id	sid	tid	token	lemma	pos
cana-1748	1	1	communications	communication	NOUN
cana-1748	1	2	on	on	ADP
cana-1748	1	3	applied	apply	VERB
cana-1748	1	4	nonlinear	nonlinear	ADJ
cana-1748	1	5	analysis	analysis	NOUN
cana-1748	1	6	issn	issn	NOUN
cana-1748	1	7	:	:	PUNCT
cana-1748	1	8	1074	1074	NUM
cana-1748	1	9	-	-	PUNCT
cana-1748	1	10	133x	133x	NUM
cana-1748	1	11	vol	vol	NOUN
cana-1748	1	12	32	32	NUM
cana-1748	1	13	no	no	NOUN
cana-1748	1	14	.	.	NOUN
cana-1748	1	15	2	2	NUM
cana-1748	1	16	(	(	PUNCT
cana-1748	1	17	2025	2025	NUM
cana-1748	1	18	)	)	PUNCT
cana-1748	1	19	367	367	NUM
cana-1748	1	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-1748	1	21	fuzzy	fuzzy	ADJ
cana-1748	1	22	traveling	travel	VERB
cana-1748	1	23	salesman	salesman	ADJ
cana-1748	1	24	problem	problem	NOUN
cana-1748	1	25	of	of	ADP
cana-1748	1	26	fuzzy	fuzzy	ADJ
cana-1748	1	27	hexagonal	hexagonal	ADJ
cana-1748	1	28	numbers	number	NOUN
cana-1748	1	29	using	use	VERB
cana-1748	1	30	ranking	ranking	NOUN
cana-1748	1	31	method	method	NOUN
cana-1748	1	32	and	and	CCONJ
cana-1748	1	33	dijkstra	dijkstra	PROPN
cana-1748	1	34	's	's	PART
cana-1748	1	35	algorithms	algorithm	NOUN
cana-1748	1	36	s.revathy	s.revathy	ADJ
cana-1748	1	37	𝟏	𝟏	NUM
cana-1748	1	38	,	,	PUNCT
cana-1748	1	39	m.pandikani	m.pandikani	X
cana-1748	1	40	𝟐,v.nirmala	𝟐,v.nirmala	ADJ
cana-1748	1	41	𝟑∗,p.megala	𝟑∗,p.megala	NOUN
cana-1748	1	42	𝟒,s.yamini	𝟒,s.yamini	PROPN
cana-1748	1	43	𝟓	𝟓	NUM
cana-1748	1	44	1	1	NUM
cana-1748	1	45	trinity	trinity	NOUN
cana-1748	1	46	college	college	NOUN
cana-1748	1	47	for	for	ADP
cana-1748	1	48	women	woman	NOUN
cana-1748	1	49	coimbatore	coimbatore	PROPN
cana-1748	1	50	,	,	PUNCT
cana-1748	1	51	periyar	periyar	PROPN
cana-1748	1	52	university	university	NOUN
cana-1748	1	53	,	,	PUNCT
cana-1748	1	54	namakkal	namakkal	NOUN
cana-1748	1	55	2	2	NUM
cana-1748	1	56	sri	sri	PROPN
cana-1748	1	57	sairam	sairam	PROPN
cana-1748	1	58	college	college	PROPN
cana-1748	1	59	of	of	ADP
cana-1748	1	60	engineering	engineering	PROPN
cana-1748	1	61	,	,	PUNCT
cana-1748	1	62	visvesvaraya	visvesvaraya	ADP
cana-1748	1	63	technological	technological	ADJ
cana-1748	1	64	university	university	NOUN
cana-1748	1	65	,	,	PUNCT
cana-1748	1	66	karnataka	karnataka	NOUN
cana-1748	1	67	-562106	-562106	PROPN
cana-1748	1	68	3	3	NUM
cana-1748	1	69	department	department	NOUN
cana-1748	1	70	of	of	ADP
cana-1748	1	71	mathematics	mathematic	NOUN
cana-1748	1	72	,	,	PUNCT
cana-1748	1	73	faculty	faculty	NOUN
cana-1748	1	74	of	of	ADP
cana-1748	1	75	engineering	engineering	PROPN
cana-1748	1	76	,	,	PUNCT
cana-1748	1	77	karpagam	karpagam	PROPN
cana-1748	1	78	academy	academy	PROPN
cana-1748	1	79	of	of	ADP
cana-1748	1	80	higher	high	ADJ
cana-1748	1	81	education	education	NOUN
cana-1748	1	82	,	,	PUNCT
cana-1748	1	83	coimbatore	coimbatore	PROPN
cana-1748	1	84	4	4	NUM
cana-1748	1	85	sri	sri	PROPN
cana-1748	1	86	eshwar	eshwar	PROPN
cana-1748	1	87	college	college	PROPN
cana-1748	1	88	of	of	ADP
cana-1748	1	89	engineering	engineering	PROPN
cana-1748	1	90	,	,	PUNCT
cana-1748	1	91	anna	anna	PROPN
cana-1748	1	92	university	university	PROPN
cana-1748	1	93	,	,	PUNCT
cana-1748	1	94	coimbatore	coimbatore	PROPN
cana-1748	1	95	.	.	PUNCT
cana-1748	1	96	5	5	NUM
cana-1748	1	97	karpagam	karpagam	PROPN
cana-1748	1	98	institute	institute	PROPN
cana-1748	1	99	of	of	ADP
cana-1748	1	100	technology	technology	PROPN
cana-1748	1	101	,	,	PUNCT
cana-1748	1	102	anna	anna	PROPN
cana-1748	1	103	university	university	PROPN
cana-1748	1	104	,	,	PUNCT
cana-1748	1	105	coimbatore	coimbatore	PROPN
cana-1748	1	106	.	.	PUNCT
cana-1748	2	1	*	*	PUNCT
cana-1748	2	2	corresponding	correspond	VERB
cana-1748	2	3	author	author	NOUN
cana-1748	2	4	,	,	PUNCT
cana-1748	2	5	e	e	NOUN
cana-1748	2	6	-	-	NOUN
cana-1748	2	7	mail	mail	NOUN
cana-1748	2	8	:	:	PUNCT
cana-1748	2	9	aaradhananirmala@gmail.com	aaradhananirmala@gmail.com	X
cana-1748	2	10	(	(	PUNCT
cana-1748	2	11	v.nirmala	v.nirmala	NOUN
cana-1748	2	12	)	)	PUNCT
cana-1748	2	13	article	article	NOUN
cana-1748	2	14	history	history	NOUN
cana-1748	2	15	:	:	PUNCT
cana-1748	2	16	received	receive	VERB
cana-1748	2	17	:	:	PUNCT
cana-1748	2	18	01	01	NUM
cana-1748	2	19	-	-	SYM
cana-1748	2	20	08	08	NUM
cana-1748	2	21	-	-	PUNCT
cana-1748	2	22	2024	2024	NUM
cana-1748	2	23	revised	revise	VERB
cana-1748	2	24	:	:	PUNCT
cana-1748	2	25	11	11	NUM
cana-1748	2	26	-	-	SYM
cana-1748	2	27	09	09	NUM
cana-1748	2	28	-	-	PUNCT
cana-1748	2	29	2024	2024	NUM
cana-1748	2	30	accepted	accept	VERB
cana-1748	2	31	:	:	PUNCT
cana-1748	2	32	20	20	NUM
cana-1748	2	33	-	-	SYM
cana-1748	2	34	09	09	NUM
cana-1748	2	35	-	-	PUNCT
cana-1748	2	36	2024	2024	NUM
cana-1748	2	37	abstract	abstract	NOUN
cana-1748	2	38	the	the	DET
cana-1748	2	39	aim	aim	NOUN
cana-1748	2	40	of	of	ADP
cana-1748	2	41	this	this	DET
cana-1748	2	42	article	article	NOUN
cana-1748	2	43	is	be	AUX
cana-1748	2	44	to	to	PART
cana-1748	2	45	find	find	VERB
cana-1748	2	46	the	the	DET
cana-1748	2	47	fuzzy	fuzzy	ADJ
cana-1748	2	48	shortest	short	ADJ
cana-1748	2	49	possible	possible	ADJ
cana-1748	2	50	distance	distance	NOUN
cana-1748	2	51	for	for	ADP
cana-1748	2	52	a	a	DET
cana-1748	2	53	fuzzy	fuzzy	ADJ
cana-1748	2	54	traveling	travel	VERB
cana-1748	2	55	salesman	salesman	ADJ
cana-1748	2	56	problem	problem	NOUN
cana-1748	2	57	of	of	ADP
cana-1748	2	58	hexagonal	hexagonal	ADJ
cana-1748	2	59	fuzzy	fuzzy	ADJ
cana-1748	2	60	numbers	number	NOUN
cana-1748	2	61	.	.	PUNCT
cana-1748	3	1	we	we	PRON
cana-1748	3	2	used	use	VERB
cana-1748	3	3	to	to	PART
cana-1748	3	4	formulate	formulate	VERB
cana-1748	3	5	the	the	DET
cana-1748	3	6	numerical	numerical	ADJ
cana-1748	3	7	example	example	NOUN
cana-1748	3	8	using	use	VERB
cana-1748	3	9	dijkstra	dijkstra	PROPN
cana-1748	3	10	's	's	PART
cana-1748	3	11	algorithm	algorithm	NOUN
cana-1748	3	12	.	.	PUNCT
cana-1748	4	1	introduction	introduction	NOUN
cana-1748	4	2	the	the	DET
cana-1748	4	3	traveling	travel	VERB
cana-1748	4	4	salesman	salesman	ADJ
cana-1748	4	5	problem	problem	NOUN
cana-1748	4	6	(	(	PUNCT
cana-1748	4	7	tsm	tsm	NOUN
cana-1748	4	8	)	)	PUNCT
cana-1748	4	9	involves	involve	VERB
cana-1748	4	10	finding	find	VERB
cana-1748	4	11	the	the	DET
cana-1748	4	12	shortest	short	ADJ
cana-1748	4	13	possible	possible	ADJ
cana-1748	4	14	route	route	NOUN
cana-1748	4	15	to	to	ADP
cana-1748	4	16	multiple	multiple	ADJ
cana-1748	4	17	destination	destination	NOUN
cana-1748	4	18	and	and	CCONJ
cana-1748	4	19	returning	return	VERB
cana-1748	4	20	to	to	ADP
cana-1748	4	21	the	the	DET
cana-1748	4	22	starting	starting	NOUN
cana-1748	4	23	point	point	NOUN
cana-1748	4	24	.	.	PUNCT
cana-1748	5	1	—	—	PUNCT
cana-1748	5	2	_	_	NOUN
cana-1748	5	3	there	there	ADV
cana-1748	5	4	we	we	PRON
cana-1748	5	5	several	several	ADJ
cana-1748	5	6	applications	application	NOUN
cana-1748	5	7	of	of	ADP
cana-1748	5	8	tsp	tsp	NOUN
cana-1748	5	9	,	,	PUNCT
cana-1748	5	10	such	such	ADJ
cana-1748	5	11	as	as	ADP
cana-1748	5	12	vehicle	vehicle	NOUN
cana-1748	5	13	routing	routing	NOUN
cana-1748	5	14	,	,	PUNCT
cana-1748	5	15	scheduling	scheduling	NOUN
cana-1748	5	16	.	.	PUNCT
cana-1748	6	1	the	the	DET
cana-1748	6	2	tsp	tsp	NOUN
cana-1748	6	3	in	in	ADP
cana-1748	6	4	a	a	DET
cana-1748	6	5	serious	serious	ADJ
cana-1748	6	6	challenge	challenge	NOUN
cana-1748	6	7	for	for	ADP
cana-1748	6	8	the	the	DET
cana-1748	6	9	logistics	logistic	NOUN
cana-1748	6	10	and	and	CCONJ
cana-1748	6	11	supply	supply	NOUN
cana-1748	6	12	chain	chain	NOUN
cana-1748	6	13	industry	industry	NOUN
cana-1748	6	14	because	because	SCONJ
cana-1748	6	15	of	of	ADP
cana-1748	6	16	involves	involve	NOUN
cana-1748	6	17	optimizing	optimize	VERB
cana-1748	6	18	the	the	DET
cana-1748	6	19	delivery	delivery	NOUN
cana-1748	6	20	router	router	NOUN
cana-1748	6	21	for	for	ADP
cana-1748	6	22	multiple	multiple	ADJ
cana-1748	6	23	destinations	destination	NOUN
cana-1748	6	24	while	while	SCONJ
cana-1748	6	25	considering	consider	VERB
cana-1748	6	26	various	various	ADJ
cana-1748	6	27	constraints	constraint	NOUN
cana-1748	6	28	such	such	ADJ
cana-1748	6	29	as	as	ADP
cana-1748	6	30	,	,	PUNCT
cana-1748	6	31	traffic	traffic	NOUN
cana-1748	6	32	,	,	PUNCT
cana-1748	6	33	delivery	delivery	NOUN
cana-1748	6	34	windows	window	NOUN
cana-1748	6	35	and	and	CCONJ
cana-1748	6	36	customer	customer	NOUN
cana-1748	6	37	request	request	NOUN
cana-1748	6	38	with	with	ADP
cana-1748	6	39	multiple	multiple	ADJ
cana-1748	6	40	vehicle	vehicle	NOUN
cana-1748	6	41	,	,	PUNCT
cana-1748	6	42	more	more	ADJ
cana-1748	6	43	cities	city	NOUN
cana-1748	6	44	and	and	CCONJ
cana-1748	6	45	multiple	multiple	ADJ
cana-1748	6	46	sales	sale	NOUN
cana-1748	6	47	professionals	professional	NOUN
cana-1748	6	48	,	,	PUNCT
cana-1748	6	49	tsp	tsp	NOUN
cana-1748	6	50	become	become	VERB
cana-1748	6	51	a	a	DET
cana-1748	6	52	more	more	ADV
cana-1748	6	53	challenging	challenging	ADJ
cana-1748	6	54	to	to	PART
cana-1748	6	55	solve	solve	VERB
cana-1748	6	56	.	.	PUNCT
cana-1748	7	1	in	in	ADP
cana-1748	7	2	this	this	DET
cana-1748	7	3	article	article	NOUN
cana-1748	7	4	we	we	PRON
cana-1748	7	5	proposed	propose	VERB
cana-1748	7	6	shorter	short	ADJ
cana-1748	7	7	possible	possible	ADJ
cana-1748	7	8	distance	distance	NOUN
cana-1748	7	9	route	route	NOUN
cana-1748	7	10	from	from	ADP
cana-1748	7	11	multiple	multiple	ADJ
cana-1748	7	12	destination	destination	NOUN
cana-1748	7	13	and	and	CCONJ
cana-1748	7	14	returning	return	VERB
cana-1748	7	15	to	to	ADP
cana-1748	7	16	the	the	DET
cana-1748	7	17	starting	starting	NOUN
cana-1748	7	18	point	point	NOUN
cana-1748	7	19	using	use	VERB
cana-1748	7	20	ranking	ranking	NOUN
cana-1748	7	21	method	method	NOUN
cana-1748	7	22	of	of	ADP
cana-1748	7	23	hexagonal	hexagonal	ADJ
cana-1748	7	24	fuzzy	fuzzy	ADJ
cana-1748	7	25	numbers	number	NOUN
cana-1748	7	26	.	.	PUNCT
cana-1748	8	1	conclusions	conclusion	NOUN
cana-1748	8	2	:	:	PUNCT
cana-1748	8	3	the	the	DET
cana-1748	8	4	ranking	rank	VERB
cana-1748	8	5	approach	approach	NOUN
cana-1748	8	6	is	be	AUX
cana-1748	8	7	used	use	VERB
cana-1748	8	8	in	in	ADP
cana-1748	8	9	this	this	DET
cana-1748	8	10	paper	paper	NOUN
cana-1748	8	11	to	to	PART
cana-1748	8	12	transform	transform	VERB
cana-1748	8	13	hexagonal	hexagonal	ADJ
cana-1748	8	14	fuzzy	fuzzy	ADJ
cana-1748	8	15	numbers	number	NOUN
cana-1748	8	16	into	into	ADP
cana-1748	8	17	expected	expect	VERB
cana-1748	8	18	time	time	NOUN
cana-1748	8	19	,	,	PUNCT
cana-1748	8	20	or	or	CCONJ
cana-1748	8	21	standard	standard	ADJ
cana-1748	8	22	time	time	NOUN
cana-1748	8	23	,	,	PUNCT
cana-1748	8	24	for	for	ADP
cana-1748	8	25	each	each	DET
cana-1748	8	26	activity	activity	NOUN
cana-1748	8	27	.	.	PUNCT
cana-1748	9	1	thus	thus	ADV
cana-1748	9	2	,	,	PUNCT
cana-1748	9	3	using	use	VERB
cana-1748	9	4	the	the	DET
cana-1748	9	5	dijkstra	dijkstra	ADJ
cana-1748	9	6	algorithm	algorithm	NOUN
cana-1748	9	7	,	,	PUNCT
cana-1748	9	8	the	the	DET
cana-1748	9	9	fuzzy	fuzzy	ADJ
cana-1748	9	10	shortest	short	ADJ
cana-1748	9	11	path	path	NOUN
cana-1748	9	12	is	be	AUX
cana-1748	9	13	found	find	VERB
cana-1748	9	14	.	.	PUNCT
cana-1748	10	1	it	it	PRON
cana-1748	10	2	assists	assist	VERB
cana-1748	10	3	decision	decision	NOUN
cana-1748	10	4	makers	maker	NOUN
cana-1748	10	5	in	in	ADP
cana-1748	10	6	selecting	select	VERB
cana-1748	10	7	the	the	DET
cana-1748	10	8	optimal	optimal	ADJ
cana-1748	10	9	,	,	PUNCT
cana-1748	10	10	shortest	short	ADJ
cana-1748	10	11	path	path	NOUN
cana-1748	10	12	in	in	ADP
cana-1748	10	13	a	a	DET
cana-1748	10	14	fuzzy	fuzzy	ADJ
cana-1748	10	15	environment	environment	NOUN
cana-1748	10	16	by	by	ADP
cana-1748	10	17	applying	apply	VERB
cana-1748	10	18	the	the	DET
cana-1748	10	19	ranking	ranking	ADJ
cana-1748	10	20	algorithm	algorithm	NOUN
cana-1748	10	21	.	.	PUNCT
cana-1748	11	1	keywords	keyword	NOUN
cana-1748	11	2	:	:	PUNCT
cana-1748	11	3	fuzzy	fuzzy	ADJ
cana-1748	11	4	number	number	NOUN
cana-1748	11	5	,	,	PUNCT
cana-1748	11	6	hexagonal	hexagonal	ADJ
cana-1748	11	7	fuzzy	fuzzy	ADJ
cana-1748	11	8	number	number	NOUN
cana-1748	11	9	,	,	PUNCT
cana-1748	11	10	dijkstra	dijkstra	PROPN
cana-1748	11	11	's	's	PART
cana-1748	11	12	algorithm	algorithm	NOUN
cana-1748	11	13	ranking	ranking	NOUN
cana-1748	11	14	algorithm	algorithm	NOUN
cana-1748	11	15	,	,	PUNCT
cana-1748	11	16	sales	sale	NOUN
cana-1748	11	17	man	man	NOUN
cana-1748	11	18	.	.	PUNCT
cana-1748	12	1	1	1	X
cana-1748	12	2	.	.	X
cana-1748	12	3	introduction	introduction	NOUN
cana-1748	12	4	the	the	DET
cana-1748	12	5	traveling	travel	VERB
cana-1748	12	6	salesman	salesman	ADJ
cana-1748	12	7	problem	problem	NOUN
cana-1748	12	8	(	(	PUNCT
cana-1748	12	9	tsm	tsm	NOUN
cana-1748	12	10	)	)	PUNCT
cana-1748	12	11	involves	involve	VERB
cana-1748	12	12	finding	find	VERB
cana-1748	12	13	the	the	DET
cana-1748	12	14	shortest	short	ADJ
cana-1748	12	15	possible	possible	ADJ
cana-1748	12	16	route	route	NOUN
cana-1748	12	17	to	to	ADP
cana-1748	12	18	multiple	multiple	ADJ
cana-1748	12	19	destination	destination	NOUN
cana-1748	12	20	and	and	CCONJ
cana-1748	12	21	returning	return	VERB
cana-1748	12	22	to	to	ADP
cana-1748	12	23	the	the	DET
cana-1748	12	24	starting	starting	NOUN
cana-1748	12	25	point	point	NOUN
cana-1748	12	26	.	.	PUNCT
cana-1748	13	1	—	—	PUNCT
cana-1748	13	2	_	_	NOUN
cana-1748	13	3	there	there	ADV
cana-1748	13	4	we	we	PRON
cana-1748	13	5	several	several	ADJ
cana-1748	13	6	applications	application	NOUN
cana-1748	13	7	of	of	ADP
cana-1748	13	8	tsp	tsp	NOUN
cana-1748	13	9	,	,	PUNCT
cana-1748	13	10	such	such	ADJ
cana-1748	13	11	as	as	ADP
cana-1748	13	12	vehicle	vehicle	NOUN
cana-1748	13	13	routing	routing	NOUN
cana-1748	13	14	,	,	PUNCT
cana-1748	13	15	scheduling	scheduling	NOUN
cana-1748	13	16	.	.	PUNCT
cana-1748	14	1	the	the	DET
cana-1748	14	2	tsp	tsp	NOUN
cana-1748	14	3	in	in	ADP
cana-1748	14	4	a	a	DET
cana-1748	14	5	serious	serious	ADJ
cana-1748	14	6	challenge	challenge	NOUN
cana-1748	14	7	for	for	ADP
cana-1748	14	8	the	the	DET
cana-1748	14	9	logistics	logistic	NOUN
cana-1748	14	10	and	and	CCONJ
cana-1748	14	11	supply	supply	NOUN
cana-1748	14	12	chain	chain	NOUN
cana-1748	14	13	industry	industry	NOUN
cana-1748	14	14	because	because	SCONJ
cana-1748	14	15	of	of	ADP
cana-1748	14	16	involves	involve	NOUN
cana-1748	14	17	optimizing	optimize	VERB
cana-1748	14	18	the	the	DET
cana-1748	14	19	delivery	delivery	NOUN
cana-1748	14	20	router	router	NOUN
cana-1748	14	21	for	for	ADP
cana-1748	14	22	multiple	multiple	ADJ
cana-1748	14	23	destinations	destination	NOUN
cana-1748	14	24	while	while	SCONJ
cana-1748	14	25	considering	consider	VERB
cana-1748	14	26	various	various	ADJ
cana-1748	14	27	constraints	constraint	NOUN
cana-1748	14	28	such	such	ADJ
cana-1748	14	29	as	as	ADP
cana-1748	14	30	,	,	PUNCT
cana-1748	14	31	traffic	traffic	NOUN
cana-1748	14	32	,	,	PUNCT
cana-1748	14	33	delivery	delivery	NOUN
cana-1748	14	34	windows	window	NOUN
cana-1748	14	35	and	and	CCONJ
cana-1748	14	36	customer	customer	NOUN
cana-1748	14	37	request.with	request.with	ADP
cana-1748	14	38	multiple	multiple	ADJ
cana-1748	14	39	vehicle	vehicle	NOUN
cana-1748	14	40	,	,	PUNCT
cana-1748	14	41	more	more	ADJ
cana-1748	14	42	cities	city	NOUN
cana-1748	14	43	and	and	CCONJ
cana-1748	14	44	multiple	multiple	ADJ
cana-1748	14	45	sales	sale	NOUN
cana-1748	14	46	professionals	professional	NOUN
cana-1748	14	47	,	,	PUNCT
cana-1748	14	48	tsp	tsp	NOUN
cana-1748	14	49	become	become	VERB
cana-1748	14	50	a	a	DET
cana-1748	14	51	more	more	ADV
cana-1748	14	52	challenging	challenging	ADJ
cana-1748	14	53	to	to	PART
cana-1748	14	54	solve	solve	VERB
cana-1748	14	55	.	.	PUNCT
cana-1748	15	1	in	in	ADP
cana-1748	15	2	this	this	DET
cana-1748	15	3	article	article	NOUN
cana-1748	15	4	we	we	PRON
cana-1748	15	5	proposed	propose	VERB
cana-1748	15	6	shorter	short	ADJ
cana-1748	15	7	possible	possible	ADJ
cana-1748	15	8	distance	distance	NOUN
cana-1748	15	9	route	route	NOUN
cana-1748	15	10	from	from	ADP
cana-1748	15	11	multiple	multiple	ADJ
cana-1748	15	12	destination	destination	NOUN
cana-1748	15	13	and	and	CCONJ
cana-1748	15	14	returning	return	VERB
cana-1748	15	15	to	to	ADP
cana-1748	15	16	the	the	DET
cana-1748	15	17	starting	starting	NOUN
cana-1748	15	18	point	point	NOUN
cana-1748	15	19	using	use	VERB
cana-1748	15	20	ranking	ranking	NOUN
cana-1748	15	21	method	method	NOUN
cana-1748	15	22	of	of	ADP
cana-1748	15	23	hexagonal	hexagonal	ADJ
cana-1748	15	24	fuzzy	fuzzy	ADJ
cana-1748	15	25	numbers	number	NOUN
cana-1748	15	26	.	.	PUNCT
cana-1748	16	1	mailto:aaradhananirmala@gmail.com	mailto:aaradhananirmala@gmail.com	PROPN
cana-1748	16	2	communications	communication	NOUN
cana-1748	16	3	on	on	ADP
cana-1748	16	4	applied	apply	VERB
cana-1748	16	5	nonlinear	nonlinear	ADJ
cana-1748	16	6	analysis	analysis	NOUN
cana-1748	16	7	issn	issn	NOUN
cana-1748	16	8	:	:	PUNCT
cana-1748	16	9	1074	1074	NUM
cana-1748	16	10	-	-	PUNCT
cana-1748	16	11	133x	133x	NUM
cana-1748	16	12	vol	vol	NOUN
cana-1748	16	13	32	32	NUM
cana-1748	16	14	no	no	NOUN
cana-1748	16	15	.	.	NOUN
cana-1748	16	16	2	2	NUM
cana-1748	16	17	(	(	PUNCT
cana-1748	16	18	2025	2025	NUM
cana-1748	16	19	)	)	PUNCT
cana-1748	16	20	368	368	NUM
cana-1748	16	21	https://internationalpubls.com	https://internationalpubls.com	SYM
cana-1748	16	22	2	2	NUM
cana-1748	16	23	preliminaries	preliminary	NOUN
cana-1748	16	24	2.1	2.1	NUM
cana-1748	16	25	definition	definition	NOUN
cana-1748	16	26	let	let	VERB
cana-1748	16	27	the	the	DET
cana-1748	16	28	universe	universe	NOUN
cana-1748	16	29	be	be	AUX
cana-1748	16	30	𝑈.	𝑈.	ADJ
cana-1748	16	31	the	the	DET
cana-1748	16	32	definition	definition	NOUN
cana-1748	16	33	of	of	ADP
cana-1748	16	34	the	the	DET
cana-1748	16	35	fuzzy	fuzzy	ADJ
cana-1748	16	36	seti	seti	NOUN
cana-1748	16	37	on	on	ADP
cana-1748	16	38	𝑈	𝑈	PROPN
cana-1748	16	39	is	be	AUX
cana-1748	16	40	as	as	SCONJ
cana-1748	16	41	follows	follow	VERB
cana-1748	16	42	,	,	PUNCT
cana-1748	16	43	i	i	PRON
cana-1748	16	44	=	=	PUNCT
cana-1748	16	45	{	{	PUNCT
cana-1748	16	46	𝑥	𝑥	NOUN
cana-1748	16	47	,	,	PUNCT
cana-1748	16	48	𝜒a(𝑥	𝜒a(𝑥	NUM
cana-1748	16	49	)	)	PUNCT
cana-1748	16	50	,	,	PUNCT
cana-1748	16	51	𝑥	𝑥	PROPN
cana-1748	16	52	∈	∈	PROPN
cana-1748	16	53	u	u	NOUN
cana-1748	16	54	}	}	PUNCT
cana-1748	16	55	in	in	ADP
cana-1748	16	56	which	which	PRON
cana-1748	16	57	𝜒a(𝑥	𝜒a(𝑥	NUM
cana-1748	16	58	):	):	PUNCT
cana-1748	16	59	u	u	NOUN
cana-1748	16	60	→	→	SYM
cana-1748	16	61	[	[	X
cana-1748	16	62	0,1	0,1	NUM
cana-1748	16	63	]	]	PUNCT
cana-1748	16	64	is	be	AUX
cana-1748	16	65	called	call	VERB
cana-1748	16	66	membership	membership	NOUN
cana-1748	16	67	2.2	2.2	NUM
cana-1748	16	68	definition	definition	NOUN
cana-1748	16	69	if	if	SCONJ
cana-1748	16	70	there	there	PRON
cana-1748	16	71	is	be	VERB
cana-1748	16	72	an	an	DET
cana-1748	16	73	element	element	NOUN
cana-1748	16	74	𝑥	𝑥	PRON
cana-1748	16	75	∈	∈	NOUN
cana-1748	16	76	u	u	NOUN
cana-1748	16	77	whose	whose	DET
cana-1748	16	78	membership	membership	NOUN
cana-1748	16	79	value	value	NOUN
cana-1748	16	80	is	be	AUX
cana-1748	16	81	one	one	NUM
cana-1748	16	82	,	,	PUNCT
cana-1748	16	83	that	that	ADV
cana-1748	16	84	is	be	AUX
cana-1748	16	85	𝜒i(𝑥	𝜒i(𝑥	NOUN
cana-1748	16	86	)	)	PUNCT
cana-1748	17	1	=	=	SYM
cana-1748	17	2	1	1	X
cana-1748	17	3	.	.	PUNCT
cana-1748	17	4	then	then	ADV
cana-1748	17	5	a	a	DET
cana-1748	17	6	fuzzy	fuzzy	ADJ
cana-1748	17	7	set	set	NOUN
cana-1748	17	8	i	i	PRON
cana-1748	17	9	is	be	AUX
cana-1748	17	10	normal	normal	ADJ
cana-1748	17	11	.	.	PUNCT
cana-1748	18	1	2.3	2.3	NUM
cana-1748	18	2	definition	definition	NOUN
cana-1748	18	3	fuzzy	fuzzy	ADJ
cana-1748	18	4	number	number	NOUN
cana-1748	18	5	is	be	AUX
cana-1748	18	6	defined	define	VERB
cana-1748	18	7	as	as	ADP
cana-1748	18	8	fuzzy	fuzzy	ADJ
cana-1748	18	9	set	set	NOUN
cana-1748	18	10	i	i	PRON
cana-1748	18	11	of	of	ADP
cana-1748	18	12	real	real	ADJ
cana-1748	18	13	line	line	NOUN
cana-1748	18	14	r	r	NOUN
cana-1748	18	15	with	with	ADP
cana-1748	18	16	membership	membership	NOUN
cana-1748	18	17	function	function	NOUN
cana-1748	18	18	𝜒i(𝑥	𝜒i(𝑥	NOUN
cana-1748	18	19	):	):	PUNCT
cana-1748	19	1	r	r	NOUN
cana-1748	19	2	→	→	SYM
cana-1748	19	3	[	[	X
cana-1748	19	4	0,1	0,1	NUM
cana-1748	19	5	]	]	X
cana-1748	19	6	if	if	SCONJ
cana-1748	19	7	(	(	PUNCT
cana-1748	19	8	i	i	NOUN
cana-1748	19	9	)	)	PUNCT
cana-1748	20	1	i	i	PRON
cana-1748	20	2	is	be	AUX
cana-1748	20	3	normal	normal	ADJ
cana-1748	20	4	and	and	CCONJ
cana-1748	20	5	convexity	convexity	NOUN
cana-1748	20	6	(	(	PUNCT
cana-1748	20	7	ii	ii	NOUN
cana-1748	20	8	)	)	PUNCT
cana-1748	20	9	i	i	PRON
cana-1748	20	10	must	must	AUX
cana-1748	20	11	be	be	AUX
cana-1748	20	12	bounded	bound	VERB
cana-1748	20	13	(	(	PUNCT
cana-1748	20	14	iii	iii	X
cana-1748	20	15	)	)	PUNCT
cana-1748	20	16	𝛼i	𝛼i	PRON
cana-1748	20	17	must	must	AUX
cana-1748	20	18	be	be	AUX
cana-1748	20	19	closed	close	VERB
cana-1748	20	20	interval	interval	NOUN
cana-1748	20	21	for	for	ADP
cana-1748	20	22	every	every	DET
cana-1748	20	23	𝛼	𝛼	PROPN
cana-1748	20	24	∈	∈	NOUN
cana-1748	20	25	[	[	X
cana-1748	20	26	0,1	0,1	NUM
cana-1748	20	27	]	]	SYM
cana-1748	20	28	2.4	2.4	NUM
cana-1748	20	29	definition	definition	NOUN
cana-1748	20	30	a	a	DET
cana-1748	20	31	fuzzy	fuzzy	ADJ
cana-1748	20	32	number	number	NOUN
cana-1748	20	33	i𝐻	i𝐻	NOUN
cana-1748	20	34	is	be	AUX
cana-1748	20	35	an	an	DET
cana-1748	20	36	hfn	hfn	NOUN
cana-1748	20	37	and	and	CCONJ
cana-1748	20	38	is	be	AUX
cana-1748	20	39	represented	represent	VERB
cana-1748	20	40	as	as	ADP
cana-1748	20	41	i𝐻	i𝐻	X
cana-1748	20	42	=	=	SYM
cana-1748	20	43	(	(	PUNCT
cana-1748	20	44	𝑛1	𝑛1	NOUN
cana-1748	20	45	,	,	PUNCT
cana-1748	20	46	𝑛2	𝑛2	NOUN
cana-1748	20	47	,	,	PUNCT
cana-1748	20	48	𝑛3	𝑛3	NOUN
cana-1748	20	49	,	,	PUNCT
cana-1748	20	50	𝑛4	𝑛4	NOUN
cana-1748	20	51	,	,	PUNCT
cana-1748	20	52	𝑛5	𝑛5	PROPN
cana-1748	20	53	,	,	PUNCT
cana-1748	20	54	𝑛6	𝑛6	PROPN
cana-1748	20	55	)	)	PUNCT
cana-1748	20	56	.	.	PUNCT
cana-1748	21	1	in	in	ADP
cana-1748	21	2	which	which	PRON
cana-1748	21	3	real	real	ADJ
cana-1748	21	4	numbers	number	NOUN
cana-1748	21	5	(	(	PUNCT
cana-1748	21	6	𝑛1	𝑛1	NOUN
cana-1748	21	7	,	,	PUNCT
cana-1748	21	8	𝑛2	𝑛2	NOUN
cana-1748	21	9	,	,	PUNCT
cana-1748	21	10	𝑛3	𝑛3	NOUN
cana-1748	21	11	,	,	PUNCT
cana-1748	21	12	𝑛4	𝑛4	NOUN
cana-1748	21	13	,	,	PUNCT
cana-1748	21	14	𝑛5	𝑛5	PROPN
cana-1748	21	15	,	,	PUNCT
cana-1748	21	16	and	and	CCONJ
cana-1748	21	17	𝑛6	𝑛6	PROPN
cana-1748	21	18	)	)	PUNCT
cana-1748	21	19	are	be	AUX
cana-1748	21	20	found	find	VERB
cana-1748	21	21	.	.	PUNCT
cana-1748	22	1	the	the	DET
cana-1748	22	2	function	function	NOUN
cana-1748	22	3	its	its	PRON
cana-1748	22	4	membership	membership	NOUN
cana-1748	22	5	is	be	AUX
cana-1748	22	6	listed	list	VERB
cana-1748	22	7	below	below	ADP
cana-1748	22	8	f(x	f(x	PROPN
cana-1748	22	9	)	)	PUNCT
cana-1748	23	1	=	=	PRON
cana-1748	23	2	{	{	PUNCT
cana-1748	23	3	0.5	0.5	NUM
cana-1748	23	4	[	[	PUNCT
cana-1748	23	5	𝑥	𝑥	X
cana-1748	23	6	−	−	X
cana-1748	23	7	𝑛1	𝑛1	ADJ
cana-1748	23	8	𝑛3	𝑛3	NOUN
cana-1748	23	9	−	−	PROPN
cana-1748	23	10	𝑛1	𝑛1	NOUN
cana-1748	23	11	]	]	PUNCT
cana-1748	23	12	for	for	ADP
cana-1748	23	13	𝑛1	𝑛1	ADJ
cana-1748	23	14	≤	≤	NUM
cana-1748	23	15	𝑥	𝑥	PRON
cana-1748	23	16	≤	≤	NUM
cana-1748	23	17	𝑛2	𝑛2	NOUN
cana-1748	23	18	0.5	0.5	NUM
cana-1748	23	19	+	+	NUM
cana-1748	23	20	0.5	0.5	NUM
cana-1748	23	21	[	[	PUNCT
cana-1748	23	22	𝑥	𝑥	NOUN
cana-1748	23	23	−	−	PROPN
cana-1748	23	24	𝑛2	𝑛2	NOUN
cana-1748	23	25	𝑛3	𝑛3	NOUN
cana-1748	23	26	−	−	PROPN
cana-1748	23	27	𝑛2	𝑛2	NOUN
cana-1748	23	28	]	]	PUNCT
cana-1748	23	29	for	for	ADP
cana-1748	23	30	𝑛2	𝑛2	NOUN
cana-1748	23	31	≤	≤	NOUN
cana-1748	23	32	𝑥	𝑥	DET
cana-1748	23	33	≤	≤	NUM
cana-1748	23	34	𝑛3	𝑛3	NOUN
cana-1748	23	35	1	1	NUM
cana-1748	23	36	for	for	ADP
cana-1748	23	37	𝑛3	𝑛3	NOUN
cana-1748	23	38	≤	≤	NUM
cana-1748	23	39	𝑥	𝑥	DET
cana-1748	23	40	≤	≤	NUM
cana-1748	23	41	𝑛4	𝑛4	NOUN
cana-1748	23	42	1	1	NUM
cana-1748	23	43	−	−	NOUN
cana-1748	23	44	0.5	0.5	NUM
cana-1748	23	45	[	[	PUNCT
cana-1748	23	46	𝑥	𝑥	PRON
cana-1748	23	47	−	−	PROPN
cana-1748	23	48	𝑛4	𝑛4	NOUN
cana-1748	23	49	𝑛5	𝑛5	NOUN
cana-1748	23	50	−	−	PROPN
cana-1748	23	51	𝑛4	𝑛4	NOUN
cana-1748	23	52	]	]	PUNCT
cana-1748	23	53	for	for	ADP
cana-1748	23	54	𝑛4	𝑛4	NOUN
cana-1748	23	55	≤	≤	NUM
cana-1748	23	56	𝑥	𝑥	PRON
cana-1748	23	57	≤	≤	NUM
cana-1748	23	58	𝑛5	𝑛5	NOUN
cana-1748	23	59	0.5	0.5	NUM
cana-1748	23	60	[	[	PUNCT
cana-1748	23	61	𝑛6	𝑛6	PROPN
cana-1748	23	62	−	−	PROPN
cana-1748	23	63	𝑥	𝑥	PROPN
cana-1748	23	64	𝑛6	𝑛6	PROPN
cana-1748	23	65	−	−	PROPN
cana-1748	23	66	𝑛5	𝑛5	PROPN
cana-1748	23	67	]	]	PUNCT
cana-1748	23	68	for	for	ADP
cana-1748	23	69	𝑛5	𝑛5	PROPN
cana-1748	23	70	≤	≤	NUM
cana-1748	23	71	𝑥	𝑥	DET
cana-1748	23	72	≤	≤	NUM
cana-1748	23	73	𝑛6	𝑛6	PROPN
cana-1748	23	74	3	3	NUM
cana-1748	23	75	operation	operation	NOUN
cana-1748	23	76	of	of	ADP
cana-1748	23	77	hexagonal	hexagonal	ADJ
cana-1748	23	78	fuzzy	fuzzy	ADJ
cana-1748	23	79	number	number	NOUN
cana-1748	23	80	assuming	assume	VERB
cana-1748	23	81	that	that	SCONJ
cana-1748	23	82	s𝐻	s𝐻	PROPN
cana-1748	23	83	=	=	SYM
cana-1748	23	84	(	(	PUNCT
cana-1748	23	85	𝑔1	𝑔1	PROPN
cana-1748	23	86	,	,	PUNCT
cana-1748	23	87	𝑔2	𝑔2	NOUN
cana-1748	23	88	,	,	PUNCT
cana-1748	23	89	𝑔3	𝑔3	ADJ
cana-1748	23	90	,	,	PUNCT
cana-1748	23	91	𝑔4	𝑔4	PROPN
cana-1748	23	92	,	,	PUNCT
cana-1748	23	93	𝑔5	𝑔5	NOUN
cana-1748	23	94	,	,	PUNCT
cana-1748	23	95	𝑔6	𝑔6	NOUN
cana-1748	23	96	)	)	PUNCT
cana-1748	23	97	and	and	CCONJ
cana-1748	23	98	t𝐻	t𝐻	NOUN
cana-1748	23	99	=	=	SYM
cana-1748	23	100	(	(	PUNCT
cana-1748	23	101	ℎ1	ℎ1	PROPN
cana-1748	23	102	,	,	PUNCT
cana-1748	23	103	ℎ2	ℎ2	NOUN
cana-1748	23	104	,	,	PUNCT
cana-1748	23	105	ℎ3	ℎ3	NOUN
cana-1748	23	106	,	,	PUNCT
cana-1748	23	107	ℎ4	ℎ4	PROPN
cana-1748	23	108	,	,	PUNCT
cana-1748	23	109	ℎ5	ℎ5	PROPN
cana-1748	23	110	,	,	PUNCT
cana-1748	23	111	ℎ6	ℎ6	ADJ
cana-1748	23	112	)	)	PUNCT
cana-1748	23	113	.	.	PUNCT
cana-1748	24	1	are	be	AUX
cana-1748	24	2	two	two	NUM
cana-1748	24	3	hexagonal	hexagonal	ADJ
cana-1748	24	4	fuzzy	fuzzy	ADJ
cana-1748	24	5	numbers	number	NOUN
cana-1748	24	6	,	,	PUNCT
cana-1748	24	7	the	the	DET
cana-1748	24	8	three	three	NUM
cana-1748	24	9	operations	operation	NOUN
cana-1748	24	10	that	that	PRON
cana-1748	24	11	can	can	AUX
cana-1748	24	12	be	be	AUX
cana-1748	24	13	carried	carry	VERB
cana-1748	24	14	out	out	ADP
cana-1748	24	15	on	on	ADP
cana-1748	24	16	them	they	PRON
cana-1748	24	17	are	be	AUX
cana-1748	24	18	as	as	SCONJ
cana-1748	24	19	follows	follow	NOUN
cana-1748	24	20	,	,	PUNCT
cana-1748	24	21	1	1	X
cana-1748	24	22	.	.	PUNCT
cana-1748	25	1	addition	addition	NOUN
cana-1748	25	2	:	:	PUNCT
cana-1748	26	1	s𝛼	s𝛼	X
cana-1748	26	2	+	+	CCONJ
cana-1748	26	3	t𝛼	t𝛼	NOUN
cana-1748	26	4	=	=	SYM
cana-1748	26	5	(	(	PUNCT
cana-1748	26	6	𝑔1	𝑔1	PROPN
cana-1748	26	7	+	+	CCONJ
cana-1748	26	8	ℎ1	ℎ1	PROPN
cana-1748	26	9	,	,	PUNCT
cana-1748	26	10	𝑔2	𝑔2	VERB
cana-1748	26	11	+	+	CCONJ
cana-1748	26	12	ℎ2	ℎ2	NOUN
cana-1748	26	13	,	,	PUNCT
cana-1748	26	14	𝑔3	𝑔3	ADJ
cana-1748	26	15	+	+	CCONJ
cana-1748	26	16	ℎ3	ℎ3	NOUN
cana-1748	26	17	,	,	PUNCT
cana-1748	26	18	𝑔4	𝑔4	NOUN
cana-1748	26	19	+	+	CCONJ
cana-1748	26	20	ℎ4	ℎ4	PROPN
cana-1748	26	21	,	,	PUNCT
cana-1748	26	22	𝑔5	𝑔5	PROPN
cana-1748	26	23	+	+	CCONJ
cana-1748	26	24	ℎ5	ℎ5	PROPN
cana-1748	26	25	,	,	PUNCT
cana-1748	26	26	𝑔6	𝑔6	NOUN
cana-1748	26	27	+	+	CCONJ
cana-1748	26	28	ℎ6	ℎ6	ADJ
cana-1748	26	29	)	)	PUNCT
cana-1748	26	30	2	2	NUM
cana-1748	26	31	.	.	X
cana-1748	26	32	subtraction	subtraction	NOUN
cana-1748	26	33	:	:	PUNCT
cana-1748	26	34	s𝛼	s𝛼	NOUN
cana-1748	26	35	−	−	NOUN
cana-1748	26	36	t𝛼	t𝛼	NOUN
cana-1748	26	37	=	=	SYM
cana-1748	26	38	(	(	PUNCT
cana-1748	26	39	𝑔1	𝑔1	PROPN
cana-1748	26	40	−	−	PROPN
cana-1748	26	41	ℎ1	ℎ1	PROPN
cana-1748	26	42	,	,	PUNCT
cana-1748	26	43	𝑔2	𝑔2	VERB
cana-1748	26	44	−	−	NOUN
cana-1748	26	45	ℎ2	ℎ2	NOUN
cana-1748	26	46	,	,	PUNCT
cana-1748	26	47	𝑔3	𝑔3	ADJ
cana-1748	26	48	−	−	PROPN
cana-1748	26	49	ℎ3	ℎ3	NOUN
cana-1748	26	50	,	,	PUNCT
cana-1748	26	51	𝑔4	𝑔4	NOUN
cana-1748	26	52	−	−	PROPN
cana-1748	26	53	ℎ4	ℎ4	PROPN
cana-1748	26	54	,	,	PUNCT
cana-1748	26	55	𝑔5	𝑔5	PROPN
cana-1748	26	56	−	−	PROPN
cana-1748	26	57	ℎ5	ℎ5	PROPN
cana-1748	26	58	,	,	PUNCT
cana-1748	26	59	𝑔6	𝑔6	NOUN
cana-1748	26	60	−	−	PROPN
cana-1748	26	61	ℎ6	ℎ6	ADJ
cana-1748	26	62	)	)	PUNCT
cana-1748	26	63	3	3	NUM
cana-1748	26	64	.	.	X
cana-1748	26	65	multiplication	multiplication	NOUN
cana-1748	26	66	:	:	PUNCT
cana-1748	26	67	s𝛼	s𝛼	NOUN
cana-1748	26	68	∗	∗	NOUN
cana-1748	26	69	t𝛼	t𝛼	NOUN
cana-1748	26	70	=	=	SYM
cana-1748	26	71	(	(	PUNCT
cana-1748	26	72	𝑔1	𝑔1	PROPN
cana-1748	26	73	∗	∗	VERB
cana-1748	26	74	ℎ1	ℎ1	PROPN
cana-1748	26	75	,	,	PUNCT
cana-1748	26	76	𝑔2	𝑔2	VERB
cana-1748	26	77	∗	∗	NOUN
cana-1748	26	78	ℎ2	ℎ2	NOUN
cana-1748	26	79	,	,	PUNCT
cana-1748	26	80	𝑔3	𝑔3	ADJ
cana-1748	26	81	∗	∗	NOUN
cana-1748	26	82	ℎ3	ℎ3	NOUN
cana-1748	26	83	,	,	PUNCT
cana-1748	26	84	𝑔4	𝑔4	NOUN
cana-1748	26	85	∗	∗	NOUN
cana-1748	26	86	ℎ4	ℎ4	PROPN
cana-1748	26	87	,	,	PUNCT
cana-1748	26	88	𝑔5	𝑔5	PROPN
cana-1748	26	89	∗	∗	PROPN
cana-1748	26	90	ℎ5	ℎ5	PROPN
cana-1748	26	91	,	,	PUNCT
cana-1748	26	92	𝑔6	𝑔6	NOUN
cana-1748	26	93	∗	∗	NOUN
cana-1748	26	94	ℎ6	ℎ6	PROPN
cana-1748	26	95	)	)	PUNCT
cana-1748	26	96	3.1𝛼-cut	3.1𝛼-cut	NUM
cana-1748	26	97	of	of	ADP
cana-1748	26	98	hexagonal	hexagonal	ADJ
cana-1748	26	99	fuzzy	fuzzy	ADJ
cana-1748	26	100	number	number	NOUN
cana-1748	26	101	the	the	DET
cana-1748	26	102	𝛼-cut	𝛼-cut	NOUN
cana-1748	26	103	of	of	ADP
cana-1748	26	104	normal	normal	ADJ
cana-1748	26	105	hexagonal	hexagonal	ADJ
cana-1748	26	106	fuzzy	fuzzy	ADJ
cana-1748	26	107	number	number	NOUN
cana-1748	26	108	s𝐻	s𝐻	NOUN
cana-1748	26	109	=	=	SYM
cana-1748	26	110	(	(	PUNCT
cana-1748	26	111	𝑔1	𝑔1	PROPN
cana-1748	26	112	,	,	PUNCT
cana-1748	26	113	𝑔2	𝑔2	NOUN
cana-1748	26	114	,	,	PUNCT
cana-1748	26	115	𝑔3	𝑔3	ADJ
cana-1748	26	116	,	,	PUNCT
cana-1748	26	117	𝑔4	𝑔4	PROPN
cana-1748	26	118	,	,	PUNCT
cana-1748	26	119	𝑔5	𝑔5	PROPN
cana-1748	26	120	,	,	PUNCT
cana-1748	26	121	𝑔6	𝑔6	NOUN
cana-1748	26	122	)	)	PUNCT
cana-1748	26	123	given	give	VERB
cana-1748	26	124	by	by	ADP
cana-1748	26	125	the	the	DET
cana-1748	26	126	definition	definition	NOUN
cana-1748	26	127	(	(	PUNCT
cana-1748	26	128	2.2	2.2	NUM
cana-1748	26	129	)	)	PUNCT
cana-1748	26	130	.	.	PUNCT
cana-1748	27	1	therefore	therefore	ADV
cana-1748	27	2	𝜒i(𝑥	𝜒i(𝑥	NOUN
cana-1748	27	3	)	)	PUNCT
cana-1748	27	4	=	=	SYM
cana-1748	27	5	1	1	NUM
cana-1748	27	6	for	for	ADP
cana-1748	27	7	all	all	DET
cana-1748	27	8	𝛼	𝛼	PRON
cana-1748	27	9	∈	∈	NOUN
cana-1748	27	10	[	[	X
cana-1748	27	11	0,1	0,1	NUM
cana-1748	27	12	]	]	X
cana-1748	27	13	communications	communication	NOUN
cana-1748	27	14	on	on	ADP
cana-1748	27	15	applied	apply	VERB
cana-1748	27	16	nonlinear	nonlinear	ADJ
cana-1748	27	17	analysis	analysis	NOUN
cana-1748	27	18	issn	issn	NOUN
cana-1748	27	19	:	:	PUNCT
cana-1748	27	20	1074	1074	NUM
cana-1748	27	21	-	-	PUNCT
cana-1748	27	22	133x	133x	NUM
cana-1748	27	23	vol	vol	NOUN
cana-1748	27	24	32	32	NUM
cana-1748	27	25	no	no	NOUN
cana-1748	27	26	.	.	NOUN
cana-1748	27	27	2	2	NUM
cana-1748	27	28	(	(	PUNCT
cana-1748	27	29	2025	2025	NUM
cana-1748	27	30	)	)	PUNCT
cana-1748	27	31	369	369	NUM
cana-1748	28	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-1748	28	2	s𝐻	s𝐻	ADJ
cana-1748	28	3	=	=	PUNCT
cana-1748	28	4	{	{	PUNCT
cana-1748	28	5	[	[	X
cana-1748	28	6	2𝛼(𝑔3	2𝛼(𝑔3	NUM
cana-1748	28	7	−	−	PROPN
cana-1748	28	8	𝑔1	𝑔1	PROPN
cana-1748	28	9	)	)	PUNCT
cana-1748	28	10	+	+	SYM
cana-1748	28	11	𝑔1	𝑔1	PROPN
cana-1748	28	12	,	,	PUNCT
cana-1748	28	13	−2𝛼(𝑔6	−2𝛼(𝑔6	PRON
cana-1748	28	14	−	−	PROPN
cana-1748	28	15	𝑔5	𝑔5	PROPN
cana-1748	28	16	)	)	PUNCT
cana-1748	29	1	+	+	SYM
cana-1748	30	1	𝑔6	𝑔6	NOUN
cana-1748	30	2	]	]	PUNCT
cana-1748	30	3	for	for	ADP
cana-1748	30	4	𝛼	𝛼	PROPN
cana-1748	30	5	∈	∈	PROPN
cana-1748	30	6	[	[	X
cana-1748	30	7	0,0.5	0,0.5	NUM
cana-1748	30	8	)	)	PUNCT
cana-1748	31	1	[	[	X
cana-1748	31	2	2𝛼(𝑔3	2𝛼(𝑔3	NUM
cana-1748	31	3	−	−	NOUN
cana-1748	31	4	𝑔2	𝑔2	NOUN
cana-1748	31	5	)	)	PUNCT
cana-1748	31	6	−	−	NOUN
cana-1748	32	1	𝑔3	𝑔3	ADJ
cana-1748	32	2	+	+	CCONJ
cana-1748	32	3	2𝑔2	2𝑔2	NUM
cana-1748	32	4	,	,	PUNCT
cana-1748	32	5	−2𝛼(𝑔5	−2𝛼(𝑔5	PROPN
cana-1748	32	6	−	−	PROPN
cana-1748	32	7	𝑔4	𝑔4	PROPN
cana-1748	32	8	)	)	PUNCT
cana-1748	33	1	+	+	CCONJ
cana-1748	33	2	2𝑔5	2𝑔5	NUM
cana-1748	33	3	−	−	PROPN
cana-1748	33	4	𝑔4	𝑔4	NOUN
cana-1748	33	5	]	]	PUNCT
cana-1748	33	6	for	for	ADP
cana-1748	33	7	𝛼	𝛼	PROPN
cana-1748	33	8	∈	∈	PROPN
cana-1748	34	1	[	[	X
cana-1748	34	2	0.5,1	0.5,1	X
cana-1748	34	3	]	]	X
cana-1748	34	4	3.2	3.2	NUM
cana-1748	34	5	preposition	preposition	NOUN
cana-1748	34	6	1	1	NUM
cana-1748	34	7	.	.	PUNCT
cana-1748	35	1	let	let	VERB
cana-1748	35	2	us	we	PRON
cana-1748	35	3	consider	consider	VERB
cana-1748	35	4	two	two	NUM
cana-1748	35	5	hfn𝐻	hfn𝐻	NOUN
cana-1748	35	6	=	=	SYM
cana-1748	35	7	(	(	PUNCT
cana-1748	35	8	𝑔1	𝑔1	PROPN
cana-1748	35	9	,	,	PUNCT
cana-1748	35	10	𝑔2	𝑔2	NOUN
cana-1748	35	11	,	,	PUNCT
cana-1748	35	12	𝑔3	𝑔3	ADJ
cana-1748	35	13	,	,	PUNCT
cana-1748	35	14	𝑔4	𝑔4	PROPN
cana-1748	35	15	,	,	PUNCT
cana-1748	35	16	𝑔5	𝑔5	NOUN
cana-1748	35	17	,	,	PUNCT
cana-1748	35	18	𝑔6	𝑔6	NOUN
cana-1748	35	19	)	)	PUNCT
cana-1748	35	20	and	and	CCONJ
cana-1748	35	21	t𝐻	t𝐻	NOUN
cana-1748	35	22	=	=	SYM
cana-1748	35	23	(	(	PUNCT
cana-1748	35	24	ℎ1	ℎ1	PROPN
cana-1748	35	25	,	,	PUNCT
cana-1748	35	26	ℎ2	ℎ2	NOUN
cana-1748	35	27	,	,	PUNCT
cana-1748	35	28	ℎ3	ℎ3	NOUN
cana-1748	35	29	,	,	PUNCT
cana-1748	35	30	ℎ4	ℎ4	PROPN
cana-1748	35	31	,	,	PUNCT
cana-1748	35	32	ℎ5	ℎ5	PROPN
cana-1748	35	33	,	,	PUNCT
cana-1748	35	34	ℎ6	ℎ6	ADJ
cana-1748	35	35	)	)	PUNCT
cana-1748	35	36	.	.	PUNCT
cana-1748	36	1	then	then	ADV
cana-1748	36	2	the	the	DET
cana-1748	36	3	addition	addition	NOUN
cana-1748	36	4	of	of	ADP
cana-1748	36	5	two	two	NUM
cana-1748	36	6	hexagonal	hexagonal	ADJ
cana-1748	36	7	fuzzy	fuzzy	ADJ
cana-1748	36	8	number	number	NOUN
cana-1748	36	9	.	.	PUNCT
cana-1748	37	1	proof	proof	NOUN
cana-1748	37	2	let	let	VERB
cana-1748	37	3	us	we	PRON
cana-1748	37	4	add	add	VERB
cana-1748	37	5	the	the	DET
cana-1748	37	6	alpha	alpha	NOUN
cana-1748	37	7	cut	cut	NOUN
cana-1748	37	8	s𝛼	s𝛼	NOUN
cana-1748	37	9	and	and	CCONJ
cana-1748	37	10	t𝛼	t𝛼	NOUN
cana-1748	37	11	of	of	ADP
cana-1748	37	12	s𝐻	s𝐻	ADJ
cana-1748	37	13	and	and	CCONJ
cana-1748	37	14	t𝐻	t𝐻	NOUN
cana-1748	37	15	using	use	VERB
cana-1748	37	16	interval	interval	NOUN
cana-1748	37	17	arithmetic	arithmetic	ADJ
cana-1748	37	18	.	.	PUNCT
cana-1748	38	1	s𝛼	s𝛼	NOUN
cana-1748	39	1	+	+	CCONJ
cana-1748	39	2	t𝛼	t𝛼	NOUN
cana-1748	39	3	=	=	PUNCT
cana-1748	39	4	{	{	PUNCT
cana-1748	40	1	[	[	X
cana-1748	40	2	2𝛼(𝑔3	2𝛼(𝑔3	NUM
cana-1748	40	3	−	−	PROPN
cana-1748	40	4	𝑔1	𝑔1	PROPN
cana-1748	40	5	)	)	PUNCT
cana-1748	41	1	+	+	SYM
cana-1748	41	2	𝑔1	𝑔1	PROPN
cana-1748	41	3	,	,	PUNCT
cana-1748	41	4	−2𝛼(𝑔6	−2𝛼(𝑔6	PRON
cana-1748	41	5	−	−	PROPN
cana-1748	41	6	𝑔5	𝑔5	PROPN
cana-1748	41	7	)	)	PUNCT
cana-1748	42	1	+	+	SYM
cana-1748	42	2	𝑔6	𝑔6	NOUN
cana-1748	42	3	]	]	PUNCT
cana-1748	42	4	+	+	CCONJ
cana-1748	42	5	[	[	X
cana-1748	42	6	2𝛼(ℎ3	2𝛼(ℎ3	NUM
cana-1748	42	7	−	−	NOUN
cana-1748	42	8	ℎ1	ℎ1	PROPN
cana-1748	42	9	)	)	PUNCT
cana-1748	42	10	+	+	CCONJ
cana-1748	42	11	ℎ1	ℎ1	PROPN
cana-1748	42	12	,	,	PUNCT
cana-1748	42	13	−2𝛼(ℎ6	−2𝛼(ℎ6	PROPN
cana-1748	42	14	−	−	PROPN
cana-1748	42	15	ℎ5	ℎ5	PROPN
cana-1748	42	16	)	)	PUNCT
cana-1748	42	17	+	+	CCONJ
cana-1748	42	18	ℎ6	ℎ6	PROPN
cana-1748	42	19	]	]	X
cana-1748	42	20	,	,	PUNCT
cana-1748	42	21	for	for	ADP
cana-1748	42	22	𝛼	𝛼	PROPN
cana-1748	42	23	∈	∈	PROPN
cana-1748	42	24	[	[	X
cana-1748	42	25	0,0.5	0,0.5	NUM
cana-1748	42	26	)	)	PUNCT
cana-1748	43	1	[	[	X
cana-1748	43	2	2𝛼(𝑔3	2𝛼(𝑔3	NUM
cana-1748	43	3	−	−	NOUN
cana-1748	43	4	𝑔2	𝑔2	NOUN
cana-1748	43	5	)	)	PUNCT
cana-1748	43	6	−	−	NOUN
cana-1748	44	1	𝑔3	𝑔3	ADJ
cana-1748	44	2	+	+	CCONJ
cana-1748	44	3	2𝑔2	2𝑔2	NUM
cana-1748	44	4	,	,	PUNCT
cana-1748	44	5	−2𝛼(𝑔5	−2𝛼(𝑔5	PROPN
cana-1748	44	6	−	−	PROPN
cana-1748	44	7	𝑔4	𝑔4	PROPN
cana-1748	44	8	)	)	PUNCT
cana-1748	45	1	+	+	CCONJ
cana-1748	45	2	2𝑔5	2𝑔5	NUM
cana-1748	45	3	−	−	PROPN
cana-1748	45	4	𝑔4	𝑔4	NOUN
cana-1748	45	5	]	]	PUNCT
cana-1748	46	1	+	+	CCONJ
cana-1748	46	2	[	[	X
cana-1748	46	3	2𝛼(ℎ3	2𝛼(ℎ3	NUM
cana-1748	46	4	−	−	NOUN
cana-1748	46	5	ℎ2	ℎ2	NOUN
cana-1748	46	6	)	)	PUNCT
cana-1748	46	7	−	−	NOUN
cana-1748	46	8	ℎ3	ℎ3	NOUN
cana-1748	46	9	+	+	CCONJ
cana-1748	46	10	2ℎ2	2ℎ2	NUM
cana-1748	46	11	,	,	PUNCT
cana-1748	46	12	−2𝛼(ℎ5	−2𝛼(ℎ5	PROPN
cana-1748	46	13	−	−	PROPN
cana-1748	46	14	ℎ4	ℎ4	PROPN
cana-1748	46	15	)	)	PUNCT
cana-1748	47	1	+	+	NOUN
cana-1748	47	2	2ℎ5	2ℎ5	NUM
cana-1748	47	3	−	−	PROPN
cana-1748	47	4	ℎ4	ℎ4	NOUN
cana-1748	47	5	]	]	PUNCT
cana-1748	47	6	,	,	PUNCT
cana-1748	47	7	for	for	ADP
cana-1748	47	8	𝛼	𝛼	PROPN
cana-1748	47	9	∈	∈	PROPN
cana-1748	47	10	[	[	X
cana-1748	47	11	0.5,1	0.5,1	X
cana-1748	47	12	]	]	X
cana-1748	47	13	s𝛼	s𝛼	NOUN
cana-1748	48	1	=	=	SYM
cana-1748	49	1	[	[	X
cana-1748	49	2	2𝛼	2𝛼	PROPN
cana-1748	49	3	+	+	X
cana-1748	49	4	𝑔1	𝑔1	PROPN
cana-1748	49	5	,	,	PUNCT
cana-1748	49	6	−2𝛼	−2𝛼	PROPN
cana-1748	49	7	+	+	X
cana-1748	49	8	𝑔6	𝑔6	NOUN
cana-1748	49	9	]	]	PUNCT
cana-1748	49	10	for	for	ADP
cana-1748	49	11	𝛼	𝛼	PROPN
cana-1748	49	12	∈	∈	PROPN
cana-1748	49	13	[	[	X
cana-1748	49	14	0,0.5	0,0.5	NUM
cana-1748	49	15	)	)	PUNCT
cana-1748	49	16	t𝛼	t𝛼	NOUN
cana-1748	49	17	=	=	PUNCT
cana-1748	50	1	[	[	X
cana-1748	50	2	4𝛼	4𝛼	NOUN
cana-1748	50	3	+	+	X
cana-1748	50	4	ℎ1	ℎ1	PROPN
cana-1748	50	5	,	,	PUNCT
cana-1748	50	6	−4𝛼	−4𝛼	PROPN
cana-1748	50	7	+	+	CCONJ
cana-1748	50	8	ℎ6	ℎ6	ADJ
cana-1748	50	9	]	]	X
cana-1748	50	10	for	for	ADP
cana-1748	50	11	𝛼	𝛼	PROPN
cana-1748	50	12	∈	∈	PROPN
cana-1748	50	13	[	[	X
cana-1748	50	14	0.5,1	0.5,1	X
cana-1748	50	15	]	]	X
cana-1748	50	16	so	so	SCONJ
cana-1748	50	17	that	that	SCONJ
cana-1748	50	18	,	,	PUNCT
cana-1748	50	19	s𝛼	s𝛼	X
cana-1748	50	20	+	+	CCONJ
cana-1748	50	21	t𝛼	t𝛼	NOUN
cana-1748	50	22	=	=	PUNCT
cana-1748	51	1	[	[	X
cana-1748	51	2	6𝛼	6𝛼	NOUN
cana-1748	51	3	+	+	SYM
cana-1748	51	4	(	(	PUNCT
cana-1748	51	5	𝑔1	𝑔1	PROPN
cana-1748	51	6	+	+	CCONJ
cana-1748	51	7	ℎ1),−6𝛼	ℎ1),−6𝛼	PROPN
cana-1748	51	8	+	+	PROPN
cana-1748	51	9	(	(	PUNCT
cana-1748	51	10	𝑔6	𝑔6	NOUN
cana-1748	51	11	+	+	CCONJ
cana-1748	51	12	ℎ6	ℎ6	ADJ
cana-1748	51	13	)	)	PUNCT
cana-1748	51	14	]	]	PUNCT
cana-1748	51	15	consider	consider	VERB
cana-1748	51	16	the	the	DET
cana-1748	51	17	example	example	NOUN
cana-1748	51	18	of	of	ADP
cana-1748	51	19	hfn	hfn	NOUN
cana-1748	51	20	s𝐻	s𝐻	PROPN
cana-1748	51	21	=	=	PUNCT
cana-1748	51	22	(	(	PUNCT
cana-1748	51	23	2,5,6,3,7,3	2,5,6,3,7,3	NUM
cana-1748	51	24	)	)	PUNCT
cana-1748	51	25	and	and	CCONJ
cana-1748	51	26	t𝐻	t𝐻	NOUN
cana-1748	51	27	=	=	SYM
cana-1748	51	28	(	(	PUNCT
cana-1748	51	29	9,7,5,1,6,4	9,7,5,1,6,4	NUM
cana-1748	51	30	)	)	PUNCT
cana-1748	51	31	s𝛼	s𝛼	NOUN
cana-1748	52	1	=	=	PUNCT
cana-1748	53	1	[	[	X
cana-1748	53	2	2𝛼	2𝛼	NOUN
cana-1748	53	3	+	+	CCONJ
cana-1748	53	4	2,−2𝛼	2,−2𝛼	NUM
cana-1748	54	1	+	+	CCONJ
cana-1748	54	2	3	3	X
cana-1748	54	3	]	]	PUNCT
cana-1748	54	4	for	for	ADP
cana-1748	54	5	𝛼	𝛼	PROPN
cana-1748	54	6	∈	∈	PROPN
cana-1748	54	7	[	[	X
cana-1748	54	8	0,0.5	0,0.5	NUM
cana-1748	54	9	)	)	PUNCT
cana-1748	54	10	t𝛼	t𝛼	NOUN
cana-1748	54	11	=	=	PUNCT
cana-1748	55	1	[	[	X
cana-1748	55	2	4𝛼	4𝛼	NOUN
cana-1748	55	3	+	+	X
cana-1748	55	4	9	9	NUM
cana-1748	55	5	,	,	PUNCT
cana-1748	55	6	−4𝛼	−4𝛼	PUNCT
cana-1748	55	7	+	+	NOUN
cana-1748	55	8	4	4	X
cana-1748	55	9	]	]	PUNCT
cana-1748	55	10	for	for	ADP
cana-1748	55	11	𝛼	𝛼	PROPN
cana-1748	55	12	∈	∈	PROPN
cana-1748	55	13	[	[	X
cana-1748	55	14	0.5,1	0.5,1	X
cana-1748	55	15	]	]	PUNCT
cana-1748	55	16	since	since	SCONJ
cana-1748	55	17	for	for	ADP
cana-1748	55	18	both	both	DET
cana-1748	55	19	𝛼	𝛼	PRON
cana-1748	55	20	∈	∈	PROPN
cana-1748	55	21	[	[	X
cana-1748	55	22	0,0.5	0,0.5	NUM
cana-1748	55	23	)	)	PUNCT
cana-1748	55	24	and	and	CCONJ
cana-1748	55	25	𝛼	𝛼	PRON
cana-1748	55	26	∈	∈	PROPN
cana-1748	55	27	[	[	X
cana-1748	55	28	0.5,1	0.5,1	X
cana-1748	55	29	]	]	X
cana-1748	55	30	arithmetic	arithmetic	ADJ
cana-1748	55	31	intervals	interval	NOUN
cana-1748	55	32	are	be	AUX
cana-1748	55	33	same	same	ADJ
cana-1748	55	34	.	.	PUNCT
cana-1748	56	1	therefore	therefore	ADV
cana-1748	56	2	s𝛼	s𝛼	X
cana-1748	57	1	+	+	CCONJ
cana-1748	57	2	t𝛼	t𝛼	NOUN
cana-1748	57	3	=	=	SYM
cana-1748	58	1	[	[	X
cana-1748	58	2	6𝛼	6𝛼	NOUN
cana-1748	58	3	+	+	X
cana-1748	58	4	11,−6𝛼	11,−6𝛼	NOUN
cana-1748	59	1	+	+	CCONJ
cana-1748	59	2	7	7	X
cana-1748	59	3	]	]	PUNCT
cana-1748	59	4	for	for	ADP
cana-1748	59	5	all	all	DET
cana-1748	59	6	𝛼	𝛼	PRON
cana-1748	59	7	∈	∈	NOUN
cana-1748	59	8	[	[	X
cana-1748	59	9	0,1	0,1	NUM
cana-1748	59	10	]	]	X
cana-1748	59	11	𝛼	𝛼	NOUN
cana-1748	59	12	=	=	SYM
cana-1748	59	13	0	0	NUM
cana-1748	59	14	⟹	⟹	NUM
cana-1748	59	15	s0	s0	PROPN
cana-1748	59	16	+	+	CCONJ
cana-1748	59	17	t0	t0	PROPN
cana-1748	59	18	=	=	PUNCT
cana-1748	60	1	[	[	X
cana-1748	60	2	11,7	11,7	X
cana-1748	60	3	]	]	X
cana-1748	60	4	𝛼	𝛼	NOUN
cana-1748	60	5	=	=	SYM
cana-1748	60	6	0.5	0.5	NUM
cana-1748	60	7	⟹	⟹	NUM
cana-1748	60	8	s0.5	s0.5	VERB
cana-1748	60	9	+	+	CCONJ
cana-1748	60	10	t0.5	t0.5	PRON
cana-1748	60	11	=	=	PUNCT
cana-1748	61	1	[	[	X
cana-1748	61	2	13,4	13,4	NUM
cana-1748	61	3	]	]	X
cana-1748	61	4	𝛼	𝛼	NOUN
cana-1748	61	5	=	=	SYM
cana-1748	61	6	1	1	NUM
cana-1748	61	7	⟹	⟹	NUM
cana-1748	61	8	s1	s1	NOUN
cana-1748	61	9	+	+	CCONJ
cana-1748	61	10	t1	t1	NOUN
cana-1748	61	11	=	=	PUNCT
cana-1748	62	1	[	[	X
cana-1748	62	2	16,1	16,1	X
cana-1748	62	3	]	]	X
cana-1748	62	4	hence	hence	ADV
cana-1748	62	5	,	,	PUNCT
cana-1748	62	6	s𝛼	s𝛼	X
cana-1748	63	1	+	+	CCONJ
cana-1748	63	2	t𝛼	t𝛼	NOUN
cana-1748	63	3	=	=	SYM
cana-1748	64	1	[	[	X
cana-1748	64	2	11,13,16,1,4,7	11,13,16,1,4,7	NOUN
cana-1748	64	3	]	]	PUNCT
cana-1748	64	4	,	,	PUNCT
cana-1748	64	5	every	every	DET
cana-1748	64	6	point	point	NOUN
cana-1748	64	7	corresponds	correspond	VERB
cana-1748	64	8	to	to	ADP
cana-1748	64	9	part	part	NOUN
cana-1748	64	10	of	of	ADP
cana-1748	64	11	the	the	DET
cana-1748	64	12	two	two	NUM
cana-1748	64	13	hfn	hfn	NOUN
cana-1748	64	14	.	.	PUNCT
cana-1748	65	1	consequently	consequently	ADV
cana-1748	65	2	,	,	PUNCT
cana-1748	65	3	the	the	DET
cana-1748	65	4	interval	interval	NOUN
cana-1748	65	5	is	be	AUX
cana-1748	65	6	covered	cover	VERB
cana-1748	65	7	by	by	ADP
cana-1748	65	8	the	the	DET
cana-1748	65	9	addition	addition	NOUN
cana-1748	65	10	of	of	ADP
cana-1748	65	11	two	two	NUM
cana-1748	65	12	𝛼-cut	𝛼-cut	VERB
cana-1748	65	13	.	.	PUNCT
cana-1748	66	1	2	2	NUM
cana-1748	66	2	if	if	SCONJ
cana-1748	66	3	we	we	PRON
cana-1748	66	4	assume	assume	VERB
cana-1748	66	5	two	two	NUM
cana-1748	66	6	hexagonal	hexagonal	ADJ
cana-1748	66	7	fuzzy	fuzzy	ADJ
cana-1748	66	8	numbers	number	NOUN
cana-1748	66	9	s	s	PART
cana-1748	66	10	=	=	SYM
cana-1748	66	11	(	(	PUNCT
cana-1748	66	12	𝑔1	𝑔1	PROPN
cana-1748	66	13	,	,	PUNCT
cana-1748	66	14	𝑔2	𝑔2	NOUN
cana-1748	66	15	,	,	PUNCT
cana-1748	66	16	𝑔3	𝑔3	ADJ
cana-1748	66	17	,	,	PUNCT
cana-1748	66	18	𝑔4	𝑔4	PROPN
cana-1748	66	19	,	,	PUNCT
cana-1748	66	20	𝑔5	𝑔5	NOUN
cana-1748	66	21	,	,	PUNCT
cana-1748	66	22	𝑔6	𝑔6	NOUN
cana-1748	66	23	)	)	PUNCT
cana-1748	66	24	and	and	CCONJ
cana-1748	66	25	h	h	NOUN
cana-1748	66	26	=	=	SYM
cana-1748	66	27	(	(	PUNCT
cana-1748	66	28	𝑡1	𝑡1	PROPN
cana-1748	66	29	,	,	PUNCT
cana-1748	66	30	𝑡2	𝑡2	PROPN
cana-1748	66	31	,	,	PUNCT
cana-1748	66	32	𝑡3	𝑡3	PROPN
cana-1748	66	33	,	,	PUNCT
cana-1748	66	34	𝑡4	𝑡4	NOUN
cana-1748	66	35	,	,	PUNCT
cana-1748	66	36	𝑡5	𝑡5	PROPN
cana-1748	66	37	,	,	PUNCT
cana-1748	66	38	𝑡6	𝑡6	NOUN
cana-1748	66	39	)	)	PUNCT
cana-1748	66	40	.	.	PUNCT
cana-1748	67	1	then	then	ADV
cana-1748	67	2	the	the	DET
cana-1748	67	3	subtraction	subtraction	NOUN
cana-1748	67	4	of	of	ADP
cana-1748	67	5	two	two	NUM
cana-1748	67	6	numbers	number	NOUN
cana-1748	67	7	.	.	PUNCT
cana-1748	68	1	proof	proof	NOUN
cana-1748	68	2	let	let	VERB
cana-1748	68	3	us	we	PRON
cana-1748	68	4	add	add	VERB
cana-1748	68	5	the	the	DET
cana-1748	68	6	alpha	alpha	NOUN
cana-1748	68	7	cut	cut	NOUN
cana-1748	68	8	s𝛼	s𝛼	NOUN
cana-1748	68	9	and	and	CCONJ
cana-1748	68	10	t𝛼	t𝛼	NOUN
cana-1748	68	11	of	of	ADP
cana-1748	68	12	s𝐻	s𝐻	ADJ
cana-1748	68	13	and	and	CCONJ
cana-1748	68	14	t𝐻	t𝐻	NOUN
cana-1748	68	15	using	use	VERB
cana-1748	68	16	interval	interval	NOUN
cana-1748	68	17	arithmetic	arithmetic	ADJ
cana-1748	68	18	.	.	PUNCT
cana-1748	69	1	s𝛼	s𝛼	NOUN
cana-1748	70	1	+	+	CCONJ
cana-1748	70	2	t𝛼	t𝛼	NOUN
cana-1748	70	3	=	=	PUNCT
cana-1748	70	4	{	{	PUNCT
cana-1748	71	1	[	[	X
cana-1748	71	2	2𝛼(𝑔3	2𝛼(𝑔3	NUM
cana-1748	71	3	−	−	PROPN
cana-1748	71	4	𝑔1	𝑔1	PROPN
cana-1748	71	5	)	)	PUNCT
cana-1748	72	1	+	+	SYM
cana-1748	72	2	𝑔1	𝑔1	PROPN
cana-1748	72	3	,	,	PUNCT
cana-1748	72	4	−2𝛼(𝑔6	−2𝛼(𝑔6	PRON
cana-1748	72	5	−	−	PROPN
cana-1748	72	6	𝑔5	𝑔5	PROPN
cana-1748	72	7	)	)	PUNCT
cana-1748	73	1	+	+	SYM
cana-1748	73	2	𝑔6	𝑔6	NOUN
cana-1748	73	3	]	]	PUNCT
cana-1748	73	4	−	−	PUNCT
cana-1748	74	1	[	[	X
cana-1748	74	2	2𝛼(ℎ3	2𝛼(ℎ3	NUM
cana-1748	74	3	−	−	NOUN
cana-1748	74	4	ℎ1	ℎ1	PROPN
cana-1748	74	5	)	)	PUNCT
cana-1748	74	6	+	+	CCONJ
cana-1748	74	7	ℎ1	ℎ1	PROPN
cana-1748	74	8	,	,	PUNCT
cana-1748	74	9	−2𝛼(ℎ6	−2𝛼(ℎ6	PROPN
cana-1748	74	10	−	−	PROPN
cana-1748	74	11	ℎ5	ℎ5	PROPN
cana-1748	74	12	)	)	PUNCT
cana-1748	74	13	+	+	CCONJ
cana-1748	74	14	ℎ6	ℎ6	PROPN
cana-1748	74	15	]	]	X
cana-1748	74	16	,	,	PUNCT
cana-1748	74	17	for	for	ADP
cana-1748	74	18	𝛼	𝛼	PROPN
cana-1748	74	19	∈	∈	PROPN
cana-1748	74	20	[	[	X
cana-1748	74	21	0,0.5	0,0.5	NUM
cana-1748	74	22	)	)	PUNCT
cana-1748	75	1	[	[	X
cana-1748	75	2	2𝛼(𝑔3	2𝛼(𝑔3	NUM
cana-1748	75	3	−	−	NOUN
cana-1748	75	4	𝑔2	𝑔2	NOUN
cana-1748	75	5	)	)	PUNCT
cana-1748	75	6	−	−	NOUN
cana-1748	76	1	𝑔3	𝑔3	ADJ
cana-1748	76	2	+	+	CCONJ
cana-1748	76	3	2𝑔2	2𝑔2	NUM
cana-1748	76	4	,	,	PUNCT
cana-1748	76	5	−2𝛼(𝑔5	−2𝛼(𝑔5	PROPN
cana-1748	76	6	−	−	PROPN
cana-1748	76	7	𝑔4	𝑔4	PROPN
cana-1748	76	8	)	)	PUNCT
cana-1748	77	1	+	+	CCONJ
cana-1748	77	2	2𝑔5	2𝑔5	NUM
cana-1748	77	3	−	−	PROPN
cana-1748	77	4	𝑔4	𝑔4	NOUN
cana-1748	77	5	]	]	PUNCT
cana-1748	77	6	−	−	PROPN
cana-1748	78	1	[	[	X
cana-1748	78	2	2𝛼(ℎ3	2𝛼(ℎ3	NUM
cana-1748	78	3	−	−	NOUN
cana-1748	78	4	ℎ2	ℎ2	NOUN
cana-1748	78	5	)	)	PUNCT
cana-1748	78	6	−	−	NOUN
cana-1748	78	7	ℎ3	ℎ3	NOUN
cana-1748	78	8	+	+	CCONJ
cana-1748	78	9	2ℎ2	2ℎ2	NUM
cana-1748	78	10	,	,	PUNCT
cana-1748	78	11	−2𝛼(ℎ5	−2𝛼(ℎ5	PROPN
cana-1748	78	12	−	−	PROPN
cana-1748	78	13	ℎ4	ℎ4	PROPN
cana-1748	78	14	)	)	PUNCT
cana-1748	79	1	+	+	NOUN
cana-1748	79	2	2ℎ5	2ℎ5	NUM
cana-1748	79	3	−	−	PROPN
cana-1748	79	4	ℎ4	ℎ4	NOUN
cana-1748	79	5	]	]	PUNCT
cana-1748	79	6	,	,	PUNCT
cana-1748	79	7	for	for	ADP
cana-1748	79	8	𝛼	𝛼	PROPN
cana-1748	79	9	∈	∈	PROPN
cana-1748	80	1	[	[	X
cana-1748	80	2	0.5,1	0.5,1	X
cana-1748	80	3	]	]	PUNCT
cana-1748	80	4	.	.	PUNCT
cana-1748	81	1	s𝛼	s𝛼	NOUN
cana-1748	81	2	=	=	PUNCT
cana-1748	82	1	[	[	X
cana-1748	82	2	2𝛼	2𝛼	PROPN
cana-1748	82	3	+	+	X
cana-1748	82	4	𝑔1	𝑔1	PROPN
cana-1748	82	5	,	,	PUNCT
cana-1748	82	6	−2𝛼	−2𝛼	PROPN
cana-1748	82	7	+	+	X
cana-1748	82	8	𝑔6	𝑔6	NOUN
cana-1748	82	9	]	]	PUNCT
cana-1748	82	10	for	for	ADP
cana-1748	82	11	𝛼	𝛼	PROPN
cana-1748	82	12	∈	∈	PROPN
cana-1748	82	13	[	[	X
cana-1748	82	14	0,0.5	0,0.5	NUM
cana-1748	82	15	)	)	PUNCT
cana-1748	82	16	t𝛼	t𝛼	NOUN
cana-1748	82	17	=	=	PUNCT
cana-1748	83	1	[	[	X
cana-1748	83	2	4𝛼	4𝛼	NOUN
cana-1748	83	3	+	+	X
cana-1748	83	4	ℎ1	ℎ1	PROPN
cana-1748	83	5	,	,	PUNCT
cana-1748	83	6	−4𝛼	−4𝛼	PROPN
cana-1748	83	7	+	+	CCONJ
cana-1748	83	8	ℎ6	ℎ6	ADJ
cana-1748	83	9	]	]	X
cana-1748	83	10	for	for	ADP
cana-1748	83	11	𝛼	𝛼	PROPN
cana-1748	83	12	∈	∈	PROPN
cana-1748	83	13	[	[	X
cana-1748	83	14	0.5,1	0.5,1	X
cana-1748	83	15	]	]	PUNCT
cana-1748	83	16	since	since	ADV
cana-1748	83	17	,	,	PUNCT
cana-1748	83	18	s𝛼	s𝛼	NOUN
cana-1748	83	19	−	−	NOUN
cana-1748	83	20	t𝛼	t𝛼	NOUN
cana-1748	84	1	=	=	PUNCT
cana-1748	85	1	[	[	X
cana-1748	85	2	−2𝛼	−2𝛼	PROPN
cana-1748	85	3	+	+	CCONJ
cana-1748	85	4	(	(	PUNCT
cana-1748	85	5	𝑔1	𝑔1	PROPN
cana-1748	85	6	−	−	PROPN
cana-1748	85	7	ℎ1	ℎ1	PROPN
cana-1748	85	8	)	)	PUNCT
cana-1748	85	9	,	,	PUNCT
cana-1748	85	10	2𝛼	2𝛼	PROPN
cana-1748	85	11	+	+	SYM
cana-1748	85	12	(	(	PUNCT
cana-1748	85	13	𝑔6	𝑔6	NOUN
cana-1748	85	14	−	−	PROPN
cana-1748	85	15	ℎ6	ℎ6	ADJ
cana-1748	85	16	)	)	PUNCT
cana-1748	85	17	]	]	PUNCT
cana-1748	85	18	communications	communication	NOUN
cana-1748	85	19	on	on	ADP
cana-1748	85	20	applied	apply	VERB
cana-1748	85	21	nonlinear	nonlinear	ADJ
cana-1748	85	22	analysis	analysis	NOUN
cana-1748	85	23	issn	issn	NOUN
cana-1748	85	24	:	:	PUNCT
cana-1748	85	25	1074	1074	NUM
cana-1748	85	26	-	-	PUNCT
cana-1748	85	27	133x	133x	NUM
cana-1748	85	28	vol	vol	NOUN
cana-1748	85	29	32	32	NUM
cana-1748	85	30	no	no	NOUN
cana-1748	85	31	.	.	NOUN
cana-1748	85	32	2	2	NUM
cana-1748	85	33	(	(	PUNCT
cana-1748	85	34	2025	2025	NUM
cana-1748	85	35	)	)	PUNCT
cana-1748	85	36	370	370	NUM
cana-1748	85	37	https://internationalpubls.com	https://internationalpubls.com	X
cana-1748	85	38	consider	consider	VERB
cana-1748	85	39	the	the	DET
cana-1748	85	40	example	example	NOUN
cana-1748	85	41	of	of	ADP
cana-1748	85	42	hfn	hfn	NOUN
cana-1748	85	43	s𝐻	s𝐻	PROPN
cana-1748	85	44	=	=	SYM
cana-1748	85	45	(	(	PUNCT
cana-1748	85	46	1,3,5,7,9,2	1,3,5,7,9,2	NUM
cana-1748	85	47	)	)	PUNCT
cana-1748	85	48	and	and	CCONJ
cana-1748	85	49	t𝐻	t𝐻	NOUN
cana-1748	85	50	=	=	SYM
cana-1748	85	51	(	(	PUNCT
cana-1748	85	52	2,4,6,8,1,10	2,4,6,8,1,10	NUM
cana-1748	85	53	)	)	PUNCT
cana-1748	85	54	s𝛼	s𝛼	NOUN
cana-1748	86	1	=	=	PUNCT
cana-1748	87	1	[	[	X
cana-1748	87	2	2𝛼	2𝛼	NOUN
cana-1748	87	3	+	+	CCONJ
cana-1748	87	4	1,−2𝛼	1,−2𝛼	NUM
cana-1748	88	1	+	+	CCONJ
cana-1748	88	2	2	2	NUM
cana-1748	88	3	]	]	PUNCT
cana-1748	88	4	for	for	ADP
cana-1748	88	5	𝛼	𝛼	PROPN
cana-1748	88	6	∈	∈	PROPN
cana-1748	88	7	[	[	X
cana-1748	88	8	0,0.5	0,0.5	NUM
cana-1748	88	9	)	)	PUNCT
cana-1748	88	10	t𝛼	t𝛼	NOUN
cana-1748	88	11	=	=	PUNCT
cana-1748	89	1	[	[	X
cana-1748	89	2	4𝛼	4𝛼	NOUN
cana-1748	89	3	+	+	X
cana-1748	89	4	2	2	NUM
cana-1748	89	5	,	,	PUNCT
cana-1748	89	6	−4𝛼	−4𝛼	PUNCT
cana-1748	89	7	+	+	PUNCT
cana-1748	89	8	10	10	NUM
cana-1748	89	9	]	]	PUNCT
cana-1748	89	10	for	for	ADP
cana-1748	89	11	𝛼	𝛼	PROPN
cana-1748	89	12	∈	∈	PROPN
cana-1748	89	13	[	[	X
cana-1748	89	14	0.5,1	0.5,1	X
cana-1748	89	15	]	]	PUNCT
cana-1748	89	16	since	since	SCONJ
cana-1748	89	17	for	for	ADP
cana-1748	89	18	both	both	DET
cana-1748	89	19	𝛼	𝛼	PRON
cana-1748	89	20	∈	∈	PROPN
cana-1748	89	21	[	[	X
cana-1748	89	22	0,0.5	0,0.5	NUM
cana-1748	89	23	)	)	PUNCT
cana-1748	89	24	and	and	CCONJ
cana-1748	89	25	𝛼	𝛼	PRON
cana-1748	89	26	∈	∈	PROPN
cana-1748	89	27	[	[	X
cana-1748	89	28	0.5,1	0.5,1	X
cana-1748	89	29	]	]	X
cana-1748	89	30	arithmetic	arithmetic	ADJ
cana-1748	89	31	intervals	interval	NOUN
cana-1748	89	32	are	be	AUX
cana-1748	89	33	same	same	ADJ
cana-1748	89	34	.	.	PUNCT
cana-1748	90	1	therefore	therefore	ADV
cana-1748	90	2	s𝛼	s𝛼	X
cana-1748	91	1	+	+	CCONJ
cana-1748	91	2	t𝛼	t𝛼	NOUN
cana-1748	91	3	=	=	SYM
cana-1748	92	1	[	[	X
cana-1748	92	2	−2𝛼	−2𝛼	PROPN
cana-1748	92	3	−	−	NOUN
cana-1748	92	4	1,2𝛼	1,2𝛼	NUM
cana-1748	92	5	−	−	NOUN
cana-1748	92	6	8	8	NUM
cana-1748	92	7	]	]	PUNCT
cana-1748	92	8	for	for	ADP
cana-1748	92	9	all	all	DET
cana-1748	92	10	𝛼	𝛼	PRON
cana-1748	92	11	∈	∈	NOUN
cana-1748	92	12	[	[	X
cana-1748	92	13	0,1	0,1	NUM
cana-1748	92	14	]	]	X
cana-1748	92	15	𝛼	𝛼	NOUN
cana-1748	92	16	=	=	SYM
cana-1748	92	17	0	0	NUM
cana-1748	92	18	⟹	⟹	NUM
cana-1748	92	19	s0	s0	PROPN
cana-1748	92	20	+	+	CCONJ
cana-1748	92	21	t0	t0	PROPN
cana-1748	92	22	=	=	PUNCT
cana-1748	93	1	[	[	X
cana-1748	93	2	−1,−8	−1,−8	X
cana-1748	93	3	]	]	X
cana-1748	93	4	𝛼	𝛼	NOUN
cana-1748	93	5	=	=	SYM
cana-1748	93	6	0.5	0.5	NUM
cana-1748	93	7	⟹	⟹	NUM
cana-1748	93	8	s0.5	s0.5	VERB
cana-1748	93	9	+	+	CCONJ
cana-1748	93	10	t0.5	t0.5	PRON
cana-1748	93	11	=	=	PUNCT
cana-1748	94	1	[	[	X
cana-1748	94	2	−2	−2	X
cana-1748	94	3	,	,	PUNCT
cana-1748	94	4	−7	−7	X
cana-1748	94	5	]	]	X
cana-1748	94	6	𝛼	𝛼	X
cana-1748	94	7	=	=	SYM
cana-1748	94	8	1	1	NUM
cana-1748	94	9	⟹	⟹	NUM
cana-1748	94	10	s1	s1	NOUN
cana-1748	94	11	+	+	CCONJ
cana-1748	94	12	t1	t1	NOUN
cana-1748	94	13	=	=	PUNCT
cana-1748	95	1	[	[	X
cana-1748	95	2	−3,−6	−3,−6	X
cana-1748	95	3	]	]	PUNCT
cana-1748	95	4	hence	hence	ADV
cana-1748	95	5	,	,	PUNCT
cana-1748	95	6	s𝛼	s𝛼	NOUN
cana-1748	95	7	−	−	NOUN
cana-1748	95	8	t𝛼	t𝛼	NOUN
cana-1748	95	9	=	=	PUNCT
cana-1748	96	1	[	[	X
cana-1748	96	2	−1,−2,−3,−6,−7,−8	−1,−2,−3,−6,−7,−8	PROPN
cana-1748	96	3	]	]	X
cana-1748	96	4	,	,	PUNCT
cana-1748	96	5	every	every	DET
cana-1748	96	6	point	point	NOUN
cana-1748	96	7	corresponds	correspond	VERB
cana-1748	96	8	to	to	ADP
cana-1748	96	9	part	part	NOUN
cana-1748	96	10	of	of	ADP
cana-1748	96	11	the	the	DET
cana-1748	96	12	two	two	NUM
cana-1748	96	13	hfn	hfn	NOUN
cana-1748	96	14	.	.	PUNCT
cana-1748	97	1	consequently	consequently	ADV
cana-1748	97	2	,	,	PUNCT
cana-1748	97	3	the	the	DET
cana-1748	97	4	interval	interval	NOUN
cana-1748	97	5	is	be	AUX
cana-1748	97	6	covered	cover	VERB
cana-1748	97	7	by	by	ADP
cana-1748	97	8	the	the	DET
cana-1748	97	9	addition	addition	NOUN
cana-1748	97	10	of	of	ADP
cana-1748	97	11	two	two	NUM
cana-1748	97	12	𝛼-cut	𝛼-cut	VERB
cana-1748	97	13	.	.	PUNCT
cana-1748	98	1	3	3	NUM
cana-1748	98	2	if	if	SCONJ
cana-1748	98	3	we	we	PRON
cana-1748	98	4	assume	assume	VERB
cana-1748	98	5	two	two	NUM
cana-1748	98	6	hexagonal	hexagonal	ADJ
cana-1748	98	7	fuzzy	fuzzy	ADJ
cana-1748	98	8	numbers	number	NOUN
cana-1748	98	9	s	s	PART
cana-1748	98	10	=	=	SYM
cana-1748	98	11	(	(	PUNCT
cana-1748	98	12	𝑔1	𝑔1	PROPN
cana-1748	98	13	,	,	PUNCT
cana-1748	98	14	𝑔2	𝑔2	NOUN
cana-1748	98	15	,	,	PUNCT
cana-1748	98	16	𝑔3	𝑔3	ADJ
cana-1748	98	17	,	,	PUNCT
cana-1748	98	18	𝑔4	𝑔4	PROPN
cana-1748	98	19	,	,	PUNCT
cana-1748	98	20	𝑔5	𝑔5	NOUN
cana-1748	98	21	,	,	PUNCT
cana-1748	98	22	𝑔6	𝑔6	NOUN
cana-1748	98	23	)	)	PUNCT
cana-1748	98	24	and	and	CCONJ
cana-1748	98	25	h	h	NOUN
cana-1748	98	26	=	=	SYM
cana-1748	98	27	(	(	PUNCT
cana-1748	98	28	𝑡1	𝑡1	PROPN
cana-1748	98	29	,	,	PUNCT
cana-1748	98	30	𝑡2	𝑡2	PROPN
cana-1748	98	31	,	,	PUNCT
cana-1748	98	32	𝑡3	𝑡3	PROPN
cana-1748	98	33	,	,	PUNCT
cana-1748	98	34	𝑡4	𝑡4	NOUN
cana-1748	98	35	,	,	PUNCT
cana-1748	98	36	𝑡5	𝑡5	PROPN
cana-1748	98	37	,	,	PUNCT
cana-1748	98	38	𝑡6	𝑡6	NOUN
cana-1748	98	39	)	)	PUNCT
cana-1748	98	40	.	.	PUNCT
cana-1748	99	1	then	then	ADV
cana-1748	99	2	the	the	DET
cana-1748	99	3	multiplication	multiplication	NOUN
cana-1748	99	4	of	of	ADP
cana-1748	99	5	two	two	NUM
cana-1748	99	6	numbers	number	NOUN
cana-1748	99	7	.	.	PUNCT
cana-1748	100	1	proof	proof	NOUN
cana-1748	100	2	let	let	VERB
cana-1748	100	3	us	we	PRON
cana-1748	100	4	add	add	VERB
cana-1748	100	5	the	the	DET
cana-1748	100	6	alpha	alpha	NOUN
cana-1748	100	7	cut	cut	NOUN
cana-1748	100	8	s𝛼	s𝛼	NOUN
cana-1748	100	9	and	and	CCONJ
cana-1748	100	10	t𝛼	t𝛼	NOUN
cana-1748	100	11	of	of	ADP
cana-1748	100	12	s𝐻	s𝐻	ADJ
cana-1748	100	13	and	and	CCONJ
cana-1748	100	14	t𝐻	t𝐻	NOUN
cana-1748	100	15	using	use	VERB
cana-1748	100	16	interval	interval	NOUN
cana-1748	100	17	arithmetic	arithmetic	ADJ
cana-1748	100	18	.	.	PUNCT
cana-1748	101	1	s𝛼	s𝛼	NOUN
cana-1748	102	1	+	+	CCONJ
cana-1748	102	2	t𝛼	t𝛼	NOUN
cana-1748	102	3	=	=	PUNCT
cana-1748	102	4	{	{	PUNCT
cana-1748	103	1	[	[	X
cana-1748	103	2	2𝛼(𝑔3	2𝛼(𝑔3	NUM
cana-1748	103	3	−	−	PROPN
cana-1748	103	4	𝑔1	𝑔1	PROPN
cana-1748	103	5	)	)	PUNCT
cana-1748	104	1	+	+	SYM
cana-1748	104	2	𝑔1	𝑔1	PROPN
cana-1748	104	3	,	,	PUNCT
cana-1748	104	4	−2𝛼(𝑔6	−2𝛼(𝑔6	PRON
cana-1748	104	5	−	−	PROPN
cana-1748	104	6	𝑔5	𝑔5	PROPN
cana-1748	104	7	)	)	PUNCT
cana-1748	105	1	+	+	SYM
cana-1748	105	2	𝑔6	𝑔6	NOUN
cana-1748	105	3	]	]	PUNCT
cana-1748	105	4	∗	∗	NOUN
cana-1748	105	5	[	[	X
cana-1748	105	6	2𝛼(ℎ3	2𝛼(ℎ3	NUM
cana-1748	105	7	−	−	NOUN
cana-1748	105	8	ℎ1	ℎ1	PROPN
cana-1748	105	9	)	)	PUNCT
cana-1748	105	10	+	+	CCONJ
cana-1748	105	11	ℎ1	ℎ1	PROPN
cana-1748	105	12	,	,	PUNCT
cana-1748	105	13	−2𝛼(ℎ6	−2𝛼(ℎ6	PROPN
cana-1748	105	14	−	−	PROPN
cana-1748	105	15	ℎ5	ℎ5	PROPN
cana-1748	105	16	)	)	PUNCT
cana-1748	105	17	+	+	CCONJ
cana-1748	105	18	ℎ6	ℎ6	PROPN
cana-1748	105	19	]	]	X
cana-1748	105	20	,	,	PUNCT
cana-1748	105	21	for	for	ADP
cana-1748	105	22	𝛼	𝛼	PROPN
cana-1748	105	23	∈	∈	PROPN
cana-1748	105	24	[	[	X
cana-1748	105	25	0,0.5	0,0.5	NUM
cana-1748	105	26	)	)	PUNCT
cana-1748	106	1	[	[	X
cana-1748	106	2	2𝛼(𝑔3	2𝛼(𝑔3	NUM
cana-1748	106	3	−	−	NOUN
cana-1748	106	4	𝑔2	𝑔2	NOUN
cana-1748	106	5	)	)	PUNCT
cana-1748	106	6	−	−	NOUN
cana-1748	107	1	𝑔3	𝑔3	ADJ
cana-1748	107	2	+	+	CCONJ
cana-1748	107	3	2𝑔2	2𝑔2	NUM
cana-1748	107	4	,	,	PUNCT
cana-1748	107	5	−2𝛼(𝑔5	−2𝛼(𝑔5	PROPN
cana-1748	107	6	−	−	PROPN
cana-1748	107	7	𝑔4	𝑔4	PROPN
cana-1748	107	8	)	)	PUNCT
cana-1748	108	1	+	+	CCONJ
cana-1748	108	2	2𝑔5	2𝑔5	NUM
cana-1748	108	3	−	−	PROPN
cana-1748	108	4	𝑔4	𝑔4	PROPN
cana-1748	108	5	]	]	X
cana-1748	108	6	∗	∗	NOUN
cana-1748	109	1	[	[	X
cana-1748	109	2	2𝛼(ℎ3	2𝛼(ℎ3	NUM
cana-1748	109	3	−	−	NOUN
cana-1748	109	4	ℎ2	ℎ2	NOUN
cana-1748	109	5	)	)	PUNCT
cana-1748	109	6	−	−	NOUN
cana-1748	109	7	ℎ3	ℎ3	NOUN
cana-1748	109	8	+	+	CCONJ
cana-1748	109	9	2ℎ2	2ℎ2	NUM
cana-1748	109	10	,	,	PUNCT
cana-1748	109	11	−2𝛼(ℎ5	−2𝛼(ℎ5	PROPN
cana-1748	109	12	−	−	PROPN
cana-1748	109	13	ℎ4	ℎ4	PROPN
cana-1748	109	14	)	)	PUNCT
cana-1748	110	1	+	+	NOUN
cana-1748	110	2	2ℎ5	2ℎ5	NUM
cana-1748	110	3	−	−	PROPN
cana-1748	110	4	ℎ4	ℎ4	NOUN
cana-1748	110	5	]	]	PUNCT
cana-1748	110	6	,	,	PUNCT
cana-1748	110	7	for	for	ADP
cana-1748	110	8	𝛼	𝛼	PROPN
cana-1748	110	9	∈	∈	PROPN
cana-1748	111	1	[	[	X
cana-1748	111	2	0.5,1	0.5,1	X
cana-1748	111	3	]	]	PUNCT
cana-1748	111	4	.	.	PUNCT
cana-1748	112	1	s𝛼	s𝛼	NOUN
cana-1748	112	2	=	=	PUNCT
cana-1748	113	1	[	[	X
cana-1748	113	2	2𝛼	2𝛼	PROPN
cana-1748	113	3	+	+	X
cana-1748	113	4	𝑔1	𝑔1	PROPN
cana-1748	113	5	,	,	PUNCT
cana-1748	113	6	−2𝛼	−2𝛼	PROPN
cana-1748	113	7	+	+	X
cana-1748	113	8	𝑔6	𝑔6	NOUN
cana-1748	113	9	]	]	PUNCT
cana-1748	113	10	for	for	ADP
cana-1748	113	11	𝛼	𝛼	PROPN
cana-1748	113	12	∈	∈	PROPN
cana-1748	113	13	[	[	X
cana-1748	113	14	0,0.5	0,0.5	NUM
cana-1748	113	15	)	)	PUNCT
cana-1748	113	16	t𝛼	t𝛼	NOUN
cana-1748	113	17	=	=	PUNCT
cana-1748	114	1	[	[	X
cana-1748	114	2	4𝛼	4𝛼	NOUN
cana-1748	114	3	+	+	X
cana-1748	114	4	ℎ1	ℎ1	PROPN
cana-1748	114	5	,	,	PUNCT
cana-1748	114	6	−4𝛼	−4𝛼	PROPN
cana-1748	114	7	+	+	CCONJ
cana-1748	114	8	ℎ6	ℎ6	ADJ
cana-1748	114	9	]	]	X
cana-1748	114	10	for	for	ADP
cana-1748	114	11	𝛼	𝛼	PROPN
cana-1748	114	12	∈	∈	PROPN
cana-1748	115	1	[	[	X
cana-1748	115	2	0.5,1	0.5,1	X
cana-1748	115	3	]	]	PUNCT
cana-1748	115	4	since	since	SCONJ
cana-1748	115	5	,	,	PUNCT
cana-1748	115	6	s𝛼	s𝛼	NOUN
cana-1748	115	7	∗	∗	NOUN
cana-1748	115	8	t𝛼	t𝛼	NOUN
cana-1748	115	9	=	=	SYM
cana-1748	116	1	[	[	X
cana-1748	116	2	(	(	PUNCT
cana-1748	116	3	2𝛼	2𝛼	PROPN
cana-1748	116	4	+	+	CCONJ
cana-1748	116	5	𝑔1)(4𝛼	𝑔1)(4𝛼	PROPN
cana-1748	116	6	+	+	CCONJ
cana-1748	116	7	ℎ1	ℎ1	PROPN
cana-1748	116	8	)	)	PUNCT
cana-1748	116	9	,	,	PUNCT
cana-1748	116	10	(	(	PUNCT
cana-1748	116	11	−2𝛼	−2𝛼	PROPN
cana-1748	116	12	+	+	CCONJ
cana-1748	116	13	𝑔6)(−4𝛼	𝑔6)(−4𝛼	PROPN
cana-1748	116	14	+	+	CCONJ
cana-1748	116	15	ℎ6	ℎ6	ADJ
cana-1748	116	16	)	)	PUNCT
cana-1748	116	17	]	]	PUNCT
cana-1748	116	18	4	4	NUM
cana-1748	116	19	if	if	SCONJ
cana-1748	116	20	we	we	PRON
cana-1748	116	21	assume	assume	VERB
cana-1748	116	22	two	two	NUM
cana-1748	116	23	hexagonal	hexagonal	ADJ
cana-1748	116	24	fuzzy	fuzzy	ADJ
cana-1748	116	25	numbers	number	NOUN
cana-1748	116	26	s	s	PART
cana-1748	116	27	=	=	SYM
cana-1748	116	28	(	(	PUNCT
cana-1748	116	29	𝑔1	𝑔1	PROPN
cana-1748	116	30	,	,	PUNCT
cana-1748	116	31	𝑔2	𝑔2	NOUN
cana-1748	116	32	,	,	PUNCT
cana-1748	116	33	𝑔3	𝑔3	ADJ
cana-1748	116	34	,	,	PUNCT
cana-1748	116	35	𝑔4	𝑔4	PROPN
cana-1748	116	36	,	,	PUNCT
cana-1748	116	37	𝑔5	𝑔5	NOUN
cana-1748	116	38	,	,	PUNCT
cana-1748	116	39	𝑔6	𝑔6	NOUN
cana-1748	116	40	)	)	PUNCT
cana-1748	116	41	and	and	CCONJ
cana-1748	116	42	h	h	NOUN
cana-1748	116	43	=	=	SYM
cana-1748	116	44	(	(	PUNCT
cana-1748	116	45	𝑡1	𝑡1	PROPN
cana-1748	116	46	,	,	PUNCT
cana-1748	116	47	𝑡2	𝑡2	PROPN
cana-1748	116	48	,	,	PUNCT
cana-1748	116	49	𝑡3	𝑡3	PROPN
cana-1748	116	50	,	,	PUNCT
cana-1748	116	51	𝑡4	𝑡4	NOUN
cana-1748	116	52	,	,	PUNCT
cana-1748	116	53	𝑡5	𝑡5	PROPN
cana-1748	116	54	,	,	PUNCT
cana-1748	116	55	𝑡6	𝑡6	NOUN
cana-1748	116	56	)	)	PUNCT
cana-1748	116	57	.	.	PUNCT
cana-1748	117	1	then	then	ADV
cana-1748	117	2	the	the	DET
cana-1748	117	3	division	division	NOUN
cana-1748	117	4	of	of	ADP
cana-1748	117	5	two	two	NUM
cana-1748	117	6	numbers	number	NOUN
cana-1748	117	7	.	.	PUNCT
cana-1748	118	1	proof	proof	NOUN
cana-1748	118	2	let	let	VERB
cana-1748	118	3	us	we	PRON
cana-1748	118	4	add	add	VERB
cana-1748	118	5	the	the	DET
cana-1748	118	6	alpha	alpha	NOUN
cana-1748	118	7	cut	cut	NOUN
cana-1748	118	8	s𝛼	s𝛼	NOUN
cana-1748	118	9	and	and	CCONJ
cana-1748	118	10	t𝛼	t𝛼	NOUN
cana-1748	118	11	of	of	ADP
cana-1748	118	12	s𝐻	s𝐻	ADJ
cana-1748	118	13	and	and	CCONJ
cana-1748	118	14	t𝐻	t𝐻	NOUN
cana-1748	118	15	using	use	VERB
cana-1748	118	16	interval	interval	NOUN
cana-1748	118	17	arithmetic	arithmetic	ADJ
cana-1748	118	18	.	.	PUNCT
cana-1748	119	1	s𝛼/t𝛼	s𝛼/t𝛼	NUM
cana-1748	119	2	=	=	SYM
cana-1748	119	3	{	{	PUNCT
cana-1748	120	1	[	[	X
cana-1748	120	2	2𝛼(𝑔3	2𝛼(𝑔3	NUM
cana-1748	120	3	−	−	PROPN
cana-1748	120	4	𝑔1	𝑔1	PROPN
cana-1748	120	5	)	)	PUNCT
cana-1748	120	6	+	+	SYM
cana-1748	120	7	𝑔1	𝑔1	PROPN
cana-1748	120	8	,	,	PUNCT
cana-1748	120	9	−2𝛼(𝑔6	−2𝛼(𝑔6	PRON
cana-1748	120	10	−	−	PROPN
cana-1748	120	11	𝑔5	𝑔5	PROPN
cana-1748	120	12	)	)	PUNCT
cana-1748	121	1	+	+	NUM
cana-1748	121	2	𝑔6]/	𝑔6]/	NOUN
cana-1748	121	3	[	[	X
cana-1748	121	4	2𝛼(ℎ3	2𝛼(ℎ3	NUM
cana-1748	121	5	−	−	NOUN
cana-1748	121	6	ℎ1	ℎ1	PROPN
cana-1748	121	7	)	)	PUNCT
cana-1748	121	8	+	+	CCONJ
cana-1748	121	9	ℎ6	ℎ6	ADJ
cana-1748	121	10	,	,	PUNCT
cana-1748	121	11	−2𝛼(ℎ6	−2𝛼(ℎ6	PROPN
cana-1748	121	12	−	−	PROPN
cana-1748	121	13	ℎ5	ℎ5	PROPN
cana-1748	121	14	)	)	PUNCT
cana-1748	121	15	+	+	CCONJ
cana-1748	121	16	ℎ6	ℎ6	PROPN
cana-1748	121	17	]	]	X
cana-1748	121	18	,	,	PUNCT
cana-1748	121	19	[	[	X
cana-1748	121	20	2𝛼(𝑔3	2𝛼(𝑔3	NUM
cana-1748	121	21	−	−	NOUN
cana-1748	121	22	𝑔2	𝑔2	NOUN
cana-1748	121	23	)	)	PUNCT
cana-1748	121	24	−	−	NOUN
cana-1748	121	25	𝑔3	𝑔3	ADJ
cana-1748	121	26	+	+	CCONJ
cana-1748	121	27	2𝑔2	2𝑔2	NUM
cana-1748	121	28	,	,	PUNCT
cana-1748	121	29	−2𝛼(𝑔5	−2𝛼(𝑔5	PROPN
cana-1748	121	30	−	−	PROPN
cana-1748	121	31	𝑔4	𝑔4	PROPN
cana-1748	121	32	)	)	PUNCT
cana-1748	122	1	+	+	CCONJ
cana-1748	122	2	2𝑔5	2𝑔5	NUM
cana-1748	122	3	−	−	NOUN
cana-1748	122	4	𝑔4]/	𝑔4]/	ADJ
cana-1748	122	5	[	[	PUNCT
cana-1748	122	6	2𝛼(ℎ3	2𝛼(ℎ3	NUM
cana-1748	122	7	−	−	NOUN
cana-1748	122	8	ℎ2	ℎ2	NOUN
cana-1748	122	9	)	)	PUNCT
cana-1748	122	10	−	−	NOUN
cana-1748	122	11	ℎ3	ℎ3	NOUN
cana-1748	122	12	+	+	CCONJ
cana-1748	122	13	2ℎ2	2ℎ2	NUM
cana-1748	122	14	,	,	PUNCT
cana-1748	122	15	−2𝛼(ℎ5	−2𝛼(ℎ5	PROPN
cana-1748	122	16	−	−	PROPN
cana-1748	122	17	ℎ4	ℎ4	PROPN
cana-1748	122	18	)	)	PUNCT
cana-1748	123	1	+	+	NOUN
cana-1748	123	2	2ℎ5	2ℎ5	NUM
cana-1748	123	3	−	−	PROPN
cana-1748	123	4	ℎ4	ℎ4	NOUN
cana-1748	123	5	]	]	PUNCT
cana-1748	123	6	,	,	PUNCT
cana-1748	123	7	for	for	ADP
cana-1748	123	8	𝛼	𝛼	PROPN
cana-1748	123	9	∈	∈	PROPN
cana-1748	123	10	[	[	X
cana-1748	123	11	0,0.5	0,0.5	NUM
cana-1748	123	12	)	)	PUNCT
cana-1748	123	13	s𝛼	s𝛼	NOUN
cana-1748	123	14	=	=	PUNCT
cana-1748	124	1	[	[	X
cana-1748	124	2	2𝛼	2𝛼	PROPN
cana-1748	124	3	+	+	X
cana-1748	124	4	𝑔1	𝑔1	PROPN
cana-1748	124	5	,	,	PUNCT
cana-1748	124	6	−2𝛼	−2𝛼	PROPN
cana-1748	124	7	+	+	X
cana-1748	124	8	𝑔6	𝑔6	NOUN
cana-1748	124	9	]	]	PUNCT
cana-1748	124	10	for	for	ADP
cana-1748	124	11	𝛼	𝛼	PROPN
cana-1748	124	12	∈	∈	PROPN
cana-1748	125	1	[	[	X
cana-1748	125	2	0.5,1	0.5,1	X
cana-1748	125	3	]	]	X
cana-1748	125	4	t𝛼	t𝛼	NOUN
cana-1748	125	5	=	=	PUNCT
cana-1748	126	1	[	[	X
cana-1748	126	2	2𝛼	2𝛼	NOUN
cana-1748	126	3	+	+	CCONJ
cana-1748	126	4	ℎ1	ℎ1	PROPN
cana-1748	126	5	,	,	PUNCT
cana-1748	126	6	−4𝛼	−4𝛼	PROPN
cana-1748	126	7	+	+	CCONJ
cana-1748	126	8	ℎ6	ℎ6	ADJ
cana-1748	126	9	]	]	X
cana-1748	126	10	for	for	ADP
cana-1748	126	11	𝛼	𝛼	PROPN
cana-1748	126	12	∈	∈	PROPN
cana-1748	127	1	[	[	X
cana-1748	127	2	0.5,1	0.5,1	X
cana-1748	127	3	]	]	PUNCT
cana-1748	127	4	since	since	SCONJ
cana-1748	127	5	,	,	PUNCT
cana-1748	127	6	s𝛼/t𝛼	s𝛼/t𝛼	NUM
cana-1748	127	7	=	=	SYM
cana-1748	128	1	[	[	X
cana-1748	128	2	(	(	PUNCT
cana-1748	128	3	2𝛼	2𝛼	PROPN
cana-1748	128	4	+	+	CCONJ
cana-1748	128	5	𝑔1)/(4𝛼	𝑔1)/(4𝛼	PROPN
cana-1748	128	6	+	+	CCONJ
cana-1748	128	7	ℎ6	ℎ6	ADJ
cana-1748	128	8	)	)	PUNCT
cana-1748	128	9	,	,	PUNCT
cana-1748	128	10	(	(	PUNCT
cana-1748	128	11	−2𝛼	−2𝛼	PROPN
cana-1748	128	12	+	+	NUM
cana-1748	128	13	𝑔6)/(−4𝛼	𝑔6)/(−4𝛼	NOUN
cana-1748	128	14	+	+	CCONJ
cana-1748	128	15	ℎ6	ℎ6	ADJ
cana-1748	128	16	)	)	PUNCT
cana-1748	128	17	]	]	PUNCT
cana-1748	128	18	4	4	NUM
cana-1748	128	19	new	new	ADJ
cana-1748	128	20	ranking	ranking	NOUN
cana-1748	128	21	function	function	NOUN
cana-1748	128	22	the	the	DET
cana-1748	128	23	classical	classical	ADJ
cana-1748	128	24	set	set	NOUN
cana-1748	128	25	i𝛼	i𝛼	ADP
cana-1748	128	26	called	call	VERB
cana-1748	128	27	alpha	alpha	NOUN
cana-1748	128	28	cut	cut	NOUN
cana-1748	128	29	set	set	VERB
cana-1748	128	30	is	be	AUX
cana-1748	128	31	the	the	DET
cana-1748	128	32	set	set	NOUN
cana-1748	128	33	of	of	ADP
cana-1748	128	34	elements	element	NOUN
cana-1748	128	35	whose	whose	DET
cana-1748	128	36	degree	degree	NOUN
cana-1748	128	37	of	of	ADP
cana-1748	128	38	membership	membership	NOUN
cana-1748	128	39	is	be	AUX
cana-1748	128	40	the	the	DET
cana-1748	128	41	set	set	NOUN
cana-1748	128	42	of	of	ADP
cana-1748	128	43	elements	element	NOUN
cana-1748	128	44	whose	whose	DET
cana-1748	128	45	degree	degree	NOUN
cana-1748	128	46	of	of	ADP
cana-1748	128	47	membership	membership	NOUN
cana-1748	128	48	in	in	ADP
cana-1748	128	49	i𝐻	i𝐻	PROPN
cana-1748	128	50	=	=	SYM
cana-1748	128	51	(	(	PUNCT
cana-1748	128	52	𝑛1	𝑛1	NOUN
cana-1748	128	53	,	,	PUNCT
cana-1748	128	54	𝑛2	𝑛2	NOUN
cana-1748	128	55	,	,	PUNCT
cana-1748	128	56	𝑛3	𝑛3	NOUN
cana-1748	128	57	,	,	PUNCT
cana-1748	128	58	𝑛4	𝑛4	NOUN
cana-1748	128	59	,	,	PUNCT
cana-1748	128	60	𝑛5	𝑛5	PROPN
cana-1748	128	61	,	,	PUNCT
cana-1748	128	62	𝑛6	𝑛6	PROPN
cana-1748	128	63	)	)	PUNCT
cana-1748	128	64	is	be	AUX
cana-1748	128	65	no	no	PRON
cana-1748	128	66	less	less	ADJ
cana-1748	128	67	than	than	ADP
cana-1748	128	68	,	,	PUNCT
cana-1748	128	69	𝛼	𝛼	VERB
cana-1748	128	70	it	it	PRON
cana-1748	128	71	is	be	AUX
cana-1748	128	72	defined	define	VERB
cana-1748	128	73	as	as	ADP
cana-1748	128	74	i	i	PRON
cana-1748	128	75	=	=	PUNCT
cana-1748	128	76	{	{	PUNCT
cana-1748	128	77	𝑥	𝑥	X
cana-1748	128	78	∈	∈	NOUN
cana-1748	128	79	u/𝜒i𝐻(𝑥	u/𝜒i𝐻(𝑥	PROPN
cana-1748	128	80	)	)	PUNCT
cana-1748	128	81	≥	≥	NOUN
cana-1748	128	82	𝛼	𝛼	NOUN
cana-1748	128	83	}	}	PUNCT
cana-1748	128	84	communications	communication	NOUN
cana-1748	128	85	on	on	ADP
cana-1748	128	86	applied	apply	VERB
cana-1748	128	87	nonlinear	nonlinear	ADJ
cana-1748	128	88	analysis	analysis	NOUN
cana-1748	128	89	issn	issn	NOUN
cana-1748	128	90	:	:	PUNCT
cana-1748	128	91	1074	1074	NUM
cana-1748	128	92	-	-	PUNCT
cana-1748	128	93	133x	133x	NUM
cana-1748	128	94	vol	vol	NOUN
cana-1748	128	95	32	32	NUM
cana-1748	128	96	no	no	NOUN
cana-1748	128	97	.	.	NOUN
cana-1748	128	98	2	2	NUM
cana-1748	128	99	(	(	PUNCT
cana-1748	128	100	2025	2025	NUM
cana-1748	128	101	)	)	PUNCT
cana-1748	128	102	371	371	NUM
cana-1748	128	103	https://internationalpubls.com	https://internationalpubls.com	X
cana-1748	128	104	=	=	PUNCT
cana-1748	128	105	{	{	PUNCT
cana-1748	128	106	[	[	X
cana-1748	128	107	p1(𝛼	p1(𝛼	NOUN
cana-1748	128	108	)	)	PUNCT
cana-1748	128	109	,	,	PUNCT
cana-1748	128	110	p2(𝛼	p2(𝛼	NOUN
cana-1748	128	111	)	)	PUNCT
cana-1748	128	112	]	]	PUNCT
cana-1748	128	113	,	,	PUNCT
cana-1748	128	114	for	for	ADP
cana-1748	128	115	𝛼	𝛼	PROPN
cana-1748	128	116	∈	∈	PROPN
cana-1748	128	117	[	[	X
cana-1748	128	118	0,0.5	0,0.5	NUM
cana-1748	128	119	)	)	PUNCT
cana-1748	129	1	[	[	X
cana-1748	129	2	q1(𝛼	q1(𝛼	NOUN
cana-1748	129	3	)	)	PUNCT
cana-1748	129	4	,	,	PUNCT
cana-1748	129	5	q2(𝛼	q2(𝛼	PROPN
cana-1748	129	6	)	)	PUNCT
cana-1748	129	7	]	]	PUNCT
cana-1748	129	8	,	,	PUNCT
cana-1748	129	9	for	for	ADP
cana-1748	129	10	𝛼	𝛼	PROPN
cana-1748	129	11	∈	∈	PROPN
cana-1748	130	1	[	[	X
cana-1748	130	2	0.5,1	0.5,1	X
cana-1748	130	3	]	]	X
cana-1748	130	4	=	=	X
cana-1748	130	5	{	{	PUNCT
cana-1748	130	6	[	[	X
cana-1748	130	7	p1(𝛼	p1(𝛼	NOUN
cana-1748	130	8	)	)	PUNCT
cana-1748	130	9	,	,	PUNCT
cana-1748	130	10	q1(𝛼	q1(𝛼	NOUN
cana-1748	130	11	)	)	PUNCT
cana-1748	130	12	]	]	PUNCT
cana-1748	130	13	,	,	PUNCT
cana-1748	130	14	for	for	ADP
cana-1748	130	15	𝛼	𝛼	PROPN
cana-1748	130	16	∈	∈	PROPN
cana-1748	130	17	[	[	X
cana-1748	130	18	0,0.5	0,0.5	NUM
cana-1748	130	19	)	)	PUNCT
cana-1748	131	1	[	[	X
cana-1748	131	2	p2(𝛼	p2(𝛼	X
cana-1748	131	3	)	)	PUNCT
cana-1748	131	4	,	,	PUNCT
cana-1748	131	5	q2(𝛼	q2(𝛼	PROPN
cana-1748	131	6	)	)	PUNCT
cana-1748	131	7	]	]	PUNCT
cana-1748	131	8	,	,	PUNCT
cana-1748	131	9	for	for	ADP
cana-1748	131	10	𝛼	𝛼	PROPN
cana-1748	131	11	∈	∈	PROPN
cana-1748	132	1	[	[	X
cana-1748	132	2	0.5,1	0.5,1	X
cana-1748	132	3	]	]	X
cana-1748	132	4	=	=	PUNCT
cana-1748	133	1	[	[	X
cana-1748	133	2	𝑛1	𝑛1	NOUN
cana-1748	133	3	+	+	CCONJ
cana-1748	133	4	𝛼(𝑛3	𝛼(𝑛3	PROPN
cana-1748	133	5	−	−	PROPN
cana-1748	133	6	𝑛1	𝑛1	PROPN
cana-1748	133	7	)	)	PUNCT
cana-1748	134	1	+	+	NUM
cana-1748	134	2	𝑛6	𝑛6	PROPN
cana-1748	134	3	+	+	CCONJ
cana-1748	134	4	𝛼(𝑛4	𝛼(𝑛4	NOUN
cana-1748	134	5	−	−	PROPN
cana-1748	134	6	𝑛6	𝑛6	PROPN
cana-1748	134	7	)	)	PUNCT
cana-1748	134	8	]	]	PUNCT
cana-1748	134	9	for	for	ADP
cana-1748	134	10	𝛼	𝛼	PROPN
cana-1748	134	11	∈	∈	PROPN
cana-1748	134	12	[	[	X
cana-1748	134	13	0,1	0,1	NUM
cana-1748	134	14	]	]	PUNCT
cana-1748	134	15	it	it	PRON
cana-1748	134	16	provides	provide	VERB
cana-1748	134	17	results	result	NOUN
cana-1748	134	18	,	,	PUNCT
cana-1748	134	19	i	i	PRON
cana-1748	134	20	is	be	AUX
cana-1748	134	21	a	a	DET
cana-1748	134	22	fuzzy	fuzzy	ADJ
cana-1748	134	23	number	number	NOUN
cana-1748	134	24	then	then	ADV
cana-1748	134	25	the	the	DET
cana-1748	134	26	ranking	ranking	NOUN
cana-1748	134	27	is	be	AUX
cana-1748	134	28	defined	define	VERB
cana-1748	134	29	by	by	ADP
cana-1748	134	30	r(i𝐻	r(i𝐻	NOUN
cana-1748	134	31	)	)	PUNCT
cana-1748	135	1	=	=	SYM
cana-1748	135	2	∫	∫	PROPN
cana-1748	135	3	0	0	NUM
cana-1748	135	4	1	1	NUM
cana-1748	135	5	 	 	SPACE
cana-1748	135	6	2(0.5)(iℎ𝛼	2(0.5)(iℎ𝛼	NUM
cana-1748	135	7	𝐿	𝐿	PROPN
cana-1748	135	8	,	,	PUNCT
cana-1748	135	9	iℎ𝛼	iℎ𝛼	NOUN
cana-1748	135	10	𝑈)𝐷𝛼	𝑈)𝐷𝛼	NOUN
cana-1748	135	11	where	where	SCONJ
cana-1748	135	12	(	(	PUNCT
cana-1748	135	13	iℎ𝛼	iℎ𝛼	NOUN
cana-1748	135	14	𝐿	𝐿	PROPN
cana-1748	135	15	,	,	PUNCT
cana-1748	135	16	iℎ𝛼	iℎ𝛼	NOUN
cana-1748	135	17	𝑈	𝑈	PROPN
cana-1748	135	18	)	)	PUNCT
cana-1748	135	19	is	be	AUX
cana-1748	135	20	the	the	DET
cana-1748	135	21	𝛼	𝛼	NOUN
cana-1748	135	22	level	level	NOUN
cana-1748	135	23	cut	cut	NOUN
cana-1748	135	24	of	of	ADP
cana-1748	135	25	the	the	DET
cana-1748	135	26	fuzzy	fuzzy	ADJ
cana-1748	135	27	number	number	NOUN
cana-1748	135	28	i𝐻	i𝐻	PROPN
cana-1748	135	29	r(i𝐻	r(i𝐻	NOUN
cana-1748	135	30	)	)	PUNCT
cana-1748	136	1	=	=	SYM
cana-1748	136	2	∫	∫	PROPN
cana-1748	136	3	0	0	NUM
cana-1748	136	4	1	1	NUM
cana-1748	136	5	 	 	SPACE
cana-1748	136	6	2(0.5)[𝑛1	2(0.5)[𝑛1	NUM
cana-1748	137	1	+	+	CCONJ
cana-1748	137	2	𝛼(𝑛3	𝛼(𝑛3	PROPN
cana-1748	137	3	−	−	PROPN
cana-1748	137	4	𝑛1	𝑛1	PROPN
cana-1748	137	5	)	)	PUNCT
cana-1748	138	1	+	+	NUM
cana-1748	138	2	𝑛6	𝑛6	PROPN
cana-1748	138	3	+	+	CCONJ
cana-1748	138	4	𝛼(𝑛4	𝛼(𝑛4	NOUN
cana-1748	138	5	−	−	NOUN
cana-1748	138	6	𝑛6)]𝐷𝛼	𝑛6)]𝐷𝛼	NOUN
cana-1748	138	7	5	5	NUM
cana-1748	138	8	description	description	NOUN
cana-1748	138	9	of	of	ADP
cana-1748	138	10	the	the	DET
cana-1748	138	11	model	model	NOUN
cana-1748	138	12	using	use	VERB
cana-1748	138	13	the	the	DET
cana-1748	138	14	ranking	ranking	ADJ
cana-1748	138	15	algorithm	algorithm	NOUN
cana-1748	138	16	r[i𝐻	r[i𝐻	PROPN
cana-1748	138	17	]	]	PUNCT
cana-1748	138	18	,	,	PUNCT
cana-1748	138	19	hexagonal	hexagonal	ADJ
cana-1748	138	20	fuzzy	fuzzy	ADJ
cana-1748	138	21	numbers	number	NOUN
cana-1748	138	22	are	be	AUX
cana-1748	138	23	transformed	transform	VERB
cana-1748	138	24	into	into	ADP
cana-1748	138	25	anticipated	anticipate	VERB
cana-1748	138	26	time	time	NOUN
cana-1748	138	27	(	(	PUNCT
cana-1748	138	28	normal	normal	ADJ
cana-1748	138	29	time	time	NOUN
cana-1748	138	30	)	)	PUNCT
cana-1748	138	31	for	for	ADP
cana-1748	138	32	every	every	DET
cana-1748	138	33	activity	activity	NOUN
cana-1748	138	34	.	.	PUNCT
cana-1748	139	1	these	these	DET
cana-1748	139	2	numbers	number	NOUN
cana-1748	139	3	are	be	AUX
cana-1748	139	4	interpreted	interpret	VERB
cana-1748	139	5	as	as	SCONJ
cana-1748	139	6	the	the	DET
cana-1748	139	7	typical	typical	ADJ
cana-1748	139	8	travel	travel	NOUN
cana-1748	139	9	time	time	NOUN
cana-1748	139	10	between	between	ADP
cana-1748	139	11	the	the	DET
cana-1748	139	12	nodes	node	NOUN
cana-1748	139	13	and	and	CCONJ
cana-1748	139	14	the	the	DET
cana-1748	139	15	provided	provide	VERB
cana-1748	139	16	algorithm	algorithm	NOUN
cana-1748	139	17	is	be	AUX
cana-1748	139	18	used	use	VERB
cana-1748	139	19	to	to	PART
cana-1748	139	20	find	find	VERB
cana-1748	139	21	the	the	DET
cana-1748	139	22	path	path	NOUN
cana-1748	139	23	,	,	PUNCT
cana-1748	139	24	or	or	CCONJ
cana-1748	139	25	least	least	ADJ
cana-1748	139	26	distance	distance	NOUN
cana-1748	139	27	.	.	PUNCT
cana-1748	140	1	5.1	5.1	NUM
cana-1748	140	2	algorithm	algorithm	NOUN
cana-1748	140	3	step	step	NOUN
cana-1748	140	4	1	1	NUM
cana-1748	140	5	:	:	PUNCT
cana-1748	140	6	create	create	VERB
cana-1748	140	7	the	the	DET
cana-1748	140	8	network	network	NOUN
cana-1748	140	9	diagram	diagram	NOUN
cana-1748	140	10	in	in	ADP
cana-1748	140	11	accordance	accordance	NOUN
cana-1748	140	12	with	with	ADP
cana-1748	140	13	the	the	DET
cana-1748	140	14	task	task	NOUN
cana-1748	140	15	assigned	assign	VERB
cana-1748	140	16	.	.	PUNCT
cana-1748	141	1	step	step	NOUN
cana-1748	141	2	2	2	NUM
cana-1748	141	3	:	:	PUNCT
cana-1748	141	4	find	find	VERB
cana-1748	141	5	the	the	DET
cana-1748	141	6	(	(	PUNCT
cana-1748	141	7	normal	normal	ADJ
cana-1748	141	8	)	)	PUNCT
cana-1748	141	9	expected	expect	VERB
cana-1748	141	10	time	time	NOUN
cana-1748	141	11	using	use	VERB
cana-1748	141	12	the	the	DET
cana-1748	141	13	ranking	rank	VERB
cana-1748	141	14	algorithm	algorithm	NOUN
cana-1748	141	15	given	give	VERB
cana-1748	141	16	the	the	DET
cana-1748	141	17	hfn	hfn	NOUN
cana-1748	141	18	.	.	PUNCT
cana-1748	142	1	step	step	NOUN
cana-1748	142	2	3	3	NUM
cana-1748	142	3	:	:	PUNCT
cana-1748	142	4	find	find	VERB
cana-1748	142	5	out	out	ADP
cana-1748	142	6	how	how	SCONJ
cana-1748	142	7	many	many	ADJ
cana-1748	142	8	paths	path	NOUN
cana-1748	142	9	,	,	PUNCT
cana-1748	142	10	or	or	CCONJ
cana-1748	142	11	possible	possible	ADJ
cana-1748	142	12	routes	route	NOUN
cana-1748	142	13	,	,	PUNCT
cana-1748	142	14	there	there	PRON
cana-1748	142	15	are	be	VERB
cana-1748	142	16	from	from	ADP
cana-1748	142	17	the	the	DET
cana-1748	142	18	starting	start	VERB
cana-1748	142	19	node	node	NOUN
cana-1748	142	20	to	to	ADP
cana-1748	142	21	the	the	DET
cana-1748	142	22	finishing	finish	VERB
cana-1748	142	23	nodes	node	NOUN
cana-1748	142	24	.	.	PUNCT
cana-1748	143	1	step	step	NOUN
cana-1748	143	2	4	4	NUM
cana-1748	143	3	:	:	PUNCT
cana-1748	143	4	finally	finally	ADV
cana-1748	143	5	,	,	PUNCT
cana-1748	143	6	dijkstra	dijkstra	PROPN
cana-1748	143	7	's	's	PART
cana-1748	143	8	algorithm	algorithm	NOUN
cana-1748	143	9	will	will	AUX
cana-1748	143	10	be	be	AUX
cana-1748	143	11	used	use	VERB
cana-1748	143	12	to	to	PART
cana-1748	143	13	find	find	VERB
cana-1748	143	14	the	the	DET
cana-1748	143	15	shortest	short	ADJ
cana-1748	143	16	path	path	NOUN
cana-1748	143	17	or	or	CCONJ
cana-1748	143	18	minimal	minimal	ADJ
cana-1748	143	19	traveling	traveling	ADJ
cana-1748	143	20	time	time	NOUN
cana-1748	143	21	.	.	PUNCT
cana-1748	144	1	6	6	NUM
cana-1748	144	2	numerical	numerical	ADJ
cana-1748	144	3	example-1	example-1	PROPN
cana-1748	144	4	think	think	NOUN
cana-1748	144	5	of	of	ADP
cana-1748	144	6	a	a	DET
cana-1748	144	7	project	project	NOUN
cana-1748	144	8	that	that	PRON
cana-1748	144	9	has	have	VERB
cana-1748	144	10	activities	activity	NOUN
cana-1748	144	11	and	and	CCONJ
cana-1748	144	12	nodes	node	NOUN
cana-1748	144	13	.	.	PUNCT
cana-1748	145	1	hfn	hfn	NOUN
cana-1748	145	2	is	be	AUX
cana-1748	145	3	a	a	DET
cana-1748	145	4	representation	representation	NOUN
cana-1748	145	5	of	of	ADP
cana-1748	145	6	the	the	DET
cana-1748	145	7	separation	separation	NOUN
cana-1748	145	8	between	between	ADP
cana-1748	145	9	them	they	PRON
cana-1748	145	10	.	.	PUNCT
cana-1748	146	1	step	step	NOUN
cana-1748	146	2	1	1	NUM
cana-1748	146	3	:	:	PUNCT
cana-1748	146	4	create	create	VERB
cana-1748	146	5	the	the	DET
cana-1748	146	6	network	network	NOUN
cana-1748	146	7	diagram	diagram	NOUN
cana-1748	146	8	in	in	ADP
cana-1748	146	9	accordance	accordance	NOUN
cana-1748	146	10	with	with	ADP
cana-1748	146	11	the	the	DET
cana-1748	146	12	task	task	NOUN
cana-1748	146	13	assigned	assign	VERB
cana-1748	146	14	.	.	PUNCT
cana-1748	147	1	communications	communication	NOUN
cana-1748	147	2	on	on	ADP
cana-1748	147	3	applied	apply	VERB
cana-1748	147	4	nonlinear	nonlinear	ADJ
cana-1748	147	5	analysis	analysis	NOUN
cana-1748	147	6	issn	issn	NOUN
cana-1748	147	7	:	:	PUNCT
cana-1748	147	8	1074	1074	NUM
cana-1748	147	9	-	-	PUNCT
cana-1748	147	10	133x	133x	NUM
cana-1748	147	11	vol	vol	NOUN
cana-1748	147	12	32	32	NUM
cana-1748	147	13	no	no	NOUN
cana-1748	147	14	.	.	NOUN
cana-1748	147	15	2	2	NUM
cana-1748	147	16	(	(	PUNCT
cana-1748	147	17	2025	2025	NUM
cana-1748	147	18	)	)	PUNCT
cana-1748	147	19	372	372	NUM
cana-1748	147	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-1748	147	21	activity	activity	NOUN
cana-1748	147	22	hfn	hfn	NOUN
cana-1748	147	23	1	1	NUM
cana-1748	147	24	−	−	NOUN
cana-1748	147	25	2	2	NUM
cana-1748	147	26	(	(	PUNCT
cana-1748	147	27	4,3,2,7,6,5	4,3,2,7,6,5	NUM
cana-1748	147	28	)	)	PUNCT
cana-1748	147	29	1	1	NUM
cana-1748	147	30	−	−	NOUN
cana-1748	147	31	3	3	NUM
cana-1748	147	32	(	(	PUNCT
cana-1748	147	33	6,5,1,14,3,9	6,5,1,14,3,9	NUM
cana-1748	147	34	)	)	PUNCT
cana-1748	147	35	3	3	NUM
cana-1748	147	36	−	−	NOUN
cana-1748	147	37	4	4	NUM
cana-1748	147	38	(	(	PUNCT
cana-1748	147	39	9,1,3,12,10,6	9,1,3,12,10,6	NUM
cana-1748	147	40	)	)	PUNCT
cana-1748	147	41	2	2	NUM
cana-1748	147	42	−	−	NOUN
cana-1748	147	43	4	4	NUM
cana-1748	147	44	(	(	PUNCT
cana-1748	147	45	1,3,10,9,7,18	1,3,10,9,7,18	NUM
cana-1748	147	46	)	)	PUNCT
cana-1748	147	47	3	3	NUM
cana-1748	147	48	−	−	NOUN
cana-1748	147	49	6	6	NUM
cana-1748	147	50	(	(	PUNCT
cana-1748	147	51	2,4,1,9,6,8	2,4,1,9,6,8	NUM
cana-1748	147	52	)	)	PUNCT
cana-1748	147	53	2	2	NUM
cana-1748	147	54	−	−	NOUN
cana-1748	147	55	6	6	NUM
cana-1748	147	56	(	(	PUNCT
cana-1748	147	57	8,4,3,14,1,9	8,4,3,14,1,9	NUM
cana-1748	147	58	)	)	PUNCT
cana-1748	147	59	5	5	NUM
cana-1748	147	60	−	−	NOUN
cana-1748	147	61	7	7	NUM
cana-1748	147	62	(	(	PUNCT
cana-1748	147	63	2,9,8,11,10,17	2,9,8,11,10,17	NUM
cana-1748	147	64	)	)	PUNCT
cana-1748	147	65	4	4	NUM
cana-1748	147	66	−	−	NOUN
cana-1748	147	67	7	7	NUM
cana-1748	147	68	(	(	PUNCT
cana-1748	147	69	4,8,10,12,13,18	4,8,10,12,13,18	NUM
cana-1748	147	70	)	)	PUNCT
cana-1748	147	71	6	6	NUM
cana-1748	147	72	−	−	NOUN
cana-1748	147	73	7	7	NUM
cana-1748	147	74	(	(	PUNCT
cana-1748	147	75	16,11,12,17,10,13	16,11,12,17,10,13	NUM
cana-1748	147	76	)	)	PUNCT
cana-1748	147	77	table	table	NOUN
cana-1748	147	78	1	1	NUM
cana-1748	147	79	:	:	PUNCT
cana-1748	147	80	activities	activity	NOUN
cana-1748	147	81	and	and	CCONJ
cana-1748	147	82	hexagonal	hexagonal	ADJ
cana-1748	147	83	fuzzy	fuzzy	ADJ
cana-1748	147	84	number	number	NOUN
cana-1748	147	85	step	step	NOUN
cana-1748	147	86	2	2	NUM
cana-1748	147	87	:	:	PUNCT
cana-1748	147	88	find	find	VERB
cana-1748	147	89	the	the	DET
cana-1748	147	90	(	(	PUNCT
cana-1748	147	91	normal	normal	ADJ
cana-1748	147	92	)	)	PUNCT
cana-1748	147	93	expected	expect	VERB
cana-1748	147	94	time	time	NOUN
cana-1748	147	95	using	use	VERB
cana-1748	147	96	the	the	DET
cana-1748	147	97	ranking	rank	VERB
cana-1748	147	98	algorithm	algorithm	NOUN
cana-1748	147	99	given	give	VERB
cana-1748	147	100	the	the	DET
cana-1748	147	101	hfn	hfn	NOUN
cana-1748	147	102	.	.	PUNCT
cana-1748	148	1	step	step	NOUN
cana-1748	148	2	3	3	NUM
cana-1748	148	3	:	:	PUNCT
cana-1748	148	4	find	find	VERB
cana-1748	148	5	out	out	ADP
cana-1748	148	6	how	how	SCONJ
cana-1748	148	7	many	many	ADJ
cana-1748	148	8	paths	path	NOUN
cana-1748	148	9	,	,	PUNCT
cana-1748	148	10	or	or	CCONJ
cana-1748	148	11	possible	possible	ADJ
cana-1748	148	12	routes	route	NOUN
cana-1748	148	13	,	,	PUNCT
cana-1748	148	14	there	there	PRON
cana-1748	148	15	are	be	VERB
cana-1748	148	16	from	from	ADP
cana-1748	148	17	the	the	DET
cana-1748	148	18	starting	start	VERB
cana-1748	148	19	node	node	NOUN
cana-1748	148	20	to	to	ADP
cana-1748	148	21	the	the	DET
cana-1748	148	22	finishing	finish	VERB
cana-1748	148	23	nodes	node	NOUN
cana-1748	148	24	.	.	PUNCT
cana-1748	149	1	1	1	NUM
cana-1748	149	2	−	−	NUM
cana-1748	149	3	2	2	NUM
cana-1748	149	4	−	−	NOUN
cana-1748	149	5	4	4	NUM
cana-1748	149	6	−	−	NOUN
cana-1748	149	7	7	7	NUM
cana-1748	149	8	45	45	NUM
cana-1748	149	9	1	1	NUM
cana-1748	149	10	−	−	NUM
cana-1748	149	11	2	2	NUM
cana-1748	149	12	−	−	NOUN
cana-1748	149	13	5	5	NUM
cana-1748	149	14	−	−	NOUN
cana-1748	149	15	7	7	NUM
cana-1748	149	16	45	45	NUM
cana-1748	149	17	1	1	NUM
cana-1748	149	18	−	−	NOUN
cana-1748	149	19	3	3	NUM
cana-1748	149	20	−	−	NOUN
cana-1748	149	21	4	4	NUM
cana-1748	149	22	−	−	NOUN
cana-1748	149	23	7	7	NUM
cana-1748	149	24	52	52	NUM
cana-1748	149	25	1	1	NUM
cana-1748	149	26	−	−	NUM
cana-1748	149	27	3	3	NUM
cana-1748	149	28	−	−	PROPN
cana-1748	149	29	6	6	NUM
cana-1748	149	30	−	−	NOUN
cana-1748	149	31	7	7	NUM
cana-1748	149	32	54	54	NUM
cana-1748	149	33	table	table	NOUN
cana-1748	149	34	2	2	NUM
cana-1748	149	35	:	:	PUNCT
cana-1748	149	36	path	path	NOUN
cana-1748	149	37	and	and	CCONJ
cana-1748	149	38	time	time	NOUN
cana-1748	149	39	using	use	VERB
cana-1748	149	40	shortest	short	ADJ
cana-1748	149	41	traveling	traveling	ADJ
cana-1748	149	42	path	path	NOUN
cana-1748	149	43	method	method	NOUN
cana-1748	149	44	step	step	NOUN
cana-1748	149	45	4	4	NUM
cana-1748	149	46	:	:	PUNCT
cana-1748	149	47	finally	finally	ADV
cana-1748	149	48	,	,	PUNCT
cana-1748	149	49	dijkstra	dijkstra	PROPN
cana-1748	149	50	's	's	PART
cana-1748	149	51	algorithm	algorithm	NOUN
cana-1748	149	52	will	will	AUX
cana-1748	149	53	be	be	AUX
cana-1748	149	54	used	use	VERB
cana-1748	149	55	to	to	PART
cana-1748	149	56	find	find	VERB
cana-1748	149	57	the	the	DET
cana-1748	149	58	shortest	short	ADJ
cana-1748	149	59	path	path	NOUN
cana-1748	149	60	or	or	CCONJ
cana-1748	149	61	minimal	minimal	ADJ
cana-1748	149	62	traveling	traveling	ADJ
cana-1748	149	63	time	time	NOUN
cana-1748	149	64	.	.	PUNCT
cana-1748	150	1	fuzzy	fuzzy	ADJ
cana-1748	150	2	shortest	short	ADJ
cana-1748	150	3	traveling	traveling	ADJ
cana-1748	150	4	path	path	NOUN
cana-1748	150	5	is	be	AUX
cana-1748	150	6	1	1	NUM
cana-1748	150	7	−	−	NUM
cana-1748	150	8	2	2	NUM
cana-1748	150	9	−	−	NOUN
cana-1748	150	10	4	4	NUM
cana-1748	150	11	−	−	NOUN
cana-1748	150	12	7	7	NUM
cana-1748	150	13	=	=	SYM
cana-1748	150	14	45	45	NUM
cana-1748	150	15	communications	communication	NOUN
cana-1748	150	16	on	on	ADP
cana-1748	150	17	applied	apply	VERB
cana-1748	150	18	nonlinear	nonlinear	ADJ
cana-1748	150	19	analysis	analysis	NOUN
cana-1748	150	20	issn	issn	NOUN
cana-1748	150	21	:	:	PUNCT
cana-1748	150	22	1074	1074	NUM
cana-1748	150	23	-	-	PUNCT
cana-1748	150	24	133x	133x	NUM
cana-1748	150	25	vol	vol	NOUN
cana-1748	150	26	32	32	NUM
cana-1748	150	27	no	no	NOUN
cana-1748	150	28	.	.	NOUN
cana-1748	150	29	2	2	NUM
cana-1748	150	30	(	(	PUNCT
cana-1748	150	31	2025	2025	NUM
cana-1748	150	32	)	)	PUNCT
cana-1748	150	33	373	373	NUM
cana-1748	150	34	https://internationalpubls.com	https://internationalpubls.com	X
cana-1748	150	35	7	7	NUM
cana-1748	150	36	numerical	numerical	ADJ
cana-1748	150	37	example-2	example-2	NUM
cana-1748	150	38	one	one	NUM
cana-1748	150	39	more	more	ADV
cana-1748	150	40	numerical	numerical	ADJ
cana-1748	150	41	illustration	illustration	NOUN
cana-1748	150	42	of	of	ADP
cana-1748	150	43	finding	find	VERB
cana-1748	150	44	the	the	DET
cana-1748	150	45	shortest	short	ADJ
cana-1748	150	46	path	path	NOUN
cana-1748	150	47	.	.	PUNCT
cana-1748	151	1	with	with	ADP
cana-1748	151	2	a	a	DET
cana-1748	151	3	few	few	ADJ
cana-1748	151	4	activities	activity	NOUN
cana-1748	151	5	and	and	CCONJ
cana-1748	151	6	nodes	node	NOUN
cana-1748	151	7	in	in	ADP
cana-1748	151	8	mind	mind	NOUN
cana-1748	151	9	,	,	PUNCT
cana-1748	151	10	the	the	DET
cana-1748	151	11	hfn	hfn	NOUN
cana-1748	151	12	represents	represent	VERB
cana-1748	151	13	the	the	DET
cana-1748	151	14	distance	distance	NOUN
cana-1748	151	15	between	between	ADP
cana-1748	151	16	them	they	PRON
cana-1748	151	17	.	.	PUNCT
cana-1748	152	1	step	step	NOUN
cana-1748	152	2	1	1	NUM
cana-1748	152	3	:	:	PUNCT
cana-1748	152	4	create	create	VERB
cana-1748	152	5	the	the	DET
cana-1748	152	6	network	network	NOUN
cana-1748	152	7	diagram	diagram	NOUN
cana-1748	152	8	in	in	ADP
cana-1748	152	9	accordance	accordance	NOUN
cana-1748	152	10	with	with	ADP
cana-1748	152	11	the	the	DET
cana-1748	152	12	task	task	NOUN
cana-1748	152	13	assigned	assign	VERB
cana-1748	152	14	.	.	PUNCT
cana-1748	153	1	table	table	NOUN
cana-1748	153	2	3	3	NUM
cana-1748	153	3	:	:	PUNCT
cana-1748	153	4	activities	activity	NOUN
cana-1748	153	5	and	and	CCONJ
cana-1748	153	6	hexagonal	hexagonal	ADJ
cana-1748	153	7	fuzzy	fuzzy	ADJ
cana-1748	153	8	number	number	NOUN
cana-1748	153	9	step	step	NOUN
cana-1748	153	10	2	2	NUM
cana-1748	153	11	:	:	PUNCT
cana-1748	153	12	find	find	VERB
cana-1748	153	13	the	the	DET
cana-1748	153	14	(	(	PUNCT
cana-1748	153	15	normal	normal	ADJ
cana-1748	153	16	)	)	PUNCT
cana-1748	153	17	expected	expect	VERB
cana-1748	153	18	time	time	NOUN
cana-1748	153	19	using	use	VERB
cana-1748	153	20	the	the	DET
cana-1748	153	21	ranking	rank	VERB
cana-1748	153	22	algorithm	algorithm	NOUN
cana-1748	153	23	given	give	VERB
cana-1748	153	24	the	the	DET
cana-1748	153	25	hfn	hfn	NOUN
cana-1748	153	26	.	.	PUNCT
cana-1748	154	1	step	step	NOUN
cana-1748	154	2	3	3	NUM
cana-1748	154	3	:	:	PUNCT
cana-1748	154	4	find	find	VERB
cana-1748	154	5	out	out	ADP
cana-1748	154	6	how	how	SCONJ
cana-1748	154	7	many	many	ADJ
cana-1748	154	8	paths	path	NOUN
cana-1748	154	9	,	,	PUNCT
cana-1748	154	10	or	or	CCONJ
cana-1748	154	11	possible	possible	ADJ
cana-1748	154	12	routes	route	NOUN
cana-1748	154	13	,	,	PUNCT
cana-1748	154	14	there	there	PRON
cana-1748	154	15	are	be	VERB
cana-1748	154	16	from	from	ADP
cana-1748	154	17	the	the	DET
cana-1748	154	18	starting	start	VERB
cana-1748	154	19	node	node	NOUN
cana-1748	154	20	to	to	ADP
cana-1748	154	21	the	the	DET
cana-1748	154	22	finishing	finish	VERB
cana-1748	154	23	nodes	node	NOUN
cana-1748	154	24	.	.	PUNCT
cana-1748	155	1	1	1	NUM
cana-1748	155	2	−	−	NUM
cana-1748	155	3	2	2	NUM
cana-1748	155	4	−	−	NOUN
cana-1748	155	5	3	3	NUM
cana-1748	155	6	−	−	NOUN
cana-1748	155	7	4	4	NUM
cana-1748	155	8	55	55	NUM
cana-1748	155	9	1	1	NUM
cana-1748	155	10	−	−	NUM
cana-1748	155	11	6	6	NUM
cana-1748	155	12	−	−	NOUN
cana-1748	155	13	5	5	NUM
cana-1748	155	14	−	−	NOUN
cana-1748	155	15	4	4	NUM
cana-1748	155	16	35	35	NUM
cana-1748	155	17	1	1	NUM
cana-1748	155	18	−	−	NUM
cana-1748	155	19	6	6	NUM
cana-1748	155	20	−	−	NOUN
cana-1748	155	21	2	2	NUM
cana-1748	155	22	−	−	NOUN
cana-1748	155	23	3	3	NUM
cana-1748	155	24	−	−	PROPN
cana-1748	155	25	4	4	NUM
cana-1748	155	26	68	68	NUM
cana-1748	155	27	communications	communication	NOUN
cana-1748	155	28	on	on	ADP
cana-1748	155	29	applied	apply	VERB
cana-1748	155	30	nonlinear	nonlinear	ADJ
cana-1748	155	31	analysis	analysis	NOUN
cana-1748	155	32	issn	issn	NOUN
cana-1748	155	33	:	:	PUNCT
cana-1748	155	34	1074	1074	NUM
cana-1748	155	35	-	-	PUNCT
cana-1748	155	36	133x	133x	NUM
cana-1748	155	37	vol	vol	NOUN
cana-1748	155	38	32	32	NUM
cana-1748	155	39	no	no	NOUN
cana-1748	155	40	.	.	NOUN
cana-1748	155	41	2	2	NUM
cana-1748	155	42	(	(	PUNCT
cana-1748	155	43	2025	2025	NUM
cana-1748	155	44	)	)	PUNCT
cana-1748	155	45	374	374	NUM
cana-1748	155	46	https://internationalpubls.com	https://internationalpubls.com	X
cana-1748	155	47	1	1	NUM
cana-1748	155	48	−	−	NOUN
cana-1748	155	49	6	6	NUM
cana-1748	155	50	−	−	NOUN
cana-1748	155	51	5	5	NUM
cana-1748	155	52	−	−	NOUN
cana-1748	155	53	3	3	NUM
cana-1748	155	54	−	−	PROPN
cana-1748	155	55	4	4	NUM
cana-1748	155	56	64	64	NUM
cana-1748	155	57	1	1	NUM
cana-1748	155	58	−	−	NUM
cana-1748	155	59	2	2	NUM
cana-1748	155	60	−	−	PROPN
cana-1748	155	61	3	3	NUM
cana-1748	155	62	−	−	PROPN
cana-1748	155	63	6	6	NUM
cana-1748	155	64	−	−	NOUN
cana-1748	155	65	5	5	NUM
cana-1748	155	66	−	−	NOUN
cana-1748	155	67	4	4	NUM
cana-1748	155	68	77	77	NUM
cana-1748	155	69	table	table	NOUN
cana-1748	155	70	4	4	NUM
cana-1748	155	71	:	:	PUNCT
cana-1748	155	72	path	path	NOUN
cana-1748	155	73	and	and	CCONJ
cana-1748	155	74	time	time	NOUN
cana-1748	155	75	using	use	VERB
cana-1748	155	76	shortest	short	ADJ
cana-1748	155	77	traveling	traveling	ADJ
cana-1748	155	78	path	path	NOUN
cana-1748	155	79	method	method	NOUN
cana-1748	155	80	step	step	NOUN
cana-1748	155	81	4	4	NUM
cana-1748	155	82	:	:	PUNCT
cana-1748	155	83	finally	finally	ADV
cana-1748	155	84	,	,	PUNCT
cana-1748	155	85	"	"	PUNCT
cana-1748	155	86	dijkstra	dijkstra	PROPN
cana-1748	155	87	's	's	PART
cana-1748	155	88	algorithm	algorithm	NOUN
cana-1748	155	89	"	"	PUNCT
cana-1748	155	90	will	will	AUX
cana-1748	155	91	be	be	AUX
cana-1748	155	92	used	use	VERB
cana-1748	155	93	to	to	PART
cana-1748	155	94	find	find	VERB
cana-1748	155	95	the	the	DET
cana-1748	155	96	shortest	short	ADJ
cana-1748	155	97	path	path	NOUN
cana-1748	155	98	or	or	CCONJ
cana-1748	155	99	minimal	minimal	ADJ
cana-1748	155	100	traveling	traveling	ADJ
cana-1748	155	101	time	time	NOUN
cana-1748	155	102	.	.	PUNCT
cana-1748	156	1	fuzzy	fuzzy	ADJ
cana-1748	156	2	shortest	short	ADJ
cana-1748	156	3	traveling	traveling	ADJ
cana-1748	156	4	path	path	NOUN
cana-1748	156	5	is	be	AUX
cana-1748	156	6	1	1	NUM
cana-1748	156	7	−	−	NOUN
cana-1748	156	8	6	6	NUM
cana-1748	156	9	−	−	NOUN
cana-1748	156	10	5	5	NUM
cana-1748	156	11	−	−	NOUN
cana-1748	156	12	4	4	NUM
cana-1748	156	13	=	=	SYM
cana-1748	156	14	35	35	NUM
cana-1748	156	15	8	8	NUM
cana-1748	156	16	conclusion	conclusion	NOUN
cana-1748	156	17	the	the	DET
cana-1748	156	18	ranking	rank	VERB
cana-1748	156	19	approach	approach	NOUN
cana-1748	156	20	is	be	AUX
cana-1748	156	21	used	use	VERB
cana-1748	156	22	in	in	ADP
cana-1748	156	23	this	this	DET
cana-1748	156	24	paper	paper	NOUN
cana-1748	156	25	to	to	PART
cana-1748	156	26	transform	transform	VERB
cana-1748	156	27	hexagonal	hexagonal	ADJ
cana-1748	156	28	fuzzy	fuzzy	ADJ
cana-1748	156	29	numbers	number	NOUN
cana-1748	156	30	into	into	ADP
cana-1748	156	31	expected	expect	VERB
cana-1748	156	32	time	time	NOUN
cana-1748	156	33	,	,	PUNCT
cana-1748	156	34	or	or	CCONJ
cana-1748	156	35	standard	standard	ADJ
cana-1748	156	36	time	time	NOUN
cana-1748	156	37	,	,	PUNCT
cana-1748	156	38	for	for	ADP
cana-1748	156	39	each	each	DET
cana-1748	156	40	activity	activity	NOUN
cana-1748	156	41	.	.	PUNCT
cana-1748	157	1	thus	thus	ADV
cana-1748	157	2	,	,	PUNCT
cana-1748	157	3	using	use	VERB
cana-1748	157	4	the	the	DET
cana-1748	157	5	dijkstra	dijkstra	ADJ
cana-1748	157	6	algorithm	algorithm	NOUN
cana-1748	157	7	,	,	PUNCT
cana-1748	157	8	the	the	DET
cana-1748	157	9	fuzzy	fuzzy	ADJ
cana-1748	157	10	shortest	short	ADJ
cana-1748	157	11	path	path	NOUN
cana-1748	157	12	is	be	AUX
cana-1748	157	13	found	find	VERB
cana-1748	157	14	.	.	PUNCT
cana-1748	158	1	it	it	PRON
cana-1748	158	2	assists	assist	VERB
cana-1748	158	3	decision	decision	NOUN
cana-1748	158	4	makers	maker	NOUN
cana-1748	158	5	in	in	ADP
cana-1748	158	6	selecting	select	VERB
cana-1748	158	7	the	the	DET
cana-1748	158	8	optimal	optimal	ADJ
cana-1748	158	9	,	,	PUNCT
cana-1748	158	10	shortest	short	ADJ
cana-1748	158	11	path	path	NOUN
cana-1748	158	12	in	in	ADP
cana-1748	158	13	a	a	DET
cana-1748	158	14	fuzzy	fuzzy	ADJ
cana-1748	158	15	environment	environment	NOUN
cana-1748	158	16	by	by	ADP
cana-1748	158	17	applying	apply	VERB
cana-1748	158	18	the	the	DET
cana-1748	158	19	ranking	ranking	ADJ
cana-1748	158	20	algorithm	algorithm	NOUN
cana-1748	158	21	.	.	PUNCT
cana-1748	159	1	9	9	NUM
cana-1748	159	2	declaration	declaration	NOUN
cana-1748	159	3	9.1	9.1	NUM
cana-1748	159	4	funding	funding	NOUN
cana-1748	159	5	of	of	ADP
cana-1748	159	6	interests	interest	NOUN
cana-1748	159	7	:	:	PUNCT
cana-1748	159	8	no	no	DET
cana-1748	159	9	funding	funding	NOUN
cana-1748	159	10	was	be	AUX
cana-1748	159	11	received	receive	VERB
cana-1748	159	12	to	to	PART
cana-1748	159	13	assist	assist	VERB
cana-1748	159	14	with	with	ADP
cana-1748	159	15	the	the	DET
cana-1748	159	16	preparation	preparation	NOUN
cana-1748	159	17	of	of	ADP
cana-1748	159	18	this	this	DET
cana-1748	159	19	manuscript	manuscript	NOUN
cana-1748	159	20	.	.	PUNCT
cana-1748	160	1	9.2	9.2	NUM
cana-1748	160	2	conflicts	conflict	NOUN
cana-1748	160	3	of	of	ADP
cana-1748	160	4	interests	interest	NOUN
cana-1748	160	5	:	:	PUNCT
cana-1748	160	6	the	the	DET
cana-1748	160	7	authors	author	NOUN
cana-1748	160	8	have	have	VERB
cana-1748	160	9	no	no	DET
cana-1748	160	10	compelling	compelling	ADJ
cana-1748	160	11	interests	interest	NOUN
cana-1748	160	12	to	to	PART
cana-1748	160	13	declare	declare	VERB
cana-1748	160	14	that	that	PRON
cana-1748	160	15	are	be	AUX
cana-1748	160	16	relevant	relevant	ADJ
cana-1748	160	17	to	to	ADP
cana-1748	160	18	the	the	DET
cana-1748	160	19	content	content	NOUN
cana-1748	160	20	of	of	ADP
cana-1748	160	21	this	this	DET
cana-1748	160	22	article	article	NOUN
cana-1748	160	23	.	.	PUNCT
cana-1748	161	1	refrences	refrence	VERB
cana-1748	161	2	[	[	X
cana-1748	161	3	1	1	X
cana-1748	161	4	]	]	X
cana-1748	161	5	abbasi.f	abbasi.f	PROPN
cana-1748	161	6	and	and	CCONJ
cana-1748	161	7	allahviranloo.t	allahviranloo.t	PROPN
cana-1748	161	8	(	(	PUNCT
cana-1748	161	9	2021	2021	NUM
cana-1748	161	10	)	)	PUNCT
cana-1748	161	11	the	the	DET
cana-1748	161	12	fuzzy	fuzzy	ADJ
cana-1748	161	13	arithmetic	arithmetic	ADJ
cana-1748	161	14	operations	operation	NOUN
cana-1748	161	15	of	of	ADP
cana-1748	161	16	transmission	transmission	NOUN
cana-1748	161	17	average	average	NOUN
cana-1748	161	18	on	on	ADP
cana-1748	161	19	pseudohexagonal	pseudohexagonal	ADJ
cana-1748	161	20	fuzzy	fuzzy	ADJ
cana-1748	161	21	numbers	number	NOUN
cana-1748	161	22	and	and	CCONJ
cana-1748	161	23	its	its	PRON
cana-1748	161	24	application	application	NOUN
cana-1748	161	25	in	in	ADP
cana-1748	161	26	fuzzy	fuzzy	ADJ
cana-1748	161	27	system	system	NOUN
cana-1748	161	28	reliability	reliability	NOUN
cana-1748	161	29	analysis	analysis	NOUN
cana-1748	161	30	,	,	PUNCT
cana-1748	161	31	fuzzy	fuzzy	ADJ
cana-1748	161	32	information	information	NOUN
cana-1748	161	33	and	and	CCONJ
cana-1748	161	34	engineering	engineering	NOUN
cana-1748	161	35	,	,	PUNCT
cana-1748	161	36	volume	volume	NOUN
cana-1748	161	37	13,58	13,58	NUM
cana-1748	161	38	-	-	SYM
cana-1748	161	39	78	78	NUM
cana-1748	162	1	[	[	X
cana-1748	162	2	2	2	NUM
cana-1748	162	3	]	]	X
cana-1748	162	4	ching	ching	NOUN
cana-1748	162	5	-	-	PUNCT
cana-1748	162	6	hsue	hsue	PROPN
cana-1748	162	7	cheng	cheng	PROPN
cana-1748	162	8	(	(	PUNCT
cana-1748	162	9	1998	1998	NUM
cana-1748	162	10	)	)	PUNCT
cana-1748	162	11	a	a	DET
cana-1748	162	12	new	new	ADJ
cana-1748	162	13	approach	approach	NOUN
cana-1748	162	14	for	for	ADP
cana-1748	162	15	ranking	rank	VERB
cana-1748	162	16	fuzzy	fuzzy	ADJ
cana-1748	162	17	numbers	number	NOUN
cana-1748	162	18	by	by	ADP
cana-1748	162	19	distance	distance	NOUN
cana-1748	162	20	method	method	NOUN
cana-1748	162	21	,	,	PUNCT
cana-1748	162	22	a	a	DET
cana-1748	162	23	new	new	ADJ
cana-1748	162	24	approach	approach	NOUN
cana-1748	162	25	for	for	ADP
cana-1748	162	26	ranking	rank	VERB
cana-1748	162	27	fuzzy	fuzzy	ADJ
cana-1748	162	28	numbers	number	NOUN
cana-1748	162	29	by	by	ADP
cana-1748	162	30	distance	distance	NOUN
cana-1748	162	31	method	method	NOUN
cana-1748	162	32	,	,	PUNCT
cana-1748	162	33	volume	volume	NOUN
cana-1748	162	34	95	95	NUM
cana-1748	162	35	,	,	PUNCT
cana-1748	162	36	307	307	NUM
cana-1748	162	37	-	-	SYM
cana-1748	162	38	317	317	NUM
cana-1748	162	39	.	.	PUNCT
cana-1748	163	1	[	[	X
cana-1748	163	2	3	3	NUM
cana-1748	163	3	]	]	X
cana-1748	163	4	deng	deng	PROPN
cana-1748	163	5	feng	feng	PROPN
cana-1748	163	6	,	,	PUNCT
cana-1748	163	7	jiang	jiang	PROPN
cana-1748	163	8	xia	xia	PROPN
cana-1748	163	9	nan	nan	PROPN
cana-1748	163	10	,	,	PUNCT
cana-1748	163	11	mao	mao	PROPN
cana-1748	163	12	jun	jun	PROPN
cana-1748	163	13	zhang	zhang	PROPN
cana-1748	163	14	,	,	PUNCT
cana-1748	163	15	venkataraman	venkataraman	PROPN
cana-1748	163	16	.	.	PUNCT
cana-1748	164	1	y	y	PROPN
cana-1748	164	2	and	and	CCONJ
cana-1748	164	3	balas.e.v	balas.e.v	PROPN
cana-1748	164	4	(	(	PUNCT
cana-1748	164	5	2010	2010	NUM
cana-1748	164	6	)	)	PUNCT
cana-1748	164	7	a	a	DET
cana-1748	164	8	ranking	ranking	NOUN
cana-1748	164	9	method	method	NOUN
cana-1748	164	10	of	of	ADP
cana-1748	164	11	triangular	triangular	NOUN
cana-1748	164	12	intuitionistic	intuitionistic	ADJ
cana-1748	164	13	fuzzy	fuzzy	ADJ
cana-1748	164	14	numbers	number	NOUN
cana-1748	164	15	and	and	CCONJ
cana-1748	164	16	application	application	NOUN
cana-1748	164	17	to	to	ADP
cana-1748	164	18	decision	decision	NOUN
cana-1748	164	19	making	making	NOUN
cana-1748	164	20	,	,	PUNCT
cana-1748	164	21	international	international	ADJ
cana-1748	164	22	journal	journal	NOUN
cana-1748	164	23	of	of	ADP
cana-1748	164	24	computational	computational	ADJ
cana-1748	164	25	intelligence	intelligence	NOUN
cana-1748	164	26	systems	system	NOUN
cana-1748	164	27	,	,	PUNCT
cana-1748	164	28	volume	volume	NOUN
cana-1748	164	29	3	3	NUM
cana-1748	164	30	,	,	PUNCT
cana-1748	164	31	522	522	NUM
cana-1748	164	32	-	-	SYM
cana-1748	164	33	530	530	NUM
cana-1748	164	34	.	.	PUNCT
cana-1748	165	1	[	[	X
cana-1748	165	2	4	4	X
cana-1748	165	3	]	]	PUNCT
cana-1748	165	4	kirtiwant	kirtiwant	ADJ
cana-1748	165	5	p.	p.	NOUN
cana-1748	165	6	and	and	CCONJ
cana-1748	165	7	pathade.a	pathade.a	PROPN
cana-1748	165	8	(	(	PUNCT
cana-1748	165	9	2016	2016	NUM
cana-1748	165	10	)	)	PUNCT
cana-1748	165	11	optimal	optimal	ADJ
cana-1748	165	12	solution	solution	NOUN
cana-1748	165	13	of	of	ADP
cana-1748	165	14	balanced	balanced	ADJ
cana-1748	165	15	and	and	CCONJ
cana-1748	165	16	unbalanced	unbalanced	ADJ
cana-1748	165	17	fuzzy	fuzzy	ADJ
cana-1748	165	18	transportation	transportation	NOUN
cana-1748	165	19	problem	problem	NOUN
cana-1748	165	20	using	use	VERB
cana-1748	165	21	hexagonal	hexagonal	ADJ
cana-1748	165	22	fuzzy	fuzzy	ADJ
cana-1748	165	23	numbers	number	NOUN
cana-1748	165	24	,	,	PUNCT
cana-1748	165	25	international	international	ADJ
cana-1748	165	26	journal	journal	NOUN
cana-1748	165	27	of	of	ADP
cana-1748	165	28	mathematical	mathematical	ADJ
cana-1748	165	29	research	research	NOUN
cana-1748	165	30	,	,	PUNCT
cana-1748	165	31	volume	volume	NOUN
cana-1748	165	32	5(2	5(2	NUM
cana-1748	165	33	)	)	PUNCT
cana-1748	165	34	,	,	PUNCT
cana-1748	165	35	131	131	NUM
cana-1748	165	36	-	-	SYM
cana-1748	165	37	137	137	NUM
cana-1748	165	38	.	.	PUNCT
cana-1748	166	1	[	[	X
cana-1748	166	2	5	5	X
cana-1748	166	3	]	]	X
cana-1748	166	4	lakshmana	lakshmana	PROPN
cana-1748	166	5	gomathi	gomathi	PROPN
cana-1748	166	6	nayagam.v	nayagam.v	PROPN
cana-1748	166	7	,	,	PUNCT
cana-1748	166	8	jagadeeswari	jagadeeswari	PROPN
cana-1748	166	9	murugan	murugan	PROPN
cana-1748	166	10	,	,	PUNCT
cana-1748	166	11	and	and	CCONJ
cana-1748	166	12	suriyapriya.k	suriyapriya.k	X
cana-1748	166	13	(	(	PUNCT
cana-1748	166	14	2020	2020	NUM
cana-1748	166	15	)	)	PUNCT
cana-1748	166	16	hexagonal	hexagonal	ADJ
cana-1748	166	17	fuzzy	fuzzy	ADJ
cana-1748	166	18	number	number	NOUN
cana-1748	166	19	inadvertences	inadvertence	NOUN
cana-1748	166	20	and	and	CCONJ
cana-1748	166	21	its	its	PRON
cana-1748	166	22	applications	application	NOUN
cana-1748	166	23	to	to	ADP
cana-1748	166	24	mcdm	mcdm	ADJ
cana-1748	166	25	and	and	CCONJ
cana-1748	166	26	hffls	hffls	ADJ
cana-1748	166	27	based	base	VERB
cana-1748	166	28	on	on	ADP
cana-1748	166	29	complete	complete	ADJ
cana-1748	166	30	ranking	ranking	NOUN
cana-1748	166	31	by	by	ADP
cana-1748	166	32	score	score	NOUN
cana-1748	166	33	functions	function	NOUN
cana-1748	166	34	,	,	PUNCT
cana-1748	166	35	computational	computational	ADJ
cana-1748	166	36	and	and	CCONJ
cana-1748	166	37	applied	applied	ADJ
cana-1748	166	38	mathematics	mathematic	NOUN
cana-1748	166	39	,	,	PUNCT
cana-1748	166	40	volume	volume	NOUN
cana-1748	166	41	39,323	39,323	NUM
cana-1748	166	42	.	.	PUNCT
cana-1748	167	1	[	[	X
cana-1748	167	2	6	6	NUM
cana-1748	167	3	]	]	PUNCT
cana-1748	167	4	najeeb	najeeb	PROPN
cana-1748	167	5	alam	alam	PROPN
cana-1748	167	6	khan	khan	PROPN
cana-1748	167	7	,	,	PUNCT
cana-1748	167	8	oyoon	oyoon	PROPN
cana-1748	167	9	abdul	abdul	PROPN
cana-1748	167	10	razzaq	razzaq	PROPN
cana-1748	167	11	,	,	PUNCT
cana-1748	167	12	avishek	avishek	PROPN
cana-1748	167	13	chakraborty	chakraborty	PROPN
cana-1748	167	14	,	,	PUNCT
cana-1748	167	15	sankar	sankar	NOUN
cana-1748	167	16	parsad	parsad	PROPN
cana-1748	167	17	mondal	mondal	PROPN
cana-1748	167	18	,	,	PUNCT
cana-1748	167	19	and	and	CCONJ
cana-1748	167	20	shariful	shariful	ADJ
cana-1748	167	21	alam	alam	PROPN
cana-1748	167	22	(	(	PUNCT
cana-1748	167	23	2020	2020	NUM
cana-1748	167	24	)	)	PUNCT
cana-1748	167	25	measures	measure	NOUN
cana-1748	167	26	of	of	ADP
cana-1748	167	27	linear	linear	ADJ
cana-1748	167	28	and	and	CCONJ
cana-1748	167	29	nonlinear	nonlinear	ADJ
cana-1748	167	30	interval	interval	NOUN
cana-1748	167	31	-	-	PUNCT
cana-1748	167	32	valued	value	VERB
cana-1748	167	33	hexagonal	hexagonal	ADJ
cana-1748	167	34	fuzzy	fuzzy	ADJ
cana-1748	167	35	number	number	NOUN
cana-1748	167	36	,	,	PUNCT
cana-1748	167	37	international	international	ADJ
cana-1748	167	38	journal	journal	NOUN
cana-1748	167	39	of	of	ADP
cana-1748	167	40	fuzzy	fuzzy	ADJ
cana-1748	167	41	system	system	NOUN
cana-1748	167	42	applications	application	NOUN
cana-1748	167	43	,	,	PUNCT
cana-1748	167	44	volume	volume	NOUN
cana-1748	167	45	9,40	9,40	NUM
cana-1748	167	46	.	.	PUNCT
cana-1748	168	1	[	[	X
cana-1748	168	2	7	7	NUM
cana-1748	168	3	]	]	SYM
cana-1748	168	4	saeidifar.a	saeidifar.a	PUNCT
cana-1748	168	5	(	(	PUNCT
cana-1748	168	6	2011	2011	NUM
cana-1748	168	7	)	)	PUNCT
cana-1748	168	8	application	application	NOUN
cana-1748	168	9	of	of	ADP
cana-1748	168	10	weighting	weight	VERB
cana-1748	168	11	functions	function	NOUN
cana-1748	168	12	to	to	ADP
cana-1748	168	13	the	the	DET
cana-1748	168	14	ranking	ranking	NOUN
cana-1748	168	15	of	of	ADP
cana-1748	168	16	fuzzy	fuzzy	ADJ
cana-1748	168	17	numbers	number	NOUN
cana-1748	168	18	,	,	PUNCT
cana-1748	168	19	computers	computer	NOUN
cana-1748	168	20	and	and	CCONJ
cana-1748	168	21	mathematics	mathematic	NOUN
cana-1748	168	22	with	with	ADP
cana-1748	168	23	applications	application	NOUN
cana-1748	168	24	,	,	PUNCT
cana-1748	168	25	volume	volume	NOUN
cana-1748	168	26	62	62	NUM
cana-1748	168	27	,	,	PUNCT
cana-1748	168	28	2246	2246	NUM
cana-1748	168	29	2258	2258	NUM
cana-1748	168	30	.	.	PUNCT
cana-1748	169	1	[	[	X
cana-1748	169	2	8	8	NUM
cana-1748	169	3	]	]	X
cana-1748	169	4	sangeetha	sangeetha	NOUN
cana-1748	169	5	.	.	PUNCT
cana-1748	170	1	k	k	PROPN
cana-1748	170	2	and	and	CCONJ
cana-1748	170	3	parimala	parimala	PROPN
cana-1748	170	4	.	.	PUNCT
cana-1748	171	1	m	m	VERB
cana-1748	171	2	(	(	PUNCT
cana-1748	171	3	2021	2021	NUM
cana-1748	171	4	)	)	PUNCT
cana-1748	172	1	on	on	ADP
cana-1748	172	2	solving	solve	VERB
cana-1748	172	3	a	a	DET
cana-1748	172	4	fuzzy	fuzzy	ADJ
cana-1748	172	5	game	game	NOUN
cana-1748	172	6	problem	problem	NOUN
cana-1748	172	7	using	use	VERB
cana-1748	172	8	hexagonal	hexagonal	ADJ
cana-1748	172	9	fuzzy	fuzzy	ADJ
cana-1748	172	10	numbers	number	NOUN
cana-1748	172	11	,	,	PUNCT
cana-1748	172	12	materials	material	NOUN
cana-1748	172	13	today	today	NOUN
cana-1748	172	14	:	:	PUNCT
cana-1748	172	15	proceedings	proceeding	NOUN
cana-1748	172	16	,	,	PUNCT
cana-1748	172	17	volume	volume	VERB
cana-1748	172	18	47,2102	47,2102	NUM
cana-1748	172	19	−	−	PROPN
cana-1748	172	20	2106	2106	NUM
cana-1748	172	21	.	.	PUNCT
cana-1748	173	1	[	[	X
cana-1748	173	2	9	9	NUM
cana-1748	173	3	]	]	PUNCT
cana-1748	173	4	tharakeswari	tharakeswari	PROPN
cana-1748	173	5	.	.	PUNCT
cana-1748	173	6	v	v	NOUN
cana-1748	173	7	,	,	PUNCT
cana-1748	173	8	kameswari	kameswari	PROPN
cana-1748	173	9	.	.	PUNCT
cana-1748	174	1	m	m	PROPN
cana-1748	174	2	,	,	PUNCT
cana-1748	174	3	mariappan	mariappan	NOUN
cana-1748	174	4	.	.	PUNCT
cana-1748	175	1	p	p	X
cana-1748	175	2	,	,	PUNCT
cana-1748	175	3	venkataraman	venkataraman	NOUN
cana-1748	175	4	.	.	PUNCT
cana-1748	176	1	y	y	PROPN
cana-1748	176	2	and	and	CCONJ
cana-1748	176	3	balas.e.v	balas.e.v	PROPN
cana-1748	176	4	(	(	PUNCT
cana-1748	176	5	2023	2023	NUM
cana-1748	176	6	)	)	PUNCT
cana-1748	176	7	role	role	NOUN
cana-1748	176	8	of	of	ADP
cana-1748	176	9	hexagonal	hexagonal	ADJ
cana-1748	176	10	fuzzy	fuzzy	ADJ
cana-1748	176	11	numbers	number	NOUN
cana-1748	176	12	while	while	SCONJ
cana-1748	176	13	applying	apply	VERB
cana-1748	176	14	the	the	DET
cana-1748	176	15	maxmin	maxmin	NOUN
cana-1748	176	16	concept	concept	NOUN
cana-1748	176	17	to	to	ADP
cana-1748	176	18	a	a	DET
cana-1748	176	19	transportation	transportation	NOUN
cana-1748	176	20	problem	problem	NOUN
cana-1748	176	21	,	,	PUNCT
cana-1748	176	22	fuzzy	fuzzy	ADJ
cana-1748	176	23	optimization	optimization	NOUN
cana-1748	176	24	,	,	PUNCT
cana-1748	176	25	decisionmaking	decisionmake	VERB
cana-1748	176	26	and	and	CCONJ
cana-1748	176	27	operations	operation	NOUN
cana-1748	176	28	research	research	NOUN
cana-1748	176	29	,	,	PUNCT
cana-1748	176	30	161	161	NUM
cana-1748	176	31	-	-	SYM
cana-1748	176	32	175	175	NUM
cana-1748	176	33	.	.	PUNCT
cana-1748	177	1	[	[	X
cana-1748	177	2	10	10	NUM
cana-1748	177	3	]	]	X
cana-1748	177	4	vincent	vincent	PROPN
cana-1748	177	5	f.	f.	PROPN
cana-1748	177	6	yu	yu	PROPN
cana-1748	177	7	,	,	PUNCT
cana-1748	177	8	luu	luu	PROPN
cana-1748	177	9	huu	huu	PROPN
cana-1748	177	10	van	van	PROPN
cana-1748	177	11	,	,	PUNCT
cana-1748	177	12	luu	luu	PROPN
cana-1748	177	13	quoc	quoc	PROPN
cana-1748	177	14	dat	dat	PROPN
cana-1748	177	15	,	,	PUNCT
cana-1748	177	16	ha	ha	INTJ
cana-1748	177	17	thi	thi	PROPN
cana-1748	177	18	xuan	xuan	PROPN
cana-1748	177	19	chi	chi	PROPN
cana-1748	177	20	,	,	PUNCT
cana-1748	177	21	shuo	shuo	NOUN
cana-1748	177	22	-	-	PUNCT
cana-1748	177	23	yan	yan	NOUN
cana-1748	177	24	chou	chou	PROPN
cana-1748	177	25	and	and	CCONJ
cana-1748	177	26	truong	truong	PROPN
cana-1748	177	27	thi	thi	PROPN
cana-1748	177	28	thuy	thuy	PROPN
cana-1748	177	29	duong	duong	PROPN
cana-1748	177	30	(	(	PUNCT
cana-1748	177	31	2016	2016	NUM
cana-1748	177	32	)	)	PUNCT
cana-1748	177	33	analyzing	analyze	VERB
cana-1748	177	34	the	the	DET
cana-1748	177	35	ranking	ranking	NOUN
cana-1748	177	36	method	method	NOUN
cana-1748	177	37	forfuzzy	forfuzzy	NOUN
cana-1748	177	38	numbers	number	NOUN
cana-1748	177	39	in	in	ADP
cana-1748	177	40	fuzzy	fuzzy	ADJ
cana-1748	177	41	decision	decision	NOUN
cana-1748	177	42	making	making	NOUN
cana-1748	177	43	based	base	VERB
cana-1748	177	44	on	on	ADP
cana-1748	177	45	the	the	DET
cana-1748	177	46	magnitude	magnitude	NOUN
cana-1748	177	47	concepts	concept	NOUN
cana-1748	177	48	,	,	PUNCT
cana-1748	177	49	international	international	ADJ
cana-1748	177	50	journal	journal	NOUN
cana-1748	177	51	of	of	ADP
cana-1748	177	52	fuzzy	fuzzy	ADJ
cana-1748	177	53	systems	system	NOUN
cana-1748	177	54	,	,	PUNCT
cana-1748	177	55	volume	volume	NOUN
cana-1748	177	56	19	19	NUM
cana-1748	177	57	,	,	PUNCT
cana-1748	177	58	1279	1279	NUM
cana-1748	177	59	-	-	SYM
cana-1748	177	60	1289	1289	NUM
cana-1748	177	61	.	.	PUNCT