id	sid	tid	token	lemma	pos
cana-826	1	1	communications	communication	NOUN
cana-826	1	2	on	on	ADP
cana-826	1	3	applied	apply	VERB
cana-826	1	4	nonlinear	nonlinear	ADJ
cana-826	1	5	analysis	analysis	NOUN
cana-826	1	6	issn	issn	NOUN
cana-826	1	7	:	:	PUNCT
cana-826	1	8	1074	1074	NUM
cana-826	1	9	-	-	PUNCT
cana-826	1	10	133x	133x	NUM
cana-826	1	11	vol	vol	NOUN
cana-826	1	12	31	31	NUM
cana-826	1	13	no	no	NOUN
cana-826	1	14	.	.	PUNCT
cana-826	2	1	4s	4s	NUM
cana-826	2	2	(	(	PUNCT
cana-826	2	3	2024	2024	NUM
cana-826	2	4	)	)	PUNCT
cana-826	2	5	9	9	NUM
cana-826	2	6	https://internationalpubls.com	https://internationalpubls.com	NUM
cana-826	2	7	intuitionistic	intuitionistic	ADJ
cana-826	2	8	fuzzy	fuzzy	ADJ
cana-826	2	9	threshold	threshold	NOUN
cana-826	2	10	hypergraphs	hypergraph	NOUN
cana-826	2	11	and	and	CCONJ
cana-826	2	12	their	their	PRON
cana-826	2	13	role	role	NOUN
cana-826	2	14	in	in	ADP
cana-826	2	15	chasing	chase	VERB
cana-826	2	16	fugitives	fugitive	NOUN
cana-826	2	17	with	with	ADP
cana-826	2	18	multi	multi	ADJ
cana-826	2	19	-	-	NOUN
cana-826	2	20	bots	bot	NOUN
cana-826	2	21	myithili.k.k1	myithili.k.k1	PROPN
cana-826	2	22	,	,	PUNCT
cana-826	2	23	nandhini.c	nandhini.c	NUM
cana-826	2	24	2	2	NUM
cana-826	2	25	1associate	1associate	NUM
cana-826	2	26	professor	professor	NOUN
cana-826	2	27	&	&	CCONJ
cana-826	2	28	head	head	PROPN
cana-826	2	29	,	,	PUNCT
cana-826	2	30	department	department	NOUN
cana-826	2	31	of	of	ADP
cana-826	2	32	mathematics(ca	mathematics(ca	PROPN
cana-826	2	33	)	)	PUNCT
cana-826	2	34	,	,	PUNCT
cana-826	2	35	vellalar	vellalar	ADJ
cana-826	2	36	college	college	NOUN
cana-826	2	37	for	for	ADP
cana-826	2	38	women	woman	NOUN
cana-826	2	39	,	,	PUNCT
cana-826	2	40	erode-638012	erode-638012	ADJ
cana-826	2	41	,	,	PUNCT
cana-826	2	42	tamilnadu	tamilnadu	ADJ
cana-826	2	43	,	,	PUNCT
cana-826	2	44	india	india	PROPN
cana-826	2	45	,	,	PUNCT
cana-826	2	46	mathsmyth@gmail.com	mathsmyth@gmail.com	X
cana-826	3	1	2research	2research	NUM
cana-826	3	2	scholar	scholar	NOUN
cana-826	3	3	,	,	PUNCT
cana-826	3	4	department	department	NOUN
cana-826	3	5	of	of	ADP
cana-826	3	6	mathematics	mathematic	NOUN
cana-826	3	7	,	,	PUNCT
cana-826	3	8	vellalar	vellalar	ADJ
cana-826	3	9	college	college	NOUN
cana-826	3	10	for	for	ADP
cana-826	3	11	women	woman	NOUN
cana-826	3	12	,	,	PUNCT
cana-826	3	13	erode-638012	erode-638012	ADJ
cana-826	3	14	,	,	PUNCT
cana-826	3	15	tamilnadu	tamilnadu	ADJ
cana-826	3	16	,	,	PUNCT
cana-826	3	17	india	india	PROPN
cana-826	3	18	,	,	PUNCT
cana-826	3	19	c.nandhini@vcw.ac.in	c.nandhini@vcw.ac.in	NOUN
cana-826	3	20	article	article	NOUN
cana-826	3	21	history	history	NOUN
cana-826	3	22	:	:	PUNCT
cana-826	3	23	received	receive	VERB
cana-826	3	24	:	:	PUNCT
cana-826	3	25	15	15	NUM
cana-826	3	26	-	-	PUNCT
cana-826	3	27	04	04	NUM
cana-826	3	28	-	-	PUNCT
cana-826	3	29	2024	2024	NUM
cana-826	3	30	revised	revise	VERB
cana-826	3	31	:	:	PUNCT
cana-826	3	32	03	03	NUM
cana-826	3	33	-	-	PUNCT
cana-826	3	34	06	06	NUM
cana-826	3	35	-	-	PUNCT
cana-826	3	36	2024	2024	NUM
cana-826	3	37	accepted	accept	VERB
cana-826	3	38	:	:	PUNCT
cana-826	3	39	22	22	NUM
cana-826	3	40	-	-	SYM
cana-826	3	41	06	06	NUM
cana-826	3	42	-	-	PUNCT
cana-826	3	43	2024	2024	NUM
cana-826	3	44	abstract	abstract	NOUN
cana-826	3	45	in	in	ADP
cana-826	3	46	this	this	DET
cana-826	3	47	paper	paper	NOUN
cana-826	3	48	,	,	PUNCT
cana-826	3	49	intuitionistic	intuitionistic	ADJ
cana-826	3	50	fuzzy	fuzzy	ADJ
cana-826	3	51	threshold	threshold	NOUN
cana-826	3	52	hypergraph	hypergraph	NOUN
cana-826	3	53	(	(	PUNCT
cana-826	3	54	ifthg	ifthg	NOUN
cana-826	3	55	)	)	PUNCT
cana-826	3	56	is	be	AUX
cana-826	3	57	described	describe	VERB
cana-826	3	58	with	with	ADP
cana-826	3	59	some	some	DET
cana-826	3	60	definitions	definition	NOUN
cana-826	3	61	,	,	PUNCT
cana-826	3	62	such	such	ADJ
cana-826	3	63	as	as	ADP
cana-826	3	64	adjacency	adjacency	NOUN
cana-826	3	65	level	level	NOUN
cana-826	3	66	,	,	PUNCT
cana-826	3	67	strength	strength	NOUN
cana-826	3	68	,	,	PUNCT
cana-826	3	69	walk	walk	VERB
cana-826	3	70	,	,	PUNCT
cana-826	3	71	hyperpath	hyperpath	NOUN
cana-826	3	72	,	,	PUNCT
cana-826	3	73	score	score	NOUN
cana-826	3	74	values	value	NOUN
cana-826	3	75	,	,	PUNCT
cana-826	3	76	connected	connected	ADJ
cana-826	3	77	and	and	CCONJ
cana-826	3	78	disconnected	disconnected	ADJ
cana-826	3	79	ifthgs	ifthgs	PROPN
cana-826	3	80	.	.	PUNCT
cana-826	4	1	ifthgs	ifthgs	PROPN
cana-826	4	2	are	be	AUX
cana-826	4	3	essential	essential	ADJ
cana-826	4	4	for	for	ADP
cana-826	4	5	modeling	model	VERB
cana-826	4	6	complex	complex	ADJ
cana-826	4	7	relationships	relationship	NOUN
cana-826	4	8	and	and	CCONJ
cana-826	4	9	uncertainties	uncertainty	NOUN
cana-826	4	10	in	in	ADP
cana-826	4	11	emergency	emergency	NOUN
cana-826	4	12	response	response	NOUN
cana-826	4	13	scenarios	scenario	NOUN
cana-826	4	14	within	within	ADP
cana-826	4	15	crowed	crow	VERB
cana-826	4	16	areas	area	NOUN
cana-826	4	17	.	.	PUNCT
cana-826	5	1	furthermore	furthermore	ADV
cana-826	5	2	,	,	PUNCT
cana-826	5	3	a	a	DET
cana-826	5	4	novel	novel	ADJ
cana-826	5	5	method	method	NOUN
cana-826	5	6	for	for	ADP
cana-826	5	7	capturing	capture	VERB
cana-826	5	8	fugitives	fugitive	NOUN
cana-826	5	9	using	use	VERB
cana-826	5	10	ifthg	ifthg	NOUN
cana-826	5	11	model	model	NOUN
cana-826	5	12	is	be	AUX
cana-826	5	13	demonstrated	demonstrate	VERB
cana-826	5	14	.	.	PUNCT
cana-826	6	1	the	the	DET
cana-826	6	2	proposed	propose	VERB
cana-826	6	3	system	system	NOUN
cana-826	6	4	initializes	initialize	VERB
cana-826	6	5	robots	robot	NOUN
cana-826	6	6	and	and	CCONJ
cana-826	6	7	implements	implement	VERB
cana-826	6	8	a	a	DET
cana-826	6	9	step	step	NOUN
cana-826	6	10	-	-	PUNCT
cana-826	6	11	by	by	ADP
cana-826	6	12	-	-	PUNCT
cana-826	6	13	step	step	NOUN
cana-826	6	14	algorithm	algorithm	NOUN
cana-826	6	15	upon	upon	SCONJ
cana-826	6	16	detecting	detect	VERB
cana-826	6	17	any	any	DET
cana-826	6	18	intrusion	intrusion	NOUN
cana-826	6	19	,	,	PUNCT
cana-826	6	20	ultimately	ultimately	ADV
cana-826	6	21	determining	determine	VERB
cana-826	6	22	the	the	DET
cana-826	6	23	nearest	near	ADJ
cana-826	6	24	robot	robot	NOUN
cana-826	6	25	to	to	PART
cana-826	6	26	capture	capture	VERB
cana-826	6	27	the	the	DET
cana-826	6	28	fugitives	fugitive	NOUN
cana-826	6	29	.	.	PUNCT
cana-826	7	1	keywords	keyword	NOUN
cana-826	7	2	:	:	PUNCT
cana-826	7	3	intuitionistic	intuitionistic	ADJ
cana-826	7	4	fuzzy	fuzzy	ADJ
cana-826	7	5	threshold	threshold	NOUN
cana-826	7	6	hypergraph	hypergraph	NOUN
cana-826	7	7	,	,	PUNCT
cana-826	7	8	multi	multi	ADJ
cana-826	7	9	robots	robot	NOUN
cana-826	7	10	,	,	PUNCT
cana-826	7	11	algorithm	algorithm	NOUN
cana-826	7	12	,	,	PUNCT
cana-826	7	13	fugitive	fugitive	ADJ
cana-826	7	14	chase	chase	NOUN
cana-826	7	15	.	.	PUNCT
cana-826	8	1	2000	2000	NUM
cana-826	8	2	mathematics	mathematic	NOUN
cana-826	8	3	subject	subject	ADJ
cana-826	8	4	classification	classification	NOUN
cana-826	8	5	:	:	PUNCT
cana-826	8	6	05c65	05c65	NOUN
cana-826	8	7	1	1	X
cana-826	8	8	.	.	X
cana-826	8	9	introduction	introduction	NOUN
cana-826	8	10	to	to	PART
cana-826	8	11	deal	deal	VERB
cana-826	8	12	with	with	ADP
cana-826	8	13	the	the	DET
cana-826	8	14	complexities	complexity	NOUN
cana-826	8	15	of	of	ADP
cana-826	8	16	application	application	NOUN
cana-826	8	17	base	base	NOUN
cana-826	8	18	,	,	PUNCT
cana-826	8	19	the	the	DET
cana-826	8	20	graph	graph	NOUN
cana-826	8	21	concept	concept	NOUN
cana-826	8	22	was	be	AUX
cana-826	8	23	expanded	expand	VERB
cana-826	8	24	to	to	PART
cana-826	8	25	provide	provide	VERB
cana-826	8	26	a	a	DET
cana-826	8	27	hypergraph	hypergraph	NOUN
cana-826	8	28	,	,	PUNCT
cana-826	8	29	which	which	PRON
cana-826	8	30	is	be	AUX
cana-826	8	31	a	a	DET
cana-826	8	32	set	set	NOUN
cana-826	8	33	of	of	ADP
cana-826	8	34	all	all	DET
cana-826	8	35	vertices	vertex	NOUN
cana-826	8	36	including	include	VERB
cana-826	8	37	a	a	DET
cana-826	8	38	collection	collection	NOUN
cana-826	8	39	of	of	ADP
cana-826	8	40	v	v	NOUN
cana-826	8	41	subsets	subset	NOUN
cana-826	8	42	.	.	PUNCT
cana-826	9	1	the	the	DET
cana-826	9	2	notions	notion	NOUN
cana-826	9	3	of	of	ADP
cana-826	9	4	hypergraph	hypergraph	NOUN
cana-826	9	5	was	be	AUX
cana-826	9	6	introduced	introduce	VERB
cana-826	9	7	by	by	ADP
cana-826	9	8	berge	berge	NOUN
cana-826	9	9	[	[	X
cana-826	9	10	5	5	NUM
cana-826	9	11	]	]	PUNCT
cana-826	9	12	.	.	PUNCT
cana-826	10	1	chvatal	chvatal	ADJ
cana-826	10	2	and	and	CCONJ
cana-826	10	3	hammer	hammer	NOUN
cana-826	10	4	were	be	AUX
cana-826	10	5	the	the	DET
cana-826	10	6	first	first	ADJ
cana-826	10	7	to	to	PART
cana-826	10	8	introduce	introduce	VERB
cana-826	10	9	threshold	threshold	NOUN
cana-826	10	10	graphs(1973	graphs(1973	NOUN
cana-826	10	11	)	)	PUNCT
cana-826	10	12	in	in	ADP
cana-826	10	13	[	[	X
cana-826	10	14	6	6	NUM
cana-826	10	15	]	]	PUNCT
cana-826	10	16	.	.	PUNCT
cana-826	11	1	in	in	ADP
cana-826	11	2	set	set	PROPN
cana-826	11	3	theory	theory	NOUN
cana-826	11	4	,	,	PUNCT
cana-826	11	5	zadeh[13	zadeh[13	NOUN
cana-826	11	6	]	]	PUNCT
cana-826	11	7	created	create	VERB
cana-826	11	8	fuzzy	fuzzy	ADJ
cana-826	11	9	sets	set	NOUN
cana-826	11	10	as	as	ADP
cana-826	11	11	a	a	DET
cana-826	11	12	technique	technique	NOUN
cana-826	11	13	of	of	ADP
cana-826	11	14	conveying	convey	VERB
cana-826	11	15	ambiguity	ambiguity	NOUN
cana-826	11	16	and	and	CCONJ
cana-826	11	17	vagueness	vagueness	NOUN
cana-826	11	18	.	.	PUNCT
cana-826	12	1	fuzzy	fuzzy	ADJ
cana-826	12	2	set	set	PROPN
cana-826	12	3	theory	theory	NOUN
cana-826	12	4	has	have	AUX
cana-826	12	5	sparked	spark	VERB
cana-826	12	6	attention	attention	NOUN
cana-826	12	7	to	to	ADP
cana-826	12	8	variety	variety	NOUN
cana-826	12	9	of	of	ADP
cana-826	12	10	fields	field	NOUN
cana-826	12	11	.	.	PUNCT
cana-826	13	1	atanassov[1	atanassov[1	ADV
cana-826	13	2	,	,	PUNCT
cana-826	13	3	3	3	NUM
cana-826	13	4	]	]	PUNCT
cana-826	13	5	came	come	VERB
cana-826	13	6	up	up	ADP
cana-826	13	7	with	with	ADP
cana-826	13	8	of	of	ADP
cana-826	13	9	intuitionistic	intuitionistic	ADJ
cana-826	13	10	fuzzy	fuzzy	ADJ
cana-826	13	11	sets(ifs	sets(if	NOUN
cana-826	13	12	)	)	PUNCT
cana-826	13	13	concept	concept	NOUN
cana-826	13	14	as	as	ADP
cana-826	13	15	a	a	DET
cana-826	13	16	generalization	generalization	NOUN
cana-826	13	17	of	of	ADP
cana-826	13	18	fuzzy	fuzzy	ADJ
cana-826	13	19	sets	set	NOUN
cana-826	13	20	&	&	CCONJ
cana-826	13	21	atanassov	atanassov	PROPN
cana-826	13	22	added	add	VERB
cana-826	13	23	an	an	DET
cana-826	13	24	additional	additional	ADJ
cana-826	13	25	module	module	NOUN
cana-826	13	26	to	to	ADP
cana-826	13	27	fuzzy	fuzzy	ADJ
cana-826	13	28	set(which	set(which	PRON
cana-826	13	29	specifies	specify	VERB
cana-826	13	30	the	the	DET
cana-826	13	31	degree	degree	NOUN
cana-826	13	32	of	of	ADP
cana-826	13	33	non	non	ADJ
cana-826	13	34	-	-	NOUN
cana-826	13	35	membership	membership	NOUN
cana-826	13	36	)	)	PUNCT
cana-826	13	37	.	.	PUNCT
cana-826	14	1	the	the	DET
cana-826	14	2	concept	concept	NOUN
cana-826	14	3	behind	behind	ADP
cana-826	14	4	intuitionistic	intuitionistic	ADJ
cana-826	14	5	fuzzy	fuzzy	ADJ
cana-826	14	6	relations	relation	NOUN
cana-826	14	7	and	and	CCONJ
cana-826	14	8	graphs	graph	NOUN
cana-826	14	9	were	be	AUX
cana-826	14	10	discussed	discuss	VERB
cana-826	14	11	in	in	ADP
cana-826	14	12	[	[	X
cana-826	14	13	2	2	NUM
cana-826	14	14	,	,	PUNCT
cana-826	14	15	4	4	NUM
cana-826	14	16	]	]	PUNCT
cana-826	14	17	.	.	PUNCT
cana-826	15	1	intuitionistic	intuitionistic	ADJ
cana-826	15	2	fuzzy	fuzzy	ADJ
cana-826	15	3	graphs(ifgs	graphs(ifgs	PROPN
cana-826	15	4	)	)	PUNCT
cana-826	15	5	,	,	PUNCT
cana-826	15	6	intuitionistic	intuitionistic	ADJ
cana-826	15	7	fuzzy	fuzzy	ADJ
cana-826	15	8	hypergraphs(ifhgs	hypergraphs(ifhgs	NOUN
cana-826	15	9	)	)	PUNCT
cana-826	15	10	and	and	CCONJ
cana-826	15	11	intuitionistic	intuitionistic	ADJ
cana-826	15	12	fuzzy	fuzzy	ADJ
cana-826	15	13	directed	direct	VERB
cana-826	15	14	hypergraphs(ifdhg	hypergraphs(ifdhg	PROPN
cana-826	15	15	)	)	PUNCT
cana-826	15	16	have	have	AUX
cana-826	15	17	been	be	AUX
cana-826	15	18	introduced	introduce	VERB
cana-826	15	19	in	in	ADP
cana-826	15	20	[	[	X
cana-826	15	21	9	9	NUM
cana-826	15	22	,	,	PUNCT
cana-826	15	23	10	10	NUM
cana-826	15	24	,	,	PUNCT
cana-826	15	25	11	11	NUM
cana-826	15	26	]	]	PUNCT
cana-826	15	27	.	.	PUNCT
cana-826	16	1	some	some	DET
cana-826	16	2	types	type	NOUN
cana-826	16	3	of	of	ADP
cana-826	16	4	ifdhgs	ifdhgs	NOUN
cana-826	16	5	are	be	AUX
cana-826	16	6	discussed	discuss	VERB
cana-826	16	7	in	in	ADP
cana-826	16	8	[	[	X
cana-826	16	9	8	8	NUM
cana-826	16	10	]	]	PUNCT
cana-826	16	11	.	.	PUNCT
cana-826	17	1	a	a	DET
cana-826	17	2	novel	novel	ADJ
cana-826	17	3	decision	decision	NOUN
cana-826	17	4	-	-	PUNCT
cana-826	17	5	making	make	VERB
cana-826	17	6	approach	approach	NOUN
cana-826	17	7	based	base	VERB
cana-826	17	8	on	on	ADP
cana-826	17	9	hypergraphs	hypergraph	NOUN
cana-826	17	10	in	in	ADP
cana-826	17	11	if	if	SCONJ
cana-826	17	12	environment	environment	NOUN
cana-826	17	13	has	have	AUX
cana-826	17	14	been	be	AUX
cana-826	17	15	discussed	discuss	VERB
cana-826	17	16	in	in	ADP
cana-826	17	17	[	[	X
cana-826	17	18	7	7	NUM
cana-826	17	19	]	]	PUNCT
cana-826	17	20	.	.	PUNCT
cana-826	18	1	lanzhen	lanzhen	PROPN
cana-826	18	2	yang	yang	PROPN
cana-826	18	3	and	and	CCONJ
cana-826	18	4	hua	hua	PROPN
cana-826	18	5	mao	mao	PROPN
cana-826	19	1	[	[	X
cana-826	19	2	12	12	NUM
cana-826	19	3	]	]	PUNCT
cana-826	19	4	introduced	introduce	VERB
cana-826	19	5	intuitionistic	intuitionistic	ADJ
cana-826	19	6	fuzzy	fuzzy	ADJ
cana-826	19	7	threshold	threshold	NOUN
cana-826	19	8	graph	graph	NOUN
cana-826	19	9	and	and	CCONJ
cana-826	19	10	explained	explain	VERB
cana-826	19	11	its	its	PRON
cana-826	19	12	applications	application	NOUN
cana-826	19	13	.	.	PUNCT
cana-826	20	1	in	in	ADP
cana-826	20	2	this	this	DET
cana-826	20	3	research	research	NOUN
cana-826	20	4	paper	paper	NOUN
cana-826	20	5	,	,	PUNCT
cana-826	20	6	section	section	NOUN
cana-826	20	7	2	2	NUM
cana-826	20	8	elaborates	elaborate	VERB
cana-826	20	9	on	on	ADP
cana-826	20	10	fundamental	fundamental	ADJ
cana-826	20	11	definitions	definition	NOUN
cana-826	20	12	,	,	PUNCT
cana-826	20	13	while	while	SCONJ
cana-826	20	14	section	section	NOUN
cana-826	20	15	3	3	NUM
cana-826	20	16	includes	include	VERB
cana-826	20	17	mathematical	mathematical	ADJ
cana-826	20	18	definitions	definition	NOUN
cana-826	20	19	of	of	ADP
cana-826	20	20	ifthg	ifthg	NOUN
cana-826	20	21	and	and	CCONJ
cana-826	20	22	its	its	PRON
cana-826	20	23	related	related	ADJ
cana-826	20	24	extensions	extension	NOUN
cana-826	20	25	.	.	PUNCT
cana-826	21	1	furthermore	furthermore	ADV
cana-826	21	2	,	,	PUNCT
cana-826	21	3	section	section	NOUN
cana-826	21	4	4	4	NUM
cana-826	21	5	outlines	outline	VERB
cana-826	21	6	the	the	DET
cana-826	21	7	implementation	implementation	NOUN
cana-826	21	8	of	of	ADP
cana-826	21	9	ifthg	ifthg	NOUN
cana-826	21	10	for	for	ADP
cana-826	21	11	fugitive	fugitive	ADJ
cana-826	21	12	determination	determination	NOUN
cana-826	21	13	,	,	PUNCT
cana-826	21	14	offering	offer	VERB
cana-826	21	15	a	a	DET
cana-826	21	16	discussion	discussion	NOUN
cana-826	21	17	on	on	ADP
cana-826	21	18	simulation	simulation	NOUN
cana-826	21	19	results	result	NOUN
cana-826	21	20	and	and	CCONJ
cana-826	21	21	examples	example	NOUN
cana-826	21	22	.	.	PUNCT
cana-826	22	1	mailto:mathsmyth@gmail.com	mailto:mathsmyth@gmail.com	X
cana-826	23	1	mailto:c.nandhini@vcw.ac.in	mailto:c.nandhini@vcw.ac.in	PART
cana-826	23	2	communications	communication	NOUN
cana-826	23	3	on	on	ADP
cana-826	23	4	applied	apply	VERB
cana-826	23	5	nonlinear	nonlinear	ADJ
cana-826	23	6	analysis	analysis	NOUN
cana-826	23	7	issn	issn	NOUN
cana-826	23	8	:	:	PUNCT
cana-826	23	9	1074	1074	NUM
cana-826	23	10	-	-	PUNCT
cana-826	23	11	133x	133x	NUM
cana-826	23	12	vol	vol	NOUN
cana-826	23	13	31	31	NUM
cana-826	23	14	no	no	NOUN
cana-826	23	15	.	.	PUNCT
cana-826	24	1	4s	4s	NUM
cana-826	24	2	(	(	PUNCT
cana-826	24	3	2024	2024	NUM
cana-826	24	4	)	)	PUNCT
cana-826	24	5	10	10	NUM
cana-826	24	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-826	24	7	2	2	NUM
cana-826	24	8	.	.	PUNCT
cana-826	24	9	preliminaries	preliminary	NOUN
cana-826	24	10	in	in	ADP
cana-826	24	11	this	this	DET
cana-826	24	12	section	section	NOUN
cana-826	24	13	,	,	PUNCT
cana-826	24	14	we	we	PRON
cana-826	24	15	go	go	VERB
cana-826	24	16	through	through	ADP
cana-826	24	17	certain	certain	ADJ
cana-826	24	18	important	important	ADJ
cana-826	24	19	concepts	concept	NOUN
cana-826	24	20	that	that	PRON
cana-826	24	21	related	relate	VERB
cana-826	24	22	to	to	ADP
cana-826	24	23	our	our	PRON
cana-826	24	24	main	main	ADJ
cana-826	24	25	concept	concept	NOUN
cana-826	24	26	.	.	PUNCT
cana-826	25	1	definition	definition	NOUN
cana-826	25	2	2.1	2.1	NUM
cana-826	25	3	.	.	PUNCT
cana-826	26	1	[	[	X
cana-826	26	2	3	3	X
cana-826	26	3	]	]	PUNCT
cana-826	26	4	let	let	VERB
cana-826	26	5	a	a	DET
cana-826	26	6	set	set	NOUN
cana-826	26	7	𝐸	𝐸	PROPN
cana-826	26	8	be	be	AUX
cana-826	26	9	fixed	fix	VERB
cana-826	26	10	.	.	PUNCT
cana-826	27	1	an	an	DET
cana-826	27	2	intuitionistic	intuitionistic	ADJ
cana-826	27	3	fuzzy	fuzzy	ADJ
cana-826	27	4	set	set	NOUN
cana-826	27	5	(	(	PUNCT
cana-826	27	6	ifs	ifs	PROPN
cana-826	27	7	)	)	PUNCT
cana-826	27	8	𝑈	𝑈	PROPN
cana-826	27	9	in	in	ADP
cana-826	27	10	𝐸	𝐸	PROPN
cana-826	27	11	is	be	AUX
cana-826	27	12	an	an	DET
cana-826	27	13	object	object	NOUN
cana-826	27	14	of	of	ADP
cana-826	27	15	the	the	DET
cana-826	27	16	form	form	NOUN
cana-826	27	17	𝑈	𝑈	NOUN
cana-826	27	18	=	=	PUNCT
cana-826	27	19	{	{	PUNCT
cana-826	27	20	<	<	X
cana-826	27	21	𝑢𝑖	𝑢𝑖	PROPN
cana-826	27	22	,	,	PUNCT
cana-826	27	23	𝜇𝑖(𝑢𝑖	𝜇𝑖(𝑢𝑖	PROPN
cana-826	27	24	)	)	PUNCT
cana-826	27	25	,	,	PUNCT
cana-826	27	26	𝜈𝑖(𝑢𝑖	𝜈𝑖(𝑢𝑖	PROPN
cana-826	27	27	)	)	PUNCT
cana-826	27	28	>	>	X
cana-826	28	1	|𝑢𝑖	|𝑢𝑖	NUM
cana-826	28	2	∈	∈	PROPN
cana-826	28	3	𝐸	𝐸	PROPN
cana-826	28	4	}	}	PUNCT
cana-826	28	5	,	,	PUNCT
cana-826	28	6	where	where	SCONJ
cana-826	28	7	the	the	DET
cana-826	28	8	function	function	NOUN
cana-826	28	9	𝜇𝑖	𝜇𝑖	ADP
cana-826	28	10	:	:	PUNCT
cana-826	28	11	𝐸	𝐸	PROPN
cana-826	28	12	→	→	SYM
cana-826	28	13	[	[	X
cana-826	28	14	0,1	0,1	NUM
cana-826	28	15	]	]	PUNCT
cana-826	28	16	and	and	CCONJ
cana-826	28	17	𝜈𝑖	𝜈𝑖	ADP
cana-826	28	18	:	:	PUNCT
cana-826	28	19	𝐸	𝐸	PROPN
cana-826	28	20	→	→	SYM
cana-826	28	21	[	[	X
cana-826	28	22	0,1	0,1	NUM
cana-826	28	23	]	]	PUNCT
cana-826	28	24	determine	determine	VERB
cana-826	28	25	the	the	DET
cana-826	28	26	degree	degree	NOUN
cana-826	28	27	of	of	ADP
cana-826	28	28	membership	membership	NOUN
cana-826	28	29	&	&	CCONJ
cana-826	28	30	the	the	DET
cana-826	28	31	degree	degree	NOUN
cana-826	28	32	of	of	ADP
cana-826	28	33	non	non	ADJ
cana-826	28	34	-	-	NOUN
cana-826	28	35	membership	membership	NOUN
cana-826	28	36	of	of	ADP
cana-826	28	37	the	the	DET
cana-826	28	38	element	element	NOUN
cana-826	28	39	𝑢𝑖	𝑢𝑖	PRON
cana-826	28	40	∈	∈	PROPN
cana-826	28	41	𝐸	𝐸	PROPN
cana-826	28	42	,	,	PUNCT
cana-826	28	43	respectively	respectively	ADV
cana-826	28	44	and	and	CCONJ
cana-826	28	45	for	for	ADP
cana-826	28	46	every	every	DET
cana-826	28	47	𝑢𝑖	𝑢𝑖	PRON
cana-826	28	48	∈	∈	PROPN
cana-826	28	49	𝐸	𝐸	PROPN
cana-826	28	50	,	,	PUNCT
cana-826	28	51	0	0	NUM
cana-826	28	52	≤	≤	NUM
cana-826	28	53	𝜇𝑖(𝑢𝑖	𝜇𝑖(𝑢𝑖	PROPN
cana-826	28	54	)	)	PUNCT
cana-826	28	55	+	+	NUM
cana-826	28	56	𝜈𝑖(𝑢𝑖	𝜈𝑖(𝑢𝑖	NOUN
cana-826	28	57	)	)	PUNCT
cana-826	28	58	≤	≤	NUM
cana-826	28	59	1	1	NUM
cana-826	28	60	.	.	PUNCT
cana-826	29	1	definition	definition	NOUN
cana-826	29	2	2.2	2.2	NUM
cana-826	29	3	.	.	PUNCT
cana-826	30	1	[	[	X
cana-826	30	2	3	3	X
cana-826	30	3	]	]	PUNCT
cana-826	30	4	let	let	VERB
cana-826	30	5	𝐸	𝐸	PRON
cana-826	30	6	be	be	AUX
cana-826	30	7	the	the	DET
cana-826	30	8	fixed	fix	VERB
cana-826	30	9	set	set	NOUN
cana-826	30	10	and	and	CCONJ
cana-826	30	11	𝑈	𝑈	PROPN
cana-826	30	12	=	=	PUNCT
cana-826	30	13	{	{	PUNCT
cana-826	30	14	<	<	X
cana-826	30	15	𝑢𝑖	𝑢𝑖	INTJ
cana-826	30	16	,	,	PUNCT
cana-826	30	17	𝜇𝑖(𝑢𝑖	𝜇𝑖(𝑢𝑖	PROPN
cana-826	30	18	)	)	PUNCT
cana-826	30	19	,	,	PUNCT
cana-826	30	20	𝜈𝑖(𝑢𝑖	𝜈𝑖(𝑢𝑖	PROPN
cana-826	30	21	)	)	PUNCT
cana-826	30	22	>	>	X
cana-826	30	23	|𝑢𝑖	|𝑢𝑖	NUM
cana-826	30	24	∈	∈	PROPN
cana-826	30	25	𝐸	𝐸	PROPN
cana-826	30	26	}	}	PUNCT
cana-826	30	27	,	,	PUNCT
cana-826	30	28	be	be	AUX
cana-826	30	29	an	an	DET
cana-826	30	30	ifs	ifs	PROPN
cana-826	30	31	.	.	PUNCT
cana-826	31	1	six	six	NUM
cana-826	31	2	types	type	NOUN
cana-826	31	3	of	of	ADP
cana-826	31	4	cartesian	cartesian	ADJ
cana-826	31	5	products	product	NOUN
cana-826	31	6	of	of	ADP
cana-826	31	7	𝑛	𝑛	DET
cana-826	31	8	subsets	subset	NOUN
cana-826	31	9	(	(	PUNCT
cana-826	31	10	crisp	crisp	ADJ
cana-826	31	11	sets	set	NOUN
cana-826	31	12	)	)	PUNCT
cana-826	31	13	𝑈1	𝑈1	PROPN
cana-826	31	14	,	,	PUNCT
cana-826	31	15	𝑈2	𝑈2	PROPN
cana-826	31	16	,	,	PUNCT
cana-826	31	17	…	…	PUNCT
cana-826	31	18	,	,	PUNCT
cana-826	31	19	𝑈𝑛	𝑈𝑛	PROPN
cana-826	31	20	of	of	ADP
cana-826	31	21	𝑈	𝑈	PROPN
cana-826	31	22	over	over	ADP
cana-826	31	23	𝐸	𝐸	PROPN
cana-826	31	24	are	be	AUX
cana-826	31	25	defined	define	VERB
cana-826	31	26	as	as	SCONJ
cana-826	31	27	follows	follow	VERB
cana-826	31	28	𝑈𝑖1	𝑈𝑖1	PROPN
cana-826	31	29	×1	×1	PROPN
cana-826	31	30	𝑈𝑖2	𝑈𝑖2	NOUN
cana-826	31	31	×1	×1	NOUN
cana-826	31	32	𝑈𝑖3	𝑈𝑖3	NOUN
cana-826	31	33	×1	×1	NOUN
cana-826	31	34	…	…	PUNCT
cana-826	31	35	×1	×1	NOUN
cana-826	31	36	𝑈𝑖𝑛	𝑈𝑖𝑛	PROPN
cana-826	31	37	=	=	SYM
cana-826	31	38	{	{	PUNCT
cana-826	31	39	〈	〈	PROPN
cana-826	31	40	(	(	PUNCT
cana-826	31	41	𝑢1	𝑢1	PROPN
cana-826	31	42	,	,	PUNCT
cana-826	31	43	𝑢2	𝑢2	PROPN
cana-826	31	44	,	,	PUNCT
cana-826	31	45	…	…	PUNCT
cana-826	31	46	,	,	PUNCT
cana-826	31	47	𝑢𝑛),∏𝜇𝑖	𝑢𝑛),∏𝜇𝑖	INTJ
cana-826	31	48	,	,	PUNCT
cana-826	31	49	𝑛	𝑛	PRON
cana-826	31	50	𝑖=1	𝑖=1	PROPN
cana-826	31	51	∏𝜈𝑖	∏𝜈𝑖	ADJ
cana-826	31	52	𝑛	𝑛	DET
cana-826	31	53	𝑖=1	𝑖=1	PROPN
cana-826	31	54	〉	〉	NOUN
cana-826	31	55	|𝑢1	|𝑢1	NOUN
cana-826	31	56	∈	∈	NOUN
cana-826	31	57	𝑈1	𝑈1	NOUN
cana-826	31	58	,	,	PUNCT
cana-826	31	59	𝑢2	𝑢2	PROPN
cana-826	31	60	∈	∈	PROPN
cana-826	31	61	𝑈2	𝑈2	PROPN
cana-826	31	62	,	,	PUNCT
cana-826	31	63	…	…	PUNCT
cana-826	31	64	,	,	PUNCT
cana-826	31	65	𝑢𝑛	𝑢𝑛	PROPN
cana-826	31	66	∈	∈	PROPN
cana-826	31	67	𝑈𝑛	𝑈𝑛	PROPN
cana-826	31	68	}	}	PUNCT
cana-826	31	69	𝑈𝑖1	𝑈𝑖1	NOUN
cana-826	31	70	×2	×2	PROPN
cana-826	31	71	𝑈𝑖2	𝑈𝑖2	VERB
cana-826	31	72	×2	×2	PROPN
cana-826	31	73	𝑈𝑖3	𝑈𝑖3	NOUN
cana-826	31	74	×2	×2	PROPN
cana-826	31	75	…	…	PUNCT
cana-826	31	76	×2	×2	PROPN
cana-826	31	77	𝑈𝑖𝑛	𝑈𝑖𝑛	PROPN
cana-826	31	78	=	=	SYM
cana-826	31	79	{	{	PUNCT
cana-826	31	80	〈	〈	PROPN
cana-826	31	81	(	(	PUNCT
cana-826	31	82	𝑢1	𝑢1	PROPN
cana-826	31	83	,	,	PUNCT
cana-826	31	84	𝑢2	𝑢2	PROPN
cana-826	31	85	,	,	PUNCT
cana-826	31	86	…	…	PUNCT
cana-826	31	87	,	,	PUNCT
cana-826	31	88	𝑢𝑛),∑𝜇𝑖	𝑢𝑛),∑𝜇𝑖	NOUN
cana-826	31	89	𝑛	𝑛	PRON
cana-826	31	90	𝑖=1	𝑖=1	PROPN
cana-826	31	91	−∑𝜇𝑖𝜇𝑗	−∑𝜇𝑖𝜇𝑗	PROPN
cana-826	31	92	+	+	CCONJ
cana-826	31	93	∑	∑	ADV
cana-826	31	94	𝜇𝑖𝜇𝑗𝜇𝑘	𝜇𝑖𝜇𝑗𝜇𝑘	ADJ
cana-826	31	95	𝑖≠𝑗≠𝑘	𝑖≠𝑗≠𝑘	X
cana-826	31	96	−⋯+	−⋯+	X
cana-826	31	97	(	(	PUNCT
cana-826	31	98	−1)𝑛−2	−1)𝑛−2	NOUN
cana-826	31	99	𝑖≠𝑗	𝑖≠𝑗	PUNCT
cana-826	31	100	∑	∑	PUNCT
cana-826	31	101	𝜇𝑖𝜇𝑗𝜇𝑘	𝜇𝑖𝜇𝑗𝜇𝑘	ADJ
cana-826	31	102	…	…	SYM
cana-826	31	103	𝜇𝑛	𝜇𝑛	NOUN
cana-826	31	104	𝑖≠𝑗≠𝑘	𝑖≠𝑗≠𝑘	NOUN
cana-826	31	105	…	…	PUNCT
cana-826	31	106	≠𝑛	≠𝑛	PRON
cana-826	31	107	+	+	CCONJ
cana-826	31	108	(	(	PUNCT
cana-826	31	109	−1)𝑛−1∏𝜇𝑖	−1)𝑛−1∏𝜇𝑖	NOUN
cana-826	31	110	,	,	PUNCT
cana-826	31	111	𝑛	𝑛	PRON
cana-826	31	112	𝑖=1	𝑖=1	PROPN
cana-826	31	113	∏𝜈𝑖	∏𝜈𝑖	ADJ
cana-826	31	114	𝑛	𝑛	DET
cana-826	31	115	𝑖=1	𝑖=1	PROPN
cana-826	31	116	〉	〉	NOUN
cana-826	31	117	|𝑢1	|𝑢1	NOUN
cana-826	31	118	∈	∈	NOUN
cana-826	31	119	𝑈1	𝑈1	NOUN
cana-826	31	120	,	,	PUNCT
cana-826	31	121	𝑢2	𝑢2	PROPN
cana-826	31	122	∈	∈	PROPN
cana-826	31	123	𝑈2	𝑈2	PROPN
cana-826	31	124	,	,	PUNCT
cana-826	31	125	…	…	PUNCT
cana-826	31	126	,	,	PUNCT
cana-826	31	127	𝑢𝑛	𝑢𝑛	PROPN
cana-826	31	128	∈	∈	PROPN
cana-826	31	129	𝑈𝑛	𝑈𝑛	PROPN
cana-826	31	130	}	}	PUNCT
cana-826	31	131	𝑈𝑖1	𝑈𝑖1	NOUN
cana-826	31	132	×3	×3	NOUN
cana-826	31	133	𝑈𝑖2	𝑈𝑖2	NOUN
cana-826	31	134	×3	×3	NOUN
cana-826	31	135	𝑈𝑖3	𝑈𝑖3	NOUN
cana-826	31	136	×3	×3	NOUN
cana-826	31	137	…	…	PUNCT
cana-826	31	138	×3	×3	NOUN
cana-826	31	139	𝑈𝑖𝑛	𝑈𝑖𝑛	PROPN
cana-826	31	140	=	=	SYM
cana-826	31	141	{	{	PUNCT
cana-826	31	142	〈	〈	PROPN
cana-826	31	143	(	(	PUNCT
cana-826	31	144	𝑢1	𝑢1	PROPN
cana-826	31	145	,	,	PUNCT
cana-826	31	146	𝑢2	𝑢2	PROPN
cana-826	31	147	,	,	PUNCT
cana-826	31	148	…	…	PUNCT
cana-826	31	149	,	,	PUNCT
cana-826	31	150	𝑢𝑛),∏𝜇𝑖	𝑢𝑛),∏𝜇𝑖	INTJ
cana-826	31	151	,	,	PUNCT
cana-826	31	152	𝑛	𝑛	PROPN
cana-826	31	153	𝑖=1	𝑖=1	PUNCT
cana-826	31	154	∑𝜈𝑖	∑𝜈𝑖	NOUN
cana-826	31	155	𝑛	𝑛	PRON
cana-826	31	156	𝑖=1	𝑖=1	PROPN
cana-826	31	157	−∑𝜈𝑖𝜈𝑗	−∑𝜈𝑖𝜈𝑗	PROPN
cana-826	31	158	+	+	CCONJ
cana-826	31	159	∑	∑	PROPN
cana-826	31	160	𝜈𝑖𝜈𝑗𝜈𝑘	𝜈𝑖𝜈𝑗𝜈𝑘	NOUN
cana-826	31	161	𝑖≠𝑗≠𝑘	𝑖≠𝑗≠𝑘	PROPN
cana-826	31	162	−⋯+	−⋯+	PROPN
cana-826	31	163	(	(	PUNCT
cana-826	31	164	−1)𝑛−2	−1)𝑛−2	NOUN
cana-826	31	165	𝑖≠𝑗	𝑖≠𝑗	PUNCT
cana-826	31	166	∑	∑	PROPN
cana-826	31	167	𝜈𝑖𝜈𝑗𝜈𝑘	𝜈𝑖𝜈𝑗𝜈𝑘	PROPN
cana-826	31	168	…	…	PUNCT
cana-826	31	169	𝜈𝑛	𝜈𝑛	ADP
cana-826	31	170	𝑖≠𝑗≠𝑘	𝑖≠𝑗≠𝑘	NOUN
cana-826	31	171	…	…	PUNCT
cana-826	31	172	≠𝑛	≠𝑛	PRON
cana-826	31	173	+	+	CCONJ
cana-826	31	174	(	(	PUNCT
cana-826	31	175	−1)𝑛−1∏𝜈𝑖	−1)𝑛−1∏𝜈𝑖	ADJ
cana-826	31	176	𝑛	𝑛	DET
cana-826	31	177	𝑖=1	𝑖=1	PROPN
cana-826	31	178	〉	〉	NOUN
cana-826	31	179	|𝑢1	|𝑢1	NOUN
cana-826	31	180	∈	∈	NOUN
cana-826	31	181	𝑈1	𝑈1	NOUN
cana-826	31	182	,	,	PUNCT
cana-826	31	183	𝑢2	𝑢2	PROPN
cana-826	31	184	∈	∈	PROPN
cana-826	31	185	𝑈2	𝑈2	PROPN
cana-826	31	186	,	,	PUNCT
cana-826	31	187	…	…	PUNCT
cana-826	31	188	,	,	PUNCT
cana-826	31	189	𝑢𝑛	𝑢𝑛	PROPN
cana-826	31	190	∈	∈	PROPN
cana-826	31	191	𝑈𝑛	𝑈𝑛	PROPN
cana-826	31	192	}	}	PUNCT
cana-826	31	193	𝑈𝑖1	𝑈𝑖1	NOUN
cana-826	31	194	×4	×4	NOUN
cana-826	31	195	𝑈𝑖2	𝑈𝑖2	VERB
cana-826	31	196	×4	×4	NOUN
cana-826	31	197	𝑈𝑖3	𝑈𝑖3	VERB
cana-826	31	198	×4	×4	NOUN
cana-826	31	199	…	…	PUNCT
cana-826	31	200	×4	×4	NOUN
cana-826	31	201	𝑈𝑖𝑛	𝑈𝑖𝑛	PROPN
cana-826	31	202	=	=	SYM
cana-826	31	203	{	{	PUNCT
cana-826	31	204	〈	〈	PROPN
cana-826	31	205	(	(	PUNCT
cana-826	31	206	𝑢1	𝑢1	PROPN
cana-826	31	207	,	,	PUNCT
cana-826	31	208	𝑢2	𝑢2	PROPN
cana-826	31	209	,	,	PUNCT
cana-826	31	210	…	…	PUNCT
cana-826	31	211	,	,	PUNCT
cana-826	31	212	𝑢𝑛),𝑚𝑖	𝑢𝑛),𝑚𝑖	PROPN
cana-826	31	213	𝑛(𝜇1	𝑛(𝜇1	NOUN
cana-826	31	214	,	,	PUNCT
cana-826	31	215	𝜇2	𝜇2	NOUN
cana-826	31	216	,	,	PUNCT
cana-826	31	217	…	…	PUNCT
cana-826	31	218	,	,	PUNCT
cana-826	31	219	𝜇𝑛	𝜇𝑛	NOUN
cana-826	31	220	)	)	PUNCT
cana-826	31	221	,	,	PUNCT
cana-826	31	222	𝑚𝑎𝑥⁡(𝜈1	𝑚𝑎𝑥⁡(𝜈1	NOUN
cana-826	31	223	,	,	PUNCT
cana-826	31	224	𝜈2	𝜈2	NOUN
cana-826	31	225	,	,	PUNCT
cana-826	31	226	…	…	PUNCT
cana-826	31	227	,	,	PUNCT
cana-826	31	228	𝜈𝑛)〉|𝑢1	𝜈𝑛)〉|𝑢1	PRON
cana-826	31	229	∈	∈	PROPN
cana-826	31	230	𝑈1	𝑈1	NOUN
cana-826	31	231	,	,	PUNCT
cana-826	31	232	𝑢2	𝑢2	PROPN
cana-826	31	233	∈	∈	PROPN
cana-826	31	234	𝑈2	𝑈2	PROPN
cana-826	31	235	,	,	PUNCT
cana-826	31	236	…	…	PUNCT
cana-826	31	237	,	,	PUNCT
cana-826	31	238	𝑢𝑛	𝑢𝑛	PROPN
cana-826	31	239	∈	∈	PROPN
cana-826	31	240	𝑈𝑛	𝑈𝑛	PROPN
cana-826	31	241	}	}	PUNCT
cana-826	31	242	𝑈𝑖1	𝑈𝑖1	NOUN
cana-826	31	243	×5	×5	NOUN
cana-826	31	244	𝑈𝑖2	𝑈𝑖2	NOUN
cana-826	31	245	×5	×5	NOUN
cana-826	31	246	𝑈𝑖3	𝑈𝑖3	ADJ
cana-826	31	247	×5	×5	NOUN
cana-826	31	248	…	…	PUNCT
cana-826	31	249	×5	×5	NOUN
cana-826	31	250	𝑈𝑖𝑛	𝑈𝑖𝑛	PROPN
cana-826	31	251	=	=	SYM
cana-826	31	252	{	{	PUNCT
cana-826	31	253	〈	〈	PROPN
cana-826	31	254	(	(	PUNCT
cana-826	31	255	𝑢1	𝑢1	PROPN
cana-826	31	256	,	,	PUNCT
cana-826	31	257	𝑢2	𝑢2	PROPN
cana-826	31	258	,	,	PUNCT
cana-826	31	259	…	…	PUNCT
cana-826	31	260	,	,	PUNCT
cana-826	31	261	𝑢𝑛),𝑚𝑎𝑥(𝜇1	𝑢𝑛),𝑚𝑎𝑥(𝜇1	PROPN
cana-826	31	262	,	,	PUNCT
cana-826	31	263	𝜇2	𝜇2	PROPN
cana-826	31	264	,	,	PUNCT
cana-826	31	265	…	…	PUNCT
cana-826	31	266	,	,	PUNCT
cana-826	31	267	𝜇𝑛	𝜇𝑛	NOUN
cana-826	31	268	)	)	PUNCT
cana-826	31	269	,	,	PUNCT
cana-826	31	270	min(𝜈1	min(𝜈1	PROPN
cana-826	31	271	,	,	PUNCT
cana-826	31	272	𝜈2	𝜈2	NOUN
cana-826	31	273	,	,	PUNCT
cana-826	31	274	…	…	PUNCT
cana-826	31	275	,	,	PUNCT
cana-826	31	276	𝜈𝑛)〉|𝑢1	𝜈𝑛)〉|𝑢1	PRON
cana-826	31	277	∈	∈	PROPN
cana-826	31	278	𝑈1	𝑈1	NOUN
cana-826	31	279	,	,	PUNCT
cana-826	31	280	𝑢2	𝑢2	PROPN
cana-826	31	281	∈	∈	PROPN
cana-826	31	282	𝑈2	𝑈2	PROPN
cana-826	31	283	,	,	PUNCT
cana-826	31	284	…	…	PUNCT
cana-826	31	285	,	,	PUNCT
cana-826	31	286	𝑢𝑛	𝑢𝑛	PROPN
cana-826	31	287	∈	∈	PROPN
cana-826	31	288	𝑈𝑛	𝑈𝑛	PROPN
cana-826	31	289	}	}	PUNCT
cana-826	31	290	communications	communication	NOUN
cana-826	31	291	on	on	ADP
cana-826	31	292	applied	apply	VERB
cana-826	31	293	nonlinear	nonlinear	ADJ
cana-826	31	294	analysis	analysis	NOUN
cana-826	31	295	issn	issn	NOUN
cana-826	31	296	:	:	PUNCT
cana-826	31	297	1074	1074	NUM
cana-826	31	298	-	-	PUNCT
cana-826	31	299	133x	133x	NUM
cana-826	31	300	vol	vol	NOUN
cana-826	31	301	31	31	NUM
cana-826	31	302	no	no	NOUN
cana-826	31	303	.	.	PUNCT
cana-826	32	1	4s	4s	NUM
cana-826	32	2	(	(	PUNCT
cana-826	32	3	2024	2024	NUM
cana-826	32	4	)	)	PUNCT
cana-826	32	5	11	11	NUM
cana-826	33	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-826	33	2	𝑈𝑖1	𝑈𝑖1	NOUN
cana-826	33	3	×6	×6	PROPN
cana-826	33	4	𝑈𝑖2	𝑈𝑖2	ADJ
cana-826	33	5	×6	×6	ADJ
cana-826	33	6	𝑈𝑖3	𝑈𝑖3	ADJ
cana-826	33	7	×6	×6	ADJ
cana-826	33	8	…	…	SYM
cana-826	33	9	×6	×6	ADJ
cana-826	33	10	𝑈𝑖𝑛	𝑈𝑖𝑛	PROPN
cana-826	33	11	=	=	SYM
cana-826	33	12	{	{	PUNCT
cana-826	33	13	〈	〈	PROPN
cana-826	33	14	(	(	PUNCT
cana-826	33	15	𝑢1	𝑢1	PROPN
cana-826	33	16	,	,	PUNCT
cana-826	33	17	𝑢2	𝑢2	PROPN
cana-826	33	18	,	,	PUNCT
cana-826	33	19	…	…	PUNCT
cana-826	33	20	,	,	PUNCT
cana-826	33	21	𝑢𝑛	𝑢𝑛	NOUN
cana-826	33	22	)	)	PUNCT
cana-826	33	23	,	,	PUNCT
cana-826	33	24	∑	∑	PROPN
cana-826	33	25	𝜇𝑖	𝜇𝑖	ADP
cana-826	33	26	𝑛	𝑛	PRON
cana-826	33	27	𝑖=1	𝑖=1	PROPN
cana-826	33	28	𝑛	𝑛	PROPN
cana-826	33	29	,	,	PUNCT
cana-826	33	30	∑	∑	PUNCT
cana-826	33	31	𝜈𝑖	𝜈𝑖	ADP
cana-826	33	32	𝑛	𝑛	PRON
cana-826	33	33	𝑖=1	𝑖=1	PUNCT
cana-826	33	34	𝑛	𝑛	VERB
cana-826	33	35	〉	〉	NOUN
cana-826	33	36	|𝑢1	|𝑢1	NOUN
cana-826	33	37	∈	∈	NOUN
cana-826	33	38	𝑈1	𝑈1	NOUN
cana-826	33	39	,	,	PUNCT
cana-826	33	40	𝑢2	𝑢2	PROPN
cana-826	33	41	∈	∈	PROPN
cana-826	33	42	𝑈2	𝑈2	PROPN
cana-826	33	43	,	,	PUNCT
cana-826	33	44	…	…	PUNCT
cana-826	33	45	,	,	PUNCT
cana-826	33	46	𝑢𝑛	𝑢𝑛	PROPN
cana-826	33	47	∈	∈	PROPN
cana-826	33	48	𝑈𝑛	𝑈𝑛	PROPN
cana-826	33	49	}	}	PUNCT
cana-826	33	50	it	it	PRON
cana-826	33	51	must	must	AUX
cana-826	33	52	be	be	AUX
cana-826	33	53	noted	note	VERB
cana-826	33	54	that	that	SCONJ
cana-826	33	55	𝑢𝑖	𝑢𝑖	NOUN
cana-826	33	56	×𝑠	×𝑠	ADP
cana-826	33	57	𝑢𝑗	𝑢𝑗	NOUN
cana-826	33	58	is	be	AUX
cana-826	33	59	an	an	DET
cana-826	33	60	ifs	ifs	PROPN
cana-826	33	61	,	,	PUNCT
cana-826	33	62	where	where	SCONJ
cana-826	33	63	𝑠	𝑠	PROPN
cana-826	33	64	=	=	SYM
cana-826	33	65	1,2,3,4,5,6	1,2,3,4,5,6	NUM
cana-826	33	66	.	.	PUNCT
cana-826	34	1	definition	definition	NOUN
cana-826	34	2	2.3	2.3	NUM
cana-826	34	3	.	.	PUNCT
cana-826	35	1	[	[	X
cana-826	35	2	9	9	NUM
cana-826	35	3	]	]	PUNCT
cana-826	35	4	an	an	DET
cana-826	35	5	intuitionistic	intuitionistic	ADJ
cana-826	35	6	fuzzy	fuzzy	ADJ
cana-826	35	7	graph	graph	NOUN
cana-826	35	8	(	(	PUNCT
cana-826	35	9	ifg	ifg	PROPN
cana-826	35	10	)	)	PUNCT
cana-826	35	11	is	be	AUX
cana-826	35	12	of	of	ADP
cana-826	35	13	the	the	DET
cana-826	35	14	form	form	NOUN
cana-826	35	15	𝐺	𝐺	NOUN
cana-826	35	16	=	=	SYM
cana-826	35	17	(	(	PUNCT
cana-826	35	18	𝑈	𝑈	PROPN
cana-826	35	19	,	,	PUNCT
cana-826	35	20	𝐸	𝐸	PROPN
cana-826	35	21	)	)	PUNCT
cana-826	35	22	,	,	PUNCT
cana-826	35	23	where	where	SCONJ
cana-826	35	24	(	(	PUNCT
cana-826	35	25	i	i	NOUN
cana-826	35	26	)	)	PUNCT
cana-826	35	27	𝑈	𝑈	NOUN
cana-826	35	28	=	=	SYM
cana-826	35	29	{	{	PUNCT
cana-826	35	30	𝑢1	𝑢1	PROPN
cana-826	35	31	,	,	PUNCT
cana-826	35	32	𝑢2	𝑢2	PROPN
cana-826	35	33	,	,	PUNCT
cana-826	35	34	…	…	PUNCT
cana-826	35	35	,	,	PUNCT
cana-826	35	36	𝑢𝑛	𝑢𝑛	X
cana-826	35	37	}	}	PUNCT
cana-826	35	38	such	such	ADJ
cana-826	35	39	that	that	SCONJ
cana-826	35	40	𝜇𝑖	𝜇𝑖	ADP
cana-826	35	41	:	:	PUNCT
cana-826	35	42	𝑈	𝑈	PROPN
cana-826	35	43	→	→	SYM
cana-826	35	44	[	[	X
cana-826	35	45	0,1	0,1	NUM
cana-826	35	46	]	]	PUNCT
cana-826	35	47	and	and	CCONJ
cana-826	35	48	𝜈𝑖	𝜈𝑖	ADP
cana-826	35	49	:	:	PUNCT
cana-826	35	50	𝑈	𝑈	PROPN
cana-826	35	51	→	→	SYM
cana-826	35	52	[	[	X
cana-826	35	53	0,1	0,1	NUM
cana-826	35	54	]	]	PUNCT
cana-826	35	55	denote	denote	VERB
cana-826	35	56	the	the	DET
cana-826	35	57	degrees	degree	NOUN
cana-826	35	58	of	of	ADP
cana-826	35	59	membership	membership	NOUN
cana-826	35	60	&	&	CCONJ
cana-826	35	61	non	non	NOUN
cana-826	35	62	-	-	NOUN
cana-826	35	63	membership	membership	NOUN
cana-826	35	64	of	of	ADP
cana-826	35	65	the	the	DET
cana-826	35	66	element	element	NOUN
cana-826	35	67	𝑢𝑖	𝑢𝑖	ADP
cana-826	35	68	∈	∈	PROPN
cana-826	35	69	𝑈	𝑈	PROPN
cana-826	35	70	respectively	respectively	ADV
cana-826	35	71	and	and	CCONJ
cana-826	35	72	0	0	NUM
cana-826	35	73	≤	≤	NOUN
cana-826	35	74	𝜇𝑖(𝑢𝑖	𝜇𝑖(𝑢𝑖	PROPN
cana-826	35	75	)	)	PUNCT
cana-826	35	76	+	+	NUM
cana-826	35	77	𝜈𝑖(𝑢𝑖	𝜈𝑖(𝑢𝑖	NOUN
cana-826	35	78	)	)	PUNCT
cana-826	35	79	≤	≤	NUM
cana-826	35	80	1	1	NUM
cana-826	35	81	for	for	ADP
cana-826	35	82	every	every	DET
cana-826	35	83	𝑢𝑖	𝑢𝑖	PRON
cana-826	35	84	∈	∈	PROPN
cana-826	35	85	𝑈	𝑈	PROPN
cana-826	35	86	,	,	PUNCT
cana-826	35	87	𝑖	𝑖	NOUN
cana-826	35	88	=	=	SYM
cana-826	35	89	1,2	1,2	NUM
cana-826	35	90	,	,	PUNCT
cana-826	35	91	…	…	PUNCT
cana-826	35	92	,	,	PUNCT
cana-826	35	93	𝑛.	𝑛.	NOUN
cana-826	35	94	(	(	PUNCT
cana-826	35	95	ii	ii	NOUN
cana-826	35	96	)	)	PUNCT
cana-826	35	97	𝐸	𝐸	PROPN
cana-826	35	98	⊆	⊆	NUM
cana-826	35	99	𝑈×𝑈	𝑈×𝑈	NOUN
cana-826	35	100	where	where	SCONJ
cana-826	35	101	𝜇𝑖𝑗	𝜇𝑖𝑗	NOUN
cana-826	35	102	:	:	PUNCT
cana-826	35	103	𝑈	𝑈	PROPN
cana-826	35	104	×	×	NOUN
cana-826	35	105	𝑈	𝑈	PROPN
cana-826	35	106	→	→	SYM
cana-826	35	107	[	[	X
cana-826	35	108	0,1	0,1	NUM
cana-826	35	109	]	]	PUNCT
cana-826	35	110	and	and	CCONJ
cana-826	35	111	𝜈𝑖𝑗	𝜈𝑖𝑗	NOUN
cana-826	35	112	:	:	PUNCT
cana-826	35	113	𝑈	𝑈	PROPN
cana-826	35	114	×	×	PROPN
cana-826	35	115	𝑈	𝑈	PROPN
cana-826	35	116	→	→	SYM
cana-826	35	117	[	[	X
cana-826	35	118	0,1	0,1	NUM
cana-826	35	119	]	]	PUNCT
cana-826	35	120	are	be	AUX
cana-826	35	121	such	such	ADJ
cana-826	35	122	that	that	DET
cana-826	35	123	𝜇𝑖𝑗	𝜇𝑖𝑗	NOUN
cana-826	35	124	≤	≤	ADV
cana-826	35	125	𝜇𝑖	𝜇𝑖	ADP
cana-826	35	126	∧	∧	PROPN
cana-826	35	127	𝜇𝑗	𝜇𝑗	PROPN
cana-826	35	128	,	,	PUNCT
cana-826	35	129	𝜈𝑖𝑗	𝜈𝑖𝑗	X
cana-826	35	130	≤	≤	NUM
cana-826	35	131	𝜈𝑖	𝜈𝑖	ADP
cana-826	35	132	∨	∨	NUM
cana-826	35	133	𝜈𝑗	𝜈𝑗	PROPN
cana-826	35	134	and	and	CCONJ
cana-826	35	135	0	0	NUM
cana-826	35	136	≤	≤	NOUN
cana-826	35	137	𝜇𝑖(𝑢𝑖	𝜇𝑖(𝑢𝑖	PROPN
cana-826	35	138	)	)	PUNCT
cana-826	36	1	+	+	NUM
cana-826	36	2	𝜈𝑖(𝑢𝑖	𝜈𝑖(𝑢𝑖	NOUN
cana-826	36	3	)	)	PUNCT
cana-826	36	4	≤	≤	NUM
cana-826	36	5	1	1	NUM
cana-826	36	6	,	,	PUNCT
cana-826	36	7	where	where	SCONJ
cana-826	36	8	𝜇𝑖𝑗	𝜇𝑖𝑗	NOUN
cana-826	36	9	and	and	CCONJ
cana-826	36	10	𝜈𝑖𝑗	𝜈𝑖𝑗	NOUN
cana-826	36	11	are	be	AUX
cana-826	36	12	the	the	DET
cana-826	36	13	membership	membership	NOUN
cana-826	36	14	&	&	CCONJ
cana-826	36	15	non	non	ADJ
cana-826	36	16	-	-	ADJ
cana-826	36	17	membership	membership	ADJ
cana-826	36	18	values	value	NOUN
cana-826	36	19	of	of	ADP
cana-826	36	20	the	the	DET
cana-826	36	21	edge	edge	NOUN
cana-826	36	22	(	(	PUNCT
cana-826	36	23	𝜈𝑖	𝜈𝑖	ADP
cana-826	36	24	,	,	PUNCT
cana-826	36	25	𝜈𝑗	𝜈𝑗	PROPN
cana-826	36	26	)	)	PUNCT
cana-826	36	27	;	;	PUNCT
cana-826	36	28	the	the	DET
cana-826	36	29	values	value	NOUN
cana-826	36	30	of	of	ADP
cana-826	36	31	𝜇𝑖	𝜇𝑖	ADP
cana-826	36	32	∧	∧	PROPN
cana-826	36	33	𝜇𝑗	𝜇𝑗	NOUN
cana-826	36	34	and	and	CCONJ
cana-826	36	35	𝜈𝑖	𝜈𝑖	ADP
cana-826	36	36	∨	∨	NUM
cana-826	36	37	𝜈𝑗	𝜈𝑗	PROPN
cana-826	36	38	can	can	AUX
cana-826	36	39	be	be	AUX
cana-826	36	40	determined	determine	VERB
cana-826	36	41	by	by	ADP
cana-826	36	42	any	any	DET
cana-826	36	43	one	one	NUM
cana-826	36	44	of	of	ADP
cana-826	36	45	the	the	DET
cana-826	36	46	cartesian	cartesian	ADJ
cana-826	36	47	products	product	NOUN
cana-826	36	48	×𝑠	×𝑠	ADP
cana-826	36	49	where	where	SCONJ
cana-826	36	50	𝑠	𝑠	PROPN
cana-826	36	51	=	=	SYM
cana-826	36	52	1,2,3,4,5,6	1,2,3,4,5,6	NUM
cana-826	36	53	,	,	PUNCT
cana-826	36	54	∀⁡𝑖⁡&⁡𝑗	∀⁡𝑖⁡&⁡𝑗	PROPN
cana-826	36	55	given	give	VERB
cana-826	36	56	in	in	ADP
cana-826	36	57	definition	definition	NOUN
cana-826	36	58	2.2	2.2	NUM
cana-826	36	59	.	.	PUNCT
cana-826	37	1	note	note	NOUN
cana-826	37	2	:	:	PUNCT
cana-826	37	3	throughout	throughout	ADP
cana-826	37	4	this	this	DET
cana-826	37	5	paper	paper	NOUN
cana-826	37	6	,	,	PUNCT
cana-826	37	7	it	it	PRON
cana-826	37	8	is	be	AUX
cana-826	37	9	assumed	assume	VERB
cana-826	37	10	that	that	SCONJ
cana-826	37	11	the	the	DET
cana-826	37	12	fourth	fourth	ADJ
cana-826	37	13	cartesian	cartesian	ADJ
cana-826	37	14	product	product	NOUN
cana-826	37	15	𝑈𝑖1	𝑈𝑖1	VERB
cana-826	37	16	×4	×4	NOUN
cana-826	37	17	𝑈𝑖2	𝑈𝑖2	VERB
cana-826	37	18	×4	×4	NOUN
cana-826	37	19	𝑈𝑖3	𝑈𝑖3	VERB
cana-826	37	20	×4	×4	NOUN
cana-826	37	21	…	…	PUNCT
cana-826	37	22	×4	×4	NOUN
cana-826	37	23	𝑈𝑖𝑛	𝑈𝑖𝑛	PROPN
cana-826	37	24	=	=	SYM
cana-826	37	25	{	{	PUNCT
cana-826	37	26	〈	〈	PROPN
cana-826	37	27	(	(	PUNCT
cana-826	37	28	𝑢1	𝑢1	PROPN
cana-826	37	29	,	,	PUNCT
cana-826	37	30	𝑢2	𝑢2	PROPN
cana-826	37	31	,	,	PUNCT
cana-826	37	32	…	…	PUNCT
cana-826	37	33	,	,	PUNCT
cana-826	37	34	𝑢𝑛	𝑢𝑛	NOUN
cana-826	37	35	)	)	PUNCT
cana-826	37	36	,	,	PUNCT
cana-826	37	37	𝑚𝑖	𝑚𝑖	NOUN
cana-826	37	38	𝑛(𝜇1	𝑛(𝜇1	NOUN
cana-826	37	39	,	,	PUNCT
cana-826	37	40	𝜇2	𝜇2	NOUN
cana-826	37	41	,	,	PUNCT
cana-826	37	42	…	…	PUNCT
cana-826	37	43	,	,	PUNCT
cana-826	37	44	𝜇𝑛	𝜇𝑛	NOUN
cana-826	37	45	)	)	PUNCT
cana-826	37	46	,	,	PUNCT
cana-826	37	47	𝑚𝑎𝑥⁡(𝜈1	𝑚𝑎𝑥⁡(𝜈1	NOUN
cana-826	37	48	,	,	PUNCT
cana-826	37	49	𝜈2	𝜈2	NOUN
cana-826	37	50	,	,	PUNCT
cana-826	37	51	…	…	PUNCT
cana-826	37	52	,	,	PUNCT
cana-826	37	53	𝜈𝑛)〉|⁡𝑢1	𝜈𝑛)〉|⁡𝑢1	PROPN
cana-826	37	54	∈	∈	PROPN
cana-826	37	55	𝑈1	𝑈1	NOUN
cana-826	37	56	,	,	PUNCT
cana-826	37	57	𝑢2	𝑢2	PROPN
cana-826	37	58	∈	∈	PROPN
cana-826	37	59	𝑈2	𝑈2	PROPN
cana-826	37	60	,	,	PUNCT
cana-826	37	61	…	…	PUNCT
cana-826	37	62	,	,	PUNCT
cana-826	37	63	𝑢𝑛	𝑢𝑛	PROPN
cana-826	37	64	∈	∈	PROPN
cana-826	37	65	𝑈𝑛	𝑈𝑛	PROPN
cana-826	37	66	}	}	PUNCT
cana-826	37	67	,	,	PUNCT
cana-826	37	68	is	be	AUX
cana-826	37	69	used	use	VERB
cana-826	37	70	to	to	PART
cana-826	37	71	determine	determine	VERB
cana-826	37	72	the	the	DET
cana-826	37	73	edge	edge	NOUN
cana-826	37	74	membership	membership	NOUN
cana-826	37	75	𝜇𝑖𝑗	𝜇𝑖𝑗	NOUN
cana-826	37	76	and	and	CCONJ
cana-826	37	77	the	the	DET
cana-826	37	78	edge	edge	NOUN
cana-826	37	79	non	non	ADJ
cana-826	37	80	-	-	ADJ
cana-826	37	81	membership	membership	ADJ
cana-826	37	82	𝜈𝑖𝑗.	𝜈𝑖𝑗.	NOUN
cana-826	37	83	definition	definition	NOUN
cana-826	37	84	2.4	2.4	NUM
cana-826	37	85	.	.	PUNCT
cana-826	38	1	[	[	X
cana-826	38	2	10	10	NUM
cana-826	38	3	]	]	X
cana-826	38	4	an	an	DET
cana-826	38	5	intuitionistic	intuitionistic	ADJ
cana-826	38	6	fuzzy	fuzzy	ADJ
cana-826	38	7	hypergraph(ifhg	hypergraph(ifhg	NOUN
cana-826	38	8	)	)	PUNCT
cana-826	38	9	is	be	AUX
cana-826	38	10	an	an	DET
cana-826	38	11	ordered	order	VERB
cana-826	38	12	pair	pair	NOUN
cana-826	38	13	𝐻	𝐻	NOUN
cana-826	38	14	=	=	PUNCT
cana-826	38	15	(	(	PUNCT
cana-826	38	16	𝑈,𝐸	𝑈,𝐸	NOUN
cana-826	38	17	)	)	PUNCT
cana-826	38	18	where	where	SCONJ
cana-826	38	19	(	(	PUNCT
cana-826	38	20	i	i	NOUN
cana-826	38	21	)	)	PUNCT
cana-826	38	22	𝑈	𝑈	NOUN
cana-826	38	23	=	=	SYM
cana-826	38	24	{	{	PUNCT
cana-826	38	25	𝑢1	𝑢1	PROPN
cana-826	38	26	,	,	PUNCT
cana-826	38	27	𝑢2	𝑢2	PROPN
cana-826	38	28	,	,	PUNCT
cana-826	38	29	…	…	PUNCT
cana-826	38	30	,	,	PUNCT
cana-826	38	31	𝑢𝑛	𝑢𝑛	NOUN
cana-826	38	32	,	,	PUNCT
cana-826	38	33	}	}	PUNCT
cana-826	38	34	,	,	PUNCT
cana-826	38	35	is	be	AUX
cana-826	38	36	a	a	DET
cana-826	38	37	finite	finite	ADJ
cana-826	38	38	set	set	NOUN
cana-826	38	39	of	of	ADP
cana-826	38	40	if	if	SCONJ
cana-826	38	41	vertices	vertex	NOUN
cana-826	38	42	,	,	PUNCT
cana-826	38	43	(	(	PUNCT
cana-826	38	44	ii	ii	NOUN
cana-826	38	45	)	)	PUNCT
cana-826	38	46	𝐸	𝐸	PROPN
cana-826	38	47	=	=	SYM
cana-826	38	48	{	{	PUNCT
cana-826	38	49	𝐸1	𝐸1	NOUN
cana-826	38	50	,	,	PUNCT
cana-826	38	51	𝐸2	𝐸2	ADJ
cana-826	38	52	,	,	PUNCT
cana-826	38	53	…	…	PUNCT
cana-826	38	54	,	,	PUNCT
cana-826	38	55	𝐸𝑚	𝐸𝑚	PROPN
cana-826	38	56	}	}	PUNCT
cana-826	38	57	is	be	AUX
cana-826	38	58	a	a	DET
cana-826	38	59	family	family	NOUN
cana-826	38	60	of	of	ADP
cana-826	38	61	crisp	crisp	ADJ
cana-826	38	62	subsets	subset	NOUN
cana-826	38	63	of	of	ADP
cana-826	38	64	𝑈	𝑈	PROPN
cana-826	38	65	,	,	PUNCT
cana-826	38	66	(	(	PUNCT
cana-826	38	67	iii	iii	NOUN
cana-826	38	68	)	)	PUNCT
cana-826	38	69	𝐸𝑗	𝐸𝑗	PROPN
cana-826	38	70	=	=	PUNCT
cana-826	38	71	{	{	PUNCT
cana-826	38	72	𝑢𝑖	𝑢𝑖	NOUN
cana-826	38	73	,	,	PUNCT
cana-826	38	74	𝜇𝑗(𝑢𝑖	𝜇𝑗(𝑢𝑖	PROPN
cana-826	38	75	)	)	PUNCT
cana-826	38	76	,	,	PUNCT
cana-826	38	77	𝜈𝑗(𝑢𝑖)|0	𝜈𝑗(𝑢𝑖)|0	PROPN
cana-826	38	78	≤	≤	NUM
cana-826	38	79	𝜇𝑗(𝑢𝑖	𝜇𝑗(𝑢𝑖	PROPN
cana-826	38	80	)	)	PUNCT
cana-826	39	1	+	+	NUM
cana-826	39	2	𝜈𝑗(𝑢𝑖	𝜈𝑗(𝑢𝑖	NOUN
cana-826	39	3	)	)	PUNCT
cana-826	39	4	≤	≤	NUM
cana-826	39	5	1	1	NUM
cana-826	39	6	}	}	PUNCT
cana-826	39	7	,	,	PUNCT
cana-826	39	8	𝑗	𝑗	NOUN
cana-826	39	9	=	=	SYM
cana-826	39	10	1,2	1,2	NUM
cana-826	39	11	,	,	PUNCT
cana-826	39	12	…	…	PUNCT
cana-826	39	13	,	,	PUNCT
cana-826	39	14	𝑚	𝑚	X
cana-826	39	15	(	(	PUNCT
cana-826	39	16	iv	iv	X
cana-826	39	17	)	)	PUNCT
cana-826	39	18	𝐸𝑗	𝐸𝑗	PROPN
cana-826	39	19	≠	≠	PROPN
cana-826	39	20	∅	∅	NOUN
cana-826	39	21	,	,	PUNCT
cana-826	39	22	𝑗	𝑗	NOUN
cana-826	39	23	=	=	SYM
cana-826	39	24	1,2	1,2	NUM
cana-826	39	25	,	,	PUNCT
cana-826	39	26	…	…	PUNCT
cana-826	39	27	,	,	PUNCT
cana-826	39	28	𝑚	𝑚	X
cana-826	39	29	(	(	PUNCT
cana-826	39	30	v	v	NOUN
cana-826	39	31	)	)	PUNCT
cana-826	39	32	⋃	⋃	NOUN
cana-826	39	33	supp(𝐸𝑗	supp(𝐸𝑗	NUM
cana-826	39	34	)	)	PUNCT
cana-826	39	35	=	=	SYM
cana-826	39	36	𝑈,𝑗	𝑈,𝑗	NOUN
cana-826	39	37	⁡𝑗	⁡𝑗	NOUN
cana-826	39	38	=	=	SYM
cana-826	39	39	1,2	1,2	NUM
cana-826	39	40	,	,	PUNCT
cana-826	39	41	…	…	PUNCT
cana-826	39	42	,	,	PUNCT
cana-826	39	43	𝑚	𝑚	X
cana-826	39	44	here	here	ADV
cana-826	39	45	,	,	PUNCT
cana-826	39	46	the	the	DET
cana-826	39	47	hyperedges	hyperedge	NOUN
cana-826	39	48	𝐸𝑗	𝐸𝑗	PROPN
cana-826	39	49	are	be	AUX
cana-826	39	50	crisp	crisp	ADJ
cana-826	39	51	sets	set	NOUN
cana-826	39	52	of	of	ADP
cana-826	39	53	if	if	SCONJ
cana-826	39	54	vertices	vertex	NOUN
cana-826	39	55	,	,	PUNCT
cana-826	39	56	𝜇𝑗(𝑢𝑖)⁡&⁡𝜈𝑗(𝑢𝑖	𝜇𝑗(𝑢𝑖)⁡&⁡𝜈𝑗(𝑢𝑖	NOUN
cana-826	39	57	)	)	PUNCT
cana-826	39	58	denotes	denote	VERB
cana-826	39	59	the	the	DET
cana-826	39	60	degrees	degree	NOUN
cana-826	39	61	of	of	ADP
cana-826	39	62	membership	membership	NOUN
cana-826	39	63	&	&	CCONJ
cana-826	39	64	non	non	ADJ
cana-826	39	65	-	-	NOUN
cana-826	39	66	membership	membership	NOUN
cana-826	39	67	of	of	ADP
cana-826	39	68	vertex	vertex	NOUN
cana-826	39	69	𝑢𝑖	𝑢𝑖	NOUN
cana-826	39	70	to	to	PART
cana-826	39	71	hyperedge	hyperedge	VERB
cana-826	39	72	𝐸𝑗.	𝐸𝑗.	PROPN
cana-826	39	73	notations	notation	NOUN
cana-826	39	74	list[8	list[8	NOUN
cana-826	39	75	]	]	X
cana-826	39	76	•	•	ADP
cana-826	39	77	<	<	X
cana-826	39	78	𝜇(𝑢𝑖	𝜇(𝑢𝑖	PROPN
cana-826	39	79	)	)	PUNCT
cana-826	39	80	,	,	PUNCT
cana-826	39	81	𝜈(𝑢𝑖	𝜈(𝑢𝑖	NOUN
cana-826	39	82	)	)	PUNCT
cana-826	39	83	>	>	X
cana-826	39	84	or	or	CCONJ
cana-826	39	85	simply	simply	ADV
cana-826	39	86	<	<	X
cana-826	39	87	𝜇𝑖	𝜇𝑖	ADP
cana-826	39	88	,	,	PUNCT
cana-826	39	89	𝜈𝑖	𝜈𝑖	ADP
cana-826	39	90	>	>	X
cana-826	39	91	denote	denote	VERB
cana-826	39	92	the	the	DET
cana-826	39	93	degrees	degree	NOUN
cana-826	39	94	of	of	ADP
cana-826	39	95	membership	membership	NOUN
cana-826	39	96	&	&	CCONJ
cana-826	39	97	nonmembership	nonmembership	NOUN
cana-826	39	98	of	of	ADP
cana-826	39	99	the	the	DET
cana-826	39	100	vertex	vertex	NOUN
cana-826	39	101	𝑢𝑖	𝑢𝑖	ADP
cana-826	39	102	∈	∈	PROPN
cana-826	39	103	𝑈	𝑈	PROPN
cana-826	39	104	such	such	ADJ
cana-826	39	105	that	that	SCONJ
cana-826	39	106	0	0	NUM
cana-826	39	107	≤	≤	NOUN
cana-826	39	108	𝜇𝑖	𝜇𝑖	ADP
cana-826	39	109	+	+	PUNCT
cana-826	39	110	𝜈𝑖	𝜈𝑖	ADP
cana-826	39	111	≤	≤	NUM
cana-826	39	112	1	1	NUM
cana-826	39	113	.	.	NOUN
cana-826	39	114	•	•	NUM
cana-826	39	115	<	<	X
cana-826	39	116	𝜇(𝑢𝑗	𝜇(𝑢𝑗	NOUN
cana-826	39	117	)	)	PUNCT
cana-826	39	118	,	,	PUNCT
cana-826	39	119	𝜈(𝑢𝑗	𝜈(𝑢𝑗	NOUN
cana-826	39	120	)	)	PUNCT
cana-826	39	121	>	>	PUNCT
cana-826	39	122	or	or	CCONJ
cana-826	39	123	simply	simply	ADV
cana-826	39	124	<	<	X
cana-826	39	125	𝜇𝑗	𝜇𝑗	X
cana-826	39	126	,	,	PUNCT
cana-826	39	127	𝜈𝑗	𝜈𝑗	PROPN
cana-826	39	128	>	>	X
cana-826	39	129	denote	denote	VERB
cana-826	39	130	the	the	DET
cana-826	39	131	degrees	degree	NOUN
cana-826	39	132	of	of	ADP
cana-826	39	133	membership	membership	NOUN
cana-826	39	134	&	&	CCONJ
cana-826	39	135	nonmembership	nonmembership	NOUN
cana-826	39	136	of	of	ADP
cana-826	39	137	the	the	DET
cana-826	39	138	hyperedge	hyperedge	NOUN
cana-826	39	139	(	(	PUNCT
cana-826	39	140	𝑢𝑖	𝑢𝑖	INTJ
cana-826	39	141	,	,	PUNCT
cana-826	39	142	𝑢𝑗	𝑢𝑗	NOUN
cana-826	39	143	)	)	PUNCT
cana-826	39	144	∈	∈	PROPN
cana-826	39	145	𝑈	𝑈	PROPN
cana-826	39	146	×𝑈	×𝑈	PROPN
cana-826	39	147	,	,	PUNCT
cana-826	39	148	such	such	ADJ
cana-826	39	149	that	that	SCONJ
cana-826	39	150	0	0	NUM
cana-826	39	151	≤	≤	NUM
cana-826	39	152	𝜇𝑗	𝜇𝑗	NOUN
cana-826	39	153	+	+	CCONJ
cana-826	39	154	𝜈𝑗	𝜈𝑗	PROPN
cana-826	39	155	≤	≤	NUM
cana-826	39	156	1	1	NUM
cana-826	39	157	.	.	NOUN
cana-826	39	158	•	•	NUM
cana-826	39	159	𝜇𝑖𝑗	𝜇𝑖𝑗	NOUN
cana-826	39	160	and	and	CCONJ
cana-826	39	161	𝜈𝑖𝑗	𝜈𝑖𝑗	NOUN
cana-826	39	162	are	be	AUX
cana-826	39	163	the	the	DET
cana-826	39	164	membership	membership	NOUN
cana-826	39	165	&	&	CCONJ
cana-826	39	166	non	non	ADJ
cana-826	39	167	-	-	ADJ
cana-826	39	168	membership	membership	ADJ
cana-826	39	169	value	value	NOUN
cana-826	39	170	of	of	ADP
cana-826	39	171	𝑖𝑡ℎ	𝑖𝑡ℎ	ADJ
cana-826	39	172	vertex	vertex	NOUN
cana-826	39	173	in	in	ADP
cana-826	39	174	𝑗𝑡ℎ	𝑗𝑡ℎ	ADJ
cana-826	39	175	hyperedge	hyperedge	NOUN
cana-826	39	176	.	.	PUNCT
cana-826	40	1	•	•	NOUN
cana-826	40	2	support	support	NOUN
cana-826	40	3	of	of	ADP
cana-826	40	4	an	an	DET
cana-826	40	5	ifs	ifs	PROPN
cana-826	40	6	𝑈	𝑈	PROPN
cana-826	40	7	in	in	ADP
cana-826	40	8	𝐸	𝐸	PROPN
cana-826	40	9	is	be	AUX
cana-826	40	10	denoted	denote	VERB
cana-826	40	11	by	by	ADP
cana-826	40	12	𝑠𝑢𝑝𝑝(𝐸𝑗	𝑠𝑢𝑝𝑝(𝐸𝑗	PROPN
cana-826	40	13	)	)	PUNCT
cana-826	40	14	=	=	SYM
cana-826	40	15	{	{	PUNCT
cana-826	40	16	𝑢𝑖	𝑢𝑖	NOUN
cana-826	40	17	│	│	ADJ
cana-826	40	18	𝜇𝑗(𝑢𝑖	𝜇𝑗(𝑢𝑖	NOUN
cana-826	40	19	)	)	PUNCT
cana-826	40	20	>	>	PUNCT
cana-826	40	21	0⁡&⁡𝜈𝑗(𝑢𝑖	0⁡&⁡𝜈𝑗(𝑢𝑖	NOUN
cana-826	40	22	)	)	PUNCT
cana-826	40	23	>	>	X
cana-826	40	24	0	0	NUM
cana-826	40	25	}	}	PUNCT
cana-826	40	26	.	.	PUNCT
cana-826	41	1	communications	communication	NOUN
cana-826	41	2	on	on	ADP
cana-826	41	3	applied	apply	VERB
cana-826	41	4	nonlinear	nonlinear	ADJ
cana-826	41	5	analysis	analysis	NOUN
cana-826	41	6	issn	issn	NOUN
cana-826	41	7	:	:	PUNCT
cana-826	41	8	1074	1074	NUM
cana-826	41	9	-	-	PUNCT
cana-826	41	10	133x	133x	NUM
cana-826	41	11	vol	vol	NOUN
cana-826	41	12	31	31	NUM
cana-826	41	13	no	no	NOUN
cana-826	41	14	.	.	PUNCT
cana-826	42	1	4s	4s	NUM
cana-826	42	2	(	(	PUNCT
cana-826	42	3	2024	2024	NUM
cana-826	42	4	)	)	PUNCT
cana-826	42	5	12	12	NUM
cana-826	42	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-826	42	7	3	3	X
cana-826	42	8	.	.	PUNCT
cana-826	42	9	intuitionistic	intuitionistic	ADJ
cana-826	42	10	fuzzy	fuzzy	ADJ
cana-826	42	11	threshold	threshold	NOUN
cana-826	42	12	hypergraph	hypergraph	NOUN
cana-826	42	13	definition	definition	NOUN
cana-826	42	14	3.1	3.1	NUM
cana-826	42	15	.	.	PUNCT
cana-826	43	1	the	the	DET
cana-826	43	2	intuitionistic	intuitionistic	ADJ
cana-826	43	3	fuzzy	fuzzy	ADJ
cana-826	43	4	threshold	threshold	NOUN
cana-826	43	5	hypergraph(ifthg	hypergraph(ifthg	PROPN
cana-826	43	6	)	)	PUNCT
cana-826	43	7	is	be	AUX
cana-826	43	8	defined	define	VERB
cana-826	43	9	as	as	ADP
cana-826	43	10	ℍ𝔾	ℍ𝔾	ADV
cana-826	43	11	=	=	SYM
cana-826	43	12	(	(	PUNCT
cana-826	43	13	𝑈	𝑈	PROPN
cana-826	43	14	,	,	PUNCT
cana-826	43	15	ℰ	ℰ	PROPN
cana-826	43	16	;	;	PUNCT
cana-826	43	17	𝑠1	𝑠1	PROPN
cana-826	43	18	,	,	PUNCT
cana-826	43	19	𝑠2	𝑠2	PROPN
cana-826	43	20	)	)	PUNCT
cana-826	43	21	where	where	SCONJ
cana-826	43	22	,	,	PUNCT
cana-826	43	23	(	(	PUNCT
cana-826	43	24	i	i	NOUN
cana-826	43	25	)	)	PUNCT
cana-826	43	26	𝑈	𝑈	NOUN
cana-826	43	27	=	=	SYM
cana-826	43	28	{	{	PUNCT
cana-826	43	29	𝑢1	𝑢1	PROPN
cana-826	43	30	,	,	PUNCT
cana-826	43	31	𝑢2	𝑢2	PROPN
cana-826	43	32	,	,	PUNCT
cana-826	43	33	…	…	PUNCT
cana-826	43	34	,	,	PUNCT
cana-826	43	35	𝑢𝑛	𝑢𝑛	NOUN
cana-826	43	36	,	,	PUNCT
cana-826	43	37	}	}	PUNCT
cana-826	43	38	is	be	AUX
cana-826	43	39	a	a	DET
cana-826	43	40	finite	finite	ADJ
cana-826	43	41	set	set	NOUN
cana-826	43	42	of	of	ADP
cana-826	43	43	if	if	SCONJ
cana-826	43	44	vertices	vertex	NOUN
cana-826	43	45	(	(	PUNCT
cana-826	43	46	ii	ii	NOUN
cana-826	43	47	)	)	PUNCT
cana-826	43	48	ℰ	ℰ	NOUN
cana-826	43	49	=	=	SYM
cana-826	43	50	{	{	PUNCT
cana-826	43	51	ℰ1	ℰ1	NOUN
cana-826	43	52	,	,	PUNCT
cana-826	43	53	ℰ2	ℰ2	NOUN
cana-826	43	54	,	,	PUNCT
cana-826	43	55	…	…	PUNCT
cana-826	43	56	,	,	PUNCT
cana-826	43	57	ℰ𝑚	ℰ𝑚	NOUN
cana-826	43	58	}	}	PUNCT
cana-826	43	59	is	be	AUX
cana-826	43	60	a	a	DET
cana-826	43	61	family	family	NOUN
cana-826	43	62	of	of	ADP
cana-826	43	63	crisp	crisp	ADJ
cana-826	43	64	subsets	subset	NOUN
cana-826	43	65	of	of	ADP
cana-826	43	66	𝑈	𝑈	PROPN
cana-826	43	67	(	(	PUNCT
cana-826	43	68	iii	iii	NOUN
cana-826	43	69	)	)	PUNCT
cana-826	43	70	ℰ𝑗	ℰ𝑗	PROPN
cana-826	43	71	=	=	SYM
cana-826	43	72	{	{	PUNCT
cana-826	43	73	𝑢𝑖	𝑢𝑖	INTJ
cana-826	43	74	,	,	PUNCT
cana-826	43	75	𝜇𝑗(𝑢𝑖	𝜇𝑗(𝑢𝑖	PROPN
cana-826	43	76	)	)	PUNCT
cana-826	43	77	,	,	PUNCT
cana-826	43	78	𝜈𝑗(𝑢𝑖)|0	𝜈𝑗(𝑢𝑖)|0	PROPN
cana-826	43	79	≤	≤	NUM
cana-826	43	80	𝜇𝑗(𝑢𝑖	𝜇𝑗(𝑢𝑖	PROPN
cana-826	43	81	)	)	PUNCT
cana-826	44	1	+	+	NUM
cana-826	44	2	𝜈𝑗(𝑢𝑖	𝜈𝑗(𝑢𝑖	NOUN
cana-826	44	3	)	)	PUNCT
cana-826	44	4	≤	≤	NUM
cana-826	44	5	1	1	NUM
cana-826	44	6	}	}	PUNCT
cana-826	44	7	,	,	PUNCT
cana-826	44	8	𝑗	𝑗	NOUN
cana-826	44	9	=	=	SYM
cana-826	44	10	1,2	1,2	NUM
cana-826	44	11	,	,	PUNCT
cana-826	44	12	…	…	PUNCT
cana-826	44	13	,	,	PUNCT
cana-826	44	14	𝑚	𝑚	X
cana-826	44	15	(	(	PUNCT
cana-826	44	16	iv	iv	X
cana-826	44	17	)	)	PUNCT
cana-826	44	18	ℰ𝑗	ℰ𝑗	PROPN
cana-826	44	19	≠	≠	PROPN
cana-826	44	20	∅	∅	NOUN
cana-826	44	21	,	,	PUNCT
cana-826	44	22	𝑗	𝑗	NOUN
cana-826	44	23	=	=	SYM
cana-826	44	24	1,2	1,2	NUM
cana-826	44	25	,	,	PUNCT
cana-826	44	26	…	…	PUNCT
cana-826	44	27	,	,	PUNCT
cana-826	44	28	𝑚	𝑚	X
cana-826	44	29	(	(	PUNCT
cana-826	44	30	v	v	NOUN
cana-826	44	31	)	)	PUNCT
cana-826	44	32	⋃	⋃	NOUN
cana-826	44	33	supp(ℰ𝑗	supp(ℰ𝑗	NOUN
cana-826	44	34	)	)	PUNCT
cana-826	44	35	=	=	SYM
cana-826	44	36	𝑈,𝑗	𝑈,𝑗	NOUN
cana-826	44	37	⁡𝑗	⁡𝑗	NOUN
cana-826	44	38	=	=	SYM
cana-826	44	39	1,2	1,2	NUM
cana-826	44	40	,	,	PUNCT
cana-826	44	41	…	…	PUNCT
cana-826	44	42	,	,	PUNCT
cana-826	44	43	𝑚	𝑚	X
cana-826	44	44	(	(	PUNCT
cana-826	44	45	vi	vi	NOUN
cana-826	44	46	)	)	PUNCT
cana-826	44	47	an	an	DET
cana-826	44	48	independent	independent	ADJ
cana-826	44	49	set	set	NOUN
cana-826	44	50	𝑉	𝑉	PROPN
cana-826	44	51	⊆	⊆	PROPN
cana-826	44	52	𝑈	𝑈	PROPN
cana-826	44	53	has	have	VERB
cana-826	44	54	a	a	DET
cana-826	44	55	set	set	NOUN
cana-826	44	56	of	of	ADP
cana-826	44	57	all	all	DET
cana-826	44	58	distinct	distinct	ADJ
cana-826	44	59	combinations	combination	NOUN
cana-826	44	60	of	of	ADP
cana-826	44	61	a	a	DET
cana-826	44	62	non	non	ADJ
cana-826	44	63	-	-	ADJ
cana-826	44	64	adjacent	adjacent	ADJ
cana-826	44	65	vertices	vertex	NOUN
cana-826	44	66	in	in	ADP
cana-826	44	67	ℍ𝔾	ℍ𝔾	PROPN
cana-826	44	68	iff	iff	PROPN
cana-826	44	69	there	there	PRON
cana-826	44	70	exists	exist	VERB
cana-826	44	71	a	a	DET
cana-826	44	72	threshold	threshold	NOUN
cana-826	44	73	values	value	NOUN
cana-826	44	74	𝑠1⁡&⁡𝑠2	𝑠1⁡&⁡𝑠2	VERB
cana-826	44	75	>	>	X
cana-826	44	76	0	0	NUM
cana-826	45	1	such	such	ADJ
cana-826	45	2	that	that	SCONJ
cana-826	45	3	∑	∑	PROPN
cana-826	45	4	𝜇𝑗(𝑢𝑖	𝜇𝑗(𝑢𝑖	PROPN
cana-826	45	5	)	)	PUNCT
cana-826	45	6	≤	≤	NUM
cana-826	45	7	𝑠1⁡𝑢𝑖∈𝑉	𝑠1⁡𝑢𝑖∈𝑉	PROPN
cana-826	45	8	&	&	CCONJ
cana-826	45	9	∑	∑	PROPN
cana-826	45	10	(	(	PUNCT
cana-826	45	11	1	1	NUM
cana-826	45	12	−	−	PROPN
cana-826	45	13	𝜈𝑗(𝑢𝑖	𝜈𝑗(𝑢𝑖	NOUN
cana-826	45	14	)	)	PUNCT
cana-826	45	15	)	)	PUNCT
cana-826	45	16	≤	≤	NUM
cana-826	45	17	𝑠2𝑢𝑖∈𝑉	𝑠2𝑢𝑖∈𝑉	ADJ
cana-826	45	18	.	.	PUNCT
cana-826	46	1	example	example	NOUN
cana-826	46	2	consider	consider	VERB
cana-826	46	3	an	an	DET
cana-826	46	4	ifthg	ifthg	NOUN
cana-826	46	5	ℍ𝔾	ℍ𝔾	ADV
cana-826	46	6	=	=	SYM
cana-826	46	7	(	(	PUNCT
cana-826	46	8	𝑈	𝑈	PROPN
cana-826	46	9	,	,	PUNCT
cana-826	46	10	ℰ	ℰ	NOUN
cana-826	46	11	;	;	PUNCT
cana-826	46	12	0.4,0.6	0.4,0.6	NUM
cana-826	46	13	)	)	PUNCT
cana-826	46	14	with	with	ADP
cana-826	46	15	𝑈	𝑈	PROPN
cana-826	46	16	=	=	SYM
cana-826	46	17	{	{	PUNCT
cana-826	46	18	𝑢1	𝑢1	PROPN
cana-826	46	19	,	,	PUNCT
cana-826	46	20	𝑢2	𝑢2	PROPN
cana-826	46	21	,	,	PUNCT
cana-826	46	22	…	…	PUNCT
cana-826	46	23	,	,	PUNCT
cana-826	46	24	𝑢7	𝑢7	PROPN
cana-826	46	25	,	,	PUNCT
cana-826	46	26	}	}	PUNCT
cana-826	46	27	,	,	PUNCT
cana-826	46	28	ℰ	ℰ	PROPN
cana-826	46	29	=	=	SYM
cana-826	46	30	{	{	PUNCT
cana-826	46	31	ℰ1	ℰ1	NOUN
cana-826	46	32	,	,	PUNCT
cana-826	46	33	ℰ2	ℰ2	PROPN
cana-826	46	34	,	,	PUNCT
cana-826	46	35	ℰ3	ℰ3	PROPN
cana-826	46	36	,	,	PUNCT
cana-826	46	37	ℰ4	ℰ4	ADJ
cana-826	46	38	}	}	PUNCT
cana-826	46	39	.	.	PUNCT
cana-826	47	1	fig	fig	NOUN
cana-826	47	2	3.1	3.1	NUM
cana-826	47	3	:	:	PUNCT
cana-826	47	4	intuitionistic	intuitionistic	ADJ
cana-826	47	5	fuzzy	fuzzy	ADJ
cana-826	47	6	threshold	threshold	NOUN
cana-826	47	7	hypergraph	hypergraph	NOUN
cana-826	47	8	hg	hg	X
cana-826	47	9	adjacency	adjacency	PROPN
cana-826	47	10	matrix	matrix	NOUN
cana-826	47	11	of	of	ADP
cana-826	47	12	the	the	DET
cana-826	47	13	above	above	ADJ
cana-826	47	14	ifthg	ifthg	NOUN
cana-826	47	15	is	be	AUX
cana-826	47	16	represented	represent	VERB
cana-826	47	17	as	as	SCONJ
cana-826	47	18	follows	follow	VERB
cana-826	47	19	:	:	PUNCT
cana-826	47	20	note	note	NOUN
cana-826	47	21	:	:	PUNCT
cana-826	47	22	intuitionistic	intuitionistic	ADJ
cana-826	47	23	fuzzy	fuzzy	ADJ
cana-826	47	24	hypergraphs	hypergraph	NOUN
cana-826	47	25	is	be	AUX
cana-826	47	26	a	a	DET
cana-826	47	27	special	special	ADJ
cana-826	47	28	case	case	NOUN
cana-826	47	29	of	of	ADP
cana-826	47	30	the	the	DET
cana-826	47	31	intuitionistic	intuitionistic	ADJ
cana-826	47	32	fuzzy	fuzzy	ADJ
cana-826	47	33	threshold	threshold	NOUN
cana-826	47	34	hypergraphs	hypergraph	NOUN
cana-826	47	35	.	.	PUNCT
cana-826	48	1	communications	communication	NOUN
cana-826	48	2	on	on	ADP
cana-826	48	3	applied	apply	VERB
cana-826	48	4	nonlinear	nonlinear	ADJ
cana-826	48	5	analysis	analysis	NOUN
cana-826	48	6	issn	issn	NOUN
cana-826	48	7	:	:	PUNCT
cana-826	48	8	1074	1074	NUM
cana-826	48	9	-	-	PUNCT
cana-826	48	10	133x	133x	NUM
cana-826	48	11	vol	vol	NOUN
cana-826	48	12	31	31	NUM
cana-826	48	13	no	no	NOUN
cana-826	48	14	.	.	PUNCT
cana-826	49	1	4s	4s	NUM
cana-826	49	2	(	(	PUNCT
cana-826	49	3	2024	2024	NUM
cana-826	49	4	)	)	PUNCT
cana-826	49	5	13	13	NUM
cana-826	49	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-826	49	7	definition	definition	NOUN
cana-826	49	8	3.2	3.2	NUM
cana-826	49	9	.	.	PUNCT
cana-826	50	1	let	let	VERB
cana-826	50	2	ℍ𝔾	ℍ𝔾	ADV
cana-826	50	3	=	=	SYM
cana-826	50	4	(	(	PUNCT
cana-826	50	5	𝑈	𝑈	PROPN
cana-826	50	6	,	,	PUNCT
cana-826	50	7	ℰ	ℰ	PROPN
cana-826	50	8	;	;	PUNCT
cana-826	50	9	𝑠1	𝑠1	PROPN
cana-826	50	10	,	,	PUNCT
cana-826	50	11	𝑠2	𝑠2	PROPN
cana-826	50	12	)	)	PUNCT
cana-826	50	13	be	be	VERB
cana-826	50	14	an	an	DET
cana-826	50	15	ifthg	ifthg	NOUN
cana-826	50	16	.	.	PUNCT
cana-826	51	1	the	the	DET
cana-826	51	2	adjacency	adjacency	NOUN
cana-826	51	3	level	level	NOUN
cana-826	51	4	between	between	ADP
cana-826	51	5	two	two	NUM
cana-826	51	6	vertices	vertex	NOUN
cana-826	51	7	𝑢𝑖	𝑢𝑖	NOUN
cana-826	51	8	and	and	CCONJ
cana-826	51	9	𝑢𝑖+1	𝑢𝑖+1	PROPN
cana-826	51	10	,	,	PUNCT
cana-826	51	11	denoted	denote	VERB
cana-826	51	12	by	by	ADP
cana-826	51	13	𝛾(𝑢𝑖	𝛾(𝑢𝑖	PROPN
cana-826	51	14	,	,	PUNCT
cana-826	51	15	𝑢𝑖+1	𝑢𝑖+1	PROPN
cana-826	51	16	)	)	PUNCT
cana-826	51	17	,	,	PUNCT
cana-826	51	18	is	be	AUX
cana-826	51	19	defined	define	VERB
cana-826	51	20	by	by	ADP
cana-826	51	21	⁡𝛾(𝑢𝑖	⁡𝛾(𝑢𝑖	NOUN
cana-826	51	22	,	,	PUNCT
cana-826	51	23	𝑢𝑖+1	𝑢𝑖+1	PROPN
cana-826	51	24	)	)	PUNCT
cana-826	51	25	=	=	SYM
cana-826	52	1	max	max	PROPN
cana-826	52	2	𝑗	𝑗	PROPN
cana-826	52	3	(	(	PUNCT
cana-826	52	4	min(𝜇𝑗(𝑢𝑖	min(𝜇𝑗(𝑢𝑖	PROPN
cana-826	52	5	)	)	PUNCT
cana-826	52	6	)	)	PUNCT
cana-826	52	7	,	,	PUNCT
cana-826	52	8	(	(	PUNCT
cana-826	52	9	𝜇𝑗(𝑢𝑖+1))),min	𝜇𝑗(𝑢𝑖+1))),min	NOUN
cana-826	52	10	𝑗	𝑗	X
cana-826	52	11	(	(	PUNCT
cana-826	52	12	max	max	PROPN
cana-826	52	13	(	(	PUNCT
cana-826	52	14	𝜈𝑗(𝑢𝑖	𝜈𝑗(𝑢𝑖	PROPN
cana-826	52	15	)	)	PUNCT
cana-826	52	16	)	)	PUNCT
cana-826	52	17	,	,	PUNCT
cana-826	52	18	(	(	PUNCT
cana-826	52	19	𝜈𝑗(𝑢𝑖+1	𝜈𝑗(𝑢𝑖+1	ADJ
cana-826	52	20	)	)	PUNCT
cana-826	52	21	)	)	PUNCT
cana-826	52	22	)	)	PUNCT
cana-826	52	23	,	,	PUNCT
cana-826	52	24	where	where	SCONJ
cana-826	52	25	𝑖	𝑖	ADP
cana-826	52	26	=	=	SYM
cana-826	52	27	1,2	1,2	NUM
cana-826	52	28	,	,	PUNCT
cana-826	52	29	…	…	PUNCT
cana-826	52	30	,	,	PUNCT
cana-826	52	31	𝑛⁡&⁡𝑗	𝑛⁡&⁡𝑗	PROPN
cana-826	52	32	=	=	SYM
cana-826	52	33	1,2	1,2	NUM
cana-826	52	34	,	,	PUNCT
cana-826	52	35	…	…	PUNCT
cana-826	52	36	,	,	PUNCT
cana-826	52	37	𝑚	𝑚	X
cana-826	52	38	for	for	ADP
cana-826	52	39	which	which	PRON
cana-826	52	40	∑	∑	PROPN
cana-826	52	41	𝜇𝑗(𝑢𝑖	𝜇𝑗(𝑢𝑖	PROPN
cana-826	52	42	)	)	PUNCT
cana-826	52	43	≤	≤	NUM
cana-826	52	44	𝑠1⁡𝑢𝑖∈𝑉	𝑠1⁡𝑢𝑖∈𝑉	PROPN
cana-826	52	45	&	&	CCONJ
cana-826	52	46	∑	∑	PROPN
cana-826	52	47	(	(	PUNCT
cana-826	52	48	1	1	NUM
cana-826	52	49	−	−	PROPN
cana-826	52	50	𝜈𝑗(𝑢𝑖	𝜈𝑗(𝑢𝑖	NOUN
cana-826	52	51	)	)	PUNCT
cana-826	52	52	)	)	PUNCT
cana-826	52	53	≤𝑢𝑖∈𝑉	≤𝑢𝑖∈𝑉	ADJ
cana-826	52	54	𝑠2	𝑠2	NOUN
cana-826	52	55	.	.	PUNCT
cana-826	53	1	definition	definition	NOUN
cana-826	53	2	3.3	3.3	NUM
cana-826	53	3	.	.	PUNCT
cana-826	54	1	let	let	VERB
cana-826	54	2	ℍ𝔾	ℍ𝔾	ADV
cana-826	54	3	=	=	SYM
cana-826	54	4	(	(	PUNCT
cana-826	54	5	𝑈	𝑈	PROPN
cana-826	54	6	,	,	PUNCT
cana-826	54	7	ℰ	ℰ	PROPN
cana-826	54	8	;	;	PUNCT
cana-826	54	9	𝑠1	𝑠1	PROPN
cana-826	54	10	,	,	PUNCT
cana-826	54	11	𝑠2	𝑠2	PROPN
cana-826	54	12	)	)	PUNCT
cana-826	54	13	be	be	VERB
cana-826	54	14	an	an	DET
cana-826	54	15	ifthg	ifthg	NOUN
cana-826	54	16	.	.	PUNCT
cana-826	55	1	the	the	DET
cana-826	55	2	adjacency	adjacency	NOUN
cana-826	55	3	level	level	NOUN
cana-826	55	4	between	between	ADP
cana-826	55	5	the	the	DET
cana-826	55	6	hyperedges	hyperedge	NOUN
cana-826	55	7	ℰ𝑗	ℰ𝑗	PROPN
cana-826	55	8	and	and	CCONJ
cana-826	55	9	ℰ𝑘	ℰ𝑘	PROPN
cana-826	55	10	,	,	PUNCT
cana-826	55	11	denoted	denote	VERB
cana-826	55	12	by	by	ADP
cana-826	55	13	𝜎(ℰ𝑗	𝜎(ℰ𝑗	NOUN
cana-826	55	14	,	,	PUNCT
cana-826	55	15	ℰ𝑘	ℰ𝑘	PROPN
cana-826	55	16	)	)	PUNCT
cana-826	55	17	,	,	PUNCT
cana-826	55	18	is	be	AUX
cana-826	55	19	defined	define	VERB
cana-826	55	20	by	by	ADP
cana-826	55	21	𝜎(ℰ𝑗	𝜎(ℰ𝑗	NOUN
cana-826	55	22	,	,	PUNCT
cana-826	55	23	ℰ𝑘	ℰ𝑘	PROPN
cana-826	55	24	)	)	PUNCT
cana-826	55	25	=	=	SYM
cana-826	56	1	max	max	PROPN
cana-826	56	2	𝑗	𝑗	X
cana-826	56	3	(	(	PUNCT
cana-826	56	4	min	min	PROPN
cana-826	56	5	(	(	PUNCT
cana-826	56	6	𝜇𝑗(𝑢𝑖	𝜇𝑗(𝑢𝑖	PROPN
cana-826	56	7	)	)	PUNCT
cana-826	56	8	)	)	PUNCT
cana-826	56	9	,	,	PUNCT
cana-826	56	10	𝜇𝑘(𝑢𝑖)),min	𝜇𝑘(𝑢𝑖)),min	PROPN
cana-826	56	11	𝑗	𝑗	X
cana-826	56	12	(	(	PUNCT
cana-826	56	13	max	max	PROPN
cana-826	56	14	(	(	PUNCT
cana-826	56	15	𝜈𝑗(𝑢𝑖	𝜈𝑗(𝑢𝑖	PROPN
cana-826	56	16	)	)	PUNCT
cana-826	56	17	)	)	PUNCT
cana-826	56	18	,	,	PUNCT
cana-826	56	19	𝜈𝑘(𝑢𝑖	𝜈𝑘(𝑢𝑖	PROPN
cana-826	56	20	)	)	PUNCT
cana-826	56	21	)	)	PUNCT
cana-826	56	22	,	,	PUNCT
cana-826	56	23	where	where	SCONJ
cana-826	56	24	𝑖	𝑖	ADP
cana-826	56	25	=	=	SYM
cana-826	56	26	1,2	1,2	NUM
cana-826	56	27	,	,	PUNCT
cana-826	56	28	…	…	PUNCT
cana-826	56	29	,	,	PUNCT
cana-826	56	30	𝑛⁡&⁡𝑗	𝑛⁡&⁡𝑗	PROPN
cana-826	56	31	,	,	PUNCT
cana-826	56	32	𝑘	𝑘	NOUN
cana-826	56	33	=	=	SYM
cana-826	56	34	1,2	1,2	NUM
cana-826	56	35	,	,	PUNCT
cana-826	56	36	…	…	PUNCT
cana-826	56	37	,	,	PUNCT
cana-826	56	38	𝑚	𝑚	X
cana-826	56	39	for	for	ADP
cana-826	56	40	which	which	PRON
cana-826	56	41	∑	∑	PROPN
cana-826	56	42	𝜇𝑗(𝑢𝑖	𝜇𝑗(𝑢𝑖	PROPN
cana-826	56	43	)	)	PUNCT
cana-826	56	44	≤	≤	NUM
cana-826	56	45	𝑠1⁡𝑢𝑖∈𝑉	𝑠1⁡𝑢𝑖∈𝑉	PROPN
cana-826	56	46	&	&	CCONJ
cana-826	56	47	∑	∑	PROPN
cana-826	56	48	(	(	PUNCT
cana-826	56	49	1	1	NUM
cana-826	56	50	−𝑢𝑖∈𝑉	−𝑢𝑖∈𝑉	NUM
cana-826	56	51	𝜈𝑗(𝑢𝑖	𝜈𝑗(𝑢𝑖	PROPN
cana-826	56	52	)	)	PUNCT
cana-826	56	53	)	)	PUNCT
cana-826	56	54	≤	≤	NUM
cana-826	56	55	𝑠2	𝑠2	NOUN
cana-826	56	56	.	.	PUNCT
cana-826	57	1	definition	definition	NOUN
cana-826	57	2	3.4	3.4	NUM
cana-826	57	3	.	.	PUNCT
cana-826	58	1	let	let	VERB
cana-826	58	2	ℍ𝔾	ℍ𝔾	ADV
cana-826	58	3	=	=	SYM
cana-826	58	4	(	(	PUNCT
cana-826	58	5	𝑈	𝑈	PROPN
cana-826	58	6	,	,	PUNCT
cana-826	58	7	ℰ	ℰ	PROPN
cana-826	58	8	;	;	PUNCT
cana-826	58	9	𝑠1	𝑠1	PROPN
cana-826	58	10	,	,	PUNCT
cana-826	58	11	𝑠2	𝑠2	PROPN
cana-826	58	12	)	)	PUNCT
cana-826	58	13	be	be	VERB
cana-826	58	14	an	an	DET
cana-826	58	15	ifthg	ifthg	NOUN
cana-826	58	16	.	.	PUNCT
cana-826	59	1	the	the	DET
cana-826	59	2	strength	strength	NOUN
cana-826	59	3	𝛿	𝛿	NOUN
cana-826	59	4	of	of	ADP
cana-826	59	5	a	a	DET
cana-826	59	6	hyperedge	hyperedge	NOUN
cana-826	59	7	ℰ𝑗	ℰ𝑗	PROPN
cana-826	59	8	is	be	AUX
cana-826	59	9	the	the	DET
cana-826	59	10	minimum	minimum	ADJ
cana-826	59	11	membership	membership	NOUN
cana-826	59	12	𝜇𝑗(𝑢𝑖	𝜇𝑗(𝑢𝑖	PROPN
cana-826	59	13	)	)	PUNCT
cana-826	59	14	and	and	CCONJ
cana-826	59	15	maximum	maximum	ADJ
cana-826	59	16	nonmembership	nonmembership	PROPN
cana-826	59	17	𝜈𝑗(𝑢𝑖	𝜈𝑗(𝑢𝑖	PROPN
cana-826	59	18	)	)	PUNCT
cana-826	59	19	of	of	ADP
cana-826	59	20	vertices	vertex	NOUN
cana-826	59	21	in	in	ADP
cana-826	59	22	the	the	DET
cana-826	59	23	hyperedge	hyperedge	NOUN
cana-826	60	1	ℰ𝑗.	ℰ𝑗.	ADV
cana-826	60	2	then	then	ADV
cana-826	60	3	,	,	PUNCT
cana-826	60	4	𝛿(ℰ𝑗	𝛿(ℰ𝑗	NOUN
cana-826	60	5	)	)	PUNCT
cana-826	60	6	=	=	SYM
cana-826	60	7	(	(	PUNCT
cana-826	60	8	min	min	NOUN
cana-826	60	9	𝑢𝑖	𝑢𝑖	INTJ
cana-826	60	10	(	(	PUNCT
cana-826	60	11	𝜇𝑗(𝑢𝑖)),max	𝜇𝑗(𝑢𝑖)),max	NOUN
cana-826	60	12	𝑢𝑖	𝑢𝑖	PROPN
cana-826	60	13	(	(	PUNCT
cana-826	60	14	𝜈𝑗(𝑢𝑖	𝜈𝑗(𝑢𝑖	PROPN
cana-826	60	15	)	)	PUNCT
cana-826	60	16	)	)	PUNCT
cana-826	60	17	for	for	ADP
cana-826	60	18	every	every	DET
cana-826	60	19	𝜇𝑗(𝑢𝑖	𝜇𝑗(𝑢𝑖	NOUN
cana-826	60	20	)	)	PUNCT
cana-826	60	21	>	>	X
cana-826	60	22	0	0	NUM
cana-826	60	23	,	,	PUNCT
cana-826	60	24	𝜈𝑗(𝑢𝑖	𝜈𝑗(𝑢𝑖	PROPN
cana-826	60	25	)	)	PUNCT
cana-826	60	26	>	>	X
cana-826	60	27	0	0	PUNCT
cana-826	61	1	for	for	ADP
cana-826	61	2	which	which	PRON
cana-826	61	3	∑	∑	PROPN
cana-826	61	4	𝜇𝑗(𝑢𝑖	𝜇𝑗(𝑢𝑖	PROPN
cana-826	61	5	)	)	PUNCT
cana-826	61	6	≤	≤	NUM
cana-826	61	7	𝑠1⁡𝑢𝑖∈𝑉	𝑠1⁡𝑢𝑖∈𝑉	PROPN
cana-826	61	8	&	&	CCONJ
cana-826	61	9	∑	∑	PROPN
cana-826	61	10	(	(	PUNCT
cana-826	61	11	1	1	NUM
cana-826	61	12	−	−	PROPN
cana-826	61	13	𝜈𝑗(𝑢𝑖	𝜈𝑗(𝑢𝑖	NOUN
cana-826	61	14	)	)	PUNCT
cana-826	61	15	)	)	PUNCT
cana-826	61	16	≤𝑢𝑖∈𝑉	≤𝑢𝑖∈𝑉	ADJ
cana-826	61	17	𝑠2	𝑠2	NOUN
cana-826	61	18	.	.	PUNCT
cana-826	62	1	definition	definition	NOUN
cana-826	62	2	3.5	3.5	NUM
cana-826	62	3	.	.	PUNCT
cana-826	63	1	let	let	VERB
cana-826	63	2	ℍ𝔾	ℍ𝔾	ADV
cana-826	63	3	=	=	SYM
cana-826	63	4	(	(	PUNCT
cana-826	63	5	𝑈	𝑈	PROPN
cana-826	63	6	,	,	PUNCT
cana-826	63	7	ℰ	ℰ	PROPN
cana-826	63	8	;	;	PUNCT
cana-826	63	9	𝑠1	𝑠1	PROPN
cana-826	63	10	,	,	PUNCT
cana-826	63	11	𝑠2	𝑠2	PROPN
cana-826	63	12	)	)	PUNCT
cana-826	63	13	be	be	VERB
cana-826	63	14	an	an	DET
cana-826	63	15	ifthg	ifthg	NOUN
cana-826	63	16	.	.	PUNCT
cana-826	64	1	then	then	ADV
cana-826	64	2	the	the	DET
cana-826	64	3	hyper	hyper	ADJ
cana-826	64	4	walk	walk	NOUN
cana-826	64	5	is	be	AUX
cana-826	64	6	a	a	DET
cana-826	64	7	sequence	sequence	NOUN
cana-826	64	8	of	of	ADP
cana-826	64	9	vertices	vertex	NOUN
cana-826	64	10	𝑢1	𝑢1	PROPN
cana-826	64	11	,	,	PUNCT
cana-826	64	12	𝑢2	𝑢2	PROPN
cana-826	64	13	,	,	PUNCT
cana-826	64	14	…	…	PUNCT
cana-826	64	15	,	,	PUNCT
cana-826	64	16	𝑢𝑛	𝑢𝑛	NOUN
cana-826	64	17	,	,	PUNCT
cana-826	64	18	not	not	PART
cana-826	64	19	necessarily	necessarily	ADV
cana-826	64	20	distinct	distinct	ADJ
cana-826	64	21	,	,	PUNCT
cana-826	64	22	if	if	SCONJ
cana-826	64	23	at	at	ADV
cana-826	64	24	least	least	ADJ
cana-826	64	25	one	one	NUM
cana-826	64	26	of	of	ADP
cana-826	64	27	the	the	DET
cana-826	64	28	𝜇𝑗(𝑢𝑖	𝜇𝑗(𝑢𝑖	PROPN
cana-826	64	29	,	,	PUNCT
cana-826	64	30	𝑢𝑖+1)⁡&⁡𝜈𝑗(𝑢𝑖	𝑢𝑖+1)⁡&⁡𝜈𝑗(𝑢𝑖	PROPN
cana-826	64	31	,	,	PUNCT
cana-826	64	32	𝑢𝑖+1	𝑢𝑖+1	PROPN
cana-826	64	33	)	)	PUNCT
cana-826	64	34	are	be	AUX
cana-826	64	35	different	different	ADJ
cana-826	64	36	from	from	ADP
cana-826	64	37	zero	zero	NUM
cana-826	64	38	,	,	PUNCT
cana-826	64	39	for	for	ADP
cana-826	64	40	which	which	PRON
cana-826	64	41	∑	∑	PROPN
cana-826	64	42	𝜇𝑗(𝑢𝑖	𝜇𝑗(𝑢𝑖	PROPN
cana-826	64	43	)	)	PUNCT
cana-826	64	44	≤	≤	NUM
cana-826	64	45	𝑠1⁡𝑢𝑖∈𝑉	𝑠1⁡𝑢𝑖∈𝑉	PROPN
cana-826	64	46	&	&	CCONJ
cana-826	64	47	∑	∑	PROPN
cana-826	64	48	(	(	PUNCT
cana-826	64	49	1	1	NUM
cana-826	64	50	−	−	PROPN
cana-826	64	51	𝜈𝑗(𝑢𝑖	𝜈𝑗(𝑢𝑖	NOUN
cana-826	64	52	)	)	PUNCT
cana-826	64	53	)	)	PUNCT
cana-826	64	54	≤	≤	NUM
cana-826	65	1	𝑠2𝑢𝑖∈𝑉	𝑠2𝑢𝑖∈𝑉	ADJ
cana-826	65	2	.	.	PUNCT
cana-826	66	1	definition	definition	NOUN
cana-826	66	2	3.6	3.6	NUM
cana-826	66	3	.	.	PUNCT
cana-826	67	1	let	let	VERB
cana-826	67	2	ℍ𝔾	ℍ𝔾	ADV
cana-826	67	3	=	=	SYM
cana-826	67	4	(	(	PUNCT
cana-826	67	5	𝑈	𝑈	PROPN
cana-826	67	6	,	,	PUNCT
cana-826	67	7	ℰ	ℰ	PROPN
cana-826	67	8	;	;	PUNCT
cana-826	67	9	𝑠1	𝑠1	PROPN
cana-826	67	10	,	,	PUNCT
cana-826	67	11	𝑠2	𝑠2	PROPN
cana-826	67	12	)	)	PUNCT
cana-826	67	13	be	be	VERB
cana-826	67	14	an	an	DET
cana-826	67	15	ifthg	ifthg	NOUN
cana-826	67	16	.	.	PUNCT
cana-826	68	1	then	then	ADV
cana-826	68	2	the	the	DET
cana-826	68	3	intuitionistic	intuitionistic	ADJ
cana-826	68	4	fuzzy	fuzzy	ADJ
cana-826	68	5	threshold	threshold	NOUN
cana-826	68	6	hyperpath	hyperpath	NOUN
cana-826	68	7	𝒫	𝒫	PROPN
cana-826	68	8	of	of	ADP
cana-826	68	9	length	length	NOUN
cana-826	68	10	𝑘	𝑘	NOUN
cana-826	68	11	in	in	ADP
cana-826	68	12	an	an	DET
cana-826	68	13	ifthg	ifthg	NOUN
cana-826	68	14	is	be	AUX
cana-826	68	15	defined	define	VERB
cana-826	68	16	as	as	ADP
cana-826	68	17	a	a	DET
cana-826	68	18	sequence	sequence	NOUN
cana-826	68	19	say	say	VERB
cana-826	68	20	,	,	PUNCT
cana-826	68	21	𝑢1⁡	𝑢1⁡	PROPN
cana-826	68	22	,	,	PUNCT
cana-826	68	23	ℰ1⁡⁡	ℰ1⁡⁡	PROPN
cana-826	68	24	,	,	PUNCT
cana-826	68	25	𝑢2⁡⁡	𝑢2⁡⁡	PROPN
cana-826	68	26	,	,	PUNCT
cana-826	68	27	ℰ2⁡	ℰ2⁡	PROPN
cana-826	68	28	,	,	PUNCT
cana-826	68	29	…	…	PUNCT
cana-826	68	30	,	,	PUNCT
cana-826	68	31	𝑢𝑘	𝑢𝑘	X
cana-826	68	32	,	,	PUNCT
cana-826	68	33	ℰ𝑘	ℰ𝑘	PROPN
cana-826	68	34	,	,	PUNCT
cana-826	68	35	𝑢𝑘+1	𝑢𝑘+1	NOUN
cana-826	68	36	of	of	ADP
cana-826	68	37	distinct	distinct	ADJ
cana-826	68	38	vertices	vertex	NOUN
cana-826	68	39	𝑢𝑖′s	𝑢𝑖′s	ADV
cana-826	68	40	and	and	CCONJ
cana-826	68	41	hyperedges	hyperedge	NOUN
cana-826	68	42	ℰ𝑗′s	ℰ𝑗′s	VERB
cana-826	68	43	such	such	ADJ
cana-826	68	44	that	that	SCONJ
cana-826	68	45	(	(	PUNCT
cana-826	68	46	i	i	NOUN
cana-826	68	47	)	)	PUNCT
cana-826	68	48	𝜇𝑗(ℰ𝑗	𝜇𝑗(ℰ𝑗	PROPN
cana-826	68	49	)	)	PUNCT
cana-826	68	50	>	>	X
cana-826	68	51	0	0	NUM
cana-826	68	52	,	,	PUNCT
cana-826	68	53	for	for	ADP
cana-826	68	54	all	all	DET
cana-826	68	55	1	1	NUM
cana-826	68	56	≤	≤	NUM
cana-826	68	57	𝑗	𝑗	PRON
cana-826	68	58	≤	≤	ADJ
cana-826	68	59	𝑘	𝑘	PRON
cana-826	68	60	(	(	PUNCT
cana-826	68	61	ii	ii	NOUN
cana-826	68	62	)	)	PUNCT
cana-826	68	63	𝑢𝑖	𝑢𝑖	NOUN
cana-826	68	64	,	,	PUNCT
cana-826	68	65	𝑢𝑖+1	𝑢𝑖+1	PROPN
cana-826	68	66	∈	∈	PROPN
cana-826	68	67	ℰ𝑗	ℰ𝑗	PROPN
cana-826	68	68	,	,	PUNCT
cana-826	68	69	for	for	ADP
cana-826	68	70	all	all	DET
cana-826	68	71	1	1	NUM
cana-826	68	72	≤	≤	NUM
cana-826	69	1	𝑗	𝑗	PRON
cana-826	69	2	≤	≤	NOUN
cana-826	69	3	𝑘	𝑘	PRON
cana-826	69	4	for	for	ADP
cana-826	69	5	which	which	PRON
cana-826	69	6	∑	∑	PROPN
cana-826	69	7	𝜇𝑗(𝑢𝑖	𝜇𝑗(𝑢𝑖	PROPN
cana-826	69	8	)	)	PUNCT
cana-826	69	9	≤	≤	NUM
cana-826	69	10	𝑠1⁡𝑢𝑖∈𝑉	𝑠1⁡𝑢𝑖∈𝑉	PROPN
cana-826	69	11	&	&	CCONJ
cana-826	69	12	∑	∑	PROPN
cana-826	69	13	(	(	PUNCT
cana-826	69	14	1	1	NUM
cana-826	69	15	−	−	PROPN
cana-826	69	16	𝜈𝑗(𝑢𝑖	𝜈𝑗(𝑢𝑖	NOUN
cana-826	69	17	)	)	PUNCT
cana-826	69	18	)	)	PUNCT
cana-826	69	19	≤	≤	NUM
cana-826	69	20	𝑠2𝑢𝑖∈𝑉	𝑠2𝑢𝑖∈𝑉	ADJ
cana-826	69	21	.	.	PUNCT
cana-826	70	1	definition	definition	NOUN
cana-826	70	2	3.7	3.7	NUM
cana-826	70	3	.	.	PUNCT
cana-826	71	1	consider	consider	VERB
cana-826	71	2	ℍ𝔾	ℍ𝔾	ADV
cana-826	71	3	=	=	SYM
cana-826	71	4	(	(	PUNCT
cana-826	71	5	𝑈	𝑈	PROPN
cana-826	71	6	,	,	PUNCT
cana-826	71	7	ℰ	ℰ	PROPN
cana-826	71	8	;	;	PUNCT
cana-826	71	9	𝑠1	𝑠1	PROPN
cana-826	71	10	,	,	PUNCT
cana-826	71	11	𝑠2	𝑠2	PROPN
cana-826	71	12	)	)	PUNCT
cana-826	71	13	be	be	VERB
cana-826	71	14	an	an	DET
cana-826	71	15	ifthg	ifthg	NOUN
cana-826	71	16	on	on	ADP
cana-826	71	17	a	a	DET
cana-826	71	18	non	non	ADJ
cana-826	71	19	-	-	ADJ
cana-826	71	20	empty	empty	ADJ
cana-826	71	21	set	set	NOUN
cana-826	71	22	𝑈	𝑈	PROPN
cana-826	71	23	is	be	AUX
cana-826	71	24	connected	connect	VERB
cana-826	71	25	if	if	SCONJ
cana-826	71	26	every	every	DET
cana-826	71	27	two	two	NUM
cana-826	71	28	distinct	distinct	ADJ
cana-826	71	29	vertices	vertex	NOUN
cana-826	71	30	in	in	ADV
cana-826	71	31	ℍ𝔾	ℍ𝔾	ADV
cana-826	71	32	are	be	AUX
cana-826	71	33	linked	link	VERB
cana-826	71	34	by	by	ADP
cana-826	71	35	an	an	DET
cana-826	71	36	intuitionistic	intuitionistic	ADJ
cana-826	71	37	fuzzy	fuzzy	ADJ
cana-826	71	38	threshold	threshold	NOUN
cana-826	71	39	hyperpath	hyperpath	NOUN
cana-826	71	40	for	for	ADP
cana-826	71	41	which	which	PRON
cana-826	71	42	∑	∑	PROPN
cana-826	71	43	𝜇𝑗(𝑢𝑖	𝜇𝑗(𝑢𝑖	PROPN
cana-826	71	44	)	)	PUNCT
cana-826	71	45	≤	≤	NUM
cana-826	71	46	𝑠1⁡𝑢𝑖∈𝑉	𝑠1⁡𝑢𝑖∈𝑉	PROPN
cana-826	71	47	&	&	CCONJ
cana-826	71	48	∑	∑	PROPN
cana-826	71	49	(	(	PUNCT
cana-826	71	50	1	1	NUM
cana-826	71	51	−	−	PROPN
cana-826	71	52	𝜈𝑗(𝑢𝑖	𝜈𝑗(𝑢𝑖	NOUN
cana-826	71	53	)	)	PUNCT
cana-826	71	54	)	)	PUNCT
cana-826	72	1	≤	≤	NUM
cana-826	72	2	𝑠2𝑢𝑖∈𝑉	𝑠2𝑢𝑖∈𝑉	ADJ
cana-826	72	3	.	.	PUNCT
cana-826	73	1	otherwise	otherwise	ADV
cana-826	73	2	,	,	PUNCT
cana-826	73	3	ℍ𝔾	ℍ𝔾	PROPN
cana-826	73	4	is	be	AUX
cana-826	73	5	disconnected	disconnect	VERB
cana-826	73	6	.	.	PUNCT
cana-826	74	1	definition	definition	NOUN
cana-826	74	2	3.8	3.8	NUM
cana-826	74	3	.	.	PUNCT
cana-826	75	1	let	let	VERB
cana-826	75	2	ℍ𝔾	ℍ𝔾	ADV
cana-826	75	3	=	=	SYM
cana-826	75	4	(	(	PUNCT
cana-826	75	5	𝑈	𝑈	PROPN
cana-826	75	6	,	,	PUNCT
cana-826	75	7	ℰ	ℰ	PROPN
cana-826	75	8	;	;	PUNCT
cana-826	75	9	𝑠1	𝑠1	PROPN
cana-826	75	10	,	,	PUNCT
cana-826	75	11	𝑠2	𝑠2	PROPN
cana-826	75	12	)	)	PUNCT
cana-826	75	13	be	be	VERB
cana-826	75	14	an	an	DET
cana-826	75	15	ifthg	ifthg	NOUN
cana-826	75	16	.	.	PUNCT
cana-826	76	1	then	then	ADV
cana-826	76	2	the	the	DET
cana-826	76	3	score	score	NOUN
cana-826	76	4	value	value	NOUN
cana-826	76	5	of	of	ADP
cana-826	76	6	a	a	DET
cana-826	76	7	vertex	vertex	NOUN
cana-826	76	8	𝑢𝑖	𝑢𝑖	NOUN
cana-826	76	9	and	and	CCONJ
cana-826	76	10	hyperedge	hyperedge	VERB
cana-826	76	11	ℰ𝑗	ℰ𝑗	PROPN
cana-826	76	12	is	be	AUX
cana-826	76	13	denoted	denote	VERB
cana-826	76	14	as	as	ADP
cana-826	76	15	𝒮(𝑢𝑖	𝒮(𝑢𝑖	NOUN
cana-826	76	16	)	)	PUNCT
cana-826	76	17	=	=	SYM
cana-826	77	1	1−𝜈𝑖(𝑢𝑖	1−𝜈𝑖(𝑢𝑖	NUM
cana-826	77	2	)	)	PUNCT
cana-826	78	1	2−𝜇𝑖(𝑢𝑖)−𝜈𝑖(𝑢𝑖	2−𝜇𝑖(𝑢𝑖)−𝜈𝑖(𝑢𝑖	NUM
cana-826	78	2	)	)	PUNCT
cana-826	78	3	&	&	CCONJ
cana-826	78	4	𝒮(ℰ𝑗	𝒮(ℰ𝑗	NOUN
cana-826	78	5	)	)	PUNCT
cana-826	78	6	=	=	SYM
cana-826	78	7	1−𝜈𝑗(ℰ𝑗	1−𝜈𝑗(ℰ𝑗	NUM
cana-826	78	8	)	)	PUNCT
cana-826	78	9	2−𝜇𝑗(ℰ𝑗)−𝜈𝑗(ℰ𝑗	2−𝜇𝑗(ℰ𝑗)−𝜈𝑗(ℰ𝑗	NUM
cana-826	78	10	)	)	PUNCT
cana-826	78	11	respectively	respectively	ADV
cana-826	78	12	,	,	PUNCT
cana-826	78	13	for	for	ADP
cana-826	78	14	which	which	PRON
cana-826	78	15	∑	∑	PROPN
cana-826	78	16	𝜇𝑗(𝑢𝑖	𝜇𝑗(𝑢𝑖	PROPN
cana-826	78	17	)	)	PUNCT
cana-826	78	18	≤	≤	NUM
cana-826	78	19	𝑠1⁡𝑢𝑖∈𝑉	𝑠1⁡𝑢𝑖∈𝑉	PROPN
cana-826	78	20	&	&	CCONJ
cana-826	78	21	∑	∑	PROPN
cana-826	79	1	(	(	PUNCT
cana-826	79	2	1	1	NUM
cana-826	79	3	−	−	PROPN
cana-826	79	4	𝜈𝑗(𝑢𝑖	𝜈𝑗(𝑢𝑖	NOUN
cana-826	79	5	)	)	PUNCT
cana-826	79	6	)	)	PUNCT
cana-826	79	7	≤	≤	NUM
cana-826	79	8	𝑠2𝑢𝑖∈𝑉	𝑠2𝑢𝑖∈𝑉	ADJ
cana-826	79	9	.	.	PUNCT
cana-826	80	1	communications	communication	NOUN
cana-826	80	2	on	on	ADP
cana-826	80	3	applied	apply	VERB
cana-826	80	4	nonlinear	nonlinear	ADJ
cana-826	80	5	analysis	analysis	NOUN
cana-826	80	6	issn	issn	NOUN
cana-826	80	7	:	:	PUNCT
cana-826	80	8	1074	1074	NUM
cana-826	80	9	-	-	PUNCT
cana-826	80	10	133x	133x	NUM
cana-826	80	11	vol	vol	NOUN
cana-826	80	12	31	31	NUM
cana-826	80	13	no	no	NOUN
cana-826	80	14	.	.	PUNCT
cana-826	81	1	4s	4s	NUM
cana-826	81	2	(	(	PUNCT
cana-826	81	3	2024	2024	NUM
cana-826	81	4	)	)	PUNCT
cana-826	81	5	14	14	NUM
cana-826	81	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-826	81	7	theorem	theorem	VERB
cana-826	81	8	3.1	3.1	NUM
cana-826	81	9	.	.	PUNCT
cana-826	82	1	if	if	SCONJ
cana-826	82	2	𝑑𝑢𝑣	𝑑𝑢𝑣	DET
cana-826	82	3	≤	≤	X
cana-826	82	4	𝑠1	𝑠1	PROPN
cana-826	82	5	and	and	CCONJ
cana-826	82	6	(	(	PUNCT
cana-826	82	7	1	1	NUM
cana-826	82	8	−	−	PROPN
cana-826	82	9	𝑑𝑢𝑣	𝑑𝑢𝑣	PROPN
cana-826	82	10	)	)	PUNCT
cana-826	82	11	≤	≤	NUM
cana-826	82	12	𝑠2	𝑠2	NOUN
cana-826	82	13	,	,	PUNCT
cana-826	82	14	∀𝑢	∀𝑢	NOUN
cana-826	82	15	,	,	PUNCT
cana-826	82	16	𝑣	𝑣	DET
cana-826	82	17	∈	∈	PROPN
cana-826	82	18	ℰ	ℰ	NOUN
cana-826	82	19	in	in	ADP
cana-826	82	20	the	the	DET
cana-826	82	21	ifthg	ifthg	NOUN
cana-826	82	22	,	,	PUNCT
cana-826	82	23	then	then	ADV
cana-826	82	24	the	the	DET
cana-826	82	25	ifthg	ifthg	NOUN
cana-826	82	26	is	be	AUX
cana-826	82	27	connected	connect	VERB
cana-826	82	28	.	.	PUNCT
cana-826	83	1	proof	proof	NOUN
cana-826	83	2	.	.	PUNCT
cana-826	84	1	let	let	VERB
cana-826	84	2	ℍ𝔾	ℍ𝔾	ADV
cana-826	84	3	=	=	SYM
cana-826	84	4	(	(	PUNCT
cana-826	84	5	𝑈	𝑈	PROPN
cana-826	84	6	,	,	PUNCT
cana-826	84	7	ℰ	ℰ	PROPN
cana-826	84	8	;	;	PUNCT
cana-826	84	9	𝑠1	𝑠1	PROPN
cana-826	84	10	,	,	PUNCT
cana-826	84	11	𝑠2	𝑠2	PROPN
cana-826	84	12	)	)	PUNCT
cana-826	84	13	be	be	VERB
cana-826	84	14	an	an	DET
cana-826	84	15	ifthg	ifthg	NOUN
cana-826	84	16	,	,	PUNCT
cana-826	84	17	where	where	SCONJ
cana-826	84	18	𝑈	𝑈	PROPN
cana-826	84	19	represents	represent	VERB
cana-826	84	20	the	the	DET
cana-826	84	21	set	set	NOUN
cana-826	84	22	of	of	ADP
cana-826	84	23	all	all	DET
cana-826	84	24	vertices	vertex	NOUN
cana-826	84	25	𝑢1	𝑢1	PROPN
cana-826	84	26	,	,	PUNCT
cana-826	84	27	𝑢2	𝑢2	PROPN
cana-826	84	28	,	,	PUNCT
cana-826	84	29	…	…	PUNCT
cana-826	84	30	,	,	PUNCT
cana-826	84	31	𝑢𝑛	𝑢𝑛	NOUN
cana-826	84	32	and	and	CCONJ
cana-826	84	33	ℰ	ℰ	PROPN
cana-826	84	34	represents	represent	VERB
cana-826	84	35	the	the	DET
cana-826	84	36	set	set	NOUN
cana-826	84	37	of	of	ADP
cana-826	84	38	all	all	DET
cana-826	84	39	hyperedges	hyperedge	NOUN
cana-826	84	40	ℰ1	ℰ1	NOUN
cana-826	84	41	,	,	PUNCT
cana-826	84	42	ℰ2	ℰ2	NOUN
cana-826	84	43	,	,	PUNCT
cana-826	84	44	…	…	PUNCT
cana-826	84	45	,	,	PUNCT
cana-826	84	46	ℰ𝑛.	ℰ𝑛.	PROPN
cana-826	84	47	let	let	VERB
cana-826	84	48	𝑑𝑢𝑣	𝑑𝑢𝑣	PROPN
cana-826	84	49	denote	denote	VERB
cana-826	84	50	the	the	DET
cana-826	84	51	distance	distance	NOUN
cana-826	84	52	between	between	ADP
cana-826	84	53	any	any	DET
cana-826	84	54	two	two	NUM
cana-826	84	55	connected	connected	ADJ
cana-826	84	56	vertices	vertex	NOUN
cana-826	84	57	u	u	NOUN
cana-826	84	58	and	and	CCONJ
cana-826	84	59	v	v	NOUN
cana-826	84	60	and	and	CCONJ
cana-826	84	61	let	let	VERB
cana-826	84	62	𝑠1	𝑠1	PROPN
cana-826	84	63	,	,	PUNCT
cana-826	84	64	𝑠2	𝑠2	PROPN
cana-826	84	65	denotes	denote	VERB
cana-826	84	66	the	the	DET
cana-826	84	67	threshold	threshold	NOUN
cana-826	84	68	values	value	NOUN
cana-826	84	69	.	.	PUNCT
cana-826	85	1	assume	assume	VERB
cana-826	85	2	two	two	NUM
cana-826	85	3	arbitrary	arbitrary	ADJ
cana-826	85	4	vertices	vertex	NOUN
cana-826	85	5	u	u	NOUN
cana-826	85	6	and	and	CCONJ
cana-826	85	7	v	v	ADP
cana-826	85	8	which	which	PRON
cana-826	85	9	are	be	AUX
cana-826	85	10	connected	connect	VERB
cana-826	85	11	in	in	ADP
cana-826	85	12	the	the	DET
cana-826	85	13	ifthg	ifthg	NOUN
cana-826	85	14	.	.	PUNCT
cana-826	86	1	∃	∃	PROPN
cana-826	86	2	a	a	DET
cana-826	86	3	path	path	NOUN
cana-826	86	4	𝑃	𝑃	NOUN
cana-826	86	5	:	:	PUNCT
cana-826	86	6	𝑢	𝑢	X
cana-826	86	7	=	=	SYM
cana-826	86	8	𝑢1⁡ℰ1⁡𝑢2⁡ℰ2	𝑢1⁡ℰ1⁡𝑢2⁡ℰ2	NOUN
cana-826	86	9	…	…	SYM
cana-826	86	10	𝑢𝑚⁡ℰ𝑚⁡𝑢𝑚+1	𝑢𝑚⁡ℰ𝑚⁡𝑢𝑚+1	NOUN
cana-826	86	11	between	between	ADP
cana-826	86	12	any	any	DET
cana-826	86	13	2	2	NUM
cana-826	86	14	vertices	vertex	NOUN
cana-826	86	15	u	u	NOUN
cana-826	86	16	&	&	CCONJ
cana-826	86	17	v	v	NOUN
cana-826	86	18	in	in	ADP
cana-826	86	19	the	the	DET
cana-826	86	20	ifthg	ifthg	NOUN
cana-826	86	21	with	with	ADP
cana-826	86	22	the	the	DET
cana-826	86	23	condition	condition	NOUN
cana-826	86	24	that	that	SCONJ
cana-826	86	25	the	the	DET
cana-826	86	26	distance	distance	NOUN
cana-826	86	27	𝑑𝑢𝑣	𝑑𝑢𝑣	NOUN
cana-826	86	28	between	between	ADP
cana-826	86	29	u	u	PROPN
cana-826	86	30	&	&	CCONJ
cana-826	86	31	v	v	PROPN
cana-826	86	32	must	must	AUX
cana-826	86	33	satisfy	satisfy	VERB
cana-826	86	34	the	the	DET
cana-826	86	35	condition	condition	NOUN
cana-826	86	36	𝑑𝑢𝑣	𝑑𝑢𝑣	PROPN
cana-826	86	37	≤	≤	ADJ
cana-826	86	38	𝑠1	𝑠1	PROPN
cana-826	86	39	and	and	CCONJ
cana-826	86	40	(	(	PUNCT
cana-826	86	41	1	1	NUM
cana-826	86	42	−	−	PROPN
cana-826	86	43	𝑑𝑢𝑣	𝑑𝑢𝑣	PROPN
cana-826	86	44	)	)	PUNCT
cana-826	86	45	≤	≤	NOUN
cana-826	86	46	𝑠2	𝑠2	NOUN
cana-826	86	47	.	.	PUNCT
cana-826	87	1	since	since	SCONJ
cana-826	87	2	all	all	DET
cana-826	87	3	the	the	DET
cana-826	87	4	hyperedges	hyperedge	NOUN
cana-826	87	5	are	be	AUX
cana-826	87	6	connected	connect	VERB
cana-826	87	7	with	with	ADP
cana-826	87	8	each	each	DET
cana-826	87	9	other	other	ADJ
cana-826	87	10	,	,	PUNCT
cana-826	87	11	it	it	PRON
cana-826	87	12	is	be	AUX
cana-826	87	13	proved	prove	VERB
cana-826	87	14	that	that	SCONJ
cana-826	87	15	the	the	DET
cana-826	87	16	ifthg	ifthg	NOUN
cana-826	87	17	is	be	AUX
cana-826	87	18	connected	connect	VERB
cana-826	87	19	.	.	PUNCT
cana-826	88	1	theorem	theorem	ADJ
cana-826	88	2	3.2	3.2	NUM
cana-826	88	3	.	.	PUNCT
cana-826	89	1	let	let	VERB
cana-826	89	2	ℍ𝔾	ℍ𝔾	ADV
cana-826	89	3	=	=	SYM
cana-826	89	4	(	(	PUNCT
cana-826	89	5	𝑈	𝑈	PROPN
cana-826	89	6	,	,	PUNCT
cana-826	89	7	ℰ	ℰ	PROPN
cana-826	89	8	;	;	PUNCT
cana-826	89	9	𝑠1	𝑠1	PROPN
cana-826	89	10	,	,	PUNCT
cana-826	89	11	𝑠2	𝑠2	PROPN
cana-826	89	12	)	)	PUNCT
cana-826	89	13	be	be	VERB
cana-826	89	14	the	the	DET
cana-826	89	15	ifthg	ifthg	NOUN
cana-826	89	16	.	.	PUNCT
cana-826	90	1	then	then	ADV
cana-826	90	2	ℍ𝔾	ℍ𝔾	PROPN
cana-826	90	3	is	be	AUX
cana-826	90	4	disconnected	disconnect	VERB
cana-826	90	5	iff	iff	PROPN
cana-826	90	6	every	every	DET
cana-826	90	7	nonempty	nonempty	ADJ
cana-826	90	8	subsets	subset	NOUN
cana-826	90	9	𝑈1	𝑈1	NOUN
cana-826	90	10	,	,	PUNCT
cana-826	90	11	𝑈2	𝑈2	NOUN
cana-826	90	12	of	of	ADP
cana-826	90	13	𝑈	𝑈	PROPN
cana-826	90	14	such	such	ADJ
cana-826	90	15	that	that	SCONJ
cana-826	90	16	𝑈1	𝑈1	PROPN
cana-826	90	17	∪	∪	ADJ
cana-826	90	18	𝑈2	𝑈2	PROPN
cana-826	90	19	=	=	PUNCT
cana-826	90	20	𝑈,𝑈1	𝑈,𝑈1	PROPN
cana-826	90	21	∩𝑈2	∩𝑈2	NOUN
cana-826	90	22	=	=	NOUN
cana-826	91	1	∅	∅	NOUN
cana-826	92	1	and	and	CCONJ
cana-826	92	2	there	there	PRON
cana-826	92	3	is	be	VERB
cana-826	92	4	no	no	DET
cana-826	92	5	hyperedge	hyperedge	NOUN
cana-826	92	6	ℰ𝑗	ℰ𝑗	PROPN
cana-826	92	7	∈	∈	NOUN
cana-826	92	8	ℰ	ℰ	NOUN
cana-826	92	9	which	which	PRON
cana-826	92	10	has	have	VERB
cana-826	92	11	one	one	NUM
cana-826	92	12	vertex	vertex	NOUN
cana-826	92	13	in	in	ADP
cana-826	92	14	𝑈1	𝑈1	NOUN
cana-826	92	15	and	and	CCONJ
cana-826	92	16	another	another	DET
cana-826	92	17	vertex	vertex	NOUN
cana-826	92	18	in	in	ADP
cana-826	92	19	𝑈2	𝑈2	PROPN
cana-826	92	20	.	.	PUNCT
cana-826	93	1	proof	proof	NOUN
cana-826	93	2	.	.	PUNCT
cana-826	94	1	suppose	suppose	VERB
cana-826	94	2	that	that	SCONJ
cana-826	94	3	ℍ𝔾	ℍ𝔾	PROPN
cana-826	94	4	=	=	SYM
cana-826	94	5	(	(	PUNCT
cana-826	94	6	𝑈	𝑈	PROPN
cana-826	94	7	,	,	PUNCT
cana-826	94	8	ℰ	ℰ	PROPN
cana-826	94	9	;	;	PUNCT
cana-826	94	10	𝑠1	𝑠1	PROPN
cana-826	94	11	,	,	PUNCT
cana-826	94	12	𝑠2	𝑠2	PROPN
cana-826	94	13	)	)	PUNCT
cana-826	94	14	is	be	AUX
cana-826	94	15	a	a	DET
cana-826	94	16	disconnected	disconnected	ADJ
cana-826	94	17	ifthg	ifthg	NOUN
cana-826	94	18	.	.	PUNCT
cana-826	95	1	then	then	ADV
cana-826	95	2	∃	∃	PROPN
cana-826	95	3	a	a	DET
cana-826	95	4	vertices	vertex	NOUN
cana-826	95	5	𝑢	𝑢	PART
cana-826	95	6	,	,	PUNCT
cana-826	95	7	𝑣⁡𝜖⁡𝑈	𝑣⁡𝜖⁡𝑈	PRON
cana-826	95	8	such	such	ADJ
cana-826	95	9	that	that	SCONJ
cana-826	95	10	there	there	PRON
cana-826	95	11	is	be	VERB
cana-826	95	12	no	no	DET
cana-826	95	13	path	path	NOUN
cana-826	95	14	between	between	ADP
cana-826	95	15	u	u	NOUN
cana-826	95	16	and	and	CCONJ
cana-826	95	17	v.	v.	CCONJ
cana-826	95	18	let	let	VERB
cana-826	95	19	𝑈𝑢	𝑈𝑢	PROPN
cana-826	95	20	=	=	PRON
cana-826	95	21	{	{	PUNCT
cana-826	95	22	𝑢	𝑢	X
cana-826	95	23	∈	∈	PROPN
cana-826	95	24	𝑈|∃⁡a⁡path⁡between⁡𝑢⁡&⁡𝑣	𝑈|∃⁡a⁡path⁡between⁡𝑢⁡&⁡𝑣	NUM
cana-826	95	25	}	}	PUNCT
cana-826	95	26	.	.	PUNCT
cana-826	96	1	then	then	ADV
cana-826	96	2	,	,	PUNCT
cana-826	96	3	clearly	clearly	ADV
cana-826	96	4	𝑈𝑢	𝑈𝑢	PROPN
cana-826	96	5	≠	≠	PROPN
cana-826	96	6	∅.	∅.	AUX
cana-826	96	7	let	let	VERB
cana-826	96	8	𝑈𝑣	𝑈𝑣	PROPN
cana-826	96	9	=	=	PROPN
cana-826	96	10	𝑈	𝑈	PROPN
cana-826	96	11	−𝑈𝑢.	−𝑈𝑢.	PROPN
cana-826	96	12	since	since	SCONJ
cana-826	96	13	𝑣	𝑣	PRON
cana-826	96	14	∉	∉	PROPN
cana-826	96	15	𝑈𝑢	𝑈𝑢	PROPN
cana-826	96	16	⟹	⟹	VERB
cana-826	96	17	𝑣	𝑣	DET
cana-826	96	18	∈	∈	PROPN
cana-826	96	19	𝑈𝑣.	𝑈𝑣.	PROPN
cana-826	96	20	now	now	ADV
cana-826	96	21	,	,	PUNCT
cana-826	96	22	𝑈𝑢	𝑈𝑢	PROPN
cana-826	96	23	≠	≠	PROPN
cana-826	96	24	∅,𝑈𝑣	∅,𝑈𝑣	NUM
cana-826	96	25	≠	≠	PROPN
cana-826	96	26	∅	∅	NOUN
cana-826	96	27	and	and	CCONJ
cana-826	96	28	𝑈𝑢	𝑈𝑢	PROPN
cana-826	96	29	∪	∪	ADP
cana-826	96	30	𝑈𝑣	𝑈𝑣	PROPN
cana-826	96	31	=	=	PUNCT
cana-826	96	32	𝑈.(also	𝑈.(also	PUNCT
cana-826	96	33	𝑈𝑢	𝑈𝑢	PROPN
cana-826	96	34	∩𝑈𝑣	∩𝑈𝑣	NOUN
cana-826	96	35	=	=	SYM
cana-826	96	36	∅	∅	NOUN
cana-826	96	37	)	)	PUNCT
cana-826	96	38	.	.	PUNCT
cana-826	97	1	suppose	suppose	VERB
cana-826	97	2	there	there	PRON
cana-826	97	3	exists	exist	VERB
cana-826	97	4	a	a	DET
cana-826	97	5	hyperedge	hyperedge	NOUN
cana-826	97	6	ℰ𝑗	ℰ𝑗	PROPN
cana-826	97	7	=	=	SYM
cana-826	97	8	{	{	PUNCT
cana-826	97	9	𝑢1	𝑢1	PROPN
cana-826	97	10	,	,	PUNCT
cana-826	97	11	𝑢2	𝑢2	PROPN
cana-826	97	12	}	}	PUNCT
cana-826	97	13	∈	∈	PROPN
cana-826	97	14	ℰ	ℰ	NOUN
cana-826	97	15	such	such	ADJ
cana-826	97	16	that	that	SCONJ
cana-826	97	17	𝑢1	𝑢1	PROPN
cana-826	97	18	∈	∈	PROPN
cana-826	97	19	𝑈𝑢	𝑈𝑢	PROPN
cana-826	97	20	,	,	PUNCT
cana-826	97	21	𝑢2	𝑢2	PROPN
cana-826	97	22	∈	∈	PROPN
cana-826	97	23	𝑈𝑣.	𝑈𝑣.	PROPN
cana-826	97	24	now	now	ADV
cana-826	97	25	𝑢1	𝑢1	PROPN
cana-826	97	26	and	and	CCONJ
cana-826	97	27	𝑢	𝑢	NOUN
cana-826	97	28	are	be	AUX
cana-826	97	29	connected	connect	VERB
cana-826	97	30	as	as	ADP
cana-826	97	31	ℰ𝑗	ℰ𝑗	PROPN
cana-826	97	32	=	=	SYM
cana-826	97	33	{	{	PUNCT
cana-826	97	34	𝑢1	𝑢1	PROPN
cana-826	97	35	,	,	PUNCT
cana-826	97	36	𝑢2	𝑢2	PROPN
cana-826	97	37	}	}	PUNCT
cana-826	97	38	⟹	⟹	NUM
cana-826	97	39	𝑢⁡and⁡𝑢2⁡	𝑢⁡and⁡𝑢2⁡	NOUN
cana-826	97	40	are	be	AUX
cana-826	97	41	also	also	ADV
cana-826	97	42	disconnected	disconnect	VERB
cana-826	97	43	.	.	PUNCT
cana-826	98	1	⇒	⇒	PROPN
cana-826	98	2	𝑢2	𝑢2	PROPN
cana-826	98	3	∈	∈	PROPN
cana-826	98	4	𝑈𝑢	𝑈𝑢	PROPN
cana-826	98	5	which	which	PRON
cana-826	98	6	is	be	AUX
cana-826	98	7	a	a	DET
cana-826	98	8	contradiction	contradiction	NOUN
cana-826	98	9	.	.	PUNCT
cana-826	99	1	hence	hence	ADV
cana-826	99	2	the	the	DET
cana-826	99	3	result	result	NOUN
cana-826	99	4	holds	hold	VERB
cana-826	99	5	good	good	ADJ
cana-826	99	6	.	.	PUNCT
cana-826	100	1	conversely	conversely	ADV
cana-826	100	2	,	,	PUNCT
cana-826	100	3	assume	assume	VERB
cana-826	100	4	that	that	SCONJ
cana-826	100	5	∃	∃	PROPN
cana-826	100	6	a	a	DET
cana-826	100	7	partition	partition	NOUN
cana-826	100	8	of	of	ADP
cana-826	100	9	𝑈	𝑈	PROPN
cana-826	101	1	such	such	ADJ
cana-826	101	2	that	that	SCONJ
cana-826	101	3	𝑈1	𝑈1	PROPN
cana-826	101	4	∪𝑈2	∪𝑈2	PROPN
cana-826	101	5	=	=	SYM
cana-826	101	6	𝑈,𝑈1	𝑈,𝑈1	PROPN
cana-826	101	7	∩	∩	PROPN
cana-826	101	8	𝑈2	𝑈2	NOUN
cana-826	101	9	=	=	SYM
cana-826	101	10	∅	∅	NOUN
cana-826	101	11	,	,	PUNCT
cana-826	101	12	⁡𝑈1	⁡𝑈1	PROPN
cana-826	101	13	≠	≠	PART
cana-826	101	14	∅,𝑈2	∅,𝑈2	NOUN
cana-826	101	15	≠	≠	PROPN
cana-826	101	16	∅⁡and	∅⁡and	PROPN
cana-826	101	17	there	there	ADV
cana-826	101	18	exists	exist	VERB
cana-826	101	19	no	no	DET
cana-826	101	20	hyperedge	hyperedge	NOUN
cana-826	101	21	ℰ𝑗	ℰ𝑗	PROPN
cana-826	101	22	∈	∈	NOUN
cana-826	101	23	ℰ	ℰ	NOUN
cana-826	101	24	having	have	VERB
cana-826	101	25	one	one	NUM
cana-826	101	26	vertex	vertex	NOUN
cana-826	101	27	in	in	ADP
cana-826	101	28	𝑈1	𝑈1	NOUN
cana-826	101	29	and	and	CCONJ
cana-826	101	30	another	another	DET
cana-826	101	31	vertex	vertex	NOUN
cana-826	101	32	in	in	ADP
cana-826	101	33	𝑈2	𝑈2	PROPN
cana-826	101	34	.	.	PUNCT
cana-826	102	1	to	to	PART
cana-826	102	2	prove	prove	VERB
cana-826	102	3	:	:	PUNCT
cana-826	102	4	ℍ𝔾	ℍ𝔾	PROPN
cana-826	102	5	is	be	AUX
cana-826	102	6	disconnected	disconnect	VERB
cana-826	102	7	.	.	PUNCT
cana-826	103	1	suppose	suppose	VERB
cana-826	103	2	ℍ𝔾	ℍ𝔾	ADV
cana-826	103	3	is	be	AUX
cana-826	103	4	connected	connect	VERB
cana-826	103	5	.	.	PUNCT
cana-826	104	1	take	take	VERB
cana-826	104	2	𝑢𝜖𝑈1	𝑢𝜖𝑈1	PROPN
cana-826	104	3	⊆	⊆	NUM
cana-826	104	4	𝑈,𝑣𝜖𝑈2	𝑈,𝑣𝜖𝑈2	PROPN
cana-826	104	5	⊆	⊆	NUM
cana-826	104	6	𝑈.	𝑈.	NOUN
cana-826	104	7	⟹	⟹	PUNCT
cana-826	105	1	𝑢,𝑣	𝑢,𝑣	VERB
cana-826	105	2	∈	∈	NOUN
cana-826	105	3	𝑈1	𝑈1	NOUN
cana-826	105	4	∪𝑈2	∪𝑈2	PROPN
cana-826	105	5	=	=	SYM
cana-826	105	6	𝑈	𝑈	PROPN
cana-826	105	7	[	[	AUX
cana-826	105	8	since	since	SCONJ
cana-826	105	9	ℍ𝔾	ℍ𝔾	ADV
cana-826	105	10	is	be	AUX
cana-826	105	11	connected	connect	VERB
cana-826	105	12	]	]	X
cana-826	105	13	.	.	PUNCT
cana-826	106	1	therefore	therefore	ADV
cana-826	106	2	,	,	PUNCT
cana-826	106	3	∃	∃	PROPN
cana-826	106	4	a	a	DET
cana-826	106	5	path	path	NOUN
cana-826	106	6	𝑃	𝑃	NOUN
cana-826	106	7	:	:	PUNCT
cana-826	106	8	𝑢	𝑢	X
cana-826	106	9	=	=	SYM
cana-826	106	10	𝑢1ℰ1𝑢2ℰ2	𝑢1ℰ1𝑢2ℰ2	X
cana-826	106	11	…	…	PUNCT
cana-826	106	12	𝑢𝑚ℰ𝑚𝑢𝑚+1	𝑢𝑚ℰ𝑚𝑢𝑚+1	NOUN
cana-826	106	13	=	=	SYM
cana-826	106	14	𝑣	𝑣	ADP
cana-826	106	15	connecting	connect	VERB
cana-826	106	16	u	u	NOUN
cana-826	106	17	and	and	CCONJ
cana-826	106	18	v.	v.	ADP
cana-826	106	19	since	since	SCONJ
cana-826	106	20	𝑢𝜖𝑈1	𝑢𝜖𝑈1	PROPN
cana-826	106	21	,	,	PUNCT
cana-826	106	22	𝑣	𝑣	PRON
cana-826	106	23	∈	∈	PROPN
cana-826	106	24	𝑈2	𝑈2	NOUN
cana-826	106	25	and	and	CCONJ
cana-826	106	26	𝑈1	𝑈1	PROPN
cana-826	106	27	∩	∩	NOUN
cana-826	106	28	𝑈2	𝑈2	NOUN
cana-826	106	29	=	=	PUNCT
cana-826	106	30	∅.	∅.	NOUN
cana-826	106	31	⟹	⟹	NUM
cana-826	106	32	there	there	ADV
cana-826	106	33	exists	exist	VERB
cana-826	106	34	an	an	DET
cana-826	106	35	i	i	PRON
cana-826	106	36	such	such	ADJ
cana-826	106	37	that	that	SCONJ
cana-826	106	38	𝑢𝑖	𝑢𝑖	DET
cana-826	106	39	∈	∈	PROPN
cana-826	106	40	𝑈1	𝑈1	NOUN
cana-826	106	41	,	,	PUNCT
cana-826	106	42	𝑢𝑖+1	𝑢𝑖+1	PROPN
cana-826	106	43	∈	∈	PROPN
cana-826	106	44	𝑈2	𝑈2	PROPN
cana-826	106	45	.	.	PUNCT
cana-826	107	1	now	now	ADV
cana-826	107	2	ℰ	ℰ	NOUN
cana-826	107	3	=	=	SYM
cana-826	107	4	{	{	PUNCT
cana-826	107	5	𝑢𝑖	𝑢𝑖	INTJ
cana-826	107	6	,	,	PUNCT
cana-826	107	7	𝑢𝑖+1	𝑢𝑖+1	PROPN
cana-826	107	8	}	}	PUNCT
cana-826	107	9	∈	∈	NOUN
cana-826	107	10	ℰ	ℰ	NOUN
cana-826	107	11	such	such	ADJ
cana-826	107	12	that	that	DET
cana-826	107	13	one	one	NUM
cana-826	107	14	vertex	vertex	NOUN
cana-826	107	15	is	be	AUX
cana-826	107	16	in	in	ADP
cana-826	107	17	𝑈1	𝑈1	NOUN
cana-826	107	18	and	and	CCONJ
cana-826	107	19	another	another	DET
cana-826	107	20	vertex	vertex	NOUN
cana-826	107	21	is	be	AUX
cana-826	107	22	in	in	ADP
cana-826	107	23	𝑈2	𝑈2	PROPN
cana-826	107	24	.	.	PUNCT
cana-826	108	1	which	which	PRON
cana-826	108	2	is	be	AUX
cana-826	108	3	contradiction	contradiction	NOUN
cana-826	108	4	.	.	PUNCT
cana-826	109	1	⟹	⟹	PROPN
cana-826	110	1	ℍ𝔾	ℍ𝔾	PROPN
cana-826	110	2	is	be	AUX
cana-826	110	3	disconnected	disconnected	ADJ
cana-826	110	4	ifthg	ifthg	NOUN
cana-826	110	5	.	.	PUNCT
cana-826	111	1	communications	communication	NOUN
cana-826	111	2	on	on	ADP
cana-826	111	3	applied	apply	VERB
cana-826	111	4	nonlinear	nonlinear	ADJ
cana-826	111	5	analysis	analysis	NOUN
cana-826	111	6	issn	issn	NOUN
cana-826	111	7	:	:	PUNCT
cana-826	111	8	1074	1074	NUM
cana-826	111	9	-	-	PUNCT
cana-826	111	10	133x	133x	NUM
cana-826	111	11	vol	vol	NOUN
cana-826	111	12	31	31	NUM
cana-826	111	13	no	no	NOUN
cana-826	111	14	.	.	PUNCT
cana-826	112	1	4s	4s	NUM
cana-826	112	2	(	(	PUNCT
cana-826	112	3	2024	2024	NUM
cana-826	112	4	)	)	PUNCT
cana-826	112	5	15	15	NUM
cana-826	112	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-826	112	7	theorem	theorem	VERB
cana-826	112	8	3.3	3.3	NUM
cana-826	112	9	.	.	PUNCT
cana-826	113	1	let	let	VERB
cana-826	113	2	ℍ𝔾	ℍ𝔾	ADV
cana-826	113	3	be	be	AUX
cana-826	113	4	an	an	DET
cana-826	113	5	ifthg	ifthg	NOUN
cana-826	113	6	,	,	PUNCT
cana-826	113	7	with	with	ADP
cana-826	113	8	vertices	vertex	NOUN
cana-826	113	9	u	u	NOUN
cana-826	113	10	,	,	PUNCT
cana-826	113	11	v	v	NOUN
cana-826	113	12	∈	∈	NOUN
cana-826	113	13	u.	u.	VERB
cana-826	113	14	there	there	PRON
cana-826	113	15	is	be	VERB
cana-826	113	16	a	a	DET
cana-826	113	17	𝑢	𝑢	ADJ
cana-826	113	18	−	−	NOUN
cana-826	113	19	𝑣	𝑣	ADP
cana-826	113	20	hyper	hyper	ADJ
cana-826	113	21	walk	walk	NOUN
cana-826	113	22	in	in	ADP
cana-826	113	23	ℍ𝔾	ℍ𝔾	PROPN
cana-826	113	24	iff	iff	PROPN
cana-826	113	25	there	there	PRON
cana-826	113	26	exists	exist	VERB
cana-826	113	27	a	a	DET
cana-826	113	28	𝑢	𝑢	ADJ
cana-826	113	29	−	−	NOUN
cana-826	113	30	𝑣	𝑣	ADP
cana-826	113	31	hyperpath	hyperpath	NOUN
cana-826	113	32	.	.	PUNCT
cana-826	114	1	proof	proof	NOUN
cana-826	114	2	.	.	PUNCT
cana-826	115	1	assume	assume	VERB
cana-826	115	2	ℍ𝔾	ℍ𝔾	PROPN
cana-826	115	3	=	=	SYM
cana-826	115	4	(	(	PUNCT
cana-826	115	5	𝑈	𝑈	PROPN
cana-826	115	6	,	,	PUNCT
cana-826	115	7	ℰ	ℰ	PROPN
cana-826	115	8	;	;	PUNCT
cana-826	115	9	𝑠1	𝑠1	PROPN
cana-826	115	10	,	,	PUNCT
cana-826	115	11	𝑠2	𝑠2	PROPN
cana-826	115	12	)	)	PUNCT
cana-826	115	13	be	be	VERB
cana-826	115	14	an	an	DET
cana-826	115	15	ifthg	ifthg	NOUN
cana-826	115	16	and	and	CCONJ
cana-826	115	17	w	w	NOUN
cana-826	115	18	is	be	AUX
cana-826	115	19	a	a	DET
cana-826	115	20	hyper	hyper	ADJ
cana-826	115	21	walk	walk	NOUN
cana-826	115	22	in	in	ADP
cana-826	115	23	ℍ𝔾.	ℍ𝔾.	X
cana-826	115	24	the	the	DET
cana-826	115	25	theorem	theorem	NOUN
cana-826	115	26	is	be	AUX
cana-826	115	27	proved	prove	VERB
cana-826	115	28	by	by	ADP
cana-826	115	29	using	use	VERB
cana-826	115	30	mathematical	mathematical	ADJ
cana-826	115	31	induction	induction	NOUN
cana-826	115	32	on	on	ADP
cana-826	115	33	length	length	NOUN
cana-826	115	34	of	of	ADP
cana-826	115	35	w	w	NOUN
cana-826	115	36	.	.	PUNCT
cana-826	116	1	if	if	SCONJ
cana-826	116	2	w	w	NOUN
cana-826	116	3	be	be	AUX
cana-826	116	4	the	the	DET
cana-826	116	5	length	length	NOUN
cana-826	116	6	1	1	NUM
cana-826	116	7	or	or	CCONJ
cana-826	116	8	2	2	NUM
cana-826	116	9	,	,	PUNCT
cana-826	116	10	then	then	ADV
cana-826	116	11	it	it	PRON
cana-826	116	12	is	be	AUX
cana-826	116	13	obvious	obvious	ADJ
cana-826	116	14	that	that	SCONJ
cana-826	116	15	w	w	NOUN
cana-826	116	16	is	be	AUX
cana-826	116	17	a	a	DET
cana-826	116	18	hyperpath	hyperpath	NOUN
cana-826	116	19	in	in	ADP
cana-826	116	20	ℍ𝔾.	ℍ𝔾.	X
cana-826	116	21	now	now	ADV
cana-826	116	22	,	,	PUNCT
cana-826	116	23	assume	assume	VERB
cana-826	116	24	the	the	DET
cana-826	116	25	result	result	NOUN
cana-826	116	26	is	be	AUX
cana-826	116	27	possible	possible	ADJ
cana-826	116	28	for	for	SCONJ
cana-826	116	29	every	every	DET
cana-826	116	30	hyperwalks	hyperwalk	NOUN
cana-826	116	31	of	of	ADP
cana-826	116	32	length	length	NOUN
cana-826	116	33	less	less	ADV
cana-826	116	34	than	than	ADP
cana-826	116	35	k	k	PROPN
cana-826	116	36	,	,	PUNCT
cana-826	116	37	and	and	CCONJ
cana-826	116	38	consider	consider	VERB
cana-826	116	39	w	w	NOUN
cana-826	116	40	has	have	VERB
cana-826	116	41	length	length	NOUN
cana-826	116	42	k	k	NOUN
cana-826	116	43	,	,	PUNCT
cana-826	116	44	which	which	PRON
cana-826	116	45	implies	imply	VERB
cana-826	116	46	w	w	NOUN
cana-826	116	47	is	be	AUX
cana-826	116	48	,	,	PUNCT
cana-826	116	49	𝑢	𝑢	X
cana-826	116	50	=	=	PROPN
cana-826	116	51	𝑢0	𝑢0	PROPN
cana-826	116	52	,	,	PUNCT
cana-826	116	53	𝑢1	𝑢1	NOUN
cana-826	116	54	,	,	PUNCT
cana-826	116	55	𝑢2	𝑢2	PROPN
cana-826	116	56	,	,	PUNCT
cana-826	116	57	…	…	PUNCT
cana-826	116	58	,	,	PUNCT
cana-826	116	59	𝑢𝑘−1	𝑢𝑘−1	PROPN
cana-826	116	60	,	,	PUNCT
cana-826	116	61	𝑢𝑘	𝑢𝑘	ADP
cana-826	116	62	=	=	PUNCT
cana-826	116	63	𝑣	𝑣	X
cana-826	116	64	where	where	SCONJ
cana-826	116	65	the	the	DET
cana-826	116	66	vertices	vertex	NOUN
cana-826	116	67	are	be	AUX
cana-826	116	68	not	not	PART
cana-826	116	69	necessarily	necessarily	ADV
cana-826	116	70	distinct	distinct	ADJ
cana-826	116	71	.	.	PUNCT
cana-826	117	1	if	if	SCONJ
cana-826	117	2	the	the	DET
cana-826	117	3	vertices	vertex	NOUN
cana-826	117	4	are	be	AUX
cana-826	117	5	distinct	distinct	ADJ
cana-826	117	6	then	then	ADV
cana-826	117	7	w	w	ADP
cana-826	117	8	itself	itself	PRON
cana-826	117	9	be	be	VERB
cana-826	117	10	a	a	DET
cana-826	117	11	desired	desire	VERB
cana-826	117	12	𝑢	𝑢	NOUN
cana-826	117	13	−	−	PROPN
cana-826	117	14	𝑣	𝑣	ADP
cana-826	117	15	hyperpath	hyperpath	NOUN
cana-826	117	16	.	.	PUNCT
cana-826	118	1	if	if	SCONJ
cana-826	118	2	not	not	PART
cana-826	118	3	,	,	PUNCT
cana-826	118	4	then	then	ADV
cana-826	118	5	assume	assume	VERB
cana-826	118	6	j	j	PROPN
cana-826	118	7	is	be	AUX
cana-826	118	8	a	a	DET
cana-826	118	9	smallest	small	ADJ
cana-826	118	10	integer	integer	NOUN
cana-826	118	11	such	such	ADJ
cana-826	118	12	that	that	DET
cana-826	118	13	𝑢𝑗	𝑢𝑗	NOUN
cana-826	118	14	=	=	PUNCT
cana-826	118	15	𝑢𝑟	𝑢𝑟	ADV
cana-826	118	16	for	for	ADP
cana-826	118	17	some	some	DET
cana-826	118	18	𝑟	𝑟	NOUN
cana-826	118	19	>	>	X
cana-826	118	20	𝑗.	𝑗.	PROPN
cana-826	118	21	assume	assume	PROPN
cana-826	118	22	w1	w1	NOUN
cana-826	118	23	is	be	AUX
cana-826	118	24	a	a	DET
cana-826	118	25	hyperwalk	hyperwalk	NOUN
cana-826	118	26	in	in	ADP
cana-826	118	27	ℍ𝔾	ℍ𝔾	PROPN
cana-826	118	28	,	,	PUNCT
cana-826	118	29	is	be	AUX
cana-826	118	30	𝑢	𝑢	PRON
cana-826	118	31	=	=	PROPN
cana-826	118	32	𝑢0	𝑢0	PROPN
cana-826	118	33	,	,	PUNCT
cana-826	118	34	𝑢1	𝑢1	NOUN
cana-826	118	35	,	,	PUNCT
cana-826	118	36	𝑢2	𝑢2	PROPN
cana-826	118	37	,	,	PUNCT
cana-826	118	38	…	…	PUNCT
cana-826	118	39	,	,	PUNCT
cana-826	118	40	𝑢𝑗	𝑢𝑗	NOUN
cana-826	118	41	,	,	PUNCT
cana-826	118	42	𝑢𝑟+1	𝑢𝑟+1	PROPN
cana-826	118	43	,	,	PUNCT
cana-826	118	44	…	…	PUNCT
cana-826	118	45	,	,	PUNCT
cana-826	118	46	𝑢𝑘	𝑢𝑘	X
cana-826	118	47	=	=	PUNCT
cana-826	118	48	𝑣.	𝑣.	NOUN
cana-826	118	49	this	this	DET
cana-826	118	50	hyperwalk	hyperwalk	NOUN
cana-826	118	51	has	have	VERB
cana-826	118	52	length	length	NOUN
cana-826	118	53	strictly	strictly	ADV
cana-826	118	54	less	less	ADJ
cana-826	118	55	than	than	ADP
cana-826	118	56	k	k	PROPN
cana-826	118	57	,	,	PUNCT
cana-826	118	58	and	and	CCONJ
cana-826	118	59	then	then	ADV
cana-826	118	60	the	the	DET
cana-826	118	61	induction	induction	NOUN
cana-826	118	62	hypothesis	hypothesis	NOUN
cana-826	118	63	gives	give	VERB
cana-826	118	64	that	that	DET
cana-826	118	65	w1	w1	NOUN
cana-826	118	66	has	have	VERB
cana-826	118	67	a	a	DET
cana-826	118	68	𝑢	𝑢	NOUN
cana-826	118	69	−	−	NOUN
cana-826	118	70	𝑣	𝑣	ADP
cana-826	118	71	hyperpath	hyperpath	NOUN
cana-826	118	72	in	in	ADP
cana-826	118	73	ℍ𝔾.	ℍ𝔾.	ADP
cana-826	118	74	this	this	PRON
cana-826	118	75	means	mean	VERB
cana-826	118	76	that	that	SCONJ
cana-826	118	77	w	w	NOUN
cana-826	118	78	contains	contain	VERB
cana-826	118	79	a	a	DET
cana-826	118	80	𝑢	𝑢	NOUN
cana-826	118	81	−	−	NOUN
cana-826	118	82	𝑣	𝑣	ADP
cana-826	118	83	hyperpath	hyperpath	NOUN
cana-826	118	84	and	and	CCONJ
cana-826	118	85	proof	proof	NOUN
cana-826	118	86	is	be	AUX
cana-826	118	87	complete	complete	ADJ
cana-826	118	88	.	.	PUNCT
cana-826	119	1	the	the	DET
cana-826	119	2	converse	converse	NOUN
cana-826	119	3	part	part	NOUN
cana-826	119	4	is	be	AUX
cana-826	119	5	obviously	obviously	ADV
cana-826	119	6	holds	hold	NOUN
cana-826	119	7	.	.	PUNCT
cana-826	120	1	4	4	X
cana-826	120	2	.	.	X
cana-826	120	3	utilizing	utilize	VERB
cana-826	120	4	the	the	DET
cana-826	120	5	ifthg	ifthg	NOUN
cana-826	120	6	model	model	NOUN
cana-826	120	7	for	for	ADP
cana-826	120	8	robot	robot	NOUN
cana-826	120	9	-	-	PUNCT
cana-826	120	10	based	base	VERB
cana-826	120	11	security	security	NOUN
cana-826	120	12	applications	application	NOUN
cana-826	120	13	the	the	DET
cana-826	120	14	ifthg	ifthg	NOUN
cana-826	120	15	model	model	NOUN
cana-826	120	16	proposes	propose	VERB
cana-826	120	17	employing	employ	VERB
cana-826	120	18	robots	robot	NOUN
cana-826	120	19	as	as	ADP
cana-826	120	20	security	security	NOUN
cana-826	120	21	guards	guard	NOUN
cana-826	120	22	in	in	ADP
cana-826	120	23	order	order	NOUN
cana-826	120	24	to	to	PART
cana-826	120	25	reduce	reduce	VERB
cana-826	120	26	risks	risk	NOUN
cana-826	120	27	and	and	CCONJ
cana-826	120	28	ensure	ensure	VERB
cana-826	120	29	public	public	ADJ
cana-826	120	30	safety	safety	NOUN
cana-826	120	31	in	in	ADP
cana-826	120	32	situations	situation	NOUN
cana-826	120	33	when	when	SCONJ
cana-826	120	34	the	the	DET
cana-826	120	35	robots	robot	NOUN
cana-826	120	36	are	be	AUX
cana-826	120	37	able	able	ADJ
cana-826	120	38	to	to	PART
cana-826	120	39	catch	catch	VERB
cana-826	120	40	fugitives	fugitive	NOUN
cana-826	120	41	and	and	CCONJ
cana-826	120	42	keep	keep	VERB
cana-826	120	43	control	control	NOUN
cana-826	120	44	until	until	SCONJ
cana-826	120	45	the	the	DET
cana-826	120	46	police	police	NOUN
cana-826	120	47	arrives	arrive	VERB
cana-826	120	48	.	.	PUNCT
cana-826	121	1	security	security	NOUN
cana-826	121	2	bots	bot	NOUN
cana-826	121	3	would	would	AUX
cana-826	121	4	be	be	AUX
cana-826	121	5	alerted	alert	VERB
cana-826	121	6	and	and	CCONJ
cana-826	121	7	transmit	transmit	VERB
cana-826	121	8	a	a	DET
cana-826	121	9	message	message	NOUN
cana-826	121	10	to	to	ADP
cana-826	121	11	the	the	DET
cana-826	121	12	control	control	NOUN
cana-826	121	13	room	room	NOUN
cana-826	121	14	in	in	ADP
cana-826	121	15	the	the	DET
cana-826	121	16	event	event	NOUN
cana-826	121	17	of	of	ADP
cana-826	121	18	an	an	DET
cana-826	121	19	unusual	unusual	ADJ
cana-826	121	20	occurrence	occurrence	NOUN
cana-826	121	21	such	such	ADJ
cana-826	121	22	as	as	ADP
cana-826	121	23	robbery	robbery	NOUN
cana-826	121	24	,	,	PUNCT
cana-826	121	25	heist	heist	NOUN
cana-826	121	26	,	,	PUNCT
cana-826	121	27	gunshot	gunshot	NOUN
cana-826	121	28	or	or	CCONJ
cana-826	121	29	accident	accident	NOUN
cana-826	121	30	.	.	PUNCT
cana-826	122	1	consider	consider	VERB
cana-826	122	2	a	a	DET
cana-826	122	3	large	large	ADJ
cana-826	122	4	mall	mall	NOUN
cana-826	122	5	comprising	comprise	VERB
cana-826	122	6	two	two	NUM
cana-826	122	7	significant	significant	ADJ
cana-826	122	8	compartments	compartment	NOUN
cana-826	122	9	with	with	ADP
cana-826	122	10	11	11	NUM
cana-826	122	11	and	and	CCONJ
cana-826	122	12	10	10	NUM
cana-826	122	13	robots	robot	NOUN
cana-826	122	14	respectively	respectively	ADV
cana-826	122	15	,	,	PUNCT
cana-826	122	16	each	each	PRON
cana-826	122	17	equipped	equip	VERB
cana-826	122	18	with	with	ADP
cana-826	122	19	a	a	DET
cana-826	122	20	primary	primary	ADJ
cana-826	122	21	control	control	NOUN
cana-826	122	22	room	room	NOUN
cana-826	122	23	.	.	PUNCT
cana-826	123	1	•	•	NOUN
cana-826	123	2	in	in	ADP
cana-826	123	3	the	the	DET
cana-826	123	4	ifthg	ifthg	NOUN
cana-826	123	5	model	model	NOUN
cana-826	123	6	,	,	PUNCT
cana-826	123	7	individual	individual	ADJ
cana-826	123	8	robots	robot	NOUN
cana-826	123	9	are	be	AUX
cana-826	123	10	represented	represent	VERB
cana-826	123	11	as	as	ADP
cana-826	123	12	vertices	vertex	NOUN
cana-826	123	13	,	,	PUNCT
cana-826	123	14	denoted	denote	VERB
cana-826	123	15	by	by	ADP
cana-826	123	16	𝑈	𝑈	PROPN
cana-826	123	17	=	=	SYM
cana-826	123	18	{	{	PUNCT
cana-826	123	19	𝑢1	𝑢1	PROPN
cana-826	123	20	,	,	PUNCT
cana-826	123	21	𝑢2	𝑢2	PROPN
cana-826	123	22	,	,	PUNCT
cana-826	123	23	.	.	PUNCT
cana-826	123	24	.	.	PUNCT
cana-826	124	1	.	.	PUNCT
cana-826	125	1	,	,	PUNCT
cana-826	125	2	𝑢21	𝑢21	VERB
cana-826	125	3	,	,	PUNCT
cana-826	125	4	𝐾	𝐾	PROPN
cana-826	125	5	,	,	PUNCT
cana-826	125	6	𝐿	𝐿	PROPN
cana-826	125	7	}	}	PUNCT
cana-826	125	8	,	,	PUNCT
cana-826	125	9	while	while	SCONJ
cana-826	125	10	hyperedges	hyperedge	NOUN
cana-826	125	11	could	could	AUX
cana-826	125	12	represent	represent	VERB
cana-826	125	13	complex	complex	ADJ
cana-826	125	14	relationships	relationship	NOUN
cana-826	125	15	or	or	CCONJ
cana-826	125	16	interactions	interaction	NOUN
cana-826	125	17	between	between	ADP
cana-826	125	18	multiple	multiple	ADJ
cana-826	125	19	robots	robot	NOUN
cana-826	125	20	in	in	ADP
cana-826	125	21	each	each	DET
cana-826	125	22	block	block	NOUN
cana-826	125	23	of	of	ADP
cana-826	125	24	mall	mall	NOUN
cana-826	125	25	which	which	PRON
cana-826	125	26	are	be	AUX
cana-826	125	27	denoted	denote	VERB
cana-826	125	28	by	by	ADP
cana-826	125	29	ℰ	ℰ	PROPN
cana-826	125	30	=	=	NOUN
cana-826	125	31	{	{	PUNCT
cana-826	125	32	ℰ1	ℰ1	NOUN
cana-826	125	33	,	,	PUNCT
cana-826	125	34	ℰ2	ℰ2	NOUN
cana-826	125	35	,	,	PUNCT
cana-826	125	36	.	.	PUNCT
cana-826	125	37	.	.	PUNCT
cana-826	126	1	.	.	PUNCT
cana-826	127	1	,	,	PUNCT
cana-826	127	2	ℰ10	ℰ10	ADJ
cana-826	127	3	}	}	PUNCT
cana-826	127	4	.	.	PUNCT
cana-826	128	1	•	•	NOUN
cana-826	128	2	every	every	DET
cana-826	128	3	robot	robot	NOUN
cana-826	128	4	is	be	AUX
cana-826	128	5	attached	attach	VERB
cana-826	128	6	to	to	ADP
cana-826	128	7	two	two	NUM
cana-826	128	8	main	main	ADJ
cana-826	128	9	processing	processing	NOUN
cana-826	128	10	systems	system	NOUN
cana-826	128	11	,	,	PUNCT
cana-826	128	12	𝐾	𝐾	PROPN
cana-826	128	13	and	and	CCONJ
cana-826	128	14	𝐿	𝐿	PROPN
cana-826	128	15	,	,	PUNCT
cana-826	128	16	which	which	PRON
cana-826	128	17	direct	direct	VERB
cana-826	128	18	the	the	DET
cana-826	128	19	robots	robot	NOUN
cana-826	128	20	on	on	ADP
cana-826	128	21	how	how	SCONJ
cana-826	128	22	to	to	PART
cana-826	128	23	act	act	VERB
cana-826	128	24	.	.	PUNCT
cana-826	129	1	•	•	INTJ
cana-826	129	2	there	there	PRON
cana-826	129	3	are	be	VERB
cana-826	129	4	two	two	NUM
cana-826	129	5	intuitionistic	intuitionistic	ADJ
cana-826	129	6	fuzzy	fuzzy	ADJ
cana-826	129	7	threshold	threshold	NOUN
cana-826	129	8	subhypergraphs(iftshgs	subhypergraphs(iftshgs	PROPN
cana-826	129	9	)	)	PUNCT
cana-826	129	10	based	base	VERB
cana-826	129	11	on	on	ADP
cana-826	129	12	the	the	DET
cana-826	129	13	major	major	ADJ
cana-826	129	14	control	control	NOUN
cana-826	129	15	systems	system	NOUN
cana-826	129	16	𝐾	𝐾	PROPN
cana-826	129	17	and	and	CCONJ
cana-826	129	18	𝐿.	𝐿.	VERB
cana-826	129	19	the	the	DET
cana-826	129	20	first	first	ADJ
cana-826	129	21	iftshg	iftshg	NOUN
cana-826	129	22	has	have	VERB
cana-826	129	23	11	11	NUM
cana-826	129	24	robots	robot	NOUN
cana-826	129	25	{	{	PUNCT
cana-826	129	26	𝑢1	𝑢1	PROPN
cana-826	129	27	,	,	PUNCT
cana-826	129	28	𝑢2	𝑢2	PROPN
cana-826	129	29	,	,	PUNCT
cana-826	129	30	.	.	PUNCT
cana-826	129	31	.	.	PUNCT
cana-826	130	1	.	.	PUNCT
cana-826	131	1	,	,	PUNCT
cana-826	131	2	𝑢11	𝑢11	PROPN
cana-826	131	3	}	}	PUNCT
cana-826	131	4	linked	link	VERB
cana-826	131	5	with	with	ADP
cana-826	131	6	main	main	ADJ
cana-826	131	7	control	control	NOUN
cana-826	131	8	system	system	NOUN
cana-826	131	9	𝐾	𝐾	PROPN
cana-826	131	10	with	with	ADP
cana-826	131	11	hyperedges	hyperedge	NOUN
cana-826	131	12	{	{	PUNCT
cana-826	131	13	ℰ1	ℰ1	NOUN
cana-826	131	14	,	,	PUNCT
cana-826	131	15	ℰ2	ℰ2	NOUN
cana-826	131	16	,	,	PUNCT
cana-826	131	17	.	.	PUNCT
cana-826	131	18	.	.	PUNCT
cana-826	132	1	.	.	PUNCT
cana-826	133	1	,	,	PUNCT
cana-826	133	2	ℰ5	ℰ5	VERB
cana-826	133	3	}	}	PUNCT
cana-826	133	4	,	,	PUNCT
cana-826	133	5	and	and	CCONJ
cana-826	133	6	the	the	DET
cana-826	133	7	second	second	ADJ
cana-826	133	8	iftshg	iftshg	NOUN
cana-826	133	9	has	have	VERB
cana-826	133	10	10	10	NUM
cana-826	133	11	robots{𝑢12	robots{𝑢12	NOUN
cana-826	133	12	,	,	PUNCT
cana-826	133	13	.	.	PUNCT
cana-826	133	14	.	.	PUNCT
cana-826	134	1	.	.	PUNCT
cana-826	135	1	,	,	PUNCT
cana-826	135	2	𝑢21	𝑢21	VERB
cana-826	135	3	}	}	PUNCT
cana-826	135	4	connected	connect	VERB
cana-826	135	5	to	to	ADP
cana-826	135	6	𝐿	𝐿	PROPN
cana-826	135	7	with	with	ADP
cana-826	135	8	hyperedges	hyperedge	NOUN
cana-826	135	9	{	{	PUNCT
cana-826	135	10	ℰ6	ℰ6	ADV
cana-826	135	11	,	,	PUNCT
cana-826	135	12	.	.	PUNCT
cana-826	135	13	.	.	PUNCT
cana-826	135	14	.	.	PUNCT
cana-826	136	1	ℰ9}⁡.	ℰ9}⁡.	ADJ
cana-826	136	2	•	•	ADV
cana-826	136	3	additionally	additionally	ADV
cana-826	136	4	,	,	PUNCT
cana-826	136	5	the	the	DET
cana-826	136	6	hyperedge	hyperedge	NOUN
cana-826	136	7	s10	s10	NOUN
cana-826	136	8	is	be	AUX
cana-826	136	9	connected	connect	VERB
cana-826	136	10	to	to	ADP
cana-826	136	11	the	the	DET
cana-826	136	12	major	major	ADJ
cana-826	136	13	control	control	PROPN
cana-826	136	14	systems	systems	PROPN
cana-826	136	15	𝐾	𝐾	PROPN
cana-826	136	16	&	&	CCONJ
cana-826	136	17	𝐿.	𝐿.	VERB
cana-826	136	18	to	to	PART
cana-826	136	19	regulate	regulate	VERB
cana-826	136	20	the	the	DET
cana-826	136	21	maximum	maximum	ADJ
cana-826	136	22	and	and	CCONJ
cana-826	136	23	minimum	minimum	ADJ
cana-826	136	24	values	value	NOUN
cana-826	136	25	for	for	ADP
cana-826	136	26	bots	bot	NOUN
cana-826	136	27	,	,	PUNCT
cana-826	136	28	threshold	threshold	NOUN
cana-826	136	29	values	value	NOUN
cana-826	136	30	are	be	AUX
cana-826	136	31	essential	essential	ADJ
cana-826	136	32	.	.	PUNCT
cana-826	137	1	vertices	vertex	NOUN
cana-826	137	2	of	of	ADP
cana-826	137	3	ifthgs	ifthgs	ADJ
cana-826	137	4	indicate	indicate	VERB
cana-826	137	5	where	where	SCONJ
cana-826	137	6	the	the	DET
cana-826	137	7	robots	robot	NOUN
cana-826	137	8	are	be	AUX
cana-826	137	9	situated	situate	VERB
cana-826	137	10	and	and	CCONJ
cana-826	137	11	how	how	SCONJ
cana-826	137	12	accessible	accessible	ADJ
cana-826	137	13	they	they	PRON
cana-826	137	14	are	be	AUX
cana-826	137	15	possible	possible	ADJ
cana-826	137	16	to	to	PART
cana-826	137	17	escape	escape	VERB
cana-826	137	18	routes	route	NOUN
cana-826	137	19	.	.	PUNCT
cana-826	138	1	almost	almost	ADV
cana-826	138	2	every	every	DET
cana-826	138	3	exit	exit	NOUN
cana-826	138	4	gate	gate	NOUN
cana-826	138	5	and	and	CCONJ
cana-826	138	6	crowded	crowded	ADJ
cana-826	138	7	area	area	NOUN
cana-826	138	8	has	have	VERB
cana-826	138	9	at	at	ADV
cana-826	138	10	least	least	ADV
cana-826	138	11	one	one	NUM
cana-826	138	12	robot	robot	NOUN
cana-826	138	13	.	.	PUNCT
cana-826	139	1	robots	robot	NOUN
cana-826	139	2	have	have	AUX
cana-826	139	3	been	be	AUX
cana-826	139	4	spread	spread	VERB
cana-826	139	5	out	out	ADP
cana-826	139	6	around	around	ADP
cana-826	139	7	the	the	DET
cana-826	139	8	area	area	NOUN
cana-826	139	9	and	and	CCONJ
cana-826	139	10	are	be	AUX
cana-826	139	11	ready	ready	ADJ
cana-826	139	12	to	to	PART
cana-826	139	13	go	go	VERB
cana-826	139	14	on	on	ADP
cana-826	139	15	tasks	task	NOUN
cana-826	139	16	before	before	ADP
cana-826	139	17	any	any	DET
cana-826	139	18	alarm	alarm	NOUN
cana-826	139	19	case	case	NOUN
cana-826	139	20	.	.	PUNCT
cana-826	140	1	this	this	DET
cana-826	140	2	algorithm	algorithm	NOUN
cana-826	140	3	is	be	AUX
cana-826	140	4	used	use	VERB
cana-826	140	5	to	to	PART
cana-826	140	6	find	find	VERB
cana-826	140	7	in	in	ADP
cana-826	140	8	which	which	PRON
cana-826	140	9	gate	gate	VERB
cana-826	140	10	the	the	DET
cana-826	140	11	fugitives	fugitive	NOUN
cana-826	140	12	are	be	AUX
cana-826	140	13	using	use	VERB
cana-826	140	14	in	in	ADP
cana-826	140	15	the	the	DET
cana-826	140	16	situation	situation	NOUN
cana-826	140	17	that	that	SCONJ
cana-826	140	18	the	the	DET
cana-826	140	19	security	security	NOUN
cana-826	140	20	department	department	NOUN
cana-826	140	21	suddenly	suddenly	ADV
cana-826	140	22	develops	develop	VERB
cana-826	140	23	an	an	DET
cana-826	140	24	alarm	alarm	NOUN
cana-826	140	25	case	case	NOUN
cana-826	140	26	concerning	concern	VERB
cana-826	140	27	any	any	DET
cana-826	140	28	suspicious	suspicious	ADJ
cana-826	140	29	persons	person	NOUN
cana-826	140	30	.	.	PUNCT
cana-826	141	1	after	after	ADP
cana-826	141	2	this	this	PRON
cana-826	141	3	,	,	PUNCT
cana-826	141	4	the	the	DET
cana-826	141	5	security	security	NOUN
cana-826	141	6	sections	section	NOUN
cana-826	141	7	goal	goal	NOUN
cana-826	141	8	is	be	AUX
cana-826	141	9	to	to	PART
cana-826	141	10	pursue	pursue	VERB
cana-826	141	11	any	any	DET
cana-826	141	12	suspicious	suspicious	ADJ
cana-826	141	13	fugitives	fugitive	NOUN
cana-826	141	14	until	until	SCONJ
cana-826	141	15	the	the	DET
cana-826	141	16	police	police	NOUN
cana-826	141	17	forces	force	NOUN
cana-826	141	18	get	get	AUX
cana-826	141	19	involved	involve	VERB
cana-826	141	20	in	in	ADP
cana-826	141	21	communications	communication	NOUN
cana-826	141	22	on	on	ADP
cana-826	141	23	applied	apply	VERB
cana-826	141	24	nonlinear	nonlinear	ADJ
cana-826	141	25	analysis	analysis	NOUN
cana-826	141	26	issn	issn	NOUN
cana-826	141	27	:	:	PUNCT
cana-826	141	28	1074	1074	NUM
cana-826	141	29	-	-	PUNCT
cana-826	141	30	133x	133x	NUM
cana-826	141	31	vol	vol	NOUN
cana-826	141	32	31	31	NUM
cana-826	141	33	no	no	NOUN
cana-826	141	34	.	.	PUNCT
cana-826	142	1	4s	4s	NUM
cana-826	142	2	(	(	PUNCT
cana-826	142	3	2024	2024	NUM
cana-826	142	4	)	)	PUNCT
cana-826	142	5	16	16	NUM
cana-826	142	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-826	142	7	this	this	DET
cana-826	142	8	pursuit	pursuit	NOUN
cana-826	142	9	.	.	PUNCT
cana-826	143	1	fig	fig	NOUN
cana-826	143	2	4.1	4.1	NUM
cana-826	143	3	:	:	PUNCT
cana-826	143	4	large	large	ADJ
cana-826	143	5	mall	mall	NOUN
cana-826	143	6	with	with	ADP
cana-826	143	7	security	security	NOUN
cana-826	143	8	robots	robot	NOUN
cana-826	143	9	some	some	DET
cana-826	143	10	notions	notion	NOUN
cana-826	143	11	of	of	ADP
cana-826	143	12	membership	membership	NOUN
cana-826	143	13	and	and	CCONJ
cana-826	143	14	non	non	ADJ
cana-826	143	15	-	-	NOUN
cana-826	143	16	membership	membership	NOUN
cana-826	143	17	in	in	ADP
cana-826	143	18	this	this	DET
cana-826	143	19	scenario	scenario	NOUN
cana-826	143	20	are	be	AUX
cana-826	143	21	denoted	denote	VERB
cana-826	143	22	as	as	SCONJ
cana-826	143	23	follows	follow	VERB
cana-826	143	24	:	:	PUNCT
cana-826	143	25	•	•	NUM
cana-826	143	26	𝜇𝑗(𝑢𝑛	𝜇𝑗(𝑢𝑛	NOUN
cana-826	143	27	)	)	PUNCT
cana-826	144	1	represents	represent	VERB
cana-826	144	2	where	where	SCONJ
cana-826	144	3	the	the	DET
cana-826	144	4	robots	robot	NOUN
cana-826	144	5	are	be	AUX
cana-826	144	6	located	locate	VERB
cana-826	144	7	and	and	CCONJ
cana-826	144	8	how	how	SCONJ
cana-826	144	9	accessible	accessible	ADJ
cana-826	144	10	they	they	PRON
cana-826	144	11	are	be	AUX
cana-826	144	12	to	to	ADP
cana-826	144	13	possible	possible	ADJ
cana-826	144	14	escape	escape	NOUN
cana-826	144	15	routes	route	NOUN
cana-826	144	16	.	.	PUNCT
cana-826	145	1	•	•	NUM
cana-826	145	2	𝑣𝑗(𝑢𝑛	𝑣𝑗(𝑢𝑛	PROPN
cana-826	145	3	)	)	PUNCT
cana-826	146	1	reflect	reflect	VERB
cana-826	146	2	how	how	SCONJ
cana-826	146	3	far	far	ADV
cana-826	146	4	a	a	DET
cana-826	146	5	robot	robot	NOUN
cana-826	146	6	is	be	AUX
cana-826	146	7	from	from	ADP
cana-826	146	8	these	these	DET
cana-826	146	9	critical	critical	ADJ
cana-826	146	10	areas	area	NOUN
cana-826	146	11	.	.	PUNCT
cana-826	147	1	•	•	NUM
cana-826	147	2	𝜇𝑖𝑗(ℰ𝑚	𝜇𝑖𝑗(ℰ𝑚	PROPN
cana-826	147	3	)	)	PUNCT
cana-826	147	4	represents	represent	VERB
cana-826	147	5	the	the	DET
cana-826	147	6	overall	overall	ADJ
cana-826	147	7	significance	significance	NOUN
cana-826	147	8	of	of	ADP
cana-826	147	9	a	a	DET
cana-826	147	10	hyperedge	hyperedge	NOUN
cana-826	147	11	in	in	ADP
cana-826	147	12	enhancing	enhance	VERB
cana-826	147	13	the	the	DET
cana-826	147	14	system	system	NOUN
cana-826	147	15	’s	’s	PART
cana-826	147	16	efficiency	efficiency	NOUN
cana-826	147	17	and	and	CCONJ
cana-826	147	18	effectiveness	effectiveness	NOUN
cana-826	147	19	within	within	ADP
cana-826	147	20	addressing	address	VERB
cana-826	147	21	block	block	NOUN
cana-826	147	22	.	.	PUNCT
cana-826	148	1	•	•	NUM
cana-826	148	2	𝑣𝑖𝑗(ℰ𝑚	𝑣𝑖𝑗(ℰ𝑚	PROPN
cana-826	148	3	)	)	PUNCT
cana-826	148	4	reflects	reflect	VERB
cana-826	148	5	the	the	DET
cana-826	148	6	degree	degree	NOUN
cana-826	148	7	of	of	ADP
cana-826	148	8	non	non	ADJ
cana-826	148	9	-	-	ADJ
cana-826	148	10	belongingness	belongingness	ADJ
cana-826	148	11	or	or	CCONJ
cana-826	148	12	lack	lack	NOUN
cana-826	148	13	of	of	ADP
cana-826	148	14	significance	significance	NOUN
cana-826	148	15	of	of	ADP
cana-826	148	16	a	a	DET
cana-826	148	17	hyperedge	hyperedge	NOUN
cana-826	148	18	within	within	ADP
cana-826	148	19	addressing	address	VERB
cana-826	148	20	block	block	NOUN
cana-826	148	21	.	.	PUNCT
cana-826	149	1	the	the	DET
cana-826	149	2	following	follow	VERB
cana-826	149	3	ifthg	ifthg	NOUN
cana-826	149	4	depicts	depict	VERB
cana-826	149	5	the	the	DET
cana-826	149	6	pictorial	pictorial	ADJ
cana-826	149	7	representation	representation	NOUN
cana-826	149	8	of	of	ADP
cana-826	149	9	fig	fig	NOUN
cana-826	149	10	.	.	PUNCT
cana-826	150	1	4.1	4.1	NUM
cana-826	150	2	fig	fig	NOUN
cana-826	150	3	4.2	4.2	NUM
cana-826	150	4	:	:	PUNCT
cana-826	150	5	ifthg	ifthg	NOUN
cana-826	150	6	linked	link	VERB
cana-826	150	7	with	with	ADP
cana-826	150	8	multi	multi	ADJ
cana-826	150	9	robot	robot	NOUN
cana-826	150	10	system	system	NOUN
cana-826	150	11	communications	communication	NOUN
cana-826	150	12	on	on	ADP
cana-826	150	13	applied	apply	VERB
cana-826	150	14	nonlinear	nonlinear	ADJ
cana-826	150	15	analysis	analysis	NOUN
cana-826	150	16	issn	issn	NOUN
cana-826	150	17	:	:	PUNCT
cana-826	150	18	1074	1074	NUM
cana-826	150	19	-	-	PUNCT
cana-826	150	20	133x	133x	NUM
cana-826	150	21	vol	vol	NOUN
cana-826	150	22	31	31	NUM
cana-826	150	23	no	no	NOUN
cana-826	150	24	.	.	PUNCT
cana-826	151	1	4s	4s	NUM
cana-826	151	2	(	(	PUNCT
cana-826	151	3	2024	2024	NUM
cana-826	151	4	)	)	PUNCT
cana-826	151	5	17	17	NUM
cana-826	151	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-826	151	7	the	the	DET
cana-826	151	8	values	value	NOUN
cana-826	151	9	of	of	ADP
cana-826	151	10	vertices	vertex	NOUN
cana-826	151	11	are	be	AUX
cana-826	151	12	tabulated	tabulate	VERB
cana-826	151	13	below	below	ADP
cana-826	151	14	:	:	PUNCT
cana-826	151	15	table	table	NOUN
cana-826	151	16	1	1	NUM
cana-826	151	17	:	:	PUNCT
cana-826	151	18	score	score	NOUN
cana-826	151	19	values	value	NOUN
cana-826	151	20	s.no	s.no	VERB
cana-826	151	21	𝑢𝑖/ℰj	𝑢𝑖/ℰj	ADV
cana-826	151	22	(	(	PUNCT
cana-826	151	23	𝜇	𝜇	X
cana-826	151	24	,	,	PUNCT
cana-826	151	25	𝜈	𝜈	NOUN
cana-826	151	26	)	)	PUNCT
cana-826	151	27	score	score	NOUN
cana-826	151	28	1	1	NUM
cana-826	151	29	u1	u1	NOUN
cana-826	151	30	(	(	PUNCT
cana-826	151	31	0.6,0.002	0.6,0.002	NOUN
cana-826	151	32	)	)	PUNCT
cana-826	151	33	0.7139	0.7139	NUM
cana-826	151	34	2	2	NUM
cana-826	151	35	u2	u2	NOUN
cana-826	151	36	(	(	PUNCT
cana-826	151	37	0.5,0.0015	0.5,0.0015	NUM
cana-826	151	38	)	)	PUNCT
cana-826	151	39	0.6663	0.6663	NUM
cana-826	151	40	3	3	NUM
cana-826	151	41	u3	u3	NOUN
cana-826	151	42	(	(	PUNCT
cana-826	151	43	0.55,0.002	0.55,0.002	NUM
cana-826	151	44	)	)	PUNCT
cana-826	151	45	0.6892	0.6892	NUM
cana-826	151	46	4	4	NUM
cana-826	151	47	u4	u4	PROPN
cana-826	151	48	(	(	PUNCT
cana-826	151	49	0.5,0.001	0.5,0.001	PROPN
cana-826	151	50	)	)	PUNCT
cana-826	151	51	0.6894	0.6894	NUM
cana-826	151	52	5	5	NUM
cana-826	151	53	u5	u5	PROPN
cana-826	151	54	(	(	PUNCT
cana-826	151	55	0.4,0.001	0.4,0.001	NOUN
cana-826	151	56	)	)	PUNCT
cana-826	151	57	0.6248	0.6248	NUM
cana-826	151	58	6	6	NUM
cana-826	151	59	u6	u6	NOUN
cana-826	151	60	(	(	PUNCT
cana-826	151	61	0.5,0.001	0.5,0.001	NOUN
cana-826	151	62	)	)	PUNCT
cana-826	151	63	0.6664	0.6664	NUM
cana-826	151	64	7	7	NUM
cana-826	151	65	u7	u7	PROPN
cana-826	151	66	(	(	PUNCT
cana-826	151	67	0.6,0.0015	0.6,0.0015	PROPN
cana-826	151	68	)	)	PUNCT
cana-826	151	69	0.7140	0.7140	NUM
cana-826	151	70	8	8	NUM
cana-826	151	71	u8	u8	X
cana-826	151	72	(	(	PUNCT
cana-826	151	73	0.3,0.004	0.3,0.004	PROPN
cana-826	151	74	)	)	PUNCT
cana-826	151	75	0.5875	0.5875	NUM
cana-826	151	76	9	9	NUM
cana-826	151	77	u9	u9	PROPN
cana-826	151	78	(	(	PUNCT
cana-826	151	79	0.5,0.005	0.5,0.005	NUM
cana-826	151	80	)	)	PUNCT
cana-826	151	81	0.6656	0.6656	NUM
cana-826	151	82	10	10	NUM
cana-826	151	83	u10	u10	NOUN
cana-826	151	84	(	(	PUNCT
cana-826	151	85	0.3,0.05	0.3,0.05	NUM
cana-826	151	86	)	)	PUNCT
cana-826	151	87	0.5758	0.5758	NUM
cana-826	151	88	11	11	NUM
cana-826	151	89	u11	u11	ADJ
cana-826	151	90	(	(	PUNCT
cana-826	151	91	0.2,0.045	0.2,0.045	NOUN
cana-826	151	92	)	)	PUNCT
cana-826	151	93	0.5442	0.5442	NUM
cana-826	151	94	12	12	NUM
cana-826	151	95	u12	u12	NOUN
cana-826	151	96	(	(	PUNCT
cana-826	151	97	0.5,0.001	0.5,0.001	NOUN
cana-826	151	98	)	)	PUNCT
cana-826	151	99	0.6664	0.6664	NUM
cana-826	151	100	13	13	NUM
cana-826	151	101	u13	u13	NOUN
cana-826	151	102	(	(	PUNCT
cana-826	151	103	0.3,0.002	0.3,0.002	NOUN
cana-826	151	104	)	)	PUNCT
cana-826	151	105	0.5878	0.5878	NUM
cana-826	151	106	14	14	NUM
cana-826	151	107	u14	u14	NOUN
cana-826	151	108	(	(	PUNCT
cana-826	151	109	0.4,0.0015	0.4,0.0015	NUM
cana-826	151	110	)	)	PUNCT
cana-826	151	111	0.6246	0.6246	NUM
cana-826	151	112	15	15	NUM
cana-826	151	113	u15	u15	NOUN
cana-826	151	114	(	(	PUNCT
cana-826	151	115	0.6,0.003	0.6,0.003	NOUN
cana-826	151	116	)	)	PUNCT
cana-826	151	117	0.7137	0.7137	NUM
cana-826	151	118	16	16	NUM
cana-826	151	119	u16	u16	NOUN
cana-826	151	120	(	(	PUNCT
cana-826	151	121	0.2,0.004	0.2,0.004	PROPN
cana-826	151	122	)	)	PUNCT
cana-826	151	123	0.5547	0.5547	NUM
cana-826	151	124	17	17	NUM
cana-826	151	125	u17	u17	NOUN
cana-826	151	126	(	(	PUNCT
cana-826	151	127	0.5,0.001	0.5,0.001	NUM
cana-826	151	128	)	)	PUNCT
cana-826	151	129	0.6664	0.6664	NUM
cana-826	151	130	18	18	NUM
cana-826	151	131	u18	u18	X
cana-826	151	132	(	(	PUNCT
cana-826	151	133	0.7,0.0015	0.7,0.0015	NUM
cana-826	151	134	)	)	PUNCT
cana-826	151	135	0.7688	0.7688	NUM
cana-826	151	136	19	19	NUM
cana-826	151	137	u19	u19	NOUN
cana-826	151	138	(	(	PUNCT
cana-826	151	139	0.6,0.001	0.6,0.001	NUM
cana-826	151	140	)	)	PUNCT
cana-826	151	141	0.7141	0.7141	NUM
cana-826	151	142	20	20	NUM
cana-826	151	143	u20	u20	NUM
cana-826	151	144	(	(	PUNCT
cana-826	151	145	0.7,0.002	0.7,0.002	NOUN
cana-826	151	146	)	)	PUNCT
cana-826	151	147	0.7689	0.7689	NUM
cana-826	151	148	21	21	NUM
cana-826	151	149	u21	u21	NOUN
cana-826	151	150	(	(	PUNCT
cana-826	151	151	0.65,0.0015	0.65,0.0015	PROPN
cana-826	151	152	)	)	PUNCT
cana-826	151	153	0.7404	0.7404	NUM
cana-826	151	154	22	22	NUM
cana-826	151	155	k	k	NOUN
cana-826	151	156	(	(	PUNCT
cana-826	151	157	0.96,0.02	0.96,0.02	NOUN
cana-826	151	158	)	)	PUNCT
cana-826	151	159	0.9608	0.9608	NUM
cana-826	151	160	23	23	NUM
cana-826	151	161	l	l	NOUN
cana-826	151	162	(	(	PUNCT
cana-826	151	163	0.92,0.04	0.92,0.04	NOUN
cana-826	151	164	)	)	PUNCT
cana-826	151	165	0.9423	0.9423	NUM
cana-826	151	166	24	24	NUM
cana-826	151	167	ℰ1	ℰ1	NOUN
cana-826	151	168	(	(	PUNCT
cana-826	151	169	0.5,0.002	0.5,0.002	NOUN
cana-826	151	170	)	)	PUNCT
cana-826	151	171	0.6662	0.6662	NUM
cana-826	151	172	25	25	NUM
cana-826	151	173	ℰ2	ℰ2	NOUN
cana-826	151	174	(	(	PUNCT
cana-826	151	175	0.4,0.01	0.4,0.01	NUM
cana-826	151	176	)	)	PUNCT
cana-826	151	177	0.6226	0.6226	NUM
cana-826	151	178	26	26	NUM
cana-826	151	179	ℰ3	ℰ3	NOUN
cana-826	151	180	(	(	PUNCT
cana-826	151	181	0.5,0.015	0.5,0.015	NUM
cana-826	151	182	)	)	PUNCT
cana-826	151	183	0.6633	0.6633	NUM
cana-826	151	184	27	27	NUM
cana-826	151	185	ℰ4	ℰ4	PROPN
cana-826	151	186	(	(	PUNCT
cana-826	151	187	0.3,0.005	0.3,0.005	NUM
cana-826	151	188	)	)	PUNCT
cana-826	151	189	0.5870	0.5870	NUM
cana-826	151	190	28	28	NUM
cana-826	151	191	ℰ5	ℰ5	NOUN
cana-826	151	192	(	(	PUNCT
cana-826	151	193	0.2,0.05	0.2,0.05	NUM
cana-826	151	194	)	)	PUNCT
cana-826	151	195	0.5429	0.5429	NUM
cana-826	151	196	29	29	NUM
cana-826	151	197	ℰ6	ℰ6	PROPN
cana-826	151	198	(	(	PUNCT
cana-826	151	199	0.3,0.002	0.3,0.002	NOUN
cana-826	151	200	)	)	PUNCT
cana-826	151	201	0.5878	0.5878	NUM
cana-826	151	202	30	30	NUM
cana-826	151	203	ℰ7	ℰ7	NOUN
cana-826	151	204	(	(	PUNCT
cana-826	151	205	0.2,0.004	0.2,0.004	PROPN
cana-826	151	206	)	)	PUNCT
cana-826	151	207	0.5546	0.5546	NUM
cana-826	151	208	31	31	NUM
cana-826	151	209	ℰ8	ℰ8	NOUN
cana-826	151	210	(	(	PUNCT
cana-826	151	211	0.5,0.0015	0.5,0.0015	NUM
cana-826	151	212	)	)	PUNCT
cana-826	151	213	0.6663	0.6663	NUM
cana-826	151	214	32	32	NUM
cana-826	151	215	ℰ9	ℰ9	NOUN
cana-826	151	216	(	(	PUNCT
cana-826	151	217	0.6,0.002	0.6,0.002	NOUN
cana-826	151	218	)	)	PUNCT
cana-826	151	219	0.7139	0.7139	NUM
cana-826	151	220	33	33	NUM
cana-826	152	1	ℰ10	ℰ10	ADV
cana-826	152	2	(	(	PUNCT
cana-826	152	3	0.6,0.006	0.6,0.006	NUM
cana-826	152	4	)	)	PUNCT
cana-826	152	5	0.7131	0.7131	NUM
cana-826	152	6	communications	communication	NOUN
cana-826	152	7	on	on	ADP
cana-826	152	8	applied	apply	VERB
cana-826	152	9	nonlinear	nonlinear	ADJ
cana-826	152	10	analysis	analysis	NOUN
cana-826	152	11	issn	issn	NOUN
cana-826	152	12	:	:	PUNCT
cana-826	152	13	1074	1074	NUM
cana-826	152	14	-	-	PUNCT
cana-826	152	15	133x	133x	NUM
cana-826	152	16	vol	vol	NOUN
cana-826	152	17	31	31	NUM
cana-826	152	18	no	no	NOUN
cana-826	152	19	.	.	PUNCT
cana-826	153	1	4s	4s	NUM
cana-826	153	2	(	(	PUNCT
cana-826	153	3	2024	2024	NUM
cana-826	153	4	)	)	PUNCT
cana-826	153	5	18	18	NUM
cana-826	153	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-826	153	7	an	an	DET
cana-826	153	8	overview	overview	NOUN
cana-826	153	9	of	of	ADP
cana-826	153	10	the	the	DET
cana-826	153	11	proposed	propose	VERB
cana-826	153	12	simulation	simulation	NOUN
cana-826	153	13	is	be	AUX
cana-826	153	14	represented	represent	VERB
cana-826	153	15	as	as	SCONJ
cana-826	153	16	follows	follow	VERB
cana-826	153	17	:	:	PUNCT
cana-826	153	18	fig	fig	NOUN
cana-826	153	19	4.3	4.3	NUM
cana-826	153	20	:	:	PUNCT
cana-826	153	21	flow	flow	VERB
cana-826	153	22	chart	chart	NOUN
cana-826	153	23	of	of	ADP
cana-826	153	24	simulated	simulate	VERB
cana-826	153	25	ifthg	ifthg	NOUN
cana-826	153	26	model	model	NOUN
cana-826	153	27	this	this	DET
cana-826	153	28	situation	situation	NOUN
cana-826	153	29	describes	describe	VERB
cana-826	153	30	a	a	DET
cana-826	153	31	scenario	scenario	NOUN
cana-826	153	32	where	where	SCONJ
cana-826	153	33	there	there	PRON
cana-826	153	34	’s	’	VERB
cana-826	153	35	a	a	DET
cana-826	153	36	main	main	ADJ
cana-826	153	37	control	control	NOUN
cana-826	153	38	system	system	NOUN
cana-826	153	39	,	,	PUNCT
cana-826	153	40	referred	refer	VERB
cana-826	153	41	to	to	ADP
cana-826	153	42	as	as	ADP
cana-826	153	43	k	k	PROPN
cana-826	153	44	,	,	PUNCT
cana-826	153	45	which	which	PRON
cana-826	153	46	is	be	AUX
cana-826	153	47	responsible	responsible	ADJ
cana-826	153	48	for	for	ADP
cana-826	153	49	overseeing	oversee	VERB
cana-826	153	50	and	and	CCONJ
cana-826	153	51	managing	manage	VERB
cana-826	153	52	a	a	DET
cana-826	153	53	certain	certain	ADJ
cana-826	153	54	environment	environment	NOUN
cana-826	153	55	or	or	CCONJ
cana-826	153	56	system	system	NOUN
cana-826	153	57	.	.	PUNCT
cana-826	154	1	when	when	SCONJ
cana-826	154	2	the	the	DET
cana-826	154	3	main	main	ADJ
cana-826	154	4	control	control	NOUN
cana-826	154	5	system	system	NOUN
cana-826	154	6	detects	detect	VERB
cana-826	154	7	an	an	DET
cana-826	154	8	intrusion	intrusion	NOUN
cana-826	154	9	or	or	CCONJ
cana-826	154	10	a	a	DET
cana-826	154	11	threat	threat	NOUN
cana-826	154	12	,	,	PUNCT
cana-826	154	13	it	it	PRON
cana-826	154	14	triggers	trigger	VERB
cana-826	154	15	an	an	DET
cana-826	154	16	algorithm	algorithm	NOUN
cana-826	154	17	to	to	PART
cana-826	154	18	initiate	initiate	VERB
cana-826	154	19	a	a	DET
cana-826	154	20	series	series	NOUN
cana-826	154	21	of	of	ADP
cana-826	154	22	calculations	calculation	NOUN
cana-826	154	23	.	.	PUNCT
cana-826	155	1	communications	communication	NOUN
cana-826	155	2	on	on	ADP
cana-826	155	3	applied	apply	VERB
cana-826	155	4	nonlinear	nonlinear	ADJ
cana-826	155	5	analysis	analysis	NOUN
cana-826	155	6	issn	issn	NOUN
cana-826	155	7	:	:	PUNCT
cana-826	155	8	1074	1074	NUM
cana-826	155	9	-	-	PUNCT
cana-826	155	10	133x	133x	NUM
cana-826	155	11	vol	vol	NOUN
cana-826	155	12	31	31	NUM
cana-826	155	13	no	no	NOUN
cana-826	155	14	.	.	PUNCT
cana-826	156	1	4s	4s	NUM
cana-826	156	2	(	(	PUNCT
cana-826	156	3	2024	2024	NUM
cana-826	156	4	)	)	PUNCT
cana-826	156	5	19	19	NUM
cana-826	156	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-826	156	7	fig:4.4	fig:4.4	NOUN
cana-826	156	8	iftshg	iftshg	NOUN
cana-826	156	9	:	:	PUNCT
cana-826	156	10	robots	robot	NOUN
cana-826	156	11	linked	link	VERB
cana-826	156	12	to	to	ADP
cana-826	156	13	k.	k.	PROPN
cana-826	156	14	the	the	DET
cana-826	156	15	following	follow	VERB
cana-826	156	16	tables	table	NOUN
cana-826	156	17	2	2	NUM
cana-826	156	18	and	and	CCONJ
cana-826	156	19	3	3	NUM
cana-826	156	20	represents	represent	VERB
cana-826	156	21	the	the	DET
cana-826	156	22	adjacency	adjacency	NOUN
cana-826	156	23	matrix	matrix	NOUN
cana-826	156	24	and	and	CCONJ
cana-826	156	25	score	score	NOUN
cana-826	156	26	values	value	NOUN
cana-826	156	27	respectively	respectively	ADV
cana-826	156	28	of	of	ADP
cana-826	156	29	fig	fig	NOUN
cana-826	156	30	.	.	PUNCT
cana-826	157	1	4.4	4.4	NUM
cana-826	158	1	if	if	SCONJ
cana-826	158	2	a	a	DET
cana-826	158	3	thread	thread	NOUN
cana-826	158	4	is	be	AUX
cana-826	158	5	detected	detect	VERB
cana-826	158	6	under	under	ADP
cana-826	158	7	the	the	DET
cana-826	158	8	major	major	ADJ
cana-826	158	9	control	control	NOUN
cana-826	158	10	system	system	NOUN
cana-826	158	11	𝐾	𝐾	PROPN
cana-826	158	12	,	,	PUNCT
cana-826	158	13	then	then	ADV
cana-826	158	14	𝐾	𝐾	PROPN
cana-826	158	15	will	will	AUX
cana-826	158	16	promptly	promptly	ADV
cana-826	158	17	initiate	initiate	VERB
cana-826	158	18	the	the	DET
cana-826	158	19	following	follow	VERB
cana-826	158	20	algorithm	algorithm	NOUN
cana-826	158	21	,	,	PUNCT
cana-826	158	22	proceeding	proceed	VERB
cana-826	158	23	step	step	NOUN
cana-826	158	24	by	by	ADP
cana-826	158	25	step	step	NOUN
cana-826	158	26	.	.	PUNCT
cana-826	159	1	communications	communication	NOUN
cana-826	159	2	on	on	ADP
cana-826	159	3	applied	apply	VERB
cana-826	159	4	nonlinear	nonlinear	ADJ
cana-826	159	5	analysis	analysis	NOUN
cana-826	159	6	issn	issn	NOUN
cana-826	159	7	:	:	PUNCT
cana-826	159	8	1074	1074	NUM
cana-826	159	9	-	-	PUNCT
cana-826	159	10	133x	133x	NUM
cana-826	159	11	vol	vol	NOUN
cana-826	159	12	31	31	NUM
cana-826	159	13	no	no	NOUN
cana-826	159	14	.	.	PUNCT
cana-826	160	1	4s	4s	NUM
cana-826	160	2	(	(	PUNCT
cana-826	160	3	2024	2024	NUM
cana-826	160	4	)	)	PUNCT
cana-826	160	5	20	20	NUM
cana-826	160	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-826	160	7	algorithm	algorithm	NOUN
cana-826	160	8	:	:	PUNCT
cana-826	160	9	step	step	NOUN
cana-826	160	10	1	1	NUM
cana-826	160	11	:	:	PUNCT
cana-826	160	12	initialize	initialize	VERB
cana-826	160	13	system	system	NOUN
cana-826	160	14	and	and	CCONJ
cana-826	160	15	robots	robot	NOUN
cana-826	160	16	class	class	NOUN
cana-826	160	17	robot	robot	NOUN
cana-826	160	18	:	:	PUNCT
cana-826	160	19	def	def	PROPN
cana-826	160	20	init	init	PROPN
cana-826	160	21	(	(	PUNCT
cana-826	160	22	self	self	NOUN
cana-826	160	23	,	,	PUNCT
cana-826	160	24	i	i	PROPN
cana-826	160	25	d	d	PROPN
cana-826	160	26	,	,	PUNCT
cana-826	160	27	location	location	NOUN
cana-826	160	28	):	):	PUNCT
cana-826	160	29	self.id	self.id	X
cana-826	160	30	=	=	SYM
cana-826	160	31	i	i	PROPN
cana-826	160	32	d	d	PROPN
cana-826	160	33	self.location	self.location	NOUN
cana-826	160	34	=	=	SYM
cana-826	160	35	location	location	NOUN
cana-826	160	36	step	step	NOUN
cana-826	160	37	2	2	NUM
cana-826	160	38	:	:	PUNCT
cana-826	160	39	find	find	VERB
cana-826	160	40	any	any	DET
cana-826	160	41	intrusion	intrusion	NOUN
cana-826	160	42	and	and	CCONJ
cana-826	160	43	determine	determine	VERB
cana-826	160	44	its	its	PRON
cana-826	160	45	location	location	NOUN
cana-826	160	46	intrusion	intrusion	NOUN
cana-826	160	47	detected	detect	VERB
cana-826	160	48	=	=	SYM
cana-826	160	49	true	true	ADJ
cana-826	160	50	step	step	NOUN
cana-826	160	51	3	3	NUM
cana-826	160	52	:	:	PUNCT
cana-826	160	53	find	find	VERB
cana-826	160	54	location	location	NOUN
cana-826	160	55	of	of	ADP
cana-826	160	56	all	all	DET
cana-826	160	57	robots	robot	NOUN
cana-826	160	58	def	def	ADJ
cana-826	160	59	find	find	VERB
cana-826	160	60	robot	robot	NOUN
cana-826	160	61	locations(robots	locations(robot	NOUN
cana-826	160	62	):	):	PUNCT
cana-826	160	63	return	return	NOUN
cana-826	160	64	robot.id	robot.id	NUM
cana-826	160	65	:	:	PUNCT
cana-826	160	66	robot.location	robot.location	NOUN
cana-826	160	67	for	for	ADP
cana-826	160	68	robot	robot	NOUN
cana-826	160	69	in	in	ADP
cana-826	160	70	robots	robot	NOUN
cana-826	160	71	robot	robot	NOUN
cana-826	160	72	locations	location	NOUN
cana-826	160	73	=	=	PRON
cana-826	160	74	find	find	VERB
cana-826	160	75	robot	robot	NOUN
cana-826	160	76	locations(robots	locations(robot	NOUN
cana-826	160	77	)	)	PUNCT
cana-826	160	78	step	step	NOUN
cana-826	160	79	4	4	NUM
cana-826	160	80	:	:	PUNCT
cana-826	160	81	find	find	VERB
cana-826	160	82	score	score	NOUN
cana-826	160	83	value	value	NOUN
cana-826	160	84	of	of	ADP
cana-826	160	85	robots	robot	NOUN
cana-826	160	86	def	def	ADJ
cana-826	160	87	calculate	calculate	NOUN
cana-826	160	88	score(1	score(1	ADJ
cana-826	160	89	-	-	PUNCT
cana-826	160	90	non	non	ADJ
cana-826	160	91	membership	membership	NOUN
cana-826	161	1	value/2	value/2	NUM
cana-826	161	2	-membership	-membership	PROPN
cana-826	161	3	valuenon	valuenon	NOUN
cana-826	161	4	membership	membership	NOUN
cana-826	161	5	value	value	NOUN
cana-826	161	6	):	):	PUNCT
cana-826	161	7	score	score	NOUN
cana-826	161	8	values	value	NOUN
cana-826	161	9	=	=	PUNCT
cana-826	161	10	for	for	ADP
cana-826	161	11	robot	robot	NOUN
cana-826	161	12	i	i	PROPN
cana-826	161	13	d	d	PROPN
cana-826	161	14	,	,	PUNCT
cana-826	161	15	location	location	NOUN
cana-826	161	16	in	in	ADP
cana-826	161	17	robot	robot	NOUN
cana-826	161	18	locations.items	locations.items	PROPN
cana-826	161	19	(	(	PUNCT
cana-826	161	20	):	):	PUNCT
cana-826	161	21	return	return	VERB
cana-826	161	22	score	score	NOUN
cana-826	161	23	values	value	NOUN
cana-826	161	24	step	step	VERB
cana-826	161	25	5	5	NUM
cana-826	161	26	:	:	PUNCT
cana-826	161	27	calculate	calculate	NOUN
cana-826	161	28	eigenvalues	eigenvalue	NOUN
cana-826	161	29	and	and	CCONJ
cana-826	161	30	eigenvectors	eigenvector	VERB
cana-826	161	31	a	a	DET
cana-826	161	32	=	=	NOUN
cana-826	161	33	np.array	np.array	X
cana-826	161	34	(	(	PUNCT
cana-826	161	35	[	[	X
cana-826	161	36	]	]	X
cana-826	161	37	)	)	PUNCT
cana-826	161	38	eigenvalues	eigenvalue	NOUN
cana-826	161	39	,	,	PUNCT
cana-826	161	40	eigenvectors	eigenvector	NOUN
cana-826	161	41	=	=	SYM
cana-826	161	42	np.linalg.eig(a	np.linalg.eig(a	X
cana-826	161	43	)	)	PUNCT
cana-826	161	44	step	step	NOUN
cana-826	161	45	6	6	NUM
cana-826	161	46	:	:	PUNCT
cana-826	161	47	assign	assign	VERB
cana-826	161	48	index	index	NOUN
cana-826	161	49	values	value	NOUN
cana-826	161	50	to	to	ADP
cana-826	161	51	robots	robot	NOUN
cana-826	161	52	based	base	VERB
cana-826	161	53	on	on	ADP
cana-826	161	54	eigenvalues	eigenvalue	NOUN
cana-826	161	55	sorted	sort	VERB
cana-826	161	56	indices	index	NOUN
cana-826	161	57	=	=	SYM
cana-826	161	58	np.argsort(eigenvalues	np.argsort(eigenvalue	NOUN
cana-826	161	59	)	)	PUNCT
cana-826	161	60	index	index	NOUN
cana-826	161	61	values	value	NOUN
cana-826	161	62	=	=	SYM
cana-826	161	63	robot	robot	NOUN
cana-826	161	64	:	:	PUNCT
cana-826	161	65	index	index	NOUN
cana-826	161	66	for	for	ADP
cana-826	161	67	index	index	NOUN
cana-826	161	68	,	,	PUNCT
cana-826	161	69	robot	robot	NOUN
cana-826	161	70	in	in	ADP
cana-826	161	71	enumerate(sorted	enumerate(sorte	VERB
cana-826	161	72	indices	index	NOUN
cana-826	161	73	)	)	PUNCT
cana-826	161	74	step	step	NOUN
cana-826	161	75	7	7	NUM
cana-826	161	76	:	:	PUNCT
cana-826	161	77	assign	assign	VERB
cana-826	161	78	task	task	NOUN
cana-826	161	79	to	to	ADP
cana-826	161	80	nearest	nearest	PROPN
cana-826	161	81	robot	robot	NOUN
cana-826	161	82	task	task	NOUN
cana-826	161	83	assigned	assign	VERB
cana-826	161	84	=	=	SYM
cana-826	161	85	f”task	f”task	AUX
cana-826	161	86	assigned	assign	VERB
cana-826	161	87	to	to	ADP
cana-826	161	88	robot	robot	NOUN
cana-826	161	89	nearest	nearest	PROPN
cana-826	161	90	robot	robot	PROPN
cana-826	161	91	i	i	PROPN
cana-826	161	92	d	d	PROPN
cana-826	161	93	”	"	PUNCT
cana-826	161	94	step	step	NOUN
cana-826	161	95	8	8	NUM
cana-826	161	96	:	:	PUNCT
cana-826	161	97	monitor	monitor	VERB
cana-826	161	98	the	the	DET
cana-826	161	99	robots	robot	NOUN
cana-826	161	100	and	and	CCONJ
cana-826	161	101	situation	situation	NOUN
cana-826	161	102	situation	situation	NOUN
cana-826	161	103	under	under	ADP
cana-826	161	104	control	control	NOUN
cana-826	161	105	=	=	SYM
cana-826	161	106	true	true	ADJ
cana-826	161	107	step	step	NOUN
cana-826	161	108	9	9	NUM
cana-826	161	109	:	:	PUNCT
cana-826	161	110	check	check	VERB
cana-826	161	111	if	if	SCONJ
cana-826	161	112	situation	situation	NOUN
cana-826	161	113	is	be	AUX
cana-826	161	114	under	under	ADP
cana-826	161	115	control	control	NOUN
cana-826	161	116	if	if	SCONJ
cana-826	161	117	situation	situation	NOUN
cana-826	161	118	under	under	ADP
cana-826	161	119	control	control	NOUN
cana-826	161	120	:	:	PUNCT
cana-826	161	121	print(“situation	print(“situation	NOUN
cana-826	161	122	is	be	AUX
cana-826	161	123	under	under	ADP
cana-826	161	124	control	control	NOUN
cana-826	161	125	.	.	PUNCT
cana-826	162	1	continuing	continue	VERB
cana-826	162	2	monitoring	monitoring	NOUN
cana-826	162	3	.	.	PUNCT
cana-826	162	4	”	"	PUNCT
cana-826	162	5	)	)	PUNCT
cana-826	163	1	else	else	ADV
cana-826	163	2	:	:	PUNCT
cana-826	163	3	print(“situation	print(“situation	NOUN
cana-826	163	4	is	be	AUX
cana-826	163	5	not	not	PART
cana-826	163	6	under	under	ADP
cana-826	163	7	control	control	NOUN
cana-826	163	8	.	.	PUNCT
cana-826	164	1	activating	activate	VERB
cana-826	164	2	alarm	alarm	NOUN
cana-826	164	3	and	and	CCONJ
cana-826	164	4	executing	execute	VERB
cana-826	164	5	emergency	emergency	NOUN
cana-826	164	6	response	response	NOUN
cana-826	164	7	plan	plan	NOUN
cana-826	164	8	.	.	PUNCT
cana-826	165	1	notifying	notify	VERB
cana-826	165	2	authorities	authority	NOUN
cana-826	165	3	.	.	PUNCT
cana-826	165	4	”	"	PUNCT
cana-826	166	1	)	)	PUNCT
cana-826	166	2	the	the	DET
cana-826	166	3	score	score	NOUN
cana-826	166	4	values	value	NOUN
cana-826	166	5	of	of	ADP
cana-826	166	6	the	the	DET
cana-826	166	7	robots	robot	NOUN
cana-826	166	8	indicate	indicate	VERB
cana-826	166	9	their	their	PRON
cana-826	166	10	accessibility	accessibility	NOUN
cana-826	166	11	.	.	PUNCT
cana-826	167	1	this	this	DET
cana-826	167	2	plot	plot	NOUN
cana-826	167	3	illustrates	illustrate	VERB
cana-826	167	4	the	the	DET
cana-826	167	5	relationship	relationship	NOUN
cana-826	167	6	between	between	ADP
cana-826	167	7	the	the	DET
cana-826	167	8	score	score	NOUN
cana-826	167	9	values	value	NOUN
cana-826	167	10	of	of	ADP
cana-826	167	11	robots	robot	NOUN
cana-826	167	12	in	in	ADP
cana-826	167	13	two	two	NUM
cana-826	167	14	compartments	compartment	NOUN
cana-826	167	15	.	.	PUNCT
cana-826	168	1	from	from	ADP
cana-826	168	2	this	this	DET
cana-826	168	3	plotted	plot	VERB
cana-826	168	4	graph	graph	NOUN
cana-826	168	5	,	,	PUNCT
cana-826	168	6	robots	robot	NOUN
cana-826	168	7	connected	connect	VERB
cana-826	168	8	to	to	ADP
cana-826	168	9	the	the	DET
cana-826	168	10	main	main	ADJ
cana-826	168	11	control	control	NOUN
cana-826	168	12	system	system	NOUN
cana-826	168	13	𝐿	𝐿	PROPN
cana-826	168	14	demonstrate	demonstrate	VERB
cana-826	168	15	higher	high	ADJ
cana-826	168	16	accessibility	accessibility	NOUN
cana-826	168	17	compared	compare	VERB
cana-826	168	18	to	to	ADP
cana-826	168	19	those	those	PRON
cana-826	168	20	connected	connect	VERB
cana-826	168	21	to	to	ADP
cana-826	168	22	𝐾.	𝐾.	PROPN
cana-826	168	23	communications	communication	NOUN
cana-826	168	24	on	on	ADP
cana-826	168	25	applied	apply	VERB
cana-826	168	26	nonlinear	nonlinear	ADJ
cana-826	168	27	analysis	analysis	NOUN
cana-826	168	28	issn	issn	NOUN
cana-826	168	29	:	:	PUNCT
cana-826	168	30	1074	1074	NUM
cana-826	168	31	-	-	PUNCT
cana-826	168	32	133x	133x	NUM
cana-826	168	33	vol	vol	NOUN
cana-826	168	34	31	31	NUM
cana-826	168	35	no	no	NOUN
cana-826	168	36	.	.	PUNCT
cana-826	169	1	4s	4s	NUM
cana-826	169	2	(	(	PUNCT
cana-826	169	3	2024	2024	NUM
cana-826	169	4	)	)	PUNCT
cana-826	169	5	21	21	NUM
cana-826	169	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-826	169	7	fig	fig	NOUN
cana-826	169	8	4.5	4.5	NUM
cana-826	169	9	:	:	PUNCT
cana-826	169	10	score	score	NOUN
cana-826	169	11	values	value	NOUN
cana-826	169	12	of	of	ADP
cana-826	169	13	the	the	DET
cana-826	169	14	robots	robot	NOUN
cana-826	169	15	are	be	AUX
cana-826	169	16	linked	link	VERB
cana-826	169	17	to	to	ADP
cana-826	169	18	𝐾⁡&⁡𝐿	𝐾⁡&⁡𝐿	NUM
cana-826	169	19	4.1	4.1	NUM
cana-826	169	20	simulation	simulation	NOUN
cana-826	169	21	results	result	VERB
cana-826	169	22	•	•	ADJ
cana-826	169	23	score	score	NOUN
cana-826	169	24	values	value	NOUN
cana-826	169	25	are	be	AUX
cana-826	169	26	employed	employ	VERB
cana-826	169	27	to	to	ADP
cana-826	169	28	precisely	precisely	ADV
cana-826	169	29	locate	locate	ADJ
cana-826	169	30	security	security	NOUN
cana-826	169	31	robots	robot	NOUN
cana-826	169	32	,	,	PUNCT
cana-826	169	33	utilizing	utilize	VERB
cana-826	169	34	the	the	DET
cana-826	169	35	ifthg	ifthg	NOUN
cana-826	169	36	model	model	NOUN
cana-826	169	37	to	to	PART
cana-826	169	38	calculate	calculate	VERB
cana-826	169	39	distances	distance	NOUN
cana-826	169	40	between	between	ADP
cana-826	169	41	them	they	PRON
cana-826	169	42	.	.	PUNCT
cana-826	170	1	these	these	DET
cana-826	170	2	robots	robot	NOUN
cana-826	170	3	establish	establish	VERB
cana-826	170	4	communication	communication	NOUN
cana-826	170	5	channels	channel	NOUN
cana-826	170	6	using	use	VERB
cana-826	170	7	radio	radio	NOUN
cana-826	170	8	frequency	frequency	NOUN
cana-826	170	9	technologies	technology	NOUN
cana-826	170	10	,	,	PUNCT
cana-826	170	11	facilitating	facilitate	VERB
cana-826	170	12	smooth	smooth	ADJ
cana-826	170	13	information	information	NOUN
cana-826	170	14	exchange	exchange	NOUN
cana-826	170	15	and	and	CCONJ
cana-826	170	16	coordination	coordination	NOUN
cana-826	170	17	in	in	ADP
cana-826	170	18	surveillance	surveillance	NOUN
cana-826	170	19	operations	operation	NOUN
cana-826	170	20	.	.	PUNCT
cana-826	171	1	•	•	NUM
cana-826	171	2	in	in	ADP
cana-826	171	3	order	order	NOUN
cana-826	171	4	to	to	PART
cana-826	171	5	obtain	obtain	VERB
cana-826	171	6	communication	communication	NOUN
cana-826	171	7	and	and	CCONJ
cana-826	171	8	distance	distance	NOUN
cana-826	171	9	information	information	NOUN
cana-826	171	10	,	,	PUNCT
cana-826	171	11	the	the	DET
cana-826	171	12	adjacency	adjacency	NOUN
cana-826	171	13	matrix	matrix	NOUN
cana-826	171	14	,	,	PUNCT
cana-826	171	15	its	its	PRON
cana-826	171	16	eigenvalues	eigenvalue	NOUN
cana-826	171	17	,	,	PUNCT
cana-826	171	18	and	and	CCONJ
cana-826	171	19	related	related	ADJ
cana-826	171	20	index	index	NOUN
cana-826	171	21	values	value	NOUN
cana-826	171	22	have	have	AUX
cana-826	171	23	been	be	AUX
cana-826	171	24	used	use	VERB
cana-826	171	25	.	.	PUNCT
cana-826	172	1	•	•	NUM
cana-826	172	2	the	the	DET
cana-826	172	3	adjacency	adjacency	NOUN
cana-826	172	4	matrix	matrix	NOUN
cana-826	172	5	illustrates	illustrate	VERB
cana-826	172	6	the	the	DET
cana-826	172	7	distances	distance	NOUN
cana-826	172	8	between	between	ADP
cana-826	172	9	robots	robot	NOUN
cana-826	172	10	that	that	PRON
cana-826	172	11	establish	establish	VERB
cana-826	172	12	communication	communication	NOUN
cana-826	172	13	links	link	NOUN
cana-826	172	14	with	with	ADP
cana-826	172	15	each	each	DET
cana-826	172	16	other	other	ADJ
cana-826	172	17	.	.	PUNCT
cana-826	173	1	•	•	NUM
cana-826	173	2	the	the	DET
cana-826	173	3	highest	high	ADJ
cana-826	173	4	eigenvalue	eigenvalue	NOUN
cana-826	173	5	represents	represent	VERB
cana-826	173	6	the	the	DET
cana-826	173	7	principal	principal	ADJ
cana-826	173	8	eigenvector	eigenvector	NOUN
cana-826	173	9	of	of	ADP
cana-826	173	10	the	the	DET
cana-826	173	11	system	system	NOUN
cana-826	173	12	,	,	PUNCT
cana-826	173	13	from	from	ADP
cana-826	173	14	which	which	PRON
cana-826	173	15	the	the	DET
cana-826	173	16	main	main	ADJ
cana-826	173	17	control	control	NOUN
cana-826	173	18	system	system	NOUN
cana-826	173	19	directs	direct	VERB
cana-826	173	20	the	the	DET
cana-826	173	21	nearest	near	ADJ
cana-826	173	22	robot	robot	NOUN
cana-826	173	23	seize	seize	VERB
cana-826	173	24	the	the	DET
cana-826	173	25	fugitives	fugitive	NOUN
cana-826	173	26	.	.	PUNCT
cana-826	174	1	5	5	X
cana-826	174	2	.	.	X
cana-826	174	3	conclusion	conclusion	NOUN
cana-826	174	4	this	this	DET
cana-826	174	5	paper	paper	NOUN
cana-826	174	6	explains	explain	VERB
cana-826	174	7	about	about	ADP
cana-826	174	8	the	the	DET
cana-826	174	9	basic	basic	ADJ
cana-826	174	10	concepts	concept	NOUN
cana-826	174	11	of	of	ADP
cana-826	174	12	ifthg	ifthg	NOUN
cana-826	174	13	and	and	CCONJ
cana-826	174	14	some	some	PRON
cana-826	174	15	of	of	ADP
cana-826	174	16	its	its	PRON
cana-826	174	17	properties	property	NOUN
cana-826	174	18	.	.	PUNCT
cana-826	175	1	ifthgs	ifthgs	AUX
cana-826	175	2	provide	provide	VERB
cana-826	175	3	a	a	DET
cana-826	175	4	more	more	ADV
cana-826	175	5	flexible	flexible	ADJ
cana-826	175	6	approach	approach	NOUN
cana-826	175	7	to	to	ADP
cana-826	175	8	real	real	ADJ
cana-826	175	9	-	-	PUNCT
cana-826	175	10	time	time	NOUN
cana-826	175	11	decision	decision	NOUN
cana-826	175	12	making	making	NOUN
cana-826	175	13	by	by	ADP
cana-826	175	14	representing	represent	VERB
cana-826	175	15	uncertainty	uncertainty	NOUN
cana-826	175	16	and	and	CCONJ
cana-826	175	17	vagueness	vagueness	NOUN
cana-826	175	18	in	in	ADP
cana-826	175	19	robot	robot	NOUN
cana-826	175	20	configuration	configuration	NOUN
cana-826	175	21	.	.	PUNCT
cana-826	176	1	also	also	ADV
cana-826	176	2	an	an	DET
cana-826	176	3	algorithm	algorithm	NOUN
cana-826	176	4	designed	design	VERB
cana-826	176	5	to	to	PART
cana-826	176	6	identify	identify	VERB
cana-826	176	7	the	the	DET
cana-826	176	8	nearest	near	ADJ
cana-826	176	9	robot	robot	NOUN
cana-826	176	10	index	index	NOUN
cana-826	176	11	to	to	PART
cana-826	176	12	seize	seize	VERB
cana-826	176	13	the	the	DET
cana-826	176	14	fugitives	fugitive	NOUN
cana-826	176	15	when	when	SCONJ
cana-826	176	16	an	an	DET
cana-826	176	17	intrusion	intrusion	NOUN
cana-826	176	18	is	be	AUX
cana-826	176	19	detected	detect	VERB
cana-826	176	20	in	in	ADP
cana-826	176	21	a	a	DET
cana-826	176	22	large	large	ADJ
cana-826	176	23	area	area	NOUN
cana-826	176	24	.	.	PUNCT
cana-826	177	1	future	future	ADJ
cana-826	177	2	work	work	NOUN
cana-826	177	3	will	will	AUX
cana-826	177	4	explore	explore	VERB
cana-826	177	5	the	the	DET
cana-826	177	6	intuitionistic	intuitionistic	ADJ
cana-826	177	7	fuzzy	fuzzy	ADJ
cana-826	177	8	hesitancy	hesitancy	NOUN
cana-826	177	9	threshold	threshold	NOUN
cana-826	177	10	hypergraphs	hypergraph	NOUN
cana-826	177	11	and	and	CCONJ
cana-826	177	12	its	its	PRON
cana-826	177	13	application	application	NOUN
cana-826	177	14	in	in	ADP
cana-826	177	15	real	real	ADJ
cana-826	177	16	life	life	NOUN
cana-826	177	17	scenario	scenario	NOUN
cana-826	177	18	.	.	PUNCT
cana-826	178	1	references	reference	NOUN
cana-826	178	2	[	[	X
cana-826	178	3	1	1	NUM
cana-826	178	4	]	]	X
cana-826	178	5	atanassov	atanassov	NOUN
cana-826	178	6	k	k	PROPN
cana-826	178	7	t	t	PROPN
cana-826	178	8	,	,	PUNCT
cana-826	178	9	intuitionistic	intuitionistic	ADJ
cana-826	178	10	fuzzy	fuzzy	ADJ
cana-826	178	11	sets	set	NOUN
cana-826	178	12	,	,	PUNCT
cana-826	178	13	fuzzy	fuzzy	ADJ
cana-826	178	14	sets	set	NOUN
cana-826	178	15	and	and	CCONJ
cana-826	178	16	systems	system	NOUN
cana-826	178	17	,	,	PUNCT
cana-826	178	18	20	20	NUM
cana-826	178	19	(	(	PUNCT
cana-826	178	20	1986	1986	NUM
cana-826	178	21	)	)	PUNCT
cana-826	178	22	,	,	PUNCT
cana-826	178	23	87–96	87–96	NUM
cana-826	178	24	.	.	PUNCT
cana-826	179	1	[	[	X
cana-826	179	2	2	2	NUM
cana-826	179	3	]	]	PUNCT
cana-826	179	4	atanassov	atanassov	NOUN
cana-826	179	5	k	k	PROPN
cana-826	179	6	t	t	PROPN
cana-826	179	7	,	,	PUNCT
cana-826	179	8	on	on	ADP
cana-826	179	9	intuitionistic	intuitionistic	ADJ
cana-826	179	10	fuzzy	fuzzy	ADJ
cana-826	179	11	graphs	graph	NOUN
cana-826	179	12	and	and	CCONJ
cana-826	179	13	intuitionistic	intuitionistic	ADJ
cana-826	179	14	fuzzy	fuzzy	ADJ
cana-826	179	15	relations	relation	NOUN
cana-826	179	16	,	,	PUNCT
cana-826	179	17	proceedings	proceeding	NOUN
cana-826	179	18	of	of	ADP
cana-826	179	19	the	the	DET
cana-826	179	20	6th	6th	ADJ
cana-826	179	21	ifsa	ifsa	PROPN
cana-826	179	22	world	world	PROPN
cana-826	179	23	congress	congress	PROPN
cana-826	179	24	,	,	PUNCT
cana-826	179	25	sao	sao	PROPN
cana-826	179	26	paulo	paulo	PROPN
cana-826	179	27	,	,	PUNCT
cana-826	179	28	brazil	brazil	PROPN
cana-826	179	29	,	,	PUNCT
cana-826	179	30	1(1995	1(1995	NUM
cana-826	179	31	)	)	PUNCT
cana-826	179	32	,	,	PUNCT
cana-826	179	33	551–554	551–554	NUM
cana-826	179	34	.	.	PUNCT
cana-826	180	1	[	[	X
cana-826	180	2	3	3	X
cana-826	180	3	]	]	X
cana-826	180	4	atanassov	atanassov	NOUN
cana-826	180	5	k	k	PROPN
cana-826	180	6	t	t	PROPN
cana-826	180	7	,	,	PUNCT
cana-826	180	8	intuitionistic	intuitionistic	ADJ
cana-826	180	9	fuzzy	fuzzy	ADJ
cana-826	180	10	sets	set	NOUN
cana-826	180	11	:	:	PUNCT
cana-826	180	12	theory	theory	NOUN
cana-826	180	13	and	and	CCONJ
cana-826	180	14	applications	application	NOUN
cana-826	180	15	,	,	PUNCT
cana-826	180	16	studies	study	NOUN
cana-826	180	17	in	in	ADP
cana-826	180	18	fuzziness	fuzziness	NOUN
cana-826	180	19	and	and	CCONJ
cana-826	180	20	soft	soft	ADJ
cana-826	180	21	computing	computing	NOUN
cana-826	180	22	,	,	PUNCT
cana-826	180	23	physica	physica	NOUN
cana-826	180	24	-	-	PUNCT
cana-826	180	25	verlag	verlag	PROPN
cana-826	180	26	,	,	PUNCT
cana-826	180	27	heidelberg	heidelberg	PROPN
cana-826	180	28	,	,	PUNCT
cana-826	180	29	new	new	PROPN
cana-826	180	30	york	york	PROPN
cana-826	180	31	,	,	PUNCT
cana-826	180	32	2012	2012	NUM
cana-826	180	33	.	.	PUNCT
cana-826	181	1	[	[	X
cana-826	181	2	4	4	X
cana-826	181	3	]	]	X
cana-826	181	4	atanassov	atanassov	NOUN
cana-826	181	5	k	k	PROPN
cana-826	181	6	t	t	PROPN
cana-826	181	7	,	,	PUNCT
cana-826	181	8	parvathi	parvathi	PROPN
cana-826	181	9	r	r	PROPN
cana-826	181	10	and	and	CCONJ
cana-826	181	11	karunambigai	karunambigai	PROPN
cana-826	181	12	mg	mg	PROPN
cana-826	181	13	,	,	PUNCT
cana-826	181	14	operations	operation	NOUN
cana-826	181	15	on	on	ADP
cana-826	181	16	intuitionistic	intuitionistic	ADJ
cana-826	181	17	fuzzy	fuzzy	ADJ
cana-826	181	18	graphs	graph	NOUN
cana-826	181	19	,	,	PUNCT
cana-826	181	20	ieee	ieee	PROPN
cana-826	181	21	international	international	ADJ
cana-826	181	22	conference	conference	NOUN
cana-826	181	23	on	on	ADP
cana-826	181	24	fuzzy	fuzzy	ADJ
cana-826	181	25	systems	system	NOUN
cana-826	181	26	,	,	PUNCT
cana-826	181	27	korea	korea	PROPN
cana-826	181	28	,	,	PUNCT
cana-826	181	29	(	(	PUNCT
cana-826	181	30	2009	2009	NUM
cana-826	181	31	)	)	PUNCT
cana-826	181	32	,	,	PUNCT
cana-826	181	33	20	20	NUM
cana-826	181	34	-	-	SYM
cana-826	181	35	24	24	NUM
cana-826	181	36	.	.	PUNCT
cana-826	182	1	[	[	X
cana-826	182	2	5	5	X
cana-826	182	3	]	]	X
cana-826	182	4	berge	berge	NOUN
cana-826	182	5	c	c	NOUN
cana-826	182	6	,	,	PUNCT
cana-826	182	7	graphs	graph	NOUN
cana-826	182	8	and	and	CCONJ
cana-826	182	9	hypergraphs	hypergraph	NOUN
cana-826	182	10	,	,	PUNCT
cana-826	182	11	north	north	NOUN
cana-826	182	12	holland	holland	PROPN
cana-826	182	13	,	,	PUNCT
cana-826	182	14	new	new	PROPN
cana-826	182	15	york	york	PROPN
cana-826	182	16	,	,	PUNCT
cana-826	182	17	1976	1976	NUM
cana-826	182	18	.	.	PUNCT
cana-826	183	1	[	[	X
cana-826	183	2	6	6	NUM
cana-826	183	3	]	]	SYM
cana-826	183	4	chvatal.v	chvatal.v	NOUN
cana-826	183	5	,	,	PUNCT
cana-826	183	6	hammer	hammer	NOUN
cana-826	183	7	.	.	PUNCT
cana-826	184	1	p.	p.	NOUN
cana-826	184	2	l	l	PROPN
cana-826	184	3	,	,	PUNCT
cana-826	185	1	set	set	NOUN
cana-826	185	2	-	-	PUNCT
cana-826	185	3	packing	pack	VERB
cana-826	185	4	problems	problem	NOUN
cana-826	185	5	and	and	CCONJ
cana-826	185	6	threshold	threshold	NOUN
cana-826	185	7	graphs	graph	NOUN
cana-826	185	8	,	,	PUNCT
cana-826	185	9	technical	technical	ADJ
cana-826	185	10	report	report	NOUN
cana-826	185	11	,	,	PUNCT
cana-826	185	12	university	university	NOUN
cana-826	185	13	of	of	ADP
cana-826	185	14	waterloo	waterloo	PROPN
cana-826	185	15	,	,	PUNCT
cana-826	185	16	canada	canada	PROPN
cana-826	185	17	,	,	PUNCT
cana-826	185	18	1973	1973	NUM
cana-826	185	19	.	.	PUNCT
cana-826	186	1	[	[	X
cana-826	186	2	7	7	X
cana-826	186	3	]	]	X
cana-826	186	4	muhammad	muhammad	PROPN
cana-826	186	5	akram	akram	PROPN
cana-826	186	6	,	,	PUNCT
cana-826	186	7	musavarah	musavarah	PROPN
cana-826	186	8	sarwar	sarwar	PROPN
cana-826	186	9	,	,	PUNCT
cana-826	186	10	rajab	rajab	PROPN
cana-826	186	11	ali	ali	PROPN
cana-826	186	12	borzooei	borzooei	PROPN
cana-826	186	13	,	,	PUNCT
cana-826	186	14	a	a	DET
cana-826	186	15	novel	novel	ADJ
cana-826	186	16	decision	decision	NOUN
cana-826	186	17	-	-	PUNCT
cana-826	186	18	making	make	VERB
cana-826	186	19	approach	approach	NOUN
cana-826	186	20	based	base	VERB
cana-826	186	21	communications	communication	NOUN
cana-826	186	22	on	on	ADP
cana-826	186	23	applied	apply	VERB
cana-826	186	24	nonlinear	nonlinear	ADJ
cana-826	186	25	analysis	analysis	NOUN
cana-826	186	26	issn	issn	NOUN
cana-826	186	27	:	:	PUNCT
cana-826	186	28	1074	1074	NUM
cana-826	186	29	-	-	PUNCT
cana-826	186	30	133x	133x	NUM
cana-826	186	31	vol	vol	NOUN
cana-826	186	32	31	31	NUM
cana-826	186	33	no	no	NOUN
cana-826	186	34	.	.	PUNCT
cana-826	187	1	4s	4s	NUM
cana-826	187	2	(	(	PUNCT
cana-826	187	3	2024	2024	NUM
cana-826	187	4	)	)	PUNCT
cana-826	187	5	22	22	NUM
cana-826	187	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-826	187	7	on	on	ADP
cana-826	187	8	hypergraphs	hypergraph	NOUN
cana-826	187	9	in	in	ADP
cana-826	187	10	intuitionistic	intuitionistic	ADJ
cana-826	187	11	fuzzy	fuzzy	ADJ
cana-826	187	12	environment	environment	NOUN
cana-826	187	13	,	,	PUNCT
cana-826	187	14	journal	journal	NOUN
cana-826	187	15	of	of	ADP
cana-826	187	16	intelligent	intelligent	ADJ
cana-826	187	17	&	&	CCONJ
cana-826	187	18	fuzzy	fuzzy	ADJ
cana-826	187	19	systems	system	NOUN
cana-826	187	20	,	,	PUNCT
cana-826	187	21	35	35	NUM
cana-826	187	22	,	,	PUNCT
cana-826	187	23	(	(	PUNCT
cana-826	187	24	2018	2018	NUM
cana-826	187	25	)	)	PUNCT
cana-826	187	26	,	,	PUNCT
cana-826	187	27	1905	1905	NUM
cana-826	187	28	1922	1922	NUM
cana-826	187	29	.	.	PUNCT
cana-826	188	1	[	[	X
cana-826	188	2	8	8	NUM
cana-826	188	3	]	]	X
cana-826	188	4	myithili	myithili	NOUN
cana-826	188	5	k	k	PROPN
cana-826	188	6	k	k	PROPN
cana-826	188	7	,	,	PUNCT
cana-826	188	8	parvathi	parvathi	PROPN
cana-826	188	9	r	r	PROPN
cana-826	188	10	and	and	CCONJ
cana-826	188	11	akram	akram	PROPN
cana-826	188	12	m	m	PROPN
cana-826	188	13	,	,	PUNCT
cana-826	188	14	certain	certain	ADJ
cana-826	188	15	types	type	NOUN
cana-826	188	16	of	of	ADP
cana-826	188	17	intuitionistic	intuitionistic	ADJ
cana-826	188	18	fuzzy	fuzzy	ADJ
cana-826	188	19	directed	direct	VERB
cana-826	188	20	hypergraphs	hypergraph	NOUN
cana-826	188	21	,	,	PUNCT
cana-826	188	22	international	international	ADJ
cana-826	188	23	journal	journal	NOUN
cana-826	188	24	of	of	ADP
cana-826	188	25	machine	machine	NOUN
cana-826	188	26	learning	learning	NOUN
cana-826	188	27	and	and	CCONJ
cana-826	188	28	cybernetics	cybernetic	NOUN
cana-826	188	29	,	,	PUNCT
cana-826	188	30	springer	springer	NOUN
cana-826	188	31	-	-	PUNCT
cana-826	188	32	verlag	verlag	PROPN
cana-826	188	33	berlin	berlin	PROPN
cana-826	188	34	heidelberg	heidelberg	PROPN
cana-826	188	35	,	,	PUNCT
cana-826	188	36	7(2	7(2	NUM
cana-826	188	37	)	)	PUNCT
cana-826	188	38	(	(	PUNCT
cana-826	188	39	2016	2016	NUM
cana-826	188	40	)	)	PUNCT
cana-826	188	41	,	,	PUNCT
cana-826	188	42	287	287	NUM
cana-826	188	43	-	-	SYM
cana-826	188	44	295	295	NUM
cana-826	188	45	.	.	PUNCT
cana-826	189	1	[	[	X
cana-826	189	2	9	9	NUM
cana-826	189	3	]	]	X
cana-826	189	4	parvathi	parvathi	PROPN
cana-826	189	5	r	r	PROPN
cana-826	189	6	,	,	PUNCT
cana-826	189	7	karunambigai	karunambigai	PROPN
cana-826	189	8	m	m	NOUN
cana-826	189	9	g	g	NOUN
cana-826	189	10	,	,	PUNCT
cana-826	189	11	intuitionistic	intuitionistic	ADJ
cana-826	189	12	fuzzy	fuzzy	ADJ
cana-826	189	13	graphs	graph	NOUN
cana-826	189	14	,	,	PUNCT
cana-826	189	15	proceedings	proceeding	NOUN
cana-826	189	16	of	of	ADP
cana-826	189	17	9th	9th	ADJ
cana-826	189	18	fuzzy	fuzzy	ADJ
cana-826	189	19	days	day	NOUN
cana-826	189	20	international	international	ADJ
cana-826	189	21	conference	conference	NOUN
cana-826	189	22	on	on	ADP
cana-826	189	23	computational	computational	ADJ
cana-826	189	24	intelligence	intelligence	NOUN
cana-826	189	25	,	,	PUNCT
cana-826	189	26	advances	advance	NOUN
cana-826	189	27	in	in	ADP
cana-826	189	28	soft	soft	ADJ
cana-826	189	29	computing	computing	NOUN
cana-826	189	30	:	:	PUNCT
cana-826	189	31	computational	computational	ADJ
cana-826	189	32	intelligence	intelligence	NOUN
cana-826	189	33	,	,	PUNCT
cana-826	189	34	theory	theory	NOUN
cana-826	189	35	and	and	CCONJ
cana-826	189	36	applications	application	NOUN
cana-826	189	37	,	,	PUNCT
cana-826	189	38	springer	springer	NOUN
cana-826	189	39	-	-	PUNCT
cana-826	189	40	verlag	verlag	PROPN
cana-826	189	41	,	,	PUNCT
cana-826	189	42	new	new	PROPN
cana-826	189	43	york	york	PROPN
cana-826	189	44	,	,	PUNCT
cana-826	189	45	20(2006	20(2006	NUM
cana-826	189	46	)	)	PUNCT
cana-826	189	47	,	,	PUNCT
cana-826	189	48	139	139	NUM
cana-826	189	49	–	–	SYM
cana-826	189	50	150	150	NUM
cana-826	189	51	.	.	PUNCT
cana-826	190	1	[	[	X
cana-826	190	2	10	10	NUM
cana-826	190	3	]	]	X
cana-826	190	4	parvathi	parvathi	PROPN
cana-826	190	5	r	r	PROPN
cana-826	190	6	,	,	PUNCT
cana-826	190	7	thilagavathi	thilagavathi	NOUN
cana-826	190	8	s	s	PART
cana-826	190	9	and	and	CCONJ
cana-826	190	10	karunambigai	karunambigai	PROPN
cana-826	190	11	m	m	PROPN
cana-826	190	12	g	g	NOUN
cana-826	190	13	,	,	PUNCT
cana-826	190	14	intuitionistic	intuitionistic	ADJ
cana-826	190	15	fuzzy	fuzzy	ADJ
cana-826	190	16	hypergraphs	hypergraph	NOUN
cana-826	190	17	,	,	PUNCT
cana-826	190	18	bulgarian	bulgarian	ADJ
cana-826	190	19	academy	academy	NOUN
cana-826	190	20	of	of	ADP
cana-826	190	21	science	science	PROPN
cana-826	190	22	,	,	PUNCT
cana-826	190	23	cybernetics	cybernetic	NOUN
cana-826	190	24	and	and	CCONJ
cana-826	190	25	information	information	NOUN
cana-826	190	26	technologies	technology	NOUN
cana-826	190	27	,	,	PUNCT
cana-826	190	28	9(2	9(2	NUM
cana-826	190	29	)	)	PUNCT
cana-826	190	30	(	(	PUNCT
cana-826	190	31	2009	2009	NUM
cana-826	190	32	)	)	PUNCT
cana-826	190	33	,	,	PUNCT
cana-826	190	34	46–53	46–53	NOUN
cana-826	190	35	.	.	PUNCT
cana-826	191	1	[	[	X
cana-826	191	2	11	11	NUM
cana-826	191	3	]	]	X
cana-826	191	4	parvathi	parvathi	PROPN
cana-826	191	5	r	r	PROPN
cana-826	191	6	,	,	PUNCT
cana-826	191	7	thilagavathi	thilagavathi	NOUN
cana-826	191	8	s	s	PART
cana-826	191	9	,	,	PUNCT
cana-826	191	10	intuitionistic	intuitionistic	ADJ
cana-826	191	11	fuzzy	fuzzy	ADJ
cana-826	191	12	directed	direct	VERB
cana-826	191	13	hypergraphs	hypergraph	NOUN
cana-826	191	14	,	,	PUNCT
cana-826	191	15	advances	advance	NOUN
cana-826	191	16	in	in	ADP
cana-826	191	17	fuzzy	fuzzy	ADJ
cana-826	191	18	sets	set	NOUN
cana-826	191	19	and	and	CCONJ
cana-826	191	20	systems	system	NOUN
cana-826	191	21	,	,	PUNCT
cana-826	191	22	pushpa	pushpa	NOUN
cana-826	191	23	publishing	publishing	PROPN
cana-826	191	24	house	house	PROPN
cana-826	191	25	,	,	PUNCT
cana-826	191	26	14(1	14(1	NUM
cana-826	191	27	)	)	PUNCT
cana-826	191	28	(	(	PUNCT
cana-826	191	29	2013	2013	NUM
cana-826	191	30	)	)	PUNCT
cana-826	191	31	,	,	PUNCT
cana-826	191	32	39–52	39–52	NUM
cana-826	191	33	.	.	PUNCT
cana-826	192	1	[	[	X
cana-826	192	2	12	12	NUM
cana-826	192	3	]	]	X
cana-826	192	4	lanzhen	lanzhen	PROPN
cana-826	192	5	yang	yang	PROPN
cana-826	192	6	,	,	PUNCT
cana-826	192	7	hua	hua	PROPN
cana-826	192	8	mao	mao	PROPN
cana-826	192	9	,	,	PUNCT
cana-826	192	10	intuitionistic	intuitionistic	ADJ
cana-826	192	11	fuzzy	fuzzy	ADJ
cana-826	192	12	threshold	threshold	NOUN
cana-826	192	13	graphs	graph	NOUN
cana-826	192	14	,	,	PUNCT
cana-826	192	15	journal	journal	NOUN
cana-826	192	16	of	of	ADP
cana-826	192	17	intelligent	intelligent	ADJ
cana-826	192	18	and	and	CCONJ
cana-826	192	19	fuzzy	fuzzy	ADJ
cana-826	192	20	systems	system	NOUN
cana-826	192	21	,	,	PUNCT
cana-826	192	22	36	36	NUM
cana-826	192	23	(	(	PUNCT
cana-826	192	24	2019	2019	NUM
cana-826	192	25	)	)	PUNCT
cana-826	192	26	,	,	PUNCT
cana-826	192	27	6641–6651	6641–6651	NUM
cana-826	192	28	.	.	PUNCT
cana-826	193	1	[	[	X
cana-826	193	2	13	13	NUM
cana-826	193	3	]	]	PUNCT
cana-826	193	4	zadeh	zadeh	PROPN
cana-826	193	5	l	l	PROPN
cana-826	193	6	a	a	X
cana-826	193	7	,	,	PUNCT
cana-826	193	8	fuzzy	fuzzy	ADJ
cana-826	193	9	sets	set	NOUN
cana-826	193	10	,	,	PUNCT
cana-826	193	11	information	information	NOUN
cana-826	193	12	and	and	CCONJ
cana-826	193	13	control	control	NOUN
cana-826	193	14	,	,	PUNCT
cana-826	193	15	8	8	NUM
cana-826	193	16	(	(	PUNCT
cana-826	193	17	1965	1965	NUM
cana-826	193	18	)	)	PUNCT
cana-826	193	19	,	,	PUNCT
cana-826	193	20	338–353	338–353	NUM