id	sid	tid	token	lemma	pos
cana-2737	1	1	communications	communication	NOUN
cana-2737	1	2	on	on	ADP
cana-2737	1	3	applied	apply	VERB
cana-2737	1	4	nonlinear	nonlinear	ADJ
cana-2737	1	5	analysis	analysis	NOUN
cana-2737	1	6	issn	issn	NOUN
cana-2737	1	7	:	:	PUNCT
cana-2737	1	8	1074	1074	NUM
cana-2737	1	9	-	-	PUNCT
cana-2737	1	10	133x	133x	NUM
cana-2737	1	11	vol	vol	NOUN
cana-2737	1	12	32	32	NUM
cana-2737	1	13	no	no	NOUN
cana-2737	1	14	.	.	PUNCT
cana-2737	2	1	4s	4s	NUM
cana-2737	2	2	(	(	PUNCT
cana-2737	2	3	2025	2025	NUM
cana-2737	2	4	)	)	PUNCT
cana-2737	2	5	26	26	NUM
cana-2737	3	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-2737	3	2	𝑴-open	𝑴-open	PROPN
cana-2737	3	3	maps	map	NOUN
cana-2737	3	4	and	and	CCONJ
cana-2737	3	5	its	its	PRON
cana-2737	3	6	applications	application	NOUN
cana-2737	3	7	in	in	ADP
cana-2737	3	8	pythagorean	pythagorean	PROPN
cana-2737	3	9	fuzzy	fuzzy	ADJ
cana-2737	3	10	topological	topological	PROPN
cana-2737	3	11	spaces	space	NOUN
cana-2737	3	12	b.	b.	PROPN
cana-2737	3	13	vijayalakshmi	vijayalakshmi	PROPN
cana-2737	3	14	𝟏	𝟏	NUM
cana-2737	3	15	,	,	PUNCT
cana-2737	3	16	m.	m.	NOUN
cana-2737	3	17	ramalakshmi	ramalakshmi	NOUN
cana-2737	3	18	𝟐	𝟐	NUM
cana-2737	3	19	,	,	PUNCT
cana-2737	3	20	a.	a.	NOUN
cana-2737	3	21	vadivel	vadivel	NOUN
cana-2737	3	22	𝟑	𝟑	PROPN
cana-2737	3	23	,	,	PUNCT
cana-2737	3	24	g.	g.	PROPN
cana-2737	3	25	saravanakumar	saravanakumar	PROPN
cana-2737	3	26	𝟒	𝟒	PROPN
cana-2737	3	27	1department	1department	NUM
cana-2737	3	28	of	of	ADP
cana-2737	3	29	mathematics	mathematic	NOUN
cana-2737	3	30	,	,	PUNCT
cana-2737	3	31	government	government	NOUN
cana-2737	3	32	arts	arts	PROPN
cana-2737	3	33	college	college	PROPN
cana-2737	3	34	,	,	PUNCT
cana-2737	3	35	chidambaram	chidambaram	PROPN
cana-2737	3	36	,	,	PUNCT
cana-2737	3	37	tamil	tamil	PROPN
cana-2737	3	38	nadu-608	nadu-608	NOUN
cana-2737	3	39	102	102	NUM
cana-2737	3	40	;	;	PUNCT
cana-2737	3	41	mathematics	mathematic	NOUN
cana-2737	3	42	section	section	NOUN
cana-2737	3	43	(	(	PUNCT
cana-2737	3	44	feat	feat	PROPN
cana-2737	3	45	)	)	PUNCT
cana-2737	3	46	,	,	PUNCT
cana-2737	3	47	annamalai	annamalai	PROPN
cana-2737	3	48	university	university	PROPN
cana-2737	3	49	,	,	PUNCT
cana-2737	3	50	annamalai	annamalai	PROPN
cana-2737	3	51	nagar	nagar	VERB
cana-2737	3	52	608	608	NUM
cana-2737	3	53	002	002	NUM
cana-2737	3	54	,	,	PUNCT
cana-2737	3	55	tamilnadu	tamilnadu	NOUN
cana-2737	3	56	.	.	PUNCT
cana-2737	4	1	2department	2department	NUM
cana-2737	4	2	of	of	ADP
cana-2737	4	3	mathematics	mathematic	NOUN
cana-2737	4	4	,	,	PUNCT
cana-2737	4	5	sri	sri	PROPN
cana-2737	4	6	meenakshi	meenakshi	PROPN
cana-2737	4	7	government	government	PROPN
cana-2737	4	8	arts	arts	PROPN
cana-2737	4	9	college	college	PROPN
cana-2737	4	10	for	for	ADP
cana-2737	4	11	women	woman	NOUN
cana-2737	4	12	(	(	PUNCT
cana-2737	4	13	a	a	X
cana-2737	4	14	)	)	PUNCT
cana-2737	4	15	,	,	PUNCT
cana-2737	4	16	madurai625	madurai625	PROPN
cana-2737	4	17	002	002	NUM
cana-2737	4	18	3	3	NUM
cana-2737	4	19	arignar	arignar	NOUN
cana-2737	4	20	anna	anna	NOUN
cana-2737	4	21	government	government	PROPN
cana-2737	4	22	arts	arts	PROPN
cana-2737	4	23	college	college	PROPN
cana-2737	4	24	,	,	PUNCT
cana-2737	4	25	namakkal	namakkal	NOUN
cana-2737	4	26	637	637	NUM
cana-2737	4	27	002	002	NUM
cana-2737	4	28	,	,	PUNCT
cana-2737	4	29	india	india	PROPN
cana-2737	4	30	.	.	PUNCT
cana-2737	5	1	3department	3department	NUM
cana-2737	5	2	of	of	ADP
cana-2737	5	3	mathematics	mathematic	NOUN
cana-2737	5	4	,	,	PUNCT
cana-2737	5	5	annamalai	annamalai	PROPN
cana-2737	5	6	university	university	PROPN
cana-2737	5	7	,	,	PUNCT
cana-2737	5	8	annamalai	annamalai	PROPN
cana-2737	5	9	nagar	nagar	VERB
cana-2737	5	10	608	608	NUM
cana-2737	5	11	002	002	NUM
cana-2737	5	12	,	,	PUNCT
cana-2737	5	13	india	india	PROPN
cana-2737	5	14	.	.	PUNCT
cana-2737	6	1	4department	4department	NUM
cana-2737	6	2	of	of	ADP
cana-2737	6	3	mathematics	mathematic	NOUN
cana-2737	6	4	,	,	PUNCT
cana-2737	7	1	vel	vel	PROPN
cana-2737	7	2	tech	tech	PROPN
cana-2737	7	3	rangarajan	rangarajan	PROPN
cana-2737	7	4	dr	dr	PROPN
cana-2737	7	5	.	.	PROPN
cana-2737	7	6	sagunthala	sagunthala	PROPN
cana-2737	7	7	r&d	r&d	PROPN
cana-2737	7	8	institute	institute	PROPN
cana-2737	7	9	of	of	ADP
cana-2737	7	10	science	science	NOUN
cana-2737	7	11	and	and	CCONJ
cana-2737	7	12	technology	technology	NOUN
cana-2737	7	13	(	(	PUNCT
cana-2737	7	14	deemed	deem	VERB
cana-2737	7	15	to	to	PART
cana-2737	7	16	be	be	AUX
cana-2737	7	17	university	university	NOUN
cana-2737	7	18	)	)	PUNCT
cana-2737	7	19	,	,	PUNCT
cana-2737	7	20	avadi	avadi	NOUN
cana-2737	7	21	,	,	PUNCT
cana-2737	7	22	chennai-600062	chennai-600062	NOUN
cana-2737	7	23	,	,	PUNCT
cana-2737	7	24	india	india	PROPN
cana-2737	7	25	1	1	NUM
cana-2737	7	26	mathvijaya2006au@gmail.com,2	mathvijaya2006au@gmail.com,2	VERB
cana-2737	7	27	ramalakshmikrishnan23@gmail.com	ramalakshmikrishnan23@gmail.com	NOUN
cana-2737	7	28	,	,	PUNCT
cana-2737	7	29	3	3	NUM
cana-2737	7	30	avmaths@gmail.com,4	avmaths@gmail.com,4	NOUN
cana-2737	7	31	saravananguru2612@gmail.com	saravananguru2612@gmail.com	X
cana-2737	7	32	article	article	NOUN
cana-2737	7	33	history	history	NOUN
cana-2737	7	34	:	:	PUNCT
cana-2737	7	35	received	receive	VERB
cana-2737	7	36	:	:	PUNCT
cana-2737	7	37	11	11	NUM
cana-2737	7	38	-	-	SYM
cana-2737	7	39	09	09	NUM
cana-2737	7	40	-	-	PUNCT
cana-2737	7	41	2024	2024	NUM
cana-2737	7	42	revised	revise	VERB
cana-2737	7	43	:	:	PUNCT
cana-2737	7	44	16	16	NUM
cana-2737	7	45	-	-	SYM
cana-2737	7	46	11	11	NUM
cana-2737	7	47	-	-	PUNCT
cana-2737	7	48	2024	2024	NUM
cana-2737	7	49	accepted	accept	VERB
cana-2737	7	50	:	:	PUNCT
cana-2737	7	51	26	26	NUM
cana-2737	7	52	-	-	SYM
cana-2737	7	53	11	11	NUM
cana-2737	7	54	-	-	PUNCT
cana-2737	7	55	2024	2024	NUM
cana-2737	7	56	abstract	abstract	NOUN
cana-2737	7	57	:	:	PUNCT
cana-2737	7	58	in	in	ADP
cana-2737	7	59	this	this	DET
cana-2737	7	60	paper	paper	NOUN
cana-2737	7	61	,	,	PUNCT
cana-2737	7	62	we	we	PRON
cana-2737	7	63	introduce	introduce	VERB
cana-2737	7	64	and	and	CCONJ
cana-2737	7	65	investigate	investigate	VERB
cana-2737	7	66	pythagorean	pythagorean	PROPN
cana-2737	7	67	fuzzy	fuzzy	NOUN
cana-2737	7	68	𝑀-open	𝑀-open	PROPN
cana-2737	7	69	and	and	CCONJ
cana-2737	7	70	closed	closed	ADJ
cana-2737	7	71	maps	map	NOUN
cana-2737	7	72	in	in	ADP
cana-2737	7	73	pythagorean	pythagorean	PROPN
cana-2737	7	74	fuzzy	fuzzy	ADJ
cana-2737	7	75	topological	topological	ADJ
cana-2737	7	76	spaces	space	NOUN
cana-2737	7	77	and	and	CCONJ
cana-2737	7	78	also	also	ADV
cana-2737	7	79	discuss	discuss	VERB
cana-2737	7	80	about	about	ADP
cana-2737	7	81	some	some	DET
cana-2737	7	82	properties	property	NOUN
cana-2737	7	83	and	and	CCONJ
cana-2737	7	84	characterization	characterization	NOUN
cana-2737	7	85	of	of	ADP
cana-2737	7	86	pythagorean	pythagorean	ADJ
cana-2737	7	87	fuzzy	fuzzy	ADJ
cana-2737	7	88	maps	map	NOUN
cana-2737	7	89	.	.	PUNCT
cana-2737	8	1	also	also	ADV
cana-2737	8	2	one	one	NUM
cana-2737	8	3	real	real	ADJ
cana-2737	8	4	life	life	NOUN
cana-2737	8	5	applications	application	NOUN
cana-2737	8	6	,	,	PUNCT
cana-2737	8	7	we	we	PRON
cana-2737	8	8	applied	apply	VERB
cana-2737	8	9	entropy	entropy	NOUN
cana-2737	8	10	measure	measure	NOUN
cana-2737	8	11	for	for	ADP
cana-2737	8	12	decision	decision	NOUN
cana-2737	8	13	making	making	NOUN
cana-2737	8	14	problem	problem	NOUN
cana-2737	8	15	of	of	ADP
cana-2737	8	16	diet	diet	NOUN
cana-2737	8	17	selection	selection	NOUN
cana-2737	8	18	based	base	VERB
cana-2737	8	19	on	on	ADP
cana-2737	8	20	the	the	DET
cana-2737	8	21	performance	performance	NOUN
cana-2737	8	22	.	.	PUNCT
cana-2737	9	1	keywords	keyword	NOUN
cana-2737	9	2	pythagorean	pythagorean	VERB
cana-2737	9	3	fuzzy	fuzzy	ADJ
cana-2737	9	4	m	m	ADJ
cana-2737	9	5	-	-	ADJ
cana-2737	9	6	open	open	ADJ
cana-2737	9	7	maps	map	NOUN
cana-2737	9	8	,	,	PUNCT
cana-2737	9	9	pythagorean	pythagorean	PROPN
cana-2737	9	10	fuzzy	fuzzy	ADJ
cana-2737	9	11	m	m	PROPN
cana-2737	9	12	-	-	ADJ
cana-2737	9	13	closed	closed	ADJ
cana-2737	9	14	maps	map	NOUN
cana-2737	9	15	,	,	PUNCT
cana-2737	9	16	pythagorean	pythagorean	PROPN
cana-2737	9	17	fuzzy	fuzzy	ADJ
cana-2737	9	18	entropy	entropy	PROPN
cana-2737	9	19	.	.	PUNCT
cana-2737	10	1	1	1	X
cana-2737	10	2	.	.	X
cana-2737	10	3	introduction	introduction	NOUN
cana-2737	10	4	considering	consider	VERB
cana-2737	10	5	the	the	DET
cana-2737	10	6	imprecision	imprecision	NOUN
cana-2737	10	7	in	in	ADP
cana-2737	10	8	decision	decision	NOUN
cana-2737	10	9	-	-	PUNCT
cana-2737	10	10	making	making	NOUN
cana-2737	10	11	,	,	PUNCT
cana-2737	10	12	zadeh	zadeh	PROPN
cana-2737	11	1	[	[	X
cana-2737	11	2	35	35	NUM
cana-2737	11	3	]	]	PUNCT
cana-2737	11	4	introduced	introduce	VERB
cana-2737	11	5	the	the	DET
cana-2737	11	6	idea	idea	NOUN
cana-2737	11	7	of	of	ADP
cana-2737	11	8	fuzzy	fuzzy	ADJ
cana-2737	11	9	set	set	NOUN
cana-2737	11	10	which	which	PRON
cana-2737	11	11	has	have	VERB
cana-2737	11	12	a	a	DET
cana-2737	11	13	membership	membership	NOUN
cana-2737	11	14	function	function	NOUN
cana-2737	11	15	,	,	PUNCT
cana-2737	11	16	𝜇	𝜇	ADP
cana-2737	11	17	that	that	DET
cana-2737	11	18	assigns	assign	NOUN
cana-2737	11	19	to	to	ADP
cana-2737	11	20	each	each	DET
cana-2737	11	21	element	element	NOUN
cana-2737	11	22	of	of	ADP
cana-2737	11	23	the	the	DET
cana-2737	11	24	universe	universe	NOUN
cana-2737	11	25	of	of	ADP
cana-2737	11	26	discourse	discourse	NOUN
cana-2737	11	27	,	,	PUNCT
cana-2737	11	28	a	a	DET
cana-2737	11	29	number	number	NOUN
cana-2737	11	30	from	from	ADP
cana-2737	11	31	the	the	DET
cana-2737	11	32	unit	unit	NOUN
cana-2737	11	33	nterval	nterval	NOUN
cana-2737	12	1	[	[	X
cana-2737	12	2	0,1	0,1	NUM
cana-2737	12	3	]	]	PUNCT
cana-2737	12	4	to	to	PART
cana-2737	12	5	indicate	indicate	VERB
cana-2737	12	6	the	the	DET
cana-2737	12	7	degree	degree	NOUN
cana-2737	12	8	of	of	ADP
cana-2737	12	9	belongingness	belongingness	NOUN
cana-2737	12	10	to	to	ADP
cana-2737	12	11	the	the	DET
cana-2737	12	12	set	set	NOUN
cana-2737	12	13	under	under	ADP
cana-2737	12	14	consideration	consideration	NOUN
cana-2737	12	15	.	.	PUNCT
cana-2737	13	1	the	the	DET
cana-2737	13	2	notion	notion	NOUN
cana-2737	13	3	of	of	ADP
cana-2737	13	4	fuzzy	fuzzy	ADJ
cana-2737	13	5	sets	set	NOUN
cana-2737	13	6	generalizes	generalize	VERB
cana-2737	13	7	classical	classical	ADJ
cana-2737	13	8	sets	set	NOUN
cana-2737	13	9	theory	theory	NOUN
cana-2737	13	10	by	by	ADP
cana-2737	13	11	allowing	allow	VERB
cana-2737	13	12	intermediate	intermediate	ADJ
cana-2737	13	13	situations	situation	NOUN
cana-2737	13	14	between	between	ADP
cana-2737	13	15	the	the	DET
cana-2737	13	16	whole	whole	NOUN
cana-2737	13	17	and	and	CCONJ
cana-2737	13	18	nothing	nothing	PRON
cana-2737	13	19	.	.	PUNCT
cana-2737	14	1	in	in	ADP
cana-2737	14	2	a	a	DET
cana-2737	14	3	fuzzy	fuzzy	ADJ
cana-2737	14	4	set	set	NOUN
cana-2737	14	5	,	,	PUNCT
cana-2737	14	6	a	a	DET
cana-2737	14	7	membership	membership	NOUN
cana-2737	14	8	function	function	NOUN
cana-2737	14	9	is	be	AUX
cana-2737	14	10	defined	define	VERB
cana-2737	14	11	to	to	PART
cana-2737	14	12	describe	describe	VERB
cana-2737	14	13	the	the	DET
cana-2737	14	14	degree	degree	NOUN
cana-2737	14	15	of	of	ADP
cana-2737	14	16	membership	membership	NOUN
cana-2737	14	17	of	of	ADP
cana-2737	14	18	an	an	DET
cana-2737	14	19	element	element	NOUN
cana-2737	14	20	to	to	ADP
cana-2737	14	21	a	a	DET
cana-2737	14	22	class	class	NOUN
cana-2737	14	23	.	.	PUNCT
cana-2737	15	1	the	the	DET
cana-2737	15	2	membership	membership	NOUN
cana-2737	15	3	value	value	NOUN
cana-2737	15	4	ranges	range	VERB
cana-2737	15	5	from	from	ADP
cana-2737	15	6	0	0	NUM
cana-2737	15	7	to	to	ADP
cana-2737	15	8	1	1	NUM
cana-2737	15	9	,	,	PUNCT
cana-2737	15	10	where	where	SCONJ
cana-2737	15	11	0	0	NUM
cana-2737	15	12	shows	show	VERB
cana-2737	15	13	that	that	SCONJ
cana-2737	15	14	the	the	DET
cana-2737	15	15	element	element	NOUN
cana-2737	15	16	does	do	AUX
cana-2737	15	17	not	not	PART
cana-2737	15	18	belong	belong	VERB
cana-2737	15	19	to	to	ADP
cana-2737	15	20	a	a	DET
cana-2737	15	21	class	class	NOUN
cana-2737	15	22	,	,	PUNCT
cana-2737	15	23	1	1	NUM
cana-2737	15	24	means	mean	NOUN
cana-2737	15	25	belongs	belong	NOUN
cana-2737	15	26	,	,	PUNCT
cana-2737	15	27	and	and	CCONJ
cana-2737	15	28	other	other	ADJ
cana-2737	15	29	values	value	NOUN
cana-2737	15	30	indicate	indicate	VERB
cana-2737	15	31	the	the	DET
cana-2737	15	32	degree	degree	NOUN
cana-2737	15	33	of	of	ADP
cana-2737	15	34	membership	membership	NOUN
cana-2737	15	35	to	to	ADP
cana-2737	15	36	a	a	DET
cana-2737	15	37	class	class	NOUN
cana-2737	15	38	.	.	PUNCT
cana-2737	16	1	for	for	ADP
cana-2737	16	2	fuzzy	fuzzy	ADJ
cana-2737	16	3	sets	set	NOUN
cana-2737	16	4	,	,	PUNCT
cana-2737	16	5	the	the	DET
cana-2737	16	6	membership	membership	NOUN
cana-2737	16	7	function	function	NOUN
cana-2737	16	8	replaced	replace	VERB
cana-2737	16	9	the	the	DET
cana-2737	16	10	characteristic	characteristic	ADJ
cana-2737	16	11	function	function	NOUN
cana-2737	16	12	in	in	ADP
cana-2737	16	13	crisp	crisp	ADJ
cana-2737	16	14	sets	set	NOUN
cana-2737	16	15	.	.	PUNCT
cana-2737	17	1	the	the	DET
cana-2737	17	2	concept	concept	NOUN
cana-2737	17	3	of	of	ADP
cana-2737	17	4	fuzzy	fuzzy	ADJ
cana-2737	17	5	set	set	NOUN
cana-2737	17	6	theory	theory	NOUN
cana-2737	17	7	seems	seem	VERB
cana-2737	17	8	to	to	PART
cana-2737	17	9	be	be	AUX
cana-2737	17	10	inconclusive	inconclusive	ADJ
cana-2737	17	11	because	because	SCONJ
cana-2737	17	12	of	of	ADP
cana-2737	17	13	the	the	DET
cana-2737	17	14	exclusion	exclusion	NOUN
cana-2737	17	15	of	of	ADP
cana-2737	17	16	nonmembership	nonmembership	NOUN
cana-2737	17	17	function	function	NOUN
cana-2737	17	18	and	and	CCONJ
cana-2737	17	19	the	the	DET
cana-2737	17	20	disregard	disregard	NOUN
cana-2737	17	21	for	for	ADP
cana-2737	17	22	the	the	DET
cana-2737	17	23	possibility	possibility	NOUN
cana-2737	17	24	of	of	ADP
cana-2737	17	25	hesitation	hesitation	NOUN
cana-2737	17	26	margin	margin	NOUN
cana-2737	17	27	.	.	PUNCT
cana-2737	18	1	atanassov	atanassov	PROPN
cana-2737	18	2	critically	critically	ADV
cana-2737	18	3	studied	study	VERB
cana-2737	18	4	these	these	DET
cana-2737	18	5	shortcomings	shortcoming	NOUN
cana-2737	18	6	and	and	CCONJ
cana-2737	18	7	proposed	propose	VERB
cana-2737	18	8	a	a	DET
cana-2737	18	9	concept	concept	NOUN
cana-2737	18	10	called	call	VERB
cana-2737	18	11	intuitionistic	intuitionistic	ADJ
cana-2737	18	12	fuzzy	fuzzy	ADJ
cana-2737	18	13	sets	set	NOUN
cana-2737	18	14	(	(	PUNCT
cana-2737	18	15	𝐼𝐹𝑆s	𝐼𝐹𝑆s	NOUN
cana-2737	18	16	)	)	PUNCT
cana-2737	19	1	[	[	X
cana-2737	19	2	1	1	NUM
cana-2737	19	3	,	,	PUNCT
cana-2737	19	4	2	2	NUM
cana-2737	19	5	,	,	PUNCT
cana-2737	19	6	4	4	NUM
cana-2737	19	7	,	,	PUNCT
cana-2737	19	8	5	5	NUM
cana-2737	19	9	]	]	PUNCT
cana-2737	19	10	.	.	PUNCT
cana-2737	20	1	the	the	DET
cana-2737	20	2	construct	construct	NOUN
cana-2737	20	3	(	(	PUNCT
cana-2737	20	4	that	that	PRON
cana-2737	20	5	is	is	ADV
cana-2737	20	6	,	,	PUNCT
cana-2737	20	7	𝐼𝐹𝑆	𝐼𝐹𝑆	PROPN
cana-2737	20	8	’s	’s	PART
cana-2737	20	9	)	)	PUNCT
cana-2737	20	10	incorporates	incorporate	VERB
cana-2737	20	11	both	both	DET
cana-2737	20	12	membership	membership	NOUN
cana-2737	20	13	function	function	NOUN
cana-2737	20	14	,	,	PUNCT
cana-2737	20	15	𝜇	𝜇	ADP
cana-2737	20	16	and	and	CCONJ
cana-2737	20	17	nonmembership	nonmembership	NOUN
cana-2737	20	18	function	function	NOUN
cana-2737	20	19	,	,	PUNCT
cana-2737	20	20	𝜈	𝜈	X
cana-2737	20	21	with	with	ADP
cana-2737	20	22	hesitation	hesitation	NOUN
cana-2737	20	23	margin	margin	NOUN
cana-2737	20	24	,	,	PUNCT
cana-2737	20	25	𝜋	𝜋	X
cana-2737	20	26	(	(	PUNCT
cana-2737	20	27	that	that	PRON
cana-2737	20	28	is	is	ADV
cana-2737	20	29	,	,	PUNCT
cana-2737	20	30	neither	neither	CCONJ
cana-2737	20	31	membership	membership	NOUN
cana-2737	20	32	nor	nor	CCONJ
cana-2737	20	33	nonmembership	nonmembership	NOUN
cana-2737	20	34	functions	function	NOUN
cana-2737	20	35	)	)	PUNCT
cana-2737	20	36	,	,	PUNCT
cana-2737	20	37	such	such	ADJ
cana-2737	20	38	that	that	SCONJ
cana-2737	20	39	𝜇	𝜇	ADP
cana-2737	20	40	+	+	X
cana-2737	20	41	𝜈	𝜈	X
cana-2737	20	42	≤	≤	NUM
cana-2737	20	43	1	1	NUM
cana-2737	20	44	and	and	CCONJ
cana-2737	20	45	𝜇	𝜇	X
cana-2737	20	46	+	+	X
cana-2737	20	47	𝜈	𝜈	X
cana-2737	20	48	+	+	CCONJ
cana-2737	20	49	𝜋	𝜋	NOUN
cana-2737	20	50	=	=	ADJ
cana-2737	20	51	1	1	X
cana-2737	20	52	.	.	X
cana-2737	20	53	atanassov	atanassov	PROPN
cana-2737	20	54	[	[	X
cana-2737	20	55	3	3	NUM
cana-2737	20	56	]	]	PUNCT
cana-2737	20	57	introduced	introduce	VERB
cana-2737	20	58	intuitionistic	intuitionistic	ADJ
cana-2737	20	59	fuzzy	fuzzy	ADJ
cana-2737	20	60	sets	set	NOUN
cana-2737	20	61	of	of	ADP
cana-2737	20	62	second	second	ADJ
cana-2737	20	63	type	type	NOUN
cana-2737	20	64	(	(	PUNCT
cana-2737	20	65	𝐼𝐹𝑆𝑆𝑇	𝐼𝐹𝑆𝑆𝑇	PROPN
cana-2737	20	66	)	)	PUNCT
cana-2737	20	67	with	with	ADP
cana-2737	20	68	the	the	DET
cana-2737	20	69	property	property	NOUN
cana-2737	20	70	that	that	PRON
cana-2737	20	71	the	the	DET
cana-2737	20	72	sum	sum	NOUN
cana-2737	20	73	of	of	ADP
cana-2737	20	74	the	the	DET
cana-2737	20	75	square	square	NOUN
cana-2737	20	76	of	of	ADP
cana-2737	20	77	the	the	DET
cana-2737	20	78	membership	membership	NOUN
cana-2737	20	79	and	and	CCONJ
cana-2737	20	80	non	non	ADJ
cana-2737	20	81	-	-	ADJ
cana-2737	20	82	membership	membership	ADJ
cana-2737	20	83	degrees	degree	NOUN
cana-2737	20	84	is	be	AUX
cana-2737	20	85	less	less	ADJ
cana-2737	20	86	than	than	ADP
cana-2737	20	87	or	or	CCONJ
cana-2737	20	88	equal	equal	ADJ
cana-2737	20	89	to	to	ADP
cana-2737	20	90	one	one	NUM
cana-2737	20	91	.	.	PUNCT
cana-2737	21	1	this	this	DET
cana-2737	21	2	concept	concept	NOUN
cana-2737	21	3	generalizes	generalize	VERB
cana-2737	21	4	𝐼𝐹𝑆	𝐼𝐹𝑆	PROPN
cana-2737	21	5	’s	’s	PART
cana-2737	21	6	in	in	ADP
cana-2737	21	7	a	a	DET
cana-2737	21	8	way	way	NOUN
cana-2737	21	9	.	.	PUNCT
cana-2737	22	1	the	the	DET
cana-2737	22	2	notion	notion	NOUN
cana-2737	22	3	of	of	ADP
cana-2737	22	4	𝐼𝐹𝑆	𝐼𝐹𝑆	PROPN
cana-2737	22	5	’s	’s	PART
cana-2737	22	6	provides	provide	VERB
cana-2737	22	7	a	a	DET
cana-2737	22	8	flexible	flexible	ADJ
cana-2737	22	9	framework	framework	NOUN
cana-2737	22	10	to	to	PART
cana-2737	22	11	elaborate	elaborate	VERB
cana-2737	22	12	uncertainty	uncertainty	NOUN
cana-2737	22	13	and	and	CCONJ
cana-2737	22	14	vagueness	vagueness	NOUN
cana-2737	22	15	.	.	PUNCT
cana-2737	23	1	communications	communication	NOUN
cana-2737	23	2	on	on	ADP
cana-2737	23	3	applied	apply	VERB
cana-2737	23	4	nonlinear	nonlinear	ADJ
cana-2737	23	5	analysis	analysis	NOUN
cana-2737	23	6	issn	issn	NOUN
cana-2737	23	7	:	:	PUNCT
cana-2737	23	8	1074	1074	NUM
cana-2737	23	9	-	-	PUNCT
cana-2737	23	10	133x	133x	NUM
cana-2737	23	11	vol	vol	NOUN
cana-2737	23	12	32	32	NUM
cana-2737	23	13	no	no	NOUN
cana-2737	23	14	.	.	PUNCT
cana-2737	24	1	4s	4s	NUM
cana-2737	24	2	(	(	PUNCT
cana-2737	24	3	2025	2025	NUM
cana-2737	24	4	)	)	PUNCT
cana-2737	24	5	27	27	NUM
cana-2737	24	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2737	24	7	the	the	DET
cana-2737	24	8	idea	idea	NOUN
cana-2737	24	9	of	of	ADP
cana-2737	24	10	𝐼𝐹𝑆	𝐼𝐹𝑆	PROPN
cana-2737	24	11	seems	seem	VERB
cana-2737	24	12	to	to	PART
cana-2737	24	13	be	be	AUX
cana-2737	24	14	resourceful	resourceful	ADJ
cana-2737	24	15	in	in	ADP
cana-2737	24	16	modelling	model	VERB
cana-2737	24	17	many	many	ADJ
cana-2737	24	18	real	real	ADJ
cana-2737	24	19	-	-	PUNCT
cana-2737	24	20	life	life	NOUN
cana-2737	24	21	situations	situation	NOUN
cana-2737	24	22	like	like	ADP
cana-2737	24	23	medical	medical	ADJ
cana-2737	24	24	diagnosis	diagnosis	NOUN
cana-2737	24	25	[	[	X
cana-2737	24	26	7	7	NUM
cana-2737	24	27	,	,	PUNCT
cana-2737	24	28	8	8	NUM
cana-2737	24	29	,	,	PUNCT
cana-2737	24	30	12	12	NUM
cana-2737	24	31	,	,	PUNCT
cana-2737	24	32	28	28	NUM
cana-2737	24	33	,	,	PUNCT
cana-2737	24	34	29	29	NUM
cana-2737	24	35	]	]	PUNCT
cana-2737	24	36	,	,	PUNCT
cana-2737	24	37	career	career	NOUN
cana-2737	24	38	determination	determination	NOUN
cana-2737	24	39	[	[	X
cana-2737	24	40	10	10	NUM
cana-2737	24	41	]	]	PUNCT
cana-2737	24	42	,	,	PUNCT
cana-2737	24	43	selection	selection	NOUN
cana-2737	24	44	process	process	NOUN
cana-2737	24	45	[	[	X
cana-2737	24	46	11	11	NUM
cana-2737	24	47	]	]	PUNCT
cana-2737	24	48	,	,	PUNCT
cana-2737	24	49	and	and	CCONJ
cana-2737	24	50	multi	multi	ADJ
cana-2737	24	51	-	-	NOUN
cana-2737	24	52	criteria	criterion	NOUN
cana-2737	24	53	decision	decision	NOUN
cana-2737	24	54	-	-	PUNCT
cana-2737	24	55	making	making	NOUN
cana-2737	24	56	[	[	X
cana-2737	24	57	15	15	NUM
cana-2737	24	58	,	,	PUNCT
cana-2737	24	59	16	16	NUM
cana-2737	24	60	,	,	PUNCT
cana-2737	24	61	17	17	NUM
cana-2737	24	62	]	]	PUNCT
cana-2737	24	63	,	,	PUNCT
cana-2737	24	64	among	among	ADP
cana-2737	24	65	others	other	NOUN
cana-2737	24	66	.	.	PUNCT
cana-2737	25	1	there	there	PRON
cana-2737	25	2	are	be	VERB
cana-2737	25	3	situations	situation	NOUN
cana-2737	25	4	where	where	SCONJ
cana-2737	25	5	𝜇	𝜇	ADP
cana-2737	25	6	+	+	CCONJ
cana-2737	25	7	𝜈	𝜈	X
cana-2737	25	8	≥	≥	NOUN
cana-2737	25	9	1	1	NUM
cana-2737	25	10	unlike	unlike	ADP
cana-2737	25	11	the	the	DET
cana-2737	25	12	cases	case	NOUN
cana-2737	25	13	capture	capture	VERB
cana-2737	25	14	in	in	ADP
cana-2737	25	15	𝐼𝐹𝑆	𝐼𝐹𝑆	PROPN
cana-2737	25	16	’s	’s	PART
cana-2737	25	17	.	.	PUNCT
cana-2737	26	1	this	this	DET
cana-2737	26	2	limitation	limitation	NOUN
cana-2737	26	3	in	in	ADP
cana-2737	26	4	𝐼𝐹𝑆	𝐼𝐹𝑆	PROPN
cana-2737	26	5	naturally	naturally	ADV
cana-2737	26	6	led	lead	VERB
cana-2737	26	7	to	to	ADP
cana-2737	26	8	a	a	DET
cana-2737	26	9	construct	construct	NOUN
cana-2737	26	10	,	,	PUNCT
cana-2737	26	11	called	call	VERB
cana-2737	26	12	pythagorean	pythagorean	PROPN
cana-2737	26	13	fuzzy	fuzzy	ADJ
cana-2737	26	14	sets	set	NOUN
cana-2737	26	15	(	(	PUNCT
cana-2737	26	16	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2737	26	17	’s	’s	PART
cana-2737	26	18	)	)	PUNCT
cana-2737	26	19	.	.	PUNCT
cana-2737	27	1	pythagorean	pythagorean	PROPN
cana-2737	27	2	fuzzy	fuzzy	ADJ
cana-2737	27	3	set	set	NOUN
cana-2737	27	4	(	(	PUNCT
cana-2737	27	5	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2737	27	6	)	)	PUNCT
cana-2737	27	7	proposed	propose	VERB
cana-2737	27	8	in	in	ADP
cana-2737	27	9	[	[	X
cana-2737	27	10	32	32	NUM
cana-2737	27	11	,	,	PUNCT
cana-2737	27	12	33	33	NUM
cana-2737	27	13	,	,	PUNCT
cana-2737	27	14	34	34	NUM
cana-2737	27	15	]	]	PUNCT
cana-2737	27	16	is	be	AUX
cana-2737	27	17	a	a	DET
cana-2737	27	18	new	new	ADJ
cana-2737	27	19	tool	tool	NOUN
cana-2737	27	20	to	to	PART
cana-2737	27	21	deal	deal	VERB
cana-2737	27	22	with	with	ADP
cana-2737	27	23	vagueness	vagueness	NOUN
cana-2737	27	24	considering	consider	VERB
cana-2737	27	25	the	the	DET
cana-2737	27	26	membership	membership	NOUN
cana-2737	27	27	grade	grade	NOUN
cana-2737	27	28	,	,	PUNCT
cana-2737	27	29	𝜇	𝜇	ADP
cana-2737	27	30	and	and	CCONJ
cana-2737	27	31	non	non	ADJ
cana-2737	27	32	-	-	ADJ
cana-2737	27	33	membership	membership	ADJ
cana-2737	27	34	grade	grade	NOUN
cana-2737	27	35	,	,	PUNCT
cana-2737	27	36	𝜈	𝜈	X
cana-2737	27	37	satisfying	satisfy	VERB
cana-2737	27	38	the	the	DET
cana-2737	27	39	conditions	condition	NOUN
cana-2737	27	40	𝜇	𝜇	ADP
cana-2737	27	41	+	+	CCONJ
cana-2737	27	42	𝜈	𝜈	X
cana-2737	27	43	≤	≤	NUM
cana-2737	27	44	1	1	NUM
cana-2737	27	45	or	or	CCONJ
cana-2737	27	46	𝜇	𝜇	X
cana-2737	27	47	+	+	CCONJ
cana-2737	27	48	𝜈	𝜈	X
cana-2737	27	49	≥	≥	NUM
cana-2737	27	50	1	1	NUM
cana-2737	27	51	,	,	PUNCT
cana-2737	27	52	and	and	CCONJ
cana-2737	27	53	also	also	ADV
cana-2737	27	54	,	,	PUNCT
cana-2737	27	55	it	it	PRON
cana-2737	27	56	follows	follow	VERB
cana-2737	27	57	that	that	SCONJ
cana-2737	27	58	𝜇2	𝜇2	PROPN
cana-2737	27	59	+	+	CCONJ
cana-2737	27	60	𝜈2	𝜈2	NOUN
cana-2737	27	61	+	+	CCONJ
cana-2737	27	62	𝜋2	𝜋2	NOUN
cana-2737	27	63	=	=	SYM
cana-2737	27	64	1	1	NUM
cana-2737	27	65	,	,	PUNCT
cana-2737	27	66	where	where	SCONJ
cana-2737	27	67	𝜋	𝜋	NOUN
cana-2737	27	68	is	be	AUX
cana-2737	27	69	the	the	DET
cana-2737	27	70	pythagorean	pythagorean	PROPN
cana-2737	27	71	fuzzy	fuzzy	ADJ
cana-2737	27	72	set	set	PROPN
cana-2737	27	73	index	index	NOUN
cana-2737	27	74	.	.	PUNCT
cana-2737	28	1	in	in	ADP
cana-2737	28	2	fact	fact	NOUN
cana-2737	28	3	,	,	PUNCT
cana-2737	28	4	the	the	DET
cana-2737	28	5	origin	origin	NOUN
cana-2737	28	6	of	of	ADP
cana-2737	28	7	pythagorean	pythagorean	PROPN
cana-2737	28	8	fuzzy	fuzzy	ADJ
cana-2737	28	9	sets	set	NOUN
cana-2737	28	10	emanated	emanate	VERB
cana-2737	28	11	from	from	ADP
cana-2737	28	12	𝐼𝐹𝑆𝑆𝑇	𝐼𝐹𝑆𝑆𝑇	PROPN
cana-2737	28	13	earlier	early	ADV
cana-2737	28	14	studied	study	VERB
cana-2737	28	15	in	in	ADP
cana-2737	28	16	the	the	DET
cana-2737	28	17	literature	literature	NOUN
cana-2737	28	18	.	.	PUNCT
cana-2737	29	1	as	as	ADP
cana-2737	29	2	a	a	DET
cana-2737	29	3	generalized	generalized	ADJ
cana-2737	29	4	set	set	NOUN
cana-2737	29	5	,	,	PUNCT
cana-2737	29	6	𝑃𝐹𝑆	𝑃𝐹𝑆	PROPN
cana-2737	29	7	has	have	VERB
cana-2737	29	8	close	close	ADJ
cana-2737	29	9	relationship	relationship	NOUN
cana-2737	29	10	with	with	ADP
cana-2737	29	11	𝐼𝐹𝑆.	𝐼𝐹𝑆.	PUNCT
cana-2737	29	12	the	the	DET
cana-2737	29	13	construct	construct	NOUN
cana-2737	29	14	of	of	ADP
cana-2737	29	15	𝑃𝐹𝑆	𝑃𝐹𝑆	PROPN
cana-2737	29	16	’s	’s	PART
cana-2737	29	17	can	can	AUX
cana-2737	29	18	be	be	AUX
cana-2737	29	19	used	use	VERB
cana-2737	29	20	to	to	PART
cana-2737	29	21	characterize	characterize	VERB
cana-2737	29	22	uncertain	uncertain	ADJ
cana-2737	29	23	information	information	NOUN
cana-2737	29	24	more	more	ADV
cana-2737	29	25	sufficiently	sufficiently	ADV
cana-2737	29	26	and	and	CCONJ
cana-2737	29	27	accurately	accurately	ADV
cana-2737	29	28	than	than	ADP
cana-2737	29	29	𝐼𝐹𝑆.	𝐼𝐹𝑆.	NUM
cana-2737	29	30	garg	garg	NOUN
cana-2737	30	1	[	[	X
cana-2737	30	2	14	14	NUM
cana-2737	30	3	]	]	PUNCT
cana-2737	30	4	presented	present	VERB
cana-2737	30	5	an	an	DET
cana-2737	30	6	improved	improved	ADJ
cana-2737	30	7	score	score	NOUN
cana-2737	30	8	function	function	NOUN
cana-2737	30	9	for	for	ADP
cana-2737	30	10	the	the	DET
cana-2737	30	11	ranking	ranking	ADJ
cana-2737	30	12	order	order	NOUN
cana-2737	30	13	of	of	ADP
cana-2737	30	14	intervalvalued	intervalvalue	VERB
cana-2737	30	15	pythagorean	pythagorean	PROPN
cana-2737	30	16	fuzzy	fuzzy	ADJ
cana-2737	30	17	sets	set	NOUN
cana-2737	30	18	(	(	PUNCT
cana-2737	30	19	𝐼𝑉𝑃𝐹𝑆s	𝐼𝑉𝑃𝐹𝑆	NOUN
cana-2737	30	20	)	)	PUNCT
cana-2737	30	21	.	.	PUNCT
cana-2737	31	1	based	base	VERB
cana-2737	31	2	on	on	ADP
cana-2737	31	3	it	it	PRON
cana-2737	31	4	,	,	PUNCT
cana-2737	31	5	a	a	DET
cana-2737	31	6	pythagorean	pythagorean	ADJ
cana-2737	31	7	fuzzy	fuzzy	ADJ
cana-2737	31	8	technique	technique	NOUN
cana-2737	31	9	for	for	ADP
cana-2737	31	10	order	order	NOUN
cana-2737	31	11	of	of	ADP
cana-2737	31	12	preference	preference	NOUN
cana-2737	31	13	by	by	ADP
cana-2737	31	14	similarity	similarity	NOUN
cana-2737	31	15	to	to	ADP
cana-2737	31	16	ideal	ideal	ADJ
cana-2737	31	17	solution	solution	NOUN
cana-2737	31	18	(	(	PUNCT
cana-2737	31	19	𝑇𝑂𝑃𝑆𝐼𝑆	𝑇𝑂𝑃𝑆𝐼𝑆	PROPN
cana-2737	31	20	)	)	PUNCT
cana-2737	31	21	method	method	NOUN
cana-2737	31	22	by	by	ADP
cana-2737	31	23	taking	take	VERB
cana-2737	31	24	the	the	DET
cana-2737	31	25	preferences	preference	NOUN
cana-2737	31	26	of	of	ADP
cana-2737	31	27	the	the	DET
cana-2737	31	28	experts	expert	NOUN
cana-2737	31	29	in	in	ADP
cana-2737	31	30	the	the	DET
cana-2737	31	31	form	form	NOUN
cana-2737	31	32	of	of	ADP
cana-2737	31	33	interval	interval	NOUN
cana-2737	31	34	-	-	PUNCT
cana-2737	31	35	valued	value	VERB
cana-2737	31	36	pythagorean	pythagorean	PROPN
cana-2737	31	37	fuzzy	fuzzy	ADJ
cana-2737	31	38	decision	decision	NOUN
cana-2737	31	39	matrices	matrix	NOUN
cana-2737	31	40	was	be	AUX
cana-2737	31	41	discussed	discuss	VERB
cana-2737	31	42	.	.	PUNCT
cana-2737	32	1	other	other	ADJ
cana-2737	32	2	explorations	exploration	NOUN
cana-2737	32	3	of	of	ADP
cana-2737	32	4	the	the	DET
cana-2737	32	5	theory	theory	NOUN
cana-2737	32	6	of	of	ADP
cana-2737	32	7	𝑃𝐹𝑆	𝑃𝐹𝑆	PROPN
cana-2737	32	8	’s	’s	PART
cana-2737	32	9	can	can	AUX
cana-2737	32	10	be	be	AUX
cana-2737	32	11	found	find	VERB
cana-2737	32	12	in	in	ADP
cana-2737	32	13	[	[	X
cana-2737	32	14	6	6	NUM
cana-2737	32	15	,	,	PUNCT
cana-2737	32	16	9	9	NUM
cana-2737	32	17	,	,	PUNCT
cana-2737	32	18	13	13	NUM
cana-2737	32	19	,	,	PUNCT
cana-2737	32	20	18	18	NUM
cana-2737	32	21	,	,	PUNCT
cana-2737	32	22	19	19	NUM
cana-2737	32	23	,	,	PUNCT
cana-2737	32	24	25	25	NUM
cana-2737	32	25	,	,	PUNCT
cana-2737	32	26	26	26	NUM
cana-2737	32	27	]	]	PUNCT
cana-2737	32	28	.	.	PUNCT
cana-2737	33	1	saha	saha	PROPN
cana-2737	34	1	[	[	X
cana-2737	34	2	27	27	NUM
cana-2737	34	3	]	]	SYM
cana-2737	34	4	defined	define	VERB
cana-2737	34	5	𝛿-open	𝛿-open	NOUN
cana-2737	34	6	sets	set	NOUN
cana-2737	34	7	in	in	ADP
cana-2737	34	8	topological	topological	ADJ
cana-2737	34	9	spaces	space	NOUN
cana-2737	34	10	.	.	PUNCT
cana-2737	35	1	vadivel	vadivel	VERB
cana-2737	35	2	et	et	PROPN
cana-2737	35	3	al	al	PROPN
cana-2737	35	4	.	.	PUNCT
cana-2737	36	1	[	[	X
cana-2737	36	2	31	31	NUM
cana-2737	36	3	]	]	PUNCT
cana-2737	36	4	introduced	introduce	VERB
cana-2737	36	5	𝛿-open	𝛿-open	NOUN
cana-2737	36	6	sets	set	NOUN
cana-2737	36	7	in	in	ADP
cana-2737	36	8	a	a	DET
cana-2737	36	9	neutrosophic	neutrosophic	ADJ
cana-2737	36	10	topological	topological	ADJ
cana-2737	36	11	space	space	NOUN
cana-2737	36	12	.	.	PUNCT
cana-2737	37	1	the	the	DET
cana-2737	37	2	notion	notion	NOUN
cana-2737	37	3	of	of	ADP
cana-2737	37	4	m	m	NOUN
cana-2737	37	5	-	-	ADJ
cana-2737	37	6	open	open	ADJ
cana-2737	37	7	sets	set	NOUN
cana-2737	37	8	in	in	ADP
cana-2737	37	9	topological	topological	ADJ
cana-2737	37	10	spaces	space	NOUN
cana-2737	37	11	were	be	AUX
cana-2737	37	12	introduced	introduce	VERB
cana-2737	37	13	by	by	ADP
cana-2737	37	14	el	el	NOUN
cana-2737	37	15	-	-	PUNCT
cana-2737	37	16	maghrabi	maghrabi	NOUN
cana-2737	37	17	and	and	CCONJ
cana-2737	37	18	al	al	PROPN
cana-2737	37	19	-	-	PUNCT
cana-2737	37	20	juhani	juhani	PROPN
cana-2737	38	1	[	[	X
cana-2737	38	2	23	23	NUM
cana-2737	38	3	]	]	PUNCT
cana-2737	38	4	in	in	ADP
cana-2737	38	5	2011	2011	NUM
cana-2737	38	6	and	and	CCONJ
cana-2737	38	7	studied	study	VERB
cana-2737	38	8	some	some	PRON
cana-2737	38	9	of	of	ADP
cana-2737	38	10	their	their	PRON
cana-2737	38	11	properties	property	NOUN
cana-2737	38	12	.	.	PUNCT
cana-2737	39	1	the	the	DET
cana-2737	39	2	class	class	NOUN
cana-2737	39	3	of	of	ADP
cana-2737	39	4	sets	set	NOUN
cana-2737	39	5	namely	namely	ADV
cana-2737	39	6	,	,	PUNCT
cana-2737	39	7	𝑀-open	𝑀-open	ADJ
cana-2737	39	8	sets	set	NOUN
cana-2737	39	9	are	be	AUX
cana-2737	39	10	playing	play	VERB
cana-2737	39	11	more	more	ADV
cana-2737	39	12	important	important	ADJ
cana-2737	39	13	role	role	NOUN
cana-2737	39	14	in	in	ADP
cana-2737	39	15	topological	topological	ADJ
cana-2737	39	16	spaces	space	NOUN
cana-2737	39	17	,	,	PUNCT
cana-2737	39	18	because	because	SCONJ
cana-2737	39	19	of	of	ADP
cana-2737	39	20	their	their	PRON
cana-2737	39	21	applications	application	NOUN
cana-2737	39	22	in	in	ADP
cana-2737	39	23	various	various	ADJ
cana-2737	39	24	fields	field	NOUN
cana-2737	39	25	of	of	ADP
cana-2737	39	26	mathematics	mathematic	NOUN
cana-2737	39	27	and	and	CCONJ
cana-2737	39	28	other	other	ADJ
cana-2737	39	29	real	real	ADJ
cana-2737	39	30	fields	field	NOUN
cana-2737	39	31	.	.	PUNCT
cana-2737	40	1	recently	recently	ADV
cana-2737	40	2	,	,	PUNCT
cana-2737	40	3	jeeva	jeeva	PROPN
cana-2737	40	4	et	et	PROPN
cana-2737	40	5	al	al	PROPN
cana-2737	40	6	.	.	PUNCT
cana-2737	41	1	[	[	X
cana-2737	41	2	20	20	NUM
cana-2737	41	3	,	,	PUNCT
cana-2737	41	4	21	21	NUM
cana-2737	41	5	,	,	PUNCT
cana-2737	41	6	22	22	NUM
cana-2737	41	7	]	]	PUNCT
cana-2737	41	8	introduced	introduce	VERB
cana-2737	41	9	neutrosophic	neutrosophic	ADJ
cana-2737	41	10	soft	soft	ADJ
cana-2737	41	11	𝑀-open	𝑀-open	PROPN
cana-2737	41	12	sets	set	NOUN
cana-2737	41	13	in	in	ADP
cana-2737	41	14	neutrosophic	neutrosophic	ADJ
cana-2737	41	15	topological	topological	ADJ
cana-2737	41	16	spaces	space	NOUN
cana-2737	41	17	and	and	CCONJ
cana-2737	41	18	developed	develop	VERB
cana-2737	41	19	the	the	DET
cana-2737	41	20	concepts	concept	NOUN
cana-2737	41	21	of	of	ADP
cana-2737	41	22	neutrosophic	neutrosophic	ADJ
cana-2737	41	23	soft	soft	ADJ
cana-2737	41	24	𝑀-continuity	𝑀-continuity	PROPN
cana-2737	41	25	and	and	CCONJ
cana-2737	41	26	𝑀-irresolute	𝑀-irresolute	PROPN
cana-2737	41	27	maps	map	NOUN
cana-2737	41	28	.	.	PUNCT
cana-2737	42	1	entropy	entropy	PROPN
cana-2737	42	2	can	can	AUX
cana-2737	42	3	be	be	AUX
cana-2737	42	4	viewed	view	VERB
cana-2737	42	5	as	as	ADP
cana-2737	42	6	a	a	DET
cana-2737	42	7	gauge	gauge	NOUN
cana-2737	42	8	of	of	ADP
cana-2737	42	9	the	the	DET
cana-2737	42	10	degree	degree	NOUN
cana-2737	42	11	of	of	ADP
cana-2737	42	12	uncertainty	uncertainty	NOUN
cana-2737	42	13	present	present	ADJ
cana-2737	42	14	in	in	ADP
cana-2737	42	15	a	a	DET
cana-2737	42	16	set	set	NOUN
cana-2737	42	17	,	,	PUNCT
cana-2737	42	18	regardless	regardless	ADV
cana-2737	42	19	of	of	ADP
cana-2737	42	20	how	how	SCONJ
cana-2737	42	21	fuzzy	fuzzy	ADJ
cana-2737	42	22	,	,	PUNCT
cana-2737	42	23	intuitionistic	intuitionistic	ADJ
cana-2737	42	24	,	,	PUNCT
cana-2737	42	25	ambiguous	ambiguous	ADJ
cana-2737	42	26	,	,	PUNCT
cana-2737	42	27	etc	etc	X
cana-2737	42	28	.	.	X
cana-2737	43	1	the	the	DET
cana-2737	43	2	set	set	NOUN
cana-2737	43	3	may	may	AUX
cana-2737	43	4	be	be	AUX
cana-2737	43	5	.	.	PUNCT
cana-2737	44	1	since	since	SCONJ
cana-2737	44	2	the	the	DET
cana-2737	44	3	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2737	44	4	in	in	ADP
cana-2737	44	5	this	this	DET
cana-2737	44	6	case	case	NOUN
cana-2737	44	7	can	can	AUX
cana-2737	44	8	also	also	ADV
cana-2737	44	9	handle	handle	VERB
cana-2737	44	10	uncertain	uncertain	ADJ
cana-2737	44	11	data	datum	NOUN
cana-2737	44	12	,	,	PUNCT
cana-2737	44	13	it	it	PRON
cana-2737	44	14	follows	follow	VERB
cana-2737	44	15	naturally	naturally	ADV
cana-2737	44	16	that	that	SCONJ
cana-2737	44	17	we	we	PRON
cana-2737	44	18	are	be	AUX
cana-2737	44	19	also	also	ADV
cana-2737	44	20	interested	interested	ADJ
cana-2737	44	21	in	in	ADP
cana-2737	44	22	determining	determine	VERB
cana-2737	44	23	the	the	DET
cana-2737	44	24	entropy	entropy	NOUN
cana-2737	44	25	of	of	ADP
cana-2737	44	26	an	an	DET
cana-2737	44	27	𝑝𝑓𝑠.	𝑝𝑓𝑠.	NOUN
cana-2737	44	28	in	in	ADP
cana-2737	44	29	1965	1965	NUM
cana-2737	44	30	,	,	PUNCT
cana-2737	44	31	zadeh	zadeh	PROPN
cana-2737	45	1	[	[	X
cana-2737	45	2	35	35	NUM
cana-2737	45	3	]	]	PUNCT
cana-2737	45	4	made	make	VERB
cana-2737	45	5	the	the	DET
cana-2737	45	6	first	first	ADJ
cana-2737	45	7	reference	reference	NOUN
cana-2737	45	8	to	to	PART
cana-2737	45	9	entropy	entropy	VERB
cana-2737	45	10	as	as	ADP
cana-2737	45	11	a	a	DET
cana-2737	45	12	fuzziness	fuzziness	NOUN
cana-2737	45	13	metric	metric	NOUN
cana-2737	45	14	.	.	PUNCT
cana-2737	46	1	more	more	ADV
cana-2737	46	2	recently	recently	ADV
cana-2737	46	3	,	,	PUNCT
cana-2737	46	4	de	de	X
cana-2737	46	5	luca	luca	X
cana-2737	46	6	-	-	PUNCT
cana-2737	46	7	termini	termini	NOUN
cana-2737	46	8	[	[	X
cana-2737	46	9	8	8	NUM
cana-2737	46	10	]	]	PUNCT
cana-2737	46	11	axiomatized	axiomatize	VERB
cana-2737	46	12	the	the	DET
cana-2737	46	13	entropy	entropy	NOUN
cana-2737	46	14	that	that	PRON
cana-2737	46	15	is	be	AUX
cana-2737	46	16	not	not	PART
cana-2737	46	17	probabilistic	probabilistic	ADJ
cana-2737	46	18	.	.	PUNCT
cana-2737	47	1	the	the	DET
cana-2737	47	2	remainder	remainder	NOUN
cana-2737	47	3	of	of	ADP
cana-2737	47	4	this	this	DET
cana-2737	47	5	paper	paper	NOUN
cana-2737	47	6	is	be	AUX
cana-2737	47	7	organized	organize	VERB
cana-2737	47	8	as	as	SCONJ
cana-2737	47	9	follows	follow	VERB
cana-2737	47	10	.	.	PUNCT
cana-2737	48	1	in	in	ADP
cana-2737	48	2	section	section	NOUN
cana-2737	48	3	2	2	NUM
cana-2737	48	4	,	,	PUNCT
cana-2737	48	5	some	some	DET
cana-2737	48	6	basic	basic	ADJ
cana-2737	48	7	definitions	definition	NOUN
cana-2737	48	8	of	of	ADP
cana-2737	48	9	𝑓𝑠	𝑓𝑠	NOUN
cana-2737	48	10	’s	’s	PART
cana-2737	48	11	,	,	PUNCT
cana-2737	48	12	𝐼𝐹𝑆	𝐼𝐹𝑆	PROPN
cana-2737	48	13	’s	’s	PART
cana-2737	48	14	and	and	CCONJ
cana-2737	48	15	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2737	48	16	’s	’	VERB
cana-2737	48	17	are	be	AUX
cana-2737	48	18	briefly	briefly	ADV
cana-2737	48	19	reviewed	review	VERB
cana-2737	48	20	.	.	PUNCT
cana-2737	49	1	in	in	ADP
cana-2737	49	2	sections	section	NOUN
cana-2737	49	3	3	3	NUM
cana-2737	49	4	and	and	CCONJ
cana-2737	49	5	4	4	NUM
cana-2737	49	6	,	,	PUNCT
cana-2737	49	7	we	we	PRON
cana-2737	49	8	develop	develop	VERB
cana-2737	49	9	the	the	DET
cana-2737	49	10	concept	concept	NOUN
cana-2737	49	11	of	of	ADP
cana-2737	49	12	some	some	DET
cana-2737	49	13	pythagorean	pythagorean	ADJ
cana-2737	49	14	fuzzy	fuzzy	ADJ
cana-2737	49	15	open	open	ADJ
cana-2737	49	16	and	and	CCONJ
cana-2737	49	17	closed	closed	ADJ
cana-2737	49	18	maps	map	NOUN
cana-2737	49	19	in	in	ADP
cana-2737	49	20	pythagorean	pythagorean	PROPN
cana-2737	49	21	fuzzy	fuzzy	ADJ
cana-2737	49	22	topological	topological	ADJ
cana-2737	49	23	space	space	NOUN
cana-2737	49	24	and	and	CCONJ
cana-2737	49	25	also	also	ADV
cana-2737	49	26	specialized	specialize	VERB
cana-2737	49	27	some	some	PRON
cana-2737	49	28	of	of	ADP
cana-2737	49	29	their	their	PRON
cana-2737	49	30	basic	basic	ADJ
cana-2737	49	31	properties	property	NOUN
cana-2737	49	32	with	with	ADP
cana-2737	49	33	examples	example	NOUN
cana-2737	49	34	.	.	PUNCT
cana-2737	50	1	finally	finally	ADV
cana-2737	50	2	,	,	PUNCT
cana-2737	50	3	we	we	PRON
cana-2737	50	4	presented	present	VERB
cana-2737	50	5	an	an	DET
cana-2737	50	6	entropy	entropy	NOUN
cana-2737	50	7	measure	measure	NOUN
cana-2737	50	8	for	for	ADP
cana-2737	50	9	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2737	50	10	’s	’s	PART
cana-2737	50	11	and	and	CCONJ
cana-2737	50	12	one	one	NUM
cana-2737	50	13	real	real	ADJ
cana-2737	50	14	world	world	NOUN
cana-2737	50	15	scenarios	scenario	NOUN
cana-2737	50	16	where	where	SCONJ
cana-2737	50	17	this	this	DET
cana-2737	50	18	entropy	entropy	NOUN
cana-2737	50	19	measure	measure	NOUN
cana-2737	50	20	can	can	AUX
cana-2737	50	21	be	be	AUX
cana-2737	50	22	used	use	VERB
cana-2737	50	23	are	be	AUX
cana-2737	50	24	mentioned	mention	VERB
cana-2737	50	25	in	in	ADP
cana-2737	50	26	section	section	NOUN
cana-2737	50	27	4	4	NUM
cana-2737	50	28	.	.	PUNCT
cana-2737	51	1	the	the	DET
cana-2737	51	2	paper	paper	NOUN
cana-2737	51	3	is	be	AUX
cana-2737	51	4	concluded	conclude	VERB
cana-2737	51	5	in	in	ADP
cana-2737	51	6	section	section	NOUN
cana-2737	51	7	5	5	NUM
cana-2737	51	8	.	.	SYM
cana-2737	51	9	2	2	NUM
cana-2737	51	10	preliminaries	preliminary	NOUN
cana-2737	51	11	we	we	PRON
cana-2737	51	12	recall	recall	VERB
cana-2737	51	13	some	some	DET
cana-2737	51	14	basic	basic	ADJ
cana-2737	51	15	notions	notion	NOUN
cana-2737	51	16	of	of	ADP
cana-2737	51	17	fuzzy	fuzzy	ADJ
cana-2737	51	18	sets	set	NOUN
cana-2737	51	19	,	,	PUNCT
cana-2737	51	20	𝐼𝐹𝑆	𝐼𝐹𝑆	PROPN
cana-2737	51	21	’s	’s	PART
cana-2737	51	22	and	and	CCONJ
cana-2737	51	23	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2737	51	24	’s	’s	PART
cana-2737	51	25	.	.	PUNCT
cana-2737	52	1	definition	definition	NOUN
cana-2737	52	2	2.1	2.1	NUM
cana-2737	52	3	[	[	SYM
cana-2737	52	4	35	35	NUM
cana-2737	52	5	]	]	PUNCT
cana-2737	52	6	let	let	VERB
cana-2737	52	7	𝑋	𝑋	NOUN
cana-2737	52	8	be	be	AUX
cana-2737	52	9	a	a	DET
cana-2737	52	10	nonempty	nonempty	ADV
cana-2737	52	11	set	set	VERB
cana-2737	52	12	.	.	PUNCT
cana-2737	53	1	a	a	DET
cana-2737	53	2	fuzzy	fuzzy	ADJ
cana-2737	53	3	set	set	VERB
cana-2737	53	4	𝐴	𝐴	PROPN
cana-2737	53	5	in	in	ADP
cana-2737	53	6	𝑋	𝑋	PROPN
cana-2737	53	7	is	be	AUX
cana-2737	53	8	characterized	characterize	VERB
cana-2737	53	9	by	by	ADP
cana-2737	53	10	a	a	DET
cana-2737	53	11	membership	membership	NOUN
cana-2737	53	12	function	function	NOUN
cana-2737	53	13	𝜇𝐴	𝜇𝐴	ADP
cana-2737	53	14	:	:	PUNCT
cana-2737	53	15	𝑋	𝑋	PROPN
cana-2737	53	16	→	→	SYM
cana-2737	54	1	[	[	X
cana-2737	54	2	0,1	0,1	NUM
cana-2737	54	3	]	]	PUNCT
cana-2737	54	4	.	.	PUNCT
cana-2737	55	1	that	that	PRON
cana-2737	55	2	is	be	AUX
cana-2737	55	3	:	:	PUNCT
cana-2737	55	4	communications	communication	NOUN
cana-2737	55	5	on	on	ADP
cana-2737	55	6	applied	apply	VERB
cana-2737	55	7	nonlinear	nonlinear	ADJ
cana-2737	55	8	analysis	analysis	NOUN
cana-2737	55	9	issn	issn	NOUN
cana-2737	55	10	:	:	PUNCT
cana-2737	55	11	1074	1074	NUM
cana-2737	55	12	-	-	PUNCT
cana-2737	55	13	133x	133x	NUM
cana-2737	55	14	vol	vol	NOUN
cana-2737	55	15	32	32	NUM
cana-2737	55	16	no	no	NOUN
cana-2737	55	17	.	.	PUNCT
cana-2737	56	1	4s	4s	NUM
cana-2737	56	2	(	(	PUNCT
cana-2737	56	3	2025	2025	NUM
cana-2737	56	4	)	)	PUNCT
cana-2737	56	5	28	28	NUM
cana-2737	56	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2737	56	7	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-2737	56	8	)	)	PUNCT
cana-2737	56	9	=	=	NOUN
cana-2737	56	10	{	{	PUNCT
cana-2737	56	11	1	1	NUM
cana-2737	56	12	,	,	PUNCT
cana-2737	56	13	if	if	SCONJ
cana-2737	56	14	𝑥	𝑥	PRON
cana-2737	56	15	∈	∈	PROPN
cana-2737	56	16	𝑋	𝑋	NOUN
cana-2737	56	17	0	0	NUM
cana-2737	56	18	,	,	PUNCT
cana-2737	56	19	if	if	SCONJ
cana-2737	56	20	𝑥	𝑥	PROPN
cana-2737	56	21	∉	∉	X
cana-2737	56	22	𝑋	𝑋	PROPN
cana-2737	56	23	(	(	PUNCT
cana-2737	56	24	0,1	0,1	NUM
cana-2737	56	25	)	)	PUNCT
cana-2737	56	26	if	if	SCONJ
cana-2737	56	27	𝑥	𝑥	NOUN
cana-2737	56	28	ispartlyin	ispartlyin	VERB
cana-2737	56	29	𝑋.	𝑋.	PROPN
cana-2737	56	30	alternatively	alternatively	ADV
cana-2737	56	31	,	,	PUNCT
cana-2737	56	32	a	a	DET
cana-2737	56	33	fuzzy	fuzzy	ADJ
cana-2737	56	34	set	set	VERB
cana-2737	56	35	𝐴	𝐴	PROPN
cana-2737	56	36	in	in	ADP
cana-2737	56	37	𝑋	𝑋	PROPN
cana-2737	56	38	is	be	AUX
cana-2737	56	39	an	an	DET
cana-2737	56	40	object	object	NOUN
cana-2737	56	41	having	have	VERB
cana-2737	56	42	the	the	DET
cana-2737	56	43	form	form	NOUN
cana-2737	56	44	𝐴	𝐴	NOUN
cana-2737	56	45	=	=	PUNCT
cana-2737	56	46	{	{	PUNCT
cana-2737	56	47	<	<	X
cana-2737	56	48	𝑥	𝑥	X
cana-2737	56	49	,	,	PUNCT
cana-2737	56	50	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-2737	56	51	)	)	PUNCT
cana-2737	56	52	>	>	PUNCT
cana-2737	57	1	|𝑥	|𝑥	PROPN
cana-2737	57	2	∈	∈	PROPN
cana-2737	57	3	𝑋	𝑋	PROPN
cana-2737	57	4	}	}	PUNCT
cana-2737	57	5	or	or	CCONJ
cana-2737	57	6	𝐴	𝐴	PROPN
cana-2737	57	7	=	=	PUNCT
cana-2737	57	8	{	{	PUNCT
cana-2737	57	9	⟨	⟨	NOUN
cana-2737	57	10	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-2737	57	11	)	)	PUNCT
cana-2737	57	12	𝑥	𝑥	DET
cana-2737	57	13	⟩	⟩	NOUN
cana-2737	57	14	|𝑥	|𝑥	NOUN
cana-2737	57	15	∈	∈	PROPN
cana-2737	57	16	𝑋	𝑋	PROPN
cana-2737	57	17	}	}	PUNCT
cana-2737	57	18	,	,	PUNCT
cana-2737	57	19	where	where	SCONJ
cana-2737	57	20	the	the	DET
cana-2737	57	21	function	function	NOUN
cana-2737	57	22	𝜇𝐴(𝑥	𝜇𝐴(𝑥	VERB
cana-2737	57	23	):	):	PUNCT
cana-2737	57	24	𝑋	𝑋	PROPN
cana-2737	57	25	→	→	SYM
cana-2737	57	26	[	[	X
cana-2737	57	27	0,1	0,1	NUM
cana-2737	57	28	]	]	PUNCT
cana-2737	57	29	defines	define	VERB
cana-2737	57	30	the	the	DET
cana-2737	57	31	degree	degree	NOUN
cana-2737	57	32	of	of	ADP
cana-2737	57	33	membership	membership	NOUN
cana-2737	57	34	of	of	ADP
cana-2737	57	35	the	the	DET
cana-2737	57	36	element	element	NOUN
cana-2737	57	37	,	,	PUNCT
cana-2737	57	38	𝑥	𝑥	PROPN
cana-2737	57	39	∈	∈	PROPN
cana-2737	57	40	𝑋.	𝑋.	PROPN
cana-2737	57	41	the	the	PRON
cana-2737	57	42	closer	close	ADV
cana-2737	57	43	the	the	DET
cana-2737	57	44	membership	membership	NOUN
cana-2737	57	45	value	value	NOUN
cana-2737	57	46	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NOUN
cana-2737	57	47	)	)	PUNCT
cana-2737	57	48	to	to	ADP
cana-2737	57	49	1	1	NUM
cana-2737	57	50	,	,	PUNCT
cana-2737	57	51	the	the	PRON
cana-2737	57	52	more	more	ADJ
cana-2737	57	53	𝑥	𝑥	NOUN
cana-2737	57	54	belongs	belong	VERB
cana-2737	57	55	to	to	ADP
cana-2737	57	56	𝐴	𝐴	PROPN
cana-2737	57	57	,	,	PUNCT
cana-2737	57	58	where	where	SCONJ
cana-2737	57	59	the	the	DET
cana-2737	57	60	grades	grade	NOUN
cana-2737	57	61	1	1	NUM
cana-2737	57	62	and	and	CCONJ
cana-2737	57	63	0	0	NUM
cana-2737	57	64	represent	represent	VERB
cana-2737	57	65	full	full	ADJ
cana-2737	57	66	membership	membership	NOUN
cana-2737	57	67	and	and	CCONJ
cana-2737	57	68	full	full	ADJ
cana-2737	57	69	nonmembership	nonmembership	NOUN
cana-2737	57	70	.	.	PUNCT
cana-2737	58	1	fuzzy	fuzzy	ADJ
cana-2737	58	2	set	set	NOUN
cana-2737	58	3	is	be	AUX
cana-2737	58	4	a	a	DET
cana-2737	58	5	collection	collection	NOUN
cana-2737	58	6	of	of	ADP
cana-2737	58	7	objects	object	NOUN
cana-2737	58	8	with	with	ADP
cana-2737	58	9	graded	grade	VERB
cana-2737	58	10	membership	membership	NOUN
cana-2737	58	11	,	,	PUNCT
cana-2737	58	12	that	that	ADV
cana-2737	58	13	is	is	ADV
cana-2737	58	14	,	,	PUNCT
cana-2737	58	15	having	have	VERB
cana-2737	58	16	degree	degree	NOUN
cana-2737	58	17	of	of	ADP
cana-2737	58	18	membership	membership	NOUN
cana-2737	58	19	.	.	PUNCT
cana-2737	59	1	fuzzy	fuzzy	ADJ
cana-2737	59	2	set	set	NOUN
cana-2737	59	3	is	be	AUX
cana-2737	59	4	an	an	DET
cana-2737	59	5	extension	extension	NOUN
cana-2737	59	6	of	of	ADP
cana-2737	59	7	the	the	DET
cana-2737	59	8	classical	classical	ADJ
cana-2737	59	9	notion	notion	NOUN
cana-2737	59	10	of	of	ADP
cana-2737	59	11	set	set	NOUN
cana-2737	59	12	.	.	PUNCT
cana-2737	60	1	in	in	ADP
cana-2737	60	2	classical	classical	ADJ
cana-2737	60	3	set	set	NOUN
cana-2737	60	4	theory	theory	NOUN
cana-2737	60	5	,	,	PUNCT
cana-2737	60	6	the	the	DET
cana-2737	60	7	membership	membership	NOUN
cana-2737	60	8	of	of	ADP
cana-2737	60	9	elements	element	NOUN
cana-2737	60	10	in	in	ADP
cana-2737	60	11	a	a	DET
cana-2737	60	12	set	set	NOUN
cana-2737	60	13	is	be	AUX
cana-2737	60	14	assessed	assess	VERB
cana-2737	60	15	in	in	ADP
cana-2737	60	16	a	a	DET
cana-2737	60	17	binary	binary	ADJ
cana-2737	60	18	terms	term	NOUN
cana-2737	60	19	according	accord	VERB
cana-2737	60	20	to	to	ADP
cana-2737	60	21	a	a	DET
cana-2737	60	22	bivalent	bivalent	ADJ
cana-2737	60	23	condition	condition	NOUN
cana-2737	60	24	;	;	PUNCT
cana-2737	60	25	an	an	DET
cana-2737	60	26	element	element	NOUN
cana-2737	60	27	either	either	CCONJ
cana-2737	60	28	belongs	belong	VERB
cana-2737	60	29	or	or	CCONJ
cana-2737	60	30	does	do	AUX
cana-2737	60	31	not	not	PART
cana-2737	60	32	belong	belong	VERB
cana-2737	60	33	to	to	ADP
cana-2737	60	34	the	the	DET
cana-2737	60	35	set	set	NOUN
cana-2737	60	36	.	.	PUNCT
cana-2737	61	1	classical	classical	ADJ
cana-2737	61	2	bivalent	bivalent	ADJ
cana-2737	61	3	sets	set	NOUN
cana-2737	61	4	are	be	AUX
cana-2737	61	5	in	in	ADP
cana-2737	61	6	fuzzy	fuzzy	ADJ
cana-2737	61	7	set	set	NOUN
cana-2737	61	8	theory	theory	NOUN
cana-2737	61	9	called	call	VERB
cana-2737	61	10	crisp	crisp	ADJ
cana-2737	61	11	sets	set	NOUN
cana-2737	61	12	.	.	PUNCT
cana-2737	62	1	fuzzy	fuzzy	ADJ
cana-2737	62	2	sets	set	NOUN
cana-2737	62	3	are	be	AUX
cana-2737	62	4	generalized	generalized	ADJ
cana-2737	62	5	classical	classical	ADJ
cana-2737	62	6	sets	set	NOUN
cana-2737	62	7	,	,	PUNCT
cana-2737	62	8	since	since	SCONJ
cana-2737	62	9	the	the	DET
cana-2737	62	10	indicator	indicator	NOUN
cana-2737	62	11	function	function	NOUN
cana-2737	62	12	of	of	ADP
cana-2737	62	13	classical	classical	ADJ
cana-2737	62	14	sets	set	NOUN
cana-2737	62	15	is	be	AUX
cana-2737	62	16	special	special	ADJ
cana-2737	62	17	cases	case	NOUN
cana-2737	62	18	of	of	ADP
cana-2737	62	19	the	the	DET
cana-2737	62	20	membership	membership	NOUN
cana-2737	62	21	functions	function	NOUN
cana-2737	62	22	of	of	ADP
cana-2737	62	23	fuzzy	fuzzy	ADJ
cana-2737	62	24	sets	set	NOUN
cana-2737	62	25	,	,	PUNCT
cana-2737	62	26	if	if	SCONJ
cana-2737	62	27	the	the	DET
cana-2737	62	28	latter	latter	ADJ
cana-2737	62	29	only	only	ADV
cana-2737	62	30	take	take	VERB
cana-2737	62	31	values	value	NOUN
cana-2737	62	32	0	0	NUM
cana-2737	62	33	or	or	CCONJ
cana-2737	62	34	1	1	NUM
cana-2737	62	35	.	.	X
cana-2737	62	36	fuzzy	fuzzy	ADJ
cana-2737	62	37	sets	set	NOUN
cana-2737	62	38	theory	theory	NOUN
cana-2737	62	39	permits	permit	VERB
cana-2737	62	40	the	the	DET
cana-2737	62	41	gradual	gradual	ADJ
cana-2737	62	42	assessment	assessment	NOUN
cana-2737	62	43	of	of	ADP
cana-2737	62	44	the	the	DET
cana-2737	62	45	membership	membership	NOUN
cana-2737	62	46	of	of	ADP
cana-2737	62	47	element	element	NOUN
cana-2737	62	48	in	in	ADP
cana-2737	62	49	a	a	DET
cana-2737	62	50	set	set	NOUN
cana-2737	62	51	;	;	PUNCT
cana-2737	62	52	this	this	PRON
cana-2737	62	53	is	be	AUX
cana-2737	62	54	described	describe	VERB
cana-2737	62	55	with	with	ADP
cana-2737	62	56	the	the	DET
cana-2737	62	57	aid	aid	NOUN
cana-2737	62	58	of	of	ADP
cana-2737	62	59	a	a	DET
cana-2737	62	60	membership	membership	NOUN
cana-2737	62	61	function	function	NOUN
cana-2737	62	62	valued	value	VERB
cana-2737	62	63	in	in	ADP
cana-2737	62	64	the	the	DET
cana-2737	62	65	real	real	ADJ
cana-2737	62	66	unit	unit	NOUN
cana-2737	62	67	interval	interval	NOUN
cana-2737	62	68	[	[	X
cana-2737	62	69	0,1	0,1	NUM
cana-2737	62	70	]	]	PUNCT
cana-2737	62	71	.	.	PUNCT
cana-2737	63	1	let	let	VERB
cana-2737	63	2	us	we	PRON
cana-2737	63	3	consider	consider	VERB
cana-2737	63	4	two	two	NUM
cana-2737	63	5	examples	example	NOUN
cana-2737	63	6	:	:	PUNCT
cana-2737	63	7	(	(	PUNCT
cana-2737	63	8	i	i	NOUN
cana-2737	63	9	)	)	PUNCT
cana-2737	63	10	all	all	DET
cana-2737	63	11	employees	employee	NOUN
cana-2737	63	12	of	of	ADP
cana-2737	63	13	𝑋𝑌𝑍	𝑋𝑌𝑍	PROPN
cana-2737	63	14	who	who	PRON
cana-2737	63	15	are	be	AUX
cana-2737	63	16	over	over	ADP
cana-2737	63	17	1.8𝑚	1.8𝑚	NUM
cana-2737	63	18	in	in	ADP
cana-2737	63	19	height	height	NOUN
cana-2737	63	20	;	;	PUNCT
cana-2737	63	21	(	(	PUNCT
cana-2737	63	22	ii	ii	NOUN
cana-2737	63	23	)	)	PUNCT
cana-2737	63	24	all	all	DET
cana-2737	63	25	employees	employee	NOUN
cana-2737	63	26	of	of	ADP
cana-2737	63	27	𝑋𝑌𝑍	𝑋𝑌𝑍	PROPN
cana-2737	63	28	who	who	PRON
cana-2737	63	29	are	be	AUX
cana-2737	63	30	tall	tall	ADJ
cana-2737	63	31	.	.	PUNCT
cana-2737	64	1	the	the	DET
cana-2737	64	2	first	first	ADJ
cana-2737	64	3	example	example	NOUN
cana-2737	64	4	is	be	AUX
cana-2737	64	5	a	a	DET
cana-2737	64	6	classical	classical	ADJ
cana-2737	64	7	set	set	NOUN
cana-2737	64	8	with	with	ADP
cana-2737	64	9	a	a	DET
cana-2737	64	10	universe	universe	NOUN
cana-2737	64	11	(	(	PUNCT
cana-2737	64	12	all	all	DET
cana-2737	64	13	𝑋𝑌𝑍	𝑋𝑌𝑍	PROPN
cana-2737	64	14	employees	employee	NOUN
cana-2737	64	15	)	)	PUNCT
cana-2737	64	16	and	and	CCONJ
cana-2737	64	17	a	a	DET
cana-2737	64	18	membership	membership	NOUN
cana-2737	64	19	rule	rule	NOUN
cana-2737	64	20	that	that	PRON
cana-2737	64	21	divides	divide	VERB
cana-2737	64	22	the	the	DET
cana-2737	64	23	universe	universe	NOUN
cana-2737	64	24	into	into	ADP
cana-2737	64	25	members	member	NOUN
cana-2737	64	26	(	(	PUNCT
cana-2737	64	27	those	those	PRON
cana-2737	64	28	over	over	ADP
cana-2737	64	29	1.8𝑚	1.8𝑚	NUM
cana-2737	64	30	)	)	PUNCT
cana-2737	64	31	and	and	CCONJ
cana-2737	64	32	nonmembers	nonmember	NOUN
cana-2737	64	33	.	.	PUNCT
cana-2737	65	1	the	the	DET
cana-2737	65	2	second	second	ADJ
cana-2737	65	3	example	example	NOUN
cana-2737	65	4	is	be	AUX
cana-2737	65	5	a	a	DET
cana-2737	65	6	fuzzy	fuzzy	ADJ
cana-2737	65	7	set	set	NOUN
cana-2737	65	8	,	,	PUNCT
cana-2737	65	9	because	because	SCONJ
cana-2737	65	10	some	some	DET
cana-2737	65	11	employees	employee	NOUN
cana-2737	65	12	are	be	AUX
cana-2737	65	13	definitely	definitely	ADV
cana-2737	65	14	in	in	ADP
cana-2737	65	15	the	the	DET
cana-2737	65	16	set	set	NOUN
cana-2737	65	17	and	and	CCONJ
cana-2737	65	18	some	some	PRON
cana-2737	65	19	are	be	AUX
cana-2737	65	20	definitely	definitely	ADV
cana-2737	65	21	not	not	PART
cana-2737	65	22	in	in	ADP
cana-2737	65	23	the	the	DET
cana-2737	65	24	set	set	NOUN
cana-2737	65	25	,	,	PUNCT
cana-2737	65	26	but	but	CCONJ
cana-2737	65	27	some	some	PRON
cana-2737	65	28	are	be	AUX
cana-2737	65	29	borderline	borderline	NOUN
cana-2737	65	30	.	.	PUNCT
cana-2737	66	1	this	this	DET
cana-2737	66	2	distinction	distinction	NOUN
cana-2737	66	3	between	between	ADP
cana-2737	66	4	the	the	DET
cana-2737	66	5	ins	in	NOUN
cana-2737	66	6	,	,	PUNCT
cana-2737	66	7	the	the	DET
cana-2737	66	8	outs	out	NOUN
cana-2737	66	9	,	,	PUNCT
cana-2737	66	10	and	and	CCONJ
cana-2737	66	11	the	the	DET
cana-2737	66	12	borderline	borderline	NOUN
cana-2737	66	13	is	be	AUX
cana-2737	66	14	made	make	VERB
cana-2737	66	15	more	more	ADV
cana-2737	66	16	exact	exact	ADJ
cana-2737	66	17	by	by	ADP
cana-2737	66	18	the	the	DET
cana-2737	66	19	membership	membership	NOUN
cana-2737	66	20	function	function	NOUN
cana-2737	66	21	,	,	PUNCT
cana-2737	66	22	𝜇.	𝜇.	ADV
cana-2737	66	23	if	if	SCONJ
cana-2737	66	24	we	we	PRON
cana-2737	66	25	return	return	VERB
cana-2737	66	26	to	to	ADP
cana-2737	66	27	our	our	PRON
cana-2737	66	28	second	second	ADJ
cana-2737	66	29	example	example	NOUN
cana-2737	66	30	and	and	CCONJ
cana-2737	66	31	let	let	VERB
cana-2737	66	32	𝐴	𝐴	PROPN
cana-2737	66	33	represent	represent	VERB
cana-2737	66	34	the	the	DET
cana-2737	66	35	fuzzy	fuzzy	ADJ
cana-2737	66	36	set	set	NOUN
cana-2737	66	37	of	of	ADP
cana-2737	66	38	all	all	DET
cana-2737	66	39	tall	tall	ADJ
cana-2737	66	40	employees	employee	NOUN
cana-2737	66	41	and	and	CCONJ
cana-2737	66	42	𝑥	𝑥	PROPN
cana-2737	66	43	represent	represent	VERB
cana-2737	66	44	a	a	DET
cana-2737	66	45	member	member	NOUN
cana-2737	66	46	of	of	ADP
cana-2737	66	47	the	the	DET
cana-2737	66	48	universe	universe	ADJ
cana-2737	66	49	𝑋	𝑋	NOUN
cana-2737	66	50	(	(	PUNCT
cana-2737	66	51	i.e.	i.e.	X
cana-2737	66	52	all	all	DET
cana-2737	66	53	employees	employee	NOUN
cana-2737	66	54	)	)	PUNCT
cana-2737	66	55	,	,	PUNCT
cana-2737	66	56	then	then	ADV
cana-2737	66	57	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-2737	66	58	)	)	PUNCT
cana-2737	66	59	would	would	AUX
cana-2737	66	60	be	be	AUX
cana-2737	66	61	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-2737	66	62	)	)	PUNCT
cana-2737	66	63	=	=	SYM
cana-2737	66	64	1	1	NUM
cana-2737	66	65	if	if	SCONJ
cana-2737	66	66	𝑥	𝑥	PRON
cana-2737	66	67	is	be	AUX
cana-2737	66	68	definitely	definitely	ADV
cana-2737	66	69	tall	tall	ADJ
cana-2737	66	70	or	or	CCONJ
cana-2737	66	71	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-2737	66	72	)	)	PUNCT
cana-2737	66	73	=	=	SYM
cana-2737	66	74	0	0	PUNCT
cana-2737	67	1	if	if	SCONJ
cana-2737	67	2	𝑥	𝑥	PRON
cana-2737	67	3	is	be	AUX
cana-2737	67	4	definitely	definitely	ADV
cana-2737	67	5	not	not	PART
cana-2737	67	6	tall	tall	ADJ
cana-2737	67	7	or	or	CCONJ
cana-2737	67	8	0	0	NUM
cana-2737	67	9	<	<	X
cana-2737	67	10	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NOUN
cana-2737	67	11	)	)	PUNCT
cana-2737	67	12	<	<	X
cana-2737	67	13	1	1	NUM
cana-2737	67	14	for	for	ADP
cana-2737	67	15	borderline	borderline	NOUN
cana-2737	67	16	cases	case	NOUN
cana-2737	67	17	.	.	PUNCT
cana-2737	68	1	definition	definition	NOUN
cana-2737	68	2	2.2	2.2	NUM
cana-2737	68	3	[	[	SYM
cana-2737	68	4	1	1	NUM
cana-2737	68	5	,	,	PUNCT
cana-2737	68	6	2	2	NUM
cana-2737	68	7	,	,	PUNCT
cana-2737	68	8	4	4	NUM
cana-2737	68	9	,	,	PUNCT
cana-2737	68	10	5	5	NUM
cana-2737	68	11	]	]	PUNCT
cana-2737	68	12	let	let	VERB
cana-2737	68	13	a	a	DET
cana-2737	68	14	nonempty	nonempty	ADV
cana-2737	68	15	set	set	VERB
cana-2737	68	16	𝑋	𝑋	NOUN
cana-2737	68	17	be	be	AUX
cana-2737	68	18	fixed	fix	VERB
cana-2737	68	19	.	.	PUNCT
cana-2737	69	1	an	an	DET
cana-2737	69	2	𝐼𝐹𝑆	𝐼𝐹𝑆	PROPN
cana-2737	69	3	𝐴	𝐴	PROPN
cana-2737	69	4	in	in	ADP
cana-2737	69	5	𝑋	𝑋	PROPN
cana-2737	69	6	is	be	AUX
cana-2737	69	7	an	an	DET
cana-2737	69	8	object	object	NOUN
cana-2737	69	9	having	have	VERB
cana-2737	69	10	the	the	DET
cana-2737	69	11	form	form	NOUN
cana-2737	69	12	:	:	PUNCT
cana-2737	69	13	𝐴	𝐴	PROPN
cana-2737	69	14	=	=	PUNCT
cana-2737	69	15	{	{	PUNCT
cana-2737	69	16	<	<	X
cana-2737	69	17	𝑥	𝑥	X
cana-2737	69	18	,	,	PUNCT
cana-2737	69	19	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NOUN
cana-2737	69	20	)	)	PUNCT
cana-2737	69	21	,	,	PUNCT
cana-2737	69	22	𝜈𝐴(𝑥	𝜈𝐴(𝑥	NUM
cana-2737	69	23	)	)	PUNCT
cana-2737	69	24	>	>	X
cana-2737	69	25	|𝑥	|𝑥	PROPN
cana-2737	69	26	∈	∈	PROPN
cana-2737	69	27	𝑋	𝑋	PROPN
cana-2737	69	28	}	}	PUNCT
cana-2737	69	29	or	or	CCONJ
cana-2737	69	30	𝐴	𝐴	PROPN
cana-2737	69	31	=	=	PUNCT
cana-2737	69	32	{	{	PUNCT
cana-2737	69	33	⟨	⟨	NOUN
cana-2737	69	34	𝜇𝐴(𝑥),𝜈𝐴(𝑥	𝜇𝐴(𝑥),𝜈𝐴(𝑥	NOUN
cana-2737	69	35	)	)	PUNCT
cana-2737	70	1	𝑥	𝑥	DET
cana-2737	70	2	⟩	⟩	NOUN
cana-2737	70	3	|𝑥	|𝑥	NOUN
cana-2737	70	4	∈	∈	PROPN
cana-2737	70	5	𝑋	𝑋	PROPN
cana-2737	70	6	}	}	PUNCT
cana-2737	70	7	,	,	PUNCT
cana-2737	70	8	where	where	SCONJ
cana-2737	70	9	the	the	DET
cana-2737	70	10	functions	function	NOUN
cana-2737	70	11	𝜇𝐴(𝑥	𝜇𝐴(𝑥	VERB
cana-2737	70	12	):	):	PUNCT
cana-2737	70	13	𝑋	𝑋	PROPN
cana-2737	70	14	→	→	SYM
cana-2737	70	15	[	[	X
cana-2737	70	16	0,1	0,1	NUM
cana-2737	70	17	]	]	PUNCT
cana-2737	70	18	and	and	CCONJ
cana-2737	70	19	𝜈𝐴(𝑥	𝜈𝐴(𝑥	NUM
cana-2737	70	20	):	):	PUNCT
cana-2737	70	21	𝑋	𝑋	PROPN
cana-2737	70	22	→	→	SYM
cana-2737	70	23	[	[	X
cana-2737	70	24	0,1	0,1	NUM
cana-2737	70	25	]	]	PUNCT
cana-2737	70	26	define	define	VERB
cana-2737	70	27	the	the	DET
cana-2737	70	28	degree	degree	NOUN
cana-2737	70	29	of	of	ADP
cana-2737	70	30	membership	membership	NOUN
cana-2737	70	31	and	and	CCONJ
cana-2737	70	32	the	the	DET
cana-2737	70	33	degree	degree	NOUN
cana-2737	70	34	of	of	ADP
cana-2737	70	35	nonmembership	nonmembership	NOUN
cana-2737	70	36	,	,	PUNCT
cana-2737	70	37	respectively	respectively	ADV
cana-2737	70	38	,	,	PUNCT
cana-2737	70	39	of	of	ADP
cana-2737	70	40	the	the	DET
cana-2737	70	41	element	element	NOUN
cana-2737	70	42	𝑥	𝑥	PRON
cana-2737	70	43	∈	∈	PROPN
cana-2737	70	44	𝑋	𝑋	NOUN
cana-2737	70	45	to	to	ADP
cana-2737	70	46	𝐴	𝐴	PROPN
cana-2737	70	47	,	,	PUNCT
cana-2737	70	48	which	which	PRON
cana-2737	70	49	is	be	AUX
cana-2737	70	50	a	a	DET
cana-2737	70	51	subset	subset	NOUN
cana-2737	70	52	of	of	ADP
cana-2737	70	53	𝑋	𝑋	PROPN
cana-2737	70	54	,	,	PUNCT
cana-2737	70	55	and	and	CCONJ
cana-2737	70	56	for	for	ADP
cana-2737	70	57	every	every	DET
cana-2737	70	58	𝑥	𝑥	PRON
cana-2737	70	59	∈	∈	PROPN
cana-2737	70	60	𝑋	𝑋	NOUN
cana-2737	70	61	:	:	PUNCT
cana-2737	70	62	0	0	NUM
cana-2737	70	63	≤	≤	NUM
cana-2737	70	64	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-2737	70	65	)	)	PUNCT
cana-2737	70	66	+	+	NUM
cana-2737	70	67	𝜈𝐴(𝑥	𝜈𝐴(𝑥	X
cana-2737	70	68	)	)	PUNCT
cana-2737	70	69	≤	≤	NUM
cana-2737	70	70	1	1	NUM
cana-2737	70	71	.	.	PUNCT
cana-2737	71	1	for	for	ADP
cana-2737	71	2	each	each	DET
cana-2737	71	3	𝐴	𝐴	PROPN
cana-2737	71	4	in	in	ADP
cana-2737	71	5	𝑋	𝑋	PROPN
cana-2737	71	6	:	:	PUNCT
cana-2737	71	7	𝜋𝐴(𝑥	𝜋𝐴(𝑥	NUM
cana-2737	71	8	)	)	PUNCT
cana-2737	71	9	=	=	SYM
cana-2737	71	10	1	1	NUM
cana-2737	71	11	−	−	NUM
cana-2737	71	12	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-2737	71	13	)	)	PUNCT
cana-2737	71	14	−	−	PROPN
cana-2737	71	15	𝜈𝐴(𝑥	𝜈𝐴(𝑥	NUM
cana-2737	71	16	)	)	PUNCT
cana-2737	71	17	is	be	AUX
cana-2737	71	18	the	the	DET
cana-2737	71	19	intuitionistic	intuitionistic	ADJ
cana-2737	71	20	fuzzy	fuzzy	ADJ
cana-2737	71	21	set	set	VERB
cana-2737	71	22	index	index	NOUN
cana-2737	71	23	or	or	CCONJ
cana-2737	71	24	hesitation	hesitation	NOUN
cana-2737	71	25	margin	margin	NOUN
cana-2737	71	26	of	of	ADP
cana-2737	71	27	𝑥	𝑥	NOUN
cana-2737	71	28	in	in	ADP
cana-2737	71	29	𝑋.	𝑋.	PROPN
cana-2737	71	30	the	the	DET
cana-2737	71	31	hesitation	hesitation	NOUN
cana-2737	71	32	margin	margin	NOUN
cana-2737	71	33	𝜋𝐴(𝑥	𝜋𝐴(𝑥	NUM
cana-2737	71	34	)	)	PUNCT
cana-2737	71	35	is	be	AUX
cana-2737	71	36	the	the	DET
cana-2737	71	37	degree	degree	NOUN
cana-2737	71	38	of	of	ADP
cana-2737	71	39	nondeterminacy	nondeterminacy	NOUN
cana-2737	71	40	of	of	ADP
cana-2737	71	41	𝑥	𝑥	DET
cana-2737	71	42	∈	∈	PROPN
cana-2737	71	43	𝑋	𝑋	NOUN
cana-2737	71	44	to	to	ADP
cana-2737	71	45	the	the	DET
cana-2737	71	46	set	set	ADJ
cana-2737	71	47	𝐴	𝐴	PROPN
cana-2737	71	48	and	and	CCONJ
cana-2737	71	49	𝜋𝐴(𝑥	𝜋𝐴(𝑥	NUM
cana-2737	71	50	)	)	PUNCT
cana-2737	71	51	∈	∈	NOUN
cana-2737	72	1	[	[	X
cana-2737	72	2	0,1	0,1	NUM
cana-2737	72	3	]	]	PUNCT
cana-2737	72	4	.	.	PUNCT
cana-2737	73	1	the	the	DET
cana-2737	73	2	hesitation	hesitation	NOUN
cana-2737	73	3	margin	margin	NOUN
cana-2737	73	4	is	be	AUX
cana-2737	73	5	the	the	DET
cana-2737	73	6	function	function	NOUN
cana-2737	73	7	that	that	PRON
cana-2737	73	8	expresses	express	VERB
cana-2737	73	9	lack	lack	NOUN
cana-2737	73	10	of	of	ADP
cana-2737	73	11	knowledge	knowledge	NOUN
cana-2737	73	12	of	of	ADP
cana-2737	73	13	whether	whether	SCONJ
cana-2737	73	14	𝑥	𝑥	PRON
cana-2737	73	15	∈	∈	PROPN
cana-2737	73	16	𝑋	𝑋	NOUN
cana-2737	73	17	or	or	CCONJ
cana-2737	73	18	𝑥	𝑥	PROPN
cana-2737	73	19	∉	∉	PROPN
cana-2737	73	20	𝑋.	𝑋.	PROPN
cana-2737	73	21	thus	thus	ADV
cana-2737	73	22	:	:	PUNCT
cana-2737	73	23	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-2737	73	24	)	)	PUNCT
cana-2737	73	25	+	+	NUM
cana-2737	73	26	𝜈𝐴(𝑥	𝜈𝐴(𝑥	NUM
cana-2737	73	27	)	)	PUNCT
cana-2737	73	28	+	+	NUM
cana-2737	73	29	𝜋𝐴(𝑥	𝜋𝐴(𝑥	NUM
cana-2737	73	30	)	)	PUNCT
cana-2737	73	31	=	=	SYM
cana-2737	73	32	1	1	X
cana-2737	73	33	.	.	PUNCT
cana-2737	73	34	example	example	NOUN
cana-2737	73	35	2.1	2.1	NUM
cana-2737	73	36	let	let	VERB
cana-2737	73	37	𝑋	𝑋	NOUN
cana-2737	73	38	=	=	SYM
cana-2737	73	39	{	{	PUNCT
cana-2737	73	40	𝑥	𝑥	PROPN
cana-2737	73	41	,	,	PUNCT
cana-2737	73	42	𝑦	𝑦	NOUN
cana-2737	73	43	,	,	PUNCT
cana-2737	73	44	𝑧	𝑧	PRON
cana-2737	73	45	}	}	PUNCT
cana-2737	73	46	be	be	AUX
cana-2737	73	47	a	a	DET
cana-2737	73	48	fixed	fix	VERB
cana-2737	73	49	universe	universe	NOUN
cana-2737	73	50	of	of	ADP
cana-2737	73	51	discourse	discourse	NOUN
cana-2737	73	52	and	and	CCONJ
cana-2737	73	53	𝐴	𝐴	PROPN
cana-2737	73	54	=	=	PUNCT
cana-2737	73	55	{	{	PUNCT
cana-2737	73	56	⟨	⟨	VERB
cana-2737	73	57	0.6,0.1	0.6,0.1	PROPN
cana-2737	73	58	𝑥	𝑥	DET
cana-2737	73	59	⟩	⟩	NOUN
cana-2737	73	60	,	,	PUNCT
cana-2737	73	61	⟨	⟨	VERB
cana-2737	73	62	0.8,0.1	0.8,0.1	PROPN
cana-2737	73	63	𝑦	𝑦	NOUN
cana-2737	73	64	⟩	⟩	NOUN
cana-2737	73	65	,	,	PUNCT
cana-2737	73	66	⟨	⟨	VERB
cana-2737	73	67	0.5,0.3	0.5,0.3	PROPN
cana-2737	73	68	𝑧	𝑧	DET
cana-2737	73	69	⟩	⟩	NOUN
cana-2737	73	70	}	}	PUNCT
cana-2737	73	71	,	,	PUNCT
cana-2737	73	72	be	be	AUX
cana-2737	73	73	the	the	DET
cana-2737	73	74	intuitionistic	intuitionistic	ADJ
cana-2737	73	75	fuzzy	fuzzy	ADJ
cana-2737	73	76	set	set	NOUN
cana-2737	73	77	in	in	ADP
cana-2737	73	78	𝑋.	𝑋.	PROPN
cana-2737	73	79	the	the	DET
cana-2737	73	80	hesitation	hesitation	NOUN
cana-2737	73	81	margins	margin	NOUN
cana-2737	73	82	of	of	ADP
cana-2737	73	83	the	the	DET
cana-2737	73	84	elements	element	NOUN
cana-2737	73	85	𝑥	𝑥	PROPN
cana-2737	73	86	,	,	PUNCT
cana-2737	73	87	𝑦	𝑦	NOUN
cana-2737	73	88	,	,	PUNCT
cana-2737	73	89	𝑧	𝑧	PUNCT
cana-2737	73	90	to	to	ADP
cana-2737	73	91	𝐴	𝐴	PROPN
cana-2737	73	92	are	be	AUX
cana-2737	73	93	as	as	SCONJ
cana-2737	73	94	follows	follow	VERB
cana-2737	73	95	:	:	PUNCT
cana-2737	73	96	𝜋𝐴(𝑥	𝜋𝐴(𝑥	NUM
cana-2737	73	97	)	)	PUNCT
cana-2737	73	98	=	=	SYM
cana-2737	73	99	0.3	0.3	NUM
cana-2737	73	100	,	,	PUNCT
cana-2737	73	101	𝜋𝐴(𝑦	𝜋𝐴(𝑦	PROPN
cana-2737	73	102	)	)	PUNCT
cana-2737	73	103	=	=	SYM
cana-2737	73	104	0.1	0.1	NUM
cana-2737	73	105	and	and	CCONJ
cana-2737	73	106	𝜋𝐴(𝑧	𝜋𝐴(𝑧	NUM
cana-2737	73	107	)	)	PUNCT
cana-2737	73	108	=	=	PUNCT
cana-2737	74	1	0.2	0.2	NUM
cana-2737	74	2	.	.	PUNCT
cana-2737	75	1	definition	definition	NOUN
cana-2737	75	2	2.3	2.3	NUM
cana-2737	76	1	[	[	X
cana-2737	76	2	32	32	NUM
cana-2737	76	3	,	,	PUNCT
cana-2737	76	4	33	33	NUM
cana-2737	76	5	,	,	PUNCT
cana-2737	76	6	34	34	NUM
cana-2737	76	7	]	]	PUNCT
cana-2737	76	8	let	let	VERB
cana-2737	76	9	𝑋	𝑋	NOUN
cana-2737	76	10	be	be	AUX
cana-2737	76	11	a	a	DET
cana-2737	76	12	universal	universal	ADJ
cana-2737	76	13	set	set	NOUN
cana-2737	76	14	.	.	PUNCT
cana-2737	77	1	then	then	ADV
cana-2737	77	2	,	,	PUNCT
cana-2737	77	3	a	a	DET
cana-2737	77	4	pythagorean	pythagorean	PROPN
cana-2737	77	5	fuzzy	fuzzy	ADJ
cana-2737	77	6	set	set	PROPN
cana-2737	77	7	𝐴	𝐴	PROPN
cana-2737	77	8	,	,	PUNCT
cana-2737	77	9	which	which	PRON
cana-2737	77	10	is	be	AUX
cana-2737	77	11	a	a	DET
cana-2737	77	12	set	set	NOUN
cana-2737	77	13	of	of	ADP
cana-2737	77	14	ordered	order	VERB
cana-2737	77	15	pairs	pair	NOUN
cana-2737	77	16	over	over	ADP
cana-2737	77	17	𝑋	𝑋	PROPN
cana-2737	77	18	,	,	PUNCT
cana-2737	77	19	is	be	AUX
cana-2737	77	20	defined	define	VERB
cana-2737	77	21	by	by	ADP
cana-2737	77	22	the	the	DET
cana-2737	77	23	following	following	NOUN
cana-2737	77	24	:	:	PUNCT
cana-2737	77	25	𝐴	𝐴	PROPN
cana-2737	77	26	=	=	PUNCT
cana-2737	77	27	{	{	PUNCT
cana-2737	77	28	<	<	X
cana-2737	77	29	𝑥	𝑥	X
cana-2737	77	30	,	,	PUNCT
cana-2737	77	31	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-2737	77	32	)	)	PUNCT
cana-2737	77	33	,	,	PUNCT
cana-2737	77	34	𝜈𝐴(𝑥)|𝑥	𝜈𝐴(𝑥)|𝑥	NOUN
cana-2737	77	35	∈	∈	PROPN
cana-2737	77	36	𝑋	𝑋	PROPN
cana-2737	77	37	}	}	PUNCT
cana-2737	77	38	or	or	CCONJ
cana-2737	77	39	𝐴	𝐴	PROPN
cana-2737	77	40	=	=	NOUN
cana-2737	77	41	communications	communication	NOUN
cana-2737	77	42	on	on	ADP
cana-2737	77	43	applied	apply	VERB
cana-2737	77	44	nonlinear	nonlinear	ADJ
cana-2737	77	45	analysis	analysis	NOUN
cana-2737	77	46	issn	issn	NOUN
cana-2737	77	47	:	:	PUNCT
cana-2737	77	48	1074	1074	NUM
cana-2737	77	49	-	-	PUNCT
cana-2737	77	50	133x	133x	NUM
cana-2737	77	51	vol	vol	NOUN
cana-2737	77	52	32	32	NUM
cana-2737	77	53	no	no	NOUN
cana-2737	77	54	.	.	PUNCT
cana-2737	78	1	4s	4s	NUM
cana-2737	78	2	(	(	PUNCT
cana-2737	78	3	2025	2025	NUM
cana-2737	78	4	)	)	PUNCT
cana-2737	78	5	29	29	NUM
cana-2737	78	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2737	78	7	{	{	PUNCT
cana-2737	78	8	⟨	⟨	NOUN
cana-2737	78	9	𝜇𝐴(𝑥),𝜈𝐴(𝑥	𝜇𝐴(𝑥),𝜈𝐴(𝑥	NOUN
cana-2737	78	10	)	)	PUNCT
cana-2737	79	1	𝑥	𝑥	DET
cana-2737	79	2	⟩	⟩	NOUN
cana-2737	79	3	|𝑥	|𝑥	NOUN
cana-2737	79	4	∈	∈	PROPN
cana-2737	79	5	𝑋	𝑋	PROPN
cana-2737	79	6	}	}	PUNCT
cana-2737	79	7	,	,	PUNCT
cana-2737	79	8	where	where	SCONJ
cana-2737	79	9	the	the	DET
cana-2737	79	10	functions	function	NOUN
cana-2737	79	11	𝜇𝐴(𝑥	𝜇𝐴(𝑥	VERB
cana-2737	79	12	):	):	PUNCT
cana-2737	79	13	𝑋	𝑋	PROPN
cana-2737	79	14	→	→	SYM
cana-2737	79	15	[	[	X
cana-2737	79	16	0,1	0,1	NUM
cana-2737	79	17	]	]	PUNCT
cana-2737	79	18	and	and	CCONJ
cana-2737	79	19	𝜈𝐴(𝑥	𝜈𝐴(𝑥	NUM
cana-2737	79	20	):	):	PUNCT
cana-2737	79	21	𝑋	𝑋	PROPN
cana-2737	79	22	→	→	SYM
cana-2737	79	23	[	[	X
cana-2737	79	24	0,1	0,1	NUM
cana-2737	79	25	]	]	PUNCT
cana-2737	79	26	define	define	VERB
cana-2737	79	27	the	the	DET
cana-2737	79	28	degree	degree	NOUN
cana-2737	79	29	of	of	ADP
cana-2737	79	30	membership	membership	NOUN
cana-2737	79	31	and	and	CCONJ
cana-2737	79	32	the	the	DET
cana-2737	79	33	degree	degree	NOUN
cana-2737	79	34	of	of	ADP
cana-2737	79	35	nonmembership	nonmembership	NOUN
cana-2737	79	36	,	,	PUNCT
cana-2737	79	37	respectively	respectively	ADV
cana-2737	79	38	,	,	PUNCT
cana-2737	79	39	of	of	ADP
cana-2737	79	40	the	the	DET
cana-2737	79	41	element	element	NOUN
cana-2737	79	42	𝑥	𝑥	PRON
cana-2737	79	43	∈	∈	PROPN
cana-2737	79	44	𝑋	𝑋	NOUN
cana-2737	79	45	to	to	ADP
cana-2737	79	46	𝐴	𝐴	PROPN
cana-2737	79	47	,	,	PUNCT
cana-2737	79	48	which	which	PRON
cana-2737	79	49	is	be	AUX
cana-2737	79	50	a	a	DET
cana-2737	79	51	subset	subset	NOUN
cana-2737	79	52	of	of	ADP
cana-2737	79	53	𝑋	𝑋	PROPN
cana-2737	79	54	,	,	PUNCT
cana-2737	79	55	and	and	CCONJ
cana-2737	79	56	for	for	ADP
cana-2737	79	57	every	every	DET
cana-2737	79	58	𝑥	𝑥	PRON
cana-2737	79	59	∈	∈	PROPN
cana-2737	79	60	𝑋	𝑋	PROPN
cana-2737	79	61	,	,	PUNCT
cana-2737	79	62	0	0	NUM
cana-2737	79	63	≤	≤	NUM
cana-2737	79	64	(	(	PUNCT
cana-2737	79	65	𝜇𝐴(𝑥))2	𝜇𝐴(𝑥))2	NOUN
cana-2737	79	66	+	+	CCONJ
cana-2737	79	67	(	(	PUNCT
cana-2737	79	68	𝜈𝐴(𝑥))2	𝜈𝐴(𝑥))2	NOUN
cana-2737	79	69	≤	≤	ADV
cana-2737	79	70	1	1	NUM
cana-2737	79	71	.	.	PUNCT
cana-2737	80	1	supposing	suppose	VERB
cana-2737	80	2	(	(	PUNCT
cana-2737	80	3	𝜇𝐴(𝑥))2	𝜇𝐴(𝑥))2	NOUN
cana-2737	80	4	+	+	CCONJ
cana-2737	80	5	(	(	PUNCT
cana-2737	80	6	𝜈𝐴(𝑥))2	𝜈𝐴(𝑥))2	NOUN
cana-2737	80	7	≤	≤	ADV
cana-2737	80	8	1	1	NUM
cana-2737	80	9	,	,	PUNCT
cana-2737	80	10	then	then	ADV
cana-2737	80	11	there	there	PRON
cana-2737	80	12	is	be	VERB
cana-2737	80	13	a	a	DET
cana-2737	80	14	degree	degree	NOUN
cana-2737	80	15	of	of	ADP
cana-2737	80	16	indeterminacy	indeterminacy	NOUN
cana-2737	80	17	of	of	ADP
cana-2737	80	18	𝑥	𝑥	DET
cana-2737	80	19	∈	∈	PROPN
cana-2737	80	20	𝑋	𝑋	NOUN
cana-2737	80	21	to	to	ADP
cana-2737	80	22	𝐴	𝐴	PROPN
cana-2737	80	23	defined	define	VERB
cana-2737	80	24	by	by	ADP
cana-2737	80	25	𝜋𝐴(𝑥	𝜋𝐴(𝑥	NUM
cana-2737	80	26	)	)	PUNCT
cana-2737	80	27	=	=	PUNCT
cana-2737	81	1	√1	√1	ADV
cana-2737	81	2	−	−	PROPN
cana-2737	82	1	[	[	X
cana-2737	82	2	(	(	PUNCT
cana-2737	82	3	𝜇𝐴(𝑥))2	𝜇𝐴(𝑥))2	NOUN
cana-2737	82	4	+	+	CCONJ
cana-2737	82	5	(	(	PUNCT
cana-2737	82	6	𝜈𝐴(𝑥))2	𝜈𝐴(𝑥))2	PROPN
cana-2737	82	7	]	]	PUNCT
cana-2737	82	8	and	and	CCONJ
cana-2737	82	9	𝜋𝐴(𝑥	𝜋𝐴(𝑥	NUM
cana-2737	82	10	)	)	PUNCT
cana-2737	82	11	∈	∈	NOUN
cana-2737	83	1	[	[	X
cana-2737	83	2	0,1	0,1	NUM
cana-2737	83	3	]	]	PUNCT
cana-2737	83	4	.	.	PUNCT
cana-2737	84	1	in	in	ADP
cana-2737	84	2	what	what	PRON
cana-2737	84	3	follows	follow	VERB
cana-2737	84	4	,	,	PUNCT
cana-2737	84	5	(	(	PUNCT
cana-2737	84	6	𝜇𝐴(𝑥))2	𝜇𝐴(𝑥))2	NOUN
cana-2737	84	7	+	+	CCONJ
cana-2737	84	8	(	(	PUNCT
cana-2737	84	9	𝜈𝐴(𝑥))2	𝜈𝐴(𝑥))2	NOUN
cana-2737	84	10	+	+	CCONJ
cana-2737	84	11	(	(	PUNCT
cana-2737	84	12	𝜋𝐴(𝑥))2	𝜋𝐴(𝑥))2	NOUN
cana-2737	84	13	=	=	SYM
cana-2737	84	14	1	1	X
cana-2737	84	15	.	.	PUNCT
cana-2737	84	16	otherwise	otherwise	ADV
cana-2737	84	17	,	,	PUNCT
cana-2737	84	18	𝜋𝐴(𝑥	𝜋𝐴(𝑥	NUM
cana-2737	84	19	)	)	PUNCT
cana-2737	84	20	=	=	SYM
cana-2737	84	21	0	0	PUNCT
cana-2737	85	1	whenever	whenever	SCONJ
cana-2737	85	2	(	(	PUNCT
cana-2737	85	3	𝜇𝐴(𝑥))2	𝜇𝐴(𝑥))2	NOUN
cana-2737	85	4	+	+	CCONJ
cana-2737	85	5	(	(	PUNCT
cana-2737	85	6	𝜈𝐴(𝑥))2	𝜈𝐴(𝑥))2	NOUN
cana-2737	85	7	=	=	SYM
cana-2737	85	8	1	1	X
cana-2737	85	9	.	.	X
cana-2737	85	10	we	we	PRON
cana-2737	85	11	denote	denote	VERB
cana-2737	85	12	the	the	DET
cana-2737	85	13	set	set	NOUN
cana-2737	85	14	of	of	ADP
cana-2737	85	15	all	all	DET
cana-2737	85	16	𝑃𝐹𝑆	𝑃𝐹𝑆	PROPN
cana-2737	85	17	’s	’s	NOUN
cana-2737	85	18	over	over	ADP
cana-2737	85	19	𝑋	𝑋	PROPN
cana-2737	85	20	by	by	ADP
cana-2737	85	21	𝑝𝑓𝑠(𝑋	𝑝𝑓𝑠(𝑋	PROPN
cana-2737	85	22	)	)	PUNCT
cana-2737	85	23	.	.	PUNCT
cana-2737	86	1	definition	definition	NOUN
cana-2737	86	2	2.4	2.4	NUM
cana-2737	86	3	[	[	SYM
cana-2737	86	4	34	34	NUM
cana-2737	86	5	]	]	PUNCT
cana-2737	86	6	let	let	VERB
cana-2737	86	7	𝐴	𝐴	PROPN
cana-2737	86	8	and	and	CCONJ
cana-2737	86	9	𝐵	𝐵	NOUN
cana-2737	86	10	be	be	AUX
cana-2737	87	1	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2737	87	2	’s	’s	NOUN
cana-2737	87	3	of	of	ADP
cana-2737	87	4	the	the	DET
cana-2737	87	5	forms	form	NOUN
cana-2737	87	6	𝐴	𝐴	NOUN
cana-2737	87	7	=	=	PUNCT
cana-2737	87	8	{	{	PUNCT
cana-2737	87	9	<	<	X
cana-2737	87	10	𝑎	𝑎	X
cana-2737	87	11	,	,	PUNCT
cana-2737	87	12	𝜆𝐴(𝑎	𝜆𝐴(𝑎	PROPN
cana-2737	87	13	)	)	PUNCT
cana-2737	87	14	,	,	PUNCT
cana-2737	87	15	𝜇𝐴(𝑎	𝜇𝐴(𝑎	PROPN
cana-2737	87	16	)	)	PUNCT
cana-2737	87	17	>	>	X
cana-2737	87	18	|𝑎	|𝑎	PROPN
cana-2737	88	1	∈	∈	PROPN
cana-2737	88	2	𝑋	𝑋	PROPN
cana-2737	88	3	}	}	PUNCT
cana-2737	88	4	and	and	CCONJ
cana-2737	88	5	𝐵	𝐵	NOUN
cana-2737	88	6	=	=	PUNCT
cana-2737	88	7	{	{	PUNCT
cana-2737	88	8	<	<	X
cana-2737	88	9	𝑎	𝑎	X
cana-2737	88	10	,	,	PUNCT
cana-2737	88	11	𝜆𝐵(𝑎	𝜆𝐵(𝑎	PRON
cana-2737	88	12	)	)	PUNCT
cana-2737	88	13	,	,	PUNCT
cana-2737	88	14	𝜇𝐵(𝑎	𝜇𝐵(𝑎	NUM
cana-2737	88	15	)	)	PUNCT
cana-2737	88	16	>	>	X
cana-2737	88	17	|𝑎	|𝑎	PROPN
cana-2737	89	1	∈	∈	PROPN
cana-2737	89	2	𝑋	𝑋	PROPN
cana-2737	89	3	}	}	PUNCT
cana-2737	89	4	.	.	PUNCT
cana-2737	90	1	then	then	ADV
cana-2737	91	1	[	[	X
cana-2737	91	2	(	(	PUNCT
cana-2737	91	3	i	i	NOUN
cana-2737	91	4	)	)	PUNCT
cana-2737	91	5	]	]	PUNCT
cana-2737	92	1	1	1	X
cana-2737	92	2	.	.	X
cana-2737	92	3	𝐴	𝐴	PROPN
cana-2737	92	4	⊆	⊆	NUM
cana-2737	92	5	𝐵	𝐵	PROPN
cana-2737	92	6	if	if	SCONJ
cana-2737	92	7	and	and	CCONJ
cana-2737	92	8	only	only	ADV
cana-2737	92	9	if	if	SCONJ
cana-2737	92	10	𝜆𝐴(𝑎	𝜆𝐴(𝑎	NOUN
cana-2737	92	11	)	)	PUNCT
cana-2737	92	12	≤	≤	NOUN
cana-2737	92	13	𝜆𝐵(𝑎	𝜆𝐵(𝑎	CCONJ
cana-2737	92	14	)	)	PUNCT
cana-2737	92	15	and	and	CCONJ
cana-2737	92	16	𝜇𝐴(𝑎	𝜇𝐴(𝑎	NUM
cana-2737	92	17	)	)	PUNCT
cana-2737	92	18	≥	≥	NOUN
cana-2737	92	19	𝜇𝐵(𝑎	𝜇𝐵(𝑎	NUM
cana-2737	92	20	)	)	PUNCT
cana-2737	92	21	for	for	ADP
cana-2737	92	22	all	all	DET
cana-2737	92	23	𝑎	𝑎	PROPN
cana-2737	92	24	∈	∈	NOUN
cana-2737	92	25	𝑋.	𝑋.	PROPN
cana-2737	92	26	2	2	NUM
cana-2737	92	27	.	.	PUNCT
cana-2737	93	1	𝐴	𝐴	NOUN
cana-2737	93	2	=	=	PROPN
cana-2737	93	3	𝐵	𝐵	PROPN
cana-2737	93	4	if	if	SCONJ
cana-2737	94	1	and	and	CCONJ
cana-2737	94	2	only	only	ADV
cana-2737	94	3	if	if	SCONJ
cana-2737	94	4	𝐴	𝐴	PROPN
cana-2737	94	5	⊆	⊆	NUM
cana-2737	94	6	𝐵	𝐵	NOUN
cana-2737	94	7	and	and	CCONJ
cana-2737	94	8	𝐵	𝐵	NOUN
cana-2737	94	9	⊆	⊆	NUM
cana-2737	94	10	𝐴.	𝐴.	PROPN
cana-2737	94	11	3	3	NUM
cana-2737	94	12	.	.	PUNCT
cana-2737	94	13	�	�	NOUN
cana-2737	94	14	̅	̅	NOUN
cana-2737	94	15	�	�	NOUN
cana-2737	94	16	=	=	SYM
cana-2737	94	17	{	{	PUNCT
cana-2737	94	18	<	<	X
cana-2737	94	19	𝑎	𝑎	NOUN
cana-2737	94	20	,	,	PUNCT
cana-2737	94	21	𝜇𝐴(𝑎	𝜇𝐴(𝑎	NOUN
cana-2737	94	22	)	)	PUNCT
cana-2737	94	23	,	,	PUNCT
cana-2737	94	24	𝜆𝐴(𝑎	𝜆𝐴(𝑎	PROPN
cana-2737	94	25	)	)	PUNCT
cana-2737	94	26	>	>	X
cana-2737	94	27	|𝑎	|𝑎	PROPN
cana-2737	95	1	∈	∈	PROPN
cana-2737	95	2	𝑋	𝑋	PROPN
cana-2737	95	3	}	}	PUNCT
cana-2737	95	4	.	.	PUNCT
cana-2737	96	1	4	4	X
cana-2737	96	2	.	.	X
cana-2737	96	3	𝐴	𝐴	PROPN
cana-2737	96	4	∩	∩	NOUN
cana-2737	96	5	𝐵	𝐵	NOUN
cana-2737	96	6	=	=	PUNCT
cana-2737	96	7	{	{	PUNCT
cana-2737	96	8	<	<	X
cana-2737	96	9	𝑎	𝑎	X
cana-2737	96	10	,	,	PUNCT
cana-2737	96	11	𝜆𝐴(𝑎	𝜆𝐴(𝑎	NOUN
cana-2737	96	12	)	)	PUNCT
cana-2737	96	13	∧	∧	NOUN
cana-2737	96	14	𝜆𝐵(𝑎	𝜆𝐵(𝑎	NOUN
cana-2737	96	15	)	)	PUNCT
cana-2737	96	16	,	,	PUNCT
cana-2737	96	17	𝜇𝐴(𝑎	𝜇𝐴(𝑎	NOUN
cana-2737	96	18	)	)	PUNCT
cana-2737	96	19	∨	∨	NUM
cana-2737	96	20	𝜇𝐵(𝑎	𝜇𝐵(𝑎	NUM
cana-2737	96	21	)	)	PUNCT
cana-2737	96	22	>	>	X
cana-2737	96	23	|𝑎	|𝑎	PROPN
cana-2737	96	24	∈	∈	PROPN
cana-2737	96	25	𝑋	𝑋	PROPN
cana-2737	96	26	}	}	PUNCT
cana-2737	96	27	.	.	PUNCT
cana-2737	97	1	5	5	X
cana-2737	97	2	.	.	X
cana-2737	97	3	𝐴	𝐴	PROPN
cana-2737	97	4	∪	∪	AUX
cana-2737	97	5	𝐵	𝐵	NOUN
cana-2737	97	6	=	=	PUNCT
cana-2737	97	7	{	{	PUNCT
cana-2737	97	8	<	<	X
cana-2737	97	9	𝑎	𝑎	X
cana-2737	97	10	,	,	PUNCT
cana-2737	97	11	𝜆𝐴(𝑎	𝜆𝐴(𝑎	NOUN
cana-2737	97	12	)	)	PUNCT
cana-2737	97	13	∨	∨	NOUN
cana-2737	97	14	𝜆𝐵(𝑎	𝜆𝐵(𝑎	NUM
cana-2737	97	15	)	)	PUNCT
cana-2737	97	16	,	,	PUNCT
cana-2737	97	17	𝜇𝐴(𝑎	𝜇𝐴(𝑎	NOUN
cana-2737	97	18	)	)	PUNCT
cana-2737	97	19	∧	∧	PROPN
cana-2737	97	20	𝜇𝐵(𝑎	𝜇𝐵(𝑎	PROPN
cana-2737	97	21	)	)	PUNCT
cana-2737	97	22	>	>	X
cana-2737	97	23	|𝑎	|𝑎	PROPN
cana-2737	97	24	∈	∈	PROPN
cana-2737	97	25	𝑋	𝑋	PROPN
cana-2737	97	26	}	}	PUNCT
cana-2737	97	27	.	.	PUNCT
cana-2737	98	1	6	6	X
cana-2737	98	2	.	.	X
cana-2737	98	3	0𝑋	0𝑋	NOUN
cana-2737	98	4	=	=	SYM
cana-2737	98	5	{	{	PUNCT
cana-2737	98	6	<	<	X
cana-2737	98	7	𝑎	𝑎	NOUN
cana-2737	98	8	,	,	PUNCT
cana-2737	98	9	0,1	0,1	NUM
cana-2737	98	10	>	>	SYM
cana-2737	98	11	|𝑎	|𝑎	NOUN
cana-2737	99	1	∈	∈	PROPN
cana-2737	99	2	𝑋	𝑋	PROPN
cana-2737	99	3	}	}	PUNCT
cana-2737	99	4	and	and	CCONJ
cana-2737	99	5	1𝑋	1𝑋	NOUN
cana-2737	99	6	=	=	SYM
cana-2737	99	7	{	{	PUNCT
cana-2737	99	8	<	<	X
cana-2737	99	9	𝑎	𝑎	PROPN
cana-2737	99	10	,	,	PUNCT
cana-2737	99	11	1,0	1,0	NUM
cana-2737	99	12	>	>	SYM
cana-2737	99	13	|𝑎	|𝑎	PROPN
cana-2737	99	14	∈	∈	PROPN
cana-2737	99	15	𝑋	𝑋	PROPN
cana-2737	99	16	}	}	PUNCT
cana-2737	99	17	.	.	PUNCT
cana-2737	100	1	7	7	X
cana-2737	100	2	.	.	X
cana-2737	100	3	1̅	1̅	NUM
cana-2737	100	4	=	=	SYM
cana-2737	100	5	0	0	NUM
cana-2737	100	6	and	and	CCONJ
cana-2737	100	7	0̅	0̅	NOUN
cana-2737	100	8	=	=	SYM
cana-2737	100	9	1	1	X
cana-2737	100	10	.	.	PUNCT
cana-2737	101	1	definition	definition	NOUN
cana-2737	101	2	2.5	2.5	NUM
cana-2737	102	1	[	[	X
cana-2737	102	2	24	24	NUM
cana-2737	102	3	]	]	PUNCT
cana-2737	102	4	an	an	DET
cana-2737	102	5	pythagorean	pythagorean	ADJ
cana-2737	102	6	fuzzy	fuzzy	ADJ
cana-2737	102	7	topology	topology	NOUN
cana-2737	102	8	by	by	ADP
cana-2737	102	9	subsets	subset	NOUN
cana-2737	102	10	of	of	ADP
cana-2737	102	11	a	a	DET
cana-2737	102	12	non	non	ADJ
cana-2737	102	13	-	-	ADJ
cana-2737	102	14	empty	empty	ADJ
cana-2737	102	15	set	set	ADJ
cana-2737	102	16	𝑋	𝑋	PROPN
cana-2737	102	17	is	be	AUX
cana-2737	102	18	a	a	DET
cana-2737	102	19	family	family	NOUN
cana-2737	102	20	𝜏	𝜏	X
cana-2737	102	21	of	of	ADP
cana-2737	102	22	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2737	102	23	’s	’s	AUX
cana-2737	102	24	satisfying	satisfy	VERB
cana-2737	102	25	the	the	DET
cana-2737	102	26	following	follow	VERB
cana-2737	102	27	axioms	axiom	NOUN
cana-2737	102	28	.	.	PUNCT
cana-2737	103	1	[	[	X
cana-2737	103	2	(	(	PUNCT
cana-2737	103	3	i	i	NOUN
cana-2737	103	4	)	)	PUNCT
cana-2737	103	5	]	]	PUNCT
cana-2737	103	6	1	1	X
cana-2737	103	7	.	.	X
cana-2737	103	8	𝜙	𝜙	X
cana-2737	103	9	,	,	PUNCT
cana-2737	103	10	𝑋	𝑋	PROPN
cana-2737	103	11	∈	∈	PROPN
cana-2737	103	12	𝜏.	𝜏.	NOUN
cana-2737	103	13	2	2	NUM
cana-2737	103	14	.	.	PROPN
cana-2737	103	15	𝐺1	𝐺1	PROPN
cana-2737	103	16	∩	∩	PROPN
cana-2737	103	17	𝐺2	𝐺2	NOUN
cana-2737	103	18	∈	∈	PROPN
cana-2737	103	19	𝜏	𝜏	NOUN
cana-2737	103	20	for	for	ADP
cana-2737	103	21	every	every	DET
cana-2737	103	22	𝐺1	𝐺1	NOUN
cana-2737	103	23	,	,	PUNCT
cana-2737	103	24	𝐺2	𝐺2	NOUN
cana-2737	103	25	∈	∈	PROPN
cana-2737	103	26	𝜏	𝜏	NOUN
cana-2737	103	27	and	and	CCONJ
cana-2737	103	28	3	3	NUM
cana-2737	103	29	.	.	PUNCT
cana-2737	103	30	⋃	⋃	PRON
cana-2737	103	31	𝐺𝑖	𝐺𝑖	VERB
cana-2737	103	32	∈	∈	PRON
cana-2737	103	33	𝜏	𝜏	NOUN
cana-2737	103	34	for	for	ADP
cana-2737	103	35	any	any	DET
cana-2737	103	36	arbitrary	arbitrary	ADJ
cana-2737	103	37	family	family	NOUN
cana-2737	103	38	{	{	PUNCT
cana-2737	103	39	𝐺𝑖|𝑖	𝐺𝑖|𝑖	PROPN
cana-2737	103	40	∈	∈	PROPN
cana-2737	103	41	𝑗	𝑗	NOUN
cana-2737	103	42	}	}	PUNCT
cana-2737	103	43	⊆	⊆	NUM
cana-2737	103	44	𝜏.	𝜏.	NOUN
cana-2737	103	45	the	the	DET
cana-2737	103	46	pair	pair	NOUN
cana-2737	103	47	(	(	PUNCT
cana-2737	103	48	𝑋	𝑋	PROPN
cana-2737	103	49	,	,	PUNCT
cana-2737	103	50	𝜏	𝜏	NOUN
cana-2737	103	51	)	)	PUNCT
cana-2737	103	52	is	be	AUX
cana-2737	103	53	called	call	VERB
cana-2737	103	54	an	an	DET
cana-2737	103	55	pythagorean	pythagorean	ADJ
cana-2737	103	56	fuzzy	fuzzy	ADJ
cana-2737	103	57	topological	topological	ADJ
cana-2737	103	58	space	space	NOUN
cana-2737	103	59	(	(	PUNCT
cana-2737	103	60	𝑝𝑓𝑡𝑠	𝑝𝑓𝑡𝑠	NOUN
cana-2737	103	61	in	in	ADP
cana-2737	103	62	short	short	ADJ
cana-2737	103	63	)	)	PUNCT
cana-2737	103	64	and	and	CCONJ
cana-2737	103	65	any	any	DET
cana-2737	103	66	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2737	103	67	𝐺	𝐺	PROPN
cana-2737	103	68	in	in	ADP
cana-2737	103	69	𝜏	𝜏	PROPN
cana-2737	103	70	is	be	AUX
cana-2737	103	71	called	call	VERB
cana-2737	103	72	an	an	DET
cana-2737	103	73	pythagorean	pythagorean	ADJ
cana-2737	103	74	fuzzy	fuzzy	ADJ
cana-2737	103	75	open	open	ADJ
cana-2737	103	76	set	set	NOUN
cana-2737	103	77	(	(	PUNCT
cana-2737	103	78	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	ADJ
cana-2737	103	79	in	in	ADP
cana-2737	103	80	short	short	ADJ
cana-2737	103	81	)	)	PUNCT
cana-2737	103	82	in	in	ADP
cana-2737	103	83	𝑋.	𝑋.	PROPN
cana-2737	103	84	the	the	DET
cana-2737	103	85	complement	complement	PROPN
cana-2737	103	86	�	�	PROPN
cana-2737	103	87	̅	̅	NOUN
cana-2737	103	88	�	�	NOUN
cana-2737	103	89	of	of	ADP
cana-2737	103	90	an	an	DET
cana-2737	103	91	pythagorean	pythagorean	ADJ
cana-2737	103	92	fuzzy	fuzzy	ADJ
cana-2737	103	93	open	open	ADJ
cana-2737	103	94	set	set	VERB
cana-2737	103	95	𝐴	𝐴	PROPN
cana-2737	103	96	in	in	ADP
cana-2737	103	97	an	an	DET
cana-2737	103	98	𝑝𝑓𝑡𝑠(𝑋	𝑝𝑓𝑡𝑠(𝑋	PROPN
cana-2737	103	99	,	,	PUNCT
cana-2737	103	100	𝜏	𝜏	NOUN
cana-2737	103	101	)	)	PUNCT
cana-2737	103	102	is	be	AUX
cana-2737	103	103	called	call	VERB
cana-2737	103	104	an	an	DET
cana-2737	103	105	pythagorean	pythagorean	ADJ
cana-2737	103	106	fuzzy	fuzzy	NOUN
cana-2737	103	107	closed	close	VERB
cana-2737	103	108	set	set	NOUN
cana-2737	103	109	(	(	PUNCT
cana-2737	103	110	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-2737	103	111	in	in	ADP
cana-2737	103	112	short	short	ADJ
cana-2737	103	113	)	)	PUNCT
cana-2737	103	114	.	.	PUNCT
cana-2737	104	1	definition	definition	NOUN
cana-2737	104	2	2.6	2.6	NUM
cana-2737	105	1	[	[	SYM
cana-2737	105	2	24	24	NUM
cana-2737	105	3	]	]	PUNCT
cana-2737	105	4	let	let	VERB
cana-2737	105	5	(	(	PUNCT
cana-2737	105	6	𝑋	𝑋	NOUN
cana-2737	105	7	,	,	PUNCT
cana-2737	105	8	𝜏	𝜏	NOUN
cana-2737	105	9	)	)	PUNCT
cana-2737	105	10	be	be	VERB
cana-2737	105	11	an	an	DET
cana-2737	105	12	𝑝𝑓𝑡𝑠	𝑝𝑓𝑡𝑠	NOUN
cana-2737	105	13	and	and	CCONJ
cana-2737	105	14	𝐴	𝐴	PROPN
cana-2737	105	15	=	=	PUNCT
cana-2737	105	16	{	{	PUNCT
cana-2737	105	17	<	<	X
cana-2737	105	18	𝑎	𝑎	X
cana-2737	105	19	,	,	PUNCT
cana-2737	105	20	𝜆𝐴(𝑎	𝜆𝐴(𝑎	PROPN
cana-2737	105	21	)	)	PUNCT
cana-2737	105	22	,	,	PUNCT
cana-2737	105	23	𝜇𝐴(𝑎	𝜇𝐴(𝑎	PROPN
cana-2737	105	24	)	)	PUNCT
cana-2737	105	25	>	>	X
cana-2737	105	26	|𝑎	|𝑎	PROPN
cana-2737	106	1	∈	∈	PROPN
cana-2737	106	2	𝑋	𝑋	PROPN
cana-2737	106	3	}	}	PUNCT
cana-2737	106	4	be	be	AUX
cana-2737	106	5	an	an	DET
cana-2737	106	6	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2737	106	7	in	in	ADP
cana-2737	106	8	𝑋.	𝑋.	PROPN
cana-2737	106	9	then	then	ADV
cana-2737	106	10	the	the	DET
cana-2737	106	11	interior	interior	NOUN
cana-2737	106	12	and	and	CCONJ
cana-2737	106	13	the	the	DET
cana-2737	106	14	closure	closure	NOUN
cana-2737	106	15	of	of	ADP
cana-2737	106	16	𝐴	𝐴	PROPN
cana-2737	106	17	are	be	AUX
cana-2737	106	18	denoted	denote	VERB
cana-2737	106	19	by	by	ADP
cana-2737	106	20	𝑝𝑓𝑖𝑛𝑡(𝐴	𝑝𝑓𝑖𝑛𝑡(𝐴	PROPN
cana-2737	106	21	)	)	PUNCT
cana-2737	106	22	and	and	CCONJ
cana-2737	106	23	𝑝𝑓𝑐𝑙(𝐴	𝑝𝑓𝑐𝑙(𝐴	NUM
cana-2737	106	24	)	)	PUNCT
cana-2737	106	25	and	and	CCONJ
cana-2737	106	26	are	be	AUX
cana-2737	106	27	defined	define	VERB
cana-2737	106	28	as	as	SCONJ
cana-2737	106	29	follows	follow	VERB
cana-2737	106	30	:	:	PUNCT
cana-2737	106	31	𝑝𝑓𝑐𝑙(𝐴	𝑝𝑓𝑐𝑙(𝐴	X
cana-2737	106	32	)	)	PUNCT
cana-2737	107	1	=	=	NOUN
cana-2737	107	2	∩	∩	NOUN
cana-2737	107	3	{	{	PUNCT
cana-2737	107	4	𝐾|𝐾	𝐾|𝐾	PRON
cana-2737	107	5	𝑖𝑠𝑎𝑛	𝑖𝑠𝑎𝑛	VERB
cana-2737	107	6	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NUM
cana-2737	107	7	𝑎𝑛𝑑	𝑎𝑛𝑑	PROPN
cana-2737	107	8	𝐴	𝐴	PROPN
cana-2737	107	9	⊆	⊆	NUM
cana-2737	107	10	𝐾	𝐾	PROPN
cana-2737	107	11	}	}	PUNCT
cana-2737	107	12	and	and	CCONJ
cana-2737	107	13	𝑝𝑓𝑖𝑛𝑡(𝐴	𝑝𝑓𝑖𝑛𝑡(𝐴	NOUN
cana-2737	107	14	)	)	PUNCT
cana-2737	107	15	=	=	SYM
cana-2737	107	16	∪	∪	X
cana-2737	107	17	{	{	PUNCT
cana-2737	107	18	𝐺|𝐺	𝐺|𝐺	NOUN
cana-2737	107	19	𝑖𝑠𝑎𝑛	𝑖𝑠𝑎𝑛	NOUN
cana-2737	107	20	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	VERB
cana-2737	107	21	𝑎𝑛𝑑	𝑎𝑛𝑑	PROPN
cana-2737	107	22	𝐺	𝐺	PROPN
cana-2737	107	23	⊆	⊆	NUM
cana-2737	107	24	𝐴	𝐴	PROPN
cana-2737	107	25	}	}	PUNCT
cana-2737	107	26	.	.	PUNCT
cana-2737	108	1	also	also	ADV
cana-2737	108	2	,	,	PUNCT
cana-2737	108	3	it	it	PRON
cana-2737	108	4	can	can	AUX
cana-2737	108	5	be	be	AUX
cana-2737	108	6	established	establish	VERB
cana-2737	108	7	that	that	DET
cana-2737	108	8	𝑝𝑓𝑐𝑙(𝐴	𝑝𝑓𝑐𝑙(𝐴	NOUN
cana-2737	108	9	)	)	PUNCT
cana-2737	108	10	is	be	AUX
cana-2737	108	11	an	an	DET
cana-2737	108	12	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-2737	108	13	and	and	CCONJ
cana-2737	108	14	𝑝𝑓𝑖𝑛𝑡(𝐴	𝑝𝑓𝑖𝑛𝑡(𝐴	NOUN
cana-2737	108	15	)	)	PUNCT
cana-2737	108	16	is	be	AUX
cana-2737	108	17	an	an	DET
cana-2737	108	18	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	ADJ
cana-2737	108	19	,	,	PUNCT
cana-2737	108	20	𝐴	𝐴	PROPN
cana-2737	108	21	is	be	AUX
cana-2737	108	22	an	an	DET
cana-2737	108	23	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-2737	108	24	if	if	SCONJ
cana-2737	109	1	and	and	CCONJ
cana-2737	109	2	only	only	ADV
cana-2737	109	3	if	if	SCONJ
cana-2737	109	4	𝑝𝑓𝑐𝑙(𝐴	𝑝𝑓𝑐𝑙(𝐴	NUM
cana-2737	109	5	)	)	PUNCT
cana-2737	109	6	=	=	SYM
cana-2737	109	7	𝐴	𝐴	PROPN
cana-2737	109	8	and	and	CCONJ
cana-2737	109	9	𝐴	𝐴	PROPN
cana-2737	109	10	is	be	AUX
cana-2737	109	11	an	an	DET
cana-2737	109	12	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	ADJ
cana-2737	109	13	if	if	SCONJ
cana-2737	109	14	and	and	CCONJ
cana-2737	109	15	only	only	ADV
cana-2737	109	16	if	if	SCONJ
cana-2737	109	17	𝑝𝑓𝑖𝑛𝑡(𝐴	𝑝𝑓𝑖𝑛𝑡(𝐴	NOUN
cana-2737	109	18	)	)	PUNCT
cana-2737	109	19	=	=	SYM
cana-2737	110	1	𝐴.	𝐴.	NOUN
cana-2737	110	2	we	we	PRON
cana-2737	110	3	say	say	VERB
cana-2737	110	4	that	that	SCONJ
cana-2737	110	5	𝐴	𝐴	PROPN
cana-2737	110	6	is	be	AUX
cana-2737	110	7	𝑝𝑓-dense	𝑝𝑓-dense	ADJ
cana-2737	110	8	if	if	SCONJ
cana-2737	110	9	𝑝𝑓𝑐𝑙(𝐴	𝑝𝑓𝑐𝑙(𝐴	NUM
cana-2737	110	10	)	)	PUNCT
cana-2737	111	1	=	=	SYM
cana-2737	111	2	𝑋.	𝑋.	PROPN
cana-2737	111	3	lemma	lemma	PROPN
cana-2737	111	4	2.1	2.1	NUM
cana-2737	112	1	[	[	SYM
cana-2737	112	2	30	30	NUM
cana-2737	112	3	]	]	PUNCT
cana-2737	112	4	for	for	ADP
cana-2737	112	5	any	any	DET
cana-2737	112	6	pythagorean	pythagorean	PROPN
cana-2737	112	7	fuzzy	fuzzy	ADJ
cana-2737	112	8	set	set	VERB
cana-2737	112	9	𝐴	𝐴	PROPN
cana-2737	112	10	in	in	ADP
cana-2737	112	11	(	(	PUNCT
cana-2737	112	12	𝑋	𝑋	PROPN
cana-2737	112	13	,	,	PUNCT
cana-2737	112	14	𝜏	𝜏	NOUN
cana-2737	112	15	)	)	PUNCT
cana-2737	112	16	,	,	PUNCT
cana-2737	112	17	we	we	PRON
cana-2737	112	18	have	have	VERB
cana-2737	112	19	𝑋	𝑋	PROPN
cana-2737	112	20	−	−	PROPN
cana-2737	112	21	𝑝𝑓𝑖𝑛𝑡(𝐴	𝑝𝑓𝑖𝑛𝑡(𝐴	PROPN
cana-2737	112	22	)	)	PUNCT
cana-2737	112	23	=	=	SYM
cana-2737	112	24	𝑝𝑓𝑐𝑙(𝑋	𝑝𝑓𝑐𝑙(𝑋	PROPN
cana-2737	112	25	−	−	PROPN
cana-2737	112	26	𝐴	𝐴	PROPN
cana-2737	112	27	)	)	PUNCT
cana-2737	112	28	and	and	CCONJ
cana-2737	112	29	𝑋	𝑋	PROPN
cana-2737	112	30	−	−	PROPN
cana-2737	112	31	𝑝𝑓𝑐𝑙(𝐴	𝑝𝑓𝑐𝑙(𝐴	PROPN
cana-2737	112	32	)	)	PUNCT
cana-2737	113	1	=	=	PRON
cana-2737	113	2	𝑝𝑓𝑖𝑛𝑡(𝑋	𝑝𝑓𝑖𝑛𝑡(𝑋	X
cana-2737	113	3	−	−	PROPN
cana-2737	113	4	𝐴	𝐴	PROPN
cana-2737	113	5	)	)	PUNCT
cana-2737	113	6	.	.	PUNCT
cana-2737	114	1	definition	definition	NOUN
cana-2737	114	2	2.7	2.7	NUM
cana-2737	114	3	[	[	SYM
cana-2737	114	4	30	30	NUM
cana-2737	114	5	]	]	X
cana-2737	114	6	let	let	NOUN
cana-2737	114	7	(	(	PUNCT
cana-2737	114	8	𝑋	𝑋	NOUN
cana-2737	114	9	,	,	PUNCT
cana-2737	114	10	𝜏	𝜏	NOUN
cana-2737	114	11	)	)	PUNCT
cana-2737	114	12	be	be	VERB
cana-2737	114	13	an	an	DET
cana-2737	114	14	𝑝𝑓𝑡𝑠	𝑝𝑓𝑡𝑠	NOUN
cana-2737	114	15	and	and	CCONJ
cana-2737	114	16	𝐴	𝐴	PROPN
cana-2737	114	17	be	be	VERB
cana-2737	114	18	an	an	DET
cana-2737	114	19	𝑝𝑓𝑠.	𝑝𝑓𝑠.	NOUN
cana-2737	114	20	then	then	ADV
cana-2737	114	21	𝐴	𝐴	PROPN
cana-2737	114	22	is	be	AUX
cana-2737	114	23	said	say	VERB
cana-2737	114	24	to	to	PART
cana-2737	114	25	be	be	AUX
cana-2737	114	26	an	an	DET
cana-2737	114	27	pythagorean	pythagorean	ADJ
cana-2737	114	28	fuzzy	fuzzy	NOUN
cana-2737	114	29	(	(	PUNCT
cana-2737	114	30	i	i	NOUN
cana-2737	114	31	)	)	PUNCT
cana-2737	114	32	regular	regular	ADJ
cana-2737	114	33	open	open	ADJ
cana-2737	114	34	set	set	NOUN
cana-2737	114	35	(	(	PUNCT
cana-2737	114	36	𝑝𝑓𝑟𝑜𝑠	𝑝𝑓𝑟𝑜𝑠	NOUN
cana-2737	114	37	in	in	ADP
cana-2737	114	38	short	short	ADJ
cana-2737	114	39	)	)	PUNCT
cana-2737	114	40	if	if	SCONJ
cana-2737	114	41	𝐴	𝐴	PROPN
cana-2737	114	42	=	=	SYM
cana-2737	114	43	𝑝𝑓𝑖𝑛𝑡(𝑝𝑓𝑐𝑙(𝐴	𝑝𝑓𝑖𝑛𝑡(𝑝𝑓𝑐𝑙(𝐴	PROPN
cana-2737	114	44	)	)	PUNCT
cana-2737	114	45	)	)	PUNCT
cana-2737	114	46	.	.	PUNCT
cana-2737	115	1	(	(	PUNCT
cana-2737	115	2	ii	ii	NOUN
cana-2737	115	3	)	)	PUNCT
cana-2737	115	4	regular	regular	ADJ
cana-2737	115	5	closed	close	VERB
cana-2737	115	6	set	set	NOUN
cana-2737	115	7	(	(	PUNCT
cana-2737	115	8	𝑝𝑓𝑟𝑐𝑠	𝑝𝑓𝑟𝑐𝑠	ADJ
cana-2737	115	9	in	in	ADP
cana-2737	115	10	short	short	ADJ
cana-2737	115	11	)	)	PUNCT
cana-2737	115	12	if	if	SCONJ
cana-2737	115	13	𝐴	𝐴	PROPN
cana-2737	115	14	=	=	SYM
cana-2737	115	15	𝑝𝑓𝑐𝑙(𝑝𝑓𝑖𝑛𝑡(𝐴	𝑝𝑓𝑐𝑙(𝑝𝑓𝑖𝑛𝑡(𝐴	NUM
cana-2737	115	16	)	)	PUNCT
cana-2737	115	17	)	)	PUNCT
cana-2737	115	18	.	.	PUNCT
cana-2737	116	1	by	by	ADP
cana-2737	116	2	lemma	lemma	PROPN
cana-2737	116	3	2.1	2.1	NUM
cana-2737	116	4	,	,	PUNCT
cana-2737	116	5	it	it	PRON
cana-2737	116	6	follows	follow	VERB
cana-2737	116	7	that	that	SCONJ
cana-2737	116	8	𝐴	𝐴	PROPN
cana-2737	116	9	is	be	AUX
cana-2737	116	10	an	an	DET
cana-2737	116	11	𝑝𝑓𝑟𝑜𝑠	𝑝𝑓𝑟𝑜𝑠	NOUN
cana-2737	116	12	iff	iff	PROPN
cana-2737	116	13	�	�	PROPN
cana-2737	116	14	̅	̅	NOUN
cana-2737	116	15	�	�	NOUN
cana-2737	116	16	is	be	AUX
cana-2737	116	17	an	an	DET
cana-2737	116	18	𝑝𝑓𝑟𝑐𝑠.	𝑝𝑓𝑟𝑐𝑠.	PROPN
cana-2737	116	19	communications	communication	NOUN
cana-2737	116	20	on	on	ADP
cana-2737	116	21	applied	apply	VERB
cana-2737	116	22	nonlinear	nonlinear	ADJ
cana-2737	116	23	analysis	analysis	NOUN
cana-2737	116	24	issn	issn	NOUN
cana-2737	116	25	:	:	PUNCT
cana-2737	116	26	1074	1074	NUM
cana-2737	116	27	-	-	PUNCT
cana-2737	116	28	133x	133x	NUM
cana-2737	116	29	vol	vol	NOUN
cana-2737	116	30	32	32	NUM
cana-2737	116	31	no	no	NOUN
cana-2737	116	32	.	.	PUNCT
cana-2737	117	1	4s	4s	NUM
cana-2737	117	2	(	(	PUNCT
cana-2737	117	3	2025	2025	NUM
cana-2737	117	4	)	)	PUNCT
cana-2737	117	5	30	30	NUM
cana-2737	117	6	https://internationalpubls.com	https://internationalpubls.com	SYM
cana-2737	117	7	3	3	NUM
cana-2737	117	8	pythagorean	pythagorean	NOUN
cana-2737	117	9	fuzzy	fuzzy	ADJ
cana-2737	117	10	𝑴-open	𝑴-open	PROPN
cana-2737	117	11	mappings	mapping	NOUN
cana-2737	117	12	definition	definition	NOUN
cana-2737	117	13	3.1	3.1	NUM
cana-2737	117	14	let	let	NOUN
cana-2737	117	15	(	(	PUNCT
cana-2737	117	16	𝑋1	𝑋1	PROPN
cana-2737	117	17	,	,	PUNCT
cana-2737	117	18	𝛤𝑃	𝛤𝑃	PROPN
cana-2737	117	19	)	)	PUNCT
cana-2737	117	20	(	(	PUNCT
cana-2737	117	21	or	or	CCONJ
cana-2737	117	22	𝑋1	𝑋1	PROPN
cana-2737	117	23	)	)	PUNCT
cana-2737	117	24	be	be	VERB
cana-2737	117	25	an	an	DET
cana-2737	117	26	𝑝𝑓𝑡𝑠	𝑝𝑓𝑡𝑠	NOUN
cana-2737	117	27	and	and	CCONJ
cana-2737	117	28	𝐴	𝐴	PROPN
cana-2737	117	29	=	=	PUNCT
cana-2737	117	30	{	{	PUNCT
cana-2737	117	31	<	<	X
cana-2737	117	32	𝑎	𝑎	X
cana-2737	117	33	,	,	PUNCT
cana-2737	117	34	𝜆𝐴(𝑎	𝜆𝐴(𝑎	PROPN
cana-2737	117	35	)	)	PUNCT
cana-2737	117	36	,	,	PUNCT
cana-2737	117	37	𝜇𝐴(𝑎	𝜇𝐴(𝑎	PROPN
cana-2737	117	38	)	)	PUNCT
cana-2737	117	39	>	>	X
cana-2737	117	40	|𝑎	|𝑎	PROPN
cana-2737	118	1	∈	∈	PROPN
cana-2737	118	2	𝑋1	𝑋1	PROPN
cana-2737	118	3	}	}	PUNCT
cana-2737	118	4	be	be	AUX
cana-2737	118	5	an	an	DET
cana-2737	118	6	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2737	118	7	in	in	ADP
cana-2737	118	8	𝑋1	𝑋1	PROPN
cana-2737	118	9	.	.	PUNCT
cana-2737	119	1	then	then	ADV
cana-2737	119	2	the	the	DET
cana-2737	119	3	(	(	PUNCT
cana-2737	119	4	i	i	NOUN
cana-2737	119	5	)	)	PUNCT
cana-2737	119	6	𝑝𝑓𝛿-interior	𝑝𝑓𝛿-interior	NOUN
cana-2737	119	7	of	of	ADP
cana-2737	119	8	𝐴	𝐴	PROPN
cana-2737	119	9	are	be	AUX
cana-2737	119	10	denoted	denote	VERB
cana-2737	119	11	by	by	ADP
cana-2737	119	12	𝑝𝑓𝛿𝑖𝑛𝑡(𝐴	𝑝𝑓𝛿𝑖𝑛𝑡(𝐴	NOUN
cana-2737	119	13	)	)	PUNCT
cana-2737	119	14	and	and	CCONJ
cana-2737	119	15	are	be	AUX
cana-2737	119	16	defined	define	VERB
cana-2737	119	17	as	as	ADP
cana-2737	119	18	follows	follow	NOUN
cana-2737	119	19	.	.	PUNCT
cana-2737	120	1	𝑝𝑓𝛿𝑖𝑛𝑡(𝐴	𝑝𝑓𝛿𝑖𝑛𝑡(𝐴	NOUN
cana-2737	120	2	)	)	PUNCT
cana-2737	121	1	=	=	SYM
cana-2737	121	2	∪	∪	X
cana-2737	121	3	{	{	PUNCT
cana-2737	121	4	𝐺|𝐺	𝐺|𝐺	PROPN
cana-2737	121	5	is	be	AUX
cana-2737	121	6	an	an	DET
cana-2737	121	7	𝑝𝑓𝑟𝑜𝑠	𝑝𝑓𝑟𝑜𝑠	NOUN
cana-2737	121	8	and	and	CCONJ
cana-2737	121	9	𝐺	𝐺	PROPN
cana-2737	121	10	⊆	⊆	NUM
cana-2737	121	11	𝐴	𝐴	PROPN
cana-2737	121	12	}	}	PUNCT
cana-2737	121	13	.	.	PUNCT
cana-2737	122	1	(	(	PUNCT
cana-2737	122	2	ii	ii	NOUN
cana-2737	122	3	)	)	PUNCT
cana-2737	122	4	𝑝𝑓𝛿-closure	𝑝𝑓𝛿-closure	NOUN
cana-2737	122	5	of	of	ADP
cana-2737	122	6	𝐴	𝐴	PROPN
cana-2737	122	7	are	be	AUX
cana-2737	122	8	denoted	denote	VERB
cana-2737	122	9	by	by	ADP
cana-2737	122	10	𝑝𝑓𝛿𝑐𝑙(𝐴	𝑝𝑓𝛿𝑐𝑙(𝐴	NOUN
cana-2737	122	11	)	)	PUNCT
cana-2737	122	12	and	and	CCONJ
cana-2737	122	13	are	be	AUX
cana-2737	122	14	defined	define	VERB
cana-2737	122	15	as	as	ADP
cana-2737	122	16	follows	follow	VERB
cana-2737	122	17	.	.	PUNCT
cana-2737	123	1	𝑝𝑓𝛿𝑐𝑙(𝐴	𝑝𝑓𝛿𝑐𝑙(𝐴	X
cana-2737	123	2	)	)	PUNCT
cana-2737	124	1	=	=	NOUN
cana-2737	124	2	∩	∩	NOUN
cana-2737	124	3	{	{	PUNCT
cana-2737	124	4	𝐾|𝐾	𝐾|𝐾	NOUN
cana-2737	124	5	is	be	AUX
cana-2737	124	6	an	an	DET
cana-2737	124	7	𝑝𝑓𝑟𝑐𝑠	𝑝𝑓𝑟𝑐𝑠	NOUN
cana-2737	124	8	and	and	CCONJ
cana-2737	124	9	𝐴	𝐴	PROPN
cana-2737	124	10	⊆	⊆	NUM
cana-2737	124	11	𝐾	𝐾	PROPN
cana-2737	124	12	}	}	PUNCT
cana-2737	124	13	.	.	PUNCT
cana-2737	125	1	definition	definition	NOUN
cana-2737	125	2	3.2	3.2	NUM
cana-2737	125	3	let	let	VERB
cana-2737	125	4	(	(	PUNCT
cana-2737	125	5	𝑋1	𝑋1	PROPN
cana-2737	125	6	,	,	PUNCT
cana-2737	125	7	𝛤𝑃	𝛤𝑃	PROPN
cana-2737	125	8	)	)	PUNCT
cana-2737	125	9	be	be	AUX
cana-2737	125	10	an	an	DET
cana-2737	125	11	𝑝𝑓𝑡𝑠	𝑝𝑓𝑡𝑠	NOUN
cana-2737	125	12	and	and	CCONJ
cana-2737	125	13	𝐴	𝐴	PROPN
cana-2737	125	14	=	=	PUNCT
cana-2737	125	15	{	{	PUNCT
cana-2737	125	16	<	<	X
cana-2737	125	17	𝑎	𝑎	X
cana-2737	125	18	,	,	PUNCT
cana-2737	125	19	𝜆𝐴(𝑎	𝜆𝐴(𝑎	PROPN
cana-2737	125	20	)	)	PUNCT
cana-2737	125	21	,	,	PUNCT
cana-2737	125	22	𝜇𝐴(𝑎	𝜇𝐴(𝑎	PROPN
cana-2737	125	23	)	)	PUNCT
cana-2737	125	24	>	>	X
cana-2737	125	25	|𝑎	|𝑎	PROPN
cana-2737	126	1	∈	∈	PROPN
cana-2737	126	2	𝑋1	𝑋1	PROPN
cana-2737	126	3	}	}	PUNCT
cana-2737	126	4	be	be	AUX
cana-2737	126	5	an	an	DET
cana-2737	126	6	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2737	126	7	in	in	ADP
cana-2737	126	8	𝑋1	𝑋1	PROPN
cana-2737	126	9	.	.	PUNCT
cana-2737	127	1	a	a	DET
cana-2737	127	2	set	set	ADJ
cana-2737	127	3	𝐴	𝐴	PROPN
cana-2737	127	4	is	be	AUX
cana-2737	127	5	said	say	VERB
cana-2737	127	6	to	to	PART
cana-2737	127	7	be	be	AUX
cana-2737	127	8	𝑝𝑓	𝑝𝑓	PRON
cana-2737	127	9	[	[	X
cana-2737	127	10	(	(	PUNCT
cana-2737	127	11	i	i	NOUN
cana-2737	127	12	)	)	PUNCT
cana-2737	127	13	]	]	PUNCT
cana-2737	128	1	1	1	X
cana-2737	128	2	.	.	X
cana-2737	128	3	𝛿-open	𝛿-open	VERB
cana-2737	128	4	set	set	NOUN
cana-2737	128	5	(	(	PUNCT
cana-2737	128	6	briefly	briefly	ADV
cana-2737	128	7	,	,	PUNCT
cana-2737	128	8	𝑝𝑓𝛿𝑜𝑠	𝑝𝑓𝛿𝑜𝑠	PROPN
cana-2737	128	9	)	)	PUNCT
cana-2737	128	10	if	if	SCONJ
cana-2737	128	11	𝐴	𝐴	PROPN
cana-2737	128	12	=	=	SYM
cana-2737	128	13	𝑝𝑓𝛿𝑖𝑛𝑡(𝐴	𝑝𝑓𝛿𝑖𝑛𝑡(𝐴	PROPN
cana-2737	128	14	)	)	PUNCT
cana-2737	128	15	,	,	PUNCT
cana-2737	128	16	2	2	X
cana-2737	128	17	.	.	X
cana-2737	128	18	𝛿-pre	𝛿-pre	PROPN
cana-2737	128	19	open	open	ADJ
cana-2737	128	20	set	set	PROPN
cana-2737	128	21	(	(	PUNCT
cana-2737	128	22	briefly	briefly	ADV
cana-2737	128	23	,	,	PUNCT
cana-2737	128	24	𝑝𝑓𝛿𝒫𝑜𝑠	𝑝𝑓𝛿𝒫𝑜𝑠	X
cana-2737	128	25	)	)	PUNCT
cana-2737	128	26	if	if	SCONJ
cana-2737	128	27	𝐴	𝐴	PROPN
cana-2737	128	28	⊆	⊆	NUM
cana-2737	128	29	𝑝𝑓𝑖𝑛𝑡(𝑝𝑓𝛿𝑐𝑙(𝐴	𝑝𝑓𝑖𝑛𝑡(𝑝𝑓𝛿𝑐𝑙(𝐴	NOUN
cana-2737	128	30	)	)	PUNCT
cana-2737	128	31	)	)	PUNCT
cana-2737	128	32	,	,	PUNCT
cana-2737	128	33	3	3	X
cana-2737	128	34	.	.	X
cana-2737	128	35	𝛿-semi	𝛿-semi	PROPN
cana-2737	128	36	open	open	ADJ
cana-2737	128	37	set	set	NOUN
cana-2737	128	38	(	(	PUNCT
cana-2737	128	39	briefly	briefly	ADV
cana-2737	128	40	,	,	PUNCT
cana-2737	128	41	𝑝𝑓𝛿𝒮𝑜𝑠	𝑝𝑓𝛿𝒮𝑜𝑠	PROPN
cana-2737	128	42	)	)	PUNCT
cana-2737	129	1	if	if	SCONJ
cana-2737	129	2	𝐴	𝐴	PROPN
cana-2737	129	3	⊆	⊆	NUM
cana-2737	129	4	𝑝𝑓𝑐𝑙(𝑝𝑓𝛿𝑖𝑛𝑡(𝐴	𝑝𝑓𝑐𝑙(𝑝𝑓𝛿𝑖𝑛𝑡(𝐴	PROPN
cana-2737	129	5	)	)	PUNCT
cana-2737	129	6	)	)	PUNCT
cana-2737	129	7	,	,	PUNCT
cana-2737	129	8	4	4	X
cana-2737	129	9	.	.	X
cana-2737	129	10	𝑒	𝑒	PROPN
cana-2737	129	11	open	open	ADJ
cana-2737	129	12	set	set	NOUN
cana-2737	129	13	(	(	PUNCT
cana-2737	129	14	briefly	briefly	ADV
cana-2737	129	15	,	,	PUNCT
cana-2737	129	16	𝑝𝑓𝑒𝑜𝑠	𝑝𝑓𝑒𝑜𝑠	VERB
cana-2737	129	17	)	)	PUNCT
cana-2737	130	1	if	if	SCONJ
cana-2737	130	2	𝐴	𝐴	PROPN
cana-2737	130	3	⊆	⊆	NUM
cana-2737	130	4	𝑝𝑓𝑐𝑙(𝑝𝑓𝛿𝑖𝑛𝑡(𝐴	𝑝𝑓𝑐𝑙(𝑝𝑓𝛿𝑖𝑛𝑡(𝐴	NOUN
cana-2737	130	5	)	)	PUNCT
cana-2737	130	6	)	)	PUNCT
cana-2737	130	7	∪	∪	ADP
cana-2737	130	8	𝑝𝑓𝑖𝑛𝑡(𝑝𝑓𝛿𝑐𝑙(𝐴	𝑝𝑓𝑖𝑛𝑡(𝑝𝑓𝛿𝑐𝑙(𝐴	PROPN
cana-2737	130	9	)	)	PUNCT
cana-2737	130	10	)	)	PUNCT
cana-2737	130	11	,	,	PUNCT
cana-2737	130	12	5	5	X
cana-2737	130	13	.	.	PUNCT
cana-2737	130	14	𝛿	𝛿	ADJ
cana-2737	130	15	(	(	PUNCT
cana-2737	130	16	resp	resp	NOUN
cana-2737	130	17	.	.	PUNCT
cana-2737	131	1	𝛿-pre	𝛿-pre	PROPN
cana-2737	131	2	,	,	PUNCT
cana-2737	131	3	𝛿-semi	𝛿-semi	VERB
cana-2737	131	4	and	and	CCONJ
cana-2737	131	5	𝑒	𝑒	X
cana-2737	131	6	)	)	PUNCT
cana-2737	131	7	dense	dense	ADJ
cana-2737	131	8	if	if	SCONJ
cana-2737	131	9	𝑝𝑓𝛿𝑐𝑙(𝐴	𝑝𝑓𝛿𝑐𝑙(𝐴	VERB
cana-2737	131	10	)	)	PUNCT
cana-2737	131	11	(	(	PUNCT
cana-2737	131	12	resp	resp	NOUN
cana-2737	131	13	.	.	PUNCT
cana-2737	132	1	𝑝𝑓𝛿𝒫𝑐𝑙(𝐴	𝑝𝑓𝛿𝒫𝑐𝑙(𝐴	NUM
cana-2737	132	2	)	)	PUNCT
cana-2737	132	3	,	,	PUNCT
cana-2737	132	4	𝑝𝑓𝛿𝒮𝑐𝑙(𝐴	𝑝𝑓𝛿𝒮𝑐𝑙(𝐴	PROPN
cana-2737	132	5	)	)	PUNCT
cana-2737	132	6	and	and	CCONJ
cana-2737	132	7	𝑝𝑓𝑒𝑐𝑙(𝐴	𝑝𝑓𝑒𝑐𝑙(𝐴	NOUN
cana-2737	132	8	)	)	PUNCT
cana-2737	132	9	)	)	PUNCT
cana-2737	133	1	=	=	SYM
cana-2737	133	2	𝑋1	𝑋1	PROPN
cana-2737	133	3	.	.	PUNCT
cana-2737	134	1	the	the	DET
cana-2737	134	2	complement	complement	NOUN
cana-2737	134	3	of	of	ADP
cana-2737	134	4	an	an	DET
cana-2737	134	5	𝑝𝑓𝛿𝑜𝑠	𝑝𝑓𝛿𝑜𝑠	NOUN
cana-2737	134	6	(	(	PUNCT
cana-2737	134	7	resp	resp	NOUN
cana-2737	134	8	.	.	PUNCT
cana-2737	135	1	𝑝𝑓𝛿𝒫𝑜𝑠	𝑝𝑓𝛿𝒫𝑜𝑠	X
cana-2737	135	2	,	,	PUNCT
cana-2737	135	3	𝑝𝑓𝛿𝒮𝑜𝑠	𝑝𝑓𝛿𝒮𝑜𝑠	PROPN
cana-2737	135	4	and	and	CCONJ
cana-2737	135	5	𝑝𝑓𝑒𝑜𝑠	𝑝𝑓𝑒𝑜𝑠	NOUN
cana-2737	135	6	)	)	PUNCT
cana-2737	135	7	is	be	AUX
cana-2737	135	8	called	call	VERB
cana-2737	135	9	an	an	DET
cana-2737	135	10	𝑝𝑓𝛿	𝑝𝑓𝛿	NOUN
cana-2737	135	11	(	(	PUNCT
cana-2737	135	12	resp	resp	NOUN
cana-2737	135	13	.	.	PUNCT
cana-2737	136	1	𝑝𝑓𝛿𝒫	𝑝𝑓𝛿𝒫	ADJ
cana-2737	136	2	,	,	PUNCT
cana-2737	136	3	𝑝𝑓𝛿𝒮	𝑝𝑓𝛿𝒮	X
cana-2737	136	4	and	and	CCONJ
cana-2737	136	5	𝑝𝑓𝑒	𝑝𝑓𝑒	ADJ
cana-2737	136	6	)	)	PUNCT
cana-2737	136	7	closed	close	VERB
cana-2737	136	8	set	set	VERB
cana-2737	136	9	(	(	PUNCT
cana-2737	136	10	briefly	briefly	ADV
cana-2737	136	11	,	,	PUNCT
cana-2737	136	12	𝑝𝑓𝛿𝑐𝑠	𝑝𝑓𝛿𝑐𝑠	PROPN
cana-2737	136	13	(	(	PUNCT
cana-2737	136	14	resp	resp	NOUN
cana-2737	136	15	.	.	PUNCT
cana-2737	137	1	𝑝𝑓𝛿𝒫𝑐𝑠	𝑝𝑓𝛿𝒫𝑐𝑠	PROPN
cana-2737	137	2	,	,	PUNCT
cana-2737	137	3	𝑝𝑓𝛿𝒮𝑐𝑠	𝑝𝑓𝛿𝒮𝑐𝑠	PROPN
cana-2737	137	4	and	and	CCONJ
cana-2737	137	5	𝑝𝑓𝑒𝑐𝑠	𝑝𝑓𝑒𝑐𝑠	PROPN
cana-2737	137	6	)	)	PUNCT
cana-2737	137	7	)	)	PUNCT
cana-2737	137	8	in	in	ADP
cana-2737	137	9	𝑋1	𝑋1	PROPN
cana-2737	137	10	.	.	PUNCT
cana-2737	138	1	the	the	DET
cana-2737	138	2	family	family	NOUN
cana-2737	138	3	of	of	ADP
cana-2737	138	4	all	all	DET
cana-2737	138	5	𝑝𝑓𝛿𝑜𝑠	𝑝𝑓𝛿𝑜𝑠	PROPN
cana-2737	138	6	(	(	PUNCT
cana-2737	138	7	resp	resp	NOUN
cana-2737	138	8	.	.	PUNCT
cana-2737	139	1	𝑝𝑓𝛿𝑐𝑠	𝑝𝑓𝛿𝑐𝑠	PROPN
cana-2737	139	2	,	,	PUNCT
cana-2737	139	3	𝑝𝑓𝛿𝒫𝑜𝑠	𝑝𝑓𝛿𝒫𝑜𝑠	PROPN
cana-2737	139	4	,	,	PUNCT
cana-2737	139	5	𝑝𝑓𝛿𝒫𝑐𝑠	𝑝𝑓𝛿𝒫𝑐𝑠	PROPN
cana-2737	139	6	,	,	PUNCT
cana-2737	139	7	𝑝𝑓𝛿𝒮𝑜𝑠	𝑝𝑓𝛿𝒮𝑜𝑠	PROPN
cana-2737	139	8	,	,	PUNCT
cana-2737	139	9	𝑝𝑓𝛿𝒮𝑐𝑠	𝑝𝑓𝛿𝒮𝑐𝑠	PROPN
cana-2737	139	10	,	,	PUNCT
cana-2737	139	11	𝑝𝑓𝑒𝑜𝑠	𝑝𝑓𝑒𝑜𝑠	VERB
cana-2737	139	12	and	and	CCONJ
cana-2737	139	13	𝑝𝑓𝑒𝑐𝑠	𝑝𝑓𝑒𝑐𝑠	NOUN
cana-2737	139	14	)	)	PUNCT
cana-2737	139	15	of	of	ADP
cana-2737	139	16	𝑋1	𝑋1	PROPN
cana-2737	139	17	is	be	AUX
cana-2737	139	18	denoted	denote	VERB
cana-2737	139	19	by	by	ADP
cana-2737	139	20	𝑝𝑓𝛿𝑂𝑆(𝑋1	𝑝𝑓𝛿𝑂𝑆(𝑋1	NOUN
cana-2737	139	21	)	)	PUNCT
cana-2737	139	22	,	,	PUNCT
cana-2737	139	23	(	(	PUNCT
cana-2737	139	24	resp	resp	NOUN
cana-2737	139	25	.	.	PUNCT
cana-2737	139	26	𝑝𝑓𝛿𝐶𝑆(𝑋1	𝑝𝑓𝛿𝐶𝑆(𝑋1	PROPN
cana-2737	139	27	)	)	PUNCT
cana-2737	139	28	,	,	PUNCT
cana-2737	139	29	𝑝𝑓𝛿𝒫𝑂𝑆(𝑋1	𝑝𝑓𝛿𝒫𝑂𝑆(𝑋1	NUM
cana-2737	139	30	)	)	PUNCT
cana-2737	139	31	,	,	PUNCT
cana-2737	139	32	𝑝𝑓𝛿𝒫𝐶𝑆(𝑋1	𝑝𝑓𝛿𝒫𝐶𝑆(𝑋1	NUM
cana-2737	139	33	)	)	PUNCT
cana-2737	139	34	,	,	PUNCT
cana-2737	139	35	𝑝𝑓𝛿𝒮𝑂𝑆(𝑋1	𝑝𝑓𝛿𝒮𝑂𝑆(𝑋1	NUM
cana-2737	139	36	)	)	PUNCT
cana-2737	139	37	,	,	PUNCT
cana-2737	139	38	𝑝𝑓𝛿𝒮𝐶𝑆(𝑋1	𝑝𝑓𝛿𝒮𝐶𝑆(𝑋1	NOUN
cana-2737	139	39	)	)	PUNCT
cana-2737	139	40	,	,	PUNCT
cana-2737	139	41	𝑝𝑓𝑒𝑂𝑆(𝑋1	𝑝𝑓𝑒𝑂𝑆(𝑋1	PROPN
cana-2737	139	42	)	)	PUNCT
cana-2737	139	43	and	and	CCONJ
cana-2737	139	44	𝑝𝑓𝑒𝐶𝑆(𝑋1	𝑝𝑓𝑒𝐶𝑆(𝑋1	NUM
cana-2737	139	45	)	)	PUNCT
cana-2737	139	46	)	)	PUNCT
cana-2737	139	47	.	.	PUNCT
cana-2737	140	1	definition	definition	NOUN
cana-2737	140	2	3.3	3.3	NUM
cana-2737	140	3	let	let	VERB
cana-2737	140	4	(	(	PUNCT
cana-2737	140	5	𝑋	𝑋	NOUN
cana-2737	140	6	,	,	PUNCT
cana-2737	140	7	𝜏	𝜏	NOUN
cana-2737	140	8	)	)	PUNCT
cana-2737	140	9	be	be	VERB
cana-2737	140	10	an	an	DET
cana-2737	140	11	𝑝𝑓𝑡𝑠	𝑝𝑓𝑡𝑠	NOUN
cana-2737	140	12	and	and	CCONJ
cana-2737	140	13	𝐴	𝐴	PROPN
cana-2737	140	14	=	=	PUNCT
cana-2737	140	15	{	{	PUNCT
cana-2737	140	16	<	<	X
cana-2737	140	17	𝑎	𝑎	X
cana-2737	140	18	,	,	PUNCT
cana-2737	140	19	𝜆𝐴(𝑎	𝜆𝐴(𝑎	PROPN
cana-2737	140	20	)	)	PUNCT
cana-2737	140	21	,	,	PUNCT
cana-2737	140	22	𝜇𝐴(𝑎	𝜇𝐴(𝑎	PROPN
cana-2737	140	23	)	)	PUNCT
cana-2737	140	24	>	>	X
cana-2737	140	25	|𝑎	|𝑎	PROPN
cana-2737	141	1	∈	∈	PROPN
cana-2737	141	2	𝑋1	𝑋1	PROPN
cana-2737	141	3	}	}	PUNCT
cana-2737	141	4	be	be	AUX
cana-2737	141	5	an	an	DET
cana-2737	141	6	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2737	141	7	in	in	ADP
cana-2737	141	8	𝑋1	𝑋1	PROPN
cana-2737	141	9	.	.	PUNCT
cana-2737	142	1	then	then	ADV
cana-2737	142	2	the	the	DET
cana-2737	142	3	(	(	PUNCT
cana-2737	142	4	i	i	NOUN
cana-2737	142	5	)	)	PUNCT
cana-2737	142	6	𝑝𝑓𝛿-pre	𝑝𝑓𝛿-pre	VERB
cana-2737	142	7	(	(	PUNCT
cana-2737	142	8	resp	resp	NOUN
cana-2737	142	9	.	.	PUNCT
cana-2737	143	1	𝑝𝑓𝛿-semi	𝑝𝑓𝛿-semi	PROPN
cana-2737	143	2	and	and	CCONJ
cana-2737	143	3	𝑝𝑓𝑒)-interior	𝑝𝑓𝑒)-interior	PROPN
cana-2737	143	4	of	of	ADP
cana-2737	143	5	𝐴	𝐴	PROPN
cana-2737	143	6	are	be	AUX
cana-2737	143	7	denoted	denote	VERB
cana-2737	143	8	by	by	ADP
cana-2737	143	9	𝑝𝑓𝛿𝒫𝑖𝑛𝑡(𝐴	𝑝𝑓𝛿𝒫𝑖𝑛𝑡(𝐴	NOUN
cana-2737	143	10	)	)	PUNCT
cana-2737	143	11	(	(	PUNCT
cana-2737	143	12	resp	resp	NOUN
cana-2737	143	13	.	.	PUNCT
cana-2737	144	1	𝑝𝑓𝛿𝒮𝑖𝑛𝑡(𝐴	𝑝𝑓𝛿𝒮𝑖𝑛𝑡(𝐴	PROPN
cana-2737	144	2	)	)	PUNCT
cana-2737	144	3	and	and	CCONJ
cana-2737	144	4	𝑝𝑓𝑒𝑖𝑛𝑡(𝐴	𝑝𝑓𝑒𝑖𝑛𝑡(𝐴	NOUN
cana-2737	144	5	)	)	PUNCT
cana-2737	144	6	)	)	PUNCT
cana-2737	145	1	and	and	CCONJ
cana-2737	145	2	are	be	AUX
cana-2737	145	3	defined	define	VERB
cana-2737	145	4	as	as	SCONJ
cana-2737	145	5	follows	follow	VERB
cana-2737	145	6	:	:	PUNCT
cana-2737	145	7	𝑝𝑓𝛿𝒫𝑖𝑛𝑡(𝐴	𝑝𝑓𝛿𝒫𝑖𝑛𝑡(𝐴	X
cana-2737	145	8	)	)	PUNCT
cana-2737	145	9	(	(	PUNCT
cana-2737	145	10	resp	resp	NOUN
cana-2737	145	11	.	.	PUNCT
cana-2737	146	1	𝑝𝑓𝛿𝒮𝑖𝑛𝑡(𝐴	𝑝𝑓𝛿𝒮𝑖𝑛𝑡(𝐴	PROPN
cana-2737	146	2	)	)	PUNCT
cana-2737	146	3	and	and	CCONJ
cana-2737	146	4	𝑝𝑓𝑒𝑖𝑛𝑡(𝐴	𝑝𝑓𝑒𝑖𝑛𝑡(𝐴	X
cana-2737	146	5	)	)	PUNCT
cana-2737	147	1	=	=	NOUN
cana-2737	147	2	∪	∪	X
cana-2737	147	3	{	{	PUNCT
cana-2737	147	4	𝐺|𝐺	𝐺|𝐺	NOUN
cana-2737	147	5	in	in	ADP
cana-2737	147	6	a	a	DET
cana-2737	147	7	𝑝𝑓𝛿𝒫𝑜𝑠	𝑝𝑓𝛿𝒫𝑜𝑠	ADJ
cana-2737	147	8	(	(	PUNCT
cana-2737	147	9	resp	resp	NOUN
cana-2737	147	10	.	.	PUNCT
cana-2737	148	1	𝑝𝑓𝛿𝒮𝑜𝑠	𝑝𝑓𝛿𝒮𝑜𝑠	PROPN
cana-2737	148	2	and	and	CCONJ
cana-2737	148	3	𝑝𝑓𝑒𝑜𝑠	𝑝𝑓𝑒𝑜𝑠	NOUN
cana-2737	148	4	)	)	PUNCT
cana-2737	148	5	and	and	CCONJ
cana-2737	148	6	𝐺	𝐺	PROPN
cana-2737	148	7	⊆	⊆	NUM
cana-2737	148	8	𝐴	𝐴	PROPN
cana-2737	148	9	}	}	PUNCT
cana-2737	148	10	,	,	PUNCT
cana-2737	148	11	(	(	PUNCT
cana-2737	148	12	ii	ii	NOUN
cana-2737	148	13	)	)	PUNCT
cana-2737	148	14	𝑝𝑓𝛿-pre	𝑝𝑓𝛿-pre	VERB
cana-2737	148	15	(	(	PUNCT
cana-2737	148	16	resp	resp	NOUN
cana-2737	148	17	.	.	PUNCT
cana-2737	149	1	𝑝𝑓𝛿-semi	𝑝𝑓𝛿-semi	PROPN
cana-2737	149	2	and	and	CCONJ
cana-2737	149	3	𝑝𝑓𝑒)-closure	𝑝𝑓𝑒)-closure	NOUN
cana-2737	149	4	of	of	ADP
cana-2737	149	5	𝐴	𝐴	PROPN
cana-2737	149	6	are	be	AUX
cana-2737	149	7	denoted	denote	VERB
cana-2737	149	8	by	by	ADP
cana-2737	149	9	𝑝𝑓𝛿𝒫𝑐𝑙(𝐴	𝑝𝑓𝛿𝒫𝑐𝑙(𝐴	PROPN
cana-2737	149	10	)	)	PUNCT
cana-2737	149	11	(	(	PUNCT
cana-2737	149	12	resp	resp	NOUN
cana-2737	149	13	.	.	PUNCT
cana-2737	150	1	𝑝𝑓𝛿𝒮𝑐𝑙(𝐴	𝑝𝑓𝛿𝒮𝑐𝑙(𝐴	PROPN
cana-2737	150	2	)	)	PUNCT
cana-2737	150	3	and	and	CCONJ
cana-2737	150	4	𝑝𝑓𝑒𝑐𝑙(𝐴	𝑝𝑓𝑒𝑐𝑙(𝐴	NOUN
cana-2737	150	5	)	)	PUNCT
cana-2737	150	6	)	)	PUNCT
cana-2737	151	1	and	and	CCONJ
cana-2737	151	2	are	be	AUX
cana-2737	151	3	defined	define	VERB
cana-2737	151	4	as	as	SCONJ
cana-2737	151	5	follows	follow	VERB
cana-2737	151	6	:	:	PUNCT
cana-2737	151	7	𝑝𝑓𝛿𝒫𝑐𝑙(𝐴	𝑝𝑓𝛿𝒫𝑐𝑙(𝐴	NUM
cana-2737	151	8	)	)	PUNCT
cana-2737	151	9	(	(	PUNCT
cana-2737	151	10	resp	resp	NOUN
cana-2737	151	11	.	.	PUNCT
cana-2737	152	1	𝑝𝑓𝛿𝒮𝑐𝑙(𝐴	𝑝𝑓𝛿𝒮𝑐𝑙(𝐴	PROPN
cana-2737	152	2	)	)	PUNCT
cana-2737	152	3	and	and	CCONJ
cana-2737	152	4	𝑝𝑓𝑒𝑐𝑙(𝐴	𝑝𝑓𝑒𝑐𝑙(𝐴	NOUN
cana-2737	152	5	)	)	PUNCT
cana-2737	152	6	)	)	PUNCT
cana-2737	153	1	=	=	NOUN
cana-2737	153	2	∩	∩	NOUN
cana-2737	153	3	{	{	PUNCT
cana-2737	153	4	𝐾|𝐾	𝐾|𝐾	NOUN
cana-2737	153	5	is	be	AUX
cana-2737	153	6	an	an	DET
cana-2737	153	7	𝑝𝑓𝛿𝒫𝑐𝑠	𝑝𝑓𝛿𝒫𝑐𝑠	NOUN
cana-2737	153	8	(	(	PUNCT
cana-2737	153	9	resp	resp	NOUN
cana-2737	153	10	.	.	PUNCT
cana-2737	154	1	𝑝𝑓𝛿𝒮𝑐𝑠	𝑝𝑓𝛿𝒮𝑐𝑠	PROPN
cana-2737	154	2	,	,	PUNCT
cana-2737	154	3	𝑝𝑓𝑒𝑐𝑠	𝑝𝑓𝑒𝑐𝑠	PROPN
cana-2737	154	4	)	)	PUNCT
cana-2737	154	5	and	and	CCONJ
cana-2737	154	6	𝐴	𝐴	PROPN
cana-2737	154	7	⊆	⊆	NUM
cana-2737	154	8	𝐾	𝐾	PROPN
cana-2737	154	9	}	}	PUNCT
cana-2737	154	10	.	.	PUNCT
cana-2737	155	1	definition	definition	NOUN
cana-2737	155	2	3.4	3.4	NUM
cana-2737	155	3	let	let	VERB
cana-2737	155	4	(	(	PUNCT
cana-2737	155	5	𝑋1	𝑋1	PROPN
cana-2737	155	6	,	,	PUNCT
cana-2737	155	7	𝛤𝑃	𝛤𝑃	PROPN
cana-2737	155	8	)	)	PUNCT
cana-2737	155	9	be	be	AUX
cana-2737	155	10	an	an	DET
cana-2737	155	11	𝑝𝑓𝑡𝑠	𝑝𝑓𝑡𝑠	NOUN
cana-2737	155	12	and	and	CCONJ
cana-2737	155	13	𝐴	𝐴	PROPN
cana-2737	155	14	=	=	PUNCT
cana-2737	155	15	{	{	PUNCT
cana-2737	155	16	<	<	X
cana-2737	155	17	𝑎	𝑎	X
cana-2737	155	18	,	,	PUNCT
cana-2737	155	19	𝜆𝐴(𝑎	𝜆𝐴(𝑎	PROPN
cana-2737	155	20	)	)	PUNCT
cana-2737	155	21	,	,	PUNCT
cana-2737	155	22	𝜇𝐴(𝑎	𝜇𝐴(𝑎	PROPN
cana-2737	155	23	)	)	PUNCT
cana-2737	155	24	>	>	X
cana-2737	155	25	|𝑎	|𝑎	PROPN
cana-2737	156	1	∈	∈	PROPN
cana-2737	156	2	𝑋1	𝑋1	PROPN
cana-2737	156	3	}	}	PUNCT
cana-2737	156	4	be	be	AUX
cana-2737	156	5	an	an	DET
cana-2737	156	6	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2737	156	7	in	in	ADP
cana-2737	156	8	𝑋1	𝑋1	PROPN
cana-2737	156	9	.	.	PUNCT
cana-2737	157	1	a	a	DET
cana-2737	157	2	set	set	ADJ
cana-2737	157	3	𝐴	𝐴	PROPN
cana-2737	157	4	is	be	AUX
cana-2737	157	5	said	say	VERB
cana-2737	157	6	to	to	PART
cana-2737	157	7	be	be	AUX
cana-2737	157	8	𝑝𝑓	𝑝𝑓	PRON
cana-2737	157	9	1	1	NUM
cana-2737	157	10	.	.	PUNCT
cana-2737	158	1	𝜃-interior	𝜃-interior	NOUN
cana-2737	158	2	of	of	ADP
cana-2737	158	3	𝐴	𝐴	PROPN
cana-2737	158	4	(	(	PUNCT
cana-2737	158	5	briefly	briefly	ADV
cana-2737	158	6	,	,	PUNCT
cana-2737	158	7	𝑝𝑓𝜃𝑖𝑛𝑡(𝐴	𝑝𝑓𝜃𝑖𝑛𝑡(𝐴	PROPN
cana-2737	158	8	)	)	PUNCT
cana-2737	158	9	)	)	PUNCT
cana-2737	158	10	is	be	AUX
cana-2737	158	11	defined	define	VERB
cana-2737	158	12	by	by	ADP
cana-2737	158	13	𝑝𝑓𝜃𝑖𝑛𝑡(𝐴	𝑝𝑓𝜃𝑖𝑛𝑡(𝐴	NOUN
cana-2737	158	14	)	)	PUNCT
cana-2737	159	1	=	=	SYM
cana-2737	159	2	∪	∪	X
cana-2737	159	3	{	{	PUNCT
cana-2737	159	4	𝑝𝑓𝑖𝑛𝑡(𝐵	𝑝𝑓𝑖𝑛𝑡(𝐵	NOUN
cana-2737	159	5	):	):	PUNCT
cana-2737	159	6	𝐵	𝐵	PROPN
cana-2737	159	7	⊆	⊆	NUM
cana-2737	159	8	𝐴	𝐴	PROPN
cana-2737	159	9	&	&	CCONJ
cana-2737	159	10	𝐵	𝐵	PROPN
cana-2737	159	11	isa	isa	VERB
cana-2737	159	12	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-2737	159	13	in	in	ADP
cana-2737	159	14	𝑋1	𝑋1	PROPN
cana-2737	159	15	}	}	PUNCT
cana-2737	159	16	.	.	PUNCT
cana-2737	160	1	2	2	X
cana-2737	160	2	.	.	X
cana-2737	160	3	𝜃-open	𝜃-open	NOUN
cana-2737	160	4	set	set	NOUN
cana-2737	160	5	(	(	PUNCT
cana-2737	160	6	briefly	briefly	ADV
cana-2737	160	7	,	,	PUNCT
cana-2737	160	8	𝑝𝑓𝜃𝑜𝑠	𝑝𝑓𝜃𝑜𝑠	NOUN
cana-2737	160	9	)	)	PUNCT
cana-2737	160	10	if	if	SCONJ
cana-2737	160	11	𝐴	𝐴	PROPN
cana-2737	160	12	=	=	SYM
cana-2737	160	13	𝑝𝑓𝜃𝑖𝑛𝑡(𝐴	𝑝𝑓𝜃𝑖𝑛𝑡(𝐴	PROPN
cana-2737	160	14	)	)	PUNCT
cana-2737	160	15	.	.	PUNCT
cana-2737	161	1	3	3	X
cana-2737	161	2	.	.	X
cana-2737	161	3	𝜃	𝜃	PRON
cana-2737	161	4	-semi	-semi	VERB
cana-2737	161	5	open	open	ADJ
cana-2737	161	6	set	set	NOUN
cana-2737	161	7	(	(	PUNCT
cana-2737	161	8	briefly	briefly	ADV
cana-2737	161	9	,	,	PUNCT
cana-2737	161	10	𝑝𝑓𝜃𝒮𝑜𝑠	𝑝𝑓𝜃𝒮𝑜𝑠	PROPN
cana-2737	161	11	)	)	PUNCT
cana-2737	161	12	if	if	SCONJ
cana-2737	161	13	𝐴	𝐴	PROPN
cana-2737	161	14	⊆	⊆	NUM
cana-2737	161	15	𝑝𝑓𝑐𝑙(𝑝𝑓𝜃𝑖𝑛𝑡(𝐴	𝑝𝑓𝑐𝑙(𝑝𝑓𝜃𝑖𝑛𝑡(𝐴	NOUN
cana-2737	161	16	)	)	PUNCT
cana-2737	161	17	)	)	PUNCT
cana-2737	161	18	.	.	PUNCT
cana-2737	162	1	4	4	X
cana-2737	162	2	.	.	X
cana-2737	163	1	𝑀-open	𝑀-open	ADJ
cana-2737	163	2	set	set	NOUN
cana-2737	163	3	(	(	PUNCT
cana-2737	163	4	briefly	briefly	ADV
cana-2737	163	5	,	,	PUNCT
cana-2737	163	6	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	ADJ
cana-2737	163	7	)	)	PUNCT
cana-2737	163	8	if	if	SCONJ
cana-2737	163	9	𝐴	𝐴	PROPN
cana-2737	163	10	⊆	⊆	NUM
cana-2737	163	11	𝑝𝑓𝑐𝑙(𝑝𝑓𝜃𝑖𝑛𝑡(𝐴	𝑝𝑓𝑐𝑙(𝑝𝑓𝜃𝑖𝑛𝑡(𝐴	NOUN
cana-2737	163	12	)	)	PUNCT
cana-2737	163	13	)	)	PUNCT
cana-2737	163	14	∪	∪	ADP
cana-2737	163	15	𝑝𝑓𝑖𝑛𝑡(𝑝𝑓𝛿𝑐𝑙(𝐴	𝑝𝑓𝑖𝑛𝑡(𝑝𝑓𝛿𝑐𝑙(𝐴	PROPN
cana-2737	163	16	)	)	PUNCT
cana-2737	163	17	)	)	PUNCT
cana-2737	163	18	.	.	PUNCT
cana-2737	164	1	the	the	DET
cana-2737	164	2	complement	complement	NOUN
cana-2737	164	3	of	of	ADP
cana-2737	164	4	a	a	DET
cana-2737	164	5	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	ADJ
cana-2737	164	6	(	(	PUNCT
cana-2737	164	7	resp	resp	NOUN
cana-2737	164	8	.	.	PUNCT
cana-2737	165	1	𝑝𝑓𝜃𝑜𝑠	𝑝𝑓𝜃𝑜𝑠	PROPN
cana-2737	165	2	&	&	CCONJ
cana-2737	165	3	𝑝𝑓𝜃𝒮𝑜𝑠	𝑝𝑓𝜃𝒮𝑜𝑠	PROPN
cana-2737	165	4	)	)	PUNCT
cana-2737	165	5	is	be	AUX
cana-2737	165	6	called	call	VERB
cana-2737	165	7	an	an	DET
cana-2737	165	8	𝑝𝑓𝑀	𝑝𝑓𝑀	NOUN
cana-2737	165	9	(	(	PUNCT
cana-2737	165	10	resp	resp	NOUN
cana-2737	165	11	.	.	PUNCT
cana-2737	166	1	𝑝𝑓𝜃	𝑝𝑓𝜃	PROPN
cana-2737	166	2	&	&	CCONJ
cana-2737	166	3	𝑝𝑓𝜃𝒮	𝑝𝑓𝜃𝒮	NOUN
cana-2737	166	4	)	)	PUNCT
cana-2737	166	5	closed	closed	ADJ
cana-2737	166	6	set	set	NOUN
cana-2737	166	7	(	(	PUNCT
cana-2737	166	8	briefly	briefly	ADV
cana-2737	166	9	,	,	PUNCT
cana-2737	166	10	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	PROPN
cana-2737	166	11	(	(	PUNCT
cana-2737	166	12	resp	resp	NOUN
cana-2737	166	13	.	.	PUNCT
cana-2737	166	14	𝑝𝑓𝜃𝑐𝑠	𝑝𝑓𝜃𝑐𝑠	PROPN
cana-2737	166	15	&	&	CCONJ
cana-2737	166	16	𝑝𝑓𝜃𝒮𝑐𝑠	𝑝𝑓𝜃𝒮𝑐𝑠	NUM
cana-2737	166	17	)	)	PUNCT
cana-2737	166	18	)	)	PUNCT
cana-2737	166	19	in	in	ADP
cana-2737	166	20	𝑋1	𝑋1	PROPN
cana-2737	166	21	.	.	PUNCT
cana-2737	167	1	communications	communication	NOUN
cana-2737	167	2	on	on	ADP
cana-2737	167	3	applied	apply	VERB
cana-2737	167	4	nonlinear	nonlinear	ADJ
cana-2737	167	5	analysis	analysis	NOUN
cana-2737	167	6	issn	issn	NOUN
cana-2737	167	7	:	:	PUNCT
cana-2737	167	8	1074	1074	NUM
cana-2737	167	9	-	-	PUNCT
cana-2737	167	10	133x	133x	NUM
cana-2737	167	11	vol	vol	NOUN
cana-2737	167	12	32	32	NUM
cana-2737	167	13	no	no	NOUN
cana-2737	167	14	.	.	PUNCT
cana-2737	168	1	4s	4s	NUM
cana-2737	168	2	(	(	PUNCT
cana-2737	168	3	2025	2025	NUM
cana-2737	168	4	)	)	PUNCT
cana-2737	168	5	31	31	NUM
cana-2737	168	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2737	168	7	the	the	DET
cana-2737	168	8	family	family	NOUN
cana-2737	168	9	of	of	ADP
cana-2737	168	10	all	all	DET
cana-2737	168	11	𝑝𝑓𝜃𝑜𝑠	𝑝𝑓𝜃𝑜𝑠	NOUN
cana-2737	168	12	(	(	PUNCT
cana-2737	168	13	resp	resp	NOUN
cana-2737	168	14	.	.	PUNCT
cana-2737	169	1	𝑝𝑓𝜃𝑐𝑠	𝑝𝑓𝜃𝑐𝑠	PROPN
cana-2737	169	2	,	,	PUNCT
cana-2737	169	3	𝑝𝑓𝜃𝒮𝑜𝑠	𝑝𝑓𝜃𝒮𝑜𝑠	PROPN
cana-2737	169	4	,	,	PUNCT
cana-2737	169	5	𝑝𝑓𝜃𝒮𝑐𝑠	𝑝𝑓𝜃𝒮𝑐𝑠	PROPN
cana-2737	169	6	,	,	PUNCT
cana-2737	169	7	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	ADJ
cana-2737	169	8	and	and	CCONJ
cana-2737	169	9	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NUM
cana-2737	169	10	)	)	PUNCT
cana-2737	169	11	of	of	ADP
cana-2737	169	12	𝑋1	𝑋1	PROPN
cana-2737	169	13	is	be	AUX
cana-2737	169	14	denoted	denote	VERB
cana-2737	169	15	by	by	ADP
cana-2737	169	16	𝑝𝑓𝜃𝑂𝑆(𝑋1	𝑝𝑓𝜃𝑂𝑆(𝑋1	NOUN
cana-2737	169	17	)	)	PUNCT
cana-2737	169	18	,	,	PUNCT
cana-2737	169	19	(	(	PUNCT
cana-2737	169	20	resp	resp	NOUN
cana-2737	169	21	.	.	PUNCT
cana-2737	170	1	𝑝𝑓𝜃𝐶𝑆(𝑋1	𝑝𝑓𝜃𝐶𝑆(𝑋1	PROPN
cana-2737	170	2	)	)	PUNCT
cana-2737	170	3	,	,	PUNCT
cana-2737	170	4	𝑝𝑓𝜃𝒮𝑂𝑆(𝑋1	𝑝𝑓𝜃𝒮𝑂𝑆(𝑋1	NUM
cana-2737	170	5	)	)	PUNCT
cana-2737	170	6	,	,	PUNCT
cana-2737	170	7	𝑝𝑓𝜃𝒮𝐶𝑆(𝑋1	𝑝𝑓𝜃𝒮𝐶𝑆(𝑋1	NUM
cana-2737	170	8	)	)	PUNCT
cana-2737	170	9	,	,	PUNCT
cana-2737	170	10	𝑝𝑓𝑀𝑂𝑆(𝑋1	𝑝𝑓𝑀𝑂𝑆(𝑋1	NUM
cana-2737	170	11	)	)	PUNCT
cana-2737	170	12	and	and	CCONJ
cana-2737	170	13	𝑝𝑓𝑀𝐶𝑆(𝑋1	𝑝𝑓𝑀𝐶𝑆(𝑋1	NUM
cana-2737	170	14	)	)	PUNCT
cana-2737	170	15	)	)	PUNCT
cana-2737	170	16	.	.	PUNCT
cana-2737	171	1	definition	definition	NOUN
cana-2737	171	2	3.5	3.5	NUM
cana-2737	171	3	let	let	VERB
cana-2737	171	4	(	(	PUNCT
cana-2737	171	5	𝑋1	𝑋1	PROPN
cana-2737	171	6	,	,	PUNCT
cana-2737	171	7	𝛤𝑃	𝛤𝑃	PROPN
cana-2737	171	8	)	)	PUNCT
cana-2737	171	9	be	be	AUX
cana-2737	171	10	an	an	DET
cana-2737	171	11	𝑝𝑓𝑡𝑠	𝑝𝑓𝑡𝑠	NOUN
cana-2737	171	12	and	and	CCONJ
cana-2737	171	13	𝐴	𝐴	PROPN
cana-2737	171	14	=	=	PUNCT
cana-2737	171	15	{	{	PUNCT
cana-2737	171	16	<	<	X
cana-2737	171	17	𝑎	𝑎	X
cana-2737	171	18	,	,	PUNCT
cana-2737	171	19	𝜆𝐴(𝑎	𝜆𝐴(𝑎	PROPN
cana-2737	171	20	)	)	PUNCT
cana-2737	171	21	,	,	PUNCT
cana-2737	171	22	𝜇𝐴(𝑎	𝜇𝐴(𝑎	PROPN
cana-2737	171	23	)	)	PUNCT
cana-2737	171	24	>	>	X
cana-2737	171	25	|𝑎	|𝑎	PROPN
cana-2737	172	1	∈	∈	PROPN
cana-2737	172	2	𝑋1	𝑋1	PROPN
cana-2737	172	3	}	}	PUNCT
cana-2737	172	4	be	be	AUX
cana-2737	172	5	an	an	DET
cana-2737	172	6	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2737	172	7	in	in	ADP
cana-2737	172	8	𝑋1	𝑋1	PROPN
cana-2737	172	9	.	.	PUNCT
cana-2737	173	1	then	then	ADV
cana-2737	173	2	the	the	DET
cana-2737	173	3	𝑝𝑓	𝑝𝑓	PROPN
cana-2737	173	4	1	1	NUM
cana-2737	173	5	.	.	PUNCT
cana-2737	173	6	𝑀	𝑀	PROPN
cana-2737	173	7	(	(	PUNCT
cana-2737	173	8	resp	resp	PROPN
cana-2737	173	9	.	.	PUNCT
cana-2737	174	1	𝑝𝑓𝜃-semi	𝑝𝑓𝜃-semi	ADJ
cana-2737	174	2	)	)	PUNCT
cana-2737	174	3	-interior	-interior	NOUN
cana-2737	174	4	of	of	ADP
cana-2737	174	5	𝐴	𝐴	PROPN
cana-2737	174	6	(	(	PUNCT
cana-2737	174	7	briefly	briefly	ADV
cana-2737	174	8	,	,	PUNCT
cana-2737	174	9	𝑝𝑓𝑀𝑖𝑛𝑡(𝐴	𝑝𝑓𝑀𝑖𝑛𝑡(𝐴	NUM
cana-2737	174	10	)	)	PUNCT
cana-2737	174	11	(	(	PUNCT
cana-2737	174	12	resp	resp	NOUN
cana-2737	174	13	.	.	PUNCT
cana-2737	175	1	𝑝𝑓𝜃𝒮𝑖𝑛𝑡(𝐴	𝑝𝑓𝜃𝒮𝑖𝑛𝑡(𝐴	NOUN
cana-2737	175	2	)	)	PUNCT
cana-2737	175	3	)	)	PUNCT
cana-2737	176	1	is	be	AUX
cana-2737	176	2	defined	define	VERB
cana-2737	176	3	by	by	ADP
cana-2737	176	4	𝑝𝑓𝑀𝑖𝑛𝑡(𝐴	𝑝𝑓𝑀𝑖𝑛𝑡(𝐴	NUM
cana-2737	176	5	)	)	PUNCT
cana-2737	176	6	(	(	PUNCT
cana-2737	176	7	resp	resp	NOUN
cana-2737	176	8	.	.	PUNCT
cana-2737	177	1	𝑝𝑓𝜃𝑖𝑛𝑡(𝐴	𝑝𝑓𝜃𝑖𝑛𝑡(𝐴	NOUN
cana-2737	177	2	)	)	PUNCT
cana-2737	177	3	and	and	CCONJ
cana-2737	177	4	𝑝𝑓𝜃𝒮𝑖𝑛𝑡(𝐴	𝑝𝑓𝜃𝒮𝑖𝑛𝑡(𝐴	NOUN
cana-2737	177	5	)	)	PUNCT
cana-2737	177	6	)	)	PUNCT
cana-2737	178	1	=	=	SYM
cana-2737	178	2	∪	∪	X
cana-2737	178	3	{	{	PUNCT
cana-2737	178	4	𝐵	𝐵	NOUN
cana-2737	178	5	:	:	PUNCT
cana-2737	178	6	𝐵	𝐵	PROPN
cana-2737	178	7	⊆	⊆	NUM
cana-2737	178	8	𝐴	𝐴	PROPN
cana-2737	178	9	and	and	CCONJ
cana-2737	178	10	𝐵	𝐵	PROPN
cana-2737	178	11	is	be	AUX
cana-2737	178	12	a	a	DET
cana-2737	178	13	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	ADJ
cana-2737	178	14	(	(	PUNCT
cana-2737	178	15	resp	resp	NOUN
cana-2737	178	16	.	.	PUNCT
cana-2737	179	1	𝑝𝑓𝜃𝒮𝑜𝑠	𝑝𝑓𝜃𝒮𝑜𝑠	PROPN
cana-2737	179	2	)	)	PUNCT
cana-2737	180	1	in	in	ADP
cana-2737	180	2	𝑋1	𝑋1	PROPN
cana-2737	180	3	}	}	PUNCT
cana-2737	180	4	.	.	PUNCT
cana-2737	181	1	2	2	X
cana-2737	181	2	.	.	X
cana-2737	181	3	𝑀	𝑀	PROPN
cana-2737	181	4	(	(	PUNCT
cana-2737	181	5	resp	resp	PROPN
cana-2737	181	6	.	.	PUNCT
cana-2737	182	1	𝜃-semi	𝜃-semi	NOUN
cana-2737	182	2	)	)	PUNCT
cana-2737	182	3	-closure	-closure	NOUN
cana-2737	182	4	of	of	ADP
cana-2737	182	5	𝐴	𝐴	PROPN
cana-2737	182	6	(	(	PUNCT
cana-2737	182	7	briefly	briefly	ADV
cana-2737	182	8	,	,	PUNCT
cana-2737	182	9	𝑝𝑓𝑀𝑐𝑙(𝐴	𝑝𝑓𝑀𝑐𝑙(𝐴	INTJ
cana-2737	182	10	)	)	PUNCT
cana-2737	182	11	(	(	PUNCT
cana-2737	182	12	resp	resp	NOUN
cana-2737	182	13	.	.	PUNCT
cana-2737	183	1	𝑝𝑓𝜃𝒮𝑐𝑙(𝐴	𝑝𝑓𝜃𝒮𝑐𝑙(𝐴	NUM
cana-2737	183	2	)	)	PUNCT
cana-2737	183	3	)	)	PUNCT
cana-2737	183	4	is	be	AUX
cana-2737	183	5	defined	define	VERB
cana-2737	183	6	by	by	ADP
cana-2737	183	7	𝑝𝑓𝑀𝑐𝑙(𝐴	𝑝𝑓𝑀𝑐𝑙(𝐴	NOUN
cana-2737	183	8	)	)	PUNCT
cana-2737	183	9	(	(	PUNCT
cana-2737	183	10	resp	resp	NOUN
cana-2737	183	11	.	.	PUNCT
cana-2737	184	1	𝑝𝑓𝜃𝒮𝑐𝑙(𝐴	𝑝𝑓𝜃𝒮𝑐𝑙(𝐴	NUM
cana-2737	184	2	)	)	PUNCT
cana-2737	184	3	)	)	PUNCT
cana-2737	185	1	=	=	NOUN
cana-2737	185	2	∩	∩	X
cana-2737	185	3	{	{	PUNCT
cana-2737	185	4	𝐵	𝐵	NOUN
cana-2737	185	5	:	:	PUNCT
cana-2737	185	6	𝐴	𝐴	PROPN
cana-2737	185	7	⊆	⊆	NUM
cana-2737	185	8	𝐵	𝐵	PROPN
cana-2737	185	9	and	and	CCONJ
cana-2737	185	10	𝐴	𝐴	PROPN
cana-2737	185	11	is	be	AUX
cana-2737	185	12	a	a	DET
cana-2737	185	13	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-2737	185	14	(	(	PUNCT
cana-2737	185	15	resp	resp	NOUN
cana-2737	185	16	.	.	PUNCT
cana-2737	186	1	𝑝𝑓𝜃𝒮𝑐𝑠	𝑝𝑓𝜃𝒮𝑐𝑠	NUM
cana-2737	186	2	)	)	PUNCT
cana-2737	187	1	in	in	ADP
cana-2737	187	2	𝑋1	𝑋1	PROPN
cana-2737	187	3	}	}	PUNCT
cana-2737	187	4	.	.	PUNCT
cana-2737	188	1	definition	definition	NOUN
cana-2737	188	2	3.6	3.6	NUM
cana-2737	188	3	let	let	VERB
cana-2737	188	4	(	(	PUNCT
cana-2737	188	5	𝑋1	𝑋1	PROPN
cana-2737	188	6	,	,	PUNCT
cana-2737	188	7	𝛤𝑃	𝛤𝑃	PROPN
cana-2737	188	8	)	)	PUNCT
cana-2737	188	9	and	and	CCONJ
cana-2737	188	10	(	(	PUNCT
cana-2737	188	11	𝑋2	𝑋2	PROPN
cana-2737	188	12	,	,	PUNCT
cana-2737	188	13	𝛹𝑃	𝛹𝑃	PROPN
cana-2737	188	14	)	)	PUNCT
cana-2737	188	15	be	be	VERB
cana-2737	188	16	any	any	DET
cana-2737	188	17	two	two	NUM
cana-2737	188	18	𝑝𝑓𝑡𝑠	𝑝𝑓𝑡𝑠	NOUN
cana-2737	188	19	’s	’s	PART
cana-2737	188	20	.	.	PUNCT
cana-2737	189	1	a	a	DET
cana-2737	189	2	mapping	mapping	NOUN
cana-2737	189	3	ℎ𝑃	ℎ𝑃	NOUN
cana-2737	189	4	:	:	PUNCT
cana-2737	189	5	(	(	PUNCT
cana-2737	189	6	𝑋1	𝑋1	PROPN
cana-2737	189	7	,	,	PUNCT
cana-2737	189	8	𝛤𝑃	𝛤𝑃	PROPN
cana-2737	189	9	)	)	PUNCT
cana-2737	189	10	→	→	PUNCT
cana-2737	189	11	(	(	PUNCT
cana-2737	189	12	𝑋2	𝑋2	PROPN
cana-2737	189	13	,	,	PUNCT
cana-2737	189	14	𝛹𝑃	𝛹𝑃	PROPN
cana-2737	189	15	)	)	PUNCT
cana-2737	189	16	is	be	AUX
cana-2737	189	17	said	say	VERB
cana-2737	189	18	to	to	PART
cana-2737	189	19	be	be	AUX
cana-2737	189	20	a	a	DET
cana-2737	189	21	pythagorean	pythagorean	ADJ
cana-2737	189	22	fuzzy	fuzzy	NOUN
cana-2737	189	23	(	(	PUNCT
cana-2737	189	24	resp	resp	NOUN
cana-2737	189	25	.	.	PUNCT
cana-2737	190	1	𝛿	𝛿	ADJ
cana-2737	190	2	,	,	PUNCT
cana-2737	190	3	𝛿𝒫	𝛿𝒫	NOUN
cana-2737	190	4	,	,	PUNCT
cana-2737	190	5	𝛿𝒮	𝛿𝒮	NOUN
cana-2737	190	6	,	,	PUNCT
cana-2737	190	7	𝑒	𝑒	NOUN
cana-2737	190	8	,	,	PUNCT
cana-2737	190	9	𝜃	𝜃	NOUN
cana-2737	190	10	,	,	PUNCT
cana-2737	190	11	𝜃𝒮	𝜃𝒮	ADJ
cana-2737	190	12	and	and	CCONJ
cana-2737	190	13	𝑀	𝑀	PROPN
cana-2737	190	14	)	)	PUNCT
cana-2737	190	15	-continuous	-continuous	ADJ
cana-2737	190	16	(	(	PUNCT
cana-2737	190	17	briefly	briefly	ADV
cana-2737	190	18	,	,	PUNCT
cana-2737	190	19	𝑝𝑓𝐶𝑡𝑠	𝑝𝑓𝐶𝑡𝑠	PROPN
cana-2737	190	20	(	(	PUNCT
cana-2737	190	21	resp	resp	NOUN
cana-2737	190	22	.	.	PUNCT
cana-2737	191	1	𝑝𝑓𝛿𝐶𝑡𝑠	𝑝𝑓𝛿𝐶𝑡𝑠	PROPN
cana-2737	191	2	,	,	PUNCT
cana-2737	191	3	𝑝𝑓𝛿𝒫𝐶𝑡𝑠	𝑝𝑓𝛿𝒫𝐶𝑡𝑠	PROPN
cana-2737	191	4	,	,	PUNCT
cana-2737	191	5	𝑝𝑓𝛿𝒮𝐶𝑡𝑠	𝑝𝑓𝛿𝒮𝐶𝑡𝑠	PROPN
cana-2737	191	6	,	,	PUNCT
cana-2737	191	7	𝑝𝑓𝑒𝐶𝑡𝑠	𝑝𝑓𝑒𝐶𝑡𝑠	NOUN
cana-2737	191	8	,	,	PUNCT
cana-2737	191	9	𝑝𝑓𝜃𝐶𝑡𝑠	𝑝𝑓𝜃𝐶𝑡𝑠	NOUN
cana-2737	191	10	,	,	PUNCT
cana-2737	191	11	𝑝𝑓𝜃𝒮𝐶𝑡𝑠	𝑝𝑓𝜃𝒮𝐶𝑡𝑠	PROPN
cana-2737	191	12	and	and	CCONJ
cana-2737	191	13	𝑝𝑓𝑀𝐶𝑡𝑠	𝑝𝑓𝑀𝐶𝑡𝑠	PROPN
cana-2737	191	14	)	)	PUNCT
cana-2737	191	15	)	)	PUNCT
cana-2737	192	1	if	if	SCONJ
cana-2737	192	2	the	the	DET
cana-2737	192	3	inverse	inverse	ADJ
cana-2737	192	4	image	image	NOUN
cana-2737	192	5	of	of	ADP
cana-2737	192	6	every	every	DET
cana-2737	192	7	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-2737	192	8	in	in	ADP
cana-2737	192	9	(	(	PUNCT
cana-2737	192	10	𝑋2	𝑋2	PROPN
cana-2737	192	11	,	,	PUNCT
cana-2737	192	12	𝛹𝑃	𝛹𝑃	PROPN
cana-2737	192	13	)	)	PUNCT
cana-2737	192	14	is	be	AUX
cana-2737	192	15	a	a	DET
cana-2737	192	16	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	ADJ
cana-2737	192	17	(	(	PUNCT
cana-2737	192	18	resp	resp	NOUN
cana-2737	192	19	.	.	PUNCT
cana-2737	193	1	𝑝𝑓𝛿𝑜𝑠	𝑝𝑓𝛿𝑜𝑠	PROPN
cana-2737	193	2	,	,	PUNCT
cana-2737	193	3	𝑝𝑓𝛿𝒫𝑜𝑠	𝑝𝑓𝛿𝒫𝑜𝑠	PROPN
cana-2737	193	4	,	,	PUNCT
cana-2737	193	5	𝑝𝑓𝛿𝒮𝑜𝑠	𝑝𝑓𝛿𝒮𝑜𝑠	PROPN
cana-2737	193	6	,	,	PUNCT
cana-2737	193	7	𝑝𝑓𝑒𝑜𝑠	𝑝𝑓𝑒𝑜𝑠	NOUN
cana-2737	193	8	,	,	PUNCT
cana-2737	193	9	𝑝𝑓𝜃𝑜𝑠	𝑝𝑓𝜃𝑜𝑠	NOUN
cana-2737	193	10	,	,	PUNCT
cana-2737	193	11	𝑝𝑓𝜃𝒮𝑜𝑠	𝑝𝑓𝜃𝒮𝑜𝑠	PROPN
cana-2737	193	12	and	and	CCONJ
cana-2737	193	13	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	ADJ
cana-2737	193	14	)	)	PUNCT
cana-2737	193	15	in	in	ADP
cana-2737	193	16	(	(	PUNCT
cana-2737	193	17	𝑋1	𝑋1	PROPN
cana-2737	193	18	,	,	PUNCT
cana-2737	193	19	𝛤𝑃	𝛤𝑃	PROPN
cana-2737	193	20	)	)	PUNCT
cana-2737	193	21	.	.	PUNCT
cana-2737	194	1	definition	definition	NOUN
cana-2737	194	2	3.7	3.7	NUM
cana-2737	194	3	let	let	VERB
cana-2737	194	4	(	(	PUNCT
cana-2737	194	5	𝑋1	𝑋1	PROPN
cana-2737	194	6	,	,	PUNCT
cana-2737	194	7	𝛤𝑃	𝛤𝑃	PROPN
cana-2737	194	8	)	)	PUNCT
cana-2737	194	9	and	and	CCONJ
cana-2737	194	10	(	(	PUNCT
cana-2737	194	11	𝑋2	𝑋2	PROPN
cana-2737	194	12	,	,	PUNCT
cana-2737	194	13	𝛹𝑃	𝛹𝑃	PROPN
cana-2737	194	14	)	)	PUNCT
cana-2737	194	15	be	be	VERB
cana-2737	194	16	any	any	DET
cana-2737	194	17	two	two	NUM
cana-2737	194	18	𝑝𝑓𝑡𝑠	𝑝𝑓𝑡𝑠	NOUN
cana-2737	194	19	’s	’s	PART
cana-2737	194	20	.	.	PUNCT
cana-2737	195	1	a	a	DET
cana-2737	195	2	mapping	mapping	NOUN
cana-2737	195	3	ℎ𝑃	ℎ𝑃	NOUN
cana-2737	195	4	:	:	PUNCT
cana-2737	195	5	(	(	PUNCT
cana-2737	195	6	𝑋1	𝑋1	PROPN
cana-2737	195	7	,	,	PUNCT
cana-2737	195	8	𝛤𝑃	𝛤𝑃	PROPN
cana-2737	195	9	)	)	PUNCT
cana-2737	195	10	→	→	PUNCT
cana-2737	195	11	(	(	PUNCT
cana-2737	195	12	𝑋2	𝑋2	PROPN
cana-2737	195	13	,	,	PUNCT
cana-2737	195	14	𝛹𝑃	𝛹𝑃	PROPN
cana-2737	195	15	)	)	PUNCT
cana-2737	195	16	is	be	AUX
cana-2737	195	17	said	say	VERB
cana-2737	195	18	to	to	PART
cana-2737	195	19	be	be	AUX
cana-2737	195	20	a	a	DET
cana-2737	195	21	pythagorean	pythagorean	ADJ
cana-2737	195	22	fuzzy	fuzzy	NOUN
cana-2737	195	23	(	(	PUNCT
cana-2737	195	24	resp	resp	NOUN
cana-2737	195	25	.	.	PUNCT
cana-2737	196	1	𝜃	𝜃	X
cana-2737	196	2	,	,	PUNCT
cana-2737	196	3	𝜃𝒮	𝜃𝒮	ADJ
cana-2737	196	4	,	,	PUNCT
cana-2737	196	5	𝛿	𝛿	ADJ
cana-2737	196	6	,	,	PUNCT
cana-2737	196	7	𝛿𝒫	𝛿𝒫	NOUN
cana-2737	196	8	,	,	PUNCT
cana-2737	196	9	𝛿𝒮	𝛿𝒮	NOUN
cana-2737	196	10	,	,	PUNCT
cana-2737	196	11	𝑀	𝑀	PROPN
cana-2737	196	12	and	and	CCONJ
cana-2737	196	13	𝑒	𝑒	PROPN
cana-2737	196	14	)	)	PUNCT
cana-2737	196	15	-open	-open	NOUN
cana-2737	196	16	(	(	PUNCT
cana-2737	196	17	briefly	briefly	ADV
cana-2737	196	18	,	,	PUNCT
cana-2737	196	19	𝑝𝑓𝑂	𝑝𝑓𝑂	PROPN
cana-2737	196	20	(	(	PUNCT
cana-2737	196	21	resp	resp	NOUN
cana-2737	196	22	.	.	PUNCT
cana-2737	197	1	𝑝𝑓𝜃𝑂	𝑝𝑓𝜃𝑂	NOUN
cana-2737	197	2	,	,	PUNCT
cana-2737	197	3	𝑝𝑓𝜃𝒮𝑂	𝑝𝑓𝜃𝒮𝑂	NOUN
cana-2737	197	4	,	,	PUNCT
cana-2737	197	5	𝑝𝑓𝛿𝑂	𝑝𝑓𝛿𝑂	NOUN
cana-2737	197	6	,	,	PUNCT
cana-2737	197	7	𝑝𝑓𝛿𝒫𝑂	𝑝𝑓𝛿𝒫𝑂	NOUN
cana-2737	197	8	,	,	PUNCT
cana-2737	197	9	𝑝𝑓𝛿𝒮𝑂	𝑝𝑓𝛿𝒮𝑂	NOUN
cana-2737	197	10	,	,	PUNCT
cana-2737	197	11	𝑝𝑓𝑀𝑂	𝑝𝑓𝑀𝑂	NOUN
cana-2737	197	12	and	and	CCONJ
cana-2737	197	13	𝑝𝑓𝑒𝑂	𝑝𝑓𝑒𝑂	NOUN
cana-2737	197	14	)	)	PUNCT
cana-2737	197	15	)	)	PUNCT
cana-2737	197	16	mapping	mapping	NOUN
cana-2737	197	17	if	if	SCONJ
cana-2737	197	18	the	the	DET
cana-2737	197	19	image	image	NOUN
cana-2737	197	20	of	of	ADP
cana-2737	197	21	every	every	DET
cana-2737	197	22	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-2737	197	23	in	in	ADP
cana-2737	197	24	(	(	PUNCT
cana-2737	197	25	𝑋1	𝑋1	PROPN
cana-2737	197	26	,	,	PUNCT
cana-2737	197	27	𝛤𝑃	𝛤𝑃	PROPN
cana-2737	197	28	)	)	PUNCT
cana-2737	197	29	is	be	AUX
cana-2737	197	30	a	a	DET
cana-2737	197	31	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	ADJ
cana-2737	197	32	(	(	PUNCT
cana-2737	197	33	resp	resp	NOUN
cana-2737	197	34	.	.	PUNCT
cana-2737	198	1	𝑝𝑓𝜃𝑜𝑠	𝑝𝑓𝜃𝑜𝑠	PROPN
cana-2737	198	2	,	,	PUNCT
cana-2737	198	3	𝑝𝑓𝜃𝒮𝑜𝑠	𝑝𝑓𝜃𝒮𝑜𝑠	PROPN
cana-2737	198	4	,	,	PUNCT
cana-2737	198	5	𝑝𝑓𝛿𝑜𝑠	𝑝𝑓𝛿𝑜𝑠	VERB
cana-2737	198	6	,	,	PUNCT
cana-2737	198	7	𝑝𝑓𝛿𝒫𝑜𝑠	𝑝𝑓𝛿𝒫𝑜𝑠	PROPN
cana-2737	198	8	,	,	PUNCT
cana-2737	198	9	𝑝𝑓𝛿𝒮𝑜𝑠	𝑝𝑓𝛿𝒮𝑜𝑠	PROPN
cana-2737	198	10	,	,	PUNCT
cana-2737	198	11	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	ADV
cana-2737	198	12	and	and	CCONJ
cana-2737	198	13	𝑝𝑓𝑒𝑜𝑠	𝑝𝑓𝑒𝑜𝑠	NOUN
cana-2737	198	14	)	)	PUNCT
cana-2737	198	15	in	in	ADP
cana-2737	198	16	(	(	PUNCT
cana-2737	198	17	𝑋2	𝑋2	PROPN
cana-2737	198	18	,	,	PUNCT
cana-2737	198	19	𝛹𝑃	𝛹𝑃	PROPN
cana-2737	198	20	)	)	PUNCT
cana-2737	198	21	.	.	PUNCT
cana-2737	199	1	proposition	proposition	NOUN
cana-2737	199	2	3.1	3.1	NUM
cana-2737	199	3	let	let	NOUN
cana-2737	199	4	(	(	PUNCT
cana-2737	199	5	𝑋1	𝑋1	PROPN
cana-2737	199	6	,	,	PUNCT
cana-2737	199	7	𝛤𝑃	𝛤𝑃	PROPN
cana-2737	199	8	)	)	PUNCT
cana-2737	199	9	&	&	CCONJ
cana-2737	199	10	(	(	PUNCT
cana-2737	199	11	𝑋2	𝑋2	PROPN
cana-2737	199	12	,	,	PUNCT
cana-2737	199	13	𝛹𝑃	𝛹𝑃	PROPN
cana-2737	199	14	)	)	PUNCT
cana-2737	199	15	be	be	VERB
cana-2737	199	16	a	a	DET
cana-2737	199	17	𝑝𝑓𝑡𝑠	𝑝𝑓𝑡𝑠	NOUN
cana-2737	199	18	’s	’s	PART
cana-2737	199	19	.	.	PUNCT
cana-2737	200	1	let	let	VERB
cana-2737	200	2	ℎ𝑃	ℎ𝑃	NOUN
cana-2737	200	3	:	:	PUNCT
cana-2737	200	4	(	(	PUNCT
cana-2737	200	5	𝑋1	𝑋1	PROPN
cana-2737	200	6	,	,	PUNCT
cana-2737	200	7	𝛤𝑃	𝛤𝑃	PROPN
cana-2737	200	8	)	)	PUNCT
cana-2737	200	9	→	→	PUNCT
cana-2737	200	10	(	(	PUNCT
cana-2737	200	11	𝑋2	𝑋2	PROPN
cana-2737	200	12	,	,	PUNCT
cana-2737	200	13	𝛹𝑃	𝛹𝑃	PROPN
cana-2737	200	14	)	)	PUNCT
cana-2737	200	15	be	be	AUX
cana-2737	200	16	a	a	DET
cana-2737	200	17	mapping	mapping	NOUN
cana-2737	200	18	.	.	PUNCT
cana-2737	201	1	then	then	ADV
cana-2737	201	2	the	the	DET
cana-2737	201	3	following	following	ADJ
cana-2737	201	4	statements	statement	NOUN
cana-2737	201	5	are	be	AUX
cana-2737	201	6	hold	hold	ADJ
cana-2737	201	7	for	for	ADP
cana-2737	201	8	𝑝𝑓𝑡𝑠	𝑝𝑓𝑡𝑠	NOUN
cana-2737	201	9	,	,	PUNCT
cana-2737	201	10	but	but	CCONJ
cana-2737	201	11	not	not	PART
cana-2737	201	12	conversely	conversely	ADV
cana-2737	201	13	.	.	PUNCT
cana-2737	202	1	1	1	X
cana-2737	202	2	.	.	X
cana-2737	202	3	every	every	DET
cana-2737	202	4	𝑝𝑓𝜃𝑂	𝑝𝑓𝜃𝑂	NOUN
cana-2737	202	5	is	be	AUX
cana-2737	202	6	a	a	DET
cana-2737	202	7	𝑝𝑓𝑂.	𝑝𝑓𝑂.	NUM
cana-2737	202	8	2	2	NUM
cana-2737	202	9	.	.	PUNCT
cana-2737	203	1	every	every	DET
cana-2737	203	2	𝑝𝑓𝜃𝑂	𝑝𝑓𝜃𝑂	NOUN
cana-2737	203	3	is	be	AUX
cana-2737	203	4	a	a	DET
cana-2737	203	5	𝑝𝑓𝜃𝒮𝑂.	𝑝𝑓𝜃𝒮𝑂.	ADJ
cana-2737	203	6	3	3	NUM
cana-2737	203	7	.	.	PUNCT
cana-2737	204	1	every	every	DET
cana-2737	204	2	𝑝𝑓𝜃𝒮𝑂	𝑝𝑓𝜃𝒮𝑂	NOUN
cana-2737	204	3	is	be	AUX
cana-2737	204	4	a	a	DET
cana-2737	204	5	𝑝𝑓𝑀𝑂.	𝑝𝑓𝑀𝑂.	NOUN
cana-2737	204	6	4	4	NUM
cana-2737	204	7	.	.	PUNCT
cana-2737	205	1	every	every	DET
cana-2737	205	2	𝑝𝑓𝛿𝑂	𝑝𝑓𝛿𝑂	NOUN
cana-2737	205	3	is	be	AUX
cana-2737	205	4	a	a	DET
cana-2737	205	5	𝑝𝑓𝛿𝒮𝑂.	𝑝𝑓𝛿𝒮𝑂.	ADJ
cana-2737	205	6	5	5	NUM
cana-2737	205	7	.	.	PUNCT
cana-2737	206	1	every	every	DET
cana-2737	206	2	𝑝𝑓𝛿𝑂	𝑝𝑓𝛿𝑂	NOUN
cana-2737	206	3	is	be	AUX
cana-2737	206	4	a	a	DET
cana-2737	206	5	𝑝𝑓𝛿𝒫𝑂.	𝑝𝑓𝛿𝒫𝑂.	PROPN
cana-2737	206	6	6	6	NUM
cana-2737	206	7	.	.	PUNCT
cana-2737	207	1	every	every	DET
cana-2737	207	2	𝑝𝑓𝛿𝒮𝑂	𝑝𝑓𝛿𝒮𝑂	NOUN
cana-2737	207	3	is	be	AUX
cana-2737	207	4	a	a	DET
cana-2737	207	5	𝑝𝑓𝑒𝑂.	𝑝𝑓𝑒𝑂.	NOUN
cana-2737	207	6	7	7	NUM
cana-2737	207	7	.	.	PUNCT
cana-2737	208	1	every	every	DET
cana-2737	208	2	𝑝𝑓𝛿𝒫𝑂	𝑝𝑓𝛿𝒫𝑂	NOUN
cana-2737	208	3	is	be	AUX
cana-2737	208	4	a	a	DET
cana-2737	208	5	𝑝𝑓𝑀𝑂.	𝑝𝑓𝑀𝑂.	NOUN
cana-2737	208	6	8	8	NUM
cana-2737	208	7	.	.	PUNCT
cana-2737	209	1	every	every	DET
cana-2737	209	2	𝑝𝑓𝑀𝑂	𝑝𝑓𝑀𝑂	NOUN
cana-2737	209	3	is	be	AUX
cana-2737	209	4	a	a	DET
cana-2737	209	5	𝑝𝑓𝑒𝑂.	𝑝𝑓𝑒𝑂.	NOUN
cana-2737	209	6	9	9	NUM
cana-2737	209	7	.	.	PUNCT
cana-2737	210	1	every	every	DET
cana-2737	210	2	𝑝𝑓𝛿𝑂	𝑝𝑓𝛿𝑂	NOUN
cana-2737	210	3	is	be	AUX
cana-2737	210	4	a	a	DET
cana-2737	210	5	𝑝𝑓𝑂.	𝑝𝑓𝑂.	PROPN
cana-2737	210	6	proof	proof	NOUN
cana-2737	210	7	.	.	PUNCT
cana-2737	211	1	1	1	X
cana-2737	211	2	.	.	X
cana-2737	211	3	let	let	VERB
cana-2737	211	4	𝐵	𝐵	PRON
cana-2737	211	5	be	be	AUX
cana-2737	211	6	a	a	DET
cana-2737	211	7	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-2737	211	8	in	in	ADP
cana-2737	211	9	(	(	PUNCT
cana-2737	211	10	𝑋1	𝑋1	NOUN
cana-2737	211	11	,	,	PUNCT
cana-2737	211	12	γ𝑃	γ𝑃	NOUN
cana-2737	211	13	)	)	PUNCT
cana-2737	211	14	.	.	PUNCT
cana-2737	212	1	since	since	SCONJ
cana-2737	212	2	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	212	3	is	be	AUX
cana-2737	212	4	𝑝𝑓𝜃𝑂	𝑝𝑓𝜃𝑂	NOUN
cana-2737	212	5	,	,	PUNCT
cana-2737	212	6	ℎ𝑃(𝐵	ℎ𝑃(𝐵	NUM
cana-2737	212	7	)	)	PUNCT
cana-2737	212	8	is	be	AUX
cana-2737	212	9	𝑝𝑓𝜃𝑜𝑠	𝑝𝑓𝜃𝑜𝑠	NOUN
cana-2737	212	10	in	in	ADP
cana-2737	212	11	(	(	PUNCT
cana-2737	212	12	𝑋2	𝑋2	ADJ
cana-2737	212	13	,	,	PUNCT
cana-2737	212	14	ψ𝑃	ψ𝑃	NOUN
cana-2737	212	15	)	)	PUNCT
cana-2737	212	16	.	.	PUNCT
cana-2737	213	1	since	since	SCONJ
cana-2737	213	2	every	every	DET
cana-2737	213	3	𝑝𝑓𝜃𝑜𝑠	𝑝𝑓𝜃𝑜𝑠	NOUN
cana-2737	213	4	is	be	AUX
cana-2737	213	5	a	a	DET
cana-2737	213	6	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	ADJ
cana-2737	213	7	,	,	PUNCT
cana-2737	213	8	ℎ𝑃(𝐵	ℎ𝑃(𝐵	NUM
cana-2737	213	9	)	)	PUNCT
cana-2737	213	10	is	be	AUX
cana-2737	213	11	a	a	DET
cana-2737	213	12	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-2737	213	13	in	in	ADP
cana-2737	213	14	(	(	PUNCT
cana-2737	213	15	𝑋2	𝑋2	ADJ
cana-2737	213	16	,	,	PUNCT
cana-2737	213	17	ψ𝑃	ψ𝑃	NOUN
cana-2737	213	18	)	)	PUNCT
cana-2737	213	19	.	.	PUNCT
cana-2737	214	1	hence	hence	ADV
cana-2737	214	2	,	,	PUNCT
cana-2737	214	3	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	214	4	is	be	AUX
cana-2737	214	5	a	a	DET
cana-2737	214	6	𝑝𝑓𝑂.	𝑝𝑓𝑂.	NUM
cana-2737	214	7	2	2	NUM
cana-2737	214	8	.	.	PUNCT
cana-2737	215	1	let	let	VERB
cana-2737	215	2	𝐵	𝐵	PRON
cana-2737	215	3	be	be	AUX
cana-2737	215	4	a	a	DET
cana-2737	215	5	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-2737	215	6	in	in	ADP
cana-2737	215	7	(	(	PUNCT
cana-2737	215	8	𝑋1	𝑋1	NOUN
cana-2737	215	9	,	,	PUNCT
cana-2737	215	10	γ𝑃	γ𝑃	NOUN
cana-2737	215	11	)	)	PUNCT
cana-2737	215	12	.	.	PUNCT
cana-2737	216	1	since	since	SCONJ
cana-2737	216	2	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	216	3	is	be	AUX
cana-2737	216	4	𝑝𝑓𝜃𝑂	𝑝𝑓𝜃𝑂	NOUN
cana-2737	216	5	,	,	PUNCT
cana-2737	216	6	ℎ𝑃(𝐵	ℎ𝑃(𝐵	NUM
cana-2737	216	7	)	)	PUNCT
cana-2737	216	8	is	be	AUX
cana-2737	216	9	𝑝𝑓𝜃𝑜𝑠	𝑝𝑓𝜃𝑜𝑠	NOUN
cana-2737	216	10	in	in	ADP
cana-2737	216	11	(	(	PUNCT
cana-2737	216	12	𝑋2	𝑋2	ADJ
cana-2737	216	13	,	,	PUNCT
cana-2737	216	14	ψ𝑃	ψ𝑃	NOUN
cana-2737	216	15	)	)	PUNCT
cana-2737	216	16	.	.	PUNCT
cana-2737	217	1	since	since	SCONJ
cana-2737	217	2	every	every	DET
cana-2737	217	3	𝑝𝑓𝜃𝑜𝑠	𝑝𝑓𝜃𝑜𝑠	NOUN
cana-2737	217	4	is	be	AUX
cana-2737	217	5	a	a	DET
cana-2737	217	6	𝑝𝑓𝜃𝒮𝑜𝑠	𝑝𝑓𝜃𝒮𝑜𝑠	PROPN
cana-2737	217	7	,	,	PUNCT
cana-2737	217	8	ℎ𝑃(𝐵	ℎ𝑃(𝐵	NUM
cana-2737	217	9	)	)	PUNCT
cana-2737	217	10	is	be	AUX
cana-2737	217	11	a	a	DET
cana-2737	217	12	𝑝𝑓𝜃𝒮𝑜𝑠	𝑝𝑓𝜃𝒮𝑜𝑠	PROPN
cana-2737	217	13	in	in	ADP
cana-2737	217	14	(	(	PUNCT
cana-2737	217	15	𝑋2	𝑋2	ADJ
cana-2737	217	16	,	,	PUNCT
cana-2737	217	17	ψ𝑃	ψ𝑃	NOUN
cana-2737	217	18	)	)	PUNCT
cana-2737	217	19	.	.	PUNCT
cana-2737	218	1	hence	hence	ADV
cana-2737	218	2	,	,	PUNCT
cana-2737	218	3	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	218	4	is	be	AUX
cana-2737	218	5	a	a	DET
cana-2737	218	6	𝑝𝑓𝜃𝒮𝑂.	𝑝𝑓𝜃𝒮𝑂.	ADJ
cana-2737	218	7	communications	communication	NOUN
cana-2737	218	8	on	on	ADP
cana-2737	218	9	applied	apply	VERB
cana-2737	218	10	nonlinear	nonlinear	ADJ
cana-2737	218	11	analysis	analysis	NOUN
cana-2737	218	12	issn	issn	NOUN
cana-2737	218	13	:	:	PUNCT
cana-2737	218	14	1074	1074	NUM
cana-2737	218	15	-	-	PUNCT
cana-2737	218	16	133x	133x	NUM
cana-2737	218	17	vol	vol	NOUN
cana-2737	218	18	32	32	NUM
cana-2737	218	19	no	no	NOUN
cana-2737	218	20	.	.	PUNCT
cana-2737	219	1	4s	4s	NUM
cana-2737	219	2	(	(	PUNCT
cana-2737	219	3	2025	2025	NUM
cana-2737	219	4	)	)	PUNCT
cana-2737	219	5	32	32	NUM
cana-2737	219	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2737	219	7	3	3	X
cana-2737	219	8	.	.	PUNCT
cana-2737	219	9	let	let	VERB
cana-2737	219	10	𝐵	𝐵	PRON
cana-2737	219	11	be	be	AUX
cana-2737	219	12	a	a	DET
cana-2737	219	13	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-2737	219	14	in	in	ADP
cana-2737	219	15	(	(	PUNCT
cana-2737	219	16	𝑋1	𝑋1	NOUN
cana-2737	219	17	,	,	PUNCT
cana-2737	219	18	γ𝑃	γ𝑃	NOUN
cana-2737	219	19	)	)	PUNCT
cana-2737	219	20	.	.	PUNCT
cana-2737	220	1	since	since	SCONJ
cana-2737	220	2	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	220	3	is	be	AUX
cana-2737	220	4	𝑝𝑓𝜃𝒮𝑂	𝑝𝑓𝜃𝒮𝑂	NOUN
cana-2737	220	5	,	,	PUNCT
cana-2737	220	6	ℎ𝑃(𝐵	ℎ𝑃(𝐵	NUM
cana-2737	220	7	)	)	PUNCT
cana-2737	220	8	is	be	AUX
cana-2737	220	9	𝑝𝑓𝜃𝒮𝑜𝑠	𝑝𝑓𝜃𝒮𝑜𝑠	PROPN
cana-2737	220	10	in	in	ADP
cana-2737	220	11	(	(	PUNCT
cana-2737	220	12	𝑋2	𝑋2	ADJ
cana-2737	220	13	,	,	PUNCT
cana-2737	220	14	ψ𝑃	ψ𝑃	NOUN
cana-2737	220	15	)	)	PUNCT
cana-2737	220	16	.	.	PUNCT
cana-2737	221	1	since	since	SCONJ
cana-2737	221	2	every	every	DET
cana-2737	221	3	𝑝𝑓𝜃𝒮𝑜𝑠	𝑝𝑓𝜃𝒮𝑜𝑠	PROPN
cana-2737	221	4	is	be	AUX
cana-2737	221	5	a	a	DET
cana-2737	221	6	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	ADJ
cana-2737	221	7	,	,	PUNCT
cana-2737	221	8	ℎ𝑃(𝐵	ℎ𝑃(𝐵	NUM
cana-2737	221	9	)	)	PUNCT
cana-2737	221	10	is	be	AUX
cana-2737	221	11	a	a	DET
cana-2737	221	12	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	NOUN
cana-2737	221	13	in	in	ADP
cana-2737	221	14	(	(	PUNCT
cana-2737	221	15	𝑋2	𝑋2	ADJ
cana-2737	221	16	,	,	PUNCT
cana-2737	221	17	ψ𝑃	ψ𝑃	NOUN
cana-2737	221	18	)	)	PUNCT
cana-2737	221	19	.	.	PUNCT
cana-2737	222	1	hence	hence	ADV
cana-2737	222	2	,	,	PUNCT
cana-2737	222	3	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	222	4	is	be	AUX
cana-2737	222	5	a	a	DET
cana-2737	222	6	𝑝𝑓𝑀𝑂.	𝑝𝑓𝑀𝑂.	NOUN
cana-2737	222	7	4	4	NUM
cana-2737	222	8	.	.	PUNCT
cana-2737	223	1	let	let	VERB
cana-2737	223	2	𝐵	𝐵	PRON
cana-2737	223	3	be	be	AUX
cana-2737	223	4	a	a	DET
cana-2737	223	5	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-2737	223	6	in	in	ADP
cana-2737	223	7	(	(	PUNCT
cana-2737	223	8	𝑋1	𝑋1	NOUN
cana-2737	223	9	,	,	PUNCT
cana-2737	223	10	γ𝑃	γ𝑃	NOUN
cana-2737	223	11	)	)	PUNCT
cana-2737	223	12	.	.	PUNCT
cana-2737	224	1	since	since	SCONJ
cana-2737	224	2	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	224	3	is	be	AUX
cana-2737	224	4	𝑝𝑓𝛿𝑂	𝑝𝑓𝛿𝑂	ADJ
cana-2737	224	5	,	,	PUNCT
cana-2737	224	6	ℎ𝑃(𝐵	ℎ𝑃(𝐵	NUM
cana-2737	224	7	)	)	PUNCT
cana-2737	224	8	is	be	AUX
cana-2737	224	9	𝑝𝑓𝛿𝑜𝑠	𝑝𝑓𝛿𝑜𝑠	NOUN
cana-2737	224	10	in	in	ADP
cana-2737	224	11	(	(	PUNCT
cana-2737	224	12	𝑋2	𝑋2	ADJ
cana-2737	224	13	,	,	PUNCT
cana-2737	224	14	ψ𝑃	ψ𝑃	NOUN
cana-2737	224	15	)	)	PUNCT
cana-2737	224	16	.	.	PUNCT
cana-2737	225	1	since	since	SCONJ
cana-2737	225	2	every	every	DET
cana-2737	225	3	𝑝𝑓𝛿𝑜𝑠	𝑝𝑓𝛿𝑜𝑠	NOUN
cana-2737	225	4	is	be	AUX
cana-2737	225	5	a	a	DET
cana-2737	225	6	𝑝𝑓𝛿𝒮𝑜𝑠	𝑝𝑓𝛿𝒮𝑜𝑠	NOUN
cana-2737	225	7	,	,	PUNCT
cana-2737	225	8	ℎ𝑃(𝐵	ℎ𝑃(𝐵	NUM
cana-2737	225	9	)	)	PUNCT
cana-2737	225	10	is	be	AUX
cana-2737	225	11	a	a	DET
cana-2737	225	12	𝑝𝑓𝛿𝒮𝑜𝑠	𝑝𝑓𝛿𝒮𝑜𝑠	PROPN
cana-2737	225	13	in	in	ADP
cana-2737	225	14	(	(	PUNCT
cana-2737	225	15	𝑋2	𝑋2	ADJ
cana-2737	225	16	,	,	PUNCT
cana-2737	225	17	ψ𝑃	ψ𝑃	NOUN
cana-2737	225	18	)	)	PUNCT
cana-2737	225	19	.	.	PUNCT
cana-2737	226	1	hence	hence	ADV
cana-2737	226	2	,	,	PUNCT
cana-2737	226	3	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	226	4	is	be	AUX
cana-2737	226	5	a	a	DET
cana-2737	226	6	𝑝𝑓𝛿𝒮𝑂.	𝑝𝑓𝛿𝒮𝑂.	ADJ
cana-2737	226	7	5	5	NUM
cana-2737	226	8	.	.	PUNCT
cana-2737	227	1	let	let	VERB
cana-2737	227	2	𝐵	𝐵	PRON
cana-2737	227	3	be	be	AUX
cana-2737	227	4	a	a	DET
cana-2737	227	5	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-2737	227	6	in	in	ADP
cana-2737	227	7	(	(	PUNCT
cana-2737	227	8	𝑋1	𝑋1	NOUN
cana-2737	227	9	,	,	PUNCT
cana-2737	227	10	γ𝑃	γ𝑃	NOUN
cana-2737	227	11	)	)	PUNCT
cana-2737	227	12	.	.	PUNCT
cana-2737	228	1	since	since	SCONJ
cana-2737	228	2	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	228	3	is	be	AUX
cana-2737	228	4	𝑝𝑓𝛿𝑂	𝑝𝑓𝛿𝑂	ADJ
cana-2737	228	5	,	,	PUNCT
cana-2737	228	6	ℎ𝑃(𝐵	ℎ𝑃(𝐵	NUM
cana-2737	228	7	)	)	PUNCT
cana-2737	228	8	is	be	AUX
cana-2737	228	9	𝑝𝑓𝛿𝑜𝑠	𝑝𝑓𝛿𝑜𝑠	NOUN
cana-2737	228	10	in	in	ADP
cana-2737	228	11	(	(	PUNCT
cana-2737	228	12	𝑋2	𝑋2	ADJ
cana-2737	228	13	,	,	PUNCT
cana-2737	228	14	ψ𝑃	ψ𝑃	NOUN
cana-2737	228	15	)	)	PUNCT
cana-2737	228	16	.	.	PUNCT
cana-2737	229	1	since	since	SCONJ
cana-2737	229	2	every	every	DET
cana-2737	229	3	𝑝𝑓𝛿𝑜𝑠	𝑝𝑓𝛿𝑜𝑠	NOUN
cana-2737	229	4	is	be	AUX
cana-2737	229	5	a	a	DET
cana-2737	229	6	𝑝𝑓𝛿𝒫𝑜𝑠	𝑝𝑓𝛿𝒫𝑜𝑠	PROPN
cana-2737	229	7	,	,	PUNCT
cana-2737	229	8	ℎ𝑃(𝐵	ℎ𝑃(𝐵	NUM
cana-2737	229	9	)	)	PUNCT
cana-2737	229	10	is	be	AUX
cana-2737	229	11	a	a	DET
cana-2737	229	12	𝑝𝑓𝛿𝒫𝑜𝑠	𝑝𝑓𝛿𝒫𝑜𝑠	ADJ
cana-2737	229	13	in	in	ADP
cana-2737	229	14	(	(	PUNCT
cana-2737	229	15	𝑋2	𝑋2	ADJ
cana-2737	229	16	,	,	PUNCT
cana-2737	229	17	ψ𝑃	ψ𝑃	NOUN
cana-2737	229	18	)	)	PUNCT
cana-2737	229	19	.	.	PUNCT
cana-2737	230	1	hence	hence	ADV
cana-2737	230	2	,	,	PUNCT
cana-2737	230	3	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	230	4	is	be	AUX
cana-2737	230	5	a	a	DET
cana-2737	230	6	𝑝𝑓𝛿𝒫𝑂.	𝑝𝑓𝛿𝒫𝑂.	PROPN
cana-2737	230	7	6	6	NUM
cana-2737	230	8	.	.	PUNCT
cana-2737	231	1	let	let	VERB
cana-2737	231	2	𝐵	𝐵	PRON
cana-2737	231	3	be	be	AUX
cana-2737	231	4	a	a	DET
cana-2737	231	5	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-2737	231	6	in	in	ADP
cana-2737	231	7	(	(	PUNCT
cana-2737	231	8	𝑋1	𝑋1	NOUN
cana-2737	231	9	,	,	PUNCT
cana-2737	231	10	γ𝑃	γ𝑃	NOUN
cana-2737	231	11	)	)	PUNCT
cana-2737	231	12	.	.	PUNCT
cana-2737	232	1	since	since	SCONJ
cana-2737	232	2	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	232	3	is	be	AUX
cana-2737	232	4	𝑝𝑓𝛿𝒮𝑂	𝑝𝑓𝛿𝒮𝑂	NOUN
cana-2737	232	5	,	,	PUNCT
cana-2737	232	6	ℎ𝑃(𝐵	ℎ𝑃(𝐵	NUM
cana-2737	232	7	)	)	PUNCT
cana-2737	232	8	is	be	AUX
cana-2737	232	9	𝑝𝑓𝛿𝒮𝑜𝑠	𝑝𝑓𝛿𝒮𝑜𝑠	PROPN
cana-2737	232	10	in	in	ADP
cana-2737	232	11	(	(	PUNCT
cana-2737	232	12	𝑋2	𝑋2	ADJ
cana-2737	232	13	,	,	PUNCT
cana-2737	232	14	ψ𝑃	ψ𝑃	NOUN
cana-2737	232	15	)	)	PUNCT
cana-2737	232	16	.	.	PUNCT
cana-2737	233	1	since	since	SCONJ
cana-2737	233	2	every	every	DET
cana-2737	233	3	𝑝𝑓𝛿𝒮𝑜𝑠	𝑝𝑓𝛿𝒮𝑜𝑠	NOUN
cana-2737	233	4	is	be	AUX
cana-2737	233	5	a	a	DET
cana-2737	233	6	𝑝𝑓𝑒𝑜𝑠	𝑝𝑓𝑒𝑜𝑠	NOUN
cana-2737	233	7	,	,	PUNCT
cana-2737	233	8	ℎ𝑃(𝐵	ℎ𝑃(𝐵	NUM
cana-2737	233	9	)	)	PUNCT
cana-2737	233	10	is	be	AUX
cana-2737	233	11	a	a	DET
cana-2737	233	12	𝑝𝑓𝑒𝑜𝑠	𝑝𝑓𝑒𝑜𝑠	NOUN
cana-2737	233	13	in	in	ADP
cana-2737	233	14	(	(	PUNCT
cana-2737	233	15	𝑋2	𝑋2	ADJ
cana-2737	233	16	,	,	PUNCT
cana-2737	233	17	ψ𝑃	ψ𝑃	NOUN
cana-2737	233	18	)	)	PUNCT
cana-2737	233	19	.	.	PUNCT
cana-2737	234	1	hence	hence	ADV
cana-2737	234	2	,	,	PUNCT
cana-2737	234	3	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	234	4	is	be	AUX
cana-2737	234	5	a	a	DET
cana-2737	234	6	𝑝𝑓𝑒𝑂.	𝑝𝑓𝑒𝑂.	NOUN
cana-2737	234	7	7	7	NUM
cana-2737	234	8	.	.	PUNCT
cana-2737	235	1	let	let	VERB
cana-2737	235	2	𝐵	𝐵	PRON
cana-2737	235	3	be	be	AUX
cana-2737	235	4	a	a	DET
cana-2737	235	5	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-2737	235	6	in	in	ADP
cana-2737	235	7	(	(	PUNCT
cana-2737	235	8	𝑋1	𝑋1	NOUN
cana-2737	235	9	,	,	PUNCT
cana-2737	235	10	γ𝑃	γ𝑃	NOUN
cana-2737	235	11	)	)	PUNCT
cana-2737	235	12	.	.	PUNCT
cana-2737	236	1	since	since	SCONJ
cana-2737	236	2	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	236	3	is	be	AUX
cana-2737	236	4	𝑝𝑓𝛿𝒫𝑂	𝑝𝑓𝛿𝒫𝑂	PROPN
cana-2737	236	5	,	,	PUNCT
cana-2737	236	6	ℎ𝑃(𝐵	ℎ𝑃(𝐵	NUM
cana-2737	236	7	)	)	PUNCT
cana-2737	236	8	is	be	AUX
cana-2737	236	9	𝑝𝑓𝛿𝒫𝑜𝑠	𝑝𝑓𝛿𝒫𝑜𝑠	ADJ
cana-2737	236	10	in	in	ADP
cana-2737	236	11	(	(	PUNCT
cana-2737	236	12	𝑋2	𝑋2	ADJ
cana-2737	236	13	,	,	PUNCT
cana-2737	236	14	ψ𝑃	ψ𝑃	NOUN
cana-2737	236	15	)	)	PUNCT
cana-2737	236	16	.	.	PUNCT
cana-2737	237	1	since	since	SCONJ
cana-2737	237	2	every	every	DET
cana-2737	237	3	𝑝𝑓𝛿𝒫𝑜𝑠	𝑝𝑓𝛿𝒫𝑜𝑠	NOUN
cana-2737	237	4	is	be	AUX
cana-2737	237	5	a	a	DET
cana-2737	237	6	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	ADJ
cana-2737	237	7	,	,	PUNCT
cana-2737	237	8	ℎ𝑃(𝐵	ℎ𝑃(𝐵	NUM
cana-2737	237	9	)	)	PUNCT
cana-2737	237	10	is	be	AUX
cana-2737	237	11	a	a	DET
cana-2737	237	12	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	NOUN
cana-2737	237	13	in	in	ADP
cana-2737	237	14	(	(	PUNCT
cana-2737	237	15	𝑋2	𝑋2	ADJ
cana-2737	237	16	,	,	PUNCT
cana-2737	237	17	ψ𝑃	ψ𝑃	NOUN
cana-2737	237	18	)	)	PUNCT
cana-2737	237	19	.	.	PUNCT
cana-2737	238	1	hence	hence	ADV
cana-2737	238	2	,	,	PUNCT
cana-2737	238	3	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	238	4	is	be	AUX
cana-2737	238	5	a	a	DET
cana-2737	238	6	𝑝𝑓𝑀𝑂.	𝑝𝑓𝑀𝑂.	NOUN
cana-2737	238	7	8	8	NUM
cana-2737	238	8	.	.	PUNCT
cana-2737	239	1	let	let	VERB
cana-2737	239	2	𝐵	𝐵	PRON
cana-2737	239	3	be	be	AUX
cana-2737	239	4	a	a	DET
cana-2737	239	5	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-2737	239	6	in	in	ADP
cana-2737	239	7	(	(	PUNCT
cana-2737	239	8	𝑋1	𝑋1	NOUN
cana-2737	239	9	,	,	PUNCT
cana-2737	239	10	γ𝑃	γ𝑃	NOUN
cana-2737	239	11	)	)	PUNCT
cana-2737	239	12	.	.	PUNCT
cana-2737	240	1	since	since	SCONJ
cana-2737	240	2	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	240	3	is	be	AUX
cana-2737	240	4	𝑝𝑓𝑀𝑂	𝑝𝑓𝑀𝑂	VERB
cana-2737	240	5	,	,	PUNCT
cana-2737	240	6	ℎ𝑃(𝐵	ℎ𝑃(𝐵	NUM
cana-2737	240	7	)	)	PUNCT
cana-2737	240	8	is	be	AUX
cana-2737	240	9	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	ADJ
cana-2737	240	10	in	in	ADP
cana-2737	240	11	(	(	PUNCT
cana-2737	240	12	𝑋2	𝑋2	ADJ
cana-2737	240	13	,	,	PUNCT
cana-2737	240	14	ψ𝑃	ψ𝑃	NOUN
cana-2737	240	15	)	)	PUNCT
cana-2737	240	16	.	.	PUNCT
cana-2737	241	1	since	since	SCONJ
cana-2737	241	2	every	every	DET
cana-2737	241	3	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	NOUN
cana-2737	241	4	is	be	AUX
cana-2737	241	5	a	a	DET
cana-2737	241	6	𝑝𝑓𝑒𝑜𝑠	𝑝𝑓𝑒𝑜𝑠	NOUN
cana-2737	241	7	,	,	PUNCT
cana-2737	241	8	ℎ𝑃(𝐵	ℎ𝑃(𝐵	NUM
cana-2737	241	9	)	)	PUNCT
cana-2737	241	10	is	be	AUX
cana-2737	241	11	a	a	DET
cana-2737	241	12	𝑝𝑓𝑒𝑜𝑠	𝑝𝑓𝑒𝑜𝑠	NOUN
cana-2737	241	13	in	in	ADP
cana-2737	241	14	(	(	PUNCT
cana-2737	241	15	𝑋2	𝑋2	ADJ
cana-2737	241	16	,	,	PUNCT
cana-2737	241	17	ψ𝑃	ψ𝑃	NOUN
cana-2737	241	18	)	)	PUNCT
cana-2737	241	19	.	.	PUNCT
cana-2737	242	1	hence	hence	ADV
cana-2737	242	2	,	,	PUNCT
cana-2737	242	3	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	242	4	is	be	AUX
cana-2737	242	5	a	a	DET
cana-2737	242	6	𝑝𝑓𝑒𝑂.	𝑝𝑓𝑒𝑂.	NOUN
cana-2737	242	7	9	9	NUM
cana-2737	242	8	.	.	PUNCT
cana-2737	243	1	let	let	VERB
cana-2737	243	2	𝐵	𝐵	PRON
cana-2737	243	3	be	be	AUX
cana-2737	243	4	a	a	DET
cana-2737	243	5	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-2737	243	6	in	in	ADP
cana-2737	243	7	(	(	PUNCT
cana-2737	243	8	𝑋1	𝑋1	NOUN
cana-2737	243	9	,	,	PUNCT
cana-2737	243	10	γ𝑃	γ𝑃	NOUN
cana-2737	243	11	)	)	PUNCT
cana-2737	243	12	.	.	PUNCT
cana-2737	244	1	since	since	SCONJ
cana-2737	244	2	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	244	3	is	be	AUX
cana-2737	244	4	𝑝𝑓𝛿𝑂	𝑝𝑓𝛿𝑂	ADJ
cana-2737	244	5	,	,	PUNCT
cana-2737	244	6	ℎ𝑃(𝐵	ℎ𝑃(𝐵	NUM
cana-2737	244	7	)	)	PUNCT
cana-2737	244	8	is	be	AUX
cana-2737	244	9	𝑝𝑓𝛿𝑜𝑠	𝑝𝑓𝛿𝑜𝑠	NOUN
cana-2737	244	10	in	in	ADP
cana-2737	244	11	(	(	PUNCT
cana-2737	244	12	𝑋2	𝑋2	ADJ
cana-2737	244	13	,	,	PUNCT
cana-2737	244	14	ψ𝑃	ψ𝑃	NOUN
cana-2737	244	15	)	)	PUNCT
cana-2737	244	16	.	.	PUNCT
cana-2737	245	1	since	since	SCONJ
cana-2737	245	2	every	every	DET
cana-2737	245	3	𝑝𝑓𝛿𝑜𝑠	𝑝𝑓𝛿𝑜𝑠	NOUN
cana-2737	245	4	is	be	AUX
cana-2737	245	5	a	a	DET
cana-2737	245	6	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	ADJ
cana-2737	245	7	,	,	PUNCT
cana-2737	245	8	ℎ𝑃(𝐵	ℎ𝑃(𝐵	NUM
cana-2737	245	9	)	)	PUNCT
cana-2737	245	10	is	be	AUX
cana-2737	245	11	a	a	DET
cana-2737	245	12	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-2737	245	13	in	in	ADP
cana-2737	245	14	(	(	PUNCT
cana-2737	245	15	𝑋2	𝑋2	ADJ
cana-2737	245	16	,	,	PUNCT
cana-2737	245	17	ψ𝑃	ψ𝑃	NOUN
cana-2737	245	18	)	)	PUNCT
cana-2737	245	19	.	.	PUNCT
cana-2737	246	1	hence	hence	ADV
cana-2737	246	2	,	,	PUNCT
cana-2737	246	3	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	246	4	is	be	AUX
cana-2737	246	5	a	a	DET
cana-2737	246	6	𝑝𝑓𝑂	𝑝𝑓𝑂	ADJ
cana-2737	246	7	remark	remark	NOUN
cana-2737	246	8	3.1	3.1	NUM
cana-2737	246	9	we	we	PRON
cana-2737	246	10	obtain	obtain	VERB
cana-2737	246	11	the	the	DET
cana-2737	246	12	following	follow	VERB
cana-2737	246	13	diagram	diagram	NOUN
cana-2737	246	14	from	from	ADP
cana-2737	246	15	the	the	DET
cana-2737	246	16	results	result	NOUN
cana-2737	246	17	are	be	AUX
cana-2737	246	18	discussed	discuss	VERB
cana-2737	246	19	above	above	ADV
cana-2737	246	20	.	.	PUNCT
cana-2737	247	1	note	note	NOUN
cana-2737	247	2	:	:	PUNCT
cana-2737	247	3	𝐴	𝐴	PROPN
cana-2737	247	4	→	→	SYM
cana-2737	247	5	𝐵	𝐵	PROPN
cana-2737	247	6	denotes	denote	NOUN
cana-2737	247	7	𝐴	𝐴	PROPN
cana-2737	247	8	implies	imply	VERB
cana-2737	247	9	𝐵	𝐵	PROPN
cana-2737	247	10	,	,	PUNCT
cana-2737	247	11	but	but	CCONJ
cana-2737	247	12	not	not	PART
cana-2737	247	13	conversely	conversely	ADV
cana-2737	247	14	.	.	PUNCT
cana-2737	248	1	example	example	NOUN
cana-2737	248	2	3.1	3.1	NUM
cana-2737	248	3	let	let	VERB
cana-2737	248	4	𝑋1	𝑋1	NOUN
cana-2737	248	5	=	=	SYM
cana-2737	248	6	𝑋2	𝑋2	VERB
cana-2737	248	7	=	=	PUNCT
cana-2737	248	8	{	{	PUNCT
cana-2737	248	9	𝑥1	𝑥1	NOUN
cana-2737	248	10	,	,	PUNCT
cana-2737	248	11	𝑥2	𝑥2	NOUN
cana-2737	248	12	}	}	PUNCT
cana-2737	248	13	and	and	CCONJ
cana-2737	248	14	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2737	248	15	’s	’s	PART
cana-2737	248	16	𝐴1	𝐴1	PROPN
cana-2737	248	17	,	,	PUNCT
cana-2737	248	18	𝐴2	𝐴2	PROPN
cana-2737	248	19	,	,	PUNCT
cana-2737	248	20	𝐴3	𝐴3	PROPN
cana-2737	248	21	&	&	CCONJ
cana-2737	248	22	𝐴4	𝐴4	PROPN
cana-2737	248	23	in	in	ADP
cana-2737	248	24	𝑋1	𝑋1	PROPN
cana-2737	248	25	are	be	AUX
cana-2737	248	26	defined	define	VERB
cana-2737	248	27	as	as	ADP
cana-2737	248	28	,	,	PUNCT
cana-2737	248	29	𝐴1	𝐴1	PROPN
cana-2737	248	30	=	=	SYM
cana-2737	248	31	{	{	PUNCT
cana-2737	248	32	<	<	X
cana-2737	248	33	𝑥1	𝑥1	PROPN
cana-2737	248	34	,	,	PUNCT
cana-2737	248	35	0.20,0.80	0.20,0.80	NOUN
cana-2737	248	36	>	>	X
cana-2737	248	37	,	,	PUNCT
cana-2737	248	38	<	<	X
cana-2737	248	39	𝑥2	𝑥2	NOUN
cana-2737	248	40	,	,	PUNCT
cana-2737	248	41	0.40,0.60	0.40,0.60	NUM
cana-2737	248	42	>	>	PUNCT
cana-2737	248	43	}	}	PUNCT
cana-2737	248	44	𝐴2	𝐴2	PROPN
cana-2737	248	45	=	=	SYM
cana-2737	248	46	{	{	PUNCT
cana-2737	248	47	<	<	X
cana-2737	248	48	𝑥1	𝑥1	PROPN
cana-2737	248	49	,	,	PUNCT
cana-2737	248	50	0.10,0.90	0.10,0.90	NUM
cana-2737	248	51	>	>	X
cana-2737	248	52	,	,	PUNCT
cana-2737	248	53	<	<	X
cana-2737	248	54	𝑥2	𝑥2	NOUN
cana-2737	248	55	,	,	PUNCT
cana-2737	248	56	0.30,0.70	0.30,0.70	PRON
cana-2737	248	57	>	>	PUNCT
cana-2737	248	58	}	}	PUNCT
cana-2737	248	59	𝐴3	𝐴3	PROPN
cana-2737	249	1	=	=	SYM
cana-2737	249	2	{	{	PUNCT
cana-2737	249	3	<	<	X
cana-2737	249	4	𝑥1	𝑥1	PROPN
cana-2737	249	5	,	,	PUNCT
cana-2737	249	6	0.90,0.10	0.90,0.10	NOUN
cana-2737	249	7	>	>	X
cana-2737	249	8	,	,	PUNCT
cana-2737	249	9	<	<	X
cana-2737	249	10	𝑥2	𝑥2	NOUN
cana-2737	249	11	,	,	PUNCT
cana-2737	249	12	0.70,0.30	0.70,0.30	NOUN
cana-2737	249	13	>	>	PUNCT
cana-2737	249	14	}	}	PUNCT
cana-2737	249	15	communications	communication	NOUN
cana-2737	249	16	on	on	ADP
cana-2737	249	17	applied	apply	VERB
cana-2737	249	18	nonlinear	nonlinear	ADJ
cana-2737	249	19	analysis	analysis	NOUN
cana-2737	249	20	issn	issn	NOUN
cana-2737	249	21	:	:	PUNCT
cana-2737	249	22	1074	1074	NUM
cana-2737	249	23	-	-	PUNCT
cana-2737	249	24	133x	133x	NUM
cana-2737	249	25	vol	vol	NOUN
cana-2737	249	26	32	32	NUM
cana-2737	249	27	no	no	NOUN
cana-2737	249	28	.	.	PUNCT
cana-2737	250	1	4s	4s	NUM
cana-2737	250	2	(	(	PUNCT
cana-2737	250	3	2025	2025	NUM
cana-2737	250	4	)	)	PUNCT
cana-2737	250	5	33	33	NUM
cana-2737	250	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2737	250	7	𝐴4	𝐴4	NOUN
cana-2737	250	8	=	=	PUNCT
cana-2737	250	9	{	{	PUNCT
cana-2737	250	10	<	<	X
cana-2737	250	11	𝑥1	𝑥1	PROPN
cana-2737	250	12	,	,	PUNCT
cana-2737	250	13	0.20,0.80	0.20,0.80	NOUN
cana-2737	250	14	>	>	X
cana-2737	250	15	,	,	PUNCT
cana-2737	250	16	<	<	X
cana-2737	250	17	𝑥2	𝑥2	NOUN
cana-2737	250	18	,	,	PUNCT
cana-2737	250	19	0.30,0.70	0.30,0.70	PRON
cana-2737	250	20	>	>	PUNCT
cana-2737	250	21	}	}	PUNCT
cana-2737	250	22	now	now	ADV
cana-2737	250	23	,	,	PUNCT
cana-2737	250	24	we	we	PRON
cana-2737	250	25	have	have	VERB
cana-2737	250	26	γ𝑃	γ𝑃	ADJ
cana-2737	250	27	=	=	PUNCT
cana-2737	250	28	ψ𝑃	ψ𝑃	NOUN
cana-2737	250	29	=	=	SYM
cana-2737	250	30	{	{	PUNCT
cana-2737	250	31	0𝑋	0𝑋	PROPN
cana-2737	250	32	,	,	PUNCT
cana-2737	250	33	1𝑋	1𝑋	PROPN
cana-2737	250	34	,	,	PUNCT
cana-2737	250	35	𝐴1	𝐴1	PROPN
cana-2737	250	36	,	,	PUNCT
cana-2737	250	37	𝐴2	𝐴2	PROPN
cana-2737	250	38	,	,	PUNCT
cana-2737	250	39	𝐴3	𝐴3	PROPN
cana-2737	250	40	,	,	PUNCT
cana-2737	250	41	𝐴4	𝐴4	PROPN
cana-2737	250	42	}	}	PUNCT
cana-2737	250	43	.	.	PUNCT
cana-2737	251	1	let	let	VERB
cana-2737	251	2	ℎ𝑃	ℎ𝑃	NOUN
cana-2737	251	3	:	:	PUNCT
cana-2737	251	4	(	(	PUNCT
cana-2737	251	5	𝑋1	𝑋1	NOUN
cana-2737	251	6	,	,	PUNCT
cana-2737	251	7	γ𝑃	γ𝑃	NOUN
cana-2737	251	8	)	)	PUNCT
cana-2737	251	9	→	→	SYM
cana-2737	251	10	(	(	PUNCT
cana-2737	251	11	𝑋2	𝑋2	ADJ
cana-2737	251	12	,	,	PUNCT
cana-2737	251	13	ψ𝑃	ψ𝑃	NOUN
cana-2737	251	14	)	)	PUNCT
cana-2737	251	15	be	be	VERB
cana-2737	251	16	an	an	DET
cana-2737	251	17	identity	identity	NOUN
cana-2737	251	18	mapping	mapping	NOUN
cana-2737	251	19	.	.	PUNCT
cana-2737	252	1	then	then	ADV
cana-2737	252	2	,	,	PUNCT
cana-2737	252	3	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	252	4	is	be	AUX
cana-2737	252	5	𝑝𝑓𝑂	𝑝𝑓𝑂	ADJ
cana-2737	252	6	but	but	CCONJ
cana-2737	252	7	not	not	PART
cana-2737	252	8	𝑝𝑓𝜃𝑂	𝑝𝑓𝜃𝑂	NOUN
cana-2737	252	9	,	,	PUNCT
cana-2737	252	10	because	because	SCONJ
cana-2737	252	11	the	the	DET
cana-2737	252	12	set	set	NOUN
cana-2737	252	13	𝐴1	𝐴1	PROPN
cana-2737	252	14	is	be	AUX
cana-2737	252	15	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	ADJ
cana-2737	252	16	in	in	ADP
cana-2737	252	17	𝑋1	𝑋1	NOUN
cana-2737	252	18	but	but	CCONJ
cana-2737	252	19	ℎ𝑃(𝐴1	ℎ𝑃(𝐴1	NOUN
cana-2737	252	20	)	)	PUNCT
cana-2737	253	1	=	=	SYM
cana-2737	253	2	𝐴1	𝐴1	PROPN
cana-2737	253	3	is	be	AUX
cana-2737	253	4	not	not	PART
cana-2737	253	5	𝑝𝑓𝜃𝑜𝑠	𝑝𝑓𝜃𝑜𝑠	NOUN
cana-2737	253	6	in	in	ADP
cana-2737	253	7	𝑋2	𝑋2	PROPN
cana-2737	253	8	.	.	PUNCT
cana-2737	254	1	example	example	NOUN
cana-2737	254	2	3.2	3.2	NUM
cana-2737	254	3	let	let	VERB
cana-2737	254	4	𝑋1	𝑋1	NOUN
cana-2737	254	5	=	=	SYM
cana-2737	254	6	𝑋2	𝑋2	VERB
cana-2737	254	7	=	=	PUNCT
cana-2737	254	8	{	{	PUNCT
cana-2737	254	9	𝑥1	𝑥1	NOUN
cana-2737	254	10	,	,	PUNCT
cana-2737	254	11	𝑥2	𝑥2	NOUN
cana-2737	254	12	}	}	PUNCT
cana-2737	254	13	and	and	CCONJ
cana-2737	254	14	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2737	254	15	’s	’s	PART
cana-2737	254	16	𝐴1	𝐴1	PROPN
cana-2737	254	17	,	,	PUNCT
cana-2737	254	18	𝐴2	𝐴2	PROPN
cana-2737	254	19	,	,	PUNCT
cana-2737	254	20	𝐴3	𝐴3	PROPN
cana-2737	254	21	,	,	PUNCT
cana-2737	254	22	𝐴4	𝐴4	PROPN
cana-2737	254	23	in	in	ADP
cana-2737	254	24	𝑋2	𝑋2	PROPN
cana-2737	254	25	&	&	CCONJ
cana-2737	254	26	𝐵1	𝐵1	PROPN
cana-2737	254	27	in	in	ADP
cana-2737	254	28	𝑋1	𝑋1	PROPN
cana-2737	254	29	are	be	AUX
cana-2737	254	30	defined	define	VERB
cana-2737	254	31	as	as	ADP
cana-2737	254	32	,	,	PUNCT
cana-2737	254	33	𝐴1	𝐴1	PROPN
cana-2737	254	34	=	=	SYM
cana-2737	254	35	{	{	PUNCT
cana-2737	254	36	<	<	X
cana-2737	254	37	𝑥1	𝑥1	PROPN
cana-2737	254	38	,	,	PUNCT
cana-2737	254	39	0.20,0.80	0.20,0.80	NOUN
cana-2737	254	40	>	>	X
cana-2737	254	41	,	,	PUNCT
cana-2737	254	42	<	<	X
cana-2737	254	43	𝑥2	𝑥2	NOUN
cana-2737	254	44	,	,	PUNCT
cana-2737	254	45	0.40,0.60	0.40,0.60	NUM
cana-2737	254	46	>	>	PUNCT
cana-2737	254	47	}	}	PUNCT
cana-2737	254	48	𝐴2	𝐴2	PROPN
cana-2737	254	49	=	=	SYM
cana-2737	254	50	{	{	PUNCT
cana-2737	254	51	<	<	X
cana-2737	254	52	𝑥1	𝑥1	PROPN
cana-2737	254	53	,	,	PUNCT
cana-2737	254	54	0.10,0.90	0.10,0.90	NUM
cana-2737	254	55	>	>	X
cana-2737	254	56	,	,	PUNCT
cana-2737	254	57	<	<	X
cana-2737	254	58	𝑥2	𝑥2	NOUN
cana-2737	254	59	,	,	PUNCT
cana-2737	254	60	0.30,0.70	0.30,0.70	PRON
cana-2737	254	61	>	>	PUNCT
cana-2737	254	62	}	}	PUNCT
cana-2737	254	63	𝐴3	𝐴3	PROPN
cana-2737	255	1	=	=	SYM
cana-2737	255	2	{	{	PUNCT
cana-2737	255	3	<	<	X
cana-2737	255	4	𝑥1	𝑥1	PROPN
cana-2737	255	5	,	,	PUNCT
cana-2737	255	6	0.90,0.10	0.90,0.10	NOUN
cana-2737	255	7	>	>	X
cana-2737	255	8	,	,	PUNCT
cana-2737	255	9	<	<	X
cana-2737	255	10	𝑥2	𝑥2	NOUN
cana-2737	255	11	,	,	PUNCT
cana-2737	255	12	0.70,0.30	0.70,0.30	NOUN
cana-2737	255	13	>	>	PUNCT
cana-2737	255	14	}	}	PUNCT
cana-2737	255	15	𝐴4	𝐴4	PROPN
cana-2737	255	16	=	=	PUNCT
cana-2737	255	17	{	{	PUNCT
cana-2737	255	18	<	<	X
cana-2737	255	19	𝑥1	𝑥1	PROPN
cana-2737	255	20	,	,	PUNCT
cana-2737	255	21	0.20,0.80	0.20,0.80	NOUN
cana-2737	255	22	>	>	X
cana-2737	255	23	,	,	PUNCT
cana-2737	255	24	<	<	X
cana-2737	255	25	𝑥2	𝑥2	NOUN
cana-2737	255	26	,	,	PUNCT
cana-2737	255	27	0.30,0.70	0.30,0.70	PRON
cana-2737	255	28	>	>	PUNCT
cana-2737	255	29	}	}	PUNCT
cana-2737	255	30	𝐵1	𝐵1	NOUN
cana-2737	255	31	=	=	PUNCT
cana-2737	255	32	{	{	PUNCT
cana-2737	255	33	<	<	X
cana-2737	255	34	𝑥1	𝑥1	PROPN
cana-2737	255	35	,	,	PUNCT
cana-2737	255	36	0.80,0.20	0.80,0.20	X
cana-2737	255	37	>	>	X
cana-2737	255	38	,	,	PUNCT
cana-2737	255	39	<	<	X
cana-2737	255	40	𝑥2	𝑥2	NOUN
cana-2737	255	41	,	,	PUNCT
cana-2737	255	42	0.60,0.40	0.60,0.40	X
cana-2737	255	43	>	>	PUNCT
cana-2737	255	44	}	}	PUNCT
cana-2737	255	45	now	now	ADV
cana-2737	255	46	,	,	PUNCT
cana-2737	255	47	we	we	PRON
cana-2737	255	48	have	have	VERB
cana-2737	255	49	γ𝑃	γ𝑃	ADJ
cana-2737	255	50	=	=	PUNCT
cana-2737	255	51	{	{	PUNCT
cana-2737	255	52	0𝑋	0𝑋	PROPN
cana-2737	255	53	,	,	PUNCT
cana-2737	255	54	1𝑋	1𝑋	PROPN
cana-2737	255	55	,	,	PUNCT
cana-2737	255	56	𝐵1	𝐵1	PROPN
cana-2737	255	57	}	}	PUNCT
cana-2737	255	58	and	and	CCONJ
cana-2737	255	59	ψ𝑃	ψ𝑃	NOUN
cana-2737	255	60	=	=	SYM
cana-2737	255	61	{	{	PUNCT
cana-2737	255	62	0𝑋	0𝑋	PROPN
cana-2737	255	63	,	,	PUNCT
cana-2737	255	64	1𝑋	1𝑋	PROPN
cana-2737	255	65	,	,	PUNCT
cana-2737	255	66	𝐴1	𝐴1	PROPN
cana-2737	255	67	,	,	PUNCT
cana-2737	255	68	𝐴2	𝐴2	PROPN
cana-2737	255	69	,	,	PUNCT
cana-2737	255	70	𝐴3	𝐴3	PROPN
cana-2737	255	71	,	,	PUNCT
cana-2737	255	72	𝐴4	𝐴4	PROPN
cana-2737	255	73	}	}	PUNCT
cana-2737	255	74	.	.	PUNCT
cana-2737	256	1	let	let	VERB
cana-2737	256	2	ℎ𝑃	ℎ𝑃	NOUN
cana-2737	256	3	:	:	PUNCT
cana-2737	256	4	(	(	PUNCT
cana-2737	256	5	𝑋1	𝑋1	NOUN
cana-2737	256	6	,	,	PUNCT
cana-2737	256	7	γ𝑃	γ𝑃	NOUN
cana-2737	256	8	)	)	PUNCT
cana-2737	256	9	→	→	SYM
cana-2737	256	10	(	(	PUNCT
cana-2737	256	11	𝑋2	𝑋2	ADJ
cana-2737	256	12	,	,	PUNCT
cana-2737	256	13	ψ𝑃	ψ𝑃	NOUN
cana-2737	256	14	)	)	PUNCT
cana-2737	256	15	be	be	VERB
cana-2737	256	16	an	an	DET
cana-2737	256	17	identity	identity	NOUN
cana-2737	256	18	mapping	mapping	NOUN
cana-2737	256	19	.	.	PUNCT
cana-2737	257	1	then	then	ADV
cana-2737	257	2	,	,	PUNCT
cana-2737	257	3	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	257	4	is	be	AUX
cana-2737	257	5	𝑝𝑓𝜃𝒮𝑂	𝑝𝑓𝜃𝒮𝑂	NOUN
cana-2737	257	6	(	(	PUNCT
cana-2737	257	7	resp	resp	NOUN
cana-2737	257	8	.	.	PUNCT
cana-2737	257	9	𝑝𝑓𝛿𝒮𝑂	𝑝𝑓𝛿𝒮𝑂	PROPN
cana-2737	257	10	)	)	PUNCT
cana-2737	257	11	but	but	CCONJ
cana-2737	257	12	not	not	PART
cana-2737	257	13	𝑝𝑓𝜃𝑂	𝑝𝑓𝜃𝑂	INTJ
cana-2737	257	14	(	(	PUNCT
cana-2737	257	15	resp	resp	NOUN
cana-2737	257	16	.	.	PUNCT
cana-2737	258	1	𝑝𝑓𝛿𝑂	𝑝𝑓𝛿𝑂	NOUN
cana-2737	258	2	)	)	PUNCT
cana-2737	258	3	,	,	PUNCT
cana-2737	258	4	because	because	SCONJ
cana-2737	258	5	the	the	DET
cana-2737	258	6	set	set	NOUN
cana-2737	258	7	𝐵1	𝐵1	NOUN
cana-2737	258	8	is	be	AUX
cana-2737	258	9	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	ADJ
cana-2737	258	10	in	in	ADP
cana-2737	258	11	𝑋1	𝑋1	PROPN
cana-2737	258	12	but	but	CCONJ
cana-2737	258	13	ℎ𝑃(𝐵1	ℎ𝑃(𝐵1	NOUN
cana-2737	258	14	)	)	PUNCT
cana-2737	259	1	=	=	SYM
cana-2737	259	2	𝐵1	𝐵1	NOUN
cana-2737	259	3	is	be	AUX
cana-2737	259	4	not	not	PART
cana-2737	259	5	𝑝𝑓𝜃𝑜𝑠	𝑝𝑓𝜃𝑜𝑠	NOUN
cana-2737	259	6	(	(	PUNCT
cana-2737	259	7	resp	resp	PROPN
cana-2737	259	8	.	.	PUNCT
cana-2737	259	9	𝑝𝑓𝛿𝑜𝑠	𝑝𝑓𝛿𝑜𝑠	PROPN
cana-2737	259	10	)	)	PUNCT
cana-2737	259	11	in	in	ADP
cana-2737	259	12	𝑋2	𝑋2	PROPN
cana-2737	259	13	.	.	PUNCT
cana-2737	260	1	example	example	NOUN
cana-2737	260	2	3.3	3.3	NUM
cana-2737	260	3	let	let	VERB
cana-2737	260	4	𝑋1	𝑋1	NOUN
cana-2737	260	5	=	=	SYM
cana-2737	260	6	𝑋2	𝑋2	VERB
cana-2737	260	7	=	=	PUNCT
cana-2737	260	8	{	{	PUNCT
cana-2737	260	9	𝑥1	𝑥1	NOUN
cana-2737	260	10	,	,	PUNCT
cana-2737	260	11	𝑥2	𝑥2	NOUN
cana-2737	260	12	}	}	PUNCT
cana-2737	260	13	and	and	CCONJ
cana-2737	260	14	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2737	260	15	’s	’s	PART
cana-2737	260	16	𝐴1	𝐴1	PROPN
cana-2737	260	17	,	,	PUNCT
cana-2737	260	18	𝐴2	𝐴2	PROPN
cana-2737	260	19	,	,	PUNCT
cana-2737	260	20	𝐴3	𝐴3	PROPN
cana-2737	260	21	,	,	PUNCT
cana-2737	260	22	𝐴4	𝐴4	PROPN
cana-2737	260	23	in	in	ADP
cana-2737	260	24	𝑋2	𝑋2	PROPN
cana-2737	260	25	&	&	CCONJ
cana-2737	260	26	𝐵1	𝐵1	PROPN
cana-2737	260	27	in	in	ADP
cana-2737	260	28	𝑋1	𝑋1	PROPN
cana-2737	260	29	are	be	AUX
cana-2737	260	30	defined	define	VERB
cana-2737	260	31	as	as	ADP
cana-2737	260	32	,	,	PUNCT
cana-2737	260	33	𝐴1	𝐴1	PROPN
cana-2737	260	34	=	=	PUNCT
cana-2737	260	35	𝐵1	𝐵1	PROPN
cana-2737	260	36	=	=	SYM
cana-2737	260	37	{	{	PUNCT
cana-2737	260	38	<	<	X
cana-2737	260	39	𝑥1	𝑥1	PROPN
cana-2737	260	40	,	,	PUNCT
cana-2737	260	41	0.20,0.80	0.20,0.80	NOUN
cana-2737	260	42	>	>	X
cana-2737	260	43	,	,	PUNCT
cana-2737	260	44	<	<	X
cana-2737	260	45	𝑥2	𝑥2	NOUN
cana-2737	260	46	,	,	PUNCT
cana-2737	260	47	0.40,0.60	0.40,0.60	NUM
cana-2737	260	48	>	>	PUNCT
cana-2737	260	49	}	}	PUNCT
cana-2737	260	50	𝐴2	𝐴2	PROPN
cana-2737	260	51	=	=	SYM
cana-2737	260	52	{	{	PUNCT
cana-2737	260	53	<	<	X
cana-2737	260	54	𝑥1	𝑥1	PROPN
cana-2737	260	55	,	,	PUNCT
cana-2737	260	56	0.10,0.90	0.10,0.90	NUM
cana-2737	260	57	>	>	X
cana-2737	260	58	,	,	PUNCT
cana-2737	260	59	<	<	X
cana-2737	260	60	𝑥2	𝑥2	NOUN
cana-2737	260	61	,	,	PUNCT
cana-2737	260	62	0.30,0.70	0.30,0.70	PRON
cana-2737	260	63	>	>	PUNCT
cana-2737	260	64	}	}	PUNCT
cana-2737	260	65	𝐴3	𝐴3	PROPN
cana-2737	260	66	=	=	SYM
cana-2737	260	67	{	{	PUNCT
cana-2737	260	68	<	<	X
cana-2737	260	69	𝑥1	𝑥1	PROPN
cana-2737	260	70	,	,	PUNCT
cana-2737	260	71	0.90,0.10	0.90,0.10	NOUN
cana-2737	260	72	>	>	X
cana-2737	260	73	,	,	PUNCT
cana-2737	260	74	<	<	X
cana-2737	260	75	𝑥2	𝑥2	NOUN
cana-2737	260	76	,	,	PUNCT
cana-2737	260	77	0.70,0.30	0.70,0.30	NOUN
cana-2737	260	78	>	>	PUNCT
cana-2737	260	79	}	}	PUNCT
cana-2737	260	80	𝐴4	𝐴4	PROPN
cana-2737	260	81	=	=	PUNCT
cana-2737	260	82	{	{	PUNCT
cana-2737	260	83	<	<	X
cana-2737	260	84	𝑥1	𝑥1	PROPN
cana-2737	260	85	,	,	PUNCT
cana-2737	260	86	0.20,0.80	0.20,0.80	NOUN
cana-2737	260	87	>	>	X
cana-2737	260	88	,	,	PUNCT
cana-2737	260	89	<	<	X
cana-2737	260	90	𝑥2	𝑥2	NOUN
cana-2737	260	91	,	,	PUNCT
cana-2737	260	92	0.30,0.70	0.30,0.70	PRON
cana-2737	260	93	>	>	PUNCT
cana-2737	260	94	}	}	PUNCT
cana-2737	260	95	now	now	ADV
cana-2737	260	96	,	,	PUNCT
cana-2737	260	97	we	we	PRON
cana-2737	260	98	have	have	VERB
cana-2737	260	99	γ𝑃	γ𝑃	ADJ
cana-2737	260	100	=	=	PUNCT
cana-2737	260	101	{	{	PUNCT
cana-2737	260	102	0𝑋	0𝑋	PROPN
cana-2737	260	103	,	,	PUNCT
cana-2737	260	104	1𝑋	1𝑋	PROPN
cana-2737	260	105	,	,	PUNCT
cana-2737	260	106	𝐵1	𝐵1	PROPN
cana-2737	260	107	}	}	PUNCT
cana-2737	260	108	and	and	CCONJ
cana-2737	260	109	ψ𝑃	ψ𝑃	NOUN
cana-2737	260	110	=	=	SYM
cana-2737	260	111	{	{	PUNCT
cana-2737	260	112	0𝑋	0𝑋	PROPN
cana-2737	260	113	,	,	PUNCT
cana-2737	260	114	1𝑋	1𝑋	PROPN
cana-2737	260	115	,	,	PUNCT
cana-2737	260	116	𝐴1	𝐴1	PROPN
cana-2737	260	117	,	,	PUNCT
cana-2737	260	118	𝐴2	𝐴2	PROPN
cana-2737	260	119	,	,	PUNCT
cana-2737	260	120	𝐴3	𝐴3	PROPN
cana-2737	260	121	,	,	PUNCT
cana-2737	260	122	𝐴4	𝐴4	PROPN
cana-2737	260	123	}	}	PUNCT
cana-2737	260	124	.	.	PUNCT
cana-2737	261	1	let	let	VERB
cana-2737	261	2	ℎ𝑃	ℎ𝑃	NOUN
cana-2737	261	3	:	:	PUNCT
cana-2737	261	4	(	(	PUNCT
cana-2737	261	5	𝑋1	𝑋1	NOUN
cana-2737	261	6	,	,	PUNCT
cana-2737	261	7	γ𝑃	γ𝑃	NOUN
cana-2737	261	8	)	)	PUNCT
cana-2737	261	9	→	→	SYM
cana-2737	261	10	(	(	PUNCT
cana-2737	261	11	𝑋2	𝑋2	ADJ
cana-2737	261	12	,	,	PUNCT
cana-2737	261	13	ψ𝑃	ψ𝑃	NOUN
cana-2737	261	14	)	)	PUNCT
cana-2737	261	15	be	be	VERB
cana-2737	261	16	an	an	DET
cana-2737	261	17	identity	identity	NOUN
cana-2737	261	18	mapping	mapping	NOUN
cana-2737	261	19	.	.	PUNCT
cana-2737	262	1	then	then	ADV
cana-2737	262	2	,	,	PUNCT
cana-2737	262	3	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	262	4	is	be	AUX
cana-2737	262	5	𝑝𝑓𝑀𝑂	𝑝𝑓𝑀𝑂	NOUN
cana-2737	262	6	but	but	CCONJ
cana-2737	262	7	not	not	PART
cana-2737	262	8	𝑝𝑓𝜃𝒮𝑂	𝑝𝑓𝜃𝒮𝑂	NOUN
cana-2737	262	9	,	,	PUNCT
cana-2737	262	10	because	because	SCONJ
cana-2737	262	11	the	the	DET
cana-2737	262	12	set	set	NOUN
cana-2737	262	13	𝐵1	𝐵1	NOUN
cana-2737	262	14	is	be	AUX
cana-2737	262	15	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	ADJ
cana-2737	262	16	in	in	ADP
cana-2737	262	17	𝑋1	𝑋1	PROPN
cana-2737	262	18	but	but	CCONJ
cana-2737	262	19	ℎ𝑃(𝐵1	ℎ𝑃(𝐵1	NOUN
cana-2737	262	20	)	)	PUNCT
cana-2737	263	1	=	=	SYM
cana-2737	263	2	𝐵1	𝐵1	NOUN
cana-2737	263	3	is	be	AUX
cana-2737	263	4	not	not	PART
cana-2737	263	5	𝑝𝑓𝜃𝒮𝑜𝑠	𝑝𝑓𝜃𝒮𝑜𝑠	PROPN
cana-2737	263	6	in	in	ADP
cana-2737	263	7	𝑋2	𝑋2	PROPN
cana-2737	263	8	.	.	PUNCT
cana-2737	264	1	example	example	NOUN
cana-2737	264	2	3.4	3.4	NUM
cana-2737	264	3	let	let	VERB
cana-2737	264	4	𝑋1	𝑋1	NOUN
cana-2737	264	5	=	=	SYM
cana-2737	264	6	𝑋2	𝑋2	VERB
cana-2737	264	7	=	=	PUNCT
cana-2737	264	8	{	{	PUNCT
cana-2737	264	9	𝑥1	𝑥1	NOUN
cana-2737	264	10	,	,	PUNCT
cana-2737	264	11	𝑥2	𝑥2	NOUN
cana-2737	264	12	}	}	PUNCT
cana-2737	264	13	and	and	CCONJ
cana-2737	264	14	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2737	264	15	’s	’s	PART
cana-2737	264	16	𝐴1	𝐴1	PROPN
cana-2737	264	17	,	,	PUNCT
cana-2737	264	18	𝐴2	𝐴2	PROPN
cana-2737	264	19	,	,	PUNCT
cana-2737	264	20	𝐴3	𝐴3	PROPN
cana-2737	264	21	,	,	PUNCT
cana-2737	264	22	𝐴4	𝐴4	PROPN
cana-2737	264	23	in	in	ADP
cana-2737	264	24	𝑋2	𝑋2	PROPN
cana-2737	264	25	&	&	CCONJ
cana-2737	264	26	𝐵1	𝐵1	PROPN
cana-2737	264	27	in	in	ADP
cana-2737	264	28	𝑋1	𝑋1	PROPN
cana-2737	264	29	are	be	AUX
cana-2737	264	30	defined	define	VERB
cana-2737	264	31	as	as	ADP
cana-2737	264	32	,	,	PUNCT
cana-2737	264	33	𝐴1	𝐴1	PROPN
cana-2737	264	34	=	=	SYM
cana-2737	264	35	{	{	PUNCT
cana-2737	264	36	<	<	X
cana-2737	264	37	𝑥1	𝑥1	PROPN
cana-2737	264	38	,	,	PUNCT
cana-2737	264	39	0.20,0.80	0.20,0.80	NOUN
cana-2737	264	40	>	>	X
cana-2737	264	41	,	,	PUNCT
cana-2737	264	42	<	<	X
cana-2737	264	43	𝑥2	𝑥2	NOUN
cana-2737	264	44	,	,	PUNCT
cana-2737	264	45	0.40,0.60	0.40,0.60	NUM
cana-2737	264	46	>	>	PUNCT
cana-2737	264	47	}	}	PUNCT
cana-2737	264	48	𝐴2	𝐴2	PROPN
cana-2737	264	49	=	=	SYM
cana-2737	264	50	{	{	PUNCT
cana-2737	264	51	<	<	X
cana-2737	264	52	𝑥1	𝑥1	PROPN
cana-2737	264	53	,	,	PUNCT
cana-2737	264	54	0.10,0.90	0.10,0.90	NUM
cana-2737	264	55	>	>	X
cana-2737	264	56	,	,	PUNCT
cana-2737	264	57	<	<	X
cana-2737	264	58	𝑥2	𝑥2	NOUN
cana-2737	264	59	,	,	PUNCT
cana-2737	264	60	0.30,0.70	0.30,0.70	PRON
cana-2737	264	61	>	>	PUNCT
cana-2737	264	62	}	}	PUNCT
cana-2737	264	63	𝐴3	𝐴3	PROPN
cana-2737	265	1	=	=	SYM
cana-2737	265	2	{	{	PUNCT
cana-2737	265	3	<	<	X
cana-2737	265	4	𝑥1	𝑥1	PROPN
cana-2737	265	5	,	,	PUNCT
cana-2737	265	6	0.90,0.10	0.90,0.10	NOUN
cana-2737	265	7	>	>	X
cana-2737	265	8	,	,	PUNCT
cana-2737	265	9	<	<	X
cana-2737	265	10	𝑥2	𝑥2	NOUN
cana-2737	265	11	,	,	PUNCT
cana-2737	265	12	0.70,0.30	0.70,0.30	NOUN
cana-2737	265	13	>	>	PUNCT
cana-2737	265	14	}	}	PUNCT
cana-2737	265	15	𝐴4	𝐴4	PROPN
cana-2737	265	16	=	=	PUNCT
cana-2737	265	17	{	{	PUNCT
cana-2737	265	18	<	<	X
cana-2737	265	19	𝑥1	𝑥1	PROPN
cana-2737	265	20	,	,	PUNCT
cana-2737	265	21	0.20,0.80	0.20,0.80	NOUN
cana-2737	265	22	>	>	X
cana-2737	265	23	,	,	PUNCT
cana-2737	265	24	<	<	X
cana-2737	265	25	𝑥2	𝑥2	NOUN
cana-2737	265	26	,	,	PUNCT
cana-2737	265	27	0.30,0.70	0.30,0.70	PRON
cana-2737	265	28	>	>	PUNCT
cana-2737	265	29	}	}	PUNCT
cana-2737	265	30	𝐵1	𝐵1	NOUN
cana-2737	265	31	=	=	PUNCT
cana-2737	265	32	{	{	PUNCT
cana-2737	265	33	<	<	X
cana-2737	265	34	𝑥1	𝑥1	PROPN
cana-2737	265	35	,	,	PUNCT
cana-2737	265	36	0.40,0.20	0.40,0.20	NOUN
cana-2737	265	37	>	>	X
cana-2737	265	38	,	,	PUNCT
cana-2737	265	39	<	<	X
cana-2737	265	40	𝑥2	𝑥2	NOUN
cana-2737	265	41	,	,	PUNCT
cana-2737	265	42	0.40,0.40	0.40,0.40	NOUN
cana-2737	265	43	>	>	X
cana-2737	265	44	}	}	PUNCT
cana-2737	265	45	now	now	ADV
cana-2737	265	46	,	,	PUNCT
cana-2737	265	47	we	we	PRON
cana-2737	265	48	have	have	VERB
cana-2737	265	49	γ𝑃	γ𝑃	ADJ
cana-2737	265	50	=	=	PUNCT
cana-2737	265	51	{	{	PUNCT
cana-2737	265	52	0𝑋	0𝑋	PROPN
cana-2737	265	53	,	,	PUNCT
cana-2737	265	54	1𝑋	1𝑋	PROPN
cana-2737	265	55	,	,	PUNCT
cana-2737	265	56	𝐵1	𝐵1	PROPN
cana-2737	265	57	}	}	PUNCT
cana-2737	265	58	and	and	CCONJ
cana-2737	265	59	ψ𝑃	ψ𝑃	NOUN
cana-2737	265	60	=	=	SYM
cana-2737	265	61	{	{	PUNCT
cana-2737	265	62	0𝑋	0𝑋	PROPN
cana-2737	265	63	,	,	PUNCT
cana-2737	265	64	1𝑋	1𝑋	PROPN
cana-2737	265	65	,	,	PUNCT
cana-2737	265	66	𝐴1	𝐴1	PROPN
cana-2737	265	67	,	,	PUNCT
cana-2737	265	68	𝐴2	𝐴2	PROPN
cana-2737	265	69	,	,	PUNCT
cana-2737	265	70	𝐴3	𝐴3	PROPN
cana-2737	265	71	,	,	PUNCT
cana-2737	265	72	𝐴4	𝐴4	PROPN
cana-2737	265	73	}	}	PUNCT
cana-2737	265	74	.	.	PUNCT
cana-2737	266	1	let	let	VERB
cana-2737	266	2	ℎ𝑃	ℎ𝑃	NOUN
cana-2737	266	3	:	:	PUNCT
cana-2737	266	4	(	(	PUNCT
cana-2737	266	5	𝑋1	𝑋1	NOUN
cana-2737	266	6	,	,	PUNCT
cana-2737	266	7	γ𝑃	γ𝑃	NOUN
cana-2737	266	8	)	)	PUNCT
cana-2737	266	9	→	→	SYM
cana-2737	266	10	(	(	PUNCT
cana-2737	266	11	𝑋2	𝑋2	ADJ
cana-2737	266	12	,	,	PUNCT
cana-2737	266	13	ψ𝑃	ψ𝑃	NOUN
cana-2737	266	14	)	)	PUNCT
cana-2737	266	15	be	be	VERB
cana-2737	266	16	an	an	DET
cana-2737	266	17	identity	identity	NOUN
cana-2737	266	18	mapping	mapping	NOUN
cana-2737	266	19	.	.	PUNCT
cana-2737	267	1	then	then	ADV
cana-2737	267	2	,	,	PUNCT
cana-2737	267	3	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	267	4	is	be	AUX
cana-2737	267	5	𝑝𝑓𝑒𝑂	𝑝𝑓𝑒𝑂	NOUN
cana-2737	267	6	but	but	CCONJ
cana-2737	267	7	not	not	PART
cana-2737	267	8	𝑝𝑓𝑀𝑂	𝑝𝑓𝑀𝑂	VERB
cana-2737	267	9	,	,	PUNCT
cana-2737	267	10	because	because	SCONJ
cana-2737	267	11	the	the	DET
cana-2737	267	12	set	set	NOUN
cana-2737	267	13	𝐵1	𝐵1	NOUN
cana-2737	267	14	is	be	AUX
cana-2737	267	15	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	ADJ
cana-2737	267	16	in	in	ADP
cana-2737	267	17	𝑋1	𝑋1	PROPN
cana-2737	267	18	but	but	CCONJ
cana-2737	267	19	ℎ𝑃(𝐵1	ℎ𝑃(𝐵1	NOUN
cana-2737	267	20	)	)	PUNCT
cana-2737	268	1	=	=	SYM
cana-2737	268	2	𝐵1	𝐵1	NOUN
cana-2737	268	3	is	be	AUX
cana-2737	268	4	not	not	PART
cana-2737	268	5	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	ADJ
cana-2737	268	6	in	in	ADP
cana-2737	268	7	𝑋2	𝑋2	PROPN
cana-2737	268	8	.	.	PUNCT
cana-2737	269	1	example	example	NOUN
cana-2737	269	2	3.5	3.5	NUM
cana-2737	269	3	let	let	VERB
cana-2737	269	4	𝑋1	𝑋1	NOUN
cana-2737	269	5	=	=	SYM
cana-2737	269	6	𝑋2	𝑋2	VERB
cana-2737	269	7	=	=	PUNCT
cana-2737	269	8	{	{	PUNCT
cana-2737	269	9	𝑥1	𝑥1	NOUN
cana-2737	269	10	,	,	PUNCT
cana-2737	269	11	𝑥2	𝑥2	NOUN
cana-2737	269	12	}	}	PUNCT
cana-2737	269	13	and	and	CCONJ
cana-2737	269	14	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2737	269	15	’s	’s	PART
cana-2737	269	16	𝐴1	𝐴1	PROPN
cana-2737	269	17	,	,	PUNCT
cana-2737	269	18	𝐴2	𝐴2	PROPN
cana-2737	269	19	,	,	PUNCT
cana-2737	269	20	𝐴3	𝐴3	PROPN
cana-2737	269	21	,	,	PUNCT
cana-2737	269	22	𝐴4	𝐴4	PROPN
cana-2737	269	23	in	in	ADP
cana-2737	269	24	𝑋2	𝑋2	PROPN
cana-2737	269	25	&	&	CCONJ
cana-2737	269	26	𝐵1	𝐵1	PROPN
cana-2737	269	27	in	in	ADP
cana-2737	269	28	𝑋1	𝑋1	PROPN
cana-2737	269	29	are	be	AUX
cana-2737	269	30	defined	define	VERB
cana-2737	269	31	as	as	ADP
cana-2737	269	32	,	,	PUNCT
cana-2737	269	33	communications	communication	NOUN
cana-2737	269	34	on	on	ADP
cana-2737	269	35	applied	apply	VERB
cana-2737	269	36	nonlinear	nonlinear	ADJ
cana-2737	269	37	analysis	analysis	NOUN
cana-2737	269	38	issn	issn	NOUN
cana-2737	269	39	:	:	PUNCT
cana-2737	269	40	1074	1074	NUM
cana-2737	269	41	-	-	PUNCT
cana-2737	269	42	133x	133x	NUM
cana-2737	269	43	vol	vol	NOUN
cana-2737	269	44	32	32	NUM
cana-2737	270	1	no	no	NOUN
cana-2737	270	2	.	.	PUNCT
cana-2737	271	1	4s	4s	NUM
cana-2737	271	2	(	(	PUNCT
cana-2737	271	3	2025	2025	NUM
cana-2737	271	4	)	)	PUNCT
cana-2737	271	5	34	34	NUM
cana-2737	272	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-2737	272	2	𝐴1	𝐴1	PROPN
cana-2737	272	3	=	=	PUNCT
cana-2737	272	4	{	{	PUNCT
cana-2737	272	5	<	<	X
cana-2737	272	6	𝑥1	𝑥1	PROPN
cana-2737	272	7	,	,	PUNCT
cana-2737	272	8	0.20,0.80	0.20,0.80	NOUN
cana-2737	272	9	>	>	X
cana-2737	272	10	,	,	PUNCT
cana-2737	272	11	<	<	X
cana-2737	272	12	𝑥2	𝑥2	NOUN
cana-2737	272	13	,	,	PUNCT
cana-2737	272	14	0.40,0.60	0.40,0.60	NUM
cana-2737	272	15	>	>	PUNCT
cana-2737	272	16	}	}	PUNCT
cana-2737	272	17	𝐴2	𝐴2	PROPN
cana-2737	272	18	=	=	SYM
cana-2737	272	19	{	{	PUNCT
cana-2737	272	20	<	<	X
cana-2737	272	21	𝑥1	𝑥1	PROPN
cana-2737	272	22	,	,	PUNCT
cana-2737	272	23	0.10,0.90	0.10,0.90	NUM
cana-2737	272	24	>	>	X
cana-2737	272	25	,	,	PUNCT
cana-2737	272	26	<	<	X
cana-2737	272	27	𝑥2	𝑥2	NOUN
cana-2737	272	28	,	,	PUNCT
cana-2737	272	29	0.30,0.70	0.30,0.70	PRON
cana-2737	272	30	>	>	PUNCT
cana-2737	272	31	}	}	PUNCT
cana-2737	272	32	𝐴3	𝐴3	PROPN
cana-2737	272	33	=	=	SYM
cana-2737	272	34	{	{	PUNCT
cana-2737	272	35	<	<	X
cana-2737	272	36	𝑥1	𝑥1	PROPN
cana-2737	272	37	,	,	PUNCT
cana-2737	272	38	0.90,0.10	0.90,0.10	NOUN
cana-2737	272	39	>	>	X
cana-2737	272	40	,	,	PUNCT
cana-2737	272	41	<	<	X
cana-2737	272	42	𝑥2	𝑥2	NOUN
cana-2737	272	43	,	,	PUNCT
cana-2737	272	44	0.70,0.30	0.70,0.30	NOUN
cana-2737	272	45	>	>	PUNCT
cana-2737	272	46	}	}	PUNCT
cana-2737	272	47	𝐵1	𝐵1	NOUN
cana-2737	272	48	=	=	PUNCT
cana-2737	272	49	𝐴4	𝐴4	PROPN
cana-2737	272	50	=	=	PUNCT
cana-2737	272	51	{	{	PUNCT
cana-2737	272	52	<	<	X
cana-2737	272	53	𝑥1	𝑥1	PROPN
cana-2737	272	54	,	,	PUNCT
cana-2737	272	55	0.20,0.80	0.20,0.80	NOUN
cana-2737	272	56	>	>	X
cana-2737	272	57	,	,	PUNCT
cana-2737	272	58	<	<	X
cana-2737	272	59	𝑥2	𝑥2	NOUN
cana-2737	272	60	,	,	PUNCT
cana-2737	272	61	0.30,0.70	0.30,0.70	PRON
cana-2737	272	62	>	>	PUNCT
cana-2737	272	63	}	}	PUNCT
cana-2737	272	64	now	now	ADV
cana-2737	272	65	,	,	PUNCT
cana-2737	272	66	we	we	PRON
cana-2737	272	67	have	have	VERB
cana-2737	272	68	γ𝑃	γ𝑃	ADJ
cana-2737	272	69	=	=	PUNCT
cana-2737	272	70	{	{	PUNCT
cana-2737	272	71	0𝑋	0𝑋	PROPN
cana-2737	272	72	,	,	PUNCT
cana-2737	272	73	1𝑋	1𝑋	PROPN
cana-2737	272	74	,	,	PUNCT
cana-2737	272	75	𝐵1	𝐵1	PROPN
cana-2737	272	76	}	}	PUNCT
cana-2737	272	77	and	and	CCONJ
cana-2737	272	78	ψ𝑃	ψ𝑃	NOUN
cana-2737	272	79	=	=	SYM
cana-2737	272	80	{	{	PUNCT
cana-2737	272	81	0𝑋	0𝑋	PROPN
cana-2737	272	82	,	,	PUNCT
cana-2737	272	83	1𝑋	1𝑋	PROPN
cana-2737	272	84	,	,	PUNCT
cana-2737	272	85	𝐴1	𝐴1	PROPN
cana-2737	272	86	,	,	PUNCT
cana-2737	272	87	𝐴2	𝐴2	PROPN
cana-2737	272	88	,	,	PUNCT
cana-2737	272	89	𝐴3	𝐴3	PROPN
cana-2737	272	90	,	,	PUNCT
cana-2737	272	91	𝐴4	𝐴4	PROPN
cana-2737	272	92	}	}	PUNCT
cana-2737	272	93	.	.	PUNCT
cana-2737	273	1	let	let	VERB
cana-2737	273	2	ℎ𝑃	ℎ𝑃	NOUN
cana-2737	273	3	:	:	PUNCT
cana-2737	273	4	(	(	PUNCT
cana-2737	273	5	𝑋1	𝑋1	NOUN
cana-2737	273	6	,	,	PUNCT
cana-2737	273	7	γ𝑃	γ𝑃	NOUN
cana-2737	273	8	)	)	PUNCT
cana-2737	273	9	→	→	SYM
cana-2737	273	10	(	(	PUNCT
cana-2737	273	11	𝑋2	𝑋2	ADJ
cana-2737	273	12	,	,	PUNCT
cana-2737	273	13	ψ𝑃	ψ𝑃	NOUN
cana-2737	273	14	)	)	PUNCT
cana-2737	273	15	be	be	VERB
cana-2737	273	16	an	an	DET
cana-2737	273	17	identity	identity	NOUN
cana-2737	273	18	mapping	mapping	NOUN
cana-2737	273	19	.	.	PUNCT
cana-2737	274	1	then	then	ADV
cana-2737	274	2	,	,	PUNCT
cana-2737	274	3	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	274	4	is	be	AUX
cana-2737	274	5	𝑝𝑓𝑂	𝑝𝑓𝑂	PROPN
cana-2737	274	6	(	(	PUNCT
cana-2737	274	7	resp	resp	NOUN
cana-2737	274	8	.	.	PUNCT
cana-2737	275	1	𝑝𝑓𝑒𝑂	𝑝𝑓𝑒𝑂	NOUN
cana-2737	275	2	and	and	CCONJ
cana-2737	275	3	𝑝𝑓𝛿𝒫𝑂	𝑝𝑓𝛿𝒫𝑂	NOUN
cana-2737	275	4	)	)	PUNCT
cana-2737	275	5	but	but	CCONJ
cana-2737	275	6	not	not	PART
cana-2737	275	7	𝑝𝑓𝛿𝑂	𝑝𝑓𝛿𝑂	X
cana-2737	275	8	(	(	PUNCT
cana-2737	275	9	resp	resp	NOUN
cana-2737	275	10	.	.	PUNCT
cana-2737	275	11	𝑝𝑓𝛿𝒮𝑂	𝑝𝑓𝛿𝒮𝑂	PROPN
cana-2737	275	12	and	and	CCONJ
cana-2737	275	13	𝑝𝑓𝛿𝑂	𝑝𝑓𝛿𝑂	NOUN
cana-2737	275	14	)	)	PUNCT
cana-2737	275	15	,	,	PUNCT
cana-2737	275	16	because	because	SCONJ
cana-2737	275	17	the	the	DET
cana-2737	275	18	set	set	NOUN
cana-2737	275	19	𝐵1	𝐵1	NOUN
cana-2737	275	20	is	be	AUX
cana-2737	275	21	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	ADJ
cana-2737	275	22	in	in	ADP
cana-2737	275	23	𝑋1	𝑋1	PROPN
cana-2737	275	24	but	but	CCONJ
cana-2737	275	25	ℎ𝑃(𝐵1	ℎ𝑃(𝐵1	NOUN
cana-2737	275	26	)	)	PUNCT
cana-2737	276	1	=	=	SYM
cana-2737	276	2	𝐵1	𝐵1	NOUN
cana-2737	276	3	is	be	AUX
cana-2737	276	4	not	not	PART
cana-2737	276	5	𝑝𝑓𝛿𝑜𝑠	𝑝𝑓𝛿𝑜𝑠	NOUN
cana-2737	276	6	(	(	PUNCT
cana-2737	276	7	resp	resp	NOUN
cana-2737	276	8	.	.	PUNCT
cana-2737	277	1	𝑝𝑓𝛿𝒮𝑜𝑠	𝑝𝑓𝛿𝒮𝑜𝑠	PROPN
cana-2737	277	2	and	and	CCONJ
cana-2737	277	3	𝑝𝑓𝛿𝑜𝑠	𝑝𝑓𝛿𝑜𝑠	PROPN
cana-2737	277	4	)	)	PUNCT
cana-2737	277	5	in	in	ADP
cana-2737	277	6	𝑋2	𝑋2	PROPN
cana-2737	277	7	.	.	PUNCT
cana-2737	278	1	example	example	NOUN
cana-2737	278	2	3.6	3.6	NUM
cana-2737	278	3	let	let	VERB
cana-2737	278	4	𝑋1	𝑋1	NOUN
cana-2737	278	5	=	=	SYM
cana-2737	278	6	𝑋2	𝑋2	VERB
cana-2737	278	7	=	=	PUNCT
cana-2737	278	8	{	{	PUNCT
cana-2737	278	9	𝑥1	𝑥1	NOUN
cana-2737	278	10	,	,	PUNCT
cana-2737	278	11	𝑥2	𝑥2	NOUN
cana-2737	278	12	}	}	PUNCT
cana-2737	278	13	and	and	CCONJ
cana-2737	278	14	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2737	278	15	’s	’s	PART
cana-2737	278	16	𝐴1	𝐴1	PROPN
cana-2737	278	17	,	,	PUNCT
cana-2737	278	18	𝐴2	𝐴2	PROPN
cana-2737	278	19	,	,	PUNCT
cana-2737	278	20	𝐴3	𝐴3	PROPN
cana-2737	278	21	,	,	PUNCT
cana-2737	278	22	𝐴4	𝐴4	PROPN
cana-2737	278	23	in	in	ADP
cana-2737	278	24	𝑋2	𝑋2	PROPN
cana-2737	278	25	&	&	CCONJ
cana-2737	278	26	𝐵1	𝐵1	PROPN
cana-2737	278	27	in	in	ADP
cana-2737	278	28	𝑋1	𝑋1	PROPN
cana-2737	278	29	are	be	AUX
cana-2737	278	30	defined	define	VERB
cana-2737	278	31	as	as	ADP
cana-2737	278	32	,	,	PUNCT
cana-2737	278	33	𝐴1	𝐴1	PROPN
cana-2737	278	34	=	=	SYM
cana-2737	278	35	{	{	PUNCT
cana-2737	278	36	<	<	X
cana-2737	278	37	𝑥1	𝑥1	PROPN
cana-2737	278	38	,	,	PUNCT
cana-2737	278	39	0.20,0.80	0.20,0.80	NOUN
cana-2737	278	40	>	>	X
cana-2737	278	41	,	,	PUNCT
cana-2737	278	42	<	<	X
cana-2737	278	43	𝑥2	𝑥2	NOUN
cana-2737	278	44	,	,	PUNCT
cana-2737	278	45	0.40,0.60	0.40,0.60	NUM
cana-2737	278	46	>	>	PUNCT
cana-2737	278	47	}	}	PUNCT
cana-2737	278	48	𝐴2	𝐴2	PROPN
cana-2737	278	49	=	=	SYM
cana-2737	278	50	{	{	PUNCT
cana-2737	278	51	<	<	X
cana-2737	278	52	𝑥1	𝑥1	PROPN
cana-2737	278	53	,	,	PUNCT
cana-2737	278	54	0.10,0.90	0.10,0.90	NUM
cana-2737	278	55	>	>	X
cana-2737	278	56	,	,	PUNCT
cana-2737	278	57	<	<	X
cana-2737	278	58	𝑥2	𝑥2	NOUN
cana-2737	278	59	,	,	PUNCT
cana-2737	278	60	0.30,0.70	0.30,0.70	PRON
cana-2737	278	61	>	>	PUNCT
cana-2737	278	62	}	}	PUNCT
cana-2737	278	63	𝐴3	𝐴3	PROPN
cana-2737	278	64	=	=	SYM
cana-2737	278	65	{	{	PUNCT
cana-2737	278	66	<	<	X
cana-2737	278	67	𝑥1	𝑥1	PROPN
cana-2737	278	68	,	,	PUNCT
cana-2737	278	69	0.90,0.10	0.90,0.10	NOUN
cana-2737	278	70	>	>	X
cana-2737	278	71	,	,	PUNCT
cana-2737	278	72	<	<	X
cana-2737	278	73	𝑥2	𝑥2	NOUN
cana-2737	278	74	,	,	PUNCT
cana-2737	278	75	0.70,0.30	0.70,0.30	NOUN
cana-2737	278	76	>	>	PUNCT
cana-2737	278	77	}	}	PUNCT
cana-2737	278	78	𝐴4	𝐴4	PROPN
cana-2737	278	79	=	=	PUNCT
cana-2737	278	80	{	{	PUNCT
cana-2737	278	81	<	<	X
cana-2737	278	82	𝑥1	𝑥1	PROPN
cana-2737	278	83	,	,	PUNCT
cana-2737	278	84	0.20,0.80	0.20,0.80	NOUN
cana-2737	278	85	>	>	X
cana-2737	278	86	,	,	PUNCT
cana-2737	278	87	<	<	X
cana-2737	278	88	𝑥2	𝑥2	NOUN
cana-2737	278	89	,	,	PUNCT
cana-2737	278	90	0.30,0.70	0.30,0.70	PRON
cana-2737	278	91	>	>	PUNCT
cana-2737	278	92	}	}	PUNCT
cana-2737	278	93	𝐵1	𝐵1	NOUN
cana-2737	278	94	=	=	PUNCT
cana-2737	278	95	{	{	PUNCT
cana-2737	278	96	<	<	X
cana-2737	278	97	𝑥1	𝑥1	PROPN
cana-2737	278	98	,	,	PUNCT
cana-2737	278	99	0.80,0.20	0.80,0.20	X
cana-2737	278	100	>	>	X
cana-2737	278	101	,	,	PUNCT
cana-2737	278	102	<	<	X
cana-2737	278	103	𝑥2	𝑥2	NOUN
cana-2737	278	104	,	,	PUNCT
cana-2737	278	105	0.60,0.30	0.60,0.30	PUNCT
cana-2737	278	106	>	>	PUNCT
cana-2737	278	107	}	}	PUNCT
cana-2737	278	108	now	now	ADV
cana-2737	278	109	,	,	PUNCT
cana-2737	278	110	we	we	PRON
cana-2737	278	111	have	have	VERB
cana-2737	278	112	γ𝑃	γ𝑃	ADJ
cana-2737	278	113	=	=	PUNCT
cana-2737	278	114	{	{	PUNCT
cana-2737	278	115	0𝑋	0𝑋	PROPN
cana-2737	278	116	,	,	PUNCT
cana-2737	278	117	1𝑋	1𝑋	PROPN
cana-2737	278	118	,	,	PUNCT
cana-2737	278	119	𝐵1	𝐵1	PROPN
cana-2737	278	120	}	}	PUNCT
cana-2737	278	121	and	and	CCONJ
cana-2737	278	122	ψ𝑃	ψ𝑃	NOUN
cana-2737	278	123	=	=	SYM
cana-2737	278	124	{	{	PUNCT
cana-2737	278	125	0𝑋	0𝑋	PROPN
cana-2737	278	126	,	,	PUNCT
cana-2737	278	127	1𝑋	1𝑋	PROPN
cana-2737	278	128	,	,	PUNCT
cana-2737	278	129	𝐴1	𝐴1	PROPN
cana-2737	278	130	,	,	PUNCT
cana-2737	278	131	𝐴2	𝐴2	PROPN
cana-2737	278	132	,	,	PUNCT
cana-2737	278	133	𝐴3	𝐴3	PROPN
cana-2737	278	134	,	,	PUNCT
cana-2737	278	135	𝐴4	𝐴4	PROPN
cana-2737	278	136	}	}	PUNCT
cana-2737	278	137	.	.	PUNCT
cana-2737	279	1	let	let	VERB
cana-2737	279	2	ℎ𝑃	ℎ𝑃	NOUN
cana-2737	279	3	:	:	PUNCT
cana-2737	279	4	(	(	PUNCT
cana-2737	279	5	𝑋1	𝑋1	NOUN
cana-2737	279	6	,	,	PUNCT
cana-2737	279	7	γ𝑃	γ𝑃	NOUN
cana-2737	279	8	)	)	PUNCT
cana-2737	279	9	→	→	SYM
cana-2737	279	10	(	(	PUNCT
cana-2737	279	11	𝑋2	𝑋2	ADJ
cana-2737	279	12	,	,	PUNCT
cana-2737	279	13	ψ𝑃	ψ𝑃	NOUN
cana-2737	279	14	)	)	PUNCT
cana-2737	279	15	be	be	VERB
cana-2737	279	16	an	an	DET
cana-2737	279	17	identity	identity	NOUN
cana-2737	279	18	mapping	mapping	NOUN
cana-2737	279	19	.	.	PUNCT
cana-2737	280	1	then	then	ADV
cana-2737	280	2	,	,	PUNCT
cana-2737	280	3	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	280	4	is	be	AUX
cana-2737	280	5	𝑝𝑓𝑀𝑂	𝑝𝑓𝑀𝑂	NOUN
cana-2737	280	6	but	but	CCONJ
cana-2737	280	7	not	not	PART
cana-2737	280	8	𝑝𝑓𝛿𝒫𝑂	𝑝𝑓𝛿𝒫𝑂	NOUN
cana-2737	280	9	,	,	PUNCT
cana-2737	280	10	because	because	SCONJ
cana-2737	280	11	the	the	DET
cana-2737	280	12	set	set	NOUN
cana-2737	280	13	𝐵1	𝐵1	NOUN
cana-2737	280	14	is	be	AUX
cana-2737	280	15	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	ADJ
cana-2737	280	16	in	in	ADP
cana-2737	280	17	𝑋1	𝑋1	PROPN
cana-2737	280	18	but	but	CCONJ
cana-2737	280	19	ℎ𝑃(𝐵1	ℎ𝑃(𝐵1	NOUN
cana-2737	280	20	)	)	PUNCT
cana-2737	281	1	=	=	SYM
cana-2737	281	2	𝐵1	𝐵1	NOUN
cana-2737	281	3	is	be	AUX
cana-2737	281	4	not	not	PART
cana-2737	281	5	𝑝𝑓𝛿𝒫𝑜𝑠	𝑝𝑓𝛿𝒫𝑜𝑠	ADJ
cana-2737	281	6	in	in	ADP
cana-2737	281	7	𝑋2	𝑋2	PROPN
cana-2737	281	8	.	.	PUNCT
cana-2737	282	1	theorem	theorem	VERB
cana-2737	282	2	3.1	3.1	NUM
cana-2737	282	3	a	a	DET
cana-2737	282	4	mapping	mapping	NOUN
cana-2737	282	5	ℎ𝑃	ℎ𝑃	NOUN
cana-2737	282	6	:	:	PUNCT
cana-2737	282	7	(	(	PUNCT
cana-2737	282	8	𝑋1	𝑋1	PROPN
cana-2737	282	9	,	,	PUNCT
cana-2737	282	10	𝛤𝑃	𝛤𝑃	PROPN
cana-2737	282	11	)	)	PUNCT
cana-2737	282	12	→	→	PUNCT
cana-2737	282	13	(	(	PUNCT
cana-2737	282	14	𝑋2	𝑋2	PROPN
cana-2737	282	15	,	,	PUNCT
cana-2737	282	16	𝛹𝑃	𝛹𝑃	PROPN
cana-2737	282	17	)	)	PUNCT
cana-2737	282	18	is	be	AUX
cana-2737	282	19	𝑝𝑓𝑀𝑂	𝑝𝑓𝑀𝑂	VERB
cana-2737	282	20	iff	iff	PROPN
cana-2737	282	21	for	for	ADP
cana-2737	282	22	every	every	DET
cana-2737	282	23	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2737	282	24	𝐾	𝐾	PROPN
cana-2737	282	25	of	of	ADP
cana-2737	282	26	(	(	PUNCT
cana-2737	282	27	𝑋1	𝑋1	PROPN
cana-2737	282	28	,	,	PUNCT
cana-2737	282	29	𝛤𝑃	𝛤𝑃	PROPN
cana-2737	282	30	)	)	PUNCT
cana-2737	282	31	,	,	PUNCT
cana-2737	282	32	ℎ𝑃(𝑝𝑓𝑖𝑛𝑡(𝐾	ℎ𝑃(𝑝𝑓𝑖𝑛𝑡(𝐾	PROPN
cana-2737	282	33	)	)	PUNCT
cana-2737	282	34	)	)	PUNCT
cana-2737	283	1	⊆	⊆	NUM
cana-2737	283	2	𝑝𝑓𝑀𝑖𝑛𝑡(ℎ𝑃(𝐾	𝑝𝑓𝑀𝑖𝑛𝑡(ℎ𝑃(𝐾	NOUN
cana-2737	283	3	)	)	PUNCT
cana-2737	283	4	)	)	PUNCT
cana-2737	283	5	.	.	PUNCT
cana-2737	284	1	proof	proof	NOUN
cana-2737	284	2	.	.	PUNCT
cana-2737	285	1	necessity	necessity	NOUN
cana-2737	285	2	:	:	PUNCT
cana-2737	285	3	let	let	VERB
cana-2737	285	4	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	285	5	be	be	AUX
cana-2737	285	6	a	a	DET
cana-2737	285	7	𝑝𝑓𝑀𝑂	𝑝𝑓𝑀𝑂	NOUN
cana-2737	285	8	mapping	mapping	NOUN
cana-2737	285	9	and	and	CCONJ
cana-2737	285	10	𝐾	𝐾	PROPN
cana-2737	285	11	be	be	VERB
cana-2737	285	12	a	a	DET
cana-2737	285	13	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-2737	285	14	in	in	ADP
cana-2737	285	15	(	(	PUNCT
cana-2737	285	16	𝑋1	𝑋1	NOUN
cana-2737	285	17	,	,	PUNCT
cana-2737	285	18	γ𝑃	γ𝑃	NOUN
cana-2737	285	19	)	)	PUNCT
cana-2737	285	20	.	.	PUNCT
cana-2737	286	1	now	now	ADV
cana-2737	286	2	,	,	PUNCT
cana-2737	286	3	𝑝𝑓𝑖𝑛𝑡(𝐾	𝑝𝑓𝑖𝑛𝑡(𝐾	PROPN
cana-2737	286	4	)	)	PUNCT
cana-2737	286	5	⊆	⊆	NUM
cana-2737	286	6	𝐾	𝐾	PROPN
cana-2737	286	7	implies	imply	VERB
cana-2737	286	8	ℎ𝑃(𝑝𝑓𝑖𝑛𝑡(𝐾	ℎ𝑃(𝑝𝑓𝑖𝑛𝑡(𝐾	PROPN
cana-2737	286	9	)	)	PUNCT
cana-2737	286	10	)	)	PUNCT
cana-2737	287	1	⊆	⊆	NUM
cana-2737	287	2	ℎ𝑃(𝐾	ℎ𝑃(𝐾	NOUN
cana-2737	287	3	)	)	PUNCT
cana-2737	287	4	.	.	PUNCT
cana-2737	288	1	since	since	SCONJ
cana-2737	288	2	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	288	3	is	be	AUX
cana-2737	288	4	a	a	DET
cana-2737	288	5	𝑝𝑓𝑀𝑂	𝑝𝑓𝑀𝑂	NOUN
cana-2737	288	6	mapping	mapping	NOUN
cana-2737	288	7	,	,	PUNCT
cana-2737	288	8	ℎ𝑃(𝑝𝑓𝑖𝑛𝑡(𝐾	ℎ𝑃(𝑝𝑓𝑖𝑛𝑡(𝐾	PROPN
cana-2737	288	9	)	)	PUNCT
cana-2737	288	10	)	)	PUNCT
cana-2737	288	11	is	be	AUX
cana-2737	288	12	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	ADJ
cana-2737	288	13	in	in	ADP
cana-2737	288	14	(	(	PUNCT
cana-2737	288	15	𝑋2	𝑋2	ADJ
cana-2737	288	16	,	,	PUNCT
cana-2737	288	17	ψ𝑃	ψ𝑃	NOUN
cana-2737	288	18	)	)	PUNCT
cana-2737	288	19	such	such	ADJ
cana-2737	288	20	that	that	SCONJ
cana-2737	288	21	ℎ𝑃(𝑝𝑓𝑖𝑛𝑡(𝐾	ℎ𝑃(𝑝𝑓𝑖𝑛𝑡(𝐾	PROPN
cana-2737	288	22	)	)	PUNCT
cana-2737	288	23	)	)	PUNCT
cana-2737	288	24	⊆	⊆	NUM
cana-2737	288	25	ℎ𝑃(𝐾	ℎ𝑃(𝐾	NOUN
cana-2737	288	26	)	)	PUNCT
cana-2737	288	27	.	.	PUNCT
cana-2737	289	1	therefore	therefore	ADV
cana-2737	289	2	ℎ𝑃(𝑝𝑓𝑖𝑛𝑡(𝐾	ℎ𝑃(𝑝𝑓𝑖𝑛𝑡(𝐾	PROPN
cana-2737	289	3	)	)	PUNCT
cana-2737	289	4	)	)	PUNCT
cana-2737	290	1	⊆	⊆	NUM
cana-2737	290	2	𝑝𝑓𝑀𝑖𝑛𝑡(ℎ𝑃(𝐾	𝑝𝑓𝑀𝑖𝑛𝑡(ℎ𝑃(𝐾	NOUN
cana-2737	290	3	)	)	PUNCT
cana-2737	290	4	)	)	PUNCT
cana-2737	290	5	.	.	PUNCT
cana-2737	291	1	sufficiency	sufficiency	NOUN
cana-2737	291	2	:	:	PUNCT
cana-2737	291	3	assume	assume	VERB
cana-2737	291	4	𝐾	𝐾	PROPN
cana-2737	291	5	is	be	AUX
cana-2737	291	6	a	a	DET
cana-2737	291	7	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-2737	291	8	of	of	ADP
cana-2737	291	9	(	(	PUNCT
cana-2737	291	10	𝑋1	𝑋1	NOUN
cana-2737	291	11	,	,	PUNCT
cana-2737	291	12	γ𝑃	γ𝑃	NOUN
cana-2737	291	13	)	)	PUNCT
cana-2737	291	14	.	.	PUNCT
cana-2737	292	1	then	then	ADV
cana-2737	292	2	ℎ𝑃(𝐾	ℎ𝑃(𝐾	NOUN
cana-2737	292	3	)	)	PUNCT
cana-2737	292	4	=	=	SYM
cana-2737	292	5	ℎ𝑃(𝑝𝑓𝑖𝑛𝑡(𝐾	ℎ𝑃(𝑝𝑓𝑖𝑛𝑡(𝐾	PROPN
cana-2737	292	6	)	)	PUNCT
cana-2737	292	7	)	)	PUNCT
cana-2737	293	1	⊆	⊆	NUM
cana-2737	293	2	𝑝𝑓𝑀𝑖𝑛𝑡(ℎ𝑃(𝐾	𝑝𝑓𝑀𝑖𝑛𝑡(ℎ𝑃(𝐾	NOUN
cana-2737	293	3	)	)	PUNCT
cana-2737	293	4	)	)	PUNCT
cana-2737	293	5	.	.	PUNCT
cana-2737	294	1	but	but	CCONJ
cana-2737	294	2	𝑝𝑓𝑀𝑖𝑛𝑡ℎ𝑃(𝐾	𝑝𝑓𝑀𝑖𝑛𝑡ℎ𝑃(𝐾	INTJ
cana-2737	294	3	)	)	PUNCT
cana-2737	294	4	⊆	⊆	NUM
cana-2737	294	5	ℎ𝑃(𝐾	ℎ𝑃(𝐾	NUM
cana-2737	294	6	)	)	PUNCT
cana-2737	294	7	.	.	PUNCT
cana-2737	295	1	so	so	ADV
cana-2737	295	2	ℎ𝑃(𝐾	ℎ𝑃(𝐾	PROPN
cana-2737	295	3	)	)	PUNCT
cana-2737	295	4	=	=	SYM
cana-2737	295	5	𝑝𝑓𝑀𝑖𝑛𝑡(𝐾	𝑝𝑓𝑀𝑖𝑛𝑡(𝐾	NOUN
cana-2737	295	6	)	)	PUNCT
cana-2737	295	7	which	which	PRON
cana-2737	295	8	implies	imply	VERB
cana-2737	295	9	ℎ𝑃(𝐾	ℎ𝑃(𝐾	NOUN
cana-2737	295	10	)	)	PUNCT
cana-2737	295	11	is	be	AUX
cana-2737	295	12	a	a	DET
cana-2737	295	13	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	NOUN
cana-2737	295	14	of	of	ADP
cana-2737	295	15	(	(	PUNCT
cana-2737	295	16	𝑋2	𝑋2	ADJ
cana-2737	295	17	,	,	PUNCT
cana-2737	295	18	ψ𝑃	ψ𝑃	NOUN
cana-2737	295	19	)	)	PUNCT
cana-2737	295	20	and	and	CCONJ
cana-2737	295	21	hence	hence	ADV
cana-2737	295	22	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	295	23	is	be	AUX
cana-2737	295	24	a	a	DET
cana-2737	295	25	𝑝𝑓𝑀𝑂	𝑝𝑓𝑀𝑂	NOUN
cana-2737	295	26	theorem	theorem	NOUN
cana-2737	295	27	3.2	3.2	NUM
cana-2737	295	28	if	if	SCONJ
cana-2737	295	29	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	295	30	:	:	PUNCT
cana-2737	295	31	(	(	PUNCT
cana-2737	295	32	𝑋1	𝑋1	PROPN
cana-2737	295	33	,	,	PUNCT
cana-2737	295	34	𝛤𝑃	𝛤𝑃	PROPN
cana-2737	295	35	)	)	PUNCT
cana-2737	295	36	→	→	PUNCT
cana-2737	295	37	(	(	PUNCT
cana-2737	295	38	𝑋2	𝑋2	PROPN
cana-2737	295	39	,	,	PUNCT
cana-2737	295	40	𝛹𝑃	𝛹𝑃	PROPN
cana-2737	295	41	)	)	PUNCT
cana-2737	295	42	is	be	AUX
cana-2737	295	43	a	a	DET
cana-2737	295	44	𝑝𝑓𝑀𝑂	𝑝𝑓𝑀𝑂	NOUN
cana-2737	295	45	mapping	mapping	NOUN
cana-2737	295	46	,	,	PUNCT
cana-2737	295	47	then	then	ADV
cana-2737	295	48	𝑝𝑓𝑖𝑛𝑡(ℎ𝑃	𝑝𝑓𝑖𝑛𝑡(ℎ𝑃	NOUN
cana-2737	295	49	−1(𝐾	−1(𝐾	NOUN
cana-2737	295	50	)	)	PUNCT
cana-2737	295	51	)	)	PUNCT
cana-2737	296	1	⊆	⊆	NUM
cana-2737	296	2	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	296	3	−1(𝑝𝑓𝑀𝑖𝑛𝑡(𝐾	−1(𝑝𝑓𝑀𝑖𝑛𝑡(𝐾	PROPN
cana-2737	296	4	)	)	PUNCT
cana-2737	296	5	)	)	PUNCT
cana-2737	296	6	for	for	ADP
cana-2737	296	7	every	every	DET
cana-2737	296	8	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2737	296	9	𝐾	𝐾	PROPN
cana-2737	296	10	of	of	ADP
cana-2737	296	11	(	(	PUNCT
cana-2737	296	12	𝑋2	𝑋2	PROPN
cana-2737	296	13	,	,	PUNCT
cana-2737	296	14	𝛹𝑃	𝛹𝑃	PROPN
cana-2737	296	15	)	)	PUNCT
cana-2737	296	16	.	.	PUNCT
cana-2737	297	1	proof	proof	NOUN
cana-2737	297	2	.	.	PUNCT
cana-2737	298	1	let	let	VERB
cana-2737	298	2	𝐾	𝐾	PRON
cana-2737	298	3	be	be	AUX
cana-2737	298	4	a	a	DET
cana-2737	298	5	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2737	298	6	of	of	ADP
cana-2737	298	7	(	(	PUNCT
cana-2737	298	8	𝑋2	𝑋2	PROPN
cana-2737	298	9	,	,	PUNCT
cana-2737	298	10	ψ𝑃	ψ𝑃	NOUN
cana-2737	298	11	)	)	PUNCT
cana-2737	298	12	.	.	PUNCT
cana-2737	299	1	then	then	ADV
cana-2737	299	2	𝑝𝑓𝑖𝑛𝑡(ℎ𝑃	𝑝𝑓𝑖𝑛𝑡(ℎ𝑃	NOUN
cana-2737	299	3	−1(𝐾	−1(𝐾	NOUN
cana-2737	299	4	)	)	PUNCT
cana-2737	299	5	)	)	PUNCT
cana-2737	299	6	is	be	AUX
cana-2737	299	7	a	a	DET
cana-2737	299	8	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-2737	299	9	in	in	ADP
cana-2737	299	10	(	(	PUNCT
cana-2737	299	11	𝑋1	𝑋1	NOUN
cana-2737	299	12	,	,	PUNCT
cana-2737	299	13	γ𝑃	γ𝑃	NOUN
cana-2737	299	14	)	)	PUNCT
cana-2737	299	15	.	.	PUNCT
cana-2737	300	1	since	since	SCONJ
cana-2737	300	2	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	300	3	is	be	AUX
cana-2737	300	4	𝑝𝑓𝑀𝑂	𝑝𝑓𝑀𝑂	VERB
cana-2737	300	5	,	,	PUNCT
cana-2737	300	6	ℎ𝑃(𝑝𝑓𝑖𝑛𝑡(ℎ𝑃	ℎ𝑃(𝑝𝑓𝑖𝑛𝑡(ℎ𝑃	PRON
cana-2737	300	7	−1(𝐾	−1(𝐾	NOUN
cana-2737	300	8	)	)	PUNCT
cana-2737	300	9	)	)	PUNCT
cana-2737	300	10	)	)	PUNCT
cana-2737	300	11	is	be	AUX
cana-2737	300	12	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	ADJ
cana-2737	300	13	in	in	ADP
cana-2737	300	14	(	(	PUNCT
cana-2737	300	15	𝑋2	𝑋2	ADJ
cana-2737	300	16	,	,	PUNCT
cana-2737	300	17	ψ𝑃	ψ𝑃	NOUN
cana-2737	300	18	)	)	PUNCT
cana-2737	300	19	and	and	CCONJ
cana-2737	300	20	hence	hence	ADV
cana-2737	300	21	ℎ𝑃(𝑝𝑓𝑖𝑛𝑡(ℎ𝑃	ℎ𝑃(𝑝𝑓𝑖𝑛𝑡(ℎ𝑃	ADJ
cana-2737	300	22	−1(𝐾	−1(𝐾	NOUN
cana-2737	300	23	)	)	PUNCT
cana-2737	300	24	)	)	PUNCT
cana-2737	300	25	)	)	PUNCT
cana-2737	301	1	⊆	⊆	NUM
cana-2737	301	2	𝑝𝑓𝑀𝑖𝑛𝑡(ℎ𝑃(ℎ𝑃	𝑝𝑓𝑀𝑖𝑛𝑡(ℎ𝑃(ℎ𝑃	NOUN
cana-2737	301	3	−1(𝐾	−1(𝐾	NOUN
cana-2737	301	4	)	)	PUNCT
cana-2737	301	5	)	)	PUNCT
cana-2737	301	6	)	)	PUNCT
cana-2737	302	1	⊆	⊆	NUM
cana-2737	302	2	𝑝𝑓𝑀𝑖𝑛𝑡(𝐾	𝑝𝑓𝑀𝑖𝑛𝑡(𝐾	NOUN
cana-2737	302	3	)	)	PUNCT
cana-2737	302	4	.	.	PUNCT
cana-2737	303	1	thus	thus	ADV
cana-2737	303	2	𝑝𝑓𝑖𝑛𝑡(ℎ𝑃	𝑝𝑓𝑖𝑛𝑡(ℎ𝑃	NOUN
cana-2737	303	3	−1(𝐾	−1(𝐾	NOUN
cana-2737	303	4	)	)	PUNCT
cana-2737	303	5	)	)	PUNCT
cana-2737	304	1	⊆	⊆	NUM
cana-2737	304	2	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	304	3	−1(𝑝𝑓𝑀𝑖𝑛𝑡(𝐾	−1(𝑝𝑓𝑀𝑖𝑛𝑡(𝐾	PROPN
cana-2737	304	4	)	)	PUNCT
cana-2737	304	5	)	)	PUNCT
cana-2737	304	6	.	.	PUNCT
cana-2737	305	1	theorem	theorem	VERB
cana-2737	305	2	3.3	3.3	NUM
cana-2737	305	3	a	a	DET
cana-2737	305	4	mapping	mapping	NOUN
cana-2737	305	5	ℎ𝑃	ℎ𝑃	NOUN
cana-2737	305	6	:	:	PUNCT
cana-2737	305	7	(	(	PUNCT
cana-2737	305	8	𝑋1	𝑋1	PROPN
cana-2737	305	9	,	,	PUNCT
cana-2737	305	10	𝛤𝑃	𝛤𝑃	PROPN
cana-2737	305	11	)	)	PUNCT
cana-2737	305	12	→	→	PUNCT
cana-2737	305	13	(	(	PUNCT
cana-2737	305	14	𝑋2	𝑋2	PROPN
cana-2737	305	15	,	,	PUNCT
cana-2737	305	16	𝛹𝑃	𝛹𝑃	PROPN
cana-2737	305	17	)	)	PUNCT
cana-2737	305	18	is	be	AUX
cana-2737	305	19	𝑝𝑓𝑀𝑂	𝑝𝑓𝑀𝑂	VERB
cana-2737	305	20	iff	iff	PROPN
cana-2737	305	21	for	for	ADP
cana-2737	305	22	each	each	DET
cana-2737	305	23	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2737	305	24	𝐺	𝐺	PROPN
cana-2737	305	25	of	of	ADP
cana-2737	305	26	(	(	PUNCT
cana-2737	305	27	𝑋2	𝑋2	PROPN
cana-2737	305	28	,	,	PUNCT
cana-2737	305	29	𝛹𝑃	𝛹𝑃	PROPN
cana-2737	305	30	)	)	PUNCT
cana-2737	305	31	and	and	CCONJ
cana-2737	305	32	for	for	ADP
cana-2737	305	33	each	each	DET
cana-2737	305	34	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-2737	305	35	𝐾	𝐾	PROPN
cana-2737	305	36	of	of	ADP
cana-2737	305	37	(	(	PUNCT
cana-2737	305	38	𝑋1	𝑋1	PROPN
cana-2737	305	39	,	,	PUNCT
cana-2737	305	40	𝛤𝑃	𝛤𝑃	PROPN
cana-2737	305	41	)	)	PUNCT
cana-2737	305	42	containing	contain	VERB
cana-2737	305	43	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	305	44	−1(𝐺	−1(𝐺	NOUN
cana-2737	305	45	)	)	PUNCT
cana-2737	305	46	,	,	PUNCT
cana-2737	305	47	there	there	PRON
cana-2737	305	48	is	be	VERB
cana-2737	305	49	a	a	DET
cana-2737	305	50	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-2737	305	51	𝐻	𝐻	PROPN
cana-2737	305	52	of	of	ADP
cana-2737	305	53	(	(	PUNCT
cana-2737	305	54	𝑋2	𝑋2	PROPN
cana-2737	305	55	,	,	PUNCT
cana-2737	305	56	𝛹𝑃	𝛹𝑃	PROPN
cana-2737	305	57	)	)	PUNCT
cana-2737	305	58	such	such	ADJ
cana-2737	305	59	that	that	SCONJ
cana-2737	305	60	𝐺	𝐺	PROPN
cana-2737	305	61	⊆	⊆	NUM
cana-2737	305	62	𝐻	𝐻	PROPN
cana-2737	305	63	and	and	CCONJ
cana-2737	305	64	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	305	65	−1(𝐻	−1(𝐻	PROPN
cana-2737	305	66	)	)	PUNCT
cana-2737	305	67	⊆	⊆	NUM
cana-2737	305	68	𝐾.	𝐾.	PROPN
cana-2737	305	69	proof	proof	NOUN
cana-2737	305	70	.	.	PUNCT
cana-2737	306	1	necessity	necessity	NOUN
cana-2737	306	2	:	:	PUNCT
cana-2737	306	3	assume	assume	VERB
cana-2737	306	4	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	306	5	is	be	AUX
cana-2737	306	6	a	a	DET
cana-2737	306	7	𝑝𝑓𝑀𝑂	𝑝𝑓𝑀𝑂	NOUN
cana-2737	306	8	mapping	mapping	NOUN
cana-2737	306	9	.	.	PUNCT
cana-2737	307	1	let	let	VERB
cana-2737	307	2	𝐺	𝐺	PRON
cana-2737	307	3	be	be	AUX
cana-2737	307	4	the	the	DET
cana-2737	307	5	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-2737	307	6	of	of	ADP
cana-2737	307	7	(	(	PUNCT
cana-2737	307	8	𝑋2	𝑋2	ADJ
cana-2737	307	9	,	,	PUNCT
cana-2737	307	10	ψ𝑃	ψ𝑃	NOUN
cana-2737	307	11	)	)	PUNCT
cana-2737	307	12	and	and	CCONJ
cana-2737	307	13	𝐾	𝐾	PROPN
cana-2737	307	14	is	be	AUX
cana-2737	307	15	a	a	DET
cana-2737	307	16	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-2737	307	17	of	of	ADP
cana-2737	307	18	(	(	PUNCT
cana-2737	307	19	𝑋1	𝑋1	NOUN
cana-2737	307	20	,	,	PUNCT
cana-2737	307	21	γ𝑃	γ𝑃	NOUN
cana-2737	307	22	)	)	PUNCT
cana-2737	307	23	such	such	ADJ
cana-2737	307	24	that	that	SCONJ
cana-2737	307	25	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	307	26	−1(𝐺	−1(𝐺	NOUN
cana-2737	307	27	)	)	PUNCT
cana-2737	308	1	⊆	⊆	X
cana-2737	308	2	𝐾.	𝐾.	NOUN
cana-2737	308	3	then	then	ADV
cana-2737	308	4	𝐻	𝐻	PROPN
cana-2737	308	5	=	=	PUNCT
cana-2737	309	1	(	(	PUNCT
cana-2737	309	2	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	309	3	−1(𝐾𝑐))𝑐	−1(𝐾𝑐))𝑐	PROPN
cana-2737	309	4	is	be	AUX
cana-2737	309	5	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	PROPN
cana-2737	309	6	of	of	ADP
cana-2737	309	7	(	(	PUNCT
cana-2737	309	8	𝑋2	𝑋2	ADJ
cana-2737	309	9	,	,	PUNCT
cana-2737	309	10	ψ𝑃	ψ𝑃	NOUN
cana-2737	309	11	)	)	PUNCT
cana-2737	309	12	such	such	ADJ
cana-2737	309	13	that	that	SCONJ
cana-2737	309	14	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	309	15	−1(𝐻	−1(𝐻	PROPN
cana-2737	309	16	)	)	PUNCT
cana-2737	309	17	⊆	⊆	NUM
cana-2737	309	18	𝐾.	𝐾.	PROPN
cana-2737	309	19	communications	communication	NOUN
cana-2737	309	20	on	on	ADP
cana-2737	309	21	applied	apply	VERB
cana-2737	309	22	nonlinear	nonlinear	ADJ
cana-2737	309	23	analysis	analysis	NOUN
cana-2737	309	24	issn	issn	NOUN
cana-2737	309	25	:	:	PUNCT
cana-2737	309	26	1074	1074	NUM
cana-2737	309	27	-	-	PUNCT
cana-2737	309	28	133x	133x	NUM
cana-2737	309	29	vol	vol	NOUN
cana-2737	309	30	32	32	NUM
cana-2737	310	1	no	no	NOUN
cana-2737	310	2	.	.	PUNCT
cana-2737	311	1	4s	4s	NUM
cana-2737	311	2	(	(	PUNCT
cana-2737	311	3	2025	2025	NUM
cana-2737	311	4	)	)	PUNCT
cana-2737	311	5	35	35	NUM
cana-2737	311	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2737	311	7	sufficiency	sufficiency	NOUN
cana-2737	311	8	:	:	PUNCT
cana-2737	311	9	assume	assume	VERB
cana-2737	311	10	𝐾	𝐾	PROPN
cana-2737	311	11	is	be	AUX
cana-2737	311	12	a	a	DET
cana-2737	311	13	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-2737	311	14	of	of	ADP
cana-2737	311	15	(	(	PUNCT
cana-2737	311	16	𝑋1	𝑋1	NOUN
cana-2737	311	17	,	,	PUNCT
cana-2737	311	18	γ𝑃	γ𝑃	NOUN
cana-2737	311	19	)	)	PUNCT
cana-2737	311	20	.	.	PUNCT
cana-2737	312	1	then	then	ADV
cana-2737	312	2	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	312	3	−1((ℎ𝑃(𝐾))𝑐	−1((ℎ𝑃(𝐾))𝑐	PROPN
cana-2737	312	4	)	)	PUNCT
cana-2737	313	1	⊆	⊆	NUM
cana-2737	313	2	𝐾𝑐	𝐾𝑐	VERB
cana-2737	313	3	and	and	CCONJ
cana-2737	313	4	𝐾𝑐	𝐾𝑐	PROPN
cana-2737	313	5	is	be	AUX
cana-2737	313	6	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-2737	313	7	in	in	ADP
cana-2737	313	8	(	(	PUNCT
cana-2737	313	9	𝑋1	𝑋1	NOUN
cana-2737	313	10	,	,	PUNCT
cana-2737	313	11	γ𝑃	γ𝑃	NOUN
cana-2737	313	12	)	)	PUNCT
cana-2737	313	13	.	.	PUNCT
cana-2737	314	1	by	by	ADP
cana-2737	314	2	hypothesis	hypothesis	NOUN
cana-2737	314	3	,	,	PUNCT
cana-2737	314	4	there	there	PRON
cana-2737	314	5	is	be	VERB
cana-2737	314	6	a	a	DET
cana-2737	314	7	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-2737	314	8	𝐻	𝐻	PROPN
cana-2737	314	9	of	of	ADP
cana-2737	314	10	(	(	PUNCT
cana-2737	314	11	𝑋2	𝑋2	ADJ
cana-2737	314	12	,	,	PUNCT
cana-2737	314	13	ψ𝑃	ψ𝑃	NOUN
cana-2737	314	14	)	)	PUNCT
cana-2737	314	15	such	such	ADJ
cana-2737	314	16	that	that	SCONJ
cana-2737	314	17	(	(	PUNCT
cana-2737	314	18	ℎ𝑃(𝐾))𝑐	ℎ𝑃(𝐾))𝑐	ADV
cana-2737	314	19	⊆	⊆	NUM
cana-2737	314	20	𝐻	𝐻	PROPN
cana-2737	314	21	and	and	CCONJ
cana-2737	314	22	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	314	23	−1(𝐻	−1(𝐻	PROPN
cana-2737	314	24	)	)	PUNCT
cana-2737	314	25	⊆	⊆	NUM
cana-2737	314	26	𝐾𝑐.	𝐾𝑐.	PROPN
cana-2737	314	27	therefore	therefore	ADV
cana-2737	314	28	𝐾	𝐾	PROPN
cana-2737	314	29	⊆	⊆	NUM
cana-2737	314	30	(	(	PUNCT
cana-2737	314	31	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	314	32	−1(𝐻))𝑐.	−1(𝐻))𝑐.	VERB
cana-2737	314	33	hence	hence	ADV
cana-2737	314	34	𝐻𝑐	𝐻𝑐	PROPN
cana-2737	314	35	⊆	⊆	NUM
cana-2737	314	36	ℎ𝑃(𝐾	ℎ𝑃(𝐾	NOUN
cana-2737	314	37	)	)	PUNCT
cana-2737	315	1	⊆	⊆	NUM
cana-2737	315	2	ℎ𝑃((ℎ𝑃	ℎ𝑃((ℎ𝑃	PROPN
cana-2737	315	3	−1(𝐻))𝑐	−1(𝐻))𝑐	PROPN
cana-2737	315	4	)	)	PUNCT
cana-2737	316	1	⊆	⊆	NUM
cana-2737	316	2	𝐻𝑐	𝐻𝑐	PROPN
cana-2737	316	3	which	which	PRON
cana-2737	316	4	implies	imply	VERB
cana-2737	316	5	ℎ𝑃(𝐾	ℎ𝑃(𝐾	NOUN
cana-2737	316	6	)	)	PUNCT
cana-2737	316	7	=	=	SYM
cana-2737	316	8	𝐻𝑐.	𝐻𝑐.	PROPN
cana-2737	316	9	since	since	SCONJ
cana-2737	316	10	𝐻𝑐	𝐻𝑐	PROPN
cana-2737	316	11	is	be	AUX
cana-2737	316	12	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	ADJ
cana-2737	316	13	of	of	ADP
cana-2737	316	14	(	(	PUNCT
cana-2737	316	15	𝑋2	𝑋2	ADJ
cana-2737	316	16	,	,	PUNCT
cana-2737	316	17	ψ𝑃	ψ𝑃	NOUN
cana-2737	316	18	)	)	PUNCT
cana-2737	316	19	,	,	PUNCT
cana-2737	316	20	ℎ𝑃(𝐾	ℎ𝑃(𝐾	PROPN
cana-2737	316	21	)	)	PUNCT
cana-2737	316	22	is	be	AUX
cana-2737	316	23	𝑝𝑓𝑀𝑂	𝑝𝑓𝑀𝑂	VERB
cana-2737	316	24	in	in	ADP
cana-2737	316	25	(	(	PUNCT
cana-2737	316	26	𝑋2	𝑋2	ADJ
cana-2737	316	27	,	,	PUNCT
cana-2737	316	28	ψ𝑃	ψ𝑃	NOUN
cana-2737	316	29	)	)	PUNCT
cana-2737	316	30	and	and	CCONJ
cana-2737	316	31	thus	thus	ADV
cana-2737	316	32	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	316	33	is	be	AUX
cana-2737	316	34	𝑝𝑓𝑀𝑂	𝑝𝑓𝑀𝑂	NOUN
cana-2737	316	35	mapping	mapping	NOUN
cana-2737	316	36	.	.	PUNCT
cana-2737	317	1	theorem	theorem	VERB
cana-2737	317	2	3.4	3.4	NUM
cana-2737	317	3	a	a	DET
cana-2737	317	4	mapping	mapping	NOUN
cana-2737	317	5	ℎ𝑃	ℎ𝑃	NOUN
cana-2737	317	6	:	:	PUNCT
cana-2737	317	7	(	(	PUNCT
cana-2737	317	8	𝑋1	𝑋1	PROPN
cana-2737	317	9	,	,	PUNCT
cana-2737	317	10	𝛤𝑃	𝛤𝑃	PROPN
cana-2737	317	11	)	)	PUNCT
cana-2737	317	12	→	→	PUNCT
cana-2737	317	13	(	(	PUNCT
cana-2737	317	14	𝑋2	𝑋2	PROPN
cana-2737	317	15	,	,	PUNCT
cana-2737	317	16	𝛹𝑃	𝛹𝑃	PROPN
cana-2737	317	17	)	)	PUNCT
cana-2737	317	18	is	be	AUX
cana-2737	317	19	𝑝𝑓𝑀𝑂	𝑝𝑓𝑀𝑂	PROPN
cana-2737	317	20	iff	iff	PROPN
cana-2737	317	21	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	317	22	−1(𝑝𝑓𝑀𝑐𝑙(𝐺	−1(𝑝𝑓𝑀𝑐𝑙(𝐺	PROPN
cana-2737	317	23	)	)	PUNCT
cana-2737	317	24	)	)	PUNCT
cana-2737	318	1	⊆	⊆	NUM
cana-2737	318	2	𝑝𝑓𝑐𝑙(ℎ𝑃	𝑝𝑓𝑐𝑙(ℎ𝑃	NOUN
cana-2737	318	3	−1(𝐺	−1(𝐺	NOUN
cana-2737	318	4	)	)	PUNCT
cana-2737	318	5	)	)	PUNCT
cana-2737	318	6	for	for	ADP
cana-2737	318	7	every	every	DET
cana-2737	318	8	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2737	318	9	𝐺	𝐺	PROPN
cana-2737	318	10	of	of	ADP
cana-2737	318	11	(	(	PUNCT
cana-2737	318	12	𝑋2	𝑋2	PROPN
cana-2737	318	13	,	,	PUNCT
cana-2737	318	14	𝛹𝑃	𝛹𝑃	PROPN
cana-2737	318	15	)	)	PUNCT
cana-2737	318	16	.	.	PUNCT
cana-2737	319	1	proof	proof	NOUN
cana-2737	319	2	.	.	PUNCT
cana-2737	320	1	necessity	necessity	NOUN
cana-2737	320	2	:	:	PUNCT
cana-2737	320	3	assume	assume	VERB
cana-2737	320	4	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	320	5	is	be	AUX
cana-2737	320	6	a	a	DET
cana-2737	320	7	𝑝𝑓𝑀𝑂	𝑝𝑓𝑀𝑂	NOUN
cana-2737	320	8	mapping	mapping	NOUN
cana-2737	320	9	.	.	PUNCT
cana-2737	321	1	for	for	ADP
cana-2737	321	2	any	any	DET
cana-2737	321	3	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2737	321	4	𝐺	𝐺	PROPN
cana-2737	321	5	of	of	ADP
cana-2737	321	6	(	(	PUNCT
cana-2737	321	7	𝑋2	𝑋2	PROPN
cana-2737	321	8	,	,	PUNCT
cana-2737	321	9	ψ𝑃	ψ𝑃	NOUN
cana-2737	321	10	)	)	PUNCT
cana-2737	321	11	,	,	PUNCT
cana-2737	321	12	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	321	13	−1(𝐺	−1(𝐺	NOUN
cana-2737	321	14	)	)	PUNCT
cana-2737	321	15	⊆	⊆	NUM
cana-2737	321	16	𝑝𝑓𝑐𝑙(ℎ𝑃	𝑝𝑓𝑐𝑙(ℎ𝑃	NOUN
cana-2737	321	17	−1(𝐺	−1(𝐺	NOUN
cana-2737	321	18	)	)	PUNCT
cana-2737	321	19	)	)	PUNCT
cana-2737	321	20	.	.	PUNCT
cana-2737	322	1	therefore	therefore	ADV
cana-2737	322	2	by	by	ADP
cana-2737	322	3	theorem	theorem	NOUN
cana-2737	322	4	3.3	3.3	NUM
cana-2737	322	5	,	,	PUNCT
cana-2737	322	6	there	there	PRON
cana-2737	322	7	exists	exist	VERB
cana-2737	322	8	a	a	DET
cana-2737	322	9	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-2737	322	10	𝐾	𝐾	NOUN
cana-2737	322	11	in	in	ADP
cana-2737	322	12	(	(	PUNCT
cana-2737	322	13	𝑋2	𝑋2	ADJ
cana-2737	322	14	,	,	PUNCT
cana-2737	322	15	ψ𝑃	ψ𝑃	NOUN
cana-2737	322	16	)	)	PUNCT
cana-2737	322	17	such	such	ADJ
cana-2737	322	18	that	that	SCONJ
cana-2737	322	19	𝐺	𝐺	PROPN
cana-2737	322	20	⊆	⊆	NUM
cana-2737	322	21	𝐾	𝐾	PROPN
cana-2737	322	22	and	and	CCONJ
cana-2737	322	23	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	322	24	−1(𝐾	−1(𝐾	NOUN
cana-2737	322	25	)	)	PUNCT
cana-2737	322	26	⊆	⊆	NUM
cana-2737	322	27	𝑝𝑓𝑐𝑙(ℎ𝑃	𝑝𝑓𝑐𝑙(ℎ𝑃	NOUN
cana-2737	322	28	−1(𝐺	−1(𝐺	NOUN
cana-2737	322	29	)	)	PUNCT
cana-2737	322	30	)	)	PUNCT
cana-2737	322	31	.	.	PUNCT
cana-2737	323	1	therefore	therefore	ADV
cana-2737	323	2	we	we	PRON
cana-2737	323	3	obtain	obtain	VERB
cana-2737	323	4	that	that	DET
cana-2737	323	5	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	323	6	−1(𝑝𝑓𝑀𝑐𝑙(𝐺	−1(𝑝𝑓𝑀𝑐𝑙(𝐺	PROPN
cana-2737	323	7	)	)	PUNCT
cana-2737	323	8	)	)	PUNCT
cana-2737	324	1	⊆	⊆	NUM
cana-2737	324	2	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	324	3	−1(𝐾	−1(𝐾	NOUN
cana-2737	324	4	)	)	PUNCT
cana-2737	324	5	⊆	⊆	NUM
cana-2737	324	6	𝑝𝑓𝑐𝑙(ℎ𝑃	𝑝𝑓𝑐𝑙(ℎ𝑃	NOUN
cana-2737	324	7	−1(𝐺	−1(𝐺	NOUN
cana-2737	324	8	)	)	PUNCT
cana-2737	324	9	)	)	PUNCT
cana-2737	324	10	.	.	PUNCT
cana-2737	325	1	sufficiency	sufficiency	NOUN
cana-2737	325	2	:	:	PUNCT
cana-2737	325	3	assume	assume	VERB
cana-2737	325	4	𝐺	𝐺	PROPN
cana-2737	325	5	is	be	AUX
cana-2737	325	6	a	a	DET
cana-2737	325	7	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2737	325	8	of	of	ADP
cana-2737	325	9	(	(	PUNCT
cana-2737	325	10	𝑋2	𝑋2	ADJ
cana-2737	325	11	,	,	PUNCT
cana-2737	325	12	ψ𝑃	ψ𝑃	NOUN
cana-2737	325	13	)	)	PUNCT
cana-2737	325	14	and	and	CCONJ
cana-2737	325	15	𝐾	𝐾	PROPN
cana-2737	325	16	is	be	AUX
cana-2737	325	17	a	a	DET
cana-2737	325	18	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-2737	325	19	of	of	ADP
cana-2737	325	20	(	(	PUNCT
cana-2737	325	21	𝑋1	𝑋1	NOUN
cana-2737	325	22	,	,	PUNCT
cana-2737	325	23	γ𝑃	γ𝑃	NOUN
cana-2737	325	24	)	)	PUNCT
cana-2737	325	25	containing	contain	VERB
cana-2737	325	26	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	325	27	−1(𝐺	−1(𝐺	NOUN
cana-2737	325	28	)	)	PUNCT
cana-2737	325	29	.	.	PUNCT
cana-2737	326	1	put	put	VERB
cana-2737	326	2	𝐻	𝐻	PROPN
cana-2737	326	3	=	=	PUNCT
cana-2737	326	4	𝑝𝑓𝑐𝑙(𝐺	𝑝𝑓𝑐𝑙(𝐺	PROPN
cana-2737	326	5	)	)	PUNCT
cana-2737	326	6	,	,	PUNCT
cana-2737	326	7	then	then	ADV
cana-2737	326	8	𝐺	𝐺	PROPN
cana-2737	326	9	⊆	⊆	NUM
cana-2737	326	10	𝐻	𝐻	PROPN
cana-2737	326	11	and	and	CCONJ
cana-2737	326	12	𝐻	𝐻	PROPN
cana-2737	326	13	is	be	AUX
cana-2737	326	14	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NUM
cana-2737	326	15	and	and	CCONJ
cana-2737	326	16	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	326	17	−1(𝐻	−1(𝐻	PROPN
cana-2737	326	18	)	)	PUNCT
cana-2737	326	19	⊊	⊊	VERB
cana-2737	326	20	𝑝𝑓𝑐𝑙(ℎ𝑃	𝑝𝑓𝑐𝑙(ℎ𝑃	ADJ
cana-2737	326	21	−1(𝐺	−1(𝐺	NOUN
cana-2737	326	22	)	)	PUNCT
cana-2737	326	23	)	)	PUNCT
cana-2737	327	1	⊆	⊆	X
cana-2737	327	2	𝐾.	𝐾.	NOUN
cana-2737	327	3	then	then	ADV
cana-2737	327	4	by	by	ADP
cana-2737	327	5	theorem	theorem	NOUN
cana-2737	327	6	3.3	3.3	NUM
cana-2737	327	7	,	,	PUNCT
cana-2737	327	8	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	327	9	is	be	AUX
cana-2737	327	10	𝑝𝑓𝑀𝑂	𝑝𝑓𝑀𝑂	NOUN
cana-2737	327	11	mapping	mapping	NOUN
cana-2737	327	12	.	.	PUNCT
cana-2737	328	1	theorem	theorem	VERB
cana-2737	328	2	3.5	3.5	NUM
cana-2737	328	3	if	if	SCONJ
cana-2737	328	4	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	328	5	:	:	PUNCT
cana-2737	328	6	(	(	PUNCT
cana-2737	328	7	𝑋1	𝑋1	PROPN
cana-2737	328	8	,	,	PUNCT
cana-2737	328	9	𝛤𝑃	𝛤𝑃	PROPN
cana-2737	328	10	)	)	PUNCT
cana-2737	328	11	→	→	PUNCT
cana-2737	328	12	(	(	PUNCT
cana-2737	328	13	𝑋2	𝑋2	PROPN
cana-2737	328	14	,	,	PUNCT
cana-2737	328	15	𝛹𝑃	𝛹𝑃	PROPN
cana-2737	328	16	)	)	PUNCT
cana-2737	328	17	and	and	CCONJ
cana-2737	328	18	𝑔𝑃	𝑔𝑃	ADJ
cana-2737	328	19	:	:	PUNCT
cana-2737	328	20	(	(	PUNCT
cana-2737	328	21	𝑋2	𝑋2	PROPN
cana-2737	328	22	,	,	PUNCT
cana-2737	328	23	𝛹𝑃	𝛹𝑃	PROPN
cana-2737	328	24	)	)	PUNCT
cana-2737	328	25	→	→	SYM
cana-2737	328	26	(	(	PUNCT
cana-2737	328	27	𝑋3	𝑋3	NOUN
cana-2737	328	28	,	,	PUNCT
cana-2737	328	29	𝛷𝑃	𝛷𝑃	PROPN
cana-2737	328	30	)	)	PUNCT
cana-2737	328	31	be	be	VERB
cana-2737	328	32	two	two	NUM
cana-2737	328	33	𝑝𝑓	𝑝𝑓	NOUN
cana-2737	328	34	mappings	mapping	NOUN
cana-2737	328	35	and	and	CCONJ
cana-2737	328	36	𝑔𝑃	𝑔𝑃	ADJ
cana-2737	328	37	∘	∘	PROPN
cana-2737	328	38	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	328	39	:	:	PUNCT
cana-2737	328	40	(	(	PUNCT
cana-2737	328	41	𝑋1	𝑋1	PROPN
cana-2737	328	42	,	,	PUNCT
cana-2737	328	43	𝛤𝑃	𝛤𝑃	PROPN
cana-2737	328	44	)	)	PUNCT
cana-2737	328	45	→	→	SYM
cana-2737	328	46	(	(	PUNCT
cana-2737	328	47	𝑋3	𝑋3	NOUN
cana-2737	328	48	,	,	PUNCT
cana-2737	328	49	𝛷𝑃	𝛷𝑃	PROPN
cana-2737	328	50	)	)	PUNCT
cana-2737	328	51	is	be	AUX
cana-2737	328	52	𝑝𝑓𝑀𝑂.	𝑝𝑓𝑀𝑂.	NOUN
cana-2737	328	53	if	if	SCONJ
cana-2737	328	54	𝑔𝑃	𝑔𝑃	VERB
cana-2737	328	55	:	:	PUNCT
cana-2737	328	56	(	(	PUNCT
cana-2737	328	57	𝑋2	𝑋2	PROPN
cana-2737	328	58	,	,	PUNCT
cana-2737	328	59	𝛹𝑃	𝛹𝑃	PROPN
cana-2737	328	60	)	)	PUNCT
cana-2737	328	61	→	→	SYM
cana-2737	328	62	(	(	PUNCT
cana-2737	328	63	𝑋3	𝑋3	NOUN
cana-2737	328	64	,	,	PUNCT
cana-2737	328	65	𝛷𝑃	𝛷𝑃	PROPN
cana-2737	328	66	)	)	PUNCT
cana-2737	328	67	is	be	AUX
cana-2737	328	68	𝑝𝑓𝑀𝐼𝑟𝑟	𝑝𝑓𝑀𝐼𝑟𝑟	PROPN
cana-2737	328	69	,	,	PUNCT
cana-2737	328	70	then	then	ADV
cana-2737	328	71	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	328	72	:	:	PUNCT
cana-2737	328	73	(	(	PUNCT
cana-2737	328	74	𝑋1	𝑋1	PROPN
cana-2737	328	75	,	,	PUNCT
cana-2737	328	76	𝛤𝑃	𝛤𝑃	PROPN
cana-2737	328	77	)	)	PUNCT
cana-2737	328	78	→	→	PUNCT
cana-2737	328	79	(	(	PUNCT
cana-2737	328	80	𝑋2	𝑋2	PROPN
cana-2737	328	81	,	,	PUNCT
cana-2737	328	82	𝛹𝑃	𝛹𝑃	PROPN
cana-2737	328	83	)	)	PUNCT
cana-2737	328	84	is	be	AUX
cana-2737	328	85	𝑝𝑓𝑀𝑂	𝑝𝑓𝑀𝑂	NOUN
cana-2737	328	86	mapping	mapping	NOUN
cana-2737	328	87	.	.	PUNCT
cana-2737	329	1	proof	proof	NOUN
cana-2737	329	2	.	.	PUNCT
cana-2737	330	1	let	let	VERB
cana-2737	330	2	𝐾	𝐾	PRON
cana-2737	330	3	be	be	AUX
cana-2737	330	4	a	a	DET
cana-2737	330	5	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-2737	330	6	in	in	ADP
cana-2737	330	7	(	(	PUNCT
cana-2737	330	8	𝑋1	𝑋1	NOUN
cana-2737	330	9	,	,	PUNCT
cana-2737	330	10	γ𝑃	γ𝑃	NOUN
cana-2737	330	11	)	)	PUNCT
cana-2737	330	12	.	.	PUNCT
cana-2737	331	1	then	then	ADV
cana-2737	331	2	(	(	PUNCT
cana-2737	331	3	𝑔𝑃	𝑔𝑃	ADP
cana-2737	331	4	∘	∘	PROPN
cana-2737	331	5	ℎ𝑃)(𝐾	ℎ𝑃)(𝐾	ADJ
cana-2737	331	6	)	)	PUNCT
cana-2737	331	7	is	be	AUX
cana-2737	331	8	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	ADJ
cana-2737	331	9	of	of	ADP
cana-2737	331	10	(	(	PUNCT
cana-2737	331	11	𝑋3	𝑋3	NOUN
cana-2737	331	12	,	,	PUNCT
cana-2737	331	13	φ𝑃	φ𝑃	NOUN
cana-2737	331	14	)	)	PUNCT
cana-2737	331	15	because	because	SCONJ
cana-2737	331	16	𝑔𝑝	𝑔𝑝	ADP
cana-2737	331	17	∘	∘	PROPN
cana-2737	331	18	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	331	19	is	be	AUX
cana-2737	331	20	𝑝𝑓𝑀𝑂	𝑝𝑓𝑀𝑂	NOUN
cana-2737	331	21	mapping	mapping	NOUN
cana-2737	331	22	.	.	PUNCT
cana-2737	332	1	since	since	SCONJ
cana-2737	332	2	𝑔𝑃	𝑔𝑃	ADJ
cana-2737	332	3	is	be	AUX
cana-2737	332	4	𝑝𝑓𝑀𝐼𝑟𝑟	𝑝𝑓𝑀𝐼𝑟𝑟	PROPN
cana-2737	332	5	and	and	CCONJ
cana-2737	332	6	(	(	PUNCT
cana-2737	332	7	𝑔𝑃	𝑔𝑃	ADP
cana-2737	332	8	∘	∘	PROPN
cana-2737	332	9	ℎ𝑃)(𝐾	ℎ𝑃)(𝐾	ADJ
cana-2737	332	10	)	)	PUNCT
cana-2737	332	11	is	be	AUX
cana-2737	332	12	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	ADJ
cana-2737	332	13	of	of	ADP
cana-2737	332	14	(	(	PUNCT
cana-2737	332	15	𝑋3	𝑋3	NOUN
cana-2737	332	16	,	,	PUNCT
cana-2737	332	17	φ𝑃	φ𝑃	NOUN
cana-2737	332	18	)	)	PUNCT
cana-2737	332	19	,	,	PUNCT
cana-2737	332	20	𝑔𝑃	𝑔𝑃	ADV
cana-2737	332	21	−1((𝑔𝑃	−1((𝑔𝑃	X
cana-2737	332	22	∘	∘	PROPN
cana-2737	332	23	ℎ𝑃)(𝐾	ℎ𝑃)(𝐾	PROPN
cana-2737	332	24	)	)	PUNCT
cana-2737	332	25	)	)	PUNCT
cana-2737	333	1	=	=	SYM
cana-2737	333	2	ℎ𝑃(𝐾	ℎ𝑃(𝐾	PROPN
cana-2737	333	3	)	)	PUNCT
cana-2737	333	4	is	be	AUX
cana-2737	333	5	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	ADJ
cana-2737	333	6	in	in	ADP
cana-2737	333	7	(	(	PUNCT
cana-2737	333	8	𝑋2	𝑋2	ADJ
cana-2737	333	9	,	,	PUNCT
cana-2737	333	10	ψ𝑃	ψ𝑃	NOUN
cana-2737	333	11	)	)	PUNCT
cana-2737	333	12	.	.	PUNCT
cana-2737	334	1	hence	hence	ADV
cana-2737	334	2	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	334	3	is	be	AUX
cana-2737	334	4	𝑝𝑓𝑀𝑂	𝑝𝑓𝑀𝑂	NOUN
cana-2737	334	5	mapping	mapping	NOUN
cana-2737	334	6	theorem	theorem	VERB
cana-2737	334	7	3.6	3.6	NUM
cana-2737	334	8	if	if	SCONJ
cana-2737	334	9	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	334	10	:	:	PUNCT
cana-2737	334	11	(	(	PUNCT
cana-2737	334	12	𝑋1	𝑋1	PROPN
cana-2737	334	13	,	,	PUNCT
cana-2737	334	14	𝛤𝑃	𝛤𝑃	PROPN
cana-2737	334	15	)	)	PUNCT
cana-2737	334	16	→	→	PUNCT
cana-2737	334	17	(	(	PUNCT
cana-2737	334	18	𝑋2	𝑋2	PROPN
cana-2737	334	19	,	,	PUNCT
cana-2737	334	20	𝛹𝑃	𝛹𝑃	PROPN
cana-2737	334	21	)	)	PUNCT
cana-2737	334	22	is	be	AUX
cana-2737	334	23	𝑝𝑓𝑂	𝑝𝑓𝑂	ADJ
cana-2737	334	24	and	and	CCONJ
cana-2737	334	25	𝑔𝑃	𝑔𝑃	ADJ
cana-2737	334	26	:	:	PUNCT
cana-2737	334	27	(	(	PUNCT
cana-2737	334	28	𝑋2	𝑋2	PROPN
cana-2737	334	29	,	,	PUNCT
cana-2737	334	30	𝛹𝑃	𝛹𝑃	PROPN
cana-2737	334	31	)	)	PUNCT
cana-2737	334	32	→	→	SYM
cana-2737	334	33	(	(	PUNCT
cana-2737	334	34	𝑋3	𝑋3	NOUN
cana-2737	334	35	,	,	PUNCT
cana-2737	334	36	𝛷𝑃	𝛷𝑃	PROPN
cana-2737	334	37	)	)	PUNCT
cana-2737	334	38	is	be	AUX
cana-2737	334	39	𝑝𝑓𝑀𝑂	𝑝𝑓𝑀𝑂	NOUN
cana-2737	334	40	mappings	mapping	NOUN
cana-2737	334	41	,	,	PUNCT
cana-2737	334	42	then	then	ADV
cana-2737	334	43	𝑔𝑃	𝑔𝑃	ADP
cana-2737	334	44	∘	∘	PROPN
cana-2737	334	45	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	334	46	:	:	PUNCT
cana-2737	334	47	(	(	PUNCT
cana-2737	334	48	𝑋1	𝑋1	PROPN
cana-2737	334	49	,	,	PUNCT
cana-2737	334	50	𝛤𝑃	𝛤𝑃	PROPN
cana-2737	334	51	)	)	PUNCT
cana-2737	334	52	→	→	SYM
cana-2737	334	53	(	(	PUNCT
cana-2737	334	54	𝑋3	𝑋3	NOUN
cana-2737	334	55	,	,	PUNCT
cana-2737	334	56	𝛷𝑃	𝛷𝑃	PROPN
cana-2737	334	57	)	)	PUNCT
cana-2737	334	58	is	be	AUX
cana-2737	334	59	𝑝𝑓𝑀𝑂.	𝑝𝑓𝑀𝑂.	NOUN
cana-2737	334	60	proof	proof	NOUN
cana-2737	334	61	.	.	PUNCT
cana-2737	335	1	let	let	VERB
cana-2737	335	2	𝐾	𝐾	PRON
cana-2737	335	3	be	be	AUX
cana-2737	335	4	a	a	DET
cana-2737	335	5	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-2737	335	6	in	in	ADP
cana-2737	335	7	(	(	PUNCT
cana-2737	335	8	𝑋1	𝑋1	NOUN
cana-2737	335	9	,	,	PUNCT
cana-2737	335	10	γ𝑃	γ𝑃	NOUN
cana-2737	335	11	)	)	PUNCT
cana-2737	335	12	.	.	PUNCT
cana-2737	336	1	then	then	ADV
cana-2737	336	2	ℎ𝑃(𝐾	ℎ𝑃(𝐾	NOUN
cana-2737	336	3	)	)	PUNCT
cana-2737	336	4	is	be	AUX
cana-2737	336	5	a	a	DET
cana-2737	336	6	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-2737	336	7	of	of	ADP
cana-2737	336	8	(	(	PUNCT
cana-2737	336	9	𝑋2	𝑋2	ADJ
cana-2737	336	10	,	,	PUNCT
cana-2737	336	11	ψ𝑃	ψ𝑃	NOUN
cana-2737	336	12	)	)	PUNCT
cana-2737	336	13	because	because	SCONJ
cana-2737	336	14	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	336	15	is	be	AUX
cana-2737	336	16	a	a	DET
cana-2737	336	17	𝑝𝑓𝑂	𝑝𝑓𝑂	ADJ
cana-2737	336	18	mapping	mapping	NOUN
cana-2737	336	19	.	.	PUNCT
cana-2737	337	1	since	since	SCONJ
cana-2737	337	2	𝑔𝑃	𝑔𝑃	PROPN
cana-2737	337	3	is	be	AUX
cana-2737	337	4	𝑝𝑓𝑀𝑂	𝑝𝑓𝑀𝑂	VERB
cana-2737	337	5	,	,	PUNCT
cana-2737	337	6	𝑔𝑃(ℎ𝑃(𝐾	𝑔𝑃(ℎ𝑃(𝐾	PROPN
cana-2737	337	7	)	)	PUNCT
cana-2737	337	8	)	)	PUNCT
cana-2737	338	1	=	=	PUNCT
cana-2737	338	2	(	(	PUNCT
cana-2737	338	3	𝑔𝑃	𝑔𝑃	ADP
cana-2737	338	4	∘	∘	PROPN
cana-2737	338	5	ℎ𝑃)(𝐾	ℎ𝑃)(𝐾	ADJ
cana-2737	338	6	)	)	PUNCT
cana-2737	338	7	is	be	AUX
cana-2737	338	8	a	a	DET
cana-2737	338	9	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	NOUN
cana-2737	338	10	of	of	ADP
cana-2737	338	11	(	(	PUNCT
cana-2737	338	12	𝑋3	𝑋3	NOUN
cana-2737	338	13	,	,	PUNCT
cana-2737	338	14	φ𝑃	φ𝑃	NOUN
cana-2737	338	15	)	)	PUNCT
cana-2737	338	16	.	.	PUNCT
cana-2737	339	1	hence	hence	ADV
cana-2737	339	2	𝑔𝑃	𝑔𝑃	ADJ
cana-2737	339	3	∘	∘	PROPN
cana-2737	339	4	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	339	5	is	be	AUX
cana-2737	339	6	𝑝𝑓𝑀𝑂	𝑝𝑓𝑀𝑂	NOUN
cana-2737	339	7	mapping	mapping	NOUN
cana-2737	339	8	.	.	PUNCT
cana-2737	340	1	4	4	NUM
cana-2737	340	2	pythagorean	pythagorean	NOUN
cana-2737	340	3	fuzzy	fuzzy	ADJ
cana-2737	340	4	𝑴-closed	𝑴-closed	ADJ
cana-2737	340	5	mapping	mapping	NOUN
cana-2737	340	6	definition	definition	NOUN
cana-2737	340	7	4.1	4.1	NUM
cana-2737	340	8	let	let	VERB
cana-2737	340	9	(	(	PUNCT
cana-2737	340	10	𝑋1	𝑋1	PROPN
cana-2737	340	11	,	,	PUNCT
cana-2737	340	12	𝛤𝑃	𝛤𝑃	PROPN
cana-2737	340	13	)	)	PUNCT
cana-2737	340	14	and	and	CCONJ
cana-2737	340	15	(	(	PUNCT
cana-2737	340	16	𝑋2	𝑋2	PROPN
cana-2737	340	17	,	,	PUNCT
cana-2737	340	18	𝛹𝑃	𝛹𝑃	PROPN
cana-2737	340	19	)	)	PUNCT
cana-2737	340	20	be	be	VERB
cana-2737	340	21	any	any	DET
cana-2737	340	22	two	two	NUM
cana-2737	340	23	𝑝𝑓𝑡𝑠	𝑝𝑓𝑡𝑠	NOUN
cana-2737	340	24	’s	’s	PART
cana-2737	340	25	.	.	PUNCT
cana-2737	341	1	a	a	DET
cana-2737	341	2	mapping	mapping	NOUN
cana-2737	341	3	ℎ𝑃	ℎ𝑃	NOUN
cana-2737	341	4	:	:	PUNCT
cana-2737	341	5	(	(	PUNCT
cana-2737	341	6	𝑋1	𝑋1	PROPN
cana-2737	341	7	,	,	PUNCT
cana-2737	341	8	𝛤𝑃	𝛤𝑃	PROPN
cana-2737	341	9	)	)	PUNCT
cana-2737	341	10	→	→	PUNCT
cana-2737	341	11	(	(	PUNCT
cana-2737	341	12	𝑋2	𝑋2	PROPN
cana-2737	341	13	,	,	PUNCT
cana-2737	341	14	𝛹𝑃	𝛹𝑃	PROPN
cana-2737	341	15	)	)	PUNCT
cana-2737	341	16	is	be	AUX
cana-2737	341	17	said	say	VERB
cana-2737	341	18	to	to	PART
cana-2737	341	19	be	be	AUX
cana-2737	341	20	a	a	DET
cana-2737	341	21	pythagorean	pythagorean	ADJ
cana-2737	341	22	fuzzy	fuzzy	NOUN
cana-2737	341	23	(	(	PUNCT
cana-2737	341	24	resp	resp	NOUN
cana-2737	341	25	.	.	PUNCT
cana-2737	342	1	𝜃	𝜃	X
cana-2737	342	2	,	,	PUNCT
cana-2737	342	3	𝜃𝒮	𝜃𝒮	ADJ
cana-2737	342	4	,	,	PUNCT
cana-2737	342	5	𝛿	𝛿	ADJ
cana-2737	342	6	,	,	PUNCT
cana-2737	342	7	𝛿𝒫	𝛿𝒫	NOUN
cana-2737	342	8	,	,	PUNCT
cana-2737	342	9	𝛿𝒮	𝛿𝒮	NOUN
cana-2737	342	10	,	,	PUNCT
cana-2737	342	11	𝑀	𝑀	PROPN
cana-2737	342	12	and	and	CCONJ
cana-2737	342	13	𝑒	𝑒	AUX
cana-2737	342	14	)	)	PUNCT
cana-2737	342	15	-closed	-close	VERB
cana-2737	342	16	(	(	PUNCT
cana-2737	342	17	briefly	briefly	ADV
cana-2737	342	18	,	,	PUNCT
cana-2737	342	19	𝑝𝑓𝐶	𝑝𝑓𝐶	PROPN
cana-2737	342	20	(	(	PUNCT
cana-2737	342	21	resp	resp	NOUN
cana-2737	342	22	.	.	PUNCT
cana-2737	343	1	𝑝𝑓𝜃𝐶	𝑝𝑓𝜃𝐶	NOUN
cana-2737	343	2	,	,	PUNCT
cana-2737	343	3	𝑝𝑓𝜃𝒮𝐶	𝑝𝑓𝜃𝒮𝐶	ADJ
cana-2737	343	4	,	,	PUNCT
cana-2737	343	5	𝑝𝑓𝛿𝐶	𝑝𝑓𝛿𝐶	ADJ
cana-2737	343	6	,	,	PUNCT
cana-2737	343	7	𝑝𝑓𝛿𝒫𝐶	𝑝𝑓𝛿𝒫𝐶	ADJ
cana-2737	343	8	,	,	PUNCT
cana-2737	343	9	𝑝𝑓𝛿𝒮𝐶	𝑝𝑓𝛿𝒮𝐶	NOUN
cana-2737	343	10	,	,	PUNCT
cana-2737	343	11	𝑝𝑓𝑀𝐶	𝑝𝑓𝑀𝐶	NOUN
cana-2737	343	12	and	and	CCONJ
cana-2737	343	13	𝑝𝑓𝑒𝐶	𝑝𝑓𝑒𝐶	NOUN
cana-2737	343	14	)	)	PUNCT
cana-2737	343	15	)	)	PUNCT
cana-2737	344	1	mapping	mapping	NOUN
cana-2737	344	2	if	if	SCONJ
cana-2737	344	3	the	the	DET
cana-2737	344	4	image	image	NOUN
cana-2737	344	5	of	of	ADP
cana-2737	344	6	every	every	DET
cana-2737	344	7	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-2737	344	8	in	in	ADP
cana-2737	344	9	(	(	PUNCT
cana-2737	344	10	𝑋1	𝑋1	PROPN
cana-2737	344	11	,	,	PUNCT
cana-2737	344	12	𝛤𝑃	𝛤𝑃	PROPN
cana-2737	344	13	)	)	PUNCT
cana-2737	344	14	is	be	AUX
cana-2737	344	15	a	a	DET
cana-2737	344	16	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-2737	344	17	(	(	PUNCT
cana-2737	344	18	resp	resp	NOUN
cana-2737	344	19	.	.	PUNCT
cana-2737	344	20	𝑝𝑓𝜃𝑐𝑠	𝑝𝑓𝜃𝑐𝑠	PROPN
cana-2737	344	21	,	,	PUNCT
cana-2737	344	22	𝑝𝑓𝜃𝒮𝑐𝑠	𝑝𝑓𝜃𝒮𝑐𝑠	PROPN
cana-2737	344	23	,	,	PUNCT
cana-2737	344	24	𝑝𝑓𝛿𝑐𝑠	𝑝𝑓𝛿𝑐𝑠	PROPN
cana-2737	344	25	,	,	PUNCT
cana-2737	344	26	𝑝𝑓𝛿𝒫𝑐𝑠	𝑝𝑓𝛿𝒫𝑐𝑠	PROPN
cana-2737	344	27	,	,	PUNCT
cana-2737	344	28	𝑝𝑓𝛿𝒮𝑐𝑠	𝑝𝑓𝛿𝒮𝑐𝑠	PROPN
cana-2737	344	29	,	,	PUNCT
cana-2737	344	30	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	PRON
cana-2737	344	31	and	and	CCONJ
cana-2737	344	32	𝑝𝑓𝑒𝑐𝑠	𝑝𝑓𝑒𝑐𝑠	NOUN
cana-2737	344	33	)	)	PUNCT
cana-2737	344	34	in	in	ADP
cana-2737	344	35	(	(	PUNCT
cana-2737	344	36	𝑋2	𝑋2	PROPN
cana-2737	344	37	,	,	PUNCT
cana-2737	344	38	𝛹𝑃	𝛹𝑃	PROPN
cana-2737	344	39	)	)	PUNCT
cana-2737	344	40	.	.	PUNCT
cana-2737	345	1	proposition	proposition	NOUN
cana-2737	345	2	4.1	4.1	NUM
cana-2737	345	3	let	let	VERB
cana-2737	345	4	(	(	PUNCT
cana-2737	345	5	𝑋1	𝑋1	PROPN
cana-2737	345	6	,	,	PUNCT
cana-2737	345	7	𝛤𝑃	𝛤𝑃	PROPN
cana-2737	345	8	)	)	PUNCT
cana-2737	345	9	&	&	CCONJ
cana-2737	345	10	(	(	PUNCT
cana-2737	345	11	𝑋2	𝑋2	PROPN
cana-2737	345	12	,	,	PUNCT
cana-2737	345	13	𝛹𝑃	𝛹𝑃	PROPN
cana-2737	345	14	)	)	PUNCT
cana-2737	345	15	be	be	VERB
cana-2737	345	16	a	a	DET
cana-2737	345	17	𝑝𝑓𝑡𝑠	𝑝𝑓𝑡𝑠	NOUN
cana-2737	345	18	’s	’s	PART
cana-2737	345	19	.	.	PUNCT
cana-2737	346	1	let	let	VERB
cana-2737	346	2	ℎ𝑃	ℎ𝑃	NOUN
cana-2737	346	3	:	:	PUNCT
cana-2737	346	4	(	(	PUNCT
cana-2737	346	5	𝑋1	𝑋1	PROPN
cana-2737	346	6	,	,	PUNCT
cana-2737	346	7	𝛤𝑃	𝛤𝑃	PROPN
cana-2737	346	8	)	)	PUNCT
cana-2737	346	9	→	→	PUNCT
cana-2737	346	10	(	(	PUNCT
cana-2737	346	11	𝑋2	𝑋2	PROPN
cana-2737	346	12	,	,	PUNCT
cana-2737	346	13	𝛹𝑃	𝛹𝑃	PROPN
cana-2737	346	14	)	)	PUNCT
cana-2737	346	15	be	be	AUX
cana-2737	346	16	a	a	DET
cana-2737	346	17	mapping	mapping	NOUN
cana-2737	346	18	.	.	PUNCT
cana-2737	347	1	then	then	ADV
cana-2737	347	2	the	the	DET
cana-2737	347	3	following	following	ADJ
cana-2737	347	4	statements	statement	NOUN
cana-2737	347	5	are	be	AUX
cana-2737	347	6	hold	hold	ADJ
cana-2737	347	7	for	for	ADP
cana-2737	347	8	𝑝𝑓𝑡𝑠	𝑝𝑓𝑡𝑠	NOUN
cana-2737	347	9	,	,	PUNCT
cana-2737	347	10	but	but	CCONJ
cana-2737	347	11	not	not	PART
cana-2737	347	12	conversely	conversely	ADV
cana-2737	347	13	.	.	PUNCT
cana-2737	348	1	1	1	X
cana-2737	348	2	.	.	X
cana-2737	349	1	every	every	DET
cana-2737	349	2	𝑝𝑓𝜃𝐶	𝑝𝑓𝜃𝐶	NOUN
cana-2737	349	3	is	be	AUX
cana-2737	349	4	a	a	DET
cana-2737	349	5	𝑝𝑓𝐶.	𝑝𝑓𝐶.	NOUN
cana-2737	349	6	2	2	NUM
cana-2737	349	7	.	.	PUNCT
cana-2737	350	1	every	every	DET
cana-2737	350	2	𝑝𝑓𝜃𝐶	𝑝𝑓𝜃𝐶	NOUN
cana-2737	350	3	is	be	AUX
cana-2737	350	4	a	a	DET
cana-2737	350	5	𝑝𝑓𝜃𝒮𝐶.	𝑝𝑓𝜃𝒮𝐶.	ADJ
cana-2737	350	6	3	3	NUM
cana-2737	350	7	.	.	PUNCT
cana-2737	351	1	every	every	DET
cana-2737	351	2	𝑝𝑓𝜃𝒮𝐶	𝑝𝑓𝜃𝒮𝐶	NOUN
cana-2737	351	3	is	be	AUX
cana-2737	351	4	a	a	DET
cana-2737	351	5	𝑝𝑓𝑀𝐶.	𝑝𝑓𝑀𝐶.	NOUN
cana-2737	351	6	4	4	NUM
cana-2737	351	7	.	.	PUNCT
cana-2737	352	1	every	every	DET
cana-2737	352	2	𝑝𝑓𝛿𝐶	𝑝𝑓𝛿𝐶	ADJ
cana-2737	352	3	is	be	AUX
cana-2737	352	4	a	a	DET
cana-2737	352	5	𝑝𝑓𝛿𝒮𝐶.	𝑝𝑓𝛿𝒮𝐶.	NOUN
cana-2737	352	6	5	5	NUM
cana-2737	352	7	.	.	PUNCT
cana-2737	353	1	every	every	DET
cana-2737	353	2	𝑝𝑓𝛿𝐶	𝑝𝑓𝛿𝐶	ADJ
cana-2737	353	3	is	be	AUX
cana-2737	353	4	a	a	DET
cana-2737	353	5	𝑝𝑓𝛿𝒫𝐶.	𝑝𝑓𝛿𝒫𝐶.	NOUN
cana-2737	353	6	communications	communication	NOUN
cana-2737	353	7	on	on	ADP
cana-2737	353	8	applied	apply	VERB
cana-2737	353	9	nonlinear	nonlinear	ADJ
cana-2737	353	10	analysis	analysis	NOUN
cana-2737	353	11	issn	issn	NOUN
cana-2737	353	12	:	:	PUNCT
cana-2737	353	13	1074	1074	NUM
cana-2737	353	14	-	-	PUNCT
cana-2737	353	15	133x	133x	NUM
cana-2737	353	16	vol	vol	NOUN
cana-2737	353	17	32	32	NUM
cana-2737	353	18	no	no	NOUN
cana-2737	353	19	.	.	PUNCT
cana-2737	354	1	4s	4s	NUM
cana-2737	354	2	(	(	PUNCT
cana-2737	354	3	2025	2025	NUM
cana-2737	354	4	)	)	PUNCT
cana-2737	354	5	36	36	NUM
cana-2737	355	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-2737	355	2	6	6	NUM
cana-2737	355	3	.	.	PUNCT
cana-2737	356	1	every	every	DET
cana-2737	356	2	𝑝𝑓𝛿𝒮𝐶	𝑝𝑓𝛿𝒮𝐶	NOUN
cana-2737	356	3	is	be	AUX
cana-2737	356	4	a	a	DET
cana-2737	356	5	𝑝𝑓𝑒𝐶.	𝑝𝑓𝑒𝐶.	NUM
cana-2737	356	6	7	7	NUM
cana-2737	356	7	.	.	PUNCT
cana-2737	357	1	every	every	DET
cana-2737	357	2	𝑝𝑓𝛿𝒫𝐶	𝑝𝑓𝛿𝒫𝐶	PROPN
cana-2737	357	3	is	be	AUX
cana-2737	357	4	a	a	DET
cana-2737	357	5	𝑝𝑓𝑀𝐶.	𝑝𝑓𝑀𝐶.	ADJ
cana-2737	357	6	8	8	NUM
cana-2737	357	7	.	.	PUNCT
cana-2737	358	1	every	every	DET
cana-2737	358	2	𝑝𝑓𝑀𝐶	𝑝𝑓𝑀𝐶	NOUN
cana-2737	358	3	is	be	AUX
cana-2737	358	4	a	a	DET
cana-2737	358	5	𝑝𝑓𝑒𝐶.	𝑝𝑓𝑒𝐶.	NUM
cana-2737	358	6	9	9	NUM
cana-2737	358	7	.	.	PUNCT
cana-2737	359	1	every	every	DET
cana-2737	359	2	𝑝𝑓𝛿𝐶	𝑝𝑓𝛿𝐶	ADJ
cana-2737	359	3	is	be	AUX
cana-2737	359	4	a	a	DET
cana-2737	359	5	𝑝𝑓𝐶.	𝑝𝑓𝐶.	NOUN
cana-2737	359	6	proof	proof	NOUN
cana-2737	359	7	.	.	PUNCT
cana-2737	360	1	1	1	X
cana-2737	360	2	.	.	X
cana-2737	360	3	let	let	VERB
cana-2737	360	4	𝐵	𝐵	PRON
cana-2737	360	5	be	be	AUX
cana-2737	360	6	a	a	DET
cana-2737	360	7	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-2737	360	8	in	in	ADP
cana-2737	360	9	(	(	PUNCT
cana-2737	360	10	𝑋1	𝑋1	NOUN
cana-2737	360	11	,	,	PUNCT
cana-2737	360	12	γ𝑃	γ𝑃	NOUN
cana-2737	360	13	)	)	PUNCT
cana-2737	360	14	.	.	PUNCT
cana-2737	361	1	since	since	SCONJ
cana-2737	361	2	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	361	3	is	be	AUX
cana-2737	361	4	𝑝𝑓𝜃𝐶	𝑝𝑓𝜃𝐶	NOUN
cana-2737	361	5	,	,	PUNCT
cana-2737	361	6	ℎ𝑃(𝐵	ℎ𝑃(𝐵	NUM
cana-2737	361	7	)	)	PUNCT
cana-2737	361	8	is	be	AUX
cana-2737	361	9	𝑝𝑓𝜃𝑐𝑠	𝑝𝑓𝜃𝑐𝑠	NOUN
cana-2737	361	10	in	in	ADP
cana-2737	361	11	(	(	PUNCT
cana-2737	361	12	𝑋2	𝑋2	ADJ
cana-2737	361	13	,	,	PUNCT
cana-2737	361	14	ψ𝑃	ψ𝑃	NOUN
cana-2737	361	15	)	)	PUNCT
cana-2737	361	16	.	.	PUNCT
cana-2737	362	1	since	since	SCONJ
cana-2737	362	2	every	every	DET
cana-2737	362	3	𝑝𝑓𝜃𝑐𝑠	𝑝𝑓𝜃𝑐𝑠	NOUN
cana-2737	362	4	is	be	AUX
cana-2737	362	5	a	a	DET
cana-2737	362	6	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	PROPN
cana-2737	362	7	,	,	PUNCT
cana-2737	362	8	ℎ𝑃(𝐵	ℎ𝑃(𝐵	NUM
cana-2737	362	9	)	)	PUNCT
cana-2737	362	10	is	be	AUX
cana-2737	362	11	a	a	DET
cana-2737	362	12	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-2737	362	13	in	in	ADP
cana-2737	362	14	(	(	PUNCT
cana-2737	362	15	𝑋2	𝑋2	ADJ
cana-2737	362	16	,	,	PUNCT
cana-2737	362	17	ψ𝑃	ψ𝑃	NOUN
cana-2737	362	18	)	)	PUNCT
cana-2737	362	19	.	.	PUNCT
cana-2737	363	1	hence	hence	ADV
cana-2737	363	2	,	,	PUNCT
cana-2737	363	3	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	363	4	is	be	AUX
cana-2737	363	5	a	a	DET
cana-2737	363	6	𝑝𝑓𝐶.	𝑝𝑓𝐶.	NOUN
cana-2737	363	7	2	2	NUM
cana-2737	363	8	.	.	PUNCT
cana-2737	364	1	let	let	VERB
cana-2737	364	2	𝐵	𝐵	PRON
cana-2737	364	3	be	be	AUX
cana-2737	364	4	a	a	DET
cana-2737	364	5	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-2737	364	6	in	in	ADP
cana-2737	364	7	(	(	PUNCT
cana-2737	364	8	𝑋1	𝑋1	NOUN
cana-2737	364	9	,	,	PUNCT
cana-2737	364	10	γ𝑃	γ𝑃	NOUN
cana-2737	364	11	)	)	PUNCT
cana-2737	364	12	.	.	PUNCT
cana-2737	365	1	since	since	SCONJ
cana-2737	365	2	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	365	3	is	be	AUX
cana-2737	365	4	𝑝𝑓𝜃𝐶	𝑝𝑓𝜃𝐶	NOUN
cana-2737	365	5	,	,	PUNCT
cana-2737	365	6	ℎ𝑃(𝐵	ℎ𝑃(𝐵	NUM
cana-2737	365	7	)	)	PUNCT
cana-2737	365	8	is	be	AUX
cana-2737	365	9	𝑝𝑓𝜃𝑐𝑠	𝑝𝑓𝜃𝑐𝑠	NOUN
cana-2737	365	10	in	in	ADP
cana-2737	365	11	(	(	PUNCT
cana-2737	365	12	𝑋2	𝑋2	ADJ
cana-2737	365	13	,	,	PUNCT
cana-2737	365	14	ψ𝑃	ψ𝑃	NOUN
cana-2737	365	15	)	)	PUNCT
cana-2737	365	16	.	.	PUNCT
cana-2737	366	1	since	since	SCONJ
cana-2737	366	2	every	every	DET
cana-2737	366	3	𝑝𝑓𝜃𝑐𝑠	𝑝𝑓𝜃𝑐𝑠	NOUN
cana-2737	366	4	is	be	AUX
cana-2737	366	5	a	a	DET
cana-2737	366	6	𝑝𝑓𝜃𝒮𝑐𝑠	𝑝𝑓𝜃𝒮𝑐𝑠	NOUN
cana-2737	366	7	,	,	PUNCT
cana-2737	366	8	ℎ𝑃(𝐵	ℎ𝑃(𝐵	NUM
cana-2737	366	9	)	)	PUNCT
cana-2737	366	10	is	be	AUX
cana-2737	366	11	a	a	DET
cana-2737	366	12	𝑝𝑓𝜃𝒮𝑐𝑠	𝑝𝑓𝜃𝒮𝑐𝑠	PROPN
cana-2737	366	13	in	in	ADP
cana-2737	366	14	(	(	PUNCT
cana-2737	366	15	𝑋2	𝑋2	ADJ
cana-2737	366	16	,	,	PUNCT
cana-2737	366	17	ψ𝑃	ψ𝑃	NOUN
cana-2737	366	18	)	)	PUNCT
cana-2737	366	19	.	.	PUNCT
cana-2737	367	1	hence	hence	ADV
cana-2737	367	2	,	,	PUNCT
cana-2737	367	3	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	367	4	is	be	AUX
cana-2737	367	5	a	a	DET
cana-2737	367	6	𝑝𝑓𝜃𝒮𝐶.	𝑝𝑓𝜃𝒮𝐶.	ADJ
cana-2737	367	7	3	3	NUM
cana-2737	367	8	.	.	PUNCT
cana-2737	368	1	let	let	VERB
cana-2737	368	2	𝐵	𝐵	PRON
cana-2737	368	3	be	be	AUX
cana-2737	368	4	a	a	DET
cana-2737	368	5	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-2737	368	6	in	in	ADP
cana-2737	368	7	(	(	PUNCT
cana-2737	368	8	𝑋1	𝑋1	NOUN
cana-2737	368	9	,	,	PUNCT
cana-2737	368	10	γ𝑃	γ𝑃	NOUN
cana-2737	368	11	)	)	PUNCT
cana-2737	368	12	.	.	PUNCT
cana-2737	369	1	since	since	SCONJ
cana-2737	369	2	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	369	3	is	be	AUX
cana-2737	369	4	𝑝𝑓𝜃𝒮𝐶	𝑝𝑓𝜃𝒮𝐶	ADJ
cana-2737	369	5	,	,	PUNCT
cana-2737	369	6	ℎ𝑃(𝐵	ℎ𝑃(𝐵	NUM
cana-2737	369	7	)	)	PUNCT
cana-2737	369	8	is	be	AUX
cana-2737	369	9	𝑝𝑓𝜃𝒮𝑐𝑠	𝑝𝑓𝜃𝒮𝑐𝑠	PROPN
cana-2737	369	10	in	in	ADP
cana-2737	369	11	(	(	PUNCT
cana-2737	369	12	𝑋2	𝑋2	ADJ
cana-2737	369	13	,	,	PUNCT
cana-2737	369	14	ψ𝑃	ψ𝑃	NOUN
cana-2737	369	15	)	)	PUNCT
cana-2737	369	16	.	.	PUNCT
cana-2737	370	1	since	since	SCONJ
cana-2737	370	2	every	every	DET
cana-2737	370	3	𝑝𝑓𝜃𝒮𝑐𝑠	𝑝𝑓𝜃𝒮𝑐𝑠	PROPN
cana-2737	370	4	is	be	AUX
cana-2737	370	5	a	a	DET
cana-2737	370	6	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-2737	370	7	,	,	PUNCT
cana-2737	370	8	ℎ𝑃(𝐵	ℎ𝑃(𝐵	NUM
cana-2737	370	9	)	)	PUNCT
cana-2737	370	10	is	be	AUX
cana-2737	370	11	a	a	DET
cana-2737	370	12	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-2737	370	13	in	in	ADP
cana-2737	370	14	(	(	PUNCT
cana-2737	370	15	𝑋2	𝑋2	ADJ
cana-2737	370	16	,	,	PUNCT
cana-2737	370	17	ψ𝑃	ψ𝑃	NOUN
cana-2737	370	18	)	)	PUNCT
cana-2737	370	19	.	.	PUNCT
cana-2737	371	1	hence	hence	ADV
cana-2737	371	2	,	,	PUNCT
cana-2737	371	3	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	371	4	is	be	AUX
cana-2737	371	5	a	a	DET
cana-2737	371	6	𝑝𝑓𝑀𝐶.	𝑝𝑓𝑀𝐶.	NOUN
cana-2737	371	7	4	4	NUM
cana-2737	371	8	.	.	PUNCT
cana-2737	372	1	let	let	VERB
cana-2737	372	2	𝐵	𝐵	PRON
cana-2737	372	3	be	be	AUX
cana-2737	372	4	a	a	DET
cana-2737	372	5	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-2737	372	6	in	in	ADP
cana-2737	372	7	(	(	PUNCT
cana-2737	372	8	𝑋1	𝑋1	NOUN
cana-2737	372	9	,	,	PUNCT
cana-2737	372	10	γ𝑃	γ𝑃	NOUN
cana-2737	372	11	)	)	PUNCT
cana-2737	372	12	.	.	PUNCT
cana-2737	373	1	since	since	SCONJ
cana-2737	373	2	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	373	3	is	be	AUX
cana-2737	373	4	𝑝𝑓𝛿𝐶	𝑝𝑓𝛿𝐶	ADJ
cana-2737	373	5	,	,	PUNCT
cana-2737	373	6	ℎ𝑃(𝐵	ℎ𝑃(𝐵	NUM
cana-2737	373	7	)	)	PUNCT
cana-2737	373	8	is	be	AUX
cana-2737	373	9	𝑝𝑓𝛿𝑐𝑠	𝑝𝑓𝛿𝑐𝑠	VERB
cana-2737	373	10	in	in	ADP
cana-2737	373	11	(	(	PUNCT
cana-2737	373	12	𝑋2	𝑋2	ADJ
cana-2737	373	13	,	,	PUNCT
cana-2737	373	14	ψ𝑃	ψ𝑃	NOUN
cana-2737	373	15	)	)	PUNCT
cana-2737	373	16	.	.	PUNCT
cana-2737	374	1	since	since	SCONJ
cana-2737	374	2	every	every	DET
cana-2737	374	3	𝑝𝑓𝛿𝑐𝑠	𝑝𝑓𝛿𝑐𝑠	NOUN
cana-2737	374	4	is	be	AUX
cana-2737	374	5	a	a	DET
cana-2737	374	6	𝑝𝑓𝛿𝒮𝑐𝑠	𝑝𝑓𝛿𝒮𝑐𝑠	PROPN
cana-2737	374	7	,	,	PUNCT
cana-2737	374	8	ℎ𝑃(𝐵	ℎ𝑃(𝐵	NUM
cana-2737	374	9	)	)	PUNCT
cana-2737	374	10	is	be	AUX
cana-2737	374	11	a	a	DET
cana-2737	374	12	𝑝𝑓𝛿𝒮𝑐𝑠	𝑝𝑓𝛿𝒮𝑐𝑠	PROPN
cana-2737	374	13	in	in	ADP
cana-2737	374	14	(	(	PUNCT
cana-2737	374	15	𝑋2	𝑋2	ADJ
cana-2737	374	16	,	,	PUNCT
cana-2737	374	17	ψ𝑃	ψ𝑃	NOUN
cana-2737	374	18	)	)	PUNCT
cana-2737	374	19	.	.	PUNCT
cana-2737	375	1	hence	hence	ADV
cana-2737	375	2	,	,	PUNCT
cana-2737	375	3	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	375	4	is	be	AUX
cana-2737	375	5	a	a	DET
cana-2737	375	6	𝑝𝑓𝛿𝒮𝐶.	𝑝𝑓𝛿𝒮𝐶.	NOUN
cana-2737	375	7	5	5	NUM
cana-2737	375	8	.	.	PUNCT
cana-2737	376	1	let	let	VERB
cana-2737	376	2	𝐵	𝐵	PRON
cana-2737	376	3	be	be	AUX
cana-2737	376	4	a	a	DET
cana-2737	376	5	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-2737	376	6	in	in	ADP
cana-2737	376	7	(	(	PUNCT
cana-2737	376	8	𝑋1	𝑋1	NOUN
cana-2737	376	9	,	,	PUNCT
cana-2737	376	10	γ𝑃	γ𝑃	NOUN
cana-2737	376	11	)	)	PUNCT
cana-2737	376	12	.	.	PUNCT
cana-2737	377	1	since	since	SCONJ
cana-2737	377	2	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	377	3	is	be	AUX
cana-2737	377	4	𝑝𝑓𝛿𝐶	𝑝𝑓𝛿𝐶	ADJ
cana-2737	377	5	,	,	PUNCT
cana-2737	377	6	ℎ𝑃(𝐵	ℎ𝑃(𝐵	NUM
cana-2737	377	7	)	)	PUNCT
cana-2737	377	8	is	be	AUX
cana-2737	377	9	𝑝𝑓𝛿𝑐𝑠	𝑝𝑓𝛿𝑐𝑠	VERB
cana-2737	377	10	in	in	ADP
cana-2737	377	11	(	(	PUNCT
cana-2737	377	12	𝑋2	𝑋2	ADJ
cana-2737	377	13	,	,	PUNCT
cana-2737	377	14	ψ𝑃	ψ𝑃	NOUN
cana-2737	377	15	)	)	PUNCT
cana-2737	377	16	.	.	PUNCT
cana-2737	378	1	since	since	SCONJ
cana-2737	378	2	every	every	DET
cana-2737	378	3	𝑝𝑓𝛿𝑐𝑠	𝑝𝑓𝛿𝑐𝑠	NOUN
cana-2737	378	4	is	be	AUX
cana-2737	378	5	a	a	DET
cana-2737	378	6	𝑝𝑓𝛿𝒫𝑐𝑠	𝑝𝑓𝛿𝒫𝑐𝑠	NOUN
cana-2737	378	7	,	,	PUNCT
cana-2737	378	8	ℎ𝑃(𝐵	ℎ𝑃(𝐵	NUM
cana-2737	378	9	)	)	PUNCT
cana-2737	378	10	is	be	AUX
cana-2737	378	11	a	a	DET
cana-2737	378	12	𝑝𝑓𝛿𝒫𝑐𝑠	𝑝𝑓𝛿𝒫𝑐𝑠	PRON
cana-2737	378	13	in	in	ADP
cana-2737	378	14	(	(	PUNCT
cana-2737	378	15	𝑋2	𝑋2	ADJ
cana-2737	378	16	,	,	PUNCT
cana-2737	378	17	ψ𝑃	ψ𝑃	NOUN
cana-2737	378	18	)	)	PUNCT
cana-2737	378	19	.	.	PUNCT
cana-2737	379	1	hence	hence	ADV
cana-2737	379	2	,	,	PUNCT
cana-2737	379	3	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	379	4	is	be	AUX
cana-2737	379	5	a	a	DET
cana-2737	379	6	𝑝𝑓𝛿𝒫𝐶.	𝑝𝑓𝛿𝒫𝐶.	NOUN
cana-2737	379	7	6	6	NUM
cana-2737	379	8	.	.	PUNCT
cana-2737	380	1	let	let	VERB
cana-2737	380	2	𝐵	𝐵	PRON
cana-2737	380	3	be	be	AUX
cana-2737	380	4	a	a	DET
cana-2737	380	5	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-2737	380	6	in	in	ADP
cana-2737	380	7	(	(	PUNCT
cana-2737	380	8	𝑋1	𝑋1	NOUN
cana-2737	380	9	,	,	PUNCT
cana-2737	380	10	γ𝑃	γ𝑃	NOUN
cana-2737	380	11	)	)	PUNCT
cana-2737	380	12	.	.	PUNCT
cana-2737	381	1	since	since	SCONJ
cana-2737	381	2	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	381	3	is	be	AUX
cana-2737	381	4	𝑝𝑓𝛿𝒮𝐶	𝑝𝑓𝛿𝒮𝐶	NOUN
cana-2737	381	5	,	,	PUNCT
cana-2737	381	6	ℎ𝑃(𝐵	ℎ𝑃(𝐵	NUM
cana-2737	381	7	)	)	PUNCT
cana-2737	381	8	is	be	AUX
cana-2737	381	9	𝑝𝑓𝛿𝒮𝑐𝑠	𝑝𝑓𝛿𝒮𝑐𝑠	PROPN
cana-2737	381	10	in	in	ADP
cana-2737	381	11	(	(	PUNCT
cana-2737	381	12	𝑋2	𝑋2	ADJ
cana-2737	381	13	,	,	PUNCT
cana-2737	381	14	ψ𝑃	ψ𝑃	NOUN
cana-2737	381	15	)	)	PUNCT
cana-2737	381	16	.	.	PUNCT
cana-2737	382	1	since	since	SCONJ
cana-2737	382	2	every	every	DET
cana-2737	382	3	𝑝𝑓𝛿𝒮𝑐𝑠	𝑝𝑓𝛿𝒮𝑐𝑠	NOUN
cana-2737	382	4	is	be	AUX
cana-2737	382	5	a	a	DET
cana-2737	382	6	𝑝𝑓𝑒𝑐𝑠	𝑝𝑓𝑒𝑐𝑠	NOUN
cana-2737	382	7	,	,	PUNCT
cana-2737	382	8	ℎ𝑃(𝐵	ℎ𝑃(𝐵	NUM
cana-2737	382	9	)	)	PUNCT
cana-2737	382	10	is	be	AUX
cana-2737	382	11	a	a	DET
cana-2737	382	12	𝑝𝑓𝑒𝑐𝑠	𝑝𝑓𝑒𝑐𝑠	NOUN
cana-2737	382	13	in	in	ADP
cana-2737	382	14	(	(	PUNCT
cana-2737	382	15	𝑋2	𝑋2	ADJ
cana-2737	382	16	,	,	PUNCT
cana-2737	382	17	ψ𝑃	ψ𝑃	NOUN
cana-2737	382	18	)	)	PUNCT
cana-2737	382	19	.	.	PUNCT
cana-2737	383	1	hence	hence	ADV
cana-2737	383	2	,	,	PUNCT
cana-2737	383	3	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	383	4	is	be	AUX
cana-2737	383	5	a	a	DET
cana-2737	383	6	𝑝𝑓𝑒𝐶.	𝑝𝑓𝑒𝐶.	NUM
cana-2737	383	7	7	7	NUM
cana-2737	383	8	.	.	PUNCT
cana-2737	384	1	let	let	VERB
cana-2737	384	2	𝐵	𝐵	PRON
cana-2737	384	3	be	be	AUX
cana-2737	384	4	a	a	DET
cana-2737	384	5	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-2737	384	6	in	in	ADP
cana-2737	384	7	(	(	PUNCT
cana-2737	384	8	𝑋1	𝑋1	NOUN
cana-2737	384	9	,	,	PUNCT
cana-2737	384	10	γ𝑃	γ𝑃	NOUN
cana-2737	384	11	)	)	PUNCT
cana-2737	384	12	.	.	PUNCT
cana-2737	385	1	since	since	SCONJ
cana-2737	385	2	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	385	3	is	be	AUX
cana-2737	385	4	𝑝𝑓𝛿𝒫𝐶	𝑝𝑓𝛿𝒫𝐶	PROPN
cana-2737	385	5	,	,	PUNCT
cana-2737	385	6	ℎ𝑃(𝐵	ℎ𝑃(𝐵	NUM
cana-2737	385	7	)	)	PUNCT
cana-2737	385	8	is	be	AUX
cana-2737	385	9	𝑝𝑓𝛿𝒫𝑐𝑠	𝑝𝑓𝛿𝒫𝑐𝑠	PRON
cana-2737	385	10	in	in	ADP
cana-2737	385	11	(	(	PUNCT
cana-2737	385	12	𝑋2	𝑋2	ADJ
cana-2737	385	13	,	,	PUNCT
cana-2737	385	14	ψ𝑃	ψ𝑃	NOUN
cana-2737	385	15	)	)	PUNCT
cana-2737	385	16	.	.	PUNCT
cana-2737	386	1	since	since	SCONJ
cana-2737	386	2	every	every	DET
cana-2737	386	3	𝑝𝑓𝛿𝒫𝑐𝑠	𝑝𝑓𝛿𝒫𝑐𝑠	PRON
cana-2737	386	4	is	be	AUX
cana-2737	386	5	a	a	DET
cana-2737	386	6	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-2737	386	7	,	,	PUNCT
cana-2737	386	8	ℎ𝑃(𝐵	ℎ𝑃(𝐵	NUM
cana-2737	386	9	)	)	PUNCT
cana-2737	386	10	is	be	AUX
cana-2737	386	11	a	a	DET
cana-2737	386	12	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-2737	386	13	in	in	ADP
cana-2737	386	14	(	(	PUNCT
cana-2737	386	15	𝑋2	𝑋2	ADJ
cana-2737	386	16	,	,	PUNCT
cana-2737	386	17	ψ𝑃	ψ𝑃	NOUN
cana-2737	386	18	)	)	PUNCT
cana-2737	386	19	.	.	PUNCT
cana-2737	387	1	hence	hence	ADV
cana-2737	387	2	,	,	PUNCT
cana-2737	387	3	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	387	4	is	be	AUX
cana-2737	387	5	a	a	DET
cana-2737	387	6	𝑝𝑓𝑀𝐶.	𝑝𝑓𝑀𝐶.	NOUN
cana-2737	387	7	8	8	NUM
cana-2737	387	8	.	.	PUNCT
cana-2737	388	1	let	let	VERB
cana-2737	388	2	𝐵	𝐵	PRON
cana-2737	388	3	be	be	AUX
cana-2737	388	4	a	a	DET
cana-2737	388	5	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-2737	388	6	in	in	ADP
cana-2737	388	7	(	(	PUNCT
cana-2737	388	8	𝑋1	𝑋1	NOUN
cana-2737	388	9	,	,	PUNCT
cana-2737	388	10	γ𝑃	γ𝑃	NOUN
cana-2737	388	11	)	)	PUNCT
cana-2737	388	12	.	.	PUNCT
cana-2737	389	1	since	since	SCONJ
cana-2737	389	2	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	389	3	is	be	AUX
cana-2737	389	4	𝑝𝑓𝑀𝐶	𝑝𝑓𝑀𝐶	NOUN
cana-2737	389	5	,	,	PUNCT
cana-2737	389	6	ℎ𝑃(𝐵	ℎ𝑃(𝐵	NUM
cana-2737	389	7	)	)	PUNCT
cana-2737	389	8	is	be	AUX
cana-2737	389	9	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-2737	389	10	in	in	ADP
cana-2737	389	11	(	(	PUNCT
cana-2737	389	12	𝑋2	𝑋2	ADJ
cana-2737	389	13	,	,	PUNCT
cana-2737	389	14	ψ𝑃	ψ𝑃	NOUN
cana-2737	389	15	)	)	PUNCT
cana-2737	389	16	.	.	PUNCT
cana-2737	390	1	since	since	SCONJ
cana-2737	390	2	every	every	DET
cana-2737	390	3	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-2737	390	4	is	be	AUX
cana-2737	390	5	a	a	DET
cana-2737	390	6	𝑝𝑓𝑒𝑐𝑠	𝑝𝑓𝑒𝑐𝑠	NOUN
cana-2737	390	7	,	,	PUNCT
cana-2737	390	8	ℎ𝑃(𝐵	ℎ𝑃(𝐵	NUM
cana-2737	390	9	)	)	PUNCT
cana-2737	390	10	is	be	AUX
cana-2737	390	11	a	a	DET
cana-2737	390	12	𝑝𝑓𝑒𝑐𝑠	𝑝𝑓𝑒𝑐𝑠	NOUN
cana-2737	390	13	in	in	ADP
cana-2737	390	14	(	(	PUNCT
cana-2737	390	15	𝑋2	𝑋2	ADJ
cana-2737	390	16	,	,	PUNCT
cana-2737	390	17	ψ𝑃	ψ𝑃	NOUN
cana-2737	390	18	)	)	PUNCT
cana-2737	390	19	.	.	PUNCT
cana-2737	391	1	hence	hence	ADV
cana-2737	391	2	,	,	PUNCT
cana-2737	391	3	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	391	4	is	be	AUX
cana-2737	391	5	a	a	DET
cana-2737	391	6	𝑝𝑓𝑒𝐶.	𝑝𝑓𝑒𝐶.	NUM
cana-2737	391	7	9	9	NUM
cana-2737	391	8	.	.	PUNCT
cana-2737	392	1	let	let	VERB
cana-2737	392	2	𝐵	𝐵	PRON
cana-2737	392	3	be	be	AUX
cana-2737	392	4	a	a	DET
cana-2737	392	5	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-2737	392	6	in	in	ADP
cana-2737	392	7	(	(	PUNCT
cana-2737	392	8	𝑋1	𝑋1	NOUN
cana-2737	392	9	,	,	PUNCT
cana-2737	392	10	γ𝑃	γ𝑃	NOUN
cana-2737	392	11	)	)	PUNCT
cana-2737	392	12	.	.	PUNCT
cana-2737	393	1	since	since	SCONJ
cana-2737	393	2	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	393	3	is	be	AUX
cana-2737	393	4	𝑝𝑓𝛿𝐶	𝑝𝑓𝛿𝐶	ADJ
cana-2737	393	5	,	,	PUNCT
cana-2737	393	6	ℎ𝑃(𝐵	ℎ𝑃(𝐵	NUM
cana-2737	393	7	)	)	PUNCT
cana-2737	393	8	is	be	AUX
cana-2737	393	9	𝑝𝑓𝛿𝑐𝑠	𝑝𝑓𝛿𝑐𝑠	VERB
cana-2737	393	10	in	in	ADP
cana-2737	393	11	(	(	PUNCT
cana-2737	393	12	𝑋2	𝑋2	ADJ
cana-2737	393	13	,	,	PUNCT
cana-2737	393	14	ψ𝑃	ψ𝑃	NOUN
cana-2737	393	15	)	)	PUNCT
cana-2737	393	16	.	.	PUNCT
cana-2737	394	1	since	since	SCONJ
cana-2737	394	2	every	every	DET
cana-2737	394	3	𝑝𝑓𝛿𝑐𝑠	𝑝𝑓𝛿𝑐𝑠	NOUN
cana-2737	394	4	is	be	AUX
cana-2737	394	5	a	a	DET
cana-2737	394	6	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	PROPN
cana-2737	394	7	,	,	PUNCT
cana-2737	394	8	ℎ𝑃(𝐵	ℎ𝑃(𝐵	NUM
cana-2737	394	9	)	)	PUNCT
cana-2737	394	10	is	be	AUX
cana-2737	394	11	a	a	DET
cana-2737	394	12	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-2737	394	13	in	in	ADP
cana-2737	394	14	(	(	PUNCT
cana-2737	394	15	𝑋2	𝑋2	ADJ
cana-2737	394	16	,	,	PUNCT
cana-2737	394	17	ψ𝑃	ψ𝑃	NOUN
cana-2737	394	18	)	)	PUNCT
cana-2737	394	19	.	.	PUNCT
cana-2737	395	1	hence	hence	ADV
cana-2737	395	2	,	,	PUNCT
cana-2737	395	3	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	395	4	is	be	AUX
cana-2737	395	5	a	a	DET
cana-2737	395	6	𝑝𝑓𝐶	𝑝𝑓𝐶	PROPN
cana-2737	395	7	remark	remark	NOUN
cana-2737	395	8	4.1	4.1	NUM
cana-2737	395	9	we	we	PRON
cana-2737	395	10	obtain	obtain	VERB
cana-2737	395	11	the	the	DET
cana-2737	395	12	following	follow	VERB
cana-2737	395	13	diagram	diagram	NOUN
cana-2737	395	14	from	from	ADP
cana-2737	395	15	the	the	DET
cana-2737	395	16	results	result	NOUN
cana-2737	395	17	are	be	AUX
cana-2737	395	18	discussed	discuss	VERB
cana-2737	395	19	above	above	ADV
cana-2737	395	20	.	.	PUNCT
cana-2737	396	1	note	note	NOUN
cana-2737	396	2	:	:	PUNCT
cana-2737	396	3	𝐴	𝐴	PROPN
cana-2737	396	4	→	→	SYM
cana-2737	396	5	𝐵	𝐵	PROPN
cana-2737	396	6	denotes	denote	NOUN
cana-2737	396	7	𝐴	𝐴	PROPN
cana-2737	396	8	implies	imply	VERB
cana-2737	396	9	𝐵	𝐵	PROPN
cana-2737	396	10	,	,	PUNCT
cana-2737	396	11	but	but	CCONJ
cana-2737	396	12	not	not	PART
cana-2737	396	13	conversely	conversely	ADV
cana-2737	396	14	.	.	PUNCT
cana-2737	397	1	communications	communication	NOUN
cana-2737	397	2	on	on	ADP
cana-2737	397	3	applied	apply	VERB
cana-2737	397	4	nonlinear	nonlinear	ADJ
cana-2737	397	5	analysis	analysis	NOUN
cana-2737	397	6	issn	issn	NOUN
cana-2737	397	7	:	:	PUNCT
cana-2737	397	8	1074	1074	NUM
cana-2737	397	9	-	-	PUNCT
cana-2737	397	10	133x	133x	NUM
cana-2737	397	11	vol	vol	NOUN
cana-2737	397	12	32	32	NUM
cana-2737	397	13	no	no	NOUN
cana-2737	397	14	.	.	PUNCT
cana-2737	398	1	4s	4s	NUM
cana-2737	398	2	(	(	PUNCT
cana-2737	398	3	2025	2025	NUM
cana-2737	398	4	)	)	PUNCT
cana-2737	398	5	37	37	NUM
cana-2737	398	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2737	398	7	example	example	NOUN
cana-2737	398	8	4.1	4.1	NUM
cana-2737	398	9	let	let	VERB
cana-2737	398	10	𝑋1	𝑋1	NOUN
cana-2737	398	11	=	=	SYM
cana-2737	398	12	𝑋2	𝑋2	VERB
cana-2737	398	13	=	=	PUNCT
cana-2737	398	14	{	{	PUNCT
cana-2737	398	15	𝑥1	𝑥1	NOUN
cana-2737	398	16	,	,	PUNCT
cana-2737	398	17	𝑥2	𝑥2	NOUN
cana-2737	398	18	}	}	PUNCT
cana-2737	398	19	and	and	CCONJ
cana-2737	398	20	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2737	398	21	’s	’s	PART
cana-2737	398	22	𝐴1	𝐴1	PROPN
cana-2737	398	23	,	,	PUNCT
cana-2737	398	24	𝐴2	𝐴2	PROPN
cana-2737	398	25	,	,	PUNCT
cana-2737	398	26	𝐴3	𝐴3	PROPN
cana-2737	398	27	&	&	CCONJ
cana-2737	398	28	𝐴4	𝐴4	PROPN
cana-2737	398	29	in	in	ADP
cana-2737	398	30	𝑋1	𝑋1	PROPN
cana-2737	398	31	are	be	AUX
cana-2737	398	32	defined	define	VERB
cana-2737	398	33	as	as	ADP
cana-2737	398	34	,	,	PUNCT
cana-2737	398	35	𝐴1	𝐴1	PROPN
cana-2737	398	36	=	=	SYM
cana-2737	398	37	{	{	PUNCT
cana-2737	398	38	<	<	X
cana-2737	398	39	𝑥1	𝑥1	PROPN
cana-2737	398	40	,	,	PUNCT
cana-2737	398	41	0.20,0.80	0.20,0.80	NOUN
cana-2737	398	42	>	>	X
cana-2737	398	43	,	,	PUNCT
cana-2737	398	44	<	<	X
cana-2737	398	45	𝑥2	𝑥2	NOUN
cana-2737	398	46	,	,	PUNCT
cana-2737	398	47	0.40,0.60	0.40,0.60	NUM
cana-2737	398	48	>	>	PUNCT
cana-2737	398	49	}	}	PUNCT
cana-2737	398	50	𝐴2	𝐴2	PROPN
cana-2737	398	51	=	=	SYM
cana-2737	398	52	{	{	PUNCT
cana-2737	398	53	<	<	X
cana-2737	398	54	𝑥1	𝑥1	PROPN
cana-2737	398	55	,	,	PUNCT
cana-2737	398	56	0.10,0.90	0.10,0.90	NUM
cana-2737	398	57	>	>	X
cana-2737	398	58	,	,	PUNCT
cana-2737	398	59	<	<	X
cana-2737	398	60	𝑥2	𝑥2	NOUN
cana-2737	398	61	,	,	PUNCT
cana-2737	398	62	0.30,0.70	0.30,0.70	PRON
cana-2737	398	63	>	>	PUNCT
cana-2737	398	64	}	}	PUNCT
cana-2737	398	65	𝐴3	𝐴3	PROPN
cana-2737	399	1	=	=	SYM
cana-2737	399	2	{	{	PUNCT
cana-2737	399	3	<	<	X
cana-2737	399	4	𝑥1	𝑥1	PROPN
cana-2737	399	5	,	,	PUNCT
cana-2737	399	6	0.90,0.10	0.90,0.10	NOUN
cana-2737	399	7	>	>	X
cana-2737	399	8	,	,	PUNCT
cana-2737	399	9	<	<	X
cana-2737	399	10	𝑥2	𝑥2	NOUN
cana-2737	399	11	,	,	PUNCT
cana-2737	399	12	0.70,0.30	0.70,0.30	NOUN
cana-2737	399	13	>	>	PUNCT
cana-2737	399	14	}	}	PUNCT
cana-2737	399	15	𝐴4	𝐴4	PROPN
cana-2737	399	16	=	=	PUNCT
cana-2737	399	17	{	{	PUNCT
cana-2737	399	18	<	<	X
cana-2737	399	19	𝑥1	𝑥1	PROPN
cana-2737	399	20	,	,	PUNCT
cana-2737	399	21	0.20,0.80	0.20,0.80	NOUN
cana-2737	399	22	>	>	X
cana-2737	399	23	,	,	PUNCT
cana-2737	399	24	<	<	X
cana-2737	399	25	𝑥2	𝑥2	NOUN
cana-2737	399	26	,	,	PUNCT
cana-2737	399	27	0.30,0.70	0.30,0.70	PRON
cana-2737	399	28	>	>	PUNCT
cana-2737	399	29	}	}	PUNCT
cana-2737	399	30	now	now	ADV
cana-2737	399	31	,	,	PUNCT
cana-2737	399	32	we	we	PRON
cana-2737	399	33	have	have	VERB
cana-2737	399	34	γ𝑃	γ𝑃	ADJ
cana-2737	399	35	=	=	PUNCT
cana-2737	399	36	ψ𝑃	ψ𝑃	NOUN
cana-2737	399	37	=	=	SYM
cana-2737	399	38	{	{	PUNCT
cana-2737	399	39	0𝑋	0𝑋	PROPN
cana-2737	399	40	,	,	PUNCT
cana-2737	399	41	1𝑋	1𝑋	PROPN
cana-2737	399	42	,	,	PUNCT
cana-2737	399	43	𝐴1	𝐴1	PROPN
cana-2737	399	44	,	,	PUNCT
cana-2737	399	45	𝐴2	𝐴2	PROPN
cana-2737	399	46	,	,	PUNCT
cana-2737	399	47	𝐴3	𝐴3	PROPN
cana-2737	399	48	,	,	PUNCT
cana-2737	399	49	𝐴4	𝐴4	PROPN
cana-2737	399	50	}	}	PUNCT
cana-2737	399	51	.	.	PUNCT
cana-2737	400	1	let	let	VERB
cana-2737	400	2	ℎ𝑃	ℎ𝑃	NOUN
cana-2737	400	3	:	:	PUNCT
cana-2737	400	4	(	(	PUNCT
cana-2737	400	5	𝑋1	𝑋1	NOUN
cana-2737	400	6	,	,	PUNCT
cana-2737	400	7	γ𝑃	γ𝑃	NOUN
cana-2737	400	8	)	)	PUNCT
cana-2737	400	9	→	→	SYM
cana-2737	400	10	(	(	PUNCT
cana-2737	400	11	𝑋2	𝑋2	ADJ
cana-2737	400	12	,	,	PUNCT
cana-2737	400	13	ψ𝑃	ψ𝑃	NOUN
cana-2737	400	14	)	)	PUNCT
cana-2737	400	15	be	be	VERB
cana-2737	400	16	an	an	DET
cana-2737	400	17	identity	identity	NOUN
cana-2737	400	18	mapping	mapping	NOUN
cana-2737	400	19	.	.	PUNCT
cana-2737	401	1	then	then	ADV
cana-2737	401	2	,	,	PUNCT
cana-2737	401	3	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	401	4	is	be	AUX
cana-2737	401	5	𝑝𝑓𝐶	𝑝𝑓𝐶	NOUN
cana-2737	401	6	but	but	CCONJ
cana-2737	401	7	not	not	PART
cana-2737	401	8	𝑝𝑓𝜃𝐶	𝑝𝑓𝜃𝐶	NOUN
cana-2737	401	9	,	,	PUNCT
cana-2737	401	10	because	because	SCONJ
cana-2737	401	11	the	the	DET
cana-2737	401	12	set	set	NOUN
cana-2737	401	13	𝐴1	𝐴1	PROPN
cana-2737	401	14	𝑐	𝑐	PROPN
cana-2737	401	15	is	be	AUX
cana-2737	401	16	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-2737	401	17	in	in	ADP
cana-2737	401	18	𝑋1	𝑋1	PROPN
cana-2737	401	19	but	but	CCONJ
cana-2737	401	20	ℎ𝑃(𝐴1	ℎ𝑃(𝐴1	NOUN
cana-2737	401	21	𝑐	𝑐	NOUN
cana-2737	401	22	)	)	PUNCT
cana-2737	401	23	=	=	PUNCT
cana-2737	402	1	𝐴1	𝐴1	PROPN
cana-2737	402	2	𝑐	𝑐	NOUN
cana-2737	402	3	is	be	AUX
cana-2737	402	4	not	not	PART
cana-2737	402	5	𝑝𝑓𝜃𝑐𝑠	𝑝𝑓𝜃𝑐𝑠	NOUN
cana-2737	402	6	in	in	ADP
cana-2737	402	7	𝑋2	𝑋2	PROPN
cana-2737	402	8	.	.	PUNCT
cana-2737	403	1	example	example	NOUN
cana-2737	403	2	4.2	4.2	NUM
cana-2737	403	3	let	let	VERB
cana-2737	403	4	𝑋1	𝑋1	NOUN
cana-2737	403	5	=	=	SYM
cana-2737	403	6	𝑋2	𝑋2	VERB
cana-2737	403	7	=	=	PUNCT
cana-2737	403	8	{	{	PUNCT
cana-2737	403	9	𝑥1	𝑥1	NOUN
cana-2737	403	10	,	,	PUNCT
cana-2737	403	11	𝑥2	𝑥2	NOUN
cana-2737	403	12	}	}	PUNCT
cana-2737	403	13	and	and	CCONJ
cana-2737	403	14	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2737	403	15	’s	’s	PART
cana-2737	403	16	𝐴1	𝐴1	PROPN
cana-2737	403	17	,	,	PUNCT
cana-2737	403	18	𝐴2	𝐴2	PROPN
cana-2737	403	19	,	,	PUNCT
cana-2737	403	20	𝐴3	𝐴3	PROPN
cana-2737	403	21	,	,	PUNCT
cana-2737	403	22	𝐴4	𝐴4	PROPN
cana-2737	403	23	in	in	ADP
cana-2737	403	24	𝑋2	𝑋2	PROPN
cana-2737	403	25	&	&	CCONJ
cana-2737	403	26	𝐵1	𝐵1	PROPN
cana-2737	403	27	in	in	ADP
cana-2737	403	28	𝑋1	𝑋1	PROPN
cana-2737	403	29	are	be	AUX
cana-2737	403	30	defined	define	VERB
cana-2737	403	31	as	as	ADP
cana-2737	403	32	,	,	PUNCT
cana-2737	403	33	𝐴1	𝐴1	PROPN
cana-2737	403	34	=	=	SYM
cana-2737	403	35	{	{	PUNCT
cana-2737	403	36	<	<	X
cana-2737	403	37	𝑥1	𝑥1	PROPN
cana-2737	403	38	,	,	PUNCT
cana-2737	403	39	0.20,0.80	0.20,0.80	NOUN
cana-2737	403	40	>	>	X
cana-2737	403	41	,	,	PUNCT
cana-2737	403	42	<	<	X
cana-2737	403	43	𝑥2	𝑥2	NOUN
cana-2737	403	44	,	,	PUNCT
cana-2737	403	45	0.40,0.60	0.40,0.60	NUM
cana-2737	403	46	>	>	PUNCT
cana-2737	403	47	}	}	PUNCT
cana-2737	403	48	𝐴2	𝐴2	PROPN
cana-2737	403	49	=	=	SYM
cana-2737	403	50	{	{	PUNCT
cana-2737	403	51	<	<	X
cana-2737	403	52	𝑥1	𝑥1	PROPN
cana-2737	403	53	,	,	PUNCT
cana-2737	403	54	0.10,0.90	0.10,0.90	NUM
cana-2737	403	55	>	>	X
cana-2737	403	56	,	,	PUNCT
cana-2737	403	57	<	<	X
cana-2737	403	58	𝑥2	𝑥2	NOUN
cana-2737	403	59	,	,	PUNCT
cana-2737	403	60	0.30,0.70	0.30,0.70	PRON
cana-2737	403	61	>	>	PUNCT
cana-2737	403	62	}	}	PUNCT
cana-2737	403	63	𝐴3	𝐴3	PROPN
cana-2737	404	1	=	=	SYM
cana-2737	404	2	{	{	PUNCT
cana-2737	404	3	<	<	X
cana-2737	404	4	𝑥1	𝑥1	PROPN
cana-2737	404	5	,	,	PUNCT
cana-2737	404	6	0.90,0.10	0.90,0.10	NOUN
cana-2737	404	7	>	>	X
cana-2737	404	8	,	,	PUNCT
cana-2737	404	9	<	<	X
cana-2737	404	10	𝑥2	𝑥2	NOUN
cana-2737	404	11	,	,	PUNCT
cana-2737	404	12	0.70,0.30	0.70,0.30	NOUN
cana-2737	404	13	>	>	PUNCT
cana-2737	404	14	}	}	PUNCT
cana-2737	404	15	𝐴4	𝐴4	PROPN
cana-2737	404	16	=	=	PUNCT
cana-2737	404	17	{	{	PUNCT
cana-2737	404	18	<	<	X
cana-2737	404	19	𝑥1	𝑥1	PROPN
cana-2737	404	20	,	,	PUNCT
cana-2737	404	21	0.20,0.80	0.20,0.80	NOUN
cana-2737	404	22	>	>	X
cana-2737	404	23	,	,	PUNCT
cana-2737	404	24	<	<	X
cana-2737	404	25	𝑥2	𝑥2	NOUN
cana-2737	404	26	,	,	PUNCT
cana-2737	404	27	0.30,0.70	0.30,0.70	PRON
cana-2737	404	28	>	>	PUNCT
cana-2737	404	29	}	}	PUNCT
cana-2737	404	30	𝐵1	𝐵1	NOUN
cana-2737	404	31	=	=	PUNCT
cana-2737	404	32	{	{	PUNCT
cana-2737	404	33	<	<	X
cana-2737	404	34	𝑥1	𝑥1	PROPN
cana-2737	404	35	,	,	PUNCT
cana-2737	404	36	0.80,0.20	0.80,0.20	X
cana-2737	404	37	>	>	X
cana-2737	404	38	,	,	PUNCT
cana-2737	404	39	<	<	X
cana-2737	404	40	𝑥2	𝑥2	NOUN
cana-2737	404	41	,	,	PUNCT
cana-2737	404	42	0.60,0.40	0.60,0.40	X
cana-2737	404	43	>	>	PUNCT
cana-2737	404	44	}	}	PUNCT
cana-2737	404	45	now	now	ADV
cana-2737	404	46	,	,	PUNCT
cana-2737	404	47	we	we	PRON
cana-2737	404	48	have	have	VERB
cana-2737	404	49	γ𝑃	γ𝑃	ADJ
cana-2737	404	50	=	=	PUNCT
cana-2737	404	51	{	{	PUNCT
cana-2737	404	52	0𝑋	0𝑋	PROPN
cana-2737	404	53	,	,	PUNCT
cana-2737	404	54	1𝑋	1𝑋	PROPN
cana-2737	404	55	,	,	PUNCT
cana-2737	404	56	𝐵1	𝐵1	PROPN
cana-2737	404	57	}	}	PUNCT
cana-2737	404	58	and	and	CCONJ
cana-2737	404	59	ψ𝑃	ψ𝑃	NOUN
cana-2737	404	60	=	=	SYM
cana-2737	404	61	{	{	PUNCT
cana-2737	404	62	0𝑋	0𝑋	PROPN
cana-2737	404	63	,	,	PUNCT
cana-2737	404	64	1𝑋	1𝑋	PROPN
cana-2737	404	65	,	,	PUNCT
cana-2737	404	66	𝐴1	𝐴1	PROPN
cana-2737	404	67	,	,	PUNCT
cana-2737	404	68	𝐴2	𝐴2	PROPN
cana-2737	404	69	,	,	PUNCT
cana-2737	404	70	𝐴3	𝐴3	PROPN
cana-2737	404	71	,	,	PUNCT
cana-2737	404	72	𝐴4	𝐴4	PROPN
cana-2737	404	73	}	}	PUNCT
cana-2737	404	74	.	.	PUNCT
cana-2737	405	1	let	let	VERB
cana-2737	405	2	ℎ𝑃	ℎ𝑃	NOUN
cana-2737	405	3	:	:	PUNCT
cana-2737	405	4	(	(	PUNCT
cana-2737	405	5	𝑋1	𝑋1	NOUN
cana-2737	405	6	,	,	PUNCT
cana-2737	405	7	γ𝑃	γ𝑃	NOUN
cana-2737	405	8	)	)	PUNCT
cana-2737	405	9	→	→	SYM
cana-2737	405	10	(	(	PUNCT
cana-2737	405	11	𝑋2	𝑋2	ADJ
cana-2737	405	12	,	,	PUNCT
cana-2737	405	13	ψ𝑃	ψ𝑃	NOUN
cana-2737	405	14	)	)	PUNCT
cana-2737	405	15	be	be	VERB
cana-2737	405	16	an	an	DET
cana-2737	405	17	identity	identity	NOUN
cana-2737	405	18	mapping	mapping	NOUN
cana-2737	405	19	.	.	PUNCT
cana-2737	406	1	then	then	ADV
cana-2737	406	2	,	,	PUNCT
cana-2737	406	3	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	406	4	is	be	AUX
cana-2737	406	5	𝑝𝑓𝜃𝒮𝐶	𝑝𝑓𝜃𝒮𝐶	ADJ
cana-2737	406	6	(	(	PUNCT
cana-2737	406	7	resp	resp	NOUN
cana-2737	406	8	.	.	PUNCT
cana-2737	407	1	𝑝𝑓𝛿𝒮𝐶	𝑝𝑓𝛿𝒮𝐶	PROPN
cana-2737	407	2	)	)	PUNCT
cana-2737	407	3	but	but	CCONJ
cana-2737	407	4	not	not	PART
cana-2737	407	5	𝑝𝑓𝜃𝐶	𝑝𝑓𝜃𝐶	NOUN
cana-2737	407	6	(	(	PUNCT
cana-2737	407	7	resp	resp	NOUN
cana-2737	407	8	.	.	PUNCT
cana-2737	408	1	𝑝𝑓𝛿𝐶	𝑝𝑓𝛿𝐶	ADJ
cana-2737	408	2	)	)	PUNCT
cana-2737	408	3	,	,	PUNCT
cana-2737	408	4	because	because	SCONJ
cana-2737	408	5	the	the	DET
cana-2737	408	6	set	set	NOUN
cana-2737	408	7	𝐵1	𝐵1	NOUN
cana-2737	408	8	𝑐	𝑐	NOUN
cana-2737	408	9	is	be	AUX
cana-2737	408	10	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-2737	408	11	in	in	ADP
cana-2737	408	12	𝑋1	𝑋1	PROPN
cana-2737	408	13	but	but	CCONJ
cana-2737	408	14	ℎ𝑃(𝐵1	ℎ𝑃(𝐵1	PROPN
cana-2737	408	15	𝑐	𝑐	NOUN
cana-2737	408	16	)	)	PUNCT
cana-2737	408	17	=	=	NOUN
cana-2737	409	1	𝐵1	𝐵1	NOUN
cana-2737	409	2	𝑐	𝑐	NOUN
cana-2737	409	3	is	be	AUX
cana-2737	409	4	not	not	PART
cana-2737	409	5	𝑝𝑓𝜃𝑐𝑠	𝑝𝑓𝜃𝑐𝑠	NOUN
cana-2737	409	6	(	(	PUNCT
cana-2737	409	7	resp	resp	NOUN
cana-2737	409	8	.	.	PUNCT
cana-2737	410	1	𝑝𝑓𝛿𝑐𝑠	𝑝𝑓𝛿𝑐𝑠	PROPN
cana-2737	410	2	)	)	PUNCT
cana-2737	410	3	in	in	ADP
cana-2737	410	4	𝑋2	𝑋2	PROPN
cana-2737	410	5	.	.	PUNCT
cana-2737	411	1	example	example	NOUN
cana-2737	411	2	4.3	4.3	NUM
cana-2737	411	3	let	let	VERB
cana-2737	411	4	𝑋1	𝑋1	NOUN
cana-2737	411	5	=	=	SYM
cana-2737	411	6	𝑋2	𝑋2	VERB
cana-2737	411	7	=	=	PUNCT
cana-2737	411	8	{	{	PUNCT
cana-2737	411	9	𝑥1	𝑥1	NOUN
cana-2737	411	10	,	,	PUNCT
cana-2737	411	11	𝑥2	𝑥2	NOUN
cana-2737	411	12	}	}	PUNCT
cana-2737	411	13	and	and	CCONJ
cana-2737	411	14	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2737	411	15	’s	’s	PART
cana-2737	411	16	𝐴1	𝐴1	PROPN
cana-2737	411	17	,	,	PUNCT
cana-2737	411	18	𝐴2	𝐴2	PROPN
cana-2737	411	19	,	,	PUNCT
cana-2737	411	20	𝐴3	𝐴3	PROPN
cana-2737	411	21	,	,	PUNCT
cana-2737	411	22	𝐴4	𝐴4	PROPN
cana-2737	411	23	in	in	ADP
cana-2737	411	24	𝑋2	𝑋2	PROPN
cana-2737	411	25	&	&	CCONJ
cana-2737	411	26	𝐵1	𝐵1	PROPN
cana-2737	411	27	in	in	ADP
cana-2737	411	28	𝑋1	𝑋1	PROPN
cana-2737	411	29	are	be	AUX
cana-2737	411	30	defined	define	VERB
cana-2737	411	31	as	as	ADP
cana-2737	411	32	,	,	PUNCT
cana-2737	411	33	𝐴1	𝐴1	PROPN
cana-2737	411	34	=	=	PUNCT
cana-2737	411	35	𝐵1	𝐵1	PROPN
cana-2737	411	36	=	=	SYM
cana-2737	411	37	{	{	PUNCT
cana-2737	411	38	<	<	X
cana-2737	411	39	𝑥1	𝑥1	PROPN
cana-2737	411	40	,	,	PUNCT
cana-2737	411	41	0.20,0.80	0.20,0.80	NOUN
cana-2737	411	42	>	>	X
cana-2737	411	43	,	,	PUNCT
cana-2737	411	44	<	<	X
cana-2737	411	45	𝑥2	𝑥2	NOUN
cana-2737	411	46	,	,	PUNCT
cana-2737	411	47	0.40,0.60	0.40,0.60	NUM
cana-2737	411	48	>	>	PUNCT
cana-2737	411	49	}	}	PUNCT
cana-2737	411	50	𝐴2	𝐴2	PROPN
cana-2737	411	51	=	=	SYM
cana-2737	411	52	{	{	PUNCT
cana-2737	411	53	<	<	X
cana-2737	411	54	𝑥1	𝑥1	PROPN
cana-2737	411	55	,	,	PUNCT
cana-2737	411	56	0.10,0.90	0.10,0.90	NUM
cana-2737	411	57	>	>	X
cana-2737	411	58	,	,	PUNCT
cana-2737	411	59	<	<	X
cana-2737	411	60	𝑥2	𝑥2	NOUN
cana-2737	411	61	,	,	PUNCT
cana-2737	411	62	0.30,0.70	0.30,0.70	PRON
cana-2737	411	63	>	>	PUNCT
cana-2737	411	64	}	}	PUNCT
cana-2737	411	65	𝐴3	𝐴3	PROPN
cana-2737	411	66	=	=	SYM
cana-2737	411	67	{	{	PUNCT
cana-2737	411	68	<	<	X
cana-2737	411	69	𝑥1	𝑥1	PROPN
cana-2737	411	70	,	,	PUNCT
cana-2737	411	71	0.90,0.10	0.90,0.10	NOUN
cana-2737	411	72	>	>	X
cana-2737	411	73	,	,	PUNCT
cana-2737	411	74	<	<	X
cana-2737	411	75	𝑥2	𝑥2	NOUN
cana-2737	411	76	,	,	PUNCT
cana-2737	411	77	0.70,0.30	0.70,0.30	NOUN
cana-2737	411	78	>	>	PUNCT
cana-2737	411	79	}	}	PUNCT
cana-2737	411	80	𝐴4	𝐴4	PROPN
cana-2737	411	81	=	=	PUNCT
cana-2737	411	82	{	{	PUNCT
cana-2737	411	83	<	<	X
cana-2737	411	84	𝑥1	𝑥1	PROPN
cana-2737	411	85	,	,	PUNCT
cana-2737	411	86	0.20,0.80	0.20,0.80	NOUN
cana-2737	411	87	>	>	X
cana-2737	411	88	,	,	PUNCT
cana-2737	411	89	<	<	X
cana-2737	411	90	𝑥2	𝑥2	NOUN
cana-2737	411	91	,	,	PUNCT
cana-2737	411	92	0.30,0.70	0.30,0.70	PRON
cana-2737	411	93	>	>	PUNCT
cana-2737	411	94	}	}	PUNCT
cana-2737	411	95	now	now	ADV
cana-2737	411	96	,	,	PUNCT
cana-2737	411	97	we	we	PRON
cana-2737	411	98	have	have	VERB
cana-2737	411	99	γ𝑃	γ𝑃	ADJ
cana-2737	411	100	=	=	PUNCT
cana-2737	411	101	{	{	PUNCT
cana-2737	411	102	0𝑋	0𝑋	PROPN
cana-2737	411	103	,	,	PUNCT
cana-2737	411	104	1𝑋	1𝑋	PROPN
cana-2737	411	105	,	,	PUNCT
cana-2737	411	106	𝐵1	𝐵1	PROPN
cana-2737	411	107	}	}	PUNCT
cana-2737	411	108	and	and	CCONJ
cana-2737	411	109	ψ𝑃	ψ𝑃	NOUN
cana-2737	411	110	=	=	SYM
cana-2737	411	111	{	{	PUNCT
cana-2737	411	112	0𝑋	0𝑋	PROPN
cana-2737	411	113	,	,	PUNCT
cana-2737	411	114	1𝑋	1𝑋	PROPN
cana-2737	411	115	,	,	PUNCT
cana-2737	411	116	𝐴1	𝐴1	PROPN
cana-2737	411	117	,	,	PUNCT
cana-2737	411	118	𝐴2	𝐴2	PROPN
cana-2737	411	119	,	,	PUNCT
cana-2737	411	120	𝐴3	𝐴3	PROPN
cana-2737	411	121	,	,	PUNCT
cana-2737	411	122	𝐴4	𝐴4	PROPN
cana-2737	411	123	}	}	PUNCT
cana-2737	411	124	.	.	PUNCT
cana-2737	412	1	let	let	VERB
cana-2737	412	2	ℎ𝑃	ℎ𝑃	NOUN
cana-2737	412	3	:	:	PUNCT
cana-2737	412	4	(	(	PUNCT
cana-2737	412	5	𝑋1	𝑋1	NOUN
cana-2737	412	6	,	,	PUNCT
cana-2737	412	7	γ𝑃	γ𝑃	NOUN
cana-2737	412	8	)	)	PUNCT
cana-2737	412	9	→	→	SYM
cana-2737	412	10	(	(	PUNCT
cana-2737	412	11	𝑋2	𝑋2	ADJ
cana-2737	412	12	,	,	PUNCT
cana-2737	412	13	ψ𝑃	ψ𝑃	NOUN
cana-2737	412	14	)	)	PUNCT
cana-2737	412	15	be	be	VERB
cana-2737	412	16	an	an	DET
cana-2737	412	17	identity	identity	NOUN
cana-2737	412	18	mapping	mapping	NOUN
cana-2737	412	19	.	.	PUNCT
cana-2737	413	1	then	then	ADV
cana-2737	413	2	,	,	PUNCT
cana-2737	413	3	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	413	4	is	be	AUX
cana-2737	413	5	𝑝𝑓𝑀𝐶	𝑝𝑓𝑀𝐶	NOUN
cana-2737	413	6	but	but	CCONJ
cana-2737	413	7	not	not	PART
cana-2737	413	8	𝑝𝑓𝜃𝒮𝐶	𝑝𝑓𝜃𝒮𝐶	ADJ
cana-2737	413	9	,	,	PUNCT
cana-2737	413	10	because	because	SCONJ
cana-2737	413	11	the	the	DET
cana-2737	413	12	set	set	NOUN
cana-2737	413	13	𝐵1	𝐵1	NOUN
cana-2737	413	14	𝑐	𝑐	NOUN
cana-2737	413	15	is	be	AUX
cana-2737	413	16	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-2737	413	17	in	in	ADP
cana-2737	413	18	𝑋1	𝑋1	PROPN
cana-2737	413	19	but	but	CCONJ
cana-2737	413	20	ℎ𝑃(𝐵1	ℎ𝑃(𝐵1	PROPN
cana-2737	413	21	𝑐	𝑐	NOUN
cana-2737	413	22	)	)	PUNCT
cana-2737	413	23	=	=	NOUN
cana-2737	414	1	𝐵1	𝐵1	NOUN
cana-2737	414	2	𝑐	𝑐	NOUN
cana-2737	414	3	is	be	AUX
cana-2737	414	4	not	not	PART
cana-2737	414	5	𝑝𝑓𝜃𝒮𝑐𝑠	𝑝𝑓𝜃𝒮𝑐𝑠	PROPN
cana-2737	414	6	in	in	ADP
cana-2737	414	7	𝑋2	𝑋2	PROPN
cana-2737	414	8	.	.	PUNCT
cana-2737	415	1	example	example	NOUN
cana-2737	415	2	4.4	4.4	NUM
cana-2737	415	3	let	let	VERB
cana-2737	415	4	𝑋1	𝑋1	NOUN
cana-2737	415	5	=	=	SYM
cana-2737	415	6	𝑋2	𝑋2	VERB
cana-2737	415	7	=	=	PUNCT
cana-2737	415	8	{	{	PUNCT
cana-2737	415	9	𝑥1	𝑥1	NOUN
cana-2737	415	10	,	,	PUNCT
cana-2737	415	11	𝑥2	𝑥2	NOUN
cana-2737	415	12	}	}	PUNCT
cana-2737	415	13	and	and	CCONJ
cana-2737	415	14	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2737	415	15	’s	’s	PART
cana-2737	415	16	𝐴1	𝐴1	PROPN
cana-2737	415	17	,	,	PUNCT
cana-2737	415	18	𝐴2	𝐴2	PROPN
cana-2737	415	19	,	,	PUNCT
cana-2737	415	20	𝐴3	𝐴3	PROPN
cana-2737	415	21	,	,	PUNCT
cana-2737	415	22	𝐴4	𝐴4	PROPN
cana-2737	415	23	in	in	ADP
cana-2737	415	24	𝑋2	𝑋2	PROPN
cana-2737	415	25	&	&	CCONJ
cana-2737	415	26	𝐵1	𝐵1	PROPN
cana-2737	415	27	in	in	ADP
cana-2737	415	28	𝑋1	𝑋1	PROPN
cana-2737	415	29	are	be	AUX
cana-2737	415	30	defined	define	VERB
cana-2737	415	31	as	as	ADP
cana-2737	415	32	,	,	PUNCT
cana-2737	415	33	𝐴1	𝐴1	PROPN
cana-2737	415	34	=	=	SYM
cana-2737	415	35	{	{	PUNCT
cana-2737	415	36	<	<	X
cana-2737	415	37	𝑥1	𝑥1	PROPN
cana-2737	415	38	,	,	PUNCT
cana-2737	415	39	0.20,0.80	0.20,0.80	NOUN
cana-2737	415	40	>	>	X
cana-2737	415	41	,	,	PUNCT
cana-2737	415	42	<	<	X
cana-2737	415	43	𝑥2	𝑥2	NOUN
cana-2737	415	44	,	,	PUNCT
cana-2737	415	45	0.40,0.60	0.40,0.60	NUM
cana-2737	415	46	>	>	PUNCT
cana-2737	415	47	}	}	PUNCT
cana-2737	415	48	𝐴2	𝐴2	PROPN
cana-2737	415	49	=	=	SYM
cana-2737	415	50	{	{	PUNCT
cana-2737	415	51	<	<	X
cana-2737	415	52	𝑥1	𝑥1	PROPN
cana-2737	415	53	,	,	PUNCT
cana-2737	415	54	0.10,0.90	0.10,0.90	NUM
cana-2737	415	55	>	>	X
cana-2737	415	56	,	,	PUNCT
cana-2737	415	57	<	<	X
cana-2737	415	58	𝑥2	𝑥2	NOUN
cana-2737	415	59	,	,	PUNCT
cana-2737	415	60	0.30,0.70	0.30,0.70	PRON
cana-2737	415	61	>	>	PUNCT
cana-2737	415	62	}	}	PUNCT
cana-2737	415	63	𝐴3	𝐴3	PROPN
cana-2737	416	1	=	=	SYM
cana-2737	416	2	{	{	PUNCT
cana-2737	416	3	<	<	X
cana-2737	416	4	𝑥1	𝑥1	PROPN
cana-2737	416	5	,	,	PUNCT
cana-2737	416	6	0.90,0.10	0.90,0.10	NOUN
cana-2737	416	7	>	>	X
cana-2737	416	8	,	,	PUNCT
cana-2737	416	9	<	<	X
cana-2737	416	10	𝑥2	𝑥2	NOUN
cana-2737	416	11	,	,	PUNCT
cana-2737	416	12	0.70,0.30	0.70,0.30	NOUN
cana-2737	416	13	>	>	PUNCT
cana-2737	416	14	}	}	PUNCT
cana-2737	416	15	𝐴4	𝐴4	PROPN
cana-2737	416	16	=	=	PUNCT
cana-2737	416	17	{	{	PUNCT
cana-2737	416	18	<	<	X
cana-2737	416	19	𝑥1	𝑥1	PROPN
cana-2737	416	20	,	,	PUNCT
cana-2737	416	21	0.20,0.80	0.20,0.80	NOUN
cana-2737	416	22	>	>	X
cana-2737	416	23	,	,	PUNCT
cana-2737	416	24	<	<	X
cana-2737	416	25	𝑥2	𝑥2	NOUN
cana-2737	416	26	,	,	PUNCT
cana-2737	416	27	0.30,0.70	0.30,0.70	PRON
cana-2737	416	28	>	>	PUNCT
cana-2737	416	29	}	}	PUNCT
cana-2737	416	30	𝐵1	𝐵1	NOUN
cana-2737	416	31	=	=	PUNCT
cana-2737	416	32	{	{	PUNCT
cana-2737	416	33	<	<	X
cana-2737	416	34	𝑥1	𝑥1	PROPN
cana-2737	416	35	,	,	PUNCT
cana-2737	416	36	0.40,0.20	0.40,0.20	NOUN
cana-2737	416	37	>	>	X
cana-2737	416	38	,	,	PUNCT
cana-2737	416	39	<	<	X
cana-2737	416	40	𝑥2	𝑥2	NOUN
cana-2737	416	41	,	,	PUNCT
cana-2737	416	42	0.40,0.40	0.40,0.40	NOUN
cana-2737	416	43	>	>	X
cana-2737	416	44	}	}	PUNCT
cana-2737	416	45	communications	communication	NOUN
cana-2737	416	46	on	on	ADP
cana-2737	416	47	applied	apply	VERB
cana-2737	416	48	nonlinear	nonlinear	ADJ
cana-2737	416	49	analysis	analysis	NOUN
cana-2737	416	50	issn	issn	NOUN
cana-2737	416	51	:	:	PUNCT
cana-2737	416	52	1074	1074	NUM
cana-2737	416	53	-	-	PUNCT
cana-2737	416	54	133x	133x	NUM
cana-2737	416	55	vol	vol	NOUN
cana-2737	416	56	32	32	NUM
cana-2737	416	57	no	no	NOUN
cana-2737	416	58	.	.	PUNCT
cana-2737	417	1	4s	4s	NUM
cana-2737	417	2	(	(	PUNCT
cana-2737	417	3	2025	2025	NUM
cana-2737	417	4	)	)	PUNCT
cana-2737	417	5	38	38	NUM
cana-2737	417	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2737	417	7	now	now	ADV
cana-2737	417	8	,	,	PUNCT
cana-2737	417	9	we	we	PRON
cana-2737	417	10	have	have	VERB
cana-2737	417	11	γ𝑃	γ𝑃	ADJ
cana-2737	417	12	=	=	PUNCT
cana-2737	417	13	{	{	PUNCT
cana-2737	417	14	0𝑋	0𝑋	PROPN
cana-2737	417	15	,	,	PUNCT
cana-2737	417	16	1𝑋	1𝑋	PROPN
cana-2737	417	17	,	,	PUNCT
cana-2737	417	18	𝐵1	𝐵1	PROPN
cana-2737	417	19	}	}	PUNCT
cana-2737	417	20	and	and	CCONJ
cana-2737	417	21	ψ𝑃	ψ𝑃	NOUN
cana-2737	417	22	=	=	SYM
cana-2737	417	23	{	{	PUNCT
cana-2737	417	24	0𝑋	0𝑋	PROPN
cana-2737	417	25	,	,	PUNCT
cana-2737	417	26	1𝑋	1𝑋	PROPN
cana-2737	417	27	,	,	PUNCT
cana-2737	417	28	𝐴1	𝐴1	PROPN
cana-2737	417	29	,	,	PUNCT
cana-2737	417	30	𝐴2	𝐴2	PROPN
cana-2737	417	31	,	,	PUNCT
cana-2737	417	32	𝐴3	𝐴3	PROPN
cana-2737	417	33	,	,	PUNCT
cana-2737	417	34	𝐴4	𝐴4	PROPN
cana-2737	417	35	}	}	PUNCT
cana-2737	417	36	.	.	PUNCT
cana-2737	418	1	let	let	VERB
cana-2737	418	2	ℎ𝑃	ℎ𝑃	NOUN
cana-2737	418	3	:	:	PUNCT
cana-2737	418	4	(	(	PUNCT
cana-2737	418	5	𝑋1	𝑋1	NOUN
cana-2737	418	6	,	,	PUNCT
cana-2737	418	7	γ𝑃	γ𝑃	NOUN
cana-2737	418	8	)	)	PUNCT
cana-2737	418	9	→	→	SYM
cana-2737	418	10	(	(	PUNCT
cana-2737	418	11	𝑋2	𝑋2	ADJ
cana-2737	418	12	,	,	PUNCT
cana-2737	418	13	ψ𝑃	ψ𝑃	NOUN
cana-2737	418	14	)	)	PUNCT
cana-2737	418	15	be	be	VERB
cana-2737	418	16	an	an	DET
cana-2737	418	17	identity	identity	NOUN
cana-2737	418	18	mapping	mapping	NOUN
cana-2737	418	19	.	.	PUNCT
cana-2737	419	1	then	then	ADV
cana-2737	419	2	,	,	PUNCT
cana-2737	419	3	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	419	4	is	be	AUX
cana-2737	419	5	𝑝𝑓𝑒𝐶	𝑝𝑓𝑒𝐶	NOUN
cana-2737	419	6	but	but	CCONJ
cana-2737	419	7	not	not	PART
cana-2737	419	8	𝑝𝑓𝑀𝐶	𝑝𝑓𝑀𝐶	NOUN
cana-2737	419	9	,	,	PUNCT
cana-2737	419	10	because	because	SCONJ
cana-2737	419	11	the	the	DET
cana-2737	419	12	set	set	NOUN
cana-2737	419	13	𝐵1	𝐵1	NOUN
cana-2737	419	14	𝑐	𝑐	NOUN
cana-2737	419	15	is	be	AUX
cana-2737	419	16	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-2737	419	17	in	in	ADP
cana-2737	419	18	𝑋1	𝑋1	PROPN
cana-2737	419	19	but	but	CCONJ
cana-2737	419	20	ℎ𝑃(𝐵1	ℎ𝑃(𝐵1	PROPN
cana-2737	419	21	𝑐	𝑐	NOUN
cana-2737	419	22	)	)	PUNCT
cana-2737	419	23	=	=	NOUN
cana-2737	420	1	𝐵1	𝐵1	NOUN
cana-2737	420	2	𝑐	𝑐	NOUN
cana-2737	420	3	is	be	AUX
cana-2737	420	4	not	not	PART
cana-2737	420	5	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-2737	420	6	in	in	ADP
cana-2737	420	7	𝑋2	𝑋2	PROPN
cana-2737	420	8	.	.	PUNCT
cana-2737	421	1	example	example	NOUN
cana-2737	421	2	4.5	4.5	NUM
cana-2737	421	3	let	let	VERB
cana-2737	421	4	𝑋1	𝑋1	NOUN
cana-2737	421	5	=	=	SYM
cana-2737	421	6	𝑋2	𝑋2	VERB
cana-2737	421	7	=	=	PUNCT
cana-2737	421	8	{	{	PUNCT
cana-2737	421	9	𝑥1	𝑥1	NOUN
cana-2737	421	10	,	,	PUNCT
cana-2737	421	11	𝑥2	𝑥2	NOUN
cana-2737	421	12	}	}	PUNCT
cana-2737	421	13	and	and	CCONJ
cana-2737	421	14	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2737	421	15	’s	’s	PART
cana-2737	421	16	𝐴1	𝐴1	PROPN
cana-2737	421	17	,	,	PUNCT
cana-2737	421	18	𝐴2	𝐴2	PROPN
cana-2737	421	19	,	,	PUNCT
cana-2737	421	20	𝐴3	𝐴3	PROPN
cana-2737	421	21	,	,	PUNCT
cana-2737	421	22	𝐴4	𝐴4	PROPN
cana-2737	421	23	in	in	ADP
cana-2737	421	24	𝑋2	𝑋2	PROPN
cana-2737	421	25	&	&	CCONJ
cana-2737	421	26	𝐵1	𝐵1	PROPN
cana-2737	421	27	in	in	ADP
cana-2737	421	28	𝑋1	𝑋1	PROPN
cana-2737	421	29	are	be	AUX
cana-2737	421	30	defined	define	VERB
cana-2737	421	31	as	as	ADP
cana-2737	421	32	,	,	PUNCT
cana-2737	421	33	𝐴1	𝐴1	PROPN
cana-2737	421	34	=	=	SYM
cana-2737	421	35	{	{	PUNCT
cana-2737	421	36	<	<	X
cana-2737	421	37	𝑥1	𝑥1	PROPN
cana-2737	421	38	,	,	PUNCT
cana-2737	421	39	0.20,0.80	0.20,0.80	NOUN
cana-2737	421	40	>	>	X
cana-2737	421	41	,	,	PUNCT
cana-2737	421	42	<	<	X
cana-2737	421	43	𝑥2	𝑥2	NOUN
cana-2737	421	44	,	,	PUNCT
cana-2737	421	45	0.40,0.60	0.40,0.60	NUM
cana-2737	421	46	>	>	PUNCT
cana-2737	421	47	}	}	PUNCT
cana-2737	421	48	𝐴2	𝐴2	PROPN
cana-2737	421	49	=	=	SYM
cana-2737	421	50	{	{	PUNCT
cana-2737	421	51	<	<	X
cana-2737	421	52	𝑥1	𝑥1	PROPN
cana-2737	421	53	,	,	PUNCT
cana-2737	421	54	0.10,0.90	0.10,0.90	NUM
cana-2737	421	55	>	>	X
cana-2737	421	56	,	,	PUNCT
cana-2737	421	57	<	<	X
cana-2737	421	58	𝑥2	𝑥2	NOUN
cana-2737	421	59	,	,	PUNCT
cana-2737	421	60	0.30,0.70	0.30,0.70	PRON
cana-2737	421	61	>	>	PUNCT
cana-2737	421	62	}	}	PUNCT
cana-2737	421	63	𝐴3	𝐴3	PROPN
cana-2737	422	1	=	=	SYM
cana-2737	422	2	{	{	PUNCT
cana-2737	422	3	<	<	X
cana-2737	422	4	𝑥1	𝑥1	PROPN
cana-2737	422	5	,	,	PUNCT
cana-2737	422	6	0.90,0.10	0.90,0.10	NOUN
cana-2737	422	7	>	>	X
cana-2737	422	8	,	,	PUNCT
cana-2737	422	9	<	<	X
cana-2737	422	10	𝑥2	𝑥2	NOUN
cana-2737	422	11	,	,	PUNCT
cana-2737	422	12	0.70,0.30	0.70,0.30	NOUN
cana-2737	422	13	>	>	PUNCT
cana-2737	422	14	}	}	PUNCT
cana-2737	422	15	𝐵1	𝐵1	NOUN
cana-2737	422	16	=	=	PUNCT
cana-2737	422	17	𝐴4	𝐴4	PROPN
cana-2737	422	18	=	=	PUNCT
cana-2737	422	19	{	{	PUNCT
cana-2737	422	20	<	<	X
cana-2737	422	21	𝑥1	𝑥1	PROPN
cana-2737	422	22	,	,	PUNCT
cana-2737	422	23	0.20,0.80	0.20,0.80	NOUN
cana-2737	422	24	>	>	X
cana-2737	422	25	,	,	PUNCT
cana-2737	422	26	<	<	X
cana-2737	422	27	𝑥2	𝑥2	NOUN
cana-2737	422	28	,	,	PUNCT
cana-2737	422	29	0.30,0.70	0.30,0.70	PRON
cana-2737	422	30	>	>	PUNCT
cana-2737	422	31	}	}	PUNCT
cana-2737	422	32	now	now	ADV
cana-2737	422	33	,	,	PUNCT
cana-2737	422	34	we	we	PRON
cana-2737	422	35	have	have	VERB
cana-2737	422	36	γ𝑃	γ𝑃	ADJ
cana-2737	422	37	=	=	PUNCT
cana-2737	422	38	{	{	PUNCT
cana-2737	422	39	0𝑋	0𝑋	PROPN
cana-2737	422	40	,	,	PUNCT
cana-2737	422	41	1𝑋	1𝑋	PROPN
cana-2737	422	42	,	,	PUNCT
cana-2737	422	43	𝐵1	𝐵1	PROPN
cana-2737	422	44	}	}	PUNCT
cana-2737	422	45	and	and	CCONJ
cana-2737	422	46	ψ𝑃	ψ𝑃	NOUN
cana-2737	422	47	=	=	SYM
cana-2737	422	48	{	{	PUNCT
cana-2737	422	49	0𝑋	0𝑋	PROPN
cana-2737	422	50	,	,	PUNCT
cana-2737	422	51	1𝑋	1𝑋	PROPN
cana-2737	422	52	,	,	PUNCT
cana-2737	422	53	𝐴1	𝐴1	PROPN
cana-2737	422	54	,	,	PUNCT
cana-2737	422	55	𝐴2	𝐴2	PROPN
cana-2737	422	56	,	,	PUNCT
cana-2737	422	57	𝐴3	𝐴3	PROPN
cana-2737	422	58	,	,	PUNCT
cana-2737	422	59	𝐴4	𝐴4	PROPN
cana-2737	422	60	}	}	PUNCT
cana-2737	422	61	.	.	PUNCT
cana-2737	423	1	let	let	VERB
cana-2737	423	2	ℎ𝑃	ℎ𝑃	NOUN
cana-2737	423	3	:	:	PUNCT
cana-2737	423	4	(	(	PUNCT
cana-2737	423	5	𝑋1	𝑋1	NOUN
cana-2737	423	6	,	,	PUNCT
cana-2737	423	7	γ𝑃	γ𝑃	NOUN
cana-2737	423	8	)	)	PUNCT
cana-2737	423	9	→	→	SYM
cana-2737	423	10	(	(	PUNCT
cana-2737	423	11	𝑋2	𝑋2	ADJ
cana-2737	423	12	,	,	PUNCT
cana-2737	423	13	ψ𝑃	ψ𝑃	NOUN
cana-2737	423	14	)	)	PUNCT
cana-2737	423	15	be	be	VERB
cana-2737	423	16	an	an	DET
cana-2737	423	17	identity	identity	NOUN
cana-2737	423	18	mapping	mapping	NOUN
cana-2737	423	19	.	.	PUNCT
cana-2737	424	1	then	then	ADV
cana-2737	424	2	,	,	PUNCT
cana-2737	424	3	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	424	4	is	be	AUX
cana-2737	424	5	𝑝𝑓𝐶	𝑝𝑓𝐶	PROPN
cana-2737	424	6	(	(	PUNCT
cana-2737	424	7	resp	resp	NOUN
cana-2737	424	8	.	.	PUNCT
cana-2737	425	1	𝑝𝑓𝑒𝐶	𝑝𝑓𝑒𝐶	NOUN
cana-2737	425	2	and	and	CCONJ
cana-2737	425	3	𝑝𝑓𝛿𝒫𝐶	𝑝𝑓𝛿𝒫𝐶	PROPN
cana-2737	425	4	)	)	PUNCT
cana-2737	425	5	but	but	CCONJ
cana-2737	425	6	not	not	PART
cana-2737	425	7	𝑝𝑓𝛿𝐶	𝑝𝑓𝛿𝐶	ADJ
cana-2737	425	8	(	(	PUNCT
cana-2737	425	9	resp	resp	NOUN
cana-2737	425	10	.	.	PUNCT
cana-2737	426	1	𝑝𝑓𝛿𝒮𝐶	𝑝𝑓𝛿𝒮𝐶	NOUN
cana-2737	426	2	and	and	CCONJ
cana-2737	426	3	𝑝𝑓𝛿𝐶	𝑝𝑓𝛿𝐶	ADJ
cana-2737	426	4	)	)	PUNCT
cana-2737	426	5	,	,	PUNCT
cana-2737	426	6	because	because	SCONJ
cana-2737	426	7	the	the	DET
cana-2737	426	8	set	set	NOUN
cana-2737	426	9	𝐵1	𝐵1	NOUN
cana-2737	426	10	𝑐	𝑐	NOUN
cana-2737	426	11	is	be	AUX
cana-2737	426	12	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-2737	426	13	in	in	ADP
cana-2737	426	14	𝑋1	𝑋1	PROPN
cana-2737	426	15	but	but	CCONJ
cana-2737	426	16	ℎ𝑃(𝐵1	ℎ𝑃(𝐵1	PROPN
cana-2737	426	17	𝑐	𝑐	NOUN
cana-2737	426	18	)	)	PUNCT
cana-2737	426	19	=	=	NOUN
cana-2737	427	1	𝐵1	𝐵1	NOUN
cana-2737	427	2	𝑐	𝑐	NOUN
cana-2737	427	3	is	be	AUX
cana-2737	427	4	not	not	PART
cana-2737	427	5	𝑝𝑓𝛿𝑐𝑠	𝑝𝑓𝛿𝑐𝑠	VERB
cana-2737	427	6	(	(	PUNCT
cana-2737	427	7	resp	resp	NOUN
cana-2737	427	8	.	.	PUNCT
cana-2737	428	1	𝑝𝑓𝛿𝒮𝑐𝑠	𝑝𝑓𝛿𝒮𝑐𝑠	PROPN
cana-2737	428	2	and	and	CCONJ
cana-2737	428	3	𝑝𝑓𝛿𝑐𝑠	𝑝𝑓𝛿𝑐𝑠	PROPN
cana-2737	428	4	)	)	PUNCT
cana-2737	428	5	in	in	ADP
cana-2737	428	6	𝑋2	𝑋2	PROPN
cana-2737	428	7	.	.	PUNCT
cana-2737	429	1	example	example	NOUN
cana-2737	429	2	4.6	4.6	NUM
cana-2737	429	3	let	let	VERB
cana-2737	429	4	𝑋1	𝑋1	NOUN
cana-2737	429	5	=	=	SYM
cana-2737	429	6	𝑋2	𝑋2	VERB
cana-2737	429	7	=	=	PUNCT
cana-2737	429	8	{	{	PUNCT
cana-2737	429	9	𝑥1	𝑥1	NOUN
cana-2737	429	10	,	,	PUNCT
cana-2737	429	11	𝑥2	𝑥2	NOUN
cana-2737	429	12	}	}	PUNCT
cana-2737	429	13	and	and	CCONJ
cana-2737	429	14	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2737	429	15	’s	’s	PART
cana-2737	429	16	𝐴1	𝐴1	PROPN
cana-2737	429	17	,	,	PUNCT
cana-2737	429	18	𝐴2	𝐴2	PROPN
cana-2737	429	19	,	,	PUNCT
cana-2737	429	20	𝐴3	𝐴3	PROPN
cana-2737	429	21	,	,	PUNCT
cana-2737	429	22	𝐴4	𝐴4	PROPN
cana-2737	429	23	in	in	ADP
cana-2737	429	24	𝑋2	𝑋2	PROPN
cana-2737	429	25	&	&	CCONJ
cana-2737	429	26	𝐵1	𝐵1	PROPN
cana-2737	429	27	in	in	ADP
cana-2737	429	28	𝑋1	𝑋1	PROPN
cana-2737	429	29	are	be	AUX
cana-2737	429	30	defined	define	VERB
cana-2737	429	31	as	as	ADP
cana-2737	429	32	,	,	PUNCT
cana-2737	429	33	𝐴1	𝐴1	PROPN
cana-2737	429	34	=	=	SYM
cana-2737	429	35	{	{	PUNCT
cana-2737	429	36	<	<	X
cana-2737	429	37	𝑥1	𝑥1	PROPN
cana-2737	429	38	,	,	PUNCT
cana-2737	429	39	0.20,0.80	0.20,0.80	NOUN
cana-2737	429	40	>	>	X
cana-2737	429	41	,	,	PUNCT
cana-2737	429	42	<	<	X
cana-2737	429	43	𝑥2	𝑥2	NOUN
cana-2737	429	44	,	,	PUNCT
cana-2737	429	45	0.40,0.60	0.40,0.60	NUM
cana-2737	429	46	>	>	PUNCT
cana-2737	429	47	}	}	PUNCT
cana-2737	429	48	𝐴2	𝐴2	PROPN
cana-2737	429	49	=	=	SYM
cana-2737	429	50	{	{	PUNCT
cana-2737	429	51	<	<	X
cana-2737	429	52	𝑥1	𝑥1	PROPN
cana-2737	429	53	,	,	PUNCT
cana-2737	429	54	0.10,0.90	0.10,0.90	NUM
cana-2737	429	55	>	>	X
cana-2737	429	56	,	,	PUNCT
cana-2737	429	57	<	<	X
cana-2737	429	58	𝑥2	𝑥2	NOUN
cana-2737	429	59	,	,	PUNCT
cana-2737	429	60	0.30,0.70	0.30,0.70	PRON
cana-2737	429	61	>	>	PUNCT
cana-2737	429	62	}	}	PUNCT
cana-2737	429	63	𝐴3	𝐴3	PROPN
cana-2737	430	1	=	=	SYM
cana-2737	430	2	{	{	PUNCT
cana-2737	430	3	<	<	X
cana-2737	430	4	𝑥1	𝑥1	PROPN
cana-2737	430	5	,	,	PUNCT
cana-2737	430	6	0.90,0.10	0.90,0.10	NOUN
cana-2737	430	7	>	>	X
cana-2737	430	8	,	,	PUNCT
cana-2737	430	9	<	<	X
cana-2737	430	10	𝑥2	𝑥2	NOUN
cana-2737	430	11	,	,	PUNCT
cana-2737	430	12	0.70,0.30	0.70,0.30	NOUN
cana-2737	430	13	>	>	PUNCT
cana-2737	430	14	}	}	PUNCT
cana-2737	430	15	𝐴4	𝐴4	PROPN
cana-2737	430	16	=	=	PUNCT
cana-2737	430	17	{	{	PUNCT
cana-2737	430	18	<	<	X
cana-2737	430	19	𝑥1	𝑥1	PROPN
cana-2737	430	20	,	,	PUNCT
cana-2737	430	21	0.20,0.80	0.20,0.80	NOUN
cana-2737	430	22	>	>	X
cana-2737	430	23	,	,	PUNCT
cana-2737	430	24	<	<	X
cana-2737	430	25	𝑥2	𝑥2	NOUN
cana-2737	430	26	,	,	PUNCT
cana-2737	430	27	0.30,0.70	0.30,0.70	PRON
cana-2737	430	28	>	>	PUNCT
cana-2737	430	29	}	}	PUNCT
cana-2737	430	30	𝐵1	𝐵1	NOUN
cana-2737	430	31	=	=	PUNCT
cana-2737	430	32	{	{	PUNCT
cana-2737	430	33	<	<	X
cana-2737	430	34	𝑥1	𝑥1	PROPN
cana-2737	430	35	,	,	PUNCT
cana-2737	430	36	0.80,0.20	0.80,0.20	X
cana-2737	430	37	>	>	X
cana-2737	430	38	,	,	PUNCT
cana-2737	430	39	<	<	X
cana-2737	430	40	𝑥2	𝑥2	NOUN
cana-2737	430	41	,	,	PUNCT
cana-2737	430	42	0.60,0.30	0.60,0.30	PUNCT
cana-2737	430	43	>	>	PUNCT
cana-2737	430	44	}	}	PUNCT
cana-2737	430	45	now	now	ADV
cana-2737	430	46	,	,	PUNCT
cana-2737	430	47	we	we	PRON
cana-2737	430	48	have	have	VERB
cana-2737	430	49	γ𝑃	γ𝑃	ADJ
cana-2737	430	50	=	=	PUNCT
cana-2737	430	51	{	{	PUNCT
cana-2737	430	52	0𝑋	0𝑋	PROPN
cana-2737	430	53	,	,	PUNCT
cana-2737	430	54	1𝑋	1𝑋	PROPN
cana-2737	430	55	,	,	PUNCT
cana-2737	430	56	𝐵1	𝐵1	PROPN
cana-2737	430	57	}	}	PUNCT
cana-2737	430	58	and	and	CCONJ
cana-2737	430	59	ψ𝑃	ψ𝑃	NOUN
cana-2737	430	60	=	=	SYM
cana-2737	430	61	{	{	PUNCT
cana-2737	430	62	0𝑋	0𝑋	PROPN
cana-2737	430	63	,	,	PUNCT
cana-2737	430	64	1𝑋	1𝑋	PROPN
cana-2737	430	65	,	,	PUNCT
cana-2737	430	66	𝐴1	𝐴1	PROPN
cana-2737	430	67	,	,	PUNCT
cana-2737	430	68	𝐴2	𝐴2	PROPN
cana-2737	430	69	,	,	PUNCT
cana-2737	430	70	𝐴3	𝐴3	PROPN
cana-2737	430	71	,	,	PUNCT
cana-2737	430	72	𝐴4	𝐴4	PROPN
cana-2737	430	73	}	}	PUNCT
cana-2737	430	74	.	.	PUNCT
cana-2737	431	1	let	let	VERB
cana-2737	431	2	ℎ𝑃	ℎ𝑃	NOUN
cana-2737	431	3	:	:	PUNCT
cana-2737	431	4	(	(	PUNCT
cana-2737	431	5	𝑋1	𝑋1	NOUN
cana-2737	431	6	,	,	PUNCT
cana-2737	431	7	γ𝑃	γ𝑃	NOUN
cana-2737	431	8	)	)	PUNCT
cana-2737	431	9	→	→	SYM
cana-2737	431	10	(	(	PUNCT
cana-2737	431	11	𝑋2	𝑋2	ADJ
cana-2737	431	12	,	,	PUNCT
cana-2737	431	13	ψ𝑃	ψ𝑃	NOUN
cana-2737	431	14	)	)	PUNCT
cana-2737	431	15	be	be	VERB
cana-2737	431	16	an	an	DET
cana-2737	431	17	identity	identity	NOUN
cana-2737	431	18	mapping	mapping	NOUN
cana-2737	431	19	.	.	PUNCT
cana-2737	432	1	then	then	ADV
cana-2737	432	2	,	,	PUNCT
cana-2737	432	3	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	432	4	is	be	AUX
cana-2737	432	5	𝑝𝑓𝑀𝐶	𝑝𝑓𝑀𝐶	NOUN
cana-2737	432	6	but	but	CCONJ
cana-2737	432	7	not	not	PART
cana-2737	432	8	𝑝𝑓𝛿𝒫𝐶	𝑝𝑓𝛿𝒫𝐶	ADJ
cana-2737	432	9	,	,	PUNCT
cana-2737	432	10	because	because	SCONJ
cana-2737	432	11	the	the	DET
cana-2737	432	12	set	set	NOUN
cana-2737	432	13	𝐵1	𝐵1	NOUN
cana-2737	432	14	𝑐	𝑐	NOUN
cana-2737	432	15	is	be	AUX
cana-2737	432	16	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-2737	432	17	in	in	ADP
cana-2737	432	18	𝑋1	𝑋1	PROPN
cana-2737	432	19	but	but	CCONJ
cana-2737	432	20	ℎ𝑃(𝐵1	ℎ𝑃(𝐵1	PROPN
cana-2737	432	21	𝑐	𝑐	NOUN
cana-2737	432	22	)	)	PUNCT
cana-2737	432	23	=	=	NOUN
cana-2737	433	1	𝐵1	𝐵1	NOUN
cana-2737	433	2	𝑐	𝑐	NOUN
cana-2737	433	3	is	be	AUX
cana-2737	433	4	not	not	PART
cana-2737	433	5	𝑝𝑓𝛿𝒫𝑐𝑠	𝑝𝑓𝛿𝒫𝑐𝑠	PRON
cana-2737	433	6	in	in	ADP
cana-2737	433	7	𝑋2	𝑋2	PROPN
cana-2737	433	8	.	.	PUNCT
cana-2737	434	1	theorem	theorem	VERB
cana-2737	434	2	4.1	4.1	NUM
cana-2737	434	3	a	a	DET
cana-2737	434	4	mapping	mapping	NOUN
cana-2737	434	5	ℎ𝑃	ℎ𝑃	NOUN
cana-2737	434	6	:	:	PUNCT
cana-2737	434	7	(	(	PUNCT
cana-2737	434	8	𝑋1	𝑋1	PROPN
cana-2737	434	9	,	,	PUNCT
cana-2737	434	10	𝛤𝑃	𝛤𝑃	PROPN
cana-2737	434	11	)	)	PUNCT
cana-2737	434	12	→	→	PUNCT
cana-2737	434	13	(	(	PUNCT
cana-2737	434	14	𝑋2	𝑋2	PROPN
cana-2737	434	15	,	,	PUNCT
cana-2737	434	16	𝛹𝑃	𝛹𝑃	PROPN
cana-2737	434	17	)	)	PUNCT
cana-2737	434	18	is	be	AUX
cana-2737	434	19	𝑝𝑓𝑀𝐶	𝑝𝑓𝑀𝐶	PROPN
cana-2737	434	20	iff	iff	PROPN
cana-2737	434	21	for	for	ADP
cana-2737	434	22	each	each	DET
cana-2737	434	23	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2737	434	24	𝐺	𝐺	PROPN
cana-2737	434	25	of	of	ADP
cana-2737	434	26	(	(	PUNCT
cana-2737	434	27	𝑋2	𝑋2	PROPN
cana-2737	434	28	,	,	PUNCT
cana-2737	434	29	𝛹𝑃	𝛹𝑃	PROPN
cana-2737	434	30	)	)	PUNCT
cana-2737	434	31	and	and	CCONJ
cana-2737	434	32	for	for	ADP
cana-2737	434	33	each	each	DET
cana-2737	434	34	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	ADJ
cana-2737	434	35	𝐾	𝐾	PROPN
cana-2737	434	36	of	of	ADP
cana-2737	434	37	(	(	PUNCT
cana-2737	434	38	𝑋1	𝑋1	PROPN
cana-2737	434	39	,	,	PUNCT
cana-2737	434	40	𝛤𝑃	𝛤𝑃	PROPN
cana-2737	434	41	)	)	PUNCT
cana-2737	434	42	containing	contain	VERB
cana-2737	434	43	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	434	44	−1(𝐺	−1(𝐺	NOUN
cana-2737	434	45	)	)	PUNCT
cana-2737	434	46	,	,	PUNCT
cana-2737	434	47	there	there	PRON
cana-2737	434	48	is	be	VERB
cana-2737	434	49	a	a	DET
cana-2737	434	50	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	ADJ
cana-2737	434	51	𝐿	𝐿	PROPN
cana-2737	434	52	of	of	ADP
cana-2737	434	53	(	(	PUNCT
cana-2737	434	54	𝑋2	𝑋2	PROPN
cana-2737	434	55	,	,	PUNCT
cana-2737	434	56	𝛹𝑃	𝛹𝑃	PROPN
cana-2737	434	57	)	)	PUNCT
cana-2737	434	58	such	such	ADJ
cana-2737	434	59	that	that	SCONJ
cana-2737	434	60	𝐺	𝐺	PROPN
cana-2737	434	61	⊆	⊆	NUM
cana-2737	434	62	𝐿	𝐿	PROPN
cana-2737	434	63	and	and	CCONJ
cana-2737	434	64	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	434	65	−1(𝐿	−1(𝐿	NOUN
cana-2737	434	66	)	)	PUNCT
cana-2737	434	67	⊆	⊆	NUM
cana-2737	434	68	𝐾.	𝐾.	PROPN
cana-2737	434	69	proof	proof	NOUN
cana-2737	434	70	.	.	PUNCT
cana-2737	435	1	necessity	necessity	NOUN
cana-2737	435	2	:	:	PUNCT
cana-2737	435	3	assume	assume	VERB
cana-2737	435	4	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	435	5	is	be	AUX
cana-2737	435	6	a	a	DET
cana-2737	435	7	𝑝𝑓𝑀𝐶	𝑝𝑓𝑀𝐶	NOUN
cana-2737	435	8	mapping	mapping	NOUN
cana-2737	435	9	.	.	PUNCT
cana-2737	436	1	let	let	VERB
cana-2737	436	2	𝐺	𝐺	PRON
cana-2737	436	3	be	be	AUX
cana-2737	436	4	the	the	DET
cana-2737	436	5	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-2737	436	6	of	of	ADP
cana-2737	436	7	(	(	PUNCT
cana-2737	436	8	𝑋2	𝑋2	ADJ
cana-2737	436	9	,	,	PUNCT
cana-2737	436	10	ψ𝑃	ψ𝑃	NOUN
cana-2737	436	11	)	)	PUNCT
cana-2737	436	12	and	and	CCONJ
cana-2737	436	13	𝐾	𝐾	PROPN
cana-2737	436	14	is	be	AUX
cana-2737	436	15	a	a	DET
cana-2737	436	16	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-2737	436	17	of	of	ADP
cana-2737	436	18	(	(	PUNCT
cana-2737	436	19	𝑋1	𝑋1	NOUN
cana-2737	436	20	,	,	PUNCT
cana-2737	436	21	γ𝑃	γ𝑃	NOUN
cana-2737	436	22	)	)	PUNCT
cana-2737	436	23	such	such	ADJ
cana-2737	436	24	that	that	SCONJ
cana-2737	436	25	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	436	26	−1(𝐺	−1(𝐺	NOUN
cana-2737	436	27	)	)	PUNCT
cana-2737	436	28	⊆	⊆	X
cana-2737	436	29	𝐾.	𝐾.	PROPN
cana-2737	436	30	then	then	ADV
cana-2737	436	31	𝐿	𝐿	PROPN
cana-2737	436	32	=	=	PUNCT
cana-2737	436	33	1𝑋	1𝑋	PROPN
cana-2737	436	34	−	−	PROPN
cana-2737	436	35	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	436	36	−1(𝐾𝑐	−1(𝐾𝑐	PROPN
cana-2737	436	37	)	)	PUNCT
cana-2737	436	38	is	be	AUX
cana-2737	436	39	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	ADJ
cana-2737	436	40	of	of	ADP
cana-2737	436	41	(	(	PUNCT
cana-2737	436	42	𝑋2	𝑋2	ADJ
cana-2737	436	43	,	,	PUNCT
cana-2737	436	44	ψ𝑃	ψ𝑃	NOUN
cana-2737	436	45	)	)	PUNCT
cana-2737	436	46	such	such	ADJ
cana-2737	436	47	that	that	SCONJ
cana-2737	436	48	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	436	49	−1(𝐿	−1(𝐿	NOUN
cana-2737	436	50	)	)	PUNCT
cana-2737	436	51	⊆	⊆	NUM
cana-2737	436	52	𝐾.	𝐾.	PROPN
cana-2737	436	53	sufficiency	sufficiency	NOUN
cana-2737	436	54	:	:	PUNCT
cana-2737	436	55	assume	assume	VERB
cana-2737	436	56	𝐾	𝐾	PROPN
cana-2737	436	57	is	be	AUX
cana-2737	436	58	a	a	DET
cana-2737	436	59	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-2737	436	60	of	of	ADP
cana-2737	436	61	(	(	PUNCT
cana-2737	436	62	𝑋1	𝑋1	NOUN
cana-2737	436	63	,	,	PUNCT
cana-2737	436	64	γ𝑃	γ𝑃	NOUN
cana-2737	436	65	)	)	PUNCT
cana-2737	436	66	.	.	PUNCT
cana-2737	437	1	then	then	ADV
cana-2737	437	2	(	(	PUNCT
cana-2737	437	3	ℎ𝑃(𝐾))𝑐	ℎ𝑃(𝐾))𝑐	ADV
cana-2737	437	4	is	be	AUX
cana-2737	437	5	a	a	DET
cana-2737	437	6	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2737	437	7	of	of	ADP
cana-2737	437	8	(	(	PUNCT
cana-2737	437	9	𝑋2	𝑋2	ADJ
cana-2737	437	10	,	,	PUNCT
cana-2737	437	11	ψ𝑃	ψ𝑃	NOUN
cana-2737	437	12	)	)	PUNCT
cana-2737	437	13	and	and	CCONJ
cana-2737	437	14	𝐾𝑐	𝐾𝑐	PROPN
cana-2737	437	15	is	be	AUX
cana-2737	437	16	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	ADJ
cana-2737	437	17	in	in	ADP
cana-2737	437	18	(	(	PUNCT
cana-2737	437	19	𝑋1	𝑋1	NOUN
cana-2737	437	20	,	,	PUNCT
cana-2737	437	21	γ𝑃	γ𝑃	NOUN
cana-2737	437	22	)	)	PUNCT
cana-2737	437	23	such	such	ADJ
cana-2737	437	24	that	that	SCONJ
cana-2737	437	25	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	437	26	−1((ℎ𝑃(𝐾))𝑐	−1((ℎ𝑃(𝐾))𝑐	PROPN
cana-2737	437	27	)	)	PUNCT
cana-2737	437	28	⊆	⊆	NUM
cana-2737	437	29	𝐾𝑐.	𝐾𝑐.	PROPN
cana-2737	437	30	by	by	ADP
cana-2737	437	31	hypothesis	hypothesis	NOUN
cana-2737	437	32	,	,	PUNCT
cana-2737	437	33	there	there	PRON
cana-2737	437	34	is	be	VERB
cana-2737	437	35	a	a	DET
cana-2737	437	36	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	ADJ
cana-2737	437	37	𝐿	𝐿	PROPN
cana-2737	437	38	of	of	ADP
cana-2737	437	39	(	(	PUNCT
cana-2737	437	40	𝑋2	𝑋2	ADJ
cana-2737	437	41	,	,	PUNCT
cana-2737	437	42	ψ𝑃	ψ𝑃	NOUN
cana-2737	437	43	)	)	PUNCT
cana-2737	437	44	such	such	ADJ
cana-2737	437	45	that	that	SCONJ
cana-2737	437	46	(	(	PUNCT
cana-2737	437	47	ℎ𝑃(𝐾))𝑐	ℎ𝑃(𝐾))𝑐	ADV
cana-2737	437	48	⊆	⊆	NUM
cana-2737	437	49	𝐿	𝐿	PROPN
cana-2737	437	50	and	and	CCONJ
cana-2737	437	51	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	437	52	−1(𝐿	−1(𝐿	NOUN
cana-2737	437	53	)	)	PUNCT
cana-2737	437	54	⊆	⊆	NUM
cana-2737	437	55	𝐾𝑐.	𝐾𝑐.	PROPN
cana-2737	437	56	therefore	therefore	ADV
cana-2737	437	57	𝐾	𝐾	PROPN
cana-2737	437	58	⊆	⊆	NUM
cana-2737	437	59	(	(	PUNCT
cana-2737	437	60	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	438	1	−1(𝐿))𝑐.	−1(𝐿))𝑐.	INTJ
cana-2737	438	2	hence	hence	ADV
cana-2737	438	3	𝐿𝑐	𝐿𝑐	VERB
cana-2737	438	4	⊆	⊆	NUM
cana-2737	438	5	ℎ𝑃(𝐿	ℎ𝑃(𝐿	NUM
cana-2737	438	6	)	)	PUNCT
cana-2737	438	7	⊆	⊆	NUM
cana-2737	438	8	ℎ𝑃((ℎ𝑃	ℎ𝑃((ℎ𝑃	NOUN
cana-2737	438	9	−1(𝐿))𝑐	−1(𝐿))𝑐	NOUN
cana-2737	438	10	)	)	PUNCT
cana-2737	438	11	⊆	⊆	X
cana-2737	439	1	𝐿𝑐	𝐿𝑐	PROPN
cana-2737	439	2	which	which	PRON
cana-2737	439	3	implies	imply	VERB
cana-2737	439	4	ℎ𝑃(𝐾	ℎ𝑃(𝐾	NOUN
cana-2737	439	5	)	)	PUNCT
cana-2737	439	6	=	=	SYM
cana-2737	439	7	𝐿𝑐.	𝐿𝑐.	PROPN
cana-2737	439	8	since	since	SCONJ
cana-2737	439	9	𝐿𝑐	𝐿𝑐	PROPN
cana-2737	439	10	is	be	AUX
cana-2737	439	11	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-2737	439	12	of	of	ADP
cana-2737	439	13	(	(	PUNCT
cana-2737	439	14	𝑋2	𝑋2	PROPN
cana-2737	439	15	,	,	PUNCT
cana-2737	439	16	ψ𝑃	ψ𝑃	NOUN
cana-2737	439	17	)	)	PUNCT
cana-2737	439	18	,	,	PUNCT
cana-2737	439	19	ℎ𝑃(𝐾	ℎ𝑃(𝐾	PROPN
cana-2737	439	20	)	)	PUNCT
cana-2737	439	21	is	be	AUX
cana-2737	439	22	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-2737	439	23	in	in	ADP
cana-2737	439	24	(	(	PUNCT
cana-2737	439	25	𝑋2	𝑋2	ADJ
cana-2737	439	26	,	,	PUNCT
cana-2737	439	27	ψ𝑃	ψ𝑃	NOUN
cana-2737	439	28	)	)	PUNCT
cana-2737	439	29	and	and	CCONJ
cana-2737	439	30	thus	thus	ADV
cana-2737	439	31	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	439	32	is	be	AUX
cana-2737	439	33	𝑝𝑓𝑀𝐶	𝑝𝑓𝑀𝐶	PROPN
cana-2737	439	34	mapping	mapping	NOUN
cana-2737	439	35	.	.	PUNCT
cana-2737	440	1	theorem	theorem	VERB
cana-2737	440	2	4.2	4.2	NUM
cana-2737	440	3	if	if	SCONJ
cana-2737	440	4	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	440	5	:	:	PUNCT
cana-2737	440	6	(	(	PUNCT
cana-2737	440	7	𝑋1	𝑋1	PROPN
cana-2737	440	8	,	,	PUNCT
cana-2737	440	9	𝛤𝑃	𝛤𝑃	PROPN
cana-2737	440	10	)	)	PUNCT
cana-2737	440	11	→	→	PUNCT
cana-2737	440	12	(	(	PUNCT
cana-2737	440	13	𝑋2	𝑋2	PROPN
cana-2737	440	14	,	,	PUNCT
cana-2737	440	15	𝛹𝑃	𝛹𝑃	PROPN
cana-2737	440	16	)	)	PUNCT
cana-2737	440	17	is	be	AUX
cana-2737	440	18	𝑝𝑓𝐶	𝑝𝑓𝐶	NOUN
cana-2737	440	19	and	and	CCONJ
cana-2737	440	20	𝑔𝑃	𝑔𝑃	ADJ
cana-2737	440	21	:	:	PUNCT
cana-2737	440	22	(	(	PUNCT
cana-2737	440	23	𝑋2	𝑋2	PROPN
cana-2737	440	24	,	,	PUNCT
cana-2737	440	25	𝛹𝑃	𝛹𝑃	PROPN
cana-2737	440	26	)	)	PUNCT
cana-2737	440	27	→	→	SYM
cana-2737	440	28	(	(	PUNCT
cana-2737	440	29	𝑋3	𝑋3	NOUN
cana-2737	440	30	,	,	PUNCT
cana-2737	440	31	𝛷𝑃	𝛷𝑃	PROPN
cana-2737	440	32	)	)	PUNCT
cana-2737	440	33	is	be	AUX
cana-2737	440	34	𝑝𝑓𝑀𝐶.	𝑝𝑓𝑀𝐶.	ADJ
cana-2737	440	35	then	then	ADV
cana-2737	440	36	𝑔𝑃	𝑔𝑃	ADJ
cana-2737	440	37	∘	∘	PROPN
cana-2737	440	38	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	440	39	:	:	PUNCT
cana-2737	440	40	(	(	PUNCT
cana-2737	440	41	𝑋1	𝑋1	PROPN
cana-2737	440	42	,	,	PUNCT
cana-2737	440	43	𝛤𝑃	𝛤𝑃	PROPN
cana-2737	440	44	)	)	PUNCT
cana-2737	440	45	→	→	SYM
cana-2737	440	46	(	(	PUNCT
cana-2737	440	47	𝑋3	𝑋3	NOUN
cana-2737	440	48	,	,	PUNCT
cana-2737	440	49	𝛷𝑃	𝛷𝑃	PROPN
cana-2737	440	50	)	)	PUNCT
cana-2737	440	51	is	be	AUX
cana-2737	440	52	𝑝𝑓𝑀𝐶.	𝑝𝑓𝑀𝐶.	ADJ
cana-2737	440	53	communications	communication	NOUN
cana-2737	440	54	on	on	ADP
cana-2737	440	55	applied	apply	VERB
cana-2737	440	56	nonlinear	nonlinear	ADJ
cana-2737	440	57	analysis	analysis	NOUN
cana-2737	440	58	issn	issn	NOUN
cana-2737	440	59	:	:	PUNCT
cana-2737	440	60	1074	1074	NUM
cana-2737	440	61	-	-	PUNCT
cana-2737	440	62	133x	133x	NUM
cana-2737	440	63	vol	vol	NOUN
cana-2737	440	64	32	32	NUM
cana-2737	440	65	no	no	NOUN
cana-2737	440	66	.	.	PUNCT
cana-2737	441	1	4s	4s	NUM
cana-2737	441	2	(	(	PUNCT
cana-2737	441	3	2025	2025	NUM
cana-2737	441	4	)	)	PUNCT
cana-2737	441	5	39	39	NUM
cana-2737	441	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2737	441	7	proof	proof	NOUN
cana-2737	441	8	.	.	PUNCT
cana-2737	442	1	let	let	VERB
cana-2737	442	2	𝐾	𝐾	PRON
cana-2737	442	3	be	be	AUX
cana-2737	442	4	a	a	DET
cana-2737	442	5	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-2737	442	6	in	in	ADP
cana-2737	442	7	(	(	PUNCT
cana-2737	442	8	𝑋1	𝑋1	NOUN
cana-2737	442	9	,	,	PUNCT
cana-2737	442	10	γ𝑃	γ𝑃	NOUN
cana-2737	442	11	)	)	PUNCT
cana-2737	442	12	.	.	PUNCT
cana-2737	443	1	then	then	ADV
cana-2737	443	2	ℎ𝑃(𝐾	ℎ𝑃(𝐾	NOUN
cana-2737	443	3	)	)	PUNCT
cana-2737	443	4	is	be	AUX
cana-2737	443	5	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-2737	443	6	of	of	ADP
cana-2737	443	7	(	(	PUNCT
cana-2737	443	8	𝑋2	𝑋2	ADJ
cana-2737	443	9	,	,	PUNCT
cana-2737	443	10	ψ𝑃	ψ𝑃	NOUN
cana-2737	443	11	)	)	PUNCT
cana-2737	443	12	because	because	SCONJ
cana-2737	443	13	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	443	14	is	be	AUX
cana-2737	443	15	𝑝𝑓𝐶	𝑝𝑓𝐶	PROPN
cana-2737	443	16	mapping	mapping	NOUN
cana-2737	443	17	.	.	PUNCT
cana-2737	444	1	now	now	ADV
cana-2737	444	2	(	(	PUNCT
cana-2737	444	3	𝑔𝑃	𝑔𝑃	ADP
cana-2737	444	4	∘	∘	PROPN
cana-2737	444	5	ℎ𝑃)(𝐾	ℎ𝑃)(𝐾	ADJ
cana-2737	444	6	)	)	PUNCT
cana-2737	444	7	=	=	PUNCT
cana-2737	444	8	𝑔𝑃(ℎ𝑃(𝐾	𝑔𝑃(ℎ𝑃(𝐾	PROPN
cana-2737	444	9	)	)	PUNCT
cana-2737	444	10	)	)	PUNCT
cana-2737	444	11	is	be	AUX
cana-2737	444	12	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-2737	444	13	in	in	ADP
cana-2737	444	14	(	(	PUNCT
cana-2737	444	15	𝑋3	𝑋3	NOUN
cana-2737	444	16	,	,	PUNCT
cana-2737	444	17	φ𝑃	φ𝑃	NOUN
cana-2737	444	18	)	)	PUNCT
cana-2737	444	19	because	because	SCONJ
cana-2737	444	20	𝑔𝑃	𝑔𝑃	ADJ
cana-2737	444	21	is	be	AUX
cana-2737	444	22	𝑝𝑓𝑀𝐶	𝑝𝑓𝑀𝐶	NOUN
cana-2737	444	23	mapping	mapping	NOUN
cana-2737	444	24	.	.	PUNCT
cana-2737	445	1	thus	thus	ADV
cana-2737	445	2	𝑔𝑃	𝑔𝑃	VERB
cana-2737	445	3	∘	∘	PROPN
cana-2737	445	4	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	445	5	is	be	AUX
cana-2737	445	6	𝑝𝑓𝑀𝐶	𝑝𝑓𝑀𝐶	PROPN
cana-2737	445	7	mapping	mapping	NOUN
cana-2737	445	8	theorem	theorem	VERB
cana-2737	445	9	4.3	4.3	NUM
cana-2737	445	10	if	if	SCONJ
cana-2737	445	11	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	445	12	:	:	PUNCT
cana-2737	445	13	(	(	PUNCT
cana-2737	445	14	𝑋1	𝑋1	PROPN
cana-2737	445	15	,	,	PUNCT
cana-2737	445	16	𝛤𝑃	𝛤𝑃	PROPN
cana-2737	445	17	)	)	PUNCT
cana-2737	445	18	→	→	PUNCT
cana-2737	445	19	(	(	PUNCT
cana-2737	445	20	𝑋2	𝑋2	PROPN
cana-2737	445	21	,	,	PUNCT
cana-2737	445	22	𝛹𝑃	𝛹𝑃	PROPN
cana-2737	445	23	)	)	PUNCT
cana-2737	445	24	is	be	AUX
cana-2737	445	25	𝑝𝑓𝑀𝐶	𝑝𝑓𝑀𝐶	NOUN
cana-2737	445	26	map	map	NOUN
cana-2737	445	27	,	,	PUNCT
cana-2737	445	28	then	then	ADV
cana-2737	445	29	𝑝𝑓𝑀𝑐𝑙(ℎ𝑃(𝐾	𝑝𝑓𝑀𝑐𝑙(ℎ𝑃(𝐾	PROPN
cana-2737	445	30	)	)	PUNCT
cana-2737	445	31	)	)	PUNCT
cana-2737	446	1	⊆	⊆	NUM
cana-2737	446	2	ℎ𝑃(𝑝𝑓𝑐𝑙(𝐾	ℎ𝑃(𝑝𝑓𝑐𝑙(𝐾	PROPN
cana-2737	446	3	)	)	PUNCT
cana-2737	446	4	)	)	PUNCT
cana-2737	446	5	.	.	PUNCT
cana-2737	447	1	proof	proof	NOUN
cana-2737	447	2	.	.	PUNCT
cana-2737	448	1	obvious	obvious	ADJ
cana-2737	448	2	.	.	PUNCT
cana-2737	449	1	theorem	theorem	VERB
cana-2737	449	2	4.4	4.4	NUM
cana-2737	449	3	let	let	VERB
cana-2737	449	4	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	449	5	:	:	PUNCT
cana-2737	449	6	(	(	PUNCT
cana-2737	449	7	𝑋1	𝑋1	PROPN
cana-2737	449	8	,	,	PUNCT
cana-2737	449	9	𝛤𝑃	𝛤𝑃	PROPN
cana-2737	449	10	)	)	PUNCT
cana-2737	449	11	→	→	PUNCT
cana-2737	449	12	(	(	PUNCT
cana-2737	449	13	𝑋2	𝑋2	PROPN
cana-2737	449	14	,	,	PUNCT
cana-2737	449	15	𝛹𝑃	𝛹𝑃	PROPN
cana-2737	449	16	)	)	PUNCT
cana-2737	449	17	and	and	CCONJ
cana-2737	449	18	𝑔𝑃	𝑔𝑃	ADJ
cana-2737	449	19	:	:	PUNCT
cana-2737	449	20	(	(	PUNCT
cana-2737	449	21	𝑋2	𝑋2	PROPN
cana-2737	449	22	,	,	PUNCT
cana-2737	449	23	𝛹𝑃	𝛹𝑃	PROPN
cana-2737	449	24	)	)	PUNCT
cana-2737	449	25	→	→	SYM
cana-2737	449	26	(	(	PUNCT
cana-2737	449	27	𝑋3	𝑋3	NOUN
cana-2737	449	28	,	,	PUNCT
cana-2737	449	29	𝛷𝑃	𝛷𝑃	PROPN
cana-2737	449	30	)	)	PUNCT
cana-2737	449	31	are	be	AUX
cana-2737	449	32	𝑝𝑓𝑀𝐶	𝑝𝑓𝑀𝐶	NOUN
cana-2737	449	33	mappings	mapping	NOUN
cana-2737	449	34	.	.	PUNCT
cana-2737	450	1	if	if	SCONJ
cana-2737	450	2	every	every	DET
cana-2737	450	3	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	PROPN
cana-2737	450	4	of	of	ADP
cana-2737	450	5	(	(	PUNCT
cana-2737	450	6	𝑋2	𝑋2	PROPN
cana-2737	450	7	,	,	PUNCT
cana-2737	450	8	𝛹𝑃	𝛹𝑃	PROPN
cana-2737	450	9	)	)	PUNCT
cana-2737	450	10	is	be	AUX
cana-2737	450	11	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	PROPN
cana-2737	450	12	,	,	PUNCT
cana-2737	450	13	then	then	ADV
cana-2737	450	14	𝑔𝑃	𝑔𝑃	ADP
cana-2737	450	15	∘	∘	PROPN
cana-2737	450	16	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	450	17	:	:	PUNCT
cana-2737	450	18	(	(	PUNCT
cana-2737	450	19	𝑋1	𝑋1	PROPN
cana-2737	450	20	,	,	PUNCT
cana-2737	450	21	𝛤𝑃	𝛤𝑃	PROPN
cana-2737	450	22	)	)	PUNCT
cana-2737	450	23	→	→	SYM
cana-2737	450	24	(	(	PUNCT
cana-2737	450	25	𝑋3	𝑋3	NOUN
cana-2737	450	26	,	,	PUNCT
cana-2737	450	27	𝛷𝑃	𝛷𝑃	PROPN
cana-2737	450	28	)	)	PUNCT
cana-2737	450	29	is	be	AUX
cana-2737	450	30	𝑝𝑓𝑀𝐶.	𝑝𝑓𝑀𝐶.	ADJ
cana-2737	450	31	proof	proof	NOUN
cana-2737	450	32	.	.	PUNCT
cana-2737	451	1	let	let	VERB
cana-2737	451	2	𝐾	𝐾	PRON
cana-2737	451	3	be	be	AUX
cana-2737	451	4	a	a	DET
cana-2737	451	5	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-2737	451	6	in	in	ADP
cana-2737	451	7	(	(	PUNCT
cana-2737	451	8	𝑋1	𝑋1	NOUN
cana-2737	451	9	,	,	PUNCT
cana-2737	451	10	γ𝑃	γ𝑃	NOUN
cana-2737	451	11	)	)	PUNCT
cana-2737	451	12	.	.	PUNCT
cana-2737	452	1	then	then	ADV
cana-2737	452	2	ℎ𝑃(𝐾	ℎ𝑃(𝐾	NOUN
cana-2737	452	3	)	)	PUNCT
cana-2737	452	4	is	be	AUX
cana-2737	452	5	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	PROPN
cana-2737	452	6	of	of	ADP
cana-2737	452	7	(	(	PUNCT
cana-2737	452	8	𝑋2	𝑋2	ADJ
cana-2737	452	9	,	,	PUNCT
cana-2737	452	10	ψ𝑃	ψ𝑃	NOUN
cana-2737	452	11	)	)	PUNCT
cana-2737	452	12	because	because	SCONJ
cana-2737	452	13	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	452	14	is	be	AUX
cana-2737	452	15	𝑝𝑓𝑀𝐶	𝑝𝑓𝑀𝐶	NOUN
cana-2737	452	16	mapping	mapping	NOUN
cana-2737	452	17	.	.	PUNCT
cana-2737	453	1	by	by	ADP
cana-2737	453	2	hypothesis	hypothesis	NOUN
cana-2737	453	3	,	,	PUNCT
cana-2737	453	4	ℎ𝑃(𝐾	ℎ𝑃(𝐾	PROPN
cana-2737	453	5	)	)	PUNCT
cana-2737	453	6	is	be	AUX
cana-2737	453	7	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-2737	453	8	of	of	ADP
cana-2737	453	9	(	(	PUNCT
cana-2737	453	10	𝑋2	𝑋2	ADJ
cana-2737	453	11	,	,	PUNCT
cana-2737	453	12	ψ𝑃	ψ𝑃	NOUN
cana-2737	453	13	)	)	PUNCT
cana-2737	453	14	.	.	PUNCT
cana-2737	454	1	now	now	ADV
cana-2737	454	2	𝑔𝑃(ℎ𝑃(𝐾	𝑔𝑃(ℎ𝑃(𝐾	NOUN
cana-2737	454	3	)	)	PUNCT
cana-2737	454	4	)	)	PUNCT
cana-2737	455	1	=	=	PRON
cana-2737	455	2	(	(	PUNCT
cana-2737	455	3	𝑔𝑃	𝑔𝑃	ADP
cana-2737	455	4	∘	∘	PROPN
cana-2737	455	5	ℎ𝑃)(𝐾	ℎ𝑃)(𝐾	ADJ
cana-2737	455	6	)	)	PUNCT
cana-2737	455	7	is	be	AUX
cana-2737	455	8	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-2737	455	9	in	in	ADP
cana-2737	455	10	(	(	PUNCT
cana-2737	455	11	𝑋3	𝑋3	NOUN
cana-2737	455	12	,	,	PUNCT
cana-2737	455	13	φ𝑃	φ𝑃	NOUN
cana-2737	455	14	)	)	PUNCT
cana-2737	455	15	because	because	SCONJ
cana-2737	455	16	𝑔𝑃	𝑔𝑃	ADJ
cana-2737	455	17	is	be	AUX
cana-2737	455	18	𝑝𝑓𝑀𝐶	𝑝𝑓𝑀𝐶	NOUN
cana-2737	455	19	mapping	mapping	NOUN
cana-2737	455	20	.	.	PUNCT
cana-2737	456	1	thus	thus	ADV
cana-2737	456	2	𝑔𝑃	𝑔𝑃	VERB
cana-2737	456	3	∘	∘	PROPN
cana-2737	456	4	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	456	5	is	be	AUX
cana-2737	456	6	𝑝𝑓𝑀𝐶	𝑝𝑓𝑀𝐶	PROPN
cana-2737	456	7	mapping	mapping	NOUN
cana-2737	456	8	theorem	theorem	VERB
cana-2737	456	9	4.5	4.5	NUM
cana-2737	456	10	let	let	VERB
cana-2737	456	11	ℎ𝑃	ℎ𝑃	NOUN
cana-2737	456	12	:	:	PUNCT
cana-2737	456	13	(	(	PUNCT
cana-2737	456	14	𝑋1	𝑋1	PROPN
cana-2737	456	15	,	,	PUNCT
cana-2737	456	16	𝛤𝑃	𝛤𝑃	PROPN
cana-2737	456	17	)	)	PUNCT
cana-2737	456	18	→	→	PUNCT
cana-2737	456	19	(	(	PUNCT
cana-2737	456	20	𝑋2	𝑋2	PROPN
cana-2737	456	21	,	,	PUNCT
cana-2737	456	22	𝛹𝑃	𝛹𝑃	PROPN
cana-2737	456	23	)	)	PUNCT
cana-2737	456	24	be	be	AUX
cana-2737	456	25	a	a	DET
cana-2737	456	26	bijective	bijective	ADJ
cana-2737	456	27	mapping	mapping	NOUN
cana-2737	456	28	.	.	PUNCT
cana-2737	457	1	then	then	ADV
cana-2737	457	2	the	the	DET
cana-2737	457	3	following	follow	VERB
cana-2737	457	4	statements	statement	NOUN
cana-2737	457	5	are	be	AUX
cana-2737	457	6	equivalent	equivalent	ADJ
cana-2737	457	7	:	:	PUNCT
cana-2737	458	1	[	[	X
cana-2737	458	2	(	(	PUNCT
cana-2737	458	3	i	i	NOUN
cana-2737	458	4	)	)	PUNCT
cana-2737	458	5	]	]	PUNCT
cana-2737	459	1	1	1	X
cana-2737	459	2	.	.	PUNCT
cana-2737	460	1	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	460	2	is	be	AUX
cana-2737	460	3	a	a	DET
cana-2737	460	4	𝑝𝑓𝑀𝑂	𝑝𝑓𝑀𝑂	NOUN
cana-2737	460	5	mapping	mapping	NOUN
cana-2737	460	6	.	.	PUNCT
cana-2737	461	1	2	2	X
cana-2737	461	2	.	.	X
cana-2737	461	3	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	461	4	is	be	AUX
cana-2737	461	5	a	a	DET
cana-2737	461	6	𝑝𝑓𝑀𝐶	𝑝𝑓𝑀𝐶	NOUN
cana-2737	461	7	mapping	mapping	NOUN
cana-2737	461	8	.	.	PUNCT
cana-2737	462	1	3	3	X
cana-2737	462	2	.	.	X
cana-2737	462	3	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	462	4	−1	−1	NOUN
cana-2737	462	5	is	be	AUX
cana-2737	462	6	𝑝𝑓𝑀𝐶𝑡𝑠	𝑝𝑓𝑀𝐶𝑡𝑠	PROPN
cana-2737	462	7	mapping	mapping	NOUN
cana-2737	462	8	.	.	PUNCT
cana-2737	463	1	proof	proof	NOUN
cana-2737	463	2	.	.	PUNCT
cana-2737	464	1	(	(	PUNCT
cana-2737	464	2	i	i	NOUN
cana-2737	464	3	)	)	PUNCT
cana-2737	464	4	⇒	⇒	PROPN
cana-2737	464	5	(	(	PUNCT
cana-2737	464	6	ii	ii	PROPN
cana-2737	464	7	):	):	PUNCT
cana-2737	464	8	let	let	VERB
cana-2737	464	9	us	we	PRON
cana-2737	464	10	assume	assume	VERB
cana-2737	464	11	that	that	SCONJ
cana-2737	464	12	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	464	13	is	be	AUX
cana-2737	464	14	a	a	DET
cana-2737	464	15	𝑝𝑓𝑀𝑂	𝑝𝑓𝑀𝑂	NOUN
cana-2737	464	16	mapping	mapping	NOUN
cana-2737	464	17	.	.	PUNCT
cana-2737	465	1	by	by	ADP
cana-2737	465	2	definition	definition	NOUN
cana-2737	465	3	,	,	PUNCT
cana-2737	465	4	𝐾	𝐾	PROPN
cana-2737	465	5	is	be	AUX
cana-2737	465	6	a	a	DET
cana-2737	465	7	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-2737	465	8	in	in	ADP
cana-2737	465	9	(	(	PUNCT
cana-2737	465	10	𝑋1	𝑋1	NOUN
cana-2737	465	11	,	,	PUNCT
cana-2737	465	12	γ𝑃	γ𝑃	NOUN
cana-2737	465	13	)	)	PUNCT
cana-2737	465	14	,	,	PUNCT
cana-2737	465	15	then	then	ADV
cana-2737	465	16	ℎ𝑃(𝐾	ℎ𝑃(𝐾	NOUN
cana-2737	465	17	)	)	PUNCT
cana-2737	465	18	is	be	AUX
cana-2737	465	19	a	a	DET
cana-2737	465	20	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	NOUN
cana-2737	465	21	in	in	ADP
cana-2737	465	22	(	(	PUNCT
cana-2737	465	23	𝑋2	𝑋2	ADJ
cana-2737	465	24	,	,	PUNCT
cana-2737	465	25	ψ𝑃	ψ𝑃	NOUN
cana-2737	465	26	)	)	PUNCT
cana-2737	465	27	.	.	PUNCT
cana-2737	466	1	here	here	ADV
cana-2737	466	2	,	,	PUNCT
cana-2737	466	3	𝐾	𝐾	PROPN
cana-2737	466	4	is	be	AUX
cana-2737	466	5	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-2737	466	6	in	in	ADP
cana-2737	466	7	(	(	PUNCT
cana-2737	466	8	𝑋1	𝑋1	NOUN
cana-2737	466	9	,	,	PUNCT
cana-2737	466	10	γ𝑃	γ𝑃	NOUN
cana-2737	466	11	)	)	PUNCT
cana-2737	466	12	.	.	PUNCT
cana-2737	467	1	then	then	ADV
cana-2737	467	2	1𝑋	1𝑋	PROPN
cana-2737	467	3	−	−	PROPN
cana-2737	467	4	𝐾	𝐾	PROPN
cana-2737	467	5	is	be	AUX
cana-2737	467	6	a	a	DET
cana-2737	467	7	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-2737	467	8	in	in	ADP
cana-2737	467	9	(	(	PUNCT
cana-2737	467	10	𝑋1	𝑋1	NOUN
cana-2737	467	11	,	,	PUNCT
cana-2737	467	12	γ𝑃	γ𝑃	NOUN
cana-2737	467	13	)	)	PUNCT
cana-2737	467	14	.	.	PUNCT
cana-2737	468	1	by	by	ADP
cana-2737	468	2	assumption	assumption	NOUN
cana-2737	468	3	,	,	PUNCT
cana-2737	468	4	ℎ𝑃(1𝑋	ℎ𝑃(1𝑋	PROPN
cana-2737	468	5	−	−	PROPN
cana-2737	468	6	𝐾	𝐾	PROPN
cana-2737	468	7	)	)	PUNCT
cana-2737	468	8	is	be	AUX
cana-2737	468	9	a	a	DET
cana-2737	468	10	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	NOUN
cana-2737	468	11	in	in	ADP
cana-2737	468	12	(	(	PUNCT
cana-2737	468	13	𝑋2	𝑋2	ADJ
cana-2737	468	14	,	,	PUNCT
cana-2737	468	15	ψ𝑃	ψ𝑃	NOUN
cana-2737	468	16	)	)	PUNCT
cana-2737	468	17	.	.	PUNCT
cana-2737	469	1	hence	hence	ADV
cana-2737	469	2	,	,	PUNCT
cana-2737	469	3	1𝑌	1𝑌	PROPN
cana-2737	469	4	−	−	PROPN
cana-2737	469	5	ℎ𝑃(1𝑋	ℎ𝑃(1𝑋	PROPN
cana-2737	469	6	−	−	PROPN
cana-2737	469	7	𝐾	𝐾	PROPN
cana-2737	469	8	)	)	PUNCT
cana-2737	469	9	is	be	AUX
cana-2737	469	10	a	a	DET
cana-2737	469	11	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-2737	469	12	in	in	ADP
cana-2737	469	13	(	(	PUNCT
cana-2737	469	14	𝑋2	𝑋2	ADJ
cana-2737	469	15	,	,	PUNCT
cana-2737	469	16	ψ𝑃	ψ𝑃	NOUN
cana-2737	469	17	)	)	PUNCT
cana-2737	469	18	.	.	PUNCT
cana-2737	470	1	therefore	therefore	ADV
cana-2737	470	2	,	,	PUNCT
cana-2737	470	3	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	470	4	is	be	AUX
cana-2737	470	5	a	a	DET
cana-2737	470	6	𝑝𝑓𝑀𝐶	𝑝𝑓𝑀𝐶	NOUN
cana-2737	470	7	mapping	mapping	NOUN
cana-2737	470	8	.	.	PUNCT
cana-2737	471	1	(	(	PUNCT
cana-2737	471	2	ii	ii	NOUN
cana-2737	471	3	)	)	PUNCT
cana-2737	471	4	⇒	⇒	NOUN
cana-2737	471	5	(	(	PUNCT
cana-2737	471	6	iii	iii	NOUN
cana-2737	471	7	):	):	PUNCT
cana-2737	471	8	let	let	VERB
cana-2737	471	9	𝐾	𝐾	PRON
cana-2737	471	10	be	be	AUX
cana-2737	471	11	a	a	DET
cana-2737	471	12	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-2737	471	13	in	in	ADP
cana-2737	471	14	(	(	PUNCT
cana-2737	471	15	𝑋1	𝑋1	NOUN
cana-2737	471	16	,	,	PUNCT
cana-2737	471	17	γ𝑃	γ𝑃	NOUN
cana-2737	471	18	)	)	PUNCT
cana-2737	471	19	by	by	ADP
cana-2737	471	20	(	(	PUNCT
cana-2737	471	21	ii	ii	NOUN
cana-2737	471	22	)	)	PUNCT
cana-2737	471	23	,	,	PUNCT
cana-2737	471	24	ℎ𝑃(𝐾	ℎ𝑃(𝐾	PROPN
cana-2737	471	25	)	)	PUNCT
cana-2737	471	26	is	be	AUX
cana-2737	471	27	a	a	DET
cana-2737	471	28	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-2737	471	29	in	in	ADP
cana-2737	471	30	(	(	PUNCT
cana-2737	471	31	𝑋2	𝑋2	ADJ
cana-2737	471	32	,	,	PUNCT
cana-2737	471	33	ψ𝑃	ψ𝑃	NOUN
cana-2737	471	34	)	)	PUNCT
cana-2737	471	35	.	.	PUNCT
cana-2737	472	1	hence	hence	ADV
cana-2737	472	2	,	,	PUNCT
cana-2737	472	3	ℎ𝑃(𝐾	ℎ𝑃(𝐾	PROPN
cana-2737	472	4	)	)	PUNCT
cana-2737	472	5	=	=	SYM
cana-2737	473	1	(	(	PUNCT
cana-2737	473	2	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	473	3	−1)−1(𝐾	−1)−1(𝐾	PROPN
cana-2737	473	4	)	)	PUNCT
cana-2737	473	5	.	.	PUNCT
cana-2737	474	1	so	so	ADV
cana-2737	474	2	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	474	3	−1	−1	NOUN
cana-2737	474	4	is	be	AUX
cana-2737	474	5	a	a	DET
cana-2737	474	6	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-2737	474	7	in	in	ADP
cana-2737	474	8	(	(	PUNCT
cana-2737	474	9	𝑋2	𝑋2	ADJ
cana-2737	474	10	,	,	PUNCT
cana-2737	474	11	ψ𝑃	ψ𝑃	NOUN
cana-2737	474	12	)	)	PUNCT
cana-2737	474	13	.	.	PUNCT
cana-2737	475	1	hence	hence	ADV
cana-2737	475	2	,	,	PUNCT
cana-2737	475	3	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	475	4	−1	−1	NOUN
cana-2737	475	5	is	be	AUX
cana-2737	475	6	𝑝𝑓𝑀𝐶𝑡𝑠.	𝑝𝑓𝑀𝐶𝑡𝑠.	NOUN
cana-2737	475	7	(	(	PUNCT
cana-2737	475	8	iii	iii	NOUN
cana-2737	475	9	)	)	PUNCT
cana-2737	475	10	⇒	⇒	NOUN
cana-2737	475	11	(	(	PUNCT
cana-2737	475	12	i	i	NOUN
cana-2737	475	13	):	):	PUNCT
cana-2737	475	14	let	let	VERB
cana-2737	475	15	𝐾	𝐾	PRON
cana-2737	475	16	be	be	AUX
cana-2737	475	17	a	a	DET
cana-2737	475	18	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-2737	475	19	in	in	ADP
cana-2737	475	20	(	(	PUNCT
cana-2737	475	21	𝑋1	𝑋1	NOUN
cana-2737	475	22	,	,	PUNCT
cana-2737	475	23	γ𝑃	γ𝑃	NOUN
cana-2737	475	24	)	)	PUNCT
cana-2737	475	25	.	.	PUNCT
cana-2737	476	1	by	by	ADP
cana-2737	476	2	(	(	PUNCT
cana-2737	476	3	iii	iii	NOUN
cana-2737	476	4	)	)	PUNCT
cana-2737	476	5	,	,	PUNCT
cana-2737	476	6	(	(	PUNCT
cana-2737	476	7	ℎ𝑃	ℎ𝑃	PROPN
cana-2737	476	8	−1)−1(𝐾	−1)−1(𝐾	NOUN
cana-2737	476	9	)	)	PUNCT
cana-2737	476	10	=	=	SYM
cana-2737	476	11	ℎ𝑃(𝐾	ℎ𝑃(𝐾	PROPN
cana-2737	476	12	)	)	PUNCT
cana-2737	476	13	is	be	AUX
cana-2737	476	14	a	a	DET
cana-2737	476	15	𝑝𝑓𝑀𝑂	𝑝𝑓𝑀𝑂	NOUN
cana-2737	476	16	mapping	mapping	NOUN
cana-2737	476	17	.	.	PUNCT
cana-2737	477	1	5	5	NUM
cana-2737	477	2	application	application	NOUN
cana-2737	477	3	entropy	entropy	NOUN
cana-2737	477	4	as	as	ADP
cana-2737	477	5	a	a	DET
cana-2737	477	6	measure	measure	NOUN
cana-2737	477	7	of	of	ADP
cana-2737	477	8	fuzziness	fuzziness	NOUN
cana-2737	477	9	was	be	AUX
cana-2737	477	10	first	first	ADV
cana-2737	477	11	proposed	propose	VERB
cana-2737	477	12	by	by	ADP
cana-2737	477	13	zadeh	zadeh	PROPN
cana-2737	477	14	[	[	X
cana-2737	477	15	35	35	NUM
cana-2737	477	16	]	]	PUNCT
cana-2737	477	17	.	.	PUNCT
cana-2737	478	1	later	later	ADV
cana-2737	478	2	many	many	ADJ
cana-2737	478	3	mathematicians	mathematician	NOUN
cana-2737	478	4	defined	define	VERB
cana-2737	478	5	several	several	ADJ
cana-2737	478	6	entropy	entropy	NOUN
cana-2737	478	7	measures	measure	NOUN
cana-2737	478	8	.	.	PUNCT
cana-2737	479	1	in	in	ADP
cana-2737	479	2	this	this	DET
cana-2737	479	3	section	section	NOUN
cana-2737	479	4	,	,	PUNCT
cana-2737	479	5	we	we	PRON
cana-2737	479	6	focus	focus	VERB
cana-2737	479	7	on	on	ADP
cana-2737	479	8	defining	define	VERB
cana-2737	479	9	an	an	DET
cana-2737	479	10	entropy	entropy	NOUN
cana-2737	479	11	measure	measure	NOUN
cana-2737	479	12	for	for	ADP
cana-2737	479	13	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2737	479	14	that	that	PRON
cana-2737	479	15	connects	connect	VERB
cana-2737	479	16	the	the	DET
cana-2737	479	17	degree	degree	NOUN
cana-2737	479	18	of	of	ADP
cana-2737	479	19	membership	membership	NOUN
cana-2737	479	20	and	and	CCONJ
cana-2737	479	21	non	non	ADJ
cana-2737	479	22	-	-	NOUN
cana-2737	479	23	membership	membership	NOUN
cana-2737	479	24	.	.	PUNCT
cana-2737	480	1	as	as	ADP
cana-2737	480	2	an	an	DET
cana-2737	480	3	example	example	NOUN
cana-2737	480	4	,	,	PUNCT
cana-2737	480	5	we	we	PRON
cana-2737	480	6	have	have	AUX
cana-2737	480	7	applied	apply	VERB
cana-2737	480	8	the	the	DET
cana-2737	480	9	proposed	propose	VERB
cana-2737	480	10	entropy	entropy	NOUN
cana-2737	480	11	measure	measure	NOUN
cana-2737	480	12	in	in	ADP
cana-2737	480	13	the	the	DET
cana-2737	480	14	field	field	NOUN
cana-2737	480	15	of	of	ADP
cana-2737	480	16	seasons	season	NOUN
cana-2737	480	17	.	.	PUNCT
cana-2737	481	1	definition	definition	NOUN
cana-2737	481	2	5.1	5.1	NUM
cana-2737	481	3	let	let	VERB
cana-2737	481	4	𝐴	𝐴	PROPN
cana-2737	481	5	=	=	PUNCT
cana-2737	481	6	{	{	PUNCT
cana-2737	481	7	<	<	X
cana-2737	481	8	𝑥	𝑥	X
cana-2737	481	9	,	,	PUNCT
cana-2737	481	10	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-2737	481	11	)	)	PUNCT
cana-2737	481	12	,	,	PUNCT
cana-2737	481	13	𝜈𝐴(𝑥)|𝑥	𝜈𝐴(𝑥)|𝑥	NOUN
cana-2737	481	14	∈	∈	PROPN
cana-2737	481	15	𝑋	𝑋	PROPN
cana-2737	481	16	}	}	PUNCT
cana-2737	481	17	be	be	AUX
cana-2737	481	18	a	a	DET
cana-2737	481	19	𝑝𝑓𝑠	𝑝𝑓𝑠	NOUN
cana-2737	481	20	in	in	ADP
cana-2737	481	21	𝑋.	𝑋.	PROPN
cana-2737	481	22	the	the	DET
cana-2737	481	23	new	new	ADJ
cana-2737	481	24	entropy	entropy	NOUN
cana-2737	481	25	measure	measure	NOUN
cana-2737	481	26	for	for	ADP
cana-2737	481	27	𝐴	𝐴	PROPN
cana-2737	481	28	denoted	denote	VERB
cana-2737	481	29	by	by	ADP
cana-2737	481	30	휀𝑝𝑓𝑠(𝐴	휀𝑝𝑓𝑠(𝐴	NOUN
cana-2737	481	31	)	)	PUNCT
cana-2737	481	32	,	,	PUNCT
cana-2737	481	33	is	be	AUX
cana-2737	481	34	a	a	DET
cana-2737	481	35	function	function	NOUN
cana-2737	481	36	,	,	PUNCT
cana-2737	481	37	휀𝑝𝑓𝑠	휀𝑝𝑓𝑠	NOUN
cana-2737	481	38	:	:	PUNCT
cana-2737	481	39	𝜏𝑝𝑓𝑠(𝑋	𝜏𝑝𝑓𝑠(𝑋	PROPN
cana-2737	481	40	)	)	PUNCT
cana-2737	481	41	→	→	PUNCT
cana-2737	482	1	[	[	X
cana-2737	482	2	0,1	0,1	NUM
cana-2737	482	3	]	]	PUNCT
cana-2737	482	4	and	and	CCONJ
cana-2737	482	5	is	be	AUX
cana-2737	482	6	defined	define	VERB
cana-2737	482	7	as	as	ADP
cana-2737	482	8	휀𝑝𝑓𝑠(𝐴	휀𝑝𝑓𝑠(𝐴	X
cana-2737	482	9	)	)	PUNCT
cana-2737	483	1	=	=	SYM
cana-2737	484	1	1	1	NUM
cana-2737	484	2	−	−	NUM
cana-2737	484	3	1	1	NUM
cana-2737	484	4	𝑛	𝑛	PRON
cana-2737	484	5	∑𝑛	∑𝑛	PROPN
cana-2737	484	6	𝑖=1	𝑖=1	PROPN
cana-2737	484	7	(	(	PUNCT
cana-2737	484	8	𝛼𝐴	𝛼𝐴	ADV
cana-2737	484	9	−	−	NOUN
cana-2737	484	10	𝛾𝐴)2	𝛾𝐴)2	ADJ
cana-2737	484	11	;	;	PUNCT
cana-2737	484	12	𝑓𝑜𝑟𝑒𝑣𝑒𝑟𝑦`𝑥𝑖	𝑓𝑜𝑟𝑒𝑣𝑒𝑟𝑦`𝑥𝑖	NUM
cana-2737	484	13	∈	∈	PROPN
cana-2737	484	14	𝐴	𝐴	PROPN
cana-2737	484	15	,	,	PUNCT
cana-2737	484	16	where	where	SCONJ
cana-2737	484	17	𝜏𝑝𝑓𝑠(𝑋	𝜏𝑝𝑓𝑠(𝑋	NOUN
cana-2737	484	18	)	)	PUNCT
cana-2737	484	19	denote	denote	VERB
cana-2737	484	20	the	the	DET
cana-2737	484	21	family	family	NOUN
cana-2737	484	22	of	of	ADP
cana-2737	484	23	all	all	PRON
cana-2737	485	1	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2737	485	2	’s	’s	NOUN
cana-2737	485	3	on	on	ADP
cana-2737	485	4	𝑋.	𝑋.	PROPN
cana-2737	485	5	example	example	NOUN
cana-2737	485	6	5.1	5.1	NUM
cana-2737	486	1	the	the	DET
cana-2737	486	2	development	development	NOUN
cana-2737	486	3	of	of	ADP
cana-2737	486	4	the	the	DET
cana-2737	486	5	each	each	DET
cana-2737	486	6	nation	nation	NOUN
cana-2737	486	7	is	be	AUX
cana-2737	486	8	measured	measure	VERB
cana-2737	486	9	by	by	ADP
cana-2737	486	10	the	the	DET
cana-2737	486	11	economical	economical	ADJ
cana-2737	486	12	development	development	NOUN
cana-2737	486	13	,	,	PUNCT
cana-2737	486	14	technical	technical	ADJ
cana-2737	486	15	development	development	NOUN
cana-2737	486	16	,	,	PUNCT
cana-2737	486	17	educational	educational	ADJ
cana-2737	486	18	growth	growth	NOUN
cana-2737	486	19	,	,	PUNCT
cana-2737	486	20	ai	ai	VERB
cana-2737	486	21	implementation	implementation	NOUN
cana-2737	486	22	,	,	PUNCT
cana-2737	486	23	import	import	NOUN
cana-2737	486	24	and	and	CCONJ
cana-2737	486	25	export	export	NOUN
cana-2737	486	26	,	,	PUNCT
cana-2737	486	27	defence	defence	NOUN
cana-2737	486	28	status	status	NOUN
cana-2737	486	29	,	,	PUNCT
cana-2737	486	30	sports	sport	NOUN
cana-2737	486	31	and	and	CCONJ
cana-2737	486	32	etc	etc	X
cana-2737	486	33	.	.	X
cana-2737	487	1	in	in	ADP
cana-2737	487	2	olympics	olympics	PROPN
cana-2737	487	3	and	and	CCONJ
cana-2737	487	4	commonwealth	commonwealth	PROPN
cana-2737	487	5	games	game	NOUN
cana-2737	487	6	the	the	DET
cana-2737	487	7	developed	develop	VERB
cana-2737	487	8	countries	country	NOUN
cana-2737	487	9	are	be	AUX
cana-2737	487	10	the	the	DET
cana-2737	487	11	toppers	topper	NOUN
cana-2737	487	12	of	of	ADP
cana-2737	487	13	the	the	DET
cana-2737	487	14	list	list	NOUN
cana-2737	487	15	,	,	PUNCT
cana-2737	487	16	so	so	CCONJ
cana-2737	487	17	the	the	DET
cana-2737	487	18	developing	develop	VERB
cana-2737	487	19	countries	country	NOUN
cana-2737	487	20	are	be	AUX
cana-2737	487	21	also	also	ADV
cana-2737	487	22	making	make	VERB
cana-2737	487	23	lot	lot	NOUN
cana-2737	487	24	of	of	ADP
cana-2737	487	25	efforts	effort	NOUN
cana-2737	487	26	and	and	CCONJ
cana-2737	487	27	allot	allot	VERB
cana-2737	487	28	funds	fund	NOUN
cana-2737	487	29	for	for	ADP
cana-2737	487	30	sports	sport	NOUN
cana-2737	487	31	.	.	PUNCT
cana-2737	488	1	even	even	ADV
cana-2737	488	2	-	-	PUNCT
cana-2737	488	3	though	though	SCONJ
cana-2737	488	4	communications	communication	NOUN
cana-2737	488	5	on	on	ADP
cana-2737	488	6	applied	apply	VERB
cana-2737	488	7	nonlinear	nonlinear	ADJ
cana-2737	488	8	analysis	analysis	NOUN
cana-2737	488	9	issn	issn	NOUN
cana-2737	488	10	:	:	PUNCT
cana-2737	488	11	1074	1074	NUM
cana-2737	488	12	-	-	PUNCT
cana-2737	488	13	133x	133x	NUM
cana-2737	488	14	vol	vol	NOUN
cana-2737	488	15	32	32	NUM
cana-2737	488	16	no	no	NOUN
cana-2737	488	17	.	.	PUNCT
cana-2737	489	1	4s	4s	NUM
cana-2737	489	2	(	(	PUNCT
cana-2737	489	3	2025	2025	NUM
cana-2737	489	4	)	)	PUNCT
cana-2737	489	5	40	40	NUM
cana-2737	489	6	https://internationalpubls.com	https://internationalpubls.com	NUM
cana-2737	489	7	practice	practice	NOUN
cana-2737	489	8	and	and	CCONJ
cana-2737	489	9	coaching	coaching	NOUN
cana-2737	489	10	plays	play	VERB
cana-2737	489	11	the	the	DET
cana-2737	489	12	major	major	ADJ
cana-2737	489	13	role	role	NOUN
cana-2737	489	14	,	,	PUNCT
cana-2737	489	15	the	the	DET
cana-2737	489	16	diet	diet	NOUN
cana-2737	489	17	supplement	supplement	NOUN
cana-2737	489	18	also	also	ADV
cana-2737	489	19	plays	play	VERB
cana-2737	489	20	a	a	DET
cana-2737	489	21	vital	vital	ADJ
cana-2737	489	22	role	role	NOUN
cana-2737	489	23	in	in	ADP
cana-2737	489	24	athlete	athlete	NOUN
cana-2737	489	25	’s	’s	PART
cana-2737	489	26	performance	performance	NOUN
cana-2737	489	27	.	.	PUNCT
cana-2737	490	1	each	each	DET
cana-2737	490	2	sports	sport	NOUN
cana-2737	490	3	academy	academy	NOUN
cana-2737	490	4	,	,	PUNCT
cana-2737	490	5	there	there	PRON
cana-2737	490	6	are	be	VERB
cana-2737	490	7	well	well	ADV
cana-2737	490	8	trained	train	VERB
cana-2737	490	9	nutritions	nutrition	NOUN
cana-2737	490	10	to	to	PART
cana-2737	490	11	plan	plan	VERB
cana-2737	490	12	for	for	ADP
cana-2737	490	13	the	the	DET
cana-2737	490	14	diet	diet	NOUN
cana-2737	490	15	of	of	ADP
cana-2737	490	16	the	the	DET
cana-2737	490	17	athlete	athlete	NOUN
cana-2737	490	18	.	.	PUNCT
cana-2737	491	1	in	in	ADP
cana-2737	491	2	a	a	DET
cana-2737	491	3	private	private	ADJ
cana-2737	491	4	sports	sport	NOUN
cana-2737	491	5	academy	academy	NOUN
cana-2737	491	6	named	name	VERB
cana-2737	491	7	as	as	SCONJ
cana-2737	491	8	𝑋	𝑋	PROPN
cana-2737	491	9	has	have	VERB
cana-2737	491	10	three	three	NUM
cana-2737	491	11	diet	diet	NOUN
cana-2737	491	12	plans	plan	NOUN
cana-2737	491	13	for	for	ADP
cana-2737	491	14	athlete	athlete	NOUN
cana-2737	491	15	who	who	PRON
cana-2737	491	16	is	be	AUX
cana-2737	491	17	on	on	ADP
cana-2737	491	18	the	the	DET
cana-2737	491	19	training	training	NOUN
cana-2737	491	20	of	of	ADP
cana-2737	491	21	the	the	DET
cana-2737	491	22	national	national	PROPN
cana-2737	491	23	games	game	NOUN
cana-2737	491	24	.	.	PUNCT
cana-2737	492	1	each	each	DET
cana-2737	492	2	diet	diet	NOUN
cana-2737	492	3	was	be	AUX
cana-2737	492	4	scheduled	schedule	VERB
cana-2737	492	5	for	for	ADP
cana-2737	492	6	a	a	DET
cana-2737	492	7	week	week	NOUN
cana-2737	492	8	,	,	PUNCT
cana-2737	492	9	implemented	implement	VERB
cana-2737	492	10	at	at	ADP
cana-2737	492	11	the	the	DET
cana-2737	492	12	gap	gap	NOUN
cana-2737	492	13	of	of	ADP
cana-2737	492	14	one	one	NUM
cana-2737	492	15	week	week	NOUN
cana-2737	492	16	difference	difference	NOUN
cana-2737	492	17	,	,	PUNCT
cana-2737	492	18	the	the	DET
cana-2737	492	19	performance	performance	NOUN
cana-2737	492	20	was	be	AUX
cana-2737	492	21	rated	rate	VERB
cana-2737	492	22	by	by	ADP
cana-2737	492	23	four	four	NUM
cana-2737	492	24	trainers	trainer	NOUN
cana-2737	492	25	,	,	PUNCT
cana-2737	492	26	for	for	ADP
cana-2737	492	27	each	each	DET
cana-2737	492	28	day	day	NOUN
cana-2737	492	29	on	on	ADP
cana-2737	492	30	the	the	DET
cana-2737	492	31	diet	diet	NOUN
cana-2737	492	32	week	week	NOUN
cana-2737	492	33	.	.	PUNCT
cana-2737	493	1	the	the	DET
cana-2737	493	2	rating	rating	NOUN
cana-2737	493	3	of	of	ADP
cana-2737	493	4	the	the	DET
cana-2737	493	5	trainers	trainer	NOUN
cana-2737	493	6	was	be	AUX
cana-2737	493	7	converted	convert	VERB
cana-2737	493	8	as	as	SCONJ
cana-2737	493	9	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2737	493	10	and	and	CCONJ
cana-2737	493	11	entropy	entropy	NOUN
cana-2737	493	12	measure	measure	NOUN
cana-2737	493	13	is	be	AUX
cana-2737	493	14	used	use	VERB
cana-2737	493	15	to	to	PART
cana-2737	493	16	select	select	VERB
cana-2737	493	17	the	the	DET
cana-2737	493	18	best	good	ADJ
cana-2737	493	19	diet	diet	NOUN
cana-2737	493	20	for	for	ADP
cana-2737	493	21	the	the	DET
cana-2737	493	22	athlete	athlete	NOUN
cana-2737	493	23	.	.	PUNCT
cana-2737	494	1	the	the	DET
cana-2737	494	2	following	follow	VERB
cana-2737	494	3	table	table	NOUN
cana-2737	494	4	displays	display	NOUN
cana-2737	494	5	𝑝𝑓𝑠	𝑝𝑓𝑠	ADP
cana-2737	494	6	of	of	ADP
cana-2737	494	7	performance	performance	NOUN
cana-2737	494	8	of	of	ADP
cana-2737	494	9	each	each	DET
cana-2737	494	10	diet	diet	NOUN
cana-2737	494	11	week	week	NOUN
cana-2737	494	12	.	.	PUNCT
cana-2737	495	1	here	here	ADV
cana-2737	495	2	we	we	PRON
cana-2737	495	3	use	use	VERB
cana-2737	495	4	the	the	DET
cana-2737	495	5	notations	notation	NOUN
cana-2737	495	6	for	for	ADP
cana-2737	495	7	diet	diet	NOUN
cana-2737	495	8	1	1	NUM
cana-2737	495	9	,	,	PUNCT
cana-2737	495	10	diet	diet	NOUN
cana-2737	495	11	2	2	NUM
cana-2737	495	12	and	and	CCONJ
cana-2737	495	13	diet	diet	PROPN
cana-2737	495	14	3	3	NUM
cana-2737	495	15	are	be	AUX
cana-2737	495	16	𝐷𝑖1	𝐷𝑖1	ADJ
cana-2737	495	17	,	,	PUNCT
cana-2737	495	18	𝐷𝑖2	𝐷𝑖2	NOUN
cana-2737	495	19	and	and	CCONJ
cana-2737	495	20	𝐷𝑖3	𝐷𝑖3	NOUN
cana-2737	495	21	.	.	PUNCT
cana-2737	496	1	table	table	NOUN
cana-2737	496	2	1	1	NUM
cana-2737	496	3	.	.	PUNCT
cana-2737	497	1	reviews	review	NOUN
cana-2737	497	2	of	of	ADP
cana-2737	497	3	the	the	DET
cana-2737	497	4	hotels	hotel	NOUN
cana-2737	497	5	based	base	VERB
cana-2737	497	6	on	on	ADP
cana-2737	497	7	the	the	DET
cana-2737	497	8	criteria	criterion	NOUN
cana-2737	497	9	day	day	NOUN
cana-2737	497	10	1	1	NUM
cana-2737	497	11	(	(	PUNCT
cana-2737	497	12	𝐷1	𝐷1	PROPN
cana-2737	497	13	)	)	PUNCT
cana-2737	497	14	day	day	NOUN
cana-2737	497	15	2	2	NUM
cana-2737	497	16	(	(	PUNCT
cana-2737	497	17	𝐷2	𝐷2	NOUN
cana-2737	497	18	)	)	PUNCT
cana-2737	497	19	day	day	NOUN
cana-2737	497	20	3	3	NUM
cana-2737	497	21	(	(	PUNCT
cana-2737	497	22	𝐷3	𝐷3	PROPN
cana-2737	497	23	)	)	PUNCT
cana-2737	497	24	day	day	NOUN
cana-2737	497	25	4	4	NUM
cana-2737	497	26	(	(	PUNCT
cana-2737	497	27	𝐷4	𝐷4	NOUN
cana-2737	497	28	)	)	PUNCT
cana-2737	497	29	𝐷𝑖1	𝐷𝑖1	NOUN
cana-2737	497	30	<	<	X
cana-2737	497	31	𝐷𝑖1	𝐷𝑖1	ADJ
cana-2737	497	32	,	,	PUNCT
cana-2737	497	33	𝐷1	𝐷1	PROPN
cana-2737	497	34	;	;	PUNCT
cana-2737	497	35	0.8,0.0	0.8,0.0	X
cana-2737	497	36	>	>	X
cana-2737	497	37	<	<	X
cana-2737	497	38	𝐷𝑖1	𝐷𝑖1	ADJ
cana-2737	497	39	,	,	PUNCT
cana-2737	497	40	𝐷2	𝐷2	NOUN
cana-2737	497	41	;	;	PUNCT
cana-2737	497	42	0.6,0.6	0.6,0.6	X
cana-2737	497	43	>	>	X
cana-2737	497	44	<	<	X
cana-2737	497	45	𝐷𝑖1	𝐷𝑖1	PROPN
cana-2737	497	46	,	,	PUNCT
cana-2737	497	47	𝐷3	𝐷3	PROPN
cana-2737	497	48	;	;	PUNCT
cana-2737	497	49	0.4,0.6	0.4,0.6	X
cana-2737	497	50	>	>	X
cana-2737	497	51	<	<	X
cana-2737	497	52	𝐷𝑖1	𝐷𝑖1	ADJ
cana-2737	497	53	,	,	PUNCT
cana-2737	497	54	𝐷4	𝐷4	PROPN
cana-2737	497	55	;	;	PUNCT
cana-2737	497	56	0.3,0.3	0.3,0.3	PROPN
cana-2737	497	57	>	>	X
cana-2737	497	58	𝐷𝑖2	𝐷𝑖2	NOUN
cana-2737	497	59	<	<	X
cana-2737	497	60	𝐷𝑖2	𝐷𝑖2	NOUN
cana-2737	497	61	,	,	PUNCT
cana-2737	497	62	𝐷1	𝐷1	PROPN
cana-2737	497	63	;	;	PUNCT
cana-2737	497	64	0.7,0.3	0.7,0.3	PROPN
cana-2737	497	65	>	>	X
cana-2737	497	66	<	<	X
cana-2737	497	67	𝐷𝑖2	𝐷𝑖2	NOUN
cana-2737	497	68	,	,	PUNCT
cana-2737	497	69	𝐷2	𝐷2	NOUN
cana-2737	497	70	;	;	PUNCT
cana-2737	497	71	0.8,0.6	0.8,0.6	PROPN
cana-2737	497	72	>	>	X
cana-2737	497	73	<	<	X
cana-2737	497	74	𝐷𝑖2	𝐷𝑖2	NOUN
cana-2737	497	75	,	,	PUNCT
cana-2737	497	76	𝐷3	𝐷3	PROPN
cana-2737	497	77	;	;	PUNCT
cana-2737	497	78	0.7,0.3	0.7,0.3	PROPN
cana-2737	497	79	>	>	X
cana-2737	497	80	<	<	X
cana-2737	497	81	𝐷𝑖2	𝐷𝑖2	NOUN
cana-2737	497	82	,	,	PUNCT
cana-2737	497	83	𝐷4	𝐷4	PROPN
cana-2737	497	84	;	;	PUNCT
cana-2737	497	85	0.8,0.2	0.8,0.2	PROPN
cana-2737	497	86	>	>	X
cana-2737	497	87	𝐷𝑖3	𝐷𝑖3	NOUN
cana-2737	497	88	<	<	X
cana-2737	497	89	𝐷𝑖3	𝐷𝑖3	NOUN
cana-2737	497	90	,	,	PUNCT
cana-2737	497	91	𝐷1	𝐷1	PROPN
cana-2737	497	92	;	;	PUNCT
cana-2737	497	93	0.7,0.1	0.7,0.1	PROPN
cana-2737	497	94	>	>	X
cana-2737	497	95	<	<	X
cana-2737	497	96	𝐷𝑖3	𝐷𝑖3	X
cana-2737	497	97	,	,	PUNCT
cana-2737	497	98	𝐷2	𝐷2	NOUN
cana-2737	497	99	;	;	PUNCT
cana-2737	497	100	0.8,0.0	0.8,0.0	NUM
cana-2737	497	101	>	>	X
cana-2737	497	102	<	<	X
cana-2737	497	103	𝐷𝑖3	𝐷𝑖3	NOUN
cana-2737	497	104	,	,	PUNCT
cana-2737	497	105	𝐷3	𝐷3	PROPN
cana-2737	497	106	;	;	PUNCT
cana-2737	497	107	0.7,0.4	0.7,0.4	NUM
cana-2737	497	108	>	>	X
cana-2737	497	109	<	<	X
cana-2737	497	110	𝐷𝑖3	𝐷𝑖3	NOUN
cana-2737	497	111	,	,	PUNCT
cana-2737	497	112	𝐷4	𝐷4	PROPN
cana-2737	497	113	;	;	PUNCT
cana-2737	497	114	0.6,0.3	0.6,0.3	PROPN
cana-2737	497	115	>	>	X
cana-2737	497	116	day	day	NOUN
cana-2737	497	117	5	5	NUM
cana-2737	497	118	(	(	PUNCT
cana-2737	497	119	𝐷5	𝐷5	PROPN
cana-2737	497	120	)	)	PUNCT
cana-2737	497	121	day	day	NOUN
cana-2737	497	122	6	6	NUM
cana-2737	497	123	(	(	PUNCT
cana-2737	497	124	𝐷6	𝐷6	NOUN
cana-2737	497	125	)	)	PUNCT
cana-2737	497	126	day	day	NOUN
cana-2737	497	127	7	7	NUM
cana-2737	497	128	(	(	PUNCT
cana-2737	497	129	𝐷7	𝐷7	PROPN
cana-2737	497	130	)	)	PUNCT
cana-2737	497	131	𝐷𝑖1	𝐷𝑖1	NOUN
cana-2737	497	132	<	<	X
cana-2737	497	133	𝐷𝑖1	𝐷𝑖1	ADJ
cana-2737	497	134	,	,	PUNCT
cana-2737	497	135	𝐷5	𝐷5	PROPN
cana-2737	497	136	;	;	PUNCT
cana-2737	497	137	0.8,0.2	0.8,0.2	NUM
cana-2737	497	138	>	>	X
cana-2737	497	139	<	<	X
cana-2737	497	140	𝐷𝑖1	𝐷𝑖1	ADJ
cana-2737	497	141	,	,	PUNCT
cana-2737	497	142	𝐷6	𝐷6	NOUN
cana-2737	497	143	;	;	PUNCT
cana-2737	497	144	0.7,0.7	0.7,0.7	PROPN
cana-2737	497	145	>	>	X
cana-2737	497	146	<	<	X
cana-2737	497	147	𝐷𝑖1	𝐷𝑖1	ADJ
cana-2737	497	148	,	,	PUNCT
cana-2737	497	149	𝐷7	𝐷7	PROPN
cana-2737	497	150	;	;	PUNCT
cana-2737	497	151	0.7,0.5	0.7,0.5	NUM
cana-2737	497	152	>	>	X
cana-2737	497	153	𝐷𝑖2	𝐷𝑖2	NOUN
cana-2737	497	154	<	<	X
cana-2737	497	155	𝐷𝑖2	𝐷𝑖2	NOUN
cana-2737	497	156	,	,	PUNCT
cana-2737	497	157	𝐷5	𝐷5	PROPN
cana-2737	497	158	;	;	PUNCT
cana-2737	497	159	0.2,0.4	0.2,0.4	PROPN
cana-2737	497	160	>	>	X
cana-2737	497	161	<	<	X
cana-2737	497	162	𝐷𝑖2	𝐷𝑖2	NOUN
cana-2737	497	163	,	,	PUNCT
cana-2737	497	164	𝐷6	𝐷6	NOUN
cana-2737	497	165	;	;	PUNCT
cana-2737	497	166	0.6,0.2	0.6,0.2	PROPN
cana-2737	497	167	>	>	X
cana-2737	497	168	<	<	X
cana-2737	497	169	𝐷𝑖2	𝐷𝑖2	NOUN
cana-2737	497	170	,	,	PUNCT
cana-2737	497	171	𝐷7	𝐷7	PROPN
cana-2737	497	172	;	;	PUNCT
cana-2737	497	173	0.7,0.5	0.7,0.5	NUM
cana-2737	497	174	>	>	X
cana-2737	497	175	𝐷𝑖3	𝐷𝑖3	NOUN
cana-2737	497	176	<	<	X
cana-2737	497	177	𝐷𝑖3	𝐷𝑖3	NOUN
cana-2737	497	178	,	,	PUNCT
cana-2737	497	179	𝐷5	𝐷5	PROPN
cana-2737	497	180	;	;	PUNCT
cana-2737	497	181	0.7,0.5	0.7,0.5	NUM
cana-2737	497	182	>	>	X
cana-2737	497	183	<	<	X
cana-2737	497	184	𝐷𝑖3	𝐷𝑖3	X
cana-2737	497	185	,	,	PUNCT
cana-2737	497	186	𝐷6	𝐷6	NOUN
cana-2737	497	187	;	;	PUNCT
cana-2737	497	188	0.7,0.2	0.7,0.2	PROPN
cana-2737	497	189	>	>	X
cana-2737	497	190	<	<	X
cana-2737	497	191	𝐷𝑖3	𝐷𝑖3	NOUN
cana-2737	497	192	,	,	PUNCT
cana-2737	497	193	𝐷7	𝐷7	PROPN
cana-2737	497	194	;	;	PUNCT
cana-2737	497	195	0.8,0.5	0.8,0.5	NUM
cana-2737	497	196	>	>	X
cana-2737	497	197	clearly	clearly	ADV
cana-2737	497	198	,	,	PUNCT
cana-2737	497	199	all	all	DET
cana-2737	497	200	values	value	NOUN
cana-2737	497	201	in	in	ADP
cana-2737	497	202	the	the	DET
cana-2737	497	203	table	table	NOUN
cana-2737	497	204	1	1	NUM
cana-2737	497	205	are	be	AUX
cana-2737	497	206	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-2737	497	207	’s	’s	NOUN
cana-2737	497	208	.	.	PUNCT
cana-2737	498	1	now	now	ADV
cana-2737	498	2	we	we	PRON
cana-2737	498	3	calculate	calculate	VERB
cana-2737	498	4	the	the	DET
cana-2737	498	5	휀𝑝𝑓𝑠	휀𝑝𝑓𝑠	NOUN
cana-2737	498	6	of	of	ADP
cana-2737	498	7	each	each	DET
cana-2737	498	8	value	value	NOUN
cana-2737	498	9	.	.	PUNCT
cana-2737	499	1	table	table	NOUN
cana-2737	499	2	2	2	NUM
cana-2737	499	3	.	.	PUNCT
cana-2737	499	4	entropy	entropy	PROPN
cana-2737	499	5	measure	measure	NOUN
cana-2737	499	6	of	of	ADP
cana-2737	499	7	each	each	DET
cana-2737	499	8	diet	diet	NOUN
cana-2737	499	9	.	.	PUNCT
cana-2737	500	1	entropy	entropy	PROPN
cana-2737	500	2	measure	measure	PROPN
cana-2737	500	3	𝐷𝑖1	𝐷𝑖1	ADJ
cana-2737	500	4	0.73	0.73	NUM
cana-2737	500	5	𝐷𝑖2	𝐷𝑖2	NOUN
cana-2737	500	6	0.76	0.76	NUM
cana-2737	500	7	𝐷𝑖3	𝐷𝑖3	NOUN
cana-2737	500	8	0.61	0.61	NUM
cana-2737	500	9	from	from	ADP
cana-2737	500	10	table	table	NOUN
cana-2737	500	11	2	2	NUM
cana-2737	500	12	,	,	PUNCT
cana-2737	500	13	clearly	clearly	ADV
cana-2737	500	14	that	that	SCONJ
cana-2737	500	15	휀𝑝𝑓𝑠(𝐷𝑖3	휀𝑝𝑓𝑠(𝐷𝑖3	ADV
cana-2737	500	16	)	)	PUNCT
cana-2737	500	17	<	<	X
cana-2737	500	18	휀𝑝𝑓𝑠(𝐷𝑖1	휀𝑝𝑓𝑠(𝐷𝑖1	PROPN
cana-2737	500	19	)	)	PUNCT
cana-2737	500	20	<	<	X
cana-2737	500	21	휀𝑝𝑓𝑠(𝐷𝑖2	휀𝑝𝑓𝑠(𝐷𝑖2	NOUN
cana-2737	500	22	)	)	PUNCT
cana-2737	500	23	.	.	PUNCT
cana-2737	501	1	hence	hence	ADV
cana-2737	501	2	we	we	PRON
cana-2737	501	3	conclude	conclude	VERB
cana-2737	501	4	that	that	PRON
cana-2737	501	5	𝐷𝑖3	𝐷𝑖3	NOUN
cana-2737	501	6	is	be	AUX
cana-2737	501	7	the	the	DET
cana-2737	501	8	best	good	ADJ
cana-2737	501	9	for	for	ADP
cana-2737	501	10	the	the	DET
cana-2737	501	11	athlete	athlete	NOUN
cana-2737	501	12	.	.	PUNCT
cana-2737	502	1	6	6	NUM
cana-2737	502	2	conclusion	conclusion	NOUN
cana-2737	502	3	in	in	ADP
cana-2737	502	4	this	this	DET
cana-2737	502	5	paper	paper	NOUN
cana-2737	502	6	,	,	PUNCT
cana-2737	502	7	we	we	PRON
cana-2737	502	8	have	have	AUX
cana-2737	502	9	studied	study	VERB
cana-2737	502	10	a	a	DET
cana-2737	502	11	new	new	ADJ
cana-2737	502	12	class	class	NOUN
cana-2737	502	13	of	of	ADP
cana-2737	502	14	maps	map	NOUN
cana-2737	502	15	called	call	VERB
cana-2737	502	16	pythagorean	pythagorean	PROPN
cana-2737	502	17	fuzzy	fuzzy	PROPN
cana-2737	502	18	𝑀	𝑀	PROPN
cana-2737	502	19	open	open	VERB
cana-2737	502	20	and	and	CCONJ
cana-2737	502	21	pythagorean	pythagorean	PROPN
cana-2737	502	22	fuzzy	fuzzy	PROPN
cana-2737	502	23	𝑀	𝑀	PROPN
cana-2737	502	24	closed	close	VERB
cana-2737	502	25	and	and	CCONJ
cana-2737	502	26	their	their	PRON
cana-2737	502	27	properties	property	NOUN
cana-2737	502	28	are	be	AUX
cana-2737	502	29	discussed	discuss	VERB
cana-2737	502	30	.	.	PUNCT
cana-2737	503	1	also	also	ADV
cana-2737	503	2	we	we	PRON
cana-2737	503	3	applied	apply	VERB
cana-2737	503	4	entropy	entropy	NOUN
cana-2737	503	5	measure	measure	NOUN
cana-2737	503	6	for	for	ADP
cana-2737	503	7	decision	decision	NOUN
cana-2737	503	8	making	making	NOUN
cana-2737	503	9	problem	problem	NOUN
cana-2737	503	10	of	of	ADP
cana-2737	503	11	calculation	calculation	NOUN
cana-2737	503	12	of	of	ADP
cana-2737	503	13	diet	diet	NOUN
cana-2737	503	14	selection	selection	NOUN
cana-2737	503	15	based	base	VERB
cana-2737	503	16	on	on	ADP
cana-2737	503	17	the	the	DET
cana-2737	503	18	performance	performance	NOUN
cana-2737	503	19	.	.	PUNCT
cana-2737	504	1	in	in	ADP
cana-2737	504	2	future	future	NOUN
cana-2737	504	3	,	,	PUNCT
cana-2737	504	4	we	we	PRON
cana-2737	504	5	decide	decide	VERB
cana-2737	504	6	to	to	PART
cana-2737	504	7	apply	apply	VERB
cana-2737	504	8	entropy	entropy	NOUN
cana-2737	504	9	measure	measure	NOUN
cana-2737	504	10	for	for	ADP
cana-2737	504	11	decision	decision	NOUN
cana-2737	504	12	making	making	NOUN
cana-2737	504	13	in	in	ADP
cana-2737	504	14	various	various	ADJ
cana-2737	504	15	fields	field	NOUN
cana-2737	504	16	.	.	PUNCT
cana-2737	505	1	references	reference	NOUN
cana-2737	505	2	[	[	X
cana-2737	505	3	1	1	NUM
cana-2737	505	4	]	]	PUNCT
cana-2737	505	5	k.	k.	PROPN
cana-2737	505	6	t.	t.	PROPN
cana-2737	505	7	atanassov	atanassov	PROPN
cana-2737	505	8	(	(	PUNCT
cana-2737	505	9	1983	1983	NUM
cana-2737	505	10	)	)	PUNCT
cana-2737	505	11	,	,	PUNCT
cana-2737	505	12	intuitionistic	intuitionistic	ADJ
cana-2737	505	13	fuzzy	fuzzy	ADJ
cana-2737	505	14	sets	set	NOUN
cana-2737	505	15	,	,	PUNCT
cana-2737	505	16	vii	vii	PROPN
cana-2737	505	17	itkrâ€	itkrâ€	PROPN
cana-2737	505	18	™	™	PROPN
cana-2737	505	19	s	s	PART
cana-2737	505	20	session	session	NOUN
cana-2737	505	21	,	,	PUNCT
cana-2737	505	22	sofia	sofia	PROPN
cana-2737	505	23	.	.	PUNCT
cana-2737	506	1	[	[	X
cana-2737	506	2	2	2	X
cana-2737	506	3	]	]	PUNCT
cana-2737	506	4	k.	k.	PROPN
cana-2737	506	5	t.	t.	PROPN
cana-2737	506	6	atanassov	atanassov	PROPN
cana-2737	506	7	(	(	PUNCT
cana-2737	506	8	1986	1986	NUM
cana-2737	506	9	)	)	PUNCT
cana-2737	506	10	,	,	PUNCT
cana-2737	506	11	intuitionistic	intuitionistic	ADJ
cana-2737	506	12	fuzzy	fuzzy	ADJ
cana-2737	506	13	sets	set	NOUN
cana-2737	506	14	,	,	PUNCT
cana-2737	506	15	fuzzy	fuzzy	ADJ
cana-2737	506	16	sets	set	NOUN
cana-2737	506	17	syst	syst	NOUN
cana-2737	506	18	.	.	PUNCT
cana-2737	507	1	20	20	NUM
cana-2737	507	2	,	,	PUNCT
cana-2737	507	3	87	87	NUM
cana-2737	507	4	-	-	SYM
cana-2737	507	5	96	96	NUM
cana-2737	507	6	.	.	PUNCT
cana-2737	508	1	[	[	X
cana-2737	508	2	3	3	X
cana-2737	508	3	]	]	PUNCT
cana-2737	508	4	k.	k.	PROPN
cana-2737	508	5	t.	t.	PROPN
cana-2737	508	6	atanassov	atanassov	PROPN
cana-2737	508	7	(	(	PUNCT
cana-2737	508	8	1989	1989	NUM
cana-2737	508	9	)	)	PUNCT
cana-2737	508	10	,	,	PUNCT
cana-2737	508	11	geometrical	geometrical	ADJ
cana-2737	508	12	interpretation	interpretation	NOUN
cana-2737	508	13	of	of	ADP
cana-2737	508	14	the	the	DET
cana-2737	508	15	elements	element	NOUN
cana-2737	508	16	of	of	ADP
cana-2737	508	17	the	the	DET
cana-2737	508	18	intuitionistic	intuitionistic	ADJ
cana-2737	508	19	fuzzy	fuzzy	ADJ
cana-2737	508	20	objects	object	NOUN
cana-2737	508	21	,	,	PUNCT
cana-2737	508	22	preprint	preprint	NOUN
cana-2737	508	23	im	im	NOUN
cana-2737	508	24	-	-	PUNCT
cana-2737	508	25	mfais-1	mfais-1	NOUN
cana-2737	508	26	-	-	SYM
cana-2737	508	27	89	89	NUM
cana-2737	508	28	,	,	PUNCT
cana-2737	508	29	sofia	sofia	NOUN
cana-2737	508	30	.	.	PUNCT
cana-2737	509	1	[	[	X
cana-2737	509	2	4	4	X
cana-2737	509	3	]	]	PUNCT
cana-2737	509	4	k.	k.	PROPN
cana-2737	509	5	t.	t.	PROPN
cana-2737	509	6	atanassov	atanassov	PROPN
cana-2737	509	7	(	(	PUNCT
cana-2737	509	8	1999	1999	NUM
cana-2737	509	9	)	)	PUNCT
cana-2737	509	10	,	,	PUNCT
cana-2737	509	11	intuitionistic	intuitionistic	ADJ
cana-2737	509	12	fuzzy	fuzzy	ADJ
cana-2737	509	13	sets	set	NOUN
cana-2737	509	14	:	:	PUNCT
cana-2737	509	15	theory	theory	NOUN
cana-2737	509	16	and	and	CCONJ
cana-2737	509	17	applications	application	NOUN
cana-2737	509	18	,	,	PUNCT
cana-2737	509	19	physica	physica	NOUN
cana-2737	509	20	,	,	PUNCT
cana-2737	509	21	heidelberg	heidelberg	NOUN
cana-2737	509	22	.	.	PUNCT
cana-2737	510	1	[	[	X
cana-2737	510	2	5	5	X
cana-2737	510	3	]	]	PUNCT
cana-2737	510	4	k.	k.	PROPN
cana-2737	510	5	t.	t.	PROPN
cana-2737	510	6	atanassov	atanassov	PROPN
cana-2737	510	7	(	(	PUNCT
cana-2737	510	8	2012	2012	NUM
cana-2737	510	9	)	)	PUNCT
cana-2737	510	10	,	,	PUNCT
cana-2737	510	11	on	on	ADP
cana-2737	510	12	intuitionistic	intuitionistic	ADJ
cana-2737	510	13	fuzzy	fuzzy	ADJ
cana-2737	510	14	sets	set	NOUN
cana-2737	510	15	theory	theory	NOUN
cana-2737	510	16	,	,	PUNCT
cana-2737	510	17	springer	springer	NOUN
cana-2737	510	18	,	,	PUNCT
cana-2737	510	19	berlin	berlin	PROPN
cana-2737	510	20	.	.	PUNCT
cana-2737	511	1	communications	communication	NOUN
cana-2737	511	2	on	on	ADP
cana-2737	511	3	applied	apply	VERB
cana-2737	511	4	nonlinear	nonlinear	ADJ
cana-2737	511	5	analysis	analysis	NOUN
cana-2737	511	6	issn	issn	NOUN
cana-2737	511	7	:	:	PUNCT
cana-2737	511	8	1074	1074	NUM
cana-2737	511	9	-	-	PUNCT
cana-2737	511	10	133x	133x	NUM
cana-2737	511	11	vol	vol	NOUN
cana-2737	511	12	32	32	NUM
cana-2737	511	13	no	no	NOUN
cana-2737	511	14	.	.	PUNCT
cana-2737	512	1	4s	4s	NUM
cana-2737	512	2	(	(	PUNCT
cana-2737	512	3	2025	2025	NUM
cana-2737	512	4	)	)	PUNCT
cana-2737	512	5	41	41	NUM
cana-2737	513	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-2737	514	1	[	[	X
cana-2737	514	2	6	6	NUM
cana-2737	514	3	]	]	X
cana-2737	514	4	g.	g.	PROPN
cana-2737	514	5	beliakov	beliakov	PROPN
cana-2737	514	6	and	and	CCONJ
cana-2737	514	7	s.	s.	PROPN
cana-2737	514	8	james	james	PROPN
cana-2737	514	9	(	(	PUNCT
cana-2737	514	10	2014	2014	NUM
cana-2737	514	11	)	)	PUNCT
cana-2737	514	12	,	,	PUNCT
cana-2737	514	13	averaging	average	VERB
cana-2737	514	14	aggregation	aggregation	NOUN
cana-2737	514	15	functions	function	NOUN
cana-2737	514	16	for	for	ADP
cana-2737	514	17	preferences	preference	NOUN
cana-2737	514	18	expressed	express	VERB
cana-2737	514	19	as	as	ADP
cana-2737	514	20	pythagorean	pythagorean	PROPN
cana-2737	514	21	membership	membership	NOUN
cana-2737	514	22	grades	grade	NOUN
cana-2737	514	23	and	and	CCONJ
cana-2737	514	24	fuzzy	fuzzy	ADJ
cana-2737	514	25	orthopairs	orthopair	NOUN
cana-2737	514	26	,	,	PUNCT
cana-2737	514	27	in	in	ADP
cana-2737	514	28	:	:	PUNCT
cana-2737	514	29	proceedings	proceeding	NOUN
cana-2737	514	30	of	of	ADP
cana-2737	514	31	the	the	DET
cana-2737	514	32	ieee	ieee	NOUN
cana-2737	514	33	international	international	PROPN
cana-2737	514	34	conference	conference	NOUN
cana-2737	514	35	on	on	ADP
cana-2737	514	36	fuzzy	fuzzy	ADJ
cana-2737	514	37	systems	system	NOUN
cana-2737	514	38	(	(	PUNCT
cana-2737	514	39	fuzz	fuzz	NOUN
cana-2737	514	40	-	-	PUNCT
cana-2737	514	41	ieee	ieee	NOUN
cana-2737	514	42	)	)	PUNCT
cana-2737	514	43	,	,	PUNCT
cana-2737	514	44	298	298	NUM
cana-2737	514	45	-	-	SYM
cana-2737	514	46	305	305	NUM
cana-2737	514	47	.	.	PUNCT
cana-2737	515	1	[	[	X
cana-2737	515	2	7	7	X
cana-2737	515	3	]	]	X
cana-2737	515	4	b.	b.	PROPN
cana-2737	515	5	davvaz	davvaz	PROPN
cana-2737	515	6	and	and	CCONJ
cana-2737	515	7	e.	e.	PROPN
cana-2737	515	8	h.	h.	PROPN
cana-2737	515	9	sadrabadi	sadrabadi	PROPN
cana-2737	515	10	(	(	PUNCT
cana-2737	515	11	2016	2016	NUM
cana-2737	515	12	)	)	PUNCT
cana-2737	515	13	,	,	PUNCT
cana-2737	515	14	an	an	DET
cana-2737	515	15	application	application	NOUN
cana-2737	515	16	of	of	ADP
cana-2737	515	17	intuitionistic	intuitionistic	ADJ
cana-2737	515	18	fuzzy	fuzzy	ADJ
cana-2737	515	19	sets	set	NOUN
cana-2737	515	20	in	in	ADP
cana-2737	515	21	medicine	medicine	NOUN
cana-2737	515	22	,	,	PUNCT
cana-2737	515	23	int	int	NOUN
cana-2737	515	24	.	.	PUNCT
cana-2737	516	1	j.	j.	PROPN
cana-2737	516	2	biomath	biomath	PROPN
cana-2737	516	3	9	9	NUM
cana-2737	516	4	,	,	PUNCT
cana-2737	516	5	(	(	PUNCT
cana-2737	516	6	3	3	NUM
cana-2737	516	7	)	)	PUNCT
cana-2737	516	8	1650037	1650037	NUM
cana-2737	516	9	.	.	PUNCT
cana-2737	517	1	[	[	X
cana-2737	517	2	8	8	NUM
cana-2737	517	3	]	]	PUNCT
cana-2737	517	4	s.	s.	PROPN
cana-2737	517	5	k.	k.	PROPN
cana-2737	517	6	de	de	PROPN
cana-2737	517	7	,	,	PUNCT
cana-2737	517	8	r.	r.	PROPN
cana-2737	517	9	biswas	biswas	PROPN
cana-2737	517	10	and	and	CCONJ
cana-2737	517	11	a.	a.	PROPN
cana-2737	517	12	r.	r.	PROPN
cana-2737	517	13	roy	roy	PROPN
cana-2737	517	14	(	(	PUNCT
cana-2737	517	15	2001	2001	NUM
cana-2737	517	16	)	)	PUNCT
cana-2737	517	17	,	,	PUNCT
cana-2737	517	18	an	an	DET
cana-2737	517	19	application	application	NOUN
cana-2737	517	20	of	of	ADP
cana-2737	517	21	intuitionistic	intuitionistic	ADJ
cana-2737	517	22	fuzzy	fuzzy	ADJ
cana-2737	517	23	sets	set	NOUN
cana-2737	517	24	in	in	ADP
cana-2737	517	25	medical	medical	ADJ
cana-2737	517	26	diagnosis	diagnosis	NOUN
cana-2737	517	27	,	,	PUNCT
cana-2737	517	28	fuzzy	fuzzy	ADJ
cana-2737	517	29	sets	set	VERB
cana-2737	517	30	syst	syst	NOUN
cana-2737	517	31	.	.	PUNCT
cana-2737	517	32	117	117	NUM
cana-2737	517	33	(	(	PUNCT
cana-2737	517	34	2	2	NUM
cana-2737	517	35	)	)	PUNCT
cana-2737	517	36	,	,	PUNCT
cana-2737	517	37	209	209	NUM
cana-2737	517	38	-	-	SYM
cana-2737	517	39	213	213	NUM
cana-2737	517	40	.	.	PUNCT
cana-2737	518	1	[	[	X
cana-2737	518	2	9	9	NUM
cana-2737	518	3	]	]	PUNCT
cana-2737	518	4	s.	s.	PROPN
cana-2737	518	5	dick	dick	PROPN
cana-2737	518	6	,	,	PUNCT
cana-2737	518	7	r.	r.	PROPN
cana-2737	518	8	r.	r.	PROPN
cana-2737	518	9	yager	yager	PROPN
cana-2737	518	10	and	and	CCONJ
cana-2737	518	11	o.	o.	PROPN
cana-2737	518	12	yazdanbakhsh	yazdanbakhsh	PROPN
cana-2737	518	13	(	(	PUNCT
cana-2737	518	14	2016	2016	NUM
cana-2737	518	15	)	)	PUNCT
cana-2737	518	16	,	,	PUNCT
cana-2737	518	17	on	on	ADP
cana-2737	518	18	pythagorean	pythagorean	PROPN
cana-2737	518	19	and	and	CCONJ
cana-2737	518	20	complex	complex	ADJ
cana-2737	518	21	fuzzy	fuzzy	ADJ
cana-2737	518	22	set	set	NOUN
cana-2737	518	23	operations	operation	NOUN
cana-2737	518	24	.	.	PUNCT
cana-2737	519	1	𝐼𝐸𝐸𝐸	𝐼𝐸𝐸𝐸	PROPN
cana-2737	519	2	trans	trans	PROPN
cana-2737	519	3	fuzzy	fuzzy	ADJ
cana-2737	519	4	syst	syst	PROPN
cana-2737	519	5	.	.	PUNCT
cana-2737	520	1	24	24	NUM
cana-2737	520	2	(	(	PUNCT
cana-2737	520	3	5	5	NUM
cana-2737	520	4	)	)	PUNCT
cana-2737	520	5	,	,	PUNCT
cana-2737	520	6	1009	1009	NUM
cana-2737	520	7	-	-	SYM
cana-2737	520	8	1021	1021	NUM
cana-2737	520	9	.	.	PUNCT
cana-2737	521	1	[	[	X
cana-2737	521	2	10	10	NUM
cana-2737	521	3	]	]	X
cana-2737	521	4	p.	p.	NOUN
cana-2737	521	5	a.	a.	NOUN
cana-2737	521	6	ejegwa	ejegwa	PROPN
cana-2737	521	7	,	,	PUNCT
cana-2737	521	8	a.	a.	PROPN
cana-2737	521	9	j.	j.	PROPN
cana-2737	521	10	akubo	akubo	PROPN
cana-2737	521	11	and	and	CCONJ
cana-2737	521	12	o.	o.	PROPN
cana-2737	521	13	m.	m.	PROPN
cana-2737	521	14	joshua	joshua	PROPN
cana-2737	521	15	(	(	PUNCT
cana-2737	521	16	2014	2014	NUM
cana-2737	521	17	)	)	PUNCT
cana-2737	521	18	,	,	PUNCT
cana-2737	521	19	intuitionistic	intuitionistic	ADJ
cana-2737	521	20	fuzzzy	fuzzzy	ADJ
cana-2737	521	21	sets	set	NOUN
cana-2737	521	22	in	in	ADP
cana-2737	521	23	career	career	NOUN
cana-2737	521	24	determination	determination	NOUN
cana-2737	521	25	,	,	PUNCT
cana-2737	521	26	j	j	PROPN
cana-2737	521	27	info	info	NOUN
cana-2737	521	28	comput	comput	NOUN
cana-2737	521	29	.	.	PUNCT
cana-2737	522	1	sci	sci	PROPN
cana-2737	522	2	.	.	PROPN
cana-2737	522	3	9	9	NUM
cana-2737	522	4	(	(	PUNCT
cana-2737	522	5	4	4	NUM
cana-2737	522	6	)	)	PUNCT
cana-2737	522	7	,	,	PUNCT
cana-2737	522	8	285	285	NUM
cana-2737	522	9	-	-	SYM
cana-2737	522	10	288	288	NUM
cana-2737	522	11	.	.	PUNCT
cana-2737	523	1	[	[	X
cana-2737	523	2	11	11	NUM
cana-2737	523	3	]	]	PUNCT
cana-2737	523	4	p.	p.	NOUN
cana-2737	523	5	a.	a.	NOUN
cana-2737	523	6	ejegwa	ejegwa	PROPN
cana-2737	523	7	(	(	PUNCT
cana-2737	523	8	2015	2015	NUM
cana-2737	523	9	)	)	PUNCT
cana-2737	523	10	,	,	PUNCT
cana-2737	523	11	intuitionistic	intuitionistic	ADJ
cana-2737	523	12	fuzzy	fuzzy	ADJ
cana-2737	523	13	sets	set	NOUN
cana-2737	523	14	approach	approach	NOUN
cana-2737	523	15	in	in	ADP
cana-2737	523	16	appointment	appointment	NOUN
cana-2737	523	17	of	of	ADP
cana-2737	523	18	positions	position	NOUN
cana-2737	523	19	in	in	ADP
cana-2737	523	20	an	an	DET
cana-2737	523	21	organization	organization	NOUN
cana-2737	523	22	via	via	ADP
cana-2737	523	23	max	max	PROPN
cana-2737	523	24	-	-	PUNCT
cana-2737	523	25	minmax	minmax	PROPN
cana-2737	523	26	rule	rule	NOUN
cana-2737	523	27	,	,	PUNCT
cana-2737	523	28	glob	glob	NOUN
cana-2737	523	29	.	.	PUNCT
cana-2737	524	1	j	j	PROPN
cana-2737	524	2	sci	sci	PROPN
cana-2737	524	3	.	.	PROPN
cana-2737	525	1	front	front	PROPN
cana-2737	525	2	res	res	PROPN
cana-2737	525	3	f	f	PROPN
cana-2737	525	4	math	math	PROPN
cana-2737	525	5	.	.	PUNCT
cana-2737	526	1	decis	decis	PROPN
cana-2737	526	2	.	.	PUNCT
cana-2737	527	1	sci	sci	PROPN
cana-2737	527	2	.	.	PROPN
cana-2737	527	3	15	15	NUM
cana-2737	527	4	(	(	PUNCT
cana-2737	527	5	6	6	NUM
cana-2737	527	6	)	)	PUNCT
cana-2737	527	7	,	,	PUNCT
cana-2737	527	8	1	1	NUM
cana-2737	527	9	-	-	SYM
cana-2737	527	10	6	6	NUM
cana-2737	527	11	.	.	PUNCT
cana-2737	528	1	[	[	X
cana-2737	528	2	12	12	NUM
cana-2737	528	3	]	]	X
cana-2737	528	4	p.	p.	NOUN
cana-2737	528	5	a.	a.	NOUN
cana-2737	528	6	ejegwa	ejegwa	PROPN
cana-2737	528	7	and	and	CCONJ
cana-2737	528	8	e.	e.	PROPN
cana-2737	528	9	s.	s.	PROPN
cana-2737	528	10	modom	modom	PROPN
cana-2737	528	11	(	(	PUNCT
cana-2737	528	12	2015	2015	NUM
cana-2737	528	13	)	)	PUNCT
cana-2737	528	14	,	,	PUNCT
cana-2737	528	15	diagnosis	diagnosis	NOUN
cana-2737	528	16	of	of	ADP
cana-2737	528	17	viral	viral	ADJ
cana-2737	528	18	hepatitis	hepatitis	NOUN
cana-2737	528	19	using	use	VERB
cana-2737	528	20	new	new	ADJ
cana-2737	528	21	distance	distance	NOUN
cana-2737	528	22	measure	measure	NOUN
cana-2737	528	23	of	of	ADP
cana-2737	528	24	intuitionistic	intuitionistic	ADJ
cana-2737	528	25	fuzzy	fuzzy	ADJ
cana-2737	528	26	sets	set	NOUN
cana-2737	528	27	,	,	PUNCT
cana-2737	528	28	int	int	NOUN
cana-2737	528	29	.	.	PUNCT
cana-2737	529	1	j.	j.	PROPN
cana-2737	529	2	fuzzy	fuzzy	PROPN
cana-2737	529	3	math	math	PROPN
cana-2737	529	4	.	.	PUNCT
cana-2737	530	1	arch	arch	NOUN
cana-2737	530	2	.	.	PUNCT
cana-2737	531	1	8	8	NUM
cana-2737	531	2	(	(	PUNCT
cana-2737	531	3	1	1	NUM
cana-2737	531	4	)	)	PUNCT
cana-2737	531	5	,	,	PUNCT
cana-2737	531	6	1	1	NUM
cana-2737	531	7	-	-	SYM
cana-2737	531	8	7	7	NUM
cana-2737	531	9	.	.	PUNCT
cana-2737	532	1	[	[	X
cana-2737	532	2	13	13	NUM
cana-2737	532	3	]	]	PUNCT
cana-2737	532	4	p.	p.	NOUN
cana-2737	532	5	a.	a.	NOUN
cana-2737	532	6	ejegwa	ejegwa	PROPN
cana-2737	532	7	(	(	PUNCT
cana-2737	532	8	2018	2018	NUM
cana-2737	532	9	)	)	PUNCT
cana-2737	532	10	,	,	PUNCT
cana-2737	532	11	distance	distance	NOUN
cana-2737	532	12	and	and	CCONJ
cana-2737	532	13	similarity	similarity	NOUN
cana-2737	532	14	measures	measure	NOUN
cana-2737	532	15	of	of	ADP
cana-2737	532	16	pythagorean	pythagorean	ADJ
cana-2737	532	17	fuzzy	fuzzy	ADJ
cana-2737	532	18	sets	set	NOUN
cana-2737	532	19	,	,	PUNCT
cana-2737	532	20	granul	granul	ADJ
cana-2737	532	21	comput	comput	NOUN
cana-2737	532	22	.	.	PUNCT
cana-2737	533	1	https://doi.org/10.1007/s41066-018-00149-z	https://doi.org/10.1007/s41066-018-00149-z	PROPN
cana-2737	533	2	.	.	PUNCT
cana-2737	534	1	[	[	X
cana-2737	534	2	14	14	NUM
cana-2737	534	3	]	]	X
cana-2737	534	4	h.	h.	PROPN
cana-2737	534	5	garg	garg	PROPN
cana-2737	534	6	(	(	PUNCT
cana-2737	534	7	2017	2017	NUM
cana-2737	534	8	)	)	PUNCT
cana-2737	534	9	,	,	PUNCT
cana-2737	534	10	a	a	DET
cana-2737	534	11	new	new	ADJ
cana-2737	534	12	improved	improve	VERB
cana-2737	534	13	score	score	NOUN
cana-2737	534	14	function	function	NOUN
cana-2737	534	15	of	of	ADP
cana-2737	534	16	an	an	DET
cana-2737	534	17	interval	interval	NOUN
cana-2737	534	18	-	-	PUNCT
cana-2737	534	19	valued	value	VERB
cana-2737	534	20	pythagorean	pythagorean	PROPN
cana-2737	534	21	fuzzy	fuzzy	PROPN
cana-2737	534	22	set	set	VERB
cana-2737	534	23	based	base	VERB
cana-2737	534	24	topsis	topsis	NOUN
cana-2737	534	25	method	method	NOUN
cana-2737	534	26	,	,	PUNCT
cana-2737	534	27	int	int	NOUN
cana-2737	534	28	.	.	PUNCT
cana-2737	535	1	j	j	PROPN
cana-2737	535	2	uncertain	uncertain	ADJ
cana-2737	535	3	quantif	quantif	PROPN
cana-2737	535	4	7	7	NUM
cana-2737	535	5	(	(	PUNCT
cana-2737	535	6	5	5	NUM
cana-2737	535	7	)	)	PUNCT
cana-2737	535	8	,	,	PUNCT
cana-2737	535	9	463	463	NUM
cana-2737	535	10	-	-	SYM
cana-2737	535	11	474	474	NUM
cana-2737	535	12	.	.	PUNCT
cana-2737	536	1	[	[	X
cana-2737	536	2	15	15	NUM
cana-2737	536	3	]	]	X
cana-2737	536	4	h.	h.	PROPN
cana-2737	536	5	garg	garg	PROPN
cana-2737	536	6	and	and	CCONJ
cana-2737	536	7	s.	s.	PROPN
cana-2737	536	8	singh	singh	PROPN
cana-2737	536	9	(	(	PUNCT
cana-2737	536	10	2018	2018	NUM
cana-2737	536	11	)	)	PUNCT
cana-2737	536	12	,	,	PUNCT
cana-2737	536	13	a	a	DET
cana-2737	536	14	novel	novel	ADJ
cana-2737	536	15	triangular	triangular	NOUN
cana-2737	536	16	interval	interval	NOUN
cana-2737	536	17	type-2	type-2	NUM
cana-2737	536	18	intuitionistic	intuitionistic	ADJ
cana-2737	536	19	fuzzy	fuzzy	ADJ
cana-2737	536	20	set	set	NOUN
cana-2737	536	21	and	and	CCONJ
cana-2737	536	22	their	their	PRON
cana-2737	536	23	aggregation	aggregation	NOUN
cana-2737	536	24	operators	operator	NOUN
cana-2737	536	25	,	,	PUNCT
cana-2737	536	26	iran	iran	PROPN
cana-2737	536	27	j	j	PROPN
cana-2737	536	28	fuzzy	fuzzy	PROPN
cana-2737	536	29	syst	syst	PROPN
cana-2737	536	30	.	.	PUNCT
cana-2737	537	1	15	15	NUM
cana-2737	537	2	(	(	PUNCT
cana-2737	537	3	5	5	NUM
cana-2737	537	4	)	)	PUNCT
cana-2737	537	5	,	,	PUNCT
cana-2737	537	6	69	69	NUM
cana-2737	537	7	-	-	SYM
cana-2737	537	8	93	93	NUM
cana-2737	537	9	.	.	PUNCT
cana-2737	538	1	[	[	X
cana-2737	538	2	16	16	NUM
cana-2737	538	3	]	]	X
cana-2737	538	4	h.	h.	PROPN
cana-2737	538	5	garg	garg	PROPN
cana-2737	538	6	and	and	CCONJ
cana-2737	538	7	k.	k.	PROPN
cana-2737	538	8	kumar	kumar	PROPN
cana-2737	538	9	(	(	PUNCT
cana-2737	538	10	2018	2018	NUM
cana-2737	538	11	)	)	PUNCT
cana-2737	538	12	,	,	PUNCT
cana-2737	538	13	distance	distance	NOUN
cana-2737	538	14	measures	measure	NOUN
cana-2737	538	15	for	for	ADP
cana-2737	538	16	connection	connection	NOUN
cana-2737	538	17	number	number	NOUN
cana-2737	538	18	sets	set	NOUN
cana-2737	538	19	based	base	VERB
cana-2737	538	20	on	on	ADP
cana-2737	538	21	set	set	VERB
cana-2737	538	22	pair	pair	NOUN
cana-2737	538	23	analysis	analysis	NOUN
cana-2737	538	24	and	and	CCONJ
cana-2737	538	25	its	its	PRON
cana-2737	538	26	applications	application	NOUN
cana-2737	538	27	to	to	PART
cana-2737	538	28	decision	decision	VERB
cana-2737	538	29	making	making	NOUN
cana-2737	538	30	process	process	NOUN
cana-2737	538	31	,	,	PUNCT
cana-2737	538	32	appl	appl	PROPN
cana-2737	538	33	.	.	PUNCT
cana-2737	539	1	intell	intell	PROPN
cana-2737	539	2	48	48	NUM
cana-2737	539	3	(	(	PUNCT
cana-2737	539	4	10	10	NUM
cana-2737	539	5	)	)	PUNCT
cana-2737	539	6	,	,	PUNCT
cana-2737	539	7	3346	3346	NUM
cana-2737	539	8	-	-	SYM
cana-2737	539	9	3359	3359	NUM
cana-2737	539	10	.	.	PUNCT
cana-2737	540	1	[	[	X
cana-2737	540	2	17	17	NUM
cana-2737	540	3	]	]	X
cana-2737	540	4	h.	h.	PROPN
cana-2737	540	5	garg	garg	PROPN
cana-2737	540	6	and	and	CCONJ
cana-2737	540	7	k.	k.	PROPN
cana-2737	540	8	kumar	kumar	PROPN
cana-2737	540	9	(	(	PUNCT
cana-2737	540	10	2018	2018	NUM
cana-2737	540	11	)	)	PUNCT
cana-2737	540	12	,	,	PUNCT
cana-2737	540	13	an	an	DET
cana-2737	540	14	advance	advance	NOUN
cana-2737	540	15	study	study	NOUN
cana-2737	540	16	on	on	ADP
cana-2737	540	17	the	the	DET
cana-2737	540	18	similarity	similarity	NOUN
cana-2737	540	19	measures	measure	NOUN
cana-2737	540	20	of	of	ADP
cana-2737	540	21	intuitionistic	intuitionistic	ADJ
cana-2737	540	22	fuzzy	fuzzy	ADJ
cana-2737	540	23	sets	set	NOUN
cana-2737	540	24	based	base	VERB
cana-2737	540	25	on	on	ADP
cana-2737	540	26	the	the	DET
cana-2737	540	27	set	set	VERB
cana-2737	540	28	pair	pair	NOUN
cana-2737	540	29	analysis	analysis	NOUN
cana-2737	540	30	theory	theory	NOUN
cana-2737	540	31	and	and	CCONJ
cana-2737	540	32	their	their	PRON
cana-2737	540	33	application	application	NOUN
cana-2737	540	34	in	in	ADP
cana-2737	540	35	decision	decision	NOUN
cana-2737	540	36	making	making	NOUN
cana-2737	540	37	,	,	PUNCT
cana-2737	540	38	soft	soft	ADJ
cana-2737	540	39	comput	comput	NOUN
cana-2737	540	40	.	.	PUNCT
cana-2737	541	1	22	22	NUM
cana-2737	541	2	(	(	PUNCT
cana-2737	541	3	15	15	NUM
cana-2737	541	4	)	)	PUNCT
cana-2737	541	5	,	,	PUNCT
cana-2737	541	6	4959	4959	NUM
cana-2737	541	7	-	-	SYM
cana-2737	541	8	4970	4970	NUM
cana-2737	541	9	.	.	PUNCT
cana-2737	542	1	[	[	X
cana-2737	542	2	18	18	NUM
cana-2737	542	3	]	]	PUNCT
cana-2737	542	4	x.	x.	NOUN
cana-2737	542	5	j.	j.	PROPN
cana-2737	542	6	gou	gou	PROPN
cana-2737	542	7	,	,	PUNCT
cana-2737	542	8	z.	z.	PROPN
cana-2737	542	9	s.	s.	PROPN
cana-2737	542	10	xu	xu	PROPN
cana-2737	542	11	and	and	CCONJ
cana-2737	542	12	p.	p.	PROPN
cana-2737	542	13	j.	j.	PROPN
cana-2737	542	14	ren	ren	PROPN
cana-2737	542	15	(	(	PUNCT
cana-2737	542	16	2016	2016	NUM
cana-2737	542	17	)	)	PUNCT
cana-2737	542	18	,	,	PUNCT
cana-2737	542	19	the	the	DET
cana-2737	542	20	properties	property	NOUN
cana-2737	542	21	of	of	ADP
cana-2737	542	22	continuous	continuous	ADJ
cana-2737	542	23	pyhagorean	pyhagorean	NOUN
cana-2737	542	24	fuzzy	fuzzy	ADJ
cana-2737	542	25	information	information	NOUN
cana-2737	542	26	,	,	PUNCT
cana-2737	542	27	int	int	NOUN
cana-2737	542	28	.	.	PUNCT
cana-2737	543	1	j	j	PROPN
cana-2737	543	2	intell	intell	PROPN
cana-2737	543	3	.	.	PUNCT
cana-2737	544	1	syst	syst	PROPN
cana-2737	544	2	.	.	PUNCT
cana-2737	545	1	31	31	NUM
cana-2737	545	2	(	(	PUNCT
cana-2737	545	3	5	5	NUM
cana-2737	545	4	)	)	PUNCT
cana-2737	545	5	,	,	PUNCT
cana-2737	545	6	401	401	NUM
cana-2737	545	7	-	-	SYM
cana-2737	545	8	424	424	NUM
cana-2737	545	9	.	.	PUNCT
cana-2737	546	1	[	[	X
cana-2737	546	2	19	19	NUM
cana-2737	546	3	]	]	PUNCT
cana-2737	546	4	x.	x.	NOUN
cana-2737	546	5	he	he	PRON
cana-2737	546	6	,	,	PUNCT
cana-2737	546	7	y.	y.	PROPN
cana-2737	546	8	du	du	PROPN
cana-2737	546	9	and	and	CCONJ
cana-2737	546	10	w.	w.	PROPN
cana-2737	546	11	liu	liu	PROPN
cana-2737	546	12	(	(	PUNCT
cana-2737	546	13	2016	2016	NUM
cana-2737	546	14	)	)	PUNCT
cana-2737	546	15	,	,	PUNCT
cana-2737	546	16	pythagorean	pythagorean	VERB
cana-2737	546	17	fuzzy	fuzzy	ADJ
cana-2737	546	18	power	power	PROPN
cana-2737	546	19	average	average	ADJ
cana-2737	546	20	operators	operator	NOUN
cana-2737	546	21	,	,	PUNCT
cana-2737	546	22	fuzzy	fuzzy	ADJ
cana-2737	546	23	syst	syst	NOUN
cana-2737	546	24	.	.	PUNCT
cana-2737	546	25	math	math	NOUN
cana-2737	546	26	.	.	PUNCT
cana-2737	547	1	30	30	NUM
cana-2737	547	2	(	(	PUNCT
cana-2737	547	3	6	6	NUM
cana-2737	547	4	)	)	PUNCT
cana-2737	547	5	,	,	PUNCT
cana-2737	547	6	116	116	NUM
cana-2737	547	7	-	-	SYM
cana-2737	547	8	124	124	NUM
cana-2737	547	9	.	.	PUNCT
cana-2737	548	1	[	[	X
cana-2737	548	2	20	20	NUM
cana-2737	548	3	]	]	X
cana-2737	548	4	d.	d.	PROPN
cana-2737	548	5	jeeva	jeeva	PROPN
cana-2737	548	6	,	,	PUNCT
cana-2737	548	7	d.sivakumar	d.sivakumar	NOUN
cana-2737	548	8	and	and	CCONJ
cana-2737	548	9	a.	a.	NOUN
cana-2737	548	10	vadivel	vadivel	NOUN
cana-2737	548	11	(	(	PUNCT
cana-2737	548	12	2023	2023	NUM
cana-2737	548	13	)	)	PUNCT
cana-2737	548	14	,	,	PUNCT
cana-2737	548	15	contra	contra	PROPN
cana-2737	548	16	𝑀-continuous	𝑀-continuous	ADJ
cana-2737	548	17	maps	map	NOUN
cana-2737	548	18	in	in	ADP
cana-2737	548	19	neutrosophic	neutrosophic	ADJ
cana-2737	548	20	soft	soft	ADJ
cana-2737	548	21	topological	topological	ADJ
cana-2737	548	22	spaces	space	NOUN
cana-2737	548	23	,	,	PUNCT
cana-2737	548	24	ijns	ijns	PROPN
cana-2737	548	25	,	,	PUNCT
cana-2737	548	26	20	20	NUM
cana-2737	548	27	(	(	PUNCT
cana-2737	548	28	3	3	NUM
cana-2737	548	29	)	)	PUNCT
cana-2737	548	30	,	,	PUNCT
cana-2737	548	31	98	98	NUM
cana-2737	548	32	-	-	SYM
cana-2737	548	33	106	106	NUM
cana-2737	548	34	.	.	PUNCT
cana-2737	549	1	[	[	X
cana-2737	549	2	21	21	NUM
cana-2737	549	3	]	]	X
cana-2737	549	4	d.	d.	PROPN
cana-2737	549	5	jeeva	jeeva	PROPN
cana-2737	549	6	,	,	PUNCT
cana-2737	549	7	a.	a.	NOUN
cana-2737	549	8	vadivel	vadivel	NOUN
cana-2737	549	9	and	and	CCONJ
cana-2737	549	10	d.	d.	PROPN
cana-2737	549	11	sivakumar	sivakumar	PROPN
cana-2737	549	12	(	(	PUNCT
cana-2737	549	13	2023	2023	NUM
cana-2737	549	14	)	)	PUNCT
cana-2737	549	15	,	,	PUNCT
cana-2737	549	16	𝑀-continuous	𝑀-continuous	PROPN
cana-2737	549	17	and	and	CCONJ
cana-2737	549	18	𝑀-irresolute	𝑀-irresolute	PROPN
cana-2737	549	19	maps	map	NOUN
cana-2737	549	20	in	in	ADP
cana-2737	549	21	neutrosophic	neutrosophic	ADJ
cana-2737	549	22	soft	soft	ADJ
cana-2737	549	23	topological	topological	ADJ
cana-2737	549	24	spaces	space	NOUN
cana-2737	549	25	,	,	PUNCT
cana-2737	549	26	aip	aip	PROPN
cana-2737	549	27	conference	conference	NOUN
cana-2737	549	28	proceedings	proceeding	NOUN
cana-2737	549	29	,	,	PUNCT
cana-2737	549	30	2852	2852	NUM
cana-2737	549	31	,	,	PUNCT
cana-2737	549	32	150001	150001	NUM
cana-2737	549	33	.	.	PUNCT
cana-2737	550	1	[	[	X
cana-2737	550	2	22	22	NUM
cana-2737	550	3	]	]	X
cana-2737	550	4	d.	d.	PROPN
cana-2737	550	5	jeeva	jeeva	PROPN
cana-2737	550	6	,	,	PUNCT
cana-2737	550	7	a.	a.	NOUN
cana-2737	550	8	vadivel	vadivel	NOUN
cana-2737	550	9	and	and	CCONJ
cana-2737	550	10	d.	d.	PROPN
cana-2737	550	11	sivakumar	sivakumar	PROPN
cana-2737	550	12	(	(	PUNCT
cana-2737	550	13	2023	2023	NUM
cana-2737	550	14	)	)	PUNCT
cana-2737	550	15	,	,	PUNCT
cana-2737	550	16	maps	map	NOUN
cana-2737	550	17	and	and	CCONJ
cana-2737	550	18	homeomorphisms	homeomorphism	NOUN
cana-2737	550	19	via	via	ADP
cana-2737	550	20	𝑀-open	𝑀-open	PROPN
cana-2737	550	21	sets	set	NOUN
cana-2737	550	22	in	in	ADP
cana-2737	550	23	neutrosophic	neutrosophic	ADJ
cana-2737	550	24	soft	soft	ADJ
cana-2737	550	25	topological	topological	ADJ
cana-2737	550	26	spaces	space	NOUN
cana-2737	550	27	,	,	PUNCT
cana-2737	550	28	south	south	PROPN
cana-2737	550	29	east	east	PROPN
cana-2737	550	30	asian	asian	PROPN
cana-2737	550	31	j.	j.	PROPN
cana-2737	550	32	of	of	ADP
cana-2737	550	33	mathematics	mathematics	PROPN
cana-2737	550	34	and	and	CCONJ
cana-2737	550	35	mathematical	mathematical	ADJ
cana-2737	550	36	sciences	science	NOUN
cana-2737	550	37	19	19	NUM
cana-2737	550	38	(	(	PUNCT
cana-2737	550	39	1	1	NUM
cana-2737	550	40	)	)	PUNCT
cana-2737	550	41	(	(	PUNCT
cana-2737	550	42	2023	2023	NUM
cana-2737	550	43	)	)	PUNCT
cana-2737	550	44	,	,	PUNCT
cana-2737	550	45	367	367	NUM
cana-2737	550	46	-	-	SYM
cana-2737	550	47	384	384	NUM
cana-2737	550	48	.	.	PUNCT
cana-2737	551	1	[	[	X
cana-2737	551	2	23	23	NUM
cana-2737	551	3	]	]	PUNCT
cana-2737	551	4	a.	a.	PROPN
cana-2737	551	5	i.	i.	PROPN
cana-2737	551	6	el	el	PROPN
cana-2737	551	7	-	-	PUNCT
cana-2737	551	8	maghrabi	maghrabi	NOUN
cana-2737	551	9	and	and	CCONJ
cana-2737	551	10	m.	m.	NOUN
cana-2737	551	11	a.	a.	PROPN
cana-2737	551	12	al	al	PROPN
cana-2737	551	13	-	-	PUNCT
cana-2737	551	14	juhani	juhani	PROPN
cana-2737	551	15	,	,	PUNCT
cana-2737	551	16	𝑀open	𝑀open	NOUN
cana-2737	551	17	sets	set	NOUN
cana-2737	551	18	in	in	ADP
cana-2737	551	19	topological	topological	ADJ
cana-2737	551	20	spaces	space	NOUN
cana-2737	551	21	,	,	PUNCT
cana-2737	551	22	pioneer	pioneer	PROPN
cana-2737	551	23	j.	j.	PROPN
cana-2737	551	24	math	math	PROPN
cana-2737	551	25	.	.	PUNCT
cana-2737	552	1	sci	sci	PROPN
cana-2737	552	2	.	.	PROPN
cana-2737	552	3	,	,	PUNCT
cana-2737	552	4	4	4	NUM
cana-2737	552	5	(	(	PUNCT
cana-2737	552	6	2	2	NUM
cana-2737	552	7	)	)	PUNCT
cana-2737	552	8	(	(	PUNCT
cana-2737	552	9	2011	2011	NUM
cana-2737	552	10	)	)	PUNCT
cana-2737	552	11	,	,	PUNCT
cana-2737	552	12	213	213	NUM
cana-2737	552	13	-	-	SYM
cana-2737	552	14	230	230	NUM
cana-2737	552	15	.	.	PUNCT
cana-2737	553	1	[	[	X
cana-2737	553	2	24	24	NUM
cana-2737	553	3	]	]	X
cana-2737	553	4	murat	murat	PROPN
cana-2737	553	5	olgun	olgun	PROPN
cana-2737	553	6	,	,	PUNCT
cana-2737	553	7	mehmet	mehmet	PROPN
cana-2737	553	8	unver	unver	PROPN
cana-2737	553	9	and	and	CCONJ
cana-2737	553	10	seyhmus	seyhmus	VERB
cana-2737	553	11	yardimci	yardimci	PROPN
cana-2737	553	12	(	(	PUNCT
cana-2737	553	13	2019	2019	NUM
cana-2737	553	14	)	)	PUNCT
cana-2737	553	15	,	,	PUNCT
cana-2737	553	16	pythagorean	pythagorean	PROPN
cana-2737	553	17	fuzzy	fuzzy	ADJ
cana-2737	553	18	topological	topological	ADJ
cana-2737	553	19	spaces	space	NOUN
cana-2737	553	20	,	,	PUNCT
cana-2737	553	21	complex	complex	ADJ
cana-2737	553	22	&	&	CCONJ
cana-2737	553	23	intelligent	intelligent	ADJ
cana-2737	553	24	systems	system	NOUN
cana-2737	553	25	.	.	PUNCT
cana-2737	554	1	https://doi.org/10.1007/s40747-019-0095-2	https://doi.org/10.1007/s40747-019-0095-2	NUM
cana-2737	554	2	.	.	PUNCT
cana-2737	555	1	[	[	X
cana-2737	555	2	25	25	NUM
cana-2737	555	3	]	]	PUNCT
cana-2737	555	4	x.	x.	NOUN
cana-2737	555	5	peng	peng	PROPN
cana-2737	555	6	and	and	CCONJ
cana-2737	555	7	y.	y.	PROPN
cana-2737	555	8	yang	yang	PROPN
cana-2737	555	9	(	(	PUNCT
cana-2737	555	10	2015	2015	NUM
cana-2737	555	11	)	)	PUNCT
cana-2737	555	12	,	,	PUNCT
cana-2737	555	13	some	some	PRON
cana-2737	555	14	results	result	VERB
cana-2737	555	15	for	for	ADP
cana-2737	555	16	pythagorean	pythagorean	ADJ
cana-2737	555	17	fuzzy	fuzzy	ADJ
cana-2737	555	18	sets	set	NOUN
cana-2737	555	19	,	,	PUNCT
cana-2737	555	20	int	int	NOUN
cana-2737	555	21	.	.	PUNCT
cana-2737	556	1	j	j	PROPN
cana-2737	556	2	intell	intell	PROPN
cana-2737	556	3	syst	syst	PROPN
cana-2737	556	4	.	.	PUNCT
cana-2737	557	1	30	30	NUM
cana-2737	557	2	,	,	PUNCT
cana-2737	557	3	1133	1133	NUM
cana-2737	557	4	-	-	SYM
cana-2737	557	5	1160	1160	NUM
cana-2737	557	6	.	.	PUNCT
cana-2737	558	1	[	[	X
cana-2737	558	2	26	26	NUM
cana-2737	558	3	]	]	PUNCT
cana-2737	558	4	x.	x.	NOUN
cana-2737	558	5	peng	peng	PROPN
cana-2737	558	6	and	and	CCONJ
cana-2737	558	7	g.	g.	PROPN
cana-2737	558	8	selvachandran	selvachandran	PROPN
cana-2737	558	9	(	(	PUNCT
cana-2737	558	10	2017	2017	NUM
cana-2737	558	11	)	)	PUNCT
cana-2737	558	12	,	,	PUNCT
cana-2737	558	13	pythagorean	pythagorean	PROPN
cana-2737	558	14	fuzzy	fuzzy	PROPN
cana-2737	558	15	set	set	VERB
cana-2737	558	16	state	state	NOUN
cana-2737	558	17	of	of	ADP
cana-2737	558	18	the	the	DET
cana-2737	558	19	art	art	NOUN
cana-2737	558	20	and	and	CCONJ
cana-2737	558	21	future	future	ADJ
cana-2737	558	22	directions	direction	NOUN
cana-2737	558	23	,	,	PUNCT
cana-2737	558	24	artif	artif	PROPN
cana-2737	558	25	intell	intell	PROPN
cana-2737	558	26	rev	rev	VERB
cana-2737	558	27	.	.	PUNCT
cana-2737	558	28	https://doi.org/10.1007/s10462-017-9596-9	https://doi.org/10.1007/s10462-017-9596-9	PROPN
cana-2737	558	29	.	.	PUNCT
cana-2737	559	1	[	[	X
cana-2737	559	2	27	27	NUM
cana-2737	559	3	]	]	X
cana-2737	559	4	supriti	supriti	PROPN
cana-2737	559	5	saha	saha	PROPN
cana-2737	559	6	,	,	PUNCT
cana-2737	559	7	fuzzy	fuzzy	ADJ
cana-2737	559	8	𝛿-continuous	𝛿-continuous	ADJ
cana-2737	559	9	mappings	mapping	NOUN
cana-2737	559	10	,	,	PUNCT
cana-2737	559	11	journal	journal	NOUN
cana-2737	559	12	of	of	ADP
cana-2737	559	13	mathematical	mathematical	ADJ
cana-2737	559	14	analysis	analysis	NOUN
cana-2737	559	15	and	and	CCONJ
cana-2737	559	16	applications	application	NOUN
cana-2737	559	17	,	,	PUNCT
cana-2737	559	18	126	126	NUM
cana-2737	559	19	(	(	PUNCT
cana-2737	559	20	1987	1987	NUM
cana-2737	559	21	)	)	PUNCT
cana-2737	559	22	,	,	PUNCT
cana-2737	559	23	130142	130142	NUM
cana-2737	559	24	.	.	PUNCT
cana-2737	560	1	[	[	X
cana-2737	560	2	28	28	NUM
cana-2737	560	3	]	]	X
cana-2737	560	4	e.	e.	PROPN
cana-2737	560	5	szmidt	szmidt	PROPN
cana-2737	560	6	and	and	CCONJ
cana-2737	560	7	j.	j.	PROPN
cana-2737	560	8	kacprzyk	kacprzyk	PROPN
cana-2737	560	9	(	(	PUNCT
cana-2737	560	10	2001	2001	NUM
cana-2737	560	11	)	)	PUNCT
cana-2737	560	12	,	,	PUNCT
cana-2737	560	13	intuitionistic	intuitionistic	ADJ
cana-2737	560	14	fuzzy	fuzzy	ADJ
cana-2737	560	15	sets	set	NOUN
cana-2737	560	16	in	in	ADP
cana-2737	560	17	some	some	DET
cana-2737	560	18	medical	medical	ADJ
cana-2737	560	19	applications	application	NOUN
cana-2737	560	20	,	,	PUNCT
cana-2737	560	21	note	note	VERB
cana-2737	560	22	ifs	ifs	PROPN
cana-2737	560	23	7	7	NUM
cana-2737	560	24	(	(	PUNCT
cana-2737	560	25	4	4	NUM
cana-2737	560	26	)	)	PUNCT
cana-2737	560	27	,	,	PUNCT
cana-2737	560	28	58	58	NUM
cana-2737	560	29	-	-	SYM
cana-2737	560	30	64	64	NUM
cana-2737	560	31	.	.	PUNCT
cana-2737	561	1	[	[	X
cana-2737	561	2	29	29	NUM
cana-2737	561	3	]	]	PUNCT
cana-2737	561	4	e.	e.	PROPN
cana-2737	561	5	szmidt	szmidt	PROPN
cana-2737	561	6	and	and	CCONJ
cana-2737	561	7	j.	j.	PROPN
cana-2737	561	8	kacprzyk	kacprzyk	PROPN
cana-2737	561	9	(	(	PUNCT
cana-2737	561	10	2004	2004	NUM
cana-2737	561	11	)	)	PUNCT
cana-2737	561	12	,	,	PUNCT
cana-2737	561	13	medical	medical	ADJ
cana-2737	561	14	diagnostic	diagnostic	ADJ
cana-2737	561	15	reasoning	reasoning	NOUN
cana-2737	561	16	using	use	VERB
cana-2737	561	17	a	a	DET
cana-2737	561	18	similarity	similarity	NOUN
cana-2737	561	19	measure	measure	NOUN
cana-2737	561	20	for	for	ADP
cana-2737	561	21	intuitionistic	intuitionistic	ADJ
cana-2737	561	22	fuzzy	fuzzy	ADJ
cana-2737	561	23	sets	set	NOUN
cana-2737	561	24	,	,	PUNCT
cana-2737	561	25	note	note	VERB
cana-2737	561	26	ifs	ifs	PROPN
cana-2737	561	27	10	10	NUM
cana-2737	561	28	(	(	PUNCT
cana-2737	561	29	4	4	NUM
cana-2737	561	30	)	)	PUNCT
cana-2737	561	31	,	,	PUNCT
cana-2737	561	32	61	61	NUM
cana-2737	561	33	-	-	SYM
cana-2737	561	34	69	69	NUM
cana-2737	561	35	.	.	PUNCT
cana-2737	562	1	[	[	X
cana-2737	562	2	30	30	NUM
cana-2737	562	3	]	]	X
cana-2737	562	4	m.	m.	NOUN
cana-2737	562	5	udhaya	udhaya	PROPN
cana-2737	562	6	shalini	shalini	PROPN
cana-2737	562	7	and	and	CCONJ
cana-2737	562	8	a.	a.	PROPN
cana-2737	562	9	stanis	stanis	PROPN
cana-2737	562	10	arul	arul	PROPN
cana-2737	562	11	mary	mary	PROPN
cana-2737	562	12	(	(	PUNCT
cana-2737	562	13	2022	2022	NUM
cana-2737	562	14	)	)	PUNCT
cana-2737	562	15	,	,	PUNCT
cana-2737	562	16	generalized	generalize	VERB
cana-2737	562	17	pre	pre	ADJ
cana-2737	562	18	-	-	ADJ
cana-2737	562	19	closed	closed	ADJ
cana-2737	562	20	sets	set	NOUN
cana-2737	562	21	in	in	ADP
cana-2737	562	22	pythagorean	pythagorean	PROPN
cana-2737	562	23	fuzzy	fuzzy	ADJ
cana-2737	562	24	topological	topological	ADJ
cana-2737	562	25	spaces	space	NOUN
cana-2737	562	26	,	,	PUNCT
cana-2737	562	27	international	international	ADJ
cana-2737	562	28	journal	journal	NOUN
cana-2737	562	29	of	of	ADP
cana-2737	562	30	creative	creative	ADJ
cana-2737	562	31	research	research	NOUN
cana-2737	562	32	thoughts	thought	NOUN
cana-2737	562	33	(	(	PUNCT
cana-2737	562	34	ijcrt	ijcrt	NOUN
cana-2737	562	35	)	)	PUNCT
cana-2737	562	36	,	,	PUNCT
cana-2737	562	37	10	10	NUM
cana-2737	562	38	(	(	PUNCT
cana-2737	562	39	30	30	NUM
cana-2737	562	40	)	)	PUNCT
cana-2737	562	41	,	,	PUNCT
cana-2737	562	42	e142	e142	PROPN
cana-2737	562	43	-	-	PUNCT
cana-2737	562	44	e147	e147	PROPN
cana-2737	562	45	.	.	PUNCT
cana-2737	563	1	[	[	X
cana-2737	563	2	31	31	NUM
cana-2737	563	3	]	]	PUNCT
cana-2737	563	4	a.	a.	NOUN
cana-2737	563	5	vadivel	vadivel	NOUN
cana-2737	563	6	,	,	PUNCT
cana-2737	563	7	m.	m.	NOUN
cana-2737	563	8	seenivasan	seenivasan	NOUN
cana-2737	563	9	and	and	CCONJ
cana-2737	563	10	c.	c.	PROPN
cana-2737	563	11	john	john	PROPN
cana-2737	563	12	sundar	sundar	PROPN
cana-2737	563	13	,	,	PUNCT
cana-2737	563	14	an	an	DET
cana-2737	563	15	introduction	introduction	NOUN
cana-2737	563	16	to	to	PART
cana-2737	563	17	𝛿-open	𝛿-open	VERB
cana-2737	563	18	sets	set	NOUN
cana-2737	563	19	in	in	ADP
cana-2737	563	20	a	a	DET
cana-2737	563	21	neutrosophic	neutrosophic	ADJ
cana-2737	563	22	topological	topological	ADJ
cana-2737	563	23	spaces	space	NOUN
cana-2737	563	24	,	,	PUNCT
cana-2737	563	25	journal	journal	NOUN
cana-2737	563	26	of	of	ADP
cana-2737	563	27	physics	physics	PROPN
cana-2737	563	28	:	:	PUNCT
cana-2737	563	29	conference	conference	NOUN
cana-2737	563	30	series	series	NOUN
cana-2737	563	31	,	,	PUNCT
cana-2737	563	32	1724	1724	NUM
cana-2737	563	33	(	(	PUNCT
cana-2737	563	34	2021	2021	NUM
cana-2737	563	35	)	)	PUNCT
cana-2737	563	36	,	,	PUNCT
cana-2737	563	37	012011	012011	NUM
cana-2737	563	38	.	.	PUNCT
cana-2737	564	1	[	[	X
cana-2737	564	2	32	32	NUM
cana-2737	564	3	]	]	PUNCT
cana-2737	564	4	r.	r.	PROPN
cana-2737	564	5	r.	r.	PROPN
cana-2737	564	6	yager	yager	PROPN
cana-2737	564	7	(	(	PUNCT
cana-2737	564	8	2013	2013	NUM
cana-2737	564	9	)	)	PUNCT
cana-2737	564	10	,	,	PUNCT
cana-2737	564	11	pythagorean	pythagorean	PROPN
cana-2737	564	12	membership	membership	NOUN
cana-2737	564	13	grades	grade	NOUN
cana-2737	564	14	in	in	ADP
cana-2737	564	15	multicriteria	multicriteria	PROPN
cana-2737	564	16	decision	decision	NOUN
cana-2737	564	17	making	making	NOUN
cana-2737	564	18	,	,	PUNCT
cana-2737	564	19	in	in	ADP
cana-2737	564	20	:	:	PUNCT
cana-2737	564	21	technical	technical	ADJ
cana-2737	564	22	report	report	NOUN
cana-2737	564	23	𝑀𝐼𝐼3301	𝑀𝐼𝐼3301	PROPN
cana-2737	564	24	.	.	PUNCT
cana-2737	565	1	machine	machine	NOUN
cana-2737	565	2	intelligence	intelligence	PROPN
cana-2737	565	3	institute	institute	PROPN
cana-2737	565	4	,	,	PUNCT
cana-2737	565	5	iona	iona	PROPN
cana-2737	565	6	college	college	PROPN
cana-2737	565	7	,	,	PUNCT
cana-2737	565	8	new	new	ADJ
cana-2737	565	9	rochelle	rochelle	NOUN
cana-2737	565	10	.	.	PUNCT
cana-2737	566	1	[	[	X
cana-2737	566	2	33	33	NUM
cana-2737	566	3	]	]	PUNCT
cana-2737	566	4	r.	r.	PROPN
cana-2737	566	5	r.	r.	PROPN
cana-2737	566	6	yager	yager	PROPN
cana-2737	566	7	(	(	PUNCT
cana-2737	566	8	2013	2013	NUM
cana-2737	566	9	)	)	PUNCT
cana-2737	566	10	,	,	PUNCT
cana-2737	566	11	pythagorean	pythagorean	PROPN
cana-2737	566	12	fuzzy	fuzzy	ADJ
cana-2737	566	13	subsets	subset	NOUN
cana-2737	566	14	,	,	PUNCT
cana-2737	566	15	in	in	ADP
cana-2737	566	16	:	:	PUNCT
cana-2737	566	17	proceedings	proceeding	NOUN
cana-2737	566	18	of	of	ADP
cana-2737	566	19	the	the	DET
cana-2737	566	20	joint	joint	ADJ
cana-2737	566	21	𝐼𝐹𝑆𝐴	𝐼𝐹𝑆𝐴	PROPN
cana-2737	566	22	world	world	PROPN
cana-2737	566	23	congress	congress	PROPN
cana-2737	566	24	𝑁𝐴𝐹𝐼𝑃𝑆	𝑁𝐴𝐹𝐼𝑃𝑆	PROPN
cana-2737	566	25	annual	annual	ADJ
cana-2737	566	26	meeting	meeting	NOUN
cana-2737	566	27	,	,	PUNCT
cana-2737	566	28	57	57	NUM
cana-2737	566	29	-	-	SYM
cana-2737	566	30	61	61	NUM
cana-2737	566	31	.	.	PUNCT
cana-2737	567	1	[	[	X
cana-2737	567	2	34	34	NUM
cana-2737	567	3	]	]	X
cana-2737	567	4	r.	r.	PROPN
cana-2737	567	5	r.	r.	PROPN
cana-2737	567	6	yager	yager	PROPN
cana-2737	567	7	(	(	PUNCT
cana-2737	567	8	2014	2014	NUM
cana-2737	567	9	)	)	PUNCT
cana-2737	567	10	,	,	PUNCT
cana-2737	567	11	pythagorean	pythagorean	PROPN
cana-2737	567	12	membership	membership	NOUN
cana-2737	567	13	grades	grade	NOUN
cana-2737	567	14	in	in	ADP
cana-2737	567	15	multicriteria	multicriteria	PROPN
cana-2737	567	16	decision	decision	NOUN
cana-2737	567	17	making	making	NOUN
cana-2737	567	18	,	,	PUNCT
cana-2737	567	19	𝐼𝐸𝐸𝐸	𝐼𝐸𝐸𝐸	PROPN
cana-2737	567	20	trans	trans	PROPN
cana-2737	567	21	fuzzy	fuzzy	PROPN
cana-2737	567	22	syst	syst	PROPN
cana-2737	567	23	.	.	PUNCT
cana-2737	568	1	22	22	NUM
cana-2737	568	2	(	(	PUNCT
cana-2737	568	3	4	4	NUM
cana-2737	568	4	)	)	PUNCT
cana-2737	568	5	,	,	PUNCT
cana-2737	568	6	958	958	NUM
cana-2737	568	7	-	-	SYM
cana-2737	568	8	965	965	NUM
cana-2737	568	9	.	.	PUNCT
cana-2737	569	1	[	[	X
cana-2737	569	2	35	35	NUM
cana-2737	569	3	]	]	X
cana-2737	569	4	l.	l.	PROPN
cana-2737	569	5	a.	a.	PROPN
cana-2737	569	6	zadeh	zadeh	PROPN
cana-2737	569	7	(	(	PUNCT
cana-2737	569	8	1965	1965	NUM
cana-2737	569	9	)	)	PUNCT
cana-2737	569	10	,	,	PUNCT
cana-2737	569	11	fuzzy	fuzzy	ADJ
cana-2737	569	12	sets	set	NOUN
cana-2737	569	13	,	,	PUNCT
cana-2737	569	14	inf	inf	PROPN
cana-2737	569	15	.	.	PROPN
cana-2737	569	16	control	control	PROPN
cana-2737	569	17	,	,	PUNCT
cana-2737	569	18	8	8	NUM
cana-2737	569	19	,	,	PUNCT
cana-2737	569	20	338	338	NUM
cana-2737	569	21	-	-	SYM
cana-2737	569	22	353	353	NUM
cana-2737	569	23	.	.	PUNCT