id	sid	tid	token	lemma	pos
cana-2861	1	1	communications	communication	NOUN
cana-2861	1	2	on	on	ADP
cana-2861	1	3	applied	apply	VERB
cana-2861	1	4	nonlinear	nonlinear	ADJ
cana-2861	1	5	analysis	analysis	NOUN
cana-2861	1	6	issn	issn	NOUN
cana-2861	1	7	:	:	PUNCT
cana-2861	1	8	1074	1074	NUM
cana-2861	1	9	-	-	PUNCT
cana-2861	1	10	133x	133x	NUM
cana-2861	1	11	vol	vol	NOUN
cana-2861	1	12	32	32	NUM
cana-2861	1	13	no	no	NOUN
cana-2861	1	14	.	.	PUNCT
cana-2861	2	1	4s	4s	NUM
cana-2861	2	2	(	(	PUNCT
cana-2861	2	3	2025	2025	NUM
cana-2861	2	4	)	)	PUNCT
cana-2861	2	5	421	421	NUM
cana-2861	3	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-2861	3	2	new	new	ADJ
cana-2861	3	3	operators	operator	NOUN
cana-2861	3	4	using	use	VERB
cana-2861	3	5	β	β	NOUN
cana-2861	3	6	-	-	ADJ
cana-2861	3	7	open	open	ADJ
cana-2861	3	8	sets	set	NOUN
cana-2861	3	9	in	in	ADP
cana-2861	3	10	a	a	DET
cana-2861	3	11	quadripartitioned	quadripartitione	VERB
cana-2861	3	12	neutrosophic	neutrosophic	ADJ
cana-2861	3	13	topological	topological	ADJ
cana-2861	3	14	spaces	space	NOUN
cana-2861	3	15	1mohanarao	1mohanarao	NUM
cana-2861	3	16	navuluri	navuluri	PROPN
cana-2861	3	17	,	,	PUNCT
cana-2861	3	18	2v	2v	PROPN
cana-2861	3	19	sathishkumar	sathishkumar	PROPN
cana-2861	3	20	1department	1department	PROPN
cana-2861	3	21	of	of	ADP
cana-2861	3	22	mathematics	mathematics	PROPN
cana-2861	3	23	,	,	PUNCT
cana-2861	3	24	annamalai	annamalai	PROPN
cana-2861	3	25	university	university	PROPN
cana-2861	3	26	,	,	PUNCT
cana-2861	3	27	annamalainagar	annamalainagar	NOUN
cana-2861	3	28	,	,	PUNCT
cana-2861	3	29	tamilnadu	tamilnadu	NOUN
cana-2861	3	30	,	,	PUNCT
cana-2861	3	31	india	india	PROPN
cana-2861	3	32	.	.	PUNCT
cana-2861	4	1	(	(	PUNCT
cana-2861	4	2	deputed	depute	VERB
cana-2861	4	3	to	to	ADP
cana-2861	4	4	government	government	NOUN
cana-2861	4	5	college	college	NOUN
cana-2861	4	6	of	of	ADP
cana-2861	4	7	engineering	engineering	NOUN
cana-2861	4	8	,	,	PUNCT
cana-2861	4	9	theni	theni	NOUN
cana-2861	4	10	,	,	PUNCT
cana-2861	4	11	tamilnadu	tamilnadu	NOUN
cana-2861	4	12	,	,	PUNCT
cana-2861	4	13	india	india	PROPN
cana-2861	4	14	.	.	PUNCT
cana-2861	4	15	)	)	PUNCT
cana-2861	5	1	2department	2department	NUM
cana-2861	5	2	of	of	ADP
cana-2861	5	3	mathematics	mathematic	NOUN
cana-2861	5	4	,	,	PUNCT
cana-2861	5	5	rajalakshmi	rajalakshmi	PROPN
cana-2861	5	6	institute	institute	PROPN
cana-2861	5	7	of	of	ADP
cana-2861	5	8	technology	technology	PROPN
cana-2861	5	9	(	(	PUNCT
cana-2861	5	10	autonomous	autonomous	ADJ
cana-2861	5	11	)	)	PUNCT
cana-2861	5	12	,	,	PUNCT
cana-2861	5	13	chennai	chennai	PROPN
cana-2861	5	14	;	;	PUNCT
cana-2861	5	15	department	department	NOUN
cana-2861	5	16	of	of	ADP
cana-2861	5	17	mathematics	mathematics	PROPN
cana-2861	5	18	,	,	PUNCT
cana-2861	5	19	annamalai	annamalai	PROPN
cana-2861	5	20	university	university	PROPN
cana-2861	5	21	,	,	PUNCT
cana-2861	5	22	annamalainagar	annamalainagar	NOUN
cana-2861	5	23	,	,	PUNCT
cana-2861	5	24	tamilnadu	tamilnadu	NOUN
cana-2861	5	25	,	,	PUNCT
cana-2861	5	26	india	india	PROPN
cana-2861	5	27	.	.	PUNCT
cana-2861	6	1	mohanaraonavuluri@gmail.com1	mohanaraonavuluri@gmail.com1	PROPN
cana-2861	6	2	,	,	PUNCT
cana-2861	6	3	vsathishkumar2020@gmail.com2	vsathishkumar2020@gmail.com2	ADP
cana-2861	6	4	article	article	NOUN
cana-2861	6	5	history	history	NOUN
cana-2861	6	6	:	:	PUNCT
cana-2861	6	7	received	receive	VERB
cana-2861	6	8	:	:	PUNCT
cana-2861	6	9	27	27	NUM
cana-2861	6	10	-	-	SYM
cana-2861	6	11	09	09	NUM
cana-2861	6	12	-	-	PUNCT
cana-2861	6	13	2024	2024	NUM
cana-2861	6	14	revised	revise	VERB
cana-2861	6	15	:	:	PUNCT
cana-2861	6	16	29	29	NUM
cana-2861	6	17	-	-	SYM
cana-2861	6	18	11	11	NUM
cana-2861	6	19	-	-	PUNCT
cana-2861	6	20	2024	2024	NUM
cana-2861	6	21	accepted	accept	VERB
cana-2861	6	22	:	:	PUNCT
cana-2861	6	23	09	09	NUM
cana-2861	6	24	-	-	SYM
cana-2861	6	25	12	12	NUM
cana-2861	6	26	-	-	PUNCT
cana-2861	6	27	2024	2024	NUM
cana-2861	6	28	abstract	abstract	NOUN
cana-2861	6	29	:	:	PUNCT
cana-2861	6	30	in	in	ADP
cana-2861	6	31	this	this	DET
cana-2861	6	32	paper	paper	NOUN
cana-2861	6	33	,	,	PUNCT
cana-2861	6	34	we	we	PRON
cana-2861	6	35	introduce	introduce	VERB
cana-2861	6	36	some	some	DET
cana-2861	6	37	new	new	ADJ
cana-2861	6	38	operators	operator	NOUN
cana-2861	6	39	called	call	VERB
cana-2861	6	40	quadri	quadri	PROPN
cana-2861	6	41	partitioned	partition	VERB
cana-2861	6	42	neuromorphic	neuromorphic	ADJ
cana-2861	6	43	β	β	PROPN
cana-2861	6	44	frontier	frontier	NOUN
cana-2861	6	45	,	,	PUNCT
cana-2861	6	46	quadripartitioned	quadripartitione	VERB
cana-2861	6	47	neutrosophic	neutrosophic	PROPN
cana-2861	6	48	β	β	X
cana-2861	6	49	border	border	NOUN
cana-2861	6	50	and	and	CCONJ
cana-2861	6	51	quadri	quadri	PROPN
cana-2861	6	52	partitioned	partition	VERB
cana-2861	6	53	neuromorphic	neuromorphic	ADJ
cana-2861	6	54	β	β	X
cana-2861	6	55	exterior	exterior	NOUN
cana-2861	6	56	with	with	ADP
cana-2861	6	57	the	the	DET
cana-2861	6	58	help	help	NOUN
cana-2861	6	59	of	of	ADP
cana-2861	6	60	quadripartitioned	quadripartitione	VERB
cana-2861	6	61	neutrosophic	neutrosophic	ADJ
cana-2861	6	62	β	β	X
cana-2861	6	63	-	-	ADJ
cana-2861	6	64	open	open	ADJ
cana-2861	6	65	sets	set	NOUN
cana-2861	6	66	in	in	ADP
cana-2861	6	67	quadripartitioned	quadripartitione	VERB
cana-2861	6	68	neutrosophic	neutrosophic	PROPN
cana-2861	6	69	topological	topological	ADJ
cana-2861	6	70	space	space	NOUN
cana-2861	6	71	.	.	PUNCT
cana-2861	7	1	also	also	ADV
cana-2861	7	2	,	,	PUNCT
cana-2861	7	3	we	we	PRON
cana-2861	7	4	discuss	discuss	VERB
cana-2861	7	5	the	the	DET
cana-2861	7	6	important	important	ADJ
cana-2861	7	7	properties	property	NOUN
cana-2861	7	8	of	of	ADP
cana-2861	7	9	them	they	PRON
cana-2861	7	10	and	and	CCONJ
cana-2861	7	11	the	the	DET
cana-2861	7	12	relations	relation	NOUN
cana-2861	7	13	between	between	ADP
cana-2861	7	14	them	they	PRON
cana-2861	7	15	.	.	PUNCT
cana-2861	8	1	keywords	keyword	NOUN
cana-2861	8	2	:	:	PUNCT
cana-2861	8	3	quadri	quadri	PROPN
cana-2861	8	4	partitioned	partition	VERB
cana-2861	8	5	neutrosophic	neutrosophic	ADJ
cana-2861	8	6	β	β	X
cana-2861	8	7	-	-	ADJ
cana-2861	8	8	open	open	ADJ
cana-2861	8	9	,	,	PUNCT
cana-2861	8	10	quadri	quadri	PROPN
cana-2861	8	11	partitioned	partition	VERB
cana-2861	8	12	neutrosophic	neutrosophic	PROPN
cana-2861	8	13	β	β	PROPN
cana-2861	8	14	frontier	frontier	NOUN
cana-2861	8	15	,	,	PUNCT
cana-2861	8	16	quadripartitioned	quadripartitione	VERB
cana-2861	8	17	neuromorphic	neuromorphic	ADJ
cana-2861	8	18	β	β	X
cana-2861	8	19	border	border	NOUN
cana-2861	8	20	,	,	PUNCT
cana-2861	8	21	quadripartitioned	quadripartitione	VERB
cana-2861	8	22	neutrosophic	neutrosophic	ADJ
cana-2861	8	23	β	β	X
cana-2861	8	24	exterior	exterior	NOUN
cana-2861	8	25	.	.	PUNCT
cana-2861	9	1	1	1	X
cana-2861	9	2	.	.	X
cana-2861	9	3	introduction	introduction	NOUN
cana-2861	9	4	in	in	ADP
cana-2861	9	5	mathematics	mathematic	NOUN
cana-2861	9	6	,	,	PUNCT
cana-2861	9	7	zadeh26	zadeh26	X
cana-2861	9	8	was	be	AUX
cana-2861	9	9	first	first	ADV
cana-2861	9	10	presented	present	VERB
cana-2861	9	11	a	a	DET
cana-2861	9	12	idea	idea	NOUN
cana-2861	9	13	of	of	ADP
cana-2861	9	14	fuzzy	fuzzy	ADJ
cana-2861	9	15	set	set	NOUN
cana-2861	9	16	between	between	ADP
cana-2861	9	17	the	the	DET
cana-2861	9	18	intervals	interval	NOUN
cana-2861	9	19	in	in	ADP
cana-2861	9	20	order	order	NOUN
cana-2861	9	21	of	of	ADP
cana-2861	9	22	logic	logic	NOUN
cana-2861	9	23	and	and	CCONJ
cana-2861	9	24	set	set	VERB
cana-2861	9	25	hypothesis	hypothesis	NOUN
cana-2861	9	26	.	.	PUNCT
cana-2861	10	1	the	the	DET
cana-2861	10	2	fuzzy	fuzzy	ADJ
cana-2861	10	3	set	set	NOUN
cana-2861	10	4	was	be	AUX
cana-2861	10	5	attempted	attempt	VERB
cana-2861	10	6	in	in	ADP
cana-2861	10	7	general	general	ADJ
cana-2861	10	8	topology	topology	NOUN
cana-2861	10	9	by	by	ADP
cana-2861	10	10	chang2	chang2	NOUN
cana-2861	10	11	as	as	ADP
cana-2861	10	12	fuzzy	fuzzy	ADJ
cana-2861	10	13	topological	topological	ADJ
cana-2861	10	14	space	space	NOUN
cana-2861	10	15	.	.	PUNCT
cana-2861	11	1	the	the	DET
cana-2861	11	2	intuitionistic	intuitionistic	ADJ
cana-2861	11	3	fuzzy	fuzzy	ADJ
cana-2861	11	4	set	set	NOUN
cana-2861	11	5	which	which	PRON
cana-2861	11	6	contains	contain	VERB
cana-2861	11	7	a	a	DET
cana-2861	11	8	membership	membership	NOUN
cana-2861	11	9	and	and	CCONJ
cana-2861	11	10	non	non	ADJ
cana-2861	11	11	-	-	ADJ
cana-2861	11	12	membership	membership	ADJ
cana-2861	11	13	values	value	NOUN
cana-2861	11	14	was	be	AUX
cana-2861	11	15	introduced	introduce	VERB
cana-2861	11	16	by	by	ADP
cana-2861	11	17	atanassov1	atanassov1	NOUN
cana-2861	11	18	in	in	ADP
cana-2861	11	19	1983	1983	NUM
cana-2861	11	20	.	.	PUNCT
cana-2861	12	1	coker4	coker4	PROPN
cana-2861	12	2	made	make	VERB
cana-2861	12	3	intuitionistic	intuitionistic	ADJ
cana-2861	12	4	fuzzy	fuzzy	ADJ
cana-2861	12	5	set	set	NOUN
cana-2861	12	6	in	in	ADP
cana-2861	12	7	a	a	DET
cana-2861	12	8	topology	topology	NOUN
cana-2861	12	9	entitled	entitle	VERB
cana-2861	12	10	as	as	ADP
cana-2861	12	11	intuitionistic	intuitionistic	ADJ
cana-2861	12	12	fuzzy	fuzzy	ADJ
cana-2861	12	13	topological	topological	ADJ
cana-2861	12	14	spaces	space	NOUN
cana-2861	12	15	.	.	PUNCT
cana-2861	13	1	the	the	DET
cana-2861	13	2	ideas	idea	NOUN
cana-2861	13	3	of	of	ADP
cana-2861	13	4	neutrosophy	neutrosophy	NOUN
cana-2861	13	5	and	and	CCONJ
cana-2861	13	6	neutrosophic	neutrosophic	ADJ
cana-2861	13	7	set	set	NOUN
cana-2861	13	8	was	be	AUX
cana-2861	13	9	presented	present	VERB
cana-2861	13	10	by	by	ADP
cana-2861	13	11	smarandache16,17	smarandache16,17	NOUN
cana-2861	13	12	toward	toward	ADP
cana-2861	13	13	the	the	DET
cana-2861	13	14	start	start	NOUN
cana-2861	13	15	of	of	ADP
cana-2861	13	16	20th	20th	ADJ
cana-2861	13	17	century	century	NOUN
cana-2861	13	18	.	.	PUNCT
cana-2861	14	1	salama	salama	NOUN
cana-2861	14	2	and	and	CCONJ
cana-2861	14	3	alblowi14,15	alblowi14,15	ADJ
cana-2861	14	4	in	in	ADP
cana-2861	14	5	2012	2012	NUM
cana-2861	14	6	,	,	PUNCT
cana-2861	14	7	originated	originate	VERB
cana-2861	14	8	neutrosophic	neutrosophic	ADJ
cana-2861	14	9	set	set	NOUN
cana-2861	14	10	and	and	CCONJ
cana-2861	14	11	neutrosophic	neutrosophic	ADJ
cana-2861	14	12	crisp	crisp	ADJ
cana-2861	14	13	set	set	NOUN
cana-2861	14	14	in	in	ADP
cana-2861	14	15	a	a	DET
cana-2861	14	16	neutrosophic	neutrosophic	ADJ
cana-2861	14	17	topological	topological	ADJ
cana-2861	14	18	space	space	NOUN
cana-2861	14	19	.	.	PUNCT
cana-2861	15	1	in	in	ADP
cana-2861	15	2	the	the	DET
cana-2861	15	3	year	year	NOUN
cana-2861	15	4	2016	2016	NUM
cana-2861	15	5	,	,	PUNCT
cana-2861	15	6	chatterjee	chatterjee	PROPN
cana-2861	15	7	et	et	NOUN
cana-2861	15	8	al.3	al.3	PROPN
cana-2861	15	9	grounded	ground	VERB
cana-2861	15	10	the	the	DET
cana-2861	15	11	idea	idea	NOUN
cana-2861	15	12	of	of	ADP
cana-2861	15	13	quadripartitioned	quadripartitione	VERB
cana-2861	15	14	neutrosophic	neutrosophic	ADJ
cana-2861	15	15	set	set	VERB
cana-2861	15	16	and	and	CCONJ
cana-2861	15	17	defined	define	VERB
cana-2861	15	18	several	several	ADJ
cana-2861	15	19	similarity	similarity	NOUN
cana-2861	15	20	measures	measure	NOUN
cana-2861	15	21	between	between	ADP
cana-2861	15	22	two	two	NUM
cana-2861	15	23	quadripartitioned	quadripartitione	VERB
cana-2861	15	24	neutrosophic	neutrosophic	ADJ
cana-2861	15	25	sets	set	NOUN
cana-2861	15	26	.	.	PUNCT
cana-2861	16	1	iswaraya	iswaraya	NOUN
cana-2861	16	2	and	and	CCONJ
cana-2861	16	3	bageerathi9	bageerathi9	PROPN
cana-2861	16	4	studied	study	VERB
cana-2861	16	5	the	the	DET
cana-2861	16	6	concept	concept	NOUN
cana-2861	16	7	of	of	ADP
cana-2861	16	8	neutrosophic	neutrosophic	ADJ
cana-2861	16	9	semi	semi	ADJ
cana-2861	16	10	-	-	ADJ
cana-2861	16	11	open	open	ADJ
cana-2861	16	12	sets	set	NOUN
cana-2861	16	13	and	and	CCONJ
cana-2861	16	14	neutrosophic	neutrosophic	ADJ
cana-2861	16	15	semi	semi	ADJ
cana-2861	16	16	-	-	ADJ
cana-2861	16	17	closed	closed	ADJ
cana-2861	16	18	sets	set	NOUN
cana-2861	16	19	.	.	PUNCT
cana-2861	17	1	pushpalatha	pushpalatha	NOUN
cana-2861	17	2	and	and	CCONJ
cana-2861	17	3	nandhini12grounded	nandhini12grounde	VERB
cana-2861	17	4	the	the	DET
cana-2861	17	5	idea	idea	NOUN
cana-2861	17	6	of	of	ADP
cana-2861	17	7	neutrosophic	neutrosophic	ADJ
cana-2861	17	8	generalized	generalize	VERB
cana-2861	17	9	closed	close	VERB
cana-2861	17	10	sets	set	NOUN
cana-2861	17	11	in	in	ADP
cana-2861	17	12	nts	nt	NOUN
cana-2861	17	13	’s	’s	PART
cana-2861	17	14	.	.	PUNCT
cana-2861	18	1	the	the	DET
cana-2861	18	2	notion	notion	NOUN
cana-2861	18	3	of	of	ADP
cana-2861	18	4	neutrosophic	neutrosophic	ADJ
cana-2861	18	5	b	b	X
cana-2861	18	6	-	-	PUNCT
cana-2861	18	7	open	open	ADJ
cana-2861	18	8	sets	set	NOUN
cana-2861	18	9	in	in	ADP
cana-2861	18	10	nts	nt	NOUN
cana-2861	18	11	’s	’s	PART
cana-2861	18	12	was	be	AUX
cana-2861	18	13	presented	present	VERB
cana-2861	18	14	by	by	ADP
cana-2861	18	15	ebenanjar	ebenanjar	PROPN
cana-2861	18	16	et	et	PROPN
cana-2861	18	17	al.8	al.8	PROPN
cana-2861	18	18	rao	rao	PROPN
cana-2861	18	19	and	and	CCONJ
cana-2861	18	20	srinivasa13	srinivasa13	NOUN
cana-2861	18	21	grounded	ground	VERB
cana-2861	18	22	the	the	DET
cana-2861	18	23	concept	concept	NOUN
cana-2861	18	24	of	of	ADP
cana-2861	18	25	pre	pre	ADJ
cana-2861	18	26	-	-	ADJ
cana-2861	18	27	open	open	ADJ
cana-2861	18	28	set	set	NOUN
cana-2861	18	29	and	and	CCONJ
cana-2861	18	30	pre	pre	VERB
cana-2861	18	31	closed	closed	ADJ
cana-2861	18	32	set	set	VERB
cana-2861	18	33	via	via	ADP
cana-2861	18	34	neutrosophic	neutrosophic	ADJ
cana-2861	18	35	topological	topological	ADJ
cana-2861	18	36	spaces	space	NOUN
cana-2861	18	37	.	.	PUNCT
cana-2861	19	1	thereafter	thereafter	ADV
cana-2861	19	2	,	,	PUNCT
cana-2861	19	3	maheswari	maheswari	PROPN
cana-2861	19	4	et	et	PROPN
cana-2861	19	5	al.10	al.10	PROPN
cana-2861	19	6	studied	study	VERB
cana-2861	19	7	the	the	DET
cana-2861	19	8	neutrosophic	neutrosophic	ADJ
cana-2861	19	9	generalized	generalized	ADJ
cana-2861	19	10	b	b	X
cana-2861	19	11	-	-	PUNCT
cana-2861	19	12	closed	closed	ADJ
cana-2861	19	13	sets	set	NOUN
cana-2861	19	14	in	in	ADP
cana-2861	19	15	nts	nt	NOUN
cana-2861	19	16	’s	’s	PART
cana-2861	19	17	.	.	PUNCT
cana-2861	20	1	in	in	ADP
cana-2861	20	2	the	the	DET
cana-2861	20	3	year	year	NOUN
cana-2861	20	4	2019	2019	NUM
cana-2861	20	5	,	,	PUNCT
cana-2861	20	6	mohammed	mohammed	PROPN
cana-2861	20	7	ali	ali	PROPN
cana-2861	20	8	jaffer	jaffer	PROPN
cana-2861	20	9	and	and	CCONJ
cana-2861	20	10	ramesh11	ramesh11	PROPN
cana-2861	20	11	studied	study	VERB
cana-2861	20	12	the	the	DET
cana-2861	20	13	concept	concept	NOUN
cana-2861	20	14	of	of	ADP
cana-2861	20	15	neutrosophic	neutrosophic	ADJ
cana-2861	20	16	generalized	generalized	ADJ
cana-2861	20	17	pre	pre	ADJ
cana-2861	20	18	-	-	ADJ
cana-2861	20	19	regular	regular	ADJ
cana-2861	20	20	closed	closed	ADJ
cana-2861	20	21	sets	set	NOUN
cana-2861	20	22	.	.	PUNCT
cana-2861	21	1	the	the	DET
cana-2861	21	2	generalized	generalize	VERB
cana-2861	21	3	neutrosophic	neutrosophic	ADJ
cana-2861	21	4	b	b	X
cana-2861	21	5	-	-	PUNCT
cana-2861	21	6	open	open	ADJ
cana-2861	21	7	sets	set	NOUN
cana-2861	21	8	in	in	ADP
cana-2861	21	9	nts	nt	NOUN
cana-2861	21	10	’s	’s	PART
cana-2861	21	11	was	be	AUX
cana-2861	21	12	introduced	introduce	VERB
cana-2861	21	13	by	by	ADP
cana-2861	21	14	das	das	PROPN
cana-2861	21	15	and	and	CCONJ
cana-2861	21	16	pramanik.6	pramanik.6	PROPN
cana-2861	21	17	das	das	PROPN
cana-2861	21	18	and	and	CCONJ
cana-2861	21	19	pramanik7	pramanik7	NOUN
cana-2861	21	20	also	also	ADV
cana-2861	21	21	defined	define	VERB
cana-2861	21	22	the	the	DET
cana-2861	21	23	neutrosophic	neutrosophic	ADJ
cana-2861	21	24	φ	φ	VERB
cana-2861	21	25	-	-	ADJ
cana-2861	21	26	open	open	ADJ
cana-2861	21	27	sets	set	NOUN
cana-2861	21	28	and	and	CCONJ
cana-2861	21	29	neutrosophic	neutrosophic	ADJ
cana-2861	21	30	φcontinuous	φcontinuous	ADJ
cana-2861	21	31	mappings	mapping	NOUN
cana-2861	21	32	via	via	ADP
cana-2861	21	33	nts	nt	NOUN
cana-2861	21	34	’s	’s	PART
cana-2861	21	35	.	.	PUNCT
cana-2861	22	1	vadivel	vadivel	VERB
cana-2861	22	2	and	and	CCONJ
cana-2861	22	3	sundar	sundar	NOUN
cana-2861	22	4	defined	define	VERB
cana-2861	22	5	γ	γ	X
cana-2861	22	6	open	open	ADJ
cana-2861	22	7	sets,18	sets,18	PROPN
cana-2861	22	8	γ	γ	PROPN
cana-2861	22	9	continuous	continuous	ADJ
cana-2861	22	10	maps,21,22	maps,21,22	PRON
cana-2861	22	11	βopen	βopen	ADJ
cana-2861	22	12	sets19	sets19	NOUN
cana-2861	22	13	and	and	CCONJ
cana-2861	22	14	β	β	X
cana-2861	22	15	continuous	continuous	ADJ
cana-2861	22	16	maps23–25	maps23–25	NOUN
cana-2861	22	17	in	in	ADP
cana-2861	22	18	n	n	CCONJ
cana-2861	22	19	-neutrosophic	-neutrosophic	ADJ
cana-2861	22	20	crisp	crisp	ADJ
cana-2861	22	21	topological	topological	ADJ
cana-2861	22	22	spaces	space	NOUN
cana-2861	22	23	and	and	CCONJ
cana-2861	22	24	defined	define	VERB
cana-2861	22	25	some	some	DET
cana-2861	22	26	operators20	operators20	ADJ
cana-2861	22	27	in	in	ADP
cana-2861	22	28	nts	nt	NOUN
cana-2861	22	29	’s	’s	PART
cana-2861	22	30	.	.	PUNCT
cana-2861	23	1	mailto	mailto	PROPN
cana-2861	23	2	:	:	PUNCT
cana-2861	23	3	mohanaraonavuluri@gmail.com1	mohanaraonavuluri@gmail.com1	PROPN
cana-2861	23	4	mailto	mailto	PROPN
cana-2861	23	5	:	:	PUNCT
cana-2861	23	6	mohanaraonavuluri@gmail.com1	mohanaraonavuluri@gmail.com1	PROPN
cana-2861	23	7	mailto	mailto	PROPN
cana-2861	23	8	:	:	PUNCT
cana-2861	23	9	vsathishkumar2020@gmail.com2	vsathishkumar2020@gmail.com2	ADP
cana-2861	23	10	communications	communication	NOUN
cana-2861	23	11	on	on	ADP
cana-2861	23	12	applied	apply	VERB
cana-2861	23	13	nonlinear	nonlinear	ADJ
cana-2861	23	14	analysis	analysis	NOUN
cana-2861	23	15	issn	issn	NOUN
cana-2861	23	16	:	:	PUNCT
cana-2861	23	17	1074	1074	NUM
cana-2861	23	18	-	-	PUNCT
cana-2861	23	19	133x	133x	NUM
cana-2861	23	20	vol	vol	NOUN
cana-2861	23	21	32	32	NUM
cana-2861	23	22	no	no	NOUN
cana-2861	23	23	.	.	PUNCT
cana-2861	24	1	4s	4s	NUM
cana-2861	24	2	(	(	PUNCT
cana-2861	24	3	2025	2025	NUM
cana-2861	24	4	)	)	PUNCT
cana-2861	24	5	422	422	NUM
cana-2861	24	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2861	24	7	∪	∪	PROPN
cana-2861	24	8	∈	∈	PROPN
cana-2861	24	9	∩	∩	NOUN
cana-2861	24	10	in	in	ADP
cana-2861	24	11	this	this	DET
cana-2861	24	12	paper	paper	NOUN
cana-2861	24	13	we	we	PRON
cana-2861	24	14	introduce	introduce	VERB
cana-2861	24	15	quadripartitioned	quadripartitione	VERB
cana-2861	24	16	neutrosophic	neutrosophic	PROPN
cana-2861	24	17	β	β	PROPN
cana-2861	24	18	frontier	frontier	NOUN
cana-2861	24	19	,	,	PUNCT
cana-2861	24	20	quadripartitioned	quadripartitione	VERB
cana-2861	24	21	neutrosophic	neutrosophic	PROPN
cana-2861	24	22	β	β	X
cana-2861	24	23	border	border	NOUN
cana-2861	24	24	and	and	CCONJ
cana-2861	24	25	quadripartitioned	quadripartitione	VERB
cana-2861	24	26	neutrosophic	neutrosophic	PROPN
cana-2861	24	27	β	β	X
cana-2861	24	28	exterior	exterior	ADJ
cana-2861	24	29	and	and	CCONJ
cana-2861	24	30	discuss	discuss	VERB
cana-2861	24	31	their	their	PRON
cana-2861	24	32	properties	property	NOUN
cana-2861	24	33	in	in	ADP
cana-2861	24	34	quadripartitioned	quadripartitione	VERB
cana-2861	24	35	neutrosophic	neutrosophic	PROPN
cana-2861	24	36	topological	topological	ADJ
cana-2861	24	37	spaces	space	NOUN
cana-2861	24	38	.	.	PUNCT
cana-2861	25	1	2	2	X
cana-2861	25	2	.	.	X
cana-2861	25	3	preliminaries	preliminary	NOUN
cana-2861	25	4	the	the	DET
cana-2861	25	5	needful	needful	ADJ
cana-2861	25	6	basic	basic	ADJ
cana-2861	25	7	definitions	definition	NOUN
cana-2861	25	8	&	&	CCONJ
cana-2861	25	9	properties	property	NOUN
cana-2861	25	10	are	be	AUX
cana-2861	25	11	discussed	discuss	VERB
cana-2861	25	12	in	in	ADP
cana-2861	25	13	this	this	DET
cana-2861	25	14	section	section	NOUN
cana-2861	25	15	.	.	PUNCT
cana-2861	26	1	definition	definition	NOUN
cana-2861	26	2	2.1	2.1	NUM
cana-2861	26	3	.	.	PUNCT
cana-2861	26	4	3	3	NUM
cana-2861	26	5	let	let	VERB
cana-2861	26	6	z	z	NOUN
cana-2861	26	7	be	be	AUX
cana-2861	26	8	a	a	DET
cana-2861	26	9	fixed	fix	VERB
cana-2861	26	10	set	set	NOUN
cana-2861	26	11	.	.	PUNCT
cana-2861	27	1	then	then	ADV
cana-2861	27	2	,	,	PUNCT
cana-2861	27	3	a	a	DET
cana-2861	27	4	quadripartitioned	quadripartitione	VERB
cana-2861	27	5	neutrosophic	neutrosophic	ADJ
cana-2861	27	6	set	set	NOUN
cana-2861	27	7	(	(	PUNCT
cana-2861	27	8	in	in	ADP
cana-2861	27	9	-	-	PUNCT
cana-2861	27	10	short	short	ADJ
cana-2861	27	11	,	,	PUNCT
cana-2861	27	12	q	q	NOUN
cana-2861	27	13	-	-	PUNCT
cana-2861	27	14	nss	nss	ADJ
cana-2861	27	15	)	)	PUNCT
cana-2861	27	16	u	u	NOUN
cana-2861	27	17	over	over	ADP
cana-2861	27	18	z	z	PROPN
cana-2861	27	19	is	be	AUX
cana-2861	27	20	defined	define	VERB
cana-2861	27	21	by	by	ADP
cana-2861	27	22	u	u	X
cana-2861	27	23	=	=	PUNCT
cana-2861	27	24	{	{	PUNCT
cana-2861	27	25	(	(	PUNCT
cana-2861	27	26	u	u	NOUN
cana-2861	27	27	,	,	PUNCT
cana-2861	27	28	tu	tu	PROPN
cana-2861	27	29	(	(	PUNCT
cana-2861	27	30	u	u	NOUN
cana-2861	27	31	)	)	PUNCT
cana-2861	27	32	,	,	PUNCT
cana-2861	27	33	cu	cu	PROPN
cana-2861	27	34	(	(	PUNCT
cana-2861	27	35	u	u	NOUN
cana-2861	27	36	)	)	PUNCT
cana-2861	27	37	,	,	PUNCT
cana-2861	27	38	iu	iu	ADP
cana-2861	27	39	(	(	PUNCT
cana-2861	27	40	u	u	NOUN
cana-2861	27	41	)	)	PUNCT
cana-2861	27	42	,	,	PUNCT
cana-2861	27	43	fu	fu	NOUN
cana-2861	27	44	(	(	PUNCT
cana-2861	27	45	u	u	NOUN
cana-2861	27	46	)	)	PUNCT
cana-2861	27	47	):	):	PUNCT
cana-2861	28	1	u	u	PROPN
cana-2861	28	2	∈	∈	PROPN
cana-2861	28	3	z	z	PROPN
cana-2861	28	4	}	}	PUNCT
cana-2861	28	5	where	where	SCONJ
cana-2861	28	6	tu	tu	PROPN
cana-2861	28	7	,	,	PUNCT
cana-2861	28	8	cu	cu	PROPN
cana-2861	28	9	,	,	PUNCT
cana-2861	28	10	iu	iu	ADP
cana-2861	28	11	and	and	CCONJ
cana-2861	28	12	fu	fu	NOUN
cana-2861	28	13	(	(	PUNCT
cana-2861	28	14	∈	∈	PROPN
cana-2861	28	15	[	[	X
cana-2861	28	16	0	0	NUM
cana-2861	28	17	,	,	PUNCT
cana-2861	28	18	1	1	NUM
cana-2861	28	19	]	]	PUNCT
cana-2861	28	20	)	)	PUNCT
cana-2861	28	21	are	be	AUX
cana-2861	28	22	the	the	DET
cana-2861	28	23	truth	truth	NOUN
cana-2861	28	24	,	,	PUNCT
cana-2861	28	25	contradiction	contradiction	NOUN
cana-2861	28	26	,	,	PUNCT
cana-2861	28	27	ignorance	ignorance	NOUN
cana-2861	28	28	,	,	PUNCT
cana-2861	28	29	and	and	CCONJ
cana-2861	28	30	falsity	falsity	NOUN
cana-2861	28	31	membership	membership	NOUN
cana-2861	28	32	values	value	NOUN
cana-2861	28	33	of	of	ADP
cana-2861	28	34	u	u	PROPN
cana-2861	28	35	∈	∈	PROPN
cana-2861	28	36	z.	z.	PROPN
cana-2861	29	1	so	so	ADV
cana-2861	29	2	,	,	PUNCT
cana-2861	29	3	0	0	NUM
cana-2861	29	4	≤	≤	PROPN
cana-2861	29	5	tu	tu	X
cana-2861	29	6	(	(	PUNCT
cana-2861	29	7	u	u	NOUN
cana-2861	29	8	)	)	PUNCT
cana-2861	29	9	+	+	CCONJ
cana-2861	29	10	cu	cu	PROPN
cana-2861	29	11	(	(	PUNCT
cana-2861	29	12	u	u	NOUN
cana-2861	29	13	)	)	PUNCT
cana-2861	29	14	+	+	CCONJ
cana-2861	29	15	iu	iu	ADP
cana-2861	29	16	(	(	PUNCT
cana-2861	29	17	u	u	NOUN
cana-2861	29	18	)	)	PUNCT
cana-2861	29	19	+	+	CCONJ
cana-2861	29	20	fu	fu	NOUN
cana-2861	29	21	(	(	PUNCT
cana-2861	29	22	u	u	NOUN
cana-2861	29	23	)	)	PUNCT
cana-2861	29	24	≤	≤	NUM
cana-2861	29	25	4	4	NUM
cana-2861	29	26	.	.	PUNCT
cana-2861	29	27	definition	definition	NOUN
cana-2861	29	28	2.2	2.2	NUM
cana-2861	29	29	.	.	NOUN
cana-2861	29	30	3	3	NUM
cana-2861	29	31	let	let	VERB
cana-2861	29	32	z	z	NOUN
cana-2861	29	33	be	be	AUX
cana-2861	29	34	a	a	DET
cana-2861	29	35	non	non	ADJ
cana-2861	29	36	-	-	ADJ
cana-2861	29	37	empty	empty	ADJ
cana-2861	29	38	set	set	NOUN
cana-2861	29	39	&	&	CCONJ
cana-2861	29	40	the	the	DET
cana-2861	29	41	q	q	NOUN
cana-2861	29	42	-	-	PUNCT
cana-2861	29	43	nss	nss	NOUN
cana-2861	29	44	’s	’s	PART
cana-2861	29	45	u	u	NOUN
cana-2861	29	46	&	&	CCONJ
cana-2861	29	47	uo	uo	NOUN
cana-2861	29	48	in	in	ADP
cana-2861	29	49	the	the	DET
cana-2861	29	50	form	form	NOUN
cana-2861	29	51	u	u	NOUN
cana-2861	29	52	=	=	X
cana-2861	29	53	{	{	PUNCT
cana-2861	29	54	(	(	PUNCT
cana-2861	29	55	u	u	NOUN
cana-2861	29	56	,	,	PUNCT
cana-2861	29	57	tu	tu	PROPN
cana-2861	29	58	(	(	PUNCT
cana-2861	29	59	u	u	NOUN
cana-2861	29	60	)	)	PUNCT
cana-2861	29	61	,	,	PUNCT
cana-2861	29	62	cu	cu	PROPN
cana-2861	29	63	(	(	PUNCT
cana-2861	29	64	u),iu	u),iu	PROPN
cana-2861	29	65	(	(	PUNCT
cana-2861	29	66	u	u	NOUN
cana-2861	29	67	)	)	PUNCT
cana-2861	29	68	,	,	PUNCT
cana-2861	29	69	fu	fu	NOUN
cana-2861	29	70	(	(	PUNCT
cana-2861	29	71	u	u	NOUN
cana-2861	29	72	)	)	PUNCT
cana-2861	29	73	)	)	PUNCT
cana-2861	29	74	:	:	PUNCT
cana-2861	30	1	u	u	PROPN
cana-2861	30	2	∈	∈	PROPN
cana-2861	30	3	z	z	PROPN
cana-2861	30	4	}	}	PUNCT
cana-2861	30	5	,	,	PUNCT
cana-2861	30	6	uo	uo	X
cana-2861	30	7	=	=	SYM
cana-2861	30	8	{	{	PUNCT
cana-2861	30	9	(	(	PUNCT
cana-2861	30	10	u	u	NOUN
cana-2861	30	11	,	,	PUNCT
cana-2861	30	12	tuo	tuo	NOUN
cana-2861	30	13	(	(	PUNCT
cana-2861	30	14	u	u	NOUN
cana-2861	30	15	)	)	PUNCT
cana-2861	30	16	,	,	PUNCT
cana-2861	30	17	cuo	cuo	PROPN
cana-2861	30	18	(	(	PUNCT
cana-2861	30	19	u	u	NOUN
cana-2861	30	20	)	)	PUNCT
cana-2861	30	21	,	,	PUNCT
cana-2861	30	22	iuo	iuo	VERB
cana-2861	30	23	(	(	PUNCT
cana-2861	30	24	u	u	NOUN
cana-2861	30	25	)	)	PUNCT
cana-2861	30	26	,	,	PUNCT
cana-2861	30	27	fuo	fuo	ADV
cana-2861	30	28	)	)	PUNCT
cana-2861	30	29	:	:	PUNCT
cana-2861	31	1	u	u	PROPN
cana-2861	31	2	∈	∈	PROPN
cana-2861	31	3	z	z	PROPN
cana-2861	31	4	}	}	PUNCT
cana-2861	31	5	,	,	PUNCT
cana-2861	31	6	then	then	ADV
cana-2861	31	7	(	(	PUNCT
cana-2861	31	8	i	i	NOUN
cana-2861	31	9	)	)	PUNCT
cana-2861	31	10	0qns	0qns	PROPN
cana-2861	32	1	=	=	PUNCT
cana-2861	32	2	(	(	PUNCT
cana-2861	32	3	u	u	NOUN
cana-2861	32	4	,	,	PUNCT
cana-2861	32	5	0	0	NUM
cana-2861	32	6	,	,	PUNCT
cana-2861	32	7	0	0	NUM
cana-2861	32	8	,	,	PUNCT
cana-2861	32	9	1	1	NUM
cana-2861	32	10	,	,	PUNCT
cana-2861	32	11	1	1	NUM
cana-2861	32	12	)	)	PUNCT
cana-2861	32	13	and	and	CCONJ
cana-2861	32	14	1qns	1qns	NUM
cana-2861	32	15	=	=	SYM
cana-2861	32	16	(	(	PUNCT
cana-2861	32	17	u	u	NOUN
cana-2861	32	18	,	,	PUNCT
cana-2861	32	19	1	1	NUM
cana-2861	32	20	,	,	PUNCT
cana-2861	32	21	1	1	NUM
cana-2861	32	22	,	,	PUNCT
cana-2861	32	23	0	0	NUM
cana-2861	32	24	,	,	PUNCT
cana-2861	32	25	0	0	NUM
cana-2861	32	26	)	)	PUNCT
cana-2861	32	27	,	,	PUNCT
cana-2861	32	28	(	(	PUNCT
cana-2861	32	29	ii	ii	NOUN
cana-2861	32	30	)	)	PUNCT
cana-2861	32	31	u	u	NOUN
cana-2861	32	32	⊆	⊆	NUM
cana-2861	32	33	uo	uo	NOUN
cana-2861	32	34	iff	iff	PROPN
cana-2861	32	35	tu	tu	PROPN
cana-2861	32	36	(	(	PUNCT
cana-2861	32	37	u	u	NOUN
cana-2861	32	38	)	)	PUNCT
cana-2861	32	39	≤	≤	ADJ
cana-2861	32	40	tuo	tuo	NOUN
cana-2861	32	41	(	(	PUNCT
cana-2861	32	42	u	u	NOUN
cana-2861	32	43	)	)	PUNCT
cana-2861	32	44	,	,	PUNCT
cana-2861	32	45	cu	cu	PROPN
cana-2861	32	46	(	(	PUNCT
cana-2861	32	47	u	u	NOUN
cana-2861	32	48	)	)	PUNCT
cana-2861	32	49	≤	≤	PROPN
cana-2861	32	50	cuo	cuo	PROPN
cana-2861	32	51	(	(	PUNCT
cana-2861	32	52	u	u	NOUN
cana-2861	32	53	)	)	PUNCT
cana-2861	32	54	,	,	PUNCT
cana-2861	32	55	iu	iu	ADP
cana-2861	32	56	(	(	PUNCT
cana-2861	32	57	u	u	NOUN
cana-2861	32	58	)	)	PUNCT
cana-2861	32	59	≥	≥	PRON
cana-2861	32	60	iuo	iuo	VERB
cana-2861	32	61	(	(	PUNCT
cana-2861	32	62	u	u	NOUN
cana-2861	32	63	)	)	PUNCT
cana-2861	32	64	&	&	CCONJ
cana-2861	32	65	fu	fu	PROPN
cana-2861	32	66	(	(	PUNCT
cana-2861	32	67	u	u	NOUN
cana-2861	32	68	)	)	PUNCT
cana-2861	32	69	≥	≥	NOUN
cana-2861	32	70	fuo	fuo	ADV
cana-2861	32	71	(	(	PUNCT
cana-2861	32	72	u	u	NOUN
cana-2861	32	73	)	)	PUNCT
cana-2861	32	74	:	:	PUNCT
cana-2861	32	75	u	u	PROPN
cana-2861	32	76	∈	∈	PROPN
cana-2861	32	77	z	z	PROPN
cana-2861	32	78	,	,	PUNCT
cana-2861	32	79	(	(	PUNCT
cana-2861	32	80	iii	iii	NOUN
cana-2861	32	81	)	)	PUNCT
cana-2861	32	82	1qns	1qns	NUM
cana-2861	32	83	−	−	PROPN
cana-2861	32	84	u	u	NOUN
cana-2861	32	85	=	=	PUNCT
cana-2861	32	86	{	{	PUNCT
cana-2861	32	87	(	(	PUNCT
cana-2861	32	88	u	u	NOUN
cana-2861	32	89	,	,	PUNCT
cana-2861	32	90	fu	fu	NOUN
cana-2861	32	91	(	(	PUNCT
cana-2861	32	92	u	u	NOUN
cana-2861	32	93	)	)	PUNCT
cana-2861	32	94	,	,	PUNCT
cana-2861	32	95	iu	iu	ADP
cana-2861	32	96	(	(	PUNCT
cana-2861	32	97	u	u	NOUN
cana-2861	32	98	)	)	PUNCT
cana-2861	32	99	,	,	PUNCT
cana-2861	32	100	cu	cu	PROPN
cana-2861	32	101	(	(	PUNCT
cana-2861	32	102	u	u	NOUN
cana-2861	32	103	)	)	PUNCT
cana-2861	32	104	,	,	PUNCT
cana-2861	32	105	tu	tu	PROPN
cana-2861	32	106	(	(	PUNCT
cana-2861	32	107	u	u	NOUN
cana-2861	32	108	)	)	PUNCT
cana-2861	32	109	)	)	PUNCT
cana-2861	32	110	:	:	PUNCT
cana-2861	33	1	u	u	PROPN
cana-2861	33	2	∈	∈	PROPN
cana-2861	33	3	z	z	NOUN
cana-2861	33	4	}	}	PUNCT
cana-2861	33	5	=	=	SYM
cana-2861	33	6	uc	uc	PROPN
cana-2861	33	7	,	,	PUNCT
cana-2861	33	8	(	(	PUNCT
cana-2861	33	9	iv	iv	X
cana-2861	33	10	)	)	PUNCT
cana-2861	33	11	u	u	NOUN
cana-2861	33	12	∪	∪	NOUN
cana-2861	33	13	uo	uo	NOUN
cana-2861	33	14	=	=	SYM
cana-2861	33	15	{	{	PUNCT
cana-2861	33	16	(	(	PUNCT
cana-2861	33	17	u	u	NOUN
cana-2861	33	18	,	,	PUNCT
cana-2861	33	19	max	max	PROPN
cana-2861	33	20	(	(	PUNCT
cana-2861	33	21	tu	tu	PROPN
cana-2861	33	22	(	(	PUNCT
cana-2861	33	23	u	u	NOUN
cana-2861	33	24	)	)	PUNCT
cana-2861	33	25	,	,	PUNCT
cana-2861	33	26	tuo	tuo	NOUN
cana-2861	33	27	(	(	PUNCT
cana-2861	33	28	u	u	NOUN
cana-2861	33	29	)	)	PUNCT
cana-2861	33	30	)	)	PUNCT
cana-2861	33	31	,	,	PUNCT
cana-2861	33	32	max	max	PROPN
cana-2861	33	33	(	(	PUNCT
cana-2861	33	34	cu	cu	PROPN
cana-2861	33	35	(	(	PUNCT
cana-2861	33	36	u	u	NOUN
cana-2861	33	37	)	)	PUNCT
cana-2861	33	38	,	,	PUNCT
cana-2861	33	39	cuo	cuo	PROPN
cana-2861	33	40	(	(	PUNCT
cana-2861	33	41	u	u	NOUN
cana-2861	33	42	)	)	PUNCT
cana-2861	33	43	)	)	PUNCT
cana-2861	33	44	,	,	PUNCT
cana-2861	33	45	min	min	PROPN
cana-2861	33	46	(	(	PUNCT
cana-2861	33	47	iu	iu	X
cana-2861	33	48	(	(	PUNCT
cana-2861	33	49	u	u	NOUN
cana-2861	33	50	)	)	PUNCT
cana-2861	33	51	,	,	PUNCT
cana-2861	33	52	iuo	iuo	VERB
cana-2861	33	53	(	(	PUNCT
cana-2861	33	54	u	u	NOUN
cana-2861	33	55	)	)	PUNCT
cana-2861	33	56	)	)	PUNCT
cana-2861	33	57	,	,	PUNCT
cana-2861	33	58	min(fu	min(fu	X
cana-2861	33	59	(	(	PUNCT
cana-2861	33	60	u	u	NOUN
cana-2861	33	61	)	)	PUNCT
cana-2861	33	62	,	,	PUNCT
cana-2861	33	63	fuo	fuo	PROPN
cana-2861	33	64	(	(	PUNCT
cana-2861	33	65	u	u	NOUN
cana-2861	33	66	)	)	PUNCT
cana-2861	33	67	)	)	PUNCT
cana-2861	33	68	)	)	PUNCT
cana-2861	33	69	:	:	PUNCT
cana-2861	34	1	u	u	NOUN
cana-2861	34	2	∈	∈	PROPN
cana-2861	34	3	z	z	PROPN
cana-2861	34	4	}	}	PUNCT
cana-2861	34	5	,	,	PUNCT
cana-2861	34	6	(	(	PUNCT
cana-2861	34	7	v	v	NOUN
cana-2861	34	8	)	)	PUNCT
cana-2861	34	9	u	u	NOUN
cana-2861	34	10	∩	∩	NOUN
cana-2861	34	11	uo	uo	NOUN
cana-2861	34	12	=	=	SYM
cana-2861	34	13	{	{	PUNCT
cana-2861	34	14	(	(	PUNCT
cana-2861	34	15	u	u	NOUN
cana-2861	34	16	,	,	PUNCT
cana-2861	34	17	min	min	PROPN
cana-2861	34	18	(	(	PUNCT
cana-2861	34	19	tu	tu	X
cana-2861	34	20	(	(	PUNCT
cana-2861	34	21	u	u	NOUN
cana-2861	34	22	)	)	PUNCT
cana-2861	34	23	,	,	PUNCT
cana-2861	34	24	tuo	tuo	NOUN
cana-2861	34	25	(	(	PUNCT
cana-2861	34	26	u	u	NOUN
cana-2861	34	27	)	)	PUNCT
cana-2861	34	28	)	)	PUNCT
cana-2861	34	29	,	,	PUNCT
cana-2861	34	30	min	min	PROPN
cana-2861	34	31	(	(	PUNCT
cana-2861	34	32	cu	cu	PROPN
cana-2861	34	33	(	(	PUNCT
cana-2861	34	34	u	u	NOUN
cana-2861	34	35	)	)	PUNCT
cana-2861	34	36	,	,	PUNCT
cana-2861	34	37	cuo	cuo	PROPN
cana-2861	34	38	(	(	PUNCT
cana-2861	34	39	u	u	NOUN
cana-2861	34	40	)	)	PUNCT
cana-2861	34	41	)	)	PUNCT
cana-2861	34	42	,	,	PUNCT
cana-2861	34	43	max	max	PROPN
cana-2861	34	44	(	(	PUNCT
cana-2861	34	45	iu	iu	X
cana-2861	34	46	(	(	PUNCT
cana-2861	34	47	u	u	NOUN
cana-2861	34	48	)	)	PUNCT
cana-2861	34	49	,	,	PUNCT
cana-2861	34	50	iuo	iuo	VERB
cana-2861	34	51	(	(	PUNCT
cana-2861	34	52	u	u	NOUN
cana-2861	34	53	)	)	PUNCT
cana-2861	34	54	)	)	PUNCT
cana-2861	34	55	,	,	PUNCT
cana-2861	34	56	max(fu	max(fu	PROPN
cana-2861	34	57	(	(	PUNCT
cana-2861	34	58	u	u	NOUN
cana-2861	34	59	)	)	PUNCT
cana-2861	34	60	,	,	PUNCT
cana-2861	34	61	fuo	fuo	PROPN
cana-2861	34	62	(	(	PUNCT
cana-2861	34	63	u	u	NOUN
cana-2861	34	64	)	)	PUNCT
cana-2861	34	65	)	)	PUNCT
cana-2861	34	66	)	)	PUNCT
cana-2861	34	67	:	:	PUNCT
cana-2861	35	1	u	u	NOUN
cana-2861	35	2	∈	∈	PROPN
cana-2861	35	3	z	z	NOUN
cana-2861	35	4	}	}	PUNCT
cana-2861	35	5	.	.	PUNCT
cana-2861	36	1	definition	definition	NOUN
cana-2861	36	2	2.3	2.3	NUM
cana-2861	36	3	.	.	PUNCT
cana-2861	36	4	5	5	NUM
cana-2861	36	5	let	let	VERB
cana-2861	36	6	z	z	PRON
cana-2861	36	7	be	be	AUX
cana-2861	36	8	a	a	DET
cana-2861	36	9	fixed	fix	VERB
cana-2861	36	10	set	set	NOUN
cana-2861	36	11	.	.	PUNCT
cana-2861	37	1	a	a	DET
cana-2861	37	2	collection	collection	NOUN
cana-2861	37	3	γq	γq	ADP
cana-2861	37	4	of	of	ADP
cana-2861	37	5	some	some	DET
cana-2861	37	6	q	q	NOUN
cana-2861	37	7	-	-	PUNCT
cana-2861	37	8	nss	nss	NOUN
cana-2861	37	9	’s	’s	NOUN
cana-2861	37	10	over	over	ADP
cana-2861	37	11	z	z	PROPN
cana-2861	37	12	is	be	AUX
cana-2861	37	13	called	call	VERB
cana-2861	37	14	a	a	DET
cana-2861	37	15	quadripartitioned	quadripartitione	VERB
cana-2861	37	16	neutrosophic	neutrosophic	ADJ
cana-2861	37	17	topology	topology	NOUN
cana-2861	37	18	(	(	PUNCT
cana-2861	37	19	in	in	ADP
cana-2861	37	20	-	-	PUNCT
cana-2861	37	21	short	short	ADJ
cana-2861	37	22	,	,	PUNCT
cana-2861	37	23	q	q	NOUN
cana-2861	37	24	-	-	PUNCT
cana-2861	37	25	nst	nst	NOUN
cana-2861	37	26	)	)	PUNCT
cana-2861	37	27	on	on	ADP
cana-2861	37	28	z	z	PROPN
cana-2861	37	29	,	,	PUNCT
cana-2861	37	30	if	if	SCONJ
cana-2861	37	31	the	the	DET
cana-2861	37	32	following	follow	VERB
cana-2861	37	33	conditions	condition	NOUN
cana-2861	37	34	holds	hold	VERB
cana-2861	37	35	:	:	PUNCT
cana-2861	37	36	(	(	PUNCT
cana-2861	37	37	i	i	NOUN
cana-2861	37	38	)	)	PUNCT
cana-2861	37	39	0n	0n	NOUN
cana-2861	37	40	,	,	PUNCT
cana-2861	38	1	1n	1n	NUM
cana-2861	38	2	∈	∈	PROPN
cana-2861	38	3	γq	γq	VERB
cana-2861	38	4	.	.	PUNCT
cana-2861	39	1	(	(	PUNCT
cana-2861	39	2	ii	ii	NOUN
cana-2861	39	3	)	)	PUNCT
cana-2861	39	4	gϕ	gϕ	PROPN
cana-2861	39	5	∩	∩	PROPN
cana-2861	39	6	gφ	gφ	PROPN
cana-2861	39	7	∈	∈	PROPN
cana-2861	39	8	γq	γq	ADP
cana-2861	39	9	for	for	ADP
cana-2861	39	10	any	any	DET
cana-2861	39	11	gϕ	gϕ	PROPN
cana-2861	39	12	,	,	PUNCT
cana-2861	39	13	gφ	gφ	PROPN
cana-2861	39	14	∈	∈	PROPN
cana-2861	39	15	γq	γq	VERB
cana-2861	39	16	.	.	PUNCT
cana-2861	40	1	(	(	PUNCT
cana-2861	40	2	iii	iii	X
cana-2861	40	3	)	)	PUNCT
cana-2861	40	4	gϕ	gϕ	PROPN
cana-2861	40	5	∈	∈	PROPN
cana-2861	40	6	γq	γq	VERB
cana-2861	40	7	,	,	PUNCT
cana-2861	40	8	∀	∀	X
cana-2861	40	9	{	{	PUNCT
cana-2861	40	10	gϕ	gϕ	PROPN
cana-2861	40	11	:	:	PUNCT
cana-2861	40	12	ϕ	ϕ	PROPN
cana-2861	40	13	∈	∈	PROPN
cana-2861	40	14	z	z	PROPN
cana-2861	40	15	}	}	PUNCT
cana-2861	40	16	⊆	⊆	NUM
cana-2861	40	17	γq	γq	NOUN
cana-2861	40	18	.	.	PUNCT
cana-2861	41	1	then	then	ADV
cana-2861	41	2	(	(	PUNCT
cana-2861	41	3	z	z	NOUN
cana-2861	41	4	,	,	PUNCT
cana-2861	41	5	γq	γq	VERB
cana-2861	41	6	)	)	PUNCT
cana-2861	41	7	is	be	AUX
cana-2861	41	8	called	call	VERB
cana-2861	41	9	a	a	DET
cana-2861	41	10	quadripartitioned	quadripartitione	VERB
cana-2861	41	11	neutrosophic	neutrosophic	ADJ
cana-2861	41	12	topological	topological	ADJ
cana-2861	41	13	space	space	NOUN
cana-2861	41	14	(	(	PUNCT
cana-2861	41	15	in	in	ADP
cana-2861	41	16	-	-	PUNCT
cana-2861	41	17	short	short	ADJ
cana-2861	41	18	,	,	PUNCT
cana-2861	41	19	q	q	NOUN
cana-2861	41	20	-	-	NOUN
cana-2861	41	21	nsts	nst	NOUN
cana-2861	41	22	)	)	PUNCT
cana-2861	41	23	in	in	ADP
cana-2861	41	24	z.	z.	PROPN
cana-2861	42	1	every	every	DET
cana-2861	42	2	element	element	NOUN
cana-2861	42	3	of	of	ADP
cana-2861	42	4	γq	γq	ADV
cana-2861	42	5	are	be	AUX
cana-2861	42	6	called	call	VERB
cana-2861	42	7	a	a	DET
cana-2861	42	8	quadripartitioned	quadripartitione	VERB
cana-2861	42	9	neutrosophic	neutrosophic	ADJ
cana-2861	42	10	open	open	ADJ
cana-2861	42	11	sets	set	NOUN
cana-2861	42	12	(	(	PUNCT
cana-2861	42	13	in	in	ADP
cana-2861	42	14	-	-	PUNCT
cana-2861	42	15	short	short	ADJ
cana-2861	42	16	,	,	PUNCT
cana-2861	42	17	q	q	ADJ
cana-2861	42	18	-	-	PUNCT
cana-2861	42	19	nso	nso	NOUN
cana-2861	42	20	set	set	NOUN
cana-2861	42	21	)	)	PUNCT
cana-2861	42	22	.	.	PUNCT
cana-2861	43	1	if	if	SCONJ
cana-2861	43	2	c	c	PRON
cana-2861	43	3	γq	γq	VERB
cana-2861	43	4	,	,	PUNCT
cana-2861	43	5	then	then	ADV
cana-2861	43	6	cc	cc	PROPN
cana-2861	43	7	is	be	AUX
cana-2861	43	8	called	call	VERB
cana-2861	43	9	a	a	DET
cana-2861	43	10	quadripartitioned	quadripartitione	VERB
cana-2861	43	11	neutrosophic	neutrosophic	ADJ
cana-2861	43	12	closed	closed	ADJ
cana-2861	43	13	sets	set	NOUN
cana-2861	43	14	(	(	PUNCT
cana-2861	43	15	in	in	ADP
cana-2861	43	16	-	-	PUNCT
cana-2861	43	17	short	short	ADJ
cana-2861	43	18	,	,	PUNCT
cana-2861	43	19	q	q	ADJ
cana-2861	43	20	-	-	PUNCT
cana-2861	43	21	nsc	nsc	NOUN
cana-2861	43	22	set	set	NOUN
cana-2861	43	23	)	)	PUNCT
cana-2861	43	24	.	.	PUNCT
cana-2861	44	1	definition	definition	NOUN
cana-2861	44	2	2.4	2.4	NUM
cana-2861	44	3	.	.	PUNCT
cana-2861	44	4	5	5	NUM
cana-2861	44	5	let	let	VERB
cana-2861	44	6	(	(	PUNCT
cana-2861	44	7	z	z	NOUN
cana-2861	44	8	,	,	PUNCT
cana-2861	44	9	γq	γq	VERB
cana-2861	44	10	)	)	PUNCT
cana-2861	44	11	be	be	AUX
cana-2861	44	12	q	q	NOUN
cana-2861	44	13	-	-	NOUN
cana-2861	44	14	nsts	nst	NOUN
cana-2861	44	15	on	on	ADP
cana-2861	44	16	z	z	PROPN
cana-2861	44	17	and	and	CCONJ
cana-2861	44	18	u	u	PRON
cana-2861	44	19	be	be	VERB
cana-2861	44	20	an	an	DET
cana-2861	44	21	q	q	NOUN
cana-2861	44	22	-	-	PUNCT
cana-2861	44	23	nss	nss	NOUN
cana-2861	44	24	on	on	ADP
cana-2861	44	25	z	z	PROPN
cana-2861	44	26	,	,	PUNCT
cana-2861	44	27	then	then	ADV
cana-2861	44	28	a	a	DET
cana-2861	44	29	quadripartitioned	quadripartitioned	ADJ
cana-2861	44	30	neutrosophic	neutrosophic	ADJ
cana-2861	44	31	interior	interior	NOUN
cana-2861	44	32	(	(	PUNCT
cana-2861	44	33	resp	resp	NOUN
cana-2861	44	34	.	.	PUNCT
cana-2861	45	1	closure	closure	NOUN
cana-2861	45	2	)	)	PUNCT
cana-2861	45	3	of	of	ADP
cana-2861	45	4	u	u	PROPN
cana-2861	45	5	(	(	PUNCT
cana-2861	45	6	in	in	ADP
cana-2861	45	7	-	-	PUNCT
cana-2861	45	8	short	short	ADJ
cana-2861	45	9	,	,	PUNCT
cana-2861	45	10	q	q	NOUN
cana-2861	45	11	-	-	PUNCT
cana-2861	45	12	nsint(u	nsint(u	PROPN
cana-2861	45	13	)	)	PUNCT
cana-2861	45	14	(	(	PUNCT
cana-2861	45	15	resp	resp	NOUN
cana-2861	45	16	.	.	PUNCT
cana-2861	46	1	q	q	X
cana-2861	46	2	-	-	PUNCT
cana-2861	46	3	nscl(u	nscl(u	NOUN
cana-2861	46	4	)	)	PUNCT
cana-2861	46	5	)	)	PUNCT
cana-2861	46	6	)	)	PUNCT
cana-2861	46	7	are	be	AUX
cana-2861	46	8	defined	define	VERB
cana-2861	46	9	as	as	ADP
cana-2861	46	10	q	q	NOUN
cana-2861	46	11	-	-	NOUN
cana-2861	46	12	nsint(u	nsint(u	ADJ
cana-2861	46	13	)	)	PUNCT
cana-2861	47	1	=	=	SYM
cana-2861	47	2	∪{uo	∪{uo	PROPN
cana-2861	47	3	:	:	PUNCT
cana-2861	47	4	uo	uo	NUM
cana-2861	47	5	⊆	⊆	NUM
cana-2861	47	6	u	u	NOUN
cana-2861	47	7	&	&	CCONJ
cana-2861	47	8	uo	uo	PROPN
cana-2861	47	9	is	be	AUX
cana-2861	47	10	a	a	DET
cana-2861	47	11	q	q	NOUN
cana-2861	47	12	-	-	NOUN
cana-2861	47	13	nso	nso	NOUN
cana-2861	47	14	in	in	ADP
cana-2861	47	15	z	z	PROPN
cana-2861	47	16	}	}	PUNCT
cana-2861	47	17	,	,	PUNCT
cana-2861	47	18	q	q	X
cana-2861	47	19	-	-	PUNCT
cana-2861	47	20	nscl(u	nscl(u	NOUN
cana-2861	47	21	)	)	PUNCT
cana-2861	48	1	=	=	NOUN
cana-2861	48	2	∩{uo	∩{uo	NOUN
cana-2861	48	3	:	:	PUNCT
cana-2861	48	4	u	u	NOUN
cana-2861	48	5	⊆	⊆	NUM
cana-2861	48	6	uo	uo	NOUN
cana-2861	48	7	&	&	CCONJ
cana-2861	48	8	uo	uo	PROPN
cana-2861	48	9	is	be	AUX
cana-2861	48	10	a	a	DET
cana-2861	48	11	q	q	NOUN
cana-2861	48	12	-	-	PUNCT
cana-2861	48	13	nsc	nsc	NOUN
cana-2861	48	14	in	in	ADP
cana-2861	48	15	z	z	PROPN
cana-2861	48	16	}	}	PUNCT
cana-2861	48	17	,	,	PUNCT
cana-2861	48	18	definition	definition	NOUN
cana-2861	48	19	2.5	2.5	NUM
cana-2861	48	20	.	.	PUNCT
cana-2861	49	1	5	5	NUM
cana-2861	49	2	let	let	VERB
cana-2861	49	3	(	(	PUNCT
cana-2861	49	4	z	z	NOUN
cana-2861	49	5	,	,	PUNCT
cana-2861	49	6	γq	γq	VERB
cana-2861	49	7	)	)	PUNCT
cana-2861	49	8	be	be	AUX
cana-2861	49	9	q	q	NOUN
cana-2861	49	10	-	-	NOUN
cana-2861	49	11	nsts	nst	NOUN
cana-2861	49	12	on	on	ADP
cana-2861	49	13	z	z	PROPN
cana-2861	49	14	and	and	CCONJ
cana-2861	49	15	u	u	PRON
cana-2861	49	16	be	be	VERB
cana-2861	49	17	an	an	DET
cana-2861	49	18	q	q	NOUN
cana-2861	49	19	-	-	PUNCT
cana-2861	49	20	nss	nss	NOUN
cana-2861	49	21	on	on	ADP
cana-2861	49	22	z.	z.	PROPN
cana-2861	49	23	then	then	ADV
cana-2861	49	24	u	u	NOUN
cana-2861	49	25	is	be	AUX
cana-2861	49	26	said	say	VERB
cana-2861	49	27	to	to	PART
cana-2861	49	28	be	be	AUX
cana-2861	49	29	a	a	DET
cana-2861	49	30	quadripartitioned	quadripartitioned	ADJ
cana-2861	49	31	neutrosophic	neutrosophic	ADJ
cana-2861	49	32	pre	pre	PROPN
cana-2861	49	33	(	(	PUNCT
cana-2861	49	34	resp	resp	NOUN
cana-2861	49	35	.	.	PUNCT
cana-2861	50	1	semi	semi	ADV
cana-2861	50	2	,	,	PUNCT
cana-2861	50	3	α	α	PROPN
cana-2861	50	4	&	&	CCONJ
cana-2861	50	5	b	b	NOUN
cana-2861	50	6	)	)	PUNCT
cana-2861	50	7	open	open	ADJ
cana-2861	50	8	set	set	NOUN
cana-2861	50	9	(	(	PUNCT
cana-2861	50	10	in	in	ADP
cana-2861	50	11	-	-	PUNCT
cana-2861	50	12	short	short	ADJ
cana-2861	50	13	,	,	PUNCT
cana-2861	50	14	q	q	NOUN
cana-2861	50	15	-	-	PUNCT
cana-2861	50	16	ns	ns	NOUN
cana-2861	50	17	ƿo	ƿo	ADP
cana-2861	50	18	set	set	NOUN
cana-2861	50	19	(	(	PUNCT
cana-2861	50	20	resp	resp	NOUN
cana-2861	50	21	.	.	PUNCT
cana-2861	51	1	q	q	X
cana-2861	51	2	-	-	PUNCT
cana-2861	51	3	ns	ns	ADJ
cana-2861	51	4	communications	communication	NOUN
cana-2861	51	5	on	on	ADP
cana-2861	51	6	applied	apply	VERB
cana-2861	51	7	nonlinear	nonlinear	ADJ
cana-2861	51	8	analysis	analysis	NOUN
cana-2861	51	9	issn	issn	NOUN
cana-2861	51	10	:	:	PUNCT
cana-2861	51	11	1074	1074	NUM
cana-2861	51	12	-	-	PUNCT
cana-2861	51	13	133x	133x	NUM
cana-2861	51	14	vol	vol	NOUN
cana-2861	51	15	32	32	NUM
cana-2861	51	16	no	no	NOUN
cana-2861	51	17	.	.	PUNCT
cana-2861	52	1	4s	4s	NUM
cana-2861	52	2	(	(	PUNCT
cana-2861	52	3	2025	2025	NUM
cana-2861	52	4	)	)	PUNCT
cana-2861	52	5	423	423	NUM
cana-2861	52	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2861	52	7	o	o	NOUN
cana-2861	52	8	set	set	NOUN
cana-2861	52	9	,	,	PUNCT
cana-2861	52	10	q	q	ADJ
cana-2861	52	11	-	-	PUNCT
cana-2861	52	12	nsαo	nsαo	NOUN
cana-2861	52	13	set	set	PROPN
cana-2861	52	14	&	&	CCONJ
cana-2861	52	15	q	q	NOUN
cana-2861	52	16	-	-	PUNCT
cana-2861	52	17	nsbo	nsbo	NOUN
cana-2861	52	18	set	set	PROPN
cana-2861	52	19	)	)	PUNCT
cana-2861	52	20	)	)	PUNCT
cana-2861	53	1	if	if	SCONJ
cana-2861	53	2	u	u	NOUN
cana-2861	53	3	⊆q	⊆q	NOUN
cana-2861	53	4	-	-	PUNCT
cana-2861	53	5	nsint(q	nsint(q	NOUN
cana-2861	53	6	-	-	PUNCT
cana-2861	53	7	nscl(u	nscl(u	NOUN
cana-2861	53	8	)	)	PUNCT
cana-2861	53	9	)	)	PUNCT
cana-2861	53	10	(	(	PUNCT
cana-2861	53	11	resp	resp	NOUN
cana-2861	53	12	.	.	PUNCT
cana-2861	54	1	u	u	PRON
cana-2861	54	2	q	q	NOUN
cana-2861	54	3	-	-	PUNCT
cana-2861	54	4	nscl(q	nscl(q	ADP
cana-2861	54	5	-	-	PUNCT
cana-2861	54	6	nsint(u	nsint(u	PROPN
cana-2861	54	7	)	)	PUNCT
cana-2861	54	8	)	)	PUNCT
cana-2861	54	9	,	,	PUNCT
cana-2861	54	10	u⊆q	u⊆q	PROPN
cana-2861	54	11	-	-	PUNCT
cana-2861	54	12	nsint(q	nsint(q	NOUN
cana-2861	54	13	-	-	PUNCT
cana-2861	54	14	nscl(q	nscl(q	ADP
cana-2861	54	15	-	-	PUNCT
cana-2861	54	16	nsint(u	nsint(u	PROPN
cana-2861	54	17	)	)	PUNCT
cana-2861	54	18	)	)	PUNCT
cana-2861	54	19	)	)	PUNCT
cana-2861	54	20	&	&	CCONJ
cana-2861	54	21	u	u	NOUN
cana-2861	54	22	⊆	⊆	NUM
cana-2861	54	23	q	q	PROPN
cana-2861	54	24	-	-	PUNCT
cana-2861	54	25	nscl(q	nscl(q	ADP
cana-2861	54	26	-	-	PUNCT
cana-2861	54	27	nsint(u	nsint(u	PROPN
cana-2861	54	28	)	)	PUNCT
cana-2861	54	29	)	)	PUNCT
cana-2861	55	1	q	q	X
cana-2861	55	2	-	-	PUNCT
cana-2861	55	3	nsint(q	nsint(q	NOUN
cana-2861	55	4	-	-	PUNCT
cana-2861	55	5	nscl(u	nscl(u	NOUN
cana-2861	55	6	)	)	PUNCT
cana-2861	55	7	)	)	PUNCT
cana-2861	55	8	)	)	PUNCT
cana-2861	55	9	.	.	PUNCT
cana-2861	56	1	the	the	DET
cana-2861	56	2	complement	complement	NOUN
cana-2861	56	3	of	of	ADP
cana-2861	56	4	an	an	DET
cana-2861	56	5	q	q	NOUN
cana-2861	56	6	-	-	PUNCT
cana-2861	56	7	ns	ns	NOUN
cana-2861	56	8	ƿo	ƿo	ADP
cana-2861	56	9	set	set	NOUN
cana-2861	56	10	(	(	PUNCT
cana-2861	56	11	resp	resp	NOUN
cana-2861	56	12	.	.	PUNCT
cana-2861	57	1	q	q	X
cana-2861	57	2	-	-	PUNCT
cana-2861	57	3	ns	ns	ADJ
cana-2861	57	4	o	o	NOUN
cana-2861	57	5	set	set	NOUN
cana-2861	57	6	,	,	PUNCT
cana-2861	57	7	q	q	ADJ
cana-2861	57	8	-	-	PUNCT
cana-2861	57	9	nsαo	nsαo	NOUN
cana-2861	57	10	set	set	PROPN
cana-2861	57	11	&	&	CCONJ
cana-2861	57	12	q	q	NOUN
cana-2861	57	13	-	-	PUNCT
cana-2861	57	14	nsbo	nsbo	PROPN
cana-2861	57	15	set	set	NOUN
cana-2861	57	16	)	)	PUNCT
cana-2861	57	17	is	be	AUX
cana-2861	57	18	called	call	VERB
cana-2861	57	19	a	a	DET
cana-2861	57	20	quadripar	quadripar	NOUN
cana-2861	57	21	titioned	titione	VERB
cana-2861	57	22	neutrosophic	neutrosophic	ADJ
cana-2861	57	23	pre	pre	X
cana-2861	57	24	(	(	PUNCT
cana-2861	57	25	resp	resp	NOUN
cana-2861	57	26	.	.	PUNCT
cana-2861	58	1	semi	semi	ADV
cana-2861	58	2	,	,	PUNCT
cana-2861	58	3	α	α	PROPN
cana-2861	58	4	&	&	CCONJ
cana-2861	58	5	b	b	PROPN
cana-2861	58	6	)	)	PUNCT
cana-2861	58	7	closed	close	VERB
cana-2861	58	8	set	set	NOUN
cana-2861	58	9	(	(	PUNCT
cana-2861	58	10	in	in	ADP
cana-2861	58	11	-	-	PUNCT
cana-2861	58	12	short	short	ADJ
cana-2861	58	13	,	,	PUNCT
cana-2861	58	14	q	q	ADJ
cana-2861	58	15	-	-	PUNCT
cana-2861	58	16	ns	ns	ADJ
cana-2861	58	17	ѕc	ѕc	NOUN
cana-2861	58	18	set	set	NOUN
cana-2861	58	19	(	(	PUNCT
cana-2861	58	20	resp	resp	NOUN
cana-2861	58	21	.	.	PUNCT
cana-2861	59	1	q	q	X
cana-2861	59	2	-	-	PUNCT
cana-2861	59	3	ns	ns	PROPN
cana-2861	59	4	c	c	NOUN
cana-2861	59	5	set	set	NOUN
cana-2861	59	6	,	,	PUNCT
cana-2861	59	7	q	q	ADJ
cana-2861	59	8	-	-	PUNCT
cana-2861	59	9	nsαc	nsαc	NOUN
cana-2861	59	10	set	set	NOUN
cana-2861	59	11	&	&	CCONJ
cana-2861	59	12	q	q	NOUN
cana-2861	59	13	-	-	PUNCT
cana-2861	59	14	nsbc	nsbc	ADJ
cana-2861	59	15	set	set	NOUN
cana-2861	59	16	)	)	PUNCT
cana-2861	59	17	)	)	PUNCT
cana-2861	60	1	in	in	ADP
cana-2861	60	2	z.	z.	PROPN
cana-2861	60	3	the	the	DET
cana-2861	60	4	family	family	NOUN
cana-2861	60	5	of	of	ADP
cana-2861	60	6	all	all	DET
cana-2861	60	7	q	q	NOUN
cana-2861	60	8	-	-	PUNCT
cana-2861	60	9	nspo	nspo	NOUN
cana-2861	60	10	set	set	NOUN
cana-2861	60	11	(	(	PUNCT
cana-2861	60	12	resp	resp	NOUN
cana-2861	60	13	.	.	PUNCT
cana-2861	61	1	q	q	X
cana-2861	61	2	-	-	PUNCT
cana-2861	61	3	nspc	nspc	NOUN
cana-2861	61	4	set	set	NOUN
cana-2861	61	5	,	,	PUNCT
cana-2861	61	6	q	q	ADJ
cana-2861	61	7	-	-	PUNCT
cana-2861	61	8	nsso	nsso	ADJ
cana-2861	61	9	set	set	NOUN
cana-2861	61	10	,	,	PUNCT
cana-2861	61	11	q	q	ADJ
cana-2861	61	12	-	-	PUNCT
cana-2861	61	13	nssc	nssc	NOUN
cana-2861	61	14	set	set	NOUN
cana-2861	61	15	,	,	PUNCT
cana-2861	61	16	q	q	ADJ
cana-2861	61	17	-	-	PUNCT
cana-2861	61	18	nsαo	nsαo	NOUN
cana-2861	61	19	set	set	NOUN
cana-2861	61	20	,	,	PUNCT
cana-2861	61	21	q	q	ADJ
cana-2861	61	22	-	-	PUNCT
cana-2861	61	23	nsαc	nsαc	NOUN
cana-2861	61	24	set	set	NOUN
cana-2861	61	25	,	,	PUNCT
cana-2861	61	26	q	q	NOUN
cana-2861	61	27	-	-	PUNCT
cana-2861	61	28	nsbo	nsbo	NOUN
cana-2861	61	29	set	set	PROPN
cana-2861	61	30	&	&	CCONJ
cana-2861	61	31	q	q	PROPN
cana-2861	61	32	-	-	PUNCT
cana-2861	61	33	nsbc	nsbc	ADJ
cana-2861	61	34	set	set	NOUN
cana-2861	61	35	)	)	PUNCT
cana-2861	61	36	of	of	ADP
cana-2861	61	37	z	z	PROPN
cana-2861	61	38	is	be	AUX
cana-2861	61	39	denoted	denote	VERB
cana-2861	61	40	by	by	ADP
cana-2861	61	41	q	q	NOUN
cana-2861	61	42	-	-	PUNCT
cana-2861	61	43	nspos(z	nspos(z	NOUN
cana-2861	61	44	)	)	PUNCT
cana-2861	61	45	(	(	PUNCT
cana-2861	61	46	resp	resp	NOUN
cana-2861	61	47	.	.	PUNCT
cana-2861	62	1	q	q	X
cana-2861	62	2	-	-	PUNCT
cana-2861	62	3	nspcs(z	nspcs(z	NOUN
cana-2861	62	4	)	)	PUNCT
cana-2861	62	5	,	,	PUNCT
cana-2861	62	6	qnssos(z	qnssos(z	NOUN
cana-2861	62	7	)	)	PUNCT
cana-2861	62	8	,	,	PUNCT
cana-2861	62	9	qnsscs(z	qnsscs(z	PROPN
cana-2861	62	10	)	)	PUNCT
cana-2861	62	11	,	,	PUNCT
cana-2861	62	12	q	q	PROPN
cana-2861	62	13	-	-	PUNCT
cana-2861	62	14	nsαos(z	nsαos(z	NOUN
cana-2861	62	15	)	)	PUNCT
cana-2861	62	16	,	,	PUNCT
cana-2861	62	17	q	q	NOUN
cana-2861	62	18	-	-	PUNCT
cana-2861	62	19	nsαcs(z	nsαcs(z	NOUN
cana-2861	62	20	)	)	PUNCT
cana-2861	62	21	,	,	PUNCT
cana-2861	62	22	q	q	NOUN
cana-2861	62	23	-	-	PUNCT
cana-2861	62	24	nsbos(z	nsbos(z	NOUN
cana-2861	62	25	)	)	PUNCT
cana-2861	62	26	&	&	CCONJ
cana-2861	62	27	q	q	NOUN
cana-2861	62	28	-	-	PUNCT
cana-2861	62	29	nsbcs(z	nsbcs(z	NOUN
cana-2861	62	30	)	)	PUNCT
cana-2861	62	31	)	)	PUNCT
cana-2861	62	32	.	.	PUNCT
cana-2861	63	1	definition	definition	NOUN
cana-2861	63	2	2.6	2.6	NUM
cana-2861	63	3	.	.	PUNCT
cana-2861	64	1	let	let	VERB
cana-2861	64	2	(	(	PUNCT
cana-2861	64	3	z	z	NOUN
cana-2861	64	4	,	,	PUNCT
cana-2861	64	5	γq	γq	AUX
cana-2861	64	6	)	)	PUNCT
cana-2861	64	7	be	be	AUX
cana-2861	64	8	q	q	NOUN
cana-2861	64	9	-	-	NOUN
cana-2861	64	10	nsts	nst	NOUN
cana-2861	64	11	on	on	ADP
cana-2861	64	12	z	z	PROPN
cana-2861	64	13	and	and	CCONJ
cana-2861	64	14	u	u	PRON
cana-2861	64	15	be	be	VERB
cana-2861	64	16	a	a	DET
cana-2861	64	17	q	q	NOUN
cana-2861	64	18	-	-	PUNCT
cana-2861	64	19	nss	nss	NOUN
cana-2861	64	20	on	on	ADP
cana-2861	64	21	z.	z.	PROPN
cana-2861	64	22	then	then	ADV
cana-2861	64	23	u	u	NOUN
cana-2861	64	24	is	be	AUX
cana-2861	64	25	said	say	VERB
cana-2861	64	26	to	to	PART
cana-2861	64	27	be	be	AUX
cana-2861	64	28	a	a	DET
cana-2861	64	29	quadripartitioned	quadripartitioned	ADJ
cana-2861	64	30	neutrosophic	neutrosophic	ADJ
cana-2861	64	31	β	β	X
cana-2861	64	32	open	open	ADJ
cana-2861	64	33	set	set	NOUN
cana-2861	64	34	(	(	PUNCT
cana-2861	64	35	in	in	ADP
cana-2861	64	36	-	-	PUNCT
cana-2861	64	37	short	short	ADJ
cana-2861	64	38	,	,	PUNCT
cana-2861	64	39	q	q	NOUN
cana-2861	64	40	-	-	PUNCT
cana-2861	64	41	nsβo	nsβo	ADJ
cana-2861	64	42	)	)	PUNCT
cana-2861	64	43	set	set	VERB
cana-2861	64	44	if	if	SCONJ
cana-2861	64	45	u	u	NOUN
cana-2861	64	46	q	q	NOUN
cana-2861	64	47	-	-	PUNCT
cana-2861	64	48	nscl(q	nscl(q	ADP
cana-2861	64	49	-	-	PUNCT
cana-2861	64	50	nsint(qnscl(u	nsint(qnscl(u	NOUN
cana-2861	64	51	)	)	PUNCT
cana-2861	64	52	)	)	PUNCT
cana-2861	64	53	)	)	PUNCT
cana-2861	64	54	.	.	PUNCT
cana-2861	65	1	the	the	DET
cana-2861	65	2	complement	complement	NOUN
cana-2861	65	3	of	of	ADP
cana-2861	65	4	an	an	DET
cana-2861	65	5	q	q	NOUN
cana-2861	65	6	-	-	PUNCT
cana-2861	65	7	nsβo	nsβo	ADJ
cana-2861	65	8	set	set	NOUN
cana-2861	65	9	is	be	AUX
cana-2861	65	10	called	call	VERB
cana-2861	65	11	a	a	DET
cana-2861	65	12	quadripartitioned	quadripartitione	VERB
cana-2861	65	13	neutrosophic	neutrosophic	PROPN
cana-2861	65	14	β	β	X
cana-2861	65	15	closed	close	VERB
cana-2861	65	16	set	set	NOUN
cana-2861	65	17	(	(	PUNCT
cana-2861	65	18	in	in	ADP
cana-2861	65	19	-	-	PUNCT
cana-2861	65	20	short	short	ADJ
cana-2861	65	21	,	,	PUNCT
cana-2861	65	22	qnsβc	qnsβc	PROPN
cana-2861	65	23	set	set	VERB
cana-2861	65	24	in	in	ADP
cana-2861	65	25	z.	z.	PROPN
cana-2861	65	26	the	the	DET
cana-2861	65	27	family	family	NOUN
cana-2861	65	28	of	of	ADP
cana-2861	65	29	all	all	DET
cana-2861	65	30	q	q	ADJ
cana-2861	65	31	-	-	PUNCT
cana-2861	65	32	nsβo	nsβo	ADJ
cana-2861	65	33	set	set	NOUN
cana-2861	65	34	(	(	PUNCT
cana-2861	65	35	resp	resp	NOUN
cana-2861	65	36	.	.	PUNCT
cana-2861	66	1	q	q	X
cana-2861	66	2	-	-	PUNCT
cana-2861	66	3	nsβc	nsβc	NOUN
cana-2861	66	4	set	set	NOUN
cana-2861	66	5	)	)	PUNCT
cana-2861	66	6	of	of	ADP
cana-2861	66	7	z	z	PROPN
cana-2861	66	8	is	be	AUX
cana-2861	66	9	denoted	denote	VERB
cana-2861	66	10	by	by	ADP
cana-2861	66	11	q	q	NOUN
cana-2861	66	12	-	-	PUNCT
cana-2861	66	13	nsβos(z	nsβos(z	NOUN
cana-2861	66	14	)	)	PUNCT
cana-2861	66	15	(	(	PUNCT
cana-2861	66	16	resp	resp	NOUN
cana-2861	66	17	.	.	PUNCT
cana-2861	67	1	qnsβcs(z	qnsβcs(z	NOUN
cana-2861	67	2	)	)	PUNCT
cana-2861	67	3	)	)	PUNCT
cana-2861	67	4	.	.	PUNCT
cana-2861	68	1	definition	definition	NOUN
cana-2861	68	2	2.7	2.7	NUM
cana-2861	68	3	.	.	PUNCT
cana-2861	69	1	the	the	DET
cana-2861	69	2	q	q	ADJ
cana-2861	69	3	-	-	PUNCT
cana-2861	69	4	nsβ	nsβ	ADJ
cana-2861	69	5	interior	interior	NOUN
cana-2861	69	6	of	of	ADP
cana-2861	69	7	u	u	PROPN
cana-2861	69	8	(	(	PUNCT
cana-2861	69	9	briefly	briefly	ADV
cana-2861	69	10	,	,	PUNCT
cana-2861	69	11	q	q	NOUN
cana-2861	69	12	-	-	NOUN
cana-2861	69	13	nsβint(u	nsβint(u	ADJ
cana-2861	69	14	)	)	PUNCT
cana-2861	69	15	)	)	PUNCT
cana-2861	69	16	and	and	CCONJ
cana-2861	69	17	q	q	X
cana-2861	69	18	-	-	PUNCT
cana-2861	69	19	nsβ	nsβ	ADV
cana-2861	69	20	closure	closure	NOUN
cana-2861	69	21	of	of	ADP
cana-2861	69	22	u	u	NOUN
cana-2861	69	23	(	(	PUNCT
cana-2861	69	24	briefly	briefly	ADV
cana-2861	69	25	,	,	PUNCT
cana-2861	69	26	q	q	NOUN
cana-2861	69	27	-	-	PUNCT
cana-2861	69	28	nsβcl(u	nsβcl(u	NOUN
cana-2861	69	29	)	)	PUNCT
cana-2861	69	30	)	)	PUNCT
cana-2861	69	31	are	be	AUX
cana-2861	69	32	defined	define	VERB
cana-2861	69	33	as	as	ADP
cana-2861	69	34	(	(	PUNCT
cana-2861	69	35	i	i	NOUN
cana-2861	69	36	)	)	PUNCT
cana-2861	69	37	q	q	NOUN
cana-2861	69	38	-	-	NOUN
cana-2861	69	39	nsβint(u	nsβint(u	ADJ
cana-2861	69	40	)	)	PUNCT
cana-2861	70	1	=	=	SYM
cana-2861	70	2	∪{uo	∪{uo	PROPN
cana-2861	70	3	:	:	PUNCT
cana-2861	70	4	uo	uo	NUM
cana-2861	70	5	⊆	⊆	NUM
cana-2861	70	6	u	u	NOUN
cana-2861	70	7	&	&	CCONJ
cana-2861	70	8	uo	uo	PROPN
cana-2861	70	9	is	be	AUX
cana-2861	70	10	a	a	DET
cana-2861	70	11	q	q	NOUN
cana-2861	70	12	-	-	PUNCT
cana-2861	70	13	nsβo	nsβo	ADJ
cana-2861	70	14	set	set	NOUN
cana-2861	70	15	in	in	ADP
cana-2861	70	16	z	z	NOUN
cana-2861	70	17	}	}	PUNCT
cana-2861	70	18	.	.	PUNCT
cana-2861	71	1	(	(	PUNCT
cana-2861	71	2	ii	ii	NOUN
cana-2861	71	3	)	)	PUNCT
cana-2861	71	4	q	q	NOUN
cana-2861	71	5	-	-	PUNCT
cana-2861	71	6	nsβcl(u	nsβcl(u	NOUN
cana-2861	71	7	)	)	PUNCT
cana-2861	72	1	=	=	PUNCT
cana-2861	72	2	∩{uo	∩{uo	NUM
cana-2861	72	3	:	:	PUNCT
cana-2861	72	4	u	u	PROPN
cana-2861	72	5	⊆	⊆	NUM
cana-2861	72	6	uo	uo	NOUN
cana-2861	72	7	&	&	CCONJ
cana-2861	72	8	uo	uo	PROPN
cana-2861	72	9	is	be	AUX
cana-2861	72	10	a	a	DET
cana-2861	72	11	q	q	ADJ
cana-2861	72	12	-	-	PUNCT
cana-2861	72	13	nsβc	nsβc	NOUN
cana-2861	72	14	set	set	NOUN
cana-2861	72	15	in	in	ADP
cana-2861	72	16	z	z	NOUN
cana-2861	72	17	}	}	PUNCT
cana-2861	72	18	.	.	PUNCT
cana-2861	73	1	theorem	theorem	VERB
cana-2861	73	2	2.8	2.8	NUM
cana-2861	73	3	.	.	PUNCT
cana-2861	74	1	let	let	VERB
cana-2861	74	2	(	(	PUNCT
cana-2861	74	3	z	z	NOUN
cana-2861	74	4	,	,	PUNCT
cana-2861	74	5	γq	γq	AUX
cana-2861	74	6	)	)	PUNCT
cana-2861	74	7	be	be	AUX
cana-2861	74	8	q	q	NOUN
cana-2861	74	9	-	-	NOUN
cana-2861	74	10	nsts	nst	NOUN
cana-2861	74	11	on	on	ADP
cana-2861	74	12	z	z	PROPN
cana-2861	74	13	and	and	CCONJ
cana-2861	74	14	g	g	PROPN
cana-2861	74	15	be	be	AUX
cana-2861	74	16	a	a	DET
cana-2861	74	17	q	q	NOUN
cana-2861	74	18	-	-	PUNCT
cana-2861	74	19	nss	nss	NOUN
cana-2861	74	20	on	on	ADP
cana-2861	74	21	z.	z.	PROPN
cana-2861	75	1	then	then	ADV
cana-2861	75	2	(	(	PUNCT
cana-2861	75	3	i	i	NOUN
cana-2861	75	4	)	)	PUNCT
cana-2861	75	5	q	q	NOUN
cana-2861	75	6	-	-	PUNCT
cana-2861	75	7	nsβcl(1	nsβcl(1	NOUN
cana-2861	75	8	−	−	NOUN
cana-2861	75	9	g	g	NOUN
cana-2861	75	10	)	)	PUNCT
cana-2861	75	11	=	=	SYM
cana-2861	75	12	1	1	NUM
cana-2861	75	13	−	−	PRON
cana-2861	75	14	q	q	NOUN
cana-2861	75	15	-	-	PUNCT
cana-2861	75	16	nsβint(g	nsβint(g	NOUN
cana-2861	75	17	)	)	PUNCT
cana-2861	75	18	.	.	PUNCT
cana-2861	76	1	(	(	PUNCT
cana-2861	76	2	ii	ii	NOUN
cana-2861	76	3	)	)	PUNCT
cana-2861	76	4	q	q	NOUN
cana-2861	76	5	-	-	PUNCT
cana-2861	76	6	nsβint(1	nsβint(1	ADJ
cana-2861	76	7	−	−	PROPN
cana-2861	76	8	g	g	NOUN
cana-2861	76	9	)	)	PUNCT
cana-2861	76	10	=	=	SYM
cana-2861	77	1	1	1	NUM
cana-2861	77	2	−	−	PRON
cana-2861	77	3	q	q	NOUN
cana-2861	77	4	-	-	PUNCT
cana-2861	77	5	nsβcl(g	nsβcl(g	NOUN
cana-2861	77	6	)	)	PUNCT
cana-2861	77	7	.	.	PUNCT
cana-2861	78	1	theorem	theorem	VERB
cana-2861	78	2	2.9	2.9	NUM
cana-2861	78	3	.	.	PUNCT
cana-2861	79	1	let	let	VERB
cana-2861	79	2	(	(	PUNCT
cana-2861	79	3	z	z	NOUN
cana-2861	79	4	,	,	PUNCT
cana-2861	79	5	γq	γq	AUX
cana-2861	79	6	)	)	PUNCT
cana-2861	79	7	be	be	AUX
cana-2861	79	8	q	q	NOUN
cana-2861	79	9	-	-	NOUN
cana-2861	79	10	nsts	nst	NOUN
cana-2861	79	11	on	on	ADP
cana-2861	79	12	z	z	PROPN
cana-2861	79	13	and	and	CCONJ
cana-2861	79	14	g	g	PROPN
cana-2861	79	15	be	be	AUX
cana-2861	79	16	an	an	DET
cana-2861	79	17	q	q	NOUN
cana-2861	79	18	-	-	PUNCT
cana-2861	79	19	nss	nss	NOUN
cana-2861	79	20	on	on	ADP
cana-2861	79	21	z.	z.	PROPN
cana-2861	80	1	then	then	ADV
cana-2861	80	2	(	(	PUNCT
cana-2861	80	3	i	i	NOUN
cana-2861	80	4	)	)	PUNCT
cana-2861	80	5	q	q	NOUN
cana-2861	80	6	-	-	PUNCT
cana-2861	80	7	nsβint(g	nsβint(g	NOUN
cana-2861	80	8	)	)	PUNCT
cana-2861	80	9	⊆	⊆	NUM
cana-2861	80	10	g.	g.	PROPN
cana-2861	80	11	(	(	PUNCT
cana-2861	80	12	ii	ii	PROPN
cana-2861	80	13	)	)	PUNCT
cana-2861	80	14	g	g	PROPN
cana-2861	80	15	is	be	AUX
cana-2861	80	16	q	q	ADJ
cana-2861	80	17	-	-	PUNCT
cana-2861	80	18	nsβo	nsβo	ADJ
cana-2861	80	19	iff	iff	PROPN
cana-2861	80	20	q	q	NOUN
cana-2861	80	21	-	-	PUNCT
cana-2861	80	22	nsβint(g	nsβint(g	NOUN
cana-2861	80	23	)	)	PUNCT
cana-2861	80	24	=	=	SYM
cana-2861	80	25	g.	g.	PROPN
cana-2861	80	26	(	(	PUNCT
cana-2861	80	27	iii	iii	NOUN
cana-2861	80	28	)	)	PUNCT
cana-2861	80	29	q	q	NOUN
cana-2861	80	30	-	-	PUNCT
cana-2861	80	31	nsβint(q	nsβint(q	NOUN
cana-2861	80	32	-	-	PUNCT
cana-2861	80	33	nsβint(g	nsβint(g	NOUN
cana-2861	80	34	)	)	PUNCT
cana-2861	80	35	)	)	PUNCT
cana-2861	81	1	=	=	SYM
cana-2861	81	2	q	q	NOUN
cana-2861	81	3	-	-	PUNCT
cana-2861	81	4	nsβint(g	nsβint(g	NOUN
cana-2861	81	5	)	)	PUNCT
cana-2861	81	6	.	.	PUNCT
cana-2861	82	1	theorem	theorem	VERB
cana-2861	82	2	2.10	2.10	NUM
cana-2861	82	3	.	.	PUNCT
cana-2861	83	1	let	let	VERB
cana-2861	83	2	(	(	PUNCT
cana-2861	83	3	z	z	NOUN
cana-2861	83	4	,	,	PUNCT
cana-2861	83	5	γq	γq	AUX
cana-2861	83	6	)	)	PUNCT
cana-2861	83	7	be	be	AUX
cana-2861	83	8	q	q	NOUN
cana-2861	83	9	-	-	NOUN
cana-2861	83	10	nsts	nst	NOUN
cana-2861	83	11	on	on	ADP
cana-2861	83	12	z.	z.	PROPN
cana-2861	83	13	let	let	VERB
cana-2861	83	14	g	g	PROPN
cana-2861	83	15	and	and	CCONJ
cana-2861	83	16	t	t	PROPN
cana-2861	83	17	be	be	AUX
cana-2861	83	18	quadripartitioned	quadripartitione	VERB
cana-2861	83	19	neutrosophic	neutrosophic	ADJ
cana-2861	83	20	subsets	subset	NOUN
cana-2861	83	21	of	of	ADP
cana-2861	83	22	z	z	PROPN
cana-2861	83	23	,	,	PUNCT
cana-2861	83	24	then	then	ADV
cana-2861	83	25	the	the	DET
cana-2861	83	26	following	following	ADJ
cana-2861	83	27	statements	statement	NOUN
cana-2861	83	28	hold	hold	VERB
cana-2861	83	29	.	.	PUNCT
cana-2861	84	1	(	(	PUNCT
cana-2861	84	2	i	i	NOUN
cana-2861	84	3	)	)	PUNCT
cana-2861	84	4	g	g	ADP
cana-2861	84	5	⊆	⊆	NUM
cana-2861	84	6	q	q	NOUN
cana-2861	84	7	-	-	PUNCT
cana-2861	84	8	nsβcl(g	nsβcl(g	NOUN
cana-2861	84	9	)	)	PUNCT
cana-2861	84	10	.	.	PUNCT
cana-2861	85	1	(	(	PUNCT
cana-2861	85	2	ii	ii	NOUN
cana-2861	85	3	)	)	PUNCT
cana-2861	85	4	g	g	PROPN
cana-2861	85	5	is	be	AUX
cana-2861	85	6	q	q	ADJ
cana-2861	85	7	-	-	PUNCT
cana-2861	85	8	nsβc	nsβc	ADJ
cana-2861	85	9	iff	iff	PROPN
cana-2861	85	10	q	q	PROPN
cana-2861	85	11	-	-	PUNCT
cana-2861	85	12	nsβcl(g	nsβcl(g	NOUN
cana-2861	85	13	)	)	PUNCT
cana-2861	85	14	=	=	SYM
cana-2861	85	15	g.	g.	PROPN
cana-2861	85	16	(	(	PUNCT
cana-2861	85	17	iii	iii	NOUN
cana-2861	85	18	)	)	PUNCT
cana-2861	85	19	q	q	ADJ
cana-2861	85	20	-	-	PUNCT
cana-2861	85	21	nsβcl(q	nsβcl(q	NOUN
cana-2861	85	22	-	-	PUNCT
cana-2861	85	23	nsβcl(g	nsβcl(g	NOUN
cana-2861	85	24	)	)	PUNCT
cana-2861	85	25	)	)	PUNCT
cana-2861	86	1	=	=	SYM
cana-2861	86	2	q	q	X
cana-2861	86	3	-	-	PUNCT
cana-2861	86	4	nsβcl(g	nsβcl(g	NOUN
cana-2861	86	5	)	)	PUNCT
cana-2861	86	6	.	.	PUNCT
cana-2861	87	1	(	(	PUNCT
cana-2861	87	2	iv	iv	X
cana-2861	87	3	)	)	PUNCT
cana-2861	87	4	g	g	PROPN
cana-2861	87	5	⊆	⊆	NUM
cana-2861	87	6	t	t	NOUN
cana-2861	87	7	⇒	⇒	NOUN
cana-2861	87	8	q	q	X
cana-2861	87	9	-	-	PUNCT
cana-2861	87	10	nsβcl(g	nsβcl(g	ADJ
cana-2861	87	11	)	)	PUNCT
cana-2861	87	12	⊆	⊆	NUM
cana-2861	87	13	q	q	NOUN
cana-2861	87	14	-	-	PUNCT
cana-2861	87	15	nsβcl(t	nsβcl(t	NOUN
cana-2861	87	16	)	)	PUNCT
cana-2861	87	17	.	.	PUNCT
cana-2861	88	1	(	(	PUNCT
cana-2861	88	2	v	v	NOUN
cana-2861	88	3	)	)	PUNCT
cana-2861	88	4	q	q	NOUN
cana-2861	88	5	-	-	PUNCT
cana-2861	88	6	nsβcl(g	nsβcl(g	ADJ
cana-2861	88	7	∩	∩	PROPN
cana-2861	88	8	t	t	NOUN
cana-2861	88	9	)	)	PUNCT
cana-2861	88	10	⊆	⊆	NUM
cana-2861	88	11	q	q	NOUN
cana-2861	88	12	-	-	PUNCT
cana-2861	88	13	nsβcl(g	nsβcl(g	ADJ
cana-2861	88	14	)	)	PUNCT
cana-2861	88	15	∩	∩	NOUN
cana-2861	88	16	q	q	NOUN
cana-2861	88	17	-	-	PUNCT
cana-2861	88	18	nsβcl(t	nsβcl(t	NOUN
cana-2861	88	19	)	)	PUNCT
cana-2861	88	20	.	.	PUNCT
cana-2861	89	1	(	(	PUNCT
cana-2861	89	2	vi	vi	NOUN
cana-2861	89	3	)	)	PUNCT
cana-2861	89	4	q	q	NOUN
cana-2861	89	5	-	-	PUNCT
cana-2861	89	6	nsβcl(g	nsβcl(g	NUM
cana-2861	89	7	∪	∪	ADJ
cana-2861	89	8	t	t	NOUN
cana-2861	89	9	)	)	PUNCT
cana-2861	90	1	=	=	PUNCT
cana-2861	90	2	q	q	X
cana-2861	90	3	-	-	PUNCT
cana-2861	90	4	nsβcl(g	nsβcl(g	NOUN
cana-2861	90	5	)	)	PUNCT
cana-2861	90	6	∪	∪	ADP
cana-2861	90	7	q	q	NOUN
cana-2861	90	8	-	-	PUNCT
cana-2861	90	9	nsβcl(t	nsβcl(t	NOUN
cana-2861	90	10	)	)	PUNCT
cana-2861	90	11	.	.	PUNCT
cana-2861	91	1	communications	communication	NOUN
cana-2861	91	2	on	on	ADP
cana-2861	91	3	applied	apply	VERB
cana-2861	91	4	nonlinear	nonlinear	ADJ
cana-2861	91	5	analysis	analysis	NOUN
cana-2861	91	6	issn	issn	NOUN
cana-2861	91	7	:	:	PUNCT
cana-2861	91	8	1074	1074	NUM
cana-2861	91	9	-	-	PUNCT
cana-2861	91	10	133x	133x	NUM
cana-2861	91	11	vol	vol	NOUN
cana-2861	91	12	32	32	NUM
cana-2861	91	13	no	no	NOUN
cana-2861	91	14	.	.	PUNCT
cana-2861	92	1	4s	4s	NUM
cana-2861	92	2	(	(	PUNCT
cana-2861	92	3	2025	2025	NUM
cana-2861	92	4	)	)	PUNCT
cana-2861	92	5	424	424	NUM
cana-2861	92	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2861	92	7	3	3	NUM
cana-2861	92	8	quadripartitioned	quadripartitione	VERB
cana-2861	92	9	neutrosophic	neutrosophic	PROPN
cana-2861	92	10	β	β	X
cana-2861	92	11	frontier	frontier	NOUN
cana-2861	92	12	in	in	ADP
cana-2861	92	13	this	this	DET
cana-2861	92	14	section	section	NOUN
cana-2861	92	15	,	,	PUNCT
cana-2861	92	16	we	we	PRON
cana-2861	92	17	introduce	introduce	VERB
cana-2861	92	18	quadripartitioned	quadripartitione	VERB
cana-2861	92	19	neutrosophic	neutrosophic	PROPN
cana-2861	92	20	β	β	X
cana-2861	92	21	frontier	frontier	NOUN
cana-2861	92	22	and	and	CCONJ
cana-2861	92	23	discuss	discuss	VERB
cana-2861	92	24	their	their	PRON
cana-2861	92	25	properties	property	NOUN
cana-2861	92	26	in	in	ADP
cana-2861	92	27	quadripartitioned	quadripartitione	VERB
cana-2861	92	28	neutrosophic	neutrosophic	ADJ
cana-2861	92	29	topological	topological	ADJ
cana-2861	92	30	spaces	space	NOUN
cana-2861	92	31	.	.	PUNCT
cana-2861	93	1	definition	definition	NOUN
cana-2861	93	2	3.1	3.1	NUM
cana-2861	93	3	.	.	PUNCT
cana-2861	94	1	let	let	AUX
cana-2861	94	2	(	(	PUNCT
cana-2861	94	3	z	z	AUX
cana-2861	94	4	,	,	PUNCT
cana-2861	94	5	γq	γq	AUX
cana-2861	94	6	)	)	PUNCT
cana-2861	94	7	be	be	AUX
cana-2861	94	8	a	a	DET
cana-2861	94	9	q	q	NOUN
cana-2861	94	10	-	-	PUNCT
cana-2861	94	11	nsts	nst	NOUN
cana-2861	94	12	with	with	ADP
cana-2861	94	13	respect	respect	NOUN
cana-2861	94	14	to	to	ADP
cana-2861	94	15	f	f	PROPN
cana-2861	94	16	where	where	SCONJ
cana-2861	94	17	f	f	PROPN
cana-2861	94	18	is	be	AUX
cana-2861	94	19	a	a	DET
cana-2861	94	20	quadripartitioned	quadripartitione	VERB
cana-2861	94	21	neutrosophic	neutrosophic	ADJ
cana-2861	94	22	subset	subset	NOUN
cana-2861	94	23	of	of	ADP
cana-2861	94	24	z.	z.	PROPN
cana-2861	94	25	let	let	VERB
cana-2861	94	26	a	a	PRON
cana-2861	94	27	be	be	AUX
cana-2861	94	28	a	a	DET
cana-2861	94	29	neutrosophic	neutrosophic	ADJ
cana-2861	94	30	subset	subset	NOUN
cana-2861	94	31	of	of	ADP
cana-2861	94	32	z.	z.	PROPN
cana-2861	95	1	then	then	ADV
cana-2861	95	2	the	the	DET
cana-2861	95	3	quadripartitioned	quadripartitioned	ADJ
cana-2861	95	4	neutrosophic	neutrosophic	PROPN
cana-2861	95	5	β	β	PROPN
cana-2861	95	6	frontier	frontier	NOUN
cana-2861	95	7	of	of	ADP
cana-2861	95	8	a	a	DET
cana-2861	95	9	quadripartitioned	quadripartitione	VERB
cana-2861	95	10	neutrosophic	neutrosophic	PROPN
cana-2861	95	11	subset	subset	VERB
cana-2861	95	12	a	a	PRON
cana-2861	95	13	is	be	AUX
cana-2861	95	14	denoted	denote	VERB
cana-2861	95	15	by	by	ADP
cana-2861	95	16	q	q	NOUN
cana-2861	95	17	-	-	PUNCT
cana-2861	95	18	nsβfr(a	nsβfr(a	NOUN
cana-2861	95	19	)	)	PUNCT
cana-2861	95	20	and	and	CCONJ
cana-2861	95	21	is	be	AUX
cana-2861	95	22	defined	define	VERB
cana-2861	95	23	by	by	ADP
cana-2861	95	24	qnsβfr(a	qnsβfr(a	NOUN
cana-2861	95	25	)	)	PUNCT
cana-2861	95	26	=	=	SYM
cana-2861	95	27	qnsβcl(a	qnsβcl(a	ADJ
cana-2861	95	28	)	)	PUNCT
cana-2861	95	29	∩	∩	ADJ
cana-2861	95	30	q	q	NOUN
cana-2861	95	31	-	-	PUNCT
cana-2861	95	32	nsβcl(ac	nsβcl(ac	NOUN
cana-2861	95	33	)	)	PUNCT
cana-2861	95	34	.	.	PUNCT
cana-2861	96	1	remark	remark	PROPN
cana-2861	96	2	3.2	3.2	NUM
cana-2861	96	3	.	.	PUNCT
cana-2861	97	1	for	for	ADP
cana-2861	97	2	a	a	DET
cana-2861	97	3	quadripartitioned	quadripartitione	VERB
cana-2861	97	4	neutrosophic	neutrosophic	PROPN
cana-2861	97	5	subset	subset	VERB
cana-2861	97	6	a	a	PRON
cana-2861	97	7	of	of	ADP
cana-2861	97	8	z	z	PROPN
cana-2861	97	9	,	,	PUNCT
cana-2861	97	10	q	q	NOUN
cana-2861	97	11	-	-	PUNCT
cana-2861	97	12	nsβfr(a	nsβfr(a	NOUN
cana-2861	97	13	)	)	PUNCT
cana-2861	97	14	is	be	AUX
cana-2861	97	15	a	a	DET
cana-2861	97	16	q	q	NOUN
cana-2861	97	17	-	-	PUNCT
cana-2861	97	18	nsβc	nsβc	ADJ
cana-2861	97	19	.	.	PUNCT
cana-2861	98	1	theorem	theorem	VERB
cana-2861	98	2	3.3	3.3	NUM
cana-2861	98	3	.	.	PUNCT
cana-2861	99	1	for	for	ADP
cana-2861	99	2	a	a	DET
cana-2861	99	3	quadripartitioned	quadripartitione	VERB
cana-2861	99	4	neutrosophic	neutrosophic	PROPN
cana-2861	99	5	subset	subset	VERB
cana-2861	99	6	a	a	DET
cana-2861	99	7	in	in	ADP
cana-2861	99	8	q	q	NOUN
cana-2861	99	9	-	-	PUNCT
cana-2861	99	10	nsts	nst	NOUN
cana-2861	99	11	(	(	PUNCT
cana-2861	99	12	z	z	NOUN
cana-2861	99	13	,	,	PUNCT
cana-2861	99	14	γq	γq	ADP
cana-2861	99	15	)	)	PUNCT
cana-2861	99	16	,	,	PUNCT
cana-2861	99	17	q	q	NOUN
cana-2861	99	18	-	-	PUNCT
cana-2861	99	19	nsβfr(a	nsβfr(a	NOUN
cana-2861	99	20	)	)	PUNCT
cana-2861	99	21	=	=	PUNCT
cana-2861	99	22	q	q	PROPN
cana-2861	99	23	nsβfr(ac	nsβfr(ac	PROPN
cana-2861	99	24	)	)	PUNCT
cana-2861	99	25	.	.	PUNCT
cana-2861	100	1	proof	proof	NOUN
cana-2861	100	2	.	.	PUNCT
cana-2861	101	1	let	let	VERB
cana-2861	101	2	a	a	DET
cana-2861	101	3	be	be	AUX
cana-2861	101	4	a	a	DET
cana-2861	101	5	quadripartitioned	quadripartitione	VERB
cana-2861	101	6	neutrosophic	neutrosophic	ADJ
cana-2861	101	7	subset	subset	NOUN
cana-2861	101	8	in	in	ADP
cana-2861	101	9	q	q	NOUN
cana-2861	101	10	-	-	PUNCT
cana-2861	101	11	nsts	nst	NOUN
cana-2861	101	12	(	(	PUNCT
cana-2861	101	13	z	z	NOUN
cana-2861	101	14	,	,	PUNCT
cana-2861	101	15	γq	γq	ADP
cana-2861	101	16	)	)	PUNCT
cana-2861	101	17	.	.	PUNCT
cana-2861	102	1	then	then	ADV
cana-2861	102	2	by	by	ADP
cana-2861	102	3	definition	definition	NOUN
cana-2861	102	4	3.1	3.1	NUM
cana-2861	102	5	,	,	PUNCT
cana-2861	102	6	qnsβfr(a	qnsβfr(a	NOUN
cana-2861	102	7	)	)	PUNCT
cana-2861	102	8	=	=	SYM
cana-2861	102	9	q	q	NOUN
cana-2861	102	10	-	-	PUNCT
cana-2861	102	11	nsβcl(a	nsβcl(a	ADJ
cana-2861	102	12	)	)	PUNCT
cana-2861	102	13	⋂	⋂	PROPN
cana-2861	102	14	q	q	ADJ
cana-2861	102	15	-	-	PUNCT
cana-2861	102	16	nsβcl(ac	nsβcl(ac	NOUN
cana-2861	102	17	)	)	PUNCT
cana-2861	102	18	=	=	SYM
cana-2861	103	1	q	q	ADJ
cana-2861	103	2	-	-	PUNCT
cana-2861	103	3	nsβcl(ac)⋂q	nsβcl(ac)⋂q	ADJ
cana-2861	103	4	-	-	NUM
cana-2861	103	5	nsβcl(a	nsβcl(a	ADJ
cana-2861	103	6	)	)	PUNCT
cana-2861	103	7	=	=	SYM
cana-2861	104	1	q	q	PROPN
cana-2861	104	2	-	-	PUNCT
cana-2861	104	3	nsβcl(ac)⋂(q	nsβcl(ac)⋂(q	NOUN
cana-2861	104	4	nsβcl(ac)c	nsβcl(ac)c	NOUN
cana-2861	104	5	)	)	PUNCT
cana-2861	104	6	.	.	PUNCT
cana-2861	105	1	again	again	ADV
cana-2861	105	2	by	by	ADP
cana-2861	105	3	definition	definition	NOUN
cana-2861	105	4	3.1	3.1	NUM
cana-2861	105	5	,	,	PUNCT
cana-2861	105	6	this	this	PRON
cana-2861	105	7	is	be	AUX
cana-2861	105	8	equal	equal	ADJ
cana-2861	105	9	to	to	ADP
cana-2861	105	10	q	q	NOUN
cana-2861	105	11	-	-	PUNCT
cana-2861	105	12	nsβfr(ac	nsβfr(ac	NOUN
cana-2861	105	13	)	)	PUNCT
cana-2861	105	14	.	.	PUNCT
cana-2861	106	1	hence	hence	ADV
cana-2861	106	2	q	q	ADV
cana-2861	106	3	-	-	PUNCT
cana-2861	106	4	nsβfr(a	nsβfr(a	NOUN
cana-2861	106	5	)	)	PUNCT
cana-2861	106	6	=	=	SYM
cana-2861	106	7	qnsβfr(ac	qnsβfr(ac	PROPN
cana-2861	106	8	)	)	PUNCT
cana-2861	106	9	.	.	PUNCT
cana-2861	106	10	theorem	theorem	VERB
cana-2861	106	11	3.4	3.4	NUM
cana-2861	106	12	.	.	PUNCT
cana-2861	107	1	let	let	VERB
cana-2861	107	2	a	a	DET
cana-2861	107	3	be	be	AUX
cana-2861	107	4	a	a	DET
cana-2861	107	5	quadripartitioned	quadripartitione	VERB
cana-2861	107	6	neutrosophic	neutrosophic	ADJ
cana-2861	107	7	subset	subset	NOUN
cana-2861	107	8	in	in	ADP
cana-2861	107	9	q	q	NOUN
cana-2861	107	10	-	-	PUNCT
cana-2861	107	11	nsts	nst	NOUN
cana-2861	107	12	(	(	PUNCT
cana-2861	107	13	z	z	NOUN
cana-2861	107	14	,	,	PUNCT
cana-2861	107	15	γq	γq	ADP
cana-2861	107	16	)	)	PUNCT
cana-2861	107	17	.	.	PUNCT
cana-2861	108	1	then	then	ADV
cana-2861	108	2	qnsβfr(a	qnsβfr(a	NOUN
cana-2861	108	3	)	)	PUNCT
cana-2861	108	4	=	=	SYM
cana-2861	108	5	q	q	NOUN
cana-2861	108	6	-	-	PUNCT
cana-2861	108	7	nsβcl(a	nsβcl(a	NOUN
cana-2861	108	8	)	)	PUNCT
cana-2861	108	9	−	−	PRON
cana-2861	108	10	q	q	NOUN
cana-2861	108	11	-	-	PUNCT
cana-2861	108	12	nsβint(a	nsβint(a	NOUN
cana-2861	108	13	)	)	PUNCT
cana-2861	108	14	.	.	PUNCT
cana-2861	109	1	proof	proof	NOUN
cana-2861	109	2	.	.	PUNCT
cana-2861	110	1	let	let	VERB
cana-2861	110	2	a	a	DET
cana-2861	110	3	be	be	AUX
cana-2861	110	4	a	a	DET
cana-2861	110	5	quadripartitioned	quadripartitione	VERB
cana-2861	110	6	neutrosophic	neutrosophic	ADJ
cana-2861	110	7	subset	subset	NOUN
cana-2861	110	8	in	in	ADP
cana-2861	110	9	q	q	NOUN
cana-2861	110	10	-	-	PUNCT
cana-2861	110	11	nsts	nst	NOUN
cana-2861	110	12	(	(	PUNCT
cana-2861	110	13	z	z	NOUN
cana-2861	110	14	,	,	PUNCT
cana-2861	110	15	γq	γq	ADP
cana-2861	110	16	)	)	PUNCT
cana-2861	110	17	.	.	PUNCT
cana-2861	111	1	by	by	ADP
cana-2861	111	2	theorem	theorem	ADJ
cana-2861	111	3	2.8	2.8	NUM
cana-2861	111	4	(	(	PUNCT
cana-2861	111	5	ii	ii	NOUN
cana-2861	111	6	)	)	PUNCT
cana-2861	111	7	,	,	PUNCT
cana-2861	111	8	(	(	PUNCT
cana-2861	111	9	q	q	PROPN
cana-2861	111	10	nsβcl(ac))c	nsβcl(ac))c	ADJ
cana-2861	111	11	=	=	SYM
cana-2861	111	12	q	q	NOUN
cana-2861	111	13	-	-	PUNCT
cana-2861	111	14	nsβint(a	nsβint(a	NOUN
cana-2861	111	15	)	)	PUNCT
cana-2861	111	16	and	and	CCONJ
cana-2861	111	17	by	by	ADP
cana-2861	111	18	definition	definition	NOUN
cana-2861	111	19	3.1	3.1	NUM
cana-2861	111	20	,	,	PUNCT
cana-2861	111	21	q	q	NOUN
cana-2861	111	22	-	-	PUNCT
cana-2861	111	23	nsβfr(a	nsβfr(a	NOUN
cana-2861	111	24	)	)	PUNCT
cana-2861	111	25	=	=	SYM
cana-2861	111	26	q	q	NOUN
cana-2861	111	27	-	-	PUNCT
cana-2861	111	28	nsβcl(a	nsβcl(a	ADJ
cana-2861	111	29	)	)	PUNCT
cana-2861	111	30	∩	∩	NOUN
cana-2861	111	31	(	(	PUNCT
cana-2861	111	32	qnsβcl(ac	qnsβcl(ac	NOUN
cana-2861	111	33	)	)	PUNCT
cana-2861	111	34	)	)	PUNCT
cana-2861	112	1	=	=	PUNCT
cana-2861	112	2	qnsβcl(a	qnsβcl(a	ADJ
cana-2861	112	3	)	)	PUNCT
cana-2861	112	4	∩	∩	NOUN
cana-2861	112	5	(	(	PUNCT
cana-2861	112	6	q	q	NOUN
cana-2861	112	7	-	-	PUNCT
cana-2861	112	8	nsβ	nsβ	ADJ
cana-2861	112	9	int(ac))c	int(ac))c	PROPN
cana-2861	112	10	.	.	PUNCT
cana-2861	112	11	by	by	ADP
cana-2861	112	12	using	use	VERB
cana-2861	112	13	a	a	DET
cana-2861	112	14	−	−	PROPN
cana-2861	112	15	b	b	NOUN
cana-2861	112	16	=	=	SYM
cana-2861	112	17	a	a	DET
cana-2861	112	18	∩	∩	ADJ
cana-2861	112	19	bc	bc	PROPN
cana-2861	112	20	,	,	PUNCT
cana-2861	112	21	q	q	NOUN
cana-2861	112	22	-	-	PUNCT
cana-2861	112	23	nsβfr(a	nsβfr(a	NOUN
cana-2861	112	24	)	)	PUNCT
cana-2861	112	25	=	=	SYM
cana-2861	113	1	qnsβcl(a	qnsβcl(a	PROPN
cana-2861	113	2	)	)	PUNCT
cana-2861	113	3	−	−	PRON
cana-2861	113	4	q	q	NOUN
cana-2861	113	5	-	-	PUNCT
cana-2861	113	6	nsβint(a	nsβint(a	NOUN
cana-2861	113	7	)	)	PUNCT
cana-2861	113	8	.	.	PUNCT
cana-2861	114	1	hence	hence	ADV
cana-2861	114	2	q	q	ADV
cana-2861	114	3	-	-	PUNCT
cana-2861	114	4	nsβfr(a	nsβfr(a	NOUN
cana-2861	114	5	)	)	PUNCT
cana-2861	114	6	=	=	SYM
cana-2861	114	7	q	q	NOUN
cana-2861	114	8	-	-	PUNCT
cana-2861	114	9	nsβcl(a	nsβcl(a	NOUN
cana-2861	114	10	)	)	PUNCT
cana-2861	114	11	−	−	PRON
cana-2861	114	12	q	q	NOUN
cana-2861	114	13	-	-	PUNCT
cana-2861	114	14	nsβint(a	nsβint(a	NOUN
cana-2861	114	15	)	)	PUNCT
cana-2861	114	16	.	.	PUNCT
cana-2861	115	1	theorem	theorem	VERB
cana-2861	115	2	3.5	3.5	NUM
cana-2861	115	3	.	.	PUNCT
cana-2861	116	1	a	a	DET
cana-2861	116	2	quadripartitioned	quadripartitione	VERB
cana-2861	116	3	neutrosophic	neutrosophic	PROPN
cana-2861	116	4	subset	subset	VERB
cana-2861	116	5	a	a	PRON
cana-2861	116	6	is	be	AUX
cana-2861	116	7	q	q	ADJ
cana-2861	116	8	-	-	PUNCT
cana-2861	116	9	nsβc	nsβc	NOUN
cana-2861	116	10	set	set	NOUN
cana-2861	116	11	in	in	ADP
cana-2861	116	12	z	z	NOUN
cana-2861	116	13	if	if	SCONJ
cana-2861	117	1	and	and	CCONJ
cana-2861	117	2	only	only	ADV
cana-2861	117	3	if	if	SCONJ
cana-2861	117	4	qnsβfr(a	qnsβfr(a	ADJ
cana-2861	117	5	)	)	PUNCT
cana-2861	117	6	⊆a	⊆a	NOUN
cana-2861	117	7	.	.	PUNCT
cana-2861	118	1	proof	proof	NOUN
cana-2861	118	2	.	.	PUNCT
cana-2861	119	1	let	let	VERB
cana-2861	119	2	a	a	DET
cana-2861	119	3	be	be	AUX
cana-2861	119	4	a	a	DET
cana-2861	119	5	q	q	ADJ
cana-2861	119	6	-	-	PUNCT
cana-2861	119	7	nsβc	nsβc	NOUN
cana-2861	119	8	set	set	NOUN
cana-2861	119	9	in	in	ADP
cana-2861	119	10	the	the	DET
cana-2861	119	11	q	q	NOUN
cana-2861	119	12	-	-	PUNCT
cana-2861	119	13	nsts	nst	NOUN
cana-2861	119	14	(	(	PUNCT
cana-2861	119	15	z	z	NOUN
cana-2861	119	16	,	,	PUNCT
cana-2861	119	17	γq	γq	ADP
cana-2861	119	18	)	)	PUNCT
cana-2861	119	19	.	.	PUNCT
cana-2861	120	1	then	then	ADV
cana-2861	120	2	by	by	ADP
cana-2861	120	3	definition	definition	NOUN
cana-2861	120	4	3.1	3.1	NUM
cana-2861	120	5	,	,	PUNCT
cana-2861	120	6	q	q	NOUN
cana-2861	120	7	-	-	PUNCT
cana-2861	120	8	nsβfr(a	nsβfr(a	NOUN
cana-2861	120	9	)	)	PUNCT
cana-2861	120	10	=	=	SYM
cana-2861	120	11	q	q	X
cana-2861	120	12	nsβcl(a	nsβcl(a	PROPN
cana-2861	120	13	)	)	PUNCT
cana-2861	120	14	∩	∩	ADJ
cana-2861	120	15	q	q	NOUN
cana-2861	120	16	-	-	PUNCT
cana-2861	120	17	nsβcl(ac	nsβcl(ac	ADJ
cana-2861	120	18	)	)	PUNCT
cana-2861	120	19	⊆	⊆	NUM
cana-2861	120	20	q	q	PROPN
cana-2861	120	21	-	-	PUNCT
cana-2861	120	22	nsβcl(a	nsβcl(a	NOUN
cana-2861	120	23	)	)	PUNCT
cana-2861	120	24	.	.	PUNCT
cana-2861	121	1	by	by	ADP
cana-2861	121	2	using	use	VERB
cana-2861	121	3	theorem	theorem	ADJ
cana-2861	121	4	2.10	2.10	NUM
cana-2861	121	5	(	(	PUNCT
cana-2861	121	6	ii	ii	NOUN
cana-2861	121	7	)	)	PUNCT
cana-2861	121	8	,	,	PUNCT
cana-2861	121	9	q	q	NOUN
cana-2861	121	10	-	-	PUNCT
cana-2861	121	11	nsβcl(a	nsβcl(a	ADJ
cana-2861	121	12	)	)	PUNCT
cana-2861	121	13	=	=	SYM
cana-2861	121	14	a.	a.	NOUN
cana-2861	121	15	hence	hence	ADV
cana-2861	121	16	qnsβfr(a	qnsβfr(a	NOUN
cana-2861	121	17	)	)	PUNCT
cana-2861	121	18	⊆	⊆	NUM
cana-2861	121	19	a	a	PRON
cana-2861	121	20	,	,	PUNCT
cana-2861	121	21	if	if	SCONJ
cana-2861	121	22	a	a	PRON
cana-2861	121	23	is	be	AUX
cana-2861	121	24	q	q	NOUN
cana-2861	121	25	-	-	PUNCT
cana-2861	121	26	nsβc	nsβc	VERB
cana-2861	121	27	in	in	ADP
cana-2861	121	28	z.	z.	PROPN
cana-2861	121	29	conversely	conversely	ADV
cana-2861	121	30	,	,	PUNCT
cana-2861	121	31	assume	assume	VERB
cana-2861	121	32	that	that	SCONJ
cana-2861	121	33	,	,	PUNCT
cana-2861	121	34	q	q	NOUN
cana-2861	121	35	-	-	PUNCT
cana-2861	121	36	nsβfr(a	nsβfr(a	ADJ
cana-2861	121	37	)	)	PUNCT
cana-2861	121	38	⊆	⊆	NUM
cana-2861	121	39	a.	a.	NOUN
cana-2861	121	40	then	then	ADV
cana-2861	121	41	q	q	PROPN
cana-2861	121	42	-	-	PUNCT
cana-2861	121	43	nsβcl(a	nsβcl(a	ADJ
cana-2861	121	44	)	)	PUNCT
cana-2861	121	45	−	−	PRON
cana-2861	121	46	q	q	NOUN
cana-2861	121	47	-	-	PUNCT
cana-2861	121	48	nsβint(a	nsβint(a	NOUN
cana-2861	121	49	)	)	PUNCT
cana-2861	121	50	⊆	⊆	NUM
cana-2861	121	51	a.	a.	NOUN
cana-2861	121	52	since	since	SCONJ
cana-2861	121	53	q	q	PROPN
cana-2861	121	54	nsβint(a	nsβint(a	PROPN
cana-2861	121	55	)	)	PUNCT
cana-2861	121	56	⊆	⊆	PROPN
cana-2861	121	57	a	a	PRON
cana-2861	121	58	,	,	PUNCT
cana-2861	121	59	we	we	PRON
cana-2861	121	60	conclude	conclude	VERB
cana-2861	121	61	that	that	DET
cana-2861	121	62	q	q	NOUN
cana-2861	121	63	-	-	PUNCT
cana-2861	121	64	nsβcl(a	nsβcl(a	ADJ
cana-2861	121	65	)	)	PUNCT
cana-2861	121	66	=	=	PUNCT
cana-2861	121	67	a	a	PRON
cana-2861	121	68	and	and	CCONJ
cana-2861	121	69	hence	hence	ADV
cana-2861	121	70	a	a	PRON
cana-2861	121	71	is	be	AUX
cana-2861	121	72	q	q	NOUN
cana-2861	121	73	-	-	PUNCT
cana-2861	121	74	nsβc	nsβc	ADJ
cana-2861	121	75	.	.	PUNCT
cana-2861	122	1	theorem	theorem	VERB
cana-2861	122	2	3.6	3.6	NUM
cana-2861	122	3	.	.	PUNCT
cana-2861	123	1	if	if	SCONJ
cana-2861	123	2	a	a	PRON
cana-2861	123	3	is	be	AUX
cana-2861	123	4	a	a	DET
cana-2861	123	5	q	q	NOUN
cana-2861	123	6	-	-	PUNCT
cana-2861	123	7	nsβo	nsβo	ADJ
cana-2861	123	8	set	set	NOUN
cana-2861	123	9	in	in	ADP
cana-2861	123	10	z	z	NOUN
cana-2861	123	11	,	,	PUNCT
cana-2861	123	12	then	then	ADV
cana-2861	123	13	q	q	NOUN
cana-2861	123	14	-	-	PUNCT
cana-2861	123	15	nsβfr(a	nsβfr(a	ADJ
cana-2861	123	16	)	)	PUNCT
cana-2861	123	17	⊆	⊆	NUM
cana-2861	123	18	ac	ac	NOUN
cana-2861	123	19	.	.	PUNCT
cana-2861	124	1	proof	proof	NOUN
cana-2861	124	2	.	.	PUNCT
cana-2861	125	1	let	let	VERB
cana-2861	125	2	a	a	PRON
cana-2861	125	3	be	be	AUX
cana-2861	125	4	a	a	DET
cana-2861	125	5	q	q	NOUN
cana-2861	125	6	-	-	PUNCT
cana-2861	125	7	nsβo	nsβo	ADJ
cana-2861	125	8	set	set	NOUN
cana-2861	125	9	in	in	ADP
cana-2861	125	10	the	the	DET
cana-2861	125	11	q	q	NOUN
cana-2861	125	12	-	-	PUNCT
cana-2861	125	13	nsts	nst	NOUN
cana-2861	125	14	(	(	PUNCT
cana-2861	125	15	z	z	NOUN
cana-2861	125	16	,	,	PUNCT
cana-2861	125	17	γq	γq	ADP
cana-2861	125	18	)	)	PUNCT
cana-2861	125	19	.	.	PUNCT
cana-2861	126	1	by	by	ADP
cana-2861	126	2	definition	definition	NOUN
cana-2861	126	3	2.6	2.6	NUM
cana-2861	126	4	,	,	PUNCT
cana-2861	126	5	ac	ac	PROPN
cana-2861	126	6	is	be	AUX
cana-2861	126	7	q	q	ADJ
cana-2861	126	8	-	-	PUNCT
cana-2861	126	9	nsβc	nsβc	VERB
cana-2861	126	10	set	set	NOUN
cana-2861	126	11	in	in	ADP
cana-2861	126	12	z.	z.	PROPN
cana-2861	126	13	by	by	ADP
cana-2861	126	14	theorem	theorem	ADJ
cana-2861	126	15	3.5	3.5	NUM
cana-2861	126	16	,	,	PUNCT
cana-2861	126	17	q	q	NOUN
cana-2861	126	18	-	-	PUNCT
cana-2861	126	19	nsβfr(ac	nsβfr(ac	NOUN
cana-2861	126	20	)	)	PUNCT
cana-2861	126	21	⊆	⊆	NUM
cana-2861	126	22	ac	ac	PROPN
cana-2861	126	23	and	and	CCONJ
cana-2861	126	24	by	by	ADP
cana-2861	126	25	theorem	theorem	NOUN
cana-2861	126	26	3.5	3.5	NUM
cana-2861	126	27	,	,	PUNCT
cana-2861	126	28	we	we	PRON
cana-2861	126	29	get	get	VERB
cana-2861	126	30	q	q	NOUN
cana-2861	126	31	-	-	PUNCT
cana-2861	126	32	nsβfr(a	nsβfr(a	ADJ
cana-2861	126	33	)	)	PUNCT
cana-2861	126	34	⊆	⊆	NUM
cana-2861	126	35	ac	ac	PROPN
cana-2861	126	36	.	.	PUNCT
cana-2861	127	1	theorem	theorem	VERB
cana-2861	127	2	3.7	3.7	NUM
cana-2861	127	3	.	.	PUNCT
cana-2861	128	1	let	let	VERB
cana-2861	128	2	a	a	DET
cana-2861	128	3	⊆	⊆	NUM
cana-2861	128	4	b	b	NOUN
cana-2861	128	5	and	and	CCONJ
cana-2861	128	6	b	b	NOUN
cana-2861	128	7	be	be	AUX
cana-2861	128	8	any	any	DET
cana-2861	128	9	q	q	ADJ
cana-2861	128	10	-	-	PUNCT
cana-2861	128	11	nsβc	nsβc	NOUN
cana-2861	128	12	set	set	NOUN
cana-2861	128	13	in	in	ADP
cana-2861	128	14	z.	z.	PROPN
cana-2861	128	15	then	then	ADV
cana-2861	128	16	q	q	PROPN
cana-2861	128	17	-	-	PUNCT
cana-2861	128	18	nsβfr(a	nsβfr(a	ADJ
cana-2861	128	19	)	)	PUNCT
cana-2861	128	20	⊆	⊆	NUM
cana-2861	128	21	b.	b.	NOUN
cana-2861	128	22	proof	proof	NOUN
cana-2861	128	23	.	.	PUNCT
cana-2861	129	1	by	by	ADP
cana-2861	129	2	theorem	theorem	ADJ
cana-2861	129	3	2.10	2.10	NUM
cana-2861	129	4	(	(	PUNCT
cana-2861	129	5	iv	iv	NUM
cana-2861	129	6	)	)	PUNCT
cana-2861	129	7	,	,	PUNCT
cana-2861	129	8	a	a	DET
cana-2861	129	9	⊆	⊆	NUM
cana-2861	129	10	b	b	NOUN
cana-2861	129	11	,	,	PUNCT
cana-2861	129	12	q	q	NOUN
cana-2861	129	13	-	-	PUNCT
cana-2861	129	14	nsβcl(a	nsβcl(a	ADJ
cana-2861	129	15	)	)	PUNCT
cana-2861	129	16	⊆	⊆	NUM
cana-2861	129	17	q	q	NOUN
cana-2861	129	18	-	-	PUNCT
cana-2861	129	19	nsβcl(b	nsβcl(b	NOUN
cana-2861	129	20	)	)	PUNCT
cana-2861	129	21	.	.	PUNCT
cana-2861	130	1	by	by	ADP
cana-2861	130	2	definition	definition	NOUN
cana-2861	130	3	3.1	3.1	NUM
cana-2861	130	4	,	,	PUNCT
cana-2861	130	5	qnsβfr(a	qnsβfr(a	NOUN
cana-2861	130	6	)	)	PUNCT
cana-2861	130	7	=	=	SYM
cana-2861	130	8	q	q	NOUN
cana-2861	130	9	-	-	PUNCT
cana-2861	130	10	nsβcl(a	nsβcl(a	ADJ
cana-2861	130	11	)	)	PUNCT
cana-2861	130	12	∩	∩	ADJ
cana-2861	130	13	q	q	NOUN
cana-2861	130	14	-	-	PUNCT
cana-2861	130	15	nsβcl(ac	nsβcl(ac	ADJ
cana-2861	130	16	)	)	PUNCT
cana-2861	130	17	⊆	⊆	NUM
cana-2861	130	18	q	q	NOUN
cana-2861	130	19	-	-	PUNCT
cana-2861	130	20	nsβcl(b	nsβcl(b	NOUN
cana-2861	130	21	)	)	PUNCT
cana-2861	130	22	∩	∩	ADJ
cana-2861	130	23	q	q	NOUN
cana-2861	130	24	-	-	PUNCT
cana-2861	130	25	nsβcl(ac	nsβcl(ac	ADJ
cana-2861	130	26	)	)	PUNCT
cana-2861	130	27	⊆	⊆	NUM
cana-2861	130	28	q	q	NOUN
cana-2861	130	29	-	-	PUNCT
cana-2861	130	30	nsβcl(b	nsβcl(b	NOUN
cana-2861	130	31	)	)	PUNCT
cana-2861	130	32	.	.	PUNCT
cana-2861	131	1	then	then	ADV
cana-2861	131	2	by	by	ADP
cana-2861	131	3	remark	remark	NOUN
cana-2861	131	4	?	?	PUNCT
cana-2861	131	5	?	?	PUNCT
cana-2861	131	6	,	,	PUNCT
cana-2861	131	7	this	this	PRON
cana-2861	131	8	is	be	AUX
cana-2861	131	9	equal	equal	ADJ
cana-2861	131	10	to	to	ADP
cana-2861	131	11	b.	b.	PROPN
cana-2861	131	12	hence	hence	ADV
cana-2861	131	13	q	q	NOUN
cana-2861	131	14	-	-	PUNCT
cana-2861	131	15	nsβfr(a	nsβfr(a	ADJ
cana-2861	131	16	)	)	PUNCT
cana-2861	131	17	⊆	⊆	PROPN
cana-2861	131	18	b.	b.	NOUN
cana-2861	131	19	communications	communication	NOUN
cana-2861	131	20	on	on	ADP
cana-2861	131	21	applied	apply	VERB
cana-2861	131	22	nonlinear	nonlinear	ADJ
cana-2861	131	23	analysis	analysis	NOUN
cana-2861	131	24	issn	issn	NOUN
cana-2861	131	25	:	:	PUNCT
cana-2861	131	26	1074	1074	NUM
cana-2861	131	27	-	-	PUNCT
cana-2861	131	28	133x	133x	NUM
cana-2861	131	29	vol	vol	NOUN
cana-2861	131	30	32	32	NUM
cana-2861	131	31	no	no	NOUN
cana-2861	131	32	.	.	PUNCT
cana-2861	132	1	4s	4s	NUM
cana-2861	132	2	(	(	PUNCT
cana-2861	132	3	2025	2025	NUM
cana-2861	132	4	)	)	PUNCT
cana-2861	132	5	425	425	NUM
cana-2861	133	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-2861	133	2	c	c	NOUN
cana-2861	133	3	∪	∪	X
cana-2861	133	4	∪	∪	X
cana-2861	133	5	theorem	theorem	ADJ
cana-2861	133	6	3.8	3.8	NUM
cana-2861	133	7	.	.	PUNCT
cana-2861	134	1	let	let	VERB
cana-2861	134	2	a	a	DET
cana-2861	134	3	be	be	AUX
cana-2861	134	4	a	a	DET
cana-2861	134	5	quadripartitioned	quadripartitione	VERB
cana-2861	134	6	neutrosophic	neutrosophic	ADJ
cana-2861	134	7	subset	subset	NOUN
cana-2861	134	8	in	in	ADP
cana-2861	134	9	the	the	DET
cana-2861	134	10	q	q	NOUN
cana-2861	134	11	-	-	PUNCT
cana-2861	134	12	nsts	nst	NOUN
cana-2861	134	13	(	(	PUNCT
cana-2861	134	14	z	z	NOUN
cana-2861	134	15	,	,	PUNCT
cana-2861	134	16	γq	γq	ADP
cana-2861	134	17	)	)	PUNCT
cana-2861	134	18	.	.	PUNCT
cana-2861	135	1	then	then	ADV
cana-2861	135	2	(	(	PUNCT
cana-2861	135	3	qnsβfr(a))c	qnsβfr(a))c	PROPN
cana-2861	135	4	=	=	ADJ
cana-2861	135	5	q	q	NOUN
cana-2861	135	6	-	-	PUNCT
cana-2861	135	7	nsβint(a	nsβint(a	NOUN
cana-2861	135	8	)	)	PUNCT
cana-2861	135	9	∪	∪	ADP
cana-2861	135	10	q	q	NOUN
cana-2861	135	11	-	-	PUNCT
cana-2861	135	12	nsβint(ac	nsβint(ac	NOUN
cana-2861	135	13	)	)	PUNCT
cana-2861	135	14	.	.	PUNCT
cana-2861	136	1	proof	proof	NOUN
cana-2861	136	2	.	.	PUNCT
cana-2861	137	1	let	let	VERB
cana-2861	137	2	a	a	DET
cana-2861	137	3	be	be	AUX
cana-2861	137	4	a	a	DET
cana-2861	137	5	quadripartitioned	quadripartitione	VERB
cana-2861	137	6	neutrosophic	neutrosophic	ADJ
cana-2861	137	7	subset	subset	NOUN
cana-2861	137	8	in	in	ADP
cana-2861	137	9	the	the	DET
cana-2861	137	10	q	q	NOUN
cana-2861	137	11	-	-	PUNCT
cana-2861	137	12	nsts	nst	NOUN
cana-2861	137	13	(	(	PUNCT
cana-2861	137	14	z	z	NOUN
cana-2861	137	15	,	,	PUNCT
cana-2861	137	16	γq	γq	ADP
cana-2861	137	17	)	)	PUNCT
cana-2861	137	18	.	.	PUNCT
cana-2861	138	1	then	then	ADV
cana-2861	138	2	by	by	ADP
cana-2861	138	3	definition	definition	NOUN
cana-2861	138	4	3.1	3.1	NUM
cana-2861	138	5	,	,	PUNCT
cana-2861	138	6	(	(	PUNCT
cana-2861	138	7	q	q	ADJ
cana-2861	138	8	-	-	ADJ
cana-2861	138	9	nsβfr(a))c	nsβfr(a))c	ADJ
cana-2861	138	10	=	=	SYM
cana-2861	138	11	(	(	PUNCT
cana-2861	138	12	q	q	ADJ
cana-2861	138	13	-	-	PUNCT
cana-2861	138	14	nsβcl(a)∩q	nsβcl(a)∩q	ADJ
cana-2861	138	15	-	-	ADJ
cana-2861	138	16	nsβcl(ac))c	nsβcl(ac))c	ADJ
cana-2861	138	17	=	=	PUNCT
cana-2861	138	18	(	(	PUNCT
cana-2861	138	19	(	(	PUNCT
cana-2861	138	20	q	q	ADJ
cana-2861	138	21	-	-	PUNCT
cana-2861	138	22	nsβcl(a))c∪(q	nsβcl(a))c∪(q	NOUN
cana-2861	138	23	-	-	PUNCT
cana-2861	138	24	nsβcl(ac))c	nsβcl(ac))c	NOUN
cana-2861	138	25	.	.	PUNCT
cana-2861	139	1	by	by	ADP
cana-2861	139	2	theorem(ii	theorem(ii	NOUN
cana-2861	139	3	)	)	PUNCT
cana-2861	139	4	,	,	PUNCT
cana-2861	139	5	which	which	PRON
cana-2861	139	6	is	be	AUX
cana-2861	139	7	equal	equal	ADJ
cana-2861	139	8	to	to	ADP
cana-2861	139	9	q	q	NOUN
cana-2861	139	10	-	-	PUNCT
cana-2861	139	11	nsβint(ac	nsβint(ac	ADJ
cana-2861	139	12	)	)	PUNCT
cana-2861	139	13	q	q	NOUN
cana-2861	139	14	-	-	PUNCT
cana-2861	139	15	nsβint(a	nsβint(a	NOUN
cana-2861	139	16	)	)	PUNCT
cana-2861	139	17	.	.	PUNCT
cana-2861	140	1	hence	hence	ADV
cana-2861	140	2	(	(	PUNCT
cana-2861	140	3	q	q	ADJ
cana-2861	140	4	-	-	ADJ
cana-2861	140	5	nsβfr(a))c	nsβfr(a))c	ADJ
cana-2861	140	6	=	=	PUNCT
cana-2861	140	7	qnsβint(a)∪qnsβint(ac	qnsβint(a)∪qnsβint(ac	NOUN
cana-2861	140	8	)	)	PUNCT
cana-2861	140	9	.	.	PUNCT
cana-2861	141	1	theorem	theorem	VERB
cana-2861	141	2	3.9	3.9	NUM
cana-2861	141	3	.	.	PUNCT
cana-2861	142	1	for	for	ADP
cana-2861	142	2	a	a	DET
cana-2861	142	3	quadripartitioned	quadripartitione	VERB
cana-2861	142	4	neutrosophic	neutrosophic	PROPN
cana-2861	142	5	subset	subset	VERB
cana-2861	142	6	a	a	PRON
cana-2861	142	7	in	in	ADP
cana-2861	142	8	the	the	DET
cana-2861	142	9	q	q	NOUN
cana-2861	142	10	-	-	PUNCT
cana-2861	142	11	nsts	nst	NOUN
cana-2861	142	12	(	(	PUNCT
cana-2861	142	13	z	z	NOUN
cana-2861	142	14	,	,	PUNCT
cana-2861	142	15	γq	γq	ADP
cana-2861	142	16	)	)	PUNCT
cana-2861	142	17	,	,	PUNCT
cana-2861	142	18	then	then	ADV
cana-2861	142	19	qnsβfr(a)⊆qnsfr(a	qnsβfr(a)⊆qnsfr(a	NOUN
cana-2861	142	20	)	)	PUNCT
cana-2861	142	21	.	.	PUNCT
cana-2861	143	1	proof	proof	NOUN
cana-2861	143	2	.	.	PUNCT
cana-2861	144	1	let	let	VERB
cana-2861	144	2	a	a	DET
cana-2861	144	3	be	be	AUX
cana-2861	144	4	a	a	DET
cana-2861	144	5	quadripartitioned	quadripartitione	VERB
cana-2861	144	6	neutrosophic	neutrosophic	ADJ
cana-2861	144	7	subset	subset	NOUN
cana-2861	144	8	in	in	ADP
cana-2861	144	9	the	the	DET
cana-2861	144	10	q	q	NOUN
cana-2861	144	11	-	-	PUNCT
cana-2861	144	12	nsts	nst	NOUN
cana-2861	144	13	(	(	PUNCT
cana-2861	144	14	z	z	NOUN
cana-2861	144	15	,	,	PUNCT
cana-2861	144	16	γq	γq	ADP
cana-2861	144	17	)	)	PUNCT
cana-2861	144	18	.	.	PUNCT
cana-2861	145	1	then	then	ADV
cana-2861	145	2	by	by	ADP
cana-2861	145	3	definition	definition	NOUN
cana-2861	145	4	2.7	2.7	NUM
cana-2861	145	5	,	,	PUNCT
cana-2861	145	6	q	q	ADJ
cana-2861	145	7	-	-	PUNCT
cana-2861	145	8	nsβcl(a)⊇q	nsβcl(a)⊇q	NOUN
cana-2861	145	9	-	-	PUNCT
cana-2861	145	10	nsβcl(a	nsβcl(a	NOUN
cana-2861	145	11	)	)	PUNCT
cana-2861	145	12	and	and	CCONJ
cana-2861	145	13	q	q	ADJ
cana-2861	145	14	-	-	PUNCT
cana-2861	145	15	nsβcl(ac)⊆q	nsβcl(ac)⊆q	NOUN
cana-2861	145	16	-	-	NOUN
cana-2861	145	17	nscl(ac	nscl(ac	NOUN
cana-2861	145	18	)	)	PUNCT
cana-2861	145	19	.	.	PUNCT
cana-2861	146	1	by	by	ADP
cana-2861	146	2	definition	definition	NOUN
cana-2861	146	3	3.1	3.1	NUM
cana-2861	146	4	,	,	PUNCT
cana-2861	146	5	q	q	NOUN
cana-2861	146	6	-	-	PUNCT
cana-2861	146	7	nsβfr(a	nsβfr(a	NOUN
cana-2861	146	8	)	)	PUNCT
cana-2861	146	9	=	=	SYM
cana-2861	146	10	qnsβcl(a)∩q	qnsβcl(a)∩q	NUM
cana-2861	146	11	-	-	PUNCT
cana-2861	146	12	nsβcl(ac)⊆q	nsβcl(ac)⊆q	NOUN
cana-2861	146	13	-	-	PUNCT
cana-2861	146	14	nscl(a)∩q	nscl(a)∩q	NOUN
cana-2861	146	15	-	-	NOUN
cana-2861	146	16	nscl(ac	nscl(ac	NOUN
cana-2861	146	17	)	)	PUNCT
cana-2861	146	18	,	,	PUNCT
cana-2861	146	19	this	this	PRON
cana-2861	146	20	is	be	AUX
cana-2861	146	21	equal	equal	ADJ
cana-2861	146	22	to	to	ADP
cana-2861	146	23	q	q	NOUN
cana-2861	146	24	-	-	PUNCT
cana-2861	146	25	nsfr(a	nsfr(a	NOUN
cana-2861	146	26	)	)	PUNCT
cana-2861	146	27	.	.	PUNCT
cana-2861	147	1	hence	hence	ADV
cana-2861	147	2	qnsβfr(a)⊆q	qnsβfr(a)⊆q	PROPN
cana-2861	147	3	-	-	PUNCT
cana-2861	147	4	nsfr(a	nsfr(a	NOUN
cana-2861	147	5	)	)	PUNCT
cana-2861	147	6	.	.	PUNCT
cana-2861	148	1	theorem	theorem	VERB
cana-2861	148	2	3.10	3.10	NUM
cana-2861	148	3	.	.	PUNCT
cana-2861	149	1	for	for	ADP
cana-2861	149	2	a	a	DET
cana-2861	149	3	quadripartitioned	quadripartitione	VERB
cana-2861	149	4	neutrosophic	neutrosophic	PROPN
cana-2861	149	5	subset	subset	VERB
cana-2861	149	6	a	a	PRON
cana-2861	149	7	in	in	ADP
cana-2861	149	8	the	the	DET
cana-2861	149	9	q	q	NOUN
cana-2861	149	10	-	-	PUNCT
cana-2861	149	11	nsts	nst	NOUN
cana-2861	149	12	(	(	PUNCT
cana-2861	149	13	z	z	NOUN
cana-2861	149	14	,	,	PUNCT
cana-2861	149	15	γq	γq	ADP
cana-2861	149	16	)	)	PUNCT
cana-2861	149	17	,	,	PUNCT
cana-2861	149	18	q	q	NOUN
cana-2861	149	19	-	-	PUNCT
cana-2861	149	20	nsβcl(qnsβfr(a))⊆	nsβcl(qnsβfr(a))⊆	NOUN
cana-2861	149	21	q	q	NOUN
cana-2861	149	22	-	-	PUNCT
cana-2861	149	23	nsβfr(a	nsβfr(a	NOUN
cana-2861	149	24	)	)	PUNCT
cana-2861	149	25	.	.	PUNCT
cana-2861	150	1	proof	proof	NOUN
cana-2861	150	2	.	.	PUNCT
cana-2861	151	1	let	let	VERB
cana-2861	151	2	a	a	DET
cana-2861	151	3	be	be	AUX
cana-2861	151	4	the	the	DET
cana-2861	151	5	quadripartitioned	quadripartitioned	ADJ
cana-2861	151	6	neutrosophic	neutrosophic	PROPN
cana-2861	151	7	subset	subset	NOUN
cana-2861	151	8	in	in	ADP
cana-2861	151	9	the	the	DET
cana-2861	151	10	q	q	NOUN
cana-2861	151	11	-	-	PUNCT
cana-2861	151	12	nsts	nst	NOUN
cana-2861	151	13	(	(	PUNCT
cana-2861	151	14	z	z	NOUN
cana-2861	151	15	,	,	PUNCT
cana-2861	151	16	γq	γq	ADP
cana-2861	151	17	)	)	PUNCT
cana-2861	151	18	.	.	PUNCT
cana-2861	152	1	then	then	ADV
cana-2861	152	2	by	by	ADP
cana-2861	152	3	definition	definition	NOUN
cana-2861	152	4	3.1,q	3.1,q	NUM
cana-2861	152	5	-	-	PUNCT
cana-2861	152	6	nsβcl(q	nsβcl(q	NOUN
cana-2861	152	7	-	-	PUNCT
cana-2861	152	8	nsβfr(a	nsβfr(a	NOUN
cana-2861	152	9	)	)	PUNCT
cana-2861	152	10	)	)	PUNCT
cana-2861	153	1	=	=	PUNCT
cana-2861	153	2	q	q	ADJ
cana-2861	153	3	-	-	PUNCT
cana-2861	153	4	nsβcl(q	nsβcl(q	NOUN
cana-2861	153	5	-	-	PUNCT
cana-2861	153	6	nsβcl(a	nsβcl(a	NOUN
cana-2861	153	7	)	)	PUNCT
cana-2861	153	8	(	(	PUNCT
cana-2861	153	9	q	q	NOUN
cana-2861	153	10	-	-	PUNCT
cana-2861	153	11	nsβcl(ac)))⊆(q	nsβcl(ac)))⊆(q	NOUN
cana-2861	153	12	-	-	PUNCT
cana-2861	153	13	nsβcl(qnsβcl(a)))∩(q	nsβcl(qnsβcl(a)))∩(q	NOUN
cana-2861	153	14	-	-	PUNCT
cana-2861	153	15	nsβcl(q	nsβcl(q	NOUN
cana-2861	153	16	-	-	PUNCT
cana-2861	153	17	nsβcl(ac	nsβcl(ac	NOUN
cana-2861	153	18	)	)	PUNCT
cana-2861	153	19	)	)	PUNCT
cana-2861	153	20	)	)	PUNCT
cana-2861	153	21	.	.	PUNCT
cana-2861	154	1	by	by	ADP
cana-2861	154	2	theorem	theorem	ADJ
cana-2861	154	3	2.10	2.10	NUM
cana-2861	154	4	(	(	PUNCT
cana-2861	154	5	iii	iii	NOUN
cana-2861	154	6	)	)	PUNCT
cana-2861	154	7	,	,	PUNCT
cana-2861	154	8	q	q	NOUN
cana-2861	154	9	-	-	PUNCT
cana-2861	154	10	nsβcl(q	nsβcl(q	NOUN
cana-2861	154	11	-	-	PUNCT
cana-2861	154	12	nsδ	nsδ	NOUN
cana-2861	154	13	fr(a	fr(a	NUM
cana-2861	154	14	)	)	PUNCT
cana-2861	154	15	)	)	PUNCT
cana-2861	155	1	=	=	SYM
cana-2861	155	2	qnsβcl(a)∩(q	qnsβcl(a)∩(q	NOUN
cana-2861	155	3	-	-	PUNCT
cana-2861	155	4	nsβcl(ac	nsβcl(ac	NOUN
cana-2861	155	5	)	)	PUNCT
cana-2861	155	6	)	)	PUNCT
cana-2861	155	7	.	.	PUNCT
cana-2861	156	1	by	by	ADP
cana-2861	156	2	definition	definition	NOUN
cana-2861	156	3	3.1	3.1	NUM
cana-2861	156	4	,	,	PUNCT
cana-2861	156	5	this	this	PRON
cana-2861	156	6	is	be	AUX
cana-2861	156	7	equal	equal	ADJ
cana-2861	156	8	to	to	ADP
cana-2861	156	9	q	q	NOUN
cana-2861	156	10	-	-	PUNCT
cana-2861	156	11	nsβfr(a	nsβfr(a	NOUN
cana-2861	156	12	)	)	PUNCT
cana-2861	156	13	.	.	PUNCT
cana-2861	157	1	theorem	theorem	PROPN
cana-2861	157	2	3.11	3.11	NUM
cana-2861	157	3	.	.	PUNCT
cana-2861	158	1	for	for	ADP
cana-2861	158	2	a	a	DET
cana-2861	158	3	quadripartitioned	quadripartitione	VERB
cana-2861	158	4	neutrosophic	neutrosophic	PROPN
cana-2861	158	5	subset	subset	VERB
cana-2861	158	6	a	a	DET
cana-2861	158	7	in	in	ADP
cana-2861	158	8	the	the	DET
cana-2861	158	9	q	q	NOUN
cana-2861	158	10	-	-	PUNCT
cana-2861	158	11	nsts	nst	NOUN
cana-2861	158	12	(	(	PUNCT
cana-2861	158	13	z	z	NOUN
cana-2861	158	14	,	,	PUNCT
cana-2861	158	15	γq	γq	ADP
cana-2861	158	16	)	)	PUNCT
cana-2861	158	17	,	,	PUNCT
cana-2861	158	18	q	q	NOUN
cana-2861	158	19	-	-	NOUN
cana-2861	158	20	nsβfr(qnsβint(a	nsβfr(qnsβint(a	NUM
cana-2861	158	21	)	)	PUNCT
cana-2861	158	22	)	)	PUNCT
cana-2861	159	1	q	q	X
cana-2861	159	2	-	-	PUNCT
cana-2861	159	3	nsβfr(a	nsβfr(a	NOUN
cana-2861	159	4	)	)	PUNCT
cana-2861	159	5	.	.	PUNCT
cana-2861	160	1	proof	proof	NOUN
cana-2861	160	2	.	.	PUNCT
cana-2861	161	1	let	let	VERB
cana-2861	161	2	a	a	DET
cana-2861	161	3	be	be	AUX
cana-2861	161	4	the	the	DET
cana-2861	161	5	quadripartitioned	quadripartitioned	ADJ
cana-2861	161	6	neutrosophic	neutrosophic	PROPN
cana-2861	161	7	subset	subset	NOUN
cana-2861	161	8	in	in	ADP
cana-2861	161	9	the	the	DET
cana-2861	161	10	q	q	NOUN
cana-2861	161	11	-	-	PUNCT
cana-2861	161	12	nsts	nst	NOUN
cana-2861	161	13	(	(	PUNCT
cana-2861	161	14	z	z	NOUN
cana-2861	161	15	,	,	PUNCT
cana-2861	161	16	γq	γq	ADP
cana-2861	161	17	)	)	PUNCT
cana-2861	161	18	.	.	PUNCT
cana-2861	162	1	then	then	ADV
cana-2861	162	2	q−nsβfr(q−nsβint(a)=q−nsβcl(q−nsint(a))∩(q−nsβcl(q−nsβint(a))c)[by	q−nsβfr(q−nsβint(a)=q−nsβcl(q−nsint(a))∩(q−nsβcl(q−nsβint(a))c)[by	NOUN
cana-2861	162	3	definition	definition	NOUN
cana-2861	162	4	3.1	3.1	NUM
cana-2861	162	5	]	]	PUNCT
cana-2861	162	6	=	=	SYM
cana-2861	162	7	q−nsβcl(q−nsβint(a))∩(q−nsβcl(q−nsβcl(ac)))[by	q−nsβcl(q−nsβint(a))∩(q−nsβcl(q−nsβcl(ac)))[by	X
cana-2861	162	8	theorem	theorem	VERB
cana-2861	162	9	2.8(i	2.8(i	NUM
cana-2861	162	10	)	)	PUNCT
cana-2861	162	11	]	]	PUNCT
cana-2861	163	1	=	=	X
cana-2861	163	2	q−nsβcl(q−nsβint(a	q−nsβcl(q−nsβint(a	NOUN
cana-2861	163	3	)	)	PUNCT
cana-2861	163	4	)	)	PUNCT
cana-2861	163	5	∩	∩	NOUN
cana-2861	163	6	(	(	PUNCT
cana-2861	163	7	q−nsβcl(ac	q−nsβcl(ac	NOUN
cana-2861	163	8	)	)	PUNCT
cana-2861	163	9	)	)	PUNCT
cana-2861	163	10	[	[	PUNCT
cana-2861	163	11	by	by	ADP
cana-2861	163	12	theorem	theorem	ADJ
cana-2861	163	13	2.10	2.10	NUM
cana-2861	163	14	(	(	PUNCT
cana-2861	163	15	iii	iii	NOUN
cana-2861	163	16	)	)	PUNCT
cana-2861	163	17	]	]	PUNCT
cana-2861	163	18	⊆q−nsβcl(a	⊆q−nsβcl(a	X
cana-2861	163	19	)	)	PUNCT
cana-2861	163	20	∩	∩	NOUN
cana-2861	163	21	q−nsβcl(ac	q−nsβcl(ac	NOUN
cana-2861	163	22	)	)	PUNCT
cana-2861	163	23	[	[	PUNCT
cana-2861	163	24	by	by	ADP
cana-2861	163	25	theorem	theorem	ADJ
cana-2861	163	26	2.9	2.9	NUM
cana-2861	163	27	(	(	PUNCT
cana-2861	163	28	i	i	NOUN
cana-2861	163	29	)	)	PUNCT
cana-2861	163	30	]	]	PUNCT
cana-2861	164	1	=	=	X
cana-2861	164	2	q−nsβfr(a	q−nsβfr(a	PROPN
cana-2861	164	3	)	)	PUNCT
cana-2861	164	4	[	[	PUNCT
cana-2861	164	5	by	by	ADP
cana-2861	164	6	definition	definition	NOUN
cana-2861	164	7	3.1	3.1	NUM
cana-2861	164	8	]	]	PUNCT
cana-2861	164	9	.	.	PUNCT
cana-2861	165	1	hence	hence	ADV
cana-2861	165	2	q	q	NOUN
cana-2861	165	3	-	-	PUNCT
cana-2861	165	4	nsβfr(q	nsβfr(q	NOUN
cana-2861	165	5	-	-	PUNCT
cana-2861	165	6	nsβint(a	nsβint(a	NOUN
cana-2861	165	7	)	)	PUNCT
cana-2861	165	8	)	)	PUNCT
cana-2861	166	1	⊆	⊆	NUM
cana-2861	166	2	(	(	PUNCT
cana-2861	166	3	q	q	NOUN
cana-2861	166	4	-	-	PUNCT
cana-2861	166	5	nsβfr(a	nsβfr(a	NOUN
cana-2861	166	6	)	)	PUNCT
cana-2861	166	7	)	)	PUNCT
cana-2861	166	8	.	.	PUNCT
cana-2861	167	1	theorem	theorem	VERB
cana-2861	167	2	3.12	3.12	NUM
cana-2861	167	3	.	.	PUNCT
cana-2861	168	1	for	for	ADP
cana-2861	168	2	a	a	DET
cana-2861	168	3	quadripartitioned	quadripartitione	VERB
cana-2861	168	4	neutrosophic	neutrosophic	PROPN
cana-2861	168	5	subset	subset	VERB
cana-2861	168	6	a	a	PRON
cana-2861	168	7	in	in	ADP
cana-2861	168	8	the	the	DET
cana-2861	168	9	q	q	NOUN
cana-2861	168	10	-	-	PUNCT
cana-2861	168	11	nsts	nst	NOUN
cana-2861	168	12	(	(	PUNCT
cana-2861	168	13	z	z	NOUN
cana-2861	168	14	,	,	PUNCT
cana-2861	168	15	γq	γq	ADP
cana-2861	168	16	)	)	PUNCT
cana-2861	168	17	,	,	PUNCT
cana-2861	168	18	then	then	ADV
cana-2861	168	19	qnsβfr(qnsβcl(a	qnsβfr(qnsβcl(a	NUM
cana-2861	168	20	)	)	PUNCT
cana-2861	168	21	)	)	PUNCT
cana-2861	169	1	⊆	⊆	NUM
cana-2861	169	2	q	q	NOUN
cana-2861	169	3	-	-	PUNCT
cana-2861	169	4	nsβfr(a	nsβfr(a	NOUN
cana-2861	169	5	)	)	PUNCT
cana-2861	169	6	.	.	PUNCT
cana-2861	170	1	proof	proof	NOUN
cana-2861	170	2	.	.	PUNCT
cana-2861	171	1	let	let	VERB
cana-2861	171	2	a	a	DET
cana-2861	171	3	be	be	AUX
cana-2861	171	4	a	a	DET
cana-2861	171	5	quadripartitioned	quadripartitione	VERB
cana-2861	171	6	neutrosophic	neutrosophic	ADJ
cana-2861	171	7	subset	subset	NOUN
cana-2861	171	8	in	in	ADP
cana-2861	171	9	the	the	DET
cana-2861	171	10	q	q	NOUN
cana-2861	171	11	-	-	PUNCT
cana-2861	171	12	nsts	nst	NOUN
cana-2861	171	13	(	(	PUNCT
cana-2861	171	14	z	z	NOUN
cana-2861	171	15	,	,	PUNCT
cana-2861	171	16	γq	γq	ADP
cana-2861	171	17	)	)	PUNCT
cana-2861	171	18	.	.	PUNCT
cana-2861	172	1	then	then	ADV
cana-2861	172	2	q−nsβfr(q−nsβcl(a))=q−nsβcl(q−nsβcl(a))∩(q−nsβcl(q−nsβcl(a))c)[bydefinition	q−nsβfr(q−nsβcl(a))=q−nsβcl(q−nsβcl(a))∩(q−nsβcl(q−nsβcl(a))c)[bydefinition	NOUN
cana-2861	172	3	3.1	3.1	NUM
cana-2861	172	4	]	]	PUNCT
cana-2861	172	5	=	=	SYM
cana-2861	172	6	q−nsβcl(a)∩(q−nsβcl(q−nsβint(ac)))[bytheorem2.8(ii)and2.10(iii)&(iv	q−nsβcl(a)∩(q−nsβcl(q−nsβint(ac)))[bytheorem2.8(ii)and2.10(iii)&(iv	NOUN
cana-2861	172	7	)	)	PUNCT
cana-2861	172	8	]	]	PUNCT
cana-2861	172	9	⊆q−nsβcl(a	⊆q−nsβcl(a	X
cana-2861	172	10	)	)	PUNCT
cana-2861	172	11	∩	∩	NOUN
cana-2861	172	12	q−nsβcl(a	q−nsβcl(a	PROPN
cana-2861	172	13	)	)	PUNCT
cana-2861	173	1	[	[	X
cana-2861	173	2	by	by	ADP
cana-2861	173	3	theorem	theorem	ADJ
cana-2861	173	4	2.9	2.9	NUM
cana-2861	173	5	(	(	PUNCT
cana-2861	173	6	i	i	NOUN
cana-2861	173	7	)	)	PUNCT
cana-2861	173	8	]	]	PUNCT
cana-2861	174	1	=	=	X
cana-2861	174	2	q−nsβfr(a)[by	q−nsβfr(a)[by	PROPN
cana-2861	174	3	definition	definition	NOUN
cana-2861	174	4	3.1	3.1	NUM
cana-2861	174	5	]	]	PUNCT
cana-2861	174	6	communications	communication	NOUN
cana-2861	174	7	on	on	ADP
cana-2861	174	8	applied	apply	VERB
cana-2861	174	9	nonlinear	nonlinear	ADJ
cana-2861	174	10	analysis	analysis	NOUN
cana-2861	174	11	issn	issn	NOUN
cana-2861	174	12	:	:	PUNCT
cana-2861	174	13	1074	1074	NUM
cana-2861	174	14	-	-	PUNCT
cana-2861	174	15	133x	133x	NUM
cana-2861	174	16	vol	vol	NOUN
cana-2861	174	17	32	32	NUM
cana-2861	174	18	no	no	NOUN
cana-2861	174	19	.	.	PUNCT
cana-2861	175	1	4s	4s	NUM
cana-2861	175	2	(	(	PUNCT
cana-2861	175	3	2025	2025	NUM
cana-2861	175	4	)	)	PUNCT
cana-2861	175	5	426	426	NUM
cana-2861	175	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2861	175	7	hence	hence	ADV
cana-2861	175	8	q	q	PROPN
cana-2861	175	9	-	-	PUNCT
cana-2861	175	10	nsβfr(q	nsβfr(q	NOUN
cana-2861	175	11	-	-	PUNCT
cana-2861	175	12	nsβcl(a))⊆	nsβcl(a))⊆	NOUN
cana-2861	175	13	q	q	NOUN
cana-2861	175	14	-	-	PUNCT
cana-2861	175	15	nsβfr(a	nsβfr(a	NOUN
cana-2861	175	16	)	)	PUNCT
cana-2861	175	17	.	.	PUNCT
cana-2861	176	1	theorem	theorem	VERB
cana-2861	176	2	3.13	3.13	NUM
cana-2861	176	3	.	.	PUNCT
cana-2861	177	1	let	let	VERB
cana-2861	177	2	a	a	DET
cana-2861	177	3	be	be	AUX
cana-2861	177	4	a	a	DET
cana-2861	177	5	quadripartitioned	quadripartitione	VERB
cana-2861	177	6	neutrosophic	neutrosophic	ADJ
cana-2861	177	7	subset	subset	NOUN
cana-2861	177	8	in	in	ADP
cana-2861	177	9	the	the	DET
cana-2861	177	10	q	q	NOUN
cana-2861	177	11	-	-	PUNCT
cana-2861	177	12	nsts	nst	NOUN
cana-2861	177	13	(	(	PUNCT
cana-2861	177	14	z	z	NOUN
cana-2861	177	15	,	,	PUNCT
cana-2861	177	16	γq	γq	ADP
cana-2861	177	17	)	)	PUNCT
cana-2861	177	18	.	.	PUNCT
cana-2861	178	1	then	then	ADV
cana-2861	178	2	qnsβint(a	qnsβint(a	NOUN
cana-2861	178	3	)	)	PUNCT
cana-2861	178	4	⊆a	⊆a	NOUN
cana-2861	178	5	−	−	PROPN
cana-2861	178	6	q	q	NOUN
cana-2861	178	7	-	-	PUNCT
cana-2861	178	8	nsβfr(a	nsβfr(a	NOUN
cana-2861	178	9	)	)	PUNCT
cana-2861	178	10	.	.	PUNCT
cana-2861	179	1	proof	proof	NOUN
cana-2861	179	2	.	.	PUNCT
cana-2861	180	1	let	let	VERB
cana-2861	180	2	a	a	DET
cana-2861	180	3	be	be	AUX
cana-2861	180	4	a	a	DET
cana-2861	180	5	quadripartitioned	quadripartitione	VERB
cana-2861	180	6	neutrosophic	neutrosophic	ADJ
cana-2861	180	7	subset	subset	NOUN
cana-2861	180	8	in	in	ADP
cana-2861	180	9	the	the	DET
cana-2861	180	10	q	q	NOUN
cana-2861	180	11	-	-	PUNCT
cana-2861	180	12	nsts(z	nsts(z	NOUN
cana-2861	180	13	,	,	PUNCT
cana-2861	180	14	γq).now	γq).now	PUNCT
cana-2861	180	15	by	by	ADP
cana-2861	180	16	definition	definition	NOUN
cana-2861	180	17	3.1	3.1	NUM
cana-2861	180	18	,	,	PUNCT
cana-2861	180	19	a	a	DET
cana-2861	180	20	−	−	PROPN
cana-2861	180	21	q−nsβfr(a	q−nsβfr(a	PROPN
cana-2861	180	22	)	)	PUNCT
cana-2861	181	1	=	=	NOUN
cana-2861	181	2	a	a	DET
cana-2861	181	3	∩	∩	NOUN
cana-2861	181	4	(	(	PUNCT
cana-2861	181	5	q−nsβfr(a))c	q−nsβfr(a))c	X
cana-2861	181	6	=	=	X
cana-2861	181	7	a	a	DET
cana-2861	181	8	∩	∩	NOUN
cana-2861	181	9	[	[	X
cana-2861	181	10	q−nsβcl(a	q−nsβcl(a	ADJ
cana-2861	181	11	)	)	PUNCT
cana-2861	181	12	∩	∩	NOUN
cana-2861	181	13	q−nsβcl(ac)]c	q−nsβcl(ac)]c	NOUN
cana-2861	181	14	=	=	NOUN
cana-2861	181	15	a	a	DET
cana-2861	181	16	∩	∩	NOUN
cana-2861	181	17	[	[	X
cana-2861	181	18	q−nsβint(ac	q−nsβint(ac	NOUN
cana-2861	181	19	)	)	PUNCT
cana-2861	181	20	∪	∪	ADP
cana-2861	181	21	q−nsβint(a	q−nsβint(a	PROPN
cana-2861	181	22	)	)	PUNCT
cana-2861	181	23	]	]	PUNCT
cana-2861	182	1	=	=	PUNCT
cana-2861	182	2	[	[	X
cana-2861	182	3	a	a	DET
cana-2861	182	4	∩	∩	X
cana-2861	182	5	q−nsβint(ac	q−nsβint(ac	NOUN
cana-2861	182	6	)	)	PUNCT
cana-2861	182	7	]	]	PUNCT
cana-2861	182	8	∪	∪	ADP
cana-2861	182	9	[	[	PUNCT
cana-2861	182	10	a	a	DET
cana-2861	182	11	∩	∩	ADJ
cana-2861	182	12	q−nsβint(a	q−nsβint(a	NOUN
cana-2861	182	13	)	)	PUNCT
cana-2861	182	14	]	]	PUNCT
cana-2861	183	1	=	=	PUNCT
cana-2861	183	2	[	[	X
cana-2861	183	3	a	a	DET
cana-2861	183	4	∩	∩	X
cana-2861	183	5	q−nsβint(ac	q−nsβint(ac	NOUN
cana-2861	183	6	)	)	PUNCT
cana-2861	183	7	]	]	PUNCT
cana-2861	183	8	∪	∪	ADP
cana-2861	183	9	q−nsβint(a	q−nsβint(a	PROPN
cana-2861	183	10	)	)	PUNCT
cana-2861	183	11	⊇	⊇	PROPN
cana-2861	183	12	q−nsβint(a	q−nsβint(a	PROPN
cana-2861	183	13	)	)	PUNCT
cana-2861	183	14	hence	hence	ADV
cana-2861	183	15	q	q	PROPN
cana-2861	183	16	-	-	PUNCT
cana-2861	183	17	nsβint(a	nsβint(a	NOUN
cana-2861	183	18	)	)	PUNCT
cana-2861	183	19	⊆	⊆	PROPN
cana-2861	183	20	a	a	DET
cana-2861	183	21	−	−	NOUN
cana-2861	183	22	q	q	NOUN
cana-2861	183	23	-	-	PUNCT
cana-2861	183	24	nsβfr(a	nsβfr(a	NOUN
cana-2861	183	25	)	)	PUNCT
cana-2861	183	26	.	.	PUNCT
cana-2861	184	1	theorem	theorem	VERB
cana-2861	184	2	3.14	3.14	NUM
cana-2861	184	3	.	.	PUNCT
cana-2861	185	1	let	let	VERB
cana-2861	185	2	a	a	PRON
cana-2861	185	3	and	and	CCONJ
cana-2861	185	4	b	b	NOUN
cana-2861	185	5	be	be	AUX
cana-2861	185	6	quadripartitioned	quadripartitione	VERB
cana-2861	185	7	neutrosophic	neutrosophic	ADJ
cana-2861	185	8	subsets	subset	NOUN
cana-2861	185	9	in	in	ADP
cana-2861	185	10	the	the	DET
cana-2861	185	11	q	q	NOUN
cana-2861	185	12	-	-	PUNCT
cana-2861	185	13	nsts	nst	NOUN
cana-2861	185	14	(	(	PUNCT
cana-2861	185	15	z	z	NOUN
cana-2861	185	16	,	,	PUNCT
cana-2861	185	17	γq	γq	ADP
cana-2861	185	18	)	)	PUNCT
cana-2861	185	19	.	.	PUNCT
cana-2861	186	1	then	then	ADV
cana-2861	186	2	qnsβfr(a	qnsβfr(a	VERB
cana-2861	186	3	∪	∪	ADP
cana-2861	186	4	b	b	NOUN
cana-2861	186	5	)	)	PUNCT
cana-2861	186	6	⊆	⊆	NUM
cana-2861	186	7	q	q	NOUN
cana-2861	186	8	-	-	PUNCT
cana-2861	186	9	nsβfr(a	nsβfr(a	NOUN
cana-2861	186	10	)	)	PUNCT
cana-2861	186	11	∪	∪	ADP
cana-2861	186	12	q	q	NOUN
cana-2861	186	13	-	-	PUNCT
cana-2861	186	14	nsβfr(b	nsβfr(b	NOUN
cana-2861	186	15	)	)	PUNCT
cana-2861	186	16	.	.	PUNCT
cana-2861	187	1	proof	proof	NOUN
cana-2861	187	2	.	.	PUNCT
cana-2861	188	1	let	let	VERB
cana-2861	188	2	a	a	PRON
cana-2861	188	3	and	and	CCONJ
cana-2861	188	4	b	b	NOUN
cana-2861	188	5	be	be	AUX
cana-2861	188	6	quadripartitioned	quadripartitione	VERB
cana-2861	188	7	neutrosophic	neutrosophic	ADJ
cana-2861	188	8	subsets	subset	NOUN
cana-2861	188	9	in	in	ADP
cana-2861	188	10	the	the	DET
cana-2861	188	11	q	q	NOUN
cana-2861	188	12	-	-	PUNCT
cana-2861	188	13	nsts	nst	NOUN
cana-2861	188	14	(	(	PUNCT
cana-2861	188	15	z	z	NOUN
cana-2861	188	16	,	,	PUNCT
cana-2861	188	17	γq	γq	ADP
cana-2861	188	18	)	)	PUNCT
cana-2861	188	19	.	.	PUNCT
cana-2861	189	1	then	then	ADV
cana-2861	189	2	q−nsβfr(a	q−nsβfr(a	PROPN
cana-2861	189	3	∪	∪	ADJ
cana-2861	189	4	b	b	NOUN
cana-2861	189	5	)	)	PUNCT
cana-2861	189	6	=	=	NOUN
cana-2861	189	7	q−nsβcl(a	q−nsβcl(a	PROPN
cana-2861	189	8	∪	∪	ADP
cana-2861	189	9	b	b	NOUN
cana-2861	189	10	)	)	PUNCT
cana-2861	189	11	∩	∩	NOUN
cana-2861	189	12	q−nsβcl(a	q−nsβcl(a	PROPN
cana-2861	189	13	∪	∪	ADP
cana-2861	189	14	b)c[by	b)c[by	PROPN
cana-2861	189	15	definition	definition	NOUN
cana-2861	189	16	3.1	3.1	NUM
cana-2861	189	17	]	]	PUNCT
cana-2861	189	18	=	=	SYM
cana-2861	189	19	q−nsβcl(a	q−nsβcl(a	PROPN
cana-2861	189	20	∪	∪	CCONJ
cana-2861	189	21	b	b	NOUN
cana-2861	189	22	)	)	PUNCT
cana-2861	189	23	∩	∩	NOUN
cana-2861	189	24	q−nsβcl(ac	q−nsβcl(ac	X
cana-2861	189	25	∩	∩	X
cana-2861	189	26	bc	bc	PROPN
cana-2861	189	27	)	)	PUNCT
cana-2861	189	28	⊆(q−nsβcl(a	⊆(q−nsβcl(a	PROPN
cana-2861	189	29	)	)	PUNCT
cana-2861	189	30	∪	∪	ADP
cana-2861	189	31	q−nsβcl(b	q−nsβcl(b	PROPN
cana-2861	189	32	)	)	PUNCT
cana-2861	189	33	∩	∩	NOUN
cana-2861	189	34	(	(	PUNCT
cana-2861	189	35	(	(	PUNCT
cana-2861	189	36	q−nsβcl(a	q−nsβcl(a	PROPN
cana-2861	189	37	)	)	PUNCT
cana-2861	189	38	)	)	PUNCT
cana-2861	189	39	)	)	PUNCT
cana-2861	189	40	∩	∩	NOUN
cana-2861	189	41	(	(	PUNCT
cana-2861	189	42	q−nsβcl(b	q−nsβcl(b	PROPN
cana-2861	189	43	)	)	PUNCT
cana-2861	189	44	)	)	PUNCT
cana-2861	190	1	[	[	X
cana-2861	190	2	by	by	ADP
cana-2861	190	3	theorem	theorem	ADJ
cana-2861	190	4	2.10	2.10	NUM
cana-2861	190	5	(	(	PUNCT
cana-2861	190	6	v	v	NOUN
cana-2861	190	7	)	)	PUNCT
cana-2861	190	8	&	&	CCONJ
cana-2861	190	9	(	(	PUNCT
cana-2861	190	10	vi	vi	NOUN
cana-2861	190	11	)	)	PUNCT
cana-2861	190	12	]	]	PUNCT
cana-2861	191	1	=	=	PUNCT
cana-2861	191	2	[	[	X
cana-2861	191	3	(	(	PUNCT
cana-2861	191	4	q−nsβcl(a	q−nsβcl(a	PROPN
cana-2861	191	5	)	)	PUNCT
cana-2861	191	6	∪	∪	NOUN
cana-2861	191	7	(	(	PUNCT
cana-2861	191	8	q−nsβcl(b	q−nsβcl(b	PROPN
cana-2861	191	9	)	)	PUNCT
cana-2861	191	10	)	)	PUNCT
cana-2861	191	11	∩	∩	NOUN
cana-2861	191	12	(	(	PUNCT
cana-2861	191	13	q−nsβcl(ac	q−nsβcl(ac	NOUN
cana-2861	191	14	)	)	PUNCT
cana-2861	191	15	)	)	PUNCT
cana-2861	191	16	)	)	PUNCT
cana-2861	191	17	]	]	PUNCT
cana-2861	192	1	∩	∩	NOUN
cana-2861	192	2	[	[	X
cana-2861	192	3	(	(	PUNCT
cana-2861	192	4	q−nsβcl(a)∪	q−nsβcl(a)∪	PROPN
cana-2861	192	5	(	(	PUNCT
cana-2861	192	6	q−nsβcl(b	q−nsβcl(b	PROPN
cana-2861	192	7	)	)	PUNCT
cana-2861	192	8	)	)	PUNCT
cana-2861	192	9	∩	∩	NOUN
cana-2861	192	10	(	(	PUNCT
cana-2861	192	11	q−nsβcl(bc	q−nsβcl(bc	NUM
cana-2861	192	12	)	)	PUNCT
cana-2861	192	13	)	)	PUNCT
cana-2861	192	14	)	)	PUNCT
cana-2861	192	15	]	]	PUNCT
cana-2861	193	1	=	=	PUNCT
cana-2861	193	2	[	[	X
cana-2861	193	3	(	(	PUNCT
cana-2861	193	4	q−nsβcl(a	q−nsβcl(a	ADJ
cana-2861	193	5	)	)	PUNCT
cana-2861	193	6	∩	∩	NOUN
cana-2861	193	7	q−nsβcl(ac	q−nsβcl(ac	NOUN
cana-2861	193	8	)	)	PUNCT
cana-2861	193	9	)	)	PUNCT
cana-2861	193	10	∪	∪	X
cana-2861	193	11	(	(	PUNCT
cana-2861	193	12	(	(	PUNCT
cana-2861	193	13	q−nsβcl(b	q−nsβcl(b	PROPN
cana-2861	193	14	)	)	PUNCT
cana-2861	193	15	∩	∩	NOUN
cana-2861	193	16	(	(	PUNCT
cana-2861	193	17	q−nsβcl(ac))))]∩	q−nsβcl(ac))))]∩	NOUN
cana-2861	193	18	[	[	X
cana-2861	193	19	(	(	PUNCT
cana-2861	193	20	q−nsβcl(a	q−nsβcl(a	ADJ
cana-2861	193	21	)	)	PUNCT
cana-2861	193	22	∩	∩	NOUN
cana-2861	193	23	(	(	PUNCT
cana-2861	193	24	q−nsβcl(bc	q−nsβcl(bc	NUM
cana-2861	193	25	)	)	PUNCT
cana-2861	193	26	)	)	PUNCT
cana-2861	193	27	)	)	PUNCT
cana-2861	193	28	∪	∪	X
cana-2861	193	29	(	(	PUNCT
cana-2861	193	30	(	(	PUNCT
cana-2861	193	31	q−nsβcl(b	q−nsβcl(b	PROPN
cana-2861	193	32	)	)	PUNCT
cana-2861	193	33	∩	∩	NOUN
cana-2861	193	34	(	(	PUNCT
cana-2861	193	35	q−nsβcl(bc	q−nsβcl(bc	NUM
cana-2861	193	36	)	)	PUNCT
cana-2861	193	37	)	)	PUNCT
cana-2861	193	38	)	)	PUNCT
cana-2861	193	39	)	)	PUNCT
cana-2861	193	40	]	]	PUNCT
cana-2861	194	1	=	=	PUNCT
cana-2861	194	2	[	[	X
cana-2861	194	3	q−nsβfr(a	q−nsβfr(a	PROPN
cana-2861	194	4	)	)	PUNCT
cana-2861	194	5	∪	∪	NOUN
cana-2861	194	6	(	(	PUNCT
cana-2861	194	7	q−nsβcl(b	q−nsβcl(b	PROPN
cana-2861	194	8	)	)	PUNCT
cana-2861	194	9	)	)	PUNCT
cana-2861	194	10	∩	∩	NOUN
cana-2861	194	11	(	(	PUNCT
cana-2861	194	12	q−nsβcl(ac	q−nsβcl(ac	NOUN
cana-2861	194	13	)	)	PUNCT
cana-2861	194	14	)	)	PUNCT
cana-2861	194	15	]	]	PUNCT
cana-2861	195	1	∩	∩	NOUN
cana-2861	195	2	[	[	X
cana-2861	195	3	(	(	PUNCT
cana-2861	195	4	q−nsβcl(a)∩	q−nsβcl(a)∩	X
cana-2861	195	5	(	(	PUNCT
cana-2861	195	6	q−nsβcl(bc	q−nsβcl(bc	NUM
cana-2861	195	7	)	)	PUNCT
cana-2861	195	8	)	)	PUNCT
cana-2861	195	9	)	)	PUNCT
cana-2861	195	10	∪	∪	ADP
cana-2861	195	11	(	(	PUNCT
cana-2861	195	12	q−nsβfr(b))][by	q−nsβfr(b))][by	NUM
cana-2861	195	13	definition	definition	NOUN
cana-2861	195	14	3.1	3.1	NUM
cana-2861	195	15	]	]	X
cana-2861	195	16	=	=	PRON
cana-2861	195	17	(	(	PUNCT
cana-2861	195	18	q−nsβfr(a	q−nsβfr(a	PROPN
cana-2861	195	19	)	)	PUNCT
cana-2861	195	20	∪	∪	ADP
cana-2861	195	21	q−nsβfr(b	q−nsβfr(b	PROPN
cana-2861	195	22	)	)	PUNCT
cana-2861	195	23	)	)	PUNCT
cana-2861	195	24	∩	∩	NOUN
cana-2861	195	25	[	[	X
cana-2861	195	26	(	(	PUNCT
cana-2861	195	27	q−nsβcl(b	q−nsβcl(b	PROPN
cana-2861	195	28	)	)	PUNCT
cana-2861	195	29	∩	∩	NOUN
cana-2861	195	30	(	(	PUNCT
cana-2861	195	31	q−nsβcl(ac)))∪	q−nsβcl(ac)))∪	PROPN
cana-2861	195	32	(	(	PUNCT
cana-2861	195	33	(	(	PUNCT
cana-2861	195	34	q−nsβcl(a	q−nsβcl(a	PROPN
cana-2861	195	35	)	)	PUNCT
cana-2861	195	36	∩	∩	NOUN
cana-2861	195	37	q−nsβcl(bc	q−nsβcl(bc	NOUN
cana-2861	195	38	)	)	PUNCT
cana-2861	195	39	)	)	PUNCT
cana-2861	195	40	)	)	PUNCT
cana-2861	195	41	]	]	PUNCT
cana-2861	196	1	⊆q−nsβfr(a	⊆q−nsβfr(a	VERB
cana-2861	196	2	)	)	PUNCT
cana-2861	196	3	∪	∪	ADP
cana-2861	196	4	q−nsβfr(b	q−nsβfr(b	PROPN
cana-2861	196	5	)	)	PUNCT
cana-2861	196	6	.	.	PUNCT
cana-2861	197	1	hence	hence	ADV
cana-2861	197	2	,	,	PUNCT
cana-2861	197	3	q	q	NOUN
cana-2861	197	4	-	-	PUNCT
cana-2861	197	5	nsβfr(a	nsβfr(a	ADV
cana-2861	197	6	∪	∪	ADJ
cana-2861	197	7	b	b	NOUN
cana-2861	197	8	)	)	PUNCT
cana-2861	197	9	⊆	⊆	NUM
cana-2861	197	10	q	q	NOUN
cana-2861	197	11	-	-	PUNCT
cana-2861	197	12	nsβfr(a	nsβfr(a	NOUN
cana-2861	197	13	)	)	PUNCT
cana-2861	197	14	∪	∪	ADP
cana-2861	197	15	q	q	NOUN
cana-2861	197	16	-	-	PUNCT
cana-2861	197	17	nsβfr(b	nsβfr(b	NOUN
cana-2861	197	18	)	)	PUNCT
cana-2861	197	19	.	.	PUNCT
cana-2861	198	1	theorem	theorem	VERB
cana-2861	198	2	3.15	3.15	NUM
cana-2861	198	3	.	.	PUNCT
cana-2861	199	1	for	for	ADP
cana-2861	199	2	any	any	DET
cana-2861	199	3	quadripartitioned	quadripartitione	VERB
cana-2861	199	4	neutrosophic	neutrosophic	ADJ
cana-2861	199	5	subsets	subset	NOUN
cana-2861	199	6	a	a	PRON
cana-2861	199	7	and	and	CCONJ
cana-2861	199	8	b	b	NOUN
cana-2861	199	9	in	in	ADP
cana-2861	199	10	the	the	DET
cana-2861	199	11	q	q	NOUN
cana-2861	199	12	-	-	PUNCT
cana-2861	199	13	nsts	nst	NOUN
cana-2861	199	14	(	(	PUNCT
cana-2861	199	15	z	z	NOUN
cana-2861	199	16	,	,	PUNCT
cana-2861	199	17	γq	γq	ADP
cana-2861	199	18	)	)	PUNCT
cana-2861	199	19	,	,	PUNCT
cana-2861	199	20	qnsβfr(a∩	qnsβfr(a∩	PROPN
cana-2861	199	21	b	b	X
cana-2861	199	22	)	)	PUNCT
cana-2861	199	23	⊆	⊆	NUM
cana-2861	199	24	(	(	PUNCT
cana-2861	199	25	q	q	NOUN
cana-2861	199	26	-	-	PUNCT
cana-2861	199	27	nsβfr(a	nsβfr(a	NOUN
cana-2861	199	28	)	)	PUNCT
cana-2861	199	29	∩	∩	NOUN
cana-2861	199	30	(	(	PUNCT
cana-2861	199	31	q	q	NOUN
cana-2861	199	32	-	-	PUNCT
cana-2861	199	33	nsβcl(b	nsβcl(b	NOUN
cana-2861	199	34	)	)	PUNCT
cana-2861	199	35	)	)	PUNCT
cana-2861	199	36	)	)	PUNCT
cana-2861	199	37	∪	∪	ADP
cana-2861	199	38	(	(	PUNCT
cana-2861	199	39	q	q	NOUN
cana-2861	199	40	-	-	PUNCT
cana-2861	199	41	nsβfr(b	nsβfr(b	ADJ
cana-2861	199	42	)	)	PUNCT
cana-2861	199	43	∩	∩	ADJ
cana-2861	199	44	q	q	X
cana-2861	199	45	-	-	PUNCT
cana-2861	199	46	nsβcl(a	nsβcl(a	NOUN
cana-2861	199	47	)	)	PUNCT
cana-2861	199	48	)	)	PUNCT
cana-2861	199	49	.	.	PUNCT
cana-2861	200	1	proof	proof	NOUN
cana-2861	200	2	.	.	PUNCT
cana-2861	201	1	let	let	VERB
cana-2861	201	2	a	a	PRON
cana-2861	201	3	and	and	CCONJ
cana-2861	201	4	b	b	NOUN
cana-2861	201	5	be	be	AUX
cana-2861	201	6	quadripartitioned	quadripartitione	VERB
cana-2861	201	7	neutrosophic	neutrosophic	ADJ
cana-2861	201	8	subsets	subset	NOUN
cana-2861	201	9	in	in	ADP
cana-2861	201	10	the	the	DET
cana-2861	201	11	q	q	NOUN
cana-2861	201	12	-	-	PUNCT
cana-2861	201	13	nsts	nst	NOUN
cana-2861	201	14	(	(	PUNCT
cana-2861	201	15	z	z	NOUN
cana-2861	201	16	,	,	PUNCT
cana-2861	201	17	γq	γq	ADP
cana-2861	201	18	)	)	PUNCT
cana-2861	201	19	.	.	PUNCT
cana-2861	202	1	then	then	ADV
cana-2861	202	2	q−nsβfr(a	q−nsβfr(a	PROPN
cana-2861	202	3	∩	∩	ADJ
cana-2861	202	4	b	b	NOUN
cana-2861	202	5	)	)	PUNCT
cana-2861	202	6	communications	communication	NOUN
cana-2861	202	7	on	on	ADP
cana-2861	202	8	applied	apply	VERB
cana-2861	202	9	nonlinear	nonlinear	ADJ
cana-2861	202	10	analysis	analysis	NOUN
cana-2861	202	11	issn	issn	NOUN
cana-2861	202	12	:	:	PUNCT
cana-2861	202	13	1074	1074	NUM
cana-2861	202	14	-	-	PUNCT
cana-2861	202	15	133x	133x	NUM
cana-2861	202	16	vol	vol	NOUN
cana-2861	202	17	32	32	NUM
cana-2861	202	18	no	no	NOUN
cana-2861	202	19	.	.	PUNCT
cana-2861	203	1	4s	4s	NUM
cana-2861	203	2	(	(	PUNCT
cana-2861	203	3	2025	2025	NUM
cana-2861	203	4	)	)	PUNCT
cana-2861	203	5	427	427	NUM
cana-2861	203	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2861	203	7	=	=	SYM
cana-2861	203	8	q−nsβcl(a	q−nsβcl(a	PROPN
cana-2861	203	9	∩	∩	ADJ
cana-2861	203	10	b	b	NOUN
cana-2861	203	11	)	)	PUNCT
cana-2861	203	12	∩	∩	NOUN
cana-2861	203	13	(	(	PUNCT
cana-2861	203	14	q−nsβcl(a	q−nsβcl(a	ADJ
cana-2861	203	15	∩	∩	ADJ
cana-2861	203	16	b)c)[by	b)c)[by	NOUN
cana-2861	203	17	definition	definition	NOUN
cana-2861	203	18	3.1	3.1	NUM
cana-2861	203	19	]	]	PUNCT
cana-2861	203	20	=	=	SYM
cana-2861	203	21	q−nsβcl(a	q−nsβcl(a	X
cana-2861	203	22	∩	∩	ADJ
cana-2861	203	23	b	b	NOUN
cana-2861	203	24	)	)	PUNCT
cana-2861	203	25	∩	∩	NOUN
cana-2861	203	26	(	(	PUNCT
cana-2861	203	27	q−nsβcl(ac	q−nsβcl(ac	X
cana-2861	203	28	∪	∪	ADJ
cana-2861	203	29	bc	bc	PROPN
cana-2861	203	30	)	)	PUNCT
cana-2861	203	31	)	)	PUNCT
cana-2861	204	1	⊆(q−nsβcl(a	⊆(q−nsβcl(a	ADJ
cana-2861	204	2	)	)	PUNCT
cana-2861	204	3	∩	∩	ADJ
cana-2861	204	4	q−nsβcl(b))∩	q−nsβcl(b))∩	NOUN
cana-2861	204	5	(	(	PUNCT
cana-2861	204	6	q−nsβcl(a	q−nsβcl(a	PROPN
cana-2861	204	7	)	)	PUNCT
cana-2861	204	8	∪	∪	ADP
cana-2861	204	9	q−nsβcl(b	q−nsβcl(b	PROPN
cana-2861	204	10	)	)	PUNCT
cana-2861	204	11	)	)	PUNCT
cana-2861	205	1	[	[	X
cana-2861	205	2	by	by	ADP
cana-2861	205	3	theorem	theorem	ADJ
cana-2861	205	4	2.10	2.10	NUM
cana-2861	205	5	(	(	PUNCT
cana-2861	205	6	v	v	NOUN
cana-2861	205	7	)	)	PUNCT
cana-2861	205	8	&	&	CCONJ
cana-2861	205	9	(	(	PUNCT
cana-2861	205	10	vi	vi	NOUN
cana-2861	205	11	)	)	PUNCT
cana-2861	205	12	]	]	PUNCT
cana-2861	206	1	=	=	PUNCT
cana-2861	206	2	[	[	X
cana-2861	206	3	(	(	PUNCT
cana-2861	206	4	q−nsβcl(a)∩q−nsβcl(b))∩q−nsβcl(ac)]∪[(q−nsβcl(a)∩q−nsβcl(b))∩	q−nsβcl(a)∩q−nsβcl(b))∩q−nsβcl(ac)]∪[(q−nsβcl(a)∩q−nsβcl(b))∩	NOUN
cana-2861	206	5	q−nsβcl(bc	q−nsβcl(bc	VERB
cana-2861	206	6	)	)	PUNCT
cana-2861	206	7	]	]	PUNCT
cana-2861	207	1	=	=	X
cana-2861	207	2	(	(	PUNCT
cana-2861	207	3	q−nsβfr(a	q−nsβfr(a	PROPN
cana-2861	207	4	)	)	PUNCT
cana-2861	207	5	∩	∩	NOUN
cana-2861	207	6	q−nsβcl(b	q−nsβcl(b	PROPN
cana-2861	207	7	)	)	PUNCT
cana-2861	207	8	)	)	PUNCT
cana-2861	207	9	∪	∪	ADP
cana-2861	207	10	(	(	PUNCT
cana-2861	207	11	q−nsβfr(b	q−nsβfr(b	ADJ
cana-2861	207	12	)	)	PUNCT
cana-2861	207	13	∩	∩	ADJ
cana-2861	207	14	q−nsβcl(a))[by	q−nsβcl(a))[by	ADJ
cana-2861	207	15	definition	definition	NOUN
cana-2861	207	16	3.1	3.1	NUM
cana-2861	207	17	]	]	PUNCT
cana-2861	207	18	.	.	PUNCT
cana-2861	208	1	hence	hence	ADV
cana-2861	208	2	q	q	ADJ
cana-2861	208	3	-	-	PUNCT
cana-2861	208	4	nsβfr(a	nsβfr(a	NOUN
cana-2861	208	5	∩	∩	ADJ
cana-2861	208	6	b)⊆((q	b)⊆((q	NOUN
cana-2861	208	7	-	-	PUNCT
cana-2861	208	8	nsβfr(a)∩(q	nsβfr(a)∩(q	PROPN
cana-2861	208	9	-	-	PUNCT
cana-2861	208	10	nsβcl(b)))∪(q	nsβcl(b)))∪(q	NOUN
cana-2861	208	11	-	-	PUNCT
cana-2861	208	12	nsβfr(b)∩(q	nsβfr(b)∩(q	NOUN
cana-2861	208	13	-	-	PUNCT
cana-2861	208	14	nsβcl(a	nsβcl(a	NOUN
cana-2861	208	15	)	)	PUNCT
cana-2861	208	16	)	)	PUNCT
cana-2861	208	17	)	)	PUNCT
cana-2861	208	18	)	)	PUNCT
cana-2861	208	19	.	.	PUNCT
cana-2861	209	1	corollary	corollary	ADJ
cana-2861	209	2	3.16	3.16	NUM
cana-2861	209	3	.	.	PUNCT
cana-2861	210	1	for	for	ADP
cana-2861	210	2	any	any	DET
cana-2861	210	3	quadripartitioned	quadripartitione	VERB
cana-2861	210	4	neutrosophic	neutrosophic	ADJ
cana-2861	210	5	subsets	subset	NOUN
cana-2861	210	6	a	a	PRON
cana-2861	210	7	and	and	CCONJ
cana-2861	210	8	b	b	NOUN
cana-2861	210	9	in	in	ADP
cana-2861	210	10	the	the	DET
cana-2861	210	11	q	q	NOUN
cana-2861	210	12	-	-	PUNCT
cana-2861	210	13	nsts	nst	NOUN
cana-2861	210	14	(	(	PUNCT
cana-2861	210	15	z	z	NOUN
cana-2861	210	16	,	,	PUNCT
cana-2861	210	17	γq	γq	ADP
cana-2861	210	18	)	)	PUNCT
cana-2861	210	19	,	,	PUNCT
cana-2861	210	20	q	q	PROPN
cana-2861	210	21	-	-	PROPN
cana-2861	210	22	nsβfr(a∩	nsβfr(a∩	PROPN
cana-2861	210	23	b	b	NOUN
cana-2861	210	24	)	)	PUNCT
cana-2861	210	25	⊆	⊆	NUM
cana-2861	210	26	q	q	NOUN
cana-2861	210	27	-	-	PUNCT
cana-2861	210	28	nsβfr(a	nsβfr(a	NOUN
cana-2861	210	29	)	)	PUNCT
cana-2861	210	30	∪	∪	ADP
cana-2861	210	31	q	q	NOUN
cana-2861	210	32	-	-	PUNCT
cana-2861	210	33	nsβfr(b	nsβfr(b	NOUN
cana-2861	210	34	)	)	PUNCT
cana-2861	210	35	.	.	PUNCT
cana-2861	211	1	proof	proof	NOUN
cana-2861	211	2	.	.	PUNCT
cana-2861	212	1	let	let	VERB
cana-2861	212	2	a	a	PRON
cana-2861	212	3	and	and	CCONJ
cana-2861	212	4	b	b	NOUN
cana-2861	212	5	be	be	AUX
cana-2861	212	6	quadripartitioned	quadripartitione	VERB
cana-2861	212	7	neutrosophic	neutrosophic	ADJ
cana-2861	212	8	subsets	subset	NOUN
cana-2861	212	9	in	in	ADP
cana-2861	212	10	the	the	DET
cana-2861	212	11	q	q	NOUN
cana-2861	212	12	-	-	PUNCT
cana-2861	212	13	nsts	nst	NOUN
cana-2861	212	14	(	(	PUNCT
cana-2861	212	15	z	z	NOUN
cana-2861	212	16	,	,	PUNCT
cana-2861	212	17	γq	γq	ADP
cana-2861	212	18	)	)	PUNCT
cana-2861	212	19	.	.	PUNCT
cana-2861	213	1	then	then	ADV
cana-2861	213	2	q−nsβfr(a	q−nsβfr(a	PROPN
cana-2861	213	3	∩	∩	ADJ
cana-2861	213	4	b	b	NOUN
cana-2861	213	5	)	)	PUNCT
cana-2861	213	6	=	=	NOUN
cana-2861	213	7	q−nsβcl(a	q−nsβcl(a	ADJ
cana-2861	213	8	∩	∩	ADJ
cana-2861	213	9	b	b	NOUN
cana-2861	213	10	)	)	PUNCT
cana-2861	213	11	∩	∩	NOUN
cana-2861	213	12	(	(	PUNCT
cana-2861	213	13	q−nsβcl(a	q−nsβcl(a	ADJ
cana-2861	213	14	∩	∩	ADJ
cana-2861	213	15	b)c)[by	b)c)[by	NOUN
cana-2861	213	16	definition	definition	NOUN
cana-2861	213	17	3.1	3.1	NUM
cana-2861	213	18	]	]	PUNCT
cana-2861	213	19	=	=	SYM
cana-2861	213	20	q−nsβcl(a	q−nsβcl(a	X
cana-2861	213	21	∩	∩	ADJ
cana-2861	213	22	b	b	NOUN
cana-2861	213	23	)	)	PUNCT
cana-2861	213	24	∩	∩	NOUN
cana-2861	213	25	(	(	PUNCT
cana-2861	213	26	q−nsβcl(ac∪bc	q−nsβcl(ac∪bc	NUM
cana-2861	213	27	)	)	PUNCT
cana-2861	213	28	⊆(q−nsβcl(a	⊆(q−nsβcl(a	ADJ
cana-2861	213	29	)	)	PUNCT
cana-2861	213	30	∩	∩	NOUN
cana-2861	213	31	q−nsβcl(b	q−nsβcl(b	PROPN
cana-2861	213	32	)	)	PUNCT
cana-2861	213	33	)	)	PUNCT
cana-2861	213	34	∩	∩	NOUN
cana-2861	213	35	(	(	PUNCT
cana-2861	213	36	q−nsβcl(a	q−nsβcl(a	PROPN
cana-2861	213	37	)	)	PUNCT
cana-2861	213	38	∪	∪	ADP
cana-2861	213	39	q−nsβcl(b	q−nsβcl(b	PROPN
cana-2861	213	40	)	)	PUNCT
cana-2861	213	41	)	)	PUNCT
cana-2861	214	1	[	[	X
cana-2861	214	2	by	by	ADP
cana-2861	214	3	theorem	theorem	ADJ
cana-2861	214	4	2.10	2.10	NUM
cana-2861	214	5	(	(	PUNCT
cana-2861	214	6	v	v	NOUN
cana-2861	214	7	)	)	PUNCT
cana-2861	214	8	&	&	CCONJ
cana-2861	214	9	(	(	PUNCT
cana-2861	214	10	vi	vi	NOUN
cana-2861	214	11	)	)	PUNCT
cana-2861	214	12	]	]	PUNCT
cana-2861	215	1	=	=	X
cana-2861	215	2	(	(	PUNCT
cana-2861	215	3	q−nsβcl(a)∩q−nsβcl(b))∩(q−nsβcl(ac)∪(q−nsβcl(a)∩q−nsβcl(b))∩	q−nsβcl(a)∩q−nsβcl(b))∩(q−nsβcl(ac)∪(q−nsβcl(a)∩q−nsβcl(b))∩	X
cana-2861	215	4	(	(	PUNCT
cana-2861	215	5	q−nsβcl(bc	q−nsβcl(bc	NUM
cana-2861	215	6	)	)	PUNCT
cana-2861	215	7	)	)	PUNCT
cana-2861	215	8	)	)	PUNCT
cana-2861	215	9	=(	=(	PROPN
cana-2861	215	10	q−nsβfr(a	q−nsβfr(a	PROPN
cana-2861	215	11	)	)	PUNCT
cana-2861	215	12	∩	∩	NOUN
cana-2861	215	13	q−nsβcl(b	q−nsβcl(b	PROPN
cana-2861	215	14	)	)	PUNCT
cana-2861	215	15	)	)	PUNCT
cana-2861	216	1	∪	∪	ADP
cana-2861	216	2	(	(	PUNCT
cana-2861	216	3	q−nsβcl(a	q−nsβcl(a	ADJ
cana-2861	216	4	)	)	PUNCT
cana-2861	216	5	∩	∩	ADJ
cana-2861	216	6	q−nsβfr(b))[by	q−nsβfr(b))[by	NOUN
cana-2861	216	7	definition	definition	NOUN
cana-2861	216	8	3.1	3.1	NUM
cana-2861	216	9	]	]	PUNCT
cana-2861	216	10	⊆q−nsβfr(a	⊆q−nsβfr(a	NOUN
cana-2861	216	11	)	)	PUNCT
cana-2861	216	12	∪	∪	NOUN
cana-2861	216	13	(	(	PUNCT
cana-2861	216	14	q−nsβfr(b	q−nsβfr(b	PROPN
cana-2861	216	15	)	)	PUNCT
cana-2861	216	16	.	.	PUNCT
cana-2861	217	1	hence	hence	ADV
cana-2861	217	2	q	q	NOUN
cana-2861	217	3	-	-	PUNCT
cana-2861	217	4	nsβfr(a	nsβfr(a	ADJ
cana-2861	217	5	∩	∩	ADJ
cana-2861	217	6	b	b	X
cana-2861	217	7	)	)	PUNCT
cana-2861	217	8	⊆	⊆	NUM
cana-2861	217	9	q	q	NOUN
cana-2861	217	10	-	-	PUNCT
cana-2861	217	11	nsβfr(a	nsβfr(a	NOUN
cana-2861	217	12	)	)	PUNCT
cana-2861	217	13	∪	∪	ADP
cana-2861	217	14	q	q	NOUN
cana-2861	217	15	-	-	PUNCT
cana-2861	217	16	nsβfr(b	nsβfr(b	NOUN
cana-2861	217	17	)	)	PUNCT
cana-2861	217	18	.	.	PUNCT
cana-2861	218	1	theorem	theorem	VERB
cana-2861	218	2	3.17	3.17	NUM
cana-2861	218	3	.	.	PUNCT
cana-2861	219	1	for	for	ADP
cana-2861	219	2	any	any	DET
cana-2861	219	3	quadripartitioned	quadripartitioned	ADJ
cana-2861	219	4	neutrosophic	neutrosophic	PROPN
cana-2861	219	5	subset	subset	VERB
cana-2861	219	6	a	a	PRON
cana-2861	219	7	in	in	ADP
cana-2861	219	8	the	the	DET
cana-2861	219	9	q	q	NOUN
cana-2861	219	10	-	-	PUNCT
cana-2861	219	11	nsts	nst	NOUN
cana-2861	219	12	(	(	PUNCT
cana-2861	219	13	z	z	NOUN
cana-2861	219	14	,	,	PUNCT
cana-2861	219	15	γq	γq	ADP
cana-2861	219	16	)	)	PUNCT
cana-2861	219	17	,	,	PUNCT
cana-2861	219	18	(	(	PUNCT
cana-2861	219	19	i	i	NOUN
cana-2861	219	20	)	)	PUNCT
cana-2861	219	21	q	q	PROPN
cana-2861	219	22	-	-	PUNCT
cana-2861	219	23	nsβfr(q	nsβfr(q	NOUN
cana-2861	219	24	-	-	PUNCT
cana-2861	219	25	nsβfr(a	nsβfr(a	NOUN
cana-2861	219	26	)	)	PUNCT
cana-2861	219	27	)	)	PUNCT
cana-2861	220	1	⊆	⊆	NUM
cana-2861	220	2	q	q	NOUN
cana-2861	220	3	-	-	PUNCT
cana-2861	220	4	nsβfr(a	nsβfr(a	NOUN
cana-2861	220	5	)	)	PUNCT
cana-2861	220	6	,	,	PUNCT
cana-2861	220	7	(	(	PUNCT
cana-2861	220	8	ii	ii	NOUN
cana-2861	220	9	)	)	PUNCT
cana-2861	220	10	q	q	PROPN
cana-2861	220	11	-	-	PUNCT
cana-2861	220	12	nsβfr(q	nsβfr(q	NOUN
cana-2861	220	13	-	-	PUNCT
cana-2861	220	14	nsβfr(q	nsβfr(q	NOUN
cana-2861	220	15	-	-	PUNCT
cana-2861	220	16	nsβfr(a	nsβfr(a	NOUN
cana-2861	220	17	)	)	PUNCT
cana-2861	220	18	)	)	PUNCT
cana-2861	220	19	)	)	PUNCT
cana-2861	221	1	⊆	⊆	X
cana-2861	221	2	q	q	X
cana-2861	221	3	-	-	PUNCT
cana-2861	221	4	nsβfr(q	nsβfr(q	NOUN
cana-2861	221	5	-	-	PUNCT
cana-2861	221	6	nsβfr(a	nsβfr(a	NOUN
cana-2861	221	7	)	)	PUNCT
cana-2861	221	8	)	)	PUNCT
cana-2861	221	9	.	.	PUNCT
cana-2861	222	1	proof	proof	NOUN
cana-2861	222	2	.	.	PUNCT
cana-2861	223	1	(	(	PUNCT
cana-2861	223	2	i	i	NOUN
cana-2861	223	3	)	)	PUNCT
cana-2861	223	4	let	let	VERB
cana-2861	223	5	a	a	PRON
cana-2861	223	6	be	be	AUX
cana-2861	223	7	a	a	DET
cana-2861	223	8	quadripartitioned	quadripartitione	VERB
cana-2861	223	9	neutrosophic	neutrosophic	ADJ
cana-2861	223	10	subset	subset	NOUN
cana-2861	223	11	in	in	ADP
cana-2861	223	12	the	the	DET
cana-2861	223	13	q	q	NOUN
cana-2861	223	14	-	-	PUNCT
cana-2861	223	15	nsts	nst	NOUN
cana-2861	223	16	(	(	PUNCT
cana-2861	223	17	z	z	NOUN
cana-2861	223	18	,	,	PUNCT
cana-2861	223	19	γq	γq	ADP
cana-2861	223	20	)	)	PUNCT
cana-2861	223	21	.	.	PUNCT
cana-2861	224	1	then	then	ADV
cana-2861	224	2	q−nsβfr(q−nsβfr(a	q−nsβfr(q−nsβfr(a	NUM
cana-2861	224	3	)	)	PUNCT
cana-2861	224	4	)	)	PUNCT
cana-2861	225	1	=	=	SYM
cana-2861	225	2	q−nsβcl(q−nsβfr(a	q−nsβcl(q−nsβfr(a	NOUN
cana-2861	225	3	)	)	PUNCT
cana-2861	225	4	)	)	PUNCT
cana-2861	225	5	∩	∩	NOUN
cana-2861	225	6	q−nsβcl(q−nsβfr(a)c	q−nsβcl(q−nsβfr(a)c	NUM
cana-2861	225	7	)	)	PUNCT
cana-2861	225	8	by	by	ADP
cana-2861	225	9	[	[	X
cana-2861	225	10	definition	definition	NOUN
cana-2861	225	11	3.1	3.1	NUM
cana-2861	225	12	]	]	PUNCT
cana-2861	225	13	=	=	SYM
cana-2861	225	14	q−nsβcl(q−nsβcl(a	q−nsβcl(q−nsβcl(a	X
cana-2861	225	15	)	)	PUNCT
cana-2861	225	16	∩	∩	NOUN
cana-2861	225	17	(	(	PUNCT
cana-2861	225	18	q−nsβcl	q−nsβcl	X
cana-2861	225	19	(	(	PUNCT
cana-2861	225	20	ac	ac	PROPN
cana-2861	225	21	)	)	PUNCT
cana-2861	225	22	)	)	PUNCT
cana-2861	225	23	∩	∩	NOUN
cana-2861	225	24	(	(	PUNCT
cana-2861	225	25	q−nsβcl(q−nsβcl(a	q−nsβcl(q−nsβcl(a	NUM
cana-2861	225	26	)	)	PUNCT
cana-2861	225	27	)	)	PUNCT
cana-2861	225	28	∩	∩	NOUN
cana-2861	225	29	(	(	PUNCT
cana-2861	225	30	q−nsβcl	q−nsβcl	X
cana-2861	225	31	(	(	PUNCT
cana-2861	225	32	ac	ac	PROPN
cana-2861	225	33	)	)	PUNCT
cana-2861	225	34	)	)	PUNCT
cana-2861	225	35	c	c	X
cana-2861	225	36	)	)	PUNCT
cana-2861	225	37	)	)	PUNCT
cana-2861	225	38	by	by	ADP
cana-2861	225	39	[	[	PUNCT
cana-2861	225	40	definition	definition	NOUN
cana-2861	225	41	3.1	3.1	NUM
cana-2861	225	42	]	]	SYM
cana-2861	225	43	⊆(n	⊆(n	PROPN
cana-2861	225	44	n	n	PRON
cana-2861	225	45	δcl(q−nsβcl(a	δcl(q−nsβcl(a	PROPN
cana-2861	225	46	)	)	PUNCT
cana-2861	225	47	)	)	PUNCT
cana-2861	225	48	∩	∩	NOUN
cana-2861	225	49	(	(	PUNCT
cana-2861	225	50	q−nsβcl(q−nsβcl(a)))∩(q−nsβcl(q−nsβint(a)))∪	q−nsβcl(q−nsβcl(a)))∩(q−nsβcl(q−nsβint(a)))∪	PROPN
cana-2861	225	51	(	(	PUNCT
cana-2861	225	52	q−nsβint(a)))[by	q−nsβint(a)))[by	NOUN
cana-2861	225	53	theorem	theorem	VERB
cana-2861	225	54	2.10	2.10	NUM
cana-2861	225	55	(	(	PUNCT
cana-2861	225	56	iii	iii	NOUN
cana-2861	225	57	)	)	PUNCT
cana-2861	225	58	&	&	CCONJ
cana-2861	225	59	(	(	PUNCT
cana-2861	225	60	v	v	NOUN
cana-2861	225	61	)	)	PUNCT
cana-2861	225	62	]	]	PUNCT
cana-2861	226	1	=	=	X
cana-2861	226	2	(	(	PUNCT
cana-2861	226	3	q−nsβcl(a	q−nsβcl(a	PROPN
cana-2861	226	4	)	)	PUNCT
cana-2861	226	5	∩	∩	NOUN
cana-2861	226	6	(	(	PUNCT
cana-2861	226	7	q−nsβcl(ac	q−nsβcl(ac	NOUN
cana-2861	226	8	)	)	PUNCT
cana-2861	226	9	)	)	PUNCT
cana-2861	226	10	∩	∩	NOUN
cana-2861	226	11	(	(	PUNCT
cana-2861	226	12	q−nsβcl(q−nsβint(a	q−nsβcl(q−nsβint(a	PROPN
cana-2861	226	13	)	)	PUNCT
cana-2861	226	14	∪	∪	ADP
cana-2861	226	15	q−nsβint(a	q−nsβint(a	PROPN
cana-2861	226	16	)	)	PUNCT
cana-2861	226	17	)	)	PUNCT
cana-2861	226	18	)	)	PUNCT
cana-2861	226	19	)	)	PUNCT
cana-2861	227	1	[	[	X
cana-2861	227	2	by	by	ADP
cana-2861	227	3	theorem	theorem	ADJ
cana-2861	227	4	2.10	2.10	NUM
cana-2861	227	5	(	(	PUNCT
cana-2861	227	6	iii	iii	NOUN
cana-2861	227	7	)	)	PUNCT
cana-2861	227	8	]	]	PUNCT
cana-2861	227	9	⊆q−nsβcl(a	⊆q−nsβcl(a	X
cana-2861	227	10	)	)	PUNCT
cana-2861	227	11	∩	∩	ADJ
cana-2861	227	12	q−nsβcl(ac	q−nsβcl(ac	NOUN
cana-2861	227	13	)	)	PUNCT
cana-2861	227	14	=	=	SYM
cana-2861	227	15	q−nsβfr(a	q−nsβfr(a	PROPN
cana-2861	227	16	)	)	PUNCT
cana-2861	228	1	[	[	X
cana-2861	228	2	by	by	ADP
cana-2861	228	3	definition	definition	NOUN
cana-2861	228	4	3.1	3.1	NUM
cana-2861	228	5	]	]	PUNCT
cana-2861	228	6	.	.	PUNCT
cana-2861	229	1	communications	communication	NOUN
cana-2861	229	2	on	on	ADP
cana-2861	229	3	applied	apply	VERB
cana-2861	229	4	nonlinear	nonlinear	ADJ
cana-2861	229	5	analysis	analysis	NOUN
cana-2861	229	6	issn	issn	NOUN
cana-2861	229	7	:	:	PUNCT
cana-2861	229	8	1074	1074	NUM
cana-2861	229	9	-	-	PUNCT
cana-2861	229	10	133x	133x	NUM
cana-2861	229	11	vol	vol	NOUN
cana-2861	229	12	32	32	NUM
cana-2861	229	13	no	no	NOUN
cana-2861	229	14	.	.	PUNCT
cana-2861	230	1	4s	4s	NUM
cana-2861	230	2	(	(	PUNCT
cana-2861	230	3	2025	2025	NUM
cana-2861	230	4	)	)	PUNCT
cana-2861	230	5	428	428	NUM
cana-2861	231	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-2861	231	2	therefore	therefore	ADV
cana-2861	231	3	q	q	PROPN
cana-2861	231	4	-	-	PUNCT
cana-2861	231	5	nsβfr(q	nsβfr(q	NOUN
cana-2861	231	6	-	-	PUNCT
cana-2861	231	7	nsβfr(a	nsβfr(a	NOUN
cana-2861	231	8	)	)	PUNCT
cana-2861	231	9	)	)	PUNCT
cana-2861	232	1	⊆	⊆	NUM
cana-2861	232	2	q	q	NOUN
cana-2861	232	3	-	-	PUNCT
cana-2861	232	4	nsβfr(a	nsβfr(a	NOUN
cana-2861	232	5	)	)	PUNCT
cana-2861	232	6	.	.	PUNCT
cana-2861	233	1	(	(	PUNCT
cana-2861	233	2	ii	ii	NOUN
cana-2861	233	3	)	)	PUNCT
cana-2861	233	4	again	again	ADV
cana-2861	233	5	,	,	PUNCT
cana-2861	233	6	q	q	NOUN
cana-2861	233	7	-	-	PUNCT
cana-2861	233	8	nsβfr(q	nsβfr(q	NOUN
cana-2861	233	9	-	-	PUNCT
cana-2861	233	10	nsβfr(q	nsβfr(q	NOUN
cana-2861	233	11	-	-	PUNCT
cana-2861	233	12	nsβfr(a	nsβfr(a	NOUN
cana-2861	233	13	)	)	PUNCT
cana-2861	233	14	)	)	PUNCT
cana-2861	233	15	)	)	PUNCT
cana-2861	234	1	⊆	⊆	X
cana-2861	234	2	q	q	X
cana-2861	234	3	-	-	PUNCT
cana-2861	234	4	nsβfr(q	nsβfr(q	NOUN
cana-2861	234	5	-	-	PUNCT
cana-2861	234	6	nsβfr(a	nsβfr(a	NOUN
cana-2861	234	7	)	)	PUNCT
cana-2861	234	8	)	)	PUNCT
cana-2861	234	9	.	.	PUNCT
cana-2861	235	1	4	4	NUM
cana-2861	235	2	quadripartitioned	quadripartitione	VERB
cana-2861	235	3	neutrosophic	neutrosophic	ADJ
cana-2861	235	4	β	β	X
cana-2861	235	5	border	border	NOUN
cana-2861	235	6	and	and	CCONJ
cana-2861	235	7	quadripartitioned	quadripartitione	VERB
cana-2861	235	8	neutrosophic	neutrosophic	PROPN
cana-2861	235	9	β	β	X
cana-2861	235	10	exterior	exterior	NOUN
cana-2861	235	11	in	in	ADP
cana-2861	235	12	this	this	DET
cana-2861	235	13	section	section	NOUN
cana-2861	235	14	,	,	PUNCT
cana-2861	235	15	we	we	PRON
cana-2861	235	16	introduce	introduce	VERB
cana-2861	235	17	the	the	DET
cana-2861	235	18	quadripartitioned	quadripartitioned	ADJ
cana-2861	235	19	neutrosophic	neutrosophic	PROPN
cana-2861	235	20	β	β	PROPN
cana-2861	235	21	border	border	NOUN
cana-2861	235	22	,	,	PUNCT
cana-2861	235	23	quadripartitioned	quadripartitione	VERB
cana-2861	235	24	neutrosophic	neutrosophic	ADJ
cana-2861	235	25	β	β	PROPN
cana-2861	235	26	exterior	exterior	PROPN
cana-2861	235	27	using	use	VERB
cana-2861	235	28	quadripartitioned	quadripartitione	VERB
cana-2861	235	29	neutrosophic	neutrosophic	PROPN
cana-2861	235	30	β	β	X
cana-2861	235	31	open	open	ADJ
cana-2861	235	32	sets	set	NOUN
cana-2861	235	33	and	and	CCONJ
cana-2861	235	34	their	their	PRON
cana-2861	235	35	properties	property	NOUN
cana-2861	235	36	are	be	AUX
cana-2861	235	37	discussed	discuss	VERB
cana-2861	235	38	in	in	ADP
cana-2861	235	39	q	q	NOUN
cana-2861	235	40	-	-	NOUN
cana-2861	235	41	nsts	nst	NOUN
cana-2861	235	42	’s	’s	PART
cana-2861	235	43	.	.	PUNCT
cana-2861	236	1	definition	definition	NOUN
cana-2861	236	2	4.1	4.1	NUM
cana-2861	236	3	.	.	PUNCT
cana-2861	237	1	let	let	VERB
cana-2861	237	2	a	a	DET
cana-2861	237	3	be	be	AUX
cana-2861	237	4	a	a	DET
cana-2861	237	5	quadripartitioned	quadripartitione	VERB
cana-2861	237	6	neutrosophic	neutrosophic	ADJ
cana-2861	237	7	subset	subset	NOUN
cana-2861	237	8	of	of	ADP
cana-2861	237	9	q	q	NOUN
cana-2861	237	10	-	-	PUNCT
cana-2861	237	11	nsts	nst	NOUN
cana-2861	237	12	(	(	PUNCT
cana-2861	237	13	z	z	NOUN
cana-2861	237	14	,	,	PUNCT
cana-2861	237	15	γq	γq	ADP
cana-2861	237	16	)	)	PUNCT
cana-2861	237	17	.	.	PUNCT
cana-2861	238	1	then	then	ADV
cana-2861	238	2	the	the	DET
cana-2861	238	3	set	set	NOUN
cana-2861	238	4	q	q	PROPN
cana-2861	238	5	nsbr(a	nsbr(a	PROPN
cana-2861	238	6	)	)	PUNCT
cana-2861	238	7	=	=	PUNCT
cana-2861	238	8	a	a	DET
cana-2861	238	9	q	q	NOUN
cana-2861	238	10	-	-	PUNCT
cana-2861	238	11	nsint(a	nsint(a	NOUN
cana-2861	238	12	)	)	PUNCT
cana-2861	238	13	(	(	PUNCT
cana-2861	238	14	resp	resp	NOUN
cana-2861	238	15	.	.	PUNCT
cana-2861	239	1	q	q	X
cana-2861	239	2	-	-	PUNCT
cana-2861	239	3	nsβbr(a	nsβbr(a	NOUN
cana-2861	239	4	)	)	PUNCT
cana-2861	239	5	=	=	SYM
cana-2861	239	6	a	a	DET
cana-2861	239	7	-q	-q	PROPN
cana-2861	239	8	-	-	NOUN
cana-2861	239	9	nsβint(a	nsβint(a	NOUN
cana-2861	239	10	)	)	PUNCT
cana-2861	239	11	)	)	PUNCT
cana-2861	239	12	is	be	AUX
cana-2861	239	13	called	call	VERB
cana-2861	239	14	the	the	DET
cana-2861	239	15	quadripartitioned	quadripartitione	VERB
cana-2861	239	16	neutrosophic	neutrosophic	ADJ
cana-2861	239	17	(	(	PUNCT
cana-2861	239	18	resp	resp	PROPN
cana-2861	239	19	.	.	PUNCT
cana-2861	240	1	quadripartitioned	quadripartitione	VERB
cana-2861	240	2	neutrosophic	neutrosophic	PROPN
cana-2861	240	3	β	β	X
cana-2861	240	4	)	)	PUNCT
cana-2861	240	5	border	border	NOUN
cana-2861	240	6	of	of	ADP
cana-2861	240	7	a.	a.	NOUN
cana-2861	240	8	theorem	theorem	NOUN
cana-2861	240	9	4.2	4.2	NUM
cana-2861	240	10	.	.	PUNCT
cana-2861	241	1	if	if	SCONJ
cana-2861	241	2	a	a	DET
cana-2861	241	3	subset	subset	NOUN
cana-2861	241	4	a	a	PRON
cana-2861	241	5	of	of	ADP
cana-2861	241	6	z	z	NOUN
cana-2861	241	7	is	be	AUX
cana-2861	241	8	q	q	NOUN
cana-2861	241	9	-	-	PUNCT
cana-2861	241	10	nsβc	nsβc	ADJ
cana-2861	241	11	,	,	PUNCT
cana-2861	241	12	then	then	ADV
cana-2861	241	13	q	q	X
cana-2861	241	14	-	-	PUNCT
cana-2861	241	15	nsβbr(a	nsβbr(a	NOUN
cana-2861	241	16	)	)	PUNCT
cana-2861	241	17	=	=	SYM
cana-2861	241	18	q	q	NOUN
cana-2861	241	19	-	-	PUNCT
cana-2861	241	20	nsβfr(a	nsβfr(a	NOUN
cana-2861	241	21	)	)	PUNCT
cana-2861	241	22	.	.	PUNCT
cana-2861	242	1	proof	proof	NOUN
cana-2861	242	2	.	.	PUNCT
cana-2861	243	1	let	let	VERB
cana-2861	243	2	a	a	DET
cana-2861	243	3	be	be	AUX
cana-2861	243	4	a	a	DET
cana-2861	243	5	q	q	ADJ
cana-2861	243	6	-	-	PUNCT
cana-2861	243	7	nsβc	nsβc	NOUN
cana-2861	243	8	subset	subset	NOUN
cana-2861	243	9	of	of	ADP
cana-2861	243	10	z.	z.	PROPN
cana-2861	243	11	then	then	ADV
cana-2861	243	12	by	by	ADP
cana-2861	243	13	theorem	theorem	ADJ
cana-2861	243	14	2.8	2.8	NUM
cana-2861	243	15	(	(	PUNCT
cana-2861	243	16	ii	ii	NOUN
cana-2861	243	17	)	)	PUNCT
cana-2861	243	18	,	,	PUNCT
cana-2861	243	19	q	q	NOUN
cana-2861	243	20	-	-	PUNCT
cana-2861	243	21	nsβcl(a	nsβcl(a	ADJ
cana-2861	243	22	)	)	PUNCT
cana-2861	243	23	=	=	SYM
cana-2861	244	1	a.	a.	NOUN
cana-2861	244	2	now	now	ADV
cana-2861	244	3	,	,	PUNCT
cana-2861	244	4	qnsβfr(a	qnsβfr(a	ADJ
cana-2861	244	5	)	)	PUNCT
cana-2861	244	6	=	=	SYM
cana-2861	245	1	q	q	NOUN
cana-2861	245	2	-	-	PUNCT
cana-2861	245	3	nsβcl(a	nsβcl(a	NOUN
cana-2861	245	4	)	)	PUNCT
cana-2861	245	5	−	−	PRON
cana-2861	245	6	q	q	NOUN
cana-2861	245	7	-	-	PUNCT
cana-2861	245	8	nsβint(a	nsβint(a	NOUN
cana-2861	245	9	)	)	PUNCT
cana-2861	245	10	=	=	PUNCT
cana-2861	246	1	a	a	DET
cana-2861	246	2	−	−	PROPN
cana-2861	246	3	q	q	NOUN
cana-2861	246	4	-	-	PUNCT
cana-2861	246	5	nsβint(a	nsβint(a	NOUN
cana-2861	246	6	)	)	PUNCT
cana-2861	246	7	=	=	SYM
cana-2861	246	8	q	q	NOUN
cana-2861	246	9	-	-	PUNCT
cana-2861	246	10	nsβbr(a	nsβbr(a	NOUN
cana-2861	246	11	)	)	PUNCT
cana-2861	246	12	.	.	PUNCT
cana-2861	247	1	theorem	theorem	VERB
cana-2861	247	2	4.3	4.3	NUM
cana-2861	247	3	.	.	PUNCT
cana-2861	248	1	for	for	ADP
cana-2861	248	2	a	a	DET
cana-2861	248	3	quadripartitioned	quadripartitione	VERB
cana-2861	248	4	neutrosophic	neutrosophic	PROPN
cana-2861	248	5	subset	subset	VERB
cana-2861	248	6	a	a	PRON
cana-2861	248	7	of	of	ADP
cana-2861	248	8	z	z	PROPN
cana-2861	248	9	,	,	PUNCT
cana-2861	248	10	a	a	DET
cana-2861	248	11	=	=	ADJ
cana-2861	248	12	q	q	NOUN
cana-2861	248	13	-	-	PUNCT
cana-2861	248	14	nsβint(a	nsβint(a	NOUN
cana-2861	248	15	)	)	PUNCT
cana-2861	248	16	∪	∪	X
cana-2861	248	17	qnsβbr(a	qnsβbr(a	NOUN
cana-2861	248	18	)	)	PUNCT
cana-2861	248	19	.	.	PUNCT
cana-2861	249	1	proof	proof	NOUN
cana-2861	249	2	.	.	PUNCT
cana-2861	250	1	let	let	VERB
cana-2861	250	2	x(e1,e2,e3,e4	x(e1,e2,e3,e4	PRON
cana-2861	250	3	)	)	PUNCT
cana-2861	250	4	∈	∈	PROPN
cana-2861	250	5	a.	a.	NOUN
cana-2861	251	1	if	if	SCONJ
cana-2861	251	2	x(e1,e2,e3,e4	x(e1,e2,e3,e4	X
cana-2861	251	3	)	)	PUNCT
cana-2861	251	4	∈	∈	PROPN
cana-2861	251	5	q	q	NOUN
cana-2861	251	6	-	-	PUNCT
cana-2861	251	7	nsβint(a	nsβint(a	NOUN
cana-2861	251	8	)	)	PUNCT
cana-2861	251	9	,	,	PUNCT
cana-2861	251	10	then	then	ADV
cana-2861	251	11	the	the	DET
cana-2861	251	12	result	result	NOUN
cana-2861	251	13	is	be	AUX
cana-2861	251	14	obvious	obvious	ADJ
cana-2861	251	15	.	.	PUNCT
cana-2861	252	1	if	if	SCONJ
cana-2861	252	2	x(e1,e2,e3,e4	x(e1,e2,e3,e4	PRON
cana-2861	252	3	)	)	PUNCT
cana-2861	252	4	̸∈	̸∈	PROPN
cana-2861	252	5	q	q	PROPN
cana-2861	252	6	-	-	PUNCT
cana-2861	252	7	nsβint(a	nsβint(a	NOUN
cana-2861	252	8	)	)	PUNCT
cana-2861	252	9	,	,	PUNCT
cana-2861	252	10	then	then	ADV
cana-2861	252	11	by	by	ADP
cana-2861	252	12	the	the	DET
cana-2861	252	13	definition	definition	NOUN
cana-2861	252	14	of	of	ADP
cana-2861	252	15	q	q	NOUN
cana-2861	252	16	-	-	PUNCT
cana-2861	252	17	nsβbr(a	nsβbr(a	NOUN
cana-2861	252	18	)	)	PUNCT
cana-2861	252	19	,	,	PUNCT
cana-2861	252	20	x(e1,e2,e3,e4	x(e1,e2,e3,e4	X
cana-2861	252	21	)	)	PUNCT
cana-2861	252	22	∈	∈	PROPN
cana-2861	252	23	qnsβbr(a	qnsβbr(a	NOUN
cana-2861	252	24	)	)	PUNCT
cana-2861	252	25	.	.	PUNCT
cana-2861	253	1	hence	hence	ADV
cana-2861	253	2	x(e1,e2,e3,e4	x(e1,e2,e3,e4	X
cana-2861	253	3	)	)	PUNCT
cana-2861	253	4	∈	∈	PROPN
cana-2861	253	5	q	q	NOUN
cana-2861	253	6	-	-	PUNCT
cana-2861	253	7	nsβint(a	nsβint(a	NOUN
cana-2861	253	8	)	)	PUNCT
cana-2861	253	9	∪	∪	ADP
cana-2861	253	10	q	q	NOUN
cana-2861	253	11	-	-	PUNCT
cana-2861	253	12	nsβbr(a	nsβbr(a	NOUN
cana-2861	253	13	)	)	PUNCT
cana-2861	253	14	and	and	CCONJ
cana-2861	253	15	so	so	ADV
cana-2861	253	16	a	a	DET
cana-2861	253	17	⊆	⊆	NUM
cana-2861	253	18	q	q	NOUN
cana-2861	253	19	-	-	PUNCT
cana-2861	253	20	nsβint(a	nsβint(a	NOUN
cana-2861	253	21	)	)	PUNCT
cana-2861	253	22	∪	∪	ADP
cana-2861	253	23	q	q	NOUN
cana-2861	253	24	-	-	PUNCT
cana-2861	253	25	nsβbr(a	nsβbr(a	NOUN
cana-2861	253	26	)	)	PUNCT
cana-2861	253	27	.	.	PUNCT
cana-2861	254	1	on	on	ADP
cana-2861	254	2	the	the	DET
cana-2861	254	3	other	other	ADJ
cana-2861	254	4	hand	hand	NOUN
cana-2861	254	5	,	,	PUNCT
cana-2861	254	6	since	since	SCONJ
cana-2861	254	7	qnsβint(a	qnsβint(a	NOUN
cana-2861	254	8	)	)	PUNCT
cana-2861	254	9	⊆	⊆	NUM
cana-2861	254	10	a	a	DET
cana-2861	254	11	and	and	CCONJ
cana-2861	254	12	q	q	NOUN
cana-2861	254	13	-	-	PUNCT
cana-2861	254	14	nsβbr(a	nsβbr(a	ADJ
cana-2861	254	15	)	)	PUNCT
cana-2861	254	16	⊆	⊆	NUM
cana-2861	254	17	a	a	PRON
cana-2861	254	18	,	,	PUNCT
cana-2861	254	19	we	we	PRON
cana-2861	254	20	have	have	AUX
cana-2861	254	21	qnsβint(a	qnsβint(a	NOUN
cana-2861	254	22	)	)	PUNCT
cana-2861	254	23	∪	∪	ADP
cana-2861	254	24	q	q	NOUN
cana-2861	254	25	-	-	PUNCT
cana-2861	254	26	nsβbr(a	nsβbr(a	ADJ
cana-2861	254	27	)	)	PUNCT
cana-2861	254	28	⊆	⊆	NUM
cana-2861	254	29	a.	a.	NOUN
cana-2861	254	30	theorem	theorem	NOUN
cana-2861	254	31	4.4.for	4.4.for	ADP
cana-2861	254	32	a	a	DET
cana-2861	254	33	quadripartitioned	quadripartitione	VERB
cana-2861	254	34	neutrosophic	neutrosophic	PROPN
cana-2861	254	35	subset	subset	VERB
cana-2861	254	36	a	a	PRON
cana-2861	254	37	of	of	ADP
cana-2861	254	38	z	z	PROPN
cana-2861	254	39	,	,	PUNCT
cana-2861	254	40	q	q	ADJ
cana-2861	254	41	-	-	PUNCT
cana-2861	254	42	nsβint(a)∩q	nsβint(a)∩q	PRON
cana-2861	254	43	-	-	PUNCT
cana-2861	254	44	nsβbr(a)=0n	nsβbr(a)=0n	ADJ
cana-2861	254	45	.	.	PUNCT
cana-2861	255	1	proof	proof	NOUN
cana-2861	255	2	.	.	PUNCT
cana-2861	256	1	suppose	suppose	VERB
cana-2861	256	2	q	q	ADJ
cana-2861	256	3	-	-	PUNCT
cana-2861	256	4	nsβint(a)∩q	nsβint(a)∩q	NOUN
cana-2861	256	5	-	-	PUNCT
cana-2861	256	6	nsβbr(a)≠0n	nsβbr(a)≠0n	NOUN
cana-2861	256	7	.let	.let	PUNCT
cana-2861	257	1	x(e1,e2,e3,e4)∈	x(e1,e2,e3,e4)∈	PROPN
cana-2861	257	2	q	q	PROPN
cana-2861	257	3	-	-	PUNCT
cana-2861	257	4	nsβint(a)∩q	nsβint(a)∩q	ADV
cana-2861	257	5	-	-	PUNCT
cana-2861	257	6	nsβbr(a	nsβbr(a	NOUN
cana-2861	257	7	)	)	PUNCT
cana-2861	257	8	.	.	PUNCT
cana-2861	258	1	then	then	ADV
cana-2861	258	2	x(e1,e2,e3,e4	x(e1,e2,e3,e4	X
cana-2861	258	3	)	)	PUNCT
cana-2861	258	4	∈	∈	PROPN
cana-2861	258	5	q	q	NOUN
cana-2861	258	6	-	-	PUNCT
cana-2861	258	7	nsβint(a	nsβint(a	NOUN
cana-2861	258	8	)	)	PUNCT
cana-2861	258	9	and	and	CCONJ
cana-2861	258	10	x(e1,e2,e3,e4	x(e1,e2,e3,e4	NUM
cana-2861	258	11	)	)	PUNCT
cana-2861	258	12	∈	∈	PROPN
cana-2861	259	1	q	q	NOUN
cana-2861	259	2	-	-	PUNCT
cana-2861	259	3	nsβbr(a	nsβbr(a	NOUN
cana-2861	259	4	)	)	PUNCT
cana-2861	259	5	.	.	PUNCT
cana-2861	260	1	since	since	SCONJ
cana-2861	260	2	q	q	NOUN
cana-2861	260	3	-	-	PUNCT
cana-2861	260	4	nsβbr(a)=	nsβbr(a)=	PROPN
cana-2861	260	5	a	a	DET
cana-2861	260	6	−	−	NOUN
cana-2861	260	7	qnsβint(a	qnsβint(a	NOUN
cana-2861	260	8	)	)	PUNCT
cana-2861	260	9	,	,	PUNCT
cana-2861	260	10	then	then	ADV
cana-2861	260	11	x(e1,e2,e3,e4	x(e1,e2,e3,e4	X
cana-2861	260	12	)	)	PUNCT
cana-2861	260	13	∈	∈	PROPN
cana-2861	260	14	a.	a.	NOUN
cana-2861	260	15	but	but	CCONJ
cana-2861	260	16	x(e1,e2,e3,e4	x(e1,e2,e3,e4	NUM
cana-2861	260	17	)	)	PUNCT
cana-2861	260	18	∈	∈	PROPN
cana-2861	260	19	q	q	NOUN
cana-2861	260	20	-	-	PUNCT
cana-2861	260	21	nsβint(a	nsβint(a	NOUN
cana-2861	260	22	)	)	PUNCT
cana-2861	260	23	,	,	PUNCT
cana-2861	260	24	x(e1,e2,e3,e4	x(e1,e2,e3,e4	X
cana-2861	260	25	)	)	PUNCT
cana-2861	260	26	∈	∈	NOUN
cana-2861	260	27	a.	a.	NOUN
cana-2861	260	28	there	there	PRON
cana-2861	260	29	is	be	VERB
cana-2861	260	30	a	a	DET
cana-2861	260	31	contradiction	contradiction	NOUN
cana-2861	260	32	.	.	PUNCT
cana-2861	261	1	hence	hence	ADV
cana-2861	261	2	q	q	PROPN
cana-2861	261	3	-	-	PUNCT
cana-2861	261	4	nsβint(a	nsβint(a	NOUN
cana-2861	261	5	)	)	PUNCT
cana-2861	261	6	∩	∩	NOUN
cana-2861	261	7	q	q	X
cana-2861	261	8	-	-	PUNCT
cana-2861	261	9	nsβbr(a	nsβbr(a	NOUN
cana-2861	261	10	)	)	PUNCT
cana-2861	261	11	=	=	NOUN
cana-2861	261	12	0n	0n	NOUN
cana-2861	261	13	.	.	PUNCT
cana-2861	262	1	theorem	theorem	VERB
cana-2861	262	2	4.5	4.5	NUM
cana-2861	262	3	.	.	PUNCT
cana-2861	263	1	for	for	ADP
cana-2861	263	2	a	a	DET
cana-2861	263	3	quadripartitioned	quadripartitione	VERB
cana-2861	263	4	neutrosophic	neutrosophic	PROPN
cana-2861	263	5	subset	subset	VERB
cana-2861	263	6	a	a	PRON
cana-2861	263	7	of	of	ADP
cana-2861	263	8	z	z	PROPN
cana-2861	263	9	,	,	PUNCT
cana-2861	263	10	a	a	PRON
cana-2861	263	11	is	be	AUX
cana-2861	263	12	a	a	DET
cana-2861	263	13	q	q	NOUN
cana-2861	263	14	-	-	PUNCT
cana-2861	263	15	nsβo	nsβo	ADJ
cana-2861	263	16	set	set	VERB
cana-2861	263	17	if	if	SCONJ
cana-2861	263	18	and	and	CCONJ
cana-2861	263	19	only	only	ADV
cana-2861	263	20	if	if	SCONJ
cana-2861	263	21	qnsβbr(a	qnsβbr(a	VERB
cana-2861	263	22	)	)	PUNCT
cana-2861	263	23	=	=	PUNCT
cana-2861	263	24	0n	0n	NOUN
cana-2861	263	25	.	.	PUNCT
cana-2861	264	1	proof	proof	NOUN
cana-2861	264	2	.	.	PUNCT
cana-2861	265	1	necessity	necessity	NOUN
cana-2861	265	2	:	:	PUNCT
cana-2861	265	3	suppose	suppose	VERB
cana-2861	265	4	a	a	PRON
cana-2861	265	5	is	be	AUX
cana-2861	265	6	q	q	NOUN
cana-2861	265	7	-	-	PUNCT
cana-2861	265	8	nsβo	nsβo	ADJ
cana-2861	265	9	.	.	PUNCT
cana-2861	266	1	then	then	ADV
cana-2861	266	2	by	by	ADP
cana-2861	266	3	theorem	theorem	ADJ
cana-2861	266	4	2.9	2.9	NUM
cana-2861	266	5	(	(	PUNCT
cana-2861	266	6	ii	ii	NOUN
cana-2861	266	7	)	)	PUNCT
cana-2861	266	8	,	,	PUNCT
cana-2861	266	9	q	q	NOUN
cana-2861	266	10	-	-	PUNCT
cana-2861	266	11	nsβint(a	nsβint(a	NOUN
cana-2861	266	12	)	)	PUNCT
cana-2861	266	13	=	=	PUNCT
cana-2861	266	14	a.	a.	NOUN
cana-2861	266	15	now	now	ADV
cana-2861	266	16	,	,	PUNCT
cana-2861	266	17	qnsβbr(a	qnsβbr(a	NOUN
cana-2861	266	18	)	)	PUNCT
cana-2861	266	19	=	=	PUNCT
cana-2861	267	1	a	a	DET
cana-2861	267	2	q	q	NOUN
cana-2861	267	3	-	-	PUNCT
cana-2861	267	4	nsβint(a	nsβint(a	NOUN
cana-2861	267	5	)	)	PUNCT
cana-2861	267	6	=	=	PUNCT
cana-2861	268	1	a	a	DET
cana-2861	268	2	a	a	DET
cana-2861	268	3	=	=	NOUN
cana-2861	268	4	0n	0n	NUM
cana-2861	268	5	.	.	PUNCT
cana-2861	269	1	sufficiency	sufficiency	NOUN
cana-2861	269	2	:	:	PUNCT
cana-2861	269	3	suppose	suppose	VERB
cana-2861	269	4	q	q	X
cana-2861	269	5	-	-	PUNCT
cana-2861	269	6	nsβbr(a	nsβbr(a	NOUN
cana-2861	269	7	)	)	PUNCT
cana-2861	269	8	=	=	PUNCT
cana-2861	269	9	0n	0n	NOUN
cana-2861	269	10	.	.	PUNCT
cana-2861	270	1	this	this	PRON
cana-2861	270	2	implies	imply	VERB
cana-2861	270	3	,	,	PUNCT
cana-2861	270	4	a	a	DET
cana-2861	270	5	q	q	NOUN
cana-2861	270	6	-	-	PUNCT
cana-2861	270	7	nsβint(a	nsβint(a	NOUN
cana-2861	270	8	)	)	PUNCT
cana-2861	270	9	=	=	PUNCT
cana-2861	270	10	0n	0n	NOUN
cana-2861	270	11	.	.	PUNCT
cana-2861	271	1	therefore	therefore	ADV
cana-2861	271	2	a	a	DET
cana-2861	271	3	=	=	SYM
cana-2861	271	4	qnsβint(a	qnsβint(a	NOUN
cana-2861	271	5	)	)	PUNCT
cana-2861	271	6	and	and	CCONJ
cana-2861	271	7	hence	hence	ADV
cana-2861	271	8	a	a	PRON
cana-2861	271	9	is	be	AUX
cana-2861	271	10	q	q	NOUN
cana-2861	271	11	-	-	PUNCT
cana-2861	271	12	nsβo	nsβo	ADJ
cana-2861	271	13	.	.	PUNCT
cana-2861	272	1	corollary	corollary	ADJ
cana-2861	272	2	4.6	4.6	NUM
cana-2861	272	3	.	.	PUNCT
cana-2861	273	1	for	for	ADP
cana-2861	273	2	a	a	DET
cana-2861	273	3	q	q	NOUN
cana-2861	273	4	-	-	NOUN
cana-2861	273	5	nsts	nst	NOUN
cana-2861	273	6	,	,	PUNCT
cana-2861	273	7	q	q	ADJ
cana-2861	273	8	-	-	ADJ
cana-2861	273	9	nsβbr(0n	nsβbr(0n	ADJ
cana-2861	273	10	)	)	PUNCT
cana-2861	273	11	=	=	NOUN
cana-2861	273	12	0n	0n	NOUN
cana-2861	273	13	and	and	CCONJ
cana-2861	273	14	q	q	NOUN
cana-2861	273	15	-	-	PUNCT
cana-2861	273	16	nsβbr(1n	nsβbr(1n	NOUN
cana-2861	273	17	)	)	PUNCT
cana-2861	273	18	=	=	PUNCT
cana-2861	273	19	0n	0n	NOUN
cana-2861	273	20	.	.	PUNCT
cana-2861	274	1	proof.since	proof.since	NOUN
cana-2861	274	2	0n	0n	NOUN
cana-2861	274	3	and	and	CCONJ
cana-2861	274	4	1n	1n	NUM
cana-2861	274	5	are	be	AUX
cana-2861	274	6	q	q	NOUN
cana-2861	274	7	-	-	PUNCT
cana-2861	274	8	nsβo	nsβo	ADJ
cana-2861	274	9	,	,	PUNCT
cana-2861	274	10	by	by	ADP
cana-2861	274	11	theorem	theorem	ADJ
cana-2861	274	12	4.5,q	4.5,q	NUM
cana-2861	274	13	-	-	NUM
cana-2861	274	14	nsβbr(0n)=0n	nsβbr(0n)=0n	NUM
cana-2861	274	15	and	and	CCONJ
cana-2861	274	16	q	q	ADJ
cana-2861	274	17	-	-	PUNCT
cana-2861	274	18	nsβbr(1n)=	nsβbr(1n)=	ADV
cana-2861	274	19	0n	0n	NOUN
cana-2861	274	20	communications	communication	NOUN
cana-2861	274	21	on	on	ADP
cana-2861	274	22	applied	apply	VERB
cana-2861	274	23	nonlinear	nonlinear	ADJ
cana-2861	274	24	analysis	analysis	NOUN
cana-2861	274	25	issn	issn	NOUN
cana-2861	274	26	:	:	PUNCT
cana-2861	274	27	1074	1074	NUM
cana-2861	274	28	-	-	PUNCT
cana-2861	274	29	133x	133x	NUM
cana-2861	274	30	vol	vol	NOUN
cana-2861	274	31	32	32	NUM
cana-2861	274	32	no	no	NOUN
cana-2861	274	33	.	.	PUNCT
cana-2861	275	1	4s	4s	NUM
cana-2861	275	2	(	(	PUNCT
cana-2861	275	3	2025	2025	NUM
cana-2861	275	4	)	)	PUNCT
cana-2861	275	5	429	429	NUM
cana-2861	275	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2861	275	7	theorem	theorem	VERB
cana-2861	275	8	4.7	4.7	NUM
cana-2861	275	9	.	.	PUNCT
cana-2861	276	1	for	for	ADP
cana-2861	276	2	a	a	DET
cana-2861	276	3	quadripartitioned	quadripartitione	VERB
cana-2861	276	4	neutrosophic	neutrosophic	PROPN
cana-2861	276	5	subset	subset	VERB
cana-2861	276	6	a	a	PRON
cana-2861	276	7	of	of	ADP
cana-2861	276	8	z	z	PROPN
cana-2861	276	9	,	,	PUNCT
cana-2861	276	10	q	q	PROPN
cana-2861	276	11	-	-	PUNCT
cana-2861	276	12	nsβbr(q	nsβbr(q	PROPN
cana-2861	276	13	-	-	PUNCT
cana-2861	276	14	nsβint(a	nsβint(a	NOUN
cana-2861	276	15	)	)	PUNCT
cana-2861	276	16	)	)	PUNCT
cana-2861	277	1	=	=	PUNCT
cana-2861	277	2	0n	0n	NOUN
cana-2861	277	3	.	.	PUNCT
cana-2861	278	1	proof	proof	NOUN
cana-2861	278	2	.	.	PUNCT
cana-2861	279	1	by	by	ADP
cana-2861	279	2	the	the	DET
cana-2861	279	3	definition	definition	NOUN
cana-2861	279	4	of	of	ADP
cana-2861	279	5	q	q	NOUN
cana-2861	279	6	-	-	PUNCT
cana-2861	279	7	nsβ	nsβ	ADJ
cana-2861	279	8	border	border	NOUN
cana-2861	279	9	,	,	PUNCT
cana-2861	279	10	q	q	PROPN
cana-2861	279	11	-	-	PUNCT
cana-2861	279	12	nsβbr(q	nsβbr(q	PROPN
cana-2861	279	13	-	-	PUNCT
cana-2861	279	14	nsβint(a	nsβint(a	NOUN
cana-2861	279	15	)	)	PUNCT
cana-2861	279	16	)	)	PUNCT
cana-2861	280	1	=	=	SYM
cana-2861	280	2	q	q	NOUN
cana-2861	280	3	-	-	PUNCT
cana-2861	280	4	nsβint(a	nsβint(a	NOUN
cana-2861	280	5	)	)	PUNCT
cana-2861	280	6	q	q	NOUN
cana-2861	280	7	-	-	PUNCT
cana-2861	280	8	nsβint(q	nsβint(q	NUM
cana-2861	280	9	nsβint(a	nsβint(a	NOUN
cana-2861	280	10	)	)	PUNCT
cana-2861	280	11	)	)	PUNCT
cana-2861	280	12	.	.	PUNCT
cana-2861	281	1	by	by	ADP
cana-2861	281	2	theorem	theorem	ADJ
cana-2861	281	3	2.9	2.9	NUM
cana-2861	281	4	(	(	PUNCT
cana-2861	281	5	iii	iii	NOUN
cana-2861	281	6	)	)	PUNCT
cana-2861	281	7	,	,	PUNCT
cana-2861	281	8	q	q	NOUN
cana-2861	281	9	-	-	PUNCT
cana-2861	281	10	nsβint(q	nsβint(q	NOUN
cana-2861	281	11	-	-	PUNCT
cana-2861	281	12	nsβint(a	nsβint(a	NOUN
cana-2861	281	13	)	)	PUNCT
cana-2861	281	14	)	)	PUNCT
cana-2861	282	1	=	=	SYM
cana-2861	282	2	q	q	NOUN
cana-2861	282	3	-	-	PUNCT
cana-2861	282	4	nsβint(a	nsβint(a	NOUN
cana-2861	282	5	)	)	PUNCT
cana-2861	282	6	and	and	CCONJ
cana-2861	282	7	hence	hence	ADV
cana-2861	282	8	qnsβbr(qnsβint(a	qnsβbr(qnsβint(a	NUM
cana-2861	282	9	)	)	PUNCT
cana-2861	282	10	)	)	PUNCT
cana-2861	283	1	=	=	PUNCT
cana-2861	283	2	0n	0n	NOUN
cana-2861	283	3	.	.	PUNCT
cana-2861	284	1	theorem	theorem	VERB
cana-2861	284	2	4.8	4.8	NUM
cana-2861	284	3	.	.	PUNCT
cana-2861	285	1	for	for	ADP
cana-2861	285	2	a	a	DET
cana-2861	285	3	quadripartitioned	quadripartitione	VERB
cana-2861	285	4	neutrosophic	neutrosophic	PROPN
cana-2861	285	5	subset	subset	VERB
cana-2861	285	6	a	a	PRON
cana-2861	285	7	of	of	ADP
cana-2861	285	8	z	z	PROPN
cana-2861	285	9	,	,	PUNCT
cana-2861	285	10	q	q	NOUN
cana-2861	285	11	-	-	PUNCT
cana-2861	285	12	nsβint(q	nsβint(q	NOUN
cana-2861	285	13	-	-	PUNCT
cana-2861	285	14	nsβbr(a))=0n	nsβbr(a))=0n	NOUN
cana-2861	285	15	.	.	PUNCT
cana-2861	286	1	proof	proof	NOUN
cana-2861	286	2	.	.	PUNCT
cana-2861	287	1	let	let	VERB
cana-2861	287	2	x(e1,e2,e3,e4	x(e1,e2,e3,e4	PRON
cana-2861	287	3	)	)	PUNCT
cana-2861	287	4	∈	∈	PROPN
cana-2861	287	5	q	q	NOUN
cana-2861	287	6	-	-	PUNCT
cana-2861	287	7	nsβint(q	nsβint(q	NOUN
cana-2861	287	8	-	-	PUNCT
cana-2861	287	9	nsβbr(a	nsβbr(a	NOUN
cana-2861	287	10	)	)	PUNCT
cana-2861	287	11	)	)	PUNCT
cana-2861	287	12	.	.	PUNCT
cana-2861	288	1	since	since	SCONJ
cana-2861	288	2	q	q	NOUN
cana-2861	288	3	-	-	PUNCT
cana-2861	288	4	nsβbr(a	nsβbr(a	NOUN
cana-2861	288	5	)	)	PUNCT
cana-2861	288	6	⊆	⊆	NUM
cana-2861	288	7	a	a	PRON
cana-2861	288	8	,	,	PUNCT
cana-2861	288	9	by	by	ADP
cana-2861	288	10	theorem	theorem	ADJ
cana-2861	288	11	2.9	2.9	NUM
cana-2861	288	12	(	(	PUNCT
cana-2861	288	13	i	i	NOUN
cana-2861	288	14	)	)	PUNCT
cana-2861	288	15	,	,	PUNCT
cana-2861	288	16	q	q	NOUN
cana-2861	288	17	-	-	PUNCT
cana-2861	288	18	nsβint(q	nsβint(q	NOUN
cana-2861	288	19	-	-	PUNCT
cana-2861	288	20	nsβbr(a	nsβbr(a	NOUN
cana-2861	288	21	)	)	PUNCT
cana-2861	288	22	)	)	PUNCT
cana-2861	289	1	⊆	⊆	NUM
cana-2861	289	2	q	q	NOUN
cana-2861	289	3	-	-	PUNCT
cana-2861	289	4	nsβint(a	nsβint(a	NOUN
cana-2861	289	5	)	)	PUNCT
cana-2861	289	6	.	.	PUNCT
cana-2861	290	1	hence	hence	ADV
cana-2861	290	2	x(e1,e2,e3,e4	x(e1,e2,e3,e4	X
cana-2861	290	3	)	)	PUNCT
cana-2861	290	4	∈	∈	PROPN
cana-2861	290	5	q	q	NOUN
cana-2861	290	6	-	-	PUNCT
cana-2861	290	7	nsβint(a	nsβint(a	NOUN
cana-2861	290	8	)	)	PUNCT
cana-2861	290	9	.	.	PUNCT
cana-2861	291	1	since	since	SCONJ
cana-2861	291	2	qnsβint(qnsβbr(a	qnsβint(qnsβbr(a	NOUN
cana-2861	291	3	)	)	PUNCT
cana-2861	291	4	)	)	PUNCT
cana-2861	292	1	⊆	⊆	NUM
cana-2861	292	2	q	q	NOUN
cana-2861	292	3	-	-	PUNCT
cana-2861	292	4	nsβbr(a	nsβbr(a	NOUN
cana-2861	292	5	)	)	PUNCT
cana-2861	292	6	,	,	PUNCT
cana-2861	292	7	x(e1,e2,e3,e4	x(e1,e2,e3,e4	SYM
cana-2861	292	8	)	)	PUNCT
cana-2861	292	9	∈	∈	PROPN
cana-2861	292	10	q	q	NOUN
cana-2861	292	11	-	-	PUNCT
cana-2861	292	12	nsβbr(a	nsβbr(a	NOUN
cana-2861	292	13	)	)	PUNCT
cana-2861	292	14	.	.	PUNCT
cana-2861	293	1	therefore	therefore	ADV
cana-2861	293	2	x(e1,e2,e3,e4	x(e1,e2,e3,e4	X
cana-2861	293	3	)	)	PUNCT
cana-2861	293	4	∈	∈	PROPN
cana-2861	293	5	q	q	NOUN
cana-2861	293	6	-	-	PUNCT
cana-2861	293	7	nsβint(a	nsβint(a	NOUN
cana-2861	293	8	)	)	PUNCT
cana-2861	293	9	∩	∩	NOUN
cana-2861	293	10	qnsβbr(a	qnsβbr(a	NUM
cana-2861	293	11	)	)	PUNCT
cana-2861	293	12	,	,	PUNCT
cana-2861	293	13	x(e1,e2,e3,e4	x(e1,e2,e3,e4	X
cana-2861	293	14	)	)	PUNCT
cana-2861	293	15	=	=	PUNCT
cana-2861	293	16	0n	0n	NOUN
cana-2861	293	17	.	.	PUNCT
cana-2861	294	1	theorem	theorem	VERB
cana-2861	294	2	4.9	4.9	NUM
cana-2861	294	3	.	.	PUNCT
cana-2861	295	1	for	for	ADP
cana-2861	295	2	a	a	DET
cana-2861	295	3	quadripartitioned	quadripartitione	VERB
cana-2861	295	4	neutrosophic	neutrosophic	PROPN
cana-2861	295	5	subset	subset	VERB
cana-2861	295	6	a	a	PRON
cana-2861	295	7	of	of	ADP
cana-2861	295	8	z	z	PROPN
cana-2861	295	9	,	,	PUNCT
cana-2861	295	10	q	q	PROPN
cana-2861	295	11	-	-	PUNCT
cana-2861	295	12	nsβbr(q	nsβbr(q	NOUN
cana-2861	295	13	-	-	PUNCT
cana-2861	295	14	nsβbr(a	nsβbr(a	NOUN
cana-2861	295	15	)	)	PUNCT
cana-2861	295	16	)	)	PUNCT
cana-2861	296	1	=	=	SYM
cana-2861	296	2	qnsβbr(a	qnsβbr(a	NUM
cana-2861	296	3	)	)	PUNCT
cana-2861	296	4	.	.	PUNCT
cana-2861	297	1	proof	proof	NOUN
cana-2861	297	2	.	.	PUNCT
cana-2861	298	1	by	by	ADP
cana-2861	298	2	the	the	DET
cana-2861	298	3	definition	definition	NOUN
cana-2861	298	4	of	of	ADP
cana-2861	298	5	q	q	NOUN
cana-2861	298	6	-	-	PUNCT
cana-2861	298	7	nsβ	nsβ	ADJ
cana-2861	298	8	border	border	NOUN
cana-2861	298	9	,	,	PUNCT
cana-2861	298	10	q	q	PROPN
cana-2861	298	11	-	-	PUNCT
cana-2861	298	12	nsβbr(q	nsβbr(q	NOUN
cana-2861	298	13	-	-	PUNCT
cana-2861	298	14	nsβbr(a	nsβbr(a	NOUN
cana-2861	298	15	)	)	PUNCT
cana-2861	298	16	)	)	PUNCT
cana-2861	299	1	=	=	SYM
cana-2861	299	2	q	q	NOUN
cana-2861	299	3	-	-	PUNCT
cana-2861	299	4	nsβbr(a	nsβbr(a	NOUN
cana-2861	299	5	)	)	PUNCT
cana-2861	299	6	qnsβint(qnsβbr(a	qnsβint(qnsβbr(a	NOUN
cana-2861	299	7	)	)	PUNCT
cana-2861	299	8	)	)	PUNCT
cana-2861	299	9	.	.	PUNCT
cana-2861	300	1	by	by	ADP
cana-2861	300	2	theorem	theorem	ADJ
cana-2861	300	3	4.8	4.8	NUM
cana-2861	300	4	q	q	NOUN
cana-2861	300	5	-	-	PUNCT
cana-2861	300	6	nsβint(q	nsβint(q	NOUN
cana-2861	300	7	-	-	PUNCT
cana-2861	300	8	nsβbr(a	nsβbr(a	NOUN
cana-2861	300	9	)	)	PUNCT
cana-2861	300	10	)	)	PUNCT
cana-2861	301	1	=	=	SYM
cana-2861	301	2	0n	0n	NOUN
cana-2861	301	3	and	and	CCONJ
cana-2861	301	4	hence	hence	ADV
cana-2861	301	5	q	q	ADV
cana-2861	301	6	-	-	PUNCT
cana-2861	301	7	nsβbr(qnsβbr(a	nsβbr(qnsβbr(a	NUM
cana-2861	301	8	)	)	PUNCT
cana-2861	301	9	)	)	PUNCT
cana-2861	302	1	=	=	SYM
cana-2861	302	2	qnsβbr(a	qnsβbr(a	NUM
cana-2861	302	3	)	)	PUNCT
cana-2861	302	4	.	.	PUNCT
cana-2861	303	1	theorem	theorem	VERB
cana-2861	303	2	4.10	4.10	NUM
cana-2861	303	3	.	.	PUNCT
cana-2861	304	1	let	let	VERB
cana-2861	304	2	a	a	DET
cana-2861	304	3	be	be	AUX
cana-2861	304	4	a	a	DET
cana-2861	304	5	quadripartitioned	quadripartitione	VERB
cana-2861	304	6	neutrosophic	neutrosophic	ADJ
cana-2861	304	7	subset	subset	NOUN
cana-2861	304	8	of	of	ADP
cana-2861	304	9	z.	z.	PROPN
cana-2861	304	10	then	then	ADV
cana-2861	304	11	,	,	PUNCT
cana-2861	304	12	q	q	NOUN
cana-2861	304	13	-	-	PUNCT
cana-2861	304	14	nsβbr(a	nsβbr(a	NOUN
cana-2861	304	15	)	)	PUNCT
cana-2861	304	16	=	=	PUNCT
cana-2861	304	17	a	a	DET
cana-2861	304	18	∩qnsβcl(ac	∩qnsβcl(ac	NOUN
cana-2861	304	19	)	)	PUNCT
cana-2861	304	20	.	.	PUNCT
cana-2861	305	1	proof	proof	NOUN
cana-2861	305	2	.	.	PUNCT
cana-2861	306	1	since	since	SCONJ
cana-2861	306	2	q	q	NOUN
cana-2861	306	3	-	-	PUNCT
cana-2861	306	4	nsβbr(a	nsβbr(a	NOUN
cana-2861	306	5	)	)	PUNCT
cana-2861	306	6	=	=	PUNCT
cana-2861	306	7	a	a	DET
cana-2861	306	8	−	−	PROPN
cana-2861	306	9	q	q	NOUN
cana-2861	306	10	-	-	PUNCT
cana-2861	306	11	nsβint(a	nsβint(a	NOUN
cana-2861	306	12	)	)	PUNCT
cana-2861	306	13	and	and	CCONJ
cana-2861	306	14	by	by	ADP
cana-2861	306	15	theorem	theorem	ADJ
cana-2861	306	16	2.10	2.10	NUM
cana-2861	306	17	,	,	PUNCT
cana-2861	306	18	q	q	NOUN
cana-2861	306	19	-	-	PUNCT
cana-2861	306	20	nsβbr(a)=a	nsβbr(a)=a	NOUN
cana-2861	306	21	−	−	PROPN
cana-2861	306	22	(	(	PUNCT
cana-2861	306	23	qnsβcl(ac))c	qnsβcl(ac))c	PROPN
cana-2861	306	24	=	=	PUNCT
cana-2861	306	25	a	a	DET
cana-2861	306	26	∩	∩	NOUN
cana-2861	306	27	(	(	PUNCT
cana-2861	306	28	q	q	NOUN
cana-2861	306	29	-	-	PUNCT
cana-2861	306	30	nsβcl	nsβcl	NOUN
cana-2861	306	31	(	(	PUNCT
cana-2861	306	32	ac)c	ac)c	PROPN
cana-2861	306	33	)	)	PUNCT
cana-2861	306	34	=	=	PUNCT
cana-2861	307	1	a	a	DET
cana-2861	307	2	∩	∩	ADJ
cana-2861	307	3	q	q	NOUN
cana-2861	307	4	-	-	PUNCT
cana-2861	307	5	nsβcl(ac	nsβcl(ac	NOUN
cana-2861	307	6	)	)	PUNCT
cana-2861	307	7	.	.	PUNCT
cana-2861	308	1	theorem	theorem	PROPN
cana-2861	308	2	4.11	4.11	NUM
cana-2861	308	3	.	.	PUNCT
cana-2861	309	1	for	for	ADP
cana-2861	309	2	a	a	DET
cana-2861	309	3	quadripartitioned	quadripartitione	VERB
cana-2861	309	4	neutrosophic	neutrosophic	PROPN
cana-2861	309	5	subset	subset	VERB
cana-2861	309	6	a	a	PRON
cana-2861	309	7	of	of	ADP
cana-2861	309	8	z	z	PROPN
cana-2861	309	9	,	,	PUNCT
cana-2861	309	10	q	q	NOUN
cana-2861	309	11	-	-	PUNCT
cana-2861	309	12	nsβbr(a	nsβbr(a	NOUN
cana-2861	309	13	)	)	PUNCT
cana-2861	309	14	⊆	⊆	NUM
cana-2861	309	15	q	q	NOUN
cana-2861	309	16	-	-	PUNCT
cana-2861	309	17	nsβfr(a	nsβfr(a	NOUN
cana-2861	309	18	)	)	PUNCT
cana-2861	309	19	.	.	PUNCT
cana-2861	310	1	proof	proof	NOUN
cana-2861	310	2	.	.	PUNCT
cana-2861	311	1	since	since	SCONJ
cana-2861	311	2	a	a	DET
cana-2861	311	3	⊆	⊆	NUM
cana-2861	311	4	q	q	NOUN
cana-2861	311	5	-	-	PUNCT
cana-2861	311	6	nsβcl(a	nsβcl(a	NOUN
cana-2861	311	7	)	)	PUNCT
cana-2861	311	8	,	,	PUNCT
cana-2861	311	9	a	a	DET
cana-2861	311	10	−	−	PROPN
cana-2861	311	11	q	q	NOUN
cana-2861	311	12	-	-	PUNCT
cana-2861	311	13	nsβint(a	nsβint(a	NOUN
cana-2861	311	14	)	)	PUNCT
cana-2861	311	15	⊆	⊆	NUM
cana-2861	311	16	q	q	PROPN
cana-2861	311	17	-	-	PUNCT
cana-2861	311	18	nsβcl(a	nsβcl(a	NOUN
cana-2861	311	19	)	)	PUNCT
cana-2861	311	20	−	−	PRON
cana-2861	311	21	q	q	NOUN
cana-2861	311	22	-	-	PUNCT
cana-2861	311	23	nsβint(a	nsβint(a	NOUN
cana-2861	311	24	)	)	PUNCT
cana-2861	311	25	.	.	PUNCT
cana-2861	312	1	that	that	PRON
cana-2861	312	2	implies	imply	VERB
cana-2861	312	3	,	,	PUNCT
cana-2861	312	4	q	q	NOUN
cana-2861	312	5	-	-	PUNCT
cana-2861	312	6	nsβbr(a	nsβbr(a	NOUN
cana-2861	312	7	)	)	PUNCT
cana-2861	312	8	⊆	⊆	NUM
cana-2861	312	9	q	q	NOUN
cana-2861	312	10	-	-	PUNCT
cana-2861	312	11	nsβfr(a	nsβfr(a	NOUN
cana-2861	312	12	)	)	PUNCT
cana-2861	312	13	.	.	PUNCT
cana-2861	313	1	definition	definition	NOUN
cana-2861	313	2	4.12	4.12	NUM
cana-2861	313	3	.	.	PUNCT
cana-2861	314	1	let	let	VERB
cana-2861	314	2	a	a	DET
cana-2861	314	3	be	be	AUX
cana-2861	314	4	a	a	DET
cana-2861	314	5	quadripartitioned	quadripartitione	VERB
cana-2861	314	6	neutrosophic	neutrosophic	ADJ
cana-2861	314	7	subset	subset	NOUN
cana-2861	314	8	of	of	ADP
cana-2861	314	9	a	a	DET
cana-2861	314	10	q	q	NOUN
cana-2861	314	11	-	-	PUNCT
cana-2861	314	12	nsts	nst	NOUN
cana-2861	314	13	(	(	PUNCT
cana-2861	314	14	z	z	NOUN
cana-2861	314	15	,	,	PUNCT
cana-2861	314	16	γq	γq	ADP
cana-2861	314	17	)	)	PUNCT
cana-2861	314	18	.	.	PUNCT
cana-2861	315	1	the	the	DET
cana-2861	315	2	quadriparti	quadriparti	NOUN
cana-2861	315	3	tioned	tione	VERB
cana-2861	315	4	neutrosophic	neutrosophic	ADJ
cana-2861	315	5	(	(	PUNCT
cana-2861	315	6	resp	resp	NOUN
cana-2861	315	7	.	.	PUNCT
cana-2861	316	1	β	β	X
cana-2861	316	2	)	)	PUNCT
cana-2861	316	3	interior	interior	NOUN
cana-2861	316	4	of	of	ADP
cana-2861	316	5	ac	ac	PROPN
cana-2861	316	6	is	be	AUX
cana-2861	316	7	called	call	VERB
cana-2861	316	8	the	the	DET
cana-2861	316	9	quadripartitioned	quadripartitione	VERB
cana-2861	316	10	neutrosophic	neutrosophic	ADJ
cana-2861	316	11	(	(	PUNCT
cana-2861	316	12	resp	resp	PROPN
cana-2861	316	13	.	.	PUNCT
cana-2861	317	1	quadripartitioned	quadripartitione	VERB
cana-2861	317	2	neutrosophic	neutrosophic	PROPN
cana-2861	317	3	β	β	X
cana-2861	317	4	)	)	PUNCT
cana-2861	317	5	exterior	exterior	NOUN
cana-2861	317	6	of	of	ADP
cana-2861	317	7	a	a	PRON
cana-2861	318	1	and	and	CCONJ
cana-2861	318	2	it	it	PRON
cana-2861	318	3	is	be	AUX
cana-2861	318	4	denoted	denote	VERB
cana-2861	318	5	by	by	ADP
cana-2861	318	6	q	q	NOUN
cana-2861	318	7	-	-	PUNCT
cana-2861	318	8	nsext(a	nsext(a	NOUN
cana-2861	318	9	)	)	PUNCT
cana-2861	318	10	(	(	PUNCT
cana-2861	318	11	resp	resp	NOUN
cana-2861	318	12	.	.	PUNCT
cana-2861	319	1	qnsβext(a	qnsβext(a	NOUN
cana-2861	319	2	)	)	PUNCT
cana-2861	319	3	)	)	PUNCT
cana-2861	319	4	.	.	PUNCT
cana-2861	320	1	that	that	PRON
cana-2861	320	2	is	be	AUX
cana-2861	320	3	,	,	PUNCT
cana-2861	320	4	q	q	NOUN
cana-2861	320	5	-	-	PUNCT
cana-2861	320	6	nsext(a	nsext(a	NOUN
cana-2861	320	7	)	)	PUNCT
cana-2861	320	8	=	=	SYM
cana-2861	320	9	q	q	ADJ
cana-2861	320	10	-	-	PUNCT
cana-2861	320	11	nsint(ac	nsint(ac	ADJ
cana-2861	320	12	)	)	PUNCT
cana-2861	320	13	(	(	PUNCT
cana-2861	320	14	resp	resp	NOUN
cana-2861	320	15	.	.	PUNCT
cana-2861	321	1	q	q	X
cana-2861	321	2	-	-	PUNCT
cana-2861	321	3	nsβext(a	nsβext(a	NOUN
cana-2861	321	4	)	)	PUNCT
cana-2861	321	5	=	=	SYM
cana-2861	322	1	q	q	ADJ
cana-2861	322	2	-	-	PUNCT
cana-2861	322	3	nsβint(ac	nsβint(ac	NOUN
cana-2861	322	4	)	)	PUNCT
cana-2861	322	5	)	)	PUNCT
cana-2861	322	6	.	.	PUNCT
cana-2861	323	1	theorem	theorem	VERB
cana-2861	323	2	4.13	4.13	NUM
cana-2861	323	3	.	.	PUNCT
cana-2861	324	1	for	for	ADP
cana-2861	324	2	a	a	DET
cana-2861	324	3	quadripartitioned	quadripartitione	VERB
cana-2861	324	4	neutrosophic	neutrosophic	PROPN
cana-2861	324	5	subset	subset	VERB
cana-2861	324	6	a	a	PRON
cana-2861	324	7	of	of	ADP
cana-2861	324	8	z	z	PROPN
cana-2861	324	9	,	,	PUNCT
cana-2861	324	10	q	q	ADJ
cana-2861	324	11	-	-	PUNCT
cana-2861	324	12	nsβext(a)=(q	nsβext(a)=(q	X
cana-2861	324	13	-	-	PUNCT
cana-2861	324	14	nsβcl(a))c	nsβcl(a))c	NOUN
cana-2861	324	15	.	.	PUNCT
cana-2861	325	1	proof	proof	NOUN
cana-2861	325	2	.	.	PUNCT
cana-2861	326	1	we	we	PRON
cana-2861	326	2	know	know	VERB
cana-2861	326	3	that	that	SCONJ
cana-2861	326	4	,	,	PUNCT
cana-2861	326	5	u	u	NOUN
cana-2861	326	6	q	q	NOUN
cana-2861	326	7	-	-	PUNCT
cana-2861	326	8	nsβcl(a	nsβcl(a	NUM
cana-2861	326	9	=	=	NOUN
cana-2861	326	10	q	q	NOUN
cana-2861	326	11	-	-	PUNCT
cana-2861	326	12	nsβint(ac	nsβint(ac	NOUN
cana-2861	326	13	)	)	PUNCT
cana-2861	326	14	,	,	PUNCT
cana-2861	326	15	then	then	ADV
cana-2861	326	16	q	q	ADJ
cana-2861	326	17	-	-	PUNCT
cana-2861	326	18	nsβext(a)=q	nsβext(a)=q	ADV
cana-2861	326	19	-	-	PUNCT
cana-2861	326	20	nsβint(ac	nsβint(ac	NOUN
cana-2861	326	21	)	)	PUNCT
cana-2861	326	22	=	=	PUNCT
cana-2861	326	23	(	(	PUNCT
cana-2861	326	24	q	q	NOUN
cana-2861	326	25	-	-	PUNCT
cana-2861	326	26	nsβcl(a))c	nsβcl(a))c	NOUN
cana-2861	326	27	.	.	PUNCT
cana-2861	327	1	theorem	theorem	VERB
cana-2861	327	2	4.14	4.14	NUM
cana-2861	327	3	.	.	PUNCT
cana-2861	328	1	for	for	ADP
cana-2861	328	2	a	a	DET
cana-2861	328	3	quadripartitioned	quadripartitione	VERB
cana-2861	328	4	neutrosophic	neutrosophic	PROPN
cana-2861	328	5	subset	subset	VERB
cana-2861	328	6	a	a	PRON
cana-2861	328	7	of	of	ADP
cana-2861	328	8	z	z	PROPN
cana-2861	328	9	,	,	PUNCT
cana-2861	328	10	q	q	ADJ
cana-2861	328	11	-	-	PUNCT
cana-2861	328	12	nsβext(q	nsβext(q	NOUN
cana-2861	328	13	-	-	PUNCT
cana-2861	328	14	nsβext(a	nsβext(a	NOUN
cana-2861	328	15	)	)	PUNCT
cana-2861	328	16	)	)	PUNCT
cana-2861	329	1	=	=	PUNCT
cana-2861	329	2	qnsβint(q	qnsβint(q	NOUN
cana-2861	329	3	-	-	PUNCT
cana-2861	329	4	nsβcl(a	nsβcl(a	NOUN
cana-2861	329	5	)	)	PUNCT
cana-2861	329	6	)	)	PUNCT
cana-2861	330	1	⊇	⊇	PROPN
cana-2861	330	2	q	q	PROPN
cana-2861	330	3	-	-	PUNCT
cana-2861	330	4	nsβint(a	nsβint(a	NOUN
cana-2861	330	5	)	)	PUNCT
cana-2861	330	6	.	.	PUNCT
cana-2861	331	1	proof	proof	NOUN
cana-2861	331	2	.	.	PUNCT
cana-2861	332	1	now	now	ADV
cana-2861	332	2	,	,	PUNCT
cana-2861	332	3	q	q	NOUN
cana-2861	332	4	-	-	PUNCT
cana-2861	332	5	nsβext(q	nsβext(q	NOUN
cana-2861	332	6	-	-	PUNCT
cana-2861	332	7	nsβext(a	nsβext(a	NOUN
cana-2861	332	8	)	)	PUNCT
cana-2861	332	9	)	)	PUNCT
cana-2861	333	1	=	=	PUNCT
cana-2861	333	2	q	q	X
cana-2861	333	3	-	-	PUNCT
cana-2861	333	4	nsβext(q	nsβext(q	NOUN
cana-2861	333	5	-	-	PUNCT
cana-2861	333	6	nsβint(ac	nsβint(ac	NOUN
cana-2861	333	7	)	)	PUNCT
cana-2861	333	8	)	)	PUNCT
cana-2861	334	1	=	=	SYM
cana-2861	334	2	q	q	ADJ
cana-2861	334	3	-	-	PUNCT
cana-2861	334	4	nsβint((qnsβint(ac))c	nsβint((qnsβint(ac))c	ADJ
cana-2861	334	5	)	)	PUNCT
cana-2861	335	1	=	=	NOUN
cana-2861	335	2	q	q	NOUN
cana-2861	335	3	-	-	PUNCT
cana-2861	335	4	nsβint(q	nsβint(q	NOUN
cana-2861	335	5	-	-	PUNCT
cana-2861	335	6	nsβcl(a	nsβcl(a	NOUN
cana-2861	335	7	)	)	PUNCT
cana-2861	335	8	)	)	PUNCT
cana-2861	336	1	⊇	⊇	PROPN
cana-2861	336	2	q	q	PROPN
cana-2861	336	3	-	-	PUNCT
cana-2861	336	4	nsβint(a	nsβint(a	NOUN
cana-2861	336	5	)	)	PUNCT
cana-2861	336	6	.	.	PUNCT
cana-2861	337	1	theorem	theorem	VERB
cana-2861	337	2	4.15	4.15	NUM
cana-2861	337	3	.	.	PUNCT
cana-2861	338	1	for	for	ADP
cana-2861	338	2	a	a	DET
cana-2861	338	3	quadripartitioned	quadripartitione	VERB
cana-2861	338	4	neutrosophic	neutrosophic	PROPN
cana-2861	338	5	subset	subset	VERB
cana-2861	338	6	a	a	PRON
cana-2861	338	7	of	of	ADP
cana-2861	338	8	z	z	PROPN
cana-2861	338	9	,	,	PUNCT
cana-2861	338	10	if	if	SCONJ
cana-2861	338	11	a⊆	a⊆	NOUN
cana-2861	338	12	b	b	NOUN
cana-2861	338	13	,	,	PUNCT
cana-2861	338	14	then	then	ADV
cana-2861	338	15	q	q	NOUN
cana-2861	338	16	-	-	PUNCT
cana-2861	338	17	nsβext(b	nsβext(b	NOUN
cana-2861	338	18	)	)	PUNCT
cana-2861	338	19	⊆qnsβext(a	⊆qnsβext(a	NOUN
cana-2861	338	20	)	)	PUNCT
cana-2861	338	21	.	.	PUNCT
cana-2861	339	1	proof	proof	NOUN
cana-2861	339	2	.	.	PUNCT
cana-2861	340	1	suppose	suppose	VERB
cana-2861	340	2	a⊆b.now	a⊆b.now	PROPN
cana-2861	340	3	,	,	PUNCT
cana-2861	340	4	q	q	ADJ
cana-2861	340	5	-	-	PUNCT
cana-2861	340	6	nsβext(b)=q	nsβext(b)=q	ADV
cana-2861	340	7	-	-	PUNCT
cana-2861	340	8	nsβint(bc	nsβint(bc	ADJ
cana-2861	340	9	)	)	PUNCT
cana-2861	340	10	⊆	⊆	NUM
cana-2861	340	11	q	q	X
cana-2861	340	12	-	-	PUNCT
cana-2861	340	13	nsβint(ac)=	nsβint(ac)=	NOUN
cana-2861	340	14	q	q	NOUN
cana-2861	340	15	-	-	PUNCT
cana-2861	340	16	nsβext(a	nsβext(a	NOUN
cana-2861	340	17	)	)	PUNCT
cana-2861	340	18	.	.	PUNCT
cana-2861	341	1	communications	communication	NOUN
cana-2861	341	2	on	on	ADP
cana-2861	341	3	applied	apply	VERB
cana-2861	341	4	nonlinear	nonlinear	ADJ
cana-2861	341	5	analysis	analysis	NOUN
cana-2861	341	6	issn	issn	NOUN
cana-2861	341	7	:	:	PUNCT
cana-2861	341	8	1074	1074	NUM
cana-2861	341	9	-	-	PUNCT
cana-2861	341	10	133x	133x	NUM
cana-2861	341	11	vol	vol	NOUN
cana-2861	341	12	32	32	NUM
cana-2861	341	13	no	no	NOUN
cana-2861	341	14	.	.	PUNCT
cana-2861	342	1	4s	4s	NUM
cana-2861	342	2	(	(	PUNCT
cana-2861	342	3	2025	2025	NUM
cana-2861	342	4	)	)	PUNCT
cana-2861	342	5	430	430	NUM
cana-2861	342	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2861	342	7	theorem	theorem	VERB
cana-2861	342	8	4.16	4.16	NUM
cana-2861	342	9	.	.	PUNCT
cana-2861	343	1	for	for	ADP
cana-2861	343	2	a	a	DET
cana-2861	343	3	quadripartitioned	quadripartitione	VERB
cana-2861	343	4	neutrosophic	neutrosophic	PROPN
cana-2861	343	5	subset	subset	VERB
cana-2861	343	6	a	a	PRON
cana-2861	343	7	of	of	ADP
cana-2861	343	8	z	z	PROPN
cana-2861	343	9	,	,	PUNCT
cana-2861	343	10	q	q	ADJ
cana-2861	343	11	-	-	PUNCT
cana-2861	343	12	nsβext(1n	nsβext(1n	ADJ
cana-2861	343	13	)	)	PUNCT
cana-2861	344	1	=	=	SYM
cana-2861	344	2	0n	0n	NOUN
cana-2861	344	3	and	and	CCONJ
cana-2861	344	4	qnsβext(0n	qnsβext(0n	NOUN
cana-2861	344	5	)	)	PUNCT
cana-2861	345	1	=	=	SYM
cana-2861	345	2	1n	1n	NUM
cana-2861	345	3	.	.	PUNCT
cana-2861	346	1	proof	proof	NOUN
cana-2861	346	2	.	.	PUNCT
cana-2861	347	1	now	now	ADV
cana-2861	347	2	,	,	PUNCT
cana-2861	347	3	q	q	ADJ
cana-2861	347	4	-	-	PUNCT
cana-2861	347	5	nsβext(1n	nsβext(1n	ADJ
cana-2861	347	6	)	)	PUNCT
cana-2861	348	1	=	=	PUNCT
cana-2861	349	1	q	q	ADJ
cana-2861	349	2	-	-	PUNCT
cana-2861	349	3	nsβint((1n	nsβint((1n	ADJ
cana-2861	349	4	)	)	PUNCT
cana-2861	349	5	c	c	X
cana-2861	349	6	)	)	PUNCT
cana-2861	349	7	=	=	SYM
cana-2861	350	1	q	q	NOUN
cana-2861	350	2	-	-	PUNCT
cana-2861	350	3	nsβint(0n	nsβint(0n	PROPN
cana-2861	350	4	)	)	PUNCT
cana-2861	350	5	and	and	CCONJ
cana-2861	350	6	q	q	ADJ
cana-2861	350	7	-	-	PUNCT
cana-2861	350	8	nsβext(0n	nsβext(0n	NOUN
cana-2861	350	9	)	)	PUNCT
cana-2861	350	10	=	=	PUNCT
cana-2861	351	1	q	q	NOUN
cana-2861	351	2	nsβint((0n	nsβint((0n	NOUN
cana-2861	351	3	)	)	PUNCT
cana-2861	351	4	c	c	X
cana-2861	351	5	)	)	PUNCT
cana-2861	351	6	=	=	SYM
cana-2861	352	1	q	q	ADJ
cana-2861	352	2	-	-	PUNCT
cana-2861	352	3	nsβint(1n	nsβint(1n	ADJ
cana-2861	352	4	)	)	PUNCT
cana-2861	352	5	.	.	PUNCT
cana-2861	353	1	since	since	SCONJ
cana-2861	353	2	0n	0n	NOUN
cana-2861	353	3	and	and	CCONJ
cana-2861	353	4	1n	1n	NUM
cana-2861	353	5	are	be	AUX
cana-2861	353	6	q	q	ADJ
cana-2861	353	7	-	-	PUNCT
cana-2861	353	8	nsβo	nsβo	ADJ
cana-2861	353	9	sets	set	NOUN
cana-2861	353	10	,	,	PUNCT
cana-2861	353	11	then	then	ADV
cana-2861	353	12	q	q	PROPN
cana-2861	353	13	-	-	PUNCT
cana-2861	353	14	nsβint(0n	nsβint(0n	NOUN
cana-2861	353	15	)	)	PUNCT
cana-2861	354	1	=	=	SYM
cana-2861	354	2	0n	0n	NOUN
cana-2861	354	3	and	and	CCONJ
cana-2861	354	4	q	q	NOUN
cana-2861	354	5	-	-	ADJ
cana-2861	354	6	nsβint(1n	nsβint(1n	ADJ
cana-2861	354	7	)	)	PUNCT
cana-2861	355	1	=	=	SYM
cana-2861	355	2	1n	1n	NUM
cana-2861	355	3	.	.	PUNCT
cana-2861	356	1	hence	hence	ADV
cana-2861	356	2	q	q	ADJ
cana-2861	356	3	-	-	PUNCT
cana-2861	356	4	nsβext(0n	nsβext(0n	NOUN
cana-2861	356	5	)	)	PUNCT
cana-2861	357	1	=	=	SYM
cana-2861	357	2	1n	1n	NUM
cana-2861	357	3	and	and	CCONJ
cana-2861	357	4	q	q	NOUN
cana-2861	357	5	-	-	ADJ
cana-2861	357	6	nsβext(1n	nsβext(1n	ADJ
cana-2861	357	7	)	)	PUNCT
cana-2861	358	1	=	=	PUNCT
cana-2861	358	2	0n	0n	NOUN
cana-2861	358	3	.	.	PUNCT
cana-2861	359	1	theorem	theorem	VERB
cana-2861	359	2	4.17	4.17	NUM
cana-2861	359	3	.	.	PUNCT
cana-2861	360	1	for	for	ADP
cana-2861	360	2	a	a	DET
cana-2861	360	3	quadripartitioned	quadripartitione	VERB
cana-2861	360	4	neutrosophic	neutrosophic	PROPN
cana-2861	360	5	subset	subset	VERB
cana-2861	360	6	a	a	PRON
cana-2861	360	7	of	of	ADP
cana-2861	360	8	z	z	PROPN
cana-2861	360	9	,	,	PUNCT
cana-2861	360	10	q	q	NOUN
cana-2861	360	11	-	-	PUNCT
cana-2861	360	12	nsβext(a	nsβext(a	NOUN
cana-2861	360	13	)	)	PUNCT
cana-2861	360	14	=	=	SYM
cana-2861	360	15	qnsβext((qnsβext(a))c	qnsβext((qnsβext(a))c	ADJ
cana-2861	360	16	)	)	PUNCT
cana-2861	360	17	.	.	PUNCT
cana-2861	361	1	proof	proof	NOUN
cana-2861	361	2	.	.	PUNCT
cana-2861	362	1	now	now	ADV
cana-2861	362	2	,	,	PUNCT
cana-2861	362	3	q	q	NOUN
cana-2861	362	4	-	-	PUNCT
cana-2861	362	5	nsβext((q	nsβext((q	NOUN
cana-2861	362	6	-	-	ADJ
cana-2861	362	7	nsβext(a))c	nsβext(a))c	ADJ
cana-2861	362	8	)	)	PUNCT
cana-2861	363	1	=	=	SYM
cana-2861	363	2	q	q	ADJ
cana-2861	363	3	-	-	PUNCT
cana-2861	363	4	nsβext((q	nsβext((q	NOUN
cana-2861	363	5	-	-	ADJ
cana-2861	363	6	nsβint(ac))c	nsβint(ac))c	ADJ
cana-2861	363	7	)	)	PUNCT
cana-2861	363	8	=	=	SYM
cana-2861	363	9	qnsβint((((qnsβint(ac))c))c	qnsβint((((qnsβint(ac))c))c	PROPN
cana-2861	363	10	)	)	PUNCT
cana-2861	363	11	=	=	SYM
cana-2861	364	1	q	q	X
cana-2861	364	2	-	-	PUNCT
cana-2861	364	3	nsβint	nsβint	NOUN
cana-2861	364	4	(	(	PUNCT
cana-2861	364	5	q	q	NOUN
cana-2861	364	6	-	-	PUNCT
cana-2861	364	7	nsβint(ac	nsβint(ac	NOUN
cana-2861	364	8	)	)	PUNCT
cana-2861	364	9	)	)	PUNCT
cana-2861	365	1	=	=	PUNCT
cana-2861	365	2	q	q	ADJ
cana-2861	365	3	-	-	PUNCT
cana-2861	365	4	nsβint(ac	nsβint(ac	ADJ
cana-2861	365	5	)	)	PUNCT
cana-2861	365	6	=	=	SYM
cana-2861	365	7	qnsβext(a	qnsβext(a	PROPN
cana-2861	365	8	)	)	PUNCT
cana-2861	365	9	.	.	PUNCT
cana-2861	366	1	theorem	theorem	VERB
cana-2861	366	2	4.18	4.18	NUM
cana-2861	366	3	.	.	PUNCT
cana-2861	367	1	for	for	SCONJ
cana-2861	367	2	a	a	DET
cana-2861	367	3	sub	sub	NOUN
cana-2861	367	4	sets	set	VERB
cana-2861	367	5	a	a	PRON
cana-2861	367	6	and	and	CCONJ
cana-2861	367	7	b	b	NOUN
cana-2861	367	8	of	of	ADP
cana-2861	367	9	z	z	PROPN
cana-2861	367	10	,	,	PUNCT
cana-2861	367	11	the	the	DET
cana-2861	367	12	followings	following	NOUN
cana-2861	367	13	are	be	AUX
cana-2861	367	14	valid	valid	ADJ
cana-2861	367	15	.	.	PUNCT
cana-2861	368	1	(	(	PUNCT
cana-2861	368	2	i	i	NOUN
cana-2861	368	3	)	)	PUNCT
cana-2861	368	4	q	q	NOUN
cana-2861	368	5	-	-	PUNCT
cana-2861	368	6	nsβext(a	nsβext(a	NOUN
cana-2861	368	7	∪	∪	NOUN
cana-2861	368	8	b	b	NOUN
cana-2861	368	9	)	)	PUNCT
cana-2861	368	10	⊆	⊆	NUM
cana-2861	368	11	q	q	PROPN
cana-2861	368	12	-	-	PUNCT
cana-2861	368	13	nsβext(a	nsβext(a	ADJ
cana-2861	368	14	)	)	PUNCT
cana-2861	368	15	∩	∩	ADJ
cana-2861	368	16	q	q	NOUN
cana-2861	368	17	-	-	PUNCT
cana-2861	368	18	nsβext(b	nsβext(b	NOUN
cana-2861	368	19	)	)	PUNCT
cana-2861	368	20	.	.	PUNCT
cana-2861	369	1	(	(	PUNCT
cana-2861	369	2	ii	ii	NOUN
cana-2861	369	3	)	)	PUNCT
cana-2861	369	4	q	q	NOUN
cana-2861	369	5	-	-	PUNCT
cana-2861	369	6	nsβext(a	nsβext(a	NOUN
cana-2861	369	7	∩	∩	ADJ
cana-2861	369	8	b	b	X
cana-2861	369	9	)	)	PUNCT
cana-2861	369	10	⊇	⊇	NOUN
cana-2861	369	11	q	q	PROPN
cana-2861	369	12	-	-	PUNCT
cana-2861	369	13	nsβext(a	nsβext(a	NOUN
cana-2861	369	14	)	)	PUNCT
cana-2861	369	15	∪	∪	ADP
cana-2861	369	16	q	q	NOUN
cana-2861	369	17	-	-	PUNCT
cana-2861	369	18	nsβext(b	nsβext(b	NOUN
cana-2861	369	19	)	)	PUNCT
cana-2861	369	20	.	.	PUNCT
cana-2861	370	1	proof	proof	NOUN
cana-2861	370	2	.	.	PUNCT
cana-2861	371	1	(	(	PUNCT
cana-2861	371	2	i	i	NOUN
cana-2861	371	3	)	)	PUNCT
cana-2861	371	4	q	q	NOUN
cana-2861	371	5	-	-	PUNCT
cana-2861	371	6	nsβext(a	nsβext(a	NOUN
cana-2861	371	7	∪	∪	NOUN
cana-2861	371	8	b	b	NOUN
cana-2861	371	9	)	)	PUNCT
cana-2861	371	10	=	=	SYM
cana-2861	371	11	q	q	X
cana-2861	371	12	-	-	PUNCT
cana-2861	371	13	nsβint((a	nsβint((a	NOUN
cana-2861	371	14	∪	∪	ADJ
cana-2861	371	15	b)c	b)c	NOUN
cana-2861	371	16	)	)	PUNCT
cana-2861	371	17	=	=	SYM
cana-2861	371	18	q	q	ADJ
cana-2861	371	19	-	-	PUNCT
cana-2861	371	20	nsβint((ac	nsβint((ac	NOUN
cana-2861	371	21	)	)	PUNCT
cana-2861	371	22	∩	∩	NOUN
cana-2861	371	23	(	(	PUNCT
cana-2861	371	24	bc	bc	PROPN
cana-2861	371	25	)	)	PUNCT
cana-2861	371	26	)	)	PUNCT
cana-2861	372	1	⊆	⊆	NUM
cana-2861	372	2	q	q	ADJ
cana-2861	372	3	-	-	PUNCT
cana-2861	372	4	nsβcl(ac	nsβcl(ac	ADJ
cana-2861	372	5	)	)	PUNCT
cana-2861	372	6	∩	∩	NOUN
cana-2861	372	7	qnsβcl(bc	qnsβcl(bc	NOUN
cana-2861	372	8	)	)	PUNCT
cana-2861	372	9	=	=	SYM
cana-2861	372	10	q	q	NOUN
cana-2861	372	11	-	-	PUNCT
cana-2861	372	12	nsβext(a	nsβext(a	ADJ
cana-2861	372	13	)	)	PUNCT
cana-2861	372	14	∩	∩	ADJ
cana-2861	372	15	q	q	NOUN
cana-2861	372	16	-	-	PUNCT
cana-2861	372	17	nsβext(b	nsβext(b	NOUN
cana-2861	372	18	)	)	PUNCT
cana-2861	372	19	.	.	PUNCT
cana-2861	373	1	(	(	PUNCT
cana-2861	373	2	ii	ii	NOUN
cana-2861	373	3	)	)	PUNCT
cana-2861	373	4	q	q	NOUN
cana-2861	373	5	-	-	PUNCT
cana-2861	373	6	nsβext(a	nsβext(a	NOUN
cana-2861	373	7	∩	∩	ADJ
cana-2861	373	8	b	b	NOUN
cana-2861	373	9	)	)	PUNCT
cana-2861	373	10	=	=	SYM
cana-2861	373	11	q	q	ADJ
cana-2861	373	12	-	-	PUNCT
cana-2861	373	13	nsβint((a	nsβint((a	NOUN
cana-2861	373	14	∩	∩	NOUN
cana-2861	373	15	b)c	b)c	ADJ
cana-2861	373	16	)	)	PUNCT
cana-2861	373	17	=	=	SYM
cana-2861	373	18	q	q	X
cana-2861	373	19	-	-	PUNCT
cana-2861	373	20	nsβint((ac	nsβint((ac	NOUN
cana-2861	373	21	)	)	PUNCT
cana-2861	373	22	∪	∪	NOUN
cana-2861	373	23	(	(	PUNCT
cana-2861	373	24	bc	bc	PROPN
cana-2861	373	25	)	)	PUNCT
cana-2861	373	26	)	)	PUNCT
cana-2861	374	1	⊇	⊇	PROPN
cana-2861	374	2	q	q	ADJ
cana-2861	374	3	-	-	PUNCT
cana-2861	374	4	nsβcl(ac	nsβcl(ac	NOUN
cana-2861	374	5	)	)	PUNCT
cana-2861	374	6	∪	∪	ADP
cana-2861	374	7	q	q	PROPN
cana-2861	374	8	nsβcl(bc	nsβcl(bc	PROPN
cana-2861	374	9	)	)	PUNCT
cana-2861	374	10	=	=	SYM
cana-2861	374	11	q	q	NOUN
cana-2861	374	12	-	-	PUNCT
cana-2861	374	13	nsβext(a	nsβext(a	NOUN
cana-2861	374	14	)	)	PUNCT
cana-2861	374	15	∪	∪	ADP
cana-2861	374	16	q	q	NOUN
cana-2861	374	17	-	-	PUNCT
cana-2861	374	18	nsβext(b	nsβext(b	NOUN
cana-2861	374	19	)	)	PUNCT
cana-2861	374	20	.	.	PUNCT
cana-2861	375	1	conclusion	conclusion	NOUN
cana-2861	375	2	in	in	ADP
cana-2861	375	3	this	this	DET
cana-2861	375	4	paper	paper	NOUN
cana-2861	375	5	,	,	PUNCT
cana-2861	375	6	we	we	PRON
cana-2861	375	7	have	have	AUX
cana-2861	375	8	studied	study	VERB
cana-2861	375	9	some	some	DET
cana-2861	375	10	new	new	ADJ
cana-2861	375	11	operators	operator	NOUN
cana-2861	375	12	called	call	VERB
cana-2861	375	13	quadripartitioned	quadripartitione	VERB
cana-2861	375	14	neutrosophic	neutrosophic	PROPN
cana-2861	375	15	β	β	PROPN
cana-2861	375	16	frontier	frontier	NOUN
cana-2861	375	17	,	,	PUNCT
cana-2861	375	18	respective	respective	ADJ
cana-2861	375	19	border	border	NOUN
cana-2861	375	20	and	and	CCONJ
cana-2861	375	21	exterior	exterior	ADJ
cana-2861	375	22	with	with	ADP
cana-2861	375	23	the	the	DET
cana-2861	375	24	help	help	NOUN
cana-2861	375	25	of	of	ADP
cana-2861	375	26	quadripartitioned	quadripartitione	VERB
cana-2861	375	27	neutrosophic	neutrosophic	ADJ
cana-2861	375	28	β	β	X
cana-2861	375	29	-	-	ADJ
cana-2861	375	30	open	open	ADJ
cana-2861	375	31	sets	set	NOUN
cana-2861	375	32	in	in	ADP
cana-2861	375	33	quadripartitioned	quadripartitione	VERB
cana-2861	375	34	neutrosophic	neutrosophic	PROPN
cana-2861	375	35	topological	topological	ADJ
cana-2861	375	36	space	space	NOUN
cana-2861	375	37	.	.	PUNCT
cana-2861	376	1	also	also	ADV
cana-2861	376	2	,	,	PUNCT
cana-2861	376	3	we	we	PRON
cana-2861	376	4	discussed	discuss	VERB
cana-2861	376	5	the	the	DET
cana-2861	376	6	important	important	ADJ
cana-2861	376	7	properties	property	NOUN
cana-2861	376	8	of	of	ADP
cana-2861	376	9	them	they	PRON
cana-2861	376	10	and	and	CCONJ
cana-2861	376	11	the	the	DET
cana-2861	376	12	relations	relation	NOUN
cana-2861	376	13	between	between	ADP
cana-2861	376	14	them	they	PRON
cana-2861	376	15	.	.	PUNCT
cana-2861	377	1	refrences	refrence	VERB
cana-2861	377	2	[	[	X
cana-2861	378	1	1	1	X
cana-2861	378	2	]	]	PUNCT
cana-2861	378	3	k.	k.	PROPN
cana-2861	378	4	atanassov	atanassov	PROPN
cana-2861	378	5	,	,	PUNCT
cana-2861	378	6	intuitionistic	intuitionistic	ADJ
cana-2861	378	7	fuzzy	fuzzy	ADJ
cana-2861	378	8	sets	set	NOUN
cana-2861	378	9	,	,	PUNCT
cana-2861	378	10	fuzzy	fuzzy	ADJ
cana-2861	378	11	sets	set	NOUN
cana-2861	378	12	and	and	CCONJ
cana-2861	378	13	systems	system	NOUN
cana-2861	378	14	,	,	PUNCT
cana-2861	378	15	20	20	NUM
cana-2861	378	16	(	(	PUNCT
cana-2861	378	17	1986	1986	NUM
cana-2861	378	18	)	)	PUNCT
cana-2861	378	19	,	,	PUNCT
cana-2861	378	20	87	87	NUM
cana-2861	378	21	-	-	SYM
cana-2861	378	22	96	96	NUM
cana-2861	378	23	.	.	PUNCT
cana-2861	379	1	[	[	X
cana-2861	379	2	2	2	NUM
cana-2861	379	3	]	]	PUNCT
cana-2861	379	4	c.	c.	PROPN
cana-2861	379	5	l.	l.	PROPN
cana-2861	379	6	chang	chang	PROPN
cana-2861	379	7	,	,	PUNCT
cana-2861	379	8	fuzzy	fuzzy	ADJ
cana-2861	379	9	topological	topological	ADJ
cana-2861	379	10	spaces	space	NOUN
cana-2861	379	11	,	,	PUNCT
cana-2861	379	12	j.	j.	PROPN
cana-2861	379	13	math	math	PROPN
cana-2861	379	14	.	.	PUNCT
cana-2861	380	1	anal	anal	PROPN
cana-2861	380	2	.	.	PUNCT
cana-2861	381	1	appl	appl	PROPN
cana-2861	381	2	.	.	PROPN
cana-2861	381	3	,	,	PUNCT
cana-2861	381	4	24	24	NUM
cana-2861	381	5	(	(	PUNCT
cana-2861	381	6	1968	1968	NUM
cana-2861	381	7	)	)	PUNCT
cana-2861	381	8	,	,	PUNCT
cana-2861	381	9	182	182	NUM
cana-2861	381	10	-	-	SYM
cana-2861	381	11	190	190	NUM
cana-2861	381	12	.	.	PUNCT
cana-2861	382	1	[	[	X
cana-2861	382	2	3	3	X
cana-2861	382	3	]	]	X
cana-2861	382	4	r.	r.	PROPN
cana-2861	382	5	chatterjee	chatterjee	PROPN
cana-2861	382	6	,	,	PUNCT
cana-2861	382	7	p.	p.	PROPN
cana-2861	382	8	majumdar	majumdar	PROPN
cana-2861	382	9	and	and	CCONJ
cana-2861	382	10	s.	s.	PROPN
cana-2861	382	11	k.	k.	PROPN
cana-2861	382	12	samanta	samanta	PROPN
cana-2861	382	13	,	,	PUNCT
cana-2861	382	14	on	on	ADP
cana-2861	382	15	some	some	DET
cana-2861	382	16	similarity	similarity	NOUN
cana-2861	382	17	measures	measure	NOUN
cana-2861	382	18	and	and	CCONJ
cana-2861	382	19	entropy	entropy	NOUN
cana-2861	382	20	on	on	ADP
cana-2861	382	21	quadripartitioned	quadripartitione	VERB
cana-2861	382	22	single	single	ADJ
cana-2861	382	23	valued	value	VERB
cana-2861	382	24	neutrosophic	neutrosophic	ADJ
cana-2861	382	25	sets	set	NOUN
cana-2861	382	26	,	,	PUNCT
cana-2861	382	27	journal	journal	NOUN
cana-2861	382	28	of	of	ADP
cana-2861	382	29	intelligent	intelligent	ADJ
cana-2861	382	30	&	&	CCONJ
cana-2861	382	31	fuzzy	fuzzy	ADJ
cana-2861	382	32	systems	system	NOUN
cana-2861	382	33	,	,	PUNCT
cana-2861	382	34	30	30	NUM
cana-2861	382	35	(	(	PUNCT
cana-2861	382	36	4	4	NUM
cana-2861	382	37	)	)	PUNCT
cana-2861	382	38	(	(	PUNCT
cana-2861	382	39	2016	2016	NUM
cana-2861	382	40	)	)	PUNCT
cana-2861	382	41	,	,	PUNCT
cana-2861	382	42	2475	2475	NUM
cana-2861	382	43	-	-	SYM
cana-2861	382	44	2485	2485	NUM
cana-2861	382	45	.	.	PUNCT
cana-2861	383	1	[	[	X
cana-2861	383	2	4	4	X
cana-2861	383	3	]	]	X
cana-2861	383	4	d.	d.	PROPN
cana-2861	383	5	coker	coker	PROPN
cana-2861	383	6	,	,	PUNCT
cana-2861	383	7	an	an	DET
cana-2861	383	8	introduction	introduction	NOUN
cana-2861	383	9	to	to	ADP
cana-2861	383	10	intuitionistic	intuitionistic	ADJ
cana-2861	383	11	fuzzy	fuzzy	ADJ
cana-2861	383	12	topological	topological	ADJ
cana-2861	383	13	spaces	space	NOUN
cana-2861	383	14	,	,	PUNCT
cana-2861	383	15	fuzzy	fuzzy	ADJ
cana-2861	383	16	sets	set	NOUN
cana-2861	383	17	and	and	CCONJ
cana-2861	383	18	systems	system	NOUN
cana-2861	383	19	,	,	PUNCT
cana-2861	383	20	88	88	NUM
cana-2861	383	21	(	(	PUNCT
cana-2861	383	22	1997	1997	NUM
cana-2861	383	23	)	)	PUNCT
cana-2861	383	24	,	,	PUNCT
cana-2861	383	25	81	81	NUM
cana-2861	383	26	-	-	SYM
cana-2861	383	27	89	89	NUM
cana-2861	383	28	.	.	PUNCT
cana-2861	384	1	[	[	X
cana-2861	384	2	5	5	X
cana-2861	384	3	]	]	PUNCT
cana-2861	384	4	s.	s.	PROPN
cana-2861	384	5	das	das	PROPN
cana-2861	384	6	,	,	PUNCT
cana-2861	384	7	r.	r.	PROPN
cana-2861	384	8	das	das	PROPN
cana-2861	384	9	and	and	CCONJ
cana-2861	384	10	c.	c.	PROPN
cana-2861	384	11	granados	granados	PROPN
cana-2861	384	12	,	,	PUNCT
cana-2861	384	13	topology	topology	NOUN
cana-2861	384	14	on	on	ADP
cana-2861	384	15	quadripartitioned	quadripartitione	VERB
cana-2861	384	16	neutrosophic	neutrosophic	ADJ
cana-2861	384	17	sets	set	NOUN
cana-2861	384	18	,	,	PUNCT
cana-2861	384	19	neutrosophic	neutrosophic	ADJ
cana-2861	384	20	sets	set	NOUN
cana-2861	384	21	and	and	CCONJ
cana-2861	384	22	systems	system	NOUN
cana-2861	384	23	,	,	PUNCT
cana-2861	384	24	45	45	NUM
cana-2861	384	25	(	(	PUNCT
cana-2861	384	26	2021	2021	NUM
cana-2861	384	27	)	)	PUNCT
cana-2861	384	28	,	,	PUNCT
cana-2861	384	29	54	54	NUM
cana-2861	384	30	-	-	SYM
cana-2861	384	31	61	61	NUM
cana-2861	384	32	.	.	PUNCT
cana-2861	385	1	[	[	X
cana-2861	385	2	6	6	NUM
cana-2861	385	3	]	]	PUNCT
cana-2861	385	4	s.	s.	PROPN
cana-2861	385	5	das	das	PROPN
cana-2861	385	6	and	and	CCONJ
cana-2861	385	7	s.	s.	PROPN
cana-2861	385	8	pramanik	pramanik	PROPN
cana-2861	385	9	,	,	PUNCT
cana-2861	385	10	generalized	generalize	VERB
cana-2861	385	11	neutrosophic	neutrosophic	ADJ
cana-2861	385	12	b	b	X
cana-2861	385	13	-	-	PUNCT
cana-2861	385	14	open	open	ADJ
cana-2861	385	15	sets	set	NOUN
cana-2861	385	16	in	in	ADP
cana-2861	385	17	neutrosophic	neutrosophic	ADJ
cana-2861	385	18	topological	topological	ADJ
cana-2861	385	19	space	space	NOUN
cana-2861	385	20	,	,	PUNCT
cana-2861	385	21	neutrosophic	neutrosophic	ADJ
cana-2861	385	22	sets	set	NOUN
cana-2861	385	23	and	and	CCONJ
cana-2861	385	24	systems	system	NOUN
cana-2861	385	25	,	,	PUNCT
cana-2861	385	26	35	35	NUM
cana-2861	385	27	(	(	PUNCT
cana-2861	385	28	2020	2020	NUM
cana-2861	385	29	)	)	PUNCT
cana-2861	385	30	,	,	PUNCT
cana-2861	385	31	522	522	NUM
cana-2861	385	32	-	-	SYM
cana-2861	385	33	530	530	NUM
cana-2861	385	34	.	.	PUNCT
cana-2861	386	1	[	[	X
cana-2861	386	2	7	7	X
cana-2861	386	3	]	]	X
cana-2861	386	4	s.	s.	PROPN
cana-2861	386	5	das	das	PROPN
cana-2861	386	6	and	and	CCONJ
cana-2861	386	7	s.	s.	PROPN
cana-2861	386	8	pramanik	pramanik	PROPN
cana-2861	386	9	,	,	PUNCT
cana-2861	386	10	neutrosophic	neutrosophic	ADJ
cana-2861	386	11	φ	φ	VERB
cana-2861	386	12	-	-	ADJ
cana-2861	386	13	open	open	ADJ
cana-2861	386	14	sets	set	NOUN
cana-2861	386	15	and	and	CCONJ
cana-2861	386	16	neutrosophic	neutrosophic	ADJ
cana-2861	386	17	φ	φ	VERB
cana-2861	386	18	-	-	ADJ
cana-2861	386	19	continuous	continuous	ADJ
cana-2861	386	20	functions	function	NOUN
cana-2861	386	21	,	,	PUNCT
cana-2861	386	22	neutrosophic	neutrosophic	ADJ
cana-2861	386	23	sets	set	NOUN
cana-2861	386	24	and	and	CCONJ
cana-2861	386	25	systems	system	NOUN
cana-2861	386	26	,	,	PUNCT
cana-2861	386	27	38	38	NUM
cana-2861	386	28	(	(	PUNCT
cana-2861	386	29	2020	2020	NUM
cana-2861	386	30	)	)	PUNCT
cana-2861	386	31	,	,	PUNCT
cana-2861	386	32	355	355	NUM
cana-2861	386	33	-	-	SYM
cana-2861	386	34	367	367	NUM
cana-2861	386	35	.	.	PUNCT
cana-2861	387	1	[	[	X
cana-2861	387	2	8	8	NUM
cana-2861	387	3	]	]	X
cana-2861	387	4	e.	e.	PROPN
cana-2861	387	5	ebenanjar	ebenanjar	PROPN
cana-2861	387	6	,	,	PUNCT
cana-2861	387	7	j.	j.	PROPN
cana-2861	387	8	immaculate	immaculate	PROPN
cana-2861	387	9	and	and	CCONJ
cana-2861	387	10	c.	c.	PROPN
cana-2861	387	11	b.	b.	PROPN
cana-2861	387	12	wilfred	wilfred	PROPN
cana-2861	387	13	,	,	PUNCT
cana-2861	387	14	on	on	ADP
cana-2861	387	15	neutrosophic	neutrosophic	ADJ
cana-2861	387	16	b	b	X
cana-2861	387	17	-	-	PUNCT
cana-2861	387	18	open	open	ADJ
cana-2861	387	19	sets	set	NOUN
cana-2861	387	20	in	in	ADP
cana-2861	387	21	neutrosophic	neutrosophic	ADJ
cana-2861	387	22	topological	topological	ADJ
cana-2861	387	23	space	space	NOUN
cana-2861	387	24	,	,	PUNCT
cana-2861	387	25	journal	journal	NOUN
cana-2861	387	26	of	of	ADP
cana-2861	387	27	physics	physics	PROPN
cana-2861	387	28	conference	conference	NOUN
cana-2861	387	29	series	series	NOUN
cana-2861	387	30	,	,	PUNCT
cana-2861	387	31	1139	1139	NUM
cana-2861	387	32	(	(	PUNCT
cana-2861	387	33	1	1	NUM
cana-2861	387	34	)	)	PUNCT
cana-2861	387	35	(	(	PUNCT
cana-2861	387	36	2018	2018	NUM
cana-2861	387	37	)	)	PUNCT
cana-2861	387	38	,	,	PUNCT
cana-2861	387	39	012062	012062	NUM
cana-2861	387	40	.	.	PUNCT
cana-2861	388	1	[	[	X
cana-2861	388	2	9	9	NUM
cana-2861	388	3	]	]	PUNCT
cana-2861	388	4	p.	p.	NOUN
cana-2861	388	5	iswarya	iswarya	PROPN
cana-2861	388	6	and	and	CCONJ
cana-2861	388	7	k.	k.	PROPN
cana-2861	388	8	bageerathi	bageerathi	PROPN
cana-2861	388	9	,	,	PUNCT
cana-2861	388	10	on	on	ADP
cana-2861	388	11	neutrosophic	neutrosophic	ADJ
cana-2861	388	12	semi	semi	ADJ
cana-2861	388	13	-	-	ADJ
cana-2861	388	14	open	open	ADJ
cana-2861	388	15	sets	set	NOUN
cana-2861	388	16	in	in	ADP
cana-2861	388	17	neutrosophic	neutrosophic	ADJ
cana-2861	388	18	topological	topological	ADJ
cana-2861	388	19	spaces	space	NOUN
cana-2861	388	20	,	,	PUNCT
cana-2861	388	21	international	international	ADJ
cana-2861	388	22	journal	journal	NOUN
cana-2861	388	23	of	of	ADP
cana-2861	388	24	mathematical	mathematical	ADJ
cana-2861	388	25	trends	trend	NOUN
cana-2861	388	26	and	and	CCONJ
cana-2861	388	27	technology	technology	NOUN
cana-2861	388	28	,	,	PUNCT
cana-2861	388	29	37	37	NUM
cana-2861	388	30	(	(	PUNCT
cana-2861	388	31	3	3	NUM
cana-2861	388	32	)	)	PUNCT
cana-2861	388	33	(	(	PUNCT
cana-2861	388	34	2016	2016	NUM
cana-2861	388	35	)	)	PUNCT
cana-2861	388	36	,	,	PUNCT
cana-2861	388	37	214	214	NUM
cana-2861	388	38	-	-	SYM
cana-2861	388	39	223	223	NUM
cana-2861	388	40	.	.	PUNCT
cana-2861	389	1	[	[	X
cana-2861	389	2	10	10	NUM
cana-2861	389	3	]	]	X
cana-2861	389	4	c.	c.	PROPN
cana-2861	389	5	maheswari	maheswari	PROPN
cana-2861	389	6	,	,	PUNCT
cana-2861	389	7	m.	m.	NOUN
cana-2861	389	8	sathyabama	sathyabama	PROPN
cana-2861	389	9	and	and	CCONJ
cana-2861	389	10	s.	s.	PROPN
cana-2861	389	11	chandrasekar	chandrasekar	PROPN
cana-2861	389	12	,	,	PUNCT
cana-2861	389	13	neutrosophic	neutrosophic	ADJ
cana-2861	389	14	generalized	generalized	ADJ
cana-2861	389	15	b	b	X
cana-2861	389	16	-	-	PUNCT
cana-2861	389	17	closed	closed	ADJ
cana-2861	389	18	sets	set	NOUN
cana-2861	389	19	in	in	ADP
cana-2861	389	20	neutrosophic	neutrosophic	ADJ
cana-2861	389	21	topological	topological	ADJ
cana-2861	389	22	spaces	space	NOUN
cana-2861	389	23	,	,	PUNCT
cana-2861	389	24	journal	journal	NOUN
cana-2861	389	25	of	of	ADP
cana-2861	389	26	physics	physics	PROPN
cana-2861	389	27	conference	conference	NOUN
cana-2861	389	28	series	series	NOUN
cana-2861	389	29	,	,	PUNCT
cana-2861	389	30	1139	1139	NUM
cana-2861	389	31	(	(	PUNCT
cana-2861	389	32	1	1	NUM
cana-2861	389	33	)	)	PUNCT
cana-2861	389	34	(	(	PUNCT
cana-2861	389	35	2018	2018	NUM
cana-2861	389	36	)	)	PUNCT
cana-2861	389	37	,	,	PUNCT
cana-2861	389	38	012065	012065	NUM
cana-2861	389	39	.	.	PUNCT
cana-2861	390	1	communications	communication	NOUN
cana-2861	390	2	on	on	ADP
cana-2861	390	3	applied	apply	VERB
cana-2861	390	4	nonlinear	nonlinear	ADJ
cana-2861	390	5	analysis	analysis	NOUN
cana-2861	390	6	issn	issn	NOUN
cana-2861	390	7	:	:	PUNCT
cana-2861	390	8	1074	1074	NUM
cana-2861	390	9	-	-	PUNCT
cana-2861	390	10	133x	133x	NUM
cana-2861	390	11	vol	vol	NOUN
cana-2861	390	12	32	32	NUM
cana-2861	390	13	no	no	NOUN
cana-2861	390	14	.	.	PUNCT
cana-2861	391	1	4s	4s	NUM
cana-2861	391	2	(	(	PUNCT
cana-2861	391	3	2025	2025	NUM
cana-2861	391	4	)	)	PUNCT
cana-2861	391	5	431	431	NUM
cana-2861	391	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2861	392	1	[	[	X
cana-2861	392	2	11	11	NUM
cana-2861	392	3	]	]	PUNCT
cana-2861	392	4	i.	i.	PROPN
cana-2861	392	5	mohammed	mohammed	PROPN
cana-2861	392	6	ali	ali	PROPN
cana-2861	392	7	jaffer	jaffer	PROPN
cana-2861	392	8	and	and	CCONJ
cana-2861	392	9	k.	k.	PROPN
cana-2861	392	10	ramesh	ramesh	PROPN
cana-2861	392	11	,	,	PUNCT
cana-2861	392	12	neutrosophic	neutrosophic	PROPN
cana-2861	392	13	generalized	generalize	VERB
cana-2861	392	14	pre	pre	X
cana-2861	392	15	regular	regular	ADJ
cana-2861	392	16	closed	closed	ADJ
cana-2861	392	17	sets	set	NOUN
cana-2861	392	18	,	,	PUNCT
cana-2861	392	19	neutrosophic	neutrosophic	ADJ
cana-2861	392	20	sets	set	NOUN
cana-2861	392	21	and	and	CCONJ
cana-2861	392	22	system	system	NOUN
cana-2861	392	23	,	,	PUNCT
cana-2861	392	24	30	30	NUM
cana-2861	392	25	(	(	PUNCT
cana-2861	392	26	2019	2019	NUM
cana-2861	392	27	)	)	PUNCT
cana-2861	392	28	,	,	PUNCT
cana-2861	392	29	171	171	NUM
cana-2861	392	30	-	-	SYM
cana-2861	392	31	181	181	NUM
cana-2861	393	1	.	.	PUNCT
cana-2861	394	1	[	[	X
cana-2861	394	2	12	12	NUM
cana-2861	394	3	]	]	PUNCT
cana-2861	394	4	a.	a.	NOUN
cana-2861	394	5	pushpalatha	pushpalatha	PROPN
cana-2861	394	6	and	and	CCONJ
cana-2861	394	7	t.	t.	PROPN
cana-2861	394	8	nandhini	nandhini	PROPN
cana-2861	394	9	,	,	PUNCT
cana-2861	394	10	generalized	generalize	VERB
cana-2861	394	11	closed	close	VERB
cana-2861	394	12	sets	set	NOUN
cana-2861	394	13	via	via	ADP
cana-2861	394	14	neutrosophic	neutrosophic	ADJ
cana-2861	394	15	topological	topological	ADJ
cana-2861	394	16	spaces	space	NOUN
cana-2861	394	17	,	,	PUNCT
cana-2861	394	18	malaya	malaya	PROPN
cana-2861	394	19	journal	journal	PROPN
cana-2861	394	20	of	of	ADP
cana-2861	394	21	matematik	matematik	PROPN
cana-2861	394	22	,	,	PUNCT
cana-2861	394	23	7	7	NUM
cana-2861	394	24	(	(	PUNCT
cana-2861	394	25	1	1	NUM
cana-2861	394	26	)	)	PUNCT
cana-2861	394	27	(	(	PUNCT
cana-2861	394	28	2019	2019	NUM
cana-2861	394	29	)	)	PUNCT
cana-2861	394	30	,	,	PUNCT
cana-2861	394	31	50	50	NUM
cana-2861	394	32	-	-	SYM
cana-2861	394	33	54	54	NUM
cana-2861	394	34	.	.	PUNCT
cana-2861	395	1	[	[	X
cana-2861	395	2	13	13	NUM
cana-2861	395	3	]	]	X
cana-2861	395	4	v.	v.	PROPN
cana-2861	395	5	v.	v.	ADP
cana-2861	395	6	rao	rao	PROPN
cana-2861	395	7	and	and	CCONJ
cana-2861	395	8	r.	r.	PROPN
cana-2861	395	9	srinivasa	srinivasa	PROPN
cana-2861	395	10	,	,	PUNCT
cana-2861	395	11	neutrosophic	neutrosophic	ADJ
cana-2861	395	12	pre	pre	ADJ
cana-2861	395	13	-	-	ADJ
cana-2861	395	14	open	open	ADJ
cana-2861	395	15	sets	set	NOUN
cana-2861	395	16	and	and	CCONJ
cana-2861	395	17	pre	pre	ADJ
cana-2861	395	18	-	-	ADJ
cana-2861	395	19	closed	closed	ADJ
cana-2861	395	20	sets	set	NOUN
cana-2861	395	21	in	in	ADP
cana-2861	395	22	neutrosophic	neutrosophic	ADJ
cana-2861	395	23	topology	topology	NOUN
cana-2861	395	24	,	,	PUNCT
cana-2861	395	25	international	international	ADJ
cana-2861	395	26	journal	journal	NOUN
cana-2861	395	27	of	of	ADP
cana-2861	395	28	chemtech	chemtech	PROPN
cana-2861	395	29	research	research	NOUN
cana-2861	395	30	,	,	PUNCT
cana-2861	395	31	10	10	NUM
cana-2861	395	32	(	(	PUNCT
cana-2861	395	33	10	10	NUM
cana-2861	395	34	)	)	PUNCT
cana-2861	395	35	(	(	PUNCT
cana-2861	395	36	2017	2017	NUM
cana-2861	395	37	)	)	PUNCT
cana-2861	395	38	,	,	PUNCT
cana-2861	395	39	449	449	NUM
cana-2861	395	40	-	-	SYM
cana-2861	395	41	458	458	NUM
cana-2861	395	42	.	.	PUNCT
cana-2861	396	1	[	[	X
cana-2861	396	2	14	14	NUM
cana-2861	396	3	]	]	PUNCT
cana-2861	396	4	a.	a.	NOUN
cana-2861	396	5	a.	a.	NOUN
cana-2861	396	6	salama	salama	PROPN
cana-2861	396	7	and	and	CCONJ
cana-2861	396	8	s.	s.	PROPN
cana-2861	396	9	a.	a.	PROPN
cana-2861	396	10	alblowi	alblowi	PROPN
cana-2861	396	11	,	,	PUNCT
cana-2861	396	12	neutrosophic	neutrosophic	ADJ
cana-2861	396	13	set	set	NOUN
cana-2861	396	14	and	and	CCONJ
cana-2861	396	15	neutrosophic	neutrosophic	ADJ
cana-2861	396	16	topological	topological	ADJ
cana-2861	396	17	spaces	space	NOUN
cana-2861	396	18	,	,	PUNCT
cana-2861	396	19	iosr	iosr	ADJ
cana-2861	396	20	journal	journal	NOUN
cana-2861	396	21	of	of	ADP
cana-2861	396	22	mathematics	mathematic	NOUN
cana-2861	396	23	,	,	PUNCT
cana-2861	396	24	3	3	NUM
cana-2861	396	25	(	(	PUNCT
cana-2861	396	26	4	4	NUM
cana-2861	396	27	)	)	PUNCT
cana-2861	396	28	(	(	PUNCT
cana-2861	396	29	2012	2012	NUM
cana-2861	396	30	)	)	PUNCT
cana-2861	396	31	,	,	PUNCT
cana-2861	396	32	31	31	NUM
cana-2861	396	33	-	-	SYM
cana-2861	396	34	35	35	NUM
cana-2861	396	35	.	.	PUNCT
cana-2861	397	1	[	[	X
cana-2861	397	2	15	15	NUM
cana-2861	397	3	]	]	PUNCT
cana-2861	397	4	a.	a.	NOUN
cana-2861	397	5	a.	a.	NOUN
cana-2861	397	6	salama	salama	PROPN
cana-2861	397	7	and	and	CCONJ
cana-2861	397	8	f.	f.	PROPN
cana-2861	397	9	smarandache	smarandache	PROPN
cana-2861	397	10	,	,	PUNCT
cana-2861	397	11	neutrosophic	neutrosophic	ADJ
cana-2861	397	12	crisp	crisp	ADJ
cana-2861	397	13	set	set	NOUN
cana-2861	397	14	theory	theory	NOUN
cana-2861	397	15	,	,	PUNCT
cana-2861	397	16	educational	educational	ADJ
cana-2861	397	17	publisher	publisher	NOUN
cana-2861	397	18	,	,	PUNCT
cana-2861	397	19	columbus	columbus	PROPN
cana-2861	397	20	,	,	PUNCT
cana-2861	397	21	ohio	ohio	PROPN
cana-2861	397	22	,	,	PUNCT
cana-2861	397	23	usa	usa	PROPN
cana-2861	397	24	,	,	PUNCT
cana-2861	397	25	2015	2015	NUM
cana-2861	397	26	.	.	PUNCT
cana-2861	398	1	[	[	X
cana-2861	398	2	16	16	NUM
cana-2861	398	3	]	]	X
cana-2861	398	4	f.	f.	PROPN
cana-2861	398	5	smarandache	smarandache	PROPN
cana-2861	398	6	,	,	PUNCT
cana-2861	398	7	a	a	DET
cana-2861	398	8	unifying	unifying	ADJ
cana-2861	398	9	field	field	NOUN
cana-2861	398	10	in	in	ADP
cana-2861	398	11	logics	logic	NOUN
cana-2861	398	12	:	:	PUNCT
cana-2861	398	13	neutrosophic	neutrosophic	ADJ
cana-2861	398	14	logic	logic	NOUN
cana-2861	398	15	.	.	PUNCT
cana-2861	399	1	neutrosophy	neutrosophy	NOUN
cana-2861	399	2	,	,	PUNCT
cana-2861	399	3	neutrosophic	neutrosophic	ADJ
cana-2861	399	4	set	set	NOUN
cana-2861	399	5	,	,	PUNCT
cana-2861	399	6	neutrosophic	neutrosophic	ADJ
cana-2861	399	7	probability	probability	NOUN
cana-2861	399	8	,	,	PUNCT
cana-2861	399	9	american	american	ADJ
cana-2861	399	10	research	research	PROPN
cana-2861	399	11	press	press	PROPN
cana-2861	399	12	,	,	PUNCT
cana-2861	399	13	rehoboth	rehoboth	PROPN
cana-2861	399	14	,	,	PUNCT
cana-2861	399	15	nm	nm	PROPN
cana-2861	399	16	,	,	PUNCT
cana-2861	399	17	(	(	PUNCT
cana-2861	399	18	1999	1999	NUM
cana-2861	399	19	)	)	PUNCT
cana-2861	399	20	.	.	PUNCT
cana-2861	400	1	[	[	X
cana-2861	400	2	17	17	NUM
cana-2861	400	3	]	]	X
cana-2861	400	4	f.	f.	PROPN
cana-2861	400	5	smarandache	smarandache	PROPN
cana-2861	400	6	,	,	PUNCT
cana-2861	400	7	neutrosophy	neutrosophy	NOUN
cana-2861	400	8	and	and	CCONJ
cana-2861	400	9	neutrosophic	neutrosophic	ADJ
cana-2861	400	10	logic	logic	NOUN
cana-2861	400	11	,	,	PUNCT
cana-2861	400	12	first	first	ADJ
cana-2861	400	13	international	international	ADJ
cana-2861	400	14	conference	conference	NOUN
cana-2861	400	15	on	on	ADP
cana-2861	400	16	neutrosophy	neutrosophy	NOUN
cana-2861	400	17	,	,	PUNCT
cana-2861	400	18	neutrosophic	neutrosophic	ADJ
cana-2861	400	19	logic	logic	NOUN
cana-2861	400	20	,	,	PUNCT
cana-2861	400	21	set	set	NOUN
cana-2861	400	22	,	,	PUNCT
cana-2861	400	23	probability	probability	NOUN
cana-2861	400	24	,	,	PUNCT
cana-2861	400	25	and	and	CCONJ
cana-2861	400	26	statistics	statistic	NOUN
cana-2861	400	27	,	,	PUNCT
cana-2861	400	28	university	university	NOUN
cana-2861	400	29	of	of	ADP
cana-2861	400	30	new	new	PROPN
cana-2861	400	31	mexico	mexico	PROPN
cana-2861	400	32	,	,	PUNCT
cana-2861	400	33	gallup	gallup	PROPN
cana-2861	400	34	,	,	PUNCT
cana-2861	400	35	nm	nm	PROPN
cana-2861	400	36	87301	87301	NUM
cana-2861	400	37	,	,	PUNCT
cana-2861	400	38	usa	usa	PROPN
cana-2861	400	39	(	(	PUNCT
cana-2861	400	40	2002	2002	NUM
cana-2861	400	41	)	)	PUNCT
cana-2861	400	42	.	.	PUNCT
cana-2861	401	1	[	[	X
cana-2861	401	2	18	18	NUM
cana-2861	401	3	]	]	PUNCT
cana-2861	401	4	a.	a.	NOUN
cana-2861	401	5	vadivel	vadivel	NOUN
cana-2861	401	6	and	and	CCONJ
cana-2861	401	7	c.	c.	PROPN
cana-2861	401	8	john	john	PROPN
cana-2861	401	9	sundar	sundar	PROPN
cana-2861	401	10	,	,	PUNCT
cana-2861	401	11	γ	γ	X
cana-2861	401	12	-	-	ADJ
cana-2861	401	13	open	open	ADJ
cana-2861	401	14	sets	set	NOUN
cana-2861	401	15	in	in	ADP
cana-2861	401	16	nnc	nnc	PROPN
cana-2861	401	17	-	-	PUNCT
cana-2861	401	18	topological	topological	ADJ
cana-2861	401	19	spaces	space	NOUN
cana-2861	401	20	,	,	PUNCT
cana-2861	401	21	advances	advance	NOUN
cana-2861	401	22	in	in	ADP
cana-2861	401	23	mathematics	mathematic	NOUN
cana-2861	401	24	:	:	PUNCT
cana-2861	401	25	scientific	scientific	ADJ
cana-2861	401	26	journal	journal	NOUN
cana-2861	401	27	,	,	PUNCT
cana-2861	401	28	9	9	NUM
cana-2861	401	29	(	(	PUNCT
cana-2861	401	30	4	4	NUM
cana-2861	401	31	)	)	PUNCT
cana-2861	401	32	(	(	PUNCT
cana-2861	401	33	2020	2020	NUM
cana-2861	401	34	)	)	PUNCT
cana-2861	401	35	,	,	PUNCT
cana-2861	401	36	2197	2197	NUM
cana-2861	401	37	-	-	SYM
cana-2861	401	38	2202	2202	NUM
cana-2861	401	39	.	.	PUNCT
cana-2861	402	1	[	[	X
cana-2861	402	2	19	19	NUM
cana-2861	402	3	]	]	PUNCT
cana-2861	402	4	a.	a.	NOUN
cana-2861	402	5	vadivel	vadivel	NOUN
cana-2861	402	6	and	and	CCONJ
cana-2861	402	7	c.	c.	PROPN
cana-2861	402	8	john	john	PROPN
cana-2861	402	9	sundar	sundar	PROPN
cana-2861	402	10	,	,	PUNCT
cana-2861	402	11	nncβ	nncβ	NOUN
cana-2861	402	12	-	-	PUNCT
cana-2861	402	13	open	open	ADJ
cana-2861	402	14	sets	set	NOUN
cana-2861	402	15	,	,	PUNCT
cana-2861	402	16	advances	advance	NOUN
cana-2861	402	17	in	in	ADP
cana-2861	402	18	mathematics	mathematic	NOUN
cana-2861	402	19	:	:	PUNCT
cana-2861	402	20	scientific	scientific	ADJ
cana-2861	402	21	journal	journal	NOUN
cana-2861	402	22	,	,	PUNCT
cana-2861	402	23	9	9	NUM
cana-2861	402	24	(	(	PUNCT
cana-2861	402	25	4	4	NUM
cana-2861	402	26	)	)	PUNCT
cana-2861	402	27	(	(	PUNCT
cana-2861	402	28	2020	2020	NUM
cana-2861	402	29	)	)	PUNCT
cana-2861	402	30	,	,	PUNCT
cana-2861	402	31	22032207	22032207	NUM
cana-2861	402	32	.	.	PUNCT
cana-2861	403	1	[	[	X
cana-2861	403	2	20	20	NUM
cana-2861	403	3	]	]	PUNCT
cana-2861	403	4	a.	a.	NOUN
cana-2861	403	5	vadivel	vadivel	NOUN
cana-2861	403	6	and	and	CCONJ
cana-2861	403	7	c.	c.	PROPN
cana-2861	403	8	john	john	PROPN
cana-2861	403	9	sundar	sundar	PROPN
cana-2861	403	10	,	,	PUNCT
cana-2861	403	11	new	new	ADJ
cana-2861	403	12	operators	operator	NOUN
cana-2861	403	13	using	use	VERB
cana-2861	403	14	neutrosophic	neutrosophic	PROPN
cana-2861	403	15	δ	δ	PROPN
cana-2861	403	16	-	-	ADJ
cana-2861	403	17	open	open	ADJ
cana-2861	403	18	set	set	NOUN
cana-2861	403	19	,	,	PUNCT
cana-2861	403	20	journal	journal	NOUN
cana-2861	403	21	of	of	ADP
cana-2861	403	22	neutrosophic	neutrosophic	ADJ
cana-2861	403	23	and	and	CCONJ
cana-2861	403	24	fuzzy	fuzzy	ADJ
cana-2861	403	25	systems	system	NOUN
cana-2861	403	26	,	,	PUNCT
cana-2861	403	27	1	1	NUM
cana-2861	403	28	(	(	PUNCT
cana-2861	403	29	2	2	NUM
cana-2861	403	30	)	)	PUNCT
cana-2861	403	31	(	(	PUNCT
cana-2861	403	32	2021	2021	NUM
cana-2861	403	33	)	)	PUNCT
cana-2861	403	34	,	,	PUNCT
cana-2861	403	35	61	61	NUM
cana-2861	403	36	-	-	SYM
cana-2861	403	37	70	70	NUM
cana-2861	403	38	.	.	PUNCT
cana-2861	404	1	[	[	X
cana-2861	404	2	21	21	NUM
cana-2861	404	3	]	]	PUNCT
cana-2861	404	4	a.	a.	NOUN
cana-2861	404	5	vadivel	vadivel	NOUN
cana-2861	404	6	and	and	CCONJ
cana-2861	404	7	c.	c.	PROPN
cana-2861	404	8	john	john	PROPN
cana-2861	404	9	sundar	sundar	PROPN
cana-2861	404	10	,	,	PUNCT
cana-2861	404	11	on	on	ADP
cana-2861	404	12	almost	almost	ADV
cana-2861	404	13	γ	γ	ADJ
cana-2861	404	14	-	-	ADJ
cana-2861	404	15	continuous	continuous	ADJ
cana-2861	404	16	functions	function	NOUN
cana-2861	404	17	in	in	ADP
cana-2861	404	18	n	n	CCONJ
cana-2861	404	19	-	-	PUNCT
cana-2861	404	20	neutrosophic	neutrosophic	ADJ
cana-2861	404	21	crisp	crisp	ADJ
cana-2861	404	22	topological	topological	ADJ
cana-2861	404	23	spaces	space	NOUN
cana-2861	404	24	,	,	PUNCT
cana-2861	404	25	palestine	palestine	PROPN
cana-2861	404	26	journal	journal	PROPN
cana-2861	404	27	of	of	ADP
cana-2861	404	28	mathematics	mathematic	NOUN
cana-2861	404	29	,	,	PUNCT
cana-2861	404	30	11	11	NUM
cana-2861	404	31	(	(	PUNCT
cana-2861	404	32	3	3	NUM
cana-2861	404	33	)	)	PUNCT
cana-2861	404	34	(	(	PUNCT
cana-2861	404	35	2022	2022	NUM
cana-2861	404	36	)	)	PUNCT
cana-2861	404	37	,	,	PUNCT
cana-2861	404	38	424	424	NUM
cana-2861	404	39	-	-	SYM
cana-2861	404	40	432	432	NUM
cana-2861	404	41	.	.	PUNCT
cana-2861	405	1	[	[	X
cana-2861	405	2	22	22	NUM
cana-2861	405	3	]	]	PUNCT
cana-2861	405	4	a.	a.	NOUN
cana-2861	405	5	vadivel	vadivel	NOUN
cana-2861	405	6	and	and	CCONJ
cana-2861	405	7	c.	c.	PROPN
cana-2861	405	8	john	john	PROPN
cana-2861	405	9	sundar	sundar	PROPN
cana-2861	405	10	,	,	PUNCT
cana-2861	405	11	nncγ	nncγ	NOUN
cana-2861	405	12	maps	map	NOUN
cana-2861	405	13	in	in	ADP
cana-2861	405	14	nnc	nnc	PROPN
cana-2861	405	15	-	-	PUNCT
cana-2861	405	16	topological	topological	ADJ
cana-2861	405	17	spaces	space	NOUN
cana-2861	405	18	,	,	PUNCT
cana-2861	405	19	international	international	ADJ
cana-2861	405	20	journal	journal	NOUN
cana-2861	405	21	of	of	ADP
cana-2861	405	22	neutrosophic	neutrosophic	ADJ
cana-2861	405	23	science	science	NOUN
cana-2861	405	24	,	,	PUNCT
cana-2861	405	25	18	18	NUM
cana-2861	405	26	(	(	PUNCT
cana-2861	405	27	3	3	NUM
cana-2861	405	28	)	)	PUNCT
cana-2861	405	29	(	(	PUNCT
cana-2861	405	30	2022	2022	NUM
cana-2861	405	31	)	)	PUNCT
cana-2861	405	32	,	,	PUNCT
cana-2861	405	33	30	30	NUM
cana-2861	405	34	-	-	SYM
cana-2861	405	35	40	40	NUM
cana-2861	405	36	.	.	PUNCT
cana-2861	406	1	[	[	X
cana-2861	406	2	23	23	NUM
cana-2861	406	3	]	]	PUNCT
cana-2861	406	4	a.	a.	NOUN
cana-2861	406	5	vadivel	vadivel	NOUN
cana-2861	406	6	and	and	CCONJ
cana-2861	406	7	c.	c.	PROPN
cana-2861	406	8	john	john	PROPN
cana-2861	406	9	sundar	sundar	PROPN
cana-2861	406	10	,	,	PUNCT
cana-2861	406	11	on	on	ADP
cana-2861	406	12	almost	almost	ADV
cana-2861	406	13	γ	γ	ADJ
cana-2861	406	14	-	-	ADJ
cana-2861	406	15	continuous	continuous	ADJ
cana-2861	406	16	functions	function	NOUN
cana-2861	406	17	in	in	ADP
cana-2861	406	18	n	n	CCONJ
cana-2861	406	19	-	-	PUNCT
cana-2861	406	20	neutrosophic	neutrosophic	ADJ
cana-2861	406	21	crisp	crisp	ADJ
cana-2861	406	22	topological	topological	ADJ
cana-2861	406	23	spaces	space	NOUN
cana-2861	406	24	,	,	PUNCT
cana-2861	406	25	palestine	palestine	PROPN
cana-2861	406	26	journal	journal	PROPN
cana-2861	406	27	of	of	ADP
cana-2861	406	28	mathematics	mathematic	NOUN
cana-2861	406	29	,	,	PUNCT
cana-2861	406	30	11	11	NUM
cana-2861	406	31	(	(	PUNCT
cana-2861	406	32	3	3	NUM
cana-2861	406	33	)	)	PUNCT
cana-2861	406	34	(	(	PUNCT
cana-2861	406	35	2022	2022	NUM
cana-2861	406	36	)	)	PUNCT
cana-2861	406	37	,	,	PUNCT
cana-2861	406	38	424	424	NUM
cana-2861	406	39	-	-	SYM
cana-2861	406	40	432	432	NUM
cana-2861	406	41	.	.	PUNCT
cana-2861	407	1	[	[	X
cana-2861	407	2	24	24	NUM
cana-2861	407	3	]	]	PUNCT
cana-2861	407	4	a.	a.	NOUN
cana-2861	407	5	vadivel	vadivel	NOUN
cana-2861	407	6	and	and	CCONJ
cana-2861	407	7	c.	c.	PROPN
cana-2861	407	8	john	john	PROPN
cana-2861	407	9	sundar	sundar	PROPN
cana-2861	407	10	,	,	PUNCT
cana-2861	407	11	(	(	PUNCT
cana-2861	407	12	r1957	r1957	NOUN
cana-2861	407	13	)	)	PUNCT
cana-2861	407	14	some	some	DET
cana-2861	407	15	types	type	NOUN
cana-2861	407	16	of	of	ADP
cana-2861	407	17	continuous	continuous	ADJ
cana-2861	407	18	function	function	NOUN
cana-2861	407	19	via	via	ADP
cana-2861	407	20	n	n	CCONJ
cana-2861	407	21	-neutrosophic	-neutrosophic	ADJ
cana-2861	407	22	crisp	crisp	ADJ
cana-2861	407	23	topological	topological	ADJ
cana-2861	407	24	spaces	space	NOUN
cana-2861	407	25	,	,	PUNCT
cana-2861	407	26	applications	application	NOUN
cana-2861	407	27	and	and	CCONJ
cana-2861	407	28	applied	apply	VERB
cana-2861	407	29	mathematics	mathematic	NOUN
cana-2861	407	30	:	:	PUNCT
cana-2861	407	31	an	an	DET
cana-2861	407	32	international	international	ADJ
cana-2861	407	33	journal	journal	NOUN
cana-2861	407	34	(	(	PUNCT
cana-2861	407	35	aam	aam	PROPN
cana-2861	407	36	)	)	PUNCT
cana-2861	407	37	,	,	PUNCT
cana-2861	407	38	18	18	NUM
cana-2861	407	39	(	(	PUNCT
cana-2861	407	40	1	1	NUM
cana-2861	407	41	)	)	PUNCT
cana-2861	407	42	(	(	PUNCT
cana-2861	407	43	2023	2023	NUM
cana-2861	407	44	)	)	PUNCT
cana-2861	407	45	,	,	PUNCT
cana-2861	407	46	article	article	NOUN
cana-2861	407	47	12	12	NUM
cana-2861	407	48	.	.	PUNCT
cana-2861	408	1	[	[	X
cana-2861	408	2	25	25	NUM
cana-2861	408	3	]	]	PUNCT
cana-2861	408	4	a.	a.	NOUN
cana-2861	408	5	vadivel	vadivel	NOUN
cana-2861	408	6	,	,	PUNCT
cana-2861	408	7	c.	c.	PROPN
cana-2861	408	8	john	john	PROPN
cana-2861	408	9	sundar	sundar	PROPN
cana-2861	408	10	and	and	CCONJ
cana-2861	408	11	p.	p.	PROPN
cana-2861	408	12	thangaraja	thangaraja	PROPN
cana-2861	408	13	,	,	PUNCT
cana-2861	408	14	nncβ	nncβ	ADJ
cana-2861	408	15	-	-	PUNCT
cana-2861	408	16	continuous	continuous	ADJ
cana-2861	408	17	maps	map	NOUN
cana-2861	408	18	,	,	PUNCT
cana-2861	408	19	south	south	PROPN
cana-2861	408	20	east	east	PROPN
cana-2861	408	21	asian	asian	PROPN
cana-2861	408	22	journal	journal	NOUN
cana-2861	408	23	of	of	ADP
cana-2861	408	24	mathematics	mathematics	PROPN
cana-2861	408	25	and	and	CCONJ
cana-2861	408	26	mathematical	mathematical	ADJ
cana-2861	408	27	sciences	science	NOUN
cana-2861	408	28	,	,	PUNCT
cana-2861	408	29	18	18	NUM
cana-2861	408	30	(	(	PUNCT
cana-2861	408	31	2	2	NUM
cana-2861	408	32	)	)	PUNCT
cana-2861	408	33	(	(	PUNCT
cana-2861	408	34	2022	2022	NUM
cana-2861	408	35	)	)	PUNCT
cana-2861	408	36	,	,	PUNCT
cana-2861	408	37	275	275	NUM
cana-2861	408	38	-	-	SYM
cana-2861	408	39	288	288	NUM
cana-2861	408	40	.	.	PUNCT
cana-2861	409	1	[	[	X
cana-2861	409	2	26	26	NUM
cana-2861	409	3	]	]	X
cana-2861	409	4	l.	l.	PROPN
cana-2861	409	5	a.	a.	PROPN
cana-2861	409	6	zadeh	zadeh	PROPN
cana-2861	409	7	,	,	PUNCT
cana-2861	409	8	fuzzy	fuzzy	ADJ
cana-2861	409	9	sets	set	NOUN
cana-2861	409	10	,	,	PUNCT
cana-2861	409	11	information	information	NOUN
cana-2861	409	12	and	and	CCONJ
cana-2861	409	13	control	control	NOUN
cana-2861	409	14	,	,	PUNCT
cana-2861	409	15	8	8	NUM
cana-2861	409	16	(	(	PUNCT
cana-2861	409	17	1965	1965	NUM
cana-2861	409	18	)	)	PUNCT
cana-2861	409	19	,	,	PUNCT
cana-2861	409	20	338	338	NUM
cana-2861	409	21	-	-	SYM
cana-2861	409	22	353	353	NUM
cana-2861	409	23	.	.	PUNCT