triangular	NOUN
cana-2411	281	16	coefficient	coefficient	NOUN
cana-2411	281	17	.	.	PUNCT
cana-2411	282	1	�	�	PROPN
cana-2411	282	2	̃	̃	PROPN
cana-2411	282	3	�	�	PROPN
cana-2411	282	4	𝒩(υ̃(κ	𝒩(υ̃(κ	NOUN
cana-2411	282	5	)	)	PUNCT
cana-2411	282	6	𝒩	𝒩	PROPN
cana-2411	282	7	)	)	PUNCT
cana-2411	282	8	.	.	PUNCT
cana-2411	283	1	step	step	NOUN
cana-2411	283	2	2	2	NUM
cana-2411	283	3	.	.	PUNCT
cana-2411	283	4	convert	convert	VERB
cana-2411	283	5	the	the	DET
cana-2411	283	6	triangular	triangular	NOUN
cana-2411	283	7	neutrosophic	neutrosophic	ADJ
cana-2411	283	8	number	number	NOUN
cana-2411	283	9	coeffecients	coeffecient	NOUN
cana-2411	283	10	into	into	ADP
cana-2411	283	11	arithmetic	arithmetic	ADJ
cana-2411	283	12	neutrosophic	neutrosophic	ADJ
cana-2411	283	13	number	number	NOUN
cana-2411	283	14	and	and	CCONJ
cana-2411	283	15	then	then	ADV
cana-2411	283	16	covert	covert	ADJ
cana-2411	283	17	to	to	ADP
cana-2411	283	18	parametric	parametric	ADJ
cana-2411	283	19	form	form	NOUN
cana-2411	283	20	.	.	PUNCT
cana-2411	284	1	step	step	NOUN
cana-2411	284	2	3	3	NUM
cana-2411	284	3	.	.	PUNCT
cana-2411	284	4	compute	compute	PROPN
cana-2411	284	5	first	first	ADJ
cana-2411	284	6	and	and	CCONJ
cana-2411	284	7	second	second	ADJ
cana-2411	284	8	derivative	derivative	NOUN
cana-2411	284	9	for	for	ADP
cana-2411	284	10	the	the	DET
cana-2411	284	11	given	give	VERB
cana-2411	284	12	function	function	NOUN
cana-2411	284	13	,	,	PUNCT
cana-2411	284	14	and	and	CCONJ
cana-2411	284	15	choose	choose	VERB
cana-2411	284	16	any	any	DET
cana-2411	284	17	initial	initial	ADJ
cana-2411	284	18	points	point	NOUN
cana-2411	284	19	.	.	PUNCT
cana-2411	285	1	step	step	NOUN
cana-2411	285	2	4	4	NUM
cana-2411	285	3	.	.	PUNCT
cana-2411	286	1	input	input	NOUN
cana-2411	286	2	υ̃(0	υ̃(0	NOUN
cana-2411	286	3	)	)	PUNCT
cana-2411	286	4	𝒩	𝒩	PROPN
cana-2411	286	5	,	,	PUNCT
cana-2411	286	6	let	let	VERB
cana-2411	286	7	κ	κ	PROPN
cana-2411	286	8	←	←	PROPN
cana-2411	286	9	0	0	NUM
cana-2411	286	10	step	step	NOUN
cana-2411	286	11	5	5	NUM
cana-2411	286	12	.	.	PUNCT
cana-2411	286	13	calculate	calculate	VERB
cana-2411	286	14	s̃i	s̃i	PROPN
cana-2411	286	15	𝒩	𝒩	PROPN
cana-2411	286	16	,	,	PUNCT
cana-2411	286	17	s̃i	s̃i	PRON
cana-2411	286	18	𝒩	𝒩	PROPN
cana-2411	286	19	=	=	PUNCT
cana-2411	286	20	−∇	−∇	PROPN
cana-2411	286	21	�	�	PROPN
cana-2411	286	22	̃	̃	PROPN
cana-2411	286	23	�	�	PROPN
cana-2411	286	24	i	i	PRON
cana-2411	286	25	𝒩	𝒩	PROPN
cana-2411	286	26	,	,	PUNCT
cana-2411	286	27	where	where	SCONJ
cana-2411	286	28	�	�	PROPN
cana-2411	286	29	̃	̃	PROPN
cana-2411	286	30	�	�	PROPN
cana-2411	286	31	i	i	NOUN
cana-2411	286	32	𝒩	𝒩	PROPN
cana-2411	286	33	=	=	SYM
cana-2411	286	34	f̃	f̃	PROPN
cana-2411	286	35	𝒩	𝒩	PROPN
cana-2411	286	36	(	(	PUNCT
cana-2411	286	37	υ̃	υ̃	PROPN
cana-2411	286	38	)	)	PUNCT
cana-2411	286	39	,	,	PUNCT
cana-2411	286	40	∇	∇	PROPN
cana-2411	286	41	�	�	PROPN
cana-2411	286	42	̃	̃	PROPN
cana-2411	286	43	�	�	PROPN
cana-2411	286	44	i	i	NOUN
cana-2411	286	45	𝒩	𝒩	PROPN
cana-2411	286	46	=	=	PUNCT
cana-2411	286	47	∇f̃	∇f̃	PROPN
cana-2411	286	48	𝒩	𝒩	PROPN
cana-2411	286	49	(	(	PUNCT
cana-2411	286	50	υ̃κ	υ̃κ	NOUN
cana-2411	286	51	)	)	PUNCT
cana-2411	286	52	.	.	PUNCT
cana-2411	287	1	and	and	CCONJ
cana-2411	287	2	s̃i+1	s̃i+1	VERB
cana-2411	287	3	𝒩	𝒩	PROPN
cana-2411	287	4	=	=	PUNCT
cana-2411	287	5	−∇	−∇	NOUN
cana-2411	287	6	�	�	PROPN
cana-2411	287	7	̃	̃	NOUN
cana-2411	287	8	�	�	PROPN
cana-2411	287	9	i	i	PRON
cana-2411	287	10	𝒩	𝒩	PROPN
cana-2411	287	11	+	+	CCONJ
cana-2411	287	12	|∇	|∇	PROPN
cana-2411	287	13	�	�	PROPN
cana-2411	287	14	̃	̃	PROPN
cana-2411	287	15	�	�	PROPN
cana-2411	287	16	i	i	PRON
cana-2411	287	17	𝒩|2	𝒩|2	VERB
cana-2411	287	18	|∇	|∇	PROPN
cana-2411	287	19	�	�	PROPN
cana-2411	287	20	̃	̃	PROPN
cana-2411	287	21	�	�	PROPN
cana-2411	287	22	i−1	i−1	PROPN
cana-2411	287	23	𝒩	𝒩	PROPN
cana-2411	287	24	|2	|2	NUM
cana-2411	287	25	s̃i	s̃i	PRON
cana-2411	287	26	𝒩	𝒩	PROPN
cana-2411	287	27	step	step	NOUN
cana-2411	287	28	6	6	NUM
cana-2411	287	29	.	.	PUNCT
cana-2411	288	1	find	find	VERB
cana-2411	288	2	hessian	hessian	NOUN
cana-2411	288	3	for	for	ADP
cana-2411	288	4	�	�	PROPN
cana-2411	288	5	̃	̃	PROPN
cana-2411	288	6	�	�	PROPN
cana-2411	288	7	i	i	PRON
cana-2411	288	8	𝒩(υ̃	𝒩(υ̃	ADV
cana-2411	288	9	)	)	PUNCT
cana-2411	288	10	step	step	NOUN
cana-2411	288	11	7	7	NUM
cana-2411	288	12	.	.	PUNCT
cana-2411	289	1	find	find	VERB
cana-2411	289	2	the	the	DET
cana-2411	289	3	(	(	PUNCT
cana-2411	289	4	υ̃κ+1)𝒩	υ̃κ+1)𝒩	NOUN
cana-2411	289	5	=	=	SYM
cana-2411	289	6	(	(	PUNCT
cana-2411	289	7	υ̃κ)𝒩	υ̃κ)𝒩	NOUN
cana-2411	289	8	−	−	X
cana-2411	289	9	(	(	PUNCT
cana-2411	289	10	γ̃	γ̃	PROPN
cana-2411	289	11	i	i	PRON
cana-2411	289	12	�	�	PROPN
cana-2411	289	13	̃	̃	PROPN
cana-2411	289	14	�	�	NOUN
cana-2411	289	15	κ)𝒩	κ)𝒩	NOUN
cana-2411	289	16	then	then	ADV
cana-2411	289	17	κ	κ	PROPN
cana-2411	289	18	←	←	PROPN
cana-2411	289	19	κ	κ	PROPN
cana-2411	290	1	+	+	PROPN
cana-2411	290	2	1	1	X
cana-2411	290	3	.	.	PUNCT
cana-2411	290	4	where	where	SCONJ
cana-2411	290	5	γ̃	γ̃	PROPN
cana-2411	290	6	=	=	SYM
cana-2411	290	7	−(∇	−(∇	X
cana-2411	290	8	�	�	PROPN
cana-2411	290	9	̃	̃	NOUN
cana-2411	290	10	�	�	PROPN
cana-2411	290	11	i	i	PROPN
cana-2411	290	12	𝒩(υ̃))ts̃i	𝒩(υ̃))ts̃i	PROPN
cana-2411	290	13	𝒩	𝒩	PROPN
cana-2411	290	14	(	(	PUNCT
cana-2411	290	15	s̃i	s̃i	PRON
cana-2411	290	16	𝒩	𝒩	PROPN
cana-2411	290	17	)	)	PUNCT
cana-2411	290	18	thi	thi	AUX
cana-2411	290	19	𝒩	𝒩	PROPN
cana-2411	290	20	s̃i	s̃i	DET
cana-2411	290	21	𝒩	𝒩	PROPN
cana-2411	290	22	step	step	NOUN
cana-2411	290	23	8	8	NUM
cana-2411	290	24	.	.	PUNCT
cana-2411	291	1	repeat	repeat	VERB
cana-2411	291	2	the	the	DET
cana-2411	291	3	process	process	NOUN
cana-2411	291	4	until	until	SCONJ
cana-2411	291	5	∥	∥	PROPN
cana-2411	291	6	∇	∇	X
cana-2411	291	7	�	�	PROPN
cana-2411	291	8	̃	̃	PROPN
cana-2411	291	9	�	�	PROPN
cana-2411	291	10	i	i	PRON
cana-2411	291	11	𝒩(υ̃κ	𝒩(υ̃κ	AUX
cana-2411	291	12	)	)	PUNCT
cana-2411	291	13	∥	∥	PUNCT
cana-2411	291	14	<	<	X
cana-2411	291	15	ε	ε	PROPN
cana-2411	291	16	(	(	PUNCT
cana-2411	291	17	or	or	CCONJ
cana-2411	291	18	)	)	PUNCT
cana-2411	291	19	∥	∥	NOUN
cana-2411	291	20	(	(	PUNCT
cana-2411	291	21	υ̃κ)𝒩	υ̃κ)𝒩	NOUN
cana-2411	291	22	−	−	PROPN
cana-2411	291	23	(	(	PUNCT
cana-2411	291	24	υ̃κ+1)𝒩	υ̃κ+1)𝒩	NOUN
cana-2411	291	25	∥	∥	PRON
cana-2411	291	26	<	<	X
cana-2411	291	27	ε	ε	PROPN
cana-2411	291	28	.	.	PUNCT
cana-2411	292	1	then	then	ADV
cana-2411	292	2	halt	halt	VERB
cana-2411	292	3	the	the	DET
cana-2411	292	4	process	process	NOUN
cana-2411	292	5	if	if	SCONJ
cana-2411	292	6	we	we	PRON
cana-2411	292	7	get	get	VERB
cana-2411	292	8	an	an	DET
cana-2411	292	9	optimal	optimal	ADJ
cana-2411	292	10	solution	solution	NOUN
cana-2411	292	11	;	;	PUNCT
cana-2411	292	12	otherwise	otherwise	ADV
cana-2411	292	13	,	,	PUNCT
cana-2411	292	14	go	go	VERB
cana-2411	292	15	to	to	PART
cana-2411	292	16	step	step	VERB
cana-2411	292	17	5	5	NUM
cana-2411	292	18	.	.	PUNCT
cana-2411	293	1	step	step	NOUN
cana-2411	293	2	9	9	NUM
cana-2411	293	3	.	.	PUNCT
cana-2411	293	4	verify	verify	VERB
cana-2411	293	5	the	the	DET
cana-2411	293	6	optimum	optimum	NOUN
cana-2411	293	7	.	.	PUNCT
cana-2411	294	1	communications	communication	NOUN
cana-2411	294	2	on	on	ADP
cana-2411	294	3	applied	apply	VERB
cana-2411	294	4	nonlinear	nonlinear	ADJ
cana-2411	294	5	analysis	analysis	NOUN
cana-2411	294	6	issn	issn	NOUN
cana-2411	294	7	:	:	PUNCT
cana-2411	294	8	1074	1074	NUM
cana-2411	294	9	-	-	PUNCT
cana-2411	294	10	133x	133x	NUM
cana-2411	294	11	vol	vol	NOUN
cana-2411	294	12	32	32	NUM
cana-2411	294	13	no	no	NOUN
cana-2411	294	14	.	.	PUNCT
cana-2411	295	1	2s	2s	NUM
cana-2411	295	2	(	(	PUNCT
cana-2411	295	3	2025	2025	NUM
cana-2411	295	4	)	)	PUNCT
cana-2411	295	5	378	378	NUM
cana-2411	295	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2411	295	7	6	6	NUM
cana-2411	295	8	.	.	PUNCT
cana-2411	295	9	numerical	numerical	ADJ
cana-2411	295	10	examples	example	NOUN
cana-2411	295	11	this	this	DET
cana-2411	295	12	section	section	NOUN
cana-2411	295	13	presents	present	VERB
cana-2411	295	14	numerical	numerical	ADJ
cana-2411	295	15	examples	example	NOUN
cana-2411	295	16	of	of	ADP
cana-2411	295	17	two	two	NUM
cana-2411	295	18	significant	significant	ADJ
cana-2411	295	19	methods	method	NOUN
cana-2411	295	20	utilized	utilize	VERB
cana-2411	295	21	in	in	ADP
cana-2411	295	22	neutrosophic	neutrosophic	ADJ
cana-2411	295	23	optimization	optimization	NOUN
cana-2411	295	24	:	:	PUNCT
cana-2411	295	25	the	the	DET
cana-2411	295	26	fletcher	fletcher	PROPN
cana-2411	295	27	-	-	PUNCT
cana-2411	295	28	reeves	reeves	PROPN
cana-2411	295	29	method	method	NOUN
cana-2411	295	30	(	(	PUNCT
cana-2411	295	31	also	also	ADV
cana-2411	295	32	known	know	VERB
cana-2411	295	33	as	as	ADP
cana-2411	295	34	the	the	DET
cana-2411	295	35	conjugate	conjugate	ADJ
cana-2411	295	36	gradient	gradient	NOUN
cana-2411	295	37	method	method	NOUN
cana-2411	295	38	)	)	PUNCT
cana-2411	295	39	and	and	CCONJ
cana-2411	295	40	the	the	DET
cana-2411	295	41	neutrosophic	neutrosophic	ADJ
cana-2411	295	42	steepest	steep	ADJ
cana-2411	295	43	descent	descent	NOUN
cana-2411	295	44	.	.	PUNCT
cana-2411	296	1	these	these	DET
cana-2411	296	2	examples	example	NOUN
cana-2411	296	3	provide	provide	VERB
cana-2411	296	4	an	an	DET
cana-2411	296	5	in	in	ADP
cana-2411	296	6	-	-	PUNCT
cana-2411	296	7	depth	depth	NOUN
cana-2411	296	8	demonstration	demonstration	NOUN
cana-2411	296	9	of	of	ADP
cana-2411	296	10	how	how	SCONJ
cana-2411	296	11	these	these	DET
cana-2411	296	12	algorithms	algorithm	NOUN
cana-2411	296	13	are	be	AUX
cana-2411	296	14	applied	apply	VERB
cana-2411	296	15	,	,	PUNCT
cana-2411	296	16	discussing	discuss	VERB
cana-2411	296	17	their	their	PRON
cana-2411	296	18	convergence	convergence	NOUN
cana-2411	296	19	properties	property	NOUN
cana-2411	296	20	and	and	CCONJ
cana-2411	296	21	their	their	PRON
cana-2411	296	22	ability	ability	NOUN
cana-2411	296	23	to	to	PART
cana-2411	296	24	traverse	traverse	VERB
cana-2411	296	25	uncertain	uncertain	ADJ
cana-2411	296	26	solution	solution	NOUN
cana-2411	296	27	domains	domain	NOUN
cana-2411	296	28	.	.	PUNCT
cana-2411	296	29	example	example	NOUN
cana-2411	296	30	6.1	6.1	NUM
cana-2411	296	31	consider	consider	VERB
cana-2411	296	32	the	the	DET
cana-2411	296	33	problem	problem	NOUN
cana-2411	296	34	of	of	ADP
cana-2411	296	35	unconstrained	unconstrained	ADJ
cana-2411	296	36	optimization	optimization	NOUN
cana-2411	296	37	with	with	ADP
cana-2411	296	38	single	single	ADV
cana-2411	296	39	-	-	PUNCT
cana-2411	296	40	valued	value	VERB
cana-2411	296	41	neutrosophic	neutrosophic	ADJ
cana-2411	296	42	triangular	triangular	NOUN
cana-2411	296	43	coefficients	coefficient	NOUN
cana-2411	296	44	.	.	PUNCT
cana-2411	297	1	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
cana-2411	297	2	f̃(υ̃1	f̃(υ̃1	NOUN
cana-2411	297	3	,	,	PUNCT
cana-2411	297	4	υ̃2	υ̃2	PROPN
cana-2411	297	5	)	)	PUNCT
cana-2411	297	6	=	=	SYM
cana-2411	297	7	(	(	PUNCT
cana-2411	297	8	19,20,21	19,20,21	NUM
cana-2411	297	9	)	)	PUNCT
cana-2411	297	10	;	;	PUNCT
cana-2411	297	11	(	(	PUNCT
cana-2411	297	12	0.69,0.51,0.52)υ̃1	0.69,0.51,0.52)υ̃1	NOUN
cana-2411	297	13	+	+	CCONJ
cana-2411	297	14	(	(	PUNCT
cana-2411	297	15	25,26,27	25,26,27	NUM
cana-2411	297	16	)	)	PUNCT
cana-2411	297	17	;	;	PUNCT
cana-2411	297	18	(	(	PUNCT
cana-2411	297	19	0.67,0.54,0.5)υ̃2	0.67,0.54,0.5)υ̃2	X
cana-2411	298	1	+	+	ADJ
cana-2411	298	2	(	(	PUNCT
cana-2411	298	3	3,4,5	3,4,5	NUM
cana-2411	298	4	)	)	PUNCT
cana-2411	298	5	;	;	PUNCT
cana-2411	298	6	(	(	PUNCT
cana-2411	298	7	0.74,0.75,0.68)υ̃1υ̃2	0.74,0.75,0.68)υ̃1υ̃2	NOUN
cana-2411	298	8	+	+	CCONJ
cana-2411	298	9	(	(	PUNCT
cana-2411	298	10	−5	−5	ADJ
cana-2411	298	11	,	,	PUNCT
cana-2411	298	12	−4	−4	PRON
cana-2411	298	13	,	,	PUNCT
cana-2411	298	14	−3	−3	PROPN
cana-2411	298	15	)	)	PUNCT
cana-2411	298	16	;	;	PUNCT
cana-2411	298	17	(	(	PUNCT
cana-2411	298	18	0.8,0.75,0.6)υ̃1	0.8,0.75,0.6)υ̃1	NOUN
cana-2411	298	19	2	2	NUM
cana-2411	298	20	+	+	NOUN
cana-2411	298	21	(	(	PUNCT
cana-2411	298	22	−4	−4	PROPN
cana-2411	298	23	,	,	PUNCT
cana-2411	298	24	−3	−3	ADJ
cana-2411	298	25	,	,	PUNCT
cana-2411	298	26	−2	−2	PROPN
cana-2411	298	27	)	)	PUNCT
cana-2411	298	28	;	;	PUNCT
cana-2411	298	29	(	(	PUNCT
cana-2411	298	30	0.7,0.65,0.75)υ̃2	0.7,0.65,0.75)υ̃2	NOUN
cana-2411	298	31	2	2	NUM
cana-2411	298	32	(	(	PUNCT
cana-2411	298	33	9	9	NUM
cana-2411	298	34	)	)	PUNCT
cana-2411	298	35	starting	start	VERB
cana-2411	298	36	with	with	ADP
cana-2411	298	37	initial	initial	ADJ
cana-2411	298	38	point	point	NOUN
cana-2411	298	39	ỹ	ỹ	PROPN
cana-2411	298	40	0	0	PUNCT
cana-2411	298	41	=	=	SYM
cana-2411	298	42	(	(	PUNCT
cana-2411	298	43	(	(	PUNCT
cana-2411	298	44	0,1,2	0,1,2	NUM
cana-2411	298	45	)	)	PUNCT
cana-2411	298	46	;	;	PUNCT
cana-2411	298	47	(	(	PUNCT
cana-2411	298	48	0.65,0.6,0.5	0.65,0.6,0.5	NUM
cana-2411	298	49	)	)	PUNCT
cana-2411	298	50	(	(	PUNCT
cana-2411	298	51	0,1,2	0,1,2	NOUN
cana-2411	298	52	)	)	PUNCT
cana-2411	298	53	;	;	PUNCT
cana-2411	298	54	(	(	PUNCT
cana-2411	298	55	0.65,0.6,0.5	0.65,0.6,0.5	NOUN
cana-2411	298	56	)	)	PUNCT
cana-2411	298	57	)	)	PUNCT
cana-2411	298	58	solution	solution	NOUN
cana-2411	298	59	:	:	PUNCT
cana-2411	298	60	the	the	DET
cana-2411	298	61	parametric	parametric	ADJ
cana-2411	298	62	form	form	NOUN
cana-2411	298	63	of	of	ADP
cana-2411	298	64	the	the	DET
cana-2411	298	65	given	give	VERB
cana-2411	298	66	svnnlpp	svnnlpp	NOUN
cana-2411	298	67	(	(	PUNCT
cana-2411	298	68	only	only	ADV
cana-2411	298	69	triplet)(9	triplet)(9	PROPN
cana-2411	298	70	)	)	PUNCT
cana-2411	298	71	is	be	AUX
cana-2411	298	72	given	give	VERB
cana-2411	298	73	by	by	ADP
cana-2411	298	74	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
cana-2411	298	75	f̃(υ̃1	f̃(υ̃1	NOUN
cana-2411	298	76	,	,	PUNCT
cana-2411	298	77	υ̃2	υ̃2	PROPN
cana-2411	298	78	)	)	PUNCT
cana-2411	298	79	=	=	PUNCT
cana-2411	299	1	(	(	PUNCT
cana-2411	299	2	20,1−	20,1−	NUM
cana-2411	299	3	r	r	NOUN
cana-2411	299	4	,	,	PUNCT
cana-2411	299	5	1	1	NUM
cana-2411	299	6	−	−	NOUN
cana-2411	299	7	r	r	NOUN
cana-2411	299	8	)	)	PUNCT
cana-2411	299	9	;	;	PUNCT
cana-2411	299	10	(	(	PUNCT
cana-2411	299	11	0.69,0.51,0.52)υ̃1	0.69,0.51,0.52)υ̃1	NOUN
cana-2411	299	12	+	+	CCONJ
cana-2411	299	13	(	(	PUNCT
cana-2411	299	14	26,1−	26,1−	NUM
cana-2411	299	15	r	r	NOUN
cana-2411	299	16	,	,	PUNCT
cana-2411	299	17	1−	1−	NUM
cana-2411	299	18	r	r	NOUN
cana-2411	299	19	)	)	PUNCT
cana-2411	299	20	;	;	PUNCT
cana-2411	299	21	(	(	PUNCT
cana-2411	299	22	0.67,0.54,0.5)υ̃2	0.67,0.54,0.5)υ̃2	X
cana-2411	300	1	+	+	CCONJ
cana-2411	300	2	(	(	PUNCT
cana-2411	300	3	4,1−	4,1−	NUM
cana-2411	300	4	r	r	NOUN
cana-2411	300	5	,	,	PUNCT
cana-2411	300	6	1−	1−	NUM
cana-2411	300	7	r	r	NOUN
cana-2411	300	8	)	)	PUNCT
cana-2411	300	9	;	;	PUNCT
cana-2411	300	10	(	(	PUNCT
cana-2411	300	11	0.74,0.75,0.68)υ̃1υ̃2	0.74,0.75,0.68)υ̃1υ̃2	PROPN
cana-2411	300	12	+	+	PROPN
cana-2411	300	13	(	(	PUNCT
cana-2411	300	14	−4,1−	−4,1−	PUNCT
cana-2411	300	15	r	r	NOUN
cana-2411	300	16	,	,	PUNCT
cana-2411	300	17	1	1	NUM
cana-2411	300	18	−	−	NOUN
cana-2411	300	19	r	r	NOUN
cana-2411	300	20	)	)	PUNCT
cana-2411	300	21	;	;	PUNCT
cana-2411	300	22	(	(	PUNCT
cana-2411	300	23	0.8,0.75,0.6)υ̃1	0.8,0.75,0.6)υ̃1	NOUN
cana-2411	300	24	2	2	NUM
cana-2411	300	25	+	+	CCONJ
cana-2411	300	26	(	(	PUNCT
cana-2411	300	27	−3,1−	−3,1−	X
cana-2411	300	28	r	r	NOUN
cana-2411	300	29	,	,	PUNCT
cana-2411	300	30	1	1	NUM
cana-2411	300	31	−	−	NOUN
cana-2411	300	32	r	r	NOUN
cana-2411	300	33	)	)	PUNCT
cana-2411	300	34	;	;	PUNCT
cana-2411	300	35	(	(	PUNCT
cana-2411	300	36	0.7,0.65,0.75)υ̃2	0.7,0.65,0.75)υ̃2	NOUN
cana-2411	300	37	2	2	NUM
cana-2411	300	38	(	(	PUNCT
cana-2411	300	39	10	10	NUM
cana-2411	300	40	)	)	PUNCT
cana-2411	300	41	ỹ	ỹ	NOUN
cana-2411	300	42	0	0	PUNCT
cana-2411	300	43	=	=	SYM
cana-2411	300	44	(	(	PUNCT
cana-2411	300	45	(	(	PUNCT
cana-2411	300	46	1,1−	1,1−	NUM
cana-2411	300	47	r	r	NOUN
cana-2411	300	48	,	,	PUNCT
cana-2411	300	49	1−	1−	NUM
cana-2411	300	50	r	r	NOUN
cana-2411	300	51	)	)	PUNCT
cana-2411	300	52	;	;	PUNCT
cana-2411	300	53	(	(	PUNCT
cana-2411	300	54	0.65,0.6,0.5	0.65,0.6,0.5	NUM
cana-2411	300	55	)	)	PUNCT
cana-2411	300	56	(	(	PUNCT
cana-2411	300	57	1,1−	1,1−	NUM
cana-2411	300	58	r	r	NOUN
cana-2411	300	59	,	,	PUNCT
cana-2411	300	60	1−	1−	NUM
cana-2411	300	61	r	r	NOUN
cana-2411	300	62	)	)	PUNCT
cana-2411	300	63	;	;	PUNCT
cana-2411	300	64	(	(	PUNCT
cana-2411	300	65	0.65,0.6,0.5	0.65,0.6,0.5	NUM
cana-2411	300	66	)	)	PUNCT
cana-2411	300	67	)	)	PUNCT
cana-2411	300	68	the	the	DET
cana-2411	300	69	condition	condition	NOUN
cana-2411	300	70	required	require	VERB
cana-2411	300	71	for	for	SCONJ
cana-2411	300	72	υ̃	υ̃	PROPN
cana-2411	300	73	to	to	PART
cana-2411	300	74	be	be	AUX
cana-2411	300	75	the	the	DET
cana-2411	300	76	optimum	optimum	ADJ
cana-2411	300	77	solution	solution	NOUN
cana-2411	300	78	for	for	ADP
cana-2411	300	79	(	(	PUNCT
cana-2411	300	80	10	10	NUM
cana-2411	300	81	)	)	PUNCT
cana-2411	300	82	∇f̃(υ̃1	∇f̃(υ̃1	NOUN
cana-2411	300	83	,	,	PUNCT
cana-2411	300	84	υ̃2	υ̃2	PROPN
cana-2411	300	85	)	)	PUNCT
cana-2411	301	1	≈	≈	NOUN
cana-2411	301	2	0̃.	0̃.	NOUN
cana-2411	302	1	hence	hence	ADV
cana-2411	302	2	we	we	PRON
cana-2411	302	3	have	have	VERB
cana-2411	302	4	∂f̃	∂f̃	NUM
cana-2411	302	5	∂υ̃1	∂υ̃1	NOUN
cana-2411	303	1	=	=	PUNCT
cana-2411	304	1	(	(	PUNCT
cana-2411	304	2	20,1−	20,1−	NUM
cana-2411	304	3	r	r	NOUN
cana-2411	304	4	,	,	PUNCT
cana-2411	304	5	1	1	NUM
cana-2411	304	6	−	−	NOUN
cana-2411	304	7	r	r	NOUN
cana-2411	304	8	)	)	PUNCT
cana-2411	304	9	;	;	PUNCT
cana-2411	304	10	(	(	PUNCT
cana-2411	304	11	0.69,0.51,0.52	0.69,0.51,0.52	NOUN
cana-2411	304	12	)	)	PUNCT
cana-2411	304	13	+	+	CCONJ
cana-2411	304	14	(	(	PUNCT
cana-2411	304	15	4,1−	4,1−	NUM
cana-2411	304	16	r	r	NOUN
cana-2411	304	17	,	,	PUNCT
cana-2411	304	18	1−	1−	NUM
cana-2411	304	19	r	r	NOUN
cana-2411	304	20	)	)	PUNCT
cana-2411	304	21	;	;	PUNCT
cana-2411	304	22	(	(	PUNCT
cana-2411	304	23	0.74,0.75,0.68)υ̃2	0.74,0.75,0.68)υ̃2	NOUN
cana-2411	304	24	+	+	PROPN
cana-2411	304	25	(	(	PUNCT
cana-2411	304	26	−8,1−	−8,1−	PROPN
cana-2411	304	27	r	r	PROPN
cana-2411	304	28	,	,	PUNCT
cana-2411	304	29	1−	1−	NUM
cana-2411	304	30	r	r	NOUN
cana-2411	304	31	)	)	PUNCT
cana-2411	304	32	;	;	PUNCT
cana-2411	304	33	(	(	PUNCT
cana-2411	304	34	0.8,0.75,0.6)υ̃1	0.8,0.75,0.6)υ̃1	NUM
cana-2411	304	35	∂f̃	∂f̃	NOUN
cana-2411	304	36	∂υ̃2	∂υ̃2	NOUN
cana-2411	304	37	=	=	PUNCT
cana-2411	304	38	(	(	PUNCT
cana-2411	304	39	26,1−	26,1−	NUM
cana-2411	304	40	r	r	NOUN
cana-2411	304	41	,	,	PUNCT
cana-2411	304	42	1	1	NUM
cana-2411	304	43	−	−	NOUN
cana-2411	304	44	r	r	NOUN
cana-2411	304	45	)	)	PUNCT
cana-2411	304	46	;	;	PUNCT
cana-2411	304	47	(	(	PUNCT
cana-2411	304	48	0.67,0.54,0.5	0.67,0.54,0.5	NUM
cana-2411	304	49	)	)	PUNCT
cana-2411	304	50	+	+	CCONJ
cana-2411	304	51	(	(	PUNCT
cana-2411	304	52	4,1−	4,1−	NUM
cana-2411	304	53	r	r	NOUN
cana-2411	304	54	,	,	PUNCT
cana-2411	304	55	1−	1−	NUM
cana-2411	304	56	r	r	NOUN
cana-2411	304	57	)	)	PUNCT
cana-2411	304	58	;	;	PUNCT
cana-2411	304	59	(	(	PUNCT
cana-2411	304	60	0.74,0.75,0.68)υ̃1	0.74,0.75,0.68)υ̃1	NOUN
cana-2411	304	61	(	(	PUNCT
cana-2411	304	62	−6,1−	−6,1−	NOUN
cana-2411	304	63	r	r	NOUN
cana-2411	304	64	,	,	PUNCT
cana-2411	304	65	1−	1−	NUM
cana-2411	304	66	r	r	NOUN
cana-2411	304	67	)	)	PUNCT
cana-2411	304	68	;	;	PUNCT
cana-2411	304	69	(	(	PUNCT
cana-2411	304	70	0.7,0.65,0.75)υ̃2	0.7,0.65,0.75)υ̃2	X
cana-2411	304	71	the	the	DET
cana-2411	304	72	condition	condition	NOUN
cana-2411	304	73	required	require	VERB
cana-2411	304	74	for	for	SCONJ
cana-2411	304	75	υ̃	υ̃	PROPN
cana-2411	304	76	to	to	PART
cana-2411	304	77	be	be	AUX
cana-2411	304	78	the	the	DET
cana-2411	304	79	optimum	optimum	ADJ
cana-2411	304	80	solution	solution	NOUN
cana-2411	304	81	for	for	ADP
cana-2411	304	82	(	(	PUNCT
cana-2411	304	83	10	10	NUM
cana-2411	304	84	)	)	PUNCT
cana-2411	304	85	∇2f̃(υ̃1	∇2f̃(υ̃1	NOUN
cana-2411	304	86	,	,	PUNCT
cana-2411	304	87	υ̃2	υ̃2	PROPN
cana-2411	304	88	)	)	PUNCT
cana-2411	305	1	≈	≈	NOUN
cana-2411	305	2	0̃.	0̃.	NOUN
cana-2411	306	1	hence	hence	ADV
cana-2411	306	2	we	we	PRON
cana-2411	306	3	have	have	VERB
cana-2411	306	4	∂2f̃	∂2f̃	PROPN
cana-2411	306	5	∂υ̃1	∂υ̃1	NOUN
cana-2411	306	6	2	2	NUM
cana-2411	306	7	=	=	SYM
cana-2411	306	8	(	(	PUNCT
cana-2411	306	9	−8,1−	−8,1−	PROPN
cana-2411	306	10	r	r	PROPN
cana-2411	306	11	,	,	PUNCT
cana-2411	306	12	1−	1−	NUM
cana-2411	306	13	r	r	NOUN
cana-2411	306	14	)	)	PUNCT
cana-2411	306	15	;	;	PUNCT
cana-2411	306	16	(	(	PUNCT
cana-2411	306	17	0.8,0.75,0.6	0.8,0.75,0.6	NOUN
cana-2411	306	18	)	)	PUNCT
cana-2411	306	19	,	,	PUNCT
cana-2411	306	20	∂2f̃	∂2f̃	NOUN
cana-2411	306	21	∂υ̃2	∂υ̃2	NOUN
cana-2411	306	22	2	2	NUM
cana-2411	306	23	=	=	SYM
cana-2411	306	24	(	(	PUNCT
cana-2411	306	25	−6,1−	−6,1−	ADP
cana-2411	306	26	r	r	NOUN
cana-2411	306	27	,	,	PUNCT
cana-2411	306	28	1−	1−	NUM
cana-2411	306	29	r	r	NOUN
cana-2411	306	30	)	)	PUNCT
cana-2411	306	31	;	;	PUNCT
cana-2411	306	32	(	(	PUNCT
cana-2411	306	33	0.7,0.65,0.75	0.7,0.65,0.75	NOUN
cana-2411	306	34	)	)	PUNCT
cana-2411	306	35	∂2f̃	∂2f̃	NOUN
cana-2411	306	36	∂υ̃1	∂υ̃1	PROPN
cana-2411	307	1	∂υ̃2	∂υ̃2	NOUN
cana-2411	307	2	=	=	PUNCT
cana-2411	307	3	(	(	PUNCT
cana-2411	307	4	4,1−	4,1−	NUM
cana-2411	307	5	r	r	NOUN
cana-2411	307	6	,	,	PUNCT
cana-2411	307	7	1−	1−	NUM
cana-2411	307	8	r	r	NOUN
cana-2411	307	9	)	)	PUNCT
cana-2411	307	10	;	;	PUNCT
cana-2411	307	11	(	(	PUNCT
cana-2411	307	12	0.74,0.75,0.68	0.74,0.75,0.68	NOUN
cana-2411	307	13	)	)	PUNCT
cana-2411	307	14	,	,	PUNCT
cana-2411	307	15	∂2f̃	∂2f̃	PROPN
cana-2411	307	16	∂υ̃2	∂υ̃2	X
cana-2411	307	17	∂υ̃1	∂υ̃1	PROPN
cana-2411	308	1	=	=	PRON
cana-2411	308	2	(	(	PUNCT
cana-2411	308	3	4,1−	4,1−	NUM
cana-2411	308	4	r	r	NOUN
cana-2411	308	5	,	,	PUNCT
cana-2411	308	6	1−	1−	NUM
cana-2411	308	7	r	r	NOUN
cana-2411	308	8	)	)	PUNCT
cana-2411	308	9	;	;	PUNCT
cana-2411	308	10	(	(	PUNCT
cana-2411	308	11	0.74,0.75,0.68	0.74,0.75,0.68	X
cana-2411	308	12	)	)	PUNCT
cana-2411	308	13	communications	communication	NOUN
cana-2411	308	14	on	on	ADP
cana-2411	308	15	applied	apply	VERB
cana-2411	308	16	nonlinear	nonlinear	ADJ
cana-2411	308	17	analysis	analysis	NOUN
cana-2411	308	18	issn	issn	NOUN
cana-2411	308	19	:	:	PUNCT
cana-2411	308	20	1074	1074	NUM
cana-2411	308	21	-	-	PUNCT
cana-2411	308	22	133x	133x	NUM
cana-2411	308	23	vol	vol	NOUN
cana-2411	308	24	32	32	NUM
cana-2411	308	25	no	no	NOUN
cana-2411	308	26	.	.	PUNCT
cana-2411	309	1	2s	2s	NUM
cana-2411	309	2	(	(	PUNCT
cana-2411	309	3	2025	2025	NUM
cana-2411	309	4	)	)	PUNCT
cana-2411	309	5	379	379	NUM
cana-2411	309	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2411	309	7	table	table	NOUN
cana-2411	309	8	1	1	NUM
cana-2411	309	9	:	:	PUNCT
cana-2411	309	10	cauchy	cauchy	PROPN
cana-2411	309	11	’s	’s	PART
cana-2411	309	12	steepest	steep	ADJ
cana-2411	309	13	descent	descent	NOUN
cana-2411	309	14	method	method	NOUN
cana-2411	309	15	iteration	iteration	NOUN
cana-2411	309	16	𝐘𝐢	𝐘𝐢	PROPN
cana-2411	309	17	=	=	SYM
cana-2411	309	18	(	(	PUNCT
cana-2411	309	19	𝛖𝟏	𝛖𝟏	ADJ
cana-2411	309	20	,	,	PUNCT
cana-2411	309	21	𝛖𝟐	𝛖𝟐	NOUN
cana-2411	309	22	)	)	PUNCT
cana-2411	309	23	�	�	PROPN
cana-2411	309	24	̃	̃	PROPN
cana-2411	309	25	�	�	PROPN
cana-2411	309	26	𝐢+𝟏	𝐢+𝟏	X
cana-2411	309	27	=	=	SYM
cana-2411	309	28	(	(	PUNCT
cana-2411	309	29	𝛖𝟏	𝛖𝟏	ADJ
cana-2411	309	30	,	,	PUNCT
cana-2411	309	31	𝛖𝟐	𝛖𝟐	NOUN
cana-2411	309	32	)	)	PUNCT
cana-2411	309	33	𝛁𝐟𝐢	𝛁𝐟𝐢	NOUN
cana-2411	309	34	1	1	NUM
cana-2411	309	35	(	(	PUNCT
cana-2411	309	36	(	(	PUNCT
cana-2411	309	37	1,1−	1,1−	NUM
cana-2411	309	38	r	r	NOUN
cana-2411	309	39	,	,	PUNCT
cana-2411	309	40	1	1	NUM
cana-2411	309	41	−	−	NOUN
cana-2411	309	42	r	r	NOUN
cana-2411	309	43	)	)	PUNCT
cana-2411	309	44	;	;	PUNCT
cana-2411	309	45	(	(	PUNCT
cana-2411	309	46	0.65,0.6,0.5	0.65,0.6,0.5	NUM
cana-2411	309	47	)	)	PUNCT
cana-2411	309	48	(	(	PUNCT
cana-2411	309	49	1,1−	1,1−	NUM
cana-2411	309	50	r	r	NOUN
cana-2411	309	51	,	,	PUNCT
cana-2411	309	52	1	1	NUM
cana-2411	309	53	−	−	NOUN
cana-2411	309	54	r	r	NOUN
cana-2411	309	55	)	)	PUNCT
cana-2411	309	56	;	;	PUNCT
cana-2411	309	57	(	(	PUNCT
cana-2411	309	58	0.65,0.6,0.5	0.65,0.6,0.5	NUM
cana-2411	309	59	)	)	PUNCT
cana-2411	309	60	)	)	PUNCT
cana-2411	310	1	(	(	PUNCT
cana-2411	310	2	(	(	PUNCT
cana-2411	310	3	6.4736,1−	6.4736,1−	PROPN
cana-2411	310	4	r	r	NOUN
cana-2411	310	5	,	,	PUNCT
cana-2411	310	6	1−	1−	NUM
cana-2411	310	7	r	r	NOUN
cana-2411	310	8	)	)	PUNCT
cana-2411	310	9	;	;	PUNCT
cana-2411	310	10	(	(	PUNCT
cana-2411	310	11	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	310	12	)	)	PUNCT
cana-2411	310	13	(	(	PUNCT
cana-2411	310	14	9.2104,1−	9.2104,1−	NOUN
cana-2411	310	15	r	r	NOUN
cana-2411	310	16	,	,	PUNCT
cana-2411	310	17	1−	1−	NUM
cana-2411	310	18	r	r	NOUN
cana-2411	310	19	)	)	PUNCT
cana-2411	310	20	;	;	PUNCT
cana-2411	310	21	(	(	PUNCT
cana-2411	310	22	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	310	23	)	)	PUNCT
cana-2411	310	24	)	)	PUNCT
cana-2411	311	1	(	(	PUNCT
cana-2411	311	2	(	(	PUNCT
cana-2411	311	3	5.0528,1−	5.0528,1−	PROPN
cana-2411	311	4	r	r	NOUN
cana-2411	311	5	,	,	PUNCT
cana-2411	311	6	1−	1−	NUM
cana-2411	311	7	r	r	NOUN
cana-2411	311	8	)	)	PUNCT
cana-2411	311	9	;	;	PUNCT
cana-2411	311	10	(	(	PUNCT
cana-2411	311	11	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	311	12	)	)	PUNCT
cana-2411	311	13	(	(	PUNCT
cana-2411	311	14	−3.368,1−	−3.368,1−	NOUN
cana-2411	311	15	r	r	NOUN
cana-2411	311	16	,	,	PUNCT
cana-2411	311	17	1−	1−	NUM
cana-2411	311	18	r	r	NOUN
cana-2411	311	19	)	)	PUNCT
cana-2411	311	20	;	;	PUNCT
cana-2411	311	21	(	(	PUNCT
cana-2411	311	22	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	311	23	)	)	PUNCT
cana-2411	311	24	)	)	PUNCT
cana-2411	311	25	2	2	NUM
cana-2411	311	26	(	(	PUNCT
cana-2411	311	27	(	(	PUNCT
cana-2411	311	28	6.4736,1−	6.4736,1−	PROPN
cana-2411	311	29	r	r	NOUN
cana-2411	311	30	,	,	PUNCT
cana-2411	311	31	1−	1−	NUM
cana-2411	311	32	r	r	NOUN
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cana-2411	311	34	;	;	PUNCT
cana-2411	311	35	(	(	PUNCT
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cana-2411	311	37	)	)	PUNCT
cana-2411	311	38	(	(	PUNCT
cana-2411	311	39	9.2104,1−	9.2104,1−	NOUN
cana-2411	311	40	r	r	NOUN
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cana-2411	311	42	1−	1−	NUM
cana-2411	311	43	r	r	NOUN
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cana-2411	311	45	;	;	PUNCT
cana-2411	311	46	(	(	PUNCT
cana-2411	311	47	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	311	48	)	)	PUNCT
cana-2411	311	49	)	)	PUNCT
cana-2411	312	1	(	(	PUNCT
cana-2411	312	2	(	(	PUNCT
cana-2411	312	3	6.9299,1−	6.9299,1−	NUM
cana-2411	312	4	r	r	NOUN
cana-2411	312	5	,	,	PUNCT
cana-2411	312	6	1−	1−	NUM
cana-2411	312	7	r	r	NOUN
cana-2411	312	8	)	)	PUNCT
cana-2411	312	9	;	;	PUNCT
cana-2411	312	10	(	(	PUNCT
cana-2411	312	11	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	312	12	)	)	PUNCT
cana-2411	312	13	(	(	PUNCT
cana-2411	312	14	8.9063,1−	8.9063,1−	NUM
cana-2411	312	15	r	r	NOUN
cana-2411	312	16	,	,	PUNCT
cana-2411	312	17	1−	1−	NUM
cana-2411	312	18	r	r	NOUN
cana-2411	312	19	)	)	PUNCT
cana-2411	312	20	;	;	PUNCT
cana-2411	312	21	(	(	PUNCT
cana-2411	312	22	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	312	23	)	)	PUNCT
cana-2411	312	24	)	)	PUNCT
cana-2411	313	1	(	(	PUNCT
cana-2411	313	2	(	(	PUNCT
cana-2411	313	3	0.186,1−	0.186,1−	NOUN
cana-2411	313	4	r	r	NOUN
cana-2411	313	5	,	,	PUNCT
cana-2411	313	6	1−	1−	NUM
cana-2411	313	7	r	r	NOUN
cana-2411	313	8	)	)	PUNCT
cana-2411	313	9	;	;	PUNCT
cana-2411	313	10	(	(	PUNCT
cana-2411	313	11	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	313	12	)	)	PUNCT
cana-2411	313	13	(	(	PUNCT
cana-2411	313	14	0.2818,1−	0.2818,1−	NOUN
cana-2411	313	15	r	r	NOUN
cana-2411	313	16	,	,	PUNCT
cana-2411	313	17	1−	1−	NUM
cana-2411	313	18	r	r	NOUN
cana-2411	313	19	)	)	PUNCT
cana-2411	313	20	;	;	PUNCT
cana-2411	313	21	(	(	PUNCT
cana-2411	313	22	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	313	23	)	)	PUNCT
cana-2411	313	24	)	)	PUNCT
cana-2411	313	25	3	3	NUM
cana-2411	313	26	(	(	PUNCT
cana-2411	313	27	(	(	PUNCT
cana-2411	313	28	6.9299,1−	6.9299,1−	NUM
cana-2411	313	29	r	r	NOUN
cana-2411	313	30	,	,	PUNCT
cana-2411	313	31	1−	1−	NUM
cana-2411	313	32	r	r	NOUN
cana-2411	313	33	)	)	PUNCT
cana-2411	313	34	;	;	PUNCT
cana-2411	313	35	(	(	PUNCT
cana-2411	313	36	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	313	37	)	)	PUNCT
cana-2411	313	38	(	(	PUNCT
cana-2411	313	39	8.9063,1−	8.9063,1−	NUM
cana-2411	313	40	r	r	NOUN
cana-2411	313	41	,	,	PUNCT
cana-2411	313	42	1−	1−	NUM
cana-2411	313	43	r	r	NOUN
cana-2411	313	44	)	)	PUNCT
cana-2411	313	45	;	;	PUNCT
cana-2411	313	46	(	(	PUNCT
cana-2411	313	47	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	313	48	)	)	PUNCT
cana-2411	313	49	)	)	PUNCT
cana-2411	313	50	(	(	PUNCT
cana-2411	313	51	(	(	PUNCT
cana-2411	313	52	6.993,1−	6.993,1−	NUM
cana-2411	313	53	r	r	NOUN
cana-2411	313	54	,	,	PUNCT
cana-2411	313	55	1−	1−	NUM
cana-2411	313	56	r	r	NOUN
cana-2411	313	57	)	)	PUNCT
cana-2411	313	58	;	;	PUNCT
cana-2411	313	59	(	(	PUNCT
cana-2411	313	60	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	313	61	)	)	PUNCT
cana-2411	313	62	(	(	PUNCT
cana-2411	313	63	9.002,1−	9.002,1−	NUM
cana-2411	313	64	r	r	NOUN
cana-2411	313	65	,	,	PUNCT
cana-2411	313	66	1−	1−	NUM
cana-2411	313	67	r	r	NOUN
cana-2411	313	68	)	)	PUNCT
cana-2411	313	69	;	;	PUNCT
cana-2411	313	70	(	(	PUNCT
cana-2411	313	71	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	313	72	)	)	PUNCT
cana-2411	313	73	)	)	PUNCT
cana-2411	313	74	(	(	PUNCT
cana-2411	313	75	(	(	PUNCT
cana-2411	313	76	0.064,1−	0.064,1−	PROPN
cana-2411	313	77	r	r	NOUN
cana-2411	313	78	,	,	PUNCT
cana-2411	313	79	1−	1−	NUM
cana-2411	313	80	r	r	NOUN
cana-2411	313	81	)	)	PUNCT
cana-2411	313	82	;	;	PUNCT
cana-2411	313	83	(	(	PUNCT
cana-2411	313	84	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	313	85	)	)	PUNCT
cana-2411	313	86	(	(	PUNCT
cana-2411	313	87	0.2818,1−	0.2818,1−	NOUN
cana-2411	313	88	r	r	NOUN
cana-2411	313	89	,	,	PUNCT
cana-2411	313	90	1−	1−	NUM
cana-2411	313	91	r	r	NOUN
cana-2411	313	92	)	)	PUNCT
cana-2411	313	93	;	;	PUNCT
cana-2411	313	94	(	(	PUNCT
cana-2411	313	95	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	313	96	)	)	PUNCT
cana-2411	313	97	)	)	PUNCT
cana-2411	313	98	4	4	NUM
cana-2411	313	99	(	(	PUNCT
cana-2411	313	100	(	(	PUNCT
cana-2411	313	101	6.993,1−	6.993,1−	NUM
cana-2411	313	102	r	r	NOUN
cana-2411	313	103	,	,	PUNCT
cana-2411	313	104	1−	1−	NUM
cana-2411	313	105	r	r	NOUN
cana-2411	313	106	)	)	PUNCT
cana-2411	313	107	;	;	PUNCT
cana-2411	313	108	(	(	PUNCT
cana-2411	313	109	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	313	110	)	)	PUNCT
cana-2411	313	111	(	(	PUNCT
cana-2411	313	112	9.002,1−	9.002,1−	NUM
cana-2411	313	113	r	r	NOUN
cana-2411	313	114	,	,	PUNCT
cana-2411	313	115	1−	1−	NUM
cana-2411	313	116	r	r	NOUN
cana-2411	313	117	)	)	PUNCT
cana-2411	313	118	;	;	PUNCT
cana-2411	313	119	(	(	PUNCT
cana-2411	313	120	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	313	121	)	)	PUNCT
cana-2411	313	122	)	)	PUNCT
cana-2411	313	123	(	(	PUNCT
cana-2411	313	124	(	(	PUNCT
cana-2411	313	125	6.9993,1−	6.9993,1−	NUM
cana-2411	313	126	r	r	NOUN
cana-2411	313	127	,	,	PUNCT
cana-2411	313	128	1−	1−	NUM
cana-2411	313	129	r	r	NOUN
cana-2411	313	130	)	)	PUNCT
cana-2411	313	131	;	;	PUNCT
cana-2411	313	132	(	(	PUNCT
cana-2411	313	133	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	313	134	)	)	PUNCT
cana-2411	313	135	(	(	PUNCT
cana-2411	313	136	9.002,1−	9.002,1−	NUM
cana-2411	313	137	r	r	NOUN
cana-2411	313	138	,	,	PUNCT
cana-2411	313	139	1−	1−	NUM
cana-2411	313	140	r	r	NOUN
cana-2411	313	141	)	)	PUNCT
cana-2411	313	142	;	;	PUNCT
cana-2411	313	143	(	(	PUNCT
cana-2411	313	144	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	313	145	)	)	PUNCT
cana-2411	313	146	)	)	PUNCT
cana-2411	313	147	(	(	PUNCT
cana-2411	313	148	(	(	PUNCT
cana-2411	313	149	0.064,1−	0.064,1−	PROPN
cana-2411	313	150	r	r	NOUN
cana-2411	313	151	,	,	PUNCT
cana-2411	313	152	1−	1−	NUM
cana-2411	313	153	r	r	NOUN
cana-2411	313	154	)	)	PUNCT
cana-2411	313	155	;	;	PUNCT
cana-2411	313	156	(	(	PUNCT
cana-2411	313	157	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	313	158	)	)	PUNCT
cana-2411	313	159	(	(	PUNCT
cana-2411	313	160	−0.04,1−	−0.04,1−	NOUN
cana-2411	313	161	r	r	NOUN
cana-2411	313	162	,	,	PUNCT
cana-2411	313	163	1−	1−	NUM
cana-2411	313	164	r	r	NOUN
cana-2411	313	165	)	)	PUNCT
cana-2411	313	166	;	;	PUNCT
cana-2411	313	167	(	(	PUNCT
cana-2411	313	168	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	313	169	)	)	PUNCT
cana-2411	313	170	)	)	PUNCT
cana-2411	313	171	table	table	NOUN
cana-2411	313	172	2	2	NUM
cana-2411	313	173	:	:	PUNCT
cana-2411	313	174	fletcher	fletcher	PROPN
cana-2411	313	175	reeves	reeves	PROPN
cana-2411	313	176	method	method	PROPN
cana-2411	313	177	iteration	iteration	PROPN
cana-2411	313	178	�	�	PROPN
cana-2411	313	179	̃	̃	PROPN
cana-2411	313	180	�	�	PROPN
cana-2411	313	181	𝐢	𝐢	NOUN
cana-2411	313	182	=	=	SYM
cana-2411	313	183	(	(	PUNCT
cana-2411	313	184	𝛖𝟏	𝛖𝟏	ADJ
cana-2411	313	185	,	,	PUNCT
cana-2411	313	186	𝛖𝟐	𝛖𝟐	NOUN
cana-2411	313	187	)	)	PUNCT
cana-2411	313	188	�	�	PROPN
cana-2411	313	189	̃	̃	PROPN
cana-2411	313	190	�	�	PROPN
cana-2411	313	191	𝐢+𝟏	𝐢+𝟏	X
cana-2411	313	192	=	=	SYM
cana-2411	313	193	(	(	PUNCT
cana-2411	313	194	𝛖𝟏	𝛖𝟏	ADJ
cana-2411	313	195	,	,	PUNCT
cana-2411	313	196	𝛖𝟐	𝛖𝟐	NOUN
cana-2411	313	197	)	)	PUNCT
cana-2411	313	198	𝛁𝐟𝐢	𝛁𝐟𝐢	NOUN
cana-2411	313	199	1	1	NUM
cana-2411	313	200	(	(	PUNCT
cana-2411	313	201	(	(	PUNCT
cana-2411	313	202	1,1−	1,1−	NUM
cana-2411	313	203	r	r	NOUN
cana-2411	313	204	,	,	PUNCT
cana-2411	313	205	1−	1−	NUM
cana-2411	313	206	r	r	NOUN
cana-2411	313	207	)	)	PUNCT
cana-2411	313	208	;	;	PUNCT
cana-2411	313	209	(	(	PUNCT
cana-2411	313	210	0.65,0.6,0.5	0.65,0.6,0.5	NUM
cana-2411	313	211	)	)	PUNCT
cana-2411	313	212	(	(	PUNCT
cana-2411	313	213	1,1−	1,1−	NUM
cana-2411	313	214	r	r	NOUN
cana-2411	313	215	,	,	PUNCT
cana-2411	313	216	1−	1−	NUM
cana-2411	313	217	r	r	NOUN
cana-2411	313	218	)	)	PUNCT
cana-2411	313	219	;	;	PUNCT
cana-2411	313	220	(	(	PUNCT
cana-2411	313	221	0.65,0.6,0.5	0.65,0.6,0.5	NUM
cana-2411	313	222	)	)	PUNCT
cana-2411	313	223	)	)	PUNCT
cana-2411	314	1	(	(	PUNCT
cana-2411	314	2	(	(	PUNCT
cana-2411	314	3	6.4736,1−	6.4736,1−	PROPN
cana-2411	314	4	r	r	NOUN
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cana-2411	314	6	1−	1−	NUM
cana-2411	314	7	r	r	NOUN
cana-2411	314	8	)	)	PUNCT
cana-2411	314	9	;	;	PUNCT
cana-2411	314	10	(	(	PUNCT
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cana-2411	314	12	)	)	PUNCT
cana-2411	314	13	(	(	PUNCT
cana-2411	314	14	9.2104,1−	9.2104,1−	NOUN
cana-2411	314	15	r	r	NOUN
cana-2411	314	16	,	,	PUNCT
cana-2411	314	17	1−	1−	NUM
cana-2411	314	18	r	r	NOUN
cana-2411	314	19	)	)	PUNCT
cana-2411	314	20	;	;	PUNCT
cana-2411	314	21	(	(	PUNCT
cana-2411	314	22	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	314	23	)	)	PUNCT
cana-2411	314	24	)	)	PUNCT
cana-2411	315	1	(	(	PUNCT
cana-2411	315	2	(	(	PUNCT
cana-2411	315	3	5.0528,1−	5.0528,1−	PROPN
cana-2411	315	4	r	r	NOUN
cana-2411	315	5	,	,	PUNCT
cana-2411	315	6	1−	1−	NUM
cana-2411	315	7	r	r	NOUN
cana-2411	315	8	)	)	PUNCT
cana-2411	315	9	;	;	PUNCT
cana-2411	315	10	(	(	PUNCT
cana-2411	315	11	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	315	12	)	)	PUNCT
cana-2411	315	13	(	(	PUNCT
cana-2411	315	14	−3.368,1−	−3.368,1−	NOUN
cana-2411	315	15	r	r	NOUN
cana-2411	315	16	,	,	PUNCT
cana-2411	315	17	1−	1−	NUM
cana-2411	315	18	r	r	NOUN
cana-2411	315	19	)	)	PUNCT
cana-2411	315	20	;	;	PUNCT
cana-2411	315	21	(	(	PUNCT
cana-2411	315	22	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	315	23	)	)	PUNCT
cana-2411	315	24	)	)	PUNCT
cana-2411	315	25	2	2	NUM
cana-2411	315	26	(	(	PUNCT
cana-2411	315	27	(	(	PUNCT
cana-2411	315	28	6.4736,1−	6.4736,1−	PROPN
cana-2411	315	29	r	r	NOUN
cana-2411	315	30	,	,	PUNCT
cana-2411	315	31	1−	1−	NUM
cana-2411	315	32	r	r	NOUN
cana-2411	315	33	)	)	PUNCT
cana-2411	315	34	;	;	PUNCT
cana-2411	315	35	(	(	PUNCT
cana-2411	315	36	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	315	37	)	)	PUNCT
cana-2411	315	38	(	(	PUNCT
cana-2411	315	39	9.2104,1−	9.2104,1−	NOUN
cana-2411	315	40	r	r	NOUN
cana-2411	315	41	,	,	PUNCT
cana-2411	315	42	1−	1−	NUM
cana-2411	315	43	r	r	NOUN
cana-2411	315	44	)	)	PUNCT
cana-2411	315	45	;	;	PUNCT
cana-2411	315	46	(	(	PUNCT
cana-2411	315	47	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	315	48	)	)	PUNCT
cana-2411	315	49	)	)	PUNCT
cana-2411	316	1	(	(	PUNCT
cana-2411	316	2	(	(	PUNCT
cana-2411	316	3	6.9975,1−	6.9975,1−	NUM
cana-2411	316	4	r	r	NOUN
cana-2411	316	5	,	,	PUNCT
cana-2411	316	6	1−	1−	NUM
cana-2411	316	7	r	r	NOUN
cana-2411	316	8	)	)	PUNCT
cana-2411	316	9	;	;	PUNCT
cana-2411	316	10	(	(	PUNCT
cana-2411	316	11	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	316	12	)	)	PUNCT
cana-2411	316	13	(	(	PUNCT
cana-2411	316	14	9.000,1−	9.000,1−	PROPN
cana-2411	316	15	r	r	NOUN
cana-2411	316	16	,	,	PUNCT
cana-2411	316	17	1−	1−	NUM
cana-2411	316	18	r	r	NOUN
cana-2411	316	19	)	)	PUNCT
cana-2411	316	20	;	;	PUNCT
cana-2411	316	21	(	(	PUNCT
cana-2411	316	22	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	316	23	)	)	PUNCT
cana-2411	316	24	)	)	PUNCT
cana-2411	317	1	(	(	PUNCT
cana-2411	317	2	(	(	PUNCT
cana-2411	317	3	0.02,1−	0.02,1−	NOUN
cana-2411	317	4	r	r	NOUN
cana-2411	317	5	,	,	PUNCT
cana-2411	317	6	1−	1−	NUM
cana-2411	317	7	r	r	NOUN
cana-2411	317	8	)	)	PUNCT
cana-2411	317	9	;	;	PUNCT
cana-2411	317	10	(	(	PUNCT
cana-2411	317	11	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	317	12	)	)	PUNCT
cana-2411	317	13	(	(	PUNCT
cana-2411	317	14	−0.01,1−	−0.01,1−	NOUN
cana-2411	317	15	r	r	NOUN
cana-2411	317	16	,	,	PUNCT
cana-2411	317	17	1−	1−	NUM
cana-2411	317	18	r	r	NOUN
cana-2411	317	19	)	)	PUNCT
cana-2411	317	20	;	;	PUNCT
cana-2411	317	21	(	(	PUNCT
cana-2411	317	22	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	317	23	)	)	PUNCT
cana-2411	317	24	)	)	PUNCT
cana-2411	317	25	3	3	NUM
cana-2411	317	26	(	(	PUNCT
cana-2411	317	27	(	(	PUNCT
cana-2411	317	28	6.9975,1−	6.9975,1−	NUM
cana-2411	317	29	r	r	NOUN
cana-2411	317	30	,	,	PUNCT
cana-2411	317	31	1−	1−	NUM
cana-2411	317	32	r	r	NOUN
cana-2411	317	33	)	)	PUNCT
cana-2411	317	34	;	;	PUNCT
cana-2411	317	35	(	(	PUNCT
cana-2411	317	36	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	317	37	)	)	PUNCT
cana-2411	317	38	(	(	PUNCT
cana-2411	317	39	9.000,1−	9.000,1−	PROPN
cana-2411	317	40	r	r	NOUN
cana-2411	317	41	,	,	PUNCT
cana-2411	317	42	1−	1−	NUM
cana-2411	317	43	r	r	NOUN
cana-2411	317	44	)	)	PUNCT
cana-2411	317	45	;	;	PUNCT
cana-2411	317	46	(	(	PUNCT
cana-2411	317	47	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	317	48	)	)	PUNCT
cana-2411	317	49	)	)	PUNCT
cana-2411	317	50	(	(	PUNCT
cana-2411	317	51	(	(	PUNCT
cana-2411	317	52	6.999,1−	6.999,1−	NUM
cana-2411	317	53	r	r	NOUN
cana-2411	317	54	,	,	PUNCT
cana-2411	317	55	1−	1−	NUM
cana-2411	317	56	r	r	NOUN
cana-2411	317	57	)	)	PUNCT
cana-2411	317	58	;	;	PUNCT
cana-2411	317	59	(	(	PUNCT
cana-2411	317	60	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	317	61	)	)	PUNCT
cana-2411	317	62	(	(	PUNCT
cana-2411	317	63	8.999,1−	8.999,1−	PROPN
cana-2411	317	64	r	r	PROPN
cana-2411	317	65	,	,	PUNCT
cana-2411	317	66	1−	1−	NUM
cana-2411	317	67	r	r	NOUN
cana-2411	317	68	)	)	PUNCT
cana-2411	317	69	;	;	PUNCT
cana-2411	317	70	(	(	PUNCT
cana-2411	317	71	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	317	72	)	)	PUNCT
cana-2411	317	73	)	)	PUNCT
cana-2411	318	1	(	(	PUNCT
cana-2411	318	2	(	(	PUNCT
cana-2411	318	3	0.001,1−	0.001,1−	NOUN
cana-2411	318	4	r	r	NOUN
cana-2411	318	5	,	,	PUNCT
cana-2411	318	6	1−	1−	NUM
cana-2411	318	7	r	r	NOUN
cana-2411	318	8	)	)	PUNCT
cana-2411	318	9	;	;	PUNCT
cana-2411	318	10	(	(	PUNCT
cana-2411	318	11	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	318	12	)	)	PUNCT
cana-2411	318	13	(	(	PUNCT
cana-2411	318	14	0.003,1−	0.003,1−	NOUN
cana-2411	318	15	r	r	NOUN
cana-2411	318	16	,	,	PUNCT
cana-2411	318	17	1−	1−	NUM
cana-2411	318	18	r	r	NOUN
cana-2411	318	19	)	)	PUNCT
cana-2411	318	20	;	;	PUNCT
cana-2411	318	21	(	(	PUNCT
cana-2411	318	22	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	318	23	)	)	PUNCT
cana-2411	318	24	)	)	PUNCT
cana-2411	318	25	from	from	ADP
cana-2411	318	26	the	the	DET
cana-2411	318	27	above	above	ADJ
cana-2411	318	28	tables(1),(2	tables(1),(2	PROPN
cana-2411	318	29	)	)	PUNCT
cana-2411	318	30	,	,	PUNCT
cana-2411	318	31	we	we	PRON
cana-2411	318	32	observed	observe	VERB
cana-2411	318	33	that	that	SCONJ
cana-2411	318	34	the	the	DET
cana-2411	318	35	sdm	sdm	NOUN
cana-2411	318	36	converges	converge	VERB
cana-2411	318	37	at	at	ADP
cana-2411	318	38	iteration	iteration	NOUN
cana-2411	318	39	4	4	NUM
cana-2411	318	40	while	while	SCONJ
cana-2411	318	41	the	the	DET
cana-2411	318	42	frm	frm	PROPN
cana-2411	318	43	at	at	ADP
cana-2411	318	44	iteration	iteration	NOUN
cana-2411	318	45	3	3	NUM
cana-2411	318	46	.	.	PUNCT
cana-2411	319	1	hence	hence	ADV
cana-2411	319	2	the	the	DET
cana-2411	319	3	optimal	optimal	ADJ
cana-2411	319	4	solution	solution	NOUN
cana-2411	319	5	of	of	ADP
cana-2411	319	6	the	the	DET
cana-2411	319	7	given	give	VERB
cana-2411	319	8	svnnlpp	svnnlpp	NOUN
cana-2411	319	9	(	(	PUNCT
cana-2411	319	10	9	9	NUM
cana-2411	319	11	)	)	PUNCT
cana-2411	319	12	is	be	AUX
cana-2411	319	13	communications	communication	NOUN
cana-2411	319	14	on	on	ADP
cana-2411	319	15	applied	apply	VERB
cana-2411	319	16	nonlinear	nonlinear	ADJ
cana-2411	319	17	analysis	analysis	NOUN
cana-2411	319	18	issn	issn	NOUN
cana-2411	319	19	:	:	PUNCT
cana-2411	319	20	1074	1074	NUM
cana-2411	319	21	-	-	PUNCT
cana-2411	319	22	133x	133x	NUM
cana-2411	319	23	vol	vol	NOUN
cana-2411	319	24	32	32	NUM
cana-2411	319	25	no	no	NOUN
cana-2411	319	26	.	.	PUNCT
cana-2411	320	1	2s	2s	NUM
cana-2411	320	2	(	(	PUNCT
cana-2411	320	3	2025	2025	NUM
cana-2411	320	4	)	)	PUNCT
cana-2411	320	5	380	380	NUM
cana-2411	320	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2411	320	7	υ̃1	υ̃1	X
cana-2411	320	8	=	=	SYM
cana-2411	320	9	(	(	PUNCT
cana-2411	320	10	6.999,1−	6.999,1−	NUM
cana-2411	320	11	r	r	NOUN
cana-2411	320	12	,	,	PUNCT
cana-2411	320	13	1	1	NUM
cana-2411	320	14	−	−	NOUN
cana-2411	320	15	r	r	NOUN
cana-2411	320	16	)	)	PUNCT
cana-2411	320	17	;	;	PUNCT
cana-2411	320	18	(	(	PUNCT
cana-2411	320	19	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	320	20	)	)	PUNCT
cana-2411	320	21	,	,	PUNCT
cana-2411	320	22	υ̃2	υ̃2	PROPN
cana-2411	320	23	=	=	SYM
cana-2411	320	24	(	(	PUNCT
cana-2411	320	25	8.999,1−	8.999,1−	PROPN
cana-2411	320	26	r	r	PROPN
cana-2411	320	27	,	,	PUNCT
cana-2411	320	28	1−	1−	NUM
cana-2411	320	29	r	r	NOUN
cana-2411	320	30	)	)	PUNCT
cana-2411	320	31	;	;	PUNCT
cana-2411	320	32	(	(	PUNCT
cana-2411	320	33	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	320	34	)	)	PUNCT
cana-2411	320	35	with	with	ADP
cana-2411	320	36	f̃(υ̃1	f̃(υ̃1	NOUN
cana-2411	320	37	,	,	PUNCT
cana-2411	320	38	υ̃2	υ̃2	PROPN
cana-2411	320	39	)	)	PUNCT
cana-2411	320	40	=	=	PUNCT
cana-2411	320	41	(	(	PUNCT
cana-2411	320	42	186.999,1−	186.999,1−	NUM
cana-2411	320	43	r	r	NOUN
cana-2411	320	44	,	,	PUNCT
cana-2411	320	45	1−	1−	NUM
cana-2411	320	46	r	r	NOUN
cana-2411	320	47	)	)	PUNCT
cana-2411	320	48	;	;	PUNCT
cana-2411	320	49	(	(	PUNCT
cana-2411	320	50	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	320	51	)	)	PUNCT
cana-2411	320	52	that	that	PRON
cana-2411	320	53	is	be	AUX
cana-2411	320	54	the	the	DET
cana-2411	320	55	optimal	optimal	ADJ
cana-2411	320	56	solution	solution	NOUN
cana-2411	320	57	of	of	ADP
cana-2411	320	58	the	the	DET
cana-2411	320	59	svnnlpp	svnnlpp	NOUN
cana-2411	320	60	(	(	PUNCT
cana-2411	320	61	9	9	NUM
cana-2411	320	62	)	)	PUNCT
cana-2411	320	63	is	be	AUX
cana-2411	320	64	υ̃1	υ̃1	NOUN
cana-2411	320	65	=	=	PUNCT
cana-2411	320	66	(	(	PUNCT
cana-2411	320	67	5.999	5.999	NUM
cana-2411	320	68	+	+	NOUN
cana-2411	320	69	r	r	NOUN
cana-2411	320	70	,	,	PUNCT
cana-2411	320	71	6.999,7.999−	6.999,7.999−	NUM
cana-2411	320	72	r	r	NOUN
cana-2411	320	73	)	)	PUNCT
cana-2411	320	74	;	;	PUNCT
cana-2411	320	75	(	(	PUNCT
cana-2411	320	76	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	320	77	)	)	PUNCT
cana-2411	320	78	,	,	PUNCT
cana-2411	321	1	υ̃2	υ̃2	PROPN
cana-2411	321	2	=	=	SYM
cana-2411	321	3	(	(	PUNCT
cana-2411	321	4	7.999	7.999	NUM
cana-2411	321	5	+	+	CCONJ
cana-2411	321	6	r	r	NOUN
cana-2411	321	7	,	,	PUNCT
cana-2411	321	8	8.999,9.999−	8.999,9.999−	NUM
cana-2411	321	9	r	r	NOUN
cana-2411	321	10	)	)	PUNCT
cana-2411	321	11	;	;	PUNCT
cana-2411	321	12	(	(	PUNCT
cana-2411	321	13	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	321	14	)	)	PUNCT
cana-2411	321	15	with	with	ADP
cana-2411	321	16	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
cana-2411	321	17	f̃(υ̃1	f̃(υ̃1	NOUN
cana-2411	321	18	,	,	PUNCT
cana-2411	321	19	υ̃2	υ̃2	PROPN
cana-2411	321	20	)	)	PUNCT
cana-2411	321	21	=	=	PUNCT
cana-2411	321	22	(	(	PUNCT
cana-2411	321	23	185.999	185.999	NUM
cana-2411	321	24	+	+	SYM
cana-2411	321	25	r	r	NOUN
cana-2411	321	26	,	,	PUNCT
cana-2411	321	27	186.999,187.999−	186.999,187.999−	NUM
cana-2411	321	28	r	r	NOUN
cana-2411	321	29	)	)	PUNCT
cana-2411	321	30	;	;	PUNCT
cana-2411	321	31	(	(	PUNCT
cana-2411	321	32	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	321	33	)	)	PUNCT
cana-2411	321	34	.	.	PUNCT
cana-2411	322	1	example	example	NOUN
cana-2411	322	2	6.2	6.2	NUM
cana-2411	322	3	consider	consider	VERB
cana-2411	322	4	the	the	DET
cana-2411	322	5	problem	problem	NOUN
cana-2411	322	6	of	of	ADP
cana-2411	322	7	unconstrained	unconstrained	ADJ
cana-2411	322	8	optimization	optimization	NOUN
cana-2411	322	9	with	with	ADP
cana-2411	322	10	single	single	ADV
cana-2411	322	11	-	-	PUNCT
cana-2411	322	12	valued	value	VERB
cana-2411	322	13	neutrosophic	neutrosophic	ADJ
cana-2411	322	14	triangular	triangular	NOUN
cana-2411	322	15	fuzzy	fuzzy	ADJ
cana-2411	322	16	coefficients	coefficient	NOUN
cana-2411	322	17	,	,	PUNCT
cana-2411	322	18	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
cana-2411	322	19	f̃(υ̃1	f̃(υ̃1	NOUN
cana-2411	322	20	,	,	PUNCT
cana-2411	322	21	υ̃2	υ̃2	PROPN
cana-2411	322	22	)	)	PUNCT
cana-2411	322	23	=	=	SYM
cana-2411	323	1	(	(	PUNCT
cana-2411	323	2	0,1,2	0,1,2	NUM
cana-2411	323	3	)	)	PUNCT
cana-2411	323	4	;	;	PUNCT
cana-2411	324	1	(	(	PUNCT
cana-2411	324	2	0.68,0.51,0.55)υ̃1	0.68,0.51,0.55)υ̃1	NOUN
cana-2411	324	3	−	−	PROPN
cana-2411	325	1	(	(	PUNCT
cana-2411	325	2	0,1,2)(0.67,0.53,0.54)υ̃2	0,1,2)(0.67,0.53,0.54)υ̃2	NOUN
cana-2411	325	3	+	+	CCONJ
cana-2411	325	4	(	(	PUNCT
cana-2411	325	5	1,2,3	1,2,3	NUM
cana-2411	325	6	)	)	PUNCT
cana-2411	325	7	;	;	PUNCT
cana-2411	325	8	(	(	PUNCT
cana-2411	325	9	0.7,0.65,0.72)υ̃1	0.7,0.65,0.72)υ̃1	NOUN
cana-2411	325	10	2	2	NUM
cana-2411	325	11	+	+	CCONJ
cana-2411	325	12	(	(	PUNCT
cana-2411	325	13	1,2,3	1,2,3	NUM
cana-2411	325	14	)	)	PUNCT
cana-2411	325	15	;	;	PUNCT
cana-2411	325	16	(	(	PUNCT
cana-2411	325	17	0.69,0.51,0.52)υ̃1υ̃2	0.69,0.51,0.52)υ̃1υ̃2	ADV
cana-2411	325	18	+	+	ADJ
cana-2411	325	19	(	(	PUNCT
cana-2411	325	20	0,1,2	0,1,2	NUM
cana-2411	325	21	)	)	PUNCT
cana-2411	325	22	;	;	PUNCT
cana-2411	325	23	(	(	PUNCT
cana-2411	325	24	0.67,0.5,0.51)υ̃2	0.67,0.5,0.51)υ̃2	NUM
cana-2411	325	25	2	2	NUM
cana-2411	325	26	(	(	PUNCT
cana-2411	325	27	11	11	NUM
cana-2411	325	28	)	)	PUNCT
cana-2411	325	29	starting	start	VERB
cana-2411	325	30	with	with	ADP
cana-2411	325	31	initial	initial	ADJ
cana-2411	325	32	point	point	NOUN
cana-2411	325	33	ỹ	ỹ	PROPN
cana-2411	325	34	0	0	PUNCT
cana-2411	325	35	=	=	SYM
cana-2411	325	36	(	(	PUNCT
cana-2411	325	37	(	(	PUNCT
cana-2411	325	38	0,0,0	0,0,0	NOUN
cana-2411	325	39	)	)	PUNCT
cana-2411	325	40	;	;	PUNCT
cana-2411	325	41	(	(	PUNCT
cana-2411	325	42	0.66,0.52,0.53	0.66,0.52,0.53	NOUN
cana-2411	325	43	)	)	PUNCT
cana-2411	325	44	(	(	PUNCT
cana-2411	325	45	0,0,0	0,0,0	NOUN
cana-2411	325	46	)	)	PUNCT
cana-2411	325	47	;	;	PUNCT
cana-2411	325	48	(	(	PUNCT
cana-2411	325	49	0.66,0.52,0.53	0.66,0.52,0.53	NOUN
cana-2411	325	50	)	)	PUNCT
cana-2411	325	51	)	)	PUNCT
cana-2411	325	52	solution	solution	NOUN
cana-2411	325	53	:	:	PUNCT
cana-2411	325	54	the	the	DET
cana-2411	325	55	parametric	parametric	ADJ
cana-2411	325	56	form	form	NOUN
cana-2411	325	57	of	of	ADP
cana-2411	325	58	the	the	DET
cana-2411	325	59	given	give	VERB
cana-2411	325	60	svnnlpp	svnnlpp	NOUN
cana-2411	325	61	(	(	PUNCT
cana-2411	325	62	only	only	ADV
cana-2411	325	63	triplet)(11	triplet)(11	PROPN
cana-2411	325	64	)	)	PUNCT
cana-2411	325	65	is	be	AUX
cana-2411	325	66	given	give	VERB
cana-2411	325	67	by	by	ADP
cana-2411	325	68	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
cana-2411	325	69	f̃(υ̃1	f̃(υ̃1	NOUN
cana-2411	325	70	,	,	PUNCT
cana-2411	325	71	υ̃2	υ̃2	PROPN
cana-2411	325	72	)	)	PUNCT
cana-2411	325	73	=	=	PUNCT
cana-2411	326	1	(	(	PUNCT
cana-2411	326	2	1,1−	1,1−	NUM
cana-2411	326	3	r	r	NOUN
cana-2411	326	4	,	,	PUNCT
cana-2411	326	5	1	1	NUM
cana-2411	326	6	−	−	NOUN
cana-2411	326	7	r	r	NOUN
cana-2411	326	8	)	)	PUNCT
cana-2411	326	9	;	;	PUNCT
cana-2411	326	10	(	(	PUNCT
cana-2411	326	11	0.68,0.51,0.55)υ̃1	0.68,0.51,0.55)υ̃1	NOUN
cana-2411	326	12	−	−	PROPN
cana-2411	326	13	(	(	PUNCT
cana-2411	326	14	1,1−	1,1−	NUM
cana-2411	326	15	r	r	NOUN
cana-2411	326	16	,	,	PUNCT
cana-2411	326	17	1−	1−	NUM
cana-2411	326	18	r	r	NOUN
cana-2411	326	19	)	)	PUNCT
cana-2411	326	20	;	;	PUNCT
cana-2411	326	21	(	(	PUNCT
cana-2411	326	22	0.67,0.53,0.54)υ̃2	0.67,0.53,0.54)υ̃2	NOUN
cana-2411	326	23	+	+	CCONJ
cana-2411	326	24	(	(	PUNCT
cana-2411	326	25	2,1−	2,1−	NUM
cana-2411	326	26	r	r	NOUN
cana-2411	326	27	,	,	PUNCT
cana-2411	326	28	1−	1−	NUM
cana-2411	326	29	r	r	NOUN
cana-2411	326	30	)	)	PUNCT
cana-2411	326	31	;	;	PUNCT
cana-2411	326	32	(	(	PUNCT
cana-2411	326	33	0.7,0.65,0.72)υ̃1	0.7,0.65,0.72)υ̃1	NOUN
cana-2411	326	34	2	2	NUM
cana-2411	327	1	+	+	NOUN
cana-2411	327	2	(	(	PUNCT
cana-2411	327	3	2,1−	2,1−	NUM
cana-2411	327	4	r	r	NOUN
cana-2411	327	5	,	,	PUNCT
cana-2411	327	6	1−	1−	NUM
cana-2411	327	7	r	r	NOUN
cana-2411	327	8	)	)	PUNCT
cana-2411	327	9	;	;	PUNCT
cana-2411	327	10	(	(	PUNCT
cana-2411	327	11	0.69,0.51,0.52)υ̃1υ̃2	0.69,0.51,0.52)υ̃1υ̃2	ADV
cana-2411	327	12	+	+	CCONJ
cana-2411	327	13	(	(	PUNCT
cana-2411	327	14	1,1−	1,1−	NUM
cana-2411	327	15	r	r	NOUN
cana-2411	327	16	,	,	PUNCT
cana-2411	327	17	1−	1−	NUM
cana-2411	327	18	r	r	NOUN
cana-2411	327	19	)	)	PUNCT
cana-2411	327	20	;	;	PUNCT
cana-2411	327	21	(	(	PUNCT
cana-2411	327	22	0.67,0.5,0.51)υ̃2	0.67,0.5,0.51)υ̃2	NUM
cana-2411	327	23	2	2	NUM
cana-2411	327	24	(	(	PUNCT
cana-2411	327	25	12	12	NUM
cana-2411	327	26	)	)	PUNCT
cana-2411	327	27	ỹ	ỹ	NOUN
cana-2411	327	28	0	0	PUNCT
cana-2411	327	29	=	=	SYM
cana-2411	327	30	(	(	PUNCT
cana-2411	327	31	(	(	PUNCT
cana-2411	327	32	0,1−	0,1−	NUM
cana-2411	327	33	r	r	NOUN
cana-2411	327	34	,	,	PUNCT
cana-2411	327	35	1−	1−	NUM
cana-2411	327	36	r	r	NOUN
cana-2411	327	37	)	)	PUNCT
cana-2411	327	38	;	;	PUNCT
cana-2411	327	39	(	(	PUNCT
cana-2411	327	40	0.66,0.52,0.53	0.66,0.52,0.53	NOUN
cana-2411	327	41	)	)	PUNCT
cana-2411	327	42	(	(	PUNCT
cana-2411	327	43	0,1−	0,1−	NUM
cana-2411	327	44	r	r	NOUN
cana-2411	327	45	,	,	PUNCT
cana-2411	327	46	1−	1−	NUM
cana-2411	327	47	r	r	NOUN
cana-2411	327	48	)	)	PUNCT
cana-2411	327	49	;	;	PUNCT
cana-2411	327	50	(	(	PUNCT
cana-2411	327	51	0.66,0.52,0.53	0.66,0.52,0.53	NOUN
cana-2411	327	52	)	)	PUNCT
cana-2411	327	53	)	)	PUNCT
cana-2411	327	54	the	the	DET
cana-2411	327	55	condition	condition	NOUN
cana-2411	327	56	required	require	VERB
cana-2411	327	57	for	for	SCONJ
cana-2411	327	58	υ̃	υ̃	PROPN
cana-2411	327	59	to	to	PART
cana-2411	327	60	be	be	AUX
cana-2411	327	61	the	the	DET
cana-2411	327	62	optimum	optimum	ADJ
cana-2411	327	63	solution	solution	NOUN
cana-2411	327	64	for	for	ADP
cana-2411	327	65	(	(	PUNCT
cana-2411	327	66	12	12	NUM
cana-2411	327	67	)	)	PUNCT
cana-2411	327	68	∇f̃(υ̃1	∇f̃(υ̃1	NOUN
cana-2411	327	69	,	,	PUNCT
cana-2411	327	70	υ̃2	υ̃2	PROPN
cana-2411	327	71	)	)	PUNCT
cana-2411	328	1	≈	≈	NOUN
cana-2411	328	2	0̃.	0̃.	NOUN
cana-2411	329	1	hence	hence	ADV
cana-2411	329	2	we	we	PRON
cana-2411	329	3	have	have	VERB
cana-2411	329	4	∂f̃	∂f̃	NUM
cana-2411	329	5	∂υ̃1	∂υ̃1	NOUN
cana-2411	330	1	=	=	PUNCT
cana-2411	331	1	(	(	PUNCT
cana-2411	331	2	1,1−	1,1−	NUM
cana-2411	331	3	r	r	NOUN
cana-2411	331	4	,	,	PUNCT
cana-2411	331	5	1	1	NUM
cana-2411	331	6	−	−	NOUN
cana-2411	331	7	r	r	NOUN
cana-2411	331	8	)	)	PUNCT
cana-2411	331	9	;	;	PUNCT
cana-2411	331	10	(	(	PUNCT
cana-2411	331	11	0.68,0.51,0.55	0.68,0.51,0.55	NOUN
cana-2411	331	12	)	)	PUNCT
cana-2411	331	13	+	+	CCONJ
cana-2411	331	14	(	(	PUNCT
cana-2411	331	15	4,1−	4,1−	NUM
cana-2411	331	16	r	r	NOUN
cana-2411	331	17	,	,	PUNCT
cana-2411	331	18	1−	1−	NUM
cana-2411	331	19	r	r	NOUN
cana-2411	331	20	)	)	PUNCT
cana-2411	331	21	;	;	PUNCT
cana-2411	331	22	(	(	PUNCT
cana-2411	331	23	0.7,0.65,0.72)υ̃1	0.7,0.65,0.72)υ̃1	X
cana-2411	332	1	+	+	NOUN
cana-2411	332	2	(	(	PUNCT
cana-2411	332	3	2,1−	2,1−	NUM
cana-2411	332	4	r	r	NOUN
cana-2411	332	5	,	,	PUNCT
cana-2411	332	6	1−	1−	NUM
cana-2411	332	7	r	r	NOUN
cana-2411	332	8	)	)	PUNCT
cana-2411	332	9	;	;	PUNCT
cana-2411	332	10	(	(	PUNCT
cana-2411	332	11	0.69,0.51,0.52)υ̃2	0.69,0.51,0.52)υ̃2	NOUN
cana-2411	332	12	∂f̃	∂f̃	NOUN
cana-2411	332	13	∂υ̃2	∂υ̃2	ADV
cana-2411	333	1	=	=	NOUN
cana-2411	333	2	−(1,1−	−(1,1−	NOUN
cana-2411	333	3	r	r	NOUN
cana-2411	333	4	,	,	PUNCT
cana-2411	333	5	1−	1−	NUM
cana-2411	333	6	r	r	NOUN
cana-2411	333	7	)	)	PUNCT
cana-2411	333	8	;	;	PUNCT
cana-2411	333	9	(	(	PUNCT
cana-2411	333	10	0.67,0.53,0.54	0.67,0.53,0.54	X
cana-2411	333	11	)	)	PUNCT
cana-2411	334	1	+	+	CCONJ
cana-2411	334	2	(	(	PUNCT
cana-2411	334	3	2,1−	2,1−	NUM
cana-2411	334	4	r	r	NOUN
cana-2411	334	5	,	,	PUNCT
cana-2411	334	6	1	1	NUM
cana-2411	334	7	−	−	NOUN
cana-2411	334	8	r	r	NOUN
cana-2411	334	9	)	)	PUNCT
cana-2411	334	10	;	;	PUNCT
cana-2411	334	11	(	(	PUNCT
cana-2411	334	12	0.69,0.51,0.52)υ̃1	0.69,0.51,0.52)υ̃1	NOUN
cana-2411	334	13	(	(	PUNCT
cana-2411	334	14	2,1−	2,1−	NUM
cana-2411	334	15	r	r	NOUN
cana-2411	334	16	,	,	PUNCT
cana-2411	334	17	1	1	NUM
cana-2411	334	18	−	−	NOUN
cana-2411	334	19	r	r	NOUN
cana-2411	334	20	)	)	PUNCT
cana-2411	334	21	;	;	PUNCT
cana-2411	334	22	(	(	PUNCT
cana-2411	334	23	0.67,0.5,0.51)υ̃2	0.67,0.5,0.51)υ̃2	ADP
cana-2411	334	24	the	the	DET
cana-2411	334	25	condition	condition	NOUN
cana-2411	334	26	required	require	VERB
cana-2411	334	27	for	for	SCONJ
cana-2411	334	28	υ̃	υ̃	PROPN
cana-2411	334	29	to	to	PART
cana-2411	334	30	be	be	AUX
cana-2411	334	31	the	the	DET
cana-2411	334	32	optimum	optimum	ADJ
cana-2411	334	33	solution	solution	NOUN
cana-2411	334	34	for	for	ADP
cana-2411	334	35	(	(	PUNCT
cana-2411	334	36	12	12	NUM
cana-2411	334	37	)	)	PUNCT
cana-2411	334	38	∇f̃(υ̃1	∇f̃(υ̃1	NOUN
cana-2411	334	39	,	,	PUNCT
cana-2411	334	40	υ̃2	υ̃2	PROPN
cana-2411	334	41	)	)	PUNCT
cana-2411	335	1	≈	≈	NOUN
cana-2411	335	2	0̃.	0̃.	NOUN
cana-2411	336	1	hence	hence	ADV
cana-2411	336	2	we	we	PRON
cana-2411	336	3	have	have	AUX
cana-2411	336	4	∂2f	∂2f	VERB
cana-2411	336	5	∂υ̃1	∂υ̃1	ADP
cana-2411	336	6	2	2	NUM
cana-2411	336	7	=	=	SYM
cana-2411	336	8	(	(	PUNCT
cana-2411	336	9	4,1−	4,1−	NUM
cana-2411	336	10	r	r	NOUN
cana-2411	336	11	,	,	PUNCT
cana-2411	336	12	1−	1−	NUM
cana-2411	336	13	r	r	NOUN
cana-2411	336	14	)	)	PUNCT
cana-2411	336	15	;	;	PUNCT
cana-2411	336	16	(	(	PUNCT
cana-2411	336	17	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	336	18	)	)	PUNCT
cana-2411	336	19	,	,	PUNCT
cana-2411	336	20	∂2f	∂2f	VERB
cana-2411	336	21	∂υ̃2	∂υ̃2	ADV
cana-2411	336	22	2	2	NUM
cana-2411	336	23	=	=	SYM
cana-2411	336	24	(	(	PUNCT
cana-2411	336	25	2,1−	2,1−	NUM
cana-2411	336	26	r	r	NOUN
cana-2411	336	27	,	,	PUNCT
cana-2411	336	28	1−	1−	NUM
cana-2411	336	29	r	r	NOUN
cana-2411	336	30	)	)	PUNCT
cana-2411	336	31	;	;	PUNCT
cana-2411	336	32	(	(	PUNCT
cana-2411	336	33	0.67,0.5,0.51	0.67,0.5,0.51	NOUN
cana-2411	336	34	)	)	PUNCT
cana-2411	336	35	∂2f	∂2f	VERB
cana-2411	336	36	∂υ̃1	∂υ̃1	NOUN
cana-2411	336	37	∂υ̃2	∂υ̃2	NOUN
cana-2411	337	1	=	=	PUNCT
cana-2411	337	2	(	(	PUNCT
cana-2411	337	3	2,1−	2,1−	NUM
cana-2411	337	4	r	r	NOUN
cana-2411	337	5	,	,	PUNCT
cana-2411	337	6	1−	1−	NUM
cana-2411	337	7	r	r	NOUN
cana-2411	337	8	)	)	PUNCT
cana-2411	337	9	;	;	PUNCT
cana-2411	337	10	(	(	PUNCT
cana-2411	337	11	0.69,0.51,0.52	0.69,0.51,0.52	NOUN
cana-2411	337	12	)	)	PUNCT
cana-2411	337	13	,	,	PUNCT
cana-2411	337	14	∂2f	∂2f	VERB
cana-2411	337	15	∂υ̃2	∂υ̃2	ADV
cana-2411	337	16	∂υ̃1	∂υ̃1	PROPN
cana-2411	338	1	=	=	PUNCT
cana-2411	338	2	(	(	PUNCT
cana-2411	338	3	2,1−	2,1−	NUM
cana-2411	338	4	r	r	NOUN
cana-2411	338	5	,	,	PUNCT
cana-2411	338	6	1−	1−	NUM
cana-2411	338	7	r	r	NOUN
cana-2411	338	8	)	)	PUNCT
cana-2411	338	9	;	;	PUNCT
cana-2411	338	10	(	(	PUNCT
cana-2411	338	11	0.69,0.51,0.52	0.69,0.51,0.52	X
cana-2411	338	12	)	)	PUNCT
cana-2411	338	13	communications	communication	NOUN
cana-2411	338	14	on	on	ADP
cana-2411	338	15	applied	apply	VERB
cana-2411	338	16	nonlinear	nonlinear	ADJ
cana-2411	338	17	analysis	analysis	NOUN
cana-2411	338	18	issn	issn	NOUN
cana-2411	338	19	:	:	PUNCT
cana-2411	338	20	1074	1074	NUM
cana-2411	338	21	-	-	PUNCT
cana-2411	338	22	133x	133x	NUM
cana-2411	338	23	vol	vol	NOUN
cana-2411	338	24	32	32	NUM
cana-2411	338	25	no	no	NOUN
cana-2411	338	26	.	.	PUNCT
cana-2411	339	1	2s	2s	NUM
cana-2411	339	2	(	(	PUNCT
cana-2411	339	3	2025	2025	NUM
cana-2411	339	4	)	)	PUNCT
cana-2411	339	5	381	381	NUM
cana-2411	339	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2411	339	7	table	table	NOUN
cana-2411	339	8	3	3	NUM
cana-2411	339	9	:	:	PUNCT
cana-2411	339	10	cauchy	cauchy	PROPN
cana-2411	339	11	’s	’s	PART
cana-2411	339	12	steepest	steep	ADJ
cana-2411	339	13	descent	descent	NOUN
cana-2411	339	14	method	method	PROPN
cana-2411	339	15	iteration	iteration	PROPN
cana-2411	339	16	�	�	PROPN
cana-2411	339	17	̃	̃	PROPN
cana-2411	339	18	�	�	PROPN
cana-2411	339	19	𝐢	𝐢	NOUN
cana-2411	339	20	=	=	SYM
cana-2411	339	21	(	(	PUNCT
cana-2411	339	22	𝛖𝟏	𝛖𝟏	ADJ
cana-2411	339	23	,	,	PUNCT
cana-2411	339	24	𝛖𝟐	𝛖𝟐	NOUN
cana-2411	339	25	)	)	PUNCT
cana-2411	339	26	�	�	PROPN
cana-2411	339	27	̃	̃	PROPN
cana-2411	339	28	�	�	PROPN
cana-2411	339	29	𝐢+𝟏	𝐢+𝟏	X
cana-2411	339	30	=	=	SYM
cana-2411	339	31	(	(	PUNCT
cana-2411	339	32	𝛖𝟏	𝛖𝟏	ADJ
cana-2411	339	33	,	,	PUNCT
cana-2411	339	34	𝛖𝟐	𝛖𝟐	NOUN
cana-2411	339	35	)	)	PUNCT
cana-2411	339	36	𝛁𝐟𝐢	𝛁𝐟𝐢	NOUN
cana-2411	339	37	1	1	NUM
cana-2411	339	38	(	(	PUNCT
cana-2411	339	39	(	(	PUNCT
cana-2411	339	40	0,1−	0,1−	NUM
cana-2411	339	41	r	r	NOUN
cana-2411	339	42	,	,	PUNCT
cana-2411	339	43	1	1	NUM
cana-2411	339	44	−	−	NOUN
cana-2411	339	45	r	r	NOUN
cana-2411	339	46	)	)	PUNCT
cana-2411	339	47	;	;	PUNCT
cana-2411	339	48	(	(	PUNCT
cana-2411	339	49	0.66,0.52,0.53	0.66,0.52,0.53	NOUN
cana-2411	339	50	)	)	PUNCT
cana-2411	339	51	(	(	PUNCT
cana-2411	339	52	0,1−	0,1−	NUM
cana-2411	339	53	r	r	NOUN
cana-2411	339	54	,	,	PUNCT
cana-2411	339	55	1	1	NUM
cana-2411	339	56	−	−	NOUN
cana-2411	339	57	r	r	NOUN
cana-2411	339	58	)	)	PUNCT
cana-2411	339	59	;	;	PUNCT
cana-2411	339	60	(	(	PUNCT
cana-2411	339	61	0.66,0.52,0.53	0.66,0.52,0.53	NOUN
cana-2411	339	62	)	)	PUNCT
cana-2411	339	63	)	)	PUNCT
cana-2411	340	1	(	(	PUNCT
cana-2411	340	2	(	(	PUNCT
cana-2411	340	3	1,1−	1,1−	NUM
cana-2411	340	4	r	r	NOUN
cana-2411	340	5	,	,	PUNCT
cana-2411	340	6	1	1	NUM
cana-2411	340	7	−	−	NOUN
cana-2411	340	8	r	r	NOUN
cana-2411	340	9	)	)	PUNCT
cana-2411	340	10	;	;	PUNCT
cana-2411	340	11	(	(	PUNCT
cana-2411	340	12	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	340	13	)	)	PUNCT
cana-2411	340	14	(	(	PUNCT
cana-2411	340	15	1,1−	1,1−	NUM
cana-2411	340	16	r	r	NOUN
cana-2411	340	17	,	,	PUNCT
cana-2411	340	18	1	1	NUM
cana-2411	340	19	−	−	NOUN
cana-2411	340	20	r	r	NOUN
cana-2411	340	21	)	)	PUNCT
cana-2411	340	22	;	;	PUNCT
cana-2411	340	23	(	(	PUNCT
cana-2411	340	24	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	340	25	)	)	PUNCT
cana-2411	340	26	)	)	PUNCT
cana-2411	340	27	(	(	PUNCT
cana-2411	340	28	(	(	PUNCT
cana-2411	340	29	−1,1−	−1,1−	PUNCT
cana-2411	340	30	r	r	NOUN
cana-2411	340	31	,	,	PUNCT
cana-2411	340	32	1−	1−	NUM
cana-2411	340	33	r	r	NOUN
cana-2411	340	34	)	)	PUNCT
cana-2411	340	35	;	;	PUNCT
cana-2411	340	36	(	(	PUNCT
cana-2411	340	37	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	340	38	)	)	PUNCT
cana-2411	340	39	(	(	PUNCT
cana-2411	340	40	−1,1−	−1,1−	PUNCT
cana-2411	340	41	r	r	NOUN
cana-2411	340	42	,	,	PUNCT
cana-2411	340	43	1−	1−	NUM
cana-2411	340	44	r	r	NOUN
cana-2411	340	45	)	)	PUNCT
cana-2411	340	46	;	;	PUNCT
cana-2411	340	47	(	(	PUNCT
cana-2411	340	48	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	340	49	)	)	PUNCT
cana-2411	340	50	)	)	PUNCT
cana-2411	340	51	2	2	NUM
cana-2411	340	52	(	(	PUNCT
cana-2411	340	53	(	(	PUNCT
cana-2411	340	54	1,1−	1,1−	NUM
cana-2411	340	55	r	r	NOUN
cana-2411	340	56	,	,	PUNCT
cana-2411	340	57	1	1	NUM
cana-2411	340	58	−	−	NOUN
cana-2411	340	59	r	r	NOUN
cana-2411	340	60	)	)	PUNCT
cana-2411	340	61	;	;	PUNCT
cana-2411	340	62	(	(	PUNCT
cana-2411	340	63	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	340	64	)	)	PUNCT
cana-2411	340	65	(	(	PUNCT
cana-2411	340	66	1,1−	1,1−	NUM
cana-2411	340	67	r	r	NOUN
cana-2411	340	68	,	,	PUNCT
cana-2411	340	69	1	1	NUM
cana-2411	340	70	−	−	NOUN
cana-2411	340	71	r	r	NOUN
cana-2411	340	72	)	)	PUNCT
cana-2411	340	73	;	;	PUNCT
cana-2411	340	74	(	(	PUNCT
cana-2411	340	75	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	340	76	)	)	PUNCT
cana-2411	340	77	)	)	PUNCT
cana-2411	341	1	(	(	PUNCT
cana-2411	341	2	(	(	PUNCT
cana-2411	341	3	−0.8,1−	−0.8,1−	NOUN
cana-2411	341	4	r	r	NOUN
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cana-2411	341	6	1−	1−	NUM
cana-2411	341	7	r	r	NOUN
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cana-2411	341	9	;	;	PUNCT
cana-2411	341	10	(	(	PUNCT
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cana-2411	341	14	1.2,1−	1.2,1−	NOUN
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cana-2411	341	17	1−	1−	NUM
cana-2411	341	18	r	r	NOUN
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cana-2411	341	20	;	;	PUNCT
cana-2411	341	21	(	(	PUNCT
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cana-2411	341	23	)	)	PUNCT
cana-2411	341	24	)	)	PUNCT
cana-2411	342	1	(	(	PUNCT
cana-2411	342	2	(	(	PUNCT
cana-2411	342	3	0.2,1−	0.2,1−	NOUN
cana-2411	342	4	r	r	NOUN
cana-2411	342	5	,	,	PUNCT
cana-2411	342	6	1−	1−	NUM
cana-2411	342	7	r	r	NOUN
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cana-2411	342	9	;	;	PUNCT
cana-2411	342	10	(	(	PUNCT
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cana-2411	342	15	r	r	PROPN
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cana-2411	342	17	1−	1−	NUM
cana-2411	342	18	r	r	NOUN
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cana-2411	342	20	;	;	PUNCT
cana-2411	342	21	(	(	PUNCT
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cana-2411	342	23	)	)	PUNCT
cana-2411	342	24	)	)	PUNCT
cana-2411	342	25	3	3	NUM
cana-2411	342	26	(	(	PUNCT
cana-2411	342	27	(	(	PUNCT
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cana-2411	342	29	r	r	NOUN
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cana-2411	342	31	1−	1−	NUM
cana-2411	342	32	r	r	NOUN
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cana-2411	342	34	;	;	PUNCT
cana-2411	342	35	(	(	PUNCT
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cana-2411	342	37	)	)	PUNCT
cana-2411	342	38	(	(	PUNCT
cana-2411	342	39	1.2,1−	1.2,1−	NOUN
cana-2411	342	40	r	r	NOUN
cana-2411	342	41	,	,	PUNCT
cana-2411	342	42	1−	1−	NUM
cana-2411	342	43	r	r	NOUN
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cana-2411	342	45	;	;	PUNCT
cana-2411	342	46	(	(	PUNCT
cana-2411	342	47	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	342	48	)	)	PUNCT
cana-2411	342	49	)	)	PUNCT
cana-2411	342	50	(	(	PUNCT
cana-2411	342	51	(	(	PUNCT
cana-2411	342	52	−1,1−	−1,1−	PUNCT
cana-2411	342	53	r	r	NOUN
cana-2411	342	54	,	,	PUNCT
cana-2411	342	55	1−	1−	NUM
cana-2411	342	56	r	r	NOUN
cana-2411	342	57	)	)	PUNCT
cana-2411	342	58	;	;	PUNCT
cana-2411	342	59	(	(	PUNCT
cana-2411	342	60	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	342	61	)	)	PUNCT
cana-2411	342	62	(	(	PUNCT
cana-2411	342	63	1.4,1−	1.4,1−	NUM
cana-2411	342	64	r	r	NOUN
cana-2411	342	65	,	,	PUNCT
cana-2411	342	66	1−	1−	NUM
cana-2411	342	67	r	r	NOUN
cana-2411	342	68	)	)	PUNCT
cana-2411	342	69	;	;	PUNCT
cana-2411	342	70	(	(	PUNCT
cana-2411	342	71	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	342	72	)	)	PUNCT
cana-2411	342	73	)	)	PUNCT
cana-2411	343	1	(	(	PUNCT
cana-2411	343	2	(	(	PUNCT
cana-2411	343	3	−0.2,1−	−0.2,1−	NOUN
cana-2411	343	4	r	r	NOUN
cana-2411	343	5	,	,	PUNCT
cana-2411	343	6	1−	1−	NUM
cana-2411	343	7	r	r	NOUN
cana-2411	343	8	)	)	PUNCT
cana-2411	343	9	;	;	PUNCT
cana-2411	343	10	(	(	PUNCT
cana-2411	343	11	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	343	12	)	)	PUNCT
cana-2411	343	13	(	(	PUNCT
cana-2411	343	14	−0.2,1−	−0.2,1−	NOUN
cana-2411	343	15	r	r	PROPN
cana-2411	343	16	,	,	PUNCT
cana-2411	343	17	1−	1−	NUM
cana-2411	343	18	r	r	NOUN
cana-2411	343	19	)	)	PUNCT
cana-2411	343	20	;	;	PUNCT
cana-2411	343	21	(	(	PUNCT
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cana-2411	343	23	)	)	PUNCT
cana-2411	343	24	)	)	PUNCT
cana-2411	343	25	4	4	NUM
cana-2411	343	26	(	(	PUNCT
cana-2411	343	27	(	(	PUNCT
cana-2411	343	28	−1,1−	−1,1−	PUNCT
cana-2411	343	29	r	r	NOUN
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cana-2411	343	31	1−	1−	NUM
cana-2411	343	32	r	r	NOUN
cana-2411	343	33	)	)	PUNCT
cana-2411	343	34	;	;	PUNCT
cana-2411	343	35	(	(	PUNCT
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cana-2411	343	37	)	)	PUNCT
cana-2411	343	38	(	(	PUNCT
cana-2411	343	39	1.4,1−	1.4,1−	NUM
cana-2411	343	40	r	r	NOUN
cana-2411	343	41	,	,	PUNCT
cana-2411	343	42	1−	1−	NUM
cana-2411	343	43	r	r	NOUN
cana-2411	343	44	)	)	PUNCT
cana-2411	343	45	;	;	PUNCT
cana-2411	343	46	(	(	PUNCT
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cana-2411	343	48	)	)	PUNCT
cana-2411	343	49	)	)	PUNCT
cana-2411	344	1	(	(	PUNCT
cana-2411	344	2	(	(	PUNCT
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cana-2411	344	4	r	r	NOUN
cana-2411	344	5	,	,	PUNCT
cana-2411	344	6	1−	1−	NUM
cana-2411	344	7	r	r	NOUN
cana-2411	344	8	)	)	PUNCT
cana-2411	344	9	;	;	PUNCT
cana-2411	344	10	(	(	PUNCT
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cana-2411	344	12	)	)	PUNCT
cana-2411	344	13	(	(	PUNCT
cana-2411	344	14	1.44,1−	1.44,1−	NOUN
cana-2411	344	15	r	r	NOUN
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cana-2411	344	17	1−	1−	NUM
cana-2411	344	18	r	r	NOUN
cana-2411	344	19	)	)	PUNCT
cana-2411	344	20	;	;	PUNCT
cana-2411	344	21	(	(	PUNCT
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cana-2411	344	23	)	)	PUNCT
cana-2411	344	24	)	)	PUNCT
cana-2411	344	25	(	(	PUNCT
cana-2411	344	26	(	(	PUNCT
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cana-2411	344	28	r	r	NOUN
cana-2411	344	29	,	,	PUNCT
cana-2411	344	30	1−	1−	NUM
cana-2411	344	31	r	r	NOUN
cana-2411	344	32	)	)	PUNCT
cana-2411	344	33	;	;	PUNCT
cana-2411	344	34	(	(	PUNCT
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cana-2411	344	36	)	)	PUNCT
cana-2411	344	37	(	(	PUNCT
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cana-2411	344	39	r	r	NOUN
cana-2411	344	40	,	,	PUNCT
cana-2411	344	41	1−	1−	NUM
cana-2411	344	42	r	r	NOUN
cana-2411	344	43	)	)	PUNCT
cana-2411	344	44	;	;	PUNCT
cana-2411	344	45	(	(	PUNCT
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cana-2411	344	47	)	)	PUNCT
cana-2411	344	48	)	)	PUNCT
cana-2411	344	49	5	5	NUM
cana-2411	344	50	(	(	PUNCT
cana-2411	344	51	(	(	PUNCT
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cana-2411	344	53	r	r	NOUN
cana-2411	344	54	,	,	PUNCT
cana-2411	344	55	1−	1−	NUM
cana-2411	344	56	r	r	NOUN
cana-2411	344	57	)	)	PUNCT
cana-2411	344	58	;	;	PUNCT
cana-2411	344	59	(	(	PUNCT
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cana-2411	344	61	)	)	PUNCT
cana-2411	344	62	(	(	PUNCT
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cana-2411	344	64	r	r	NOUN
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cana-2411	344	66	1−	1−	NUM
cana-2411	344	67	r	r	NOUN
cana-2411	344	68	)	)	PUNCT
cana-2411	344	69	;	;	PUNCT
cana-2411	344	70	(	(	PUNCT
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cana-2411	344	72	)	)	PUNCT
cana-2411	344	73	)	)	PUNCT
cana-2411	344	74	(	(	PUNCT
cana-2411	344	75	(	(	PUNCT
cana-2411	344	76	−1,1−	−1,1−	PUNCT
cana-2411	344	77	r	r	NOUN
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cana-2411	344	79	1−	1−	NUM
cana-2411	344	80	r	r	NOUN
cana-2411	344	81	)	)	PUNCT
cana-2411	344	82	;	;	PUNCT
cana-2411	344	83	(	(	PUNCT
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cana-2411	344	85	)	)	PUNCT
cana-2411	344	86	(	(	PUNCT
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cana-2411	344	88	r	r	NOUN
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cana-2411	344	90	1−	1−	NUM
cana-2411	344	91	r	r	NOUN
cana-2411	344	92	)	)	PUNCT
cana-2411	344	93	;	;	PUNCT
cana-2411	344	94	(	(	PUNCT
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cana-2411	344	96	)	)	PUNCT
cana-2411	344	97	)	)	PUNCT
cana-2411	345	1	(	(	PUNCT
cana-2411	345	2	(	(	PUNCT
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cana-2411	345	4	r	r	NOUN
cana-2411	345	5	,	,	PUNCT
cana-2411	345	6	1−	1−	NUM
cana-2411	345	7	r	r	NOUN
cana-2411	345	8	)	)	PUNCT
cana-2411	345	9	;	;	PUNCT
cana-2411	345	10	(	(	PUNCT
cana-2411	345	11	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	345	12	)	)	PUNCT
cana-2411	345	13	(	(	PUNCT
cana-2411	345	14	−0.04,1−	−0.04,1−	NOUN
cana-2411	345	15	r	r	NOUN
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cana-2411	345	17	1−	1−	NUM
cana-2411	345	18	r	r	NOUN
cana-2411	345	19	)	)	PUNCT
cana-2411	345	20	;	;	PUNCT
cana-2411	345	21	(	(	PUNCT
cana-2411	345	22	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	345	23	)	)	PUNCT
cana-2411	345	24	)	)	PUNCT
cana-2411	345	25	6	6	NUM
cana-2411	345	26	(	(	PUNCT
cana-2411	345	27	(	(	PUNCT
cana-2411	345	28	−1,1−	−1,1−	PUNCT
cana-2411	345	29	r	r	NOUN
cana-2411	345	30	,	,	PUNCT
cana-2411	345	31	1−	1−	NUM
cana-2411	345	32	r	r	NOUN
cana-2411	345	33	)	)	PUNCT
cana-2411	345	34	;	;	PUNCT
cana-2411	345	35	(	(	PUNCT
cana-2411	345	36	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	345	37	)	)	PUNCT
cana-2411	345	38	(	(	PUNCT
cana-2411	345	39	1.48,1−	1.48,1−	NUM
cana-2411	345	40	r	r	NOUN
cana-2411	345	41	,	,	PUNCT
cana-2411	345	42	1−	1−	NUM
cana-2411	345	43	r	r	NOUN
cana-2411	345	44	)	)	PUNCT
cana-2411	345	45	;	;	PUNCT
cana-2411	345	46	(	(	PUNCT
cana-2411	345	47	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	345	48	)	)	PUNCT
cana-2411	345	49	)	)	PUNCT
cana-2411	345	50	(	(	PUNCT
cana-2411	345	51	(	(	PUNCT
cana-2411	345	52	−0.992,1−	−0.992,1−	VERB
cana-2411	345	53	r	r	NOUN
cana-2411	345	54	,	,	PUNCT
cana-2411	345	55	1−	1−	NUM
cana-2411	345	56	r	r	NOUN
cana-2411	345	57	)	)	PUNCT
cana-2411	345	58	;	;	PUNCT
cana-2411	345	59	(	(	PUNCT
cana-2411	345	60	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	345	61	)	)	PUNCT
cana-2411	345	62	(	(	PUNCT
cana-2411	345	63	1.488,1−	1.488,1−	NUM
cana-2411	345	64	r	r	NOUN
cana-2411	345	65	,	,	PUNCT
cana-2411	345	66	1−	1−	NUM
cana-2411	345	67	r	r	NOUN
cana-2411	345	68	)	)	PUNCT
cana-2411	345	69	;	;	PUNCT
cana-2411	345	70	(	(	PUNCT
cana-2411	345	71	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	345	72	)	)	PUNCT
cana-2411	345	73	)	)	PUNCT
cana-2411	345	74	(	(	PUNCT
cana-2411	345	75	(	(	PUNCT
cana-2411	345	76	0.008,1−	0.008,1−	NUM
cana-2411	345	77	r	r	NOUN
cana-2411	345	78	,	,	PUNCT
cana-2411	345	79	1−	1−	NUM
cana-2411	345	80	r	r	NOUN
cana-2411	345	81	)	)	PUNCT
cana-2411	345	82	;	;	PUNCT
cana-2411	345	83	(	(	PUNCT
cana-2411	345	84	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	345	85	)	)	PUNCT
cana-2411	345	86	(	(	PUNCT
cana-2411	345	87	−0.008,1−	−0.008,1−	PROPN
cana-2411	345	88	r	r	NOUN
cana-2411	345	89	,	,	PUNCT
cana-2411	345	90	1−	1−	NUM
cana-2411	345	91	r	r	NOUN
cana-2411	345	92	)	)	PUNCT
cana-2411	345	93	;	;	PUNCT
cana-2411	345	94	(	(	PUNCT
cana-2411	345	95	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	345	96	)	)	PUNCT
cana-2411	345	97	)	)	PUNCT
cana-2411	345	98	table	table	NOUN
cana-2411	345	99	4	4	NUM
cana-2411	345	100	:	:	PUNCT
cana-2411	345	101	fletcher	fletcher	PROPN
cana-2411	345	102	-	-	PUNCT
cana-2411	345	103	reeves	reeves	PROPN
cana-2411	345	104	method	method	PROPN
cana-2411	345	105	iteration	iteration	PROPN
cana-2411	345	106	�	�	PROPN
cana-2411	345	107	̃	̃	PROPN
cana-2411	345	108	�	�	PROPN
cana-2411	345	109	𝐢	𝐢	NOUN
cana-2411	345	110	=	=	SYM
cana-2411	345	111	(	(	PUNCT
cana-2411	345	112	𝛖𝟏	𝛖𝟏	ADJ
cana-2411	345	113	,	,	PUNCT
cana-2411	345	114	𝛖𝟐	𝛖𝟐	NOUN
cana-2411	345	115	)	)	PUNCT
cana-2411	345	116	�	�	PROPN
cana-2411	345	117	̃	̃	PROPN
cana-2411	345	118	�	�	PROPN
cana-2411	345	119	𝐢+𝟏	𝐢+𝟏	X
cana-2411	345	120	=	=	SYM
cana-2411	345	121	(	(	PUNCT
cana-2411	345	122	𝛖𝟏	𝛖𝟏	ADJ
cana-2411	345	123	,	,	PUNCT
cana-2411	345	124	𝛖𝟐	𝛖𝟐	NOUN
cana-2411	345	125	)	)	PUNCT
cana-2411	345	126	𝛁𝐟𝐢	𝛁𝐟𝐢	NOUN
cana-2411	345	127	1	1	NUM
cana-2411	345	128	(	(	PUNCT
cana-2411	345	129	(	(	PUNCT
cana-2411	345	130	0,1−	0,1−	NUM
cana-2411	345	131	r	r	NOUN
cana-2411	345	132	,	,	PUNCT
cana-2411	345	133	1	1	NUM
cana-2411	345	134	−	−	NOUN
cana-2411	345	135	r	r	NOUN
cana-2411	345	136	)	)	PUNCT
cana-2411	345	137	;	;	PUNCT
cana-2411	345	138	(	(	PUNCT
cana-2411	345	139	0.66,0.52,0.53	0.66,0.52,0.53	NOUN
cana-2411	345	140	)	)	PUNCT
cana-2411	345	141	(	(	PUNCT
cana-2411	345	142	0,1−	0,1−	NUM
cana-2411	345	143	r	r	NOUN
cana-2411	345	144	,	,	PUNCT
cana-2411	345	145	1	1	NUM
cana-2411	345	146	−	−	NOUN
cana-2411	345	147	r	r	NOUN
cana-2411	345	148	)	)	PUNCT
cana-2411	345	149	;	;	PUNCT
cana-2411	345	150	(	(	PUNCT
cana-2411	345	151	0.66,0.52,0.53	0.66,0.52,0.53	NOUN
cana-2411	345	152	)	)	PUNCT
cana-2411	345	153	)	)	PUNCT
cana-2411	346	1	(	(	PUNCT
cana-2411	346	2	(	(	PUNCT
cana-2411	346	3	1,1−	1,1−	NUM
cana-2411	346	4	r	r	NOUN
cana-2411	346	5	,	,	PUNCT
cana-2411	346	6	1	1	NUM
cana-2411	346	7	−	−	NOUN
cana-2411	346	8	r	r	NOUN
cana-2411	346	9	)	)	PUNCT
cana-2411	346	10	;	;	PUNCT
cana-2411	346	11	(	(	PUNCT
cana-2411	346	12	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	346	13	)	)	PUNCT
cana-2411	346	14	(	(	PUNCT
cana-2411	346	15	1,1−	1,1−	NUM
cana-2411	346	16	r	r	NOUN
cana-2411	346	17	,	,	PUNCT
cana-2411	346	18	1	1	NUM
cana-2411	346	19	−	−	NOUN
cana-2411	346	20	r	r	NOUN
cana-2411	346	21	)	)	PUNCT
cana-2411	346	22	;	;	PUNCT
cana-2411	346	23	(	(	PUNCT
cana-2411	346	24	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	346	25	)	)	PUNCT
cana-2411	346	26	)	)	PUNCT
cana-2411	346	27	(	(	PUNCT
cana-2411	346	28	(	(	PUNCT
cana-2411	346	29	−1,1−	−1,1−	PUNCT
cana-2411	346	30	r	r	NOUN
cana-2411	346	31	,	,	PUNCT
cana-2411	346	32	1−	1−	NUM
cana-2411	346	33	r	r	NOUN
cana-2411	346	34	)	)	PUNCT
cana-2411	346	35	;	;	PUNCT
cana-2411	346	36	(	(	PUNCT
cana-2411	346	37	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	346	38	)	)	PUNCT
cana-2411	346	39	(	(	PUNCT
cana-2411	346	40	−1,1−	−1,1−	PUNCT
cana-2411	346	41	r	r	NOUN
cana-2411	346	42	,	,	PUNCT
cana-2411	346	43	1−	1−	NUM
cana-2411	346	44	r	r	NOUN
cana-2411	346	45	)	)	PUNCT
cana-2411	346	46	;	;	PUNCT
cana-2411	346	47	(	(	PUNCT
cana-2411	346	48	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	346	49	)	)	PUNCT
cana-2411	346	50	)	)	PUNCT
cana-2411	346	51	2	2	NUM
cana-2411	346	52	(	(	PUNCT
cana-2411	346	53	(	(	PUNCT
cana-2411	346	54	1,1−	1,1−	NUM
cana-2411	346	55	r	r	NOUN
cana-2411	346	56	,	,	PUNCT
cana-2411	346	57	1	1	NUM
cana-2411	346	58	−	−	NOUN
cana-2411	346	59	r	r	NOUN
cana-2411	346	60	)	)	PUNCT
cana-2411	346	61	;	;	PUNCT
cana-2411	346	62	(	(	PUNCT
cana-2411	346	63	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	346	64	)	)	PUNCT
cana-2411	346	65	(	(	PUNCT
cana-2411	346	66	1,1−	1,1−	NUM
cana-2411	346	67	r	r	NOUN
cana-2411	346	68	,	,	PUNCT
cana-2411	346	69	1	1	NUM
cana-2411	346	70	−	−	NOUN
cana-2411	346	71	r	r	NOUN
cana-2411	346	72	)	)	PUNCT
cana-2411	346	73	;	;	PUNCT
cana-2411	346	74	(	(	PUNCT
cana-2411	346	75	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	346	76	)	)	PUNCT
cana-2411	346	77	)	)	PUNCT
cana-2411	347	1	(	(	PUNCT
cana-2411	347	2	(	(	PUNCT
cana-2411	347	3	−1,1−	−1,1−	PUNCT
cana-2411	347	4	r	r	NOUN
cana-2411	347	5	,	,	PUNCT
cana-2411	347	6	1−	1−	NUM
cana-2411	347	7	r	r	NOUN
cana-2411	347	8	)	)	PUNCT
cana-2411	347	9	;	;	PUNCT
cana-2411	347	10	(	(	PUNCT
cana-2411	347	11	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	347	12	)	)	PUNCT
cana-2411	347	13	(	(	PUNCT
cana-2411	347	14	1.5,1−	1.5,1−	NUM
cana-2411	347	15	r	r	NOUN
cana-2411	347	16	,	,	PUNCT
cana-2411	347	17	1−	1−	NUM
cana-2411	347	18	r	r	NOUN
cana-2411	347	19	)	)	PUNCT
cana-2411	347	20	;	;	PUNCT
cana-2411	347	21	(	(	PUNCT
cana-2411	347	22	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	347	23	)	)	PUNCT
cana-2411	347	24	)	)	PUNCT
cana-2411	348	1	(	(	PUNCT
cana-2411	348	2	(	(	PUNCT
cana-2411	348	3	0,1−	0,1−	NUM
cana-2411	348	4	r	r	NOUN
cana-2411	348	5	,	,	PUNCT
cana-2411	348	6	1	1	NUM
cana-2411	348	7	−	−	NOUN
cana-2411	348	8	r	r	NOUN
cana-2411	348	9	)	)	PUNCT
cana-2411	348	10	;	;	PUNCT
cana-2411	348	11	(	(	PUNCT
cana-2411	348	12	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	348	13	)	)	PUNCT
cana-2411	348	14	(	(	PUNCT
cana-2411	348	15	0,1−	0,1−	NUM
cana-2411	348	16	r	r	NOUN
cana-2411	348	17	,	,	PUNCT
cana-2411	348	18	1	1	NUM
cana-2411	348	19	−	−	NOUN
cana-2411	348	20	r	r	NOUN
cana-2411	348	21	)	)	PUNCT
cana-2411	348	22	;	;	PUNCT
cana-2411	348	23	(	(	PUNCT
cana-2411	348	24	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	348	25	)	)	PUNCT
cana-2411	348	26	)	)	PUNCT
cana-2411	348	27	communications	communication	NOUN
cana-2411	348	28	on	on	ADP
cana-2411	348	29	applied	apply	VERB
cana-2411	348	30	nonlinear	nonlinear	ADJ
cana-2411	348	31	analysis	analysis	NOUN
cana-2411	348	32	issn	issn	NOUN
cana-2411	348	33	:	:	PUNCT
cana-2411	348	34	1074	1074	NUM
cana-2411	348	35	-	-	PUNCT
cana-2411	348	36	133x	133x	NUM
cana-2411	348	37	vol	vol	NOUN
cana-2411	348	38	32	32	NUM
cana-2411	348	39	no	no	NOUN
cana-2411	348	40	.	.	PUNCT
cana-2411	349	1	2s	2s	NUM
cana-2411	349	2	(	(	PUNCT
cana-2411	349	3	2025	2025	NUM
cana-2411	349	4	)	)	PUNCT
cana-2411	349	5	382	382	NUM
cana-2411	349	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2411	349	7	from	from	ADP
cana-2411	349	8	the	the	DET
cana-2411	349	9	above	above	ADJ
cana-2411	349	10	tables(3),(4	tables(3),(4	PROPN
cana-2411	349	11	)	)	PUNCT
cana-2411	349	12	,	,	PUNCT
cana-2411	349	13	we	we	PRON
cana-2411	349	14	observed	observe	VERB
cana-2411	349	15	that	that	SCONJ
cana-2411	349	16	the	the	DET
cana-2411	349	17	csdm	csdm	NOUN
cana-2411	349	18	converges	converge	VERB
cana-2411	349	19	at	at	ADP
cana-2411	349	20	iteration	iteration	NOUN
cana-2411	349	21	6	6	NUM
cana-2411	349	22	and	and	CCONJ
cana-2411	349	23	the	the	DET
cana-2411	349	24	frm	frm	PROPN
cana-2411	349	25	converges	converge	VERB
cana-2411	349	26	at	at	ADP
cana-2411	349	27	iteration	iteration	NOUN
cana-2411	349	28	2	2	NUM
cana-2411	349	29	.	.	PUNCT
cana-2411	350	1	hence	hence	ADV
cana-2411	350	2	the	the	DET
cana-2411	350	3	optimal	optimal	ADJ
cana-2411	350	4	solution	solution	NOUN
cana-2411	350	5	of	of	ADP
cana-2411	350	6	the	the	DET
cana-2411	350	7	given	give	VERB
cana-2411	350	8	svnnlpp	svnnlpp	NOUN
cana-2411	350	9	(	(	PUNCT
cana-2411	350	10	11	11	NUM
cana-2411	350	11	)	)	PUNCT
cana-2411	350	12	is	be	AUX
cana-2411	350	13	υ̃1	υ̃1	NOUN
cana-2411	350	14	=	=	PUNCT
cana-2411	350	15	(	(	PUNCT
cana-2411	350	16	−1,1−	−1,1−	PUNCT
cana-2411	350	17	r	r	NOUN
cana-2411	350	18	,	,	PUNCT
cana-2411	350	19	1−	1−	NUM
cana-2411	350	20	r	r	NOUN
cana-2411	350	21	)	)	PUNCT
cana-2411	350	22	;	;	PUNCT
cana-2411	350	23	(	(	PUNCT
cana-2411	350	24	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	350	25	)	)	PUNCT
cana-2411	350	26	,	,	PUNCT
cana-2411	351	1	υ̃2	υ̃2	PROPN
cana-2411	351	2	=	=	SYM
cana-2411	351	3	(	(	PUNCT
cana-2411	351	4	1.5,1−	1.5,1−	NUM
cana-2411	351	5	r	r	NOUN
cana-2411	351	6	,	,	PUNCT
cana-2411	351	7	1−	1−	NUM
cana-2411	351	8	r	r	NOUN
cana-2411	351	9	)	)	PUNCT
cana-2411	351	10	;	;	PUNCT
cana-2411	351	11	(	(	PUNCT
cana-2411	351	12	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	351	13	)	)	PUNCT
cana-2411	351	14	with	with	ADP
cana-2411	351	15	f̃(υ̃1	f̃(υ̃1	NOUN
cana-2411	351	16	,	,	PUNCT
cana-2411	351	17	υ̃2	υ̃2	PROPN
cana-2411	351	18	)	)	PUNCT
cana-2411	351	19	=	=	PUNCT
cana-2411	351	20	(	(	PUNCT
cana-2411	351	21	−1.25,1−	−1.25,1−	PROPN
cana-2411	351	22	r	r	NOUN
cana-2411	351	23	,	,	PUNCT
cana-2411	351	24	1−	1−	NUM
cana-2411	351	25	r	r	NOUN
cana-2411	351	26	)	)	PUNCT
cana-2411	351	27	;	;	PUNCT
cana-2411	351	28	(	(	PUNCT
cana-2411	351	29	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	351	30	)	)	PUNCT
cana-2411	351	31	that	that	PRON
cana-2411	351	32	is	be	AUX
cana-2411	351	33	the	the	DET
cana-2411	351	34	optimal	optimal	ADJ
cana-2411	351	35	solution	solution	NOUN
cana-2411	351	36	of	of	ADP
cana-2411	351	37	the	the	DET
cana-2411	351	38	svnnlpp	svnnlpp	NOUN
cana-2411	351	39	(	(	PUNCT
cana-2411	351	40	11	11	NUM
cana-2411	351	41	)	)	PUNCT
cana-2411	351	42	is	be	AUX
cana-2411	351	43	υ̃1	υ̃1	NOUN
cana-2411	351	44	=	=	PUNCT
cana-2411	351	45	(	(	PUNCT
cana-2411	351	46	−2	−2	NOUN
cana-2411	351	47	+	+	CCONJ
cana-2411	351	48	r	r	NOUN
cana-2411	351	49	,	,	PUNCT
cana-2411	351	50	−1,0−	−1,0−	INTJ
cana-2411	351	51	r	r	NOUN
cana-2411	351	52	)	)	PUNCT
cana-2411	351	53	;	;	PUNCT
cana-2411	351	54	(	(	PUNCT
cana-2411	351	55	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	351	56	)	)	PUNCT
cana-2411	351	57	,	,	PUNCT
cana-2411	352	1	υ̃2	υ̃2	PROPN
cana-2411	352	2	=	=	SYM
cana-2411	352	3	(	(	PUNCT
cana-2411	352	4	0.5	0.5	NUM
cana-2411	352	5	+	+	CCONJ
cana-2411	352	6	r	r	NOUN
cana-2411	352	7	,	,	PUNCT
cana-2411	352	8	1.5,2.5−	1.5,2.5−	NUM
cana-2411	352	9	r	r	NOUN
cana-2411	352	10	)	)	PUNCT
cana-2411	352	11	;	;	PUNCT
cana-2411	352	12	(	(	PUNCT
cana-2411	352	13	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	352	14	)	)	PUNCT
cana-2411	352	15	with	with	ADP
cana-2411	352	16	f̃(υ̃1	f̃(υ̃1	NOUN
cana-2411	352	17	,	,	PUNCT
cana-2411	352	18	υ̃2	υ̃2	PROPN
cana-2411	352	19	)	)	PUNCT
cana-2411	352	20	=	=	PUNCT
cana-2411	352	21	(	(	PUNCT
cana-2411	352	22	−2.25	−2.25	NOUN
cana-2411	352	23	+	+	X
cana-2411	352	24	r	r	NOUN
cana-2411	352	25	,	,	PUNCT
cana-2411	352	26	−1.25	−1.25	PROPN
cana-2411	352	27	,	,	PUNCT
cana-2411	352	28	−0.25−	−0.25−	X
cana-2411	352	29	r	r	NOUN
cana-2411	352	30	)	)	PUNCT
cana-2411	352	31	;	;	PUNCT
cana-2411	352	32	(	(	PUNCT
cana-2411	352	33	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	352	34	)	)	PUNCT
cana-2411	352	35	7	7	NUM
cana-2411	352	36	.	.	X
cana-2411	352	37	result	result	NOUN
cana-2411	352	38	and	and	CCONJ
cana-2411	352	39	discussion	discussion	NOUN
cana-2411	352	40	we	we	PRON
cana-2411	352	41	focused	focus	VERB
cana-2411	352	42	on	on	ADP
cana-2411	352	43	using	use	VERB
cana-2411	352	44	the	the	DET
cana-2411	352	45	fletcher	fletcher	PROPN
cana-2411	352	46	-	-	PUNCT
cana-2411	352	47	reeves	reeves	PROPN
cana-2411	352	48	method	method	PROPN
cana-2411	352	49	table	table	NOUN
cana-2411	352	50	(	(	PUNCT
cana-2411	352	51	2	2	NUM
cana-2411	352	52	)	)	PUNCT
cana-2411	352	53	table	table	NOUN
cana-2411	352	54	(	(	PUNCT
cana-2411	352	55	4	4	NUM
cana-2411	352	56	)	)	PUNCT
cana-2411	352	57	and	and	CCONJ
cana-2411	352	58	the	the	DET
cana-2411	352	59	cauchy	cauchy	NOUN
cana-2411	352	60	's	's	PART
cana-2411	352	61	steepest	steep	ADJ
cana-2411	352	62	descent	descent	NOUN
cana-2411	352	63	method	method	NOUN
cana-2411	352	64	table	table	NOUN
cana-2411	352	65	(	(	PUNCT
cana-2411	352	66	1	1	NUM
cana-2411	352	67	)	)	PUNCT
cana-2411	352	68	,	,	PUNCT
cana-2411	352	69	table	table	NOUN
cana-2411	352	70	(	(	PUNCT
cana-2411	352	71	3	3	NUM
cana-2411	352	72	)	)	PUNCT
cana-2411	352	73	to	to	PART
cana-2411	352	74	solve	solve	VERB
cana-2411	352	75	two	two	NUM
cana-2411	352	76	different	different	ADJ
cana-2411	352	77	problems	problem	NOUN
cana-2411	352	78	,	,	PUNCT
cana-2411	352	79	each	each	PRON
cana-2411	352	80	with	with	ADP
cana-2411	352	81	a	a	DET
cana-2411	352	82	unique	unique	ADJ
cana-2411	352	83	set	set	NOUN
cana-2411	352	84	of	of	ADP
cana-2411	352	85	notations	notation	NOUN
cana-2411	352	86	.	.	PUNCT
cana-2411	353	1	our	our	PRON
cana-2411	353	2	study	study	NOUN
cana-2411	353	3	determined	determine	VERB
cana-2411	353	4	that	that	SCONJ
cana-2411	353	5	both	both	DET
cana-2411	353	6	methods	method	NOUN
cana-2411	353	7	produced	produce	VERB
cana-2411	353	8	the	the	DET
cana-2411	353	9	same	same	ADJ
cana-2411	353	10	solution	solution	NOUN
cana-2411	353	11	,	,	PUNCT
cana-2411	353	12	but	but	CCONJ
cana-2411	353	13	the	the	DET
cana-2411	353	14	fletcherreeves	fletcherreeve	NOUN
cana-2411	353	15	method	method	VERB
cana-2411	353	16	converged	converge	VERB
cana-2411	353	17	to	to	ADP
cana-2411	353	18	the	the	DET
cana-2411	353	19	solution	solution	NOUN
cana-2411	353	20	in	in	ADP
cana-2411	353	21	fewer	few	ADJ
cana-2411	353	22	iterations	iteration	NOUN
cana-2411	353	23	than	than	ADP
cana-2411	353	24	the	the	DET
cana-2411	353	25	steepest	steep	ADJ
cana-2411	353	26	descent	descent	NOUN
cana-2411	353	27	method	method	NOUN
cana-2411	353	28	,	,	PUNCT
cana-2411	353	29	making	make	VERB
cana-2411	353	30	it	it	PRON
cana-2411	353	31	the	the	DET
cana-2411	353	32	more	more	ADV
cana-2411	353	33	efficient	efficient	ADJ
cana-2411	353	34	method	method	NOUN
cana-2411	353	35	for	for	ADP
cana-2411	353	36	obtaining	obtain	VERB
cana-2411	353	37	the	the	DET
cana-2411	353	38	single	single	ADV
cana-2411	353	39	-	-	PUNCT
cana-2411	353	40	valued	value	VERB
cana-2411	353	41	neutrosophic	neutrosophic	ADJ
cana-2411	353	42	optimal	optimal	ADJ
cana-2411	353	43	solution	solution	NOUN
cana-2411	353	44	to	to	ADP
cana-2411	353	45	the	the	DET
cana-2411	353	46	problems	problem	NOUN
cana-2411	353	47	.	.	PUNCT
cana-2411	354	1	table	table	NOUN
cana-2411	354	2	(	(	PUNCT
cana-2411	354	3	5),(6	5),(6	NUM
cana-2411	354	4	)	)	PUNCT
cana-2411	354	5	represent	represent	VERB
cana-2411	354	6	the	the	DET
cana-2411	354	7	single	single	ADV
cana-2411	354	8	-	-	PUNCT
cana-2411	354	9	valued	value	VERB
cana-2411	354	10	neutrosophic	neutrosophic	ADJ
cana-2411	354	11	optimal	optimal	ADJ
cana-2411	354	12	solution	solution	NOUN
cana-2411	354	13	of	of	ADP
cana-2411	354	14	the	the	DET
cana-2411	354	15	svnnlpp	svnnlpp	NOUN
cana-2411	354	16	(	(	PUNCT
cana-2411	354	17	9	9	NUM
cana-2411	354	18	)	)	PUNCT
cana-2411	354	19	for	for	ADP
cana-2411	354	20	various	various	ADJ
cana-2411	354	21	values	value	NOUN
cana-2411	354	22	of	of	ADP
cana-2411	354	23	r.	r.	PROPN
cana-2411	354	24	table	table	NOUN
cana-2411	354	25	5	5	NUM
cana-2411	354	26	:	:	PUNCT
cana-2411	354	27	neutrosophic	neutrosophic	ADJ
cana-2411	354	28	the	the	DET
cana-2411	354	29	optimum	optimum	ADJ
cana-2411	354	30	technique	technique	NOUN
cana-2411	354	31	to	to	PART
cana-2411	354	32	solve	solve	VERB
cana-2411	354	33	the	the	DET
cana-2411	354	34	provided	provide	VERB
cana-2411	354	35	neutrosophic	neutrosophic	ADJ
cana-2411	354	36	a	a	DET
cana-2411	354	37	triangular	triangular	NOUN
cana-2411	354	38	coefficients	coefficient	NOUN
cana-2411	354	39	for	for	ADP
cana-2411	354	40	different	different	ADJ
cana-2411	354	41	values	value	NOUN
cana-2411	354	42	of	of	ADP
cana-2411	354	43	r	r	NOUN
cana-2411	354	44	∈	∈	PROPN
cana-2411	355	1	[	[	X
cana-2411	355	2	0,1	0,1	NUM
cana-2411	355	3	]	]	X
cana-2411	355	4	𝐫	𝐫	PROPN
cana-2411	355	5	𝛖𝟏	𝛖𝟏	ADJ
cana-2411	355	6	𝛖𝟐	𝛖𝟐	NOUN
cana-2411	355	7	0	0	PUNCT
cana-2411	355	8	(	(	PUNCT
cana-2411	355	9	5.999,6.999,7.999	5.999,6.999,7.999	NUM
cana-2411	355	10	)	)	PUNCT
cana-2411	355	11	;	;	PUNCT
cana-2411	355	12	(	(	PUNCT
cana-2411	355	13	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	355	14	)	)	PUNCT
cana-2411	355	15	(	(	PUNCT
cana-2411	355	16	7.999,8.999,9.999	7.999,8.999,9.999	NOUN
cana-2411	355	17	)	)	PUNCT
cana-2411	355	18	;	;	PUNCT
cana-2411	355	19	(	(	PUNCT
cana-2411	355	20	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	355	21	)	)	PUNCT
cana-2411	355	22	0.25	0.25	NUM
cana-2411	355	23	(	(	PUNCT
cana-2411	355	24	6.249,6.999,7.749	6.249,6.999,7.749	NOUN
cana-2411	355	25	)	)	PUNCT
cana-2411	355	26	;	;	PUNCT
cana-2411	355	27	(	(	PUNCT
cana-2411	355	28	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	355	29	)	)	PUNCT
cana-2411	355	30	(	(	PUNCT
cana-2411	355	31	8.249,8.999,9.749	8.249,8.999,9.749	NOUN
cana-2411	355	32	)	)	PUNCT
cana-2411	355	33	;	;	PUNCT
cana-2411	355	34	(	(	PUNCT
cana-2411	355	35	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	355	36	)	)	PUNCT
cana-2411	355	37	0.5	0.5	NUM
cana-2411	355	38	(	(	PUNCT
cana-2411	355	39	6.499,6.999,7.499	6.499,6.999,7.499	NUM
cana-2411	355	40	)	)	PUNCT
cana-2411	355	41	;	;	PUNCT
cana-2411	355	42	(	(	PUNCT
cana-2411	355	43	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	355	44	)	)	PUNCT
cana-2411	355	45	(	(	PUNCT
cana-2411	355	46	8.499,8.999,9.499	8.499,8.999,9.499	NUM
cana-2411	355	47	)	)	PUNCT
cana-2411	355	48	;	;	PUNCT
cana-2411	355	49	(	(	PUNCT
cana-2411	355	50	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	355	51	)	)	PUNCT
cana-2411	355	52	0.75	0.75	NUM
cana-2411	355	53	(	(	PUNCT
cana-2411	355	54	6.749,6.999,7.249	6.749,6.999,7.249	NOUN
cana-2411	355	55	)	)	PUNCT
cana-2411	355	56	;	;	PUNCT
cana-2411	355	57	(	(	PUNCT
cana-2411	355	58	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	355	59	)	)	PUNCT
cana-2411	355	60	(	(	PUNCT
cana-2411	355	61	8.749,8.999,9.249	8.749,8.999,9.249	NUM
cana-2411	355	62	)	)	PUNCT
cana-2411	355	63	;	;	PUNCT
cana-2411	355	64	(	(	PUNCT
cana-2411	355	65	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	355	66	)	)	PUNCT
cana-2411	355	67	1	1	NUM
cana-2411	355	68	(	(	PUNCT
cana-2411	355	69	6.999,6.999,6.999	6.999,6.999,6.999	NOUN
cana-2411	355	70	)	)	PUNCT
cana-2411	355	71	;	;	PUNCT
cana-2411	355	72	(	(	PUNCT
cana-2411	355	73	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	355	74	)	)	PUNCT
cana-2411	355	75	(	(	PUNCT
cana-2411	355	76	8.999,8.999,8.999	8.999,8.999,8.999	NUM
cana-2411	355	77	)	)	PUNCT
cana-2411	355	78	;	;	PUNCT
cana-2411	355	79	(	(	PUNCT
cana-2411	355	80	0.8,0.75,0.75	0.8,0.75,0.75	ADJ
cana-2411	355	81	)	)	PUNCT
cana-2411	355	82	table	table	NOUN
cana-2411	355	83	6	6	NUM
cana-2411	355	84	:	:	PUNCT
cana-2411	355	85	continue	continue	VERB
cana-2411	355	86	on	on	ADP
cana-2411	355	87	the	the	DET
cana-2411	355	88	table	table	NOUN
cana-2411	355	89	(	(	PUNCT
cana-2411	355	90	5	5	NUM
cana-2411	355	91	)	)	PUNCT
cana-2411	355	92	𝐫	𝐫	NOUN
cana-2411	355	93	𝐟(𝛖𝟏	𝐟(𝛖𝟏	NOUN
cana-2411	355	94	,	,	PUNCT
cana-2411	355	95	𝛖𝟐	𝛖𝟐	NOUN
cana-2411	355	96	)	)	PUNCT
cana-2411	355	97	0	0	NUM
cana-2411	356	1	(	(	PUNCT
cana-2411	356	2	185.999,186.999,187.999	185.999,186.999,187.999	NUM
cana-2411	356	3	)	)	PUNCT
cana-2411	356	4	;	;	PUNCT
cana-2411	356	5	(	(	PUNCT
cana-2411	356	6	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	356	7	)	)	PUNCT
cana-2411	356	8	0.25	0.25	NUM
cana-2411	356	9	(	(	PUNCT
cana-2411	356	10	186.249,186.999,187.749	186.249,186.999,187.749	NOUN
cana-2411	356	11	)	)	PUNCT
cana-2411	356	12	;	;	PUNCT
cana-2411	356	13	(	(	PUNCT
cana-2411	356	14	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	356	15	)	)	PUNCT
cana-2411	356	16	0.5	0.5	NUM
cana-2411	356	17	(	(	PUNCT
cana-2411	356	18	186.499,186.999,187.499	186.499,186.999,187.499	NUM
cana-2411	356	19	)	)	PUNCT
cana-2411	356	20	;	;	PUNCT
cana-2411	356	21	(	(	PUNCT
cana-2411	356	22	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	356	23	)	)	PUNCT
cana-2411	356	24	0.75	0.75	NUM
cana-2411	356	25	(	(	PUNCT
cana-2411	356	26	186.749,186.999,187.249	186.749,186.999,187.249	NUM
cana-2411	356	27	)	)	PUNCT
cana-2411	356	28	;	;	PUNCT
cana-2411	356	29	(	(	PUNCT
cana-2411	356	30	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	356	31	)	)	PUNCT
cana-2411	356	32	1	1	NUM
cana-2411	356	33	(	(	PUNCT
cana-2411	356	34	186.999,186.999,186.999	186.999,186.999,186.999	NUM
cana-2411	356	35	)	)	PUNCT
cana-2411	356	36	;	;	PUNCT
cana-2411	356	37	(	(	PUNCT
cana-2411	356	38	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	356	39	)	)	PUNCT
cana-2411	356	40	when	when	SCONJ
cana-2411	356	41	r	r	NOUN
cana-2411	356	42	=	=	SYM
cana-2411	356	43	1	1	NUM
cana-2411	356	44	,	,	PUNCT
cana-2411	356	45	we	we	PRON
cana-2411	356	46	see	see	VERB
cana-2411	356	47	that	that	DET
cana-2411	356	48	𝛖𝟏	𝛖𝟏	NOUN
cana-2411	356	49	=	=	SYM
cana-2411	356	50	(	(	PUNCT
cana-2411	356	51	6.999,6.999,6.999	6.999,6.999,6.999	NOUN
cana-2411	356	52	)	)	PUNCT
cana-2411	356	53	;	;	PUNCT
cana-2411	356	54	(	(	PUNCT
cana-2411	356	55	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	356	56	)	)	PUNCT
cana-2411	356	57	,	,	PUNCT
cana-2411	356	58	𝛖𝟐	𝛖𝟐	NOUN
cana-2411	356	59	=	=	SYM
cana-2411	356	60	(	(	PUNCT
cana-2411	356	61	8.999,8.999,8.999	8.999,8.999,8.999	NUM
cana-2411	356	62	)	)	PUNCT
cana-2411	356	63	;	;	PUNCT
cana-2411	356	64	(	(	PUNCT
cana-2411	356	65	0.8,0.75,0.75	0.8,0.75,0.75	NOUN
cana-2411	356	66	)	)	PUNCT
cana-2411	356	67	and	and	CCONJ
cana-2411	356	68	𝑚𝑖𝑛	𝑚𝑖𝑛	PROPN
cana-2411	356	69	𝐟(	𝐟(	PROPN
cana-2411	356	70	�	�	PROPN
cana-2411	356	71	̃	̃	PROPN
cana-2411	356	72	�	�	PROPN
cana-2411	356	73	𝟏	𝟏	NUM
cana-2411	356	74	,	,	PUNCT
cana-2411	356	75	𝛖𝟐	𝛖𝟐	NOUN
cana-2411	356	76	)	)	PUNCT
cana-2411	356	77	=	=	PUNCT
cana-2411	356	78	(	(	PUNCT
cana-2411	356	79	186.999,186.999,186.999	186.999,186.999,186.999	NUM
cana-2411	356	80	)	)	PUNCT
cana-2411	356	81	;	;	PUNCT
cana-2411	356	82	(	(	PUNCT
cana-2411	356	83	0.8,0.75,0.75	0.8,0.75,0.75	ADJ
cana-2411	356	84	)	)	PUNCT
cana-2411	356	85	table	table	NOUN
cana-2411	356	86	(	(	PUNCT
cana-2411	356	87	7	7	NUM
cana-2411	356	88	)	)	PUNCT
cana-2411	356	89	,	,	PUNCT
cana-2411	356	90	(	(	PUNCT
cana-2411	356	91	8)	8)	NUM
cana-2411	356	92	represent	represent	VERB
cana-2411	356	93	the	the	DET
cana-2411	356	94	single	single	ADV
cana-2411	356	95	-	-	PUNCT
cana-2411	356	96	valued	value	VERB
cana-2411	356	97	neutrosophic	neutrosophic	ADJ
cana-2411	356	98	optimal	optimal	ADJ
cana-2411	356	99	solution	solution	NOUN
cana-2411	356	100	of	of	ADP
cana-2411	356	101	the	the	DET
cana-2411	356	102	svnnlpp	svnnlpp	NOUN
cana-2411	356	103	(	(	PUNCT
cana-2411	356	104	11	11	NUM
cana-2411	356	105	)	)	PUNCT
cana-2411	356	106	for	for	ADP
cana-2411	356	107	various	various	ADJ
cana-2411	356	108	values	value	NOUN
cana-2411	356	109	of	of	ADP
cana-2411	356	110	r.	r.	PROPN
cana-2411	356	111	communications	communication	NOUN
cana-2411	356	112	on	on	ADP
cana-2411	356	113	applied	apply	VERB
cana-2411	356	114	nonlinear	nonlinear	ADJ
cana-2411	356	115	analysis	analysis	NOUN
cana-2411	356	116	issn	issn	NOUN
cana-2411	356	117	:	:	PUNCT
cana-2411	356	118	1074	1074	NUM
cana-2411	356	119	-	-	PUNCT
cana-2411	356	120	133x	133x	NUM
cana-2411	356	121	vol	vol	NOUN
cana-2411	356	122	32	32	NUM
cana-2411	356	123	no	no	NOUN
cana-2411	356	124	.	.	PUNCT
cana-2411	357	1	2s	2s	NUM
cana-2411	357	2	(	(	PUNCT
cana-2411	357	3	2025	2025	NUM
cana-2411	357	4	)	)	PUNCT
cana-2411	357	5	383	383	NUM
cana-2411	357	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2411	357	7	table	table	NOUN
cana-2411	357	8	7	7	NUM
cana-2411	357	9	:	:	PUNCT
cana-2411	357	10	neutrosophic	neutrosophic	ADJ
cana-2411	357	11	the	the	DET
cana-2411	357	12	optimum	optimum	ADJ
cana-2411	357	13	technique	technique	NOUN
cana-2411	357	14	to	to	PART
cana-2411	357	15	solve	solve	VERB
cana-2411	357	16	the	the	DET
cana-2411	357	17	provided	provide	VERB
cana-2411	357	18	neutrosophic	neutrosophic	ADJ
cana-2411	357	19	a	a	DET
cana-2411	357	20	triangular	triangular	NOUN
cana-2411	357	21	coefficients	coefficient	NOUN
cana-2411	357	22	for	for	ADP
cana-2411	357	23	different	different	ADJ
cana-2411	357	24	values	value	NOUN
cana-2411	357	25	of	of	ADP
cana-2411	357	26	r	r	NOUN
cana-2411	357	27	∈	∈	PROPN
cana-2411	358	1	[	[	X
cana-2411	358	2	0,1	0,1	NUM
cana-2411	358	3	]	]	X
cana-2411	358	4	𝐫	𝐫	PROPN
cana-2411	358	5	𝛖𝟏	𝛖𝟏	ADJ
cana-2411	358	6	𝛖𝟐	𝛖𝟐	NOUN
cana-2411	358	7	0	0	PUNCT
cana-2411	358	8	(	(	PUNCT
cana-2411	358	9	−2	−2	NOUN
cana-2411	358	10	,	,	PUNCT
cana-2411	358	11	−1,0	−1,0	NOUN
cana-2411	358	12	)	)	PUNCT
cana-2411	358	13	;	;	PUNCT
cana-2411	358	14	(	(	PUNCT
cana-2411	358	15	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	358	16	)	)	PUNCT
cana-2411	358	17	(	(	PUNCT
cana-2411	358	18	0.5,1.5,2.5	0.5,1.5,2.5	PROPN
cana-2411	358	19	)	)	PUNCT
cana-2411	358	20	;	;	PUNCT
cana-2411	358	21	(	(	PUNCT
cana-2411	358	22	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	358	23	)	)	PUNCT
cana-2411	358	24	0.25	0.25	NUM
cana-2411	358	25	(	(	PUNCT
cana-2411	358	26	−1.75	−1.75	ADJ
cana-2411	358	27	,	,	PUNCT
cana-2411	358	28	−1	−1	ADV
cana-2411	358	29	,	,	PUNCT
cana-2411	358	30	−0.25	−0.25	ADJ
cana-2411	358	31	)	)	PUNCT
cana-2411	358	32	;	;	PUNCT
cana-2411	358	33	(	(	PUNCT
cana-2411	358	34	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	358	35	)	)	PUNCT
cana-2411	358	36	(	(	PUNCT
cana-2411	358	37	0.75,1.5,2.25	0.75,1.5,2.25	NOUN
cana-2411	358	38	)	)	PUNCT
cana-2411	358	39	;	;	PUNCT
cana-2411	358	40	(	(	PUNCT
cana-2411	358	41	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	358	42	)	)	PUNCT
cana-2411	358	43	0.5	0.5	NUM
cana-2411	358	44	(	(	PUNCT
cana-2411	358	45	−1.5	−1.5	PROPN
cana-2411	358	46	,	,	PUNCT
cana-2411	358	47	−1	−1	NOUN
cana-2411	358	48	,	,	PUNCT
cana-2411	358	49	−0.5	−0.5	PROPN
cana-2411	358	50	)	)	PUNCT
cana-2411	358	51	;	;	PUNCT
cana-2411	358	52	(	(	PUNCT
cana-2411	358	53	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	358	54	)	)	PUNCT
cana-2411	358	55	(	(	PUNCT
cana-2411	358	56	1,1.5,2	1,1.5,2	NUM
cana-2411	358	57	)	)	PUNCT
cana-2411	358	58	;	;	PUNCT
cana-2411	358	59	(	(	PUNCT
cana-2411	358	60	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	358	61	)	)	PUNCT
cana-2411	358	62	0.75	0.75	NUM
cana-2411	358	63	(	(	PUNCT
cana-2411	358	64	−1.25	−1.25	NOUN
cana-2411	358	65	,	,	PUNCT
cana-2411	358	66	−1	−1	PRON
cana-2411	358	67	,	,	PUNCT
cana-2411	358	68	−0.75	−0.75	ADJ
cana-2411	358	69	)	)	PUNCT
cana-2411	358	70	;	;	PUNCT
cana-2411	358	71	(	(	PUNCT
cana-2411	358	72	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	358	73	)	)	PUNCT
cana-2411	358	74	(	(	PUNCT
cana-2411	358	75	1.25,1.5,1.75	1.25,1.5,1.75	NUM
cana-2411	358	76	)	)	PUNCT
cana-2411	358	77	;	;	PUNCT
cana-2411	358	78	(	(	PUNCT
cana-2411	358	79	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	358	80	)	)	PUNCT
cana-2411	358	81	1	1	NUM
cana-2411	358	82	(	(	PUNCT
cana-2411	358	83	−1	−1	NOUN
cana-2411	358	84	,	,	PUNCT
cana-2411	358	85	−1	−1	NOUN
cana-2411	358	86	,	,	PUNCT
cana-2411	358	87	−1	−1	NOUN
cana-2411	358	88	)	)	PUNCT
cana-2411	358	89	;	;	PUNCT
cana-2411	358	90	(	(	PUNCT
cana-2411	358	91	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	358	92	)	)	PUNCT
cana-2411	358	93	(	(	PUNCT
cana-2411	358	94	1.5,1.5,1.5	1.5,1.5,1.5	NUM
cana-2411	358	95	)	)	PUNCT
cana-2411	358	96	;	;	PUNCT
cana-2411	358	97	(	(	PUNCT
cana-2411	358	98	0.7,0.65,0.72	0.7,0.65,0.72	ADJ
cana-2411	358	99	)	)	PUNCT
cana-2411	358	100	table	table	NOUN
cana-2411	358	101	8	8	NUM
cana-2411	358	102	:	:	PUNCT
cana-2411	358	103	continue	continue	VERB
cana-2411	358	104	on	on	ADP
cana-2411	358	105	the	the	DET
cana-2411	358	106	table	table	NOUN
cana-2411	358	107	(	(	PUNCT
cana-2411	358	108	7	7	NUM
cana-2411	358	109	)	)	PUNCT
cana-2411	358	110	𝐫	𝐫	NOUN
cana-2411	358	111	𝐟(𝛖𝟏	𝐟(𝛖𝟏	NOUN
cana-2411	358	112	,	,	PUNCT
cana-2411	358	113	𝛖𝟐	𝛖𝟐	NOUN
cana-2411	358	114	)	)	PUNCT
cana-2411	358	115	0	0	NUM
cana-2411	359	1	(	(	PUNCT
cana-2411	359	2	−2.25	−2.25	NOUN
cana-2411	359	3	,	,	PUNCT
cana-2411	359	4	−1.25	−1.25	NOUN
cana-2411	359	5	,	,	PUNCT
cana-2411	359	6	−0.25	−0.25	NOUN
cana-2411	359	7	)	)	PUNCT
cana-2411	359	8	;	;	PUNCT
cana-2411	359	9	(	(	PUNCT
cana-2411	359	10	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	359	11	)	)	PUNCT
cana-2411	359	12	0.25	0.25	NUM
cana-2411	359	13	(	(	PUNCT
cana-2411	359	14	−2	−2	PROPN
cana-2411	359	15	,	,	PUNCT
cana-2411	359	16	−1.25	−1.25	NOUN
cana-2411	359	17	,	,	PUNCT
cana-2411	359	18	−0.5	−0.5	PROPN
cana-2411	359	19	)	)	PUNCT
cana-2411	359	20	;	;	PUNCT
cana-2411	359	21	(	(	PUNCT
cana-2411	359	22	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	359	23	)	)	PUNCT
cana-2411	359	24	0.5	0.5	NUM
cana-2411	359	25	(	(	PUNCT
cana-2411	359	26	−1.75	−1.75	PROPN
cana-2411	359	27	,	,	PUNCT
cana-2411	359	28	−1.25	−1.25	NOUN
cana-2411	359	29	,	,	PUNCT
cana-2411	359	30	−0.75	−0.75	ADJ
cana-2411	359	31	)	)	PUNCT
cana-2411	359	32	;	;	PUNCT
cana-2411	359	33	(	(	PUNCT
cana-2411	359	34	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	359	35	)	)	PUNCT
cana-2411	359	36	0.75	0.75	NUM
cana-2411	359	37	(	(	PUNCT
cana-2411	359	38	−1.25	−1.25	NOUN
cana-2411	359	39	,	,	PUNCT
cana-2411	359	40	−1.25	−1.25	NOUN
cana-2411	359	41	,	,	PUNCT
cana-2411	359	42	−1	−1	NOUN
cana-2411	359	43	)	)	PUNCT
cana-2411	359	44	;	;	PUNCT
cana-2411	359	45	(	(	PUNCT
cana-2411	359	46	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	359	47	)	)	PUNCT
cana-2411	359	48	1	1	NUM
cana-2411	359	49	(	(	PUNCT
cana-2411	359	50	−1.25	−1.25	NOUN
cana-2411	359	51	,	,	PUNCT
cana-2411	359	52	−1.25	−1.25	PROPN
cana-2411	359	53	,	,	PUNCT
cana-2411	359	54	−1.25	−1.25	NOUN
cana-2411	359	55	)	)	PUNCT
cana-2411	359	56	;	;	PUNCT
cana-2411	359	57	(	(	PUNCT
cana-2411	359	58	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	359	59	)	)	PUNCT
cana-2411	359	60	when	when	SCONJ
cana-2411	359	61	r	r	NOUN
cana-2411	359	62	=	=	SYM
cana-2411	359	63	1	1	NUM
cana-2411	359	64	,	,	PUNCT
cana-2411	359	65	we	we	PRON
cana-2411	359	66	see	see	VERB
cana-2411	359	67	that	that	PRON
cana-2411	359	68	𝛖𝟏	𝛖𝟏	NOUN
cana-2411	359	69	=	=	SYM
cana-2411	359	70	(	(	PUNCT
cana-2411	359	71	−1	−1	NOUN
cana-2411	359	72	,	,	PUNCT
cana-2411	359	73	−1	−1	NOUN
cana-2411	359	74	,	,	PUNCT
cana-2411	359	75	−1	−1	NOUN
cana-2411	359	76	)	)	PUNCT
cana-2411	359	77	;	;	PUNCT
cana-2411	359	78	(	(	PUNCT
cana-2411	359	79	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	359	80	)	)	PUNCT
cana-2411	359	81	,	,	PUNCT
cana-2411	359	82	𝛖𝟐	𝛖𝟐	NOUN
cana-2411	359	83	=	=	SYM
cana-2411	359	84	(	(	PUNCT
cana-2411	359	85	1.5,1.5,1.5	1.5,1.5,1.5	NUM
cana-2411	359	86	)	)	PUNCT
cana-2411	359	87	;	;	PUNCT
cana-2411	359	88	(	(	PUNCT
cana-2411	359	89	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	359	90	)	)	PUNCT
cana-2411	359	91	and	and	CCONJ
cana-2411	359	92	𝑚𝑖𝑛	𝑚𝑖𝑛	PROPN
cana-2411	359	93	𝐟(	𝐟(	PROPN
cana-2411	359	94	�	�	PROPN
cana-2411	359	95	̃	̃	PROPN
cana-2411	359	96	�	�	PROPN
cana-2411	359	97	𝟏	𝟏	NUM
cana-2411	359	98	,	,	PUNCT
cana-2411	359	99	𝛖𝟐	𝛖𝟐	NOUN
cana-2411	359	100	)	)	PUNCT
cana-2411	359	101	=	=	PUNCT
cana-2411	359	102	(	(	PUNCT
cana-2411	359	103	−1.25	−1.25	NOUN
cana-2411	359	104	,	,	PUNCT
cana-2411	359	105	−1.25	−1.25	PROPN
cana-2411	359	106	,	,	PUNCT
cana-2411	359	107	−1.25	−1.25	NOUN
cana-2411	359	108	)	)	PUNCT
cana-2411	359	109	;	;	PUNCT
cana-2411	359	110	(	(	PUNCT
cana-2411	359	111	0.7,0.65,0.72	0.7,0.65,0.72	NOUN
cana-2411	359	112	)	)	PUNCT
cana-2411	359	113	the	the	DET
cana-2411	359	114	above	above	ADJ
cana-2411	359	115	tables	table	NOUN
cana-2411	359	116	(	(	PUNCT
cana-2411	359	117	5	5	NUM
cana-2411	359	118	)	)	PUNCT
cana-2411	359	119	,	,	PUNCT
cana-2411	359	120	(	(	PUNCT
cana-2411	359	121	6	6	NUM
cana-2411	359	122	)	)	PUNCT
cana-2411	359	123	,	,	PUNCT
cana-2411	359	124	(	(	PUNCT
cana-2411	359	125	7	7	NUM
cana-2411	359	126	)	)	PUNCT
cana-2411	359	127	,	,	PUNCT
cana-2411	359	128	and	and	CCONJ
cana-2411	359	129	(	(	PUNCT
cana-2411	359	130	8)	8)	NUM
cana-2411	359	131	illustrate	illustrate	VERB
cana-2411	359	132	that	that	SCONJ
cana-2411	359	133	the	the	DET
cana-2411	359	134	proposed	propose	VERB
cana-2411	359	135	method	method	NOUN
cana-2411	359	136	provides	provide	VERB
cana-2411	359	137	decision	decision	NOUN
cana-2411	359	138	makers	maker	NOUN
cana-2411	359	139	with	with	ADP
cana-2411	359	140	the	the	DET
cana-2411	359	141	flexibility	flexibility	NOUN
cana-2411	359	142	to	to	PART
cana-2411	359	143	select	select	VERB
cana-2411	359	144	their	their	PRON
cana-2411	359	145	preferred	prefer	VERB
cana-2411	359	146	solutions	solution	NOUN
cana-2411	359	147	by	by	ADP
cana-2411	359	148	making	make	VERB
cana-2411	359	149	appropriate	appropriate	ADJ
cana-2411	359	150	choices	choice	NOUN
cana-2411	359	151	of	of	ADP
cana-2411	359	152	r.	r.	PROPN
cana-2411	359	153	8	8	NUM
cana-2411	359	154	.	.	PUNCT
cana-2411	360	1	conclusion	conclusion	NOUN
cana-2411	360	2	in	in	ADP
cana-2411	360	3	this	this	DET
cana-2411	360	4	paper	paper	NOUN
cana-2411	360	5	,	,	PUNCT
cana-2411	360	6	we	we	PRON
cana-2411	360	7	discussed	discuss	VERB
cana-2411	360	8	a	a	DET
cana-2411	360	9	solution	solution	NOUN
cana-2411	360	10	concept	concept	NOUN
cana-2411	360	11	for	for	ADP
cana-2411	360	12	svnnlpp	svnnlpp	NOUN
cana-2411	360	13	involving	involve	VERB
cana-2411	360	14	neutrosophic	neutrosophic	ADJ
cana-2411	360	15	triangular	triangular	NOUN
cana-2411	360	16	numbers	number	NOUN
cana-2411	360	17	.	.	PUNCT
cana-2411	361	1	first	first	ADV
cana-2411	361	2	,	,	PUNCT
cana-2411	361	3	the	the	DET
cana-2411	361	4	given	give	VERB
cana-2411	361	5	svnnlpp	svnnlpp	NOUN
cana-2411	361	6	is	be	AUX
cana-2411	361	7	expressed	express	VERB
cana-2411	361	8	in	in	ADP
cana-2411	361	9	terms	term	NOUN
cana-2411	361	10	of	of	ADP
cana-2411	361	11	its	its	PRON
cana-2411	361	12	location	location	NOUN
cana-2411	361	13	index	index	NOUN
cana-2411	361	14	number	number	NOUN
cana-2411	361	15	,	,	PUNCT
cana-2411	361	16	left	leave	VERB
cana-2411	361	17	and	and	CCONJ
cana-2411	361	18	right	right	ADJ
cana-2411	361	19	fuzziness	fuzziness	NOUN
cana-2411	361	20	index	index	NOUN
cana-2411	361	21	functions	function	NOUN
cana-2411	361	22	.	.	PUNCT
cana-2411	362	1	in	in	ADP
cana-2411	362	2	the	the	DET
cana-2411	362	3	parametric	parametric	ADJ
cana-2411	362	4	forms	form	NOUN
cana-2411	362	5	of	of	ADP
cana-2411	362	6	neutrosophic	neutrosophic	ADJ
cana-2411	362	7	numbers	number	NOUN
cana-2411	362	8	,	,	PUNCT
cana-2411	362	9	a	a	DET
cana-2411	362	10	new	new	ADJ
cana-2411	362	11	type	type	NOUN
cana-2411	362	12	of	of	ADP
cana-2411	362	13	neutrosophic	neutrosophic	ADJ
cana-2411	362	14	arithmetic	arithmetic	ADJ
cana-2411	362	15	and	and	CCONJ
cana-2411	362	16	neutrosophic	neutrosophic	ADJ
cana-2411	362	17	ranking	ranking	NOUN
cana-2411	362	18	are	be	AUX
cana-2411	362	19	introduced	introduce	VERB
cana-2411	362	20	and	and	CCONJ
cana-2411	362	21	utilized	utilize	VERB
cana-2411	362	22	.	.	PUNCT
cana-2411	363	1	the	the	DET
cana-2411	363	2	neutrosophic	neutrosophic	ADJ
cana-2411	363	3	quadratic	quadratic	ADJ
cana-2411	363	4	and	and	CCONJ
cana-2411	363	5	neutrosophic	neutrosophic	ADJ
cana-2411	363	6	conjugate	conjugate	ADJ
cana-2411	363	7	gradient	gradient	NOUN
cana-2411	363	8	theorems	theorem	NOUN
cana-2411	363	9	for	for	ADP
cana-2411	363	10	svnnlpp	svnnlpp	NOUN
cana-2411	363	11	are	be	AUX
cana-2411	363	12	established	establish	VERB
cana-2411	363	13	.	.	PUNCT
cana-2411	364	1	the	the	DET
cana-2411	364	2	neutrosophic	neutrosophic	ADJ
cana-2411	364	3	versions	version	NOUN
cana-2411	364	4	of	of	ADP
cana-2411	364	5	the	the	DET
cana-2411	364	6	csdm	csdm	NOUN
cana-2411	364	7	and	and	CCONJ
cana-2411	364	8	the	the	DET
cana-2411	364	9	frm	frm	PROPN
cana-2411	364	10	are	be	AUX
cana-2411	364	11	used	use	VERB
cana-2411	364	12	,	,	PUNCT
cana-2411	364	13	and	and	CCONJ
cana-2411	364	14	the	the	DET
cana-2411	364	15	neutrosophic	neutrosophic	ADJ
cana-2411	364	16	optimal	optimal	ADJ
cana-2411	364	17	solution	solution	NOUN
cana-2411	364	18	of	of	ADP
cana-2411	364	19	the	the	DET
cana-2411	364	20	svnnlpp	svnnlpp	NOUN
cana-2411	364	21	is	be	AUX
cana-2411	364	22	obtained	obtain	VERB
cana-2411	364	23	without	without	ADP
cana-2411	364	24	having	have	VERB
cana-2411	364	25	to	to	PART
cana-2411	364	26	convert	convert	VERB
cana-2411	364	27	the	the	DET
cana-2411	364	28	given	give	VERB
cana-2411	364	29	problem	problem	NOUN
cana-2411	364	30	.	.	PUNCT
cana-2411	365	1	the	the	DET
cana-2411	365	2	neutrosophic	neutrosophic	ADJ
cana-2411	365	3	fuzzy	fuzzy	ADJ
cana-2411	365	4	optimal	optimal	ADJ
cana-2411	365	5	solution	solution	NOUN
cana-2411	365	6	of	of	ADP
cana-2411	365	7	the	the	DET
cana-2411	365	8	given	give	VERB
cana-2411	365	9	svnnlpp	svnnlpp	NOUN
cana-2411	365	10	is	be	AUX
cana-2411	365	11	tabulated	tabulate	VERB
cana-2411	365	12	for	for	ADP
cana-2411	365	13	different	different	ADJ
cana-2411	365	14	values	value	NOUN
cana-2411	365	15	of	of	ADP
cana-2411	365	16	r	r	NOUN
cana-2411	365	17	∈	∈	PROPN
cana-2411	366	1	[	[	X
cana-2411	366	2	0,1	0,1	NUM
cana-2411	366	3	]	]	PUNCT
cana-2411	366	4	.	.	PUNCT
cana-2411	367	1	it	it	PRON
cana-2411	367	2	is	be	AUX
cana-2411	367	3	important	important	ADJ
cana-2411	367	4	to	to	PART
cana-2411	367	5	note	note	VERB
cana-2411	367	6	that	that	SCONJ
cana-2411	367	7	by	by	ADP
cana-2411	367	8	utilizing	utilize	VERB
cana-2411	367	9	the	the	DET
cana-2411	367	10	suggested	suggest	VERB
cana-2411	367	11	procedure	procedure	NOUN
cana-2411	367	12	and	and	CCONJ
cana-2411	367	13	selecting	select	VERB
cana-2411	367	14	an	an	DET
cana-2411	367	15	appropriate	appropriate	ADJ
cana-2411	367	16	value	value	NOUN
cana-2411	367	17	for	for	ADP
cana-2411	367	18	r	r	NOUN
cana-2411	367	19	∈	∈	PROPN
cana-2411	367	20	[	[	X
cana-2411	367	21	0,1	0,1	NUM
cana-2411	367	22	]	]	PUNCT
cana-2411	367	23	,	,	PUNCT
cana-2411	367	24	the	the	DET
cana-2411	367	25	decision	decision	NOUN
cana-2411	367	26	maker	maker	NOUN
cana-2411	367	27	has	have	VERB
cana-2411	367	28	the	the	DET
cana-2411	367	29	flexibility	flexibility	NOUN
cana-2411	367	30	to	to	PART
cana-2411	367	31	select	select	VERB
cana-2411	367	32	his	his	PRON
cana-2411	367	33	or	or	CCONJ
cana-2411	367	34	her	her	PRON
cana-2411	367	35	preferred	preferred	ADJ
cana-2411	367	36	optimal	optimal	ADJ
cana-2411	367	37	solution	solution	NOUN
cana-2411	367	38	based	base	VERB
cana-2411	367	39	on	on	ADP
cana-2411	367	40	the	the	DET
cana-2411	367	41	situation	situation	NOUN
cana-2411	367	42	.	.	PUNCT
cana-2411	368	1	the	the	DET
cana-2411	368	2	numerical	numerical	ADJ
cana-2411	368	3	solutions	solution	NOUN
cana-2411	368	4	have	have	AUX
cana-2411	368	5	been	be	AUX
cana-2411	368	6	presented	present	VERB
cana-2411	368	7	and	and	CCONJ
cana-2411	368	8	discussed	discuss	VERB
cana-2411	368	9	.	.	PUNCT
cana-2411	369	1	both	both	DET
cana-2411	369	2	methods	method	NOUN
cana-2411	369	3	provide	provide	VERB
cana-2411	369	4	same	same	ADJ
cana-2411	369	5	solution	solution	NOUN
cana-2411	369	6	but	but	CCONJ
cana-2411	369	7	frm	frm	PROPN
cana-2411	369	8	requires	require	VERB
cana-2411	369	9	less	less	ADJ
cana-2411	369	10	number	number	NOUN
cana-2411	369	11	itreration	itreration	NOUN
cana-2411	369	12	comparing	compare	VERB
cana-2411	369	13	with	with	ADP
cana-2411	369	14	csdm	csdm	NOUN
cana-2411	369	15	.	.	PUNCT
cana-2411	370	1	conflicts	conflict	NOUN
cana-2411	370	2	of	of	ADP
cana-2411	370	3	interest	interest	NOUN
cana-2411	370	4	:	:	PUNCT
cana-2411	370	5	the	the	DET
cana-2411	370	6	authors	author	NOUN
cana-2411	370	7	have	have	VERB
cana-2411	370	8	no	no	DET
cana-2411	370	9	conflicting	conflict	VERB
cana-2411	370	10	interests	interest	NOUN
cana-2411	370	11	related	relate	VERB
cana-2411	370	12	to	to	ADP
cana-2411	370	13	the	the	DET
cana-2411	370	14	content	content	NOUN
cana-2411	370	15	of	of	ADP
cana-2411	370	16	this	this	DET
cana-2411	370	17	article	article	NOUN
cana-2411	370	18	to	to	PART
cana-2411	370	19	declare	declare	VERB
cana-2411	370	20	.	.	PUNCT
cana-2411	371	1	communications	communication	NOUN
cana-2411	371	2	on	on	ADP
cana-2411	371	3	applied	apply	VERB
cana-2411	371	4	nonlinear	nonlinear	ADJ
cana-2411	371	5	analysis	analysis	NOUN
cana-2411	371	6	issn	issn	NOUN
cana-2411	371	7	:	:	PUNCT
cana-2411	371	8	1074	1074	NUM
cana-2411	371	9	-	-	PUNCT
cana-2411	371	10	133x	133x	NUM
cana-2411	371	11	vol	vol	NOUN
cana-2411	371	12	32	32	NUM
cana-2411	371	13	no	no	NOUN
cana-2411	371	14	.	.	PUNCT
cana-2411	372	1	2s	2s	NUM
cana-2411	372	2	(	(	PUNCT
cana-2411	372	3	2025	2025	NUM
cana-2411	372	4	)	)	PUNCT
cana-2411	372	5	384	384	NUM
cana-2411	372	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2411	372	7	references	reference	NOUN
cana-2411	372	8	[	[	X
cana-2411	372	9	1	1	NUM
cana-2411	372	10	]	]	X
cana-2411	372	11	al	al	PROPN
cana-2411	372	12	-	-	PUNCT
cana-2411	372	13	naemi	naemi	NOUN
cana-2411	372	14	,	,	PUNCT
cana-2411	372	15	g.	g.	PROPN
cana-2411	372	16	m.	m.	PROPN
cana-2411	372	17	,	,	PUNCT
cana-2411	372	18	the	the	DET
cana-2411	372	19	convergent	convergent	NOUN
cana-2411	372	20	properties	property	NOUN
cana-2411	372	21	of	of	ADP
cana-2411	372	22	a	a	DET
cana-2411	372	23	new	new	ADJ
cana-2411	372	24	parameter	parameter	NOUN
cana-2411	372	25	for	for	ADP
cana-2411	372	26	unconstrained	unconstrained	ADJ
cana-2411	372	27	optimization	optimization	NOUN
cana-2411	372	28	,	,	PUNCT
cana-2411	372	29	european	european	PROPN
cana-2411	372	30	journal	journal	PROPN
cana-2411	372	31	of	of	ADP
cana-2411	372	32	pure	pure	ADJ
cana-2411	372	33	and	and	CCONJ
cana-2411	372	34	applied	applied	ADJ
cana-2411	372	35	mathematics	mathematic	NOUN
cana-2411	372	36	,	,	PUNCT
cana-2411	372	37	(	(	PUNCT
cana-2411	372	38	2022	2022	NUM
cana-2411	372	39	)	)	PUNCT
cana-2411	372	40	,	,	PUNCT
cana-2411	372	41	15(4	15(4	NUM
cana-2411	372	42	):	):	PUNCT
cana-2411	372	43	1683	1683	NUM
cana-2411	372	44	-	-	SYM
cana-2411	372	45	1693	1693	NUM
cana-2411	372	46	.	.	PUNCT
cana-2411	373	1	https://doi.org/10.29020/nybg.ejpam.v15i4.4538	https://doi.org/10.29020/nybg.ejpam.v15i4.4538	X
cana-2411	373	2	.	.	PUNCT
cana-2411	374	1	[	[	X
cana-2411	374	2	2	2	NUM
cana-2411	374	3	]	]	X
cana-2411	374	4	andrei	andrei	NOUN
cana-2411	374	5	,	,	PUNCT
cana-2411	374	6	n.	n.	NOUN
cana-2411	374	7	,	,	PUNCT
cana-2411	374	8	steepest	steepest	ADJ
cana-2411	374	9	descent	descent	NOUN
cana-2411	374	10	methods	method	NOUN
cana-2411	374	11	.	.	PUNCT
cana-2411	375	1	in	in	ADP
cana-2411	375	2	:	:	PUNCT
cana-2411	375	3	modern	modern	ADJ
cana-2411	375	4	numerical	numerical	PROPN
cana-2411	375	5	nonlinear	nonlinear	PROPN
cana-2411	375	6	optimization	optimization	NOUN
cana-2411	375	7	springer	springer	NOUN
cana-2411	375	8	optimization	optimization	NOUN
cana-2411	375	9	and	and	CCONJ
cana-2411	375	10	its	its	PRON
cana-2411	375	11	applications	application	NOUN
cana-2411	375	12	,	,	PUNCT
cana-2411	375	13	(	(	PUNCT
cana-2411	375	14	2022	2022	NUM
cana-2411	375	15	)	)	PUNCT
cana-2411	375	16	,	,	PUNCT
cana-2411	375	17	195	195	NUM
cana-2411	375	18	,	,	PUNCT
cana-2411	375	19	springer	springer	NOUN
cana-2411	375	20	,	,	PUNCT
cana-2411	375	21	cham	cham	PROPN
cana-2411	375	22	,	,	PUNCT
cana-2411	375	23	https://doi.org/10.1007/978-3-031-08720-2_3	https://doi.org/10.1007/978-3-031-08720-2_3	X
cana-2411	375	24	[	[	X
cana-2411	375	25	3	3	NUM
cana-2411	375	26	]	]	X
cana-2411	375	27	antczak	antczak	NOUN
cana-2411	375	28	,	,	PUNCT
cana-2411	375	29	t.	t.	NOUN
cana-2411	375	30	,	,	PUNCT
cana-2411	375	31	optimality	optimality	NOUN
cana-2411	375	32	conditions	condition	NOUN
cana-2411	375	33	for	for	ADP
cana-2411	375	34	invex	invex	NOUN
cana-2411	375	35	nonsmooth	nonsmooth	NOUN
cana-2411	375	36	optimization	optimization	NOUN
cana-2411	375	37	problems	problem	NOUN
cana-2411	375	38	with	with	ADP
cana-2411	375	39	fuzzy	fuzzy	ADJ
cana-2411	375	40	objective	objective	ADJ
cana-2411	375	41	functions	function	NOUN
cana-2411	375	42	,	,	PUNCT
cana-2411	375	43	fuzzy	fuzzy	ADJ
cana-2411	375	44	optim	optim	ADJ
cana-2411	375	45	.	.	PUNCT
cana-2411	376	1	decis	decis	PROPN
cana-2411	376	2	.	.	PUNCT
cana-2411	377	1	making	make	VERB
cana-2411	377	2	,	,	PUNCT
cana-2411	377	3	(	(	PUNCT
cana-2411	377	4	2023	2023	NUM
cana-2411	377	5	)	)	PUNCT
cana-2411	377	6	,	,	PUNCT
cana-2411	377	7	22	22	NUM
cana-2411	377	8	,	,	PUNCT
cana-2411	377	9	121	121	NUM
cana-2411	377	10	,	,	PUNCT
cana-2411	377	11	https://doi.org/10.1007/s10700-022-09381-4	https://doi.org/10.1007/s10700-022-09381-4	NUM
cana-2411	377	12	.	.	PUNCT
cana-2411	378	1	[	[	X
cana-2411	378	2	4	4	NUM
cana-2411	378	3	]	]	X
cana-2411	378	4	basim	basim	NOUN
cana-2411	378	5	,	,	PUNCT
cana-2411	378	6	a.h	a.h	PROPN
cana-2411	378	7	,	,	PUNCT
cana-2411	378	8	hawraz	hawraz	PROPN
cana-2411	378	9	,	,	PUNCT
cana-2411	378	10	n.j	n.j	PROPN
cana-2411	378	11	,	,	PUNCT
cana-2411	378	12	yoksal	yoksal	PROPN
cana-2411	378	13	,	,	PUNCT
cana-2411	378	14	a.l	a.l	PROPN
cana-2411	378	15	,	,	PUNCT
cana-2411	378	16	issam	issam	PROPN
cana-2411	378	17	abdul	abdul	PROPN
cana-2411	378	18	rahman	rahman	PROPN
cana-2411	378	19	moghrabi	moghrabi	PROPN
cana-2411	378	20	&	&	CCONJ
cana-2411	378	21	ali	ali	PROPN
cana-2411	378	22	joma	joma	PROPN
cana-2411	378	23	alissa	alissa	PROPN
cana-2411	378	24	,	,	PUNCT
cana-2411	378	25	an	an	DET
cana-2411	378	26	enhanced	enhanced	ADJ
cana-2411	378	27	fletcherreeves	fletcherreeve	NOUN
cana-2411	378	28	-	-	PUNCT
cana-2411	378	29	like	like	ADJ
cana-2411	378	30	conjugate	conjugate	ADJ
cana-2411	378	31	gradient	gradient	ADJ
cana-2411	378	32	methods	method	NOUN
cana-2411	378	33	for	for	ADP
cana-2411	378	34	image	image	NOUN
cana-2411	378	35	restoration	restoration	NOUN
cana-2411	378	36	,	,	PUNCT
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cana-2411	378	38	journal	journal	NOUN
cana-2411	378	39	of	of	ADP
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cana-2411	378	41	and	and	CCONJ
cana-2411	378	42	computer	computer	NOUN
cana-2411	378	43	engineering	engineering	NOUN
cana-2411	378	44	(	(	PUNCT
cana-2411	378	45	ijece	ijece	PROPN
cana-2411	378	46	)	)	PUNCT
cana-2411	378	47	,	,	PUNCT
cana-2411	378	48	(	(	PUNCT
cana-2411	378	49	2023	2023	NUM
cana-2411	378	50	)	)	PUNCT
cana-2411	378	51	,	,	PUNCT
cana-2411	378	52	13(6	13(6	NUM
cana-2411	378	53	)	)	PUNCT
cana-2411	378	54	,	,	PUNCT
cana-2411	378	55	6268	6268	NUM
cana-2411	378	56	-	-	SYM
cana-2411	378	57	6276	6276	NUM
cana-2411	378	58	,	,	PUNCT
cana-2411	378	59	doi	doi	NOUN
cana-2411	378	60	:	:	PUNCT
cana-2411	378	61	10.11591	10.11591	NUM
cana-2411	378	62	/	/	SYM
cana-2411	378	63	ijece.v13i6.pp6268	ijece.v13i6.pp6268	PROPN
cana-2411	378	64	-	-	PUNCT
cana-2411	378	65	6276	6276	NUM
cana-2411	378	66	.	.	PUNCT
cana-2411	379	1	[	[	X
cana-2411	379	2	5	5	NUM
cana-2411	379	3	]	]	X
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cana-2411	379	5	,	,	PUNCT
cana-2411	379	6	r.e	r.e	PROPN
cana-2411	379	7	.	.	PROPN
cana-2411	379	8	&	&	CCONJ
cana-2411	379	9	zadeh	zadeh	PROPN
cana-2411	379	10	,	,	PUNCT
cana-2411	379	11	l.a	l.a	PROPN
cana-2411	379	12	.	.	PROPN
cana-2411	379	13	,	,	PUNCT
cana-2411	379	14	decision	decision	NOUN
cana-2411	379	15	making	making	NOUN
cana-2411	379	16	in	in	ADP
cana-2411	379	17	a	a	DET
cana-2411	379	18	fuzzy	fuzzy	ADJ
cana-2411	379	19	environment	environment	NOUN
cana-2411	379	20	,	,	PUNCT
cana-2411	379	21	management	management	NOUN
cana-2411	379	22	sci	sci	PROPN
cana-2411	379	23	.	.	PROPN
cana-2411	379	24	,	,	PUNCT
cana-2411	379	25	(	(	PUNCT
cana-2411	379	26	1970	1970	NUM
cana-2411	379	27	)	)	PUNCT
cana-2411	379	28	,	,	PUNCT
cana-2411	379	29	17	17	NUM
cana-2411	379	30	,	,	PUNCT
cana-2411	379	31	141	141	NUM
cana-2411	379	32	-	-	SYM
cana-2411	379	33	164	164	NUM
cana-2411	379	34	,	,	PUNCT
cana-2411	379	35	https://doi.org/10.1287/mnsc.17.4.b141	https://doi.org/10.1287/mnsc.17.4.b141	NOUN
cana-2411	379	36	.	.	PUNCT
cana-2411	380	1	[	[	X
cana-2411	380	2	6	6	NUM
cana-2411	380	3	]	]	SYM
cana-2411	380	4	chakraborty	chakraborty	PROPN
cana-2411	380	5	,	,	PUNCT
cana-2411	380	6	a.	a.	NOUN
cana-2411	380	7	,	,	PUNCT
cana-2411	380	8	mondal	mondal	PROPN
cana-2411	380	9	,	,	PUNCT
cana-2411	380	10	s.p	s.p	PROPN
cana-2411	380	11	.	.	PROPN
cana-2411	380	12	,	,	PUNCT
cana-2411	380	13	mahata	mahata	PROPN
cana-2411	380	14	,	,	PUNCT
cana-2411	380	15	a.	a.	PROPN
cana-2411	380	16	&	&	CCONJ
cana-2411	380	17	alam	alam	PROPN
cana-2411	380	18	,	,	PUNCT
cana-2411	380	19	s.	s.	PROPN
cana-2411	380	20	,	,	PUNCT
cana-2411	380	21	different	different	ADJ
cana-2411	380	22	linear	linear	ADJ
cana-2411	380	23	and	and	CCONJ
cana-2411	380	24	non	non	ADJ
cana-2411	380	25	-	-	ADJ
cana-2411	380	26	linear	linear	ADJ
cana-2411	380	27	form	form	NOUN
cana-2411	380	28	of	of	ADP
cana-2411	380	29	trapezoidal	trapezoidal	ADJ
cana-2411	380	30	neutrosophic	neutrosophic	ADJ
cana-2411	380	31	numbers	number	NOUN
cana-2411	380	32	,	,	PUNCT
cana-2411	380	33	de	de	ADJ
cana-2411	380	34	-	-	NOUN
cana-2411	380	35	neutrosophication	neutrosophication	NOUN
cana-2411	380	36	techniques	technique	NOUN
cana-2411	380	37	and	and	CCONJ
cana-2411	380	38	its	its	PRON
cana-2411	380	39	application	application	NOUN
cana-2411	380	40	in	in	ADP
cana-2411	380	41	time	time	NOUN
cana-2411	380	42	-	-	PUNCT
cana-2411	380	43	cost	cost	NOUN
cana-2411	380	44	optimization	optimization	NOUN
cana-2411	380	45	technique	technique	NOUN
cana-2411	380	46	,	,	PUNCT
cana-2411	380	47	sequencing	sequencing	NOUN
cana-2411	380	48	problem	problem	NOUN
cana-2411	380	49	,	,	PUNCT
cana-2411	380	50	rairo	rairo	PROPN
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cana-2411	380	52	research	research	NOUN
cana-2411	380	53	,	,	PUNCT
cana-2411	380	54	(	(	PUNCT
cana-2411	380	55	2021	2021	NUM
cana-2411	380	56	)	)	PUNCT
cana-2411	380	57	,	,	PUNCT
cana-2411	380	58	55	55	NUM
cana-2411	380	59	,	,	PUNCT
cana-2411	380	60	s97	s97	NOUN
cana-2411	380	61	-	-	PUNCT
cana-2411	380	62	s118	s118	PROPN
cana-2411	380	63	,	,	PUNCT
cana-2411	380	64	doi:10.1051	doi:10.1051	NOUN
cana-2411	380	65	/	/	SYM
cana-2411	380	66	ro/2019090	ro/2019090	NOUN
cana-2411	380	67	.	.	PUNCT
cana-2411	381	1	[	[	X
cana-2411	381	2	7	7	NUM
cana-2411	381	3	]	]	X
cana-2411	381	4	hanachi	hanachi	PROPN
cana-2411	381	5	,	,	PUNCT
cana-2411	381	6	s.b	s.b	PROPN
cana-2411	381	7	.	.	PROPN
cana-2411	381	8	,	,	PUNCT
cana-2411	381	9	sellami	sellami	PROPN
cana-2411	381	10	,	,	PUNCT
cana-2411	381	11	b.	b.	PROPN
cana-2411	381	12	&	&	CCONJ
cana-2411	381	13	belloufi	belloufi	PROPN
cana-2411	381	14	,	,	PUNCT
cana-2411	381	15	m.	m.	NOUN
cana-2411	381	16	,	,	PUNCT
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cana-2411	381	18	iterative	iterative	NOUN
cana-2411	381	19	conjugate	conjugate	ADJ
cana-2411	381	20	gradient	gradient	NOUN
cana-2411	381	21	method	method	NOUN
cana-2411	381	22	for	for	ADP
cana-2411	381	23	nonlinear	nonlinear	ADJ
cana-2411	381	24	unconstrained	unconstrained	ADJ
cana-2411	381	25	optimization	optimization	NOUN
cana-2411	381	26	,	,	PUNCT
cana-2411	381	27	rairo	rairo	NOUN
cana-2411	381	28	-	-	PUNCT
cana-2411	381	29	operations	operation	NOUN
cana-2411	381	30	research	research	NOUN
cana-2411	381	31	,	,	PUNCT
cana-2411	381	32	(	(	PUNCT
cana-2411	381	33	2022	2022	NUM
cana-2411	381	34	)	)	PUNCT
cana-2411	381	35	,	,	PUNCT
cana-2411	381	36	56(4	56(4	NOUN
cana-2411	381	37	)	)	PUNCT
cana-2411	381	38	,	,	PUNCT
cana-2411	381	39	2315	2315	NUM
cana-2411	381	40	-	-	SYM
cana-2411	381	41	2327	2327	NUM
cana-2411	381	42	,	,	PUNCT
cana-2411	381	43	https://doi.org/10.1051/ro/2022109	https://doi.org/10.1051/ro/2022109	VERB
cana-2411	381	44	.	.	PUNCT
cana-2411	382	1	[	[	X
cana-2411	382	2	8	8	NUM
cana-2411	382	3	]	]	X
cana-2411	382	4	hassan	hassan	PROPN
cana-2411	382	5	,	,	PUNCT
cana-2411	382	6	b.a	b.a	PROPN
cana-2411	382	7	.	.	PROPN
cana-2411	382	8	,	,	PUNCT
cana-2411	382	9	jabbar	jabbar	PROPN
cana-2411	382	10	,	,	PUNCT
cana-2411	382	11	h.n	h.n	PROPN
cana-2411	382	12	.	.	PROPN
cana-2411	382	13	,	,	PUNCT
cana-2411	382	14	laylani	laylani	NOUN
cana-2411	382	15	,	,	PUNCT
cana-2411	382	16	y.a	y.a	PROPN
cana-2411	382	17	.	.	PROPN
cana-2411	382	18	,	,	PUNCT
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cana-2411	382	20	,	,	PUNCT
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cana-2411	382	22	.	.	PROPN
cana-2411	382	23	,	,	PUNCT
cana-2411	382	24	alissa	alissa	PROPN
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cana-2411	382	26	a.j	a.j	PROPN
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cana-2411	382	28	:	:	PUNCT
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cana-2411	382	32	-	-	PUNCT
cana-2411	382	33	reeves	reeve	NOUN
cana-2411	382	34	-	-	PUNCT
cana-2411	382	35	like	like	ADJ
cana-2411	382	36	conjugate	conjugate	ADJ
cana-2411	382	37	gradient	gradient	ADJ
cana-2411	382	38	methods	method	NOUN
cana-2411	382	39	for	for	ADP
cana-2411	382	40	image	image	NOUN
cana-2411	382	41	restoration	restoration	NOUN
cana-2411	382	42	.	.	PUNCT
cana-2411	383	1	international	international	ADJ
cana-2411	383	2	journal	journal	NOUN
cana-2411	383	3	of	of	ADP
cana-2411	383	4	electrical	electrical	ADJ
cana-2411	383	5	and	and	CCONJ
cana-2411	383	6	computer	computer	NOUN
cana-2411	383	7	engineering	engineering	NOUN
cana-2411	383	8	(	(	PUNCT
cana-2411	383	9	ijece	ijece	PROPN
cana-2411	383	10	)	)	PUNCT
cana-2411	383	11	,	,	PUNCT
cana-2411	383	12	(	(	PUNCT
cana-2411	383	13	2023	2023	NUM
cana-2411	383	14	)	)	PUNCT
cana-2411	383	15	,	,	PUNCT
cana-2411	383	16	13(6	13(6	NUM
cana-2411	383	17	)	)	PUNCT
cana-2411	383	18	,	,	PUNCT
cana-2411	383	19	6268	6268	NUM
cana-2411	383	20	-	-	SYM
cana-2411	383	21	6276	6276	NUM
cana-2411	383	22	.	.	PUNCT
cana-2411	384	1	[	[	X
cana-2411	384	2	9	9	NUM
cana-2411	384	3	]	]	X
cana-2411	384	4	husin	husin	PROPN
cana-2411	384	5	,	,	PUNCT
cana-2411	384	6	s.f	s.f	PROPN
cana-2411	384	7	.	.	PROPN
cana-2411	384	8	,	,	PUNCT
cana-2411	384	9	mamat	mamat	PROPN
cana-2411	384	10	,	,	PUNCT
cana-2411	384	11	m.	m.	NOUN
cana-2411	384	12	,	,	PUNCT
cana-2411	384	13	rivaie	rivaie	PROPN
cana-2411	384	14	,	,	PUNCT
cana-2411	384	15	m.	m.	NOUN
cana-2411	384	16	,	,	PUNCT
cana-2411	384	17	mohamed	mohamed	PROPN
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cana-2411	384	19	m.a	m.a	PROPN
cana-2411	384	20	.	.	PROPN
cana-2411	384	21	&	&	CCONJ
cana-2411	384	22	ibrahim	ibrahim	PROPN
cana-2411	384	23	,	,	PUNCT
cana-2411	384	24	h.	h.	PROPN
cana-2411	384	25	,	,	PUNCT
cana-2411	384	26	modification	modification	NOUN
cana-2411	384	27	of	of	ADP
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cana-2411	384	29	direction	direction	NOUN
cana-2411	384	30	in	in	ADP
cana-2411	384	31	steepest	steep	ADJ
cana-2411	384	32	descent	descent	NOUN
cana-2411	384	33	method	method	NOUN
cana-2411	384	34	and	and	CCONJ
cana-2411	384	35	its	its	PRON
cana-2411	384	36	application	application	NOUN
cana-2411	384	37	in	in	ADP
cana-2411	384	38	regression	regression	NOUN
cana-2411	384	39	analysis	analysis	NOUN
cana-2411	384	40	,	,	PUNCT
cana-2411	384	41	international	international	ADJ
cana-2411	384	42	journal	journal	NOUN
cana-2411	384	43	of	of	ADP
cana-2411	384	44	advanced	advanced	ADJ
cana-2411	384	45	trends	trend	NOUN
cana-2411	384	46	in	in	ADP
cana-2411	384	47	computer	computer	NOUN
cana-2411	384	48	science	science	NOUN
cana-2411	384	49	and	and	CCONJ
cana-2411	384	50	engineering	engineering	NOUN
cana-2411	384	51	,	,	PUNCT
cana-2411	384	52	(	(	PUNCT
cana-2411	384	53	2020	2020	NUM
cana-2411	384	54	)	)	PUNCT
cana-2411	384	55	,	,	PUNCT
cana-2411	384	56	9(1	9(1	NUM
cana-2411	384	57	)	)	PUNCT
cana-2411	384	58	,	,	PUNCT
cana-2411	384	59	1	1	NUM
cana-2411	384	60	,	,	PUNCT
cana-2411	384	61	doi	doi	NOUN
cana-2411	384	62	:	:	PUNCT
cana-2411	384	63	10.30534	10.30534	NUM
cana-2411	384	64	/	/	SYM
cana-2411	384	65	ijatcse/2020/1791.12020	ijatcse/2020/1791.12020	PROPN
cana-2411	384	66	.	.	PUNCT
cana-2411	385	1	[	[	X
cana-2411	385	2	10	10	NUM
cana-2411	385	3	]	]	X
cana-2411	385	4	hepzibah	hepzibah	PROPN
cana-2411	385	5	r.i	r.i	PROPN
cana-2411	385	6	,	,	PUNCT
cana-2411	385	7	&	&	CCONJ
cana-2411	385	8	shilpa	shilpa	PROPN
cana-2411	385	9	ivin	ivin	PROPN
cana-2411	385	10	emimal	emimal	PROPN
cana-2411	385	11	s.	s.	PROPN
cana-2411	385	12	,	,	PUNCT
cana-2411	385	13	on	on	ADP
cana-2411	385	14	solving	solve	VERB
cana-2411	385	15	neutrosophic	neutrosophic	ADJ
cana-2411	385	16	unconstrained	unconstrained	ADJ
cana-2411	385	17	optimization	optimization	NOUN
cana-2411	385	18	problems	problem	NOUN
cana-2411	385	19	by	by	ADP
cana-2411	385	20	steepest	steepest	ADJ
cana-2411	385	21	descent	descent	NOUN
cana-2411	385	22	method	method	NOUN
cana-2411	385	23	and	and	CCONJ
cana-2411	385	24	fletcher	fletcher	PROPN
cana-2411	385	25	reeves	reeves	PROPN
cana-2411	385	26	method	method	PROPN
cana-2411	385	27	,	,	PUNCT
cana-2411	385	28	intern	intern	NOUN
cana-2411	385	29	.	.	PUNCT
cana-2411	386	1	j.	j.	PROPN
cana-2411	386	2	fuzzy	fuzzy	PROPN
cana-2411	386	3	mathematical	mathematical	PROPN
cana-2411	386	4	archive	archive	NOUN
cana-2411	386	5	,	,	PUNCT
cana-2411	386	6	(	(	PUNCT
cana-2411	386	7	2021	2021	NUM
cana-2411	386	8	)	)	PUNCT
cana-2411	386	9	,	,	PUNCT
cana-2411	386	10	19(2	19(2	NUM
cana-2411	386	11	)	)	PUNCT
cana-2411	386	12	,	,	PUNCT
cana-2411	386	13	111122	111122	NUM
cana-2411	386	14	,	,	PUNCT
cana-2411	386	15	doi	doi	NOUN
cana-2411	386	16	:	:	PUNCT
cana-2411	386	17	http://dx.doi.org/10.22457/ijfma.v19n2a02230	http://dx.doi.org/10.22457/ijfma.v19n2a02230	NOUN
cana-2411	386	18	.	.	PUNCT
cana-2411	387	1	[	[	X
cana-2411	387	2	11	11	NUM
cana-2411	387	3	]	]	X
cana-2411	387	4	hepzibah	hepzibah	ADJ
cana-2411	387	5	,	,	PUNCT
cana-2411	387	6	r.i	r.i	PROPN
cana-2411	387	7	.	.	PROPN
cana-2411	387	8	&	&	CCONJ
cana-2411	387	9	emimal	emimal	ADJ
cana-2411	387	10	,	,	PUNCT
cana-2411	387	11	s.s.i	s.s.i	ADJ
cana-2411	387	12	.	.	PROPN
cana-2411	387	13	,	,	PUNCT
cana-2411	387	14	solving	solve	VERB
cana-2411	387	15	fuzzy	fuzzy	ADJ
cana-2411	387	16	unconstrained	unconstraine	VERB
cana-2411	387	17	optimization	optimization	NOUN
cana-2411	387	18	problems	problem	NOUN
cana-2411	387	19	using	use	VERB
cana-2411	387	20	interval	interval	PROPN
cana-2411	387	21	newton	newton	PROPN
cana-2411	387	22	’s	’s	PART
cana-2411	387	23	method	method	NOUN
cana-2411	387	24	,	,	PUNCT
cana-2411	387	25	advances	advance	NOUN
cana-2411	387	26	and	and	CCONJ
cana-2411	387	27	applications	application	NOUN
cana-2411	387	28	in	in	ADP
cana-2411	387	29	mathematical	mathematical	ADJ
cana-2411	387	30	sciences	science	NOUN
cana-2411	387	31	,	,	PUNCT
cana-2411	387	32	(	(	PUNCT
cana-2411	387	33	2022	2022	NUM
cana-2411	387	34	)	)	PUNCT
cana-2411	387	35	,	,	PUNCT
cana-2411	387	36	21(3	21(3	NUM
cana-2411	387	37	)	)	PUNCT
cana-2411	387	38	,	,	PUNCT
cana-2411	387	39	1463	1463	NUM
cana-2411	387	40	-	-	SYM
cana-2411	387	41	1477	1477	NUM
cana-2411	387	42	.	.	PUNCT
cana-2411	388	1	[	[	X
cana-2411	388	2	12	12	NUM
cana-2411	388	3	]	]	X
cana-2411	388	4	kaliyaperumal	kaliyaperumal	PROPN
cana-2411	388	5	,	,	PUNCT
cana-2411	388	6	p.	p.	PROPN
cana-2411	388	7	,	,	PUNCT
cana-2411	388	8	&	&	CCONJ
cana-2411	388	9	das	das	PROPN
cana-2411	388	10	,	,	PUNCT
cana-2411	388	11	a.	a.	PROPN
cana-2411	388	12	,	,	PUNCT
cana-2411	388	13	a	a	DET
cana-2411	388	14	mathematical	mathematical	ADJ
cana-2411	388	15	model	model	NOUN
cana-2411	388	16	for	for	ADP
cana-2411	388	17	nonlinear	nonlinear	ADJ
cana-2411	388	18	optimization	optimization	NOUN
cana-2411	388	19	which	which	PRON
cana-2411	388	20	attempts	attempt	VERB
cana-2411	388	21	membership	membership	NOUN
cana-2411	388	22	functions	function	NOUN
cana-2411	388	23	to	to	PART
cana-2411	388	24	address	address	VERB
cana-2411	388	25	the	the	DET
cana-2411	388	26	uncertainties	uncertainty	NOUN
cana-2411	388	27	,	,	PUNCT
cana-2411	388	28	multidisciplinary	multidisciplinary	ADJ
cana-2411	388	29	digit	digit	NOUN
cana-2411	388	30	.	.	PUNCT
cana-2411	389	1	publishing	publish	VERB
cana-2411	389	2	inst	inst	PROPN
cana-2411	389	3	.	.	PUNCT
cana-2411	390	1	(	(	PUNCT
cana-2411	390	2	math	math	NOUN
cana-2411	390	3	.	.	PUNCT
cana-2411	390	4	)	)	PUNCT
cana-2411	390	5	,	,	PUNCT
cana-2411	390	6	(	(	PUNCT
cana-2411	390	7	2022	2022	NUM
cana-2411	390	8	)	)	PUNCT
cana-2411	390	9	,	,	PUNCT
cana-2411	390	10	10(10	10(10	NUM
cana-2411	390	11	)	)	PUNCT
cana-2411	390	12	,	,	PUNCT
cana-2411	390	13	1743	1743	NUM
cana-2411	390	14	,	,	PUNCT
cana-2411	390	15	https://doi.org/10.3390/math10101743	https://doi.org/10.3390/math10101743	NOUN
cana-2411	390	16	.	.	PUNCT
cana-2411	391	1	[	[	X
cana-2411	391	2	13	13	NUM
cana-2411	391	3	]	]	X
cana-2411	391	4	kanaya	kanaya	PROPN
cana-2411	391	5	,	,	PUNCT
cana-2411	391	6	z.	z.	PROPN
cana-2411	391	7	a.	a.	PROPN
cana-2411	391	8	,	,	PUNCT
cana-2411	391	9	an	an	DET
cana-2411	391	10	interactive	interactive	ADJ
cana-2411	391	11	method	method	NOUN
cana-2411	391	12	for	for	ADP
cana-2411	391	13	fuzzy	fuzzy	ADJ
cana-2411	391	14	multi	multi	ADJ
cana-2411	391	15	objective	objective	ADJ
cana-2411	391	16	nonlinear	nonlinear	ADJ
cana-2411	391	17	programming	programming	NOUN
cana-2411	391	18	problems	problem	NOUN
cana-2411	391	19	,	,	PUNCT
cana-2411	391	20	jkau	jkau	PROPN
cana-2411	391	21	sci	sci	PROPN
cana-2411	391	22	.	.	PROPN
cana-2411	391	23	,	,	PUNCT
cana-2411	391	24	(	(	PUNCT
cana-2411	391	25	2010	2010	NUM
cana-2411	391	26	)	)	PUNCT
cana-2411	391	27	,	,	PUNCT
cana-2411	391	28	22(1	22(1	NUM
cana-2411	391	29	)	)	PUNCT
cana-2411	391	30	,	,	PUNCT
cana-2411	391	31	103	103	NUM
cana-2411	391	32	-	-	SYM
cana-2411	391	33	112	112	NUM
cana-2411	391	34	,	,	PUNCT
cana-2411	391	35	doi	doi	NOUN
cana-2411	391	36	:	:	PUNCT
cana-2411	391	37	10.4197	10.4197	NUM
cana-2411	391	38	/	/	SYM
cana-2411	391	39	sci	sci	PROPN
cana-2411	391	40	.	.	PROPN
cana-2411	391	41	22	22	NUM
cana-2411	391	42	-	-	SYM
cana-2411	391	43	1.8	1.8	NUM
cana-2411	391	44	.	.	PUNCT
cana-2411	392	1	[	[	X
cana-2411	392	2	14	14	NUM
cana-2411	392	3	]	]	X
cana-2411	392	4	lachhwani	lachhwani	PROPN
cana-2411	392	5	,	,	PUNCT
cana-2411	392	6	k.	k.	PROPN
cana-2411	392	7	,	,	PUNCT
cana-2411	392	8	solving	solve	VERB
cana-2411	392	9	non	non	ADJ
cana-2411	392	10	-	-	ADJ
cana-2411	392	11	linear	linear	ADJ
cana-2411	392	12	neutrosophic	neutrosophic	ADJ
cana-2411	392	13	linear	linear	ADJ
cana-2411	392	14	programming	programming	NOUN
cana-2411	392	15	problems	problem	NOUN
cana-2411	392	16	,	,	PUNCT
cana-2411	392	17	neutrosophic	neutrosophic	ADJ
cana-2411	392	18	sets	set	NOUN
cana-2411	392	19	and	and	CCONJ
cana-2411	392	20	systems	system	NOUN
cana-2411	392	21	,	,	PUNCT
cana-2411	392	22	(	(	PUNCT
cana-2411	392	23	2023	2023	NUM
cana-2411	392	24	)	)	PUNCT
cana-2411	392	25	,	,	PUNCT
cana-2411	392	26	60(1	60(1	NUM
cana-2411	392	27	)	)	PUNCT
cana-2411	392	28	,	,	PUNCT
cana-2411	392	29	2	2	X
cana-2411	392	30	.	.	PUNCT
cana-2411	393	1	[	[	X
cana-2411	393	2	15	15	NUM
cana-2411	393	3	]	]	X
cana-2411	393	4	maissam	maissam	PROPN
cana-2411	393	5	jdid	jdid	PROPN
cana-2411	393	6	&	&	CCONJ
cana-2411	393	7	florentin	florentin	PROPN
cana-2411	393	8	smarandache	smarandache	PROPN
cana-2411	393	9	.	.	PUNCT
cana-2411	393	10	,	,	PUNCT
cana-2411	393	11	the	the	DET
cana-2411	393	12	use	use	NOUN
cana-2411	393	13	of	of	ADP
cana-2411	393	14	neutrosophic	neutrosophic	ADJ
cana-2411	393	15	methods	method	NOUN
cana-2411	393	16	of	of	ADP
cana-2411	393	17	operation	operation	NOUN
cana-2411	393	18	research	research	NOUN
cana-2411	393	19	in	in	ADP
cana-2411	393	20	the	the	DET
cana-2411	393	21	management	management	NOUN
cana-2411	393	22	of	of	ADP
cana-2411	393	23	corporate	corporate	ADJ
cana-2411	393	24	work	work	NOUN
cana-2411	393	25	,	,	PUNCT
cana-2411	393	26	neutrosophic	neutrosophic	ADJ
cana-2411	393	27	systems	system	NOUN
cana-2411	393	28	with	with	ADP
cana-2411	393	29	applications	application	NOUN
cana-2411	393	30	,	,	PUNCT
cana-2411	393	31	(	(	PUNCT
cana-2411	393	32	2023	2023	NUM
cana-2411	393	33	)	)	PUNCT
cana-2411	393	34	,	,	PUNCT
cana-2411	393	35	3	3	NUM
cana-2411	393	36	,	,	PUNCT
cana-2411	393	37	1	1	NUM
cana-2411	393	38	-	-	SYM
cana-2411	393	39	16	16	NUM
cana-2411	393	40	,	,	PUNCT
cana-2411	393	41	https://doi.org/10.61356/j.nswa.2023.11	https://doi.org/10.61356/j.nswa.2023.11	NOUN
cana-2411	393	42	.	.	PUNCT
cana-2411	394	1	[	[	X
cana-2411	394	2	16	16	NUM
cana-2411	394	3	]	]	X
cana-2411	394	4	ming	ming	PROPN
cana-2411	394	5	ma	ma	PROPN
cana-2411	394	6	,	,	PUNCT
cana-2411	394	7	menahem	menahem	PROPN
cana-2411	394	8	friedman	friedman	PROPN
cana-2411	394	9	,	,	PUNCT
cana-2411	394	10	&	&	CCONJ
cana-2411	394	11	abraham	abraham	PROPN
cana-2411	394	12	kandel	kandel	PROPN
cana-2411	394	13	,	,	PUNCT
cana-2411	394	14	a	a	DET
cana-2411	394	15	new	new	ADJ
cana-2411	394	16	fuzzy	fuzzy	ADJ
cana-2411	394	17	arithmetic	arithmetic	ADJ
cana-2411	394	18	,	,	PUNCT
cana-2411	394	19	fuzzy	fuzzy	ADJ
cana-2411	394	20	sets	set	NOUN
cana-2411	394	21	and	and	CCONJ
cana-2411	394	22	systems	system	NOUN
cana-2411	394	23	,	,	PUNCT
cana-2411	394	24	(	(	PUNCT
cana-2411	394	25	1999	1999	NUM
cana-2411	394	26	)	)	PUNCT
cana-2411	394	27	,	,	PUNCT
cana-2411	394	28	108(1	108(1	NUM
cana-2411	394	29	)	)	PUNCT
cana-2411	394	30	,	,	PUNCT
cana-2411	394	31	83	83	NUM
cana-2411	394	32	-	-	SYM
cana-2411	394	33	90	90	NUM
cana-2411	394	34	.	.	PUNCT
cana-2411	394	35	https://doi.org/10.1016/s0165-0114(97)00310-2	https://doi.org/10.1016/s0165-0114(97)00310-2	PROPN
cana-2411	394	36	.	.	PUNCT
cana-2411	395	1	[	[	X
cana-2411	395	2	17	17	NUM
cana-2411	395	3	]	]	SYM
cana-2411	395	4	nagoorgani	nagoorgani	PROPN
cana-2411	395	5	,	,	PUNCT
cana-2411	395	6	a.	a.	PROPN
cana-2411	395	7	&	&	CCONJ
cana-2411	395	8	sudha	sudha	PROPN
cana-2411	395	9	,	,	PUNCT
cana-2411	395	10	k.	k.	PROPN
cana-2411	395	11	,	,	PUNCT
cana-2411	395	12	optimality	optimality	NOUN
cana-2411	395	13	conditions	condition	NOUN
cana-2411	395	14	for	for	ADP
cana-2411	395	15	fuzzy	fuzzy	ADJ
cana-2411	395	16	non	non	ADJ
cana-2411	395	17	-	-	ADJ
cana-2411	395	18	linear	linear	ADJ
cana-2411	395	19	unconstrained	unconstrained	ADJ
cana-2411	395	20	minimization	minimization	NOUN
cana-2411	395	21	problems	problem	NOUN
cana-2411	395	22	,	,	PUNCT
cana-2411	395	23	bull	bull	NOUN
cana-2411	395	24	.	.	PUNCT
cana-2411	396	1	pure	pure	ADJ
cana-2411	396	2	appl	appl	PROPN
cana-2411	396	3	.	.	PUNCT
cana-2411	397	1	sci	sci	PROPN
cana-2411	397	2	.	.	PROPN
cana-2411	397	3	,	,	PUNCT
cana-2411	397	4	(	(	PUNCT
cana-2411	397	5	2019	2019	NUM
cana-2411	397	6	)	)	PUNCT
cana-2411	397	7	,	,	PUNCT
cana-2411	397	8	38(1	38(1	NUM
cana-2411	397	9	)	)	PUNCT
cana-2411	397	10	,	,	PUNCT
cana-2411	397	11	378	378	NUM
cana-2411	397	12	-	-	SYM
cana-2411	397	13	384	384	NUM
cana-2411	397	14	,	,	PUNCT
cana-2411	397	15	doi	doi	NOUN
cana-2411	397	16	:	:	PUNCT
cana-2411	397	17	10.5958/2320	10.5958/2320	NUM
cana-2411	397	18	-	-	SYM
cana-2411	397	19	3226.2019.00041.9	3226.2019.00041.9	NUM
cana-2411	397	20	.	.	PUNCT
cana-2411	398	1	[	[	X
cana-2411	398	2	18	18	NUM
cana-2411	398	3	]	]	PUNCT
cana-2411	398	4	reig	reig	NOUN
cana-2411	398	5	-	-	PUNCT
cana-2411	398	6	mullor	mullor	NOUN
cana-2411	398	7	,	,	PUNCT
cana-2411	398	8	j.	j.	PROPN
cana-2411	398	9	&	&	CCONJ
cana-2411	398	10	salas	salas	PROPN
cana-2411	398	11	-	-	PUNCT
cana-2411	398	12	molina	molina	PROPN
cana-2411	398	13	,	,	PUNCT
cana-2411	398	14	f.	f.	PROPN
cana-2411	398	15	,	,	PUNCT
cana-2411	398	16	non	non	ADJ
cana-2411	398	17	-	-	ADJ
cana-2411	398	18	linear	linear	ADJ
cana-2411	398	19	neutrosophic	neutrosophic	ADJ
cana-2411	398	20	numbers	number	NOUN
cana-2411	398	21	and	and	CCONJ
cana-2411	398	22	its	its	PRON
cana-2411	398	23	application	application	NOUN
cana-2411	398	24	to	to	ADP
cana-2411	398	25	multiple	multiple	ADJ
cana-2411	398	26	criteria	criterion	NOUN
cana-2411	398	27	performance	performance	NOUN
cana-2411	398	28	assessment	assessment	NOUN
cana-2411	398	29	,	,	PUNCT
cana-2411	398	30	international	international	ADJ
cana-2411	398	31	journal	journal	NOUN
cana-2411	398	32	of	of	ADP
cana-2411	398	33	fuzzy	fuzzy	ADJ
cana-2411	398	34	systems	system	NOUN
cana-2411	398	35	,	,	PUNCT
cana-2411	398	36	(	(	PUNCT
cana-2411	398	37	2022	2022	NUM
cana-2411	398	38	)	)	PUNCT
cana-2411	398	39	,	,	PUNCT
cana-2411	398	40	24	24	NUM
cana-2411	398	41	,	,	PUNCT
cana-2411	398	42	2889	2889	NUM
cana-2411	398	43	-	-	SYM
cana-2411	398	44	2904	2904	NUM
cana-2411	398	45	,	,	PUNCT
cana-2411	398	46	doi:10.1007	doi:10.1007	NOUN
cana-2411	398	47	/	/	SYM
cana-2411	398	48	s40815	s40815	NUM
cana-2411	398	49	-	-	PUNCT
cana-2411	398	50	02201295	02201295	NUM
cana-2411	398	51	-	-	PUNCT
cana-2411	398	52	y.	y.	NOUN
cana-2411	398	53	[	[	X
cana-2411	398	54	19	19	NUM
cana-2411	398	55	]	]	PUNCT
cana-2411	398	56	seikh	seikh	NOUN
cana-2411	398	57	,	,	PUNCT
cana-2411	398	58	mijanur	mijanur	NOUN
cana-2411	398	59	rahaman	rahaman	NOUN
cana-2411	398	60	&	&	CCONJ
cana-2411	398	61	shibaji	shibaji	PROPN
cana-2411	398	62	dutta	dutta	PROPN
cana-2411	398	63	,	,	PUNCT
cana-2411	398	64	a	a	DET
cana-2411	398	65	nonlinear	nonlinear	ADJ
cana-2411	398	66	programming	programming	NOUN
cana-2411	398	67	model	model	NOUN
cana-2411	398	68	to	to	PART
cana-2411	398	69	solve	solve	VERB
cana-2411	398	70	matrix	matrix	NOUN
cana-2411	398	71	games	game	NOUN
cana-2411	398	72	with	with	ADP
cana-2411	398	73	pay	pay	NOUN
cana-2411	398	74	-	-	PUNCT
cana-2411	398	75	offs	off	NOUN
cana-2411	398	76	of	of	ADP
cana-2411	398	77	single	single	ADV
cana-2411	398	78	-	-	PUNCT
cana-2411	398	79	valued	value	VERB
cana-2411	398	80	neutrosophic	neutrosophic	ADJ
cana-2411	398	81	numbers	number	NOUN
cana-2411	398	82	,	,	PUNCT
cana-2411	398	83	neutrosophic	neutrosophic	ADJ
cana-2411	398	84	sets	set	NOUN
cana-2411	398	85	and	and	CCONJ
cana-2411	398	86	systems	system	NOUN
cana-2411	398	87	,	,	PUNCT
cana-2411	398	88	(	(	PUNCT
cana-2411	398	89	2021	2021	NUM
cana-2411	398	90	)	)	PUNCT
cana-2411	398	91	,	,	PUNCT
cana-2411	398	92	47	47	NUM
cana-2411	398	93	,	,	PUNCT
cana-2411	398	94	1	1	NUM
cana-2411	398	95	,	,	PUNCT
cana-2411	398	96	https://digitalrepository.unm.edu/nss-journal/vol47/iss1/24	https://digitalrepository.unm.edu/nss-journal/vol47/iss1/24	NOUN
cana-2411	398	97	.	.	PUNCT
cana-2411	399	1	https://doi.org/10.29020/nybg.ejpam.v15i4.4538	https://doi.org/10.29020/nybg.ejpam.v15i4.4538	SYM
cana-2411	399	2	https://doi.org/10.1007/978-3-031-08720-2_3	https://doi.org/10.1007/978-3-031-08720-2_3	NOUN
cana-2411	399	3	https://doi.org/10.1007/s10700-022-09381-4	https://doi.org/10.1007/s10700-022-09381-4	NUM
cana-2411	399	4	https://doi.org/10.1287/mnsc.17.4.b141	https://doi.org/10.1287/mnsc.17.4.b141	NOUN
cana-2411	399	5	https://doi.org/10.1051/ro/2022109	https://doi.org/10.1051/ro/2022109	ADJ
cana-2411	399	6	https://doi.org/10.3390/math10101743	https://doi.org/10.3390/math10101743	NOUN
cana-2411	399	7	https://doi.org/10.61356/j.nswa.2023.11	https://doi.org/10.61356/j.nswa.2023.11	ADJ
cana-2411	399	8	https://doi.org/10.1016/s0165-0114(97)00310-2	https://doi.org/10.1016/s0165-0114(97)00310-2	NOUN
cana-2411	399	9	https://digitalrepository.unm.edu/nss-journal/vol47/iss1/24	https://digitalrepository.unm.edu/nss-journal/vol47/iss1/24	VERB
cana-2411	399	10	communications	communication	NOUN
cana-2411	399	11	on	on	ADP
cana-2411	399	12	applied	apply	VERB
cana-2411	399	13	nonlinear	nonlinear	ADJ
cana-2411	399	14	analysis	analysis	NOUN
cana-2411	399	15	issn	issn	NOUN
cana-2411	399	16	:	:	PUNCT
cana-2411	399	17	1074	1074	NUM
cana-2411	399	18	-	-	PUNCT
cana-2411	399	19	133x	133x	NUM
cana-2411	399	20	vol	vol	NOUN
cana-2411	399	21	32	32	NUM
cana-2411	399	22	no	no	NOUN
cana-2411	399	23	.	.	PUNCT
cana-2411	400	1	2s	2s	NUM
cana-2411	400	2	(	(	PUNCT
cana-2411	400	3	2025	2025	NUM
cana-2411	400	4	)	)	PUNCT
cana-2411	400	5	385	385	NUM
cana-2411	400	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2411	401	1	[	[	X
cana-2411	401	2	20	20	NUM
cana-2411	401	3	]	]	PUNCT
cana-2411	401	4	s.	s.	PROPN
cana-2411	401	5	shilpa	shilpa	PROPN
cana-2411	401	6	ivin	ivin	PROPN
cana-2411	401	7	emimal	emimal	PROPN
cana-2411	401	8	,	,	PUNCT
cana-2411	401	9	r.	r.	PROPN
cana-2411	401	10	irene	irene	PROPN
cana-2411	401	11	hepzibah	hepzibah	PROPN
cana-2411	401	12	,	,	PUNCT
cana-2411	401	13	solving	solve	VERB
cana-2411	401	14	intuitionistic	intuitionistic	ADJ
cana-2411	401	15	fuzzy	fuzzy	ADJ
cana-2411	401	16	unconstrained	unconstrained	ADJ
cana-2411	401	17	optimization	optimization	NOUN
cana-2411	401	18	problems	problem	NOUN
cana-2411	401	19	using	use	VERB
cana-2411	401	20	interval	interval	PROPN
cana-2411	401	21	newton	newton	PROPN
cana-2411	401	22	’s	’s	PART
cana-2411	401	23	method	method	NOUN
cana-2411	401	24	,	,	PUNCT
cana-2411	401	25	communications	communication	NOUN
cana-2411	401	26	on	on	ADP
cana-2411	401	27	applied	apply	VERB
cana-2411	401	28	nonlinear	nonlinear	ADJ
cana-2411	401	29	analysis	analysis	NOUN
cana-2411	401	30	,	,	PUNCT
cana-2411	401	31	(	(	PUNCT
cana-2411	401	32	2024	2024	NUM
cana-2411	401	33	)	)	PUNCT
cana-2411	401	34	,	,	PUNCT
cana-2411	401	35	31	31	NUM
cana-2411	401	36	(	(	PUNCT
cana-2411	401	37	4s	4s	NUM
cana-2411	401	38	)	)	PUNCT
cana-2411	401	39	,	,	PUNCT
cana-2411	401	40	366	366	NUM
cana-2411	401	41	-	-	SYM
cana-2411	401	42	383	383	NUM
cana-2411	401	43	.	.	PUNCT
cana-2411	402	1	https://doi.org/10.52783/cana.v31.835	https://doi.org/10.52783/cana.v31.835	VERB
cana-2411	402	2	[	[	PUNCT
cana-2411	402	3	21	21	NUM
cana-2411	402	4	]	]	X
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cana-2411	402	6	,	,	PUNCT
cana-2411	402	7	f.	f.	PROPN
cana-2411	402	8	,	,	PUNCT
cana-2411	402	9	neutrosophy	neutrosophy	NOUN
cana-2411	402	10	:	:	PUNCT
cana-2411	402	11	neutrosophic	neutrosophic	ADJ
cana-2411	402	12	probability	probability	NOUN
cana-2411	402	13	set	set	NOUN
cana-2411	402	14	and	and	CCONJ
cana-2411	402	15	logic	logic	NOUN
cana-2411	402	16	,	,	PUNCT
cana-2411	402	17	rehoboth	rehoboth	PROPN
cana-2411	402	18	:	:	PUNCT
cana-2411	402	19	american	american	PROPN
cana-2411	402	20	research	research	PROPN
cana-2411	402	21	press	press	PROPN
cana-2411	402	22	,	,	PUNCT
cana-2411	402	23	(	(	PUNCT
cana-2411	402	24	1998	1998	NUM
cana-2411	402	25	)	)	PUNCT
cana-2411	402	26	.	.	PUNCT
cana-2411	403	1	[	[	X
cana-2411	403	2	22	22	NUM
cana-2411	403	3	]	]	X
cana-2411	403	4	sujit	sujit	PROPN
cana-2411	403	5	,	,	PUNCT
cana-2411	403	6	d.	d.	PROPN
cana-2411	403	7	,	,	PUNCT
cana-2411	403	8	bikash	bikash	PROPN
cana-2411	403	9	,	,	PUNCT
cana-2411	403	10	k.r	k.r	PROPN
cana-2411	403	11	.	.	PROPN
cana-2411	403	12	,	,	PUNCT
cana-2411	403	13	mohuya	mohuya	PROPN
cana-2411	403	14	,	,	PUNCT
cana-2411	403	15	b.k	b.k	PROPN
cana-2411	403	16	.	.	PROPN
cana-2411	403	17	,	,	PUNCT
cana-2411	403	18	samarjit	samarjit	PROPN
cana-2411	403	19	,	,	PUNCT
cana-2411	403	20	k.	k.	PROPN
cana-2411	403	21	&	&	CCONJ
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cana-2411	403	25	,	,	PUNCT
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cana-2411	403	28	set	set	NOUN
cana-2411	403	29	and	and	CCONJ
cana-2411	403	30	its	its	PRON
cana-2411	403	31	application	application	NOUN
cana-2411	403	32	in	in	ADP
cana-2411	403	33	decision	decision	NOUN
cana-2411	403	34	making	making	NOUN
cana-2411	403	35	,	,	PUNCT
cana-2411	403	36	journal	journal	NOUN
cana-2411	403	37	of	of	ADP
cana-2411	403	38	ambient	ambient	ADJ
cana-2411	403	39	intelligence	intelligence	NOUN
cana-2411	403	40	and	and	CCONJ
cana-2411	403	41	humanized	humanize	VERB
cana-2411	403	42	computing,(2020),11(3	computing,(2020),11(3	NUM
cana-2411	403	43	)	)	PUNCT
cana-2411	403	44	,	,	PUNCT
cana-2411	403	45	5017	5017	NUM
cana-2411	403	46	–	–	PUNCT
cana-2411	403	47	5029	5029	NUM
cana-2411	403	48	.	.	PUNCT
cana-2411	404	1	https://doi.org/10.1007/s12652-020-01808-3	https://doi.org/10.1007/s12652-020-01808-3	PROPN
cana-2411	404	2	.	.	PUNCT
cana-2411	405	1	[	[	X
cana-2411	405	2	23	23	NUM
cana-2411	405	3	]	]	PUNCT
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cana-2411	405	5	p.	p.	PROPN
cana-2411	405	6	&	&	CCONJ
cana-2411	405	7	ganesan	ganesan	PROPN
cana-2411	405	8	k.	k.	PROPN
cana-2411	405	9	,	,	PUNCT
cana-2411	405	10	a	a	DET
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cana-2411	405	12	approach	approach	NOUN
cana-2411	405	13	for	for	ADP
cana-2411	405	14	the	the	DET
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cana-2411	405	16	of	of	ADP
cana-2411	405	17	unconstrained	unconstrained	ADJ
cana-2411	405	18	fuzzy	fuzzy	ADJ
cana-2411	405	19	optimization	optimization	NOUN
cana-2411	405	20	problems	problem	NOUN
cana-2411	405	21	,	,	PUNCT
cana-2411	405	22	aip	aip	PROPN
cana-2411	405	23	conference	conference	NOUN
cana-2411	405	24	proceedings,(2019	proceedings,(2019	NOUN
cana-2411	405	25	)	)	PUNCT
cana-2411	405	26	,	,	PUNCT
cana-2411	405	27	2112	2112	NUM
cana-2411	405	28	,	,	PUNCT
cana-2411	405	29	020004	020004	NUM
cana-2411	405	30	,	,	PUNCT
cana-2411	405	31	https://doi.org/10.1063/1.5112189	https://doi.org/10.1063/1.5112189	PROPN
cana-2411	405	32	.	.	PUNCT
cana-2411	406	1	[	[	X
cana-2411	406	2	24	24	NUM
cana-2411	406	3	]	]	SYM
cana-2411	406	4	vanaja	vanaja	NOUN
cana-2411	406	5	,	,	PUNCT
cana-2411	406	6	g.	g.	PROPN
cana-2411	406	7	,	,	PUNCT
cana-2411	406	8	ganesan	ganesan	PROPN
cana-2411	406	9	,	,	PUNCT
cana-2411	406	10	k.	k.	PROPN
cana-2411	406	11	,	,	PUNCT
cana-2411	406	12	&	&	CCONJ
cana-2411	406	13	rathour	rathour	PROPN
cana-2411	406	14	laxmi	laxmi	PROPN
cana-2411	406	15	.	.	PUNCT
cana-2411	406	16	,	,	PUNCT
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cana-2411	406	18	fuzzy	fuzzy	ADJ
cana-2411	406	19	nonlinear	nonlinear	ADJ
cana-2411	406	20	programming	programming	NOUN
cana-2411	406	21	problems	problem	NOUN
cana-2411	406	22	with	with	ADP
cana-2411	406	23	exterior	exterior	ADJ
cana-2411	406	24	penalty	penalty	NOUN
cana-2411	406	25	fuzzy	fuzzy	ADJ
cana-2411	406	26	valued	value	VERB
cana-2411	406	27	functions	function	NOUN
cana-2411	406	28	,	,	PUNCT
cana-2411	406	29	advanced	advanced	ADJ
cana-2411	406	30	mathematical	mathematical	ADJ
cana-2411	406	31	models	model	NOUN
cana-2411	406	32	&	&	CCONJ
cana-2411	406	33	applications	application	NOUN
cana-2411	406	34	,	,	PUNCT
cana-2411	406	35	(	(	PUNCT
cana-2411	406	36	2024	2024	NUM
cana-2411	406	37	)	)	PUNCT
cana-2411	406	38	,	,	PUNCT
cana-2411	406	39	9(1	9(1	NUM
cana-2411	406	40	)	)	PUNCT
cana-2411	406	41	,	,	PUNCT
cana-2411	406	42	130–146	130–146	NUM
cana-2411	406	43	.	.	PUNCT
cana-2411	406	44	https://doi.org/10.62476/amma9130	https://doi.org/10.62476/amma9130	NOUN
cana-2411	406	45	.	.	PUNCT
cana-2411	407	1	[	[	X
cana-2411	407	2	25	25	NUM
cana-2411	407	3	]	]	SYM
cana-2411	407	4	vanaja	vanaja	PROPN
cana-2411	407	5	,	,	PUNCT
cana-2411	407	6	g.	g.	PROPN
cana-2411	407	7	,	,	PUNCT
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cana-2411	407	10	k.	k.	PROPN
cana-2411	407	11	,	,	PUNCT
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cana-2411	407	22	problems	problem	NOUN
cana-2411	407	23	,	,	PUNCT
cana-2411	407	24	bulletin	bulletin	NOUN
cana-2411	407	25	of	of	ADP
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cana-2411	407	27	engineering	engineering	NOUN
cana-2411	407	28	\	\	PROPN
cana-2411	407	29	&	&	CCONJ
cana-2411	407	30	informatics	informatic	NOUN
cana-2411	407	31	,	,	PUNCT
cana-2411	407	32	(	(	PUNCT
cana-2411	407	33	2024	2024	NUM
cana-2411	407	34	)	)	PUNCT
cana-2411	407	35	,	,	PUNCT
cana-2411	407	36	13(3	13(3	NUM
cana-2411	407	37	)	)	PUNCT
cana-2411	407	38	,	,	PUNCT
cana-2411	407	39	2320	2320	NUM
cana-2411	407	40	-	-	SYM
cana-2411	407	41	2330	2330	NUM
cana-2411	407	42	,	,	PUNCT
cana-2411	407	43	doi	doi	NOUN
cana-2411	407	44	:	:	PUNCT
cana-2411	407	45	10.11591	10.11591	NUM
cana-2411	407	46	/	/	SYM
cana-2411	407	47	eei.v13i3.7047	eei.v13i3.7047	PROPN
cana-2411	407	48	.	.	PUNCT
cana-2411	408	1	[	[	X
cana-2411	408	2	26	26	NUM
cana-2411	408	3	]	]	SYM
cana-2411	408	4	ye	ye	PROPN
cana-2411	408	5	,	,	PUNCT
cana-2411	408	6	jun	jun	PROPN
cana-2411	408	7	,	,	PUNCT
cana-2411	408	8	wenhua	wenhua	PROPN
cana-2411	408	9	cui	cui	PROPN
cana-2411	408	10	,	,	PUNCT
cana-2411	408	11	&	&	CCONJ
cana-2411	408	12	zhikang	zhikang	PROPN
cana-2411	408	13	lu	lu	PROPN
cana-2411	408	14	.	.	PROPN
cana-2411	408	15	,	,	PUNCT
cana-2411	408	16	neutrosophic	neutrosophic	ADJ
cana-2411	408	17	number	number	NOUN
cana-2411	408	18	nonlinear	nonlinear	ADJ
cana-2411	408	19	programming	programming	NOUN
cana-2411	408	20	problems	problem	NOUN
cana-2411	408	21	and	and	CCONJ
cana-2411	408	22	their	their	PRON
cana-2411	408	23	general	general	ADJ
cana-2411	408	24	solution	solution	NOUN
cana-2411	408	25	methods	method	NOUN
cana-2411	408	26	under	under	ADP
cana-2411	408	27	neutrosophic	neutrosophic	ADJ
cana-2411	408	28	number	number	NOUN
cana-2411	408	29	environments	environment	NOUN
cana-2411	408	30	,	,	PUNCT
cana-2411	408	31	axioms	axiom	NOUN
cana-2411	408	32	,	,	PUNCT
cana-2411	408	33	(	(	PUNCT
cana-2411	408	34	2018	2018	NUM
cana-2411	408	35	)	)	PUNCT
cana-2411	408	36	,	,	PUNCT
cana-2411	408	37	7(1	7(1	NUM
cana-2411	408	38	)	)	PUNCT
cana-2411	408	39	,	,	PUNCT
cana-2411	408	40	13	13	NUM
cana-2411	408	41	.	.	PUNCT
cana-2411	408	42	https://doi.org/10.3390/axioms7010013	https://doi.org/10.3390/axioms7010013	VERB
cana-2411	408	43	.	.	PUNCT
cana-2411	409	1	[	[	X
cana-2411	409	2	27	27	NUM
cana-2411	409	3	]	]	X
cana-2411	409	4	zadeh	zadeh	PROPN
cana-2411	409	5	,	,	PUNCT
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cana-2411	409	7	.	.	PROPN
cana-2411	409	8	,	,	PUNCT
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cana-2411	409	10	sets	set	NOUN
cana-2411	409	11	,	,	PUNCT
cana-2411	409	12	information	information	NOUN
cana-2411	409	13	and	and	CCONJ
cana-2411	409	14	control	control	NOUN
cana-2411	409	15	,	,	PUNCT
cana-2411	409	16	(	(	PUNCT
cana-2411	409	17	1965	1965	NUM
cana-2411	409	18	)	)	PUNCT
cana-2411	409	19	8(3	8(3	NUM
cana-2411	409	20	)	)	PUNCT
cana-2411	409	21	,	,	PUNCT
cana-2411	409	22	338	338	NUM
cana-2411	409	23	-	-	SYM
cana-2411	409	24	353	353	NUM
cana-2411	409	25	,	,	PUNCT
cana-2411	409	26	https://doi.org/10.1016/	https://doi.org/10.1016/	PROPN
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cana-2411	409	28	-	-	PUNCT
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