id	sid	tid	token	lemma	pos
cana-5360	1	1	communications	communication	NOUN
cana-5360	1	2	on	on	ADP
cana-5360	1	3	applied	apply	VERB
cana-5360	1	4	nonlinear	nonlinear	ADJ
cana-5360	1	5	analysis	analysis	NOUN
cana-5360	1	6	issn	issn	NOUN
cana-5360	1	7	:	:	PUNCT
cana-5360	1	8	1074	1074	NUM
cana-5360	1	9	-	-	PUNCT
cana-5360	1	10	133x	133x	NUM
cana-5360	1	11	vol	vol	VERB
cana-5360	1	12	32	32	NUM
cana-5360	1	13	no	no	NOUN
cana-5360	1	14	.	.	PUNCT
cana-5360	2	1	10s	10	NOUN
cana-5360	2	2	(	(	PUNCT
cana-5360	2	3	2025	2025	NUM
cana-5360	2	4	)	)	PUNCT
cana-5360	2	5	1925	1925	NUM
cana-5360	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5360	2	7	more	more	ADV
cana-5360	2	8	on	on	ADP
cana-5360	2	9	contra	contra	PROPN
cana-5360	2	10	continuous	continuous	ADJ
cana-5360	2	11	,	,	PUNCT
cana-5360	2	12	irresolute	irresolute	ADJ
cana-5360	2	13	maps	map	NOUN
cana-5360	2	14	in	in	ADP
cana-5360	2	15	pythagorean	pythagorean	PROPN
cana-5360	2	16	fuzzy	fuzzy	ADJ
cana-5360	2	17	nano	nano	PROPN
cana-5360	2	18	topological	topological	ADJ
cana-5360	2	19	spaces	space	NOUN
cana-5360	2	20	and	and	CCONJ
cana-5360	2	21	application	application	NOUN
cana-5360	2	22	in	in	ADP
cana-5360	2	23	𝐌𝐂𝐃𝐌	𝐌𝐂𝐃𝐌	PROPN
cana-5360	2	24	k.	k.	PROPN
cana-5360	2	25	balasubramaniyan1	balasubramaniyan1	PROPN
cana-5360	2	26	,	,	PUNCT
cana-5360	2	27	k.	k.	PROPN
cana-5360	2	28	nijanthan2	nijanthan2	PROPN
cana-5360	2	29	,	,	PUNCT
cana-5360	2	30	a.	a.	PROPN
cana-5360	2	31	vadivel3	vadivel3	PROPN
cana-5360	2	32	and	and	CCONJ
cana-5360	2	33	k.	k.	PROPN
cana-5360	2	34	shantha	shantha	PROPN
cana-5360	3	1	lakshmi4	lakshmi4	PROPN
cana-5360	3	2	1department	1department	NUM
cana-5360	3	3	of	of	ADP
cana-5360	3	4	mathematics	mathematic	NOUN
cana-5360	3	5	,	,	PUNCT
cana-5360	3	6	arignar	arignar	ADJ
cana-5360	3	7	anna	anna	PROPN
cana-5360	3	8	government	government	PROPN
cana-5360	3	9	arts	arts	PROPN
cana-5360	3	10	college	college	PROPN
cana-5360	3	11	,	,	PUNCT
cana-5360	3	12	attur	attur	VERB
cana-5360	3	13	636	636	NUM
cana-5360	3	14	121	121	NUM
cana-5360	3	15	,	,	PUNCT
cana-5360	3	16	india	india	PROPN
cana-5360	3	17	.	.	PUNCT
cana-5360	4	1	kgbalumaths@gmail.com	kgbalumaths@gmail.com	PROPN
cana-5360	5	1	3department	3department	NUM
cana-5360	5	2	of	of	ADP
cana-5360	5	3	mathematics	mathematic	NOUN
cana-5360	5	4	,	,	PUNCT
cana-5360	5	5	arignar	arignar	ADJ
cana-5360	5	6	anna	anna	PROPN
cana-5360	5	7	government	government	PROPN
cana-5360	5	8	arts	arts	PROPN
cana-5360	5	9	college	college	PROPN
cana-5360	5	10	,	,	PUNCT
cana-5360	5	11	namakkal	namakkal	NOUN
cana-5360	5	12	637	637	NUM
cana-5360	5	13	002	002	NUM
cana-5360	5	14	,	,	PUNCT
cana-5360	5	15	india	india	PROPN
cana-5360	5	16	.	.	PUNCT
cana-5360	5	17	nijanthanvdl1996@gmail.com	nijanthanvdl1996@gmail.com	PROPN
cana-5360	6	1	4department	4department	NUM
cana-5360	6	2	of	of	ADP
cana-5360	6	3	mathematics	mathematic	NOUN
cana-5360	6	4	,	,	PUNCT
cana-5360	6	5	m.kumarasamy	m.kumarasamy	ADJ
cana-5360	6	6	college	college	NOUN
cana-5360	6	7	of	of	ADP
cana-5360	6	8	engineering	engineering	PROPN
cana-5360	6	9	,	,	PUNCT
cana-5360	6	10	karur	karur	PROPN
cana-5360	6	11	639	639	NUM
cana-5360	6	12	113	113	NUM
cana-5360	6	13	,	,	PUNCT
cana-5360	6	14	india	india	PROPN
cana-5360	6	15	.	.	PUNCT
cana-5360	7	1	avmaths@gmail.com	avmaths@gmail.com	X
cana-5360	8	1	1,2,3,4department	1,2,3,4department	NOUN
cana-5360	8	2	of	of	ADP
cana-5360	8	3	mathematics	mathematic	NOUN
cana-5360	8	4	,	,	PUNCT
cana-5360	8	5	annamalai	annamalai	PROPN
cana-5360	8	6	university	university	PROPN
cana-5360	8	7	,	,	PUNCT
cana-5360	8	8	annamalai	annamalai	PROPN
cana-5360	8	9	nagar	nagar	VERB
cana-5360	8	10	608	608	NUM
cana-5360	8	11	002	002	NUM
cana-5360	8	12	,	,	PUNCT
cana-5360	8	13	india	india	PROPN
cana-5360	8	14	.	.	PUNCT
cana-5360	9	1	kslakshmi20@gmail.com	kslakshmi20@gmail.com	PROPN
cana-5360	9	2	;	;	PUNCT
cana-5360	9	3	corresponding	correspond	VERB
cana-5360	9	4	author	author	PROPN
cana-5360	9	5	k.	k.	PROPN
cana-5360	9	6	shantha	shantha	PROPN
cana-5360	9	7	lakshmi	lakshmi	PROPN
cana-5360	9	8	and	and	CCONJ
cana-5360	9	9	k.	k.	PROPN
cana-5360	9	10	nijanthan	nijanthan	PROPN
cana-5360	9	11	article	article	PROPN
cana-5360	9	12	history	history	NOUN
cana-5360	9	13	:	:	PUNCT
cana-5360	9	14	received	receive	VERB
cana-5360	9	15	:	:	PUNCT
cana-5360	9	16	12	12	NUM
cana-5360	9	17	-	-	SYM
cana-5360	9	18	01	01	NUM
cana-5360	9	19	-	-	PUNCT
cana-5360	9	20	2025	2025	NUM
cana-5360	9	21	revised	revise	VERB
cana-5360	9	22	:	:	PUNCT
cana-5360	9	23	15	15	NUM
cana-5360	9	24	-	-	NUM
cana-5360	9	25	02	02	NUM
cana-5360	9	26	-	-	PUNCT
cana-5360	9	27	2025	2025	NUM
cana-5360	9	28	accepted	accept	VERB
cana-5360	9	29	:	:	PUNCT
cana-5360	9	30	01	01	NUM
cana-5360	9	31	-	-	SYM
cana-5360	9	32	03	03	NUM
cana-5360	9	33	-	-	PUNCT
cana-5360	9	34	2025	2025	NUM
cana-5360	9	35	abstract	abstract	NOUN
cana-5360	9	36	:	:	PUNCT
cana-5360	9	37	in	in	ADP
cana-5360	9	38	our	our	PRON
cana-5360	9	39	daily	daily	ADJ
cana-5360	9	40	life	life	NOUN
cana-5360	9	41	we	we	PRON
cana-5360	9	42	come	come	VERB
cana-5360	9	43	across	across	ADP
cana-5360	9	44	many	many	ADJ
cana-5360	9	45	situation	situation	NOUN
cana-5360	9	46	which	which	PRON
cana-5360	9	47	are	be	AUX
cana-5360	9	48	non	non	X
cana-5360	9	49	probabilistic	probabilistic	ADJ
cana-5360	9	50	and	and	CCONJ
cana-5360	9	51	underestimation	underestimation	NOUN
cana-5360	9	52	category	category	NOUN
cana-5360	9	53	.	.	PUNCT
cana-5360	10	1	since	since	SCONJ
cana-5360	10	2	they	they	PRON
cana-5360	10	3	are	be	AUX
cana-5360	10	4	unpredictable	unpredictable	ADJ
cana-5360	10	5	,	,	PUNCT
cana-5360	10	6	innumerable	innumerable	ADJ
cana-5360	10	7	real	real	ADJ
cana-5360	10	8	life	life	NOUN
cana-5360	10	9	problems	problem	NOUN
cana-5360	10	10	are	be	AUX
cana-5360	10	11	in	in	ADP
cana-5360	10	12	abundant	abundant	ADJ
cana-5360	10	13	condition	condition	NOUN
cana-5360	10	14	for	for	ADP
cana-5360	10	15	decision	decision	NOUN
cana-5360	10	16	making	make	VERB
cana-5360	10	17	from	from	ADP
cana-5360	10	18	earlier	early	ADJ
cana-5360	10	19	20th	20th	ADJ
cana-5360	10	20	century	century	NOUN
cana-5360	10	21	.	.	PUNCT
cana-5360	11	1	fuzzy	fuzzy	ADJ
cana-5360	11	2	sets	set	NOUN
cana-5360	11	3	,	,	PUNCT
cana-5360	11	4	intuitionstic	intuitionstic	ADJ
cana-5360	11	5	fuzzy	fuzzy	ADJ
cana-5360	11	6	sets	set	NOUN
cana-5360	11	7	and	and	CCONJ
cana-5360	11	8	pythagorean	pythagorean	PROPN
cana-5360	11	9	fuzzy	fuzzy	ADJ
cana-5360	11	10	sets	set	NOUN
cana-5360	11	11	emerged	emerge	VERB
cana-5360	11	12	one	one	NUM
cana-5360	11	13	by	by	ADP
cana-5360	11	14	one	one	NUM
cana-5360	11	15	and	and	CCONJ
cana-5360	11	16	many	many	ADJ
cana-5360	11	17	literature	literature	NOUN
cana-5360	11	18	are	be	AUX
cana-5360	11	19	adding	add	VERB
cana-5360	11	20	on	on	ADP
cana-5360	11	21	every	every	DET
cana-5360	11	22	day	day	NOUN
cana-5360	11	23	.	.	PUNCT
cana-5360	12	1	the	the	DET
cana-5360	12	2	concept	concept	NOUN
cana-5360	12	3	of	of	ADP
cana-5360	12	4	pythagorean	pythagorean	PROPN
cana-5360	12	5	fuzzy	fuzzy	ADJ
cana-5360	12	6	nano	nano	PROPN
cana-5360	12	7	(	(	PUNCT
cana-5360	12	8	resp	resp	NOUN
cana-5360	12	9	.	.	PUNCT
cana-5360	13	1	𝛿	𝛿	ADJ
cana-5360	13	2	,	,	PUNCT
cana-5360	13	3	𝛿𝒫	𝛿𝒫	NOUN
cana-5360	13	4	,	,	PUNCT
cana-5360	13	5	𝛿𝒮	𝛿𝒮	NOUN
cana-5360	13	6	,	,	PUNCT
cana-5360	13	7	𝛿𝛼	𝛿𝛼	PROPN
cana-5360	13	8	&	&	CCONJ
cana-5360	13	9	𝛿𝛽	𝛿𝛽	PROPN
cana-5360	13	10	or	or	CCONJ
cana-5360	13	11	𝑒∗	𝑒∗	VERB
cana-5360	13	12	)	)	PUNCT
cana-5360	13	13	-continuity	-continuity	PROPN
cana-5360	13	14	in	in	ADP
cana-5360	13	15	pythagorean	pythagorean	PROPN
cana-5360	13	16	fuzzy	fuzzy	ADJ
cana-5360	13	17	nano	nano	PROPN
cana-5360	13	18	topological	topological	ADJ
cana-5360	13	19	spaces	space	NOUN
cana-5360	13	20	and	and	CCONJ
cana-5360	13	21	specialize	specialize	VERB
cana-5360	13	22	some	some	PRON
cana-5360	13	23	of	of	ADP
cana-5360	13	24	their	their	PRON
cana-5360	13	25	basic	basic	ADJ
cana-5360	13	26	properties	property	NOUN
cana-5360	13	27	with	with	ADP
cana-5360	13	28	examples	example	NOUN
cana-5360	13	29	is	be	AUX
cana-5360	13	30	our	our	PRON
cana-5360	13	31	main	main	ADJ
cana-5360	13	32	contribution	contribution	NOUN
cana-5360	13	33	to	to	ADP
cana-5360	13	34	those	those	DET
cana-5360	13	35	literature	literature	NOUN
cana-5360	13	36	.	.	PUNCT
cana-5360	14	1	also	also	ADV
cana-5360	14	2	,	,	PUNCT
cana-5360	14	3	we	we	PRON
cana-5360	14	4	discuss	discuss	VERB
cana-5360	14	5	about	about	ADP
cana-5360	14	6	properties	property	NOUN
cana-5360	14	7	and	and	CCONJ
cana-5360	14	8	characterization	characterization	NOUN
cana-5360	14	9	of	of	ADP
cana-5360	14	10	pythagorean	pythagorean	PROPN
cana-5360	14	11	fuzzy	fuzzy	ADJ
cana-5360	14	12	irresolute	irresolute	ADJ
cana-5360	14	13	maps	map	NOUN
cana-5360	14	14	and	and	CCONJ
cana-5360	14	15	application	application	NOUN
cana-5360	14	16	of	of	ADP
cana-5360	14	17	multiple	multiple	ADJ
cana-5360	14	18	criteria	criterion	NOUN
cana-5360	14	19	decision	decision	NOUN
cana-5360	14	20	making	making	NOUN
cana-5360	14	21	(	(	PUNCT
cana-5360	14	22	mcdm	mcdm	ADJ
cana-5360	14	23	)	)	PUNCT
cana-5360	14	24	techniques	technique	NOUN
cana-5360	14	25	to	to	ADP
cana-5360	14	26	the	the	DET
cana-5360	14	27	real	real	ADJ
cana-5360	14	28	-	-	PUNCT
cana-5360	14	29	world	world	NOUN
cana-5360	14	30	problem	problem	NOUN
cana-5360	14	31	using	use	VERB
cana-5360	14	32	a	a	DET
cana-5360	14	33	proposed	propose	VERB
cana-5360	14	34	similarity	similarity	NOUN
cana-5360	14	35	measure	measure	NOUN
cana-5360	14	36	in	in	ADP
cana-5360	14	37	pythagorean	pythagorean	PROPN
cana-5360	14	38	fuzzy	fuzzy	ADJ
cana-5360	14	39	nano	nano	PROPN
cana-5360	14	40	topological	topological	ADJ
cana-5360	14	41	spaces	space	NOUN
cana-5360	14	42	.	.	PUNCT
cana-5360	15	1	keywords	keyword	NOUN
cana-5360	15	2	:	:	PUNCT
cana-5360	15	3	pythagorean	pythagorean	VERB
cana-5360	15	4	fuzzy	fuzzy	ADJ
cana-5360	15	5	nano	nano	PROPN
cana-5360	15	6	topological	topological	ADJ
cana-5360	15	7	spaces	space	NOUN
cana-5360	15	8	,	,	PUNCT
cana-5360	15	9	𝒫ℱ𝔑𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	𝒫ℱ𝔑𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	PRON
cana-5360	15	10	,	,	PUNCT
cana-5360	15	11	𝒫ℱ𝔑𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	𝒫ℱ𝔑𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	PROPN
cana-5360	15	12	,	,	PUNCT
cana-5360	15	13	𝒫ℱ𝔑	𝒫ℱ𝔑	PROPN
cana-5360	15	14	𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐼𝑟𝑟	𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐼𝑟𝑟	PROPN
cana-5360	15	15	,	,	PUNCT
cana-5360	15	16	𝒫ℱ𝔑𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	𝒫ℱ𝔑𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	PROPN
cana-5360	15	17	and	and	CCONJ
cana-5360	15	18	zhang	zhang	PROPN
cana-5360	15	19	similarity	similarity	NOUN
cana-5360	15	20	measure	measure	NOUN
cana-5360	15	21	.	.	PUNCT
cana-5360	16	1	ams	am	NOUN
cana-5360	16	2	(	(	PUNCT
cana-5360	16	3	2000	2000	NUM
cana-5360	16	4	)	)	PUNCT
cana-5360	16	5	subject	subject	ADJ
cana-5360	16	6	classification	classification	NOUN
cana-5360	16	7	:	:	PUNCT
cana-5360	16	8	03e72	03e72	NUM
cana-5360	16	9	,	,	PUNCT
cana-5360	16	10	54a40	54a40	NUM
cana-5360	16	11	,	,	PUNCT
cana-5360	16	12	54c05	54c05	NUM
cana-5360	16	13	,	,	PUNCT
cana-5360	16	14	94d05	94d05	NUM
cana-5360	16	15	1	1	NUM
cana-5360	16	16	introduction	introduction	NOUN
cana-5360	16	17	in	in	ADP
cana-5360	16	18	1965	1965	NUM
cana-5360	16	19	,	,	PUNCT
cana-5360	16	20	zadeh	zadeh	PROPN
cana-5360	17	1	[	[	X
cana-5360	17	2	40	40	NUM
cana-5360	17	3	]	]	PUNCT
cana-5360	17	4	familiarized	familiarize	VERB
cana-5360	17	5	the	the	DET
cana-5360	17	6	concept	concept	NOUN
cana-5360	17	7	of	of	ADP
cana-5360	17	8	fuzzy	fuzzy	ADJ
cana-5360	17	9	set	set	NOUN
cana-5360	17	10	which	which	PRON
cana-5360	17	11	has	have	VERB
cana-5360	17	12	several	several	ADJ
cana-5360	17	13	applications	application	NOUN
cana-5360	17	14	in	in	ADP
cana-5360	17	15	decision	decision	NOUN
cana-5360	17	16	theory	theory	NOUN
cana-5360	17	17	,	,	PUNCT
cana-5360	17	18	artificial	artificial	ADJ
cana-5360	17	19	intelligence	intelligence	NOUN
cana-5360	17	20	,	,	PUNCT
cana-5360	17	21	operations	operation	NOUN
cana-5360	17	22	research	research	NOUN
cana-5360	17	23	,	,	PUNCT
cana-5360	17	24	expert	expert	NOUN
cana-5360	17	25	systems	system	NOUN
cana-5360	17	26	,	,	PUNCT
cana-5360	17	27	computer	computer	NOUN
cana-5360	17	28	science	science	NOUN
cana-5360	17	29	,	,	PUNCT
cana-5360	17	30	data	datum	NOUN
cana-5360	17	31	analytics	analytic	NOUN
cana-5360	17	32	,	,	PUNCT
cana-5360	17	33	pattern	pattern	NOUN
cana-5360	17	34	recognition	recognition	NOUN
cana-5360	17	35	,	,	PUNCT
cana-5360	17	36	management	management	NOUN
cana-5360	17	37	science	science	NOUN
cana-5360	17	38	and	and	CCONJ
cana-5360	17	39	robotics	robotic	NOUN
cana-5360	17	40	.	.	PUNCT
cana-5360	18	1	in	in	ADP
cana-5360	18	2	1968	1968	NUM
cana-5360	18	3	,	,	PUNCT
cana-5360	18	4	chang	chang	PROPN
cana-5360	18	5	and	and	CCONJ
cana-5360	18	6	warren	warren	PROPN
cana-5360	18	7	[	[	X
cana-5360	18	8	14	14	NUM
cana-5360	18	9	,	,	PUNCT
cana-5360	18	10	34	34	NUM
cana-5360	18	11	]	]	PUNCT
cana-5360	18	12	defined	define	VERB
cana-5360	18	13	fuzzy	fuzzy	ADJ
cana-5360	18	14	topological	topological	ADJ
cana-5360	18	15	spaces	space	NOUN
cana-5360	18	16	,	,	PUNCT
cana-5360	18	17	the	the	DET
cana-5360	18	18	basic	basic	ADJ
cana-5360	18	19	philosophies	philosophy	NOUN
cana-5360	18	20	of	of	ADP
cana-5360	18	21	topology	topology	NOUN
cana-5360	18	22	such	such	ADJ
cana-5360	18	23	as	as	ADP
cana-5360	18	24	open	open	ADJ
cana-5360	18	25	set	set	NOUN
cana-5360	18	26	,	,	PUNCT
cana-5360	18	27	closed	closed	ADJ
cana-5360	18	28	set	set	NOUN
cana-5360	18	29	,	,	PUNCT
cana-5360	18	30	neighbourhood	neighbourhood	NOUN
cana-5360	18	31	,	,	PUNCT
cana-5360	18	32	interior	interior	ADJ
cana-5360	18	33	set	set	NOUN
cana-5360	18	34	,	,	PUNCT
cana-5360	18	35	closure	closure	NOUN
cana-5360	18	36	,	,	PUNCT
cana-5360	18	37	continuity	continuity	NOUN
cana-5360	18	38	,	,	PUNCT
cana-5360	18	39	compactness	compactness	NOUN
cana-5360	18	40	to	to	ADP
cana-5360	18	41	fuzzy	fuzzy	ADJ
cana-5360	18	42	topological	topological	ADJ
cana-5360	18	43	spaces	space	NOUN
cana-5360	18	44	(	(	PUNCT
cana-5360	18	45	𝐹𝑇𝑆	𝐹𝑇𝑆	PROPN
cana-5360	18	46	)	)	PUNCT
cana-5360	18	47	.	.	PUNCT
cana-5360	19	1	applications	application	NOUN
cana-5360	19	2	of	of	ADP
cana-5360	19	3	fuzzy	fuzzy	ADJ
cana-5360	19	4	sets	set	NOUN
cana-5360	19	5	were	be	AUX
cana-5360	19	6	studied	study	VERB
cana-5360	19	7	[	[	PUNCT
cana-5360	19	8	1	1	NUM
cana-5360	19	9	,	,	PUNCT
cana-5360	19	10	13	13	NUM
cana-5360	19	11	,	,	PUNCT
cana-5360	19	12	25	25	NUM
cana-5360	19	13	,	,	PUNCT
cana-5360	19	14	30	30	NUM
cana-5360	19	15	]	]	PUNCT
cana-5360	19	16	.	.	PUNCT
cana-5360	20	1	later	later	ADV
cana-5360	20	2	numerous	numerous	ADJ
cana-5360	20	3	fuzzy	fuzzy	ADJ
cana-5360	20	4	topological	topological	ADJ
cana-5360	20	5	spaces	space	NOUN
cana-5360	20	6	raised	raise	VERB
cana-5360	20	7	which	which	PRON
cana-5360	20	8	have	have	VERB
cana-5360	20	9	unique	unique	ADJ
cana-5360	20	10	properties	property	NOUN
cana-5360	20	11	.	.	PUNCT
cana-5360	21	1	in	in	ADP
cana-5360	21	2	1997	1997	NUM
cana-5360	21	3	,	,	PUNCT
cana-5360	21	4	dogan	dogan	PROPN
cana-5360	21	5	coker	coker	NOUN
cana-5360	22	1	[	[	X
cana-5360	22	2	9	9	NUM
cana-5360	22	3	,	,	PUNCT
cana-5360	22	4	15	15	NUM
cana-5360	22	5	,	,	PUNCT
cana-5360	22	6	19	19	NUM
cana-5360	22	7	]	]	PUNCT
cana-5360	22	8	introduced	introduce	VERB
cana-5360	22	9	intuitionistic	intuitionistic	ADJ
cana-5360	22	10	fuzzy	fuzzy	ADJ
cana-5360	22	11	topological	topological	ADJ
cana-5360	22	12	spaces	space	NOUN
cana-5360	22	13	and	and	CCONJ
cana-5360	22	14	studied	study	VERB
cana-5360	22	15	its	its	PRON
cana-5360	22	16	continuity	continuity	NOUN
cana-5360	22	17	and	and	CCONJ
cana-5360	22	18	compactness	compactness	NOUN
cana-5360	22	19	.	.	PUNCT
cana-5360	23	1	intuitionistic	intuitionistic	ADJ
cana-5360	23	2	fuzzy	fuzzy	ADJ
cana-5360	23	3	sets	set	NOUN
cana-5360	23	4	have	have	VERB
cana-5360	23	5	many	many	ADJ
cana-5360	23	6	applications	application	NOUN
cana-5360	23	7	[	[	X
cana-5360	23	8	30	30	NUM
cana-5360	23	9	,	,	PUNCT
cana-5360	23	10	27	27	NUM
cana-5360	23	11	]	]	PUNCT
cana-5360	23	12	and	and	CCONJ
cana-5360	23	13	also	also	ADV
cana-5360	23	14	flagged	flag	VERB
cana-5360	23	15	approach	approach	NOUN
cana-5360	23	16	to	to	PART
cana-5360	23	17	study	study	VERB
cana-5360	23	18	pythagorean	pythagorean	PROPN
cana-5360	23	19	fuzzy	fuzzy	ADJ
cana-5360	23	20	sets	set	NOUN
cana-5360	23	21	.	.	PUNCT
cana-5360	24	1	in	in	ADP
cana-5360	24	2	both	both	CCONJ
cana-5360	24	3	the	the	DET
cana-5360	24	4	sets	set	NOUN
cana-5360	24	5	membership	membership	NOUN
cana-5360	24	6	and	and	CCONJ
cana-5360	24	7	non	non	ADJ
cana-5360	24	8	-	-	ADJ
cana-5360	24	9	membership	membership	NOUN
cana-5360	24	10	are	be	AUX
cana-5360	24	11	incorporated	incorporate	VERB
cana-5360	24	12	in	in	ADP
cana-5360	24	13	a	a	DET
cana-5360	24	14	different	different	ADJ
cana-5360	24	15	way	way	NOUN
cana-5360	24	16	.	.	PUNCT
cana-5360	25	1	in	in	ADP
cana-5360	25	2	intuitionistic	intuitionistic	ADJ
cana-5360	25	3	fuzzy	fuzzy	ADJ
cana-5360	25	4	set	set	VERB
cana-5360	25	5	the	the	DET
cana-5360	25	6	communications	communication	NOUN
cana-5360	25	7	on	on	ADP
cana-5360	25	8	applied	apply	VERB
cana-5360	25	9	nonlinear	nonlinear	ADJ
cana-5360	25	10	analysis	analysis	NOUN
cana-5360	25	11	issn	issn	NOUN
cana-5360	25	12	:	:	PUNCT
cana-5360	25	13	1074	1074	NUM
cana-5360	25	14	-	-	PUNCT
cana-5360	25	15	133x	133x	NUM
cana-5360	25	16	vol	vol	VERB
cana-5360	25	17	32	32	NUM
cana-5360	25	18	no	no	NOUN
cana-5360	25	19	.	.	PUNCT
cana-5360	26	1	10s	10	NOUN
cana-5360	26	2	(	(	PUNCT
cana-5360	26	3	2025	2025	NUM
cana-5360	26	4	)	)	PUNCT
cana-5360	26	5	1926	1926	NUM
cana-5360	26	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5360	26	7	membership	membership	NOUN
cana-5360	26	8	𝜇	𝜇	ADP
cana-5360	26	9	and	and	CCONJ
cana-5360	26	10	non	non	ADJ
cana-5360	26	11	-	-	NOUN
cana-5360	26	12	membership	membership	ADJ
cana-5360	26	13	𝜆	𝜆	NOUN
cana-5360	26	14	are	be	AUX
cana-5360	26	15	incorporated	incorporate	VERB
cana-5360	26	16	in	in	ADP
cana-5360	26	17	such	such	DET
cana-5360	26	18	a	a	DET
cana-5360	26	19	way	way	NOUN
cana-5360	26	20	that	that	PRON
cana-5360	26	21	𝜇	𝜇	ADP
cana-5360	26	22	+	+	X
cana-5360	26	23	𝜆	𝜆	SYM
cana-5360	26	24	≤	≤	NUM
cana-5360	26	25	1	1	NUM
cana-5360	26	26	where	where	SCONJ
cana-5360	26	27	as	as	ADP
cana-5360	26	28	in	in	ADP
cana-5360	26	29	pythagorean	pythagorean	PROPN
cana-5360	26	30	fuzzy	fuzzy	PROPN
cana-5360	26	31	set	set	VERB
cana-5360	26	32	it	it	PRON
cana-5360	26	33	is	be	AUX
cana-5360	26	34	𝜇2	𝜇2	ADJ
cana-5360	26	35	+	+	CCONJ
cana-5360	26	36	𝜆2	𝜆2	NOUN
cana-5360	26	37	≤	≤	ADV
cana-5360	26	38	1	1	NUM
cana-5360	26	39	.	.	PUNCT
cana-5360	27	1	in	in	ADP
cana-5360	27	2	2013	2013	NUM
cana-5360	27	3	,	,	PUNCT
cana-5360	27	4	yager	yager	NOUN
cana-5360	28	1	[	[	X
cana-5360	28	2	37	37	NUM
cana-5360	28	3	]	]	PUNCT
cana-5360	28	4	introduced	introduce	VERB
cana-5360	28	5	the	the	DET
cana-5360	28	6	non	non	ADJ
cana-5360	28	7	-	-	ADJ
cana-5360	28	8	standard	standard	ADJ
cana-5360	28	9	fuzzy	fuzzy	ADJ
cana-5360	28	10	sets	set	NOUN
cana-5360	28	11	called	call	VERB
cana-5360	28	12	pythagorean	pythagorean	PROPN
cana-5360	28	13	fuzzy	fuzzy	ADJ
cana-5360	28	14	sets	set	NOUN
cana-5360	28	15	in	in	ADP
cana-5360	28	16	comparison	comparison	NOUN
cana-5360	28	17	with	with	ADP
cana-5360	28	18	intuitionistic	intuitionistic	ADJ
cana-5360	28	19	fuzzy	fuzzy	ADJ
cana-5360	28	20	sets	set	NOUN
cana-5360	28	21	.	.	PUNCT
cana-5360	29	1	he	he	PRON
cana-5360	29	2	gave	give	VERB
cana-5360	29	3	the	the	DET
cana-5360	29	4	basic	basic	ADJ
cana-5360	29	5	definition	definition	NOUN
cana-5360	29	6	of	of	ADP
cana-5360	29	7	pythagorean	pythagorean	PROPN
cana-5360	29	8	fuzzy	fuzzy	ADJ
cana-5360	29	9	set	set	NOUN
cana-5360	29	10	(	(	PUNCT
cana-5360	29	11	𝑃𝐹𝑆	𝑃𝐹𝑆	PROPN
cana-5360	29	12	)	)	PUNCT
cana-5360	29	13	and	and	CCONJ
cana-5360	29	14	its	its	PRON
cana-5360	29	15	application	application	NOUN
cana-5360	29	16	in	in	ADP
cana-5360	29	17	decision	decision	NOUN
cana-5360	29	18	making	make	VERB
cana-5360	29	19	[	[	X
cana-5360	29	20	3	3	NUM
cana-5360	29	21	,	,	PUNCT
cana-5360	29	22	39	39	NUM
cana-5360	29	23	,	,	PUNCT
cana-5360	29	24	38	38	NUM
cana-5360	29	25	]	]	PUNCT
cana-5360	29	26	.	.	PUNCT
cana-5360	30	1	𝑃𝐹𝑆	𝑃𝐹𝑆	PROPN
cana-5360	30	2	has	have	VERB
cana-5360	30	3	its	its	PRON
cana-5360	30	4	applications	application	NOUN
cana-5360	30	5	in	in	ADP
cana-5360	30	6	career	career	NOUN
cana-5360	30	7	placements	placement	NOUN
cana-5360	30	8	based	base	VERB
cana-5360	30	9	on	on	ADP
cana-5360	30	10	academic	academic	ADJ
cana-5360	30	11	performance	performance	NOUN
cana-5360	30	12	[	[	X
cana-5360	30	13	20	20	NUM
cana-5360	30	14	]	]	PUNCT
cana-5360	30	15	,	,	PUNCT
cana-5360	30	16	selection	selection	NOUN
cana-5360	30	17	of	of	ADP
cana-5360	30	18	mask	mask	NOUN
cana-5360	30	19	during	during	ADP
cana-5360	30	20	covid-19	covid-19	PROPN
cana-5360	30	21	pandemic	pandemic	ADJ
cana-5360	30	22	using	use	VERB
cana-5360	30	23	pythagorean	pythagorean	PROPN
cana-5360	30	24	topsis	topsis	NOUN
cana-5360	30	25	technique	technique	NOUN
cana-5360	30	26	[	[	X
cana-5360	30	27	24	24	NUM
cana-5360	30	28	]	]	PUNCT
cana-5360	30	29	,	,	PUNCT
cana-5360	30	30	etc	etc	X
cana-5360	30	31	.	.	X
cana-5360	30	32	later	later	PROPN
cana-5360	30	33	murat	murat	PROPN
cana-5360	30	34	et.al	et.al	PROPN
cana-5360	31	1	[	[	X
cana-5360	31	2	18	18	NUM
cana-5360	31	3	]	]	PUNCT
cana-5360	31	4	introduced	introduce	VERB
cana-5360	31	5	the	the	DET
cana-5360	31	6	conception	conception	NOUN
cana-5360	31	7	of	of	ADP
cana-5360	31	8	pythagorean	pythagorean	PROPN
cana-5360	31	9	fuzzy	fuzzy	ADJ
cana-5360	31	10	topological	topological	ADJ
cana-5360	31	11	space	space	NOUN
cana-5360	31	12	(	(	PUNCT
cana-5360	31	13	𝑃𝐹𝑇𝑆	𝑃𝐹𝑇𝑆	PROPN
cana-5360	31	14	)	)	PUNCT
cana-5360	31	15	by	by	ADP
cana-5360	31	16	provoking	provoke	VERB
cana-5360	31	17	from	from	ADP
cana-5360	31	18	the	the	DET
cana-5360	31	19	conviction	conviction	NOUN
cana-5360	31	20	of	of	ADP
cana-5360	31	21	𝐹𝑇𝑆	𝐹𝑇𝑆	PROPN
cana-5360	32	1	[	[	X
cana-5360	32	2	16	16	NUM
cana-5360	32	3	,	,	PUNCT
cana-5360	32	4	17	17	NUM
cana-5360	32	5	,	,	PUNCT
cana-5360	32	6	23	23	NUM
cana-5360	32	7	]	]	PUNCT
cana-5360	32	8	.	.	PUNCT
cana-5360	33	1	he	he	PRON
cana-5360	33	2	defined	define	VERB
cana-5360	33	3	pythagorean	pythagorean	PROPN
cana-5360	33	4	fuzzy	fuzzy	ADJ
cana-5360	33	5	continuous	continuous	ADJ
cana-5360	33	6	function	function	NOUN
cana-5360	33	7	between	between	ADP
cana-5360	33	8	𝑃𝐹𝑇𝑆.	𝑃𝐹𝑇𝑆.	X
cana-5360	33	9	saha	saha	PROPN
cana-5360	34	1	[	[	X
cana-5360	34	2	26	26	NUM
cana-5360	34	3	]	]	SYM
cana-5360	34	4	defined	define	VERB
cana-5360	34	5	𝛿-open	𝛿-open	NOUN
cana-5360	34	6	sets	set	NOUN
cana-5360	34	7	in	in	ADP
cana-5360	34	8	fuzzy	fuzzy	ADJ
cana-5360	34	9	topological	topological	ADJ
cana-5360	34	10	spaces	space	NOUN
cana-5360	34	11	.	.	PUNCT
cana-5360	35	1	in	in	ADP
cana-5360	35	2	2019	2019	NUM
cana-5360	35	3	,	,	PUNCT
cana-5360	35	4	acikgoz	acikgoz	ADJ
cana-5360	35	5	and	and	CCONJ
cana-5360	35	6	esenbel	esenbel	VERB
cana-5360	36	1	[	[	X
cana-5360	36	2	2	2	NUM
cana-5360	36	3	]	]	PUNCT
cana-5360	36	4	defined	define	VERB
cana-5360	36	5	neutrosophic	neutrosophic	ADJ
cana-5360	36	6	soft	soft	ADJ
cana-5360	36	7	𝛿-topology	𝛿-topology	NOUN
cana-5360	36	8	.	.	PUNCT
cana-5360	37	1	aranganayagi	aranganayagi	NOUN
cana-5360	37	2	et	et	PROPN
cana-5360	37	3	al	al	PROPN
cana-5360	37	4	.	.	PROPN
cana-5360	37	5	,	,	PUNCT
cana-5360	37	6	surendra	surendra	PROPN
cana-5360	37	7	et	et	PROPN
cana-5360	37	8	al	al	PROPN
cana-5360	37	9	.	.	PROPN
cana-5360	38	1	and	and	CCONJ
cana-5360	38	2	vadivel	vadivel	VERB
cana-5360	38	3	et	et	PROPN
cana-5360	38	4	al	al	PROPN
cana-5360	38	5	.	.	PUNCT
cana-5360	39	1	[	[	X
cana-5360	39	2	7	7	NUM
cana-5360	39	3	,	,	PUNCT
cana-5360	39	4	8	8	NUM
cana-5360	39	5	,	,	PUNCT
cana-5360	39	6	28	28	NUM
cana-5360	39	7	,	,	PUNCT
cana-5360	39	8	29	29	NUM
cana-5360	39	9	,	,	PUNCT
cana-5360	39	10	32	32	NUM
cana-5360	39	11	,	,	PUNCT
cana-5360	39	12	33	33	NUM
cana-5360	39	13	]	]	PUNCT
cana-5360	39	14	introduced	introduce	VERB
cana-5360	39	15	𝛿	𝛿	DET
cana-5360	39	16	-open	-open	ADJ
cana-5360	39	17	sets	set	NOUN
cana-5360	39	18	in	in	ADP
cana-5360	39	19	neutrosophic	neutrosophic	ADJ
cana-5360	39	20	,	,	PUNCT
cana-5360	39	21	neutrosophic	neutrosophic	ADJ
cana-5360	39	22	soft	soft	ADJ
cana-5360	39	23	,	,	PUNCT
cana-5360	39	24	neutrosophic	neutrosophic	ADJ
cana-5360	39	25	hypersoft	hypersoft	NOUN
cana-5360	39	26	and	and	CCONJ
cana-5360	39	27	neutrosophic	neutrosophic	ADJ
cana-5360	39	28	nano	nano	NOUN
cana-5360	39	29	topological	topological	ADJ
cana-5360	39	30	spaces	space	NOUN
cana-5360	39	31	and	and	CCONJ
cana-5360	39	32	studied	study	VERB
cana-5360	39	33	its	its	PRON
cana-5360	39	34	maps	map	NOUN
cana-5360	39	35	and	and	CCONJ
cana-5360	39	36	separation	separation	NOUN
cana-5360	39	37	axioms	axiom	NOUN
cana-5360	39	38	.	.	PUNCT
cana-5360	40	1	similarity	similarity	NOUN
cana-5360	40	2	measure	measure	NOUN
cana-5360	40	3	is	be	AUX
cana-5360	40	4	a	a	DET
cana-5360	40	5	significant	significant	ADJ
cana-5360	40	6	means	mean	NOUN
cana-5360	40	7	for	for	ADP
cana-5360	40	8	measuring	measure	VERB
cana-5360	40	9	the	the	DET
cana-5360	40	10	uncertain	uncertain	ADJ
cana-5360	40	11	information	information	NOUN
cana-5360	40	12	.	.	PUNCT
cana-5360	41	1	the	the	DET
cana-5360	41	2	fuzzy	fuzzy	ADJ
cana-5360	41	3	similarity	similarity	NOUN
cana-5360	41	4	measure	measure	NOUN
cana-5360	41	5	is	be	AUX
cana-5360	41	6	a	a	DET
cana-5360	41	7	measure	measure	NOUN
cana-5360	41	8	that	that	PRON
cana-5360	41	9	depicts	depict	VERB
cana-5360	41	10	the	the	DET
cana-5360	41	11	closeness	closeness	NOUN
cana-5360	41	12	(	(	PUNCT
cana-5360	41	13	difference	difference	NOUN
cana-5360	41	14	)	)	PUNCT
cana-5360	41	15	among	among	ADP
cana-5360	41	16	fuzzy	fuzzy	ADJ
cana-5360	41	17	sets	set	NOUN
cana-5360	41	18	.	.	PUNCT
cana-5360	42	1	zhang	zhang	X
cana-5360	43	1	[	[	X
cana-5360	43	2	42	42	NUM
cana-5360	43	3	]	]	PUNCT
cana-5360	43	4	proposed	propose	VERB
cana-5360	43	5	the	the	DET
cana-5360	43	6	pythagorean	pythagorean	PROPN
cana-5360	43	7	fuzzy	fuzzy	ADJ
cana-5360	43	8	similarity	similarity	NOUN
cana-5360	43	9	measures	measure	NOUN
cana-5360	43	10	for	for	ADP
cana-5360	43	11	dealing	deal	VERB
cana-5360	43	12	the	the	DET
cana-5360	43	13	multi	multi	ADJ
cana-5360	43	14	-	-	ADJ
cana-5360	43	15	attribute	attribute	NOUN
cana-5360	43	16	decision	decision	NOUN
cana-5360	43	17	-	-	PUNCT
cana-5360	43	18	making	make	VERB
cana-5360	43	19	problems	problem	NOUN
cana-5360	43	20	.	.	PUNCT
cana-5360	44	1	peng	peng	PROPN
cana-5360	44	2	et	et	PROPN
cana-5360	44	3	al	al	PROPN
cana-5360	44	4	.	.	PUNCT
cana-5360	45	1	[	[	X
cana-5360	45	2	21	21	NUM
cana-5360	45	3	]	]	PUNCT
cana-5360	45	4	proposed	propose	VERB
cana-5360	45	5	the	the	DET
cana-5360	45	6	many	many	ADJ
cana-5360	45	7	new	new	ADJ
cana-5360	45	8	distance	distance	NOUN
cana-5360	45	9	measures	measure	NOUN
cana-5360	45	10	and	and	CCONJ
cana-5360	45	11	similarity	similarity	NOUN
cana-5360	45	12	measures	measure	NOUN
cana-5360	45	13	for	for	ADP
cana-5360	45	14	dealing	deal	VERB
cana-5360	45	15	the	the	DET
cana-5360	45	16	issues	issue	NOUN
cana-5360	45	17	of	of	ADP
cana-5360	45	18	pattern	pattern	NOUN
cana-5360	45	19	recognition	recognition	NOUN
cana-5360	45	20	,	,	PUNCT
cana-5360	45	21	medical	medical	ADJ
cana-5360	45	22	diagnosis	diagnosis	NOUN
cana-5360	45	23	and	and	CCONJ
cana-5360	45	24	clustering	cluster	VERB
cana-5360	45	25	analysis	analysis	NOUN
cana-5360	45	26	,	,	PUNCT
cana-5360	45	27	and	and	CCONJ
cana-5360	45	28	discussed	discuss	VERB
cana-5360	45	29	their	their	PRON
cana-5360	45	30	transformation	transformation	NOUN
cana-5360	45	31	relations	relation	NOUN
cana-5360	45	32	.	.	PUNCT
cana-5360	46	1	wei	wei	PROPN
cana-5360	46	2	and	and	CCONJ
cana-5360	46	3	wei	wei	PROPN
cana-5360	47	1	[	[	X
cana-5360	47	2	35	35	NUM
cana-5360	47	3	]	]	PUNCT
cana-5360	47	4	presented	present	VERB
cana-5360	47	5	some	some	DET
cana-5360	47	6	pythagorean	pythagorean	PROPN
cana-5360	47	7	fuzzy	fuzzy	ADJ
cana-5360	47	8	cosine	cosine	NOUN
cana-5360	47	9	function	function	NOUN
cana-5360	47	10	for	for	ADP
cana-5360	47	11	dealing	deal	VERB
cana-5360	47	12	with	with	ADP
cana-5360	47	13	the	the	DET
cana-5360	47	14	decision	decision	NOUN
cana-5360	47	15	-	-	PUNCT
cana-5360	47	16	making	make	VERB
cana-5360	47	17	problems	problem	NOUN
cana-5360	47	18	.	.	PUNCT
cana-5360	48	1	however	however	ADV
cana-5360	48	2	,	,	PUNCT
cana-5360	48	3	some	some	DET
cana-5360	48	4	existing	exist	VERB
cana-5360	48	5	similarity	similarity	NOUN
cana-5360	48	6	measures	measure	NOUN
cana-5360	48	7	/	/	SYM
cana-5360	48	8	distance	distance	NOUN
cana-5360	48	9	measures	measure	NOUN
cana-5360	48	10	can	can	AUX
cana-5360	48	11	not	not	PART
cana-5360	48	12	obey	obey	VERB
cana-5360	48	13	the	the	DET
cana-5360	48	14	third	third	ADJ
cana-5360	48	15	or	or	CCONJ
cana-5360	48	16	fourth	fourth	ADJ
cana-5360	48	17	axiom	axiom	NOUN
cana-5360	48	18	,	,	PUNCT
cana-5360	48	19	and	and	CCONJ
cana-5360	48	20	also	also	ADV
cana-5360	48	21	have	have	VERB
cana-5360	48	22	no	no	DET
cana-5360	48	23	power	power	NOUN
cana-5360	48	24	to	to	PART
cana-5360	48	25	differentiate	differentiate	VERB
cana-5360	48	26	positive	positive	ADJ
cana-5360	48	27	difference	difference	NOUN
cana-5360	48	28	and	and	CCONJ
cana-5360	48	29	negative	negative	ADJ
cana-5360	48	30	difference	difference	NOUN
cana-5360	48	31	or	or	CCONJ
cana-5360	48	32	deal	deal	VERB
cana-5360	48	33	with	with	ADP
cana-5360	48	34	the	the	DET
cana-5360	48	35	division	division	NOUN
cana-5360	48	36	by	by	ADP
cana-5360	48	37	the	the	DET
cana-5360	48	38	zero	zero	NUM
cana-5360	48	39	problem	problem	NOUN
cana-5360	48	40	.	.	PUNCT
cana-5360	49	1	due	due	ADP
cana-5360	49	2	to	to	ADP
cana-5360	49	3	the	the	DET
cana-5360	49	4	above	above	ADJ
cana-5360	49	5	counter	counter	ADJ
cana-5360	49	6	-	-	ADJ
cana-5360	49	7	intuitive	intuitive	ADJ
cana-5360	49	8	phenomena	phenomenon	NOUN
cana-5360	49	9	[	[	X
cana-5360	49	10	35	35	NUM
cana-5360	49	11	,	,	PUNCT
cana-5360	49	12	42	42	NUM
cana-5360	49	13	,	,	PUNCT
cana-5360	49	14	21	21	NUM
cana-5360	49	15	]	]	PUNCT
cana-5360	49	16	of	of	ADP
cana-5360	49	17	the	the	DET
cana-5360	49	18	existing	exist	VERB
cana-5360	49	19	similarity	similarity	NOUN
cana-5360	49	20	measures	measure	NOUN
cana-5360	49	21	of	of	ADP
cana-5360	49	22	𝒫ℱ𝑠	𝒫ℱ𝑠	PROPN
cana-5360	49	23	’s	’s	PART
cana-5360	49	24	,	,	PUNCT
cana-5360	49	25	they	they	PRON
cana-5360	49	26	may	may	AUX
cana-5360	49	27	be	be	AUX
cana-5360	49	28	hard	hard	ADJ
cana-5360	49	29	for	for	ADP
cana-5360	49	30	𝐷𝑀	𝐷𝑀	PROPN
cana-5360	49	31	’s	’s	PART
cana-5360	49	32	to	to	PART
cana-5360	49	33	choose	choose	VERB
cana-5360	49	34	convincible	convincible	ADJ
cana-5360	49	35	or	or	CCONJ
cana-5360	49	36	optimal	optimal	ADJ
cana-5360	49	37	alternatives	alternative	NOUN
cana-5360	49	38	.	.	PUNCT
cana-5360	50	1	as	as	ADP
cana-5360	50	2	a	a	DET
cana-5360	50	3	consequence	consequence	NOUN
cana-5360	50	4	,	,	PUNCT
cana-5360	50	5	the	the	DET
cana-5360	50	6	goal	goal	NOUN
cana-5360	50	7	of	of	ADP
cana-5360	50	8	this	this	DET
cana-5360	50	9	paper	paper	NOUN
cana-5360	50	10	is	be	AUX
cana-5360	50	11	to	to	PART
cana-5360	50	12	deal	deal	VERB
cana-5360	50	13	with	with	ADP
cana-5360	50	14	the	the	DET
cana-5360	50	15	above	above	ADJ
cana-5360	50	16	issue	issue	NOUN
cana-5360	50	17	by	by	ADP
cana-5360	50	18	proposing	propose	VERB
cana-5360	50	19	a	a	DET
cana-5360	50	20	novel	novel	ADJ
cana-5360	50	21	similarity	similarity	NOUN
cana-5360	50	22	measure	measure	NOUN
cana-5360	50	23	for	for	ADP
cana-5360	50	24	pythagorean	pythagorean	PROPN
cana-5360	50	25	fuzzy	fuzzy	ADJ
cana-5360	50	26	set	set	NOUN
cana-5360	50	27	,	,	PUNCT
cana-5360	50	28	which	which	PRON
cana-5360	50	29	can	can	AUX
cana-5360	50	30	be	be	AUX
cana-5360	50	31	without	without	ADP
cana-5360	50	32	counter	counter	ADJ
cana-5360	50	33	intuitive	intuitive	ADJ
cana-5360	50	34	phenomena	phenomenon	NOUN
cana-5360	50	35	.	.	PUNCT
cana-5360	51	1	research	research	NOUN
cana-5360	51	2	gap	gap	NOUN
cana-5360	51	3	:	:	PUNCT
cana-5360	51	4	no	no	DET
cana-5360	51	5	investigation	investigation	NOUN
cana-5360	51	6	on	on	ADP
cana-5360	51	7	some	some	DET
cana-5360	51	8	stronger	strong	ADJ
cana-5360	51	9	and	and	CCONJ
cana-5360	51	10	weaker	weak	ADJ
cana-5360	51	11	forms	form	NOUN
cana-5360	51	12	of	of	ADP
cana-5360	51	13	pythagorean	pythagorean	ADJ
cana-5360	51	14	fuzzy	fuzzy	ADJ
cana-5360	51	15	continuous	continuous	ADJ
cana-5360	51	16	and	and	CCONJ
cana-5360	51	17	irresolute	irresolute	ADJ
cana-5360	51	18	maps	map	NOUN
cana-5360	51	19	such	such	ADJ
cana-5360	51	20	as	as	ADP
cana-5360	51	21	pythagorean	pythagorean	PROPN
cana-5360	51	22	fuzzy	fuzzy	PROPN
cana-5360	51	23	nano	nano	PROPN
cana-5360	51	24	𝑐𝑜𝑛𝑡𝑟𝑎𝛿	𝑐𝑜𝑛𝑡𝑟𝑎𝛿	PROPN
cana-5360	51	25	open	open	PROPN
cana-5360	51	26	map	map	NOUN
cana-5360	51	27	,	,	PUNCT
cana-5360	51	28	pythagorean	pythagorean	PROPN
cana-5360	51	29	fuzzy	fuzzy	ADJ
cana-5360	51	30	nano	nano	NOUN
cana-5360	51	31	𝑐𝑜𝑛𝑡𝑟𝑎𝛿-semi	𝑐𝑜𝑛𝑡𝑟𝑎𝛿-semi	PRON
cana-5360	51	32	open	open	ADJ
cana-5360	51	33	map	map	NOUN
cana-5360	51	34	,	,	PUNCT
cana-5360	51	35	pythagorean	pythagorean	PROPN
cana-5360	51	36	fuzzy	fuzzy	ADJ
cana-5360	51	37	nano	nano	PROPN
cana-5360	51	38	𝑐𝑜𝑛𝑡𝑟𝑎𝛿-pre	𝑐𝑜𝑛𝑡𝑟𝑎𝛿-pre	ADJ
cana-5360	51	39	open	open	ADJ
cana-5360	51	40	map	map	NOUN
cana-5360	51	41	,	,	PUNCT
cana-5360	51	42	pythagorean	pythagorean	PROPN
cana-5360	51	43	fuzzy	fuzzy	ADJ
cana-5360	51	44	nano	nano	NOUN
cana-5360	51	45	𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼	𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼	NOUN
cana-5360	51	46	open	open	ADJ
cana-5360	51	47	map	map	NOUN
cana-5360	51	48	and	and	CCONJ
cana-5360	51	49	pythagorean	pythagorean	VERB
cana-5360	51	50	fuzzy	fuzzy	ADJ
cana-5360	51	51	nano	nano	NOUN
cana-5360	51	52	𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽	𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽	NOUN
cana-5360	51	53	open	open	ADJ
cana-5360	51	54	maps	map	NOUN
cana-5360	51	55	on	on	ADP
cana-5360	51	56	pythagorean	pythagorean	PROPN
cana-5360	51	57	fuzzy	fuzzy	ADJ
cana-5360	51	58	nano	nano	PROPN
cana-5360	51	59	topological	topological	ADJ
cana-5360	51	60	space	space	NOUN
cana-5360	51	61	has	have	AUX
cana-5360	51	62	been	be	AUX
cana-5360	51	63	reported	report	VERB
cana-5360	51	64	in	in	ADP
cana-5360	51	65	the	the	DET
cana-5360	51	66	pythagorean	pythagorean	PROPN
cana-5360	51	67	fuzzy	fuzzy	ADJ
cana-5360	51	68	nano	nano	NOUN
cana-5360	51	69	literature	literature	NOUN
cana-5360	51	70	.	.	PUNCT
cana-5360	52	1	this	this	PRON
cana-5360	52	2	leads	lead	VERB
cana-5360	52	3	to	to	PART
cana-5360	52	4	encompass	encompass	VERB
cana-5360	52	5	the	the	DET
cana-5360	52	6	notion	notion	NOUN
cana-5360	52	7	of	of	ADP
cana-5360	52	8	𝑃𝐹𝑁𝑡𝑠	𝑃𝐹𝑁𝑡𝑠	PROPN
cana-5360	52	9	by	by	ADP
cana-5360	52	10	introducing	introduce	VERB
cana-5360	52	11	pythagorean	pythagorean	PROPN
cana-5360	52	12	fuzzy	fuzzy	ADJ
cana-5360	52	13	nano	nano	PROPN
cana-5360	52	14	𝑐𝑜𝑛𝑡𝑟𝑎𝛿	𝑐𝑜𝑛𝑡𝑟𝑎𝛿	PROPN
cana-5360	52	15	(	(	PUNCT
cana-5360	52	16	resp	resp	PROPN
cana-5360	52	17	.	.	PUNCT
cana-5360	53	1	𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼	𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼	NOUN
cana-5360	53	2	,	,	PUNCT
cana-5360	53	3	𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮	𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮	NOUN
cana-5360	53	4	,	,	PUNCT
cana-5360	53	5	𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫	𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫	PROPN
cana-5360	53	6	&	&	CCONJ
cana-5360	53	7	𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽	𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽	NOUN
cana-5360	53	8	or	or	CCONJ
cana-5360	53	9	𝑐𝑜𝑛𝑡𝑟𝑎𝑒∗	𝑐𝑜𝑛𝑡𝑟𝑎𝑒∗	ADJ
cana-5360	53	10	)	)	PUNCT
cana-5360	53	11	-continuous	-continuous	ADJ
cana-5360	53	12	and	and	CCONJ
cana-5360	53	13	discuss	discuss	VERB
cana-5360	53	14	its	its	PRON
cana-5360	53	15	properties	property	NOUN
cana-5360	53	16	.	.	PUNCT
cana-5360	54	1	also	also	ADV
cana-5360	54	2	,	,	PUNCT
cana-5360	54	3	we	we	PRON
cana-5360	54	4	introduce	introduce	VERB
cana-5360	54	5	the	the	DET
cana-5360	54	6	concept	concept	NOUN
cana-5360	54	7	of	of	ADP
cana-5360	54	8	pythagorean	pythagorean	PROPN
cana-5360	54	9	fuzzy	fuzzy	ADJ
cana-5360	54	10	nano	nano	PROPN
cana-5360	54	11	irresoluteness	irresoluteness	NOUN
cana-5360	54	12	called	call	VERB
cana-5360	54	13	pythagorean	pythagorean	PROPN
cana-5360	54	14	fuzzy	fuzzy	PROPN
cana-5360	54	15	nano	nano	PROPN
cana-5360	54	16	𝑐𝑜𝑛𝑡𝑟𝑎𝛿	𝑐𝑜𝑛𝑡𝑟𝑎𝛿	PROPN
cana-5360	54	17	(	(	PUNCT
cana-5360	54	18	resp	resp	NOUN
cana-5360	54	19	.	.	PUNCT
cana-5360	55	1	𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫	𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫	NOUN
cana-5360	55	2	,	,	PUNCT
cana-5360	55	3	𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮	𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮	NOUN
cana-5360	55	4	,	,	PUNCT
cana-5360	55	5	𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼	𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼	NOUN
cana-5360	55	6	and	and	CCONJ
cana-5360	55	7	𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽	𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽	NOUN
cana-5360	55	8	)	)	PUNCT
cana-5360	55	9	-irresolute	-irresolute	ADJ
cana-5360	55	10	maps	map	NOUN
cana-5360	55	11	by	by	ADP
cana-5360	55	12	using	use	VERB
cana-5360	55	13	𝒫ℱ𝒩𝒮𝑜𝑠	𝒫ℱ𝒩𝒮𝑜𝑠	PROPN
cana-5360	55	14	(	(	PUNCT
cana-5360	55	15	resp	resp	NOUN
cana-5360	55	16	.	.	PUNCT
cana-5360	56	1	𝒫ℱ𝒩𝛿𝑜𝑠	𝒫ℱ𝒩𝛿𝑜𝑠	PROPN
cana-5360	56	2	,	,	PUNCT
cana-5360	56	3	𝒫ℱ𝒩𝛿𝒫𝑜𝑠	𝒫ℱ𝒩𝛿𝒫𝑜𝑠	NUM
cana-5360	56	4	,	,	PUNCT
cana-5360	56	5	𝑝𝑓𝒩𝛿𝒮𝑜𝑠	𝑝𝑓𝒩𝛿𝒮𝑜𝑠	PROPN
cana-5360	56	6	,	,	PUNCT
cana-5360	56	7	𝑝𝑓𝒩𝛿𝛼𝑜𝑠	𝑝𝑓𝒩𝛿𝛼𝑜𝑠	PROPN
cana-5360	56	8	and	and	CCONJ
cana-5360	56	9	𝒫ℱ𝒩𝛿𝛽𝑜𝑠	𝒫ℱ𝒩𝛿𝛽𝑜𝑠	PROPN
cana-5360	56	10	)	)	PUNCT
cana-5360	56	11	’s	’	VERB
cana-5360	56	12	and	and	CCONJ
cana-5360	56	13	study	study	VERB
cana-5360	56	14	some	some	PRON
cana-5360	56	15	of	of	ADP
cana-5360	56	16	their	their	PRON
cana-5360	56	17	basic	basic	ADJ
cana-5360	56	18	properties	property	NOUN
cana-5360	56	19	.	.	PUNCT
cana-5360	57	1	communications	communication	NOUN
cana-5360	57	2	on	on	ADP
cana-5360	57	3	applied	apply	VERB
cana-5360	57	4	nonlinear	nonlinear	ADJ
cana-5360	57	5	analysis	analysis	NOUN
cana-5360	57	6	issn	issn	NOUN
cana-5360	57	7	:	:	PUNCT
cana-5360	57	8	1074	1074	NUM
cana-5360	57	9	-	-	PUNCT
cana-5360	57	10	133x	133x	NUM
cana-5360	57	11	vol	vol	VERB
cana-5360	57	12	32	32	NUM
cana-5360	57	13	no	no	NOUN
cana-5360	57	14	.	.	PUNCT
cana-5360	58	1	10s	10	NOUN
cana-5360	58	2	(	(	PUNCT
cana-5360	58	3	2025	2025	NUM
cana-5360	58	4	)	)	PUNCT
cana-5360	58	5	1927	1927	NUM
cana-5360	58	6	https://internationalpubls.com	https://internationalpubls.com	SYM
cana-5360	58	7	2	2	NUM
cana-5360	58	8	preliminaries	preliminary	NOUN
cana-5360	58	9	we	we	PRON
cana-5360	58	10	recall	recall	VERB
cana-5360	58	11	some	some	DET
cana-5360	58	12	basic	basic	ADJ
cana-5360	58	13	notions	notion	NOUN
cana-5360	58	14	of	of	ADP
cana-5360	58	15	fuzzy	fuzzy	ADJ
cana-5360	58	16	sets	set	NOUN
cana-5360	58	17	,	,	PUNCT
cana-5360	58	18	𝐼𝐹𝑆	𝐼𝐹𝑆	PROPN
cana-5360	58	19	’s	’s	PART
cana-5360	58	20	and	and	CCONJ
cana-5360	58	21	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-5360	58	22	’s	’s	PART
cana-5360	58	23	.	.	PUNCT
cana-5360	59	1	definition	definition	NOUN
cana-5360	59	2	2.1	2.1	NUM
cana-5360	59	3	[	[	SYM
cana-5360	59	4	40	40	NUM
cana-5360	59	5	]	]	PUNCT
cana-5360	59	6	let	let	VERB
cana-5360	59	7	𝑋	𝑋	NOUN
cana-5360	59	8	be	be	AUX
cana-5360	59	9	a	a	DET
cana-5360	59	10	nonempty	nonempty	ADV
cana-5360	59	11	set	set	VERB
cana-5360	59	12	.	.	PUNCT
cana-5360	60	1	a	a	DET
cana-5360	60	2	fuzzy	fuzzy	ADJ
cana-5360	60	3	set	set	VERB
cana-5360	60	4	𝐴	𝐴	PROPN
cana-5360	60	5	in	in	ADP
cana-5360	60	6	𝑋	𝑋	PROPN
cana-5360	60	7	is	be	AUX
cana-5360	60	8	characterized	characterize	VERB
cana-5360	60	9	by	by	ADP
cana-5360	60	10	a	a	DET
cana-5360	60	11	membership	membership	NOUN
cana-5360	60	12	function	function	NOUN
cana-5360	60	13	𝜇𝐴	𝜇𝐴	ADP
cana-5360	60	14	:	:	PUNCT
cana-5360	60	15	𝑋	𝑋	PROPN
cana-5360	60	16	→	→	SYM
cana-5360	61	1	[	[	X
cana-5360	61	2	0,1	0,1	NUM
cana-5360	61	3	]	]	PUNCT
cana-5360	61	4	.	.	PUNCT
cana-5360	62	1	that	that	PRON
cana-5360	62	2	is	be	AUX
cana-5360	62	3	:	:	PUNCT
cana-5360	62	4	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-5360	62	5	)	)	PUNCT
cana-5360	62	6	=	=	NOUN
cana-5360	62	7	{	{	PUNCT
cana-5360	63	1	1	1	NUM
cana-5360	63	2	,	,	PUNCT
cana-5360	63	3	if	if	SCONJ
cana-5360	63	4	𝑥	𝑥	PRON
cana-5360	63	5	∈	∈	PROPN
cana-5360	63	6	𝑋	𝑋	NOUN
cana-5360	63	7	0	0	NUM
cana-5360	63	8	,	,	PUNCT
cana-5360	63	9	if	if	SCONJ
cana-5360	63	10	𝑥	𝑥	PROPN
cana-5360	63	11	∉	∉	X
cana-5360	63	12	𝑋	𝑋	PROPN
cana-5360	63	13	(	(	PUNCT
cana-5360	63	14	0,1	0,1	NUM
cana-5360	63	15	)	)	PUNCT
cana-5360	63	16	if	if	SCONJ
cana-5360	63	17	𝑥	𝑥	NOUN
cana-5360	63	18	ispartlyin	ispartlyin	VERB
cana-5360	63	19	𝑋.	𝑋.	PROPN
cana-5360	63	20	alternatively	alternatively	ADV
cana-5360	63	21	,	,	PUNCT
cana-5360	63	22	a	a	DET
cana-5360	63	23	fuzzy	fuzzy	ADJ
cana-5360	63	24	set	set	VERB
cana-5360	63	25	𝐴	𝐴	PROPN
cana-5360	63	26	in	in	ADP
cana-5360	63	27	𝑋	𝑋	PROPN
cana-5360	63	28	is	be	AUX
cana-5360	63	29	an	an	DET
cana-5360	63	30	object	object	NOUN
cana-5360	63	31	having	have	VERB
cana-5360	63	32	the	the	DET
cana-5360	63	33	form	form	NOUN
cana-5360	63	34	𝐴	𝐴	NOUN
cana-5360	63	35	=	=	PUNCT
cana-5360	63	36	{	{	PUNCT
cana-5360	63	37	<	<	X
cana-5360	63	38	𝑥	𝑥	X
cana-5360	63	39	,	,	PUNCT
cana-5360	63	40	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-5360	63	41	)	)	PUNCT
cana-5360	63	42	>	>	PUNCT
cana-5360	64	1	|𝑥	|𝑥	PROPN
cana-5360	64	2	∈	∈	PROPN
cana-5360	64	3	𝑋	𝑋	PROPN
cana-5360	64	4	}	}	PUNCT
cana-5360	64	5	or	or	CCONJ
cana-5360	64	6	𝐴	𝐴	PROPN
cana-5360	64	7	=	=	PUNCT
cana-5360	64	8	{	{	PUNCT
cana-5360	64	9	⟨	⟨	NOUN
cana-5360	64	10	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-5360	64	11	)	)	PUNCT
cana-5360	64	12	𝑥	𝑥	DET
cana-5360	64	13	⟩	⟩	NOUN
cana-5360	64	14	|𝑥	|𝑥	NOUN
cana-5360	64	15	∈	∈	PROPN
cana-5360	64	16	𝑋	𝑋	PROPN
cana-5360	64	17	}	}	PUNCT
cana-5360	64	18	,	,	PUNCT
cana-5360	64	19	where	where	SCONJ
cana-5360	64	20	the	the	DET
cana-5360	64	21	function	function	NOUN
cana-5360	64	22	𝜇𝐴(𝑥	𝜇𝐴(𝑥	VERB
cana-5360	64	23	):	):	PUNCT
cana-5360	64	24	𝑋	𝑋	PROPN
cana-5360	64	25	→	→	SYM
cana-5360	64	26	[	[	X
cana-5360	64	27	0,1	0,1	NUM
cana-5360	64	28	]	]	PUNCT
cana-5360	64	29	defines	define	VERB
cana-5360	64	30	the	the	DET
cana-5360	64	31	degree	degree	NOUN
cana-5360	64	32	of	of	ADP
cana-5360	64	33	membership	membership	NOUN
cana-5360	64	34	of	of	ADP
cana-5360	64	35	the	the	DET
cana-5360	64	36	element	element	NOUN
cana-5360	64	37	,	,	PUNCT
cana-5360	64	38	𝑥	𝑥	PROPN
cana-5360	64	39	∈	∈	PROPN
cana-5360	64	40	𝑋.	𝑋.	PROPN
cana-5360	64	41	the	the	PRON
cana-5360	64	42	closer	close	ADV
cana-5360	64	43	the	the	DET
cana-5360	64	44	membership	membership	NOUN
cana-5360	64	45	value	value	NOUN
cana-5360	64	46	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NOUN
cana-5360	64	47	)	)	PUNCT
cana-5360	64	48	to	to	ADP
cana-5360	64	49	1	1	NUM
cana-5360	64	50	,	,	PUNCT
cana-5360	64	51	the	the	PRON
cana-5360	64	52	more	more	ADJ
cana-5360	64	53	𝑥	𝑥	NOUN
cana-5360	64	54	belongs	belong	VERB
cana-5360	64	55	to	to	ADP
cana-5360	64	56	𝐴	𝐴	PROPN
cana-5360	64	57	,	,	PUNCT
cana-5360	64	58	where	where	SCONJ
cana-5360	64	59	the	the	DET
cana-5360	64	60	grades	grade	NOUN
cana-5360	64	61	1	1	NUM
cana-5360	64	62	and	and	CCONJ
cana-5360	64	63	0	0	NUM
cana-5360	64	64	represent	represent	VERB
cana-5360	64	65	full	full	ADJ
cana-5360	64	66	membership	membership	NOUN
cana-5360	64	67	and	and	CCONJ
cana-5360	64	68	full	full	ADJ
cana-5360	64	69	nonmembership	nonmembership	NOUN
cana-5360	64	70	.	.	PUNCT
cana-5360	65	1	fuzzy	fuzzy	ADJ
cana-5360	65	2	set	set	NOUN
cana-5360	65	3	is	be	AUX
cana-5360	65	4	a	a	DET
cana-5360	65	5	collection	collection	NOUN
cana-5360	65	6	of	of	ADP
cana-5360	65	7	objects	object	NOUN
cana-5360	65	8	with	with	ADP
cana-5360	65	9	graded	grade	VERB
cana-5360	65	10	membership	membership	NOUN
cana-5360	65	11	,	,	PUNCT
cana-5360	65	12	that	that	ADV
cana-5360	65	13	is	is	ADV
cana-5360	65	14	,	,	PUNCT
cana-5360	65	15	having	have	VERB
cana-5360	65	16	degree	degree	NOUN
cana-5360	65	17	of	of	ADP
cana-5360	65	18	membership	membership	NOUN
cana-5360	65	19	.	.	PUNCT
cana-5360	66	1	fuzzy	fuzzy	ADJ
cana-5360	66	2	set	set	NOUN
cana-5360	66	3	is	be	AUX
cana-5360	66	4	an	an	DET
cana-5360	66	5	extension	extension	NOUN
cana-5360	66	6	of	of	ADP
cana-5360	66	7	the	the	DET
cana-5360	66	8	classical	classical	ADJ
cana-5360	66	9	notion	notion	NOUN
cana-5360	66	10	of	of	ADP
cana-5360	66	11	set	set	NOUN
cana-5360	66	12	.	.	PUNCT
cana-5360	67	1	in	in	ADP
cana-5360	67	2	classical	classical	ADJ
cana-5360	67	3	set	set	NOUN
cana-5360	67	4	theory	theory	NOUN
cana-5360	67	5	,	,	PUNCT
cana-5360	67	6	the	the	DET
cana-5360	67	7	membership	membership	NOUN
cana-5360	67	8	of	of	ADP
cana-5360	67	9	elements	element	NOUN
cana-5360	67	10	in	in	ADP
cana-5360	67	11	a	a	DET
cana-5360	67	12	set	set	NOUN
cana-5360	67	13	is	be	AUX
cana-5360	67	14	assessed	assess	VERB
cana-5360	67	15	in	in	ADP
cana-5360	67	16	a	a	DET
cana-5360	67	17	binary	binary	ADJ
cana-5360	67	18	terms	term	NOUN
cana-5360	67	19	according	accord	VERB
cana-5360	67	20	to	to	ADP
cana-5360	67	21	a	a	DET
cana-5360	67	22	bivalent	bivalent	ADJ
cana-5360	67	23	condition	condition	NOUN
cana-5360	67	24	;	;	PUNCT
cana-5360	67	25	an	an	DET
cana-5360	67	26	element	element	NOUN
cana-5360	67	27	either	either	CCONJ
cana-5360	67	28	belongs	belong	VERB
cana-5360	67	29	or	or	CCONJ
cana-5360	67	30	does	do	AUX
cana-5360	67	31	not	not	PART
cana-5360	67	32	belong	belong	VERB
cana-5360	67	33	to	to	ADP
cana-5360	67	34	the	the	DET
cana-5360	67	35	set	set	NOUN
cana-5360	67	36	.	.	PUNCT
cana-5360	68	1	classical	classical	ADJ
cana-5360	68	2	bivalent	bivalent	ADJ
cana-5360	68	3	sets	set	NOUN
cana-5360	68	4	are	be	AUX
cana-5360	68	5	in	in	ADP
cana-5360	68	6	fuzzy	fuzzy	ADJ
cana-5360	68	7	set	set	NOUN
cana-5360	68	8	theory	theory	NOUN
cana-5360	68	9	called	call	VERB
cana-5360	68	10	crisp	crisp	ADJ
cana-5360	68	11	sets	set	NOUN
cana-5360	68	12	.	.	PUNCT
cana-5360	69	1	fuzzy	fuzzy	ADJ
cana-5360	69	2	sets	set	NOUN
cana-5360	69	3	are	be	AUX
cana-5360	69	4	generalized	generalized	ADJ
cana-5360	69	5	classical	classical	ADJ
cana-5360	69	6	sets	set	NOUN
cana-5360	69	7	,	,	PUNCT
cana-5360	69	8	since	since	SCONJ
cana-5360	69	9	the	the	DET
cana-5360	69	10	indicator	indicator	NOUN
cana-5360	69	11	function	function	NOUN
cana-5360	69	12	of	of	ADP
cana-5360	69	13	classical	classical	ADJ
cana-5360	69	14	sets	set	NOUN
cana-5360	69	15	is	be	AUX
cana-5360	69	16	special	special	ADJ
cana-5360	69	17	cases	case	NOUN
cana-5360	69	18	of	of	ADP
cana-5360	69	19	the	the	DET
cana-5360	69	20	membership	membership	NOUN
cana-5360	69	21	functions	function	NOUN
cana-5360	69	22	of	of	ADP
cana-5360	69	23	fuzzy	fuzzy	ADJ
cana-5360	69	24	sets	set	NOUN
cana-5360	69	25	,	,	PUNCT
cana-5360	69	26	if	if	SCONJ
cana-5360	69	27	the	the	DET
cana-5360	69	28	latter	latter	ADJ
cana-5360	69	29	only	only	ADV
cana-5360	69	30	take	take	VERB
cana-5360	69	31	values	value	NOUN
cana-5360	69	32	0	0	NUM
cana-5360	69	33	or	or	CCONJ
cana-5360	69	34	1	1	NUM
cana-5360	69	35	.	.	X
cana-5360	69	36	fuzzy	fuzzy	ADJ
cana-5360	69	37	sets	set	NOUN
cana-5360	69	38	theory	theory	NOUN
cana-5360	69	39	permits	permit	VERB
cana-5360	69	40	the	the	DET
cana-5360	69	41	gradual	gradual	ADJ
cana-5360	69	42	assessment	assessment	NOUN
cana-5360	69	43	of	of	ADP
cana-5360	69	44	the	the	DET
cana-5360	69	45	membership	membership	NOUN
cana-5360	69	46	of	of	ADP
cana-5360	69	47	element	element	NOUN
cana-5360	69	48	in	in	ADP
cana-5360	69	49	a	a	DET
cana-5360	69	50	set	set	NOUN
cana-5360	69	51	;	;	PUNCT
cana-5360	69	52	this	this	PRON
cana-5360	69	53	is	be	AUX
cana-5360	69	54	described	describe	VERB
cana-5360	69	55	with	with	ADP
cana-5360	69	56	the	the	DET
cana-5360	69	57	aid	aid	NOUN
cana-5360	69	58	of	of	ADP
cana-5360	69	59	a	a	DET
cana-5360	69	60	membership	membership	NOUN
cana-5360	69	61	function	function	NOUN
cana-5360	69	62	valued	value	VERB
cana-5360	69	63	in	in	ADP
cana-5360	69	64	the	the	DET
cana-5360	69	65	real	real	ADJ
cana-5360	69	66	unit	unit	NOUN
cana-5360	69	67	interval	interval	NOUN
cana-5360	69	68	[	[	X
cana-5360	69	69	0,1	0,1	NUM
cana-5360	69	70	]	]	PUNCT
cana-5360	69	71	.	.	PUNCT
cana-5360	70	1	let	let	VERB
cana-5360	70	2	us	we	PRON
cana-5360	70	3	consider	consider	VERB
cana-5360	70	4	two	two	NUM
cana-5360	70	5	examples	example	NOUN
cana-5360	70	6	:	:	PUNCT
cana-5360	70	7	(	(	PUNCT
cana-5360	70	8	i	i	NOUN
cana-5360	70	9	)	)	PUNCT
cana-5360	70	10	all	all	DET
cana-5360	70	11	employees	employee	NOUN
cana-5360	70	12	of	of	ADP
cana-5360	70	13	𝑋𝑌𝑍	𝑋𝑌𝑍	PROPN
cana-5360	70	14	who	who	PRON
cana-5360	70	15	are	be	AUX
cana-5360	70	16	over	over	ADP
cana-5360	70	17	1.8𝑚	1.8𝑚	NUM
cana-5360	70	18	in	in	ADP
cana-5360	70	19	height	height	NOUN
cana-5360	70	20	;	;	PUNCT
cana-5360	70	21	(	(	PUNCT
cana-5360	70	22	ii	ii	NOUN
cana-5360	70	23	)	)	PUNCT
cana-5360	70	24	all	all	DET
cana-5360	70	25	employees	employee	NOUN
cana-5360	70	26	of	of	ADP
cana-5360	70	27	𝑋𝑌𝑍	𝑋𝑌𝑍	PROPN
cana-5360	70	28	who	who	PRON
cana-5360	70	29	are	be	AUX
cana-5360	70	30	tall	tall	ADJ
cana-5360	70	31	.	.	PUNCT
cana-5360	71	1	the	the	DET
cana-5360	71	2	first	first	ADJ
cana-5360	71	3	example	example	NOUN
cana-5360	71	4	is	be	AUX
cana-5360	71	5	a	a	DET
cana-5360	71	6	classical	classical	ADJ
cana-5360	71	7	set	set	NOUN
cana-5360	71	8	with	with	ADP
cana-5360	71	9	a	a	DET
cana-5360	71	10	universe	universe	NOUN
cana-5360	71	11	(	(	PUNCT
cana-5360	71	12	all	all	DET
cana-5360	71	13	𝑋𝑌𝑍	𝑋𝑌𝑍	PROPN
cana-5360	71	14	employees	employee	NOUN
cana-5360	71	15	)	)	PUNCT
cana-5360	71	16	and	and	CCONJ
cana-5360	71	17	a	a	DET
cana-5360	71	18	membership	membership	NOUN
cana-5360	71	19	rule	rule	NOUN
cana-5360	71	20	that	that	PRON
cana-5360	71	21	divides	divide	VERB
cana-5360	71	22	the	the	DET
cana-5360	71	23	universe	universe	NOUN
cana-5360	71	24	into	into	ADP
cana-5360	71	25	members	member	NOUN
cana-5360	71	26	(	(	PUNCT
cana-5360	71	27	those	those	PRON
cana-5360	71	28	over	over	ADP
cana-5360	71	29	1.8𝑚	1.8𝑚	NUM
cana-5360	71	30	)	)	PUNCT
cana-5360	71	31	and	and	CCONJ
cana-5360	71	32	nonmembers	nonmember	NOUN
cana-5360	71	33	.	.	PUNCT
cana-5360	72	1	the	the	DET
cana-5360	72	2	second	second	ADJ
cana-5360	72	3	example	example	NOUN
cana-5360	72	4	is	be	AUX
cana-5360	72	5	a	a	DET
cana-5360	72	6	fuzzy	fuzzy	ADJ
cana-5360	72	7	set	set	NOUN
cana-5360	72	8	,	,	PUNCT
cana-5360	72	9	because	because	SCONJ
cana-5360	72	10	some	some	DET
cana-5360	72	11	employees	employee	NOUN
cana-5360	72	12	are	be	AUX
cana-5360	72	13	definitely	definitely	ADV
cana-5360	72	14	in	in	ADP
cana-5360	72	15	the	the	DET
cana-5360	72	16	set	set	NOUN
cana-5360	72	17	and	and	CCONJ
cana-5360	72	18	some	some	PRON
cana-5360	72	19	are	be	AUX
cana-5360	72	20	definitely	definitely	ADV
cana-5360	72	21	not	not	PART
cana-5360	72	22	in	in	ADP
cana-5360	72	23	the	the	DET
cana-5360	72	24	set	set	NOUN
cana-5360	72	25	,	,	PUNCT
cana-5360	72	26	but	but	CCONJ
cana-5360	72	27	some	some	PRON
cana-5360	72	28	are	be	AUX
cana-5360	72	29	borderline	borderline	NOUN
cana-5360	72	30	.	.	PUNCT
cana-5360	73	1	this	this	DET
cana-5360	73	2	distinction	distinction	NOUN
cana-5360	73	3	between	between	ADP
cana-5360	73	4	the	the	DET
cana-5360	73	5	ins	in	NOUN
cana-5360	73	6	,	,	PUNCT
cana-5360	73	7	the	the	DET
cana-5360	73	8	outs	out	NOUN
cana-5360	73	9	,	,	PUNCT
cana-5360	73	10	and	and	CCONJ
cana-5360	73	11	the	the	DET
cana-5360	73	12	borderline	borderline	NOUN
cana-5360	73	13	is	be	AUX
cana-5360	73	14	made	make	VERB
cana-5360	73	15	more	more	ADV
cana-5360	73	16	exact	exact	ADJ
cana-5360	73	17	by	by	ADP
cana-5360	73	18	the	the	DET
cana-5360	73	19	membership	membership	NOUN
cana-5360	73	20	function	function	NOUN
cana-5360	73	21	,	,	PUNCT
cana-5360	73	22	𝜇.	𝜇.	ADV
cana-5360	73	23	if	if	SCONJ
cana-5360	73	24	we	we	PRON
cana-5360	73	25	return	return	VERB
cana-5360	73	26	to	to	ADP
cana-5360	73	27	our	our	PRON
cana-5360	73	28	second	second	ADJ
cana-5360	73	29	example	example	NOUN
cana-5360	73	30	and	and	CCONJ
cana-5360	73	31	let	let	VERB
cana-5360	73	32	𝐴	𝐴	PROPN
cana-5360	73	33	represent	represent	VERB
cana-5360	73	34	the	the	DET
cana-5360	73	35	fuzzy	fuzzy	ADJ
cana-5360	73	36	set	set	NOUN
cana-5360	73	37	of	of	ADP
cana-5360	73	38	all	all	DET
cana-5360	73	39	tall	tall	ADJ
cana-5360	73	40	employees	employee	NOUN
cana-5360	73	41	and	and	CCONJ
cana-5360	73	42	𝑥	𝑥	PROPN
cana-5360	73	43	represent	represent	VERB
cana-5360	73	44	a	a	DET
cana-5360	73	45	member	member	NOUN
cana-5360	73	46	of	of	ADP
cana-5360	73	47	the	the	DET
cana-5360	73	48	universe	universe	ADJ
cana-5360	73	49	𝑋	𝑋	NOUN
cana-5360	73	50	(	(	PUNCT
cana-5360	73	51	i.e.	i.e.	X
cana-5360	73	52	all	all	DET
cana-5360	73	53	employees	employee	NOUN
cana-5360	73	54	)	)	PUNCT
cana-5360	73	55	,	,	PUNCT
cana-5360	73	56	then	then	ADV
cana-5360	73	57	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-5360	73	58	)	)	PUNCT
cana-5360	73	59	would	would	AUX
cana-5360	73	60	be	be	AUX
cana-5360	73	61	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-5360	73	62	)	)	PUNCT
cana-5360	73	63	=	=	SYM
cana-5360	73	64	1	1	NUM
cana-5360	73	65	if	if	SCONJ
cana-5360	73	66	𝑥	𝑥	PRON
cana-5360	73	67	is	be	AUX
cana-5360	73	68	definitely	definitely	ADV
cana-5360	73	69	tall	tall	ADJ
cana-5360	73	70	or	or	CCONJ
cana-5360	73	71	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-5360	73	72	)	)	PUNCT
cana-5360	73	73	=	=	SYM
cana-5360	73	74	0	0	PUNCT
cana-5360	74	1	if	if	SCONJ
cana-5360	74	2	𝑥	𝑥	PRON
cana-5360	74	3	is	be	AUX
cana-5360	74	4	definitely	definitely	ADV
cana-5360	74	5	not	not	PART
cana-5360	74	6	tall	tall	ADJ
cana-5360	74	7	or	or	CCONJ
cana-5360	74	8	0	0	NUM
cana-5360	74	9	<	<	X
cana-5360	74	10	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NOUN
cana-5360	74	11	)	)	PUNCT
cana-5360	74	12	<	<	X
cana-5360	74	13	1	1	NUM
cana-5360	74	14	for	for	ADP
cana-5360	74	15	borderline	borderline	NOUN
cana-5360	74	16	cases	case	NOUN
cana-5360	74	17	.	.	PUNCT
cana-5360	75	1	definition	definition	NOUN
cana-5360	75	2	2.2	2.2	NUM
cana-5360	76	1	[	[	SYM
cana-5360	76	2	9	9	NUM
cana-5360	76	3	,	,	PUNCT
cana-5360	76	4	10	10	NUM
cana-5360	76	5	,	,	PUNCT
cana-5360	76	6	11	11	NUM
cana-5360	76	7	,	,	PUNCT
cana-5360	76	8	12	12	NUM
cana-5360	76	9	]	]	PUNCT
cana-5360	76	10	let	let	VERB
cana-5360	76	11	a	a	DET
cana-5360	76	12	nonempty	nonempty	ADV
cana-5360	76	13	set	set	VERB
cana-5360	76	14	𝑋	𝑋	NOUN
cana-5360	76	15	be	be	AUX
cana-5360	76	16	fixed	fix	VERB
cana-5360	76	17	.	.	PUNCT
cana-5360	77	1	an	an	DET
cana-5360	77	2	𝐼𝐹𝑆	𝐼𝐹𝑆	PROPN
cana-5360	77	3	𝐴	𝐴	PROPN
cana-5360	77	4	in	in	ADP
cana-5360	77	5	𝑋	𝑋	PROPN
cana-5360	77	6	is	be	AUX
cana-5360	77	7	an	an	DET
cana-5360	77	8	object	object	NOUN
cana-5360	77	9	having	have	VERB
cana-5360	77	10	the	the	DET
cana-5360	77	11	form	form	NOUN
cana-5360	77	12	:	:	PUNCT
cana-5360	77	13	𝐴	𝐴	PROPN
cana-5360	77	14	=	=	PUNCT
cana-5360	77	15	{	{	PUNCT
cana-5360	77	16	<	<	X
cana-5360	77	17	𝑥	𝑥	X
cana-5360	77	18	,	,	PUNCT
cana-5360	77	19	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-5360	77	20	)	)	PUNCT
cana-5360	77	21	,	,	PUNCT
cana-5360	77	22	𝜆𝐴(𝑥	𝜆𝐴(𝑥	PROPN
cana-5360	77	23	)	)	PUNCT
cana-5360	77	24	>	>	PUNCT
cana-5360	78	1	|𝑥	|𝑥	PROPN
cana-5360	78	2	∈	∈	PROPN
cana-5360	78	3	𝑋	𝑋	PROPN
cana-5360	78	4	}	}	PUNCT
cana-5360	78	5	or	or	CCONJ
cana-5360	78	6	𝐴	𝐴	PROPN
cana-5360	78	7	=	=	PUNCT
cana-5360	78	8	{	{	PUNCT
cana-5360	78	9	⟨	⟨	NOUN
cana-5360	78	10	𝜇𝐴(𝑥),𝜆𝐴(𝑥	𝜇𝐴(𝑥),𝜆𝐴(𝑥	PUNCT
cana-5360	78	11	)	)	PUNCT
cana-5360	78	12	𝑥	𝑥	PRON
cana-5360	78	13	⟩	⟩	NOUN
cana-5360	78	14	|𝑥	|𝑥	NOUN
cana-5360	78	15	∈	∈	PROPN
cana-5360	78	16	𝑋	𝑋	PROPN
cana-5360	78	17	}	}	PUNCT
cana-5360	78	18	,	,	PUNCT
cana-5360	78	19	where	where	SCONJ
cana-5360	78	20	the	the	DET
cana-5360	78	21	functions	function	NOUN
cana-5360	78	22	𝜇𝐴(𝑥	𝜇𝐴(𝑥	VERB
cana-5360	78	23	):	):	PUNCT
cana-5360	78	24	𝑋	𝑋	PROPN
cana-5360	78	25	→	→	SYM
cana-5360	78	26	[	[	X
cana-5360	78	27	0,1	0,1	NUM
cana-5360	78	28	]	]	PUNCT
cana-5360	78	29	and	and	CCONJ
cana-5360	78	30	𝜆𝐴(𝑥	𝜆𝐴(𝑥	NUM
cana-5360	78	31	):	):	PUNCT
cana-5360	78	32	𝑋	𝑋	PROPN
cana-5360	78	33	→	→	SYM
cana-5360	78	34	[	[	X
cana-5360	78	35	0,1	0,1	NUM
cana-5360	78	36	]	]	PUNCT
cana-5360	78	37	define	define	VERB
cana-5360	78	38	the	the	DET
cana-5360	78	39	degree	degree	NOUN
cana-5360	78	40	of	of	ADP
cana-5360	78	41	membership	membership	NOUN
cana-5360	78	42	and	and	CCONJ
cana-5360	78	43	the	the	DET
cana-5360	78	44	degree	degree	NOUN
cana-5360	78	45	of	of	ADP
cana-5360	78	46	nonmembership	nonmembership	NOUN
cana-5360	78	47	,	,	PUNCT
cana-5360	78	48	respectively	respectively	ADV
cana-5360	78	49	,	,	PUNCT
cana-5360	78	50	of	of	ADP
cana-5360	78	51	the	the	DET
cana-5360	78	52	element	element	NOUN
cana-5360	78	53	𝑥	𝑥	PRON
cana-5360	78	54	∈	∈	PROPN
cana-5360	78	55	𝑋	𝑋	NOUN
cana-5360	78	56	to	to	ADP
cana-5360	78	57	𝐴	𝐴	PROPN
cana-5360	78	58	,	,	PUNCT
cana-5360	78	59	which	which	PRON
cana-5360	78	60	is	be	AUX
cana-5360	78	61	a	a	DET
cana-5360	78	62	subset	subset	NOUN
cana-5360	78	63	of	of	ADP
cana-5360	78	64	𝑋	𝑋	PROPN
cana-5360	78	65	,	,	PUNCT
cana-5360	78	66	and	and	CCONJ
cana-5360	78	67	for	for	ADP
cana-5360	78	68	every	every	DET
cana-5360	78	69	𝑥	𝑥	PRON
cana-5360	78	70	∈	∈	PROPN
cana-5360	78	71	𝑋	𝑋	NOUN
cana-5360	78	72	:	:	PUNCT
cana-5360	78	73	0	0	NUM
cana-5360	78	74	≤	≤	NUM
cana-5360	78	75	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-5360	78	76	)	)	PUNCT
cana-5360	79	1	+	+	NUM
cana-5360	79	2	𝜆𝐴(𝑥	𝜆𝐴(𝑥	X
cana-5360	79	3	)	)	PUNCT
cana-5360	79	4	≤	≤	NUM
cana-5360	79	5	1	1	NUM
cana-5360	79	6	.	.	PUNCT
cana-5360	80	1	for	for	ADP
cana-5360	80	2	each	each	DET
cana-5360	80	3	𝐴	𝐴	PROPN
cana-5360	80	4	in	in	ADP
cana-5360	80	5	𝑋	𝑋	PROPN
cana-5360	80	6	:	:	PUNCT
cana-5360	80	7	𝜋𝐴(𝑥	𝜋𝐴(𝑥	NUM
cana-5360	80	8	)	)	PUNCT
cana-5360	80	9	=	=	SYM
cana-5360	80	10	1	1	NUM
cana-5360	80	11	−	−	NUM
cana-5360	80	12	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-5360	80	13	)	)	PUNCT
cana-5360	80	14	−	−	PUNCT
cana-5360	80	15	𝜆𝐴(𝑥	𝜆𝐴(𝑥	NOUN
cana-5360	80	16	)	)	PUNCT
cana-5360	80	17	is	be	AUX
cana-5360	80	18	the	the	DET
cana-5360	80	19	intuitionistic	intuitionistic	ADJ
cana-5360	80	20	fuzzy	fuzzy	ADJ
cana-5360	80	21	set	set	VERB
cana-5360	80	22	index	index	NOUN
cana-5360	80	23	or	or	CCONJ
cana-5360	80	24	hesitation	hesitation	NOUN
cana-5360	80	25	margin	margin	NOUN
cana-5360	80	26	of	of	ADP
cana-5360	80	27	𝑥	𝑥	NOUN
cana-5360	80	28	in	in	ADP
cana-5360	80	29	𝑋.	𝑋.	PROPN
cana-5360	80	30	the	the	DET
cana-5360	80	31	hesitation	hesitation	NOUN
cana-5360	80	32	margin	margin	NOUN
cana-5360	80	33	𝜋𝐴(𝑥	𝜋𝐴(𝑥	NUM
cana-5360	80	34	)	)	PUNCT
cana-5360	80	35	is	be	AUX
cana-5360	80	36	the	the	DET
cana-5360	80	37	degree	degree	NOUN
cana-5360	80	38	of	of	ADP
cana-5360	80	39	nondeterminacy	nondeterminacy	NOUN
cana-5360	80	40	of	of	ADP
cana-5360	80	41	𝑥	𝑥	DET
cana-5360	80	42	∈	∈	PROPN
cana-5360	80	43	𝑋	𝑋	NOUN
cana-5360	80	44	to	to	ADP
cana-5360	80	45	the	the	DET
cana-5360	80	46	set	set	ADJ
cana-5360	80	47	𝐴	𝐴	PROPN
cana-5360	80	48	and	and	CCONJ
cana-5360	80	49	𝜋𝐴(𝑥	𝜋𝐴(𝑥	NUM
cana-5360	80	50	)	)	PUNCT
cana-5360	80	51	∈	∈	NOUN
cana-5360	81	1	[	[	X
cana-5360	81	2	0,1	0,1	NUM
cana-5360	81	3	]	]	PUNCT
cana-5360	81	4	.	.	PUNCT
cana-5360	82	1	the	the	DET
cana-5360	82	2	hesitation	hesitation	NOUN
cana-5360	82	3	margin	margin	NOUN
cana-5360	82	4	is	be	AUX
cana-5360	82	5	the	the	DET
cana-5360	82	6	function	function	NOUN
cana-5360	82	7	that	that	PRON
cana-5360	82	8	expresses	express	VERB
cana-5360	82	9	lack	lack	NOUN
cana-5360	82	10	of	of	ADP
cana-5360	82	11	knowledge	knowledge	NOUN
cana-5360	82	12	of	of	ADP
cana-5360	82	13	whether	whether	SCONJ
cana-5360	82	14	𝑥	𝑥	PRON
cana-5360	82	15	∈	∈	PROPN
cana-5360	82	16	𝑋	𝑋	NOUN
cana-5360	82	17	or	or	CCONJ
cana-5360	82	18	𝑥	𝑥	PROPN
cana-5360	82	19	∉	∉	PROPN
cana-5360	82	20	𝑋.	𝑋.	PROPN
cana-5360	82	21	thus	thus	ADV
cana-5360	82	22	:	:	PUNCT
cana-5360	82	23	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-5360	82	24	)	)	PUNCT
cana-5360	82	25	+	+	CCONJ
cana-5360	82	26	𝜆𝐴(𝑥	𝜆𝐴(𝑥	X
cana-5360	82	27	)	)	PUNCT
cana-5360	82	28	+	+	NUM
cana-5360	82	29	𝜋𝐴(𝑥	𝜋𝐴(𝑥	NUM
cana-5360	82	30	)	)	PUNCT
cana-5360	82	31	=	=	SYM
cana-5360	82	32	1	1	X
cana-5360	82	33	.	.	X
cana-5360	82	34	communications	communication	NOUN
cana-5360	82	35	on	on	ADP
cana-5360	82	36	applied	apply	VERB
cana-5360	82	37	nonlinear	nonlinear	ADJ
cana-5360	82	38	analysis	analysis	NOUN
cana-5360	82	39	issn	issn	NOUN
cana-5360	82	40	:	:	PUNCT
cana-5360	82	41	1074	1074	NUM
cana-5360	82	42	-	-	PUNCT
cana-5360	82	43	133x	133x	NUM
cana-5360	82	44	vol	vol	VERB
cana-5360	82	45	32	32	NUM
cana-5360	82	46	no	no	NOUN
cana-5360	82	47	.	.	PUNCT
cana-5360	83	1	10s	10	NOUN
cana-5360	83	2	(	(	PUNCT
cana-5360	83	3	2025	2025	NUM
cana-5360	83	4	)	)	PUNCT
cana-5360	83	5	1928	1928	NUM
cana-5360	83	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5360	83	7	example	example	NOUN
cana-5360	83	8	2.1	2.1	NUM
cana-5360	83	9	let	let	VERB
cana-5360	83	10	𝑋	𝑋	NOUN
cana-5360	83	11	=	=	SYM
cana-5360	83	12	{	{	PUNCT
cana-5360	83	13	𝑥	𝑥	PROPN
cana-5360	83	14	,	,	PUNCT
cana-5360	83	15	𝑦	𝑦	NOUN
cana-5360	83	16	,	,	PUNCT
cana-5360	83	17	𝑧	𝑧	PRON
cana-5360	83	18	}	}	PUNCT
cana-5360	83	19	be	be	AUX
cana-5360	83	20	a	a	DET
cana-5360	83	21	fixed	fix	VERB
cana-5360	83	22	universe	universe	NOUN
cana-5360	83	23	of	of	ADP
cana-5360	83	24	discourse	discourse	NOUN
cana-5360	83	25	and	and	CCONJ
cana-5360	83	26	𝐴	𝐴	PROPN
cana-5360	83	27	=	=	PUNCT
cana-5360	83	28	{	{	PUNCT
cana-5360	83	29	⟨	⟨	VERB
cana-5360	83	30	0.6,0.1	0.6,0.1	PROPN
cana-5360	83	31	𝑥	𝑥	DET
cana-5360	83	32	⟩	⟩	NOUN
cana-5360	83	33	,	,	PUNCT
cana-5360	83	34	⟨	⟨	VERB
cana-5360	83	35	0.8,0.1	0.8,0.1	PROPN
cana-5360	83	36	𝑦	𝑦	NOUN
cana-5360	83	37	⟩	⟩	NOUN
cana-5360	83	38	,	,	PUNCT
cana-5360	83	39	⟨	⟨	VERB
cana-5360	83	40	0.5,0.3	0.5,0.3	PROPN
cana-5360	83	41	𝑧	𝑧	DET
cana-5360	83	42	⟩	⟩	NOUN
cana-5360	83	43	}	}	PUNCT
cana-5360	83	44	,	,	PUNCT
cana-5360	83	45	be	be	AUX
cana-5360	83	46	the	the	DET
cana-5360	83	47	intuitionistic	intuitionistic	ADJ
cana-5360	83	48	fuzzy	fuzzy	ADJ
cana-5360	83	49	set	set	NOUN
cana-5360	83	50	in	in	ADP
cana-5360	83	51	𝑋.	𝑋.	PROPN
cana-5360	83	52	the	the	DET
cana-5360	83	53	hesitation	hesitation	NOUN
cana-5360	83	54	margins	margin	NOUN
cana-5360	83	55	of	of	ADP
cana-5360	83	56	the	the	DET
cana-5360	83	57	elements	element	NOUN
cana-5360	83	58	𝑥	𝑥	PROPN
cana-5360	83	59	,	,	PUNCT
cana-5360	83	60	𝑦	𝑦	NOUN
cana-5360	83	61	,	,	PUNCT
cana-5360	83	62	𝑧	𝑧	PUNCT
cana-5360	83	63	to	to	ADP
cana-5360	83	64	𝐴	𝐴	PROPN
cana-5360	83	65	are	be	AUX
cana-5360	83	66	as	as	SCONJ
cana-5360	83	67	follows	follow	VERB
cana-5360	83	68	:	:	PUNCT
cana-5360	83	69	𝜋𝐴(𝑥	𝜋𝐴(𝑥	NUM
cana-5360	83	70	)	)	PUNCT
cana-5360	83	71	=	=	SYM
cana-5360	83	72	0.3	0.3	NUM
cana-5360	83	73	,	,	PUNCT
cana-5360	83	74	𝜋𝐴(𝑦	𝜋𝐴(𝑦	PROPN
cana-5360	83	75	)	)	PUNCT
cana-5360	83	76	=	=	SYM
cana-5360	83	77	0.1	0.1	NUM
cana-5360	83	78	and	and	CCONJ
cana-5360	83	79	𝜋𝐴(𝑧	𝜋𝐴(𝑧	NUM
cana-5360	83	80	)	)	PUNCT
cana-5360	83	81	=	=	PUNCT
cana-5360	84	1	0.2	0.2	NUM
cana-5360	84	2	.	.	PUNCT
cana-5360	85	1	definition	definition	NOUN
cana-5360	85	2	2.3	2.3	NUM
cana-5360	86	1	[	[	X
cana-5360	86	2	36	36	NUM
cana-5360	86	3	,	,	PUNCT
cana-5360	86	4	37	37	NUM
cana-5360	86	5	,	,	PUNCT
cana-5360	86	6	39	39	NUM
cana-5360	86	7	]	]	PUNCT
cana-5360	86	8	let	let	VERB
cana-5360	86	9	a	a	DET
cana-5360	86	10	non	non	ADJ
cana-5360	86	11	empty	empty	ADJ
cana-5360	86	12	set	set	ADJ
cana-5360	86	13	𝑋	𝑋	NOUN
cana-5360	86	14	be	be	VERB
cana-5360	86	15	a	a	DET
cana-5360	86	16	universal	universal	ADJ
cana-5360	86	17	set	set	NOUN
cana-5360	86	18	.	.	PUNCT
cana-5360	87	1	then	then	ADV
cana-5360	87	2	,	,	PUNCT
cana-5360	87	3	a	a	DET
cana-5360	87	4	pythagorean	pythagorean	PROPN
cana-5360	87	5	fuzzy	fuzzy	ADJ
cana-5360	87	6	set	set	PROPN
cana-5360	87	7	𝐴	𝐴	PROPN
cana-5360	87	8	,	,	PUNCT
cana-5360	87	9	which	which	PRON
cana-5360	87	10	is	be	AUX
cana-5360	87	11	a	a	DET
cana-5360	87	12	set	set	NOUN
cana-5360	87	13	of	of	ADP
cana-5360	87	14	ordered	order	VERB
cana-5360	87	15	pairs	pair	NOUN
cana-5360	87	16	over	over	ADP
cana-5360	87	17	𝑋	𝑋	PROPN
cana-5360	87	18	,	,	PUNCT
cana-5360	87	19	is	be	AUX
cana-5360	87	20	defined	define	VERB
cana-5360	87	21	by	by	ADP
cana-5360	87	22	the	the	DET
cana-5360	87	23	following	following	NOUN
cana-5360	87	24	:	:	PUNCT
cana-5360	87	25	𝐴	𝐴	PROPN
cana-5360	87	26	=	=	PUNCT
cana-5360	87	27	{	{	PUNCT
cana-5360	87	28	<	<	X
cana-5360	87	29	𝑥	𝑥	X
cana-5360	87	30	,	,	PUNCT
cana-5360	87	31	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-5360	87	32	)	)	PUNCT
cana-5360	87	33	,	,	PUNCT
cana-5360	87	34	𝜆𝐴(𝑥)|𝑥	𝜆𝐴(𝑥)|𝑥	NOUN
cana-5360	87	35	∈	∈	PROPN
cana-5360	87	36	𝑋	𝑋	PROPN
cana-5360	87	37	}	}	PUNCT
cana-5360	87	38	or	or	CCONJ
cana-5360	87	39	𝐴	𝐴	PROPN
cana-5360	87	40	=	=	PUNCT
cana-5360	87	41	{	{	PUNCT
cana-5360	87	42	⟨	⟨	NOUN
cana-5360	87	43	𝜇𝐴(𝑥),𝜆𝐴(𝑥	𝜇𝐴(𝑥),𝜆𝐴(𝑥	PUNCT
cana-5360	87	44	)	)	PUNCT
cana-5360	87	45	𝑥	𝑥	PRON
cana-5360	87	46	⟩	⟩	NOUN
cana-5360	87	47	|𝑥	|𝑥	NOUN
cana-5360	87	48	∈	∈	PROPN
cana-5360	87	49	𝑋	𝑋	PROPN
cana-5360	87	50	}	}	PUNCT
cana-5360	87	51	,	,	PUNCT
cana-5360	87	52	where	where	SCONJ
cana-5360	87	53	the	the	DET
cana-5360	87	54	functions	function	NOUN
cana-5360	87	55	𝜇𝐴(𝑥	𝜇𝐴(𝑥	VERB
cana-5360	87	56	):	):	PUNCT
cana-5360	87	57	𝑋	𝑋	PROPN
cana-5360	87	58	→	→	SYM
cana-5360	87	59	[	[	X
cana-5360	87	60	0,1	0,1	NUM
cana-5360	87	61	]	]	PUNCT
cana-5360	87	62	and	and	CCONJ
cana-5360	87	63	𝜆𝐴(𝑥	𝜆𝐴(𝑥	NUM
cana-5360	87	64	):	):	PUNCT
cana-5360	87	65	𝑋	𝑋	PROPN
cana-5360	87	66	→	→	SYM
cana-5360	87	67	[	[	X
cana-5360	87	68	0,1	0,1	NUM
cana-5360	87	69	]	]	PUNCT
cana-5360	87	70	define	define	VERB
cana-5360	87	71	the	the	DET
cana-5360	87	72	degree	degree	NOUN
cana-5360	87	73	of	of	ADP
cana-5360	87	74	membership	membership	NOUN
cana-5360	87	75	and	and	CCONJ
cana-5360	87	76	the	the	DET
cana-5360	87	77	degree	degree	NOUN
cana-5360	87	78	of	of	ADP
cana-5360	87	79	nonmembership	nonmembership	NOUN
cana-5360	87	80	,	,	PUNCT
cana-5360	87	81	respectively	respectively	ADV
cana-5360	87	82	,	,	PUNCT
cana-5360	87	83	of	of	ADP
cana-5360	87	84	the	the	DET
cana-5360	87	85	element	element	NOUN
cana-5360	87	86	𝑥	𝑥	PRON
cana-5360	87	87	∈	∈	PROPN
cana-5360	87	88	𝑋	𝑋	NOUN
cana-5360	87	89	to	to	ADP
cana-5360	87	90	𝐴	𝐴	PROPN
cana-5360	87	91	,	,	PUNCT
cana-5360	87	92	which	which	PRON
cana-5360	87	93	is	be	AUX
cana-5360	87	94	a	a	DET
cana-5360	87	95	subset	subset	NOUN
cana-5360	87	96	of	of	ADP
cana-5360	87	97	𝑋	𝑋	PROPN
cana-5360	87	98	,	,	PUNCT
cana-5360	87	99	and	and	CCONJ
cana-5360	87	100	for	for	ADP
cana-5360	87	101	every	every	DET
cana-5360	87	102	𝑥	𝑥	PRON
cana-5360	87	103	∈	∈	PROPN
cana-5360	87	104	𝑋	𝑋	PROPN
cana-5360	87	105	,	,	PUNCT
cana-5360	87	106	0	0	NUM
cana-5360	87	107	≤	≤	NUM
cana-5360	87	108	(	(	PUNCT
cana-5360	87	109	𝜇𝐴(𝑥))2	𝜇𝐴(𝑥))2	NOUN
cana-5360	87	110	+	+	CCONJ
cana-5360	87	111	(	(	PUNCT
cana-5360	87	112	𝜆𝐴(𝑥))2	𝜆𝐴(𝑥))2	NOUN
cana-5360	87	113	≤	≤	NOUN
cana-5360	87	114	1	1	NUM
cana-5360	87	115	.	.	PUNCT
cana-5360	88	1	supposing	suppose	VERB
cana-5360	88	2	(	(	PUNCT
cana-5360	88	3	𝜇𝐴(𝑥))2	𝜇𝐴(𝑥))2	NOUN
cana-5360	88	4	+	+	CCONJ
cana-5360	88	5	(	(	PUNCT
cana-5360	88	6	𝜆𝐴(𝑥))2	𝜆𝐴(𝑥))2	NOUN
cana-5360	88	7	≤	≤	NUM
cana-5360	88	8	1	1	NUM
cana-5360	88	9	,	,	PUNCT
cana-5360	88	10	then	then	ADV
cana-5360	88	11	there	there	PRON
cana-5360	88	12	is	be	VERB
cana-5360	88	13	a	a	DET
cana-5360	88	14	degree	degree	NOUN
cana-5360	88	15	of	of	ADP
cana-5360	88	16	indeterminacy	indeterminacy	NOUN
cana-5360	88	17	of	of	ADP
cana-5360	88	18	𝑥	𝑥	DET
cana-5360	88	19	∈	∈	PROPN
cana-5360	88	20	𝑋	𝑋	NOUN
cana-5360	88	21	to	to	ADP
cana-5360	88	22	𝐴	𝐴	PROPN
cana-5360	88	23	defined	define	VERB
cana-5360	88	24	by	by	ADP
cana-5360	88	25	𝜋𝐴(𝑥	𝜋𝐴(𝑥	NUM
cana-5360	88	26	)	)	PUNCT
cana-5360	88	27	=	=	PUNCT
cana-5360	89	1	√1	√1	ADV
cana-5360	89	2	−	−	PROPN
cana-5360	90	1	[	[	X
cana-5360	90	2	(	(	PUNCT
cana-5360	90	3	𝜇𝐴(𝑥))2	𝜇𝐴(𝑥))2	NOUN
cana-5360	90	4	+	+	CCONJ
cana-5360	90	5	(	(	PUNCT
cana-5360	90	6	𝜆𝐴(𝑥))2	𝜆𝐴(𝑥))2	NOUN
cana-5360	90	7	]	]	PUNCT
cana-5360	90	8	and	and	CCONJ
cana-5360	90	9	𝜋𝐴(𝑥	𝜋𝐴(𝑥	NUM
cana-5360	90	10	)	)	PUNCT
cana-5360	90	11	∈	∈	NOUN
cana-5360	91	1	[	[	X
cana-5360	91	2	0,1	0,1	NUM
cana-5360	91	3	]	]	PUNCT
cana-5360	91	4	.	.	PUNCT
cana-5360	92	1	in	in	ADP
cana-5360	92	2	what	what	PRON
cana-5360	92	3	follows	follow	VERB
cana-5360	92	4	,	,	PUNCT
cana-5360	92	5	(	(	PUNCT
cana-5360	92	6	𝜇𝐴(𝑥))2	𝜇𝐴(𝑥))2	NOUN
cana-5360	92	7	+	+	CCONJ
cana-5360	92	8	(	(	PUNCT
cana-5360	92	9	𝜆𝐴(𝑥))2	𝜆𝐴(𝑥))2	NOUN
cana-5360	92	10	+	+	CCONJ
cana-5360	92	11	(	(	PUNCT
cana-5360	92	12	𝜋𝐴(𝑥))2	𝜋𝐴(𝑥))2	NOUN
cana-5360	92	13	=	=	SYM
cana-5360	92	14	1	1	X
cana-5360	92	15	.	.	PUNCT
cana-5360	92	16	otherwise	otherwise	ADV
cana-5360	92	17	,	,	PUNCT
cana-5360	92	18	𝜋𝐴(𝑥	𝜋𝐴(𝑥	NUM
cana-5360	92	19	)	)	PUNCT
cana-5360	92	20	=	=	SYM
cana-5360	92	21	0	0	PUNCT
cana-5360	92	22	whenever	whenever	SCONJ
cana-5360	92	23	(	(	PUNCT
cana-5360	92	24	𝜇𝐴(𝑥))2	𝜇𝐴(𝑥))2	NOUN
cana-5360	92	25	+	+	CCONJ
cana-5360	92	26	(	(	PUNCT
cana-5360	92	27	𝜆𝐴(𝑥))2	𝜆𝐴(𝑥))2	NOUN
cana-5360	92	28	=	=	SYM
cana-5360	92	29	1	1	X
cana-5360	92	30	.	.	X
cana-5360	93	1	we	we	PRON
cana-5360	93	2	denote	denote	VERB
cana-5360	93	3	the	the	DET
cana-5360	93	4	set	set	NOUN
cana-5360	93	5	of	of	ADP
cana-5360	93	6	all	all	DET
cana-5360	93	7	𝑃𝐹𝑆	𝑃𝐹𝑆	PROPN
cana-5360	93	8	’s	’s	NOUN
cana-5360	93	9	over	over	ADP
cana-5360	93	10	𝑋	𝑋	PROPN
cana-5360	93	11	by	by	ADP
cana-5360	93	12	𝑝𝑓𝑠(𝑋	𝑝𝑓𝑠(𝑋	PROPN
cana-5360	93	13	)	)	PUNCT
cana-5360	93	14	.	.	PUNCT
cana-5360	94	1	definition	definition	NOUN
cana-5360	94	2	2.4	2.4	NUM
cana-5360	94	3	[	[	SYM
cana-5360	94	4	39	39	NUM
cana-5360	94	5	]	]	PUNCT
cana-5360	94	6	let	let	VERB
cana-5360	94	7	𝐴	𝐴	PROPN
cana-5360	94	8	and	and	CCONJ
cana-5360	94	9	𝐵	𝐵	NOUN
cana-5360	94	10	be	be	AUX
cana-5360	95	1	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-5360	95	2	’s	’s	NOUN
cana-5360	95	3	of	of	ADP
cana-5360	95	4	the	the	DET
cana-5360	95	5	forms	form	NOUN
cana-5360	95	6	𝐴	𝐴	NOUN
cana-5360	95	7	=	=	PUNCT
cana-5360	95	8	{	{	PUNCT
cana-5360	95	9	<	<	X
cana-5360	95	10	𝑎	𝑎	NOUN
cana-5360	95	11	,	,	PUNCT
cana-5360	95	12	𝜇𝐴(𝑎	𝜇𝐴(𝑎	NOUN
cana-5360	95	13	)	)	PUNCT
cana-5360	95	14	,	,	PUNCT
cana-5360	95	15	𝜆𝐴(𝑎	𝜆𝐴(𝑎	PROPN
cana-5360	95	16	)	)	PUNCT
cana-5360	95	17	>	>	X
cana-5360	95	18	|𝑎	|𝑎	PROPN
cana-5360	96	1	∈	∈	PROPN
cana-5360	96	2	𝑋	𝑋	PROPN
cana-5360	96	3	}	}	PUNCT
cana-5360	96	4	and	and	CCONJ
cana-5360	96	5	𝐵	𝐵	NOUN
cana-5360	96	6	=	=	PUNCT
cana-5360	96	7	{	{	PUNCT
cana-5360	96	8	<	<	X
cana-5360	96	9	𝑎	𝑎	PROPN
cana-5360	96	10	,	,	PUNCT
cana-5360	96	11	𝜇𝐵(𝑎	𝜇𝐵(𝑎	NUM
cana-5360	96	12	)	)	PUNCT
cana-5360	96	13	,	,	PUNCT
cana-5360	96	14	𝜆𝐵(𝑎	𝜆𝐵(𝑎	PROPN
cana-5360	96	15	)	)	PUNCT
cana-5360	96	16	>	>	X
cana-5360	96	17	|𝑎	|𝑎	PROPN
cana-5360	97	1	∈	∈	PROPN
cana-5360	97	2	𝑋	𝑋	PROPN
cana-5360	97	3	}	}	PUNCT
cana-5360	97	4	.	.	PUNCT
cana-5360	98	1	then	then	ADV
cana-5360	99	1	[	[	X
cana-5360	99	2	(	(	PUNCT
cana-5360	99	3	i	i	NOUN
cana-5360	99	4	)	)	PUNCT
cana-5360	99	5	]	]	PUNCT
cana-5360	100	1	1	1	X
cana-5360	100	2	.	.	X
cana-5360	100	3	𝐴	𝐴	PROPN
cana-5360	100	4	⊆	⊆	NUM
cana-5360	100	5	𝐵	𝐵	PROPN
cana-5360	100	6	if	if	SCONJ
cana-5360	100	7	and	and	CCONJ
cana-5360	100	8	only	only	ADV
cana-5360	100	9	if	if	SCONJ
cana-5360	100	10	𝜇𝐴(𝑎	𝜇𝐴(𝑎	NUM
cana-5360	100	11	)	)	PUNCT
cana-5360	100	12	≤	≤	NUM
cana-5360	100	13	𝜇𝐵(𝑎	𝜇𝐵(𝑎	NUM
cana-5360	100	14	)	)	PUNCT
cana-5360	100	15	and	and	CCONJ
cana-5360	100	16	𝜆𝐴(𝑎	𝜆𝐴(𝑎	PROPN
cana-5360	100	17	)	)	PUNCT
cana-5360	100	18	≥	≥	NOUN
cana-5360	100	19	𝜆𝐵(𝑎	𝜆𝐵(𝑎	INTJ
cana-5360	100	20	)	)	PUNCT
cana-5360	100	21	for	for	ADP
cana-5360	100	22	all	all	DET
cana-5360	100	23	𝑎	𝑎	PROPN
cana-5360	100	24	∈	∈	NOUN
cana-5360	100	25	𝑋.	𝑋.	PROPN
cana-5360	100	26	2	2	NUM
cana-5360	100	27	.	.	PUNCT
cana-5360	101	1	𝐴	𝐴	NOUN
cana-5360	101	2	=	=	PROPN
cana-5360	101	3	𝐵	𝐵	PROPN
cana-5360	101	4	if	if	SCONJ
cana-5360	102	1	and	and	CCONJ
cana-5360	102	2	only	only	ADV
cana-5360	102	3	if	if	SCONJ
cana-5360	102	4	𝐴	𝐴	PROPN
cana-5360	102	5	⊆	⊆	NUM
cana-5360	102	6	𝐵	𝐵	NOUN
cana-5360	102	7	and	and	CCONJ
cana-5360	102	8	𝐵	𝐵	NOUN
cana-5360	102	9	⊆	⊆	NUM
cana-5360	102	10	𝐴.	𝐴.	PROPN
cana-5360	102	11	3	3	NUM
cana-5360	102	12	.	.	PUNCT
cana-5360	102	13	𝐴̅	𝐴̅	NOUN
cana-5360	102	14	=	=	PUNCT
cana-5360	102	15	{	{	PUNCT
cana-5360	102	16	<	<	X
cana-5360	102	17	𝑎	𝑎	X
cana-5360	102	18	,	,	PUNCT
cana-5360	102	19	𝜆𝐴(𝑎	𝜆𝐴(𝑎	PROPN
cana-5360	102	20	)	)	PUNCT
cana-5360	102	21	,	,	PUNCT
cana-5360	102	22	𝜇𝐴(𝑎	𝜇𝐴(𝑎	PROPN
cana-5360	102	23	)	)	PUNCT
cana-5360	102	24	>	>	X
cana-5360	102	25	|𝑎	|𝑎	PROPN
cana-5360	103	1	∈	∈	PROPN
cana-5360	103	2	𝑋	𝑋	PROPN
cana-5360	103	3	}	}	PUNCT
cana-5360	103	4	.	.	PUNCT
cana-5360	104	1	4	4	X
cana-5360	104	2	.	.	X
cana-5360	104	3	𝐴	𝐴	PROPN
cana-5360	104	4	∩	∩	NOUN
cana-5360	104	5	𝐵	𝐵	NOUN
cana-5360	104	6	=	=	PUNCT
cana-5360	104	7	{	{	PUNCT
cana-5360	104	8	<	<	X
cana-5360	104	9	𝑎	𝑎	X
cana-5360	104	10	,	,	PUNCT
cana-5360	104	11	𝜇𝐴(𝑎	𝜇𝐴(𝑎	NOUN
cana-5360	104	12	)	)	PUNCT
cana-5360	104	13	∧	∧	PROPN
cana-5360	104	14	𝜇𝐵(𝑎	𝜇𝐵(𝑎	NUM
cana-5360	104	15	)	)	PUNCT
cana-5360	104	16	,	,	PUNCT
cana-5360	104	17	𝜆𝐴(𝑎	𝜆𝐴(𝑎	PROPN
cana-5360	104	18	)	)	PUNCT
cana-5360	104	19	∨	∨	NOUN
cana-5360	104	20	𝜆𝐵(𝑎	𝜆𝐵(𝑎	NUM
cana-5360	104	21	)	)	PUNCT
cana-5360	104	22	>	>	X
cana-5360	104	23	|𝑎	|𝑎	PROPN
cana-5360	104	24	∈	∈	PROPN
cana-5360	104	25	𝑋	𝑋	PROPN
cana-5360	104	26	}	}	PUNCT
cana-5360	104	27	.	.	PUNCT
cana-5360	105	1	5	5	X
cana-5360	105	2	.	.	X
cana-5360	105	3	𝐴	𝐴	PROPN
cana-5360	105	4	∪	∪	AUX
cana-5360	105	5	𝐵	𝐵	NOUN
cana-5360	105	6	=	=	PUNCT
cana-5360	105	7	{	{	PUNCT
cana-5360	105	8	<	<	X
cana-5360	105	9	𝑎	𝑎	NOUN
cana-5360	105	10	,	,	PUNCT
cana-5360	105	11	𝜇𝐴(𝑎	𝜇𝐴(𝑎	NOUN
cana-5360	105	12	)	)	PUNCT
cana-5360	105	13	∨	∨	NUM
cana-5360	105	14	𝜇𝐵(𝑎	𝜇𝐵(𝑎	NUM
cana-5360	105	15	)	)	PUNCT
cana-5360	105	16	,	,	PUNCT
cana-5360	105	17	𝜆𝐴(𝑎	𝜆𝐴(𝑎	PROPN
cana-5360	105	18	)	)	PUNCT
cana-5360	105	19	∧	∧	NOUN
cana-5360	105	20	𝜆𝐵(𝑎	𝜆𝐵(𝑎	PROPN
cana-5360	105	21	)	)	PUNCT
cana-5360	105	22	>	>	X
cana-5360	105	23	|𝑎	|𝑎	PROPN
cana-5360	105	24	∈	∈	PROPN
cana-5360	105	25	𝑋	𝑋	PROPN
cana-5360	105	26	}	}	PUNCT
cana-5360	105	27	.	.	PUNCT
cana-5360	106	1	6	6	NUM
cana-5360	106	2	.	.	X
cana-5360	106	3	0𝑃	0𝑃	NOUN
cana-5360	106	4	=	=	SYM
cana-5360	106	5	{	{	PUNCT
cana-5360	106	6	<	<	X
cana-5360	106	7	𝑎	𝑎	NOUN
cana-5360	106	8	,	,	PUNCT
cana-5360	106	9	0,1	0,1	NUM
cana-5360	106	10	>	>	SYM
cana-5360	106	11	|𝑎	|𝑎	NOUN
cana-5360	106	12	∈	∈	PROPN
cana-5360	106	13	𝑋	𝑋	PROPN
cana-5360	106	14	}	}	PUNCT
cana-5360	106	15	and	and	CCONJ
cana-5360	106	16	1𝑃	1𝑃	NOUN
cana-5360	106	17	=	=	SYM
cana-5360	106	18	{	{	PUNCT
cana-5360	106	19	<	<	X
cana-5360	106	20	𝑎	𝑎	PROPN
cana-5360	106	21	,	,	PUNCT
cana-5360	106	22	1,0	1,0	NUM
cana-5360	106	23	>	>	SYM
cana-5360	106	24	|𝑎	|𝑎	PROPN
cana-5360	106	25	∈	∈	PROPN
cana-5360	106	26	𝑋	𝑋	PROPN
cana-5360	106	27	}	}	PUNCT
cana-5360	106	28	.	.	PUNCT
cana-5360	107	1	7	7	X
cana-5360	107	2	.	.	X
cana-5360	107	3	1̅𝑃	1̅𝑃	NUM
cana-5360	107	4	=	=	NOUN
cana-5360	107	5	0𝑃	0𝑃	NOUN
cana-5360	107	6	and	and	CCONJ
cana-5360	107	7	0̅𝑃	0̅𝑃	NOUN
cana-5360	108	1	=	=	SYM
cana-5360	109	1	1𝑃.	1𝑃.	NUM
cana-5360	109	2	definition	definition	NOUN
cana-5360	109	3	2.5	2.5	NUM
cana-5360	109	4	[	[	X
cana-5360	109	5	4	4	X
cana-5360	109	6	]	]	PUNCT
cana-5360	109	7	let	let	VERB
cana-5360	109	8	𝑈	𝑈	PROPN
cana-5360	109	9	be	be	AUX
cana-5360	109	10	a	a	DET
cana-5360	109	11	non	non	ADJ
cana-5360	109	12	-	-	ADJ
cana-5360	109	13	empty	empty	ADJ
cana-5360	109	14	set	set	NOUN
cana-5360	109	15	and	and	CCONJ
cana-5360	109	16	𝑅	𝑅	PROPN
cana-5360	109	17	be	be	AUX
cana-5360	109	18	an	an	DET
cana-5360	109	19	equivalence	equivalence	NOUN
cana-5360	109	20	relation	relation	NOUN
cana-5360	109	21	on	on	ADP
cana-5360	109	22	𝑈.	𝑈.	PROPN
cana-5360	109	23	let	let	VERB
cana-5360	109	24	𝐴	𝐴	PROPN
cana-5360	109	25	be	be	AUX
cana-5360	109	26	a	a	DET
cana-5360	109	27	pythagorean	pythagorean	ADJ
cana-5360	109	28	fuzzy	fuzzy	NOUN
cana-5360	109	29	set	set	VERB
cana-5360	109	30	in	in	ADP
cana-5360	109	31	𝑈	𝑈	PROPN
cana-5360	109	32	with	with	ADP
cana-5360	109	33	the	the	DET
cana-5360	109	34	membership	membership	NOUN
cana-5360	109	35	function	function	VERB
cana-5360	109	36	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-5360	109	37	)	)	PUNCT
cana-5360	109	38	and	and	CCONJ
cana-5360	109	39	non	non	ADJ
cana-5360	109	40	membership	membership	NOUN
cana-5360	109	41	function	function	NOUN
cana-5360	109	42	𝜆𝐴(𝑥	𝜆𝐴(𝑥	NOUN
cana-5360	109	43	)	)	PUNCT
cana-5360	109	44	,	,	PUNCT
cana-5360	109	45	∀	∀	PUNCT
cana-5360	109	46	𝑥	𝑥	DET
cana-5360	109	47	∈	∈	NOUN
cana-5360	109	48	𝑈.	𝑈.	PROPN
cana-5360	109	49	the	the	DET
cana-5360	109	50	pythagorean	pythagorean	PROPN
cana-5360	109	51	fuzzy	fuzzy	ADJ
cana-5360	109	52	nano	nano	NOUN
cana-5360	109	53	lower	low	ADJ
cana-5360	109	54	,	,	PUNCT
cana-5360	109	55	pythagorean	pythagorean	PROPN
cana-5360	109	56	fuzzy	fuzzy	ADJ
cana-5360	109	57	nano	nano	PROPN
cana-5360	109	58	upper	upper	ADJ
cana-5360	109	59	approximation	approximation	NOUN
cana-5360	109	60	and	and	CCONJ
cana-5360	109	61	pythagorean	pythagorean	PROPN
cana-5360	109	62	fuzzy	fuzzy	ADJ
cana-5360	109	63	nano	nano	NOUN
cana-5360	109	64	boundary	boundary	NOUN
cana-5360	109	65	of	of	ADP
cana-5360	109	66	𝐴	𝐴	PROPN
cana-5360	109	67	in	in	ADP
cana-5360	109	68	the	the	DET
cana-5360	109	69	approximation	approximation	NOUN
cana-5360	109	70	(	(	PUNCT
cana-5360	109	71	𝑈	𝑈	PROPN
cana-5360	109	72	,	,	PUNCT
cana-5360	109	73	𝑅	𝑅	PROPN
cana-5360	109	74	)	)	PUNCT
cana-5360	109	75	denoted	denote	VERB
cana-5360	109	76	by	by	ADP
cana-5360	109	77	𝒫ℱ𝒩(𝐴	𝒫ℱ𝒩(𝐴	NOUN
cana-5360	109	78	)	)	PUNCT
cana-5360	109	79	,	,	PUNCT
cana-5360	109	80	𝒫ℱ𝒩(𝐴	𝒫ℱ𝒩(𝐴	NOUN
cana-5360	109	81	)	)	PUNCT
cana-5360	109	82	and	and	CCONJ
cana-5360	109	83	𝐵𝒫ℱ𝒩(𝐴	𝐵𝒫ℱ𝒩(𝐴	NOUN
cana-5360	109	84	)	)	PUNCT
cana-5360	109	85	are	be	AUX
cana-5360	109	86	respectively	respectively	ADV
cana-5360	109	87	defined	define	VERB
cana-5360	109	88	as	as	SCONJ
cana-5360	109	89	follows	follow	VERB
cana-5360	109	90	:	:	PUNCT
cana-5360	110	1	[	[	X
cana-5360	110	2	(	(	PUNCT
cana-5360	110	3	i	i	NOUN
cana-5360	110	4	)	)	PUNCT
cana-5360	110	5	]	]	PUNCT
cana-5360	110	6	1	1	X
cana-5360	110	7	.	.	X
cana-5360	110	8	𝒫ℱ𝒩(𝐴	𝒫ℱ𝒩(𝐴	NOUN
cana-5360	110	9	)	)	PUNCT
cana-5360	110	10	=	=	PRON
cana-5360	110	11	{	{	PUNCT
cana-5360	110	12	〈	〈	NOUN
cana-5360	110	13	𝑥	𝑥	NOUN
cana-5360	110	14	,	,	PUNCT
cana-5360	110	15	𝜇𝑅(𝐴)(𝑥	𝜇𝑅(𝐴)(𝑥	NOUN
cana-5360	110	16	)	)	PUNCT
cana-5360	110	17	,	,	PUNCT
cana-5360	110	18	𝜆𝑅(𝐴)(𝑥)〉/𝑦	𝜆𝑅(𝐴)(𝑥)〉/𝑦	PROPN
cana-5360	110	19	∈	∈	PROPN
cana-5360	111	1	[	[	X
cana-5360	111	2	𝑥]𝑅	𝑥]𝑅	NOUN
cana-5360	111	3	,	,	PUNCT
cana-5360	111	4	𝑥	𝑥	PRON
cana-5360	111	5	∈	∈	PROPN
cana-5360	111	6	𝑈	𝑈	PROPN
cana-5360	111	7	}	}	PUNCT
cana-5360	111	8	2	2	NUM
cana-5360	111	9	.	.	PUNCT
cana-5360	111	10	𝒫ℱ𝒩(𝐹	𝒫ℱ𝒩(𝐹	NOUN
cana-5360	111	11	)	)	PUNCT
cana-5360	111	12	=	=	PRON
cana-5360	111	13	{	{	PUNCT
cana-5360	111	14	〈	〈	NOUN
cana-5360	111	15	𝑥	𝑥	NOUN
cana-5360	111	16	,	,	PUNCT
cana-5360	111	17	𝜇𝑅(𝐴)(𝑥	𝜇𝑅(𝐴)(𝑥	NOUN
cana-5360	111	18	)	)	PUNCT
cana-5360	111	19	,	,	PUNCT
cana-5360	111	20	𝜆𝑅(𝐴)(𝑥)〉/𝑦	𝜆𝑅(𝐴)(𝑥)〉/𝑦	PROPN
cana-5360	111	21	∈	∈	PROPN
cana-5360	112	1	[	[	X
cana-5360	112	2	𝑥]𝑅	𝑥]𝑅	ADV
cana-5360	112	3	,	,	PUNCT
cana-5360	112	4	𝑥	𝑥	PRON
cana-5360	112	5	∈	∈	PROPN
cana-5360	112	6	𝑈	𝑈	PROPN
cana-5360	112	7	}	}	PUNCT
cana-5360	112	8	3	3	NUM
cana-5360	112	9	.	.	PUNCT
cana-5360	112	10	𝐵𝒫ℱ𝒩(𝐹	𝐵𝒫ℱ𝒩(𝐹	NUM
cana-5360	112	11	)	)	PUNCT
cana-5360	112	12	=	=	PUNCT
cana-5360	112	13	𝒫ℱ𝒩(𝐹	𝒫ℱ𝒩(𝐹	NOUN
cana-5360	112	14	)	)	PUNCT
cana-5360	112	15	−	−	PROPN
cana-5360	112	16	𝒫ℱ𝒩(𝐹	𝒫ℱ𝒩(𝐹	NOUN
cana-5360	112	17	)	)	PUNCT
cana-5360	112	18	where	where	SCONJ
cana-5360	112	19	𝜇𝑅(𝐴)(𝑥	𝜇𝑅(𝐴)(𝑥	NOUN
cana-5360	112	20	)	)	PUNCT
cana-5360	113	1	=	=	NOUN
cana-5360	113	2	∧𝑦∈[𝑥]𝑅	∧𝑦∈[𝑥]𝑅	NOUN
cana-5360	113	3	𝜇𝐴(𝑦	𝜇𝐴(𝑦	NUM
cana-5360	113	4	)	)	PUNCT
cana-5360	113	5	𝜆𝑅(𝐴)(𝑥	𝜆𝑅(𝐴)(𝑥	ADP
cana-5360	113	6	)	)	PUNCT
cana-5360	114	1	=	=	X
cana-5360	114	2	∧𝑦∈[𝑥]𝑅	∧𝑦∈[𝑥]𝑅	NOUN
cana-5360	114	3	𝜆𝐴(𝑦	𝜆𝐴(𝑦	NOUN
cana-5360	114	4	)	)	PUNCT
cana-5360	114	5	,	,	PUNCT
cana-5360	114	6	𝜇𝑅(𝐴)(𝑥	𝜇𝑅(𝐴)(𝑥	NOUN
cana-5360	114	7	)	)	PUNCT
cana-5360	114	8	=	=	NOUN
cana-5360	114	9	∨𝑦∈[𝑥]𝑅	∨𝑦∈[𝑥]𝑅	NOUN
cana-5360	114	10	𝜇𝐴(𝑦	𝜇𝐴(𝑦	NOUN
cana-5360	114	11	)	)	PUNCT
cana-5360	114	12	,	,	PUNCT
cana-5360	114	13	communications	communication	NOUN
cana-5360	114	14	on	on	ADP
cana-5360	114	15	applied	apply	VERB
cana-5360	114	16	nonlinear	nonlinear	ADJ
cana-5360	114	17	analysis	analysis	NOUN
cana-5360	114	18	issn	issn	NOUN
cana-5360	114	19	:	:	PUNCT
cana-5360	114	20	1074	1074	NUM
cana-5360	114	21	-	-	PUNCT
cana-5360	114	22	133x	133x	NUM
cana-5360	114	23	vol	vol	VERB
cana-5360	114	24	32	32	NUM
cana-5360	114	25	no	no	NOUN
cana-5360	114	26	.	.	PUNCT
cana-5360	115	1	10s	10	NOUN
cana-5360	115	2	(	(	PUNCT
cana-5360	115	3	2025	2025	NUM
cana-5360	115	4	)	)	PUNCT
cana-5360	115	5	1929	1929	NUM
cana-5360	115	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5360	115	7	𝜆𝑅(𝐴)(𝑥	𝜆𝑅(𝐴)(𝑥	X
cana-5360	115	8	)	)	PUNCT
cana-5360	116	1	=	=	NOUN
cana-5360	116	2	∨𝑦∈[𝑥]𝑅	∨𝑦∈[𝑥]𝑅	NOUN
cana-5360	116	3	𝜆𝐴(𝑦	𝜆𝐴(𝑦	NOUN
cana-5360	116	4	)	)	PUNCT
cana-5360	116	5	.	.	PUNCT
cana-5360	117	1	definition	definition	NOUN
cana-5360	117	2	2.6	2.6	NUM
cana-5360	118	1	[	[	X
cana-5360	118	2	4	4	NUM
cana-5360	118	3	]	]	PUNCT
cana-5360	118	4	let	let	VERB
cana-5360	118	5	𝑈	𝑈	PROPN
cana-5360	118	6	be	be	AUX
cana-5360	118	7	an	an	DET
cana-5360	118	8	universe	universe	NOUN
cana-5360	118	9	of	of	ADP
cana-5360	118	10	discourse	discourse	NOUN
cana-5360	118	11	,	,	PUNCT
cana-5360	118	12	𝑅	𝑅	PROPN
cana-5360	118	13	be	be	AUX
cana-5360	118	14	an	an	DET
cana-5360	118	15	equivalence	equivalence	NOUN
cana-5360	118	16	relation	relation	NOUN
cana-5360	118	17	on	on	ADP
cana-5360	118	18	𝑈	𝑈	PROPN
cana-5360	118	19	and	and	CCONJ
cana-5360	118	20	𝐴	𝐴	PROPN
cana-5360	118	21	be	be	VERB
cana-5360	118	22	a	a	DET
cana-5360	118	23	pythagorean	pythagorean	ADJ
cana-5360	118	24	fuzzy	fuzzy	ADJ
cana-5360	118	25	set	set	VERB
cana-5360	118	26	in	in	ADP
cana-5360	118	27	𝑈	𝑈	PROPN
cana-5360	118	28	and	and	CCONJ
cana-5360	118	29	if	if	SCONJ
cana-5360	118	30	the	the	DET
cana-5360	118	31	collection	collection	NOUN
cana-5360	118	32	𝜏ℛ(𝐴	𝜏ℛ(𝐴	NOUN
cana-5360	118	33	)	)	PUNCT
cana-5360	118	34	=	=	PRON
cana-5360	118	35	{	{	PUNCT
cana-5360	118	36	0𝒫	0𝒫	NOUN
cana-5360	118	37	,	,	PUNCT
cana-5360	118	38	1𝒫	1𝒫	INTJ
cana-5360	118	39	,	,	PUNCT
cana-5360	118	40	𝒫ℱ𝒩(𝐴	𝒫ℱ𝒩(𝐴	NOUN
cana-5360	118	41	)	)	PUNCT
cana-5360	118	42	,	,	PUNCT
cana-5360	118	43	𝒫ℱ𝒩(𝐴	𝒫ℱ𝒩(𝐴	NOUN
cana-5360	118	44	)	)	PUNCT
cana-5360	118	45	,	,	PUNCT
cana-5360	118	46	𝐵𝒫ℱ𝒩(𝐴	𝐵𝒫ℱ𝒩(𝐴	NOUN
cana-5360	118	47	)	)	PUNCT
cana-5360	118	48	}	}	PUNCT
cana-5360	118	49	forms	form	VERB
cana-5360	118	50	a	a	DET
cana-5360	118	51	topology	topology	NOUN
cana-5360	118	52	then	then	ADV
cana-5360	118	53	it	it	PRON
cana-5360	118	54	is	be	AUX
cana-5360	118	55	said	say	VERB
cana-5360	118	56	to	to	PART
cana-5360	118	57	be	be	AUX
cana-5360	118	58	a	a	DET
cana-5360	118	59	pythagorean	pythagorean	ADJ
cana-5360	118	60	fuzzy	fuzzy	ADJ
cana-5360	118	61	nano	nano	NOUN
cana-5360	118	62	topology	topology	NOUN
cana-5360	118	63	.	.	PUNCT
cana-5360	119	1	we	we	PRON
cana-5360	119	2	call	call	VERB
cana-5360	119	3	(	(	PUNCT
cana-5360	119	4	𝑈	𝑈	PROPN
cana-5360	119	5	,	,	PUNCT
cana-5360	119	6	𝜏ℛ(𝐴	𝜏ℛ(𝐴	NOUN
cana-5360	119	7	)	)	PUNCT
cana-5360	119	8	)	)	PUNCT
cana-5360	120	1	(	(	PUNCT
cana-5360	120	2	or	or	CCONJ
cana-5360	120	3	simply	simply	ADV
cana-5360	120	4	𝑈	𝑈	PROPN
cana-5360	120	5	)	)	PUNCT
cana-5360	120	6	as	as	ADP
cana-5360	120	7	the	the	DET
cana-5360	120	8	pythagorean	pythagorean	PROPN
cana-5360	120	9	fuzzy	fuzzy	ADJ
cana-5360	120	10	nano	nano	NOUN
cana-5360	120	11	topological	topological	ADJ
cana-5360	120	12	space	space	NOUN
cana-5360	120	13	.	.	PUNCT
cana-5360	121	1	the	the	DET
cana-5360	121	2	elements	element	NOUN
cana-5360	121	3	of	of	ADP
cana-5360	121	4	𝜏ℛ(𝐴	𝜏ℛ(𝐴	NOUN
cana-5360	121	5	)	)	PUNCT
cana-5360	121	6	are	be	AUX
cana-5360	121	7	called	call	VERB
cana-5360	121	8	pythagorean	pythagorean	PROPN
cana-5360	121	9	fuzzy	fuzzy	ADJ
cana-5360	121	10	nano	nano	NOUN
cana-5360	121	11	open	open	ADJ
cana-5360	121	12	(	(	PUNCT
cana-5360	121	13	briefly	briefly	ADV
cana-5360	121	14	,	,	PUNCT
cana-5360	121	15	𝒫ℱ𝒩𝑜	𝒫ℱ𝒩𝑜	PROPN
cana-5360	121	16	)	)	PUNCT
cana-5360	121	17	sets	set	NOUN
cana-5360	121	18	.	.	PUNCT
cana-5360	122	1	remark	remark	VERB
cana-5360	122	2	2.1	2.1	NUM
cana-5360	122	3	[	[	SYM
cana-5360	122	4	4	4	NUM
cana-5360	122	5	]	]	X
cana-5360	122	6	[	[	X
cana-5360	122	7	𝜏ℛ(𝐴)]𝑐	𝜏ℛ(𝐴)]𝑐	NOUN
cana-5360	122	8	is	be	AUX
cana-5360	122	9	called	call	VERB
cana-5360	122	10	the	the	DET
cana-5360	122	11	dual	dual	ADJ
cana-5360	122	12	fuzzy	fuzzy	ADJ
cana-5360	122	13	nano	nano	NOUN
cana-5360	122	14	topology	topology	NOUN
cana-5360	122	15	of	of	ADP
cana-5360	122	16	𝜏ℛ(𝐴	𝜏ℛ(𝐴	NOUN
cana-5360	122	17	)	)	PUNCT
cana-5360	122	18	.	.	PUNCT
cana-5360	123	1	elements	element	NOUN
cana-5360	123	2	of	of	ADP
cana-5360	123	3	[	[	X
cana-5360	123	4	𝜏ℛ(𝐴)]𝑐	𝜏ℛ(𝐴)]𝑐	NOUN
cana-5360	123	5	are	be	AUX
cana-5360	123	6	called	call	VERB
cana-5360	123	7	pythagorean	pythagorean	PROPN
cana-5360	123	8	fuzzy	fuzzy	PROPN
cana-5360	123	9	nano	nano	PROPN
cana-5360	123	10	closed	close	VERB
cana-5360	123	11	(	(	PUNCT
cana-5360	123	12	briefly	briefly	ADV
cana-5360	123	13	,	,	PUNCT
cana-5360	123	14	𝒫ℱ𝒩𝑐	𝒫ℱ𝒩𝑐	NOUN
cana-5360	123	15	)	)	PUNCT
cana-5360	123	16	sets	set	NOUN
cana-5360	123	17	.	.	PUNCT
cana-5360	124	1	thus	thus	ADV
cana-5360	124	2	,	,	PUNCT
cana-5360	124	3	we	we	PRON
cana-5360	124	4	note	note	VERB
cana-5360	124	5	that	that	SCONJ
cana-5360	124	6	a	a	DET
cana-5360	124	7	pythagorean	pythagorean	PROPN
cana-5360	124	8	fuzzy	fuzzy	NOUN
cana-5360	124	9	set	set	VERB
cana-5360	124	10	𝐺	𝐺	PROPN
cana-5360	124	11	of	of	ADP
cana-5360	124	12	𝑈	𝑈	PROPN
cana-5360	124	13	is	be	AUX
cana-5360	124	14	pythagorean	pythagorean	PROPN
cana-5360	124	15	fuzzy	fuzzy	ADJ
cana-5360	124	16	nano	nano	NOUN
cana-5360	124	17	closed	close	VERB
cana-5360	124	18	in	in	ADP
cana-5360	124	19	𝜏ℛ(𝐴	𝜏ℛ(𝐴	NOUN
cana-5360	124	20	)	)	PUNCT
cana-5360	124	21	if	if	SCONJ
cana-5360	124	22	and	and	CCONJ
cana-5360	124	23	only	only	ADV
cana-5360	124	24	if	if	SCONJ
cana-5360	124	25	1𝑃	1𝑃	PROPN
cana-5360	124	26	−	−	PROPN
cana-5360	124	27	𝐺	𝐺	PROPN
cana-5360	124	28	is	be	AUX
cana-5360	124	29	pythagorean	pythagorean	ADJ
cana-5360	124	30	fuzzy	fuzzy	ADJ
cana-5360	124	31	nano	nano	NOUN
cana-5360	124	32	open	open	ADJ
cana-5360	124	33	in	in	ADP
cana-5360	124	34	𝜏ℛ(𝐴	𝜏ℛ(𝐴	NOUN
cana-5360	124	35	)	)	PUNCT
cana-5360	124	36	.	.	PUNCT
cana-5360	125	1	definition	definition	NOUN
cana-5360	125	2	2.7	2.7	NUM
cana-5360	126	1	[	[	SYM
cana-5360	126	2	4	4	NUM
cana-5360	126	3	,	,	PUNCT
cana-5360	126	4	5	5	NUM
cana-5360	126	5	]	]	PUNCT
cana-5360	126	6	let	let	VERB
cana-5360	126	7	(	(	PUNCT
cana-5360	126	8	𝑈	𝑈	PROPN
cana-5360	126	9	,	,	PUNCT
cana-5360	126	10	𝜏𝒫(𝐴	𝜏𝒫(𝐴	NOUN
cana-5360	126	11	)	)	PUNCT
cana-5360	126	12	)	)	PUNCT
cana-5360	126	13	be	be	AUX
cana-5360	126	14	a	a	DET
cana-5360	126	15	𝒫ℱ𝒩𝑡𝑠	𝒫ℱ𝒩𝑡𝑠	NOUN
cana-5360	126	16	with	with	ADP
cana-5360	126	17	respect	respect	NOUN
cana-5360	126	18	to	to	ADP
cana-5360	126	19	𝐴	𝐴	PROPN
cana-5360	126	20	where	where	SCONJ
cana-5360	126	21	𝐴	𝐴	PROPN
cana-5360	126	22	is	be	AUX
cana-5360	126	23	a	a	DET
cana-5360	126	24	pythagorean	pythagorean	ADJ
cana-5360	126	25	fuzzy	fuzzy	ADJ
cana-5360	126	26	subset	subset	NOUN
cana-5360	126	27	of	of	ADP
cana-5360	126	28	𝑈.	𝑈.	PROPN
cana-5360	126	29	let	let	VERB
cana-5360	126	30	𝑆	𝑆	PROPN
cana-5360	126	31	be	be	AUX
cana-5360	126	32	a	a	DET
cana-5360	126	33	pythagorean	pythagorean	ADJ
cana-5360	126	34	fuzzy	fuzzy	ADJ
cana-5360	126	35	subset	subset	NOUN
cana-5360	126	36	of	of	ADP
cana-5360	126	37	𝑈.	𝑈.	PROPN
cana-5360	126	38	then	then	ADV
cana-5360	126	39	pythagorean	pythagorean	VERB
cana-5360	126	40	fuzzy	fuzzy	ADJ
cana-5360	126	41	nano	nano	PROPN
cana-5360	127	1	[	[	X
cana-5360	127	2	(	(	PUNCT
cana-5360	127	3	i	i	NOUN
cana-5360	127	4	)	)	PUNCT
cana-5360	127	5	]	]	PUNCT
cana-5360	127	6	1	1	X
cana-5360	127	7	.	.	X
cana-5360	127	8	interior	interior	NOUN
cana-5360	127	9	of	of	ADP
cana-5360	127	10	𝑆	𝑆	PROPN
cana-5360	127	11	(	(	PUNCT
cana-5360	127	12	briefly	briefly	ADV
cana-5360	127	13	,	,	PUNCT
cana-5360	127	14	𝒫ℱ𝒩𝑖𝑛𝑡(𝑆	𝒫ℱ𝒩𝑖𝑛𝑡(𝑆	X
cana-5360	127	15	)	)	PUNCT
cana-5360	127	16	)	)	PUNCT
cana-5360	127	17	is	be	AUX
cana-5360	127	18	defined	define	VERB
cana-5360	127	19	by	by	ADP
cana-5360	127	20	𝒫ℱ𝒩𝑖𝑛𝑡(𝑆	𝒫ℱ𝒩𝑖𝑛𝑡(𝑆	NOUN
cana-5360	127	21	)	)	PUNCT
cana-5360	127	22	=	=	NOUN
cana-5360	127	23	∪	∪	X
cana-5360	127	24	{	{	PUNCT
cana-5360	127	25	𝐼	𝐼	NOUN
cana-5360	127	26	:	:	PUNCT
cana-5360	127	27	𝐼	𝐼	PROPN
cana-5360	127	28	≤	≤	ADJ
cana-5360	127	29	𝑆	𝑆	PROPN
cana-5360	127	30	&	&	CCONJ
cana-5360	127	31	𝐼isa𝒫ℱ𝒩𝑜set	𝐼isa𝒫ℱ𝒩𝑜set	PROPN
cana-5360	127	32	in𝑈	in𝑈	PROPN
cana-5360	127	33	}	}	PUNCT
cana-5360	127	34	.	.	PUNCT
cana-5360	128	1	2	2	X
cana-5360	128	2	.	.	X
cana-5360	128	3	closure	closure	NOUN
cana-5360	128	4	of	of	ADP
cana-5360	128	5	𝑆	𝑆	PROPN
cana-5360	128	6	(	(	PUNCT
cana-5360	128	7	briefly	briefly	ADV
cana-5360	128	8	,	,	PUNCT
cana-5360	128	9	𝒫ℱ𝒩𝑐𝑙(𝑆	𝒫ℱ𝒩𝑐𝑙(𝑆	PUNCT
cana-5360	128	10	)	)	PUNCT
cana-5360	128	11	)	)	PUNCT
cana-5360	128	12	is	be	AUX
cana-5360	128	13	defined	define	VERB
cana-5360	128	14	by	by	ADP
cana-5360	128	15	𝒫ℱ𝒩𝑐𝑙(𝑆	𝒫ℱ𝒩𝑐𝑙(𝑆	NOUN
cana-5360	128	16	)	)	PUNCT
cana-5360	128	17	=	=	NOUN
cana-5360	128	18	∩	∩	X
cana-5360	128	19	{	{	PUNCT
cana-5360	128	20	𝐴	𝐴	PROPN
cana-5360	128	21	:	:	PUNCT
cana-5360	128	22	𝑆	𝑆	PROPN
cana-5360	128	23	≤	≤	PROPN
cana-5360	128	24	𝐴	𝐴	PROPN
cana-5360	128	25	&	&	CCONJ
cana-5360	128	26	𝐴isa𝒫ℱ𝒩𝑐set	𝐴isa𝒫ℱ𝒩𝑐set	PROPN
cana-5360	128	27	in𝑈	in𝑈	PROPN
cana-5360	128	28	}	}	PUNCT
cana-5360	128	29	.	.	PUNCT
cana-5360	129	1	3	3	X
cana-5360	129	2	.	.	X
cana-5360	129	3	regular	regular	ADJ
cana-5360	129	4	open	open	ADJ
cana-5360	129	5	(	(	PUNCT
cana-5360	129	6	briefly	briefly	ADV
cana-5360	129	7	,	,	PUNCT
cana-5360	129	8	𝒫ℱ𝒩𝑟𝑜	𝒫ℱ𝒩𝑟𝑜	NUM
cana-5360	129	9	)	)	PUNCT
cana-5360	129	10	set	set	VERB
cana-5360	129	11	if	if	SCONJ
cana-5360	129	12	𝑆	𝑆	PROPN
cana-5360	129	13	=	=	PUNCT
cana-5360	129	14	𝒫ℱ𝒩𝑖𝑛𝑡(𝒫ℱ𝒩𝑐𝑙(𝑆	𝒫ℱ𝒩𝑖𝑛𝑡(𝒫ℱ𝒩𝑐𝑙(𝑆	NOUN
cana-5360	129	15	)	)	PUNCT
cana-5360	129	16	)	)	PUNCT
cana-5360	129	17	.	.	PUNCT
cana-5360	130	1	4	4	X
cana-5360	130	2	.	.	X
cana-5360	130	3	regular	regular	ADJ
cana-5360	130	4	closed	close	VERB
cana-5360	130	5	(	(	PUNCT
cana-5360	130	6	briefly	briefly	ADV
cana-5360	130	7	,	,	PUNCT
cana-5360	130	8	𝒫ℱ𝒩𝑟𝑐	𝒫ℱ𝒩𝑟𝑐	PROPN
cana-5360	130	9	)	)	PUNCT
cana-5360	130	10	set	set	VERB
cana-5360	130	11	if	if	SCONJ
cana-5360	130	12	𝑆	𝑆	PROPN
cana-5360	130	13	=	=	SYM
cana-5360	130	14	𝒫ℱ𝒩𝑐𝑙(𝒫ℱ𝒩𝑖𝑛𝑡(𝑆	𝒫ℱ𝒩𝑐𝑙(𝒫ℱ𝒩𝑖𝑛𝑡(𝑆	PROPN
cana-5360	130	15	)	)	PUNCT
cana-5360	130	16	)	)	PUNCT
cana-5360	130	17	.	.	PUNCT
cana-5360	131	1	definition	definition	NOUN
cana-5360	131	2	2.8	2.8	NUM
cana-5360	131	3	[	[	X
cana-5360	131	4	6	6	NUM
cana-5360	131	5	]	]	PUNCT
cana-5360	131	6	let	let	ADJ
cana-5360	131	7	(	(	PUNCT
cana-5360	131	8	𝑈1	𝑈1	NOUN
cana-5360	131	9	,	,	PUNCT
cana-5360	131	10	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	131	11	)	)	PUNCT
cana-5360	131	12	)	)	PUNCT
cana-5360	131	13	and	and	CCONJ
cana-5360	131	14	(	(	PUNCT
cana-5360	131	15	𝑈2	𝑈2	NOUN
cana-5360	131	16	,	,	PUNCT
cana-5360	131	17	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	131	18	)	)	PUNCT
cana-5360	131	19	)	)	PUNCT
cana-5360	131	20	be	be	AUX
cana-5360	131	21	two	two	NUM
cana-5360	131	22	𝑝𝑓𝒩𝑡𝑠	𝑝𝑓𝒩𝑡𝑠	X
cana-5360	131	23	’s	’s	NOUN
cana-5360	131	24	.	.	PUNCT
cana-5360	132	1	then	then	ADV
cana-5360	132	2	a	a	DET
cana-5360	132	3	function	function	NOUN
cana-5360	132	4	ℎ𝑃	ℎ𝑃	NOUN
cana-5360	132	5	:	:	PUNCT
cana-5360	132	6	𝑈1	𝑈1	PROPN
cana-5360	132	7	→	→	SYM
cana-5360	132	8	𝑈2	𝑈2	PROPN
cana-5360	132	9	is	be	AUX
cana-5360	132	10	said	say	VERB
cana-5360	132	11	to	to	PART
cana-5360	132	12	be	be	AUX
cana-5360	132	13	a	a	DET
cana-5360	132	14	pythagorean	pythagorean	ADJ
cana-5360	132	15	fuzzy	fuzzy	ADJ
cana-5360	132	16	nano	nano	NOUN
cana-5360	132	17	continuous	continuous	ADJ
cana-5360	132	18	(	(	PUNCT
cana-5360	132	19	briefly	briefly	ADV
cana-5360	132	20	,	,	PUNCT
cana-5360	132	21	𝒫ℱ𝒩𝐶𝑡𝑠	𝒫ℱ𝒩𝐶𝑡𝑠	PROPN
cana-5360	132	22	)	)	PUNCT
cana-5360	132	23	function	function	NOUN
cana-5360	132	24	if	if	SCONJ
cana-5360	132	25	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	132	26	−1(𝐺	−1(𝐺	NOUN
cana-5360	132	27	)	)	PUNCT
cana-5360	132	28	is	be	AUX
cana-5360	132	29	𝒫ℱ𝒩𝑜	𝒫ℱ𝒩𝑜	PROPN
cana-5360	132	30	set	set	VERB
cana-5360	132	31	in	in	ADP
cana-5360	132	32	𝑈1	𝑈1	NOUN
cana-5360	132	33	for	for	ADP
cana-5360	132	34	all	all	DET
cana-5360	132	35	𝒫ℱ𝒩𝑜	𝒫ℱ𝒩𝑜	PROPN
cana-5360	132	36	set	set	VERB
cana-5360	132	37	𝐺	𝐺	PROPN
cana-5360	132	38	in	in	ADP
cana-5360	132	39	𝑈2	𝑈2	PROPN
cana-5360	132	40	.	.	PUNCT
cana-5360	133	1	definition	definition	NOUN
cana-5360	133	2	2.9	2.9	NUM
cana-5360	134	1	[	[	X
cana-5360	134	2	22	22	NUM
cana-5360	134	3	]	]	PUNCT
cana-5360	134	4	let	let	VERB
cana-5360	134	5	𝑀	𝑀	PROPN
cana-5360	134	6	,	,	PUNCT
cana-5360	134	7	𝑁	𝑁	PROPN
cana-5360	134	8	and	and	CCONJ
cana-5360	134	9	𝑂	𝑂	PROPN
cana-5360	134	10	be	be	VERB
cana-5360	134	11	three	three	NUM
cana-5360	134	12	𝑝𝑓𝑠	𝑝𝑓𝑠	NOUN
cana-5360	134	13	’s	’s	NOUN
cana-5360	134	14	on	on	ADP
cana-5360	134	15	𝑋	𝑋	PROPN
cana-5360	134	16	.	.	PUNCT
cana-5360	135	1	a	a	DET
cana-5360	135	2	similarity	similarity	NOUN
cana-5360	135	3	measure	measure	NOUN
cana-5360	135	4	𝑆(𝑀	𝑆(𝑀	PROPN
cana-5360	135	5	,	,	PUNCT
cana-5360	135	6	𝑁	𝑁	PROPN
cana-5360	135	7	)	)	PUNCT
cana-5360	135	8	is	be	AUX
cana-5360	135	9	mapping	map	VERB
cana-5360	135	10	𝑆	𝑆	PROPN
cana-5360	135	11	:	:	PUNCT
cana-5360	135	12	𝑝𝑓𝑠(𝑋	𝑝𝑓𝑠(𝑋	NUM
cana-5360	135	13	)	)	PUNCT
cana-5360	135	14	×	×	NOUN
cana-5360	135	15	𝑝𝑓𝑠(𝑋	𝑝𝑓𝑠(𝑋	NUM
cana-5360	135	16	)	)	PUNCT
cana-5360	135	17	→	→	PUNCT
cana-5360	136	1	[	[	X
cana-5360	136	2	0,1	0,1	NUM
cana-5360	136	3	]	]	PUNCT
cana-5360	136	4	,	,	PUNCT
cana-5360	136	5	possessing	possess	VERB
cana-5360	136	6	the	the	DET
cana-5360	136	7	following	follow	VERB
cana-5360	136	8	properties	property	NOUN
cana-5360	136	9	:	:	PUNCT
cana-5360	136	10	[	[	X
cana-5360	136	11	(	(	PUNCT
cana-5360	136	12	s1	s1	NOUN
cana-5360	136	13	)	)	PUNCT
cana-5360	136	14	]	]	PUNCT
cana-5360	137	1	1	1	NUM
cana-5360	137	2	.	.	NOUN
cana-5360	137	3	0	0	NUM
cana-5360	137	4	≤	≤	NUM
cana-5360	137	5	𝑆(𝑀	𝑆(𝑀	PROPN
cana-5360	137	6	,	,	PUNCT
cana-5360	137	7	𝑁	𝑁	PROPN
cana-5360	137	8	)	)	PUNCT
cana-5360	137	9	≤	≤	NOUN
cana-5360	137	10	1	1	NUM
cana-5360	137	11	;	;	PUNCT
cana-5360	137	12	2	2	NUM
cana-5360	137	13	.	.	X
cana-5360	137	14	𝑆(𝑀	𝑆(𝑀	PROPN
cana-5360	137	15	,	,	PUNCT
cana-5360	137	16	𝑁	𝑁	PROPN
cana-5360	137	17	)	)	PUNCT
cana-5360	137	18	=	=	SYM
cana-5360	137	19	𝑆(𝑁	𝑆(𝑁	NOUN
cana-5360	137	20	,	,	PUNCT
cana-5360	137	21	𝑀	𝑀	PROPN
cana-5360	137	22	)	)	PUNCT
cana-5360	137	23	;	;	PUNCT
cana-5360	137	24	3	3	X
cana-5360	137	25	.	.	X
cana-5360	137	26	𝑆(𝑀	𝑆(𝑀	PROPN
cana-5360	137	27	,	,	PUNCT
cana-5360	137	28	𝑁	𝑁	PROPN
cana-5360	137	29	)	)	PUNCT
cana-5360	137	30	=	=	SYM
cana-5360	137	31	1	1	NUM
cana-5360	137	32	iff	iff	PROPN
cana-5360	137	33	𝑀	𝑀	PROPN
cana-5360	137	34	=	=	PUNCT
cana-5360	137	35	𝑁	𝑁	PROPN
cana-5360	137	36	;	;	PUNCT
cana-5360	137	37	4	4	NUM
cana-5360	137	38	.	.	X
cana-5360	137	39	𝑆(𝑀	𝑆(𝑀	ADJ
cana-5360	137	40	,	,	PUNCT
cana-5360	137	41	𝑀𝑐	𝑀𝑐	PROPN
cana-5360	137	42	)	)	PUNCT
cana-5360	137	43	=	=	SYM
cana-5360	137	44	0	0	NUM
cana-5360	137	45	iff	iff	PROPN
cana-5360	137	46	𝑀	𝑀	PROPN
cana-5360	137	47	is	be	AUX
cana-5360	137	48	a	a	DET
cana-5360	137	49	crisp	crisp	ADJ
cana-5360	137	50	set	set	NOUN
cana-5360	137	51	;	;	PUNCT
cana-5360	137	52	5	5	X
cana-5360	137	53	.	.	X
cana-5360	138	1	if	if	SCONJ
cana-5360	138	2	𝑀	𝑀	PROPN
cana-5360	138	3	⊆	⊆	NUM
cana-5360	138	4	𝑁	𝑁	PROPN
cana-5360	138	5	⊆	⊆	NUM
cana-5360	138	6	𝑂	𝑂	PROPN
cana-5360	138	7	,	,	PUNCT
cana-5360	138	8	then	then	ADV
cana-5360	138	9	𝑆(𝑀	𝑆(𝑀	PROPN
cana-5360	138	10	,	,	PUNCT
cana-5360	138	11	𝑂	𝑂	PROPN
cana-5360	138	12	)	)	PUNCT
cana-5360	138	13	≤	≤	NOUN
cana-5360	138	14	𝑆(𝑀	𝑆(𝑀	PROPN
cana-5360	138	15	,	,	PUNCT
cana-5360	138	16	𝑁	𝑁	PROPN
cana-5360	138	17	)	)	PUNCT
cana-5360	138	18	and	and	CCONJ
cana-5360	138	19	𝑆(𝑀	𝑆(𝑀	PROPN
cana-5360	138	20	,	,	PUNCT
cana-5360	138	21	𝑂	𝑂	PROPN
cana-5360	138	22	)	)	PUNCT
cana-5360	138	23	≤	≤	NOUN
cana-5360	138	24	𝑆(𝑁	𝑆(𝑁	NOUN
cana-5360	138	25	,	,	PUNCT
cana-5360	138	26	𝑂	𝑂	PROPN
cana-5360	138	27	)	)	PUNCT
cana-5360	138	28	.	.	PUNCT
cana-5360	139	1	let	let	VERB
cana-5360	139	2	𝑋	𝑋	PROPN
cana-5360	139	3	=	=	PROPN
cana-5360	139	4	𝑥1	𝑥1	PROPN
cana-5360	139	5	,	,	PUNCT
cana-5360	139	6	𝑥2	𝑥2	NOUN
cana-5360	139	7	,	,	PUNCT
cana-5360	139	8	…	…	PUNCT
cana-5360	139	9	,	,	PUNCT
cana-5360	139	10	𝑥𝑛	𝑥𝑛	AUX
cana-5360	139	11	be	be	AUX
cana-5360	139	12	a	a	DET
cana-5360	139	13	finite	finite	ADJ
cana-5360	139	14	universe	universe	NOUN
cana-5360	139	15	of	of	ADP
cana-5360	139	16	discourse	discourse	NOUN
cana-5360	139	17	,	,	PUNCT
cana-5360	139	18	and	and	CCONJ
cana-5360	139	19	𝐴	𝐴	PROPN
cana-5360	139	20	and	and	CCONJ
cana-5360	139	21	𝐵	𝐵	NOUN
cana-5360	139	22	be	be	VERB
cana-5360	139	23	two	two	NUM
cana-5360	139	24	𝑃𝐹𝑆	𝑃𝐹𝑆	PROPN
cana-5360	139	25	’s	’s	NOUN
cana-5360	139	26	in	in	ADP
cana-5360	139	27	𝑋	𝑋	PROPN
cana-5360	139	28	,	,	PUNCT
cana-5360	139	29	in	in	ADP
cana-5360	139	30	which	which	PRON
cana-5360	139	31	𝐴	𝐴	PROPN
cana-5360	139	32	=	=	PRON
cana-5360	139	33	{	{	PUNCT
cana-5360	139	34	<	<	X
cana-5360	139	35	𝑥𝑖	𝑥𝑖	PROPN
cana-5360	139	36	,	,	PUNCT
cana-5360	139	37	𝜇𝐴(𝑥𝑖	𝜇𝐴(𝑥𝑖	PROPN
cana-5360	139	38	)	)	PUNCT
cana-5360	139	39	,	,	PUNCT
cana-5360	139	40	𝜆𝐴(𝑥𝑖	𝜆𝐴(𝑥𝑖	PROPN
cana-5360	139	41	)	)	PUNCT
cana-5360	139	42	>	>	X
cana-5360	139	43	|𝑥𝑖	|𝑥𝑖	PROPN
cana-5360	139	44	∈	∈	PROPN
cana-5360	139	45	𝑋	𝑋	PROPN
cana-5360	139	46	}	}	PUNCT
cana-5360	139	47	and	and	CCONJ
cana-5360	139	48	𝐵	𝐵	NOUN
cana-5360	139	49	=	=	PUNCT
cana-5360	139	50	{	{	PUNCT
cana-5360	139	51	<	<	X
cana-5360	139	52	𝑥𝑖	𝑥𝑖	PROPN
cana-5360	139	53	,	,	PUNCT
cana-5360	139	54	𝜇𝐵(𝑥𝑖	𝜇𝐵(𝑥𝑖	PROPN
cana-5360	139	55	)	)	PUNCT
cana-5360	139	56	,	,	PUNCT
cana-5360	139	57	𝜆𝐵(𝑥𝑖	𝜆𝐵(𝑥𝑖	PROPN
cana-5360	139	58	)	)	PUNCT
cana-5360	139	59	>	>	X
cana-5360	140	1	|𝑥𝑖	|𝑥𝑖	PROPN
cana-5360	140	2	∈	∈	PROPN
cana-5360	140	3	𝑋	𝑋	PROPN
cana-5360	140	4	}	}	PUNCT
cana-5360	140	5	.	.	PUNCT
cana-5360	141	1	using	use	VERB
cana-5360	141	2	the	the	DET
cana-5360	141	3	similarity	similarity	NOUN
cana-5360	141	4	measure	measure	NOUN
cana-5360	141	5	in	in	ADP
cana-5360	141	6	section	section	NOUN
cana-5360	141	7	4	4	NUM
cana-5360	141	8	,	,	PUNCT
cana-5360	141	9	we	we	PRON
cana-5360	141	10	have	have	VERB
cana-5360	141	11	the	the	DET
cana-5360	141	12	zhang	zhang	PROPN
cana-5360	142	1	[	[	X
cana-5360	142	2	42	42	NUM
cana-5360	142	3	]	]	X
cana-5360	142	4	similarity	similarity	NOUN
cana-5360	142	5	measure	measure	NOUN
cana-5360	142	6	are	be	AUX
cana-5360	142	7	defined	define	VERB
cana-5360	142	8	by	by	ADP
cana-5360	142	9	𝑆𝑍(𝐴	𝑆𝑍(𝐴	NOUN
cana-5360	142	10	,	,	PUNCT
cana-5360	142	11	𝐵	𝐵	NOUN
cana-5360	142	12	)	)	PUNCT
cana-5360	142	13	=	=	SYM
cana-5360	143	1	1	1	NUM
cana-5360	143	2	2	2	NUM
cana-5360	143	3	∑𝑛	∑𝑛	PROPN
cana-5360	143	4	𝑖=1	𝑖=1	PROPN
cana-5360	143	5	(	(	PUNCT
cana-5360	143	6	|𝜇𝐴	|𝜇𝐴	PROPN
cana-5360	143	7	2	2	NUM
cana-5360	143	8	(	(	PUNCT
cana-5360	143	9	𝑥𝑖)−𝜈𝐵	𝑥𝑖)−𝜈𝐵	NOUN
cana-5360	143	10	2	2	NUM
cana-5360	143	11	(	(	PUNCT
cana-5360	143	12	𝑥𝑖)|+|𝜈𝐴	𝑥𝑖)|+|𝜈𝐴	PROPN
cana-5360	143	13	2	2	NUM
cana-5360	143	14	(	(	PUNCT
cana-5360	143	15	𝑥𝑖)−𝜇𝐵	𝑥𝑖)−𝜇𝐵	PROPN
cana-5360	143	16	2	2	NUM
cana-5360	143	17	(	(	PUNCT
cana-5360	143	18	𝑥𝑖)|+|𝜋𝐴	𝑥𝑖)|+|𝜋𝐴	ADJ
cana-5360	143	19	2	2	NUM
cana-5360	143	20	(	(	PUNCT
cana-5360	143	21	𝑥𝑖)−𝜋𝐵	𝑥𝑖)−𝜋𝐵	NUM
cana-5360	143	22	2	2	NUM
cana-5360	143	23	(	(	PUNCT
cana-5360	143	24	𝑥𝑖)|	𝑥𝑖)|	PROPN
cana-5360	143	25	)	)	PUNCT
cana-5360	143	26	|𝜇𝐴	|𝜇𝐴	PROPN
cana-5360	143	27	2	2	NUM
cana-5360	143	28	(	(	PUNCT
cana-5360	143	29	𝑥𝑖)−𝜇𝐵	𝑥𝑖)−𝜇𝐵	PROPN
cana-5360	143	30	2	2	NUM
cana-5360	143	31	(	(	PUNCT
cana-5360	143	32	𝑥𝑖)|+|𝜈𝐴	𝑥𝑖)|+|𝜈𝐴	PROPN
cana-5360	143	33	2	2	NUM
cana-5360	143	34	(	(	PUNCT
cana-5360	143	35	𝑥𝑖)−𝜈𝐵	𝑥𝑖)−𝜈𝐵	NOUN
cana-5360	143	36	2	2	NUM
cana-5360	143	37	(	(	PUNCT
cana-5360	143	38	𝑥𝑖)|+|𝜋𝐴	𝑥𝑖)|+|𝜋𝐴	ADJ
cana-5360	143	39	2	2	NUM
cana-5360	143	40	(	(	PUNCT
cana-5360	143	41	𝑥𝑖)−𝜋𝐵	𝑥𝑖)−𝜋𝐵	NUM
cana-5360	143	42	2	2	NUM
cana-5360	143	43	(	(	PUNCT
cana-5360	143	44	𝑥𝑖)|+|𝜇𝐴	𝑥𝑖)|+|𝜇𝐴	NOUN
cana-5360	143	45	2	2	NUM
cana-5360	143	46	(	(	PUNCT
cana-5360	143	47	𝑥𝑖)−𝜈𝐵	𝑥𝑖)−𝜈𝐵	NOUN
cana-5360	143	48	2	2	NUM
cana-5360	143	49	(	(	PUNCT
cana-5360	143	50	𝑥𝑖)|+|𝜈𝐴	𝑥𝑖)|+|𝜈𝐴	PROPN
cana-5360	143	51	2	2	NUM
cana-5360	143	52	(	(	PUNCT
cana-5360	143	53	𝑥𝑖)−𝜇𝐵	𝑥𝑖)−𝜇𝐵	PROPN
cana-5360	143	54	2	2	NUM
cana-5360	143	55	(	(	PUNCT
cana-5360	143	56	𝑥𝑖)|+|𝜋𝐴	𝑥𝑖)|+|𝜋𝐴	ADJ
cana-5360	143	57	2	2	NUM
cana-5360	143	58	(	(	PUNCT
cana-5360	143	59	𝑥𝑖)−𝜋𝐵	𝑥𝑖)−𝜋𝐵	NUM
cana-5360	143	60	2	2	NUM
cana-5360	143	61	(	(	PUNCT
cana-5360	143	62	𝑥𝑖)|	𝑥𝑖)|	PROPN
cana-5360	143	63	.	.	PUNCT
cana-5360	144	1	communications	communication	NOUN
cana-5360	144	2	on	on	ADP
cana-5360	144	3	applied	apply	VERB
cana-5360	144	4	nonlinear	nonlinear	ADJ
cana-5360	144	5	analysis	analysis	NOUN
cana-5360	144	6	issn	issn	NOUN
cana-5360	144	7	:	:	PUNCT
cana-5360	144	8	1074	1074	NUM
cana-5360	144	9	-	-	PUNCT
cana-5360	144	10	133x	133x	NUM
cana-5360	144	11	vol	vol	VERB
cana-5360	144	12	32	32	NUM
cana-5360	144	13	no	no	NOUN
cana-5360	144	14	.	.	PUNCT
cana-5360	145	1	10s	10	NOUN
cana-5360	145	2	(	(	PUNCT
cana-5360	145	3	2025	2025	NUM
cana-5360	145	4	)	)	PUNCT
cana-5360	145	5	1930	1930	NUM
cana-5360	145	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5360	145	7	3	3	NUM
cana-5360	145	8	pythagorean	pythagorean	PROPN
cana-5360	145	9	fuzzy	fuzzy	ADJ
cana-5360	145	10	nano	nano	NOUN
cana-5360	145	11	contra	contra	PROPN
cana-5360	145	12	𝜹	𝜹	X
cana-5360	145	13	(	(	PUNCT
cana-5360	145	14	resp	resp	NOUN
cana-5360	145	15	.	.	PUNCT
cana-5360	146	1	𝜹	𝜹	X
cana-5360	146	2	pre	pre	ADJ
cana-5360	146	3	,	,	PUNCT
cana-5360	146	4	𝜹	𝜹	X
cana-5360	146	5	semi	semi	ADV
cana-5360	146	6	,	,	PUNCT
cana-5360	146	7	𝜹𝜶	𝜹𝜶	VERB
cana-5360	146	8	and	and	CCONJ
cana-5360	146	9	𝜹𝜷)-continuous	𝜹𝜷)-continuous	ADJ
cana-5360	146	10	mappings	mapping	NOUN
cana-5360	146	11	in	in	ADP
cana-5360	146	12	this	this	DET
cana-5360	146	13	section	section	NOUN
cana-5360	146	14	,	,	PUNCT
cana-5360	146	15	we	we	PRON
cana-5360	146	16	introduce	introduce	VERB
cana-5360	146	17	pythagorean	pythagorean	PROPN
cana-5360	146	18	fuzzy	fuzzy	ADJ
cana-5360	146	19	nano	nano	PROPN
cana-5360	146	20	contra	contra	PROPN
cana-5360	146	21	𝛿	𝛿	PROPN
cana-5360	146	22	(	(	PUNCT
cana-5360	146	23	resp	resp	NOUN
cana-5360	146	24	.	.	PUNCT
cana-5360	147	1	𝛿	𝛿	DET
cana-5360	147	2	pre	pre	NOUN
cana-5360	147	3	,	,	PUNCT
cana-5360	147	4	𝛿	𝛿	ADJ
cana-5360	147	5	semi	semi	ADJ
cana-5360	147	6	,	,	PUNCT
cana-5360	147	7	𝛿𝛼	𝛿𝛼	NOUN
cana-5360	147	8	and	and	CCONJ
cana-5360	147	9	𝛿𝛽)-continuous	𝛿𝛽)-continuous	ADJ
cana-5360	147	10	mappings	mapping	NOUN
cana-5360	147	11	and	and	CCONJ
cana-5360	147	12	discuss	discuss	VERB
cana-5360	147	13	some	some	PRON
cana-5360	147	14	of	of	ADP
cana-5360	147	15	their	their	PRON
cana-5360	147	16	properties	property	NOUN
cana-5360	147	17	.	.	PUNCT
cana-5360	148	1	definition	definition	NOUN
cana-5360	148	2	3.1	3.1	NUM
cana-5360	148	3	let	let	NOUN
cana-5360	148	4	(	(	PUNCT
cana-5360	148	5	𝑈	𝑈	PROPN
cana-5360	148	6	,	,	PUNCT
cana-5360	148	7	𝜏𝒫(𝐴	𝜏𝒫(𝐴	NOUN
cana-5360	148	8	)	)	PUNCT
cana-5360	148	9	)	)	PUNCT
cana-5360	148	10	be	be	AUX
cana-5360	148	11	a	a	DET
cana-5360	148	12	𝒫ℱ𝔑𝑡𝑠	𝒫ℱ𝔑𝑡𝑠	NOUN
cana-5360	148	13	with	with	ADP
cana-5360	148	14	respect	respect	NOUN
cana-5360	148	15	to	to	ADP
cana-5360	148	16	𝐴	𝐴	PROPN
cana-5360	148	17	where	where	SCONJ
cana-5360	148	18	𝐴	𝐴	PROPN
cana-5360	148	19	is	be	AUX
cana-5360	148	20	a	a	DET
cana-5360	148	21	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-5360	148	22	of	of	ADP
cana-5360	148	23	𝑈.	𝑈.	PROPN
cana-5360	148	24	let	let	VERB
cana-5360	148	25	𝑆	𝑆	PROPN
cana-5360	148	26	be	be	AUX
cana-5360	148	27	a	a	DET
cana-5360	148	28	𝑝𝑓𝑠	𝑝𝑓𝑠	NOUN
cana-5360	148	29	of	of	ADP
cana-5360	148	30	𝑈.	𝑈.	PROPN
cana-5360	149	1	then	then	ADV
cana-5360	150	1	[	[	X
cana-5360	150	2	(	(	PUNCT
cana-5360	150	3	i	i	NOUN
cana-5360	150	4	)	)	PUNCT
cana-5360	150	5	]	]	PUNCT
cana-5360	150	6	1	1	X
cana-5360	150	7	.	.	X
cana-5360	150	8	pythagorean	pythagorean	PROPN
cana-5360	150	9	fuzzy	fuzzy	ADJ
cana-5360	150	10	nano	nano	PROPN
cana-5360	150	11	𝛿	𝛿	DET
cana-5360	150	12	interior	interior	NOUN
cana-5360	150	13	of	of	ADP
cana-5360	150	14	𝑆	𝑆	PROPN
cana-5360	150	15	(	(	PUNCT
cana-5360	150	16	briefly	briefly	ADV
cana-5360	150	17	,	,	PUNCT
cana-5360	150	18	𝒫ℱ𝔑𝛿𝑖𝑛𝑡(𝑆	𝒫ℱ𝔑𝛿𝑖𝑛𝑡(𝑆	NUM
cana-5360	150	19	)	)	PUNCT
cana-5360	150	20	)	)	PUNCT
cana-5360	150	21	is	be	AUX
cana-5360	150	22	defined	define	VERB
cana-5360	150	23	by	by	ADP
cana-5360	150	24	𝒫ℱ𝔑𝛿𝑖𝑛𝑡(𝑆	𝒫ℱ𝔑𝛿𝑖𝑛𝑡(𝑆	NOUN
cana-5360	150	25	)	)	PUNCT
cana-5360	150	26	=	=	NOUN
cana-5360	150	27	∪	∪	X
cana-5360	150	28	{	{	PUNCT
cana-5360	150	29	𝐼	𝐼	NOUN
cana-5360	150	30	:	:	PUNCT
cana-5360	150	31	𝐼	𝐼	PROPN
cana-5360	150	32	⊆	⊆	NUM
cana-5360	150	33	𝑆	𝑆	PROPN
cana-5360	150	34	&	&	CCONJ
cana-5360	150	35	𝐼isa𝒫ℱ𝔑𝑟𝑜	𝐼isa𝒫ℱ𝔑𝑟𝑜	NOUN
cana-5360	150	36	set	set	VERB
cana-5360	150	37	in𝑈	in𝑈	NOUN
cana-5360	150	38	}	}	PUNCT
cana-5360	150	39	.	.	PUNCT
cana-5360	151	1	2	2	X
cana-5360	151	2	.	.	X
cana-5360	151	3	pythagorean	pythagorean	PROPN
cana-5360	151	4	fuzzy	fuzzy	ADJ
cana-5360	151	5	nano	nano	PROPN
cana-5360	151	6	𝛿	𝛿	ADJ
cana-5360	151	7	closure	closure	NOUN
cana-5360	151	8	of	of	ADP
cana-5360	151	9	𝑆	𝑆	PROPN
cana-5360	151	10	(	(	PUNCT
cana-5360	151	11	briefly	briefly	ADV
cana-5360	151	12	,	,	PUNCT
cana-5360	151	13	𝒫ℱ𝔑𝛿𝑐𝑙(𝑆	𝒫ℱ𝔑𝛿𝑐𝑙(𝑆	PROPN
cana-5360	151	14	)	)	PUNCT
cana-5360	151	15	)	)	PUNCT
cana-5360	151	16	is	be	AUX
cana-5360	151	17	defined	define	VERB
cana-5360	151	18	by	by	ADP
cana-5360	151	19	𝒫ℱ𝔑𝛿𝑐𝑙(𝑆	𝒫ℱ𝔑𝛿𝑐𝑙(𝑆	ADP
cana-5360	151	20	)	)	PUNCT
cana-5360	152	1	=	=	NOUN
cana-5360	152	2	∩	∩	NOUN
cana-5360	152	3	{	{	PUNCT
cana-5360	152	4	𝐴	𝐴	PROPN
cana-5360	152	5	:	:	PUNCT
cana-5360	152	6	𝑆	𝑆	PROPN
cana-5360	152	7	⊆	⊆	NUM
cana-5360	152	8	𝐴	𝐴	PROPN
cana-5360	152	9	&	&	CCONJ
cana-5360	152	10	𝐴isa𝒫ℱ𝔑𝑟𝑐	𝐴isa𝒫ℱ𝔑𝑟𝑐	NOUN
cana-5360	152	11	set	set	VERB
cana-5360	152	12	in	in	ADP
cana-5360	152	13	𝑈	𝑈	PROPN
cana-5360	152	14	}	}	PUNCT
cana-5360	152	15	.	.	PUNCT
cana-5360	153	1	definition	definition	NOUN
cana-5360	153	2	3.2	3.2	NUM
cana-5360	153	3	let	let	VERB
cana-5360	153	4	(	(	PUNCT
cana-5360	153	5	𝑈	𝑈	PROPN
cana-5360	153	6	,	,	PUNCT
cana-5360	153	7	𝜏𝒫(𝐴	𝜏𝒫(𝐴	NOUN
cana-5360	153	8	)	)	PUNCT
cana-5360	153	9	)	)	PUNCT
cana-5360	153	10	be	be	AUX
cana-5360	153	11	a	a	DET
cana-5360	153	12	𝒫ℱ𝔑𝑡𝑠	𝒫ℱ𝔑𝑡𝑠	NOUN
cana-5360	153	13	with	with	ADP
cana-5360	153	14	respect	respect	NOUN
cana-5360	153	15	to	to	ADP
cana-5360	153	16	𝐴	𝐴	PROPN
cana-5360	153	17	where	where	SCONJ
cana-5360	153	18	𝐴	𝐴	PROPN
cana-5360	153	19	is	be	AUX
cana-5360	153	20	a	a	DET
cana-5360	153	21	𝑝𝑓𝑠	𝑝𝑓𝑠	NOUN
cana-5360	153	22	of	of	ADP
cana-5360	153	23	𝑈.	𝑈.	PROPN
cana-5360	153	24	then	then	ADV
cana-5360	153	25	a	a	DET
cana-5360	153	26	𝒫ℱ𝑠	𝒫ℱ𝑠	X
cana-5360	153	27	𝑆	𝑆	PROPN
cana-5360	153	28	in	in	ADP
cana-5360	153	29	𝑈	𝑈	PROPN
cana-5360	153	30	is	be	AUX
cana-5360	153	31	said	say	VERB
cana-5360	153	32	to	to	PART
cana-5360	153	33	be	be	AUX
cana-5360	153	34	pythagorean	pythagorean	NOUN
cana-5360	153	35	:	:	PUNCT
cana-5360	154	1	[	[	X
cana-5360	154	2	(	(	PUNCT
cana-5360	154	3	i	i	NOUN
cana-5360	154	4	)	)	PUNCT
cana-5360	154	5	]	]	PUNCT
cana-5360	154	6	1	1	X
cana-5360	154	7	.	.	X
cana-5360	154	8	fuzzy	fuzzy	ADJ
cana-5360	154	9	nano	nano	NOUN
cana-5360	154	10	𝛿-open	𝛿-open	NOUN
cana-5360	154	11	set	set	NOUN
cana-5360	154	12	(	(	PUNCT
cana-5360	154	13	briefly	briefly	ADV
cana-5360	154	14	,	,	PUNCT
cana-5360	154	15	𝒫ℱ𝔑𝛿𝑜𝑠	𝒫ℱ𝔑𝛿𝑜𝑠	PROPN
cana-5360	154	16	)	)	PUNCT
cana-5360	154	17	if	if	SCONJ
cana-5360	154	18	𝑆	𝑆	PROPN
cana-5360	154	19	=	=	SYM
cana-5360	154	20	𝒫ℱ𝔑𝛿𝑖𝑛𝑡(𝑆	𝒫ℱ𝔑𝛿𝑖𝑛𝑡(𝑆	NUM
cana-5360	154	21	)	)	PUNCT
cana-5360	154	22	.	.	PUNCT
cana-5360	155	1	2	2	X
cana-5360	155	2	.	.	X
cana-5360	155	3	fuzzy	fuzzy	ADJ
cana-5360	155	4	nano	nano	NOUN
cana-5360	155	5	𝛿𝒫-open	𝛿𝒫-open	NOUN
cana-5360	155	6	set	set	VERB
cana-5360	155	7	(	(	PUNCT
cana-5360	155	8	briefly	briefly	ADV
cana-5360	155	9	,	,	PUNCT
cana-5360	155	10	𝒫ℱ𝔑𝛿𝒫𝑜𝑠	𝒫ℱ𝔑𝛿𝒫𝑜𝑠	PROPN
cana-5360	155	11	)	)	PUNCT
cana-5360	155	12	if	if	SCONJ
cana-5360	155	13	𝑆	𝑆	PROPN
cana-5360	155	14	⊆	⊆	NUM
cana-5360	155	15	𝒫ℱ𝔑𝑖𝑛𝑡(𝒫ℱ𝔑𝛿𝑐𝑙(𝑆	𝒫ℱ𝔑𝑖𝑛𝑡(𝒫ℱ𝔑𝛿𝑐𝑙(𝑆	PROPN
cana-5360	155	16	)	)	PUNCT
cana-5360	155	17	)	)	PUNCT
cana-5360	155	18	.	.	PUNCT
cana-5360	156	1	3	3	X
cana-5360	156	2	.	.	X
cana-5360	156	3	fuzzy	fuzzy	ADJ
cana-5360	156	4	nano	nano	ADJ
cana-5360	156	5	𝛿𝒮-open	𝛿𝒮-open	NOUN
cana-5360	156	6	set	set	NOUN
cana-5360	156	7	(	(	PUNCT
cana-5360	156	8	briefly	briefly	ADV
cana-5360	156	9	,	,	PUNCT
cana-5360	156	10	𝒫ℱ𝔑𝛿𝒮𝑜𝑠	𝒫ℱ𝔑𝛿𝒮𝑜𝑠	NOUN
cana-5360	156	11	)	)	PUNCT
cana-5360	156	12	if	if	SCONJ
cana-5360	156	13	𝑆	𝑆	PROPN
cana-5360	156	14	⊆	⊆	NUM
cana-5360	156	15	𝒫ℱ𝔑𝑐𝑙(𝒫ℱ𝔑𝛿𝑖𝑛𝑡(𝑆	𝒫ℱ𝔑𝑐𝑙(𝒫ℱ𝔑𝛿𝑖𝑛𝑡(𝑆	PROPN
cana-5360	156	16	)	)	PUNCT
cana-5360	156	17	)	)	PUNCT
cana-5360	156	18	.	.	PUNCT
cana-5360	157	1	4	4	X
cana-5360	157	2	.	.	X
cana-5360	157	3	fuzzy	fuzzy	ADJ
cana-5360	157	4	nano	nano	NOUN
cana-5360	157	5	𝛿𝛼	𝛿𝛼	ADP
cana-5360	157	6	or	or	CCONJ
cana-5360	157	7	𝑎	𝑎	PRON
cana-5360	157	8	-open	-open	NOUN
cana-5360	157	9	set	set	NOUN
cana-5360	157	10	(	(	PUNCT
cana-5360	157	11	briefly	briefly	ADV
cana-5360	157	12	,	,	PUNCT
cana-5360	157	13	𝒫ℱ𝔑𝛿𝛼𝑜𝑠	𝒫ℱ𝔑𝛿𝛼𝑜𝑠	PROPN
cana-5360	157	14	or	or	CCONJ
cana-5360	157	15	𝒫ℱ𝔑𝑎𝑜𝑠	𝒫ℱ𝔑𝑎𝑜𝑠	PROPN
cana-5360	157	16	)	)	PUNCT
cana-5360	158	1	if	if	SCONJ
cana-5360	158	2	𝑆	𝑆	PROPN
cana-5360	158	3	⊆	⊆	NUM
cana-5360	158	4	𝒫ℱ𝔑𝑖𝑛𝑡(𝒫ℱ𝔑𝑐𝑙(𝒫ℱ𝔑𝛿𝑖𝑛𝑡(𝑆	𝒫ℱ𝔑𝑖𝑛𝑡(𝒫ℱ𝔑𝑐𝑙(𝒫ℱ𝔑𝛿𝑖𝑛𝑡(𝑆	NOUN
cana-5360	158	5	)	)	PUNCT
cana-5360	158	6	)	)	PUNCT
cana-5360	158	7	)	)	PUNCT
cana-5360	158	8	.	.	PUNCT
cana-5360	159	1	5	5	X
cana-5360	159	2	.	.	X
cana-5360	159	3	fuzzy	fuzzy	ADJ
cana-5360	159	4	nano	nano	ADJ
cana-5360	159	5	𝛿𝛽	𝛿𝛽	NOUN
cana-5360	159	6	or	or	CCONJ
cana-5360	159	7	𝑒∗	𝑒∗	PROPN
cana-5360	159	8	-open	-open	ADJ
cana-5360	159	9	set	set	NOUN
cana-5360	159	10	(	(	PUNCT
cana-5360	159	11	briefly	briefly	ADV
cana-5360	159	12	,	,	PUNCT
cana-5360	159	13	𝒫ℱ𝔑𝛿𝛽𝑜𝑠	𝒫ℱ𝔑𝛿𝛽𝑜𝑠	PROPN
cana-5360	159	14	or	or	CCONJ
cana-5360	159	15	𝒫ℱ𝔑𝑒∗𝑜𝑠	𝒫ℱ𝔑𝑒∗𝑜𝑠	NUM
cana-5360	159	16	)	)	PUNCT
cana-5360	160	1	if	if	SCONJ
cana-5360	160	2	𝑆	𝑆	PROPN
cana-5360	160	3	⊆	⊆	NUM
cana-5360	160	4	𝒫ℱ𝔑𝑐𝑙(𝒫ℱ𝔑𝑖𝑛𝑡(𝒫ℱ𝔑𝛿𝑐𝑙(𝑆	𝒫ℱ𝔑𝑐𝑙(𝒫ℱ𝔑𝑖𝑛𝑡(𝒫ℱ𝔑𝛿𝑐𝑙(𝑆	NUM
cana-5360	160	5	)	)	PUNCT
cana-5360	160	6	)	)	PUNCT
cana-5360	160	7	)	)	PUNCT
cana-5360	160	8	.	.	PUNCT
cana-5360	161	1	the	the	DET
cana-5360	161	2	complement	complement	NOUN
cana-5360	161	3	of	of	ADP
cana-5360	161	4	a	a	DET
cana-5360	161	5	𝒫ℱ𝔑𝛿𝑜𝑠	𝒫ℱ𝔑𝛿𝑜𝑠	PROPN
cana-5360	161	6	(	(	PUNCT
cana-5360	161	7	resp	resp	NOUN
cana-5360	161	8	.	.	PUNCT
cana-5360	162	1	𝒫ℱ𝔑𝛿𝒫𝑜𝑠	𝒫ℱ𝔑𝛿𝒫𝑜𝑠	NOUN
cana-5360	162	2	,	,	PUNCT
cana-5360	162	3	𝒫ℱ𝔑𝛿𝒮𝑜𝑠	𝒫ℱ𝔑𝛿𝒮𝑜𝑠	PROPN
cana-5360	162	4	,	,	PUNCT
cana-5360	162	5	𝒫ℱ𝔑𝛿𝛼𝑜𝑠	𝒫ℱ𝔑𝛿𝛼𝑜𝑠	PROPN
cana-5360	162	6	&	&	CCONJ
cana-5360	162	7	𝒫ℱ𝔑𝛿𝛽𝑜𝑠	𝒫ℱ𝔑𝛿𝛽𝑜𝑠	PROPN
cana-5360	162	8	)	)	PUNCT
cana-5360	162	9	is	be	AUX
cana-5360	162	10	called	call	VERB
cana-5360	162	11	a	a	DET
cana-5360	162	12	pythagorean	pythagorean	ADJ
cana-5360	162	13	fuzzy	fuzzy	ADJ
cana-5360	162	14	nano	nano	PROPN
cana-5360	162	15	𝛿	𝛿	ADJ
cana-5360	162	16	(	(	PUNCT
cana-5360	162	17	resp	resp	NOUN
cana-5360	162	18	.	.	PUNCT
cana-5360	163	1	𝛿𝒫	𝛿𝒫	ADV
cana-5360	163	2	,	,	PUNCT
cana-5360	163	3	𝛿𝒮	𝛿𝒮	NOUN
cana-5360	163	4	,	,	PUNCT
cana-5360	163	5	𝛿𝛼	𝛿𝛼	NOUN
cana-5360	163	6	and	and	CCONJ
cana-5360	163	7	𝛿𝛽	𝛿𝛽	VERB
cana-5360	163	8	)	)	PUNCT
cana-5360	163	9	closed	close	VERB
cana-5360	163	10	set	set	VERB
cana-5360	163	11	(	(	PUNCT
cana-5360	163	12	briefly	briefly	ADV
cana-5360	163	13	,	,	PUNCT
cana-5360	163	14	𝒫ℱ𝔑𝛿𝑐𝑠	𝒫ℱ𝔑𝛿𝑐𝑠	PROPN
cana-5360	163	15	(	(	PUNCT
cana-5360	163	16	resp	resp	NOUN
cana-5360	163	17	.	.	PUNCT
cana-5360	164	1	𝒫ℱ𝔑𝛿𝒫𝑐𝑠	𝒫ℱ𝔑𝛿𝒫𝑐𝑠	PROPN
cana-5360	164	2	,	,	PUNCT
cana-5360	164	3	𝒫ℱ𝔑𝛿𝒮𝑐𝑠	𝒫ℱ𝔑𝛿𝒮𝑐𝑠	PROPN
cana-5360	164	4	,	,	PUNCT
cana-5360	164	5	𝒫ℱ𝔑𝛿𝛼𝑐𝑠	𝒫ℱ𝔑𝛿𝛼𝑐𝑠	NOUN
cana-5360	164	6	and	and	CCONJ
cana-5360	164	7	𝒫ℱ𝔑𝛿𝛽𝑐𝑠	𝒫ℱ𝔑𝛿𝛽𝑐𝑠	PROPN
cana-5360	164	8	)	)	PUNCT
cana-5360	164	9	)	)	PUNCT
cana-5360	164	10	in	in	ADP
cana-5360	164	11	𝑈.	𝑈.	PROPN
cana-5360	164	12	the	the	DET
cana-5360	164	13	family	family	NOUN
cana-5360	164	14	of	of	ADP
cana-5360	164	15	all	all	DET
cana-5360	164	16	𝒫ℱ𝔑𝛿𝑜𝑠	𝒫ℱ𝔑𝛿𝑜𝑠	PROPN
cana-5360	164	17	(	(	PUNCT
cana-5360	164	18	resp	resp	NOUN
cana-5360	164	19	.	.	PUNCT
cana-5360	165	1	𝒫ℱ𝔑𝛿𝑐𝑠	𝒫ℱ𝔑𝛿𝑐𝑠	PROPN
cana-5360	165	2	,	,	PUNCT
cana-5360	165	3	𝒫ℱ𝔑𝛿𝒫𝑜𝑠	𝒫ℱ𝔑𝛿𝒫𝑜𝑠	PROPN
cana-5360	165	4	,	,	PUNCT
cana-5360	165	5	𝒫ℱ𝔑𝛿𝒫𝑐𝑠	𝒫ℱ𝔑𝛿𝒫𝑐𝑠	PROPN
cana-5360	165	6	,	,	PUNCT
cana-5360	165	7	𝒫ℱ𝔑𝛿𝒮𝑜𝑠	𝒫ℱ𝔑𝛿𝒮𝑜𝑠	PROPN
cana-5360	165	8	,	,	PUNCT
cana-5360	165	9	𝒫ℱ𝔑𝛿𝒮𝑐𝑠	𝒫ℱ𝔑𝛿𝒮𝑐𝑠	PROPN
cana-5360	165	10	,	,	PUNCT
cana-5360	165	11	𝒫ℱ𝔑𝛿𝛼𝑜𝑠	𝒫ℱ𝔑𝛿𝛼𝑜𝑠	PROPN
cana-5360	165	12	,	,	PUNCT
cana-5360	165	13	𝒫ℱ𝔑𝛿𝛼𝑐𝑠	𝒫ℱ𝔑𝛿𝛼𝑐𝑠	PROPN
cana-5360	165	14	,	,	PUNCT
cana-5360	165	15	𝒫ℱ𝔑𝛿𝛽𝑜𝑠	𝒫ℱ𝔑𝛿𝛽𝑜𝑠	PROPN
cana-5360	165	16	and	and	CCONJ
cana-5360	165	17	𝒫ℱ𝔑𝛿𝛽𝑐𝑠	𝒫ℱ𝔑𝛿𝛽𝑐𝑠	PROPN
cana-5360	165	18	)	)	PUNCT
cana-5360	165	19	of	of	ADP
cana-5360	165	20	𝑈	𝑈	PROPN
cana-5360	165	21	is	be	AUX
cana-5360	165	22	denoted	denote	VERB
cana-5360	165	23	by	by	ADP
cana-5360	165	24	𝒫ℱ𝔑𝛿𝑂𝑆(𝑈	𝒫ℱ𝔑𝛿𝑂𝑆(𝑈	NOUN
cana-5360	165	25	)	)	PUNCT
cana-5360	165	26	(	(	PUNCT
cana-5360	165	27	resp	resp	NOUN
cana-5360	165	28	.	.	PUNCT
cana-5360	166	1	𝒫ℱ𝔑𝛿𝐶𝑆(𝑈	𝒫ℱ𝔑𝛿𝐶𝑆(𝑈	X
cana-5360	166	2	)	)	PUNCT
cana-5360	167	1	,	,	PUNCT
cana-5360	167	2	𝒫ℱ𝔑𝛿𝒫𝑂𝑆(𝑈	𝒫ℱ𝔑𝛿𝒫𝑂𝑆(𝑈	NOUN
cana-5360	167	3	)	)	PUNCT
cana-5360	167	4	,	,	PUNCT
cana-5360	167	5	𝒫ℱ𝔑𝛿𝒫𝐶𝑆(𝑈	𝒫ℱ𝔑𝛿𝒫𝐶𝑆(𝑈	PROPN
cana-5360	167	6	)	)	PUNCT
cana-5360	167	7	,	,	PUNCT
cana-5360	167	8	𝒫ℱ𝔑𝛿𝒮𝑂𝑆(𝑈	𝒫ℱ𝔑𝛿𝒮𝑂𝑆(𝑈	NOUN
cana-5360	167	9	)	)	PUNCT
cana-5360	167	10	,	,	PUNCT
cana-5360	167	11	𝒫ℱ𝔑𝛿𝒮𝐶𝑆(𝑈	𝒫ℱ𝔑𝛿𝒮𝐶𝑆(𝑈	ADV
cana-5360	167	12	)	)	PUNCT
cana-5360	167	13	,	,	PUNCT
cana-5360	167	14	𝒫ℱ𝔑𝛿𝛼𝑂𝑆(𝑈	𝒫ℱ𝔑𝛿𝛼𝑂𝑆(𝑈	ADV
cana-5360	167	15	)	)	PUNCT
cana-5360	167	16	,	,	PUNCT
cana-5360	167	17	𝒫ℱ𝔑𝛿𝛼𝐶𝑆(𝑈	𝒫ℱ𝔑𝛿𝛼𝐶𝑆(𝑈	PROPN
cana-5360	167	18	)	)	PUNCT
cana-5360	167	19	,	,	PUNCT
cana-5360	167	20	𝒫ℱ𝔑𝛿𝛽𝑂𝑆(𝑈	𝒫ℱ𝔑𝛿𝛽𝑂𝑆(𝑈	NUM
cana-5360	167	21	)	)	PUNCT
cana-5360	167	22	and	and	CCONJ
cana-5360	167	23	𝒫ℱ𝔑𝛿𝛽𝐶𝑆(𝑈	𝒫ℱ𝔑𝛿𝛽𝐶𝑆(𝑈	NUM
cana-5360	167	24	)	)	PUNCT
cana-5360	167	25	)	)	PUNCT
cana-5360	167	26	.	.	PUNCT
cana-5360	168	1	definition	definition	NOUN
cana-5360	168	2	3.3	3.3	NUM
cana-5360	168	3	let	let	VERB
cana-5360	168	4	(	(	PUNCT
cana-5360	168	5	𝑈	𝑈	PROPN
cana-5360	168	6	,	,	PUNCT
cana-5360	168	7	𝜏𝒫(𝐴	𝜏𝒫(𝐴	NOUN
cana-5360	168	8	)	)	PUNCT
cana-5360	168	9	)	)	PUNCT
cana-5360	168	10	be	be	AUX
cana-5360	168	11	a	a	DET
cana-5360	168	12	𝒫ℱ𝔑𝑡𝑠	𝒫ℱ𝔑𝑡𝑠	NOUN
cana-5360	168	13	with	with	ADP
cana-5360	168	14	respect	respect	NOUN
cana-5360	168	15	to	to	ADP
cana-5360	168	16	𝐴	𝐴	PROPN
cana-5360	168	17	where	where	SCONJ
cana-5360	168	18	𝐴	𝐴	PROPN
cana-5360	168	19	is	be	AUX
cana-5360	168	20	a	a	DET
cana-5360	168	21	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-5360	168	22	of	of	ADP
cana-5360	168	23	𝑈.	𝑈.	PROPN
cana-5360	168	24	let	let	VERB
cana-5360	168	25	𝑆	𝑆	PROPN
cana-5360	168	26	be	be	AUX
cana-5360	168	27	a	a	DET
cana-5360	168	28	𝑝𝑓𝑠	𝑝𝑓𝑠	NOUN
cana-5360	168	29	of	of	ADP
cana-5360	168	30	𝑈.	𝑈.	PROPN
cana-5360	168	31	then	then	ADV
cana-5360	168	32	pythagorean	pythagorean	VERB
cana-5360	168	33	fuzzy	fuzzy	ADJ
cana-5360	168	34	nano	nano	PROPN
cana-5360	169	1	[	[	X
cana-5360	169	2	(	(	PUNCT
cana-5360	169	3	i	i	NOUN
cana-5360	169	4	)	)	PUNCT
cana-5360	169	5	]	]	PUNCT
cana-5360	170	1	1	1	X
cana-5360	170	2	.	.	PUNCT
cana-5360	171	1	𝛿	𝛿	PRON
cana-5360	171	2	pre	pre	X
cana-5360	171	3	(	(	PUNCT
cana-5360	171	4	resp	resp	NOUN
cana-5360	171	5	.	.	PUNCT
cana-5360	172	1	𝛿	𝛿	ADJ
cana-5360	172	2	semi	semi	ADJ
cana-5360	172	3	,	,	PUNCT
cana-5360	172	4	𝛿𝛼	𝛿𝛼	ADP
cana-5360	172	5	and	and	CCONJ
cana-5360	172	6	𝛿𝛽	𝛿𝛽	ADJ
cana-5360	172	7	)	)	PUNCT
cana-5360	172	8	interior	interior	NOUN
cana-5360	172	9	of	of	ADP
cana-5360	172	10	𝑆	𝑆	PROPN
cana-5360	172	11	(	(	PUNCT
cana-5360	172	12	briefly	briefly	ADV
cana-5360	172	13	,	,	PUNCT
cana-5360	172	14	𝒫ℱ𝔑𝛿𝒫𝑖𝑛𝑡(𝑆	𝒫ℱ𝔑𝛿𝒫𝑖𝑛𝑡(𝑆	PROPN
cana-5360	172	15	)	)	PUNCT
cana-5360	172	16	(	(	PUNCT
cana-5360	172	17	resp	resp	NOUN
cana-5360	172	18	.	.	PUNCT
cana-5360	173	1	𝒫ℱ𝔑𝛿𝒮𝑖𝑛𝑡(𝑆	𝒫ℱ𝔑𝛿𝒮𝑖𝑛𝑡(𝑆	PROPN
cana-5360	173	2	)	)	PUNCT
cana-5360	173	3	,	,	PUNCT
cana-5360	173	4	𝒫ℱ𝔑𝛿𝛼𝑖𝑛𝑡(𝑆	𝒫ℱ𝔑𝛿𝛼𝑖𝑛𝑡(𝑆	X
cana-5360	173	5	)	)	PUNCT
cana-5360	173	6	and	and	CCONJ
cana-5360	173	7	𝒫ℱ𝔑𝛿𝛽𝑖𝑛𝑡(𝑆	𝒫ℱ𝔑𝛿𝛽𝑖𝑛𝑡(𝑆	NOUN
cana-5360	173	8	)	)	PUNCT
cana-5360	173	9	)	)	PUNCT
cana-5360	173	10	)	)	PUNCT
cana-5360	173	11	is	be	AUX
cana-5360	173	12	defined	define	VERB
cana-5360	173	13	by	by	ADP
cana-5360	173	14	𝒫ℱ𝔑𝛿𝒫𝑖𝑛𝑡(𝑆	𝒫ℱ𝔑𝛿𝒫𝑖𝑛𝑡(𝑆	PROPN
cana-5360	173	15	)	)	PUNCT
cana-5360	173	16	(	(	PUNCT
cana-5360	173	17	resp	resp	NOUN
cana-5360	173	18	.	.	PUNCT
cana-5360	174	1	𝒫ℱ𝔑𝛿𝒮𝑖𝑛𝑡(𝑆	𝒫ℱ𝔑𝛿𝒮𝑖𝑛𝑡(𝑆	PROPN
cana-5360	174	2	)	)	PUNCT
cana-5360	174	3	,	,	PUNCT
cana-5360	174	4	𝒫ℱ𝔑𝛿𝛼𝑖𝑛𝑡(𝑆	𝒫ℱ𝔑𝛿𝛼𝑖𝑛𝑡(𝑆	X
cana-5360	174	5	)	)	PUNCT
cana-5360	174	6	and	and	CCONJ
cana-5360	174	7	𝒫ℱ𝔑𝛿𝛽𝑖𝑛𝑡(𝑆	𝒫ℱ𝔑𝛿𝛽𝑖𝑛𝑡(𝑆	NOUN
cana-5360	174	8	)	)	PUNCT
cana-5360	174	9	)	)	PUNCT
cana-5360	175	1	=	=	SYM
cana-5360	175	2	∪	∪	X
cana-5360	175	3	{	{	PUNCT
cana-5360	175	4	𝐼	𝐼	NOUN
cana-5360	175	5	:	:	PUNCT
cana-5360	175	6	𝐼	𝐼	PROPN
cana-5360	175	7	⊆	⊆	NUM
cana-5360	175	8	𝑆	𝑆	PROPN
cana-5360	175	9	&	&	CCONJ
cana-5360	175	10	𝐼isa𝒫ℱ𝔑𝛿𝒫𝑜	𝐼isa𝒫ℱ𝔑𝛿𝒫𝑜	NOUN
cana-5360	175	11	(	(	PUNCT
cana-5360	175	12	resp	resp	NOUN
cana-5360	175	13	.	.	PUNCT
cana-5360	176	1	𝒫ℱ𝔑𝛿𝒮𝑜	𝒫ℱ𝔑𝛿𝒮𝑜	PROPN
cana-5360	176	2	,	,	PUNCT
cana-5360	176	3	𝒫ℱ𝔑𝛿𝛼𝑜	𝒫ℱ𝔑𝛿𝛼𝑜	PROPN
cana-5360	176	4	&	&	CCONJ
cana-5360	176	5	𝒫ℱ𝔑𝛿𝛽𝑜	𝒫ℱ𝔑𝛿𝛽𝑜	PROPN
cana-5360	176	6	)	)	PUNCT
cana-5360	176	7	set	set	VERB
cana-5360	176	8	in𝑈	in𝑈	NOUN
cana-5360	176	9	}	}	PUNCT
cana-5360	176	10	.	.	PUNCT
cana-5360	177	1	2	2	X
cana-5360	177	2	.	.	X
cana-5360	177	3	𝛿	𝛿	PRON
cana-5360	177	4	pre	pre	X
cana-5360	177	5	(	(	PUNCT
cana-5360	177	6	resp	resp	NOUN
cana-5360	177	7	.	.	PUNCT
cana-5360	178	1	𝛿	𝛿	ADJ
cana-5360	178	2	semi	semi	ADJ
cana-5360	178	3	,	,	PUNCT
cana-5360	178	4	𝛿𝛼	𝛿𝛼	ADP
cana-5360	178	5	and	and	CCONJ
cana-5360	178	6	𝛿𝛽	𝛿𝛽	ADJ
cana-5360	178	7	)	)	PUNCT
cana-5360	178	8	closure	closure	NOUN
cana-5360	178	9	of	of	ADP
cana-5360	178	10	𝑆	𝑆	PROPN
cana-5360	178	11	(	(	PUNCT
cana-5360	178	12	briefly	briefly	ADV
cana-5360	178	13	,	,	PUNCT
cana-5360	178	14	𝒫ℱ𝔑𝛿𝒫𝑐𝑙(𝑆	𝒫ℱ𝔑𝛿𝒫𝑐𝑙(𝑆	PROPN
cana-5360	178	15	)	)	PUNCT
cana-5360	178	16	(	(	PUNCT
cana-5360	178	17	resp	resp	NOUN
cana-5360	178	18	.	.	PUNCT
cana-5360	179	1	𝒫ℱ𝔑𝛿𝒮𝑐𝑙(𝑆	𝒫ℱ𝔑𝛿𝒮𝑐𝑙(𝑆	NOUN
cana-5360	179	2	)	)	PUNCT
cana-5360	179	3	,	,	PUNCT
cana-5360	179	4	𝒫ℱ𝔑𝛿𝛼𝑐𝑙(𝑆	𝒫ℱ𝔑𝛿𝛼𝑐𝑙(𝑆	ADP
cana-5360	179	5	)	)	PUNCT
cana-5360	179	6	and	and	CCONJ
cana-5360	179	7	𝒫ℱ𝔑𝛿𝛽𝑐𝑙(𝑆	𝒫ℱ𝔑𝛿𝛽𝑐𝑙(𝑆	NOUN
cana-5360	179	8	)	)	PUNCT
cana-5360	179	9	)	)	PUNCT
cana-5360	179	10	)	)	PUNCT
cana-5360	180	1	is	be	AUX
cana-5360	180	2	defined	define	VERB
cana-5360	180	3	by	by	ADP
cana-5360	180	4	𝒫ℱ𝔑𝛿𝒫𝑐𝑙(𝑆	𝒫ℱ𝔑𝛿𝒫𝑐𝑙(𝑆	PROPN
cana-5360	180	5	)	)	PUNCT
cana-5360	180	6	(	(	PUNCT
cana-5360	180	7	resp	resp	NOUN
cana-5360	180	8	.	.	PUNCT
cana-5360	181	1	𝒫ℱ𝔑𝛿𝒮𝑐𝑙(𝑆	𝒫ℱ𝔑𝛿𝒮𝑐𝑙(𝑆	NOUN
cana-5360	181	2	)	)	PUNCT
cana-5360	181	3	,	,	PUNCT
cana-5360	181	4	𝒫ℱ𝔑𝛿𝛼𝑐𝑙(𝑆	𝒫ℱ𝔑𝛿𝛼𝑐𝑙(𝑆	ADP
cana-5360	181	5	)	)	PUNCT
cana-5360	181	6	and	and	CCONJ
cana-5360	181	7	𝒫ℱ𝔑𝛿𝛽𝑐𝑙(𝑆	𝒫ℱ𝔑𝛿𝛽𝑐𝑙(𝑆	NOUN
cana-5360	181	8	)	)	PUNCT
cana-5360	181	9	)	)	PUNCT
cana-5360	182	1	=	=	NOUN
cana-5360	182	2	∩	∩	X
cana-5360	182	3	{	{	PUNCT
cana-5360	182	4	𝐴	𝐴	PROPN
cana-5360	182	5	:	:	PUNCT
cana-5360	182	6	𝑆	𝑆	PROPN
cana-5360	182	7	⊆	⊆	NUM
cana-5360	182	8	𝐴	𝐴	PROPN
cana-5360	182	9	&	&	CCONJ
cana-5360	182	10	𝐴isa𝒫ℱ𝔑𝛿𝒫𝑐	𝐴isa𝒫ℱ𝔑𝛿𝒫𝑐	PROPN
cana-5360	182	11	(	(	PUNCT
cana-5360	182	12	resp	resp	NOUN
cana-5360	182	13	.	.	PUNCT
cana-5360	183	1	𝒫ℱ𝔑𝛿𝒮𝑐	𝒫ℱ𝔑𝛿𝒮𝑐	PROPN
cana-5360	183	2	,	,	PUNCT
cana-5360	183	3	𝒫ℱ𝔑𝛿𝛼𝑐	𝒫ℱ𝔑𝛿𝛼𝑐	PROPN
cana-5360	183	4	&	&	CCONJ
cana-5360	183	5	𝒫ℱ𝔑𝛿𝛽𝑐	𝒫ℱ𝔑𝛿𝛽𝑐	PROPN
cana-5360	183	6	)	)	PUNCT
cana-5360	183	7	set	set	VERB
cana-5360	183	8	in	in	ADP
cana-5360	183	9	𝑈	𝑈	PROPN
cana-5360	183	10	}	}	PUNCT
cana-5360	183	11	.	.	PUNCT
cana-5360	184	1	communications	communication	NOUN
cana-5360	184	2	on	on	ADP
cana-5360	184	3	applied	apply	VERB
cana-5360	184	4	nonlinear	nonlinear	ADJ
cana-5360	184	5	analysis	analysis	NOUN
cana-5360	184	6	issn	issn	NOUN
cana-5360	184	7	:	:	PUNCT
cana-5360	184	8	1074	1074	NUM
cana-5360	184	9	-	-	PUNCT
cana-5360	184	10	133x	133x	NUM
cana-5360	184	11	vol	vol	VERB
cana-5360	184	12	32	32	NUM
cana-5360	184	13	no	no	NOUN
cana-5360	184	14	.	.	PUNCT
cana-5360	185	1	10s	10	NOUN
cana-5360	185	2	(	(	PUNCT
cana-5360	185	3	2025	2025	NUM
cana-5360	185	4	)	)	PUNCT
cana-5360	185	5	1931	1931	NUM
cana-5360	185	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5360	185	7	definition	definition	NOUN
cana-5360	185	8	3.4	3.4	NUM
cana-5360	185	9	let	let	VERB
cana-5360	185	10	(	(	PUNCT
cana-5360	185	11	𝑈	𝑈	PROPN
cana-5360	185	12	,	,	PUNCT
cana-5360	185	13	𝜏𝒫(𝐴	𝜏𝒫(𝐴	NOUN
cana-5360	185	14	)	)	PUNCT
cana-5360	185	15	)	)	PUNCT
cana-5360	185	16	be	be	AUX
cana-5360	185	17	a	a	DET
cana-5360	185	18	𝒫ℱ𝔑𝑡𝑠	𝒫ℱ𝔑𝑡𝑠	NOUN
cana-5360	185	19	with	with	ADP
cana-5360	185	20	respect	respect	NOUN
cana-5360	185	21	to	to	ADP
cana-5360	185	22	𝐴	𝐴	PROPN
cana-5360	185	23	where	where	SCONJ
cana-5360	185	24	𝐴	𝐴	PROPN
cana-5360	185	25	is	be	AUX
cana-5360	185	26	a	a	DET
cana-5360	185	27	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-5360	185	28	of	of	ADP
cana-5360	185	29	𝑈.	𝑈.	PROPN
cana-5360	185	30	let	let	VERB
cana-5360	185	31	𝑆	𝑆	PROPN
cana-5360	185	32	be	be	AUX
cana-5360	185	33	a	a	DET
cana-5360	185	34	𝑝𝑓𝑠	𝑝𝑓𝑠	NOUN
cana-5360	185	35	of	of	ADP
cana-5360	185	36	𝑈.	𝑈.	PROPN
cana-5360	186	1	then	then	ADV
cana-5360	187	1	[	[	X
cana-5360	187	2	(	(	PUNCT
cana-5360	187	3	i	i	NOUN
cana-5360	187	4	)	)	PUNCT
cana-5360	187	5	]	]	PUNCT
cana-5360	187	6	1	1	X
cana-5360	187	7	.	.	X
cana-5360	187	8	pythagorean	pythagorean	PROPN
cana-5360	187	9	fuzzy	fuzzy	ADJ
cana-5360	187	10	nano	nano	PROPN
cana-5360	187	11	𝛿	𝛿	DET
cana-5360	187	12	interior	interior	NOUN
cana-5360	187	13	of	of	ADP
cana-5360	187	14	𝑆	𝑆	PROPN
cana-5360	187	15	(	(	PUNCT
cana-5360	187	16	briefly	briefly	ADV
cana-5360	187	17	,	,	PUNCT
cana-5360	187	18	𝒫ℱ𝔑𝛿𝑖𝑛𝑡(𝑆	𝒫ℱ𝔑𝛿𝑖𝑛𝑡(𝑆	NUM
cana-5360	187	19	)	)	PUNCT
cana-5360	187	20	)	)	PUNCT
cana-5360	187	21	is	be	AUX
cana-5360	187	22	defined	define	VERB
cana-5360	187	23	by	by	ADP
cana-5360	187	24	𝒫ℱ𝔑𝛿𝑖𝑛𝑡(𝑆	𝒫ℱ𝔑𝛿𝑖𝑛𝑡(𝑆	NOUN
cana-5360	187	25	)	)	PUNCT
cana-5360	187	26	=	=	NOUN
cana-5360	187	27	∪	∪	X
cana-5360	187	28	{	{	PUNCT
cana-5360	187	29	𝐼	𝐼	NOUN
cana-5360	187	30	:	:	PUNCT
cana-5360	187	31	𝐼	𝐼	PROPN
cana-5360	187	32	⊆	⊆	NUM
cana-5360	187	33	𝑆	𝑆	PROPN
cana-5360	187	34	&	&	CCONJ
cana-5360	187	35	𝐼isa𝒫ℱ𝔑𝑟𝑜	𝐼isa𝒫ℱ𝔑𝑟𝑜	NOUN
cana-5360	187	36	set	set	VERB
cana-5360	187	37	in𝑈	in𝑈	NOUN
cana-5360	187	38	}	}	PUNCT
cana-5360	187	39	.	.	PUNCT
cana-5360	188	1	2	2	X
cana-5360	188	2	.	.	X
cana-5360	188	3	pythagorean	pythagorean	PROPN
cana-5360	188	4	fuzzy	fuzzy	ADJ
cana-5360	188	5	nano	nano	PROPN
cana-5360	188	6	𝛿	𝛿	ADJ
cana-5360	188	7	closure	closure	NOUN
cana-5360	188	8	of	of	ADP
cana-5360	188	9	𝑆	𝑆	PROPN
cana-5360	188	10	(	(	PUNCT
cana-5360	188	11	briefly	briefly	ADV
cana-5360	188	12	,	,	PUNCT
cana-5360	188	13	𝒫ℱ𝔑𝛿𝑐𝑙(𝑆	𝒫ℱ𝔑𝛿𝑐𝑙(𝑆	PROPN
cana-5360	188	14	)	)	PUNCT
cana-5360	188	15	)	)	PUNCT
cana-5360	188	16	is	be	AUX
cana-5360	188	17	defined	define	VERB
cana-5360	188	18	by	by	ADP
cana-5360	188	19	𝒫ℱ𝔑𝛿𝑐𝑙(𝑆	𝒫ℱ𝔑𝛿𝑐𝑙(𝑆	ADP
cana-5360	188	20	)	)	PUNCT
cana-5360	189	1	=	=	NOUN
cana-5360	189	2	∩	∩	NOUN
cana-5360	189	3	{	{	PUNCT
cana-5360	189	4	𝐴	𝐴	PROPN
cana-5360	189	5	:	:	PUNCT
cana-5360	189	6	𝑆	𝑆	PROPN
cana-5360	189	7	⊆	⊆	NUM
cana-5360	189	8	𝐴	𝐴	PROPN
cana-5360	189	9	&	&	CCONJ
cana-5360	189	10	𝐴isa𝒫ℱ𝔑𝑟𝑐	𝐴isa𝒫ℱ𝔑𝑟𝑐	NOUN
cana-5360	189	11	set	set	VERB
cana-5360	189	12	in	in	ADP
cana-5360	189	13	𝑈	𝑈	PROPN
cana-5360	189	14	}	}	PUNCT
cana-5360	189	15	.	.	PUNCT
cana-5360	190	1	definition	definition	NOUN
cana-5360	190	2	3.5	3.5	NUM
cana-5360	190	3	let	let	NOUN
cana-5360	190	4	(	(	PUNCT
cana-5360	190	5	𝑈	𝑈	PROPN
cana-5360	190	6	,	,	PUNCT
cana-5360	190	7	𝜏𝒫(𝐴	𝜏𝒫(𝐴	NOUN
cana-5360	190	8	)	)	PUNCT
cana-5360	190	9	)	)	PUNCT
cana-5360	190	10	be	be	AUX
cana-5360	190	11	a	a	DET
cana-5360	190	12	𝒫ℱ𝔑𝑡𝑠	𝒫ℱ𝔑𝑡𝑠	NOUN
cana-5360	190	13	with	with	ADP
cana-5360	190	14	respect	respect	NOUN
cana-5360	190	15	to	to	ADP
cana-5360	190	16	𝐴	𝐴	PROPN
cana-5360	190	17	where	where	SCONJ
cana-5360	190	18	𝐴	𝐴	PROPN
cana-5360	190	19	is	be	AUX
cana-5360	190	20	a	a	DET
cana-5360	190	21	𝑝𝑓𝑠	𝑝𝑓𝑠	NOUN
cana-5360	190	22	of	of	ADP
cana-5360	190	23	𝑈.	𝑈.	PROPN
cana-5360	190	24	then	then	ADV
cana-5360	190	25	a	a	DET
cana-5360	190	26	𝒫ℱ𝑠	𝒫ℱ𝑠	X
cana-5360	190	27	𝑆	𝑆	PROPN
cana-5360	190	28	in	in	ADP
cana-5360	190	29	𝑈	𝑈	PROPN
cana-5360	190	30	is	be	AUX
cana-5360	190	31	said	say	VERB
cana-5360	190	32	to	to	PART
cana-5360	190	33	be	be	AUX
cana-5360	190	34	pythagorean	pythagorean	NOUN
cana-5360	190	35	:	:	PUNCT
cana-5360	191	1	[	[	X
cana-5360	191	2	(	(	PUNCT
cana-5360	191	3	i	i	NOUN
cana-5360	191	4	)	)	PUNCT
cana-5360	191	5	]	]	PUNCT
cana-5360	191	6	1	1	X
cana-5360	191	7	.	.	X
cana-5360	191	8	fuzzy	fuzzy	ADJ
cana-5360	191	9	nano	nano	NOUN
cana-5360	191	10	𝛿-open	𝛿-open	NOUN
cana-5360	191	11	set	set	NOUN
cana-5360	191	12	(	(	PUNCT
cana-5360	191	13	briefly	briefly	ADV
cana-5360	191	14	,	,	PUNCT
cana-5360	191	15	𝒫ℱ𝔑𝛿𝑜𝑠	𝒫ℱ𝔑𝛿𝑜𝑠	PROPN
cana-5360	191	16	)	)	PUNCT
cana-5360	191	17	if	if	SCONJ
cana-5360	191	18	𝑆	𝑆	PROPN
cana-5360	191	19	=	=	SYM
cana-5360	191	20	𝒫ℱ𝔑𝛿𝑖𝑛𝑡(𝑆	𝒫ℱ𝔑𝛿𝑖𝑛𝑡(𝑆	NUM
cana-5360	191	21	)	)	PUNCT
cana-5360	191	22	.	.	PUNCT
cana-5360	192	1	2	2	X
cana-5360	192	2	.	.	X
cana-5360	192	3	fuzzy	fuzzy	ADJ
cana-5360	192	4	nano	nano	NOUN
cana-5360	192	5	𝛿𝒫-open	𝛿𝒫-open	NOUN
cana-5360	192	6	set	set	VERB
cana-5360	192	7	(	(	PUNCT
cana-5360	192	8	briefly	briefly	ADV
cana-5360	192	9	,	,	PUNCT
cana-5360	192	10	𝒫ℱ𝔑𝛿𝒫𝑜𝑠	𝒫ℱ𝔑𝛿𝒫𝑜𝑠	PROPN
cana-5360	192	11	)	)	PUNCT
cana-5360	192	12	if	if	SCONJ
cana-5360	192	13	𝑆	𝑆	PROPN
cana-5360	192	14	⊆	⊆	NUM
cana-5360	192	15	𝒫ℱ𝔑𝑖𝑛𝑡(𝒫ℱ𝔑𝛿𝑐𝑙(𝑆	𝒫ℱ𝔑𝑖𝑛𝑡(𝒫ℱ𝔑𝛿𝑐𝑙(𝑆	PROPN
cana-5360	192	16	)	)	PUNCT
cana-5360	192	17	)	)	PUNCT
cana-5360	192	18	.	.	PUNCT
cana-5360	193	1	3	3	X
cana-5360	193	2	.	.	X
cana-5360	193	3	fuzzy	fuzzy	ADJ
cana-5360	193	4	nano	nano	ADJ
cana-5360	193	5	𝛿𝒮-open	𝛿𝒮-open	NOUN
cana-5360	193	6	set	set	NOUN
cana-5360	193	7	(	(	PUNCT
cana-5360	193	8	briefly	briefly	ADV
cana-5360	193	9	,	,	PUNCT
cana-5360	193	10	𝒫ℱ𝔑𝛿𝒮𝑜𝑠	𝒫ℱ𝔑𝛿𝒮𝑜𝑠	NOUN
cana-5360	193	11	)	)	PUNCT
cana-5360	193	12	if	if	SCONJ
cana-5360	193	13	𝑆	𝑆	PROPN
cana-5360	193	14	⊆	⊆	NUM
cana-5360	193	15	𝒫ℱ𝔑𝑐𝑙(𝒫ℱ𝔑𝛿𝑖𝑛𝑡(𝑆	𝒫ℱ𝔑𝑐𝑙(𝒫ℱ𝔑𝛿𝑖𝑛𝑡(𝑆	PROPN
cana-5360	193	16	)	)	PUNCT
cana-5360	193	17	)	)	PUNCT
cana-5360	193	18	.	.	PUNCT
cana-5360	194	1	4	4	X
cana-5360	194	2	.	.	X
cana-5360	194	3	fuzzy	fuzzy	ADJ
cana-5360	194	4	nano	nano	NOUN
cana-5360	194	5	𝛿𝛼	𝛿𝛼	ADP
cana-5360	194	6	or	or	CCONJ
cana-5360	194	7	𝑎	𝑎	PRON
cana-5360	194	8	-open	-open	NOUN
cana-5360	194	9	set	set	NOUN
cana-5360	194	10	(	(	PUNCT
cana-5360	194	11	briefly	briefly	ADV
cana-5360	194	12	,	,	PUNCT
cana-5360	194	13	𝒫ℱ𝔑𝛿𝛼𝑜𝑠	𝒫ℱ𝔑𝛿𝛼𝑜𝑠	PROPN
cana-5360	194	14	or	or	CCONJ
cana-5360	194	15	𝒫ℱ𝔑𝑎𝑜𝑠	𝒫ℱ𝔑𝑎𝑜𝑠	PROPN
cana-5360	194	16	)	)	PUNCT
cana-5360	195	1	if	if	SCONJ
cana-5360	195	2	𝑆	𝑆	PROPN
cana-5360	195	3	⊆	⊆	NUM
cana-5360	195	4	𝒫ℱ𝔑𝑖𝑛𝑡(𝒫ℱ𝔑𝑐𝑙(𝒫ℱ𝔑𝛿𝑖𝑛𝑡(𝑆	𝒫ℱ𝔑𝑖𝑛𝑡(𝒫ℱ𝔑𝑐𝑙(𝒫ℱ𝔑𝛿𝑖𝑛𝑡(𝑆	NOUN
cana-5360	195	5	)	)	PUNCT
cana-5360	195	6	)	)	PUNCT
cana-5360	195	7	)	)	PUNCT
cana-5360	195	8	.	.	PUNCT
cana-5360	196	1	5	5	X
cana-5360	196	2	.	.	X
cana-5360	196	3	fuzzy	fuzzy	ADJ
cana-5360	196	4	nano	nano	ADJ
cana-5360	196	5	𝛿𝛽	𝛿𝛽	NOUN
cana-5360	196	6	or	or	CCONJ
cana-5360	196	7	𝑒∗	𝑒∗	PROPN
cana-5360	196	8	-open	-open	ADJ
cana-5360	196	9	set	set	NOUN
cana-5360	196	10	(	(	PUNCT
cana-5360	196	11	briefly	briefly	ADV
cana-5360	196	12	,	,	PUNCT
cana-5360	196	13	𝒫ℱ𝔑𝛿𝛽𝑜𝑠	𝒫ℱ𝔑𝛿𝛽𝑜𝑠	PROPN
cana-5360	196	14	or	or	CCONJ
cana-5360	196	15	𝒫ℱ𝔑𝑒∗𝑜𝑠	𝒫ℱ𝔑𝑒∗𝑜𝑠	NUM
cana-5360	196	16	)	)	PUNCT
cana-5360	197	1	if	if	SCONJ
cana-5360	197	2	𝑆	𝑆	PROPN
cana-5360	197	3	⊆	⊆	NUM
cana-5360	197	4	𝒫ℱ𝔑𝑐𝑙(𝒫ℱ𝔑𝑖𝑛𝑡(𝒫ℱ𝔑𝛿𝑐𝑙(𝑆	𝒫ℱ𝔑𝑐𝑙(𝒫ℱ𝔑𝑖𝑛𝑡(𝒫ℱ𝔑𝛿𝑐𝑙(𝑆	NUM
cana-5360	197	5	)	)	PUNCT
cana-5360	197	6	)	)	PUNCT
cana-5360	197	7	)	)	PUNCT
cana-5360	197	8	.	.	PUNCT
cana-5360	198	1	the	the	DET
cana-5360	198	2	complement	complement	NOUN
cana-5360	198	3	of	of	ADP
cana-5360	198	4	a	a	DET
cana-5360	198	5	𝒫ℱ𝔑𝛿𝑜𝑠	𝒫ℱ𝔑𝛿𝑜𝑠	PROPN
cana-5360	198	6	(	(	PUNCT
cana-5360	198	7	resp	resp	NOUN
cana-5360	198	8	.	.	PUNCT
cana-5360	199	1	𝒫ℱ𝔑𝛿𝒫𝑜𝑠	𝒫ℱ𝔑𝛿𝒫𝑜𝑠	NOUN
cana-5360	199	2	,	,	PUNCT
cana-5360	199	3	𝒫ℱ𝔑𝛿𝒮𝑜𝑠	𝒫ℱ𝔑𝛿𝒮𝑜𝑠	PROPN
cana-5360	199	4	,	,	PUNCT
cana-5360	199	5	𝒫ℱ𝔑𝛿𝛼𝑜𝑠	𝒫ℱ𝔑𝛿𝛼𝑜𝑠	PROPN
cana-5360	199	6	&	&	CCONJ
cana-5360	199	7	𝒫ℱ𝔑𝛿𝛽𝑜𝑠	𝒫ℱ𝔑𝛿𝛽𝑜𝑠	PROPN
cana-5360	199	8	)	)	PUNCT
cana-5360	199	9	is	be	AUX
cana-5360	199	10	called	call	VERB
cana-5360	199	11	a	a	DET
cana-5360	199	12	pythagorean	pythagorean	ADJ
cana-5360	199	13	fuzzy	fuzzy	ADJ
cana-5360	199	14	nano	nano	PROPN
cana-5360	199	15	𝛿	𝛿	ADJ
cana-5360	199	16	(	(	PUNCT
cana-5360	199	17	resp	resp	NOUN
cana-5360	199	18	.	.	PUNCT
cana-5360	200	1	𝛿𝒫	𝛿𝒫	ADV
cana-5360	200	2	,	,	PUNCT
cana-5360	200	3	𝛿𝒮	𝛿𝒮	NOUN
cana-5360	200	4	,	,	PUNCT
cana-5360	200	5	𝛿𝛼	𝛿𝛼	NOUN
cana-5360	200	6	and	and	CCONJ
cana-5360	200	7	𝛿𝛽	𝛿𝛽	VERB
cana-5360	200	8	)	)	PUNCT
cana-5360	200	9	closed	close	VERB
cana-5360	200	10	set	set	VERB
cana-5360	200	11	(	(	PUNCT
cana-5360	200	12	briefly	briefly	ADV
cana-5360	200	13	,	,	PUNCT
cana-5360	200	14	𝒫ℱ𝔑𝛿𝑐𝑠	𝒫ℱ𝔑𝛿𝑐𝑠	PROPN
cana-5360	200	15	(	(	PUNCT
cana-5360	200	16	resp	resp	NOUN
cana-5360	200	17	.	.	PUNCT
cana-5360	201	1	𝒫ℱ𝔑𝛿𝒫𝑐𝑠	𝒫ℱ𝔑𝛿𝒫𝑐𝑠	PROPN
cana-5360	201	2	,	,	PUNCT
cana-5360	201	3	𝒫ℱ𝔑𝛿𝒮𝑐𝑠	𝒫ℱ𝔑𝛿𝒮𝑐𝑠	PROPN
cana-5360	201	4	,	,	PUNCT
cana-5360	201	5	𝒫ℱ𝔑𝛿𝛼𝑐𝑠	𝒫ℱ𝔑𝛿𝛼𝑐𝑠	NOUN
cana-5360	201	6	and	and	CCONJ
cana-5360	201	7	𝒫ℱ𝔑𝛿𝛽𝑐𝑠	𝒫ℱ𝔑𝛿𝛽𝑐𝑠	PROPN
cana-5360	201	8	)	)	PUNCT
cana-5360	201	9	)	)	PUNCT
cana-5360	201	10	in	in	ADP
cana-5360	201	11	𝑈.	𝑈.	PROPN
cana-5360	201	12	the	the	DET
cana-5360	201	13	family	family	NOUN
cana-5360	201	14	of	of	ADP
cana-5360	201	15	all	all	DET
cana-5360	201	16	𝒫ℱ𝔑𝛿𝑜𝑠	𝒫ℱ𝔑𝛿𝑜𝑠	PROPN
cana-5360	201	17	(	(	PUNCT
cana-5360	201	18	resp	resp	NOUN
cana-5360	201	19	.	.	PUNCT
cana-5360	202	1	𝒫ℱ𝔑𝛿𝑐𝑠	𝒫ℱ𝔑𝛿𝑐𝑠	PROPN
cana-5360	202	2	,	,	PUNCT
cana-5360	202	3	𝒫ℱ𝔑𝛿𝒫𝑜𝑠	𝒫ℱ𝔑𝛿𝒫𝑜𝑠	PROPN
cana-5360	202	4	,	,	PUNCT
cana-5360	202	5	𝒫ℱ𝔑𝛿𝒫𝑐𝑠	𝒫ℱ𝔑𝛿𝒫𝑐𝑠	PROPN
cana-5360	202	6	,	,	PUNCT
cana-5360	202	7	𝒫ℱ𝔑𝛿𝒮𝑜𝑠	𝒫ℱ𝔑𝛿𝒮𝑜𝑠	PROPN
cana-5360	202	8	,	,	PUNCT
cana-5360	202	9	𝒫ℱ𝔑𝛿𝒮𝑐𝑠	𝒫ℱ𝔑𝛿𝒮𝑐𝑠	PROPN
cana-5360	202	10	,	,	PUNCT
cana-5360	202	11	𝒫ℱ𝔑𝛿𝛼𝑜𝑠	𝒫ℱ𝔑𝛿𝛼𝑜𝑠	PROPN
cana-5360	202	12	,	,	PUNCT
cana-5360	202	13	𝒫ℱ𝔑𝛿𝛼𝑐𝑠	𝒫ℱ𝔑𝛿𝛼𝑐𝑠	PROPN
cana-5360	202	14	,	,	PUNCT
cana-5360	202	15	𝒫ℱ𝔑𝛿𝛽𝑜𝑠	𝒫ℱ𝔑𝛿𝛽𝑜𝑠	PROPN
cana-5360	202	16	and	and	CCONJ
cana-5360	202	17	𝒫ℱ𝔑𝛿𝛽𝑐𝑠	𝒫ℱ𝔑𝛿𝛽𝑐𝑠	PROPN
cana-5360	202	18	)	)	PUNCT
cana-5360	202	19	of	of	ADP
cana-5360	202	20	𝑈	𝑈	PROPN
cana-5360	202	21	is	be	AUX
cana-5360	202	22	denoted	denote	VERB
cana-5360	202	23	by	by	ADP
cana-5360	202	24	𝒫ℱ𝔑𝛿𝑂𝑆(𝑈	𝒫ℱ𝔑𝛿𝑂𝑆(𝑈	NOUN
cana-5360	202	25	)	)	PUNCT
cana-5360	202	26	,	,	PUNCT
cana-5360	202	27	(	(	PUNCT
cana-5360	202	28	resp	resp	NOUN
cana-5360	202	29	.	.	PUNCT
cana-5360	203	1	𝒫ℱ𝔑𝛿𝐶𝑆(𝑈	𝒫ℱ𝔑𝛿𝐶𝑆(𝑈	X
cana-5360	203	2	)	)	PUNCT
cana-5360	204	1	,	,	PUNCT
cana-5360	204	2	𝒫ℱ𝔑𝛿𝒫𝑂𝑆(𝑈	𝒫ℱ𝔑𝛿𝒫𝑂𝑆(𝑈	NOUN
cana-5360	204	3	)	)	PUNCT
cana-5360	204	4	,	,	PUNCT
cana-5360	204	5	𝒫ℱ𝔑𝛿𝒫𝐶𝑆(𝑈	𝒫ℱ𝔑𝛿𝒫𝐶𝑆(𝑈	PROPN
cana-5360	204	6	)	)	PUNCT
cana-5360	204	7	,	,	PUNCT
cana-5360	204	8	𝒫ℱ𝔑𝛿𝒮𝑂𝑆(𝑈	𝒫ℱ𝔑𝛿𝒮𝑂𝑆(𝑈	NOUN
cana-5360	204	9	)	)	PUNCT
cana-5360	204	10	,	,	PUNCT
cana-5360	204	11	𝒫ℱ𝔑𝛿𝒮𝐶𝑆(𝑈	𝒫ℱ𝔑𝛿𝒮𝐶𝑆(𝑈	ADV
cana-5360	204	12	)	)	PUNCT
cana-5360	204	13	,	,	PUNCT
cana-5360	204	14	𝒫ℱ𝔑𝛿𝛼𝑂𝑆(𝑈	𝒫ℱ𝔑𝛿𝛼𝑂𝑆(𝑈	ADV
cana-5360	204	15	)	)	PUNCT
cana-5360	204	16	,	,	PUNCT
cana-5360	204	17	𝒫ℱ𝔑𝛿𝛼𝐶𝑆(𝑈	𝒫ℱ𝔑𝛿𝛼𝐶𝑆(𝑈	PROPN
cana-5360	204	18	)	)	PUNCT
cana-5360	204	19	,	,	PUNCT
cana-5360	204	20	𝒫ℱ𝔑𝛿𝛽𝑂𝑆(𝑈	𝒫ℱ𝔑𝛿𝛽𝑂𝑆(𝑈	NUM
cana-5360	204	21	)	)	PUNCT
cana-5360	204	22	and	and	CCONJ
cana-5360	204	23	𝒫ℱ𝔑𝛿𝛽𝐶𝑆(𝑈	𝒫ℱ𝔑𝛿𝛽𝐶𝑆(𝑈	NUM
cana-5360	204	24	)	)	PUNCT
cana-5360	204	25	)	)	PUNCT
cana-5360	204	26	.	.	PUNCT
cana-5360	205	1	definition	definition	NOUN
cana-5360	205	2	3.6	3.6	NUM
cana-5360	205	3	let	let	VERB
cana-5360	205	4	(	(	PUNCT
cana-5360	205	5	𝑈	𝑈	PROPN
cana-5360	205	6	,	,	PUNCT
cana-5360	205	7	𝜏𝒫(𝐴	𝜏𝒫(𝐴	NOUN
cana-5360	205	8	)	)	PUNCT
cana-5360	205	9	)	)	PUNCT
cana-5360	205	10	be	be	AUX
cana-5360	205	11	a	a	DET
cana-5360	205	12	𝒫ℱ𝔑𝑡𝑠	𝒫ℱ𝔑𝑡𝑠	NOUN
cana-5360	205	13	with	with	ADP
cana-5360	205	14	respect	respect	NOUN
cana-5360	205	15	to	to	ADP
cana-5360	205	16	𝐴	𝐴	PROPN
cana-5360	205	17	where	where	SCONJ
cana-5360	205	18	𝐴	𝐴	PROPN
cana-5360	205	19	is	be	AUX
cana-5360	205	20	a	a	DET
cana-5360	205	21	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-5360	205	22	of	of	ADP
cana-5360	205	23	𝑈.	𝑈.	PROPN
cana-5360	205	24	let	let	VERB
cana-5360	205	25	𝑆	𝑆	PROPN
cana-5360	205	26	be	be	AUX
cana-5360	205	27	a	a	DET
cana-5360	205	28	𝑝𝑓𝑠	𝑝𝑓𝑠	NOUN
cana-5360	205	29	of	of	ADP
cana-5360	205	30	𝑈.	𝑈.	PROPN
cana-5360	205	31	then	then	ADV
cana-5360	205	32	pythagorean	pythagorean	VERB
cana-5360	205	33	fuzzy	fuzzy	ADJ
cana-5360	205	34	nano	nano	PROPN
cana-5360	206	1	[	[	X
cana-5360	206	2	(	(	PUNCT
cana-5360	206	3	i	i	NOUN
cana-5360	206	4	)	)	PUNCT
cana-5360	206	5	]	]	PUNCT
cana-5360	207	1	1	1	X
cana-5360	207	2	.	.	PUNCT
cana-5360	208	1	𝛿	𝛿	PRON
cana-5360	208	2	pre	pre	X
cana-5360	208	3	(	(	PUNCT
cana-5360	208	4	resp	resp	NOUN
cana-5360	208	5	.	.	PUNCT
cana-5360	209	1	𝛿	𝛿	ADJ
cana-5360	209	2	semi	semi	ADJ
cana-5360	209	3	,	,	PUNCT
cana-5360	209	4	𝛿𝛼	𝛿𝛼	ADP
cana-5360	209	5	and	and	CCONJ
cana-5360	209	6	𝛿𝛽	𝛿𝛽	ADJ
cana-5360	209	7	)	)	PUNCT
cana-5360	209	8	interior	interior	NOUN
cana-5360	209	9	of	of	ADP
cana-5360	209	10	𝑆	𝑆	PROPN
cana-5360	209	11	(	(	PUNCT
cana-5360	209	12	briefly	briefly	ADV
cana-5360	209	13	,	,	PUNCT
cana-5360	209	14	𝒫ℱ𝔑𝛿𝒫𝑖𝑛𝑡(𝑆	𝒫ℱ𝔑𝛿𝒫𝑖𝑛𝑡(𝑆	PROPN
cana-5360	209	15	)	)	PUNCT
cana-5360	209	16	(	(	PUNCT
cana-5360	209	17	resp	resp	NOUN
cana-5360	209	18	.	.	PUNCT
cana-5360	210	1	𝒫ℱ𝔑𝛿𝒮𝑖𝑛𝑡(𝑆	𝒫ℱ𝔑𝛿𝒮𝑖𝑛𝑡(𝑆	PROPN
cana-5360	210	2	)	)	PUNCT
cana-5360	210	3	,	,	PUNCT
cana-5360	210	4	𝒫ℱ𝔑𝛿𝛼𝑖𝑛𝑡(𝑆	𝒫ℱ𝔑𝛿𝛼𝑖𝑛𝑡(𝑆	X
cana-5360	210	5	)	)	PUNCT
cana-5360	210	6	and	and	CCONJ
cana-5360	210	7	𝒫ℱ𝔑𝛿𝛽𝑖𝑛𝑡(𝑆	𝒫ℱ𝔑𝛿𝛽𝑖𝑛𝑡(𝑆	NOUN
cana-5360	210	8	)	)	PUNCT
cana-5360	210	9	)	)	PUNCT
cana-5360	210	10	)	)	PUNCT
cana-5360	210	11	is	be	AUX
cana-5360	210	12	defined	define	VERB
cana-5360	210	13	by	by	ADP
cana-5360	210	14	𝒫ℱ𝔑𝛿𝒫𝑖𝑛𝑡(𝑆	𝒫ℱ𝔑𝛿𝒫𝑖𝑛𝑡(𝑆	PROPN
cana-5360	210	15	)	)	PUNCT
cana-5360	210	16	(	(	PUNCT
cana-5360	210	17	resp	resp	NOUN
cana-5360	210	18	.	.	PUNCT
cana-5360	211	1	𝒫ℱ𝔑𝛿𝒮𝑖𝑛𝑡(𝑆	𝒫ℱ𝔑𝛿𝒮𝑖𝑛𝑡(𝑆	PROPN
cana-5360	211	2	)	)	PUNCT
cana-5360	211	3	,	,	PUNCT
cana-5360	211	4	𝒫ℱ𝔑𝛿𝛼𝑖𝑛𝑡(𝑆	𝒫ℱ𝔑𝛿𝛼𝑖𝑛𝑡(𝑆	X
cana-5360	211	5	)	)	PUNCT
cana-5360	211	6	and	and	CCONJ
cana-5360	211	7	𝒫ℱ𝔑𝛿𝛽𝑖𝑛𝑡(𝑆	𝒫ℱ𝔑𝛿𝛽𝑖𝑛𝑡(𝑆	NOUN
cana-5360	211	8	)	)	PUNCT
cana-5360	211	9	)	)	PUNCT
cana-5360	212	1	=	=	SYM
cana-5360	212	2	∪	∪	X
cana-5360	212	3	{	{	PUNCT
cana-5360	212	4	𝐼	𝐼	NOUN
cana-5360	212	5	:	:	PUNCT
cana-5360	212	6	𝐼	𝐼	PROPN
cana-5360	212	7	⊆	⊆	NUM
cana-5360	212	8	𝑆	𝑆	PROPN
cana-5360	212	9	&	&	CCONJ
cana-5360	212	10	𝐼isa𝒫ℱ𝔑𝛿𝒫𝑜	𝐼isa𝒫ℱ𝔑𝛿𝒫𝑜	NOUN
cana-5360	212	11	(	(	PUNCT
cana-5360	212	12	resp	resp	NOUN
cana-5360	212	13	.	.	PUNCT
cana-5360	213	1	𝒫ℱ𝔑𝛿𝒮𝑜	𝒫ℱ𝔑𝛿𝒮𝑜	PROPN
cana-5360	213	2	,	,	PUNCT
cana-5360	213	3	𝒫ℱ𝔑𝛿𝛼𝑜	𝒫ℱ𝔑𝛿𝛼𝑜	PROPN
cana-5360	213	4	&	&	CCONJ
cana-5360	213	5	𝒫ℱ𝔑𝛿𝛽𝑜	𝒫ℱ𝔑𝛿𝛽𝑜	PROPN
cana-5360	213	6	)	)	PUNCT
cana-5360	213	7	set	set	VERB
cana-5360	213	8	in𝑈	in𝑈	NOUN
cana-5360	213	9	}	}	PUNCT
cana-5360	213	10	.	.	PUNCT
cana-5360	214	1	2	2	X
cana-5360	214	2	.	.	X
cana-5360	214	3	𝛿	𝛿	PRON
cana-5360	214	4	pre	pre	X
cana-5360	214	5	(	(	PUNCT
cana-5360	214	6	resp	resp	NOUN
cana-5360	214	7	.	.	PUNCT
cana-5360	215	1	𝛿	𝛿	ADJ
cana-5360	215	2	semi	semi	ADJ
cana-5360	215	3	,	,	PUNCT
cana-5360	215	4	𝛿𝛼	𝛿𝛼	ADP
cana-5360	215	5	and	and	CCONJ
cana-5360	215	6	𝛿𝛽	𝛿𝛽	ADJ
cana-5360	215	7	)	)	PUNCT
cana-5360	215	8	closure	closure	NOUN
cana-5360	215	9	of	of	ADP
cana-5360	215	10	𝑆	𝑆	PROPN
cana-5360	215	11	(	(	PUNCT
cana-5360	215	12	briefly	briefly	ADV
cana-5360	215	13	,	,	PUNCT
cana-5360	215	14	𝒫ℱ𝔑𝛿𝒫𝑐𝑙(𝑆	𝒫ℱ𝔑𝛿𝒫𝑐𝑙(𝑆	PROPN
cana-5360	215	15	)	)	PUNCT
cana-5360	215	16	(	(	PUNCT
cana-5360	215	17	resp	resp	NOUN
cana-5360	215	18	.	.	PUNCT
cana-5360	216	1	𝒫ℱ𝔑𝛿𝒮𝑐𝑙(𝑆	𝒫ℱ𝔑𝛿𝒮𝑐𝑙(𝑆	NOUN
cana-5360	216	2	)	)	PUNCT
cana-5360	216	3	,	,	PUNCT
cana-5360	216	4	𝒫ℱ𝔑𝛿𝛼𝑐𝑙(𝑆	𝒫ℱ𝔑𝛿𝛼𝑐𝑙(𝑆	ADP
cana-5360	216	5	)	)	PUNCT
cana-5360	216	6	and	and	CCONJ
cana-5360	216	7	𝒫ℱ𝔑𝛿𝛽𝑐𝑙(𝑆	𝒫ℱ𝔑𝛿𝛽𝑐𝑙(𝑆	NOUN
cana-5360	216	8	)	)	PUNCT
cana-5360	216	9	)	)	PUNCT
cana-5360	216	10	)	)	PUNCT
cana-5360	217	1	is	be	AUX
cana-5360	217	2	defined	define	VERB
cana-5360	217	3	by	by	ADP
cana-5360	217	4	𝒫ℱ𝔑𝛿𝒫𝑐𝑙(𝑆	𝒫ℱ𝔑𝛿𝒫𝑐𝑙(𝑆	PROPN
cana-5360	217	5	)	)	PUNCT
cana-5360	217	6	(	(	PUNCT
cana-5360	217	7	resp	resp	NOUN
cana-5360	217	8	.	.	PUNCT
cana-5360	218	1	𝒫ℱ𝔑𝛿𝒮𝑐𝑙(𝑆	𝒫ℱ𝔑𝛿𝒮𝑐𝑙(𝑆	NOUN
cana-5360	218	2	)	)	PUNCT
cana-5360	218	3	,	,	PUNCT
cana-5360	218	4	𝒫ℱ𝔑𝛿𝛼𝑐𝑙(𝑆	𝒫ℱ𝔑𝛿𝛼𝑐𝑙(𝑆	ADP
cana-5360	218	5	)	)	PUNCT
cana-5360	218	6	and	and	CCONJ
cana-5360	218	7	𝒫ℱ𝔑𝛿𝛽𝑐𝑙(𝑆	𝒫ℱ𝔑𝛿𝛽𝑐𝑙(𝑆	NOUN
cana-5360	218	8	)	)	PUNCT
cana-5360	218	9	)	)	PUNCT
cana-5360	219	1	=	=	NOUN
cana-5360	219	2	∩	∩	X
cana-5360	219	3	{	{	PUNCT
cana-5360	219	4	𝐴	𝐴	PROPN
cana-5360	219	5	:	:	PUNCT
cana-5360	219	6	𝑆	𝑆	PROPN
cana-5360	219	7	⊆	⊆	NUM
cana-5360	219	8	𝐴	𝐴	PROPN
cana-5360	219	9	&	&	CCONJ
cana-5360	219	10	𝐴isa𝒫ℱ𝔑𝛿𝒫𝑐	𝐴isa𝒫ℱ𝔑𝛿𝒫𝑐	PROPN
cana-5360	219	11	(	(	PUNCT
cana-5360	219	12	resp	resp	NOUN
cana-5360	219	13	.	.	PUNCT
cana-5360	220	1	𝒫ℱ𝔑𝛿𝒮𝑐	𝒫ℱ𝔑𝛿𝒮𝑐	PROPN
cana-5360	220	2	,	,	PUNCT
cana-5360	220	3	𝒫ℱ𝔑𝛿𝛼𝑐	𝒫ℱ𝔑𝛿𝛼𝑐	PROPN
cana-5360	220	4	&	&	CCONJ
cana-5360	220	5	𝒫ℱ𝔑𝛿𝛽𝑐	𝒫ℱ𝔑𝛿𝛽𝑐	PROPN
cana-5360	220	6	)	)	PUNCT
cana-5360	220	7	set	set	VERB
cana-5360	220	8	in	in	ADP
cana-5360	220	9	𝑈	𝑈	PROPN
cana-5360	220	10	}	}	PUNCT
cana-5360	220	11	.	.	PUNCT
cana-5360	221	1	definition	definition	NOUN
cana-5360	221	2	3.7	3.7	NUM
cana-5360	221	3	let	let	VERB
cana-5360	221	4	(	(	PUNCT
cana-5360	221	5	𝑈1	𝑈1	NOUN
cana-5360	221	6	,	,	PUNCT
cana-5360	221	7	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	221	8	)	)	PUNCT
cana-5360	221	9	)	)	PUNCT
cana-5360	222	1	and	and	CCONJ
cana-5360	222	2	(	(	PUNCT
cana-5360	222	3	𝑈2	𝑈2	NOUN
cana-5360	222	4	,	,	PUNCT
cana-5360	222	5	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	222	6	)	)	PUNCT
cana-5360	222	7	)	)	PUNCT
cana-5360	222	8	be	be	AUX
cana-5360	222	9	two	two	NUM
cana-5360	222	10	𝑃𝐹𝒩𝑡𝑠	𝑃𝐹𝒩𝑡𝑠	NOUN
cana-5360	222	11	’	'	PUNCT
cana-5360	222	12	s.	s.	PROPN
cana-5360	222	13	then	then	ADV
cana-5360	222	14	a	a	DET
cana-5360	222	15	function	function	NOUN
cana-5360	222	16	ℎ𝑃	ℎ𝑃	NOUN
cana-5360	222	17	:	:	PUNCT
cana-5360	222	18	(	(	PUNCT
cana-5360	222	19	𝑈1	𝑈1	NOUN
cana-5360	222	20	,	,	PUNCT
cana-5360	222	21	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	222	22	)	)	PUNCT
cana-5360	222	23	)	)	PUNCT
cana-5360	223	1	→	→	SYM
cana-5360	223	2	(	(	PUNCT
cana-5360	223	3	𝑈2	𝑈2	PROPN
cana-5360	223	4	,	,	PUNCT
cana-5360	223	5	𝜏𝑝(𝐴2	𝜏𝑝(𝐴2	NUM
cana-5360	223	6	)	)	PUNCT
cana-5360	223	7	)	)	PUNCT
cana-5360	223	8	is	be	AUX
cana-5360	223	9	said	say	VERB
cana-5360	223	10	to	to	PART
cana-5360	223	11	be	be	AUX
cana-5360	223	12	a	a	DET
cana-5360	223	13	pythagorean	pythagorean	ADJ
cana-5360	223	14	fuzzy	fuzzy	ADJ
cana-5360	223	15	nano	nano	PROPN
cana-5360	223	16	𝛿	𝛿	ADJ
cana-5360	223	17	(	(	PUNCT
cana-5360	223	18	resp	resp	NOUN
cana-5360	223	19	.	.	PUNCT
cana-5360	224	1	𝛿	𝛿	DET
cana-5360	224	2	pre	pre	NOUN
cana-5360	224	3	,	,	PUNCT
cana-5360	224	4	𝛿	𝛿	ADJ
cana-5360	224	5	semi	semi	ADJ
cana-5360	224	6	,	,	PUNCT
cana-5360	224	7	𝛿𝛼	𝛿𝛼	ADP
cana-5360	224	8	and	and	CCONJ
cana-5360	224	9	𝛿𝛽	𝛿𝛽	VERB
cana-5360	224	10	)	)	PUNCT
cana-5360	224	11	continuous	continuous	ADJ
cana-5360	224	12	(	(	PUNCT
cana-5360	224	13	briefly	briefly	ADV
cana-5360	224	14	,	,	PUNCT
cana-5360	224	15	𝒫ℱ𝒩𝛿𝐶𝑡𝑠	𝒫ℱ𝒩𝛿𝐶𝑡𝑠	PROPN
cana-5360	224	16	(	(	PUNCT
cana-5360	224	17	resp	resp	NOUN
cana-5360	224	18	.	.	PUNCT
cana-5360	225	1	𝒫ℱ𝒩𝛿𝒫𝐶𝑡𝑠	𝒫ℱ𝒩𝛿𝒫𝐶𝑡𝑠	PRON
cana-5360	225	2	,	,	PUNCT
cana-5360	225	3	𝒫ℱ𝒩𝛿𝒮𝐶𝑡𝑠	𝒫ℱ𝒩𝛿𝒮𝐶𝑡𝑠	AUX
cana-5360	225	4	,	,	PUNCT
cana-5360	225	5	𝒫ℱ𝒩𝛿𝛼𝐶𝑡𝑠	𝒫ℱ𝒩𝛿𝛼𝐶𝑡𝑠	PROPN
cana-5360	225	6	and	and	CCONJ
cana-5360	225	7	𝒫ℱ𝒩𝛿𝛽𝐶𝑡𝑠	𝒫ℱ𝒩𝛿𝛽𝐶𝑡𝑠	PROPN
cana-5360	225	8	)	)	PUNCT
cana-5360	225	9	)	)	PUNCT
cana-5360	225	10	function	function	VERB
cana-5360	225	11	if	if	SCONJ
cana-5360	225	12	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	225	13	−1(𝐺	−1(𝐺	NOUN
cana-5360	225	14	)	)	PUNCT
cana-5360	225	15	is	be	AUX
cana-5360	225	16	𝒫ℱ𝒩𝛿𝑜	𝒫ℱ𝒩𝛿𝑜	PROPN
cana-5360	225	17	(	(	PUNCT
cana-5360	225	18	resp	resp	NOUN
cana-5360	225	19	.	.	PUNCT
cana-5360	226	1	𝒫ℱ𝒩𝛿𝒫𝑜	𝒫ℱ𝒩𝛿𝒫𝑜	NOUN
cana-5360	226	2	,	,	PUNCT
cana-5360	226	3	𝒫ℱ𝒩𝛿𝒮𝑜	𝒫ℱ𝒩𝛿𝒮𝑜	PROPN
cana-5360	226	4	,	,	PUNCT
cana-5360	226	5	𝒫ℱ𝒩𝛿𝛼𝑜	𝒫ℱ𝒩𝛿𝛼𝑜	PROPN
cana-5360	226	6	&	&	CCONJ
cana-5360	226	7	communications	communication	NOUN
cana-5360	226	8	on	on	ADP
cana-5360	226	9	applied	apply	VERB
cana-5360	226	10	nonlinear	nonlinear	ADJ
cana-5360	226	11	analysis	analysis	NOUN
cana-5360	226	12	issn	issn	NOUN
cana-5360	226	13	:	:	PUNCT
cana-5360	226	14	1074	1074	NUM
cana-5360	226	15	-	-	PUNCT
cana-5360	226	16	133x	133x	NUM
cana-5360	226	17	vol	vol	VERB
cana-5360	226	18	32	32	NUM
cana-5360	226	19	no	no	NOUN
cana-5360	226	20	.	.	PUNCT
cana-5360	227	1	10s	10	NOUN
cana-5360	227	2	(	(	PUNCT
cana-5360	227	3	2025	2025	NUM
cana-5360	227	4	)	)	PUNCT
cana-5360	227	5	1932	1932	NUM
cana-5360	227	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5360	227	7	𝒫ℱ𝒩𝛿𝛽𝑜	𝒫ℱ𝒩𝛿𝛽𝑜	PROPN
cana-5360	227	8	)	)	PUNCT
cana-5360	227	9	set	set	VERB
cana-5360	227	10	in	in	ADP
cana-5360	227	11	𝑈1	𝑈1	NOUN
cana-5360	227	12	for	for	ADP
cana-5360	227	13	all	all	DET
cana-5360	227	14	𝒫ℱ𝒩𝑜	𝒫ℱ𝒩𝑜	PROPN
cana-5360	227	15	set	set	VERB
cana-5360	227	16	𝐺	𝐺	PROPN
cana-5360	227	17	in	in	ADP
cana-5360	227	18	𝑈2	𝑈2	PROPN
cana-5360	227	19	.	.	PUNCT
cana-5360	228	1	definition	definition	NOUN
cana-5360	228	2	3.8	3.8	NUM
cana-5360	228	3	let	let	VERB
cana-5360	228	4	(	(	PUNCT
cana-5360	228	5	𝑈1	𝑈1	NOUN
cana-5360	228	6	,	,	PUNCT
cana-5360	228	7	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	228	8	)	)	PUNCT
cana-5360	228	9	)	)	PUNCT
cana-5360	229	1	and	and	CCONJ
cana-5360	229	2	(	(	PUNCT
cana-5360	229	3	𝑈2	𝑈2	NOUN
cana-5360	229	4	,	,	PUNCT
cana-5360	229	5	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	229	6	)	)	PUNCT
cana-5360	229	7	)	)	PUNCT
cana-5360	229	8	be	be	AUX
cana-5360	229	9	two	two	NUM
cana-5360	229	10	𝑃𝐹𝒩𝑡𝑠	𝑃𝐹𝒩𝑡𝑠	NOUN
cana-5360	229	11	’	'	PUNCT
cana-5360	229	12	s.	s.	PROPN
cana-5360	229	13	then	then	ADV
cana-5360	229	14	a	a	DET
cana-5360	229	15	function	function	NOUN
cana-5360	229	16	ℎ𝑃	ℎ𝑃	NOUN
cana-5360	229	17	:	:	PUNCT
cana-5360	229	18	(	(	PUNCT
cana-5360	229	19	𝑈1	𝑈1	NOUN
cana-5360	229	20	,	,	PUNCT
cana-5360	229	21	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	229	22	)	)	PUNCT
cana-5360	229	23	)	)	PUNCT
cana-5360	230	1	→	→	SYM
cana-5360	230	2	(	(	PUNCT
cana-5360	230	3	𝑈2	𝑈2	PROPN
cana-5360	230	4	,	,	PUNCT
cana-5360	230	5	𝜏𝑝(𝐴2	𝜏𝑝(𝐴2	NUM
cana-5360	230	6	)	)	PUNCT
cana-5360	230	7	)	)	PUNCT
cana-5360	230	8	is	be	AUX
cana-5360	230	9	said	say	VERB
cana-5360	230	10	to	to	PART
cana-5360	230	11	be	be	AUX
cana-5360	230	12	a	a	DET
cana-5360	230	13	pythagorean	pythagorean	ADJ
cana-5360	230	14	fuzzy	fuzzy	ADJ
cana-5360	230	15	nano	nano	PROPN
cana-5360	230	16	contra	contra	PROPN
cana-5360	230	17	𝛿	𝛿	PROPN
cana-5360	230	18	(	(	PUNCT
cana-5360	230	19	resp	resp	NOUN
cana-5360	230	20	.	.	PUNCT
cana-5360	231	1	𝛿	𝛿	DET
cana-5360	231	2	pre	pre	NOUN
cana-5360	231	3	,	,	PUNCT
cana-5360	231	4	𝛿	𝛿	ADJ
cana-5360	231	5	semi	semi	ADJ
cana-5360	231	6	,	,	PUNCT
cana-5360	231	7	𝛿𝛼	𝛿𝛼	ADP
cana-5360	231	8	and	and	CCONJ
cana-5360	231	9	𝛿𝛽	𝛿𝛽	VERB
cana-5360	231	10	)	)	PUNCT
cana-5360	231	11	continuous	continuous	ADJ
cana-5360	231	12	(	(	PUNCT
cana-5360	231	13	briefly	briefly	ADV
cana-5360	231	14	,	,	PUNCT
cana-5360	231	15	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	PROPN
cana-5360	231	16	(	(	PUNCT
cana-5360	231	17	resp	resp	NOUN
cana-5360	231	18	.	.	PUNCT
cana-5360	232	1	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	PROPN
cana-5360	232	2	,	,	PUNCT
cana-5360	232	3	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	PROPN
cana-5360	232	4	,	,	PUNCT
cana-5360	232	5	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐶𝑡𝑠	PRON
cana-5360	232	6	and	and	CCONJ
cana-5360	232	7	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠	NUM
cana-5360	232	8	)	)	PUNCT
cana-5360	232	9	)	)	PUNCT
cana-5360	232	10	function	function	VERB
cana-5360	232	11	if	if	SCONJ
cana-5360	232	12	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	232	13	−1(𝐺	−1(𝐺	NOUN
cana-5360	232	14	)	)	PUNCT
cana-5360	232	15	is	be	AUX
cana-5360	232	16	𝒫ℱ𝒩𝛿𝑐	𝒫ℱ𝒩𝛿𝑐	NUM
cana-5360	232	17	(	(	PUNCT
cana-5360	232	18	resp	resp	NOUN
cana-5360	232	19	.	.	PUNCT
cana-5360	233	1	𝒫ℱ𝒩𝛿𝒫𝑐	𝒫ℱ𝒩𝛿𝒫𝑐	PROPN
cana-5360	233	2	,	,	PUNCT
cana-5360	233	3	𝒫ℱ𝒩𝛿𝒮𝑐	𝒫ℱ𝒩𝛿𝒮𝑐	PROPN
cana-5360	233	4	,	,	PUNCT
cana-5360	233	5	𝒫ℱ𝒩𝛿𝛼𝑐	𝒫ℱ𝒩𝛿𝛼𝑐	PROPN
cana-5360	233	6	&	&	CCONJ
cana-5360	233	7	𝒫ℱ𝒩𝛿𝛽𝑐	𝒫ℱ𝒩𝛿𝛽𝑐	PROPN
cana-5360	233	8	)	)	PUNCT
cana-5360	233	9	set	set	VERB
cana-5360	233	10	in	in	ADP
cana-5360	233	11	𝑈1	𝑈1	NOUN
cana-5360	233	12	for	for	ADP
cana-5360	233	13	all	all	DET
cana-5360	233	14	𝒫ℱ𝒩𝑜	𝒫ℱ𝒩𝑜	PROPN
cana-5360	233	15	set	set	VERB
cana-5360	233	16	𝐺	𝐺	PROPN
cana-5360	233	17	in	in	ADP
cana-5360	233	18	𝑈2	𝑈2	PROPN
cana-5360	233	19	.	.	PUNCT
cana-5360	234	1	lemma	lemma	PROPN
cana-5360	234	2	3.1	3.1	NUM
cana-5360	234	3	let	let	VERB
cana-5360	234	4	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	234	5	:	:	PUNCT
cana-5360	234	6	(	(	PUNCT
cana-5360	234	7	𝑈1	𝑈1	NOUN
cana-5360	234	8	,	,	PUNCT
cana-5360	234	9	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	234	10	)	)	PUNCT
cana-5360	234	11	)	)	PUNCT
cana-5360	234	12	→	→	SYM
cana-5360	234	13	(	(	PUNCT
cana-5360	234	14	𝑈2	𝑈2	NOUN
cana-5360	234	15	,	,	PUNCT
cana-5360	234	16	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	234	17	)	)	PUNCT
cana-5360	234	18	)	)	PUNCT
cana-5360	234	19	be	be	AUX
cana-5360	234	20	a	a	DET
cana-5360	234	21	function	function	NOUN
cana-5360	234	22	.	.	PUNCT
cana-5360	235	1	then	then	ADV
cana-5360	235	2	the	the	DET
cana-5360	235	3	following	follow	VERB
cana-5360	235	4	statements	statement	NOUN
cana-5360	235	5	hold	hold	VERB
cana-5360	235	6	.	.	PUNCT
cana-5360	236	1	1	1	X
cana-5360	236	2	.	.	X
cana-5360	236	3	if	if	SCONJ
cana-5360	236	4	𝑆	𝑆	PROPN
cana-5360	236	5	and	and	CCONJ
cana-5360	236	6	𝑇	𝑇	PROPN
cana-5360	236	7	are	be	AUX
cana-5360	236	8	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-5360	236	9	’s	’s	NOUN
cana-5360	236	10	of	of	ADP
cana-5360	236	11	𝑈1	𝑈1	NOUN
cana-5360	236	12	such	such	ADJ
cana-5360	236	13	that	that	SCONJ
cana-5360	236	14	𝑆	𝑆	PROPN
cana-5360	236	15	⊆	⊆	NUM
cana-5360	236	16	𝑇	𝑇	PROPN
cana-5360	236	17	,	,	PUNCT
cana-5360	236	18	then	then	ADV
cana-5360	236	19	ℎ𝑃(𝑆	ℎ𝑃(𝑆	NUM
cana-5360	236	20	)	)	PUNCT
cana-5360	236	21	⊆	⊆	NUM
cana-5360	236	22	ℎ𝑃(𝑇	ℎ𝑃(𝑇	NOUN
cana-5360	236	23	)	)	PUNCT
cana-5360	236	24	.	.	PUNCT
cana-5360	237	1	2	2	X
cana-5360	237	2	.	.	X
cana-5360	237	3	if	if	SCONJ
cana-5360	237	4	𝑆	𝑆	PROPN
cana-5360	237	5	and	and	CCONJ
cana-5360	237	6	𝑇	𝑇	PROPN
cana-5360	237	7	are	be	AUX
cana-5360	237	8	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-5360	237	9	’s	’s	NOUN
cana-5360	237	10	of	of	ADP
cana-5360	237	11	𝑈2	𝑈2	PROPN
cana-5360	237	12	such	such	ADJ
cana-5360	237	13	that	that	SCONJ
cana-5360	237	14	𝑆	𝑆	PROPN
cana-5360	237	15	⊆	⊆	NUM
cana-5360	237	16	𝑇	𝑇	PROPN
cana-5360	237	17	,	,	PUNCT
cana-5360	237	18	then	then	ADV
cana-5360	237	19	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	237	20	−1(𝑆	−1(𝑆	PROPN
cana-5360	237	21	)	)	PUNCT
cana-5360	237	22	⊆	⊆	NUM
cana-5360	237	23	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	237	24	−1(𝑇	−1(𝑇	PROPN
cana-5360	237	25	)	)	PUNCT
cana-5360	237	26	.	.	PUNCT
cana-5360	238	1	lemma	lemma	PROPN
cana-5360	238	2	3.2	3.2	NUM
cana-5360	238	3	let	let	VERB
cana-5360	238	4	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	238	5	:	:	PUNCT
cana-5360	238	6	(	(	PUNCT
cana-5360	238	7	𝑈1	𝑈1	NOUN
cana-5360	238	8	,	,	PUNCT
cana-5360	238	9	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	238	10	)	)	PUNCT
cana-5360	238	11	)	)	PUNCT
cana-5360	238	12	→	→	SYM
cana-5360	238	13	(	(	PUNCT
cana-5360	238	14	𝑈2	𝑈2	NOUN
cana-5360	238	15	,	,	PUNCT
cana-5360	238	16	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	238	17	)	)	PUNCT
cana-5360	238	18	)	)	PUNCT
cana-5360	238	19	be	be	AUX
cana-5360	238	20	a	a	DET
cana-5360	238	21	function	function	NOUN
cana-5360	238	22	.	.	PUNCT
cana-5360	239	1	if	if	SCONJ
cana-5360	239	2	𝑆	𝑆	PROPN
cana-5360	239	3	is	be	AUX
cana-5360	239	4	a	a	DET
cana-5360	239	5	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-5360	239	6	of	of	ADP
cana-5360	239	7	𝑈1	𝑈1	NOUN
cana-5360	239	8	and	and	CCONJ
cana-5360	239	9	𝑇	𝑇	PROPN
cana-5360	239	10	is	be	AUX
cana-5360	239	11	a	a	DET
cana-5360	239	12	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-5360	239	13	of	of	ADP
cana-5360	239	14	𝑈2	𝑈2	PROPN
cana-5360	239	15	.	.	PUNCT
cana-5360	240	1	then	then	ADV
cana-5360	240	2	1	1	X
cana-5360	240	3	.	.	PUNCT
cana-5360	240	4	ℎ𝑃(ℎ𝑃	ℎ𝑃(ℎ𝑃	PROPN
cana-5360	240	5	−1(𝑆	−1(𝑆	ADV
cana-5360	240	6	)	)	PUNCT
cana-5360	240	7	)	)	PUNCT
cana-5360	241	1	⊆	⊆	X
cana-5360	241	2	𝑆	𝑆	PROPN
cana-5360	241	3	2	2	NUM
cana-5360	241	4	.	.	PUNCT
cana-5360	241	5	ℎ𝑃(ℎ𝑃	ℎ𝑃(ℎ𝑃	PROPN
cana-5360	241	6	−1(𝑆	−1(𝑆	ADV
cana-5360	241	7	)	)	PUNCT
cana-5360	241	8	)	)	PUNCT
cana-5360	242	1	=	=	SYM
cana-5360	242	2	𝑆	𝑆	PROPN
cana-5360	242	3	⇔	⇔	PROPN
cana-5360	242	4	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	242	5	is	be	AUX
cana-5360	242	6	surjective	surjective	ADJ
cana-5360	242	7	.	.	PUNCT
cana-5360	243	1	3	3	X
cana-5360	243	2	.	.	X
cana-5360	243	3	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	243	4	−1(ℎ𝑃(𝑆	−1(ℎ𝑃(𝑆	NOUN
cana-5360	243	5	)	)	PUNCT
cana-5360	243	6	)	)	PUNCT
cana-5360	244	1	⊇	⊇	PROPN
cana-5360	244	2	𝑆	𝑆	PROPN
cana-5360	244	3	4	4	NUM
cana-5360	244	4	.	.	PUNCT
cana-5360	245	1	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	245	2	−1(ℎ𝑃(𝑆	−1(ℎ𝑃(𝑆	NOUN
cana-5360	245	3	)	)	PUNCT
cana-5360	245	4	)	)	PUNCT
cana-5360	246	1	=	=	PUNCT
cana-5360	246	2	𝑆	𝑆	PROPN
cana-5360	246	3	whenever	whenever	SCONJ
cana-5360	246	4	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	246	5	is	be	AUX
cana-5360	246	6	injective	injective	ADJ
cana-5360	246	7	.	.	PUNCT
cana-5360	247	1	theorem	theorem	VERB
cana-5360	247	2	3.1	3.1	NUM
cana-5360	247	3	let	let	NOUN
cana-5360	247	4	(	(	PUNCT
cana-5360	247	5	𝑈1	𝑈1	NOUN
cana-5360	247	6	,	,	PUNCT
cana-5360	247	7	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	247	8	)	)	PUNCT
cana-5360	247	9	)	)	PUNCT
cana-5360	248	1	and	and	CCONJ
cana-5360	248	2	(	(	PUNCT
cana-5360	248	3	𝑈2	𝑈2	NOUN
cana-5360	248	4	,	,	PUNCT
cana-5360	248	5	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	248	6	)	)	PUNCT
cana-5360	248	7	)	)	PUNCT
cana-5360	248	8	be	be	AUX
cana-5360	248	9	two	two	NUM
cana-5360	248	10	𝑃𝑁𝒩𝑡𝑠	𝑃𝑁𝒩𝑡𝑠	NOUN
cana-5360	248	11	’s	’s	NOUN
cana-5360	248	12	and	and	CCONJ
cana-5360	248	13	let	let	VERB
cana-5360	248	14	ℎ𝑃	ℎ𝑃	NOUN
cana-5360	248	15	:	:	PUNCT
cana-5360	248	16	(	(	PUNCT
cana-5360	248	17	𝑈1	𝑈1	NOUN
cana-5360	248	18	,	,	PUNCT
cana-5360	248	19	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	248	20	)	)	PUNCT
cana-5360	248	21	)	)	PUNCT
cana-5360	249	1	→	→	SYM
cana-5360	249	2	(	(	PUNCT
cana-5360	249	3	𝑈2	𝑈2	NOUN
cana-5360	249	4	,	,	PUNCT
cana-5360	249	5	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	249	6	)	)	PUNCT
cana-5360	249	7	)	)	PUNCT
cana-5360	249	8	,	,	PUNCT
cana-5360	249	9	then	then	ADV
cana-5360	249	10	(	(	PUNCT
cana-5360	249	11	i	i	NOUN
cana-5360	249	12	)	)	PUNCT
cana-5360	249	13	every	every	DET
cana-5360	249	14	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	NOUN
cana-5360	249	15	is	be	AUX
cana-5360	249	16	a	a	DET
cana-5360	249	17	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠.	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠.	PROPN
cana-5360	249	18	(	(	PUNCT
cana-5360	249	19	ii	ii	NOUN
cana-5360	249	20	)	)	PUNCT
cana-5360	249	21	every	every	DET
cana-5360	249	22	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	NOUN
cana-5360	249	23	is	be	AUX
cana-5360	249	24	a	a	DET
cana-5360	249	25	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠.	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠.	PROPN
cana-5360	249	26	(	(	PUNCT
cana-5360	249	27	iii	iii	NOUN
cana-5360	249	28	)	)	PUNCT
cana-5360	249	29	every	every	DET
cana-5360	249	30	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	NOUN
cana-5360	249	31	is	be	AUX
cana-5360	249	32	a	a	DET
cana-5360	249	33	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠.	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠.	PROPN
cana-5360	249	34	(	(	PUNCT
cana-5360	249	35	iv	iv	X
cana-5360	249	36	)	)	PUNCT
cana-5360	249	37	every	every	DET
cana-5360	249	38	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	NOUN
cana-5360	249	39	is	be	AUX
cana-5360	249	40	a	a	DET
cana-5360	249	41	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠.	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠.	PROPN
cana-5360	249	42	(	(	PUNCT
cana-5360	249	43	v	v	NOUN
cana-5360	249	44	)	)	PUNCT
cana-5360	249	45	every	every	DET
cana-5360	249	46	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	PROPN
cana-5360	249	47	is	be	AUX
cana-5360	249	48	a	a	DET
cana-5360	249	49	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠.	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠.	PROPN
cana-5360	249	50	(	(	PUNCT
cana-5360	249	51	vi	vi	NOUN
cana-5360	249	52	)	)	PUNCT
cana-5360	249	53	every	every	PRON
cana-5360	249	54	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐶𝑡𝑠	NOUN
cana-5360	249	55	is	be	AUX
cana-5360	249	56	a	a	DET
cana-5360	249	57	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠.	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠.	PROPN
cana-5360	249	58	(	(	PUNCT
cana-5360	249	59	vii	vii	PROPN
cana-5360	249	60	)	)	PUNCT
cana-5360	249	61	every	every	PRON
cana-5360	249	62	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐶𝑡𝑠	NOUN
cana-5360	249	63	is	be	AUX
cana-5360	249	64	a	a	DET
cana-5360	249	65	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠.	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠.	PROPN
cana-5360	249	66	but	but	CCONJ
cana-5360	249	67	not	not	PART
cana-5360	249	68	converse	converse	NOUN
cana-5360	249	69	.	.	PUNCT
cana-5360	250	1	proof	proof	NOUN
cana-5360	250	2	.	.	PUNCT
cana-5360	251	1	(	(	PUNCT
cana-5360	251	2	i	i	NOUN
cana-5360	251	3	)	)	PUNCT
cana-5360	251	4	let	let	VERB
cana-5360	251	5	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	251	6	:	:	PUNCT
cana-5360	251	7	(	(	PUNCT
cana-5360	251	8	𝑈1	𝑈1	NOUN
cana-5360	251	9	,	,	PUNCT
cana-5360	251	10	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	251	11	)	)	PUNCT
cana-5360	251	12	)	)	PUNCT
cana-5360	251	13	→	→	SYM
cana-5360	251	14	(	(	PUNCT
cana-5360	251	15	𝑈2	𝑈2	NOUN
cana-5360	251	16	,	,	PUNCT
cana-5360	251	17	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	251	18	)	)	PUNCT
cana-5360	251	19	)	)	PUNCT
cana-5360	251	20	be	be	AUX
cana-5360	251	21	a	a	DET
cana-5360	251	22	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠.	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠.	NOUN
cana-5360	251	23	let	let	VERB
cana-5360	251	24	𝑆	𝑆	PROPN
cana-5360	251	25	be	be	AUX
cana-5360	251	26	a	a	DET
cana-5360	251	27	𝒫ℱ𝒩𝑜	𝒫ℱ𝒩𝑜	PROPN
cana-5360	251	28	set	set	VERB
cana-5360	251	29	in	in	ADP
cana-5360	251	30	(	(	PUNCT
cana-5360	251	31	𝑈2	𝑈2	NOUN
cana-5360	251	32	,	,	PUNCT
cana-5360	251	33	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	251	34	)	)	PUNCT
cana-5360	251	35	)	)	PUNCT
cana-5360	251	36	.	.	PUNCT
cana-5360	252	1	then	then	ADV
cana-5360	252	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	252	3	−1(𝑆	−1(𝑆	PROPN
cana-5360	252	4	)	)	PUNCT
cana-5360	252	5	is	be	AUX
cana-5360	252	6	𝒫ℱ𝒩𝛿𝑐	𝒫ℱ𝒩𝛿𝑐	NUM
cana-5360	252	7	set	set	NOUN
cana-5360	252	8	in	in	ADP
cana-5360	252	9	(	(	PUNCT
cana-5360	252	10	𝑈1	𝑈1	NOUN
cana-5360	252	11	,	,	PUNCT
cana-5360	252	12	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	252	13	)	)	PUNCT
cana-5360	252	14	)	)	PUNCT
cana-5360	252	15	.	.	PUNCT
cana-5360	253	1	since	since	SCONJ
cana-5360	253	2	every	every	DET
cana-5360	253	3	𝒫ℱ𝒩𝛿𝑐	𝒫ℱ𝒩𝛿𝑐	NUM
cana-5360	253	4	set	set	NOUN
cana-5360	253	5	is	be	AUX
cana-5360	253	6	𝒫ℱ𝒩𝑐𝑠	𝒫ℱ𝒩𝑐𝑠	NOUN
cana-5360	253	7	,	,	PUNCT
cana-5360	253	8	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	253	9	−1(𝑆	−1(𝑆	NOUN
cana-5360	253	10	)	)	PUNCT
cana-5360	253	11	is	be	AUX
cana-5360	253	12	𝑝𝑓𝒩𝑐	𝑝𝑓𝒩𝑐	PROPN
cana-5360	253	13	set	set	VERB
cana-5360	253	14	in	in	ADP
cana-5360	253	15	(	(	PUNCT
cana-5360	253	16	𝑈1	𝑈1	NOUN
cana-5360	253	17	,	,	PUNCT
cana-5360	253	18	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	253	19	)	)	PUNCT
cana-5360	253	20	)	)	PUNCT
cana-5360	253	21	.	.	PUNCT
cana-5360	254	1	hence	hence	ADV
cana-5360	254	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	254	3	is	be	AUX
cana-5360	254	4	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	PROPN
cana-5360	254	5	function	function	NOUN
cana-5360	254	6	.	.	PUNCT
cana-5360	255	1	(	(	PUNCT
cana-5360	255	2	ii	ii	NOUN
cana-5360	255	3	)	)	PUNCT
cana-5360	255	4	let	let	VERB
cana-5360	255	5	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	255	6	:	:	PUNCT
cana-5360	255	7	(	(	PUNCT
cana-5360	255	8	𝑈1	𝑈1	NOUN
cana-5360	255	9	,	,	PUNCT
cana-5360	255	10	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	255	11	)	)	PUNCT
cana-5360	255	12	)	)	PUNCT
cana-5360	255	13	→	→	SYM
cana-5360	255	14	(	(	PUNCT
cana-5360	255	15	𝑈2	𝑈2	NOUN
cana-5360	255	16	,	,	PUNCT
cana-5360	255	17	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	255	18	)	)	PUNCT
cana-5360	255	19	)	)	PUNCT
cana-5360	255	20	be	be	AUX
cana-5360	255	21	a	a	DET
cana-5360	255	22	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	NOUN
cana-5360	255	23	.	.	PUNCT
cana-5360	256	1	let	let	VERB
cana-5360	256	2	𝑆	𝑆	PROPN
cana-5360	256	3	be	be	AUX
cana-5360	256	4	a	a	DET
cana-5360	256	5	𝒫ℱ𝒩𝑜	𝒫ℱ𝒩𝑜	PROPN
cana-5360	256	6	set	set	VERB
cana-5360	256	7	in	in	ADP
cana-5360	256	8	(	(	PUNCT
cana-5360	256	9	𝑈2	𝑈2	NOUN
cana-5360	256	10	,	,	PUNCT
cana-5360	256	11	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	256	12	)	)	PUNCT
cana-5360	256	13	)	)	PUNCT
cana-5360	256	14	.	.	PUNCT
cana-5360	257	1	then	then	ADV
cana-5360	257	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	257	3	−1(𝑆	−1(𝑆	PROPN
cana-5360	257	4	)	)	PUNCT
cana-5360	257	5	is	be	AUX
cana-5360	257	6	𝒫ℱ𝒩𝛿𝑐	𝒫ℱ𝒩𝛿𝑐	NUM
cana-5360	257	7	set	set	NOUN
cana-5360	257	8	in	in	ADP
cana-5360	257	9	(	(	PUNCT
cana-5360	257	10	𝑈1	𝑈1	NOUN
cana-5360	257	11	,	,	PUNCT
cana-5360	257	12	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	257	13	)	)	PUNCT
cana-5360	257	14	)	)	PUNCT
cana-5360	257	15	.	.	PUNCT
cana-5360	258	1	since	since	SCONJ
cana-5360	258	2	every	every	DET
cana-5360	258	3	𝒫ℱ𝒩𝛿𝑐	𝒫ℱ𝒩𝛿𝑐	NUM
cana-5360	258	4	set	set	NOUN
cana-5360	258	5	is	be	AUX
cana-5360	258	6	𝒫ℱ𝒩𝛿𝒫𝑐𝑠	𝒫ℱ𝒩𝛿𝒫𝑐𝑠	PROPN
cana-5360	258	7	,	,	PUNCT
cana-5360	258	8	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	258	9	−1(𝑆	−1(𝑆	NOUN
cana-5360	258	10	)	)	PUNCT
cana-5360	258	11	is	be	AUX
cana-5360	258	12	𝑝𝑓𝒩𝛿𝒫𝑐	𝑝𝑓𝒩𝛿𝒫𝑐	NOUN
cana-5360	258	13	set	set	VERB
cana-5360	258	14	in	in	ADP
cana-5360	258	15	(	(	PUNCT
cana-5360	258	16	𝑈1	𝑈1	NOUN
cana-5360	258	17	,	,	PUNCT
cana-5360	258	18	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	258	19	)	)	PUNCT
cana-5360	258	20	)	)	PUNCT
cana-5360	258	21	.	.	PUNCT
cana-5360	259	1	hence	hence	ADV
cana-5360	259	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	259	3	is	be	AUX
cana-5360	259	4	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	PROPN
cana-5360	259	5	function	function	NOUN
cana-5360	259	6	.	.	PUNCT
cana-5360	260	1	(	(	PUNCT
cana-5360	260	2	iii	iii	X
cana-5360	260	3	)	)	PUNCT
cana-5360	260	4	let	let	VERB
cana-5360	260	5	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	260	6	:	:	PUNCT
cana-5360	260	7	(	(	PUNCT
cana-5360	260	8	𝑈1	𝑈1	NOUN
cana-5360	260	9	,	,	PUNCT
cana-5360	260	10	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	260	11	)	)	PUNCT
cana-5360	260	12	)	)	PUNCT
cana-5360	260	13	→	→	SYM
cana-5360	260	14	(	(	PUNCT
cana-5360	260	15	𝑈2	𝑈2	NOUN
cana-5360	260	16	,	,	PUNCT
cana-5360	260	17	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	260	18	)	)	PUNCT
cana-5360	260	19	)	)	PUNCT
cana-5360	260	20	be	be	AUX
cana-5360	260	21	a	a	DET
cana-5360	260	22	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	NOUN
cana-5360	260	23	.	.	PUNCT
cana-5360	261	1	let	let	VERB
cana-5360	261	2	𝑆	𝑆	PROPN
cana-5360	261	3	be	be	AUX
cana-5360	261	4	a	a	DET
cana-5360	261	5	𝒫ℱ𝒩𝑜	𝒫ℱ𝒩𝑜	ADJ
cana-5360	261	6	set	set	NOUN
cana-5360	261	7	in	in	ADP
cana-5360	261	8	communications	communication	NOUN
cana-5360	261	9	on	on	ADP
cana-5360	261	10	applied	apply	VERB
cana-5360	261	11	nonlinear	nonlinear	ADJ
cana-5360	261	12	analysis	analysis	NOUN
cana-5360	261	13	issn	issn	NOUN
cana-5360	261	14	:	:	PUNCT
cana-5360	261	15	1074	1074	NUM
cana-5360	261	16	-	-	PUNCT
cana-5360	261	17	133x	133x	NUM
cana-5360	261	18	vol	vol	VERB
cana-5360	261	19	32	32	NUM
cana-5360	261	20	no	no	NOUN
cana-5360	261	21	.	.	PUNCT
cana-5360	262	1	10s	10	NOUN
cana-5360	262	2	(	(	PUNCT
cana-5360	262	3	2025	2025	NUM
cana-5360	262	4	)	)	PUNCT
cana-5360	262	5	1933	1933	NUM
cana-5360	263	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-5360	263	2	(	(	PUNCT
cana-5360	263	3	𝑈2	𝑈2	NOUN
cana-5360	263	4	,	,	PUNCT
cana-5360	263	5	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	263	6	)	)	PUNCT
cana-5360	263	7	)	)	PUNCT
cana-5360	263	8	.	.	PUNCT
cana-5360	264	1	then	then	ADV
cana-5360	264	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	264	3	−1(𝑆	−1(𝑆	PROPN
cana-5360	264	4	)	)	PUNCT
cana-5360	264	5	is	be	AUX
cana-5360	264	6	𝒫ℱ𝒩𝛿𝑐	𝒫ℱ𝒩𝛿𝑐	NUM
cana-5360	264	7	set	set	NOUN
cana-5360	264	8	in	in	ADP
cana-5360	264	9	(	(	PUNCT
cana-5360	264	10	𝑈1	𝑈1	NOUN
cana-5360	264	11	,	,	PUNCT
cana-5360	264	12	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	264	13	)	)	PUNCT
cana-5360	264	14	)	)	PUNCT
cana-5360	264	15	.	.	PUNCT
cana-5360	265	1	since	since	SCONJ
cana-5360	265	2	every	every	DET
cana-5360	265	3	𝒫ℱ𝒩𝛿𝑐	𝒫ℱ𝒩𝛿𝑐	NOUN
cana-5360	265	4	set	set	NOUN
cana-5360	265	5	is	be	AUX
cana-5360	265	6	𝒫ℱ𝒩𝛿𝒮𝑐𝑠	𝒫ℱ𝒩𝛿𝒮𝑐𝑠	PROPN
cana-5360	265	7	,	,	PUNCT
cana-5360	265	8	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	265	9	−1(𝑆	−1(𝑆	NOUN
cana-5360	265	10	)	)	PUNCT
cana-5360	265	11	is	be	AUX
cana-5360	265	12	𝑝𝑓𝒩𝛿𝒮𝑐	𝑝𝑓𝒩𝛿𝒮𝑐	VERB
cana-5360	265	13	set	set	VERB
cana-5360	265	14	in	in	ADP
cana-5360	265	15	(	(	PUNCT
cana-5360	265	16	𝑈1	𝑈1	NOUN
cana-5360	265	17	,	,	PUNCT
cana-5360	265	18	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	265	19	)	)	PUNCT
cana-5360	265	20	)	)	PUNCT
cana-5360	265	21	.	.	PUNCT
cana-5360	266	1	hence	hence	ADV
cana-5360	266	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	266	3	is	be	AUX
cana-5360	266	4	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	NOUN
cana-5360	266	5	function	function	NOUN
cana-5360	266	6	.	.	PUNCT
cana-5360	267	1	(	(	PUNCT
cana-5360	267	2	iv	iv	X
cana-5360	267	3	)	)	PUNCT
cana-5360	267	4	let	let	VERB
cana-5360	267	5	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	267	6	:	:	PUNCT
cana-5360	267	7	(	(	PUNCT
cana-5360	267	8	𝑈1	𝑈1	NOUN
cana-5360	267	9	,	,	PUNCT
cana-5360	267	10	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	267	11	)	)	PUNCT
cana-5360	267	12	)	)	PUNCT
cana-5360	268	1	→	→	SYM
cana-5360	268	2	(	(	PUNCT
cana-5360	268	3	𝑈2	𝑈2	NOUN
cana-5360	268	4	,	,	PUNCT
cana-5360	268	5	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	268	6	)	)	PUNCT
cana-5360	268	7	)	)	PUNCT
cana-5360	268	8	be	be	AUX
cana-5360	268	9	a	a	DET
cana-5360	268	10	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	NOUN
cana-5360	268	11	.	.	PUNCT
cana-5360	269	1	let	let	VERB
cana-5360	269	2	𝑆	𝑆	PROPN
cana-5360	269	3	be	be	AUX
cana-5360	269	4	a	a	DET
cana-5360	269	5	𝒫ℱ𝒩𝑜	𝒫ℱ𝒩𝑜	PROPN
cana-5360	269	6	set	set	VERB
cana-5360	269	7	in	in	ADP
cana-5360	269	8	(	(	PUNCT
cana-5360	269	9	𝑈2	𝑈2	NOUN
cana-5360	269	10	,	,	PUNCT
cana-5360	269	11	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	269	12	)	)	PUNCT
cana-5360	269	13	)	)	PUNCT
cana-5360	269	14	.	.	PUNCT
cana-5360	270	1	then	then	ADV
cana-5360	270	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	270	3	−1(𝑆	−1(𝑆	PROPN
cana-5360	270	4	)	)	PUNCT
cana-5360	270	5	is	be	AUX
cana-5360	270	6	𝒫ℱ𝒩𝛿𝒮𝑐	𝒫ℱ𝒩𝛿𝒮𝑐	PROPN
cana-5360	270	7	set	set	VERB
cana-5360	270	8	in	in	ADP
cana-5360	270	9	(	(	PUNCT
cana-5360	270	10	𝑈1	𝑈1	NOUN
cana-5360	270	11	,	,	PUNCT
cana-5360	270	12	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	270	13	)	)	PUNCT
cana-5360	270	14	)	)	PUNCT
cana-5360	270	15	.	.	PUNCT
cana-5360	271	1	since	since	SCONJ
cana-5360	271	2	every	every	DET
cana-5360	271	3	𝒫ℱ𝒩𝛿𝒮𝑐	𝒫ℱ𝒩𝛿𝒮𝑐	PROPN
cana-5360	271	4	set	set	NOUN
cana-5360	271	5	is	be	AUX
cana-5360	271	6	𝒫ℱ𝒩𝛿𝛽𝑐𝑠	𝒫ℱ𝒩𝛿𝛽𝑐𝑠	PROPN
cana-5360	271	7	,	,	PUNCT
cana-5360	271	8	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	271	9	−1(𝑆	−1(𝑆	NOUN
cana-5360	271	10	)	)	PUNCT
cana-5360	271	11	is	be	AUX
cana-5360	271	12	𝑝𝑓𝒩𝛿𝛽𝑐	𝑝𝑓𝒩𝛿𝛽𝑐	NOUN
cana-5360	271	13	set	set	VERB
cana-5360	271	14	in	in	ADP
cana-5360	271	15	(	(	PUNCT
cana-5360	271	16	𝑈1	𝑈1	NOUN
cana-5360	271	17	,	,	PUNCT
cana-5360	271	18	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	271	19	)	)	PUNCT
cana-5360	271	20	)	)	PUNCT
cana-5360	271	21	.	.	PUNCT
cana-5360	272	1	hence	hence	ADV
cana-5360	272	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	272	3	is	be	AUX
cana-5360	272	4	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠	PROPN
cana-5360	272	5	function	function	NOUN
cana-5360	272	6	.	.	PUNCT
cana-5360	273	1	(	(	PUNCT
cana-5360	273	2	v	v	NOUN
cana-5360	273	3	)	)	PUNCT
cana-5360	273	4	let	let	VERB
cana-5360	273	5	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	273	6	:	:	PUNCT
cana-5360	273	7	(	(	PUNCT
cana-5360	273	8	𝑈1	𝑈1	NOUN
cana-5360	273	9	,	,	PUNCT
cana-5360	273	10	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	273	11	)	)	PUNCT
cana-5360	273	12	)	)	PUNCT
cana-5360	274	1	→	→	SYM
cana-5360	274	2	(	(	PUNCT
cana-5360	274	3	𝑈2	𝑈2	NOUN
cana-5360	274	4	,	,	PUNCT
cana-5360	274	5	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	274	6	)	)	PUNCT
cana-5360	274	7	)	)	PUNCT
cana-5360	274	8	be	be	AUX
cana-5360	274	9	a	a	DET
cana-5360	274	10	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	PROPN
cana-5360	274	11	.	.	PUNCT
cana-5360	275	1	let	let	VERB
cana-5360	275	2	𝑆	𝑆	PROPN
cana-5360	275	3	be	be	AUX
cana-5360	275	4	a	a	DET
cana-5360	275	5	𝒫ℱ𝒩𝑐	𝒫ℱ𝒩𝑐	NOUN
cana-5360	275	6	set	set	VERB
cana-5360	275	7	in	in	ADP
cana-5360	275	8	(	(	PUNCT
cana-5360	275	9	𝑈2	𝑈2	NOUN
cana-5360	275	10	,	,	PUNCT
cana-5360	275	11	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	275	12	)	)	PUNCT
cana-5360	275	13	)	)	PUNCT
cana-5360	275	14	.	.	PUNCT
cana-5360	276	1	then	then	ADV
cana-5360	276	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	276	3	−1(𝑆	−1(𝑆	PROPN
cana-5360	276	4	)	)	PUNCT
cana-5360	276	5	is	be	AUX
cana-5360	276	6	𝒫ℱ𝒩𝛿𝒫𝑐	𝒫ℱ𝒩𝛿𝒫𝑐	PROPN
cana-5360	276	7	set	set	VERB
cana-5360	276	8	in	in	ADP
cana-5360	276	9	(	(	PUNCT
cana-5360	276	10	𝑈1	𝑈1	NOUN
cana-5360	276	11	,	,	PUNCT
cana-5360	276	12	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	276	13	)	)	PUNCT
cana-5360	276	14	)	)	PUNCT
cana-5360	276	15	.	.	PUNCT
cana-5360	277	1	since	since	SCONJ
cana-5360	277	2	every	every	DET
cana-5360	277	3	𝒫ℱ𝒩𝛿𝒫𝑐	𝒫ℱ𝒩𝛿𝒫𝑐	PROPN
cana-5360	277	4	set	set	NOUN
cana-5360	277	5	is	be	AUX
cana-5360	277	6	𝒫ℱ𝒩𝛿𝛽𝑐𝑠	𝒫ℱ𝒩𝛿𝛽𝑐𝑠	PROPN
cana-5360	277	7	,	,	PUNCT
cana-5360	277	8	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	277	9	−1(𝑆	−1(𝑆	NOUN
cana-5360	277	10	)	)	PUNCT
cana-5360	277	11	is	be	AUX
cana-5360	277	12	𝑝𝑓𝒩𝛿𝛽𝑐	𝑝𝑓𝒩𝛿𝛽𝑐	NOUN
cana-5360	277	13	set	set	VERB
cana-5360	277	14	in	in	ADP
cana-5360	277	15	(	(	PUNCT
cana-5360	277	16	𝑈1	𝑈1	NOUN
cana-5360	277	17	,	,	PUNCT
cana-5360	277	18	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	277	19	)	)	PUNCT
cana-5360	277	20	)	)	PUNCT
cana-5360	277	21	.	.	PUNCT
cana-5360	278	1	hence	hence	ADV
cana-5360	278	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	278	3	is	be	AUX
cana-5360	278	4	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠	PROPN
cana-5360	278	5	function	function	NOUN
cana-5360	278	6	.	.	PUNCT
cana-5360	279	1	(	(	PUNCT
cana-5360	279	2	vi	vi	X
cana-5360	279	3	)	)	PUNCT
cana-5360	279	4	let	let	VERB
cana-5360	279	5	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	279	6	:	:	PUNCT
cana-5360	279	7	(	(	PUNCT
cana-5360	279	8	𝑈1	𝑈1	NOUN
cana-5360	279	9	,	,	PUNCT
cana-5360	279	10	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	279	11	)	)	PUNCT
cana-5360	279	12	)	)	PUNCT
cana-5360	279	13	→	→	SYM
cana-5360	279	14	(	(	PUNCT
cana-5360	279	15	𝑈2	𝑈2	NOUN
cana-5360	279	16	,	,	PUNCT
cana-5360	279	17	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	279	18	)	)	PUNCT
cana-5360	279	19	)	)	PUNCT
cana-5360	279	20	be	be	AUX
cana-5360	279	21	a	a	DET
cana-5360	279	22	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐶𝑡𝑠	X
cana-5360	279	23	.	.	PUNCT
cana-5360	280	1	let	let	VERB
cana-5360	280	2	𝑆	𝑆	PROPN
cana-5360	280	3	be	be	AUX
cana-5360	280	4	a	a	DET
cana-5360	280	5	𝒫ℱ𝒩𝑜	𝒫ℱ𝒩𝑜	PROPN
cana-5360	280	6	set	set	VERB
cana-5360	280	7	in	in	ADP
cana-5360	280	8	(	(	PUNCT
cana-5360	280	9	𝑈2	𝑈2	NOUN
cana-5360	280	10	,	,	PUNCT
cana-5360	280	11	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	280	12	)	)	PUNCT
cana-5360	280	13	)	)	PUNCT
cana-5360	280	14	.	.	PUNCT
cana-5360	281	1	then	then	ADV
cana-5360	281	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	281	3	−1(𝑆	−1(𝑆	PROPN
cana-5360	281	4	)	)	PUNCT
cana-5360	281	5	is	be	AUX
cana-5360	281	6	𝒫ℱ𝒩𝛿𝛼𝑐	𝒫ℱ𝒩𝛿𝛼𝑐	PROPN
cana-5360	281	7	set	set	VERB
cana-5360	281	8	in	in	ADP
cana-5360	281	9	(	(	PUNCT
cana-5360	281	10	𝑈1	𝑈1	NOUN
cana-5360	281	11	,	,	PUNCT
cana-5360	281	12	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	281	13	)	)	PUNCT
cana-5360	281	14	)	)	PUNCT
cana-5360	281	15	.	.	PUNCT
cana-5360	282	1	since	since	SCONJ
cana-5360	282	2	every	every	DET
cana-5360	282	3	𝒫ℱ𝒩𝛿𝛼𝑐	𝒫ℱ𝒩𝛿𝛼𝑐	PROPN
cana-5360	282	4	set	set	NOUN
cana-5360	282	5	is	be	AUX
cana-5360	282	6	𝒫ℱ𝒩𝛿𝒫𝑐𝑠	𝒫ℱ𝒩𝛿𝒫𝑐𝑠	PROPN
cana-5360	282	7	,	,	PUNCT
cana-5360	282	8	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	282	9	−1(𝑆	−1(𝑆	NOUN
cana-5360	282	10	)	)	PUNCT
cana-5360	282	11	is	be	AUX
cana-5360	282	12	𝑝𝑓𝒩𝛿𝒫𝑐	𝑝𝑓𝒩𝛿𝒫𝑐	NOUN
cana-5360	282	13	set	set	VERB
cana-5360	282	14	in	in	ADP
cana-5360	282	15	(	(	PUNCT
cana-5360	282	16	𝑈1	𝑈1	NOUN
cana-5360	282	17	,	,	PUNCT
cana-5360	282	18	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	282	19	)	)	PUNCT
cana-5360	282	20	)	)	PUNCT
cana-5360	282	21	.	.	PUNCT
cana-5360	283	1	hence	hence	ADV
cana-5360	283	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	283	3	is	be	AUX
cana-5360	283	4	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	PROPN
cana-5360	283	5	function	function	NOUN
cana-5360	283	6	.	.	PUNCT
cana-5360	284	1	(	(	PUNCT
cana-5360	284	2	vii	vii	PROPN
cana-5360	284	3	)	)	PUNCT
cana-5360	284	4	let	let	VERB
cana-5360	284	5	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	284	6	:	:	PUNCT
cana-5360	284	7	(	(	PUNCT
cana-5360	284	8	𝑈1	𝑈1	NOUN
cana-5360	284	9	,	,	PUNCT
cana-5360	284	10	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	284	11	)	)	PUNCT
cana-5360	284	12	)	)	PUNCT
cana-5360	284	13	→	→	SYM
cana-5360	284	14	(	(	PUNCT
cana-5360	284	15	𝑈2	𝑈2	NOUN
cana-5360	284	16	,	,	PUNCT
cana-5360	284	17	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	284	18	)	)	PUNCT
cana-5360	284	19	)	)	PUNCT
cana-5360	284	20	be	be	AUX
cana-5360	284	21	a	a	DET
cana-5360	284	22	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐶𝑡𝑠	X
cana-5360	284	23	.	.	PUNCT
cana-5360	285	1	let	let	VERB
cana-5360	285	2	𝑆	𝑆	PROPN
cana-5360	285	3	be	be	AUX
cana-5360	285	4	a	a	DET
cana-5360	285	5	𝒫ℱ𝒩𝑜	𝒫ℱ𝒩𝑜	PROPN
cana-5360	285	6	set	set	VERB
cana-5360	285	7	in	in	ADP
cana-5360	285	8	(	(	PUNCT
cana-5360	285	9	𝑈2	𝑈2	NOUN
cana-5360	285	10	,	,	PUNCT
cana-5360	285	11	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	285	12	)	)	PUNCT
cana-5360	285	13	)	)	PUNCT
cana-5360	285	14	.	.	PUNCT
cana-5360	286	1	then	then	ADV
cana-5360	286	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	286	3	−1(𝑆	−1(𝑆	PROPN
cana-5360	286	4	)	)	PUNCT
cana-5360	286	5	is	be	AUX
cana-5360	286	6	𝒫ℱ𝒩𝛿𝛼𝑐	𝒫ℱ𝒩𝛿𝛼𝑐	PROPN
cana-5360	286	7	set	set	VERB
cana-5360	286	8	in	in	ADP
cana-5360	286	9	(	(	PUNCT
cana-5360	286	10	𝑈1	𝑈1	NOUN
cana-5360	286	11	,	,	PUNCT
cana-5360	286	12	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	286	13	)	)	PUNCT
cana-5360	286	14	)	)	PUNCT
cana-5360	286	15	.	.	PUNCT
cana-5360	287	1	since	since	SCONJ
cana-5360	287	2	every	every	DET
cana-5360	287	3	𝒫ℱ𝒩𝛿𝛼𝑐	𝒫ℱ𝒩𝛿𝛼𝑐	PROPN
cana-5360	287	4	set	set	NOUN
cana-5360	287	5	is	be	AUX
cana-5360	287	6	𝒫ℱ𝒩𝛿𝒮𝑐𝑠	𝒫ℱ𝒩𝛿𝒮𝑐𝑠	PROPN
cana-5360	287	7	,	,	PUNCT
cana-5360	287	8	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	287	9	−1(𝑆	−1(𝑆	NOUN
cana-5360	287	10	)	)	PUNCT
cana-5360	287	11	is	be	AUX
cana-5360	287	12	𝑝𝑓𝒩𝛿𝒮𝑐	𝑝𝑓𝒩𝛿𝒮𝑐	VERB
cana-5360	287	13	set	set	VERB
cana-5360	287	14	in	in	ADP
cana-5360	287	15	(	(	PUNCT
cana-5360	287	16	𝑈1	𝑈1	NOUN
cana-5360	287	17	,	,	PUNCT
cana-5360	287	18	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	287	19	)	)	PUNCT
cana-5360	287	20	)	)	PUNCT
cana-5360	287	21	.	.	PUNCT
cana-5360	288	1	hence	hence	ADV
cana-5360	288	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	288	3	is	be	AUX
cana-5360	288	4	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	PRON
cana-5360	288	5	function	function	NOUN
cana-5360	288	6	.	.	PUNCT
cana-5360	289	1	remark	remark	PROPN
cana-5360	289	2	3.1	3.1	NUM
cana-5360	289	3	the	the	DET
cana-5360	289	4	following	follow	VERB
cana-5360	289	5	figure	figure	NOUN
cana-5360	289	6	shows	show	VERB
cana-5360	289	7	the	the	DET
cana-5360	289	8	relations	relation	NOUN
cana-5360	289	9	among	among	ADP
cana-5360	289	10	the	the	DET
cana-5360	289	11	different	different	ADJ
cana-5360	289	12	types	type	NOUN
cana-5360	289	13	of	of	ADP
cana-5360	289	14	pythagorean	pythagorean	PROPN
cana-5360	289	15	fuzzy	fuzzy	ADJ
cana-5360	289	16	𝛿	𝛿	PRON
cana-5360	289	17	continuous	continuous	ADJ
cana-5360	289	18	mappings	mapping	NOUN
cana-5360	289	19	that	that	PRON
cana-5360	289	20	were	be	AUX
cana-5360	289	21	studied	study	VERB
cana-5360	289	22	in	in	ADP
cana-5360	289	23	this	this	DET
cana-5360	289	24	section	section	NOUN
cana-5360	289	25	.	.	PUNCT
cana-5360	290	1	figure	figure	NOUN
cana-5360	290	2	:	:	PUNCT
cana-5360	290	3	𝓟𝓕𝓝𝒄𝒐𝒏𝒕𝒓𝒂𝜹𝑪𝒕𝒔	𝓟𝓕𝓝𝒄𝒐𝒏𝒕𝒓𝒂𝜹𝑪𝒕𝒔	NOUN
cana-5360	290	4	mappings	mapping	NOUN
cana-5360	290	5	in	in	ADP
cana-5360	290	6	𝓟𝓕𝓝𝒄𝒐𝒏𝒕𝒓𝒂𝑪𝒕𝒔	𝓟𝓕𝓝𝒄𝒐𝒏𝒕𝒓𝒂𝑪𝒕𝒔	PROPN
cana-5360	290	7	example	example	NOUN
cana-5360	290	8	3.1	3.1	NUM
cana-5360	290	9	assume	assume	VERB
cana-5360	290	10	𝑈1	𝑈1	NOUN
cana-5360	290	11	=	=	PRON
cana-5360	290	12	𝑈2	𝑈2	PROPN
cana-5360	290	13	=	=	PUNCT
cana-5360	290	14	𝑈	𝑈	PROPN
cana-5360	290	15	=	=	SYM
cana-5360	290	16	{	{	PUNCT
cana-5360	290	17	𝑠1	𝑠1	PROPN
cana-5360	290	18	,	,	PUNCT
cana-5360	290	19	𝑠2	𝑠2	NOUN
cana-5360	290	20	,	,	PUNCT
cana-5360	290	21	𝑠3	𝑠3	NOUN
cana-5360	290	22	,	,	PUNCT
cana-5360	290	23	𝑠4	𝑠4	PROPN
cana-5360	290	24	}	}	PUNCT
cana-5360	290	25	be	be	VERB
cana-5360	290	26	the	the	DET
cana-5360	290	27	universe	universe	NOUN
cana-5360	290	28	set	set	VERB
cana-5360	290	29	and	and	CCONJ
cana-5360	290	30	the	the	DET
cana-5360	290	31	equivalence	equivalence	NOUN
cana-5360	290	32	relation	relation	NOUN
cana-5360	290	33	is	be	AUX
cana-5360	290	34	𝑈/𝑅	𝑈/𝑅	ADJ
cana-5360	290	35	=	=	SYM
cana-5360	290	36	{	{	PUNCT
cana-5360	290	37	{	{	PUNCT
cana-5360	290	38	𝑠1	𝑠1	PROPN
cana-5360	290	39	,	,	PUNCT
cana-5360	290	40	𝑠4	𝑠4	PROPN
cana-5360	290	41	}	}	PUNCT
cana-5360	290	42	,	,	PUNCT
cana-5360	290	43	{	{	PUNCT
cana-5360	290	44	𝑠2	𝑠2	NOUN
cana-5360	290	45	}	}	PUNCT
cana-5360	290	46	,	,	PUNCT
cana-5360	290	47	{	{	PUNCT
cana-5360	290	48	𝑠3	𝑠3	NOUN
cana-5360	290	49	}	}	PUNCT
cana-5360	290	50	}	}	PUNCT
cana-5360	290	51	.	.	PUNCT
cana-5360	291	1	let	let	VERB
cana-5360	291	2	𝐴	𝐴	PROPN
cana-5360	291	3	=	=	PUNCT
cana-5360	291	4	{	{	PUNCT
cana-5360	291	5	⟨	⟨	X
cana-5360	291	6	𝑠1	𝑠1	PROPN
cana-5360	291	7	0.3,0.1	0.3,0.1	PROPN
cana-5360	291	8	⟩	⟩	NOUN
cana-5360	291	9	,	,	PUNCT
cana-5360	291	10	⟨	⟨	VERB
cana-5360	291	11	𝑠2	𝑠2	NOUN
cana-5360	291	12	0.1,0.5	0.1,0.5	PROPN
cana-5360	291	13	⟩	⟩	NOUN
cana-5360	291	14	,	,	PUNCT
cana-5360	291	15	⟨	⟨	VERB
cana-5360	291	16	𝑠3	𝑠3	PROPN
cana-5360	291	17	0.2,0.45	0.2,0.45	NUM
cana-5360	291	18	⟩	⟩	NOUN
cana-5360	291	19	,	,	PUNCT
cana-5360	291	20	⟨	⟨	VERB
cana-5360	291	21	𝑠4	𝑠4	PROPN
cana-5360	291	22	0.4,0.25	0.4,0.25	NUM
cana-5360	291	23	⟩	⟩	NOUN
cana-5360	291	24	}	}	PUNCT
cana-5360	291	25	be	be	AUX
cana-5360	291	26	a	a	DET
cana-5360	291	27	pythagorean	pythagorean	ADJ
cana-5360	291	28	fuzzy	fuzzy	ADJ
cana-5360	291	29	subset	subset	NOUN
cana-5360	291	30	of	of	ADP
cana-5360	291	31	𝑈.	𝑈.	PROPN
cana-5360	291	32	𝒫ℱ𝔑(𝐴	𝒫ℱ𝔑(𝐴	PROPN
cana-5360	291	33	)	)	PUNCT
cana-5360	291	34	=	=	NOUN
cana-5360	291	35	{	{	PUNCT
cana-5360	291	36	⟨	⟨	ADP
cana-5360	291	37	𝑠1,𝑠4	𝑠1,𝑠4	PROPN
cana-5360	291	38	0.3,0.25	0.3,0.25	NUM
cana-5360	291	39	⟩	⟩	NOUN
cana-5360	291	40	,	,	PUNCT
cana-5360	291	41	⟨	⟨	VERB
cana-5360	291	42	𝑠2	𝑠2	NOUN
cana-5360	291	43	0.1,0.5	0.1,0.5	PROPN
cana-5360	291	44	⟩	⟩	NOUN
cana-5360	291	45	,	,	PUNCT
cana-5360	291	46	⟨	⟨	VERB
cana-5360	291	47	𝑠3	𝑠3	PROPN
cana-5360	291	48	0.2,0.45	0.2,0.45	NUM
cana-5360	291	49	⟩	⟩	NOUN
cana-5360	291	50	}	}	PUNCT
cana-5360	291	51	,	,	PUNCT
cana-5360	291	52	𝒫ℱ𝔑(𝐴	𝒫ℱ𝔑(𝐴	INTJ
cana-5360	291	53	)	)	PUNCT
cana-5360	291	54	=	=	NOUN
cana-5360	291	55	{	{	PUNCT
cana-5360	291	56	⟨	⟨	ADP
cana-5360	291	57	𝑠1,𝑠4	𝑠1,𝑠4	PROPN
cana-5360	291	58	0.4,0.1	0.4,0.1	PROPN
cana-5360	291	59	⟩	⟩	NOUN
cana-5360	291	60	,	,	PUNCT
cana-5360	291	61	⟨	⟨	VERB
cana-5360	291	62	𝑠2	𝑠2	NOUN
cana-5360	291	63	0.1,0.5	0.1,0.5	PROPN
cana-5360	291	64	⟩	⟩	NOUN
cana-5360	291	65	,	,	PUNCT
cana-5360	291	66	⟨	⟨	VERB
cana-5360	291	67	𝑠3	𝑠3	PROPN
cana-5360	291	68	0.2,0.45	0.2,0.45	PUNCT
cana-5360	291	69	⟩	⟩	NOUN
cana-5360	291	70	}	}	PUNCT
cana-5360	291	71	,	,	PUNCT
cana-5360	291	72	𝐵𝒫ℱ𝔑(𝐴	𝐵𝒫ℱ𝔑(𝐴	PROPN
cana-5360	291	73	)	)	PUNCT
cana-5360	292	1	=	=	NOUN
cana-5360	292	2	{	{	PUNCT
cana-5360	292	3	⟨	⟨	ADP
cana-5360	292	4	𝑠1,𝑠4	𝑠1,𝑠4	PROPN
cana-5360	292	5	0.25,0.3	0.25,0.3	NOUN
cana-5360	292	6	⟩	⟩	NOUN
cana-5360	292	7	,	,	PUNCT
cana-5360	292	8	⟨	⟨	VERB
cana-5360	292	9	𝑠2	𝑠2	NOUN
cana-5360	292	10	0.1,0.5	0.1,0.5	PROPN
cana-5360	292	11	⟩	⟩	NOUN
cana-5360	292	12	,	,	PUNCT
cana-5360	292	13	⟨	⟨	VERB
cana-5360	292	14	𝑠3	𝑠3	PROPN
cana-5360	292	15	0.2,0.45	0.2,0.45	NUM
cana-5360	292	16	⟩	⟩	NOUN
cana-5360	292	17	}	}	PUNCT
cana-5360	292	18	.	.	PUNCT
cana-5360	293	1	now	now	ADV
cana-5360	293	2	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	VERB
cana-5360	293	3	)	)	PUNCT
cana-5360	293	4	=	=	PRON
cana-5360	293	5	{	{	PUNCT
cana-5360	293	6	0𝒫	0𝒫	NOUN
cana-5360	293	7	,	,	PUNCT
cana-5360	293	8	1𝒫	1𝒫	INTJ
cana-5360	293	9	,	,	PUNCT
cana-5360	293	10	𝒫ℱ𝔑(𝐴	𝒫ℱ𝔑(𝐴	NOUN
cana-5360	293	11	)	)	PUNCT
cana-5360	293	12	,	,	PUNCT
cana-5360	293	13	𝒫ℱ𝔑(𝐴	𝒫ℱ𝔑(𝐴	NOUN
cana-5360	293	14	)	)	PUNCT
cana-5360	293	15	,	,	PUNCT
cana-5360	293	16	𝐵𝒫ℱ𝔑(𝐴	𝐵𝒫ℱ𝔑(𝐴	PROPN
cana-5360	293	17	)	)	PUNCT
cana-5360	293	18	}	}	PUNCT
cana-5360	293	19	and	and	CCONJ
cana-5360	293	20	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NUM
cana-5360	293	21	)	)	PUNCT
cana-5360	294	1	=	=	PRON
cana-5360	294	2	{	{	PUNCT
cana-5360	294	3	0𝒫	0𝒫	NOUN
cana-5360	294	4	,	,	PUNCT
cana-5360	294	5	1𝒫	1𝒫	INTJ
cana-5360	294	6	,	,	PUNCT
cana-5360	294	7	(	(	PUNCT
cana-5360	294	8	𝒫ℱ𝔑(𝐴))𝑐	𝒫ℱ𝔑(𝐴))𝑐	X
cana-5360	294	9	,	,	PUNCT
cana-5360	294	10	communications	communication	NOUN
cana-5360	294	11	on	on	ADP
cana-5360	294	12	applied	apply	VERB
cana-5360	294	13	nonlinear	nonlinear	ADJ
cana-5360	294	14	analysis	analysis	NOUN
cana-5360	294	15	issn	issn	NOUN
cana-5360	294	16	:	:	PUNCT
cana-5360	294	17	1074	1074	NUM
cana-5360	294	18	-	-	PUNCT
cana-5360	294	19	133x	133x	NUM
cana-5360	294	20	vol	vol	VERB
cana-5360	294	21	32	32	NUM
cana-5360	294	22	no	no	NOUN
cana-5360	294	23	.	.	PUNCT
cana-5360	295	1	10s	10	NOUN
cana-5360	295	2	(	(	PUNCT
cana-5360	295	3	2025	2025	NUM
cana-5360	295	4	)	)	PUNCT
cana-5360	295	5	1934	1934	NUM
cana-5360	295	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5360	295	7	(	(	PUNCT
cana-5360	295	8	𝒫ℱ𝔑(𝐴))𝑐	𝒫ℱ𝔑(𝐴))𝑐	NUM
cana-5360	295	9	,	,	PUNCT
cana-5360	295	10	(	(	PUNCT
cana-5360	295	11	𝐵𝒫ℱ𝔑(𝐴))𝑐	𝐵𝒫ℱ𝔑(𝐴))𝑐	X
cana-5360	295	12	}	}	PUNCT
cana-5360	295	13	.	.	PUNCT
cana-5360	296	1	let	let	VERB
cana-5360	296	2	ℎ𝑃	ℎ𝑃	NOUN
cana-5360	296	3	:	:	PUNCT
cana-5360	296	4	(	(	PUNCT
cana-5360	296	5	𝑈	𝑈	NOUN
cana-5360	296	6	,	,	PUNCT
cana-5360	296	7	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	296	8	)	)	PUNCT
cana-5360	296	9	)	)	PUNCT
cana-5360	296	10	→	→	PUNCT
cana-5360	296	11	(	(	PUNCT
cana-5360	296	12	𝑈	𝑈	PROPN
cana-5360	296	13	,	,	PUNCT
cana-5360	296	14	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NUM
cana-5360	296	15	)	)	PUNCT
cana-5360	296	16	)	)	PUNCT
cana-5360	296	17	be	be	AUX
cana-5360	296	18	an	an	DET
cana-5360	296	19	identity	identity	NOUN
cana-5360	296	20	function	function	NOUN
cana-5360	296	21	,	,	PUNCT
cana-5360	296	22	then	then	ADV
cana-5360	296	23	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	296	24	is	be	AUX
cana-5360	296	25	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	PROPN
cana-5360	296	26	but	but	CCONJ
cana-5360	296	27	not	not	PART
cana-5360	296	28	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	NOUN
cana-5360	296	29	.	.	PUNCT
cana-5360	297	1	since	since	ADV
cana-5360	297	2	,	,	PUNCT
cana-5360	297	3	𝒫ℱ𝔑(𝐴	𝒫ℱ𝔑(𝐴	NOUN
cana-5360	297	4	)	)	PUNCT
cana-5360	297	5	is	be	AUX
cana-5360	297	6	a	a	DET
cana-5360	297	7	𝒫ℱ𝒩𝑜	𝒫ℱ𝒩𝑜	PROPN
cana-5360	297	8	set	set	NOUN
cana-5360	297	9	in	in	ADP
cana-5360	297	10	𝑈2	𝑈2	PROPN
cana-5360	298	1	but	but	CCONJ
cana-5360	298	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	298	3	−1(𝒫ℱ𝔑(𝐴	−1(𝒫ℱ𝔑(𝐴	PROPN
cana-5360	298	4	)	)	PUNCT
cana-5360	298	5	)	)	PUNCT
cana-5360	299	1	=	=	SYM
cana-5360	299	2	𝒫ℱ𝔑(𝐴	𝒫ℱ𝔑(𝐴	NOUN
cana-5360	299	3	)	)	PUNCT
cana-5360	299	4	is	be	AUX
cana-5360	299	5	not	not	PART
cana-5360	299	6	𝒫ℱ𝒩𝛿𝑐	𝒫ℱ𝒩𝛿𝑐	NUM
cana-5360	299	7	set	set	VERB
cana-5360	299	8	in	in	ADP
cana-5360	299	9	𝑈1	𝑈1	PROPN
cana-5360	299	10	.	.	PUNCT
cana-5360	300	1	example	example	NOUN
cana-5360	300	2	3.2	3.2	NUM
cana-5360	300	3	let	let	VERB
cana-5360	300	4	𝑈1	𝑈1	NOUN
cana-5360	300	5	=	=	SYM
cana-5360	300	6	{	{	PUNCT
cana-5360	300	7	𝑠1	𝑠1	PROPN
cana-5360	300	8	,	,	PUNCT
cana-5360	300	9	𝑠2	𝑠2	NOUN
cana-5360	300	10	,	,	PUNCT
cana-5360	300	11	𝑠3	𝑠3	NOUN
cana-5360	300	12	,	,	PUNCT
cana-5360	300	13	𝑠4	𝑠4	PROPN
cana-5360	300	14	}	}	PUNCT
cana-5360	300	15	,	,	PUNCT
cana-5360	300	16	𝑈2	𝑈2	PROPN
cana-5360	300	17	=	=	PUNCT
cana-5360	300	18	{	{	PUNCT
cana-5360	300	19	𝑡1	𝑡1	PROPN
cana-5360	300	20	,	,	PUNCT
cana-5360	300	21	𝑡2	𝑡2	PROPN
cana-5360	300	22	,	,	PUNCT
cana-5360	300	23	𝑡3	𝑡3	PROPN
cana-5360	300	24	,	,	PUNCT
cana-5360	300	25	𝑡4	𝑡4	PROPN
cana-5360	300	26	}	}	PUNCT
cana-5360	300	27	are	be	AUX
cana-5360	300	28	the	the	DET
cana-5360	300	29	universe	universe	NOUN
cana-5360	300	30	sets	set	NOUN
cana-5360	300	31	and	and	CCONJ
cana-5360	300	32	the	the	DET
cana-5360	300	33	equivalence	equivalence	NOUN
cana-5360	300	34	relations	relation	NOUN
cana-5360	300	35	are	be	AUX
cana-5360	300	36	𝑈1/𝑅	𝑈1/𝑅	X
cana-5360	300	37	=	=	SYM
cana-5360	300	38	{	{	PUNCT
cana-5360	300	39	{	{	PUNCT
cana-5360	300	40	𝑠1	𝑠1	NOUN
cana-5360	300	41	,	,	PUNCT
cana-5360	300	42	𝑠3	𝑠3	PROPN
cana-5360	300	43	}	}	PUNCT
cana-5360	300	44	,	,	PUNCT
cana-5360	300	45	{	{	PUNCT
cana-5360	300	46	𝑠2	𝑠2	NOUN
cana-5360	300	47	,	,	PUNCT
cana-5360	300	48	𝑠4	𝑠4	PROPN
cana-5360	300	49	}	}	PUNCT
cana-5360	300	50	}	}	PUNCT
cana-5360	300	51	and	and	CCONJ
cana-5360	300	52	𝑈2/𝑅	𝑈2/𝑅	PUNCT
cana-5360	300	53	=	=	PRON
cana-5360	300	54	{	{	PUNCT
cana-5360	300	55	{	{	PUNCT
cana-5360	300	56	𝑡1	𝑡1	NOUN
cana-5360	300	57	,	,	PUNCT
cana-5360	300	58	𝑡3	𝑡3	PROPN
cana-5360	300	59	}	}	PUNCT
cana-5360	300	60	,	,	PUNCT
cana-5360	300	61	{	{	PUNCT
cana-5360	300	62	𝑡2	𝑡2	PROPN
cana-5360	300	63	,	,	PUNCT
cana-5360	300	64	𝑡4	𝑡4	PROPN
cana-5360	300	65	}	}	PUNCT
cana-5360	300	66	}	}	PUNCT
cana-5360	300	67	.	.	PUNCT
cana-5360	301	1	let	let	VERB
cana-5360	301	2	𝐴1	𝐴1	PROPN
cana-5360	301	3	=	=	PUNCT
cana-5360	301	4	{	{	PUNCT
cana-5360	301	5	⟨	⟨	X
cana-5360	301	6	𝑠1	𝑠1	PROPN
cana-5360	301	7	0.4,0.8	0.4,0.8	PROPN
cana-5360	301	8	⟩	⟩	NOUN
cana-5360	301	9	,	,	PUNCT
cana-5360	301	10	⟨	⟨	VERB
cana-5360	301	11	𝑠2	𝑠2	NOUN
cana-5360	301	12	0.5,0.4	0.5,0.4	PROPN
cana-5360	301	13	⟩	⟩	NOUN
cana-5360	301	14	,	,	PUNCT
cana-5360	301	15	⟨	⟨	VERB
cana-5360	301	16	𝑠3	𝑠3	PROPN
cana-5360	301	17	0.6,0.6	0.6,0.6	PROPN
cana-5360	301	18	⟩	⟩	NOUN
cana-5360	301	19	,	,	PUNCT
cana-5360	301	20	⟨	⟨	VERB
cana-5360	301	21	𝑠4	𝑠4	PROPN
cana-5360	301	22	0.7,0.6	0.7,0.6	PROPN
cana-5360	301	23	⟩	⟩	NOUN
cana-5360	301	24	}	}	PUNCT
cana-5360	301	25	and	and	CCONJ
cana-5360	301	26	𝐴2	𝐴2	PROPN
cana-5360	301	27	=	=	PUNCT
cana-5360	301	28	{	{	PUNCT
cana-5360	301	29	⟨	⟨	NOUN
cana-5360	301	30	𝑡1	𝑡1	NOUN
cana-5360	301	31	0.4,0.8	0.4,0.8	NUM
cana-5360	301	32	⟩	⟩	NOUN
cana-5360	301	33	,	,	PUNCT
cana-5360	301	34	⟨	⟨	VERB
cana-5360	301	35	𝑡2	𝑡2	PROPN
cana-5360	301	36	0.5,0.7	0.5,0.7	PROPN
cana-5360	301	37	⟩	⟩	NOUN
cana-5360	301	38	,	,	PUNCT
cana-5360	301	39	⟨	⟨	VERB
cana-5360	301	40	𝑡3	𝑡3	PROPN
cana-5360	301	41	0.4,0.6	0.4,0.6	PROPN
cana-5360	301	42	⟩	⟩	NOUN
cana-5360	301	43	,	,	PUNCT
cana-5360	301	44	⟨	⟨	VERB
cana-5360	301	45	𝑡4	𝑡4	PROPN
cana-5360	301	46	0.3,0.7	0.3,0.7	PROPN
cana-5360	301	47	⟩	⟩	PROPN
cana-5360	301	48	}	}	PUNCT
cana-5360	301	49	be	be	VERB
cana-5360	301	50	a	a	DET
cana-5360	301	51	pythagorean	pythagorean	ADJ
cana-5360	301	52	fuzzy	fuzzy	ADJ
cana-5360	301	53	subsets	subset	NOUN
cana-5360	301	54	of	of	ADP
cana-5360	301	55	𝑈1	𝑈1	NOUN
cana-5360	301	56	and	and	CCONJ
cana-5360	301	57	𝑈2	𝑈2	NOUN
cana-5360	301	58	respectively	respectively	ADV
cana-5360	301	59	.	.	PUNCT
cana-5360	302	1	𝒫ℱ𝔑(𝐴1	𝒫ℱ𝔑(𝐴1	NUM
cana-5360	302	2	)	)	PUNCT
cana-5360	302	3	=	=	PRON
cana-5360	302	4	{	{	PUNCT
cana-5360	302	5	⟨	⟨	VERB
cana-5360	302	6	𝑠1,𝑠3	𝑠1,𝑠3	PROPN
cana-5360	302	7	0.4,0.8	0.4,0.8	NUM
cana-5360	302	8	⟩	⟩	NOUN
cana-5360	302	9	,	,	PUNCT
cana-5360	302	10	⟨	⟨	VERB
cana-5360	302	11	𝑠2,𝑠4	𝑠2,𝑠4	PROPN
cana-5360	302	12	0.5,0.6	0.5,0.6	PROPN
cana-5360	302	13	⟩	⟩	PROPN
cana-5360	302	14	}	}	PUNCT
cana-5360	302	15	𝒫ℱ𝔑(𝐴1	𝒫ℱ𝔑(𝐴1	NUM
cana-5360	302	16	)	)	PUNCT
cana-5360	302	17	=	=	PRON
cana-5360	302	18	{	{	PUNCT
cana-5360	302	19	⟨	⟨	VERB
cana-5360	302	20	𝑠1,𝑠3	𝑠1,𝑠3	PROPN
cana-5360	302	21	0.6,0.6	0.6,0.6	PROPN
cana-5360	302	22	⟩	⟩	NOUN
cana-5360	302	23	,	,	PUNCT
cana-5360	302	24	⟨	⟨	VERB
cana-5360	302	25	𝑠2,𝑠4	𝑠2,𝑠4	PROPN
cana-5360	302	26	0.7,0.4	0.7,0.4	PROPN
cana-5360	302	27	⟩	⟩	NOUN
cana-5360	302	28	}	}	PUNCT
cana-5360	302	29	𝐵𝒫ℱ𝔑(𝐴1	𝐵𝒫ℱ𝔑(𝐴1	NOUN
cana-5360	302	30	)	)	PUNCT
cana-5360	303	1	=	=	PRON
cana-5360	303	2	{	{	PUNCT
cana-5360	303	3	⟨	⟨	VERB
cana-5360	303	4	𝑠1,𝑠3	𝑠1,𝑠3	PROPN
cana-5360	303	5	0.6,0.6	0.6,0.6	PROPN
cana-5360	303	6	⟩	⟩	NOUN
cana-5360	303	7	,	,	PUNCT
cana-5360	303	8	⟨	⟨	VERB
cana-5360	303	9	𝑠2,𝑠4	𝑠2,𝑠4	PROPN
cana-5360	303	10	0.6,0.5	0.6,0.5	NUM
cana-5360	303	11	⟩	⟩	PROPN
cana-5360	303	12	}	}	PUNCT
cana-5360	303	13	𝒫ℱ𝔑(𝐴2	𝒫ℱ𝔑(𝐴2	NUM
cana-5360	303	14	)	)	PUNCT
cana-5360	303	15	=	=	PRON
cana-5360	303	16	{	{	PUNCT
cana-5360	303	17	⟨	⟨	ADP
cana-5360	303	18	𝑡1,𝑡3	𝑡1,𝑡3	PROPN
cana-5360	303	19	0.4,0.7	0.4,0.7	PROPN
cana-5360	303	20	⟩	⟩	NOUN
cana-5360	303	21	,	,	PUNCT
cana-5360	303	22	⟨	⟨	VERB
cana-5360	303	23	𝑡2,𝑡4	𝑡2,𝑡4	PROPN
cana-5360	303	24	0.3,0.7	0.3,0.7	PROPN
cana-5360	303	25	⟩	⟩	PROPN
cana-5360	303	26	}	}	PUNCT
cana-5360	303	27	𝐵𝒫ℱ𝔑(𝐴2	𝐵𝒫ℱ𝔑(𝐴2	PROPN
cana-5360	303	28	)	)	PUNCT
cana-5360	303	29	=	=	SYM
cana-5360	303	30	𝒫ℱ𝔑(𝐴2	𝒫ℱ𝔑(𝐴2	NUM
cana-5360	303	31	)	)	PUNCT
cana-5360	303	32	=	=	PRON
cana-5360	303	33	{	{	PUNCT
cana-5360	303	34	⟨	⟨	NOUN
cana-5360	303	35	𝑡1,𝑡3	𝑡1,𝑡3	PROPN
cana-5360	303	36	0.4,0.6	0.4,0.6	PROPN
cana-5360	303	37	⟩	⟩	NOUN
cana-5360	303	38	,	,	PUNCT
cana-5360	303	39	⟨	⟨	VERB
cana-5360	303	40	𝑡2,𝑡4	𝑡2,𝑡4	PROPN
cana-5360	303	41	0.5,0.7	0.5,0.7	PROPN
cana-5360	303	42	⟩	⟩	NOUN
cana-5360	303	43	}	}	PUNCT
cana-5360	303	44	.	.	PUNCT
cana-5360	304	1	now	now	ADV
cana-5360	304	2	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	VERB
cana-5360	304	3	)	)	PUNCT
cana-5360	304	4	=	=	PRON
cana-5360	304	5	{	{	PUNCT
cana-5360	304	6	0𝒫	0𝒫	NOUN
cana-5360	304	7	,	,	PUNCT
cana-5360	304	8	1𝒫	1𝒫	INTJ
cana-5360	304	9	,	,	PUNCT
cana-5360	304	10	𝒫ℱ𝔑(𝐴1	𝒫ℱ𝔑(𝐴1	NUM
cana-5360	304	11	)	)	PUNCT
cana-5360	304	12	,	,	PUNCT
cana-5360	304	13	𝒫ℱ𝔑(𝐴1	𝒫ℱ𝔑(𝐴1	NUM
cana-5360	304	14	)	)	PUNCT
cana-5360	304	15	,	,	PUNCT
cana-5360	304	16	𝐵𝒫ℱ𝔑(𝐴1	𝐵𝒫ℱ𝔑(𝐴1	NOUN
cana-5360	304	17	)	)	PUNCT
cana-5360	304	18	}	}	PUNCT
cana-5360	304	19	,	,	PUNCT
cana-5360	304	20	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	X
cana-5360	304	21	)	)	PUNCT
cana-5360	305	1	=	=	PRON
cana-5360	305	2	{	{	PUNCT
cana-5360	305	3	0𝒫	0𝒫	NOUN
cana-5360	305	4	,	,	PUNCT
cana-5360	305	5	1𝒫	1𝒫	INTJ
cana-5360	305	6	,	,	PUNCT
cana-5360	305	7	𝒫ℱ𝔑(𝐴2	𝒫ℱ𝔑(𝐴2	PROPN
cana-5360	305	8	)	)	PUNCT
cana-5360	305	9	,	,	PUNCT
cana-5360	305	10	𝒫ℱ𝔑(𝐴2	𝒫ℱ𝔑(𝐴2	NUM
cana-5360	305	11	)	)	PUNCT
cana-5360	305	12	=	=	SYM
cana-5360	305	13	𝐵𝒫ℱ𝔑(𝐴2	𝐵𝒫ℱ𝔑(𝐴2	PROPN
cana-5360	305	14	)	)	PUNCT
cana-5360	305	15	}	}	PUNCT
cana-5360	305	16	.	.	PUNCT
cana-5360	306	1	let	let	VERB
cana-5360	306	2	ℎ𝑃	ℎ𝑃	NOUN
cana-5360	306	3	:	:	PUNCT
cana-5360	306	4	(	(	PUNCT
cana-5360	306	5	𝑈1	𝑈1	NOUN
cana-5360	306	6	,	,	PUNCT
cana-5360	306	7	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	306	8	)	)	PUNCT
cana-5360	306	9	)	)	PUNCT
cana-5360	306	10	→	→	SYM
cana-5360	306	11	(	(	PUNCT
cana-5360	306	12	𝑈2	𝑈2	NOUN
cana-5360	306	13	,	,	PUNCT
cana-5360	306	14	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	306	15	)	)	PUNCT
cana-5360	306	16	)	)	PUNCT
cana-5360	306	17	be	be	AUX
cana-5360	306	18	an	an	DET
cana-5360	306	19	identity	identity	NOUN
cana-5360	306	20	function	function	NOUN
cana-5360	306	21	,	,	PUNCT
cana-5360	306	22	then	then	ADV
cana-5360	306	23	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	306	24	is	be	AUX
cana-5360	306	25	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	PROPN
cana-5360	306	26	(	(	PUNCT
cana-5360	306	27	resp	resp	NOUN
cana-5360	306	28	.	.	PUNCT
cana-5360	307	1	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠	PRON
cana-5360	307	2	and	and	CCONJ
cana-5360	307	3	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	PROPN
cana-5360	307	4	)	)	PUNCT
cana-5360	307	5	but	but	CCONJ
cana-5360	307	6	not	not	PART
cana-5360	307	7	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	NOUN
cana-5360	307	8	(	(	PUNCT
cana-5360	307	9	resp	resp	NOUN
cana-5360	307	10	.	.	PUNCT
cana-5360	308	1	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	NOUN
cana-5360	308	2	and	and	CCONJ
cana-5360	308	3	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐶𝑡𝑠	NUM
cana-5360	308	4	)	)	PUNCT
cana-5360	308	5	.	.	PUNCT
cana-5360	309	1	since	since	SCONJ
cana-5360	309	2	,	,	PUNCT
cana-5360	309	3	𝒫ℱ𝔑(𝐴2	𝒫ℱ𝔑(𝐴2	NUM
cana-5360	309	4	)	)	PUNCT
cana-5360	309	5	is	be	AUX
cana-5360	309	6	a	a	DET
cana-5360	309	7	𝒫ℱ𝒩𝑜	𝒫ℱ𝒩𝑜	PROPN
cana-5360	309	8	set	set	NOUN
cana-5360	309	9	in	in	ADP
cana-5360	309	10	𝑈2	𝑈2	PROPN
cana-5360	309	11	but	but	CCONJ
cana-5360	309	12	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	309	13	−1(𝒫ℱ𝔑(𝐴2	−1(𝒫ℱ𝔑(𝐴2	PROPN
cana-5360	309	14	)	)	PUNCT
cana-5360	309	15	)	)	PUNCT
cana-5360	310	1	=	=	SYM
cana-5360	310	2	𝒫ℱ𝔑(𝐴2	𝒫ℱ𝔑(𝐴2	PROPN
cana-5360	310	3	)	)	PUNCT
cana-5360	310	4	is	be	AUX
cana-5360	310	5	not	not	PART
cana-5360	310	6	𝒫ℱ𝒩𝛿𝑐	𝒫ℱ𝒩𝛿𝑐	NUM
cana-5360	310	7	(	(	PUNCT
cana-5360	310	8	resp	resp	NOUN
cana-5360	310	9	.	.	PUNCT
cana-5360	311	1	𝒫ℱ𝒩𝛿𝒮𝑐	𝒫ℱ𝒩𝛿𝒮𝑐	PROPN
cana-5360	311	2	and	and	CCONJ
cana-5360	311	3	𝒫ℱ𝒩𝛿𝛼𝑐	𝒫ℱ𝒩𝛿𝛼𝑐	PROPN
cana-5360	311	4	)	)	PUNCT
cana-5360	311	5	set	set	VERB
cana-5360	311	6	in	in	ADP
cana-5360	311	7	𝑈1	𝑈1	PROPN
cana-5360	311	8	.	.	PUNCT
cana-5360	312	1	example	example	NOUN
cana-5360	312	2	3.3	3.3	NUM
cana-5360	312	3	let	let	VERB
cana-5360	312	4	𝑈1	𝑈1	NOUN
cana-5360	312	5	=	=	SYM
cana-5360	312	6	{	{	PUNCT
cana-5360	312	7	𝑠1	𝑠1	PROPN
cana-5360	312	8	,	,	PUNCT
cana-5360	312	9	𝑠2	𝑠2	NOUN
cana-5360	312	10	,	,	PUNCT
cana-5360	312	11	𝑠3	𝑠3	NOUN
cana-5360	312	12	,	,	PUNCT
cana-5360	312	13	𝑠4	𝑠4	PROPN
cana-5360	312	14	}	}	PUNCT
cana-5360	312	15	,	,	PUNCT
cana-5360	312	16	𝑈2	𝑈2	PROPN
cana-5360	312	17	=	=	PUNCT
cana-5360	312	18	{	{	PUNCT
cana-5360	312	19	𝑡1	𝑡1	PROPN
cana-5360	312	20	,	,	PUNCT
cana-5360	312	21	𝑡2	𝑡2	PROPN
cana-5360	312	22	,	,	PUNCT
cana-5360	312	23	𝑡3	𝑡3	PROPN
cana-5360	312	24	,	,	PUNCT
cana-5360	312	25	𝑡4	𝑡4	PROPN
cana-5360	312	26	}	}	PUNCT
cana-5360	312	27	are	be	AUX
cana-5360	312	28	the	the	DET
cana-5360	312	29	universe	universe	NOUN
cana-5360	312	30	sets	set	NOUN
cana-5360	312	31	and	and	CCONJ
cana-5360	312	32	the	the	DET
cana-5360	312	33	equivalence	equivalence	NOUN
cana-5360	312	34	relations	relation	NOUN
cana-5360	312	35	are	be	AUX
cana-5360	312	36	𝑈1/𝑅	𝑈1/𝑅	X
cana-5360	312	37	=	=	SYM
cana-5360	312	38	{	{	PUNCT
cana-5360	312	39	{	{	PUNCT
cana-5360	312	40	𝑠1	𝑠1	PROPN
cana-5360	312	41	,	,	PUNCT
cana-5360	312	42	𝑠4	𝑠4	PROPN
cana-5360	312	43	}	}	PUNCT
cana-5360	312	44	,	,	PUNCT
cana-5360	312	45	{	{	PUNCT
cana-5360	312	46	𝑠2	𝑠2	NOUN
cana-5360	312	47	}	}	PUNCT
cana-5360	312	48	,	,	PUNCT
cana-5360	312	49	{	{	PUNCT
cana-5360	312	50	𝑠3	𝑠3	NOUN
cana-5360	312	51	}	}	PUNCT
cana-5360	312	52	}	}	PUNCT
cana-5360	312	53	and	and	CCONJ
cana-5360	312	54	𝑈2/𝑅	𝑈2/𝑅	PUNCT
cana-5360	312	55	=	=	PRON
cana-5360	312	56	{	{	PUNCT
cana-5360	312	57	{	{	PUNCT
cana-5360	312	58	𝑡1	𝑡1	NOUN
cana-5360	312	59	,	,	PUNCT
cana-5360	312	60	𝑡4	𝑡4	PROPN
cana-5360	312	61	}	}	PUNCT
cana-5360	312	62	,	,	PUNCT
cana-5360	312	63	{	{	PUNCT
cana-5360	312	64	𝑡2	𝑡2	NOUN
cana-5360	312	65	}	}	PUNCT
cana-5360	312	66	,	,	PUNCT
cana-5360	312	67	{	{	PUNCT
cana-5360	312	68	𝑡3	𝑡3	PROPN
cana-5360	312	69	}	}	PUNCT
cana-5360	312	70	}	}	PUNCT
cana-5360	312	71	.	.	PUNCT
cana-5360	313	1	let	let	VERB
cana-5360	313	2	𝐴1	𝐴1	PROPN
cana-5360	313	3	=	=	PUNCT
cana-5360	313	4	{	{	PUNCT
cana-5360	313	5	⟨	⟨	ADP
cana-5360	313	6	𝑠1	𝑠1	PROPN
cana-5360	313	7	0.3,0.7	0.3,0.7	PROPN
cana-5360	313	8	⟩	⟩	NOUN
cana-5360	313	9	,	,	PUNCT
cana-5360	313	10	⟨	⟨	VERB
cana-5360	313	11	𝑠2	𝑠2	PROPN
cana-5360	313	12	0.1,0.6	0.1,0.6	PROPN
cana-5360	313	13	⟩	⟩	NOUN
cana-5360	313	14	,	,	PUNCT
cana-5360	313	15	⟨	⟨	VERB
cana-5360	313	16	𝑠3	𝑠3	PROPN
cana-5360	313	17	0.4,0.6	0.4,0.6	PROPN
cana-5360	313	18	⟩	⟩	NOUN
cana-5360	313	19	,	,	PUNCT
cana-5360	313	20	⟨	⟨	VERB
cana-5360	313	21	𝑠4	𝑠4	PROPN
cana-5360	313	22	0.4,0.6	0.4,0.6	PROPN
cana-5360	313	23	⟩	⟩	NOUN
cana-5360	313	24	}	}	PUNCT
cana-5360	313	25	and	and	CCONJ
cana-5360	313	26	𝐴2	𝐴2	PROPN
cana-5360	313	27	=	=	PUNCT
cana-5360	313	28	{	{	PUNCT
cana-5360	313	29	⟨	⟨	VERB
cana-5360	313	30	𝑡1	𝑡1	NOUN
cana-5360	313	31	0.6,0.4	0.6,0.4	PROPN
cana-5360	313	32	⟩	⟩	NOUN
cana-5360	313	33	,	,	PUNCT
cana-5360	313	34	⟨	⟨	VERB
cana-5360	313	35	𝑡2	𝑡2	PROPN
cana-5360	313	36	0.6,0.2	0.6,0.2	PROPN
cana-5360	313	37	⟩	⟩	NOUN
cana-5360	313	38	,	,	PUNCT
cana-5360	313	39	⟨	⟨	VERB
cana-5360	313	40	𝑡3	𝑡3	PROPN
cana-5360	313	41	0.6,0.4	0.6,0.4	PROPN
cana-5360	313	42	⟩	⟩	NOUN
cana-5360	313	43	,	,	PUNCT
cana-5360	313	44	⟨	⟨	VERB
cana-5360	313	45	𝑡4	𝑡4	PROPN
cana-5360	313	46	0.6,0.4	0.6,0.4	PROPN
cana-5360	313	47	⟩	⟩	PROPN
cana-5360	313	48	}	}	PUNCT
cana-5360	313	49	be	be	VERB
cana-5360	313	50	a	a	DET
cana-5360	313	51	pythagorean	pythagorean	ADJ
cana-5360	313	52	fuzzy	fuzzy	ADJ
cana-5360	313	53	subsets	subset	NOUN
cana-5360	313	54	of	of	ADP
cana-5360	313	55	𝑈1	𝑈1	NOUN
cana-5360	313	56	and	and	CCONJ
cana-5360	313	57	𝑈2	𝑈2	NOUN
cana-5360	313	58	respectively	respectively	ADV
cana-5360	313	59	.	.	PUNCT
cana-5360	314	1	𝒫ℱ𝔑(𝐴1	𝒫ℱ𝔑(𝐴1	NUM
cana-5360	314	2	)	)	PUNCT
cana-5360	314	3	=	=	PRON
cana-5360	314	4	{	{	PUNCT
cana-5360	314	5	⟨	⟨	ADP
cana-5360	314	6	𝑠1,𝑠4	𝑠1,𝑠4	PROPN
cana-5360	314	7	0.3,0.7	0.3,0.7	PROPN
cana-5360	314	8	⟩	⟩	NOUN
cana-5360	314	9	,	,	PUNCT
cana-5360	314	10	⟨	⟨	VERB
cana-5360	314	11	𝑠2	𝑠2	PROPN
cana-5360	314	12	0.1,0.6	0.1,0.6	PROPN
cana-5360	314	13	⟩	⟩	NOUN
cana-5360	314	14	,	,	PUNCT
cana-5360	314	15	⟨	⟨	VERB
cana-5360	314	16	𝑠3	𝑠3	PROPN
cana-5360	314	17	0.4,0.6	0.4,0.6	PROPN
cana-5360	314	18	⟩	⟩	NOUN
cana-5360	314	19	}	}	PUNCT
cana-5360	314	20	,	,	PUNCT
cana-5360	314	21	𝐵𝒫ℱ𝔑(𝐴1	𝐵𝒫ℱ𝔑(𝐴1	NOUN
cana-5360	314	22	)	)	PUNCT
cana-5360	314	23	=	=	SYM
cana-5360	315	1	𝒫ℱ𝔑(𝐴1	𝒫ℱ𝔑(𝐴1	NUM
cana-5360	315	2	)	)	PUNCT
cana-5360	315	3	=	=	PRON
cana-5360	315	4	{	{	PUNCT
cana-5360	315	5	⟨	⟨	ADP
cana-5360	315	6	𝑠1,𝑠4	𝑠1,𝑠4	PROPN
cana-5360	315	7	0.4,0.6	0.4,0.6	PROPN
cana-5360	315	8	⟩	⟩	NOUN
cana-5360	315	9	,	,	PUNCT
cana-5360	315	10	⟨	⟨	VERB
cana-5360	315	11	𝑠2	𝑠2	PROPN
cana-5360	315	12	0.1,0.6	0.1,0.6	PROPN
cana-5360	315	13	⟩	⟩	NOUN
cana-5360	315	14	,	,	PUNCT
cana-5360	315	15	⟨	⟨	VERB
cana-5360	315	16	𝑠3	𝑠3	PROPN
cana-5360	315	17	0.4,0.6	0.4,0.6	PROPN
cana-5360	315	18	⟩	⟩	NOUN
cana-5360	315	19	}	}	PUNCT
cana-5360	315	20	,	,	PUNCT
cana-5360	315	21	𝒫ℱ𝔑(𝐴2	𝒫ℱ𝔑(𝐴2	NUM
cana-5360	315	22	)	)	PUNCT
cana-5360	315	23	=	=	PRON
cana-5360	315	24	{	{	PUNCT
cana-5360	315	25	⟨	⟨	VERB
cana-5360	315	26	𝑡1,𝑡4	𝑡1,𝑡4	PROPN
cana-5360	315	27	0.6,0.4	0.6,0.4	PROPN
cana-5360	315	28	⟩	⟩	NOUN
cana-5360	315	29	,	,	PUNCT
cana-5360	315	30	⟨	⟨	VERB
cana-5360	315	31	𝑡2	𝑡2	PROPN
cana-5360	315	32	0.6,0.2	0.6,0.2	PROPN
cana-5360	315	33	⟩	⟩	NOUN
cana-5360	315	34	,	,	PUNCT
cana-5360	315	35	⟨	⟨	VERB
cana-5360	315	36	𝑡3	𝑡3	PROPN
cana-5360	315	37	0.6,0.4	0.6,0.4	PROPN
cana-5360	315	38	⟩	⟩	PROPN
cana-5360	315	39	}	}	PUNCT
cana-5360	315	40	,	,	PUNCT
cana-5360	315	41	𝒫ℱ𝔑(𝐴2	𝒫ℱ𝔑(𝐴2	NUM
cana-5360	315	42	)	)	PUNCT
cana-5360	316	1	=	=	PRON
cana-5360	316	2	{	{	PUNCT
cana-5360	316	3	⟨	⟨	VERB
cana-5360	316	4	𝑡1,𝑡4	𝑡1,𝑡4	PROPN
cana-5360	316	5	0.6,0.4	0.6,0.4	PROPN
cana-5360	316	6	⟩	⟩	NOUN
cana-5360	316	7	,	,	PUNCT
cana-5360	316	8	⟨	⟨	VERB
cana-5360	316	9	𝑡2	𝑡2	PROPN
cana-5360	316	10	0.6,0.2	0.6,0.2	PROPN
cana-5360	316	11	⟩	⟩	NOUN
cana-5360	316	12	,	,	PUNCT
cana-5360	316	13	⟨	⟨	VERB
cana-5360	316	14	𝑡3	𝑡3	PROPN
cana-5360	316	15	0.6,0.4	0.6,0.4	PROPN
cana-5360	316	16	⟩	⟩	PROPN
cana-5360	316	17	}	}	PUNCT
cana-5360	316	18	,	,	PUNCT
cana-5360	316	19	𝐵𝒫ℱ𝔑(𝐴2	𝐵𝒫ℱ𝔑(𝐴2	PROPN
cana-5360	316	20	)	)	PUNCT
cana-5360	316	21	=	=	PRON
cana-5360	316	22	{	{	PUNCT
cana-5360	316	23	⟨	⟨	PROPN
cana-5360	316	24	𝑡1,𝑡4	𝑡1,𝑡4	PROPN
cana-5360	316	25	0.4,0.6	0.4,0.6	PROPN
cana-5360	316	26	⟩	⟩	NOUN
cana-5360	316	27	,	,	PUNCT
cana-5360	316	28	⟨	⟨	VERB
cana-5360	316	29	𝑡2	𝑡2	PROPN
cana-5360	316	30	0.2,0.6	0.2,0.6	PROPN
cana-5360	316	31	⟩	⟩	NOUN
cana-5360	316	32	,	,	PUNCT
cana-5360	316	33	⟨	⟨	VERB
cana-5360	316	34	𝑡3	𝑡3	PROPN
cana-5360	316	35	0.4,0.6	0.4,0.6	PROPN
cana-5360	316	36	⟩	⟩	NOUN
cana-5360	316	37	}	}	PUNCT
cana-5360	316	38	.	.	PUNCT
cana-5360	317	1	communications	communication	NOUN
cana-5360	317	2	on	on	ADP
cana-5360	317	3	applied	apply	VERB
cana-5360	317	4	nonlinear	nonlinear	ADJ
cana-5360	317	5	analysis	analysis	NOUN
cana-5360	317	6	issn	issn	NOUN
cana-5360	317	7	:	:	PUNCT
cana-5360	317	8	1074	1074	NUM
cana-5360	317	9	-	-	PUNCT
cana-5360	317	10	133x	133x	NUM
cana-5360	317	11	vol	vol	VERB
cana-5360	317	12	32	32	NUM
cana-5360	317	13	no	no	NOUN
cana-5360	317	14	.	.	PUNCT
cana-5360	318	1	10s	10	NOUN
cana-5360	318	2	(	(	PUNCT
cana-5360	318	3	2025	2025	NUM
cana-5360	318	4	)	)	PUNCT
cana-5360	318	5	1935	1935	NUM
cana-5360	318	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5360	318	7	now	now	ADV
cana-5360	318	8	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	318	9	)	)	PUNCT
cana-5360	318	10	=	=	PRON
cana-5360	318	11	{	{	PUNCT
cana-5360	318	12	0𝒫	0𝒫	NOUN
cana-5360	318	13	,	,	PUNCT
cana-5360	318	14	1𝒫	1𝒫	INTJ
cana-5360	318	15	,	,	PUNCT
cana-5360	318	16	𝒫ℱ𝔑(𝐴1	𝒫ℱ𝔑(𝐴1	NUM
cana-5360	318	17	)	)	PUNCT
cana-5360	318	18	,	,	PUNCT
cana-5360	318	19	𝒫ℱ𝔑(𝐴1	𝒫ℱ𝔑(𝐴1	NUM
cana-5360	318	20	)	)	PUNCT
cana-5360	318	21	=	=	SYM
cana-5360	318	22	𝐵𝒫ℱ𝔑(𝐴1	𝐵𝒫ℱ𝔑(𝐴1	NOUN
cana-5360	318	23	)	)	PUNCT
cana-5360	318	24	}	}	PUNCT
cana-5360	318	25	,	,	PUNCT
cana-5360	318	26	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	X
cana-5360	318	27	)	)	PUNCT
cana-5360	319	1	=	=	PRON
cana-5360	319	2	{	{	PUNCT
cana-5360	319	3	0𝒫	0𝒫	NOUN
cana-5360	319	4	,	,	PUNCT
cana-5360	319	5	1𝒫	1𝒫	INTJ
cana-5360	319	6	,	,	PUNCT
cana-5360	319	7	𝒫ℱ𝔑(𝐴2	𝒫ℱ𝔑(𝐴2	PROPN
cana-5360	319	8	)	)	PUNCT
cana-5360	319	9	,	,	PUNCT
cana-5360	319	10	𝒫ℱ𝔑(𝐴2	𝒫ℱ𝔑(𝐴2	NUM
cana-5360	319	11	)	)	PUNCT
cana-5360	319	12	,	,	PUNCT
cana-5360	319	13	𝐵𝒫ℱ𝔑(𝐴2	𝐵𝒫ℱ𝔑(𝐴2	PROPN
cana-5360	319	14	)	)	PUNCT
cana-5360	319	15	}	}	PUNCT
cana-5360	319	16	.	.	PUNCT
cana-5360	320	1	let	let	VERB
cana-5360	320	2	ℎ𝑃	ℎ𝑃	NOUN
cana-5360	320	3	:	:	PUNCT
cana-5360	320	4	(	(	PUNCT
cana-5360	320	5	𝑈1	𝑈1	NOUN
cana-5360	320	6	,	,	PUNCT
cana-5360	320	7	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	320	8	)	)	PUNCT
cana-5360	320	9	)	)	PUNCT
cana-5360	320	10	→	→	SYM
cana-5360	320	11	(	(	PUNCT
cana-5360	320	12	𝑈2	𝑈2	NOUN
cana-5360	320	13	,	,	PUNCT
cana-5360	320	14	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	320	15	)	)	PUNCT
cana-5360	320	16	)	)	PUNCT
cana-5360	320	17	be	be	AUX
cana-5360	320	18	an	an	DET
cana-5360	320	19	identity	identity	NOUN
cana-5360	320	20	function	function	NOUN
cana-5360	320	21	,	,	PUNCT
cana-5360	320	22	then	then	ADV
cana-5360	320	23	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	320	24	is	be	AUX
cana-5360	320	25	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	NOUN
cana-5360	320	26	(	(	PUNCT
cana-5360	320	27	resp	resp	NOUN
cana-5360	320	28	.	.	PUNCT
cana-5360	321	1	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	NOUN
cana-5360	321	2	)	)	PUNCT
cana-5360	321	3	but	but	CCONJ
cana-5360	321	4	not	not	PART
cana-5360	321	5	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	NOUN
cana-5360	321	6	(	(	PUNCT
cana-5360	321	7	resp	resp	NOUN
cana-5360	321	8	.	.	PUNCT
cana-5360	321	9	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐶𝑡𝑠	PROPN
cana-5360	321	10	)	)	PUNCT
cana-5360	321	11	.	.	PUNCT
cana-5360	322	1	since	since	SCONJ
cana-5360	322	2	,	,	PUNCT
cana-5360	322	3	𝒫ℱ𝔑(𝐴2	𝒫ℱ𝔑(𝐴2	NUM
cana-5360	322	4	)	)	PUNCT
cana-5360	322	5	is	be	AUX
cana-5360	322	6	a	a	DET
cana-5360	322	7	𝒫ℱ𝒩𝑜	𝒫ℱ𝒩𝑜	PROPN
cana-5360	322	8	set	set	NOUN
cana-5360	322	9	in	in	ADP
cana-5360	322	10	𝑈2	𝑈2	PROPN
cana-5360	322	11	but	but	CCONJ
cana-5360	322	12	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	322	13	−1(𝒫ℱ𝔑(𝐴2	−1(𝒫ℱ𝔑(𝐴2	PROPN
cana-5360	322	14	)	)	PUNCT
cana-5360	322	15	)	)	PUNCT
cana-5360	323	1	=	=	SYM
cana-5360	323	2	𝒫ℱ𝔑(𝐴2	𝒫ℱ𝔑(𝐴2	PROPN
cana-5360	323	3	)	)	PUNCT
cana-5360	323	4	is	be	AUX
cana-5360	323	5	not	not	PART
cana-5360	323	6	𝒫ℱ𝒩𝛿𝑐	𝒫ℱ𝒩𝛿𝑐	NUM
cana-5360	323	7	(	(	PUNCT
cana-5360	323	8	resp	resp	NOUN
cana-5360	323	9	.	.	PUNCT
cana-5360	324	1	𝒫ℱ𝒩𝛿𝛼𝑐	𝒫ℱ𝒩𝛿𝛼𝑐	NOUN
cana-5360	324	2	)	)	PUNCT
cana-5360	324	3	set	set	VERB
cana-5360	324	4	in	in	ADP
cana-5360	324	5	𝑈1	𝑈1	PROPN
cana-5360	324	6	.	.	PUNCT
cana-5360	325	1	example	example	NOUN
cana-5360	325	2	3.4	3.4	NUM
cana-5360	325	3	let	let	VERB
cana-5360	325	4	𝑈1	𝑈1	NOUN
cana-5360	325	5	=	=	SYM
cana-5360	325	6	{	{	PUNCT
cana-5360	325	7	𝑠1	𝑠1	PROPN
cana-5360	325	8	,	,	PUNCT
cana-5360	325	9	𝑠2	𝑠2	NOUN
cana-5360	325	10	,	,	PUNCT
cana-5360	325	11	𝑠3	𝑠3	NOUN
cana-5360	325	12	,	,	PUNCT
cana-5360	325	13	𝑠4	𝑠4	PROPN
cana-5360	325	14	}	}	PUNCT
cana-5360	325	15	,	,	PUNCT
cana-5360	325	16	𝑈2	𝑈2	PROPN
cana-5360	325	17	=	=	PUNCT
cana-5360	325	18	{	{	PUNCT
cana-5360	325	19	𝑡1	𝑡1	PROPN
cana-5360	325	20	,	,	PUNCT
cana-5360	325	21	𝑡2	𝑡2	PROPN
cana-5360	325	22	,	,	PUNCT
cana-5360	325	23	𝑡3	𝑡3	PROPN
cana-5360	325	24	,	,	PUNCT
cana-5360	325	25	𝑡4	𝑡4	PROPN
cana-5360	325	26	}	}	PUNCT
cana-5360	325	27	are	be	AUX
cana-5360	325	28	the	the	DET
cana-5360	325	29	universe	universe	NOUN
cana-5360	325	30	sets	set	NOUN
cana-5360	325	31	and	and	CCONJ
cana-5360	325	32	the	the	DET
cana-5360	325	33	equivalence	equivalence	NOUN
cana-5360	325	34	relations	relation	NOUN
cana-5360	325	35	are	be	AUX
cana-5360	325	36	𝑈1/𝑅	𝑈1/𝑅	X
cana-5360	325	37	=	=	SYM
cana-5360	325	38	{	{	PUNCT
cana-5360	325	39	{	{	PUNCT
cana-5360	325	40	𝑠1	𝑠1	NOUN
cana-5360	325	41	,	,	PUNCT
cana-5360	325	42	𝑠3	𝑠3	PROPN
cana-5360	325	43	}	}	PUNCT
cana-5360	325	44	,	,	PUNCT
cana-5360	325	45	{	{	PUNCT
cana-5360	325	46	𝑠2	𝑠2	NOUN
cana-5360	325	47	,	,	PUNCT
cana-5360	325	48	𝑠4	𝑠4	PROPN
cana-5360	325	49	}	}	PUNCT
cana-5360	325	50	}	}	PUNCT
cana-5360	325	51	and	and	CCONJ
cana-5360	325	52	𝑈2/𝑅	𝑈2/𝑅	PUNCT
cana-5360	325	53	=	=	PRON
cana-5360	325	54	{	{	PUNCT
cana-5360	325	55	{	{	PUNCT
cana-5360	325	56	𝑡1	𝑡1	NOUN
cana-5360	325	57	,	,	PUNCT
cana-5360	325	58	𝑡3	𝑡3	PROPN
cana-5360	325	59	}	}	PUNCT
cana-5360	325	60	,	,	PUNCT
cana-5360	325	61	{	{	PUNCT
cana-5360	325	62	𝑡2	𝑡2	PROPN
cana-5360	325	63	,	,	PUNCT
cana-5360	325	64	𝑡4	𝑡4	PROPN
cana-5360	325	65	}	}	PUNCT
cana-5360	325	66	}	}	PUNCT
cana-5360	325	67	.	.	PUNCT
cana-5360	326	1	let	let	VERB
cana-5360	326	2	𝐴1	𝐴1	PROPN
cana-5360	326	3	=	=	PUNCT
cana-5360	326	4	{	{	PUNCT
cana-5360	326	5	⟨	⟨	ADP
cana-5360	326	6	𝑠1	𝑠1	PROPN
cana-5360	326	7	0.4,0.7	0.4,0.7	PROPN
cana-5360	326	8	⟩	⟩	PROPN
cana-5360	326	9	,	,	PUNCT
cana-5360	326	10	⟨	⟨	VERB
cana-5360	326	11	𝑠2	𝑠2	PROPN
cana-5360	326	12	0.5,0.7	0.5,0.7	PROPN
cana-5360	326	13	⟩	⟩	NOUN
cana-5360	326	14	,	,	PUNCT
cana-5360	326	15	⟨	⟨	VERB
cana-5360	326	16	𝑠3	𝑠3	PROPN
cana-5360	326	17	0.4,0.6	0.4,0.6	PROPN
cana-5360	326	18	⟩	⟩	NOUN
cana-5360	326	19	,	,	PUNCT
cana-5360	326	20	⟨	⟨	VERB
cana-5360	326	21	𝑠4	𝑠4	PROPN
cana-5360	326	22	0.3,0.7	0.3,0.7	PROPN
cana-5360	326	23	⟩	⟩	PROPN
cana-5360	326	24	}	}	PUNCT
cana-5360	326	25	and	and	CCONJ
cana-5360	326	26	𝐴2	𝐴2	PROPN
cana-5360	326	27	=	=	PUNCT
cana-5360	326	28	{	{	PUNCT
cana-5360	326	29	⟨	⟨	NOUN
cana-5360	326	30	𝑡1	𝑡1	NOUN
cana-5360	326	31	0.4,0.8	0.4,0.8	NUM
cana-5360	326	32	⟩	⟩	NOUN
cana-5360	326	33	,	,	PUNCT
cana-5360	326	34	⟨	⟨	VERB
cana-5360	326	35	𝑡2	𝑡2	PROPN
cana-5360	326	36	0.5,0.4	0.5,0.4	PROPN
cana-5360	327	1	⟩	⟩	NOUN
cana-5360	327	2	,	,	PUNCT
cana-5360	327	3	⟨	⟨	VERB
cana-5360	327	4	𝑡3	𝑡3	PROPN
cana-5360	327	5	0.6,0.6	0.6,0.6	PROPN
cana-5360	327	6	⟩	⟩	NOUN
cana-5360	327	7	,	,	PUNCT
cana-5360	327	8	⟨	⟨	VERB
cana-5360	327	9	𝑡4	𝑡4	PROPN
cana-5360	327	10	0.7,0.6	0.7,0.6	NOUN
cana-5360	327	11	⟩	⟩	NOUN
cana-5360	327	12	}	}	PUNCT
cana-5360	327	13	be	be	VERB
cana-5360	327	14	a	a	DET
cana-5360	327	15	pythagorean	pythagorean	ADJ
cana-5360	327	16	fuzzy	fuzzy	ADJ
cana-5360	327	17	subsets	subset	NOUN
cana-5360	327	18	of	of	ADP
cana-5360	327	19	𝑈1	𝑈1	NOUN
cana-5360	327	20	and	and	CCONJ
cana-5360	327	21	𝑈2	𝑈2	NOUN
cana-5360	327	22	respectively	respectively	ADV
cana-5360	327	23	.	.	PUNCT
cana-5360	328	1	𝒫ℱ𝔑(𝐴1	𝒫ℱ𝔑(𝐴1	NUM
cana-5360	328	2	)	)	PUNCT
cana-5360	328	3	=	=	PRON
cana-5360	328	4	{	{	PUNCT
cana-5360	328	5	⟨	⟨	VERB
cana-5360	328	6	𝑠1,𝑠3	𝑠1,𝑠3	PROPN
cana-5360	328	7	0.4,0.7	0.4,0.7	PROPN
cana-5360	328	8	⟩	⟩	NOUN
cana-5360	328	9	,	,	PUNCT
cana-5360	328	10	⟨	⟨	VERB
cana-5360	328	11	𝑠2,𝑠4	𝑠2,𝑠4	PROPN
cana-5360	328	12	0.3,0.7	0.3,0.7	PROPN
cana-5360	328	13	⟩	⟩	PROPN
cana-5360	328	14	}	}	PUNCT
cana-5360	328	15	𝒫ℱ𝔑(𝐴1	𝒫ℱ𝔑(𝐴1	NUM
cana-5360	328	16	)	)	PUNCT
cana-5360	328	17	=	=	PRON
cana-5360	328	18	{	{	PUNCT
cana-5360	328	19	⟨	⟨	VERB
cana-5360	328	20	𝑠1,𝑠3	𝑠1,𝑠3	PROPN
cana-5360	328	21	0.4,0.6	0.4,0.6	PROPN
cana-5360	328	22	⟩	⟩	NOUN
cana-5360	328	23	,	,	PUNCT
cana-5360	328	24	⟨	⟨	VERB
cana-5360	328	25	𝑠2,𝑠4	𝑠2,𝑠4	PROPN
cana-5360	328	26	0.5,0.7	0.5,0.7	PROPN
cana-5360	328	27	⟩	⟩	NOUN
cana-5360	328	28	}	}	PUNCT
cana-5360	328	29	𝐵𝒫ℱ𝔑(𝐴1	𝐵𝒫ℱ𝔑(𝐴1	NOUN
cana-5360	328	30	)	)	PUNCT
cana-5360	329	1	=	=	PRON
cana-5360	329	2	{	{	PUNCT
cana-5360	329	3	⟨	⟨	VERB
cana-5360	329	4	𝑠1,𝑠3	𝑠1,𝑠3	PROPN
cana-5360	329	5	0.4,0.6	0.4,0.6	PROPN
cana-5360	329	6	⟩	⟩	NOUN
cana-5360	329	7	,	,	PUNCT
cana-5360	329	8	⟨	⟨	VERB
cana-5360	329	9	𝑠2,𝑠4	𝑠2,𝑠4	PROPN
cana-5360	329	10	0.5,0.7	0.5,0.7	PROPN
cana-5360	329	11	⟩	⟩	PROPN
cana-5360	329	12	}	}	PUNCT
cana-5360	329	13	𝒫ℱ𝔑(𝐴2	𝒫ℱ𝔑(𝐴2	PROPN
cana-5360	329	14	)	)	PUNCT
cana-5360	329	15	=	=	PRON
cana-5360	329	16	{	{	PUNCT
cana-5360	329	17	⟨	⟨	X
cana-5360	329	18	𝑡1,𝑡3	𝑡1,𝑡3	PROPN
cana-5360	329	19	0.4,0.8	0.4,0.8	NUM
cana-5360	329	20	⟩	⟩	NOUN
cana-5360	329	21	,	,	PUNCT
cana-5360	329	22	⟨	⟨	VERB
cana-5360	329	23	𝑡2,𝑡4	𝑡2,𝑡4	PROPN
cana-5360	329	24	0.5,0.6	0.5,0.6	PROPN
cana-5360	329	25	⟩	⟩	PROPN
cana-5360	329	26	}	}	PUNCT
cana-5360	329	27	𝒫ℱ𝔑(𝐴2	𝒫ℱ𝔑(𝐴2	PROPN
cana-5360	329	28	)	)	PUNCT
cana-5360	330	1	=	=	PRON
cana-5360	330	2	{	{	PUNCT
cana-5360	330	3	⟨	⟨	NOUN
cana-5360	330	4	𝑡1,𝑡3	𝑡1,𝑡3	PROPN
cana-5360	330	5	0.6,0.6	0.6,0.6	PROPN
cana-5360	330	6	⟩	⟩	NOUN
cana-5360	330	7	,	,	PUNCT
cana-5360	330	8	⟨	⟨	VERB
cana-5360	330	9	𝑡2,𝑡4	𝑡2,𝑡4	PROPN
cana-5360	330	10	0.7,0.4	0.7,0.4	NUM
cana-5360	330	11	⟩	⟩	NOUN
cana-5360	330	12	}	}	PUNCT
cana-5360	330	13	𝐵𝒫ℱ𝔑(𝐴2	𝐵𝒫ℱ𝔑(𝐴2	PROPN
cana-5360	330	14	)	)	PUNCT
cana-5360	330	15	=	=	PRON
cana-5360	330	16	{	{	PUNCT
cana-5360	330	17	⟨	⟨	NOUN
cana-5360	330	18	𝑡1,𝑡3	𝑡1,𝑡3	PROPN
cana-5360	330	19	0.6,0.6	0.6,0.6	PROPN
cana-5360	330	20	⟩	⟩	NOUN
cana-5360	330	21	,	,	PUNCT
cana-5360	330	22	⟨	⟨	VERB
cana-5360	330	23	𝑡2,𝑡4	𝑡2,𝑡4	PROPN
cana-5360	330	24	0.6,0.5	0.6,0.5	NUM
cana-5360	330	25	⟩	⟩	NOUN
cana-5360	330	26	}	}	PUNCT
cana-5360	330	27	.	.	PUNCT
cana-5360	331	1	now	now	ADV
cana-5360	331	2	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	VERB
cana-5360	331	3	)	)	PUNCT
cana-5360	331	4	=	=	PRON
cana-5360	331	5	{	{	PUNCT
cana-5360	331	6	0𝒫	0𝒫	NOUN
cana-5360	331	7	,	,	PUNCT
cana-5360	331	8	1𝒫	1𝒫	INTJ
cana-5360	331	9	,	,	PUNCT
cana-5360	331	10	𝒫ℱ𝔑(𝐴1	𝒫ℱ𝔑(𝐴1	NUM
cana-5360	331	11	)	)	PUNCT
cana-5360	331	12	,	,	PUNCT
cana-5360	331	13	𝒫ℱ𝔑(𝐴1	𝒫ℱ𝔑(𝐴1	NUM
cana-5360	331	14	)	)	PUNCT
cana-5360	331	15	,	,	PUNCT
cana-5360	331	16	𝐵𝒫ℱ𝔑(𝐴1	𝐵𝒫ℱ𝔑(𝐴1	NOUN
cana-5360	331	17	)	)	PUNCT
cana-5360	331	18	}	}	PUNCT
cana-5360	331	19	,	,	PUNCT
cana-5360	331	20	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	X
cana-5360	331	21	)	)	PUNCT
cana-5360	332	1	=	=	PRON
cana-5360	332	2	{	{	PUNCT
cana-5360	332	3	0𝒫	0𝒫	NOUN
cana-5360	332	4	,	,	PUNCT
cana-5360	332	5	1𝒫	1𝒫	INTJ
cana-5360	332	6	,	,	PUNCT
cana-5360	332	7	𝒫ℱ𝔑(𝐴2	𝒫ℱ𝔑(𝐴2	PROPN
cana-5360	332	8	)	)	PUNCT
cana-5360	332	9	,	,	PUNCT
cana-5360	332	10	𝒫ℱ𝔑(𝐴2	𝒫ℱ𝔑(𝐴2	NUM
cana-5360	332	11	)	)	PUNCT
cana-5360	332	12	,	,	PUNCT
cana-5360	332	13	𝐵𝒫ℱ𝔑(𝐴2	𝐵𝒫ℱ𝔑(𝐴2	PROPN
cana-5360	332	14	)	)	PUNCT
cana-5360	332	15	}	}	PUNCT
cana-5360	332	16	.	.	PUNCT
cana-5360	333	1	let	let	VERB
cana-5360	333	2	ℎ𝑃	ℎ𝑃	NOUN
cana-5360	333	3	:	:	PUNCT
cana-5360	333	4	(	(	PUNCT
cana-5360	333	5	𝑈1	𝑈1	NOUN
cana-5360	333	6	,	,	PUNCT
cana-5360	333	7	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	333	8	)	)	PUNCT
cana-5360	333	9	)	)	PUNCT
cana-5360	333	10	→	→	SYM
cana-5360	333	11	(	(	PUNCT
cana-5360	333	12	𝑈2	𝑈2	NOUN
cana-5360	333	13	,	,	PUNCT
cana-5360	333	14	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	333	15	)	)	PUNCT
cana-5360	333	16	)	)	PUNCT
cana-5360	333	17	be	be	AUX
cana-5360	333	18	an	an	DET
cana-5360	333	19	identity	identity	NOUN
cana-5360	333	20	function	function	NOUN
cana-5360	333	21	,	,	PUNCT
cana-5360	333	22	then	then	ADV
cana-5360	333	23	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	333	24	is	be	AUX
cana-5360	333	25	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠	PRON
cana-5360	333	26	but	but	CCONJ
cana-5360	333	27	not	not	PART
cana-5360	333	28	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	PROPN
cana-5360	333	29	.	.	PUNCT
cana-5360	334	1	since	since	SCONJ
cana-5360	334	2	,	,	PUNCT
cana-5360	334	3	𝒫ℱ𝔑(𝐴2	𝒫ℱ𝔑(𝐴2	NUM
cana-5360	334	4	)	)	PUNCT
cana-5360	334	5	is	be	AUX
cana-5360	334	6	a	a	DET
cana-5360	334	7	𝒫ℱ𝒩𝑜	𝒫ℱ𝒩𝑜	PROPN
cana-5360	334	8	set	set	NOUN
cana-5360	334	9	in	in	ADP
cana-5360	334	10	𝑈2	𝑈2	PROPN
cana-5360	334	11	but	but	CCONJ
cana-5360	334	12	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	334	13	−1(𝒫ℱ𝔑(𝐴2	−1(𝒫ℱ𝔑(𝐴2	PROPN
cana-5360	334	14	)	)	PUNCT
cana-5360	334	15	)	)	PUNCT
cana-5360	335	1	=	=	SYM
cana-5360	335	2	𝒫ℱ𝔑(𝐴2	𝒫ℱ𝔑(𝐴2	PROPN
cana-5360	335	3	)	)	PUNCT
cana-5360	335	4	is	be	AUX
cana-5360	335	5	not	not	PART
cana-5360	335	6	𝒫ℱ𝒩𝛿𝒫𝑐	𝒫ℱ𝒩𝛿𝒫𝑐	PROPN
cana-5360	335	7	set	set	VERB
cana-5360	335	8	in	in	ADP
cana-5360	335	9	𝑈1	𝑈1	PROPN
cana-5360	335	10	.	.	PUNCT
cana-5360	336	1	theorem	theorem	VERB
cana-5360	336	2	3.2	3.2	NUM
cana-5360	336	3	let	let	VERB
cana-5360	336	4	(	(	PUNCT
cana-5360	336	5	𝑈1	𝑈1	NOUN
cana-5360	336	6	,	,	PUNCT
cana-5360	336	7	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	336	8	)	)	PUNCT
cana-5360	336	9	)	)	PUNCT
cana-5360	337	1	&	&	CCONJ
cana-5360	337	2	(	(	PUNCT
cana-5360	337	3	𝑈2	𝑈2	PROPN
cana-5360	337	4	,	,	PUNCT
cana-5360	337	5	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	337	6	)	)	PUNCT
cana-5360	337	7	)	)	PUNCT
cana-5360	337	8	be	be	AUX
cana-5360	337	9	a	a	DET
cana-5360	337	10	𝒫ℱ𝒩𝑡𝑠	𝒫ℱ𝒩𝑡𝑠	NOUN
cana-5360	337	11	’s	’s	NOUN
cana-5360	337	12	.	.	PUNCT
cana-5360	338	1	a	a	DET
cana-5360	338	2	mapping	mapping	NOUN
cana-5360	338	3	ℎ𝑃	ℎ𝑃	NOUN
cana-5360	338	4	:	:	PUNCT
cana-5360	338	5	(	(	PUNCT
cana-5360	338	6	𝑈1	𝑈1	NOUN
cana-5360	338	7	,	,	PUNCT
cana-5360	338	8	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	338	9	)	)	PUNCT
cana-5360	338	10	)	)	PUNCT
cana-5360	338	11	→	→	SYM
cana-5360	338	12	(	(	PUNCT
cana-5360	338	13	𝑈2	𝑈2	NOUN
cana-5360	338	14	,	,	PUNCT
cana-5360	338	15	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	338	16	)	)	PUNCT
cana-5360	338	17	)	)	PUNCT
cana-5360	338	18	satisfies	satisfy	VERB
cana-5360	338	19	the	the	DET
cana-5360	338	20	following	follow	VERB
cana-5360	338	21	conditions	condition	NOUN
cana-5360	338	22	are	be	AUX
cana-5360	338	23	equivalent	equivalent	ADJ
cana-5360	338	24	.	.	PUNCT
cana-5360	339	1	(	(	PUNCT
cana-5360	339	2	i	i	NOUN
cana-5360	339	3	)	)	PUNCT
cana-5360	339	4	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	339	5	is	be	AUX
cana-5360	339	6	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠	NUM
cana-5360	339	7	;	;	PUNCT
cana-5360	339	8	(	(	PUNCT
cana-5360	339	9	ii	ii	NOUN
cana-5360	339	10	)	)	PUNCT
cana-5360	339	11	the	the	DET
cana-5360	339	12	inverse	inverse	NOUN
cana-5360	339	13	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	339	14	−1(𝐾	−1(𝐾	NOUN
cana-5360	339	15	)	)	PUNCT
cana-5360	339	16	of	of	ADP
cana-5360	339	17	all	all	DET
cana-5360	339	18	𝒫ℱ𝒩𝑐𝑠	𝒫ℱ𝒩𝑐𝑠	NUM
cana-5360	339	19	set	set	VERB
cana-5360	339	20	𝐾	𝐾	PROPN
cana-5360	339	21	in	in	ADP
cana-5360	339	22	𝑈2	𝑈2	PROPN
cana-5360	339	23	is	be	AUX
cana-5360	339	24	𝒫ℱ𝒩𝛿𝛽𝑜𝑠	𝒫ℱ𝒩𝛿𝛽𝑜𝑠	PROPN
cana-5360	339	25	in	in	ADP
cana-5360	339	26	𝑈1	𝑈1	NOUN
cana-5360	339	27	.	.	PUNCT
cana-5360	340	1	proof	proof	NOUN
cana-5360	340	2	.	.	PUNCT
cana-5360	341	1	(	(	PUNCT
cana-5360	341	2	i	i	NOUN
cana-5360	341	3	)	)	PUNCT
cana-5360	341	4	→	→	SYM
cana-5360	341	5	(	(	PUNCT
cana-5360	341	6	ii	ii	NOUN
cana-5360	341	7	):	):	PUNCT
cana-5360	341	8	consider	consider	VERB
cana-5360	341	9	a	a	DET
cana-5360	341	10	𝒫ℱ𝒩𝑐𝑠	𝒫ℱ𝒩𝑐𝑠	NOUN
cana-5360	341	11	𝐾	𝐾	PROPN
cana-5360	341	12	in	in	ADP
cana-5360	341	13	𝑈2	𝑈2	PROPN
cana-5360	341	14	.	.	PUNCT
cana-5360	342	1	then	then	ADV
cana-5360	342	2	𝐾𝑐	𝐾𝑐	VERB
cana-5360	342	3	is	be	AUX
cana-5360	342	4	𝒫ℱ𝒩𝑜𝑠	𝒫ℱ𝒩𝑜𝑠	ADJ
cana-5360	342	5	in	in	ADP
cana-5360	342	6	𝑈2	𝑈2	PROPN
cana-5360	342	7	.	.	PUNCT
cana-5360	343	1	as	as	SCONJ
cana-5360	343	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	343	3	is	be	AUX
cana-5360	343	4	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠	PRON
cana-5360	343	5	,	,	PUNCT
cana-5360	343	6	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	343	7	−1(𝐾𝑐	−1(𝐾𝑐	X
cana-5360	343	8	)	)	PUNCT
cana-5360	343	9	is	be	AUX
cana-5360	343	10	𝒫ℱ𝒩𝛿𝛽𝑐𝑠	𝒫ℱ𝒩𝛿𝛽𝑐𝑠	PROPN
cana-5360	343	11	in	in	ADP
cana-5360	343	12	𝑈1	𝑈1	NOUN
cana-5360	343	13	.	.	PUNCT
cana-5360	344	1	as	as	ADP
cana-5360	344	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	344	3	−1(𝐾𝑐	−1(𝐾𝑐	PROPN
cana-5360	344	4	)	)	PUNCT
cana-5360	345	1	=	=	PRON
cana-5360	345	2	(	(	PUNCT
cana-5360	345	3	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	345	4	−1(𝐾))𝑐	−1(𝐾))𝑐	X
cana-5360	345	5	,	,	PUNCT
cana-5360	345	6	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	345	7	−1(𝐾	−1(𝐾	NOUN
cana-5360	345	8	)	)	PUNCT
cana-5360	345	9	is	be	AUX
cana-5360	345	10	a	a	DET
cana-5360	345	11	𝒫ℱ𝒩𝛿𝛽𝑜𝑠	𝒫ℱ𝒩𝛿𝛽𝑜𝑠	PROPN
cana-5360	345	12	in	in	ADP
cana-5360	345	13	𝑈1	𝑈1	PROPN
cana-5360	345	14	.	.	PUNCT
cana-5360	346	1	(	(	PUNCT
cana-5360	346	2	ii	ii	NOUN
cana-5360	346	3	)	)	PUNCT
cana-5360	346	4	→	→	SYM
cana-5360	346	5	(	(	PUNCT
cana-5360	346	6	i	i	NOUN
cana-5360	346	7	):	):	PUNCT
cana-5360	346	8	consider	consider	VERB
cana-5360	346	9	a	a	DET
cana-5360	346	10	𝒫ℱ𝒩𝑐𝑠	𝒫ℱ𝒩𝑐𝑠	NOUN
cana-5360	346	11	𝐾	𝐾	PROPN
cana-5360	346	12	in	in	ADP
cana-5360	346	13	𝑈2	𝑈2	PROPN
cana-5360	346	14	.	.	PUNCT
cana-5360	347	1	so	so	ADV
cana-5360	347	2	𝐾𝑐	𝐾𝑐	VERB
cana-5360	347	3	is	be	AUX
cana-5360	347	4	a	a	DET
cana-5360	347	5	𝒫ℱ𝒩𝑜𝑠	𝒫ℱ𝒩𝑜𝑠	NOUN
cana-5360	347	6	in	in	ADP
cana-5360	347	7	𝑈2	𝑈2	PROPN
cana-5360	347	8	.	.	PUNCT
cana-5360	348	1	by	by	ADP
cana-5360	348	2	presumption	presumption	NOUN
cana-5360	348	3	,	,	PUNCT
cana-5360	348	4	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	348	5	−1(𝐾𝑐	−1(𝐾𝑐	X
cana-5360	348	6	)	)	PUNCT
cana-5360	348	7	is	be	AUX
cana-5360	348	8	𝒫ℱ𝒩𝛿𝛽𝑐𝑠	𝒫ℱ𝒩𝛿𝛽𝑐𝑠	PROPN
cana-5360	348	9	in	in	ADP
cana-5360	348	10	𝑈1	𝑈1	NOUN
cana-5360	348	11	.	.	PUNCT
cana-5360	349	1	as	as	ADP
cana-5360	349	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	349	3	−1(𝐾𝑐	−1(𝐾𝑐	PROPN
cana-5360	349	4	)	)	PUNCT
cana-5360	350	1	=	=	PRON
cana-5360	350	2	(	(	PUNCT
cana-5360	350	3	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	350	4	−1𝐾)𝑐	−1𝐾)𝑐	NOUN
cana-5360	350	5	,	,	PUNCT
cana-5360	350	6	(	(	PUNCT
cana-5360	350	7	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	350	8	−1(𝐾))𝑐	−1(𝐾))𝑐	PRON
cana-5360	350	9	is	be	AUX
cana-5360	350	10	a	a	DET
cana-5360	350	11	𝒫ℱ𝒩𝛿𝛽𝑐𝑠	𝒫ℱ𝒩𝛿𝛽𝑐𝑠	PROPN
cana-5360	350	12	in	in	ADP
cana-5360	350	13	𝑈1	𝑈1	NOUN
cana-5360	350	14	.	.	PUNCT
cana-5360	351	1	hence	hence	ADV
cana-5360	351	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	351	3	−1(𝐾	−1(𝐾	NOUN
cana-5360	351	4	)	)	PUNCT
cana-5360	351	5	is	be	AUX
cana-5360	351	6	a	a	DET
cana-5360	351	7	𝒫ℱ𝒩𝛿𝛽𝑜𝑠	𝒫ℱ𝒩𝛿𝛽𝑜𝑠	PROPN
cana-5360	351	8	in	in	ADP
cana-5360	351	9	𝑈1	𝑈1	NOUN
cana-5360	351	10	.	.	PUNCT
cana-5360	352	1	thus	thus	ADV
cana-5360	352	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	352	3	is	be	AUX
cana-5360	352	4	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠.	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠.	PROPN
cana-5360	352	5	communications	communication	NOUN
cana-5360	352	6	on	on	ADP
cana-5360	352	7	applied	apply	VERB
cana-5360	352	8	nonlinear	nonlinear	ADJ
cana-5360	352	9	analysis	analysis	NOUN
cana-5360	352	10	issn	issn	NOUN
cana-5360	352	11	:	:	PUNCT
cana-5360	352	12	1074	1074	NUM
cana-5360	352	13	-	-	PUNCT
cana-5360	352	14	133x	133x	NUM
cana-5360	352	15	vol	vol	VERB
cana-5360	352	16	32	32	NUM
cana-5360	352	17	no	no	NOUN
cana-5360	352	18	.	.	PUNCT
cana-5360	353	1	10s	10	NOUN
cana-5360	353	2	(	(	PUNCT
cana-5360	353	3	2025	2025	NUM
cana-5360	353	4	)	)	PUNCT
cana-5360	353	5	1936	1936	NUM
cana-5360	353	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5360	353	7	theorem	theorem	VERB
cana-5360	353	8	3.3	3.3	NUM
cana-5360	353	9	let	let	NOUN
cana-5360	353	10	(	(	PUNCT
cana-5360	353	11	𝑈1	𝑈1	NOUN
cana-5360	353	12	,	,	PUNCT
cana-5360	353	13	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	353	14	)	)	PUNCT
cana-5360	353	15	)	)	PUNCT
cana-5360	353	16	&	&	CCONJ
cana-5360	353	17	(	(	PUNCT
cana-5360	353	18	𝑈2	𝑈2	PROPN
cana-5360	353	19	,	,	PUNCT
cana-5360	353	20	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	353	21	)	)	PUNCT
cana-5360	353	22	)	)	PUNCT
cana-5360	353	23	be	be	AUX
cana-5360	353	24	a	a	DET
cana-5360	353	25	𝒫ℱ𝒩𝑡𝑠	𝒫ℱ𝒩𝑡𝑠	NOUN
cana-5360	353	26	’s	’s	NOUN
cana-5360	353	27	.	.	PUNCT
cana-5360	354	1	a	a	DET
cana-5360	354	2	mapping	mapping	NOUN
cana-5360	354	3	ℎ𝑃	ℎ𝑃	NOUN
cana-5360	354	4	:	:	PUNCT
cana-5360	354	5	(	(	PUNCT
cana-5360	354	6	𝑈1	𝑈1	NOUN
cana-5360	354	7	,	,	PUNCT
cana-5360	354	8	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	354	9	)	)	PUNCT
cana-5360	354	10	)	)	PUNCT
cana-5360	354	11	→	→	SYM
cana-5360	354	12	(	(	PUNCT
cana-5360	354	13	𝑈2	𝑈2	NOUN
cana-5360	354	14	,	,	PUNCT
cana-5360	354	15	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	354	16	)	)	PUNCT
cana-5360	354	17	)	)	PUNCT
cana-5360	354	18	is	be	AUX
cana-5360	354	19	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠	PRON
cana-5360	354	20	satisfies	satisfy	VERB
cana-5360	354	21	the	the	DET
cana-5360	354	22	following	follow	VERB
cana-5360	354	23	conditions	condition	NOUN
cana-5360	354	24	are	be	AUX
cana-5360	354	25	hold	hold	ADJ
cana-5360	354	26	.	.	PUNCT
cana-5360	355	1	(	(	PUNCT
cana-5360	355	2	i	i	NOUN
cana-5360	355	3	)	)	PUNCT
cana-5360	355	4	ℎ𝑃(𝒫ℱ𝒩𝛿𝛽𝑐𝑙(𝐿	ℎ𝑃(𝒫ℱ𝒩𝛿𝛽𝑐𝑙(𝐿	PROPN
cana-5360	355	5	)	)	PUNCT
cana-5360	355	6	)	)	PUNCT
cana-5360	356	1	⊇	⊇	PROPN
cana-5360	356	2	𝒫ℱ𝒩𝛿𝑖𝑛𝑡(ℎ𝑃(𝐿	𝒫ℱ𝒩𝛿𝑖𝑛𝑡(ℎ𝑃(𝐿	NOUN
cana-5360	356	3	)	)	PUNCT
cana-5360	356	4	)	)	PUNCT
cana-5360	356	5	,	,	PUNCT
cana-5360	356	6	for	for	ADP
cana-5360	356	7	all	all	PRON
cana-5360	356	8	𝑝𝑓𝑠	𝑝𝑓𝑠	ADP
cana-5360	356	9	𝐿	𝐿	PROPN
cana-5360	356	10	in	in	ADP
cana-5360	356	11	𝑈1	𝑈1	PROPN
cana-5360	356	12	.	.	PUNCT
cana-5360	357	1	(	(	PUNCT
cana-5360	357	2	ii	ii	NOUN
cana-5360	357	3	)	)	PUNCT
cana-5360	357	4	𝒫ℱ𝒩𝛿𝛽𝑐𝑙(ℎ𝑃	𝒫ℱ𝒩𝛿𝛽𝑐𝑙(ℎ𝑃	PROPN
cana-5360	357	5	−1(𝐾	−1(𝐾	NOUN
cana-5360	357	6	)	)	PUNCT
cana-5360	357	7	)	)	PUNCT
cana-5360	358	1	⊇	⊇	PROPN
cana-5360	358	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	358	3	−1(𝒫ℱ𝒩𝛿𝑖𝑛𝑡(𝐾	−1(𝒫ℱ𝒩𝛿𝑖𝑛𝑡(𝐾	PROPN
cana-5360	358	4	)	)	PUNCT
cana-5360	358	5	)	)	PUNCT
cana-5360	358	6	,	,	PUNCT
cana-5360	358	7	for	for	ADP
cana-5360	358	8	all	all	PRON
cana-5360	358	9	𝑝𝑓𝑠	𝑝𝑓𝑠	ADP
cana-5360	358	10	𝐾	𝐾	PROPN
cana-5360	358	11	in	in	ADP
cana-5360	358	12	𝑈2	𝑈2	PROPN
cana-5360	358	13	.	.	PUNCT
cana-5360	359	1	proof	proof	NOUN
cana-5360	359	2	.	.	PUNCT
cana-5360	360	1	(	(	PUNCT
cana-5360	360	2	i	i	NOUN
cana-5360	360	3	)	)	PUNCT
cana-5360	360	4	since	since	SCONJ
cana-5360	360	5	𝒫ℱ𝒩𝛿𝑐𝑙(ℎ𝑃(𝐿	𝒫ℱ𝒩𝛿𝑐𝑙(ℎ𝑃(𝐿	NUM
cana-5360	360	6	)	)	PUNCT
cana-5360	360	7	)	)	PUNCT
cana-5360	360	8	is	be	AUX
cana-5360	360	9	a	a	DET
cana-5360	360	10	𝒫ℱ𝒩𝛿𝑐𝑠	𝒫ℱ𝒩𝛿𝑐𝑠	PROPN
cana-5360	360	11	in	in	ADP
cana-5360	360	12	𝑈2	𝑈2	PROPN
cana-5360	360	13	and	and	CCONJ
cana-5360	360	14	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	360	15	is	be	AUX
cana-5360	360	16	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠	PRON
cana-5360	360	17	,	,	PUNCT
cana-5360	360	18	then	then	ADV
cana-5360	360	19	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	360	20	−1(𝒫ℱ𝒩𝛿𝑖𝑛𝑡	−1(𝒫ℱ𝒩𝛿𝑖𝑛𝑡	PROPN
cana-5360	360	21	(	(	PUNCT
cana-5360	360	22	ℎ𝑃(𝐿	ℎ𝑃(𝐿	NOUN
cana-5360	360	23	)	)	PUNCT
cana-5360	360	24	)	)	PUNCT
cana-5360	360	25	)	)	PUNCT
cana-5360	360	26	is	be	AUX
cana-5360	360	27	𝒫ℱ𝒩𝛿𝛽𝑜𝑠	𝒫ℱ𝒩𝛿𝛽𝑜𝑠	PROPN
cana-5360	360	28	in	in	ADP
cana-5360	360	29	𝑈1	𝑈1	NOUN
cana-5360	360	30	.	.	PUNCT
cana-5360	361	1	now	now	ADV
cana-5360	361	2	,	,	PUNCT
cana-5360	361	3	since	since	SCONJ
cana-5360	361	4	𝐿	𝐿	PROPN
cana-5360	361	5	⊇	⊇	PROPN
cana-5360	361	6	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	361	7	−1(𝒫ℱ𝒩𝛿𝑖𝑛𝑡(ℎ𝑃(𝐿	−1(𝒫ℱ𝒩𝛿𝑖𝑛𝑡(ℎ𝑃(𝐿	PROPN
cana-5360	361	8	)	)	PUNCT
cana-5360	361	9	)	)	PUNCT
cana-5360	361	10	)	)	PUNCT
cana-5360	361	11	,	,	PUNCT
cana-5360	361	12	𝒫ℱ𝒩𝛿𝛽𝑐𝑙(𝐿	𝒫ℱ𝒩𝛿𝛽𝑐𝑙(𝐿	NUM
cana-5360	361	13	)	)	PUNCT
cana-5360	361	14	⊇	⊇	PROPN
cana-5360	361	15	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	361	16	−1(𝒫ℱ𝒩𝛿𝑖𝑛𝑡(ℎ𝑃(𝐿	−1(𝒫ℱ𝒩𝛿𝑖𝑛𝑡(ℎ𝑃(𝐿	PROPN
cana-5360	361	17	)	)	PUNCT
cana-5360	361	18	)	)	PUNCT
cana-5360	361	19	)	)	PUNCT
cana-5360	361	20	.	.	PUNCT
cana-5360	362	1	therefore	therefore	ADV
cana-5360	362	2	,	,	PUNCT
cana-5360	362	3	ℎ𝑃(𝒫ℱ𝒩𝛿𝛽𝑐𝑙(𝐿	ℎ𝑃(𝒫ℱ𝒩𝛿𝛽𝑐𝑙(𝐿	PROPN
cana-5360	362	4	)	)	PUNCT
cana-5360	362	5	)	)	PUNCT
cana-5360	362	6	⊇	⊇	PROPN
cana-5360	362	7	𝒫ℱ𝒩𝛿𝑖𝑛𝑡(ℎ𝑃(𝐿	𝒫ℱ𝒩𝛿𝑖𝑛𝑡(ℎ𝑃(𝐿	NOUN
cana-5360	362	8	)	)	PUNCT
cana-5360	362	9	)	)	PUNCT
cana-5360	362	10	.	.	PUNCT
cana-5360	363	1	(	(	PUNCT
cana-5360	363	2	ii	ii	NOUN
cana-5360	363	3	)	)	PUNCT
cana-5360	363	4	by	by	ADP
cana-5360	363	5	replacing	replace	VERB
cana-5360	363	6	𝐿	𝐿	PROPN
cana-5360	363	7	with	with	ADP
cana-5360	363	8	𝐾	𝐾	PROPN
cana-5360	363	9	in	in	ADP
cana-5360	363	10	(	(	PUNCT
cana-5360	363	11	i	i	NOUN
cana-5360	363	12	)	)	PUNCT
cana-5360	363	13	,	,	PUNCT
cana-5360	363	14	we	we	PRON
cana-5360	363	15	obtain	obtain	VERB
cana-5360	363	16	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	363	17	(	(	PUNCT
cana-5360	363	18	𝒫ℱ𝒩𝛿𝛽𝑐𝑙(ℎ𝑃	𝒫ℱ𝒩𝛿𝛽𝑐𝑙(ℎ𝑃	NOUN
cana-5360	363	19	−1(𝐾	−1(𝐾	NOUN
cana-5360	363	20	)	)	PUNCT
cana-5360	363	21	)	)	PUNCT
cana-5360	363	22	)	)	PUNCT
cana-5360	363	23	⊇	⊇	PROPN
cana-5360	363	24	𝒫ℱ𝒩𝛿𝑖𝑛𝑡(ℎ𝑃(ℎ𝑃	𝒫ℱ𝒩𝛿𝑖𝑛𝑡(ℎ𝑃(ℎ𝑃	ADJ
cana-5360	363	25	−1(𝐾	−1(𝐾	NOUN
cana-5360	363	26	)	)	PUNCT
cana-5360	363	27	)	)	PUNCT
cana-5360	363	28	)	)	PUNCT
cana-5360	363	29	⊇	⊇	PROPN
cana-5360	363	30	𝒫ℱ𝒩𝛿𝑖𝑛(𝐾	𝒫ℱ𝒩𝛿𝑖𝑛(𝐾	NOUN
cana-5360	363	31	)	)	PUNCT
cana-5360	363	32	.	.	PUNCT
cana-5360	364	1	hence	hence	ADV
cana-5360	364	2	,	,	PUNCT
cana-5360	364	3	𝒫ℱ𝒩𝛿𝛽𝑐𝑙(ℎ𝑃	𝒫ℱ𝒩𝛿𝛽𝑐𝑙(ℎ𝑃	NOUN
cana-5360	364	4	−1(𝐾	−1(𝐾	NOUN
cana-5360	364	5	)	)	PUNCT
cana-5360	364	6	)	)	PUNCT
cana-5360	365	1	⊇	⊇	PROPN
cana-5360	365	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	365	3	−1(𝒫ℱ𝒩𝛿𝑖𝑛𝑡(𝐾	−1(𝒫ℱ𝒩𝛿𝑖𝑛𝑡(𝐾	PROPN
cana-5360	365	4	)	)	PUNCT
cana-5360	365	5	)	)	PUNCT
cana-5360	365	6	.	.	PUNCT
cana-5360	366	1	remark	remark	PROPN
cana-5360	366	2	3.2	3.2	NUM
cana-5360	366	3	let	let	VERB
cana-5360	366	4	(	(	PUNCT
cana-5360	366	5	𝑈1	𝑈1	NOUN
cana-5360	366	6	,	,	PUNCT
cana-5360	366	7	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	366	8	)	)	PUNCT
cana-5360	366	9	)	)	PUNCT
cana-5360	366	10	&	&	CCONJ
cana-5360	366	11	(	(	PUNCT
cana-5360	366	12	𝑈2	𝑈2	PROPN
cana-5360	366	13	,	,	PUNCT
cana-5360	366	14	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	366	15	)	)	PUNCT
cana-5360	366	16	)	)	PUNCT
cana-5360	367	1	be	be	AUX
cana-5360	367	2	a	a	DET
cana-5360	367	3	𝒫ℱ𝒩𝑡𝑠	𝒫ℱ𝒩𝑡𝑠	PROPN
cana-5360	367	4	’	'	PUNCT
cana-5360	367	5	s.	s.	PROPN
cana-5360	367	6	let	let	VERB
cana-5360	367	7	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	367	8	:	:	PUNCT
cana-5360	367	9	(	(	PUNCT
cana-5360	367	10	𝑈1	𝑈1	NOUN
cana-5360	367	11	,	,	PUNCT
cana-5360	367	12	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	367	13	)	)	PUNCT
cana-5360	367	14	)	)	PUNCT
cana-5360	368	1	→	→	SYM
cana-5360	368	2	(	(	PUNCT
cana-5360	368	3	𝑈2	𝑈2	NOUN
cana-5360	368	4	,	,	PUNCT
cana-5360	368	5	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	368	6	)	)	PUNCT
cana-5360	368	7	)	)	PUNCT
cana-5360	368	8	be	be	AUX
cana-5360	368	9	a	a	DET
cana-5360	368	10	mapping	mapping	NOUN
cana-5360	368	11	.	.	PUNCT
cana-5360	369	1	if	if	SCONJ
cana-5360	369	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	369	3	is	be	AUX
cana-5360	369	4	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠	PRON
cana-5360	369	5	,	,	PUNCT
cana-5360	369	6	then	then	ADV
cana-5360	369	7	1	1	NUM
cana-5360	369	8	.	.	PUNCT
cana-5360	369	9	ℎ𝑃(𝒫ℱ𝒩𝛿𝛽𝑐𝑙(𝐿	ℎ𝑃(𝒫ℱ𝒩𝛿𝛽𝑐𝑙(𝐿	PROPN
cana-5360	369	10	)	)	PUNCT
cana-5360	369	11	)	)	PUNCT
cana-5360	369	12	is	be	AUX
cana-5360	369	13	not	not	PART
cana-5360	369	14	necessarily	necessarily	ADV
cana-5360	369	15	equal	equal	ADJ
cana-5360	369	16	to	to	PART
cana-5360	369	17	𝒫ℱ𝒩𝛿𝑖𝑛𝑡(ℎ𝑃(𝐿	𝒫ℱ𝒩𝛿𝑖𝑛𝑡(ℎ𝑃(𝐿	VERB
cana-5360	369	18	)	)	PUNCT
cana-5360	369	19	)	)	PUNCT
cana-5360	369	20	where	where	SCONJ
cana-5360	369	21	𝐿	𝐿	PROPN
cana-5360	369	22	∈	∈	PROPN
cana-5360	369	23	𝑈1	𝑈1	NOUN
cana-5360	369	24	.	.	PUNCT
cana-5360	370	1	2	2	X
cana-5360	370	2	.	.	X
cana-5360	370	3	𝒫ℱ𝒩𝛿𝛽𝑐𝑙(ℎ𝑃	𝒫ℱ𝒩𝛿𝛽𝑐𝑙(ℎ𝑃	PROPN
cana-5360	370	4	−1(𝐾	−1(𝐾	NOUN
cana-5360	370	5	)	)	PUNCT
cana-5360	370	6	)	)	PUNCT
cana-5360	370	7	is	be	AUX
cana-5360	370	8	not	not	PART
cana-5360	370	9	necessarily	necessarily	ADV
cana-5360	370	10	equal	equal	ADJ
cana-5360	370	11	to	to	ADP
cana-5360	370	12	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	370	13	−1(𝒫ℱ𝒩𝛿𝑖𝑛𝑡(𝐾	−1(𝒫ℱ𝒩𝛿𝑖𝑛𝑡(𝐾	PROPN
cana-5360	370	14	)	)	PUNCT
cana-5360	370	15	)	)	PUNCT
cana-5360	370	16	where	where	SCONJ
cana-5360	370	17	𝐾	𝐾	PROPN
cana-5360	370	18	∈	∈	PROPN
cana-5360	370	19	𝑈2	𝑈2	PROPN
cana-5360	370	20	.	.	PUNCT
cana-5360	371	1	example	example	NOUN
cana-5360	371	2	3.5	3.5	NUM
cana-5360	371	3	assume	assume	VERB
cana-5360	371	4	𝑈1	𝑈1	NOUN
cana-5360	371	5	=	=	SYM
cana-5360	371	6	𝑈2	𝑈2	PROPN
cana-5360	371	7	=	=	PUNCT
cana-5360	371	8	𝑈	𝑈	PROPN
cana-5360	371	9	=	=	SYM
cana-5360	371	10	{	{	PUNCT
cana-5360	371	11	𝑠1	𝑠1	PROPN
cana-5360	371	12	,	,	PUNCT
cana-5360	371	13	𝑠2	𝑠2	NOUN
cana-5360	371	14	,	,	PUNCT
cana-5360	371	15	𝑠3	𝑠3	NOUN
cana-5360	371	16	,	,	PUNCT
cana-5360	371	17	𝑠4	𝑠4	PROPN
cana-5360	371	18	}	}	PUNCT
cana-5360	371	19	be	be	VERB
cana-5360	371	20	the	the	DET
cana-5360	371	21	universe	universe	NOUN
cana-5360	371	22	set	set	VERB
cana-5360	371	23	and	and	CCONJ
cana-5360	371	24	the	the	DET
cana-5360	371	25	equivalence	equivalence	NOUN
cana-5360	371	26	relation	relation	NOUN
cana-5360	371	27	is	be	AUX
cana-5360	371	28	𝑈/𝑅	𝑈/𝑅	ADJ
cana-5360	371	29	=	=	SYM
cana-5360	371	30	{	{	PUNCT
cana-5360	371	31	{	{	PUNCT
cana-5360	371	32	𝑠1	𝑠1	PROPN
cana-5360	371	33	,	,	PUNCT
cana-5360	371	34	𝑠4	𝑠4	PROPN
cana-5360	371	35	}	}	PUNCT
cana-5360	371	36	,	,	PUNCT
cana-5360	371	37	{	{	PUNCT
cana-5360	371	38	𝑠2	𝑠2	NOUN
cana-5360	371	39	}	}	PUNCT
cana-5360	371	40	,	,	PUNCT
cana-5360	371	41	{	{	PUNCT
cana-5360	371	42	𝑠3	𝑠3	NOUN
cana-5360	371	43	}	}	PUNCT
cana-5360	371	44	}	}	PUNCT
cana-5360	371	45	.	.	PUNCT
cana-5360	372	1	let	let	VERB
cana-5360	372	2	𝐴	𝐴	PROPN
cana-5360	372	3	=	=	PUNCT
cana-5360	372	4	{	{	PUNCT
cana-5360	372	5	⟨	⟨	X
cana-5360	372	6	𝑠1	𝑠1	PROPN
cana-5360	372	7	0.3,0.1	0.3,0.1	PROPN
cana-5360	372	8	⟩	⟩	NOUN
cana-5360	372	9	,	,	PUNCT
cana-5360	372	10	⟨	⟨	VERB
cana-5360	372	11	𝑠2	𝑠2	NOUN
cana-5360	372	12	0.1,0.5	0.1,0.5	PROPN
cana-5360	372	13	⟩	⟩	NOUN
cana-5360	372	14	,	,	PUNCT
cana-5360	372	15	⟨	⟨	VERB
cana-5360	372	16	𝑠3	𝑠3	PROPN
cana-5360	372	17	0.2,0.45	0.2,0.45	NUM
cana-5360	372	18	⟩	⟩	NOUN
cana-5360	372	19	,	,	PUNCT
cana-5360	372	20	⟨	⟨	VERB
cana-5360	372	21	𝑠4	𝑠4	PROPN
cana-5360	372	22	0.4,0.25	0.4,0.25	NUM
cana-5360	372	23	⟩	⟩	NOUN
cana-5360	372	24	}	}	PUNCT
cana-5360	372	25	be	be	AUX
cana-5360	372	26	a	a	DET
cana-5360	372	27	pythagorean	pythagorean	ADJ
cana-5360	372	28	fuzzy	fuzzy	ADJ
cana-5360	372	29	subset	subset	NOUN
cana-5360	372	30	of	of	ADP
cana-5360	372	31	𝑈.	𝑈.	PROPN
cana-5360	372	32	𝒫ℱ𝔑(𝐴	𝒫ℱ𝔑(𝐴	PROPN
cana-5360	372	33	)	)	PUNCT
cana-5360	372	34	=	=	NOUN
cana-5360	372	35	{	{	PUNCT
cana-5360	372	36	⟨	⟨	ADP
cana-5360	372	37	𝑠1,𝑠4	𝑠1,𝑠4	PROPN
cana-5360	372	38	0.3,0.25	0.3,0.25	NUM
cana-5360	372	39	⟩	⟩	NOUN
cana-5360	372	40	,	,	PUNCT
cana-5360	372	41	⟨	⟨	VERB
cana-5360	372	42	𝑠2	𝑠2	NOUN
cana-5360	372	43	0.1,0.5	0.1,0.5	PROPN
cana-5360	372	44	⟩	⟩	NOUN
cana-5360	372	45	,	,	PUNCT
cana-5360	372	46	⟨	⟨	VERB
cana-5360	372	47	𝑠3	𝑠3	PROPN
cana-5360	372	48	0.2,0.45	0.2,0.45	NUM
cana-5360	372	49	⟩	⟩	NOUN
cana-5360	372	50	}	}	PUNCT
cana-5360	372	51	,	,	PUNCT
cana-5360	372	52	𝒫ℱ𝔑(𝐴	𝒫ℱ𝔑(𝐴	INTJ
cana-5360	372	53	)	)	PUNCT
cana-5360	372	54	=	=	NOUN
cana-5360	372	55	{	{	PUNCT
cana-5360	372	56	⟨	⟨	ADP
cana-5360	372	57	𝑠1,𝑠4	𝑠1,𝑠4	PROPN
cana-5360	372	58	0.4,0.1	0.4,0.1	PROPN
cana-5360	372	59	⟩	⟩	NOUN
cana-5360	372	60	,	,	PUNCT
cana-5360	372	61	⟨	⟨	VERB
cana-5360	372	62	𝑠2	𝑠2	NOUN
cana-5360	372	63	0.1,0.5	0.1,0.5	PROPN
cana-5360	372	64	⟩	⟩	NOUN
cana-5360	372	65	,	,	PUNCT
cana-5360	372	66	⟨	⟨	VERB
cana-5360	372	67	𝑠3	𝑠3	PROPN
cana-5360	372	68	0.2,0.45	0.2,0.45	PUNCT
cana-5360	372	69	⟩	⟩	NOUN
cana-5360	372	70	}	}	PUNCT
cana-5360	372	71	,	,	PUNCT
cana-5360	372	72	𝐵𝒫ℱ𝔑(𝐴	𝐵𝒫ℱ𝔑(𝐴	PROPN
cana-5360	372	73	)	)	PUNCT
cana-5360	373	1	=	=	NOUN
cana-5360	373	2	{	{	PUNCT
cana-5360	373	3	⟨	⟨	ADP
cana-5360	373	4	𝑠1,𝑠4	𝑠1,𝑠4	PROPN
cana-5360	373	5	0.25,0.3	0.25,0.3	NOUN
cana-5360	373	6	⟩	⟩	NOUN
cana-5360	373	7	,	,	PUNCT
cana-5360	373	8	⟨	⟨	VERB
cana-5360	373	9	𝑠2	𝑠2	NOUN
cana-5360	373	10	0.1,0.5	0.1,0.5	PROPN
cana-5360	373	11	⟩	⟩	NOUN
cana-5360	373	12	,	,	PUNCT
cana-5360	373	13	⟨	⟨	VERB
cana-5360	373	14	𝑠3	𝑠3	PROPN
cana-5360	373	15	0.2,0.45	0.2,0.45	NUM
cana-5360	373	16	⟩	⟩	NOUN
cana-5360	373	17	}	}	PUNCT
cana-5360	373	18	.	.	PUNCT
cana-5360	374	1	now	now	ADV
cana-5360	374	2	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	VERB
cana-5360	374	3	)	)	PUNCT
cana-5360	374	4	=	=	PUNCT
cana-5360	374	5	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	X
cana-5360	374	6	)	)	PUNCT
cana-5360	375	1	=	=	SYM
cana-5360	375	2	𝜏𝑃(𝐴	𝜏𝑃(𝐴	ADJ
cana-5360	375	3	)	)	PUNCT
cana-5360	375	4	=	=	PRON
cana-5360	375	5	{	{	PUNCT
cana-5360	375	6	0𝒫	0𝒫	NOUN
cana-5360	375	7	,	,	PUNCT
cana-5360	375	8	1𝒫	1𝒫	INTJ
cana-5360	375	9	,	,	PUNCT
cana-5360	375	10	𝒫ℱ𝔑(𝐴	𝒫ℱ𝔑(𝐴	NOUN
cana-5360	375	11	)	)	PUNCT
cana-5360	375	12	,	,	PUNCT
cana-5360	375	13	𝒫ℱ𝔑(𝐴	𝒫ℱ𝔑(𝐴	NOUN
cana-5360	375	14	)	)	PUNCT
cana-5360	375	15	,	,	PUNCT
cana-5360	375	16	𝐵𝒫ℱ𝔑(𝐴	𝐵𝒫ℱ𝔑(𝐴	PROPN
cana-5360	375	17	)	)	PUNCT
cana-5360	375	18	}	}	PUNCT
cana-5360	375	19	is	be	AUX
cana-5360	375	20	a	a	DET
cana-5360	375	21	𝒫ℱ𝒩𝑡𝑠	𝒫ℱ𝒩𝑡𝑠	PROPN
cana-5360	375	22	.	.	PUNCT
cana-5360	376	1	let	let	VERB
cana-5360	376	2	ℎ𝑃	ℎ𝑃	NOUN
cana-5360	376	3	:	:	PUNCT
cana-5360	376	4	(	(	PUNCT
cana-5360	376	5	𝑈	𝑈	NOUN
cana-5360	376	6	,	,	PUNCT
cana-5360	376	7	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	376	8	)	)	PUNCT
cana-5360	376	9	)	)	PUNCT
cana-5360	377	1	→	→	PUNCT
cana-5360	377	2	(	(	PUNCT
cana-5360	377	3	𝑈	𝑈	PROPN
cana-5360	377	4	,	,	PUNCT
cana-5360	377	5	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NUM
cana-5360	377	6	)	)	PUNCT
cana-5360	377	7	)	)	PUNCT
cana-5360	377	8	be	be	AUX
cana-5360	377	9	an	an	DET
cana-5360	377	10	identity	identity	NOUN
cana-5360	377	11	function	function	NOUN
cana-5360	377	12	,	,	PUNCT
cana-5360	377	13	then	then	ADV
cana-5360	377	14	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	377	15	is	be	AUX
cana-5360	377	16	𝒫ℱ𝒩𝛿𝛽𝐶𝑡𝑠.	𝒫ℱ𝒩𝛿𝛽𝐶𝑡𝑠.	PROPN
cana-5360	377	17	1	1	NUM
cana-5360	377	18	.	.	PUNCT
cana-5360	377	19	ℎ𝑃(𝒫ℱ𝒩𝛿𝛽𝑐𝑙(𝒫ℱ𝔑(𝐴	ℎ𝑃(𝒫ℱ𝒩𝛿𝛽𝑐𝑙(𝒫ℱ𝔑(𝐴	NOUN
cana-5360	377	20	)	)	PUNCT
cana-5360	377	21	)	)	PUNCT
cana-5360	377	22	)	)	PUNCT
cana-5360	378	1	=	=	SYM
cana-5360	378	2	𝐵𝒫ℱ𝔑(𝐴	𝐵𝒫ℱ𝔑(𝐴	PROPN
cana-5360	378	3	)	)	PUNCT
cana-5360	378	4	.	.	PUNCT
cana-5360	379	1	but	but	CCONJ
cana-5360	379	2	𝒫ℱ𝒩𝛿𝑐𝑙	𝒫ℱ𝒩𝛿𝑐𝑙	PROPN
cana-5360	379	3	(	(	PUNCT
cana-5360	379	4	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	379	5	(	(	PUNCT
cana-5360	379	6	𝒫ℱ𝔑(𝐴	𝒫ℱ𝔑(𝐴	NOUN
cana-5360	379	7	)	)	PUNCT
cana-5360	379	8	)	)	PUNCT
cana-5360	379	9	)	)	PUNCT
cana-5360	380	1	=	=	SYM
cana-5360	380	2	𝐵𝒫ℱ𝔑(𝐴)𝑐.	𝐵𝒫ℱ𝔑(𝐴)𝑐.	ADV
cana-5360	380	3	thus	thus	ADV
cana-5360	380	4	ℎ𝑃(𝒫ℱ𝒩𝛿𝛽𝑐𝑙(𝒫ℱ𝔑(𝐴	ℎ𝑃(𝒫ℱ𝒩𝛿𝛽𝑐𝑙(𝒫ℱ𝔑(𝐴	NOUN
cana-5360	380	5	)	)	PUNCT
cana-5360	380	6	)	)	PUNCT
cana-5360	380	7	)	)	PUNCT
cana-5360	381	1	≠	≠	PROPN
cana-5360	381	2	𝒫ℱ𝒩𝛿𝑐𝑙(ℎ𝑃(𝒫ℱ𝔑(𝐴	𝒫ℱ𝒩𝛿𝑐𝑙(ℎ𝑃(𝒫ℱ𝔑(𝐴	NOUN
cana-5360	381	3	)	)	PUNCT
cana-5360	381	4	)	)	PUNCT
cana-5360	381	5	)	)	PUNCT
cana-5360	381	6	.	.	PUNCT
cana-5360	382	1	2	2	X
cana-5360	382	2	.	.	X
cana-5360	382	3	𝒫ℱ𝒩𝛿𝛽𝑐𝑙(ℎ𝑃	𝒫ℱ𝒩𝛿𝛽𝑐𝑙(ℎ𝑃	PROPN
cana-5360	382	4	−1(𝒫ℱ𝔑(𝐴	−1(𝒫ℱ𝔑(𝐴	PROPN
cana-5360	382	5	)	)	PUNCT
cana-5360	382	6	)	)	PUNCT
cana-5360	382	7	)	)	PUNCT
cana-5360	383	1	=	=	SYM
cana-5360	383	2	𝐵𝒫ℱ𝔑(𝐴	𝐵𝒫ℱ𝔑(𝐴	PROPN
cana-5360	383	3	)	)	PUNCT
cana-5360	383	4	.	.	PUNCT
cana-5360	384	1	but	but	CCONJ
cana-5360	384	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	384	3	−1(𝒫ℱ𝒩𝛿𝑐𝑙(𝒫ℱ𝔑(𝐴	−1(𝒫ℱ𝒩𝛿𝑐𝑙(𝒫ℱ𝔑(𝐴	NOUN
cana-5360	384	4	)	)	PUNCT
cana-5360	384	5	)	)	PUNCT
cana-5360	384	6	)	)	PUNCT
cana-5360	385	1	=	=	PUNCT
cana-5360	385	2	𝐵𝒫ℱ𝔑(𝐴)𝑐	𝐵𝒫ℱ𝔑(𝐴)𝑐	INTJ
cana-5360	385	3	.	.	PUNCT
cana-5360	386	1	thus	thus	ADV
cana-5360	386	2	𝒫ℱ𝒩𝛿𝛽𝑐𝑙(ℎ𝑃	𝒫ℱ𝒩𝛿𝛽𝑐𝑙(ℎ𝑃	NOUN
cana-5360	386	3	−1(𝒫ℱ𝔑(𝐴	−1(𝒫ℱ𝔑(𝐴	PROPN
cana-5360	386	4	)	)	PUNCT
cana-5360	386	5	)	)	PUNCT
cana-5360	386	6	)	)	PUNCT
cana-5360	387	1	≠	≠	PROPN
cana-5360	387	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	387	3	−1(𝒫ℱ𝒩𝛿𝑐𝑙(𝒫ℱ𝔑(𝐴	−1(𝒫ℱ𝒩𝛿𝑐𝑙(𝒫ℱ𝔑(𝐴	NOUN
cana-5360	387	4	)	)	PUNCT
cana-5360	387	5	)	)	PUNCT
cana-5360	387	6	)	)	PUNCT
cana-5360	387	7	.	.	PUNCT
cana-5360	388	1	4	4	NUM
cana-5360	388	2	pythagorean	pythagorean	PROPN
cana-5360	388	3	fuzzy	fuzzy	ADJ
cana-5360	388	4	nano	nano	NOUN
cana-5360	388	5	contra	contra	PROPN
cana-5360	388	6	𝜹	𝜹	X
cana-5360	388	7	(	(	PUNCT
cana-5360	388	8	resp	resp	NOUN
cana-5360	388	9	.	.	PUNCT
cana-5360	389	1	𝜹	𝜹	X
cana-5360	389	2	pre	pre	ADJ
cana-5360	389	3	,	,	PUNCT
cana-5360	389	4	𝜹	𝜹	X
cana-5360	389	5	semi	semi	ADV
cana-5360	389	6	,	,	PUNCT
cana-5360	389	7	𝜹𝜶	𝜹𝜶	VERB
cana-5360	389	8	and	and	CCONJ
cana-5360	389	9	𝜹𝜷)-irresolute	𝜹𝜷)-irresolute	ADJ
cana-5360	389	10	maps	map	NOUN
cana-5360	389	11	in	in	ADP
cana-5360	389	12	this	this	DET
cana-5360	389	13	section	section	NOUN
cana-5360	389	14	,	,	PUNCT
cana-5360	389	15	we	we	PRON
cana-5360	389	16	introduce	introduce	VERB
cana-5360	389	17	the	the	DET
cana-5360	389	18	concept	concept	NOUN
cana-5360	389	19	of	of	ADP
cana-5360	389	20	pythagorean	pythagorean	PROPN
cana-5360	389	21	fuzzy	fuzzy	ADJ
cana-5360	389	22	nano	nano	PROPN
cana-5360	389	23	contra	contra	PROPN
cana-5360	389	24	irresoluteness	irresoluteness	PROPN
cana-5360	389	25	called	call	VERB
cana-5360	389	26	pythagorean	pythagorean	PROPN
cana-5360	389	27	fuzzy	fuzzy	ADJ
cana-5360	389	28	nano	nano	PROPN
cana-5360	389	29	contra	contra	PROPN
cana-5360	389	30	(	(	PUNCT
cana-5360	389	31	resp	resp	NOUN
cana-5360	389	32	.	.	PUNCT
cana-5360	390	1	𝛿	𝛿	ADJ
cana-5360	390	2	,	,	PUNCT
cana-5360	390	3	𝛿𝒫	𝛿𝒫	NOUN
cana-5360	390	4	,	,	PUNCT
cana-5360	390	5	𝛿𝒮	𝛿𝒮	NOUN
cana-5360	390	6	,	,	PUNCT
cana-5360	390	7	𝛿𝛼	𝛿𝛼	NOUN
cana-5360	390	8	and	and	CCONJ
cana-5360	390	9	𝛿𝛽)-irresolute	𝛿𝛽)-irresolute	PROPN
cana-5360	390	10	maps	map	NOUN
cana-5360	390	11	by	by	ADP
cana-5360	390	12	using	use	VERB
cana-5360	390	13	𝒫ℱ𝒩𝒮𝑜𝑠	𝒫ℱ𝒩𝒮𝑜𝑠	PROPN
cana-5360	390	14	(	(	PUNCT
cana-5360	390	15	resp	resp	NOUN
cana-5360	390	16	.	.	PUNCT
cana-5360	391	1	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝑜𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝑜𝑠	NUM
cana-5360	391	2	,	,	PUNCT
cana-5360	391	3	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝑜𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝑜𝑠	PROPN
cana-5360	391	4	,	,	PUNCT
cana-5360	391	5	𝒫ℱ𝒩	𝒫ℱ𝒩	PROPN
cana-5360	391	6	𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝑜𝑠	𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝑜𝑠	PROPN
cana-5360	391	7	,	,	PUNCT
cana-5360	391	8	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝑜𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝑜𝑠	PROPN
cana-5360	391	9	and	and	CCONJ
cana-5360	391	10	communications	communication	NOUN
cana-5360	391	11	on	on	ADP
cana-5360	391	12	applied	apply	VERB
cana-5360	391	13	nonlinear	nonlinear	ADJ
cana-5360	391	14	analysis	analysis	NOUN
cana-5360	391	15	issn	issn	NOUN
cana-5360	391	16	:	:	PUNCT
cana-5360	391	17	1074	1074	NUM
cana-5360	391	18	-	-	PUNCT
cana-5360	391	19	133x	133x	NUM
cana-5360	391	20	vol	vol	VERB
cana-5360	391	21	32	32	NUM
cana-5360	391	22	no	no	NOUN
cana-5360	391	23	.	.	PUNCT
cana-5360	392	1	10s	10	NOUN
cana-5360	392	2	(	(	PUNCT
cana-5360	392	3	2025	2025	NUM
cana-5360	392	4	)	)	PUNCT
cana-5360	392	5	1937	1937	NUM
cana-5360	392	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5360	392	7	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝑜𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝑜𝑠	PROPN
cana-5360	392	8	)	)	PUNCT
cana-5360	392	9	’s	’	VERB
cana-5360	392	10	and	and	CCONJ
cana-5360	392	11	study	study	VERB
cana-5360	392	12	some	some	PRON
cana-5360	392	13	of	of	ADP
cana-5360	392	14	their	their	PRON
cana-5360	392	15	basic	basic	ADJ
cana-5360	392	16	properties	property	NOUN
cana-5360	392	17	.	.	PUNCT
cana-5360	393	1	this	this	DET
cana-5360	393	2	definition	definition	NOUN
cana-5360	393	3	enables	enable	VERB
cana-5360	393	4	us	we	PRON
cana-5360	393	5	to	to	PART
cana-5360	393	6	obtain	obtain	VERB
cana-5360	393	7	conditions	condition	NOUN
cana-5360	393	8	under	under	ADP
cana-5360	393	9	which	which	PRON
cana-5360	393	10	maps	map	NOUN
cana-5360	393	11	and	and	CCONJ
cana-5360	393	12	inverse	inverse	NOUN
cana-5360	393	13	maps	map	NOUN
cana-5360	393	14	preserve	preserve	VERB
cana-5360	393	15	respective	respective	ADJ
cana-5360	393	16	open	open	ADJ
cana-5360	393	17	sets	set	NOUN
cana-5360	393	18	.	.	PUNCT
cana-5360	394	1	definition	definition	NOUN
cana-5360	394	2	4.1	4.1	NUM
cana-5360	394	3	a	a	DET
cana-5360	394	4	map	map	NOUN
cana-5360	394	5	ℎ𝑃	ℎ𝑃	NOUN
cana-5360	394	6	:	:	PUNCT
cana-5360	394	7	(	(	PUNCT
cana-5360	394	8	𝑈1	𝑈1	NOUN
cana-5360	394	9	,	,	PUNCT
cana-5360	394	10	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	394	11	)	)	PUNCT
cana-5360	394	12	)	)	PUNCT
cana-5360	394	13	→	→	SYM
cana-5360	394	14	(	(	PUNCT
cana-5360	394	15	𝑈2	𝑈2	NOUN
cana-5360	394	16	,	,	PUNCT
cana-5360	394	17	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	394	18	)	)	PUNCT
cana-5360	394	19	)	)	PUNCT
cana-5360	394	20	is	be	AUX
cana-5360	394	21	said	say	VERB
cana-5360	394	22	to	to	PART
cana-5360	394	23	be	be	AUX
cana-5360	394	24	pythagorean	pythagorean	PROPN
cana-5360	394	25	fuzzy	fuzzy	ADJ
cana-5360	394	26	nano	nano	NOUN
cana-5360	394	27	contra	contra	PROPN
cana-5360	394	28	(	(	PUNCT
cana-5360	394	29	resp	resp	NOUN
cana-5360	394	30	.	.	PUNCT
cana-5360	395	1	𝛿	𝛿	ADJ
cana-5360	395	2	,	,	PUNCT
cana-5360	395	3	𝛿𝒫	𝛿𝒫	NOUN
cana-5360	395	4	,	,	PUNCT
cana-5360	395	5	𝛿𝒮	𝛿𝒮	NOUN
cana-5360	395	6	,	,	PUNCT
cana-5360	395	7	𝛿𝛼	𝛿𝛼	NOUN
cana-5360	395	8	and	and	CCONJ
cana-5360	395	9	𝛿𝛽	𝛿𝛽	ADJ
cana-5360	395	10	)	)	PUNCT
cana-5360	395	11	-irresolute	-irresolute	NOUN
cana-5360	395	12	(	(	PUNCT
cana-5360	395	13	in	in	ADP
cana-5360	395	14	short	short	ADJ
cana-5360	395	15	,	,	PUNCT
cana-5360	395	16	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝐼𝑟𝑟	PROPN
cana-5360	395	17	(	(	PUNCT
cana-5360	395	18	resp	resp	NOUN
cana-5360	395	19	.	.	PUNCT
cana-5360	395	20	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐼𝑟𝑟	NUM
cana-5360	395	21	,	,	PUNCT
cana-5360	396	1	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	PROPN
cana-5360	396	2	,	,	PUNCT
cana-5360	396	3	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	PROPN
cana-5360	396	4	,	,	PUNCT
cana-5360	396	5	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐼𝑟𝑟	PROPN
cana-5360	396	6	and	and	CCONJ
cana-5360	396	7	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐼𝑟𝑟	PROPN
cana-5360	396	8	)	)	PUNCT
cana-5360	396	9	)	)	PUNCT
cana-5360	396	10	map	map	VERB
cana-5360	396	11	if	if	SCONJ
cana-5360	396	12	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	396	13	−1(𝐾	−1(𝐾	NOUN
cana-5360	396	14	)	)	PUNCT
cana-5360	396	15	is	be	AUX
cana-5360	396	16	a	a	DET
cana-5360	396	17	𝒫ℱ𝒩𝒮𝑐𝑠	𝒫ℱ𝒩𝒮𝑐𝑠	PROPN
cana-5360	396	18	(	(	PUNCT
cana-5360	396	19	resp	resp	NOUN
cana-5360	396	20	.	.	PUNCT
cana-5360	397	1	𝒫ℱ𝒩𝛿𝑐𝑠	𝒫ℱ𝒩𝛿𝑐𝑠	PROPN
cana-5360	397	2	,	,	PUNCT
cana-5360	397	3	𝒫ℱ𝒩𝛿𝒫𝑐𝑠	𝒫ℱ𝒩𝛿𝒫𝑐𝑠	PROPN
cana-5360	397	4	,	,	PUNCT
cana-5360	397	5	𝒫ℱ𝒩𝛿𝒮𝑐𝑠	𝒫ℱ𝒩𝛿𝒮𝑐𝑠	PROPN
cana-5360	397	6	,	,	PUNCT
cana-5360	397	7	𝒫ℱ𝒩𝛿𝛼𝑐𝑠	𝒫ℱ𝒩𝛿𝛼𝑐𝑠	PROPN
cana-5360	397	8	and	and	CCONJ
cana-5360	397	9	𝒫ℱ𝒩𝛿𝛽𝑐𝑠	𝒫ℱ𝒩𝛿𝛽𝑐𝑠	PROPN
cana-5360	397	10	)	)	PUNCT
cana-5360	397	11	in	in	ADP
cana-5360	397	12	(	(	PUNCT
cana-5360	397	13	𝑈1	𝑈1	NOUN
cana-5360	397	14	,	,	PUNCT
cana-5360	397	15	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	397	16	)	)	PUNCT
cana-5360	397	17	)	)	PUNCT
cana-5360	397	18	for	for	ADP
cana-5360	397	19	each	each	DET
cana-5360	397	20	𝒫ℱ𝒩𝒮𝑜𝑠	𝒫ℱ𝒩𝒮𝑜𝑠	PROPN
cana-5360	397	21	(	(	PUNCT
cana-5360	397	22	resp	resp	NOUN
cana-5360	397	23	.	.	PUNCT
cana-5360	398	1	𝒫ℱ𝒩𝛿𝑜𝑠	𝒫ℱ𝒩𝛿𝑜𝑠	PROPN
cana-5360	398	2	,	,	PUNCT
cana-5360	398	3	𝒫ℱ𝒩𝛿𝒫𝑜𝑠	𝒫ℱ𝒩𝛿𝒫𝑜𝑠	NUM
cana-5360	398	4	,	,	PUNCT
cana-5360	398	5	𝒫ℱ𝒩𝛿𝒮𝑜𝑠	𝒫ℱ𝒩𝛿𝒮𝑜𝑠	PROPN
cana-5360	398	6	,	,	PUNCT
cana-5360	398	7	𝒫ℱ𝒩𝛿𝛼𝑜𝑠	𝒫ℱ𝒩𝛿𝛼𝑜𝑠	PROPN
cana-5360	398	8	and	and	CCONJ
cana-5360	398	9	𝒫ℱ𝒩𝛿𝛽𝑜𝑠	𝒫ℱ𝒩𝛿𝛽𝑜𝑠	PROPN
cana-5360	398	10	)	)	PUNCT
cana-5360	398	11	𝐾	𝐾	PROPN
cana-5360	398	12	of	of	ADP
cana-5360	398	13	(	(	PUNCT
cana-5360	398	14	𝑈2	𝑈2	PROPN
cana-5360	398	15	,	,	PUNCT
cana-5360	398	16	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	398	17	)	)	PUNCT
cana-5360	398	18	)	)	PUNCT
cana-5360	398	19	.	.	PUNCT
cana-5360	399	1	theorem	theorem	VERB
cana-5360	399	2	4.1	4.1	NUM
cana-5360	399	3	let	let	NOUN
cana-5360	399	4	(	(	PUNCT
cana-5360	399	5	𝑈1	𝑈1	NOUN
cana-5360	399	6	,	,	PUNCT
cana-5360	399	7	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	399	8	)	)	PUNCT
cana-5360	399	9	)	)	PUNCT
cana-5360	399	10	&	&	CCONJ
cana-5360	399	11	(	(	PUNCT
cana-5360	399	12	𝑈2	𝑈2	PROPN
cana-5360	399	13	,	,	PUNCT
cana-5360	399	14	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	399	15	)	)	PUNCT
cana-5360	399	16	)	)	PUNCT
cana-5360	400	1	be	be	AUX
cana-5360	400	2	a	a	DET
cana-5360	400	3	𝒫ℱ𝒩𝑡𝑠	𝒫ℱ𝒩𝑡𝑠	PROPN
cana-5360	400	4	’	'	PUNCT
cana-5360	400	5	s.	s.	PROPN
cana-5360	400	6	let	let	VERB
cana-5360	400	7	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	400	8	:	:	PUNCT
cana-5360	400	9	(	(	PUNCT
cana-5360	400	10	𝑈1	𝑈1	NOUN
cana-5360	400	11	,	,	PUNCT
cana-5360	400	12	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	400	13	)	)	PUNCT
cana-5360	400	14	)	)	PUNCT
cana-5360	401	1	→	→	SYM
cana-5360	401	2	(	(	PUNCT
cana-5360	401	3	𝑈2	𝑈2	NOUN
cana-5360	401	4	,	,	PUNCT
cana-5360	401	5	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	401	6	)	)	PUNCT
cana-5360	401	7	)	)	PUNCT
cana-5360	401	8	be	be	AUX
cana-5360	401	9	a	a	DET
cana-5360	401	10	mapping	mapping	NOUN
cana-5360	401	11	.	.	PUNCT
cana-5360	402	1	then	then	ADV
cana-5360	402	2	the	the	DET
cana-5360	402	3	following	following	ADJ
cana-5360	402	4	statements	statement	NOUN
cana-5360	402	5	are	be	AUX
cana-5360	402	6	hold	hold	ADJ
cana-5360	402	7	for	for	ADP
cana-5360	402	8	𝒫ℱ𝒩𝑡𝑠	𝒫ℱ𝒩𝑡𝑠	NOUN
cana-5360	402	9	,	,	PUNCT
cana-5360	402	10	but	but	CCONJ
cana-5360	402	11	not	not	PART
cana-5360	402	12	conversely	conversely	ADV
cana-5360	402	13	.	.	PUNCT
cana-5360	403	1	(	(	PUNCT
cana-5360	403	2	i	i	NOUN
cana-5360	403	3	)	)	PUNCT
cana-5360	403	4	every	every	DET
cana-5360	403	5	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝐼𝑟𝑟	PROPN
cana-5360	403	6	map	map	NOUN
cana-5360	403	7	is	be	AUX
cana-5360	403	8	a	a	DET
cana-5360	403	9	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝒮𝐶𝑡𝑠.	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝒮𝐶𝑡𝑠.	PROPN
cana-5360	403	10	(	(	PUNCT
cana-5360	403	11	ii	ii	NOUN
cana-5360	403	12	)	)	PUNCT
cana-5360	403	13	every	every	DET
cana-5360	403	14	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	PROPN
cana-5360	403	15	map	map	NOUN
cana-5360	403	16	is	be	AUX
cana-5360	403	17	a	a	DET
cana-5360	403	18	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠.	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠.	PROPN
cana-5360	403	19	(	(	PUNCT
cana-5360	403	20	iii	iii	NOUN
cana-5360	403	21	)	)	PUNCT
cana-5360	403	22	every	every	PRON
cana-5360	403	23	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	ADJ
cana-5360	403	24	map	map	NOUN
cana-5360	403	25	is	be	AUX
cana-5360	403	26	a	a	DET
cana-5360	403	27	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠.	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠.	NOUN
cana-5360	403	28	(	(	PUNCT
cana-5360	403	29	iv	iv	X
cana-5360	403	30	)	)	PUNCT
cana-5360	403	31	every	every	DET
cana-5360	403	32	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐼𝑟𝑟	PROPN
cana-5360	403	33	map	map	NOUN
cana-5360	403	34	is	be	AUX
cana-5360	403	35	a	a	DET
cana-5360	403	36	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐶𝑡𝑠.	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐶𝑡𝑠.	NOUN
cana-5360	403	37	(	(	PUNCT
cana-5360	403	38	v	v	NOUN
cana-5360	403	39	)	)	PUNCT
cana-5360	403	40	every	every	DET
cana-5360	403	41	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐼𝑟𝑟	PROPN
cana-5360	403	42	map	map	NOUN
cana-5360	403	43	is	be	AUX
cana-5360	403	44	a	a	DET
cana-5360	403	45	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠.	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠.	PROPN
cana-5360	403	46	proof	proof	NOUN
cana-5360	403	47	.	.	PUNCT
cana-5360	404	1	(	(	PUNCT
cana-5360	404	2	i	i	NOUN
cana-5360	404	3	)	)	PUNCT
cana-5360	404	4	consider	consider	VERB
cana-5360	404	5	a	a	DET
cana-5360	404	6	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝐼𝑟𝑟	PROPN
cana-5360	404	7	map	map	NOUN
cana-5360	404	8	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	404	9	and	and	CCONJ
cana-5360	404	10	a	a	DET
cana-5360	404	11	𝒫ℱ𝒩𝑜𝑠	𝒫ℱ𝒩𝑜𝑠	PROPN
cana-5360	404	12	𝐾	𝐾	PROPN
cana-5360	404	13	in	in	ADP
cana-5360	404	14	𝑈2	𝑈2	PROPN
cana-5360	404	15	.	.	PUNCT
cana-5360	405	1	as	as	SCONJ
cana-5360	405	2	each	each	DET
cana-5360	405	3	𝒫ℱ𝒩𝑜𝑠	𝒫ℱ𝒩𝑜𝑠	NOUN
cana-5360	405	4	is	be	AUX
cana-5360	405	5	a	a	DET
cana-5360	405	6	𝒫ℱ𝒩𝒮𝑜𝑠	𝒫ℱ𝒩𝒮𝑜𝑠	PROPN
cana-5360	405	7	,	,	PUNCT
cana-5360	405	8	𝐾	𝐾	PROPN
cana-5360	405	9	is	be	AUX
cana-5360	405	10	a	a	DET
cana-5360	405	11	𝒫ℱ𝒩𝒮𝑜𝑠	𝒫ℱ𝒩𝒮𝑜𝑠	PROPN
cana-5360	405	12	in	in	ADP
cana-5360	405	13	𝑈2	𝑈2	PROPN
cana-5360	405	14	.	.	PUNCT
cana-5360	406	1	by	by	ADP
cana-5360	406	2	presumption	presumption	NOUN
cana-5360	406	3	,	,	PUNCT
cana-5360	406	4	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	406	5	−1(𝐾	−1(𝐾	NOUN
cana-5360	406	6	)	)	PUNCT
cana-5360	406	7	is	be	AUX
cana-5360	406	8	a	a	DET
cana-5360	406	9	𝒫ℱ𝒩𝒮𝑐𝑠	𝒫ℱ𝒩𝒮𝑐𝑠	PROPN
cana-5360	406	10	in	in	ADP
cana-5360	406	11	𝑈1	𝑈1	NOUN
cana-5360	406	12	.	.	PUNCT
cana-5360	407	1	thus	thus	ADV
cana-5360	407	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	407	3	is	be	AUX
cana-5360	407	4	a	a	DET
cana-5360	407	5	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝒮𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝒮𝐶𝑡𝑠	PROPN
cana-5360	407	6	map	map	NOUN
cana-5360	407	7	.	.	PUNCT
cana-5360	408	1	(	(	PUNCT
cana-5360	408	2	ii	ii	NOUN
cana-5360	408	3	)	)	PUNCT
cana-5360	408	4	consider	consider	VERB
cana-5360	408	5	a	a	DET
cana-5360	408	6	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	PROPN
cana-5360	408	7	map	map	VERB
cana-5360	408	8	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	408	9	and	and	CCONJ
cana-5360	408	10	a	a	DET
cana-5360	408	11	𝒫ℱ𝒩𝛿𝑜𝑠	𝒫ℱ𝒩𝛿𝑜𝑠	PROPN
cana-5360	408	12	𝐾	𝐾	PROPN
cana-5360	408	13	in	in	ADP
cana-5360	408	14	𝑈2	𝑈2	PROPN
cana-5360	408	15	.	.	PUNCT
cana-5360	409	1	as	as	SCONJ
cana-5360	409	2	each	each	DET
cana-5360	409	3	𝒫ℱ𝒩𝛿𝑜𝑠	𝒫ℱ𝒩𝛿𝑜𝑠	PROPN
cana-5360	409	4	is	be	AUX
cana-5360	409	5	a	a	DET
cana-5360	409	6	𝒫ℱ𝒩𝑜𝑠	𝒫ℱ𝒩𝑜𝑠	NOUN
cana-5360	409	7	and	and	CCONJ
cana-5360	409	8	𝒫ℱ𝒩𝛿𝒮𝑜𝑠	𝒫ℱ𝒩𝛿𝒮𝑜𝑠	NUM
cana-5360	409	9	,	,	PUNCT
cana-5360	409	10	𝐾	𝐾	PROPN
cana-5360	409	11	is	be	AUX
cana-5360	409	12	a	a	DET
cana-5360	409	13	𝒫ℱ𝒩𝛿𝑜𝑠	𝒫ℱ𝒩𝛿𝑜𝑠	PROPN
cana-5360	409	14	and	and	CCONJ
cana-5360	409	15	𝒫ℱ𝒩𝛿𝒮𝑜𝑠	𝒫ℱ𝒩𝛿𝒮𝑜𝑠	NUM
cana-5360	409	16	in	in	ADP
cana-5360	409	17	𝑈2	𝑈2	PROPN
cana-5360	409	18	.	.	PUNCT
cana-5360	410	1	by	by	ADP
cana-5360	410	2	presumption	presumption	NOUN
cana-5360	410	3	,	,	PUNCT
cana-5360	410	4	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	410	5	−1(𝐾	−1(𝐾	NOUN
cana-5360	410	6	)	)	PUNCT
cana-5360	410	7	is	be	AUX
cana-5360	410	8	a	a	DET
cana-5360	410	9	𝒫ℱ𝒩𝛿𝒮𝑐𝑠	𝒫ℱ𝒩𝛿𝒮𝑐𝑠	PROPN
cana-5360	410	10	in	in	ADP
cana-5360	410	11	𝑈1	𝑈1	NOUN
cana-5360	410	12	.	.	PUNCT
cana-5360	411	1	thus	thus	ADV
cana-5360	411	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	411	3	is	be	AUX
cana-5360	411	4	a	a	DET
cana-5360	411	5	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	NOUN
cana-5360	411	6	map	map	NOUN
cana-5360	411	7	.	.	PUNCT
cana-5360	412	1	(	(	PUNCT
cana-5360	412	2	iii	iii	X
cana-5360	412	3	)	)	PUNCT
cana-5360	412	4	consider	consider	VERB
cana-5360	412	5	a	a	DET
cana-5360	412	6	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	ADJ
cana-5360	412	7	map	map	NOUN
cana-5360	412	8	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	412	9	and	and	CCONJ
cana-5360	412	10	a	a	DET
cana-5360	412	11	𝒫ℱ𝒩𝛿𝑜𝑠	𝒫ℱ𝒩𝛿𝑜𝑠	PROPN
cana-5360	412	12	𝐾	𝐾	PROPN
cana-5360	412	13	in	in	ADP
cana-5360	412	14	𝑈2	𝑈2	PROPN
cana-5360	412	15	.	.	PUNCT
cana-5360	413	1	as	as	SCONJ
cana-5360	413	2	each	each	DET
cana-5360	413	3	𝒫ℱ𝒩𝛿𝑜𝑠	𝒫ℱ𝒩𝛿𝑜𝑠	PROPN
cana-5360	413	4	is	be	AUX
cana-5360	413	5	a	a	DET
cana-5360	413	6	𝒫ℱ𝒩𝑜𝑠	𝒫ℱ𝒩𝑜𝑠	ADJ
cana-5360	413	7	and	and	CCONJ
cana-5360	413	8	𝒫ℱ𝒩𝛿𝒫𝑜𝑠	𝒫ℱ𝒩𝛿𝒫𝑜𝑠	NUM
cana-5360	413	9	,	,	PUNCT
cana-5360	413	10	𝐾	𝐾	PROPN
cana-5360	413	11	is	be	AUX
cana-5360	413	12	a	a	DET
cana-5360	413	13	𝒫ℱ𝒩𝛿𝑜𝑠	𝒫ℱ𝒩𝛿𝑜𝑠	PROPN
cana-5360	413	14	and	and	CCONJ
cana-5360	413	15	𝒫ℱ𝒩𝛿𝒫𝑜𝑠	𝒫ℱ𝒩𝛿𝒫𝑜𝑠	NUM
cana-5360	413	16	in	in	ADP
cana-5360	413	17	𝑈2	𝑈2	PROPN
cana-5360	413	18	.	.	PUNCT
cana-5360	414	1	by	by	ADP
cana-5360	414	2	presumption	presumption	NOUN
cana-5360	414	3	,	,	PUNCT
cana-5360	414	4	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	414	5	−1(𝐾	−1(𝐾	NOUN
cana-5360	414	6	)	)	PUNCT
cana-5360	414	7	is	be	AUX
cana-5360	414	8	a	a	DET
cana-5360	414	9	𝒫ℱ𝒩𝛿𝒫𝑐𝑠	𝒫ℱ𝒩𝛿𝒫𝑐𝑠	PROPN
cana-5360	414	10	in	in	ADP
cana-5360	414	11	𝑈1	𝑈1	NOUN
cana-5360	414	12	.	.	PUNCT
cana-5360	415	1	thus	thus	ADV
cana-5360	415	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	415	3	is	be	AUX
cana-5360	415	4	a	a	DET
cana-5360	415	5	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	PROPN
cana-5360	415	6	map	map	NOUN
cana-5360	415	7	.	.	PUNCT
cana-5360	416	1	(	(	PUNCT
cana-5360	416	2	iv	iv	X
cana-5360	416	3	)	)	PUNCT
cana-5360	416	4	consider	consider	VERB
cana-5360	416	5	a	a	DET
cana-5360	416	6	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐼𝑟𝑟	PROPN
cana-5360	416	7	map	map	VERB
cana-5360	416	8	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	416	9	and	and	CCONJ
cana-5360	416	10	a	a	DET
cana-5360	416	11	𝒫ℱ𝒩𝛿𝑜𝑠	𝒫ℱ𝒩𝛿𝑜𝑠	PROPN
cana-5360	416	12	𝐾	𝐾	PROPN
cana-5360	416	13	in	in	ADP
cana-5360	416	14	𝑈2	𝑈2	PROPN
cana-5360	416	15	.	.	PUNCT
cana-5360	417	1	as	as	SCONJ
cana-5360	417	2	each	each	DET
cana-5360	417	3	𝒫ℱ𝒩𝛿𝑜𝑠	𝒫ℱ𝒩𝛿𝑜𝑠	PROPN
cana-5360	417	4	is	be	AUX
cana-5360	417	5	a	a	DET
cana-5360	417	6	𝒫ℱ𝒩𝑜𝑠	𝒫ℱ𝒩𝑜𝑠	PROPN
cana-5360	417	7	and	and	CCONJ
cana-5360	417	8	𝒫ℱ𝒩𝛿𝛼𝑜𝑠	𝒫ℱ𝒩𝛿𝛼𝑜𝑠	PROPN
cana-5360	417	9	,	,	PUNCT
cana-5360	417	10	𝐾	𝐾	PROPN
cana-5360	417	11	is	be	AUX
cana-5360	417	12	a	a	DET
cana-5360	417	13	𝒫ℱ𝒩𝛿𝑜𝑠	𝒫ℱ𝒩𝛿𝑜𝑠	PROPN
cana-5360	417	14	and	and	CCONJ
cana-5360	417	15	𝒫ℱ𝒩𝛿𝛼𝑜𝑠	𝒫ℱ𝒩𝛿𝛼𝑜𝑠	PROPN
cana-5360	417	16	in	in	ADP
cana-5360	417	17	𝑈2	𝑈2	PROPN
cana-5360	417	18	.	.	PUNCT
cana-5360	418	1	by	by	ADP
cana-5360	418	2	presumption	presumption	NOUN
cana-5360	418	3	,	,	PUNCT
cana-5360	418	4	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	418	5	−1(𝐾	−1(𝐾	NOUN
cana-5360	418	6	)	)	PUNCT
cana-5360	418	7	is	be	AUX
cana-5360	418	8	a	a	DET
cana-5360	418	9	𝒫ℱ𝒩𝛿𝛼𝑐𝑠	𝒫ℱ𝒩𝛿𝛼𝑐𝑠	PROPN
cana-5360	418	10	in	in	ADP
cana-5360	418	11	𝑈1	𝑈1	NOUN
cana-5360	418	12	.	.	PUNCT
cana-5360	419	1	thus	thus	ADV
cana-5360	419	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	419	3	is	be	AUX
cana-5360	419	4	a	a	DET
cana-5360	419	5	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐶𝑡𝑠	PROPN
cana-5360	419	6	map	map	NOUN
cana-5360	419	7	.	.	PUNCT
cana-5360	420	1	(	(	PUNCT
cana-5360	420	2	v	v	NOUN
cana-5360	420	3	)	)	PUNCT
cana-5360	420	4	consider	consider	VERB
cana-5360	420	5	a	a	DET
cana-5360	420	6	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐼𝑟𝑟	PROPN
cana-5360	420	7	map	map	NOUN
cana-5360	420	8	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	420	9	and	and	CCONJ
cana-5360	420	10	a	a	DET
cana-5360	420	11	𝒫ℱ𝒩𝛿𝑜𝑠	𝒫ℱ𝒩𝛿𝑜𝑠	PROPN
cana-5360	420	12	𝐾	𝐾	PROPN
cana-5360	420	13	in	in	ADP
cana-5360	420	14	𝑈2	𝑈2	PROPN
cana-5360	420	15	.	.	PUNCT
cana-5360	421	1	as	as	SCONJ
cana-5360	421	2	each	each	DET
cana-5360	421	3	𝒫ℱ𝒩𝛿𝑜𝑠	𝒫ℱ𝒩𝛿𝑜𝑠	PROPN
cana-5360	421	4	is	be	AUX
cana-5360	421	5	a	a	DET
cana-5360	421	6	𝒫ℱ𝒩𝑜𝑠	𝒫ℱ𝒩𝑜𝑠	NOUN
cana-5360	421	7	and	and	CCONJ
cana-5360	421	8	𝒫ℱ𝒩𝛿𝛽𝑜𝑠	𝒫ℱ𝒩𝛿𝛽𝑜𝑠	PROPN
cana-5360	421	9	,	,	PUNCT
cana-5360	421	10	𝐾	𝐾	PROPN
cana-5360	421	11	is	be	AUX
cana-5360	421	12	a	a	DET
cana-5360	421	13	𝒫ℱ𝒩𝛿𝑜𝑠	𝒫ℱ𝒩𝛿𝑜𝑠	PROPN
cana-5360	421	14	and	and	CCONJ
cana-5360	421	15	𝒫ℱ𝒩𝛿𝛽𝑜𝑠	𝒫ℱ𝒩𝛿𝛽𝑜𝑠	PROPN
cana-5360	421	16	in	in	ADP
cana-5360	421	17	𝑈2	𝑈2	PROPN
cana-5360	421	18	.	.	PUNCT
cana-5360	422	1	by	by	ADP
cana-5360	422	2	presumption	presumption	NOUN
cana-5360	422	3	,	,	PUNCT
cana-5360	422	4	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	422	5	−1(𝐾	−1(𝐾	NOUN
cana-5360	422	6	)	)	PUNCT
cana-5360	422	7	is	be	AUX
cana-5360	422	8	a	a	DET
cana-5360	422	9	𝒫ℱ𝒩𝛿𝛽𝑐𝑠	𝒫ℱ𝒩𝛿𝛽𝑐𝑠	PROPN
cana-5360	422	10	in	in	ADP
cana-5360	422	11	𝑈1	𝑈1	NOUN
cana-5360	422	12	.	.	PUNCT
cana-5360	423	1	thus	thus	ADV
cana-5360	423	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	423	3	is	be	AUX
cana-5360	423	4	a	a	DET
cana-5360	423	5	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠	PROPN
cana-5360	423	6	map	map	NOUN
cana-5360	423	7	.	.	PUNCT
cana-5360	424	1	example	example	NOUN
cana-5360	424	2	4.1	4.1	NUM
cana-5360	424	3	let	let	VERB
cana-5360	424	4	𝑈1	𝑈1	NOUN
cana-5360	424	5	=	=	SYM
cana-5360	424	6	{	{	PUNCT
cana-5360	424	7	𝑠1	𝑠1	PROPN
cana-5360	424	8	,	,	PUNCT
cana-5360	424	9	𝑠2	𝑠2	NOUN
cana-5360	424	10	,	,	PUNCT
cana-5360	424	11	𝑠3	𝑠3	NOUN
cana-5360	424	12	,	,	PUNCT
cana-5360	424	13	𝑠4	𝑠4	PROPN
cana-5360	424	14	}	}	PUNCT
cana-5360	424	15	,	,	PUNCT
cana-5360	424	16	𝑈2	𝑈2	PROPN
cana-5360	424	17	=	=	PUNCT
cana-5360	424	18	{	{	PUNCT
cana-5360	424	19	𝑡1	𝑡1	PROPN
cana-5360	424	20	,	,	PUNCT
cana-5360	424	21	𝑡2	𝑡2	PROPN
cana-5360	424	22	,	,	PUNCT
cana-5360	424	23	𝑡3	𝑡3	PROPN
cana-5360	424	24	,	,	PUNCT
cana-5360	424	25	𝑡4	𝑡4	PROPN
cana-5360	424	26	}	}	PUNCT
cana-5360	424	27	are	be	AUX
cana-5360	424	28	the	the	DET
cana-5360	424	29	universe	universe	NOUN
cana-5360	424	30	sets	set	NOUN
cana-5360	424	31	and	and	CCONJ
cana-5360	424	32	the	the	DET
cana-5360	424	33	equivalence	equivalence	NOUN
cana-5360	424	34	relations	relation	NOUN
cana-5360	424	35	are	be	AUX
cana-5360	424	36	𝑈1/𝑅	𝑈1/𝑅	X
cana-5360	424	37	=	=	SYM
cana-5360	424	38	{	{	PUNCT
cana-5360	424	39	{	{	PUNCT
cana-5360	424	40	𝑠1	𝑠1	NOUN
cana-5360	424	41	,	,	PUNCT
cana-5360	424	42	𝑠3	𝑠3	PROPN
cana-5360	424	43	}	}	PUNCT
cana-5360	424	44	,	,	PUNCT
cana-5360	424	45	{	{	PUNCT
cana-5360	424	46	𝑠2	𝑠2	NOUN
cana-5360	424	47	,	,	PUNCT
cana-5360	424	48	𝑠4	𝑠4	PROPN
cana-5360	424	49	}	}	PUNCT
cana-5360	424	50	}	}	PUNCT
cana-5360	424	51	and	and	CCONJ
cana-5360	424	52	𝑈2/𝑅	𝑈2/𝑅	PUNCT
cana-5360	424	53	=	=	PRON
cana-5360	424	54	{	{	PUNCT
cana-5360	424	55	{	{	PUNCT
cana-5360	424	56	𝑡1	𝑡1	NOUN
cana-5360	424	57	,	,	PUNCT
cana-5360	424	58	𝑡3	𝑡3	PROPN
cana-5360	424	59	}	}	PUNCT
cana-5360	424	60	,	,	PUNCT
cana-5360	424	61	{	{	PUNCT
cana-5360	424	62	𝑡2	𝑡2	PROPN
cana-5360	424	63	,	,	PUNCT
cana-5360	424	64	𝑡4	𝑡4	PROPN
cana-5360	424	65	}	}	PUNCT
cana-5360	424	66	}	}	PUNCT
cana-5360	424	67	.	.	PUNCT
cana-5360	425	1	let	let	VERB
cana-5360	425	2	𝐴1	𝐴1	PROPN
cana-5360	425	3	=	=	PUNCT
cana-5360	425	4	{	{	PUNCT
cana-5360	425	5	⟨	⟨	X
cana-5360	425	6	𝑠1	𝑠1	PROPN
cana-5360	425	7	0.1,0.8	0.1,0.8	PROPN
cana-5360	425	8	⟩	⟩	NOUN
cana-5360	425	9	,	,	PUNCT
cana-5360	425	10	⟨	⟨	VERB
cana-5360	425	11	𝑠2	𝑠2	PROPN
cana-5360	425	12	0.3,0.7	0.3,0.7	PROPN
cana-5360	425	13	⟩	⟩	NOUN
cana-5360	425	14	,	,	PUNCT
cana-5360	425	15	⟨	⟨	VERB
cana-5360	425	16	𝑠3	𝑠3	PROPN
cana-5360	425	17	0.2,0.9	0.2,0.9	PROPN
cana-5360	425	18	⟩	⟩	NOUN
cana-5360	425	19	,	,	PUNCT
cana-5360	425	20	⟨	⟨	VERB
cana-5360	425	21	𝑠4	𝑠4	PROPN
cana-5360	425	22	0.4,0.6	0.4,0.6	PROPN
cana-5360	425	23	⟩	⟩	NOUN
cana-5360	425	24	}	}	PUNCT
cana-5360	425	25	and	and	CCONJ
cana-5360	425	26	𝐴2	𝐴2	PROPN
cana-5360	425	27	=	=	PUNCT
cana-5360	425	28	{	{	PUNCT
cana-5360	425	29	⟨	⟨	NOUN
cana-5360	425	30	𝑡1	𝑡1	NOUN
cana-5360	425	31	0.4,0.8	0.4,0.8	NUM
cana-5360	425	32	⟩	⟩	NOUN
cana-5360	425	33	,	,	PUNCT
cana-5360	425	34	⟨	⟨	VERB
cana-5360	425	35	𝑡2	𝑡2	PROPN
cana-5360	425	36	0.5,0.4	0.5,0.4	PROPN
cana-5360	426	1	⟩	⟩	NOUN
cana-5360	426	2	,	,	PUNCT
cana-5360	426	3	⟨	⟨	VERB
cana-5360	426	4	𝑡3	𝑡3	PROPN
cana-5360	426	5	0.6,0.6	0.6,0.6	PROPN
cana-5360	426	6	⟩	⟩	NOUN
cana-5360	426	7	,	,	PUNCT
cana-5360	426	8	⟨	⟨	VERB
cana-5360	426	9	𝑡4	𝑡4	PROPN
cana-5360	426	10	0.7,0.6	0.7,0.6	NOUN
cana-5360	426	11	⟩	⟩	NOUN
cana-5360	426	12	}	}	PUNCT
cana-5360	426	13	be	be	VERB
cana-5360	426	14	a	a	DET
cana-5360	426	15	pythagorean	pythagorean	ADJ
cana-5360	426	16	fuzzy	fuzzy	ADJ
cana-5360	426	17	subsets	subset	NOUN
cana-5360	426	18	of	of	ADP
cana-5360	426	19	𝑈1	𝑈1	NOUN
cana-5360	426	20	and	and	CCONJ
cana-5360	426	21	𝑈2	𝑈2	NOUN
cana-5360	426	22	respectively	respectively	ADV
cana-5360	426	23	.	.	PUNCT
cana-5360	427	1	𝒫ℱ𝔑(𝐴1	𝒫ℱ𝔑(𝐴1	NUM
cana-5360	427	2	)	)	PUNCT
cana-5360	427	3	=	=	PRON
cana-5360	427	4	{	{	PUNCT
cana-5360	427	5	⟨	⟨	VERB
cana-5360	427	6	𝑠1,𝑠3	𝑠1,𝑠3	PROPN
cana-5360	427	7	0.1,0.9	0.1,0.9	PROPN
cana-5360	427	8	⟩	⟩	NOUN
cana-5360	427	9	,	,	PUNCT
cana-5360	427	10	⟨	⟨	VERB
cana-5360	427	11	𝑠2,𝑠4	𝑠2,𝑠4	PROPN
cana-5360	427	12	0.3,0.7	0.3,0.7	PROPN
cana-5360	427	13	⟩	⟩	PROPN
cana-5360	427	14	}	}	PUNCT
cana-5360	427	15	,	,	PUNCT
cana-5360	427	16	communications	communication	NOUN
cana-5360	427	17	on	on	ADP
cana-5360	427	18	applied	apply	VERB
cana-5360	427	19	nonlinear	nonlinear	ADJ
cana-5360	427	20	analysis	analysis	NOUN
cana-5360	427	21	issn	issn	NOUN
cana-5360	427	22	:	:	PUNCT
cana-5360	427	23	1074	1074	NUM
cana-5360	427	24	-	-	PUNCT
cana-5360	427	25	133x	133x	NUM
cana-5360	427	26	vol	vol	VERB
cana-5360	427	27	32	32	NUM
cana-5360	427	28	no	no	NOUN
cana-5360	427	29	.	.	PUNCT
cana-5360	428	1	10s	10	NOUN
cana-5360	428	2	(	(	PUNCT
cana-5360	428	3	2025	2025	NUM
cana-5360	428	4	)	)	PUNCT
cana-5360	428	5	1938	1938	NUM
cana-5360	428	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5360	428	7	𝐵𝒫ℱ𝔑(𝐴1	𝐵𝒫ℱ𝔑(𝐴1	NOUN
cana-5360	428	8	)	)	PUNCT
cana-5360	428	9	=	=	SYM
cana-5360	428	10	𝒫ℱ𝔑(𝐴1	𝒫ℱ𝔑(𝐴1	NUM
cana-5360	428	11	)	)	PUNCT
cana-5360	428	12	=	=	PRON
cana-5360	428	13	{	{	PUNCT
cana-5360	428	14	⟨	⟨	VERB
cana-5360	428	15	𝑠1,𝑠3	𝑠1,𝑠3	PROPN
cana-5360	428	16	0.2,0.8	0.2,0.8	PROPN
cana-5360	428	17	⟩	⟩	NOUN
cana-5360	428	18	,	,	PUNCT
cana-5360	428	19	⟨	⟨	VERB
cana-5360	428	20	𝑠2,𝑠4	𝑠2,𝑠4	PROPN
cana-5360	428	21	0.4,0.6	0.4,0.6	PROPN
cana-5360	428	22	⟩	⟩	NOUN
cana-5360	428	23	}	}	PUNCT
cana-5360	428	24	,	,	PUNCT
cana-5360	428	25	𝒫ℱ𝔑(𝐴2	𝒫ℱ𝔑(𝐴2	NUM
cana-5360	428	26	)	)	PUNCT
cana-5360	429	1	=	=	PRON
cana-5360	429	2	{	{	PUNCT
cana-5360	429	3	⟨	⟨	X
cana-5360	429	4	𝑡1,𝑡3	𝑡1,𝑡3	PROPN
cana-5360	429	5	0.4,0.8	0.4,0.8	NUM
cana-5360	429	6	⟩	⟩	NOUN
cana-5360	429	7	,	,	PUNCT
cana-5360	429	8	⟨	⟨	VERB
cana-5360	429	9	𝑡2,𝑡4	𝑡2,𝑡4	PROPN
cana-5360	429	10	0.5,0.6	0.5,0.6	PROPN
cana-5360	429	11	⟩	⟩	NOUN
cana-5360	429	12	}	}	PUNCT
cana-5360	429	13	,	,	PUNCT
cana-5360	429	14	𝒫ℱ𝔑(𝐴2	𝒫ℱ𝔑(𝐴2	NUM
cana-5360	429	15	)	)	PUNCT
cana-5360	429	16	=	=	PRON
cana-5360	429	17	{	{	PUNCT
cana-5360	429	18	⟨	⟨	NOUN
cana-5360	429	19	𝑡1,𝑡3	𝑡1,𝑡3	PROPN
cana-5360	429	20	0.6,0.6	0.6,0.6	PROPN
cana-5360	429	21	⟩	⟩	NOUN
cana-5360	429	22	,	,	PUNCT
cana-5360	429	23	⟨	⟨	VERB
cana-5360	429	24	𝑡2,𝑡4	𝑡2,𝑡4	PROPN
cana-5360	429	25	0.7,0.4	0.7,0.4	NUM
cana-5360	429	26	⟩	⟩	NOUN
cana-5360	429	27	}	}	PUNCT
cana-5360	429	28	,	,	PUNCT
cana-5360	429	29	𝐵𝒫ℱ𝔑(𝐴2	𝐵𝒫ℱ𝔑(𝐴2	PROPN
cana-5360	429	30	)	)	PUNCT
cana-5360	429	31	=	=	PRON
cana-5360	429	32	{	{	PUNCT
cana-5360	429	33	⟨	⟨	NOUN
cana-5360	429	34	𝑡1,𝑡3	𝑡1,𝑡3	PROPN
cana-5360	429	35	0.6,0.6	0.6,0.6	PROPN
cana-5360	429	36	⟩	⟩	NOUN
cana-5360	429	37	,	,	PUNCT
cana-5360	429	38	⟨	⟨	VERB
cana-5360	429	39	𝑡2,𝑡4	𝑡2,𝑡4	PROPN
cana-5360	429	40	0.6,0.5	0.6,0.5	PROPN
cana-5360	429	41	⟩	⟩	NOUN
cana-5360	429	42	}	}	PUNCT
cana-5360	429	43	.	.	PUNCT
cana-5360	430	1	here	here	ADV
cana-5360	430	2	𝜏𝑝(𝐴1	𝜏𝑝(𝐴1	ADP
cana-5360	430	3	)	)	PUNCT
cana-5360	430	4	=	=	SYM
cana-5360	430	5	{	{	PUNCT
cana-5360	430	6	0𝑃	0𝑃	PROPN
cana-5360	430	7	,	,	PUNCT
cana-5360	430	8	1𝑃	1𝑃	NOUN
cana-5360	430	9	,	,	PUNCT
cana-5360	430	10	𝒫ℱ𝔑(𝐴1	𝒫ℱ𝔑(𝐴1	NUM
cana-5360	430	11	)	)	PUNCT
cana-5360	430	12	,	,	PUNCT
cana-5360	430	13	𝒫ℱ𝔑(𝐴1	𝒫ℱ𝔑(𝐴1	NUM
cana-5360	430	14	)	)	PUNCT
cana-5360	430	15	=	=	SYM
cana-5360	430	16	𝐵𝒫ℱ𝔑(𝐴1	𝐵𝒫ℱ𝔑(𝐴1	NOUN
cana-5360	430	17	)	)	PUNCT
cana-5360	430	18	}	}	PUNCT
cana-5360	430	19	and	and	CCONJ
cana-5360	430	20	𝜏𝑝(𝐴2	𝜏𝑝(𝐴2	NUM
cana-5360	430	21	)	)	PUNCT
cana-5360	430	22	=	=	PRON
cana-5360	430	23	{	{	PUNCT
cana-5360	430	24	0𝑃	0𝑃	PROPN
cana-5360	430	25	,	,	PUNCT
cana-5360	430	26	1𝑃	1𝑃	NOUN
cana-5360	430	27	,	,	PUNCT
cana-5360	430	28	𝒫ℱ𝔑(𝐴2	𝒫ℱ𝔑(𝐴2	PROPN
cana-5360	430	29	)	)	PUNCT
cana-5360	430	30	,	,	PUNCT
cana-5360	430	31	𝒫ℱ𝔑(𝐴2	𝒫ℱ𝔑(𝐴2	NUM
cana-5360	430	32	)	)	PUNCT
cana-5360	430	33	,	,	PUNCT
cana-5360	430	34	𝐵𝒫ℱ𝔑(𝐴2	𝐵𝒫ℱ𝔑(𝐴2	PROPN
cana-5360	430	35	)	)	PUNCT
cana-5360	430	36	}	}	PUNCT
cana-5360	430	37	are	be	AUX
cana-5360	430	38	the	the	DET
cana-5360	430	39	𝒫ℱ𝒩𝑡𝑠′𝑠	𝒫ℱ𝒩𝑡𝑠′𝑠	PROPN
cana-5360	430	40	on	on	ADP
cana-5360	430	41	𝑈1	𝑈1	NOUN
cana-5360	430	42	and	and	CCONJ
cana-5360	430	43	𝑈2	𝑈2	NOUN
cana-5360	430	44	respectively	respectively	ADV
cana-5360	430	45	.	.	PUNCT
cana-5360	431	1	let	let	VERB
cana-5360	431	2	ℎ𝑃	ℎ𝑃	NOUN
cana-5360	431	3	:	:	PUNCT
cana-5360	431	4	(	(	PUNCT
cana-5360	431	5	𝑈1	𝑈1	NOUN
cana-5360	431	6	,	,	PUNCT
cana-5360	431	7	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	431	8	)	)	PUNCT
cana-5360	431	9	)	)	PUNCT
cana-5360	431	10	→	→	SYM
cana-5360	431	11	(	(	PUNCT
cana-5360	431	12	𝑈2	𝑈2	NOUN
cana-5360	431	13	,	,	PUNCT
cana-5360	431	14	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	431	15	)	)	PUNCT
cana-5360	431	16	)	)	PUNCT
cana-5360	431	17	be	be	AUX
cana-5360	431	18	an	an	DET
cana-5360	431	19	identity	identity	NOUN
cana-5360	431	20	function	function	NOUN
cana-5360	431	21	,	,	PUNCT
cana-5360	431	22	then	then	ADV
cana-5360	431	23	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	431	24	is	be	AUX
cana-5360	431	25	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝒮𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝒮𝐶𝑡𝑠	PROPN
cana-5360	431	26	but	but	CCONJ
cana-5360	431	27	not	not	PART
cana-5360	431	28	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝐼𝑟𝑟	PROPN
cana-5360	431	29	,	,	PUNCT
cana-5360	431	30	because	because	SCONJ
cana-5360	431	31	the	the	DET
cana-5360	431	32	set	set	NOUN
cana-5360	431	33	(	(	PUNCT
cana-5360	431	34	𝒫ℱ𝔑(𝐴2))𝑐	𝒫ℱ𝔑(𝐴2))𝑐	PROPN
cana-5360	431	35	is	be	AUX
cana-5360	431	36	a	a	DET
cana-5360	431	37	𝒫ℱ𝒩𝒮𝑜𝑠	𝒫ℱ𝒩𝒮𝑜𝑠	PROPN
cana-5360	431	38	in	in	ADP
cana-5360	431	39	𝑈2	𝑈2	PROPN
cana-5360	431	40	but	but	CCONJ
cana-5360	431	41	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	431	42	−1((𝒫ℱ𝔑(𝐴2))𝑐	−1((𝒫ℱ𝔑(𝐴2))𝑐	NOUN
cana-5360	431	43	)	)	PUNCT
cana-5360	432	1	=	=	SYM
cana-5360	432	2	(	(	PUNCT
cana-5360	432	3	𝒫ℱ𝔑(𝐴2))𝑐	𝒫ℱ𝔑(𝐴2))𝑐	PROPN
cana-5360	432	4	is	be	AUX
cana-5360	432	5	not	not	PART
cana-5360	432	6	𝒫ℱ𝒩𝒮𝑐𝑠	𝒫ℱ𝒩𝒮𝑐𝑠	PROPN
cana-5360	432	7	in	in	ADP
cana-5360	432	8	𝑈1	𝑈1	PROPN
cana-5360	432	9	.	.	PUNCT
cana-5360	433	1	example	example	NOUN
cana-5360	433	2	4.2	4.2	NUM
cana-5360	433	3	let	let	VERB
cana-5360	433	4	𝑈1	𝑈1	NOUN
cana-5360	433	5	=	=	SYM
cana-5360	433	6	{	{	PUNCT
cana-5360	433	7	𝑠1	𝑠1	PROPN
cana-5360	433	8	,	,	PUNCT
cana-5360	433	9	𝑠2	𝑠2	NOUN
cana-5360	433	10	,	,	PUNCT
cana-5360	433	11	𝑠3	𝑠3	NOUN
cana-5360	433	12	,	,	PUNCT
cana-5360	433	13	𝑠4	𝑠4	PROPN
cana-5360	433	14	}	}	PUNCT
cana-5360	433	15	,	,	PUNCT
cana-5360	433	16	𝑈2	𝑈2	PROPN
cana-5360	433	17	=	=	PUNCT
cana-5360	433	18	{	{	PUNCT
cana-5360	433	19	𝑡1	𝑡1	PROPN
cana-5360	433	20	,	,	PUNCT
cana-5360	433	21	𝑡2	𝑡2	PROPN
cana-5360	433	22	,	,	PUNCT
cana-5360	433	23	𝑡3	𝑡3	PROPN
cana-5360	433	24	,	,	PUNCT
cana-5360	433	25	𝑡4	𝑡4	PROPN
cana-5360	433	26	}	}	PUNCT
cana-5360	433	27	are	be	AUX
cana-5360	433	28	the	the	DET
cana-5360	433	29	universe	universe	NOUN
cana-5360	433	30	sets	set	NOUN
cana-5360	433	31	and	and	CCONJ
cana-5360	433	32	the	the	DET
cana-5360	433	33	equivalence	equivalence	NOUN
cana-5360	433	34	relations	relation	NOUN
cana-5360	433	35	are	be	AUX
cana-5360	433	36	𝑈1/𝑅	𝑈1/𝑅	X
cana-5360	433	37	=	=	SYM
cana-5360	433	38	{	{	PUNCT
cana-5360	433	39	{	{	PUNCT
cana-5360	433	40	𝑠1	𝑠1	NOUN
cana-5360	433	41	,	,	PUNCT
cana-5360	433	42	𝑠3	𝑠3	PROPN
cana-5360	433	43	}	}	PUNCT
cana-5360	433	44	,	,	PUNCT
cana-5360	433	45	{	{	PUNCT
cana-5360	433	46	𝑠2	𝑠2	NOUN
cana-5360	433	47	,	,	PUNCT
cana-5360	433	48	𝑠4	𝑠4	PROPN
cana-5360	433	49	}	}	PUNCT
cana-5360	433	50	}	}	PUNCT
cana-5360	433	51	and	and	CCONJ
cana-5360	433	52	𝑈2/𝑅	𝑈2/𝑅	PUNCT
cana-5360	433	53	=	=	PRON
cana-5360	433	54	{	{	PUNCT
cana-5360	433	55	{	{	PUNCT
cana-5360	433	56	𝑡1	𝑡1	NOUN
cana-5360	433	57	,	,	PUNCT
cana-5360	433	58	𝑡3	𝑡3	PROPN
cana-5360	433	59	}	}	PUNCT
cana-5360	433	60	,	,	PUNCT
cana-5360	433	61	{	{	PUNCT
cana-5360	433	62	𝑡2	𝑡2	PROPN
cana-5360	433	63	,	,	PUNCT
cana-5360	433	64	𝑡4	𝑡4	PROPN
cana-5360	433	65	}	}	PUNCT
cana-5360	433	66	}	}	PUNCT
cana-5360	433	67	.	.	PUNCT
cana-5360	434	1	let	let	VERB
cana-5360	434	2	𝐴1	𝐴1	PROPN
cana-5360	434	3	=	=	PUNCT
cana-5360	434	4	{	{	PUNCT
cana-5360	434	5	⟨	⟨	ADP
cana-5360	434	6	𝑠1	𝑠1	PROPN
cana-5360	434	7	0.4,0.7	0.4,0.7	PROPN
cana-5360	434	8	⟩	⟩	PROPN
cana-5360	434	9	,	,	PUNCT
cana-5360	434	10	⟨	⟨	VERB
cana-5360	434	11	𝑠2	𝑠2	PROPN
cana-5360	434	12	0.5,0.7	0.5,0.7	PROPN
cana-5360	434	13	⟩	⟩	NOUN
cana-5360	434	14	,	,	PUNCT
cana-5360	434	15	⟨	⟨	VERB
cana-5360	434	16	𝑠3	𝑠3	PROPN
cana-5360	434	17	0.4,0.6	0.4,0.6	PROPN
cana-5360	434	18	⟩	⟩	NOUN
cana-5360	434	19	,	,	PUNCT
cana-5360	434	20	⟨	⟨	VERB
cana-5360	434	21	𝑠4	𝑠4	PROPN
cana-5360	434	22	0.3,0.7	0.3,0.7	PROPN
cana-5360	434	23	⟩	⟩	PROPN
cana-5360	434	24	}	}	PUNCT
cana-5360	434	25	and	and	CCONJ
cana-5360	434	26	𝐴2	𝐴2	PROPN
cana-5360	434	27	=	=	PUNCT
cana-5360	434	28	{	{	PUNCT
cana-5360	434	29	⟨	⟨	NOUN
cana-5360	434	30	𝑡1	𝑡1	NOUN
cana-5360	434	31	0.4,0.8	0.4,0.8	NUM
cana-5360	434	32	⟩	⟩	NOUN
cana-5360	434	33	,	,	PUNCT
cana-5360	434	34	⟨	⟨	VERB
cana-5360	434	35	𝑡2	𝑡2	PROPN
cana-5360	434	36	0.5,0.4	0.5,0.4	PROPN
cana-5360	435	1	⟩	⟩	NOUN
cana-5360	435	2	,	,	PUNCT
cana-5360	435	3	⟨	⟨	VERB
cana-5360	435	4	𝑡3	𝑡3	PROPN
cana-5360	435	5	0.6,0.6	0.6,0.6	PROPN
cana-5360	435	6	⟩	⟩	NOUN
cana-5360	435	7	,	,	PUNCT
cana-5360	435	8	⟨	⟨	VERB
cana-5360	435	9	𝑡4	𝑡4	PROPN
cana-5360	435	10	0.7,0.6	0.7,0.6	NOUN
cana-5360	435	11	⟩	⟩	NOUN
cana-5360	435	12	}	}	PUNCT
cana-5360	435	13	be	be	VERB
cana-5360	435	14	a	a	DET
cana-5360	435	15	pythagorean	pythagorean	ADJ
cana-5360	435	16	fuzzy	fuzzy	ADJ
cana-5360	435	17	subsets	subset	NOUN
cana-5360	435	18	of	of	ADP
cana-5360	435	19	𝑈1	𝑈1	NOUN
cana-5360	435	20	and	and	CCONJ
cana-5360	435	21	𝑈2	𝑈2	NOUN
cana-5360	435	22	respectively	respectively	ADV
cana-5360	435	23	.	.	PUNCT
cana-5360	436	1	𝒫ℱ𝔑(𝐴1	𝒫ℱ𝔑(𝐴1	NUM
cana-5360	436	2	)	)	PUNCT
cana-5360	436	3	=	=	PRON
cana-5360	436	4	{	{	PUNCT
cana-5360	436	5	⟨	⟨	VERB
cana-5360	436	6	𝑠1,𝑠3	𝑠1,𝑠3	PROPN
cana-5360	436	7	0.4,0.7	0.4,0.7	PROPN
cana-5360	436	8	⟩	⟩	NOUN
cana-5360	436	9	,	,	PUNCT
cana-5360	436	10	⟨	⟨	VERB
cana-5360	436	11	𝑠2,𝑠4	𝑠2,𝑠4	PROPN
cana-5360	436	12	0.3,0.7	0.3,0.7	PROPN
cana-5360	436	13	⟩	⟩	PROPN
cana-5360	436	14	}	}	PUNCT
cana-5360	436	15	𝒫ℱ𝔑(𝐴1	𝒫ℱ𝔑(𝐴1	NUM
cana-5360	436	16	)	)	PUNCT
cana-5360	436	17	=	=	PRON
cana-5360	436	18	{	{	PUNCT
cana-5360	436	19	⟨	⟨	VERB
cana-5360	436	20	𝑠1,𝑠3	𝑠1,𝑠3	PROPN
cana-5360	436	21	0.4,0.6	0.4,0.6	PROPN
cana-5360	436	22	⟩	⟩	NOUN
cana-5360	436	23	,	,	PUNCT
cana-5360	436	24	⟨	⟨	VERB
cana-5360	436	25	𝑠2,𝑠4	𝑠2,𝑠4	PROPN
cana-5360	436	26	0.5,0.7	0.5,0.7	PROPN
cana-5360	436	27	⟩	⟩	NOUN
cana-5360	436	28	}	}	PUNCT
cana-5360	436	29	𝐵𝒫ℱ𝔑(𝐴1	𝐵𝒫ℱ𝔑(𝐴1	NOUN
cana-5360	436	30	)	)	PUNCT
cana-5360	437	1	=	=	PRON
cana-5360	437	2	{	{	PUNCT
cana-5360	437	3	⟨	⟨	VERB
cana-5360	437	4	𝑠1,𝑠3	𝑠1,𝑠3	PROPN
cana-5360	437	5	0.4,0.6	0.4,0.6	PROPN
cana-5360	437	6	⟩	⟩	NOUN
cana-5360	437	7	,	,	PUNCT
cana-5360	437	8	⟨	⟨	VERB
cana-5360	437	9	𝑠2,𝑠4	𝑠2,𝑠4	PROPN
cana-5360	437	10	0.5,0.7	0.5,0.7	PROPN
cana-5360	437	11	⟩	⟩	PROPN
cana-5360	437	12	}	}	PUNCT
cana-5360	437	13	𝒫ℱ𝔑(𝐴2	𝒫ℱ𝔑(𝐴2	PROPN
cana-5360	437	14	)	)	PUNCT
cana-5360	437	15	=	=	PRON
cana-5360	437	16	{	{	PUNCT
cana-5360	437	17	⟨	⟨	X
cana-5360	437	18	𝑡1,𝑡3	𝑡1,𝑡3	PROPN
cana-5360	437	19	0.4,0.8	0.4,0.8	NUM
cana-5360	437	20	⟩	⟩	NOUN
cana-5360	437	21	,	,	PUNCT
cana-5360	437	22	⟨	⟨	VERB
cana-5360	437	23	𝑡2,𝑡4	𝑡2,𝑡4	PROPN
cana-5360	437	24	0.5,0.6	0.5,0.6	PROPN
cana-5360	437	25	⟩	⟩	PROPN
cana-5360	437	26	}	}	PUNCT
cana-5360	437	27	𝒫ℱ𝔑(𝐴2	𝒫ℱ𝔑(𝐴2	PROPN
cana-5360	437	28	)	)	PUNCT
cana-5360	438	1	=	=	PRON
cana-5360	438	2	{	{	PUNCT
cana-5360	438	3	⟨	⟨	NOUN
cana-5360	438	4	𝑡1,𝑡3	𝑡1,𝑡3	PROPN
cana-5360	438	5	0.6,0.6	0.6,0.6	PROPN
cana-5360	438	6	⟩	⟩	NOUN
cana-5360	438	7	,	,	PUNCT
cana-5360	438	8	⟨	⟨	VERB
cana-5360	438	9	𝑡2,𝑡4	𝑡2,𝑡4	PROPN
cana-5360	438	10	0.7,0.4	0.7,0.4	NUM
cana-5360	438	11	⟩	⟩	NOUN
cana-5360	438	12	}	}	PUNCT
cana-5360	438	13	𝐵𝒫ℱ𝔑(𝐴2	𝐵𝒫ℱ𝔑(𝐴2	PROPN
cana-5360	438	14	)	)	PUNCT
cana-5360	438	15	=	=	PRON
cana-5360	438	16	{	{	PUNCT
cana-5360	438	17	⟨	⟨	NOUN
cana-5360	438	18	𝑡1,𝑡3	𝑡1,𝑡3	PROPN
cana-5360	438	19	0.6,0.6	0.6,0.6	PROPN
cana-5360	438	20	⟩	⟩	NOUN
cana-5360	438	21	,	,	PUNCT
cana-5360	438	22	⟨	⟨	VERB
cana-5360	438	23	𝑡2,𝑡4	𝑡2,𝑡4	PROPN
cana-5360	438	24	0.6,0.5	0.6,0.5	PROPN
cana-5360	438	25	⟩	⟩	NOUN
cana-5360	438	26	}	}	PUNCT
cana-5360	438	27	now	now	ADV
cana-5360	438	28	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	VERB
cana-5360	438	29	)	)	PUNCT
cana-5360	438	30	=	=	PRON
cana-5360	438	31	{	{	PUNCT
cana-5360	438	32	0𝒫	0𝒫	NOUN
cana-5360	438	33	,	,	PUNCT
cana-5360	438	34	1𝒫	1𝒫	INTJ
cana-5360	438	35	,	,	PUNCT
cana-5360	438	36	𝒫ℱ𝔑(𝐴1	𝒫ℱ𝔑(𝐴1	NUM
cana-5360	438	37	)	)	PUNCT
cana-5360	438	38	,	,	PUNCT
cana-5360	438	39	𝒫ℱ𝔑(𝐴1	𝒫ℱ𝔑(𝐴1	NUM
cana-5360	438	40	)	)	PUNCT
cana-5360	438	41	,	,	PUNCT
cana-5360	438	42	𝐵𝒫ℱ𝔑(𝐴1	𝐵𝒫ℱ𝔑(𝐴1	NOUN
cana-5360	438	43	)	)	PUNCT
cana-5360	438	44	}	}	PUNCT
cana-5360	438	45	,	,	PUNCT
cana-5360	438	46	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	X
cana-5360	438	47	)	)	PUNCT
cana-5360	438	48	=	=	PRON
cana-5360	438	49	{	{	PUNCT
cana-5360	438	50	0𝒫	0𝒫	NOUN
cana-5360	438	51	,	,	PUNCT
cana-5360	438	52	1𝒫	1𝒫	INTJ
cana-5360	438	53	,	,	PUNCT
cana-5360	438	54	𝒫ℱ𝔑(𝐴2	𝒫ℱ𝔑(𝐴2	PROPN
cana-5360	438	55	)	)	PUNCT
cana-5360	438	56	,	,	PUNCT
cana-5360	438	57	𝒫ℱ𝔑(𝐴2	𝒫ℱ𝔑(𝐴2	NUM
cana-5360	438	58	)	)	PUNCT
cana-5360	438	59	,	,	PUNCT
cana-5360	438	60	𝐵𝒫ℱ𝔑(𝐴2	𝐵𝒫ℱ𝔑(𝐴2	PROPN
cana-5360	438	61	)	)	PUNCT
cana-5360	438	62	}	}	PUNCT
cana-5360	438	63	.	.	PUNCT
cana-5360	439	1	let	let	VERB
cana-5360	439	2	ℎ𝑃	ℎ𝑃	NOUN
cana-5360	439	3	:	:	PUNCT
cana-5360	439	4	(	(	PUNCT
cana-5360	439	5	𝑈1	𝑈1	NOUN
cana-5360	439	6	,	,	PUNCT
cana-5360	439	7	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	439	8	)	)	PUNCT
cana-5360	439	9	)	)	PUNCT
cana-5360	439	10	→	→	SYM
cana-5360	439	11	(	(	PUNCT
cana-5360	439	12	𝑈2	𝑈2	NOUN
cana-5360	439	13	,	,	PUNCT
cana-5360	439	14	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	439	15	)	)	PUNCT
cana-5360	439	16	)	)	PUNCT
cana-5360	439	17	be	be	AUX
cana-5360	439	18	an	an	DET
cana-5360	439	19	identity	identity	NOUN
cana-5360	439	20	function	function	NOUN
cana-5360	439	21	,	,	PUNCT
cana-5360	439	22	then	then	ADV
cana-5360	439	23	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	439	24	is	be	AUX
cana-5360	439	25	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	PROPN
cana-5360	439	26	but	but	CCONJ
cana-5360	439	27	not	not	PART
cana-5360	439	28	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	PROPN
cana-5360	439	29	.	.	PUNCT
cana-5360	440	1	since	since	SCONJ
cana-5360	440	2	,	,	PUNCT
cana-5360	440	3	(	(	PUNCT
cana-5360	440	4	𝒫ℱ𝔑(𝐴2))𝑐	𝒫ℱ𝔑(𝐴2))𝑐	PROPN
cana-5360	440	5	is	be	AUX
cana-5360	440	6	a	a	DET
cana-5360	440	7	𝒫ℱ𝒩𝛿𝒫𝑜	𝒫ℱ𝒩𝛿𝒫𝑜	NOUN
cana-5360	440	8	set	set	VERB
cana-5360	440	9	in	in	ADP
cana-5360	440	10	𝑈2	𝑈2	PROPN
cana-5360	440	11	but	but	CCONJ
cana-5360	440	12	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	440	13	−1((𝒫ℱ𝔑(𝐴2))𝑐	−1((𝒫ℱ𝔑(𝐴2))𝑐	NOUN
cana-5360	440	14	)	)	PUNCT
cana-5360	440	15	=	=	SYM
cana-5360	440	16	(	(	PUNCT
cana-5360	440	17	𝒫ℱ𝔑(𝐴2))𝑐	𝒫ℱ𝔑(𝐴2))𝑐	PROPN
cana-5360	440	18	is	be	AUX
cana-5360	440	19	not	not	PART
cana-5360	440	20	𝒫ℱ𝒩𝛿𝒫𝑐	𝒫ℱ𝒩𝛿𝒫𝑐	PROPN
cana-5360	440	21	set	set	VERB
cana-5360	440	22	in	in	ADP
cana-5360	440	23	𝑈1	𝑈1	PROPN
cana-5360	440	24	.	.	PUNCT
cana-5360	441	1	example	example	NOUN
cana-5360	441	2	4.3	4.3	NUM
cana-5360	441	3	let	let	VERB
cana-5360	441	4	𝑈1	𝑈1	NOUN
cana-5360	441	5	=	=	SYM
cana-5360	441	6	{	{	PUNCT
cana-5360	441	7	𝑠1	𝑠1	PROPN
cana-5360	441	8	,	,	PUNCT
cana-5360	441	9	𝑠2	𝑠2	NOUN
cana-5360	441	10	,	,	PUNCT
cana-5360	441	11	𝑠3	𝑠3	NOUN
cana-5360	441	12	,	,	PUNCT
cana-5360	441	13	𝑠4	𝑠4	PROPN
cana-5360	441	14	}	}	PUNCT
cana-5360	441	15	,	,	PUNCT
cana-5360	441	16	𝑈2	𝑈2	PROPN
cana-5360	441	17	=	=	PUNCT
cana-5360	441	18	{	{	PUNCT
cana-5360	441	19	𝑡1	𝑡1	PROPN
cana-5360	441	20	,	,	PUNCT
cana-5360	441	21	𝑡2	𝑡2	PROPN
cana-5360	441	22	,	,	PUNCT
cana-5360	441	23	𝑡3	𝑡3	PROPN
cana-5360	441	24	,	,	PUNCT
cana-5360	441	25	𝑡4	𝑡4	PROPN
cana-5360	441	26	}	}	PUNCT
cana-5360	441	27	are	be	AUX
cana-5360	441	28	the	the	DET
cana-5360	441	29	universe	universe	NOUN
cana-5360	441	30	sets	set	NOUN
cana-5360	441	31	and	and	CCONJ
cana-5360	441	32	the	the	DET
cana-5360	441	33	equivalence	equivalence	NOUN
cana-5360	441	34	relations	relation	NOUN
cana-5360	441	35	are	be	AUX
cana-5360	441	36	𝑈1/𝑅	𝑈1/𝑅	X
cana-5360	441	37	=	=	SYM
cana-5360	441	38	{	{	PUNCT
cana-5360	441	39	{	{	PUNCT
cana-5360	441	40	𝑠1	𝑠1	PROPN
cana-5360	441	41	,	,	PUNCT
cana-5360	441	42	𝑠4	𝑠4	PROPN
cana-5360	441	43	}	}	PUNCT
cana-5360	441	44	,	,	PUNCT
cana-5360	441	45	{	{	PUNCT
cana-5360	441	46	𝑠2	𝑠2	NOUN
cana-5360	441	47	}	}	PUNCT
cana-5360	441	48	,	,	PUNCT
cana-5360	441	49	{	{	PUNCT
cana-5360	441	50	𝑠3	𝑠3	NOUN
cana-5360	441	51	}	}	PUNCT
cana-5360	441	52	}	}	PUNCT
cana-5360	441	53	and	and	CCONJ
cana-5360	441	54	𝑈2/𝑅	𝑈2/𝑅	PUNCT
cana-5360	441	55	=	=	PRON
cana-5360	441	56	{	{	PUNCT
cana-5360	441	57	{	{	PUNCT
cana-5360	441	58	𝑡1	𝑡1	NOUN
cana-5360	441	59	,	,	PUNCT
cana-5360	441	60	𝑡4	𝑡4	PROPN
cana-5360	441	61	}	}	PUNCT
cana-5360	441	62	,	,	PUNCT
cana-5360	441	63	{	{	PUNCT
cana-5360	441	64	𝑡2	𝑡2	NOUN
cana-5360	441	65	}	}	PUNCT
cana-5360	441	66	,	,	PUNCT
cana-5360	441	67	{	{	PUNCT
cana-5360	441	68	𝑡3	𝑡3	PROPN
cana-5360	441	69	}	}	PUNCT
cana-5360	441	70	}	}	PUNCT
cana-5360	441	71	.	.	PUNCT
cana-5360	442	1	let	let	VERB
cana-5360	442	2	𝐴1	𝐴1	PROPN
cana-5360	442	3	=	=	PUNCT
cana-5360	442	4	{	{	PUNCT
cana-5360	442	5	⟨	⟨	ADP
cana-5360	442	6	𝑠1	𝑠1	PROPN
cana-5360	442	7	0.4,0.3	0.4,0.3	PROPN
cana-5360	442	8	⟩	⟩	NOUN
cana-5360	442	9	,	,	PUNCT
cana-5360	442	10	⟨	⟨	VERB
cana-5360	442	11	𝑠2	𝑠2	NOUN
cana-5360	442	12	0.4,0.2	0.4,0.2	PROPN
cana-5360	442	13	⟩	⟩	NOUN
cana-5360	442	14	,	,	PUNCT
cana-5360	442	15	⟨	⟨	VERB
cana-5360	442	16	𝑠3	𝑠3	PROPN
cana-5360	442	17	0.5,0.5	0.5,0.5	PROPN
cana-5360	443	1	⟩	⟩	NOUN
cana-5360	443	2	,	,	PUNCT
cana-5360	443	3	⟨	⟨	VERB
cana-5360	443	4	𝑠4	𝑠4	PROPN
cana-5360	443	5	0.5,0.2	0.5,0.2	PROPN
cana-5360	443	6	⟩	⟩	PROPN
cana-5360	443	7	}	}	PUNCT
cana-5360	443	8	and	and	CCONJ
cana-5360	443	9	𝐴2	𝐴2	PROPN
cana-5360	443	10	=	=	PUNCT
cana-5360	443	11	{	{	PUNCT
cana-5360	443	12	⟨	⟨	VERB
cana-5360	443	13	𝑡1	𝑡1	PROPN
cana-5360	443	14	0.3,0.1	0.3,0.1	PROPN
cana-5360	443	15	⟩	⟩	NOUN
cana-5360	443	16	,	,	PUNCT
cana-5360	443	17	⟨	⟨	VERB
cana-5360	443	18	𝑡2	𝑡2	PROPN
cana-5360	443	19	0.1,0.5	0.1,0.5	PROPN
cana-5360	443	20	⟩	⟩	NOUN
cana-5360	443	21	,	,	PUNCT
cana-5360	443	22	⟨	⟨	VERB
cana-5360	443	23	𝑡3	𝑡3	PROPN
cana-5360	443	24	0.2,0.45	0.2,0.45	NUM
cana-5360	443	25	⟩	⟩	NOUN
cana-5360	443	26	,	,	PUNCT
cana-5360	443	27	⟨	⟨	VERB
cana-5360	443	28	𝑡4	𝑡4	PROPN
cana-5360	443	29	0.4,0.25	0.4,0.25	NUM
cana-5360	443	30	⟩	⟩	NOUN
cana-5360	443	31	}	}	PUNCT
cana-5360	443	32	be	be	AUX
cana-5360	443	33	a	a	DET
cana-5360	443	34	pythagorean	pythagorean	ADJ
cana-5360	443	35	fuzzy	fuzzy	ADJ
cana-5360	443	36	subsets	subset	NOUN
cana-5360	443	37	of	of	ADP
cana-5360	443	38	𝑈1	𝑈1	NOUN
cana-5360	443	39	and	and	CCONJ
cana-5360	443	40	𝑈2	𝑈2	NOUN
cana-5360	443	41	respectively	respectively	ADV
cana-5360	443	42	.	.	PUNCT
cana-5360	444	1	communications	communication	NOUN
cana-5360	444	2	on	on	ADP
cana-5360	444	3	applied	apply	VERB
cana-5360	444	4	nonlinear	nonlinear	ADJ
cana-5360	444	5	analysis	analysis	NOUN
cana-5360	444	6	issn	issn	NOUN
cana-5360	444	7	:	:	PUNCT
cana-5360	444	8	1074	1074	NUM
cana-5360	444	9	-	-	PUNCT
cana-5360	444	10	133x	133x	NUM
cana-5360	444	11	vol	vol	VERB
cana-5360	444	12	32	32	NUM
cana-5360	444	13	no	no	NOUN
cana-5360	444	14	.	.	PUNCT
cana-5360	445	1	10s	10	NOUN
cana-5360	445	2	(	(	PUNCT
cana-5360	445	3	2025	2025	NUM
cana-5360	445	4	)	)	PUNCT
cana-5360	445	5	1939	1939	NUM
cana-5360	445	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5360	445	7	𝒫ℱ𝔑(𝐴1	𝒫ℱ𝔑(𝐴1	NUM
cana-5360	445	8	)	)	PUNCT
cana-5360	445	9	=	=	NOUN
cana-5360	445	10	{	{	PUNCT
cana-5360	445	11	⟨	⟨	ADP
cana-5360	445	12	𝑠1,𝑠4	𝑠1,𝑠4	PROPN
cana-5360	445	13	0.4,0.3	0.4,0.3	PROPN
cana-5360	445	14	⟩	⟩	NOUN
cana-5360	445	15	,	,	PUNCT
cana-5360	445	16	⟨	⟨	VERB
cana-5360	445	17	𝑠2	𝑠2	NOUN
cana-5360	445	18	0.4,0.2	0.4,0.2	PROPN
cana-5360	445	19	⟩	⟩	NOUN
cana-5360	445	20	,	,	PUNCT
cana-5360	445	21	⟨	⟨	VERB
cana-5360	445	22	𝑠3	𝑠3	PROPN
cana-5360	445	23	0.5,0.3	0.5,0.3	PROPN
cana-5360	445	24	⟩	⟩	NOUN
cana-5360	445	25	}	}	PUNCT
cana-5360	445	26	,	,	PUNCT
cana-5360	445	27	𝒫ℱ𝔑(𝐴1	𝒫ℱ𝔑(𝐴1	NUM
cana-5360	445	28	)	)	PUNCT
cana-5360	446	1	=	=	PRON
cana-5360	446	2	{	{	PUNCT
cana-5360	446	3	⟨	⟨	ADP
cana-5360	446	4	𝑠1,𝑠4	𝑠1,𝑠4	PROPN
cana-5360	446	5	0.5,0.2	0.5,0.2	PROPN
cana-5360	446	6	⟩	⟩	NOUN
cana-5360	446	7	,	,	PUNCT
cana-5360	446	8	⟨	⟨	VERB
cana-5360	446	9	𝑠2	𝑠2	NOUN
cana-5360	446	10	0.4,0.2	0.4,0.2	PROPN
cana-5360	446	11	⟩	⟩	NOUN
cana-5360	446	12	,	,	PUNCT
cana-5360	446	13	⟨	⟨	VERB
cana-5360	446	14	𝑠3	𝑠3	PROPN
cana-5360	446	15	0.5,0.3	0.5,0.3	PROPN
cana-5360	446	16	⟩	⟩	NOUN
cana-5360	446	17	}	}	PUNCT
cana-5360	446	18	,	,	PUNCT
cana-5360	446	19	𝐵𝒫ℱ𝔑(𝐴1	𝐵𝒫ℱ𝔑(𝐴1	NOUN
cana-5360	446	20	)	)	PUNCT
cana-5360	446	21	=	=	PRON
cana-5360	446	22	{	{	PUNCT
cana-5360	446	23	⟨	⟨	ADP
cana-5360	446	24	𝑠1,𝑠4	𝑠1,𝑠4	PROPN
cana-5360	446	25	0.3,0.4	0.3,0.4	PROPN
cana-5360	446	26	⟩	⟩	NOUN
cana-5360	446	27	,	,	PUNCT
cana-5360	446	28	⟨	⟨	VERB
cana-5360	446	29	𝑠2	𝑠2	NOUN
cana-5360	446	30	0.2,0.4	0.2,0.4	PROPN
cana-5360	446	31	⟩	⟩	PROPN
cana-5360	446	32	,	,	PUNCT
cana-5360	446	33	⟨	⟨	VERB
cana-5360	446	34	𝑠3	𝑠3	PROPN
cana-5360	446	35	0.3,0.5	0.3,0.5	NUM
cana-5360	446	36	⟩	⟩	NOUN
cana-5360	446	37	}	}	PUNCT
cana-5360	446	38	,	,	PUNCT
cana-5360	446	39	𝒫ℱ𝔑(𝐴2	𝒫ℱ𝔑(𝐴2	NUM
cana-5360	446	40	)	)	PUNCT
cana-5360	447	1	=	=	PRON
cana-5360	447	2	{	{	PUNCT
cana-5360	447	3	⟨	⟨	PROPN
cana-5360	447	4	𝑡1,𝑡4	𝑡1,𝑡4	PROPN
cana-5360	447	5	0.3,0.25	0.3,0.25	NUM
cana-5360	447	6	⟩	⟩	NOUN
cana-5360	447	7	,	,	PUNCT
cana-5360	447	8	⟨	⟨	VERB
cana-5360	447	9	𝑡2	𝑡2	PROPN
cana-5360	447	10	0.1,0.5	0.1,0.5	PROPN
cana-5360	447	11	⟩	⟩	NOUN
cana-5360	447	12	,	,	PUNCT
cana-5360	447	13	⟨	⟨	VERB
cana-5360	447	14	𝑡3	𝑡3	PROPN
cana-5360	447	15	0.2,0.45	0.2,0.45	NUM
cana-5360	447	16	⟩	⟩	NOUN
cana-5360	447	17	}	}	PUNCT
cana-5360	447	18	,	,	PUNCT
cana-5360	447	19	𝒫ℱ𝔑(𝐴2	𝒫ℱ𝔑(𝐴2	NUM
cana-5360	447	20	)	)	PUNCT
cana-5360	448	1	=	=	PRON
cana-5360	448	2	{	{	PUNCT
cana-5360	448	3	⟨	⟨	PROPN
cana-5360	448	4	𝑡1,𝑡4	𝑡1,𝑡4	PROPN
cana-5360	448	5	0.4,0.1	0.4,0.1	PROPN
cana-5360	448	6	⟩	⟩	NOUN
cana-5360	448	7	,	,	PUNCT
cana-5360	448	8	⟨	⟨	VERB
cana-5360	448	9	𝑡2	𝑡2	PROPN
cana-5360	448	10	0.1,0.5	0.1,0.5	PROPN
cana-5360	448	11	⟩	⟩	NOUN
cana-5360	448	12	,	,	PUNCT
cana-5360	448	13	⟨	⟨	VERB
cana-5360	448	14	𝑡3	𝑡3	PROPN
cana-5360	448	15	0.2,0.45	0.2,0.45	NUM
cana-5360	448	16	⟩	⟩	NOUN
cana-5360	448	17	}	}	PUNCT
cana-5360	448	18	,	,	PUNCT
cana-5360	448	19	𝐵𝒫ℱ𝔑(𝐴2	𝐵𝒫ℱ𝔑(𝐴2	PROPN
cana-5360	448	20	)	)	PUNCT
cana-5360	448	21	=	=	PRON
cana-5360	448	22	{	{	PUNCT
cana-5360	448	23	⟨	⟨	VERB
cana-5360	448	24	𝑡1,𝑡4	𝑡1,𝑡4	PROPN
cana-5360	448	25	0.25,0.3	0.25,0.3	NOUN
cana-5360	448	26	⟩	⟩	NOUN
cana-5360	448	27	,	,	PUNCT
cana-5360	448	28	⟨	⟨	VERB
cana-5360	448	29	𝑡2	𝑡2	PROPN
cana-5360	448	30	0.1,0.5	0.1,0.5	PROPN
cana-5360	448	31	⟩	⟩	NOUN
cana-5360	448	32	,	,	PUNCT
cana-5360	448	33	⟨	⟨	VERB
cana-5360	448	34	𝑡3	𝑡3	PROPN
cana-5360	448	35	0.2,0.45	0.2,0.45	NUM
cana-5360	448	36	⟩	⟩	NOUN
cana-5360	448	37	}	}	PUNCT
cana-5360	448	38	.	.	PUNCT
cana-5360	449	1	here	here	ADV
cana-5360	449	2	𝜏𝑝(𝐴1	𝜏𝑝(𝐴1	ADP
cana-5360	449	3	)	)	PUNCT
cana-5360	449	4	=	=	SYM
cana-5360	449	5	{	{	PUNCT
cana-5360	449	6	0𝑃	0𝑃	PROPN
cana-5360	449	7	,	,	PUNCT
cana-5360	449	8	1𝑃	1𝑃	NOUN
cana-5360	449	9	,	,	PUNCT
cana-5360	449	10	𝒫ℱ𝔑(𝐴1	𝒫ℱ𝔑(𝐴1	NUM
cana-5360	449	11	)	)	PUNCT
cana-5360	449	12	,	,	PUNCT
cana-5360	449	13	𝒫ℱ𝔑(𝐴1	𝒫ℱ𝔑(𝐴1	NUM
cana-5360	449	14	)	)	PUNCT
cana-5360	449	15	,	,	PUNCT
cana-5360	449	16	𝐵𝒫ℱ𝔑(𝐴1	𝐵𝒫ℱ𝔑(𝐴1	NOUN
cana-5360	449	17	)	)	PUNCT
cana-5360	449	18	}	}	PUNCT
cana-5360	449	19	and	and	CCONJ
cana-5360	449	20	𝜏𝑝(𝐴2	𝜏𝑝(𝐴2	NUM
cana-5360	449	21	)	)	PUNCT
cana-5360	449	22	=	=	PRON
cana-5360	449	23	{	{	PUNCT
cana-5360	449	24	0𝑃	0𝑃	PROPN
cana-5360	449	25	,	,	PUNCT
cana-5360	449	26	1𝑃	1𝑃	PROPN
cana-5360	449	27	,	,	PUNCT
cana-5360	449	28	𝒫ℱ𝔑(𝐴2	𝒫ℱ𝔑(𝐴2	PROPN
cana-5360	449	29	)	)	PUNCT
cana-5360	449	30	,	,	PUNCT
cana-5360	449	31	𝒫ℱ𝔑(𝐴2	𝒫ℱ𝔑(𝐴2	NUM
cana-5360	449	32	)	)	PUNCT
cana-5360	449	33	,	,	PUNCT
cana-5360	449	34	𝐵𝒫ℱ𝔑(𝐴2	𝐵𝒫ℱ𝔑(𝐴2	PROPN
cana-5360	449	35	)	)	PUNCT
cana-5360	449	36	}	}	PUNCT
cana-5360	449	37	are	be	AUX
cana-5360	449	38	the	the	DET
cana-5360	449	39	𝒫ℱ𝒩𝑡𝑠′𝑠	𝒫ℱ𝒩𝑡𝑠′𝑠	PROPN
cana-5360	449	40	on	on	ADP
cana-5360	449	41	𝑈1	𝑈1	NOUN
cana-5360	449	42	and	and	CCONJ
cana-5360	449	43	𝑈2	𝑈2	NOUN
cana-5360	449	44	respectively	respectively	ADV
cana-5360	449	45	.	.	PUNCT
cana-5360	450	1	let	let	VERB
cana-5360	450	2	ℎ𝑃	ℎ𝑃	NOUN
cana-5360	450	3	:	:	PUNCT
cana-5360	450	4	(	(	PUNCT
cana-5360	450	5	𝑈1	𝑈1	NOUN
cana-5360	450	6	,	,	PUNCT
cana-5360	450	7	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	450	8	)	)	PUNCT
cana-5360	450	9	)	)	PUNCT
cana-5360	450	10	→	→	SYM
cana-5360	450	11	(	(	PUNCT
cana-5360	450	12	𝑈2	𝑈2	NOUN
cana-5360	450	13	,	,	PUNCT
cana-5360	450	14	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	450	15	)	)	PUNCT
cana-5360	450	16	)	)	PUNCT
cana-5360	450	17	be	be	AUX
cana-5360	450	18	an	an	DET
cana-5360	450	19	identity	identity	NOUN
cana-5360	450	20	function	function	NOUN
cana-5360	450	21	,	,	PUNCT
cana-5360	450	22	then	then	ADV
cana-5360	450	23	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	450	24	is	be	AUX
cana-5360	450	25	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠	PRON
cana-5360	450	26	but	but	CCONJ
cana-5360	450	27	not	not	PART
cana-5360	450	28	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐼𝑟𝑟	PROPN
cana-5360	450	29	,	,	PUNCT
cana-5360	450	30	because	because	SCONJ
cana-5360	450	31	the	the	DET
cana-5360	450	32	set	set	NOUN
cana-5360	450	33	𝐵	𝐵	NOUN
cana-5360	450	34	=	=	PUNCT
cana-5360	450	35	{	{	PUNCT
cana-5360	450	36	⟨	⟨	PROPN
cana-5360	450	37	𝑡1,𝑡4	𝑡1,𝑡4	PROPN
cana-5360	450	38	0.4,0.1	0.4,0.1	PROPN
cana-5360	450	39	⟩	⟩	NOUN
cana-5360	450	40	,	,	PUNCT
cana-5360	450	41	⟨	⟨	VERB
cana-5360	450	42	𝑡2	𝑡2	PROPN
cana-5360	450	43	0.4,0.2	0.4,0.2	PROPN
cana-5360	450	44	⟩	⟩	NOUN
cana-5360	450	45	,	,	PUNCT
cana-5360	450	46	⟨	⟨	VERB
cana-5360	450	47	𝑡3	𝑡3	PROPN
cana-5360	450	48	0.2,0.3	0.2,0.3	PROPN
cana-5360	450	49	⟩	⟩	NOUN
cana-5360	450	50	}	}	PUNCT
cana-5360	450	51	is	be	AUX
cana-5360	450	52	𝒫ℱ𝒩𝛿𝛽𝑜𝑠	𝒫ℱ𝒩𝛿𝛽𝑜𝑠	PROPN
cana-5360	450	53	in	in	ADP
cana-5360	450	54	𝑈2	𝑈2	PROPN
cana-5360	451	1	but	but	CCONJ
cana-5360	451	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	451	3	−1(𝐵	−1(𝐵	NOUN
cana-5360	451	4	)	)	PUNCT
cana-5360	452	1	=	=	SYM
cana-5360	452	2	𝐵	𝐵	NOUN
cana-5360	452	3	is	be	AUX
cana-5360	452	4	not	not	PART
cana-5360	452	5	𝒫ℱ𝒩𝛿𝛽𝑐𝑠	𝒫ℱ𝒩𝛿𝛽𝑐𝑠	PROPN
cana-5360	452	6	in	in	ADP
cana-5360	452	7	𝑈1	𝑈1	NOUN
cana-5360	452	8	.	.	PUNCT
cana-5360	453	1	definition	definition	NOUN
cana-5360	453	2	4.2	4.2	NUM
cana-5360	453	3	a	a	DET
cana-5360	453	4	𝒫ℱ𝒩𝑡𝑠	𝒫ℱ𝒩𝑡𝑠	PROPN
cana-5360	453	5	(	(	PUNCT
cana-5360	453	6	𝑈1	𝑈1	NOUN
cana-5360	453	7	,	,	PUNCT
cana-5360	453	8	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	453	9	)	)	PUNCT
cana-5360	453	10	)	)	PUNCT
cana-5360	453	11	is	be	AUX
cana-5360	453	12	known	know	VERB
cana-5360	453	13	as	as	ADP
cana-5360	453	14	a	a	DET
cana-5360	453	15	pythagorean	pythagorean	ADJ
cana-5360	453	16	fuzzy	fuzzy	ADJ
cana-5360	453	17	nano	nano	NOUN
cana-5360	453	18	𝛿𝒮𝑈1	𝛿𝒮𝑈1	NOUN
cana-5360	453	19	2	2	NUM
cana-5360	453	20	(	(	PUNCT
cana-5360	453	21	resp	resp	NOUN
cana-5360	453	22	.	.	PUNCT
cana-5360	454	1	𝛿𝒫𝑈1	𝛿𝒫𝑈1	NOUN
cana-5360	454	2	2	2	NUM
cana-5360	454	3	,	,	PUNCT
cana-5360	454	4	𝛿𝛼𝑈1	𝛿𝛼𝑈1	NOUN
cana-5360	454	5	2	2	NUM
cana-5360	454	6	and	and	CCONJ
cana-5360	454	7	𝛿𝛽𝑈1	𝛿𝛽𝑈1	NOUN
cana-5360	454	8	2	2	NUM
cana-5360	454	9	)	)	PUNCT
cana-5360	454	10	(	(	PUNCT
cana-5360	454	11	in	in	ADP
cana-5360	454	12	short	short	ADJ
cana-5360	454	13	,	,	PUNCT
cana-5360	454	14	𝒫ℱ𝒩𝛿𝒮𝑈1	𝒫ℱ𝒩𝛿𝒮𝑈1	NOUN
cana-5360	454	15	2	2	NUM
cana-5360	454	16	(	(	PUNCT
cana-5360	454	17	resp	resp	NOUN
cana-5360	454	18	.	.	PUNCT
cana-5360	455	1	𝒫ℱ𝒩𝛿𝒫𝑈1	𝒫ℱ𝒩𝛿𝒫𝑈1	NOUN
cana-5360	455	2	2	2	NUM
cana-5360	455	3	,	,	PUNCT
cana-5360	455	4	𝒫ℱ𝒩𝛿𝛼𝑈1	𝒫ℱ𝒩𝛿𝛼𝑈1	X
cana-5360	455	5	2	2	NUM
cana-5360	455	6	and	and	CCONJ
cana-5360	455	7	𝒫ℱ𝒩𝛿𝛽𝑈1	𝒫ℱ𝒩𝛿𝛽𝑈1	NUM
cana-5360	455	8	2	2	NUM
cana-5360	455	9	)	)	PUNCT
cana-5360	455	10	)	)	PUNCT
cana-5360	455	11	-space	-space	NOUN
cana-5360	455	12	,	,	PUNCT
cana-5360	455	13	if	if	SCONJ
cana-5360	455	14	each	each	DET
cana-5360	455	15	𝒫ℱ𝒩𝛿𝒮𝑜𝑠	𝒫ℱ𝒩𝛿𝒮𝑜𝑠	PROPN
cana-5360	455	16	(	(	PUNCT
cana-5360	455	17	resp	resp	NOUN
cana-5360	455	18	.	.	PUNCT
cana-5360	456	1	𝒫ℱ𝒩𝛿𝒫𝑜𝑠	𝒫ℱ𝒩𝛿𝒫𝑜𝑠	X
cana-5360	456	2	,	,	PUNCT
cana-5360	456	3	𝒫ℱ𝒩𝛿𝛼𝑜𝑠	𝒫ℱ𝒩𝛿𝛼𝑜𝑠	PROPN
cana-5360	456	4	and	and	CCONJ
cana-5360	456	5	𝒫ℱ𝒩𝛿𝛽𝑜𝑠	𝒫ℱ𝒩𝛿𝛽𝑜𝑠	PROPN
cana-5360	456	6	)	)	PUNCT
cana-5360	456	7	in	in	ADP
cana-5360	456	8	𝑋	𝑋	PROPN
cana-5360	456	9	is	be	AUX
cana-5360	456	10	𝒫ℱ𝒩𝑜𝑠	𝒫ℱ𝒩𝑜𝑠	ADJ
cana-5360	456	11	in	in	ADP
cana-5360	456	12	𝑈1	𝑈1	PROPN
cana-5360	456	13	.	.	PUNCT
cana-5360	457	1	theorem	theorem	VERB
cana-5360	457	2	4.2	4.2	NUM
cana-5360	457	3	let	let	VERB
cana-5360	457	4	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	457	5	:	:	PUNCT
cana-5360	457	6	(	(	PUNCT
cana-5360	457	7	𝑈1	𝑈1	NOUN
cana-5360	457	8	,	,	PUNCT
cana-5360	457	9	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	457	10	)	)	PUNCT
cana-5360	457	11	)	)	PUNCT
cana-5360	458	1	→	→	SYM
cana-5360	458	2	(	(	PUNCT
cana-5360	458	3	𝑈2	𝑈2	NOUN
cana-5360	458	4	,	,	PUNCT
cana-5360	458	5	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	458	6	)	)	PUNCT
cana-5360	458	7	)	)	PUNCT
cana-5360	458	8	be	be	AUX
cana-5360	458	9	a	a	DET
cana-5360	458	10	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	PROPN
cana-5360	458	11	(	(	PUNCT
cana-5360	458	12	resp	resp	NOUN
cana-5360	458	13	.	.	PUNCT
cana-5360	459	1	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	ADJ
cana-5360	459	2	,	,	PUNCT
cana-5360	459	3	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐼𝑟𝑟	PROPN
cana-5360	459	4	and	and	CCONJ
cana-5360	459	5	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐼𝑟𝑟	PROPN
cana-5360	459	6	)	)	PUNCT
cana-5360	459	7	map	map	NOUN
cana-5360	459	8	.	.	PUNCT
cana-5360	460	1	then	then	ADV
cana-5360	460	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	460	3	is	be	AUX
cana-5360	460	4	a	a	DET
cana-5360	460	5	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	NOUN
cana-5360	460	6	map	map	NOUN
cana-5360	460	7	if	if	SCONJ
cana-5360	460	8	𝑋	𝑋	PROPN
cana-5360	460	9	is	be	AUX
cana-5360	460	10	a	a	DET
cana-5360	460	11	𝒫ℱ𝒩𝛿𝒮𝑈1	𝒫ℱ𝒩𝛿𝒮𝑈1	NOUN
cana-5360	460	12	2	2	NUM
cana-5360	460	13	(	(	PUNCT
cana-5360	460	14	resp	resp	NOUN
cana-5360	460	15	.	.	PUNCT
cana-5360	461	1	𝒫ℱ𝒩𝛿𝒫𝑈1	𝒫ℱ𝒩𝛿𝒫𝑈1	NOUN
cana-5360	461	2	2	2	NUM
cana-5360	461	3	,	,	PUNCT
cana-5360	461	4	𝒫ℱ𝒩𝛿𝛼𝑈1	𝒫ℱ𝒩𝛿𝛼𝑈1	X
cana-5360	461	5	2	2	NUM
cana-5360	461	6	and	and	CCONJ
cana-5360	461	7	𝒫ℱ𝒩𝛿𝛽𝑈1	𝒫ℱ𝒩𝛿𝛽𝑈1	NUM
cana-5360	461	8	2	2	NUM
cana-5360	461	9	)	)	PUNCT
cana-5360	461	10	-space	-space	NOUN
cana-5360	461	11	.	.	PUNCT
cana-5360	462	1	proof	proof	NOUN
cana-5360	462	2	.	.	PUNCT
cana-5360	463	1	(	(	PUNCT
cana-5360	463	2	i	i	NOUN
cana-5360	463	3	)	)	PUNCT
cana-5360	463	4	consider	consider	VERB
cana-5360	463	5	a	a	DET
cana-5360	463	6	𝒫ℱ𝒩𝑜𝑠	𝒫ℱ𝒩𝑜𝑠	PROPN
cana-5360	463	7	𝐾	𝐾	PROPN
cana-5360	463	8	in	in	ADP
cana-5360	463	9	𝑈2	𝑈2	PROPN
cana-5360	463	10	.	.	PUNCT
cana-5360	464	1	then	then	ADV
cana-5360	464	2	𝐾	𝐾	PROPN
cana-5360	464	3	is	be	AUX
cana-5360	464	4	a	a	DET
cana-5360	464	5	𝒫ℱ𝒩𝛿𝒮𝑜𝑠	𝒫ℱ𝒩𝛿𝒮𝑜𝑠	PROPN
cana-5360	464	6	in	in	ADP
cana-5360	464	7	𝑈2	𝑈2	PROPN
cana-5360	464	8	.	.	PUNCT
cana-5360	465	1	therefore	therefore	ADV
cana-5360	465	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	465	3	−1(𝐾	−1(𝐾	NOUN
cana-5360	465	4	)	)	PUNCT
cana-5360	465	5	is	be	AUX
cana-5360	465	6	a	a	DET
cana-5360	465	7	𝒫ℱ𝒩𝛿𝒮𝑐𝑠	𝒫ℱ𝒩𝛿𝒮𝑐𝑠	PROPN
cana-5360	465	8	in	in	ADP
cana-5360	465	9	𝑈1	𝑈1	NOUN
cana-5360	465	10	.	.	PUNCT
cana-5360	466	1	since	since	SCONJ
cana-5360	466	2	𝑈1	𝑈1	NOUN
cana-5360	466	3	is	be	AUX
cana-5360	466	4	a	a	DET
cana-5360	466	5	𝒫ℱ𝒩𝛿𝒮𝑈1	𝒫ℱ𝒩𝛿𝒮𝑈1	NOUN
cana-5360	466	6	2	2	NUM
cana-5360	466	7	-space	-space	NOUN
cana-5360	466	8	,	,	PUNCT
cana-5360	466	9	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	466	10	−1(𝐾	−1(𝐾	NOUN
cana-5360	466	11	)	)	PUNCT
cana-5360	466	12	is	be	AUX
cana-5360	466	13	a	a	DET
cana-5360	466	14	𝒫ℱ𝒩𝑐𝑠	𝒫ℱ𝒩𝑐𝑠	NOUN
cana-5360	466	15	in	in	ADP
cana-5360	466	16	𝑈1	𝑈1	NOUN
cana-5360	466	17	.	.	PUNCT
cana-5360	467	1	hence	hence	ADV
cana-5360	467	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	467	3	is	be	AUX
cana-5360	467	4	a	a	DET
cana-5360	467	5	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	NOUN
cana-5360	467	6	map	map	NOUN
cana-5360	467	7	.	.	PUNCT
cana-5360	468	1	(	(	PUNCT
cana-5360	468	2	ii	ii	NOUN
cana-5360	468	3	)	)	PUNCT
cana-5360	468	4	consider	consider	VERB
cana-5360	468	5	a	a	DET
cana-5360	468	6	𝒫ℱ𝒩𝑜𝑠	𝒫ℱ𝒩𝑜𝑠	PROPN
cana-5360	468	7	𝐾	𝐾	PROPN
cana-5360	468	8	in	in	ADP
cana-5360	468	9	𝑈2	𝑈2	PROPN
cana-5360	468	10	.	.	PUNCT
cana-5360	469	1	then	then	ADV
cana-5360	469	2	𝐾	𝐾	PROPN
cana-5360	469	3	is	be	AUX
cana-5360	469	4	a	a	DET
cana-5360	469	5	𝒫ℱ𝒩𝛿𝒫𝑜𝑠	𝒫ℱ𝒩𝛿𝒫𝑜𝑠	ADJ
cana-5360	469	6	in	in	ADP
cana-5360	469	7	𝑈2	𝑈2	PROPN
cana-5360	469	8	.	.	PUNCT
cana-5360	470	1	therefore	therefore	ADV
cana-5360	470	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	470	3	−1(𝐾	−1(𝐾	NOUN
cana-5360	470	4	)	)	PUNCT
cana-5360	470	5	is	be	AUX
cana-5360	470	6	a	a	DET
cana-5360	470	7	𝒫ℱ𝒩𝛿𝒫𝑐𝑠	𝒫ℱ𝒩𝛿𝒫𝑐𝑠	PROPN
cana-5360	470	8	in	in	ADP
cana-5360	470	9	𝑈1	𝑈1	NOUN
cana-5360	470	10	.	.	PUNCT
cana-5360	471	1	since	since	SCONJ
cana-5360	471	2	𝑋	𝑋	PROPN
cana-5360	471	3	is	be	AUX
cana-5360	471	4	a	a	DET
cana-5360	471	5	𝒫ℱ𝒩𝛿𝒫𝑈1	𝒫ℱ𝒩𝛿𝒫𝑈1	ADJ
cana-5360	471	6	2	2	NUM
cana-5360	471	7	-space	-space	NOUN
cana-5360	471	8	,	,	PUNCT
cana-5360	471	9	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	471	10	−1(𝐾	−1(𝐾	NOUN
cana-5360	471	11	)	)	PUNCT
cana-5360	471	12	is	be	AUX
cana-5360	471	13	a	a	DET
cana-5360	471	14	𝒫ℱ𝒩𝑐𝑠	𝒫ℱ𝒩𝑐𝑠	NOUN
cana-5360	471	15	in	in	ADP
cana-5360	471	16	𝑈1	𝑈1	NOUN
cana-5360	471	17	.	.	PUNCT
cana-5360	472	1	hence	hence	ADV
cana-5360	472	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	472	3	is	be	AUX
cana-5360	472	4	a	a	DET
cana-5360	472	5	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	NOUN
cana-5360	472	6	map	map	NOUN
cana-5360	472	7	.	.	PUNCT
cana-5360	473	1	(	(	PUNCT
cana-5360	473	2	iii	iii	X
cana-5360	473	3	)	)	PUNCT
cana-5360	473	4	consider	consider	VERB
cana-5360	473	5	a	a	DET
cana-5360	473	6	𝒫ℱ𝒩𝑜𝑠	𝒫ℱ𝒩𝑜𝑠	PROPN
cana-5360	473	7	𝐾	𝐾	PROPN
cana-5360	473	8	in	in	ADP
cana-5360	473	9	𝑈2	𝑈2	PROPN
cana-5360	473	10	.	.	PUNCT
cana-5360	474	1	then	then	ADV
cana-5360	474	2	𝐾	𝐾	PROPN
cana-5360	474	3	is	be	AUX
cana-5360	474	4	a	a	DET
cana-5360	474	5	𝒫ℱ𝒩𝛿𝛼𝑜𝑠	𝒫ℱ𝒩𝛿𝛼𝑜𝑠	PROPN
cana-5360	474	6	in	in	ADP
cana-5360	474	7	𝑈2	𝑈2	PROPN
cana-5360	474	8	.	.	PUNCT
cana-5360	475	1	therefore	therefore	ADV
cana-5360	475	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	475	3	−1(𝐾	−1(𝐾	NOUN
cana-5360	475	4	)	)	PUNCT
cana-5360	475	5	is	be	AUX
cana-5360	475	6	a	a	DET
cana-5360	475	7	𝒫ℱ𝒩𝛿𝛼𝑐𝑠	𝒫ℱ𝒩𝛿𝛼𝑐𝑠	PROPN
cana-5360	475	8	in	in	ADP
cana-5360	475	9	𝑈1	𝑈1	NOUN
cana-5360	475	10	.	.	PUNCT
cana-5360	476	1	since	since	SCONJ
cana-5360	476	2	𝑈1	𝑈1	NOUN
cana-5360	476	3	is	be	AUX
cana-5360	476	4	a	a	DET
cana-5360	476	5	𝒫ℱ𝒩𝛿𝛼𝑈1	𝒫ℱ𝒩𝛿𝛼𝑈1	NUM
cana-5360	476	6	2	2	NUM
cana-5360	476	7	-space	-space	NOUN
cana-5360	476	8	,	,	PUNCT
cana-5360	476	9	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	476	10	−1(𝐾	−1(𝐾	NOUN
cana-5360	476	11	)	)	PUNCT
cana-5360	476	12	is	be	AUX
cana-5360	476	13	a	a	DET
cana-5360	476	14	𝒫ℱ𝒩𝑐𝑠	𝒫ℱ𝒩𝑐𝑠	NOUN
cana-5360	476	15	in	in	ADP
cana-5360	476	16	𝑈1	𝑈1	NOUN
cana-5360	476	17	.	.	PUNCT
cana-5360	477	1	hence	hence	ADV
cana-5360	477	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	477	3	is	be	AUX
cana-5360	477	4	a	a	DET
cana-5360	477	5	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	NOUN
cana-5360	477	6	map	map	NOUN
cana-5360	477	7	.	.	PUNCT
cana-5360	478	1	(	(	PUNCT
cana-5360	478	2	iv	iv	X
cana-5360	478	3	)	)	PUNCT
cana-5360	478	4	consider	consider	VERB
cana-5360	478	5	a	a	DET
cana-5360	478	6	𝒫ℱ𝒩𝑜𝑠	𝒫ℱ𝒩𝑜𝑠	PROPN
cana-5360	478	7	𝐾	𝐾	PROPN
cana-5360	478	8	in	in	ADP
cana-5360	478	9	𝑈2	𝑈2	PROPN
cana-5360	478	10	.	.	PUNCT
cana-5360	479	1	then	then	ADV
cana-5360	479	2	𝐾	𝐾	PROPN
cana-5360	479	3	is	be	AUX
cana-5360	479	4	a	a	DET
cana-5360	479	5	𝒫ℱ𝒩𝛿𝛽𝑜𝑠	𝒫ℱ𝒩𝛿𝛽𝑜𝑠	PROPN
cana-5360	479	6	in	in	ADP
cana-5360	479	7	𝑈2	𝑈2	PROPN
cana-5360	479	8	.	.	PUNCT
cana-5360	480	1	therefore	therefore	ADV
cana-5360	480	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	480	3	−1(𝐾	−1(𝐾	NOUN
cana-5360	480	4	)	)	PUNCT
cana-5360	480	5	is	be	AUX
cana-5360	480	6	a	a	DET
cana-5360	480	7	communications	communication	NOUN
cana-5360	480	8	on	on	ADP
cana-5360	480	9	applied	apply	VERB
cana-5360	480	10	nonlinear	nonlinear	ADJ
cana-5360	480	11	analysis	analysis	NOUN
cana-5360	480	12	issn	issn	NOUN
cana-5360	480	13	:	:	PUNCT
cana-5360	480	14	1074	1074	NUM
cana-5360	480	15	-	-	PUNCT
cana-5360	480	16	133x	133x	NUM
cana-5360	480	17	vol	vol	VERB
cana-5360	480	18	32	32	NUM
cana-5360	480	19	no	no	NOUN
cana-5360	480	20	.	.	PUNCT
cana-5360	481	1	10s	10	NOUN
cana-5360	481	2	(	(	PUNCT
cana-5360	481	3	2025	2025	NUM
cana-5360	481	4	)	)	PUNCT
cana-5360	481	5	1940	1940	NUM
cana-5360	481	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5360	481	7	𝒫ℱ𝒩𝛿𝛽𝑐𝑠	𝒫ℱ𝒩𝛿𝛽𝑐𝑠	PROPN
cana-5360	481	8	in	in	ADP
cana-5360	481	9	𝑈1	𝑈1	NOUN
cana-5360	481	10	.	.	PUNCT
cana-5360	482	1	since	since	SCONJ
cana-5360	482	2	𝑈1	𝑈1	NOUN
cana-5360	482	3	is	be	AUX
cana-5360	482	4	a	a	DET
cana-5360	482	5	𝒫ℱ𝒩𝛿𝛽𝑈1	𝒫ℱ𝒩𝛿𝛽𝑈1	NUM
cana-5360	482	6	2	2	NUM
cana-5360	482	7	-space	-space	NOUN
cana-5360	482	8	,	,	PUNCT
cana-5360	482	9	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	482	10	−1(𝐾	−1(𝐾	NOUN
cana-5360	482	11	)	)	PUNCT
cana-5360	482	12	is	be	AUX
cana-5360	482	13	a	a	DET
cana-5360	482	14	𝒫ℱ𝒩𝑐𝑠	𝒫ℱ𝒩𝑐𝑠	NOUN
cana-5360	482	15	in	in	ADP
cana-5360	482	16	𝑈1	𝑈1	NOUN
cana-5360	482	17	.	.	PUNCT
cana-5360	483	1	hence	hence	ADV
cana-5360	483	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	483	3	is	be	AUX
cana-5360	483	4	a	a	DET
cana-5360	483	5	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	PROPN
cana-5360	483	6	map	map	NOUN
cana-5360	483	7	.	.	PUNCT
cana-5360	484	1	theorem	theorem	VERB
cana-5360	484	2	4.3	4.3	NUM
cana-5360	484	3	let	let	VERB
cana-5360	484	4	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	484	5	:	:	PUNCT
cana-5360	484	6	(	(	PUNCT
cana-5360	484	7	𝑈1	𝑈1	NOUN
cana-5360	484	8	,	,	PUNCT
cana-5360	484	9	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	484	10	)	)	PUNCT
cana-5360	484	11	)	)	PUNCT
cana-5360	485	1	→	→	SYM
cana-5360	485	2	(	(	PUNCT
cana-5360	485	3	𝑈2	𝑈2	NOUN
cana-5360	485	4	,	,	PUNCT
cana-5360	485	5	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	485	6	)	)	PUNCT
cana-5360	485	7	)	)	PUNCT
cana-5360	485	8	and	and	CCONJ
cana-5360	485	9	𝑔𝑃	𝑔𝑃	ADJ
cana-5360	485	10	:	:	PUNCT
cana-5360	485	11	(	(	PUNCT
cana-5360	485	12	𝑈2	𝑈2	NOUN
cana-5360	485	13	,	,	PUNCT
cana-5360	485	14	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	485	15	)	)	PUNCT
cana-5360	485	16	)	)	PUNCT
cana-5360	485	17	→	→	PUNCT
cana-5360	485	18	(	(	PUNCT
cana-5360	485	19	𝑈3	𝑈3	NOUN
cana-5360	485	20	,	,	PUNCT
cana-5360	485	21	𝜏𝑃(𝐴3	𝜏𝑃(𝐴3	NOUN
cana-5360	485	22	)	)	PUNCT
cana-5360	485	23	)	)	PUNCT
cana-5360	485	24	be	be	AUX
cana-5360	485	25	mappings	mapping	NOUN
cana-5360	485	26	.	.	PUNCT
cana-5360	486	1	then	then	ADV
cana-5360	486	2	𝑔𝑃	𝑔𝑃	PROPN
cana-5360	486	3	∘	∘	PROPN
cana-5360	486	4	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	486	5	:	:	PUNCT
cana-5360	486	6	(	(	PUNCT
cana-5360	486	7	𝑈1	𝑈1	NOUN
cana-5360	486	8	,	,	PUNCT
cana-5360	486	9	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	486	10	)	)	PUNCT
cana-5360	486	11	)	)	PUNCT
cana-5360	486	12	→	→	PUNCT
cana-5360	486	13	(	(	PUNCT
cana-5360	486	14	𝑈3	𝑈3	NOUN
cana-5360	486	15	,	,	PUNCT
cana-5360	486	16	𝜏𝑃(𝐴3	𝜏𝑃(𝐴3	NOUN
cana-5360	486	17	)	)	PUNCT
cana-5360	486	18	)	)	PUNCT
cana-5360	487	1	is	be	AUX
cana-5360	487	2	(	(	PUNCT
cana-5360	487	3	i	i	NOUN
cana-5360	487	4	)	)	PUNCT
cana-5360	487	5	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	PROPN
cana-5360	487	6	(	(	PUNCT
cana-5360	487	7	resp	resp	NOUN
cana-5360	487	8	.	.	PUNCT
cana-5360	488	1	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	NOUN
cana-5360	488	2	,	,	PUNCT
cana-5360	488	3	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	NOUN
cana-5360	488	4	,	,	PUNCT
cana-5360	488	5	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐶𝑡𝑠	PRON
cana-5360	488	6	and	and	CCONJ
cana-5360	488	7	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠	PRON
cana-5360	488	8	)	)	PUNCT
cana-5360	488	9	if	if	SCONJ
cana-5360	488	10	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	488	11	is	be	AUX
cana-5360	488	12	𝒫ℱ𝒩𝛿𝐼𝑟𝑟	𝒫ℱ𝒩𝛿𝐼𝑟𝑟	PROPN
cana-5360	488	13	(	(	PUNCT
cana-5360	488	14	resp	resp	NOUN
cana-5360	488	15	.	.	PUNCT
cana-5360	489	1	𝒫ℱ𝒩𝛿𝒮𝐼𝑟𝑟	𝒫ℱ𝒩𝛿𝒮𝐼𝑟𝑟	ADJ
cana-5360	489	2	,	,	PUNCT
cana-5360	489	3	𝒫ℱ𝒩𝛿𝒫𝐼𝑟𝑟	𝒫ℱ𝒩𝛿𝒫𝐼𝑟𝑟	PROPN
cana-5360	489	4	,	,	PUNCT
cana-5360	489	5	𝒫ℱ𝒩𝛿𝛼𝐼𝑟𝑟	𝒫ℱ𝒩𝛿𝛼𝐼𝑟𝑟	PROPN
cana-5360	489	6	and	and	CCONJ
cana-5360	489	7	𝒫ℱ𝒩𝛿𝛽𝐼𝑟𝑟	𝒫ℱ𝒩𝛿𝛽𝐼𝑟𝑟	PROPN
cana-5360	489	8	)	)	PUNCT
cana-5360	489	9	maps	map	NOUN
cana-5360	489	10	and	and	CCONJ
cana-5360	489	11	𝑔𝑃	𝑔𝑃	NOUN
cana-5360	489	12	is	be	AUX
cana-5360	489	13	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	NOUN
cana-5360	489	14	(	(	PUNCT
cana-5360	489	15	resp	resp	NOUN
cana-5360	489	16	.	.	PUNCT
cana-5360	490	1	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	PROPN
cana-5360	490	2	,	,	PUNCT
cana-5360	490	3	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	PROPN
cana-5360	490	4	,	,	PUNCT
cana-5360	490	5	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐶𝑡𝑠	PROPN
cana-5360	490	6	and	and	CCONJ
cana-5360	490	7	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠	NUM
cana-5360	490	8	)	)	PUNCT
cana-5360	490	9	.	.	PUNCT
cana-5360	491	1	(	(	PUNCT
cana-5360	491	2	ii	ii	NOUN
cana-5360	491	3	)	)	PUNCT
cana-5360	491	4	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝐼𝑟𝑟	PROPN
cana-5360	491	5	(	(	PUNCT
cana-5360	491	6	resp	resp	NOUN
cana-5360	491	7	.	.	PUNCT
cana-5360	491	8	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐼𝑟𝑟	NUM
cana-5360	491	9	,	,	PUNCT
cana-5360	491	10	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	PROPN
cana-5360	491	11	,	,	PUNCT
cana-5360	491	12	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	PROPN
cana-5360	491	13	,	,	PUNCT
cana-5360	491	14	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐼𝑟𝑟	PROPN
cana-5360	491	15	and	and	CCONJ
cana-5360	491	16	𝒫ℱ𝒩	𝒫ℱ𝒩	PROPN
cana-5360	491	17	𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐼𝑟𝑟	𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐼𝑟𝑟	PROPN
cana-5360	491	18	)	)	PUNCT
cana-5360	491	19	if	if	SCONJ
cana-5360	491	20	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	491	21	is	be	AUX
cana-5360	491	22	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝐼𝑟𝑟	PROPN
cana-5360	491	23	(	(	PUNCT
cana-5360	491	24	resp	resp	NOUN
cana-5360	491	25	.	.	PUNCT
cana-5360	492	1	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐼𝑟𝑟	PROPN
cana-5360	492	2	,	,	PUNCT
cana-5360	492	3	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	PROPN
cana-5360	492	4	,	,	PUNCT
cana-5360	492	5	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	PROPN
cana-5360	492	6	,	,	PUNCT
cana-5360	492	7	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐼𝑟𝑟	PROPN
cana-5360	492	8	and	and	CCONJ
cana-5360	492	9	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐼𝑟𝑟	PROPN
cana-5360	492	10	)	)	PUNCT
cana-5360	492	11	and	and	CCONJ
cana-5360	492	12	𝑔𝑃	𝑔𝑃	PROPN
cana-5360	492	13	is	be	AUX
cana-5360	492	14	𝒫ℱ𝒩𝛿𝐼𝑟𝑟	𝒫ℱ𝒩𝛿𝐼𝑟𝑟	NOUN
cana-5360	492	15	(	(	PUNCT
cana-5360	492	16	resp	resp	NOUN
cana-5360	492	17	.	.	PUNCT
cana-5360	493	1	𝒫ℱ𝒩𝛿𝒮𝐼𝑟𝑟	𝒫ℱ𝒩𝛿𝒮𝐼𝑟𝑟	ADJ
cana-5360	493	2	,	,	PUNCT
cana-5360	493	3	𝒫ℱ𝒩𝛿𝒫𝐼𝑟𝑟	𝒫ℱ𝒩𝛿𝒫𝐼𝑟𝑟	PROPN
cana-5360	493	4	,	,	PUNCT
cana-5360	493	5	𝒫ℱ𝒩𝛿𝛼𝐼𝑟𝑟	𝒫ℱ𝒩𝛿𝛼𝐼𝑟𝑟	PROPN
cana-5360	493	6	and	and	CCONJ
cana-5360	493	7	𝒫ℱ𝒩𝛿𝛽𝐼𝑟𝑟	𝒫ℱ𝒩𝛿𝛽𝐼𝑟𝑟	PROPN
cana-5360	493	8	)	)	PUNCT
cana-5360	493	9	.	.	PUNCT
cana-5360	494	1	(	(	PUNCT
cana-5360	494	2	iii	iii	X
cana-5360	494	3	)	)	PUNCT
cana-5360	494	4	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝐼𝑟𝑟	PROPN
cana-5360	494	5	(	(	PUNCT
cana-5360	494	6	resp	resp	NOUN
cana-5360	494	7	.	.	PUNCT
cana-5360	495	1	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐼𝑟𝑟	PROPN
cana-5360	495	2	,	,	PUNCT
cana-5360	495	3	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	PROPN
cana-5360	495	4	,	,	PUNCT
cana-5360	495	5	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	PROPN
cana-5360	495	6	,	,	PUNCT
cana-5360	495	7	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐼𝑟𝑟	PROPN
cana-5360	495	8	and	and	CCONJ
cana-5360	495	9	𝒫ℱ𝒩	𝒫ℱ𝒩	PROPN
cana-5360	495	10	𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐼𝑟𝑟	𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐼𝑟𝑟	PROPN
cana-5360	495	11	)	)	PUNCT
cana-5360	495	12	if	if	SCONJ
cana-5360	495	13	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	495	14	is	be	AUX
cana-5360	495	15	𝒫ℱ𝒩𝛿𝐼𝑟𝑟	𝒫ℱ𝒩𝛿𝐼𝑟𝑟	PROPN
cana-5360	495	16	(	(	PUNCT
cana-5360	495	17	resp	resp	NOUN
cana-5360	495	18	.	.	PUNCT
cana-5360	496	1	𝒫ℱ𝒩𝛿𝒮𝐼𝑟𝑟	𝒫ℱ𝒩𝛿𝒮𝐼𝑟𝑟	ADJ
cana-5360	496	2	,	,	PUNCT
cana-5360	496	3	𝒫ℱ𝒩𝛿𝒫𝐼𝑟𝑟	𝒫ℱ𝒩𝛿𝒫𝐼𝑟𝑟	PROPN
cana-5360	496	4	,	,	PUNCT
cana-5360	496	5	𝒫ℱ𝒩𝛿𝛼𝐼𝑟𝑟	𝒫ℱ𝒩𝛿𝛼𝐼𝑟𝑟	PROPN
cana-5360	496	6	and	and	CCONJ
cana-5360	496	7	𝒫ℱ𝒩𝛿𝛽𝐼𝑟𝑟	𝒫ℱ𝒩𝛿𝛽𝐼𝑟𝑟	PROPN
cana-5360	496	8	)	)	PUNCT
cana-5360	496	9	and	and	CCONJ
cana-5360	496	10	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝐼𝑟𝑟	PROPN
cana-5360	496	11	(	(	PUNCT
cana-5360	496	12	resp	resp	NOUN
cana-5360	496	13	.	.	PUNCT
cana-5360	497	1	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐼𝑟𝑟	PROPN
cana-5360	497	2	,	,	PUNCT
cana-5360	497	3	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	PROPN
cana-5360	497	4	,	,	PUNCT
cana-5360	497	5	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	PROPN
cana-5360	497	6	,	,	PUNCT
cana-5360	497	7	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐼𝑟𝑟	PROPN
cana-5360	497	8	&	&	CCONJ
cana-5360	497	9	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐼𝑟𝑟	PROPN
cana-5360	497	10	)	)	PUNCT
cana-5360	497	11	.	.	PUNCT
cana-5360	498	1	proof	proof	NOUN
cana-5360	498	2	.	.	PUNCT
cana-5360	499	1	(	(	PUNCT
cana-5360	499	2	i	i	NOUN
cana-5360	499	3	)	)	PUNCT
cana-5360	499	4	let	let	VERB
cana-5360	499	5	𝐾	𝐾	PRON
cana-5360	499	6	be	be	AUX
cana-5360	499	7	a	a	DET
cana-5360	499	8	𝒫ℱ𝒩𝑜𝑠	𝒫ℱ𝒩𝑜𝑠	NOUN
cana-5360	499	9	in	in	ADP
cana-5360	499	10	𝑈3	𝑈3	NOUN
cana-5360	499	11	.	.	PUNCT
cana-5360	500	1	then	then	ADV
cana-5360	500	2	𝑔𝑃	𝑔𝑃	ADJ
cana-5360	500	3	−1(𝐾	−1(𝐾	NOUN
cana-5360	500	4	)	)	PUNCT
cana-5360	500	5	is	be	AUX
cana-5360	500	6	a	a	DET
cana-5360	500	7	𝒫ℱ𝒩𝛿𝛽𝑐𝑠	𝒫ℱ𝒩𝛿𝛽𝑐𝑠	PROPN
cana-5360	500	8	in	in	ADP
cana-5360	500	9	𝑈2	𝑈2	PROPN
cana-5360	500	10	.	.	PUNCT
cana-5360	501	1	as	as	SCONJ
cana-5360	501	2	𝑔𝑃	𝑔𝑃	PROPN
cana-5360	501	3	is	be	AUX
cana-5360	501	4	a	a	DET
cana-5360	501	5	𝒫ℱ𝒩𝛿𝛽𝐼𝑟𝑟	𝒫ℱ𝒩𝛿𝛽𝐼𝑟𝑟	PROPN
cana-5360	501	6	,	,	PUNCT
cana-5360	501	7	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	501	8	−1(𝑔𝑃	−1(𝑔𝑃	NOUN
cana-5360	501	9	−1(𝐾	−1(𝐾	NOUN
cana-5360	501	10	)	)	PUNCT
cana-5360	501	11	)	)	PUNCT
cana-5360	501	12	is	be	AUX
cana-5360	501	13	a	a	DET
cana-5360	501	14	𝒫ℱ𝒩𝛿𝛽𝑐𝑠	𝒫ℱ𝒩𝛿𝛽𝑐𝑠	PROPN
cana-5360	501	15	in	in	ADP
cana-5360	501	16	𝑈1	𝑈1	NOUN
cana-5360	501	17	.	.	PUNCT
cana-5360	502	1	thus	thus	ADV
cana-5360	502	2	𝑔𝑃	𝑔𝑃	VERB
cana-5360	502	3	∘	∘	PROPN
cana-5360	502	4	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	502	5	is	be	AUX
cana-5360	502	6	a	a	DET
cana-5360	502	7	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	NOUN
cana-5360	502	8	map	map	NOUN
cana-5360	502	9	.	.	PUNCT
cana-5360	503	1	the	the	DET
cana-5360	503	2	other	other	ADJ
cana-5360	503	3	cases	case	NOUN
cana-5360	503	4	are	be	AUX
cana-5360	503	5	similar	similar	ADJ
cana-5360	503	6	.	.	PUNCT
cana-5360	504	1	theorem	theorem	VERB
cana-5360	504	2	4.4	4.4	NUM
cana-5360	504	3	let	let	VERB
cana-5360	504	4	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	504	5	:	:	PUNCT
cana-5360	504	6	(	(	PUNCT
cana-5360	504	7	𝑈1	𝑈1	NOUN
cana-5360	504	8	,	,	PUNCT
cana-5360	504	9	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	504	10	)	)	PUNCT
cana-5360	504	11	)	)	PUNCT
cana-5360	505	1	→	→	SYM
cana-5360	505	2	(	(	PUNCT
cana-5360	505	3	𝑈2	𝑈2	NOUN
cana-5360	505	4	,	,	PUNCT
cana-5360	505	5	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	505	6	)	)	PUNCT
cana-5360	505	7	)	)	PUNCT
cana-5360	505	8	be	be	AUX
cana-5360	505	9	a	a	DET
cana-5360	505	10	mapping	mapping	NOUN
cana-5360	505	11	.	.	PUNCT
cana-5360	506	1	(	(	PUNCT
cana-5360	506	2	i	i	NOUN
cana-5360	506	3	)	)	PUNCT
cana-5360	506	4	if	if	SCONJ
cana-5360	506	5	(	(	PUNCT
cana-5360	506	6	𝑈1	𝑈1	NOUN
cana-5360	506	7	,	,	PUNCT
cana-5360	506	8	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	506	9	)	)	PUNCT
cana-5360	506	10	)	)	PUNCT
cana-5360	506	11	is	be	AUX
cana-5360	506	12	𝒫ℱ𝒩𝛿𝒮𝑈1	𝒫ℱ𝒩𝛿𝒮𝑈1	NOUN
cana-5360	506	13	2	2	NUM
cana-5360	506	14	(	(	PUNCT
cana-5360	506	15	resp	resp	NOUN
cana-5360	506	16	.	.	PUNCT
cana-5360	507	1	𝒫ℱ𝒩𝛿𝒫𝑈1	𝒫ℱ𝒩𝛿𝒫𝑈1	NOUN
cana-5360	507	2	2	2	NUM
cana-5360	507	3	,	,	PUNCT
cana-5360	507	4	𝒫ℱ𝒩𝛿𝛼𝑈1	𝒫ℱ𝒩𝛿𝛼𝑈1	X
cana-5360	507	5	2	2	NUM
cana-5360	507	6	and	and	CCONJ
cana-5360	507	7	𝒫ℱ𝒩𝛿𝛽𝑈1	𝒫ℱ𝒩𝛿𝛽𝑈1	NUM
cana-5360	507	8	2	2	NUM
cana-5360	507	9	)	)	PUNCT
cana-5360	507	10	-space	-space	NOUN
cana-5360	507	11	,	,	PUNCT
cana-5360	508	1	then	then	ADV
cana-5360	508	2	the	the	DET
cana-5360	508	3	concepts	concept	NOUN
cana-5360	508	4	of	of	ADP
cana-5360	508	5	𝒫ℱ𝒩	𝒫ℱ𝒩	PROPN
cana-5360	508	6	𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	PROPN
cana-5360	508	7	and	and	CCONJ
cana-5360	508	8	𝒫ℱ𝒩𝛿𝒮𝐶𝑡𝑠	𝒫ℱ𝒩𝛿𝒮𝐶𝑡𝑠	ADJ
cana-5360	508	9	(	(	PUNCT
cana-5360	508	10	resp	resp	NOUN
cana-5360	508	11	.	.	PUNCT
cana-5360	509	1	𝒫ℱ𝒩𝛿𝒫𝐶𝑡𝑠	𝒫ℱ𝒩𝛿𝒫𝐶𝑡𝑠	PRON
cana-5360	509	2	,	,	PUNCT
cana-5360	509	3	𝒫ℱ𝒩𝛿𝛼𝐶𝑡𝑠	𝒫ℱ𝒩𝛿𝛼𝐶𝑡𝑠	PROPN
cana-5360	509	4	and	and	CCONJ
cana-5360	509	5	𝒫ℱ𝒩𝛿𝛽𝐶𝑡𝑠	𝒫ℱ𝒩𝛿𝛽𝐶𝑡𝑠	PROPN
cana-5360	509	6	)	)	PUNCT
cana-5360	509	7	are	be	AUX
cana-5360	509	8	equivalent	equivalent	ADJ
cana-5360	509	9	.	.	PUNCT
cana-5360	510	1	(	(	PUNCT
cana-5360	510	2	ii	ii	NOUN
cana-5360	510	3	)	)	PUNCT
cana-5360	510	4	if	if	SCONJ
cana-5360	510	5	𝑔𝑃	𝑔𝑃	PROPN
cana-5360	510	6	is	be	AUX
cana-5360	510	7	𝒫ℱ𝒩𝛿𝒮𝑈1	𝒫ℱ𝒩𝛿𝒮𝑈1	NOUN
cana-5360	510	8	2	2	NUM
cana-5360	510	9	(	(	PUNCT
cana-5360	510	10	resp	resp	NOUN
cana-5360	510	11	.	.	PUNCT
cana-5360	511	1	𝒫ℱ𝒩𝛿𝒫𝑈1	𝒫ℱ𝒩𝛿𝒫𝑈1	NOUN
cana-5360	511	2	2	2	NUM
cana-5360	511	3	,	,	PUNCT
cana-5360	511	4	𝒫ℱ𝒩𝛿𝛼𝑈1	𝒫ℱ𝒩𝛿𝛼𝑈1	X
cana-5360	511	5	2	2	NUM
cana-5360	511	6	and	and	CCONJ
cana-5360	511	7	𝒫ℱ𝒩𝛿𝛽𝑈1	𝒫ℱ𝒩𝛿𝛽𝑈1	NUM
cana-5360	511	8	2	2	NUM
cana-5360	511	9	)	)	PUNCT
cana-5360	511	10	-space	-space	NOUN
cana-5360	511	11	,	,	PUNCT
cana-5360	511	12	then	then	ADV
cana-5360	511	13	the	the	DET
cana-5360	511	14	concepts	concept	NOUN
cana-5360	511	15	of	of	ADP
cana-5360	511	16	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	PROPN
cana-5360	511	17	(	(	PUNCT
cana-5360	511	18	resp	resp	NOUN
cana-5360	511	19	.	.	PUNCT
cana-5360	512	1	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	PROPN
cana-5360	512	2	,	,	PUNCT
cana-5360	512	3	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐶𝑡𝑠	PROPN
cana-5360	512	4	and	and	CCONJ
cana-5360	512	5	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠	NUM
cana-5360	512	6	)	)	PUNCT
cana-5360	512	7	and	and	CCONJ
cana-5360	512	8	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	PROPN
cana-5360	512	9	(	(	PUNCT
cana-5360	512	10	resp	resp	NOUN
cana-5360	512	11	.	.	PUNCT
cana-5360	513	1	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	ADJ
cana-5360	513	2	,	,	PUNCT
cana-5360	513	3	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐼𝑟𝑟	PROPN
cana-5360	513	4	and	and	CCONJ
cana-5360	513	5	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐼𝑟𝑟	PROPN
cana-5360	513	6	)	)	PUNCT
cana-5360	513	7	are	be	AUX
cana-5360	513	8	equivalent	equivalent	ADJ
cana-5360	513	9	.	.	PUNCT
cana-5360	514	1	(	(	PUNCT
cana-5360	514	2	iii	iii	X
cana-5360	514	3	)	)	PUNCT
cana-5360	514	4	if	if	SCONJ
cana-5360	514	5	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	514	6	and	and	CCONJ
cana-5360	514	7	𝑔𝑃	𝑔𝑃	PROPN
cana-5360	514	8	are	be	AUX
cana-5360	514	9	𝒫ℱ𝒩𝛿𝒮𝑈1	𝒫ℱ𝒩𝛿𝒮𝑈1	NOUN
cana-5360	514	10	2	2	NUM
cana-5360	514	11	(	(	PUNCT
cana-5360	514	12	resp	resp	NOUN
cana-5360	514	13	.	.	PUNCT
cana-5360	515	1	𝒫ℱ𝒩𝛿𝒫𝑈1	𝒫ℱ𝒩𝛿𝒫𝑈1	NOUN
cana-5360	515	2	2	2	NUM
cana-5360	515	3	,	,	PUNCT
cana-5360	515	4	𝒫ℱ𝒩𝛿𝛼𝑈1	𝒫ℱ𝒩𝛿𝛼𝑈1	X
cana-5360	515	5	2	2	NUM
cana-5360	515	6	and	and	CCONJ
cana-5360	515	7	𝒫ℱ𝒩𝛿𝛽𝑈1	𝒫ℱ𝒩𝛿𝛽𝑈1	NUM
cana-5360	515	8	2	2	NUM
cana-5360	515	9	)	)	PUNCT
cana-5360	515	10	-spaces	-space	NOUN
cana-5360	515	11	,	,	PUNCT
cana-5360	515	12	then	then	ADV
cana-5360	515	13	the	the	DET
cana-5360	515	14	concepts	concept	NOUN
cana-5360	515	15	of	of	ADP
cana-5360	515	16	𝑁𝑠𝑆𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	𝑁𝑠𝑆𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	PROPN
cana-5360	515	17	,	,	PUNCT
cana-5360	515	18	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	PROPN
cana-5360	515	19	(	(	PUNCT
cana-5360	515	20	resp	resp	NOUN
cana-5360	515	21	.	.	PUNCT
cana-5360	516	1	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	PROPN
cana-5360	516	2	,	,	PUNCT
cana-5360	516	3	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐶𝑡𝑠	PROPN
cana-5360	516	4	and	and	CCONJ
cana-5360	516	5	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠	PRON
cana-5360	516	6	)	)	PUNCT
cana-5360	516	7	and	and	CCONJ
cana-5360	516	8	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	PROPN
cana-5360	516	9	(	(	PUNCT
cana-5360	516	10	resp	resp	NOUN
cana-5360	516	11	.	.	PUNCT
cana-5360	517	1	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	ADJ
cana-5360	517	2	,	,	PUNCT
cana-5360	517	3	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐼𝑟𝑟	PROPN
cana-5360	517	4	and	and	CCONJ
cana-5360	517	5	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐼𝑟𝑟	PROPN
cana-5360	517	6	)	)	PUNCT
cana-5360	517	7	are	be	AUX
cana-5360	517	8	equivalent	equivalent	ADJ
cana-5360	517	9	.	.	PUNCT
cana-5360	518	1	proof	proof	NOUN
cana-5360	518	2	.	.	PUNCT
cana-5360	519	1	(	(	PUNCT
cana-5360	519	2	i	i	NOUN
cana-5360	519	3	)	)	PUNCT
cana-5360	519	4	let	let	VERB
cana-5360	519	5	𝐾	𝐾	PRON
cana-5360	519	6	be	be	AUX
cana-5360	519	7	a	a	DET
cana-5360	519	8	𝒫ℱ𝒩𝑐𝑠	𝒫ℱ𝒩𝑐𝑠	NOUN
cana-5360	519	9	in	in	ADP
cana-5360	519	10	𝑈2	𝑈2	PROPN
cana-5360	519	11	.	.	PUNCT
cana-5360	520	1	then	then	ADV
cana-5360	520	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	520	3	−1(𝐾	−1(𝐾	NOUN
cana-5360	520	4	)	)	PUNCT
cana-5360	520	5	is	be	AUX
cana-5360	520	6	a	a	DET
cana-5360	520	7	𝒫ℱ𝒩𝛿𝛽𝑜𝑠	𝒫ℱ𝒩𝛿𝛽𝑜𝑠	PROPN
cana-5360	520	8	in	in	ADP
cana-5360	520	9	𝑈1	𝑈1	NOUN
cana-5360	520	10	if	if	SCONJ
cana-5360	520	11	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	520	12	is	be	AUX
cana-5360	520	13	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠.	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠.	PROPN
cana-5360	520	14	as	as	SCONJ
cana-5360	520	15	𝑈1	𝑈1	NOUN
cana-5360	520	16	is	be	AUX
cana-5360	520	17	a	a	DET
cana-5360	520	18	𝒫ℱ𝒩𝛿𝛽𝑈1	𝒫ℱ𝒩𝛿𝛽𝑈1	NUM
cana-5360	520	19	2	2	NUM
cana-5360	520	20	-space	-space	NOUN
cana-5360	520	21	,	,	PUNCT
cana-5360	520	22	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	520	23	−1(𝐾	−1(𝐾	NOUN
cana-5360	520	24	)	)	PUNCT
cana-5360	520	25	is	be	AUX
cana-5360	520	26	a	a	DET
cana-5360	520	27	𝒫ℱ𝒩𝑆𝑜𝑠	𝒫ℱ𝒩𝑆𝑜𝑠	PROPN
cana-5360	520	28	in	in	ADP
cana-5360	520	29	𝑈1	𝑈1	NOUN
cana-5360	520	30	.	.	PUNCT
cana-5360	521	1	hence	hence	ADV
cana-5360	521	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	521	3	is	be	AUX
cana-5360	521	4	also	also	ADV
cana-5360	521	5	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	PROPN
cana-5360	521	6	communications	communication	NOUN
cana-5360	521	7	on	on	ADP
cana-5360	521	8	applied	apply	VERB
cana-5360	521	9	nonlinear	nonlinear	ADJ
cana-5360	521	10	analysis	analysis	NOUN
cana-5360	521	11	issn	issn	NOUN
cana-5360	521	12	:	:	PUNCT
cana-5360	521	13	1074	1074	NUM
cana-5360	521	14	-	-	PUNCT
cana-5360	521	15	133x	133x	NUM
cana-5360	521	16	vol	vol	VERB
cana-5360	521	17	32	32	NUM
cana-5360	521	18	no	no	NOUN
cana-5360	521	19	.	.	PUNCT
cana-5360	522	1	10s	10	NOUN
cana-5360	522	2	(	(	PUNCT
cana-5360	522	3	2025	2025	NUM
cana-5360	522	4	)	)	PUNCT
cana-5360	522	5	1941	1941	NUM
cana-5360	522	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5360	522	7	map	map	NOUN
cana-5360	522	8	.	.	PUNCT
cana-5360	523	1	the	the	DET
cana-5360	523	2	other	other	ADJ
cana-5360	523	3	cases	case	NOUN
cana-5360	523	4	are	be	AUX
cana-5360	523	5	similar	similar	ADJ
cana-5360	523	6	.	.	PUNCT
cana-5360	524	1	theorem	theorem	VERB
cana-5360	524	2	4.5	4.5	NUM
cana-5360	524	3	let	let	VERB
cana-5360	524	4	ℎ𝑃	ℎ𝑃	NOUN
cana-5360	524	5	:	:	PUNCT
cana-5360	524	6	(	(	PUNCT
cana-5360	524	7	𝑈1	𝑈1	NOUN
cana-5360	524	8	,	,	PUNCT
cana-5360	524	9	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	524	10	)	)	PUNCT
cana-5360	524	11	)	)	PUNCT
cana-5360	525	1	→	→	SYM
cana-5360	525	2	(	(	PUNCT
cana-5360	525	3	𝑈2	𝑈2	NOUN
cana-5360	525	4	,	,	PUNCT
cana-5360	525	5	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	525	6	)	)	PUNCT
cana-5360	525	7	)	)	PUNCT
cana-5360	525	8	and	and	CCONJ
cana-5360	525	9	𝑔𝑃	𝑔𝑃	ADJ
cana-5360	525	10	:	:	PUNCT
cana-5360	525	11	(	(	PUNCT
cana-5360	525	12	𝑈2	𝑈2	NOUN
cana-5360	525	13	,	,	PUNCT
cana-5360	525	14	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	525	15	)	)	PUNCT
cana-5360	525	16	)	)	PUNCT
cana-5360	525	17	→	→	PUNCT
cana-5360	525	18	(	(	PUNCT
cana-5360	525	19	𝑈3	𝑈3	NOUN
cana-5360	525	20	,	,	PUNCT
cana-5360	525	21	𝜏𝑃(𝐴3	𝜏𝑃(𝐴3	NOUN
cana-5360	525	22	)	)	PUNCT
cana-5360	525	23	)	)	PUNCT
cana-5360	525	24	be	be	AUX
cana-5360	525	25	𝒫ℱ𝒩𝛿𝒮𝐶𝑡𝑠	𝒫ℱ𝒩𝛿𝒮𝐶𝑡𝑠	ADJ
cana-5360	525	26	(	(	PUNCT
cana-5360	525	27	resp	resp	NOUN
cana-5360	525	28	.	.	PUNCT
cana-5360	526	1	𝒫ℱ𝒩𝛿𝒫𝐶𝑡𝑠	𝒫ℱ𝒩𝛿𝒫𝐶𝑡𝑠	PRON
cana-5360	526	2	,	,	PUNCT
cana-5360	526	3	𝒫ℱ𝒩𝛿𝛼𝐶𝑡𝑠	𝒫ℱ𝒩𝛿𝛼𝐶𝑡𝑠	PROPN
cana-5360	526	4	and	and	CCONJ
cana-5360	526	5	𝒫ℱ𝒩𝛿𝛽𝐶𝑡𝑠	𝒫ℱ𝒩𝛿𝛽𝐶𝑡𝑠	PROPN
cana-5360	526	6	)	)	PUNCT
cana-5360	526	7	mappings	mapping	NOUN
cana-5360	526	8	and	and	CCONJ
cana-5360	526	9	𝑈2	𝑈2	PROPN
cana-5360	526	10	be	be	AUX
cana-5360	526	11	a	a	DET
cana-5360	526	12	𝒫ℱ𝒩𝛿𝒮𝑈1	𝒫ℱ𝒩𝛿𝒮𝑈1	NOUN
cana-5360	526	13	2	2	NUM
cana-5360	526	14	(	(	PUNCT
cana-5360	526	15	resp	resp	NOUN
cana-5360	526	16	.	.	PUNCT
cana-5360	527	1	𝒫ℱ𝒩𝛿𝒫𝑈1	𝒫ℱ𝒩𝛿𝒫𝑈1	NOUN
cana-5360	527	2	2	2	NUM
cana-5360	527	3	,	,	PUNCT
cana-5360	527	4	𝒫ℱ𝒩𝛿𝛼𝑈1	𝒫ℱ𝒩𝛿𝛼𝑈1	X
cana-5360	527	5	2	2	NUM
cana-5360	527	6	and	and	CCONJ
cana-5360	527	7	𝒫ℱ𝒩𝛿𝛽𝑈1	𝒫ℱ𝒩𝛿𝛽𝑈1	NUM
cana-5360	527	8	2	2	NUM
cana-5360	527	9	)	)	PUNCT
cana-5360	527	10	-spaces	-space	NOUN
cana-5360	527	11	.	.	PUNCT
cana-5360	528	1	then	then	ADV
cana-5360	528	2	𝑔𝑃	𝑔𝑃	PROPN
cana-5360	528	3	∘	∘	PROPN
cana-5360	528	4	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	528	5	:	:	PUNCT
cana-5360	528	6	(	(	PUNCT
cana-5360	528	7	𝑈1	𝑈1	NOUN
cana-5360	528	8	,	,	PUNCT
cana-5360	528	9	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	528	10	)	)	PUNCT
cana-5360	528	11	)	)	PUNCT
cana-5360	528	12	→	→	PUNCT
cana-5360	528	13	(	(	PUNCT
cana-5360	528	14	𝑈3	𝑈3	NOUN
cana-5360	528	15	,	,	PUNCT
cana-5360	528	16	𝜏𝑃(𝐴3	𝜏𝑃(𝐴3	NOUN
cana-5360	528	17	)	)	PUNCT
cana-5360	528	18	)	)	PUNCT
cana-5360	528	19	is	be	AUX
cana-5360	528	20	𝒫ℱ𝒩𝛿𝒮𝐶𝑡𝑠	𝒫ℱ𝒩𝛿𝒮𝐶𝑡𝑠	ADJ
cana-5360	528	21	(	(	PUNCT
cana-5360	528	22	resp	resp	NOUN
cana-5360	528	23	.	.	PUNCT
cana-5360	529	1	𝒫ℱ𝒩𝛿𝒫𝐶𝑡𝑠	𝒫ℱ𝒩𝛿𝒫𝐶𝑡𝑠	PRON
cana-5360	529	2	,	,	PUNCT
cana-5360	529	3	𝒫ℱ𝒩𝛿𝛼𝐶𝑡𝑠	𝒫ℱ𝒩𝛿𝛼𝐶𝑡𝑠	PROPN
cana-5360	529	4	and	and	CCONJ
cana-5360	529	5	𝒫ℱ𝒩𝛿𝛽𝐶𝑡𝑠	𝒫ℱ𝒩𝛿𝛽𝐶𝑡𝑠	PROPN
cana-5360	529	6	)	)	PUNCT
cana-5360	529	7	.	.	PUNCT
cana-5360	530	1	proof	proof	NOUN
cana-5360	530	2	.	.	PUNCT
cana-5360	531	1	let	let	VERB
cana-5360	531	2	𝐾	𝐾	PRON
cana-5360	531	3	be	be	AUX
cana-5360	531	4	a	a	DET
cana-5360	531	5	𝒫ℱ𝒩𝑐𝑠	𝒫ℱ𝒩𝑐𝑠	NOUN
cana-5360	531	6	in	in	ADP
cana-5360	531	7	𝑈3	𝑈3	NOUN
cana-5360	531	8	.	.	PUNCT
cana-5360	532	1	then	then	ADV
cana-5360	532	2	𝑔𝑃	𝑔𝑃	ADJ
cana-5360	532	3	−1(𝐾	−1(𝐾	NOUN
cana-5360	532	4	)	)	PUNCT
cana-5360	532	5	is	be	AUX
cana-5360	532	6	a	a	DET
cana-5360	532	7	𝒫ℱ𝒩𝛿𝛽𝑜𝑠	𝒫ℱ𝒩𝛿𝛽𝑜𝑠	PROPN
cana-5360	532	8	in	in	ADP
cana-5360	532	9	𝑈2	𝑈2	PROPN
cana-5360	532	10	since	since	SCONJ
cana-5360	532	11	𝑔𝑃	𝑔𝑃	PROPN
cana-5360	532	12	is	be	AUX
cana-5360	532	13	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠.	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠.	PROPN
cana-5360	532	14	as	as	SCONJ
cana-5360	532	15	𝑈2	𝑈2	PROPN
cana-5360	532	16	is	be	AUX
cana-5360	532	17	a	a	DET
cana-5360	532	18	𝒫ℱ𝒩𝛿𝛽𝑈1	𝒫ℱ𝒩𝛿𝛽𝑈1	NUM
cana-5360	532	19	2	2	NUM
cana-5360	532	20	-space	-space	NOUN
cana-5360	532	21	,	,	PUNCT
cana-5360	532	22	𝑔𝑃	𝑔𝑃	ADJ
cana-5360	532	23	−1(𝐾	−1(𝐾	NOUN
cana-5360	532	24	)	)	PUNCT
cana-5360	532	25	is	be	AUX
cana-5360	532	26	a	a	DET
cana-5360	532	27	𝒫ℱ𝒩𝑜𝑠	𝒫ℱ𝒩𝑜𝑠	NOUN
cana-5360	532	28	in	in	ADP
cana-5360	532	29	𝑈2	𝑈2	PROPN
cana-5360	532	30	.	.	PUNCT
cana-5360	533	1	then	then	ADV
cana-5360	533	2	,	,	PUNCT
cana-5360	533	3	𝑔𝑃(ℎ𝑃	𝑔𝑃(ℎ𝑃	NOUN
cana-5360	533	4	−1(𝐾	−1(𝐾	NOUN
cana-5360	533	5	)	)	PUNCT
cana-5360	533	6	)	)	PUNCT
cana-5360	533	7	is	be	AUX
cana-5360	533	8	𝒫ℱ𝒩𝛿𝛽𝑐𝑠	𝒫ℱ𝒩𝛿𝛽𝑐𝑠	PROPN
cana-5360	533	9	in	in	ADP
cana-5360	533	10	𝑈1	𝑈1	NOUN
cana-5360	533	11	because	because	SCONJ
cana-5360	533	12	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	533	13	is	be	AUX
cana-5360	533	14	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠.	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠.	PROPN
cana-5360	533	15	hence	hence	ADV
cana-5360	533	16	,	,	PUNCT
cana-5360	533	17	𝑔𝑃	𝑔𝑃	ADJ
cana-5360	533	18	∘	∘	PROPN
cana-5360	533	19	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	533	20	is	be	AUX
cana-5360	533	21	a	a	DET
cana-5360	533	22	𝒫ℱ𝒩𝛿𝛽𝐶𝑡𝑠	𝒫ℱ𝒩𝛿𝛽𝐶𝑡𝑠	PROPN
cana-5360	533	23	map	map	NOUN
cana-5360	533	24	.	.	PUNCT
cana-5360	534	1	theorem	theorem	VERB
cana-5360	534	2	4.6	4.6	NUM
cana-5360	534	3	let	let	VERB
cana-5360	534	4	a	a	DET
cana-5360	534	5	map	map	NOUN
cana-5360	534	6	ℎ𝑃	ℎ𝑃	NOUN
cana-5360	534	7	:	:	PUNCT
cana-5360	534	8	(	(	PUNCT
cana-5360	534	9	𝑈1	𝑈1	NOUN
cana-5360	534	10	,	,	PUNCT
cana-5360	534	11	𝜏𝑃(𝐴1	𝜏𝑃(𝐴1	NOUN
cana-5360	534	12	)	)	PUNCT
cana-5360	534	13	)	)	PUNCT
cana-5360	535	1	→	→	SYM
cana-5360	535	2	(	(	PUNCT
cana-5360	535	3	𝑈2	𝑈2	NOUN
cana-5360	535	4	,	,	PUNCT
cana-5360	535	5	𝜏𝑃(𝐴2	𝜏𝑃(𝐴2	NOUN
cana-5360	535	6	)	)	PUNCT
cana-5360	535	7	)	)	PUNCT
cana-5360	535	8	.	.	PUNCT
cana-5360	536	1	then	then	ADV
cana-5360	536	2	the	the	DET
cana-5360	536	3	following	follow	VERB
cana-5360	536	4	conditions	condition	NOUN
cana-5360	536	5	are	be	AUX
cana-5360	536	6	equivalent	equivalent	ADJ
cana-5360	536	7	if	if	SCONJ
cana-5360	536	8	𝑈1	𝑈1	NOUN
cana-5360	536	9	and	and	CCONJ
cana-5360	536	10	𝑈2	𝑈2	PROPN
cana-5360	536	11	are	be	AUX
cana-5360	536	12	𝒫ℱ𝒩𝛿𝒮𝑈1	𝒫ℱ𝒩𝛿𝒮𝑈1	NOUN
cana-5360	536	13	2	2	NUM
cana-5360	536	14	(	(	PUNCT
cana-5360	536	15	resp	resp	NOUN
cana-5360	536	16	.	.	PUNCT
cana-5360	537	1	𝒫ℱ𝒩𝛿𝒫𝑈1	𝒫ℱ𝒩𝛿𝒫𝑈1	NOUN
cana-5360	537	2	2	2	NUM
cana-5360	537	3	,	,	PUNCT
cana-5360	537	4	𝒫ℱ𝒩𝛿𝛼𝑈1	𝒫ℱ𝒩𝛿𝛼𝑈1	X
cana-5360	537	5	2	2	NUM
cana-5360	537	6	and	and	CCONJ
cana-5360	537	7	𝒫ℱ𝒩𝛿𝛽𝑈1	𝒫ℱ𝒩𝛿𝛽𝑈1	NUM
cana-5360	537	8	2	2	NUM
cana-5360	537	9	)	)	PUNCT
cana-5360	537	10	-spaces	-space	NOUN
cana-5360	537	11	.	.	PUNCT
cana-5360	538	1	(	(	PUNCT
cana-5360	538	2	i	i	NOUN
cana-5360	538	3	)	)	PUNCT
cana-5360	538	4	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	538	5	is	be	AUX
cana-5360	538	6	a	a	DET
cana-5360	538	7	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	PROPN
cana-5360	538	8	(	(	PUNCT
cana-5360	538	9	resp	resp	NOUN
cana-5360	538	10	.	.	PUNCT
cana-5360	539	1	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	ADJ
cana-5360	539	2	,	,	PUNCT
cana-5360	539	3	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐼𝑟𝑟	PROPN
cana-5360	539	4	and	and	CCONJ
cana-5360	539	5	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐼𝑟𝑟	PROPN
cana-5360	539	6	)	)	PUNCT
cana-5360	539	7	map	map	NOUN
cana-5360	539	8	.	.	PUNCT
cana-5360	540	1	(	(	PUNCT
cana-5360	540	2	ii	ii	NOUN
cana-5360	540	3	)	)	PUNCT
cana-5360	540	4	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	540	5	−1(𝐵	−1(𝐵	NOUN
cana-5360	540	6	)	)	PUNCT
cana-5360	540	7	is	be	AUX
cana-5360	540	8	a	a	DET
cana-5360	540	9	𝒫ℱ𝒩𝛿𝒮𝑜𝑠	𝒫ℱ𝒩𝛿𝒮𝑜𝑠	PROPN
cana-5360	540	10	(	(	PUNCT
cana-5360	540	11	resp	resp	NOUN
cana-5360	540	12	.	.	PUNCT
cana-5360	541	1	𝒫ℱ𝒩𝛿𝒫𝑜𝑠	𝒫ℱ𝒩𝛿𝒫𝑜𝑠	X
cana-5360	541	2	,	,	PUNCT
cana-5360	541	3	𝒫ℱ𝒩𝛿𝛼𝑜𝑠	𝒫ℱ𝒩𝛿𝛼𝑜𝑠	PROPN
cana-5360	541	4	and	and	CCONJ
cana-5360	541	5	𝒫ℱ𝒩𝛿𝛽𝑜𝑠	𝒫ℱ𝒩𝛿𝛽𝑜𝑠	PROPN
cana-5360	541	6	)	)	PUNCT
cana-5360	541	7	in	in	ADP
cana-5360	541	8	𝑈1	𝑈1	NOUN
cana-5360	541	9	,	,	PUNCT
cana-5360	541	10	for	for	ADP
cana-5360	541	11	each	each	DET
cana-5360	541	12	𝒫ℱ𝒩𝛿𝒮𝑐𝑠	𝒫ℱ𝒩𝛿𝒮𝑐𝑠	PROPN
cana-5360	541	13	(	(	PUNCT
cana-5360	541	14	resp	resp	PROPN
cana-5360	541	15	.	.	PUNCT
cana-5360	542	1	𝒫ℱ𝒩𝛿𝒫𝑐𝑠	𝒫ℱ𝒩𝛿𝒫𝑐𝑠	PROPN
cana-5360	542	2	,	,	PUNCT
cana-5360	542	3	𝒫ℱ𝒩𝛿𝛼𝑐𝑠	𝒫ℱ𝒩𝛿𝛼𝑐𝑠	PROPN
cana-5360	542	4	and	and	CCONJ
cana-5360	542	5	𝒫ℱ𝒩𝛿𝛽𝑐𝑠	𝒫ℱ𝒩𝛿𝛽𝑐𝑠	PROPN
cana-5360	542	6	)	)	PUNCT
cana-5360	542	7	𝐵	𝐵	NOUN
cana-5360	542	8	in	in	ADP
cana-5360	542	9	𝑈2	𝑈2	PROPN
cana-5360	542	10	.	.	PUNCT
cana-5360	543	1	(	(	PUNCT
cana-5360	543	2	iii	iii	X
cana-5360	543	3	)	)	PUNCT
cana-5360	543	4	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	PROPN
cana-5360	543	5	,	,	PUNCT
cana-5360	543	6	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	PROPN
cana-5360	543	7	,	,	PUNCT
cana-5360	543	8	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐼𝑟𝑟	PROPN
cana-5360	543	9	𝒫ℱ𝒩𝑐𝑙(ℎ𝑃	𝒫ℱ𝒩𝑐𝑙(ℎ𝑃	PROPN
cana-5360	543	10	−1(𝐵	−1(𝐵	NOUN
cana-5360	543	11	)	)	PUNCT
cana-5360	543	12	)	)	PUNCT
cana-5360	544	1	⊇	⊇	PROPN
cana-5360	544	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	544	3	−1(𝒫ℱ𝒩𝑖𝑛𝑡(𝐵	−1(𝒫ℱ𝒩𝑖𝑛𝑡(𝐵	PROPN
cana-5360	544	4	)	)	PUNCT
cana-5360	544	5	)	)	PUNCT
cana-5360	544	6	,	,	PUNCT
cana-5360	544	7	for	for	ADP
cana-5360	544	8	each	each	DET
cana-5360	544	9	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-5360	544	10	𝐵	𝐵	PROPN
cana-5360	544	11	of	of	ADP
cana-5360	544	12	𝑈2	𝑈2	PROPN
cana-5360	544	13	.	.	PUNCT
cana-5360	545	1	proof	proof	NOUN
cana-5360	545	2	.	.	PUNCT
cana-5360	546	1	(	(	PUNCT
cana-5360	546	2	i	i	NOUN
cana-5360	546	3	)	)	PUNCT
cana-5360	546	4	→	→	SYM
cana-5360	546	5	(	(	PUNCT
cana-5360	546	6	ii	ii	NOUN
cana-5360	546	7	):	):	PUNCT
cana-5360	546	8	let	let	VERB
cana-5360	546	9	𝐵	𝐵	PRON
cana-5360	546	10	be	be	AUX
cana-5360	546	11	any	any	DET
cana-5360	546	12	𝒫ℱ𝒩𝛿𝛽𝑐𝑠	𝒫ℱ𝒩𝛿𝛽𝑐𝑠	PROPN
cana-5360	546	13	in	in	ADP
cana-5360	546	14	𝑈2	𝑈2	PROPN
cana-5360	546	15	.	.	PUNCT
cana-5360	547	1	then	then	ADV
cana-5360	547	2	,	,	PUNCT
cana-5360	547	3	𝐵𝑐	𝐵𝑐	PROPN
cana-5360	547	4	is	be	AUX
cana-5360	547	5	a	a	DET
cana-5360	547	6	𝒫ℱ𝒩𝛿𝛽𝑜𝑠	𝒫ℱ𝒩𝛿𝛽𝑜𝑠	PROPN
cana-5360	547	7	in	in	ADP
cana-5360	547	8	𝑈2	𝑈2	PROPN
cana-5360	547	9	.	.	PUNCT
cana-5360	548	1	since	since	SCONJ
cana-5360	548	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	548	3	is	be	AUX
cana-5360	548	4	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐼𝑟𝑟	PROPN
cana-5360	548	5	,	,	PUNCT
cana-5360	548	6	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	548	7	−1(𝐵𝑐	−1(𝐵𝑐	PROPN
cana-5360	548	8	)	)	PUNCT
cana-5360	548	9	is	be	AUX
cana-5360	548	10	a	a	DET
cana-5360	548	11	𝒫ℱ𝒩𝛿𝛽𝑐𝑠	𝒫ℱ𝒩𝛿𝛽𝑐𝑠	PROPN
cana-5360	548	12	in	in	ADP
cana-5360	548	13	𝑈1	𝑈1	NOUN
cana-5360	548	14	.	.	PUNCT
cana-5360	549	1	but	but	CCONJ
cana-5360	549	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	549	3	−1(𝐵𝑐	−1(𝐵𝑐	PROPN
cana-5360	549	4	)	)	PUNCT
cana-5360	550	1	=	=	PRON
cana-5360	550	2	(	(	PUNCT
cana-5360	550	3	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	550	4	−1(𝐵))𝑐	−1(𝐵))𝑐	PROPN
cana-5360	550	5	.	.	PUNCT
cana-5360	551	1	therefore	therefore	ADV
cana-5360	551	2	,	,	PUNCT
cana-5360	551	3	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	551	4	−1(𝐵	−1(𝐵	NOUN
cana-5360	551	5	)	)	PUNCT
cana-5360	551	6	is	be	AUX
cana-5360	551	7	a	a	DET
cana-5360	551	8	𝒫ℱ𝒩𝛿𝛽𝑐𝑠	𝒫ℱ𝒩𝛿𝛽𝑐𝑠	PROPN
cana-5360	551	9	in	in	ADP
cana-5360	551	10	𝑈1	𝑈1	NOUN
cana-5360	551	11	.	.	PUNCT
cana-5360	552	1	(	(	PUNCT
cana-5360	552	2	ii	ii	NOUN
cana-5360	552	3	)	)	PUNCT
cana-5360	552	4	→	→	SYM
cana-5360	552	5	(	(	PUNCT
cana-5360	552	6	iii	iii	NOUN
cana-5360	552	7	)	)	PUNCT
cana-5360	552	8	:	:	PUNCT
cana-5360	552	9	let	let	VERB
cana-5360	552	10	𝐵	𝐵	PRON
cana-5360	552	11	be	be	AUX
cana-5360	552	12	any	any	DET
cana-5360	552	13	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-5360	552	14	in	in	ADP
cana-5360	552	15	𝑈2	𝑈2	PROPN
cana-5360	552	16	and	and	CCONJ
cana-5360	552	17	𝒫ℱ𝒩𝑖𝑛𝑡(𝐵	𝒫ℱ𝒩𝑖𝑛𝑡(𝐵	NOUN
cana-5360	552	18	)	)	PUNCT
cana-5360	552	19	⊆	⊆	NUM
cana-5360	552	20	𝐵.	𝐵.	PROPN
cana-5360	552	21	then	then	ADV
cana-5360	552	22	,	,	PUNCT
cana-5360	552	23	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	552	24	−1(𝒫ℱ𝒩𝑐𝑙(𝐵	−1(𝒫ℱ𝒩𝑐𝑙(𝐵	PROPN
cana-5360	552	25	)	)	PUNCT
cana-5360	552	26	)	)	PUNCT
cana-5360	553	1	⊆	⊆	NUM
cana-5360	553	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	553	3	−1(𝐵	−1(𝐵	NOUN
cana-5360	553	4	)	)	PUNCT
cana-5360	553	5	.	.	PUNCT
cana-5360	554	1	since	since	SCONJ
cana-5360	554	2	𝒫ℱ𝒩𝑖𝑛𝑡(𝐵	𝒫ℱ𝒩𝑖𝑛𝑡(𝐵	NOUN
cana-5360	554	3	)	)	PUNCT
cana-5360	554	4	is	be	AUX
cana-5360	554	5	a	a	DET
cana-5360	554	6	𝒫ℱ𝒩𝑜𝑠	𝒫ℱ𝒩𝑜𝑠	NOUN
cana-5360	554	7	in	in	ADP
cana-5360	554	8	𝑈2	𝑈2	PROPN
cana-5360	554	9	,	,	PUNCT
cana-5360	554	10	𝒫ℱ𝒩𝑖𝑛𝑡(𝐵	𝒫ℱ𝒩𝑖𝑛𝑡(𝐵	NOUN
cana-5360	554	11	)	)	PUNCT
cana-5360	554	12	is	be	AUX
cana-5360	554	13	a	a	DET
cana-5360	554	14	𝒫ℱ𝒩𝛿𝛽𝑜𝑠	𝒫ℱ𝒩𝛿𝛽𝑜𝑠	PROPN
cana-5360	554	15	in	in	ADP
cana-5360	554	16	𝑈2	𝑈2	PROPN
cana-5360	554	17	.	.	PUNCT
cana-5360	555	1	therefore	therefore	ADV
cana-5360	555	2	,	,	PUNCT
cana-5360	555	3	(	(	PUNCT
cana-5360	555	4	𝒫ℱ𝒩𝑖𝑛𝑡(𝐵))𝑐	𝒫ℱ𝒩𝑖𝑛𝑡(𝐵))𝑐	PROPN
cana-5360	555	5	is	be	AUX
cana-5360	555	6	a	a	DET
cana-5360	555	7	𝒫ℱ𝒩𝛿𝛽𝑐𝑠	𝒫ℱ𝒩𝛿𝛽𝑐𝑠	PROPN
cana-5360	555	8	in	in	ADP
cana-5360	555	9	𝑈2	𝑈2	PROPN
cana-5360	555	10	.	.	PUNCT
cana-5360	556	1	by	by	ADP
cana-5360	556	2	hypothesis	hypothesis	NOUN
cana-5360	556	3	,	,	PUNCT
cana-5360	556	4	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	556	5	−1((𝒫ℱ𝒩𝑖𝑛𝑡(𝐵))𝑐	−1((𝒫ℱ𝒩𝑖𝑛𝑡(𝐵))𝑐	PROPN
cana-5360	556	6	)	)	PUNCT
cana-5360	556	7	is	be	AUX
cana-5360	556	8	a	a	DET
cana-5360	556	9	𝒫ℱ𝒩𝛿𝛽𝑜𝑠	𝒫ℱ𝒩𝛿𝛽𝑜𝑠	PROPN
cana-5360	556	10	in	in	ADP
cana-5360	556	11	𝑈1	𝑈1	NOUN
cana-5360	556	12	.	.	PUNCT
cana-5360	557	1	since	since	SCONJ
cana-5360	557	2	,	,	PUNCT
cana-5360	557	3	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	557	4	−1((𝒫ℱ𝒩𝑖𝑛𝑡(𝐵))𝑐	−1((𝒫ℱ𝒩𝑖𝑛𝑡(𝐵))𝑐	PROPN
cana-5360	557	5	)	)	PUNCT
cana-5360	557	6	=	=	PRON
cana-5360	557	7	(	(	PUNCT
cana-5360	557	8	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	557	9	−1(𝒫ℱ𝒩𝑖𝑛𝑡(𝐵)))𝑐	−1(𝒫ℱ𝒩𝑖𝑛𝑡(𝐵)))𝑐	PROPN
cana-5360	557	10	,	,	PUNCT
cana-5360	557	11	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	557	12	−1(𝒫ℱ𝒩𝑖𝑛𝑡(𝐵	−1(𝒫ℱ𝒩𝑖𝑛𝑡(𝐵	NUM
cana-5360	557	13	)	)	PUNCT
cana-5360	557	14	)	)	PUNCT
cana-5360	557	15	is	be	AUX
cana-5360	557	16	a	a	DET
cana-5360	557	17	𝒫ℱ𝒩𝛿𝛽𝑜𝑠	𝒫ℱ𝒩𝛿𝛽𝑜𝑠	PROPN
cana-5360	557	18	in	in	ADP
cana-5360	557	19	𝑈1	𝑈1	NOUN
cana-5360	557	20	.	.	PUNCT
cana-5360	558	1	since	since	SCONJ
cana-5360	558	2	,	,	PUNCT
cana-5360	558	3	𝑈1	𝑈1	PROPN
cana-5360	558	4	is	be	AUX
cana-5360	558	5	a	a	DET
cana-5360	558	6	𝒫ℱ𝒩𝛿𝛽𝑈1/2	𝒫ℱ𝒩𝛿𝛽𝑈1/2	PROPN
cana-5360	558	7	-space	-space	NOUN
cana-5360	558	8	,	,	PUNCT
cana-5360	558	9	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	558	10	−1(𝒫ℱ𝒩𝑖𝑛𝑡(𝐵	−1(𝒫ℱ𝒩𝑖𝑛𝑡(𝐵	NUM
cana-5360	558	11	)	)	PUNCT
cana-5360	558	12	)	)	PUNCT
cana-5360	558	13	is	be	AUX
cana-5360	558	14	a	a	DET
cana-5360	558	15	𝒫ℱ𝒩𝑜𝑠	𝒫ℱ𝒩𝑜𝑠	NOUN
cana-5360	558	16	in	in	ADP
cana-5360	558	17	𝑈1	𝑈1	NOUN
cana-5360	558	18	.	.	PUNCT
cana-5360	559	1	hence	hence	ADV
cana-5360	559	2	,	,	PUNCT
cana-5360	559	3	𝒫ℱ𝒩𝑐𝑙(ℎ𝑃	𝒫ℱ𝒩𝑐𝑙(ℎ𝑃	PROPN
cana-5360	559	4	−1(𝐵	−1(𝐵	NOUN
cana-5360	559	5	)	)	PUNCT
cana-5360	559	6	)	)	PUNCT
cana-5360	560	1	⊇	⊇	PROPN
cana-5360	560	2	𝒫ℱ𝒩𝑐𝑙(ℎ𝑃	𝒫ℱ𝒩𝑐𝑙(ℎ𝑃	PROPN
cana-5360	560	3	−1(𝒫ℱ𝒩𝑖𝑛𝑡(𝐵	−1(𝒫ℱ𝒩𝑖𝑛𝑡(𝐵	PROPN
cana-5360	560	4	)	)	PUNCT
cana-5360	560	5	)	)	PUNCT
cana-5360	560	6	)	)	PUNCT
cana-5360	561	1	=	=	SYM
cana-5360	561	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	561	3	−1(𝒫ℱ𝒩𝑖𝑛𝑡(𝐵	−1(𝒫ℱ𝒩𝑖𝑛𝑡(𝐵	NUM
cana-5360	561	4	)	)	PUNCT
cana-5360	561	5	)	)	PUNCT
cana-5360	561	6	.	.	PUNCT
cana-5360	562	1	that	that	PRON
cana-5360	562	2	is	be	AUX
cana-5360	562	3	,	,	PUNCT
cana-5360	562	4	𝒫ℱ𝒩𝑐𝑙(ℎ𝑃	𝒫ℱ𝒩𝑐𝑙(ℎ𝑃	PROPN
cana-5360	562	5	−1(𝐵	−1(𝐵	NOUN
cana-5360	562	6	)	)	PUNCT
cana-5360	562	7	)	)	PUNCT
cana-5360	563	1	⊇	⊇	PROPN
cana-5360	563	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	563	3	−1(𝒫ℱ𝒩𝑖𝑛𝑡(𝐵	−1(𝒫ℱ𝒩𝑖𝑛𝑡(𝐵	PROPN
cana-5360	563	4	)	)	PUNCT
cana-5360	563	5	)	)	PUNCT
cana-5360	563	6	.	.	PUNCT
cana-5360	564	1	(	(	PUNCT
cana-5360	564	2	iii	iii	NOUN
cana-5360	564	3	)	)	PUNCT
cana-5360	564	4	→	→	SYM
cana-5360	564	5	(	(	PUNCT
cana-5360	564	6	i	i	NOUN
cana-5360	564	7	)	)	PUNCT
cana-5360	564	8	:	:	PUNCT
cana-5360	564	9	let	let	VERB
cana-5360	564	10	𝐵	𝐵	PRON
cana-5360	564	11	be	be	AUX
cana-5360	564	12	any	any	DET
cana-5360	564	13	𝒫ℱ𝒩𝛿𝛽𝑐𝑠	𝒫ℱ𝒩𝛿𝛽𝑐𝑠	PROPN
cana-5360	564	14	in	in	ADP
cana-5360	564	15	𝑈2	𝑈2	PROPN
cana-5360	564	16	.	.	PUNCT
cana-5360	565	1	since	since	SCONJ
cana-5360	565	2	𝑈2	𝑈2	PROPN
cana-5360	565	3	is	be	AUX
cana-5360	565	4	a	a	DET
cana-5360	565	5	𝒫ℱ𝒩𝛿𝛽𝑈1/2	𝒫ℱ𝒩𝛿𝛽𝑈1/2	NOUN
cana-5360	565	6	-	-	PUNCT
cana-5360	565	7	space	space	NOUN
cana-5360	565	8	,	,	PUNCT
cana-5360	565	9	𝐵	𝐵	NOUN
cana-5360	565	10	is	be	AUX
cana-5360	565	11	a	a	DET
cana-5360	565	12	𝒫ℱ𝒩𝑐𝑠	𝒫ℱ𝒩𝑐𝑠	NOUN
cana-5360	565	13	in	in	ADP
cana-5360	565	14	𝑈2	𝑈2	PROPN
cana-5360	565	15	and	and	CCONJ
cana-5360	565	16	𝒫ℱ𝒩𝑐𝑙(𝐵	𝒫ℱ𝒩𝑐𝑙(𝐵	PRON
cana-5360	565	17	)	)	PUNCT
cana-5360	566	1	=	=	SYM
cana-5360	566	2	𝐵.	𝐵.	PROPN
cana-5360	566	3	hence	hence	ADV
cana-5360	566	4	,	,	PUNCT
cana-5360	566	5	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	566	6	−1(𝐵	−1(𝐵	NOUN
cana-5360	566	7	)	)	PUNCT
cana-5360	567	1	=	=	SYM
cana-5360	567	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	567	3	−1(𝒫ℱ𝒩𝛿𝛽𝑐𝑙(𝐵	−1(𝒫ℱ𝒩𝛿𝛽𝑐𝑙(𝐵	NOUN
cana-5360	567	4	)	)	PUNCT
cana-5360	567	5	)	)	PUNCT
cana-5360	568	1	⊇	⊇	PROPN
cana-5360	568	2	𝒫ℱ𝒩𝛿𝛽𝑖𝑛𝑡(ℎ𝑃	𝒫ℱ𝒩𝛿𝛽𝑖𝑛𝑡(ℎ𝑃	ADJ
cana-5360	568	3	−1(𝐵	−1(𝐵	NOUN
cana-5360	568	4	)	)	PUNCT
cana-5360	568	5	)	)	PUNCT
cana-5360	568	6	.	.	PUNCT
cana-5360	569	1	but	but	CCONJ
cana-5360	569	2	clearly	clearly	ADV
cana-5360	569	3	,	,	PUNCT
cana-5360	569	4	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	569	5	−1(𝐵	−1(𝐵	NOUN
cana-5360	569	6	)	)	PUNCT
cana-5360	569	7	⊇	⊇	PROPN
cana-5360	569	8	𝒫ℱ𝒩𝑖𝑛𝑡(ℎ𝑃	𝒫ℱ𝒩𝑖𝑛𝑡(ℎ𝑃	PROPN
cana-5360	569	9	−1(𝐵	−1(𝐵	NOUN
cana-5360	569	10	)	)	PUNCT
cana-5360	569	11	)	)	PUNCT
cana-5360	569	12	.	.	PUNCT
cana-5360	570	1	therefore	therefore	ADV
cana-5360	570	2	,	,	PUNCT
cana-5360	570	3	𝒫ℱ𝒩𝑖𝑛𝑡(ℎ𝑃	𝒫ℱ𝒩𝑖𝑛𝑡(ℎ𝑃	PROPN
cana-5360	570	4	−1(𝐵	−1(𝐵	NOUN
cana-5360	570	5	)	)	PUNCT
cana-5360	570	6	)	)	PUNCT
cana-5360	571	1	=	=	PUNCT
cana-5360	571	2	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	571	3	−1(𝐵	−1(𝐵	NOUN
cana-5360	571	4	)	)	PUNCT
cana-5360	571	5	.	.	PUNCT
cana-5360	572	1	this	this	PRON
cana-5360	572	2	implies	imply	VERB
cana-5360	572	3	,	,	PUNCT
cana-5360	572	4	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	572	5	−1(𝐵	−1(𝐵	NOUN
cana-5360	572	6	)	)	PUNCT
cana-5360	572	7	is	be	AUX
cana-5360	572	8	a	a	DET
cana-5360	572	9	𝒫ℱ𝒩𝑜𝑠	𝒫ℱ𝒩𝑜𝑠	NOUN
cana-5360	572	10	and	and	CCONJ
cana-5360	572	11	hence	hence	ADV
cana-5360	572	12	,	,	PUNCT
cana-5360	572	13	it	it	PRON
cana-5360	572	14	is	be	AUX
cana-5360	572	15	a	a	DET
cana-5360	572	16	𝒫ℱ𝒩𝛿𝛽𝑜𝑠	𝒫ℱ𝒩𝛿𝛽𝑜𝑠	PROPN
cana-5360	572	17	in	in	ADP
cana-5360	572	18	𝑋1	𝑋1	PROPN
cana-5360	572	19	.	.	PUNCT
cana-5360	573	1	thus	thus	ADV
cana-5360	573	2	,	,	PUNCT
cana-5360	573	3	ℎ𝑃	ℎ𝑃	PROPN
cana-5360	573	4	is	be	AUX
cana-5360	573	5	a	a	DET
cana-5360	573	6	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐼𝑟𝑟	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐼𝑟𝑟	PROPN
cana-5360	573	7	map	map	NOUN
cana-5360	573	8	.	.	PUNCT
cana-5360	574	1	the	the	DET
cana-5360	574	2	proof	proof	NOUN
cana-5360	574	3	of	of	ADP
cana-5360	574	4	the	the	DET
cana-5360	574	5	others	other	NOUN
cana-5360	574	6	are	be	AUX
cana-5360	574	7	similar	similar	ADJ
cana-5360	574	8	.	.	PUNCT
cana-5360	575	1	width	width	VERB
cana-5360	575	2	0.22	0.22	NUM
cana-5360	575	3	true	true	ADJ
cana-5360	575	4	cm	cm	NOUN
cana-5360	575	5	height	height	NOUN
cana-5360	575	6	0.22	0.22	NUM
cana-5360	575	7	true	true	ADJ
cana-5360	575	8	cm	cm	NOUN
cana-5360	575	9	depth	depth	NOUN
cana-5360	575	10	0pt	0pt	NOUN
cana-5360	575	11	5	5	NUM
cana-5360	575	12	application	application	NOUN
cana-5360	575	13	measures	measure	NOUN
cana-5360	575	14	of	of	ADP
cana-5360	575	15	similarity	similarity	NOUN
cana-5360	575	16	is	be	AUX
cana-5360	575	17	a	a	DET
cana-5360	575	18	real	real	ADV
cana-5360	575	19	-	-	PUNCT
cana-5360	575	20	valued	value	VERB
cana-5360	575	21	function	function	NOUN
cana-5360	575	22	which	which	PRON
cana-5360	575	23	quantifies	quantify	VERB
cana-5360	575	24	the	the	DET
cana-5360	575	25	similarity	similarity	NOUN
cana-5360	575	26	between	between	ADP
cana-5360	575	27	two	two	NUM
cana-5360	575	28	pythagoren	pythagoren	NOUN
cana-5360	575	29	fuzzy	fuzzy	ADJ
cana-5360	575	30	sets	set	NOUN
cana-5360	575	31	and	and	CCONJ
cana-5360	575	32	its	its	PRON
cana-5360	575	33	value	value	NOUN
cana-5360	575	34	is	be	AUX
cana-5360	575	35	always	always	ADV
cana-5360	575	36	expressed	express	VERB
cana-5360	575	37	as	as	ADP
cana-5360	575	38	a	a	DET
cana-5360	575	39	number	number	NOUN
cana-5360	575	40	between	between	ADP
cana-5360	575	41	0	0	NUM
cana-5360	575	42	and	and	CCONJ
cana-5360	575	43	1	1	NUM
cana-5360	575	44	.	.	NOUN
cana-5360	575	45	0	0	NUM
cana-5360	575	46	,	,	PUNCT
cana-5360	575	47	a	a	DET
cana-5360	575	48	low	low	ADJ
cana-5360	575	49	level	level	NOUN
cana-5360	575	50	of	of	ADP
cana-5360	575	51	similarity	similarity	NOUN
cana-5360	575	52	and	and	CCONJ
cana-5360	575	53	1	1	NUM
cana-5360	575	54	,	,	PUNCT
cana-5360	575	55	a	a	DET
cana-5360	575	56	high	high	ADJ
cana-5360	575	57	level	level	NOUN
cana-5360	575	58	of	of	ADP
cana-5360	575	59	similarity	similarity	NOUN
cana-5360	575	60	.	.	PUNCT
cana-5360	576	1	communications	communication	NOUN
cana-5360	576	2	on	on	ADP
cana-5360	576	3	applied	apply	VERB
cana-5360	576	4	nonlinear	nonlinear	ADJ
cana-5360	576	5	analysis	analysis	NOUN
cana-5360	576	6	issn	issn	NOUN
cana-5360	576	7	:	:	PUNCT
cana-5360	576	8	1074	1074	NUM
cana-5360	576	9	-	-	PUNCT
cana-5360	576	10	133x	133x	NUM
cana-5360	576	11	vol	vol	VERB
cana-5360	576	12	32	32	NUM
cana-5360	576	13	no	no	NOUN
cana-5360	576	14	.	.	PUNCT
cana-5360	577	1	10s	10	NOUN
cana-5360	577	2	(	(	PUNCT
cana-5360	577	3	2025	2025	NUM
cana-5360	577	4	)	)	PUNCT
cana-5360	577	5	1942	1942	NUM
cana-5360	577	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5360	577	7	example	example	NOUN
cana-5360	577	8	5.1	5.1	NUM
cana-5360	577	9	gemstones	gemstone	NOUN
cana-5360	577	10	within	within	ADP
cana-5360	577	11	a	a	DET
cana-5360	577	12	species	specie	NOUN
cana-5360	577	13	can	can	AUX
cana-5360	577	14	exhibit	exhibit	VERB
cana-5360	577	15	distinct	distinct	ADJ
cana-5360	577	16	colors	color	NOUN
cana-5360	577	17	or	or	CCONJ
cana-5360	577	18	optical	optical	ADJ
cana-5360	577	19	characteristics	characteristic	NOUN
cana-5360	577	20	,	,	PUNCT
cana-5360	577	21	which	which	PRON
cana-5360	577	22	are	be	AUX
cana-5360	577	23	prized	prize	VERB
cana-5360	577	24	by	by	ADP
cana-5360	577	25	gemologists	gemologist	NOUN
cana-5360	577	26	and	and	CCONJ
cana-5360	577	27	enthusiasts	enthusiast	NOUN
cana-5360	577	28	alike	alike	ADV
cana-5360	577	29	.	.	PUNCT
cana-5360	578	1	these	these	DET
cana-5360	578	2	unique	unique	ADJ
cana-5360	578	3	features	feature	NOUN
cana-5360	578	4	play	play	VERB
cana-5360	578	5	a	a	DET
cana-5360	578	6	crucial	crucial	ADJ
cana-5360	578	7	role	role	NOUN
cana-5360	578	8	in	in	ADP
cana-5360	578	9	determining	determine	VERB
cana-5360	578	10	the	the	DET
cana-5360	578	11	gemstone	gemstone	NOUN
cana-5360	578	12	’s	’s	PART
cana-5360	578	13	beauty	beauty	NOUN
cana-5360	578	14	,	,	PUNCT
cana-5360	578	15	rarity	rarity	NOUN
cana-5360	578	16	,	,	PUNCT
cana-5360	578	17	and	and	CCONJ
cana-5360	578	18	ultimately	ultimately	ADV
cana-5360	578	19	,	,	PUNCT
cana-5360	578	20	its	its	PRON
cana-5360	578	21	value	value	NOUN
cana-5360	578	22	.	.	PUNCT
cana-5360	579	1	a	a	DET
cana-5360	579	2	vast	vast	ADJ
cana-5360	579	3	array	array	NOUN
cana-5360	579	4	of	of	ADP
cana-5360	579	5	vibrant	vibrant	ADJ
cana-5360	579	6	and	and	CCONJ
cana-5360	579	7	colorful	colorful	ADJ
cana-5360	579	8	gemstones	gemstone	NOUN
cana-5360	579	9	,	,	PUNCT
cana-5360	579	10	representing	represent	VERB
cana-5360	579	11	various	various	ADJ
cana-5360	579	12	types	type	NOUN
cana-5360	579	13	,	,	PUNCT
cana-5360	579	14	can	can	AUX
cana-5360	579	15	be	be	AUX
cana-5360	579	16	found	find	VERB
cana-5360	579	17	in	in	ADP
cana-5360	579	18	different	different	ADJ
cana-5360	579	19	regions	region	NOUN
cana-5360	579	20	of	of	ADP
cana-5360	579	21	particular	particular	ADJ
cana-5360	579	22	area	area	NOUN
cana-5360	579	23	.	.	PUNCT
cana-5360	580	1	a	a	DET
cana-5360	580	2	panel	panel	NOUN
cana-5360	580	3	of	of	ADP
cana-5360	580	4	experts	expert	NOUN
cana-5360	580	5	specializing	specialize	VERB
cana-5360	580	6	in	in	ADP
cana-5360	580	7	gemology	gemology	NOUN
cana-5360	580	8	aims	aim	VERB
cana-5360	580	9	to	to	PART
cana-5360	580	10	rank	rank	VERB
cana-5360	580	11	several	several	ADJ
cana-5360	580	12	of	of	ADP
cana-5360	580	13	these	these	DET
cana-5360	580	14	gemstone	gemstone	NOUN
cana-5360	580	15	varieties	variety	NOUN
cana-5360	580	16	in	in	ADP
cana-5360	580	17	order	order	NOUN
cana-5360	580	18	of	of	ADP
cana-5360	580	19	preference	preference	NOUN
cana-5360	580	20	based	base	VERB
cana-5360	580	21	on	on	ADP
cana-5360	580	22	a	a	DET
cana-5360	580	23	set	set	NOUN
cana-5360	580	24	of	of	ADP
cana-5360	580	25	predetermined	predetermine	VERB
cana-5360	580	26	criteria	criterion	NOUN
cana-5360	580	27	.	.	PUNCT
cana-5360	581	1	after	after	ADP
cana-5360	581	2	thorough	thorough	ADJ
cana-5360	581	3	discussion	discussion	NOUN
cana-5360	581	4	and	and	CCONJ
cana-5360	581	5	deliberation	deliberation	NOUN
cana-5360	581	6	,	,	PUNCT
cana-5360	581	7	the	the	DET
cana-5360	581	8	experts	expert	NOUN
cana-5360	581	9	have	have	AUX
cana-5360	581	10	identified	identify	VERB
cana-5360	581	11	five	five	NUM
cana-5360	581	12	gemstone	gemstone	NOUN
cana-5360	581	13	varieties	variety	NOUN
cana-5360	581	14	𝑆1	𝑆1	NOUN
cana-5360	581	15	,	,	PUNCT
cana-5360	581	16	𝑆2	𝑆2	PROPN
cana-5360	581	17	,	,	PUNCT
cana-5360	581	18	𝑆3	𝑆3	PROPN
cana-5360	581	19	,	,	PUNCT
cana-5360	581	20	𝑆4	𝑆4	PROPN
cana-5360	581	21	and	and	CCONJ
cana-5360	581	22	𝑆5	𝑆5	PROPN
cana-5360	581	23	as	as	ADP
cana-5360	581	24	alternatives	alternative	NOUN
cana-5360	581	25	for	for	ADP
cana-5360	581	26	ranking	ranking	NOUN
cana-5360	581	27	.	.	PUNCT
cana-5360	582	1	the	the	DET
cana-5360	582	2	ranking	rank	VERB
cana-5360	582	3	decision	decision	NOUN
cana-5360	582	4	will	will	AUX
cana-5360	582	5	be	be	AUX
cana-5360	582	6	based	base	VERB
cana-5360	582	7	on	on	ADP
cana-5360	582	8	the	the	DET
cana-5360	582	9	following	follow	VERB
cana-5360	582	10	four	four	NUM
cana-5360	582	11	key	key	ADJ
cana-5360	582	12	criteria	criterion	NOUN
cana-5360	582	13	’s	’s	PART
cana-5360	582	14	𝐶𝑗	𝐶𝑗	NOUN
cana-5360	582	15	,	,	PUNCT
cana-5360	582	16	𝑗	𝑗	NOUN
cana-5360	582	17	=	=	SYM
cana-5360	582	18	1	1	NUM
cana-5360	582	19	,	,	PUNCT
cana-5360	582	20	2	2	NUM
cana-5360	582	21	,	,	PUNCT
cana-5360	582	22	3	3	NUM
cana-5360	582	23	,	,	PUNCT
cana-5360	582	24	4	4	NUM
cana-5360	582	25	:	:	PUNCT
cana-5360	582	26	color	color	NOUN
cana-5360	582	27	and	and	CCONJ
cana-5360	582	28	clarity	clarity	NOUN
cana-5360	582	29	is	be	AUX
cana-5360	582	30	𝐶1	𝐶1	PRON
cana-5360	582	31	,	,	PUNCT
cana-5360	582	32	cut	cut	VERB
cana-5360	582	33	and	and	CCONJ
cana-5360	582	34	polish	polish	NOUN
cana-5360	582	35	is	be	AUX
cana-5360	582	36	𝐶2	𝐶2	ADJ
cana-5360	582	37	,	,	PUNCT
cana-5360	582	38	carat	carat	NOUN
cana-5360	582	39	and	and	CCONJ
cana-5360	582	40	luster	luster	NOUN
cana-5360	582	41	or	or	CCONJ
cana-5360	582	42	originality	originality	NOUN
cana-5360	582	43	is	be	AUX
cana-5360	582	44	𝐶3	𝐶3	ADJ
cana-5360	582	45	and	and	CCONJ
cana-5360	582	46	hardness	hardness	NOUN
cana-5360	582	47	is	be	AUX
cana-5360	582	48	𝐶4	𝐶4	NOUN
cana-5360	582	49	.	.	PUNCT
cana-5360	583	1	now	now	ADV
cana-5360	583	2	,	,	PUNCT
cana-5360	583	3	the	the	DET
cana-5360	583	4	experts	expert	NOUN
cana-5360	583	5	evaluate	evaluate	VERB
cana-5360	583	6	the	the	DET
cana-5360	583	7	alternatives	alternative	NOUN
cana-5360	583	8	𝑆𝑖	𝑆𝑖	PROPN
cana-5360	583	9	,	,	PUNCT
cana-5360	583	10	𝑖	𝑖	SYM
cana-5360	583	11	=	=	NOUN
cana-5360	583	12	1,2,3,4	1,2,3,4	NUM
cana-5360	583	13	under	under	ADP
cana-5360	583	14	the	the	DET
cana-5360	583	15	criteria𝐶𝑗	criteria𝐶𝑗	NOUN
cana-5360	583	16	,	,	PUNCT
cana-5360	583	17	𝑗	𝑗	PROPN
cana-5360	583	18	=	=	NOUN
cana-5360	583	19	1,2,3,4	1,2,3,4	NUM
cana-5360	583	20	which	which	PRON
cana-5360	583	21	can	can	AUX
cana-5360	583	22	be	be	AUX
cana-5360	583	23	represented	represent	VERB
cana-5360	583	24	by	by	ADP
cana-5360	583	25	the	the	DET
cana-5360	583	26	following	follow	VERB
cana-5360	583	27	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-5360	583	28	’s	’s	NOUN
cana-5360	583	29	.	.	PUNCT
cana-5360	584	1	𝑆1	𝑆1	NOUN
cana-5360	584	2	=	=	SYM
cana-5360	584	3	{	{	PUNCT
cana-5360	584	4	<	<	X
cana-5360	584	5	𝐶1	𝐶1	PROPN
cana-5360	584	6	;	;	PUNCT
cana-5360	584	7	0.8,0.4	0.8,0.4	NUM
cana-5360	585	1	>	>	PUNCT
cana-5360	585	2	,	,	PUNCT
cana-5360	585	3	<	<	X
cana-5360	585	4	𝐶2	𝐶2	PROPN
cana-5360	585	5	;	;	PUNCT
cana-5360	585	6	0.3,0.8	0.3,0.8	PROPN
cana-5360	585	7	>	>	X
cana-5360	585	8	,	,	PUNCT
cana-5360	585	9	<	<	X
cana-5360	585	10	𝐶3	𝐶3	PROPN
cana-5360	585	11	;	;	PUNCT
cana-5360	585	12	0.6,0.3	0.6,0.3	PROPN
cana-5360	585	13	>	>	X
cana-5360	585	14	,	,	PUNCT
cana-5360	585	15	<	<	X
cana-5360	585	16	𝐶4	𝐶4	NOUN
cana-5360	585	17	;	;	PUNCT
cana-5360	585	18	0.6,0.4	0.6,0.4	NUM
cana-5360	585	19	>	>	PUNCT
cana-5360	585	20	}	}	PUNCT
cana-5360	585	21	𝑆2	𝑆2	PROPN
cana-5360	585	22	=	=	PUNCT
cana-5360	585	23	{	{	PUNCT
cana-5360	585	24	<	<	X
cana-5360	585	25	𝐶1	𝐶1	PROPN
cana-5360	585	26	;	;	PUNCT
cana-5360	585	27	0.4,0.7	0.4,0.7	PROPN
cana-5360	585	28	>	>	X
cana-5360	585	29	,	,	PUNCT
cana-5360	585	30	<	<	X
cana-5360	585	31	𝐶2	𝐶2	PROPN
cana-5360	585	32	;	;	PUNCT
cana-5360	585	33	0.3,0.8	0.3,0.8	PROPN
cana-5360	585	34	>	>	X
cana-5360	585	35	,	,	PUNCT
cana-5360	585	36	<	<	X
cana-5360	585	37	𝐶3	𝐶3	PROPN
cana-5360	585	38	;	;	PUNCT
cana-5360	585	39	0.5,0.6	0.5,0.6	PROPN
cana-5360	585	40	>	>	X
cana-5360	585	41	,	,	PUNCT
cana-5360	585	42	<	<	X
cana-5360	585	43	𝐶4	𝐶4	NOUN
cana-5360	585	44	;	;	PUNCT
cana-5360	585	45	0.6,0.5	0.6,0.5	NUM
cana-5360	585	46	>	>	SYM
cana-5360	585	47	}	}	PUNCT
cana-5360	585	48	𝑆3	𝑆3	PROPN
cana-5360	585	49	=	=	PUNCT
cana-5360	585	50	{	{	PUNCT
cana-5360	585	51	<	<	X
cana-5360	585	52	𝐶1	𝐶1	PROPN
cana-5360	585	53	;	;	PUNCT
cana-5360	585	54	0.6,0.5	0.6,0.5	NUM
cana-5360	585	55	>	>	X
cana-5360	585	56	,	,	PUNCT
cana-5360	585	57	<	<	X
cana-5360	585	58	𝐶2	𝐶2	PROPN
cana-5360	585	59	;	;	PUNCT
cana-5360	585	60	0.7,0.4	0.7,0.4	NUM
cana-5360	585	61	>	>	PUNCT
cana-5360	585	62	,	,	PUNCT
cana-5360	585	63	<	<	X
cana-5360	585	64	𝐶3	𝐶3	PROPN
cana-5360	585	65	;	;	PUNCT
cana-5360	585	66	0.3,0.8	0.3,0.8	PROPN
cana-5360	585	67	>	>	X
cana-5360	585	68	,	,	PUNCT
cana-5360	585	69	<	<	X
cana-5360	585	70	𝐶4	𝐶4	PROPN
cana-5360	585	71	;	;	PUNCT
cana-5360	585	72	0.3,0.5	0.3,0.5	NUM
cana-5360	585	73	>	>	PUNCT
cana-5360	585	74	}	}	PUNCT
cana-5360	585	75	𝑆4	𝑆4	PROPN
cana-5360	585	76	=	=	SYM
cana-5360	585	77	{	{	PUNCT
cana-5360	585	78	<	<	X
cana-5360	585	79	𝐶1	𝐶1	PROPN
cana-5360	585	80	;	;	PUNCT
cana-5360	585	81	0.7,0.4	0.7,0.4	NUM
cana-5360	585	82	>	>	PUNCT
cana-5360	585	83	,	,	PUNCT
cana-5360	585	84	<	<	X
cana-5360	585	85	𝐶2	𝐶2	PROPN
cana-5360	585	86	;	;	PUNCT
cana-5360	585	87	0.4,0.7	0.4,0.7	PROPN
cana-5360	585	88	>	>	X
cana-5360	585	89	,	,	PUNCT
cana-5360	585	90	<	<	X
cana-5360	585	91	𝐶3	𝐶3	PROPN
cana-5360	585	92	;	;	PUNCT
cana-5360	585	93	0.5,0.7	0.5,0.7	PROPN
cana-5360	585	94	>	>	PUNCT
cana-5360	585	95	,	,	PUNCT
cana-5360	585	96	<	<	X
cana-5360	585	97	𝐶4	𝐶4	NOUN
cana-5360	585	98	;	;	PUNCT
cana-5360	585	99	0.6,0.4	0.6,0.4	NUM
cana-5360	585	100	>	>	PUNCT
cana-5360	585	101	}	}	PUNCT
cana-5360	585	102	𝑆5	𝑆5	PROPN
cana-5360	585	103	=	=	SYM
cana-5360	585	104	{	{	PUNCT
cana-5360	585	105	<	<	X
cana-5360	585	106	𝐶1	𝐶1	PROPN
cana-5360	585	107	;	;	PUNCT
cana-5360	585	108	0.9,0.2	0.9,0.2	PROPN
cana-5360	585	109	>	>	X
cana-5360	585	110	,	,	PUNCT
cana-5360	585	111	<	<	X
cana-5360	585	112	𝐶2	𝐶2	X
cana-5360	585	113	;	;	PUNCT
cana-5360	585	114	0.4,0.8	0.4,0.8	PROPN
cana-5360	585	115	>	>	X
cana-5360	585	116	,	,	PUNCT
cana-5360	585	117	<	<	X
cana-5360	585	118	𝐶3	𝐶3	PROPN
cana-5360	585	119	;	;	PUNCT
cana-5360	585	120	0.6,0.3	0.6,0.3	PROPN
cana-5360	585	121	>	>	X
cana-5360	585	122	,	,	PUNCT
cana-5360	585	123	<	<	X
cana-5360	585	124	𝐶4	𝐶4	PROPN
cana-5360	585	125	;	;	PUNCT
cana-5360	585	126	0.7,0.2	0.7,0.2	PROPN
cana-5360	585	127	>	>	PUNCT
cana-5360	585	128	}	}	PUNCT
cana-5360	585	129	these	these	DET
cana-5360	585	130	𝑝𝑓𝑠s	𝑝𝑓𝑠s	NOUN
cana-5360	585	131	are	be	AUX
cana-5360	585	132	shown	show	VERB
cana-5360	585	133	with	with	ADP
cana-5360	585	134	the	the	DET
cana-5360	585	135	help	help	NOUN
cana-5360	585	136	of	of	ADP
cana-5360	585	137	decision	decision	NOUN
cana-5360	585	138	matrix	matrix	NOUN
cana-5360	585	139	in	in	ADP
cana-5360	585	140	table	table	NOUN
cana-5360	585	141	1	1	NUM
cana-5360	585	142	.	.	PUNCT
cana-5360	586	1	the	the	DET
cana-5360	586	2	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-5360	586	3	of	of	ADP
cana-5360	586	4	positive	positive	ADJ
cana-5360	586	5	index	index	NOUN
cana-5360	586	6	set	set	VERB
cana-5360	586	7	and	and	CCONJ
cana-5360	586	8	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-5360	586	9	of	of	ADP
cana-5360	586	10	negative	negative	ADJ
cana-5360	586	11	index	index	NOUN
cana-5360	586	12	set	set	NOUN
cana-5360	586	13	are	be	AUX
cana-5360	586	14	constructed	construct	VERB
cana-5360	586	15	respectively	respectively	ADV
cana-5360	586	16	as	as	SCONJ
cana-5360	586	17	follows	follow	VERB
cana-5360	586	18	:	:	PUNCT
cana-5360	587	1	𝑆𝑝	𝑆𝑝	PROPN
cana-5360	587	2	=	=	PUNCT
cana-5360	587	3	{	{	PUNCT
cana-5360	587	4	<	<	X
cana-5360	587	5	𝐶1	𝐶1	PROPN
cana-5360	587	6	;	;	PUNCT
cana-5360	587	7	1,0	1,0	NUM
cana-5360	587	8	>	>	PUNCT
cana-5360	587	9	,	,	PUNCT
cana-5360	587	10	<	<	X
cana-5360	587	11	𝐶2	𝐶2	PROPN
cana-5360	587	12	;	;	PUNCT
cana-5360	587	13	1,0	1,0	NUM
cana-5360	587	14	>	>	PUNCT
cana-5360	587	15	,	,	PUNCT
cana-5360	587	16	<	<	X
cana-5360	587	17	𝐶1	𝐶1	ADJ
cana-5360	587	18	;	;	PUNCT
cana-5360	587	19	1,0	1,0	NUM
cana-5360	587	20	>	>	PUNCT
cana-5360	587	21	,	,	PUNCT
cana-5360	587	22	<	<	X
cana-5360	587	23	𝐶2	𝐶2	PROPN
cana-5360	587	24	;	;	PUNCT
cana-5360	587	25	1,0	1,0	NUM
cana-5360	587	26	>	>	PUNCT
cana-5360	587	27	}	}	PUNCT
cana-5360	587	28	𝑆𝑛	𝑆𝑛	NOUN
cana-5360	587	29	=	=	PUNCT
cana-5360	587	30	{	{	PUNCT
cana-5360	587	31	<	<	X
cana-5360	587	32	𝐶1	𝐶1	PROPN
cana-5360	587	33	;	;	PUNCT
cana-5360	587	34	0,1	0,1	NUM
cana-5360	587	35	>	>	PUNCT
cana-5360	587	36	,	,	PUNCT
cana-5360	587	37	<	<	X
cana-5360	587	38	𝐶2	𝐶2	X
cana-5360	587	39	;	;	PUNCT
cana-5360	587	40	0,1	0,1	NUM
cana-5360	587	41	>	>	PUNCT
cana-5360	587	42	,	,	PUNCT
cana-5360	587	43	<	<	X
cana-5360	587	44	𝐶1	𝐶1	X
cana-5360	587	45	;	;	PUNCT
cana-5360	587	46	0,1	0,1	NUM
cana-5360	587	47	>	>	PUNCT
cana-5360	587	48	,	,	PUNCT
cana-5360	587	49	<	<	X
cana-5360	587	50	𝐶2	𝐶2	X
cana-5360	587	51	;	;	PUNCT
cana-5360	587	52	0,1	0,1	NUM
cana-5360	587	53	>	>	PUNCT
cana-5360	587	54	}	}	PUNCT
cana-5360	587	55	next	next	ADV
cana-5360	587	56	,	,	PUNCT
cana-5360	587	57	calculating	calculate	VERB
cana-5360	587	58	the	the	DET
cana-5360	587	59	zhang	zhang	PROPN
cana-5360	587	60	similarity	similarity	NOUN
cana-5360	587	61	between	between	ADP
cana-5360	587	62	each	each	DET
cana-5360	587	63	alternatives	alternative	NOUN
cana-5360	587	64	𝑆𝑖	𝑆𝑖	PROPN
cana-5360	587	65	to	to	ADP
cana-5360	587	66	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-5360	587	67	of	of	ADP
cana-5360	587	68	positive	positive	ADJ
cana-5360	587	69	index	index	NOUN
cana-5360	587	70	set	set	VERB
cana-5360	587	71	and	and	CCONJ
cana-5360	587	72	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-5360	587	73	of	of	ADP
cana-5360	587	74	negative	negative	ADJ
cana-5360	587	75	index	index	NOUN
cana-5360	587	76	set	set	VERB
cana-5360	587	77	respectively	respectively	ADV
cana-5360	587	78	.	.	PUNCT
cana-5360	588	1	the	the	DET
cana-5360	588	2	the	the	DET
cana-5360	588	3	results	result	NOUN
cana-5360	588	4	are	be	AUX
cana-5360	588	5	shown	show	VERB
cana-5360	588	6	in	in	ADP
cana-5360	588	7	the	the	DET
cana-5360	588	8	table	table	NOUN
cana-5360	588	9	2.the	2.the	DET
cana-5360	588	10	similarity	similarity	NOUN
cana-5360	588	11	between	between	ADP
cana-5360	588	12	each	each	DET
cana-5360	588	13	alternative	alternative	ADJ
cana-5360	588	14	𝑆𝑖	𝑆𝑖	PROPN
cana-5360	588	15	to	to	ADP
cana-5360	588	16	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-5360	588	17	of	of	ADP
cana-5360	588	18	positive	positive	ADJ
cana-5360	588	19	index	index	NOUN
cana-5360	588	20	set	set	VERB
cana-5360	588	21	and	and	CCONJ
cana-5360	588	22	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-5360	588	23	of	of	ADP
cana-5360	588	24	negative	negative	ADJ
cana-5360	588	25	index	index	NOUN
cana-5360	588	26	set	set	VERB
cana-5360	588	27	respectively	respectively	ADV
cana-5360	588	28	are	be	AUX
cana-5360	588	29	utilized	utilize	VERB
cana-5360	588	30	to	to	PART
cana-5360	588	31	calculate	calculate	VERB
cana-5360	588	32	the	the	DET
cana-5360	588	33	degree	degree	NOUN
cana-5360	588	34	of	of	ADP
cana-5360	588	35	closeness	closeness	NOUN
cana-5360	589	1	[	[	X
cana-5360	589	2	41	41	NUM
cana-5360	589	3	]	]	SYM
cana-5360	589	4	𝒟𝒞(𝑆𝑖	𝒟𝒞(𝑆𝑖	NOUN
cana-5360	589	5	)	)	PUNCT
cana-5360	589	6	is	be	AUX
cana-5360	589	7	calculated	calculate	VERB
cana-5360	589	8	as	as	ADP
cana-5360	589	9	follows	follow	NOUN
cana-5360	589	10	.	.	PUNCT
cana-5360	590	1	𝒟𝒞(𝑆𝑖	𝒟𝒞(𝑆𝑖	X
cana-5360	590	2	)	)	PUNCT
cana-5360	591	1	=	=	SYM
cana-5360	591	2	𝒮𝑍(𝑆𝑛,𝑆𝑖	𝒮𝑍(𝑆𝑛,𝑆𝑖	X
cana-5360	591	3	)	)	PUNCT
cana-5360	591	4	𝒮𝑍(𝑆𝑝,𝑆𝑖)+𝒮𝑍(𝑆𝑛,𝑆𝑖	𝒮𝑍(𝑆𝑝,𝑆𝑖)+𝒮𝑍(𝑆𝑛,𝑆𝑖	NUM
cana-5360	591	5	)	)	PUNCT
cana-5360	591	6	and	and	CCONJ
cana-5360	591	7	the	the	DET
cana-5360	591	8	results	result	NOUN
cana-5360	591	9	are	be	AUX
cana-5360	591	10	display	display	NOUN
cana-5360	591	11	in	in	ADP
cana-5360	591	12	the	the	DET
cana-5360	591	13	table	table	NOUN
cana-5360	591	14	3	3	NUM
cana-5360	591	15	.	.	PUNCT
cana-5360	591	16	table	table	NOUN
cana-5360	591	17	3	3	NUM
cana-5360	591	18	,	,	PUNCT
cana-5360	591	19	shows	show	VERB
cana-5360	591	20	the	the	DET
cana-5360	591	21	degree	degree	NOUN
cana-5360	591	22	of	of	ADP
cana-5360	591	23	closeness	closeness	NOUN
cana-5360	591	24	of	of	ADP
cana-5360	591	25	each	each	DET
cana-5360	591	26	alternative	alternative	ADJ
cana-5360	591	27	𝑆𝑖	𝑆𝑖	PROPN
cana-5360	591	28	over	over	ADP
cana-5360	591	29	the	the	DET
cana-5360	591	30	criteria	criterion	NOUN
cana-5360	592	1	𝐶𝑗	𝐶𝑗	NOUN
cana-5360	592	2	:	:	PUNCT
cana-5360	592	3	the	the	DET
cana-5360	592	4	degree	degree	NOUN
cana-5360	592	5	of	of	ADP
cana-5360	592	6	closeness	closeness	NOUN
cana-5360	592	7	is	be	AUX
cana-5360	592	8	used	use	VERB
cana-5360	592	9	to	to	PART
cana-5360	592	10	rank	rank	VERB
cana-5360	592	11	the	the	DET
cana-5360	592	12	alternative	alternative	ADJ
cana-5360	592	13	𝑆𝑖	𝑆𝑖	PROPN
cana-5360	592	14	in	in	ADP
cana-5360	592	15	preference	preference	NOUN
cana-5360	592	16	order	order	NOUN
cana-5360	592	17	.	.	PUNCT
cana-5360	593	1	the	the	DET
cana-5360	593	2	results	result	NOUN
cana-5360	593	3	are	be	AUX
cana-5360	593	4	exhibited	exhibit	VERB
cana-5360	593	5	in	in	ADP
cana-5360	593	6	table	table	NOUN
cana-5360	593	7	4	4	NUM
cana-5360	593	8	.	.	PUNCT
cana-5360	593	9	table	table	NOUN
cana-5360	593	10	4	4	NUM
cana-5360	593	11	,	,	PUNCT
cana-5360	593	12	shows	show	VERB
cana-5360	593	13	the	the	DET
cana-5360	593	14	rank	rank	NOUN
cana-5360	593	15	of	of	ADP
cana-5360	593	16	alternative	alternative	ADJ
cana-5360	593	17	𝑆𝑖	𝑆𝑖	PROPN
cana-5360	593	18	according	accord	VERB
cana-5360	593	19	to	to	ADP
cana-5360	593	20	the	the	DET
cana-5360	593	21	degree	degree	NOUN
cana-5360	593	22	of	of	ADP
cana-5360	593	23	closeness	closeness	NOUN
cana-5360	593	24	in	in	ADP
cana-5360	593	25	preferred	preferred	ADJ
cana-5360	593	26	order.the	order.the	DET
cana-5360	593	27	alternative	alternative	ADJ
cana-5360	593	28	𝑆𝑖	𝑆𝑖	PROPN
cana-5360	593	29	with	with	ADP
cana-5360	593	30	the	the	DET
cana-5360	593	31	largest	large	ADJ
cana-5360	593	32	degree	degree	NOUN
cana-5360	593	33	of	of	ADP
cana-5360	593	34	closeness	closeness	NOUN
cana-5360	593	35	is	be	AUX
cana-5360	593	36	considered	consider	VERB
cana-5360	593	37	as	as	ADP
cana-5360	593	38	the	the	DET
cana-5360	593	39	best	good	ADJ
cana-5360	593	40	alternative	alternative	NOUN
cana-5360	593	41	.	.	PUNCT
cana-5360	594	1	table	table	NOUN
cana-5360	594	2	1:𝒑𝒇𝒔	1:𝒑𝒇𝒔	NOUN
cana-5360	594	3	’s	’s	NOUN
cana-5360	594	4	of	of	ADP
cana-5360	594	5	alternatives	alternative	NOUN
cana-5360	594	6	alternative	alternative	ADJ
cana-5360	594	7	criteria	criterion	NOUN
cana-5360	594	8	1	1	NUM
cana-5360	594	9	(	(	PUNCT
cana-5360	594	10	𝐶1	𝐶1	NOUN
cana-5360	594	11	)	)	PUNCT
cana-5360	594	12	criteria	criterion	NOUN
cana-5360	594	13	2	2	NUM
cana-5360	594	14	(	(	PUNCT
cana-5360	594	15	𝐶2	𝐶2	ADJ
cana-5360	594	16	)	)	PUNCT
cana-5360	594	17	criteria	criterion	NOUN
cana-5360	594	18	3	3	NUM
cana-5360	594	19	(	(	PUNCT
cana-5360	594	20	𝐶3	𝐶3	NOUN
cana-5360	594	21	)	)	PUNCT
cana-5360	594	22	criteria	criterion	NOUN
cana-5360	594	23	4	4	NUM
cana-5360	594	24	(	(	PUNCT
cana-5360	594	25	𝐶4	𝐶4	NOUN
cana-5360	594	26	)	)	PUNCT
cana-5360	594	27	𝑆1	𝑆1	NOUN
cana-5360	594	28	<	<	X
cana-5360	594	29	𝑆1	𝑆1	NOUN
cana-5360	594	30	,	,	PUNCT
cana-5360	594	31	𝐶1	𝐶1	PRON
cana-5360	594	32	;	;	PUNCT
cana-5360	595	1	0.8,0.4	0.8,0.4	NUM
cana-5360	595	2	>	>	X
cana-5360	595	3	<	<	X
cana-5360	595	4	𝑆1	𝑆1	PROPN
cana-5360	595	5	,	,	PUNCT
cana-5360	595	6	𝐶2	𝐶2	ADJ
cana-5360	595	7	;	;	PUNCT
cana-5360	595	8	0.3,0.8	0.3,0.8	NUM
cana-5360	595	9	>	>	X
cana-5360	595	10	<	<	X
cana-5360	595	11	𝑆1	𝑆1	PROPN
cana-5360	595	12	,	,	PUNCT
cana-5360	595	13	𝐶3	𝐶3	PROPN
cana-5360	595	14	;	;	PUNCT
cana-5360	595	15	0.6,0.3	0.6,0.3	PROPN
cana-5360	595	16	>	>	X
cana-5360	595	17	<	<	X
cana-5360	595	18	𝑆1	𝑆1	PROPN
cana-5360	595	19	,	,	PUNCT
cana-5360	595	20	𝐶4	𝐶4	NOUN
cana-5360	595	21	;	;	PUNCT
cana-5360	595	22	0.6,0.4	0.6,0.4	NUM
cana-5360	595	23	>	>	X
cana-5360	595	24	𝑆2	𝑆2	PROPN
cana-5360	595	25	<	<	X
cana-5360	595	26	𝑆2	𝑆2	PROPN
cana-5360	595	27	,	,	PUNCT
cana-5360	595	28	𝐶1	𝐶1	PRON
cana-5360	595	29	;	;	PUNCT
cana-5360	595	30	0.4,0.7	0.4,0.7	PROPN
cana-5360	595	31	>	>	X
cana-5360	595	32	<	<	X
cana-5360	595	33	𝑆2	𝑆2	PROPN
cana-5360	595	34	,	,	PUNCT
cana-5360	595	35	𝐶2	𝐶2	ADJ
cana-5360	595	36	;	;	PUNCT
cana-5360	595	37	0.3,0.8	0.3,0.8	NUM
cana-5360	595	38	>	>	X
cana-5360	595	39	<	<	X
cana-5360	595	40	𝑆2	𝑆2	PROPN
cana-5360	595	41	,	,	PUNCT
cana-5360	595	42	𝐶3	𝐶3	PROPN
cana-5360	595	43	;	;	PUNCT
cana-5360	595	44	0.5,0.6	0.5,0.6	X
cana-5360	595	45	>	>	X
cana-5360	595	46	<	<	X
cana-5360	595	47	𝑆2	𝑆2	PROPN
cana-5360	595	48	,	,	PUNCT
cana-5360	595	49	𝐶4	𝐶4	NOUN
cana-5360	595	50	;	;	PUNCT
cana-5360	595	51	0.6,0.5	0.6,0.5	NUM
cana-5360	595	52	>	>	SYM
cana-5360	595	53	communications	communication	NOUN
cana-5360	595	54	on	on	ADP
cana-5360	595	55	applied	apply	VERB
cana-5360	595	56	nonlinear	nonlinear	ADJ
cana-5360	595	57	analysis	analysis	NOUN
cana-5360	595	58	issn	issn	NOUN
cana-5360	595	59	:	:	PUNCT
cana-5360	595	60	1074	1074	NUM
cana-5360	595	61	-	-	PUNCT
cana-5360	595	62	133x	133x	NUM
cana-5360	595	63	vol	vol	VERB
cana-5360	595	64	32	32	NUM
cana-5360	595	65	no	no	NOUN
cana-5360	595	66	.	.	PUNCT
cana-5360	596	1	10s	10	NOUN
cana-5360	596	2	(	(	PUNCT
cana-5360	596	3	2025	2025	NUM
cana-5360	596	4	)	)	PUNCT
cana-5360	596	5	1943	1943	NUM
cana-5360	596	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5360	597	1	𝑆3	𝑆3	PROPN
cana-5360	597	2	<	<	X
cana-5360	597	3	𝑆3	𝑆3	PROPN
cana-5360	597	4	,	,	PUNCT
cana-5360	597	5	𝐶1	𝐶1	PRON
cana-5360	597	6	;	;	PUNCT
cana-5360	597	7	0.6,0.5	0.6,0.5	NUM
cana-5360	597	8	>	>	SYM
cana-5360	597	9	<	<	X
cana-5360	597	10	𝑆3	𝑆3	PROPN
cana-5360	597	11	,	,	PUNCT
cana-5360	597	12	𝐶2	𝐶2	ADJ
cana-5360	597	13	;	;	PUNCT
cana-5360	597	14	0.7,0.4	0.7,0.4	NUM
cana-5360	597	15	>	>	X
cana-5360	597	16	<	<	X
cana-5360	597	17	𝑆3	𝑆3	PROPN
cana-5360	597	18	,	,	PUNCT
cana-5360	597	19	𝐶3	𝐶3	NOUN
cana-5360	597	20	;	;	PUNCT
cana-5360	597	21	0.3,0.8	0.3,0.8	NUM
cana-5360	597	22	>	>	X
cana-5360	597	23	<	<	X
cana-5360	597	24	𝑆3	𝑆3	PROPN
cana-5360	597	25	,	,	PUNCT
cana-5360	597	26	𝐶4	𝐶4	NOUN
cana-5360	597	27	;	;	PUNCT
cana-5360	597	28	0.3,0.5	0.3,0.5	NUM
cana-5360	597	29	>	>	X
cana-5360	597	30	𝑆4	𝑆4	PROPN
cana-5360	597	31	<	<	X
cana-5360	597	32	𝑆4	𝑆4	PROPN
cana-5360	597	33	,	,	PUNCT
cana-5360	597	34	𝐶1	𝐶1	PRON
cana-5360	597	35	;	;	PUNCT
cana-5360	597	36	0.7,0.4	0.7,0.4	NUM
cana-5360	597	37	>	>	X
cana-5360	597	38	<	<	X
cana-5360	597	39	𝑆4	𝑆4	PROPN
cana-5360	597	40	,	,	PUNCT
cana-5360	597	41	𝐶2	𝐶2	PROPN
cana-5360	597	42	;	;	PUNCT
cana-5360	597	43	0.4,0.7	0.4,0.7	PROPN
cana-5360	597	44	>	>	X
cana-5360	597	45	<	<	X
cana-5360	597	46	𝑆4	𝑆4	PROPN
cana-5360	597	47	,	,	PUNCT
cana-5360	597	48	𝐶3	𝐶3	PROPN
cana-5360	597	49	;	;	PUNCT
cana-5360	597	50	0.5,0.7	0.5,0.7	PROPN
cana-5360	597	51	>	>	X
cana-5360	597	52	<	<	X
cana-5360	597	53	𝑆4	𝑆4	PROPN
cana-5360	597	54	,	,	PUNCT
cana-5360	597	55	𝐶4	𝐶4	NOUN
cana-5360	597	56	;	;	PUNCT
cana-5360	598	1	0.6,0.4	0.6,0.4	NUM
cana-5360	598	2	>	>	X
cana-5360	599	1	𝑆5	𝑆5	PROPN
cana-5360	599	2	<	<	X
cana-5360	599	3	𝑆5	𝑆5	PROPN
cana-5360	599	4	,	,	PUNCT
cana-5360	599	5	𝐶1	𝐶1	PRON
cana-5360	599	6	;	;	PUNCT
cana-5360	599	7	0.9,0.2	0.9,0.2	X
cana-5360	599	8	>	>	X
cana-5360	599	9	<	<	X
cana-5360	599	10	𝑆5	𝑆5	PROPN
cana-5360	599	11	,	,	PUNCT
cana-5360	599	12	𝐶2	𝐶2	ADJ
cana-5360	599	13	;	;	PUNCT
cana-5360	599	14	0.4,0.8	0.4,0.8	PROPN
cana-5360	599	15	>	>	X
cana-5360	599	16	<	<	X
cana-5360	599	17	𝑆5	𝑆5	PROPN
cana-5360	599	18	,	,	PUNCT
cana-5360	599	19	𝐶3	𝐶3	PROPN
cana-5360	599	20	;	;	PUNCT
cana-5360	599	21	0.6,0.3	0.6,0.3	PROPN
cana-5360	599	22	>	>	X
cana-5360	599	23	<	<	X
cana-5360	599	24	𝑆5	𝑆5	PROPN
cana-5360	599	25	,	,	PUNCT
cana-5360	599	26	𝐶4	𝐶4	NOUN
cana-5360	599	27	;	;	PUNCT
cana-5360	599	28	0.7,0.2	0.7,0.2	PROPN
cana-5360	599	29	>	>	PUNCT
cana-5360	599	30	table	table	NOUN
cana-5360	600	1	2	2	NUM
cana-5360	600	2	:	:	PUNCT
cana-5360	600	3	zhang	zhang	PROPN
cana-5360	600	4	similarity	similarity	PROPN
cana-5360	600	5	measure	measure	NOUN
cana-5360	600	6	of	of	ADP
cana-5360	600	7	each	each	DET
cana-5360	600	8	alternative	alternative	NOUN
cana-5360	600	9	with	with	ADP
cana-5360	600	10	𝑺𝒑	𝑺𝒑	PROPN
cana-5360	600	11	and	and	CCONJ
cana-5360	600	12	𝑺𝒏	𝑺𝒏	PROPN
cana-5360	600	13	alternative	alternative	ADJ
cana-5360	600	14	𝒮𝑍(𝑆𝑝	𝒮𝑍(𝑆𝑝	NUM
cana-5360	600	15	,	,	PUNCT
cana-5360	600	16	𝑆𝑖	𝑆𝑖	PROPN
cana-5360	600	17	)	)	PUNCT
cana-5360	600	18	𝒮𝑍(𝑆𝑛	𝒮𝑍(𝑆𝑛	PROPN
cana-5360	600	19	,	,	PUNCT
cana-5360	600	20	𝑆𝑖	𝑆𝑖	PROPN
cana-5360	600	21	)	)	PUNCT
cana-5360	600	22	𝑆1	𝑆1	NOUN
cana-5360	600	23	0.476	0.476	NUM
cana-5360	600	24	1.000	1.000	NUM
cana-5360	600	25	𝑆2	𝑆2	NOUN
cana-5360	600	26	0.618	0.618	NUM
cana-5360	600	27	1.000	1.000	NUM
cana-5360	600	28	𝑆3	𝑆3	PROPN
cana-5360	600	29	0.536	0.536	NUM
cana-5360	600	30	1.000	1.000	NUM
cana-5360	600	31	𝑆4	𝑆4	PROPN
cana-5360	600	32	0.495	0.495	NUM
cana-5360	600	33	0.181	0.181	NUM
cana-5360	600	34	𝑆5	𝑆5	PROPN
cana-5360	600	35	0.588	0.588	NUM
cana-5360	600	36	0.090	0.090	NUM
cana-5360	600	37	table	table	NOUN
cana-5360	600	38	3	3	NUM
cana-5360	600	39	:	:	PUNCT
cana-5360	600	40	degree	degree	NOUN
cana-5360	600	41	of	of	ADP
cana-5360	600	42	closeness	closeness	NOUN
cana-5360	600	43	of	of	ADP
cana-5360	600	44	each	each	DET
cana-5360	600	45	alternative	alternative	ADJ
cana-5360	600	46	alternative	alternative	ADJ
cana-5360	600	47	𝒟𝒞(𝑆𝑖	𝒟𝒞(𝑆𝑖	NOUN
cana-5360	600	48	)	)	PUNCT
cana-5360	600	49	𝑆1	𝑆1	NOUN
cana-5360	600	50	0.68	0.68	NUM
cana-5360	600	51	𝑆2	𝑆2	NOUN
cana-5360	600	52	0.62	0.62	NUM
cana-5360	600	53	𝑆3	𝑆3	PROPN
cana-5360	600	54	0.65	0.65	NUM
cana-5360	600	55	𝑆4	𝑆4	PROPN
cana-5360	600	56	0.27	0.27	NUM
cana-5360	600	57	𝑆5	𝑆5	PROPN
cana-5360	600	58	0.13	0.13	NUM
cana-5360	600	59	table	table	NOUN
cana-5360	600	60	4	4	NUM
cana-5360	600	61	:	:	PUNCT
cana-5360	600	62	ranking	rank	VERB
cana-5360	600	63	of	of	ADP
cana-5360	600	64	each	each	DET
cana-5360	600	65	alternative	alternative	ADJ
cana-5360	600	66	similarity	similarity	NOUN
cana-5360	600	67	ranking	rank	VERB
cana-5360	600	68	𝒮𝑍(𝑆𝑖	𝒮𝑍(𝑆𝑖	NOUN
cana-5360	600	69	)	)	PUNCT
cana-5360	600	70	𝒟𝒞(𝑆5	𝒟𝒞(𝑆5	PROPN
cana-5360	600	71	)	)	PUNCT
cana-5360	600	72	<	<	X
cana-5360	600	73	𝒟𝒞(𝑆4	𝒟𝒞(𝑆4	NOUN
cana-5360	600	74	)	)	PUNCT
cana-5360	600	75	<	<	X
cana-5360	600	76	𝒟𝒞(𝑆2	𝒟𝒞(𝑆2	PROPN
cana-5360	600	77	)	)	PUNCT
cana-5360	600	78	<	<	X
cana-5360	600	79	𝒟𝒞(𝑆3	𝒟𝒞(𝑆3	NOUN
cana-5360	600	80	)	)	PUNCT
cana-5360	600	81	<	<	X
cana-5360	600	82	𝒟𝒞(𝑆1	𝒟𝒞(𝑆1	NOUN
cana-5360	600	83	)	)	PUNCT
cana-5360	600	84	hence	hence	ADV
cana-5360	600	85	,	,	PUNCT
cana-5360	600	86	the	the	DET
cana-5360	600	87	alternative	alternative	ADJ
cana-5360	600	88	𝑆1	𝑆1	NOUN
cana-5360	600	89	is	be	AUX
cana-5360	600	90	selected	select	VERB
cana-5360	600	91	as	as	ADP
cana-5360	600	92	the	the	DET
cana-5360	600	93	best	good	ADJ
cana-5360	600	94	alternative	alternative	NOUN
cana-5360	600	95	.	.	PUNCT
cana-5360	601	1	6	6	NUM
cana-5360	601	2	conclusion	conclusion	NOUN
cana-5360	601	3	in	in	ADP
cana-5360	601	4	this	this	DET
cana-5360	601	5	paper	paper	NOUN
cana-5360	601	6	,	,	PUNCT
cana-5360	601	7	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	PROPN
cana-5360	601	8	,	,	PUNCT
cana-5360	601	9	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	PROPN
cana-5360	601	10	,	,	PUNCT
cana-5360	601	11	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	NOUN
cana-5360	601	12	,	,	PUNCT
cana-5360	601	13	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	PROPN
cana-5360	601	14	,	,	PUNCT
cana-5360	601	15	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐶𝑡𝑠	𝒫ℱ𝒩𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛼𝐶𝑡𝑠	PRON
cana-5360	601	16	,	,	PUNCT
cana-5360	601	17	and	and	CCONJ
cana-5360	601	18	𝒫ℱ𝒩	𝒫ℱ𝒩	PROPN
cana-5360	601	19	𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠	𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝛽𝐶𝑡𝑠	PRON
cana-5360	601	20	respective	respective	ADJ
cana-5360	601	21	irresolute	irresolute	ADJ
cana-5360	601	22	map	map	NOUN
cana-5360	601	23	is	be	AUX
cana-5360	601	24	defined	define	VERB
cana-5360	601	25	using	use	VERB
cana-5360	601	26	𝒫ℱ𝒩𝛿𝑜	𝒫ℱ𝒩𝛿𝑜	NOUN
cana-5360	601	27	,	,	PUNCT
cana-5360	601	28	𝒫ℱ𝒩𝛿𝒮𝑜	𝒫ℱ𝒩𝛿𝒮𝑜	PROPN
cana-5360	601	29	,	,	PUNCT
cana-5360	601	30	𝒫ℱ𝒩𝛿𝒫𝑜	𝒫ℱ𝒩𝛿𝒫𝑜	NOUN
cana-5360	601	31	,	,	PUNCT
cana-5360	601	32	𝒫ℱ𝒩𝛿𝛼𝑜	𝒫ℱ𝒩𝛿𝛼𝑜	PROPN
cana-5360	601	33	and	and	CCONJ
cana-5360	601	34	𝒫ℱ𝒩𝛿𝛽𝑜	𝒫ℱ𝒩𝛿𝛽𝑜	PROPN
cana-5360	601	35	set	set	NOUN
cana-5360	601	36	and	and	CCONJ
cana-5360	601	37	its	its	PRON
cana-5360	601	38	properties	property	NOUN
cana-5360	601	39	are	be	AUX
cana-5360	601	40	analyzed	analyze	VERB
cana-5360	601	41	with	with	ADP
cana-5360	601	42	the	the	DET
cana-5360	601	43	examples	example	NOUN
cana-5360	601	44	.	.	PUNCT
cana-5360	602	1	also	also	ADV
cana-5360	602	2	we	we	PRON
cana-5360	602	3	extended	extend	VERB
cana-5360	602	4	the	the	DET
cana-5360	602	5	concept	concept	NOUN
cana-5360	602	6	of	of	ADP
cana-5360	602	7	pythagorean	pythagorean	PROPN
cana-5360	602	8	fuzzy	fuzzy	PROPN
cana-5360	602	9	contra	contra	PROPN
cana-5360	602	10	irresolute	irresolute	PROPN
cana-5360	602	11	maps	map	NOUN
cana-5360	602	12	in	in	ADP
cana-5360	602	13	pythagorean	pythagorean	PROPN
cana-5360	602	14	communications	communication	NOUN
cana-5360	602	15	on	on	ADP
cana-5360	602	16	applied	apply	VERB
cana-5360	602	17	nonlinear	nonlinear	ADJ
cana-5360	602	18	analysis	analysis	NOUN
cana-5360	602	19	issn	issn	NOUN
cana-5360	602	20	:	:	PUNCT
cana-5360	602	21	1074	1074	NUM
cana-5360	602	22	-	-	PUNCT
cana-5360	602	23	133x	133x	NUM
cana-5360	602	24	vol	vol	VERB
cana-5360	602	25	32	32	NUM
cana-5360	602	26	no	no	NOUN
cana-5360	602	27	.	.	PUNCT
cana-5360	602	28	10s	10	NOUN
cana-5360	602	29	(	(	PUNCT
cana-5360	602	30	2025	2025	NUM
cana-5360	602	31	)	)	PUNCT
cana-5360	602	32	1944	1944	NUM
cana-5360	602	33	https://internationalpubls.com	https://internationalpubls.com	X
cana-5360	602	34	fuzzy	fuzzy	ADJ
cana-5360	602	35	topological	topological	ADJ
cana-5360	602	36	spaces	space	NOUN
cana-5360	602	37	using	use	VERB
cana-5360	602	38	above	above	ADV
cana-5360	602	39	mentioned	mention	VERB
cana-5360	602	40	open	open	ADJ
cana-5360	602	41	sets	set	NOUN
cana-5360	602	42	.	.	PUNCT
cana-5360	603	1	some	some	DET
cana-5360	603	2	examples	example	NOUN
cana-5360	603	3	and	and	CCONJ
cana-5360	603	4	basic	basic	ADJ
cana-5360	603	5	relationships	relationship	NOUN
cana-5360	603	6	between	between	ADP
cana-5360	603	7	the	the	DET
cana-5360	603	8	contra	contra	PROPN
cana-5360	603	9	irresolute	irresolute	PROPN
cana-5360	603	10	mappings	mapping	NOUN
cana-5360	603	11	were	be	AUX
cana-5360	603	12	also	also	ADV
cana-5360	603	13	discussed	discuss	VERB
cana-5360	603	14	.	.	PUNCT
cana-5360	604	1	in	in	ADP
cana-5360	604	2	future	future	NOUN
cana-5360	604	3	,	,	PUNCT
cana-5360	604	4	these	these	PRON
cana-5360	604	5	can	can	AUX
cana-5360	604	6	be	be	AUX
cana-5360	604	7	extended	extend	VERB
cana-5360	604	8	to	to	PART
cana-5360	604	9	pythagorean	pythagorean	VERB
cana-5360	604	10	fuzzy	fuzzy	ADJ
cana-5360	604	11	open	open	ADJ
cana-5360	604	12	,	,	PUNCT
cana-5360	604	13	closed	closed	ADJ
cana-5360	604	14	,	,	PUNCT
cana-5360	604	15	homeomorphism	homeomorphism	PROPN
cana-5360	604	16	and	and	CCONJ
cana-5360	604	17	contra	contra	PROPN
cana-5360	604	18	maps	map	NOUN
cana-5360	604	19	.	.	PUNCT
cana-5360	605	1	application	application	NOUN
cana-5360	605	2	for	for	ADP
cana-5360	605	3	economical	economical	ADJ
cana-5360	605	4	decision	decision	NOUN
cana-5360	605	5	making	make	VERB
cana-5360	605	6	problem	problem	NOUN
cana-5360	605	7	was	be	AUX
cana-5360	605	8	solved	solve	VERB
cana-5360	605	9	with	with	ADP
cana-5360	605	10	the	the	DET
cana-5360	605	11	proposed	propose	VERB
cana-5360	605	12	similarity	similarity	NOUN
cana-5360	605	13	measure	measure	NOUN
cana-5360	605	14	.	.	PUNCT
cana-5360	606	1	in	in	ADP
cana-5360	606	2	future	future	NOUN
cana-5360	606	3	,	,	PUNCT
cana-5360	606	4	mcdm	mcdm	ADJ
cana-5360	606	5	to	to	ADP
cana-5360	606	6	the	the	DET
cana-5360	606	7	field	field	NOUN
cana-5360	606	8	of	of	ADP
cana-5360	606	9	medical	medical	ADJ
cana-5360	606	10	diagnostic	diagnostic	NOUN
cana-5360	606	11	can	can	AUX
cana-5360	606	12	be	be	AUX
cana-5360	606	13	develope	develope	NOUN
cana-5360	606	14	to	to	ADP
cana-5360	606	15	the	the	DET
cana-5360	606	16	𝒫ℱ𝒩𝑡𝑠.	𝒫ℱ𝒩𝑡𝑠.	PROPN
cana-5360	606	17	references	reference	NOUN
cana-5360	606	18	[	[	X
cana-5360	606	19	1	1	X
cana-5360	606	20	]	]	PUNCT
cana-5360	606	21	s.	s.	PROPN
cana-5360	606	22	e.	e.	PROPN
cana-5360	606	23	abbas	abbas	PROPN
cana-5360	606	24	(	(	PUNCT
cana-5360	606	25	2012	2012	NUM
cana-5360	606	26	)	)	PUNCT
cana-5360	606	27	,	,	PUNCT
cana-5360	606	28	weaker	weak	ADJ
cana-5360	606	29	forms	form	NOUN
cana-5360	606	30	of	of	ADP
cana-5360	606	31	fuzzy	fuzzy	ADJ
cana-5360	606	32	contra	contra	NOUN
cana-5360	606	33	-	-	NOUN
cana-5360	606	34	continuity	continuity	NOUN
cana-5360	606	35	,	,	PUNCT
cana-5360	606	36	the	the	DET
cana-5360	606	37	journal	journal	NOUN
cana-5360	606	38	of	of	ADP
cana-5360	606	39	fuzzy	fuzzy	ADJ
cana-5360	606	40	mathematics	mathematic	NOUN
cana-5360	606	41	,	,	PUNCT
cana-5360	606	42	2010	2010	NUM
cana-5360	606	43	.	.	PUNCT
cana-5360	607	1	[	[	X
cana-5360	607	2	2	2	NUM
cana-5360	607	3	]	]	PUNCT
cana-5360	607	4	a.	a.	NOUN
cana-5360	607	5	acikgoz	acikgoz	PROPN
cana-5360	607	6	and	and	CCONJ
cana-5360	607	7	f.	f.	PROPN
cana-5360	607	8	esenbel	esenbel	PROPN
cana-5360	607	9	,	,	PUNCT
cana-5360	607	10	neutrosophic	neutrosophic	ADJ
cana-5360	607	11	soft	soft	ADJ
cana-5360	607	12	𝛿-topology	𝛿-topology	NOUN
cana-5360	607	13	and	and	CCONJ
cana-5360	607	14	neutrosophic	neutrosophic	ADJ
cana-5360	607	15	soft	soft	ADJ
cana-5360	607	16	compactness	compactness	NOUN
cana-5360	607	17	,	,	PUNCT
cana-5360	607	18	aip	aip	PROPN
cana-5360	607	19	conference	conference	NOUN
cana-5360	607	20	proceedings	proceeding	NOUN
cana-5360	607	21	2183	2183	NUM
cana-5360	607	22	,	,	PUNCT
cana-5360	607	23	030002	030002	NUM
cana-5360	607	24	,	,	PUNCT
cana-5360	607	25	(	(	PUNCT
cana-5360	607	26	2019	2019	NUM
cana-5360	607	27	)	)	PUNCT
cana-5360	607	28	.	.	PUNCT
cana-5360	608	1	[	[	X
cana-5360	608	2	3	3	X
cana-5360	608	3	]	]	PUNCT
cana-5360	608	4	m.	m.	NOUN
cana-5360	608	5	adabitabar	adabitabar	PROPN
cana-5360	608	6	firozja	firozja	PROPN
cana-5360	608	7	,	,	PUNCT
cana-5360	608	8	b.	b.	PROPN
cana-5360	608	9	agheli	agheli	PROPN
cana-5360	608	10	and	and	CCONJ
cana-5360	608	11	e.	e.	PROPN
cana-5360	608	12	baloui	baloui	PROPN
cana-5360	608	13	jamkhaneh	jamkhaneh	PROPN
cana-5360	608	14	(	(	PUNCT
cana-5360	608	15	2019	2019	NUM
cana-5360	608	16	)	)	PUNCT
cana-5360	608	17	,	,	PUNCT
cana-5360	608	18	a	a	DET
cana-5360	608	19	new	new	ADJ
cana-5360	608	20	similarity	similarity	NOUN
cana-5360	608	21	measure	measure	NOUN
cana-5360	608	22	for	for	ADP
cana-5360	608	23	pythagorean	pythagorean	ADJ
cana-5360	608	24	fuzzy	fuzzy	ADJ
cana-5360	608	25	sets	set	NOUN
cana-5360	608	26	,	,	PUNCT
cana-5360	608	27	complex	complex	ADJ
cana-5360	608	28	and	and	CCONJ
cana-5360	608	29	intelligent	intelligent	ADJ
cana-5360	608	30	systems	system	NOUN
cana-5360	608	31	.	.	PUNCT
cana-5360	609	1	[	[	X
cana-5360	609	2	4	4	X
cana-5360	609	3	]	]	X
cana-5360	609	4	d.	d.	PROPN
cana-5360	609	5	ajay	ajay	PROPN
cana-5360	609	6	and	and	CCONJ
cana-5360	609	7	j.	j.	PROPN
cana-5360	609	8	joseline	joseline	PROPN
cana-5360	609	9	charisma	charisma	PROPN
cana-5360	609	10	,	,	PUNCT
cana-5360	609	11	pythagorean	pythagorean	PROPN
cana-5360	609	12	nano	nano	PROPN
cana-5360	609	13	topological	topological	ADJ
cana-5360	609	14	space	space	NOUN
cana-5360	609	15	,	,	PUNCT
cana-5360	609	16	international	international	ADJ
cana-5360	609	17	journal	journal	NOUN
cana-5360	609	18	of	of	ADP
cana-5360	609	19	recent	recent	ADJ
cana-5360	609	20	technology	technology	NOUN
cana-5360	609	21	and	and	CCONJ
cana-5360	609	22	engineering	engineering	NOUN
cana-5360	609	23	,	,	PUNCT
cana-5360	609	24	8	8	NUM
cana-5360	609	25	(	(	PUNCT
cana-5360	609	26	2020	2020	NUM
cana-5360	609	27	)	)	PUNCT
cana-5360	609	28	,	,	PUNCT
cana-5360	609	29	3415	3415	NUM
cana-5360	609	30	-	-	SYM
cana-5360	609	31	3419	3419	NUM
cana-5360	609	32	.	.	PUNCT
cana-5360	610	1	[	[	X
cana-5360	610	2	5	5	NUM
cana-5360	610	3	]	]	PUNCT
cana-5360	610	4	d.	d.	PROPN
cana-5360	610	5	ajay	ajay	PROPN
cana-5360	610	6	and	and	CCONJ
cana-5360	610	7	j.	j.	PROPN
cana-5360	610	8	joseline	joseline	PROPN
cana-5360	610	9	charisma	charisma	PROPN
cana-5360	610	10	,	,	PUNCT
cana-5360	610	11	on	on	ADP
cana-5360	610	12	weak	weak	ADJ
cana-5360	610	13	forms	form	NOUN
cana-5360	610	14	of	of	ADP
cana-5360	610	15	pythagorean	pythagorean	PROPN
cana-5360	610	16	nano	nano	NOUN
cana-5360	610	17	open	open	ADJ
cana-5360	610	18	sets	set	NOUN
cana-5360	610	19	,	,	PUNCT
cana-5360	610	20	advances	advance	NOUN
cana-5360	610	21	in	in	ADP
cana-5360	610	22	mathematics	mathematic	NOUN
cana-5360	610	23	:	:	PUNCT
cana-5360	610	24	scientific	scientific	ADJ
cana-5360	610	25	journal	journal	NOUN
cana-5360	610	26	,	,	PUNCT
cana-5360	610	27	9	9	NUM
cana-5360	610	28	(	(	PUNCT
cana-5360	610	29	2020	2020	NUM
cana-5360	610	30	)	)	PUNCT
cana-5360	610	31	,	,	PUNCT
cana-5360	610	32	5953	5953	NUM
cana-5360	610	33	-	-	SYM
cana-5360	610	34	5963	5963	NUM
cana-5360	610	35	.	.	PUNCT
cana-5360	611	1	[	[	X
cana-5360	611	2	6	6	NUM
cana-5360	611	3	]	]	X
cana-5360	611	4	d.	d.	PROPN
cana-5360	611	5	ajay	ajay	PROPN
cana-5360	611	6	and	and	CCONJ
cana-5360	611	7	j.	j.	PROPN
cana-5360	611	8	joseline	joseline	PROPN
cana-5360	611	9	charisma	charisma	PROPN
cana-5360	611	10	,	,	PUNCT
cana-5360	611	11	pythagorean	pythagorean	PROPN
cana-5360	611	12	nano	nano	NOUN
cana-5360	611	13	continuity	continuity	NOUN
cana-5360	611	14	,	,	PUNCT
cana-5360	611	15	advances	advance	NOUN
cana-5360	611	16	in	in	ADP
cana-5360	611	17	mathematics	mathematic	NOUN
cana-5360	611	18	:	:	PUNCT
cana-5360	611	19	scientific	scientific	ADJ
cana-5360	611	20	journal	journal	NOUN
cana-5360	611	21	,	,	PUNCT
cana-5360	611	22	9	9	NUM
cana-5360	611	23	(	(	PUNCT
cana-5360	611	24	8)	8)	NUM
cana-5360	611	25	(	(	PUNCT
cana-5360	611	26	2020	2020	NUM
cana-5360	611	27	)	)	PUNCT
cana-5360	611	28	,	,	PUNCT
cana-5360	611	29	6291	6291	NUM
cana-5360	611	30	-	-	SYM
cana-5360	611	31	6298	6298	NUM
cana-5360	611	32	.	.	PUNCT
cana-5360	612	1	[	[	X
cana-5360	612	2	7	7	X
cana-5360	612	3	]	]	PUNCT
cana-5360	612	4	s.	s.	PROPN
cana-5360	612	5	aranganayagi	aranganayagi	PROPN
cana-5360	612	6	,	,	PUNCT
cana-5360	612	7	m.	m.	NOUN
cana-5360	612	8	saraswathi	saraswathi	PROPN
cana-5360	612	9	and	and	CCONJ
cana-5360	612	10	k.	k.	PROPN
cana-5360	612	11	chitirakala	chitirakala	PROPN
cana-5360	612	12	,	,	PUNCT
cana-5360	612	13	more	more	ADJ
cana-5360	612	14	on	on	ADP
cana-5360	612	15	open	open	ADJ
cana-5360	612	16	maps	map	NOUN
cana-5360	612	17	and	and	CCONJ
cana-5360	612	18	closed	closed	ADJ
cana-5360	612	19	maps	map	NOUN
cana-5360	612	20	in	in	ADP
cana-5360	612	21	fuzzy	fuzzy	ADJ
cana-5360	612	22	hypersoft	hypersoft	PROPN
cana-5360	612	23	topological	topological	ADJ
cana-5360	612	24	spaces	space	NOUN
cana-5360	612	25	and	and	CCONJ
cana-5360	612	26	application	application	NOUN
cana-5360	612	27	in	in	ADP
cana-5360	612	28	covid-19	covid-19	PROPN
cana-5360	612	29	diagnosis	diagnosis	NOUN
cana-5360	612	30	using	use	VERB
cana-5360	612	31	cotangent	cotangent	NOUN
cana-5360	612	32	similarity	similarity	NOUN
cana-5360	612	33	measure	measure	NOUN
cana-5360	612	34	,	,	PUNCT
cana-5360	612	35	international	international	ADJ
cana-5360	612	36	journal	journal	NOUN
cana-5360	612	37	of	of	ADP
cana-5360	612	38	neutrosophic	neutrosophic	ADJ
cana-5360	612	39	science	science	NOUN
cana-5360	612	40	,	,	PUNCT
cana-5360	612	41	21(2	21(2	NUM
cana-5360	612	42	)	)	PUNCT
cana-5360	612	43	,	,	PUNCT
cana-5360	612	44	(	(	PUNCT
cana-5360	612	45	2023	2023	NUM
cana-5360	612	46	)	)	PUNCT
cana-5360	612	47	,	,	PUNCT
cana-5360	612	48	32	32	NUM
cana-5360	612	49	-	-	SYM
cana-5360	612	50	58	58	NUM
cana-5360	612	51	.	.	PUNCT
cana-5360	613	1	[	[	X
cana-5360	613	2	8	8	X
cana-5360	613	3	]	]	PUNCT
cana-5360	613	4	s.	s.	PROPN
cana-5360	613	5	aranganayagi	aranganayagi	PROPN
cana-5360	613	6	,	,	PUNCT
cana-5360	613	7	m.	m.	NOUN
cana-5360	613	8	saraswathi	saraswathi	PROPN
cana-5360	613	9	,	,	PUNCT
cana-5360	613	10	k.	k.	PROPN
cana-5360	613	11	chitirakala	chitirakala	PROPN
cana-5360	613	12	and	and	CCONJ
cana-5360	613	13	a.	a.	NOUN
cana-5360	613	14	vadivel	vadivel	PROPN
cana-5360	613	15	,	,	PUNCT
cana-5360	613	16	the	the	DET
cana-5360	613	17	𝑒	𝑒	PROPN
cana-5360	613	18	-open	-open	ADJ
cana-5360	613	19	sets	set	NOUN
cana-5360	613	20	in	in	ADP
cana-5360	613	21	neutrosophic	neutrosophic	ADJ
cana-5360	613	22	hypersoft	hypersoft	ADJ
cana-5360	613	23	topologial	topologial	ADJ
cana-5360	613	24	spaces	space	NOUN
cana-5360	613	25	and	and	CCONJ
cana-5360	613	26	application	application	NOUN
cana-5360	613	27	in	in	ADP
cana-5360	613	28	covid-19	covid-19	PROPN
cana-5360	613	29	diagnosis	diagnosis	NOUN
cana-5360	613	30	using	use	VERB
cana-5360	613	31	normalized	normalize	VERB
cana-5360	613	32	hamming	hamming	NOUN
cana-5360	613	33	distance	distance	NOUN
cana-5360	613	34	,	,	PUNCT
cana-5360	613	35	journal	journal	NOUN
cana-5360	613	36	of	of	ADP
cana-5360	613	37	the	the	DET
cana-5360	613	38	indonesian	indonesian	PROPN
cana-5360	613	39	mathematical	mathematical	ADJ
cana-5360	613	40	society	society	NOUN
cana-5360	613	41	,	,	PUNCT
cana-5360	613	42	29(2	29(2	NUM
cana-5360	613	43	)	)	PUNCT
cana-5360	613	44	,	,	PUNCT
cana-5360	613	45	(	(	PUNCT
cana-5360	613	46	2023	2023	NUM
cana-5360	613	47	)	)	PUNCT
cana-5360	613	48	,	,	PUNCT
cana-5360	613	49	177	177	NUM
cana-5360	613	50	-	-	SYM
cana-5360	613	51	196	196	NUM
cana-5360	613	52	.	.	PUNCT
cana-5360	614	1	[	[	X
cana-5360	614	2	9	9	NUM
cana-5360	614	3	]	]	PUNCT
cana-5360	614	4	k.	k.	PROPN
cana-5360	614	5	t.	t.	PROPN
cana-5360	614	6	atanassov	atanassov	PROPN
cana-5360	614	7	(	(	PUNCT
cana-5360	614	8	1983	1983	NUM
cana-5360	614	9	)	)	PUNCT
cana-5360	614	10	,	,	PUNCT
cana-5360	614	11	intuitionistic	intuitionistic	ADJ
cana-5360	614	12	fuzzy	fuzzy	ADJ
cana-5360	614	13	sets	set	NOUN
cana-5360	614	14	,	,	PUNCT
cana-5360	614	15	vii	vii	PROPN
cana-5360	614	16	itkrâ€	itkrâ€	PROPN
cana-5360	614	17	™	™	PROPN
cana-5360	614	18	s	s	PART
cana-5360	614	19	session	session	NOUN
cana-5360	614	20	,	,	PUNCT
cana-5360	614	21	sofia	sofia	PROPN
cana-5360	614	22	.	.	PUNCT
cana-5360	615	1	[	[	X
cana-5360	615	2	10	10	NUM
cana-5360	615	3	]	]	PUNCT
cana-5360	615	4	k.	k.	PROPN
cana-5360	615	5	t.	t.	PROPN
cana-5360	615	6	atanassov	atanassov	PROPN
cana-5360	615	7	(	(	PUNCT
cana-5360	615	8	1986	1986	NUM
cana-5360	615	9	)	)	PUNCT
cana-5360	615	10	,	,	PUNCT
cana-5360	615	11	intuitionistic	intuitionistic	ADJ
cana-5360	615	12	fuzzy	fuzzy	ADJ
cana-5360	615	13	sets	set	NOUN
cana-5360	615	14	,	,	PUNCT
cana-5360	615	15	fuzzy	fuzzy	ADJ
cana-5360	615	16	sets	set	NOUN
cana-5360	615	17	syst	syst	NOUN
cana-5360	615	18	.	.	PUNCT
cana-5360	616	1	20	20	NUM
cana-5360	616	2	,	,	PUNCT
cana-5360	616	3	87	87	NUM
cana-5360	616	4	-	-	SYM
cana-5360	616	5	96	96	NUM
cana-5360	616	6	.	.	PUNCT
cana-5360	617	1	[	[	X
cana-5360	617	2	11	11	NUM
cana-5360	617	3	]	]	PUNCT
cana-5360	617	4	k.	k.	PROPN
cana-5360	617	5	t.	t.	PROPN
cana-5360	617	6	atanassov	atanassov	PROPN
cana-5360	617	7	(	(	PUNCT
cana-5360	617	8	1999	1999	NUM
cana-5360	617	9	)	)	PUNCT
cana-5360	617	10	,	,	PUNCT
cana-5360	617	11	intuitionistic	intuitionistic	ADJ
cana-5360	617	12	fuzzy	fuzzy	ADJ
cana-5360	617	13	sets	set	NOUN
cana-5360	617	14	:	:	PUNCT
cana-5360	617	15	theory	theory	NOUN
cana-5360	617	16	and	and	CCONJ
cana-5360	617	17	applications	application	NOUN
cana-5360	617	18	,	,	PUNCT
cana-5360	617	19	physica	physica	NOUN
cana-5360	617	20	,	,	PUNCT
cana-5360	617	21	heidelberg	heidelberg	NOUN
cana-5360	617	22	.	.	PUNCT
cana-5360	618	1	[	[	X
cana-5360	618	2	12	12	NUM
cana-5360	618	3	]	]	PUNCT
cana-5360	618	4	k.	k.	PROPN
cana-5360	618	5	t.	t.	PROPN
cana-5360	618	6	atanassov	atanassov	PROPN
cana-5360	618	7	(	(	PUNCT
cana-5360	618	8	2012	2012	NUM
cana-5360	618	9	)	)	PUNCT
cana-5360	618	10	,	,	PUNCT
cana-5360	618	11	on	on	ADP
cana-5360	618	12	intuitionistic	intuitionistic	ADJ
cana-5360	618	13	fuzzy	fuzzy	ADJ
cana-5360	618	14	sets	set	NOUN
cana-5360	618	15	theory	theory	NOUN
cana-5360	618	16	,	,	PUNCT
cana-5360	618	17	springer	springer	NOUN
cana-5360	618	18	,	,	PUNCT
cana-5360	618	19	berlin	berlin	PROPN
cana-5360	618	20	.	.	PUNCT
cana-5360	619	1	[	[	X
cana-5360	619	2	13	13	NUM
cana-5360	619	3	]	]	PUNCT
cana-5360	619	4	k.	k.	PROPN
cana-5360	620	1	k.	k.	PROPN
cana-5360	620	2	azad	azad	PROPN
cana-5360	620	3	(	(	PUNCT
cana-5360	620	4	1981	1981	NUM
cana-5360	620	5	)	)	PUNCT
cana-5360	620	6	,	,	PUNCT
cana-5360	620	7	on	on	ADP
cana-5360	620	8	fuzzy	fuzzy	ADJ
cana-5360	620	9	semi	semi	ADJ
cana-5360	620	10	continuity	continuity	NOUN
cana-5360	620	11	,	,	PUNCT
cana-5360	620	12	fuzzy	fuzzy	ADJ
cana-5360	620	13	almost	almost	ADV
cana-5360	620	14	continuity	continuity	NOUN
cana-5360	620	15	and	and	CCONJ
cana-5360	620	16	fuzzy	fuzzy	ADJ
cana-5360	620	17	weakly	weakly	ADJ
cana-5360	620	18	continuity	continuity	NOUN
cana-5360	620	19	,	,	PUNCT
cana-5360	620	20	j.	j.	PROPN
cana-5360	620	21	math	math	PROPN
cana-5360	620	22	.	.	PUNCT
cana-5360	621	1	anal	anal	PROPN
cana-5360	621	2	.	.	PUNCT
cana-5360	622	1	app	app	PROPN
cana-5360	622	2	,	,	PUNCT
cana-5360	622	3	(	(	PUNCT
cana-5360	622	4	82	82	NUM
cana-5360	622	5	)	)	PUNCT
cana-5360	622	6	,	,	PUNCT
cana-5360	622	7	14	14	NUM
cana-5360	622	8	-	-	SYM
cana-5360	622	9	32	32	NUM
cana-5360	622	10	.	.	PUNCT
cana-5360	623	1	[	[	X
cana-5360	623	2	14	14	NUM
cana-5360	623	3	]	]	X
cana-5360	623	4	c.	c.	PROPN
cana-5360	623	5	l.	l.	PROPN
cana-5360	623	6	chang	chang	PROPN
cana-5360	623	7	(	(	PUNCT
cana-5360	623	8	1968	1968	NUM
cana-5360	623	9	)	)	PUNCT
cana-5360	623	10	,	,	PUNCT
cana-5360	623	11	fuzzy	fuzzy	ADJ
cana-5360	623	12	topological	topological	ADJ
cana-5360	623	13	spaces	space	NOUN
cana-5360	623	14	,	,	PUNCT
cana-5360	623	15	j.	j.	PROPN
cana-5360	623	16	math	math	PROPN
cana-5360	623	17	.	.	PUNCT
cana-5360	624	1	anal	anal	PROPN
cana-5360	624	2	.	.	PUNCT
cana-5360	624	3	appi	appi	PROPN
cana-5360	624	4	.	.	PUNCT
cana-5360	625	1	(	(	PUNCT
cana-5360	625	2	24	24	NUM
cana-5360	625	3	)	)	PUNCT
cana-5360	625	4	,	,	PUNCT
cana-5360	625	5	182	182	NUM
cana-5360	625	6	-	-	SYM
cana-5360	625	7	190	190	NUM
cana-5360	625	8	.	.	PUNCT
cana-5360	626	1	[	[	X
cana-5360	626	2	15	15	NUM
cana-5360	626	3	]	]	X
cana-5360	626	4	dogan	dogan	PROPN
cana-5360	626	5	coker	coker	NOUN
cana-5360	626	6	(	(	PUNCT
cana-5360	626	7	1997	1997	NUM
cana-5360	626	8	)	)	PUNCT
cana-5360	626	9	,	,	PUNCT
cana-5360	626	10	an	an	DET
cana-5360	626	11	introduction	introduction	NOUN
cana-5360	626	12	to	to	ADP
cana-5360	626	13	intuitionistic	intuitionistic	ADJ
cana-5360	626	14	fuzzy	fuzzy	ADJ
cana-5360	626	15	topological	topological	ADJ
cana-5360	626	16	spaces	space	NOUN
cana-5360	626	17	,	,	PUNCT
cana-5360	626	18	fuzzy	fuzzy	ADJ
cana-5360	626	19	sets	set	NOUN
cana-5360	626	20	and	and	CCONJ
cana-5360	626	21	systems	system	NOUN
cana-5360	626	22	,	,	PUNCT
cana-5360	626	23	(	(	PUNCT
cana-5360	626	24	88	88	NUM
cana-5360	626	25	)	)	PUNCT
cana-5360	626	26	,	,	PUNCT
cana-5360	626	27	81	81	NUM
cana-5360	626	28	-	-	SYM
cana-5360	626	29	89	89	NUM
cana-5360	626	30	.	.	PUNCT
cana-5360	627	1	[	[	X
cana-5360	627	2	16	16	NUM
cana-5360	627	3	]	]	X
cana-5360	627	4	n.	n.	PROPN
cana-5360	627	5	b.	b.	PROPN
cana-5360	627	6	gnanachristy	gnanachristy	PROPN
cana-5360	627	7	and	and	CCONJ
cana-5360	627	8	g.	g.	PROPN
cana-5360	627	9	k.	k.	PROPN
cana-5360	627	10	revathi	revathi	PROPN
cana-5360	627	11	(	(	PUNCT
cana-5360	627	12	2020	2020	NUM
cana-5360	627	13	)	)	PUNCT
cana-5360	627	14	,	,	PUNCT
cana-5360	627	15	analysis	analysis	NOUN
cana-5360	627	16	of	of	ADP
cana-5360	627	17	various	various	ADJ
cana-5360	627	18	fuzzy	fuzzy	ADJ
cana-5360	627	19	topological	topological	ADJ
cana-5360	627	20	spaces	space	NOUN
cana-5360	627	21	,	,	PUNCT
cana-5360	627	22	communications	communication	NOUN
cana-5360	627	23	on	on	ADP
cana-5360	627	24	applied	apply	VERB
cana-5360	627	25	nonlinear	nonlinear	ADJ
cana-5360	627	26	analysis	analysis	NOUN
cana-5360	627	27	issn	issn	NOUN
cana-5360	627	28	:	:	PUNCT
cana-5360	627	29	1074	1074	NUM
cana-5360	627	30	-	-	PUNCT
cana-5360	627	31	133x	133x	NUM
cana-5360	627	32	vol	vol	VERB
cana-5360	627	33	32	32	NUM
cana-5360	627	34	no	no	NOUN
cana-5360	627	35	.	.	PUNCT
cana-5360	628	1	10s	10	NOUN
cana-5360	628	2	(	(	PUNCT
cana-5360	628	3	2025	2025	NUM
cana-5360	628	4	)	)	PUNCT
cana-5360	628	5	1945	1945	NUM
cana-5360	628	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5360	628	7	journal	journal	NOUN
cana-5360	628	8	of	of	ADP
cana-5360	628	9	critical	critical	ADJ
cana-5360	628	10	reviews	review	NOUN
cana-5360	628	11	(	(	PUNCT
cana-5360	628	12	7	7	NUM
cana-5360	628	13	)	)	PUNCT
cana-5360	628	14	,	,	PUNCT
cana-5360	628	15	2394	2394	NUM
cana-5360	628	16	-	-	SYM
cana-5360	628	17	5125	5125	NUM
cana-5360	628	18	.	.	PUNCT
cana-5360	629	1	[	[	X
cana-5360	629	2	17	17	NUM
cana-5360	629	3	]	]	X
cana-5360	629	4	n.	n.	PROPN
cana-5360	629	5	b.	b.	PROPN
cana-5360	629	6	gnanachristy	gnanachristy	PROPN
cana-5360	629	7	and	and	CCONJ
cana-5360	629	8	g.	g.	PROPN
cana-5360	629	9	k.	k.	PROPN
cana-5360	629	10	revathi	revathi	PROPN
cana-5360	629	11	,	,	PUNCT
cana-5360	629	12	(	(	PUNCT
cana-5360	629	13	2021	2021	NUM
cana-5360	629	14	)	)	PUNCT
cana-5360	629	15	a	a	DET
cana-5360	629	16	view	view	NOUN
cana-5360	629	17	on	on	ADP
cana-5360	629	18	pythagorean	pythagorean	PROPN
cana-5360	629	19	fuzzy	fuzzy	ADJ
cana-5360	629	20	contra	contra	PROPN
cana-5360	629	21	𝒢	𝒢	PROPN
cana-5360	629	22	continuous	continuous	ADJ
cana-5360	629	23	function	function	NOUN
cana-5360	629	24	,	,	PUNCT
cana-5360	629	25	journal	journal	NOUN
cana-5360	629	26	of	of	ADP
cana-5360	629	27	physics	physics	PROPN
cana-5360	629	28	conference	conference	NOUN
cana-5360	629	29	series	series	PROPN
cana-5360	629	30	,	,	PUNCT
cana-5360	629	31	(	(	PUNCT
cana-5360	629	32	2115	2115	NUM
cana-5360	629	33	)	)	PUNCT
cana-5360	629	34	,	,	PUNCT
cana-5360	629	35	012041	012041	NUM
cana-5360	629	36	.	.	PUNCT
cana-5360	630	1	[	[	X
cana-5360	630	2	18	18	NUM
cana-5360	630	3	]	]	X
cana-5360	630	4	murat	murat	PROPN
cana-5360	630	5	olgun	olgun	PROPN
cana-5360	630	6	,	,	PUNCT
cana-5360	630	7	mehmet	mehmet	PROPN
cana-5360	630	8	unver	unver	PROPN
cana-5360	630	9	and	and	CCONJ
cana-5360	630	10	seyhmus	seyhmus	VERB
cana-5360	630	11	yardimci	yardimci	PROPN
cana-5360	630	12	(	(	PUNCT
cana-5360	630	13	2019	2019	NUM
cana-5360	630	14	)	)	PUNCT
cana-5360	630	15	,	,	PUNCT
cana-5360	630	16	pythagorean	pythagorean	PROPN
cana-5360	630	17	fuzzy	fuzzy	ADJ
cana-5360	630	18	topological	topological	ADJ
cana-5360	630	19	spaces	space	NOUN
cana-5360	630	20	,	,	PUNCT
cana-5360	630	21	complex	complex	ADJ
cana-5360	630	22	&	&	CCONJ
cana-5360	630	23	intelligent	intelligent	ADJ
cana-5360	630	24	systems	system	NOUN
cana-5360	630	25	.	.	PUNCT
cana-5360	631	1	https://doi.org/10.1007/s40747-019-0095-2	https://doi.org/10.1007/s40747-019-0095-2	NUM
cana-5360	631	2	.	.	PUNCT
cana-5360	632	1	[	[	X
cana-5360	632	2	19	19	NUM
cana-5360	632	3	]	]	SYM
cana-5360	632	4	necla	necla	NOUN
cana-5360	632	5	turanli	turanli	NOUN
cana-5360	632	6	and	and	CCONJ
cana-5360	632	7	dogan	dogan	PROPN
cana-5360	632	8	coker	coker	NOUN
cana-5360	632	9	(	(	PUNCT
cana-5360	632	10	2000	2000	NUM
cana-5360	632	11	)	)	PUNCT
cana-5360	632	12	,	,	PUNCT
cana-5360	632	13	fuzzy	fuzzy	ADJ
cana-5360	632	14	connectedness	connectedness	NOUN
cana-5360	632	15	in	in	ADP
cana-5360	632	16	intuitionistic	intuitionistic	ADJ
cana-5360	632	17	fuzzy	fuzzy	ADJ
cana-5360	632	18	topological	topological	ADJ
cana-5360	632	19	spaces	space	NOUN
cana-5360	632	20	,	,	PUNCT
cana-5360	632	21	fuzzy	fuzzy	ADJ
cana-5360	632	22	sets	set	NOUN
cana-5360	632	23	and	and	CCONJ
cana-5360	632	24	systems	system	NOUN
cana-5360	632	25	,	,	PUNCT
cana-5360	632	26	(	(	PUNCT
cana-5360	632	27	116	116	NUM
cana-5360	632	28	)	)	PUNCT
cana-5360	632	29	369	369	NUM
cana-5360	632	30	-	-	SYM
cana-5360	632	31	375	375	NUM
cana-5360	632	32	.	.	PUNCT
cana-5360	633	1	[	[	X
cana-5360	633	2	20	20	NUM
cana-5360	633	3	]	]	X
cana-5360	633	4	paul	paul	PROPN
cana-5360	633	5	augustine	augustine	PROPN
cana-5360	633	6	ejegwa	ejegwa	PROPN
cana-5360	633	7	(	(	PUNCT
cana-5360	633	8	2019	2019	NUM
cana-5360	633	9	)	)	PUNCT
cana-5360	633	10	,	,	PUNCT
cana-5360	633	11	pythagorean	pythagorean	PROPN
cana-5360	633	12	fuzzy	fuzzy	PROPN
cana-5360	633	13	set	set	NOUN
cana-5360	633	14	and	and	CCONJ
cana-5360	633	15	its	its	PRON
cana-5360	633	16	application	application	NOUN
cana-5360	633	17	in	in	ADP
cana-5360	633	18	career	career	NOUN
cana-5360	633	19	placements	placement	NOUN
cana-5360	633	20	based	base	VERB
cana-5360	633	21	on	on	ADP
cana-5360	633	22	academic	academic	ADJ
cana-5360	633	23	performance	performance	NOUN
cana-5360	633	24	using	use	VERB
cana-5360	633	25	max	max	PROPN
cana-5360	633	26	-	-	PUNCT
cana-5360	633	27	min	min	PROPN
cana-5360	633	28	-	-	ADJ
cana-5360	633	29	max	max	PROPN
cana-5360	633	30	composition	composition	NOUN
cana-5360	633	31	complex	complex	ADJ
cana-5360	633	32	and	and	CCONJ
cana-5360	633	33	intelligent	intelligent	ADJ
cana-5360	633	34	systems	system	NOUN
cana-5360	633	35	.	.	PUNCT
cana-5360	634	1	[	[	X
cana-5360	634	2	21	21	NUM
cana-5360	634	3	]	]	PUNCT
cana-5360	634	4	x.	x.	PROPN
cana-5360	634	5	peng	peng	PROPN
cana-5360	634	6	and	and	CCONJ
cana-5360	634	7	y.	y.	PROPN
cana-5360	634	8	yang	yang	PROPN
cana-5360	634	9	(	(	PUNCT
cana-5360	634	10	2015	2015	NUM
cana-5360	634	11	)	)	PUNCT
cana-5360	634	12	,	,	PUNCT
cana-5360	634	13	some	some	PRON
cana-5360	634	14	results	result	VERB
cana-5360	634	15	for	for	ADP
cana-5360	634	16	pythagorean	pythagorean	ADJ
cana-5360	634	17	fuzzy	fuzzy	ADJ
cana-5360	634	18	sets	set	NOUN
cana-5360	634	19	,	,	PUNCT
cana-5360	634	20	int	int	NOUN
cana-5360	634	21	.	.	PUNCT
cana-5360	635	1	j	j	PROPN
cana-5360	635	2	intell	intell	PROPN
cana-5360	635	3	syst	syst	PROPN
cana-5360	635	4	.	.	PUNCT
cana-5360	636	1	30	30	NUM
cana-5360	636	2	,	,	PUNCT
cana-5360	636	3	1133	1133	NUM
cana-5360	636	4	-	-	SYM
cana-5360	636	5	1160	1160	NUM
cana-5360	636	6	.	.	PUNCT
cana-5360	637	1	[	[	X
cana-5360	637	2	22	22	NUM
cana-5360	637	3	]	]	PUNCT
cana-5360	637	4	x.	x.	NOUN
cana-5360	637	5	peng	peng	PROPN
cana-5360	637	6	and	and	CCONJ
cana-5360	637	7	g.	g.	PROPN
cana-5360	637	8	selvachandran	selvachandran	PROPN
cana-5360	637	9	(	(	PUNCT
cana-5360	637	10	2017	2017	NUM
cana-5360	637	11	)	)	PUNCT
cana-5360	637	12	,	,	PUNCT
cana-5360	637	13	pythagorean	pythagorean	PROPN
cana-5360	637	14	fuzzy	fuzzy	PROPN
cana-5360	637	15	set	set	VERB
cana-5360	637	16	state	state	NOUN
cana-5360	637	17	of	of	ADP
cana-5360	637	18	the	the	DET
cana-5360	637	19	art	art	NOUN
cana-5360	637	20	and	and	CCONJ
cana-5360	637	21	future	future	ADJ
cana-5360	637	22	directions	direction	NOUN
cana-5360	637	23	,	,	PUNCT
cana-5360	637	24	artif	artif	PROPN
cana-5360	637	25	intell	intell	PROPN
cana-5360	637	26	rev	rev	VERB
cana-5360	637	27	.	.	PUNCT
cana-5360	637	28	https://doi.org/10.1007/s10462-017-9596-9	https://doi.org/10.1007/s10462-017-9596-9	PROPN
cana-5360	637	29	.	.	PUNCT
cana-5360	638	1	[	[	X
cana-5360	638	2	23	23	NUM
cana-5360	638	3	]	]	X
cana-5360	638	4	n.	n.	NOUN
cana-5360	638	5	preethi	preethi	ADV
cana-5360	638	6	and	and	CCONJ
cana-5360	638	7	g.	g.	PROPN
cana-5360	638	8	k.	k.	PROPN
cana-5360	638	9	revathi	revathi	PROPN
cana-5360	638	10	(	(	PUNCT
cana-5360	638	11	2020	2020	NUM
cana-5360	638	12	)	)	PUNCT
cana-5360	638	13	,	,	PUNCT
cana-5360	638	14	a	a	DET
cana-5360	638	15	conceptual	conceptual	ADJ
cana-5360	638	16	view	view	NOUN
cana-5360	638	17	on	on	ADP
cana-5360	638	18	𝑃𝐹𝐷	𝑃𝐹𝐷	PROPN
cana-5360	638	19	functions	function	NOUN
cana-5360	638	20	and	and	CCONJ
cana-5360	638	21	its	its	PRON
cana-5360	638	22	properties	property	NOUN
cana-5360	638	23	,	,	PUNCT
cana-5360	638	24	test	test	NOUN
cana-5360	638	25	engineering	engineering	NOUN
cana-5360	638	26	and	and	CCONJ
cana-5360	638	27	management	management	NOUN
cana-5360	638	28	,	,	PUNCT
cana-5360	638	29	0913	0913	NUM
cana-5360	638	30	-	-	SYM
cana-5360	638	31	4120	4120	NUM
cana-5360	638	32	.	.	PUNCT
cana-5360	639	1	[	[	X
cana-5360	639	2	24	24	NUM
cana-5360	639	3	]	]	X
cana-5360	639	4	rana	rana	PROPN
cana-5360	639	5	muhammad	muhammad	PROPN
cana-5360	639	6	zulqarnain	zulqarnain	PROPN
cana-5360	639	7	et	et	PROPN
cana-5360	639	8	al	al	PROPN
cana-5360	639	9	(	(	PUNCT
cana-5360	639	10	2021	2021	NUM
cana-5360	639	11	)	)	PUNCT
cana-5360	639	12	,	,	PUNCT
cana-5360	639	13	development	development	NOUN
cana-5360	639	14	of	of	ADP
cana-5360	639	15	topsis	topsis	NOUN
cana-5360	639	16	technique	technique	NOUN
cana-5360	639	17	under	under	ADP
cana-5360	639	18	pythagorean	pythagorean	PROPN
cana-5360	639	19	fuzzy	fuzzy	ADJ
cana-5360	639	20	hypersoft	hypersoft	PROPN
cana-5360	639	21	environment	environment	NOUN
cana-5360	639	22	based	base	VERB
cana-5360	639	23	on	on	ADP
cana-5360	639	24	correlation	correlation	NOUN
cana-5360	639	25	coefficient	coefficient	NOUN
cana-5360	639	26	and	and	CCONJ
cana-5360	639	27	its	its	PRON
cana-5360	639	28	application	application	NOUN
cana-5360	639	29	towards	towards	ADP
cana-5360	639	30	the	the	DET
cana-5360	639	31	selection	selection	NOUN
cana-5360	639	32	of	of	ADP
cana-5360	639	33	antivirus	antivirus	NOUN
cana-5360	639	34	mask	mask	NOUN
cana-5360	639	35	in	in	ADP
cana-5360	639	36	covid-19	covid-19	PROPN
cana-5360	639	37	pandemic	pandemic	ADJ
cana-5360	639	38	hindawi	hindawi	ADJ
cana-5360	639	39	complexity	complexity	NOUN
cana-5360	639	40	.	.	PUNCT
cana-5360	640	1	[	[	X
cana-5360	640	2	25	25	NUM
cana-5360	640	3	]	]	PUNCT
cana-5360	640	4	g.	g.	PROPN
cana-5360	640	5	k.	k.	PROPN
cana-5360	640	6	revathi	revathi	PROPN
cana-5360	640	7	,	,	PUNCT
cana-5360	640	8	e.	e.	PROPN
cana-5360	640	9	roja	roja	PROPN
cana-5360	640	10	and	and	CCONJ
cana-5360	640	11	m.	m.	PROPN
cana-5360	640	12	k.	k.	PROPN
cana-5360	640	13	uma	uma	PROPN
cana-5360	640	14	(	(	PUNCT
cana-5360	640	15	2010	2010	NUM
cana-5360	640	16	)	)	PUNCT
cana-5360	640	17	fuzzy	fuzzy	ADJ
cana-5360	640	18	contra	contra	PROPN
cana-5360	640	19	g	g	PROPN
cana-5360	640	20	continuous	continuous	ADJ
cana-5360	640	21	functions	function	NOUN
cana-5360	640	22	,	,	PUNCT
cana-5360	640	23	international	international	ADJ
cana-5360	640	24	review	review	NOUN
cana-5360	640	25	of	of	ADP
cana-5360	640	26	fuzzy	fuzzy	ADJ
cana-5360	640	27	mathematics	mathematic	NOUN
cana-5360	640	28	,	,	PUNCT
cana-5360	640	29	(	(	PUNCT
cana-5360	640	30	5	5	NUM
cana-5360	640	31	)	)	PUNCT
cana-5360	640	32	,	,	PUNCT
cana-5360	640	33	81	81	NUM
cana-5360	640	34	-	-	SYM
cana-5360	640	35	91	91	NUM
cana-5360	640	36	.	.	PUNCT
cana-5360	641	1	[	[	X
cana-5360	641	2	26	26	NUM
cana-5360	641	3	]	]	X
cana-5360	641	4	s.	s.	PROPN
cana-5360	641	5	saha	saha	PROPN
cana-5360	641	6	,	,	PUNCT
cana-5360	641	7	fuzzy	fuzzy	ADJ
cana-5360	641	8	𝛿-continuous	𝛿-continuous	ADJ
cana-5360	641	9	mappings	mapping	NOUN
cana-5360	641	10	,	,	PUNCT
cana-5360	641	11	journal	journal	NOUN
cana-5360	641	12	of	of	ADP
cana-5360	641	13	mathematical	mathematical	ADJ
cana-5360	641	14	analysis	analysis	NOUN
cana-5360	641	15	and	and	CCONJ
cana-5360	641	16	applications	application	NOUN
cana-5360	641	17	,	,	PUNCT
cana-5360	641	18	126	126	NUM
cana-5360	641	19	(	(	PUNCT
cana-5360	641	20	1987	1987	NUM
cana-5360	641	21	)	)	PUNCT
cana-5360	641	22	,	,	PUNCT
cana-5360	641	23	130	130	NUM
cana-5360	641	24	-	-	SYM
cana-5360	641	25	142	142	NUM
cana-5360	641	26	.	.	PUNCT
cana-5360	642	1	[	[	X
cana-5360	642	2	27	27	NUM
cana-5360	642	3	]	]	X
cana-5360	642	4	r.	r.	PROPN
cana-5360	642	5	santhi	santhi	PROPN
cana-5360	642	6	and	and	CCONJ
cana-5360	642	7	k.	k.	PROPN
cana-5360	642	8	arul	arul	PROPN
cana-5360	642	9	prakash	prakash	PROPN
cana-5360	642	10	(	(	PUNCT
cana-5360	642	11	2011	2011	NUM
cana-5360	642	12	)	)	PUNCT
cana-5360	642	13	,	,	PUNCT
cana-5360	642	14	intuitionistic	intuitionistic	ADJ
cana-5360	642	15	fuzzy	fuzzy	ADJ
cana-5360	642	16	contra	contra	PROPN
cana-5360	642	17	semi	semi	ADJ
cana-5360	642	18	-	-	ADJ
cana-5360	642	19	generalised	generalised	ADJ
cana-5360	642	20	continuous	continuous	ADJ
cana-5360	642	21	mappings	mapping	NOUN
cana-5360	642	22	,	,	PUNCT
cana-5360	642	23	(	(	PUNCT
cana-5360	642	24	3	3	NUM
cana-5360	642	25	)	)	PUNCT
cana-5360	642	26	,	,	PUNCT
cana-5360	642	27	30	30	NUM
cana-5360	642	28	-	-	SYM
cana-5360	642	29	40	40	NUM
cana-5360	642	30	.	.	PUNCT
cana-5360	643	1	[	[	X
cana-5360	643	2	28	28	NUM
cana-5360	643	3	]	]	X
cana-5360	643	4	p.	p.	PROPN
cana-5360	643	5	surendra	surendra	PROPN
cana-5360	643	6	,	,	PUNCT
cana-5360	643	7	k.	k.	PROPN
cana-5360	643	8	chitirakala	chitirakala	PROPN
cana-5360	643	9	and	and	CCONJ
cana-5360	643	10	a.	a.	NOUN
cana-5360	643	11	vadivel	vadivel	NOUN
cana-5360	643	12	,	,	PUNCT
cana-5360	643	13	𝛿-open	𝛿-open	VERB
cana-5360	643	14	sets	set	NOUN
cana-5360	643	15	in	in	ADP
cana-5360	643	16	neutrosophic	neutrosophic	ADJ
cana-5360	643	17	hypersoft	hypersoft	PROPN
cana-5360	643	18	topological	topological	ADJ
cana-5360	643	19	spaces	space	NOUN
cana-5360	643	20	,	,	PUNCT
cana-5360	643	21	international	international	ADJ
cana-5360	643	22	journal	journal	NOUN
cana-5360	643	23	of	of	ADP
cana-5360	643	24	neutrosophic	neutrosophic	ADJ
cana-5360	643	25	science	science	NOUN
cana-5360	643	26	,	,	PUNCT
cana-5360	643	27	20	20	NUM
cana-5360	643	28	(	(	PUNCT
cana-5360	643	29	4	4	NUM
cana-5360	643	30	)	)	PUNCT
cana-5360	643	31	,	,	PUNCT
cana-5360	643	32	(	(	PUNCT
cana-5360	643	33	2023	2023	NUM
cana-5360	643	34	)	)	PUNCT
cana-5360	643	35	,	,	PUNCT
cana-5360	643	36	93	93	NUM
cana-5360	643	37	-	-	SYM
cana-5360	643	38	105	105	NUM
cana-5360	643	39	.	.	PUNCT
cana-5360	644	1	[	[	X
cana-5360	644	2	29	29	NUM
cana-5360	644	3	]	]	X
cana-5360	644	4	p.	p.	PROPN
cana-5360	644	5	surendra	surendra	PROPN
cana-5360	644	6	,	,	PUNCT
cana-5360	644	7	a.	a.	NOUN
cana-5360	644	8	vadivel	vadivel	NOUN
cana-5360	644	9	and	and	CCONJ
cana-5360	644	10	k.	k.	PROPN
cana-5360	644	11	chitirakala	chitirakala	PROPN
cana-5360	644	12	,	,	PUNCT
cana-5360	644	13	𝛿	𝛿	DET
cana-5360	644	14	-separation	-separation	PROPN
cana-5360	644	15	axioms	axiom	NOUN
cana-5360	644	16	on	on	ADP
cana-5360	644	17	fuzzy	fuzzy	ADJ
cana-5360	644	18	hypersoft	hypersoft	PROPN
cana-5360	644	19	topological	topological	ADJ
cana-5360	644	20	spaces	space	NOUN
cana-5360	644	21	,	,	PUNCT
cana-5360	644	22	international	international	ADJ
cana-5360	644	23	journal	journal	NOUN
cana-5360	644	24	of	of	ADP
cana-5360	644	25	neutrosophic	neutrosophic	ADJ
cana-5360	644	26	science	science	NOUN
cana-5360	644	27	,	,	PUNCT
cana-5360	644	28	23	23	NUM
cana-5360	644	29	(	(	PUNCT
cana-5360	644	30	1	1	NUM
cana-5360	644	31	)	)	PUNCT
cana-5360	644	32	,	,	PUNCT
cana-5360	644	33	(	(	PUNCT
cana-5360	644	34	2024	2024	NUM
cana-5360	644	35	)	)	PUNCT
cana-5360	644	36	,	,	PUNCT
cana-5360	644	37	17	17	NUM
cana-5360	644	38	-	-	SYM
cana-5360	644	39	26	26	NUM
cana-5360	644	40	.	.	PUNCT
cana-5360	645	1	[	[	X
cana-5360	645	2	30	30	NUM
cana-5360	645	3	]	]	PUNCT
cana-5360	645	4	m.	m.	NOUN
cana-5360	645	5	shukla	shukla	NOUN
cana-5360	645	6	(	(	PUNCT
cana-5360	645	7	2013	2013	NUM
cana-5360	645	8	)	)	PUNCT
cana-5360	645	9	,	,	PUNCT
cana-5360	645	10	on	on	ADP
cana-5360	645	11	fuzzy	fuzzy	ADJ
cana-5360	645	12	contra	contra	PROPN
cana-5360	645	13	𝑔∗	𝑔∗	PROPN
cana-5360	645	14	semi	semi	ADJ
cana-5360	645	15	-	-	ADJ
cana-5360	645	16	continuous	continuous	ADJ
cana-5360	645	17	functions	function	NOUN
cana-5360	645	18	,	,	PUNCT
cana-5360	645	19	international	international	ADJ
cana-5360	645	20	journal	journal	NOUN
cana-5360	645	21	of	of	ADP
cana-5360	645	22	scientific	scientific	ADJ
cana-5360	645	23	and	and	CCONJ
cana-5360	645	24	engineering	engineering	NOUN
cana-5360	645	25	research	research	NOUN
cana-5360	645	26	(	(	PUNCT
cana-5360	645	27	4	4	NUM
cana-5360	645	28	)	)	PUNCT
cana-5360	645	29	.	.	PUNCT
cana-5360	646	1	[	[	X
cana-5360	646	2	31	31	NUM
cana-5360	646	3	]	]	PUNCT
cana-5360	646	4	m.	m.	NOUN
cana-5360	646	5	udhaya	udhaya	PROPN
cana-5360	646	6	shalini	shalini	PROPN
cana-5360	646	7	and	and	CCONJ
cana-5360	646	8	a.	a.	PROPN
cana-5360	646	9	stanis	stanis	PROPN
cana-5360	646	10	arul	arul	PROPN
cana-5360	646	11	mary	mary	PROPN
cana-5360	646	12	(	(	PUNCT
cana-5360	646	13	2022	2022	NUM
cana-5360	646	14	)	)	PUNCT
cana-5360	646	15	,	,	PUNCT
cana-5360	646	16	generalized	generalize	VERB
cana-5360	646	17	pre	pre	ADJ
cana-5360	646	18	-	-	ADJ
cana-5360	646	19	closed	closed	ADJ
cana-5360	646	20	sets	set	NOUN
cana-5360	646	21	in	in	ADP
cana-5360	646	22	pythagorean	pythagorean	PROPN
cana-5360	646	23	fuzzy	fuzzy	ADJ
cana-5360	646	24	topological	topological	ADJ
cana-5360	646	25	spaces	space	NOUN
cana-5360	646	26	,	,	PUNCT
cana-5360	646	27	international	international	ADJ
cana-5360	646	28	journal	journal	NOUN
cana-5360	646	29	of	of	ADP
cana-5360	646	30	creative	creative	ADJ
cana-5360	646	31	research	research	NOUN
cana-5360	646	32	thoughts	thought	NOUN
cana-5360	646	33	(	(	PUNCT
cana-5360	646	34	ijcrt	ijcrt	NOUN
cana-5360	646	35	)	)	PUNCT
cana-5360	646	36	,	,	PUNCT
cana-5360	646	37	10	10	NUM
cana-5360	646	38	(	(	PUNCT
cana-5360	646	39	30	30	NUM
cana-5360	646	40	)	)	PUNCT
cana-5360	646	41	,	,	PUNCT
cana-5360	646	42	e142	e142	PROPN
cana-5360	646	43	-	-	PUNCT
cana-5360	646	44	e147	e147	PROPN
cana-5360	646	45	.	.	PUNCT
cana-5360	647	1	[	[	X
cana-5360	647	2	32	32	NUM
cana-5360	647	3	]	]	PUNCT
cana-5360	647	4	a.	a.	NOUN
cana-5360	647	5	vadivel	vadivel	NOUN
cana-5360	647	6	,	,	PUNCT
cana-5360	647	7	m.	m.	NOUN
cana-5360	647	8	seenivasan	seenivasan	NOUN
cana-5360	647	9	and	and	CCONJ
cana-5360	647	10	c.	c.	PROPN
cana-5360	647	11	john	john	PROPN
cana-5360	647	12	sundar	sundar	PROPN
cana-5360	647	13	,	,	PUNCT
cana-5360	647	14	an	an	DET
cana-5360	647	15	introduction	introduction	NOUN
cana-5360	647	16	to	to	ADP
cana-5360	647	17	𝛿	𝛿	PRON
cana-5360	647	18	-open	-open	ADJ
cana-5360	647	19	sets	set	NOUN
cana-5360	647	20	in	in	ADP
cana-5360	647	21	a	a	DET
cana-5360	647	22	communications	communication	NOUN
cana-5360	647	23	on	on	ADP
cana-5360	647	24	applied	apply	VERB
cana-5360	647	25	nonlinear	nonlinear	ADJ
cana-5360	647	26	analysis	analysis	NOUN
cana-5360	647	27	issn	issn	NOUN
cana-5360	647	28	:	:	PUNCT
cana-5360	647	29	1074	1074	NUM
cana-5360	647	30	-	-	PUNCT
cana-5360	647	31	133x	133x	NUM
cana-5360	647	32	vol	vol	VERB
cana-5360	647	33	32	32	NUM
cana-5360	647	34	no	no	NOUN
cana-5360	647	35	.	.	PUNCT
cana-5360	648	1	10s	10	NOUN
cana-5360	648	2	(	(	PUNCT
cana-5360	648	3	2025	2025	NUM
cana-5360	648	4	)	)	PUNCT
cana-5360	648	5	1946	1946	NUM
cana-5360	648	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5360	648	7	neutrosophic	neutrosophic	PROPN
cana-5360	648	8	topological	topological	ADJ
cana-5360	648	9	spaces	space	NOUN
cana-5360	648	10	,	,	PUNCT
cana-5360	648	11	journal	journal	NOUN
cana-5360	648	12	of	of	ADP
cana-5360	648	13	physics	physics	PROPN
cana-5360	648	14	:	:	PUNCT
cana-5360	648	15	conference	conference	NOUN
cana-5360	648	16	series	series	NOUN
cana-5360	648	17	,	,	PUNCT
cana-5360	648	18	1724	1724	NUM
cana-5360	648	19	(	(	PUNCT
cana-5360	648	20	2021	2021	NUM
cana-5360	648	21	)	)	PUNCT
cana-5360	648	22	,	,	PUNCT
cana-5360	648	23	012011	012011	NUM
cana-5360	648	24	.	.	PUNCT
cana-5360	649	1	[	[	X
cana-5360	649	2	33	33	NUM
cana-5360	649	3	]	]	PUNCT
cana-5360	649	4	a.	a.	NOUN
cana-5360	649	5	vadivel	vadivel	NOUN
cana-5360	649	6	,	,	PUNCT
cana-5360	649	7	c.	c.	PROPN
cana-5360	649	8	john	john	PROPN
cana-5360	649	9	sundar	sundar	PROPN
cana-5360	649	10	,	,	PUNCT
cana-5360	649	11	k.	k.	PROPN
cana-5360	649	12	kirubadevi	kirubadevi	PROPN
cana-5360	649	13	and	and	CCONJ
cana-5360	649	14	s.	s.	PROPN
cana-5360	649	15	tamilselvan	tamilselvan	PROPN
cana-5360	649	16	,	,	PUNCT
cana-5360	649	17	more	more	ADJ
cana-5360	649	18	on	on	ADP
cana-5360	649	19	neutrosophic	neutrosophic	ADJ
cana-5360	649	20	nano	nano	NOUN
cana-5360	649	21	open	open	ADJ
cana-5360	649	22	sets	set	NOUN
cana-5360	649	23	,	,	PUNCT
cana-5360	649	24	international	international	ADJ
cana-5360	649	25	journal	journal	NOUN
cana-5360	649	26	of	of	ADP
cana-5360	649	27	neutrosophic	neutrosophic	ADJ
cana-5360	649	28	science	science	NOUN
cana-5360	649	29	(	(	PUNCT
cana-5360	649	30	ijns	ijns	PROPN
cana-5360	649	31	)	)	PUNCT
cana-5360	649	32	,	,	PUNCT
cana-5360	649	33	18	18	NUM
cana-5360	649	34	(	(	PUNCT
cana-5360	649	35	4	4	NUM
cana-5360	649	36	)	)	PUNCT
cana-5360	649	37	(	(	PUNCT
cana-5360	649	38	2022	2022	NUM
cana-5360	649	39	)	)	PUNCT
cana-5360	649	40	,	,	PUNCT
cana-5360	649	41	204	204	NUM
cana-5360	649	42	-	-	SYM
cana-5360	649	43	222	222	NUM
cana-5360	649	44	.	.	PUNCT
cana-5360	650	1	[	[	X
cana-5360	650	2	34	34	NUM
cana-5360	650	3	]	]	X
cana-5360	650	4	r.	r.	PROPN
cana-5360	650	5	h.	h.	PROPN
cana-5360	650	6	warren	warren	PROPN
cana-5360	650	7	(	(	PUNCT
cana-5360	650	8	1978	1978	NUM
cana-5360	650	9	)	)	PUNCT
cana-5360	650	10	,	,	PUNCT
cana-5360	650	11	neighborhoods	neighborhood	NOUN
cana-5360	650	12	,	,	PUNCT
cana-5360	650	13	bases	basis	NOUN
cana-5360	650	14	and	and	CCONJ
cana-5360	650	15	continuity	continuity	NOUN
cana-5360	650	16	in	in	ADP
cana-5360	650	17	fuzzy	fuzzy	ADJ
cana-5360	650	18	topological	topological	ADJ
cana-5360	650	19	spaces	space	NOUN
cana-5360	650	20	,	,	PUNCT
cana-5360	650	21	rocky	rocky	ADJ
cana-5360	650	22	mountain	mountain	NOUN
cana-5360	650	23	journal	journal	NOUN
cana-5360	650	24	of	of	ADP
cana-5360	650	25	mathematics	mathematic	NOUN
cana-5360	650	26	,	,	PUNCT
cana-5360	650	27	(	(	PUNCT
cana-5360	650	28	8)	8)	NUM
cana-5360	650	29	.	.	PUNCT
cana-5360	651	1	[	[	X
cana-5360	651	2	35	35	NUM
cana-5360	651	3	]	]	X
cana-5360	651	4	gw	gw	PROPN
cana-5360	651	5	.	.	PUNCT
cana-5360	651	6	wei	wei	PROPN
cana-5360	651	7	and	and	CCONJ
cana-5360	651	8	g.	g.	PROPN
cana-5360	651	9	lan	lan	PROPN
cana-5360	651	10	grey	grey	PROPN
cana-5360	651	11	(	(	PUNCT
cana-5360	651	12	2008	2008	NUM
cana-5360	651	13	)	)	PUNCT
cana-5360	651	14	,	,	PUNCT
cana-5360	651	15	relational	relational	ADJ
cana-5360	651	16	analysis	analysis	NOUN
cana-5360	651	17	method	method	NOUN
cana-5360	651	18	for	for	ADP
cana-5360	651	19	interval	interval	NOUN
cana-5360	651	20	valued	value	VERB
cana-5360	651	21	intuitionistic	intuitionistic	ADJ
cana-5360	651	22	fuzzy	fuzzy	ADJ
cana-5360	651	23	multiple	multiple	ADJ
cana-5360	651	24	attribute	attribute	NOUN
cana-5360	651	25	decision	decision	NOUN
cana-5360	651	26	making	making	NOUN
cana-5360	651	27	,	,	PUNCT
cana-5360	651	28	in	in	ADP
cana-5360	651	29	fifth	fifth	ADJ
cana-5360	651	30	international	international	ADJ
cana-5360	651	31	conference	conference	NOUN
cana-5360	651	32	on	on	ADP
cana-5360	651	33	fuzzy	fuzzy	ADJ
cana-5360	651	34	systems	system	NOUN
cana-5360	651	35	and	and	CCONJ
cana-5360	651	36	knowledge	knowledge	NOUN
cana-5360	651	37	discovery	discovery	NOUN
cana-5360	651	38	,	,	PUNCT
cana-5360	651	39	291	291	NUM
cana-5360	651	40	-	-	SYM
cana-5360	651	41	295	295	NUM
cana-5360	651	42	.	.	PUNCT
cana-5360	652	1	[	[	X
cana-5360	652	2	36	36	NUM
cana-5360	652	3	]	]	X
cana-5360	652	4	r.	r.	PROPN
cana-5360	652	5	r.	r.	PROPN
cana-5360	652	6	yager	yager	PROPN
cana-5360	652	7	(	(	PUNCT
cana-5360	652	8	2013	2013	NUM
cana-5360	652	9	)	)	PUNCT
cana-5360	652	10	,	,	PUNCT
cana-5360	652	11	pythagorean	pythagorean	PROPN
cana-5360	652	12	membership	membership	NOUN
cana-5360	652	13	grades	grade	NOUN
cana-5360	652	14	in	in	ADP
cana-5360	652	15	multicriteria	multicriteria	PROPN
cana-5360	652	16	decision	decision	NOUN
cana-5360	652	17	making	making	NOUN
cana-5360	652	18	,	,	PUNCT
cana-5360	652	19	in	in	ADP
cana-5360	652	20	:	:	PUNCT
cana-5360	652	21	technical	technical	ADJ
cana-5360	652	22	report	report	NOUN
cana-5360	652	23	𝑀𝐼𝐼-3301	𝑀𝐼𝐼-3301	PROPN
cana-5360	652	24	.	.	PUNCT
cana-5360	653	1	machine	machine	NOUN
cana-5360	653	2	intelligence	intelligence	PROPN
cana-5360	653	3	institute	institute	PROPN
cana-5360	653	4	,	,	PUNCT
cana-5360	653	5	iona	iona	PROPN
cana-5360	653	6	college	college	PROPN
cana-5360	653	7	,	,	PUNCT
cana-5360	653	8	new	new	ADJ
cana-5360	653	9	rochelle	rochelle	NOUN
cana-5360	653	10	.	.	PUNCT
cana-5360	654	1	[	[	X
cana-5360	654	2	37	37	NUM
cana-5360	654	3	]	]	X
cana-5360	654	4	r.	r.	PROPN
cana-5360	654	5	r.	r.	PROPN
cana-5360	654	6	yager	yager	PROPN
cana-5360	654	7	(	(	PUNCT
cana-5360	654	8	2013	2013	NUM
cana-5360	654	9	)	)	PUNCT
cana-5360	654	10	,	,	PUNCT
cana-5360	654	11	pythagorean	pythagorean	PROPN
cana-5360	654	12	fuzzy	fuzzy	ADJ
cana-5360	654	13	subsets	subset	NOUN
cana-5360	654	14	,	,	PUNCT
cana-5360	654	15	in	in	ADP
cana-5360	654	16	:	:	PUNCT
cana-5360	654	17	proceedings	proceeding	NOUN
cana-5360	654	18	of	of	ADP
cana-5360	654	19	the	the	DET
cana-5360	654	20	joint	joint	ADJ
cana-5360	654	21	𝐼𝐹𝑆𝐴	𝐼𝐹𝑆𝐴	PROPN
cana-5360	654	22	world	world	PROPN
cana-5360	654	23	congress	congress	PROPN
cana-5360	654	24	𝑁𝐴𝐹𝐼𝑃𝑆	𝑁𝐴𝐹𝐼𝑃𝑆	PROPN
cana-5360	654	25	annual	annual	ADJ
cana-5360	654	26	meeting	meeting	NOUN
cana-5360	654	27	,	,	PUNCT
cana-5360	654	28	57	57	NUM
cana-5360	654	29	-	-	SYM
cana-5360	654	30	61	61	NUM
cana-5360	654	31	.	.	PUNCT
cana-5360	655	1	[	[	X
cana-5360	655	2	38	38	NUM
cana-5360	655	3	]	]	PUNCT
cana-5360	655	4	r.	r.	PROPN
cana-5360	655	5	r.	r.	PROPN
cana-5360	655	6	yager	yager	PROPN
cana-5360	655	7	and	and	CCONJ
cana-5360	655	8	a.	a.	NOUN
cana-5360	655	9	m.	m.	NOUN
cana-5360	655	10	abbasov	abbasov	PROPN
cana-5360	655	11	(	(	PUNCT
cana-5360	655	12	2013	2013	NUM
cana-5360	655	13	)	)	PUNCT
cana-5360	655	14	,	,	PUNCT
cana-5360	655	15	pythagorean	pythagorean	PROPN
cana-5360	655	16	membership	membership	NOUN
cana-5360	655	17	grades	grade	NOUN
cana-5360	655	18	,	,	PUNCT
cana-5360	655	19	complex	complex	ADJ
cana-5360	655	20	numbers	number	NOUN
cana-5360	655	21	,	,	PUNCT
cana-5360	655	22	and	and	CCONJ
cana-5360	655	23	decision	decision	NOUN
cana-5360	655	24	making	making	NOUN
cana-5360	655	25	,	,	PUNCT
cana-5360	655	26	int	int	PROPN
cana-5360	655	27	j	j	PROPN
cana-5360	655	28	intell	intell	PROPN
cana-5360	655	29	syst	syst	PROPN
cana-5360	655	30	(	(	PUNCT
cana-5360	655	31	28	28	NUM
cana-5360	655	32	)	)	PUNCT
cana-5360	655	33	,	,	PUNCT
cana-5360	655	34	436	436	NUM
cana-5360	655	35	-	-	SYM
cana-5360	655	36	452	452	NUM
cana-5360	655	37	.	.	PUNCT
cana-5360	656	1	[	[	X
cana-5360	656	2	39	39	NUM
cana-5360	656	3	]	]	PUNCT
cana-5360	656	4	r.	r.	PROPN
cana-5360	656	5	r.	r.	PROPN
cana-5360	656	6	yager	yager	PROPN
cana-5360	656	7	(	(	PUNCT
cana-5360	656	8	2014	2014	NUM
cana-5360	656	9	)	)	PUNCT
cana-5360	656	10	,	,	PUNCT
cana-5360	656	11	pythagorean	pythagorean	PROPN
cana-5360	656	12	membership	membership	NOUN
cana-5360	656	13	grades	grade	NOUN
cana-5360	656	14	in	in	ADP
cana-5360	656	15	multicriteria	multicriteria	PROPN
cana-5360	656	16	decision	decision	NOUN
cana-5360	656	17	making	making	NOUN
cana-5360	656	18	,	,	PUNCT
cana-5360	656	19	𝐼𝐸𝐸𝐸	𝐼𝐸𝐸𝐸	PROPN
cana-5360	656	20	trans	trans	PROPN
cana-5360	656	21	fuzzy	fuzzy	PROPN
cana-5360	656	22	syst	syst	PROPN
cana-5360	656	23	.	.	PUNCT
cana-5360	657	1	22	22	NUM
cana-5360	657	2	(	(	PUNCT
cana-5360	657	3	4	4	NUM
cana-5360	657	4	)	)	PUNCT
cana-5360	657	5	,	,	PUNCT
cana-5360	657	6	958	958	NUM
cana-5360	657	7	-	-	SYM
cana-5360	657	8	965	965	NUM
cana-5360	657	9	.	.	PUNCT
cana-5360	658	1	[	[	X
cana-5360	658	2	40	40	NUM
cana-5360	658	3	]	]	PUNCT
cana-5360	658	4	l.	l.	PROPN
cana-5360	658	5	a.	a.	PROPN
cana-5360	658	6	zadeh	zadeh	PROPN
cana-5360	658	7	(	(	PUNCT
cana-5360	658	8	1965	1965	NUM
cana-5360	658	9	)	)	PUNCT
cana-5360	658	10	,	,	PUNCT
cana-5360	658	11	fuzzy	fuzzy	ADJ
cana-5360	658	12	sets	set	NOUN
cana-5360	658	13	,	,	PUNCT
cana-5360	658	14	inf	inf	PROPN
cana-5360	658	15	.	.	PROPN
cana-5360	658	16	control	control	PROPN
cana-5360	658	17	,	,	PUNCT
cana-5360	658	18	8	8	NUM
cana-5360	658	19	,	,	PUNCT
cana-5360	658	20	338	338	NUM
cana-5360	658	21	-	-	SYM
cana-5360	658	22	353	353	NUM
cana-5360	658	23	.	.	PUNCT
cana-5360	659	1	[	[	X
cana-5360	659	2	41	41	NUM
cana-5360	659	3	]	]	X
cana-5360	659	4	zahid	zahid	PROPN
cana-5360	659	5	hussain	hussain	PROPN
cana-5360	659	6	,	,	PUNCT
cana-5360	659	7	sherbaz	sherbaz	PROPN
cana-5360	659	8	alam	alam	PROPN
cana-5360	659	9	,	,	PUNCT
cana-5360	659	10	rashid	rashid	PROPN
cana-5360	659	11	hussian	hussian	PROPN
cana-5360	659	12	and	and	CCONJ
cana-5360	659	13	shams	sham	VERB
cana-5360	659	14	ur	ur	PROPN
cana-5360	659	15	rahman	rahman	PROPN
cana-5360	659	16	(	(	PUNCT
cana-5360	659	17	2024	2024	NUM
cana-5360	659	18	)	)	PUNCT
cana-5360	659	19	,	,	PUNCT
cana-5360	659	20	new	new	ADJ
cana-5360	659	21	similarity	similarity	NOUN
cana-5360	659	22	measure	measure	NOUN
cana-5360	659	23	of	of	ADP
cana-5360	659	24	pythagorean	pythagorean	PROPN
cana-5360	659	25	fuzzy	fuzzy	ADJ
cana-5360	659	26	sets	set	NOUN
cana-5360	659	27	based	base	VERB
cana-5360	659	28	on	on	ADP
cana-5360	659	29	the	the	DET
cana-5360	659	30	jaccard	jaccard	ADJ
cana-5360	659	31	index	index	NOUN
cana-5360	659	32	with	with	ADP
cana-5360	659	33	its	its	PRON
cana-5360	659	34	application	application	NOUN
cana-5360	659	35	to	to	ADP
cana-5360	659	36	clustering	clustering	NOUN
cana-5360	659	37	,	,	PUNCT
cana-5360	659	38	ain	ain	NOUN
cana-5360	659	39	shams	sham	NOUN
cana-5360	659	40	engineering	engineering	NOUN
cana-5360	659	41	journal	journal	NOUN
cana-5360	659	42	,	,	PUNCT
cana-5360	659	43	15	15	NUM
cana-5360	659	44	,	,	PUNCT
cana-5360	659	45	102294	102294	NUM
cana-5360	659	46	.	.	PUNCT
cana-5360	660	1	[	[	X
cana-5360	660	2	42	42	NUM
cana-5360	660	3	]	]	PUNCT
cana-5360	660	4	x.	x.	NOUN
cana-5360	660	5	zhang	zhang	PROPN
cana-5360	660	6	(	(	PUNCT
cana-5360	660	7	2016	2016	NUM
cana-5360	660	8	)	)	PUNCT
cana-5360	660	9	,	,	PUNCT
cana-5360	660	10	a	a	DET
cana-5360	660	11	novel	novel	ADJ
cana-5360	660	12	approach	approach	NOUN
cana-5360	660	13	based	base	VERB
cana-5360	660	14	on	on	ADP
cana-5360	660	15	similarity	similarity	NOUN
cana-5360	660	16	measure	measure	NOUN
cana-5360	660	17	for	for	ADP
cana-5360	660	18	pythagorean	pythagorean	PROPN
cana-5360	660	19	fuzzy	fuzzy	ADJ
cana-5360	660	20	multiple	multiple	ADJ
cana-5360	660	21	criteria	criterion	NOUN
cana-5360	660	22	group	group	NOUN
cana-5360	660	23	decision	decision	NOUN
cana-5360	660	24	making	making	NOUN
cana-5360	660	25	,	,	PUNCT
cana-5360	660	26	int	int	PROPN
cana-5360	660	27	j	j	PROPN
cana-5360	660	28	intell	intell	PROPN
cana-5360	660	29	syst	syst	PROPN
cana-5360	660	30	(	(	PUNCT
cana-5360	660	31	31	31	NUM
cana-5360	660	32	)	)	PUNCT
cana-5360	660	33	,	,	PUNCT
cana-5360	660	34	593	593	NUM
cana-5360	660	35	-	-	SYM
cana-5360	660	36	611	611	NUM
cana-5360	660	37	.	.	PUNCT