id	sid	tid	token	lemma	pos
cana-4835	1	1	communications	communication	NOUN
cana-4835	1	2	on	on	ADP
cana-4835	1	3	applied	apply	VERB
cana-4835	1	4	nonlinear	nonlinear	ADJ
cana-4835	1	5	analysis	analysis	NOUN
cana-4835	1	6	issn	issn	NOUN
cana-4835	1	7	:	:	PUNCT
cana-4835	1	8	1074	1074	NUM
cana-4835	1	9	-	-	PUNCT
cana-4835	1	10	133x	133x	NUM
cana-4835	1	11	vol	vol	VERB
cana-4835	1	12	32	32	NUM
cana-4835	1	13	no	no	NOUN
cana-4835	1	14	.	.	PUNCT
cana-4835	2	1	10s	10	NOUN
cana-4835	2	2	(	(	PUNCT
cana-4835	2	3	2025	2025	NUM
cana-4835	2	4	)	)	PUNCT
cana-4835	2	5	428	428	NUM
cana-4835	3	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-4835	3	2	neutrosophic	neutrosophic	ADJ
cana-4835	3	3	fuzzy	fuzzy	NOUN
cana-4835	3	4	𝜶	𝜶	ADP
cana-4835	3	5	composition	composition	NOUN
cana-4835	3	6	r.	r.	PROPN
cana-4835	3	7	vijayalakshmi1	vijayalakshmi1	PROPN
cana-4835	3	8	*	*	PROPN
cana-4835	3	9	,	,	PUNCT
cana-4835	3	10	r.	r.	PROPN
cana-4835	3	11	rushma2	rushma2	PROPN
cana-4835	3	12	,	,	PUNCT
cana-4835	3	13	b.	b.	PROPN
cana-4835	3	14	kumaraswamy	kumaraswamy	PROPN
cana-4835	3	15	achari3	achari3	PROPN
cana-4835	3	16	,	,	PUNCT
cana-4835	3	17	k.	k.	PROPN
cana-4835	3	18	hemabala4	hemabala4	PROPN
cana-4835	3	19	,	,	PUNCT
cana-4835	3	20	nainaru	nainaru	NOUN
cana-4835	3	21	tarakaramu5	tarakaramu5	NOUN
cana-4835	3	22	1department	1department	NUM
cana-4835	3	23	of	of	ADP
cana-4835	3	24	mathematics	mathematic	NOUN
cana-4835	3	25	,	,	PUNCT
cana-4835	3	26	sri	sri	PROPN
cana-4835	3	27	venkateswara	venkateswara	PROPN
cana-4835	3	28	college	college	PROPN
cana-4835	3	29	of	of	ADP
cana-4835	3	30	engineering	engineering	NOUN
cana-4835	3	31	(	(	PUNCT
cana-4835	3	32	autonomous	autonomous	ADJ
cana-4835	3	33	)	)	PUNCT
cana-4835	3	34	,	,	PUNCT
cana-4835	3	35	karkambadi	karkambadi	NOUN
cana-4835	3	36	road	road	NOUN
cana-4835	3	37	,	,	PUNCT
cana-4835	3	38	tirupati517507	tirupati517507	PROPN
cana-4835	3	39	,	,	PUNCT
cana-4835	3	40	a.p	a.p	PROPN
cana-4835	3	41	,	,	PUNCT
cana-4835	3	42	india	india	PROPN
cana-4835	3	43	2department	2department	PROPN
cana-4835	3	44	of	of	ADP
cana-4835	3	45	mathematics	mathematic	NOUN
cana-4835	3	46	,	,	PUNCT
cana-4835	3	47	government	government	NOUN
cana-4835	3	48	degree	degree	NOUN
cana-4835	3	49	college	college	NOUN
cana-4835	3	50	,	,	PUNCT
cana-4835	3	51	vedurukuppam-517569	vedurukuppam-517569	NOUN
cana-4835	3	52	,	,	PUNCT
cana-4835	3	53	chittoor	chittoor	PROPN
cana-4835	3	54	district	district	PROPN
cana-4835	3	55	,	,	PUNCT
cana-4835	3	56	a.p	a.p	PROPN
cana-4835	3	57	,	,	PUNCT
cana-4835	3	58	india	india	PROPN
cana-4835	3	59	3department	3department	PROPN
cana-4835	3	60	of	of	ADP
cana-4835	3	61	mathematics	mathematic	NOUN
cana-4835	3	62	,	,	PUNCT
cana-4835	3	63	academic	academic	ADJ
cana-4835	3	64	consultant	consultant	NOUN
cana-4835	3	65	,	,	PUNCT
cana-4835	3	66	sri	sri	PROPN
cana-4835	3	67	venkateswara	venkateswara	PROPN
cana-4835	3	68	university	university	PROPN
cana-4835	3	69	,	,	PUNCT
cana-4835	3	70	tiruppati-517102	tiruppati-517102	NOUN
cana-4835	3	71	,	,	PUNCT
cana-4835	3	72	a.p	a.p	PROPN
cana-4835	3	73	,	,	PUNCT
cana-4835	3	74	india	india	PROPN
cana-4835	3	75	4department	4department	NUM
cana-4835	3	76	of	of	ADP
cana-4835	3	77	mathematics	mathematics	PROPN
cana-4835	3	78	,	,	PUNCT
cana-4835	3	79	sree	sree	PROPN
cana-4835	3	80	rama	rama	PROPN
cana-4835	3	81	engineering	engineering	PROPN
cana-4835	3	82	college	college	PROPN
cana-4835	3	83	(	(	PUNCT
cana-4835	3	84	autonomous	autonomous	ADJ
cana-4835	3	85	)	)	PUNCT
cana-4835	3	86	,	,	PUNCT
cana-4835	3	87	karkambadi	karkambadi	NOUN
cana-4835	3	88	road	road	NOUN
cana-4835	3	89	,	,	PUNCT
cana-4835	3	90	tirupati-517507	tirupati-517507	NOUN
cana-4835	3	91	,	,	PUNCT
cana-4835	3	92	a.p	a.p	PROPN
cana-4835	3	93	,	,	PUNCT
cana-4835	3	94	india	india	PROPN
cana-4835	3	95	5department	5department	NUM
cana-4835	3	96	of	of	ADP
cana-4835	3	97	mathematics	mathematic	NOUN
cana-4835	3	98	,	,	PUNCT
cana-4835	3	99	school	school	NOUN
cana-4835	3	100	of	of	ADP
cana-4835	3	101	liberal	liberal	ADJ
cana-4835	3	102	arts	art	NOUN
cana-4835	3	103	and	and	CCONJ
cana-4835	3	104	sciences	science	NOUN
cana-4835	3	105	,	,	PUNCT
cana-4835	3	106	mohan	mohan	PROPN
cana-4835	3	107	babu	babu	PROPN
cana-4835	3	108	university	university	PROPN
cana-4835	3	109	,	,	PUNCT
cana-4835	3	110	sree	sree	PROPN
cana-4835	3	111	sainath	sainath	PROPN
cana-4835	3	112	nagar	nagar	PROPN
cana-4835	3	113	,	,	PUNCT
cana-4835	3	114	tirupati-517102	tirupati-517102	NOUN
cana-4835	3	115	,	,	PUNCT
cana-4835	3	116	a.p	a.p	PROPN
cana-4835	3	117	,	,	PUNCT
cana-4835	3	118	india	india	PROPN
cana-4835	3	119	*	*	PUNCT
cana-4835	3	120	corresponding	correspond	VERB
cana-4835	3	121	author	author	NOUN
cana-4835	3	122	:	:	PUNCT
cana-4835	3	123	vijayalakshmi.r@svce.edu.in	vijayalakshmi.r@svce.edu.in	NOUN
cana-4835	3	124	article	article	NOUN
cana-4835	3	125	history	history	NOUN
cana-4835	3	126	:	:	PUNCT
cana-4835	3	127	received	receive	VERB
cana-4835	3	128	:	:	PUNCT
cana-4835	3	129	12	12	NUM
cana-4835	3	130	-	-	SYM
cana-4835	3	131	01	01	NUM
cana-4835	3	132	-	-	PUNCT
cana-4835	3	133	2025	2025	NUM
cana-4835	3	134	revised	revise	VERB
cana-4835	3	135	:	:	PUNCT
cana-4835	3	136	15	15	NUM
cana-4835	3	137	-	-	NUM
cana-4835	3	138	02	02	NUM
cana-4835	3	139	-	-	PUNCT
cana-4835	3	140	2025	2025	NUM
cana-4835	3	141	accepted	accept	VERB
cana-4835	3	142	:	:	PUNCT
cana-4835	3	143	01	01	NUM
cana-4835	3	144	-	-	SYM
cana-4835	3	145	03	03	NUM
cana-4835	3	146	-	-	PUNCT
cana-4835	3	147	2025	2025	NUM
cana-4835	3	148	abstract	abstract	NOUN
cana-4835	3	149	:	:	PUNCT
cana-4835	3	150	we	we	PRON
cana-4835	3	151	discussed	discuss	VERB
cana-4835	3	152	the	the	DET
cana-4835	3	153	methods	method	NOUN
cana-4835	3	154	for	for	ADP
cana-4835	3	155	finding	find	VERB
cana-4835	3	156	the	the	DET
cana-4835	3	157	optimal	optimal	ADJ
cana-4835	3	158	(	(	PUNCT
cana-4835	3	159	maximum	maximum	ADJ
cana-4835	3	160	and	and	CCONJ
cana-4835	3	161	minimum	minimum	ADJ
cana-4835	3	162	)	)	PUNCT
cana-4835	3	163	solution	solution	NOUN
cana-4835	3	164	of	of	ADP
cana-4835	3	165	inverse	inverse	ADJ
cana-4835	3	166	problem	problem	NOUN
cana-4835	3	167	of	of	ADP
cana-4835	3	168	neutrosophic	neutrosophic	ADJ
cana-4835	3	169	fuzzy	fuzzy	ADJ
cana-4835	3	170	relation	relation	NOUN
cana-4835	3	171	equation	equation	NOUN
cana-4835	3	172	of	of	ADP
cana-4835	3	173	the	the	DET
cana-4835	3	174	form	form	NOUN
cana-4835	3	175	r	r	NOUN
cana-4835	3	176	◦	◦	NOUN
cana-4835	3	177	q	q	NOUN
cana-4835	3	178	=	=	PUNCT
cana-4835	3	179	t	t	NOUN
cana-4835	3	180	where	where	SCONJ
cana-4835	3	181	for	for	ADP
cana-4835	3	182	both	both	DET
cana-4835	3	183	cases	case	NOUN
cana-4835	3	184	r	r	NOUN
cana-4835	3	185	and	and	CCONJ
cana-4835	3	186	q	q	NOUN
cana-4835	3	187	are	be	AUX
cana-4835	3	188	kept	keep	VERB
cana-4835	3	189	unknown	unknown	ADJ
cana-4835	3	190	interchangeably	interchangeably	ADV
cana-4835	3	191	using	use	VERB
cana-4835	3	192	alpha	alpha	NOUN
cana-4835	3	193	operator	operator	NOUN
cana-4835	3	194	.	.	PUNCT
cana-4835	4	1	keywords	keyword	NOUN
cana-4835	4	2	:	:	PUNCT
cana-4835	4	3	fuzzy	fuzzy	ADJ
cana-4835	4	4	set	set	NOUN
cana-4835	4	5	,	,	PUNCT
cana-4835	4	6	neutrosophic	neutrosophic	ADJ
cana-4835	4	7	fuzzy	fuzzy	ADJ
cana-4835	4	8	set	set	NOUN
cana-4835	4	9	,	,	PUNCT
cana-4835	4	10	alpha	alpha	NOUN
cana-4835	4	11	operator	operator	NOUN
cana-4835	4	12	,	,	PUNCT
cana-4835	4	13	composition	composition	NOUN
cana-4835	4	14	.	.	PUNCT
cana-4835	5	1	1	1	X
cana-4835	5	2	.	.	X
cana-4835	5	3	introduction	introduction	NOUN
cana-4835	5	4	in	in	ADP
cana-4835	5	5	1965	1965	NUM
cana-4835	5	6	,	,	PUNCT
cana-4835	5	7	zadeh[1	zadeh[1	NUM
cana-4835	5	8	]	]	PUNCT
cana-4835	5	9	introduced	introduce	VERB
cana-4835	5	10	the	the	DET
cana-4835	5	11	concept	concept	NOUN
cana-4835	5	12	of	of	ADP
cana-4835	5	13	fuzzy	fuzzy	ADJ
cana-4835	5	14	set	set	NOUN
cana-4835	5	15	which	which	PRON
cana-4835	5	16	takes	take	VERB
cana-4835	5	17	the	the	DET
cana-4835	5	18	values	value	NOUN
cana-4835	5	19	between	between	ADP
cana-4835	5	20	0	0	NUM
cana-4835	5	21	&	&	CCONJ
cana-4835	5	22	1	1	NUM
cana-4835	5	23	.	.	PUNCT
cana-4835	6	1	later	later	ADV
cana-4835	6	2	many	many	ADJ
cana-4835	6	3	authors	author	NOUN
cana-4835	6	4	developed	develop	VERB
cana-4835	6	5	different	different	ADJ
cana-4835	6	6	algebras	algebra	NOUN
cana-4835	6	7	,	,	PUNCT
cana-4835	6	8	concepts	concept	NOUN
cana-4835	6	9	and	and	CCONJ
cana-4835	6	10	results	result	NOUN
cana-4835	6	11	in	in	ADP
cana-4835	6	12	fuzzy	fuzzy	ADJ
cana-4835	6	13	sets	set	NOUN
cana-4835	6	14	.	.	PUNCT
cana-4835	7	1	in	in	ADP
cana-4835	7	2	vast	vast	ADJ
cana-4835	7	3	theories	theory	NOUN
cana-4835	7	4	we	we	PRON
cana-4835	7	5	are	be	AUX
cana-4835	7	6	studied	study	VERB
cana-4835	7	7	few	few	ADJ
cana-4835	7	8	literature	literature	NOUN
cana-4835	7	9	on	on	ADP
cana-4835	7	10	algebraic	algebraic	ADJ
cana-4835	7	11	structures	structure	NOUN
cana-4835	7	12	.	.	PUNCT
cana-4835	8	1	uzair	uzair	PROPN
cana-4835	8	2	ahmed	ahmed	PROPN
cana-4835	8	3	developed	develop	VERB
cana-4835	8	4	optimal	optimal	ADJ
cana-4835	8	5	solution	solution	NOUN
cana-4835	8	6	of	of	ADP
cana-4835	8	7	fuzzy	fuzzy	ADJ
cana-4835	8	8	relation	relation	NOUN
cana-4835	8	9	equations	equation	NOUN
cana-4835	8	10	.	.	PUNCT
cana-4835	9	1	in	in	ADP
cana-4835	9	2	fuzzy	fuzzy	ADJ
cana-4835	9	3	set	set	VERB
cana-4835	9	4	only	only	ADV
cana-4835	9	5	true	true	ADJ
cana-4835	9	6	values	value	NOUN
cana-4835	9	7	are	be	AUX
cana-4835	9	8	included	include	VERB
cana-4835	9	9	.	.	PUNCT
cana-4835	10	1	but	but	CCONJ
cana-4835	10	2	in	in	ADP
cana-4835	10	3	some	some	DET
cana-4835	10	4	situations	situation	NOUN
cana-4835	10	5	indeterminacy	indeterminacy	NOUN
cana-4835	10	6	and	and	CCONJ
cana-4835	10	7	falsity	falsity	NOUN
cana-4835	10	8	included	include	VERB
cana-4835	10	9	.	.	PUNCT
cana-4835	11	1	to	to	PART
cana-4835	11	2	counter	counter	VERB
cana-4835	11	3	this	this	DET
cana-4835	11	4	situation	situation	NOUN
cana-4835	11	5	.	.	PUNCT
cana-4835	12	1	smarandache	smarandache	PROPN
cana-4835	12	2	introduced	introduce	VERB
cana-4835	12	3	and	and	CCONJ
cana-4835	12	4	developed	develop	VERB
cana-4835	12	5	concepts	concept	NOUN
cana-4835	12	6	of	of	ADP
cana-4835	12	7	neutrosophic	neutrosophic	ADJ
cana-4835	12	8	sets	set	NOUN
cana-4835	12	9	.	.	PUNCT
cana-4835	13	1	later	later	ADV
cana-4835	13	2	many	many	ADJ
cana-4835	13	3	authors	author	NOUN
cana-4835	13	4	start	start	VERB
cana-4835	13	5	working	work	VERB
cana-4835	13	6	on	on	ADP
cana-4835	13	7	ns	ns	NUM
cana-4835	13	8	sets	set	NOUN
cana-4835	13	9	.	.	PUNCT
cana-4835	14	1	hemabala	hemabala	PROPN
cana-4835	14	2	srinivasa	srinivasa	PROPN
cana-4835	14	3	kumar[14	kumar[14	PROPN
cana-4835	14	4	-	-	PUNCT
cana-4835	14	5	16	16	NUM
cana-4835	14	6	]	]	PUNCT
cana-4835	14	7	developed	develop	VERB
cana-4835	14	8	algebrac	algebrac	ADJ
cana-4835	14	9	structures	structure	NOUN
cana-4835	14	10	in	in	ADP
cana-4835	14	11	neutrosophic	neutrosophic	ADJ
cana-4835	14	12	multi	multi	ADJ
cana-4835	14	13	fuzzy	fuzzy	ADJ
cana-4835	14	14	sets	set	NOUN
cana-4835	14	15	.	.	PUNCT
cana-4835	15	1	in	in	ADP
cana-4835	15	2	this	this	DET
cana-4835	15	3	paper	paper	NOUN
cana-4835	15	4	particularly	particularly	ADV
cana-4835	15	5	emphasize	emphasize	VERB
cana-4835	15	6	finding	find	VERB
cana-4835	15	7	the	the	DET
cana-4835	15	8	maximum	maximum	ADJ
cana-4835	15	9	solution	solution	NOUN
cana-4835	15	10	of	of	ADP
cana-4835	15	11	neutrosophic	neutrosophic	ADJ
cana-4835	15	12	fuzzy	fuzzy	ADJ
cana-4835	15	13	relation	relation	NOUN
cana-4835	15	14	equations	equation	NOUN
cana-4835	15	15	through	through	ADP
cana-4835	15	16	the	the	DET
cana-4835	15	17	use	use	NOUN
cana-4835	15	18	of	of	ADP
cana-4835	15	19	alpha	alpha	NOUN
cana-4835	15	20	operator	operator	NOUN
cana-4835	15	21	and	and	CCONJ
cana-4835	15	22	inverse	inverse	NOUN
cana-4835	15	23	relations	relation	NOUN
cana-4835	15	24	.	.	PUNCT
cana-4835	16	1	2	2	X
cana-4835	16	2	.	.	X
cana-4835	16	3	preliminaries	preliminary	NOUN
cana-4835	16	4	fuzzy	fuzzy	ADV
cana-4835	16	5	set	set	VERB
cana-4835	16	6	2.1	2.1	NUM
cana-4835	16	7	fuzzy	fuzzy	ADJ
cana-4835	16	8	set	set	NOUN
cana-4835	16	9	was	be	AUX
cana-4835	16	10	first	first	ADV
cana-4835	16	11	defined	define	VERB
cana-4835	16	12	by	by	ADP
cana-4835	16	13	lofti	lofti	NOUN
cana-4835	16	14	a.zadeh[1	a.zadeh[1	ADP
cana-4835	16	15	]	]	PUNCT
cana-4835	16	16	in	in	ADP
cana-4835	16	17	1965	1965	NUM
cana-4835	16	18	.	.	PUNCT
cana-4835	17	1	he	he	PRON
cana-4835	17	2	defined	define	VERB
cana-4835	17	3	a	a	DET
cana-4835	17	4	fuzzy	fuzzy	ADJ
cana-4835	17	5	set	set	NOUN
cana-4835	17	6	as	as	ADP
cana-4835	17	7	a	a	DET
cana-4835	17	8	collection	collection	NOUN
cana-4835	17	9	of	of	ADP
cana-4835	17	10	objects	object	NOUN
cana-4835	17	11	with	with	ADP
cana-4835	17	12	membership	membership	NOUN
cana-4835	17	13	values	value	NOUN
cana-4835	17	14	in	in	ADP
cana-4835	17	15	the	the	DET
cana-4835	17	16	interval	interval	NOUN
cana-4835	17	17	[	[	X
cana-4835	17	18	0,1	0,1	NUM
cana-4835	17	19	]	]	PUNCT
cana-4835	17	20	.	.	PUNCT
cana-4835	18	1	these	these	DET
cana-4835	18	2	membership	membership	NOUN
cana-4835	18	3	values	value	NOUN
cana-4835	18	4	represent	represent	VERB
cana-4835	18	5	the	the	DET
cana-4835	18	6	grades	grade	NOUN
cana-4835	18	7	of	of	ADP
cana-4835	18	8	membership	membership	NOUN
cana-4835	18	9	with	with	ADP
cana-4835	18	10	the	the	DET
cana-4835	18	11	properties	property	NOUN
cana-4835	18	12	and	and	CCONJ
cana-4835	18	13	distinct	distinct	ADJ
cana-4835	18	14	features	feature	NOUN
cana-4835	18	15	of	of	ADP
cana-4835	18	16	the	the	DET
cana-4835	18	17	collection	collection	NOUN
cana-4835	18	18	.	.	PUNCT
cana-4835	19	1	communications	communication	NOUN
cana-4835	19	2	on	on	ADP
cana-4835	19	3	applied	apply	VERB
cana-4835	19	4	nonlinear	nonlinear	ADJ
cana-4835	19	5	analysis	analysis	NOUN
cana-4835	19	6	issn	issn	NOUN
cana-4835	19	7	:	:	PUNCT
cana-4835	19	8	1074	1074	NUM
cana-4835	19	9	-	-	PUNCT
cana-4835	19	10	133x	133x	NUM
cana-4835	19	11	vol	vol	VERB
cana-4835	19	12	32	32	NUM
cana-4835	19	13	no	no	NOUN
cana-4835	19	14	.	.	PUNCT
cana-4835	20	1	10s	10	NOUN
cana-4835	20	2	(	(	PUNCT
cana-4835	20	3	2025	2025	NUM
cana-4835	20	4	)	)	PUNCT
cana-4835	20	5	429	429	NUM
cana-4835	20	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4835	20	7	fuzzy	fuzzy	ADJ
cana-4835	20	8	sets	set	NOUN
cana-4835	20	9	are	be	AUX
cana-4835	20	10	mathematically	mathematically	ADV
cana-4835	20	11	defined	define	VERB
cana-4835	20	12	as	as	SCONJ
cana-4835	20	13	follows	follow	VERB
cana-4835	20	14	:	:	PUNCT
cana-4835	20	15	“	"	PUNCT
cana-4835	20	16	a	a	DET
cana-4835	20	17	subset	subset	NOUN
cana-4835	20	18	a	a	PRON
cana-4835	20	19	of	of	ADP
cana-4835	20	20	universe	universe	NOUN
cana-4835	20	21	x	x	PUNCT
cana-4835	20	22	with	with	ADP
cana-4835	20	23	the	the	DET
cana-4835	20	24	membership	membership	NOUN
cana-4835	20	25	function	function	NOUN
cana-4835	20	26	µ(x	µ(x	NOUN
cana-4835	20	27	)	)	PUNCT
cana-4835	20	28	which	which	PRON
cana-4835	20	29	may	may	AUX
cana-4835	20	30	take	take	VERB
cana-4835	20	31	any	any	DET
cana-4835	20	32	value	value	NOUN
cana-4835	20	33	in	in	ADP
cana-4835	20	34	the	the	DET
cana-4835	20	35	interval	interval	NOUN
cana-4835	20	36	[	[	X
cana-4835	20	37	0,1	0,1	NUM
cana-4835	20	38	]	]	PUNCT
cana-4835	20	39	is	be	AUX
cana-4835	20	40	called	call	VERB
cana-4835	20	41	fuzzy	fuzzy	ADJ
cana-4835	20	42	set	set	NOUN
cana-4835	20	43	”	"	PUNCT
cana-4835	20	44	.	.	PUNCT
cana-4835	21	1	𝜇𝐴	𝜇𝐴	ADP
cana-4835	21	2	:	:	PUNCT
cana-4835	21	3	x	x	X
cana-4835	21	4	→	→	SYM
cana-4835	21	5	[	[	X
cana-4835	21	6	0,1	0,1	NUM
cana-4835	21	7	]	]	PUNCT
cana-4835	21	8	is	be	AUX
cana-4835	21	9	called	call	VERB
cana-4835	21	10	a	a	DET
cana-4835	21	11	fuzzy	fuzzy	ADJ
cana-4835	21	12	subset	subset	NOUN
cana-4835	21	13	of	of	ADP
cana-4835	21	14	x.	x.	PROPN
cana-4835	21	15	neutrosophic	neutrosophic	PROPN
cana-4835	21	16	fuzzy	fuzzy	ADJ
cana-4835	21	17	set	set	VERB
cana-4835	21	18	2.2	2.2	NUM
cana-4835	21	19	let	let	VERB
cana-4835	21	20	x	x	PRON
cana-4835	21	21	be	be	AUX
cana-4835	21	22	a	a	DET
cana-4835	21	23	non	non	X
cana-4835	21	24	empty	empty	ADJ
cana-4835	21	25	set	set	NOUN
cana-4835	21	26	.	.	PUNCT
cana-4835	22	1	a	a	DET
cana-4835	22	2	neutrosophic	neutrosophic	ADJ
cana-4835	22	3	fuzzy	fuzzy	NOUN
cana-4835	22	4	set	set	NOUN
cana-4835	22	5	𝒩on	𝒩on	PROPN
cana-4835	22	6	x	x	PUNCT
cana-4835	22	7	can	can	AUX
cana-4835	22	8	be	be	AUX
cana-4835	22	9	defined	define	VERB
cana-4835	22	10	as	as	SCONJ
cana-4835	22	11	follows	follow	VERB
cana-4835	22	12	𝒩=	𝒩=	PROPN
cana-4835	22	13	{	{	PUNCT
cana-4835	22	14	<	<	X
cana-4835	22	15	𝑥,(𝓉𝒩(𝑥	𝑥,(𝓉𝒩(𝑥	NOUN
cana-4835	22	16	)	)	PUNCT
cana-4835	22	17	,	,	PUNCT
cana-4835	22	18	𝒾𝒩(𝑥	𝒾𝒩(𝑥	PROPN
cana-4835	22	19	)	)	PUNCT
cana-4835	22	20	,	,	PUNCT
cana-4835	22	21	𝒻𝒩(𝑥	𝒻𝒩(𝑥	PROPN
cana-4835	22	22	)	)	PUNCT
cana-4835	22	23	>	>	PUNCT
cana-4835	22	24	/𝑥	/𝑥	PUNCT
cana-4835	23	1	∈	∈	PROPN
cana-4835	23	2	x	x	X
cana-4835	23	3	}	}	PUNCT
cana-4835	23	4	where	where	SCONJ
cana-4835	23	5	𝓉𝒩(𝑥	𝓉𝒩(𝑥	ADP
cana-4835	23	6	)	)	PUNCT
cana-4835	23	7	:	:	PUNCT
cana-4835	23	8	x	x	SYM
cana-4835	23	9	→[0,1	→[0,1	PROPN
cana-4835	23	10	]	]	PUNCT
cana-4835	23	11	𝒾𝒩(𝑥	𝒾𝒩(𝑥	NUM
cana-4835	23	12	)	)	PUNCT
cana-4835	23	13	∶	∶	NOUN
cana-4835	23	14	x	x	X
cana-4835	23	15	→[0,1	→[0,1	NOUN
cana-4835	23	16	]	]	X
cana-4835	23	17	𝒻𝒩(𝑥	𝒻𝒩(𝑥	X
cana-4835	23	18	)	)	PUNCT
cana-4835	23	19	∶	∶	NOUN
cana-4835	23	20	x	x	PUNCT
cana-4835	23	21	→[0,1	→[0,1	NOUN
cana-4835	23	22	]	]	PUNCT
cana-4835	23	23	0	0	NUM
cana-4835	23	24	≤	≤	PROPN
cana-4835	23	25	sup𝓉𝒩(𝑥	sup𝓉𝒩(𝑥	PROPN
cana-4835	23	26	)	)	PUNCT
cana-4835	24	1	+	+	CCONJ
cana-4835	25	1	𝑠𝑢𝑝𝒾𝒩(𝑥	𝑠𝑢𝑝𝒾𝒩(𝑥	ADJ
cana-4835	25	2	)	)	PUNCT
cana-4835	26	1	+	+	CCONJ
cana-4835	26	2	sup𝒻𝒩(𝑥	sup𝒻𝒩(𝑥	PROPN
cana-4835	26	3	)	)	PUNCT
cana-4835	26	4	≤	≤	NOUN
cana-4835	26	5	3	3	NUM
cana-4835	26	6	𝓉𝒩(𝑥	𝓉𝒩(𝑥	NUM
cana-4835	26	7	)	)	PUNCT
cana-4835	26	8	is	be	AUX
cana-4835	26	9	the	the	DET
cana-4835	26	10	truth	truth	NOUN
cana-4835	26	11	membership	membership	NOUN
cana-4835	26	12	value	value	NOUN
cana-4835	26	13	,	,	PUNCT
cana-4835	26	14	𝒾𝒩(𝑥	𝒾𝒩(𝑥	NUM
cana-4835	26	15	)	)	PUNCT
cana-4835	26	16	is	be	AUX
cana-4835	26	17	the	the	DET
cana-4835	26	18	indeterminacy	indeterminacy	NOUN
cana-4835	26	19	membership	membership	NOUN
cana-4835	26	20	value	value	NOUN
cana-4835	26	21	and	and	CCONJ
cana-4835	26	22	𝒻𝒩(𝑥)falsity	𝒻𝒩(𝑥)falsity	NOUN
cana-4835	26	23	membership	membership	NOUN
cana-4835	26	24	value	value	NOUN
cana-4835	26	25	.	.	PUNCT
cana-4835	27	1	properties	property	NOUN
cana-4835	27	2	2.3	2.3	NUM
cana-4835	27	3	:	:	PUNCT
cana-4835	27	4	let	let	VERB
cana-4835	27	5	x	x	PRON
cana-4835	27	6	be	be	AUX
cana-4835	27	7	a	a	DET
cana-4835	27	8	non	non	X
cana-4835	27	9	empty	empty	ADJ
cana-4835	27	10	set	set	NOUN
cana-4835	27	11	and	and	CCONJ
cana-4835	27	12	𝒩and	𝒩and	PROPN
cana-4835	27	13	ℳneutrosophic	ℳneutrosophic	ADJ
cana-4835	27	14	fuzzy	fuzzy	ADJ
cana-4835	27	15	sets	set	NOUN
cana-4835	27	16	of	of	ADP
cana-4835	27	17	x.	x.	NOUN
cana-4835	27	18	then	then	ADV
cana-4835	27	19	1	1	X
cana-4835	27	20	.	.	PUNCT
cana-4835	28	1	𝒩	𝒩	PROPN
cana-4835	28	2	∪	∪	ADJ
cana-4835	28	3	ℳ	ℳ	NOUN
cana-4835	28	4	=	=	PUNCT
cana-4835	28	5	{	{	PUNCT
cana-4835	28	6	<	<	X
cana-4835	28	7	x	x	NOUN
cana-4835	28	8	,	,	PUNCT
cana-4835	28	9	𝓉𝒩	𝓉𝒩	NOUN
cana-4835	28	10	∪	∪	NOUN
cana-4835	28	11	ℳ	ℳ	PROPN
cana-4835	28	12	(	(	PUNCT
cana-4835	28	13	𝑥	𝑥	NOUN
cana-4835	28	14	)	)	PUNCT
cana-4835	28	15	,	,	PUNCT
cana-4835	28	16	𝒾𝒩	𝒾𝒩	NOUN
cana-4835	28	17	∪	∪	VERB
cana-4835	28	18	ℳ	ℳ	PROPN
cana-4835	28	19	(	(	PUNCT
cana-4835	28	20	𝑥	𝑥	NOUN
cana-4835	28	21	)	)	PUNCT
cana-4835	28	22	,	,	PUNCT
cana-4835	28	23	𝒻𝒩	𝒻𝒩	NOUN
cana-4835	28	24	∪	∪	ADP
cana-4835	28	25	ℳ	ℳ	PROPN
cana-4835	28	26	(	(	PUNCT
cana-4835	28	27	𝑥	𝑥	NOUN
cana-4835	28	28	)	)	PUNCT
cana-4835	28	29	>	>	PUNCT
cana-4835	28	30	/𝑥	/𝑥	PUNCT
cana-4835	28	31	∈	∈	PROPN
cana-4835	28	32	𝑋	𝑋	PROPN
cana-4835	28	33	}	}	PUNCT
cana-4835	28	34	,	,	PUNCT
cana-4835	28	35	where	where	SCONJ
cana-4835	28	36	𝓉𝒩	𝓉𝒩	NOUN
cana-4835	28	37	∪	∪	ADP
cana-4835	28	38	ℳ	ℳ	PROPN
cana-4835	28	39	(	(	PUNCT
cana-4835	28	40	𝑥	𝑥	NOUN
cana-4835	28	41	)	)	PUNCT
cana-4835	28	42	=	=	SYM
cana-4835	28	43	max	max	PROPN
cana-4835	28	44	(	(	PUNCT
cana-4835	28	45	𝓉𝒩(𝑥	𝓉𝒩(𝑥	PROPN
cana-4835	28	46	)	)	PUNCT
cana-4835	28	47	,	,	PUNCT
cana-4835	28	48	𝓉	𝓉	PROPN
cana-4835	28	49	ℳ	ℳ	PROPN
cana-4835	28	50	(	(	PUNCT
cana-4835	28	51	𝑥	𝑥	NOUN
cana-4835	28	52	)	)	PUNCT
cana-4835	28	53	)	)	PUNCT
cana-4835	29	1	𝒾𝒩	𝒾𝒩	NOUN
cana-4835	29	2	∪	∪	VERB
cana-4835	29	3	ℳ	ℳ	PROPN
cana-4835	29	4	(	(	PUNCT
cana-4835	29	5	𝑥	𝑥	NOUN
cana-4835	29	6	)	)	PUNCT
cana-4835	29	7	=	=	SYM
cana-4835	29	8	min	min	NOUN
cana-4835	29	9	(	(	PUNCT
cana-4835	29	10	𝒾𝒩	𝒾𝒩	NOUN
cana-4835	29	11	(	(	PUNCT
cana-4835	29	12	𝑥	𝑥	NOUN
cana-4835	29	13	)	)	PUNCT
cana-4835	29	14	,	,	PUNCT
cana-4835	29	15	𝒾	𝒾	PROPN
cana-4835	29	16	ℳ	ℳ	PROPN
cana-4835	29	17	(	(	PUNCT
cana-4835	29	18	𝑥	𝑥	NOUN
cana-4835	29	19	)	)	PUNCT
cana-4835	29	20	)	)	PUNCT
cana-4835	30	1	𝒻𝒩	𝒻𝒩	ADP
cana-4835	30	2	∪	∪	X
cana-4835	30	3	ℳ	ℳ	PROPN
cana-4835	30	4	(	(	PUNCT
cana-4835	30	5	𝑥	𝑥	NOUN
cana-4835	30	6	)	)	PUNCT
cana-4835	30	7	=	=	SYM
cana-4835	30	8	min	min	NOUN
cana-4835	30	9	(	(	PUNCT
cana-4835	30	10	𝒻𝒩(𝑥	𝒻𝒩(𝑥	PROPN
cana-4835	30	11	)	)	PUNCT
cana-4835	30	12	,	,	PUNCT
cana-4835	30	13	𝒻	𝒻	PROPN
cana-4835	30	14	ℳ	ℳ	PROPN
cana-4835	30	15	(	(	PUNCT
cana-4835	30	16	𝑥	𝑥	NOUN
cana-4835	30	17	)	)	PUNCT
cana-4835	30	18	)	)	PUNCT
cana-4835	30	19	,	,	PUNCT
cana-4835	30	20	2	2	X
cana-4835	30	21	.	.	X
cana-4835	30	22	𝒩	𝒩	NOUN
cana-4835	30	23	∩	∩	NOUN
cana-4835	30	24	ℳ	ℳ	NOUN
cana-4835	30	25	=	=	SYM
cana-4835	30	26	{	{	PUNCT
cana-4835	30	27	<	<	X
cana-4835	30	28	x	x	PROPN
cana-4835	30	29	,	,	PUNCT
cana-4835	30	30	𝓉𝒩	𝓉𝒩	NOUN
cana-4835	30	31	∩	∩	NOUN
cana-4835	30	32	ℳ	ℳ	X
cana-4835	30	33	(	(	PUNCT
cana-4835	30	34	𝑥	𝑥	NOUN
cana-4835	30	35	)	)	PUNCT
cana-4835	30	36	,	,	PUNCT
cana-4835	30	37	𝒾𝒩	𝒾𝒩	NOUN
cana-4835	30	38	∩	∩	ADJ
cana-4835	30	39	ℳ	ℳ	PROPN
cana-4835	30	40	(	(	PUNCT
cana-4835	30	41	𝑥	𝑥	NOUN
cana-4835	30	42	)	)	PUNCT
cana-4835	30	43	,	,	PUNCT
cana-4835	30	44	𝒻𝒩	𝒻𝒩	NOUN
cana-4835	30	45	∩	∩	NOUN
cana-4835	30	46	ℳ	ℳ	X
cana-4835	30	47	(	(	PUNCT
cana-4835	30	48	𝑥	𝑥	NOUN
cana-4835	30	49	)	)	PUNCT
cana-4835	30	50	>	>	PUNCT
cana-4835	30	51	/𝑥	/𝑥	PUNCT
cana-4835	30	52	∈	∈	PROPN
cana-4835	30	53	𝑋	𝑋	PROPN
cana-4835	30	54	}	}	PUNCT
cana-4835	30	55	,	,	PUNCT
cana-4835	30	56	where	where	SCONJ
cana-4835	30	57	𝓉𝒩	𝓉𝒩	NOUN
cana-4835	30	58	∩	∩	ADJ
cana-4835	30	59	ℳ	ℳ	X
cana-4835	30	60	(	(	PUNCT
cana-4835	30	61	𝑥	𝑥	NOUN
cana-4835	30	62	)	)	PUNCT
cana-4835	30	63	=	=	SYM
cana-4835	30	64	min	min	PROPN
cana-4835	30	65	(	(	PUNCT
cana-4835	30	66	𝓉𝒩	𝓉𝒩	NOUN
cana-4835	30	67	(	(	PUNCT
cana-4835	30	68	𝑥	𝑥	NOUN
cana-4835	30	69	)	)	PUNCT
cana-4835	30	70	,	,	PUNCT
cana-4835	30	71	𝓉	𝓉	PROPN
cana-4835	30	72	ℳ	ℳ	PROPN
cana-4835	30	73	(	(	PUNCT
cana-4835	30	74	𝑥	𝑥	NOUN
cana-4835	30	75	)	)	PUNCT
cana-4835	30	76	)	)	PUNCT
cana-4835	30	77	𝒾𝒩	𝒾𝒩	NOUN
cana-4835	30	78	∩	∩	NOUN
cana-4835	30	79	ℳ	ℳ	PROPN
cana-4835	30	80	(	(	PUNCT
cana-4835	30	81	𝑥	𝑥	NOUN
cana-4835	30	82	)	)	PUNCT
cana-4835	30	83	=	=	SYM
cana-4835	30	84	max	max	PROPN
cana-4835	30	85	(	(	PUNCT
cana-4835	30	86	𝒾𝒩	𝒾𝒩	NOUN
cana-4835	30	87	(	(	PUNCT
cana-4835	30	88	𝑥	𝑥	NOUN
cana-4835	30	89	)	)	PUNCT
cana-4835	30	90	,	,	PUNCT
cana-4835	30	91	𝒾	𝒾	PROPN
cana-4835	30	92	ℳ	ℳ	PROPN
cana-4835	30	93	(	(	PUNCT
cana-4835	30	94	𝑥	𝑥	NOUN
cana-4835	30	95	)	)	PUNCT
cana-4835	30	96	)	)	PUNCT
cana-4835	31	1	𝒻𝒩	𝒻𝒩	ADP
cana-4835	31	2	∩	∩	NOUN
cana-4835	31	3	ℳ	ℳ	PROPN
cana-4835	31	4	(	(	PUNCT
cana-4835	31	5	𝑥	𝑥	NOUN
cana-4835	31	6	)	)	PUNCT
cana-4835	32	1	=	=	SYM
cana-4835	32	2	max	max	PROPN
cana-4835	32	3	(	(	PUNCT
cana-4835	32	4	𝒻𝒩	𝒻𝒩	NOUN
cana-4835	32	5	(	(	PUNCT
cana-4835	32	6	𝑥	𝑥	NOUN
cana-4835	32	7	)	)	PUNCT
cana-4835	32	8	,	,	PUNCT
cana-4835	32	9	𝒻	𝒻	PROPN
cana-4835	32	10	ℳ	ℳ	PROPN
cana-4835	32	11	(	(	PUNCT
cana-4835	32	12	𝑥	𝑥	NOUN
cana-4835	32	13	)	)	PUNCT
cana-4835	32	14	)	)	PUNCT
cana-4835	32	15	,	,	PUNCT
cana-4835	32	16	definition	definition	NOUN
cana-4835	32	17	2.4	2.4	NUM
cana-4835	32	18	:	:	PUNCT
cana-4835	32	19	a	a	DET
cana-4835	32	20	neutrosophic	neutrosophic	ADJ
cana-4835	32	21	set	set	NOUN
cana-4835	32	22	𝒩	𝒩	PROPN
cana-4835	32	23	is	be	AUX
cana-4835	32	24	contained	contain	VERB
cana-4835	32	25	in	in	ADP
cana-4835	32	26	another	another	DET
cana-4835	32	27	neutrosophic	neutrosophic	ADJ
cana-4835	32	28	set	set	NOUN
cana-4835	32	29	ℳ	ℳ	PROPN
cana-4835	32	30	if	if	SCONJ
cana-4835	32	31	𝓉𝒩	𝓉𝒩	NOUN
cana-4835	32	32	(	(	PUNCT
cana-4835	32	33	𝑥	𝑥	NOUN
cana-4835	32	34	)	)	PUNCT
cana-4835	32	35	≤	≤	NOUN
cana-4835	32	36	𝓉	𝓉	PROPN
cana-4835	32	37	ℳ	ℳ	PROPN
cana-4835	32	38	(	(	PUNCT
cana-4835	32	39	𝑥	𝑥	NOUN
cana-4835	32	40	)	)	PUNCT
cana-4835	32	41	,	,	PUNCT
cana-4835	32	42	𝒾𝒩	𝒾𝒩	PROPN
cana-4835	32	43	(	(	PUNCT
cana-4835	32	44	𝑥	𝑥	X
cana-4835	32	45	)	)	PUNCT
cana-4835	32	46	≥	≥	NOUN
cana-4835	32	47	𝒾	𝒾	PROPN
cana-4835	32	48	ℳ	ℳ	PROPN
cana-4835	32	49	(	(	PUNCT
cana-4835	32	50	𝑥	𝑥	NOUN
cana-4835	32	51	)	)	PUNCT
cana-4835	32	52	,	,	PUNCT
cana-4835	32	53	𝒻𝒩	𝒻𝒩	PROPN
cana-4835	32	54	(	(	PUNCT
cana-4835	32	55	𝑥	𝑥	NOUN
cana-4835	32	56	)	)	PUNCT
cana-4835	32	57	≥	≥	NOUN
cana-4835	32	58	𝒻	𝒻	PROPN
cana-4835	32	59	ℳ	ℳ	PROPN
cana-4835	32	60	(	(	PUNCT
cana-4835	32	61	𝑥	𝑥	NOUN
cana-4835	32	62	)	)	PUNCT
cana-4835	32	63	definition	definition	NOUN
cana-4835	32	64	2.5	2.5	NUM
cana-4835	32	65	:	:	PUNCT
cana-4835	32	66	two	two	NUM
cana-4835	32	67	neutrosophic	neutrosophic	ADJ
cana-4835	32	68	sets	set	NOUN
cana-4835	32	69	𝒩	𝒩	PROPN
cana-4835	32	70	and	and	CCONJ
cana-4835	32	71	ℳ	ℳ	PROPN
cana-4835	32	72	are	be	AUX
cana-4835	32	73	said	say	VERB
cana-4835	32	74	to	to	PART
cana-4835	32	75	be	be	AUX
cana-4835	32	76	equal	equal	ADJ
cana-4835	32	77	if	if	SCONJ
cana-4835	32	78	𝓉𝒩	𝓉𝒩	NOUN
cana-4835	32	79	(	(	PUNCT
cana-4835	32	80	𝑥	𝑥	NOUN
cana-4835	32	81	)	)	PUNCT
cana-4835	32	82	=	=	SYM
cana-4835	32	83	𝓉	𝓉	PROPN
cana-4835	32	84	ℳ	ℳ	PROPN
cana-4835	32	85	(	(	PUNCT
cana-4835	32	86	𝑥	𝑥	NOUN
cana-4835	32	87	)	)	PUNCT
cana-4835	32	88	,	,	PUNCT
cana-4835	32	89	𝒾𝒩	𝒾𝒩	PROPN
cana-4835	32	90	(	(	PUNCT
cana-4835	32	91	𝑥	𝑥	X
cana-4835	32	92	)	)	PUNCT
cana-4835	32	93	=	=	SYM
cana-4835	32	94	𝒾	𝒾	X
cana-4835	32	95	ℳ	ℳ	PROPN
cana-4835	32	96	(	(	PUNCT
cana-4835	32	97	𝑥	𝑥	NOUN
cana-4835	32	98	)	)	PUNCT
cana-4835	32	99	,	,	PUNCT
cana-4835	32	100	𝒻𝒩	𝒻𝒩	PROPN
cana-4835	32	101	(	(	PUNCT
cana-4835	32	102	𝑥	𝑥	NOUN
cana-4835	32	103	)	)	PUNCT
cana-4835	32	104	=	=	SYM
cana-4835	32	105	𝒻	𝒻	PROPN
cana-4835	32	106	ℳ	ℳ	PROPN
cana-4835	32	107	(	(	PUNCT
cana-4835	32	108	𝑥	𝑥	NOUN
cana-4835	32	109	)	)	PUNCT
cana-4835	32	110	communications	communication	NOUN
cana-4835	32	111	on	on	ADP
cana-4835	32	112	applied	apply	VERB
cana-4835	32	113	nonlinear	nonlinear	ADJ
cana-4835	32	114	analysis	analysis	NOUN
cana-4835	32	115	issn	issn	NOUN
cana-4835	32	116	:	:	PUNCT
cana-4835	32	117	1074	1074	NUM
cana-4835	32	118	-	-	PUNCT
cana-4835	32	119	133x	133x	NUM
cana-4835	32	120	vol	vol	VERB
cana-4835	32	121	32	32	NUM
cana-4835	32	122	no	no	NOUN
cana-4835	32	123	.	.	PUNCT
cana-4835	33	1	10s	10	NOUN
cana-4835	33	2	(	(	PUNCT
cana-4835	33	3	2025	2025	NUM
cana-4835	33	4	)	)	PUNCT
cana-4835	33	5	430	430	NUM
cana-4835	33	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4835	33	7	definition	definition	NOUN
cana-4835	33	8	2.6	2.6	NUM
cana-4835	33	9	:	:	PUNCT
cana-4835	33	10	a	a	DET
cana-4835	33	11	lattice	lattice	NOUN
cana-4835	33	12	is	be	AUX
cana-4835	33	13	a	a	DET
cana-4835	33	14	partially	partially	ADV
cana-4835	33	15	ordered	order	VERB
cana-4835	33	16	set	set	NOUN
cana-4835	33	17	(	(	PUNCT
cana-4835	33	18	poset	poset	NOUN
cana-4835	33	19	)	)	PUNCT
cana-4835	33	20	l	l	NOUN
cana-4835	33	21	in	in	ADP
cana-4835	33	22	which	which	PRON
cana-4835	33	23	any	any	DET
cana-4835	33	24	two	two	NUM
cana-4835	33	25	elements	element	NOUN
cana-4835	33	26	“	"	PUNCT
cana-4835	33	27	x	x	NOUN
cana-4835	33	28	”	"	PUNCT
cana-4835	33	29	and	and	CCONJ
cana-4835	33	30	“	"	PUNCT
cana-4835	33	31	y	y	NOUN
cana-4835	33	32	”	"	PUNCT
cana-4835	33	33	have	have	VERB
cana-4835	33	34	a	a	DET
cana-4835	33	35	greatest	greatest	ADV
cana-4835	33	36	lower	lower	ADV
cana-4835	33	37	bound	bind	VERB
cana-4835	33	38	(	(	PUNCT
cana-4835	33	39	inf	inf	NOUN
cana-4835	33	40	)	)	PUNCT
cana-4835	33	41	denoted	denote	VERB
cana-4835	33	42	by	by	ADP
cana-4835	33	43	x	x	PROPN
cana-4835	33	44	∧	∧	PROPN
cana-4835	33	45	y	y	PROPN
cana-4835	33	46	=	=	SYM
cana-4835	33	47	min(x	min(x	PROPN
cana-4835	33	48	,	,	PUNCT
cana-4835	33	49	y	y	PROPN
cana-4835	33	50	)	)	PUNCT
cana-4835	33	51	and	and	CCONJ
cana-4835	33	52	a	a	DET
cana-4835	33	53	least	least	ADV
cana-4835	33	54	upper	upper	ADJ
cana-4835	33	55	bound	bind	VERB
cana-4835	33	56	(	(	PUNCT
cana-4835	33	57	sup	sup	NOUN
cana-4835	33	58	)	)	PUNCT
cana-4835	33	59	denoted	denote	VERB
cana-4835	33	60	by	by	ADP
cana-4835	33	61	x	x	PROPN
cana-4835	33	62	∨	∨	PROPN
cana-4835	33	63	y	y	PROPN
cana-4835	33	64	=	=	SYM
cana-4835	33	65	max(x	max(x	PROPN
cana-4835	33	66	,	,	PUNCT
cana-4835	33	67	y	y	NOUN
cana-4835	33	68	)	)	PUNCT
cana-4835	33	69	.	.	PUNCT
cana-4835	34	1	definition	definition	NOUN
cana-4835	34	2	2.7	2.7	NUM
cana-4835	34	3	:	:	PUNCT
cana-4835	34	4	a	a	DET
cana-4835	34	5	brouwerian	brouwerian	ADJ
cana-4835	34	6	lattice	lattice	NOUN
cana-4835	34	7	is	be	AUX
cana-4835	34	8	a	a	DET
cana-4835	34	9	lattice	lattice	ADJ
cana-4835	34	10	l	l	NOUN
cana-4835	35	1	[	[	X
cana-4835	35	2	2	2	NUM
cana-4835	35	3	]	]	PUNCT
cana-4835	35	4	in	in	ADP
cana-4835	35	5	which	which	PRON
cana-4835	35	6	for	for	ADP
cana-4835	35	7	any	any	DET
cana-4835	35	8	given	give	VERB
cana-4835	35	9	elements	element	NOUN
cana-4835	35	10	“	"	PUNCT
cana-4835	35	11	a	a	PRON
cana-4835	35	12	”	"	PUNCT
cana-4835	35	13	and	and	CCONJ
cana-4835	35	14	“	"	PUNCT
cana-4835	35	15	b	b	X
cana-4835	35	16	”	"	PUNCT
cana-4835	35	17	,	,	PUNCT
cana-4835	35	18	the	the	DET
cana-4835	35	19	set	set	NOUN
cana-4835	35	20	of	of	ADP
cana-4835	35	21	all	all	DET
cana-4835	35	22	x	x	SYM
cana-4835	35	23	∈	∈	NOUN
cana-4835	35	24	l	l	NOUN
cana-4835	35	25	such	such	ADJ
cana-4835	35	26	that	that	SCONJ
cana-4835	35	27	a	a	DET
cana-4835	35	28	∨	∨	NOUN
cana-4835	35	29	x	x	SYM
cana-4835	35	30	≤	≤	PROPN
cana-4835	35	31	b	b	PROPN
cana-4835	35	32	contains	contain	VERB
cana-4835	35	33	a	a	DET
cana-4835	35	34	greatest	great	ADJ
cana-4835	35	35	element	element	NOUN
cana-4835	35	36	,	,	PUNCT
cana-4835	35	37	denoted	denote	VERB
cana-4835	35	38	“	"	PUNCT
cana-4835	35	39	a	a	DET
cana-4835	35	40	α	α	NOUN
cana-4835	35	41	b	b	NOUN
cana-4835	35	42	”	"	PUNCT
cana-4835	35	43	,	,	PUNCT
cana-4835	35	44	the	the	DET
cana-4835	35	45	relative	relative	ADJ
cana-4835	35	46	pseudo	pseudo	NOUN
cana-4835	35	47	complement	complement	NOUN
cana-4835	35	48	of	of	ADP
cana-4835	35	49	a	a	PRON
cana-4835	35	50	in	in	ADP
cana-4835	35	51	b.	b.	PROPN
cana-4835	35	52	definition	definition	NOUN
cana-4835	35	53	2.8	2.8	NUM
cana-4835	35	54	:	:	PUNCT
cana-4835	35	55	for	for	ADP
cana-4835	35	56	any	any	PRON
cana-4835	35	57	given	give	VERB
cana-4835	35	58	a	a	PRON
cana-4835	35	59	and	and	CCONJ
cana-4835	35	60	b	b	NOUN
cana-4835	35	61	in	in	ADP
cana-4835	35	62	lattice	lattice	PROPN
cana-4835	35	63	l	l	PROPN
cana-4835	35	64	∈	∈	PROPN
cana-4835	35	65	[	[	X
cana-4835	35	66	0,1	0,1	NUM
cana-4835	35	67	]	]	PUNCT
cana-4835	35	68	,	,	PUNCT
cana-4835	35	69	α	α	PRON
cana-4835	35	70	operator	operator	NOUN
cana-4835	35	71	is	be	AUX
cana-4835	35	72	defined	define	VERB
cana-4835	35	73	as	as	ADP
cana-4835	35	74	a	a	DET
cana-4835	35	75	α	α	NOUN
cana-4835	35	76	b	b	NOUN
cana-4835	35	77	=	=	PRON
cana-4835	35	78	{	{	PUNCT
cana-4835	35	79	1	1	NUM
cana-4835	35	80	𝑖𝑓	𝑖𝑓	ADP
cana-4835	36	1	𝑎	𝑎	NOUN
cana-4835	36	2	≤	≤	NUM
cana-4835	36	3	𝑏	𝑏	PRON
cana-4835	36	4	𝑏	𝑏	NOUN
cana-4835	36	5	𝑖𝑓	𝑖𝑓	ADP
cana-4835	36	6	𝑎	𝑎	X
cana-4835	36	7	>	>	X
cana-4835	36	8	𝑏	𝑏	PROPN
cana-4835	36	9	it	it	PRON
cana-4835	36	10	is	be	AUX
cana-4835	36	11	also	also	ADV
cana-4835	36	12	called	call	VERB
cana-4835	36	13	sanchez	sanchez	NOUN
cana-4835	36	14	operator	operator	NOUN
cana-4835	36	15	example	example	NOUN
cana-4835	36	16	1	1	NUM
cana-4835	36	17	:	:	PUNCT
cana-4835	36	18	for	for	ADP
cana-4835	36	19	different	different	ADJ
cana-4835	36	20	values	value	NOUN
cana-4835	36	21	of	of	ADP
cana-4835	36	22	a	a	PRON
cana-4835	36	23	and	and	CCONJ
cana-4835	36	24	b	b	NOUN
cana-4835	36	25	,	,	PUNCT
cana-4835	36	26	α	α	PRON
cana-4835	36	27	operator	operator	NOUN
cana-4835	36	28	will	will	AUX
cana-4835	36	29	defned	defne	VERB
cana-4835	36	30	as	as	ADP
cana-4835	36	31	:	:	PUNCT
cana-4835	36	32	0.8α0.5	0.8α0.5	NUM
cana-4835	36	33	=	=	SYM
cana-4835	36	34	0.5	0.5	NUM
cana-4835	36	35	,	,	PUNCT
cana-4835	36	36	0.5α0.6	0.5α0.6	NOUN
cana-4835	36	37	=	=	SYM
cana-4835	36	38	1	1	NUM
cana-4835	36	39	,	,	PUNCT
cana-4835	36	40	0.3α0.3	0.3α0.3	ADJ
cana-4835	36	41	=	=	SYM
cana-4835	36	42	1	1	NUM
cana-4835	36	43	,	,	PUNCT
cana-4835	36	44	0.6α0.3	0.6α0.3	NOUN
cana-4835	36	45	=	=	PUNCT
cana-4835	36	46	0.3	0.3	NUM
cana-4835	36	47	properties	property	NOUN
cana-4835	36	48	of	of	ADP
cana-4835	36	49	α	α	PRON
cana-4835	36	50	operator	operator	NOUN
cana-4835	36	51	2.9	2.9	NUM
cana-4835	36	52	:	:	SYM
cana-4835	37	1	1	1	NUM
cana-4835	37	2	.	.	X
cana-4835	38	1	if	if	SCONJ
cana-4835	38	2	b	b	X
cana-4835	38	3	=	=	NOUN
cana-4835	38	4	0	0	X
cana-4835	38	5	then	then	ADV
cana-4835	38	6	“	"	PUNCT
cana-4835	38	7	a	a	DET
cana-4835	38	8	α	α	PROPN
cana-4835	38	9	b	b	NOUN
cana-4835	38	10	”	"	PUNCT
cana-4835	38	11	will	will	AUX
cana-4835	38	12	be	be	AUX
cana-4835	38	13	given	give	VERB
cana-4835	38	14	as	as	ADP
cana-4835	38	15	a	a	DET
cana-4835	38	16	α	α	NOUN
cana-4835	38	17	0	0	PUNCT
cana-4835	39	1	=	=	NOUN
cana-4835	39	2	{	{	PUNCT
cana-4835	39	3	1	1	NUM
cana-4835	39	4	𝑖𝑓	𝑖𝑓	NUM
cana-4835	39	5	𝑎	𝑎	X
cana-4835	39	6	=	=	SYM
cana-4835	39	7	𝑏	𝑏	NOUN
cana-4835	39	8	𝑏	𝑏	NOUN
cana-4835	39	9	𝑖𝑓	𝑖𝑓	ADP
cana-4835	39	10	𝑎	𝑎	X
cana-4835	39	11	>	>	X
cana-4835	39	12	𝑏	𝑏	PROPN
cana-4835	39	13	2	2	NUM
cana-4835	39	14	.	.	PUNCT
cana-4835	40	1	if	if	SCONJ
cana-4835	40	2	a	a	PRON
cana-4835	40	3	=	=	NOUN
cana-4835	40	4	0	0	X
cana-4835	40	5	then	then	ADV
cana-4835	40	6	“	"	PUNCT
cana-4835	40	7	a	a	DET
cana-4835	40	8	α	α	PROPN
cana-4835	40	9	b	b	NOUN
cana-4835	40	10	”	"	PUNCT
cana-4835	40	11	will	will	AUX
cana-4835	40	12	be	be	AUX
cana-4835	40	13	given	give	VERB
cana-4835	40	14	as	as	ADP
cana-4835	40	15	:	:	PUNCT
cana-4835	40	16	0	0	NUM
cana-4835	41	1	α	α	PRON
cana-4835	41	2	b	b	X
cana-4835	41	3	=	=	SYM
cana-4835	41	4	1hh	1hh	NOUN
cana-4835	41	5	3	3	X
cana-4835	41	6	.	.	PUNCT
cana-4835	42	1	if	if	SCONJ
cana-4835	42	2	b	b	NOUN
cana-4835	42	3	=	=	NOUN
cana-4835	42	4	1	1	NUM
cana-4835	42	5	then	then	ADV
cana-4835	42	6	“	"	PUNCT
cana-4835	42	7	a	a	DET
cana-4835	42	8	α	α	PROPN
cana-4835	42	9	b	b	NOUN
cana-4835	42	10	”	"	PUNCT
cana-4835	42	11	will	will	AUX
cana-4835	42	12	be	be	AUX
cana-4835	42	13	given	give	VERB
cana-4835	42	14	as	as	ADP
cana-4835	42	15	:	:	PUNCT
cana-4835	42	16	a	a	DET
cana-4835	42	17	α	α	NOUN
cana-4835	42	18	1	1	X
cana-4835	42	19	=	=	SYM
cana-4835	42	20	1	1	NUM
cana-4835	42	21	4	4	NUM
cana-4835	42	22	.	.	PUNCT
cana-4835	43	1	if	if	SCONJ
cana-4835	43	2	a	a	PRON
cana-4835	43	3	=	=	NOUN
cana-4835	43	4	1	1	NUM
cana-4835	43	5	then	then	ADV
cana-4835	43	6	“	"	PUNCT
cana-4835	43	7	a	a	DET
cana-4835	43	8	α	α	PROPN
cana-4835	43	9	b	b	NOUN
cana-4835	43	10	”	"	PUNCT
cana-4835	43	11	will	will	AUX
cana-4835	43	12	be	be	AUX
cana-4835	43	13	given	give	VERB
cana-4835	43	14	as	as	ADP
cana-4835	43	15	:	:	PUNCT
cana-4835	43	16	1	1	NUM
cana-4835	43	17	α	α	NOUN
cana-4835	43	18	b	b	X
cana-4835	44	1	=	=	SYM
cana-4835	44	2	b	b	PROPN
cana-4835	44	3	5	5	NUM
cana-4835	44	4	.	.	PUNCT
cana-4835	44	5	α	α	PRON
cana-4835	44	6	operator	operator	NOUN
cana-4835	44	7	is	be	AUX
cana-4835	44	8	not	not	PART
cana-4835	44	9	commutative	commutative	ADJ
cana-4835	44	10	.	.	PUNCT
cana-4835	45	1	a	a	DET
cana-4835	45	2	α	α	NOUN
cana-4835	45	3	b	b	PROPN
cana-4835	45	4	≠	≠	PROPN
cana-4835	45	5	b	b	PROPN
cana-4835	45	6	α	α	PRON
cana-4835	45	7	a	a	DET
cana-4835	45	8	(	(	PUNCT
cana-4835	45	9	not	not	PART
cana-4835	45	10	commutative	commutative	ADJ
cana-4835	45	11	)	)	PUNCT
cana-4835	45	12	communications	communication	NOUN
cana-4835	45	13	on	on	ADP
cana-4835	45	14	applied	apply	VERB
cana-4835	45	15	nonlinear	nonlinear	ADJ
cana-4835	45	16	analysis	analysis	NOUN
cana-4835	45	17	issn	issn	NOUN
cana-4835	45	18	:	:	PUNCT
cana-4835	45	19	1074	1074	NUM
cana-4835	45	20	-	-	PUNCT
cana-4835	45	21	133x	133x	NUM
cana-4835	45	22	vol	vol	VERB
cana-4835	45	23	32	32	NUM
cana-4835	45	24	no	no	NOUN
cana-4835	45	25	.	.	PUNCT
cana-4835	46	1	10s	10	NOUN
cana-4835	46	2	(	(	PUNCT
cana-4835	46	3	2025	2025	NUM
cana-4835	46	4	)	)	PUNCT
cana-4835	46	5	431	431	NUM
cana-4835	46	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4835	46	7	6	6	NUM
cana-4835	46	8	.	.	PUNCT
cana-4835	47	1	α	α	PRON
cana-4835	47	2	operator	operator	NOUN
cana-4835	47	3	is	be	AUX
cana-4835	47	4	not	not	PART
cana-4835	47	5	associative	associative	ADJ
cana-4835	47	6	.	.	PUNCT
cana-4835	48	1	a	a	DET
cana-4835	48	2	α	α	NOUN
cana-4835	48	3	(	(	PUNCT
cana-4835	48	4	b	b	NOUN
cana-4835	48	5	α	α	NOUN
cana-4835	48	6	c	c	NOUN
cana-4835	48	7	)	)	PUNCT
cana-4835	48	8	≠	≠	PROPN
cana-4835	48	9	(	(	PUNCT
cana-4835	48	10	a	a	DET
cana-4835	48	11	α	α	PROPN
cana-4835	48	12	b	b	NOUN
cana-4835	48	13	)	)	PUNCT
cana-4835	48	14	α	α	PROPN
cana-4835	48	15	c	c	NOUN
cana-4835	48	16	(	(	PUNCT
cana-4835	48	17	not	not	PART
cana-4835	48	18	associative	associative	ADJ
cana-4835	48	19	)	)	PUNCT
cana-4835	48	20	3	3	NUM
cana-4835	48	21	.	.	X
cana-4835	48	22	neutrosophic	neutrosophic	ADJ
cana-4835	48	23	composition	composition	NOUN
cana-4835	48	24	of	of	ADP
cana-4835	48	25	the	the	DET
cana-4835	48	26	α	α	NOUN
cana-4835	48	27	–	–	PUNCT
cana-4835	48	28	operator	operator	NOUN
cana-4835	48	29	type	type	NOUN
cana-4835	48	30	in	in	ADP
cana-4835	48	31	this	this	DET
cana-4835	48	32	section	section	NOUN
cana-4835	48	33	we	we	PRON
cana-4835	48	34	will	will	AUX
cana-4835	48	35	discuss	discuss	VERB
cana-4835	48	36	the	the	DET
cana-4835	48	37	methods	method	NOUN
cana-4835	48	38	of	of	ADP
cana-4835	48	39	finding	find	VERB
cana-4835	48	40	the	the	DET
cana-4835	48	41	maximal	maximal	ADJ
cana-4835	48	42	solution	solution	NOUN
cana-4835	48	43	of	of	ADP
cana-4835	48	44	neutrosophic	neutrosophic	ADJ
cana-4835	48	45	fuzzy	fuzzy	ADJ
cana-4835	48	46	relation	relation	NOUN
cana-4835	48	47	equation	equation	NOUN
cana-4835	48	48	with	with	ADP
cana-4835	48	49	respect	respect	NOUN
cana-4835	48	50	to	to	ADP
cana-4835	48	51	unknowns	unknown	NOUN
cana-4835	48	52	r	r	NOUN
cana-4835	48	53	and	and	CCONJ
cana-4835	48	54	q.	q.	NOUN
cana-4835	48	55	we	we	PRON
cana-4835	48	56	will	will	AUX
cana-4835	48	57	discuss	discuss	VERB
cana-4835	48	58	the	the	DET
cana-4835	48	59	methods	method	NOUN
cana-4835	48	60	for	for	ADP
cana-4835	48	61	finding	find	VERB
cana-4835	48	62	the	the	DET
cana-4835	48	63	maximal	maximal	ADJ
cana-4835	48	64	“	"	PUNCT
cana-4835	48	65	q	q	NOUN
cana-4835	48	66	”	"	PUNCT
cana-4835	48	67	and	and	CCONJ
cana-4835	48	68	maximal	maximal	ADJ
cana-4835	48	69	“	"	PUNCT
cana-4835	48	70	r	r	NOUN
cana-4835	48	71	”	"	PUNCT
cana-4835	48	72	respectively	respectively	ADV
cana-4835	48	73	for	for	ADP
cana-4835	48	74	nfre	nfre	ADJ
cana-4835	48	75	of	of	ADP
cana-4835	48	76	the	the	DET
cana-4835	48	77	form	form	NOUN
cana-4835	48	78	r	r	NOUN
cana-4835	48	79	◦	◦	NOUN
cana-4835	48	80	q	q	NOUN
cana-4835	48	81	=	=	SYM
cana-4835	48	82	t.	t.	NOUN
cana-4835	48	83	here	here	ADV
cana-4835	48	84	“	"	PUNCT
cana-4835	48	85	∇	∇	X
cana-4835	48	86	”	"	PUNCT
cana-4835	48	87	denotes	denote	VERB
cana-4835	48	88	the	the	DET
cana-4835	48	89	maximal	maximal	ADJ
cana-4835	48	90	solution	solution	NOUN
cana-4835	48	91	.	.	PUNCT
cana-4835	49	1	definition	definition	NOUN
cana-4835	49	2	3.1	3.1	NUM
cana-4835	49	3	:	:	PUNCT
cana-4835	49	4	consider	consider	VERB
cana-4835	49	5	two	two	NUM
cana-4835	49	6	neutrosophic	neutrosophic	ADJ
cana-4835	49	7	fuzzy	fuzzy	ADJ
cana-4835	49	8	relations	relation	NOUN
cana-4835	49	9	r	r	NOUN
cana-4835	49	10	⊆	⊆	NUM
cana-4835	49	11	x	x	SYM
cana-4835	49	12	×	×	PROPN
cana-4835	49	13	y	y	PROPN
cana-4835	49	14	and	and	CCONJ
cana-4835	49	15	q	q	NOUN
cana-4835	50	1	⊆	⊆	NUM
cana-4835	50	2	y	y	PROPN
cana-4835	50	3	×	×	PROPN
cana-4835	50	4	z.	z.	PROPN
cana-4835	50	5	relationship	relationship	NOUN
cana-4835	50	6	between	between	ADP
cana-4835	50	7	these	these	DET
cana-4835	50	8	two	two	NUM
cana-4835	50	9	neutrosophic	neutrosophic	ADJ
cana-4835	50	10	fuzzy	fuzzy	ADJ
cana-4835	50	11	relations	relation	NOUN
cana-4835	50	12	when	when	SCONJ
cana-4835	50	13	using	use	VERB
cana-4835	50	14	@	@	ADP
cana-4835	50	15	composition	composition	NOUN
cana-4835	50	16	is	be	AUX
cana-4835	50	17	defined	define	VERB
cana-4835	50	18	as	as	ADP
cana-4835	50	19	r	r	NOUN
cana-4835	50	20	@	@	ADP
cana-4835	50	21	q	q	NOUN
cana-4835	51	1	⊆	⊆	NUM
cana-4835	51	2	x	x	SYM
cana-4835	51	3	×	×	PROPN
cana-4835	51	4	z	z	NOUN
cana-4835	51	5	with	with	ADP
cana-4835	51	6	the	the	DET
cana-4835	51	7	membership	membership	NOUN
cana-4835	51	8	function	function	NOUN
cana-4835	51	9	defined	define	VERB
cana-4835	51	10	as	as	ADP
cana-4835	51	11	:	:	PUNCT
cana-4835	51	12	𝜇𝑅@𝑄(𝑥	𝜇𝑅@𝑄(𝑥	NUM
cana-4835	51	13	,	,	PUNCT
cana-4835	51	14	𝑧	𝑧	NOUN
cana-4835	51	15	)	)	PUNCT
cana-4835	51	16	=	=	SYM
cana-4835	51	17	(	(	PUNCT
cana-4835	51	18	∧	∧	PROPN
cana-4835	51	19	{	{	PUNCT
cana-4835	51	20	𝜇𝑅𝑇(𝑥	𝜇𝑅𝑇(𝑥	PROPN
cana-4835	51	21	,	,	PUNCT
cana-4835	51	22	𝑦)𝛼𝜇𝑄𝑇(𝑦	𝑦)𝛼𝜇𝑄𝑇(𝑦	NUM
cana-4835	51	23	,	,	PUNCT
cana-4835	51	24	𝑧)},∨	𝑧)},∨	PROPN
cana-4835	51	25	{	{	PUNCT
cana-4835	51	26	𝜇𝑅𝐼(𝑥	𝜇𝑅𝐼(𝑥	PROPN
cana-4835	51	27	,	,	PUNCT
cana-4835	51	28	𝑦)𝛼𝜇𝑄𝐼(𝑦	𝑦)𝛼𝜇𝑄𝐼(𝑦	NOUN
cana-4835	51	29	,	,	PUNCT
cana-4835	51	30	𝑧)},∨	𝑧)},∨	PROPN
cana-4835	51	31	{	{	PUNCT
cana-4835	51	32	𝜇𝑅𝐹(𝑥	𝜇𝑅𝐹(𝑥	VERB
cana-4835	51	33	,	,	PUNCT
cana-4835	51	34	𝑦)𝛼𝜇𝑄𝐹(𝑦	𝑦)𝛼𝜇𝑄𝐹(𝑦	NUM
cana-4835	51	35	,	,	PUNCT
cana-4835	51	36	𝑧	𝑧	NOUN
cana-4835	51	37	)	)	PUNCT
cana-4835	51	38	}	}	PUNCT
cana-4835	51	39	)	)	PUNCT
cana-4835	51	40	∀	∀	X
cana-4835	52	1	x	x	X
cana-4835	52	2	∈	∈	NOUN
cana-4835	52	3	x	x	NOUN
cana-4835	52	4	,	,	PUNCT
cana-4835	52	5	y	y	PROPN
cana-4835	52	6	∈	∈	PROPN
cana-4835	52	7	y	y	PROPN
cana-4835	52	8	and	and	CCONJ
cana-4835	52	9	z	z	PROPN
cana-4835	52	10	∈	∈	PROPN
cana-4835	52	11	z	z	NOUN
cana-4835	52	12	example	example	NOUN
cana-4835	52	13	2	2	NUM
cana-4835	52	14	:	:	PUNCT
cana-4835	52	15	let	let	VERB
cana-4835	52	16	x	x	PUNCT
cana-4835	52	17	=	=	PRON
cana-4835	52	18	{	{	PUNCT
cana-4835	52	19	x1	x1	PROPN
cana-4835	52	20	,	,	PUNCT
cana-4835	52	21	x2	x2	PROPN
cana-4835	52	22	,	,	PUNCT
cana-4835	52	23	x3	x3	ADJ
cana-4835	52	24	}	}	PUNCT
cana-4835	52	25	,	,	PUNCT
cana-4835	52	26	y	y	PROPN
cana-4835	52	27	=	=	PRON
cana-4835	52	28	{	{	PUNCT
cana-4835	52	29	y1	y1	PROPN
cana-4835	52	30	,	,	PUNCT
cana-4835	52	31	y2	y2	PROPN
cana-4835	52	32	,	,	PUNCT
cana-4835	52	33	y3	y3	PROPN
cana-4835	52	34	}	}	PUNCT
cana-4835	52	35	and	and	CCONJ
cana-4835	52	36	z	z	NOUN
cana-4835	52	37	=	=	SYM
cana-4835	52	38	{	{	PUNCT
cana-4835	52	39	z1	z1	PROPN
cana-4835	52	40	,	,	PUNCT
cana-4835	52	41	z2	z2	PROPN
cana-4835	52	42	,	,	PUNCT
cana-4835	52	43	z3	z3	PROPN
cana-4835	52	44	}	}	PUNCT
cana-4835	52	45	consider	consider	VERB
cana-4835	52	46	two	two	NUM
cana-4835	52	47	fuzzy	fuzzy	ADJ
cana-4835	52	48	relations	relation	NOUN
cana-4835	52	49	r	r	NOUN
cana-4835	52	50	⊆	⊆	NUM
cana-4835	52	51	x	x	SYM
cana-4835	52	52	×	×	PROPN
cana-4835	52	53	y	y	PROPN
cana-4835	52	54	and	and	CCONJ
cana-4835	52	55	q	q	NOUN
cana-4835	52	56	⊆	⊆	NUM
cana-4835	52	57	y	y	SYM
cana-4835	52	58	×	×	PROPN
cana-4835	52	59	z	z	NOUN
cana-4835	52	60	which	which	PRON
cana-4835	52	61	are	be	AUX
cana-4835	52	62	given	give	VERB
cana-4835	52	63	below	below	ADP
cana-4835	52	64	respectively	respectively	ADV
cana-4835	52	65	.we	.we	NUM
cana-4835	52	66	are	be	AUX
cana-4835	52	67	to	to	PART
cana-4835	52	68	compute	compute	VERB
cana-4835	52	69	t	t	PROPN
cana-4835	52	70	⊆	⊆	NUM
cana-4835	52	71	x	x	SYM
cana-4835	52	72	×	×	PROPN
cana-4835	52	73	z	z	NOUN
cana-4835	52	74	using	use	VERB
cana-4835	52	75	“	"	PUNCT
cana-4835	52	76	@	@	ADP
cana-4835	52	77	”	"	PUNCT
cana-4835	52	78	composition	composition	NOUN
cana-4835	52	79	(	(	PUNCT
cana-4835	52	80	)	)	PUNCT
cana-4835	52	81	(	(	PUNCT
cana-4835	52	82	)	)	PUNCT
cana-4835	52	83	(	(	PUNCT
cana-4835	52	84	)	)	PUNCT
cana-4835	52	85	(	(	PUNCT
cana-4835	52	86	)	)	PUNCT
cana-4835	52	87	(	(	PUNCT
cana-4835	52	88	)	)	PUNCT
cana-4835	52	89	(	(	PUNCT
cana-4835	52	90	)	)	PUNCT
cana-4835	52	91	(	(	PUNCT
cana-4835	52	92	)	)	PUNCT
cana-4835	52	93	(	(	PUNCT
cana-4835	52	94	)	)	PUNCT
cana-4835	52	95	(	(	PUNCT
cana-4835	52	96	)	)	PUNCT
cana-4835	52	97	1	1	NUM
cana-4835	52	98	2	2	NUM
cana-4835	52	99	3	3	NUM
cana-4835	52	100	1	1	NUM
cana-4835	52	101	2	2	NUM
cana-4835	52	102	3	3	NUM
cana-4835	52	103	0.1,0.2,0.7	0.1,0.2,0.7	NOUN
cana-4835	52	104	0,0,0	0,0,0	NOUN
cana-4835	52	105	0.5,0.4,0.1	0.5,0.4,0.1	NUM
cana-4835	52	106	1,0,0	1,0,0	NUM
cana-4835	52	107	0.6,0.3,0.1	0.6,0.3,0.1	NUM
cana-4835	52	108	0.8,0.1,0.1	0.8,0.1,0.1	NOUN
cana-4835	52	109	0.3,0.3,0.4	0.3,0.3,0.4	NUM
cana-4835	53	1	0.4,0.2,0.4	0.4,0.2,0.4	NOUN
cana-4835	53	2	0.1,0.5,0.4	0.1,0.5,0.4	NUM
cana-4835	54	1	y	y	PROPN
cana-4835	54	2	y	y	PROPN
cana-4835	54	3	y	y	PROPN
cana-4835	54	4	x	x	PUNCT
cana-4835	54	5	r	r	NOUN
cana-4835	54	6	x	x	PUNCT
cana-4835	54	7	x	x	SYM
cana-4835	54	8			PROPN
cana-4835	54	9			NOUN
cana-4835	54	10			NOUN
cana-4835	54	11			NOUN
cana-4835	54	12	=	=	SYM
cana-4835	54	13			NOUN
cana-4835	54	14			NOUN
cana-4835	54	15			NOUN
cana-4835	54	16			NOUN
cana-4835	54	17			NOUN
cana-4835	54	18			PROPN
cana-4835	54	19	(	(	PUNCT
cana-4835	54	20	)	)	PUNCT
cana-4835	54	21	(	(	PUNCT
cana-4835	54	22	)	)	PUNCT
cana-4835	54	23	(	(	PUNCT
cana-4835	54	24	)	)	PUNCT
cana-4835	54	25	(	(	PUNCT
cana-4835	54	26	)	)	PUNCT
cana-4835	54	27	(	(	PUNCT
cana-4835	54	28	)	)	PUNCT
cana-4835	54	29	(	(	PUNCT
cana-4835	54	30	)	)	PUNCT
cana-4835	54	31	(	(	PUNCT
cana-4835	54	32	)	)	PUNCT
cana-4835	54	33	(	(	PUNCT
cana-4835	54	34	)	)	PUNCT
cana-4835	54	35	(	(	PUNCT
cana-4835	54	36	)	)	PUNCT
cana-4835	54	37	1	1	NUM
cana-4835	54	38	2	2	NUM
cana-4835	54	39	3	3	NUM
cana-4835	54	40	1	1	NUM
cana-4835	54	41	2	2	NUM
cana-4835	54	42	3	3	NUM
cana-4835	54	43	1,0,0	1,0,0	NUM
cana-4835	54	44	0.9,0,0.1	0.9,0,0.1	NOUN
cana-4835	54	45	0.6,0.4,0	0.6,0.4,0	NOUN
cana-4835	55	1	0.5,0.2,0.3	0.5,0.2,0.3	NUM
cana-4835	55	2	0,0,0	0,0,0	NOUN
cana-4835	55	3	0.2,0.1,0.1	0.2,0.1,0.1	NUM
cana-4835	55	4	0,0,0.1	0,0,0.1	NOUN
cana-4835	55	5	0.6,0.3,0.1	0.6,0.3,0.1	NOUN
cana-4835	56	1	0.1,0.2,0.3	0.1,0.2,0.3	NUM
cana-4835	57	1	z	z	NOUN
cana-4835	57	2	z	z	NOUN
cana-4835	57	3	z	z	NOUN
cana-4835	57	4	y	y	PROPN
cana-4835	57	5	q	q	PROPN
cana-4835	57	6	y	y	PROPN
cana-4835	57	7	y	y	PROPN
cana-4835	57	8			PROPN
cana-4835	57	9			NOUN
cana-4835	57	10			NOUN
cana-4835	57	11			NOUN
cana-4835	57	12	=	=	SYM
cana-4835	57	13			NOUN
cana-4835	57	14			NOUN
cana-4835	57	15			NOUN
cana-4835	57	16			NOUN
cana-4835	57	17			VERB
cana-4835	57	18			PROPN
cana-4835	57	19	t(x	t(x	PROPN
cana-4835	57	20	,	,	PUNCT
cana-4835	57	21	z	z	NOUN
cana-4835	57	22	)	)	PUNCT
cana-4835	57	23	=	=	PUNCT
cana-4835	58	1	𝜇𝑅@𝑄(𝑥	𝜇𝑅@𝑄(𝑥	PROPN
cana-4835	58	2	,	,	PUNCT
cana-4835	58	3	𝑧	𝑧	NOUN
cana-4835	58	4	)	)	PUNCT
cana-4835	58	5	∀	∀	X
cana-4835	58	6	x	x	SYM
cana-4835	58	7	∈	∈	NOUN
cana-4835	58	8	x	x	X
cana-4835	58	9	and	and	CCONJ
cana-4835	58	10	z	z	NOUN
cana-4835	58	11	∈	∈	PROPN
cana-4835	58	12	z	z	NOUN
cana-4835	58	13	communications	communication	NOUN
cana-4835	58	14	on	on	ADP
cana-4835	58	15	applied	apply	VERB
cana-4835	58	16	nonlinear	nonlinear	ADJ
cana-4835	58	17	analysis	analysis	NOUN
cana-4835	58	18	issn	issn	NOUN
cana-4835	58	19	:	:	PUNCT
cana-4835	58	20	1074	1074	NUM
cana-4835	58	21	-	-	PUNCT
cana-4835	58	22	133x	133x	NUM
cana-4835	58	23	vol	vol	VERB
cana-4835	58	24	32	32	NUM
cana-4835	58	25	no	no	NOUN
cana-4835	58	26	.	.	PUNCT
cana-4835	59	1	10s	10	NOUN
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cana-4835	62	11	(	(	PUNCT
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cana-4835	62	15	(	(	PUNCT
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cana-4835	62	17	(	(	PUNCT
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cana-4835	62	19	(	(	PUNCT
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cana-4835	62	29	3	3	NUM
cana-4835	62	30	1	1	NUM
cana-4835	62	31	2	2	NUM
cana-4835	62	32	3	3	NUM
cana-4835	62	33	0,1,1	0,1,1	NUM
cana-4835	62	34	1,1,1	1,1,1	NUM
cana-4835	62	35	0.1,1,1	0.1,1,1	NUM
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cana-4835	64	4	x	x	SYM
cana-4835	64	5			PROPN
cana-4835	64	6			ADJ
cana-4835	64	7			NOUN
cana-4835	64	8			PROPN
cana-4835	64	9			NOUN
cana-4835	64	10			NOUN
cana-4835	64	11			NOUN
cana-4835	64	12			NOUN
cana-4835	64	13			PROPN
cana-4835	64	14			PROPN
cana-4835	64	15	lemma	lemma	PROPN
cana-4835	64	16	3.2	3.2	NUM
cana-4835	64	17	:	:	PUNCT
cana-4835	64	18	if	if	SCONJ
cana-4835	64	19	we	we	PRON
cana-4835	64	20	have	have	VERB
cana-4835	64	21	two	two	NUM
cana-4835	64	22	fuzzy	fuzzy	ADJ
cana-4835	64	23	relations	relation	NOUN
cana-4835	64	24	r	r	NOUN
cana-4835	64	25	⊆	⊆	NUM
cana-4835	64	26	x	x	SYM
cana-4835	64	27	×	×	PROPN
cana-4835	64	28	y	y	PROPN
cana-4835	64	29	and	and	CCONJ
cana-4835	64	30	q	q	NOUN
cana-4835	64	31	⊆	⊆	NUM
cana-4835	64	32	y	y	PROPN
cana-4835	64	33	×	×	PROPN
cana-4835	64	34	z	z	NOUN
cana-4835	64	35	then	then	ADV
cana-4835	64	36	the	the	DET
cana-4835	64	37	following	follow	VERB
cana-4835	64	38	inclusion	inclusion	NOUN
cana-4835	64	39	will	will	AUX
cana-4835	64	40	hold	hold	VERB
cana-4835	64	41	:	:	PUNCT
cana-4835	64	42	𝜇𝑄	𝜇𝑄	ADJ
cana-4835	64	43	𝑇	𝑇	NOUN
cana-4835	64	44	≤	≤	NOUN
cana-4835	64	45	𝜇r−1@(r	𝜇r−1@(r	PROPN
cana-4835	64	46	◦	◦	VERB
cana-4835	64	47	q	q	ADJ
cana-4835	64	48	)	)	PUNCT
cana-4835	64	49	𝑇	𝑇	PROPN
cana-4835	64	50	,	,	PUNCT
cana-4835	64	51	𝜇r−1@(r	𝜇r−1@(r	PROPN
cana-4835	64	52	◦	◦	VERB
cana-4835	64	53	q	q	NOUN
cana-4835	64	54	)	)	PUNCT
cana-4835	64	55	𝐼	𝐼	NOUN
cana-4835	64	56	=	=	SYM
cana-4835	64	57	1	1	NUM
cana-4835	64	58	,	,	PUNCT
cana-4835	64	59	𝜇r−1@(r	𝜇r−1@(r	PROPN
cana-4835	64	60	◦	◦	NOUN
cana-4835	64	61	q	q	NOUN
cana-4835	64	62	)	)	PUNCT
cana-4835	64	63	𝐹	𝐹	PROPN
cana-4835	65	1	=	=	NOUN
cana-4835	65	2	1	1	NUM
cana-4835	65	3	if	if	SCONJ
cana-4835	65	4	r	r	NOUN
cana-4835	65	5	⊆	⊆	NUM
cana-4835	65	6	q	q	NOUN
cana-4835	65	7	or	or	CCONJ
cana-4835	65	8	q	q	NOUN
cana-4835	66	1	⊆	⊆	NUM
cana-4835	66	2	r	r	NOUN
cana-4835	66	3	where	where	SCONJ
cana-4835	66	4	“	"	PUNCT
cana-4835	66	5	◦	◦	NOUN
cana-4835	66	6	”	"	PUNCT
cana-4835	66	7	denotes	denote	VERB
cana-4835	66	8	the	the	DET
cana-4835	66	9	max	max	PROPN
cana-4835	66	10	min	min	PROPN
cana-4835	66	11	composition	composition	NOUN
cana-4835	66	12	and	and	CCONJ
cana-4835	66	13	“	"	PUNCT
cana-4835	66	14	@	@	ADP
cana-4835	66	15	”	"	PUNCT
cana-4835	66	16	is	be	AUX
cana-4835	66	17	the	the	DET
cana-4835	66	18	composition	composition	NOUN
cana-4835	66	19	made	make	VERB
cana-4835	66	20	by	by	ADP
cana-4835	66	21	α	α	NOUN
cana-4835	66	22	operator	operator	NOUN
cana-4835	66	23	.	.	PUNCT
cana-4835	67	1	proof	proof	NOUN
cana-4835	67	2	:	:	PUNCT
cana-4835	67	3	let	let	VERB
cana-4835	67	4	a	a	PRON
cana-4835	67	5	be	be	AUX
cana-4835	67	6	the	the	DET
cana-4835	67	7	neutrosophic	neutrosophic	ADJ
cana-4835	67	8	fuzzy	fuzzy	ADJ
cana-4835	67	9	set	set	NOUN
cana-4835	67	10	consider	consider	VERB
cana-4835	67	11	,	,	PUNCT
cana-4835	67	12	a	a	DET
cana-4835	67	13	=	=	NOUN
cana-4835	67	14	r-1@(r	r-1@(r	NUM
cana-4835	67	15	◦	◦	NOUN
cana-4835	67	16	q	q	NOUN
cana-4835	67	17	)	)	PUNCT
cana-4835	67	18	⊆	⊆	NUM
cana-4835	67	19	y	y	PROPN
cana-4835	67	20	×	×	PROPN
cana-4835	67	21	z.	z.	PROPN
cana-4835	67	22	communications	communication	NOUN
cana-4835	67	23	on	on	ADP
cana-4835	67	24	applied	apply	VERB
cana-4835	67	25	nonlinear	nonlinear	ADJ
cana-4835	67	26	analysis	analysis	NOUN
cana-4835	67	27	issn	issn	NOUN
cana-4835	67	28	:	:	PUNCT
cana-4835	67	29	1074	1074	NUM
cana-4835	67	30	-	-	PUNCT
cana-4835	67	31	133x	133x	NUM
cana-4835	67	32	vol	vol	VERB
cana-4835	67	33	32	32	NUM
cana-4835	67	34	no	no	NOUN
cana-4835	67	35	.	.	PUNCT
cana-4835	68	1	10s	10	NOUN
cana-4835	68	2	(	(	PUNCT
cana-4835	68	3	2025	2025	NUM
cana-4835	68	4	)	)	PUNCT
cana-4835	68	5	433	433	NUM
cana-4835	68	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4835	68	7	𝜇𝐴(𝑦	𝜇𝐴(𝑦	PROPN
cana-4835	68	8	,	,	PUNCT
cana-4835	68	9	𝑧	𝑧	NOUN
cana-4835	68	10	)	)	PUNCT
cana-4835	68	11	=	=	SYM
cana-4835	68	12	{	{	PUNCT
cana-4835	68	13	𝜇𝑅−1(𝑦	𝜇𝑅−1(𝑦	NOUN
cana-4835	68	14	,	,	PUNCT
cana-4835	68	15	𝑥)𝛼𝜇𝑅𝑜𝑄(𝑥	𝑥)𝛼𝜇𝑅𝑜𝑄(𝑥	VERB
cana-4835	68	16	,	,	PUNCT
cana-4835	68	17	𝑧	𝑧	X
cana-4835	68	18	)	)	PUNCT
cana-4835	68	19	}	}	PUNCT
cana-4835	68	20	∀	∀	X
cana-4835	68	21	x	x	SYM
cana-4835	68	22	∈	∈	NOUN
cana-4835	68	23	x	x	SYM
cana-4835	68	24	=	=	PRON
cana-4835	68	25	{	{	PUNCT
cana-4835	68	26	𝜇𝑅(𝑥	𝜇𝑅(𝑥	PROPN
cana-4835	68	27	,	,	PUNCT
cana-4835	68	28	𝑦)𝛼𝜇𝑅𝑜𝑄(𝑥	𝑦)𝛼𝜇𝑅𝑜𝑄(𝑥	NOUN
cana-4835	68	29	,	,	PUNCT
cana-4835	68	30	𝑧	𝑧	NOUN
cana-4835	68	31	)	)	PUNCT
cana-4835	68	32	}	}	PUNCT
cana-4835	68	33	∀	∀	X
cana-4835	68	34	x	x	SYM
cana-4835	68	35	∈	∈	NOUN
cana-4835	68	36	x	x	X
cana-4835	68	37	=	=	PRON
cana-4835	68	38	{	{	PUNCT
cana-4835	68	39	𝜇𝑅	𝜇𝑅	PROPN
cana-4835	68	40	𝑇(𝑥	𝑇(𝑥	PROPN
cana-4835	68	41	,	,	PUNCT
cana-4835	68	42	𝑦)𝛼	𝑦)𝛼	ADJ
cana-4835	68	43	(	(	PUNCT
cana-4835	68	44	∨	∨	X
cana-4835	68	45	(	(	PUNCT
cana-4835	68	46	𝜇𝑅	𝜇𝑅	PROPN
cana-4835	68	47	𝑇(𝑥	𝑇(𝑥	PROPN
cana-4835	68	48	,	,	PUNCT
cana-4835	68	49	𝑡	𝑡	NOUN
cana-4835	68	50	)	)	PUNCT
cana-4835	68	51	∧	∧	NOUN
cana-4835	68	52	𝜇𝑄	𝜇𝑄	NOUN
cana-4835	68	53	𝑇(𝑡	𝑇(𝑡	NOUN
cana-4835	68	54	,	,	PUNCT
cana-4835	68	55	𝑧	𝑧	NOUN
cana-4835	68	56	)	)	PUNCT
cana-4835	68	57	)	)	PUNCT
cana-4835	68	58	)	)	PUNCT
cana-4835	68	59	,	,	PUNCT
cana-4835	68	60	1,1	1,1	NUM
cana-4835	68	61	}	}	PUNCT
cana-4835	68	62	since	since	SCONJ
cana-4835	68	63	r	r	NOUN
cana-4835	68	64	⊆	⊆	NUM
cana-4835	68	65	q	q	NOUN
cana-4835	68	66	and	and	CCONJ
cana-4835	68	67	α	α	NOUN
cana-4835	68	68	operator	operator	NOUN
cana-4835	68	69	(	(	PUNCT
cana-4835	68	70	𝜇𝐴	𝜇𝐴	ADP
cana-4835	68	71	𝑇(𝑦	𝑇(𝑦	NOUN
cana-4835	68	72	,	,	PUNCT
cana-4835	68	73	𝑧	𝑧	NOUN
cana-4835	68	74	)	)	PUNCT
cana-4835	68	75	,	,	PUNCT
cana-4835	68	76	𝜇𝐴	𝜇𝐴	ADP
cana-4835	68	77	𝐼	𝐼	PROPN
cana-4835	68	78	(	(	PUNCT
cana-4835	68	79	𝑦	𝑦	NOUN
cana-4835	68	80	,	,	PUNCT
cana-4835	68	81	𝑧	𝑧	NOUN
cana-4835	68	82	)	)	PUNCT
cana-4835	68	83	,	,	PUNCT
cana-4835	68	84	𝜇𝐴	𝜇𝐴	ADP
cana-4835	68	85	𝐹(𝑦	𝐹(𝑦	NUM
cana-4835	68	86	,	,	PUNCT
cana-4835	68	87	𝑧	𝑧	NOUN
cana-4835	68	88	)	)	PUNCT
cana-4835	68	89	)	)	PUNCT
cana-4835	69	1	=	=	PRON
cana-4835	69	2	{	{	PUNCT
cana-4835	69	3	𝜇𝑅	𝜇𝑅	PROPN
cana-4835	69	4	𝑇(𝑥	𝑇(𝑥	PROPN
cana-4835	69	5	,	,	PUNCT
cana-4835	69	6	𝑦)𝛼((𝜇𝑅	𝑦)𝛼((𝜇𝑅	PROPN
cana-4835	69	7	𝑇(𝑥	𝑇(𝑥	PROPN
cana-4835	69	8	,	,	PUNCT
cana-4835	69	9	𝑦	𝑦	NOUN
cana-4835	69	10	)	)	PUNCT
cana-4835	69	11	∧	∧	PROPN
cana-4835	69	12	𝜇𝑄	𝜇𝑄	NOUN
cana-4835	69	13	𝑇(𝑦	𝑇(𝑦	NOUN
cana-4835	69	14	,	,	PUNCT
cana-4835	69	15	𝑧	𝑧	NOUN
cana-4835	69	16	)	)	PUNCT
cana-4835	69	17	)	)	PUNCT
cana-4835	69	18	∧∨𝑡≠𝑦	∧∨𝑡≠𝑦	ADP
cana-4835	69	19	(	(	PUNCT
cana-4835	69	20	∨	∨	NUM
cana-4835	69	21	𝜇𝑅	𝜇𝑅	ADJ
cana-4835	69	22	𝑇	𝑇	PROPN
cana-4835	69	23	(	(	PUNCT
cana-4835	69	24	(	(	PUNCT
cana-4835	69	25	𝑥	𝑥	NOUN
cana-4835	69	26	,	,	PUNCT
cana-4835	69	27	𝑡	𝑡	NOUN
cana-4835	69	28	)	)	PUNCT
cana-4835	69	29	∧	∧	NOUN
cana-4835	69	30	𝜇𝑄	𝜇𝑄	NOUN
cana-4835	69	31	𝑇(𝑡	𝑇(𝑡	NOUN
cana-4835	69	32	,	,	PUNCT
cana-4835	69	33	𝑧	𝑧	NOUN
cana-4835	69	34	)	)	PUNCT
cana-4835	69	35	)	)	PUNCT
cana-4835	69	36	)	)	PUNCT
cana-4835	69	37	,	,	PUNCT
cana-4835	69	38	1,1	1,1	NUM
cana-4835	69	39	}	}	PUNCT
cana-4835	69	40	𝜇𝐴	𝜇𝐴	ADP
cana-4835	69	41	𝑇(𝑦	𝑇(𝑦	NOUN
cana-4835	69	42	,	,	PUNCT
cana-4835	69	43	𝑧	𝑧	NOUN
cana-4835	69	44	)	)	PUNCT
cana-4835	69	45	=	=	SYM
cana-4835	69	46	{	{	PUNCT
cana-4835	69	47	𝜇𝑅	𝜇𝑅	PROPN
cana-4835	69	48	𝑇(𝑥	𝑇(𝑥	PROPN
cana-4835	69	49	,	,	PUNCT
cana-4835	69	50	𝑦)𝛼((𝜇𝑅	𝑦)𝛼((𝜇𝑅	PROPN
cana-4835	69	51	𝑇(𝑥	𝑇(𝑥	PROPN
cana-4835	69	52	,	,	PUNCT
cana-4835	69	53	𝑦	𝑦	NOUN
cana-4835	69	54	)	)	PUNCT
cana-4835	69	55	∧	∧	PROPN
cana-4835	69	56	𝜇𝑄	𝜇𝑄	NOUN
cana-4835	69	57	𝑇(𝑦	𝑇(𝑦	NOUN
cana-4835	69	58	,	,	PUNCT
cana-4835	69	59	𝑧	𝑧	NOUN
cana-4835	69	60	)	)	PUNCT
cana-4835	69	61	)	)	PUNCT
cana-4835	69	62	∧∨𝑡≠𝑦	∧∨𝑡≠𝑦	ADP
cana-4835	69	63	(	(	PUNCT
cana-4835	69	64	∨	∨	NUM
cana-4835	69	65	𝜇𝑅	𝜇𝑅	ADJ
cana-4835	69	66	𝑇	𝑇	PROPN
cana-4835	69	67	(	(	PUNCT
cana-4835	69	68	(	(	PUNCT
cana-4835	69	69	𝑥	𝑥	NOUN
cana-4835	69	70	,	,	PUNCT
cana-4835	69	71	𝑡	𝑡	NOUN
cana-4835	69	72	)	)	PUNCT
cana-4835	69	73	∧	∧	NOUN
cana-4835	69	74	𝜇𝑄	𝜇𝑄	NOUN
cana-4835	69	75	𝑇(𝑡	𝑇(𝑡	NOUN
cana-4835	69	76	,	,	PUNCT
cana-4835	69	77	𝑧	𝑧	NOUN
cana-4835	69	78	)	)	PUNCT
cana-4835	69	79	)	)	PUNCT
cana-4835	69	80	)	)	PUNCT
cana-4835	70	1	𝜇𝐴	𝜇𝐴	ADP
cana-4835	70	2	𝐼	𝐼	PROPN
cana-4835	70	3	(	(	PUNCT
cana-4835	70	4	𝑦	𝑦	NOUN
cana-4835	70	5	,	,	PUNCT
cana-4835	70	6	𝑧)=1	𝑧)=1	VERB
cana-4835	70	7	𝜇𝐴	𝜇𝐴	ADP
cana-4835	70	8	𝐹(𝑦	𝐹(𝑦	NUM
cana-4835	70	9	,	,	PUNCT
cana-4835	70	10	𝑧)=1	𝑧)=1	VERB
cana-4835	70	11	𝜇𝐴	𝜇𝐴	ADP
cana-4835	70	12	𝑇(𝑦	𝑇(𝑦	NOUN
cana-4835	70	13	,	,	PUNCT
cana-4835	70	14	𝑧	𝑧	NOUN
cana-4835	70	15	)	)	PUNCT
cana-4835	70	16	≥{𝜇𝑅(𝑥	≥{𝜇𝑅(𝑥	PROPN
cana-4835	70	17	,	,	PUNCT
cana-4835	70	18	𝑦)𝛼((𝜇𝑅(𝑥	𝑦)𝛼((𝜇𝑅(𝑥	PROPN
cana-4835	70	19	,	,	PUNCT
cana-4835	70	20	𝑦	𝑦	NOUN
cana-4835	70	21	)	)	PUNCT
cana-4835	70	22	∧	∧	PROPN
cana-4835	70	23	𝜇𝑄(𝑦	𝜇𝑄(𝑦	PROPN
cana-4835	70	24	,	,	PUNCT
cana-4835	70	25	𝑧	𝑧	NOUN
cana-4835	70	26	)	)	PUNCT
cana-4835	70	27	)	)	PUNCT
cana-4835	70	28	}	}	PUNCT
cana-4835	70	29	since	since	SCONJ
cana-4835	70	30	a	a	DET
cana-4835	70	31	α	α	NOUN
cana-4835	70	32	(	(	PUNCT
cana-4835	70	33	a	a	DET
cana-4835	70	34	∧	∧	PROPN
cana-4835	70	35	b	b	PROPN
cana-4835	70	36	)	)	PUNCT
cana-4835	70	37	≥	≥	NOUN
cana-4835	70	38	b	b	NOUN
cana-4835	70	39	𝜇𝐴(𝑦	𝜇𝐴(𝑦	PROPN
cana-4835	70	40	,	,	PUNCT
cana-4835	70	41	𝑧	𝑧	NOUN
cana-4835	70	42	)	)	PUNCT
cana-4835	70	43	≥	≥	NOUN
cana-4835	70	44	𝜇𝑄(𝑦	𝜇𝑄(𝑦	PROPN
cana-4835	70	45	,	,	PUNCT
cana-4835	70	46	𝑧	𝑧	PRON
cana-4835	70	47	)	)	PUNCT
cana-4835	70	48	example	example	NOUN
cana-4835	70	49	3	3	NUM
cana-4835	70	50	:	:	PUNCT
cana-4835	70	51	consider	consider	VERB
cana-4835	70	52	x	x	X
cana-4835	70	53	=	=	PRON
cana-4835	70	54	{	{	PUNCT
cana-4835	70	55	x1	x1	PROPN
cana-4835	70	56	,	,	PUNCT
cana-4835	70	57	x2	x2	PROPN
cana-4835	70	58	,	,	PUNCT
cana-4835	70	59	x3	x3	ADJ
cana-4835	70	60	}	}	PUNCT
cana-4835	70	61	,	,	PUNCT
cana-4835	70	62	y	y	PROPN
cana-4835	70	63	=	=	PRON
cana-4835	70	64	{	{	PUNCT
cana-4835	70	65	y1	y1	PROPN
cana-4835	70	66	,	,	PUNCT
cana-4835	70	67	y2	y2	PROPN
cana-4835	70	68	,	,	PUNCT
cana-4835	70	69	y3	y3	PROPN
cana-4835	70	70	}	}	PUNCT
cana-4835	70	71	and	and	CCONJ
cana-4835	70	72	z	z	NOUN
cana-4835	70	73	=	=	SYM
cana-4835	70	74	{	{	PUNCT
cana-4835	70	75	z1	z1	PROPN
cana-4835	70	76	,	,	PUNCT
cana-4835	70	77	z2	z2	PROPN
cana-4835	70	78	,	,	PUNCT
cana-4835	70	79	z3	z3	PROPN
cana-4835	70	80	}	}	PUNCT
cana-4835	70	81	.	.	PUNCT
cana-4835	71	1	(	(	PUNCT
cana-4835	71	2	)	)	PUNCT
cana-4835	71	3	(	(	PUNCT
cana-4835	71	4	)	)	PUNCT
cana-4835	71	5	(	(	PUNCT
cana-4835	71	6	)	)	PUNCT
cana-4835	71	7	(	(	PUNCT
cana-4835	71	8	)	)	PUNCT
cana-4835	71	9	(	(	PUNCT
cana-4835	71	10	)	)	PUNCT
cana-4835	71	11	(	(	PUNCT
cana-4835	71	12	)	)	PUNCT
cana-4835	71	13	(	(	PUNCT
cana-4835	71	14	)	)	PUNCT
cana-4835	71	15	(	(	PUNCT
cana-4835	71	16	)	)	PUNCT
cana-4835	71	17	(	(	PUNCT
cana-4835	71	18	)	)	PUNCT
cana-4835	71	19	1	1	NUM
cana-4835	71	20	2	2	NUM
cana-4835	71	21	3	3	NUM
cana-4835	71	22	1	1	NUM
cana-4835	71	23	2	2	NUM
cana-4835	71	24	3	3	NUM
cana-4835	71	25	0.5,0.9,0.8	0.5,0.9,0.8	NUM
cana-4835	71	26	0.6,0.3,0.2	0.6,0.3,0.2	NUM
cana-4835	71	27	0.4,0.5,0.1	0.4,0.5,0.1	NUM
cana-4835	72	1	0.3,0.2,0.3	0.3,0.2,0.3	NUM
cana-4835	73	1	0.2,0.7,0.6	0.2,0.7,0.6	NUM
cana-4835	73	2	0.8,0.2,0.2	0.8,0.2,0.2	NUM
cana-4835	74	1	1,0.3,0.2	1,0.3,0.2	NUM
cana-4835	74	2	0.0,0.7,0.6	0.0,0.7,0.6	NUM
cana-4835	74	3	0.6,0.3,0.2	0.6,0.3,0.2	NOUN
cana-4835	75	1	y	y	PROPN
cana-4835	75	2	y	y	NOUN
cana-4835	75	3	y	y	PROPN
cana-4835	75	4	x	x	PUNCT
cana-4835	75	5	r	r	NOUN
cana-4835	75	6	x	x	PUNCT
cana-4835	75	7	x	x	SYM
cana-4835	75	8			PROPN
cana-4835	75	9			NOUN
cana-4835	75	10			NOUN
cana-4835	75	11			NOUN
cana-4835	75	12	=	=	SYM
cana-4835	75	13			NOUN
cana-4835	75	14			NOUN
cana-4835	75	15			NOUN
cana-4835	75	16			NOUN
cana-4835	75	17			NOUN
cana-4835	75	18			PROPN
cana-4835	75	19	(	(	PUNCT
cana-4835	75	20	)	)	PUNCT
cana-4835	75	21	(	(	PUNCT
cana-4835	75	22	)	)	PUNCT
cana-4835	75	23	(	(	PUNCT
cana-4835	75	24	)	)	PUNCT
cana-4835	75	25	(	(	PUNCT
cana-4835	75	26	)	)	PUNCT
cana-4835	75	27	(	(	PUNCT
cana-4835	75	28	)	)	PUNCT
cana-4835	75	29	(	(	PUNCT
cana-4835	75	30	)	)	PUNCT
cana-4835	75	31	(	(	PUNCT
cana-4835	75	32	)	)	PUNCT
cana-4835	75	33	(	(	PUNCT
cana-4835	75	34	)	)	PUNCT
cana-4835	75	35	(	(	PUNCT
cana-4835	75	36	)	)	PUNCT
cana-4835	75	37	1	1	NUM
cana-4835	75	38	2	2	NUM
cana-4835	75	39	3	3	NUM
cana-4835	75	40	1	1	NUM
cana-4835	75	41	2	2	NUM
cana-4835	75	42	3	3	NUM
cana-4835	75	43	0.7,0.8,0.6	0.7,0.8,0.6	NUM
cana-4835	75	44	0.8,0.2,0.1	0.8,0.2,0.1	NUM
cana-4835	75	45	0.5,0.4,0	0.5,0.4,0	PUNCT
cana-4835	75	46	0.5,0.1,0.2	0.5,0.1,0.2	NUM
cana-4835	76	1	0.4,0.5,0.5	0.4,0.5,0.5	NUM
cana-4835	76	2	0.9,0.1,0.1	0.9,0.1,0.1	NUM
cana-4835	76	3	1,0.2,0.1	1,0.2,0.1	NOUN
cana-4835	76	4	0.3,0.6,0.5	0.3,0.6,0.5	NUM
cana-4835	76	5	0.8,0.2,0.1	0.8,0.2,0.1	NUM
cana-4835	77	1	z	z	NOUN
cana-4835	77	2	z	z	PROPN
cana-4835	77	3	z	z	PUNCT
cana-4835	77	4	y	y	PROPN
cana-4835	77	5	q	q	PROPN
cana-4835	77	6	y	y	PROPN
cana-4835	77	7	y	y	PROPN
cana-4835	77	8			PROPN
cana-4835	77	9			NOUN
cana-4835	77	10			NOUN
cana-4835	77	11			NOUN
cana-4835	77	12	=	=	SYM
cana-4835	77	13			NOUN
cana-4835	77	14			NOUN
cana-4835	77	15			NOUN
cana-4835	77	16			NOUN
cana-4835	77	17			NOUN
cana-4835	77	18			PROPN
cana-4835	77	19	(	(	PUNCT
cana-4835	77	20	)	)	PUNCT
cana-4835	77	21	(	(	PUNCT
cana-4835	77	22	)	)	PUNCT
cana-4835	78	1	(	(	PUNCT
cana-4835	78	2	)	)	PUNCT
cana-4835	78	3	(	(	PUNCT
cana-4835	78	4	)	)	PUNCT
cana-4835	78	5	(	(	PUNCT
cana-4835	78	6	)	)	PUNCT
cana-4835	78	7	(	(	PUNCT
cana-4835	78	8	)	)	PUNCT
cana-4835	78	9	(	(	PUNCT
cana-4835	78	10	)	)	PUNCT
cana-4835	78	11	(	(	PUNCT
cana-4835	78	12	)	)	PUNCT
cana-4835	78	13	(	(	PUNCT
cana-4835	78	14	)	)	PUNCT
cana-4835	78	15	1	1	NUM
cana-4835	78	16	2	2	NUM
cana-4835	78	17	3	3	NUM
cana-4835	78	18	1	1	NUM
cana-4835	78	19	1	1	NUM
cana-4835	78	20	2	2	NUM
cana-4835	78	21	3	3	NUM
cana-4835	78	22	0.5,0.9,0.8	0.5,0.9,0.8	NUM
cana-4835	78	23	0.3,0.2,0.3	0.3,0.2,0.3	NUM
cana-4835	78	24	1,0.3,0.2	1,0.3,0.2	NUM
cana-4835	78	25	0.6,0.3,0.2	0.6,0.3,0.2	NOUN
cana-4835	78	26	0.2,0.7,0.6	0.2,0.7,0.6	NOUN
cana-4835	78	27	0.0,0.7,0.6	0.0,0.7,0.6	NUM
cana-4835	79	1	0.4,0.5,0.1	0.4,0.5,0.1	NUM
cana-4835	79	2	0.8,0.2,0.2	0.8,0.2,0.2	PUNCT
cana-4835	80	1	0.6,0.3,0.2	0.6,0.3,0.2	NUM
cana-4835	81	1	x	x	PUNCT
cana-4835	81	2	x	x	PUNCT
cana-4835	81	3	x	x	PUNCT
cana-4835	81	4	y	y	NOUN
cana-4835	81	5	r	r	NOUN
cana-4835	81	6	y	y	PROPN
cana-4835	81	7	y	y	PROPN
cana-4835	81	8	−	−	PROPN
cana-4835	81	9			PROPN
cana-4835	81	10			ADJ
cana-4835	81	11			NOUN
cana-4835	81	12			NOUN
cana-4835	81	13	=	=	SYM
cana-4835	81	14			NOUN
cana-4835	81	15			NOUN
cana-4835	81	16			NOUN
cana-4835	81	17			NOUN
cana-4835	81	18			NOUN
cana-4835	81	19			PROPN
cana-4835	81	20	communications	communication	NOUN
cana-4835	81	21	on	on	ADP
cana-4835	81	22	applied	apply	VERB
cana-4835	81	23	nonlinear	nonlinear	ADJ
cana-4835	81	24	analysis	analysis	NOUN
cana-4835	81	25	issn	issn	NOUN
cana-4835	81	26	:	:	PUNCT
cana-4835	81	27	1074	1074	NUM
cana-4835	81	28	-	-	PUNCT
cana-4835	81	29	133x	133x	NUM
cana-4835	81	30	vol	vol	VERB
cana-4835	81	31	32	32	NUM
cana-4835	81	32	no	no	NOUN
cana-4835	81	33	.	.	PUNCT
cana-4835	82	1	10s	10	NOUN
cana-4835	82	2	(	(	PUNCT
cana-4835	82	3	2025	2025	NUM
cana-4835	82	4	)	)	PUNCT
cana-4835	82	5	434	434	NUM
cana-4835	82	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4835	82	7	(	(	PUNCT
cana-4835	82	8	)	)	PUNCT
cana-4835	82	9	(	(	PUNCT
cana-4835	82	10	)	)	PUNCT
cana-4835	82	11	(	(	PUNCT
cana-4835	82	12	)	)	PUNCT
cana-4835	82	13	(	(	PUNCT
cana-4835	82	14	)	)	PUNCT
cana-4835	82	15	(	(	PUNCT
cana-4835	82	16	)	)	PUNCT
cana-4835	82	17	(	(	PUNCT
cana-4835	82	18	)	)	PUNCT
cana-4835	82	19	(	(	PUNCT
cana-4835	82	20	)	)	PUNCT
cana-4835	82	21	(	(	PUNCT
cana-4835	82	22	)	)	PUNCT
cana-4835	82	23	(	(	PUNCT
cana-4835	82	24	)	)	PUNCT
cana-4835	82	25	1	1	NUM
cana-4835	82	26	2	2	NUM
cana-4835	82	27	3	3	NUM
cana-4835	82	28	1	1	NUM
cana-4835	82	29	2	2	NUM
cana-4835	82	30	3	3	NUM
cana-4835	82	31	0.5,0.3,0.2	0.5,0.3,0.2	NOUN
cana-4835	82	32	0.5,0.5,0.5	0.5,0.5,0.5	NUM
cana-4835	82	33	0.6,0.3,0.2	0.6,0.3,0.2	NUM
cana-4835	82	34	0.8,0.2,0.2	0.8,0.2,0.2	NUM
cana-4835	83	1	0.3,0.2,0.3	0.3,0.2,0.3	NUM
cana-4835	83	2	0.8,0.2,0.2	0.8,0.2,0.2	NUM
cana-4835	84	1	0.7,0.3,0.2	0.7,0.3,0.2	NUM
cana-4835	85	1	0.8,0.3,0.2	0.8,0.3,0.2	INTJ
cana-4835	86	1	0.6,0.3,0.2	0.6,0.3,0.2	NOUN
cana-4835	87	1	z	z	NOUN
cana-4835	87	2	z	z	NOUN
cana-4835	87	3	z	z	NOUN
cana-4835	88	1	x	x	PUNCT
cana-4835	88	2	roq	roq	NOUN
cana-4835	88	3	x	x	PUNCT
cana-4835	88	4	x	x	X
cana-4835	88	5			PROPN
cana-4835	88	6			NOUN
cana-4835	88	7			NOUN
cana-4835	88	8			NOUN
cana-4835	88	9	=	=	SYM
cana-4835	88	10			NOUN
cana-4835	88	11			NOUN
cana-4835	88	12			NOUN
cana-4835	88	13			NOUN
cana-4835	88	14			NOUN
cana-4835	88	15			PROPN
cana-4835	88	16	(	(	PUNCT
cana-4835	88	17	)	)	PUNCT
cana-4835	88	18	(	(	PUNCT
cana-4835	88	19	)	)	PUNCT
cana-4835	88	20	(	(	PUNCT
cana-4835	88	21	)	)	PUNCT
cana-4835	88	22	(	(	PUNCT
cana-4835	88	23	)	)	PUNCT
cana-4835	88	24	(	(	PUNCT
cana-4835	88	25	)	)	PUNCT
cana-4835	88	26	(	(	PUNCT
cana-4835	88	27	)	)	PUNCT
cana-4835	88	28	(	(	PUNCT
cana-4835	88	29	)	)	PUNCT
cana-4835	88	30	(	(	PUNCT
cana-4835	88	31	)	)	PUNCT
cana-4835	88	32	(	(	PUNCT
cana-4835	88	33	)	)	PUNCT
cana-4835	88	34	1	1	NUM
cana-4835	88	35	2	2	NUM
cana-4835	88	36	3	3	NUM
cana-4835	88	37	1	1	NUM
cana-4835	88	38	2	2	NUM
cana-4835	88	39	3	3	NUM
cana-4835	88	40	1	1	NUM
cana-4835	88	41	0.7,1,1	0.7,1,1	NOUN
cana-4835	88	42	0.8,1,1	0.8,1,1	NUM
cana-4835	88	43	0.5,1,1	0.5,1,1	NUM
cana-4835	88	44	0.5,1,1	0.5,1,1	NUM
cana-4835	88	45	0.5,1,1	0.5,1,1	NUM
cana-4835	88	46	0.6,1,1	0.6,1,1	NOUN
cana-4835	88	47	1,1,1	1,1,1	NUM
cana-4835	88	48	0.3,1,1	0.3,1,1	NOUN
cana-4835	88	49	1,1	1,1	NUM
cana-4835	88	50	@	@	ADP
cana-4835	88	51	,	,	PUNCT
cana-4835	88	52	1	1	NUM
cana-4835	88	53	r	r	NOUN
cana-4835	88	54	z	z	NOUN
cana-4835	88	55	z	z	NOUN
cana-4835	89	1	y	y	NOUN
cana-4835	89	2	yoq	yoq	NOUN
cana-4835	90	1	y	y	PROPN
cana-4835	90	2	r	r	NOUN
cana-4835	90	3	z	z	NOUN
cana-4835	90	4	−	−	PROPN
cana-4835	91	1			NUM
cana-4835	91	2			ADJ
cana-4835	91	3			NOUN
cana-4835	91	4			NOUN
cana-4835	91	5	=	=	SYM
cana-4835	91	6			NOUN
cana-4835	91	7			NOUN
cana-4835	91	8			NOUN
cana-4835	91	9			NOUN
cana-4835	91	10			VERB
cana-4835	91	11			PROPN
cana-4835	91	12	so	so	SCONJ
cana-4835	91	13	this	this	DET
cana-4835	91	14	example	example	NOUN
cana-4835	91	15	shows	show	VERB
cana-4835	91	16	that	that	SCONJ
cana-4835	91	17	𝜇𝑄	𝜇𝑄	NOUN
cana-4835	91	18	𝑇	𝑇	PROPN
cana-4835	91	19	≤	≤	NOUN
cana-4835	91	20	𝜇r−1@(r	𝜇r−1@(r	PROPN
cana-4835	91	21	◦	◦	VERB
cana-4835	91	22	q	q	ADJ
cana-4835	91	23	)	)	PUNCT
cana-4835	91	24	𝑇	𝑇	PROPN
cana-4835	91	25	,	,	PUNCT
cana-4835	91	26	𝜇r−1@(r	𝜇r−1@(r	PROPN
cana-4835	91	27	◦	◦	VERB
cana-4835	91	28	q	q	NOUN
cana-4835	91	29	)	)	PUNCT
cana-4835	91	30	𝐼	𝐼	NOUN
cana-4835	91	31	=	=	SYM
cana-4835	91	32	1	1	NUM
cana-4835	91	33	,	,	PUNCT
cana-4835	91	34	𝜇r−1@(r	𝜇r−1@(r	PROPN
cana-4835	91	35	◦	◦	NOUN
cana-4835	91	36	q	q	NOUN
cana-4835	91	37	)	)	PUNCT
cana-4835	91	38	𝐹	𝐹	PROPN
cana-4835	91	39	=	=	NOUN
cana-4835	92	1	1	1	NUM
cana-4835	92	2	hence	hence	ADV
cana-4835	92	3	it	it	PRON
cana-4835	92	4	clearly	clearly	ADV
cana-4835	92	5	satisfies	satisfy	VERB
cana-4835	92	6	the	the	DET
cana-4835	92	7	lemma	lemma	PROPN
cana-4835	92	8	lemma	lemma	PROPN
cana-4835	92	9	3.3	3.3	NUM
cana-4835	92	10	:	:	PUNCT
cana-4835	92	11	assume	assume	VERB
cana-4835	92	12	that	that	SCONJ
cana-4835	92	13	we	we	PRON
cana-4835	92	14	have	have	VERB
cana-4835	92	15	two	two	NUM
cana-4835	92	16	fuzzy	fuzzy	ADJ
cana-4835	92	17	relations	relation	NOUN
cana-4835	92	18	r	r	NOUN
cana-4835	92	19	⊆	⊆	NUM
cana-4835	92	20	x	x	SYM
cana-4835	92	21	×	×	PROPN
cana-4835	92	22	y	y	PROPN
cana-4835	92	23	and	and	CCONJ
cana-4835	92	24	t	t	PROPN
cana-4835	92	25	⊆	⊆	NUM
cana-4835	92	26	x	x	SYM
cana-4835	92	27	×	×	PROPN
cana-4835	92	28	z	z	NOUN
cana-4835	92	29	then	then	ADV
cana-4835	92	30	the	the	DET
cana-4835	92	31	following	follow	VERB
cana-4835	92	32	inclusion	inclusion	NOUN
cana-4835	92	33	holds	hold	VERB
cana-4835	92	34	:	:	PUNCT
cana-4835	92	35	r	r	NOUN
cana-4835	92	36	◦	◦	NOUN
cana-4835	92	37	(	(	PUNCT
cana-4835	92	38	r	r	NOUN
cana-4835	92	39	−1@t	−1@t	PROPN
cana-4835	92	40	)	)	PUNCT
cana-4835	92	41	⊂	⊂	PROPN
cana-4835	92	42	t	t	X
cana-4835	92	43	where	where	SCONJ
cana-4835	92	44	“	"	PUNCT
cana-4835	92	45	◦	◦	NOUN
cana-4835	92	46	”	"	PUNCT
cana-4835	92	47	denotes	denote	VERB
cana-4835	92	48	the	the	DET
cana-4835	92	49	max	max	PROPN
cana-4835	92	50	-	-	PUNCT
cana-4835	92	51	min	min	NOUN
cana-4835	92	52	composition	composition	NOUN
cana-4835	92	53	and	and	CCONJ
cana-4835	92	54	“	"	PUNCT
cana-4835	92	55	@	@	ADP
cana-4835	92	56	”	"	PUNCT
cana-4835	92	57	is	be	AUX
cana-4835	92	58	the	the	DET
cana-4835	92	59	composition	composition	NOUN
cana-4835	92	60	of	of	ADP
cana-4835	92	61	α	α	PRON
cana-4835	92	62	operator	operator	NOUN
cana-4835	92	63	.	.	PUNCT
cana-4835	93	1	the	the	DET
cana-4835	93	2	proof	proof	NOUN
cana-4835	93	3	of	of	ADP
cana-4835	93	4	this	this	DET
cana-4835	93	5	lemma	lemma	PROPN
cana-4835	93	6	is	be	AUX
cana-4835	93	7	analogous	analogous	ADJ
cana-4835	93	8	to	to	ADP
cana-4835	93	9	the	the	DET
cana-4835	93	10	proof	proof	NOUN
cana-4835	93	11	of	of	ADP
cana-4835	93	12	lemma	lemma	PROPN
cana-4835	93	13	lemma	lemma	PROPN
cana-4835	93	14	3.4	3.4	NUM
cana-4835	93	15	:	:	PUNCT
cana-4835	93	16	consider	consider	VERB
cana-4835	93	17	we	we	PRON
cana-4835	93	18	have	have	VERB
cana-4835	93	19	two	two	NUM
cana-4835	93	20	fuzzy	fuzzy	ADJ
cana-4835	93	21	relations	relation	NOUN
cana-4835	93	22	r	r	NOUN
cana-4835	93	23	⊆	⊆	NUM
cana-4835	93	24	x	x	SYM
cana-4835	93	25	×	×	PROPN
cana-4835	93	26	y	y	PROPN
cana-4835	93	27	and	and	CCONJ
cana-4835	93	28	q	q	NOUN
cana-4835	94	1	⊆	⊆	NUM
cana-4835	94	2	y	y	PROPN
cana-4835	94	3	×	×	PROPN
cana-4835	94	4	z	z	NOUN
cana-4835	94	5	then	then	ADV
cana-4835	94	6	the	the	DET
cana-4835	94	7	following	follow	VERB
cana-4835	94	8	inclusion	inclusion	NOUN
cana-4835	94	9	holds	hold	VERB
cana-4835	94	10	:	:	PUNCT
cana-4835	94	11	r	r	NOUN
cana-4835	94	12	⊆	⊆	NUM
cana-4835	94	13	(	(	PUNCT
cana-4835	94	14	q@	q@	PROPN
cana-4835	94	15	(	(	PUNCT
cana-4835	94	16	r	r	NOUN
cana-4835	94	17	◦	◦	NOUN
cana-4835	94	18	q	q	NOUN
cana-4835	94	19	)	)	PUNCT
cana-4835	94	20	−1	−1	NOUN
cana-4835	94	21	)	)	PUNCT
cana-4835	94	22	−1	−1	NOUN
cana-4835	94	23	lemma	lemma	PROPN
cana-4835	94	24	3.5	3.5	NUM
cana-4835	94	25	:	:	PUNCT
cana-4835	94	26	consider	consider	VERB
cana-4835	94	27	we	we	PRON
cana-4835	94	28	have	have	VERB
cana-4835	94	29	two	two	NUM
cana-4835	94	30	fuzzy	fuzzy	ADJ
cana-4835	94	31	relations	relation	NOUN
cana-4835	94	32	q	q	NOUN
cana-4835	94	33	⊆	⊆	NUM
cana-4835	94	34	y	y	PROPN
cana-4835	94	35	×	×	PROPN
cana-4835	94	36	z	z	NOUN
cana-4835	94	37	and	and	CCONJ
cana-4835	94	38	t	t	PROPN
cana-4835	94	39	⊆	⊆	NUM
cana-4835	94	40	x	x	SYM
cana-4835	94	41	×	×	PROPN
cana-4835	94	42	z	z	NOUN
cana-4835	95	1	then	then	ADV
cana-4835	95	2	the	the	DET
cana-4835	95	3	following	follow	VERB
cana-4835	95	4	inclusion	inclusion	NOUN
cana-4835	95	5	holds	hold	VERB
cana-4835	95	6	:	:	PUNCT
cana-4835	95	7	(	(	PUNCT
cana-4835	95	8	q@t	q@t	NOUN
cana-4835	95	9	−1	−1	NOUN
cana-4835	95	10	)	)	PUNCT
cana-4835	95	11	−1	−1	NOUN
cana-4835	96	1	◦	◦	NOUN
cana-4835	96	2	q	q	PUNCT
cana-4835	96	3	⊂	⊂	PROPN
cana-4835	96	4	t	t	PROPN
cana-4835	96	5	theorem	theorem	VERB
cana-4835	96	6	3.6	3.6	NUM
cana-4835	96	7	:	:	PUNCT
cana-4835	96	8	let	let	VERB
cana-4835	96	9	r	r	NOUN
cana-4835	96	10	⊆	⊆	NUM
cana-4835	96	11	x	x	SYM
cana-4835	96	12	×	×	PROPN
cana-4835	96	13	y	y	PROPN
cana-4835	96	14	and	and	CCONJ
cana-4835	96	15	t	t	PROPN
cana-4835	96	16	⊆	⊆	NUM
cana-4835	96	17	x	x	SYM
cana-4835	96	18	×	×	PROPN
cana-4835	96	19	z	z	NOUN
cana-4835	96	20	be	be	AUX
cana-4835	96	21	the	the	DET
cana-4835	96	22	two	two	NUM
cana-4835	96	23	fuzzy	fuzzy	ADJ
cana-4835	96	24	relations	relation	NOUN
cana-4835	96	25	,	,	PUNCT
cana-4835	96	26	s(q	s(q	NOUN
cana-4835	96	27	)	)	PUNCT
cana-4835	96	28	be	be	VERB
cana-4835	96	29	the	the	DET
cana-4835	96	30	set	set	NOUN
cana-4835	96	31	of	of	ADP
cana-4835	96	32	fuzzy	fuzzy	ADJ
cana-4835	96	33	relations	relation	NOUN
cana-4835	97	1	q	q	PROPN
cana-4835	97	2	∈	∈	PROPN
cana-4835	97	3	y	y	PROPN
cana-4835	97	4	×	×	PROPN
cana-4835	97	5	z	z	NOUN
cana-4835	97	6	such	such	ADJ
cana-4835	97	7	that	that	DET
cana-4835	97	8	r	r	NOUN
cana-4835	97	9	◦	◦	NOUN
cana-4835	97	10	q	q	NOUN
cana-4835	97	11	=	=	PUNCT
cana-4835	97	12	t.	t.	NOUN
cana-4835	97	13	s(q	s(q	NOUN
cana-4835	97	14	)	)	PUNCT
cana-4835	97	15	=	=	PRON
cana-4835	97	16	{	{	PUNCT
cana-4835	97	17	q	q	NOUN
cana-4835	97	18	∈	∈	PROPN
cana-4835	97	19	y	y	PROPN
cana-4835	97	20	×	×	NOUN
cana-4835	97	21	z	z	NOUN
cana-4835	97	22	|	|	NOUN
cana-4835	97	23	r	r	NOUN
cana-4835	97	24	◦	◦	NOUN
cana-4835	97	25	q	q	NOUN
cana-4835	97	26	=	=	SYM
cana-4835	97	27	t	t	PROPN
cana-4835	97	28	}	}	PUNCT
cana-4835	97	29	≠	≠	PROPN
cana-4835	97	30	𝜑	𝜑	NOUN
cana-4835	97	31	,	,	PUNCT
cana-4835	97	32	if	if	SCONJ
cana-4835	97	33	and	and	CCONJ
cana-4835	97	34	only	only	ADV
cana-4835	97	35	if	if	SCONJ
cana-4835	97	36	r−1@t	r−1@t	NOUN
cana-4835	97	37	∈	∈	PROPN
cana-4835	97	38	s(q	s(q	NOUN
cana-4835	97	39	)	)	PUNCT
cana-4835	97	40	then	then	ADV
cana-4835	97	41	“	"	PUNCT
cana-4835	97	42	r−1@t	r−1@t	NOUN
cana-4835	97	43	”	"	PUNCT
cana-4835	97	44	is	be	AUX
cana-4835	97	45	the	the	DET
cana-4835	97	46	the	the	DET
cana-4835	97	47	greatest	great	ADJ
cana-4835	97	48	element	element	NOUN
cana-4835	97	49	in	in	ADP
cana-4835	97	50	s(q	s(q	NOUN
cana-4835	97	51	)	)	PUNCT
cana-4835	97	52	.	.	PUNCT
cana-4835	98	1	theorem	theorem	VERB
cana-4835	98	2	3.7	3.7	NUM
cana-4835	98	3	:	:	PUNCT
cana-4835	98	4	let	let	VERB
cana-4835	98	5	r	r	NOUN
cana-4835	98	6	⊆	⊆	NUM
cana-4835	98	7	x	x	SYM
cana-4835	98	8	×	×	PROPN
cana-4835	98	9	y	y	PROPN
cana-4835	98	10	and	and	CCONJ
cana-4835	98	11	t	t	PROPN
cana-4835	98	12	⊆	⊆	NUM
cana-4835	98	13	x	x	SYM
cana-4835	98	14	×	×	PROPN
cana-4835	98	15	z	z	NOUN
cana-4835	98	16	be	be	AUX
cana-4835	98	17	the	the	DET
cana-4835	98	18	two	two	NUM
cana-4835	98	19	fuzzy	fuzzy	ADJ
cana-4835	98	20	relations	relation	NOUN
cana-4835	98	21	,	,	PUNCT
cana-4835	98	22	the	the	DET
cana-4835	98	23	set	set	NOUN
cana-4835	98	24	of	of	ADP
cana-4835	98	25	fuzzy	fuzzy	ADJ
cana-4835	98	26	relations	relation	NOUN
cana-4835	99	1	q	q	PROPN
cana-4835	99	2	∈	∈	PROPN
cana-4835	99	3	y	y	PROPN
cana-4835	99	4	×	×	PROPN
cana-4835	99	5	z	z	NOUN
cana-4835	99	6	such	such	ADJ
cana-4835	99	7	that	that	DET
cana-4835	99	8	r	r	NOUN
cana-4835	99	9	◦	◦	NOUN
cana-4835	99	10	q	q	NOUN
cana-4835	99	11	⊆	⊆	NUM
cana-4835	99	12	t	t	NOUN
cana-4835	99	13	contains	contain	VERB
cana-4835	99	14	a	a	DET
cana-4835	99	15	greatest	great	ADJ
cana-4835	99	16	element	element	NOUN
cana-4835	99	17	r−1@t	r−1@t	NOUN
cana-4835	99	18	.	.	PUNCT
cana-4835	100	1	communications	communication	NOUN
cana-4835	100	2	on	on	ADP
cana-4835	100	3	applied	apply	VERB
cana-4835	100	4	nonlinear	nonlinear	ADJ
cana-4835	100	5	analysis	analysis	NOUN
cana-4835	100	6	issn	issn	NOUN
cana-4835	100	7	:	:	PUNCT
cana-4835	100	8	1074	1074	NUM
cana-4835	100	9	-	-	PUNCT
cana-4835	100	10	133x	133x	NUM
cana-4835	100	11	vol	vol	VERB
cana-4835	100	12	32	32	NUM
cana-4835	100	13	no	no	NOUN
cana-4835	100	14	.	.	PUNCT
cana-4835	101	1	10s	10	NOUN
cana-4835	101	2	(	(	PUNCT
cana-4835	101	3	2025	2025	NUM
cana-4835	101	4	)	)	PUNCT
cana-4835	101	5	435	435	NUM
cana-4835	101	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4835	101	7	proof	proof	NOUN
cana-4835	101	8	:	:	PUNCT
cana-4835	101	9	let	let	VERB
cana-4835	101	10	s(q	s(q	NOUN
cana-4835	101	11	)	)	PUNCT
cana-4835	101	12	=	=	PRON
cana-4835	101	13	{	{	PUNCT
cana-4835	101	14	q	q	NOUN
cana-4835	101	15	∈	∈	PROPN
cana-4835	101	16	(	(	PUNCT
cana-4835	101	17	y	y	PROPN
cana-4835	101	18	×	×	PROPN
cana-4835	101	19	z	z	PROPN
cana-4835	101	20	)	)	PUNCT
cana-4835	102	1	|	|	ADV
cana-4835	102	2	r	r	NOUN
cana-4835	102	3	◦	◦	NOUN
cana-4835	102	4	q	q	NOUN
cana-4835	102	5	⊆	⊆	NUM
cana-4835	102	6	t	t	PROPN
cana-4835	102	7	}	}	PUNCT
cana-4835	102	8	≠	≠	PROPN
cana-4835	102	9	φ	φ	NUM
cana-4835	102	10	.	.	PUNCT
cana-4835	103	1	let	let	VERB
cana-4835	103	2	q	q	NOUN
cana-4835	103	3	⊆	⊆	NUM
cana-4835	103	4	s(q	s(q	NOUN
cana-4835	103	5	):	):	PUNCT
cana-4835	103	6	r	r	NOUN
cana-4835	103	7	◦	◦	NOUN
cana-4835	103	8	q	q	NOUN
cana-4835	104	1	=	=	SYM
cana-4835	104	2	t	t	NOUN
cana-4835	104	3	then	then	ADV
cana-4835	104	4	we	we	PRON
cana-4835	104	5	have	have	VERB
cana-4835	104	6	r−1@	r−1@	VERB
cana-4835	104	7	(	(	PUNCT
cana-4835	104	8	r	r	NOUN
cana-4835	104	9	◦	◦	NOUN
cana-4835	104	10	q	q	NOUN
cana-4835	104	11	)	)	PUNCT
cana-4835	104	12	⊆	⊆	NUM
cana-4835	104	13	r−1@t	r−1@t	NOUN
cana-4835	104	14	,	,	PUNCT
cana-4835	104	15	but	but	CCONJ
cana-4835	104	16	q	q	PROPN
cana-4835	104	17	⊂	⊂	PROPN
cana-4835	104	18	r−1@	r−1@	X
cana-4835	104	19	(	(	PUNCT
cana-4835	104	20	r	r	NOUN
cana-4835	104	21	◦	◦	NOUN
cana-4835	104	22	q	q	X
cana-4835	104	23	)	)	PUNCT
cana-4835	104	24	then	then	ADV
cana-4835	104	25	it	it	PRON
cana-4835	104	26	shows	show	VERB
cana-4835	104	27	q	q	PROPN
cana-4835	104	28	⊂	⊂	PROPN
cana-4835	104	29	r−1@t	r−1@t	NOUN
cana-4835	104	30	we	we	PRON
cana-4835	104	31	have	have	VERB
cana-4835	104	32	r−1@t	r−1@t	NOUN
cana-4835	104	33	∈	∈	PROPN
cana-4835	104	34	s(q	s(q	NOUN
cana-4835	104	35	)	)	PUNCT
cana-4835	104	36	.	.	PUNCT
cana-4835	105	1	then	then	ADV
cana-4835	105	2	it	it	PRON
cana-4835	105	3	shows	show	VERB
cana-4835	105	4	that	that	SCONJ
cana-4835	105	5	r−1@t	r−1@t	NOUN
cana-4835	105	6	∈	∈	PROPN
cana-4835	105	7	s(q	s(q	NOUN
cana-4835	105	8	)	)	PUNCT
cana-4835	105	9	.	.	PUNCT
cana-4835	106	1	then	then	ADV
cana-4835	106	2	r−1@t	r−1@t	NOUN
cana-4835	106	3	will	will	AUX
cana-4835	106	4	be	be	AUX
cana-4835	106	5	the	the	DET
cana-4835	106	6	greatest	great	ADJ
cana-4835	106	7	element	element	NOUN
cana-4835	106	8	in	in	ADP
cana-4835	106	9	s(q	s(q	NOUN
cana-4835	106	10	)	)	PUNCT
cana-4835	106	11	.	.	PUNCT
cana-4835	107	1	hence	hence	ADV
cana-4835	107	2	r−1@t	r−1@t	NOUN
cana-4835	107	3	be	be	AUX
cana-4835	107	4	the	the	DET
cana-4835	107	5	greatest	great	ADJ
cana-4835	107	6	element	element	NOUN
cana-4835	107	7	in	in	ADP
cana-4835	107	8	s(q	s(q	NOUN
cana-4835	107	9	)	)	PUNCT
cana-4835	107	10	.	.	PUNCT
cana-4835	108	1	then	then	ADV
cana-4835	108	2	q	q	X
cana-4835	108	3	∇	∇	X
cana-4835	108	4	=	=	SYM
cana-4835	108	5	r	r	NOUN
cana-4835	108	6	−1@	−1@	PUNCT
cana-4835	108	7	t	t	NOUN
cana-4835	108	8	which	which	PRON
cana-4835	108	9	is	be	AUX
cana-4835	108	10	the	the	DET
cana-4835	108	11	maximum	maximum	ADJ
cana-4835	108	12	relation	relation	NOUN
cana-4835	108	13	“	"	PUNCT
cana-4835	108	14	q	q	NOUN
cana-4835	108	15	”	"	PUNCT
cana-4835	108	16	satisfying	satisfy	VERB
cana-4835	108	17	the	the	DET
cana-4835	108	18	equation	equation	NOUN
cana-4835	108	19	r	r	NOUN
cana-4835	108	20	◦	◦	NOUN
cana-4835	108	21	q	q	NOUN
cana-4835	108	22	=	=	SYM
cana-4835	108	23	t	t	PROPN
cana-4835	108	24	4	4	NUM
cana-4835	108	25	.	.	PUNCT
cana-4835	109	1	conclusion	conclusion	NOUN
cana-4835	109	2	:	:	PUNCT
cana-4835	109	3	our	our	PRON
cana-4835	109	4	findings	finding	NOUN
cana-4835	109	5	suggest	suggest	VERB
cana-4835	109	6	that	that	SCONJ
cana-4835	109	7	the	the	DET
cana-4835	109	8	identification	identification	NOUN
cana-4835	109	9	of	of	ADP
cana-4835	109	10	an	an	DET
cana-4835	109	11	optimal	optimal	ADJ
cana-4835	109	12	solution	solution	NOUN
cana-4835	109	13	among	among	ADP
cana-4835	109	14	various	various	ADJ
cana-4835	109	15	alternatives	alternative	NOUN
cana-4835	109	16	in	in	ADP
cana-4835	109	17	a	a	DET
cana-4835	109	18	given	give	VERB
cana-4835	109	19	problem	problem	NOUN
cana-4835	109	20	can	can	AUX
cana-4835	109	21	be	be	AUX
cana-4835	109	22	achieved	achieve	VERB
cana-4835	109	23	through	through	ADP
cana-4835	109	24	the	the	DET
cana-4835	109	25	utilization	utilization	NOUN
cana-4835	109	26	of	of	ADP
cana-4835	109	27	nonlinear	nonlinear	ADJ
cana-4835	109	28	fuzzy	fuzzy	ADJ
cana-4835	109	29	regression	regression	NOUN
cana-4835	109	30	equation	equation	NOUN
cana-4835	109	31	.	.	PUNCT
cana-4835	110	1	after	after	ADP
cana-4835	110	2	conducting	conduct	VERB
cana-4835	110	3	extensive	extensive	ADJ
cana-4835	110	4	calculations	calculation	NOUN
cana-4835	110	5	using	use	VERB
cana-4835	110	6	nfres	nfre	NOUN
cana-4835	110	7	in	in	ADP
cana-4835	110	8	the	the	DET
cana-4835	110	9	context	context	NOUN
cana-4835	110	10	of	of	ADP
cana-4835	110	11	our	our	PRON
cana-4835	110	12	proposed	propose	VERB
cana-4835	110	13	scenarios	scenario	NOUN
cana-4835	110	14	in	in	ADP
cana-4835	110	15	civil	civil	ADJ
cana-4835	110	16	engineering	engineering	NOUN
cana-4835	110	17	,	,	PUNCT
cana-4835	110	18	we	we	PRON
cana-4835	110	19	have	have	AUX
cana-4835	110	20	been	be	AUX
cana-4835	110	21	able	able	ADJ
cana-4835	110	22	to	to	PART
cana-4835	110	23	discern	discern	VERB
cana-4835	110	24	the	the	DET
cana-4835	110	25	most	most	ADV
cana-4835	110	26	favourable	favourable	ADJ
cana-4835	110	27	outcome	outcome	NOUN
cana-4835	110	28	among	among	ADP
cana-4835	110	29	the	the	DET
cana-4835	110	30	presented	present	VERB
cana-4835	110	31	options	option	NOUN
cana-4835	110	32	.	.	PUNCT
cana-4835	111	1	the	the	DET
cana-4835	111	2	application	application	NOUN
cana-4835	111	3	of	of	ADP
cana-4835	111	4	fuzzy	fuzzy	ADJ
cana-4835	111	5	relation	relation	NOUN
cana-4835	111	6	operations	operation	NOUN
cana-4835	111	7	played	play	VERB
cana-4835	111	8	a	a	DET
cana-4835	111	9	crucial	crucial	ADJ
cana-4835	111	10	role	role	NOUN
cana-4835	111	11	in	in	ADP
cana-4835	111	12	assessing	assess	VERB
cana-4835	111	13	and	and	CCONJ
cana-4835	111	14	determining	determine	VERB
cana-4835	111	15	the	the	DET
cana-4835	111	16	best	good	ADJ
cana-4835	111	17	project	project	NOUN
cana-4835	111	18	outcome	outcome	NOUN
cana-4835	111	19	.	.	PUNCT
cana-4835	112	1	a	a	DET
cana-4835	112	2	potential	potential	ADJ
cana-4835	112	3	avenue	avenue	NOUN
cana-4835	112	4	for	for	ADP
cana-4835	112	5	future	future	ADJ
cana-4835	112	6	research	research	NOUN
cana-4835	112	7	could	could	AUX
cana-4835	112	8	involve	involve	VERB
cana-4835	112	9	optimizing	optimize	VERB
cana-4835	112	10	the	the	DET
cana-4835	112	11	influence	influence	NOUN
cana-4835	112	12	factors	factor	NOUN
cana-4835	112	13	rather	rather	ADV
cana-4835	112	14	than	than	ADP
cana-4835	112	15	solely	solely	ADV
cana-4835	112	16	focusing	focus	VERB
cana-4835	112	17	on	on	ADP
cana-4835	112	18	identifying	identify	VERB
cana-4835	112	19	the	the	DET
cana-4835	112	20	best	good	ADJ
cana-4835	112	21	project	project	NOUN
cana-4835	112	22	.	.	PUNCT
cana-4835	113	1	refrences	refrence	VERB
cana-4835	113	2	[	[	X
cana-4835	113	3	1	1	NUM
cana-4835	113	4	]	]	PUNCT
cana-4835	113	5	l.a.zadeh	l.a.zadeh	NOUN
cana-4835	113	6	,	,	PUNCT
cana-4835	113	7	fuzzy	fuzzy	ADJ
cana-4835	113	8	sets	set	NOUN
cana-4835	113	9	,	,	PUNCT
cana-4835	113	10	information	information	NOUN
cana-4835	113	11	and	and	CCONJ
cana-4835	113	12	control	control	NOUN
cana-4835	113	13	,	,	PUNCT
cana-4835	113	14	8(1965	8(1965	NUM
cana-4835	113	15	)	)	PUNCT
cana-4835	113	16	,	,	PUNCT
cana-4835	113	17	338	338	NUM
cana-4835	113	18	-	-	SYM
cana-4835	113	19	353	353	NUM
cana-4835	113	20	.	.	PUNCT
cana-4835	114	1	[	[	X
cana-4835	114	2	2	2	NUM
cana-4835	114	3	]	]	PUNCT
cana-4835	114	4	sanchez.e	sanchez.e	PROPN
cana-4835	114	5	.	.	PUNCT
cana-4835	114	6	,	,	PUNCT
cana-4835	114	7	“	"	PUNCT
cana-4835	114	8	resolution	resolution	NOUN
cana-4835	114	9	fo	fo	ADP
cana-4835	114	10	composite	composite	ADJ
cana-4835	114	11	fuzzy	fuzzy	ADJ
cana-4835	114	12	relation	relation	NOUN
cana-4835	114	13	equations.inf	equations.inf	NOUN
cana-4835	114	14	and	and	CCONJ
cana-4835	114	15	control	control	NOUN
cana-4835	114	16	.	.	PUNCT
cana-4835	114	17	”	"	PUNCT
cana-4835	114	18	vol	vol	NOUN
cana-4835	114	19	.	.	PROPN
cana-4835	114	20	30	30	NUM
cana-4835	114	21	,	,	PUNCT
cana-4835	114	22	1976	1976	NUM
cana-4835	114	23	.	.	PUNCT
cana-4835	114	24	,	,	PUNCT
cana-4835	115	1	pp	pp	ADJ
cana-4835	115	2	.	.	PUNCT
cana-4835	116	1	48–58	48–58	INTJ
cana-4835	116	2	.	.	PUNCT
cana-4835	117	1	[	[	X
cana-4835	117	2	3	3	X
cana-4835	117	3	]	]	X
cana-4835	117	4	g.	g.	PROPN
cana-4835	117	5	m.	m.	PROPN
cana-4835	117	6	m.	m.	PROPN
cana-4835	117	7	s.	s.	PROPN
cana-4835	117	8	g.	g.	PROPN
cana-4835	117	9	n.	n.	PROPN
cana-4835	117	10	g.	g.	PROPN
cana-4835	117	11	b.	b.	PROPN
cana-4835	117	12	.r.(red	.r.(red	PROPN
cana-4835	117	13	)	)	PUNCT
cana-4835	117	14	,	,	PUNCT
cana-4835	117	15	sanchez	sanchez	PROPN
cana-4835	117	16	e.	e.	PROPN
cana-4835	117	17	solutions	solutions	PROPN
cana-4835	117	18	in	in	ADP
cana-4835	117	19	composite	composite	ADJ
cana-4835	117	20	fuzzy	fuzzy	ADJ
cana-4835	117	21	relation	relation	NOUN
cana-4835	117	22	equations	equation	NOUN
cana-4835	117	23	:	:	PUNCT
cana-4835	118	1	application	application	NOUN
cana-4835	118	2	to	to	ADP
cana-4835	118	3	medical	medical	ADJ
cana-4835	118	4	diagnosis	diagnosis	NOUN
cana-4835	118	5	in	in	ADP
cana-4835	118	6	brouwerian	brouwerian	ADJ
cana-4835	118	7	logic	logic	NOUN
cana-4835	118	8	.	.	PUNCT
cana-4835	119	1	,	,	PUNCT
cana-4835	119	2	amsterdam	amsterdam	PROPN
cana-4835	119	3	:	:	PUNCT
cana-4835	119	4	northholland	northholland	ADJ
cana-4835	119	5	,	,	PUNCT
cana-4835	119	6	1977	1977	NUM
cana-4835	119	7	.	.	PUNCT
cana-4835	120	1	communications	communication	NOUN
cana-4835	120	2	on	on	ADP
cana-4835	120	3	applied	apply	VERB
cana-4835	120	4	nonlinear	nonlinear	ADJ
cana-4835	120	5	analysis	analysis	NOUN
cana-4835	120	6	issn	issn	NOUN
cana-4835	120	7	:	:	PUNCT
cana-4835	120	8	1074	1074	NUM
cana-4835	120	9	-	-	PUNCT
cana-4835	120	10	133x	133x	NUM
cana-4835	120	11	vol	vol	VERB
cana-4835	120	12	32	32	NUM
cana-4835	120	13	no	no	NOUN
cana-4835	120	14	.	.	PUNCT
cana-4835	121	1	10s	10	NOUN
cana-4835	121	2	(	(	PUNCT
cana-4835	121	3	2025	2025	NUM
cana-4835	121	4	)	)	PUNCT
cana-4835	121	5	436	436	NUM
cana-4835	121	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4835	122	1	[	[	X
cana-4835	122	2	4	4	X
cana-4835	122	3	]	]	PUNCT
cana-4835	122	4	sanchez.e	sanchez.e	PROPN
cana-4835	122	5	.	.	PUNCT
cana-4835	122	6	,	,	PUNCT
cana-4835	122	7	“	"	PUNCT
cana-4835	122	8	functional	functional	ADJ
cana-4835	122	9	relations	relation	NOUN
cana-4835	122	10	and	and	CCONJ
cana-4835	122	11	fuzzy	fuzzy	ADJ
cana-4835	122	12	relational	relational	ADJ
cana-4835	122	13	equations	equation	NOUN
cana-4835	122	14	,	,	PUNCT
cana-4835	122	15	”	"	PUNCT
cana-4835	122	16	in	in	ADP
cana-4835	122	17	ieee	ieee	NOUN
cana-4835	122	18	faculty	faculty	NOUN
cana-4835	122	19	de	de	X
cana-4835	122	20	medicine.marsylia	medicine.marsylia	PROPN
cana-4835	122	21	,	,	PUNCT
cana-4835	122	22	france	france	PROPN
cana-4835	122	23	,	,	PUNCT
cana-4835	122	24	2002	2002	NUM
cana-4835	122	25	.	.	PUNCT
cana-4835	123	1	[	[	X
cana-4835	123	2	5	5	X
cana-4835	123	3	]	]	PUNCT
cana-4835	123	4	l.	l.	PROPN
cana-4835	123	5	c.	c.	PROPN
cana-4835	123	6	.paul.wang	.paul.wang	PROPN
cana-4835	123	7	,	,	PUNCT
cana-4835	123	8	“	"	PUNCT
cana-4835	123	9	fuzzy	fuzzy	ADJ
cana-4835	123	10	relation	relation	NOUN
cana-4835	123	11	equations(ll):the	equations(ll):the	DET
cana-4835	123	12	branch	branch	NOUN
cana-4835	123	13	-point	-point	PROPN
cana-4835	123	14	-	-	PUNCT
cana-4835	123	15	solutions	solution	NOUN
cana-4835	123	16	and	and	CCONJ
cana-4835	123	17	the	the	DET
cana-4835	123	18	categorized	categorize	VERB
cana-4835	123	19	minimal	minimal	ADJ
cana-4835	123	20	solutions	solution	NOUN
cana-4835	123	21	.	.	PUNCT
cana-4835	123	22	”	"	PUNCT
cana-4835	123	23	springer	springer	NOUN
cana-4835	123	24	,	,	PUNCT
cana-4835	123	25	2006	2006	NUM
cana-4835	123	26	.	.	PUNCT
cana-4835	124	1	[	[	X
cana-4835	124	2	6	6	NUM
cana-4835	124	3	]	]	PUNCT
cana-4835	124	4	j.	j.	PROPN
cana-4835	124	5	g.	g.	PROPN
cana-4835	124	6	b.	b.	PROPN
cana-4835	124	7	c.	c.	PROPN
cana-4835	124	8	w.c.amaral	w.c.amaral	PROPN
cana-4835	124	9	,	,	PUNCT
cana-4835	124	10	“	"	PUNCT
cana-4835	124	11	hierarchical	hierarchical	ADJ
cana-4835	124	12	fuzzy	fuzzy	ADJ
cana-4835	124	13	relational	relational	ADJ
cana-4835	124	14	models	model	NOUN
cana-4835	124	15	:	:	PUNCT
cana-4835	124	16	linguistic	linguistic	ADJ
cana-4835	124	17	interpretation	interpretation	NOUN
cana-4835	124	18	,	,	PUNCT
cana-4835	124	19	”	"	PUNCT
cana-4835	124	20	in	in	ADP
cana-4835	124	21	ieee	ieee	NOUN
cana-4835	124	22	,	,	PUNCT
cana-4835	124	23	university	university	NOUN
cana-4835	124	24	of	of	ADP
cana-4835	124	25	campinas(unicamp).brazil	campinas(unicamp).brazil	PROPN
cana-4835	124	26	.	.	PUNCT
cana-4835	125	1	2002	2002	NUM
cana-4835	125	2	.	.	PUNCT
cana-4835	126	1	[	[	X
cana-4835	126	2	7	7	X
cana-4835	126	3	]	]	PUNCT
cana-4835	126	4	t.	t.	PROPN
cana-4835	126	5	kiseliova	kiseliova	PROPN
cana-4835	126	6	,	,	PUNCT
cana-4835	126	7	“	"	PUNCT
cana-4835	126	8	a	a	DET
cana-4835	126	9	theoretical	theoretical	ADJ
cana-4835	126	10	comparison	comparison	NOUN
cana-4835	126	11	of	of	ADP
cana-4835	126	12	disco	disco	NOUN
cana-4835	126	13	and	and	CCONJ
cana-4835	126	14	cadiag	cadiag	NOUN
cana-4835	126	15	-	-	PUNCT
cana-4835	126	16	ll	ll	NOUN
cana-4835	126	17	-	-	PUNCT
cana-4835	126	18	likesystems	likesystem	NOUN
cana-4835	126	19	for	for	ADP
cana-4835	126	20	medical	medical	ADJ
cana-4835	126	21	diagnoses	diagnosis	NOUN
cana-4835	126	22	,	,	PUNCT
cana-4835	126	23	”	"	PUNCT
cana-4835	126	24	vol	vol	NOUN
cana-4835	126	25	.	.	PUNCT
cana-4835	127	1	42	42	NUM
cana-4835	127	2	.	.	PUNCT
cana-4835	128	1	new	new	PROPN
cana-4835	128	2	york	york	PROPN
cana-4835	128	3	:	:	PUNCT
cana-4835	128	4	john	john	PROPN
cana-4835	128	5	wiley	wiley	PROPN
cana-4835	128	6	&	&	CCONJ
cana-4835	128	7	sons	son	NOUN
cana-4835	128	8	,	,	PUNCT
cana-4835	128	9	2006	2006	NUM
cana-4835	128	10	,	,	PUNCT
cana-4835	128	11	pp	pp	ADV
cana-4835	128	12	.	.	PUNCT
cana-4835	129	1	723–748	723–748	X
cana-4835	129	2	.	.	PUNCT
cana-4835	130	1	[	[	X
cana-4835	130	2	8	8	NUM
cana-4835	130	3	]	]	X
cana-4835	130	4	y.-k	y.-k	NOUN
cana-4835	130	5	.	.	PUNCT
cana-4835	131	1	l.	l.	PROPN
cana-4835	131	2	leh	leh	PROPN
cana-4835	131	3	luoh	luoh	PROPN
cana-4835	131	4	,	,	PUNCT
cana-4835	131	5	wen	wen	PROPN
cana-4835	131	6	-	-	PROPN
cana-4835	131	7	june	june	PROPN
cana-4835	131	8	wang	wang	PROPN
cana-4835	131	9	,	,	PUNCT
cana-4835	131	10	“	"	PUNCT
cana-4835	131	11	new	new	ADJ
cana-4835	131	12	algorithms	algorithm	NOUN
cana-4835	131	13	for	for	ADP
cana-4835	131	14	solving	solve	VERB
cana-4835	131	15	fuzzy	fuzzy	ADJ
cana-4835	131	16	relation	relation	NOUN
cana-4835	131	17	equations	equation	NOUN
cana-4835	131	18	,	,	PUNCT
cana-4835	131	19	”	"	PUNCT
cana-4835	131	20	may	may	PROPN
cana-4835	131	21	3	3	NUM
cana-4835	131	22	,	,	PUNCT
cana-4835	131	23	2002	2002	NUM
cana-4835	131	24	.	.	PUNCT
cana-4835	132	1	[	[	X
cana-4835	132	2	9	9	NUM
cana-4835	132	3	]	]	PUNCT
cana-4835	132	4	l.	l.	PROPN
cana-4835	132	5	n.	n.	PROPN
cana-4835	132	6	martin.st.epni.cka	martin.st.epni.cka	PROPN
cana-4835	132	7	,	,	PUNCT
cana-4835	132	8	bernard	bernard	PROPN
cana-4835	132	9	de	de	PROPN
cana-4835	132	10	baets	baet	NOUN
cana-4835	132	11	,	,	PUNCT
cana-4835	132	12	“	"	PUNCT
cana-4835	132	13	arthmetic	arthmetic	ADJ
cana-4835	132	14	fuzzy	fuzzy	ADJ
cana-4835	132	15	models	model	NOUN
cana-4835	132	16	,	,	PUNCT
cana-4835	132	17	”	"	PUNCT
cana-4835	132	18	in	in	ADP
cana-4835	132	19	ieee	ieee	NOUN
cana-4835	132	20	tranasactions	tranasaction	NOUN
cana-4835	132	21	on	on	ADP
cana-4835	132	22	fuzzy	fuzzy	ADJ
cana-4835	132	23	systems	system	NOUN
cana-4835	132	24	,	,	PUNCT
cana-4835	132	25	university	university	NOUN
cana-4835	132	26	of	of	ADP
cana-4835	132	27	ostrava	ostrava	PROPN
cana-4835	132	28	,	,	PUNCT
cana-4835	132	29	2010	2010	NUM
cana-4835	132	30	.	.	PUNCT
cana-4835	133	1	[	[	X
cana-4835	133	2	10	10	NUM
cana-4835	133	3	]	]	PUNCT
cana-4835	133	4	s.sapana	s.sapana	NOUN
cana-4835	133	5	and	and	CCONJ
cana-4835	133	6	d.	d.	PROPN
cana-4835	133	7	.a.tamilarasi	.a.tamilarasi	PROPN
cana-4835	133	8	,	,	PUNCT
cana-4835	133	9	“	"	PUNCT
cana-4835	133	10	fuzzy	fuzzy	ADJ
cana-4835	133	11	relations	relation	NOUN
cana-4835	133	12	equations	equation	NOUN
cana-4835	133	13	in	in	ADP
cana-4835	133	14	preventin	preventin	ADJ
cana-4835	133	15	neuropathy	neuropathy	ADJ
cana-4835	133	16	diabetic	diabetic	NOUN
cana-4835	133	17	,	,	PUNCT
cana-4835	133	18	”	"	PUNCT
cana-4835	133	19	vol	vol	NOUN
cana-4835	133	20	.	.	PROPN
cana-4835	134	1	2	2	NUM
cana-4835	134	2	,	,	PUNCT
cana-4835	134	3	no	no	INTJ
cana-4835	134	4	.	.	NOUN
cana-4835	134	5	4	4	NUM
cana-4835	134	6	.	.	PUNCT
cana-4835	134	7	recent	recent	ADJ
cana-4835	134	8	trends	trend	NOUN
cana-4835	134	9	in	in	ADP
cana-4835	134	10	engineering	engineering	NOUN
cana-4835	134	11	,	,	PUNCT
cana-4835	134	12	nov	nov	PROPN
cana-4835	134	13	2009	2009	NUM
cana-4835	134	14	.	.	PUNCT
cana-4835	135	1	[	[	X
cana-4835	135	2	11	11	NUM
cana-4835	135	3	]	]	PUNCT
cana-4835	135	4	s.	s.	PROPN
cana-4835	135	5	jain	jain	PROPN
cana-4835	135	6	and	and	CCONJ
cana-4835	135	7	k.	k.	PROPN
cana-4835	135	8	lachhwani	lachhwani	PROPN
cana-4835	135	9	,	,	PUNCT
cana-4835	135	10	“	"	PUNCT
cana-4835	135	11	multiobjective	multiobjective	ADJ
cana-4835	135	12	programming	programming	NOUN
cana-4835	135	13	problem	problem	NOUN
cana-4835	135	14	with	with	ADP
cana-4835	135	15	fuzzy	fuzzy	ADJ
cana-4835	135	16	relatinal	relatinal	ADJ
cana-4835	135	17	equations	equation	NOUN
cana-4835	135	18	,	,	PUNCT
cana-4835	135	19	”	"	PUNCT
cana-4835	135	20	2009	2009	NUM
cana-4835	135	21	.	.	PUNCT
cana-4835	136	1	[	[	X
cana-4835	136	2	12	12	NUM
cana-4835	136	3	]	]	X
cana-4835	136	4	p.n.smith	p.n.smith	NOUN
cana-4835	136	5	,	,	PUNCT
cana-4835	136	6	application	application	NOUN
cana-4835	136	7	of	of	ADP
cana-4835	136	8	fuzzy	fuzzy	ADJ
cana-4835	136	9	relation	relation	NOUN
cana-4835	136	10	equations	equation	NOUN
cana-4835	136	11	in	in	ADP
cana-4835	136	12	transport	transport	NOUN
cana-4835	136	13	project	project	NOUN
cana-4835	136	14	evalution	evalution	NOUN
cana-4835	136	15	.department	.department	ADJ
cana-4835	136	16	of	of	ADP
cana-4835	136	17	geographical	geographical	ADJ
cana-4835	136	18	sciences	science	NOUN
cana-4835	136	19	and	and	CCONJ
cana-4835	136	20	planning	planning	NOUN
cana-4835	136	21	.	.	PUNCT
cana-4835	137	1	the	the	DET
cana-4835	137	2	university	university	PROPN
cana-4835	137	3	of	of	ADP
cana-4835	137	4	queenland	queenland	PROPN
cana-4835	137	5	st.lucia	st.lucia	PROPN
cana-4835	137	6	,	,	PUNCT
cana-4835	137	7	queenland	queenland	NOUN
cana-4835	137	8	.	.	PUNCT
cana-4835	137	9	,	,	PUNCT
cana-4835	137	10	australia	australia	PROPN
cana-4835	137	11	,	,	PUNCT
cana-4835	137	12	1999	1999	NUM
cana-4835	137	13	.	.	PUNCT
cana-4835	138	1	55	55	NUM
cana-4835	138	2	56	56	NUM
cana-4835	138	3	bibliography	bibliography	NOUN
cana-4835	138	4	[	[	X
cana-4835	138	5	13	13	NUM
cana-4835	138	6	]	]	PUNCT
cana-4835	138	7	ayyub.b.m	ayyub.b.m	NOUN
cana-4835	138	8	.	.	PUNCT
cana-4835	138	9	,	,	PUNCT
cana-4835	138	10	“	"	PUNCT
cana-4835	138	11	fuzzy	fuzzy	ADJ
cana-4835	138	12	sets	set	NOUN
cana-4835	138	13	in	in	ADP
cana-4835	138	14	civil	civil	ADJ
cana-4835	138	15	engineering	engineering	NOUN
cana-4835	138	16	,	,	PUNCT
cana-4835	138	17	”	"	PUNCT
cana-4835	138	18	in	in	ADP
cana-4835	138	19	fuzzy	fuzzy	ADJ
cana-4835	138	20	sets	set	NOUN
cana-4835	138	21	and	and	CCONJ
cana-4835	138	22	systems,40	systems,40	VERB
cana-4835	138	23	,	,	PUNCT
cana-4835	138	24	killarney	killarney	NOUN
cana-4835	138	25	,	,	PUNCT
cana-4835	138	26	ireland	ireland	PROPN
cana-4835	138	27	,	,	PUNCT
cana-4835	138	28	1991	1991	NUM
cana-4835	138	29	,	,	PUNCT
cana-4835	138	30	pp	pp	ADV
cana-4835	138	31	.	.	PUNCT
cana-4835	139	1	491–5	491–5	X
cana-4835	139	2	.	.	PUNCT
cana-4835	140	1	[	[	X
cana-4835	140	2	14	14	NUM
cana-4835	140	3	]	]	PUNCT
cana-4835	140	4	k.	k.	PROPN
cana-4835	140	5	hemabala	hemabala	PROPN
cana-4835	140	6	,	,	PUNCT
cana-4835	140	7	srinivasa	srinivasa	PROPN
cana-4835	140	8	kumar	kumar	PROPN
cana-4835	140	9	,	,	PUNCT
cana-4835	140	10	cartesian	cartesian	ADJ
cana-4835	140	11	product	product	NOUN
cana-4835	140	12	of	of	ADP
cana-4835	140	13	multi	multi	ADJ
cana-4835	140	14	𝐿	𝐿	PROPN
cana-4835	140	15	fuzzy	fuzzy	ADJ
cana-4835	140	16	ideals	ideal	NOUN
cana-4835	140	17	of	of	ADP
cana-4835	140	18	г	г	PROPN
cana-4835	140	19	near	near	ADP
cana-4835	140	20	ring	ring	NOUN
cana-4835	140	21	,	,	PUNCT
cana-4835	140	22	advances	advance	NOUN
cana-4835	140	23	in	in	ADP
cana-4835	140	24	mathematics	mathematic	NOUN
cana-4835	140	25	:	:	PUNCT
cana-4835	140	26	scientific	scientific	ADJ
cana-4835	140	27	journal	journal	NOUN
cana-4835	140	28	9(2020	9(2020	NOUN
cana-4835	140	29	)	)	PUNCT
cana-4835	140	30	,	,	PUNCT
cana-4835	140	31	no.7	no.7	PROPN
cana-4835	140	32	,	,	PUNCT
cana-4835	140	33	5273	5273	NUM
cana-4835	140	34	-	-	SYM
cana-4835	140	35	5281	5281	NUM
cana-4835	140	36	.	.	PUNCT
cana-4835	141	1	[	[	X
cana-4835	141	2	15	15	NUM
cana-4835	141	3	]	]	PUNCT
cana-4835	141	4	k.	k.	NOUN
cana-4835	141	5	hemabala	hemabala	PROPN
cana-4835	141	6	,	,	PUNCT
cana-4835	141	7	srinivasa	srinivasa	PROPN
cana-4835	141	8	kumar	kumar	PROPN
cana-4835	141	9	,	,	PUNCT
cana-4835	141	10	anti	anti	PROPN
cana-4835	141	11	neutrosophic	neutrosophic	ADJ
cana-4835	141	12	multi	multi	ADJ
cana-4835	141	13	fuzzy	fuzzy	ADJ
cana-4835	141	14	ideals	ideal	NOUN
cana-4835	141	15	of	of	ADP
cana-4835	141	16	г	г	PROPN
cana-4835	141	17	near	near	ADP
cana-4835	141	18	ring	ring	NOUN
cana-4835	141	19	,	,	PUNCT
cana-4835	141	20	neutrosophic	neutrosophic	ADJ
cana-4835	141	21	sets	set	NOUN
cana-4835	141	22	and	and	CCONJ
cana-4835	141	23	systems	system	NOUN
cana-4835	141	24	,	,	PUNCT
cana-4835	141	25	vol48(2022	vol48(2022	PROPN
cana-4835	141	26	)	)	PUNCT
cana-4835	141	27	.	.	PUNCT
cana-4835	142	1	[	[	X
cana-4835	142	2	16	16	NUM
cana-4835	142	3	]	]	PUNCT
cana-4835	142	4	k.	k.	PROPN
cana-4835	142	5	hemabala	hemabala	PROPN
cana-4835	142	6	,	,	PUNCT
cana-4835	142	7	srinivasa	srinivasa	PROPN
cana-4835	142	8	kumar	kumar	PROPN
cana-4835	142	9	,	,	PUNCT
cana-4835	142	10	neutrosophic	neutrosophic	ADJ
cana-4835	142	11	multi	multi	ADJ
cana-4835	142	12	fuzzy	fuzzy	ADJ
cana-4835	142	13	ideals	ideal	NOUN
cana-4835	142	14	of	of	ADP
cana-4835	142	15	г	г	PROPN
cana-4835	142	16	near	near	ADP
cana-4835	142	17	ring	ring	NOUN
cana-4835	142	18	,	,	PUNCT
cana-4835	142	19	neutrosophic	neutrosophic	ADJ
cana-4835	142	20	sets	set	NOUN
cana-4835	142	21	and	and	CCONJ
cana-4835	142	22	systems	system	NOUN
cana-4835	142	23	,	,	PUNCT
cana-4835	142	24	vol49(2022	vol49(2022	PROPN
cana-4835	142	25	)	)	PUNCT
cana-4835	142	26	.	.	PUNCT