id	sid	tid	token	lemma	pos
cana-2738	1	1	communications	communication	NOUN
cana-2738	1	2	on	on	ADP
cana-2738	1	3	applied	apply	VERB
cana-2738	1	4	nonlinear	nonlinear	ADJ
cana-2738	1	5	analysis	analysis	NOUN
cana-2738	1	6	issn	issn	NOUN
cana-2738	1	7	:	:	PUNCT
cana-2738	1	8	1074	1074	NUM
cana-2738	1	9	-	-	PUNCT
cana-2738	1	10	133x	133x	NUM
cana-2738	1	11	vol	vol	NOUN
cana-2738	1	12	32	32	NUM
cana-2738	1	13	no	no	NOUN
cana-2738	1	14	.	.	PUNCT
cana-2738	2	1	4s	4s	NUM
cana-2738	2	2	(	(	PUNCT
cana-2738	2	3	2025	2025	NUM
cana-2738	2	4	)	)	PUNCT
cana-2738	2	5	42	42	NUM
cana-2738	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2738	2	7	open	open	ADJ
cana-2738	2	8	maps	map	NOUN
cana-2738	2	9	via	via	ADP
cana-2738	2	10	𝜹-open	𝜹-open	NOUN
cana-2738	2	11	sets	set	NOUN
cana-2738	2	12	in	in	ADP
cana-2738	2	13	pythagorean	pythagorean	PROPN
cana-2738	2	14	fuzzy	fuzzy	ADJ
cana-2738	2	15	topological	topological	ADJ
cana-2738	2	16	spaces	space	NOUN
cana-2738	2	17	and	and	CCONJ
cana-2738	2	18	its	its	PRON
cana-2738	2	19	applications	application	NOUN
cana-2738	2	20	a.	a.	NOUN
cana-2738	2	21	vadivel	vadivel	NOUN
cana-2738	2	22	𝟏	𝟏	PROPN
cana-2738	2	23	,	,	PUNCT
cana-2738	2	24	g.	g.	PROPN
cana-2738	2	25	gavaskar	gavaskar	PROPN
cana-2738	2	26	𝟐	𝟐	NUM
cana-2738	2	27	,	,	PUNCT
cana-2738	2	28	g.	g.	PROPN
cana-2738	2	29	saravanakumar	saravanakumar	PROPN
cana-2738	2	30	𝟑	𝟑	NUM
cana-2738	2	31	1pg	1pg	ADJ
cana-2738	2	32	and	and	CCONJ
cana-2738	2	33	research	research	NOUN
cana-2738	2	34	department	department	PROPN
cana-2738	2	35	of	of	ADP
cana-2738	2	36	mathematics	mathematic	NOUN
cana-2738	2	37	,	,	PUNCT
cana-2738	2	38	arignar	arignar	ADJ
cana-2738	2	39	anna	anna	PROPN
cana-2738	2	40	government	government	PROPN
cana-2738	2	41	arts	arts	PROPN
cana-2738	2	42	college	college	PROPN
cana-2738	2	43	,	,	PUNCT
cana-2738	2	44	namakkal	namakkal	NOUN
cana-2738	2	45	637	637	NUM
cana-2738	2	46	002	002	NUM
cana-2738	2	47	,	,	PUNCT
cana-2738	2	48	india	india	PROPN
cana-2738	2	49	.	.	PUNCT
cana-2738	3	1	1,2department	1,2department	NUM
cana-2738	3	2	of	of	ADP
cana-2738	3	3	mathematics	mathematic	NOUN
cana-2738	3	4	,	,	PUNCT
cana-2738	3	5	annamalai	annamalai	PROPN
cana-2738	3	6	university	university	PROPN
cana-2738	3	7	,	,	PUNCT
cana-2738	3	8	annamalai	annamalai	PROPN
cana-2738	3	9	nagar	nagar	VERB
cana-2738	3	10	608	608	NUM
cana-2738	3	11	002	002	NUM
cana-2738	3	12	,	,	PUNCT
cana-2738	3	13	india	india	PROPN
cana-2738	3	14	.	.	PUNCT
cana-2738	4	1	3department	3department	NUM
cana-2738	4	2	of	of	ADP
cana-2738	4	3	mathematics	mathematic	NOUN
cana-2738	4	4	,	,	PUNCT
cana-2738	4	5	vel	vel	ADJ
cana-2738	4	6	tech	tech	NOUN
cana-2738	4	7	rangarajan	rangarajan	NOUN
cana-2738	4	8	dr.sagunthala	dr.sagunthala	NOUN
cana-2738	4	9	r&d	r&d	PROPN
cana-2738	4	10	institute	institute	PROPN
cana-2738	4	11	of	of	ADP
cana-2738	4	12	science	science	NOUN
cana-2738	4	13	and	and	CCONJ
cana-2738	4	14	technology	technology	NOUN
cana-2738	4	15	(	(	PUNCT
cana-2738	4	16	deemed	deem	VERB
cana-2738	4	17	to	to	PART
cana-2738	4	18	be	be	AUX
cana-2738	4	19	university	university	NOUN
cana-2738	4	20	)	)	PUNCT
cana-2738	4	21	,	,	PUNCT
cana-2738	4	22	avadi	avadi	NOUN
cana-2738	4	23	,	,	PUNCT
cana-2738	4	24	chennai-600062	chennai-600062	NOUN
cana-2738	4	25	,	,	PUNCT
cana-2738	4	26	india	india	PROPN
cana-2738	4	27	e	e	PROPN
cana-2738	4	28	-	-	NOUN
cana-2738	4	29	mail	mail	NOUN
cana-2738	4	30	:	:	PUNCT
cana-2738	4	31	1avmaths@gmail.com,2gurugavaskar001@gmail.com	1avmaths@gmail.com,2gurugavaskar001@gmail.com	NUM
cana-2738	4	32	,	,	PUNCT
cana-2738	4	33	3saravananguru2612@gmail.com	3saravananguru2612@gmail.com	NUM
cana-2738	4	34	article	article	NOUN
cana-2738	4	35	history	history	NOUN
cana-2738	4	36	:	:	PUNCT
cana-2738	4	37	received	receive	VERB
cana-2738	4	38	:	:	PUNCT
cana-2738	4	39	12	12	NUM
cana-2738	4	40	-	-	SYM
cana-2738	4	41	09	09	NUM
cana-2738	4	42	-	-	PUNCT
cana-2738	4	43	2024	2024	NUM
cana-2738	4	44	revised	revise	VERB
cana-2738	4	45	:	:	PUNCT
cana-2738	4	46	17	17	NUM
cana-2738	4	47	-	-	SYM
cana-2738	4	48	11	11	NUM
cana-2738	4	49	-	-	PUNCT
cana-2738	4	50	2024	2024	NUM
cana-2738	4	51	accepted	accept	VERB
cana-2738	4	52	:	:	PUNCT
cana-2738	4	53	27	27	NUM
cana-2738	4	54	-	-	SYM
cana-2738	4	55	11	11	NUM
cana-2738	4	56	-	-	PUNCT
cana-2738	4	57	2024	2024	NUM
cana-2738	4	58	abstract	abstract	NOUN
cana-2738	4	59	:	:	PUNCT
cana-2738	4	60	in	in	ADP
cana-2738	4	61	this	this	DET
cana-2738	4	62	paper	paper	NOUN
cana-2738	4	63	,	,	PUNCT
cana-2738	4	64	we	we	PRON
cana-2738	4	65	introduce	introduce	VERB
cana-2738	4	66	the	the	DET
cana-2738	4	67	concept	concept	NOUN
cana-2738	4	68	of	of	ADP
cana-2738	4	69	pythagorean	pythagorean	PROPN
cana-2738	4	70	fuzzy	fuzzy	ADJ
cana-2738	4	71	𝛿	𝛿	ADJ
cana-2738	4	72	(	(	PUNCT
cana-2738	4	73	resp	resp	NOUN
cana-2738	4	74	.	.	PUNCT
cana-2738	5	1	𝛿𝛼	𝛿𝛼	NOUN
cana-2738	5	2	,	,	PUNCT
cana-2738	5	3	𝛿𝒮	𝛿𝒮	NOUN
cana-2738	5	4	,	,	PUNCT
cana-2738	5	5	𝛿𝒫	𝛿𝒫	NOUN
cana-2738	5	6	&	&	CCONJ
cana-2738	5	7	𝛿𝛽	𝛿𝛽	NOUN
cana-2738	5	8	or	or	CCONJ
cana-2738	5	9	𝑒∗)-open	𝑒∗)-open	ADJ
cana-2738	5	10	mappings	mapping	NOUN
cana-2738	5	11	are	be	AUX
cana-2738	5	12	introduced	introduce	VERB
cana-2738	5	13	and	and	CCONJ
cana-2738	5	14	their	their	PRON
cana-2738	5	15	properties	property	NOUN
cana-2738	5	16	are	be	AUX
cana-2738	5	17	discussed	discuss	VERB
cana-2738	5	18	.	.	PUNCT
cana-2738	6	1	in	in	ADP
cana-2738	6	2	current	current	ADJ
cana-2738	6	3	scenario	scenario	NOUN
cana-2738	6	4	people	people	NOUN
cana-2738	6	5	with	with	ADP
cana-2738	6	6	symptom	symptom	NOUN
cana-2738	6	7	of	of	ADP
cana-2738	6	8	covid-19	covid-19	PROPN
cana-2738	6	9	like	like	ADP
cana-2738	6	10	fever	fever	NOUN
cana-2738	6	11	,	,	PUNCT
cana-2738	6	12	cough	cough	NOUN
cana-2738	6	13	,	,	PUNCT
cana-2738	6	14	sneezing	sneeze	VERB
cana-2738	6	15	,	,	PUNCT
cana-2738	6	16	sore	sore	ADJ
cana-2738	6	17	throat	throat	NOUN
cana-2738	6	18	,	,	PUNCT
cana-2738	6	19	loss	loss	NOUN
cana-2738	6	20	of	of	ADP
cana-2738	6	21	taste	taste	NOUN
cana-2738	6	22	and	and	CCONJ
cana-2738	6	23	smell	smell	NOUN
cana-2738	6	24	etc	etc	X
cana-2738	6	25	.	.	X
cana-2738	6	26	,	,	PUNCT
cana-2738	6	27	were	be	AUX
cana-2738	6	28	panic	panic	NOUN
cana-2738	6	29	about	about	ADP
cana-2738	6	30	the	the	DET
cana-2738	6	31	disease	disease	NOUN
cana-2738	6	32	,	,	PUNCT
cana-2738	6	33	and	and	CCONJ
cana-2738	6	34	the	the	DET
cana-2738	6	35	diagnosis	diagnosis	NOUN
cana-2738	6	36	of	of	ADP
cana-2738	6	37	covid-19	covid-19	PROPN
cana-2738	6	38	takes	take	VERB
cana-2738	6	39	many	many	ADJ
cana-2738	6	40	hours	hour	NOUN
cana-2738	6	41	and	and	CCONJ
cana-2738	6	42	people	people	NOUN
cana-2738	6	43	can	can	AUX
cana-2738	6	44	not	not	PART
cana-2738	6	45	go	go	VERB
cana-2738	6	46	for	for	ADP
cana-2738	6	47	the	the	DET
cana-2738	6	48	test	test	NOUN
cana-2738	6	49	frequently	frequently	ADV
cana-2738	6	50	.	.	PUNCT
cana-2738	7	1	some	some	DET
cana-2738	7	2	other	other	ADJ
cana-2738	7	3	diseases	disease	NOUN
cana-2738	7	4	like	like	ADP
cana-2738	7	5	flu	flu	NOUN
cana-2738	7	6	,	,	PUNCT
cana-2738	7	7	pneumonia	pneumonia	NOUN
cana-2738	7	8	,	,	PUNCT
cana-2738	7	9	cold	cold	ADJ
cana-2738	7	10	etc	etc	X
cana-2738	7	11	.	.	X
cana-2738	7	12	,	,	PUNCT
cana-2738	7	13	also	also	ADV
cana-2738	7	14	has	have	VERB
cana-2738	7	15	the	the	DET
cana-2738	7	16	same	same	ADJ
cana-2738	7	17	symptoms	symptom	NOUN
cana-2738	7	18	.	.	PUNCT
cana-2738	8	1	each	each	DET
cana-2738	8	2	patients	patient	NOUN
cana-2738	8	3	has	have	VERB
cana-2738	8	4	unique	unique	ADJ
cana-2738	8	5	experience	experience	NOUN
cana-2738	8	6	of	of	ADP
cana-2738	8	7	that	that	DET
cana-2738	8	8	particular	particular	ADJ
cana-2738	8	9	symptom	symptom	NOUN
cana-2738	8	10	and	and	CCONJ
cana-2738	8	11	some	some	DET
cana-2738	8	12	time	time	NOUN
cana-2738	8	13	they	they	PRON
cana-2738	8	14	may	may	AUX
cana-2738	8	15	not	not	PART
cana-2738	8	16	experience	experience	VERB
cana-2738	8	17	that	that	DET
cana-2738	8	18	symptom	symptom	NOUN
cana-2738	8	19	even	even	ADV
cana-2738	8	20	though	though	SCONJ
cana-2738	8	21	they	they	PRON
cana-2738	8	22	were	be	AUX
cana-2738	8	23	affected	affect	VERB
cana-2738	8	24	by	by	ADP
cana-2738	8	25	the	the	DET
cana-2738	8	26	covid-19	covid-19	PROPN
cana-2738	8	27	.	.	PUNCT
cana-2738	9	1	also	also	ADV
cana-2738	9	2	,	,	PUNCT
cana-2738	9	3	in	in	ADP
cana-2738	9	4	this	this	DET
cana-2738	9	5	paper	paper	NOUN
cana-2738	9	6	we	we	PRON
cana-2738	9	7	tried	try	VERB
cana-2738	9	8	to	to	PART
cana-2738	9	9	diagnosis	diagnosis	VERB
cana-2738	9	10	covid-19	covid-19	PROPN
cana-2738	9	11	with	with	ADP
cana-2738	9	12	the	the	DET
cana-2738	9	13	help	help	NOUN
cana-2738	9	14	of	of	ADP
cana-2738	9	15	picture	picture	NOUN
cana-2738	9	16	fuzzy	fuzzy	ADJ
cana-2738	9	17	sets	set	NOUN
cana-2738	9	18	which	which	PRON
cana-2738	9	19	helps	help	VERB
cana-2738	9	20	to	to	PART
cana-2738	9	21	record	record	VERB
cana-2738	9	22	all	all	DET
cana-2738	9	23	symptoms	symptom	NOUN
cana-2738	9	24	in	in	ADP
cana-2738	9	25	prã	prã	PROPN
cana-2738	9	26	©	©	PROPN
cana-2738	9	27	cised	cise	VERB
cana-2738	9	28	manner	manner	NOUN
cana-2738	9	29	.	.	PUNCT
cana-2738	10	1	introduction	introduction	NOUN
cana-2738	10	2	:	:	PUNCT
cana-2738	10	3	this	this	DET
cana-2738	10	4	paper	paper	NOUN
cana-2738	10	5	introduces	introduce	VERB
cana-2738	10	6	the	the	DET
cana-2738	10	7	concept	concept	NOUN
cana-2738	10	8	of	of	ADP
cana-2738	10	9	pythagorean	pythagorean	PROPN
cana-2738	10	10	fuzzy	fuzzy	ADJ
cana-2738	10	11	open	open	ADJ
cana-2738	10	12	mappings	mapping	NOUN
cana-2738	10	13	and	and	CCONJ
cana-2738	10	14	their	their	PRON
cana-2738	10	15	relevance	relevance	NOUN
cana-2738	10	16	to	to	ADP
cana-2738	10	17	covid-19	covid-19	PROPN
cana-2738	10	18	symptom	symptom	NOUN
cana-2738	10	19	diagnosis	diagnosis	NOUN
cana-2738	10	20	.	.	PUNCT
cana-2738	11	1	due	due	ADP
cana-2738	11	2	to	to	ADP
cana-2738	11	3	the	the	DET
cana-2738	11	4	overlapping	overlap	VERB
cana-2738	11	5	symptoms	symptom	NOUN
cana-2738	11	6	of	of	ADP
cana-2738	11	7	covid-19	covid-19	PROPN
cana-2738	11	8	with	with	ADP
cana-2738	11	9	other	other	ADJ
cana-2738	11	10	illnesses	illness	NOUN
cana-2738	11	11	,	,	PUNCT
cana-2738	11	12	a	a	DET
cana-2738	11	13	pythagorean	pythagorean	ADJ
cana-2738	11	14	fuzzy	fuzzy	ADJ
cana-2738	11	15	set	set	NOUN
cana-2738	11	16	approach	approach	NOUN
cana-2738	11	17	is	be	AUX
cana-2738	11	18	utilized	utilize	VERB
cana-2738	11	19	to	to	AUX
cana-2738	11	20	more	more	ADV
cana-2738	11	21	accurately	accurately	ADV
cana-2738	11	22	capture	capture	VERB
cana-2738	11	23	and	and	CCONJ
cana-2738	11	24	analyze	analyze	VERB
cana-2738	11	25	symptom	symptom	NOUN
cana-2738	11	26	patterns	pattern	NOUN
cana-2738	11	27	.	.	PUNCT
cana-2738	12	1	objectives	objective	NOUN
cana-2738	12	2	:	:	PUNCT
cana-2738	12	3	the	the	DET
cana-2738	12	4	objective	objective	NOUN
cana-2738	12	5	is	be	AUX
cana-2738	12	6	to	to	PART
cana-2738	12	7	develop	develop	VERB
cana-2738	12	8	a	a	DET
cana-2738	12	9	precise	precise	ADJ
cana-2738	12	10	mapping	mapping	NOUN
cana-2738	12	11	model	model	NOUN
cana-2738	12	12	that	that	PRON
cana-2738	12	13	utilizes	utilize	VERB
cana-2738	12	14	pythagorean	pythagorean	PROPN
cana-2738	12	15	fuzzy	fuzzy	ADJ
cana-2738	12	16	sets	set	NOUN
cana-2738	12	17	to	to	PART
cana-2738	12	18	differentiate	differentiate	VERB
cana-2738	12	19	between	between	ADP
cana-2738	12	20	covid-19	covid-19	PROPN
cana-2738	12	21	symptoms	symptom	NOUN
cana-2738	12	22	and	and	CCONJ
cana-2738	12	23	other	other	ADJ
cana-2738	12	24	similar	similar	ADJ
cana-2738	12	25	conditions	condition	NOUN
cana-2738	12	26	,	,	PUNCT
cana-2738	12	27	aiming	aim	VERB
cana-2738	12	28	to	to	PART
cana-2738	12	29	improve	improve	VERB
cana-2738	12	30	diagnostic	diagnostic	ADJ
cana-2738	12	31	speed	speed	NOUN
cana-2738	12	32	and	and	CCONJ
cana-2738	12	33	accuracy	accuracy	NOUN
cana-2738	12	34	.	.	PUNCT
cana-2738	13	1	methods	method	NOUN
cana-2738	13	2	:	:	PUNCT
cana-2738	13	3	the	the	DET
cana-2738	13	4	method	method	NOUN
cana-2738	13	5	involves	involve	VERB
cana-2738	13	6	formulating	formulate	VERB
cana-2738	13	7	fuzzy	fuzzy	ADJ
cana-2738	13	8	sets	set	NOUN
cana-2738	13	9	based	base	VERB
cana-2738	13	10	on	on	ADP
cana-2738	13	11	covid-19	covid-19	PROPN
cana-2738	13	12	symptoms	symptom	NOUN
cana-2738	13	13	,	,	PUNCT
cana-2738	13	14	computing	computing	NOUN
cana-2738	13	15	distances	distance	NOUN
cana-2738	13	16	(	(	PUNCT
cana-2738	13	17	hamming	hamming	NOUN
cana-2738	13	18	,	,	PUNCT
cana-2738	13	19	euclidean	euclidean	NOUN
cana-2738	13	20	)	)	PUNCT
cana-2738	13	21	between	between	ADP
cana-2738	13	22	patients	patient	NOUN
cana-2738	13	23	'	'	PART
cana-2738	13	24	symptoms	symptom	NOUN
cana-2738	13	25	and	and	CCONJ
cana-2738	13	26	ideal	ideal	ADJ
cana-2738	13	27	symptom	symptom	NOUN
cana-2738	13	28	patterns	pattern	NOUN
cana-2738	13	29	,	,	PUNCT
cana-2738	13	30	and	and	CCONJ
cana-2738	13	31	identifying	identify	VERB
cana-2738	13	32	cases	case	NOUN
cana-2738	13	33	with	with	ADP
cana-2738	13	34	higher	high	ADJ
cana-2738	13	35	covid-19	covid-19	PROPN
cana-2738	13	36	risk	risk	NOUN
cana-2738	13	37	.	.	PUNCT
cana-2738	14	1	results	result	NOUN
cana-2738	14	2	:	:	PUNCT
cana-2738	14	3	the	the	DET
cana-2738	14	4	approach	approach	NOUN
cana-2738	14	5	successfully	successfully	ADV
cana-2738	14	6	identifies	identify	VERB
cana-2738	14	7	patients	patient	NOUN
cana-2738	14	8	with	with	ADP
cana-2738	14	9	symptoms	symptom	NOUN
cana-2738	14	10	closest	close	ADJ
cana-2738	14	11	to	to	ADP
cana-2738	14	12	covid19	covid19	NOUN
cana-2738	14	13	indicators	indicator	NOUN
cana-2738	14	14	,	,	PUNCT
cana-2738	14	15	offering	offer	VERB
cana-2738	14	16	a	a	DET
cana-2738	14	17	more	more	ADV
cana-2738	14	18	systematic	systematic	ADJ
cana-2738	14	19	and	and	CCONJ
cana-2738	14	20	timely	timely	ADJ
cana-2738	14	21	diagnosis	diagnosis	NOUN
cana-2738	14	22	.	.	PUNCT
cana-2738	15	1	results	result	NOUN
cana-2738	15	2	suggest	suggest	VERB
cana-2738	15	3	that	that	SCONJ
cana-2738	15	4	this	this	DET
cana-2738	15	5	fuzzy	fuzzy	ADJ
cana-2738	15	6	set	set	NOUN
cana-2738	15	7	model	model	NOUN
cana-2738	15	8	can	can	AUX
cana-2738	15	9	enhance	enhance	VERB
cana-2738	15	10	early	early	ADJ
cana-2738	15	11	detection	detection	NOUN
cana-2738	15	12	and	and	CCONJ
cana-2738	15	13	intervention	intervention	NOUN
cana-2738	15	14	for	for	ADP
cana-2738	15	15	affected	affected	ADJ
cana-2738	15	16	individuals	individual	NOUN
cana-2738	15	17	conclusions	conclusion	NOUN
cana-2738	15	18	:	:	PUNCT
cana-2738	15	19	in	in	ADP
cana-2738	15	20	this	this	DET
cana-2738	15	21	paper	paper	NOUN
cana-2738	15	22	,	,	PUNCT
cana-2738	15	23	some	some	DET
cana-2738	15	24	new	new	ADJ
cana-2738	15	25	notions	notion	NOUN
cana-2738	15	26	of	of	ADP
cana-2738	15	27	strongly	strongly	ADV
cana-2738	15	28	pythagorean	pythagorean	ADJ
cana-2738	15	29	fuzzy	fuzzy	ADJ
cana-2738	15	30	open	open	ADJ
cana-2738	15	31	(	(	PUNCT
cana-2738	15	32	closed	closed	ADJ
cana-2738	15	33	)	)	PUNCT
cana-2738	15	34	maps	map	NOUN
cana-2738	15	35	called	call	VERB
cana-2738	15	36	pythagorean	pythagorean	PROPN
cana-2738	15	37	fuzzy	fuzzy	PROPN
cana-2738	15	38	𝛿-open	𝛿-open	VERB
cana-2738	15	39	and	and	CCONJ
cana-2738	15	40	pythagorean	pythagorean	PROPN
cana-2738	15	41	fuzzy	fuzzy	ADJ
cana-2738	15	42	𝛿-closed	𝛿-close	VERB
cana-2738	15	43	maps	map	NOUN
cana-2738	15	44	are	be	AUX
cana-2738	15	45	introduced	introduce	VERB
cana-2738	15	46	and	and	CCONJ
cana-2738	15	47	discussed	discuss	VERB
cana-2738	15	48	their	their	PRON
cana-2738	15	49	relationship	relationship	NOUN
cana-2738	15	50	between	between	ADP
cana-2738	15	51	their	their	PRON
cana-2738	15	52	near	near	ADJ
cana-2738	15	53	mappings	mapping	NOUN
cana-2738	15	54	with	with	ADP
cana-2738	15	55	examples	example	NOUN
cana-2738	15	56	.	.	PUNCT
cana-2738	16	1	also	also	ADV
cana-2738	16	2	,	,	PUNCT
cana-2738	16	3	we	we	PRON
cana-2738	16	4	have	have	AUX
cana-2738	16	5	tried	try	VERB
cana-2738	16	6	to	to	PART
cana-2738	16	7	diagnosis	diagnosis	VERB
cana-2738	16	8	covid-19	covid-19	PROPN
cana-2738	16	9	with	with	ADP
cana-2738	16	10	the	the	DET
cana-2738	16	11	help	help	NOUN
cana-2738	16	12	of	of	ADP
cana-2738	16	13	pythagorean	pythagorean	PROPN
cana-2738	16	14	fuzzy	fuzzy	ADJ
cana-2738	16	15	sets	set	NOUN
cana-2738	16	16	which	which	PRON
cana-2738	16	17	helps	help	VERB
cana-2738	16	18	to	to	PART
cana-2738	16	19	record	record	VERB
cana-2738	16	20	all	all	DET
cana-2738	16	21	symptoms	symptom	NOUN
cana-2738	16	22	in	in	ADP
cana-2738	16	23	prã	prã	PROPN
cana-2738	16	24	©	©	PROPN
cana-2738	16	25	cised	cise	VERB
cana-2738	16	26	manner	manner	NOUN
cana-2738	16	27	.	.	PUNCT
cana-2738	17	1	in	in	ADP
cana-2738	17	2	future	future	NOUN
cana-2738	17	3	,	,	PUNCT
cana-2738	17	4	researchers	researcher	NOUN
cana-2738	17	5	can	can	AUX
cana-2738	17	6	extend	extend	VERB
cana-2738	17	7	this	this	DET
cana-2738	17	8	model	model	NOUN
cana-2738	17	9	to	to	ADP
cana-2738	17	10	other	other	ADJ
cana-2738	17	11	extensions	extension	NOUN
cana-2738	17	12	of	of	ADP
cana-2738	17	13	fuzzy	fuzzy	ADJ
cana-2738	17	14	sets	set	NOUN
cana-2738	17	15	such	such	ADJ
cana-2738	17	16	as	as	ADP
cana-2738	17	17	rough	rough	ADJ
cana-2738	17	18	sets	set	NOUN
cana-2738	17	19	and	and	CCONJ
cana-2738	17	20	utilize	utilize	VERB
cana-2738	17	21	the	the	DET
cana-2738	17	22	interdependency	interdependency	NOUN
cana-2738	17	23	among	among	ADP
cana-2738	17	24	the	the	DET
cana-2738	17	25	various	various	ADJ
cana-2738	17	26	evaluation	evaluation	NOUN
cana-2738	17	27	criteria	criterion	NOUN
cana-2738	17	28	for	for	ADP
cana-2738	17	29	better	well	ADJ
cana-2738	17	30	judgement	judgement	NOUN
cana-2738	17	31	.	.	PUNCT
cana-2738	18	1	keywords	keyword	NOUN
cana-2738	18	2	:	:	PUNCT
cana-2738	18	3	pythagorean	pythagorean	VERB
cana-2738	18	4	fuzzy	fuzzy	ADJ
cana-2738	18	5	𝛿-open	𝛿-open	NOUN
cana-2738	18	6	mappings	mapping	NOUN
cana-2738	18	7	,	,	PUNCT
cana-2738	18	8	distance	distance	NOUN
cana-2738	18	9	between	between	ADP
cana-2738	18	10	fuzzy	fuzzy	ADJ
cana-2738	18	11	sets	set	NOUN
cana-2738	18	12	,	,	PUNCT
cana-2738	18	13	covid-19	covid-19	PROPN
cana-2738	18	14	patientrecord	patientrecord	VERB
cana-2738	18	15	all	all	DET
cana-2738	18	16	symptoms	symptom	NOUN
cana-2738	18	17	in	in	ADP
cana-2738	18	18	precise	precise	ADJ
cana-2738	18	19	manner	manner	NOUN
cana-2738	18	20	.	.	PUNCT
cana-2738	19	1	communications	communication	NOUN
cana-2738	19	2	on	on	ADP
cana-2738	19	3	applied	apply	VERB
cana-2738	19	4	nonlinear	nonlinear	ADJ
cana-2738	19	5	analysis	analysis	NOUN
cana-2738	19	6	issn	issn	NOUN
cana-2738	19	7	:	:	PUNCT
cana-2738	19	8	1074	1074	NUM
cana-2738	19	9	-	-	PUNCT
cana-2738	19	10	133x	133x	NUM
cana-2738	19	11	vol	vol	NOUN
cana-2738	19	12	32	32	NUM
cana-2738	19	13	no	no	NOUN
cana-2738	19	14	.	.	PUNCT
cana-2738	20	1	4s	4s	NUM
cana-2738	20	2	(	(	PUNCT
cana-2738	20	3	2025	2025	NUM
cana-2738	20	4	)	)	PUNCT
cana-2738	20	5	43	43	NUM
cana-2738	21	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-2738	21	2	1	1	X
cana-2738	21	3	.	.	PUNCT
cana-2738	21	4	introduction	introduction	NOUN
cana-2738	21	5	traditional	traditional	ADJ
cana-2738	21	6	logic	logic	NOUN
cana-2738	21	7	,	,	PUNCT
cana-2738	21	8	which	which	PRON
cana-2738	21	9	is	be	AUX
cana-2738	21	10	interpreted	interpret	VERB
cana-2738	21	11	as	as	ADP
cana-2738	21	12	either	either	CCONJ
cana-2738	21	13	true	true	ADJ
cana-2738	21	14	or	or	CCONJ
cana-2738	21	15	false	false	ADJ
cana-2738	21	16	,	,	PUNCT
cana-2738	21	17	found	find	VERB
cana-2738	21	18	to	to	PART
cana-2738	21	19	be	be	AUX
cana-2738	21	20	difficult	difficult	ADJ
cana-2738	21	21	to	to	PART
cana-2738	21	22	solve	solve	VERB
cana-2738	21	23	uncertain	uncertain	ADJ
cana-2738	21	24	real	real	ADJ
cana-2738	21	25	-	-	PUNCT
cana-2738	21	26	life	life	NOUN
cana-2738	21	27	problems	problem	NOUN
cana-2738	21	28	.	.	PUNCT
cana-2738	22	1	as	as	ADP
cana-2738	22	2	a	a	DET
cana-2738	22	3	counter	counter	NOUN
cana-2738	22	4	measure	measure	NOUN
cana-2738	22	5	,	,	PUNCT
cana-2738	22	6	zadeh	zadeh	PROPN
cana-2738	22	7	(	(	PUNCT
cana-2738	22	8	1965	1965	NUM
cana-2738	22	9	)	)	PUNCT
cana-2738	23	1	[	[	X
cana-2738	23	2	35	35	NUM
cana-2738	23	3	]	]	PUNCT
cana-2738	23	4	invented	invent	VERB
cana-2738	23	5	fuzzy	fuzzy	ADJ
cana-2738	23	6	set	set	NOUN
cana-2738	23	7	theory	theory	NOUN
cana-2738	23	8	,	,	PUNCT
cana-2738	23	9	where	where	SCONJ
cana-2738	23	10	the	the	DET
cana-2738	23	11	involvement	involvement	NOUN
cana-2738	23	12	of	of	ADP
cana-2738	23	13	elements	element	NOUN
cana-2738	23	14	in	in	ADP
cana-2738	23	15	a	a	DET
cana-2738	23	16	set	set	NOUN
cana-2738	23	17	is	be	AUX
cana-2738	23	18	characterized	characterize	VERB
cana-2738	23	19	by	by	ADP
cana-2738	23	20	membership	membership	NOUN
cana-2738	23	21	grade	grade	NOUN
cana-2738	23	22	,	,	PUNCT
cana-2738	23	23	which	which	PRON
cana-2738	23	24	belongs	belong	VERB
cana-2738	23	25	to	to	ADP
cana-2738	23	26	[	[	X
cana-2738	23	27	0,1	0,1	NUM
cana-2738	23	28	]	]	PUNCT
cana-2738	23	29	.	.	PUNCT
cana-2738	24	1	to	to	PART
cana-2738	24	2	handle	handle	VERB
cana-2738	24	3	much	much	ADJ
cana-2738	24	4	uncertainty	uncertainty	NOUN
cana-2738	24	5	,	,	PUNCT
cana-2738	24	6	fuzzy	fuzzy	ADJ
cana-2738	24	7	sets	set	NOUN
cana-2738	24	8	were	be	AUX
cana-2738	24	9	extended	extend	VERB
cana-2738	24	10	by	by	ADP
cana-2738	24	11	the	the	DET
cana-2738	24	12	different	different	ADJ
cana-2738	24	13	researchers	researcher	NOUN
cana-2738	24	14	in	in	ADP
cana-2738	24	15	different	different	ADJ
cana-2738	24	16	ways	way	NOUN
cana-2738	24	17	such	such	ADJ
cana-2738	24	18	as	as	ADP
cana-2738	24	19	vague	vague	ADJ
cana-2738	24	20	set	set	NOUN
cana-2738	24	21	(	(	PUNCT
cana-2738	24	22	gau	gau	NOUN
cana-2738	24	23	and	and	CCONJ
cana-2738	24	24	buehrer	buehrer	NOUN
cana-2738	24	25	1993	1993	NUM
cana-2738	24	26	)	)	PUNCT
cana-2738	25	1	[	[	X
cana-2738	25	2	15	15	NUM
cana-2738	25	3	]	]	PUNCT
cana-2738	25	4	,	,	PUNCT
cana-2738	25	5	intuitionistic	intuitionistic	ADJ
cana-2738	25	6	fuzzy	fuzzy	ADJ
cana-2738	25	7	set	set	NOUN
cana-2738	25	8	(	(	PUNCT
cana-2738	25	9	ifs	ifs	PROPN
cana-2738	25	10	)	)	PUNCT
cana-2738	25	11	(	(	PUNCT
cana-2738	25	12	atanassov	atanassov	PROPN
cana-2738	25	13	1986a	1986a	NOUN
cana-2738	25	14	,	,	PUNCT
cana-2738	25	15	1986b	1986b	NUM
cana-2738	25	16	)	)	PUNCT
cana-2738	26	1	[	[	X
cana-2738	26	2	1	1	NUM
cana-2738	26	3	,	,	PUNCT
cana-2738	26	4	2	2	NUM
cana-2738	26	5	]	]	PUNCT
cana-2738	26	6	,	,	PUNCT
cana-2738	26	7	fuzzy	fuzzy	ADJ
cana-2738	26	8	soft	soft	ADJ
cana-2738	26	9	set	set	NOUN
cana-2738	26	10	(	(	PUNCT
cana-2738	26	11	das	das	PROPN
cana-2738	26	12	et	et	PROPN
cana-2738	26	13	al	al	PROPN
cana-2738	26	14	.	.	PROPN
cana-2738	26	15	2018	2018	NUM
cana-2738	26	16	)	)	PUNCT
cana-2738	27	1	[	[	X
cana-2738	27	2	12	12	NUM
cana-2738	27	3	]	]	PUNCT
cana-2738	27	4	,	,	PUNCT
cana-2738	27	5	rough	rough	ADJ
cana-2738	27	6	set	set	NOUN
cana-2738	27	7	(	(	PUNCT
cana-2738	27	8	pawlak	pawlak	ADJ
cana-2738	27	9	1982	1982	NUM
cana-2738	27	10	)	)	PUNCT
cana-2738	28	1	[	[	X
cana-2738	28	2	25	25	NUM
cana-2738	28	3	]	]	PUNCT
cana-2738	28	4	,	,	PUNCT
cana-2738	28	5	fuzzy	fuzzy	ADJ
cana-2738	28	6	interval	interval	NOUN
cana-2738	28	7	theory	theory	NOUN
cana-2738	28	8	(	(	PUNCT
cana-2738	28	9	gorzalczany	gorzalczany	NOUN
cana-2738	28	10	1987	1987	NUM
cana-2738	28	11	)	)	PUNCT
cana-2738	29	1	[	[	X
cana-2738	29	2	18	18	NUM
cana-2738	29	3	]	]	PUNCT
cana-2738	29	4	,	,	PUNCT
cana-2738	29	5	intuitionistic	intuitionistic	ADJ
cana-2738	29	6	multi	multi	ADJ
cana-2738	29	7	fuzzy	fuzzy	ADJ
cana-2738	29	8	set	set	NOUN
cana-2738	29	9	(	(	PUNCT
cana-2738	29	10	das	das	PROPN
cana-2738	29	11	et	et	PROPN
cana-2738	29	12	al	al	PROPN
cana-2738	29	13	.	.	PROPN
cana-2738	29	14	2013	2013	NUM
cana-2738	29	15	)	)	PUNCT
cana-2738	30	1	[	[	X
cana-2738	30	2	11	11	NUM
cana-2738	30	3	]	]	PUNCT
cana-2738	30	4	,	,	PUNCT
cana-2738	30	5	interval	interval	NOUN
cana-2738	30	6	-	-	PUNCT
cana-2738	30	7	valued	value	VERB
cana-2738	30	8	intuitionistic	intuitionistic	ADJ
cana-2738	30	9	fuzzy	fuzzy	ADJ
cana-2738	30	10	set	set	NOUN
cana-2738	30	11	(	(	PUNCT
cana-2738	30	12	park	park	NOUN
cana-2738	30	13	et	et	PROPN
cana-2738	30	14	al	al	PROPN
cana-2738	30	15	.	.	PROPN
cana-2738	30	16	2008	2008	NUM
cana-2738	30	17	)	)	PUNCT
cana-2738	31	1	[	[	X
cana-2738	31	2	26	26	NUM
cana-2738	31	3	]	]	PUNCT
cana-2738	31	4	,	,	PUNCT
cana-2738	31	5	intuitionistic	intuitionistic	ADJ
cana-2738	31	6	fuzzy	fuzzy	ADJ
cana-2738	31	7	soft	soft	ADJ
cana-2738	31	8	set	set	NOUN
cana-2738	31	9	(	(	PUNCT
cana-2738	31	10	deng	deng	PROPN
cana-2738	31	11	1982	1982	NUM
cana-2738	31	12	)	)	PUNCT
cana-2738	32	1	[	[	X
cana-2738	32	2	14	14	NUM
cana-2738	32	3	]	]	PUNCT
cana-2738	32	4	and	and	CCONJ
cana-2738	32	5	neutrosophic	neutrosophic	ADJ
cana-2738	32	6	soft	soft	ADJ
cana-2738	32	7	set	set	NOUN
cana-2738	32	8	(	(	PUNCT
cana-2738	32	9	das	das	PROPN
cana-2738	32	10	et	et	PROPN
cana-2738	32	11	al	al	PROPN
cana-2738	32	12	.	.	PROPN
cana-2738	32	13	2019	2019	NUM
cana-2738	32	14	)	)	PUNCT
cana-2738	33	1	[	[	X
cana-2738	33	2	13	13	NUM
cana-2738	33	3	]	]	PUNCT
cana-2738	33	4	.	.	PUNCT
cana-2738	34	1	consequently	consequently	ADV
cana-2738	34	2	,	,	PUNCT
cana-2738	34	3	the	the	DET
cana-2738	34	4	application	application	NOUN
cana-2738	34	5	of	of	ADP
cana-2738	34	6	fuzzy	fuzzy	ADJ
cana-2738	34	7	set	set	NOUN
cana-2738	34	8	theory	theory	NOUN
cana-2738	34	9	and	and	CCONJ
cana-2738	34	10	its	its	PRON
cana-2738	34	11	extensions	extension	NOUN
cana-2738	34	12	increased	increase	VERB
cana-2738	34	13	rapidly	rapidly	ADV
cana-2738	34	14	in	in	ADP
cana-2738	34	15	the	the	DET
cana-2738	34	16	decision	decision	NOUN
cana-2738	34	17	-	-	PUNCT
cana-2738	34	18	making	make	VERB
cana-2738	34	19	methods	method	NOUN
cana-2738	34	20	in	in	ADP
cana-2738	34	21	various	various	ADJ
cana-2738	34	22	domains	domain	NOUN
cana-2738	34	23	like	like	ADP
cana-2738	34	24	medical	medical	ADJ
cana-2738	34	25	diagnosis	diagnosis	NOUN
cana-2738	34	26	(	(	PUNCT
cana-2738	34	27	das	das	PROPN
cana-2738	34	28	et	et	PROPN
cana-2738	34	29	al	al	PROPN
cana-2738	34	30	.	.	PROPN
cana-2738	34	31	2013	2013	NUM
cana-2738	34	32	)	)	PUNCT
cana-2738	35	1	[	[	X
cana-2738	35	2	11	11	NUM
cana-2738	35	3	]	]	PUNCT
cana-2738	35	4	,	,	PUNCT
cana-2738	35	5	pattern	pattern	NOUN
cana-2738	35	6	recognition	recognition	NOUN
cana-2738	35	7	(	(	PUNCT
cana-2738	35	8	wei	wei	PROPN
cana-2738	35	9	and	and	CCONJ
cana-2738	35	10	lan	lan	PROPN
cana-2738	35	11	2008	2008	NUM
cana-2738	35	12	)	)	PUNCT
cana-2738	36	1	[	[	X
cana-2738	36	2	30	30	NUM
cana-2738	36	3	]	]	PUNCT
cana-2738	36	4	,	,	PUNCT
cana-2738	36	5	data	data	VERB
cana-2738	36	6	analysis	analysis	NOUN
cana-2738	36	7	(	(	PUNCT
cana-2738	36	8	zou	zou	PROPN
cana-2738	36	9	and	and	CCONJ
cana-2738	36	10	xiao	xiao	PROPN
cana-2738	36	11	2008	2008	NUM
cana-2738	36	12	)	)	PUNCT
cana-2738	37	1	[	[	X
cana-2738	37	2	36	36	NUM
cana-2738	37	3	]	]	PUNCT
cana-2738	37	4	,	,	PUNCT
cana-2738	37	5	forecasting	forecasting	NOUN
cana-2738	37	6	(	(	PUNCT
cana-2738	37	7	xiao	xiao	PROPN
cana-2738	37	8	et	et	PROPN
cana-2738	37	9	al	al	PROPN
cana-2738	37	10	.	.	PROPN
cana-2738	37	11	2011	2011	NUM
cana-2738	37	12	)	)	PUNCT
cana-2738	38	1	[	[	X
cana-2738	38	2	31	31	NUM
cana-2738	38	3	]	]	PUNCT
cana-2738	38	4	,	,	PUNCT
cana-2738	38	5	optimization	optimization	NOUN
cana-2738	38	6	(	(	PUNCT
cana-2738	38	7	kov	kov	PROPN
cana-2738	38	8	-	-	PUNCT
cana-2738	38	9	kov	kov	PROPN
cana-2738	38	10	et	et	PROPN
cana-2738	38	11	al	al	PROPN
cana-2738	38	12	.	.	PROPN
cana-2738	38	13	2007	2007	NUM
cana-2738	38	14	)	)	PUNCT
cana-2738	39	1	[	[	X
cana-2738	39	2	20	20	NUM
cana-2738	39	3	]	]	PUNCT
cana-2738	39	4	,	,	PUNCT
cana-2738	39	5	simulation	simulation	NOUN
cana-2738	39	6	(	(	PUNCT
cana-2738	39	7	kalayathankal	kalayathankal	PROPN
cana-2738	39	8	and	and	CCONJ
cana-2738	39	9	singh	singh	PROPN
cana-2738	39	10	2010	2010	NUM
cana-2738	39	11	)	)	PUNCT
cana-2738	40	1	[	[	X
cana-2738	40	2	19	19	NUM
cana-2738	40	3	]	]	PUNCT
cana-2738	40	4	and	and	CCONJ
cana-2738	40	5	texture	texture	ADJ
cana-2738	40	6	classification	classification	NOUN
cana-2738	40	7	(	(	PUNCT
cana-2738	40	8	mushrif	mushrif	NOUN
cana-2738	40	9	et	et	PROPN
cana-2738	40	10	al	al	PROPN
cana-2738	40	11	.	.	PROPN
cana-2738	40	12	2006	2006	NUM
cana-2738	40	13	)	)	PUNCT
cana-2738	41	1	[	[	X
cana-2738	41	2	23	23	NUM
cana-2738	41	3	]	]	PUNCT
cana-2738	41	4	.	.	PUNCT
cana-2738	42	1	recently	recently	ADV
cana-2738	42	2	in	in	ADP
cana-2738	42	3	2014	2014	NUM
cana-2738	42	4	,	,	PUNCT
cana-2738	42	5	cuong	cuong	PROPN
cana-2738	42	6	(	(	PUNCT
cana-2738	42	7	2014)[10	2014)[10	NUM
cana-2738	42	8	]	]	PUNCT
cana-2738	42	9	developed	develop	VERB
cana-2738	42	10	the	the	DET
cana-2738	42	11	picture	picture	NOUN
cana-2738	42	12	fuzzy	fuzzy	ADJ
cana-2738	42	13	set	set	NOUN
cana-2738	42	14	(	(	PUNCT
cana-2738	42	15	pfs	pfs	PROPN
cana-2738	42	16	)	)	PUNCT
cana-2738	42	17	as	as	ADP
cana-2738	42	18	the	the	DET
cana-2738	42	19	generalized	generalized	ADJ
cana-2738	42	20	form	form	NOUN
cana-2738	42	21	of	of	ADP
cana-2738	42	22	fuzzy	fuzzy	ADJ
cana-2738	42	23	set	set	NOUN
cana-2738	42	24	and	and	CCONJ
cana-2738	42	25	ifs	ifs	PROPN
cana-2738	42	26	.	.	PUNCT
cana-2738	43	1	the	the	DET
cana-2738	43	2	pfs	pfs	PROPN
cana-2738	43	3	approaches	approach	NOUN
cana-2738	43	4	are	be	AUX
cana-2738	43	5	found	find	VERB
cana-2738	43	6	to	to	PART
cana-2738	43	7	be	be	AUX
cana-2738	43	8	more	more	ADV
cana-2738	43	9	appropriate	appropriate	ADJ
cana-2738	43	10	in	in	ADP
cana-2738	43	11	those	those	DET
cana-2738	43	12	cases	case	NOUN
cana-2738	43	13	when	when	SCONJ
cana-2738	43	14	the	the	DET
cana-2738	43	15	views	view	NOUN
cana-2738	43	16	of	of	ADP
cana-2738	43	17	someone	someone	PRON
cana-2738	43	18	contain	contain	VERB
cana-2738	43	19	more	more	ADJ
cana-2738	43	20	option	option	NOUN
cana-2738	43	21	types	type	NOUN
cana-2738	43	22	like	like	ADP
cana-2738	43	23	yes	yes	INTJ
cana-2738	43	24	,	,	PUNCT
cana-2738	43	25	abstain	abstain	NOUN
cana-2738	43	26	,	,	PUNCT
cana-2738	43	27	no	no	PRON
cana-2738	43	28	and	and	CCONJ
cana-2738	43	29	refusal	refusal	NOUN
cana-2738	43	30	.	.	PUNCT
cana-2738	44	1	the	the	DET
cana-2738	44	2	general	general	ADJ
cana-2738	44	3	election	election	NOUN
cana-2738	44	4	of	of	ADP
cana-2738	44	5	a	a	DET
cana-2738	44	6	country	country	NOUN
cana-2738	44	7	is	be	AUX
cana-2738	44	8	noted	note	VERB
cana-2738	44	9	as	as	ADP
cana-2738	44	10	a	a	DET
cana-2738	44	11	good	good	ADJ
cana-2738	44	12	example	example	NOUN
cana-2738	44	13	to	to	PART
cana-2738	44	14	describe	describe	VERB
cana-2738	44	15	pfs	pfs	PROPN
cana-2738	44	16	,	,	PUNCT
cana-2738	44	17	where	where	SCONJ
cana-2738	44	18	a	a	DET
cana-2738	44	19	voter	voter	NOUN
cana-2738	44	20	can	can	AUX
cana-2738	44	21	cast	cast	VERB
cana-2738	44	22	his	his	PRON
cana-2738	44	23	vote	vote	NOUN
cana-2738	44	24	in	in	ADP
cana-2738	44	25	favour	favour	NOUN
cana-2738	44	26	of	of	ADP
cana-2738	44	27	the	the	DET
cana-2738	44	28	candidate	candidate	NOUN
cana-2738	44	29	(	(	PUNCT
cana-2738	44	30	yes	yes	INTJ
cana-2738	44	31	)	)	PUNCT
cana-2738	44	32	,	,	PUNCT
cana-2738	44	33	against	against	ADP
cana-2738	44	34	the	the	DET
cana-2738	44	35	candidate	candidate	NOUN
cana-2738	44	36	(	(	PUNCT
cana-2738	44	37	no	no	INTJ
cana-2738	44	38	)	)	PUNCT
cana-2738	44	39	,	,	PUNCT
cana-2738	44	40	may	may	AUX
cana-2738	44	41	not	not	PART
cana-2738	44	42	cast	cast	VERB
cana-2738	44	43	his	his	PRON
cana-2738	44	44	vote	vote	NOUN
cana-2738	44	45	(	(	PUNCT
cana-2738	44	46	abstain	abstain	NOUN
cana-2738	44	47	)	)	PUNCT
cana-2738	44	48	or	or	CCONJ
cana-2738	44	49	may	may	AUX
cana-2738	44	50	refuse	refuse	VERB
cana-2738	44	51	to	to	PART
cana-2738	44	52	cast	cast	VERB
cana-2738	44	53	his	his	PRON
cana-2738	44	54	vote	vote	NOUN
cana-2738	44	55	in	in	ADP
cana-2738	44	56	favour	favour	NOUN
cana-2738	44	57	of	of	ADP
cana-2738	44	58	the	the	DET
cana-2738	44	59	given	give	VERB
cana-2738	44	60	candidates	candidate	NOUN
cana-2738	44	61	and	and	CCONJ
cana-2738	44	62	prefer	prefer	VERB
cana-2738	44	63	for	for	ADP
cana-2738	44	64	nota	nota	NOUN
cana-2738	44	65	(	(	PUNCT
cana-2738	44	66	refusal	refusal	NOUN
cana-2738	44	67	)	)	PUNCT
cana-2738	44	68	(	(	PUNCT
cana-2738	44	69	cong	cong	NOUN
cana-2738	44	70	and	and	CCONJ
cana-2738	44	71	son	son	NOUN
cana-2738	44	72	2015	2015	NUM
cana-2738	44	73	)	)	PUNCT
cana-2738	45	1	[	[	X
cana-2738	45	2	9	9	NUM
cana-2738	45	3	]	]	PUNCT
cana-2738	45	4	.	.	PUNCT
cana-2738	46	1	nowadays	nowadays	ADV
cana-2738	46	2	,	,	PUNCT
cana-2738	46	3	the	the	DET
cana-2738	46	4	whole	whole	ADJ
cana-2738	46	5	world	world	NOUN
cana-2738	46	6	has	have	AUX
cana-2738	46	7	become	become	VERB
cana-2738	46	8	fully	fully	ADV
cana-2738	46	9	unbalanced	unbalanced	ADJ
cana-2738	46	10	and	and	CCONJ
cana-2738	46	11	passing	pass	VERB
cana-2738	46	12	through	through	ADP
cana-2738	46	13	an	an	DET
cana-2738	46	14	uncontrolled	uncontrolled	ADJ
cana-2738	46	15	situation	situation	NOUN
cana-2738	46	16	due	due	ADP
cana-2738	46	17	to	to	ADP
cana-2738	46	18	the	the	DET
cana-2738	46	19	dangerous	dangerous	ADJ
cana-2738	46	20	and	and	CCONJ
cana-2738	46	21	novel	novel	ADJ
cana-2738	46	22	virus	virus	NOUN
cana-2738	46	23	covid-19	covid-19	PROPN
cana-2738	46	24	.	.	PUNCT
cana-2738	47	1	most	most	ADJ
cana-2738	47	2	countries	country	NOUN
cana-2738	47	3	are	be	AUX
cana-2738	47	4	totally	totally	ADV
cana-2738	47	5	stagnant	stagnant	ADJ
cana-2738	47	6	and	and	CCONJ
cana-2738	47	7	the	the	DET
cana-2738	47	8	people	people	NOUN
cana-2738	47	9	are	be	AUX
cana-2738	47	10	quarantined	quarantine	VERB
cana-2738	47	11	to	to	PART
cana-2738	47	12	make	make	VERB
cana-2738	47	13	themselves	themselves	PRON
cana-2738	47	14	safe	safe	ADJ
cana-2738	47	15	from	from	ADP
cana-2738	47	16	covid-19	covid-19	PROPN
cana-2738	47	17	(	(	PUNCT
cana-2738	47	18	ren	ren	NOUN
cana-2738	47	19	et	et	PROPN
cana-2738	47	20	al	al	PROPN
cana-2738	47	21	.	.	PROPN
cana-2738	47	22	2020	2020	NUM
cana-2738	47	23	)	)	PUNCT
cana-2738	48	1	[	[	X
cana-2738	48	2	27	27	NUM
cana-2738	48	3	]	]	PUNCT
cana-2738	48	4	.	.	PUNCT
cana-2738	49	1	many	many	ADJ
cana-2738	49	2	researchers	researcher	NOUN
cana-2738	49	3	are	be	AUX
cana-2738	49	4	continuously	continuously	ADV
cana-2738	49	5	contributing	contribute	VERB
cana-2738	49	6	to	to	ADP
cana-2738	49	7	developing	develop	VERB
cana-2738	49	8	various	various	ADJ
cana-2738	49	9	type	type	NOUN
cana-2738	49	10	of	of	ADP
cana-2738	49	11	mathematical	mathematical	ADJ
cana-2738	49	12	and	and	CCONJ
cana-2738	49	13	hybrid	hybrid	NOUN
cana-2738	49	14	models	model	NOUN
cana-2738	49	15	to	to	PART
cana-2738	49	16	predict	predict	VERB
cana-2738	49	17	the	the	DET
cana-2738	49	18	future	future	ADJ
cana-2738	49	19	trends	trend	NOUN
cana-2738	49	20	,	,	PUNCT
cana-2738	49	21	strength	strength	NOUN
cana-2738	49	22	and	and	CCONJ
cana-2738	49	23	transmission	transmission	NOUN
cana-2738	49	24	capability	capability	NOUN
cana-2738	49	25	of	of	ADP
cana-2738	49	26	covid-19	covid-19	PROPN
cana-2738	49	27	virus	virus	NOUN
cana-2738	49	28	,	,	PUNCT
cana-2738	49	29	and	and	CCONJ
cana-2738	49	30	have	have	AUX
cana-2738	49	31	drawn	draw	VERB
cana-2738	49	32	some	some	DET
cana-2738	49	33	useful	useful	ADJ
cana-2738	49	34	conclusions	conclusion	NOUN
cana-2738	49	35	which	which	PRON
cana-2738	49	36	assist	assist	VERB
cana-2738	49	37	the	the	DET
cana-2738	49	38	health	health	NOUN
cana-2738	49	39	department	department	PROPN
cana-2738	49	40	to	to	PART
cana-2738	49	41	take	take	VERB
cana-2738	49	42	the	the	DET
cana-2738	49	43	necessary	necessary	ADJ
cana-2738	49	44	precaution	precaution	NOUN
cana-2738	49	45	to	to	PART
cana-2738	49	46	track	track	VERB
cana-2738	49	47	and	and	CCONJ
cana-2738	49	48	handle	handle	VERB
cana-2738	49	49	the	the	DET
cana-2738	49	50	covid-19	covid-19	PROPN
cana-2738	49	51	situations	situation	NOUN
cana-2738	49	52	.	.	PUNCT
cana-2738	50	1	the	the	DET
cana-2738	50	2	authors	author	NOUN
cana-2738	50	3	in	in	ADP
cana-2738	50	4	melin	melin	PROPN
cana-2738	50	5	et	et	PROPN
cana-2738	50	6	al	al	PROPN
cana-2738	50	7	.	.	PROPN
cana-2738	50	8	(	(	PUNCT
cana-2738	50	9	2020	2020	NUM
cana-2738	50	10	)	)	PUNCT
cana-2738	51	1	[	[	X
cana-2738	51	2	22	22	NUM
cana-2738	51	3	]	]	PUNCT
cana-2738	51	4	introduced	introduce	VERB
cana-2738	51	5	a	a	DET
cana-2738	51	6	novel	novel	ADJ
cana-2738	51	7	hybrid	hybrid	NOUN
cana-2738	51	8	prediction	prediction	NOUN
cana-2738	51	9	model	model	NOUN
cana-2738	51	10	that	that	PRON
cana-2738	51	11	can	can	AUX
cana-2738	51	12	mergethe	mergethe	VERB
cana-2738	51	13	ensemble	ensemble	ADJ
cana-2738	51	14	architectures	architecture	NOUN
cana-2738	51	15	of	of	ADP
cana-2738	51	16	fuzzy	fuzzy	ADJ
cana-2738	51	17	logic	logic	NOUN
cana-2738	51	18	-	-	PUNCT
cana-2738	51	19	based	base	VERB
cana-2738	51	20	neural	neural	ADJ
cana-2738	51	21	networks	network	NOUN
cana-2738	51	22	for	for	ADP
cana-2738	51	23	response	response	NOUN
cana-2738	51	24	integration	integration	NOUN
cana-2738	51	25	.	.	PUNCT
cana-2738	52	1	the	the	DET
cana-2738	52	2	fundamental	fundamental	ADJ
cana-2738	52	3	concept	concept	NOUN
cana-2738	52	4	of	of	ADP
cana-2738	52	5	the	the	DET
cana-2738	52	6	proposed	propose	VERB
cana-2738	52	7	model	model	NOUN
cana-2738	52	8	is	be	AUX
cana-2738	52	9	to	to	PART
cana-2738	52	10	merge	merge	VERB
cana-2738	52	11	several	several	ADJ
cana-2738	52	12	fuzzy	fuzzy	ADV
cana-2738	52	13	-	-	PUNCT
cana-2738	52	14	based	base	VERB
cana-2738	52	15	neural	neural	ADJ
cana-2738	52	16	network	network	NOUN
cana-2738	52	17	predictors	predictor	NOUN
cana-2738	52	18	,	,	PUNCT
cana-2738	52	19	control	control	VERB
cana-2738	52	20	the	the	DET
cana-2738	52	21	uncertainty	uncertainty	NOUN
cana-2738	52	22	of	of	ADP
cana-2738	52	23	the	the	DET
cana-2738	52	24	individual	individual	ADJ
cana-2738	52	25	networks	network	NOUN
cana-2738	52	26	and	and	CCONJ
cana-2738	52	27	try	try	VERB
cana-2738	52	28	to	to	PART
cana-2738	52	29	reduce	reduce	VERB
cana-2738	52	30	the	the	DET
cana-2738	52	31	uncertainty	uncertainty	NOUN
cana-2738	52	32	of	of	ADP
cana-2738	52	33	the	the	DET
cana-2738	52	34	total	total	ADJ
cana-2738	52	35	predictions	prediction	NOUN
cana-2738	52	36	.	.	PUNCT
cana-2738	53	1	this	this	DET
cana-2738	53	2	model	model	NOUN
cana-2738	53	3	was	be	AUX
cana-2738	53	4	able	able	ADJ
cana-2738	53	5	to	to	PART
cana-2738	53	6	predict	predict	VERB
cana-2738	53	7	the	the	DET
cana-2738	53	8	future	future	ADJ
cana-2738	53	9	trends	trend	NOUN
cana-2738	53	10	of	of	ADP
cana-2738	53	11	covid-19	covid-19	PROPN
cana-2738	53	12	up	up	ADP
cana-2738	53	13	to	to	ADP
cana-2738	53	14	some	some	DET
cana-2738	53	15	extent	extent	NOUN
cana-2738	53	16	and	and	CCONJ
cana-2738	53	17	help	help	VERB
cana-2738	53	18	the	the	DET
cana-2738	53	19	authorities	authority	NOUN
cana-2738	53	20	make	make	VERB
cana-2738	53	21	the	the	DET
cana-2738	53	22	necessary	necessary	ADJ
cana-2738	53	23	decision	decision	NOUN
cana-2738	53	24	to	to	PART
cana-2738	53	25	handle	handle	VERB
cana-2738	53	26	the	the	DET
cana-2738	53	27	health	health	NOUN
cana-2738	53	28	care	care	NOUN
cana-2738	53	29	system	system	NOUN
cana-2738	53	30	in	in	ADP
cana-2738	53	31	a	a	DET
cana-2738	53	32	better	well	ADJ
cana-2738	53	33	manner	manner	NOUN
cana-2738	53	34	.	.	PUNCT
cana-2738	54	1	the	the	DET
cana-2738	54	2	authors	author	NOUN
cana-2738	54	3	in	in	ADP
cana-2738	54	4	sun	sun	PROPN
cana-2738	54	5	and	and	CCONJ
cana-2738	54	6	wang	wang	PROPN
cana-2738	54	7	(	(	PUNCT
cana-2738	54	8	2020	2020	NUM
cana-2738	54	9	)	)	PUNCT
cana-2738	55	1	[	[	X
cana-2738	55	2	28	28	NUM
cana-2738	55	3	]	]	PUNCT
cana-2738	55	4	collected	collect	VERB
cana-2738	55	5	the	the	DET
cana-2738	55	6	covid-19	covid-19	PROPN
cana-2738	55	7	data	datum	NOUN
cana-2738	55	8	from	from	ADP
cana-2738	55	9	a	a	DET
cana-2738	55	10	decided	decide	VERB
cana-2738	55	11	location	location	NOUN
cana-2738	55	12	within	within	ADP
cana-2738	55	13	a	a	DET
cana-2738	55	14	specific	specific	ADJ
cana-2738	55	15	time	time	NOUN
cana-2738	55	16	interval	interval	NOUN
cana-2738	55	17	and	and	CCONJ
cana-2738	55	18	trained	train	VERB
cana-2738	55	19	through	through	ADP
cana-2738	55	20	the	the	DET
cana-2738	55	21	ordinary	ordinary	ADJ
cana-2738	55	22	differential	differential	ADJ
cana-2738	55	23	equation	equation	NOUN
cana-2738	55	24	model	model	NOUN
cana-2738	55	25	for	for	ADP
cana-2738	55	26	fitting.then	fitting.then	ADV
cana-2738	55	27	,	,	PUNCT
cana-2738	55	28	they	they	PRON
cana-2738	55	29	modified	modify	VERB
cana-2738	55	30	the	the	DET
cana-2738	55	31	simulation	simulation	NOUN
cana-2738	55	32	by	by	ADP
cana-2738	55	33	the	the	DET
cana-2738	55	34	trained	train	VERB
cana-2738	55	35	model	model	NOUN
cana-2738	55	36	to	to	PART
cana-2738	55	37	realize	realize	VERB
cana-2738	55	38	the	the	DET
cana-2738	55	39	effect	effect	NOUN
cana-2738	55	40	of	of	ADP
cana-2738	55	41	the	the	DET
cana-2738	55	42	covid-19	covid-19	PROPN
cana-2738	55	43	affected	affected	ADJ
cana-2738	55	44	visitors	visitor	NOUN
cana-2738	55	45	.	.	PUNCT
cana-2738	56	1	they	they	PRON
cana-2738	56	2	found	find	VERB
cana-2738	56	3	that	that	SCONJ
cana-2738	56	4	the	the	DET
cana-2738	56	5	affected	affected	ADJ
cana-2738	56	6	visitors	visitor	NOUN
cana-2738	56	7	have	have	VERB
cana-2738	56	8	a	a	DET
cana-2738	56	9	great	great	ADJ
cana-2738	56	10	role	role	NOUN
cana-2738	56	11	in	in	ADP
cana-2738	56	12	the	the	DET
cana-2738	56	13	newly	newly	ADV
cana-2738	56	14	introduced	introduce	VERB
cana-2738	56	15	case	case	NOUN
cana-2738	56	16	of	of	ADP
cana-2738	56	17	covid-19	covid-19	PROPN
cana-2738	56	18	.	.	PUNCT
cana-2738	57	1	stochastic	stochastic	ADJ
cana-2738	57	2	simulations	simulation	NOUN
cana-2738	57	3	proved	prove	VERB
cana-2738	57	4	that	that	SCONJ
cana-2738	57	5	the	the	DET
cana-2738	57	6	physical	physical	ADJ
cana-2738	57	7	connections	connection	NOUN
cana-2738	57	8	could	could	AUX
cana-2738	57	9	be	be	AUX
cana-2738	57	10	rapidly	rapidly	ADV
cana-2738	57	11	increased	increase	VERB
cana-2738	57	12	due	due	ADP
cana-2738	57	13	to	to	ADP
cana-2738	57	14	the	the	DET
cana-2738	57	15	affected	affected	ADJ
cana-2738	57	16	visitors	visitor	NOUN
cana-2738	57	17	which	which	PRON
cana-2738	57	18	are	be	AUX
cana-2738	57	19	considered	consider	VERB
cana-2738	57	20	sufficient	sufficient	ADJ
cana-2738	57	21	for	for	ADP
cana-2738	57	22	the	the	DET
cana-2738	57	23	local	local	ADJ
cana-2738	57	24	outbreak	outbreak	NOUN
cana-2738	57	25	of	of	ADP
cana-2738	57	26	covid-19	covid-19	PROPN
cana-2738	57	27	.	.	PUNCT
cana-2738	58	1	the	the	DET
cana-2738	58	2	confirmed	confirm	VERB
cana-2738	58	3	case	case	NOUN
cana-2738	58	4	of	of	ADP
cana-2738	58	5	asymptomatic	asymptomatic	ADJ
cana-2738	58	6	patients	patient	NOUN
cana-2738	58	7	was	be	AUX
cana-2738	58	8	significantly	significantly	ADV
cana-2738	58	9	less	less	ADJ
cana-2738	58	10	than	than	ADP
cana-2738	58	11	the	the	DET
cana-2738	58	12	model	model	NOUN
cana-2738	58	13	predictions	prediction	NOUN
cana-2738	58	14	quantity	quantity	NOUN
cana-2738	58	15	.	.	PUNCT
cana-2738	59	1	this	this	PRON
cana-2738	59	2	indicated	indicate	VERB
cana-2738	59	3	that	that	SCONJ
cana-2738	59	4	a	a	DET
cana-2738	59	5	major	major	ADJ
cana-2738	59	6	portion	portion	NOUN
cana-2738	59	7	of	of	ADP
cana-2738	59	8	asymptomatic	asymptomatic	ADJ
cana-2738	59	9	patients	patient	NOUN
cana-2738	59	10	are	be	AUX
cana-2738	59	11	not	not	PART
cana-2738	59	12	identified	identify	VERB
cana-2738	59	13	/	/	SYM
cana-2738	59	14	found	find	VERB
cana-2738	59	15	.	.	PUNCT
cana-2738	60	1	fuzzy	fuzzy	ADJ
cana-2738	60	2	-	-	PUNCT
cana-2738	60	3	based	base	VERB
cana-2738	60	4	hybrid	hybrid	ADJ
cana-2738	60	5	approaches	approach	NOUN
cana-2738	60	6	for	for	ADP
cana-2738	60	7	forecasting	forecast	VERB
cana-2738	60	8	the	the	DET
cana-2738	60	9	confirmed	confirm	VERB
cana-2738	60	10	cases	case	NOUN
cana-2738	60	11	and	and	CCONJ
cana-2738	60	12	deaths	death	NOUN
cana-2738	60	13	of	of	ADP
cana-2738	60	14	the	the	DET
cana-2738	60	15	communications	communication	NOUN
cana-2738	60	16	on	on	ADP
cana-2738	60	17	applied	apply	VERB
cana-2738	60	18	nonlinear	nonlinear	ADJ
cana-2738	60	19	analysis	analysis	NOUN
cana-2738	60	20	issn	issn	NOUN
cana-2738	60	21	:	:	PUNCT
cana-2738	60	22	1074	1074	NUM
cana-2738	60	23	-	-	PUNCT
cana-2738	60	24	133x	133x	NUM
cana-2738	60	25	vol	vol	NOUN
cana-2738	60	26	32	32	NUM
cana-2738	60	27	no	no	NOUN
cana-2738	60	28	.	.	PUNCT
cana-2738	61	1	4s	4s	NUM
cana-2738	61	2	(	(	PUNCT
cana-2738	61	3	2025	2025	NUM
cana-2738	61	4	)	)	PUNCT
cana-2738	61	5	44	44	NUM
cana-2738	61	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2738	61	7	countries	country	NOUN
cana-2738	61	8	according	accord	VERB
cana-2738	61	9	to	to	ADP
cana-2738	61	10	their	their	PRON
cana-2738	61	11	time	time	NOUN
cana-2738	61	12	series	series	NOUN
cana-2738	61	13	are	be	AUX
cana-2738	61	14	given	give	VERB
cana-2738	61	15	in	in	ADP
cana-2738	61	16	castillo	castillo	PROPN
cana-2738	61	17	and	and	CCONJ
cana-2738	61	18	melin	melin	PROPN
cana-2738	61	19	(	(	PUNCT
cana-2738	61	20	2020	2020	NUM
cana-2738	61	21	)	)	PUNCT
cana-2738	62	1	[	[	X
cana-2738	62	2	6	6	NUM
cana-2738	62	3	]	]	PUNCT
cana-2738	62	4	.	.	PUNCT
cana-2738	63	1	the	the	DET
cana-2738	63	2	fundamental	fundamental	ADJ
cana-2738	63	3	concept	concept	NOUN
cana-2738	63	4	of	of	ADP
cana-2738	63	5	this	this	DET
cana-2738	63	6	proposed	propose	VERB
cana-2738	63	7	hybrid	hybrid	NOUN
cana-2738	63	8	method	method	NOUN
cana-2738	63	9	(	(	PUNCT
cana-2738	63	10	castillo	castillo	PROPN
cana-2738	63	11	and	and	CCONJ
cana-2738	63	12	melin	melin	PROPN
cana-2738	63	13	2020	2020	NUM
cana-2738	63	14	)	)	PUNCT
cana-2738	64	1	[	[	X
cana-2738	64	2	6	6	NUM
cana-2738	64	3	]	]	PUNCT
cana-2738	64	4	is	be	AUX
cana-2738	64	5	to	to	PART
cana-2738	64	6	combine	combine	VERB
cana-2738	64	7	the	the	DET
cana-2738	64	8	fractal	fractal	ADJ
cana-2738	64	9	dimension	dimension	NOUN
cana-2738	64	10	and	and	CCONJ
cana-2738	64	11	fuzzy	fuzzy	ADJ
cana-2738	64	12	logic	logic	NOUN
cana-2738	64	13	for	for	ADP
cana-2738	64	14	enabling	enable	VERB
cana-2738	64	15	efficient	efficient	ADJ
cana-2738	64	16	and	and	CCONJ
cana-2738	64	17	accurate	accurate	ADJ
cana-2738	64	18	forecasting	forecasting	NOUN
cana-2738	64	19	of	of	ADP
cana-2738	64	20	covid-19	covid-19	PROPN
cana-2738	64	21	time	time	NOUN
cana-2738	64	22	series	series	NOUN
cana-2738	64	23	.	.	PUNCT
cana-2738	65	1	the	the	DET
cana-2738	65	2	fractal	fractal	ADJ
cana-2738	65	3	dimension	dimension	NOUN
cana-2738	65	4	is	be	AUX
cana-2738	65	5	provided	provide	VERB
cana-2738	65	6	to	to	PART
cana-2738	65	7	differentiate	differentiate	VERB
cana-2738	65	8	and	and	CCONJ
cana-2738	65	9	categorize	categorize	VERB
cana-2738	65	10	the	the	DET
cana-2738	65	11	object	object	NOUN
cana-2738	65	12	.	.	PUNCT
cana-2738	66	1	they	they	PRON
cana-2738	66	2	introduced	introduce	VERB
cana-2738	66	3	a	a	DET
cana-2738	66	4	fuzzy	fuzzy	ADJ
cana-2738	66	5	rulebased	rulebase	VERB
cana-2738	66	6	system	system	NOUN
cana-2738	66	7	to	to	PART
cana-2738	66	8	represent	represent	VERB
cana-2738	66	9	the	the	DET
cana-2738	66	10	knowledge	knowledge	NOUN
cana-2738	66	11	about	about	ADP
cana-2738	66	12	the	the	DET
cana-2738	66	13	forecasting	forecasting	NOUN
cana-2738	66	14	time	time	NOUN
cana-2738	66	15	series	series	NOUN
cana-2738	66	16	of	of	ADP
cana-2738	66	17	the	the	DET
cana-2738	66	18	countries	country	NOUN
cana-2738	66	19	.	.	PUNCT
cana-2738	67	1	the	the	DET
cana-2738	67	2	authors	author	NOUN
cana-2738	67	3	in	in	ADP
cana-2738	67	4	castillo	castillo	PROPN
cana-2738	67	5	and	and	CCONJ
cana-2738	67	6	melin	melin	PROPN
cana-2738	67	7	(	(	PUNCT
cana-2738	67	8	2021	2021	NUM
cana-2738	67	9	)	)	PUNCT
cana-2738	68	1	[	[	X
cana-2738	68	2	7	7	X
cana-2738	68	3	]	]	PUNCT
cana-2738	68	4	introduced	introduce	VERB
cana-2738	68	5	the	the	DET
cana-2738	68	6	hybrid	hybrid	ADJ
cana-2738	68	7	procedure	procedure	NOUN
cana-2738	68	8	for	for	ADP
cana-2738	68	9	composing	compose	VERB
cana-2738	68	10	the	the	DET
cana-2738	68	11	fuzzy	fuzzy	ADJ
cana-2738	68	12	logic	logic	NOUN
cana-2738	68	13	and	and	CCONJ
cana-2738	68	14	fractal	fractal	ADJ
cana-2738	68	15	dimension	dimension	NOUN
cana-2738	68	16	which	which	PRON
cana-2738	68	17	measured	measure	VERB
cana-2738	68	18	the	the	DET
cana-2738	68	19	uncommon	uncommon	ADJ
cana-2738	68	20	activities	activity	NOUN
cana-2738	68	21	of	of	ADP
cana-2738	68	22	times	times	PROPN
cana-2738	68	23	series	series	NOUN
cana-2738	68	24	to	to	PART
cana-2738	68	25	classify	classify	VERB
cana-2738	68	26	countries	country	NOUN
cana-2738	68	27	according	accord	VERB
cana-2738	68	28	to	to	ADP
cana-2738	68	29	their	their	PRON
cana-2738	68	30	covid-19	covid-19	PROPN
cana-2738	68	31	time	time	NOUN
cana-2738	68	32	series	series	PROPN
cana-2738	68	33	data	data	PROPN
cana-2738	68	34	.	.	PUNCT
cana-2738	69	1	the	the	DET
cana-2738	69	2	proposed	propose	VERB
cana-2738	69	3	method	method	NOUN
cana-2738	69	4	generates	generate	VERB
cana-2738	69	5	an	an	DET
cana-2738	69	6	accurate	accurate	ADJ
cana-2738	69	7	classification	classification	NOUN
cana-2738	69	8	of	of	ADP
cana-2738	69	9	countries	country	NOUN
cana-2738	69	10	based	base	VERB
cana-2738	69	11	on	on	ADP
cana-2738	69	12	the	the	DET
cana-2738	69	13	complexity	complexity	NOUN
cana-2738	69	14	of	of	ADP
cana-2738	69	15	the	the	DET
cana-2738	69	16	covid-19	covid-19	PROPN
cana-2738	69	17	time	time	NOUN
cana-2738	69	18	series	series	PROPN
cana-2738	69	19	data	data	PROPN
cana-2738	69	20	.	.	PUNCT
cana-2738	70	1	editors	editor	NOUN
cana-2738	70	2	(	(	PUNCT
cana-2738	70	3	boccaletti	boccaletti	PROPN
cana-2738	70	4	et	et	PROPN
cana-2738	70	5	al	al	PROPN
cana-2738	70	6	.	.	PROPN
cana-2738	70	7	2020	2020	NUM
cana-2738	70	8	)	)	PUNCT
cana-2738	71	1	[	[	X
cana-2738	71	2	5	5	NUM
cana-2738	71	3	]	]	PUNCT
cana-2738	71	4	of	of	ADP
cana-2738	71	5	the	the	DET
cana-2738	71	6	journal	journal	PROPN
cana-2738	71	7	‘‘chaos	‘‘chaos	PROPN
cana-2738	71	8	,	,	PUNCT
cana-2738	71	9	solitons	soliton	NOUN
cana-2738	71	10	and	and	CCONJ
cana-2738	71	11	fractalsâ€	fractalsâ€	VERB
cana-2738	71	12	™	™	NOUN
cana-2738	71	13	â€	â€	NOUN
cana-2738	71	14	™	™	NOUN
cana-2738	71	15	analysed	analyse	VERB
cana-2738	71	16	the	the	DET
cana-2738	71	17	impact	impact	NOUN
cana-2738	71	18	of	of	ADP
cana-2738	71	19	covid-19	covid-19	PROPN
cana-2738	71	20	pandemic	pandemic	NOUN
cana-2738	71	21	throughout	throughout	ADP
cana-2738	71	22	the	the	DET
cana-2738	71	23	world	world	NOUN
cana-2738	71	24	and	and	CCONJ
cana-2738	71	25	felt	feel	VERB
cana-2738	71	26	the	the	DET
cana-2738	71	27	necessity	necessity	NOUN
cana-2738	71	28	to	to	PART
cana-2738	71	29	create	create	VERB
cana-2738	71	30	a	a	DET
cana-2738	71	31	unique	unique	ADJ
cana-2738	71	32	platform	platform	NOUN
cana-2738	71	33	for	for	ADP
cana-2738	71	34	the	the	DET
cana-2738	71	35	researchers	researcher	NOUN
cana-2738	71	36	to	to	PART
cana-2738	71	37	help	help	VERB
cana-2738	71	38	the	the	DET
cana-2738	71	39	society	society	NOUN
cana-2738	71	40	to	to	PART
cana-2738	71	41	avoid	avoid	VERB
cana-2738	71	42	the	the	DET
cana-2738	71	43	worst	bad	ADJ
cana-2738	71	44	effects	effect	NOUN
cana-2738	71	45	of	of	ADP
cana-2738	71	46	future	future	ADJ
cana-2738	71	47	pandemics	pandemic	NOUN
cana-2738	71	48	.	.	PUNCT
cana-2738	72	1	recently	recently	ADV
cana-2738	72	2	,	,	PUNCT
cana-2738	72	3	mishra	mishra	PROPN
cana-2738	72	4	et	et	PROPN
cana-2738	72	5	al	al	PROPN
cana-2738	72	6	.	.	PROPN
cana-2738	72	7	(	(	PUNCT
cana-2738	72	8	2021	2021	NUM
cana-2738	72	9	)	)	PUNCT
cana-2738	73	1	[	[	X
cana-2738	73	2	27	27	NUM
cana-2738	73	3	]	]	PUNCT
cana-2738	73	4	proposed	propose	VERB
cana-2738	73	5	an	an	DET
cana-2738	73	6	extended	extended	ADJ
cana-2738	73	7	fuzzy	fuzzy	ADJ
cana-2738	73	8	decision	decision	NOUN
cana-2738	73	9	-	-	PUNCT
cana-2738	73	10	making	make	VERB
cana-2738	73	11	framework	framework	NOUN
cana-2738	73	12	using	use	VERB
cana-2738	73	13	hesitant	hesitant	ADJ
cana-2738	73	14	fuzzy	fuzzy	ADJ
cana-2738	73	15	sets	set	NOUN
cana-2738	73	16	for	for	ADP
cana-2738	73	17	the	the	DET
cana-2738	73	18	drug	drug	NOUN
cana-2738	73	19	selection	selection	NOUN
cana-2738	73	20	to	to	PART
cana-2738	73	21	treat	treat	VERB
cana-2738	73	22	the	the	DET
cana-2738	73	23	mild	mild	ADJ
cana-2738	73	24	symptoms	symptom	NOUN
cana-2738	73	25	of	of	ADP
cana-2738	73	26	covid-19	covid-19	PROPN
cana-2738	73	27	.	.	PUNCT
cana-2738	74	1	although	although	SCONJ
cana-2738	74	2	the	the	DET
cana-2738	74	3	researchers	researcher	NOUN
cana-2738	74	4	are	be	AUX
cana-2738	74	5	working	work	VERB
cana-2738	74	6	hard	hard	ADV
cana-2738	74	7	,	,	PUNCT
cana-2738	74	8	they	they	PRON
cana-2738	74	9	are	be	AUX
cana-2738	74	10	still	still	ADV
cana-2738	74	11	struggling	struggle	VERB
cana-2738	74	12	to	to	PART
cana-2738	74	13	recover	recover	VERB
cana-2738	74	14	from	from	ADP
cana-2738	74	15	this	this	DET
cana-2738	74	16	unwanted	unwanted	ADJ
cana-2738	74	17	situation	situation	NOUN
cana-2738	74	18	.	.	PUNCT
cana-2738	75	1	the	the	DET
cana-2738	75	2	scientists	scientist	NOUN
cana-2738	75	3	from	from	ADP
cana-2738	75	4	different	different	ADJ
cana-2738	75	5	domains	domain	NOUN
cana-2738	75	6	are	be	AUX
cana-2738	75	7	consistently	consistently	ADV
cana-2738	75	8	trying	try	VERB
cana-2738	75	9	to	to	PART
cana-2738	75	10	apply	apply	VERB
cana-2738	75	11	their	their	PRON
cana-2738	75	12	knowledge	knowledge	NOUN
cana-2738	75	13	in	in	ADP
cana-2738	75	14	different	different	ADJ
cana-2738	75	15	perspectives	perspective	NOUN
cana-2738	75	16	such	such	ADJ
cana-2738	75	17	as	as	ADP
cana-2738	75	18	dominating	dominate	VERB
cana-2738	75	19	the	the	DET
cana-2738	75	20	virus	virus	NOUN
cana-2738	75	21	,	,	PUNCT
cana-2738	75	22	identifying	identify	VERB
cana-2738	75	23	the	the	DET
cana-2738	75	24	virus	virus	NOUN
cana-2738	75	25	,	,	PUNCT
cana-2738	75	26	isolating	isolate	VERB
cana-2738	75	27	from	from	ADP
cana-2738	75	28	the	the	DET
cana-2738	75	29	virus	virus	NOUN
cana-2738	75	30	,	,	PUNCT
cana-2738	75	31	protecting	protect	VERB
cana-2738	75	32	from	from	ADP
cana-2738	75	33	the	the	DET
cana-2738	75	34	virus	virus	NOUN
cana-2738	75	35	,	,	PUNCT
cana-2738	75	36	and	and	CCONJ
cana-2738	75	37	finding	find	VERB
cana-2738	75	38	the	the	DET
cana-2738	75	39	treatment	treatment	NOUN
cana-2738	75	40	of	of	ADP
cana-2738	75	41	the	the	DET
cana-2738	75	42	virus	virus	NOUN
cana-2738	75	43	affected	affect	VERB
cana-2738	75	44	patients	patient	NOUN
cana-2738	75	45	,	,	PUNCT
cana-2738	75	46	to	to	PART
cana-2738	75	47	manage	manage	VERB
cana-2738	75	48	the	the	DET
cana-2738	75	49	superfluous	superfluous	ADJ
cana-2738	75	50	situation	situation	NOUN
cana-2738	75	51	(	(	PUNCT
cana-2738	75	52	kumar	kumar	PROPN
cana-2738	75	53	et	et	PROPN
cana-2738	75	54	al	al	PROPN
cana-2738	75	55	.	.	PROPN
cana-2738	75	56	,	,	PUNCT
cana-2738	75	57	2020	2020	NUM
cana-2738	76	1	[	[	X
cana-2738	76	2	21	21	NUM
cana-2738	76	3	]	]	PUNCT
cana-2738	76	4	,	,	PUNCT
cana-2738	76	5	ghosh	ghosh	PROPN
cana-2738	76	6	et	et	PROPN
cana-2738	76	7	al	al	PROPN
cana-2738	76	8	.	.	PROPN
cana-2738	76	9	,	,	PUNCT
cana-2738	76	10	2020	2020	NUM
cana-2738	76	11	)	)	PUNCT
cana-2738	77	1	[	[	X
cana-2738	77	2	17	17	NUM
cana-2738	77	3	]	]	PUNCT
cana-2738	77	4	,	,	PUNCT
cana-2738	77	5	which	which	PRON
cana-2738	77	6	are	be	AUX
cana-2738	77	7	considered	consider	VERB
cana-2738	77	8	to	to	PART
cana-2738	77	9	be	be	AUX
cana-2738	77	10	the	the	DET
cana-2738	77	11	long	long	ADJ
cana-2738	77	12	term	term	NOUN
cana-2738	77	13	project	project	NOUN
cana-2738	77	14	.	.	PUNCT
cana-2738	78	1	as	as	ADP
cana-2738	78	2	an	an	DET
cana-2738	78	3	intermediate	intermediate	ADJ
cana-2738	78	4	solution	solution	NOUN
cana-2738	78	5	,	,	PUNCT
cana-2738	78	6	the	the	DET
cana-2738	78	7	most	most	ADV
cana-2738	78	8	important	important	ADJ
cana-2738	78	9	aspect	aspect	NOUN
cana-2738	78	10	is	be	AUX
cana-2738	78	11	to	to	PART
cana-2738	78	12	provide	provide	VERB
cana-2738	78	13	suitable	suitable	ADJ
cana-2738	78	14	medical	medical	ADJ
cana-2738	78	15	service	service	NOUN
cana-2738	78	16	to	to	ADP
cana-2738	78	17	the	the	DET
cana-2738	78	18	affected	affected	ADJ
cana-2738	78	19	patients	patient	NOUN
cana-2738	78	20	and	and	CCONJ
cana-2738	78	21	recover	recover	VERB
cana-2738	78	22	those	those	PRON
cana-2738	78	23	who	who	PRON
cana-2738	78	24	are	be	AUX
cana-2738	78	25	critically	critically	ADV
cana-2738	78	26	ill	ill	ADJ
cana-2738	78	27	due	due	ADJ
cana-2738	78	28	to	to	ADP
cana-2738	78	29	perilous	perilous	ADJ
cana-2738	78	30	virus	virus	NOUN
cana-2738	78	31	covid-19	covid-19	PROPN
cana-2738	78	32	.	.	PUNCT
cana-2738	79	1	the	the	DET
cana-2738	79	2	health	health	PROPN
cana-2738	79	3	department	department	PROPN
cana-2738	79	4	of	of	ADP
cana-2738	79	5	india	india	PROPN
cana-2738	79	6	has	have	AUX
cana-2738	79	7	classified	classify	VERB
cana-2738	79	8	the	the	DET
cana-2738	79	9	covid19	covid19	NOUN
cana-2738	79	10	affected	affect	VERB
cana-2738	79	11	patients	patient	NOUN
cana-2738	79	12	into	into	ADP
cana-2738	79	13	some	some	DET
cana-2738	79	14	categories	category	NOUN
cana-2738	79	15	according	accord	VERB
cana-2738	79	16	to	to	ADP
cana-2738	79	17	the	the	DET
cana-2738	79	18	patients	patient	NOUN
cana-2738	79	19	physical	physical	ADJ
cana-2738	79	20	condition	condition	NOUN
cana-2738	79	21	.	.	PUNCT
cana-2738	80	1	the	the	DET
cana-2738	80	2	extreme	extreme	ADJ
cana-2738	80	3	condition	condition	NOUN
cana-2738	80	4	is	be	AUX
cana-2738	80	5	called	call	VERB
cana-2738	80	6	severe	severe	ADJ
cana-2738	80	7	cases	case	NOUN
cana-2738	80	8	,	,	PUNCT
cana-2738	80	9	and	and	CCONJ
cana-2738	80	10	this	this	DET
cana-2738	80	11	type	type	NOUN
cana-2738	80	12	of	of	ADP
cana-2738	80	13	patient	patient	NOUN
cana-2738	80	14	requires	require	VERB
cana-2738	80	15	quality	quality	NOUN
cana-2738	80	16	treatment	treatment	NOUN
cana-2738	80	17	(	(	PUNCT
cana-2738	80	18	clinical	clinical	ADJ
cana-2738	80	19	management	management	NOUN
cana-2738	80	20	protocol	protocol	NOUN
cana-2738	80	21	2020	2020	NUM
cana-2738	80	22	)	)	PUNCT
cana-2738	81	1	[	[	X
cana-2738	81	2	8	8	NUM
cana-2738	81	3	]	]	PUNCT
cana-2738	81	4	.	.	PUNCT
cana-2738	82	1	in	in	ADP
cana-2738	82	2	current	current	ADJ
cana-2738	82	3	scenario	scenario	NOUN
cana-2738	82	4	people	people	NOUN
cana-2738	82	5	with	with	ADP
cana-2738	82	6	symptom	symptom	NOUN
cana-2738	82	7	of	of	ADP
cana-2738	82	8	covid-19	covid-19	PROPN
cana-2738	82	9	like	like	ADP
cana-2738	82	10	fever	fever	NOUN
cana-2738	82	11	,	,	PUNCT
cana-2738	82	12	cough	cough	NOUN
cana-2738	82	13	,	,	PUNCT
cana-2738	82	14	sneezing	sneeze	VERB
cana-2738	82	15	,	,	PUNCT
cana-2738	82	16	sore	sore	ADJ
cana-2738	82	17	throat	throat	NOUN
cana-2738	82	18	,	,	PUNCT
cana-2738	82	19	loss	loss	NOUN
cana-2738	82	20	of	of	ADP
cana-2738	82	21	taste	taste	NOUN
cana-2738	82	22	and	and	CCONJ
cana-2738	82	23	smell	smell	NOUN
cana-2738	82	24	etc	etc	X
cana-2738	82	25	.	.	X
cana-2738	82	26	,	,	PUNCT
cana-2738	82	27	were	be	AUX
cana-2738	82	28	panic	panic	NOUN
cana-2738	82	29	about	about	ADP
cana-2738	82	30	the	the	DET
cana-2738	82	31	disease	disease	NOUN
cana-2738	82	32	,	,	PUNCT
cana-2738	82	33	and	and	CCONJ
cana-2738	82	34	the	the	DET
cana-2738	82	35	diagnosis	diagnosis	NOUN
cana-2738	82	36	of	of	ADP
cana-2738	82	37	covid-19	covid-19	PROPN
cana-2738	82	38	takes	take	VERB
cana-2738	82	39	many	many	ADJ
cana-2738	82	40	hours	hour	NOUN
cana-2738	82	41	and	and	CCONJ
cana-2738	82	42	people	people	NOUN
cana-2738	82	43	can	can	AUX
cana-2738	82	44	not	not	PART
cana-2738	82	45	go	go	VERB
cana-2738	82	46	for	for	ADP
cana-2738	82	47	the	the	DET
cana-2738	82	48	test	test	NOUN
cana-2738	82	49	frequently	frequently	ADV
cana-2738	82	50	.	.	PUNCT
cana-2738	83	1	some	some	DET
cana-2738	83	2	other	other	ADJ
cana-2738	83	3	diseases	disease	NOUN
cana-2738	83	4	like	like	ADP
cana-2738	83	5	flu	flu	NOUN
cana-2738	83	6	,	,	PUNCT
cana-2738	83	7	pneumonia	pneumonia	NOUN
cana-2738	83	8	,	,	PUNCT
cana-2738	83	9	cold	cold	ADJ
cana-2738	83	10	etc	etc	X
cana-2738	83	11	.	.	X
cana-2738	83	12	,	,	PUNCT
cana-2738	83	13	also	also	ADV
cana-2738	83	14	has	have	VERB
cana-2738	83	15	the	the	DET
cana-2738	83	16	same	same	ADJ
cana-2738	83	17	symptoms	symptom	NOUN
cana-2738	83	18	.	.	PUNCT
cana-2738	84	1	each	each	DET
cana-2738	84	2	patients	patient	NOUN
cana-2738	84	3	has	have	VERB
cana-2738	84	4	unique	unique	ADJ
cana-2738	84	5	experience	experience	NOUN
cana-2738	84	6	of	of	ADP
cana-2738	84	7	that	that	DET
cana-2738	84	8	particular	particular	ADJ
cana-2738	84	9	symptom	symptom	NOUN
cana-2738	84	10	and	and	CCONJ
cana-2738	84	11	some	some	DET
cana-2738	84	12	time	time	NOUN
cana-2738	84	13	they	they	PRON
cana-2738	84	14	may	may	AUX
cana-2738	84	15	not	not	PART
cana-2738	84	16	experience	experience	VERB
cana-2738	84	17	that	that	DET
cana-2738	84	18	symptom	symptom	NOUN
cana-2738	84	19	even	even	ADV
cana-2738	84	20	though	though	SCONJ
cana-2738	84	21	they	they	PRON
cana-2738	84	22	were	be	AUX
cana-2738	84	23	affected	affect	VERB
cana-2738	84	24	by	by	ADP
cana-2738	84	25	the	the	DET
cana-2738	84	26	covid-19	covid-19	PROPN
cana-2738	84	27	.	.	PUNCT
cana-2738	84	28	to	to	PART
cana-2738	84	29	fill	fill	VERB
cana-2738	84	30	up	up	ADP
cana-2738	84	31	this	this	DET
cana-2738	84	32	research	research	NOUN
cana-2738	84	33	gap	gap	NOUN
cana-2738	84	34	,	,	PUNCT
cana-2738	84	35	this	this	DET
cana-2738	84	36	paper	paper	NOUN
cana-2738	84	37	proposes	propose	VERB
cana-2738	84	38	pythagorean	pythagorean	PROPN
cana-2738	84	39	fuzzy	fuzzy	ADJ
cana-2738	84	40	𝛿	𝛿	ADJ
cana-2738	84	41	(	(	PUNCT
cana-2738	84	42	resp	resp	NOUN
cana-2738	84	43	.	.	PUNCT
cana-2738	85	1	𝛿𝛼	𝛿𝛼	NOUN
cana-2738	85	2	,	,	PUNCT
cana-2738	85	3	𝛿𝒮	𝛿𝒮	NOUN
cana-2738	85	4	,	,	PUNCT
cana-2738	85	5	𝛿𝒫	𝛿𝒫	NOUN
cana-2738	85	6	&	&	CCONJ
cana-2738	85	7	𝛿𝛽	𝛿𝛽	NOUN
cana-2738	85	8	or	or	CCONJ
cana-2738	85	9	𝑒∗)open	𝑒∗)open	NUM
cana-2738	85	10	,	,	PUNCT
cana-2738	85	11	closed	closed	ADJ
cana-2738	85	12	mappings	mapping	NOUN
cana-2738	85	13	and	and	CCONJ
cana-2738	85	14	an	an	DET
cana-2738	85	15	alternative	alternative	ADJ
cana-2738	85	16	pythagorean	pythagorean	NOUN
cana-2738	85	17	fuzzy	fuzzy	ADJ
cana-2738	85	18	set	set	VERB
cana-2738	85	19	based	base	VERB
cana-2738	85	20	approach	approach	NOUN
cana-2738	85	21	,	,	PUNCT
cana-2738	85	22	here	here	ADV
cana-2738	85	23	we	we	PRON
cana-2738	85	24	tried	try	VERB
cana-2738	85	25	to	to	PART
cana-2738	85	26	diagnosis	diagnosis	VERB
cana-2738	85	27	covid-19	covid-19	PROPN
cana-2738	85	28	with	with	ADP
cana-2738	85	29	the	the	DET
cana-2738	85	30	help	help	NOUN
cana-2738	85	31	of	of	ADP
cana-2738	85	32	pythagorean	pythagorean	PROPN
cana-2738	85	33	fuzzy	fuzzy	ADJ
cana-2738	85	34	sets	set	NOUN
cana-2738	85	35	which	which	PRON
cana-2738	85	36	helps	help	VERB
cana-2738	85	37	to	to	PART
cana-2738	85	38	record	record	VERB
cana-2738	85	39	all	all	DET
cana-2738	85	40	symptoms	symptom	NOUN
cana-2738	85	41	in	in	ADP
cana-2738	85	42	preccised	preccised	ADJ
cana-2738	85	43	manner	manner	NOUN
cana-2738	85	44	.	.	PUNCT
cana-2738	86	1	2	2	NUM
cana-2738	86	2	preliminaries	preliminary	NOUN
cana-2738	86	3	we	we	PRON
cana-2738	86	4	recall	recall	VERB
cana-2738	86	5	some	some	DET
cana-2738	86	6	basic	basic	ADJ
cana-2738	86	7	notions	notion	NOUN
cana-2738	86	8	of	of	ADP
cana-2738	86	9	fuzzy	fuzzy	ADJ
cana-2738	86	10	sets	set	NOUN
cana-2738	86	11	,	,	PUNCT
cana-2738	86	12	𝐼𝐹𝑆	𝐼𝐹𝑆	PROPN
cana-2738	86	13	’s	’s	PART
cana-2738	86	14	and	and	CCONJ
cana-2738	86	15	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2738	86	16	’s	’s	PART
cana-2738	86	17	.	.	PUNCT
cana-2738	87	1	definition	definition	NOUN
cana-2738	87	2	2.1	2.1	NUM
cana-2738	87	3	[	[	SYM
cana-2738	87	4	35	35	NUM
cana-2738	87	5	]	]	PUNCT
cana-2738	87	6	let	let	VERB
cana-2738	87	7	𝑋	𝑋	NOUN
cana-2738	87	8	be	be	AUX
cana-2738	87	9	a	a	DET
cana-2738	87	10	nonempty	nonempty	ADV
cana-2738	87	11	set	set	VERB
cana-2738	87	12	.	.	PUNCT
cana-2738	88	1	a	a	DET
cana-2738	88	2	fuzzy	fuzzy	ADJ
cana-2738	88	3	set	set	VERB
cana-2738	88	4	𝐴	𝐴	PROPN
cana-2738	88	5	in	in	ADP
cana-2738	88	6	𝑋	𝑋	PROPN
cana-2738	88	7	is	be	AUX
cana-2738	88	8	characterized	characterize	VERB
cana-2738	88	9	by	by	ADP
cana-2738	88	10	a	a	DET
cana-2738	88	11	membership	membership	NOUN
cana-2738	88	12	function	function	NOUN
cana-2738	88	13	𝜇𝐴	𝜇𝐴	ADP
cana-2738	88	14	:	:	PUNCT
cana-2738	88	15	𝑋	𝑋	PROPN
cana-2738	88	16	→	→	SYM
cana-2738	89	1	[	[	X
cana-2738	89	2	0,1	0,1	NUM
cana-2738	89	3	]	]	PUNCT
cana-2738	89	4	.	.	PUNCT
cana-2738	90	1	that	that	PRON
cana-2738	90	2	is	be	AUX
cana-2738	90	3	:	:	PUNCT
cana-2738	90	4	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-2738	90	5	)	)	PUNCT
cana-2738	90	6	=	=	NOUN
cana-2738	90	7	{	{	PUNCT
cana-2738	90	8	1	1	NUM
cana-2738	90	9	,	,	PUNCT
cana-2738	90	10	if	if	SCONJ
cana-2738	90	11	𝑥	𝑥	PRON
cana-2738	90	12	∈	∈	PROPN
cana-2738	90	13	𝑋	𝑋	NOUN
cana-2738	90	14	0	0	NUM
cana-2738	90	15	,	,	PUNCT
cana-2738	90	16	if	if	SCONJ
cana-2738	90	17	𝑥	𝑥	PROPN
cana-2738	90	18	∉	∉	X
cana-2738	90	19	𝑋	𝑋	PROPN
cana-2738	90	20	(	(	PUNCT
cana-2738	90	21	0,1	0,1	NUM
cana-2738	90	22	)	)	PUNCT
cana-2738	90	23	if	if	SCONJ
cana-2738	90	24	𝑥	𝑥	PRON
cana-2738	90	25	ispartlyin	ispartlyin	VERB
cana-2738	90	26	𝑋.	𝑋.	PROPN
cana-2738	90	27	communications	communication	NOUN
cana-2738	90	28	on	on	ADP
cana-2738	90	29	applied	apply	VERB
cana-2738	90	30	nonlinear	nonlinear	ADJ
cana-2738	90	31	analysis	analysis	NOUN
cana-2738	90	32	issn	issn	NOUN
cana-2738	90	33	:	:	PUNCT
cana-2738	90	34	1074	1074	NUM
cana-2738	90	35	-	-	PUNCT
cana-2738	90	36	133x	133x	NUM
cana-2738	90	37	vol	vol	NOUN
cana-2738	90	38	32	32	NUM
cana-2738	90	39	no	no	NOUN
cana-2738	90	40	.	.	PUNCT
cana-2738	91	1	4s	4s	NUM
cana-2738	91	2	(	(	PUNCT
cana-2738	91	3	2025	2025	NUM
cana-2738	91	4	)	)	PUNCT
cana-2738	91	5	45	45	NUM
cana-2738	91	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2738	91	7	alternatively	alternatively	ADV
cana-2738	91	8	,	,	PUNCT
cana-2738	91	9	a	a	DET
cana-2738	91	10	fuzzy	fuzzy	ADJ
cana-2738	91	11	set	set	VERB
cana-2738	91	12	𝐴	𝐴	PROPN
cana-2738	91	13	in	in	ADP
cana-2738	91	14	𝑋	𝑋	PROPN
cana-2738	91	15	is	be	AUX
cana-2738	91	16	an	an	DET
cana-2738	91	17	object	object	NOUN
cana-2738	91	18	having	have	VERB
cana-2738	91	19	the	the	DET
cana-2738	91	20	form	form	NOUN
cana-2738	91	21	𝐴	𝐴	NOUN
cana-2738	91	22	=	=	PUNCT
cana-2738	91	23	{	{	PUNCT
cana-2738	91	24	<	<	X
cana-2738	91	25	𝑥	𝑥	X
cana-2738	91	26	,	,	PUNCT
cana-2738	91	27	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-2738	91	28	)	)	PUNCT
cana-2738	91	29	>	>	PUNCT
cana-2738	92	1	|𝑥	|𝑥	PROPN
cana-2738	92	2	∈	∈	PROPN
cana-2738	92	3	𝑋	𝑋	PROPN
cana-2738	92	4	}	}	PUNCT
cana-2738	92	5	or	or	CCONJ
cana-2738	92	6	𝐴	𝐴	PROPN
cana-2738	92	7	=	=	PUNCT
cana-2738	92	8	{	{	PUNCT
cana-2738	92	9	⟨	⟨	NOUN
cana-2738	92	10	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-2738	92	11	)	)	PUNCT
cana-2738	92	12	𝑥	𝑥	DET
cana-2738	92	13	⟩	⟩	NOUN
cana-2738	92	14	|𝑥	|𝑥	NOUN
cana-2738	92	15	∈	∈	PROPN
cana-2738	92	16	𝑋	𝑋	PROPN
cana-2738	92	17	}	}	PUNCT
cana-2738	92	18	,	,	PUNCT
cana-2738	92	19	where	where	SCONJ
cana-2738	92	20	the	the	DET
cana-2738	92	21	function	function	NOUN
cana-2738	92	22	𝜇𝐴(𝑥	𝜇𝐴(𝑥	VERB
cana-2738	92	23	):	):	PUNCT
cana-2738	92	24	𝑋	𝑋	PROPN
cana-2738	92	25	→	→	SYM
cana-2738	92	26	[	[	X
cana-2738	92	27	0,1	0,1	NUM
cana-2738	92	28	]	]	PUNCT
cana-2738	92	29	defines	define	VERB
cana-2738	92	30	the	the	DET
cana-2738	92	31	degree	degree	NOUN
cana-2738	92	32	of	of	ADP
cana-2738	92	33	membership	membership	NOUN
cana-2738	92	34	of	of	ADP
cana-2738	92	35	the	the	DET
cana-2738	92	36	element	element	NOUN
cana-2738	92	37	,	,	PUNCT
cana-2738	92	38	𝑥	𝑥	PROPN
cana-2738	92	39	∈	∈	PROPN
cana-2738	92	40	𝑋.	𝑋.	PROPN
cana-2738	92	41	the	the	PRON
cana-2738	92	42	closer	close	ADV
cana-2738	92	43	the	the	DET
cana-2738	92	44	membership	membership	NOUN
cana-2738	92	45	value	value	NOUN
cana-2738	92	46	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NOUN
cana-2738	92	47	)	)	PUNCT
cana-2738	92	48	to	to	ADP
cana-2738	92	49	1	1	NUM
cana-2738	92	50	,	,	PUNCT
cana-2738	92	51	the	the	PRON
cana-2738	92	52	more	more	ADJ
cana-2738	92	53	𝑥	𝑥	NOUN
cana-2738	92	54	belongs	belong	VERB
cana-2738	92	55	to	to	ADP
cana-2738	92	56	𝐴	𝐴	PROPN
cana-2738	92	57	,	,	PUNCT
cana-2738	92	58	where	where	SCONJ
cana-2738	92	59	the	the	DET
cana-2738	92	60	grades	grade	NOUN
cana-2738	92	61	1	1	NUM
cana-2738	92	62	and	and	CCONJ
cana-2738	92	63	0	0	NUM
cana-2738	92	64	represent	represent	VERB
cana-2738	92	65	full	full	ADJ
cana-2738	92	66	membership	membership	NOUN
cana-2738	92	67	and	and	CCONJ
cana-2738	92	68	full	full	ADJ
cana-2738	92	69	nonmembership	nonmembership	NOUN
cana-2738	92	70	.	.	PUNCT
cana-2738	93	1	fuzzy	fuzzy	ADJ
cana-2738	93	2	set	set	NOUN
cana-2738	93	3	is	be	AUX
cana-2738	93	4	a	a	DET
cana-2738	93	5	collection	collection	NOUN
cana-2738	93	6	of	of	ADP
cana-2738	93	7	objects	object	NOUN
cana-2738	93	8	with	with	ADP
cana-2738	93	9	graded	grade	VERB
cana-2738	93	10	membership	membership	NOUN
cana-2738	93	11	,	,	PUNCT
cana-2738	93	12	that	that	ADV
cana-2738	93	13	is	is	ADV
cana-2738	93	14	,	,	PUNCT
cana-2738	93	15	having	have	VERB
cana-2738	93	16	degree	degree	NOUN
cana-2738	93	17	of	of	ADP
cana-2738	93	18	membership	membership	NOUN
cana-2738	93	19	.	.	PUNCT
cana-2738	94	1	fuzzy	fuzzy	ADJ
cana-2738	94	2	set	set	NOUN
cana-2738	94	3	is	be	AUX
cana-2738	94	4	an	an	DET
cana-2738	94	5	extension	extension	NOUN
cana-2738	94	6	of	of	ADP
cana-2738	94	7	the	the	DET
cana-2738	94	8	classical	classical	ADJ
cana-2738	94	9	notion	notion	NOUN
cana-2738	94	10	of	of	ADP
cana-2738	94	11	set	set	NOUN
cana-2738	94	12	.	.	PUNCT
cana-2738	95	1	in	in	ADP
cana-2738	95	2	classical	classical	ADJ
cana-2738	95	3	set	set	NOUN
cana-2738	95	4	theory	theory	NOUN
cana-2738	95	5	,	,	PUNCT
cana-2738	95	6	the	the	DET
cana-2738	95	7	membership	membership	NOUN
cana-2738	95	8	of	of	ADP
cana-2738	95	9	elements	element	NOUN
cana-2738	95	10	in	in	ADP
cana-2738	95	11	a	a	DET
cana-2738	95	12	set	set	NOUN
cana-2738	95	13	is	be	AUX
cana-2738	95	14	assessed	assess	VERB
cana-2738	95	15	in	in	ADP
cana-2738	95	16	a	a	DET
cana-2738	95	17	binary	binary	ADJ
cana-2738	95	18	terms	term	NOUN
cana-2738	95	19	according	accord	VERB
cana-2738	95	20	to	to	ADP
cana-2738	95	21	a	a	DET
cana-2738	95	22	bivalent	bivalent	ADJ
cana-2738	95	23	condition	condition	NOUN
cana-2738	95	24	;	;	PUNCT
cana-2738	95	25	an	an	DET
cana-2738	95	26	element	element	NOUN
cana-2738	95	27	either	either	CCONJ
cana-2738	95	28	belongs	belong	VERB
cana-2738	95	29	or	or	CCONJ
cana-2738	95	30	does	do	AUX
cana-2738	95	31	not	not	PART
cana-2738	95	32	belong	belong	VERB
cana-2738	95	33	to	to	ADP
cana-2738	95	34	the	the	DET
cana-2738	95	35	set	set	NOUN
cana-2738	95	36	.	.	PUNCT
cana-2738	96	1	classical	classical	ADJ
cana-2738	96	2	bivalent	bivalent	ADJ
cana-2738	96	3	sets	set	NOUN
cana-2738	96	4	are	be	AUX
cana-2738	96	5	in	in	ADP
cana-2738	96	6	fuzzy	fuzzy	ADJ
cana-2738	96	7	set	set	NOUN
cana-2738	96	8	theory	theory	NOUN
cana-2738	96	9	called	call	VERB
cana-2738	96	10	crisp	crisp	ADJ
cana-2738	96	11	sets	set	NOUN
cana-2738	96	12	.	.	PUNCT
cana-2738	97	1	fuzzy	fuzzy	ADJ
cana-2738	97	2	sets	set	NOUN
cana-2738	97	3	are	be	AUX
cana-2738	97	4	generalized	generalized	ADJ
cana-2738	97	5	classical	classical	ADJ
cana-2738	97	6	sets	set	NOUN
cana-2738	97	7	,	,	PUNCT
cana-2738	97	8	since	since	SCONJ
cana-2738	97	9	the	the	DET
cana-2738	97	10	indicator	indicator	NOUN
cana-2738	97	11	function	function	NOUN
cana-2738	97	12	of	of	ADP
cana-2738	97	13	classical	classical	ADJ
cana-2738	97	14	sets	set	NOUN
cana-2738	97	15	is	be	AUX
cana-2738	97	16	special	special	ADJ
cana-2738	97	17	cases	case	NOUN
cana-2738	97	18	of	of	ADP
cana-2738	97	19	the	the	DET
cana-2738	97	20	membership	membership	NOUN
cana-2738	97	21	functions	function	NOUN
cana-2738	97	22	of	of	ADP
cana-2738	97	23	fuzzy	fuzzy	ADJ
cana-2738	97	24	sets	set	NOUN
cana-2738	97	25	,	,	PUNCT
cana-2738	97	26	if	if	SCONJ
cana-2738	97	27	the	the	DET
cana-2738	97	28	latter	latter	ADJ
cana-2738	97	29	only	only	ADV
cana-2738	97	30	take	take	VERB
cana-2738	97	31	values	value	NOUN
cana-2738	97	32	0	0	NUM
cana-2738	97	33	or	or	CCONJ
cana-2738	97	34	1	1	NUM
cana-2738	97	35	.	.	X
cana-2738	97	36	fuzzy	fuzzy	ADJ
cana-2738	97	37	sets	set	NOUN
cana-2738	97	38	theory	theory	NOUN
cana-2738	97	39	permits	permit	VERB
cana-2738	97	40	the	the	DET
cana-2738	97	41	gradual	gradual	ADJ
cana-2738	97	42	assessment	assessment	NOUN
cana-2738	97	43	of	of	ADP
cana-2738	97	44	the	the	DET
cana-2738	97	45	membership	membership	NOUN
cana-2738	97	46	of	of	ADP
cana-2738	97	47	element	element	NOUN
cana-2738	97	48	in	in	ADP
cana-2738	97	49	a	a	DET
cana-2738	97	50	set	set	NOUN
cana-2738	97	51	;	;	PUNCT
cana-2738	97	52	this	this	PRON
cana-2738	97	53	is	be	AUX
cana-2738	97	54	described	describe	VERB
cana-2738	97	55	with	with	ADP
cana-2738	97	56	the	the	DET
cana-2738	97	57	aid	aid	NOUN
cana-2738	97	58	of	of	ADP
cana-2738	97	59	a	a	DET
cana-2738	97	60	membership	membership	NOUN
cana-2738	97	61	function	function	NOUN
cana-2738	97	62	valued	value	VERB
cana-2738	97	63	in	in	ADP
cana-2738	97	64	the	the	DET
cana-2738	97	65	real	real	ADJ
cana-2738	97	66	unit	unit	NOUN
cana-2738	97	67	interval	interval	NOUN
cana-2738	97	68	[	[	X
cana-2738	97	69	0,1	0,1	NUM
cana-2738	97	70	]	]	PUNCT
cana-2738	97	71	.	.	PUNCT
cana-2738	98	1	let	let	VERB
cana-2738	98	2	us	we	PRON
cana-2738	98	3	consider	consider	VERB
cana-2738	98	4	two	two	NUM
cana-2738	98	5	examples	example	NOUN
cana-2738	98	6	:	:	PUNCT
cana-2738	98	7	(	(	PUNCT
cana-2738	98	8	i	i	NOUN
cana-2738	98	9	)	)	PUNCT
cana-2738	98	10	all	all	DET
cana-2738	98	11	employees	employee	NOUN
cana-2738	98	12	of	of	ADP
cana-2738	98	13	𝑋𝑌𝑍	𝑋𝑌𝑍	PROPN
cana-2738	98	14	who	who	PRON
cana-2738	98	15	are	be	AUX
cana-2738	98	16	over	over	ADP
cana-2738	98	17	1.8𝑚	1.8𝑚	NUM
cana-2738	98	18	in	in	ADP
cana-2738	98	19	height	height	NOUN
cana-2738	98	20	;	;	PUNCT
cana-2738	98	21	(	(	PUNCT
cana-2738	98	22	ii	ii	NOUN
cana-2738	98	23	)	)	PUNCT
cana-2738	98	24	all	all	DET
cana-2738	98	25	employees	employee	NOUN
cana-2738	98	26	of	of	ADP
cana-2738	98	27	𝑋𝑌𝑍	𝑋𝑌𝑍	PROPN
cana-2738	98	28	who	who	PRON
cana-2738	98	29	are	be	AUX
cana-2738	98	30	tall	tall	ADJ
cana-2738	98	31	.	.	PUNCT
cana-2738	99	1	the	the	DET
cana-2738	99	2	first	first	ADJ
cana-2738	99	3	example	example	NOUN
cana-2738	99	4	is	be	AUX
cana-2738	99	5	a	a	DET
cana-2738	99	6	classical	classical	ADJ
cana-2738	99	7	set	set	NOUN
cana-2738	99	8	with	with	ADP
cana-2738	99	9	a	a	DET
cana-2738	99	10	universe	universe	NOUN
cana-2738	99	11	(	(	PUNCT
cana-2738	99	12	all	all	DET
cana-2738	99	13	𝑋𝑌𝑍	𝑋𝑌𝑍	PROPN
cana-2738	99	14	employees	employee	NOUN
cana-2738	99	15	)	)	PUNCT
cana-2738	99	16	and	and	CCONJ
cana-2738	99	17	a	a	DET
cana-2738	99	18	membership	membership	NOUN
cana-2738	99	19	rule	rule	NOUN
cana-2738	99	20	that	that	PRON
cana-2738	99	21	divides	divide	VERB
cana-2738	99	22	the	the	DET
cana-2738	99	23	universe	universe	NOUN
cana-2738	99	24	into	into	ADP
cana-2738	99	25	members	member	NOUN
cana-2738	99	26	(	(	PUNCT
cana-2738	99	27	those	those	PRON
cana-2738	99	28	over	over	ADP
cana-2738	99	29	1.8𝑚	1.8𝑚	NUM
cana-2738	99	30	)	)	PUNCT
cana-2738	99	31	and	and	CCONJ
cana-2738	99	32	nonmembers	nonmember	NOUN
cana-2738	99	33	.	.	PUNCT
cana-2738	100	1	the	the	DET
cana-2738	100	2	second	second	ADJ
cana-2738	100	3	example	example	NOUN
cana-2738	100	4	is	be	AUX
cana-2738	100	5	a	a	DET
cana-2738	100	6	fuzzy	fuzzy	ADJ
cana-2738	100	7	set	set	NOUN
cana-2738	100	8	,	,	PUNCT
cana-2738	100	9	because	because	SCONJ
cana-2738	100	10	some	some	DET
cana-2738	100	11	employees	employee	NOUN
cana-2738	100	12	are	be	AUX
cana-2738	100	13	definitely	definitely	ADV
cana-2738	100	14	in	in	ADP
cana-2738	100	15	the	the	DET
cana-2738	100	16	set	set	NOUN
cana-2738	100	17	and	and	CCONJ
cana-2738	100	18	some	some	PRON
cana-2738	100	19	are	be	AUX
cana-2738	100	20	definitely	definitely	ADV
cana-2738	100	21	not	not	PART
cana-2738	100	22	in	in	ADP
cana-2738	100	23	the	the	DET
cana-2738	100	24	set	set	NOUN
cana-2738	100	25	,	,	PUNCT
cana-2738	100	26	but	but	CCONJ
cana-2738	100	27	some	some	PRON
cana-2738	100	28	are	be	AUX
cana-2738	100	29	borderline	borderline	NOUN
cana-2738	100	30	.	.	PUNCT
cana-2738	101	1	this	this	DET
cana-2738	101	2	distinction	distinction	NOUN
cana-2738	101	3	between	between	ADP
cana-2738	101	4	the	the	DET
cana-2738	101	5	ins	in	NOUN
cana-2738	101	6	,	,	PUNCT
cana-2738	101	7	the	the	DET
cana-2738	101	8	outs	out	NOUN
cana-2738	101	9	,	,	PUNCT
cana-2738	101	10	and	and	CCONJ
cana-2738	101	11	the	the	DET
cana-2738	101	12	borderline	borderline	NOUN
cana-2738	101	13	is	be	AUX
cana-2738	101	14	made	make	VERB
cana-2738	101	15	more	more	ADV
cana-2738	101	16	exact	exact	ADJ
cana-2738	101	17	by	by	ADP
cana-2738	101	18	the	the	DET
cana-2738	101	19	membership	membership	NOUN
cana-2738	101	20	function	function	NOUN
cana-2738	101	21	,	,	PUNCT
cana-2738	101	22	𝜇.	𝜇.	ADV
cana-2738	101	23	if	if	SCONJ
cana-2738	101	24	we	we	PRON
cana-2738	101	25	return	return	VERB
cana-2738	101	26	to	to	ADP
cana-2738	101	27	our	our	PRON
cana-2738	101	28	second	second	ADJ
cana-2738	101	29	example	example	NOUN
cana-2738	101	30	and	and	CCONJ
cana-2738	101	31	let	let	VERB
cana-2738	101	32	𝐴	𝐴	PROPN
cana-2738	101	33	represent	represent	VERB
cana-2738	101	34	the	the	DET
cana-2738	101	35	fuzzy	fuzzy	ADJ
cana-2738	101	36	set	set	NOUN
cana-2738	101	37	of	of	ADP
cana-2738	101	38	all	all	DET
cana-2738	101	39	tall	tall	ADJ
cana-2738	101	40	employees	employee	NOUN
cana-2738	101	41	and	and	CCONJ
cana-2738	101	42	𝑥	𝑥	PROPN
cana-2738	101	43	represent	represent	VERB
cana-2738	101	44	a	a	DET
cana-2738	101	45	member	member	NOUN
cana-2738	101	46	of	of	ADP
cana-2738	101	47	the	the	DET
cana-2738	101	48	universe	universe	ADJ
cana-2738	101	49	𝑋	𝑋	NOUN
cana-2738	101	50	(	(	PUNCT
cana-2738	101	51	i.e.	i.e.	X
cana-2738	101	52	all	all	DET
cana-2738	101	53	employees	employee	NOUN
cana-2738	101	54	)	)	PUNCT
cana-2738	101	55	,	,	PUNCT
cana-2738	101	56	then	then	ADV
cana-2738	101	57	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-2738	101	58	)	)	PUNCT
cana-2738	101	59	would	would	AUX
cana-2738	101	60	be	be	AUX
cana-2738	101	61	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-2738	101	62	)	)	PUNCT
cana-2738	101	63	=	=	SYM
cana-2738	101	64	1	1	NUM
cana-2738	101	65	if	if	SCONJ
cana-2738	101	66	𝑥	𝑥	PRON
cana-2738	101	67	is	be	AUX
cana-2738	101	68	definitely	definitely	ADV
cana-2738	101	69	tall	tall	ADJ
cana-2738	101	70	or	or	CCONJ
cana-2738	101	71	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-2738	101	72	)	)	PUNCT
cana-2738	101	73	=	=	SYM
cana-2738	101	74	0	0	PUNCT
cana-2738	102	1	if	if	SCONJ
cana-2738	102	2	𝑥	𝑥	PRON
cana-2738	102	3	is	be	AUX
cana-2738	102	4	definitely	definitely	ADV
cana-2738	102	5	not	not	PART
cana-2738	102	6	tall	tall	ADJ
cana-2738	102	7	or	or	CCONJ
cana-2738	102	8	0	0	NUM
cana-2738	102	9	<	<	X
cana-2738	102	10	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NOUN
cana-2738	102	11	)	)	PUNCT
cana-2738	102	12	<	<	X
cana-2738	102	13	1	1	NUM
cana-2738	102	14	for	for	ADP
cana-2738	102	15	borderline	borderline	NOUN
cana-2738	102	16	cases	case	NOUN
cana-2738	102	17	.	.	PUNCT
cana-2738	103	1	definition	definition	NOUN
cana-2738	103	2	2.2	2.2	NUM
cana-2738	103	3	[	[	SYM
cana-2738	103	4	1	1	NUM
cana-2738	103	5	,	,	PUNCT
cana-2738	103	6	2	2	NUM
cana-2738	103	7	,	,	PUNCT
cana-2738	103	8	3	3	NUM
cana-2738	103	9	,	,	PUNCT
cana-2738	103	10	4	4	NUM
cana-2738	103	11	]	]	PUNCT
cana-2738	103	12	let	let	VERB
cana-2738	103	13	a	a	DET
cana-2738	103	14	nonempty	nonempty	ADV
cana-2738	103	15	set	set	VERB
cana-2738	103	16	x	x	PART
cana-2738	103	17	be	be	AUX
cana-2738	103	18	fixed	fix	VERB
cana-2738	103	19	.	.	PUNCT
cana-2738	104	1	an	an	DET
cana-2738	104	2	ifs	ifs	PROPN
cana-2738	104	3	a	a	PRON
cana-2738	104	4	in	in	NOUN
cana-2738	104	5	x	x	PROPN
cana-2738	104	6	is	be	AUX
cana-2738	104	7	an	an	DET
cana-2738	104	8	object	object	NOUN
cana-2738	104	9	having	have	VERB
cana-2738	104	10	the	the	DET
cana-2738	104	11	form	form	NOUN
cana-2738	104	12	:	:	PUNCT
cana-2738	104	13	a	a	DET
cana-2738	104	14	=	=	X
cana-2738	104	15	{	{	PUNCT
cana-2738	104	16	<	<	X
cana-2738	104	17	x	x	PROPN
cana-2738	104	18	,	,	PUNCT
cana-2738	104	19	μ	μ	PROPN
cana-2738	104	20	a	a	PRON
cana-2738	104	21	(	(	PUNCT
cana-2738	104	22	x	x	NOUN
cana-2738	104	23	)	)	PUNCT
cana-2738	104	24	,	,	PUNCT
cana-2738	104	25	νa(x	νa(x	NOUN
cana-2738	104	26	)	)	PUNCT
cana-2738	104	27	>	>	PUNCT
cana-2738	105	1	|x	|x	PROPN
cana-2738	105	2	∈	∈	PROPN
cana-2738	105	3	x	x	X
cana-2738	105	4	}	}	PUNCT
cana-2738	105	5	or	or	CCONJ
cana-2738	105	6	a	a	DET
cana-2738	105	7	=	=	X
cana-2738	105	8	{	{	PUNCT
cana-2738	105	9	⟨	⟨	NOUN
cana-2738	105	10	μa(x),νa(x	μa(x),νa(x	NUM
cana-2738	105	11	)	)	PUNCT
cana-2738	105	12	x	x	SYM
cana-2738	105	13	⟩	⟩	NOUN
cana-2738	105	14	|x	|x	NOUN
cana-2738	105	15	∈	∈	PROPN
cana-2738	105	16	x	x	NOUN
cana-2738	105	17	}	}	PUNCT
cana-2738	105	18	,	,	PUNCT
cana-2738	105	19	where	where	SCONJ
cana-2738	105	20	the	the	DET
cana-2738	105	21	functions	function	NOUN
cana-2738	105	22	μ	μ	PROPN
cana-2738	105	23	a	a	PRON
cana-2738	105	24	(	(	PUNCT
cana-2738	105	25	x	x	NOUN
cana-2738	105	26	):	):	PUNCT
cana-2738	105	27	x	x	X
cana-2738	105	28	→	→	SYM
cana-2738	106	1	[	[	X
cana-2738	106	2	0,1	0,1	NUM
cana-2738	106	3	]	]	PUNCT
cana-2738	106	4	and	and	CCONJ
cana-2738	106	5	νa(x	νa(x	NOUN
cana-2738	106	6	):	):	PUNCT
cana-2738	106	7	x	x	SYM
cana-2738	106	8	→	→	SYM
cana-2738	107	1	[	[	X
cana-2738	107	2	0,1	0,1	NUM
cana-2738	107	3	]	]	PUNCT
cana-2738	107	4	define	define	VERB
cana-2738	107	5	the	the	DET
cana-2738	107	6	degree	degree	NOUN
cana-2738	107	7	of	of	ADP
cana-2738	107	8	membership	membership	NOUN
cana-2738	107	9	and	and	CCONJ
cana-2738	107	10	the	the	DET
cana-2738	107	11	degree	degree	NOUN
cana-2738	107	12	of	of	ADP
cana-2738	107	13	nonmembership	nonmembership	NOUN
cana-2738	107	14	,	,	PUNCT
cana-2738	107	15	respectively	respectively	ADV
cana-2738	107	16	,	,	PUNCT
cana-2738	107	17	of	of	ADP
cana-2738	107	18	the	the	DET
cana-2738	107	19	element	element	NOUN
cana-2738	107	20	x	x	SYM
cana-2738	107	21	∈	∈	PROPN
cana-2738	107	22	x	x	X
cana-2738	107	23	to	to	ADP
cana-2738	107	24	a	a	PRON
cana-2738	107	25	,	,	PUNCT
cana-2738	107	26	which	which	PRON
cana-2738	107	27	is	be	AUX
cana-2738	107	28	a	a	DET
cana-2738	107	29	subset	subset	NOUN
cana-2738	107	30	of	of	ADP
cana-2738	107	31	x	x	X
cana-2738	107	32	,	,	PUNCT
cana-2738	107	33	and	and	CCONJ
cana-2738	107	34	for	for	ADP
cana-2738	107	35	every	every	DET
cana-2738	107	36	x	x	SYM
cana-2738	107	37	∈	∈	PROPN
cana-2738	107	38	x	x	X
cana-2738	107	39	:	:	PUNCT
cana-2738	107	40	0	0	NUM
cana-2738	107	41	≤	≤	NUM
cana-2738	107	42	μ	μ	NUM
cana-2738	107	43	a	a	DET
cana-2738	107	44	(	(	PUNCT
cana-2738	107	45	x	x	NOUN
cana-2738	107	46	)	)	PUNCT
cana-2738	107	47	+	+	NUM
cana-2738	107	48	νa(x	νa(x	NOUN
cana-2738	107	49	)	)	PUNCT
cana-2738	107	50	≤	≤	NUM
cana-2738	107	51	1	1	NUM
cana-2738	107	52	.	.	PUNCT
cana-2738	108	1	for	for	ADP
cana-2738	108	2	each	each	DET
cana-2738	108	3	a	a	PRON
cana-2738	108	4	in	in	ADP
cana-2738	108	5	x	x	NOUN
cana-2738	108	6	:	:	PUNCT
cana-2738	108	7	πa(x	πa(x	NOUN
cana-2738	108	8	)	)	PUNCT
cana-2738	108	9	=	=	SYM
cana-2738	108	10	1	1	NUM
cana-2738	108	11	−	−	PROPN
cana-2738	108	12	μ	μ	PROPN
cana-2738	108	13	a	a	DET
cana-2738	108	14	(	(	PUNCT
cana-2738	108	15	x	x	NOUN
cana-2738	108	16	)	)	PUNCT
cana-2738	108	17	−	−	NOUN
cana-2738	108	18	νa(x	νa(x	NOUN
cana-2738	108	19	)	)	PUNCT
cana-2738	108	20	is	be	AUX
cana-2738	108	21	the	the	DET
cana-2738	108	22	intuitionistic	intuitionistic	ADJ
cana-2738	108	23	fuzzy	fuzzy	ADJ
cana-2738	108	24	set	set	VERB
cana-2738	108	25	index	index	NOUN
cana-2738	108	26	or	or	CCONJ
cana-2738	108	27	hesitation	hesitation	NOUN
cana-2738	108	28	margin	margin	NOUN
cana-2738	108	29	of	of	ADP
cana-2738	108	30	x	x	PUNCT
cana-2738	108	31	in	in	ADP
cana-2738	108	32	x.	x.	NOUN
cana-2738	108	33	the	the	DET
cana-2738	108	34	hesitation	hesitation	NOUN
cana-2738	108	35	margin	margin	NOUN
cana-2738	108	36	πa(x	πa(x	NOUN
cana-2738	108	37	)	)	PUNCT
cana-2738	109	1	is	be	AUX
cana-2738	109	2	the	the	DET
cana-2738	109	3	degree	degree	NOUN
cana-2738	109	4	of	of	ADP
cana-2738	109	5	nondeterminacy	nondeterminacy	NOUN
cana-2738	109	6	of	of	ADP
cana-2738	109	7	x	x	X
cana-2738	109	8	∈	∈	PROPN
cana-2738	109	9	x	x	PUNCT
cana-2738	109	10	to	to	ADP
cana-2738	109	11	the	the	DET
cana-2738	109	12	set	set	NOUN
cana-2738	109	13	a	a	PRON
cana-2738	109	14	and	and	CCONJ
cana-2738	109	15	πa(x	πa(x	NOUN
cana-2738	109	16	)	)	PUNCT
cana-2738	109	17	∈	∈	NOUN
cana-2738	110	1	[	[	X
cana-2738	110	2	0,1	0,1	NUM
cana-2738	110	3	]	]	PUNCT
cana-2738	110	4	.	.	PUNCT
cana-2738	111	1	the	the	DET
cana-2738	111	2	hesitation	hesitation	NOUN
cana-2738	111	3	margin	margin	NOUN
cana-2738	111	4	is	be	AUX
cana-2738	111	5	the	the	DET
cana-2738	111	6	function	function	NOUN
cana-2738	111	7	that	that	PRON
cana-2738	111	8	expresses	express	VERB
cana-2738	111	9	lack	lack	NOUN
cana-2738	111	10	of	of	ADP
cana-2738	111	11	knowledge	knowledge	NOUN
cana-2738	111	12	of	of	ADP
cana-2738	111	13	whether	whether	SCONJ
cana-2738	111	14	x	x	SYM
cana-2738	111	15	∈	∈	NOUN
cana-2738	111	16	x	x	X
cana-2738	111	17	or	or	CCONJ
cana-2738	111	18	x	x	PROPN
cana-2738	111	19	∉	∉	PROPN
cana-2738	111	20	x.	x.	PROPN
cana-2738	111	21	thus	thus	ADV
cana-2738	111	22	:	:	PUNCT
cana-2738	111	23	μ	μ	PROPN
cana-2738	111	24	a	a	PRON
cana-2738	111	25	(	(	PUNCT
cana-2738	111	26	x	x	NOUN
cana-2738	111	27	)	)	PUNCT
cana-2738	111	28	+	+	NUM
cana-2738	111	29	νa(x	νa(x	NOUN
cana-2738	111	30	)	)	PUNCT
cana-2738	111	31	+	+	CCONJ
cana-2738	111	32	πa(x	πa(x	NOUN
cana-2738	111	33	)	)	PUNCT
cana-2738	111	34	=	=	SYM
cana-2738	111	35	1	1	X
cana-2738	111	36	.	.	PUNCT
cana-2738	111	37	example	example	NOUN
cana-2738	111	38	2.1	2.1	NUM
cana-2738	111	39	let	let	VERB
cana-2738	111	40	x	x	PUNCT
cana-2738	111	41	=	=	PRON
cana-2738	111	42	{	{	PUNCT
cana-2738	111	43	x	x	PROPN
cana-2738	111	44	,	,	PUNCT
cana-2738	111	45	y	y	PROPN
cana-2738	111	46	,	,	PUNCT
cana-2738	111	47	z	z	NOUN
cana-2738	111	48	}	}	PUNCT
cana-2738	111	49	be	be	AUX
cana-2738	111	50	a	a	DET
cana-2738	111	51	fixed	fix	VERB
cana-2738	111	52	universe	universe	NOUN
cana-2738	111	53	of	of	ADP
cana-2738	111	54	discourse	discourse	NOUN
cana-2738	111	55	and	and	CCONJ
cana-2738	111	56	a	a	DET
cana-2738	111	57	=	=	X
cana-2738	111	58	{	{	PUNCT
cana-2738	111	59	⟨	⟨	VERB
cana-2738	111	60	0.6,0.1	0.6,0.1	NOUN
cana-2738	111	61	x	x	SYM
cana-2738	111	62	⟩	⟩	NOUN
cana-2738	111	63	,	,	PUNCT
cana-2738	111	64	⟨	⟨	VERB
cana-2738	111	65	0.8,0.1	0.8,0.1	PROPN
cana-2738	111	66	y	y	PROPN
cana-2738	111	67	⟩	⟩	PROPN
cana-2738	111	68	,	,	PUNCT
cana-2738	111	69	⟨	⟨	VERB
cana-2738	111	70	0.5,0.3	0.5,0.3	PROPN
cana-2738	111	71	z	z	PROPN
cana-2738	111	72	⟩	⟩	PROPN
cana-2738	111	73	}	}	PUNCT
cana-2738	111	74	,	,	PUNCT
cana-2738	111	75	be	be	AUX
cana-2738	111	76	the	the	DET
cana-2738	111	77	intuitionistic	intuitionistic	ADJ
cana-2738	111	78	fuzzy	fuzzy	ADJ
cana-2738	111	79	set	set	NOUN
cana-2738	111	80	in	in	ADP
cana-2738	111	81	x.	x.	NOUN
cana-2738	111	82	the	the	DET
cana-2738	111	83	hesitation	hesitation	NOUN
cana-2738	111	84	margins	margin	NOUN
cana-2738	111	85	of	of	ADP
cana-2738	111	86	the	the	DET
cana-2738	111	87	elements	element	NOUN
cana-2738	111	88	x	x	NOUN
cana-2738	111	89	,	,	PUNCT
cana-2738	111	90	y	y	PROPN
cana-2738	111	91	,	,	PUNCT
cana-2738	111	92	z	z	NOUN
cana-2738	111	93	to	to	ADP
cana-2738	111	94	a	a	DET
cana-2738	111	95	are	be	AUX
cana-2738	111	96	as	as	SCONJ
cana-2738	111	97	follows	follow	VERB
cana-2738	111	98	:	:	PUNCT
cana-2738	111	99	πa(x	πa(x	NOUN
cana-2738	111	100	)	)	PUNCT
cana-2738	111	101	=	=	SYM
cana-2738	111	102	0.3	0.3	NUM
cana-2738	111	103	,	,	PUNCT
cana-2738	111	104	πa(y	πa(y	X
cana-2738	111	105	)	)	PUNCT
cana-2738	111	106	=	=	SYM
cana-2738	111	107	0.1	0.1	NUM
cana-2738	111	108	and	and	CCONJ
cana-2738	111	109	πa(z	πa(z	NOUN
cana-2738	111	110	)	)	PUNCT
cana-2738	111	111	=	=	SYM
cana-2738	111	112	0.2	0.2	NUM
cana-2738	111	113	.	.	PUNCT
cana-2738	112	1	definition	definition	NOUN
cana-2738	112	2	2.3	2.3	NUM
cana-2738	113	1	[	[	X
cana-2738	113	2	32	32	NUM
cana-2738	113	3	,	,	PUNCT
cana-2738	113	4	33	33	NUM
cana-2738	113	5	,	,	PUNCT
cana-2738	113	6	34	34	NUM
cana-2738	113	7	]	]	PUNCT
cana-2738	113	8	let	let	VERB
cana-2738	113	9	x	x	PRON
cana-2738	113	10	be	be	AUX
cana-2738	113	11	a	a	DET
cana-2738	113	12	universal	universal	ADJ
cana-2738	113	13	set	set	NOUN
cana-2738	113	14	.	.	PUNCT
cana-2738	114	1	then	then	ADV
cana-2738	114	2	,	,	PUNCT
cana-2738	114	3	a	a	DET
cana-2738	114	4	pythagorean	pythagorean	PROPN
cana-2738	114	5	fuzzy	fuzzy	NOUN
cana-2738	114	6	set	set	VERB
cana-2738	114	7	a	a	PRON
cana-2738	114	8	,	,	PUNCT
cana-2738	114	9	which	which	PRON
cana-2738	114	10	is	be	AUX
cana-2738	114	11	a	a	DET
cana-2738	114	12	set	set	NOUN
cana-2738	114	13	of	of	ADP
cana-2738	114	14	ordered	order	VERB
cana-2738	114	15	pairs	pair	NOUN
cana-2738	114	16	over	over	ADP
cana-2738	114	17	x	x	NOUN
cana-2738	114	18	,	,	PUNCT
cana-2738	114	19	is	be	AUX
cana-2738	114	20	defined	define	VERB
cana-2738	114	21	by	by	ADP
cana-2738	114	22	the	the	DET
cana-2738	114	23	following	following	NOUN
cana-2738	114	24	:	:	PUNCT
cana-2738	114	25	a	a	X
cana-2738	114	26	=	=	X
cana-2738	114	27	{	{	PUNCT
cana-2738	114	28	<	<	X
cana-2738	114	29	x	x	PROPN
cana-2738	114	30	,	,	PUNCT
cana-2738	114	31	μ	μ	PROPN
cana-2738	114	32	a	a	PRON
cana-2738	114	33	(	(	PUNCT
cana-2738	114	34	x	x	NOUN
cana-2738	114	35	)	)	PUNCT
cana-2738	114	36	,	,	PUNCT
cana-2738	114	37	νa(x)|x	νa(x)|x	NOUN
cana-2738	114	38	∈	∈	NOUN
cana-2738	114	39	x	x	X
cana-2738	114	40	}	}	PUNCT
cana-2738	114	41	or	or	CCONJ
cana-2738	114	42	a	a	DET
cana-2738	114	43	=	=	X
cana-2738	114	44	{	{	PUNCT
cana-2738	114	45	⟨	⟨	NOUN
cana-2738	114	46	μa(x),νa(x	μa(x),νa(x	NUM
cana-2738	114	47	)	)	PUNCT
cana-2738	114	48	x	x	SYM
cana-2738	114	49	⟩	⟩	NOUN
cana-2738	114	50	|x	|x	NOUN
cana-2738	114	51	∈	∈	PROPN
cana-2738	114	52	x	x	NOUN
cana-2738	114	53	}	}	PUNCT
cana-2738	114	54	,	,	PUNCT
cana-2738	114	55	where	where	SCONJ
cana-2738	114	56	the	the	DET
cana-2738	114	57	functions	function	NOUN
cana-2738	114	58	μ	μ	PROPN
cana-2738	114	59	a	a	PRON
cana-2738	114	60	(	(	PUNCT
cana-2738	114	61	x	x	NOUN
cana-2738	114	62	):	):	PUNCT
cana-2738	114	63	x	x	X
cana-2738	114	64	→	→	SYM
cana-2738	115	1	[	[	X
cana-2738	115	2	0,1	0,1	NUM
cana-2738	115	3	]	]	PUNCT
cana-2738	115	4	and	and	CCONJ
cana-2738	115	5	νa(x	νa(x	NOUN
cana-2738	115	6	):	):	PUNCT
cana-2738	115	7	x	x	SYM
cana-2738	115	8	→	→	SYM
cana-2738	116	1	[	[	X
cana-2738	116	2	0,1	0,1	NUM
cana-2738	116	3	]	]	PUNCT
cana-2738	116	4	define	define	VERB
cana-2738	116	5	the	the	DET
cana-2738	116	6	degree	degree	NOUN
cana-2738	116	7	of	of	ADP
cana-2738	116	8	membership	membership	NOUN
cana-2738	116	9	and	and	CCONJ
cana-2738	116	10	the	the	DET
cana-2738	116	11	degree	degree	NOUN
cana-2738	116	12	of	of	ADP
cana-2738	116	13	nonmembership	nonmembership	NOUN
cana-2738	116	14	,	,	PUNCT
cana-2738	116	15	respectively	respectively	ADV
cana-2738	116	16	,	,	PUNCT
cana-2738	116	17	of	of	ADP
cana-2738	116	18	the	the	DET
cana-2738	116	19	element	element	NOUN
cana-2738	116	20	x	x	SYM
cana-2738	116	21	∈	∈	PROPN
cana-2738	116	22	x	x	X
cana-2738	116	23	to	to	ADP
cana-2738	116	24	a	a	PRON
cana-2738	116	25	,	,	PUNCT
cana-2738	116	26	which	which	PRON
cana-2738	116	27	is	be	AUX
cana-2738	116	28	a	a	DET
cana-2738	116	29	communications	communication	NOUN
cana-2738	116	30	on	on	ADP
cana-2738	116	31	applied	apply	VERB
cana-2738	116	32	nonlinear	nonlinear	ADJ
cana-2738	116	33	analysis	analysis	NOUN
cana-2738	116	34	issn	issn	NOUN
cana-2738	116	35	:	:	PUNCT
cana-2738	116	36	1074	1074	NUM
cana-2738	116	37	-	-	PUNCT
cana-2738	116	38	133x	133x	NUM
cana-2738	116	39	vol	vol	NOUN
cana-2738	116	40	32	32	NUM
cana-2738	116	41	no	no	NOUN
cana-2738	116	42	.	.	PUNCT
cana-2738	117	1	4s	4s	NUM
cana-2738	117	2	(	(	PUNCT
cana-2738	117	3	2025	2025	NUM
cana-2738	117	4	)	)	PUNCT
cana-2738	117	5	46	46	NUM
cana-2738	117	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2738	117	7	subset	subset	NOUN
cana-2738	117	8	of	of	ADP
cana-2738	117	9	x	x	X
cana-2738	117	10	,	,	PUNCT
cana-2738	117	11	and	and	CCONJ
cana-2738	117	12	for	for	ADP
cana-2738	117	13	every	every	DET
cana-2738	117	14	x	x	SYM
cana-2738	117	15	∈	∈	PROPN
cana-2738	117	16	x	x	X
cana-2738	117	17	,	,	PUNCT
cana-2738	117	18	0	0	NUM
cana-2738	117	19	≤	≤	NUM
cana-2738	117	20	(	(	PUNCT
cana-2738	117	21	μ	μ	PROPN
cana-2738	117	22	a	a	X
cana-2738	117	23	(	(	PUNCT
cana-2738	117	24	x))2	x))2	X
cana-2738	117	25	+	+	CCONJ
cana-2738	117	26	(	(	PUNCT
cana-2738	117	27	νa(x))2	νa(x))2	NOUN
cana-2738	117	28	≤	≤	NOUN
cana-2738	117	29	1	1	NUM
cana-2738	117	30	.	.	PUNCT
cana-2738	118	1	supposing	suppose	VERB
cana-2738	118	2	(	(	PUNCT
cana-2738	118	3	μ	μ	PROPN
cana-2738	118	4	a	a	X
cana-2738	118	5	(	(	PUNCT
cana-2738	118	6	x))2	x))2	X
cana-2738	118	7	+	+	CCONJ
cana-2738	118	8	(	(	PUNCT
cana-2738	118	9	νa(x))2	νa(x))2	NOUN
cana-2738	118	10	≤	≤	NOUN
cana-2738	118	11	1	1	NUM
cana-2738	118	12	,	,	PUNCT
cana-2738	118	13	then	then	ADV
cana-2738	118	14	there	there	PRON
cana-2738	118	15	is	be	VERB
cana-2738	118	16	a	a	DET
cana-2738	118	17	degree	degree	NOUN
cana-2738	118	18	of	of	ADP
cana-2738	118	19	indeterminacy	indeterminacy	NOUN
cana-2738	118	20	of	of	ADP
cana-2738	118	21	x	x	X
cana-2738	118	22	∈	∈	PROPN
cana-2738	118	23	x	x	PUNCT
cana-2738	118	24	to	to	ADP
cana-2738	118	25	a	a	PRON
cana-2738	118	26	defined	define	VERB
cana-2738	118	27	by	by	ADP
cana-2738	118	28	πa(x	πa(x	NOUN
cana-2738	118	29	)	)	PUNCT
cana-2738	118	30	=	=	PUNCT
cana-2738	119	1	√1	√1	ADV
cana-2738	119	2	−	−	PROPN
cana-2738	120	1	[	[	X
cana-2738	120	2	(	(	PUNCT
cana-2738	120	3	μ	μ	PROPN
cana-2738	120	4	a	a	X
cana-2738	120	5	(	(	PUNCT
cana-2738	120	6	x))2	x))2	PROPN
cana-2738	120	7	+	+	CCONJ
cana-2738	120	8	(	(	PUNCT
cana-2738	120	9	νa(x))2	νa(x))2	NOUN
cana-2738	120	10	]	]	PUNCT
cana-2738	120	11	and	and	CCONJ
cana-2738	120	12	πa(x	πa(x	NOUN
cana-2738	120	13	)	)	PUNCT
cana-2738	120	14	∈	∈	NOUN
cana-2738	121	1	[	[	X
cana-2738	121	2	0,1	0,1	NUM
cana-2738	121	3	]	]	PUNCT
cana-2738	121	4	.	.	PUNCT
cana-2738	122	1	in	in	ADP
cana-2738	122	2	what	what	PRON
cana-2738	122	3	follows	follow	VERB
cana-2738	122	4	,	,	PUNCT
cana-2738	122	5	(	(	PUNCT
cana-2738	122	6	μ	μ	PROPN
cana-2738	122	7	a	a	X
cana-2738	122	8	(	(	PUNCT
cana-2738	122	9	x))2	x))2	X
cana-2738	122	10	+	+	CCONJ
cana-2738	122	11	(	(	PUNCT
cana-2738	122	12	νa(x))2	νa(x))2	NOUN
cana-2738	122	13	+	+	CCONJ
cana-2738	122	14	(	(	PUNCT
cana-2738	122	15	πa(x))2	πa(x))2	PROPN
cana-2738	122	16	=	=	SYM
cana-2738	122	17	1	1	X
cana-2738	122	18	.	.	PUNCT
cana-2738	122	19	otherwise	otherwise	ADV
cana-2738	122	20	,	,	PUNCT
cana-2738	122	21	πa(x	πa(x	NOUN
cana-2738	122	22	)	)	PUNCT
cana-2738	122	23	=	=	SYM
cana-2738	122	24	0	0	PUNCT
cana-2738	123	1	whenever	whenever	SCONJ
cana-2738	123	2	(	(	PUNCT
cana-2738	123	3	μ	μ	PROPN
cana-2738	123	4	a	a	X
cana-2738	123	5	(	(	PUNCT
cana-2738	123	6	x))2	x))2	X
cana-2738	123	7	+	+	CCONJ
cana-2738	123	8	(	(	PUNCT
cana-2738	123	9	νa(x))2	νa(x))2	NOUN
cana-2738	123	10	=	=	SYM
cana-2738	123	11	1	1	X
cana-2738	123	12	.	.	X
cana-2738	123	13	we	we	PRON
cana-2738	123	14	denote	denote	VERB
cana-2738	123	15	the	the	DET
cana-2738	123	16	set	set	NOUN
cana-2738	123	17	of	of	ADP
cana-2738	123	18	all	all	DET
cana-2738	123	19	pfs	pfs	PROPN
cana-2738	123	20	’s	’s	NOUN
cana-2738	123	21	over	over	ADV
cana-2738	123	22	x	x	PUNCT
cana-2738	123	23	by	by	ADP
cana-2738	123	24	pfs(x	pfs(x	PROPN
cana-2738	123	25	)	)	PUNCT
cana-2738	123	26	.	.	PUNCT
cana-2738	124	1	definition	definition	NOUN
cana-2738	124	2	2.4	2.4	NUM
cana-2738	124	3	[	[	SYM
cana-2738	124	4	34	34	NUM
cana-2738	124	5	]	]	PUNCT
cana-2738	124	6	let	let	VERB
cana-2738	124	7	a	a	PRON
cana-2738	124	8	and	and	CCONJ
cana-2738	124	9	b	b	NOUN
cana-2738	124	10	be	be	AUX
cana-2738	124	11	pfs	pf	VERB
cana-2738	124	12	’s	’s	NOUN
cana-2738	124	13	of	of	ADP
cana-2738	124	14	the	the	DET
cana-2738	124	15	forms	form	NOUN
cana-2738	124	16	a	a	PRON
cana-2738	124	17	=	=	X
cana-2738	124	18	{	{	PUNCT
cana-2738	124	19	<	<	X
cana-2738	124	20	a	a	PRON
cana-2738	124	21	,	,	PUNCT
cana-2738	124	22	λa(a	λa(a	PROPN
cana-2738	124	23	)	)	PUNCT
cana-2738	124	24	,	,	PUNCT
cana-2738	124	25	μ	μ	PROPN
cana-2738	124	26	a	a	PROPN
cana-2738	124	27	(	(	PUNCT
cana-2738	124	28	a	a	NOUN
cana-2738	124	29	)	)	PUNCT
cana-2738	124	30	>	>	PUNCT
cana-2738	124	31	|a	|a	X
cana-2738	124	32	∈	∈	PROPN
cana-2738	124	33	x	x	PRON
cana-2738	124	34	}	}	PUNCT
cana-2738	124	35	and	and	CCONJ
cana-2738	124	36	b	b	X
cana-2738	124	37	=	=	PRON
cana-2738	124	38	{	{	PUNCT
cana-2738	124	39	<	<	X
cana-2738	124	40	a	a	PRON
cana-2738	124	41	,	,	PUNCT
cana-2738	124	42	λb(a	λb(a	NUM
cana-2738	124	43	)	)	PUNCT
cana-2738	124	44	,	,	PUNCT
cana-2738	124	45	μ	μ	PROPN
cana-2738	124	46	b	b	PROPN
cana-2738	124	47	(	(	PUNCT
cana-2738	124	48	a	a	NOUN
cana-2738	124	49	)	)	PUNCT
cana-2738	124	50	>	>	PUNCT
cana-2738	124	51	|a	|a	X
cana-2738	124	52	∈	∈	PROPN
cana-2738	124	53	x	x	PRON
cana-2738	124	54	}	}	PUNCT
cana-2738	124	55	.	.	PUNCT
cana-2738	125	1	then	then	ADV
cana-2738	125	2	1	1	X
cana-2738	125	3	.	.	PUNCT
cana-2738	125	4	a	a	DET
cana-2738	125	5	⊆	⊆	NUM
cana-2738	125	6	b	b	NOUN
cana-2738	125	7	if	if	SCONJ
cana-2738	125	8	and	and	CCONJ
cana-2738	125	9	only	only	ADV
cana-2738	125	10	if	if	SCONJ
cana-2738	125	11	λa(a	λa(a	PUNCT
cana-2738	125	12	)	)	PUNCT
cana-2738	125	13	≤	≤	NOUN
cana-2738	125	14	λb(a	λb(a	NOUN
cana-2738	125	15	)	)	PUNCT
cana-2738	125	16	and	and	CCONJ
cana-2738	125	17	μ	μ	NUM
cana-2738	125	18	a	a	PRON
cana-2738	125	19	(	(	PUNCT
cana-2738	125	20	a	a	NOUN
cana-2738	125	21	)	)	PUNCT
cana-2738	125	22	≥	≥	PROPN
cana-2738	125	23	μ	μ	PROPN
cana-2738	125	24	b	b	PROPN
cana-2738	125	25	(	(	PUNCT
cana-2738	125	26	a	a	NOUN
cana-2738	125	27	)	)	PUNCT
cana-2738	125	28	for	for	ADP
cana-2738	125	29	all	all	DET
cana-2738	125	30	a	a	DET
cana-2738	125	31	∈	∈	NOUN
cana-2738	125	32	x.	x.	NOUN
cana-2738	125	33	2	2	X
cana-2738	125	34	.	.	PUNCT
cana-2738	125	35	a	a	DET
cana-2738	125	36	=	=	SYM
cana-2738	125	37	b	b	NOUN
cana-2738	125	38	if	if	SCONJ
cana-2738	125	39	and	and	CCONJ
cana-2738	125	40	only	only	ADV
cana-2738	125	41	if	if	SCONJ
cana-2738	125	42	a	a	DET
cana-2738	125	43	⊆	⊆	NUM
cana-2738	125	44	b	b	NOUN
cana-2738	125	45	and	and	CCONJ
cana-2738	125	46	b	b	NOUN
cana-2738	125	47	⊆	⊆	NUM
cana-2738	125	48	a.	a.	NOUN
cana-2738	125	49	3	3	NUM
cana-2738	125	50	.	.	PUNCT
cana-2738	125	51	a̅	a̅	PROPN
cana-2738	126	1	=	=	PUNCT
cana-2738	126	2	{	{	PUNCT
cana-2738	126	3	<	<	X
cana-2738	126	4	a	a	PROPN
cana-2738	126	5	,	,	PUNCT
cana-2738	126	6	μ	μ	PROPN
cana-2738	126	7	a	a	DET
cana-2738	126	8	(	(	PUNCT
cana-2738	126	9	a	a	NOUN
cana-2738	126	10	)	)	PUNCT
cana-2738	126	11	,	,	PUNCT
cana-2738	126	12	λa(a	λa(a	PUNCT
cana-2738	126	13	)	)	PUNCT
cana-2738	126	14	>	>	PUNCT
cana-2738	126	15	|a	|a	X
cana-2738	126	16	∈	∈	PROPN
cana-2738	126	17	x	x	PRON
cana-2738	126	18	}	}	PUNCT
cana-2738	126	19	.	.	PUNCT
cana-2738	127	1	4	4	X
cana-2738	127	2	.	.	X
cana-2738	127	3	a	a	DET
cana-2738	127	4	∩	∩	ADJ
cana-2738	127	5	b	b	NOUN
cana-2738	127	6	=	=	SYM
cana-2738	127	7	{	{	PUNCT
cana-2738	127	8	<	<	X
cana-2738	127	9	a	a	PRON
cana-2738	127	10	,	,	PUNCT
cana-2738	127	11	λa(a	λa(a	ADJ
cana-2738	127	12	)	)	PUNCT
cana-2738	127	13	∧	∧	NOUN
cana-2738	127	14	λb(a	λb(a	NOUN
cana-2738	127	15	)	)	PUNCT
cana-2738	127	16	,	,	PUNCT
cana-2738	127	17	μ	μ	PROPN
cana-2738	127	18	a	a	PROPN
cana-2738	127	19	(	(	PUNCT
cana-2738	127	20	a	a	NOUN
cana-2738	127	21	)	)	PUNCT
cana-2738	127	22	∨	∨	PROPN
cana-2738	127	23	μ	μ	PROPN
cana-2738	127	24	b	b	PROPN
cana-2738	127	25	(	(	PUNCT
cana-2738	127	26	a	a	NOUN
cana-2738	127	27	)	)	PUNCT
cana-2738	127	28	>	>	PUNCT
cana-2738	127	29	|a	|a	X
cana-2738	127	30	∈	∈	PROPN
cana-2738	127	31	x	x	PRON
cana-2738	127	32	}	}	PUNCT
cana-2738	127	33	.	.	PUNCT
cana-2738	128	1	5	5	X
cana-2738	128	2	.	.	X
cana-2738	128	3	a	a	DET
cana-2738	128	4	∪	∪	X
cana-2738	128	5	b	b	NOUN
cana-2738	128	6	=	=	PUNCT
cana-2738	128	7	{	{	PUNCT
cana-2738	128	8	<	<	X
cana-2738	128	9	a	a	PRON
cana-2738	128	10	,	,	PUNCT
cana-2738	128	11	λa(a	λa(a	NUM
cana-2738	128	12	)	)	PUNCT
cana-2738	128	13	∨	∨	NUM
cana-2738	128	14	λb(a	λb(a	NUM
cana-2738	128	15	)	)	PUNCT
cana-2738	128	16	,	,	PUNCT
cana-2738	128	17	μ	μ	PROPN
cana-2738	128	18	a	a	PROPN
cana-2738	128	19	(	(	PUNCT
cana-2738	128	20	a	a	NOUN
cana-2738	128	21	)	)	PUNCT
cana-2738	128	22	∧	∧	PROPN
cana-2738	128	23	μ	μ	PROPN
cana-2738	128	24	b	b	PROPN
cana-2738	128	25	(	(	PUNCT
cana-2738	128	26	a	a	NOUN
cana-2738	128	27	)	)	PUNCT
cana-2738	128	28	>	>	PUNCT
cana-2738	128	29	|a	|a	X
cana-2738	128	30	∈	∈	PROPN
cana-2738	128	31	x	x	PRON
cana-2738	128	32	}	}	PUNCT
cana-2738	128	33	.	.	PUNCT
cana-2738	129	1	6	6	X
cana-2738	129	2	.	.	X
cana-2738	129	3	ϕ	ϕ	X
cana-2738	130	1	=	=	X
cana-2738	131	1	{	{	PUNCT
cana-2738	131	2	<	<	X
cana-2738	131	3	a	a	PROPN
cana-2738	131	4	,	,	PUNCT
cana-2738	131	5	ϕ	ϕ	NOUN
cana-2738	131	6	,	,	PUNCT
cana-2738	131	7	x	x	X
cana-2738	131	8	>	>	X
cana-2738	131	9	|a	|a	X
cana-2738	131	10	∈	∈	PROPN
cana-2738	131	11	x	x	PRON
cana-2738	131	12	}	}	PUNCT
cana-2738	131	13	and	and	CCONJ
cana-2738	131	14	x	x	X
cana-2738	132	1	=	=	X
cana-2738	132	2	{	{	PUNCT
cana-2738	132	3	<	<	X
cana-2738	132	4	a	a	X
cana-2738	132	5	,	,	PUNCT
cana-2738	132	6	x	x	X
cana-2738	132	7	,	,	PUNCT
cana-2738	132	8	ϕ	ϕ	X
cana-2738	132	9	>	>	X
cana-2738	132	10	|a	|a	X
cana-2738	132	11	∈	∈	PROPN
cana-2738	132	12	x	x	PRON
cana-2738	132	13	}	}	PUNCT
cana-2738	132	14	.	.	PUNCT
cana-2738	133	1	7	7	X
cana-2738	133	2	.	.	X
cana-2738	133	3	x̅	x̅	NOUN
cana-2738	133	4	=	=	SYM
cana-2738	133	5	ϕ	ϕ	PROPN
cana-2738	133	6	and	and	CCONJ
cana-2738	133	7	ϕ̅	ϕ̅	PUNCT
cana-2738	133	8	=	=	SYM
cana-2738	134	1	x.	x.	NOUN
cana-2738	134	2	definition	definition	NOUN
cana-2738	134	3	2.5	2.5	NUM
cana-2738	135	1	[	[	X
cana-2738	135	2	24	24	NUM
cana-2738	135	3	]	]	PUNCT
cana-2738	135	4	an	an	DET
cana-2738	135	5	pythagorean	pythagorean	ADJ
cana-2738	135	6	fuzzy	fuzzy	ADJ
cana-2738	135	7	topology	topology	NOUN
cana-2738	135	8	by	by	ADP
cana-2738	135	9	subsets	subset	NOUN
cana-2738	135	10	of	of	ADP
cana-2738	135	11	a	a	DET
cana-2738	135	12	non	non	ADJ
cana-2738	135	13	-	-	ADJ
cana-2738	135	14	empty	empty	ADJ
cana-2738	135	15	set	set	NOUN
cana-2738	135	16	x	x	PUNCT
cana-2738	135	17	is	be	AUX
cana-2738	135	18	a	a	DET
cana-2738	135	19	family	family	NOUN
cana-2738	135	20	τ	τ	PROPN
cana-2738	135	21	of	of	ADP
cana-2738	135	22	pfs	pfs	PROPN
cana-2738	135	23	’s	’s	PART
cana-2738	135	24	satisfying	satisfy	VERB
cana-2738	135	25	the	the	DET
cana-2738	135	26	following	follow	VERB
cana-2738	135	27	axioms	axiom	NOUN
cana-2738	135	28	.	.	PUNCT
cana-2738	136	1	[	[	X
cana-2738	136	2	(	(	PUNCT
cana-2738	136	3	i	i	NOUN
cana-2738	136	4	)	)	PUNCT
cana-2738	136	5	]	]	PUNCT
cana-2738	136	6	1	1	X
cana-2738	136	7	.	.	X
cana-2738	136	8	ϕ	ϕ	NOUN
cana-2738	136	9	,	,	PUNCT
cana-2738	136	10	x	x	PROPN
cana-2738	136	11	∈	∈	PROPN
cana-2738	136	12	τ	τ	PROPN
cana-2738	136	13	.	.	PROPN
cana-2738	136	14	2	2	NUM
cana-2738	136	15	.	.	PUNCT
cana-2738	136	16	g1	g1	PROPN
cana-2738	136	17	∩	∩	PROPN
cana-2738	136	18	g2	g2	PROPN
cana-2738	136	19	∈	∈	PROPN
cana-2738	136	20	τ	τ	PROPN
cana-2738	136	21	for	for	ADP
cana-2738	136	22	every	every	DET
cana-2738	136	23	g1	g1	NOUN
cana-2738	136	24	,	,	PUNCT
cana-2738	136	25	g2	g2	PROPN
cana-2738	136	26	∈	∈	PROPN
cana-2738	136	27	τ	τ	X
cana-2738	136	28	and	and	CCONJ
cana-2738	136	29	3	3	NUM
cana-2738	136	30	.	.	X
cana-2738	137	1	⋃	⋃	NOUN
cana-2738	137	2	gi	gi	NOUN
cana-2738	137	3	∈	∈	PROPN
cana-2738	137	4	τ	τ	PROPN
cana-2738	137	5	for	for	ADP
cana-2738	137	6	any	any	DET
cana-2738	137	7	arbitrary	arbitrary	ADJ
cana-2738	137	8	family	family	NOUN
cana-2738	137	9	{	{	PUNCT
cana-2738	137	10	gi|i	gi|i	NOUN
cana-2738	137	11	∈	∈	PROPN
cana-2738	137	12	j	j	PROPN
cana-2738	137	13	}	}	PUNCT
cana-2738	137	14	⊆	⊆	NUM
cana-2738	137	15	τ	τ	X
cana-2738	137	16	.	.	PUNCT
cana-2738	138	1	the	the	DET
cana-2738	138	2	pair	pair	NOUN
cana-2738	138	3	(	(	PUNCT
cana-2738	138	4	x	x	X
cana-2738	138	5	,	,	PUNCT
cana-2738	138	6	τ	τ	X
cana-2738	138	7	)	)	PUNCT
cana-2738	138	8	is	be	AUX
cana-2738	138	9	called	call	VERB
cana-2738	138	10	an	an	DET
cana-2738	138	11	pythagorean	pythagorean	ADJ
cana-2738	138	12	fuzzy	fuzzy	ADJ
cana-2738	138	13	topological	topological	ADJ
cana-2738	138	14	space	space	NOUN
cana-2738	138	15	(	(	PUNCT
cana-2738	138	16	pfts	pft	NOUN
cana-2738	138	17	in	in	ADP
cana-2738	138	18	short	short	ADJ
cana-2738	138	19	)	)	PUNCT
cana-2738	138	20	and	and	CCONJ
cana-2738	138	21	any	any	DET
cana-2738	138	22	pfs	pfs	PROPN
cana-2738	138	23	g	g	PROPN
cana-2738	138	24	in	in	ADP
cana-2738	138	25	τ	τ	PROPN
cana-2738	138	26	is	be	AUX
cana-2738	138	27	called	call	VERB
cana-2738	138	28	an	an	DET
cana-2738	138	29	pythagorean	pythagorean	ADJ
cana-2738	138	30	fuzzy	fuzzy	ADJ
cana-2738	138	31	open	open	ADJ
cana-2738	138	32	set	set	NOUN
cana-2738	138	33	(	(	PUNCT
cana-2738	138	34	pfos	pfos	NOUN
cana-2738	138	35	in	in	ADP
cana-2738	138	36	short	short	ADJ
cana-2738	138	37	)	)	PUNCT
cana-2738	138	38	in	in	ADP
cana-2738	138	39	x.	x.	NOUN
cana-2738	138	40	the	the	DET
cana-2738	138	41	complement	complement	NOUN
cana-2738	138	42	a̅	a̅	PROPN
cana-2738	138	43	of	of	ADP
cana-2738	138	44	an	an	DET
cana-2738	138	45	pythagorean	pythagorean	ADJ
cana-2738	138	46	fuzzy	fuzzy	ADJ
cana-2738	138	47	open	open	NOUN
cana-2738	138	48	set	set	VERB
cana-2738	138	49	a	a	PRON
cana-2738	138	50	in	in	ADP
cana-2738	138	51	an	an	DET
cana-2738	138	52	pfts(x	pfts(x	PROPN
cana-2738	138	53	,	,	PUNCT
cana-2738	138	54	τ	τ	X
cana-2738	138	55	)	)	PUNCT
cana-2738	138	56	is	be	AUX
cana-2738	138	57	called	call	VERB
cana-2738	138	58	an	an	DET
cana-2738	138	59	pythagorean	pythagorean	ADJ
cana-2738	138	60	fuzzy	fuzzy	NOUN
cana-2738	138	61	closed	close	VERB
cana-2738	138	62	set	set	NOUN
cana-2738	138	63	(	(	PUNCT
cana-2738	138	64	pfcs	pfc	VERB
cana-2738	138	65	in	in	ADP
cana-2738	138	66	short	short	ADJ
cana-2738	138	67	)	)	PUNCT
cana-2738	138	68	.	.	PUNCT
cana-2738	139	1	definition	definition	NOUN
cana-2738	139	2	2.6	2.6	NUM
cana-2738	140	1	[	[	SYM
cana-2738	140	2	24	24	NUM
cana-2738	140	3	]	]	PUNCT
cana-2738	140	4	let	let	VERB
cana-2738	140	5	(	(	PUNCT
cana-2738	140	6	x	x	NOUN
cana-2738	140	7	,	,	PUNCT
cana-2738	140	8	τ	τ	X
cana-2738	140	9	)	)	PUNCT
cana-2738	140	10	be	be	VERB
cana-2738	140	11	an	an	DET
cana-2738	140	12	pfts	pft	NOUN
cana-2738	140	13	and	and	CCONJ
cana-2738	140	14	a	a	DET
cana-2738	140	15	=	=	X
cana-2738	140	16	{	{	PUNCT
cana-2738	140	17	<	<	X
cana-2738	140	18	a	a	PRON
cana-2738	140	19	,	,	PUNCT
cana-2738	140	20	λa(a	λa(a	PROPN
cana-2738	140	21	)	)	PUNCT
cana-2738	140	22	,	,	PUNCT
cana-2738	140	23	μ	μ	PROPN
cana-2738	140	24	a	a	PROPN
cana-2738	140	25	(	(	PUNCT
cana-2738	140	26	a	a	NOUN
cana-2738	140	27	)	)	PUNCT
cana-2738	140	28	>	>	PUNCT
cana-2738	140	29	|a	|a	X
cana-2738	140	30	∈	∈	PROPN
cana-2738	140	31	x	x	AUX
cana-2738	140	32	}	}	PUNCT
cana-2738	140	33	be	be	AUX
cana-2738	140	34	an	an	DET
cana-2738	140	35	pfs	pfs	NOUN
cana-2738	140	36	in	in	ADP
cana-2738	140	37	x.	x.	PROPN
cana-2738	140	38	then	then	ADV
cana-2738	140	39	the	the	DET
cana-2738	140	40	interior	interior	NOUN
cana-2738	140	41	and	and	CCONJ
cana-2738	140	42	the	the	DET
cana-2738	140	43	closure	closure	NOUN
cana-2738	140	44	of	of	ADP
cana-2738	140	45	a	a	PRON
cana-2738	140	46	are	be	AUX
cana-2738	140	47	denoted	denote	VERB
cana-2738	140	48	by	by	ADP
cana-2738	140	49	pfint(a	pfint(a	PROPN
cana-2738	140	50	)	)	PUNCT
cana-2738	140	51	and	and	CCONJ
cana-2738	140	52	pfcl(a	pfcl(a	NOUN
cana-2738	140	53	)	)	PUNCT
cana-2738	140	54	and	and	CCONJ
cana-2738	140	55	are	be	AUX
cana-2738	140	56	defined	define	VERB
cana-2738	140	57	as	as	SCONJ
cana-2738	140	58	follows	follow	VERB
cana-2738	140	59	:	:	PUNCT
cana-2738	140	60	pfcl(a	pfcl(a	ADJ
cana-2738	140	61	)	)	PUNCT
cana-2738	140	62	=	=	NOUN
cana-2738	140	63	∩	∩	NOUN
cana-2738	140	64	{	{	PUNCT
cana-2738	140	65	k|k	k|k	PROPN
cana-2738	140	66	isan	isan	PROPN
cana-2738	140	67	pfcs	pfc	VERB
cana-2738	140	68	and	and	CCONJ
cana-2738	140	69	a	a	DET
cana-2738	140	70	⊆	⊆	NUM
cana-2738	140	71	k	k	NOUN
cana-2738	140	72	}	}	PUNCT
cana-2738	140	73	and	and	CCONJ
cana-2738	140	74	pfint(a	pfint(a	NOUN
cana-2738	140	75	)	)	PUNCT
cana-2738	140	76	=	=	SYM
cana-2738	140	77	∪	∪	X
cana-2738	140	78	{	{	PUNCT
cana-2738	140	79	g|g	g|g	NOUN
cana-2738	140	80	isan	isan	ADJ
cana-2738	140	81	pfos	pfos	NOUN
cana-2738	140	82	and	and	CCONJ
cana-2738	140	83	g	g	PROPN
cana-2738	140	84	⊆	⊆	NUM
cana-2738	140	85	a	a	PRON
cana-2738	140	86	}	}	PUNCT
cana-2738	140	87	.	.	PUNCT
cana-2738	141	1	also	also	ADV
cana-2738	141	2	,	,	PUNCT
cana-2738	141	3	it	it	PRON
cana-2738	141	4	can	can	AUX
cana-2738	141	5	be	be	AUX
cana-2738	141	6	established	establish	VERB
cana-2738	141	7	that	that	SCONJ
cana-2738	141	8	pfcl(a	pfcl(a	NOUN
cana-2738	141	9	)	)	PUNCT
cana-2738	141	10	is	be	AUX
cana-2738	141	11	an	an	DET
cana-2738	141	12	pfcs	pfc	NOUN
cana-2738	141	13	and	and	CCONJ
cana-2738	141	14	pfint(a	pfint(a	NOUN
cana-2738	141	15	)	)	PUNCT
cana-2738	141	16	is	be	AUX
cana-2738	141	17	an	an	DET
cana-2738	141	18	pfos	pfos	NOUN
cana-2738	141	19	,	,	PUNCT
cana-2738	141	20	a	a	PRON
cana-2738	141	21	is	be	AUX
cana-2738	141	22	an	an	DET
cana-2738	141	23	pfcs	pfcs	NOUN
cana-2738	141	24	if	if	SCONJ
cana-2738	142	1	and	and	CCONJ
cana-2738	142	2	only	only	ADV
cana-2738	142	3	if	if	SCONJ
cana-2738	142	4	pfcl(a	pfcl(a	PROPN
cana-2738	142	5	)	)	PUNCT
cana-2738	142	6	=	=	SYM
cana-2738	143	1	a	a	PRON
cana-2738	143	2	and	and	CCONJ
cana-2738	143	3	a	a	PRON
cana-2738	143	4	is	be	AUX
cana-2738	143	5	an	an	DET
cana-2738	143	6	pfos	pfos	NOUN
cana-2738	143	7	if	if	SCONJ
cana-2738	143	8	and	and	CCONJ
cana-2738	143	9	only	only	ADV
cana-2738	143	10	if	if	SCONJ
cana-2738	143	11	pfint(a	pfint(a	NOUN
cana-2738	143	12	)	)	PUNCT
cana-2738	143	13	=	=	SYM
cana-2738	144	1	a.	a.	NOUN
cana-2738	144	2	we	we	PRON
cana-2738	144	3	say	say	VERB
cana-2738	144	4	that	that	SCONJ
cana-2738	144	5	a	a	PRON
cana-2738	144	6	is	be	AUX
cana-2738	144	7	pf	pf	NOUN
cana-2738	144	8	-	-	PUNCT
cana-2738	144	9	dense	dense	ADJ
cana-2738	144	10	if	if	SCONJ
cana-2738	144	11	pfcl(a	pfcl(a	NOUN
cana-2738	144	12	)	)	PUNCT
cana-2738	144	13	=	=	PUNCT
cana-2738	144	14	x.	x.	NOUN
cana-2738	144	15	lemma	lemma	PROPN
cana-2738	144	16	2.1	2.1	NUM
cana-2738	145	1	[	[	X
cana-2738	145	2	29	29	NUM
cana-2738	145	3	]	]	PUNCT
cana-2738	145	4	for	for	ADP
cana-2738	145	5	any	any	DET
cana-2738	145	6	pythagorean	pythagorean	PROPN
cana-2738	145	7	fuzzy	fuzzy	NOUN
cana-2738	145	8	set	set	VERB
cana-2738	145	9	a	a	DET
cana-2738	145	10	in	in	ADP
cana-2738	145	11	(	(	PUNCT
cana-2738	145	12	x	x	NOUN
cana-2738	145	13	,	,	PUNCT
cana-2738	145	14	τ	τ	PROPN
cana-2738	145	15	)	)	PUNCT
cana-2738	145	16	,	,	PUNCT
cana-2738	145	17	we	we	PRON
cana-2738	145	18	have	have	VERB
cana-2738	145	19	x	x	X
cana-2738	145	20	−	−	PROPN
cana-2738	145	21	pfint(a	pfint(a	NOUN
cana-2738	145	22	)	)	PUNCT
cana-2738	146	1	=	=	SYM
cana-2738	146	2	pfcl(x	pfcl(x	PROPN
cana-2738	146	3	−	−	PROPN
cana-2738	146	4	a	a	NOUN
cana-2738	146	5	)	)	PUNCT
cana-2738	146	6	and	and	CCONJ
cana-2738	146	7	x	x	PART
cana-2738	146	8	−	−	PROPN
cana-2738	146	9	pfcl(a	pfcl(a	PROPN
cana-2738	146	10	)	)	PUNCT
cana-2738	146	11	=	=	PUNCT
cana-2738	147	1	pfint(x	pfint(x	PROPN
cana-2738	147	2	−	−	NOUN
cana-2738	147	3	a	a	NOUN
cana-2738	147	4	)	)	PUNCT
cana-2738	147	5	.	.	PUNCT
cana-2738	148	1	definition	definition	NOUN
cana-2738	148	2	2.7	2.7	NUM
cana-2738	148	3	[	[	SYM
cana-2738	148	4	29	29	NUM
cana-2738	148	5	]	]	X
cana-2738	148	6	let	let	VERB
cana-2738	148	7	(	(	PUNCT
cana-2738	148	8	x	x	NOUN
cana-2738	148	9	,	,	PUNCT
cana-2738	148	10	τ	τ	X
cana-2738	148	11	)	)	PUNCT
cana-2738	148	12	be	be	VERB
cana-2738	148	13	an	an	DET
cana-2738	148	14	pfts	pft	NOUN
cana-2738	148	15	and	and	CCONJ
cana-2738	148	16	a	a	DET
cana-2738	148	17	be	be	AUX
cana-2738	148	18	an	an	DET
cana-2738	148	19	pfs	pfs	PROPN
cana-2738	148	20	.	.	PUNCT
cana-2738	149	1	then	then	ADV
cana-2738	149	2	a	a	PRON
cana-2738	149	3	is	be	AUX
cana-2738	149	4	said	say	VERB
cana-2738	149	5	to	to	PART
cana-2738	149	6	be	be	AUX
cana-2738	149	7	an	an	DET
cana-2738	149	8	pythagorean	pythagorean	ADJ
cana-2738	149	9	fuzzy	fuzzy	NOUN
cana-2738	149	10	(	(	PUNCT
cana-2738	149	11	i	i	NOUN
cana-2738	149	12	)	)	PUNCT
cana-2738	149	13	regular	regular	ADJ
cana-2738	149	14	open	open	ADJ
cana-2738	149	15	set	set	NOUN
cana-2738	149	16	(	(	PUNCT
cana-2738	149	17	pfros	pfro	NOUN
cana-2738	149	18	in	in	ADP
cana-2738	149	19	short	short	ADJ
cana-2738	149	20	)	)	PUNCT
cana-2738	149	21	if	if	SCONJ
cana-2738	149	22	a	a	DET
cana-2738	149	23	=	=	SYM
cana-2738	149	24	pfint(pfcl(a	pfint(pfcl(a	NUM
cana-2738	149	25	)	)	PUNCT
cana-2738	149	26	)	)	PUNCT
cana-2738	149	27	.	.	PUNCT
cana-2738	150	1	(	(	PUNCT
cana-2738	150	2	ii	ii	NOUN
cana-2738	150	3	)	)	PUNCT
cana-2738	150	4	regular	regular	ADJ
cana-2738	150	5	closed	close	VERB
cana-2738	150	6	set	set	NOUN
cana-2738	150	7	(	(	PUNCT
cana-2738	150	8	pfrcs	pfrcs	PROPN
cana-2738	150	9	in	in	ADP
cana-2738	150	10	short	short	ADJ
cana-2738	150	11	)	)	PUNCT
cana-2738	150	12	if	if	SCONJ
cana-2738	150	13	a	a	PRON
cana-2738	150	14	=	=	NOUN
cana-2738	150	15	pfcl(pfint(a	pfcl(pfint(a	NUM
cana-2738	150	16	)	)	PUNCT
cana-2738	150	17	)	)	PUNCT
cana-2738	150	18	.	.	PUNCT
cana-2738	151	1	by	by	ADP
cana-2738	151	2	lemma	lemma	PROPN
cana-2738	151	3	2.1	2.1	NUM
cana-2738	151	4	,	,	PUNCT
cana-2738	151	5	it	it	PRON
cana-2738	151	6	follows	follow	VERB
cana-2738	151	7	that	that	SCONJ
cana-2738	151	8	a	a	PRON
cana-2738	151	9	is	be	AUX
cana-2738	151	10	an	an	DET
cana-2738	151	11	pfros	pfro	NOUN
cana-2738	151	12	iff	iff	NOUN
cana-2738	151	13	a̅	a̅	PROPN
cana-2738	151	14	is	be	AUX
cana-2738	151	15	an	an	DET
cana-2738	151	16	pfrcs	pfrcs	NOUN
cana-2738	151	17	.	.	PUNCT
cana-2738	152	1	communications	communication	NOUN
cana-2738	152	2	on	on	ADP
cana-2738	152	3	applied	apply	VERB
cana-2738	152	4	nonlinear	nonlinear	ADJ
cana-2738	152	5	analysis	analysis	NOUN
cana-2738	152	6	issn	issn	NOUN
cana-2738	152	7	:	:	PUNCT
cana-2738	152	8	1074	1074	NUM
cana-2738	152	9	-	-	PUNCT
cana-2738	152	10	133x	133x	NUM
cana-2738	152	11	vol	vol	NOUN
cana-2738	152	12	32	32	NUM
cana-2738	152	13	no	no	NOUN
cana-2738	152	14	.	.	PUNCT
cana-2738	153	1	4s	4s	NUM
cana-2738	153	2	(	(	PUNCT
cana-2738	153	3	2025	2025	NUM
cana-2738	153	4	)	)	PUNCT
cana-2738	154	1	47	47	NUM
cana-2738	154	2	https://internationalpubls.com	https://internationalpubls.com	X
cana-2738	154	3	definition	definition	NOUN
cana-2738	154	4	2.8	2.8	NUM
cana-2738	154	5	[	[	X
cana-2738	154	6	16	16	NUM
cana-2738	154	7	]	]	X
cana-2738	154	8	let	let	VERB
cana-2738	154	9	(	(	PUNCT
cana-2738	154	10	x1	x1	ADJ
cana-2738	154	11	,	,	PUNCT
cana-2738	154	12	γp	γp	PROPN
cana-2738	154	13	)	)	PUNCT
cana-2738	154	14	&	&	CCONJ
cana-2738	154	15	(	(	PUNCT
cana-2738	154	16	x2	x2	PROPN
cana-2738	154	17	,	,	PUNCT
cana-2738	154	18	ψp	ψp	PRON
cana-2738	154	19	)	)	PUNCT
cana-2738	154	20	be	be	AUX
cana-2738	154	21	a	a	DET
cana-2738	154	22	pfts	pft	NOUN
cana-2738	154	23	’s	’s	PART
cana-2738	154	24	.	.	PUNCT
cana-2738	155	1	a	a	DET
cana-2738	155	2	mapping	mapping	NOUN
cana-2738	155	3	hp	hp	NOUN
cana-2738	155	4	:	:	PUNCT
cana-2738	155	5	(	(	PUNCT
cana-2738	155	6	x1	x1	PROPN
cana-2738	155	7	,	,	PUNCT
cana-2738	155	8	γp	γp	PROPN
cana-2738	155	9	)	)	PUNCT
cana-2738	155	10	→	→	SYM
cana-2738	155	11	(	(	PUNCT
cana-2738	155	12	x2	x2	PROPN
cana-2738	155	13	,	,	PUNCT
cana-2738	155	14	ψp	ψp	NOUN
cana-2738	155	15	)	)	PUNCT
cana-2738	155	16	is	be	AUX
cana-2738	155	17	said	say	VERB
cana-2738	155	18	to	to	PART
cana-2738	155	19	be	be	AUX
cana-2738	155	20	a	a	DET
cana-2738	155	21	pythagorean	pythagorean	ADJ
cana-2738	155	22	fuzzy	fuzzy	ADJ
cana-2738	155	23	continuous	continuous	ADJ
cana-2738	155	24	(	(	PUNCT
cana-2738	155	25	briefly	briefly	ADV
cana-2738	155	26	,	,	PUNCT
cana-2738	155	27	pfcts	pfct	VERB
cana-2738	155	28	)	)	PUNCT
cana-2738	155	29	if	if	SCONJ
cana-2738	155	30	the	the	DET
cana-2738	155	31	inverse	inverse	ADJ
cana-2738	155	32	image	image	NOUN
cana-2738	155	33	of	of	ADP
cana-2738	155	34	every	every	DET
cana-2738	155	35	pfos	pfos	NOUN
cana-2738	155	36	in	in	ADP
cana-2738	155	37	(	(	PUNCT
cana-2738	155	38	x2	x2	INTJ
cana-2738	155	39	,	,	PUNCT
cana-2738	155	40	ψp	ψp	PROPN
cana-2738	155	41	)	)	PUNCT
cana-2738	155	42	is	be	AUX
cana-2738	155	43	a	a	DET
cana-2738	155	44	pfos	pfos	NOUN
cana-2738	155	45	.	.	PUNCT
cana-2738	156	1	3	3	NUM
cana-2738	156	2	pythagorean	pythagorean	PROPN
cana-2738	156	3	fuzzy	fuzzy	ADJ
cana-2738	156	4	𝜹-open	𝜹-open	PROPN
cana-2738	156	5	mapping	mapping	NOUN
cana-2738	156	6	definition	definition	NOUN
cana-2738	156	7	3.1	3.1	NUM
cana-2738	156	8	let	let	VERB
cana-2738	156	9	(	(	PUNCT
cana-2738	156	10	x	x	NOUN
cana-2738	156	11	,	,	PUNCT
cana-2738	156	12	τ	τ	X
cana-2738	156	13	)	)	PUNCT
cana-2738	156	14	be	be	VERB
cana-2738	156	15	an	an	DET
cana-2738	156	16	pfts	pft	NOUN
cana-2738	156	17	and	and	CCONJ
cana-2738	156	18	a	a	DET
cana-2738	156	19	=	=	X
cana-2738	156	20	{	{	PUNCT
cana-2738	156	21	<	<	X
cana-2738	156	22	a	a	PRON
cana-2738	156	23	,	,	PUNCT
cana-2738	156	24	λa(a	λa(a	PROPN
cana-2738	156	25	)	)	PUNCT
cana-2738	156	26	,	,	PUNCT
cana-2738	156	27	μ	μ	PROPN
cana-2738	156	28	a	a	PROPN
cana-2738	156	29	(	(	PUNCT
cana-2738	156	30	a	a	NOUN
cana-2738	156	31	)	)	PUNCT
cana-2738	156	32	>	>	PUNCT
cana-2738	156	33	|a	|a	X
cana-2738	156	34	∈	∈	PROPN
cana-2738	156	35	x	x	AUX
cana-2738	156	36	}	}	PUNCT
cana-2738	156	37	be	be	AUX
cana-2738	156	38	an	an	DET
cana-2738	156	39	pfs	pfs	NOUN
cana-2738	156	40	in	in	ADP
cana-2738	156	41	x.	x.	PROPN
cana-2738	156	42	then	then	ADV
cana-2738	156	43	the	the	DET
cana-2738	156	44	δ	δ	PROPN
cana-2738	156	45	-	-	PROPN
cana-2738	156	46	interior	interior	PROPN
cana-2738	156	47	and	and	CCONJ
cana-2738	156	48	the	the	DET
cana-2738	156	49	δ	δ	PROPN
cana-2738	156	50	-	-	PUNCT
cana-2738	156	51	closure	closure	NOUN
cana-2738	156	52	of	of	ADP
cana-2738	156	53	a	a	PRON
cana-2738	156	54	are	be	AUX
cana-2738	156	55	denoted	denote	VERB
cana-2738	156	56	by	by	ADP
cana-2738	156	57	pfδint(a	pfδint(a	NOUN
cana-2738	156	58	)	)	PUNCT
cana-2738	156	59	and	and	CCONJ
cana-2738	156	60	pfδcl(a	pfδcl(a	NOUN
cana-2738	156	61	)	)	PUNCT
cana-2738	156	62	and	and	CCONJ
cana-2738	156	63	are	be	AUX
cana-2738	156	64	defined	define	VERB
cana-2738	156	65	as	as	ADP
cana-2738	156	66	follows	follow	VERB
cana-2738	156	67	.	.	PUNCT
cana-2738	157	1	pfδcl(a	pfδcl(a	X
cana-2738	157	2	)	)	PUNCT
cana-2738	157	3	=	=	NOUN
cana-2738	157	4	∩	∩	NOUN
cana-2738	157	5	{	{	PUNCT
cana-2738	157	6	k|k	k|k	PROPN
cana-2738	157	7	is	be	AUX
cana-2738	157	8	an	an	DET
cana-2738	157	9	pfrcs	pfrcs	NOUN
cana-2738	157	10	and	and	CCONJ
cana-2738	157	11	a	a	DET
cana-2738	157	12	⊆	⊆	NUM
cana-2738	157	13	k	k	NOUN
cana-2738	157	14	}	}	PUNCT
cana-2738	157	15	,	,	PUNCT
cana-2738	157	16	(	(	PUNCT
cana-2738	157	17	pfδint(a	pfδint(a	NOUN
cana-2738	157	18	)	)	PUNCT
cana-2738	157	19	=	=	SYM
cana-2738	157	20	∪	∪	X
cana-2738	157	21	{	{	PUNCT
cana-2738	157	22	g|g	g|g	NOUN
cana-2738	157	23	is	be	AUX
cana-2738	157	24	an	an	DET
cana-2738	157	25	pfros	pfro	NOUN
cana-2738	157	26	and	and	CCONJ
cana-2738	157	27	g	g	PROPN
cana-2738	157	28	⊆	⊆	NUM
cana-2738	157	29	a	a	PRON
cana-2738	157	30	}	}	PUNCT
cana-2738	157	31	.	.	PUNCT
cana-2738	158	1	definition	definition	NOUN
cana-2738	158	2	3.2	3.2	NUM
cana-2738	158	3	let	let	VERB
cana-2738	158	4	(	(	PUNCT
cana-2738	158	5	x	x	NOUN
cana-2738	158	6	,	,	PUNCT
cana-2738	158	7	τ	τ	X
cana-2738	158	8	)	)	PUNCT
cana-2738	158	9	be	be	VERB
cana-2738	158	10	an	an	DET
cana-2738	158	11	pfts	pft	NOUN
cana-2738	158	12	and	and	CCONJ
cana-2738	158	13	a	a	DET
cana-2738	158	14	=	=	X
cana-2738	158	15	{	{	PUNCT
cana-2738	158	16	<	<	X
cana-2738	158	17	a	a	PRON
cana-2738	158	18	,	,	PUNCT
cana-2738	158	19	λa(a	λa(a	PROPN
cana-2738	158	20	)	)	PUNCT
cana-2738	158	21	,	,	PUNCT
cana-2738	158	22	μ	μ	PROPN
cana-2738	158	23	a	a	PROPN
cana-2738	158	24	(	(	PUNCT
cana-2738	158	25	a	a	NOUN
cana-2738	158	26	)	)	PUNCT
cana-2738	158	27	>	>	PUNCT
cana-2738	158	28	|a	|a	X
cana-2738	158	29	∈	∈	PROPN
cana-2738	158	30	x	x	AUX
cana-2738	158	31	}	}	PUNCT
cana-2738	158	32	be	be	AUX
cana-2738	158	33	an	an	DET
cana-2738	158	34	pfs	pfs	NOUN
cana-2738	158	35	in	in	ADP
cana-2738	158	36	x.	x.	PROPN
cana-2738	158	37	a	a	DET
cana-2738	158	38	set	set	NOUN
cana-2738	158	39	a	a	PRON
cana-2738	158	40	is	be	AUX
cana-2738	158	41	said	say	VERB
cana-2738	158	42	to	to	PART
cana-2738	158	43	be	be	AUX
cana-2738	158	44	pf	pf	PROPN
cana-2738	158	45	1	1	NUM
cana-2738	158	46	.	.	PUNCT
cana-2738	159	1	δ	δ	NOUN
cana-2738	159	2	-	-	ADJ
cana-2738	159	3	open	open	ADJ
cana-2738	159	4	set	set	NOUN
cana-2738	159	5	(	(	PUNCT
cana-2738	159	6	briefly	briefly	ADV
cana-2738	159	7	,	,	PUNCT
cana-2738	159	8	pfδos	pfδos	PROPN
cana-2738	159	9	)	)	PUNCT
cana-2738	159	10	if	if	SCONJ
cana-2738	159	11	a	a	DET
cana-2738	159	12	=	=	SYM
cana-2738	159	13	pfδint(a	pfδint(a	NOUN
cana-2738	159	14	)	)	PUNCT
cana-2738	159	15	,	,	PUNCT
cana-2738	159	16	2	2	NUM
cana-2738	159	17	.	.	X
cana-2738	159	18	δ	δ	NOUN
cana-2738	159	19	-	-	PUNCT
cana-2738	159	20	pre	pre	X
cana-2738	159	21	open	open	ADJ
cana-2738	159	22	set	set	NOUN
cana-2738	159	23	(	(	PUNCT
cana-2738	159	24	briefly	briefly	ADV
cana-2738	159	25	,	,	PUNCT
cana-2738	159	26	pfδ𝒫os	pfδ𝒫os	PROPN
cana-2738	159	27	)	)	PUNCT
cana-2738	159	28	if	if	SCONJ
cana-2738	159	29	a	a	DET
cana-2738	159	30	⊆	⊆	NUM
cana-2738	159	31	pfint(pfδcl(a	pfint(pfδcl(a	NUM
cana-2738	159	32	)	)	PUNCT
cana-2738	159	33	)	)	PUNCT
cana-2738	159	34	.	.	PUNCT
cana-2738	160	1	3	3	X
cana-2738	160	2	.	.	X
cana-2738	160	3	δ	δ	NOUN
cana-2738	160	4	-	-	PUNCT
cana-2738	160	5	semi	semi	ADV
cana-2738	160	6	open	open	ADJ
cana-2738	160	7	set	set	NOUN
cana-2738	160	8	(	(	PUNCT
cana-2738	160	9	briefly	briefly	ADV
cana-2738	160	10	,	,	PUNCT
cana-2738	160	11	pfδ𝒮os	pfδ𝒮os	NOUN
cana-2738	160	12	)	)	PUNCT
cana-2738	160	13	if	if	SCONJ
cana-2738	160	14	a	a	DET
cana-2738	160	15	⊆	⊆	NUM
cana-2738	160	16	pfcl(pfδint(a	pfcl(pfδint(a	NUM
cana-2738	160	17	)	)	PUNCT
cana-2738	160	18	)	)	PUNCT
cana-2738	160	19	.	.	PUNCT
cana-2738	161	1	4	4	X
cana-2738	161	2	.	.	X
cana-2738	161	3	δ	δ	PROPN
cana-2738	161	4	-	-	PUNCT
cana-2738	161	5	α	α	PRON
cana-2738	161	6	open	open	ADJ
cana-2738	161	7	set	set	NOUN
cana-2738	161	8	or	or	CCONJ
cana-2738	161	9	a	a	DET
cana-2738	161	10	-	-	PUNCT
cana-2738	161	11	open	open	ADJ
cana-2738	161	12	set	set	NOUN
cana-2738	161	13	(	(	PUNCT
cana-2738	161	14	briefly	briefly	ADV
cana-2738	161	15	,	,	PUNCT
cana-2738	161	16	pfδαos	pfδαo	NOUN
cana-2738	161	17	or	or	CCONJ
cana-2738	161	18	pfaos	pfao	NOUN
cana-2738	161	19	)	)	PUNCT
cana-2738	161	20	if	if	SCONJ
cana-2738	161	21	a	a	DET
cana-2738	161	22	⊆	⊆	NUM
cana-2738	161	23	pfint(pfcl(pfδint(a	pfint(pfcl(pfδint(a	NOUN
cana-2738	161	24	)	)	PUNCT
cana-2738	161	25	)	)	PUNCT
cana-2738	161	26	)	)	PUNCT
cana-2738	161	27	.	.	PUNCT
cana-2738	162	1	5	5	X
cana-2738	162	2	.	.	X
cana-2738	162	3	δ	δ	PROPN
cana-2738	162	4	-	-	PUNCT
cana-2738	162	5	β	β	X
cana-2738	162	6	open	open	ADJ
cana-2738	162	7	set	set	NOUN
cana-2738	162	8	or	or	CCONJ
cana-2738	162	9	e∗-open	e∗-open	ADJ
cana-2738	162	10	set	set	NOUN
cana-2738	162	11	(	(	PUNCT
cana-2738	162	12	briefly	briefly	ADV
cana-2738	162	13	,	,	PUNCT
cana-2738	162	14	pfδβos	pfδβos	PROPN
cana-2738	162	15	or	or	CCONJ
cana-2738	162	16	pfe∗os	pfe∗os	NOUN
cana-2738	162	17	)	)	PUNCT
cana-2738	162	18	if	if	SCONJ
cana-2738	162	19	a	a	DET
cana-2738	162	20	⊆	⊆	NUM
cana-2738	162	21	pfcl(pfint(pfδcl(a	pfcl(pfint(pfδcl(a	NOUN
cana-2738	162	22	)	)	PUNCT
cana-2738	162	23	)	)	PUNCT
cana-2738	162	24	)	)	PUNCT
cana-2738	162	25	.	.	PUNCT
cana-2738	163	1	6	6	X
cana-2738	163	2	.	.	X
cana-2738	163	3	δ	δ	PROPN
cana-2738	163	4	(	(	PUNCT
cana-2738	163	5	resp	resp	PROPN
cana-2738	163	6	.	.	PUNCT
cana-2738	164	1	δ	δ	PROPN
cana-2738	164	2	-	-	PUNCT
cana-2738	164	3	pre	pre	PROPN
cana-2738	164	4	,	,	PUNCT
cana-2738	164	5	δ	δ	PROPN
cana-2738	164	6	-	-	PUNCT
cana-2738	164	7	semi	semi	ADV
cana-2738	164	8	,	,	PUNCT
cana-2738	164	9	δ	δ	PROPN
cana-2738	164	10	-	-	PUNCT
cana-2738	164	11	α	α	PROPN
cana-2738	164	12	and	and	CCONJ
cana-2738	164	13	δ	δ	PROPN
cana-2738	164	14	-	-	PUNCT
cana-2738	164	15	β	β	NOUN
cana-2738	164	16	)	)	PUNCT
cana-2738	164	17	dense	dense	ADJ
cana-2738	164	18	if	if	SCONJ
cana-2738	164	19	pfδcl(a	pfδcl(a	NUM
cana-2738	164	20	)	)	PUNCT
cana-2738	164	21	(	(	PUNCT
cana-2738	164	22	resp	resp	NOUN
cana-2738	164	23	.	.	PUNCT
cana-2738	165	1	pfδpcl(a	pfδpcl(a	NUM
cana-2738	165	2	)	)	PUNCT
cana-2738	165	3	,	,	PUNCT
cana-2738	165	4	pfδ𝒮cl(a	pfδ𝒮cl(a	NOUN
cana-2738	165	5	)	)	PUNCT
cana-2738	165	6	,	,	PUNCT
cana-2738	165	7	pfδαcl(a	pfδαcl(a	PROPN
cana-2738	165	8	)	)	PUNCT
cana-2738	165	9	and	and	CCONJ
cana-2738	165	10	pfδβcl(a	pfδβcl(a	NOUN
cana-2738	165	11	)	)	PUNCT
cana-2738	165	12	)	)	PUNCT
cana-2738	166	1	=	=	PUNCT
cana-2738	166	2	x.	x.	NOUN
cana-2738	166	3	the	the	DET
cana-2738	166	4	complement	complement	NOUN
cana-2738	166	5	of	of	ADP
cana-2738	166	6	an	an	DET
cana-2738	166	7	pfδos	pfδos	PROPN
cana-2738	166	8	(	(	PUNCT
cana-2738	166	9	resp	resp	NOUN
cana-2738	166	10	.	.	PUNCT
cana-2738	167	1	pfδ𝒫os	pfδ𝒫os	PROPN
cana-2738	167	2	,	,	PUNCT
cana-2738	167	3	pfδ𝒮os	pfδ𝒮os	NOUN
cana-2738	167	4	,	,	PUNCT
cana-2738	167	5	pfδαos	pfδαo	NOUN
cana-2738	167	6	and	and	CCONJ
cana-2738	167	7	pfδβos	pfδβos	NOUN
cana-2738	167	8	)	)	PUNCT
cana-2738	167	9	is	be	AUX
cana-2738	167	10	called	call	VERB
cana-2738	167	11	an	an	DET
cana-2738	167	12	pfδ	pfδ	NOUN
cana-2738	167	13	(	(	PUNCT
cana-2738	167	14	resp	resp	NOUN
cana-2738	167	15	.	.	PUNCT
cana-2738	168	1	pfδ𝒫	pfδ𝒫	ADJ
cana-2738	168	2	,	,	PUNCT
cana-2738	168	3	pfδ𝒮	pfδ𝒮	ADJ
cana-2738	168	4	,	,	PUNCT
cana-2738	168	5	pfδα	pfδα	NOUN
cana-2738	168	6	and	and	CCONJ
cana-2738	168	7	pfδβ	pfδβ	ADJ
cana-2738	168	8	)	)	PUNCT
cana-2738	168	9	closed	close	VERB
cana-2738	168	10	set	set	NOUN
cana-2738	168	11	(	(	PUNCT
cana-2738	168	12	briefly	briefly	ADV
cana-2738	168	13	,	,	PUNCT
cana-2738	168	14	pfδcs	pfδcs	NOUN
cana-2738	168	15	(	(	PUNCT
cana-2738	168	16	resp	resp	NOUN
cana-2738	168	17	.	.	PUNCT
cana-2738	169	1	pfδ𝒫cs	pfδ𝒫cs	PROPN
cana-2738	169	2	,	,	PUNCT
cana-2738	169	3	pfδ𝒮cs	pfδ𝒮cs	PROPN
cana-2738	169	4	,	,	PUNCT
cana-2738	169	5	pfδαcs	pfδαcs	NOUN
cana-2738	169	6	and	and	CCONJ
cana-2738	169	7	pfδβcs	pfδβcs	VERB
cana-2738	169	8	in	in	ADP
cana-2738	169	9	x.	x.	NOUN
cana-2738	169	10	the	the	DET
cana-2738	169	11	family	family	NOUN
cana-2738	169	12	of	of	ADP
cana-2738	169	13	all	all	DET
cana-2738	169	14	pfδos	pfδos	PROPN
cana-2738	169	15	(	(	PUNCT
cana-2738	169	16	resp	resp	NOUN
cana-2738	169	17	.	.	PUNCT
cana-2738	170	1	pfδcs	pfδcs	PROPN
cana-2738	170	2	,	,	PUNCT
cana-2738	170	3	pfδ𝒫os	pfδ𝒫os	PROPN
cana-2738	170	4	,	,	PUNCT
cana-2738	170	5	pfδ𝒫cs	pfδ𝒫cs	ADJ
cana-2738	170	6	,	,	PUNCT
cana-2738	170	7	pfδ𝒮os	pfδ𝒮os	NOUN
cana-2738	170	8	,	,	PUNCT
cana-2738	170	9	pfδ𝒮cs	pfδ𝒮cs	PROPN
cana-2738	170	10	,	,	PUNCT
cana-2738	170	11	pfδαos	pfδαo	NOUN
cana-2738	170	12	,	,	PUNCT
cana-2738	170	13	pfδαcs	pfδαcs	NOUN
cana-2738	170	14	,	,	PUNCT
cana-2738	170	15	pfδβos	pfδβos	NOUN
cana-2738	170	16	and	and	CCONJ
cana-2738	170	17	pfδβcs	pfδβc	VERB
cana-2738	170	18	)	)	PUNCT
cana-2738	170	19	of	of	ADP
cana-2738	170	20	x	x	PRON
cana-2738	170	21	is	be	AUX
cana-2738	170	22	denoted	denote	VERB
cana-2738	170	23	by	by	ADP
cana-2738	170	24	pfδos(x	pfδos(x	PROPN
cana-2738	170	25	)	)	PUNCT
cana-2738	170	26	,	,	PUNCT
cana-2738	170	27	(	(	PUNCT
cana-2738	170	28	resp	resp	NOUN
cana-2738	170	29	.	.	PUNCT
cana-2738	171	1	pfδcs(x	pfδcs(x	NOUN
cana-2738	171	2	)	)	PUNCT
cana-2738	171	3	,	,	PUNCT
cana-2738	171	4	pfδ𝒫os(x	pfδ𝒫os(x	NOUN
cana-2738	171	5	)	)	PUNCT
cana-2738	171	6	,	,	PUNCT
cana-2738	171	7	pfδ𝒫cs(x	pfδ𝒫cs(x	PROPN
cana-2738	171	8	)	)	PUNCT
cana-2738	171	9	,	,	PUNCT
cana-2738	171	10	pfδ𝒮os(x	pfδ𝒮os(x	NOUN
cana-2738	171	11	)	)	PUNCT
cana-2738	171	12	,	,	PUNCT
cana-2738	171	13	pfδ𝒮cs(x	pfδ𝒮cs(x	NOUN
cana-2738	171	14	)	)	PUNCT
cana-2738	171	15	,	,	PUNCT
cana-2738	171	16	pfδαos(x	pfδαos(x	PROPN
cana-2738	171	17	)	)	PUNCT
cana-2738	171	18	,	,	PUNCT
cana-2738	171	19	pfδαcs(x	pfδαcs(x	NOUN
cana-2738	171	20	)	)	PUNCT
cana-2738	171	21	,	,	PUNCT
cana-2738	171	22	pfδβos(x	pfδβos(x	PROPN
cana-2738	171	23	)	)	PUNCT
cana-2738	171	24	and	and	CCONJ
cana-2738	171	25	pfδβcs(x	pfδβcs(x	NOUN
cana-2738	171	26	)	)	PUNCT
cana-2738	171	27	)	)	PUNCT
cana-2738	171	28	.	.	PUNCT
cana-2738	172	1	definition	definition	NOUN
cana-2738	172	2	3.3	3.3	NUM
cana-2738	172	3	let	let	VERB
cana-2738	172	4	(	(	PUNCT
cana-2738	172	5	x	x	NOUN
cana-2738	172	6	,	,	PUNCT
cana-2738	172	7	τ	τ	X
cana-2738	172	8	)	)	PUNCT
cana-2738	172	9	be	be	VERB
cana-2738	172	10	an	an	DET
cana-2738	172	11	pfts	pft	NOUN
cana-2738	172	12	and	and	CCONJ
cana-2738	172	13	a	a	DET
cana-2738	172	14	=	=	X
cana-2738	172	15	{	{	PUNCT
cana-2738	172	16	<	<	X
cana-2738	172	17	a	a	PRON
cana-2738	172	18	,	,	PUNCT
cana-2738	172	19	λa(a	λa(a	PROPN
cana-2738	172	20	)	)	PUNCT
cana-2738	172	21	,	,	PUNCT
cana-2738	172	22	μ	μ	PROPN
cana-2738	172	23	a	a	PROPN
cana-2738	172	24	(	(	PUNCT
cana-2738	172	25	a	a	NOUN
cana-2738	172	26	)	)	PUNCT
cana-2738	172	27	>	>	PUNCT
cana-2738	172	28	|a	|a	X
cana-2738	172	29	∈	∈	PROPN
cana-2738	172	30	x	x	AUX
cana-2738	172	31	}	}	PUNCT
cana-2738	172	32	be	be	AUX
cana-2738	172	33	an	an	DET
cana-2738	172	34	pfs	pfs	NOUN
cana-2738	172	35	in	in	ADP
cana-2738	172	36	x.	x.	PROPN
cana-2738	172	37	then	then	ADV
cana-2738	172	38	the	the	DET
cana-2738	172	39	pfδ	pfδ	NOUN
cana-2738	172	40	-	-	PUNCT
cana-2738	172	41	pre	pre	NOUN
cana-2738	172	42	(	(	PUNCT
cana-2738	172	43	resp	resp	NOUN
cana-2738	172	44	.	.	PUNCT
cana-2738	173	1	pfδ	pfδ	NOUN
cana-2738	173	2	-	-	PUNCT
cana-2738	173	3	semi	semi	ADJ
cana-2738	173	4	,	,	PUNCT
cana-2738	173	5	pfδα	pfδα	NOUN
cana-2738	173	6	and	and	CCONJ
cana-2738	173	7	pfδβ)-interior	pfδβ)-interior	PROPN
cana-2738	173	8	and	and	CCONJ
cana-2738	173	9	the	the	DET
cana-2738	173	10	pfδ	pfδ	NOUN
cana-2738	173	11	-	-	PUNCT
cana-2738	173	12	pre	pre	NOUN
cana-2738	173	13	(	(	PUNCT
cana-2738	173	14	resp	resp	NOUN
cana-2738	173	15	.	.	PUNCT
cana-2738	174	1	pfδ	pfδ	NOUN
cana-2738	174	2	-	-	PUNCT
cana-2738	174	3	semi	semi	ADJ
cana-2738	174	4	,	,	PUNCT
cana-2738	174	5	pfδα	pfδα	NOUN
cana-2738	174	6	and	and	CCONJ
cana-2738	174	7	pfδβ)-closure	pfδβ)-closure	PROPN
cana-2738	174	8	of	of	ADP
cana-2738	174	9	a	a	PRON
cana-2738	174	10	are	be	AUX
cana-2738	174	11	denoted	denote	VERB
cana-2738	174	12	by	by	ADP
cana-2738	174	13	pfδ𝒫int(a	pfδ𝒫int(a	PROPN
cana-2738	174	14	)	)	PUNCT
cana-2738	174	15	(	(	PUNCT
cana-2738	174	16	resp	resp	NOUN
cana-2738	174	17	.	.	PUNCT
cana-2738	175	1	pfδ𝒮int(a	pfδ𝒮int(a	ADJ
cana-2738	175	2	)	)	PUNCT
cana-2738	175	3	,	,	PUNCT
cana-2738	175	4	pfδαint(a	pfδαint(a	PROPN
cana-2738	175	5	)	)	PUNCT
cana-2738	175	6	and	and	CCONJ
cana-2738	175	7	pfδβint(a	pfδβint(a	PROPN
cana-2738	175	8	)	)	PUNCT
cana-2738	175	9	)	)	PUNCT
cana-2738	175	10	and	and	CCONJ
cana-2738	175	11	the	the	DET
cana-2738	175	12	pfδ𝒫cl(a	pfδ𝒫cl(a	NUM
cana-2738	175	13	)	)	PUNCT
cana-2738	175	14	(	(	PUNCT
cana-2738	175	15	resp	resp	NOUN
cana-2738	175	16	.	.	PUNCT
cana-2738	176	1	pfδ𝒮cl(a	pfδ𝒮cl(a	NOUN
cana-2738	176	2	)	)	PUNCT
cana-2738	176	3	,	,	PUNCT
cana-2738	176	4	pfδαcl(a	pfδαcl(a	PROPN
cana-2738	176	5	)	)	PUNCT
cana-2738	176	6	and	and	CCONJ
cana-2738	176	7	pfδβcl(a	pfδβcl(a	NOUN
cana-2738	176	8	)	)	PUNCT
cana-2738	176	9	and	and	CCONJ
cana-2738	176	10	are	be	AUX
cana-2738	176	11	defined	define	VERB
cana-2738	176	12	as	as	SCONJ
cana-2738	176	13	follows	follow	VERB
cana-2738	176	14	:	:	PUNCT
cana-2738	176	15	pfδ𝒫int(a	pfδ𝒫int(a	PROPN
cana-2738	176	16	)	)	PUNCT
cana-2738	176	17	(	(	PUNCT
cana-2738	176	18	resp	resp	NOUN
cana-2738	176	19	.	.	PUNCT
cana-2738	177	1	pfδ𝒮int(a	pfδ𝒮int(a	ADJ
cana-2738	177	2	)	)	PUNCT
cana-2738	177	3	,	,	PUNCT
cana-2738	177	4	pfδαint(a	pfδαint(a	PROPN
cana-2738	177	5	)	)	PUNCT
cana-2738	177	6	and	and	CCONJ
cana-2738	177	7	pfδβint(a	pfδβint(a	NOUN
cana-2738	177	8	)	)	PUNCT
cana-2738	177	9	=	=	NOUN
cana-2738	177	10	∪	∪	X
cana-2738	177	11	{	{	PUNCT
cana-2738	177	12	g|g	g|g	NOUN
cana-2738	177	13	in	in	ADP
cana-2738	177	14	a	a	DET
cana-2738	177	15	pfδ𝒫os	pfδ𝒫os	NOUN
cana-2738	177	16	(	(	PUNCT
cana-2738	177	17	resp	resp	NOUN
cana-2738	177	18	.	.	PUNCT
cana-2738	178	1	pfδ𝒮os	pfδ𝒮os	NOUN
cana-2738	178	2	,	,	PUNCT
cana-2738	178	3	pfδαos	pfδαo	NOUN
cana-2738	178	4	and	and	CCONJ
cana-2738	178	5	pfδβos	pfδβos	NOUN
cana-2738	178	6	)	)	PUNCT
cana-2738	178	7	and	and	CCONJ
cana-2738	178	8	g	g	PROPN
cana-2738	178	9	⊆	⊆	NUM
cana-2738	178	10	a	a	PRON
cana-2738	178	11	}	}	PUNCT
cana-2738	178	12	and	and	CCONJ
cana-2738	178	13	pfδ𝒫cl(a	pfδ𝒫cl(a	NUM
cana-2738	178	14	)	)	PUNCT
cana-2738	178	15	(	(	PUNCT
cana-2738	178	16	resp	resp	NOUN
cana-2738	178	17	.	.	PUNCT
cana-2738	179	1	pfδ𝒮cl(a	pfδ𝒮cl(a	NOUN
cana-2738	179	2	)	)	PUNCT
cana-2738	179	3	,	,	PUNCT
cana-2738	179	4	pfδαcl(a	pfδαcl(a	PROPN
cana-2738	179	5	)	)	PUNCT
cana-2738	179	6	and	and	CCONJ
cana-2738	179	7	pfδβcl(a	pfδβcl(a	NOUN
cana-2738	179	8	)	)	PUNCT
cana-2738	179	9	=	=	NOUN
cana-2738	179	10	∩	∩	NOUN
cana-2738	179	11	{	{	PUNCT
cana-2738	179	12	k|k	k|k	PROPN
cana-2738	179	13	is	be	AUX
cana-2738	179	14	an	an	DET
cana-2738	179	15	pfδ𝒫cs	pfδ𝒫cs	NOUN
cana-2738	179	16	(	(	PUNCT
cana-2738	179	17	resp	resp	NOUN
cana-2738	179	18	.	.	PUNCT
cana-2738	180	1	pfδ𝒮cs	pfδ𝒮cs	PROPN
cana-2738	180	2	,	,	PUNCT
cana-2738	180	3	pfδαcs	pfδαcs	NOUN
cana-2738	180	4	,	,	PUNCT
cana-2738	180	5	pfδβcs	pfδβcs	PROPN
cana-2738	180	6	)	)	PUNCT
cana-2738	180	7	and	and	CCONJ
cana-2738	180	8	a	a	DET
cana-2738	180	9	⊆	⊆	NUM
cana-2738	180	10	k	k	NOUN
cana-2738	180	11	}	}	PUNCT
cana-2738	180	12	.	.	PUNCT
cana-2738	181	1	definition	definition	NOUN
cana-2738	181	2	3.4	3.4	NUM
cana-2738	181	3	let	let	VERB
cana-2738	181	4	(	(	PUNCT
cana-2738	181	5	x1	x1	PROPN
cana-2738	181	6	,	,	PUNCT
cana-2738	181	7	γp	γp	PROPN
cana-2738	181	8	)	)	PUNCT
cana-2738	181	9	&	&	CCONJ
cana-2738	181	10	(	(	PUNCT
cana-2738	181	11	x2	x2	PROPN
cana-2738	181	12	,	,	PUNCT
cana-2738	181	13	ψp	ψp	PRON
cana-2738	181	14	)	)	PUNCT
cana-2738	181	15	be	be	AUX
cana-2738	181	16	a	a	DET
cana-2738	181	17	pfts	pft	NOUN
cana-2738	181	18	’s	’s	PART
cana-2738	181	19	.	.	PUNCT
cana-2738	182	1	a	a	DET
cana-2738	182	2	mapping	mapping	NOUN
cana-2738	182	3	hp	hp	NOUN
cana-2738	182	4	:	:	PUNCT
cana-2738	182	5	(	(	PUNCT
cana-2738	182	6	x1	x1	PROPN
cana-2738	182	7	,	,	PUNCT
cana-2738	182	8	γp	γp	PROPN
cana-2738	182	9	)	)	PUNCT
cana-2738	182	10	→	→	SYM
cana-2738	182	11	(	(	PUNCT
cana-2738	182	12	x2	x2	PROPN
cana-2738	182	13	,	,	PUNCT
cana-2738	182	14	ψp	ψp	NOUN
cana-2738	182	15	)	)	PUNCT
cana-2738	182	16	is	be	AUX
cana-2738	182	17	said	say	VERB
cana-2738	182	18	to	to	PART
cana-2738	182	19	be	be	AUX
cana-2738	182	20	a	a	DET
cana-2738	182	21	pythagorean	pythagorean	ADJ
cana-2738	182	22	fuzzy	fuzzy	ADJ
cana-2738	182	23	δ	δ	PROPN
cana-2738	182	24	(	(	PUNCT
cana-2738	182	25	resp	resp	PROPN
cana-2738	182	26	.	.	PUNCT
cana-2738	183	1	δα	δα	PROPN
cana-2738	183	2	,	,	PUNCT
cana-2738	183	3	δ𝒮	δ𝒮	X
cana-2738	183	4	,	,	PUNCT
cana-2738	183	5	δ𝒫	δ𝒫	PROPN
cana-2738	183	6	&	&	CCONJ
cana-2738	183	7	δβ	δβ	NOUN
cana-2738	183	8	or	or	CCONJ
cana-2738	183	9	e∗)-continuous	e∗)-continuous	ADJ
cana-2738	183	10	(	(	PUNCT
cana-2738	183	11	briefly	briefly	ADV
cana-2738	183	12	,	,	PUNCT
cana-2738	183	13	pfδcts	pfδct	NOUN
cana-2738	183	14	(	(	PUNCT
cana-2738	183	15	resp	resp	NOUN
cana-2738	183	16	.	.	PUNCT
cana-2738	184	1	pfδαcts	pfδαct	NOUN
cana-2738	184	2	,	,	PUNCT
cana-2738	184	3	pfδ𝒮cts	pfδ𝒮ct	NOUN
cana-2738	184	4	,	,	PUNCT
cana-2738	184	5	pfδ𝒫cts	pfδ𝒫ct	NOUN
cana-2738	184	6	&	&	CCONJ
cana-2738	184	7	pfδβcts	pfδβct	NOUN
cana-2738	184	8	or	or	CCONJ
cana-2738	184	9	pfe∗cts	pfe∗ct	NOUN
cana-2738	184	10	)	)	PUNCT
cana-2738	184	11	)	)	PUNCT
cana-2738	185	1	if	if	SCONJ
cana-2738	185	2	the	the	DET
cana-2738	185	3	inverse	inverse	ADJ
cana-2738	185	4	image	image	NOUN
cana-2738	185	5	of	of	ADP
cana-2738	185	6	every	every	DET
cana-2738	185	7	pfos	pfos	NOUN
cana-2738	185	8	in	in	ADP
cana-2738	185	9	(	(	PUNCT
cana-2738	185	10	x2	x2	INTJ
cana-2738	185	11	,	,	PUNCT
cana-2738	185	12	ψp	ψp	PROPN
cana-2738	185	13	)	)	PUNCT
cana-2738	185	14	is	be	AUX
cana-2738	185	15	a	a	DET
cana-2738	185	16	pfδos	pfδos	PROPN
cana-2738	185	17	(	(	PUNCT
cana-2738	185	18	resp	resp	NOUN
cana-2738	185	19	.	.	PUNCT
cana-2738	186	1	pfδαos	pfδαo	NOUN
cana-2738	186	2	,	,	PUNCT
cana-2738	186	3	pfδ𝒮os	pfδ𝒮os	NOUN
cana-2738	186	4	,	,	PUNCT
cana-2738	186	5	pfδ𝒫os	pfδ𝒫os	PROPN
cana-2738	186	6	&	&	CCONJ
cana-2738	186	7	pfδβos	pfδβos	PROPN
cana-2738	186	8	or	or	CCONJ
cana-2738	186	9	pfe∗os	pfe∗os	NOUN
cana-2738	186	10	)	)	PUNCT
cana-2738	186	11	in	in	ADP
cana-2738	186	12	(	(	PUNCT
cana-2738	186	13	x1	x1	PROPN
cana-2738	186	14	,	,	PUNCT
cana-2738	186	15	γp	γp	PROPN
cana-2738	186	16	)	)	PUNCT
cana-2738	186	17	.	.	PUNCT
cana-2738	187	1	communications	communication	NOUN
cana-2738	187	2	on	on	ADP
cana-2738	187	3	applied	apply	VERB
cana-2738	187	4	nonlinear	nonlinear	ADJ
cana-2738	187	5	analysis	analysis	NOUN
cana-2738	187	6	issn	issn	NOUN
cana-2738	187	7	:	:	PUNCT
cana-2738	187	8	1074	1074	NUM
cana-2738	187	9	-	-	PUNCT
cana-2738	187	10	133x	133x	NUM
cana-2738	187	11	vol	vol	NOUN
cana-2738	187	12	32	32	NUM
cana-2738	187	13	no	no	NOUN
cana-2738	187	14	.	.	PUNCT
cana-2738	188	1	4s	4s	NUM
cana-2738	188	2	(	(	PUNCT
cana-2738	188	3	2025	2025	NUM
cana-2738	188	4	)	)	PUNCT
cana-2738	188	5	48	48	NUM
cana-2738	188	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2738	188	7	definition	definition	NOUN
cana-2738	188	8	3.5	3.5	NUM
cana-2738	188	9	let	let	VERB
cana-2738	188	10	(	(	PUNCT
cana-2738	188	11	x1	x1	PROPN
cana-2738	188	12	,	,	PUNCT
cana-2738	188	13	γp	γp	PROPN
cana-2738	188	14	)	)	PUNCT
cana-2738	188	15	&	&	CCONJ
cana-2738	188	16	(	(	PUNCT
cana-2738	188	17	x2	x2	PROPN
cana-2738	188	18	,	,	PUNCT
cana-2738	188	19	ψp	ψp	PRON
cana-2738	188	20	)	)	PUNCT
cana-2738	188	21	be	be	AUX
cana-2738	188	22	a	a	DET
cana-2738	188	23	pfts	pft	NOUN
cana-2738	188	24	’s	’s	PART
cana-2738	188	25	.	.	PUNCT
cana-2738	189	1	a	a	DET
cana-2738	189	2	mapping	mapping	NOUN
cana-2738	189	3	hp	hp	NOUN
cana-2738	189	4	:	:	PUNCT
cana-2738	189	5	(	(	PUNCT
cana-2738	189	6	x1	x1	PROPN
cana-2738	189	7	,	,	PUNCT
cana-2738	189	8	γp	γp	PROPN
cana-2738	189	9	)	)	PUNCT
cana-2738	189	10	→	→	SYM
cana-2738	189	11	(	(	PUNCT
cana-2738	189	12	x2	x2	PROPN
cana-2738	189	13	,	,	PUNCT
cana-2738	189	14	ψp	ψp	NOUN
cana-2738	189	15	)	)	PUNCT
cana-2738	189	16	is	be	AUX
cana-2738	189	17	said	say	VERB
cana-2738	189	18	to	to	PART
cana-2738	189	19	be	be	AUX
cana-2738	189	20	a	a	DET
cana-2738	189	21	pythagorean	pythagorean	ADJ
cana-2738	189	22	fuzzy	fuzzy	NOUN
cana-2738	189	23	(	(	PUNCT
cana-2738	189	24	resp	resp	NOUN
cana-2738	189	25	.	.	PUNCT
cana-2738	190	1	δ	δ	PROPN
cana-2738	190	2	,	,	PUNCT
cana-2738	190	3	δα	δα	VERB
cana-2738	190	4	,	,	PUNCT
cana-2738	190	5	δ𝒮	δ𝒮	NOUN
cana-2738	190	6	,	,	PUNCT
cana-2738	190	7	δ𝒫	δ𝒫	PROPN
cana-2738	190	8	&	&	CCONJ
cana-2738	190	9	δβ	δβ	NOUN
cana-2738	190	10	or	or	CCONJ
cana-2738	190	11	e∗)-open	e∗)-open	ADJ
cana-2738	190	12	map	map	NOUN
cana-2738	190	13	(	(	PUNCT
cana-2738	190	14	briefly	briefly	ADV
cana-2738	190	15	,	,	PUNCT
cana-2738	190	16	pfo	pfo	PROPN
cana-2738	190	17	(	(	PUNCT
cana-2738	190	18	resp	resp	PROPN
cana-2738	190	19	.	.	PUNCT
cana-2738	191	1	pfδo	pfδo	ADJ
cana-2738	191	2	,	,	PUNCT
cana-2738	191	3	pfδαo	pfδαo	NOUN
cana-2738	191	4	,	,	PUNCT
cana-2738	191	5	pfδ𝒮o	pfδ𝒮o	ADJ
cana-2738	191	6	,	,	PUNCT
cana-2738	191	7	pfδ𝒫o	pfδ𝒫o	ADJ
cana-2738	191	8	&	&	CCONJ
cana-2738	191	9	pfδβo	pfδβo	PROPN
cana-2738	191	10	or	or	CCONJ
cana-2738	191	11	pfe∗o	pfe∗o	NUM
cana-2738	191	12	)	)	PUNCT
cana-2738	191	13	)	)	PUNCT
cana-2738	192	1	if	if	SCONJ
cana-2738	192	2	the	the	DET
cana-2738	192	3	image	image	NOUN
cana-2738	192	4	of	of	ADP
cana-2738	192	5	every	every	DET
cana-2738	192	6	pfos	pfos	NOUN
cana-2738	192	7	in	in	ADP
cana-2738	192	8	(	(	PUNCT
cana-2738	192	9	x1	x1	PROPN
cana-2738	192	10	,	,	PUNCT
cana-2738	192	11	γp	γp	PROPN
cana-2738	192	12	)	)	PUNCT
cana-2738	192	13	is	be	AUX
cana-2738	192	14	a	a	DET
cana-2738	192	15	pfos	pfos	NOUN
cana-2738	192	16	(	(	PUNCT
cana-2738	192	17	resp	resp	NOUN
cana-2738	192	18	.	.	PUNCT
cana-2738	193	1	pfδos	pfδos	PROPN
cana-2738	193	2	,	,	PUNCT
cana-2738	193	3	pfδαos	pfδαo	NOUN
cana-2738	193	4	,	,	PUNCT
cana-2738	193	5	pfδ𝒮os	pfδ𝒮os	NOUN
cana-2738	193	6	,	,	PUNCT
cana-2738	193	7	pfδ𝒫os	pfδ𝒫os	PROPN
cana-2738	193	8	&	&	CCONJ
cana-2738	193	9	pfδβos	pfδβos	PROPN
cana-2738	193	10	or	or	CCONJ
cana-2738	193	11	pfe∗os	pfe∗os	NOUN
cana-2738	193	12	)	)	PUNCT
cana-2738	193	13	in	in	ADP
cana-2738	193	14	(	(	PUNCT
cana-2738	193	15	x2	x2	INTJ
cana-2738	193	16	,	,	PUNCT
cana-2738	193	17	ψp	ψp	NOUN
cana-2738	193	18	)	)	PUNCT
cana-2738	193	19	.	.	PUNCT
cana-2738	194	1	theorem	theorem	VERB
cana-2738	194	2	3.1	3.1	NUM
cana-2738	194	3	let	let	NOUN
cana-2738	194	4	(	(	PUNCT
cana-2738	194	5	x1	x1	PROPN
cana-2738	194	6	,	,	PUNCT
cana-2738	194	7	γp	γp	PROPN
cana-2738	194	8	)	)	PUNCT
cana-2738	194	9	&	&	CCONJ
cana-2738	194	10	(	(	PUNCT
cana-2738	194	11	x2	x2	PROPN
cana-2738	194	12	,	,	PUNCT
cana-2738	194	13	ψp	ψp	PRON
cana-2738	194	14	)	)	PUNCT
cana-2738	194	15	be	be	AUX
cana-2738	194	16	a	a	DET
cana-2738	194	17	pfts	pft	NOUN
cana-2738	194	18	’s	’s	PART
cana-2738	194	19	.	.	PUNCT
cana-2738	195	1	let	let	VERB
cana-2738	195	2	hp	hp	VERB
cana-2738	195	3	:	:	PUNCT
cana-2738	195	4	(	(	PUNCT
cana-2738	195	5	x1	x1	PROPN
cana-2738	195	6	,	,	PUNCT
cana-2738	195	7	γp	γp	PROPN
cana-2738	195	8	)	)	PUNCT
cana-2738	195	9	→	→	SYM
cana-2738	195	10	(	(	PUNCT
cana-2738	195	11	x2	x2	PROPN
cana-2738	195	12	,	,	PUNCT
cana-2738	195	13	ψp	ψp	PRON
cana-2738	195	14	)	)	PUNCT
cana-2738	195	15	be	be	AUX
cana-2738	195	16	a	a	DET
cana-2738	195	17	mapping	mapping	NOUN
cana-2738	195	18	.	.	PUNCT
cana-2738	196	1	then	then	ADV
cana-2738	196	2	the	the	DET
cana-2738	196	3	following	following	ADJ
cana-2738	196	4	statements	statement	NOUN
cana-2738	196	5	are	be	AUX
cana-2738	196	6	hold	hold	ADJ
cana-2738	196	7	for	for	ADP
cana-2738	196	8	pfts	pft	NOUN
cana-2738	196	9	,	,	PUNCT
cana-2738	196	10	but	but	CCONJ
cana-2738	196	11	not	not	PART
cana-2738	196	12	conversely	conversely	ADV
cana-2738	196	13	.	.	PUNCT
cana-2738	197	1	1	1	X
cana-2738	197	2	.	.	X
cana-2738	197	3	every	every	DET
cana-2738	197	4	pfδo	pfδo	ADJ
cana-2738	197	5	mapping	mapping	NOUN
cana-2738	197	6	is	be	AUX
cana-2738	197	7	a	a	DET
cana-2738	197	8	pfo	pfo	NOUN
cana-2738	197	9	mapping	mapping	NOUN
cana-2738	197	10	.	.	PUNCT
cana-2738	198	1	2	2	X
cana-2738	198	2	.	.	X
cana-2738	198	3	every	every	DET
cana-2738	198	4	pfδo	pfδo	ADJ
cana-2738	198	5	mapping	mapping	NOUN
cana-2738	198	6	is	be	AUX
cana-2738	198	7	a	a	DET
cana-2738	198	8	pfδ𝒮o	pfδ𝒮o	ADJ
cana-2738	198	9	mapping	mapping	NOUN
cana-2738	198	10	.	.	PUNCT
cana-2738	199	1	3	3	X
cana-2738	199	2	.	.	X
cana-2738	199	3	every	every	DET
cana-2738	199	4	pfδo	pfδo	ADJ
cana-2738	199	5	mapping	mapping	NOUN
cana-2738	199	6	is	be	AUX
cana-2738	199	7	a	a	DET
cana-2738	199	8	pfδ𝒫o	pfδ𝒫o	ADJ
cana-2738	199	9	mapping	mapping	NOUN
cana-2738	199	10	.	.	PUNCT
cana-2738	200	1	4	4	X
cana-2738	200	2	.	.	X
cana-2738	200	3	every	every	DET
cana-2738	200	4	pfδ𝒮o	pfδ𝒮o	ADJ
cana-2738	200	5	mapping	mapping	NOUN
cana-2738	200	6	is	be	AUX
cana-2738	200	7	a	a	DET
cana-2738	200	8	pfδβo	pfδβo	ADJ
cana-2738	200	9	mapping	mapping	NOUN
cana-2738	200	10	.	.	PUNCT
cana-2738	201	1	5	5	X
cana-2738	201	2	.	.	X
cana-2738	201	3	every	every	DET
cana-2738	201	4	pfδ𝒫o	pfδ𝒫o	ADJ
cana-2738	201	5	mapping	mapping	NOUN
cana-2738	201	6	is	be	AUX
cana-2738	201	7	a	a	DET
cana-2738	201	8	pfδβo	pfδβo	ADJ
cana-2738	201	9	mapping	mapping	NOUN
cana-2738	201	10	.	.	PUNCT
cana-2738	202	1	6	6	X
cana-2738	202	2	.	.	X
cana-2738	202	3	every	every	DET
cana-2738	202	4	pfδαo	pfδαo	NOUN
cana-2738	202	5	mapping	mapping	NOUN
cana-2738	202	6	is	be	AUX
cana-2738	202	7	a	a	DET
cana-2738	202	8	pfδ𝒮o	pfδ𝒮o	ADJ
cana-2738	202	9	mapping	mapping	NOUN
cana-2738	202	10	.	.	PUNCT
cana-2738	203	1	7	7	X
cana-2738	203	2	.	.	X
cana-2738	203	3	every	every	DET
cana-2738	203	4	pfδαo	pfδαo	NOUN
cana-2738	203	5	mapping	mapping	NOUN
cana-2738	203	6	is	be	AUX
cana-2738	203	7	a	a	DET
cana-2738	203	8	pfδ𝒫o	pfδ𝒫o	ADJ
cana-2738	203	9	mapping	mapping	NOUN
cana-2738	203	10	.	.	PUNCT
cana-2738	204	1	proof	proof	NOUN
cana-2738	204	2	.	.	PUNCT
cana-2738	205	1	(	(	PUNCT
cana-2738	205	2	i	i	NOUN
cana-2738	205	3	)	)	PUNCT
cana-2738	205	4	let	let	VERB
cana-2738	205	5	m	m	PRON
cana-2738	205	6	be	be	AUX
cana-2738	205	7	a	a	DET
cana-2738	205	8	pfos	pfos	NOUN
cana-2738	205	9	in	in	ADP
cana-2738	205	10	x1	x1	PROPN
cana-2738	205	11	.	.	PUNCT
cana-2738	206	1	since	since	SCONJ
cana-2738	206	2	hp	hp	PROPN
cana-2738	206	3	is	be	AUX
cana-2738	206	4	pfδo	pfδo	ADJ
cana-2738	206	5	map	map	NOUN
cana-2738	206	6	,	,	PUNCT
cana-2738	206	7	hp(m	hp(m	X
cana-2738	206	8	)	)	PUNCT
cana-2738	206	9	is	be	AUX
cana-2738	206	10	a	a	DET
cana-2738	206	11	pfδos	pfδo	NOUN
cana-2738	206	12	in	in	ADP
cana-2738	206	13	x2	x2	PROPN
cana-2738	206	14	.	.	PUNCT
cana-2738	207	1	since	since	SCONJ
cana-2738	207	2	every	every	DET
cana-2738	207	3	pfδos	pfδo	NOUN
cana-2738	207	4	is	be	AUX
cana-2738	207	5	a	a	DET
cana-2738	207	6	pfos	pfos	NOUN
cana-2738	207	7	,	,	PUNCT
cana-2738	207	8	hp(m	hp(m	X
cana-2738	207	9	)	)	PUNCT
cana-2738	207	10	is	be	AUX
cana-2738	207	11	a	a	DET
cana-2738	207	12	pfos	pfos	NOUN
cana-2738	207	13	in	in	ADP
cana-2738	207	14	x2	x2	PROPN
cana-2738	207	15	.	.	PUNCT
cana-2738	208	1	hence	hence	ADV
cana-2738	208	2	hp	hp	PROPN
cana-2738	208	3	is	be	AUX
cana-2738	208	4	a	a	DET
cana-2738	208	5	pfo	pfo	NOUN
cana-2738	208	6	.	.	PUNCT
cana-2738	209	1	(	(	PUNCT
cana-2738	209	2	ii	ii	NOUN
cana-2738	209	3	)	)	PUNCT
cana-2738	209	4	let	let	VERB
cana-2738	209	5	m	m	PRON
cana-2738	209	6	be	be	AUX
cana-2738	209	7	a	a	DET
cana-2738	209	8	pfos	pfos	NOUN
cana-2738	209	9	in	in	ADP
cana-2738	209	10	x1	x1	PROPN
cana-2738	209	11	.	.	PUNCT
cana-2738	210	1	since	since	SCONJ
cana-2738	210	2	hp	hp	PROPN
cana-2738	210	3	is	be	AUX
cana-2738	210	4	pfo	pfo	NOUN
cana-2738	210	5	map	map	NOUN
cana-2738	210	6	,	,	PUNCT
cana-2738	210	7	hp(m	hp(m	X
cana-2738	210	8	)	)	PUNCT
cana-2738	210	9	is	be	AUX
cana-2738	210	10	a	a	DET
cana-2738	210	11	pfos	pfos	NOUN
cana-2738	210	12	in	in	ADP
cana-2738	210	13	x2	x2	PROPN
cana-2738	210	14	.	.	PUNCT
cana-2738	211	1	since	since	SCONJ
cana-2738	211	2	every	every	DET
cana-2738	211	3	pfos	pfos	NOUN
cana-2738	211	4	is	be	AUX
cana-2738	211	5	a	a	DET
cana-2738	211	6	pfδ𝒮os	pfδ𝒮os	NOUN
cana-2738	211	7	,	,	PUNCT
cana-2738	211	8	hp(m	hp(m	X
cana-2738	211	9	)	)	PUNCT
cana-2738	211	10	is	be	AUX
cana-2738	211	11	a	a	DET
cana-2738	211	12	pfδ𝒮os	pfδ𝒮os	NOUN
cana-2738	211	13	in	in	ADP
cana-2738	211	14	x2	x2	PROPN
cana-2738	211	15	.	.	PUNCT
cana-2738	212	1	hence	hence	ADV
cana-2738	212	2	hp	hp	PROPN
cana-2738	212	3	is	be	AUX
cana-2738	212	4	a	a	DET
cana-2738	212	5	pfδ𝒮o	pfδ𝒮o	NOUN
cana-2738	212	6	.	.	PUNCT
cana-2738	213	1	(	(	PUNCT
cana-2738	213	2	iii	iii	X
cana-2738	213	3	)	)	PUNCT
cana-2738	213	4	let	let	VERB
cana-2738	213	5	m	m	PRON
cana-2738	213	6	be	be	AUX
cana-2738	213	7	a	a	DET
cana-2738	213	8	pfos	pfos	NOUN
cana-2738	213	9	in	in	ADP
cana-2738	213	10	x1	x1	PROPN
cana-2738	213	11	.	.	PUNCT
cana-2738	214	1	since	since	SCONJ
cana-2738	214	2	hp	hp	PROPN
cana-2738	214	3	is	be	AUX
cana-2738	214	4	pfo	pfo	NOUN
cana-2738	214	5	map	map	NOUN
cana-2738	214	6	,	,	PUNCT
cana-2738	214	7	hp(m	hp(m	X
cana-2738	214	8	)	)	PUNCT
cana-2738	214	9	is	be	AUX
cana-2738	214	10	a	a	DET
cana-2738	214	11	pfos	pfos	NOUN
cana-2738	214	12	in	in	ADP
cana-2738	214	13	x2	x2	PROPN
cana-2738	214	14	.	.	PUNCT
cana-2738	215	1	since	since	SCONJ
cana-2738	215	2	every	every	DET
cana-2738	215	3	pfos	pfos	NOUN
cana-2738	215	4	is	be	AUX
cana-2738	215	5	a	a	DET
cana-2738	215	6	pfδ𝒫os	pfδ𝒫os	PROPN
cana-2738	215	7	,	,	PUNCT
cana-2738	215	8	hp(m	hp(m	X
cana-2738	215	9	)	)	PUNCT
cana-2738	215	10	is	be	AUX
cana-2738	215	11	a	a	DET
cana-2738	215	12	pfδ𝒫os	pfδ𝒫os	NOUN
cana-2738	215	13	in	in	ADP
cana-2738	215	14	x2	x2	PROPN
cana-2738	215	15	.	.	PUNCT
cana-2738	216	1	hence	hence	ADV
cana-2738	216	2	hp	hp	PROPN
cana-2738	216	3	is	be	AUX
cana-2738	216	4	a	a	DET
cana-2738	216	5	pfδ𝒫o	pfδ𝒫o	NOUN
cana-2738	216	6	.	.	PUNCT
cana-2738	217	1	(	(	PUNCT
cana-2738	217	2	iv	iv	X
cana-2738	217	3	)	)	PUNCT
cana-2738	217	4	let	let	VERB
cana-2738	217	5	m	m	PRON
cana-2738	217	6	be	be	AUX
cana-2738	217	7	a	a	DET
cana-2738	217	8	pfos	pfos	NOUN
cana-2738	217	9	in	in	ADP
cana-2738	217	10	x1	x1	PROPN
cana-2738	217	11	.	.	PUNCT
cana-2738	218	1	since	since	SCONJ
cana-2738	218	2	hp	hp	PROPN
cana-2738	218	3	is	be	AUX
cana-2738	218	4	pfδ𝒮o	pfδ𝒮o	ADJ
cana-2738	218	5	map	map	NOUN
cana-2738	218	6	,	,	PUNCT
cana-2738	218	7	hp(m	hp(m	X
cana-2738	218	8	)	)	PUNCT
cana-2738	218	9	is	be	AUX
cana-2738	218	10	a	a	DET
cana-2738	218	11	pfδ𝒮os	pfδ𝒮os	NOUN
cana-2738	218	12	in	in	ADP
cana-2738	218	13	x2	x2	PROPN
cana-2738	218	14	.	.	PUNCT
cana-2738	219	1	since	since	SCONJ
cana-2738	219	2	every	every	DET
cana-2738	219	3	pfδ𝒮os	pfδ𝒮os	NOUN
cana-2738	219	4	is	be	AUX
cana-2738	219	5	a	a	DET
cana-2738	219	6	pfδβos	pfδβos	NOUN
cana-2738	219	7	,	,	PUNCT
cana-2738	219	8	hp(m	hp(m	X
cana-2738	219	9	)	)	PUNCT
cana-2738	219	10	is	be	AUX
cana-2738	219	11	a	a	DET
cana-2738	219	12	pfδβos	pfδβos	NOUN
cana-2738	219	13	in	in	ADP
cana-2738	219	14	x2	x2	PROPN
cana-2738	219	15	.	.	PUNCT
cana-2738	220	1	hence	hence	ADV
cana-2738	220	2	hp	hp	PROPN
cana-2738	220	3	is	be	AUX
cana-2738	220	4	a	a	DET
cana-2738	220	5	pfδβo	pfδβo	NOUN
cana-2738	220	6	.	.	PUNCT
cana-2738	221	1	(	(	PUNCT
cana-2738	221	2	v	v	NOUN
cana-2738	221	3	)	)	PUNCT
cana-2738	221	4	let	let	VERB
cana-2738	221	5	m	m	PRON
cana-2738	221	6	be	be	AUX
cana-2738	221	7	a	a	DET
cana-2738	221	8	pfos	pfos	NOUN
cana-2738	221	9	in	in	ADP
cana-2738	221	10	x1	x1	PROPN
cana-2738	221	11	.	.	PUNCT
cana-2738	222	1	since	since	SCONJ
cana-2738	222	2	hp	hp	PROPN
cana-2738	222	3	is	be	AUX
cana-2738	222	4	pfδ𝒫o	pfδ𝒫o	ADJ
cana-2738	222	5	map	map	NOUN
cana-2738	222	6	,	,	PUNCT
cana-2738	222	7	hp(m	hp(m	X
cana-2738	222	8	)	)	PUNCT
cana-2738	222	9	is	be	AUX
cana-2738	222	10	a	a	DET
cana-2738	222	11	pfδ𝒫os	pfδ𝒫os	NOUN
cana-2738	222	12	in	in	ADP
cana-2738	222	13	x2	x2	PROPN
cana-2738	222	14	.	.	PUNCT
cana-2738	223	1	since	since	SCONJ
cana-2738	223	2	every	every	DET
cana-2738	223	3	pfδ𝒫os	pfδ𝒫os	NOUN
cana-2738	223	4	is	be	AUX
cana-2738	223	5	a	a	DET
cana-2738	223	6	pfδβos	pfδβos	NOUN
cana-2738	223	7	,	,	PUNCT
cana-2738	223	8	hp(m	hp(m	X
cana-2738	223	9	)	)	PUNCT
cana-2738	223	10	is	be	AUX
cana-2738	223	11	a	a	DET
cana-2738	223	12	pfδβos	pfδβos	NOUN
cana-2738	223	13	in	in	ADP
cana-2738	223	14	x2	x2	PROPN
cana-2738	223	15	.	.	PUNCT
cana-2738	224	1	hence	hence	ADV
cana-2738	224	2	hp	hp	PROPN
cana-2738	224	3	is	be	AUX
cana-2738	224	4	a	a	DET
cana-2738	224	5	pfδβo	pfδβo	NOUN
cana-2738	224	6	.	.	PUNCT
cana-2738	225	1	(	(	PUNCT
cana-2738	225	2	vi	vi	X
cana-2738	225	3	)	)	PUNCT
cana-2738	225	4	let	let	VERB
cana-2738	225	5	m	m	PRON
cana-2738	225	6	be	be	AUX
cana-2738	225	7	a	a	DET
cana-2738	225	8	pfos	pfos	NOUN
cana-2738	225	9	in	in	ADP
cana-2738	225	10	x1	x1	PROPN
cana-2738	225	11	.	.	PUNCT
cana-2738	226	1	since	since	SCONJ
cana-2738	226	2	hp	hp	PROPN
cana-2738	226	3	is	be	AUX
cana-2738	226	4	pfδαo	pfδαo	NOUN
cana-2738	226	5	map	map	NOUN
cana-2738	226	6	,	,	PUNCT
cana-2738	226	7	hp(m	hp(m	X
cana-2738	226	8	)	)	PUNCT
cana-2738	226	9	is	be	AUX
cana-2738	226	10	a	a	DET
cana-2738	226	11	pfδαos	pfδαo	NOUN
cana-2738	226	12	in	in	ADP
cana-2738	226	13	x2	x2	PROPN
cana-2738	226	14	.	.	PUNCT
cana-2738	227	1	since	since	SCONJ
cana-2738	227	2	every	every	DET
cana-2738	227	3	pfδαos	pfδαo	NOUN
cana-2738	227	4	is	be	AUX
cana-2738	227	5	a	a	DET
cana-2738	227	6	pfδ𝒮os	pfδ𝒮os	NOUN
cana-2738	227	7	,	,	PUNCT
cana-2738	227	8	hp(m	hp(m	X
cana-2738	227	9	)	)	PUNCT
cana-2738	227	10	is	be	AUX
cana-2738	227	11	a	a	DET
cana-2738	227	12	pfδ𝒮os	pfδ𝒮os	NOUN
cana-2738	227	13	in	in	ADP
cana-2738	227	14	x2	x2	PROPN
cana-2738	227	15	.	.	PUNCT
cana-2738	228	1	hence	hence	ADV
cana-2738	228	2	hp	hp	PROPN
cana-2738	228	3	is	be	AUX
cana-2738	228	4	a	a	DET
cana-2738	228	5	pfδ𝒮o	pfδ𝒮o	NOUN
cana-2738	228	6	.	.	PUNCT
cana-2738	229	1	(	(	PUNCT
cana-2738	229	2	vii	vii	PROPN
cana-2738	229	3	)	)	PUNCT
cana-2738	229	4	let	let	VERB
cana-2738	229	5	m	m	PRON
cana-2738	229	6	be	be	AUX
cana-2738	229	7	a	a	DET
cana-2738	229	8	pfos	pfos	NOUN
cana-2738	229	9	in	in	ADP
cana-2738	229	10	x1	x1	PROPN
cana-2738	229	11	.	.	PUNCT
cana-2738	230	1	since	since	SCONJ
cana-2738	230	2	hp	hp	PROPN
cana-2738	230	3	is	be	AUX
cana-2738	230	4	pfδαo	pfδαo	NOUN
cana-2738	230	5	map	map	NOUN
cana-2738	230	6	,	,	PUNCT
cana-2738	230	7	hp(m	hp(m	X
cana-2738	230	8	)	)	PUNCT
cana-2738	230	9	is	be	AUX
cana-2738	230	10	a	a	DET
cana-2738	230	11	pfδαos	pfδαo	NOUN
cana-2738	230	12	in	in	ADP
cana-2738	230	13	x2	x2	PROPN
cana-2738	230	14	.	.	PUNCT
cana-2738	231	1	since	since	SCONJ
cana-2738	231	2	every	every	DET
cana-2738	231	3	pfδαos	pfδαo	NOUN
cana-2738	231	4	is	be	AUX
cana-2738	231	5	a	a	DET
cana-2738	231	6	pfδ𝒫os	pfδ𝒫os	PROPN
cana-2738	231	7	,	,	PUNCT
cana-2738	231	8	hp(m	hp(m	X
cana-2738	231	9	)	)	PUNCT
cana-2738	231	10	is	be	AUX
cana-2738	231	11	a	a	DET
cana-2738	231	12	pfδ𝒫os	pfδ𝒫os	NOUN
cana-2738	231	13	in	in	ADP
cana-2738	231	14	x2	x2	PROPN
cana-2738	231	15	.	.	PUNCT
cana-2738	232	1	hence	hence	ADV
cana-2738	232	2	hp	hp	PROPN
cana-2738	232	3	is	be	AUX
cana-2738	232	4	a	a	DET
cana-2738	232	5	pfδ𝒫o	pfδ𝒫o	ADJ
cana-2738	232	6	.	.	PUNCT
cana-2738	233	1	remark	remark	PROPN
cana-2738	233	2	3.1	3.1	NUM
cana-2738	233	3	we	we	PRON
cana-2738	233	4	obtain	obtain	VERB
cana-2738	233	5	the	the	DET
cana-2738	233	6	following	follow	VERB
cana-2738	233	7	diagram	diagram	NOUN
cana-2738	233	8	from	from	ADP
cana-2738	233	9	the	the	DET
cana-2738	233	10	results	result	NOUN
cana-2738	233	11	we	we	PRON
cana-2738	233	12	discussed	discuss	VERB
cana-2738	233	13	above	above	ADV
cana-2738	233	14	.	.	PUNCT
cana-2738	234	1	communications	communication	NOUN
cana-2738	234	2	on	on	ADP
cana-2738	234	3	applied	apply	VERB
cana-2738	234	4	nonlinear	nonlinear	ADJ
cana-2738	234	5	analysis	analysis	NOUN
cana-2738	234	6	issn	issn	NOUN
cana-2738	234	7	:	:	PUNCT
cana-2738	234	8	1074	1074	NUM
cana-2738	234	9	-	-	PUNCT
cana-2738	234	10	133x	133x	NUM
cana-2738	234	11	vol	vol	NOUN
cana-2738	234	12	32	32	NUM
cana-2738	234	13	no	no	NOUN
cana-2738	234	14	.	.	PUNCT
cana-2738	235	1	4s	4s	NUM
cana-2738	235	2	(	(	PUNCT
cana-2738	235	3	2025	2025	NUM
cana-2738	235	4	)	)	PUNCT
cana-2738	235	5	49	49	NUM
cana-2738	235	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2738	235	7	fig	fig	NOUN
cana-2738	235	8	.	.	PUNCT
cana-2738	236	1	1	1	NUM
cana-2738	236	2	:	:	PUNCT
cana-2738	236	3	𝑝𝑓𝛿𝑂	𝑝𝑓𝛿𝑂	VERB
cana-2738	236	4	mappings	mapping	NOUN
cana-2738	236	5	in	in	ADP
cana-2738	236	6	𝑝𝑓𝑡𝑠.	𝑝𝑓𝑡𝑠.	PROPN
cana-2738	236	7	note	note	NOUN
cana-2738	236	8	:	:	PUNCT
cana-2738	236	9	𝐴	𝐴	PROPN
cana-2738	236	10	→	→	SYM
cana-2738	236	11	𝐵	𝐵	NOUN
cana-2738	236	12	denotes	denote	NOUN
cana-2738	236	13	𝐴	𝐴	PROPN
cana-2738	236	14	implies	imply	VERB
cana-2738	236	15	𝐵.	𝐵.	PROPN
cana-2738	236	16	but	but	CCONJ
cana-2738	236	17	not	not	PART
cana-2738	236	18	conversely	conversely	ADV
cana-2738	236	19	.	.	PUNCT
cana-2738	237	1	example	example	NOUN
cana-2738	237	2	3.1	3.1	NUM
cana-2738	237	3	let	let	VERB
cana-2738	237	4	x	x	X
cana-2738	238	1	=	=	SYM
cana-2738	238	2	x1	x1	PROPN
cana-2738	238	3	=	=	PUNCT
cana-2738	239	1	x2	x2	PROPN
cana-2738	239	2	=	=	PUNCT
cana-2738	239	3	x3	x3	PROPN
cana-2738	239	4	=	=	SYM
cana-2738	239	5	x4	x4	PROPN
cana-2738	239	6	=	=	SYM
cana-2738	239	7	x5	x5	PROPN
cana-2738	239	8	=	=	SYM
cana-2738	239	9	{	{	PUNCT
cana-2738	239	10	x1	x1	PROPN
cana-2738	239	11	,	,	PUNCT
cana-2738	239	12	x2	x2	PROPN
cana-2738	239	13	}	}	PUNCT
cana-2738	239	14	and	and	CCONJ
cana-2738	239	15	the	the	DET
cana-2738	239	16	pfs	pfs	PROPN
cana-2738	239	17	’s	’s	PART
cana-2738	239	18	a1	a1	NOUN
cana-2738	239	19	,	,	PUNCT
cana-2738	239	20	a2	a2	PROPN
cana-2738	239	21	and	and	CCONJ
cana-2738	239	22	a3	a3	NOUN
cana-2738	239	23	are	be	AUX
cana-2738	239	24	defined	define	VERB
cana-2738	239	25	as	as	ADP
cana-2738	239	26	a1	a1	NOUN
cana-2738	239	27	=	=	PUNCT
cana-2738	239	28	{	{	PUNCT
cana-2738	239	29	<	<	X
cana-2738	239	30	x1	x1	PROPN
cana-2738	239	31	,	,	PUNCT
cana-2738	239	32	0.020,0.040	0.020,0.040	NUM
cana-2738	239	33	>	>	PUNCT
cana-2738	239	34	,	,	PUNCT
cana-2738	239	35	<	<	X
cana-2738	239	36	x2	x2	PROPN
cana-2738	239	37	,	,	PUNCT
cana-2738	239	38	0.050,0.050	0.050,0.050	PROPN
cana-2738	239	39	>	>	PUNCT
cana-2738	239	40	}	}	PUNCT
cana-2738	239	41	a2	a2	PROPN
cana-2738	239	42	=	=	PUNCT
cana-2738	239	43	{	{	PUNCT
cana-2738	239	44	<	<	X
cana-2738	239	45	x1	x1	PROPN
cana-2738	239	46	,	,	PUNCT
cana-2738	239	47	0.010,0.040	0.010,0.040	NUM
cana-2738	239	48	>	>	PUNCT
cana-2738	239	49	,	,	PUNCT
cana-2738	239	50	<	<	X
cana-2738	239	51	x2	x2	PROPN
cana-2738	239	52	,	,	PUNCT
cana-2738	239	53	0.050,0.050	0.050,0.050	PROPN
cana-2738	239	54	>	>	PUNCT
cana-2738	239	55	}	}	PUNCT
cana-2738	239	56	a3	a3	NOUN
cana-2738	239	57	=	=	PRON
cana-2738	239	58	{	{	PUNCT
cana-2738	239	59	<	<	X
cana-2738	239	60	x1	x1	PROPN
cana-2738	239	61	,	,	PUNCT
cana-2738	239	62	0.020,0.030	0.020,0.030	PROPN
cana-2738	239	63	>	>	PUNCT
cana-2738	239	64	,	,	PUNCT
cana-2738	239	65	<	<	X
cana-2738	239	66	x2	x2	PROPN
cana-2738	239	67	,	,	PUNCT
cana-2738	239	68	0.050,0.050	0.050,0.050	PROPN
cana-2738	239	69	>	>	PUNCT
cana-2738	239	70	}	}	PUNCT
cana-2738	239	71	here	here	ADV
cana-2738	239	72	we	we	PRON
cana-2738	239	73	have	have	VERB
cana-2738	239	74	τ1	τ1	NOUN
cana-2738	239	75	=	=	SYM
cana-2738	239	76	{	{	PUNCT
cana-2738	239	77	0x1	0x1	NOUN
cana-2738	239	78	,	,	PUNCT
cana-2738	239	79	1x1	1x1	NUM
cana-2738	239	80	,	,	PUNCT
cana-2738	239	81	a1	a1	NOUN
cana-2738	239	82	,	,	PUNCT
cana-2738	239	83	a2	a2	PROPN
cana-2738	239	84	}	}	PUNCT
cana-2738	239	85	,	,	PUNCT
cana-2738	240	1	τ2	τ2	NOUN
cana-2738	240	2	=	=	SYM
cana-2738	240	3	{	{	PUNCT
cana-2738	240	4	0x2	0x2	NOUN
cana-2738	240	5	,	,	PUNCT
cana-2738	240	6	1x2	1x2	NUM
cana-2738	240	7	,	,	PUNCT
cana-2738	240	8	a2	a2	PROPN
cana-2738	240	9	}	}	PUNCT
cana-2738	240	10	,	,	PUNCT
cana-2738	240	11	τ3	τ3	NOUN
cana-2738	240	12	=	=	SYM
cana-2738	240	13	{	{	PUNCT
cana-2738	240	14	0x3	0x3	PROPN
cana-2738	240	15	,	,	PUNCT
cana-2738	240	16	1x3	1x3	PROPN
cana-2738	240	17	,	,	PUNCT
cana-2738	240	18	a1	a1	NOUN
cana-2738	240	19	c	c	PROPN
cana-2738	240	20	}	}	PUNCT
cana-2738	240	21	,	,	PUNCT
cana-2738	240	22	τ4	τ4	NOUN
cana-2738	240	23	=	=	SYM
cana-2738	240	24	{	{	PUNCT
cana-2738	240	25	0x4	0x4	NUM
cana-2738	240	26	,	,	PUNCT
cana-2738	240	27	1x4	1x4	NUM
cana-2738	240	28	,	,	PUNCT
cana-2738	240	29	a2	a2	PROPN
cana-2738	240	30	c	c	NOUN
cana-2738	240	31	}	}	PUNCT
cana-2738	240	32	and	and	CCONJ
cana-2738	240	33	τ5	τ5	NOUN
cana-2738	240	34	=	=	SYM
cana-2738	240	35	{	{	PUNCT
cana-2738	240	36	0x5	0x5	NUM
cana-2738	240	37	,	,	PUNCT
cana-2738	240	38	1x5	1x5	NUM
cana-2738	240	39	,	,	PUNCT
cana-2738	240	40	a3	a3	NOUN
cana-2738	240	41	}	}	PUNCT
cana-2738	240	42	be	be	VERB
cana-2738	240	43	a	a	DET
cana-2738	240	44	pfts	pft	NOUN
cana-2738	240	45	’s	’s	NOUN
cana-2738	240	46	on	on	ADP
cana-2738	240	47	x.	x.	NOUN
cana-2738	240	48	let	let	VERB
cana-2738	240	49	h1p	h1p	NOUN
cana-2738	240	50	:	:	PUNCT
cana-2738	240	51	(	(	PUNCT
cana-2738	240	52	x2	x2	PROPN
cana-2738	240	53	,	,	PUNCT
cana-2738	240	54	τ2	τ2	PROPN
cana-2738	240	55	)	)	PUNCT
cana-2738	240	56	→	→	SYM
cana-2738	240	57	(	(	PUNCT
cana-2738	240	58	x1	x1	ADJ
cana-2738	240	59	,	,	PUNCT
cana-2738	240	60	τ1	τ1	NOUN
cana-2738	240	61	)	)	PUNCT
cana-2738	240	62	,	,	PUNCT
cana-2738	240	63	h2p	h2p	PROPN
cana-2738	240	64	:	:	PUNCT
cana-2738	240	65	(	(	PUNCT
cana-2738	240	66	x3	x3	ADJ
cana-2738	240	67	,	,	PUNCT
cana-2738	240	68	τ3	τ3	NOUN
cana-2738	240	69	)	)	PUNCT
cana-2738	240	70	→	→	SYM
cana-2738	240	71	(	(	PUNCT
cana-2738	240	72	x1	x1	ADJ
cana-2738	240	73	,	,	PUNCT
cana-2738	240	74	τ1	τ1	NOUN
cana-2738	240	75	)	)	PUNCT
cana-2738	240	76	,	,	PUNCT
cana-2738	240	77	h3p	h3p	PROPN
cana-2738	240	78	:	:	PUNCT
cana-2738	240	79	(	(	PUNCT
cana-2738	240	80	x4	x4	PROPN
cana-2738	240	81	,	,	PUNCT
cana-2738	240	82	τ4	τ4	PROPN
cana-2738	240	83	)	)	PUNCT
cana-2738	240	84	→	→	PUNCT
cana-2738	240	85	(	(	PUNCT
cana-2738	240	86	x1	x1	ADJ
cana-2738	240	87	,	,	PUNCT
cana-2738	240	88	τ1	τ1	NOUN
cana-2738	240	89	)	)	PUNCT
cana-2738	240	90	,	,	PUNCT
cana-2738	240	91	h4p	h4p	PROPN
cana-2738	240	92	:	:	PUNCT
cana-2738	240	93	(	(	PUNCT
cana-2738	240	94	x5	x5	NOUN
cana-2738	240	95	,	,	PUNCT
cana-2738	240	96	τ5	τ5	NUM
cana-2738	240	97	)	)	PUNCT
cana-2738	240	98	→	→	SYM
cana-2738	240	99	(	(	PUNCT
cana-2738	240	100	x1	x1	ADJ
cana-2738	240	101	,	,	PUNCT
cana-2738	240	102	τ1	τ1	NOUN
cana-2738	240	103	)	)	PUNCT
cana-2738	240	104	be	be	VERB
cana-2738	240	105	an	an	DET
cana-2738	240	106	identity	identity	NOUN
cana-2738	240	107	mapping	mapping	NOUN
cana-2738	240	108	.	.	PUNCT
cana-2738	241	1	then	then	ADV
cana-2738	241	2	1	1	X
cana-2738	241	3	.	.	PUNCT
cana-2738	241	4	h1p	h1p	NOUN
cana-2738	241	5	is	be	AUX
cana-2738	241	6	pfo	pfo	PROPN
cana-2738	241	7	(	(	PUNCT
cana-2738	241	8	resp	resp	PROPN
cana-2738	241	9	.	.	PUNCT
cana-2738	241	10	pfδβo	pfδβo	NOUN
cana-2738	241	11	and	and	CCONJ
cana-2738	241	12	pfδ𝒫o	pfδ𝒫o	ADJ
cana-2738	241	13	)	)	PUNCT
cana-2738	241	14	but	but	CCONJ
cana-2738	241	15	not	not	PART
cana-2738	241	16	pfδo	pfδo	ADJ
cana-2738	241	17	(	(	PUNCT
cana-2738	241	18	resp	resp	NOUN
cana-2738	241	19	.	.	PUNCT
cana-2738	242	1	pfδ𝒮o	pfδ𝒮o	PROPN
cana-2738	242	2	and	and	CCONJ
cana-2738	242	3	pfδαo	pfδαo	NOUN
cana-2738	242	4	)	)	PUNCT
cana-2738	242	5	,	,	PUNCT
cana-2738	242	6	because	because	SCONJ
cana-2738	242	7	the	the	DET
cana-2738	242	8	set	set	NOUN
cana-2738	242	9	a2	a2	PROPN
cana-2738	242	10	is	be	AUX
cana-2738	242	11	a	a	DET
cana-2738	242	12	pfos	pfos	NOUN
cana-2738	242	13	in	in	ADP
cana-2738	242	14	x2	x2	PROPN
cana-2738	242	15	but	but	CCONJ
cana-2738	242	16	h1p(a2	h1p(a2	PROPN
cana-2738	242	17	)	)	PUNCT
cana-2738	243	1	=	=	PUNCT
cana-2738	243	2	a2	a2	PROPN
cana-2738	243	3	is	be	AUX
cana-2738	243	4	not	not	PART
cana-2738	243	5	pfδos	pfδo	NOUN
cana-2738	243	6	(	(	PUNCT
cana-2738	243	7	resp	resp	NOUN
cana-2738	243	8	.	.	PUNCT
cana-2738	244	1	pfδ𝒮os	pfδ𝒮os	NOUN
cana-2738	244	2	and	and	CCONJ
cana-2738	244	3	pfδαos	pfδαo	NOUN
cana-2738	244	4	)	)	PUNCT
cana-2738	244	5	in	in	ADP
cana-2738	244	6	x1	x1	PROPN
cana-2738	244	7	.	.	PUNCT
cana-2738	245	1	2	2	X
cana-2738	245	2	.	.	X
cana-2738	245	3	h2p	h2p	PROPN
cana-2738	245	4	is	be	AUX
cana-2738	245	5	pfδ𝒮o	pfδ𝒮o	ADJ
cana-2738	245	6	but	but	CCONJ
cana-2738	245	7	not	not	PART
cana-2738	245	8	pfδo	pfδo	ADJ
cana-2738	245	9	,	,	PUNCT
cana-2738	245	10	because	because	SCONJ
cana-2738	245	11	the	the	DET
cana-2738	245	12	set	set	NOUN
cana-2738	245	13	a1	a1	NOUN
cana-2738	245	14	c	c	NOUN
cana-2738	245	15	is	be	AUX
cana-2738	245	16	a	a	DET
cana-2738	245	17	pfos	pfos	NOUN
cana-2738	245	18	x3	x3	ADJ
cana-2738	245	19	but	but	CCONJ
cana-2738	245	20	h2p(a1	h2p(a1	PROPN
cana-2738	245	21	c	c	AUX
cana-2738	245	22	)	)	PUNCT
cana-2738	245	23	=	=	NOUN
cana-2738	245	24	a1	a1	NOUN
cana-2738	245	25	c	c	NOUN
cana-2738	245	26	is	be	AUX
cana-2738	245	27	not	not	PART
cana-2738	245	28	pfδos	pfδo	NOUN
cana-2738	245	29	in	in	ADP
cana-2738	245	30	x1	x1	PROPN
cana-2738	245	31	.	.	PUNCT
cana-2738	246	1	3	3	X
cana-2738	246	2	.	.	X
cana-2738	246	3	h3p	h3p	PRON
cana-2738	246	4	is	be	AUX
cana-2738	246	5	pfδ𝒫o	pfδ𝒫o	ADJ
cana-2738	246	6	but	but	CCONJ
cana-2738	246	7	not	not	PART
cana-2738	246	8	pfδo	pfδo	ADJ
cana-2738	246	9	,	,	PUNCT
cana-2738	246	10	because	because	SCONJ
cana-2738	246	11	the	the	DET
cana-2738	246	12	set	set	NOUN
cana-2738	246	13	a2	a2	PROPN
cana-2738	246	14	c	c	PROPN
cana-2738	246	15	is	be	AUX
cana-2738	246	16	a	a	DET
cana-2738	246	17	pfos	pfos	NOUN
cana-2738	246	18	x4	x4	PROPN
cana-2738	247	1	but	but	CCONJ
cana-2738	247	2	h3p(a2	h3p(a2	PROPN
cana-2738	247	3	c	c	NOUN
cana-2738	247	4	)	)	PUNCT
cana-2738	247	5	=	=	SYM
cana-2738	247	6	a2	a2	PROPN
cana-2738	247	7	c	c	PROPN
cana-2738	247	8	is	be	AUX
cana-2738	247	9	not	not	PART
cana-2738	247	10	pfδ𝒫os	pfδ𝒫os	ADJ
cana-2738	247	11	in	in	ADP
cana-2738	247	12	x1	x1	PROPN
cana-2738	247	13	.	.	PUNCT
cana-2738	248	1	4	4	X
cana-2738	248	2	.	.	X
cana-2738	248	3	h4p	h4p	PROPN
cana-2738	248	4	is	be	AUX
cana-2738	248	5	pfδβo	pfδβo	ADJ
cana-2738	248	6	(	(	PUNCT
cana-2738	248	7	resp	resp	NOUN
cana-2738	248	8	.	.	PUNCT
cana-2738	249	1	pfδ𝒮o	pfδ𝒮o	PROPN
cana-2738	249	2	)	)	PUNCT
cana-2738	250	1	but	but	CCONJ
cana-2738	250	2	not	not	PART
cana-2738	250	3	pfδ𝒫o	pfδ𝒫o	ADJ
cana-2738	250	4	(	(	PUNCT
cana-2738	250	5	resp	resp	NOUN
cana-2738	250	6	.	.	PUNCT
cana-2738	251	1	pfδαo	pfδαo	NOUN
cana-2738	251	2	)	)	PUNCT
cana-2738	251	3	,	,	PUNCT
cana-2738	251	4	because	because	SCONJ
cana-2738	251	5	the	the	DET
cana-2738	251	6	set	set	NOUN
cana-2738	251	7	a3	a3	NOUN
cana-2738	251	8	is	be	AUX
cana-2738	251	9	a	a	DET
cana-2738	251	10	pfos	pfos	NOUN
cana-2738	251	11	x5	x5	NOUN
cana-2738	251	12	but	but	CCONJ
cana-2738	251	13	h4(a3	h4(a3	NOUN
cana-2738	251	14	)	)	PUNCT
cana-2738	251	15	=	=	NOUN
cana-2738	251	16	a3	a3	NOUN
cana-2738	251	17	is	be	AUX
cana-2738	251	18	not	not	PART
cana-2738	251	19	pfδ𝒫os	pfδ𝒫os	NOUN
cana-2738	251	20	(	(	PUNCT
cana-2738	251	21	resp	resp	NOUN
cana-2738	251	22	.	.	PUNCT
cana-2738	252	1	pfδαos	pfδαo	NOUN
cana-2738	252	2	)	)	PUNCT
cana-2738	252	3	in	in	ADP
cana-2738	252	4	x1	x1	PROPN
cana-2738	252	5	.	.	PUNCT
cana-2738	253	1	theorem	theorem	ADJ
cana-2738	253	2	3.2	3.2	NUM
cana-2738	253	3	let	let	VERB
cana-2738	253	4	(	(	PUNCT
cana-2738	253	5	x1	x1	PROPN
cana-2738	253	6	,	,	PUNCT
cana-2738	253	7	γp	γp	PROPN
cana-2738	253	8	)	)	PUNCT
cana-2738	253	9	&	&	CCONJ
cana-2738	253	10	(	(	PUNCT
cana-2738	253	11	x2	x2	PROPN
cana-2738	253	12	,	,	PUNCT
cana-2738	253	13	ψp	ψp	PRON
cana-2738	253	14	)	)	PUNCT
cana-2738	253	15	be	be	AUX
cana-2738	253	16	any	any	DET
cana-2738	253	17	pfts	pft	NOUN
cana-2738	253	18	’s	’s	PART
cana-2738	253	19	.	.	PUNCT
cana-2738	254	1	a	a	DET
cana-2738	254	2	mapping	mapping	NOUN
cana-2738	254	3	hp	hp	NOUN
cana-2738	254	4	:	:	PUNCT
cana-2738	254	5	(	(	PUNCT
cana-2738	254	6	x1	x1	PROPN
cana-2738	254	7	,	,	PUNCT
cana-2738	254	8	γp	γp	PROPN
cana-2738	254	9	)	)	PUNCT
cana-2738	254	10	→	→	SYM
cana-2738	254	11	(	(	PUNCT
cana-2738	254	12	x2	x2	PROPN
cana-2738	254	13	,	,	PUNCT
cana-2738	254	14	ψp	ψp	NOUN
cana-2738	254	15	)	)	PUNCT
cana-2738	254	16	is	be	AUX
cana-2738	254	17	pfδβo	pfδβo	ADJ
cana-2738	254	18	iff	iff	PROPN
cana-2738	254	19	for	for	ADP
cana-2738	254	20	every	every	DET
cana-2738	254	21	pfs	pfs	PROPN
cana-2738	254	22	m	m	PROPN
cana-2738	254	23	of	of	ADP
cana-2738	254	24	(	(	PUNCT
cana-2738	254	25	x1	x1	PROPN
cana-2738	254	26	,	,	PUNCT
cana-2738	254	27	γp	γp	PROPN
cana-2738	254	28	)	)	PUNCT
cana-2738	254	29	,	,	PUNCT
cana-2738	254	30	hp(pfint(m	hp(pfint(m	PROPN
cana-2738	254	31	)	)	PUNCT
cana-2738	254	32	)	)	PUNCT
cana-2738	255	1	⊆	⊆	NUM
cana-2738	255	2	pfδβint(hp(m	pfδβint(hp(m	NOUN
cana-2738	255	3	)	)	PUNCT
cana-2738	255	4	)	)	PUNCT
cana-2738	255	5	.	.	PUNCT
cana-2738	256	1	necessity	necessity	NOUN
cana-2738	256	2	:	:	PUNCT
cana-2738	256	3	let	let	VERB
cana-2738	256	4	hp	hp	PROPN
cana-2738	256	5	be	be	AUX
cana-2738	256	6	a	a	DET
cana-2738	256	7	pfδβo	pfδβo	NOUN
cana-2738	256	8	and	and	CCONJ
cana-2738	256	9	m	m	AUX
cana-2738	256	10	be	be	AUX
cana-2738	256	11	a	a	DET
cana-2738	256	12	pfos	pfos	NOUN
cana-2738	256	13	in	in	ADP
cana-2738	256	14	(	(	PUNCT
cana-2738	256	15	x1	x1	PROPN
cana-2738	256	16	,	,	PUNCT
cana-2738	256	17	γp	γp	PROPN
cana-2738	256	18	)	)	PUNCT
cana-2738	256	19	.	.	PUNCT
cana-2738	257	1	now	now	ADV
cana-2738	257	2	,	,	PUNCT
cana-2738	257	3	pfint(m	pfint(m	NOUN
cana-2738	257	4	)	)	PUNCT
cana-2738	257	5	⊆	⊆	NUM
cana-2738	257	6	m	m	NOUN
cana-2738	257	7	implies	imply	VERB
cana-2738	257	8	hp(pfint(m	hp(pfint(m	NOUN
cana-2738	257	9	)	)	PUNCT
cana-2738	257	10	)	)	PUNCT
cana-2738	258	1	⊆	⊆	NUM
cana-2738	258	2	hp(m	hp(m	NOUN
cana-2738	258	3	)	)	PUNCT
cana-2738	258	4	.	.	PUNCT
cana-2738	259	1	since	since	SCONJ
cana-2738	259	2	hp	hp	PROPN
cana-2738	259	3	is	be	AUX
cana-2738	259	4	a	a	DET
cana-2738	259	5	pfδβo	pfδβo	NOUN
cana-2738	259	6	,	,	PUNCT
cana-2738	259	7	hp(pfint(m	hp(pfint(m	NOUN
cana-2738	259	8	)	)	PUNCT
cana-2738	259	9	)	)	PUNCT
cana-2738	259	10	is	be	AUX
cana-2738	259	11	pfδβos	pfδβos	NOUN
cana-2738	259	12	in	in	ADP
cana-2738	259	13	(	(	PUNCT
cana-2738	259	14	x2	x2	INTJ
cana-2738	259	15	,	,	PUNCT
cana-2738	259	16	ψp	ψp	NOUN
cana-2738	259	17	)	)	PUNCT
cana-2738	259	18	such	such	ADJ
cana-2738	259	19	that	that	SCONJ
cana-2738	259	20	hp(pfint(m	hp(pfint(m	PROPN
cana-2738	259	21	)	)	PUNCT
cana-2738	259	22	)	)	PUNCT
cana-2738	260	1	⊆	⊆	NUM
cana-2738	260	2	hp(m	hp(m	NOUN
cana-2738	260	3	)	)	PUNCT
cana-2738	260	4	therefore	therefore	ADV
cana-2738	260	5	hp(pfint(m	hp(pfint(m	PROPN
cana-2738	260	6	)	)	PUNCT
cana-2738	260	7	)	)	PUNCT
cana-2738	261	1	⊆	⊆	NUM
cana-2738	261	2	pfδβint(hp(m	pfδβint(hp(m	NOUN
cana-2738	261	3	)	)	PUNCT
cana-2738	261	4	)	)	PUNCT
cana-2738	261	5	.	.	PUNCT
cana-2738	262	1	sufficiency	sufficiency	NOUN
cana-2738	262	2	:	:	PUNCT
cana-2738	262	3	assume	assume	VERB
cana-2738	262	4	m	m	NOUN
cana-2738	262	5	is	be	AUX
cana-2738	262	6	a	a	DET
cana-2738	262	7	pfos	pfos	NOUN
cana-2738	262	8	of	of	ADP
cana-2738	262	9	(	(	PUNCT
cana-2738	262	10	x1	x1	PROPN
cana-2738	262	11	,	,	PUNCT
cana-2738	262	12	γp	γp	PROPN
cana-2738	262	13	)	)	PUNCT
cana-2738	262	14	.	.	PUNCT
cana-2738	263	1	then	then	ADV
cana-2738	263	2	hp(m	hp(m	VERB
cana-2738	263	3	)	)	PUNCT
cana-2738	263	4	=	=	SYM
cana-2738	263	5	hp(pfint(m	hp(pfint(m	NOUN
cana-2738	263	6	)	)	PUNCT
cana-2738	263	7	)	)	PUNCT
cana-2738	264	1	⊆	⊆	NUM
cana-2738	264	2	pfδβint(hp(m	pfδβint(hp(m	NOUN
cana-2738	264	3	)	)	PUNCT
cana-2738	264	4	)	)	PUNCT
cana-2738	264	5	.	.	PUNCT
cana-2738	265	1	but	but	CCONJ
cana-2738	265	2	pfδβint	pfδβint	NOUN
cana-2738	265	3	(	(	PUNCT
cana-2738	265	4	hp(m	hp(m	NOUN
cana-2738	265	5	)	)	PUNCT
cana-2738	265	6	)	)	PUNCT
cana-2738	266	1	⊆	⊆	NUM
cana-2738	266	2	hp(m	hp(m	NOUN
cana-2738	266	3	)	)	PUNCT
cana-2738	266	4	.	.	PUNCT
cana-2738	267	1	so	so	ADV
cana-2738	267	2	hp(m	hp(m	NOUN
cana-2738	267	3	)	)	PUNCT
cana-2738	267	4	=	=	SYM
cana-2738	267	5	pfδβint(m	pfδβint(m	PROPN
cana-2738	267	6	)	)	PUNCT
cana-2738	267	7	which	which	PRON
cana-2738	267	8	implies	imply	VERB
cana-2738	267	9	hp(m	hp(m	NOUN
cana-2738	267	10	)	)	PUNCT
cana-2738	267	11	is	be	AUX
cana-2738	267	12	a	a	DET
cana-2738	267	13	pfδβos	pfδβos	NOUN
cana-2738	267	14	of	of	ADP
cana-2738	267	15	(	(	PUNCT
cana-2738	267	16	x2	x2	PROPN
cana-2738	267	17	,	,	PUNCT
cana-2738	267	18	ψp	ψp	NOUN
cana-2738	267	19	)	)	PUNCT
cana-2738	267	20	and	and	CCONJ
cana-2738	267	21	hence	hence	ADV
cana-2738	267	22	hp	hp	PROPN
cana-2738	267	23	is	be	AUX
cana-2738	267	24	a	a	DET
cana-2738	267	25	pfδβo	pfδβo	NOUN
cana-2738	267	26	.	.	PUNCT
cana-2738	268	1	communications	communication	NOUN
cana-2738	268	2	on	on	ADP
cana-2738	268	3	applied	apply	VERB
cana-2738	268	4	nonlinear	nonlinear	ADJ
cana-2738	268	5	analysis	analysis	NOUN
cana-2738	268	6	issn	issn	NOUN
cana-2738	268	7	:	:	PUNCT
cana-2738	268	8	1074	1074	NUM
cana-2738	268	9	-	-	PUNCT
cana-2738	268	10	133x	133x	NUM
cana-2738	268	11	vol	vol	NOUN
cana-2738	268	12	32	32	NUM
cana-2738	268	13	no	no	NOUN
cana-2738	268	14	.	.	PUNCT
cana-2738	269	1	4s	4s	NUM
cana-2738	269	2	(	(	PUNCT
cana-2738	269	3	2025	2025	NUM
cana-2738	269	4	)	)	PUNCT
cana-2738	269	5	50	50	NUM
cana-2738	269	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2738	269	7	theorem	theorem	VERB
cana-2738	269	8	3.3	3.3	NUM
cana-2738	269	9	let	let	VERB
cana-2738	269	10	(	(	PUNCT
cana-2738	269	11	x1	x1	PROPN
cana-2738	269	12	,	,	PUNCT
cana-2738	269	13	γp	γp	PROPN
cana-2738	269	14	)	)	PUNCT
cana-2738	269	15	&	&	CCONJ
cana-2738	269	16	(	(	PUNCT
cana-2738	269	17	x2	x2	PROPN
cana-2738	269	18	,	,	PUNCT
cana-2738	269	19	ψp	ψp	PRON
cana-2738	269	20	)	)	PUNCT
cana-2738	269	21	be	be	VERB
cana-2738	269	22	any	any	DET
cana-2738	269	23	pfts	pft	NOUN
cana-2738	269	24	’s	’s	PART
cana-2738	269	25	.	.	PUNCT
cana-2738	270	1	let	let	VERB
cana-2738	270	2	hp	hp	VERB
cana-2738	270	3	:	:	PUNCT
cana-2738	270	4	(	(	PUNCT
cana-2738	270	5	x1	x1	PROPN
cana-2738	270	6	,	,	PUNCT
cana-2738	270	7	γp	γp	PROPN
cana-2738	270	8	)	)	PUNCT
cana-2738	270	9	→	→	SYM
cana-2738	270	10	(	(	PUNCT
cana-2738	270	11	x2	x2	PROPN
cana-2738	270	12	,	,	PUNCT
cana-2738	270	13	ψp	ψp	PRON
cana-2738	270	14	)	)	PUNCT
cana-2738	270	15	be	be	AUX
cana-2738	270	16	a	a	DET
cana-2738	270	17	mapping	mapping	NOUN
cana-2738	270	18	.	.	PUNCT
cana-2738	271	1	if	if	SCONJ
cana-2738	271	2	hp	hp	VERB
cana-2738	271	3	:	:	PUNCT
cana-2738	271	4	(	(	PUNCT
cana-2738	271	5	x1	x1	PROPN
cana-2738	271	6	,	,	PUNCT
cana-2738	271	7	γp	γp	PROPN
cana-2738	271	8	)	)	PUNCT
cana-2738	271	9	→	→	SYM
cana-2738	271	10	(	(	PUNCT
cana-2738	271	11	x2	x2	PROPN
cana-2738	271	12	,	,	PUNCT
cana-2738	271	13	ψp	ψp	PROPN
cana-2738	271	14	)	)	PUNCT
cana-2738	271	15	is	be	AUX
cana-2738	271	16	a	a	DET
cana-2738	271	17	pfδβo	pfδβo	NOUN
cana-2738	271	18	,	,	PUNCT
cana-2738	271	19	then	then	ADV
cana-2738	271	20	pfint(hp	pfint(hp	ADJ
cana-2738	271	21	−1(m	−1(m	NOUN
cana-2738	271	22	)	)	PUNCT
cana-2738	271	23	)	)	PUNCT
cana-2738	272	1	⊆	⊆	NUM
cana-2738	272	2	hp	hp	ADJ
cana-2738	272	3	−1(pfδβint(m	−1(pfδβint(m	NUM
cana-2738	272	4	)	)	PUNCT
cana-2738	272	5	)	)	PUNCT
cana-2738	272	6	for	for	ADP
cana-2738	272	7	every	every	DET
cana-2738	272	8	pfs	pfs	PROPN
cana-2738	272	9	m	m	PROPN
cana-2738	272	10	of	of	ADP
cana-2738	272	11	(	(	PUNCT
cana-2738	272	12	x2	x2	PROPN
cana-2738	272	13	,	,	PUNCT
cana-2738	272	14	ψp	ψp	NOUN
cana-2738	272	15	)	)	PUNCT
cana-2738	272	16	.	.	PUNCT
cana-2738	273	1	proof	proof	NOUN
cana-2738	273	2	.	.	PUNCT
cana-2738	274	1	let	let	VERB
cana-2738	274	2	m	m	PRON
cana-2738	274	3	be	be	AUX
cana-2738	274	4	a	a	DET
cana-2738	274	5	pfs	pfs	NOUN
cana-2738	274	6	of	of	ADP
cana-2738	274	7	(	(	PUNCT
cana-2738	274	8	x2	x2	PROPN
cana-2738	274	9	,	,	PUNCT
cana-2738	274	10	ψp	ψp	NOUN
cana-2738	274	11	)	)	PUNCT
cana-2738	274	12	.	.	PUNCT
cana-2738	275	1	then	then	ADV
cana-2738	275	2	pfint(hp	pfint(hp	ADJ
cana-2738	275	3	−1(m	−1(m	NOUN
cana-2738	275	4	)	)	PUNCT
cana-2738	275	5	)	)	PUNCT
cana-2738	275	6	is	be	AUX
cana-2738	275	7	a	a	DET
cana-2738	275	8	pfos	pfos	NOUN
cana-2738	275	9	in	in	ADP
cana-2738	275	10	(	(	PUNCT
cana-2738	275	11	x1	x1	PROPN
cana-2738	275	12	,	,	PUNCT
cana-2738	275	13	γp	γp	PROPN
cana-2738	275	14	)	)	PUNCT
cana-2738	275	15	.	.	PUNCT
cana-2738	276	1	since	since	SCONJ
cana-2738	276	2	hp	hp	PROPN
cana-2738	276	3	is	be	AUX
cana-2738	276	4	pfδβo	pfδβo	ADJ
cana-2738	276	5	,	,	PUNCT
cana-2738	276	6	hp(pfint	hp(pfint	PROPN
cana-2738	276	7	(	(	PUNCT
cana-2738	276	8	hp	hp	PROPN
cana-2738	276	9	−1(m	−1(m	NOUN
cana-2738	276	10	)	)	PUNCT
cana-2738	276	11	)	)	PUNCT
cana-2738	276	12	is	be	AUX
cana-2738	276	13	pfδβo	pfδβo	ADJ
cana-2738	276	14	in	in	ADP
cana-2738	276	15	(	(	PUNCT
cana-2738	276	16	x2	x2	INTJ
cana-2738	276	17	,	,	PUNCT
cana-2738	276	18	ψp	ψp	NOUN
cana-2738	276	19	)	)	PUNCT
cana-2738	276	20	and	and	CCONJ
cana-2738	276	21	hence	hence	ADV
cana-2738	276	22	hp(pfint(hp	hp(pfint(hp	ADJ
cana-2738	276	23	−1	−1	NOUN
cana-2738	276	24	(	(	PUNCT
cana-2738	276	25	λ	λ	NOUN
cana-2738	276	26	)	)	PUNCT
cana-2738	276	27	)	)	PUNCT
cana-2738	276	28	)	)	PUNCT
cana-2738	277	1	⊆	⊆	NUM
cana-2738	277	2	pfδβint(hp(hp	pfδβint(hp(hp	ADJ
cana-2738	277	3	−1(m	−1(m	NOUN
cana-2738	277	4	)	)	PUNCT
cana-2738	277	5	)	)	PUNCT
cana-2738	277	6	)	)	PUNCT
cana-2738	278	1	⊆	⊆	NUM
cana-2738	278	2	pfδβint(m	pfδβint(m	PROPN
cana-2738	278	3	)	)	PUNCT
cana-2738	278	4	.	.	PUNCT
cana-2738	279	1	thus	thus	ADV
cana-2738	279	2	pfint(hp	pfint(hp	ADJ
cana-2738	279	3	−1(m	−1(m	NOUN
cana-2738	279	4	)	)	PUNCT
cana-2738	279	5	)	)	PUNCT
cana-2738	280	1	⊆	⊆	NUM
cana-2738	280	2	hp	hp	ADJ
cana-2738	280	3	−1(pfδβint(m	−1(pfδβint(m	NUM
cana-2738	280	4	)	)	PUNCT
cana-2738	280	5	)	)	PUNCT
cana-2738	280	6	.	.	PUNCT
cana-2738	281	1	theorem	theorem	VERB
cana-2738	281	2	3.4	3.4	NUM
cana-2738	281	3	let	let	VERB
cana-2738	281	4	(	(	PUNCT
cana-2738	281	5	x1	x1	PROPN
cana-2738	281	6	,	,	PUNCT
cana-2738	281	7	γp	γp	PROPN
cana-2738	281	8	)	)	PUNCT
cana-2738	281	9	&	&	CCONJ
cana-2738	281	10	(	(	PUNCT
cana-2738	281	11	x2	x2	PROPN
cana-2738	281	12	,	,	PUNCT
cana-2738	281	13	ψp	ψp	PRON
cana-2738	281	14	)	)	PUNCT
cana-2738	281	15	be	be	VERB
cana-2738	281	16	any	any	DET
cana-2738	281	17	pfts	pft	NOUN
cana-2738	281	18	’s	’s	PART
cana-2738	281	19	.	.	PUNCT
cana-2738	282	1	a	a	DET
cana-2738	282	2	mapping	mapping	NOUN
cana-2738	282	3	hp	hp	NOUN
cana-2738	282	4	:	:	PUNCT
cana-2738	282	5	(	(	PUNCT
cana-2738	282	6	x1	x1	PROPN
cana-2738	282	7	,	,	PUNCT
cana-2738	282	8	γp	γp	PROPN
cana-2738	282	9	)	)	PUNCT
cana-2738	282	10	→	→	SYM
cana-2738	282	11	(	(	PUNCT
cana-2738	282	12	x2	x2	PROPN
cana-2738	282	13	,	,	PUNCT
cana-2738	282	14	ψp	ψp	NOUN
cana-2738	282	15	)	)	PUNCT
cana-2738	282	16	is	be	AUX
cana-2738	282	17	pfδβo	pfδβo	ADJ
cana-2738	282	18	iff	iff	PROPN
cana-2738	282	19	for	for	ADP
cana-2738	282	20	each	each	DET
cana-2738	282	21	pfs	pfs	PROPN
cana-2738	282	22	μ	μ	PROPN
cana-2738	282	23	1	1	NUM
cana-2738	282	24	of	of	ADP
cana-2738	282	25	(	(	PUNCT
cana-2738	282	26	x2	x2	PROPN
cana-2738	282	27	,	,	PUNCT
cana-2738	282	28	ψp	ψp	NOUN
cana-2738	282	29	)	)	PUNCT
cana-2738	282	30	and	and	CCONJ
cana-2738	282	31	for	for	ADP
cana-2738	282	32	each	each	DET
cana-2738	282	33	pfs	pfs	PROPN
cana-2738	282	34	μ	μ	PROPN
cana-2738	282	35	2	2	NUM
cana-2738	282	36	of	of	ADP
cana-2738	282	37	(	(	PUNCT
cana-2738	282	38	x1	x1	PROPN
cana-2738	282	39	,	,	PUNCT
cana-2738	282	40	γp	γp	NOUN
cana-2738	282	41	)	)	PUNCT
cana-2738	282	42	containing	contain	VERB
cana-2738	282	43	hp	hp	PROPN
cana-2738	282	44	−1(μ	−1(μ	PROPN
cana-2738	282	45	)	)	PUNCT
cana-2738	282	46	there	there	PRON
cana-2738	282	47	is	be	VERB
cana-2738	282	48	an	an	DET
cana-2738	282	49	pfδβcs	pfδβcs	ADJ
cana-2738	282	50	ν	ν	NOUN
cana-2738	282	51	of	of	ADP
cana-2738	282	52	(	(	PUNCT
cana-2738	282	53	x2	x2	PROPN
cana-2738	282	54	,	,	PUNCT
cana-2738	282	55	ψp	ψp	NOUN
cana-2738	282	56	)	)	PUNCT
cana-2738	282	57	such	such	ADJ
cana-2738	283	1	that	that	SCONJ
cana-2738	283	2	μ	μ	PROPN
cana-2738	283	3	1	1	NUM
cana-2738	283	4	⊆	⊆	NUM
cana-2738	283	5	μ	μ	NUM
cana-2738	283	6	2	2	NUM
cana-2738	283	7	and	and	CCONJ
cana-2738	283	8	hp	hp	PROPN
cana-2738	283	9	−1(ν	−1(ν	PROPN
cana-2738	283	10	)	)	PUNCT
cana-2738	283	11	⊆	⊆	NUM
cana-2738	283	12	μ	μ	NUM
cana-2738	283	13	2	2	NUM
cana-2738	283	14	.	.	PUNCT
cana-2738	284	1	necessity	necessity	NOUN
cana-2738	284	2	:	:	PUNCT
cana-2738	284	3	assume	assume	VERB
cana-2738	284	4	hp	hp	PROPN
cana-2738	284	5	is	be	AUX
cana-2738	284	6	a	a	DET
cana-2738	284	7	pfδβo	pfδβo	NOUN
cana-2738	284	8	.	.	PUNCT
cana-2738	285	1	let	let	VERB
cana-2738	285	2	μ	μ	NOUN
cana-2738	285	3	1	1	NUM
cana-2738	285	4	be	be	AUX
cana-2738	285	5	the	the	DET
cana-2738	285	6	pfcs	pfc	NOUN
cana-2738	285	7	of	of	ADP
cana-2738	285	8	(	(	PUNCT
cana-2738	285	9	x2	x2	INTJ
cana-2738	285	10	,	,	PUNCT
cana-2738	285	11	ψp	ψp	NOUN
cana-2738	285	12	)	)	PUNCT
cana-2738	285	13	and	and	CCONJ
cana-2738	285	14	μ	μ	PROPN
cana-2738	285	15	2	2	NUM
cana-2738	285	16	is	be	AUX
cana-2738	285	17	a	a	DET
cana-2738	285	18	pfcs	pfcs	NOUN
cana-2738	285	19	of	of	ADP
cana-2738	285	20	(	(	PUNCT
cana-2738	285	21	x1	x1	PROPN
cana-2738	285	22	,	,	PUNCT
cana-2738	285	23	γp	γp	NOUN
cana-2738	285	24	)	)	PUNCT
cana-2738	286	1	such	such	ADJ
cana-2738	286	2	that	that	SCONJ
cana-2738	286	3	hp	hp	PROPN
cana-2738	286	4	−1(μ	−1(μ	X
cana-2738	286	5	1	1	NUM
cana-2738	286	6	)	)	PUNCT
cana-2738	286	7	⊆	⊆	NUM
cana-2738	286	8	μ	μ	NUM
cana-2738	286	9	2	2	NUM
cana-2738	286	10	.	.	PUNCT
cana-2738	287	1	then	then	ADV
cana-2738	287	2	ν	ν	X
cana-2738	287	3	=	=	SYM
cana-2738	287	4	(	(	PUNCT
cana-2738	287	5	hp	hp	X
cana-2738	287	6	−1(μ	−1(μ	NOUN
cana-2738	287	7	2	2	NUM
cana-2738	287	8	c))c	c))c	NOUN
cana-2738	287	9	is	be	AUX
cana-2738	287	10	pfδβcs	pfδβcs	ADJ
cana-2738	287	11	of	of	ADP
cana-2738	287	12	(	(	PUNCT
cana-2738	287	13	x2	x2	PROPN
cana-2738	287	14	,	,	PUNCT
cana-2738	287	15	ψp	ψp	NOUN
cana-2738	287	16	)	)	PUNCT
cana-2738	287	17	such	such	ADJ
cana-2738	287	18	that	that	SCONJ
cana-2738	287	19	hp	hp	PROPN
cana-2738	287	20	−1(ν	−1(ν	NOUN
cana-2738	287	21	)	)	PUNCT
cana-2738	287	22	⊆	⊆	NUM
cana-2738	287	23	μ	μ	PROPN
cana-2738	287	24	2	2	NUM
cana-2738	287	25	.	.	PUNCT
cana-2738	288	1	sufficiency	sufficiency	NOUN
cana-2738	288	2	:	:	PUNCT
cana-2738	288	3	assume	assume	VERB
cana-2738	288	4	ω	ω	PROPN
cana-2738	288	5	is	be	AUX
cana-2738	288	6	a	a	DET
cana-2738	288	7	pfos	pfos	NOUN
cana-2738	288	8	of	of	ADP
cana-2738	288	9	(	(	PUNCT
cana-2738	288	10	x1	x1	PROPN
cana-2738	288	11	,	,	PUNCT
cana-2738	288	12	γp	γp	PROPN
cana-2738	288	13	)	)	PUNCT
cana-2738	288	14	.	.	PUNCT
cana-2738	289	1	then	then	ADV
cana-2738	289	2	hp	hp	VERB
cana-2738	289	3	−1((hp(ω))c	−1((hp(ω))c	PROPN
cana-2738	289	4	⊆	⊆	NUM
cana-2738	289	5	ωc	ωc	X
cana-2738	289	6	and	and	CCONJ
cana-2738	289	7	ωc	ωc	PROPN
cana-2738	289	8	is	be	AUX
cana-2738	289	9	pfcs	pfc	VERB
cana-2738	289	10	in	in	ADP
cana-2738	289	11	(	(	PUNCT
cana-2738	289	12	x1	x1	PROPN
cana-2738	289	13	,	,	PUNCT
cana-2738	289	14	γp	γp	PROPN
cana-2738	289	15	)	)	PUNCT
cana-2738	289	16	.	.	PUNCT
cana-2738	290	1	by	by	ADP
cana-2738	290	2	hypothesis	hypothesis	NOUN
cana-2738	290	3	there	there	PRON
cana-2738	290	4	is	be	VERB
cana-2738	290	5	a	a	DET
cana-2738	290	6	pfδβcs	pfδβcs	ADJ
cana-2738	290	7	ν	ν	NOUN
cana-2738	290	8	of	of	ADP
cana-2738	290	9	(	(	PUNCT
cana-2738	290	10	x2	x2	PROPN
cana-2738	290	11	,	,	PUNCT
cana-2738	290	12	ψp	ψp	NOUN
cana-2738	290	13	)	)	PUNCT
cana-2738	290	14	such	such	ADJ
cana-2738	290	15	that	that	SCONJ
cana-2738	290	16	(	(	PUNCT
cana-2738	290	17	hp(ω))c	hp(ω))c	PROPN
cana-2738	290	18	⊆	⊆	NUM
cana-2738	290	19	ν	ν	NOUN
cana-2738	290	20	and	and	CCONJ
cana-2738	290	21	hp	hp	PROPN
cana-2738	290	22	−1(ν	−1(ν	PROPN
cana-2738	290	23	)	)	PUNCT
cana-2738	290	24	⊆	⊆	NUM
cana-2738	290	25	ωc	ωc	PROPN
cana-2738	290	26	.	.	PUNCT
cana-2738	291	1	therefore	therefore	ADV
cana-2738	291	2	ω	ω	PROPN
cana-2738	291	3	⊆	⊆	NUM
cana-2738	291	4	(	(	PUNCT
cana-2738	291	5	hp	hp	PROPN
cana-2738	291	6	−1(ν))c	−1(ν))c	PROPN
cana-2738	291	7	.	.	PUNCT
cana-2738	291	8	hence	hence	ADV
cana-2738	291	9	νc	νc	ADP
cana-2738	291	10	⊆	⊆	NUM
cana-2738	291	11	hp(ω	hp(ω	NOUN
cana-2738	291	12	)	)	PUNCT
cana-2738	291	13	⊆	⊆	NUM
cana-2738	291	14	hp((hp	hp((hp	PROPN
cana-2738	291	15	−1(ν))c	−1(ν))c	PROPN
cana-2738	291	16	)	)	PUNCT
cana-2738	291	17	⊆	⊆	NUM
cana-2738	291	18	νc	νc	NOUN
cana-2738	291	19	which	which	PRON
cana-2738	291	20	implies	imply	VERB
cana-2738	291	21	hp(ω	hp(ω	X
cana-2738	291	22	)	)	PUNCT
cana-2738	291	23	=	=	SYM
cana-2738	291	24	νc	νc	PROPN
cana-2738	291	25	.	.	NOUN
cana-2738	292	1	since	since	SCONJ
cana-2738	292	2	νc	νc	PROPN
cana-2738	292	3	is	be	AUX
cana-2738	292	4	pfδβos	pfδβos	NOUN
cana-2738	292	5	of	of	ADP
cana-2738	292	6	(	(	PUNCT
cana-2738	292	7	x2	x2	PROPN
cana-2738	292	8	,	,	PUNCT
cana-2738	292	9	ψp	ψp	NOUN
cana-2738	292	10	)	)	PUNCT
cana-2738	292	11	.	.	PUNCT
cana-2738	293	1	hence	hence	ADV
cana-2738	293	2	hp(ω	hp(ω	NUM
cana-2738	293	3	)	)	PUNCT
cana-2738	293	4	is	be	AUX
cana-2738	293	5	pfδβo	pfδβo	ADJ
cana-2738	293	6	in	in	ADP
cana-2738	293	7	(	(	PUNCT
cana-2738	293	8	x2	x2	INTJ
cana-2738	293	9	,	,	PUNCT
cana-2738	293	10	ψp	ψp	NOUN
cana-2738	293	11	)	)	PUNCT
cana-2738	293	12	and	and	CCONJ
cana-2738	293	13	thus	thus	ADV
cana-2738	293	14	hp	hp	PROPN
cana-2738	293	15	is	be	AUX
cana-2738	293	16	pfδβo	pfδβo	ADJ
cana-2738	293	17	.	.	PUNCT
cana-2738	294	1	theorem	theorem	VERB
cana-2738	294	2	3.5	3.5	NUM
cana-2738	294	3	let	let	NOUN
cana-2738	294	4	(	(	PUNCT
cana-2738	294	5	x1	x1	PROPN
cana-2738	294	6	,	,	PUNCT
cana-2738	294	7	γp	γp	PROPN
cana-2738	294	8	)	)	PUNCT
cana-2738	294	9	&	&	CCONJ
cana-2738	294	10	(	(	PUNCT
cana-2738	294	11	x2	x2	PROPN
cana-2738	294	12	,	,	PUNCT
cana-2738	294	13	ψp	ψp	PRON
cana-2738	294	14	)	)	PUNCT
cana-2738	294	15	be	be	AUX
cana-2738	294	16	any	any	DET
cana-2738	294	17	pfts	pft	NOUN
cana-2738	294	18	’s	’s	PART
cana-2738	294	19	.	.	PUNCT
cana-2738	295	1	a	a	DET
cana-2738	295	2	mapping	mapping	NOUN
cana-2738	295	3	hp	hp	NOUN
cana-2738	295	4	:	:	PUNCT
cana-2738	295	5	(	(	PUNCT
cana-2738	295	6	x1	x1	PROPN
cana-2738	295	7	,	,	PUNCT
cana-2738	295	8	γp	γp	PROPN
cana-2738	295	9	)	)	PUNCT
cana-2738	295	10	→	→	SYM
cana-2738	295	11	(	(	PUNCT
cana-2738	295	12	x2	x2	PROPN
cana-2738	295	13	,	,	PUNCT
cana-2738	295	14	ψp	ψp	NOUN
cana-2738	295	15	)	)	PUNCT
cana-2738	295	16	is	be	AUX
cana-2738	295	17	pfδβo	pfδβo	ADJ
cana-2738	295	18	iff	iff	PROPN
cana-2738	295	19	hp	hp	PROPN
cana-2738	295	20	−1(pfδβcl(m	−1(pfδβcl(m	NUM
cana-2738	295	21	)	)	PUNCT
cana-2738	295	22	⊆	⊆	NUM
cana-2738	295	23	pfcl(hp	pfcl(hp	ADJ
cana-2738	295	24	−1(m	−1(m	NOUN
cana-2738	295	25	)	)	PUNCT
cana-2738	295	26	)	)	PUNCT
cana-2738	295	27	for	for	ADP
cana-2738	295	28	every	every	DET
cana-2738	295	29	pfs	pfs	PROPN
cana-2738	295	30	m	m	PROPN
cana-2738	295	31	of	of	ADP
cana-2738	295	32	(	(	PUNCT
cana-2738	295	33	x2	x2	PROPN
cana-2738	295	34	,	,	PUNCT
cana-2738	295	35	ψp	ψp	NOUN
cana-2738	295	36	)	)	PUNCT
cana-2738	295	37	.	.	PUNCT
cana-2738	296	1	proof	proof	NOUN
cana-2738	296	2	.	.	PUNCT
cana-2738	297	1	necessity	necessity	NOUN
cana-2738	297	2	:	:	PUNCT
cana-2738	297	3	assume	assume	VERB
cana-2738	297	4	hp	hp	PROPN
cana-2738	297	5	is	be	AUX
cana-2738	297	6	a	a	DET
cana-2738	297	7	pfδβo	pfδβo	NOUN
cana-2738	297	8	.	.	PUNCT
cana-2738	298	1	for	for	ADP
cana-2738	298	2	any	any	DET
cana-2738	298	3	pfs	pfs	PROPN
cana-2738	298	4	m	m	PROPN
cana-2738	298	5	of	of	ADP
cana-2738	298	6	(	(	PUNCT
cana-2738	298	7	x2	x2	PROPN
cana-2738	298	8	,	,	PUNCT
cana-2738	298	9	ψp	ψp	NOUN
cana-2738	298	10	)	)	PUNCT
cana-2738	298	11	,	,	PUNCT
cana-2738	298	12	hp	hp	PROPN
cana-2738	298	13	−1(m	−1(m	PROPN
cana-2738	298	14	)	)	PUNCT
cana-2738	298	15	⊆	⊆	NUM
cana-2738	298	16	pfcl(hp	pfcl(hp	ADJ
cana-2738	298	17	−1(m	−1(m	NOUN
cana-2738	298	18	)	)	PUNCT
cana-2738	298	19	)	)	PUNCT
cana-2738	298	20	.	.	PUNCT
cana-2738	299	1	therefore	therefore	ADV
cana-2738	299	2	by	by	ADP
cana-2738	299	3	theorem	theorem	NOUN
cana-2738	299	4	3.4	3.4	NUM
cana-2738	299	5	,	,	PUNCT
cana-2738	299	6	there	there	PRON
cana-2738	299	7	exists	exist	VERB
cana-2738	299	8	a	a	DET
cana-2738	299	9	pfδβcs	pfδβcs	PROPN
cana-2738	299	10	μ	μ	PROPN
cana-2738	299	11	in	in	ADP
cana-2738	299	12	(	(	PUNCT
cana-2738	299	13	x2	x2	PROPN
cana-2738	299	14	,	,	PUNCT
cana-2738	299	15	ψp	ψp	NOUN
cana-2738	299	16	)	)	PUNCT
cana-2738	299	17	such	such	ADJ
cana-2738	299	18	that	that	SCONJ
cana-2738	299	19	λ	λ	PROPN
cana-2738	299	20	⊆	⊆	NUM
cana-2738	299	21	μ	μ	NOUN
cana-2738	299	22	and	and	CCONJ
cana-2738	299	23	hp	hp	PROPN
cana-2738	299	24	−1(μ	−1(μ	PROPN
cana-2738	299	25	)	)	PUNCT
cana-2738	299	26	⊆	⊆	NUM
cana-2738	299	27	pfcl(hp	pfcl(hp	ADJ
cana-2738	299	28	−1(m	−1(m	NOUN
cana-2738	299	29	)	)	PUNCT
cana-2738	299	30	)	)	PUNCT
cana-2738	299	31	.	.	PUNCT
cana-2738	300	1	therefore	therefore	ADV
cana-2738	300	2	we	we	PRON
cana-2738	300	3	obtain	obtain	VERB
cana-2738	300	4	that	that	DET
cana-2738	300	5	hp	hp	PROPN
cana-2738	300	6	−1(pfδβcl(m	−1(pfδβcl(m	NUM
cana-2738	300	7	)	)	PUNCT
cana-2738	300	8	)	)	PUNCT
cana-2738	301	1	⊆	⊆	NUM
cana-2738	301	2	hp	hp	PROPN
cana-2738	301	3	−1(μ	−1(μ	PROPN
cana-2738	301	4	)	)	PUNCT
cana-2738	301	5	⊆	⊆	NUM
cana-2738	301	6	pfcl(hp	pfcl(hp	ADJ
cana-2738	301	7	−1(m	−1(m	NOUN
cana-2738	301	8	)	)	PUNCT
cana-2738	301	9	)	)	PUNCT
cana-2738	301	10	.	.	PUNCT
cana-2738	302	1	sufficiency	sufficiency	NOUN
cana-2738	302	2	:	:	PUNCT
cana-2738	302	3	assume	assume	VERB
cana-2738	302	4	m	m	NOUN
cana-2738	302	5	is	be	AUX
cana-2738	302	6	a	a	DET
cana-2738	302	7	pfs	pfs	NOUN
cana-2738	302	8	of	of	ADP
cana-2738	302	9	(	(	PUNCT
cana-2738	302	10	x2	x2	PROPN
cana-2738	302	11	,	,	PUNCT
cana-2738	302	12	ψp	ψp	NOUN
cana-2738	302	13	)	)	PUNCT
cana-2738	302	14	and	and	CCONJ
cana-2738	302	15	μ	μ	PROPN
cana-2738	302	16	is	be	AUX
cana-2738	302	17	a	a	DET
cana-2738	302	18	pfos	pfos	NOUN
cana-2738	302	19	of	of	ADP
cana-2738	302	20	(	(	PUNCT
cana-2738	302	21	x1	x1	PROPN
cana-2738	302	22	,	,	PUNCT
cana-2738	302	23	γp	γp	NOUN
cana-2738	302	24	)	)	PUNCT
cana-2738	302	25	containing	contain	VERB
cana-2738	302	26	hp	hp	ADJ
cana-2738	302	27	−1(m	−1(m	NOUN
cana-2738	302	28	)	)	PUNCT
cana-2738	302	29	.	.	PUNCT
cana-2738	303	1	put	put	VERB
cana-2738	303	2	ζ	ζ	NOUN
cana-2738	303	3	=	=	SYM
cana-2738	303	4	cl(m	cl(m	NOUN
cana-2738	303	5	)	)	PUNCT
cana-2738	303	6	,	,	PUNCT
cana-2738	303	7	then	then	ADV
cana-2738	303	8	m	m	VERB
cana-2738	303	9	⊆	⊆	NUM
cana-2738	303	10	ζ	ζ	NOUN
cana-2738	303	11	and	and	CCONJ
cana-2738	303	12	ζ	ζ	NOUN
cana-2738	303	13	is	be	AUX
cana-2738	303	14	pfδβc	pfδβc	NOUN
cana-2738	303	15	and	and	CCONJ
cana-2738	303	16	hp	hp	PROPN
cana-2738	303	17	−1(ζ	−1(ζ	PROPN
cana-2738	303	18	)	)	PUNCT
cana-2738	303	19	⊊	⊊	VERB
cana-2738	303	20	cl(hp	cl(hp	ADJ
cana-2738	303	21	−1(m	−1(m	NOUN
cana-2738	303	22	)	)	PUNCT
cana-2738	303	23	)	)	PUNCT
cana-2738	304	1	⊆	⊆	NUM
cana-2738	304	2	μ	μ	NOUN
cana-2738	304	3	.	.	PUNCT
cana-2738	305	1	then	then	ADV
cana-2738	305	2	by	by	ADP
cana-2738	305	3	theorem	theorem	NOUN
cana-2738	305	4	3.4	3.4	NUM
cana-2738	305	5	,	,	PUNCT
cana-2738	305	6	hp	hp	PROPN
cana-2738	305	7	is	be	AUX
cana-2738	305	8	pfδβo	pfδβo	ADJ
cana-2738	305	9	map	map	NOUN
cana-2738	305	10	.	.	PUNCT
cana-2738	306	1	theorem	theorem	VERB
cana-2738	306	2	3.6	3.6	NUM
cana-2738	306	3	let	let	VERB
cana-2738	306	4	(	(	PUNCT
cana-2738	306	5	x1	x1	PROPN
cana-2738	306	6	,	,	PUNCT
cana-2738	306	7	γp	γp	PROPN
cana-2738	306	8	)	)	PUNCT
cana-2738	306	9	,	,	PUNCT
cana-2738	306	10	(	(	PUNCT
cana-2738	306	11	x2	x2	INTJ
cana-2738	306	12	,	,	PUNCT
cana-2738	306	13	ψp	ψp	PROPN
cana-2738	306	14	)	)	PUNCT
cana-2738	306	15	&	&	CCONJ
cana-2738	306	16	(	(	PUNCT
cana-2738	306	17	x3	x3	PROPN
cana-2738	306	18	,	,	PUNCT
cana-2738	306	19	φp	φp	NOUN
cana-2738	306	20	)	)	PUNCT
cana-2738	306	21	be	be	VERB
cana-2738	306	22	any	any	DET
cana-2738	306	23	pfts	pft	NOUN
cana-2738	306	24	’s	’s	PART
cana-2738	306	25	.	.	PUNCT
cana-2738	307	1	if	if	SCONJ
cana-2738	307	2	hp	hp	VERB
cana-2738	307	3	:	:	PUNCT
cana-2738	307	4	(	(	PUNCT
cana-2738	307	5	x1	x1	PROPN
cana-2738	307	6	,	,	PUNCT
cana-2738	307	7	γp	γp	PROPN
cana-2738	307	8	)	)	PUNCT
cana-2738	307	9	→	→	SYM
cana-2738	307	10	(	(	PUNCT
cana-2738	307	11	x2	x2	PROPN
cana-2738	307	12	,	,	PUNCT
cana-2738	307	13	ψp	ψp	NOUN
cana-2738	307	14	)	)	PUNCT
cana-2738	307	15	and	and	CCONJ
cana-2738	307	16	g	g	PROPN
cana-2738	307	17	p	p	X
cana-2738	307	18	:	:	PUNCT
cana-2738	307	19	(	(	PUNCT
cana-2738	307	20	x2	x2	ADJ
cana-2738	307	21	,	,	PUNCT
cana-2738	307	22	ψp	ψp	NOUN
cana-2738	307	23	)	)	PUNCT
cana-2738	307	24	→	→	SYM
cana-2738	307	25	(	(	PUNCT
cana-2738	307	26	x3	x3	ADJ
cana-2738	307	27	,	,	PUNCT
cana-2738	307	28	φp	φp	NOUN
cana-2738	307	29	)	)	PUNCT
cana-2738	307	30	are	be	AUX
cana-2738	307	31	mappings	mapping	NOUN
cana-2738	307	32	and	and	CCONJ
cana-2738	307	33	g	g	PROPN
cana-2738	307	34	p	p	PROPN
cana-2738	307	35	∘	∘	PROPN
cana-2738	307	36	hp	hp	PROPN
cana-2738	307	37	:	:	PUNCT
cana-2738	307	38	(	(	PUNCT
cana-2738	307	39	x1	x1	PROPN
cana-2738	307	40	,	,	PUNCT
cana-2738	307	41	γp	γp	PROPN
cana-2738	307	42	)	)	PUNCT
cana-2738	307	43	→	→	SYM
cana-2738	307	44	(	(	PUNCT
cana-2738	307	45	x3	x3	ADJ
cana-2738	307	46	,	,	PUNCT
cana-2738	307	47	φp	φp	NOUN
cana-2738	307	48	)	)	PUNCT
cana-2738	307	49	is	be	AUX
cana-2738	307	50	pfδβo	pfδβo	ADJ
cana-2738	307	51	.	.	PUNCT
cana-2738	308	1	if	if	SCONJ
cana-2738	308	2	g	g	PROPN
cana-2738	308	3	p	p	X
cana-2738	308	4	:	:	PUNCT
cana-2738	308	5	(	(	PUNCT
cana-2738	308	6	x2	x2	ADJ
cana-2738	308	7	,	,	PUNCT
cana-2738	308	8	ψp	ψp	NOUN
cana-2738	308	9	)	)	PUNCT
cana-2738	308	10	→	→	SYM
cana-2738	308	11	(	(	PUNCT
cana-2738	308	12	x3	x3	ADJ
cana-2738	308	13	,	,	PUNCT
cana-2738	308	14	φp	φp	NOUN
cana-2738	308	15	)	)	PUNCT
cana-2738	308	16	is	be	AUX
cana-2738	308	17	pfδβirr	pfδβirr	NOUN
cana-2738	308	18	then	then	ADV
cana-2738	308	19	hp	hp	X
cana-2738	308	20	:	:	PUNCT
cana-2738	308	21	(	(	PUNCT
cana-2738	308	22	x1	x1	PROPN
cana-2738	308	23	,	,	PUNCT
cana-2738	308	24	γp	γp	PROPN
cana-2738	308	25	)	)	PUNCT
cana-2738	308	26	→	→	SYM
cana-2738	308	27	(	(	PUNCT
cana-2738	308	28	x2	x2	PROPN
cana-2738	308	29	,	,	PUNCT
cana-2738	308	30	ψp	ψp	NOUN
cana-2738	308	31	)	)	PUNCT
cana-2738	308	32	is	be	AUX
cana-2738	308	33	pfδβo	pfδβo	ADJ
cana-2738	308	34	.	.	PUNCT
cana-2738	309	1	proof	proof	NOUN
cana-2738	309	2	.	.	PUNCT
cana-2738	310	1	let	let	VERB
cana-2738	310	2	ν	ν	NOUN
cana-2738	310	3	be	be	AUX
cana-2738	310	4	a	a	DET
cana-2738	310	5	pfos	pfos	NOUN
cana-2738	310	6	in	in	ADP
cana-2738	310	7	(	(	PUNCT
cana-2738	310	8	x1	x1	PROPN
cana-2738	310	9	,	,	PUNCT
cana-2738	310	10	γp	γp	PROPN
cana-2738	310	11	)	)	PUNCT
cana-2738	310	12	.	.	PUNCT
cana-2738	311	1	then	then	ADV
cana-2738	311	2	g	g	PROPN
cana-2738	311	3	p	p	PROPN
cana-2738	311	4	∘	∘	PROPN
cana-2738	311	5	hp(ν	hp(ν	X
cana-2738	311	6	)	)	PUNCT
cana-2738	311	7	is	be	AUX
cana-2738	311	8	pfδβos	pfδβos	NOUN
cana-2738	311	9	of	of	ADP
cana-2738	311	10	(	(	PUNCT
cana-2738	311	11	x3	x3	ADJ
cana-2738	311	12	,	,	PUNCT
cana-2738	311	13	φp	φp	ADP
cana-2738	311	14	)	)	PUNCT
cana-2738	311	15	because	because	SCONJ
cana-2738	311	16	g	g	PROPN
cana-2738	311	17	p	p	PROPN
cana-2738	311	18	∘	∘	PROPN
cana-2738	311	19	hp	hp	PROPN
cana-2738	311	20	is	be	AUX
cana-2738	311	21	pfδβo	pfδβo	ADJ
cana-2738	311	22	.	.	PUNCT
cana-2738	312	1	since	since	SCONJ
cana-2738	312	2	g	g	PROPN
cana-2738	312	3	p	p	PROPN
cana-2738	312	4	is	be	AUX
cana-2738	312	5	pfδβirr	pfδβirr	ADJ
cana-2738	312	6	and	and	CCONJ
cana-2738	312	7	g	g	NOUN
cana-2738	312	8	p	p	PROPN
cana-2738	312	9	∘	∘	PROPN
cana-2738	312	10	hp(ψ	hp(ψ	NOUN
cana-2738	312	11	)	)	PUNCT
cana-2738	312	12	is	be	AUX
cana-2738	312	13	pfδβos	pfδβos	NOUN
cana-2738	312	14	of	of	ADP
cana-2738	312	15	(	(	PUNCT
cana-2738	312	16	x3	x3	ADJ
cana-2738	312	17	,	,	PUNCT
cana-2738	312	18	φp	φp	ADJ
cana-2738	312	19	)	)	PUNCT
cana-2738	312	20	,	,	PUNCT
cana-2738	312	21	g	g	PROPN
cana-2738	312	22	p	p	X
cana-2738	312	23	−1(g	−1(g	X
cana-2738	312	24	p	p	NOUN
cana-2738	312	25	∘	∘	NOUN
cana-2738	312	26	hp(ψ	hp(ψ	NOUN
cana-2738	312	27	)	)	PUNCT
cana-2738	312	28	)	)	PUNCT
cana-2738	313	1	=	=	PUNCT
cana-2738	313	2	hp(ψ	hp(ψ	NOUN
cana-2738	313	3	)	)	PUNCT
cana-2738	313	4	is	be	AUX
cana-2738	313	5	pfδβos	pfδβos	NOUN
cana-2738	313	6	in	in	ADP
cana-2738	313	7	(	(	PUNCT
cana-2738	313	8	x2	x2	INTJ
cana-2738	313	9	,	,	PUNCT
cana-2738	313	10	ψp	ψp	NOUN
cana-2738	313	11	)	)	PUNCT
cana-2738	313	12	.	.	PUNCT
cana-2738	314	1	hence	hence	ADV
cana-2738	314	2	hp	hp	PROPN
cana-2738	314	3	is	be	AUX
cana-2738	314	4	pfδβo	pfδβo	ADJ
cana-2738	314	5	.	.	PUNCT
cana-2738	315	1	theorem	theorem	VERB
cana-2738	315	2	3.7	3.7	NUM
cana-2738	315	3	let	let	VERB
cana-2738	315	4	(	(	PUNCT
cana-2738	315	5	x1	x1	PROPN
cana-2738	315	6	,	,	PUNCT
cana-2738	315	7	γp	γp	PROPN
cana-2738	315	8	)	)	PUNCT
cana-2738	315	9	,	,	PUNCT
cana-2738	315	10	(	(	PUNCT
cana-2738	315	11	x2	x2	INTJ
cana-2738	315	12	,	,	PUNCT
cana-2738	315	13	ψp	ψp	PROPN
cana-2738	315	14	)	)	PUNCT
cana-2738	315	15	&	&	CCONJ
cana-2738	315	16	(	(	PUNCT
cana-2738	315	17	x3	x3	PROPN
cana-2738	315	18	,	,	PUNCT
cana-2738	315	19	φp	φp	NOUN
cana-2738	315	20	)	)	PUNCT
cana-2738	315	21	be	be	VERB
cana-2738	315	22	any	any	DET
cana-2738	315	23	pfts	pft	NOUN
cana-2738	315	24	’s	’s	PART
cana-2738	315	25	.	.	PUNCT
cana-2738	316	1	if	if	SCONJ
cana-2738	316	2	hp	hp	VERB
cana-2738	316	3	:	:	PUNCT
cana-2738	316	4	(	(	PUNCT
cana-2738	316	5	x1	x1	PROPN
cana-2738	316	6	,	,	PUNCT
cana-2738	316	7	γp	γp	PROPN
cana-2738	316	8	)	)	PUNCT
cana-2738	316	9	→	→	SYM
cana-2738	316	10	(	(	PUNCT
cana-2738	316	11	x2	x2	PROPN
cana-2738	316	12	,	,	PUNCT
cana-2738	316	13	ψp	ψp	PROPN
cana-2738	316	14	)	)	PUNCT
cana-2738	316	15	is	be	AUX
cana-2738	316	16	pfo	pfo	PROPN
cana-2738	316	17	and	and	CCONJ
cana-2738	316	18	g	g	PROPN
cana-2738	316	19	p	p	X
cana-2738	316	20	:	:	PUNCT
cana-2738	316	21	(	(	PUNCT
cana-2738	316	22	x2	x2	ADJ
cana-2738	316	23	,	,	PUNCT
cana-2738	316	24	ψp	ψp	NOUN
cana-2738	316	25	)	)	PUNCT
cana-2738	316	26	→	→	SYM
cana-2738	316	27	(	(	PUNCT
cana-2738	316	28	x3	x3	ADJ
cana-2738	316	29	,	,	PUNCT
cana-2738	316	30	φp	φp	NOUN
cana-2738	316	31	)	)	PUNCT
cana-2738	316	32	is	be	AUX
cana-2738	316	33	pfδβo	pfδβo	ADJ
cana-2738	316	34	,	,	PUNCT
cana-2738	316	35	then	then	ADV
cana-2738	316	36	g	g	PROPN
cana-2738	316	37	p	p	PROPN
cana-2738	316	38	∘	∘	PROPN
cana-2738	316	39	hp	hp	PROPN
cana-2738	316	40	:	:	PUNCT
cana-2738	316	41	(	(	PUNCT
cana-2738	316	42	x1	x1	PROPN
cana-2738	316	43	,	,	PUNCT
cana-2738	316	44	γp	γp	PROPN
cana-2738	316	45	)	)	PUNCT
cana-2738	316	46	→	→	SYM
cana-2738	316	47	(	(	PUNCT
cana-2738	316	48	x3	x3	ADJ
cana-2738	316	49	,	,	PUNCT
cana-2738	316	50	φp	φp	NOUN
cana-2738	316	51	)	)	PUNCT
cana-2738	316	52	is	be	AUX
cana-2738	316	53	pfδβo	pfδβo	ADJ
cana-2738	316	54	.	.	PUNCT
cana-2738	317	1	proof	proof	NOUN
cana-2738	317	2	.	.	PUNCT
cana-2738	318	1	let	let	VERB
cana-2738	318	2	ψ	ψ	PART
cana-2738	318	3	be	be	AUX
cana-2738	318	4	a	a	DET
cana-2738	318	5	pfos	pfos	NOUN
cana-2738	318	6	in	in	ADP
cana-2738	318	7	(	(	PUNCT
cana-2738	318	8	x1	x1	PROPN
cana-2738	318	9	,	,	PUNCT
cana-2738	318	10	γp	γp	PROPN
cana-2738	318	11	)	)	PUNCT
cana-2738	318	12	.	.	PUNCT
cana-2738	319	1	then	then	ADV
cana-2738	319	2	hp(ψ	hp(ψ	NOUN
cana-2738	319	3	)	)	PUNCT
cana-2738	319	4	is	be	AUX
cana-2738	319	5	a	a	DET
cana-2738	319	6	pfos	pfos	NOUN
cana-2738	319	7	of	of	ADP
cana-2738	319	8	(	(	PUNCT
cana-2738	319	9	x2	x2	PROPN
cana-2738	319	10	,	,	PUNCT
cana-2738	319	11	ψp	ψp	NOUN
cana-2738	319	12	)	)	PUNCT
cana-2738	319	13	because	because	SCONJ
cana-2738	319	14	hp	hp	PROPN
cana-2738	319	15	is	be	AUX
cana-2738	319	16	a	a	DET
cana-2738	319	17	pfo	pfo	NOUN
cana-2738	319	18	map	map	NOUN
cana-2738	319	19	.	.	PUNCT
cana-2738	320	1	since	since	SCONJ
cana-2738	320	2	g	g	PROPN
cana-2738	320	3	p	p	PROPN
cana-2738	320	4	is	be	AUX
cana-2738	320	5	pfδβo	pfδβo	ADJ
cana-2738	320	6	,	,	PUNCT
cana-2738	320	7	g	g	PROPN
cana-2738	320	8	p	p	X
cana-2738	320	9	(	(	PUNCT
cana-2738	320	10	hp(ψ	hp(ψ	NOUN
cana-2738	320	11	)	)	PUNCT
cana-2738	320	12	)	)	PUNCT
cana-2738	321	1	=	=	PRON
cana-2738	321	2	(	(	PUNCT
cana-2738	321	3	g	g	PROPN
cana-2738	321	4	p	p	PROPN
cana-2738	321	5	∘	∘	PROPN
cana-2738	321	6	h)(ψ	h)(ψ	NOUN
cana-2738	321	7	)	)	PUNCT
cana-2738	321	8	is	be	AUX
cana-2738	321	9	pfδβos	pfδβos	NOUN
cana-2738	321	10	of	of	ADP
cana-2738	321	11	(	(	PUNCT
cana-2738	321	12	x3	x3	ADJ
cana-2738	321	13	,	,	PUNCT
cana-2738	321	14	φp	φp	ADJ
cana-2738	321	15	)	)	PUNCT
cana-2738	321	16	.	.	PUNCT
cana-2738	322	1	hence	hence	ADV
cana-2738	322	2	g	g	PROPN
cana-2738	322	3	p	p	PROPN
cana-2738	322	4	∘	∘	PROPN
cana-2738	322	5	hp	hp	PROPN
cana-2738	322	6	is	be	AUX
cana-2738	322	7	pfδβo	pfδβo	ADJ
cana-2738	322	8	map	map	NOUN
cana-2738	322	9	.	.	PUNCT
cana-2738	323	1	remark	remark	VERB
cana-2738	323	2	3.2	3.2	NUM
cana-2738	323	3	theorems	theorem	NOUN
cana-2738	323	4	3.2	3.2	NUM
cana-2738	323	5	to	to	PART
cana-2738	323	6	3.7	3.7	NUM
cana-2738	323	7	is	be	AUX
cana-2738	323	8	also	also	ADV
cana-2738	323	9	holds	hold	NOUN
cana-2738	323	10	for	for	ADP
cana-2738	323	11	pfo	pfo	PROPN
cana-2738	323	12	(	(	PUNCT
cana-2738	323	13	resp	resp	PROPN
cana-2738	323	14	.	.	PUNCT
cana-2738	324	1	pfδo	pfδo	ADJ
cana-2738	324	2	,	,	PUNCT
cana-2738	324	3	pfδ𝒮o	pfδ𝒮o	ADJ
cana-2738	324	4	and	and	CCONJ
cana-2738	324	5	pfδ𝒫o	pfδ𝒫o	ADJ
cana-2738	324	6	)	)	PUNCT
cana-2738	324	7	mappings	mapping	NOUN
cana-2738	324	8	.	.	PUNCT
cana-2738	325	1	communications	communication	NOUN
cana-2738	325	2	on	on	ADP
cana-2738	325	3	applied	apply	VERB
cana-2738	325	4	nonlinear	nonlinear	ADJ
cana-2738	325	5	analysis	analysis	NOUN
cana-2738	325	6	issn	issn	NOUN
cana-2738	325	7	:	:	PUNCT
cana-2738	325	8	1074	1074	NUM
cana-2738	325	9	-	-	PUNCT
cana-2738	325	10	133x	133x	NUM
cana-2738	325	11	vol	vol	NOUN
cana-2738	325	12	32	32	NUM
cana-2738	325	13	no	no	NOUN
cana-2738	325	14	.	.	PUNCT
cana-2738	326	1	4s	4s	NUM
cana-2738	326	2	(	(	PUNCT
cana-2738	326	3	2025	2025	NUM
cana-2738	326	4	)	)	PUNCT
cana-2738	326	5	51	51	NUM
cana-2738	326	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2738	326	7	4	4	NUM
cana-2738	326	8	pythagorean	pythagorean	NOUN
cana-2738	326	9	fuzzy	fuzzy	ADJ
cana-2738	326	10	𝜹-closed	𝜹-close	VERB
cana-2738	326	11	mappings	mapping	NOUN
cana-2738	326	12	in	in	ADP
cana-2738	326	13	this	this	DET
cana-2738	326	14	section	section	NOUN
cana-2738	326	15	,	,	PUNCT
cana-2738	326	16	pythagorean	pythagorean	PROPN
cana-2738	326	17	fuzzy	fuzzy	PROPN
cana-2738	326	18	δ	δ	PROPN
cana-2738	326	19	-	-	PUNCT
cana-2738	326	20	closed	close	VERB
cana-2738	326	21	mappings	mapping	NOUN
cana-2738	326	22	are	be	AUX
cana-2738	326	23	introduced	introduce	VERB
cana-2738	326	24	and	and	CCONJ
cana-2738	326	25	studied	study	VERB
cana-2738	326	26	their	their	PRON
cana-2738	326	27	properties	property	NOUN
cana-2738	326	28	.	.	PUNCT
cana-2738	327	1	definition	definition	NOUN
cana-2738	327	2	4.1	4.1	NUM
cana-2738	327	3	let	let	VERB
cana-2738	327	4	(	(	PUNCT
cana-2738	327	5	x1	x1	PROPN
cana-2738	327	6	,	,	PUNCT
cana-2738	327	7	γp	γp	PROPN
cana-2738	327	8	)	)	PUNCT
cana-2738	327	9	&	&	CCONJ
cana-2738	327	10	(	(	PUNCT
cana-2738	327	11	x2	x2	PROPN
cana-2738	327	12	,	,	PUNCT
cana-2738	327	13	ψp	ψp	PRON
cana-2738	327	14	)	)	PUNCT
cana-2738	327	15	be	be	VERB
cana-2738	327	16	any	any	DET
cana-2738	327	17	two	two	NUM
cana-2738	327	18	pfts	pft	NOUN
cana-2738	327	19	’s	’s	PART
cana-2738	327	20	.	.	PUNCT
cana-2738	328	1	a	a	DET
cana-2738	328	2	mapping	mapping	NOUN
cana-2738	328	3	hp	hp	NOUN
cana-2738	328	4	:	:	PUNCT
cana-2738	328	5	(	(	PUNCT
cana-2738	328	6	x1	x1	PROPN
cana-2738	328	7	,	,	PUNCT
cana-2738	328	8	γp	γp	PROPN
cana-2738	328	9	)	)	PUNCT
cana-2738	328	10	→	→	SYM
cana-2738	328	11	(	(	PUNCT
cana-2738	328	12	x2	x2	PROPN
cana-2738	328	13	,	,	PUNCT
cana-2738	328	14	ψp	ψp	NOUN
cana-2738	328	15	)	)	PUNCT
cana-2738	328	16	is	be	AUX
cana-2738	328	17	said	say	VERB
cana-2738	328	18	to	to	PART
cana-2738	328	19	be	be	AUX
cana-2738	328	20	pythagorean	pythagorean	PROPN
cana-2738	328	21	fuzzy	fuzzy	ADJ
cana-2738	328	22	(	(	PUNCT
cana-2738	328	23	resp	resp	NOUN
cana-2738	328	24	.	.	PUNCT
cana-2738	329	1	δ	δ	PROPN
cana-2738	329	2	,	,	PUNCT
cana-2738	329	3	δ𝒮	δ𝒮	PROPN
cana-2738	329	4	,	,	PUNCT
cana-2738	329	5	δ𝒫	δ𝒫	PROPN
cana-2738	329	6	and	and	CCONJ
cana-2738	329	7	δβ	δβ	NOUN
cana-2738	329	8	)	)	PUNCT
cana-2738	329	9	closed	closed	ADJ
cana-2738	329	10	map	map	NOUN
cana-2738	329	11	(	(	PUNCT
cana-2738	329	12	briefly	briefly	ADV
cana-2738	329	13	,	,	PUNCT
cana-2738	329	14	pfc	pfc	PROPN
cana-2738	329	15	(	(	PUNCT
cana-2738	329	16	resp	resp	PROPN
cana-2738	329	17	.	.	PUNCT
cana-2738	330	1	pfδc	pfδc	NOUN
cana-2738	330	2	,	,	PUNCT
cana-2738	330	3	pfδ𝒮c	pfδ𝒮c	NOUN
cana-2738	330	4	,	,	PUNCT
cana-2738	330	5	pfδ𝒫c	pfδ𝒫c	NOUN
cana-2738	330	6	and	and	CCONJ
cana-2738	330	7	pfδβc	pfδβc	NOUN
cana-2738	330	8	)	)	PUNCT
cana-2738	330	9	)	)	PUNCT
cana-2738	331	1	if	if	SCONJ
cana-2738	331	2	the	the	DET
cana-2738	331	3	image	image	NOUN
cana-2738	331	4	of	of	ADP
cana-2738	331	5	every	every	DET
cana-2738	331	6	pfcs	pfc	NOUN
cana-2738	331	7	in	in	ADP
cana-2738	331	8	(	(	PUNCT
cana-2738	331	9	x1	x1	PROPN
cana-2738	331	10	,	,	PUNCT
cana-2738	331	11	γp	γp	PROPN
cana-2738	331	12	)	)	PUNCT
cana-2738	331	13	is	be	AUX
cana-2738	331	14	a	a	DET
cana-2738	331	15	pfcs	pfc	NOUN
cana-2738	331	16	(	(	PUNCT
cana-2738	331	17	resp	resp	NOUN
cana-2738	331	18	.	.	PUNCT
cana-2738	332	1	pfδcs	pfδcs	PROPN
cana-2738	332	2	,	,	PUNCT
cana-2738	332	3	pfδ𝒮cs	pfδ𝒮cs	PROPN
cana-2738	332	4	,	,	PUNCT
cana-2738	332	5	pfδ𝒫cs	pfδ𝒫cs	VERB
cana-2738	332	6	and	and	CCONJ
cana-2738	332	7	pfδβcs	pfδβcs	VERB
cana-2738	332	8	)	)	PUNCT
cana-2738	332	9	in	in	ADP
cana-2738	332	10	(	(	PUNCT
cana-2738	332	11	x2	x2	INTJ
cana-2738	332	12	,	,	PUNCT
cana-2738	332	13	ψp	ψp	NOUN
cana-2738	332	14	)	)	PUNCT
cana-2738	332	15	.	.	PUNCT
cana-2738	333	1	theorem	theorem	VERB
cana-2738	333	2	4.1	4.1	NUM
cana-2738	333	3	let	let	VERB
cana-2738	333	4	(	(	PUNCT
cana-2738	333	5	x1	x1	PROPN
cana-2738	333	6	,	,	PUNCT
cana-2738	333	7	γp	γp	PROPN
cana-2738	333	8	)	)	PUNCT
cana-2738	333	9	&	&	CCONJ
cana-2738	333	10	(	(	PUNCT
cana-2738	333	11	x2	x2	PROPN
cana-2738	333	12	,	,	PUNCT
cana-2738	333	13	ψp	ψp	PRON
cana-2738	333	14	)	)	PUNCT
cana-2738	333	15	be	be	AUX
cana-2738	333	16	any	any	DET
cana-2738	333	17	pfts	pft	NOUN
cana-2738	333	18	’s	’s	PART
cana-2738	333	19	.	.	PUNCT
cana-2738	334	1	let	let	VERB
cana-2738	334	2	hp	hp	VERB
cana-2738	334	3	:	:	PUNCT
cana-2738	334	4	(	(	PUNCT
cana-2738	334	5	x1	x1	PROPN
cana-2738	334	6	,	,	PUNCT
cana-2738	334	7	γp	γp	PROPN
cana-2738	334	8	)	)	PUNCT
cana-2738	334	9	→	→	SYM
cana-2738	334	10	(	(	PUNCT
cana-2738	334	11	x2	x2	PROPN
cana-2738	334	12	,	,	PUNCT
cana-2738	334	13	ψp	ψp	PRON
cana-2738	334	14	)	)	PUNCT
cana-2738	334	15	be	be	AUX
cana-2738	334	16	a	a	DET
cana-2738	334	17	mapping	mapping	NOUN
cana-2738	334	18	.	.	PUNCT
cana-2738	335	1	then	then	ADV
cana-2738	335	2	the	the	DET
cana-2738	335	3	following	following	ADJ
cana-2738	335	4	statements	statement	NOUN
cana-2738	335	5	are	be	AUX
cana-2738	335	6	hold	hold	ADJ
cana-2738	335	7	.	.	PUNCT
cana-2738	336	1	1	1	X
cana-2738	336	2	.	.	X
cana-2738	337	1	every	every	DET
cana-2738	337	2	pfδc	pfδc	NOUN
cana-2738	337	3	map	map	NOUN
cana-2738	337	4	is	be	AUX
cana-2738	337	5	a	a	DET
cana-2738	337	6	pfc	pfc	NOUN
cana-2738	337	7	map	map	NOUN
cana-2738	337	8	.	.	PUNCT
cana-2738	338	1	2	2	X
cana-2738	338	2	.	.	X
cana-2738	338	3	every	every	DET
cana-2738	338	4	pfc	pfc	NOUN
cana-2738	338	5	map	map	NOUN
cana-2738	338	6	is	be	AUX
cana-2738	338	7	a	a	DET
cana-2738	338	8	pfδ𝒮c	pfδ𝒮c	ADJ
cana-2738	338	9	map	map	NOUN
cana-2738	338	10	.	.	PUNCT
cana-2738	339	1	3	3	X
cana-2738	339	2	.	.	X
cana-2738	339	3	every	every	DET
cana-2738	339	4	pfc	pfc	NOUN
cana-2738	339	5	map	map	NOUN
cana-2738	339	6	is	be	AUX
cana-2738	339	7	a	a	DET
cana-2738	339	8	pfδ𝒫c	pfδ𝒫c	NOUN
cana-2738	339	9	map	map	NOUN
cana-2738	339	10	.	.	PUNCT
cana-2738	340	1	4	4	X
cana-2738	340	2	.	.	X
cana-2738	340	3	every	every	DET
cana-2738	340	4	pfδ𝒮c	pfδ𝒮c	ADJ
cana-2738	340	5	map	map	NOUN
cana-2738	340	6	is	be	AUX
cana-2738	340	7	a	a	DET
cana-2738	340	8	pfδβc	pfδβc	NOUN
cana-2738	340	9	map	map	NOUN
cana-2738	340	10	.	.	PUNCT
cana-2738	341	1	5	5	X
cana-2738	341	2	.	.	X
cana-2738	341	3	every	every	DET
cana-2738	341	4	pfδ𝒫c	pfδ𝒫c	NOUN
cana-2738	341	5	map	map	NOUN
cana-2738	341	6	is	be	AUX
cana-2738	341	7	a	a	DET
cana-2738	341	8	pfδβc	pfδβc	NOUN
cana-2738	341	9	map	map	NOUN
cana-2738	341	10	.	.	PUNCT
cana-2738	342	1	6	6	X
cana-2738	342	2	.	.	X
cana-2738	342	3	every	every	DET
cana-2738	342	4	pfδαc	pfδαc	NOUN
cana-2738	342	5	map	map	NOUN
cana-2738	342	6	is	be	AUX
cana-2738	342	7	a	a	DET
cana-2738	342	8	pfδ𝒮c	pfδ𝒮c	ADJ
cana-2738	342	9	map	map	NOUN
cana-2738	342	10	.	.	PUNCT
cana-2738	343	1	7	7	X
cana-2738	343	2	.	.	X
cana-2738	343	3	every	every	DET
cana-2738	343	4	pfδαc	pfδαc	NOUN
cana-2738	343	5	map	map	NOUN
cana-2738	343	6	is	be	AUX
cana-2738	343	7	a	a	DET
cana-2738	343	8	pfδ𝒫c	pfδ𝒫c	NOUN
cana-2738	343	9	map	map	NOUN
cana-2738	343	10	.	.	PUNCT
cana-2738	344	1	proof	proof	NOUN
cana-2738	344	2	.	.	PUNCT
cana-2738	345	1	(	(	PUNCT
cana-2738	345	2	i	i	NOUN
cana-2738	345	3	)	)	PUNCT
cana-2738	345	4	let	let	VERB
cana-2738	345	5	m	m	PRON
cana-2738	345	6	be	be	AUX
cana-2738	345	7	a	a	DET
cana-2738	345	8	pfcs	pfcs	NOUN
cana-2738	345	9	in	in	ADP
cana-2738	345	10	x1	x1	PROPN
cana-2738	345	11	.	.	PUNCT
cana-2738	346	1	since	since	SCONJ
cana-2738	346	2	hp	hp	PROPN
cana-2738	346	3	is	be	AUX
cana-2738	346	4	pfδc	pfδc	NOUN
cana-2738	346	5	map	map	NOUN
cana-2738	346	6	,	,	PUNCT
cana-2738	346	7	hp(m	hp(m	X
cana-2738	346	8	)	)	PUNCT
cana-2738	346	9	is	be	AUX
cana-2738	346	10	a	a	DET
cana-2738	346	11	pfδcs	pfδcs	NOUN
cana-2738	346	12	in	in	ADP
cana-2738	346	13	x2	x2	PROPN
cana-2738	346	14	.	.	PUNCT
cana-2738	347	1	since	since	SCONJ
cana-2738	347	2	every	every	DET
cana-2738	347	3	pfδcs	pfδcs	NOUN
cana-2738	347	4	is	be	AUX
cana-2738	347	5	a	a	DET
cana-2738	347	6	pfcs	pfc	NOUN
cana-2738	347	7	,	,	PUNCT
cana-2738	347	8	hp(m	hp(m	X
cana-2738	347	9	)	)	PUNCT
cana-2738	347	10	is	be	AUX
cana-2738	347	11	a	a	DET
cana-2738	347	12	pfcs	pfcs	NOUN
cana-2738	347	13	in	in	ADP
cana-2738	347	14	x2	x2	PROPN
cana-2738	347	15	.	.	PUNCT
cana-2738	348	1	hence	hence	ADV
cana-2738	348	2	hp	hp	PROPN
cana-2738	348	3	is	be	AUX
cana-2738	348	4	a	a	DET
cana-2738	348	5	pfc	pfc	NOUN
cana-2738	348	6	.	.	PUNCT
cana-2738	349	1	(	(	PUNCT
cana-2738	349	2	ii	ii	NOUN
cana-2738	349	3	)	)	PUNCT
cana-2738	349	4	let	let	VERB
cana-2738	349	5	m	m	PRON
cana-2738	349	6	be	be	AUX
cana-2738	349	7	a	a	DET
cana-2738	349	8	pfcs	pfcs	NOUN
cana-2738	349	9	in	in	ADP
cana-2738	349	10	x1	x1	PROPN
cana-2738	349	11	.	.	PUNCT
cana-2738	350	1	since	since	SCONJ
cana-2738	350	2	hp	hp	PROPN
cana-2738	350	3	is	be	AUX
cana-2738	350	4	pfc	pfc	NOUN
cana-2738	350	5	map	map	NOUN
cana-2738	350	6	,	,	PUNCT
cana-2738	350	7	hp(m	hp(m	X
cana-2738	350	8	)	)	PUNCT
cana-2738	350	9	is	be	AUX
cana-2738	350	10	a	a	DET
cana-2738	350	11	pfcs	pfcs	NOUN
cana-2738	350	12	in	in	ADP
cana-2738	350	13	x2	x2	PROPN
cana-2738	350	14	.	.	PUNCT
cana-2738	351	1	since	since	SCONJ
cana-2738	351	2	every	every	DET
cana-2738	351	3	pfcs	pfcs	NOUN
cana-2738	351	4	is	be	AUX
cana-2738	351	5	a	a	DET
cana-2738	351	6	pfδ𝒮cs	pfδ𝒮cs	PROPN
cana-2738	351	7	,	,	PUNCT
cana-2738	351	8	hp(m	hp(m	X
cana-2738	351	9	)	)	PUNCT
cana-2738	351	10	is	be	AUX
cana-2738	351	11	a	a	DET
cana-2738	351	12	pfδ𝒮cs	pfδ𝒮cs	NOUN
cana-2738	351	13	in	in	ADP
cana-2738	351	14	x2	x2	PROPN
cana-2738	351	15	.	.	PUNCT
cana-2738	352	1	hence	hence	ADV
cana-2738	352	2	hp	hp	PROPN
cana-2738	352	3	is	be	AUX
cana-2738	352	4	a	a	DET
cana-2738	352	5	pfδ𝒮c	pfδ𝒮c	NOUN
cana-2738	352	6	.	.	PUNCT
cana-2738	353	1	(	(	PUNCT
cana-2738	353	2	iii	iii	X
cana-2738	353	3	)	)	PUNCT
cana-2738	353	4	let	let	VERB
cana-2738	353	5	m	m	PRON
cana-2738	353	6	be	be	AUX
cana-2738	353	7	a	a	DET
cana-2738	353	8	pfcs	pfcs	NOUN
cana-2738	353	9	in	in	ADP
cana-2738	353	10	x1	x1	PROPN
cana-2738	353	11	.	.	PUNCT
cana-2738	354	1	since	since	SCONJ
cana-2738	354	2	hp	hp	PROPN
cana-2738	354	3	is	be	AUX
cana-2738	354	4	pfc	pfc	NOUN
cana-2738	354	5	map	map	NOUN
cana-2738	354	6	,	,	PUNCT
cana-2738	354	7	hp(m	hp(m	X
cana-2738	354	8	)	)	PUNCT
cana-2738	354	9	is	be	AUX
cana-2738	354	10	a	a	DET
cana-2738	354	11	pfcs	pfcs	NOUN
cana-2738	354	12	in	in	ADP
cana-2738	354	13	x2	x2	PROPN
cana-2738	354	14	.	.	PUNCT
cana-2738	355	1	since	since	SCONJ
cana-2738	355	2	every	every	DET
cana-2738	355	3	pfcs	pfcs	NOUN
cana-2738	355	4	is	be	AUX
cana-2738	355	5	a	a	DET
cana-2738	355	6	pfδ𝒫cs	pfδ𝒫cs	NOUN
cana-2738	355	7	,	,	PUNCT
cana-2738	355	8	hp(m	hp(m	X
cana-2738	355	9	)	)	PUNCT
cana-2738	355	10	is	be	AUX
cana-2738	355	11	a	a	DET
cana-2738	355	12	pfδ𝒫cs	pfδ𝒫cs	NOUN
cana-2738	355	13	in	in	ADP
cana-2738	355	14	x2	x2	PROPN
cana-2738	355	15	.	.	PUNCT
cana-2738	356	1	hence	hence	ADV
cana-2738	356	2	hp	hp	PROPN
cana-2738	356	3	is	be	AUX
cana-2738	356	4	a	a	DET
cana-2738	356	5	pfδ𝒫c	pfδ𝒫c	PROPN
cana-2738	356	6	.	.	PUNCT
cana-2738	357	1	(	(	PUNCT
cana-2738	357	2	iv	iv	X
cana-2738	357	3	)	)	PUNCT
cana-2738	357	4	let	let	VERB
cana-2738	357	5	m	m	PRON
cana-2738	357	6	be	be	AUX
cana-2738	357	7	a	a	DET
cana-2738	357	8	pfcs	pfcs	NOUN
cana-2738	357	9	in	in	ADP
cana-2738	357	10	x1	x1	PROPN
cana-2738	357	11	.	.	PUNCT
cana-2738	358	1	since	since	SCONJ
cana-2738	358	2	hp	hp	PROPN
cana-2738	358	3	is	be	AUX
cana-2738	358	4	pfδ𝒮c	pfδ𝒮c	ADJ
cana-2738	358	5	map	map	NOUN
cana-2738	358	6	,	,	PUNCT
cana-2738	358	7	hp(m	hp(m	X
cana-2738	358	8	)	)	PUNCT
cana-2738	358	9	is	be	AUX
cana-2738	358	10	a	a	DET
cana-2738	358	11	pfδ𝒮cs	pfδ𝒮cs	NOUN
cana-2738	358	12	in	in	ADP
cana-2738	358	13	x2	x2	PROPN
cana-2738	358	14	.	.	PUNCT
cana-2738	359	1	since	since	SCONJ
cana-2738	359	2	every	every	DET
cana-2738	359	3	pfδ𝒮cs	pfδ𝒮cs	PROPN
cana-2738	359	4	is	be	AUX
cana-2738	359	5	a	a	DET
cana-2738	359	6	pfδβcs	pfδβcs	NOUN
cana-2738	359	7	,	,	PUNCT
cana-2738	359	8	hp(m	hp(m	X
cana-2738	359	9	)	)	PUNCT
cana-2738	359	10	is	be	AUX
cana-2738	359	11	a	a	DET
cana-2738	359	12	pfδβcs	pfδβcs	NOUN
cana-2738	359	13	in	in	ADP
cana-2738	359	14	x2	x2	PROPN
cana-2738	359	15	.	.	PUNCT
cana-2738	360	1	hence	hence	ADV
cana-2738	360	2	hp	hp	PROPN
cana-2738	360	3	is	be	AUX
cana-2738	360	4	a	a	DET
cana-2738	360	5	pfδβc	pfδβc	NOUN
cana-2738	360	6	.	.	PUNCT
cana-2738	361	1	(	(	PUNCT
cana-2738	361	2	v	v	NOUN
cana-2738	361	3	)	)	PUNCT
cana-2738	361	4	let	let	VERB
cana-2738	361	5	m	m	PRON
cana-2738	361	6	be	be	AUX
cana-2738	361	7	a	a	DET
cana-2738	361	8	pfcs	pfcs	NOUN
cana-2738	361	9	in	in	ADP
cana-2738	361	10	x1	x1	PROPN
cana-2738	361	11	.	.	PUNCT
cana-2738	362	1	since	since	SCONJ
cana-2738	362	2	hp	hp	PROPN
cana-2738	362	3	is	be	AUX
cana-2738	362	4	pfδ𝒫c	pfδ𝒫c	NOUN
cana-2738	362	5	map	map	NOUN
cana-2738	362	6	,	,	PUNCT
cana-2738	362	7	hp(m	hp(m	X
cana-2738	362	8	)	)	PUNCT
cana-2738	362	9	is	be	AUX
cana-2738	362	10	a	a	DET
cana-2738	362	11	pfδ𝒫cs	pfδ𝒫cs	NOUN
cana-2738	362	12	in	in	ADP
cana-2738	362	13	x2	x2	PROPN
cana-2738	362	14	.	.	PUNCT
cana-2738	363	1	since	since	SCONJ
cana-2738	363	2	every	every	DET
cana-2738	363	3	pfδ𝒫cs	pfδ𝒫cs	NOUN
cana-2738	363	4	is	be	AUX
cana-2738	363	5	a	a	DET
cana-2738	363	6	pfδβcs	pfδβcs	NOUN
cana-2738	363	7	,	,	PUNCT
cana-2738	363	8	hp(m	hp(m	X
cana-2738	363	9	)	)	PUNCT
cana-2738	363	10	is	be	AUX
cana-2738	363	11	a	a	DET
cana-2738	363	12	pfδβcs	pfδβcs	NOUN
cana-2738	363	13	in	in	ADP
cana-2738	363	14	x2	x2	PROPN
cana-2738	363	15	.	.	PUNCT
cana-2738	364	1	hence	hence	ADV
cana-2738	364	2	hp	hp	PROPN
cana-2738	364	3	is	be	AUX
cana-2738	364	4	a	a	DET
cana-2738	364	5	pfδβc	pfδβc	NOUN
cana-2738	364	6	.	.	PUNCT
cana-2738	365	1	(	(	PUNCT
cana-2738	365	2	vi	vi	X
cana-2738	365	3	)	)	PUNCT
cana-2738	365	4	let	let	VERB
cana-2738	365	5	m	m	PRON
cana-2738	365	6	be	be	AUX
cana-2738	365	7	a	a	DET
cana-2738	365	8	pfcs	pfcs	NOUN
cana-2738	365	9	in	in	ADP
cana-2738	365	10	x1	x1	PROPN
cana-2738	365	11	.	.	PUNCT
cana-2738	366	1	since	since	SCONJ
cana-2738	366	2	hp	hp	PROPN
cana-2738	366	3	is	be	AUX
cana-2738	366	4	pfδαc	pfδαc	NOUN
cana-2738	366	5	map	map	NOUN
cana-2738	366	6	,	,	PUNCT
cana-2738	366	7	hp(m	hp(m	X
cana-2738	366	8	)	)	PUNCT
cana-2738	366	9	is	be	AUX
cana-2738	366	10	a	a	DET
cana-2738	366	11	pfδαcs	pfδαcs	NOUN
cana-2738	366	12	in	in	ADP
cana-2738	366	13	x2	x2	PROPN
cana-2738	366	14	.	.	PUNCT
cana-2738	367	1	since	since	SCONJ
cana-2738	367	2	every	every	DET
cana-2738	367	3	pfδαcs	pfδαcs	NOUN
cana-2738	367	4	is	be	AUX
cana-2738	367	5	a	a	DET
cana-2738	367	6	pfδ𝒮cs	pfδ𝒮cs	PROPN
cana-2738	367	7	,	,	PUNCT
cana-2738	367	8	hp(m	hp(m	X
cana-2738	367	9	)	)	PUNCT
cana-2738	367	10	is	be	AUX
cana-2738	367	11	a	a	DET
cana-2738	367	12	pfδ𝒮cs	pfδ𝒮cs	NOUN
cana-2738	367	13	in	in	ADP
cana-2738	367	14	x2	x2	PROPN
cana-2738	367	15	.	.	PUNCT
cana-2738	368	1	hence	hence	ADV
cana-2738	368	2	hp	hp	PROPN
cana-2738	368	3	is	be	AUX
cana-2738	368	4	a	a	DET
cana-2738	368	5	pfδ𝒮c	pfδ𝒮c	NOUN
cana-2738	368	6	.	.	PUNCT
cana-2738	369	1	(	(	PUNCT
cana-2738	369	2	vii	vii	PROPN
cana-2738	369	3	)	)	PUNCT
cana-2738	369	4	let	let	VERB
cana-2738	369	5	m	m	PRON
cana-2738	369	6	be	be	AUX
cana-2738	369	7	a	a	DET
cana-2738	369	8	pfcs	pfcs	NOUN
cana-2738	369	9	in	in	ADP
cana-2738	369	10	x1	x1	PROPN
cana-2738	369	11	.	.	PUNCT
cana-2738	370	1	since	since	SCONJ
cana-2738	370	2	hp	hp	PROPN
cana-2738	370	3	is	be	AUX
cana-2738	370	4	pfδαc	pfδαc	NOUN
cana-2738	370	5	map	map	NOUN
cana-2738	370	6	,	,	PUNCT
cana-2738	370	7	hp(m	hp(m	X
cana-2738	370	8	)	)	PUNCT
cana-2738	370	9	is	be	AUX
cana-2738	370	10	a	a	DET
cana-2738	370	11	pfδαcs	pfδαcs	NOUN
cana-2738	370	12	in	in	ADP
cana-2738	370	13	x2	x2	PROPN
cana-2738	370	14	.	.	PUNCT
cana-2738	371	1	since	since	SCONJ
cana-2738	371	2	every	every	DET
cana-2738	371	3	pfδαcs	pfδαcs	NOUN
cana-2738	371	4	is	be	AUX
cana-2738	371	5	a	a	DET
cana-2738	371	6	pfδ𝒫cs	pfδ𝒫cs	NOUN
cana-2738	371	7	,	,	PUNCT
cana-2738	371	8	hp(m	hp(m	X
cana-2738	371	9	)	)	PUNCT
cana-2738	371	10	is	be	AUX
cana-2738	371	11	a	a	DET
cana-2738	371	12	pfδ𝒫cs	pfδ𝒫cs	NOUN
cana-2738	371	13	in	in	ADP
cana-2738	371	14	x2	x2	PROPN
cana-2738	371	15	.	.	PUNCT
cana-2738	372	1	hence	hence	ADV
cana-2738	372	2	hp	hp	PROPN
cana-2738	372	3	is	be	AUX
cana-2738	372	4	a	a	DET
cana-2738	372	5	pfδ𝒫c	pfδ𝒫c	PROPN
cana-2738	372	6	.	.	PUNCT
cana-2738	372	7	example	example	NOUN
cana-2738	372	8	4.1	4.1	NUM
cana-2738	372	9	let	let	VERB
cana-2738	372	10	x	x	PUNCT
cana-2738	373	1	=	=	SYM
cana-2738	373	2	x1	x1	PROPN
cana-2738	373	3	=	=	PUNCT
cana-2738	374	1	x2	x2	PROPN
cana-2738	374	2	=	=	PUNCT
cana-2738	374	3	x3	x3	PROPN
cana-2738	374	4	=	=	SYM
cana-2738	374	5	x4	x4	PROPN
cana-2738	374	6	=	=	SYM
cana-2738	374	7	x5	x5	PROPN
cana-2738	374	8	=	=	SYM
cana-2738	374	9	{	{	PUNCT
cana-2738	374	10	x1	x1	PROPN
cana-2738	374	11	,	,	PUNCT
cana-2738	374	12	x2	x2	PROPN
cana-2738	374	13	}	}	PUNCT
cana-2738	374	14	and	and	CCONJ
cana-2738	374	15	the	the	DET
cana-2738	374	16	pfs	pfs	PROPN
cana-2738	374	17	’s	’s	PART
cana-2738	374	18	a1	a1	NOUN
cana-2738	374	19	,	,	PUNCT
cana-2738	374	20	a2	a2	PROPN
cana-2738	374	21	and	and	CCONJ
cana-2738	374	22	a3	a3	NOUN
cana-2738	374	23	are	be	AUX
cana-2738	374	24	defined	define	VERB
cana-2738	374	25	as	as	ADP
cana-2738	374	26	a1	a1	NOUN
cana-2738	374	27	=	=	PUNCT
cana-2738	374	28	{	{	PUNCT
cana-2738	374	29	<	<	X
cana-2738	374	30	x1	x1	PROPN
cana-2738	374	31	,	,	PUNCT
cana-2738	374	32	0.020,0.040	0.020,0.040	NUM
cana-2738	374	33	>	>	PUNCT
cana-2738	374	34	,	,	PUNCT
cana-2738	374	35	<	<	X
cana-2738	374	36	x2	x2	PROPN
cana-2738	374	37	,	,	PUNCT
cana-2738	374	38	0.050,0.050	0.050,0.050	PROPN
cana-2738	374	39	>	>	PUNCT
cana-2738	374	40	}	}	PUNCT
cana-2738	374	41	a2	a2	PROPN
cana-2738	374	42	=	=	PUNCT
cana-2738	374	43	{	{	PUNCT
cana-2738	374	44	<	<	X
cana-2738	374	45	x1	x1	PROPN
cana-2738	374	46	,	,	PUNCT
cana-2738	374	47	0.010,0.040	0.010,0.040	NUM
cana-2738	374	48	>	>	PUNCT
cana-2738	374	49	,	,	PUNCT
cana-2738	374	50	<	<	X
cana-2738	374	51	x2	x2	PROPN
cana-2738	374	52	,	,	PUNCT
cana-2738	374	53	0.050,0.050	0.050,0.050	PROPN
cana-2738	374	54	>	>	X
cana-2738	374	55	}	}	PUNCT
cana-2738	374	56	communications	communication	NOUN
cana-2738	374	57	on	on	ADP
cana-2738	374	58	applied	apply	VERB
cana-2738	374	59	nonlinear	nonlinear	ADJ
cana-2738	374	60	analysis	analysis	NOUN
cana-2738	374	61	issn	issn	NOUN
cana-2738	374	62	:	:	PUNCT
cana-2738	374	63	1074	1074	NUM
cana-2738	374	64	-	-	PUNCT
cana-2738	374	65	133x	133x	NUM
cana-2738	374	66	vol	vol	NOUN
cana-2738	374	67	32	32	NUM
cana-2738	375	1	no	no	NOUN
cana-2738	375	2	.	.	PUNCT
cana-2738	376	1	4s	4s	NUM
cana-2738	376	2	(	(	PUNCT
cana-2738	376	3	2025	2025	NUM
cana-2738	376	4	)	)	PUNCT
cana-2738	376	5	52	52	NUM
cana-2738	376	6	https://internationalpubls.com	https://internationalpubls.com	NUM
cana-2738	376	7	a3	a3	NOUN
cana-2738	376	8	=	=	SYM
cana-2738	376	9	{	{	PUNCT
cana-2738	376	10	<	<	X
cana-2738	376	11	x1	x1	PROPN
cana-2738	376	12	,	,	PUNCT
cana-2738	376	13	0.020,0.030	0.020,0.030	PROPN
cana-2738	376	14	>	>	PUNCT
cana-2738	376	15	,	,	PUNCT
cana-2738	376	16	<	<	X
cana-2738	376	17	x2	x2	PROPN
cana-2738	376	18	,	,	PUNCT
cana-2738	376	19	0.050,0.050	0.050,0.050	PROPN
cana-2738	376	20	>	>	PUNCT
cana-2738	376	21	}	}	PUNCT
cana-2738	376	22	here	here	ADV
cana-2738	376	23	we	we	PRON
cana-2738	376	24	have	have	VERB
cana-2738	376	25	τ1	τ1	NOUN
cana-2738	376	26	=	=	SYM
cana-2738	376	27	{	{	PUNCT
cana-2738	376	28	0x1	0x1	NOUN
cana-2738	376	29	,	,	PUNCT
cana-2738	376	30	1x1	1x1	NUM
cana-2738	376	31	,	,	PUNCT
cana-2738	376	32	a1	a1	NOUN
cana-2738	376	33	,	,	PUNCT
cana-2738	376	34	a2	a2	PROPN
cana-2738	376	35	}	}	PUNCT
cana-2738	376	36	,	,	PUNCT
cana-2738	376	37	τ2	τ2	NOUN
cana-2738	376	38	=	=	SYM
cana-2738	376	39	{	{	PUNCT
cana-2738	376	40	0x2	0x2	NOUN
cana-2738	376	41	,	,	PUNCT
cana-2738	376	42	1x2	1x2	NUM
cana-2738	376	43	,	,	PUNCT
cana-2738	376	44	a2	a2	PROPN
cana-2738	376	45	}	}	PUNCT
cana-2738	376	46	,	,	PUNCT
cana-2738	376	47	τ3	τ3	NOUN
cana-2738	376	48	=	=	SYM
cana-2738	376	49	{	{	PUNCT
cana-2738	376	50	0x3	0x3	PROPN
cana-2738	376	51	,	,	PUNCT
cana-2738	376	52	1x3	1x3	PROPN
cana-2738	376	53	,	,	PUNCT
cana-2738	376	54	a1	a1	NOUN
cana-2738	376	55	c	c	PROPN
cana-2738	376	56	}	}	PUNCT
cana-2738	376	57	,	,	PUNCT
cana-2738	376	58	τ4	τ4	NOUN
cana-2738	376	59	=	=	SYM
cana-2738	376	60	{	{	PUNCT
cana-2738	376	61	0x4	0x4	NUM
cana-2738	376	62	,	,	PUNCT
cana-2738	376	63	1x4	1x4	NUM
cana-2738	376	64	,	,	PUNCT
cana-2738	376	65	a2	a2	PROPN
cana-2738	376	66	c	c	NOUN
cana-2738	376	67	}	}	PUNCT
cana-2738	376	68	and	and	CCONJ
cana-2738	376	69	τ5	τ5	NOUN
cana-2738	376	70	=	=	SYM
cana-2738	376	71	{	{	PUNCT
cana-2738	376	72	0x5	0x5	NUM
cana-2738	376	73	,	,	PUNCT
cana-2738	376	74	1x5	1x5	NUM
cana-2738	376	75	,	,	PUNCT
cana-2738	376	76	a3	a3	NOUN
cana-2738	376	77	}	}	PUNCT
cana-2738	376	78	be	be	VERB
cana-2738	376	79	a	a	DET
cana-2738	376	80	pfts	pft	NOUN
cana-2738	376	81	’s	’s	NOUN
cana-2738	376	82	on	on	ADP
cana-2738	376	83	x.	x.	NOUN
cana-2738	376	84	let	let	VERB
cana-2738	376	85	h1p	h1p	NOUN
cana-2738	376	86	:	:	PUNCT
cana-2738	376	87	(	(	PUNCT
cana-2738	376	88	x2	x2	PROPN
cana-2738	376	89	,	,	PUNCT
cana-2738	376	90	τ2	τ2	PROPN
cana-2738	376	91	)	)	PUNCT
cana-2738	376	92	→	→	SYM
cana-2738	376	93	(	(	PUNCT
cana-2738	376	94	x1	x1	ADJ
cana-2738	376	95	,	,	PUNCT
cana-2738	376	96	τ1	τ1	NOUN
cana-2738	376	97	)	)	PUNCT
cana-2738	376	98	,	,	PUNCT
cana-2738	376	99	h2p	h2p	PROPN
cana-2738	376	100	:	:	PUNCT
cana-2738	376	101	(	(	PUNCT
cana-2738	376	102	x3	x3	ADJ
cana-2738	376	103	,	,	PUNCT
cana-2738	376	104	τ3	τ3	NOUN
cana-2738	376	105	)	)	PUNCT
cana-2738	376	106	→	→	SYM
cana-2738	376	107	(	(	PUNCT
cana-2738	376	108	x1	x1	ADJ
cana-2738	376	109	,	,	PUNCT
cana-2738	376	110	τ1	τ1	NOUN
cana-2738	376	111	)	)	PUNCT
cana-2738	376	112	,	,	PUNCT
cana-2738	376	113	h3p	h3p	PROPN
cana-2738	376	114	:	:	PUNCT
cana-2738	376	115	(	(	PUNCT
cana-2738	376	116	x4	x4	PROPN
cana-2738	376	117	,	,	PUNCT
cana-2738	376	118	τ4	τ4	PROPN
cana-2738	376	119	)	)	PUNCT
cana-2738	376	120	→	→	PUNCT
cana-2738	376	121	(	(	PUNCT
cana-2738	376	122	x1	x1	ADJ
cana-2738	376	123	,	,	PUNCT
cana-2738	376	124	τ1	τ1	NOUN
cana-2738	376	125	)	)	PUNCT
cana-2738	376	126	,	,	PUNCT
cana-2738	376	127	h4p	h4p	PROPN
cana-2738	376	128	:	:	PUNCT
cana-2738	376	129	(	(	PUNCT
cana-2738	376	130	x5	x5	NOUN
cana-2738	376	131	,	,	PUNCT
cana-2738	376	132	τ5	τ5	NUM
cana-2738	376	133	)	)	PUNCT
cana-2738	376	134	→	→	SYM
cana-2738	376	135	(	(	PUNCT
cana-2738	376	136	x1	x1	ADJ
cana-2738	376	137	,	,	PUNCT
cana-2738	376	138	τ1	τ1	NOUN
cana-2738	376	139	)	)	PUNCT
cana-2738	376	140	be	be	VERB
cana-2738	376	141	an	an	DET
cana-2738	376	142	identity	identity	NOUN
cana-2738	376	143	mapping	mapping	NOUN
cana-2738	376	144	.	.	PUNCT
cana-2738	377	1	then	then	ADV
cana-2738	377	2	[	[	X
cana-2738	377	3	(	(	PUNCT
cana-2738	377	4	i	i	NOUN
cana-2738	377	5	)	)	PUNCT
cana-2738	377	6	]	]	PUNCT
cana-2738	377	7	1	1	X
cana-2738	377	8	.	.	X
cana-2738	377	9	h1p	h1p	NOUN
cana-2738	377	10	is	be	AUX
cana-2738	377	11	pfc	pfc	NOUN
cana-2738	377	12	(	(	PUNCT
cana-2738	377	13	resp	resp	NOUN
cana-2738	377	14	.	.	PUNCT
cana-2738	378	1	pfδβc	pfδβc	PROPN
cana-2738	378	2	and	and	CCONJ
cana-2738	378	3	pfδ𝒫c	pfδ𝒫c	PROPN
cana-2738	378	4	)	)	PUNCT
cana-2738	378	5	but	but	CCONJ
cana-2738	378	6	not	not	PART
cana-2738	378	7	pfδc	pfδc	NOUN
cana-2738	378	8	(	(	PUNCT
cana-2738	378	9	resp	resp	NOUN
cana-2738	378	10	.	.	PUNCT
cana-2738	379	1	pfδ𝒮c	pfδ𝒮c	ADJ
cana-2738	379	2	and	and	CCONJ
cana-2738	379	3	pfδαc	pfδαc	NOUN
cana-2738	379	4	)	)	PUNCT
cana-2738	379	5	,	,	PUNCT
cana-2738	379	6	because	because	SCONJ
cana-2738	379	7	the	the	DET
cana-2738	379	8	set	set	NOUN
cana-2738	379	9	a2	a2	PROPN
cana-2738	379	10	c	c	PROPN
cana-2738	379	11	is	be	AUX
cana-2738	379	12	a	a	DET
cana-2738	379	13	pfcs	pfcs	NOUN
cana-2738	379	14	in	in	ADP
cana-2738	379	15	x2	x2	PROPN
cana-2738	380	1	but	but	CCONJ
cana-2738	380	2	h1p(a2	h1p(a2	NOUN
cana-2738	380	3	c	c	NOUN
cana-2738	380	4	)	)	PUNCT
cana-2738	380	5	=	=	SYM
cana-2738	380	6	a2	a2	PROPN
cana-2738	380	7	c	c	PROPN
cana-2738	380	8	is	be	AUX
cana-2738	380	9	not	not	PART
cana-2738	380	10	pfδcs	pfδcs	NOUN
cana-2738	380	11	(	(	PUNCT
cana-2738	380	12	resp	resp	NOUN
cana-2738	380	13	.	.	PUNCT
cana-2738	381	1	pfδ𝒮cs	pfδ𝒮cs	PROPN
cana-2738	381	2	and	and	CCONJ
cana-2738	381	3	pfδαcs	pfδαcs	NOUN
cana-2738	381	4	)	)	PUNCT
cana-2738	381	5	in	in	ADP
cana-2738	381	6	x1	x1	PROPN
cana-2738	381	7	.	.	PROPN
cana-2738	382	1	2	2	X
cana-2738	382	2	.	.	X
cana-2738	382	3	h2p	h2p	PROPN
cana-2738	382	4	is	be	AUX
cana-2738	382	5	pfδ𝒮c	pfδ𝒮c	ADJ
cana-2738	382	6	but	but	CCONJ
cana-2738	382	7	not	not	PART
cana-2738	382	8	pfδc	pfδc	VERB
cana-2738	382	9	,	,	PUNCT
cana-2738	382	10	because	because	SCONJ
cana-2738	382	11	the	the	DET
cana-2738	382	12	set	set	NOUN
cana-2738	382	13	a1	a1	NOUN
cana-2738	382	14	is	be	AUX
cana-2738	382	15	a	a	DET
cana-2738	382	16	pfcs	pfcs	NOUN
cana-2738	382	17	x3	x3	ADJ
cana-2738	382	18	but	but	CCONJ
cana-2738	382	19	h2p(a1	h2p(a1	NOUN
cana-2738	382	20	)	)	PUNCT
cana-2738	383	1	=	=	NOUN
cana-2738	383	2	a1	a1	NOUN
cana-2738	383	3	is	be	AUX
cana-2738	383	4	not	not	PART
cana-2738	383	5	pfδcs	pfδc	NOUN
cana-2738	383	6	in	in	ADP
cana-2738	383	7	x1	x1	PROPN
cana-2738	383	8	.	.	PUNCT
cana-2738	384	1	3	3	X
cana-2738	384	2	.	.	X
cana-2738	384	3	h3p	h3p	PRON
cana-2738	384	4	is	be	AUX
cana-2738	384	5	pfδ𝒫c	pfδ𝒫c	PROPN
cana-2738	384	6	but	but	CCONJ
cana-2738	384	7	not	not	PART
cana-2738	384	8	pfδc	pfδc	NOUN
cana-2738	384	9	,	,	PUNCT
cana-2738	384	10	because	because	SCONJ
cana-2738	384	11	the	the	DET
cana-2738	384	12	set	set	NOUN
cana-2738	384	13	a2	a2	PROPN
cana-2738	384	14	is	be	AUX
cana-2738	384	15	a	a	DET
cana-2738	384	16	pfcs	pfc	NOUN
cana-2738	385	1	x4	x4	PROPN
cana-2738	385	2	but	but	CCONJ
cana-2738	385	3	h3p(a2	h3p(a2	PROPN
cana-2738	385	4	)	)	PUNCT
cana-2738	385	5	=	=	PROPN
cana-2738	385	6	a2	a2	PROPN
cana-2738	385	7	is	be	AUX
cana-2738	385	8	not	not	PART
cana-2738	385	9	pfδ𝒫cs	pfδ𝒫cs	ADJ
cana-2738	385	10	in	in	ADP
cana-2738	385	11	x1	x1	PROPN
cana-2738	385	12	.	.	PUNCT
cana-2738	386	1	4	4	X
cana-2738	386	2	.	.	X
cana-2738	386	3	h4p	h4p	PROPN
cana-2738	386	4	is	be	AUX
cana-2738	386	5	pfδβc	pfδβc	NOUN
cana-2738	386	6	(	(	PUNCT
cana-2738	386	7	resp	resp	NOUN
cana-2738	386	8	.	.	PUNCT
cana-2738	387	1	pfδ𝒮c	pfδ𝒮c	ADJ
cana-2738	387	2	)	)	PUNCT
cana-2738	388	1	but	but	CCONJ
cana-2738	388	2	not	not	PART
cana-2738	388	3	pfδ𝒫c	pfδ𝒫c	PROPN
cana-2738	388	4	(	(	PUNCT
cana-2738	388	5	resp	resp	NOUN
cana-2738	388	6	.	.	PUNCT
cana-2738	389	1	pfδαc	pfδαc	NOUN
cana-2738	389	2	)	)	PUNCT
cana-2738	389	3	,	,	PUNCT
cana-2738	389	4	because	because	SCONJ
cana-2738	389	5	the	the	DET
cana-2738	389	6	set	set	NOUN
cana-2738	389	7	a3	a3	NOUN
cana-2738	389	8	c	c	PROPN
cana-2738	389	9	is	be	AUX
cana-2738	389	10	a	a	DET
cana-2738	389	11	pfcs	pfcs	NOUN
cana-2738	389	12	in	in	ADP
cana-2738	389	13	x5	x5	PROPN
cana-2738	389	14	but	but	CCONJ
cana-2738	389	15	h4(a3	h4(a3	NOUN
cana-2738	389	16	c	c	NOUN
cana-2738	389	17	)	)	PUNCT
cana-2738	389	18	=	=	NOUN
cana-2738	389	19	a3	a3	NOUN
cana-2738	389	20	c	c	NOUN
cana-2738	389	21	is	be	AUX
cana-2738	389	22	not	not	PART
cana-2738	389	23	pfδ𝒫cs	pfδ𝒫cs	ADJ
cana-2738	389	24	(	(	PUNCT
cana-2738	389	25	resp	resp	NOUN
cana-2738	389	26	.	.	PUNCT
cana-2738	390	1	pfδαcs	pfδαcs	PROPN
cana-2738	390	2	)	)	PUNCT
cana-2738	390	3	in	in	ADP
cana-2738	390	4	x1	x1	PROPN
cana-2738	390	5	.	.	PUNCT
cana-2738	391	1	fig	fig	NOUN
cana-2738	391	2	.	.	PUNCT
cana-2738	392	1	2	2	NUM
cana-2738	392	2	:	:	PUNCT
cana-2738	392	3	𝑝𝑓𝛿𝐶	𝑝𝑓𝛿𝐶	ADJ
cana-2738	392	4	mappings	mapping	NOUN
cana-2738	392	5	in	in	ADP
cana-2738	392	6	𝑝𝑓𝑡𝑠.	𝑝𝑓𝑡𝑠.	PROPN
cana-2738	392	7	theorem	theorem	VERB
cana-2738	392	8	4.2	4.2	NUM
cana-2738	392	9	let	let	VERB
cana-2738	392	10	(	(	PUNCT
cana-2738	392	11	x1	x1	PROPN
cana-2738	392	12	,	,	PUNCT
cana-2738	392	13	γp	γp	PROPN
cana-2738	392	14	)	)	PUNCT
cana-2738	392	15	&	&	CCONJ
cana-2738	392	16	(	(	PUNCT
cana-2738	392	17	x2	x2	PROPN
cana-2738	392	18	,	,	PUNCT
cana-2738	392	19	ψp	ψp	PRON
cana-2738	392	20	)	)	PUNCT
cana-2738	392	21	be	be	VERB
cana-2738	392	22	any	any	DET
cana-2738	392	23	pfts	pft	NOUN
cana-2738	392	24	’s	’s	PART
cana-2738	392	25	.	.	PUNCT
cana-2738	393	1	a	a	DET
cana-2738	393	2	mapping	mapping	NOUN
cana-2738	393	3	hp	hp	NOUN
cana-2738	393	4	:	:	PUNCT
cana-2738	393	5	(	(	PUNCT
cana-2738	393	6	x1	x1	PROPN
cana-2738	393	7	,	,	PUNCT
cana-2738	393	8	γp	γp	PROPN
cana-2738	393	9	)	)	PUNCT
cana-2738	393	10	→	→	SYM
cana-2738	393	11	(	(	PUNCT
cana-2738	393	12	x2	x2	PROPN
cana-2738	393	13	,	,	PUNCT
cana-2738	393	14	ψp	ψp	NOUN
cana-2738	393	15	)	)	PUNCT
cana-2738	393	16	is	be	AUX
cana-2738	393	17	pfδβc	pfδβc	ADJ
cana-2738	393	18	iff	iff	PROPN
cana-2738	393	19	for	for	ADP
cana-2738	393	20	each	each	DET
cana-2738	393	21	pfs	pfs	PROPN
cana-2738	393	22	μ	μ	PROPN
cana-2738	393	23	of	of	ADP
cana-2738	393	24	(	(	PUNCT
cana-2738	393	25	x2	x2	PROPN
cana-2738	393	26	,	,	PUNCT
cana-2738	393	27	ψp	ψp	NOUN
cana-2738	393	28	)	)	PUNCT
cana-2738	393	29	and	and	CCONJ
cana-2738	393	30	for	for	ADP
cana-2738	393	31	each	each	DET
cana-2738	393	32	pfos	pfos	NOUN
cana-2738	393	33	m	m	NOUN
cana-2738	393	34	of	of	ADP
cana-2738	393	35	(	(	PUNCT
cana-2738	393	36	x1	x1	PROPN
cana-2738	393	37	,	,	PUNCT
cana-2738	393	38	γp	γp	NOUN
cana-2738	393	39	)	)	PUNCT
cana-2738	393	40	containing	contain	VERB
cana-2738	393	41	hp	hp	PROPN
cana-2738	393	42	−1(μ	−1(μ	PROPN
cana-2738	393	43	)	)	PUNCT
cana-2738	393	44	there	there	PRON
cana-2738	393	45	is	be	VERB
cana-2738	393	46	an	an	DET
cana-2738	393	47	pfδβos	pfδβos	NOUN
cana-2738	393	48	ψ	ψ	X
cana-2738	393	49	of	of	ADP
cana-2738	393	50	(	(	PUNCT
cana-2738	393	51	x2	x2	PROPN
cana-2738	393	52	,	,	PUNCT
cana-2738	393	53	ψp	ψp	NOUN
cana-2738	393	54	)	)	PUNCT
cana-2738	393	55	such	such	ADJ
cana-2738	393	56	that	that	SCONJ
cana-2738	393	57	μ	μ	PROPN
cana-2738	393	58	⊆	⊆	NUM
cana-2738	393	59	ψ	ψ	NOUN
cana-2738	393	60	and	and	CCONJ
cana-2738	393	61	hp	hp	PROPN
cana-2738	393	62	−1(ψ	−1(ψ	NOUN
cana-2738	393	63	)	)	PUNCT
cana-2738	393	64	⊆	⊆	NUM
cana-2738	393	65	m.	m.	NOUN
cana-2738	393	66	proof	proof	NOUN
cana-2738	393	67	.	.	PUNCT
cana-2738	394	1	necessity	necessity	NOUN
cana-2738	394	2	:	:	PUNCT
cana-2738	394	3	assume	assume	VERB
cana-2738	394	4	hp	hp	PROPN
cana-2738	394	5	is	be	AUX
cana-2738	394	6	a	a	DET
cana-2738	394	7	pfδβc	pfδβc	NOUN
cana-2738	394	8	.	.	PUNCT
cana-2738	395	1	let	let	VERB
cana-2738	395	2	μ	μ	NOUN
cana-2738	395	3	be	be	AUX
cana-2738	395	4	the	the	DET
cana-2738	395	5	pfcs	pfc	NOUN
cana-2738	395	6	of	of	ADP
cana-2738	395	7	(	(	PUNCT
cana-2738	395	8	x2	x2	INTJ
cana-2738	395	9	,	,	PUNCT
cana-2738	395	10	ψp	ψp	NOUN
cana-2738	395	11	)	)	PUNCT
cana-2738	395	12	and	and	CCONJ
cana-2738	395	13	m	m	PROPN
cana-2738	395	14	is	be	AUX
cana-2738	395	15	a	a	DET
cana-2738	395	16	pfos	pfos	NOUN
cana-2738	395	17	of	of	ADP
cana-2738	395	18	(	(	PUNCT
cana-2738	395	19	x1	x1	PROPN
cana-2738	395	20	,	,	PUNCT
cana-2738	395	21	γp	γp	NOUN
cana-2738	395	22	)	)	PUNCT
cana-2738	396	1	such	such	ADJ
cana-2738	396	2	that	that	PRON
cana-2738	396	3	hp	hp	PROPN
cana-2738	396	4	−1(μ	−1(μ	PROPN
cana-2738	396	5	)	)	PUNCT
cana-2738	396	6	⊆	⊆	NUM
cana-2738	396	7	m.	m.	NOUN
cana-2738	396	8	then	then	ADV
cana-2738	396	9	ψ	ψ	ADP
cana-2738	396	10	=	=	SYM
cana-2738	396	11	y	y	PROPN
cana-2738	396	12	−	−	PROPN
cana-2738	396	13	hp	hp	PROPN
cana-2738	396	14	−1(mc	−1(mc	VERB
cana-2738	396	15	)	)	PUNCT
cana-2738	396	16	is	be	AUX
cana-2738	396	17	pfδβos	pfδβos	NOUN
cana-2738	396	18	of	of	ADP
cana-2738	396	19	(	(	PUNCT
cana-2738	396	20	x2	x2	PROPN
cana-2738	396	21	,	,	PUNCT
cana-2738	396	22	ψp	ψp	NOUN
cana-2738	396	23	)	)	PUNCT
cana-2738	396	24	such	such	ADJ
cana-2738	396	25	that	that	PRON
cana-2738	396	26	hp	hp	ADJ
cana-2738	396	27	−1(ψ	−1(ψ	NOUN
cana-2738	396	28	)	)	PUNCT
cana-2738	396	29	⊆	⊆	NUM
cana-2738	396	30	m.	m.	NOUN
cana-2738	396	31	sufficiency	sufficiency	NOUN
cana-2738	396	32	:	:	PUNCT
cana-2738	396	33	assume	assume	VERB
cana-2738	396	34	ψ	ψ	SYM
cana-2738	396	35	is	be	AUX
cana-2738	396	36	a	a	DET
cana-2738	396	37	pfcs	pfcs	NOUN
cana-2738	396	38	of	of	ADP
cana-2738	396	39	(	(	PUNCT
cana-2738	396	40	x1	x1	PROPN
cana-2738	396	41	,	,	PUNCT
cana-2738	396	42	γp	γp	PROPN
cana-2738	396	43	)	)	PUNCT
cana-2738	396	44	.	.	PUNCT
cana-2738	397	1	then	then	ADV
cana-2738	397	2	(	(	PUNCT
cana-2738	397	3	hp(ψ))c	hp(ψ))c	X
cana-2738	397	4	is	be	AUX
cana-2738	397	5	a	a	DET
cana-2738	397	6	pfs	pfs	NOUN
cana-2738	397	7	of	of	ADP
cana-2738	397	8	(	(	PUNCT
cana-2738	397	9	x2	x2	PROPN
cana-2738	397	10	,	,	PUNCT
cana-2738	397	11	ψp	ψp	NOUN
cana-2738	397	12	)	)	PUNCT
cana-2738	397	13	and	and	CCONJ
cana-2738	397	14	ψc	ψc	PRON
cana-2738	397	15	is	be	AUX
cana-2738	397	16	pfos	pfos	NOUN
cana-2738	397	17	in	in	ADP
cana-2738	397	18	(	(	PUNCT
cana-2738	397	19	x1	x1	PROPN
cana-2738	397	20	,	,	PUNCT
cana-2738	397	21	γp	γp	NOUN
cana-2738	397	22	)	)	PUNCT
cana-2738	397	23	such	such	ADJ
cana-2738	397	24	that	that	SCONJ
cana-2738	397	25	hp	hp	PROPN
cana-2738	397	26	−1((hp(ψ))c	−1((hp(ψ))c	PROPN
cana-2738	397	27	)	)	PUNCT
cana-2738	397	28	⊆	⊆	NUM
cana-2738	397	29	ψc	ψc	NOUN
cana-2738	397	30	.	.	PUNCT
cana-2738	398	1	by	by	ADP
cana-2738	398	2	hypothesis	hypothesis	NOUN
cana-2738	398	3	there	there	PRON
cana-2738	398	4	is	be	VERB
cana-2738	398	5	a	a	DET
cana-2738	398	6	pfδβos	pfδβos	NOUN
cana-2738	398	7	ψ	ψ	X
cana-2738	398	8	of	of	ADP
cana-2738	398	9	(	(	PUNCT
cana-2738	398	10	x2	x2	PROPN
cana-2738	398	11	,	,	PUNCT
cana-2738	398	12	ψp	ψp	NOUN
cana-2738	398	13	)	)	PUNCT
cana-2738	398	14	such	such	ADJ
cana-2738	398	15	that	that	SCONJ
cana-2738	398	16	(	(	PUNCT
cana-2738	398	17	hp(ψ))c	hp(ψ))c	X
cana-2738	398	18	⊆	⊆	NUM
cana-2738	398	19	ψ	ψ	NOUN
cana-2738	398	20	and	and	CCONJ
cana-2738	398	21	hp	hp	PROPN
cana-2738	398	22	−1(ψ	−1(ψ	NOUN
cana-2738	398	23	)	)	PUNCT
cana-2738	398	24	⊆	⊆	NUM
cana-2738	398	25	ψc	ψc	NOUN
cana-2738	398	26	.	.	PUNCT
cana-2738	399	1	therefore	therefore	ADV
cana-2738	399	2	ψ	ψ	X
cana-2738	399	3	⊆	⊆	NUM
cana-2738	399	4	(	(	PUNCT
cana-2738	399	5	hp	hp	PROPN
cana-2738	399	6	−1(ψ))c	−1(ψ))c	PROPN
cana-2738	399	7	.	.	PUNCT
cana-2738	400	1	hence	hence	ADV
cana-2738	400	2	ψc	ψc	VERB
cana-2738	400	3	⊆	⊆	NUM
cana-2738	400	4	hp(ψ	hp(ψ	NOUN
cana-2738	400	5	)	)	PUNCT
cana-2738	400	6	⊆	⊆	NUM
cana-2738	400	7	hp((hp	hp((hp	VERB
cana-2738	400	8	−1(ψ))c	−1(ψ))c	PROPN
cana-2738	400	9	)	)	PUNCT
cana-2738	400	10	⊆	⊆	NUM
cana-2738	400	11	ψc	ψc	ADP
cana-2738	400	12	which	which	PRON
cana-2738	400	13	implies	imply	VERB
cana-2738	400	14	hp(ψ	hp(ψ	NOUN
cana-2738	400	15	)	)	PUNCT
cana-2738	400	16	=	=	SYM
cana-2738	400	17	ψc	ψc	VERB
cana-2738	400	18	.	.	PUNCT
cana-2738	401	1	since	since	SCONJ
cana-2738	401	2	ψc	ψc	NOUN
cana-2738	401	3	is	be	AUX
cana-2738	401	4	pfδβcs	pfδβc	VERB
cana-2738	401	5	of	of	ADP
cana-2738	401	6	(	(	PUNCT
cana-2738	401	7	x2	x2	PROPN
cana-2738	401	8	,	,	PUNCT
cana-2738	401	9	ψp	ψp	NOUN
cana-2738	401	10	)	)	PUNCT
cana-2738	401	11	.	.	PUNCT
cana-2738	402	1	hence	hence	ADV
cana-2738	402	2	hp(ψ	hp(ψ	NOUN
cana-2738	402	3	)	)	PUNCT
cana-2738	402	4	is	be	AUX
cana-2738	402	5	pfδβc	pfδβc	ADJ
cana-2738	402	6	in	in	ADP
cana-2738	402	7	(	(	PUNCT
cana-2738	402	8	x2	x2	INTJ
cana-2738	402	9	,	,	PUNCT
cana-2738	402	10	ψp	ψp	NOUN
cana-2738	402	11	)	)	PUNCT
cana-2738	402	12	and	and	CCONJ
cana-2738	402	13	thus	thus	ADV
cana-2738	402	14	hp	hp	PROPN
cana-2738	402	15	is	be	AUX
cana-2738	402	16	pfδβc	pfδβc	NOUN
cana-2738	402	17	.	.	PUNCT
cana-2738	403	1	theorem	theorem	VERB
cana-2738	403	2	4.3	4.3	NUM
cana-2738	403	3	let	let	VERB
cana-2738	403	4	(	(	PUNCT
cana-2738	403	5	x1	x1	PROPN
cana-2738	403	6	,	,	PUNCT
cana-2738	403	7	γp	γp	PROPN
cana-2738	403	8	)	)	PUNCT
cana-2738	403	9	,	,	PUNCT
cana-2738	403	10	(	(	PUNCT
cana-2738	403	11	x2	x2	INTJ
cana-2738	403	12	,	,	PUNCT
cana-2738	403	13	ψp	ψp	PROPN
cana-2738	403	14	)	)	PUNCT
cana-2738	403	15	&	&	CCONJ
cana-2738	403	16	(	(	PUNCT
cana-2738	403	17	x3	x3	PROPN
cana-2738	403	18	,	,	PUNCT
cana-2738	403	19	φp	φp	NOUN
cana-2738	403	20	)	)	PUNCT
cana-2738	403	21	be	be	VERB
cana-2738	403	22	any	any	DET
cana-2738	403	23	pfts	pft	NOUN
cana-2738	403	24	’s	’s	PART
cana-2738	403	25	.	.	PUNCT
cana-2738	404	1	if	if	SCONJ
cana-2738	404	2	hp	hp	VERB
cana-2738	404	3	:	:	PUNCT
cana-2738	404	4	(	(	PUNCT
cana-2738	404	5	x1	x1	PROPN
cana-2738	404	6	,	,	PUNCT
cana-2738	404	7	γp	γp	PROPN
cana-2738	404	8	)	)	PUNCT
cana-2738	404	9	→	→	SYM
cana-2738	404	10	(	(	PUNCT
cana-2738	404	11	x2	x2	PROPN
cana-2738	404	12	,	,	PUNCT
cana-2738	404	13	ψp	ψp	NOUN
cana-2738	404	14	)	)	PUNCT
cana-2738	404	15	is	be	AUX
cana-2738	404	16	pfc	pfc	NOUN
cana-2738	404	17	and	and	CCONJ
cana-2738	404	18	g	g	PROPN
cana-2738	404	19	p	p	X
cana-2738	404	20	:	:	PUNCT
cana-2738	404	21	(	(	PUNCT
cana-2738	404	22	x2	x2	ADJ
cana-2738	404	23	,	,	PUNCT
cana-2738	404	24	ψp	ψp	NOUN
cana-2738	404	25	)	)	PUNCT
cana-2738	404	26	→	→	SYM
cana-2738	404	27	(	(	PUNCT
cana-2738	404	28	x3	x3	ADJ
cana-2738	404	29	,	,	PUNCT
cana-2738	404	30	φp	φp	NOUN
cana-2738	404	31	)	)	PUNCT
cana-2738	404	32	is	be	AUX
cana-2738	404	33	pfδβc	pfδβc	NOUN
cana-2738	404	34	,	,	PUNCT
cana-2738	404	35	then	then	ADV
cana-2738	404	36	g	g	PROPN
cana-2738	404	37	p	p	PROPN
cana-2738	404	38	∘	∘	PROPN
cana-2738	404	39	hp	hp	PROPN
cana-2738	404	40	:	:	PUNCT
cana-2738	404	41	(	(	PUNCT
cana-2738	404	42	x1	x1	PROPN
cana-2738	404	43	,	,	PUNCT
cana-2738	404	44	γp	γp	PROPN
cana-2738	404	45	)	)	PUNCT
cana-2738	404	46	→	→	SYM
cana-2738	404	47	(	(	PUNCT
cana-2738	404	48	x3	x3	ADJ
cana-2738	404	49	,	,	PUNCT
cana-2738	404	50	φp	φp	NOUN
cana-2738	404	51	)	)	PUNCT
cana-2738	404	52	is	be	AUX
cana-2738	404	53	pfδβc	pfδβc	NOUN
cana-2738	404	54	.	.	PUNCT
cana-2738	405	1	proof	proof	NOUN
cana-2738	405	2	.	.	PUNCT
cana-2738	406	1	let	let	VERB
cana-2738	406	2	ψ	ψ	PART
cana-2738	406	3	be	be	AUX
cana-2738	406	4	a	a	DET
cana-2738	406	5	pfcs	pfcs	NOUN
cana-2738	406	6	in	in	ADP
cana-2738	406	7	(	(	PUNCT
cana-2738	406	8	x1	x1	PROPN
cana-2738	406	9	,	,	PUNCT
cana-2738	406	10	γp	γp	PROPN
cana-2738	406	11	)	)	PUNCT
cana-2738	406	12	.	.	PUNCT
cana-2738	407	1	then	then	ADV
cana-2738	407	2	hp(ψ	hp(ψ	NOUN
cana-2738	407	3	)	)	PUNCT
cana-2738	407	4	is	be	AUX
cana-2738	407	5	pfcs	pfc	VERB
cana-2738	407	6	of	of	ADP
cana-2738	407	7	(	(	PUNCT
cana-2738	407	8	x2	x2	INTJ
cana-2738	407	9	,	,	PUNCT
cana-2738	407	10	ψp	ψp	NOUN
cana-2738	407	11	)	)	PUNCT
cana-2738	407	12	because	because	SCONJ
cana-2738	407	13	hp	hp	PROPN
cana-2738	407	14	is	be	AUX
cana-2738	407	15	pfc	pfc	NOUN
cana-2738	407	16	.	.	PUNCT
cana-2738	408	1	now	now	ADV
cana-2738	408	2	(	(	PUNCT
cana-2738	408	3	g	g	PROPN
cana-2738	408	4	p	p	PROPN
cana-2738	408	5	∘	∘	PROPN
cana-2738	408	6	hp)(ψ	hp)(ψ	PROPN
cana-2738	408	7	)	)	PUNCT
cana-2738	409	1	=	=	PUNCT
cana-2738	410	1	g	g	PROPN
cana-2738	410	2	p	p	X
cana-2738	410	3	(	(	PUNCT
cana-2738	410	4	hp(ψ	hp(ψ	NOUN
cana-2738	410	5	)	)	PUNCT
cana-2738	410	6	)	)	PUNCT
cana-2738	410	7	is	be	AUX
cana-2738	410	8	pfδβcs	pfδβc	VERB
cana-2738	410	9	in	in	ADP
cana-2738	410	10	(	(	PUNCT
cana-2738	410	11	x3	x3	ADJ
cana-2738	410	12	,	,	PUNCT
cana-2738	410	13	φp	φp	ADP
cana-2738	410	14	)	)	PUNCT
cana-2738	410	15	because	because	SCONJ
cana-2738	410	16	g	g	PROPN
cana-2738	410	17	p	p	PROPN
cana-2738	410	18	is	be	AUX
cana-2738	410	19	pfδβc	pfδβc	ADJ
cana-2738	410	20	.	.	PUNCT
cana-2738	411	1	thus	thus	ADV
cana-2738	411	2	g	g	ADP
cana-2738	411	3	p	p	PROPN
cana-2738	411	4	∘	∘	PROPN
cana-2738	411	5	hp	hp	PROPN
cana-2738	411	6	is	be	AUX
cana-2738	411	7	pfδβc	pfδβc	NOUN
cana-2738	411	8	.	.	PUNCT
cana-2738	412	1	communications	communication	NOUN
cana-2738	412	2	on	on	ADP
cana-2738	412	3	applied	apply	VERB
cana-2738	412	4	nonlinear	nonlinear	ADJ
cana-2738	412	5	analysis	analysis	NOUN
cana-2738	412	6	issn	issn	NOUN
cana-2738	412	7	:	:	PUNCT
cana-2738	412	8	1074	1074	NUM
cana-2738	412	9	-	-	PUNCT
cana-2738	412	10	133x	133x	NUM
cana-2738	412	11	vol	vol	NOUN
cana-2738	412	12	32	32	NUM
cana-2738	412	13	no	no	NOUN
cana-2738	412	14	.	.	PUNCT
cana-2738	413	1	4s	4s	NUM
cana-2738	413	2	(	(	PUNCT
cana-2738	413	3	2025	2025	NUM
cana-2738	413	4	)	)	PUNCT
cana-2738	413	5	53	53	NUM
cana-2738	413	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2738	413	7	theorem	theorem	VERB
cana-2738	413	8	4.4	4.4	NUM
cana-2738	413	9	let	let	VERB
cana-2738	413	10	(	(	PUNCT
cana-2738	413	11	x1	x1	PROPN
cana-2738	413	12	,	,	PUNCT
cana-2738	413	13	γp	γp	PROPN
cana-2738	413	14	)	)	PUNCT
cana-2738	413	15	&	&	CCONJ
cana-2738	413	16	(	(	PUNCT
cana-2738	413	17	x2	x2	PROPN
cana-2738	413	18	,	,	PUNCT
cana-2738	413	19	ψp	ψp	PRON
cana-2738	413	20	)	)	PUNCT
cana-2738	413	21	be	be	VERB
cana-2738	413	22	any	any	DET
cana-2738	413	23	pfts	pft	NOUN
cana-2738	413	24	’s	’s	PART
cana-2738	413	25	.	.	PUNCT
cana-2738	414	1	if	if	SCONJ
cana-2738	414	2	hp	hp	VERB
cana-2738	414	3	:	:	PUNCT
cana-2738	414	4	(	(	PUNCT
cana-2738	414	5	x1	x1	PROPN
cana-2738	414	6	,	,	PUNCT
cana-2738	414	7	γp	γp	PROPN
cana-2738	414	8	)	)	PUNCT
cana-2738	414	9	→	→	SYM
cana-2738	414	10	(	(	PUNCT
cana-2738	414	11	x2	x2	PROPN
cana-2738	414	12	,	,	PUNCT
cana-2738	414	13	ψp	ψp	NOUN
cana-2738	414	14	)	)	PUNCT
cana-2738	414	15	is	be	AUX
cana-2738	414	16	pfδβc	pfδβc	NOUN
cana-2738	414	17	,	,	PUNCT
cana-2738	414	18	then	then	ADV
cana-2738	414	19	pfδβcl(hp(ψ	pfδβcl(hp(ψ	ADV
cana-2738	414	20	)	)	PUNCT
cana-2738	414	21	)	)	PUNCT
cana-2738	415	1	⊊	⊊	VERB
cana-2738	415	2	hp(pfcl(ψ	hp(pfcl(ψ	PROPN
cana-2738	415	3	)	)	PUNCT
cana-2738	415	4	)	)	PUNCT
cana-2738	415	5	.	.	PUNCT
cana-2738	416	1	proof	proof	NOUN
cana-2738	416	2	.	.	PUNCT
cana-2738	417	1	necessity	necessity	NOUN
cana-2738	417	2	:	:	PUNCT
cana-2738	417	3	let	let	VERB
cana-2738	417	4	hp	hp	PROPN
cana-2738	417	5	be	be	AUX
cana-2738	417	6	a	a	DET
cana-2738	417	7	pfδβc	pfδβc	NOUN
cana-2738	417	8	and	and	CCONJ
cana-2738	417	9	k	k	PROPN
cana-2738	417	10	be	be	AUX
cana-2738	417	11	a	a	DET
cana-2738	417	12	pfcs	pfcs	NOUN
cana-2738	417	13	in	in	ADP
cana-2738	417	14	(	(	PUNCT
cana-2738	417	15	x1	x1	PROPN
cana-2738	417	16	,	,	PUNCT
cana-2738	417	17	γp	γp	PROPN
cana-2738	417	18	)	)	PUNCT
cana-2738	417	19	.	.	PUNCT
cana-2738	418	1	now	now	ADV
cana-2738	418	2	,	,	PUNCT
cana-2738	418	3	k	k	PROPN
cana-2738	418	4	⊆	⊆	NUM
cana-2738	418	5	pfcl(k	pfcl(k	NOUN
cana-2738	418	6	)	)	PUNCT
cana-2738	418	7	implies	imply	VERB
cana-2738	418	8	hp(k	hp(k	NOUN
cana-2738	418	9	)	)	PUNCT
cana-2738	418	10	⊆	⊆	NUM
cana-2738	418	11	hp(pfcl(k	hp(pfcl(k	NUM
cana-2738	418	12	)	)	PUNCT
cana-2738	418	13	)	)	PUNCT
cana-2738	418	14	.	.	PUNCT
cana-2738	419	1	since	since	SCONJ
cana-2738	419	2	hp	hp	PROPN
cana-2738	419	3	is	be	AUX
cana-2738	419	4	a	a	DET
cana-2738	419	5	pfδβc	pfδβc	NOUN
cana-2738	419	6	,	,	PUNCT
cana-2738	419	7	(	(	PUNCT
cana-2738	419	8	pfδβcl(hp(k	pfδβcl(hp(k	NOUN
cana-2738	419	9	)	)	PUNCT
cana-2738	419	10	)	)	PUNCT
cana-2738	419	11	is	be	AUX
cana-2738	419	12	pfδβcs	pfδβc	VERB
cana-2738	419	13	in	in	ADP
cana-2738	419	14	(	(	PUNCT
cana-2738	419	15	x2	x2	INTJ
cana-2738	419	16	,	,	PUNCT
cana-2738	419	17	ψp	ψp	NOUN
cana-2738	419	18	)	)	PUNCT
cana-2738	419	19	such	such	ADJ
cana-2738	419	20	that	that	SCONJ
cana-2738	419	21	hp(k	hp(k	NOUN
cana-2738	419	22	)	)	PUNCT
cana-2738	419	23	⊆	⊆	NUM
cana-2738	419	24	pfδβcl(hp(k	pfδβcl(hp(k	NOUN
cana-2738	419	25	)	)	PUNCT
cana-2738	419	26	)	)	PUNCT
cana-2738	419	27	therefore	therefore	ADV
cana-2738	419	28	pfδβcl(hp(k	pfδβcl(hp(k	PROPN
cana-2738	419	29	)	)	PUNCT
cana-2738	419	30	)	)	PUNCT
cana-2738	420	1	⊆	⊆	NUM
cana-2738	420	2	hp(pfcl(k	hp(pfcl(k	NUM
cana-2738	420	3	)	)	PUNCT
cana-2738	420	4	)	)	PUNCT
cana-2738	420	5	.	.	PUNCT
cana-2738	421	1	sufficiency	sufficiency	NOUN
cana-2738	421	2	:	:	PUNCT
cana-2738	421	3	assume	assume	VERB
cana-2738	421	4	k	k	PROPN
cana-2738	421	5	is	be	AUX
cana-2738	421	6	a	a	DET
cana-2738	421	7	pfcs	pfcs	NOUN
cana-2738	421	8	of	of	ADP
cana-2738	421	9	(	(	PUNCT
cana-2738	421	10	x1	x1	PROPN
cana-2738	421	11	,	,	PUNCT
cana-2738	421	12	γp	γp	PROPN
cana-2738	421	13	)	)	PUNCT
cana-2738	421	14	.	.	PUNCT
cana-2738	422	1	then	then	ADV
cana-2738	422	2	hp(k	hp(k	NOUN
cana-2738	422	3	)	)	PUNCT
cana-2738	422	4	=	=	SYM
cana-2738	422	5	pfδβcl(hp(k	pfδβcl(hp(k	NOUN
cana-2738	422	6	)	)	PUNCT
cana-2738	422	7	)	)	PUNCT
cana-2738	423	1	⊆	⊆	NUM
cana-2738	423	2	hp(pfcl(k	hp(pfcl(k	NUM
cana-2738	423	3	)	)	PUNCT
cana-2738	423	4	)	)	PUNCT
cana-2738	423	5	.	.	PUNCT
cana-2738	424	1	but	but	CCONJ
cana-2738	424	2	hp(k	hp(k	NOUN
cana-2738	424	3	)	)	PUNCT
cana-2738	424	4	⊆	⊆	NUM
cana-2738	424	5	pfδβcl(hp(k	pfδβcl(hp(k	NOUN
cana-2738	424	6	)	)	PUNCT
cana-2738	424	7	)	)	PUNCT
cana-2738	424	8	.	.	PUNCT
cana-2738	425	1	so	so	ADV
cana-2738	425	2	hp(k	hp(k	NOUN
cana-2738	425	3	)	)	PUNCT
cana-2738	425	4	=	=	SYM
cana-2738	425	5	pfδβcl(k	pfδβcl(k	NOUN
cana-2738	425	6	)	)	PUNCT
cana-2738	425	7	which	which	PRON
cana-2738	425	8	implies	imply	VERB
cana-2738	425	9	hp(k	hp(k	NOUN
cana-2738	425	10	)	)	PUNCT
cana-2738	425	11	is	be	AUX
cana-2738	425	12	a	a	DET
cana-2738	425	13	pfδβcs	pfδβcs	NOUN
cana-2738	425	14	of	of	ADP
cana-2738	425	15	(	(	PUNCT
cana-2738	425	16	x2	x2	PROPN
cana-2738	425	17	,	,	PUNCT
cana-2738	425	18	ψp	ψp	NOUN
cana-2738	425	19	)	)	PUNCT
cana-2738	425	20	and	and	CCONJ
cana-2738	425	21	hence	hence	ADV
cana-2738	425	22	hp	hp	PROPN
cana-2738	425	23	is	be	AUX
cana-2738	425	24	a	a	DET
cana-2738	425	25	pfδβc	pfδβc	NOUN
cana-2738	425	26	.	.	PUNCT
cana-2738	426	1	theorem	theorem	VERB
cana-2738	426	2	4.5	4.5	NUM
cana-2738	426	3	let	let	VERB
cana-2738	426	4	hp	hp	NOUN
cana-2738	426	5	:	:	PUNCT
cana-2738	426	6	(	(	PUNCT
cana-2738	426	7	x1	x1	PROPN
cana-2738	426	8	,	,	PUNCT
cana-2738	426	9	γp	γp	PROPN
cana-2738	426	10	)	)	PUNCT
cana-2738	426	11	→	→	SYM
cana-2738	426	12	(	(	PUNCT
cana-2738	426	13	x2	x2	PROPN
cana-2738	426	14	,	,	PUNCT
cana-2738	426	15	ψp	ψp	NOUN
cana-2738	426	16	)	)	PUNCT
cana-2738	426	17	and	and	CCONJ
cana-2738	426	18	g	g	PROPN
cana-2738	426	19	p	p	X
cana-2738	426	20	:	:	PUNCT
cana-2738	426	21	(	(	PUNCT
cana-2738	426	22	x2	x2	ADJ
cana-2738	426	23	,	,	PUNCT
cana-2738	426	24	ψp	ψp	NOUN
cana-2738	426	25	)	)	PUNCT
cana-2738	426	26	→	→	SYM
cana-2738	426	27	(	(	PUNCT
cana-2738	426	28	x3	x3	ADJ
cana-2738	426	29	,	,	PUNCT
cana-2738	426	30	φp	φp	NOUN
cana-2738	426	31	)	)	PUNCT
cana-2738	426	32	be	be	AUX
cana-2738	426	33	pfδβc	pfδβc	NOUN
cana-2738	426	34	mappings	mapping	NOUN
cana-2738	426	35	.	.	PUNCT
cana-2738	427	1	if	if	SCONJ
cana-2738	427	2	every	every	DET
cana-2738	427	3	pfδβcs	pfδβcs	NOUN
cana-2738	427	4	of	of	ADP
cana-2738	427	5	(	(	PUNCT
cana-2738	427	6	x2	x2	PROPN
cana-2738	427	7	,	,	PUNCT
cana-2738	427	8	ψp	ψp	NOUN
cana-2738	427	9	)	)	PUNCT
cana-2738	427	10	is	be	AUX
cana-2738	427	11	pfc	pfc	NOUN
cana-2738	427	12	then	then	ADV
cana-2738	427	13	,	,	PUNCT
cana-2738	427	14	g	g	PROPN
cana-2738	427	15	p	p	PROPN
cana-2738	427	16	∘	∘	PROPN
cana-2738	427	17	hp	hp	PROPN
cana-2738	427	18	:	:	PUNCT
cana-2738	427	19	(	(	PUNCT
cana-2738	427	20	x1	x1	PROPN
cana-2738	427	21	,	,	PUNCT
cana-2738	427	22	γp	γp	PROPN
cana-2738	427	23	)	)	PUNCT
cana-2738	427	24	→	→	SYM
cana-2738	427	25	(	(	PUNCT
cana-2738	427	26	x3	x3	ADJ
cana-2738	427	27	,	,	PUNCT
cana-2738	427	28	φp	φp	NOUN
cana-2738	427	29	)	)	PUNCT
cana-2738	427	30	is	be	AUX
cana-2738	427	31	pfδβc	pfδβc	NOUN
cana-2738	427	32	.	.	PUNCT
cana-2738	428	1	proof	proof	NOUN
cana-2738	428	2	.	.	PUNCT
cana-2738	429	1	let	let	VERB
cana-2738	429	2	ψ	ψ	PART
cana-2738	429	3	be	be	AUX
cana-2738	429	4	a	a	DET
cana-2738	429	5	pfcs	pfcs	NOUN
cana-2738	429	6	in	in	ADP
cana-2738	429	7	(	(	PUNCT
cana-2738	429	8	x1	x1	PROPN
cana-2738	429	9	,	,	PUNCT
cana-2738	429	10	γp	γp	PROPN
cana-2738	429	11	)	)	PUNCT
cana-2738	429	12	.	.	PUNCT
cana-2738	430	1	then	then	ADV
cana-2738	430	2	hp(ψ	hp(ψ	NOUN
cana-2738	430	3	)	)	PUNCT
cana-2738	430	4	is	be	AUX
cana-2738	430	5	pfδβcs	pfδβc	VERB
cana-2738	430	6	of	of	ADP
cana-2738	430	7	(	(	PUNCT
cana-2738	430	8	x2	x2	PROPN
cana-2738	430	9	,	,	PUNCT
cana-2738	430	10	ψp	ψp	NOUN
cana-2738	430	11	)	)	PUNCT
cana-2738	430	12	because	because	SCONJ
cana-2738	430	13	hp	hp	PROPN
cana-2738	430	14	is	be	AUX
cana-2738	430	15	pfδβc	pfδβc	NOUN
cana-2738	430	16	.	.	PUNCT
cana-2738	431	1	by	by	ADP
cana-2738	431	2	hypothesis	hypothesis	NOUN
cana-2738	431	3	hp(ψ	hp(ψ	NOUN
cana-2738	431	4	)	)	PUNCT
cana-2738	431	5	is	be	AUX
cana-2738	431	6	pfcs	pfc	VERB
cana-2738	431	7	of	of	ADP
cana-2738	431	8	(	(	PUNCT
cana-2738	431	9	x2	x2	PROPN
cana-2738	431	10	,	,	PUNCT
cana-2738	431	11	ψp	ψp	NOUN
cana-2738	431	12	)	)	PUNCT
cana-2738	431	13	.	.	PUNCT
cana-2738	432	1	now	now	ADV
cana-2738	432	2	g	g	PROPN
cana-2738	432	3	p	p	X
cana-2738	432	4	(	(	PUNCT
cana-2738	432	5	hp(ψ	hp(ψ	NOUN
cana-2738	432	6	)	)	PUNCT
cana-2738	432	7	)	)	PUNCT
cana-2738	433	1	=	=	PRON
cana-2738	433	2	(	(	PUNCT
cana-2738	433	3	g	g	PROPN
cana-2738	433	4	p	p	PROPN
cana-2738	433	5	∘	∘	PROPN
cana-2738	433	6	h)(ψ	h)(ψ	NOUN
cana-2738	433	7	)	)	PUNCT
cana-2738	433	8	is	be	AUX
cana-2738	433	9	pfδβcs	pfδβc	VERB
cana-2738	433	10	in	in	ADP
cana-2738	433	11	(	(	PUNCT
cana-2738	433	12	x3	x3	ADJ
cana-2738	433	13	,	,	PUNCT
cana-2738	433	14	φp	φp	ADP
cana-2738	433	15	)	)	PUNCT
cana-2738	433	16	because	because	SCONJ
cana-2738	433	17	g	g	PROPN
cana-2738	433	18	p	p	PROPN
cana-2738	433	19	is	be	AUX
cana-2738	433	20	pfδβc	pfδβc	ADJ
cana-2738	433	21	.	.	PUNCT
cana-2738	434	1	thus	thus	ADV
cana-2738	434	2	g	g	ADP
cana-2738	434	3	p	p	PROPN
cana-2738	434	4	∘	∘	PROPN
cana-2738	434	5	hp	hp	PROPN
cana-2738	434	6	is	be	AUX
cana-2738	434	7	pfδβc	pfδβc	NOUN
cana-2738	434	8	.	.	PUNCT
cana-2738	435	1	theorem	theorem	VERB
cana-2738	435	2	4.6	4.6	NUM
cana-2738	435	3	let	let	VERB
cana-2738	435	4	(	(	PUNCT
cana-2738	435	5	x1	x1	PROPN
cana-2738	435	6	,	,	PUNCT
cana-2738	435	7	γp	γp	PROPN
cana-2738	435	8	)	)	PUNCT
cana-2738	435	9	&	&	CCONJ
cana-2738	435	10	(	(	PUNCT
cana-2738	435	11	x2	x2	PROPN
cana-2738	435	12	,	,	PUNCT
cana-2738	435	13	ψp	ψp	PRON
cana-2738	435	14	)	)	PUNCT
cana-2738	435	15	be	be	AUX
cana-2738	435	16	any	any	DET
cana-2738	435	17	pfts	pft	NOUN
cana-2738	435	18	’s	’s	PART
cana-2738	435	19	.	.	PUNCT
cana-2738	436	1	let	let	VERB
cana-2738	436	2	hp	hp	VERB
cana-2738	436	3	:	:	PUNCT
cana-2738	436	4	(	(	PUNCT
cana-2738	436	5	x1	x1	PROPN
cana-2738	436	6	,	,	PUNCT
cana-2738	436	7	γp	γp	PROPN
cana-2738	436	8	)	)	PUNCT
cana-2738	436	9	→	→	SYM
cana-2738	436	10	(	(	PUNCT
cana-2738	436	11	x2	x2	PROPN
cana-2738	436	12	,	,	PUNCT
cana-2738	436	13	ψp	ψp	PRON
cana-2738	436	14	)	)	PUNCT
cana-2738	436	15	be	be	AUX
cana-2738	436	16	a	a	DET
cana-2738	436	17	map	map	NOUN
cana-2738	436	18	,	,	PUNCT
cana-2738	436	19	then	then	ADV
cana-2738	436	20	the	the	DET
cana-2738	436	21	following	following	ADJ
cana-2738	436	22	statements	statement	NOUN
cana-2738	436	23	are	be	AUX
cana-2738	436	24	equivalent	equivalent	ADJ
cana-2738	436	25	:	:	PUNCT
cana-2738	436	26	1	1	X
cana-2738	436	27	.	.	X
cana-2738	436	28	hp	hp	PROPN
cana-2738	436	29	is	be	AUX
cana-2738	436	30	a	a	DET
cana-2738	436	31	pfδβo	pfδβo	NOUN
cana-2738	436	32	.	.	PUNCT
cana-2738	437	1	2	2	X
cana-2738	437	2	.	.	X
cana-2738	437	3	hp	hp	PROPN
cana-2738	437	4	is	be	AUX
cana-2738	437	5	a	a	DET
cana-2738	437	6	pfδβc	pfδβc	NOUN
cana-2738	437	7	.	.	PUNCT
cana-2738	438	1	3	3	X
cana-2738	438	2	.	.	X
cana-2738	438	3	hp	hp	PROPN
cana-2738	438	4	−1	−1	NOUN
cana-2738	438	5	is	be	AUX
cana-2738	438	6	pfδβcts	pfδβct	NOUN
cana-2738	438	7	.	.	PUNCT
cana-2738	439	1	proof	proof	NOUN
cana-2738	439	2	.	.	PUNCT
cana-2738	440	1	(	(	PUNCT
cana-2738	440	2	i	i	NOUN
cana-2738	440	3	)	)	PUNCT
cana-2738	440	4	⇒	⇒	PROPN
cana-2738	440	5	(	(	PUNCT
cana-2738	440	6	ii	ii	PROPN
cana-2738	440	7	):	):	PUNCT
cana-2738	440	8	let	let	VERB
cana-2738	440	9	us	we	PRON
cana-2738	440	10	assume	assume	VERB
cana-2738	440	11	that	that	SCONJ
cana-2738	440	12	hp	hp	PROPN
cana-2738	440	13	is	be	AUX
cana-2738	440	14	a	a	DET
cana-2738	440	15	pfδβo	pfδβo	NOUN
cana-2738	440	16	.	.	PUNCT
cana-2738	441	1	by	by	ADP
cana-2738	441	2	definition	definition	NOUN
cana-2738	441	3	,	,	PUNCT
cana-2738	441	4	ψ	ψ	NOUN
cana-2738	441	5	is	be	AUX
cana-2738	441	6	a	a	DET
cana-2738	441	7	pfos	pfos	NOUN
cana-2738	441	8	in	in	ADP
cana-2738	441	9	(	(	PUNCT
cana-2738	441	10	x1	x1	PROPN
cana-2738	441	11	,	,	PUNCT
cana-2738	441	12	γp	γp	PROPN
cana-2738	441	13	)	)	PUNCT
cana-2738	441	14	,	,	PUNCT
cana-2738	441	15	then	then	ADV
cana-2738	441	16	hp(ψ	hp(ψ	NOUN
cana-2738	441	17	)	)	PUNCT
cana-2738	441	18	is	be	AUX
cana-2738	441	19	a	a	DET
cana-2738	441	20	pfδβos	pfδβos	NOUN
cana-2738	441	21	in	in	ADP
cana-2738	441	22	(	(	PUNCT
cana-2738	441	23	x2	x2	INTJ
cana-2738	441	24	,	,	PUNCT
cana-2738	441	25	ψp	ψp	NOUN
cana-2738	441	26	)	)	PUNCT
cana-2738	441	27	.	.	PUNCT
cana-2738	442	1	here	here	ADV
cana-2738	442	2	,	,	PUNCT
cana-2738	442	3	ψ	ψ	X
cana-2738	442	4	is	be	AUX
cana-2738	442	5	pfcs	pfc	VERB
cana-2738	442	6	in	in	ADP
cana-2738	442	7	(	(	PUNCT
cana-2738	442	8	x1	x1	PROPN
cana-2738	442	9	,	,	PUNCT
cana-2738	442	10	γp	γp	PROPN
cana-2738	442	11	)	)	PUNCT
cana-2738	442	12	,	,	PUNCT
cana-2738	442	13	then	then	ADV
cana-2738	442	14	x	x	PART
cana-2738	442	15	−	−	PROPN
cana-2738	442	16	ψ	ψ	NOUN
cana-2738	442	17	is	be	AUX
cana-2738	442	18	a	a	DET
cana-2738	442	19	pfos	pfos	NOUN
cana-2738	442	20	in	in	ADP
cana-2738	442	21	(	(	PUNCT
cana-2738	442	22	x1	x1	PROPN
cana-2738	442	23	,	,	PUNCT
cana-2738	442	24	γp	γp	PROPN
cana-2738	442	25	)	)	PUNCT
cana-2738	442	26	.	.	PUNCT
cana-2738	443	1	by	by	ADP
cana-2738	443	2	assumption	assumption	NOUN
cana-2738	443	3	,	,	PUNCT
cana-2738	443	4	hp(x	hp(x	X
cana-2738	443	5	−	−	PROPN
cana-2738	443	6	ψ	ψ	X
cana-2738	443	7	)	)	PUNCT
cana-2738	443	8	is	be	AUX
cana-2738	443	9	a	a	DET
cana-2738	443	10	pfδβos	pfδβos	NOUN
cana-2738	443	11	in	in	ADP
cana-2738	443	12	(	(	PUNCT
cana-2738	443	13	x2	x2	INTJ
cana-2738	443	14	,	,	PUNCT
cana-2738	443	15	ψp	ψp	NOUN
cana-2738	443	16	)	)	PUNCT
cana-2738	443	17	.	.	PUNCT
cana-2738	444	1	hence	hence	ADV
cana-2738	444	2	,	,	PUNCT
cana-2738	444	3	y	y	PROPN
cana-2738	444	4	−	−	PROPN
cana-2738	444	5	hp(x	hp(x	PUNCT
cana-2738	444	6	−	−	PROPN
cana-2738	444	7	ψ	ψ	X
cana-2738	444	8	)	)	PUNCT
cana-2738	444	9	is	be	AUX
cana-2738	444	10	a	a	DET
cana-2738	444	11	pfδβcs	pfδβcs	NOUN
cana-2738	444	12	in	in	ADP
cana-2738	444	13	(	(	PUNCT
cana-2738	444	14	x2	x2	PROPN
cana-2738	444	15	,	,	PUNCT
cana-2738	444	16	ψp	ψp	NOUN
cana-2738	444	17	)	)	PUNCT
cana-2738	444	18	.	.	PUNCT
cana-2738	445	1	therefore	therefore	ADV
cana-2738	445	2	,	,	PUNCT
cana-2738	445	3	hp	hp	PROPN
cana-2738	445	4	is	be	AUX
cana-2738	445	5	a	a	DET
cana-2738	445	6	pfδβc	pfδβc	NOUN
cana-2738	445	7	.	.	PUNCT
cana-2738	446	1	(	(	PUNCT
cana-2738	446	2	ii	ii	NOUN
cana-2738	446	3	)	)	PUNCT
cana-2738	446	4	⇒	⇒	NOUN
cana-2738	446	5	(	(	PUNCT
cana-2738	446	6	iii	iii	NOUN
cana-2738	446	7	):	):	PUNCT
cana-2738	446	8	let	let	VERB
cana-2738	446	9	ψ	ψ	PART
cana-2738	446	10	be	be	AUX
cana-2738	446	11	a	a	DET
cana-2738	446	12	pfcs	pfcs	NOUN
cana-2738	446	13	in	in	ADP
cana-2738	446	14	(	(	PUNCT
cana-2738	446	15	x1	x1	PROPN
cana-2738	446	16	,	,	PUNCT
cana-2738	446	17	γp	γp	PROPN
cana-2738	446	18	)	)	PUNCT
cana-2738	446	19	by	by	ADP
cana-2738	446	20	(	(	PUNCT
cana-2738	446	21	ii	ii	NOUN
cana-2738	446	22	)	)	PUNCT
cana-2738	446	23	,	,	PUNCT
cana-2738	446	24	hp(ψ	hp(ψ	NOUN
cana-2738	446	25	)	)	PUNCT
cana-2738	446	26	is	be	AUX
cana-2738	446	27	a	a	DET
cana-2738	446	28	pfδβcs	pfδβcs	NOUN
cana-2738	446	29	in	in	ADP
cana-2738	446	30	(	(	PUNCT
cana-2738	446	31	x2	x2	PROPN
cana-2738	446	32	,	,	PUNCT
cana-2738	446	33	ψp	ψp	NOUN
cana-2738	446	34	)	)	PUNCT
cana-2738	446	35	.	.	PUNCT
cana-2738	447	1	hence	hence	ADV
cana-2738	447	2	,	,	PUNCT
cana-2738	447	3	hp(ψ	hp(ψ	NOUN
cana-2738	447	4	)	)	PUNCT
cana-2738	447	5	=	=	SYM
cana-2738	448	1	(	(	PUNCT
cana-2738	448	2	hp	hp	PROPN
cana-2738	448	3	−1)−1(ψ	−1)−1(ψ	PROPN
cana-2738	448	4	)	)	PUNCT
cana-2738	448	5	,	,	PUNCT
cana-2738	448	6	so	so	ADV
cana-2738	448	7	hp	hp	PROPN
cana-2738	448	8	−1	−1	NOUN
cana-2738	448	9	is	be	AUX
cana-2738	448	10	a	a	DET
cana-2738	448	11	pfδβcs	pfδβcs	NOUN
cana-2738	448	12	in	in	ADP
cana-2738	448	13	(	(	PUNCT
cana-2738	448	14	x2	x2	PROPN
cana-2738	448	15	,	,	PUNCT
cana-2738	448	16	ψp	ψp	NOUN
cana-2738	448	17	)	)	PUNCT
cana-2738	448	18	.	.	PUNCT
cana-2738	449	1	hence	hence	ADV
cana-2738	449	2	,	,	PUNCT
cana-2738	449	3	hp	hp	ADJ
cana-2738	449	4	−1	−1	NOUN
cana-2738	449	5	is	be	AUX
cana-2738	449	6	pfδβcts	pfδβct	NOUN
cana-2738	449	7	.	.	PUNCT
cana-2738	450	1	(	(	PUNCT
cana-2738	450	2	iii	iii	X
cana-2738	450	3	)	)	PUNCT
cana-2738	450	4	⇒	⇒	NOUN
cana-2738	450	5	(	(	PUNCT
cana-2738	450	6	i	i	NOUN
cana-2738	450	7	):	):	PUNCT
cana-2738	450	8	let	let	VERB
cana-2738	450	9	ψ	ψ	PART
cana-2738	450	10	be	be	AUX
cana-2738	450	11	a	a	DET
cana-2738	450	12	pfos	pfos	NOUN
cana-2738	450	13	in	in	ADP
cana-2738	450	14	(	(	PUNCT
cana-2738	450	15	x1	x1	PROPN
cana-2738	450	16	,	,	PUNCT
cana-2738	450	17	γp	γp	PROPN
cana-2738	450	18	)	)	PUNCT
cana-2738	450	19	.	.	PUNCT
cana-2738	451	1	by	by	ADP
cana-2738	451	2	(	(	PUNCT
cana-2738	451	3	iii	iii	NOUN
cana-2738	451	4	)	)	PUNCT
cana-2738	451	5	,	,	PUNCT
cana-2738	451	6	(	(	PUNCT
cana-2738	451	7	hp	hp	PROPN
cana-2738	451	8	−1)−1(ψ	−1)−1(ψ	PROPN
cana-2738	451	9	)	)	PUNCT
cana-2738	451	10	=	=	SYM
cana-2738	451	11	hp(ψ	hp(ψ	NOUN
cana-2738	451	12	)	)	PUNCT
cana-2738	451	13	is	be	AUX
cana-2738	451	14	a	a	DET
cana-2738	451	15	pfδβo	pfδβo	NOUN
cana-2738	451	16	.	.	PUNCT
cana-2738	452	1	5	5	NUM
cana-2738	452	2	application	application	NOUN
cana-2738	452	3	in	in	ADP
cana-2738	452	4	current	current	ADJ
cana-2738	452	5	scenario	scenario	NOUN
cana-2738	452	6	people	people	NOUN
cana-2738	452	7	with	with	ADP
cana-2738	452	8	symptom	symptom	NOUN
cana-2738	452	9	of	of	ADP
cana-2738	452	10	covid-19	covid-19	PROPN
cana-2738	452	11	like	like	ADP
cana-2738	452	12	fever	fever	NOUN
cana-2738	452	13	,	,	PUNCT
cana-2738	452	14	cough	cough	NOUN
cana-2738	452	15	,	,	PUNCT
cana-2738	452	16	sneezing	sneeze	VERB
cana-2738	452	17	,	,	PUNCT
cana-2738	452	18	sore	sore	ADJ
cana-2738	452	19	throat	throat	NOUN
cana-2738	452	20	,	,	PUNCT
cana-2738	452	21	loss	loss	NOUN
cana-2738	452	22	of	of	ADP
cana-2738	452	23	taste	taste	NOUN
cana-2738	452	24	and	and	CCONJ
cana-2738	452	25	smell	smell	NOUN
cana-2738	452	26	etc	etc	X
cana-2738	452	27	.	.	X
cana-2738	452	28	,	,	PUNCT
cana-2738	452	29	were	be	AUX
cana-2738	452	30	panic	panic	NOUN
cana-2738	452	31	about	about	ADP
cana-2738	452	32	the	the	DET
cana-2738	452	33	disease	disease	NOUN
cana-2738	452	34	,	,	PUNCT
cana-2738	452	35	and	and	CCONJ
cana-2738	452	36	the	the	DET
cana-2738	452	37	diagnosis	diagnosis	NOUN
cana-2738	452	38	of	of	ADP
cana-2738	452	39	covid-19	covid-19	PROPN
cana-2738	452	40	takes	take	VERB
cana-2738	452	41	many	many	ADJ
cana-2738	452	42	hours	hour	NOUN
cana-2738	452	43	and	and	CCONJ
cana-2738	452	44	people	people	NOUN
cana-2738	452	45	can	can	AUX
cana-2738	452	46	not	not	PART
cana-2738	452	47	go	go	VERB
cana-2738	452	48	for	for	ADP
cana-2738	452	49	the	the	DET
cana-2738	452	50	test	test	NOUN
cana-2738	452	51	frequently	frequently	ADV
cana-2738	452	52	.	.	PUNCT
cana-2738	453	1	some	some	DET
cana-2738	453	2	other	other	ADJ
cana-2738	453	3	diseases	disease	NOUN
cana-2738	453	4	like	like	ADP
cana-2738	453	5	flu	flu	NOUN
cana-2738	453	6	,	,	PUNCT
cana-2738	453	7	pneumonia	pneumonia	NOUN
cana-2738	453	8	,	,	PUNCT
cana-2738	453	9	cold	cold	ADJ
cana-2738	453	10	etc	etc	X
cana-2738	453	11	.	.	X
cana-2738	453	12	,	,	PUNCT
cana-2738	453	13	also	also	ADV
cana-2738	453	14	has	have	VERB
cana-2738	453	15	the	the	DET
cana-2738	453	16	same	same	ADJ
cana-2738	453	17	symptoms	symptom	NOUN
cana-2738	453	18	.	.	PUNCT
cana-2738	454	1	each	each	DET
cana-2738	454	2	patients	patient	NOUN
cana-2738	454	3	has	have	VERB
cana-2738	454	4	unique	unique	ADJ
cana-2738	454	5	experience	experience	NOUN
cana-2738	454	6	of	of	ADP
cana-2738	454	7	that	that	DET
cana-2738	454	8	particular	particular	ADJ
cana-2738	454	9	symptom	symptom	NOUN
cana-2738	454	10	and	and	CCONJ
cana-2738	454	11	some	some	DET
cana-2738	454	12	time	time	NOUN
cana-2738	454	13	they	they	PRON
cana-2738	454	14	may	may	AUX
cana-2738	454	15	not	not	PART
cana-2738	454	16	experience	experience	VERB
cana-2738	454	17	that	that	DET
cana-2738	454	18	symptom	symptom	NOUN
cana-2738	454	19	even	even	ADV
cana-2738	454	20	though	though	SCONJ
cana-2738	454	21	they	they	PRON
cana-2738	454	22	were	be	AUX
cana-2738	454	23	affected	affect	VERB
cana-2738	454	24	by	by	ADP
cana-2738	454	25	the	the	DET
cana-2738	454	26	covid-19	covid-19	PROPN
cana-2738	454	27	.	.	PUNCT
cana-2738	454	28	communications	communication	NOUN
cana-2738	454	29	on	on	ADP
cana-2738	454	30	applied	apply	VERB
cana-2738	454	31	nonlinear	nonlinear	ADJ
cana-2738	454	32	analysis	analysis	NOUN
cana-2738	454	33	issn	issn	NOUN
cana-2738	454	34	:	:	PUNCT
cana-2738	454	35	1074	1074	NUM
cana-2738	454	36	-	-	PUNCT
cana-2738	454	37	133x	133x	NUM
cana-2738	454	38	vol	vol	NOUN
cana-2738	454	39	32	32	NUM
cana-2738	454	40	no	no	NOUN
cana-2738	454	41	.	.	PUNCT
cana-2738	455	1	4s	4s	NUM
cana-2738	455	2	(	(	PUNCT
cana-2738	455	3	2025	2025	NUM
cana-2738	455	4	)	)	PUNCT
cana-2738	455	5	54	54	NUM
cana-2738	456	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-2738	456	2	here	here	ADV
cana-2738	456	3	we	we	PRON
cana-2738	456	4	tried	try	VERB
cana-2738	456	5	to	to	PART
cana-2738	456	6	diagnosis	diagnosis	VERB
cana-2738	456	7	covid-19	covid-19	PROPN
cana-2738	456	8	with	with	ADP
cana-2738	456	9	the	the	DET
cana-2738	456	10	help	help	NOUN
cana-2738	456	11	of	of	ADP
cana-2738	456	12	pythagorean	pythagorean	PROPN
cana-2738	456	13	fuzzy	fuzzy	ADJ
cana-2738	456	14	sets	set	NOUN
cana-2738	456	15	(	(	PUNCT
cana-2738	456	16	in	in	ADP
cana-2738	456	17	short	short	PROPN
cana-2738	456	18	pfs	pfs	PROPN
cana-2738	456	19	’s	’s	PART
cana-2738	456	20	)	)	PUNCT
cana-2738	456	21	which	which	PRON
cana-2738	456	22	helps	help	VERB
cana-2738	456	23	to	to	PART
cana-2738	456	24	record	record	VERB
cana-2738	456	25	all	all	DET
cana-2738	456	26	symptoms	symptom	NOUN
cana-2738	456	27	in	in	ADP
cana-2738	456	28	prã	prã	PROPN
cana-2738	456	29	©	©	PROPN
cana-2738	456	30	cised	cise	VERB
cana-2738	456	31	manner	manner	NOUN
cana-2738	456	32	.	.	PUNCT
cana-2738	457	1	5.1	5.1	NUM
cana-2738	457	2	algorithm	algorithm	NOUN
cana-2738	457	3	and	and	CCONJ
cana-2738	457	4	flow	flow	VERB
cana-2738	457	5	chart	chart	NOUN
cana-2738	457	6	this	this	DET
cana-2738	457	7	section	section	NOUN
cana-2738	457	8	includes	include	VERB
cana-2738	457	9	the	the	DET
cana-2738	457	10	algorithm	algorithm	NOUN
cana-2738	457	11	based	base	VERB
cana-2738	457	12	on	on	ADP
cana-2738	457	13	the	the	DET
cana-2738	457	14	computation	computation	NOUN
cana-2738	457	15	of	of	ADP
cana-2738	457	16	the	the	DET
cana-2738	457	17	hamming	hamming	NOUN
cana-2738	457	18	distance	distance	NOUN
cana-2738	457	19	,	,	PUNCT
cana-2738	457	20	normalized	normalize	VERB
cana-2738	457	21	hamming	hamming	NOUN
cana-2738	457	22	distance	distance	NOUN
cana-2738	457	23	,	,	PUNCT
cana-2738	457	24	euclidean	euclidean	ADJ
cana-2738	457	25	distance	distance	NOUN
cana-2738	457	26	and	and	CCONJ
cana-2738	457	27	normalized	normalize	VERB
cana-2738	457	28	euclidean	euclidean	ADJ
cana-2738	457	29	distance	distance	NOUN
cana-2738	457	30	between	between	ADP
cana-2738	457	31	the	the	DET
cana-2738	457	32	pfs	pfs	PROPN
cana-2738	457	33	’s	’s	PART
cana-2738	457	34	.	.	PUNCT
cana-2738	458	1	step:1	step:1	PRON
cana-2738	458	2	identify	identify	VERB
cana-2738	458	3	the	the	DET
cana-2738	458	4	universe	universe	NOUN
cana-2738	458	5	set	set	VERB
cana-2738	458	6	with	with	ADP
cana-2738	458	7	most	most	ADJ
cana-2738	458	8	common	common	ADJ
cana-2738	458	9	symptoms	symptom	NOUN
cana-2738	458	10	of	of	ADP
cana-2738	458	11	the	the	DET
cana-2738	458	12	covid-19	covid-19	PROPN
cana-2738	458	13	patients	patient	NOUN
cana-2738	458	14	.	.	PUNCT
cana-2738	459	1	step:2	step:2	NOUN
cana-2738	459	2	formulates	formulate	VERB
cana-2738	459	3	the	the	DET
cana-2738	459	4	pfs	pfs	PROPN
cana-2738	459	5	of	of	ADP
cana-2738	459	6	each	each	DET
cana-2738	459	7	patient	patient	NOUN
cana-2738	459	8	based	base	VERB
cana-2738	459	9	on	on	ADP
cana-2738	459	10	their	their	PRON
cana-2738	459	11	experience	experience	NOUN
cana-2738	459	12	of	of	ADP
cana-2738	459	13	each	each	DET
cana-2738	459	14	symptom	symptom	NOUN
cana-2738	459	15	of	of	ADP
cana-2738	459	16	universe	universe	NOUN
cana-2738	459	17	set	set	NOUN
cana-2738	459	18	.	.	PUNCT
cana-2738	460	1	step:3	step:3	PROPN
cana-2738	460	2	formulates	formulate	VERB
cana-2738	460	3	the	the	DET
cana-2738	460	4	ideal	ideal	ADJ
cana-2738	460	5	pfs	pfs	PROPN
cana-2738	460	6	from	from	ADP
cana-2738	460	7	the	the	DET
cana-2738	460	8	patients	patient	NOUN
cana-2738	460	9	who	who	PRON
cana-2738	460	10	affected	affect	VERB
cana-2738	460	11	by	by	ADP
cana-2738	460	12	covid-19	covid-19	PROPN
cana-2738	460	13	based	base	VERB
cana-2738	460	14	on	on	ADP
cana-2738	460	15	their	their	PRON
cana-2738	460	16	experience	experience	NOUN
cana-2738	460	17	of	of	ADP
cana-2738	460	18	each	each	DET
cana-2738	460	19	symptom	symptom	NOUN
cana-2738	460	20	of	of	ADP
cana-2738	460	21	covid-19	covid-19	PROPN
cana-2738	460	22	.	.	PUNCT
cana-2738	460	23	step:4	step:4	PROPN
cana-2738	460	24	compute	compute	NOUN
cana-2738	461	1	the	the	DET
cana-2738	461	2	various	various	ADJ
cana-2738	461	3	distances	distance	NOUN
cana-2738	461	4	between	between	ADP
cana-2738	461	5	the	the	DET
cana-2738	461	6	ideal	ideal	ADJ
cana-2738	461	7	pfs	pfs	PROPN
cana-2738	461	8	of	of	ADP
cana-2738	461	9	covid-19	covid-19	PROPN
cana-2738	461	10	affected	affect	VERB
cana-2738	461	11	patients	patient	NOUN
cana-2738	461	12	and	and	CCONJ
cana-2738	461	13	the	the	DET
cana-2738	461	14	pfs	pfs	PROPN
cana-2738	461	15	of	of	ADP
cana-2738	461	16	the	the	DET
cana-2738	461	17	patient	patient	NOUN
cana-2738	461	18	who	who	PRON
cana-2738	461	19	experiences	experience	VERB
cana-2738	461	20	the	the	DET
cana-2738	461	21	symptoms	symptom	NOUN
cana-2738	461	22	of	of	ADP
cana-2738	461	23	covid-19	covid-19	PROPN
cana-2738	461	24	.	.	PUNCT
cana-2738	461	25	step:5	step:5	PROPN
cana-2738	461	26	compare	compare	VERB
cana-2738	461	27	the	the	DET
cana-2738	461	28	distance	distance	NOUN
cana-2738	461	29	between	between	ADP
cana-2738	461	30	the	the	DET
cana-2738	461	31	pfs	pfs	PROPN
cana-2738	461	32	sets	set	NOUN
cana-2738	461	33	and	and	CCONJ
cana-2738	461	34	also	also	ADV
cana-2738	461	35	between	between	ADP
cana-2738	461	36	the	the	DET
cana-2738	461	37	various	various	ADJ
cana-2738	461	38	distances	distance	NOUN
cana-2738	461	39	.	.	PUNCT
cana-2738	462	1	step:6	step:6	NOUN
cana-2738	462	2	conclude	conclude	VERB
cana-2738	462	3	,	,	PUNCT
cana-2738	462	4	the	the	DET
cana-2738	462	5	patient	patient	NOUN
cana-2738	462	6	with	with	ADP
cana-2738	462	7	minimum	minimum	ADJ
cana-2738	462	8	distance	distance	NOUN
cana-2738	462	9	from	from	ADP
cana-2738	462	10	the	the	DET
cana-2738	462	11	pfs	pfs	PROPN
cana-2738	462	12	of	of	ADP
cana-2738	462	13	covid-19	covid-19	PROPN
cana-2738	462	14	patient	patient	NOUN
cana-2738	462	15	has	have	VERB
cana-2738	462	16	the	the	DET
cana-2738	462	17	huge	huge	ADJ
cana-2738	462	18	chance	chance	NOUN
cana-2738	462	19	to	to	PART
cana-2738	462	20	affected	affect	VERB
cana-2738	462	21	by	by	ADP
cana-2738	462	22	covid-19	covid-19	PROPN
cana-2738	462	23	virus	virus	NOUN
cana-2738	462	24	.	.	PUNCT
cana-2738	463	1	5.2	5.2	NUM
cana-2738	463	2	flow	flow	NOUN
cana-2738	463	3	chart	chart	NOUN
cana-2738	463	4	identify	identify	VERB
cana-2738	463	5	universe	universe	ADJ
cana-2738	463	6	set	set	NOUN
cana-2738	463	7	of	of	ADP
cana-2738	463	8	covid-19	covid-19	PROPN
cana-2738	463	9	symptoms	symptom	NOUN
cana-2738	463	10	↓	↓	NOUN
cana-2738	463	11	formulates	formulate	VERB
cana-2738	463	12	the	the	DET
cana-2738	463	13	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2738	463	14	of	of	ADP
cana-2738	463	15	each	each	DET
cana-2738	463	16	patient	patient	NOUN
cana-2738	463	17	↓	↓	NOUN
cana-2738	463	18	formulates	formulate	VERB
cana-2738	463	19	the	the	DET
cana-2738	463	20	ideal	ideal	NOUN
cana-2738	463	21	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2738	463	22	from	from	ADP
cana-2738	463	23	the	the	DET
cana-2738	463	24	covid-19	covid-19	PROPN
cana-2738	463	25	patient	patient	ADJ
cana-2738	463	26	↓	↓	NOUN
cana-2738	463	27	compute	compute	NOUN
cana-2738	463	28	distance	distance	NOUN
cana-2738	463	29	between	between	ADP
cana-2738	463	30	the	the	DET
cana-2738	463	31	ideal	ideal	NOUN
cana-2738	464	1	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2738	464	2	the	the	DET
cana-2738	464	3	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2738	464	4	of	of	ADP
cana-2738	464	5	the	the	DET
cana-2738	464	6	patient	patient	NOUN
cana-2738	464	7	↓	↓	PROPN
cana-2738	464	8	conclude	conclude	PROPN
cana-2738	464	9	,	,	PUNCT
cana-2738	464	10	huge	huge	ADJ
cana-2738	464	11	chance	chance	NOUN
cana-2738	464	12	for	for	ADP
cana-2738	464	13	affected	affect	VERB
cana-2738	464	14	by	by	ADP
cana-2738	464	15	covid-19	covid-19	PROPN
cana-2738	464	16	by	by	ADP
cana-2738	464	17	who	who	PRON
cana-2738	464	18	has	have	AUX
cana-2738	464	19	minimum	minimum	ADJ
cana-2738	464	20	distance	distance	NOUN
cana-2738	464	21	.	.	PUNCT
cana-2738	465	1	5.3	5.3	NUM
cana-2738	465	2	example	example	NOUN
cana-2738	465	3	let	let	VERB
cana-2738	465	4	𝐴	𝐴	PROPN
cana-2738	465	5	,	,	PUNCT
cana-2738	465	6	𝐵	𝐵	PROPN
cana-2738	465	7	,	,	PUNCT
cana-2738	465	8	𝐶	𝐶	PROPN
cana-2738	465	9	denote	denote	VERB
cana-2738	465	10	the	the	DET
cana-2738	465	11	patients	patient	NOUN
cana-2738	465	12	who	who	PRON
cana-2738	465	13	has	have	VERB
cana-2738	465	14	the	the	DET
cana-2738	465	15	symptoms	symptom	NOUN
cana-2738	465	16	of	of	ADP
cana-2738	465	17	covid-19	covid-19	PROPN
cana-2738	465	18	.	.	PUNCT
cana-2738	466	1	now	now	ADV
cana-2738	466	2	their	their	PRON
cana-2738	466	3	symptoms	symptom	NOUN
cana-2738	466	4	can	can	AUX
cana-2738	466	5	be	be	AUX
cana-2738	466	6	represented	represent	VERB
cana-2738	466	7	by	by	ADP
cana-2738	466	8	the	the	DET
cana-2738	466	9	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2738	466	10	and	and	CCONJ
cana-2738	466	11	their	their	PRON
cana-2738	466	12	members	member	NOUN
cana-2738	466	13	are	be	AUX
cana-2738	466	14	taken	take	VERB
cana-2738	466	15	from	from	ADP
cana-2738	466	16	the	the	DET
cana-2738	466	17	universe	universe	NOUN
cana-2738	466	18	set	set	VERB
cana-2738	466	19	𝑋	𝑋	NOUN
cana-2738	466	20	which	which	PRON
cana-2738	466	21	includes	include	VERB
cana-2738	466	22	the	the	DET
cana-2738	466	23	all	all	DET
cana-2738	466	24	possible	possible	ADJ
cana-2738	466	25	symptoms	symptom	NOUN
cana-2738	466	26	of	of	ADP
cana-2738	466	27	covid-19	covid-19	PROPN
cana-2738	466	28	are	be	AUX
cana-2738	466	29	𝑓	𝑓	DET
cana-2738	466	30	denotes	denote	NOUN
cana-2738	466	31	fever	fever	NOUN
cana-2738	466	32	,	,	PUNCT
cana-2738	466	33	𝑡	𝑡	PROPN
cana-2738	466	34	denotes	denote	NOUN
cana-2738	466	35	tiredness	tiredness	VERB
cana-2738	466	36	,	,	PUNCT
cana-2738	466	37	𝑑	𝑑	PROPN
cana-2738	466	38	denotes	denote	NOUN
cana-2738	466	39	dry	dry	ADJ
cana-2738	466	40	cough	cough	NOUN
cana-2738	466	41	,	,	PUNCT
cana-2738	466	42	𝑠	𝑠	PROPN
cana-2738	466	43	denotes	denote	VERB
cana-2738	466	44	shortness	shortness	NOUN
cana-2738	466	45	of	of	ADP
cana-2738	466	46	breath	breath	NOUN
cana-2738	466	47	,	,	PUNCT
cana-2738	466	48	𝑝	𝑝	NOUN
cana-2738	466	49	denotes	denote	NOUN
cana-2738	466	50	body	body	NOUN
cana-2738	466	51	pain	pain	NOUN
cana-2738	466	52	/	/	SYM
cana-2738	466	53	chest	chest	NOUN
cana-2738	466	54	pain	pain	NOUN
cana-2738	466	55	,	,	PUNCT
cana-2738	466	56	𝑎	𝑎	DET
cana-2738	466	57	denotes	denote	NOUN
cana-2738	466	58	diarrhea	diarrhea	PROPN
cana-2738	466	59	,	,	PUNCT
cana-2738	466	60	𝑙	𝑙	PRON
cana-2738	466	61	denotes	denote	VERB
cana-2738	466	62	loss	loss	NOUN
cana-2738	466	63	of	of	ADP
cana-2738	466	64	taste	taste	NOUN
cana-2738	466	65	or	or	CCONJ
cana-2738	466	66	smell	smell	NOUN
cana-2738	466	67	,	,	PUNCT
cana-2738	466	68	𝑠𝑡	𝑠𝑡	PROPN
cana-2738	466	69	denotes	denote	VERB
cana-2738	466	70	sore	sore	ADJ
cana-2738	466	71	throat	throat	NOUN
cana-2738	466	72	,	,	PUNCT
cana-2738	466	73	𝑏	𝑏	PROPN
cana-2738	466	74	denotes	denote	VERB
cana-2738	466	75	difficulty	difficulty	NOUN
cana-2738	466	76	in	in	ADP
cana-2738	466	77	breathing	breathing	NOUN
cana-2738	466	78	and	and	CCONJ
cana-2738	466	79	𝑟	𝑟	PRON
cana-2738	466	80	denotes	denotes	PROPN
cana-2738	466	81	rhinorrhea	rhinorrhea	PROPN
cana-2738	466	82	.	.	PUNCT
cana-2738	467	1	we	we	PRON
cana-2738	467	2	convert	convert	VERB
cana-2738	467	3	the	the	DET
cana-2738	467	4	frequency	frequency	NOUN
cana-2738	467	5	of	of	ADP
cana-2738	467	6	experience	experience	NOUN
cana-2738	467	7	of	of	ADP
cana-2738	467	8	the	the	DET
cana-2738	467	9	symptoms	symptom	NOUN
cana-2738	467	10	of	of	ADP
cana-2738	467	11	the	the	DET
cana-2738	467	12	patients	patient	NOUN
cana-2738	467	13	from	from	ADP
cana-2738	467	14	last	last	ADJ
cana-2738	467	15	three	three	NUM
cana-2738	467	16	days	day	NOUN
cana-2738	467	17	as	as	ADP
cana-2738	467	18	pythagorean	pythagorean	PROPN
cana-2738	467	19	fuzzy	fuzzy	NOUN
cana-2738	467	20	set	set	VERB
cana-2738	467	21	by	by	ADP
cana-2738	467	22	considering	consider	VERB
cana-2738	467	23	the	the	DET
cana-2738	467	24	severe	severe	ADJ
cana-2738	467	25	symptom	symptom	NOUN
cana-2738	467	26	as	as	ADP
cana-2738	467	27	the	the	DET
cana-2738	467	28	degree	degree	NOUN
cana-2738	467	29	of	of	ADP
cana-2738	467	30	positive	positive	ADJ
cana-2738	467	31	membership	membership	NOUN
cana-2738	467	32	,	,	PUNCT
cana-2738	467	33	mild	mild	ADJ
cana-2738	467	34	symptom	symptom	NOUN
cana-2738	467	35	as	as	ADP
cana-2738	467	36	the	the	DET
cana-2738	467	37	degree	degree	NOUN
cana-2738	467	38	of	of	ADP
cana-2738	467	39	nutral	nutral	ADJ
cana-2738	467	40	membership	membership	NOUN
cana-2738	467	41	and	and	CCONJ
cana-2738	467	42	no	no	DET
cana-2738	467	43	experience	experience	NOUN
cana-2738	467	44	of	of	ADP
cana-2738	467	45	that	that	DET
cana-2738	467	46	symptom	symptom	NOUN
cana-2738	467	47	as	as	ADP
cana-2738	467	48	the	the	DET
cana-2738	467	49	degree	degree	NOUN
cana-2738	467	50	of	of	ADP
cana-2738	467	51	negative	negative	ADJ
cana-2738	467	52	membership	membership	NOUN
cana-2738	467	53	.	.	PUNCT
cana-2738	468	1	communications	communication	NOUN
cana-2738	468	2	on	on	ADP
cana-2738	468	3	applied	apply	VERB
cana-2738	468	4	nonlinear	nonlinear	ADJ
cana-2738	468	5	analysis	analysis	NOUN
cana-2738	468	6	issn	issn	NOUN
cana-2738	468	7	:	:	PUNCT
cana-2738	468	8	1074	1074	NUM
cana-2738	468	9	-	-	PUNCT
cana-2738	468	10	133x	133x	NUM
cana-2738	468	11	vol	vol	NOUN
cana-2738	468	12	32	32	NUM
cana-2738	468	13	no	no	NOUN
cana-2738	468	14	.	.	PUNCT
cana-2738	469	1	4s	4s	NUM
cana-2738	469	2	(	(	PUNCT
cana-2738	469	3	2025	2025	NUM
cana-2738	469	4	)	)	PUNCT
cana-2738	469	5	55	55	NUM
cana-2738	469	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2738	469	7	now	now	ADV
cana-2738	469	8	,	,	PUNCT
cana-2738	469	9	the	the	DET
cana-2738	469	10	ideal	ideal	ADJ
cana-2738	469	11	pythagorean	pythagorean	PROPN
cana-2738	469	12	fuzzy	fuzzy	NOUN
cana-2738	469	13	set	set	VERB
cana-2738	469	14	𝐼	𝐼	ADV
cana-2738	469	15	=	=	PUNCT
cana-2738	469	16	{	{	PUNCT
cana-2738	469	17	(	(	PUNCT
cana-2738	469	18	𝑥	𝑥	NOUN
cana-2738	469	19	,	,	PUNCT
cana-2738	469	20	𝜇𝑖(𝑥	𝜇𝑖(𝑥	NUM
cana-2738	469	21	)	)	PUNCT
cana-2738	469	22	,	,	PUNCT
cana-2738	469	23	𝜈𝑖(𝑥))/𝑥	𝜈𝑖(𝑥))/𝑥	PROPN
cana-2738	469	24	∈	∈	PROPN
cana-2738	469	25	𝑋	𝑋	PROPN
cana-2738	469	26	}	}	PUNCT
cana-2738	469	27	denotes	denote	VERB
cana-2738	469	28	the	the	DET
cana-2738	469	29	model	model	NOUN
cana-2738	469	30	set	set	VERB
cana-2738	469	31	for	for	ADP
cana-2738	469	32	the	the	DET
cana-2738	469	33	covid-19	covid-19	PROPN
cana-2738	469	34	patient	patient	NOUN
cana-2738	469	35	which	which	PRON
cana-2738	469	36	is	be	AUX
cana-2738	469	37	framed	frame	VERB
cana-2738	469	38	by	by	ADP
cana-2738	469	39	the	the	DET
cana-2738	469	40	data	datum	NOUN
cana-2738	469	41	collected	collect	VERB
cana-2738	469	42	from	from	ADP
cana-2738	469	43	the	the	DET
cana-2738	469	44	hospital	hospital	NOUN
cana-2738	469	45	resources	resource	NOUN
cana-2738	469	46	.	.	PUNCT
cana-2738	470	1	the	the	DET
cana-2738	470	2	membership	membership	NOUN
cana-2738	470	3	values	value	NOUN
cana-2738	470	4	of	of	ADP
cana-2738	470	5	the	the	DET
cana-2738	470	6	elements	element	NOUN
cana-2738	470	7	of	of	ADP
cana-2738	470	8	𝐼	𝐼	PROPN
cana-2738	470	9	are	be	AUX
cana-2738	470	10	(	(	PUNCT
cana-2738	470	11	𝑓	𝑓	ADV
cana-2738	470	12	,	,	PUNCT
cana-2738	470	13	𝜇𝑖(𝑓	𝜇𝑖(𝑓	NOUN
cana-2738	470	14	)	)	PUNCT
cana-2738	470	15	,	,	PUNCT
cana-2738	470	16	𝜈𝑖(𝑓	𝜈𝑖(𝑓	NUM
cana-2738	470	17	)	)	PUNCT
cana-2738	470	18	)	)	PUNCT
cana-2738	470	19	,	,	PUNCT
cana-2738	470	20	where	where	SCONJ
cana-2738	470	21	𝜇𝑖(𝑓	𝜇𝑖(𝑓	NOUN
cana-2738	470	22	)	)	PUNCT
cana-2738	470	23	≥	≥	NOUN
cana-2738	470	24	0.8	0.8	NUM
cana-2738	470	25	,	,	PUNCT
cana-2738	470	26	𝜈𝑖(𝑓	𝜈𝑖(𝑓	NUM
cana-2738	470	27	)	)	PUNCT
cana-2738	470	28	≥	≥	NOUN
cana-2738	470	29	0.1	0.1	NUM
cana-2738	470	30	(	(	PUNCT
cana-2738	470	31	𝑡	𝑡	X
cana-2738	470	32	,	,	PUNCT
cana-2738	470	33	𝜇𝑖(𝑡	𝜇𝑖(𝑡	ADJ
cana-2738	470	34	)	)	PUNCT
cana-2738	470	35	,	,	PUNCT
cana-2738	470	36	𝜈𝑖(𝑡	𝜈𝑖(𝑡	NUM
cana-2738	470	37	)	)	PUNCT
cana-2738	470	38	)	)	PUNCT
cana-2738	470	39	,	,	PUNCT
cana-2738	470	40	where	where	SCONJ
cana-2738	470	41	𝜇𝑖(𝑡	𝜇𝑖(𝑡	PUNCT
cana-2738	470	42	)	)	PUNCT
cana-2738	470	43	≥	≥	NOUN
cana-2738	470	44	0.5	0.5	NUM
cana-2738	470	45	,	,	PUNCT
cana-2738	470	46	𝜈𝑖(𝑡	𝜈𝑖(𝑡	NUM
cana-2738	470	47	)	)	PUNCT
cana-2738	470	48	≥	≥	NOUN
cana-2738	470	49	0.02	0.02	NUM
cana-2738	470	50	(	(	PUNCT
cana-2738	470	51	𝑑	𝑑	NOUN
cana-2738	470	52	,	,	PUNCT
cana-2738	470	53	𝜇𝑖(𝑑	𝜇𝑖(𝑑	ADJ
cana-2738	470	54	)	)	PUNCT
cana-2738	470	55	,	,	PUNCT
cana-2738	470	56	𝜈𝑖(𝑑	𝜈𝑖(𝑑	PROPN
cana-2738	470	57	)	)	PUNCT
cana-2738	470	58	)	)	PUNCT
cana-2738	470	59	,	,	PUNCT
cana-2738	470	60	where	where	SCONJ
cana-2738	470	61	𝜇𝑖(𝑑	𝜇𝑖(𝑑	NUM
cana-2738	470	62	)	)	PUNCT
cana-2738	470	63	≥	≥	NOUN
cana-2738	470	64	0.7	0.7	NUM
cana-2738	470	65	,	,	PUNCT
cana-2738	470	66	𝜈𝑖(𝑑	𝜈𝑖(𝑑	NUM
cana-2738	470	67	)	)	PUNCT
cana-2738	470	68	≥	≥	NOUN
cana-2738	470	69	0.02	0.02	NUM
cana-2738	470	70	(	(	PUNCT
cana-2738	470	71	𝑠	𝑠	NOUN
cana-2738	470	72	,	,	PUNCT
cana-2738	470	73	𝜇𝑖(𝑠	𝜇𝑖(𝑠	PROPN
cana-2738	470	74	)	)	PUNCT
cana-2738	470	75	,	,	PUNCT
cana-2738	470	76	𝜈𝑖(𝑠	𝜈𝑖(𝑠	NOUN
cana-2738	470	77	)	)	PUNCT
cana-2738	470	78	)	)	PUNCT
cana-2738	470	79	,	,	PUNCT
cana-2738	470	80	where	where	SCONJ
cana-2738	470	81	𝜇𝑖(𝑠	𝜇𝑖(𝑠	NOUN
cana-2738	470	82	)	)	PUNCT
cana-2738	470	83	≥	≥	NOUN
cana-2738	470	84	0.6	0.6	NUM
cana-2738	470	85	,	,	PUNCT
cana-2738	470	86	𝜈𝑖(𝑠	𝜈𝑖(𝑠	NOUN
cana-2738	470	87	)	)	PUNCT
cana-2738	470	88	≥	≥	NOUN
cana-2738	470	89	0.04	0.04	NUM
cana-2738	470	90	(	(	PUNCT
cana-2738	470	91	𝑝	𝑝	NOUN
cana-2738	470	92	,	,	PUNCT
cana-2738	470	93	𝜇𝑖(𝑝	𝜇𝑖(𝑝	ADJ
cana-2738	470	94	)	)	PUNCT
cana-2738	470	95	,	,	PUNCT
cana-2738	470	96	𝜈𝑖(𝑝	𝜈𝑖(𝑝	X
cana-2738	470	97	)	)	PUNCT
cana-2738	470	98	)	)	PUNCT
cana-2738	470	99	,	,	PUNCT
cana-2738	470	100	where	where	SCONJ
cana-2738	470	101	𝜇𝑖(𝑝	𝜇𝑖(𝑝	PUNCT
cana-2738	470	102	)	)	PUNCT
cana-2738	470	103	≥	≥	NOUN
cana-2738	470	104	0.4	0.4	NUM
cana-2738	470	105	,	,	PUNCT
cana-2738	470	106	𝜈𝑖(𝑝	𝜈𝑖(𝑝	NUM
cana-2738	470	107	)	)	PUNCT
cana-2738	470	108	≥	≥	NOUN
cana-2738	470	109	0.05	0.05	NUM
cana-2738	470	110	(	(	PUNCT
cana-2738	470	111	𝑎	𝑎	NOUN
cana-2738	470	112	,	,	PUNCT
cana-2738	470	113	𝜇𝑖(𝑎	𝜇𝑖(𝑎	NUM
cana-2738	470	114	)	)	PUNCT
cana-2738	470	115	,	,	PUNCT
cana-2738	470	116	𝜈𝑖(𝑎	𝜈𝑖(𝑎	NUM
cana-2738	470	117	)	)	PUNCT
cana-2738	470	118	)	)	PUNCT
cana-2738	470	119	,	,	PUNCT
cana-2738	470	120	where	where	SCONJ
cana-2738	470	121	𝜇𝑖(𝑎	𝜇𝑖(𝑎	NUM
cana-2738	470	122	)	)	PUNCT
cana-2738	470	123	≥	≥	NOUN
cana-2738	470	124	0.2	0.2	NUM
cana-2738	470	125	,	,	PUNCT
cana-2738	470	126	𝜈𝑖(𝑎	𝜈𝑖(𝑎	NUM
cana-2738	470	127	)	)	PUNCT
cana-2738	470	128	≥	≥	NOUN
cana-2738	470	129	0.4	0.4	NUM
cana-2738	470	130	(	(	PUNCT
cana-2738	470	131	𝑙	𝑙	NOUN
cana-2738	470	132	,	,	PUNCT
cana-2738	470	133	𝜇𝑖(𝑙	𝜇𝑖(𝑙	NUM
cana-2738	470	134	)	)	PUNCT
cana-2738	470	135	,	,	PUNCT
cana-2738	470	136	𝜈𝑖(𝑙	𝜈𝑖(𝑙	NUM
cana-2738	470	137	)	)	PUNCT
cana-2738	470	138	)	)	PUNCT
cana-2738	470	139	,	,	PUNCT
cana-2738	470	140	where	where	SCONJ
cana-2738	470	141	𝜇𝑖(𝑙	𝜇𝑖(𝑙	NUM
cana-2738	470	142	)	)	PUNCT
cana-2738	470	143	≥	≥	NOUN
cana-2738	470	144	0.6	0.6	NUM
cana-2738	470	145	,	,	PUNCT
cana-2738	470	146	𝜈𝑖(𝑙	𝜈𝑖(𝑙	NUM
cana-2738	470	147	)	)	PUNCT
cana-2738	470	148	≥	≥	NUM
cana-2738	470	149	0.06	0.06	NUM
cana-2738	470	150	(	(	PUNCT
cana-2738	470	151	𝑠𝑡	𝑠𝑡	PROPN
cana-2738	470	152	,	,	PUNCT
cana-2738	470	153	𝜇𝑖(𝑠𝑡	𝜇𝑖(𝑠𝑡	PROPN
cana-2738	470	154	)	)	PUNCT
cana-2738	470	155	,	,	PUNCT
cana-2738	470	156	𝜈𝑖(𝑠𝑡	𝜈𝑖(𝑠𝑡	PROPN
cana-2738	470	157	)	)	PUNCT
cana-2738	470	158	)	)	PUNCT
cana-2738	470	159	,	,	PUNCT
cana-2738	470	160	where	where	SCONJ
cana-2738	470	161	𝜇𝑖(𝑠𝑡	𝜇𝑖(𝑠𝑡	PROPN
cana-2738	470	162	)	)	PUNCT
cana-2738	470	163	≥	≥	NOUN
cana-2738	470	164	0.7	0.7	NUM
cana-2738	470	165	,	,	PUNCT
cana-2738	470	166	𝜈𝑖(𝑠𝑡	𝜈𝑖(𝑠𝑡	PROPN
cana-2738	470	167	)	)	PUNCT
cana-2738	470	168	≥	≥	NOUN
cana-2738	470	169	0.02	0.02	NUM
cana-2738	470	170	(	(	PUNCT
cana-2738	470	171	𝑏	𝑏	NOUN
cana-2738	470	172	,	,	PUNCT
cana-2738	470	173	𝜇𝑖(𝑏	𝜇𝑖(𝑏	NUM
cana-2738	470	174	)	)	PUNCT
cana-2738	470	175	,	,	PUNCT
cana-2738	470	176	𝜈𝑖(𝑏	𝜈𝑖(𝑏	NOUN
cana-2738	470	177	)	)	PUNCT
cana-2738	470	178	)	)	PUNCT
cana-2738	470	179	,	,	PUNCT
cana-2738	470	180	where	where	SCONJ
cana-2738	470	181	𝜇𝑖(𝑏	𝜇𝑖(𝑏	NOUN
cana-2738	470	182	)	)	PUNCT
cana-2738	470	183	≥	≥	NOUN
cana-2738	470	184	0.5	0.5	NUM
cana-2738	470	185	,	,	PUNCT
cana-2738	470	186	𝜈𝑖(𝑏	𝜈𝑖(𝑏	NOUN
cana-2738	470	187	)	)	PUNCT
cana-2738	470	188	≥	≥	NOUN
cana-2738	470	189	0.16	0.16	NUM
cana-2738	470	190	(	(	PUNCT
cana-2738	470	191	𝑟	𝑟	NOUN
cana-2738	470	192	,	,	PUNCT
cana-2738	470	193	𝜇𝑖(𝑟	𝜇𝑖(𝑟	NUM
cana-2738	470	194	)	)	PUNCT
cana-2738	470	195	,	,	PUNCT
cana-2738	470	196	𝜈𝑖(𝑟	𝜈𝑖(𝑟	PUNCT
cana-2738	470	197	)	)	PUNCT
cana-2738	470	198	)	)	PUNCT
cana-2738	470	199	,	,	PUNCT
cana-2738	470	200	where	where	SCONJ
cana-2738	470	201	𝜇𝑖(𝑟	𝜇𝑖(𝑟	PUNCT
cana-2738	470	202	)	)	PUNCT
cana-2738	470	203	≥	≥	NOUN
cana-2738	470	204	0.78	0.78	NUM
cana-2738	470	205	,	,	PUNCT
cana-2738	470	206	𝜈𝑖(𝑟	𝜈𝑖(𝑟	PUNCT
cana-2738	470	207	)	)	PUNCT
cana-2738	470	208	≥	≥	NOUN
cana-2738	470	209	0.01	0.01	NUM
cana-2738	470	210	𝜇𝑖(𝑥	𝜇𝑖(𝑥	NUM
cana-2738	470	211	)	)	PUNCT
cana-2738	470	212	severe	severe	ADJ
cana-2738	470	213	symptom	symptom	NOUN
cana-2738	470	214	,	,	PUNCT
cana-2738	470	215	𝜈𝑖(𝑥	𝜈𝑖(𝑥	NOUN
cana-2738	470	216	)	)	PUNCT
cana-2738	471	1	no	no	DET
cana-2738	471	2	symptom	symptom	NOUN
cana-2738	471	3	and	and	CCONJ
cana-2738	471	4	0	0	NUM
cana-2738	471	5	≤	≤	NUM
cana-2738	471	6	(	(	PUNCT
cana-2738	471	7	𝜇𝑖(𝑥))2	𝜇𝑖(𝑥))2	PROPN
cana-2738	471	8	+	+	CCONJ
cana-2738	471	9	(	(	PUNCT
cana-2738	471	10	𝜈𝑖(𝑥))2	𝜈𝑖(𝑥))2	NOUN
cana-2738	471	11	≤	≤	ADV
cana-2738	471	12	1	1	NUM
cana-2738	471	13	.	.	PUNCT
cana-2738	472	1	the	the	DET
cana-2738	472	2	decision	decision	NOUN
cana-2738	472	3	can	can	AUX
cana-2738	472	4	be	be	AUX
cana-2738	472	5	made	make	VERB
cana-2738	472	6	,	,	PUNCT
cana-2738	472	7	which	which	DET
cana-2738	472	8	patient	patient	NOUN
cana-2738	472	9	have	have	VERB
cana-2738	472	10	the	the	DET
cana-2738	472	11	more	more	ADJ
cana-2738	472	12	chances	chance	NOUN
cana-2738	472	13	to	to	PART
cana-2738	472	14	have	have	VERB
cana-2738	472	15	the	the	DET
cana-2738	472	16	covid-19	covid-19	PROPN
cana-2738	472	17	by	by	ADP
cana-2738	472	18	finding	find	VERB
cana-2738	472	19	the	the	DET
cana-2738	472	20	distance	distance	NOUN
cana-2738	472	21	between	between	ADP
cana-2738	472	22	the	the	DET
cana-2738	472	23	ideal	ideal	NOUN
cana-2738	473	1	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2738	474	1	and	and	CCONJ
cana-2738	474	2	the	the	DET
cana-2738	474	3	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2738	474	4	’s	’s	NOUN
cana-2738	474	5	of	of	ADP
cana-2738	474	6	the	the	DET
cana-2738	474	7	patients	patient	NOUN
cana-2738	474	8	𝐴	𝐴	PROPN
cana-2738	474	9	,	,	PUNCT
cana-2738	474	10	𝐵	𝐵	PROPN
cana-2738	474	11	,	,	PUNCT
cana-2738	474	12	𝐶.	𝐶.	PROPN
cana-2738	474	13	in	in	ADP
cana-2738	474	14	the	the	DET
cana-2738	474	15	following	follow	VERB
cana-2738	474	16	table	table	NOUN
cana-2738	474	17	symptom	symptom	NOUN
cana-2738	474	18	,	,	PUNCT
cana-2738	474	19	membership	membership	NOUN
cana-2738	474	20	values	value	NOUN
cana-2738	474	21	,	,	PUNCT
cana-2738	474	22	ideal	ideal	ADJ
cana-2738	474	23	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2738	474	24	,	,	PUNCT
cana-2738	474	25	patient	patient	PROPN
cana-2738	474	26	𝐴	𝐴	PROPN
cana-2738	474	27	,	,	PUNCT
cana-2738	474	28	patient	patient	ADJ
cana-2738	474	29	𝐵	𝐵	NOUN
cana-2738	474	30	,	,	PUNCT
cana-2738	474	31	patient	patient	NOUN
cana-2738	474	32	𝐶	𝐶	PROPN
cana-2738	474	33	,	,	PUNCT
cana-2738	474	34	hamming	hamming	NOUN
cana-2738	474	35	distance	distance	NOUN
cana-2738	474	36	(	(	PUNCT
cana-2738	474	37	𝐼	𝐼	PROPN
cana-2738	474	38	,	,	PUNCT
cana-2738	474	39	𝐴	𝐴	PROPN
cana-2738	474	40	)	)	PUNCT
cana-2738	474	41	,	,	PUNCT
cana-2738	474	42	hamming	ham	VERB
cana-2738	474	43	distance	distance	NOUN
cana-2738	474	44	(	(	PUNCT
cana-2738	474	45	𝐼	𝐼	PROPN
cana-2738	474	46	,	,	PUNCT
cana-2738	474	47	𝐵	𝐵	PROPN
cana-2738	474	48	)	)	PUNCT
cana-2738	474	49	,	,	PUNCT
cana-2738	474	50	hamming	ham	VERB
cana-2738	474	51	distance	distance	NOUN
cana-2738	474	52	(	(	PUNCT
cana-2738	474	53	𝐼	𝐼	PROPN
cana-2738	474	54	,	,	PUNCT
cana-2738	474	55	𝐶	𝐶	PROPN
cana-2738	474	56	)	)	PUNCT
cana-2738	474	57	,	,	PUNCT
cana-2738	474	58	euclidean	euclidean	ADJ
cana-2738	474	59	distance	distance	NOUN
cana-2738	474	60	(	(	PUNCT
cana-2738	474	61	𝐼	𝐼	PROPN
cana-2738	474	62	,	,	PUNCT
cana-2738	474	63	𝐴	𝐴	PROPN
cana-2738	474	64	)	)	PUNCT
cana-2738	474	65	,	,	PUNCT
cana-2738	474	66	euclidean	euclidean	ADJ
cana-2738	474	67	distance	distance	NOUN
cana-2738	474	68	(	(	PUNCT
cana-2738	474	69	𝐼	𝐼	PROPN
cana-2738	474	70	,	,	PUNCT
cana-2738	474	71	𝐵	𝐵	NOUN
cana-2738	474	72	)	)	PUNCT
cana-2738	474	73	and	and	CCONJ
cana-2738	474	74	euclidean	euclidean	ADJ
cana-2738	474	75	distance	distance	NOUN
cana-2738	474	76	(	(	PUNCT
cana-2738	474	77	𝐼	𝐼	PROPN
cana-2738	474	78	,	,	PUNCT
cana-2738	474	79	𝐶	𝐶	PROPN
cana-2738	474	80	)	)	PUNCT
cana-2738	474	81	are	be	AUX
cana-2738	474	82	briefly	briefly	ADV
cana-2738	474	83	denoted	denote	VERB
cana-2738	474	84	as	as	ADP
cana-2738	474	85	sym	sym	NOUN
cana-2738	474	86	,	,	PUNCT
cana-2738	474	87	mval	mval	NOUN
cana-2738	474	88	,	,	PUNCT
cana-2738	474	89	𝐼𝑃𝐹𝑆	𝐼𝑃𝐹𝑆	PROPN
cana-2738	474	90	,	,	PUNCT
cana-2738	474	91	𝑃𝐴	𝑃𝐴	PROPN
cana-2738	474	92	,	,	PUNCT
cana-2738	474	93	𝑃𝐵	𝑃𝐵	PROPN
cana-2738	474	94	,	,	PUNCT
cana-2738	474	95	𝑃𝐶	𝑃𝐶	PROPN
cana-2738	474	96	,	,	PUNCT
cana-2738	474	97	𝐻𝐷(𝐼	𝐻𝐷(𝐼	NOUN
cana-2738	474	98	,	,	PUNCT
cana-2738	474	99	𝐴	𝐴	PROPN
cana-2738	474	100	)	)	PUNCT
cana-2738	474	101	,	,	PUNCT
cana-2738	474	102	𝐻𝐷(𝐼	𝐻𝐷(𝐼	NOUN
cana-2738	474	103	,	,	PUNCT
cana-2738	474	104	𝐵	𝐵	PROPN
cana-2738	474	105	)	)	PUNCT
cana-2738	474	106	,	,	PUNCT
cana-2738	474	107	𝐻𝐷(𝐼	𝐻𝐷(𝐼	NUM
cana-2738	474	108	,	,	PUNCT
cana-2738	474	109	𝐶	𝐶	PROPN
cana-2738	474	110	)	)	PUNCT
cana-2738	474	111	,	,	PUNCT
cana-2738	474	112	𝐸𝐷(𝐼	𝐸𝐷(𝐼	PROPN
cana-2738	474	113	,	,	PUNCT
cana-2738	474	114	𝐴	𝐴	PROPN
cana-2738	474	115	)	)	PUNCT
cana-2738	474	116	,	,	PUNCT
cana-2738	474	117	𝐸𝐷(𝐼	𝐸𝐷(𝐼	PROPN
cana-2738	474	118	,	,	PUNCT
cana-2738	474	119	𝐵	𝐵	NOUN
cana-2738	474	120	)	)	PUNCT
cana-2738	474	121	and	and	CCONJ
cana-2738	474	122	𝐸𝐷(𝐼	𝐸𝐷(𝐼	PROPN
cana-2738	474	123	,	,	PUNCT
cana-2738	474	124	𝐶	𝐶	PROPN
cana-2738	474	125	)	)	PUNCT
cana-2738	474	126	.	.	PUNCT
cana-2738	475	1	communications	communication	NOUN
cana-2738	475	2	on	on	ADP
cana-2738	475	3	applied	apply	VERB
cana-2738	475	4	nonlinear	nonlinear	ADJ
cana-2738	475	5	analysis	analysis	NOUN
cana-2738	475	6	issn	issn	NOUN
cana-2738	475	7	:	:	PUNCT
cana-2738	475	8	1074	1074	NUM
cana-2738	475	9	-	-	PUNCT
cana-2738	475	10	133x	133x	NUM
cana-2738	475	11	vol	vol	NOUN
cana-2738	475	12	32	32	NUM
cana-2738	475	13	no	no	NOUN
cana-2738	475	14	.	.	PUNCT
cana-2738	476	1	4s	4s	NUM
cana-2738	476	2	(	(	PUNCT
cana-2738	476	3	2025	2025	NUM
cana-2738	476	4	)	)	PUNCT
cana-2738	476	5	56	56	NUM
cana-2738	476	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2738	476	7	calculation	calculation	NOUN
cana-2738	476	8	:	:	PUNCT
cana-2738	476	9	hamming	hamming	NOUN
cana-2738	476	10	distance	distance	NOUN
cana-2738	476	11	:	:	PUNCT
cana-2738	476	12	𝑑𝐻𝐷(𝐼	𝑑𝐻𝐷(𝐼	PROPN
cana-2738	476	13	,	,	PUNCT
cana-2738	476	14	𝐴	𝐴	PROPN
cana-2738	476	15	)	)	PUNCT
cana-2738	476	16	=	=	PUNCT
cana-2738	477	1	1.075	1.075	NUM
cana-2738	477	2	𝑑𝐻𝐷(𝐼	𝑑𝐻𝐷(𝐼	PROPN
cana-2738	477	3	,	,	PUNCT
cana-2738	477	4	𝐵	𝐵	NOUN
cana-2738	477	5	)	)	PUNCT
cana-2738	477	6	=	=	PUNCT
cana-2738	477	7	1.660	1.660	NUM
cana-2738	477	8	𝑑𝐻𝐷(𝐼	𝑑𝐻𝐷(𝐼	PROPN
cana-2738	477	9	,	,	PUNCT
cana-2738	477	10	𝐶	𝐶	PROPN
cana-2738	477	11	)	)	PUNCT
cana-2738	477	12	=	=	SYM
cana-2738	477	13	3.220	3.220	NUM
cana-2738	477	14	normalized	normalize	VERB
cana-2738	477	15	hamming	hamming	NOUN
cana-2738	477	16	distance	distance	NOUN
cana-2738	477	17	:	:	PUNCT
cana-2738	477	18	𝑑𝑁𝐻𝐷(𝐼	𝑑𝑁𝐻𝐷(𝐼	NOUN
cana-2738	477	19	,	,	PUNCT
cana-2738	477	20	𝐴	𝐴	PROPN
cana-2738	477	21	)	)	PUNCT
cana-2738	477	22	=	=	PUNCT
cana-2738	477	23	0.108	0.108	NUM
cana-2738	477	24	𝑑𝑁𝐻𝐷(𝐼	𝑑𝑁𝐻𝐷(𝐼	NOUN
cana-2738	477	25	,	,	PUNCT
cana-2738	477	26	𝐵	𝐵	NOUN
cana-2738	477	27	)	)	PUNCT
cana-2738	477	28	=	=	NOUN
cana-2738	477	29	0.166	0.166	NUM
cana-2738	477	30	𝑑𝑁𝐻𝐷(𝐼	𝑑𝑁𝐻𝐷(𝐼	NOUN
cana-2738	477	31	,	,	PUNCT
cana-2738	477	32	𝐶	𝐶	PROPN
cana-2738	477	33	)	)	PUNCT
cana-2738	477	34	=	=	PUNCT
cana-2738	477	35	0.322	0.322	NUM
cana-2738	477	36	euclidean	euclidean	ADJ
cana-2738	477	37	distance	distance	NOUN
cana-2738	477	38	:	:	PUNCT
cana-2738	477	39	𝐸𝐷(𝐼	𝐸𝐷(𝐼	NOUN
cana-2738	477	40	,	,	PUNCT
cana-2738	477	41	𝐴	𝐴	PROPN
cana-2738	477	42	)	)	PUNCT
cana-2738	477	43	=	=	SYM
cana-2738	477	44	0.550	0.550	NUM
cana-2738	477	45	𝐸𝐷(𝐼	𝐸𝐷(𝐼	NOUN
cana-2738	477	46	,	,	PUNCT
cana-2738	477	47	𝐵	𝐵	NOUN
cana-2738	477	48	)	)	PUNCT
cana-2738	477	49	=	=	NOUN
cana-2738	477	50	0.677	0.677	NUM
cana-2738	477	51	𝐸𝐷(𝐼	𝐸𝐷(𝐼	NOUN
cana-2738	477	52	,	,	PUNCT
cana-2738	477	53	𝐶	𝐶	PROPN
cana-2738	477	54	)	)	PUNCT
cana-2738	477	55	=	=	SYM
cana-2738	477	56	1.128	1.128	NUM
cana-2738	477	57	normalized	normalize	VERB
cana-2738	477	58	euclidean	euclidean	ADJ
cana-2738	477	59	distance	distance	NOUN
cana-2738	477	60	:	:	PUNCT
cana-2738	477	61	𝑁𝐸𝐷(𝐼	𝑁𝐸𝐷(𝐼	NOUN
cana-2738	477	62	,	,	PUNCT
cana-2738	477	63	𝐴	𝐴	PROPN
cana-2738	477	64	)	)	PUNCT
cana-2738	477	65	=	=	PUNCT
cana-2738	477	66	0.174	0.174	NUM
cana-2738	477	67	𝑁𝐸𝐷(𝐼	𝑁𝐸𝐷(𝐼	NOUN
cana-2738	477	68	,	,	PUNCT
cana-2738	477	69	𝐵	𝐵	NOUN
cana-2738	477	70	)	)	PUNCT
cana-2738	477	71	=	=	PUNCT
cana-2738	477	72	0.214	0.214	NUM
cana-2738	477	73	𝑁𝐸𝐷(𝐼	𝑁𝐸𝐷(𝐼	NOUN
cana-2738	477	74	,	,	PUNCT
cana-2738	477	75	𝐶	𝐶	PROPN
cana-2738	477	76	)	)	PUNCT
cana-2738	477	77	=	=	SYM
cana-2738	477	78	0.357	0.357	NUM
cana-2738	477	79	threfore	threfore	NOUN
cana-2738	477	80	,	,	PUNCT
cana-2738	477	81	from	from	ADP
cana-2738	477	82	the	the	DET
cana-2738	477	83	above	above	ADJ
cana-2738	477	84	table	table	NOUN
cana-2738	477	85	we	we	PRON
cana-2738	477	86	observe	observe	VERB
cana-2738	477	87	that	that	SCONJ
cana-2738	477	88	𝑑𝐻𝐷(𝐼	𝑑𝐻𝐷(𝐼	PROPN
cana-2738	477	89	,	,	PUNCT
cana-2738	477	90	𝐴	𝐴	PROPN
cana-2738	477	91	)	)	PUNCT
cana-2738	477	92	<	<	X
cana-2738	477	93	𝑑𝐻𝐷(𝐼	𝑑𝐻𝐷(𝐼	PROPN
cana-2738	477	94	,	,	PUNCT
cana-2738	477	95	𝐵	𝐵	NOUN
cana-2738	477	96	)	)	PUNCT
cana-2738	477	97	<	<	X
cana-2738	477	98	𝑑𝐻𝐷(𝐼	𝑑𝐻𝐷(𝐼	PROPN
cana-2738	477	99	,	,	PUNCT
cana-2738	477	100	𝐶	𝐶	PROPN
cana-2738	477	101	)	)	PUNCT
cana-2738	477	102	communications	communication	NOUN
cana-2738	477	103	on	on	ADP
cana-2738	477	104	applied	apply	VERB
cana-2738	477	105	nonlinear	nonlinear	ADJ
cana-2738	477	106	analysis	analysis	NOUN
cana-2738	477	107	issn	issn	NOUN
cana-2738	477	108	:	:	PUNCT
cana-2738	477	109	1074	1074	NUM
cana-2738	477	110	-	-	PUNCT
cana-2738	477	111	133x	133x	NUM
cana-2738	477	112	vol	vol	NOUN
cana-2738	477	113	32	32	NUM
cana-2738	477	114	no	no	NOUN
cana-2738	477	115	.	.	PUNCT
cana-2738	478	1	4s	4s	NUM
cana-2738	478	2	(	(	PUNCT
cana-2738	478	3	2025	2025	NUM
cana-2738	478	4	)	)	PUNCT
cana-2738	478	5	57	57	NUM
cana-2738	478	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2738	478	7	𝑑𝑁𝐻𝐷(𝐼	𝑑𝑁𝐻𝐷(𝐼	NOUN
cana-2738	478	8	,	,	PUNCT
cana-2738	478	9	𝐴	𝐴	PROPN
cana-2738	478	10	)	)	PUNCT
cana-2738	478	11	<	<	X
cana-2738	478	12	𝑑𝑁𝐻𝐷(𝐼	𝑑𝑁𝐻𝐷(𝐼	NOUN
cana-2738	478	13	,	,	PUNCT
cana-2738	478	14	𝐵	𝐵	NOUN
cana-2738	478	15	)	)	PUNCT
cana-2738	478	16	<	<	X
cana-2738	478	17	𝑑𝑁𝐻𝐷(𝐼	𝑑𝑁𝐻𝐷(𝐼	PROPN
cana-2738	478	18	,	,	PUNCT
cana-2738	478	19	𝐶	𝐶	PROPN
cana-2738	478	20	)	)	PUNCT
cana-2738	478	21	𝐸𝐷(𝐼	𝐸𝐷(𝐼	PROPN
cana-2738	478	22	,	,	PUNCT
cana-2738	478	23	𝐴	𝐴	PROPN
cana-2738	478	24	)	)	PUNCT
cana-2738	478	25	<	<	X
cana-2738	478	26	𝐸𝐷(𝐼	𝐸𝐷(𝐼	PROPN
cana-2738	478	27	,	,	PUNCT
cana-2738	478	28	𝐵	𝐵	NOUN
cana-2738	478	29	)	)	PUNCT
cana-2738	478	30	<	<	X
cana-2738	478	31	𝐸𝐷(𝐼	𝐸𝐷(𝐼	PROPN
cana-2738	478	32	,	,	PUNCT
cana-2738	478	33	𝐶	𝐶	PROPN
cana-2738	478	34	)	)	PUNCT
cana-2738	478	35	and	and	CCONJ
cana-2738	478	36	𝑁𝐸𝐷(𝐼	𝑁𝐸𝐷(𝐼	NOUN
cana-2738	478	37	,	,	PUNCT
cana-2738	478	38	𝐴	𝐴	PROPN
cana-2738	478	39	)	)	PUNCT
cana-2738	478	40	<	<	X
cana-2738	479	1	𝑁𝐸𝐷(𝐼	𝑁𝐸𝐷(𝐼	PROPN
cana-2738	479	2	,	,	PUNCT
cana-2738	479	3	𝐵	𝐵	NOUN
cana-2738	479	4	)	)	PUNCT
cana-2738	479	5	<	<	X
cana-2738	479	6	𝑁𝐸𝐷(𝐼	𝑁𝐸𝐷(𝐼	PROPN
cana-2738	479	7	,	,	PUNCT
cana-2738	479	8	𝐶	𝐶	PROPN
cana-2738	479	9	)	)	PUNCT
cana-2738	479	10	with	with	ADP
cana-2738	479	11	this	this	DET
cana-2738	479	12	evidence	evidence	NOUN
cana-2738	479	13	we	we	PRON
cana-2738	479	14	may	may	AUX
cana-2738	479	15	conclude	conclude	VERB
cana-2738	479	16	that	that	SCONJ
cana-2738	479	17	the	the	DET
cana-2738	479	18	patient	patient	NOUN
cana-2738	479	19	𝐴	𝐴	PROPN
cana-2738	479	20	have	have	VERB
cana-2738	479	21	the	the	DET
cana-2738	479	22	more	more	ADJ
cana-2738	479	23	chance	chance	NOUN
cana-2738	479	24	to	to	PART
cana-2738	479	25	affected	affect	VERB
cana-2738	479	26	by	by	ADP
cana-2738	479	27	the	the	DET
cana-2738	479	28	covid19	covid19	NOUN
cana-2738	479	29	among	among	ADP
cana-2738	479	30	these	these	DET
cana-2738	479	31	three	three	NUM
cana-2738	479	32	patients	patient	NOUN
cana-2738	479	33	.	.	PUNCT
cana-2738	480	1	6	6	NUM
cana-2738	480	2	conclusion	conclusion	NOUN
cana-2738	480	3	in	in	ADP
cana-2738	480	4	this	this	DET
cana-2738	480	5	paper	paper	NOUN
cana-2738	480	6	,	,	PUNCT
cana-2738	480	7	some	some	DET
cana-2738	480	8	new	new	ADJ
cana-2738	480	9	notions	notion	NOUN
cana-2738	480	10	of	of	ADP
cana-2738	480	11	strongly	strongly	ADV
cana-2738	480	12	pythagorean	pythagorean	ADJ
cana-2738	480	13	fuzzy	fuzzy	ADJ
cana-2738	480	14	open	open	ADJ
cana-2738	480	15	(	(	PUNCT
cana-2738	480	16	closed	closed	ADJ
cana-2738	480	17	)	)	PUNCT
cana-2738	480	18	maps	map	NOUN
cana-2738	480	19	called	call	VERB
cana-2738	480	20	pythagorean	pythagorean	PROPN
cana-2738	480	21	fuzzy	fuzzy	PROPN
cana-2738	480	22	𝛿-open	𝛿-open	VERB
cana-2738	480	23	and	and	CCONJ
cana-2738	480	24	pythagorean	pythagorean	PROPN
cana-2738	480	25	fuzzy	fuzzy	ADJ
cana-2738	480	26	𝛿-closed	𝛿-close	VERB
cana-2738	480	27	maps	map	NOUN
cana-2738	480	28	are	be	AUX
cana-2738	480	29	introduced	introduce	VERB
cana-2738	480	30	and	and	CCONJ
cana-2738	480	31	discussed	discuss	VERB
cana-2738	480	32	their	their	PRON
cana-2738	480	33	relationship	relationship	NOUN
cana-2738	480	34	between	between	ADP
cana-2738	480	35	their	their	PRON
cana-2738	480	36	near	near	ADJ
cana-2738	480	37	mappings	mapping	NOUN
cana-2738	480	38	with	with	ADP
cana-2738	480	39	examples	example	NOUN
cana-2738	480	40	.	.	PUNCT
cana-2738	481	1	also	also	ADV
cana-2738	481	2	,	,	PUNCT
cana-2738	481	3	we	we	PRON
cana-2738	481	4	have	have	AUX
cana-2738	481	5	tried	try	VERB
cana-2738	481	6	to	to	PART
cana-2738	481	7	diagnosis	diagnosis	VERB
cana-2738	481	8	covid-19	covid-19	PROPN
cana-2738	481	9	with	with	ADP
cana-2738	481	10	the	the	DET
cana-2738	481	11	help	help	NOUN
cana-2738	481	12	of	of	ADP
cana-2738	481	13	pythagorean	pythagorean	PROPN
cana-2738	481	14	fuzzy	fuzzy	ADJ
cana-2738	481	15	sets	set	NOUN
cana-2738	481	16	which	which	PRON
cana-2738	481	17	helps	help	VERB
cana-2738	481	18	to	to	PART
cana-2738	481	19	record	record	VERB
cana-2738	481	20	all	all	DET
cana-2738	481	21	symptoms	symptom	NOUN
cana-2738	481	22	in	in	ADP
cana-2738	481	23	prã	prã	PROPN
cana-2738	481	24	©	©	PROPN
cana-2738	481	25	cised	cise	VERB
cana-2738	481	26	manner	manner	NOUN
cana-2738	481	27	.	.	PUNCT
cana-2738	482	1	in	in	ADP
cana-2738	482	2	future	future	NOUN
cana-2738	482	3	,	,	PUNCT
cana-2738	482	4	researchers	researcher	NOUN
cana-2738	482	5	can	can	AUX
cana-2738	482	6	extend	extend	VERB
cana-2738	482	7	this	this	DET
cana-2738	482	8	model	model	NOUN
cana-2738	482	9	to	to	ADP
cana-2738	482	10	other	other	ADJ
cana-2738	482	11	extensions	extension	NOUN
cana-2738	482	12	of	of	ADP
cana-2738	482	13	fuzzy	fuzzy	ADJ
cana-2738	482	14	sets	set	NOUN
cana-2738	482	15	such	such	ADJ
cana-2738	482	16	as	as	ADP
cana-2738	482	17	rough	rough	ADJ
cana-2738	482	18	sets	set	NOUN
cana-2738	482	19	and	and	CCONJ
cana-2738	482	20	utilize	utilize	VERB
cana-2738	482	21	the	the	DET
cana-2738	482	22	interdependency	interdependency	NOUN
cana-2738	482	23	among	among	ADP
cana-2738	482	24	the	the	DET
cana-2738	482	25	various	various	ADJ
cana-2738	482	26	evaluation	evaluation	NOUN
cana-2738	482	27	criteria	criterion	NOUN
cana-2738	482	28	for	for	ADP
cana-2738	482	29	better	well	ADJ
cana-2738	482	30	judgement	judgement	NOUN
cana-2738	482	31	.	.	PUNCT
cana-2738	483	1	√	√	PROPN
cana-2738	483	2	(	(	PUNCT
cana-2738	483	3	𝑎	𝑎	PROPN
cana-2738	483	4	𝑏	𝑏	NOUN
cana-2738	483	5	+	+	PROPN
cana-2738	483	6	𝑐	𝑐	PROPN
cana-2738	483	7	𝑑	𝑑	NOUN
cana-2738	483	8	)	)	PUNCT
cana-2738	483	9	2	2	NUM
cana-2738	484	1	+	+	CCONJ
cana-2738	484	2	(	(	PUNCT
cana-2738	484	3	𝑒	𝑒	PROPN
cana-2738	484	4	𝑓	𝑓	PROPN
cana-2738	484	5	+	+	PROPN
cana-2738	484	6	𝑔	𝑔	PROPN
cana-2738	484	7	ℎ	ℎ	NOUN
cana-2738	484	8	)	)	PUNCT
cana-2738	484	9	2	2	NUM
cana-2738	485	1	+	+	CCONJ
cana-2738	485	2	(	(	PUNCT
cana-2738	485	3	𝑖	𝑖	SYM
cana-2738	485	4	𝑗	𝑗	VERB
cana-2738	485	5	+	+	X
cana-2738	485	6	𝑘	𝑘	PRON
cana-2738	485	7	𝑙	𝑙	NOUN
cana-2738	485	8	)	)	PUNCT
cana-2738	485	9	2	2	NUM
cana-2738	485	10	(	(	PUNCT
cana-2738	485	11	1	1	NUM
cana-2738	485	12	)	)	PUNCT
cana-2738	485	13	√	√	PROPN
cana-2738	485	14	(	(	PUNCT
cana-2738	485	15	𝑎	𝑎	PROPN
cana-2738	485	16	𝑏	𝑏	NOUN
cana-2738	485	17	+	+	PROPN
cana-2738	485	18	𝑐	𝑐	PROPN
cana-2738	485	19	𝑑	𝑑	NOUN
cana-2738	485	20	)	)	PUNCT
cana-2738	485	21	2	2	NUM
cana-2738	486	1	+	+	CCONJ
cana-2738	486	2	(	(	PUNCT
cana-2738	486	3	𝑒	𝑒	PROPN
cana-2738	486	4	𝑓	𝑓	PROPN
cana-2738	486	5	+	+	PROPN
cana-2738	486	6	𝑔	𝑔	PROPN
cana-2738	486	7	ℎ	ℎ	NOUN
cana-2738	486	8	)	)	PUNCT
cana-2738	486	9	2	2	NUM
cana-2738	487	1	+	+	CCONJ
cana-2738	487	2	(	(	PUNCT
cana-2738	487	3	𝑖	𝑖	SYM
cana-2738	487	4	𝑗	𝑗	VERB
cana-2738	487	5	+	+	X
cana-2738	487	6	𝑘	𝑘	PRON
cana-2738	487	7	𝑙	𝑙	NOUN
cana-2738	487	8	)	)	PUNCT
cana-2738	487	9	2	2	NUM
cana-2738	487	10	(	(	PUNCT
cana-2738	487	11	2	2	NUM
cana-2738	487	12	)	)	PUNCT
cana-2738	487	13	refrences	refrence	NOUN
cana-2738	488	1	[	[	X
cana-2738	488	2	1	1	X
cana-2738	488	3	]	]	SYM
cana-2738	488	4	kt	kt	PROPN
cana-2738	488	5	.	.	PROPN
cana-2738	488	6	atanassov	atanassov	PROPN
cana-2738	488	7	,	,	PUNCT
cana-2738	488	8	intuitionistic	intuitionistic	ADJ
cana-2738	488	9	fuzzy	fuzzy	ADJ
cana-2738	488	10	sets	set	NOUN
cana-2738	488	11	,	,	PUNCT
cana-2738	488	12	fuzzy	fuzzy	ADJ
cana-2738	488	13	sets	set	NOUN
cana-2738	488	14	syst	syst	NOUN
cana-2738	488	15	,	,	PUNCT
cana-2738	488	16	20	20	NUM
cana-2738	488	17	(	(	PUNCT
cana-2738	488	18	1986a	1986a	NUM
cana-2738	488	19	)	)	PUNCT
cana-2738	488	20	,	,	PUNCT
cana-2738	488	21	87	87	NUM
cana-2738	488	22	-	-	SYM
cana-2738	488	23	96	96	NUM
cana-2738	488	24	.	.	PUNCT
cana-2738	489	1	[	[	X
cana-2738	489	2	2	2	NUM
cana-2738	489	3	]	]	SYM
cana-2738	489	4	kt	kt	PROPN
cana-2738	489	5	.	.	PROPN
cana-2738	489	6	atanassov	atanassov	PROPN
cana-2738	489	7	,	,	PUNCT
cana-2738	489	8	intuitionistic	intuitionistic	ADJ
cana-2738	489	9	fuzzy	fuzzy	ADJ
cana-2738	489	10	sets	set	NOUN
cana-2738	489	11	,	,	PUNCT
cana-2738	489	12	fuzzy	fuzzy	ADJ
cana-2738	489	13	sets	set	NOUN
cana-2738	489	14	syst	syst	NOUN
cana-2738	489	15	,	,	PUNCT
cana-2738	489	16	20(1	20(1	NUM
cana-2738	489	17	)	)	PUNCT
cana-2738	489	18	(	(	PUNCT
cana-2738	489	19	1986b	1986b	NUM
cana-2738	489	20	)	)	PUNCT
cana-2738	489	21	,	,	PUNCT
cana-2738	489	22	87	87	NUM
cana-2738	489	23	-	-	SYM
cana-2738	489	24	96	96	NUM
cana-2738	489	25	.	.	PUNCT
cana-2738	490	1	[	[	X
cana-2738	490	2	3	3	X
cana-2738	490	3	]	]	PUNCT
cana-2738	490	4	k.	k.	PROPN
cana-2738	490	5	t.	t.	PROPN
cana-2738	490	6	atanassov	atanassov	PROPN
cana-2738	490	7	(	(	PUNCT
cana-2738	490	8	1999	1999	NUM
cana-2738	490	9	)	)	PUNCT
cana-2738	490	10	,	,	PUNCT
cana-2738	490	11	intuitionistic	intuitionistic	ADJ
cana-2738	490	12	fuzzy	fuzzy	ADJ
cana-2738	490	13	sets	set	NOUN
cana-2738	490	14	:	:	PUNCT
cana-2738	490	15	theory	theory	NOUN
cana-2738	490	16	and	and	CCONJ
cana-2738	490	17	applications	application	NOUN
cana-2738	490	18	,	,	PUNCT
cana-2738	490	19	physica	physica	NOUN
cana-2738	490	20	,	,	PUNCT
cana-2738	490	21	heidelberg	heidelberg	NOUN
cana-2738	490	22	.	.	PUNCT
cana-2738	491	1	[	[	X
cana-2738	491	2	4	4	X
cana-2738	491	3	]	]	PUNCT
cana-2738	491	4	k.	k.	PROPN
cana-2738	491	5	t.	t.	PROPN
cana-2738	491	6	atanassov	atanassov	PROPN
cana-2738	491	7	(	(	PUNCT
cana-2738	491	8	2012	2012	NUM
cana-2738	491	9	)	)	PUNCT
cana-2738	491	10	,	,	PUNCT
cana-2738	491	11	on	on	ADP
cana-2738	491	12	intuitionistic	intuitionistic	ADJ
cana-2738	491	13	fuzzy	fuzzy	ADJ
cana-2738	491	14	sets	set	NOUN
cana-2738	491	15	theory	theory	NOUN
cana-2738	491	16	,	,	PUNCT
cana-2738	491	17	springer	springer	NOUN
cana-2738	491	18	,	,	PUNCT
cana-2738	491	19	berlin	berlin	PROPN
cana-2738	491	20	.	.	PUNCT
cana-2738	492	1	[	[	X
cana-2738	492	2	5	5	X
cana-2738	492	3	]	]	PUNCT
cana-2738	492	4	s.	s.	PROPN
cana-2738	492	5	boccaletti	boccaletti	PROPN
cana-2738	492	6	,	,	PUNCT
cana-2738	492	7	w.	w.	PROPN
cana-2738	492	8	ditto	ditto	PROPN
cana-2738	492	9	,	,	PUNCT
cana-2738	492	10	g.	g.	PROPN
cana-2738	492	11	mindlin	mindlin	PROPN
cana-2738	492	12	and	and	CCONJ
cana-2738	492	13	a.	a.	PROPN
cana-2738	492	14	atangana	atangana	PROPN
cana-2738	492	15	,	,	PUNCT
cana-2738	492	16	modeling	modeling	NOUN
cana-2738	492	17	and	and	CCONJ
cana-2738	492	18	forecasting	forecasting	NOUN
cana-2738	492	19	of	of	ADP
cana-2738	492	20	epidemic	epidemic	NOUN
cana-2738	492	21	spreading	spread	VERB
cana-2738	492	22	the	the	DET
cana-2738	492	23	case	case	NOUN
cana-2738	492	24	of	of	ADP
cana-2738	492	25	covid-19	covid-19	PROPN
cana-2738	492	26	and	and	CCONJ
cana-2738	492	27	beyond	beyond	ADP
cana-2738	492	28	.	.	PUNCT
cana-2738	493	1	chaos	chaos	NOUN
cana-2738	493	2	,	,	PUNCT
cana-2738	493	3	(	(	PUNCT
cana-2738	493	4	2020	2020	NUM
cana-2738	493	5	)	)	PUNCT
cana-2738	493	6	solitons	soliton	NOUN
cana-2738	493	7	fractals	fractal	NOUN
cana-2738	493	8	135:109794	135:109794	NOUN
cana-2738	493	9	[	[	X
cana-2738	493	10	6	6	NUM
cana-2738	493	11	]	]	PUNCT
cana-2738	493	12	o.	o.	PROPN
cana-2738	493	13	castillo	castillo	PROPN
cana-2738	493	14	and	and	CCONJ
cana-2738	493	15	p.	p.	PROPN
cana-2738	493	16	melin	melin	PROPN
cana-2738	493	17	,	,	PUNCT
cana-2738	493	18	forecasting	forecasting	NOUN
cana-2738	493	19	of	of	ADP
cana-2738	493	20	covid-19	covid-19	PROPN
cana-2738	493	21	time	time	NOUN
cana-2738	493	22	series	series	NOUN
cana-2738	493	23	for	for	ADP
cana-2738	493	24	countries	country	NOUN
cana-2738	493	25	in	in	ADP
cana-2738	493	26	the	the	DET
cana-2738	493	27	world	world	NOUN
cana-2738	493	28	based	base	VERB
cana-2738	493	29	on	on	ADP
cana-2738	493	30	a	a	DET
cana-2738	493	31	hybrid	hybrid	ADJ
cana-2738	493	32	approach	approach	NOUN
cana-2738	493	33	combining	combine	VERB
cana-2738	493	34	the	the	DET
cana-2738	493	35	fractal	fractal	ADJ
cana-2738	493	36	dimension	dimension	NOUN
cana-2738	493	37	and	and	CCONJ
cana-2738	493	38	fuzzy	fuzzy	ADJ
cana-2738	493	39	logic	logic	NOUN
cana-2738	493	40	.	.	PUNCT
cana-2738	494	1	chaos	chaos	NOUN
cana-2738	494	2	,	,	PUNCT
cana-2738	494	3	(	(	PUNCT
cana-2738	494	4	2020	2020	NUM
cana-2738	494	5	)	)	PUNCT
cana-2738	494	6	solitons	soliton	NOUN
cana-2738	494	7	fractals	fractal	NOUN
cana-2738	494	8	140:110242	140:110242	NUM
cana-2738	494	9	.	.	PUNCT
cana-2738	495	1	[	[	X
cana-2738	495	2	7	7	X
cana-2738	495	3	]	]	X
cana-2738	495	4	o.	o.	PROPN
cana-2738	495	5	castillo	castillo	PROPN
cana-2738	495	6	and	and	CCONJ
cana-2738	495	7	p.	p.	PROPN
cana-2738	495	8	melin	melin	PROPN
cana-2738	495	9	,	,	PUNCT
cana-2738	495	10	a	a	DET
cana-2738	495	11	novel	novel	ADJ
cana-2738	495	12	method	method	NOUN
cana-2738	495	13	for	for	ADP
cana-2738	495	14	a	a	DET
cana-2738	495	15	covid-19	covid-19	PROPN
cana-2738	495	16	classification	classification	NOUN
cana-2738	495	17	of	of	ADP
cana-2738	495	18	countries	country	NOUN
cana-2738	495	19	based	base	VERB
cana-2738	495	20	on	on	ADP
cana-2738	495	21	an	an	DET
cana-2738	495	22	intelligent	intelligent	ADJ
cana-2738	495	23	fuzzy	fuzzy	ADJ
cana-2738	495	24	fractal	fractal	ADJ
cana-2738	495	25	approach	approach	NOUN
cana-2738	495	26	,	,	PUNCT
cana-2738	495	27	(	(	PUNCT
cana-2738	495	28	2021	2021	NUM
cana-2738	495	29	)	)	PUNCT
cana-2738	495	30	healthcare	healthcare	PROPN
cana-2738	495	31	9:196	9:196	NUM
cana-2738	495	32	.	.	PUNCT
cana-2738	496	1	https://doi.org/10.3390/	https://doi.org/10.3390/	PROPN
cana-2738	496	2	healthcare9020196	healthcare9020196	PROPN
cana-2738	496	3	.	.	PUNCT
cana-2738	497	1	[	[	X
cana-2738	497	2	8	8	NUM
cana-2738	497	3	]	]	X
cana-2738	497	4	clinical	clinical	ADJ
cana-2738	497	5	management	management	NOUN
cana-2738	497	6	protocol	protocol	NOUN
cana-2738	497	7	,	,	PUNCT
cana-2738	497	8	covid-19government	covid-19government	PROPN
cana-2738	497	9	of	of	ADP
cana-2738	497	10	india	india	PROPN
cana-2738	497	11	ministry	ministry	PROPN
cana-2738	497	12	of	of	ADP
cana-2738	497	13	health	health	PROPN
cana-2738	497	14	and	and	CCONJ
cana-2738	497	15	family	family	NOUN
cana-2738	497	16	welfare	welfare	NOUN
cana-2738	497	17	directorate	directorate	ADJ
cana-2738	497	18	general	general	NOUN
cana-2738	497	19	of	of	ADP
cana-2738	497	20	health	health	NOUN
cana-2738	497	21	services	service	NOUN
cana-2738	497	22	,	,	PUNCT
cana-2738	497	23	emr	emr	PROPN
cana-2738	497	24	division	division	NOUN
cana-2738	497	25	(	(	PUNCT
cana-2738	497	26	2020	2020	NUM
cana-2738	497	27	)	)	PUNCT
cana-2738	497	28	.	.	PUNCT
cana-2738	498	1	[	[	X
cana-2738	498	2	9	9	NUM
cana-2738	498	3	]	]	X
cana-2738	498	4	cb	cb	PROPN
cana-2738	498	5	.	.	PROPN
cana-2738	498	6	cong	cong	PROPN
cana-2738	498	7	and	and	CCONJ
cana-2738	498	8	lh	lh	PROPN
cana-2738	498	9	.	.	PROPN
cana-2738	498	10	son	son	PROPN
cana-2738	498	11	,	,	PUNCT
cana-2738	498	12	some	some	DET
cana-2738	498	13	selected	select	VERB
cana-2738	498	14	problems	problem	NOUN
cana-2738	498	15	of	of	ADP
cana-2738	498	16	modern	modern	ADJ
cana-2738	498	17	soft	soft	ADJ
cana-2738	498	18	computing	computing	NOUN
cana-2738	498	19	,	,	PUNCT
cana-2738	498	20	(	(	PUNCT
cana-2738	498	21	2015	2015	NUM
cana-2738	498	22	)	)	PUNCT
cana-2738	498	23	.	.	PUNCT
cana-2738	499	1	https://doi.org/10.15625/vap.2015.000203	https://doi.org/10.15625/vap.2015.000203	ADJ
cana-2738	499	2	[	[	X
cana-2738	499	3	10	10	NUM
cana-2738	499	4	]	]	X
cana-2738	499	5	bc	bc	PROPN
cana-2738	499	6	.	.	PROPN
cana-2738	499	7	cuong	cuong	PROPN
cana-2738	499	8	and	and	CCONJ
cana-2738	499	9	v.	v.	ADP
cana-2738	499	10	kreinovich	kreinovich	ADJ
cana-2738	499	11	,	,	PUNCT
cana-2738	499	12	picture	picture	NOUN
cana-2738	499	13	fuzzy	fuzzy	ADJ
cana-2738	499	14	sets	set	NOUN
cana-2738	499	15	,	,	PUNCT
cana-2738	499	16	j	j	PROPN
cana-2738	499	17	comput	comput	VERB
cana-2738	499	18	sci	sci	PROPN
cana-2738	499	19	cybern	cybern	PROPN
cana-2738	499	20	30(4	30(4	PROPN
cana-2738	499	21	)	)	PUNCT
cana-2738	499	22	(	(	PUNCT
cana-2738	499	23	2014	2014	NUM
cana-2738	499	24	)	)	PUNCT
cana-2738	499	25	,	,	PUNCT
cana-2738	500	1	409–416	409–416	INTJ
cana-2738	500	2	.	.	PUNCT
cana-2738	501	1	[	[	X
cana-2738	501	2	11	11	NUM
cana-2738	501	3	]	]	PUNCT
cana-2738	501	4	s.	s.	PROPN
cana-2738	501	5	das	das	PROPN
cana-2738	501	6	,	,	PUNCT
cana-2738	501	7	mb	mb	PROPN
cana-2738	501	8	.	.	PROPN
cana-2738	501	9	kar	kar	PROPN
cana-2738	501	10	and	and	CCONJ
cana-2738	501	11	s.	s.	PROPN
cana-2738	501	12	kar	kar	PROPN
cana-2738	501	13	,	,	PUNCT
cana-2738	501	14	group	group	NOUN
cana-2738	501	15	multi	multi	ADJ
cana-2738	501	16	-	-	ADJ
cana-2738	501	17	criteria	criterion	NOUN
cana-2738	501	18	decision	decision	NOUN
cana-2738	501	19	making	make	VERB
cana-2738	501	20	using	use	VERB
cana-2738	501	21	intuitionistic	intuitionistic	ADJ
cana-2738	501	22	multi	multi	ADJ
cana-2738	501	23	-	-	ADJ
cana-2738	501	24	fuzzy	fuzzy	ADJ
cana-2738	501	25	sets	set	NOUN
cana-2738	501	26	,	,	PUNCT
cana-2738	501	27	journal	journal	NOUN
cana-2738	501	28	of	of	ADP
cana-2738	501	29	uncertainty	uncertainty	NOUN
cana-2738	501	30	analysis	analysis	NOUN
cana-2738	501	31	and	and	CCONJ
cana-2738	501	32	applications	application	NOUN
cana-2738	501	33	(	(	PUNCT
cana-2738	501	34	2013	2013	NUM
cana-2738	501	35	)	)	PUNCT
cana-2738	501	36	.	.	PUNCT
cana-2738	502	1	http://www.juaa-journal.com/content/1/1/10	http://www.juaa-journal.com/content/1/1/10	PROPN
cana-2738	503	1	[	[	X
cana-2738	503	2	12	12	NUM
cana-2738	503	3	]	]	PUNCT
cana-2738	503	4	s.	s.	PROPN
cana-2738	503	5	das	das	PROPN
cana-2738	503	6	,	,	PUNCT
cana-2738	503	7	d.	d.	PROPN
cana-2738	503	8	malakar	malakar	PROPN
cana-2738	503	9	,	,	PUNCT
cana-2738	503	10	s.	s.	PROPN
cana-2738	503	11	kar	kar	PROPN
cana-2738	503	12	and	and	CCONJ
cana-2738	503	13	t.	t.	PROPN
cana-2738	503	14	pal	pal	NOUN
cana-2738	503	15	,	,	PUNCT
cana-2738	503	16	a	a	DET
cana-2738	503	17	brief	brief	ADJ
cana-2738	503	18	review	review	NOUN
cana-2738	503	19	and	and	CCONJ
cana-2738	503	20	future	future	ADJ
cana-2738	503	21	outline	outline	NOUN
cana-2738	503	22	on	on	ADP
cana-2738	503	23	decision	decision	NOUN
cana-2738	503	24	making	make	VERB
cana-2738	503	25	using	use	VERB
cana-2738	503	26	fuzzy	fuzzy	ADJ
cana-2738	503	27	soft	soft	ADJ
cana-2738	503	28	set	set	NOUN
cana-2738	503	29	,	,	PUNCT
cana-2738	503	30	int	int	NOUN
cana-2738	503	31	j	j	PROPN
cana-2738	503	32	fuzzy	fuzzy	ADJ
cana-2738	503	33	syst	syst	PROPN
cana-2738	503	34	appl	appl	PROPN
cana-2738	503	35	7(2	7(2	PROPN
cana-2738	503	36	)	)	PUNCT
cana-2738	503	37	(	(	PUNCT
cana-2738	503	38	2018	2018	NUM
cana-2738	503	39	)	)	PUNCT
cana-2738	503	40	,	,	PUNCT
cana-2738	503	41	1	1	NUM
cana-2738	503	42	-	-	SYM
cana-2738	503	43	43	43	NUM
cana-2738	503	44	.	.	PUNCT
cana-2738	504	1	[	[	X
cana-2738	504	2	13	13	NUM
cana-2738	504	3	]	]	PUNCT
cana-2738	504	4	s.	s.	PROPN
cana-2738	504	5	das	das	PROPN
cana-2738	504	6	,	,	PUNCT
cana-2738	504	7	s.	s.	PROPN
cana-2738	504	8	kumar	kumar	PROPN
cana-2738	504	9	,	,	PUNCT
cana-2738	504	10	s.	s.	PROPN
cana-2738	504	11	kar	kar	PROPN
cana-2738	504	12	and	and	CCONJ
cana-2738	504	13	t.	t.	PROPN
cana-2738	504	14	pal	pal	NOUN
cana-2738	504	15	,	,	PUNCT
cana-2738	504	16	group	group	NOUN
cana-2738	504	17	decision	decision	NOUN
cana-2738	504	18	making	make	VERB
cana-2738	504	19	using	use	VERB
cana-2738	504	20	neutrosophic	neutrosophic	ADJ
cana-2738	504	21	soft	soft	ADJ
cana-2738	504	22	matrix	matrix	NOUN
cana-2738	504	23	an	an	DET
cana-2738	504	24	algorithmic	algorithmic	ADJ
cana-2738	504	25	approach	approach	NOUN
cana-2738	504	26	,	,	PUNCT
cana-2738	504	27	j	j	PROPN
cana-2738	504	28	king	king	PROPN
cana-2738	504	29	saud	saud	PROPN
cana-2738	504	30	univ	univ	PROPN
cana-2738	504	31	comput	comput	PROPN
cana-2738	504	32	inf	inf	PROPN
cana-2738	504	33	sci	sci	PROPN
cana-2738	504	34	31(4	31(4	NUM
cana-2738	504	35	)	)	PUNCT
cana-2738	504	36	(	(	PUNCT
cana-2738	504	37	2019	2019	NUM
cana-2738	504	38	)	)	PUNCT
cana-2738	504	39	,	,	PUNCT
cana-2738	504	40	459	459	NUM
cana-2738	504	41	-	-	SYM
cana-2738	504	42	468	468	NUM
cana-2738	504	43	.	.	PUNCT
cana-2738	505	1	[	[	X
cana-2738	505	2	14	14	NUM
cana-2738	505	3	]	]	PUNCT
cana-2738	505	4	j.	j.	PROPN
cana-2738	505	5	deng	deng	PROPN
cana-2738	505	6	,	,	PUNCT
cana-2738	505	7	control	control	NOUN
cana-2738	505	8	problems	problem	NOUN
cana-2738	505	9	of	of	ADP
cana-2738	505	10	grey	grey	PROPN
cana-2738	505	11	systems	system	NOUN
cana-2738	505	12	,	,	PUNCT
cana-2738	505	13	syst	syst	PROPN
cana-2738	505	14	control	control	PROPN
cana-2738	505	15	lett	lett	PROPN
cana-2738	505	16	1(5	1(5	PROPN
cana-2738	505	17	)	)	PUNCT
cana-2738	505	18	(	(	PUNCT
cana-2738	505	19	1982	1982	NUM
cana-2738	505	20	)	)	PUNCT
cana-2738	505	21	,	,	PUNCT
cana-2738	505	22	288	288	NUM
cana-2738	505	23	-	-	SYM
cana-2738	505	24	294	294	NUM
cana-2738	505	25	.	.	PUNCT
cana-2738	506	1	[	[	X
cana-2738	506	2	15	15	NUM
cana-2738	506	3	]	]	X
cana-2738	506	4	wl	wl	PROPN
cana-2738	506	5	.	.	PUNCT
cana-2738	506	6	gau	gau	PROPN
cana-2738	506	7	and	and	CCONJ
cana-2738	506	8	dj	dj	NOUN
cana-2738	506	9	.	.	PUNCT
cana-2738	506	10	buehrer	buehrer	NOUN
cana-2738	506	11	,	,	PUNCT
cana-2738	506	12	vague	vague	ADJ
cana-2738	506	13	sets	set	NOUN
cana-2738	506	14	,	,	PUNCT
cana-2738	506	15	ieee	ieee	PROPN
cana-2738	506	16	trans	trans	PROPN
cana-2738	506	17	syst	syst	PROPN
cana-2738	506	18	man	man	PROPN
cana-2738	506	19	cybern	cybern	NOUN
cana-2738	506	20	23	23	NUM
cana-2738	506	21	(	(	PUNCT
cana-2738	506	22	1993	1993	NUM
cana-2738	506	23	)	)	PUNCT
cana-2738	506	24	,	,	PUNCT
cana-2738	506	25	610	610	NUM
cana-2738	506	26	-	-	SYM
cana-2738	506	27	614	614	NUM
cana-2738	506	28	.	.	PUNCT
cana-2738	507	1	[	[	X
cana-2738	507	2	16	16	NUM
cana-2738	507	3	]	]	X
cana-2738	507	4	n.	n.	PROPN
cana-2738	507	5	b.	b.	PROPN
cana-2738	507	6	gnanachristy	gnanachristy	PROPN
cana-2738	507	7	and	and	CCONJ
cana-2738	507	8	g.	g.	PROPN
cana-2738	507	9	k.	k.	PROPN
cana-2738	507	10	revathi	revathi	PROPN
cana-2738	507	11	,	,	PUNCT
cana-2738	507	12	(	(	PUNCT
cana-2738	507	13	2021	2021	NUM
cana-2738	507	14	)	)	PUNCT
cana-2738	507	15	a	a	DET
cana-2738	507	16	view	view	NOUN
cana-2738	507	17	on	on	ADP
cana-2738	507	18	pythagorean	pythagorean	PROPN
cana-2738	507	19	fuzzy	fuzzy	ADJ
cana-2738	507	20	contra	contra	PROPN
cana-2738	507	21	𝒢	𝒢	PROPN
cana-2738	507	22	continuous	continuous	ADJ
cana-2738	507	23	function	function	NOUN
cana-2738	507	24	,	,	PUNCT
cana-2738	507	25	journal	journal	NOUN
cana-2738	507	26	of	of	ADP
cana-2738	507	27	physics	physics	PROPN
cana-2738	507	28	conference	conference	NOUN
cana-2738	507	29	series	series	PROPN
cana-2738	507	30	,	,	PUNCT
cana-2738	507	31	(	(	PUNCT
cana-2738	507	32	2115	2115	NUM
cana-2738	507	33	)	)	PUNCT
cana-2738	507	34	,	,	PUNCT
cana-2738	507	35	012041	012041	NUM
cana-2738	507	36	.	.	PUNCT
cana-2738	508	1	communications	communication	NOUN
cana-2738	508	2	on	on	ADP
cana-2738	508	3	applied	apply	VERB
cana-2738	508	4	nonlinear	nonlinear	ADJ
cana-2738	508	5	analysis	analysis	NOUN
cana-2738	508	6	issn	issn	NOUN
cana-2738	508	7	:	:	PUNCT
cana-2738	508	8	1074	1074	NUM
cana-2738	508	9	-	-	PUNCT
cana-2738	508	10	133x	133x	NUM
cana-2738	508	11	vol	vol	NOUN
cana-2738	508	12	32	32	NUM
cana-2738	508	13	no	no	NOUN
cana-2738	508	14	.	.	PUNCT
cana-2738	509	1	4s	4s	NUM
cana-2738	509	2	(	(	PUNCT
cana-2738	509	3	2025	2025	NUM
cana-2738	509	4	)	)	PUNCT
cana-2738	509	5	58	58	NUM
cana-2738	510	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-2738	511	1	[	[	X
cana-2738	511	2	17	17	NUM
cana-2738	511	3	]	]	X
cana-2738	511	4	p.	p.	PROPN
cana-2738	511	5	ghosh	ghosh	PROPN
cana-2738	511	6	,	,	PUNCT
cana-2738	511	7	r.	r.	PROPN
cana-2738	511	8	ghosh	ghosh	PROPN
cana-2738	511	9	and	and	CCONJ
cana-2738	511	10	b.	b.	PROPN
cana-2738	511	11	chakraborty	chakraborty	PROPN
cana-2738	511	12	,	,	PUNCT
cana-2738	511	13	covid-19	covid-19	PROPN
cana-2738	511	14	in	in	ADP
cana-2738	511	15	india	india	PROPN
cana-2738	511	16	statewise	statewise	NOUN
cana-2738	511	17	analysis	analysis	NOUN
cana-2738	511	18	and	and	CCONJ
cana-2738	511	19	prediction	prediction	NOUN
cana-2738	511	20	,	,	PUNCT
cana-2738	511	21	jmir	jmir	PROPN
cana-2738	511	22	publ	publ	PROPN
cana-2738	511	23	health	health	NOUN
cana-2738	511	24	surv	surv	NOUN
cana-2738	511	25	6	6	NUM
cana-2738	511	26	(	(	PUNCT
cana-2738	511	27	2020	2020	NUM
cana-2738	511	28	)	)	PUNCT
cana-2738	511	29	,	,	PUNCT
cana-2738	511	30	20341	20341	NUM
cana-2738	511	31	.	.	PUNCT
cana-2738	512	1	https://doi.org/10.1101/2020.04.24.20077792	https://doi.org/10.1101/2020.04.24.20077792	PROPN
cana-2738	512	2	[	[	X
cana-2738	512	3	18	18	NUM
cana-2738	512	4	]	]	SYM
cana-2738	512	5	mb	mb	ADJ
cana-2738	512	6	.	.	PROPN
cana-2738	512	7	gorzalczany	gorzalczany	NOUN
cana-2738	512	8	,	,	PUNCT
cana-2738	512	9	a	a	DET
cana-2738	512	10	method	method	NOUN
cana-2738	512	11	of	of	ADP
cana-2738	512	12	inference	inference	NOUN
cana-2738	512	13	in	in	ADP
cana-2738	512	14	approximate	approximate	ADJ
cana-2738	512	15	reasoning	reasoning	NOUN
cana-2738	512	16	based	base	VERB
cana-2738	512	17	on	on	ADP
cana-2738	512	18	interval	interval	NOUN
cana-2738	512	19	-	-	PUNCT
cana-2738	512	20	valued	value	VERB
cana-2738	512	21	fuzzy	fuzzy	ADJ
cana-2738	512	22	sets	set	NOUN
cana-2738	512	23	,	,	PUNCT
cana-2738	512	24	fuzzy	fuzzy	ADJ
cana-2738	512	25	sets	set	VERB
cana-2738	512	26	syst	syst	NOUN
cana-2738	512	27	21(1	21(1	NUM
cana-2738	512	28	)	)	PUNCT
cana-2738	512	29	(	(	PUNCT
cana-2738	512	30	1987	1987	NUM
cana-2738	512	31	)	)	PUNCT
cana-2738	512	32	,	,	PUNCT
cana-2738	512	33	1	1	NUM
cana-2738	512	34	-	-	SYM
cana-2738	512	35	17	17	NUM
cana-2738	512	36	.	.	PUNCT
cana-2738	513	1	[	[	X
cana-2738	513	2	19	19	NUM
cana-2738	513	3	]	]	PUNCT
cana-2738	513	4	sj	sj	PROPN
cana-2738	513	5	.	.	PROPN
cana-2738	513	6	kalayathankal	kalayathankal	PROPN
cana-2738	513	7	and	and	CCONJ
cana-2738	513	8	gs	gs	INTJ
cana-2738	513	9	.	.	PUNCT
cana-2738	513	10	singh	singh	PROPN
cana-2738	513	11	,	,	PUNCT
cana-2738	513	12	a	a	DET
cana-2738	513	13	fuzzy	fuzzy	ADJ
cana-2738	513	14	soft	soft	ADJ
cana-2738	513	15	flood	flood	NOUN
cana-2738	513	16	alarm	alarm	NOUN
cana-2738	513	17	model	model	NOUN
cana-2738	513	18	,	,	PUNCT
cana-2738	513	19	math	math	NOUN
cana-2738	513	20	comput	comput	NOUN
cana-2738	513	21	simul	simul	PROPN
cana-2738	513	22	80(5	80(5	PROPN
cana-2738	513	23	)	)	PUNCT
cana-2738	513	24	(	(	PUNCT
cana-2738	513	25	2010	2010	NUM
cana-2738	513	26	)	)	PUNCT
cana-2738	513	27	,	,	PUNCT
cana-2738	513	28	887	887	NUM
cana-2738	513	29	-	-	SYM
cana-2738	513	30	893	893	NUM
cana-2738	513	31	.	.	PUNCT
cana-2738	514	1	[	[	X
cana-2738	514	2	20	20	NUM
cana-2738	514	3	]	]	X
cana-2738	514	4	dv	dv	PROPN
cana-2738	514	5	.	.	PROPN
cana-2738	514	6	kovkov	kovkov	PROPN
cana-2738	514	7	,	,	PUNCT
cana-2738	514	8	vm	vm	PROPN
cana-2738	514	9	.	.	PROPN
cana-2738	514	10	kolbanov	kolbanov	PROPN
cana-2738	514	11	and	and	CCONJ
cana-2738	514	12	da	da	PROPN
cana-2738	514	13	.	.	PUNCT
cana-2738	515	1	molodtsov	molodtsov	PROPN
cana-2738	515	2	soft	soft	ADJ
cana-2738	515	3	set	set	NOUN
cana-2738	515	4	theory	theory	NOUN
cana-2738	515	5	based	base	VERB
cana-2738	515	6	optimization	optimization	NOUN
cana-2738	515	7	,	,	PUNCT
cana-2738	515	8	j	j	PROPN
cana-2738	515	9	comput	comput	PROPN
cana-2738	515	10	syst	syst	PROPN
cana-2738	515	11	sci	sci	PROPN
cana-2738	515	12	int	int	PROPN
cana-2738	515	13	46(6	46(6	NOUN
cana-2738	515	14	)	)	PUNCT
cana-2738	515	15	(	(	PUNCT
cana-2738	515	16	2007	2007	NUM
cana-2738	515	17	)	)	PUNCT
cana-2738	515	18	,	,	PUNCT
cana-2738	515	19	872	872	NUM
cana-2738	515	20	-	-	SYM
cana-2738	515	21	880	880	NUM
cana-2738	515	22	.	.	PUNCT
cana-2738	516	1	[	[	X
cana-2738	516	2	21	21	NUM
cana-2738	516	3	]	]	SYM
cana-2738	516	4	su	su	PROPN
cana-2738	516	5	.	.	PROPN
cana-2738	516	6	kumar	kumar	PROPN
cana-2738	516	7	,	,	PUNCT
cana-2738	516	8	dt	dt	PROPN
cana-2738	516	9	.	.	PUNCT
cana-2738	517	1	kumar	kumar	PROPN
cana-2738	517	2	,	,	PUNCT
cana-2738	517	3	bp	bp	PROPN
cana-2738	517	4	.	.	PROPN
cana-2738	517	5	christopher	christopher	PROPN
cana-2738	517	6	and	and	CCONJ
cana-2738	517	7	cgp	cgp	PROPN
cana-2738	517	8	.	.	PUNCT
cana-2738	518	1	doss	doss	PROPN
cana-2738	518	2	,	,	PUNCT
cana-2738	518	3	the	the	DET
cana-2738	518	4	rise	rise	NOUN
cana-2738	518	5	and	and	CCONJ
cana-2738	518	6	impact	impact	NOUN
cana-2738	518	7	of	of	ADP
cana-2738	518	8	covid-19	covid-19	PROPN
cana-2738	518	9	in	in	ADP
cana-2738	518	10	india	india	PROPN
cana-2738	518	11	,	,	PUNCT
cana-2738	518	12	frontiers	frontier	NOUN
cana-2738	518	13	in	in	ADP
cana-2738	518	14	medicine	medicine	NOUN
cana-2738	518	15	.	.	PUNCT
cana-2738	519	1	front	front	NOUN
cana-2738	519	2	med	med	ADJ
cana-2738	519	3	7	7	NUM
cana-2738	519	4	(	(	PUNCT
cana-2738	519	5	2020	2020	NUM
cana-2738	519	6	)	)	PUNCT
cana-2738	519	7	,	,	PUNCT
cana-2738	519	8	250	250	NUM
cana-2738	519	9	.	.	PUNCT
cana-2738	520	1	https://doi.org/10.3389/fmed.2020.00250	https://doi.org/10.3389/fmed.2020.00250	PROPN
cana-2738	521	1	[	[	X
cana-2738	521	2	22	22	NUM
cana-2738	521	3	]	]	PUNCT
cana-2738	521	4	p.	p.	NOUN
cana-2738	521	5	melin	melin	PROPN
cana-2738	521	6	,	,	PUNCT
cana-2738	521	7	jc	jc	PROPN
cana-2738	521	8	.	.	PROPN
cana-2738	521	9	monica	monica	PROPN
cana-2738	521	10	,	,	PUNCT
cana-2738	521	11	d.	d.	PROPN
cana-2738	521	12	sanchez	sanchez	PROPN
cana-2738	521	13	and	and	CCONJ
cana-2738	521	14	o.	o.	PROPN
cana-2738	521	15	castillo	castillo	PROPN
cana-2738	521	16	,	,	PUNCT
cana-2738	521	17	multiple	multiple	ADJ
cana-2738	521	18	ensemble	ensemble	ADJ
cana-2738	521	19	neural	neural	ADJ
cana-2738	521	20	network	network	NOUN
cana-2738	521	21	models	model	NOUN
cana-2738	521	22	with	with	ADP
cana-2738	521	23	fuzzy	fuzzy	ADJ
cana-2738	521	24	response	response	NOUN
cana-2738	521	25	aggregation	aggregation	NOUN
cana-2738	521	26	for	for	ADP
cana-2738	521	27	predicting	predict	VERB
cana-2738	521	28	covid-19	covid-19	PROPN
cana-2738	521	29	time	time	NOUN
cana-2738	521	30	series	series	NOUN
cana-2738	521	31	,	,	PUNCT
cana-2738	521	32	the	the	DET
cana-2738	521	33	case	case	NOUN
cana-2738	521	34	of	of	ADP
cana-2738	521	35	mexico	mexico	PROPN
cana-2738	521	36	,	,	PUNCT
cana-2738	521	37	healthcare	healthcare	NOUN
cana-2738	521	38	8	8	NUM
cana-2738	521	39	(	(	PUNCT
cana-2738	521	40	2020	2020	NUM
cana-2738	521	41	)	)	PUNCT
cana-2738	521	42	181	181	NUM
cana-2738	521	43	.	.	PUNCT
cana-2738	522	1	https://doi.org/10.3390/healthcare8020181	https://doi.org/10.3390/healthcare8020181	VERB
cana-2738	522	2	[	[	X
cana-2738	522	3	23	23	NUM
cana-2738	522	4	]	]	SYM
cana-2738	522	5	mm	mm	X
cana-2738	522	6	.	.	PROPN
cana-2738	522	7	mushrif	mushrif	PROPN
cana-2738	522	8	,	,	PUNCT
cana-2738	522	9	s.	s.	PROPN
cana-2738	522	10	sengupta	sengupta	PROPN
cana-2738	522	11	and	and	CCONJ
cana-2738	522	12	ak	ak	PROPN
cana-2738	522	13	.	.	PROPN
cana-2738	522	14	roy	roy	PROPN
cana-2738	522	15	,	,	PUNCT
cana-2738	522	16	texture	texture	ADJ
cana-2738	522	17	classification	classification	NOUN
cana-2738	522	18	using	use	VERB
cana-2738	522	19	novel	novel	NOUN
cana-2738	522	20	,	,	PUNCT
cana-2738	522	21	soft	soft	ADJ
cana-2738	522	22	set	set	NOUN
cana-2738	522	23	theory	theory	NOUN
cana-2738	522	24	based	base	VERB
cana-2738	522	25	classification	classification	NOUN
cana-2738	522	26	algorithm	algorithm	NOUN
cana-2738	522	27	,	,	PUNCT
cana-2738	522	28	in	in	ADP
cana-2738	522	29	pj	pj	PROPN
cana-2738	522	30	.	.	PUNCT
cana-2738	523	1	narayanan	narayanan	PROPN
cana-2738	523	2	,	,	PUNCT
cana-2738	523	3	sk	sk	PROPN
cana-2738	523	4	.	.	PROPN
cana-2738	523	5	nayar	nayar	PROPN
cana-2738	523	6	,	,	PUNCT
cana-2738	523	7	hy	hy	PROPN
cana-2738	523	8	.	.	PUNCT
cana-2738	523	9	shum	shum	PROPN
cana-2738	523	10	(	(	PUNCT
cana-2738	523	11	eds	ed	NOUN
cana-2738	523	12	)	)	PUNCT
cana-2738	523	13	proceedings	proceeding	NOUN
cana-2738	523	14	of	of	ADP
cana-2738	523	15	the	the	DET
cana-2738	523	16	7th	7th	ADJ
cana-2738	523	17	asian	asian	ADJ
cana-2738	523	18	conference	conference	NOUN
cana-2738	523	19	on	on	ADP
cana-2738	523	20	computer	computer	NOUN
cana-2738	523	21	vision	vision	NOUN
cana-2738	523	22	,	,	PUNCT
cana-2738	523	23	lecture	lecture	NOUN
cana-2738	523	24	notes	note	NOUN
cana-2738	523	25	in	in	ADP
cana-2738	523	26	computer	computer	NOUN
cana-2738	523	27	science	science	NOUN
cana-2738	523	28	,	,	PUNCT
cana-2738	523	29	3851	3851	NUM
cana-2738	523	30	springer	springer	NOUN
cana-2738	523	31	(	(	PUNCT
cana-2738	523	32	2006	2006	NUM
cana-2738	523	33	)	)	PUNCT
cana-2738	523	34	,	,	PUNCT
cana-2738	523	35	246	246	NUM
cana-2738	523	36	-	-	SYM
cana-2738	523	37	254	254	NUM
cana-2738	523	38	.	.	PUNCT
cana-2738	524	1	[	[	X
cana-2738	524	2	24	24	NUM
cana-2738	524	3	]	]	X
cana-2738	524	4	murat	murat	PROPN
cana-2738	524	5	olgun	olgun	PROPN
cana-2738	524	6	,	,	PUNCT
cana-2738	524	7	mehmet	mehmet	PROPN
cana-2738	524	8	unver	unver	PROPN
cana-2738	524	9	and	and	CCONJ
cana-2738	524	10	seyhmus	seyhmus	VERB
cana-2738	524	11	yardimci	yardimci	PROPN
cana-2738	524	12	(	(	PUNCT
cana-2738	524	13	2019	2019	NUM
cana-2738	524	14	)	)	PUNCT
cana-2738	524	15	,	,	PUNCT
cana-2738	524	16	pythagorean	pythagorean	PROPN
cana-2738	524	17	fuzzy	fuzzy	ADJ
cana-2738	524	18	topological	topological	ADJ
cana-2738	524	19	spaces	space	NOUN
cana-2738	524	20	,	,	PUNCT
cana-2738	524	21	complex	complex	ADJ
cana-2738	524	22	&	&	CCONJ
cana-2738	524	23	intelligent	intelligent	ADJ
cana-2738	524	24	systems	system	NOUN
cana-2738	524	25	.	.	PUNCT
cana-2738	525	1	https://doi.org/10.1007/s40747-019-0095-2	https://doi.org/10.1007/s40747-019-0095-2	NUM
cana-2738	525	2	.	.	PUNCT
cana-2738	526	1	[	[	X
cana-2738	526	2	25	25	NUM
cana-2738	526	3	]	]	X
cana-2738	526	4	jh	jh	PROPN
cana-2738	526	5	.	.	PUNCT
cana-2738	526	6	park	park	PROPN
cana-2738	526	7	,	,	PUNCT
cana-2738	526	8	km	km	PROPN
cana-2738	526	9	.	.	PUNCT
cana-2738	527	1	lim	lim	PROPN
cana-2738	527	2	and	and	CCONJ
cana-2738	527	3	js	js	PROPN
cana-2738	527	4	.	.	PUNCT
cana-2738	528	1	park	park	PROPN
cana-2738	528	2	,	,	PUNCT
cana-2738	528	3	distances	distance	NOUN
cana-2738	528	4	between	between	ADP
cana-2738	528	5	interval	interval	NOUN
cana-2738	528	6	-	-	PUNCT
cana-2738	528	7	valued	value	VERB
cana-2738	528	8	intuitionistic	intuitionistic	ADJ
cana-2738	528	9	fuzzy	fuzzy	ADJ
cana-2738	528	10	sets	set	NOUN
cana-2738	528	11	,	,	PUNCT
cana-2738	528	12	2007	2007	NUM
cana-2738	528	13	international	international	ADJ
cana-2738	528	14	symposium	symposium	NOUN
cana-2738	528	15	on	on	ADP
cana-2738	528	16	nonlinear	nonlinear	ADJ
cana-2738	528	17	dynamics	dynamic	NOUN
cana-2738	528	18	,	,	PUNCT
cana-2738	528	19	j	j	PROPN
cana-2738	528	20	phys	phys	PROPN
cana-2738	528	21	:	:	PUNCT
cana-2738	528	22	conf	conf	NOUN
cana-2738	528	23	ser	ser	NOUN
cana-2738	528	24	(	(	PUNCT
cana-2738	528	25	2008	2008	NUM
cana-2738	528	26	)	)	PUNCT
cana-2738	528	27	96:18	96:18	NUM
cana-2738	528	28	.	.	PUNCT
cana-2738	529	1	[	[	X
cana-2738	529	2	26	26	NUM
cana-2738	529	3	]	]	PUNCT
cana-2738	529	4	z.	z.	PROPN
cana-2738	529	5	pawlak	pawlak	PROPN
cana-2738	529	6	,	,	PUNCT
cana-2738	529	7	rough	rough	ADJ
cana-2738	529	8	sets	set	NOUN
cana-2738	529	9	,	,	PUNCT
cana-2738	529	10	int	int	PROPN
cana-2738	529	11	j	j	PROPN
cana-2738	529	12	inf	inf	PROPN
cana-2738	529	13	comput	comput	VERB
cana-2738	529	14	sci	sci	PROPN
cana-2738	529	15	11	11	NUM
cana-2738	529	16	(	(	PUNCT
cana-2738	529	17	1982	1982	NUM
cana-2738	529	18	)	)	PUNCT
cana-2738	529	19	,	,	PUNCT
cana-2738	529	20	341	341	NUM
cana-2738	529	21	-	-	SYM
cana-2738	529	22	356	356	NUM
cana-2738	529	23	.	.	PUNCT
cana-2738	530	1	[	[	X
cana-2738	530	2	27	27	NUM
cana-2738	530	3	]	]	PUNCT
cana-2738	530	4	z.	z.	PROPN
cana-2738	530	5	ren	ren	PROPN
cana-2738	530	6	,	,	PUNCT
cana-2738	530	7	h.	h.	PROPN
cana-2738	530	8	liao	liao	PROPN
cana-2738	530	9	and	and	CCONJ
cana-2738	530	10	y.	y.	PROPN
cana-2738	530	11	liu	liu	PROPN
cana-2738	530	12	,	,	PUNCT
cana-2738	530	13	generalized	generalize	VERB
cana-2738	530	14	𝑍-numbers	𝑍-numbers	PROPN
cana-2738	530	15	with	with	ADP
cana-2738	530	16	hesitant	hesitant	ADJ
cana-2738	530	17	fuzzy	fuzzy	ADJ
cana-2738	530	18	linguistic	linguistic	ADJ
cana-2738	530	19	information	information	NOUN
cana-2738	530	20	and	and	CCONJ
cana-2738	530	21	its	its	PRON
cana-2738	530	22	application	application	NOUN
cana-2738	530	23	to	to	ADP
cana-2738	530	24	medicine	medicine	NOUN
cana-2738	530	25	selection	selection	NOUN
cana-2738	530	26	for	for	ADP
cana-2738	530	27	the	the	DET
cana-2738	530	28	patients	patient	NOUN
cana-2738	530	29	with	with	ADP
cana-2738	530	30	mild	mild	ADJ
cana-2738	530	31	symptoms	symptom	NOUN
cana-2738	530	32	of	of	ADP
cana-2738	530	33	the	the	DET
cana-2738	530	34	covid-19	covid-19	PROPN
cana-2738	530	35	,	,	PUNCT
cana-2738	530	36	comput	comput	ADJ
cana-2738	530	37	ind	ind	NOUN
cana-2738	530	38	eng	eng	PROPN
cana-2738	530	39	145	145	NUM
cana-2738	530	40	(	(	PUNCT
cana-2738	530	41	2020	2020	NUM
cana-2738	530	42	)	)	PUNCT
cana-2738	530	43	,	,	PUNCT
cana-2738	530	44	106517	106517	NUM
cana-2738	530	45	.	.	PUNCT
cana-2738	531	1	[	[	X
cana-2738	531	2	28	28	NUM
cana-2738	531	3	]	]	X
cana-2738	531	4	ct	ct	PROPN
cana-2738	531	5	.	.	PUNCT
cana-2738	531	6	sun	sun	PROPN
cana-2738	531	7	and	and	CCONJ
cana-2738	531	8	y.	y.	PROPN
cana-2738	531	9	wang	wang	PROPN
cana-2738	531	10	,	,	PUNCT
cana-2738	531	11	modeling	model	VERB
cana-2738	531	12	covid-19	covid-19	PROPN
cana-2738	531	13	epidemic	epidemic	NOUN
cana-2738	531	14	in	in	ADP
cana-2738	531	15	heilongjiang	heilongjiang	PROPN
cana-2738	531	16	province	province	PROPN
cana-2738	531	17	,	,	PUNCT
cana-2738	531	18	chaos	chaos	NOUN
cana-2738	531	19	,	,	PUNCT
cana-2738	531	20	solitons	soliton	NOUN
cana-2738	531	21	fractals	fractal	VERB
cana-2738	531	22	138	138	NUM
cana-2738	531	23	(	(	PUNCT
cana-2738	531	24	2020	2020	NUM
cana-2738	531	25	)	)	PUNCT
cana-2738	531	26	109949	109949	NUM
cana-2738	531	27	.	.	PUNCT
cana-2738	532	1	[	[	X
cana-2738	532	2	29	29	NUM
cana-2738	532	3	]	]	PUNCT
cana-2738	532	4	m.	m.	NOUN
cana-2738	532	5	udhaya	udhaya	PROPN
cana-2738	532	6	shalini	shalini	PROPN
cana-2738	532	7	and	and	CCONJ
cana-2738	532	8	a.	a.	PROPN
cana-2738	532	9	stanis	stanis	PROPN
cana-2738	532	10	arul	arul	PROPN
cana-2738	532	11	mary	mary	PROPN
cana-2738	532	12	(	(	PUNCT
cana-2738	532	13	2022	2022	NUM
cana-2738	532	14	)	)	PUNCT
cana-2738	532	15	,	,	PUNCT
cana-2738	532	16	generalized	generalize	VERB
cana-2738	532	17	pre	pre	ADJ
cana-2738	532	18	-	-	ADJ
cana-2738	532	19	closed	closed	ADJ
cana-2738	532	20	sets	set	NOUN
cana-2738	532	21	in	in	ADP
cana-2738	532	22	pythagorean	pythagorean	PROPN
cana-2738	532	23	fuzzy	fuzzy	ADJ
cana-2738	532	24	topological	topological	ADJ
cana-2738	532	25	spaces	space	NOUN
cana-2738	532	26	,	,	PUNCT
cana-2738	532	27	international	international	ADJ
cana-2738	532	28	journal	journal	NOUN
cana-2738	532	29	of	of	ADP
cana-2738	532	30	creative	creative	ADJ
cana-2738	532	31	research	research	NOUN
cana-2738	532	32	thoughts	thought	NOUN
cana-2738	532	33	(	(	PUNCT
cana-2738	532	34	ijcrt	ijcrt	NOUN
cana-2738	532	35	)	)	PUNCT
cana-2738	532	36	,	,	PUNCT
cana-2738	532	37	10	10	NUM
cana-2738	532	38	(	(	PUNCT
cana-2738	532	39	30	30	NUM
cana-2738	532	40	)	)	PUNCT
cana-2738	532	41	,	,	PUNCT
cana-2738	532	42	e142	e142	PROPN
cana-2738	532	43	-	-	PUNCT
cana-2738	532	44	e147	e147	PROPN
cana-2738	532	45	.	.	PUNCT
cana-2738	533	1	[	[	X
cana-2738	533	2	30	30	NUM
cana-2738	533	3	]	]	X
cana-2738	533	4	gw	gw	PROPN
cana-2738	533	5	.	.	PUNCT
cana-2738	533	6	wei	wei	PROPN
cana-2738	533	7	and	and	CCONJ
cana-2738	533	8	g.	g.	PROPN
cana-2738	533	9	lan	lan	PROPN
cana-2738	533	10	grey	grey	PROPN
cana-2738	533	11	,	,	PUNCT
cana-2738	533	12	relational	relational	ADJ
cana-2738	533	13	analysis	analysis	NOUN
cana-2738	533	14	method	method	NOUN
cana-2738	533	15	for	for	ADP
cana-2738	533	16	interval	interval	NOUN
cana-2738	533	17	valued	value	VERB
cana-2738	533	18	intuitionistic	intuitionistic	ADJ
cana-2738	533	19	fuzzy	fuzzy	ADJ
cana-2738	533	20	multiple	multiple	ADJ
cana-2738	533	21	attribute	attribute	NOUN
cana-2738	533	22	decision	decision	NOUN
cana-2738	533	23	making	making	NOUN
cana-2738	533	24	,	,	PUNCT
cana-2738	533	25	in	in	ADP
cana-2738	533	26	fifth	fifth	ADJ
cana-2738	533	27	international	international	ADJ
cana-2738	533	28	conference	conference	NOUN
cana-2738	533	29	on	on	ADP
cana-2738	533	30	fuzzy	fuzzy	ADJ
cana-2738	533	31	systems	system	NOUN
cana-2738	533	32	and	and	CCONJ
cana-2738	533	33	knowledge	knowledge	NOUN
cana-2738	533	34	discovery	discovery	PROPN
cana-2738	533	35	(	(	PUNCT
cana-2738	533	36	2008	2008	NUM
cana-2738	533	37	)	)	PUNCT
cana-2738	533	38	291295	291295	NUM
cana-2738	533	39	.	.	PUNCT
cana-2738	534	1	[	[	X
cana-2738	534	2	31	31	NUM
cana-2738	534	3	]	]	PUNCT
cana-2738	534	4	z.	z.	PROPN
cana-2738	534	5	xiao	xiao	PROPN
cana-2738	534	6	,	,	PUNCT
cana-2738	534	7	k.	k.	PROPN
cana-2738	534	8	gong	gong	PROPN
cana-2738	534	9	and	and	CCONJ
cana-2738	534	10	y.	y.	PROPN
cana-2738	534	11	zou	zou	PROPN
cana-2738	534	12	,	,	PUNCT
cana-2738	534	13	a	a	DET
cana-2738	534	14	combined	combine	VERB
cana-2738	534	15	forecasting	forecasting	NOUN
cana-2738	534	16	approach	approach	NOUN
cana-2738	534	17	based	base	VERB
cana-2738	534	18	on	on	ADP
cana-2738	534	19	fuzzy	fuzzy	ADJ
cana-2738	534	20	soft	soft	ADJ
cana-2738	534	21	sets	set	NOUN
cana-2738	534	22	,	,	PUNCT
cana-2738	534	23	j	j	PROPN
cana-2738	534	24	comput	comput	PROPN
cana-2738	534	25	appl	appl	PROPN
cana-2738	534	26	math	math	PROPN
cana-2738	534	27	61(3	61(3	PROPN
cana-2738	534	28	)	)	PUNCT
cana-2738	534	29	(	(	PUNCT
cana-2738	534	30	2011	2011	NUM
cana-2738	534	31	)	)	PUNCT
cana-2738	534	32	,	,	PUNCT
cana-2738	534	33	651	651	NUM
cana-2738	534	34	-	-	SYM
cana-2738	534	35	662	662	NUM
cana-2738	534	36	.	.	PUNCT
cana-2738	535	1	[	[	X
cana-2738	535	2	32	32	NUM
cana-2738	535	3	]	]	PUNCT
cana-2738	535	4	r.	r.	PROPN
cana-2738	535	5	r.	r.	PROPN
cana-2738	535	6	yager	yager	PROPN
cana-2738	535	7	(	(	PUNCT
cana-2738	535	8	2013	2013	NUM
cana-2738	535	9	)	)	PUNCT
cana-2738	535	10	,	,	PUNCT
cana-2738	535	11	pythagorean	pythagorean	PROPN
cana-2738	535	12	membership	membership	NOUN
cana-2738	535	13	grades	grade	NOUN
cana-2738	535	14	in	in	ADP
cana-2738	535	15	multicriteria	multicriteria	PROPN
cana-2738	535	16	decision	decision	NOUN
cana-2738	535	17	making	making	NOUN
cana-2738	535	18	,	,	PUNCT
cana-2738	535	19	in	in	ADP
cana-2738	535	20	:	:	PUNCT
cana-2738	535	21	technical	technical	ADJ
cana-2738	535	22	report	report	NOUN
cana-2738	535	23	𝑀𝐼𝐼3301	𝑀𝐼𝐼3301	PROPN
cana-2738	535	24	.	.	PUNCT
cana-2738	536	1	machine	machine	NOUN
cana-2738	536	2	intelligence	intelligence	PROPN
cana-2738	536	3	institute	institute	PROPN
cana-2738	536	4	,	,	PUNCT
cana-2738	536	5	iona	iona	PROPN
cana-2738	536	6	college	college	PROPN
cana-2738	536	7	,	,	PUNCT
cana-2738	536	8	new	new	ADJ
cana-2738	536	9	rochelle	rochelle	NOUN
cana-2738	536	10	.	.	PUNCT
cana-2738	537	1	[	[	X
cana-2738	537	2	33	33	NUM
cana-2738	537	3	]	]	PUNCT
cana-2738	537	4	r.	r.	PROPN
cana-2738	537	5	r.	r.	PROPN
cana-2738	537	6	yager	yager	PROPN
cana-2738	537	7	(	(	PUNCT
cana-2738	537	8	2013	2013	NUM
cana-2738	537	9	)	)	PUNCT
cana-2738	537	10	,	,	PUNCT
cana-2738	537	11	pythagorean	pythagorean	PROPN
cana-2738	537	12	fuzzy	fuzzy	ADJ
cana-2738	537	13	subsets	subset	NOUN
cana-2738	537	14	,	,	PUNCT
cana-2738	537	15	in	in	ADP
cana-2738	537	16	:	:	PUNCT
cana-2738	537	17	proceedings	proceeding	NOUN
cana-2738	537	18	of	of	ADP
cana-2738	537	19	the	the	DET
cana-2738	537	20	joint	joint	ADJ
cana-2738	537	21	𝐼𝐹𝑆𝐴	𝐼𝐹𝑆𝐴	PROPN
cana-2738	537	22	world	world	PROPN
cana-2738	537	23	congress	congress	PROPN
cana-2738	537	24	𝑁𝐴𝐹𝐼𝑃𝑆	𝑁𝐴𝐹𝐼𝑃𝑆	PROPN
cana-2738	537	25	annual	annual	ADJ
cana-2738	537	26	meeting	meeting	NOUN
cana-2738	537	27	,	,	PUNCT
cana-2738	537	28	57	57	NUM
cana-2738	537	29	-	-	SYM
cana-2738	537	30	61	61	NUM
cana-2738	537	31	.	.	PUNCT
cana-2738	538	1	[	[	X
cana-2738	538	2	34	34	NUM
cana-2738	538	3	]	]	X
cana-2738	538	4	r.	r.	PROPN
cana-2738	538	5	r.	r.	PROPN
cana-2738	538	6	yager	yager	PROPN
cana-2738	538	7	(	(	PUNCT
cana-2738	538	8	2014	2014	NUM
cana-2738	538	9	)	)	PUNCT
cana-2738	538	10	,	,	PUNCT
cana-2738	538	11	pythagorean	pythagorean	PROPN
cana-2738	538	12	membership	membership	NOUN
cana-2738	538	13	grades	grade	NOUN
cana-2738	538	14	in	in	ADP
cana-2738	538	15	multicriteria	multicriteria	PROPN
cana-2738	538	16	decision	decision	NOUN
cana-2738	538	17	making	making	NOUN
cana-2738	538	18	,	,	PUNCT
cana-2738	538	19	𝐼𝐸𝐸𝐸	𝐼𝐸𝐸𝐸	PROPN
cana-2738	538	20	trans	trans	PROPN
cana-2738	538	21	fuzzy	fuzzy	PROPN
cana-2738	538	22	syst	syst	PROPN
cana-2738	538	23	.	.	PUNCT
cana-2738	539	1	22	22	NUM
cana-2738	539	2	(	(	PUNCT
cana-2738	539	3	4	4	NUM
cana-2738	539	4	)	)	PUNCT
cana-2738	539	5	,	,	PUNCT
cana-2738	539	6	958	958	NUM
cana-2738	539	7	-	-	SYM
cana-2738	539	8	965	965	NUM
cana-2738	539	9	.	.	PUNCT
cana-2738	540	1	[	[	X
cana-2738	540	2	35	35	NUM
cana-2738	540	3	]	]	SYM
cana-2738	540	4	la	la	PROPN
cana-2738	540	5	.	.	PUNCT
cana-2738	540	6	zadeh	zadeh	PROPN
cana-2738	540	7	,	,	PUNCT
cana-2738	540	8	fuzzy	fuzzy	ADJ
cana-2738	540	9	sets	set	NOUN
cana-2738	540	10	,	,	PUNCT
cana-2738	540	11	inf	inf	PROPN
cana-2738	540	12	control	control	NOUN
cana-2738	540	13	,	,	PUNCT
cana-2738	540	14	8	8	NUM
cana-2738	540	15	(	(	PUNCT
cana-2738	540	16	1965	1965	NUM
cana-2738	540	17	)	)	PUNCT
cana-2738	540	18	,	,	PUNCT
cana-2738	540	19	338	338	NUM
cana-2738	540	20	-	-	SYM
cana-2738	540	21	353	353	NUM
cana-2738	540	22	.	.	PUNCT
cana-2738	541	1	[	[	X
cana-2738	541	2	36	36	NUM
cana-2738	541	3	]	]	X
cana-2738	541	4	y.	y.	PROPN
cana-2738	541	5	zou	zou	PROPN
cana-2738	541	6	and	and	CCONJ
cana-2738	541	7	z.	z.	PROPN
cana-2738	541	8	xiao	xiao	PROPN
cana-2738	541	9	,	,	PUNCT
cana-2738	541	10	data	data	VERB
cana-2738	541	11	analysis	analysis	NOUN
cana-2738	541	12	approaches	approach	NOUN
cana-2738	541	13	of	of	ADP
cana-2738	541	14	soft	soft	ADJ
cana-2738	541	15	sets	set	NOUN
cana-2738	541	16	under	under	ADP
cana-2738	541	17	incomplete	incomplete	ADJ
cana-2738	541	18	information	information	NOUN
cana-2738	541	19	,	,	PUNCT
cana-2738	541	20	knowl	knowl	NOUN
cana-2738	541	21	-	-	PUNCT
cana-2738	541	22	based	base	VERB
cana-2738	541	23	syst	syst	NOUN
cana-2738	541	24	21(8	21(8	NUM
cana-2738	541	25	)	)	PUNCT
cana-2738	541	26	(	(	PUNCT
cana-2738	541	27	2008	2008	NUM
cana-2738	541	28	)	)	PUNCT
cana-2738	541	29	,	,	PUNCT
cana-2738	541	30	941	941	NUM
cana-2738	541	31	-	-	SYM
cana-2738	541	32	945	945	NUM
cana-2738	541	33	.	.	PUNCT