id	sid	tid	token	lemma	pos
cana-5829	1	1	communications	communication	NOUN
cana-5829	1	2	on	on	ADP
cana-5829	1	3	applied	apply	VERB
cana-5829	1	4	nonlinear	nonlinear	ADJ
cana-5829	1	5	analysis	analysis	NOUN
cana-5829	1	6	issn	issn	NOUN
cana-5829	1	7	:	:	PUNCT
cana-5829	1	8	1074	1074	NUM
cana-5829	1	9	-	-	PUNCT
cana-5829	1	10	133x	133x	NUM
cana-5829	1	11	vol	vol	VERB
cana-5829	1	12	32	32	NUM
cana-5829	1	13	no	no	NOUN
cana-5829	1	14	.	.	PUNCT
cana-5829	2	1	10s	10	NOUN
cana-5829	2	2	(	(	PUNCT
cana-5829	2	3	2025	2025	NUM
cana-5829	2	4	)	)	PUNCT
cana-5829	2	5	2923	2923	NUM
cana-5829	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5829	3	1	the	the	DET
cana-5829	3	2	normalization	normalization	NOUN
cana-5829	3	3	of	of	ADP
cana-5829	3	4	complex	complex	ADJ
cana-5829	3	5	intuitionistic	intuitionistic	ADJ
cana-5829	3	6	fuzzy	fuzzy	ADJ
cana-5829	3	7	matrices	matrix	NOUN
cana-5829	3	8	jaikumar	jaikumar	PROPN
cana-5829	3	9	.	.	PUNCT
cana-5829	4	1	s1	s1	NOUN
cana-5829	4	2	,	,	PUNCT
cana-5829	4	3	ragavan	ragavan	NOUN
cana-5829	4	4	.	.	PUNCT
cana-5829	5	1	c1	c1	PROPN
cana-5829	5	2	*	*	PROPN
cana-5829	5	3	1	1	NUM
cana-5829	5	4	,	,	PUNCT
cana-5829	5	5	department	department	NOUN
cana-5829	5	6	of	of	ADP
cana-5829	5	7	mathematics	mathematic	NOUN
cana-5829	5	8	,	,	PUNCT
cana-5829	5	9	sri	sri	PROPN
cana-5829	5	10	vidya	vidya	PROPN
cana-5829	5	11	mandir	mandir	PROPN
cana-5829	5	12	arts	arts	PROPN
cana-5829	5	13	&	&	CCONJ
cana-5829	5	14	science	science	PROPN
cana-5829	5	15	college	college	PROPN
cana-5829	5	16	(	(	PUNCT
cana-5829	5	17	autonomous	autonomous	ADJ
cana-5829	5	18	)	)	PUNCT
cana-5829	5	19	,	,	PUNCT
cana-5829	5	20	uthangarai	uthangarai	PROPN
cana-5829	5	21	,	,	PUNCT
cana-5829	5	22	krishnagiri	krishnagiri	PROPN
cana-5829	5	23	,	,	PUNCT
cana-5829	5	24	tamilnadu	tamilnadu	PROPN
cana-5829	5	25	,	,	PUNCT
cana-5829	5	26	india	india	PROPN
cana-5829	5	27	sjaisan18@gmail.com	sjaisan18@gmail.com	PROPN
cana-5829	5	28	,	,	PUNCT
cana-5829	5	29	ragavanshana@gmail.com	ragavanshana@gmail.com	PROPN
cana-5829	5	30	article	article	NOUN
cana-5829	5	31	history	history	NOUN
cana-5829	5	32	:	:	PUNCT
cana-5829	5	33	received	receive	VERB
cana-5829	5	34	:	:	PUNCT
cana-5829	5	35	14	14	NUM
cana-5829	5	36	-	-	SYM
cana-5829	5	37	01	01	NUM
cana-5829	5	38	-	-	PUNCT
cana-5829	5	39	2025	2025	NUM
cana-5829	5	40	revised	revise	VERB
cana-5829	5	41	:	:	PUNCT
cana-5829	5	42	15	15	NUM
cana-5829	5	43	-	-	SYM
cana-5829	5	44	03	03	NUM
cana-5829	5	45	-	-	PUNCT
cana-5829	5	46	2025	2025	NUM
cana-5829	5	47	accepted	accept	VERB
cana-5829	5	48	:	:	PUNCT
cana-5829	5	49	21	21	NUM
cana-5829	5	50	-	-	SYM
cana-5829	5	51	03	03	NUM
cana-5829	5	52	-	-	PUNCT
cana-5829	5	53	2025	2025	NUM
cana-5829	5	54	abstract	abstract	NOUN
cana-5829	5	55	:	:	PUNCT
cana-5829	5	56	the	the	DET
cana-5829	5	57	concept	concept	NOUN
cana-5829	5	58	of	of	ADP
cana-5829	5	59	intuitionistic	intuitionistic	ADJ
cana-5829	5	60	fuzzy	fuzzy	ADJ
cana-5829	5	61	sets	set	NOUN
cana-5829	5	62	(	(	PUNCT
cana-5829	5	63	ifs	ifs	PROPN
cana-5829	5	64	)	)	PUNCT
cana-5829	5	65	provides	provide	VERB
cana-5829	5	66	a	a	DET
cana-5829	5	67	comprehensive	comprehensive	ADJ
cana-5829	5	68	framework	framework	NOUN
cana-5829	5	69	for	for	ADP
cana-5829	5	70	dealing	deal	VERB
cana-5829	5	71	with	with	ADP
cana-5829	5	72	uncertainty	uncertainty	NOUN
cana-5829	5	73	,	,	PUNCT
cana-5829	5	74	incorporating	incorporate	VERB
cana-5829	5	75	both	both	CCONJ
cana-5829	5	76	membership	membership	NOUN
cana-5829	5	77	and	and	CCONJ
cana-5829	5	78	non	non	ADJ
cana-5829	5	79	-	-	ADJ
cana-5829	5	80	membership	membership	ADJ
cana-5829	5	81	functions	function	NOUN
cana-5829	5	82	.	.	PUNCT
cana-5829	6	1	normalization	normalization	NOUN
cana-5829	6	2	of	of	ADP
cana-5829	6	3	intuitionistic	intuitionistic	ADJ
cana-5829	6	4	fuzzy	fuzzy	ADJ
cana-5829	6	5	matrices	matrix	NOUN
cana-5829	6	6	is	be	AUX
cana-5829	6	7	an	an	DET
cana-5829	6	8	essential	essential	ADJ
cana-5829	6	9	process	process	NOUN
cana-5829	6	10	in	in	ADP
cana-5829	6	11	decision	decision	NOUN
cana-5829	6	12	-	-	PUNCT
cana-5829	6	13	making	make	VERB
cana-5829	6	14	and	and	CCONJ
cana-5829	6	15	data	datum	NOUN
cana-5829	6	16	analysis	analysis	NOUN
cana-5829	6	17	where	where	SCONJ
cana-5829	6	18	the	the	DET
cana-5829	6	19	matrix	matrix	NOUN
cana-5829	6	20	entries	entry	NOUN
cana-5829	6	21	are	be	AUX
cana-5829	6	22	expressed	express	VERB
cana-5829	6	23	in	in	ADP
cana-5829	6	24	terms	term	NOUN
cana-5829	6	25	of	of	ADP
cana-5829	6	26	intuitionistic	intuitionistic	ADJ
cana-5829	6	27	fuzzy	fuzzy	ADJ
cana-5829	6	28	numbers	number	NOUN
cana-5829	6	29	(	(	PUNCT
cana-5829	6	30	ifns	ifns	NOUN
cana-5829	6	31	)	)	PUNCT
cana-5829	6	32	.	.	PUNCT
cana-5829	7	1	this	this	DET
cana-5829	7	2	paper	paper	NOUN
cana-5829	7	3	explores	explore	VERB
cana-5829	7	4	the	the	DET
cana-5829	7	5	methods	method	NOUN
cana-5829	7	6	and	and	CCONJ
cana-5829	7	7	techniques	technique	NOUN
cana-5829	7	8	for	for	ADP
cana-5829	7	9	normalizing	normalize	VERB
cana-5829	7	10	intuitionistic	intuitionistic	ADJ
cana-5829	7	11	fuzzy	fuzzy	ADJ
cana-5829	7	12	matrices	matrix	NOUN
cana-5829	7	13	to	to	PART
cana-5829	7	14	ensure	ensure	VERB
cana-5829	7	15	that	that	SCONJ
cana-5829	7	16	the	the	DET
cana-5829	7	17	degree	degree	NOUN
cana-5829	7	18	of	of	ADP
cana-5829	7	19	membership	membership	NOUN
cana-5829	7	20	and	and	CCONJ
cana-5829	7	21	non	non	ADJ
cana-5829	7	22	-	-	ADJ
cana-5829	7	23	membership	membership	ADJ
cana-5829	7	24	values	value	NOUN
cana-5829	7	25	are	be	AUX
cana-5829	7	26	consistent	consistent	ADJ
cana-5829	7	27	,	,	PUNCT
cana-5829	7	28	thus	thus	ADV
cana-5829	7	29	enhancing	enhance	VERB
cana-5829	7	30	the	the	DET
cana-5829	7	31	reliability	reliability	NOUN
cana-5829	7	32	of	of	ADP
cana-5829	7	33	the	the	DET
cana-5829	7	34	matrix	matrix	NOUN
cana-5829	7	35	in	in	ADP
cana-5829	7	36	decision	decision	NOUN
cana-5829	7	37	analysis	analysis	NOUN
cana-5829	7	38	problems	problem	NOUN
cana-5829	7	39	.	.	PUNCT
cana-5829	8	1	we	we	PRON
cana-5829	8	2	propose	propose	VERB
cana-5829	8	3	an	an	DET
cana-5829	8	4	efficient	efficient	ADJ
cana-5829	8	5	approach	approach	NOUN
cana-5829	8	6	to	to	PART
cana-5829	8	7	normalize	normalize	VERB
cana-5829	8	8	intuitionistic	intuitionistic	ADJ
cana-5829	8	9	fuzzy	fuzzy	ADJ
cana-5829	8	10	matrices	matrix	NOUN
cana-5829	8	11	,	,	PUNCT
cana-5829	8	12	ensuring	ensure	VERB
cana-5829	8	13	the	the	DET
cana-5829	8	14	transformed	transform	VERB
cana-5829	8	15	values	value	NOUN
cana-5829	8	16	retain	retain	VERB
cana-5829	8	17	their	their	PRON
cana-5829	8	18	essential	essential	ADJ
cana-5829	8	19	characteristics	characteristic	NOUN
cana-5829	8	20	while	while	SCONJ
cana-5829	8	21	adhering	adhere	VERB
cana-5829	8	22	to	to	ADP
cana-5829	8	23	the	the	DET
cana-5829	8	24	constraints	constraint	NOUN
cana-5829	8	25	of	of	ADP
cana-5829	8	26	the	the	DET
cana-5829	8	27	fuzzy	fuzzy	ADJ
cana-5829	8	28	set	set	NOUN
cana-5829	8	29	theory	theory	NOUN
cana-5829	8	30	.	.	PUNCT
cana-5829	9	1	the	the	DET
cana-5829	9	2	study	study	NOUN
cana-5829	9	3	also	also	ADV
cana-5829	9	4	addresses	address	VERB
cana-5829	9	5	the	the	DET
cana-5829	9	6	application	application	NOUN
cana-5829	9	7	of	of	ADP
cana-5829	9	8	normalized	normalize	VERB
cana-5829	9	9	intuitionistic	intuitionistic	ADJ
cana-5829	9	10	fuzzy	fuzzy	ADJ
cana-5829	9	11	matrices	matrix	NOUN
cana-5829	9	12	in	in	ADP
cana-5829	9	13	multi	multi	ADJ
cana-5829	9	14	-	-	ADJ
cana-5829	9	15	criteria	criterion	NOUN
cana-5829	9	16	decision	decision	NOUN
cana-5829	9	17	-	-	PUNCT
cana-5829	9	18	making	making	NOUN
cana-5829	9	19	(	(	PUNCT
cana-5829	9	20	mcdm	mcdm	ADJ
cana-5829	9	21	)	)	PUNCT
cana-5829	9	22	and	and	CCONJ
cana-5829	9	23	other	other	ADJ
cana-5829	9	24	relevant	relevant	ADJ
cana-5829	9	25	areas	area	NOUN
cana-5829	9	26	such	such	ADJ
cana-5829	9	27	as	as	ADP
cana-5829	9	28	image	image	NOUN
cana-5829	9	29	processing	processing	NOUN
cana-5829	9	30	,	,	PUNCT
cana-5829	9	31	pattern	pattern	NOUN
cana-5829	9	32	recognition	recognition	NOUN
cana-5829	9	33	,	,	PUNCT
cana-5829	9	34	and	and	CCONJ
cana-5829	9	35	system	system	NOUN
cana-5829	9	36	modelling	modelling	NOUN
cana-5829	9	37	.	.	PUNCT
cana-5829	10	1	several	several	ADJ
cana-5829	10	2	illustrative	illustrative	ADJ
cana-5829	10	3	examples	example	NOUN
cana-5829	10	4	are	be	AUX
cana-5829	10	5	provided	provide	VERB
cana-5829	10	6	to	to	PART
cana-5829	10	7	demonstrate	demonstrate	VERB
cana-5829	10	8	the	the	DET
cana-5829	10	9	effectiveness	effectiveness	NOUN
cana-5829	10	10	of	of	ADP
cana-5829	10	11	the	the	DET
cana-5829	10	12	proposed	propose	VERB
cana-5829	10	13	normalization	normalization	NOUN
cana-5829	10	14	techniques	technique	NOUN
cana-5829	10	15	keywords	keyword	NOUN
cana-5829	10	16	:	:	PUNCT
cana-5829	10	17	complex	complex	ADJ
cana-5829	10	18	intuitionistic	intuitionistic	ADJ
cana-5829	10	19	fuzzy	fuzzy	ADJ
cana-5829	10	20	sets	set	NOUN
cana-5829	10	21	,	,	PUNCT
cana-5829	10	22	fuzzy	fuzzy	ADJ
cana-5829	10	23	matrices	matrix	NOUN
cana-5829	10	24	,	,	PUNCT
cana-5829	10	25	normalization	normalization	NOUN
cana-5829	10	26	techniques	technique	NOUN
cana-5829	10	27	,	,	PUNCT
cana-5829	10	28	membership	membership	NOUN
cana-5829	10	29	and	and	CCONJ
cana-5829	10	30	non	non	ADJ
cana-5829	10	31	-	-	ADJ
cana-5829	10	32	membership	membership	ADJ
cana-5829	10	33	functions	function	NOUN
cana-5829	10	34	,	,	PUNCT
cana-5829	10	35	fuzzy	fuzzy	ADJ
cana-5829	10	36	logic	logic	NOUN
cana-5829	10	37	,	,	PUNCT
cana-5829	10	38	matrix	matrix	NOUN
cana-5829	10	39	normalization	normalization	NOUN
cana-5829	10	40	,	,	PUNCT
cana-5829	10	41	intuitionistic	intuitionistic	ADJ
cana-5829	10	42	fuzzy	fuzzy	ADJ
cana-5829	10	43	logic	logic	NOUN
cana-5829	10	44	.	.	PUNCT
cana-5829	11	1	1	1	X
cana-5829	11	2	.	.	X
cana-5829	11	3	introduction	introduction	NOUN
cana-5829	11	4	:	:	PUNCT
cana-5829	11	5	atanassov	atanassov	ADJ
cana-5829	11	6	.	.	PUNCT
cana-5829	12	1	k	k	X
cana-5829	13	1	[	[	X
cana-5829	13	2	1	1	NUM
cana-5829	13	3	]	]	PUNCT
cana-5829	13	4	,	,	PUNCT
cana-5829	13	5	discussed	discuss	VERB
cana-5829	13	6	“	"	PUNCT
cana-5829	13	7	intuitionistic	intuitionistic	ADJ
cana-5829	13	8	fuzzy	fuzzy	ADJ
cana-5829	13	9	sets	set	NOUN
cana-5829	13	10	”	"	PUNCT
cana-5829	13	11	,	,	PUNCT
cana-5829	13	12	fuzzy	fuzzy	ADJ
cana-5829	13	13	sets	set	NOUN
cana-5829	13	14	and	and	CCONJ
cana-5829	13	15	systems	system	NOUN
cana-5829	13	16	in	in	ADP
cana-5829	13	17	this	this	DET
cana-5829	13	18	year	year	NOUN
cana-5829	13	19	1986	1986	NUM
cana-5829	13	20	.	.	PUNCT
cana-5829	14	1	ahmad	ahmad	PROPN
cana-5829	14	2	b	b	PROPN
cana-5829	15	1	[	[	X
cana-5829	15	2	2	2	NUM
cana-5829	15	3	]	]	PUNCT
cana-5829	15	4	,	,	PUNCT
cana-5829	15	5	discussed	discuss	VERB
cana-5829	15	6	on	on	ADP
cana-5829	15	7	fuzzy	fuzzy	ADJ
cana-5829	15	8	soft	soft	ADJ
cana-5829	15	9	sets	set	NOUN
cana-5829	15	10	,	,	PUNCT
cana-5829	15	11	advances	advance	NOUN
cana-5829	15	12	in	in	ADP
cana-5829	15	13	fuzzy	fuzzy	ADJ
cana-5829	15	14	systems	system	NOUN
cana-5829	15	15	in	in	ADP
cana-5829	15	16	this	this	DET
cana-5829	15	17	year	year	NOUN
cana-5829	15	18	2009	2009	NUM
cana-5829	15	19	.	.	PUNCT
cana-5829	16	1	barbacioru	barbacioru	NOUN
cana-5829	16	2	i.	i.	PROPN
cana-5829	16	3	c	c	PROPN
cana-5829	17	1	[	[	X
cana-5829	17	2	3	3	NUM
cana-5829	17	3	]	]	PUNCT
cana-5829	17	4	,	,	PUNCT
cana-5829	17	5	discussed	discuss	VERB
cana-5829	17	6	“	"	PUNCT
cana-5829	17	7	multiplication	multiplication	NOUN
cana-5829	17	8	operation	operation	NOUN
cana-5829	17	9	on	on	ADP
cana-5829	17	10	intuitionistic	intuitionistic	ADJ
cana-5829	17	11	fuzzy	fuzzy	ADJ
cana-5829	17	12	numbers	number	NOUN
cana-5829	17	13	”	"	PUNCT
cana-5829	17	14	in	in	ADP
cana-5829	17	15	this	this	DET
cana-5829	17	16	year	year	NOUN
cana-5829	17	17	2018	2018	NUM
cana-5829	17	18	.	.	PUNCT
cana-5829	18	1	babitha	babitha	PROPN
cana-5829	18	2	k.v	k.v	PROPN
cana-5829	18	3	.	.	PUNCT
cana-5829	19	1	[	[	X
cana-5829	19	2	4	4	NUM
cana-5829	19	3	]	]	PUNCT
cana-5829	19	4	,	,	PUNCT
cana-5829	19	5	discussed	discuss	VERB
cana-5829	19	6	generalized	generalized	ADJ
cana-5829	19	7	intuitionistic	intuitionistic	ADJ
cana-5829	19	8	fuzzy	fuzzy	ADJ
cana-5829	19	9	soft	soft	ADJ
cana-5829	19	10	sets	set	NOUN
cana-5829	19	11	and	and	CCONJ
cana-5829	19	12	its	its	PRON
cana-5829	19	13	applications	application	NOUN
cana-5829	19	14	in	in	ADP
cana-5829	19	15	this	this	DET
cana-5829	19	16	year	year	NOUN
cana-5829	19	17	2011	2011	NUM
cana-5829	19	18	.	.	PUNCT
cana-5829	20	1	chetia.b	chetia.b	PUNCT
cana-5829	21	1	[	[	X
cana-5829	21	2	5	5	NUM
cana-5829	21	3	]	]	PUNCT
cana-5829	21	4	,	,	PUNCT
cana-5829	21	5	discussed	discuss	VERB
cana-5829	21	6	some	some	DET
cana-5829	21	7	result	result	NOUN
cana-5829	21	8	of	of	ADP
cana-5829	21	9	intuitionistic	intuitionistic	ADJ
cana-5829	21	10	fuzzy	fuzzy	ADJ
cana-5829	21	11	soft	soft	ADJ
cana-5829	21	12	matrix	matrix	NOUN
cana-5829	21	13	theory	theory	NOUN
cana-5829	21	14	in	in	ADP
cana-5829	21	15	this	this	DET
cana-5829	21	16	year	year	NOUN
cana-5829	21	17	2012.cagman	2012.cagman	NOUN
cana-5829	21	18	.	.	PUNCT
cana-5829	22	1	n	n	PRON
cana-5829	23	1	[	[	X
cana-5829	23	2	6	6	NUM
cana-5829	23	3	]	]	PUNCT
cana-5829	23	4	discussed	discuss	VERB
cana-5829	23	5	fuzzy	fuzzy	ADJ
cana-5829	23	6	soft	soft	ADJ
cana-5829	23	7	matrix	matrix	NOUN
cana-5829	23	8	theory	theory	NOUN
cana-5829	23	9	and	and	CCONJ
cana-5829	23	10	its	its	PRON
cana-5829	23	11	application	application	NOUN
cana-5829	23	12	in	in	ADP
cana-5829	23	13	decision	decision	NOUN
cana-5829	23	14	making	making	NOUN
cana-5829	23	15	,	,	PUNCT
cana-5829	23	16	international	international	ADJ
cana-5829	23	17	journal	journal	NOUN
cana-5829	23	18	of	of	ADP
cana-5829	23	19	fuzzy	fuzzy	ADJ
cana-5829	23	20	systems	system	NOUN
cana-5829	23	21	in	in	ADP
cana-5829	23	22	this	this	DET
cana-5829	23	23	year	year	NOUN
cana-5829	23	24	2012.djatna	2012.djatna	NOUN
cana-5829	23	25	.	.	PUNCT
cana-5829	24	1	t	t	PROPN
cana-5829	25	1	[	[	X
cana-5829	25	2	7	7	X
cana-5829	25	3	]	]	PUNCT
cana-5829	25	4	discussed	discuss	VERB
cana-5829	25	5	“	"	PUNCT
cana-5829	25	6	an	an	DET
cana-5829	25	7	intuitionistic	intuitionistic	ADJ
cana-5829	25	8	fuzzy	fuzzy	ADJ
cana-5829	25	9	diagnosis	diagnosis	NOUN
cana-5829	25	10	analytics	analytic	NOUN
cana-5829	25	11	for	for	ADP
cana-5829	25	12	stroke	stroke	NOUN
cana-5829	25	13	disease	disease	NOUN
cana-5829	25	14	”	"	PUNCT
cana-5829	25	15	,	,	PUNCT
cana-5829	25	16	journal	journal	NOUN
cana-5829	25	17	of	of	ADP
cana-5829	25	18	big	big	ADJ
cana-5829	25	19	data	datum	NOUN
cana-5829	25	20	,	,	PUNCT
cana-5829	25	21	in	in	ADP
cana-5829	25	22	this	this	DET
cana-5829	25	23	year	year	NOUN
cana-5829	25	24	2018.dubois	2018.dubois	NOUN
cana-5829	25	25	.	.	PUNCT
cana-5829	26	1	d	d	X
cana-5829	27	1	[	[	X
cana-5829	27	2	8	8	NUM
cana-5829	27	3	]	]	PUNCT
cana-5829	27	4	,	,	PUNCT
cana-5829	27	5	discussed	discuss	VERB
cana-5829	27	6	fuzzy	fuzzy	ADJ
cana-5829	27	7	sets	set	NOUN
cana-5829	27	8	and	and	CCONJ
cana-5829	27	9	systems	system	NOUN
cana-5829	27	10	:	:	PUNCT
cana-5829	27	11	theory	theory	NOUN
cana-5829	27	12	and	and	CCONJ
cana-5829	27	13	applications	application	NOUN
cana-5829	27	14	in	in	ADP
cana-5829	27	15	this	this	DET
cana-5829	27	16	year1980	year1980	PROPN
cana-5829	27	17	.	.	PUNCT
cana-5829	28	1	emam	emam	PROPN
cana-5829	28	2	e.g	e.g	PROPN
cana-5829	29	1	[	[	X
cana-5829	29	2	9	9	NUM
cana-5829	29	3	]	]	PUNCT
cana-5829	29	4	,	,	PUNCT
cana-5829	29	5	discussed	discuss	VERB
cana-5829	29	6	“	"	PUNCT
cana-5829	29	7	intuitionistic	intuitionistic	ADJ
cana-5829	29	8	circular	circular	ADJ
cana-5829	29	9	bifuzzy	bifuzzy	NOUN
cana-5829	29	10	matrices	matrix	NOUN
cana-5829	29	11	“	"	PUNCT
cana-5829	29	12	in	in	ADP
cana-5829	29	13	this	this	DET
cana-5829	29	14	year	year	NOUN
cana-5829	29	15	2017	2017	NUM
cana-5829	29	16	.	.	PUNCT
cana-5829	30	1	emam	emam	PROPN
cana-5829	30	2	e.g	e.g	PROPN
cana-5829	31	1	[	[	X
cana-5829	31	2	10	10	NUM
cana-5829	31	3	]	]	PUNCT
cana-5829	31	4	,	,	PUNCT
cana-5829	31	5	discussed	discuss	VERB
cana-5829	31	6	the	the	DET
cana-5829	31	7	determinant	determinant	ADJ
cana-5829	31	8	and	and	CCONJ
cana-5829	31	9	adjoint	adjoint	NOUN
cana-5829	31	10	of	of	ADP
cana-5829	31	11	a	a	DET
cana-5829	31	12	square	square	ADJ
cana-5829	31	13	fuzzy	fuzzy	ADJ
cana-5829	31	14	matrix	matrix	NOUN
cana-5829	31	15	,	,	PUNCT
cana-5829	31	16	information	information	NOUN
cana-5829	31	17	sciences	science	NOUN
cana-5829	31	18	in	in	ADP
cana-5829	31	19	this	this	DET
cana-5829	31	20	year1995	year1995	PROPN
cana-5829	31	21	.	.	PUNCT
cana-5829	32	1	enginoǧlu	enginoǧlu	PROPN
cana-5829	32	2	s	s	PART
cana-5829	32	3	[	[	X
cana-5829	32	4	11	11	NUM
cana-5829	32	5	]	]	PUNCT
cana-5829	32	6	,	,	PUNCT
cana-5829	32	7	discussed	discuss	VERB
cana-5829	32	8	“	"	PUNCT
cana-5829	32	9	intuitionistic	intuitionistic	ADJ
cana-5829	32	10	fuzzy	fuzzy	ADJ
cana-5829	32	11	parameterized	parameterized	ADJ
cana-5829	32	12	intuitionistic	intuitionistic	ADJ
cana-5829	32	13	fuzzy	fuzzy	ADJ
cana-5829	32	14	soft	soft	ADJ
cana-5829	32	15	matrices	matrix	NOUN
cana-5829	32	16	and	and	CCONJ
cana-5829	32	17	their	their	PRON
cana-5829	32	18	application	application	NOUN
cana-5829	32	19	in	in	ADP
cana-5829	32	20	decision	decision	NOUN
cana-5829	32	21	-	-	PUNCT
cana-5829	32	22	making	making	NOUN
cana-5829	32	23	”	"	PUNCT
cana-5829	32	24	in	in	ADP
cana-5829	32	25	this	this	DET
cana-5829	32	26	year	year	NOUN
cana-5829	33	1	2020.eklund	2020.eklund	NOUN
cana-5829	33	2	p.w	p.w	PROPN
cana-5829	34	1	[	[	X
cana-5829	34	2	12	12	NUM
cana-5829	34	3	]	]	PUNCT
cana-5829	34	4	,	,	PUNCT
cana-5829	34	5	discussed	discuss	VERB
cana-5829	34	6	fuzzy	fuzzy	ADJ
cana-5829	34	7	matrices	matrix	NOUN
cana-5829	34	8	:	:	PUNCT
cana-5829	34	9	an	an	DET
cana-5829	34	10	application	application	NOUN
cana-5829	34	11	in	in	ADP
cana-5829	34	12	agriculture	agriculture	NOUN
cana-5829	34	13	in	in	ADP
cana-5829	34	14	this	this	DET
cana-5829	34	15	year	year	NOUN
cana-5829	34	16	1995	1995	NUM
cana-5829	34	17	.	.	PUNCT
cana-5829	35	1	engino	engino	PROPN
cana-5829	35	2	glu	glu	PROPN
cana-5829	35	3	.	.	PUNCT
cana-5829	35	4	s	s	PART
cana-5829	36	1	[	[	X
cana-5829	36	2	13	13	NUM
cana-5829	36	3	]	]	PUNCT
cana-5829	36	4	,	,	PUNCT
cana-5829	36	5	discussed	discuss	VERB
cana-5829	36	6	fuzzy	fuzzy	ADJ
cana-5829	36	7	parameterized	parameterized	ADJ
cana-5829	36	8	fuzzy	fuzzy	ADJ
cana-5829	36	9	soft	soft	ADJ
cana-5829	36	10	set	set	NOUN
cana-5829	36	11	theory	theory	NOUN
cana-5829	36	12	and	and	CCONJ
cana-5829	36	13	its	its	PRON
cana-5829	36	14	applications	application	NOUN
cana-5829	36	15	in	in	ADP
cana-5829	36	16	this	this	DET
cana-5829	36	17	year	year	NOUN
cana-5829	36	18	2010.feng	2010.feng	NOUN
cana-5829	36	19	.	.	PUNCT
cana-5829	37	1	f	f	X
cana-5829	38	1	[	[	X
cana-5829	38	2	14	14	NUM
cana-5829	38	3	]	]	PUNCT
cana-5829	38	4	,	,	PUNCT
cana-5829	38	5	discussed	discuss	VERB
cana-5829	38	6	,	,	PUNCT
cana-5829	38	7	an	an	DET
cana-5829	38	8	adjustable	adjustable	ADJ
cana-5829	38	9	approach	approach	NOUN
cana-5829	38	10	to	to	ADP
cana-5829	38	11	fuzzy	fuzzy	ADJ
cana-5829	38	12	soft	soft	ADJ
cana-5829	38	13	set	set	NOUN
cana-5829	38	14	based	base	VERB
cana-5829	38	15	decision	decision	NOUN
cana-5829	38	16	making	making	NOUN
cana-5829	38	17	,	,	PUNCT
cana-5829	38	18	journal	journal	NOUN
cana-5829	38	19	of	of	ADP
cana-5829	38	20	computational	computational	ADJ
cana-5829	38	21	and	and	CCONJ
cana-5829	38	22	applied	applied	ADJ
cana-5829	38	23	mathematics	mathematic	NOUN
cana-5829	38	24	in	in	ADP
cana-5829	38	25	this	this	DET
cana-5829	38	26	year	year	NOUN
cana-5829	38	27	2010.hans	2010.hans	PROPN
cana-5829	38	28	-	-	PROPN
cana-5829	38	29	jürgen	jürgen	PROPN
cana-5829	38	30	zimmermann	zimmermann	PROPN
cana-5829	38	31	kluwer	kluwer	PROPN
cana-5829	39	1	[	[	X
cana-5829	39	2	15	15	NUM
cana-5829	39	3	]	]	PUNCT
cana-5829	39	4	,	,	PUNCT
cana-5829	39	5	discussed	discuss	VERB
cana-5829	39	6	fuzzy	fuzzy	ADJ
cana-5829	39	7	set	set	NOUN
cana-5829	39	8	theory	theory	NOUN
cana-5829	39	9	and	and	CCONJ
cana-5829	39	10	its	its	PRON
cana-5829	39	11	applications	application	NOUN
cana-5829	39	12	in	in	ADP
cana-5829	39	13	communications	communication	NOUN
cana-5829	39	14	on	on	ADP
cana-5829	39	15	applied	apply	VERB
cana-5829	39	16	nonlinear	nonlinear	ADJ
cana-5829	39	17	analysis	analysis	NOUN
cana-5829	39	18	issn	issn	NOUN
cana-5829	39	19	:	:	PUNCT
cana-5829	39	20	1074	1074	NUM
cana-5829	39	21	-	-	PUNCT
cana-5829	39	22	133x	133x	NUM
cana-5829	39	23	vol	vol	VERB
cana-5829	39	24	32	32	NUM
cana-5829	39	25	no	no	NOUN
cana-5829	39	26	.	.	PUNCT
cana-5829	40	1	10s	10	NOUN
cana-5829	40	2	(	(	PUNCT
cana-5829	40	3	2025	2025	NUM
cana-5829	40	4	)	)	PUNCT
cana-5829	40	5	2924	2924	NUM
cana-5829	40	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5829	41	1	this	this	DET
cana-5829	41	2	year	year	NOUN
cana-5829	41	3	1992.irfan	1992.irfan	NUM
cana-5829	41	4	deli	deli	NOUN
cana-5829	42	1	[	[	X
cana-5829	42	2	16	16	NUM
cana-5829	42	3	]	]	PUNCT
cana-5829	42	4	discussed	discuss	VERB
cana-5829	42	5	,	,	PUNCT
cana-5829	42	6	intuitionistic	intuitionistic	ADJ
cana-5829	42	7	fuzzy	fuzzy	ADJ
cana-5829	42	8	parameterized	parameterized	ADJ
cana-5829	42	9	soft	soft	ADJ
cana-5829	42	10	set	set	NOUN
cana-5829	42	11	theory	theory	NOUN
cana-5829	42	12	and	and	CCONJ
cana-5829	42	13	its	its	PRON
cana-5829	42	14	decision	decision	NOUN
cana-5829	42	15	making	make	VERB
cana-5829	42	16	in	in	ADP
cana-5829	42	17	this	this	DET
cana-5829	42	18	year	year	NOUN
cana-5829	42	19	2013	2013	NUM
cana-5829	42	20	.	.	PUNCT
cana-5829	43	1	kalra	kalra	PROPN
cana-5829	43	2	.	.	PUNCT
cana-5829	44	1	n[17	n[17	PROPN
cana-5829	44	2	]	]	PUNCT
cana-5829	44	3	,	,	PUNCT
cana-5829	44	4	discussed	discuss	VERB
cana-5829	44	5	“	"	PUNCT
cana-5829	44	6	a	a	DET
cana-5829	44	7	study	study	NOUN
cana-5829	44	8	of	of	ADP
cana-5829	44	9	fuzzy	fuzzy	ADJ
cana-5829	44	10	,	,	PUNCT
cana-5829	44	11	super	super	ADJ
cana-5829	44	12	and	and	CCONJ
cana-5829	44	13	super	super	ADV
cana-5829	44	14	fuzzy	fuzzy	ADJ
cana-5829	44	15	matrix	matrix	NOUN
cana-5829	44	16	theory	theory	NOUN
cana-5829	44	17	”	"	PUNCT
cana-5829	44	18	in	in	ADP
cana-5829	44	19	this	this	DET
cana-5829	44	20	year	year	NOUN
cana-5829	44	21	2010	2010	NUM
cana-5829	44	22	.	.	PUNCT
cana-5829	45	1	krishnamohan	krishnamohan	PROPN
cana-5829	45	2	.k.s[18	.k.s[18	PROPN
cana-5829	45	3	]	]	PUNCT
cana-5829	45	4	,	,	PUNCT
cana-5829	45	5	discussed	discuss	VERB
cana-5829	45	6	generalisation	generalisation	NOUN
cana-5829	45	7	of	of	ADP
cana-5829	45	8	idempotent	idempotent	ADJ
cana-5829	45	9	fuzzy	fuzzy	ADJ
cana-5829	45	10	matrices	matrix	NOUN
cana-5829	45	11	in	in	ADP
cana-5829	45	12	this	this	DET
cana-5829	45	13	year	year	NOUN
cana-5829	45	14	2018	2018	NUM
cana-5829	45	15	.	.	PUNCT
cana-5829	46	1	kaliraja.m[19	kaliraja.m[19	PROPN
cana-5829	46	2	]	]	PUNCT
cana-5829	46	3	discussed	discuss	VERB
cana-5829	46	4	an	an	DET
cana-5829	46	5	application	application	NOUN
cana-5829	46	6	of	of	ADP
cana-5829	46	7	interval	interval	NOUN
cana-5829	46	8	valued	value	VERB
cana-5829	46	9	fuzzy	fuzzy	ADJ
cana-5829	46	10	matrices	matrix	NOUN
cana-5829	46	11	in	in	ADP
cana-5829	46	12	medical	medical	ADJ
cana-5829	46	13	diagnosis	diagnosis	NOUN
cana-5829	46	14	in	in	ADP
cana-5829	46	15	this	this	DET
cana-5829	46	16	year	year	NOUN
cana-5829	46	17	2011	2011	NUM
cana-5829	46	18	.	.	PUNCT
cana-5829	47	1	kandle.a[20	kandle.a[20	PROPN
cana-5829	47	2	]	]	PUNCT
cana-5829	47	3	,	,	PUNCT
cana-5829	47	4	discussed	discuss	VERB
cana-5829	47	5	fuzzy	fuzzy	ADJ
cana-5829	47	6	sets	set	NOUN
cana-5829	47	7	,	,	PUNCT
cana-5829	47	8	fuzzy	fuzzy	ADJ
cana-5829	47	9	algebra	algebra	NOUN
cana-5829	47	10	,	,	PUNCT
cana-5829	47	11	and	and	CCONJ
cana-5829	47	12	fuzzy	fuzzy	ADJ
cana-5829	47	13	statistics	statistic	NOUN
cana-5829	47	14	in	in	ADP
cana-5829	47	15	this	this	DET
cana-5829	47	16	year	year	NOUN
cana-5829	47	17	1978	1978	NUM
cana-5829	47	18	.	.	PUNCT
cana-5829	48	1	leon	leon	PROPN
cana-5829	48	2	-	-	PUNCT
cana-5829	48	3	castro	castro	PROPN
cana-5829	48	4	e	e	PROPN
cana-5829	48	5	.[21	.[21	PROPN
cana-5829	48	6	]	]	PUNCT
cana-5829	48	7	discussed	discuss	VERB
cana-5829	48	8	“	"	PUNCT
cana-5829	48	9	computational	computational	ADJ
cana-5829	48	10	and	and	CCONJ
cana-5829	48	11	mathematical	mathematical	ADJ
cana-5829	48	12	organization	organization	NOUN
cana-5829	48	13	theory	theory	NOUN
cana-5829	48	14	”	"	PUNCT
cana-5829	48	15	,	,	PUNCT
cana-5829	48	16	fuzzy	fuzzy	ADJ
cana-5829	48	17	systems	system	NOUN
cana-5829	48	18	in	in	ADP
cana-5829	48	19	innovation	innovation	NOUN
cana-5829	48	20	and	and	CCONJ
cana-5829	48	21	sustainability	sustainability	NOUN
cana-5829	48	22	,	,	PUNCT
cana-5829	48	23	in	in	ADP
cana-5829	48	24	this	this	DET
cana-5829	48	25	year	year	NOUN
cana-5829	48	26	2021.p	2021.p	PROPN
cana-5829	48	27	.	.	PUNCT
cana-5829	48	28	k.	k.	PROPN
cana-5829	49	1	maji[22	maji[22	PROPN
cana-5829	49	2	]	]	PUNCT
cana-5829	49	3	discussed	discuss	VERB
cana-5829	49	4	“	"	PUNCT
cana-5829	49	5	fuzzy	fuzzy	ADJ
cana-5829	49	6	soft	soft	ADJ
cana-5829	49	7	sets	set	NOUN
cana-5829	49	8	”	"	PUNCT
cana-5829	49	9	,	,	PUNCT
cana-5829	49	10	journal	journal	NOUN
cana-5829	49	11	of	of	ADP
cana-5829	49	12	fuzzy	fuzzy	ADJ
cana-5829	49	13	mathematics	mathematic	NOUN
cana-5829	49	14	in	in	ADP
cana-5829	49	15	this	this	DET
cana-5829	49	16	year	year	NOUN
cana-5829	49	17	2001.mondal	2001.mondal	NOUN
cana-5829	49	18	,	,	PUNCT
cana-5829	49	19	s[23	s[23	PROPN
cana-5829	49	20	]	]	PUNCT
cana-5829	49	21	,	,	PUNCT
cana-5829	49	22	discussed	discuss	VERB
cana-5829	49	23	“	"	PUNCT
cana-5829	49	24	intuitionistic	intuitionistic	ADJ
cana-5829	49	25	fuzzy	fuzzy	ADJ
cana-5829	49	26	incline	incline	NOUN
cana-5829	49	27	matrix	matrix	NOUN
cana-5829	49	28	and	and	CCONJ
cana-5829	49	29	determinant	determinant	ADJ
cana-5829	49	30	”	"	PUNCT
cana-5829	49	31	in	in	ADP
cana-5829	49	32	this	this	DET
cana-5829	49	33	year	year	NOUN
cana-5829	49	34	2003.muthuraji	2003.muthuraji	NUM
cana-5829	49	35	,	,	PUNCT
cana-5829	49	36	t[24	t[24	PROPN
cana-5829	49	37	]	]	PUNCT
cana-5829	49	38	,	,	PUNCT
cana-5829	49	39	discussed	discuss	VERB
cana-5829	49	40	“	"	PUNCT
cana-5829	49	41	decomposition	decomposition	NOUN
cana-5829	49	42	of	of	ADP
cana-5829	49	43	intuitionistic	intuitionistic	ADJ
cana-5829	49	44	fuzzy	fuzzy	ADJ
cana-5829	49	45	matrices	matrix	NOUN
cana-5829	49	46	”	"	PUNCT
cana-5829	49	47	in	in	ADP
cana-5829	49	48	the	the	DET
cana-5829	49	49	year	year	NOUN
cana-5829	49	50	2016	2016	NUM
cana-5829	49	51	.	.	PUNCT
cana-5829	50	1	otadi	otadi	NOUN
cana-5829	50	2	,	,	PUNCT
cana-5829	50	3	m.	m.	NOUN
cana-5829	51	1	[	[	X
cana-5829	51	2	25	25	NUM
cana-5829	51	3	]	]	PUNCT
cana-5829	51	4	discussed	discuss	VERB
cana-5829	51	5	“	"	PUNCT
cana-5829	51	6	solving	solve	VERB
cana-5829	51	7	fully	fully	ADV
cana-5829	51	8	fuzzy	fuzzy	ADJ
cana-5829	51	9	matrix	matrix	NOUN
cana-5829	51	10	equations	equation	NOUN
cana-5829	51	11	”	"	PUNCT
cana-5829	51	12	,	,	PUNCT
cana-5829	51	13	applied	apply	VERB
cana-5829	51	14	mathematical	mathematical	ADJ
cana-5829	51	15	modelling	modelling	NOUN
cana-5829	51	16	in	in	ADP
cana-5829	51	17	this	this	DET
cana-5829	51	18	year	year	NOUN
cana-5829	51	19	2012	2012	NUM
cana-5829	51	20	.	.	PUNCT
cana-5829	52	1	wolkenhauer	wolkenhauer	NOUN
cana-5829	53	1	[	[	X
cana-5829	53	2	26	26	NUM
cana-5829	53	3	]	]	PUNCT
cana-5829	53	4	,	,	PUNCT
cana-5829	53	5	discussed	discuss	VERB
cana-5829	53	6	]	]	PUNCT
cana-5829	53	7	fuzzy	fuzzy	ADJ
cana-5829	53	8	set	set	NOUN
cana-5829	53	9	theory	theory	NOUN
cana-5829	53	10	and	and	CCONJ
cana-5829	53	11	its	its	PRON
cana-5829	53	12	applications	application	NOUN
cana-5829	53	13	in	in	ADP
cana-5829	53	14	this	this	DET
cana-5829	53	15	year	year	NOUN
cana-5829	53	16	1998.pal	1998.pal	NUM
cana-5829	53	17	,	,	PUNCT
cana-5829	53	18	m	m	VERB
cana-5829	53	19	[	[	X
cana-5829	53	20	27	27	NUM
cana-5829	53	21	]	]	X
cana-5829	53	22	discussed“intuitionistic	discussed“intuitionistic	ADJ
cana-5829	53	23	fuzzy	fuzzy	ADJ
cana-5829	54	1	matrices”in	matrices”in	NOUN
cana-5829	54	2	this	this	DET
cana-5829	54	3	year	year	NOUN
cana-5829	54	4	2002	2002	NUM
cana-5829	54	5	.	.	PUNCT
cana-5829	55	1	pradhan	pradhan	PROPN
cana-5829	55	2	,	,	PUNCT
cana-5829	55	3	r[28	r[28	PROPN
cana-5829	55	4	]	]	PUNCT
cana-5829	55	5	,	,	PUNCT
cana-5829	55	6	discussed	discuss	VERB
cana-5829	55	7	“	"	PUNCT
cana-5829	55	8	the	the	DET
cana-5829	55	9	generalized	generalized	ADJ
cana-5829	55	10	inverse	inverse	NOUN
cana-5829	55	11	of	of	ADP
cana-5829	55	12	atanassov	atanassov	PROPN
cana-5829	55	13	’s	’s	PART
cana-5829	55	14	intuitionistic	intuitionistic	ADJ
cana-5829	55	15	fuzzy	fuzzy	ADJ
cana-5829	55	16	matrices”in	matrices”in	NOUN
cana-5829	55	17	this	this	DET
cana-5829	55	18	year	year	NOUN
cana-5829	55	19	2014	2014	NUM
cana-5829	55	20	.	.	PUNCT
cana-5829	56	1	prade.h	prade.h	X
cana-5829	57	1	[	[	X
cana-5829	57	2	29	29	NUM
cana-5829	57	3	]	]	PUNCT
cana-5829	57	4	,	,	PUNCT
cana-5829	57	5	discussed	discuss	VERB
cana-5829	57	6	fuzzy	fuzzy	ADJ
cana-5829	57	7	sets	set	NOUN
cana-5829	57	8	and	and	CCONJ
cana-5829	57	9	systems	system	NOUN
cana-5829	57	10	theory	theory	NOUN
cana-5829	57	11	and	and	CCONJ
cana-5829	57	12	application	application	NOUN
cana-5829	57	13	in	in	ADP
cana-5829	57	14	this	this	DET
cana-5829	57	15	year	year	NOUN
cana-5829	57	16	1980	1980	NUM
cana-5829	57	17	.	.	PUNCT
cana-5829	58	1	rajarajeswari.p[30	rajarajeswari.p[30	PROPN
cana-5829	58	2	]	]	PUNCT
cana-5829	58	3	,	,	PUNCT
cana-5829	58	4	discussed	discuss	VERB
cana-5829	58	5	intuitionistic	intuitionistic	ADJ
cana-5829	58	6	fuzzy	fuzzy	ADJ
cana-5829	58	7	soft	soft	ADJ
cana-5829	58	8	matrix	matrix	NOUN
cana-5829	58	9	theory	theory	NOUN
cana-5829	58	10	and	and	CCONJ
cana-5829	58	11	its	its	PRON
cana-5829	58	12	application	application	NOUN
cana-5829	58	13	in	in	ADP
cana-5829	58	14	decision	decision	NOUN
cana-5829	58	15	making	making	NOUN
cana-5829	58	16	in	in	ADP
cana-5829	58	17	this	this	DET
cana-5829	58	18	year	year	NOUN
cana-5829	58	19	2013	2013	NUM
cana-5829	58	20	.	.	PUNCT
cana-5829	59	1	sahni	sahni	PROPN
cana-5829	59	2	,	,	PUNCT
cana-5829	59	3	m[31	m[31	PROPN
cana-5829	59	4	]	]	PUNCT
cana-5829	59	5	,	,	PUNCT
cana-5829	59	6	discussed	discuss	VERB
cana-5829	59	7	“	"	PUNCT
cana-5829	59	8	generalized	generalized	ADJ
cana-5829	59	9	trapezoidal	trapezoidal	ADJ
cana-5829	59	10	intuitionistic	intuitionistic	ADJ
cana-5829	59	11	fuzzy	fuzzy	ADJ
cana-5829	59	12	number	number	NOUN
cana-5829	59	13	for	for	ADP
cana-5829	59	14	finding	find	VERB
cana-5829	59	15	radial	radial	ADJ
cana-5829	59	16	displacement	displacement	NOUN
cana-5829	59	17	of	of	ADP
cana-5829	59	18	a	a	DET
cana-5829	59	19	solid	solid	ADJ
cana-5829	59	20	disk”in	disk”in	NOUN
cana-5829	59	21	this	this	DET
cana-5829	59	22	year	year	NOUN
cana-5829	59	23	2019	2019	NUM
cana-5829	59	24	.	.	PUNCT
cana-5829	60	1	saw	see	VERB
cana-5829	60	2	b.c	b.c	PROPN
cana-5829	61	1	[	[	X
cana-5829	61	2	32	32	NUM
cana-5829	61	3	]	]	PUNCT
cana-5829	61	4	,	,	PUNCT
cana-5829	61	5	discussed	discuss	VERB
cana-5829	61	6	“	"	PUNCT
cana-5829	61	7	𝛼	𝛼	PROPN
cana-5829	61	8	,	,	PUNCT
cana-5829	61	9	𝛽	𝛽	NOUN
cana-5829	61	10	,	,	PUNCT
cana-5829	61	11	𝛾	𝛾	PROPN
cana-5829	61	12	,	,	PUNCT
cana-5829	61	13	𝛿	𝛿	DET
cana-5829	61	14	parametric	parametric	ADJ
cana-5829	61	15	form	form	NOUN
cana-5829	61	16	for	for	ADP
cana-5829	61	17	solving	solve	VERB
cana-5829	61	18	intuitionistic	intuitionistic	ADJ
cana-5829	61	19	fuzzy	fuzzy	ADJ
cana-5829	61	20	linear	linear	ADJ
cana-5829	61	21	system	system	NOUN
cana-5829	61	22	of	of	ADP
cana-5829	61	23	equations	equation	NOUN
cana-5829	61	24	”	"	PUNCT
cana-5829	61	25	in	in	ADP
cana-5829	61	26	this	this	DET
cana-5829	61	27	year	year	NOUN
cana-5829	61	28	2021.smarandache	2021.smarandache	NUM
cana-5829	61	29	.	.	PUNCT
cana-5829	62	1	f	f	X
cana-5829	63	1	[	[	X
cana-5829	63	2	33	33	NUM
cana-5829	63	3	]	]	PUNCT
cana-5829	63	4	,	,	PUNCT
cana-5829	63	5	discussed	discuss	VERB
cana-5829	63	6	“	"	PUNCT
cana-5829	63	7	neutrosophic	neutrosophic	ADJ
cana-5829	63	8	set	set	NOUN
cana-5829	63	9	-	-	PUNCT
cana-5829	63	10	a	a	DET
cana-5829	63	11	generalization	generalization	NOUN
cana-5829	63	12	of	of	ADP
cana-5829	63	13	intuitionistic	intuitionistic	ADJ
cana-5829	63	14	fuzzy	fuzzy	ADJ
cana-5829	63	15	sets”in	sets”in	PROPN
cana-5829	63	16	this	this	DET
cana-5829	63	17	year	year	NOUN
cana-5829	63	18	2005	2005	NUM
cana-5829	63	19	.	.	PUNCT
cana-5829	64	1	thomason	thomason	PROPN
cana-5829	64	2	,	,	PUNCT
cana-5829	64	3	m.	m.	NOUN
cana-5829	64	4	g[34	g[34	PROPN
cana-5829	64	5	]	]	PUNCT
cana-5829	64	6	,	,	PUNCT
cana-5829	64	7	discussed	discuss	VERB
cana-5829	64	8	“	"	PUNCT
cana-5829	64	9	convergence	convergence	NOUN
cana-5829	64	10	of	of	ADP
cana-5829	64	11	powers	power	NOUN
cana-5829	64	12	of	of	ADP
cana-5829	64	13	a	a	DET
cana-5829	64	14	fuzzy	fuzzy	ADJ
cana-5829	64	15	matrix	matrix	NOUN
cana-5829	64	16	”	"	PUNCT
cana-5829	64	17	in	in	ADP
cana-5829	64	18	this	this	DET
cana-5829	64	19	year	year	NOUN
cana-5829	64	20	1977	1977	NUM
cana-5829	64	21	.	.	PUNCT
cana-5829	65	1	f.	f.	PROPN
cana-5829	65	2	c_tak	c_tak	PROPN
cana-5829	66	1	[	[	X
cana-5829	66	2	35	35	NUM
cana-5829	66	3	]	]	PUNCT
cana-5829	66	4	,	,	PUNCT
cana-5829	66	5	discussed	discuss	VERB
cana-5829	66	6	fuzzy	fuzzy	ADJ
cana-5829	66	7	parameterized	parameterized	ADJ
cana-5829	66	8	fuzzy	fuzzy	ADJ
cana-5829	66	9	soft	soft	ADJ
cana-5829	66	10	set	set	NOUN
cana-5829	66	11	theory	theory	NOUN
cana-5829	66	12	and	and	CCONJ
cana-5829	66	13	its	its	PRON
cana-5829	66	14	applications	application	NOUN
cana-5829	66	15	,	,	PUNCT
cana-5829	66	16	turkish	turkish	ADJ
cana-5829	66	17	journal	journal	NOUN
cana-5829	66	18	of	of	ADP
cana-5829	66	19	fuzzy	fuzzy	ADJ
cana-5829	66	20	systems	system	NOUN
cana-5829	66	21	in	in	ADP
cana-5829	66	22	this	this	DET
cana-5829	66	23	year	year	NOUN
cana-5829	66	24	2010	2010	NUM
cana-5829	66	25	.	.	PUNCT
cana-5829	67	1	venkatesan	venkatesan	ADJ
cana-5829	67	2	,	,	PUNCT
cana-5829	67	3	d[36	d[36	PROPN
cana-5829	67	4	]	]	PUNCT
cana-5829	67	5	,	,	PUNCT
cana-5829	67	6	discussed	discuss	VERB
cana-5829	67	7	“	"	PUNCT
cana-5829	67	8	remarks	remark	NOUN
cana-5829	67	9	on	on	ADP
cana-5829	67	10	the	the	DET
cana-5829	67	11	multiplicative	multiplicative	ADJ
cana-5829	67	12	operations	operation	NOUN
cana-5829	67	13	of	of	ADP
cana-5829	67	14	intuitionistic	intuitionistic	ADJ
cana-5829	67	15	fuzzy	fuzzy	ADJ
cana-5829	67	16	matrices	matrix	NOUN
cana-5829	67	17	”	"	PUNCT
cana-5829	67	18	in	in	ADP
cana-5829	67	19	this	this	DET
cana-5829	67	20	year	year	NOUN
cana-5829	67	21	2021.p.j.m	2021.p.j.m	PROPN
cana-5829	67	22	.	.	PUNCT
cana-5829	68	1	van	van	PROPN
cana-5829	68	2	laarhoven[37	laarhoven[37	PROPN
cana-5829	68	3	]	]	PUNCT
cana-5829	68	4	,	,	PUNCT
cana-5829	68	5	discussed	discuss	VERB
cana-5829	68	6	a	a	DET
cana-5829	68	7	fuzzy	fuzzy	ADJ
cana-5829	68	8	extension	extension	NOUN
cana-5829	68	9	of	of	ADP
cana-5829	68	10	saaty	saaty	NOUN
cana-5829	68	11	's	's	PART
cana-5829	68	12	priority	priority	NOUN
cana-5829	68	13	theory	theory	NOUN
cana-5829	68	14	,	,	PUNCT
cana-5829	68	15	fuzzy	fuzzy	ADJ
cana-5829	68	16	sets	set	NOUN
cana-5829	68	17	and	and	CCONJ
cana-5829	68	18	systems	system	NOUN
cana-5829	68	19	in	in	ADP
cana-5829	68	20	the	the	DET
cana-5829	68	21	year	year	NOUN
cana-5829	68	22	1983	1983	NUM
cana-5829	68	23	.	.	PUNCT
cana-5829	69	1	verma	verma	PROPN
cana-5829	69	2	r[38	r[38	PROPN
cana-5829	69	3	]	]	PUNCT
cana-5829	69	4	,	,	PUNCT
cana-5829	69	5	discussed	discuss	VERB
cana-5829	69	6	“	"	PUNCT
cana-5829	69	7	on	on	ADP
cana-5829	69	8	sharma	sharma	PROPN
cana-5829	69	9	-	-	PUNCT
cana-5829	69	10	mittal	mittal	PROPN
cana-5829	69	11	’s	’s	PART
cana-5829	69	12	entropy	entropy	NOUN
cana-5829	69	13	under	under	ADP
cana-5829	69	14	intuitionistic	intuitionistic	ADJ
cana-5829	69	15	fuzzy	fuzzy	ADJ
cana-5829	69	16	environment	environment	NOUN
cana-5829	69	17	”	"	PUNCT
cana-5829	69	18	in	in	ADP
cana-5829	69	19	this	this	DET
cana-5829	69	20	year	year	NOUN
cana-5829	69	21	2021.wagenknecht.m[39	2021.wagenknecht.m[39	NUM
cana-5829	69	22	]	]	PUNCT
cana-5829	69	23	,	,	PUNCT
cana-5829	69	24	discussed	discuss	VERB
cana-5829	69	25	on	on	ADP
cana-5829	69	26	fuzzy	fuzzy	ADJ
cana-5829	69	27	rank	rank	NOUN
cana-5829	69	28	-	-	PUNCT
cana-5829	69	29	ordering	ordering	NOUN
cana-5829	69	30	in	in	ADP
cana-5829	69	31	polyoptimization	polyoptimization	NOUN
cana-5829	69	32	,	,	PUNCT
cana-5829	69	33	fuzzy	fuzzy	ADJ
cana-5829	69	34	sets	set	NOUN
cana-5829	69	35	and	and	CCONJ
cana-5829	69	36	systems	system	NOUN
cana-5829	69	37	in	in	ADP
cana-5829	69	38	thi	thi	PROPN
cana-5829	69	39	year	year	NOUN
cana-5829	69	40	1983.xu	1983.xu	NOUN
cana-5829	69	41	,	,	PUNCT
cana-5829	69	42	z[40	z[40	PROPN
cana-5829	69	43	]	]	PUNCT
cana-5829	69	44	,	,	PUNCT
cana-5829	69	45	discussed	discuss	VERB
cana-5829	69	46	“	"	PUNCT
cana-5829	69	47	multi	multi	ADJ
cana-5829	69	48	-	-	ADJ
cana-5829	69	49	person	person	ADJ
cana-5829	69	50	multi	multi	ADJ
cana-5829	69	51	-	-	ADJ
cana-5829	69	52	attribute	attribute	ADJ
cana-5829	69	53	decision	decision	NOUN
cana-5829	69	54	making	make	VERB
cana-5829	69	55	models	model	NOUN
cana-5829	69	56	under	under	ADP
cana-5829	69	57	intuitionistic	intuitionistic	ADJ
cana-5829	69	58	fuzzy	fuzzy	ADJ
cana-5829	69	59	environment”in	environment”in	PROPN
cana-5829	69	60	this	this	DET
cana-5829	69	61	year	year	NOUN
cana-5829	69	62	2007	2007	NUM
cana-5829	69	63	.	.	PUNCT
cana-5829	70	1	yager	yager	PROPN
cana-5829	70	2	,	,	PUNCT
cana-5829	70	3	r.	r.	PROPN
cana-5829	70	4	r[41	r[41	PROPN
cana-5829	70	5	]	]	PUNCT
cana-5829	70	6	,	,	PUNCT
cana-5829	70	7	discussed	discuss	VERB
cana-5829	70	8	“	"	PUNCT
cana-5829	70	9	some	some	DET
cana-5829	70	10	aspects	aspect	NOUN
cana-5829	70	11	of	of	ADP
cana-5829	70	12	intuitionistic	intuitionistic	ADJ
cana-5829	70	13	fuzzy	fuzzy	ADJ
cana-5829	70	14	sets”,in	sets”,in	NOUN
cana-5829	70	15	this	this	DET
cana-5829	70	16	year	year	NOUN
cana-5829	70	17	2009	2009	NUM
cana-5829	70	18	.	.	PUNCT
cana-5829	71	1	yung	yung	NOUN
cana-5829	71	2	-	-	PUNCT
cana-5829	71	3	yih	yih	NOUN
cana-5829	71	4	lur[42	lur[42	PROPN
cana-5829	71	5	]	]	PUNCT
cana-5829	71	6	,	,	PUNCT
cana-5829	71	7	discussed	discuss	VERB
cana-5829	71	8	“	"	PUNCT
cana-5829	71	9	on	on	ADP
cana-5829	71	10	infinite	infinite	ADJ
cana-5829	71	11	products	product	NOUN
cana-5829	71	12	of	of	ADP
cana-5829	71	13	fuzzy	fuzzy	ADJ
cana-5829	71	14	matrices”in	matrices”in	NOUN
cana-5829	71	15	this	this	DET
cana-5829	71	16	year	year	NOUN
cana-5829	71	17	2001.zhou	2001.zhou	NUM
cana-5829	71	18	,	,	PUNCT
cana-5829	71	19	x.	x.	PUNCT
cana-5829	72	1	g[43	g[43	PROPN
cana-5829	72	2	]	]	PUNCT
cana-5829	72	3	,	,	PUNCT
cana-5829	72	4	discussed	discuss	VERB
cana-5829	72	5	“	"	PUNCT
cana-5829	72	6	study	study	NOUN
cana-5829	72	7	on	on	ADP
cana-5829	72	8	bond	bond	NOUN
cana-5829	72	9	selection	selection	NOUN
cana-5829	72	10	under	under	ADP
cana-5829	72	11	intuitionistic	intuitionistic	ADJ
cana-5829	72	12	fuzzy	fuzzy	ADJ
cana-5829	72	13	conditions”in	conditions”in	PROPN
cana-5829	72	14	this	this	DET
cana-5829	72	15	year	year	NOUN
cana-5829	72	16	2018.zhang	2018.zhang	NUM
cana-5829	72	17	,	,	PUNCT
cana-5829	72	18	f.	f.	PROPN
cana-5829	72	19	w[44	w[44	PROPN
cana-5829	72	20	]	]	PUNCT
cana-5829	72	21	,	,	PUNCT
cana-5829	72	22	discussed	discuss	VERB
cana-5829	72	23	“	"	PUNCT
cana-5829	72	24	generalized	generalize	VERB
cana-5829	72	25	fuzzy	fuzzy	ADJ
cana-5829	72	26	additive	additive	ADJ
cana-5829	72	27	operators	operator	NOUN
cana-5829	72	28	on	on	ADP
cana-5829	72	29	intuitionistic	intuitionistic	ADJ
cana-5829	72	30	fuzzy	fuzzy	ADJ
cana-5829	72	31	sets	set	NOUN
cana-5829	72	32	and	and	CCONJ
cana-5829	72	33	interval	interval	NOUN
cana-5829	72	34	-	-	PUNCT
cana-5829	72	35	valued	value	VERB
cana-5829	72	36	intuitionistic	intuitionistic	ADJ
cana-5829	72	37	fuzzy	fuzzy	ADJ
cana-5829	72	38	sets	set	NOUN
cana-5829	72	39	and	and	CCONJ
cana-5829	72	40	their	their	PRON
cana-5829	72	41	application”in	application”in	NOUN
cana-5829	72	42	this	this	DET
cana-5829	72	43	year	year	NOUN
cana-5829	72	44	2019.zadeh	2019.zadeh	NUM
cana-5829	72	45	,	,	PUNCT
cana-5829	72	46	l.a	l.a	PROPN
cana-5829	73	1	[	[	X
cana-5829	73	2	45	45	NUM
cana-5829	73	3	]	]	PUNCT
cana-5829	73	4	,	,	PUNCT
cana-5829	73	5	discussed	discuss	VERB
cana-5829	73	6	“	"	PUNCT
cana-5829	73	7	fuzzy	fuzzy	ADJ
cana-5829	73	8	sets”in	sets”in	NOUN
cana-5829	73	9	this	this	DET
cana-5829	73	10	year	year	NOUN
cana-5829	73	11	1965.l.a.zadeh[46]discussed	1965.l.a.zadeh[46]discusse	VERB
cana-5829	73	12	fuzzysets	fuzzyset	NOUN
cana-5829	73	13	,	,	PUNCT
cana-5829	73	14	information	information	NOUN
cana-5829	73	15	and	and	CCONJ
cana-5829	73	16	control	control	NOUN
cana-5829	73	17	in	in	ADP
cana-5829	73	18	this	this	DET
cana-5829	73	19	year	year	NOUN
cana-5829	73	20	1965	1965	NUM
cana-5829	73	21	.	.	PUNCT
cana-5829	74	1	objective	objective	NOUN
cana-5829	74	2	:	:	PUNCT
cana-5829	74	3	the	the	DET
cana-5829	74	4	objective	objective	NOUN
cana-5829	74	5	of	of	ADP
cana-5829	74	6	normalization	normalization	NOUN
cana-5829	74	7	of	of	ADP
cana-5829	74	8	intuitionistic	intuitionistic	ADJ
cana-5829	74	9	fuzzy	fuzzy	ADJ
cana-5829	74	10	matrices	matrix	NOUN
cana-5829	74	11	(	(	PUNCT
cana-5829	74	12	ifms	ifms	NOUN
cana-5829	74	13	)	)	PUNCT
cana-5829	74	14	is	be	AUX
cana-5829	74	15	to	to	PART
cana-5829	74	16	transform	transform	VERB
cana-5829	74	17	the	the	DET
cana-5829	74	18	matrix	matrix	NOUN
cana-5829	74	19	elements	element	NOUN
cana-5829	74	20	,	,	PUNCT
cana-5829	74	21	which	which	PRON
cana-5829	74	22	represent	represent	VERB
cana-5829	74	23	uncertain	uncertain	ADJ
cana-5829	74	24	or	or	CCONJ
cana-5829	74	25	vague	vague	ADJ
cana-5829	74	26	information	information	NOUN
cana-5829	74	27	,	,	PUNCT
cana-5829	74	28	into	into	ADP
cana-5829	74	29	a	a	DET
cana-5829	74	30	standardized	standardized	ADJ
cana-5829	74	31	form	form	NOUN
cana-5829	74	32	while	while	SCONJ
cana-5829	74	33	preserving	preserve	VERB
cana-5829	74	34	the	the	DET
cana-5829	74	35	relationships	relationship	NOUN
cana-5829	74	36	and	and	CCONJ
cana-5829	74	37	inherent	inherent	ADJ
cana-5829	74	38	structure	structure	NOUN
cana-5829	74	39	of	of	ADP
cana-5829	74	40	the	the	DET
cana-5829	74	41	fuzzy	fuzzy	ADJ
cana-5829	74	42	data	datum	NOUN
cana-5829	74	43	.	.	PUNCT
cana-5829	75	1	the	the	DET
cana-5829	75	2	purpose	purpose	NOUN
cana-5829	75	3	of	of	ADP
cana-5829	75	4	normalization	normalization	NOUN
cana-5829	75	5	is	be	AUX
cana-5829	75	6	to	to	PART
cana-5829	75	7	ensure	ensure	VERB
cana-5829	75	8	that	that	SCONJ
cana-5829	75	9	the	the	DET
cana-5829	75	10	elements	element	NOUN
cana-5829	75	11	in	in	ADP
cana-5829	75	12	the	the	DET
cana-5829	75	13	matrix	matrix	NOUN
cana-5829	75	14	are	be	AUX
cana-5829	75	15	comparable	comparable	ADJ
cana-5829	75	16	and	and	CCONJ
cana-5829	75	17	consistent	consistent	ADJ
cana-5829	75	18	,	,	PUNCT
cana-5829	75	19	allowing	allow	VERB
cana-5829	75	20	for	for	ADP
cana-5829	75	21	more	more	ADV
cana-5829	75	22	accurate	accurate	ADJ
cana-5829	75	23	and	and	CCONJ
cana-5829	75	24	reliable	reliable	ADJ
cana-5829	75	25	decision	decision	NOUN
cana-5829	75	26	-	-	PUNCT
cana-5829	75	27	making	making	NOUN
cana-5829	75	28	or	or	CCONJ
cana-5829	75	29	analysis	analysis	NOUN
cana-5829	75	30	2.preliminary	2.preliminary	NUM
cana-5829	75	31	2.1definition	2.1definition	NUM
cana-5829	75	32	of	of	ADP
cana-5829	75	33	fuzzy	fuzzy	ADJ
cana-5829	75	34	:	:	PUNCT
cana-5829	75	35	fuzzy	fuzzy	ADJ
cana-5829	75	36	refers	refer	VERB
cana-5829	75	37	to	to	ADP
cana-5829	75	38	something	something	PRON
cana-5829	75	39	that	that	PRON
cana-5829	75	40	is	be	AUX
cana-5829	75	41	unclear	unclear	ADJ
cana-5829	75	42	,	,	PUNCT
cana-5829	75	43	imprecise	imprecise	ADV
cana-5829	75	44	,	,	PUNCT
cana-5829	75	45	or	or	CCONJ
cana-5829	75	46	ambiguous	ambiguous	ADJ
cana-5829	75	47	.	.	PUNCT
cana-5829	76	1	it	it	PRON
cana-5829	76	2	often	often	ADV
cana-5829	76	3	describes	describe	VERB
cana-5829	76	4	situations	situation	NOUN
cana-5829	76	5	where	where	SCONJ
cana-5829	76	6	boundaries	boundary	NOUN
cana-5829	76	7	or	or	CCONJ
cana-5829	76	8	definitions	definition	NOUN
cana-5829	76	9	are	be	AUX
cana-5829	76	10	not	not	PART
cana-5829	76	11	strictly	strictly	ADV
cana-5829	76	12	defined	define	VERB
cana-5829	76	13	,	,	PUNCT
cana-5829	76	14	leading	lead	VERB
cana-5829	76	15	to	to	ADP
cana-5829	76	16	a	a	DET
cana-5829	76	17	certain	certain	ADJ
cana-5829	76	18	level	level	NOUN
cana-5829	76	19	of	of	ADP
cana-5829	76	20	vagueness	vagueness	NOUN
cana-5829	76	21	.	.	PUNCT
cana-5829	77	1	in	in	ADP
cana-5829	77	2	various	various	ADJ
cana-5829	77	3	fields	field	NOUN
cana-5829	77	4	,	,	PUNCT
cana-5829	77	5	"	"	PUNCT
cana-5829	77	6	fuzzy	fuzzy	ADJ
cana-5829	77	7	"	"	PUNCT
cana-5829	77	8	can	can	AUX
cana-5829	77	9	have	have	VERB
cana-5829	77	10	different	different	ADJ
cana-5829	77	11	connotations	connotation	NOUN
cana-5829	77	12	,	,	PUNCT
cana-5829	77	13	but	but	CCONJ
cana-5829	77	14	the	the	DET
cana-5829	77	15	core	core	NOUN
cana-5829	77	16	idea	idea	NOUN
cana-5829	77	17	revolves	revolve	VERB
cana-5829	77	18	around	around	ADP
cana-5829	77	19	uncertainty	uncertainty	NOUN
cana-5829	77	20	or	or	CCONJ
cana-5829	77	21	a	a	DET
cana-5829	77	22	lack	lack	NOUN
cana-5829	77	23	of	of	ADP
cana-5829	77	24	exact	exact	ADJ
cana-5829	77	25	precision	precision	NOUN
cana-5829	77	26	.	.	PUNCT
cana-5829	78	1	1.physical/visual	1.physical/visual	NUM
cana-5829	78	2	context	context	NOUN
cana-5829	78	3	:	:	PUNCT
cana-5829	78	4	when	when	SCONJ
cana-5829	78	5	something	something	PRON
cana-5829	78	6	is	be	AUX
cana-5829	78	7	blurry	blurry	ADJ
cana-5829	78	8	,	,	PUNCT
cana-5829	78	9	soft	soft	ADJ
cana-5829	78	10	,	,	PUNCT
cana-5829	78	11	or	or	CCONJ
cana-5829	78	12	lacking	lack	VERB
cana-5829	78	13	sharp	sharp	ADJ
cana-5829	78	14	details	detail	NOUN
cana-5829	78	15	,	,	PUNCT
cana-5829	78	16	it	it	PRON
cana-5829	78	17	is	be	AUX
cana-5829	78	18	often	often	ADV
cana-5829	78	19	described	describe	VERB
cana-5829	78	20	as	as	ADP
cana-5829	78	21	fuzzy	fuzzy	ADJ
cana-5829	78	22	.	.	PUNCT
cana-5829	79	1	for	for	ADP
cana-5829	79	2	example	example	NOUN
cana-5829	79	3	,	,	PUNCT
cana-5829	79	4	"	"	PUNCT
cana-5829	79	5	the	the	DET
cana-5829	79	6	picture	picture	NOUN
cana-5829	79	7	is	be	AUX
cana-5829	79	8	fuzzy	fuzzy	ADJ
cana-5829	79	9	"	"	PUNCT
cana-5829	79	10	means	mean	VERB
cana-5829	79	11	the	the	DET
cana-5829	79	12	image	image	NOUN
cana-5829	79	13	is	be	AUX
cana-5829	79	14	n't	not	PART
cana-5829	79	15	clear	clear	ADJ
cana-5829	79	16	.	.	PUNCT
cana-5829	80	1	communications	communication	NOUN
cana-5829	80	2	on	on	ADP
cana-5829	80	3	applied	apply	VERB
cana-5829	80	4	nonlinear	nonlinear	ADJ
cana-5829	80	5	analysis	analysis	NOUN
cana-5829	80	6	issn	issn	NOUN
cana-5829	80	7	:	:	PUNCT
cana-5829	80	8	1074	1074	NUM
cana-5829	80	9	-	-	PUNCT
cana-5829	80	10	133x	133x	NUM
cana-5829	80	11	vol	vol	VERB
cana-5829	80	12	32	32	NUM
cana-5829	80	13	no	no	NOUN
cana-5829	80	14	.	.	PUNCT
cana-5829	81	1	10s	10	NOUN
cana-5829	81	2	(	(	PUNCT
cana-5829	81	3	2025	2025	NUM
cana-5829	81	4	)	)	PUNCT
cana-5829	81	5	2925	2925	NUM
cana-5829	81	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5829	81	7	2.metaphorical/conceptual	2.metaphorical/conceptual	NUM
cana-5829	81	8	context	context	NOUN
cana-5829	81	9	:	:	PUNCT
cana-5829	81	10	it	it	PRON
cana-5829	81	11	can	can	AUX
cana-5829	81	12	refer	refer	VERB
cana-5829	81	13	to	to	ADP
cana-5829	81	14	something	something	PRON
cana-5829	81	15	vague	vague	ADJ
cana-5829	81	16	,	,	PUNCT
cana-5829	81	17	ambiguous	ambiguous	ADJ
cana-5829	81	18	,	,	PUNCT
cana-5829	81	19	or	or	CCONJ
cana-5829	81	20	hard	hard	ADJ
cana-5829	81	21	to	to	PART
cana-5829	81	22	understand	understand	VERB
cana-5829	81	23	.	.	PUNCT
cana-5829	82	1	for	for	ADP
cana-5829	82	2	example	example	NOUN
cana-5829	82	3	,	,	PUNCT
cana-5829	82	4	"	"	PUNCT
cana-5829	82	5	his	his	PRON
cana-5829	82	6	explanation	explanation	NOUN
cana-5829	82	7	was	be	AUX
cana-5829	82	8	fuzzy	fuzzy	ADJ
cana-5829	82	9	"	"	PUNCT
cana-5829	82	10	means	mean	VERB
cana-5829	82	11	the	the	DET
cana-5829	82	12	explanation	explanation	NOUN
cana-5829	82	13	was	be	AUX
cana-5829	82	14	unclear	unclear	ADJ
cana-5829	82	15	or	or	CCONJ
cana-5829	82	16	imprecise	imprecise	NOUN
cana-5829	82	17	.	.	PUNCT
cana-5829	83	1	a	a	DET
cana-5829	83	2	fuzzy	fuzzy	ADJ
cana-5829	83	3	set	set	NOUN
cana-5829	83	4	can	can	AUX
cana-5829	83	5	be	be	AUX
cana-5829	83	6	represented	represent	VERB
cana-5829	83	7	in	in	ADP
cana-5829	83	8	a	a	DET
cana-5829	83	9	matrix	matrix	NOUN
cana-5829	83	10	form	form	NOUN
cana-5829	83	11	,	,	PUNCT
cana-5829	83	12	where	where	SCONJ
cana-5829	83	13	the	the	DET
cana-5829	83	14	membership	membership	NOUN
cana-5829	83	15	values	value	NOUN
cana-5829	83	16	of	of	ADP
cana-5829	83	17	elements	element	NOUN
cana-5829	83	18	are	be	AUX
cana-5829	83	19	arranged	arrange	VERB
cana-5829	83	20	in	in	ADP
cana-5829	83	21	rows	row	NOUN
cana-5829	83	22	and	and	CCONJ
cana-5829	83	23	columns	column	NOUN
cana-5829	83	24	.	.	PUNCT
cana-5829	84	1	each	each	DET
cana-5829	84	2	element	element	NOUN
cana-5829	84	3	in	in	ADP
cana-5829	84	4	the	the	DET
cana-5829	84	5	matrix	matrix	NOUN
cana-5829	84	6	corresponds	correspond	VERB
cana-5829	84	7	to	to	ADP
cana-5829	84	8	a	a	DET
cana-5829	84	9	specific	specific	ADJ
cana-5829	84	10	item	item	NOUN
cana-5829	84	11	,	,	PUNCT
cana-5829	84	12	and	and	CCONJ
cana-5829	84	13	the	the	DET
cana-5829	84	14	values	value	NOUN
cana-5829	84	15	in	in	ADP
cana-5829	84	16	the	the	DET
cana-5829	84	17	matrix	matrix	NOUN
cana-5829	84	18	represent	represent	VERB
cana-5829	84	19	the	the	DET
cana-5829	84	20	degree	degree	NOUN
cana-5829	84	21	of	of	ADP
cana-5829	84	22	membership	membership	NOUN
cana-5829	84	23	of	of	ADP
cana-5829	84	24	that	that	DET
cana-5829	84	25	item	item	NOUN
cana-5829	84	26	in	in	ADP
cana-5829	84	27	the	the	DET
cana-5829	84	28	fuzzy	fuzzy	ADJ
cana-5829	84	29	set	set	NOUN
cana-5829	84	30	.	.	PUNCT
cana-5829	85	1	2.2	2.2	NUM
cana-5829	85	2	examples	example	NOUN
cana-5829	85	3	2.2.1	2.2.1	NUM
cana-5829	85	4	.	.	PUNCT
cana-5829	85	5	temperature	temperature	NOUN
cana-5829	85	6	(	(	PUNCT
cana-5829	85	7	hot	hot	ADJ
cana-5829	85	8	vs.	vs.	ADP
cana-5829	85	9	cold	cold	ADJ
cana-5829	85	10	):	):	PUNCT
cana-5829	85	11	set	set	ADJ
cana-5829	85	12	description	description	NOUN
cana-5829	85	13	:	:	PUNCT
cana-5829	85	14	we	we	PRON
cana-5829	85	15	can	can	AUX
cana-5829	85	16	define	define	VERB
cana-5829	85	17	a	a	DET
cana-5829	85	18	fuzzy	fuzzy	ADJ
cana-5829	85	19	set	set	NOUN
cana-5829	85	20	for	for	ADP
cana-5829	85	21	temperature	temperature	NOUN
cana-5829	85	22	,	,	PUNCT
cana-5829	85	23	where	where	SCONJ
cana-5829	85	24	the	the	DET
cana-5829	85	25	degree	degree	NOUN
cana-5829	85	26	of	of	ADP
cana-5829	85	27	membership	membership	NOUN
cana-5829	85	28	represents	represent	VERB
cana-5829	85	29	how	how	SCONJ
cana-5829	85	30	hot	hot	ADJ
cana-5829	85	31	or	or	CCONJ
cana-5829	85	32	cold	cold	ADJ
cana-5829	85	33	a	a	DET
cana-5829	85	34	temperature	temperature	NOUN
cana-5829	85	35	is	be	AUX
cana-5829	85	36	,	,	PUNCT
cana-5829	85	37	example	example	NOUN
cana-5829	85	38	:	:	PUNCT
cana-5829	85	39	consider	consider	VERB
cana-5829	85	40	the	the	DET
cana-5829	85	41	fuzzy	fuzzy	ADJ
cana-5829	85	42	set	set	NOUN
cana-5829	85	43	"	"	PUNCT
cana-5829	85	44	hot	hot	ADJ
cana-5829	85	45	temperatures	temperature	NOUN
cana-5829	85	46	"	"	PUNCT
cana-5829	85	47	where	where	SCONJ
cana-5829	85	48	:	:	PUNCT
cana-5829	85	49	0	0	NUM
cana-5829	85	50	°	°	ADP
cana-5829	85	51	c	c	NOUN
cana-5829	85	52	→	→	SYM
cana-5829	85	53	membership	membership	NOUN
cana-5829	85	54	degree	degree	NOUN
cana-5829	85	55	of	of	ADP
cana-5829	85	56	0	0	NUM
cana-5829	85	57	(	(	PUNCT
cana-5829	85	58	completely	completely	ADV
cana-5829	85	59	cold	cold	ADJ
cana-5829	85	60	)	)	PUNCT
cana-5829	85	61	20	20	NUM
cana-5829	86	1	°	°	NUM
cana-5829	86	2	c	c	NOUN
cana-5829	86	3	→	→	SYM
cana-5829	86	4	membership	membership	NOUN
cana-5829	86	5	degree	degree	NOUN
cana-5829	86	6	of	of	ADP
cana-5829	86	7	0.2	0.2	NUM
cana-5829	86	8	(	(	PUNCT
cana-5829	86	9	slightly	slightly	ADV
cana-5829	86	10	hot	hot	ADJ
cana-5829	86	11	)	)	PUNCT
cana-5829	86	12	30	30	NUM
cana-5829	86	13	°	°	NUM
cana-5829	86	14	c	c	NOUN
cana-5829	86	15	→	→	SYM
cana-5829	86	16	membership	membership	NOUN
cana-5829	86	17	degree	degree	NOUN
cana-5829	86	18	of	of	ADP
cana-5829	86	19	0.5	0.5	NUM
cana-5829	86	20	(	(	PUNCT
cana-5829	86	21	moderately	moderately	ADV
cana-5829	86	22	hot	hot	ADJ
cana-5829	86	23	)	)	PUNCT
cana-5829	86	24	40	40	NUM
cana-5829	87	1	°	°	NUM
cana-5829	87	2	c	c	NOUN
cana-5829	87	3	→	→	SYM
cana-5829	87	4	membership	membership	NOUN
cana-5829	87	5	degree	degree	NOUN
cana-5829	87	6	of	of	ADP
cana-5829	87	7	0.8	0.8	NUM
cana-5829	87	8	(	(	PUNCT
cana-5829	87	9	very	very	ADV
cana-5829	87	10	hot	hot	ADJ
cana-5829	87	11	)	)	PUNCT
cana-5829	88	1	50	50	NUM
cana-5829	88	2	°	°	ADP
cana-5829	88	3	c	c	NOUN
cana-5829	88	4	→	→	SYM
cana-5829	88	5	membership	membership	NOUN
cana-5829	88	6	degree	degree	NOUN
cana-5829	88	7	of	of	ADP
cana-5829	88	8	1	1	NUM
cana-5829	88	9	(	(	PUNCT
cana-5829	88	10	completely	completely	ADV
cana-5829	88	11	hot	hot	ADJ
cana-5829	88	12	)	)	PUNCT
cana-5829	88	13	2.2.2	2.2.2	NUM
cana-5829	88	14	.	.	PUNCT
cana-5829	89	1	height	height	NOUN
cana-5829	89	2	(	(	PUNCT
cana-5829	89	3	tall	tall	ADJ
cana-5829	89	4	vs.	vs.	ADP
cana-5829	89	5	short	short	ADJ
cana-5829	89	6	):	):	PUNCT
cana-5829	89	7	set	set	ADJ
cana-5829	89	8	description	description	NOUN
cana-5829	89	9	:	:	PUNCT
cana-5829	89	10	a	a	DET
cana-5829	89	11	fuzzy	fuzzy	ADJ
cana-5829	89	12	set	set	NOUN
cana-5829	89	13	can	can	AUX
cana-5829	89	14	be	be	AUX
cana-5829	89	15	defined	define	VERB
cana-5829	89	16	for	for	ADP
cana-5829	89	17	the	the	DET
cana-5829	89	18	height	height	NOUN
cana-5829	89	19	of	of	ADP
cana-5829	89	20	a	a	DET
cana-5829	89	21	person	person	NOUN
cana-5829	89	22	,	,	PUNCT
cana-5829	89	23	with	with	ADP
cana-5829	89	24	the	the	DET
cana-5829	89	25	degree	degree	NOUN
cana-5829	89	26	of	of	ADP
cana-5829	89	27	membership	membership	NOUN
cana-5829	89	28	indicating	indicate	VERB
cana-5829	89	29	how	how	SCONJ
cana-5829	89	30	tall	tall	ADJ
cana-5829	89	31	someone	someone	PRON
cana-5829	89	32	is	be	AUX
cana-5829	89	33	,	,	PUNCT
cana-5829	89	34	example	example	NOUN
cana-5829	89	35	:	:	PUNCT
cana-5829	89	36	consider	consider	VERB
cana-5829	89	37	the	the	DET
cana-5829	89	38	fuzzy	fuzzy	ADJ
cana-5829	89	39	set	set	NOUN
cana-5829	89	40	"	"	PUNCT
cana-5829	89	41	tall	tall	ADJ
cana-5829	89	42	people	people	NOUN
cana-5829	89	43	"	"	PUNCT
cana-5829	89	44	where	where	SCONJ
cana-5829	89	45	150	150	NUM
cana-5829	89	46	cm	cm	NOUN
cana-5829	89	47	→	→	SYM
cana-5829	89	48	membership	membership	NOUN
cana-5829	89	49	degree	degree	NOUN
cana-5829	89	50	of	of	ADP
cana-5829	89	51	0.2	0.2	NUM
cana-5829	89	52	(	(	PUNCT
cana-5829	89	53	slightly	slightly	ADV
cana-5829	89	54	tall	tall	ADJ
cana-5829	89	55	)	)	PUNCT
cana-5829	89	56	160	160	NUM
cana-5829	89	57	cm	cm	NOUN
cana-5829	89	58	→	→	SYM
cana-5829	89	59	membership	membership	NOUN
cana-5829	89	60	degree	degree	NOUN
cana-5829	89	61	of	of	ADP
cana-5829	89	62	0.4	0.4	NUM
cana-5829	89	63	(	(	PUNCT
cana-5829	89	64	moderately	moderately	ADV
cana-5829	89	65	tall	tall	ADJ
cana-5829	89	66	)	)	PUNCT
cana-5829	89	67	170	170	NUM
cana-5829	89	68	cm	cm	NOUN
cana-5829	89	69	→	→	SYM
cana-5829	89	70	membership	membership	NOUN
cana-5829	89	71	degree	degree	NOUN
cana-5829	89	72	of	of	ADP
cana-5829	89	73	0.7	0.7	NUM
cana-5829	89	74	(	(	PUNCT
cana-5829	89	75	fairly	fairly	ADV
cana-5829	89	76	tall	tall	ADJ
cana-5829	89	77	)	)	PUNCT
cana-5829	89	78	180	180	NUM
cana-5829	89	79	cm	cm	NOUN
cana-5829	89	80	→	→	SYM
cana-5829	89	81	membership	membership	NOUN
cana-5829	89	82	degree	degree	NOUN
cana-5829	89	83	of	of	ADP
cana-5829	89	84	1	1	NUM
cana-5829	89	85	(	(	PUNCT
cana-5829	89	86	completely	completely	ADV
cana-5829	89	87	tall	tall	ADJ
cana-5829	89	88	)	)	PUNCT
cana-5829	89	89	2.3	2.3	NUM
cana-5829	89	90	application	application	NOUN
cana-5829	89	91	of	of	ADP
cana-5829	89	92	fuzzy	fuzzy	ADJ
cana-5829	89	93	2.3.1	2.3.1	NUM
cana-5829	89	94	.	.	PUNCT
cana-5829	90	1	in	in	ADP
cana-5829	90	2	mathematics	mathematic	NOUN
cana-5829	90	3	and	and	CCONJ
cana-5829	90	4	logic	logic	NOUN
cana-5829	90	5	:	:	PUNCT
cana-5829	90	6	in	in	ADP
cana-5829	90	7	fuzzy	fuzzy	ADJ
cana-5829	90	8	logic	logic	NOUN
cana-5829	90	9	,	,	PUNCT
cana-5829	90	10	values	value	NOUN
cana-5829	90	11	are	be	AUX
cana-5829	90	12	not	not	PART
cana-5829	90	13	limited	limit	VERB
cana-5829	90	14	to	to	ADP
cana-5829	90	15	just	just	ADV
cana-5829	90	16	true	true	ADJ
cana-5829	90	17	or	or	CCONJ
cana-5829	90	18	false	false	ADJ
cana-5829	90	19	(	(	PUNCT
cana-5829	90	20	1	1	NUM
cana-5829	90	21	or	or	CCONJ
cana-5829	90	22	0	0	NUM
cana-5829	90	23	)	)	PUNCT
cana-5829	90	24	,	,	PUNCT
cana-5829	90	25	but	but	CCONJ
cana-5829	90	26	can	can	AUX
cana-5829	90	27	take	take	VERB
cana-5829	90	28	on	on	ADP
cana-5829	90	29	any	any	DET
cana-5829	90	30	value	value	NOUN
cana-5829	90	31	between	between	ADP
cana-5829	90	32	0	0	NUM
cana-5829	90	33	and	and	CCONJ
cana-5829	90	34	1	1	NUM
cana-5829	90	35	,	,	PUNCT
cana-5829	90	36	reflecting	reflect	VERB
cana-5829	90	37	degrees	degree	NOUN
cana-5829	90	38	of	of	ADP
cana-5829	90	39	truth	truth	NOUN
cana-5829	90	40	.	.	PUNCT
cana-5829	91	1	for	for	ADP
cana-5829	91	2	example	example	NOUN
cana-5829	91	3	,	,	PUNCT
cana-5829	91	4	instead	instead	ADV
cana-5829	91	5	of	of	ADP
cana-5829	91	6	saying	say	VERB
cana-5829	91	7	"	"	PUNCT
cana-5829	91	8	a	a	DET
cana-5829	91	9	person	person	NOUN
cana-5829	91	10	is	be	AUX
cana-5829	91	11	tall	tall	ADJ
cana-5829	91	12	"	"	PUNCT
cana-5829	91	13	as	as	SCONJ
cana-5829	91	14	either	either	CCONJ
cana-5829	91	15	true	true	ADJ
cana-5829	91	16	or	or	CCONJ
cana-5829	91	17	false	false	ADJ
cana-5829	91	18	,	,	PUNCT
cana-5829	91	19	fuzzy	fuzzy	ADJ
cana-5829	91	20	logic	logic	NOUN
cana-5829	91	21	might	might	AUX
cana-5829	91	22	say	say	VERB
cana-5829	91	23	they	they	PRON
cana-5829	91	24	are	be	AUX
cana-5829	91	25	0.7	0.7	NUM
cana-5829	91	26	tall	tall	ADJ
cana-5829	91	27	(	(	PUNCT
cana-5829	91	28	indicating	indicate	VERB
cana-5829	91	29	they	they	PRON
cana-5829	91	30	are	be	AUX
cana-5829	91	31	somewhat	somewhat	ADV
cana-5829	91	32	tall	tall	ADJ
cana-5829	91	33	but	but	CCONJ
cana-5829	91	34	not	not	PART
cana-5829	91	35	extremely	extremely	ADV
cana-5829	91	36	so	so	ADV
cana-5829	91	37	)	)	PUNCT
cana-5829	91	38	.	.	PUNCT
cana-5829	92	1	2.3.2	2.3.2	NUM
cana-5829	92	2	in	in	ADP
cana-5829	92	3	computing	compute	VERB
cana-5829	92	4	:	:	PUNCT
cana-5829	92	5	a	a	DET
cana-5829	92	6	fuzzy	fuzzy	ADJ
cana-5829	92	7	search	search	NOUN
cana-5829	92	8	allows	allow	VERB
cana-5829	92	9	for	for	ADP
cana-5829	92	10	approximate	approximate	ADJ
cana-5829	92	11	matches	match	NOUN
cana-5829	92	12	rather	rather	ADV
cana-5829	92	13	than	than	ADP
cana-5829	92	14	exact	exact	ADJ
cana-5829	92	15	ones	one	NOUN
cana-5829	92	16	.	.	PUNCT
cana-5829	93	1	for	for	ADP
cana-5829	93	2	example	example	NOUN
cana-5829	93	3	,	,	PUNCT
cana-5829	93	4	searching	search	VERB
cana-5829	93	5	for	for	ADP
cana-5829	93	6	"	"	PUNCT
cana-5829	93	7	appl	appl	NOUN
cana-5829	93	8	"	"	PUNCT
cana-5829	93	9	might	might	AUX
cana-5829	93	10	also	also	ADV
cana-5829	93	11	return	return	VERB
cana-5829	93	12	"	"	PUNCT
cana-5829	93	13	apple	apple	NOUN
cana-5829	93	14	"	"	PUNCT
cana-5829	93	15	or	or	CCONJ
cana-5829	93	16	"	"	PUNCT
cana-5829	93	17	applause	applause	NOUN
cana-5829	93	18	"	"	PUNCT
cana-5829	93	19	because	because	SCONJ
cana-5829	93	20	the	the	DET
cana-5829	93	21	system	system	NOUN
cana-5829	93	22	is	be	AUX
cana-5829	93	23	designed	design	VERB
cana-5829	93	24	to	to	PART
cana-5829	93	25	tolerate	tolerate	VERB
cana-5829	93	26	small	small	ADJ
cana-5829	93	27	errors	error	NOUN
cana-5829	93	28	in	in	ADP
cana-5829	93	29	spelling	spelling	NOUN
cana-5829	93	30	or	or	CCONJ
cana-5829	93	31	typing	typing	NOUN
cana-5829	93	32	.	.	PUNCT
cana-5829	94	1	2.3.3	2.3.3	X
cana-5829	94	2	.	.	PUNCT
cana-5829	94	3	computer	computer	NOUN
cana-5829	94	4	science	science	NOUN
cana-5829	94	5	and	and	CCONJ
cana-5829	94	6	mathematics	mathematic	NOUN
cana-5829	94	7	:	:	PUNCT
cana-5829	94	8	in	in	ADP
cana-5829	94	9	traditional	traditional	ADJ
cana-5829	94	10	binary	binary	ADJ
cana-5829	94	11	logic	logic	NOUN
cana-5829	94	12	,	,	PUNCT
cana-5829	94	13	something	something	PRON
cana-5829	94	14	is	be	AUX
cana-5829	94	15	either	either	CCONJ
cana-5829	94	16	true	true	ADJ
cana-5829	94	17	or	or	CCONJ
cana-5829	94	18	false	false	ADJ
cana-5829	94	19	(	(	PUNCT
cana-5829	94	20	1	1	NUM
cana-5829	94	21	or	or	CCONJ
cana-5829	94	22	0	0	NUM
cana-5829	94	23	)	)	PUNCT
cana-5829	94	24	,	,	PUNCT
cana-5829	94	25	but	but	CCONJ
cana-5829	94	26	in	in	ADP
cana-5829	94	27	fuzzy	fuzzy	ADJ
cana-5829	94	28	logic	logic	NOUN
cana-5829	94	29	,	,	PUNCT
cana-5829	94	30	truth	truth	NOUN
cana-5829	94	31	values	value	NOUN
cana-5829	94	32	can	can	AUX
cana-5829	94	33	be	be	AUX
cana-5829	94	34	any	any	DET
cana-5829	94	35	number	number	NOUN
cana-5829	94	36	between	between	ADP
cana-5829	94	37	0	0	NUM
cana-5829	94	38	and	and	CCONJ
cana-5829	94	39	1	1	NUM
cana-5829	94	40	,	,	PUNCT
cana-5829	94	41	representing	represent	VERB
cana-5829	94	42	degrees	degree	NOUN
cana-5829	94	43	of	of	ADP
cana-5829	94	44	truth	truth	NOUN
cana-5829	94	45	.	.	PUNCT
cana-5829	95	1	example	example	NOUN
cana-5829	95	2	:	:	PUNCT
cana-5829	95	3	a	a	DET
cana-5829	95	4	thermostat	thermostat	NOUN
cana-5829	95	5	that	that	PRON
cana-5829	95	6	adjusts	adjust	VERB
cana-5829	95	7	the	the	DET
cana-5829	95	8	temperature	temperature	NOUN
cana-5829	95	9	gradually	gradually	ADV
cana-5829	95	10	based	base	VERB
cana-5829	95	11	on	on	ADP
cana-5829	95	12	a	a	DET
cana-5829	95	13	range	range	NOUN
cana-5829	95	14	,	,	PUNCT
cana-5829	95	15	not	not	PART
cana-5829	95	16	just	just	ADV
cana-5829	95	17	switching	switch	VERB
cana-5829	95	18	between	between	ADP
cana-5829	95	19	"	"	PUNCT
cana-5829	95	20	on	on	ADP
cana-5829	95	21	"	"	PUNCT
cana-5829	95	22	and	and	CCONJ
cana-5829	95	23	"	"	PUNCT
cana-5829	95	24	off	off	ADP
cana-5829	95	25	.	.	PUNCT
cana-5829	95	26	"	"	PUNCT
cana-5829	96	1	if	if	SCONJ
cana-5829	96	2	the	the	DET
cana-5829	96	3	target	target	NOUN
cana-5829	96	4	temperature	temperature	NOUN
cana-5829	96	5	is	be	AUX
cana-5829	96	6	70	70	NUM
cana-5829	96	7	°	°	NOUN
cana-5829	96	8	f	f	NUM
cana-5829	96	9	,	,	PUNCT
cana-5829	96	10	and	and	CCONJ
cana-5829	96	11	the	the	DET
cana-5829	96	12	room	room	NOUN
cana-5829	96	13	temperature	temperature	NOUN
cana-5829	96	14	is	be	AUX
cana-5829	96	15	68	68	NUM
cana-5829	96	16	°	°	NOUN
cana-5829	96	17	f	f	NOUN
cana-5829	96	18	,	,	PUNCT
cana-5829	96	19	the	the	DET
cana-5829	96	20	thermostat	thermostat	NOUN
cana-5829	96	21	may	may	AUX
cana-5829	96	22	turn	turn	VERB
cana-5829	96	23	on	on	ADP
cana-5829	96	24	at	at	ADP
cana-5829	96	25	50	50	NUM
cana-5829	96	26	%	%	NOUN
cana-5829	96	27	power	power	NOUN
cana-5829	96	28	instead	instead	ADV
cana-5829	96	29	of	of	ADP
cana-5829	96	30	100	100	NUM
cana-5829	96	31	%	%	NOUN
cana-5829	96	32	.	.	PUNCT
cana-5829	97	1	2.3.4	2.3.4	X
cana-5829	97	2	.	.	PUNCT
cana-5829	97	3	technology	technology	NOUN
cana-5829	97	4	:	:	PUNCT
cana-5829	97	5	in	in	ADP
cana-5829	97	6	searching	search	VERB
cana-5829	97	7	algorithms	algorithm	NOUN
cana-5829	97	8	,	,	PUNCT
cana-5829	97	9	fuzzy	fuzzy	ADJ
cana-5829	97	10	search	search	NOUN
cana-5829	97	11	allows	allow	VERB
cana-5829	97	12	for	for	ADP
cana-5829	97	13	matching	match	VERB
cana-5829	97	14	terms	term	NOUN
cana-5829	97	15	that	that	PRON
cana-5829	97	16	are	be	AUX
cana-5829	97	17	similar	similar	ADJ
cana-5829	97	18	but	but	CCONJ
cana-5829	97	19	not	not	PART
cana-5829	97	20	identical	identical	ADJ
cana-5829	97	21	.	.	PUNCT
cana-5829	98	1	this	this	PRON
cana-5829	98	2	can	can	AUX
cana-5829	98	3	be	be	AUX
cana-5829	98	4	used	use	VERB
cana-5829	98	5	when	when	SCONJ
cana-5829	98	6	users	user	NOUN
cana-5829	98	7	make	make	VERB
cana-5829	98	8	spelling	spelling	NOUN
cana-5829	98	9	errors	error	NOUN
cana-5829	98	10	or	or	CCONJ
cana-5829	98	11	variations	variation	NOUN
cana-5829	98	12	.	.	PUNCT
cana-5829	99	1	example	example	NOUN
cana-5829	99	2	:	:	PUNCT
cana-5829	99	3	searching	search	VERB
cana-5829	99	4	for	for	ADP
cana-5829	99	5	"	"	PUNCT
cana-5829	99	6	apple	apple	NOUN
cana-5829	99	7	"	"	PUNCT
cana-5829	99	8	could	could	AUX
cana-5829	99	9	also	also	ADV
cana-5829	99	10	return	return	VERB
cana-5829	99	11	results	result	NOUN
cana-5829	99	12	for	for	ADP
cana-5829	99	13	"	"	PUNCT
cana-5829	99	14	apple	apple	NOUN
cana-5829	99	15	,	,	PUNCT
cana-5829	99	16	"	"	PUNCT
cana-5829	99	17	"	"	PUNCT
cana-5829	99	18	appl	appl	NOUN
cana-5829	99	19	,	,	PUNCT
cana-5829	99	20	"	"	PUNCT
cana-5829	99	21	or	or	CCONJ
cana-5829	99	22	"	"	PUNCT
cana-5829	99	23	apples	apple	NOUN
cana-5829	99	24	.	.	PUNCT
cana-5829	99	25	"	"	PUNCT
cana-5829	100	1	2.3.5	2.3.5	NUM
cana-5829	100	2	.	.	PUNCT
cana-5829	100	3	fuzzy	fuzzy	ADJ
cana-5829	100	4	concepts	concept	NOUN
cana-5829	100	5	(	(	PUNCT
cana-5829	100	6	philosophy	philosophy	NOUN
cana-5829	100	7	and	and	CCONJ
cana-5829	100	8	linguistics	linguistic	NOUN
cana-5829	100	9	):	):	PUNCT
cana-5829	100	10	a	a	DET
cana-5829	100	11	fuzzy	fuzzy	ADJ
cana-5829	100	12	concept	concept	NOUN
cana-5829	100	13	refers	refer	VERB
cana-5829	100	14	to	to	ADP
cana-5829	100	15	something	something	PRON
cana-5829	100	16	that	that	PRON
cana-5829	100	17	does	do	AUX
cana-5829	100	18	n’t	not	PART
cana-5829	100	19	have	have	VERB
cana-5829	100	20	clear	clear	ADJ
cana-5829	100	21	-	-	PUNCT
cana-5829	100	22	cut	cut	VERB
cana-5829	100	23	boundaries	boundary	NOUN
cana-5829	100	24	or	or	CCONJ
cana-5829	100	25	definitions	definition	NOUN
cana-5829	100	26	.	.	PUNCT
cana-5829	101	1	it	it	PRON
cana-5829	101	2	’s	’	VERB
cana-5829	101	3	often	often	ADV
cana-5829	101	4	subjective	subjective	ADJ
cana-5829	101	5	.	.	PUNCT
cana-5829	102	1	example	example	NOUN
cana-5829	102	2	:	:	PUNCT
cana-5829	102	3	the	the	DET
cana-5829	102	4	term	term	NOUN
cana-5829	102	5	"	"	PUNCT
cana-5829	102	6	tall	tall	ADJ
cana-5829	102	7	"	"	PUNCT
cana-5829	102	8	is	be	AUX
cana-5829	102	9	fuzzy	fuzzy	ADJ
cana-5829	102	10	communications	communication	NOUN
cana-5829	102	11	on	on	ADP
cana-5829	102	12	applied	apply	VERB
cana-5829	102	13	nonlinear	nonlinear	ADJ
cana-5829	102	14	analysis	analysis	NOUN
cana-5829	102	15	issn	issn	NOUN
cana-5829	102	16	:	:	PUNCT
cana-5829	102	17	1074	1074	NUM
cana-5829	102	18	-	-	PUNCT
cana-5829	102	19	133x	133x	NUM
cana-5829	102	20	vol	vol	VERB
cana-5829	102	21	32	32	NUM
cana-5829	102	22	no	no	NOUN
cana-5829	102	23	.	.	PUNCT
cana-5829	103	1	10s	10	NOUN
cana-5829	103	2	(	(	PUNCT
cana-5829	103	3	2025	2025	NUM
cana-5829	103	4	)	)	PUNCT
cana-5829	103	5	2926	2926	NUM
cana-5829	103	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5829	103	7	because	because	SCONJ
cana-5829	103	8	what	what	PRON
cana-5829	103	9	one	one	NUM
cana-5829	103	10	person	person	NOUN
cana-5829	103	11	considers	consider	VERB
cana-5829	103	12	tall	tall	ADJ
cana-5829	103	13	(	(	PUNCT
cana-5829	103	14	e.g.	e.g.	ADJ
cana-5829	103	15	,	,	PUNCT
cana-5829	103	16	6	6	NUM
cana-5829	103	17	feet	foot	NOUN
cana-5829	103	18	)	)	PUNCT
cana-5829	103	19	might	might	AUX
cana-5829	103	20	be	be	AUX
cana-5829	103	21	different	different	ADJ
cana-5829	103	22	from	from	ADP
cana-5829	103	23	another	another	DET
cana-5829	103	24	person	person	NOUN
cana-5829	103	25	’s	’s	PART
cana-5829	103	26	perception	perception	NOUN
cana-5829	103	27	(	(	PUNCT
cana-5829	103	28	e.g.	e.g.	ADV
cana-5829	103	29	,	,	PUNCT
cana-5829	103	30	5'10	5'10	NUM
cana-5829	103	31	"	"	PUNCT
cana-5829	103	32	)	)	PUNCT
cana-5829	103	33	.	.	PUNCT
cana-5829	104	1	2.3.6	2.3.6	NUM
cana-5829	104	2	.	.	PUNCT
cana-5829	104	3	fuzzy	fuzzy	ADJ
cana-5829	104	4	logic	logic	NOUN
cana-5829	104	5	in	in	ADP
cana-5829	104	6	everyday	everyday	ADJ
cana-5829	104	7	life	life	NOUN
cana-5829	104	8	:	:	PUNCT
cana-5829	104	9	using	use	VERB
cana-5829	104	10	fuzzy	fuzzy	ADJ
cana-5829	104	11	reasoning	reasoning	NOUN
cana-5829	104	12	in	in	ADP
cana-5829	104	13	everyday	everyday	ADJ
cana-5829	104	14	decisions	decision	NOUN
cana-5829	104	15	,	,	PUNCT
cana-5829	104	16	where	where	SCONJ
cana-5829	104	17	things	thing	NOUN
cana-5829	104	18	are	be	AUX
cana-5829	104	19	n’t	not	PART
cana-5829	104	20	just	just	ADV
cana-5829	104	21	black	black	ADJ
cana-5829	104	22	and	and	CCONJ
cana-5829	104	23	white	white	ADJ
cana-5829	104	24	.	.	PUNCT
cana-5829	105	1	example	example	NOUN
cana-5829	105	2	:	:	PUNCT
cana-5829	105	3	deciding	decide	VERB
cana-5829	105	4	whether	whether	SCONJ
cana-5829	105	5	to	to	PART
cana-5829	105	6	go	go	VERB
cana-5829	105	7	outside	outside	ADV
cana-5829	105	8	when	when	SCONJ
cana-5829	105	9	the	the	DET
cana-5829	105	10	weather	weather	NOUN
cana-5829	105	11	is	be	AUX
cana-5829	105	12	"	"	PUNCT
cana-5829	105	13	a	a	DET
cana-5829	105	14	little	little	ADJ
cana-5829	105	15	rainy	rainy	ADJ
cana-5829	105	16	"	"	PUNCT
cana-5829	105	17	is	be	AUX
cana-5829	105	18	a	a	DET
cana-5829	105	19	fuzzy	fuzzy	ADJ
cana-5829	105	20	decision	decision	NOUN
cana-5829	105	21	it	it	PRON
cana-5829	105	22	's	be	AUX
cana-5829	105	23	not	not	PART
cana-5829	105	24	a	a	DET
cana-5829	105	25	simple	simple	ADJ
cana-5829	105	26	"	"	PUNCT
cana-5829	105	27	yes	yes	INTJ
cana-5829	105	28	"	"	PUNCT
cana-5829	105	29	or	or	CCONJ
cana-5829	105	30	"	"	PUNCT
cana-5829	105	31	no	no	DET
cana-5829	105	32	"	"	PUNCT
cana-5829	105	33	answer	answer	NOUN
cana-5829	105	34	,	,	PUNCT
cana-5829	105	35	but	but	CCONJ
cana-5829	105	36	something	something	PRON
cana-5829	105	37	in	in	ADP
cana-5829	105	38	between	between	ADP
cana-5829	105	39	based	base	VERB
cana-5829	105	40	on	on	ADP
cana-5829	105	41	personal	personal	ADJ
cana-5829	105	42	comfort	comfort	NOUN
cana-5829	105	43	.	.	PUNCT
cana-5829	106	1	2.4	2.4	NUM
cana-5829	106	2	fuzzy	fuzzy	ADJ
cana-5829	106	3	matrix	matrix	NOUN
cana-5829	106	4	2.4.1definition	2.4.1definition	NOUN
cana-5829	106	5	of	of	ADP
cana-5829	106	6	fuzzy	fuzzy	ADJ
cana-5829	106	7	matrix	matrix	NOUN
cana-5829	106	8	:	:	PUNCT
cana-5829	106	9	a	a	DET
cana-5829	106	10	fuzzy	fuzzy	ADJ
cana-5829	106	11	matrix	matrix	NOUN
cana-5829	106	12	is	be	AUX
cana-5829	106	13	a	a	DET
cana-5829	106	14	mathematical	mathematical	ADJ
cana-5829	106	15	structure	structure	NOUN
cana-5829	106	16	used	use	VERB
cana-5829	106	17	to	to	PART
cana-5829	106	18	represent	represent	VERB
cana-5829	106	19	data	datum	NOUN
cana-5829	106	20	where	where	SCONJ
cana-5829	106	21	the	the	DET
cana-5829	106	22	relationships	relationship	NOUN
cana-5829	106	23	between	between	ADP
cana-5829	106	24	elements	element	NOUN
cana-5829	106	25	are	be	AUX
cana-5829	106	26	not	not	PART
cana-5829	106	27	precisely	precisely	ADV
cana-5829	106	28	defined	define	VERB
cana-5829	106	29	,	,	PUNCT
cana-5829	106	30	but	but	CCONJ
cana-5829	106	31	instead	instead	ADV
cana-5829	106	32	are	be	AUX
cana-5829	106	33	characterized	characterize	VERB
cana-5829	106	34	by	by	ADP
cana-5829	106	35	degrees	degree	NOUN
cana-5829	106	36	of	of	ADP
cana-5829	106	37	membership	membership	NOUN
cana-5829	106	38	.	.	PUNCT
cana-5829	107	1	this	this	DET
cana-5829	107	2	concept	concept	NOUN
cana-5829	107	3	stems	stem	VERB
cana-5829	107	4	from	from	ADP
cana-5829	107	5	fuzzy	fuzzy	ADJ
cana-5829	107	6	set	set	NOUN
cana-5829	107	7	theory	theory	NOUN
cana-5829	107	8	,	,	PUNCT
cana-5829	107	9	which	which	PRON
cana-5829	107	10	allows	allow	VERB
cana-5829	107	11	for	for	ADP
cana-5829	107	12	partial	partial	ADJ
cana-5829	107	13	membership	membership	NOUN
cana-5829	107	14	in	in	ADP
cana-5829	107	15	a	a	DET
cana-5829	107	16	set	set	NOUN
cana-5829	107	17	rather	rather	ADV
cana-5829	107	18	than	than	ADP
cana-5829	107	19	a	a	DET
cana-5829	107	20	strict	strict	ADJ
cana-5829	107	21	binary	binary	ADJ
cana-5829	107	22	classification	classification	NOUN
cana-5829	107	23	(	(	PUNCT
cana-5829	107	24	where	where	SCONJ
cana-5829	107	25	something	something	PRON
cana-5829	107	26	is	be	AUX
cana-5829	107	27	either	either	CCONJ
cana-5829	107	28	in	in	ADP
cana-5829	107	29	the	the	DET
cana-5829	107	30	set	set	NOUN
cana-5829	107	31	or	or	CCONJ
cana-5829	107	32	not	not	PART
cana-5829	107	33	)	)	PUNCT
cana-5829	107	34	.	.	PUNCT
cana-5829	108	1	in	in	ADP
cana-5829	108	2	a	a	DET
cana-5829	108	3	fuzzy	fuzzy	ADJ
cana-5829	108	4	matrix	matrix	NOUN
cana-5829	108	5	,	,	PUNCT
cana-5829	108	6	each	each	DET
cana-5829	108	7	element	element	NOUN
cana-5829	108	8	in	in	ADP
cana-5829	108	9	the	the	DET
cana-5829	108	10	matrix	matrix	NOUN
cana-5829	108	11	represents	represent	VERB
cana-5829	108	12	a	a	DET
cana-5829	108	13	relationship	relationship	NOUN
cana-5829	108	14	or	or	CCONJ
cana-5829	108	15	association	association	NOUN
cana-5829	108	16	between	between	ADP
cana-5829	108	17	two	two	NUM
cana-5829	108	18	entities	entity	NOUN
cana-5829	108	19	,	,	PUNCT
cana-5829	108	20	and	and	CCONJ
cana-5829	108	21	the	the	DET
cana-5829	108	22	value	value	NOUN
cana-5829	108	23	in	in	ADP
cana-5829	108	24	the	the	DET
cana-5829	108	25	matrix	matrix	NOUN
cana-5829	108	26	is	be	AUX
cana-5829	108	27	a	a	DET
cana-5829	108	28	fuzzy	fuzzy	ADJ
cana-5829	108	29	number	number	NOUN
cana-5829	108	30	(	(	PUNCT
cana-5829	108	31	typically	typically	ADV
cana-5829	108	32	ranging	range	VERB
cana-5829	108	33	from	from	ADP
cana-5829	108	34	0	0	NUM
cana-5829	108	35	to	to	ADP
cana-5829	108	36	1	1	NUM
cana-5829	108	37	)	)	PUNCT
cana-5829	108	38	that	that	PRON
cana-5829	108	39	indicates	indicate	VERB
cana-5829	108	40	the	the	DET
cana-5829	108	41	degree	degree	NOUN
cana-5829	108	42	of	of	ADP
cana-5829	108	43	association	association	NOUN
cana-5829	108	44	.	.	PUNCT
cana-5829	109	1	a	a	DET
cana-5829	109	2	value	value	NOUN
cana-5829	109	3	of	of	ADP
cana-5829	109	4	0	0	NUM
cana-5829	109	5	might	might	AUX
cana-5829	109	6	mean	mean	VERB
cana-5829	109	7	"	"	PUNCT
cana-5829	109	8	no	no	DET
cana-5829	109	9	association	association	NOUN
cana-5829	109	10	,	,	PUNCT
cana-5829	109	11	"	"	PUNCT
cana-5829	109	12	while	while	SCONJ
cana-5829	109	13	a	a	DET
cana-5829	109	14	value	value	NOUN
cana-5829	109	15	of	of	ADP
cana-5829	109	16	1	1	NUM
cana-5829	109	17	could	could	AUX
cana-5829	109	18	represent	represent	VERB
cana-5829	109	19	"	"	PUNCT
cana-5829	109	20	full	full	ADJ
cana-5829	109	21	association	association	NOUN
cana-5829	109	22	,	,	PUNCT
cana-5829	109	23	"	"	PUNCT
cana-5829	109	24	and	and	CCONJ
cana-5829	109	25	values	value	NOUN
cana-5829	109	26	in	in	ADP
cana-5829	109	27	between	between	ADP
cana-5829	109	28	indicate	indicate	VERB
cana-5829	109	29	partial	partial	ADJ
cana-5829	109	30	associations	association	NOUN
cana-5829	109	31	.	.	PUNCT
cana-5829	110	1	membership	membership	NOUN
cana-5829	110	2	degrees	degree	NOUN
cana-5829	110	3	:	:	PUNCT
cana-5829	110	4	instead	instead	ADV
cana-5829	110	5	of	of	ADP
cana-5829	110	6	having	have	VERB
cana-5829	110	7	binary	binary	ADJ
cana-5829	110	8	values	value	NOUN
cana-5829	110	9	(	(	PUNCT
cana-5829	110	10	0	0	NUM
cana-5829	110	11	or	or	CCONJ
cana-5829	110	12	1	1	NUM
cana-5829	110	13	)	)	PUNCT
cana-5829	110	14	,	,	PUNCT
cana-5829	110	15	fuzzy	fuzzy	ADJ
cana-5829	110	16	matrices	matrix	NOUN
cana-5829	110	17	contain	contain	VERB
cana-5829	110	18	values	value	NOUN
cana-5829	110	19	between	between	ADP
cana-5829	110	20	0	0	NUM
cana-5829	110	21	and	and	CCONJ
cana-5829	110	22	1	1	NUM
cana-5829	110	23	,	,	PUNCT
cana-5829	110	24	representing	represent	VERB
cana-5829	110	25	the	the	DET
cana-5829	110	26	degree	degree	NOUN
cana-5829	110	27	of	of	ADP
cana-5829	110	28	membership	membership	NOUN
cana-5829	110	29	.	.	PUNCT
cana-5829	111	1	symmetry	symmetry	NOUN
cana-5829	111	2	:	:	PUNCT
cana-5829	111	3	in	in	ADP
cana-5829	111	4	some	some	DET
cana-5829	111	5	applications	application	NOUN
cana-5829	111	6	,	,	PUNCT
cana-5829	111	7	the	the	DET
cana-5829	111	8	fuzzy	fuzzy	ADJ
cana-5829	111	9	matrix	matrix	NOUN
cana-5829	111	10	can	can	AUX
cana-5829	111	11	be	be	AUX
cana-5829	111	12	symmetric	symmetric	ADJ
cana-5829	111	13	,	,	PUNCT
cana-5829	111	14	meaning	mean	VERB
cana-5829	111	15	that	that	SCONJ
cana-5829	111	16	if	if	SCONJ
cana-5829	111	17	element	element	NOUN
cana-5829	111	18	a	a	PRON
cana-5829	111	19	is	be	AUX
cana-5829	111	20	related	relate	VERB
cana-5829	111	21	to	to	PART
cana-5829	111	22	element	element	VERB
cana-5829	111	23	bbb	bbb	PROPN
cana-5829	111	24	to	to	ADP
cana-5829	111	25	some	some	DET
cana-5829	111	26	degree	degree	NOUN
cana-5829	111	27	,	,	PUNCT
cana-5829	111	28	element	element	NOUN
cana-5829	111	29	bbb	bbb	PROPN
cana-5829	111	30	is	be	AUX
cana-5829	111	31	related	relate	VERB
cana-5829	111	32	to	to	PART
cana-5829	111	33	element	element	VERB
cana-5829	111	34	a	a	PRON
cana-5829	111	35	to	to	ADP
cana-5829	111	36	the	the	DET
cana-5829	111	37	same	same	ADJ
cana-5829	111	38	degree	degree	NOUN
cana-5829	111	39	.	.	PUNCT
cana-5829	112	1	application	application	NOUN
cana-5829	112	2	:	:	PUNCT
cana-5829	112	3	fuzzy	fuzzy	ADJ
cana-5829	112	4	matrices	matrix	NOUN
cana-5829	112	5	are	be	AUX
cana-5829	112	6	widely	widely	ADV
cana-5829	112	7	used	use	VERB
cana-5829	112	8	in	in	ADP
cana-5829	112	9	decision	decision	NOUN
cana-5829	112	10	-	-	PUNCT
cana-5829	112	11	making	make	VERB
cana-5829	112	12	processes	process	NOUN
cana-5829	112	13	,	,	PUNCT
cana-5829	112	14	pattern	pattern	NOUN
cana-5829	112	15	recognition	recognition	NOUN
cana-5829	112	16	,	,	PUNCT
cana-5829	112	17	image	image	NOUN
cana-5829	112	18	processing	processing	NOUN
cana-5829	112	19	,	,	PUNCT
cana-5829	112	20	and	and	CCONJ
cana-5829	112	21	systems	system	NOUN
cana-5829	112	22	where	where	SCONJ
cana-5829	112	23	uncertainty	uncertainty	NOUN
cana-5829	112	24	or	or	CCONJ
cana-5829	112	25	vagueness	vagueness	NOUN
cana-5829	112	26	in	in	ADP
cana-5829	112	27	data	datum	NOUN
cana-5829	112	28	exists	exist	VERB
cana-5829	112	29	.	.	PUNCT
cana-5829	113	1	2.5	2.5	NUM
cana-5829	113	2	examples	example	NOUN
cana-5829	113	3	of	of	ADP
cana-5829	113	4	fuzzy	fuzzy	ADJ
cana-5829	113	5	matrix	matrix	NOUN
cana-5829	113	6	:	:	PUNCT
cana-5829	113	7	a	a	DET
cana-5829	113	8	fuzzy	fuzzy	ADJ
cana-5829	113	9	matrix	matrix	NOUN
cana-5829	113	10	is	be	AUX
cana-5829	113	11	a	a	DET
cana-5829	113	12	matrix	matrix	NOUN
cana-5829	113	13	in	in	ADP
cana-5829	113	14	which	which	PRON
cana-5829	113	15	the	the	DET
cana-5829	113	16	elements	element	NOUN
cana-5829	113	17	are	be	AUX
cana-5829	113	18	fuzzy	fuzzy	ADJ
cana-5829	113	19	values	value	NOUN
cana-5829	113	20	,	,	PUNCT
cana-5829	113	21	typically	typically	ADV
cana-5829	113	22	represented	represent	VERB
cana-5829	113	23	by	by	ADP
cana-5829	113	24	fuzzy	fuzzy	ADJ
cana-5829	113	25	numbers	number	NOUN
cana-5829	113	26	or	or	CCONJ
cana-5829	113	27	membership	membership	NOUN
cana-5829	113	28	functions	function	NOUN
cana-5829	113	29	.	.	PUNCT
cana-5829	114	1	fuzzy	fuzzy	ADJ
cana-5829	114	2	matrices	matrix	NOUN
cana-5829	114	3	are	be	AUX
cana-5829	114	4	used	use	VERB
cana-5829	114	5	in	in	ADP
cana-5829	114	6	various	various	ADJ
cana-5829	114	7	fields	field	NOUN
cana-5829	114	8	,	,	PUNCT
cana-5829	114	9	such	such	ADJ
cana-5829	114	10	as	as	ADP
cana-5829	114	11	fuzzy	fuzzy	ADJ
cana-5829	114	12	logic	logic	NOUN
cana-5829	114	13	,	,	PUNCT
cana-5829	114	14	fuzzy	fuzzy	ADJ
cana-5829	114	15	systems	system	NOUN
cana-5829	114	16	,	,	PUNCT
cana-5829	114	17	and	and	CCONJ
cana-5829	114	18	decision	decision	NOUN
cana-5829	114	19	-	-	PUNCT
cana-5829	114	20	making	make	VERB
cana-5829	114	21	processes	process	NOUN
cana-5829	114	22	,	,	PUNCT
cana-5829	114	23	to	to	PART
cana-5829	114	24	handle	handle	VERB
cana-5829	114	25	imprecision	imprecision	NOUN
cana-5829	114	26	and	and	CCONJ
cana-5829	114	27	uncertainty	uncertainty	NOUN
cana-5829	114	28	.	.	PUNCT
cana-5829	115	1	let	let	VERB
cana-5829	115	2	's	us	PRON
cana-5829	115	3	consider	consider	VERB
cana-5829	115	4	a	a	DET
cana-5829	115	5	fuzzy	fuzzy	ADJ
cana-5829	115	6	matrix	matrix	NOUN
cana-5829	115	7	representing	represent	VERB
cana-5829	115	8	the	the	DET
cana-5829	115	9	relationship	relationship	NOUN
cana-5829	115	10	between	between	ADP
cana-5829	115	11	three	three	NUM
cana-5829	115	12	factors	factor	NOUN
cana-5829	115	13	(	(	PUNCT
cana-5829	115	14	a	a	DET
cana-5829	115	15	,	,	PUNCT
cana-5829	115	16	b	b	NOUN
cana-5829	115	17	,	,	PUNCT
cana-5829	115	18	c	c	NOUN
cana-5829	115	19	)	)	PUNCT
cana-5829	115	20	and	and	CCONJ
cana-5829	115	21	their	their	PRON
cana-5829	115	22	membership	membership	NOUN
cana-5829	115	23	values	value	NOUN
cana-5829	115	24	.	.	PUNCT
cana-5829	116	1	here	here	ADV
cana-5829	116	2	,	,	PUNCT
cana-5829	116	3	each	each	DET
cana-5829	116	4	element	element	NOUN
cana-5829	116	5	in	in	ADP
cana-5829	116	6	the	the	DET
cana-5829	116	7	matrix	matrix	NOUN
cana-5829	116	8	could	could	AUX
cana-5829	116	9	represent	represent	VERB
cana-5829	116	10	a	a	DET
cana-5829	116	11	degree	degree	NOUN
cana-5829	116	12	of	of	ADP
cana-5829	116	13	relationship	relationship	NOUN
cana-5829	116	14	or	or	CCONJ
cana-5829	116	15	membership	membership	NOUN
cana-5829	116	16	function	function	NOUN
cana-5829	116	17	value	value	NOUN
cana-5829	116	18	ranging	range	VERB
cana-5829	116	19	from	from	ADP
cana-5829	116	20	0	0	NUM
cana-5829	116	21	to	to	ADP
cana-5829	116	22	1	1	NUM
cana-5829	116	23	.	.	PUNCT
cana-5829	116	24	fuzzy	fuzzy	ADJ
cana-5829	116	25	matrix	matrix	NOUN
cana-5829	116	26	:	:	PUNCT
cana-5829	116	27	[	[	PUNCT
cana-5829	116	28	0.8	0.8	NUM
cana-5829	116	29	0.6	0.6	NUM
cana-5829	116	30	0.4	0.4	NUM
cana-5829	116	31	0.5	0.5	NUM
cana-5829	116	32	0.7	0.7	NUM
cana-5829	116	33	0.9	0.9	NUM
cana-5829	116	34	0.3	0.3	NUM
cana-5829	116	35	0.6	0.6	NUM
cana-5829	116	36	0.8	0.8	NUM
cana-5829	116	37	]	]	PUNCT
cana-5829	116	38	in	in	ADP
cana-5829	116	39	this	this	DET
cana-5829	116	40	matrix	matrix	NOUN
cana-5829	116	41	,	,	PUNCT
cana-5829	116	42	the	the	DET
cana-5829	116	43	value	value	NOUN
cana-5829	116	44	0.8	0.8	NUM
cana-5829	116	45	in	in	ADP
cana-5829	116	46	the	the	DET
cana-5829	116	47	first	first	ADJ
cana-5829	116	48	row	row	NOUN
cana-5829	116	49	and	and	CCONJ
cana-5829	116	50	first	first	ADJ
cana-5829	116	51	column	column	NOUN
cana-5829	116	52	indicates	indicate	VERB
cana-5829	116	53	a	a	DET
cana-5829	116	54	high	high	ADJ
cana-5829	116	55	degree	degree	NOUN
cana-5829	116	56	of	of	ADP
cana-5829	116	57	membership	membership	NOUN
cana-5829	116	58	or	or	CCONJ
cana-5829	116	59	relationship	relationship	NOUN
cana-5829	116	60	between	between	ADP
cana-5829	116	61	factor	factor	NOUN
cana-5829	116	62	a	a	NOUN
cana-5829	116	63	and	and	CCONJ
cana-5829	116	64	itself	itself	PRON
cana-5829	116	65	.	.	PUNCT
cana-5829	117	1	the	the	DET
cana-5829	117	2	value	value	NOUN
cana-5829	117	3	0.6	0.6	NUM
cana-5829	117	4	in	in	ADP
cana-5829	117	5	the	the	DET
cana-5829	117	6	first	first	ADJ
cana-5829	117	7	row	row	NOUN
cana-5829	117	8	and	and	CCONJ
cana-5829	117	9	second	second	ADJ
cana-5829	117	10	column	column	NOUN
cana-5829	117	11	represents	represent	VERB
cana-5829	117	12	a	a	DET
cana-5829	117	13	medium	medium	ADJ
cana-5829	117	14	degree	degree	NOUN
cana-5829	117	15	of	of	ADP
cana-5829	117	16	membership	membership	NOUN
cana-5829	117	17	between	between	ADP
cana-5829	117	18	factor	factor	NOUN
cana-5829	117	19	a	a	NOUN
cana-5829	117	20	and	and	CCONJ
cana-5829	117	21	b.	b.	X
cana-5829	117	22	the	the	DET
cana-5829	117	23	value	value	NOUN
cana-5829	117	24	0.4	0.4	NUM
cana-5829	117	25	in	in	ADP
cana-5829	117	26	the	the	DET
cana-5829	117	27	first	first	ADJ
cana-5829	117	28	row	row	NOUN
cana-5829	117	29	and	and	CCONJ
cana-5829	117	30	third	third	ADJ
cana-5829	117	31	column	column	NOUN
cana-5829	117	32	indicates	indicate	VERB
cana-5829	117	33	a	a	DET
cana-5829	117	34	low	low	ADJ
cana-5829	117	35	degree	degree	NOUN
cana-5829	117	36	of	of	ADP
cana-5829	117	37	relationship	relationship	NOUN
cana-5829	117	38	between	between	ADP
cana-5829	117	39	a	a	PRON
cana-5829	117	40	and	and	CCONJ
cana-5829	117	41	c.	c.	NOUN
cana-5829	117	42	each	each	DET
cana-5829	117	43	element	element	NOUN
cana-5829	117	44	in	in	ADP
cana-5829	117	45	the	the	DET
cana-5829	117	46	matrix	matrix	NOUN
cana-5829	117	47	is	be	AUX
cana-5829	117	48	a	a	DET
cana-5829	117	49	fuzzy	fuzzy	ADJ
cana-5829	117	50	value	value	NOUN
cana-5829	117	51	between	between	ADP
cana-5829	117	52	0	0	NUM
cana-5829	117	53	and	and	CCONJ
cana-5829	117	54	1	1	NUM
cana-5829	117	55	,	,	PUNCT
cana-5829	117	56	where	where	SCONJ
cana-5829	117	57	0	0	NUM
cana-5829	117	58	means	mean	VERB
cana-5829	117	59	no	no	DET
cana-5829	117	60	membership	membership	NOUN
cana-5829	117	61	or	or	CCONJ
cana-5829	117	62	no	no	DET
cana-5829	117	63	relationship	relationship	NOUN
cana-5829	117	64	.	.	PUNCT
cana-5829	118	1	1	1	NUM
cana-5829	118	2	means	mean	VERB
cana-5829	118	3	full	full	ADJ
cana-5829	118	4	membership	membership	NOUN
cana-5829	118	5	or	or	CCONJ
cana-5829	118	6	a	a	DET
cana-5829	118	7	strong	strong	ADJ
cana-5829	118	8	relationship	relationship	NOUN
cana-5829	118	9	.	.	PUNCT
cana-5829	119	1	2.5.1	2.5.1	NUM
cana-5829	119	2	.	.	PUNCT
cana-5829	119	3	basic	basic	ADJ
cana-5829	119	4	fuzzy	fuzzy	ADJ
cana-5829	119	5	matrix	matrix	NOUN
cana-5829	119	6	(	(	PUNCT
cana-5829	119	7	binary	binary	ADJ
cana-5829	119	8	fuzzy	fuzzy	ADJ
cana-5829	119	9	matrix	matrix	NOUN
cana-5829	119	10	):	):	PUNCT
cana-5829	119	11	the	the	DET
cana-5829	119	12	matrix	matrix	NOUN
cana-5829	119	13	represents	represent	VERB
cana-5829	119	14	relationships	relationship	NOUN
cana-5829	119	15	between	between	ADP
cana-5829	119	16	elements	element	NOUN
cana-5829	119	17	using	use	VERB
cana-5829	119	18	values	value	NOUN
cana-5829	119	19	in	in	ADP
cana-5829	119	20	[	[	X
cana-5829	119	21	0,1	0,1	NUM
cana-5829	119	22	]	]	PUNCT
cana-5829	119	23	a=	a=	PROPN
cana-5829	119	24	[	[	PUNCT
cana-5829	119	25	0.8	0.8	NUM
cana-5829	119	26	0.4	0.4	NUM
cana-5829	119	27	0.6	0.6	NUM
cana-5829	119	28	0.3	0.3	NUM
cana-5829	119	29	1.0	1.0	NUM
cana-5829	119	30	0.7	0.7	NUM
cana-5829	119	31	0.5	0.5	NUM
cana-5829	119	32	0.2	0.2	NUM
cana-5829	119	33	0.9	0.9	NUM
cana-5829	119	34	]	]	PUNCT
cana-5829	119	35	communications	communication	NOUN
cana-5829	119	36	on	on	ADP
cana-5829	119	37	applied	apply	VERB
cana-5829	119	38	nonlinear	nonlinear	ADJ
cana-5829	119	39	analysis	analysis	NOUN
cana-5829	119	40	issn	issn	NOUN
cana-5829	119	41	:	:	PUNCT
cana-5829	119	42	1074	1074	NUM
cana-5829	119	43	-	-	PUNCT
cana-5829	119	44	133x	133x	NUM
cana-5829	119	45	vol	vol	VERB
cana-5829	119	46	32	32	NUM
cana-5829	119	47	no	no	NOUN
cana-5829	119	48	.	.	PUNCT
cana-5829	120	1	10s	10	NOUN
cana-5829	120	2	(	(	PUNCT
cana-5829	120	3	2025	2025	NUM
cana-5829	120	4	)	)	PUNCT
cana-5829	120	5	2927	2927	NUM
cana-5829	120	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5829	120	7	where	where	SCONJ
cana-5829	120	8	𝑎𝑖𝑗	𝑎𝑖𝑗	NOUN
cana-5829	120	9	represents	represent	VERB
cana-5829	120	10	the	the	DET
cana-5829	120	11	degree	degree	NOUN
cana-5829	120	12	of	of	ADP
cana-5829	120	13	membership	membership	NOUN
cana-5829	120	14	or	or	CCONJ
cana-5829	120	15	confidence	confidence	NOUN
cana-5829	120	16	in	in	ADP
cana-5829	120	17	a	a	DET
cana-5829	120	18	relationship	relationship	NOUN
cana-5829	120	19	between	between	ADP
cana-5829	120	20	elements	element	NOUN
cana-5829	120	21	.	.	PUNCT
cana-5829	121	1	2.5.2	2.5.2	NUM
cana-5829	121	2	fuzzy	fuzzy	ADJ
cana-5829	121	3	adjacency	adjacency	NOUN
cana-5829	121	4	matrix	matrix	NOUN
cana-5829	121	5	:	:	PUNCT
cana-5829	121	6	in	in	ADP
cana-5829	121	7	a	a	DET
cana-5829	121	8	fuzzy	fuzzy	ADJ
cana-5829	121	9	graph	graph	NOUN
cana-5829	121	10	,	,	PUNCT
cana-5829	121	11	has	have	VERB
cana-5829	121	12	three	three	NUM
cana-5829	121	13	nodes	node	NOUN
cana-5829	121	14	with	with	ADP
cana-5829	121	15	fuzzy	fuzzy	ADJ
cana-5829	121	16	edges	edge	NOUN
cana-5829	121	17	weights	weight	NOUN
cana-5829	121	18	,	,	PUNCT
cana-5829	121	19	its	its	PRON
cana-5829	121	20	adjacency	adjacency	NOUN
cana-5829	121	21	matrix	matrix	NOUN
cana-5829	121	22	may	may	AUX
cana-5829	121	23	look	look	VERB
cana-5829	121	24	like	like	ADP
cana-5829	121	25	:	:	PUNCT
cana-5829	121	26	m=	m=	X
cana-5829	121	27	[	[	PUNCT
cana-5829	121	28	0	0	NUM
cana-5829	121	29	0.7	0.7	NUM
cana-5829	121	30	0.5	0.5	NUM
cana-5829	121	31	0.7	0.7	NUM
cana-5829	121	32	0	0	NUM
cana-5829	121	33	0.8	0.8	NUM
cana-5829	121	34	0.5	0.5	NUM
cana-5829	121	35	0.8	0.8	NUM
cana-5829	121	36	0	0	NUM
cana-5829	121	37	]	]	PUNCT
cana-5829	121	38	where	where	SCONJ
cana-5829	121	39	𝑀𝑖𝑗	𝑀𝑖𝑗	PROPN
cana-5829	121	40	represents	represent	VERB
cana-5829	121	41	the	the	DET
cana-5829	121	42	fuzzy	fuzzy	ADJ
cana-5829	121	43	weight	weight	NOUN
cana-5829	121	44	of	of	ADP
cana-5829	121	45	the	the	DET
cana-5829	121	46	edge	edge	NOUN
cana-5829	121	47	between	between	ADP
cana-5829	121	48	nodes	node	NOUN
cana-5829	121	49	i	i	PRON
cana-5829	121	50	and	and	CCONJ
cana-5829	121	51	j	j	PROPN
cana-5829	121	52	2.5.3	2.5.3	NUM
cana-5829	121	53	.	.	PUNCT
cana-5829	121	54	fuzzy	fuzzy	ADJ
cana-5829	121	55	relation	relation	NOUN
cana-5829	121	56	matrix	matrix	NOUN
cana-5829	121	57	:	:	PUNCT
cana-5829	121	58	a	a	DET
cana-5829	121	59	fuzzy	fuzzy	ADJ
cana-5829	121	60	matrix	matrix	NOUN
cana-5829	121	61	showing	show	VERB
cana-5829	121	62	relationships	relationship	NOUN
cana-5829	121	63	between	between	ADP
cana-5829	121	64	elements	element	NOUN
cana-5829	121	65	of	of	ADP
cana-5829	121	66	two	two	NUM
cana-5829	121	67	sets	set	NOUN
cana-5829	121	68	r=	r=	NOUN
cana-5829	121	69	[	[	PUNCT
cana-5829	121	70	0.9	0.9	NUM
cana-5829	121	71	0.6	0.6	NUM
cana-5829	121	72	0.3	0.3	NUM
cana-5829	121	73	0.5	0.5	NUM
cana-5829	121	74	0.8	0.8	NUM
cana-5829	121	75	0.7	0.7	NUM
cana-5829	121	76	0.4	0.4	NUM
cana-5829	121	77	0.2	0.2	NUM
cana-5829	121	78	0.1	0.1	NUM
cana-5829	121	79	]	]	PUNCT
cana-5829	121	80	where	where	SCONJ
cana-5829	121	81	represents	represent	VERB
cana-5829	121	82	the	the	DET
cana-5829	121	83	fuzzy	fuzzy	ADJ
cana-5829	121	84	relationships	relationship	NOUN
cana-5829	121	85	strength	strength	NOUN
cana-5829	121	86	between	between	ADP
cana-5829	121	87	elements	element	NOUN
cana-5829	121	88	of	of	ADP
cana-5829	121	89	two	two	NUM
cana-5829	121	90	sets	set	NOUN
cana-5829	121	91	2.6	2.6	NUM
cana-5829	121	92	fuzzy	fuzzy	ADJ
cana-5829	121	93	matrix	matrix	NOUN
cana-5829	121	94	application	application	NOUN
cana-5829	121	95	:	:	PUNCT
cana-5829	121	96	a	a	DET
cana-5829	121	97	fuzzy	fuzzy	ADJ
cana-5829	121	98	matrix	matrix	NOUN
cana-5829	121	99	is	be	AUX
cana-5829	121	100	a	a	DET
cana-5829	121	101	generalization	generalization	NOUN
cana-5829	121	102	of	of	ADP
cana-5829	121	103	a	a	DET
cana-5829	121	104	traditional	traditional	ADJ
cana-5829	121	105	matrix	matrix	NOUN
cana-5829	121	106	that	that	PRON
cana-5829	121	107	deals	deal	VERB
cana-5829	121	108	with	with	ADP
cana-5829	121	109	fuzzy	fuzzy	ADJ
cana-5829	121	110	relations	relation	NOUN
cana-5829	121	111	and	and	CCONJ
cana-5829	121	112	fuzzy	fuzzy	ADJ
cana-5829	121	113	logic	logic	NOUN
cana-5829	121	114	.	.	PUNCT
cana-5829	122	1	in	in	ADP
cana-5829	122	2	a	a	DET
cana-5829	122	3	fuzzy	fuzzy	ADJ
cana-5829	122	4	matrix	matrix	NOUN
cana-5829	122	5	,	,	PUNCT
cana-5829	122	6	elements	element	NOUN
cana-5829	122	7	represent	represent	VERB
cana-5829	122	8	degrees	degree	NOUN
cana-5829	122	9	of	of	ADP
cana-5829	122	10	membership	membership	NOUN
cana-5829	122	11	to	to	ADP
cana-5829	122	12	certain	certain	ADJ
cana-5829	122	13	sets	set	NOUN
cana-5829	122	14	,	,	PUNCT
cana-5829	122	15	usually	usually	ADV
cana-5829	122	16	expressed	express	VERB
cana-5829	122	17	as	as	ADP
cana-5829	122	18	values	value	NOUN
cana-5829	122	19	in	in	ADP
cana-5829	122	20	the	the	DET
cana-5829	122	21	range	range	NOUN
cana-5829	122	22	[	[	X
cana-5829	122	23	0	0	NUM
cana-5829	122	24	,	,	PUNCT
cana-5829	122	25	1	1	NUM
cana-5829	122	26	]	]	PUNCT
cana-5829	122	27	,	,	PUNCT
cana-5829	122	28	where	where	SCONJ
cana-5829	122	29	0	0	NUM
cana-5829	122	30	means	mean	VERB
cana-5829	122	31	no	no	DET
cana-5829	122	32	membership	membership	NOUN
cana-5829	122	33	,	,	PUNCT
cana-5829	122	34	1	1	NUM
cana-5829	122	35	means	mean	VERB
cana-5829	122	36	full	full	ADJ
cana-5829	122	37	membership	membership	NOUN
cana-5829	122	38	,	,	PUNCT
cana-5829	122	39	and	and	CCONJ
cana-5829	122	40	intermediate	intermediate	ADJ
cana-5829	122	41	values	value	NOUN
cana-5829	122	42	represent	represent	VERB
cana-5829	122	43	partial	partial	ADJ
cana-5829	122	44	membership	membership	NOUN
cana-5829	122	45	.	.	PUNCT
cana-5829	123	1	this	this	DET
cana-5829	123	2	concept	concept	NOUN
cana-5829	123	3	is	be	AUX
cana-5829	123	4	widely	widely	ADV
cana-5829	123	5	applied	apply	VERB
cana-5829	123	6	in	in	ADP
cana-5829	123	7	fields	field	NOUN
cana-5829	123	8	where	where	SCONJ
cana-5829	123	9	uncertainty	uncertainty	NOUN
cana-5829	123	10	,	,	PUNCT
cana-5829	123	11	vagueness	vagueness	NOUN
cana-5829	123	12	,	,	PUNCT
cana-5829	123	13	or	or	CCONJ
cana-5829	123	14	imprecision	imprecision	NOUN
cana-5829	123	15	is	be	AUX
cana-5829	123	16	present	present	ADJ
cana-5829	123	17	.	.	PUNCT
cana-5829	124	1	below	below	ADV
cana-5829	124	2	are	be	AUX
cana-5829	124	3	some	some	DET
cana-5829	124	4	applications	application	NOUN
cana-5829	124	5	of	of	ADP
cana-5829	124	6	fuzzy	fuzzy	ADJ
cana-5829	124	7	matrices	matrix	NOUN
cana-5829	124	8	:	:	PUNCT
cana-5829	124	9	2.6.1	2.6.1	NUM
cana-5829	124	10	fuzzy	fuzzy	ADJ
cana-5829	124	11	logic	logic	NOUN
cana-5829	124	12	systems	system	NOUN
cana-5829	124	13	:	:	PUNCT
cana-5829	124	14	fuzzy	fuzzy	ADJ
cana-5829	124	15	matrices	matrix	NOUN
cana-5829	124	16	are	be	AUX
cana-5829	124	17	used	use	VERB
cana-5829	124	18	in	in	ADP
cana-5829	124	19	fuzzy	fuzzy	ADJ
cana-5829	124	20	logic	logic	NOUN
cana-5829	124	21	systems	system	NOUN
cana-5829	124	22	for	for	ADP
cana-5829	124	23	decision	decision	NOUN
cana-5829	124	24	-	-	PUNCT
cana-5829	124	25	making	making	NOUN
cana-5829	124	26	,	,	PUNCT
cana-5829	124	27	where	where	SCONJ
cana-5829	124	28	each	each	DET
cana-5829	124	29	element	element	NOUN
cana-5829	124	30	in	in	ADP
cana-5829	124	31	the	the	DET
cana-5829	124	32	matrix	matrix	NOUN
cana-5829	124	33	represents	represent	VERB
cana-5829	124	34	the	the	DET
cana-5829	124	35	degree	degree	NOUN
cana-5829	124	36	of	of	ADP
cana-5829	124	37	truth	truth	NOUN
cana-5829	124	38	for	for	ADP
cana-5829	124	39	a	a	DET
cana-5829	124	40	given	give	VERB
cana-5829	124	41	fuzzy	fuzzy	ADJ
cana-5829	124	42	relationship	relationship	NOUN
cana-5829	124	43	between	between	ADP
cana-5829	124	44	variables	variable	NOUN
cana-5829	124	45	.	.	PUNCT
cana-5829	125	1	for	for	ADP
cana-5829	125	2	example	example	NOUN
cana-5829	125	3	,	,	PUNCT
cana-5829	125	4	in	in	ADP
cana-5829	125	5	a	a	DET
cana-5829	125	6	fuzzy	fuzzy	ADJ
cana-5829	125	7	control	control	NOUN
cana-5829	125	8	system	system	NOUN
cana-5829	125	9	for	for	ADP
cana-5829	125	10	a	a	DET
cana-5829	125	11	thermostat	thermostat	NOUN
cana-5829	125	12	,	,	PUNCT
cana-5829	125	13	the	the	DET
cana-5829	125	14	fuzzy	fuzzy	ADJ
cana-5829	125	15	matrix	matrix	NOUN
cana-5829	125	16	can	can	AUX
cana-5829	125	17	represent	represent	VERB
cana-5829	125	18	rules	rule	NOUN
cana-5829	125	19	and	and	CCONJ
cana-5829	125	20	conditions	condition	NOUN
cana-5829	125	21	like	like	SCONJ
cana-5829	125	22	"	"	PUNCT
cana-5829	125	23	temperature	temperature	NOUN
cana-5829	125	24	is	be	AUX
cana-5829	125	25	somewhat	somewhat	ADV
cana-5829	125	26	high	high	ADJ
cana-5829	125	27	,	,	PUNCT
cana-5829	125	28	"	"	PUNCT
cana-5829	125	29	"	"	PUNCT
cana-5829	125	30	humidity	humidity	NOUN
cana-5829	125	31	is	be	AUX
cana-5829	125	32	low	low	ADJ
cana-5829	125	33	,	,	PUNCT
cana-5829	125	34	"	"	PUNCT
cana-5829	125	35	etc	etc	X
cana-5829	125	36	.	.	X
cana-5829	125	37	,	,	PUNCT
cana-5829	125	38	and	and	CCONJ
cana-5829	125	39	the	the	DET
cana-5829	125	40	matrix	matrix	NOUN
cana-5829	125	41	helps	help	VERB
cana-5829	125	42	to	to	PART
cana-5829	125	43	decide	decide	VERB
cana-5829	125	44	the	the	DET
cana-5829	125	45	appropriate	appropriate	ADJ
cana-5829	125	46	output	output	NOUN
cana-5829	125	47	(	(	PUNCT
cana-5829	125	48	e.g.	e.g.	ADV
cana-5829	125	49	,	,	PUNCT
cana-5829	125	50	turn	turn	VERB
cana-5829	125	51	on	on	ADP
cana-5829	125	52	the	the	DET
cana-5829	125	53	air	air	NOUN
cana-5829	125	54	conditioning	conditioning	NOUN
cana-5829	125	55	)	)	PUNCT
cana-5829	125	56	.	.	PUNCT
cana-5829	126	1	2.6.2	2.6.2	NUM
cana-5829	126	2	fuzzy	fuzzy	ADJ
cana-5829	126	3	graph	graph	NOUN
cana-5829	126	4	theory	theory	NOUN
cana-5829	126	5	:	:	PUNCT
cana-5829	126	6	in	in	ADP
cana-5829	126	7	fuzzy	fuzzy	ADJ
cana-5829	126	8	graphs	graph	NOUN
cana-5829	126	9	,	,	PUNCT
cana-5829	126	10	the	the	DET
cana-5829	126	11	adjacency	adjacency	NOUN
cana-5829	126	12	matrix	matrix	NOUN
cana-5829	126	13	can	can	AUX
cana-5829	126	14	have	have	VERB
cana-5829	126	15	values	value	NOUN
cana-5829	126	16	between	between	ADP
cana-5829	126	17	0	0	NUM
cana-5829	126	18	and	and	CCONJ
cana-5829	126	19	1	1	NUM
cana-5829	126	20	,	,	PUNCT
cana-5829	126	21	indicating	indicate	VERB
cana-5829	126	22	the	the	DET
cana-5829	126	23	degree	degree	NOUN
cana-5829	126	24	of	of	ADP
cana-5829	126	25	connection	connection	NOUN
cana-5829	126	26	between	between	ADP
cana-5829	126	27	two	two	NUM
cana-5829	126	28	nodes	node	NOUN
cana-5829	126	29	.	.	PUNCT
cana-5829	127	1	this	this	DET
cana-5829	127	2	approach	approach	NOUN
cana-5829	127	3	is	be	AUX
cana-5829	127	4	useful	useful	ADJ
cana-5829	127	5	in	in	ADP
cana-5829	127	6	networks	network	NOUN
cana-5829	127	7	where	where	SCONJ
cana-5829	127	8	relationships	relationship	NOUN
cana-5829	127	9	between	between	ADP
cana-5829	127	10	nodes	node	NOUN
cana-5829	127	11	are	be	AUX
cana-5829	127	12	not	not	PART
cana-5829	127	13	binary	binary	ADJ
cana-5829	127	14	,	,	PUNCT
cana-5829	127	15	such	such	ADJ
cana-5829	127	16	as	as	ADP
cana-5829	127	17	in	in	ADP
cana-5829	127	18	social	social	ADJ
cana-5829	127	19	networks	network	NOUN
cana-5829	127	20	,	,	PUNCT
cana-5829	127	21	recommendation	recommendation	NOUN
cana-5829	127	22	systems	system	NOUN
cana-5829	127	23	,	,	PUNCT
cana-5829	127	24	or	or	CCONJ
cana-5829	127	25	transportation	transportation	NOUN
cana-5829	127	26	networks	network	NOUN
cana-5829	127	27	.	.	PUNCT
cana-5829	128	1	it	it	PRON
cana-5829	128	2	allows	allow	VERB
cana-5829	128	3	the	the	DET
cana-5829	128	4	representation	representation	NOUN
cana-5829	128	5	of	of	ADP
cana-5829	128	6	relationships	relationship	NOUN
cana-5829	128	7	that	that	PRON
cana-5829	128	8	are	be	AUX
cana-5829	128	9	n't	not	PART
cana-5829	128	10	just	just	ADV
cana-5829	128	11	"	"	PUNCT
cana-5829	128	12	connected	connect	VERB
cana-5829	128	13	"	"	PUNCT
cana-5829	128	14	or	or	CCONJ
cana-5829	128	15	"	"	PUNCT
cana-5829	128	16	not	not	PART
cana-5829	128	17	connected	connect	VERB
cana-5829	128	18	"	"	PUNCT
cana-5829	128	19	but	but	CCONJ
cana-5829	128	20	instead	instead	ADV
cana-5829	128	21	have	have	VERB
cana-5829	128	22	varying	vary	VERB
cana-5829	128	23	strengths	strength	NOUN
cana-5829	128	24	.	.	PUNCT
cana-5829	129	1	2.6.3	2.6.3	NUM
cana-5829	129	2	fuzzy	fuzzy	ADJ
cana-5829	129	3	relational	relational	ADJ
cana-5829	129	4	databases	database	NOUN
cana-5829	129	5	:	:	PUNCT
cana-5829	129	6	fuzzy	fuzzy	ADJ
cana-5829	129	7	matrices	matrix	NOUN
cana-5829	129	8	can	can	AUX
cana-5829	129	9	be	be	AUX
cana-5829	129	10	used	use	VERB
cana-5829	129	11	in	in	ADP
cana-5829	129	12	fuzzy	fuzzy	ADJ
cana-5829	129	13	relational	relational	ADJ
cana-5829	129	14	databases	database	NOUN
cana-5829	129	15	where	where	SCONJ
cana-5829	129	16	database	database	NOUN
cana-5829	129	17	relationships	relationship	NOUN
cana-5829	129	18	(	(	PUNCT
cana-5829	129	19	such	such	ADJ
cana-5829	129	20	as	as	ADP
cana-5829	129	21	queries	query	NOUN
cana-5829	129	22	or	or	CCONJ
cana-5829	129	23	connections	connection	NOUN
cana-5829	129	24	between	between	ADP
cana-5829	129	25	tables	table	NOUN
cana-5829	129	26	)	)	PUNCT
cana-5829	129	27	are	be	AUX
cana-5829	129	28	not	not	PART
cana-5829	129	29	precise	precise	ADJ
cana-5829	129	30	but	but	CCONJ
cana-5829	129	31	instead	instead	ADV
cana-5829	129	32	have	have	VERB
cana-5829	129	33	degrees	degree	NOUN
cana-5829	129	34	of	of	ADP
cana-5829	129	35	certainty	certainty	NOUN
cana-5829	129	36	.	.	PUNCT
cana-5829	130	1	for	for	ADP
cana-5829	130	2	instance	instance	NOUN
cana-5829	130	3	,	,	PUNCT
cana-5829	130	4	in	in	ADP
cana-5829	130	5	a	a	DET
cana-5829	130	6	database	database	NOUN
cana-5829	130	7	of	of	ADP
cana-5829	130	8	products	product	NOUN
cana-5829	130	9	,	,	PUNCT
cana-5829	130	10	a	a	DET
cana-5829	130	11	fuzzy	fuzzy	ADJ
cana-5829	130	12	matrix	matrix	NOUN
cana-5829	130	13	could	could	AUX
cana-5829	130	14	represent	represent	VERB
cana-5829	130	15	the	the	DET
cana-5829	130	16	degree	degree	NOUN
cana-5829	130	17	of	of	ADP
cana-5829	130	18	similarity	similarity	NOUN
cana-5829	130	19	between	between	ADP
cana-5829	130	20	different	different	ADJ
cana-5829	130	21	items	item	NOUN
cana-5829	130	22	,	,	PUNCT
cana-5829	130	23	which	which	PRON
cana-5829	130	24	can	can	AUX
cana-5829	130	25	help	help	VERB
cana-5829	130	26	with	with	ADP
cana-5829	130	27	fuzzy	fuzzy	ADJ
cana-5829	130	28	searching	searching	NOUN
cana-5829	130	29	or	or	CCONJ
cana-5829	130	30	recommendation	recommendation	NOUN
cana-5829	130	31	engines	engine	NOUN
cana-5829	130	32	.	.	PUNCT
cana-5829	131	1	2.6.4	2.6.4	NUM
cana-5829	131	2	fuzzy	fuzzy	ADJ
cana-5829	131	3	control	control	NOUN
cana-5829	131	4	systems	system	NOUN
cana-5829	131	5	:	:	PUNCT
cana-5829	131	6	in	in	ADP
cana-5829	131	7	fuzzy	fuzzy	ADJ
cana-5829	131	8	control	control	NOUN
cana-5829	131	9	,	,	PUNCT
cana-5829	131	10	fuzzy	fuzzy	ADJ
cana-5829	131	11	matrices	matrix	NOUN
cana-5829	131	12	are	be	AUX
cana-5829	131	13	often	often	ADV
cana-5829	131	14	used	use	VERB
cana-5829	131	15	to	to	PART
cana-5829	131	16	represent	represent	VERB
cana-5829	131	17	the	the	DET
cana-5829	131	18	relationship	relationship	NOUN
cana-5829	131	19	between	between	ADP
cana-5829	131	20	input	input	NOUN
cana-5829	131	21	and	and	CCONJ
cana-5829	131	22	output	output	NOUN
cana-5829	131	23	variables	variable	NOUN
cana-5829	131	24	in	in	ADP
cana-5829	131	25	fuzzy	fuzzy	ADJ
cana-5829	131	26	inference	inference	NOUN
cana-5829	131	27	systems	system	NOUN
cana-5829	131	28	(	(	PUNCT
cana-5829	131	29	fis	fis	PROPN
cana-5829	131	30	)	)	PUNCT
cana-5829	131	31	.	.	PUNCT
cana-5829	132	1	for	for	ADP
cana-5829	132	2	example	example	NOUN
cana-5829	132	3	,	,	PUNCT
cana-5829	132	4	in	in	ADP
cana-5829	132	5	controlling	control	VERB
cana-5829	132	6	the	the	DET
cana-5829	132	7	speed	speed	NOUN
cana-5829	132	8	of	of	ADP
cana-5829	132	9	a	a	DET
cana-5829	132	10	fan	fan	NOUN
cana-5829	132	11	based	base	VERB
cana-5829	132	12	on	on	ADP
cana-5829	132	13	temperature	temperature	NOUN
cana-5829	132	14	readings	reading	NOUN
cana-5829	132	15	,	,	PUNCT
cana-5829	132	16	a	a	DET
cana-5829	132	17	fuzzy	fuzzy	ADJ
cana-5829	132	18	matrix	matrix	NOUN
cana-5829	132	19	might	might	AUX
cana-5829	132	20	define	define	VERB
cana-5829	132	21	how	how	SCONJ
cana-5829	132	22	the	the	DET
cana-5829	132	23	degree	degree	NOUN
cana-5829	132	24	of	of	ADP
cana-5829	132	25	"	"	PUNCT
cana-5829	132	26	high	high	ADJ
cana-5829	132	27	temperature	temperature	NOUN
cana-5829	132	28	"	"	PUNCT
cana-5829	132	29	should	should	AUX
cana-5829	132	30	correlate	correlate	VERB
cana-5829	132	31	to	to	ADP
cana-5829	132	32	the	the	DET
cana-5829	132	33	fan	fan	NOUN
cana-5829	132	34	's	's	PART
cana-5829	132	35	speed	speed	NOUN
cana-5829	132	36	in	in	ADP
cana-5829	132	37	a	a	DET
cana-5829	132	38	fuzzy	fuzzy	ADJ
cana-5829	132	39	way	way	NOUN
cana-5829	132	40	.	.	PUNCT
cana-5829	133	1	2.6.5	2.6.5	NUM
cana-5829	133	2	pattern	pattern	NOUN
cana-5829	133	3	recognition	recognition	NOUN
cana-5829	133	4	and	and	CCONJ
cana-5829	133	5	classification	classification	NOUN
cana-5829	133	6	:	:	PUNCT
cana-5829	133	7	fuzzy	fuzzy	ADJ
cana-5829	133	8	matrices	matrix	NOUN
cana-5829	133	9	are	be	AUX
cana-5829	133	10	employed	employ	VERB
cana-5829	133	11	in	in	ADP
cana-5829	133	12	fuzzy	fuzzy	ADJ
cana-5829	133	13	pattern	pattern	NOUN
cana-5829	133	14	recognition	recognition	NOUN
cana-5829	133	15	to	to	PART
cana-5829	133	16	classify	classify	VERB
cana-5829	133	17	patterns	pattern	NOUN
cana-5829	133	18	when	when	SCONJ
cana-5829	133	19	there	there	PRON
cana-5829	133	20	is	be	VERB
cana-5829	133	21	ambiguity	ambiguity	NOUN
cana-5829	133	22	or	or	CCONJ
cana-5829	133	23	overlap	overlap	NOUN
cana-5829	133	24	between	between	ADP
cana-5829	133	25	classes	class	NOUN
cana-5829	133	26	.	.	PUNCT
cana-5829	134	1	a	a	DET
cana-5829	134	2	fuzzy	fuzzy	ADJ
cana-5829	134	3	matrix	matrix	NOUN
cana-5829	134	4	can	can	AUX
cana-5829	134	5	represent	represent	VERB
cana-5829	134	6	the	the	DET
cana-5829	134	7	degree	degree	NOUN
cana-5829	134	8	to	to	PART
cana-5829	134	9	which	which	PRON
cana-5829	134	10	a	a	DET
cana-5829	134	11	certain	certain	ADJ
cana-5829	134	12	input	input	NOUN
cana-5829	134	13	belongs	belong	VERB
cana-5829	134	14	to	to	ADP
cana-5829	134	15	multiple	multiple	ADJ
cana-5829	134	16	classes	class	NOUN
cana-5829	134	17	simultaneously	simultaneously	ADV
cana-5829	134	18	.	.	PUNCT
cana-5829	135	1	this	this	PRON
cana-5829	135	2	is	be	AUX
cana-5829	135	3	useful	useful	ADJ
cana-5829	135	4	in	in	ADP
cana-5829	135	5	applications	application	NOUN
cana-5829	135	6	like	like	ADP
cana-5829	135	7	handwriting	handwriting	NOUN
cana-5829	135	8	recognition	recognition	NOUN
cana-5829	135	9	,	,	PUNCT
cana-5829	135	10	image	image	NOUN
cana-5829	135	11	segmentation	segmentation	NOUN
cana-5829	135	12	,	,	PUNCT
cana-5829	135	13	and	and	CCONJ
cana-5829	135	14	speech	speech	NOUN
cana-5829	135	15	recognition	recognition	NOUN
cana-5829	135	16	,	,	PUNCT
cana-5829	135	17	where	where	SCONJ
cana-5829	135	18	categories	category	NOUN
cana-5829	135	19	are	be	AUX
cana-5829	135	20	not	not	PART
cana-5829	135	21	perfectly	perfectly	ADV
cana-5829	135	22	distinct	distinct	ADJ
cana-5829	135	23	.	.	PUNCT
cana-5829	136	1	2.6	2.6	NUM
cana-5829	136	2	.	.	NOUN
cana-5829	136	3	6	6	NUM
cana-5829	136	4	fuzzy	fuzzy	ADJ
cana-5829	136	5	decision	decision	NOUN
cana-5829	136	6	making	making	NOUN
cana-5829	136	7	:	:	PUNCT
cana-5829	136	8	in	in	ADP
cana-5829	136	9	multi	multi	ADJ
cana-5829	136	10	-	-	ADJ
cana-5829	136	11	criteria	criteria	ADJ
cana-5829	136	12	decision	decision	NOUN
cana-5829	136	13	analysis	analysis	NOUN
cana-5829	136	14	(	(	PUNCT
cana-5829	136	15	mcda	mcda	NOUN
cana-5829	136	16	)	)	PUNCT
cana-5829	136	17	,	,	PUNCT
cana-5829	136	18	fuzzy	fuzzy	ADJ
cana-5829	136	19	matrices	matrix	NOUN
cana-5829	136	20	can	can	AUX
cana-5829	136	21	represent	represent	VERB
cana-5829	136	22	the	the	DET
cana-5829	136	23	degrees	degree	NOUN
cana-5829	136	24	of	of	ADP
cana-5829	136	25	importance	importance	NOUN
cana-5829	136	26	or	or	CCONJ
cana-5829	136	27	preference	preference	NOUN
cana-5829	136	28	for	for	ADP
cana-5829	136	29	various	various	ADJ
cana-5829	136	30	criteria	criterion	NOUN
cana-5829	136	31	under	under	ADP
cana-5829	136	32	uncertain	uncertain	ADJ
cana-5829	136	33	conditions	condition	NOUN
cana-5829	136	34	.	.	PUNCT
cana-5829	137	1	for	for	ADP
cana-5829	137	2	example	example	NOUN
cana-5829	137	3	,	,	PUNCT
cana-5829	137	4	in	in	ADP
cana-5829	137	5	selecting	select	VERB
cana-5829	137	6	a	a	DET
cana-5829	137	7	vendor	vendor	NOUN
cana-5829	137	8	for	for	ADP
cana-5829	137	9	a	a	DET
cana-5829	137	10	project	project	NOUN
cana-5829	137	11	,	,	PUNCT
cana-5829	137	12	decision	decision	NOUN
cana-5829	137	13	-	-	PUNCT
cana-5829	137	14	makers	maker	NOUN
cana-5829	137	15	might	might	AUX
cana-5829	137	16	use	use	VERB
cana-5829	137	17	a	a	DET
cana-5829	137	18	fuzzy	fuzzy	ADJ
cana-5829	137	19	matrix	matrix	NOUN
cana-5829	137	20	to	to	PART
cana-5829	137	21	rank	rank	VERB
cana-5829	137	22	multiple	multiple	ADJ
cana-5829	137	23	communications	communication	NOUN
cana-5829	137	24	on	on	ADP
cana-5829	137	25	applied	apply	VERB
cana-5829	137	26	nonlinear	nonlinear	ADJ
cana-5829	137	27	analysis	analysis	NOUN
cana-5829	137	28	issn	issn	NOUN
cana-5829	137	29	:	:	PUNCT
cana-5829	137	30	1074	1074	NUM
cana-5829	137	31	-	-	PUNCT
cana-5829	137	32	133x	133x	NUM
cana-5829	137	33	vol	vol	VERB
cana-5829	137	34	32	32	NUM
cana-5829	137	35	no	no	NOUN
cana-5829	137	36	.	.	PUNCT
cana-5829	138	1	10s	10	NOUN
cana-5829	138	2	(	(	PUNCT
cana-5829	138	3	2025	2025	NUM
cana-5829	138	4	)	)	PUNCT
cana-5829	138	5	2928	2928	NUM
cana-5829	138	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5829	138	7	options	option	NOUN
cana-5829	138	8	based	base	VERB
cana-5829	138	9	on	on	ADP
cana-5829	138	10	subjective	subjective	ADJ
cana-5829	138	11	and	and	CCONJ
cana-5829	138	12	vague	vague	ADJ
cana-5829	138	13	criteria	criterion	NOUN
cana-5829	138	14	like	like	ADP
cana-5829	138	15	"	"	PUNCT
cana-5829	138	16	trustworthiness	trustworthiness	NOUN
cana-5829	138	17	"	"	PUNCT
cana-5829	138	18	or	or	CCONJ
cana-5829	138	19	"	"	PUNCT
cana-5829	138	20	reliability	reliability	NOUN
cana-5829	138	21	,	,	PUNCT
cana-5829	138	22	"	"	PUNCT
cana-5829	138	23	which	which	PRON
cana-5829	138	24	are	be	AUX
cana-5829	138	25	not	not	PART
cana-5829	138	26	easily	easily	ADV
cana-5829	138	27	quantifiable	quantifiable	ADJ
cana-5829	138	28	.	.	PUNCT
cana-5829	139	1	2.6.7	2.6.7	NUM
cana-5829	139	2	fuzzy	fuzzy	ADJ
cana-5829	139	3	systems	system	NOUN
cana-5829	139	4	in	in	ADP
cana-5829	139	5	ai	ai	ADJ
cana-5829	139	6	:	:	PUNCT
cana-5829	139	7	fuzzy	fuzzy	ADJ
cana-5829	139	8	matrices	matrix	NOUN
cana-5829	139	9	can	can	AUX
cana-5829	139	10	be	be	AUX
cana-5829	139	11	used	use	VERB
cana-5829	139	12	in	in	ADP
cana-5829	139	13	ai	ai	ADV
cana-5829	139	14	-	-	PUNCT
cana-5829	139	15	based	base	VERB
cana-5829	139	16	decision	decision	NOUN
cana-5829	139	17	support	support	NOUN
cana-5829	139	18	systems	system	NOUN
cana-5829	139	19	,	,	PUNCT
cana-5829	139	20	where	where	SCONJ
cana-5829	139	21	the	the	DET
cana-5829	139	22	relationships	relationship	NOUN
cana-5829	139	23	between	between	ADP
cana-5829	139	24	inputs	input	NOUN
cana-5829	139	25	and	and	CCONJ
cana-5829	139	26	outputs	output	NOUN
cana-5829	139	27	are	be	AUX
cana-5829	139	28	not	not	PART
cana-5829	139	29	deterministic	deterministic	ADJ
cana-5829	139	30	.	.	PUNCT
cana-5829	140	1	they	they	PRON
cana-5829	140	2	allow	allow	VERB
cana-5829	140	3	ai	ai	VERB
cana-5829	140	4	systems	system	NOUN
cana-5829	140	5	to	to	PART
cana-5829	140	6	handle	handle	VERB
cana-5829	140	7	uncertainty	uncertainty	NOUN
cana-5829	140	8	and	and	CCONJ
cana-5829	140	9	vagueness	vagueness	NOUN
cana-5829	140	10	,	,	PUNCT
cana-5829	140	11	which	which	PRON
cana-5829	140	12	is	be	AUX
cana-5829	140	13	essential	essential	ADJ
cana-5829	140	14	when	when	SCONJ
cana-5829	140	15	processing	process	VERB
cana-5829	140	16	real	real	ADJ
cana-5829	140	17	-	-	PUNCT
cana-5829	140	18	world	world	NOUN
cana-5829	140	19	data	datum	NOUN
cana-5829	140	20	,	,	PUNCT
cana-5829	140	21	such	such	ADJ
cana-5829	140	22	as	as	ADP
cana-5829	140	23	in	in	ADP
cana-5829	140	24	natural	natural	ADJ
cana-5829	140	25	language	language	NOUN
cana-5829	140	26	processing	processing	NOUN
cana-5829	140	27	or	or	CCONJ
cana-5829	140	28	autonomous	autonomous	ADJ
cana-5829	140	29	driving	driving	NOUN
cana-5829	140	30	.	.	PUNCT
cana-5829	141	1	2.6	2.6	NUM
cana-5829	141	2	.	.	NOUN
cana-5829	141	3	8	8	NUM
cana-5829	141	4	fuzzy	fuzzy	ADJ
cana-5829	141	5	optimization	optimization	NOUN
cana-5829	141	6	problems	problem	NOUN
cana-5829	141	7	:	:	PUNCT
cana-5829	141	8	in	in	ADP
cana-5829	141	9	optimization	optimization	NOUN
cana-5829	141	10	problems	problem	NOUN
cana-5829	141	11	,	,	PUNCT
cana-5829	141	12	fuzzy	fuzzy	ADJ
cana-5829	141	13	matrices	matrix	NOUN
cana-5829	141	14	can	can	AUX
cana-5829	141	15	be	be	AUX
cana-5829	141	16	used	use	VERB
cana-5829	141	17	to	to	PART
cana-5829	141	18	represent	represent	VERB
cana-5829	141	19	uncertainty	uncertainty	NOUN
cana-5829	141	20	in	in	ADP
cana-5829	141	21	constraints	constraint	NOUN
cana-5829	141	22	or	or	CCONJ
cana-5829	141	23	objective	objective	ADJ
cana-5829	141	24	functions	function	NOUN
cana-5829	141	25	.	.	PUNCT
cana-5829	142	1	this	this	PRON
cana-5829	142	2	is	be	AUX
cana-5829	142	3	particularly	particularly	ADV
cana-5829	142	4	useful	useful	ADJ
cana-5829	142	5	in	in	ADP
cana-5829	142	6	cases	case	NOUN
cana-5829	142	7	where	where	SCONJ
cana-5829	142	8	the	the	DET
cana-5829	142	9	optimization	optimization	NOUN
cana-5829	142	10	criteria	criterion	NOUN
cana-5829	142	11	are	be	AUX
cana-5829	142	12	vague	vague	ADJ
cana-5829	142	13	or	or	CCONJ
cana-5829	142	14	approximate	approximate	ADJ
cana-5829	142	15	,	,	PUNCT
cana-5829	142	16	such	such	ADJ
cana-5829	142	17	as	as	ADP
cana-5829	142	18	in	in	ADP
cana-5829	142	19	supply	supply	NOUN
cana-5829	142	20	chain	chain	NOUN
cana-5829	142	21	management	management	NOUN
cana-5829	142	22	,	,	PUNCT
cana-5829	142	23	where	where	SCONJ
cana-5829	142	24	costs	cost	NOUN
cana-5829	142	25	and	and	CCONJ
cana-5829	142	26	demand	demand	NOUN
cana-5829	142	27	are	be	AUX
cana-5829	142	28	uncertain	uncertain	ADJ
cana-5829	142	29	,	,	PUNCT
cana-5829	142	30	and	and	CCONJ
cana-5829	142	31	solutions	solution	NOUN
cana-5829	142	32	need	need	VERB
cana-5829	142	33	to	to	PART
cana-5829	142	34	be	be	AUX
cana-5829	142	35	found	find	VERB
cana-5829	142	36	that	that	SCONJ
cana-5829	142	37	work	work	VERB
cana-5829	142	38	well	well	ADV
cana-5829	142	39	under	under	ADP
cana-5829	142	40	a	a	DET
cana-5829	142	41	range	range	NOUN
cana-5829	142	42	of	of	ADP
cana-5829	142	43	possible	possible	ADJ
cana-5829	142	44	conditions	condition	NOUN
cana-5829	142	45	2.6.9	2.6.9	NUM
cana-5829	142	46	image	image	NOUN
cana-5829	142	47	processing	processing	NOUN
cana-5829	142	48	:	:	PUNCT
cana-5829	142	49	fuzzy	fuzzy	ADJ
cana-5829	142	50	matrices	matrix	NOUN
cana-5829	142	51	are	be	AUX
cana-5829	142	52	often	often	ADV
cana-5829	142	53	applied	apply	VERB
cana-5829	142	54	in	in	ADP
cana-5829	142	55	fuzzy	fuzzy	ADJ
cana-5829	142	56	image	image	NOUN
cana-5829	142	57	processing	processing	NOUN
cana-5829	142	58	,	,	PUNCT
cana-5829	142	59	where	where	SCONJ
cana-5829	142	60	an	an	DET
cana-5829	142	61	image	image	NOUN
cana-5829	142	62	's	's	PART
cana-5829	142	63	pixel	pixel	NOUN
cana-5829	142	64	intensities	intensity	NOUN
cana-5829	142	65	are	be	AUX
cana-5829	142	66	considered	consider	VERB
cana-5829	142	67	fuzzy	fuzzy	ADJ
cana-5829	142	68	rather	rather	ADV
cana-5829	142	69	than	than	ADP
cana-5829	142	70	precise	precise	ADJ
cana-5829	142	71	.	.	PUNCT
cana-5829	143	1	this	this	PRON
cana-5829	143	2	can	can	AUX
cana-5829	143	3	help	help	VERB
cana-5829	143	4	with	with	ADP
cana-5829	143	5	tasks	task	NOUN
cana-5829	143	6	like	like	ADP
cana-5829	143	7	image	image	NOUN
cana-5829	143	8	denoising	denoising	NOUN
cana-5829	143	9	,	,	PUNCT
cana-5829	143	10	edge	edge	NOUN
cana-5829	143	11	detection	detection	NOUN
cana-5829	143	12	,	,	PUNCT
cana-5829	143	13	or	or	CCONJ
cana-5829	143	14	segmentation	segmentation	NOUN
cana-5829	143	15	,	,	PUNCT
cana-5829	143	16	where	where	SCONJ
cana-5829	143	17	the	the	DET
cana-5829	143	18	boundaries	boundary	NOUN
cana-5829	143	19	between	between	ADP
cana-5829	143	20	objects	object	NOUN
cana-5829	143	21	in	in	ADP
cana-5829	143	22	an	an	DET
cana-5829	143	23	image	image	NOUN
cana-5829	143	24	are	be	AUX
cana-5829	143	25	not	not	PART
cana-5829	143	26	perfectly	perfectly	ADV
cana-5829	143	27	clear	clear	ADJ
cana-5829	143	28	.	.	PUNCT
cana-5829	144	1	2.6.10	2.6.10	NUM
cana-5829	144	2	fuzzy	fuzzy	ADJ
cana-5829	144	3	clustering	clustering	NOUN
cana-5829	144	4	:	:	PUNCT
cana-5829	144	5	in	in	ADP
cana-5829	144	6	fuzzy	fuzzy	ADJ
cana-5829	144	7	clustering	clustering	ADJ
cana-5829	144	8	algorithms	algorithm	NOUN
cana-5829	144	9	(	(	PUNCT
cana-5829	144	10	e.g.	e.g.	ADV
cana-5829	144	11	,	,	PUNCT
cana-5829	144	12	fuzzy	fuzzy	ADJ
cana-5829	144	13	c	c	NOUN
cana-5829	144	14	-	-	PUNCT
cana-5829	144	15	means	mean	NOUN
cana-5829	144	16	)	)	PUNCT
cana-5829	144	17	,	,	PUNCT
cana-5829	144	18	fuzzy	fuzzy	ADJ
cana-5829	144	19	matrices	matrix	NOUN
cana-5829	144	20	represent	represent	VERB
cana-5829	144	21	the	the	DET
cana-5829	144	22	degree	degree	NOUN
cana-5829	144	23	of	of	ADP
cana-5829	144	24	membership	membership	NOUN
cana-5829	144	25	of	of	ADP
cana-5829	144	26	data	datum	NOUN
cana-5829	144	27	points	point	NOUN
cana-5829	144	28	in	in	ADP
cana-5829	144	29	different	different	ADJ
cana-5829	144	30	clusters	cluster	NOUN
cana-5829	144	31	.	.	PUNCT
cana-5829	145	1	this	this	PRON
cana-5829	145	2	allows	allow	VERB
cana-5829	145	3	for	for	ADP
cana-5829	145	4	the	the	DET
cana-5829	145	5	classification	classification	NOUN
cana-5829	145	6	of	of	ADP
cana-5829	145	7	points	point	NOUN
cana-5829	145	8	that	that	PRON
cana-5829	145	9	belong	belong	VERB
cana-5829	145	10	partially	partially	ADV
cana-5829	145	11	to	to	ADP
cana-5829	145	12	multiple	multiple	ADJ
cana-5829	145	13	clusters	cluster	NOUN
cana-5829	145	14	,	,	PUNCT
cana-5829	145	15	which	which	PRON
cana-5829	145	16	is	be	AUX
cana-5829	145	17	useful	useful	ADJ
cana-5829	145	18	in	in	ADP
cana-5829	145	19	situations	situation	NOUN
cana-5829	145	20	like	like	ADP
cana-5829	145	21	market	market	NOUN
cana-5829	145	22	segmentation	segmentation	NOUN
cana-5829	145	23	,	,	PUNCT
cana-5829	145	24	medical	medical	ADJ
cana-5829	145	25	diagnosis	diagnosis	NOUN
cana-5829	145	26	,	,	PUNCT
cana-5829	145	27	and	and	CCONJ
cana-5829	145	28	customer	customer	NOUN
cana-5829	145	29	behaviour	behaviour	NOUN
cana-5829	145	30	analysis	analysis	NOUN
cana-5829	145	31	.	.	PUNCT
cana-5829	146	1	3.intuitionistic	3.intuitionistic	NUM
cana-5829	146	2	fuzzy	fuzzy	ADJ
cana-5829	146	3	matrix	matrix	NOUN
cana-5829	146	4	3.1definition	3.1definition	NOUN
cana-5829	146	5	of	of	ADP
cana-5829	146	6	intuitionistic	intuitionistic	ADJ
cana-5829	146	7	fuzzy	fuzzy	ADJ
cana-5829	146	8	matrix	matrix	NOUN
cana-5829	146	9	:	:	PUNCT
cana-5829	146	10	an	an	DET
cana-5829	146	11	intuitionistic	intuitionistic	ADJ
cana-5829	146	12	fuzzy	fuzzy	ADJ
cana-5829	146	13	matrix	matrix	NOUN
cana-5829	146	14	a	a	PRON
cana-5829	146	15	of	of	ADP
cana-5829	146	16	order	order	NOUN
cana-5829	146	17	m	m	VERB
cana-5829	146	18	×	×	NOUN
cana-5829	146	19	r	r	NOUN
cana-5829	146	20	is	be	AUX
cana-5829	146	21	defined	define	VERB
cana-5829	146	22	as	as	ADP
cana-5829	146	23	:	:	PUNCT
cana-5829	146	24	a=[(µ𝑖𝑗	a=[(µ𝑖𝑗	PROPN
cana-5829	146	25	,	,	PUNCT
cana-5829	146	26	𝜗𝑖𝑗)]𝑚×n	𝜗𝑖𝑗)]𝑚×n	VERB
cana-5829	146	27	where	where	SCONJ
cana-5829	146	28	,	,	PUNCT
cana-5829	146	29	µ𝑖𝑗is	µ𝑖𝑗is	PROPN
cana-5829	146	30	the	the	DET
cana-5829	146	31	membership	membership	NOUN
cana-5829	146	32	degree	degree	NOUN
cana-5829	146	33	of	of	ADP
cana-5829	146	34	the	the	DET
cana-5829	146	35	element	element	NOUN
cana-5829	146	36	(	(	PUNCT
cana-5829	146	37	i	i	PROPN
cana-5829	146	38	,	,	PUNCT
cana-5829	146	39	j	j	PROPN
cana-5829	146	40	)	)	PUNCT
cana-5829	146	41	,	,	PUNCT
cana-5829	146	42	representing	represent	VERB
cana-5829	146	43	the	the	DET
cana-5829	146	44	degree	degree	NOUN
cana-5829	146	45	of	of	ADP
cana-5829	146	46	belonging	belong	VERB
cana-5829	146	47	to	to	ADP
cana-5829	146	48	a	a	DET
cana-5829	146	49	set	set	NOUN
cana-5829	146	50	.	.	PUNCT
cana-5829	147	1	𝜗𝑖𝑗	𝜗𝑖𝑗	PROPN
cana-5829	147	2	is	be	AUX
cana-5829	147	3	the	the	DET
cana-5829	147	4	non	non	ADJ
cana-5829	147	5	membership	membership	NOUN
cana-5829	147	6	degree	degree	NOUN
cana-5829	147	7	,	,	PUNCT
cana-5829	147	8	representing	represent	VERB
cana-5829	147	9	the	the	DET
cana-5829	147	10	degree	degree	NOUN
cana-5829	147	11	of	of	ADP
cana-5829	147	12	not	not	PART
cana-5829	147	13	belonging	belong	VERB
cana-5829	147	14	to	to	ADP
cana-5829	147	15	a	a	DET
cana-5829	147	16	set	set	NOUN
cana-5829	147	17	.	.	PUNCT
cana-5829	148	1	for	for	ADP
cana-5829	148	2	every	every	DET
cana-5829	148	3	elements	element	NOUN
cana-5829	148	4	(	(	PUNCT
cana-5829	148	5	i	i	PRON
cana-5829	148	6	,	,	PUNCT
cana-5829	148	7	j	j	PROPN
cana-5829	148	8	the	the	DET
cana-5829	148	9	sum	sum	NOUN
cana-5829	148	10	of	of	ADP
cana-5829	148	11	membership	membership	NOUN
cana-5829	148	12	and	and	CCONJ
cana-5829	148	13	non	non	ADJ
cana-5829	148	14	-	-	ADJ
cana-5829	148	15	membership	membership	ADJ
cana-5829	148	16	degree	degree	NOUN
cana-5829	148	17	satisfies	satisfie	NOUN
cana-5829	148	18	:	:	PUNCT
cana-5829	148	19	0	0	NUM
cana-5829	148	20	≤	≤	NUM
cana-5829	148	21	µ𝑖𝑗	µ𝑖𝑗	VERB
cana-5829	148	22	+	+	CCONJ
cana-5829	148	23	𝜗𝑖𝑗	𝜗𝑖𝑗	PROPN
cana-5829	148	24	≤	≤	PROPN
cana-5829	148	25	1𝑓𝑜𝑟	1𝑓𝑜𝑟	NUM
cana-5829	148	26	𝑎𝑙𝑙	𝑎𝑙𝑙	NOUN
cana-5829	148	27	𝑖	𝑖	NOUN
cana-5829	148	28	,	,	PUNCT
cana-5829	148	29	the	the	DET
cana-5829	148	30	uncertainty	uncertainty	NOUN
cana-5829	148	31	degree	degree	NOUN
cana-5829	148	32	(	(	PUNCT
cana-5829	148	33	hesitancy)is	hesitancy)is	ADJ
cana-5829	148	34	given	give	VERB
cana-5829	148	35	by	by	ADP
cana-5829	148	36	(	(	PUNCT
cana-5829	148	37	µ𝑖𝑗	µ𝑖𝑗	PROPN
cana-5829	148	38	+	+	CCONJ
cana-5829	148	39	𝜗𝑖𝑗	𝜗𝑖𝑗	NOUN
cana-5829	148	40	)	)	PUNCT
cana-5829	148	41	which	which	PRON
cana-5829	148	42	quantifies	quantify	VERB
cana-5829	148	43	the	the	DET
cana-5829	148	44	hesitation	hesitation	NOUN
cana-5829	148	45	or	or	CCONJ
cana-5829	148	46	lack	lack	NOUN
cana-5829	148	47	of	of	ADP
cana-5829	148	48	complete	complete	ADJ
cana-5829	148	49	knowledge	knowledge	NOUN
cana-5829	148	50	about	about	ADP
cana-5829	148	51	the	the	DET
cana-5829	148	52	membership	membership	NOUN
cana-5829	148	53	status	status	NOUN
cana-5829	148	54	.	.	PUNCT
cana-5829	149	1	3.2	3.2	NUM
cana-5829	149	2	examples	example	NOUN
cana-5829	149	3	of	of	ADP
cana-5829	149	4	intuitionistic	intuitionistic	ADJ
cana-5829	149	5	fuzzy	fuzzy	ADJ
cana-5829	149	6	matrix	matrix	NOUN
cana-5829	149	7	:	:	PUNCT
cana-5829	149	8	intuitionistic	intuitionistic	ADJ
cana-5829	149	9	fuzzy	fuzzy	ADJ
cana-5829	149	10	sets	set	NOUN
cana-5829	149	11	(	(	PUNCT
cana-5829	149	12	ifs	ifs	NOUN
cana-5829	149	13	)	)	PUNCT
cana-5829	149	14	extend	extend	VERB
cana-5829	149	15	traditional	traditional	ADJ
cana-5829	149	16	fuzzy	fuzzy	ADJ
cana-5829	149	17	sets	set	NOUN
cana-5829	149	18	by	by	ADP
cana-5829	149	19	incorporating	incorporate	VERB
cana-5829	149	20	both	both	CCONJ
cana-5829	149	21	membership	membership	NOUN
cana-5829	149	22	and	and	CCONJ
cana-5829	149	23	nonmembership	nonmembership	NOUN
cana-5829	149	24	functions	function	NOUN
cana-5829	149	25	,	,	PUNCT
cana-5829	149	26	as	as	ADV
cana-5829	149	27	well	well	ADV
cana-5829	149	28	as	as	ADP
cana-5829	149	29	a	a	DET
cana-5829	149	30	degree	degree	NOUN
cana-5829	149	31	of	of	ADP
cana-5829	149	32	hesitation	hesitation	NOUN
cana-5829	149	33	.	.	PUNCT
cana-5829	150	1	in	in	ADP
cana-5829	150	2	an	an	DET
cana-5829	150	3	intuitionistic	intuitionistic	ADJ
cana-5829	150	4	fuzzy	fuzzy	ADJ
cana-5829	150	5	matrix	matrix	NOUN
cana-5829	150	6	,	,	PUNCT
cana-5829	150	7	each	each	DET
cana-5829	150	8	element	element	NOUN
cana-5829	150	9	has	have	VERB
cana-5829	150	10	three	three	NUM
cana-5829	150	11	components	component	NOUN
cana-5829	150	12	:	:	PUNCT
cana-5829	150	13	membership	membership	NOUN
cana-5829	150	14	degree	degree	NOUN
cana-5829	150	15	(	(	PUNCT
cana-5829	150	16	µ	µ	NOUN
cana-5829	150	17	):	):	PUNCT
cana-5829	150	18	the	the	DET
cana-5829	150	19	degree	degree	NOUN
cana-5829	150	20	to	to	PART
cana-5829	150	21	which	which	PRON
cana-5829	150	22	an	an	DET
cana-5829	150	23	element	element	NOUN
cana-5829	150	24	belongs	belong	VERB
cana-5829	150	25	to	to	ADP
cana-5829	150	26	the	the	DET
cana-5829	150	27	set	set	NOUN
cana-5829	150	28	.	.	PUNCT
cana-5829	151	1	non	non	ADJ
cana-5829	151	2	-	-	ADJ
cana-5829	151	3	membership	membership	ADJ
cana-5829	151	4	degree	degree	NOUN
cana-5829	151	5	(	(	PUNCT
cana-5829	151	6	ν	ν	NOUN
cana-5829	151	7	):	):	PUNCT
cana-5829	151	8	the	the	DET
cana-5829	151	9	degree	degree	NOUN
cana-5829	151	10	to	to	PART
cana-5829	151	11	which	which	PRON
cana-5829	151	12	an	an	DET
cana-5829	151	13	element	element	NOUN
cana-5829	151	14	does	do	AUX
cana-5829	151	15	not	not	PART
cana-5829	151	16	belong	belong	VERB
cana-5829	151	17	to	to	ADP
cana-5829	151	18	the	the	DET
cana-5829	151	19	set	set	NOUN
cana-5829	151	20	.	.	PUNCT
cana-5829	152	1	hesitation	hesitation	NOUN
cana-5829	152	2	degree	degree	NOUN
cana-5829	152	3	(	(	PUNCT
cana-5829	152	4	π	π	NOUN
cana-5829	152	5	):	):	PUNCT
cana-5829	152	6	the	the	DET
cana-5829	152	7	degree	degree	NOUN
cana-5829	152	8	of	of	ADP
cana-5829	152	9	uncertainty	uncertainty	NOUN
cana-5829	152	10	or	or	CCONJ
cana-5829	152	11	hesitation	hesitation	NOUN
cana-5829	152	12	,	,	PUNCT
cana-5829	152	13	calculated	calculate	VERB
cana-5829	152	14	as	as	ADP
cana-5829	152	15	π=1−μ−ν	π=1−μ−ν	NOUN
cana-5829	152	16	1.a	1.a	NUM
cana-5829	152	17	2×2	2×2	NUM
cana-5829	152	18	intuitionistic	intuitionistic	ADJ
cana-5829	152	19	fuzzy	fuzzy	ADJ
cana-5829	152	20	matrix	matrix	NOUN
cana-5829	152	21	:	:	PUNCT
cana-5829	152	22	a=	a=	PROPN
cana-5829	152	23	[	[	PUNCT
cana-5829	152	24	(	(	PUNCT
cana-5829	152	25	0.7	0.7	NUM
cana-5829	152	26	,	,	PUNCT
cana-5829	152	27	0.2	0.2	NUM
cana-5829	152	28	)	)	PUNCT
cana-5829	152	29	(	(	PUNCT
cana-5829	152	30	0.5	0.5	NUM
cana-5829	152	31	0.3	0.3	NUM
cana-5829	152	32	)	)	PUNCT
cana-5829	152	33	(	(	PUNCT
cana-5829	152	34	0.6	0.6	NUM
cana-5829	152	35	0.1	0.1	NUM
cana-5829	152	36	)	)	PUNCT
cana-5829	152	37	(	(	PUNCT
cana-5829	152	38	0.4	0.4	NUM
cana-5829	152	39	0.4	0.4	NUM
cana-5829	152	40	)	)	PUNCT
cana-5829	152	41	]	]	PUNCT
cana-5829	153	1	membership=0.7	membership=0.7	X
cana-5829	153	2	,	,	PUNCT
cana-5829	153	3	non	non	AUX
cana-5829	153	4	–	–	PUNCT
cana-5829	153	5	membership=0.2	membership=0.2	ADJ
cana-5829	153	6	and	and	CCONJ
cana-5829	153	7	hesitation	hesitation	NOUN
cana-5829	153	8	degree=1-(0.7	degree=1-(0.7	PROPN
cana-5829	153	9	+	+	PROPN
cana-5829	153	10	0.2	0.2	NUM
cana-5829	153	11	)	)	PUNCT
cana-5829	153	12	=	=	NOUN
cana-5829	153	13	0.1	0.1	NUM
cana-5829	153	14	2	2	NUM
cana-5829	153	15	.	.	PUNCT
cana-5829	154	1	a	a	DET
cana-5829	154	2	2×3	2×3	NUM
cana-5829	154	3	intuitionistic	intuitionistic	ADJ
cana-5829	154	4	fuzzy	fuzzy	ADJ
cana-5829	154	5	matrix	matrix	NOUN
cana-5829	154	6	:	:	PUNCT
cana-5829	154	7	b=	b=	NOUN
cana-5829	154	8	[	[	PUNCT
cana-5829	154	9	〈	〈	NOUN
cana-5829	154	10	0.8	0.8	NUM
cana-5829	154	11	0.1	0.1	NUM
cana-5829	154	12	〉	〉	NOUN
cana-5829	154	13	〈	〈	NOUN
cana-5829	154	14	0.6	0.6	NUM
cana-5829	154	15	0.2	0.2	NUM
cana-5829	154	16	〉	〉	NOUN
cana-5829	154	17	〈	〈	ADP
cana-5829	154	18	0.5	0.5	NUM
cana-5829	154	19	0.3	0.3	NUM
cana-5829	154	20	〉	〉	NOUN
cana-5829	154	21	〈	〈	ADP
cana-5829	154	22	0.7	0.7	NUM
cana-5829	154	23	0.2	0.2	NUM
cana-5829	154	24	〉	〉	NOUN
cana-5829	154	25	〈	〈	ADP
cana-5829	154	26	0.4	0.4	NUM
cana-5829	154	27	0.4	0.4	NUM
cana-5829	154	28	〉	〉	NOUN
cana-5829	154	29	〈	〈	ADP
cana-5829	154	30	0.3	0.3	NUM
cana-5829	154	31	0.5	0.5	NUM
cana-5829	154	32	〉	〉	NOUN
cana-5829	154	33	]	]	PUNCT
cana-5829	154	34	membership=0.3	membership=0.3	X
cana-5829	154	35	,	,	PUNCT
cana-5829	154	36	non	non	ADJ
cana-5829	154	37	–	–	PUNCT
cana-5829	154	38	membership=0.5	membership=0.5	ADJ
cana-5829	154	39	and	and	CCONJ
cana-5829	154	40	hesitation	hesitation	NOUN
cana-5829	154	41	degree=1-(0.3	degree=1-(0.3	PROPN
cana-5829	154	42	+	+	NOUN
cana-5829	154	43	0.5	0.5	NUM
cana-5829	154	44	)	)	PUNCT
cana-5829	155	1	=	=	NOUN
cana-5829	155	2	0.2	0.2	NUM
cana-5829	155	3	3.a	3.a	NUM
cana-5829	155	4	3×3	3×3	NUM
cana-5829	155	5	intuitionistic	intuitionistic	ADJ
cana-5829	155	6	fuzzy	fuzzy	ADJ
cana-5829	155	7	matrix	matrix	NOUN
cana-5829	155	8	:	:	PUNCT
cana-5829	155	9	c=	c=	NOUN
cana-5829	155	10	[	[	PUNCT
cana-5829	155	11	〈	〈	PROPN
cana-5829	155	12	0.6	0.6	NUM
cana-5829	155	13	0.3	0.3	NUM
cana-5829	155	14	〉	〉	NOUN
cana-5829	155	15	〈	〈	ADP
cana-5829	155	16	0.7	0.7	NUM
cana-5829	155	17	0.2	0.2	NUM
cana-5829	155	18	〉	〉	NOUN
cana-5829	155	19	〈	〈	ADP
cana-5829	155	20	0.5	0.5	NUM
cana-5829	155	21	0.4	0.4	NUM
cana-5829	155	22	〉	〉	NOUN
cana-5829	155	23	〈	〈	ADP
cana-5829	155	24	0.8	0.8	NUM
cana-5829	155	25	0.1	0.1	NUM
cana-5829	155	26	〉	〉	NOUN
cana-5829	155	27	〈	〈	ADP
cana-5829	155	28	0.4	0.4	NUM
cana-5829	155	29	0.5	0.5	NUM
cana-5829	155	30	〉	〉	NOUN
cana-5829	155	31	〈	〈	ADP
cana-5829	155	32	0.6	0.6	NUM
cana-5829	155	33	0.3	0.3	NUM
cana-5829	155	34	〉	〉	NOUN
cana-5829	155	35	〈	〈	ADP
cana-5829	155	36	0.3	0.3	NUM
cana-5829	155	37	0.6	0.6	NUM
cana-5829	155	38	〉	〉	NOUN
cana-5829	155	39	〈	〈	ADP
cana-5829	155	40	0.5	0.5	NUM
cana-5829	155	41	0.3	0.3	NUM
cana-5829	155	42	〉	〉	NOUN
cana-5829	155	43	〈	〈	ADP
cana-5829	155	44	0.7	0.7	NUM
cana-5829	155	45	0.2	0.2	NUM
cana-5829	155	46	〉	〉	NOUN
cana-5829	155	47	]	]	PUNCT
cana-5829	155	48	communications	communication	NOUN
cana-5829	155	49	on	on	ADP
cana-5829	155	50	applied	apply	VERB
cana-5829	155	51	nonlinear	nonlinear	ADJ
cana-5829	155	52	analysis	analysis	NOUN
cana-5829	155	53	issn	issn	NOUN
cana-5829	155	54	:	:	PUNCT
cana-5829	155	55	1074	1074	NUM
cana-5829	155	56	-	-	PUNCT
cana-5829	155	57	133x	133x	NUM
cana-5829	155	58	vol	vol	VERB
cana-5829	155	59	32	32	NUM
cana-5829	155	60	no	no	NOUN
cana-5829	155	61	.	.	PUNCT
cana-5829	155	62	10s	10	NOUN
cana-5829	155	63	(	(	PUNCT
cana-5829	155	64	2025	2025	NUM
cana-5829	155	65	)	)	PUNCT
cana-5829	155	66	2929	2929	NUM
cana-5829	155	67	https://internationalpubls.com	https://internationalpubls.com	X
cana-5829	155	68	membership=0.3	membership=0.3	X
cana-5829	155	69	,	,	PUNCT
cana-5829	155	70	non	non	ADJ
cana-5829	155	71	–	–	PUNCT
cana-5829	155	72	membership=0.5	membership=0.5	ADJ
cana-5829	155	73	and	and	CCONJ
cana-5829	155	74	hesitation	hesitation	NOUN
cana-5829	155	75	degree=1-(0.3	degree=1-(0.3	PROPN
cana-5829	155	76	+	+	NOUN
cana-5829	155	77	0.5	0.5	NUM
cana-5829	155	78	)	)	PUNCT
cana-5829	155	79	=	=	NOUN
cana-5829	155	80	0.2	0.2	NUM
cana-5829	155	81	3.3	3.3	NUM
cana-5829	155	82	application	application	NOUN
cana-5829	155	83	of	of	ADP
cana-5829	155	84	intuitionistic	intuitionistic	ADJ
cana-5829	155	85	fuzzy	fuzzy	ADJ
cana-5829	155	86	matrix	matrix	NOUN
cana-5829	155	87	:	:	PUNCT
cana-5829	155	88	3.3.1	3.3.1	NUM
cana-5829	155	89	decision	decision	NOUN
cana-5829	155	90	-	-	PUNCT
cana-5829	155	91	making	make	VERB
cana-5829	155	92	problems	problem	NOUN
cana-5829	155	93	(	(	PUNCT
cana-5829	155	94	multi	multi	ADJ
cana-5829	155	95	-	-	ADJ
cana-5829	155	96	criteria	criterion	NOUN
cana-5829	155	97	decision	decision	NOUN
cana-5829	155	98	analysis	analysis	NOUN
cana-5829	155	99	):	):	PUNCT
cana-5829	155	100	intuitionistic	intuitionistic	ADJ
cana-5829	155	101	fuzzy	fuzzy	ADJ
cana-5829	155	102	matrices	matrix	NOUN
cana-5829	155	103	are	be	AUX
cana-5829	155	104	often	often	ADV
cana-5829	155	105	used	use	VERB
cana-5829	155	106	in	in	ADP
cana-5829	155	107	decision	decision	NOUN
cana-5829	155	108	-	-	PUNCT
cana-5829	155	109	making	make	VERB
cana-5829	155	110	problems	problem	NOUN
cana-5829	155	111	where	where	SCONJ
cana-5829	155	112	decisions	decision	NOUN
cana-5829	155	113	depend	depend	VERB
cana-5829	155	114	on	on	ADP
cana-5829	155	115	multiple	multiple	ADJ
cana-5829	155	116	criteria	criterion	NOUN
cana-5829	155	117	,	,	PUNCT
cana-5829	155	118	and	and	CCONJ
cana-5829	155	119	there	there	PRON
cana-5829	155	120	is	be	VERB
cana-5829	155	121	uncertainty	uncertainty	NOUN
cana-5829	155	122	in	in	ADP
cana-5829	155	123	the	the	DET
cana-5829	155	124	assessment	assessment	NOUN
cana-5829	155	125	of	of	ADP
cana-5829	155	126	each	each	DET
cana-5829	155	127	criterion	criterion	NOUN
cana-5829	155	128	.	.	PUNCT
cana-5829	156	1	example	example	NOUN
cana-5829	156	2	:	:	PUNCT
cana-5829	156	3	in	in	ADP
cana-5829	156	4	a	a	DET
cana-5829	156	5	decision	decision	NOUN
cana-5829	156	6	-	-	PUNCT
cana-5829	156	7	making	make	VERB
cana-5829	156	8	process	process	NOUN
cana-5829	156	9	for	for	ADP
cana-5829	156	10	selecting	select	VERB
cana-5829	156	11	the	the	DET
cana-5829	156	12	best	good	ADJ
cana-5829	156	13	supplier	supplier	NOUN
cana-5829	156	14	from	from	ADP
cana-5829	156	15	a	a	DET
cana-5829	156	16	set	set	NOUN
cana-5829	156	17	of	of	ADP
cana-5829	156	18	alternatives	alternative	NOUN
cana-5829	156	19	,	,	PUNCT
cana-5829	156	20	each	each	DET
cana-5829	156	21	criterion	criterion	NOUN
cana-5829	156	22	(	(	PUNCT
cana-5829	156	23	e.g.	e.g.	ADV
cana-5829	156	24	,	,	PUNCT
cana-5829	156	25	cost	cost	NOUN
cana-5829	156	26	,	,	PUNCT
cana-5829	156	27	quality	quality	NOUN
cana-5829	156	28	,	,	PUNCT
cana-5829	156	29	delivery	delivery	NOUN
cana-5829	156	30	time	time	NOUN
cana-5829	156	31	)	)	PUNCT
cana-5829	156	32	may	may	AUX
cana-5829	156	33	have	have	VERB
cana-5829	156	34	uncertainty	uncertainty	NOUN
cana-5829	156	35	.	.	PUNCT
cana-5829	157	1	intuitionistic	intuitionistic	ADJ
cana-5829	157	2	fuzzy	fuzzy	ADJ
cana-5829	157	3	matrices	matrix	NOUN
cana-5829	157	4	help	help	VERB
cana-5829	157	5	incorporate	incorporate	VERB
cana-5829	157	6	both	both	DET
cana-5829	157	7	membership	membership	NOUN
cana-5829	157	8	(	(	PUNCT
cana-5829	157	9	degree	degree	NOUN
cana-5829	157	10	of	of	ADP
cana-5829	157	11	suitability	suitability	NOUN
cana-5829	157	12	)	)	PUNCT
cana-5829	157	13	and	and	CCONJ
cana-5829	157	14	non	non	ADJ
cana-5829	157	15	-	-	ADJ
cana-5829	157	16	membership	membership	ADJ
cana-5829	157	17	(	(	PUNCT
cana-5829	157	18	degree	degree	NOUN
cana-5829	157	19	of	of	ADP
cana-5829	157	20	unsuitability	unsuitability	NOUN
cana-5829	157	21	)	)	PUNCT
cana-5829	157	22	values	value	NOUN
cana-5829	157	23	into	into	ADP
cana-5829	157	24	the	the	DET
cana-5829	157	25	decision	decision	NOUN
cana-5829	157	26	matrix	matrix	NOUN
cana-5829	157	27	.	.	PUNCT
cana-5829	158	1	3.3.2	3.3.2	NUM
cana-5829	158	2	pattern	pattern	NOUN
cana-5829	158	3	recognition	recognition	NOUN
cana-5829	158	4	:	:	PUNCT
cana-5829	158	5	in	in	ADP
cana-5829	158	6	pattern	pattern	NOUN
cana-5829	158	7	recognition	recognition	NOUN
cana-5829	158	8	,	,	PUNCT
cana-5829	158	9	intuitionistic	intuitionistic	ADJ
cana-5829	158	10	fuzzy	fuzzy	ADJ
cana-5829	158	11	matrices	matrix	NOUN
cana-5829	158	12	can	can	AUX
cana-5829	158	13	be	be	AUX
cana-5829	158	14	used	use	VERB
cana-5829	158	15	to	to	PART
cana-5829	158	16	represent	represent	VERB
cana-5829	158	17	the	the	DET
cana-5829	158	18	degree	degree	NOUN
cana-5829	158	19	of	of	ADP
cana-5829	158	20	similarity	similarity	NOUN
cana-5829	158	21	and	and	CCONJ
cana-5829	158	22	dissimilarity	dissimilarity	NOUN
cana-5829	158	23	between	between	ADP
cana-5829	158	24	patterns	pattern	NOUN
cana-5829	158	25	,	,	PUNCT
cana-5829	158	26	making	make	VERB
cana-5829	158	27	it	it	PRON
cana-5829	158	28	easier	easy	ADJ
cana-5829	158	29	to	to	PART
cana-5829	158	30	classify	classify	VERB
cana-5829	158	31	patterns	pattern	NOUN
cana-5829	158	32	with	with	ADP
cana-5829	158	33	uncertainties	uncertainty	NOUN
cana-5829	158	34	.	.	PUNCT
cana-5829	159	1	example	example	NOUN
cana-5829	159	2	:	:	PUNCT
cana-5829	159	3	in	in	ADP
cana-5829	159	4	image	image	NOUN
cana-5829	159	5	processing	processing	NOUN
cana-5829	159	6	or	or	CCONJ
cana-5829	159	7	speech	speech	NOUN
cana-5829	159	8	recognition	recognition	NOUN
cana-5829	159	9	,	,	PUNCT
cana-5829	159	10	patterns	pattern	NOUN
cana-5829	159	11	may	may	AUX
cana-5829	159	12	not	not	PART
cana-5829	159	13	always	always	ADV
cana-5829	159	14	be	be	AUX
cana-5829	159	15	perfectly	perfectly	ADV
cana-5829	159	16	clear	clear	ADJ
cana-5829	159	17	.	.	PUNCT
cana-5829	160	1	intuitionistic	intuitionistic	ADJ
cana-5829	160	2	fuzzy	fuzzy	ADJ
cana-5829	160	3	matrices	matrix	NOUN
cana-5829	160	4	provide	provide	VERB
cana-5829	160	5	a	a	DET
cana-5829	160	6	way	way	NOUN
cana-5829	160	7	to	to	PART
cana-5829	160	8	handle	handle	VERB
cana-5829	160	9	imprecise	imprecise	ADJ
cana-5829	160	10	or	or	CCONJ
cana-5829	160	11	incomplete	incomplete	ADJ
cana-5829	160	12	data	datum	NOUN
cana-5829	160	13	,	,	PUNCT
cana-5829	160	14	allowing	allow	VERB
cana-5829	160	15	more	more	ADV
cana-5829	160	16	flexible	flexible	ADJ
cana-5829	160	17	and	and	CCONJ
cana-5829	160	18	accurate	accurate	ADJ
cana-5829	160	19	classification	classification	NOUN
cana-5829	160	20	.	.	PUNCT
cana-5829	161	1	3.3.3	3.3.3	NUM
cana-5829	161	2	data	datum	NOUN
cana-5829	161	3	mining	mining	NOUN
cana-5829	161	4	and	and	CCONJ
cana-5829	161	5	clustering	clustering	NOUN
cana-5829	161	6	:	:	PUNCT
cana-5829	161	7	intuitionistic	intuitionistic	ADJ
cana-5829	161	8	fuzzy	fuzzy	ADJ
cana-5829	161	9	clustering	clustering	ADJ
cana-5829	161	10	algorithms	algorithm	NOUN
cana-5829	161	11	,	,	PUNCT
cana-5829	161	12	where	where	SCONJ
cana-5829	161	13	each	each	DET
cana-5829	161	14	data	datum	NOUN
cana-5829	161	15	point	point	NOUN
cana-5829	161	16	belongs	belong	VERB
cana-5829	161	17	to	to	ADP
cana-5829	161	18	multiple	multiple	ADJ
cana-5829	161	19	clusters	cluster	NOUN
cana-5829	161	20	with	with	ADP
cana-5829	161	21	varying	vary	VERB
cana-5829	161	22	degrees	degree	NOUN
cana-5829	161	23	of	of	ADP
cana-5829	161	24	membership	membership	NOUN
cana-5829	161	25	and	and	CCONJ
cana-5829	161	26	non	non	ADJ
cana-5829	161	27	-	-	NOUN
cana-5829	161	28	membership	membership	NOUN
cana-5829	161	29	,	,	PUNCT
cana-5829	161	30	can	can	AUX
cana-5829	161	31	benefit	benefit	VERB
cana-5829	161	32	from	from	ADP
cana-5829	161	33	intuitionistic	intuitionistic	ADJ
cana-5829	161	34	fuzzy	fuzzy	ADJ
cana-5829	161	35	matrices	matrix	NOUN
cana-5829	161	36	.	.	PUNCT
cana-5829	162	1	example	example	NOUN
cana-5829	162	2	:	:	PUNCT
cana-5829	162	3	in	in	ADP
cana-5829	162	4	customer	customer	NOUN
cana-5829	162	5	segmentation	segmentation	NOUN
cana-5829	162	6	,	,	PUNCT
cana-5829	162	7	instead	instead	ADV
cana-5829	162	8	of	of	ADP
cana-5829	162	9	classifying	classify	VERB
cana-5829	162	10	customers	customer	NOUN
cana-5829	162	11	strictly	strictly	ADV
cana-5829	162	12	into	into	ADP
cana-5829	162	13	one	one	NUM
cana-5829	162	14	segment	segment	NOUN
cana-5829	162	15	,	,	PUNCT
cana-5829	162	16	intuitionistic	intuitionistic	ADJ
cana-5829	162	17	fuzzy	fuzzy	ADJ
cana-5829	162	18	clustering	clustering	NOUN
cana-5829	162	19	allows	allow	VERB
cana-5829	162	20	a	a	DET
cana-5829	162	21	customer	customer	NOUN
cana-5829	162	22	to	to	PART
cana-5829	162	23	belong	belong	VERB
cana-5829	162	24	to	to	ADP
cana-5829	162	25	multiple	multiple	ADJ
cana-5829	162	26	segments	segment	NOUN
cana-5829	162	27	with	with	ADP
cana-5829	162	28	different	different	ADJ
cana-5829	162	29	degrees	degree	NOUN
cana-5829	162	30	of	of	ADP
cana-5829	162	31	membership	membership	NOUN
cana-5829	162	32	and	and	CCONJ
cana-5829	162	33	non	non	ADJ
cana-5829	162	34	-	-	NOUN
cana-5829	162	35	membership	membership	NOUN
cana-5829	162	36	,	,	PUNCT
cana-5829	162	37	representing	represent	VERB
cana-5829	162	38	their	their	PRON
cana-5829	162	39	preferences	preference	NOUN
cana-5829	162	40	or	or	CCONJ
cana-5829	162	41	behaviours	behaviour	NOUN
cana-5829	162	42	more	more	ADV
cana-5829	162	43	flexibly	flexibly	ADV
cana-5829	162	44	.	.	PUNCT
cana-5829	163	1	3.3.4	3.3.4	NUM
cana-5829	163	2	control	control	NOUN
cana-5829	163	3	systems	system	NOUN
cana-5829	163	4	:	:	PUNCT
cana-5829	163	5	in	in	ADP
cana-5829	163	6	fuzzy	fuzzy	ADJ
cana-5829	163	7	control	control	NOUN
cana-5829	163	8	systems	system	NOUN
cana-5829	163	9	,	,	PUNCT
cana-5829	163	10	where	where	SCONJ
cana-5829	163	11	control	control	NOUN
cana-5829	163	12	rules	rule	NOUN
cana-5829	163	13	are	be	AUX
cana-5829	163	14	designed	design	VERB
cana-5829	163	15	based	base	VERB
cana-5829	163	16	on	on	ADP
cana-5829	163	17	uncertain	uncertain	ADJ
cana-5829	163	18	or	or	CCONJ
cana-5829	163	19	imprecise	imprecise	ADJ
cana-5829	163	20	data	datum	NOUN
cana-5829	163	21	,	,	PUNCT
cana-5829	163	22	intuitionistic	intuitionistic	ADJ
cana-5829	163	23	fuzzy	fuzzy	ADJ
cana-5829	163	24	matrices	matrix	NOUN
cana-5829	163	25	help	help	VERB
cana-5829	163	26	incorporate	incorporate	VERB
cana-5829	163	27	the	the	DET
cana-5829	163	28	uncertainty	uncertainty	NOUN
cana-5829	163	29	of	of	ADP
cana-5829	163	30	the	the	DET
cana-5829	163	31	system	system	NOUN
cana-5829	163	32	's	's	PART
cana-5829	163	33	parameters	parameter	NOUN
cana-5829	163	34	.	.	PUNCT
cana-5829	164	1	example	example	NOUN
cana-5829	164	2	:	:	PUNCT
cana-5829	164	3	in	in	ADP
cana-5829	164	4	temperature	temperature	NOUN
cana-5829	164	5	control	control	NOUN
cana-5829	164	6	of	of	ADP
cana-5829	164	7	a	a	DET
cana-5829	164	8	system	system	NOUN
cana-5829	164	9	,	,	PUNCT
cana-5829	164	10	intuitionistic	intuitionistic	ADJ
cana-5829	164	11	fuzzy	fuzzy	ADJ
cana-5829	164	12	matrices	matrix	NOUN
cana-5829	164	13	can	can	AUX
cana-5829	164	14	help	help	VERB
cana-5829	164	15	model	model	VERB
cana-5829	164	16	the	the	DET
cana-5829	164	17	uncertainty	uncertainty	NOUN
cana-5829	164	18	in	in	ADP
cana-5829	164	19	sensor	sensor	NOUN
cana-5829	164	20	readings	reading	NOUN
cana-5829	164	21	and	and	CCONJ
cana-5829	164	22	adjust	adjust	VERB
cana-5829	164	23	the	the	DET
cana-5829	164	24	control	control	NOUN
cana-5829	164	25	system	system	NOUN
cana-5829	164	26	’s	’s	PART
cana-5829	164	27	response	response	NOUN
cana-5829	164	28	accordingly	accordingly	ADV
cana-5829	164	29	.	.	PUNCT
cana-5829	165	1	3.3.5	3.3.5	NUM
cana-5829	165	2	optimization	optimization	NOUN
cana-5829	165	3	problem	problem	NOUN
cana-5829	165	4	:	:	PUNCT
cana-5829	165	5	in	in	ADP
cana-5829	165	6	optimization	optimization	NOUN
cana-5829	165	7	problems	problem	NOUN
cana-5829	165	8	with	with	ADP
cana-5829	165	9	imprecise	imprecise	ADJ
cana-5829	165	10	constraints	constraint	NOUN
cana-5829	165	11	or	or	CCONJ
cana-5829	165	12	objective	objective	ADJ
cana-5829	165	13	functions	function	NOUN
cana-5829	165	14	,	,	PUNCT
cana-5829	165	15	intuitionistic	intuitionistic	ADJ
cana-5829	165	16	fuzzy	fuzzy	ADJ
cana-5829	165	17	matrices	matrix	NOUN
cana-5829	165	18	can	can	AUX
cana-5829	165	19	be	be	AUX
cana-5829	165	20	used	use	VERB
cana-5829	165	21	to	to	PART
cana-5829	165	22	represent	represent	VERB
cana-5829	165	23	the	the	DET
cana-5829	165	24	uncertainty	uncertainty	NOUN
cana-5829	165	25	in	in	ADP
cana-5829	165	26	the	the	DET
cana-5829	165	27	data	data	NOUN
cana-5829	165	28	,	,	PUNCT
cana-5829	165	29	allowing	allow	VERB
cana-5829	165	30	for	for	ADP
cana-5829	165	31	more	more	ADV
cana-5829	165	32	robust	robust	ADJ
cana-5829	165	33	optimization	optimization	NOUN
cana-5829	165	34	results	result	NOUN
cana-5829	165	35	.	.	PUNCT
cana-5829	166	1	example	example	NOUN
cana-5829	166	2	:	:	PUNCT
cana-5829	166	3	in	in	ADP
cana-5829	166	4	supply	supply	NOUN
cana-5829	166	5	chain	chain	NOUN
cana-5829	166	6	optimization	optimization	NOUN
cana-5829	166	7	,	,	PUNCT
cana-5829	166	8	the	the	DET
cana-5829	166	9	cost	cost	NOUN
cana-5829	166	10	or	or	CCONJ
cana-5829	166	11	demand	demand	NOUN
cana-5829	166	12	may	may	AUX
cana-5829	166	13	have	have	VERB
cana-5829	166	14	uncertainty	uncertainty	NOUN
cana-5829	166	15	.	.	PUNCT
cana-5829	167	1	using	use	VERB
cana-5829	167	2	intuitionistic	intuitionistic	ADJ
cana-5829	167	3	fuzzy	fuzzy	ADJ
cana-5829	167	4	matrices	matrix	NOUN
cana-5829	167	5	to	to	PART
cana-5829	167	6	model	model	VERB
cana-5829	167	7	these	these	DET
cana-5829	167	8	uncertainties	uncertainty	NOUN
cana-5829	167	9	helps	help	VERB
cana-5829	167	10	in	in	ADP
cana-5829	167	11	obtaining	obtain	VERB
cana-5829	167	12	optimal	optimal	ADJ
cana-5829	167	13	solutions	solution	NOUN
cana-5829	167	14	under	under	ADP
cana-5829	167	15	varying	vary	VERB
cana-5829	167	16	levels	level	NOUN
cana-5829	167	17	of	of	ADP
cana-5829	167	18	confidence	confidence	NOUN
cana-5829	167	19	.	.	PUNCT
cana-5829	168	1	3.3.6	3.3.6	NUM
cana-5829	168	2	fault	fault	NOUN
cana-5829	168	3	diagnosis	diagnosis	NOUN
cana-5829	168	4	and	and	CCONJ
cana-5829	168	5	reliability	reliability	NOUN
cana-5829	168	6	analysis	analysis	NOUN
cana-5829	168	7	:	:	PUNCT
cana-5829	168	8	intuitionistic	intuitionistic	ADJ
cana-5829	168	9	fuzzy	fuzzy	ADJ
cana-5829	168	10	matrices	matrix	NOUN
cana-5829	168	11	are	be	AUX
cana-5829	168	12	useful	useful	ADJ
cana-5829	168	13	in	in	ADP
cana-5829	168	14	fault	fault	NOUN
cana-5829	168	15	diagnosis	diagnosis	NOUN
cana-5829	168	16	systems	system	NOUN
cana-5829	168	17	where	where	SCONJ
cana-5829	168	18	the	the	DET
cana-5829	168	19	exact	exact	ADJ
cana-5829	168	20	cause	cause	NOUN
cana-5829	168	21	of	of	ADP
cana-5829	168	22	a	a	DET
cana-5829	168	23	fault	fault	NOUN
cana-5829	168	24	is	be	AUX
cana-5829	168	25	not	not	PART
cana-5829	168	26	immediately	immediately	ADV
cana-5829	168	27	clear	clear	ADJ
cana-5829	168	28	,	,	PUNCT
cana-5829	168	29	and	and	CCONJ
cana-5829	168	30	multiple	multiple	ADJ
cana-5829	168	31	possible	possible	ADJ
cana-5829	168	32	faults	fault	NOUN
cana-5829	168	33	need	need	VERB
cana-5829	168	34	to	to	PART
cana-5829	168	35	be	be	AUX
cana-5829	168	36	considered	consider	VERB
cana-5829	168	37	with	with	ADP
cana-5829	168	38	varying	vary	VERB
cana-5829	168	39	levels	level	NOUN
cana-5829	168	40	of	of	ADP
cana-5829	168	41	confidence	confidence	NOUN
cana-5829	168	42	.	.	PUNCT
cana-5829	169	1	example	example	NOUN
cana-5829	169	2	:	:	PUNCT
cana-5829	169	3	in	in	ADP
cana-5829	169	4	industrial	industrial	ADJ
cana-5829	169	5	systems	system	NOUN
cana-5829	169	6	,	,	PUNCT
cana-5829	169	7	intuitionistic	intuitionistic	ADJ
cana-5829	169	8	fuzzy	fuzzy	ADJ
cana-5829	169	9	matrices	matrix	NOUN
cana-5829	169	10	can	can	AUX
cana-5829	169	11	help	help	VERB
cana-5829	169	12	in	in	ADP
cana-5829	169	13	analysing	analyse	VERB
cana-5829	169	14	machine	machine	NOUN
cana-5829	169	15	faults	fault	NOUN
cana-5829	169	16	by	by	ADP
cana-5829	169	17	considering	consider	VERB
cana-5829	169	18	various	various	ADJ
cana-5829	169	19	possible	possible	ADJ
cana-5829	169	20	failure	failure	NOUN
cana-5829	169	21	modes	mode	NOUN
cana-5829	169	22	,	,	PUNCT
cana-5829	169	23	each	each	PRON
cana-5829	169	24	with	with	ADP
cana-5829	169	25	a	a	DET
cana-5829	169	26	degree	degree	NOUN
cana-5829	169	27	of	of	ADP
cana-5829	169	28	membership	membership	NOUN
cana-5829	169	29	(	(	PUNCT
cana-5829	169	30	how	how	SCONJ
cana-5829	169	31	likely	likely	ADV
cana-5829	169	32	the	the	DET
cana-5829	169	33	fault	fault	NOUN
cana-5829	169	34	is	be	AUX
cana-5829	169	35	)	)	PUNCT
cana-5829	169	36	and	and	CCONJ
cana-5829	169	37	non	non	ADJ
cana-5829	169	38	-	-	NOUN
cana-5829	169	39	membership	membership	NOUN
cana-5829	169	40	(	(	PUNCT
cana-5829	169	41	how	how	SCONJ
cana-5829	169	42	unlikely	unlikely	ADJ
cana-5829	169	43	it	it	PRON
cana-5829	169	44	is	be	AUX
cana-5829	169	45	)	)	PUNCT
cana-5829	169	46	.	.	PUNCT
cana-5829	170	1	3.3.7	3.3.7	NUM
cana-5829	170	2	expert	expert	NOUN
cana-5829	170	3	systems	system	NOUN
cana-5829	170	4	and	and	CCONJ
cana-5829	170	5	knowledge	knowledge	NOUN
cana-5829	170	6	representation	representation	NOUN
cana-5829	170	7	:	:	PUNCT
cana-5829	170	8	intuitionistic	intuitionistic	ADJ
cana-5829	170	9	fuzzy	fuzzy	ADJ
cana-5829	170	10	matrices	matrix	NOUN
cana-5829	170	11	can	can	AUX
cana-5829	170	12	enhance	enhance	VERB
cana-5829	170	13	expert	expert	NOUN
cana-5829	170	14	systems	system	NOUN
cana-5829	170	15	by	by	ADP
cana-5829	170	16	handling	handle	VERB
cana-5829	170	17	uncertainty	uncertainty	NOUN
cana-5829	170	18	in	in	ADP
cana-5829	170	19	expert	expert	ADJ
cana-5829	170	20	knowledge	knowledge	NOUN
cana-5829	170	21	and	and	CCONJ
cana-5829	170	22	decision	decision	NOUN
cana-5829	170	23	rules	rule	NOUN
cana-5829	170	24	.	.	PUNCT
cana-5829	171	1	example	example	NOUN
cana-5829	171	2	:	:	PUNCT
cana-5829	171	3	in	in	ADP
cana-5829	171	4	medical	medical	ADJ
cana-5829	171	5	diagnosis	diagnosis	NOUN
cana-5829	171	6	systems	system	NOUN
cana-5829	171	7	,	,	PUNCT
cana-5829	171	8	intuitionistic	intuitionistic	ADJ
cana-5829	171	9	fuzzy	fuzzy	ADJ
cana-5829	171	10	matrices	matrix	NOUN
cana-5829	171	11	can	can	AUX
cana-5829	171	12	model	model	VERB
cana-5829	171	13	the	the	DET
cana-5829	171	14	uncertainty	uncertainty	NOUN
cana-5829	171	15	in	in	ADP
cana-5829	171	16	diagnosing	diagnose	VERB
cana-5829	171	17	a	a	DET
cana-5829	171	18	disease	disease	NOUN
cana-5829	171	19	based	base	VERB
cana-5829	171	20	on	on	ADP
cana-5829	171	21	symptoms	symptom	NOUN
cana-5829	171	22	and	and	CCONJ
cana-5829	171	23	test	test	NOUN
cana-5829	171	24	results	result	NOUN
cana-5829	171	25	,	,	PUNCT
cana-5829	171	26	where	where	SCONJ
cana-5829	171	27	the	the	DET
cana-5829	171	28	certainty	certainty	NOUN
cana-5829	171	29	of	of	ADP
cana-5829	171	30	a	a	DET
cana-5829	171	31	diagnosis	diagnosis	NOUN
cana-5829	171	32	may	may	AUX
cana-5829	171	33	not	not	PART
cana-5829	171	34	be	be	AUX
cana-5829	171	35	absolute	absolute	ADJ
cana-5829	171	36	communications	communication	NOUN
cana-5829	171	37	on	on	ADP
cana-5829	171	38	applied	apply	VERB
cana-5829	171	39	nonlinear	nonlinear	ADJ
cana-5829	171	40	analysis	analysis	NOUN
cana-5829	171	41	issn	issn	NOUN
cana-5829	171	42	:	:	PUNCT
cana-5829	171	43	1074	1074	NUM
cana-5829	171	44	-	-	PUNCT
cana-5829	171	45	133x	133x	NUM
cana-5829	171	46	vol	vol	VERB
cana-5829	171	47	32	32	NUM
cana-5829	171	48	no	no	NOUN
cana-5829	171	49	.	.	PUNCT
cana-5829	172	1	10s	10	NOUN
cana-5829	172	2	(	(	PUNCT
cana-5829	172	3	2025	2025	NUM
cana-5829	172	4	)	)	PUNCT
cana-5829	172	5	2930	2930	NUM
cana-5829	173	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-5829	173	2	3.3.8	3.3.8	NUM
cana-5829	173	3	recommendation	recommendation	NOUN
cana-5829	173	4	systems	system	NOUN
cana-5829	173	5	:	:	PUNCT
cana-5829	173	6	in	in	ADP
cana-5829	173	7	recommendation	recommendation	NOUN
cana-5829	173	8	systems	system	NOUN
cana-5829	173	9	,	,	PUNCT
cana-5829	173	10	intuitionistic	intuitionistic	ADJ
cana-5829	173	11	fuzzy	fuzzy	ADJ
cana-5829	173	12	matrices	matrix	NOUN
cana-5829	173	13	can	can	AUX
cana-5829	173	14	be	be	AUX
cana-5829	173	15	used	use	VERB
cana-5829	173	16	to	to	PART
cana-5829	173	17	represent	represent	VERB
cana-5829	173	18	the	the	DET
cana-5829	173	19	preferences	preference	NOUN
cana-5829	173	20	of	of	ADP
cana-5829	173	21	users	user	NOUN
cana-5829	173	22	and	and	CCONJ
cana-5829	173	23	the	the	DET
cana-5829	173	24	uncertainty	uncertainty	NOUN
cana-5829	173	25	in	in	ADP
cana-5829	173	26	their	their	PRON
cana-5829	173	27	preferences	preference	NOUN
cana-5829	173	28	for	for	ADP
cana-5829	173	29	different	different	ADJ
cana-5829	173	30	items	item	NOUN
cana-5829	173	31	or	or	CCONJ
cana-5829	173	32	services	service	NOUN
cana-5829	173	33	.	.	PUNCT
cana-5829	174	1	example	example	NOUN
cana-5829	174	2	:	:	PUNCT
cana-5829	174	3	in	in	ADP
cana-5829	174	4	an	an	DET
cana-5829	174	5	e	e	NOUN
cana-5829	174	6	-	-	NOUN
cana-5829	174	7	commerce	commerce	NOUN
cana-5829	174	8	platform	platform	NOUN
cana-5829	174	9	,	,	PUNCT
cana-5829	174	10	users	user	NOUN
cana-5829	174	11	may	may	AUX
cana-5829	174	12	have	have	VERB
cana-5829	174	13	different	different	ADJ
cana-5829	174	14	levels	level	NOUN
cana-5829	174	15	of	of	ADP
cana-5829	174	16	preference	preference	NOUN
cana-5829	174	17	for	for	ADP
cana-5829	174	18	products	product	NOUN
cana-5829	174	19	,	,	PUNCT
cana-5829	174	20	but	but	CCONJ
cana-5829	174	21	these	these	DET
cana-5829	174	22	preferences	preference	NOUN
cana-5829	174	23	may	may	AUX
cana-5829	174	24	also	also	ADV
cana-5829	174	25	be	be	AUX
cana-5829	174	26	uncertain	uncertain	ADJ
cana-5829	174	27	or	or	CCONJ
cana-5829	174	28	ambiguous	ambiguous	ADJ
cana-5829	174	29	.	.	PUNCT
cana-5829	175	1	intuitionistic	intuitionistic	ADJ
cana-5829	175	2	fuzzy	fuzzy	ADJ
cana-5829	175	3	matrices	matrix	NOUN
cana-5829	175	4	can	can	AUX
cana-5829	175	5	help	help	VERB
cana-5829	175	6	provide	provide	VERB
cana-5829	175	7	better	well	ADJ
cana-5829	175	8	personalized	personalize	VERB
cana-5829	175	9	recommendations	recommendation	NOUN
cana-5829	175	10	by	by	ADP
cana-5829	175	11	taking	take	VERB
cana-5829	175	12	into	into	ADP
cana-5829	175	13	account	account	NOUN
cana-5829	175	14	both	both	PRON
cana-5829	175	15	positive	positive	ADJ
cana-5829	175	16	preferences	preference	NOUN
cana-5829	175	17	and	and	CCONJ
cana-5829	175	18	the	the	DET
cana-5829	175	19	lack	lack	NOUN
cana-5829	175	20	of	of	ADP
cana-5829	175	21	preference	preference	NOUN
cana-5829	175	22	.	.	PUNCT
cana-5829	176	1	3.3	3.3	NUM
cana-5829	176	2	.	.	X
cana-5829	176	3	9	9	NUM
cana-5829	176	4	social	social	ADJ
cana-5829	176	5	network	network	NOUN
cana-5829	176	6	analysis	analysis	NOUN
cana-5829	176	7	:	:	PUNCT
cana-5829	176	8	in	in	ADP
cana-5829	176	9	analysing	analyse	VERB
cana-5829	176	10	social	social	ADJ
cana-5829	176	11	networks	network	NOUN
cana-5829	176	12	,	,	PUNCT
cana-5829	176	13	intuitionistic	intuitionistic	ADJ
cana-5829	176	14	fuzzy	fuzzy	ADJ
cana-5829	176	15	matrices	matrix	NOUN
cana-5829	176	16	can	can	AUX
cana-5829	176	17	model	model	VERB
cana-5829	176	18	relationships	relationship	NOUN
cana-5829	176	19	between	between	ADP
cana-5829	176	20	individuals	individual	NOUN
cana-5829	176	21	,	,	PUNCT
cana-5829	176	22	where	where	SCONJ
cana-5829	176	23	relationships	relationship	NOUN
cana-5829	176	24	may	may	AUX
cana-5829	176	25	have	have	VERB
cana-5829	176	26	different	different	ADJ
cana-5829	176	27	levels	level	NOUN
cana-5829	176	28	of	of	ADP
cana-5829	176	29	strength	strength	NOUN
cana-5829	176	30	and	and	CCONJ
cana-5829	176	31	uncertainty	uncertainty	NOUN
cana-5829	176	32	.	.	PUNCT
cana-5829	177	1	example	example	NOUN
cana-5829	177	2	:	:	PUNCT
cana-5829	177	3	in	in	ADP
cana-5829	177	4	social	social	ADJ
cana-5829	177	5	media	medium	NOUN
cana-5829	177	6	platforms	platform	NOUN
cana-5829	177	7	,	,	PUNCT
cana-5829	177	8	the	the	DET
cana-5829	177	9	relationship	relationship	NOUN
cana-5829	177	10	strength	strength	NOUN
cana-5829	177	11	between	between	ADP
cana-5829	177	12	two	two	NUM
cana-5829	177	13	users	user	NOUN
cana-5829	177	14	may	may	AUX
cana-5829	177	15	be	be	AUX
cana-5829	177	16	uncertain	uncertain	ADJ
cana-5829	177	17	(	(	PUNCT
cana-5829	177	18	not	not	PART
cana-5829	177	19	just	just	ADV
cana-5829	177	20	strong	strong	ADJ
cana-5829	177	21	or	or	CCONJ
cana-5829	177	22	weak	weak	ADJ
cana-5829	177	23	)	)	PUNCT
cana-5829	177	24	and	and	CCONJ
cana-5829	177	25	could	could	AUX
cana-5829	177	26	vary	vary	VERB
cana-5829	177	27	over	over	ADP
cana-5829	177	28	time	time	NOUN
cana-5829	177	29	.	.	PUNCT
cana-5829	178	1	intuitionistic	intuitionistic	ADJ
cana-5829	178	2	fuzzy	fuzzy	ADJ
cana-5829	178	3	matrices	matrix	NOUN
cana-5829	178	4	help	help	NOUN
cana-5829	178	5	represent	represent	VERB
cana-5829	178	6	this	this	DET
cana-5829	178	7	uncertainty	uncertainty	NOUN
cana-5829	178	8	in	in	ADP
cana-5829	178	9	social	social	ADJ
cana-5829	178	10	network	network	NOUN
cana-5829	178	11	analysis	analysis	NOUN
cana-5829	178	12	.	.	PUNCT
cana-5829	179	1	3.3.10	3.3.10	NUM
cana-5829	179	2	medical	medical	ADJ
cana-5829	179	3	diagnostics	diagnostic	NOUN
cana-5829	179	4	and	and	CCONJ
cana-5829	179	5	health	health	NOUN
cana-5829	179	6	monitoring	monitoring	NOUN
cana-5829	179	7	:	:	PUNCT
cana-5829	179	8	intuitionistic	intuitionistic	ADJ
cana-5829	179	9	fuzzy	fuzzy	ADJ
cana-5829	179	10	matrices	matrix	NOUN
cana-5829	179	11	can	can	AUX
cana-5829	179	12	be	be	AUX
cana-5829	179	13	applied	apply	VERB
cana-5829	179	14	in	in	ADP
cana-5829	179	15	the	the	DET
cana-5829	179	16	representation	representation	NOUN
cana-5829	179	17	of	of	ADP
cana-5829	179	18	medical	medical	ADJ
cana-5829	179	19	data	datum	NOUN
cana-5829	179	20	,	,	PUNCT
cana-5829	179	21	where	where	SCONJ
cana-5829	179	22	diagnostic	diagnostic	ADJ
cana-5829	179	23	results	result	NOUN
cana-5829	179	24	may	may	AUX
cana-5829	179	25	have	have	VERB
cana-5829	179	26	both	both	DET
cana-5829	179	27	degrees	degree	NOUN
cana-5829	179	28	of	of	ADP
cana-5829	179	29	certainty	certainty	NOUN
cana-5829	179	30	and	and	CCONJ
cana-5829	179	31	uncertainty	uncertainty	NOUN
cana-5829	179	32	,	,	PUNCT
cana-5829	179	33	especially	especially	ADV
cana-5829	179	34	when	when	SCONJ
cana-5829	179	35	dealing	deal	VERB
cana-5829	179	36	with	with	ADP
cana-5829	179	37	incomplete	incomplete	ADJ
cana-5829	179	38	or	or	CCONJ
cana-5829	179	39	ambiguous	ambiguous	ADJ
cana-5829	179	40	information	information	NOUN
cana-5829	179	41	.	.	PUNCT
cana-5829	180	1	example	example	NOUN
cana-5829	180	2	:	:	PUNCT
cana-5829	180	3	in	in	ADP
cana-5829	180	4	health	health	NOUN
cana-5829	180	5	monitoring	monitoring	NOUN
cana-5829	180	6	,	,	PUNCT
cana-5829	180	7	an	an	DET
cana-5829	180	8	intuitionistic	intuitionistic	ADJ
cana-5829	180	9	fuzzy	fuzzy	ADJ
cana-5829	180	10	matrix	matrix	NOUN
cana-5829	180	11	can	can	AUX
cana-5829	180	12	represent	represent	VERB
cana-5829	180	13	various	various	ADJ
cana-5829	180	14	symptoms	symptom	NOUN
cana-5829	180	15	and	and	CCONJ
cana-5829	180	16	their	their	PRON
cana-5829	180	17	relationships	relationship	NOUN
cana-5829	180	18	to	to	ADP
cana-5829	180	19	potential	potential	ADJ
cana-5829	180	20	diseases	disease	NOUN
cana-5829	180	21	,	,	PUNCT
cana-5829	180	22	with	with	ADP
cana-5829	180	23	both	both	CCONJ
cana-5829	180	24	membership	membership	NOUN
cana-5829	180	25	and	and	CCONJ
cana-5829	180	26	non	non	ADJ
cana-5829	180	27	-	-	ADJ
cana-5829	180	28	membership	membership	ADJ
cana-5829	180	29	values	value	NOUN
cana-5829	180	30	indicating	indicate	VERB
cana-5829	180	31	the	the	DET
cana-5829	180	32	degree	degree	NOUN
cana-5829	180	33	of	of	ADP
cana-5829	180	34	certainty	certainty	NOUN
cana-5829	180	35	about	about	ADP
cana-5829	180	36	the	the	DET
cana-5829	180	37	presence	presence	NOUN
cana-5829	180	38	of	of	ADP
cana-5829	180	39	a	a	DET
cana-5829	180	40	condition	condition	NOUN
cana-5829	180	41	.	.	PUNCT
cana-5829	181	1	4	4	NUM
cana-5829	181	2	overview	overview	NOUN
cana-5829	181	3	on	on	ADP
cana-5829	181	4	normalization	normalization	NOUN
cana-5829	181	5	and	and	CCONJ
cana-5829	181	6	cartesian	cartesian	ADJ
cana-5829	181	7	product	product	NOUN
cana-5829	181	8	of	of	ADP
cana-5829	181	9	intuitionistic	intuitionistic	ADJ
cana-5829	181	10	fuzzy	fuzzy	ADJ
cana-5829	181	11	matrices	matrix	NOUN
cana-5829	181	12	:	:	PUNCT
cana-5829	181	13	4.1definition	4.1definition	NOUN
cana-5829	181	14	:	:	PUNCT
cana-5829	181	15	the	the	DET
cana-5829	181	16	normalization	normalization	NOUN
cana-5829	181	17	of	of	ADP
cana-5829	181	18	an	an	DET
cana-5829	181	19	intuitionistic	intuitionistic	ADJ
cana-5829	181	20	fuzzy	fuzzy	ADJ
cana-5829	181	21	matrix	matrix	NOUN
cana-5829	181	22	(	(	PUNCT
cana-5829	181	23	ifm	ifm	NOUN
cana-5829	181	24	)	)	PUNCT
cana-5829	181	25	refers	refer	VERB
cana-5829	181	26	to	to	ADP
cana-5829	181	27	the	the	DET
cana-5829	181	28	process	process	NOUN
cana-5829	181	29	of	of	ADP
cana-5829	181	30	transforming	transform	VERB
cana-5829	181	31	an	an	DET
cana-5829	181	32	intuitionistic	intuitionistic	ADJ
cana-5829	181	33	fuzzy	fuzzy	ADJ
cana-5829	181	34	matrix	matrix	NOUN
cana-5829	181	35	into	into	ADP
cana-5829	181	36	a	a	DET
cana-5829	181	37	standardized	standardized	ADJ
cana-5829	181	38	form	form	NOUN
cana-5829	181	39	while	while	SCONJ
cana-5829	181	40	preserving	preserve	VERB
cana-5829	181	41	its	its	PRON
cana-5829	181	42	essential	essential	ADJ
cana-5829	181	43	characteristics	characteristic	NOUN
cana-5829	181	44	.an	.an	PUNCT
cana-5829	182	1	intuitionistic	intuitionistic	ADJ
cana-5829	182	2	fuzzy	fuzzy	ADJ
cana-5829	182	3	matrix	matrix	NOUN
cana-5829	182	4	is	be	AUX
cana-5829	182	5	a	a	DET
cana-5829	182	6	matrix	matrix	NOUN
cana-5829	182	7	in	in	ADP
cana-5829	182	8	which	which	PRON
cana-5829	182	9	each	each	DET
cana-5829	182	10	element	element	NOUN
cana-5829	182	11	is	be	AUX
cana-5829	182	12	represented	represent	VERB
cana-5829	182	13	as	as	ADP
cana-5829	182	14	an	an	DET
cana-5829	182	15	intuitionistic	intuitionistic	ADJ
cana-5829	182	16	fuzzy	fuzzy	ADJ
cana-5829	182	17	number	number	NOUN
cana-5829	182	18	(	(	PUNCT
cana-5829	182	19	ifm	ifm	NOUN
cana-5829	182	20	)	)	PUNCT
cana-5829	182	21	,	,	PUNCT
cana-5829	182	22	typically	typically	ADV
cana-5829	182	23	denoted	denote	VERB
cana-5829	182	24	as	as	ADP
cana-5829	182	25	a	a	DET
cana-5829	182	26	pair	pair	NOUN
cana-5829	182	27	(	(	PUNCT
cana-5829	182	28	µ𝑖𝑗	µ𝑖𝑗	NOUN
cana-5829	182	29	,	,	PUNCT
cana-5829	182	30	𝜗𝑖𝑗	𝜗𝑖𝑗	PROPN
cana-5829	182	31	)	)	PUNCT
cana-5829	182	32	,	,	PUNCT
cana-5829	182	33	where	where	SCONJ
cana-5829	182	34	,	,	PUNCT
cana-5829	182	35	µ𝑖𝑗is	µ𝑖𝑗is	PROPN
cana-5829	182	36	the	the	DET
cana-5829	182	37	membership	membership	NOUN
cana-5829	182	38	degree	degree	NOUN
cana-5829	182	39	of	of	ADP
cana-5829	182	40	the	the	DET
cana-5829	182	41	element	element	NOUN
cana-5829	182	42	(	(	PUNCT
cana-5829	182	43	i	i	NOUN
cana-5829	182	44	,	,	PUNCT
cana-5829	182	45	j),representing	j),represente	VERB
cana-5829	182	46	the	the	DET
cana-5829	182	47	degree	degree	NOUN
cana-5829	182	48	of	of	ADP
cana-5829	182	49	belonging	belong	VERB
cana-5829	182	50	to	to	ADP
cana-5829	182	51	a	a	DET
cana-5829	182	52	set	set	NOUN
cana-5829	182	53	.	.	PUNCT
cana-5829	183	1	𝜗𝑖𝑗	𝜗𝑖𝑗	PROPN
cana-5829	183	2	is	be	AUX
cana-5829	183	3	the	the	DET
cana-5829	183	4	non	non	ADJ
cana-5829	183	5	membership	membership	NOUN
cana-5829	183	6	degree	degree	NOUN
cana-5829	183	7	,	,	PUNCT
cana-5829	183	8	representing	represent	VERB
cana-5829	183	9	the	the	DET
cana-5829	183	10	degree	degree	NOUN
cana-5829	183	11	of	of	ADP
cana-5829	183	12	not	not	PART
cana-5829	183	13	belonging	belong	VERB
cana-5829	183	14	to	to	ADP
cana-5829	183	15	a	a	DET
cana-5829	183	16	set	set	NOUN
cana-5829	183	17	.	.	PUNCT
cana-5829	184	1	the	the	DET
cana-5829	184	2	hesitation	hesitation	NOUN
cana-5829	184	3	degree	degree	NOUN
cana-5829	184	4	is	be	AUX
cana-5829	184	5	given	give	VERB
cana-5829	184	6	by	by	ADP
cana-5829	184	7	𝜋𝑖𝑗	𝜋𝑖𝑗	NOUN
cana-5829	184	8	=	=	SYM
cana-5829	184	9	1	1	NUM
cana-5829	184	10	−	−	NOUN
cana-5829	184	11	(	(	PUNCT
cana-5829	184	12	µ𝑖𝑗	µ𝑖𝑗	NOUN
cana-5829	184	13	+	+	CCONJ
cana-5829	184	14	𝜗𝑖𝑗	𝜗𝑖𝑗	NOUN
cana-5829	184	15	)	)	PUNCT
cana-5829	184	16	normalization	normalization	NOUN
cana-5829	184	17	in	in	ADP
cana-5829	184	18	this	this	DET
cana-5829	184	19	context	context	NOUN
cana-5829	184	20	ensures	ensure	VERB
cana-5829	184	21	that	that	SCONJ
cana-5829	184	22	the	the	DET
cana-5829	184	23	fuzzy	fuzzy	ADJ
cana-5829	184	24	matrix	matrix	NOUN
cana-5829	184	25	values	value	NOUN
cana-5829	184	26	are	be	AUX
cana-5829	184	27	on	on	ADP
cana-5829	184	28	the	the	DET
cana-5829	184	29	same	same	ADJ
cana-5829	184	30	scale	scale	NOUN
cana-5829	184	31	,	,	PUNCT
cana-5829	184	32	which	which	PRON
cana-5829	184	33	is	be	AUX
cana-5829	184	34	important	important	ADJ
cana-5829	184	35	for	for	ADP
cana-5829	184	36	:	:	PUNCT
cana-5829	184	37	reducing	reduce	VERB
cana-5829	184	38	the	the	DET
cana-5829	184	39	impact	impact	NOUN
cana-5829	184	40	of	of	ADP
cana-5829	184	41	extreme	extreme	ADJ
cana-5829	184	42	values	value	NOUN
cana-5829	184	43	.	.	PUNCT
cana-5829	185	1	making	make	VERB
cana-5829	185	2	the	the	DET
cana-5829	185	3	matrix	matrix	NOUN
cana-5829	185	4	more	more	ADJ
cana-5829	185	5	uniform	uniform	NOUN
cana-5829	185	6	for	for	ADP
cana-5829	185	7	better	well	ADJ
cana-5829	185	8	comparison	comparison	NOUN
cana-5829	185	9	and	and	CCONJ
cana-5829	185	10	analysis	analysis	NOUN
cana-5829	185	11	.	.	PUNCT
cana-5829	186	1	ensuring	ensure	VERB
cana-5829	186	2	consistency	consistency	NOUN
cana-5829	186	3	when	when	SCONJ
cana-5829	186	4	aggregating	aggregate	VERB
cana-5829	186	5	or	or	CCONJ
cana-5829	186	6	combining	combine	VERB
cana-5829	186	7	intuitionistic	intuitionistic	ADJ
cana-5829	186	8	fuzzy	fuzzy	ADJ
cana-5829	186	9	information	information	NOUN
cana-5829	186	10	across	across	ADP
cana-5829	186	11	different	different	ADJ
cana-5829	186	12	decision	decision	NOUN
cana-5829	186	13	criteria	criterion	NOUN
cana-5829	186	14	or	or	CCONJ
cana-5829	186	15	alternatives	alternative	NOUN
cana-5829	186	16	.	.	PUNCT
cana-5829	187	1	4.2normalization	4.2normalization	NUM
cana-5829	187	2	methods	method	NOUN
cana-5829	187	3	for	for	ADP
cana-5829	187	4	intuitionistic	intuitionistic	ADJ
cana-5829	187	5	fuzzy	fuzzy	ADJ
cana-5829	187	6	matrices	matrix	NOUN
cana-5829	187	7	:	:	PUNCT
cana-5829	187	8	normalization	normalization	NOUN
cana-5829	187	9	of	of	ADP
cana-5829	187	10	ifms	ifms	NOUN
cana-5829	187	11	helps	help	VERB
cana-5829	187	12	to	to	PART
cana-5829	187	13	standardize	standardize	VERB
cana-5829	187	14	the	the	DET
cana-5829	187	15	values	value	NOUN
cana-5829	187	16	of	of	ADP
cana-5829	187	17	the	the	DET
cana-5829	187	18	matrix	matrix	NOUN
cana-5829	187	19	to	to	ADP
cana-5829	187	20	a	a	DET
cana-5829	187	21	common	common	ADJ
cana-5829	187	22	range	range	NOUN
cana-5829	187	23	,	,	PUNCT
cana-5829	187	24	typically	typically	ADV
cana-5829	187	25	between	between	ADP
cana-5829	187	26	0	0	NUM
cana-5829	187	27	and	and	CCONJ
cana-5829	187	28	1	1	NUM
cana-5829	187	29	,	,	PUNCT
cana-5829	187	30	to	to	PART
cana-5829	187	31	ensure	ensure	VERB
cana-5829	187	32	that	that	SCONJ
cana-5829	187	33	they	they	PRON
cana-5829	187	34	are	be	AUX
cana-5829	187	35	comparable	comparable	ADJ
cana-5829	187	36	across	across	ADP
cana-5829	187	37	different	different	ADJ
cana-5829	187	38	criteria	criterion	NOUN
cana-5829	187	39	or	or	CCONJ
cana-5829	187	40	decision	decision	NOUN
cana-5829	187	41	-	-	PUNCT
cana-5829	187	42	making	make	VERB
cana-5829	187	43	factors	factor	NOUN
cana-5829	187	44	.	.	PUNCT
cana-5829	188	1	here	here	ADV
cana-5829	188	2	are	be	AUX
cana-5829	188	3	some	some	DET
cana-5829	188	4	common	common	ADJ
cana-5829	188	5	normalization	normalization	NOUN
cana-5829	188	6	methods	method	NOUN
cana-5829	188	7	:	:	PUNCT
cana-5829	188	8	4.2.1	4.2.1	NUM
cana-5829	188	9	linear	linear	ADJ
cana-5829	188	10	normalization	normalization	NOUN
cana-5829	188	11	:	:	PUNCT
cana-5829	188	12	in	in	ADP
cana-5829	188	13	this	this	DET
cana-5829	188	14	method	method	NOUN
cana-5829	188	15	,	,	PUNCT
cana-5829	188	16	the	the	DET
cana-5829	188	17	values	value	NOUN
cana-5829	188	18	of	of	ADP
cana-5829	188	19	the	the	DET
cana-5829	188	20	membership	membership	NOUN
cana-5829	188	21	,	,	PUNCT
cana-5829	188	22	non	non	ADJ
cana-5829	188	23	-	-	NOUN
cana-5829	188	24	membership	membership	NOUN
cana-5829	188	25	,	,	PUNCT
cana-5829	188	26	and	and	CCONJ
cana-5829	188	27	uncertainty	uncertainty	NOUN
cana-5829	188	28	degrees	degree	NOUN
cana-5829	188	29	are	be	AUX
cana-5829	188	30	normalized	normalize	VERB
cana-5829	188	31	based	base	VERB
cana-5829	188	32	on	on	ADP
cana-5829	188	33	their	their	PRON
cana-5829	188	34	maximum	maximum	ADJ
cana-5829	188	35	and	and	CCONJ
cana-5829	188	36	minimum	minimum	ADJ
cana-5829	188	37	values	value	NOUN
cana-5829	188	38	across	across	ADP
cana-5829	188	39	the	the	DET
cana-5829	188	40	entire	entire	ADJ
cana-5829	188	41	matrix	matrix	NOUN
cana-5829	188	42	.	.	PUNCT
cana-5829	189	1	the	the	DET
cana-5829	189	2	formula	formula	NOUN
cana-5829	189	3	for	for	ADP
cana-5829	189	4	normalization	normalization	NOUN
cana-5829	189	5	of	of	ADP
cana-5829	189	6	an	an	DET
cana-5829	189	7	element	element	NOUN
cana-5829	189	8	aij	aij	NOUN
cana-5829	189	9	=	=	PUNCT
cana-5829	189	10	(	(	PUNCT
cana-5829	189	11	µ(x	µ(x	NOUN
cana-5829	189	12	)	)	PUNCT
cana-5829	189	13	,	,	PUNCT
cana-5829	189	14	ν(x	ν(x	PROPN
cana-5829	189	15	)	)	PUNCT
cana-5829	189	16	,	,	PUNCT
cana-5829	189	17	π(x	π(x	NOUN
cana-5829	189	18	)	)	PUNCT
cana-5829	189	19	)	)	PUNCT
cana-5829	189	20	is	be	AUX
cana-5829	189	21	given	give	VERB
cana-5829	189	22	as	as	ADP
cana-5829	189	23	𝑎𝑖𝑗=	𝑎𝑖𝑗=	PROPN
cana-5829	189	24	(	(	PUNCT
cana-5829	189	25	µ(x)−µ𝑚𝑖𝑛	µ(x)−µ𝑚𝑖𝑛	PROPN
cana-5829	189	26	µ𝑚𝑎𝑥−µ𝑚𝑖𝑛	µ𝑚𝑎𝑥−µ𝑚𝑖𝑛	PROPN
cana-5829	189	27	,	,	PUNCT
cana-5829	189	28	ν(x)−𝜗𝑚𝑖𝑛	ν(x)−𝜗𝑚𝑖𝑛	PROPN
cana-5829	189	29	𝜗𝑚𝑎𝑥−𝜗𝑚𝑖𝑛	𝜗𝑚𝑎𝑥−𝜗𝑚𝑖𝑛	NUM
cana-5829	189	30	,	,	PUNCT
cana-5829	189	31	π(x)−𝜋𝑚𝑖𝑛	π(x)−𝜋𝑚𝑖𝑛	PROPN
cana-5829	189	32	𝜋𝑚𝑎𝑥−𝜋𝑚𝑖𝑛	𝜋𝑚𝑎𝑥−𝜋𝑚𝑖𝑛	NUM
cana-5829	189	33	)	)	PUNCT
cana-5829	189	34	where	where	SCONJ
cana-5829	189	35	µ𝑚𝑖𝑛	µ𝑚𝑖𝑛	NOUN
cana-5829	189	36	,	,	PUNCT
cana-5829	189	37	µ𝑚𝑎𝑥	µ𝑚𝑎𝑥	NOUN
cana-5829	189	38	are	be	AUX
cana-5829	189	39	the	the	DET
cana-5829	189	40	minimum	minimum	ADJ
cana-5829	189	41	and	and	CCONJ
cana-5829	189	42	maximum	maximum	ADJ
cana-5829	189	43	membership	membership	NOUN
cana-5829	189	44	values	value	NOUN
cana-5829	189	45	across	across	ADP
cana-5829	189	46	all	all	DET
cana-5829	189	47	elements	element	NOUN
cana-5829	189	48	.	.	PUNCT
cana-5829	190	1	communications	communication	NOUN
cana-5829	190	2	on	on	ADP
cana-5829	190	3	applied	apply	VERB
cana-5829	190	4	nonlinear	nonlinear	ADJ
cana-5829	190	5	analysis	analysis	NOUN
cana-5829	190	6	issn	issn	NOUN
cana-5829	190	7	:	:	PUNCT
cana-5829	190	8	1074	1074	NUM
cana-5829	190	9	-	-	PUNCT
cana-5829	190	10	133x	133x	NUM
cana-5829	190	11	vol	vol	VERB
cana-5829	190	12	32	32	NUM
cana-5829	190	13	no	no	NOUN
cana-5829	190	14	.	.	PUNCT
cana-5829	191	1	10s	10	NOUN
cana-5829	191	2	(	(	PUNCT
cana-5829	191	3	2025	2025	NUM
cana-5829	191	4	)	)	PUNCT
cana-5829	191	5	2931	2931	NUM
cana-5829	191	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5829	191	7	𝜗𝑚𝑖𝑛	𝜗𝑚𝑖𝑛	NOUN
cana-5829	191	8	,	,	PUNCT
cana-5829	191	9	𝜗𝑚𝑎𝑥	𝜗𝑚𝑎𝑥	PROPN
cana-5829	191	10	are	be	AUX
cana-5829	191	11	the	the	DET
cana-5829	191	12	minimum	minimum	ADJ
cana-5829	191	13	and	and	CCONJ
cana-5829	191	14	maximum	maximum	ADJ
cana-5829	191	15	non	non	ADJ
cana-5829	191	16	-	-	ADJ
cana-5829	191	17	membership	membership	ADJ
cana-5829	191	18	values	value	NOUN
cana-5829	191	19	across	across	ADP
cana-5829	191	20	all	all	DET
cana-5829	191	21	elements	element	NOUN
cana-5829	191	22	.	.	PUNCT
cana-5829	192	1	𝜋𝑚𝑖𝑛	𝜋𝑚𝑖𝑛	NOUN
cana-5829	192	2	,	,	PUNCT
cana-5829	192	3	𝜋𝑚𝑎𝑥	𝜋𝑚𝑎𝑥	PROPN
cana-5829	192	4	are	be	AUX
cana-5829	192	5	the	the	DET
cana-5829	192	6	minimum	minimum	ADJ
cana-5829	192	7	and	and	CCONJ
cana-5829	192	8	maximum	maximum	ADJ
cana-5829	192	9	uncertainty	uncertainty	NOUN
cana-5829	192	10	values	value	NOUN
cana-5829	192	11	across	across	ADP
cana-5829	192	12	all	all	DET
cana-5829	192	13	elements	element	NOUN
cana-5829	192	14	.	.	PUNCT
cana-5829	193	1	4.2.2column	4.2.2column	NOUN
cana-5829	193	2	-	-	PUNCT
cana-5829	193	3	wise	wise	ADJ
cana-5829	193	4	normalization	normalization	NOUN
cana-5829	193	5	:	:	PUNCT
cana-5829	193	6	in	in	ADP
cana-5829	193	7	this	this	DET
cana-5829	193	8	approach	approach	NOUN
cana-5829	193	9	,	,	PUNCT
cana-5829	193	10	normalization	normalization	NOUN
cana-5829	193	11	is	be	AUX
cana-5829	193	12	done	do	VERB
cana-5829	193	13	separately	separately	ADV
cana-5829	193	14	for	for	ADP
cana-5829	193	15	each	each	DET
cana-5829	193	16	column	column	NOUN
cana-5829	193	17	of	of	ADP
cana-5829	193	18	the	the	DET
cana-5829	193	19	intuitionistic	intuitionistic	ADJ
cana-5829	193	20	fuzzy	fuzzy	ADJ
cana-5829	193	21	matrix	matrix	NOUN
cana-5829	193	22	.	.	PUNCT
cana-5829	194	1	each	each	DET
cana-5829	194	2	element	element	NOUN
cana-5829	194	3	in	in	ADP
cana-5829	194	4	a	a	DET
cana-5829	194	5	column	column	NOUN
cana-5829	194	6	is	be	AUX
cana-5829	194	7	normalized	normalize	VERB
cana-5829	194	8	by	by	ADP
cana-5829	194	9	dividing	divide	VERB
cana-5829	194	10	by	by	ADP
cana-5829	194	11	the	the	DET
cana-5829	194	12	sum	sum	NOUN
cana-5829	194	13	of	of	ADP
cana-5829	194	14	the	the	DET
cana-5829	194	15	membership	membership	NOUN
cana-5829	194	16	,	,	PUNCT
cana-5829	194	17	non	non	ADJ
cana-5829	194	18	-	-	NOUN
cana-5829	194	19	membership	membership	NOUN
cana-5829	194	20	,	,	PUNCT
cana-5829	194	21	and	and	CCONJ
cana-5829	194	22	uncertainty	uncertainty	NOUN
cana-5829	194	23	values	value	NOUN
cana-5829	194	24	in	in	ADP
cana-5829	194	25	that	that	DET
cana-5829	194	26	column	column	NOUN
cana-5829	194	27	.	.	PUNCT
cana-5829	195	1	for	for	ADP
cana-5829	195	2	an	an	DET
cana-5829	195	3	element	element	NOUN
cana-5829	195	4	aij	aij	PROPN
cana-5829	195	5	=	=	PUNCT
cana-5829	195	6	(	(	PUNCT
cana-5829	195	7	µ(x	µ(x	NOUN
cana-5829	195	8	)	)	PUNCT
cana-5829	195	9	,	,	PUNCT
cana-5829	195	10	ν(x	ν(x	PROPN
cana-5829	195	11	)	)	PUNCT
cana-5829	195	12	,	,	PUNCT
cana-5829	195	13	π(x	π(x	NOUN
cana-5829	195	14	)	)	PUNCT
cana-5829	195	15	)	)	PUNCT
cana-5829	196	1	the	the	DET
cana-5829	196	2	normalization	normalization	NOUN
cana-5829	196	3	formula	formula	NOUN
cana-5829	196	4	is	be	AUX
cana-5829	196	5	𝑎𝑖𝑗	𝑎𝑖𝑗	NOUN
cana-5829	196	6	=	=	SYM
cana-5829	196	7	(	(	PUNCT
cana-5829	196	8	µ(x	µ(x	X
cana-5829	196	9	)	)	PUNCT
cana-5829	196	10	∑	∑	ADV
cana-5829	196	11	µ𝑘𝑗	µ𝑘𝑗	NOUN
cana-5829	196	12	𝑚	𝑚	ADP
cana-5829	196	13	𝑘=1	𝑘=1	X
cana-5829	196	14	,	,	PUNCT
cana-5829	196	15	ϑ(x	ϑ(x	PROPN
cana-5829	196	16	)	)	PUNCT
cana-5829	196	17	∑	∑	ADV
cana-5829	196	18	𝜗𝑘𝑗	𝜗𝑘𝑗	NOUN
cana-5829	196	19	𝑚	𝑚	ADP
cana-5829	196	20	𝑘=1	𝑘=1	NOUN
cana-5829	196	21	,	,	PUNCT
cana-5829	196	22	μ(x	μ(x	PROPN
cana-5829	196	23	)	)	PUNCT
cana-5829	196	24	∑	∑	PUNCT
cana-5829	196	25	𝜋𝑘𝑗	𝜋𝑘𝑗	ADJ
cana-5829	196	26	𝑚	𝑚	PROPN
cana-5829	196	27	𝑘=1	𝑘=1	PROPN
cana-5829	196	28	)	)	PUNCT
cana-5829	196	29	where	where	SCONJ
cana-5829	196	30	m	m	NOUN
cana-5829	196	31	is	be	AUX
cana-5829	196	32	the	the	DET
cana-5829	196	33	number	number	NOUN
cana-5829	196	34	of	of	ADP
cana-5829	196	35	rows	row	NOUN
cana-5829	196	36	in	in	ADP
cana-5829	196	37	the	the	DET
cana-5829	196	38	matrix	matrix	NOUN
cana-5829	196	39	.	.	PUNCT
cana-5829	197	1	4.3.3	4.3.3	NUM
cana-5829	197	2	max	max	PROPN
cana-5829	197	3	-	-	PUNCT
cana-5829	197	4	min	min	NOUN
cana-5829	197	5	normalization	normalization	NOUN
cana-5829	197	6	:	:	PUNCT
cana-5829	197	7	this	this	DET
cana-5829	197	8	method	method	NOUN
cana-5829	197	9	normalizes	normalize	VERB
cana-5829	197	10	the	the	DET
cana-5829	197	11	elements	element	NOUN
cana-5829	197	12	of	of	ADP
cana-5829	197	13	the	the	DET
cana-5829	197	14	intuitionistic	intuitionistic	ADJ
cana-5829	197	15	fuzzy	fuzzy	ADJ
cana-5829	197	16	matrix	matrix	NOUN
cana-5829	197	17	using	use	VERB
cana-5829	197	18	the	the	DET
cana-5829	197	19	maximum	maximum	ADJ
cana-5829	197	20	and	and	CCONJ
cana-5829	197	21	minimum	minimum	ADJ
cana-5829	197	22	values	value	NOUN
cana-5829	197	23	across	across	ADP
cana-5829	197	24	each	each	DET
cana-5829	197	25	row	row	NOUN
cana-5829	197	26	.	.	PUNCT
cana-5829	198	1	for	for	ADP
cana-5829	198	2	an	an	DET
cana-5829	198	3	element	element	NOUN
cana-5829	198	4	aij=(µ(x	aij=(µ(x	PROPN
cana-5829	198	5	)	)	PUNCT
cana-5829	198	6	,	,	PUNCT
cana-5829	198	7	ν(x	ν(x	PROPN
cana-5829	198	8	)	)	PUNCT
cana-5829	198	9	,	,	PUNCT
cana-5829	198	10	π(x	π(x	ADP
cana-5829	198	11	)	)	PUNCT
cana-5829	198	12	,	,	PUNCT
cana-5829	198	13	the	the	DET
cana-5829	198	14	normalization	normalization	NOUN
cana-5829	198	15	is	be	AUX
cana-5829	198	16	:	:	PUNCT
cana-5829	198	17	𝑎𝑖𝑗	𝑎𝑖𝑗	NOUN
cana-5829	198	18	=	=	SYM
cana-5829	198	19	(	(	PUNCT
cana-5829	198	20	µ(x)−min	µ(x)−min	X
cana-5829	198	21	(	(	PUNCT
cana-5829	198	22	µ	µ	NOUN
cana-5829	198	23	)	)	PUNCT
cana-5829	198	24	max(µ)−min	max(µ)−min	NOUN
cana-5829	198	25	(	(	PUNCT
cana-5829	198	26	µ	µ	NOUN
cana-5829	198	27	)	)	PUNCT
cana-5829	198	28	,	,	PUNCT
cana-5829	198	29	ϑ(x)−min	ϑ(x)−min	X
cana-5829	198	30	(	(	PUNCT
cana-5829	198	31	𝜗	𝜗	NOUN
cana-5829	198	32	)	)	PUNCT
cana-5829	198	33	max(𝜗)−min	max(𝜗)−min	NOUN
cana-5829	198	34	(	(	PUNCT
cana-5829	198	35	𝜗	𝜗	NOUN
cana-5829	198	36	)	)	PUNCT
cana-5829	198	37	,	,	PUNCT
cana-5829	198	38	π(x)−min	π(x)−min	X
cana-5829	198	39	(	(	PUNCT
cana-5829	198	40	π	π	X
cana-5829	198	41	)	)	PUNCT
cana-5829	198	42	max(π)−min	max(π)−min	PROPN
cana-5829	198	43	(	(	PUNCT
cana-5829	198	44	π	π	NOUN
cana-5829	198	45	)	)	PUNCT
cana-5829	198	46	)	)	PUNCT
cana-5829	199	1	this	this	DET
cana-5829	199	2	method	method	NOUN
cana-5829	199	3	uses	use	VERB
cana-5829	199	4	the	the	DET
cana-5829	199	5	maximum	maximum	ADJ
cana-5829	199	6	and	and	CCONJ
cana-5829	199	7	minimum	minimum	ADJ
cana-5829	199	8	values	value	NOUN
cana-5829	199	9	for	for	ADP
cana-5829	199	10	each	each	DET
cana-5829	199	11	degree	degree	NOUN
cana-5829	199	12	across	across	ADP
cana-5829	199	13	the	the	DET
cana-5829	199	14	matrix	matrix	NOUN
cana-5829	199	15	to	to	PART
cana-5829	199	16	scale	scale	VERB
cana-5829	199	17	the	the	DET
cana-5829	199	18	values	value	NOUN
cana-5829	199	19	.	.	PUNCT
cana-5829	200	1	4.3.4	4.3.4	X
cana-5829	200	2	.	.	PUNCT
cana-5829	201	1	vector	vector	NOUN
cana-5829	201	2	–	–	PUNCT
cana-5829	201	3	based	base	VERB
cana-5829	201	4	normalization	normalization	NOUN
cana-5829	201	5	:	:	PUNCT
cana-5829	201	6	this	this	DET
cana-5829	201	7	method	method	NOUN
cana-5829	201	8	normalizes	normalize	VERB
cana-5829	201	9	each	each	DET
cana-5829	201	10	element	element	NOUN
cana-5829	201	11	in	in	ADP
cana-5829	201	12	the	the	DET
cana-5829	201	13	matrix	matrix	NOUN
cana-5829	201	14	by	by	ADP
cana-5829	201	15	considering	consider	VERB
cana-5829	201	16	the	the	DET
cana-5829	201	17	vector	vector	NOUN
cana-5829	201	18	magnitude	magnitude	NOUN
cana-5829	201	19	of	of	ADP
cana-5829	201	20	its	its	PRON
cana-5829	201	21	components	component	NOUN
cana-5829	201	22	.	.	PUNCT
cana-5829	202	1	given	give	VERB
cana-5829	202	2	that	that	SCONJ
cana-5829	202	3	each	each	DET
cana-5829	202	4	element	element	NOUN
cana-5829	202	5	is	be	AUX
cana-5829	202	6	a	a	DET
cana-5829	202	7	triplet	triplet	NOUN
cana-5829	202	8	,	,	PUNCT
cana-5829	202	9	the	the	DET
cana-5829	202	10	normalization	normalization	NOUN
cana-5829	202	11	is	be	AUX
cana-5829	202	12	based	base	VERB
cana-5829	202	13	on	on	ADP
cana-5829	202	14	the	the	DET
cana-5829	202	15	euclined	eucline	VERB
cana-5829	202	16	norm	norm	NOUN
cana-5829	202	17	or	or	CCONJ
cana-5829	202	18	magnitude	magnitude	NOUN
cana-5829	202	19	of	of	ADP
cana-5829	202	20	the	the	DET
cana-5829	202	21	triplet	triplet	NOUN
cana-5829	202	22	vector	vector	NOUN
cana-5829	202	23	(	(	PUNCT
cana-5829	202	24	µ(x	µ(x	NOUN
cana-5829	202	25	)	)	PUNCT
cana-5829	202	26	,	,	PUNCT
cana-5829	202	27	ν(x	ν(x	PROPN
cana-5829	202	28	)	)	PUNCT
cana-5829	202	29	,	,	PUNCT
cana-5829	202	30	π(x	π(x	NOUN
cana-5829	202	31	)	)	PUNCT
cana-5829	202	32	)	)	PUNCT
cana-5829	202	33	.	.	PUNCT
cana-5829	203	1	the	the	DET
cana-5829	203	2	formula	formula	NOUN
cana-5829	203	3	for	for	ADP
cana-5829	203	4	normalization	normalization	NOUN
cana-5829	203	5	is	be	AUX
cana-5829	203	6	:	:	PUNCT
cana-5829	203	7	𝑎𝑖𝑗	𝑎𝑖𝑗	NOUN
cana-5829	203	8	=	=	SYM
cana-5829	203	9	(	(	PUNCT
cana-5829	203	10	µ(x	µ(x	X
cana-5829	203	11	)	)	PUNCT
cana-5829	203	12	√µ(x)2+ϑ(x)2+π(x)2	√µ(x)2+ϑ(x)2+π(x)2	NOUN
cana-5829	203	13	,	,	PUNCT
cana-5829	203	14	ϑ(x	ϑ(x	PROPN
cana-5829	203	15	)	)	PUNCT
cana-5829	203	16	√µ(x)2+ϑ(x)2+π(x)2	√µ(x)2+ϑ(x)2+π(x)2	VERB
cana-5829	203	17	,	,	PUNCT
cana-5829	203	18	π(x	π(x	ADP
cana-5829	203	19	)	)	PUNCT
cana-5829	203	20	√µ(x)2+ϑ(x)2+π(x)2	√µ(x)2+ϑ(x)2+π(x)2	VERB
cana-5829	203	21	)	)	PUNCT
cana-5829	203	22	this	this	DET
cana-5829	203	23	method	method	NOUN
cana-5829	203	24	ensures	ensure	VERB
cana-5829	203	25	that	that	SCONJ
cana-5829	203	26	the	the	DET
cana-5829	203	27	sum	sum	NOUN
cana-5829	203	28	of	of	ADP
cana-5829	203	29	the	the	DET
cana-5829	203	30	squares	square	NOUN
cana-5829	203	31	of	of	ADP
cana-5829	203	32	the	the	DET
cana-5829	203	33	components	component	NOUN
cana-5829	203	34	of	of	ADP
cana-5829	203	35	each	each	DET
cana-5829	203	36	element	element	NOUN
cana-5829	203	37	in	in	ADP
cana-5829	203	38	the	the	DET
cana-5829	203	39	matrix	matrix	NOUN
cana-5829	203	40	equals1	equals1	VERB
cana-5829	203	41	effectively	effectively	ADV
cana-5829	203	42	standardizing	standardize	VERB
cana-5829	203	43	the	the	DET
cana-5829	203	44	values	value	NOUN
cana-5829	203	45	.	.	PUNCT
cana-5829	204	1	4.4	4.4	NUM
cana-5829	204	2	examples	example	NOUN
cana-5829	204	3	:	:	PUNCT
cana-5829	204	4	steps	step	NOUN
cana-5829	204	5	for	for	ADP
cana-5829	204	6	normalization	normalization	NOUN
cana-5829	204	7	of	of	ADP
cana-5829	204	8	intuitionistic	intuitionistic	ADJ
cana-5829	204	9	fuzzy	fuzzy	ADJ
cana-5829	204	10	matrices	matrix	NOUN
cana-5829	204	11	:	:	PUNCT
cana-5829	204	12	1.identify	1.identify	NUM
cana-5829	204	13	the	the	DET
cana-5829	204	14	maximum	maximum	ADJ
cana-5829	204	15	and	and	CCONJ
cana-5829	204	16	minimum	minimum	ADJ
cana-5829	204	17	values	value	NOUN
cana-5829	204	18	for	for	ADP
cana-5829	204	19	each	each	DET
cana-5829	204	20	component	component	NOUN
cana-5829	204	21	(	(	PUNCT
cana-5829	204	22	membership	membership	NOUN
cana-5829	204	23	,	,	PUNCT
cana-5829	204	24	non	non	ADJ
cana-5829	204	25	-	-	NOUN
cana-5829	204	26	membership	membership	NOUN
cana-5829	204	27	,	,	PUNCT
cana-5829	204	28	and	and	CCONJ
cana-5829	204	29	indeterminacy	indeterminacy	NOUN
cana-5829	204	30	)	)	PUNCT
cana-5829	204	31	across	across	ADP
cana-5829	204	32	the	the	DET
cana-5829	204	33	entire	entire	ADJ
cana-5829	204	34	matrix	matrix	NOUN
cana-5829	204	35	.	.	PUNCT
cana-5829	205	1	2.normalize	2.normalize	NUM
cana-5829	205	2	each	each	DET
cana-5829	205	3	component	component	NOUN
cana-5829	205	4	by	by	ADP
cana-5829	205	5	applying	apply	VERB
cana-5829	205	6	a	a	DET
cana-5829	205	7	normalization	normalization	NOUN
cana-5829	205	8	function	function	NOUN
cana-5829	205	9	.	.	PUNCT
cana-5829	206	1	the	the	DET
cana-5829	206	2	most	most	ADV
cana-5829	206	3	common	common	ADJ
cana-5829	206	4	normalization	normalization	NOUN
cana-5829	206	5	method	method	NOUN
cana-5829	206	6	is	be	AUX
cana-5829	206	7	min	min	ADJ
cana-5829	206	8	-	-	ADJ
cana-5829	206	9	max	max	PROPN
cana-5829	206	10	normalization	normalization	NOUN
cana-5829	206	11	,	,	PUNCT
cana-5829	206	12	where	where	SCONJ
cana-5829	206	13	the	the	DET
cana-5829	206	14	values	value	NOUN
cana-5829	206	15	are	be	AUX
cana-5829	206	16	mapped	map	VERB
cana-5829	206	17	to	to	ADP
cana-5829	206	18	a	a	DET
cana-5829	206	19	desired	desire	VERB
cana-5829	206	20	range	range	NOUN
cana-5829	206	21	,	,	PUNCT
cana-5829	206	22	typically	typically	ADV
cana-5829	206	23	[	[	X
cana-5829	206	24	0	0	NUM
cana-5829	206	25	,	,	PUNCT
cana-5829	206	26	1	1	NUM
cana-5829	206	27	]	]	PUNCT
cana-5829	206	28	.	.	PUNCT
cana-5829	207	1	for	for	ADP
cana-5829	207	2	each	each	DET
cana-5829	207	3	component	component	NOUN
cana-5829	207	4	𝑥𝑖𝑗	𝑥𝑖𝑗	PROPN
cana-5829	207	5	of	of	ADP
cana-5829	207	6	the	the	DET
cana-5829	207	7	matrix	matrix	NOUN
cana-5829	207	8	(	(	PUNCT
cana-5829	207	9	whether	whether	SCONJ
cana-5829	207	10	it	it	PRON
cana-5829	207	11	's	be	AUX
cana-5829	207	12	the	the	DET
cana-5829	207	13	membership	membership	NOUN
cana-5829	207	14	,	,	PUNCT
cana-5829	207	15	non	non	ADJ
cana-5829	207	16	-	-	NOUN
cana-5829	207	17	membership	membership	ADJ
cana-5829	207	18	,	,	PUNCT
cana-5829	207	19	or	or	CCONJ
cana-5829	207	20	indeterminacy	indeterminacy	NOUN
cana-5829	207	21	)	)	PUNCT
cana-5829	207	22	,	,	PUNCT
cana-5829	207	23	the	the	DET
cana-5829	207	24	normalized	normalize	VERB
cana-5829	207	25	value	value	NOUN
cana-5829	207	26	𝑥′𝑖𝑗	𝑥′𝑖𝑗	NOUN
cana-5829	207	27	can	can	AUX
cana-5829	207	28	be	be	AUX
cana-5829	207	29	computed	compute	VERB
cana-5829	207	30	as	as	ADP
cana-5829	207	31	=	=	NOUN
cana-5829	207	32	𝑥𝑖𝑗−𝑚𝑖𝑛(𝑥	𝑥𝑖𝑗−𝑚𝑖𝑛(𝑥	NOUN
cana-5829	207	33	)	)	PUNCT
cana-5829	207	34	max(𝑥)−min(𝑥	max(𝑥)−min(𝑥	NOUN
cana-5829	207	35	)	)	PUNCT
cana-5829	207	36	,	,	PUNCT
cana-5829	207	37	where	where	SCONJ
cana-5829	207	38	min(x	min(x	X
cana-5829	207	39	)	)	PUNCT
cana-5829	207	40	and	and	CCONJ
cana-5829	207	41	max(x	max(x	PROPN
cana-5829	207	42	)	)	PUNCT
cana-5829	207	43	are	be	AUX
cana-5829	207	44	the	the	DET
cana-5829	207	45	minimum	minimum	ADJ
cana-5829	207	46	and	and	CCONJ
cana-5829	207	47	maximum	maximum	ADJ
cana-5829	207	48	values	value	NOUN
cana-5829	207	49	of	of	ADP
cana-5829	207	50	the	the	DET
cana-5829	207	51	respective	respective	ADJ
cana-5829	207	52	component	component	NOUN
cana-5829	207	53	across	across	ADP
cana-5829	207	54	the	the	DET
cana-5829	207	55	entire	entire	ADJ
cana-5829	207	56	matrix	matrix	NOUN
cana-5829	207	57	.	.	PUNCT
cana-5829	208	1	3.adjust	3.adjust	NUM
cana-5829	208	2	the	the	DET
cana-5829	208	3	indeterminacy	indeterminacy	NOUN
cana-5829	208	4	(	(	PUNCT
cana-5829	208	5	if	if	SCONJ
cana-5829	208	6	required	require	VERB
cana-5829	208	7	)	)	PUNCT
cana-5829	208	8	.	.	PUNCT
cana-5829	209	1	after	after	ADP
cana-5829	209	2	normalizing	normalize	VERB
cana-5829	209	3	the	the	DET
cana-5829	209	4	membership	membership	NOUN
cana-5829	209	5	and	and	CCONJ
cana-5829	209	6	non	non	ADJ
cana-5829	209	7	-	-	ADJ
cana-5829	209	8	membership	membership	ADJ
cana-5829	209	9	components	component	NOUN
cana-5829	209	10	,	,	PUNCT
cana-5829	209	11	you	you	PRON
cana-5829	209	12	may	may	AUX
cana-5829	209	13	need	need	VERB
cana-5829	209	14	to	to	PART
cana-5829	209	15	adjust	adjust	VERB
cana-5829	209	16	the	the	DET
cana-5829	209	17	indeterminacy	indeterminacy	NOUN
cana-5829	209	18	to	to	PART
cana-5829	209	19	ensure	ensure	VERB
cana-5829	209	20	that	that	SCONJ
cana-5829	209	21	the	the	DET
cana-5829	209	22	sum	sum	NOUN
cana-5829	209	23	of	of	ADP
cana-5829	209	24	membership	membership	NOUN
cana-5829	209	25	,	,	PUNCT
cana-5829	209	26	nonmembership	nonmembership	NOUN
cana-5829	209	27	,	,	PUNCT
cana-5829	209	28	and	and	CCONJ
cana-5829	209	29	indeterminacy	indeterminacy	NOUN
cana-5829	209	30	still	still	ADV
cana-5829	209	31	equals	equal	VERB
cana-5829	209	32	1	1	NUM
cana-5829	209	33	.	.	PUNCT
cana-5829	210	1	you	you	PRON
cana-5829	210	2	normalize	normalize	VERB
cana-5829	210	3	the	the	DET
cana-5829	210	4	membership	membership	NOUN
cana-5829	210	5	and	and	CCONJ
cana-5829	210	6	non	non	ADJ
cana-5829	210	7	-	-	ADJ
cana-5829	210	8	membership	membership	ADJ
cana-5829	210	9	components	component	NOUN
cana-5829	210	10	first	first	ADV
cana-5829	210	11	;	;	PUNCT
cana-5829	210	12	you	you	PRON
cana-5829	210	13	can	can	AUX
cana-5829	210	14	calculate	calculate	VERB
cana-5829	210	15	the	the	DET
cana-5829	210	16	indeterminacy	indeterminacy	NOUN
cana-5829	210	17	for	for	ADP
cana-5829	210	18	each	each	DET
cana-5829	210	19	element	element	NOUN
cana-5829	210	20	as	as	ADP
cana-5829	210	21	:	:	PUNCT
cana-5829	210	22	𝜋′𝑖𝑗	𝜋′𝑖𝑗	NOUN
cana-5829	210	23	=	=	SYM
cana-5829	210	24	1	1	NUM
cana-5829	210	25	−	−	NOUN
cana-5829	210	26	µ′	µ′	NOUN
cana-5829	210	27	𝑖𝑗	𝑖𝑗	ADP
cana-5829	210	28	−	−	PROPN
cana-5829	210	29	𝜗′	𝜗′	VERB
cana-5829	210	30	𝑖𝑗	𝑖𝑗	ADP
cana-5829	210	31	this	this	PRON
cana-5829	210	32	ensures	ensure	VERB
cana-5829	210	33	that	that	SCONJ
cana-5829	210	34	the	the	DET
cana-5829	210	35	sum	sum	NOUN
cana-5829	210	36	of	of	ADP
cana-5829	210	37	the	the	DET
cana-5829	210	38	normalized	normalize	VERB
cana-5829	210	39	membership	membership	NOUN
cana-5829	210	40	,	,	PUNCT
cana-5829	210	41	non	non	ADJ
cana-5829	210	42	-	-	NOUN
cana-5829	210	43	membership	membership	NOUN
cana-5829	210	44	,	,	PUNCT
cana-5829	210	45	and	and	CCONJ
cana-5829	210	46	indeterminacy	indeterminacy	NOUN
cana-5829	210	47	remains	remain	VERB
cana-5829	210	48	1	1	NUM
cana-5829	210	49	for	for	ADP
cana-5829	210	50	each	each	DET
cana-5829	210	51	element	element	NOUN
cana-5829	210	52	.	.	PUNCT
cana-5829	211	1	example	example	NOUN
cana-5829	211	2	of	of	ADP
cana-5829	211	3	normalization	normalization	NOUN
cana-5829	211	4	:	:	PUNCT
cana-5829	211	5	consider	consider	VERB
cana-5829	211	6	an	an	DET
cana-5829	211	7	intuitionistic	intuitionistic	ADJ
cana-5829	211	8	fuzzy	fuzzy	ADJ
cana-5829	211	9	matrix	matrix	NOUN
cana-5829	211	10	with	with	ADP
cana-5829	211	11	the	the	DET
cana-5829	211	12	following	follow	VERB
cana-5829	211	13	entries	entry	NOUN
cana-5829	211	14	a	a	PRON
cana-5829	211	15	=	=	X
cana-5829	211	16	(	(	PUNCT
cana-5829	211	17	(	(	PUNCT
cana-5829	211	18	0.6,0.2	0.6,0.2	INTJ
cana-5829	211	19	,	,	PUNCT
cana-5829	211	20	0.2	0.2	NUM
cana-5829	211	21	)	)	PUNCT
cana-5829	211	22	(	(	PUNCT
cana-5829	211	23	0.8,0.1	0.8,0.1	NOUN
cana-5829	211	24	,	,	PUNCT
cana-5829	211	25	0.1	0.1	NUM
cana-5829	211	26	)	)	PUNCT
cana-5829	211	27	(	(	PUNCT
cana-5829	211	28	0.4,0.3	0.4,0.3	PROPN
cana-5829	211	29	,	,	PUNCT
cana-5829	211	30	0.3	0.3	NUM
cana-5829	211	31	)	)	PUNCT
cana-5829	211	32	(	(	PUNCT
cana-5829	211	33	0.7,0.2	0.7,0.2	PROPN
cana-5829	211	34	,	,	PUNCT
cana-5829	211	35	0.1	0.1	NUM
cana-5829	211	36	)	)	PUNCT
cana-5829	211	37	)	)	PUNCT
cana-5829	212	1	step	step	NOUN
cana-5829	212	2	1	1	NUM
cana-5829	212	3	:	:	PUNCT
cana-5829	212	4	identify	identify	VERB
cana-5829	212	5	the	the	DET
cana-5829	212	6	max	max	PROPN
cana-5829	212	7	and	and	CCONJ
cana-5829	212	8	min	min	NOUN
cana-5829	212	9	values	value	NOUN
cana-5829	212	10	for	for	ADP
cana-5829	212	11	each	each	DET
cana-5829	212	12	component	component	NOUN
cana-5829	212	13	.	.	PUNCT
cana-5829	213	1	communications	communication	NOUN
cana-5829	213	2	on	on	ADP
cana-5829	213	3	applied	apply	VERB
cana-5829	213	4	nonlinear	nonlinear	ADJ
cana-5829	213	5	analysis	analysis	NOUN
cana-5829	213	6	issn	issn	NOUN
cana-5829	213	7	:	:	PUNCT
cana-5829	213	8	1074	1074	NUM
cana-5829	213	9	-	-	PUNCT
cana-5829	213	10	133x	133x	NUM
cana-5829	213	11	vol	vol	VERB
cana-5829	213	12	32	32	NUM
cana-5829	213	13	no	no	NOUN
cana-5829	213	14	.	.	PUNCT
cana-5829	214	1	10s	10	NOUN
cana-5829	214	2	(	(	PUNCT
cana-5829	214	3	2025	2025	NUM
cana-5829	214	4	)	)	PUNCT
cana-5829	214	5	2932	2932	NUM
cana-5829	214	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5829	214	7	for	for	ADP
cana-5829	214	8	membership	membership	NOUN
cana-5829	214	9	(	(	PUNCT
cana-5829	214	10	µ	µ	NOUN
cana-5829	214	11	)	)	PUNCT
cana-5829	214	12	:	:	PUNCT
cana-5829	214	13	max(µ)=0.8	max(µ)=0.8	NOUN
cana-5829	214	14	,	,	PUNCT
cana-5829	214	15	min(µ)=0.4	min(µ)=0.4	ADV
cana-5829	214	16	for	for	ADP
cana-5829	214	17	non	non	ADJ
cana-5829	214	18	-	-	ADJ
cana-5829	214	19	membership	membership	ADJ
cana-5829	214	20	(	(	PUNCT
cana-5829	214	21	𝜗	𝜗	NOUN
cana-5829	214	22	)	)	PUNCT
cana-5829	214	23	:	:	PUNCT
cana-5829	214	24	max(𝜗)=0.3	max(𝜗)=0.3	NOUN
cana-5829	214	25	,	,	PUNCT
cana-5829	214	26	min(𝜗)=0.1	min(𝜗)=0.1	NOUN
cana-5829	214	27	for	for	ADP
cana-5829	214	28	indeterminacy	indeterminacy	NOUN
cana-5829	214	29	(	(	PUNCT
cana-5829	214	30	𝜋	𝜋	NOUN
cana-5829	214	31	)	)	PUNCT
cana-5829	214	32	:	:	PUNCT
cana-5829	214	33	max(𝜋)=0.3	max(𝜋)=0.3	NOUN
cana-5829	214	34	,	,	PUNCT
cana-5829	214	35	min(𝜋)=0.1	min(𝜋)=0.1	X
cana-5829	214	36	step	step	NOUN
cana-5829	214	37	2	2	NUM
cana-5829	214	38	:	:	PUNCT
cana-5829	214	39	normalize	normalize	VERB
cana-5829	214	40	the	the	DET
cana-5829	214	41	membership	membership	NOUN
cana-5829	214	42	and	and	CCONJ
cana-5829	214	43	non	non	ADJ
cana-5829	214	44	-	-	ADJ
cana-5829	214	45	membership	membership	ADJ
cana-5829	214	46	components	component	NOUN
cana-5829	214	47	using	use	VERB
cana-5829	214	48	min	min	ADJ
cana-5829	214	49	-	-	ADJ
cana-5829	214	50	max	max	PROPN
cana-5829	214	51	normalization	normalization	NOUN
cana-5829	214	52	.	.	PUNCT
cana-5829	215	1	for	for	ADP
cana-5829	215	2	each	each	DET
cana-5829	215	3	𝑎𝑖𝑗	𝑎𝑖𝑗	NOUN
cana-5829	215	4	=	=	SYM
cana-5829	215	5	(	(	PUNCT
cana-5829	215	6	µ𝑖𝑗	µ𝑖𝑗	PROPN
cana-5829	215	7	,	,	PUNCT
cana-5829	215	8	𝜗𝑖𝑗	𝜗𝑖𝑗	NOUN
cana-5829	215	9	,	,	PUNCT
cana-5829	215	10	𝜋𝑖𝑗	𝜋𝑖𝑗	PROPN
cana-5829	215	11	)	)	PUNCT
cana-5829	215	12	,	,	PUNCT
cana-5829	215	13	we	we	PRON
cana-5829	215	14	apply	apply	VERB
cana-5829	215	15	the	the	DET
cana-5829	215	16	normalization	normalization	NOUN
cana-5829	215	17	for	for	ADP
cana-5829	215	18	µ11	µ11	NOUN
cana-5829	215	19	=	=	SYM
cana-5829	215	20	0.6	0.6	NUM
cana-5829	215	21	:	:	PUNCT
cana-5829	215	22	µ′11	µ′11	NOUN
cana-5829	215	23	=	=	SYM
cana-5829	215	24	0.6−0.4	0.6−0.4	NOUN
cana-5829	215	25	0.8−0.4	0.8−0.4	NOUN
cana-5829	215	26	=	=	NOUN
cana-5829	216	1	0.2	0.2	NUM
cana-5829	216	2	0.4	0.4	NUM
cana-5829	216	3	=	=	SYM
cana-5829	216	4	0.5	0.5	NUM
cana-5829	216	5	for	for	ADP
cana-5829	216	6	𝜗11	𝜗11	NOUN
cana-5829	216	7	=	=	NUM
cana-5829	216	8	0.2	0.2	NUM
cana-5829	216	9	𝜗′11	𝜗′11	NOUN
cana-5829	216	10	=	=	SYM
cana-5829	216	11	0.2−0.1	0.2−0.1	NOUN
cana-5829	216	12	0.3−0.1	0.3−0.1	NOUN
cana-5829	217	1	=	=	NOUN
cana-5829	217	2	0.1	0.1	NUM
cana-5829	217	3	0.2	0.2	NUM
cana-5829	217	4	=	=	SYM
cana-5829	217	5	0.5	0.5	NUM
cana-5829	217	6	for	for	ADP
cana-5829	217	7	𝜋11	𝜋11	NOUN
cana-5829	217	8	=	=	NUM
cana-5829	217	9	0.2	0.2	NUM
cana-5829	217	10	𝜋′11	𝜋′11	NOUN
cana-5829	217	11	=	=	SYM
cana-5829	218	1	1	1	NUM
cana-5829	218	2	−	−	NOUN
cana-5829	218	3	0.5	0.5	NUM
cana-5829	218	4	=	=	SYM
cana-5829	218	5	0.5	0.5	NUM
cana-5829	218	6	=	=	SYM
cana-5829	218	7	0	0	PUNCT
cana-5829	218	8	now	now	ADV
cana-5829	218	9	,	,	PUNCT
cana-5829	218	10	apply	apply	VERB
cana-5829	218	11	the	the	DET
cana-5829	218	12	same	same	ADJ
cana-5829	218	13	normalization	normalization	NOUN
cana-5829	218	14	for	for	ADP
cana-5829	218	15	the	the	DET
cana-5829	218	16	other	other	ADJ
cana-5829	218	17	elements	element	NOUN
cana-5829	218	18	of	of	ADP
cana-5829	218	19	the	the	DET
cana-5829	218	20	matrix	matrix	NOUN
cana-5829	218	21	.	.	PUNCT
cana-5829	219	1	step	step	NOUN
cana-5829	219	2	3	3	NUM
cana-5829	219	3	:	:	PUNCT
cana-5829	219	4	adjust	adjust	VERB
cana-5829	219	5	indeterminacy	indeterminacy	NOUN
cana-5829	219	6	.	.	PUNCT
cana-5829	220	1	after	after	ADP
cana-5829	220	2	normalizing	normalize	VERB
cana-5829	220	3	the	the	DET
cana-5829	220	4	membership	membership	NOUN
cana-5829	220	5	and	and	CCONJ
cana-5829	220	6	non	non	ADJ
cana-5829	220	7	-	-	ADJ
cana-5829	220	8	membership	membership	ADJ
cana-5829	220	9	values	value	NOUN
cana-5829	220	10	,	,	PUNCT
cana-5829	220	11	the	the	DET
cana-5829	220	12	indeterminacy	indeterminacy	NOUN
cana-5829	220	13	values	value	NOUN
cana-5829	220	14	are	be	AUX
cana-5829	220	15	recalculated	recalculate	VERB
cana-5829	220	16	as	as	ADP
cana-5829	220	17	:	:	PUNCT
cana-5829	220	18	𝜋′	𝜋′	X
cana-5829	220	19	𝑖𝑗	𝑖𝑗	X
cana-5829	220	20	=	=	SYM
cana-5829	220	21	1	1	NUM
cana-5829	220	22	−	−	NOUN
cana-5829	220	23	µ′	µ′	NOUN
cana-5829	220	24	𝑖𝑗	𝑖𝑗	ADP
cana-5829	220	25	−	−	PROPN
cana-5829	220	26	𝜗′	𝜗′	NOUN
cana-5829	220	27	𝑖𝑗	𝑖𝑗	ADP
cana-5829	220	28	the	the	DET
cana-5829	220	29	final	final	ADJ
cana-5829	220	30	normalized	normalize	VERB
cana-5829	220	31	matrix	matrix	NOUN
cana-5829	220	32	will	will	AUX
cana-5829	220	33	have	have	VERB
cana-5829	220	34	the	the	DET
cana-5829	220	35	form	form	NOUN
cana-5829	220	36	𝐴′	𝐴′	ADJ
cana-5829	220	37	=	=	SYM
cana-5829	220	38	(	(	PUNCT
cana-5829	220	39	(	(	PUNCT
cana-5829	220	40	0.5,0.5	0.5,0.5	NUM
cana-5829	220	41	,	,	PUNCT
cana-5829	220	42	0	0	NUM
cana-5829	220	43	)	)	PUNCT
cana-5829	220	44	(	(	PUNCT
cana-5829	220	45	1	1	NUM
cana-5829	220	46	,	,	PUNCT
cana-5829	220	47	0	0	NUM
cana-5829	220	48	,	,	PUNCT
cana-5829	220	49	0	0	NUM
cana-5829	220	50	)	)	PUNCT
cana-5829	220	51	(	(	PUNCT
cana-5829	220	52	0	0	NUM
cana-5829	220	53	,	,	PUNCT
cana-5829	220	54	0	0	NUM
cana-5829	220	55	)	)	PUNCT
cana-5829	220	56	(	(	PUNCT
cana-5829	220	57	0.75	0.75	NUM
cana-5829	220	58	,	,	PUNCT
cana-5829	220	59	0.25	0.25	NUM
cana-5829	220	60	)	)	PUNCT
cana-5829	220	61	)	)	PUNCT
cana-5829	221	1	2.consider	2.consider	NUM
cana-5829	221	2	a	a	DET
cana-5829	221	3	2.2	2.2	NUM
cana-5829	221	4	intuitionistic	intuitionistic	ADJ
cana-5829	221	5	fuzzy	fuzzy	ADJ
cana-5829	221	6	matrix	matrix	NOUN
cana-5829	221	7	𝐴	𝐴	NOUN
cana-5829	221	8	=	=	PUNCT
cana-5829	221	9	[	[	PUNCT
cana-5829	221	10	(	(	PUNCT
cana-5829	221	11	0.5	0.5	NUM
cana-5829	221	12	,	,	PUNCT
cana-5829	221	13	0.3	0.3	NUM
cana-5829	221	14	)	)	PUNCT
cana-5829	221	15	(	(	PUNCT
cana-5829	221	16	0.7	0.7	NUM
cana-5829	221	17	,	,	PUNCT
cana-5829	221	18	0.2	0.2	NUM
cana-5829	221	19	)	)	PUNCT
cana-5829	221	20	(	(	PUNCT
cana-5829	221	21	0.4	0.4	NUM
cana-5829	221	22	,	,	PUNCT
cana-5829	221	23	0.4	0.4	NUM
cana-5829	221	24	)	)	PUNCT
cana-5829	221	25	(	(	PUNCT
cana-5829	221	26	0.6	0.6	NUM
cana-5829	221	27	,	,	PUNCT
cana-5829	221	28	0.1	0.1	NUM
cana-5829	221	29	)	)	PUNCT
cana-5829	221	30	]	]	PUNCT
cana-5829	222	1	using	use	VERB
cana-5829	222	2	the	the	DET
cana-5829	222	3	normalization	normalization	NOUN
cana-5829	222	4	:	:	PUNCT
cana-5829	222	5	µ′11	µ′11	NOUN
cana-5829	222	6	=	=	NOUN
cana-5829	222	7	0.5	0.5	NUM
cana-5829	222	8	0.5	0.5	NUM
cana-5829	222	9	+	+	SYM
cana-5829	222	10	0.3	0.3	NUM
cana-5829	222	11	=	=	SYM
cana-5829	222	12	0.625	0.625	NUM
cana-5829	222	13	𝜗′11	𝜗′11	NOUN
cana-5829	222	14	=	=	SYM
cana-5829	222	15	0.3	0.3	NUM
cana-5829	222	16	0.5	0.5	NUM
cana-5829	222	17	+	+	NUM
cana-5829	222	18	0.3	0.3	NUM
cana-5829	222	19	=	=	SYM
cana-5829	222	20	0.37	0.37	NUM
cana-5829	222	21	µ′12	µ′12	NOUN
cana-5829	222	22	=	=	NOUN
cana-5829	223	1	0.7	0.7	NUM
cana-5829	223	2	0.7	0.7	NUM
cana-5829	223	3	+	+	NUM
cana-5829	223	4	0.2	0.2	NUM
cana-5829	223	5	=	=	SYM
cana-5829	223	6	0.777	0.777	NUM
cana-5829	223	7	𝜗′12	𝜗′12	NOUN
cana-5829	223	8	=	=	PUNCT
cana-5829	223	9	0.2	0.2	NUM
cana-5829	223	10	0.7	0.7	NUM
cana-5829	223	11	+	+	NUM
cana-5829	223	12	0.2	0.2	NUM
cana-5829	223	13	=	=	SYM
cana-5829	223	14	0.22	0.22	NUM
cana-5829	223	15	µ′21	µ′21	NOUN
cana-5829	223	16	=	=	NOUN
cana-5829	223	17	0.4	0.4	NUM
cana-5829	223	18	0.4	0.4	NUM
cana-5829	224	1	+	+	SYM
cana-5829	224	2	0.4	0.4	NUM
cana-5829	224	3	=	=	SYM
cana-5829	224	4	0.5	0.5	NUM
cana-5829	224	5	𝜗′21	𝜗′21	NOUN
cana-5829	224	6	=	=	NOUN
cana-5829	224	7	0.4	0.4	NUM
cana-5829	224	8	0.4	0.4	NUM
cana-5829	225	1	+	+	SYM
cana-5829	225	2	0.4	0.4	NUM
cana-5829	225	3	=	=	SYM
cana-5829	225	4	0	0	NUM
cana-5829	225	5	µ′22	µ′22	PROPN
cana-5829	225	6	=	=	SYM
cana-5829	225	7	0.6	0.6	NUM
cana-5829	225	8	0.6	0.6	NUM
cana-5829	225	9	+	+	NUM
cana-5829	225	10	0.1	0.1	NUM
cana-5829	225	11	=	=	SYM
cana-5829	225	12	0.857	0.857	NUM
cana-5829	225	13	𝜗′22	𝜗′22	ADJ
cana-5829	225	14	=	=	NUM
cana-5829	225	15	0.1	0.1	NUM
cana-5829	225	16	0.6	0.6	NUM
cana-5829	226	1	+	+	SYM
cana-5829	226	2	0.1	0.1	NUM
cana-5829	226	3	=	=	SYM
cana-5829	226	4	0.143	0.143	NUM
cana-5829	226	5	the	the	DET
cana-5829	226	6	normalised	normalise	VERB
cana-5829	226	7	matrix	matrix	NOUN
cana-5829	226	8	becomes	become	VERB
cana-5829	226	9	𝐴′	𝐴′	PROPN
cana-5829	226	10	=	=	SYM
cana-5829	226	11	(	(	PUNCT
cana-5829	226	12	(	(	PUNCT
cana-5829	226	13	0.625	0.625	NUM
cana-5829	226	14	,	,	PUNCT
cana-5829	226	15	0.375	0.375	NUM
cana-5829	226	16	)	)	PUNCT
cana-5829	226	17	(	(	PUNCT
cana-5829	226	18	0.777	0.777	NUM
cana-5829	226	19	,	,	PUNCT
cana-5829	226	20	0.222	0.222	NUM
cana-5829	226	21	)	)	PUNCT
cana-5829	226	22	(	(	PUNCT
cana-5829	226	23	0.5	0.5	NUM
cana-5829	226	24	,	,	PUNCT
cana-5829	226	25	0.5	0.5	NUM
cana-5829	226	26	)	)	PUNCT
cana-5829	226	27	(	(	PUNCT
cana-5829	226	28	0.857	0.857	NUM
cana-5829	226	29	,	,	PUNCT
cana-5829	226	30	0.143	0.143	NUM
cana-5829	226	31	)	)	PUNCT
cana-5829	226	32	)	)	PUNCT
cana-5829	227	1	4.5	4.5	NUM
cana-5829	227	2	.	.	PUNCT
cana-5829	228	1	applications	application	NOUN
cana-5829	228	2	of	of	ADP
cana-5829	228	3	normalization	normalization	NOUN
cana-5829	228	4	of	of	ADP
cana-5829	228	5	intuitionistic	intuitionistic	ADJ
cana-5829	228	6	fuzzy	fuzzy	ADJ
cana-5829	228	7	matrices	matrix	NOUN
cana-5829	228	8	1	1	NUM
cana-5829	228	9	.	.	PUNCT
cana-5829	229	1	multi	multi	ADJ
cana-5829	229	2	-	-	ADJ
cana-5829	229	3	criteria	criterion	NOUN
cana-5829	229	4	decision	decision	NOUN
cana-5829	229	5	making	making	NOUN
cana-5829	229	6	(	(	PUNCT
cana-5829	229	7	mcdm	mcdm	ADJ
cana-5829	229	8	)	)	PUNCT
cana-5829	229	9	2	2	NUM
cana-5829	229	10	.	.	PUNCT
cana-5829	229	11	pattern	pattern	NOUN
cana-5829	229	12	recognition	recognition	NOUN
cana-5829	229	13	3.machine	3.machine	NUM
cana-5829	229	14	learning	learning	NOUN
cana-5829	229	15	&	&	CCONJ
cana-5829	229	16	ai	ai	VERB
cana-5829	229	17	1	1	NUM
cana-5829	229	18	.	.	PUNCT
cana-5829	230	1	multi	multi	ADJ
cana-5829	230	2	-	-	ADJ
cana-5829	230	3	criteria	criterion	NOUN
cana-5829	230	4	decision	decision	NOUN
cana-5829	230	5	analysis	analysis	NOUN
cana-5829	230	6	(	(	PUNCT
cana-5829	230	7	mcda	mcda	NOUN
cana-5829	230	8	):	):	PUNCT
cana-5829	230	9	when	when	SCONJ
cana-5829	230	10	dealing	deal	VERB
cana-5829	230	11	with	with	ADP
cana-5829	230	12	multi	multi	ADJ
cana-5829	230	13	-	-	ADJ
cana-5829	230	14	criteria	criterion	NOUN
cana-5829	230	15	decision	decision	NOUN
cana-5829	230	16	-	-	PUNCT
cana-5829	230	17	making	make	VERB
cana-5829	230	18	problems	problem	NOUN
cana-5829	230	19	,	,	PUNCT
cana-5829	230	20	intuitionistic	intuitionistic	ADJ
cana-5829	230	21	fuzzy	fuzzy	ADJ
cana-5829	230	22	matrices	matrix	NOUN
cana-5829	230	23	allow	allow	VERB
cana-5829	230	24	capturing	capture	VERB
cana-5829	230	25	the	the	DET
cana-5829	230	26	hesitancy	hesitancy	NOUN
cana-5829	230	27	or	or	CCONJ
cana-5829	230	28	uncertainty	uncertainty	NOUN
cana-5829	230	29	associated	associate	VERB
cana-5829	230	30	with	with	ADP
cana-5829	230	31	expert	expert	NOUN
cana-5829	230	32	judgments	judgment	NOUN
cana-5829	230	33	.	.	PUNCT
cana-5829	231	1	normalizing	normalize	VERB
cana-5829	231	2	the	the	DET
cana-5829	231	3	ifm	ifm	NOUN
cana-5829	231	4	helps	help	VERB
cana-5829	231	5	standardize	standardize	VERB
cana-5829	231	6	the	the	DET
cana-5829	231	7	fuzzy	fuzzy	ADJ
cana-5829	231	8	decision	decision	NOUN
cana-5829	231	9	criteria	criterion	NOUN
cana-5829	231	10	to	to	ADP
cana-5829	231	11	a	a	DET
cana-5829	231	12	common	common	ADJ
cana-5829	231	13	scale	scale	NOUN
cana-5829	231	14	,	,	PUNCT
cana-5829	231	15	making	make	VERB
cana-5829	231	16	it	it	PRON
cana-5829	231	17	easier	easy	ADJ
cana-5829	231	18	to	to	PART
cana-5829	231	19	compare	compare	VERB
cana-5829	231	20	alternatives	alternative	NOUN
cana-5829	231	21	across	across	ADP
cana-5829	231	22	different	different	ADJ
cana-5829	231	23	criteria	criterion	NOUN
cana-5829	231	24	and	and	CCONJ
cana-5829	231	25	achieve	achieve	VERB
cana-5829	231	26	more	more	ADV
cana-5829	231	27	reliable	reliable	ADJ
cana-5829	231	28	ranking	ranking	NOUN
cana-5829	231	29	.	.	PUNCT
cana-5829	232	1	fuzzy	fuzzy	ADJ
cana-5829	232	2	topsis	topsis	NOUN
cana-5829	232	3	method	method	NOUN
cana-5829	232	4	:	:	PUNCT
cana-5829	232	5	in	in	ADP
cana-5829	232	6	methods	method	NOUN
cana-5829	232	7	like	like	ADP
cana-5829	232	8	topsis	topsis	NOUN
cana-5829	232	9	(	(	PUNCT
cana-5829	232	10	technique	technique	NOUN
cana-5829	232	11	for	for	ADP
cana-5829	232	12	order	order	NOUN
cana-5829	232	13	preference	preference	NOUN
cana-5829	232	14	by	by	ADP
cana-5829	232	15	similarity	similarity	NOUN
cana-5829	232	16	to	to	ADP
cana-5829	232	17	ideal	ideal	ADJ
cana-5829	232	18	solution	solution	NOUN
cana-5829	232	19	)	)	PUNCT
cana-5829	232	20	,	,	PUNCT
cana-5829	232	21	normalization	normalization	NOUN
cana-5829	232	22	of	of	ADP
cana-5829	232	23	intuitionistic	intuitionistic	ADJ
cana-5829	232	24	fuzzy	fuzzy	ADJ
cana-5829	232	25	matrices	matrix	NOUN
cana-5829	232	26	allows	allow	VERB
cana-5829	232	27	a	a	DET
cana-5829	232	28	consistent	consistent	ADJ
cana-5829	232	29	comparison	comparison	NOUN
cana-5829	232	30	of	of	ADP
cana-5829	232	31	alternatives	alternative	NOUN
cana-5829	232	32	by	by	ADP
cana-5829	232	33	transforming	transform	VERB
cana-5829	232	34	the	the	DET
cana-5829	232	35	fuzzy	fuzzy	ADJ
cana-5829	232	36	values	value	NOUN
cana-5829	232	37	into	into	ADP
cana-5829	232	38	a	a	DET
cana-5829	232	39	comparable	comparable	ADJ
cana-5829	232	40	scale	scale	NOUN
cana-5829	232	41	,	,	PUNCT
cana-5829	232	42	reducing	reduce	VERB
cana-5829	232	43	inconsistencies	inconsistency	NOUN
cana-5829	232	44	and	and	CCONJ
cana-5829	232	45	ambiguities	ambiguity	NOUN
cana-5829	232	46	in	in	ADP
cana-5829	232	47	decision	decision	NOUN
cana-5829	232	48	-	-	PUNCT
cana-5829	232	49	making	making	NOUN
cana-5829	232	50	.	.	PUNCT
cana-5829	233	1	communications	communication	NOUN
cana-5829	233	2	on	on	ADP
cana-5829	233	3	applied	apply	VERB
cana-5829	233	4	nonlinear	nonlinear	ADJ
cana-5829	233	5	analysis	analysis	NOUN
cana-5829	233	6	issn	issn	NOUN
cana-5829	233	7	:	:	PUNCT
cana-5829	233	8	1074	1074	NUM
cana-5829	233	9	-	-	PUNCT
cana-5829	233	10	133x	133x	NUM
cana-5829	233	11	vol	vol	VERB
cana-5829	233	12	32	32	NUM
cana-5829	233	13	no	no	NOUN
cana-5829	233	14	.	.	PUNCT
cana-5829	234	1	10s	10	NOUN
cana-5829	234	2	(	(	PUNCT
cana-5829	234	3	2025	2025	NUM
cana-5829	234	4	)	)	PUNCT
cana-5829	234	5	2933	2933	NUM
cana-5829	234	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5829	234	7	2.image	2.image	NUM
cana-5829	234	8	processing	processing	NOUN
cana-5829	234	9	:	:	PUNCT
cana-5829	234	10	fuzzy	fuzzy	ADJ
cana-5829	234	11	image	image	NOUN
cana-5829	234	12	segmentation	segmentation	NOUN
cana-5829	234	13	:	:	PUNCT
cana-5829	234	14	in	in	ADP
cana-5829	234	15	image	image	NOUN
cana-5829	234	16	processing	processing	NOUN
cana-5829	234	17	,	,	PUNCT
cana-5829	234	18	intuitionistic	intuitionistic	ADJ
cana-5829	234	19	fuzzy	fuzzy	ADJ
cana-5829	234	20	matrices	matrix	NOUN
cana-5829	234	21	can	can	AUX
cana-5829	234	22	be	be	AUX
cana-5829	234	23	used	use	VERB
cana-5829	234	24	to	to	PART
cana-5829	234	25	represent	represent	VERB
cana-5829	234	26	uncertain	uncertain	ADJ
cana-5829	234	27	or	or	CCONJ
cana-5829	234	28	vague	vague	ADJ
cana-5829	234	29	image	image	NOUN
cana-5829	234	30	boundaries	boundary	NOUN
cana-5829	234	31	.	.	PUNCT
cana-5829	235	1	normalization	normalization	NOUN
cana-5829	235	2	helps	help	VERB
cana-5829	235	3	in	in	ADP
cana-5829	235	4	adjusting	adjust	VERB
cana-5829	235	5	pixel	pixel	ADJ
cana-5829	235	6	intensities	intensity	NOUN
cana-5829	235	7	and	and	CCONJ
cana-5829	235	8	related	relate	VERB
cana-5829	235	9	fuzzy	fuzzy	ADJ
cana-5829	235	10	values	value	NOUN
cana-5829	235	11	(	(	PUNCT
cana-5829	235	12	membership	membership	NOUN
cana-5829	235	13	and	and	CCONJ
cana-5829	235	14	non	non	ADJ
cana-5829	235	15	-	-	NOUN
cana-5829	235	16	membership	membership	NOUN
cana-5829	235	17	)	)	PUNCT
cana-5829	235	18	to	to	PART
cana-5829	235	19	ensure	ensure	VERB
cana-5829	235	20	proper	proper	ADJ
cana-5829	235	21	image	image	NOUN
cana-5829	235	22	segmentation	segmentation	NOUN
cana-5829	235	23	,	,	PUNCT
cana-5829	235	24	enhancing	enhance	VERB
cana-5829	235	25	the	the	DET
cana-5829	235	26	performance	performance	NOUN
cana-5829	235	27	of	of	ADP
cana-5829	235	28	algorithms	algorithm	NOUN
cana-5829	235	29	that	that	PRON
cana-5829	235	30	rely	rely	VERB
cana-5829	235	31	on	on	ADP
cana-5829	235	32	fuzzy	fuzzy	ADJ
cana-5829	235	33	logic	logic	NOUN
cana-5829	235	34	.	.	PUNCT
cana-5829	236	1	3.pattern	3.pattern	NUM
cana-5829	236	2	recognition	recognition	NOUN
cana-5829	236	3	and	and	CCONJ
cana-5829	236	4	classification	classification	NOUN
cana-5829	236	5	:	:	PUNCT
cana-5829	236	6	feature	feature	NOUN
cana-5829	236	7	extraction	extraction	NOUN
cana-5829	236	8	and	and	CCONJ
cana-5829	236	9	classification	classification	NOUN
cana-5829	236	10	:	:	PUNCT
cana-5829	236	11	in	in	ADP
cana-5829	236	12	pattern	pattern	NOUN
cana-5829	236	13	recognition	recognition	NOUN
cana-5829	236	14	,	,	PUNCT
cana-5829	236	15	normalized	normalize	VERB
cana-5829	236	16	intuitionistic	intuitionistic	ADJ
cana-5829	236	17	fuzzy	fuzzy	ADJ
cana-5829	236	18	matrices	matrix	NOUN
cana-5829	236	19	can	can	AUX
cana-5829	236	20	be	be	AUX
cana-5829	236	21	used	use	VERB
cana-5829	236	22	to	to	PART
cana-5829	236	23	extract	extract	VERB
cana-5829	236	24	features	feature	NOUN
cana-5829	236	25	from	from	ADP
cana-5829	236	26	data	datum	NOUN
cana-5829	236	27	sets	set	NOUN
cana-5829	236	28	where	where	SCONJ
cana-5829	236	29	uncertainty	uncertainty	NOUN
cana-5829	236	30	is	be	AUX
cana-5829	236	31	present	present	ADJ
cana-5829	236	32	.	.	PUNCT
cana-5829	237	1	the	the	DET
cana-5829	237	2	normalization	normalization	NOUN
cana-5829	237	3	ensures	ensure	VERB
cana-5829	237	4	that	that	SCONJ
cana-5829	237	5	the	the	DET
cana-5829	237	6	features	feature	NOUN
cana-5829	237	7	,	,	PUNCT
cana-5829	237	8	expressed	express	VERB
cana-5829	237	9	in	in	ADP
cana-5829	237	10	fuzzy	fuzzy	ADJ
cana-5829	237	11	terms	term	NOUN
cana-5829	237	12	,	,	PUNCT
cana-5829	237	13	are	be	AUX
cana-5829	237	14	on	on	ADP
cana-5829	237	15	the	the	DET
cana-5829	237	16	same	same	ADJ
cana-5829	237	17	scale	scale	NOUN
cana-5829	237	18	,	,	PUNCT
cana-5829	237	19	allowing	allow	VERB
cana-5829	237	20	more	more	ADV
cana-5829	237	21	effective	effective	ADJ
cana-5829	237	22	classification	classification	NOUN
cana-5829	237	23	and	and	CCONJ
cana-5829	237	24	pattern	pattern	NOUN
cana-5829	237	25	recognition	recognition	NOUN
cana-5829	237	26	by	by	ADP
cana-5829	237	27	algorithms	algorithm	NOUN
cana-5829	237	28	such	such	ADJ
cana-5829	237	29	as	as	ADP
cana-5829	237	30	fuzzy	fuzzy	ADJ
cana-5829	237	31	clustering	clustering	NOUN
cana-5829	237	32	or	or	CCONJ
cana-5829	237	33	fuzzy	fuzzy	ADJ
cana-5829	237	34	decision	decision	NOUN
cana-5829	237	35	trees	tree	NOUN
cana-5829	237	36	.	.	PUNCT
cana-5829	238	1	4.control	4.control	NUM
cana-5829	238	2	systems	system	NOUN
cana-5829	238	3	:	:	PUNCT
cana-5829	238	4	fuzzy	fuzzy	ADJ
cana-5829	238	5	logic	logic	NOUN
cana-5829	238	6	controllers	controller	NOUN
cana-5829	238	7	:	:	PUNCT
cana-5829	238	8	in	in	ADP
cana-5829	238	9	control	control	NOUN
cana-5829	238	10	systems	system	NOUN
cana-5829	238	11	,	,	PUNCT
cana-5829	238	12	intuitionistic	intuitionistic	ADJ
cana-5829	238	13	fuzzy	fuzzy	ADJ
cana-5829	238	14	matrices	matrix	NOUN
cana-5829	238	15	can	can	AUX
cana-5829	238	16	represent	represent	VERB
cana-5829	238	17	uncertain	uncertain	ADJ
cana-5829	238	18	inputs	input	NOUN
cana-5829	238	19	and	and	CCONJ
cana-5829	238	20	outputs	output	NOUN
cana-5829	238	21	.	.	PUNCT
cana-5829	239	1	normalizing	normalize	VERB
cana-5829	239	2	the	the	DET
cana-5829	239	3	ifm	ifm	NOUN
cana-5829	239	4	ensures	ensure	VERB
cana-5829	239	5	that	that	SCONJ
cana-5829	239	6	the	the	DET
cana-5829	239	7	fuzzy	fuzzy	ADJ
cana-5829	239	8	rules	rule	NOUN
cana-5829	239	9	and	and	CCONJ
cana-5829	239	10	control	control	NOUN
cana-5829	239	11	outputs	output	NOUN
cana-5829	239	12	are	be	AUX
cana-5829	239	13	consistent	consistent	ADJ
cana-5829	239	14	,	,	PUNCT
cana-5829	239	15	leading	lead	VERB
cana-5829	239	16	to	to	ADP
cana-5829	239	17	better	well	ADJ
cana-5829	239	18	control	control	VERB
cana-5829	239	19	decisions	decision	NOUN
cana-5829	239	20	in	in	ADP
cana-5829	239	21	real	real	ADJ
cana-5829	239	22	-	-	PUNCT
cana-5829	239	23	time	time	NOUN
cana-5829	239	24	applications	application	NOUN
cana-5829	239	25	such	such	ADJ
cana-5829	239	26	as	as	ADP
cana-5829	239	27	robotic	robotic	ADJ
cana-5829	239	28	navigation	navigation	NOUN
cana-5829	239	29	,	,	PUNCT
cana-5829	239	30	industrial	industrial	ADJ
cana-5829	239	31	automation	automation	NOUN
cana-5829	239	32	,	,	PUNCT
cana-5829	239	33	and	and	CCONJ
cana-5829	239	34	hvac	hvac	PROPN
cana-5829	239	35	systems	system	NOUN
cana-5829	239	36	.	.	PUNCT
cana-5829	240	1	5.risk	5.risk	NUM
cana-5829	240	2	assessment	assessment	NOUN
cana-5829	240	3	and	and	CCONJ
cana-5829	240	4	reliability	reliability	NOUN
cana-5829	240	5	analysis	analysis	NOUN
cana-5829	240	6	:	:	PUNCT
cana-5829	240	7	risk	risk	NOUN
cana-5829	240	8	modelling	modelling	NOUN
cana-5829	240	9	:	:	PUNCT
cana-5829	240	10	in	in	ADP
cana-5829	240	11	assessing	assess	VERB
cana-5829	240	12	the	the	DET
cana-5829	240	13	risk	risk	NOUN
cana-5829	240	14	in	in	ADP
cana-5829	240	15	uncertain	uncertain	ADJ
cana-5829	240	16	environments	environment	NOUN
cana-5829	240	17	,	,	PUNCT
cana-5829	240	18	intuitionistic	intuitionistic	ADJ
cana-5829	240	19	fuzzy	fuzzy	ADJ
cana-5829	240	20	matrices	matrix	NOUN
cana-5829	240	21	allow	allow	VERB
cana-5829	240	22	the	the	DET
cana-5829	240	23	modelling	modelling	NOUN
cana-5829	240	24	of	of	ADP
cana-5829	240	25	both	both	DET
cana-5829	240	26	membership	membership	NOUN
cana-5829	240	27	(	(	PUNCT
cana-5829	240	28	degree	degree	NOUN
cana-5829	240	29	of	of	ADP
cana-5829	240	30	risk	risk	NOUN
cana-5829	240	31	)	)	PUNCT
cana-5829	240	32	and	and	CCONJ
cana-5829	240	33	non	non	ADJ
cana-5829	240	34	-	-	ADJ
cana-5829	240	35	membership	membership	ADJ
cana-5829	240	36	(	(	PUNCT
cana-5829	240	37	degree	degree	NOUN
cana-5829	240	38	of	of	ADP
cana-5829	240	39	safety	safety	NOUN
cana-5829	240	40	)	)	PUNCT
cana-5829	240	41	.	.	PUNCT
cana-5829	241	1	normalization	normalization	NOUN
cana-5829	241	2	of	of	ADP
cana-5829	241	3	such	such	ADJ
cana-5829	241	4	matrices	matrix	NOUN
cana-5829	241	5	ensures	ensure	VERB
cana-5829	241	6	that	that	SCONJ
cana-5829	241	7	risk	risk	NOUN
cana-5829	241	8	factors	factor	NOUN
cana-5829	241	9	are	be	AUX
cana-5829	241	10	represented	represent	VERB
cana-5829	241	11	proportionately	proportionately	ADV
cana-5829	241	12	,	,	PUNCT
cana-5829	241	13	aiding	aid	VERB
cana-5829	241	14	in	in	ADP
cana-5829	241	15	better	well	ADJ
cana-5829	241	16	decisionmaking	decisionmake	VERB
cana-5829	241	17	for	for	ADP
cana-5829	241	18	risk	risk	NOUN
cana-5829	241	19	mitigation	mitigation	NOUN
cana-5829	241	20	strategies	strategy	NOUN
cana-5829	241	21	.	.	PUNCT
cana-5829	242	1	6.data	6.data	NUM
cana-5829	242	2	fusion	fusion	NOUN
cana-5829	242	3	:	:	PUNCT
cana-5829	242	4	sensor	sensor	NOUN
cana-5829	242	5	data	datum	NOUN
cana-5829	242	6	fusion	fusion	NOUN
cana-5829	242	7	:	:	PUNCT
cana-5829	242	8	in	in	ADP
cana-5829	242	9	applications	application	NOUN
cana-5829	242	10	like	like	ADP
cana-5829	242	11	sensor	sensor	NOUN
cana-5829	242	12	networks	network	NOUN
cana-5829	242	13	or	or	CCONJ
cana-5829	242	14	multi	multi	ADJ
cana-5829	242	15	-	-	ADJ
cana-5829	242	16	source	source	ADJ
cana-5829	242	17	information	information	NOUN
cana-5829	242	18	integration	integration	NOUN
cana-5829	242	19	,	,	PUNCT
cana-5829	242	20	normalization	normalization	NOUN
cana-5829	242	21	of	of	ADP
cana-5829	242	22	intuitionistic	intuitionistic	ADJ
cana-5829	242	23	fuzzy	fuzzy	ADJ
cana-5829	242	24	matrices	matrix	NOUN
cana-5829	242	25	can	can	AUX
cana-5829	242	26	combine	combine	VERB
cana-5829	242	27	data	datum	NOUN
cana-5829	242	28	from	from	ADP
cana-5829	242	29	multiple	multiple	ADJ
cana-5829	242	30	sources	source	NOUN
cana-5829	242	31	while	while	SCONJ
cana-5829	242	32	adjusting	adjust	VERB
cana-5829	242	33	for	for	ADP
cana-5829	242	34	different	different	ADJ
cana-5829	242	35	degrees	degree	NOUN
cana-5829	242	36	of	of	ADP
cana-5829	242	37	uncertainty	uncertainty	NOUN
cana-5829	242	38	across	across	ADP
cana-5829	242	39	sensors	sensor	NOUN
cana-5829	242	40	.	.	PUNCT
cana-5829	243	1	this	this	PRON
cana-5829	243	2	leads	lead	VERB
cana-5829	243	3	to	to	ADP
cana-5829	243	4	a	a	DET
cana-5829	243	5	more	more	ADV
cana-5829	243	6	accurate	accurate	ADJ
cana-5829	243	7	and	and	CCONJ
cana-5829	243	8	reliable	reliable	ADJ
cana-5829	243	9	fused	fuse	VERB
cana-5829	243	10	data	datum	NOUN
cana-5829	243	11	set	set	VERB
cana-5829	243	12	.	.	PUNCT
cana-5829	244	1	7.healthcare	7.healthcare	NUM
cana-5829	244	2	and	and	CCONJ
cana-5829	244	3	medical	medical	ADJ
cana-5829	244	4	diagnosis	diagnosis	NOUN
cana-5829	244	5	:	:	PUNCT
cana-5829	244	6	medical	medical	ADJ
cana-5829	244	7	decision	decision	NOUN
cana-5829	244	8	support	support	NOUN
cana-5829	244	9	systems	system	NOUN
cana-5829	244	10	:	:	PUNCT
cana-5829	244	11	in	in	ADP
cana-5829	244	12	healthcare	healthcare	PROPN
cana-5829	244	13	,	,	PUNCT
cana-5829	244	14	intuitionistic	intuitionistic	ADJ
cana-5829	244	15	fuzzy	fuzzy	ADJ
cana-5829	244	16	matrices	matrix	NOUN
cana-5829	244	17	are	be	AUX
cana-5829	244	18	used	use	VERB
cana-5829	244	19	to	to	PART
cana-5829	244	20	represent	represent	VERB
cana-5829	244	21	patient	patient	ADJ
cana-5829	244	22	data	datum	NOUN
cana-5829	244	23	,	,	PUNCT
cana-5829	244	24	symptoms	symptom	NOUN
cana-5829	244	25	,	,	PUNCT
cana-5829	244	26	and	and	CCONJ
cana-5829	244	27	diagnostic	diagnostic	ADJ
cana-5829	244	28	criteria	criterion	NOUN
cana-5829	244	29	under	under	ADP
cana-5829	244	30	uncertainty	uncertainty	NOUN
cana-5829	244	31	.	.	PUNCT
cana-5829	245	1	normalization	normalization	NOUN
cana-5829	245	2	helps	help	VERB
cana-5829	245	3	to	to	PART
cana-5829	245	4	align	align	VERB
cana-5829	245	5	various	various	ADJ
cana-5829	245	6	medical	medical	ADJ
cana-5829	245	7	parameters	parameter	NOUN
cana-5829	245	8	and	and	CCONJ
cana-5829	245	9	judgment	judgment	NOUN
cana-5829	245	10	values	value	NOUN
cana-5829	245	11	,	,	PUNCT
cana-5829	245	12	ensuring	ensure	VERB
cana-5829	245	13	that	that	SCONJ
cana-5829	245	14	the	the	DET
cana-5829	245	15	final	final	ADJ
cana-5829	245	16	diagnosis	diagnosis	NOUN
cana-5829	245	17	or	or	CCONJ
cana-5829	245	18	treatment	treatment	NOUN
cana-5829	245	19	plan	plan	NOUN
cana-5829	245	20	is	be	AUX
cana-5829	245	21	consistent	consistent	ADJ
cana-5829	245	22	with	with	ADP
cana-5829	245	23	all	all	DET
cana-5829	245	24	available	available	ADJ
cana-5829	245	25	information	information	NOUN
cana-5829	245	26	.	.	PUNCT
cana-5829	246	1	4.6	4.6	NUM
cana-5829	246	2	importance	importance	NOUN
cana-5829	246	3	:	:	PUNCT
cana-5829	246	4	consistent	consistent	ADJ
cana-5829	246	5	comparison	comparison	NOUN
cana-5829	246	6	of	of	ADP
cana-5829	246	7	data	datum	NOUN
cana-5829	246	8	:	:	PUNCT
cana-5829	246	9	normalization	normalization	NOUN
cana-5829	246	10	ensures	ensure	VERB
cana-5829	246	11	that	that	SCONJ
cana-5829	246	12	the	the	DET
cana-5829	246	13	elements	element	NOUN
cana-5829	246	14	in	in	ADP
cana-5829	246	15	the	the	DET
cana-5829	246	16	intuitionistic	intuitionistic	ADJ
cana-5829	246	17	fuzzy	fuzzy	ADJ
cana-5829	246	18	matrix	matrix	NOUN
cana-5829	246	19	are	be	AUX
cana-5829	246	20	scaled	scale	VERB
cana-5829	246	21	to	to	ADP
cana-5829	246	22	a	a	DET
cana-5829	246	23	standard	standard	ADJ
cana-5829	246	24	range	range	NOUN
cana-5829	246	25	(	(	PUNCT
cana-5829	246	26	typically	typically	ADV
cana-5829	246	27	[	[	X
cana-5829	246	28	0	0	NUM
cana-5829	246	29	,	,	PUNCT
cana-5829	246	30	1	1	NUM
cana-5829	246	31	]	]	NUM
cana-5829	246	32	)	)	PUNCT
cana-5829	246	33	,	,	PUNCT
cana-5829	246	34	making	make	VERB
cana-5829	246	35	it	it	PRON
cana-5829	246	36	easier	easy	ADJ
cana-5829	246	37	to	to	PART
cana-5829	246	38	compare	compare	VERB
cana-5829	246	39	and	and	CCONJ
cana-5829	246	40	combine	combine	VERB
cana-5829	246	41	information	information	NOUN
cana-5829	246	42	from	from	ADP
cana-5829	246	43	different	different	ADJ
cana-5829	246	44	sources	source	NOUN
cana-5829	246	45	.	.	PUNCT
cana-5829	247	1	without	without	ADP
cana-5829	247	2	normalization	normalization	NOUN
cana-5829	247	3	,	,	PUNCT
cana-5829	247	4	the	the	DET
cana-5829	247	5	data	datum	NOUN
cana-5829	247	6	might	might	AUX
cana-5829	247	7	be	be	AUX
cana-5829	247	8	inconsistent	inconsistent	ADJ
cana-5829	247	9	and	and	CCONJ
cana-5829	247	10	difficult	difficult	ADJ
cana-5829	247	11	to	to	PART
cana-5829	247	12	interpret	interpret	VERB
cana-5829	247	13	,	,	PUNCT
cana-5829	247	14	especially	especially	ADV
cana-5829	247	15	when	when	SCONJ
cana-5829	247	16	the	the	DET
cana-5829	247	17	membership	membership	NOUN
cana-5829	247	18	and	and	CCONJ
cana-5829	247	19	non	non	ADJ
cana-5829	247	20	-	-	ADJ
cana-5829	247	21	membership	membership	ADJ
cana-5829	247	22	values	value	NOUN
cana-5829	247	23	vary	vary	VERB
cana-5829	247	24	across	across	ADP
cana-5829	247	25	different	different	ADJ
cana-5829	247	26	scales	scale	NOUN
cana-5829	247	27	or	or	CCONJ
cana-5829	247	28	ranges	range	NOUN
cana-5829	247	29	.	.	PUNCT
cana-5829	248	1	improving	improve	VERB
cana-5829	248	2	accuracy	accuracy	NOUN
cana-5829	248	3	in	in	ADP
cana-5829	248	4	decision	decision	NOUN
cana-5829	248	5	making	making	NOUN
cana-5829	248	6	:	:	PUNCT
cana-5829	248	7	in	in	ADP
cana-5829	248	8	decision	decision	NOUN
cana-5829	248	9	-	-	PUNCT
cana-5829	248	10	making	make	VERB
cana-5829	248	11	problems	problem	NOUN
cana-5829	248	12	(	(	PUNCT
cana-5829	248	13	like	like	ADP
cana-5829	248	14	multi	multi	ADJ
cana-5829	248	15	-	-	ADJ
cana-5829	248	16	criteria	criterion	NOUN
cana-5829	248	17	decision	decision	NOUN
cana-5829	248	18	analysis	analysis	NOUN
cana-5829	248	19	or	or	CCONJ
cana-5829	248	20	decision	decision	NOUN
cana-5829	248	21	support	support	NOUN
cana-5829	248	22	systems	system	NOUN
cana-5829	248	23	)	)	PUNCT
cana-5829	248	24	,	,	PUNCT
cana-5829	248	25	normalization	normalization	NOUN
cana-5829	248	26	helps	help	VERB
cana-5829	248	27	to	to	PART
cana-5829	248	28	make	make	VERB
cana-5829	248	29	sure	sure	ADJ
cana-5829	248	30	that	that	SCONJ
cana-5829	248	31	all	all	DET
cana-5829	248	32	the	the	DET
cana-5829	248	33	criteria	criterion	NOUN
cana-5829	248	34	or	or	CCONJ
cana-5829	248	35	attributes	attribute	NOUN
cana-5829	248	36	are	be	AUX
cana-5829	248	37	comparable	comparable	ADJ
cana-5829	248	38	on	on	ADP
cana-5829	248	39	the	the	DET
cana-5829	248	40	same	same	ADJ
cana-5829	248	41	scale	scale	NOUN
cana-5829	248	42	.	.	PUNCT
cana-5829	249	1	this	this	PRON
cana-5829	249	2	improves	improve	VERB
cana-5829	249	3	the	the	DET
cana-5829	249	4	accuracy	accuracy	NOUN
cana-5829	249	5	and	and	CCONJ
cana-5829	249	6	reliability	reliability	NOUN
cana-5829	249	7	of	of	ADP
cana-5829	249	8	the	the	DET
cana-5829	249	9	decision	decision	NOUN
cana-5829	249	10	-	-	PUNCT
cana-5829	249	11	making	make	VERB
cana-5829	249	12	process	process	NOUN
cana-5829	249	13	.	.	PUNCT
cana-5829	250	1	eliminating	eliminate	VERB
cana-5829	250	2	bias	bias	NOUN
cana-5829	250	3	due	due	ADP
cana-5829	250	4	to	to	PART
cana-5829	250	5	scale	scale	VERB
cana-5829	250	6	differences	difference	NOUN
cana-5829	250	7	:	:	PUNCT
cana-5829	250	8	different	different	ADJ
cana-5829	250	9	elements	element	NOUN
cana-5829	250	10	of	of	ADP
cana-5829	250	11	an	an	DET
cana-5829	250	12	intuitionistic	intuitionistic	ADJ
cana-5829	250	13	fuzzy	fuzzy	ADJ
cana-5829	250	14	matrix	matrix	NOUN
cana-5829	250	15	can	can	AUX
cana-5829	250	16	have	have	VERB
cana-5829	250	17	different	different	ADJ
cana-5829	250	18	scales	scale	NOUN
cana-5829	250	19	,	,	PUNCT
cana-5829	250	20	leading	lead	VERB
cana-5829	250	21	to	to	ADP
cana-5829	250	22	biases	bias	NOUN
cana-5829	250	23	in	in	ADP
cana-5829	250	24	the	the	DET
cana-5829	250	25	analysis	analysis	NOUN
cana-5829	250	26	.	.	PUNCT
cana-5829	251	1	normalization	normalization	NOUN
cana-5829	251	2	removes	remove	VERB
cana-5829	251	3	such	such	ADJ
cana-5829	251	4	biases	bias	NOUN
cana-5829	251	5	by	by	ADP
cana-5829	251	6	ensuring	ensure	VERB
cana-5829	251	7	that	that	SCONJ
cana-5829	251	8	all	all	DET
cana-5829	251	9	values	value	NOUN
cana-5829	251	10	contribute	contribute	VERB
cana-5829	251	11	equally	equally	ADV
cana-5829	251	12	to	to	ADP
cana-5829	251	13	the	the	DET
cana-5829	251	14	outcome	outcome	NOUN
cana-5829	251	15	.	.	PUNCT
cana-5829	252	1	this	this	PRON
cana-5829	252	2	is	be	AUX
cana-5829	252	3	important	important	ADJ
cana-5829	252	4	when	when	SCONJ
cana-5829	252	5	the	the	DET
cana-5829	252	6	matrix	matrix	NOUN
cana-5829	252	7	represents	represent	VERB
cana-5829	252	8	the	the	DET
cana-5829	252	9	relationship	relationship	NOUN
cana-5829	252	10	between	between	ADP
cana-5829	252	11	various	various	ADJ
cana-5829	252	12	factors	factor	NOUN
cana-5829	252	13	or	or	CCONJ
cana-5829	252	14	alternatives	alternative	NOUN
cana-5829	252	15	in	in	ADP
cana-5829	252	16	a	a	DET
cana-5829	252	17	decision	decision	NOUN
cana-5829	252	18	-	-	PUNCT
cana-5829	252	19	making	make	VERB
cana-5829	252	20	problem	problem	NOUN
cana-5829	252	21	.	.	PUNCT
cana-5829	253	1	handling	handle	VERB
cana-5829	253	2	uncertainty	uncertainty	NOUN
cana-5829	253	3	effectively	effectively	ADV
cana-5829	253	4	:	:	PUNCT
cana-5829	253	5	communications	communication	NOUN
cana-5829	253	6	on	on	ADP
cana-5829	253	7	applied	apply	VERB
cana-5829	253	8	nonlinear	nonlinear	ADJ
cana-5829	253	9	analysis	analysis	NOUN
cana-5829	253	10	issn	issn	NOUN
cana-5829	253	11	:	:	PUNCT
cana-5829	253	12	1074	1074	NUM
cana-5829	253	13	-	-	PUNCT
cana-5829	253	14	133x	133x	NUM
cana-5829	253	15	vol	vol	VERB
cana-5829	253	16	32	32	NUM
cana-5829	253	17	no	no	NOUN
cana-5829	253	18	.	.	PUNCT
cana-5829	254	1	10s	10	NOUN
cana-5829	254	2	(	(	PUNCT
cana-5829	254	3	2025	2025	NUM
cana-5829	254	4	)	)	PUNCT
cana-5829	254	5	2934	2934	NUM
cana-5829	254	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5829	254	7	intuitionistic	intuitionistic	ADJ
cana-5829	254	8	fuzzy	fuzzy	ADJ
cana-5829	254	9	sets	set	NOUN
cana-5829	254	10	deal	deal	VERB
cana-5829	254	11	with	with	ADP
cana-5829	254	12	both	both	CCONJ
cana-5829	254	13	membership	membership	NOUN
cana-5829	254	14	and	and	CCONJ
cana-5829	254	15	non	non	ADJ
cana-5829	254	16	-	-	NOUN
cana-5829	254	17	membership	membership	NOUN
cana-5829	254	18	,	,	PUNCT
cana-5829	254	19	leaving	leave	VERB
cana-5829	254	20	room	room	NOUN
cana-5829	254	21	for	for	ADP
cana-5829	254	22	uncertainty	uncertainty	NOUN
cana-5829	254	23	(	(	PUNCT
cana-5829	254	24	indeterminacy	indeterminacy	NOUN
cana-5829	254	25	)	)	PUNCT
cana-5829	254	26	.	.	PUNCT
cana-5829	255	1	normalization	normalization	NOUN
cana-5829	255	2	allows	allow	VERB
cana-5829	255	3	better	well	ADJ
cana-5829	255	4	handling	handling	NOUN
cana-5829	255	5	and	and	CCONJ
cana-5829	255	6	representation	representation	NOUN
cana-5829	255	7	of	of	ADP
cana-5829	255	8	this	this	DET
cana-5829	255	9	uncertainty	uncertainty	NOUN
cana-5829	255	10	,	,	PUNCT
cana-5829	255	11	ensuring	ensure	VERB
cana-5829	255	12	that	that	SCONJ
cana-5829	255	13	the	the	DET
cana-5829	255	14	resulting	result	VERB
cana-5829	255	15	matrix	matrix	NOUN
cana-5829	255	16	values	value	NOUN
cana-5829	255	17	still	still	ADV
cana-5829	255	18	remain	remain	VERB
cana-5829	255	19	meaningful	meaningful	ADJ
cana-5829	255	20	even	even	ADV
cana-5829	255	21	when	when	SCONJ
cana-5829	255	22	there	there	PRON
cana-5829	255	23	is	be	VERB
cana-5829	255	24	incomplete	incomplete	ADJ
cana-5829	255	25	or	or	CCONJ
cana-5829	255	26	imprecise	imprecise	ADJ
cana-5829	255	27	data	datum	NOUN
cana-5829	255	28	.	.	PUNCT
cana-5829	256	1	facilitating	facilitate	VERB
cana-5829	256	2	aggregation	aggregation	NOUN
cana-5829	256	3	of	of	ADP
cana-5829	256	4	data	datum	NOUN
cana-5829	256	5	:	:	PUNCT
cana-5829	256	6	when	when	SCONJ
cana-5829	256	7	working	work	VERB
cana-5829	256	8	with	with	ADP
cana-5829	256	9	multiple	multiple	ADJ
cana-5829	256	10	intuitionistic	intuitionistic	ADJ
cana-5829	256	11	fuzzy	fuzzy	ADJ
cana-5829	256	12	matrices	matrix	NOUN
cana-5829	256	13	,	,	PUNCT
cana-5829	256	14	normalization	normalization	NOUN
cana-5829	256	15	allows	allow	VERB
cana-5829	256	16	for	for	ADP
cana-5829	256	17	the	the	DET
cana-5829	256	18	proper	proper	ADJ
cana-5829	256	19	aggregation	aggregation	NOUN
cana-5829	256	20	of	of	ADP
cana-5829	256	21	data	datum	NOUN
cana-5829	256	22	from	from	ADP
cana-5829	256	23	various	various	ADJ
cana-5829	256	24	sources	source	NOUN
cana-5829	256	25	.	.	PUNCT
cana-5829	257	1	this	this	PRON
cana-5829	257	2	is	be	AUX
cana-5829	257	3	particularly	particularly	ADV
cana-5829	257	4	important	important	ADJ
cana-5829	257	5	in	in	ADP
cana-5829	257	6	fields	field	NOUN
cana-5829	257	7	such	such	ADJ
cana-5829	257	8	as	as	ADP
cana-5829	257	9	multi	multi	ADJ
cana-5829	257	10	-	-	ADJ
cana-5829	257	11	criteria	criteria	ADJ
cana-5829	257	12	decision	decision	NOUN
cana-5829	257	13	analysis	analysis	NOUN
cana-5829	257	14	,	,	PUNCT
cana-5829	257	15	where	where	SCONJ
cana-5829	257	16	data	datum	NOUN
cana-5829	257	17	from	from	ADP
cana-5829	257	18	different	different	ADJ
cana-5829	257	19	criteria	criterion	NOUN
cana-5829	257	20	need	need	VERB
cana-5829	257	21	to	to	PART
cana-5829	257	22	be	be	AUX
cana-5829	257	23	aggregated	aggregate	VERB
cana-5829	257	24	into	into	ADP
cana-5829	257	25	a	a	DET
cana-5829	257	26	final	final	ADJ
cana-5829	257	27	decision	decision	NOUN
cana-5829	257	28	.	.	PUNCT
cana-5829	258	1	simplifying	simplify	VERB
cana-5829	258	2	further	further	ADJ
cana-5829	258	3	mathematical	mathematical	ADJ
cana-5829	258	4	operations	operation	NOUN
cana-5829	258	5	:	:	PUNCT
cana-5829	258	6	normalized	normalize	VERB
cana-5829	258	7	values	value	NOUN
cana-5829	258	8	in	in	ADP
cana-5829	258	9	intuitionistic	intuitionistic	ADJ
cana-5829	258	10	fuzzy	fuzzy	ADJ
cana-5829	258	11	matrices	matrix	NOUN
cana-5829	258	12	make	make	VERB
cana-5829	258	13	it	it	PRON
cana-5829	258	14	easier	easy	ADJ
cana-5829	258	15	to	to	PART
cana-5829	258	16	apply	apply	VERB
cana-5829	258	17	further	further	ADJ
cana-5829	258	18	operations	operation	NOUN
cana-5829	258	19	like	like	ADP
cana-5829	258	20	addition	addition	NOUN
cana-5829	258	21	,	,	PUNCT
cana-5829	258	22	multiplication	multiplication	NOUN
cana-5829	258	23	,	,	PUNCT
cana-5829	258	24	or	or	CCONJ
cana-5829	258	25	averaging	averaging	NOUN
cana-5829	258	26	,	,	PUNCT
cana-5829	258	27	which	which	PRON
cana-5829	258	28	are	be	AUX
cana-5829	258	29	common	common	ADJ
cana-5829	258	30	in	in	ADP
cana-5829	258	31	matrix	matrix	NOUN
cana-5829	258	32	-	-	PUNCT
cana-5829	258	33	based	base	VERB
cana-5829	258	34	decision	decision	NOUN
cana-5829	258	35	-	-	PUNCT
cana-5829	258	36	making	make	VERB
cana-5829	258	37	methods	method	NOUN
cana-5829	258	38	(	(	PUNCT
cana-5829	258	39	e.g.	e.g.	ADV
cana-5829	258	40	,	,	PUNCT
cana-5829	258	41	ahp	ahp	NOUN
cana-5829	258	42	,	,	PUNCT
cana-5829	258	43	topsis	topsis	NOUN
cana-5829	258	44	,	,	PUNCT
cana-5829	258	45	etc	etc	X
cana-5829	258	46	.	.	X
cana-5829	258	47	)	)	PUNCT
cana-5829	258	48	.	.	PUNCT
cana-5829	259	1	without	without	ADP
cana-5829	259	2	normalization	normalization	NOUN
cana-5829	259	3	,	,	PUNCT
cana-5829	259	4	the	the	DET
cana-5829	259	5	results	result	NOUN
cana-5829	259	6	of	of	ADP
cana-5829	259	7	these	these	DET
cana-5829	259	8	operations	operation	NOUN
cana-5829	259	9	may	may	AUX
cana-5829	259	10	be	be	AUX
cana-5829	259	11	skewed	skew	VERB
cana-5829	259	12	due	due	ADP
cana-5829	259	13	to	to	ADP
cana-5829	259	14	differences	difference	NOUN
cana-5829	259	15	in	in	ADP
cana-5829	259	16	scale	scale	NOUN
cana-5829	259	17	between	between	ADP
cana-5829	259	18	different	different	ADJ
cana-5829	259	19	elements	element	NOUN
cana-5829	259	20	of	of	ADP
cana-5829	259	21	the	the	DET
cana-5829	259	22	matrix	matrix	NOUN
cana-5829	259	23	.	.	PUNCT
cana-5829	260	1	ensuring	ensure	VERB
cana-5829	260	2	feasibility	feasibility	NOUN
cana-5829	260	3	and	and	CCONJ
cana-5829	260	4	validity	validity	NOUN
cana-5829	260	5	of	of	ADP
cana-5829	260	6	results	result	NOUN
cana-5829	260	7	:	:	PUNCT
cana-5829	260	8	for	for	ADP
cana-5829	260	9	certain	certain	ADJ
cana-5829	260	10	algorithms	algorithm	NOUN
cana-5829	260	11	or	or	CCONJ
cana-5829	260	12	applications	application	NOUN
cana-5829	260	13	,	,	PUNCT
cana-5829	260	14	it	it	PRON
cana-5829	260	15	's	be	AUX
cana-5829	260	16	necessary	necessary	ADJ
cana-5829	260	17	that	that	SCONJ
cana-5829	260	18	the	the	DET
cana-5829	260	19	values	value	NOUN
cana-5829	260	20	in	in	ADP
cana-5829	260	21	the	the	DET
cana-5829	260	22	intuitionistic	intuitionistic	ADJ
cana-5829	260	23	fuzzy	fuzzy	ADJ
cana-5829	260	24	matrix	matrix	NOUN
cana-5829	260	25	sum	sum	NOUN
cana-5829	260	26	to	to	ADP
cana-5829	260	27	a	a	DET
cana-5829	260	28	specific	specific	ADJ
cana-5829	260	29	value	value	NOUN
cana-5829	260	30	(	(	PUNCT
cana-5829	260	31	such	such	ADJ
cana-5829	260	32	as	as	ADP
cana-5829	260	33	1	1	NUM
cana-5829	260	34	)	)	PUNCT
cana-5829	260	35	.	.	PUNCT
cana-5829	261	1	normalization	normalization	NOUN
cana-5829	261	2	ensures	ensure	VERB
cana-5829	261	3	that	that	SCONJ
cana-5829	261	4	the	the	DET
cana-5829	261	5	sum	sum	NOUN
cana-5829	261	6	of	of	ADP
cana-5829	261	7	membership	membership	NOUN
cana-5829	261	8	and	and	CCONJ
cana-5829	261	9	nonmembership	nonmembership	NOUN
cana-5829	261	10	functions	function	NOUN
cana-5829	261	11	,	,	PUNCT
cana-5829	261	12	along	along	ADP
cana-5829	261	13	with	with	ADP
cana-5829	261	14	the	the	DET
cana-5829	261	15	degree	degree	NOUN
cana-5829	261	16	of	of	ADP
cana-5829	261	17	indeterminacy	indeterminacy	NOUN
cana-5829	261	18	,	,	PUNCT
cana-5829	261	19	remains	remain	VERB
cana-5829	261	20	valid	valid	ADJ
cana-5829	261	21	for	for	ADP
cana-5829	261	22	further	further	ADJ
cana-5829	261	23	processing	processing	NOUN
cana-5829	261	24	.	.	PUNCT
cana-5829	262	1	enhancing	enhance	VERB
cana-5829	262	2	robustness	robustness	NOUN
cana-5829	262	3	of	of	ADP
cana-5829	262	4	algorithms	algorithm	NOUN
cana-5829	262	5	many	many	ADJ
cana-5829	262	6	machines	machine	NOUN
cana-5829	262	7	learning	learn	VERB
cana-5829	262	8	or	or	CCONJ
cana-5829	262	9	optimization	optimization	NOUN
cana-5829	262	10	algorithms	algorithm	NOUN
cana-5829	262	11	require	require	VERB
cana-5829	262	12	data	datum	NOUN
cana-5829	262	13	in	in	ADP
cana-5829	262	14	a	a	DET
cana-5829	262	15	specific	specific	ADJ
cana-5829	262	16	form	form	NOUN
cana-5829	262	17	for	for	ADP
cana-5829	262	18	stable	stable	ADJ
cana-5829	262	19	convergence	convergence	NOUN
cana-5829	262	20	.	.	PUNCT
cana-5829	263	1	normalized	normalize	VERB
cana-5829	263	2	intuitionistic	intuitionistic	ADJ
cana-5829	263	3	fuzzy	fuzzy	ADJ
cana-5829	263	4	matrices	matrix	NOUN
cana-5829	263	5	help	help	VERB
cana-5829	263	6	improve	improve	VERB
cana-5829	263	7	the	the	DET
cana-5829	263	8	robustness	robustness	NOUN
cana-5829	263	9	and	and	CCONJ
cana-5829	263	10	convergence	convergence	NOUN
cana-5829	263	11	speed	speed	NOUN
cana-5829	263	12	of	of	ADP
cana-5829	263	13	these	these	DET
cana-5829	263	14	algorithms	algorithm	NOUN
cana-5829	263	15	,	,	PUNCT
cana-5829	263	16	preventing	prevent	VERB
cana-5829	263	17	issues	issue	NOUN
cana-5829	263	18	caused	cause	VERB
cana-5829	263	19	by	by	ADP
cana-5829	263	20	extreme	extreme	ADJ
cana-5829	263	21	or	or	CCONJ
cana-5829	263	22	unbalanced	unbalanced	ADJ
cana-5829	263	23	values	value	NOUN
cana-5829	263	24	.	.	PUNCT
cana-5829	264	1	we	we	PRON
cana-5829	264	2	define	define	VERB
cana-5829	264	3	over	over	ADP
cana-5829	264	4	the	the	DET
cana-5829	264	5	set	set	NOUN
cana-5829	264	6	of	of	ADP
cana-5829	264	7	ifs	ifs	PROPN
cana-5829	264	8	,	,	PUNCT
cana-5829	264	9	two	two	NUM
cana-5829	264	10	modal	modal	ADJ
cana-5829	264	11	operators	operator	NOUN
cana-5829	264	12	which	which	PRON
cana-5829	264	13	transform	transform	VERB
cana-5829	264	14	every	every	DET
cana-5829	264	15	ifs	ifs	PROPN
cana-5829	264	16	into	into	ADP
cana-5829	264	17	fuzzy	fuzzy	ADJ
cana-5829	264	18	set	set	NOUN
cana-5829	264	19	.	.	PUNCT
cana-5829	265	1	these	these	DET
cana-5829	265	2	operators	operator	NOUN
cana-5829	265	3	are	be	AUX
cana-5829	265	4	similar	similar	ADJ
cana-5829	265	5	to	to	ADP
cana-5829	265	6	the	the	DET
cana-5829	265	7	operator	operator	NOUN
cana-5829	265	8	’s	’s	PART
cana-5829	265	9	‘	'	PUNCT
cana-5829	265	10	necessity	necessity	NOUN
cana-5829	265	11	’	'	PUNCT
cana-5829	265	12	and	and	CCONJ
cana-5829	265	13	‘	'	PUNCT
cana-5829	265	14	possibility	possibility	NOUN
cana-5829	265	15	’	'	PUNCT
cana-5829	265	16	defined	define	VERB
cana-5829	265	17	in	in	ADP
cana-5829	265	18	some	some	DET
cana-5829	265	19	modal	modal	ADJ
cana-5829	265	20	logics	logic	NOUN
cana-5829	265	21	.	.	PUNCT
cana-5829	266	1	this	this	DET
cana-5829	266	2	idea	idea	NOUN
cana-5829	266	3	is	be	AUX
cana-5829	266	4	drawn	draw	VERB
cana-5829	266	5	from	from	ADP
cana-5829	266	6	the	the	DET
cana-5829	266	7	modal	modal	ADJ
cana-5829	266	8	operators	operator	NOUN
cana-5829	266	9	on	on	ADP
cana-5829	266	10	ifs	ifs	PROPN
cana-5829	266	11	proposed	propose	VERB
cana-5829	266	12	by	by	ADP
cana-5829	266	13	[	[	X
cana-5829	266	14	3	3	NUM
cana-5829	266	15	]	]	PUNCT
cana-5829	266	16	.	.	PUNCT
cana-5829	267	1	5	5	X
cana-5829	267	2	.	.	X
cana-5829	267	3	overview	overview	NOUN
cana-5829	267	4	on	on	ADP
cana-5829	267	5	normalization	normalization	NOUN
cana-5829	267	6	and	and	CCONJ
cana-5829	267	7	cartesian	cartesian	ADJ
cana-5829	267	8	product	product	NOUN
cana-5829	267	9	of	of	ADP
cana-5829	267	10	intuitionistic	intuitionistic	ADJ
cana-5829	267	11	fuzzy	fuzzy	ADJ
cana-5829	267	12	matrices	matrix	NOUN
cana-5829	267	13	5.1	5.1	NUM
cana-5829	267	14	definition	definition	NOUN
cana-5829	267	15	:	:	PUNCT
cana-5829	267	16	[	[	X
cana-5829	267	17	modal	modal	ADJ
cana-5829	267	18	operators	operator	NOUN
cana-5829	267	19	’	'	PUNCT
cana-5829	267	20	necessity	necessity	NOUN
cana-5829	267	21	]	]	PUNCT
cana-5829	267	22	:	:	PUNCT
cana-5829	267	23	let	let	VERB
cana-5829	267	24	x	x	PRON
cana-5829	267	25	be	be	AUX
cana-5829	267	26	nonempty	nonempty	ADJ
cana-5829	267	27	.	.	PUNCT
cana-5829	268	1	if	if	SCONJ
cana-5829	268	2	a	a	PRON
cana-5829	268	3	is	be	AUX
cana-5829	268	4	an	an	DET
cana-5829	268	5	ifs	ifs	NOUN
cana-5829	268	6	drawn	draw	VERB
cana-5829	268	7	from	from	ADP
cana-5829	268	8	x	x	PRON
cana-5829	268	9	,	,	PUNCT
cana-5829	268	10	then	then	ADV
cana-5829	268	11	a	a	PROPN
cana-5829	268	12	=	=	PUNCT
cana-5829	268	13	{	{	PUNCT
cana-5829	268	14	x	x	NOUN
cana-5829	268	15	,	,	PUNCT
cana-5829	268	16	μa(x	μa(x	NOUN
cana-5829	268	17	):	):	PUNCT
cana-5829	268	18	xx	xx	SYM
cana-5829	268	19	}	}	PUNCT
cana-5829	268	20	=	=	SYM
cana-5829	268	21	{	{	PUNCT
cana-5829	268	22	x	x	NOUN
cana-5829	268	23	,	,	PUNCT
cana-5829	268	24	μa(x	μa(x	NOUN
cana-5829	268	25	)	)	PUNCT
cana-5829	268	26	,	,	PUNCT
cana-5829	268	27	1	1	NUM
cana-5829	268	28	−	−	NOUN
cana-5829	268	29	𝜇𝐴(x	𝜇𝐴(x	PROPN
cana-5829	268	30	):	):	PUNCT
cana-5829	268	31	xx	xx	X
cana-5829	268	32	}	}	PUNCT
cana-5829	268	33	definition	definition	NOUN
cana-5829	268	34	:	:	PUNCT
cana-5829	268	35	[	[	X
cana-5829	268	36	modal	modal	ADJ
cana-5829	268	37	operators	operator	NOUN
cana-5829	268	38	’	'	PUNCT
cana-5829	268	39	possibility	possibility	NOUN
cana-5829	268	40	]	]	X
cana-5829	268	41	:	:	PUNCT
cana-5829	268	42	let	let	VERB
cana-5829	268	43	x	x	PRON
cana-5829	268	44	be	be	AUX
cana-5829	268	45	nonempty	nonempty	ADJ
cana-5829	268	46	.	.	PUNCT
cana-5829	269	1	if	if	SCONJ
cana-5829	269	2	a	a	PRON
cana-5829	269	3	is	be	AUX
cana-5829	269	4	an	an	DET
cana-5829	269	5	ifs	ifs	NOUN
cana-5829	269	6	drawn	draw	VERB
cana-5829	269	7	from	from	ADP
cana-5829	269	8	x	x	PRON
cana-5829	269	9	,	,	PUNCT
cana-5829	269	10	then	then	ADV
cana-5829	269	11	a	a	NOUN
cana-5829	269	12	=	=	PUNCT
cana-5829	269	13	{	{	PUNCT
cana-5829	269	14	x	x	NOUN
cana-5829	269	15	,	,	PUNCT
cana-5829	269	16	1	1	NUM
cana-5829	269	17	−	−	NOUN
cana-5829	269	18	𝜗𝐴(x	𝜗𝐴(x	NUM
cana-5829	269	19	):	):	PUNCT
cana-5829	269	20	xx	xx	PRON
cana-5829	269	21	}	}	PUNCT
cana-5829	269	22	=	=	SYM
cana-5829	269	23	{	{	PUNCT
cana-5829	269	24	x	x	NOUN
cana-5829	269	25	,	,	PUNCT
cana-5829	269	26	1	1	NUM
cana-5829	269	27	−	−	PROPN
cana-5829	269	28	𝜗𝐴(x	𝜗𝐴(x	NUM
cana-5829	269	29	)	)	PUNCT
cana-5829	269	30	,	,	PUNCT
cana-5829	269	31	𝜗𝐴(x	𝜗𝐴(x	NUM
cana-5829	269	32	):	):	PUNCT
cana-5829	269	33	xx	xx	NOUN
cana-5829	269	34	}	}	PUNCT
cana-5829	269	35	definition	definition	NOUN
cana-5829	269	36	:	:	PUNCT
cana-5829	269	37	if	if	SCONJ
cana-5829	269	38	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	269	39	and	and	CCONJ
cana-5829	269	40	𝐵𝐹	𝐵𝐹	PROPN
cana-5829	269	41	are	be	AUX
cana-5829	269	42	two	two	NUM
cana-5829	269	43	ifss	ifss	ADJ
cana-5829	269	44	over	over	ADP
cana-5829	269	45	different	different	ADJ
cana-5829	269	46	universes	universe	NOUN
cana-5829	269	47	e	e	NOUN
cana-5829	269	48	and	and	CCONJ
cana-5829	269	49	f	f	PROPN
cana-5829	269	50	gives	give	VERB
cana-5829	269	51	as	as	ADP
cana-5829	269	52	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	269	53	=	=	SYM
cana-5829	269	54	{	{	PUNCT
cana-5829	269	55	x	x	NOUN
cana-5829	269	56	,	,	PUNCT
cana-5829	269	57	μa(x	μa(x	NOUN
cana-5829	269	58	)	)	PUNCT
cana-5829	269	59	,	,	PUNCT
cana-5829	269	60	𝜗𝐴(x	𝜗𝐴(x	NUM
cana-5829	269	61	):	):	PUNCT
cana-5829	269	62	xe	xe	PRON
cana-5829	269	63	}	}	PUNCT
cana-5829	269	64	and	and	CCONJ
cana-5829	269	65	𝐵𝐹=	𝐵𝐹=	X
cana-5829	269	66	{	{	PUNCT
cana-5829	269	67	y	y	PROPN
cana-5829	269	68	,	,	PUNCT
cana-5829	269	69	𝜇𝐵(y	𝜇𝐵(y	PROPN
cana-5829	269	70	)	)	PUNCT
cana-5829	269	71	,	,	PUNCT
cana-5829	269	72	𝜗𝐵(y	𝜗𝐵(y	NUM
cana-5829	269	73	):	):	PUNCT
cana-5829	269	74	yf	yf	NOUN
cana-5829	269	75	}	}	PUNCT
cana-5829	269	76	definition	definition	NOUN
cana-5829	269	77	:	:	PUNCT
cana-5829	269	78	if	if	SCONJ
cana-5829	269	79	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	269	80	̅̅̅̅	̅̅̅̅	NOUN
cana-5829	269	81	and𝐵𝐹	and𝐵𝐹	PROPN
cana-5829	269	82	̅̅̅̅	̅̅̅̅	ADJ
cana-5829	269	83	are	be	AUX
cana-5829	269	84	two	two	NUM
cana-5829	269	85	ifss	ifss	ADJ
cana-5829	269	86	over	over	ADP
cana-5829	269	87	different	different	ADJ
cana-5829	269	88	universes	universe	NOUN
cana-5829	269	89	e	e	NOUN
cana-5829	269	90	and	and	CCONJ
cana-5829	269	91	f	f	PROPN
cana-5829	269	92	gives	give	VERB
cana-5829	269	93	as	as	ADP
cana-5829	269	94	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	269	95	̅̅̅̅	̅̅̅̅	NOUN
cana-5829	270	1	=	=	X
cana-5829	270	2	{	{	PUNCT
cana-5829	270	3	x	x	NOUN
cana-5829	270	4	,	,	PUNCT
cana-5829	270	5	𝜗𝐴(x	𝜗𝐴(x	NUM
cana-5829	270	6	)	)	PUNCT
cana-5829	270	7	,	,	PUNCT
cana-5829	270	8	μa(x	μa(x	PROPN
cana-5829	270	9	):	):	PUNCT
cana-5829	270	10	xe	xe	PRON
cana-5829	270	11	}	}	PUNCT
cana-5829	270	12	and	and	CCONJ
cana-5829	270	13	𝐵𝐹	𝐵𝐹	NOUN
cana-5829	270	14	̅̅̅̅	̅̅̅̅	NOUN
cana-5829	270	15	=	=	PUNCT
cana-5829	270	16	{	{	PUNCT
cana-5829	270	17	y	y	PROPN
cana-5829	270	18	,	,	PUNCT
cana-5829	270	19	𝜗𝐵(y	𝜗𝐵(y	NUM
cana-5829	270	20	)	)	PUNCT
cana-5829	270	21	,	,	PUNCT
cana-5829	270	22	𝜇𝐵(y	𝜇𝐵(y	NUM
cana-5829	270	23	):	):	PUNCT
cana-5829	270	24	yf	yf	NOUN
cana-5829	270	25	}	}	PUNCT
cana-5829	270	26	definition	definition	NOUN
cana-5829	270	27	:	:	PUNCT
cana-5829	270	28	if	if	SCONJ
cana-5829	270	29	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	270	30	and	and	CCONJ
cana-5829	270	31	𝐵𝐹	𝐵𝐹	PROPN
cana-5829	270	32	are	be	AUX
cana-5829	270	33	two	two	NUM
cana-5829	270	34	ifss	ifss	ADJ
cana-5829	270	35	over	over	ADP
cana-5829	270	36	different	different	ADJ
cana-5829	270	37	universes	universe	NOUN
cana-5829	270	38	e	e	NOUN
cana-5829	270	39	and	and	CCONJ
cana-5829	270	40	f	f	PROPN
cana-5829	270	41	gives	give	VERB
cana-5829	270	42	as	as	ADP
cana-5829	270	43	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	270	44	=	=	SYM
cana-5829	270	45	{	{	PUNCT
cana-5829	270	46	x	x	NOUN
cana-5829	270	47	,	,	PUNCT
cana-5829	270	48	μa(x	μa(x	NOUN
cana-5829	270	49	)	)	PUNCT
cana-5829	270	50	,	,	PUNCT
cana-5829	270	51	𝜗𝐴(x	𝜗𝐴(x	NUM
cana-5829	270	52	):	):	PUNCT
cana-5829	270	53	xe	xe	PRON
cana-5829	270	54	}	}	PUNCT
cana-5829	270	55	and	and	CCONJ
cana-5829	270	56	𝐵𝐹=	𝐵𝐹=	X
cana-5829	270	57	{	{	PUNCT
cana-5829	270	58	y	y	PROPN
cana-5829	270	59	,	,	PUNCT
cana-5829	270	60	𝜇𝐵(y	𝜇𝐵(y	PROPN
cana-5829	270	61	)	)	PUNCT
cana-5829	270	62	,	,	PUNCT
cana-5829	270	63	𝜗𝐵(y	𝜗𝐵(y	NUM
cana-5829	270	64	):	):	PUNCT
cana-5829	270	65	yf	yf	NOUN
cana-5829	270	66	}	}	PUNCT
cana-5829	270	67	definition	definition	NOUN
cana-5829	270	68	:	:	PUNCT
cana-5829	270	69	if	if	SCONJ
cana-5829	270	70	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	270	71	̅̅̅̅	̅̅̅̅	NOUN
cana-5829	270	72	and𝐵𝐹	and𝐵𝐹	PROPN
cana-5829	270	73	̅̅̅̅	̅̅̅̅	ADJ
cana-5829	270	74	are	be	AUX
cana-5829	270	75	two	two	NUM
cana-5829	270	76	ifss	ifss	ADJ
cana-5829	270	77	over	over	ADP
cana-5829	270	78	different	different	ADJ
cana-5829	270	79	universes	universe	NOUN
cana-5829	270	80	e	e	NOUN
cana-5829	270	81	and	and	CCONJ
cana-5829	270	82	f	f	PROPN
cana-5829	270	83	gives	give	VERB
cana-5829	270	84	as	as	ADP
cana-5829	270	85	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	270	86	̅̅̅̅	̅̅̅̅	NOUN
cana-5829	271	1	=	=	X
cana-5829	271	2	{	{	PUNCT
cana-5829	271	3	x	x	NOUN
cana-5829	271	4	,	,	PUNCT
cana-5829	271	5	𝜗𝐴(x	𝜗𝐴(x	NUM
cana-5829	271	6	)	)	PUNCT
cana-5829	271	7	,	,	PUNCT
cana-5829	271	8	μa(x	μa(x	PROPN
cana-5829	271	9	):	):	PUNCT
cana-5829	271	10	xe	xe	PRON
cana-5829	271	11	}	}	PUNCT
cana-5829	271	12	and	and	CCONJ
cana-5829	271	13	𝐵𝐹	𝐵𝐹	NOUN
cana-5829	271	14	̅̅̅̅	̅̅̅̅	NOUN
cana-5829	271	15	=	=	PUNCT
cana-5829	271	16	{	{	PUNCT
cana-5829	271	17	y	y	PROPN
cana-5829	271	18	,	,	PUNCT
cana-5829	271	19	𝜗𝐵(y	𝜗𝐵(y	NUM
cana-5829	271	20	)	)	PUNCT
cana-5829	271	21	,	,	PUNCT
cana-5829	271	22	𝜇𝐵(y	𝜇𝐵(y	NUM
cana-5829	271	23	):	):	PUNCT
cana-5829	271	24	yf	yf	NOUN
cana-5829	271	25	}	}	PUNCT
cana-5829	271	26	communications	communication	NOUN
cana-5829	271	27	on	on	ADP
cana-5829	271	28	applied	apply	VERB
cana-5829	271	29	nonlinear	nonlinear	ADJ
cana-5829	271	30	analysis	analysis	NOUN
cana-5829	271	31	issn	issn	NOUN
cana-5829	271	32	:	:	PUNCT
cana-5829	271	33	1074	1074	NUM
cana-5829	271	34	-	-	PUNCT
cana-5829	271	35	133x	133x	NUM
cana-5829	271	36	vol	vol	VERB
cana-5829	271	37	32	32	NUM
cana-5829	271	38	no	no	NOUN
cana-5829	271	39	.	.	PUNCT
cana-5829	272	1	10s	10	NOUN
cana-5829	272	2	(	(	PUNCT
cana-5829	272	3	2025	2025	NUM
cana-5829	272	4	)	)	PUNCT
cana-5829	272	5	2935	2935	NUM
cana-5829	272	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5829	272	7	5.2	5.2	NUM
cana-5829	272	8	definition	definition	NOUN
cana-5829	272	9	:	:	PUNCT
cana-5829	272	10	let	let	VERB
cana-5829	272	11	e	e	PRON
cana-5829	272	12	be	be	AUX
cana-5829	272	13	non	non	ADJ
cana-5829	272	14	-	-	ADJ
cana-5829	272	15	empty	empty	ADJ
cana-5829	272	16	universe	universe	NOUN
cana-5829	272	17	set	set	NOUN
cana-5829	272	18	.	.	PUNCT
cana-5829	273	1	the	the	DET
cana-5829	273	2	normalization	normalization	NOUN
cana-5829	273	3	of	of	ADP
cana-5829	273	4	intuitionistic	intuitionistic	ADJ
cana-5829	273	5	fuzzy	fuzzy	ADJ
cana-5829	273	6	sets	set	NOUN
cana-5829	273	7	a	a	DET
cana-5829	273	8	denoted	denote	VERB
cana-5829	273	9	by	by	ADP
cana-5829	273	10	norm	norm	NOUN
cana-5829	273	11	(	(	PUNCT
cana-5829	273	12	a	a	X
cana-5829	273	13	)	)	PUNCT
cana-5829	273	14	is	be	AUX
cana-5829	273	15	defined	define	VERB
cana-5829	273	16	as	as	ADP
cana-5829	273	17	norm	norm	NOUN
cana-5829	273	18	(	(	PUNCT
cana-5829	273	19	a	a	X
cana-5829	273	20	)	)	PUNCT
cana-5829	273	21	=	=	SYM
cana-5829	273	22	{	{	PUNCT
cana-5829	273	23	x	x	NOUN
cana-5829	273	24	,	,	PUNCT
cana-5829	273	25	𝜇𝑁𝑜𝑟𝑚(𝐴)(x	𝜇𝑁𝑜𝑟𝑚(𝐴)(x	PROPN
cana-5829	273	26	)	)	PUNCT
cana-5829	273	27	,	,	PUNCT
cana-5829	273	28	𝜗𝑁𝑜𝑟𝑚(𝐴)(x	𝜗𝑁𝑜𝑟𝑚(𝐴)(x	NOUN
cana-5829	273	29	):	):	PUNCT
cana-5829	273	30	xe	xe	PRON
cana-5829	273	31	}	}	PUNCT
cana-5829	273	32	,	,	PUNCT
cana-5829	273	33	where	where	SCONJ
cana-5829	273	34	μnorm(a)(x	μnorm(a)(x	NOUN
cana-5829	273	35	)	)	PUNCT
cana-5829	273	36	=	=	PUNCT
cana-5829	273	37	μa(x	μa(x	PRON
cana-5829	273	38	)	)	PUNCT
cana-5829	273	39	sup	sup	NOUN
cana-5829	273	40	(	(	PUNCT
cana-5829	273	41	μa(x	μa(x	NOUN
cana-5829	273	42	)	)	PUNCT
cana-5829	273	43	)	)	PUNCT
cana-5829	273	44	and	and	CCONJ
cana-5829	273	45	ϑnorm(a)(x	ϑnorm(a)(x	PROPN
cana-5829	273	46	)	)	PUNCT
cana-5829	274	1	=	=	SYM
cana-5829	274	2	ϑa(x)−	ϑa(x)−	PROPN
cana-5829	274	3	inf	inf	PROPN
cana-5829	274	4	(	(	PUNCT
cana-5829	274	5	ϑa(x	ϑa(x	NOUN
cana-5829	274	6	)	)	PUNCT
cana-5829	274	7	)	)	PUNCT
cana-5829	274	8	1−inf	1−inf	NUM
cana-5829	274	9	(	(	PUNCT
cana-5829	274	10	ϑa(x	ϑa(x	NOUN
cana-5829	274	11	)	)	PUNCT
cana-5829	274	12	)	)	PUNCT
cana-5829	274	13	.	.	PUNCT
cana-5829	275	1	definition5.2.1	definition5.2.1	NOUN
cana-5829	275	2	:	:	PUNCT
cana-5829	275	3	if	if	SCONJ
cana-5829	275	4	ae	ae	PROPN
cana-5829	275	5	and	and	CCONJ
cana-5829	275	6	bf	bf	NOUN
cana-5829	275	7	are	be	AUX
cana-5829	275	8	two	two	NUM
cana-5829	275	9	ifss	ifss	ADJ
cana-5829	275	10	over	over	ADP
cana-5829	275	11	different	different	ADJ
cana-5829	275	12	universes	universe	NOUN
cana-5829	275	13	sets	set	VERB
cana-5829	275	14	e	e	NOUN
cana-5829	275	15	and	and	CCONJ
cana-5829	275	16	f	f	PROPN
cana-5829	275	17	gives	give	VERB
cana-5829	275	18	as	as	ADP
cana-5829	275	19	ae	ae	PROPN
cana-5829	275	20	=	=	PROPN
cana-5829	275	21	{	{	PUNCT
cana-5829	275	22	x	x	NOUN
cana-5829	275	23	,	,	PUNCT
cana-5829	275	24	μa(x	μa(x	NOUN
cana-5829	275	25	)	)	PUNCT
cana-5829	275	26	,	,	PUNCT
cana-5829	275	27	ϑa(x	ϑa(x	NOUN
cana-5829	275	28	):	):	PUNCT
cana-5829	275	29	xe	xe	PRON
cana-5829	275	30	}	}	PUNCT
cana-5829	275	31	and	and	CCONJ
cana-5829	275	32	bf=	bf=	VERB
cana-5829	275	33	{	{	PUNCT
cana-5829	275	34	y	y	NOUN
cana-5829	275	35	,	,	PUNCT
cana-5829	275	36	μb(y	μb(y	NUM
cana-5829	275	37	)	)	PUNCT
cana-5829	275	38	,	,	PUNCT
cana-5829	275	39	ϑb(y	ϑb(y	ADV
cana-5829	275	40	):	):	PUNCT
cana-5829	275	41	yf	yf	NOUN
cana-5829	275	42	}	}	PUNCT
cana-5829	275	43	.	.	PUNCT
cana-5829	276	1	1.aebf	1.aebf	X
cana-5829	276	2	=	=	PRON
cana-5829	276	3	{	{	PUNCT
cana-5829	276	4	(	(	PUNCT
cana-5829	276	5	x	x	NOUN
cana-5829	276	6	,	,	PUNCT
cana-5829	276	7	y	y	PROPN
cana-5829	276	8	)	)	PUNCT
cana-5829	276	9	,	,	PUNCT
cana-5829	276	10	min	min	PROPN
cana-5829	276	11	(	(	PUNCT
cana-5829	276	12	μa(x	μa(x	NOUN
cana-5829	276	13	)	)	PUNCT
cana-5829	276	14	,	,	PUNCT
cana-5829	276	15	μb(y	μb(y	NUM
cana-5829	276	16	)	)	PUNCT
cana-5829	276	17	)	)	PUNCT
cana-5829	276	18	,	,	PUNCT
cana-5829	276	19	max	max	PROPN
cana-5829	276	20	(	(	PUNCT
cana-5829	276	21	ϑa(x	ϑa(x	NOUN
cana-5829	276	22	)	)	PUNCT
cana-5829	276	23	,	,	PUNCT
cana-5829	276	24	ϑb(x	ϑb(x	NUM
cana-5829	276	25	)	)	PUNCT
cana-5829	276	26	):	):	PUNCT
cana-5829	276	27	xe	xe	PROPN
cana-5829	276	28	,	,	PUNCT
cana-5829	276	29	yf	yf	ADJ
cana-5829	276	30	}	}	PUNCT
cana-5829	276	31	2	2	NUM
cana-5829	276	32	.	.	X
cana-5829	276	33	aebf	aebf	X
cana-5829	276	34	=	=	PRON
cana-5829	276	35	{	{	PUNCT
cana-5829	276	36	(	(	PUNCT
cana-5829	276	37	x	x	NOUN
cana-5829	276	38	,	,	PUNCT
cana-5829	276	39	y	y	PROPN
cana-5829	276	40	)	)	PUNCT
cana-5829	276	41	,	,	PUNCT
cana-5829	276	42	max	max	PROPN
cana-5829	276	43	(	(	PUNCT
cana-5829	276	44	μa(x	μa(x	NOUN
cana-5829	276	45	)	)	PUNCT
cana-5829	276	46	,	,	PUNCT
cana-5829	276	47	μb(y	μb(y	NUM
cana-5829	276	48	)	)	PUNCT
cana-5829	276	49	)	)	PUNCT
cana-5829	276	50	,	,	PUNCT
cana-5829	276	51	min	min	PROPN
cana-5829	276	52	(	(	PUNCT
cana-5829	276	53	ϑa(x	ϑa(x	NOUN
cana-5829	276	54	)	)	PUNCT
cana-5829	276	55	,	,	PUNCT
cana-5829	276	56	ϑb(x	ϑb(x	NUM
cana-5829	276	57	)	)	PUNCT
cana-5829	276	58	):	):	PUNCT
cana-5829	276	59	xe	xe	PROPN
cana-5829	276	60	,	,	PUNCT
cana-5829	276	61	yf	yf	ADJ
cana-5829	276	62	}	}	PUNCT
cana-5829	276	63	3	3	NUM
cana-5829	276	64	.	.	PUNCT
cana-5829	276	65	aebf	aebf	X
cana-5829	277	1	=	=	PRON
cana-5829	277	2	{	{	PUNCT
cana-5829	277	3	(	(	PUNCT
cana-5829	277	4	x	x	NOUN
cana-5829	277	5	,	,	PUNCT
cana-5829	277	6	y	y	PROPN
cana-5829	277	7	)	)	PUNCT
cana-5829	277	8	,	,	PUNCT
cana-5829	277	9	(	(	PUNCT
cana-5829	277	10	μa(x	μa(x	X
cana-5829	277	11	)	)	PUNCT
cana-5829	278	1	+	+	CCONJ
cana-5829	278	2	μb(y	μb(y	NUM
cana-5829	278	3	)	)	PUNCT
cana-5829	278	4	)	)	PUNCT
cana-5829	278	5	μa(x	μa(x	NOUN
cana-5829	278	6	)	)	PUNCT
cana-5829	278	7	.	.	PUNCT
cana-5829	279	1	μb(y	μb(y	NUM
cana-5829	279	2	)	)	PUNCT
cana-5829	280	1	,	,	PUNCT
cana-5829	280	2	ϑa(x).ϑb(y	ϑa(x).ϑb(y	ADJ
cana-5829	280	3	):	):	PUNCT
cana-5829	280	4	xe	xe	PROPN
cana-5829	280	5	,	,	PUNCT
cana-5829	280	6	yf	yf	ADJ
cana-5829	280	7	}	}	PUNCT
cana-5829	280	8	4	4	NUM
cana-5829	280	9	.	.	PUNCT
cana-5829	280	10	aebf	aebf	X
cana-5829	281	1	=	=	PRON
cana-5829	281	2	{	{	PUNCT
cana-5829	281	3	(	(	PUNCT
cana-5829	281	4	x	x	NOUN
cana-5829	281	5	,	,	PUNCT
cana-5829	281	6	y	y	PROPN
cana-5829	281	7	)	)	PUNCT
cana-5829	281	8	,	,	PUNCT
cana-5829	281	9	μa(x	μa(x	NOUN
cana-5829	281	10	)	)	PUNCT
cana-5829	281	11	.	.	PUNCT
cana-5829	282	1	μb(y	μb(y	NUM
cana-5829	282	2	)	)	PUNCT
cana-5829	282	3	,	,	PUNCT
cana-5829	282	4	ϑa(x	ϑa(x	NOUN
cana-5829	282	5	)	)	PUNCT
cana-5829	282	6	+	+	ADJ
cana-5829	282	7	ϑb(y	ϑb(y	X
cana-5829	282	8	)	)	PUNCT
cana-5829	282	9	ϑa(x).ϑb(y	ϑa(x).ϑb(y	ADJ
cana-5829	282	10	):	):	PUNCT
cana-5829	282	11	xe	xe	PROPN
cana-5829	282	12	,	,	PUNCT
cana-5829	282	13	yf	yf	ADJ
cana-5829	282	14	}	}	PUNCT
cana-5829	282	15	5	5	NUM
cana-5829	282	16	.	.	PUNCT
cana-5829	283	1	ae@bf	ae@bf	NOUN
cana-5829	283	2	=	=	SYM
cana-5829	283	3	{	{	PUNCT
cana-5829	283	4	(	(	PUNCT
cana-5829	283	5	x	x	NOUN
cana-5829	283	6	,	,	PUNCT
cana-5829	283	7	y	y	PROPN
cana-5829	283	8	)	)	PUNCT
cana-5829	283	9	,	,	PUNCT
cana-5829	283	10	μa(x)+	μa(x)+	NOUN
cana-5829	283	11	μb(y	μb(y	NUM
cana-5829	283	12	)	)	PUNCT
cana-5829	283	13	2	2	NUM
cana-5829	283	14	,	,	PUNCT
cana-5829	283	15	ϑa(x)+ϑb(y	ϑa(x)+ϑb(y	ADJ
cana-5829	283	16	)	)	PUNCT
cana-5829	283	17	2	2	NUM
cana-5829	283	18	:	:	PUNCT
cana-5829	283	19	xe	xe	NUM
cana-5829	283	20	,	,	PUNCT
cana-5829	283	21	yf	yf	ADJ
cana-5829	283	22	}	}	PUNCT
cana-5829	283	23	6	6	NUM
cana-5829	283	24	.	.	PUNCT
cana-5829	283	25	a#bf	a#bf	NOUN
cana-5829	284	1	=	=	PUNCT
cana-5829	284	2	{	{	PUNCT
cana-5829	284	3	(	(	PUNCT
cana-5829	284	4	x	x	NOUN
cana-5829	284	5	,	,	PUNCT
cana-5829	284	6	y	y	PROPN
cana-5829	284	7	)	)	PUNCT
cana-5829	284	8	,	,	PUNCT
cana-5829	284	9	2μa(x).μb(y	2μa(x).μb(y	NUM
cana-5829	284	10	)	)	PUNCT
cana-5829	284	11	μa(x)+ϑb(y	μa(x)+ϑb(y	PROPN
cana-5829	284	12	)	)	PUNCT
cana-5829	284	13	,	,	PUNCT
cana-5829	284	14	2ϑa(x).ϑb(y	2ϑa(x).ϑb(y	NUM
cana-5829	284	15	)	)	PUNCT
cana-5829	284	16	ϑa(x)+ϑb(y	ϑa(x)+ϑb(y	PROPN
cana-5829	284	17	)	)	PUNCT
cana-5829	284	18	:	:	PUNCT
cana-5829	285	1	xe	xe	PROPN
cana-5829	285	2	,	,	PUNCT
cana-5829	285	3	yf	yf	ADJ
cana-5829	285	4	}	}	PUNCT
cana-5829	285	5	7	7	NUM
cana-5829	285	6	.	.	PUNCT
cana-5829	286	1	ae$bf	ae$bf	PROPN
cana-5829	286	2	=	=	PUNCT
cana-5829	286	3	{	{	PUNCT
cana-5829	286	4	(	(	PUNCT
cana-5829	286	5	x	x	NOUN
cana-5829	286	6	,	,	PUNCT
cana-5829	286	7	y),√μa(x	y),√μa(x	PROPN
cana-5829	286	8	)	)	PUNCT
cana-5829	286	9	.	.	PUNCT
cana-5829	287	1	μb(y	μb(y	NUM
cana-5829	287	2	)	)	PUNCT
cana-5829	287	3	,	,	PUNCT
cana-5829	287	4	√ϑa(x	√ϑa(x	NOUN
cana-5829	287	5	)	)	PUNCT
cana-5829	287	6	.	.	PUNCT
cana-5829	288	1	ϑb(y)xe	ϑb(y)xe	NOUN
cana-5829	288	2	,	,	PUNCT
cana-5829	288	3	yf	yf	ADJ
cana-5829	288	4	}	}	SYM
cana-5829	288	5	8	8	NUM
cana-5829	288	6	.	.	PUNCT
cana-5829	288	7	ae*bf	ae*bf	PROPN
cana-5829	288	8	=	=	PRON
cana-5829	288	9	{	{	PUNCT
cana-5829	288	10	(	(	PUNCT
cana-5829	288	11	x	x	NOUN
cana-5829	288	12	,	,	PUNCT
cana-5829	288	13	y	y	PROPN
cana-5829	288	14	)	)	PUNCT
cana-5829	288	15	,	,	PUNCT
cana-5829	288	16	μa(x)+	μa(x)+	NOUN
cana-5829	288	17	μb(y	μb(y	NUM
cana-5829	288	18	)	)	PUNCT
cana-5829	288	19	2(μa(x	2(μa(x	NOUN
cana-5829	288	20	)	)	PUNCT
cana-5829	288	21	.	.	PUNCT
cana-5829	289	1	μb(y)+1	μb(y)+1	NUM
cana-5829	289	2	)	)	PUNCT
cana-5829	289	3	,	,	PUNCT
cana-5829	290	1	ϑa(x)+ϑb(y	ϑa(x)+ϑb(y	ADJ
cana-5829	290	2	)	)	PUNCT
cana-5829	290	3	2(ϑa(x).ϑb(x)+1	2(ϑa(x).ϑb(x)+1	NUM
cana-5829	290	4	)	)	PUNCT
cana-5829	291	1	:	:	PUNCT
cana-5829	291	2	xe	xe	PROPN
cana-5829	291	3	,	,	PUNCT
cana-5829	291	4	yf	yf	NUM
cana-5829	291	5	}	}	PUNCT
cana-5829	291	6	9	9	NUM
cana-5829	291	7	.	.	PUNCT
cana-5829	291	8	ae∆bf	ae∆bf	X
cana-5829	292	1	=	=	PRON
cana-5829	292	2	{	{	PUNCT
cana-5829	292	3	(	(	PUNCT
cana-5829	292	4	x	x	NOUN
cana-5829	292	5	,	,	PUNCT
cana-5829	292	6	y	y	PROPN
cana-5829	292	7	)	)	PUNCT
cana-5829	292	8	,	,	PUNCT
cana-5829	292	9	μa(x)+	μa(x)+	NOUN
cana-5829	292	10	μb(y	μb(y	NUM
cana-5829	292	11	)	)	PUNCT
cana-5829	292	12	μa(x)+	μa(x)+	X
cana-5829	292	13	μb(y)+ϑa(x)+ϑb(y	μb(y)+ϑa(x)+ϑb(y	NUM
cana-5829	292	14	)	)	PUNCT
cana-5829	292	15	,	,	PUNCT
cana-5829	292	16	ϑa(x)+ϑb(y	ϑa(x)+ϑb(y	ADJ
cana-5829	292	17	)	)	PUNCT
cana-5829	292	18	μa(x)+	μa(x)+	NUM
cana-5829	292	19	μb(y)+ϑa(x)+ϑb(y	μb(y)+ϑa(x)+ϑb(y	NUM
cana-5829	292	20	)	)	PUNCT
cana-5829	292	21	∶	∶	NOUN
cana-5829	292	22	xe	xe	X
cana-5829	292	23	,	,	PUNCT
cana-5829	292	24	yf	yf	NUM
cana-5829	292	25	}	}	PUNCT
cana-5829	292	26	theorem	theorem	VERB
cana-5829	292	27	5.2.1	5.2.1	NOUN
cana-5829	292	28	:	:	PUNCT
cana-5829	292	29	if	if	SCONJ
cana-5829	292	30	e	e	PROPN
cana-5829	292	31	and	and	CCONJ
cana-5829	292	32	f	f	PROPN
cana-5829	292	33	be	be	AUX
cana-5829	292	34	two	two	NUM
cana-5829	292	35	universal	universal	ADJ
cana-5829	292	36	sets	set	NOUN
cana-5829	292	37	.	.	PUNCT
cana-5829	293	1	for	for	ADP
cana-5829	293	2	every	every	DET
cana-5829	293	3	normalization	normalization	NOUN
cana-5829	293	4	of	of	ADP
cana-5829	293	5	complex	complex	ADJ
cana-5829	293	6	intuitionistic	intuitionistic	ADJ
cana-5829	293	7	fuzzy	fuzzy	ADJ
cana-5829	293	8	matrices	matrix	NOUN
cana-5829	293	9	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	293	10	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-5829	293	11	𝐵𝐹	𝐵𝐹	PROPN
cana-5829	293	12	are	be	AUX
cana-5829	293	13	in	in	ADP
cana-5829	293	14	e	e	PROPN
cana-5829	293	15	and	and	CCONJ
cana-5829	293	16	f	f	PROPN
cana-5829	293	17	then	then	ADV
cana-5829	293	18	norm	norm	VERB
cana-5829	293	19	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	293	20	∩	∩	NOUN
cana-5829	293	21	𝑁𝑜𝑟𝑚	𝑁𝑜𝑟𝑚	PROPN
cana-5829	293	22	𝐵𝐹	𝐵𝐹	PROPN
cana-5829	293	23	is	be	AUX
cana-5829	293	24	also	also	ADV
cana-5829	293	25	normalization	normalization	NOUN
cana-5829	293	26	of	of	ADP
cana-5829	293	27	complex	complex	ADJ
cana-5829	293	28	intuitionistic	intuitionistic	ADJ
cana-5829	293	29	fuzzy	fuzzy	ADJ
cana-5829	293	30	matrices	matrix	NOUN
cana-5829	293	31	.	.	PUNCT
cana-5829	294	1	proof	proof	NOUN
cana-5829	294	2	:	:	PUNCT
cana-5829	294	3	if	if	SCONJ
cana-5829	294	4	norm	norm	NOUN
cana-5829	294	5	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	294	6	and	and	CCONJ
cana-5829	294	7	𝑁𝑜𝑟𝑚	𝑁𝑜𝑟𝑚	PROPN
cana-5829	294	8	𝐵𝐹	𝐵𝐹	PROPN
cana-5829	294	9	are	be	AUX
cana-5829	294	10	two	two	NUM
cana-5829	294	11	normalization	normalization	NOUN
cana-5829	294	12	intuitionistic	intuitionistic	ADJ
cana-5829	294	13	fuzzy	fuzzy	ADJ
cana-5829	294	14	matrices	matrix	NOUN
cana-5829	294	15	over	over	ADP
cana-5829	294	16	different	different	ADJ
cana-5829	294	17	unive𝑟𝑠𝑒𝑠	unive𝑟𝑠𝑒𝑠	ADJ
cana-5829	294	18	𝑠𝑒𝑡𝑠	𝑠𝑒𝑡𝑠	PROPN
cana-5829	294	19	𝐸	𝐸	PROPN
cana-5829	294	20	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-5829	294	21	𝐹.	𝐹.	PROPN
cana-5829	294	22	if	if	SCONJ
cana-5829	294	23	we	we	PRON
cana-5829	294	24	consider	consider	VERB
cana-5829	294	25	two	two	NUM
cana-5829	294	26	2	2	NUM
cana-5829	294	27	×	×	NOUN
cana-5829	294	28	2	2	NUM
cana-5829	294	29	normalization	normalization	NOUN
cana-5829	294	30	intuitionistic	intuitionistic	ADJ
cana-5829	294	31	fuzzy	fuzzy	ADJ
cana-5829	294	32	matrices	matrix	NOUN
cana-5829	294	33	,	,	PUNCT
cana-5829	294	34	norm	norm	NOUN
cana-5829	294	35	𝐴𝐸𝑎𝑛𝑑	𝐴𝐸𝑎𝑛𝑑	PROPN
cana-5829	294	36	𝑁𝑜𝑟𝑚	𝑁𝑜𝑟𝑚	PROPN
cana-5829	294	37	𝐵𝐹.	𝐵𝐹.	NOUN
cana-5829	294	38	let	let	VERB
cana-5829	294	39	norm	norm	VERB
cana-5829	294	40	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	294	41	=	=	SYM
cana-5829	294	42	(	(	PUNCT
cana-5829	294	43	(	(	PUNCT
cana-5829	294	44	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	294	45	(	(	PUNCT
cana-5829	294	46	𝛼11	𝛼11	NOUN
cana-5829	294	47	+	+	PROPN
cana-5829	294	48	𝑖𝛽11	𝑖𝛽11	PROPN
cana-5829	294	49	)	)	PUNCT
cana-5829	294	50	𝑁𝑜𝑟𝑚µ𝐸11	𝑁𝑜𝑟𝑚µ𝐸11	NOUN
cana-5829	294	51	(	(	PUNCT
cana-5829	294	52	𝛾11	𝛾11	VERB
cana-5829	294	53	+	+	CCONJ
cana-5829	294	54	𝑖𝛿11	𝑖𝛿11	PROPN
cana-5829	294	55	)	)	PUNCT
cana-5829	294	56	)	)	PUNCT
cana-5829	294	57	(	(	PUNCT
cana-5829	294	58	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	NOUN
cana-5829	294	59	(	(	PUNCT
cana-5829	294	60	𝛼12	𝛼12	NOUN
cana-5829	294	61	+	+	CCONJ
cana-5829	294	62	𝑖𝛽12	𝑖𝛽12	PROPN
cana-5829	294	63	)	)	PUNCT
cana-5829	294	64	𝑁𝑜𝑟𝑚µ𝐸12	𝑁𝑜𝑟𝑚µ𝐸12	NOUN
cana-5829	294	65	(	(	PUNCT
cana-5829	294	66	𝛾12	𝛾12	VERB
cana-5829	294	67	+	+	CCONJ
cana-5829	294	68	𝑖𝛿12	𝑖𝛿12	PROPN
cana-5829	294	69	)	)	PUNCT
cana-5829	294	70	)	)	PUNCT
cana-5829	295	1	(	(	PUNCT
cana-5829	295	2	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	X
cana-5829	295	3	(	(	PUNCT
cana-5829	295	4	𝛼21	𝛼21	NOUN
cana-5829	295	5	+	+	X
cana-5829	295	6	𝑖𝛽21	𝑖𝛽21	PROPN
cana-5829	295	7	)	)	PUNCT
cana-5829	295	8	𝑁𝑜𝑟𝑚µ𝐸21	𝑁𝑜𝑟𝑚µ𝐸21	NOUN
cana-5829	295	9	(	(	PUNCT
cana-5829	295	10	𝛾21	𝛾21	NOUN
cana-5829	295	11	+	+	CCONJ
cana-5829	296	1	𝑖𝛿21	𝑖𝛿21	PROPN
cana-5829	296	2	)	)	PUNCT
cana-5829	296	3	)	)	PUNCT
cana-5829	297	1	(	(	PUNCT
cana-5829	297	2	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	X
cana-5829	297	3	(	(	PUNCT
cana-5829	297	4	𝛼22	𝛼22	NOUN
cana-5829	297	5	+	+	CCONJ
cana-5829	297	6	𝑖𝛽22	𝑖𝛽22	PROPN
cana-5829	297	7	)	)	PUNCT
cana-5829	297	8	𝑁𝑜𝑟𝑚µ𝐸22	𝑁𝑜𝑟𝑚µ𝐸22	NOUN
cana-5829	297	9	(	(	PUNCT
cana-5829	297	10	𝛾22	𝛾22	PROPN
cana-5829	297	11	+	+	PROPN
cana-5829	297	12	𝑖𝛿22	𝑖𝛿22	PROPN
cana-5829	297	13	)	)	PUNCT
cana-5829	297	14	)	)	PUNCT
cana-5829	297	15	)	)	PUNCT
cana-5829	298	1	and	and	CCONJ
cana-5829	298	2	𝑁𝑜𝑟𝑚	𝑁𝑜𝑟𝑚	PROPN
cana-5829	298	3	𝐵𝐹	𝐵𝐹	NOUN
cana-5829	298	4	=	=	SYM
cana-5829	298	5	(	(	PUNCT
cana-5829	298	6	(	(	PUNCT
cana-5829	298	7	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	298	8	(	(	PUNCT
cana-5829	298	9	𝑥11	𝑥11	ADV
cana-5829	298	10	+	+	CCONJ
cana-5829	298	11	𝑖𝑦11	𝑖𝑦11	NOUN
cana-5829	298	12	)	)	PUNCT
cana-5829	298	13	𝑁𝑜𝑟𝑚𝛾𝐹11	𝑁𝑜𝑟𝑚𝛾𝐹11	X
cana-5829	298	14	(	(	PUNCT
cana-5829	298	15	𝜇11	𝜇11	PROPN
cana-5829	298	16	+	+	PROPN
cana-5829	298	17	𝑖𝜃11	𝑖𝜃11	PROPN
cana-5829	298	18	)	)	PUNCT
cana-5829	298	19	)	)	PUNCT
cana-5829	299	1	(	(	PUNCT
cana-5829	299	2	𝑁𝑜𝑟𝑚𝛿𝐹12	𝑁𝑜𝑟𝑚𝛿𝐹12	X
cana-5829	299	3	(	(	PUNCT
cana-5829	299	4	𝑥12	𝑥12	VERB
cana-5829	299	5	+	+	CCONJ
cana-5829	299	6	𝑖𝑦12	𝑖𝑦12	PROPN
cana-5829	299	7	)	)	PUNCT
cana-5829	299	8	𝑁𝑜𝑟𝑚𝛾𝐹12	𝑁𝑜𝑟𝑚𝛾𝐹12	NOUN
cana-5829	299	9	(	(	PUNCT
cana-5829	299	10	𝜇12	𝜇12	NOUN
cana-5829	299	11	+	+	CCONJ
cana-5829	300	1	𝑖𝜃12	𝑖𝜃12	PROPN
cana-5829	300	2	)	)	PUNCT
cana-5829	300	3	)	)	PUNCT
cana-5829	301	1	(	(	PUNCT
cana-5829	301	2	𝑁𝑜𝑟𝑚𝛿𝐹21	𝑁𝑜𝑟𝑚𝛿𝐹21	X
cana-5829	301	3	(	(	PUNCT
cana-5829	301	4	𝑥21	𝑥21	PROPN
cana-5829	301	5	+	+	CCONJ
cana-5829	301	6	𝑖𝑦21	𝑖𝑦21	PROPN
cana-5829	301	7	)	)	PUNCT
cana-5829	301	8	𝑁𝑜𝑟𝑚𝛾𝐹21	𝑁𝑜𝑟𝑚𝛾𝐹21	ADV
cana-5829	301	9	(	(	PUNCT
cana-5829	301	10	𝜇21	𝜇21	VERB
cana-5829	301	11	+	+	CCONJ
cana-5829	301	12	𝑖𝜃21	𝑖𝜃21	PROPN
cana-5829	301	13	)	)	PUNCT
cana-5829	301	14	)	)	PUNCT
cana-5829	301	15	(	(	PUNCT
cana-5829	301	16	𝑁𝑜𝑟𝑚𝛿𝐹22	𝑁𝑜𝑟𝑚𝛿𝐹22	X
cana-5829	301	17	(	(	PUNCT
cana-5829	301	18	𝑥22	𝑥22	NOUN
cana-5829	301	19	+	+	X
cana-5829	301	20	𝑖𝑦22	𝑖𝑦22	PROPN
cana-5829	301	21	)	)	PUNCT
cana-5829	301	22	𝑁𝑜𝑟𝑚𝛾𝐹22	𝑁𝑜𝑟𝑚𝛾𝐹22	NOUN
cana-5829	301	23	(	(	PUNCT
cana-5829	301	24	𝜇22	𝜇22	NOUN
cana-5829	301	25	+	+	CCONJ
cana-5829	301	26	𝑖𝜃22	𝑖𝜃22	PROPN
cana-5829	301	27	)	)	PUNCT
cana-5829	301	28	)	)	PUNCT
cana-5829	301	29	)	)	PUNCT
cana-5829	301	30	are	be	AUX
cana-5829	301	31	two	two	NUM
cana-5829	301	32	normalization	normalization	NOUN
cana-5829	301	33	intuitionistic	intuitionistic	ADJ
cana-5829	301	34	fuzzy	fuzzy	ADJ
cana-5829	301	35	matrices	matrix	NOUN
cana-5829	301	36	.	.	PUNCT
cana-5829	302	1	now	now	ADV
cana-5829	302	2	applying	apply	VERB
cana-5829	302	3	both	both	DET
cana-5829	302	4	side	side	NOUN
cana-5829	302	5	on	on	ADP
cana-5829	302	6	intersection	intersection	NOUN
cana-5829	302	7	,	,	PUNCT
cana-5829	302	8	we	we	PRON
cana-5829	302	9	have	have	AUX
cana-5829	302	10	norm	norm	VERB
cana-5829	302	11	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	302	12			PUNCT
cana-5829	302	13	𝑁𝑜𝑟𝑚	𝑁𝑜𝑟𝑚	PROPN
cana-5829	302	14	𝐵𝐹	𝐵𝐹	NOUN
cana-5829	302	15	=	=	SYM
cana-5829	302	16	(	(	PUNCT
cana-5829	302	17	(	(	PUNCT
cana-5829	302	18	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	302	19	(	(	PUNCT
cana-5829	302	20	𝛼11	𝛼11	NOUN
cana-5829	302	21	+	+	PROPN
cana-5829	302	22	𝑖𝛽11	𝑖𝛽11	PROPN
cana-5829	302	23	)	)	PUNCT
cana-5829	302	24	𝑁𝑜𝑟𝑚µ𝐸11	𝑁𝑜𝑟𝑚µ𝐸11	NOUN
cana-5829	302	25	(	(	PUNCT
cana-5829	302	26	𝛾11	𝛾11	VERB
cana-5829	302	27	+	+	CCONJ
cana-5829	303	1	𝑖𝛿11	𝑖𝛿11	PROPN
cana-5829	303	2	)	)	PUNCT
cana-5829	303	3	)	)	PUNCT
cana-5829	303	4	(	(	PUNCT
cana-5829	303	5	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	NOUN
cana-5829	303	6	(	(	PUNCT
cana-5829	303	7	𝛼12	𝛼12	NOUN
cana-5829	303	8	+	+	CCONJ
cana-5829	303	9	𝑖𝛽12	𝑖𝛽12	PROPN
cana-5829	303	10	)	)	PUNCT
cana-5829	303	11	𝑁𝑜𝑟𝑚µ𝐸12	𝑁𝑜𝑟𝑚µ𝐸12	NOUN
cana-5829	303	12	(	(	PUNCT
cana-5829	303	13	𝛾12	𝛾12	VERB
cana-5829	303	14	+	+	CCONJ
cana-5829	303	15	𝑖𝛿12	𝑖𝛿12	PROPN
cana-5829	303	16	)	)	PUNCT
cana-5829	303	17	)	)	PUNCT
cana-5829	304	1	(	(	PUNCT
cana-5829	304	2	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	X
cana-5829	304	3	(	(	PUNCT
cana-5829	304	4	𝛼21	𝛼21	NOUN
cana-5829	304	5	+	+	X
cana-5829	304	6	𝑖𝛽21	𝑖𝛽21	PROPN
cana-5829	304	7	)	)	PUNCT
cana-5829	304	8	𝑁𝑜𝑟𝑚µ𝐸21	𝑁𝑜𝑟𝑚µ𝐸21	NOUN
cana-5829	304	9	(	(	PUNCT
cana-5829	304	10	𝛾21	𝛾21	NOUN
cana-5829	304	11	+	+	CCONJ
cana-5829	305	1	𝑖𝛿21	𝑖𝛿21	PROPN
cana-5829	305	2	)	)	PUNCT
cana-5829	305	3	)	)	PUNCT
cana-5829	306	1	(	(	PUNCT
cana-5829	306	2	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	X
cana-5829	306	3	(	(	PUNCT
cana-5829	306	4	𝛼22	𝛼22	NOUN
cana-5829	306	5	+	+	CCONJ
cana-5829	306	6	𝑖𝛽22	𝑖𝛽22	PROPN
cana-5829	306	7	)	)	PUNCT
cana-5829	306	8	𝑁𝑜𝑟𝑚µ𝐸22	𝑁𝑜𝑟𝑚µ𝐸22	NOUN
cana-5829	306	9	(	(	PUNCT
cana-5829	306	10	𝛾22	𝛾22	PROPN
cana-5829	306	11	+	+	PROPN
cana-5829	306	12	𝑖𝛿22	𝑖𝛿22	PROPN
cana-5829	306	13	)	)	PUNCT
cana-5829	306	14	)	)	PUNCT
cana-5829	306	15	)	)	PUNCT
cana-5829	306	16	∩	∩	NOUN
cana-5829	306	17	(	(	PUNCT
cana-5829	306	18	(	(	PUNCT
cana-5829	306	19	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	306	20	(	(	PUNCT
cana-5829	306	21	𝑥11	𝑥11	ADV
cana-5829	306	22	+	+	CCONJ
cana-5829	306	23	𝑖𝑦11	𝑖𝑦11	NOUN
cana-5829	306	24	)	)	PUNCT
cana-5829	306	25	𝑁𝑜𝑟𝑚𝛾𝐹11	𝑁𝑜𝑟𝑚𝛾𝐹11	X
cana-5829	306	26	(	(	PUNCT
cana-5829	306	27	𝜇11	𝜇11	PROPN
cana-5829	306	28	+	+	PROPN
cana-5829	306	29	𝑖𝜃11	𝑖𝜃11	PROPN
cana-5829	306	30	)	)	PUNCT
cana-5829	306	31	)	)	PUNCT
cana-5829	306	32	(	(	PUNCT
cana-5829	306	33	𝑁𝑜𝑟𝑚𝛿𝐹12	𝑁𝑜𝑟𝑚𝛿𝐹12	X
cana-5829	306	34	(	(	PUNCT
cana-5829	306	35	𝑥12	𝑥12	VERB
cana-5829	306	36	+	+	CCONJ
cana-5829	306	37	𝑖𝑦12	𝑖𝑦12	PROPN
cana-5829	306	38	)	)	PUNCT
cana-5829	306	39	𝑁𝑜𝑟𝑚𝛾𝐹12	𝑁𝑜𝑟𝑚𝛾𝐹12	NOUN
cana-5829	306	40	(	(	PUNCT
cana-5829	306	41	𝜇12	𝜇12	NOUN
cana-5829	306	42	+	+	CCONJ
cana-5829	306	43	𝑖𝜃12	𝑖𝜃12	PROPN
cana-5829	306	44	)	)	PUNCT
cana-5829	306	45	)	)	PUNCT
cana-5829	306	46	(	(	PUNCT
cana-5829	306	47	𝑁𝑜𝑟𝑚𝛿𝐹21	𝑁𝑜𝑟𝑚𝛿𝐹21	X
cana-5829	306	48	(	(	PUNCT
cana-5829	306	49	𝑥21	𝑥21	PROPN
cana-5829	306	50	+	+	CCONJ
cana-5829	306	51	𝑖𝑦21	𝑖𝑦21	PROPN
cana-5829	306	52	)	)	PUNCT
cana-5829	306	53	𝑁𝑜𝑟𝑚𝛾𝐹21	𝑁𝑜𝑟𝑚𝛾𝐹21	ADV
cana-5829	306	54	(	(	PUNCT
cana-5829	306	55	𝜇21	𝜇21	VERB
cana-5829	306	56	+	+	CCONJ
cana-5829	306	57	𝑖𝜃21	𝑖𝜃21	PROPN
cana-5829	306	58	)	)	PUNCT
cana-5829	306	59	)	)	PUNCT
cana-5829	306	60	(	(	PUNCT
cana-5829	306	61	𝑁𝑜𝑟𝑚𝛿𝐹22	𝑁𝑜𝑟𝑚𝛿𝐹22	X
cana-5829	306	62	(	(	PUNCT
cana-5829	306	63	𝑥22	𝑥22	NOUN
cana-5829	306	64	+	+	X
cana-5829	306	65	𝑖𝑦22	𝑖𝑦22	PROPN
cana-5829	306	66	)	)	PUNCT
cana-5829	306	67	𝑁𝑜𝑟𝑚𝛾𝐹22	𝑁𝑜𝑟𝑚𝛾𝐹22	NOUN
cana-5829	306	68	(	(	PUNCT
cana-5829	306	69	𝜇22	𝜇22	NOUN
cana-5829	306	70	+	+	CCONJ
cana-5829	306	71	𝑖𝜃22	𝑖𝜃22	PROPN
cana-5829	306	72	)	)	PUNCT
cana-5829	306	73	)	)	PUNCT
cana-5829	306	74	)	)	PUNCT
cana-5829	307	1	communications	communication	NOUN
cana-5829	307	2	on	on	ADP
cana-5829	307	3	applied	apply	VERB
cana-5829	307	4	nonlinear	nonlinear	ADJ
cana-5829	307	5	analysis	analysis	NOUN
cana-5829	307	6	issn	issn	NOUN
cana-5829	307	7	:	:	PUNCT
cana-5829	307	8	1074	1074	NUM
cana-5829	307	9	-	-	PUNCT
cana-5829	307	10	133x	133x	NUM
cana-5829	307	11	vol	vol	VERB
cana-5829	307	12	32	32	NUM
cana-5829	307	13	no	no	NOUN
cana-5829	307	14	.	.	PUNCT
cana-5829	308	1	10s	10	NOUN
cana-5829	308	2	(	(	PUNCT
cana-5829	308	3	2025	2025	NUM
cana-5829	308	4	)	)	PUNCT
cana-5829	308	5	2936	2936	NUM
cana-5829	308	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5829	308	7	calculate	calculate	NOUN
cana-5829	308	8	,	,	PUNCT
cana-5829	308	9	𝑋11	𝑋11	PROPN
cana-5829	308	10	,	,	PUNCT
cana-5829	308	11	𝑋12	𝑋12	PROPN
cana-5829	308	12	,	,	PUNCT
cana-5829	308	13	𝑋21and	𝑋21and	PROPN
cana-5829	308	14	𝑋22	𝑋22	PROPN
cana-5829	308	15	,	,	PUNCT
cana-5829	308	16	we	we	PRON
cana-5829	308	17	have	have	VERB
cana-5829	308	18	x11	x11	PROPN
cana-5829	308	19	=(	=(	NOUN
cana-5829	308	20	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	308	21	(	(	PUNCT
cana-5829	308	22	𝛼11	𝛼11	NOUN
cana-5829	308	23	+	+	PROPN
cana-5829	308	24	𝑖𝛽11	𝑖𝛽11	PROPN
cana-5829	308	25	)	)	PUNCT
cana-5829	308	26	𝑁𝑜𝑟𝑚µ𝐸11	𝑁𝑜𝑟𝑚µ𝐸11	NOUN
cana-5829	308	27	(	(	PUNCT
cana-5829	308	28	𝛾11	𝛾11	VERB
cana-5829	308	29	+	+	CCONJ
cana-5829	308	30	𝑖𝛿11	𝑖𝛿11	PROPN
cana-5829	308	31	)	)	PUNCT
cana-5829	308	32	)	)	PUNCT
cana-5829	308	33	(𝑁𝑜𝑟𝑚𝛿𝐹11	(𝑁𝑜𝑟𝑚𝛿𝐹11	ADJ
cana-5829	308	34	(	(	PUNCT
cana-5829	308	35	𝑥11	𝑥11	ADV
cana-5829	308	36	+	+	CCONJ
cana-5829	308	37	𝑖𝑦11	𝑖𝑦11	NOUN
cana-5829	308	38	)	)	PUNCT
cana-5829	308	39	𝑁𝑜𝑟𝑚𝛾𝐹11	𝑁𝑜𝑟𝑚𝛾𝐹11	X
cana-5829	308	40	(	(	PUNCT
cana-5829	308	41	𝜇11	𝜇11	PROPN
cana-5829	308	42	+	+	PROPN
cana-5829	308	43	𝑖𝜃11	𝑖𝜃11	PROPN
cana-5829	308	44	)	)	PUNCT
cana-5829	308	45	)	)	PUNCT
cana-5829	308	46	x12	x12	NUM
cana-5829	308	47	=(	=(	NOUN
cana-5829	308	48	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	NOUN
cana-5829	308	49	(	(	PUNCT
cana-5829	308	50	𝛼12	𝛼12	NOUN
cana-5829	308	51	+	+	CCONJ
cana-5829	308	52	𝑖𝛽12	𝑖𝛽12	PROPN
cana-5829	308	53	)	)	PUNCT
cana-5829	308	54	𝑁𝑜𝑟𝑚µ𝐸12	𝑁𝑜𝑟𝑚µ𝐸12	NOUN
cana-5829	308	55	(	(	PUNCT
cana-5829	308	56	𝛾12	𝛾12	VERB
cana-5829	308	57	+	+	CCONJ
cana-5829	308	58	𝑖𝛿12	𝑖𝛿12	PROPN
cana-5829	308	59	)	)	PUNCT
cana-5829	308	60	)	)	PUNCT
cana-5829	309	1			NOUN
cana-5829	309	2	(	(	PUNCT
cana-5829	309	3	𝑁𝑜𝑟𝑚𝛿𝐹12	𝑁𝑜𝑟𝑚𝛿𝐹12	X
cana-5829	309	4	(	(	PUNCT
cana-5829	309	5	𝑥12	𝑥12	VERB
cana-5829	309	6	+	+	CCONJ
cana-5829	309	7	𝑖𝑦12	𝑖𝑦12	PROPN
cana-5829	309	8	)	)	PUNCT
cana-5829	309	9	𝑁𝑜𝑟𝑚𝛾𝐹12	𝑁𝑜𝑟𝑚𝛾𝐹12	NOUN
cana-5829	310	1	(	(	PUNCT
cana-5829	310	2	𝜇12	𝜇12	NOUN
cana-5829	310	3	+	+	CCONJ
cana-5829	310	4	𝑖𝜃12	𝑖𝜃12	PROPN
cana-5829	310	5	)	)	PUNCT
cana-5829	310	6	)	)	PUNCT
cana-5829	311	1	x21	x21	NUM
cana-5829	311	2	=(	=(	NOUN
cana-5829	311	3	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	PROPN
cana-5829	311	4	(	(	PUNCT
cana-5829	311	5	𝛼21	𝛼21	NOUN
cana-5829	311	6	+	+	X
cana-5829	311	7	𝑖𝛽21	𝑖𝛽21	PROPN
cana-5829	311	8	)	)	PUNCT
cana-5829	311	9	𝑁𝑜𝑟𝑚µ𝐸21	𝑁𝑜𝑟𝑚µ𝐸21	NOUN
cana-5829	311	10	(	(	PUNCT
cana-5829	311	11	𝛾21	𝛾21	NOUN
cana-5829	311	12	+	+	CCONJ
cana-5829	312	1	𝑖𝛿21	𝑖𝛿21	PROPN
cana-5829	312	2	)	)	PUNCT
cana-5829	312	3	)	)	PUNCT
cana-5829	313	1			NOUN
cana-5829	313	2	(	(	PUNCT
cana-5829	313	3	𝑁𝑜𝑟𝑚𝛿𝐹21	𝑁𝑜𝑟𝑚𝛿𝐹21	X
cana-5829	313	4	(	(	PUNCT
cana-5829	313	5	𝑥21	𝑥21	PROPN
cana-5829	313	6	+	+	CCONJ
cana-5829	313	7	𝑖𝑦21	𝑖𝑦21	PROPN
cana-5829	313	8	)	)	PUNCT
cana-5829	313	9	𝑁𝑜𝑟𝑚𝛾𝐹21	𝑁𝑜𝑟𝑚𝛾𝐹21	ADV
cana-5829	313	10	(	(	PUNCT
cana-5829	313	11	𝜇21	𝜇21	VERB
cana-5829	313	12	+	+	CCONJ
cana-5829	313	13	𝑖𝜃21	𝑖𝜃21	PROPN
cana-5829	313	14	)	)	PUNCT
cana-5829	313	15	)	)	PUNCT
cana-5829	314	1	x22	x22	NUM
cana-5829	314	2	=(	=(	NOUN
cana-5829	314	3	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	PROPN
cana-5829	314	4	(	(	PUNCT
cana-5829	314	5	𝛼22	𝛼22	NOUN
cana-5829	314	6	+	+	CCONJ
cana-5829	314	7	𝑖𝛽22	𝑖𝛽22	PROPN
cana-5829	314	8	)	)	PUNCT
cana-5829	314	9	𝑁𝑜𝑟𝑚µ𝐸22	𝑁𝑜𝑟𝑚µ𝐸22	NOUN
cana-5829	314	10	(	(	PUNCT
cana-5829	314	11	𝛾22	𝛾22	PROPN
cana-5829	314	12	+	+	PROPN
cana-5829	314	13	𝑖𝛿22	𝑖𝛿22	PROPN
cana-5829	314	14	)	)	PUNCT
cana-5829	314	15	)	)	PUNCT
cana-5829	314	16			NOUN
cana-5829	314	17	(	(	PUNCT
cana-5829	314	18	𝑁𝑜𝑟𝑚𝛿𝐹22	𝑁𝑜𝑟𝑚𝛿𝐹22	X
cana-5829	314	19	(	(	PUNCT
cana-5829	314	20	𝑥22	𝑥22	NOUN
cana-5829	314	21	+	+	X
cana-5829	314	22	𝑖𝑦22	𝑖𝑦22	PROPN
cana-5829	314	23	)	)	PUNCT
cana-5829	314	24	𝑁𝑜𝑟𝑚𝛾𝐹22	𝑁𝑜𝑟𝑚𝛾𝐹22	NOUN
cana-5829	314	25	(	(	PUNCT
cana-5829	314	26	𝜇22	𝜇22	NOUN
cana-5829	314	27	+	+	CCONJ
cana-5829	314	28	𝑖𝜃22	𝑖𝜃22	PROPN
cana-5829	314	29	)	)	PUNCT
cana-5829	314	30	)	)	PUNCT
cana-5829	314	31	applying	apply	VERB
cana-5829	314	32	formula	formula	NOUN
cana-5829	314	33	aebf	aebf	ADP
cana-5829	314	34	=	=	SYM
cana-5829	314	35	{	{	PUNCT
cana-5829	314	36	(	(	PUNCT
cana-5829	314	37	x	x	NOUN
cana-5829	314	38	,	,	PUNCT
cana-5829	314	39	y	y	PROPN
cana-5829	314	40	)	)	PUNCT
cana-5829	314	41	,	,	PUNCT
cana-5829	314	42	min	min	PROPN
cana-5829	314	43	(	(	PUNCT
cana-5829	314	44	μa(x	μa(x	NOUN
cana-5829	314	45	)	)	PUNCT
cana-5829	314	46	,	,	PUNCT
cana-5829	314	47	μb(y	μb(y	NUM
cana-5829	314	48	)	)	PUNCT
cana-5829	314	49	)	)	PUNCT
cana-5829	314	50	,	,	PUNCT
cana-5829	314	51	max	max	PROPN
cana-5829	314	52	(	(	PUNCT
cana-5829	314	53	ϑa(x	ϑa(x	NOUN
cana-5829	314	54	)	)	PUNCT
cana-5829	314	55	,	,	PUNCT
cana-5829	314	56	ϑb(x	ϑb(x	NUM
cana-5829	314	57	)	)	PUNCT
cana-5829	314	58	):	):	PUNCT
cana-5829	314	59	xe	xe	PROPN
cana-5829	314	60	,	,	PUNCT
cana-5829	314	61	yf	yf	NUM
cana-5829	314	62	}	}	PUNCT
cana-5829	314	63	x11	x11	NOUN
cana-5829	315	1	=	=	NOUN
cana-5829	315	2	{	{	PUNCT
cana-5829	315	3	min	min	NOUN
cana-5829	315	4	(	(	PUNCT
cana-5829	315	5	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	315	6	(	(	PUNCT
cana-5829	315	7	𝛼11	𝛼11	NOUN
cana-5829	315	8	+	+	PROPN
cana-5829	315	9	𝑖𝛽11	𝑖𝛽11	PROPN
cana-5829	315	10	)	)	PUNCT
cana-5829	315	11	,	,	PUNCT
cana-5829	315	12	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	315	13	(	(	PUNCT
cana-5829	315	14	𝑥11	𝑥11	ADV
cana-5829	315	15	+	+	CCONJ
cana-5829	315	16	𝑖𝑦11	𝑖𝑦11	PROPN
cana-5829	315	17	)	)	PUNCT
cana-5829	315	18	,	,	PUNCT
cana-5829	315	19	max	max	PROPN
cana-5829	315	20	(	(	PUNCT
cana-5829	315	21	normµe11	normµe11	NOUN
cana-5829	315	22	(	(	PUNCT
cana-5829	315	23	𝛾11	𝛾11	VERB
cana-5829	315	24	+	+	CCONJ
cana-5829	315	25	𝑖𝛿11	𝑖𝛿11	PROPN
cana-5829	315	26	)	)	PUNCT
cana-5829	315	27	,	,	PUNCT
cana-5829	315	28	normγe11	normγe11	NOUN
cana-5829	315	29	(	(	PUNCT
cana-5829	315	30	𝜇11	𝜇11	PROPN
cana-5829	315	31	+	+	PROPN
cana-5829	315	32	𝑖𝜃11	𝑖𝜃11	PROPN
cana-5829	315	33	)	)	PUNCT
cana-5829	315	34	}	}	PUNCT
cana-5829	315	35	where	where	SCONJ
cana-5829	315	36	∣μ11∣=	∣μ11∣=	NOUN
cana-5829	315	37	(	(	PUNCT
cana-5829	315	38	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	315	39	(	(	PUNCT
cana-5829	315	40	𝛼11))2	𝛼11))2	PROPN
cana-5829	315	41	+	+	CCONJ
cana-5829	315	42	(	(	PUNCT
cana-5829	315	43	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	315	44	(	(	PUNCT
cana-5829	315	45	𝛽11))2	𝛽11))2	X
cana-5829	315	46	<	<	X
cana-5829	315	47	1	1	NUM
cana-5829	315	48	,	,	PUNCT
cana-5829	315	49	∣ν11∣=	∣ν11∣=	PROPN
cana-5829	315	50	(	(	PUNCT
cana-5829	315	51	normµe11	normµe11	PROPN
cana-5829	315	52	(	(	PUNCT
cana-5829	315	53	𝛾11))2	𝛾11))2	X
cana-5829	315	54	+	+	CCONJ
cana-5829	315	55	(	(	PUNCT
cana-5829	315	56	normγe11	normγe11	NOUN
cana-5829	315	57	(	(	PUNCT
cana-5829	315	58	𝛿11	𝛿11	NOUN
cana-5829	315	59	)	)	PUNCT
cana-5829	315	60	)	)	PUNCT
cana-5829	315	61	2	2	NUM
cana-5829	315	62	<	<	SYM
cana-5829	315	63	1	1	NUM
cana-5829	315	64	,	,	PUNCT
cana-5829	315	65	∣μ11∣+∣ν11∣	∣μ11∣+∣ν11∣	VERB
cana-5829	315	66	≤	≤	NUM
cana-5829	315	67	1	1	NUM
cana-5829	315	68	.	.	NUM
cana-5829	315	69	x12	x12	NUM
cana-5829	316	1	=	=	SYM
cana-5829	316	2	{	{	PUNCT
cana-5829	316	3	min	min	PROPN
cana-5829	316	4	(	(	PUNCT
cana-5829	316	5	normϑe12	normϑe12	PROPN
cana-5829	316	6	(	(	PUNCT
cana-5829	316	7	𝛼12	𝛼12	NUM
cana-5829	316	8	+	+	CCONJ
cana-5829	316	9	𝑖𝛽12	𝑖𝛽12	PROPN
cana-5829	316	10	)	)	PUNCT
cana-5829	316	11	,	,	PUNCT
cana-5829	316	12	normδf12	normδf12	NOUN
cana-5829	316	13	(	(	PUNCT
cana-5829	316	14	𝑥12	𝑥12	VERB
cana-5829	316	15	+	+	CCONJ
cana-5829	316	16	𝑖𝑦12	𝑖𝑦12	PROPN
cana-5829	316	17	)	)	PUNCT
cana-5829	316	18	,	,	PUNCT
cana-5829	316	19	min	min	PROPN
cana-5829	316	20	(	(	PUNCT
cana-5829	316	21	normµe12	normµe12	NOUN
cana-5829	316	22	(	(	PUNCT
cana-5829	316	23	𝛾12	𝛾12	VERB
cana-5829	316	24	+	+	CCONJ
cana-5829	316	25	𝑖𝛿12	𝑖𝛿12	PROPN
cana-5829	316	26	)	)	PUNCT
cana-5829	316	27	,	,	PUNCT
cana-5829	316	28	normγe12	normγe12	NOUN
cana-5829	316	29	(	(	PUNCT
cana-5829	316	30	𝜇12	𝜇12	NOUN
cana-5829	316	31	+	+	X
cana-5829	316	32	𝑖𝜃12	𝑖𝜃12	PROPN
cana-5829	316	33	)	)	PUNCT
cana-5829	316	34	}	}	PUNCT
cana-5829	316	35	where	where	SCONJ
cana-5829	316	36	∣μ12∣=	∣μ12∣=	X
cana-5829	316	37	(	(	PUNCT
cana-5829	316	38	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	NOUN
cana-5829	316	39	(	(	PUNCT
cana-5829	316	40	𝛼12))2	𝛼12))2	X
cana-5829	316	41	+	+	CCONJ
cana-5829	316	42	(	(	PUNCT
cana-5829	316	43	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	NOUN
cana-5829	316	44	(	(	PUNCT
cana-5829	316	45	𝛽12))2	𝛽12))2	X
cana-5829	316	46	<	<	X
cana-5829	316	47	1	1	NUM
cana-5829	316	48	,	,	PUNCT
cana-5829	316	49	∣ν11∣=	∣ν11∣=	PROPN
cana-5829	316	50	(	(	PUNCT
cana-5829	316	51	normµe12	normµe12	VERB
cana-5829	316	52	(	(	PUNCT
cana-5829	316	53	𝛾12))2	𝛾12))2	X
cana-5829	316	54	+	+	CCONJ
cana-5829	316	55	(	(	PUNCT
cana-5829	316	56	normγe12	normγe12	ADJ
cana-5829	316	57	(	(	PUNCT
cana-5829	316	58	𝛿12	𝛿12	NOUN
cana-5829	316	59	)	)	PUNCT
cana-5829	316	60	)	)	PUNCT
cana-5829	316	61	2	2	NUM
cana-5829	316	62	<	<	X
cana-5829	316	63	1	1	NUM
cana-5829	316	64	,	,	PUNCT
cana-5829	316	65	∣μ12∣+∣ν12∣	∣μ12∣+∣ν12∣	ADJ
cana-5829	316	66	≤	≤	NUM
cana-5829	316	67	1	1	NUM
cana-5829	316	68	.	.	PUNCT
cana-5829	317	1	x21	x21	NUM
cana-5829	318	1	=	=	SYM
cana-5829	318	2	{	{	PUNCT
cana-5829	318	3	max	max	PROPN
cana-5829	318	4	(	(	PUNCT
cana-5829	318	5	normϑe21	normϑe21	PROPN
cana-5829	318	6	(	(	PUNCT
cana-5829	318	7	𝛼21	𝛼21	NOUN
cana-5829	318	8	+	+	X
cana-5829	318	9	𝑖𝛽21	𝑖𝛽21	PROPN
cana-5829	318	10	)	)	PUNCT
cana-5829	318	11	,	,	PUNCT
cana-5829	318	12	normδf21	normδf21	NOUN
cana-5829	318	13	(	(	PUNCT
cana-5829	318	14	𝑥21	𝑥21	NOUN
cana-5829	318	15	+	+	CCONJ
cana-5829	318	16	𝑖𝑦21	𝑖𝑦21	PROPN
cana-5829	318	17	)	)	PUNCT
cana-5829	318	18	,	,	PUNCT
cana-5829	318	19	min	min	PROPN
cana-5829	318	20	(	(	PUNCT
cana-5829	318	21	normµe21	normµe21	X
cana-5829	318	22	(	(	PUNCT
cana-5829	318	23	𝛾21	𝛾21	NOUN
cana-5829	318	24	+	+	CCONJ
cana-5829	318	25	𝑖𝛿21	𝑖𝛿21	PROPN
cana-5829	318	26	)	)	PUNCT
cana-5829	318	27	,	,	PUNCT
cana-5829	318	28	normγe21	normγe21	ADV
cana-5829	318	29	(	(	PUNCT
cana-5829	318	30	𝜇21	𝜇21	VERB
cana-5829	318	31	+	+	CCONJ
cana-5829	318	32	𝑖𝜃21	𝑖𝜃21	PROPN
cana-5829	318	33	)	)	PUNCT
cana-5829	318	34	}	}	PUNCT
cana-5829	318	35	where	where	SCONJ
cana-5829	318	36	∣μ21∣=	∣μ21∣=	X
cana-5829	318	37	(	(	PUNCT
cana-5829	318	38	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	X
cana-5829	318	39	(	(	PUNCT
cana-5829	318	40	𝛼21))2	𝛼21))2	X
cana-5829	318	41	+	+	CCONJ
cana-5829	318	42	(	(	PUNCT
cana-5829	318	43	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	X
cana-5829	318	44	(	(	PUNCT
cana-5829	318	45	𝛽21))2	𝛽21))2	X
cana-5829	318	46	<	<	X
cana-5829	318	47	1	1	NUM
cana-5829	318	48	,	,	PUNCT
cana-5829	318	49	∣ν21∣=	∣ν21∣=	PROPN
cana-5829	318	50	(	(	PUNCT
cana-5829	318	51	normµe21	normµe21	X
cana-5829	318	52	(	(	PUNCT
cana-5829	318	53	𝛾21))2	𝛾21))2	X
cana-5829	319	1	+	+	CCONJ
cana-5829	319	2	(	(	PUNCT
cana-5829	319	3	normγe21	normγe21	INTJ
cana-5829	319	4	(	(	PUNCT
cana-5829	319	5	𝛿21	𝛿21	PROPN
cana-5829	319	6	)	)	PUNCT
cana-5829	319	7	)	)	PUNCT
cana-5829	319	8	2	2	NUM
cana-5829	319	9	<	<	SYM
cana-5829	319	10	1	1	NUM
cana-5829	319	11	,	,	PUNCT
cana-5829	319	12	∣μ21∣+∣ν21∣	∣μ21∣+∣ν21∣	VERB
cana-5829	319	13	≤	≤	NUM
cana-5829	319	14	1	1	NUM
cana-5829	319	15	.	.	PUNCT
cana-5829	319	16	x22	x22	NOUN
cana-5829	320	1	=	=	SYM
cana-5829	320	2	{	{	PUNCT
cana-5829	320	3	max	max	PROPN
cana-5829	320	4	(	(	PUNCT
cana-5829	320	5	normϑe22	normϑe22	NOUN
cana-5829	320	6	(	(	PUNCT
cana-5829	320	7	𝛼22	𝛼22	NOUN
cana-5829	320	8	,	,	PUNCT
cana-5829	320	9	𝑥22	𝑥22	NOUN
cana-5829	320	10	)	)	PUNCT
cana-5829	320	11	+	+	CCONJ
cana-5829	320	12	𝑖𝛽22	𝑖𝛽22	PROPN
cana-5829	320	13	)	)	PUNCT
cana-5829	320	14	,	,	PUNCT
cana-5829	320	15	inormδf22	inormδf22	NOUN
cana-5829	320	16	(	(	PUNCT
cana-5829	320	17	+	+	PROPN
cana-5829	320	18	𝑖𝑦22	𝑖𝑦22	PROPN
cana-5829	320	19	)	)	PUNCT
cana-5829	320	20	,	,	PUNCT
cana-5829	320	21	min	min	NOUN
cana-5829	320	22	(	(	PUNCT
cana-5829	320	23	normµe22	normµe22	X
cana-5829	320	24	(	(	PUNCT
cana-5829	320	25	𝛾22	𝛾22	PROPN
cana-5829	320	26	+	+	PROPN
cana-5829	320	27	𝑖𝛿22	𝑖𝛿22	PROPN
cana-5829	320	28	)	)	PUNCT
cana-5829	320	29	,	,	PUNCT
cana-5829	320	30	normγe22	normγe22	NOUN
cana-5829	320	31	(	(	PUNCT
cana-5829	320	32	𝜇22	𝜇22	NOUN
cana-5829	320	33	+	+	CCONJ
cana-5829	320	34	𝑖𝜃22	𝑖𝜃22	PROPN
cana-5829	320	35	)	)	PUNCT
cana-5829	320	36	}	}	PUNCT
cana-5829	320	37	where	where	SCONJ
cana-5829	320	38	∣μ22∣=	∣μ22∣=	PROPN
cana-5829	320	39	(	(	PUNCT
cana-5829	320	40	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	PROPN
cana-5829	320	41	(	(	PUNCT
cana-5829	320	42	𝛼22))2	𝛼22))2	PUNCT
cana-5829	320	43	+	+	CCONJ
cana-5829	320	44	(	(	PUNCT
cana-5829	320	45	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	NUM
cana-5829	320	46	(	(	PUNCT
cana-5829	320	47	𝛽22))2	𝛽22))2	X
cana-5829	320	48	<	<	X
cana-5829	320	49	1	1	NUM
cana-5829	320	50	,	,	PUNCT
cana-5829	320	51	∣ν11∣=	∣ν11∣=	X
cana-5829	320	52	(	(	PUNCT
cana-5829	320	53	normµe22	normµe22	X
cana-5829	320	54	(	(	PUNCT
cana-5829	320	55	𝛾22))2	𝛾22))2	X
cana-5829	320	56	+	+	CCONJ
cana-5829	320	57	(	(	PUNCT
cana-5829	320	58	normγe22	normγe22	X
cana-5829	320	59	(	(	PUNCT
cana-5829	320	60	𝛿22	𝛿22	NOUN
cana-5829	320	61	)	)	PUNCT
cana-5829	320	62	)	)	PUNCT
cana-5829	320	63	2	2	NUM
cana-5829	320	64	<	<	X
cana-5829	320	65	1	1	NUM
cana-5829	320	66	,	,	PUNCT
cana-5829	320	67	∣μ22∣+∣ν22∣	∣μ22∣+∣ν22∣	ADV
cana-5829	320	68	≤	≤	NUM
cana-5829	320	69	1	1	NUM
cana-5829	320	70	.	.	PUNCT
cana-5829	320	71	x11	x11	PROPN
cana-5829	320	72	=(	=(	PROPN
cana-5829	320	73	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	320	74	(	(	PUNCT
cana-5829	320	75	min	min	NOUN
cana-5829	320	76	(	(	PUNCT
cana-5829	320	77	𝛼11	𝛼11	ADJ
cana-5829	320	78	,	,	PUNCT
cana-5829	320	79	𝑥11	𝑥11	ADV
cana-5829	320	80	)	)	PUNCT
cana-5829	320	81	+	+	CCONJ
cana-5829	320	82	𝑖	𝑖	SYM
cana-5829	320	83	min	min	NOUN
cana-5829	320	84	(	(	PUNCT
cana-5829	320	85	𝛽11	𝛽11	NOUN
cana-5829	320	86	,	,	PUNCT
cana-5829	320	87	𝑦11	𝑦11	NOUN
cana-5829	320	88	)	)	PUNCT
cana-5829	320	89	)	)	PUNCT
cana-5829	320	90	)	)	PUNCT
cana-5829	320	91	,	,	PUNCT
cana-5829	320	92	normµe11	normµe11	NOUN
cana-5829	320	93	(	(	PUNCT
cana-5829	320	94	max	max	PROPN
cana-5829	320	95	(	(	PUNCT
cana-5829	320	96	𝛾11	𝛾11	ADJ
cana-5829	320	97	,	,	PUNCT
cana-5829	320	98	𝜇11	𝜇11	ADJ
cana-5829	320	99	)	)	PUNCT
cana-5829	320	100	+	+	NUM
cana-5829	320	101	𝑖max	𝑖max	X
cana-5829	320	102	(	(	PUNCT
cana-5829	320	103	𝛿11	𝛿11	NOUN
cana-5829	320	104	,	,	PUNCT
cana-5829	320	105	𝜃11	𝜃11	NOUN
cana-5829	320	106	)	)	PUNCT
cana-5829	320	107	)	)	PUNCT
cana-5829	320	108	where	where	SCONJ
cana-5829	320	109	∣μ11∣=	∣μ11∣=	NOUN
cana-5829	320	110	(	(	PUNCT
cana-5829	320	111	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	320	112	(	(	PUNCT
cana-5829	320	113	min(𝛼11	min(𝛼11	NOUN
cana-5829	320	114	,	,	PUNCT
cana-5829	320	115	𝑥11))2	𝑥11))2	PUNCT
cana-5829	320	116	+	+	CCONJ
cana-5829	320	117	(	(	PUNCT
cana-5829	320	118	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	320	119	min(𝛽11	min(𝛽11	NOUN
cana-5829	320	120	,	,	PUNCT
cana-5829	320	121	𝑦11))2	𝑦11))2	X
cana-5829	321	1	+	+	ADJ
cana-5829	321	2	(	(	PUNCT
cana-5829	321	3	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	321	4	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
cana-5829	321	5	(	(	PUNCT
cana-5829	321	6	𝛾11	𝛾11	VERB
cana-5829	321	7	,	,	PUNCT
cana-5829	321	8	𝜇11))2	𝜇11))2	ADJ
cana-5829	321	9	+	+	ADJ
cana-5829	321	10	(	(	PUNCT
cana-5829	321	11	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	321	12	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
cana-5829	321	13	(	(	PUNCT
cana-5829	321	14	𝛾11	𝛾11	VERB
cana-5829	321	15	,	,	PUNCT
cana-5829	321	16	𝜇11))2	𝜇11))2	PRON
cana-5829	321	17	<	<	X
cana-5829	321	18	1	1	NUM
cana-5829	321	19	,	,	PUNCT
cana-5829	321	20	∣ν11∣=	∣ν11∣=	PROPN
cana-5829	321	21	(	(	PUNCT
cana-5829	321	22	normµe11	normµe11	NOUN
cana-5829	321	23	𝑚𝑎𝑥(𝛾11	𝑚𝑎𝑥(𝛾11	NUM
cana-5829	321	24	,	,	PUNCT
cana-5829	321	25	𝜇11))2	𝜇11))2	X
cana-5829	321	26	+	+	ADJ
cana-5829	321	27	(	(	PUNCT
cana-5829	321	28	𝑁𝑜𝑟𝑚𝛾𝐸11	𝑁𝑜𝑟𝑚𝛾𝐸11	NOUN
cana-5829	321	29	𝑚𝑎𝑥(𝛿11	𝑚𝑎𝑥(𝛿11	NOUN
cana-5829	321	30	,	,	PUNCT
cana-5829	321	31	𝜃11))2	𝜃11))2	PUNCT
cana-5829	321	32	<	<	X
cana-5829	321	33	1	1	NUM
cana-5829	321	34	,	,	PUNCT
cana-5829	321	35	∣μ11∣+∣ν11∣	∣μ11∣+∣ν11∣	VERB
cana-5829	321	36	≤	≤	NUM
cana-5829	321	37	1	1	NUM
cana-5829	321	38	.	.	PUNCT
cana-5829	322	1	x12	x12	NUM
cana-5829	322	2	=(	=(	NOUN
cana-5829	322	3	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	NOUN
cana-5829	322	4	(	(	PUNCT
cana-5829	322	5	min	min	NOUN
cana-5829	322	6	(	(	PUNCT
cana-5829	322	7	𝛼12	𝛼12	NUM
cana-5829	322	8	,	,	PUNCT
cana-5829	322	9	𝑥12	𝑥12	VERB
cana-5829	322	10	)	)	PUNCT
cana-5829	323	1	+	+	CCONJ
cana-5829	323	2	𝑖	𝑖	SYM
cana-5829	323	3	min	min	NOUN
cana-5829	323	4	(	(	PUNCT
cana-5829	323	5	𝛽12	𝛽12	PROPN
cana-5829	323	6	,	,	PUNCT
cana-5829	323	7	𝑦12	𝑦12	NOUN
cana-5829	323	8	)	)	PUNCT
cana-5829	323	9	)	)	PUNCT
cana-5829	323	10	,	,	PUNCT
cana-5829	323	11	normµe12	normµe12	NOUN
cana-5829	323	12	(	(	PUNCT
cana-5829	323	13	max	max	PROPN
cana-5829	323	14	(	(	PUNCT
cana-5829	323	15	𝛾12	𝛾12	PROPN
cana-5829	323	16	,	,	PUNCT
cana-5829	323	17	𝜇12	𝜇12	NOUN
cana-5829	323	18	)	)	PUNCT
cana-5829	324	1	+	+	NUM
cana-5829	324	2	𝑖max	𝑖max	ADJ
cana-5829	324	3	(	(	PUNCT
cana-5829	324	4	𝛿12	𝛿12	NOUN
cana-5829	324	5	,	,	PUNCT
cana-5829	324	6	𝜃12	𝜃12	NUM
cana-5829	324	7	)	)	PUNCT
cana-5829	324	8	)	)	PUNCT
cana-5829	324	9	communications	communication	NOUN
cana-5829	324	10	on	on	ADP
cana-5829	324	11	applied	apply	VERB
cana-5829	324	12	nonlinear	nonlinear	ADJ
cana-5829	324	13	analysis	analysis	NOUN
cana-5829	324	14	issn	issn	NOUN
cana-5829	324	15	:	:	PUNCT
cana-5829	324	16	1074	1074	NUM
cana-5829	324	17	-	-	PUNCT
cana-5829	324	18	133x	133x	NUM
cana-5829	324	19	vol	vol	VERB
cana-5829	324	20	32	32	NUM
cana-5829	324	21	no	no	NOUN
cana-5829	324	22	.	.	PUNCT
cana-5829	325	1	10s	10	NOUN
cana-5829	325	2	(	(	PUNCT
cana-5829	325	3	2025	2025	NUM
cana-5829	325	4	)	)	PUNCT
cana-5829	325	5	2937	2937	NUM
cana-5829	325	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5829	326	1	where	where	SCONJ
cana-5829	326	2	∣μ12∣=(𝑁𝑜𝑟𝑚𝜗𝐸12	∣μ12∣=(𝑁𝑜𝑟𝑚𝜗𝐸12	PROPN
cana-5829	326	3	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
cana-5829	326	4	(	(	PUNCT
cana-5829	326	5	𝛼12	𝛼12	PROPN
cana-5829	326	6	,	,	PUNCT
cana-5829	326	7	𝑥12))2	𝑥12))2	X
cana-5829	326	8	+	+	ADJ
cana-5829	326	9	(	(	PUNCT
cana-5829	326	10	𝑁𝑜𝑟𝑚𝛿𝐹12	𝑁𝑜𝑟𝑚𝛿𝐹12	ADJ
cana-5829	326	11	𝑚𝑖𝑛	𝑚𝑖𝑛	PROPN
cana-5829	326	12	(	(	PUNCT
cana-5829	326	13	𝛽12	𝛽12	PROPN
cana-5829	326	14	,	,	PUNCT
cana-5829	326	15	𝑦12))2	𝑦12))2	X
cana-5829	326	16	<	<	X
cana-5829	326	17	1	1	NUM
cana-5829	326	18	,	,	PUNCT
cana-5829	326	19	∣ν12∣=	∣ν12∣=	X
cana-5829	326	20	(	(	PUNCT
cana-5829	326	21	normµe12	normµe12	NOUN
cana-5829	326	22	𝑚𝑎𝑥(𝛾12	𝑚𝑎𝑥(𝛾12	AUX
cana-5829	326	23	,	,	PUNCT
cana-5829	326	24	𝜇12))2	𝜇12))2	X
cana-5829	326	25	+	+	ADJ
cana-5829	326	26	(	(	PUNCT
cana-5829	326	27	𝑁𝑜𝑟𝑚𝛾𝐸12	𝑁𝑜𝑟𝑚𝛾𝐸12	X
cana-5829	326	28	𝑚𝑎𝑥	𝑚𝑎𝑥	NOUN
cana-5829	326	29	(	(	PUNCT
cana-5829	326	30	(	(	PUNCT
cana-5829	326	31	𝛿12	𝛿12	NOUN
cana-5829	326	32	,	,	PUNCT
cana-5829	326	33	𝜃12))2	𝜃12))2	X
cana-5829	326	34	<	<	X
cana-5829	326	35	1	1	NUM
cana-5829	326	36	,	,	PUNCT
cana-5829	326	37	∣μ12∣+∣ν12∣	∣μ12∣+∣ν12∣	ADJ
cana-5829	326	38	≤	≤	NUM
cana-5829	326	39	1	1	NUM
cana-5829	326	40	.	.	PUNCT
cana-5829	327	1	x21	x21	NUM
cana-5829	328	1	=	=	PRON
cana-5829	328	2	{	{	PUNCT
cana-5829	328	3	(	(	PUNCT
cana-5829	328	4	normϑe21	normϑe21	ADJ
cana-5829	328	5	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
cana-5829	328	6	(	(	PUNCT
cana-5829	328	7	𝛼21	𝛼21	NOUN
cana-5829	328	8	,	,	PUNCT
cana-5829	328	9	𝑥21	𝑥21	NOUN
cana-5829	328	10	)	)	PUNCT
cana-5829	328	11	+	+	NUM
cana-5829	328	12	inormδf21	inormδf21	NOUN
cana-5829	328	13	(	(	PUNCT
cana-5829	328	14	𝛽21	𝛽21	PROPN
cana-5829	328	15	,	,	PUNCT
cana-5829	328	16	𝑦21	𝑦21	PROPN
cana-5829	328	17	)	)	PUNCT
cana-5829	328	18	,	,	PUNCT
cana-5829	328	19	max	max	PROPN
cana-5829	328	20	(	(	PUNCT
cana-5829	328	21	normµe21	normµe21	PROPN
cana-5829	328	22	(	(	PUNCT
cana-5829	328	23	𝛾21	𝛾21	ADJ
cana-5829	328	24	,	,	PUNCT
cana-5829	328	25	𝜇21	𝜇21	NOUN
cana-5829	328	26	)	)	PUNCT
cana-5829	329	1	+	+	CCONJ
cana-5829	329	2	inormγe21	inormγe21	ADV
cana-5829	329	3	(	(	PUNCT
cana-5829	329	4	𝛿21	𝛿21	NOUN
cana-5829	329	5	,	,	PUNCT
cana-5829	329	6	𝜃21	𝜃21	NOUN
cana-5829	329	7	)	)	PUNCT
cana-5829	329	8	}	}	PUNCT
cana-5829	329	9	where	where	SCONJ
cana-5829	329	10	∣μ21∣=(𝑁𝑜𝑟𝑚𝜗𝐸21	∣μ21∣=(𝑁𝑜𝑟𝑚𝜗𝐸21	NOUN
cana-5829	329	11	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
cana-5829	329	12	(	(	PUNCT
cana-5829	329	13	𝛼21	𝛼21	NOUN
cana-5829	329	14	,	,	PUNCT
cana-5829	329	15	𝑥21))2	𝑥21))2	X
cana-5829	330	1	+	+	ADJ
cana-5829	330	2	(	(	PUNCT
cana-5829	330	3	𝑁𝑜𝑟𝑚𝛿𝐹21	𝑁𝑜𝑟𝑚𝛿𝐹21	ADP
cana-5829	330	4	𝑚𝑖𝑛	𝑚𝑖𝑛	PROPN
cana-5829	330	5	(	(	PUNCT
cana-5829	330	6	𝛽21	𝛽21	PROPN
cana-5829	330	7	,	,	PUNCT
cana-5829	330	8	𝑦21))2	𝑦21))2	PROPN
cana-5829	330	9	<	<	X
cana-5829	330	10	1	1	NUM
cana-5829	330	11	,	,	PUNCT
cana-5829	330	12	∣ν21∣=	∣ν21∣=	PRON
cana-5829	330	13	(	(	PUNCT
cana-5829	330	14	normµe21	normµe21	NOUN
cana-5829	330	15	𝑚𝑎𝑥(𝛾21	𝑚𝑎𝑥(𝛾21	PROPN
cana-5829	330	16	,	,	PUNCT
cana-5829	330	17	𝜇21))2	𝜇21))2	PROPN
cana-5829	331	1	+	+	ADJ
cana-5829	331	2	(	(	PUNCT
cana-5829	331	3	𝑁𝑜𝑟𝑚𝛾𝐸21	𝑁𝑜𝑟𝑚𝛾𝐸21	X
cana-5829	331	4	𝑚𝑎𝑥	𝑚𝑎𝑥	NOUN
cana-5829	331	5	(	(	PUNCT
cana-5829	331	6	(	(	PUNCT
cana-5829	331	7	𝛿21	𝛿21	PROPN
cana-5829	331	8	,	,	PUNCT
cana-5829	331	9	𝜃21))2	𝜃21))2	X
cana-5829	331	10	<	<	X
cana-5829	331	11	1	1	NUM
cana-5829	331	12	,	,	PUNCT
cana-5829	331	13	∣μ21∣+∣ν21∣	∣μ21∣+∣ν21∣	VERB
cana-5829	331	14	≤	≤	NUM
cana-5829	331	15	1	1	NUM
cana-5829	331	16	.	.	PUNCT
cana-5829	331	17	x22	x22	NOUN
cana-5829	332	1	=	=	SYM
cana-5829	332	2	{	{	PUNCT
cana-5829	332	3	max	max	PROPN
cana-5829	332	4	(	(	PUNCT
cana-5829	332	5	normϑe22	normϑe22	NOUN
cana-5829	332	6	(	(	PUNCT
cana-5829	332	7	𝛼22	𝛼22	NOUN
cana-5829	332	8	,	,	PUNCT
cana-5829	332	9	𝑥22	𝑥22	NOUN
cana-5829	332	10	)	)	PUNCT
cana-5829	332	11	)	)	PUNCT
cana-5829	332	12	,	,	PUNCT
cana-5829	332	13	inormδf22	inormδf22	NOUN
cana-5829	332	14	𝑚𝑖𝑛	𝑚𝑖𝑛	PROPN
cana-5829	332	15	(	(	PUNCT
cana-5829	332	16	𝛽22	𝛽22	NOUN
cana-5829	332	17	,	,	PUNCT
cana-5829	332	18	𝑦22	𝑦22	NUM
cana-5829	332	19	)	)	PUNCT
cana-5829	332	20	,	,	PUNCT
cana-5829	332	21	max	max	PROPN
cana-5829	332	22	(	(	PUNCT
cana-5829	332	23	normµe22	normµe22	X
cana-5829	332	24	(	(	PUNCT
cana-5829	332	25	𝛾22	𝛾22	ADJ
cana-5829	332	26	,	,	PUNCT
cana-5829	332	27	𝜇21	𝜇21	NOUN
cana-5829	332	28	)	)	PUNCT
cana-5829	332	29	,	,	PUNCT
cana-5829	332	30	normγe22	normγe22	NOUN
cana-5829	332	31	(	(	PUNCT
cana-5829	332	32	𝛿22	𝛿22	NOUN
cana-5829	332	33	,	,	PUNCT
cana-5829	332	34	𝜃22	𝜃22	NOUN
cana-5829	332	35	)	)	PUNCT
cana-5829	332	36	}	}	PUNCT
cana-5829	332	37	where	where	SCONJ
cana-5829	332	38	∣μ22∣=(𝑁𝑜𝑟𝑚𝜗𝐸22	∣μ22∣=(𝑁𝑜𝑟𝑚𝜗𝐸22	PROPN
cana-5829	332	39	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
cana-5829	332	40	(	(	PUNCT
cana-5829	332	41	𝛼22	𝛼22	NOUN
cana-5829	332	42	,	,	PUNCT
cana-5829	332	43	𝑥22))2	𝑥22))2	VERB
cana-5829	333	1	+	+	ADV
cana-5829	333	2	(	(	PUNCT
cana-5829	333	3	𝑁𝑜𝑟𝑚𝛿𝐹22	𝑁𝑜𝑟𝑚𝛿𝐹22	ADJ
cana-5829	333	4	𝑚𝑖𝑛	𝑚𝑖𝑛	PROPN
cana-5829	333	5	(	(	PUNCT
cana-5829	333	6	𝛽22	𝛽22	VERB
cana-5829	333	7	,	,	PUNCT
cana-5829	333	8	𝑦22))2	𝑦22))2	X
cana-5829	333	9	<	<	X
cana-5829	333	10	1	1	NUM
cana-5829	333	11	,	,	PUNCT
cana-5829	333	12	∣ν21∣=	∣ν21∣=	PRON
cana-5829	333	13	(	(	PUNCT
cana-5829	333	14	normµe22	normµe22	PROPN
cana-5829	333	15	𝑚𝑎𝑥(𝛾22	𝑚𝑎𝑥(𝛾22	NUM
cana-5829	333	16	,	,	PUNCT
cana-5829	333	17	𝜇22))2	𝜇22))2	X
cana-5829	334	1	+	+	ADJ
cana-5829	334	2	(	(	PUNCT
cana-5829	334	3	𝑁𝑜𝑟𝑚𝛾𝐸22	𝑁𝑜𝑟𝑚𝛾𝐸22	X
cana-5829	334	4	𝑚𝑎𝑥	𝑚𝑎𝑥	ADJ
cana-5829	334	5	(	(	PUNCT
cana-5829	334	6	(	(	PUNCT
cana-5829	334	7	𝛿22	𝛿22	NOUN
cana-5829	334	8	,	,	PUNCT
cana-5829	334	9	𝜃22))2	𝜃22))2	PUNCT
cana-5829	334	10	<	<	X
cana-5829	334	11	1	1	NUM
cana-5829	334	12	,	,	PUNCT
cana-5829	334	13	∣μ22∣+∣ν22∣	∣μ22∣+∣ν22∣	ADV
cana-5829	334	14	≤	≤	NUM
cana-5829	334	15	1	1	NUM
cana-5829	334	16	.	.	PUNCT
cana-5829	335	1	we	we	PRON
cana-5829	335	2	have	have	AUX
cana-5829	335	3	norm	norm	VERB
cana-5829	335	4	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	335	5			PUNCT
cana-5829	335	6	𝑁𝑜𝑟𝑚	𝑁𝑜𝑟𝑚	PROPN
cana-5829	335	7	𝐵𝐹	𝐵𝐹	NOUN
cana-5829	335	8	=	=	SYM
cana-5829	336	1	(	(	PUNCT
cana-5829	336	2	𝑋11	𝑋11	PROPN
cana-5829	336	3	𝑋12	𝑋12	PROPN
cana-5829	336	4	𝑋21	𝑋21	NOUN
cana-5829	336	5	𝑋22	𝑋22	ADJ
cana-5829	336	6	)	)	PUNCT
cana-5829	336	7	is	be	AUX
cana-5829	336	8	also	also	ADV
cana-5829	336	9	normalization	normalization	NOUN
cana-5829	336	10	of	of	ADP
cana-5829	336	11	complex	complex	ADJ
cana-5829	336	12	intuitionistic	intuitionistic	ADJ
cana-5829	336	13	fuzzy	fuzzy	ADJ
cana-5829	336	14	matrix	matrix	NOUN
cana-5829	336	15	.	.	PUNCT
cana-5829	337	1	example5.2.2	example5.2.2	VERB
cana-5829	337	2	:	:	PUNCT
cana-5829	337	3	if	if	SCONJ
cana-5829	337	4	𝐴𝐸=	𝐴𝐸=	NOUN
cana-5829	337	5	(	(	PUNCT
cana-5829	337	6	(	(	PUNCT
cana-5829	337	7	0.6	0.6	NUM
cana-5829	337	8	+	+	CCONJ
cana-5829	337	9	0.2i	0.2i	ADJ
cana-5829	337	10	,	,	PUNCT
cana-5829	337	11	0.3	0.3	NUM
cana-5829	337	12	+	+	NOUN
cana-5829	337	13	0.1i)(0.4	0.1i)(0.4	X
cana-5829	338	1	+	+	CCONJ
cana-5829	338	2	0.1i	0.1i	NOUN
cana-5829	338	3	,	,	PUNCT
cana-5829	338	4	0.5	0.5	NUM
cana-5829	338	5	+	+	NUM
cana-5829	338	6	0.2i	0.2i	NUM
cana-5829	338	7	)	)	PUNCT
cana-5829	338	8	(	(	PUNCT
cana-5829	338	9	0.5	0.5	NUM
cana-5829	338	10	+	+	CCONJ
cana-5829	338	11	0.3i	0.3i	NOUN
cana-5829	338	12	,	,	PUNCT
cana-5829	338	13	0.2	0.2	NUM
cana-5829	338	14	+	+	CCONJ
cana-5829	338	15	0.1i)(0.3	0.1i)(0.3	PRON
cana-5829	338	16	+	+	CCONJ
cana-5829	338	17	0.2i	0.2i	ADJ
cana-5829	338	18	,	,	PUNCT
cana-5829	338	19	0.6	0.6	NUM
cana-5829	338	20	+	+	NUM
cana-5829	338	21	0.1i	0.1i	NOUN
cana-5829	338	22	)	)	PUNCT
cana-5829	338	23	)	)	PUNCT
cana-5829	338	24	and	and	CCONJ
cana-5829	338	25	bf	bf	NOUN
cana-5829	338	26	=	=	SYM
cana-5829	338	27	(	(	PUNCT
cana-5829	338	28	(	(	PUNCT
cana-5829	338	29	0.4	0.4	NUM
cana-5829	338	30	+	+	CCONJ
cana-5829	338	31	0.3i	0.3i	NOUN
cana-5829	338	32	,	,	PUNCT
cana-5829	338	33	0.5	0.5	NUM
cana-5829	338	34	+	+	CCONJ
cana-5829	338	35	0.1i)(0.3	0.1i)(0.3	PRON
cana-5829	338	36	+	+	CCONJ
cana-5829	338	37	0.4i	0.4i	NOUN
cana-5829	338	38	,	,	PUNCT
cana-5829	338	39	0.4	0.4	NUM
cana-5829	338	40	+	+	CCONJ
cana-5829	338	41	0.2i	0.2i	NUM
cana-5829	338	42	)	)	PUNCT
cana-5829	338	43	(	(	PUNCT
cana-5829	338	44	0.6	0.6	NUM
cana-5829	338	45	+	+	CCONJ
cana-5829	338	46	0.2i	0.2i	ADJ
cana-5829	338	47	,	,	PUNCT
cana-5829	338	48	0.2	0.2	NUM
cana-5829	338	49	+	+	CCONJ
cana-5829	338	50	0.2i)(0.5	0.2i)(0.5	X
cana-5829	339	1	+	+	CCONJ
cana-5829	339	2	0.1i	0.1i	NOUN
cana-5829	339	3	,	,	PUNCT
cana-5829	339	4	0.4	0.4	NUM
cana-5829	339	5	+	+	CCONJ
cana-5829	339	6	0.3i	0.3i	NOUN
cana-5829	339	7	)	)	PUNCT
cana-5829	339	8	)	)	PUNCT
cana-5829	339	9	are	be	AUX
cana-5829	339	10	normalization	normalization	NOUN
cana-5829	339	11	of	of	ADP
cana-5829	339	12	complex	complex	ADJ
cana-5829	339	13	intuitionistic	intuitionistic	ADJ
cana-5829	339	14	fuzzy	fuzzy	ADJ
cana-5829	339	15	matrix	matrix	NOUN
cana-5829	339	16	two	two	NUM
cana-5829	339	17	intuitionistic	intuitionistic	ADJ
cana-5829	339	18	fuzzy	fuzzy	ADJ
cana-5829	339	19	matrices	matrix	NOUN
cana-5829	339	20	over	over	ADP
cana-5829	339	21	different	different	ADJ
cana-5829	339	22	universe	universe	NOUN
cana-5829	339	23	e	e	NOUN
cana-5829	339	24	and	and	CCONJ
cana-5829	339	25	f	f	PROPN
cana-5829	339	26	then	then	ADV
cana-5829	339	27	norm	norm	VERB
cana-5829	339	28	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	339	29			PUNCT
cana-5829	339	30	𝑁𝑜𝑟𝑚	𝑁𝑜𝑟𝑚	PROPN
cana-5829	339	31	𝐵𝐹	𝐵𝐹	PROPN
cana-5829	339	32	is	be	AUX
cana-5829	339	33	also	also	ADV
cana-5829	339	34	normalization	normalization	NOUN
cana-5829	339	35	of	of	ADP
cana-5829	339	36	complex	complex	ADJ
cana-5829	339	37	intuitionistic	intuitionistic	ADJ
cana-5829	339	38	fuzzy	fuzzy	ADJ
cana-5829	339	39	matrix	matrix	NOUN
cana-5829	339	40	.	.	PUNCT
cana-5829	340	1	proof	proof	NOUN
cana-5829	340	2	:	:	PUNCT
cana-5829	340	3	given	give	VERB
cana-5829	340	4	𝑨𝑬=	𝑨𝑬=	PROPN
cana-5829	340	5	(	(	PUNCT
cana-5829	340	6	(	(	PUNCT
cana-5829	340	7	0.6	0.6	NUM
cana-5829	340	8	+	+	CCONJ
cana-5829	340	9	0.2i	0.2i	ADJ
cana-5829	340	10	,	,	PUNCT
cana-5829	340	11	0.3	0.3	NUM
cana-5829	340	12	+	+	NOUN
cana-5829	340	13	0.1i)(0.4	0.1i)(0.4	X
cana-5829	341	1	+	+	CCONJ
cana-5829	341	2	0.1i	0.1i	NOUN
cana-5829	341	3	,	,	PUNCT
cana-5829	341	4	0.5	0.5	NUM
cana-5829	341	5	+	+	NUM
cana-5829	341	6	0.2i	0.2i	NUM
cana-5829	341	7	)	)	PUNCT
cana-5829	341	8	(	(	PUNCT
cana-5829	341	9	0.5	0.5	NUM
cana-5829	341	10	+	+	CCONJ
cana-5829	341	11	0.3i	0.3i	NOUN
cana-5829	341	12	,	,	PUNCT
cana-5829	341	13	0.2	0.2	NUM
cana-5829	341	14	+	+	CCONJ
cana-5829	341	15	0.1i)(0.3	0.1i)(0.3	PRON
cana-5829	341	16	+	+	CCONJ
cana-5829	341	17	0.2i	0.2i	ADJ
cana-5829	341	18	,	,	PUNCT
cana-5829	341	19	0.6	0.6	NUM
cana-5829	341	20	+	+	NUM
cana-5829	341	21	0.1i	0.1i	NOUN
cana-5829	341	22	)	)	PUNCT
cana-5829	341	23	)	)	PUNCT
cana-5829	341	24	and	and	CCONJ
cana-5829	341	25	𝑩𝑭	𝑩𝑭	PROPN
cana-5829	341	26	=	=	SYM
cana-5829	341	27	(	(	PUNCT
cana-5829	341	28	(	(	PUNCT
cana-5829	341	29	0.4	0.4	NUM
cana-5829	341	30	+	+	CCONJ
cana-5829	341	31	0.3i	0.3i	NOUN
cana-5829	341	32	,	,	PUNCT
cana-5829	341	33	0.5	0.5	NUM
cana-5829	341	34	+	+	CCONJ
cana-5829	341	35	0.1i)(0.3	0.1i)(0.3	PRON
cana-5829	341	36	+	+	CCONJ
cana-5829	341	37	0.4i	0.4i	NOUN
cana-5829	341	38	,	,	PUNCT
cana-5829	341	39	0.4	0.4	NUM
cana-5829	341	40	+	+	CCONJ
cana-5829	341	41	0.2i	0.2i	NUM
cana-5829	341	42	)	)	PUNCT
cana-5829	341	43	(	(	PUNCT
cana-5829	341	44	0.6	0.6	NUM
cana-5829	341	45	+	+	CCONJ
cana-5829	341	46	0.2i	0.2i	ADJ
cana-5829	341	47	,	,	PUNCT
cana-5829	341	48	0.2	0.2	NUM
cana-5829	341	49	+	+	CCONJ
cana-5829	341	50	0.2i)(0.5	0.2i)(0.5	X
cana-5829	342	1	+	+	CCONJ
cana-5829	342	2	0.1i	0.1i	NOUN
cana-5829	342	3	,	,	PUNCT
cana-5829	342	4	0.4	0.4	NUM
cana-5829	342	5	+	+	CCONJ
cana-5829	342	6	0.3i	0.3i	NOUN
cana-5829	342	7	)	)	PUNCT
cana-5829	342	8	)	)	PUNCT
cana-5829	342	9	norm	norm	VERB
cana-5829	342	10	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	342	11	=	=	SYM
cana-5829	343	1	(	(	PUNCT
cana-5829	343	2	(	(	PUNCT
cana-5829	343	3	1	1	NUM
cana-5829	343	4	+	+	NUM
cana-5829	343	5	0.67𝑖	0.67𝑖	NUM
cana-5829	343	6	0.125	0.125	NUM
cana-5829	343	7	+	+	NUM
cana-5829	343	8	0𝑖	0𝑖	NOUN
cana-5829	343	9	)	)	PUNCT
cana-5829	343	10	(	(	PUNCT
cana-5829	343	11	0.67	0.67	NUM
cana-5829	343	12	+	+	CCONJ
cana-5829	343	13	0.33𝑖	0.33𝑖	NUM
cana-5829	343	14	0.30	0.30	NUM
cana-5829	343	15	+	+	CCONJ
cana-5829	343	16	0.10𝑖	0.10𝑖	NOUN
cana-5829	343	17	)	)	PUNCT
cana-5829	343	18	(	(	PUNCT
cana-5829	343	19	0.83	0.83	NUM
cana-5829	343	20	+	+	NUM
cana-5829	343	21	1𝑖	1𝑖	NOUN
cana-5829	343	22	0	0	NUM
cana-5829	344	1	+	+	NUM
cana-5829	344	2	0𝑖	0𝑖	NOUN
cana-5829	344	3	)	)	PUNCT
cana-5829	344	4	(	(	PUNCT
cana-5829	344	5	0.5	0.5	NUM
cana-5829	344	6	+	+	NUM
cana-5829	344	7	0.67𝑖	0.67𝑖	NUM
cana-5829	344	8	0.5	0.5	NUM
cana-5829	344	9	+	+	NUM
cana-5829	344	10	0𝑖	0𝑖	NOUN
cana-5829	344	11	)	)	PUNCT
cana-5829	344	12	)	)	PUNCT
cana-5829	345	1	𝑁𝑜𝑟𝑚	𝑁𝑜𝑟𝑚	NOUN
cana-5829	345	2	𝐵𝐹=	𝐵𝐹=	ADP
cana-5829	345	3	(	(	PUNCT
cana-5829	345	4	(	(	PUNCT
cana-5829	345	5	0.67	0.67	NUM
cana-5829	345	6	+	+	CCONJ
cana-5829	345	7	0.75𝑖	0.75𝑖	PROPN
cana-5829	345	8	0.375	0.375	NUM
cana-5829	345	9	+	+	NUM
cana-5829	345	10	0𝑖	0𝑖	NOUN
cana-5829	345	11	)	)	PUNCT
cana-5829	345	12	(	(	PUNCT
cana-5829	345	13	0.5	0.5	NUM
cana-5829	345	14	+	+	NUM
cana-5829	345	15	1𝑖	1𝑖	NUM
cana-5829	345	16	0.25	0.25	NUM
cana-5829	345	17	+	+	CCONJ
cana-5829	345	18	0.11𝑖	0.11𝑖	NUM
cana-5829	345	19	)	)	PUNCT
cana-5829	345	20	(	(	PUNCT
cana-5829	345	21	1	1	NUM
cana-5829	345	22	+	+	NUM
cana-5829	345	23	0.5𝑖	0.5𝑖	NOUN
cana-5829	345	24	0	0	NUM
cana-5829	346	1	+	+	CCONJ
cana-5829	346	2	0.11𝑖	0.11𝑖	NUM
cana-5829	346	3	)	)	PUNCT
cana-5829	346	4	(	(	PUNCT
cana-5829	346	5	0.83	0.83	NUM
cana-5829	346	6	+	+	NUM
cana-5829	346	7	0.25𝑖	0.25𝑖	NOUN
cana-5829	346	8	0.25	0.25	NUM
cana-5829	346	9	+	+	PUNCT
cana-5829	346	10	0.22𝑖	0.22𝑖	NUM
cana-5829	346	11	)	)	PUNCT
cana-5829	346	12	)	)	PUNCT
cana-5829	347	1	norm	norm	NOUN
cana-5829	347	2	𝐴𝐸𝑁𝑜𝑟𝑚	𝐴𝐸𝑁𝑜𝑟𝑚	PROPN
cana-5829	347	3	𝐵𝐹	𝐵𝐹	PROPN
cana-5829	347	4	=	=	SYM
cana-5829	347	5	(	(	PUNCT
cana-5829	347	6	(	(	PUNCT
cana-5829	347	7	1	1	NUM
cana-5829	347	8	+	+	NUM
cana-5829	347	9	0.67𝑖	0.67𝑖	NUM
cana-5829	347	10	0.125	0.125	NUM
cana-5829	348	1	+	+	NUM
cana-5829	348	2	0𝑖	0𝑖	NOUN
cana-5829	348	3	)	)	PUNCT
cana-5829	348	4	(	(	PUNCT
cana-5829	348	5	0.67	0.67	NUM
cana-5829	348	6	+	+	CCONJ
cana-5829	348	7	0.33𝑖	0.33𝑖	NUM
cana-5829	348	8	0.30	0.30	NUM
cana-5829	348	9	+	+	CCONJ
cana-5829	348	10	0.10𝑖	0.10𝑖	NOUN
cana-5829	348	11	)	)	PUNCT
cana-5829	348	12	(	(	PUNCT
cana-5829	348	13	0.83	0.83	NUM
cana-5829	348	14	+	+	NUM
cana-5829	348	15	1𝑖	1𝑖	NOUN
cana-5829	348	16	0	0	NUM
cana-5829	349	1	+	+	NUM
cana-5829	349	2	0𝑖	0𝑖	NOUN
cana-5829	349	3	)	)	PUNCT
cana-5829	349	4	(	(	PUNCT
cana-5829	349	5	0.5	0.5	NUM
cana-5829	349	6	+	+	NUM
cana-5829	349	7	0.67𝑖	0.67𝑖	NUM
cana-5829	349	8	0.5	0.5	NUM
cana-5829	349	9	+	+	NUM
cana-5829	349	10	0𝑖	0𝑖	NOUN
cana-5829	349	11	)	)	PUNCT
cana-5829	349	12	)	)	PUNCT
cana-5829	349	13			NOUN
cana-5829	349	14	(	(	PUNCT
cana-5829	349	15	(	(	PUNCT
cana-5829	349	16	0.67	0.67	NUM
cana-5829	350	1	+	+	CCONJ
cana-5829	350	2	0.75𝑖	0.75𝑖	PROPN
cana-5829	350	3	0.375	0.375	NUM
cana-5829	350	4	+	+	NUM
cana-5829	350	5	0𝑖	0𝑖	NOUN
cana-5829	350	6	)	)	PUNCT
cana-5829	350	7	(	(	PUNCT
cana-5829	350	8	0.5	0.5	NUM
cana-5829	350	9	+	+	NUM
cana-5829	350	10	1𝑖	1𝑖	NUM
cana-5829	350	11	0.25	0.25	NUM
cana-5829	350	12	+	+	CCONJ
cana-5829	350	13	0.11𝑖	0.11𝑖	NUM
cana-5829	350	14	)	)	PUNCT
cana-5829	350	15	(	(	PUNCT
cana-5829	350	16	1	1	NUM
cana-5829	351	1	+	+	NUM
cana-5829	351	2	0.5𝑖	0.5𝑖	NOUN
cana-5829	351	3	0	0	NUM
cana-5829	352	1	+	+	CCONJ
cana-5829	352	2	0.11𝑖	0.11𝑖	NUM
cana-5829	352	3	)	)	PUNCT
cana-5829	352	4	(	(	PUNCT
cana-5829	353	1	0.83	0.83	NUM
cana-5829	353	2	+	+	NUM
cana-5829	353	3	0.25𝑖	0.25𝑖	NOUN
cana-5829	353	4	0.25	0.25	NUM
cana-5829	353	5	+	+	PUNCT
cana-5829	353	6	0.22𝑖	0.22𝑖	NUM
cana-5829	353	7	)	)	PUNCT
cana-5829	353	8	)	)	PUNCT
cana-5829	354	1	𝑋11	𝑋11	PROPN
cana-5829	354	2	=	=	PUNCT
cana-5829	354	3	(	(	PUNCT
cana-5829	354	4	1	1	NUM
cana-5829	354	5	+	+	NUM
cana-5829	354	6	0.67𝑖	0.67𝑖	NUM
cana-5829	354	7	0.125	0.125	NUM
cana-5829	354	8	+	+	NUM
cana-5829	354	9	0𝑖	0𝑖	NOUN
cana-5829	354	10	)	)	PUNCT
cana-5829	355	1	∩	∩	NOUN
cana-5829	355	2	(	(	PUNCT
cana-5829	355	3	0.67	0.67	NUM
cana-5829	356	1	+	+	CCONJ
cana-5829	356	2	0.75𝑖	0.75𝑖	PROPN
cana-5829	356	3	0.375	0.375	NUM
cana-5829	356	4	+	+	NUM
cana-5829	356	5	0𝑖	0𝑖	NOUN
cana-5829	356	6	)	)	PUNCT
cana-5829	356	7	𝑋12	𝑋12	PROPN
cana-5829	356	8	=	=	PUNCT
cana-5829	356	9	(	(	PUNCT
cana-5829	356	10	0.67	0.67	NUM
cana-5829	356	11	+	+	CCONJ
cana-5829	356	12	0.33𝑖	0.33𝑖	NUM
cana-5829	356	13	0.30	0.30	NUM
cana-5829	356	14	+	+	CCONJ
cana-5829	356	15	0.10𝑖	0.10𝑖	NOUN
cana-5829	356	16	)	)	PUNCT
cana-5829	356	17	∩	∩	NOUN
cana-5829	356	18	(	(	PUNCT
cana-5829	356	19	0.5	0.5	NUM
cana-5829	356	20	+	+	NUM
cana-5829	356	21	1𝑖	1𝑖	NUM
cana-5829	356	22	0.25	0.25	NUM
cana-5829	356	23	+	+	CCONJ
cana-5829	356	24	0.11𝑖	0.11𝑖	NUM
cana-5829	356	25	)	)	PUNCT
cana-5829	356	26	𝑋21	𝑋21	NOUN
cana-5829	356	27	=	=	SYM
cana-5829	356	28	(	(	PUNCT
cana-5829	356	29	0.83	0.83	NUM
cana-5829	356	30	+	+	NUM
cana-5829	356	31	1𝑖	1𝑖	NOUN
cana-5829	356	32	0	0	NUM
cana-5829	357	1	+	+	NUM
cana-5829	357	2	0𝑖	0𝑖	NOUN
cana-5829	357	3	)	)	PUNCT
cana-5829	357	4	∩	∩	NOUN
cana-5829	357	5	(	(	PUNCT
cana-5829	357	6	1	1	NUM
cana-5829	357	7	+	+	NUM
cana-5829	357	8	0.5𝑖	0.5𝑖	NOUN
cana-5829	357	9	0	0	NUM
cana-5829	358	1	+	+	CCONJ
cana-5829	358	2	0.11𝑖	0.11𝑖	NUM
cana-5829	358	3	)	)	PUNCT
cana-5829	359	1	𝑋22	𝑋22	ADJ
cana-5829	359	2	=	=	PUNCT
cana-5829	359	3	(	(	PUNCT
cana-5829	359	4	0.5	0.5	NUM
cana-5829	359	5	+	+	NUM
cana-5829	359	6	0.67𝑖	0.67𝑖	NUM
cana-5829	359	7	0.5	0.5	NUM
cana-5829	359	8	+	+	NUM
cana-5829	359	9	0𝑖	0𝑖	NOUN
cana-5829	359	10	)	)	PUNCT
cana-5829	359	11	∩	∩	NOUN
cana-5829	359	12	(	(	PUNCT
cana-5829	359	13	0.83	0.83	NUM
cana-5829	360	1	+	+	NUM
cana-5829	360	2	0.25𝑖	0.25𝑖	NUM
cana-5829	360	3	0.25	0.25	NUM
cana-5829	360	4	+	+	CCONJ
cana-5829	360	5	0.22𝑖	0.22𝑖	NOUN
cana-5829	360	6	)	)	PUNCT
cana-5829	360	7	applying	apply	VERB
cana-5829	360	8	formula	formula	NOUN
cana-5829	360	9	aebf	aebf	ADP
cana-5829	360	10	=	=	SYM
cana-5829	360	11	{	{	PUNCT
cana-5829	360	12	(	(	PUNCT
cana-5829	360	13	x	x	NOUN
cana-5829	360	14	,	,	PUNCT
cana-5829	360	15	y	y	PROPN
cana-5829	360	16	)	)	PUNCT
cana-5829	360	17	,	,	PUNCT
cana-5829	360	18	min	min	PROPN
cana-5829	360	19	(	(	PUNCT
cana-5829	360	20	μa(x	μa(x	NOUN
cana-5829	360	21	)	)	PUNCT
cana-5829	360	22	,	,	PUNCT
cana-5829	360	23	μb(y	μb(y	NUM
cana-5829	360	24	)	)	PUNCT
cana-5829	360	25	)	)	PUNCT
cana-5829	360	26	,	,	PUNCT
cana-5829	360	27	max	max	PROPN
cana-5829	360	28	(	(	PUNCT
cana-5829	360	29	ϑa(x	ϑa(x	NOUN
cana-5829	360	30	)	)	PUNCT
cana-5829	360	31	,	,	PUNCT
cana-5829	360	32	ϑb(x	ϑb(x	NUM
cana-5829	360	33	)	)	PUNCT
cana-5829	360	34	):	):	PUNCT
cana-5829	360	35	xe	xe	PROPN
cana-5829	360	36	,	,	PUNCT
cana-5829	360	37	yf	yf	NOUN
cana-5829	360	38	}	}	PUNCT
cana-5829	360	39	communications	communication	NOUN
cana-5829	360	40	on	on	ADP
cana-5829	360	41	applied	apply	VERB
cana-5829	360	42	nonlinear	nonlinear	ADJ
cana-5829	360	43	analysis	analysis	NOUN
cana-5829	360	44	issn	issn	NOUN
cana-5829	360	45	:	:	PUNCT
cana-5829	360	46	1074	1074	NUM
cana-5829	360	47	-	-	PUNCT
cana-5829	360	48	133x	133x	NUM
cana-5829	360	49	vol	vol	VERB
cana-5829	360	50	32	32	NUM
cana-5829	360	51	no	no	NOUN
cana-5829	360	52	.	.	PUNCT
cana-5829	361	1	10s	10	NOUN
cana-5829	361	2	(	(	PUNCT
cana-5829	361	3	2025	2025	NUM
cana-5829	361	4	)	)	PUNCT
cana-5829	361	5	2938	2938	NUM
cana-5829	361	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5829	362	1	𝑋11	𝑋11	PROPN
cana-5829	362	2	=	=	PRON
cana-5829	362	3	{	{	PUNCT
cana-5829	362	4	𝑚𝑖𝑛(1	𝑚𝑖𝑛(1	NOUN
cana-5829	362	5	+	+	CCONJ
cana-5829	362	6	0.67𝑖	0.67𝑖	NOUN
cana-5829	362	7	,	,	PUNCT
cana-5829	362	8	0.67	0.67	NUM
cana-5829	362	9	+	+	CCONJ
cana-5829	362	10	0.75𝑖	0.75𝑖	PROPN
cana-5829	362	11	)	)	PUNCT
cana-5829	362	12	,	,	PUNCT
cana-5829	363	1	𝑚𝑎𝑥(0.125	𝑚𝑎𝑥(0.125	PRON
cana-5829	363	2	+	+	NUM
cana-5829	363	3	0𝑖	0𝑖	NOUN
cana-5829	363	4	,	,	PUNCT
cana-5829	363	5	0.375	0.375	NUM
cana-5829	363	6	+	+	NUM
cana-5829	363	7	0𝑖	0𝑖	NOUN
cana-5829	363	8	)	)	PUNCT
cana-5829	363	9	}	}	PUNCT
cana-5829	364	1	𝑋12	𝑋12	VERB
cana-5829	364	2	=	=	PRON
cana-5829	364	3	{	{	PUNCT
cana-5829	364	4	𝑚𝑖𝑛(0.67	𝑚𝑖𝑛(0.67	PRON
cana-5829	364	5	+	+	CCONJ
cana-5829	364	6	0.33𝑖	0.33𝑖	ADJ
cana-5829	364	7	,	,	PUNCT
cana-5829	364	8	0.5	0.5	NUM
cana-5829	364	9	+	+	NUM
cana-5829	364	10	1𝑖	1𝑖	NUM
cana-5829	364	11	)	)	PUNCT
cana-5829	364	12	,	,	PUNCT
cana-5829	364	13	𝑚𝑎𝑥(0.30	𝑚𝑎𝑥(0.30	X
cana-5829	364	14	+	+	CCONJ
cana-5829	364	15	0.10𝑖	0.10𝑖	NOUN
cana-5829	364	16	,	,	PUNCT
cana-5829	364	17	0.25	0.25	NUM
cana-5829	364	18	+	+	X
cana-5829	364	19	0.11𝑖	0.11𝑖	NUM
cana-5829	364	20	)	)	PUNCT
cana-5829	364	21	}	}	PUNCT
cana-5829	365	1	𝑋21	𝑋21	VERB
cana-5829	365	2	=	=	PRON
cana-5829	365	3	{	{	PUNCT
cana-5829	365	4	𝑚𝑖𝑛(0.83	𝑚𝑖𝑛(0.83	ADJ
cana-5829	365	5	+	+	NUM
cana-5829	365	6	1𝑖	1𝑖	NOUN
cana-5829	365	7	,	,	PUNCT
cana-5829	365	8	1	1	NUM
cana-5829	365	9	+	+	SYM
cana-5829	365	10	0.5𝑖	0.5𝑖	NOUN
cana-5829	365	11	)	)	PUNCT
cana-5829	365	12	,	,	PUNCT
cana-5829	365	13	𝑚𝑎𝑥(0	𝑚𝑎𝑥(0	ADJ
cana-5829	365	14	+	+	CCONJ
cana-5829	365	15	0𝑖	0𝑖	NOUN
cana-5829	365	16	,	,	PUNCT
cana-5829	365	17	0	0	NUM
cana-5829	366	1	+	+	CCONJ
cana-5829	366	2	0.11𝑖	0.11𝑖	NUM
cana-5829	366	3	)	)	PUNCT
cana-5829	366	4	}	}	PUNCT
cana-5829	367	1	𝑋22	𝑋22	VERB
cana-5829	367	2	=	=	PRON
cana-5829	367	3	{	{	PUNCT
cana-5829	367	4	𝑚𝑖𝑛(0.5	𝑚𝑖𝑛(0.5	NUM
cana-5829	367	5	+	+	CCONJ
cana-5829	367	6	0.67𝑖	0.67𝑖	NUM
cana-5829	367	7	,	,	PUNCT
cana-5829	367	8	0.83	0.83	NUM
cana-5829	367	9	+	+	NUM
cana-5829	367	10	0.25𝑖	0.25𝑖	NUM
cana-5829	367	11	)	)	PUNCT
cana-5829	367	12	,	,	PUNCT
cana-5829	368	1	𝑚𝑎𝑥(0.5	𝑚𝑎𝑥(0.5	X
cana-5829	368	2	+	+	NUM
cana-5829	368	3	0𝑖	0𝑖	NOUN
cana-5829	368	4	,	,	PUNCT
cana-5829	368	5	0.25	0.25	NUM
cana-5829	368	6	+	+	CCONJ
cana-5829	368	7	0.22𝑖	0.22𝑖	NUM
cana-5829	368	8	)	)	PUNCT
cana-5829	368	9	}	}	PUNCT
cana-5829	368	10	𝑋11	𝑋11	PROPN
cana-5829	368	11	=	=	PRON
cana-5829	368	12	{	{	PUNCT
cana-5829	368	13	0.67	0.67	NUM
cana-5829	368	14	+	+	NOUN
cana-5829	368	15	0.67i	0.67i	NOUN
cana-5829	368	16	,	,	PUNCT
cana-5829	368	17	0.375	0.375	NUM
cana-5829	368	18	+	+	NOUN
cana-5829	368	19	0i	0i	X
cana-5829	368	20	}	}	PUNCT
cana-5829	368	21	𝑋12	𝑋12	PROPN
cana-5829	368	22	=	=	PRON
cana-5829	368	23	{	{	PUNCT
cana-5829	368	24	0.5	0.5	NUM
cana-5829	368	25	+	+	NOUN
cana-5829	368	26	0.33i	0.33i	PROPN
cana-5829	368	27	,	,	PUNCT
cana-5829	368	28	0.3	0.3	NUM
cana-5829	368	29	+	+	ADJ
cana-5829	368	30	0.11i	0.11i	NOUN
cana-5829	368	31	}	}	PUNCT
cana-5829	368	32	𝑋21	𝑋21	NOUN
cana-5829	368	33	=	=	NUM
cana-5829	368	34	{	{	PUNCT
cana-5829	368	35	0.83	0.83	NUM
cana-5829	368	36	+	+	NOUN
cana-5829	368	37	0.5i	0.5i	NUM
cana-5829	368	38	,	,	PUNCT
cana-5829	368	39	0	0	PUNCT
cana-5829	368	40	+	+	NUM
cana-5829	368	41	0.11i	0.11i	NOUN
cana-5829	368	42	}	}	PUNCT
cana-5829	368	43	𝑋22	𝑋22	VERB
cana-5829	368	44	=	=	X
cana-5829	368	45	{	{	PUNCT
cana-5829	368	46	0.5	0.5	NUM
cana-5829	368	47	+	+	NOUN
cana-5829	368	48	0.25i	0.25i	NOUN
cana-5829	368	49	,	,	PUNCT
cana-5829	368	50	0.5	0.5	NUM
cana-5829	368	51	+	+	NUM
cana-5829	368	52	0.22i	0.22i	NOUN
cana-5829	368	53	}	}	PUNCT
cana-5829	368	54	we	we	PRON
cana-5829	368	55	have	have	AUX
cana-5829	368	56	norm	norm	VERB
cana-5829	368	57	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	368	58			PUNCT
cana-5829	368	59	𝑁𝑜𝑟𝑚	𝑁𝑜𝑟𝑚	PROPN
cana-5829	368	60	𝐵𝐹	𝐵𝐹	NOUN
cana-5829	368	61	=	=	SYM
cana-5829	368	62	(	(	PUNCT
cana-5829	368	63	(	(	PUNCT
cana-5829	368	64	0.67	0.67	NUM
cana-5829	368	65	+	+	CCONJ
cana-5829	368	66	0.67i	0.67i	NUM
cana-5829	368	67	,	,	PUNCT
cana-5829	368	68	0.375	0.375	NUM
cana-5829	368	69	+	+	NUM
cana-5829	368	70	0i	0i	NOUN
cana-5829	368	71	)	)	PUNCT
cana-5829	368	72	(	(	PUNCT
cana-5829	368	73	0.5	0.5	NUM
cana-5829	368	74	+	+	CCONJ
cana-5829	368	75	0.33i	0.33i	NUM
cana-5829	368	76	,	,	PUNCT
cana-5829	368	77	0.3	0.3	NUM
cana-5829	368	78	+	+	NUM
cana-5829	368	79	0.11i	0.11i	NOUN
cana-5829	368	80	)	)	PUNCT
cana-5829	368	81	(	(	PUNCT
cana-5829	368	82	0.83	0.83	NUM
cana-5829	368	83	+	+	CCONJ
cana-5829	368	84	0.5i	0.5i	NUM
cana-5829	368	85	,	,	PUNCT
cana-5829	368	86	0	0	NUM
cana-5829	369	1	+	+	NUM
cana-5829	369	2	0.11i	0.11i	NOUN
cana-5829	369	3	)	)	PUNCT
cana-5829	369	4	(	(	PUNCT
cana-5829	369	5	0.5	0.5	NUM
cana-5829	369	6	+	+	CCONJ
cana-5829	369	7	0.25i	0.25i	NOUN
cana-5829	369	8	,	,	PUNCT
cana-5829	369	9	0.5	0.5	NUM
cana-5829	369	10	+	+	NUM
cana-5829	369	11	0.22i	0.22i	NOUN
cana-5829	369	12	)	)	PUNCT
cana-5829	369	13	)	)	PUNCT
cana-5829	369	14	is	be	AUX
cana-5829	369	15	also	also	ADV
cana-5829	369	16	normalization	normalization	NOUN
cana-5829	369	17	of	of	ADP
cana-5829	369	18	complex	complex	ADJ
cana-5829	369	19	intuitionistic	intuitionistic	ADJ
cana-5829	369	20	fuzzy	fuzzy	ADJ
cana-5829	369	21	matrix	matrix	NOUN
cana-5829	369	22	.	.	PUNCT
cana-5829	370	1	theorem	theorem	VERB
cana-5829	370	2	5.2.3	5.2.3	NUM
cana-5829	370	3	:	:	PUNCT
cana-5829	370	4	if	if	SCONJ
cana-5829	370	5	e	e	PROPN
cana-5829	370	6	and	and	CCONJ
cana-5829	370	7	f	f	PROPN
cana-5829	370	8	be	be	AUX
cana-5829	370	9	two	two	NUM
cana-5829	370	10	universal	universal	ADJ
cana-5829	370	11	sets	set	NOUN
cana-5829	370	12	.	.	PUNCT
cana-5829	371	1	for	for	ADP
cana-5829	371	2	every	every	DET
cana-5829	371	3	normalization	normalization	NOUN
cana-5829	371	4	of	of	ADP
cana-5829	371	5	complex	complex	ADJ
cana-5829	371	6	intuitionistic	intuitionistic	ADJ
cana-5829	371	7	fuzzy	fuzzy	ADJ
cana-5829	371	8	matrices	matrix	NOUN
cana-5829	371	9	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	371	10	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-5829	371	11	𝐵𝐹	𝐵𝐹	PROPN
cana-5829	371	12	are	be	AUX
cana-5829	371	13	in	in	ADP
cana-5829	371	14	e	e	PROPN
cana-5829	371	15	and	and	CCONJ
cana-5829	371	16	f	f	PROPN
cana-5829	371	17	then	then	ADV
cana-5829	371	18	norm	norm	VERB
cana-5829	371	19	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	371	20	∪	∪	ADJ
cana-5829	371	21	𝑁𝑜𝑟𝑚	𝑁𝑜𝑟𝑚	PROPN
cana-5829	371	22	𝐵𝐹	𝐵𝐹	PROPN
cana-5829	371	23	is	be	AUX
cana-5829	371	24	also	also	ADV
cana-5829	371	25	normalization	normalization	NOUN
cana-5829	371	26	of	of	ADP
cana-5829	371	27	complex	complex	ADJ
cana-5829	371	28	intuitionistic	intuitionistic	ADJ
cana-5829	371	29	fuzzy	fuzzy	ADJ
cana-5829	371	30	matrices	matrix	NOUN
cana-5829	371	31	.	.	PUNCT
cana-5829	372	1	proof	proof	NOUN
cana-5829	372	2	:	:	PUNCT
cana-5829	372	3	if	if	SCONJ
cana-5829	372	4	norm	norm	NOUN
cana-5829	372	5	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	372	6	and	and	CCONJ
cana-5829	372	7	𝑁𝑜𝑟𝑚	𝑁𝑜𝑟𝑚	PROPN
cana-5829	372	8	𝐵𝐹	𝐵𝐹	PROPN
cana-5829	372	9	are	be	AUX
cana-5829	372	10	two	two	NUM
cana-5829	372	11	normalization	normalization	NOUN
cana-5829	372	12	intuitionistic	intuitionistic	ADJ
cana-5829	372	13	fuzzy	fuzzy	ADJ
cana-5829	372	14	matrices	matrix	NOUN
cana-5829	372	15	over	over	ADP
cana-5829	372	16	different	different	ADJ
cana-5829	372	17	unive𝑟𝑠𝑒𝑠	unive𝑟𝑠𝑒𝑠	ADJ
cana-5829	372	18	𝑠𝑒𝑡𝑠	𝑠𝑒𝑡𝑠	PROPN
cana-5829	372	19	𝐸	𝐸	PROPN
cana-5829	372	20	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-5829	372	21	𝐹.	𝐹.	PROPN
cana-5829	372	22	if	if	SCONJ
cana-5829	372	23	we	we	PRON
cana-5829	372	24	consider	consider	VERB
cana-5829	372	25	two	two	NUM
cana-5829	372	26	2	2	NUM
cana-5829	372	27	×	×	NOUN
cana-5829	372	28	2	2	NUM
cana-5829	372	29	normalization	normalization	NOUN
cana-5829	372	30	intuitionistic	intuitionistic	ADJ
cana-5829	372	31	fuzzy	fuzzy	ADJ
cana-5829	372	32	matrices	matrix	NOUN
cana-5829	372	33	,	,	PUNCT
cana-5829	372	34	norm	norm	NOUN
cana-5829	372	35	𝐴𝐸𝑎𝑛𝑑	𝐴𝐸𝑎𝑛𝑑	PROPN
cana-5829	372	36	𝑁𝑜𝑟𝑚	𝑁𝑜𝑟𝑚	PROPN
cana-5829	372	37	𝐵𝐹.	𝐵𝐹.	NOUN
cana-5829	372	38	let	let	VERB
cana-5829	372	39	norm	norm	VERB
cana-5829	372	40	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	372	41	=	=	SYM
cana-5829	372	42	(	(	PUNCT
cana-5829	372	43	(	(	PUNCT
cana-5829	372	44	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	372	45	(	(	PUNCT
cana-5829	372	46	𝛼11	𝛼11	NOUN
cana-5829	372	47	+	+	PROPN
cana-5829	372	48	𝑖𝛽11	𝑖𝛽11	PROPN
cana-5829	372	49	)	)	PUNCT
cana-5829	372	50	𝑁𝑜𝑟𝑚µ𝐸11	𝑁𝑜𝑟𝑚µ𝐸11	NOUN
cana-5829	372	51	(	(	PUNCT
cana-5829	372	52	𝛾11	𝛾11	VERB
cana-5829	372	53	+	+	CCONJ
cana-5829	372	54	𝑖𝛿11	𝑖𝛿11	PROPN
cana-5829	372	55	)	)	PUNCT
cana-5829	372	56	)	)	PUNCT
cana-5829	372	57	(	(	PUNCT
cana-5829	372	58	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	NOUN
cana-5829	372	59	(	(	PUNCT
cana-5829	372	60	𝛼12	𝛼12	NOUN
cana-5829	372	61	+	+	CCONJ
cana-5829	372	62	𝑖𝛽12	𝑖𝛽12	PROPN
cana-5829	372	63	)	)	PUNCT
cana-5829	372	64	𝑁𝑜𝑟𝑚µ𝐸12	𝑁𝑜𝑟𝑚µ𝐸12	NOUN
cana-5829	372	65	(	(	PUNCT
cana-5829	372	66	𝛾12	𝛾12	VERB
cana-5829	372	67	+	+	CCONJ
cana-5829	372	68	𝑖𝛿12	𝑖𝛿12	PROPN
cana-5829	372	69	)	)	PUNCT
cana-5829	372	70	)	)	PUNCT
cana-5829	373	1	(	(	PUNCT
cana-5829	373	2	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	X
cana-5829	373	3	(	(	PUNCT
cana-5829	373	4	𝛼21	𝛼21	NOUN
cana-5829	373	5	+	+	X
cana-5829	373	6	𝑖𝛽21	𝑖𝛽21	PROPN
cana-5829	373	7	)	)	PUNCT
cana-5829	373	8	𝑁𝑜𝑟𝑚µ𝐸21	𝑁𝑜𝑟𝑚µ𝐸21	NOUN
cana-5829	373	9	(	(	PUNCT
cana-5829	373	10	𝛾21	𝛾21	NOUN
cana-5829	373	11	+	+	CCONJ
cana-5829	374	1	𝑖𝛿21	𝑖𝛿21	PROPN
cana-5829	374	2	)	)	PUNCT
cana-5829	374	3	)	)	PUNCT
cana-5829	375	1	(	(	PUNCT
cana-5829	375	2	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	X
cana-5829	375	3	(	(	PUNCT
cana-5829	375	4	𝛼22	𝛼22	NOUN
cana-5829	375	5	+	+	CCONJ
cana-5829	375	6	𝑖𝛽22	𝑖𝛽22	PROPN
cana-5829	375	7	)	)	PUNCT
cana-5829	375	8	𝑁𝑜𝑟𝑚µ𝐸22	𝑁𝑜𝑟𝑚µ𝐸22	NOUN
cana-5829	375	9	(	(	PUNCT
cana-5829	375	10	𝛾22	𝛾22	PROPN
cana-5829	375	11	+	+	PROPN
cana-5829	375	12	𝑖𝛿22	𝑖𝛿22	PROPN
cana-5829	375	13	)	)	PUNCT
cana-5829	375	14	)	)	PUNCT
cana-5829	375	15	)	)	PUNCT
cana-5829	376	1	and	and	CCONJ
cana-5829	376	2	𝑁𝑜𝑟𝑚	𝑁𝑜𝑟𝑚	PROPN
cana-5829	376	3	𝐵𝐹	𝐵𝐹	NOUN
cana-5829	376	4	=	=	SYM
cana-5829	376	5	(	(	PUNCT
cana-5829	376	6	(	(	PUNCT
cana-5829	376	7	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	376	8	(	(	PUNCT
cana-5829	376	9	𝑥11	𝑥11	ADV
cana-5829	376	10	+	+	CCONJ
cana-5829	376	11	𝑖𝑦11	𝑖𝑦11	NOUN
cana-5829	376	12	)	)	PUNCT
cana-5829	376	13	𝑁𝑜𝑟𝑚𝛾𝐹11	𝑁𝑜𝑟𝑚𝛾𝐹11	X
cana-5829	376	14	(	(	PUNCT
cana-5829	376	15	𝜇11	𝜇11	PROPN
cana-5829	376	16	+	+	PROPN
cana-5829	376	17	𝑖𝜃11	𝑖𝜃11	PROPN
cana-5829	376	18	)	)	PUNCT
cana-5829	376	19	)	)	PUNCT
cana-5829	377	1	(	(	PUNCT
cana-5829	377	2	𝑁𝑜𝑟𝑚𝛿𝐹12	𝑁𝑜𝑟𝑚𝛿𝐹12	X
cana-5829	377	3	(	(	PUNCT
cana-5829	377	4	𝑥12	𝑥12	VERB
cana-5829	377	5	+	+	CCONJ
cana-5829	377	6	𝑖𝑦12	𝑖𝑦12	PROPN
cana-5829	377	7	)	)	PUNCT
cana-5829	377	8	𝑁𝑜𝑟𝑚𝛾𝐹12	𝑁𝑜𝑟𝑚𝛾𝐹12	NOUN
cana-5829	377	9	(	(	PUNCT
cana-5829	377	10	𝜇12	𝜇12	NOUN
cana-5829	377	11	+	+	CCONJ
cana-5829	378	1	𝑖𝜃12	𝑖𝜃12	PROPN
cana-5829	378	2	)	)	PUNCT
cana-5829	378	3	)	)	PUNCT
cana-5829	379	1	(	(	PUNCT
cana-5829	379	2	𝑁𝑜𝑟𝑚𝛿𝐹21	𝑁𝑜𝑟𝑚𝛿𝐹21	X
cana-5829	379	3	(	(	PUNCT
cana-5829	379	4	𝑥21	𝑥21	PROPN
cana-5829	379	5	+	+	CCONJ
cana-5829	379	6	𝑖𝑦21	𝑖𝑦21	PROPN
cana-5829	379	7	)	)	PUNCT
cana-5829	379	8	𝑁𝑜𝑟𝑚𝛾𝐹21	𝑁𝑜𝑟𝑚𝛾𝐹21	ADV
cana-5829	379	9	(	(	PUNCT
cana-5829	379	10	𝜇21	𝜇21	VERB
cana-5829	379	11	+	+	CCONJ
cana-5829	379	12	𝑖𝜃21	𝑖𝜃21	PROPN
cana-5829	379	13	)	)	PUNCT
cana-5829	379	14	)	)	PUNCT
cana-5829	379	15	(	(	PUNCT
cana-5829	379	16	𝑁𝑜𝑟𝑚𝛿𝐹22	𝑁𝑜𝑟𝑚𝛿𝐹22	X
cana-5829	379	17	(	(	PUNCT
cana-5829	379	18	𝑥22	𝑥22	NOUN
cana-5829	379	19	+	+	X
cana-5829	379	20	𝑖𝑦22	𝑖𝑦22	PROPN
cana-5829	379	21	)	)	PUNCT
cana-5829	379	22	𝑁𝑜𝑟𝑚𝛾𝐹22	𝑁𝑜𝑟𝑚𝛾𝐹22	NOUN
cana-5829	379	23	(	(	PUNCT
cana-5829	379	24	𝜇22	𝜇22	NOUN
cana-5829	379	25	+	+	CCONJ
cana-5829	379	26	𝑖𝜃22	𝑖𝜃22	PROPN
cana-5829	379	27	)	)	PUNCT
cana-5829	379	28	)	)	PUNCT
cana-5829	379	29	)	)	PUNCT
cana-5829	379	30	are	be	AUX
cana-5829	379	31	two	two	NUM
cana-5829	379	32	normalization	normalization	NOUN
cana-5829	379	33	intuitionistic	intuitionistic	ADJ
cana-5829	379	34	fuzzy	fuzzy	ADJ
cana-5829	379	35	matrices	matrix	NOUN
cana-5829	379	36	.	.	PUNCT
cana-5829	380	1	norm𝐴𝐸	norm𝐴𝐸	NOUN
cana-5829	380	2	∪	∪	VERB
cana-5829	380	3	𝑁𝑜𝑟𝑚𝐵𝐹	𝑁𝑜𝑟𝑚𝐵𝐹	PROPN
cana-5829	380	4	=	=	PUNCT
cana-5829	380	5	(	(	PUNCT
cana-5829	380	6	(	(	PUNCT
cana-5829	380	7	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	380	8	(	(	PUNCT
cana-5829	380	9	𝛼11	𝛼11	NOUN
cana-5829	380	10	+	+	PROPN
cana-5829	380	11	𝑖𝛽11	𝑖𝛽11	PROPN
cana-5829	380	12	)	)	PUNCT
cana-5829	380	13	𝑁𝑜𝑟𝑚µ𝐸11	𝑁𝑜𝑟𝑚µ𝐸11	NOUN
cana-5829	380	14	(	(	PUNCT
cana-5829	380	15	𝛾11	𝛾11	VERB
cana-5829	380	16	+	+	CCONJ
cana-5829	380	17	𝑖𝛿11	𝑖𝛿11	PROPN
cana-5829	380	18	)	)	PUNCT
cana-5829	380	19	)	)	PUNCT
cana-5829	380	20	(	(	PUNCT
cana-5829	380	21	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	NOUN
cana-5829	380	22	(	(	PUNCT
cana-5829	380	23	𝛼12	𝛼12	NOUN
cana-5829	380	24	+	+	CCONJ
cana-5829	380	25	𝑖𝛽12	𝑖𝛽12	PROPN
cana-5829	380	26	)	)	PUNCT
cana-5829	380	27	𝑁𝑜𝑟𝑚µ𝐸12	𝑁𝑜𝑟𝑚µ𝐸12	NOUN
cana-5829	380	28	(	(	PUNCT
cana-5829	380	29	𝛾12	𝛾12	VERB
cana-5829	380	30	+	+	CCONJ
cana-5829	380	31	𝑖𝛿12	𝑖𝛿12	PROPN
cana-5829	380	32	)	)	PUNCT
cana-5829	380	33	)	)	PUNCT
cana-5829	380	34	(	(	PUNCT
cana-5829	380	35	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	X
cana-5829	380	36	(	(	PUNCT
cana-5829	380	37	𝛼21	𝛼21	NOUN
cana-5829	380	38	+	+	X
cana-5829	380	39	𝑖𝛽21	𝑖𝛽21	PROPN
cana-5829	380	40	)	)	PUNCT
cana-5829	380	41	𝑁𝑜𝑟𝑚µ𝐸21	𝑁𝑜𝑟𝑚µ𝐸21	NOUN
cana-5829	380	42	(	(	PUNCT
cana-5829	380	43	𝛾21	𝛾21	NOUN
cana-5829	380	44	+	+	CCONJ
cana-5829	381	1	𝑖𝛿21	𝑖𝛿21	PROPN
cana-5829	381	2	)	)	PUNCT
cana-5829	381	3	)	)	PUNCT
cana-5829	382	1	(	(	PUNCT
cana-5829	382	2	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	X
cana-5829	382	3	(	(	PUNCT
cana-5829	382	4	𝛼22	𝛼22	NOUN
cana-5829	382	5	+	+	CCONJ
cana-5829	382	6	𝑖𝛽22	𝑖𝛽22	PROPN
cana-5829	382	7	)	)	PUNCT
cana-5829	382	8	𝑁𝑜𝑟𝑚µ𝐸22	𝑁𝑜𝑟𝑚µ𝐸22	NOUN
cana-5829	382	9	(	(	PUNCT
cana-5829	382	10	𝛾22	𝛾22	PROPN
cana-5829	382	11	+	+	PROPN
cana-5829	382	12	𝑖𝛿22	𝑖𝛿22	PROPN
cana-5829	382	13	)	)	PUNCT
cana-5829	382	14	)	)	PUNCT
cana-5829	382	15	)	)	PUNCT
cana-5829	382	16	∪	∪	ADV
cana-5829	382	17	(	(	PUNCT
cana-5829	382	18	(	(	PUNCT
cana-5829	382	19	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	382	20	(	(	PUNCT
cana-5829	382	21	𝑥11	𝑥11	ADV
cana-5829	382	22	+	+	CCONJ
cana-5829	382	23	𝑖𝑦11	𝑖𝑦11	NOUN
cana-5829	382	24	)	)	PUNCT
cana-5829	382	25	𝑁𝑜𝑟𝑚𝛾𝐹11	𝑁𝑜𝑟𝑚𝛾𝐹11	X
cana-5829	382	26	(	(	PUNCT
cana-5829	382	27	𝜇11	𝜇11	PROPN
cana-5829	382	28	+	+	PROPN
cana-5829	382	29	𝑖𝜃11	𝑖𝜃11	PROPN
cana-5829	382	30	)	)	PUNCT
cana-5829	382	31	)	)	PUNCT
cana-5829	382	32	(	(	PUNCT
cana-5829	382	33	𝑁𝑜𝑟𝑚𝛿𝐹12	𝑁𝑜𝑟𝑚𝛿𝐹12	X
cana-5829	382	34	(	(	PUNCT
cana-5829	382	35	𝑥12	𝑥12	VERB
cana-5829	382	36	+	+	CCONJ
cana-5829	382	37	𝑖𝑦12	𝑖𝑦12	PROPN
cana-5829	382	38	)	)	PUNCT
cana-5829	382	39	𝑁𝑜𝑟𝑚𝛾𝐹12	𝑁𝑜𝑟𝑚𝛾𝐹12	NOUN
cana-5829	382	40	(	(	PUNCT
cana-5829	382	41	𝜇12	𝜇12	NOUN
cana-5829	382	42	+	+	CCONJ
cana-5829	382	43	𝑖𝜃12	𝑖𝜃12	PROPN
cana-5829	382	44	)	)	PUNCT
cana-5829	382	45	)	)	PUNCT
cana-5829	382	46	(	(	PUNCT
cana-5829	382	47	𝑁𝑜𝑟𝑚𝛿𝐹21	𝑁𝑜𝑟𝑚𝛿𝐹21	X
cana-5829	382	48	(	(	PUNCT
cana-5829	382	49	𝑥21	𝑥21	PROPN
cana-5829	382	50	+	+	CCONJ
cana-5829	382	51	𝑖𝑦21	𝑖𝑦21	PROPN
cana-5829	382	52	)	)	PUNCT
cana-5829	382	53	𝑁𝑜𝑟𝑚𝛾𝐹21	𝑁𝑜𝑟𝑚𝛾𝐹21	ADV
cana-5829	382	54	(	(	PUNCT
cana-5829	382	55	𝜇21	𝜇21	VERB
cana-5829	382	56	+	+	CCONJ
cana-5829	382	57	𝑖𝜃21	𝑖𝜃21	PROPN
cana-5829	382	58	)	)	PUNCT
cana-5829	382	59	)	)	PUNCT
cana-5829	382	60	(	(	PUNCT
cana-5829	382	61	𝑁𝑜𝑟𝑚𝛿𝐹22	𝑁𝑜𝑟𝑚𝛿𝐹22	X
cana-5829	382	62	(	(	PUNCT
cana-5829	382	63	𝑥22	𝑥22	NOUN
cana-5829	382	64	+	+	X
cana-5829	382	65	𝑖𝑦22	𝑖𝑦22	PROPN
cana-5829	382	66	)	)	PUNCT
cana-5829	382	67	𝑁𝑜𝑟𝑚𝛾𝐹22	𝑁𝑜𝑟𝑚𝛾𝐹22	NOUN
cana-5829	382	68	(	(	PUNCT
cana-5829	382	69	𝜇22	𝜇22	NOUN
cana-5829	382	70	+	+	CCONJ
cana-5829	382	71	𝑖𝜃22	𝑖𝜃22	PROPN
cana-5829	382	72	)	)	PUNCT
cana-5829	382	73	)	)	PUNCT
cana-5829	382	74	)	)	PUNCT
cana-5829	382	75	calculate	calculate	NOUN
cana-5829	382	76	,	,	PUNCT
cana-5829	382	77	𝑋11	𝑋11	PROPN
cana-5829	382	78	,	,	PUNCT
cana-5829	382	79	𝑋12	𝑋12	PROPN
cana-5829	382	80	,	,	PUNCT
cana-5829	382	81	𝑋21and	𝑋21and	PROPN
cana-5829	382	82	𝑋22	𝑋22	PROPN
cana-5829	382	83	,	,	PUNCT
cana-5829	382	84	we	we	PRON
cana-5829	382	85	have	have	VERB
cana-5829	382	86	.	.	PUNCT
cana-5829	383	1	now	now	ADV
cana-5829	383	2	applying	apply	VERB
cana-5829	383	3	both	both	DET
cana-5829	383	4	side	side	NOUN
cana-5829	383	5	on	on	ADP
cana-5829	383	6	intersection	intersection	NOUN
cana-5829	383	7	,	,	PUNCT
cana-5829	383	8	we	we	PRON
cana-5829	383	9	have	have	AUX
cana-5829	383	10	norm	norm	VERB
cana-5829	383	11	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	383	12	∪	∪	ADJ
cana-5829	383	13	𝑁𝑜𝑟𝑚	𝑁𝑜𝑟𝑚	PROPN
cana-5829	383	14	𝐵𝐹	𝐵𝐹	NOUN
cana-5829	383	15	=	=	SYM
cana-5829	383	16	(	(	PUNCT
cana-5829	383	17	(	(	PUNCT
cana-5829	383	18	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	383	19	(	(	PUNCT
cana-5829	383	20	𝛼11	𝛼11	NOUN
cana-5829	383	21	+	+	PROPN
cana-5829	383	22	𝑖𝛽11	𝑖𝛽11	PROPN
cana-5829	383	23	)	)	PUNCT
cana-5829	383	24	𝑁𝑜𝑟𝑚µ𝐸11	𝑁𝑜𝑟𝑚µ𝐸11	NOUN
cana-5829	383	25	(	(	PUNCT
cana-5829	383	26	𝛾11	𝛾11	VERB
cana-5829	383	27	+	+	CCONJ
cana-5829	383	28	𝑖𝛿11	𝑖𝛿11	PROPN
cana-5829	383	29	)	)	PUNCT
cana-5829	383	30	)	)	PUNCT
cana-5829	383	31	(	(	PUNCT
cana-5829	383	32	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	NOUN
cana-5829	383	33	(	(	PUNCT
cana-5829	383	34	𝛼12	𝛼12	NOUN
cana-5829	383	35	+	+	CCONJ
cana-5829	383	36	𝑖𝛽12	𝑖𝛽12	PROPN
cana-5829	383	37	)	)	PUNCT
cana-5829	383	38	𝑁𝑜𝑟𝑚µ𝐸12	𝑁𝑜𝑟𝑚µ𝐸12	NOUN
cana-5829	383	39	(	(	PUNCT
cana-5829	383	40	𝛾12	𝛾12	VERB
cana-5829	383	41	+	+	CCONJ
cana-5829	383	42	𝑖𝛿12	𝑖𝛿12	PROPN
cana-5829	383	43	)	)	PUNCT
cana-5829	383	44	)	)	PUNCT
cana-5829	384	1	(	(	PUNCT
cana-5829	384	2	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	X
cana-5829	384	3	(	(	PUNCT
cana-5829	384	4	𝛼21	𝛼21	NOUN
cana-5829	384	5	+	+	X
cana-5829	384	6	𝑖𝛽21	𝑖𝛽21	PROPN
cana-5829	384	7	)	)	PUNCT
cana-5829	384	8	𝑁𝑜𝑟𝑚µ𝐸21	𝑁𝑜𝑟𝑚µ𝐸21	NOUN
cana-5829	384	9	(	(	PUNCT
cana-5829	384	10	𝛾21	𝛾21	NOUN
cana-5829	384	11	+	+	CCONJ
cana-5829	385	1	𝑖𝛿21	𝑖𝛿21	PROPN
cana-5829	385	2	)	)	PUNCT
cana-5829	385	3	)	)	PUNCT
cana-5829	386	1	(	(	PUNCT
cana-5829	386	2	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	X
cana-5829	386	3	(	(	PUNCT
cana-5829	386	4	𝛼22	𝛼22	NOUN
cana-5829	386	5	+	+	CCONJ
cana-5829	386	6	𝑖𝛽22	𝑖𝛽22	PROPN
cana-5829	386	7	)	)	PUNCT
cana-5829	386	8	𝑁𝑜𝑟𝑚µ𝐸22	𝑁𝑜𝑟𝑚µ𝐸22	NOUN
cana-5829	386	9	(	(	PUNCT
cana-5829	386	10	𝛾22	𝛾22	PROPN
cana-5829	386	11	+	+	PROPN
cana-5829	386	12	𝑖𝛿22	𝑖𝛿22	PROPN
cana-5829	386	13	)	)	PUNCT
cana-5829	386	14	)	)	PUNCT
cana-5829	386	15	)	)	PUNCT
cana-5829	386	16	∪	∪	ADV
cana-5829	386	17	(	(	PUNCT
cana-5829	386	18	(	(	PUNCT
cana-5829	386	19	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	386	20	(	(	PUNCT
cana-5829	386	21	𝑥11	𝑥11	ADV
cana-5829	386	22	+	+	CCONJ
cana-5829	386	23	𝑖𝑦11	𝑖𝑦11	NOUN
cana-5829	386	24	)	)	PUNCT
cana-5829	386	25	𝑁𝑜𝑟𝑚𝛾𝐹11	𝑁𝑜𝑟𝑚𝛾𝐹11	X
cana-5829	386	26	(	(	PUNCT
cana-5829	386	27	𝜇11	𝜇11	PROPN
cana-5829	386	28	+	+	PROPN
cana-5829	386	29	𝑖𝜃11	𝑖𝜃11	PROPN
cana-5829	386	30	)	)	PUNCT
cana-5829	386	31	)	)	PUNCT
cana-5829	386	32	(	(	PUNCT
cana-5829	386	33	𝑁𝑜𝑟𝑚𝛿𝐹12	𝑁𝑜𝑟𝑚𝛿𝐹12	X
cana-5829	386	34	(	(	PUNCT
cana-5829	386	35	𝑥12	𝑥12	VERB
cana-5829	386	36	+	+	CCONJ
cana-5829	386	37	𝑖𝑦12	𝑖𝑦12	PROPN
cana-5829	386	38	)	)	PUNCT
cana-5829	386	39	𝑁𝑜𝑟𝑚𝛾𝐹12	𝑁𝑜𝑟𝑚𝛾𝐹12	NOUN
cana-5829	386	40	(	(	PUNCT
cana-5829	386	41	𝜇12	𝜇12	NOUN
cana-5829	386	42	+	+	CCONJ
cana-5829	386	43	𝑖𝜃12	𝑖𝜃12	PROPN
cana-5829	386	44	)	)	PUNCT
cana-5829	386	45	)	)	PUNCT
cana-5829	386	46	(	(	PUNCT
cana-5829	386	47	𝑁𝑜𝑟𝑚𝛿𝐹21	𝑁𝑜𝑟𝑚𝛿𝐹21	X
cana-5829	386	48	(	(	PUNCT
cana-5829	386	49	𝑥21	𝑥21	PROPN
cana-5829	386	50	+	+	CCONJ
cana-5829	386	51	𝑖𝑦21	𝑖𝑦21	PROPN
cana-5829	386	52	)	)	PUNCT
cana-5829	386	53	𝑁𝑜𝑟𝑚𝛾𝐹21	𝑁𝑜𝑟𝑚𝛾𝐹21	ADV
cana-5829	386	54	(	(	PUNCT
cana-5829	386	55	𝜇21	𝜇21	VERB
cana-5829	386	56	+	+	CCONJ
cana-5829	386	57	𝑖𝜃21	𝑖𝜃21	PROPN
cana-5829	386	58	)	)	PUNCT
cana-5829	386	59	)	)	PUNCT
cana-5829	386	60	(	(	PUNCT
cana-5829	386	61	𝑁𝑜𝑟𝑚𝛿𝐹22	𝑁𝑜𝑟𝑚𝛿𝐹22	X
cana-5829	386	62	(	(	PUNCT
cana-5829	386	63	𝑥22	𝑥22	NOUN
cana-5829	386	64	+	+	X
cana-5829	386	65	𝑖𝑦22	𝑖𝑦22	PROPN
cana-5829	386	66	)	)	PUNCT
cana-5829	386	67	𝑁𝑜𝑟𝑚𝛾𝐹22	𝑁𝑜𝑟𝑚𝛾𝐹22	NOUN
cana-5829	386	68	(	(	PUNCT
cana-5829	386	69	𝜇22	𝜇22	NOUN
cana-5829	386	70	+	+	CCONJ
cana-5829	386	71	𝑖𝜃22	𝑖𝜃22	PROPN
cana-5829	386	72	)	)	PUNCT
cana-5829	386	73	)	)	PUNCT
cana-5829	386	74	)	)	PUNCT
cana-5829	386	75	calculate	calculate	NOUN
cana-5829	386	76	,	,	PUNCT
cana-5829	386	77	𝑋11	𝑋11	PROPN
cana-5829	386	78	,	,	PUNCT
cana-5829	386	79	𝑋12	𝑋12	PROPN
cana-5829	386	80	,	,	PUNCT
cana-5829	386	81	𝑋21and	𝑋21and	PROPN
cana-5829	386	82	𝑋22	𝑋22	PROPN
cana-5829	386	83	,	,	PUNCT
cana-5829	386	84	we	we	PRON
cana-5829	386	85	have	have	VERB
cana-5829	386	86	communications	communication	NOUN
cana-5829	386	87	on	on	ADP
cana-5829	386	88	applied	apply	VERB
cana-5829	386	89	nonlinear	nonlinear	ADJ
cana-5829	386	90	analysis	analysis	NOUN
cana-5829	386	91	issn	issn	NOUN
cana-5829	386	92	:	:	PUNCT
cana-5829	386	93	1074	1074	NUM
cana-5829	386	94	-	-	PUNCT
cana-5829	386	95	133x	133x	NUM
cana-5829	386	96	vol	vol	VERB
cana-5829	386	97	32	32	NUM
cana-5829	386	98	no	no	NOUN
cana-5829	386	99	.	.	PUNCT
cana-5829	387	1	10s	10	NOUN
cana-5829	387	2	(	(	PUNCT
cana-5829	387	3	2025	2025	NUM
cana-5829	387	4	)	)	PUNCT
cana-5829	387	5	2939	2939	NUM
cana-5829	387	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5829	387	7	x11	x11	PROPN
cana-5829	387	8	=(	=(	NOUN
cana-5829	387	9	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	387	10	(	(	PUNCT
cana-5829	387	11	𝛼11	𝛼11	NOUN
cana-5829	387	12	+	+	PROPN
cana-5829	387	13	𝑖𝛽11	𝑖𝛽11	PROPN
cana-5829	387	14	)	)	PUNCT
cana-5829	387	15	𝑁𝑜𝑟𝑚µ𝐸11	𝑁𝑜𝑟𝑚µ𝐸11	NOUN
cana-5829	387	16	(	(	PUNCT
cana-5829	387	17	𝛾11	𝛾11	VERB
cana-5829	387	18	+	+	CCONJ
cana-5829	387	19	𝑖𝛿11	𝑖𝛿11	PROPN
cana-5829	387	20	)	)	PUNCT
cana-5829	387	21	)	)	PUNCT
cana-5829	387	22	∪	∪	ADV
cana-5829	387	23	(	(	PUNCT
cana-5829	387	24	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	387	25	(	(	PUNCT
cana-5829	387	26	𝑥11	𝑥11	ADV
cana-5829	387	27	+	+	CCONJ
cana-5829	387	28	𝑖𝑦11	𝑖𝑦11	NOUN
cana-5829	387	29	)	)	PUNCT
cana-5829	387	30	𝑁𝑜𝑟𝑚𝛾𝐹11	𝑁𝑜𝑟𝑚𝛾𝐹11	X
cana-5829	387	31	(	(	PUNCT
cana-5829	387	32	𝜇11	𝜇11	PROPN
cana-5829	387	33	+	+	PROPN
cana-5829	387	34	𝑖𝜃11	𝑖𝜃11	PROPN
cana-5829	387	35	)	)	PUNCT
cana-5829	387	36	)	)	PUNCT
cana-5829	387	37	x12	x12	NUM
cana-5829	387	38	=(	=(	NOUN
cana-5829	387	39	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	NOUN
cana-5829	387	40	(	(	PUNCT
cana-5829	387	41	𝛼12	𝛼12	NOUN
cana-5829	387	42	+	+	CCONJ
cana-5829	387	43	𝑖𝛽12	𝑖𝛽12	PROPN
cana-5829	387	44	)	)	PUNCT
cana-5829	387	45	𝑁𝑜𝑟𝑚µ𝐸12	𝑁𝑜𝑟𝑚µ𝐸12	NOUN
cana-5829	387	46	(	(	PUNCT
cana-5829	387	47	𝛾12	𝛾12	VERB
cana-5829	387	48	+	+	CCONJ
cana-5829	387	49	𝑖𝛿12	𝑖𝛿12	PROPN
cana-5829	387	50	)	)	PUNCT
cana-5829	387	51	)	)	PUNCT
cana-5829	387	52	∪	∪	NOUN
cana-5829	387	53	(	(	PUNCT
cana-5829	387	54	𝑁𝑜𝑟𝑚𝛿𝐹12	𝑁𝑜𝑟𝑚𝛿𝐹12	X
cana-5829	387	55	(	(	PUNCT
cana-5829	387	56	𝑥12	𝑥12	VERB
cana-5829	387	57	+	+	CCONJ
cana-5829	387	58	𝑖𝑦12	𝑖𝑦12	PROPN
cana-5829	387	59	)	)	PUNCT
cana-5829	387	60	𝑁𝑜𝑟𝑚𝛾𝐹12	𝑁𝑜𝑟𝑚𝛾𝐹12	NOUN
cana-5829	388	1	(	(	PUNCT
cana-5829	388	2	𝜇12	𝜇12	NOUN
cana-5829	388	3	+	+	CCONJ
cana-5829	388	4	𝑖𝜃12	𝑖𝜃12	PROPN
cana-5829	388	5	)	)	PUNCT
cana-5829	388	6	)	)	PUNCT
cana-5829	389	1	x21	x21	NUM
cana-5829	389	2	=(	=(	NOUN
cana-5829	389	3	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	PROPN
cana-5829	389	4	(	(	PUNCT
cana-5829	389	5	𝛼21	𝛼21	NOUN
cana-5829	389	6	+	+	X
cana-5829	389	7	𝑖𝛽21	𝑖𝛽21	PROPN
cana-5829	389	8	)	)	PUNCT
cana-5829	389	9	𝑁𝑜𝑟𝑚µ𝐸21	𝑁𝑜𝑟𝑚µ𝐸21	NOUN
cana-5829	389	10	(	(	PUNCT
cana-5829	389	11	𝛾21	𝛾21	NOUN
cana-5829	389	12	+	+	CCONJ
cana-5829	390	1	𝑖𝛿21	𝑖𝛿21	PROPN
cana-5829	390	2	)	)	PUNCT
cana-5829	390	3	)	)	PUNCT
cana-5829	391	1	∪	∪	ADV
cana-5829	391	2	(	(	PUNCT
cana-5829	391	3	𝑁𝑜𝑟𝑚𝛿𝐹21	𝑁𝑜𝑟𝑚𝛿𝐹21	ADP
cana-5829	391	4	(	(	PUNCT
cana-5829	391	5	𝑥21	𝑥21	NOUN
cana-5829	391	6	+	+	CCONJ
cana-5829	391	7	𝑖𝑦21	𝑖𝑦21	PROPN
cana-5829	391	8	)	)	PUNCT
cana-5829	391	9	𝑁𝑜𝑟𝑚𝛾𝐹21	𝑁𝑜𝑟𝑚𝛾𝐹21	ADV
cana-5829	391	10	(	(	PUNCT
cana-5829	391	11	𝜇21	𝜇21	VERB
cana-5829	391	12	+	+	CCONJ
cana-5829	391	13	𝑖𝜃21	𝑖𝜃21	PROPN
cana-5829	391	14	)	)	PUNCT
cana-5829	391	15	)	)	PUNCT
cana-5829	391	16	x22	x22	NUM
cana-5829	392	1	=(	=(	NOUN
cana-5829	392	2	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	PROPN
cana-5829	392	3	(	(	PUNCT
cana-5829	392	4	𝛼22	𝛼22	NOUN
cana-5829	392	5	+	+	CCONJ
cana-5829	392	6	𝑖𝛽22	𝑖𝛽22	PROPN
cana-5829	392	7	)	)	PUNCT
cana-5829	392	8	𝑁𝑜𝑟𝑚µ𝐸22	𝑁𝑜𝑟𝑚µ𝐸22	NOUN
cana-5829	392	9	(	(	PUNCT
cana-5829	392	10	𝛾22	𝛾22	PROPN
cana-5829	392	11	+	+	PROPN
cana-5829	392	12	𝑖𝛿22	𝑖𝛿22	PROPN
cana-5829	392	13	)	)	PUNCT
cana-5829	392	14	)	)	PUNCT
cana-5829	392	15	∪	∪	ADP
cana-5829	392	16	(	(	PUNCT
cana-5829	392	17	𝑁𝑜𝑟𝑚𝛿𝐹22	𝑁𝑜𝑟𝑚𝛿𝐹22	X
cana-5829	392	18	(	(	PUNCT
cana-5829	392	19	𝑥22	𝑥22	NOUN
cana-5829	392	20	+	+	X
cana-5829	392	21	𝑖𝑦22	𝑖𝑦22	PROPN
cana-5829	392	22	)	)	PUNCT
cana-5829	392	23	𝑁𝑜𝑟𝑚𝛾𝐹22	𝑁𝑜𝑟𝑚𝛾𝐹22	NOUN
cana-5829	392	24	(	(	PUNCT
cana-5829	392	25	𝜇22	𝜇22	NOUN
cana-5829	392	26	+	+	CCONJ
cana-5829	392	27	𝑖𝜃22	𝑖𝜃22	PROPN
cana-5829	392	28	)	)	PUNCT
cana-5829	392	29	)	)	PUNCT
cana-5829	392	30	applying	apply	VERB
cana-5829	392	31	formula	formula	NOUN
cana-5829	392	32	aebf	aebf	NOUN
cana-5829	392	33	=	=	SYM
cana-5829	392	34	{	{	PUNCT
cana-5829	392	35	(	(	PUNCT
cana-5829	392	36	x	x	NOUN
cana-5829	392	37	,	,	PUNCT
cana-5829	392	38	y	y	PROPN
cana-5829	392	39	)	)	PUNCT
cana-5829	392	40	,	,	PUNCT
cana-5829	392	41	max	max	PROPN
cana-5829	392	42	(	(	PUNCT
cana-5829	392	43	μa(x	μa(x	NOUN
cana-5829	392	44	)	)	PUNCT
cana-5829	392	45	,	,	PUNCT
cana-5829	392	46	μb(y	μb(y	NUM
cana-5829	392	47	)	)	PUNCT
cana-5829	392	48	)	)	PUNCT
cana-5829	392	49	,	,	PUNCT
cana-5829	392	50	min	min	PROPN
cana-5829	392	51	(	(	PUNCT
cana-5829	392	52	ϑa(x	ϑa(x	NOUN
cana-5829	392	53	)	)	PUNCT
cana-5829	392	54	,	,	PUNCT
cana-5829	392	55	ϑb(x	ϑb(x	NUM
cana-5829	392	56	)	)	PUNCT
cana-5829	392	57	):	):	PUNCT
cana-5829	392	58	xe	xe	PROPN
cana-5829	392	59	,	,	PUNCT
cana-5829	392	60	yf	yf	NUM
cana-5829	392	61	}	}	PUNCT
cana-5829	392	62	x11	x11	NOUN
cana-5829	393	1	=	=	NOUN
cana-5829	393	2	{	{	PUNCT
cana-5829	393	3	max	max	PROPN
cana-5829	393	4	(	(	PUNCT
cana-5829	393	5	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	393	6	(	(	PUNCT
cana-5829	393	7	𝛼11	𝛼11	NOUN
cana-5829	393	8	+	+	PROPN
cana-5829	393	9	𝑖𝛽11	𝑖𝛽11	PROPN
cana-5829	393	10	)	)	PUNCT
cana-5829	393	11	,	,	PUNCT
cana-5829	393	12	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	393	13	(	(	PUNCT
cana-5829	393	14	𝑥11	𝑥11	ADV
cana-5829	393	15	+	+	CCONJ
cana-5829	393	16	𝑖𝑦11	𝑖𝑦11	PROPN
cana-5829	393	17	)	)	PUNCT
cana-5829	393	18	,	,	PUNCT
cana-5829	393	19	min	min	PROPN
cana-5829	393	20	(	(	PUNCT
cana-5829	393	21	normµe11	normµe11	NOUN
cana-5829	393	22	(	(	PUNCT
cana-5829	393	23	𝛾11	𝛾11	VERB
cana-5829	393	24	+	+	CCONJ
cana-5829	393	25	𝑖𝛿11	𝑖𝛿11	PROPN
cana-5829	393	26	)	)	PUNCT
cana-5829	393	27	,	,	PUNCT
cana-5829	393	28	normγe11	normγe11	NOUN
cana-5829	393	29	(	(	PUNCT
cana-5829	393	30	𝜇11	𝜇11	PROPN
cana-5829	393	31	+	+	PROPN
cana-5829	393	32	𝑖𝜃11	𝑖𝜃11	PROPN
cana-5829	393	33	)	)	PUNCT
cana-5829	393	34	}	}	PUNCT
cana-5829	393	35	where	where	SCONJ
cana-5829	393	36	∣μ11∣=	∣μ11∣=	NOUN
cana-5829	393	37	(	(	PUNCT
cana-5829	393	38	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	393	39	(	(	PUNCT
cana-5829	393	40	𝛼11))2	𝛼11))2	PROPN
cana-5829	393	41	+	+	CCONJ
cana-5829	393	42	(	(	PUNCT
cana-5829	393	43	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	393	44	(	(	PUNCT
cana-5829	393	45	𝛽11))2	𝛽11))2	X
cana-5829	393	46	<	<	X
cana-5829	393	47	1	1	NUM
cana-5829	393	48	,	,	PUNCT
cana-5829	393	49	∣ν11∣=	∣ν11∣=	PROPN
cana-5829	393	50	(	(	PUNCT
cana-5829	393	51	normµe11	normµe11	PROPN
cana-5829	393	52	(	(	PUNCT
cana-5829	393	53	𝛾11))2	𝛾11))2	X
cana-5829	393	54	+	+	CCONJ
cana-5829	393	55	(	(	PUNCT
cana-5829	393	56	normγe11	normγe11	NOUN
cana-5829	393	57	(	(	PUNCT
cana-5829	393	58	𝛿11	𝛿11	NOUN
cana-5829	393	59	)	)	PUNCT
cana-5829	393	60	)	)	PUNCT
cana-5829	393	61	2	2	NUM
cana-5829	393	62	<	<	SYM
cana-5829	393	63	1	1	NUM
cana-5829	393	64	,	,	PUNCT
cana-5829	393	65	∣μ11∣+∣ν11∣	∣μ11∣+∣ν11∣	VERB
cana-5829	393	66	≤	≤	NUM
cana-5829	393	67	1	1	NUM
cana-5829	393	68	.	.	NUM
cana-5829	393	69	x12	x12	NUM
cana-5829	394	1	=	=	SYM
cana-5829	394	2	{	{	PUNCT
cana-5829	394	3	max	max	PROPN
cana-5829	394	4	(	(	PUNCT
cana-5829	394	5	normϑe12	normϑe12	PROPN
cana-5829	394	6	(	(	PUNCT
cana-5829	394	7	𝛼12	𝛼12	NUM
cana-5829	394	8	+	+	CCONJ
cana-5829	394	9	𝑖𝛽12	𝑖𝛽12	PROPN
cana-5829	394	10	)	)	PUNCT
cana-5829	394	11	,	,	PUNCT
cana-5829	394	12	normδf12	normδf12	NOUN
cana-5829	394	13	(	(	PUNCT
cana-5829	394	14	𝑥12	𝑥12	VERB
cana-5829	394	15	+	+	CCONJ
cana-5829	394	16	𝑖𝑦12	𝑖𝑦12	PROPN
cana-5829	394	17	)	)	PUNCT
cana-5829	394	18	,	,	PUNCT
cana-5829	394	19	min	min	PROPN
cana-5829	394	20	(	(	PUNCT
cana-5829	394	21	normµe12	normµe12	NOUN
cana-5829	394	22	(	(	PUNCT
cana-5829	394	23	𝛾12	𝛾12	VERB
cana-5829	394	24	+	+	CCONJ
cana-5829	394	25	𝑖𝛿12	𝑖𝛿12	PROPN
cana-5829	394	26	)	)	PUNCT
cana-5829	394	27	,	,	PUNCT
cana-5829	394	28	normγe12	normγe12	NOUN
cana-5829	394	29	(	(	PUNCT
cana-5829	394	30	𝜇12	𝜇12	NOUN
cana-5829	394	31	+	+	X
cana-5829	394	32	𝑖𝜃12	𝑖𝜃12	PROPN
cana-5829	394	33	)	)	PUNCT
cana-5829	394	34	}	}	PUNCT
cana-5829	394	35	where	where	SCONJ
cana-5829	394	36	∣μ12∣=	∣μ12∣=	X
cana-5829	394	37	(	(	PUNCT
cana-5829	394	38	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	NOUN
cana-5829	394	39	(	(	PUNCT
cana-5829	394	40	𝛼12))2	𝛼12))2	X
cana-5829	394	41	+	+	CCONJ
cana-5829	394	42	(	(	PUNCT
cana-5829	394	43	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	NOUN
cana-5829	394	44	(	(	PUNCT
cana-5829	394	45	𝛽12))2	𝛽12))2	X
cana-5829	394	46	<	<	X
cana-5829	394	47	1	1	NUM
cana-5829	394	48	,	,	PUNCT
cana-5829	394	49	∣ν11∣=	∣ν11∣=	PROPN
cana-5829	394	50	(	(	PUNCT
cana-5829	394	51	normµe12	normµe12	VERB
cana-5829	394	52	(	(	PUNCT
cana-5829	394	53	𝛾12))2	𝛾12))2	X
cana-5829	394	54	+	+	CCONJ
cana-5829	394	55	(	(	PUNCT
cana-5829	394	56	normγe12	normγe12	ADJ
cana-5829	394	57	(	(	PUNCT
cana-5829	394	58	𝛿12	𝛿12	NOUN
cana-5829	394	59	)	)	PUNCT
cana-5829	394	60	)	)	PUNCT
cana-5829	394	61	2	2	NUM
cana-5829	394	62	<	<	X
cana-5829	394	63	1	1	NUM
cana-5829	394	64	,	,	PUNCT
cana-5829	394	65	∣μ12∣+∣ν12∣	∣μ12∣+∣ν12∣	ADJ
cana-5829	394	66	≤	≤	NUM
cana-5829	394	67	1	1	NUM
cana-5829	394	68	.	.	PUNCT
cana-5829	395	1	x21	x21	NUM
cana-5829	396	1	=	=	SYM
cana-5829	396	2	{	{	PUNCT
cana-5829	396	3	max	max	PROPN
cana-5829	396	4	(	(	PUNCT
cana-5829	396	5	normϑe21	normϑe21	PROPN
cana-5829	396	6	(	(	PUNCT
cana-5829	396	7	𝛼21	𝛼21	NOUN
cana-5829	396	8	+	+	X
cana-5829	396	9	𝑖𝛽21	𝑖𝛽21	PROPN
cana-5829	396	10	)	)	PUNCT
cana-5829	396	11	,	,	PUNCT
cana-5829	396	12	normδf21	normδf21	NOUN
cana-5829	396	13	(	(	PUNCT
cana-5829	396	14	𝑥21	𝑥21	NOUN
cana-5829	396	15	+	+	CCONJ
cana-5829	396	16	𝑖𝑦21	𝑖𝑦21	PROPN
cana-5829	396	17	)	)	PUNCT
cana-5829	396	18	,	,	PUNCT
cana-5829	396	19	min	min	PROPN
cana-5829	396	20	(	(	PUNCT
cana-5829	396	21	normµe21	normµe21	X
cana-5829	396	22	(	(	PUNCT
cana-5829	396	23	𝛾21	𝛾21	NOUN
cana-5829	396	24	+	+	CCONJ
cana-5829	396	25	𝑖𝛿21	𝑖𝛿21	PROPN
cana-5829	396	26	)	)	PUNCT
cana-5829	396	27	,	,	PUNCT
cana-5829	396	28	normγe21	normγe21	ADV
cana-5829	396	29	(	(	PUNCT
cana-5829	396	30	𝜇21	𝜇21	VERB
cana-5829	396	31	+	+	CCONJ
cana-5829	396	32	𝑖𝜃21	𝑖𝜃21	PROPN
cana-5829	396	33	)	)	PUNCT
cana-5829	396	34	}	}	PUNCT
cana-5829	396	35	where	where	SCONJ
cana-5829	396	36	∣μ21∣=	∣μ21∣=	X
cana-5829	396	37	(	(	PUNCT
cana-5829	396	38	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	X
cana-5829	396	39	(	(	PUNCT
cana-5829	396	40	𝛼21))2	𝛼21))2	X
cana-5829	396	41	+	+	CCONJ
cana-5829	396	42	(	(	PUNCT
cana-5829	396	43	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	X
cana-5829	396	44	(	(	PUNCT
cana-5829	396	45	𝛽21))2	𝛽21))2	X
cana-5829	396	46	<	<	X
cana-5829	396	47	1	1	NUM
cana-5829	396	48	,	,	PUNCT
cana-5829	396	49	∣ν21∣=	∣ν21∣=	PROPN
cana-5829	396	50	(	(	PUNCT
cana-5829	396	51	normµe21	normµe21	X
cana-5829	396	52	(	(	PUNCT
cana-5829	396	53	𝛾21))2	𝛾21))2	X
cana-5829	397	1	+	+	CCONJ
cana-5829	397	2	(	(	PUNCT
cana-5829	397	3	normγe21	normγe21	INTJ
cana-5829	397	4	(	(	PUNCT
cana-5829	397	5	𝛿21	𝛿21	PROPN
cana-5829	397	6	)	)	PUNCT
cana-5829	397	7	)	)	PUNCT
cana-5829	397	8	2	2	NUM
cana-5829	397	9	<	<	SYM
cana-5829	397	10	1	1	NUM
cana-5829	397	11	,	,	PUNCT
cana-5829	397	12	∣μ21∣+∣ν21∣	∣μ21∣+∣ν21∣	VERB
cana-5829	397	13	≤	≤	NUM
cana-5829	397	14	1	1	NUM
cana-5829	397	15	.	.	PUNCT
cana-5829	397	16	x22	x22	NOUN
cana-5829	398	1	=	=	PRON
cana-5829	398	2	{	{	PUNCT
cana-5829	398	3	max	max	PROPN
cana-5829	398	4	(	(	PUNCT
cana-5829	398	5	normϑe22	normϑe22	NOUN
cana-5829	398	6	(	(	PUNCT
cana-5829	398	7	𝛼22	𝛼22	NOUN
cana-5829	398	8	,	,	PUNCT
cana-5829	398	9	𝑥22	𝑥22	NOUN
cana-5829	398	10	)	)	PUNCT
cana-5829	398	11	+	+	CCONJ
cana-5829	398	12	𝑖𝛽22	𝑖𝛽22	PROPN
cana-5829	398	13	)	)	PUNCT
cana-5829	398	14	,	,	PUNCT
cana-5829	398	15	inormδf22	inormδf22	NOUN
cana-5829	398	16	(	(	PUNCT
cana-5829	398	17	+	+	PROPN
cana-5829	398	18	𝑖𝑦22	𝑖𝑦22	PROPN
cana-5829	398	19	)	)	PUNCT
cana-5829	398	20	,	,	PUNCT
cana-5829	398	21	min	min	NOUN
cana-5829	398	22	(	(	PUNCT
cana-5829	398	23	normµe22	normµe22	X
cana-5829	398	24	(	(	PUNCT
cana-5829	398	25	𝛾22	𝛾22	PROPN
cana-5829	398	26	+	+	PROPN
cana-5829	398	27	𝑖𝛿22	𝑖𝛿22	PROPN
cana-5829	398	28	)	)	PUNCT
cana-5829	398	29	,	,	PUNCT
cana-5829	398	30	normγe22	normγe22	NOUN
cana-5829	398	31	(	(	PUNCT
cana-5829	398	32	𝜇22	𝜇22	NOUN
cana-5829	398	33	+	+	CCONJ
cana-5829	398	34	𝑖𝜃22	𝑖𝜃22	PROPN
cana-5829	398	35	)	)	PUNCT
cana-5829	398	36	}	}	PUNCT
cana-5829	398	37	where	where	SCONJ
cana-5829	398	38	∣μ22∣=	∣μ22∣=	PROPN
cana-5829	398	39	(	(	PUNCT
cana-5829	398	40	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	PROPN
cana-5829	398	41	(	(	PUNCT
cana-5829	398	42	𝛼22))2	𝛼22))2	PUNCT
cana-5829	398	43	+	+	CCONJ
cana-5829	398	44	(	(	PUNCT
cana-5829	398	45	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	NUM
cana-5829	398	46	(	(	PUNCT
cana-5829	398	47	𝛽22))2	𝛽22))2	X
cana-5829	398	48	<	<	X
cana-5829	398	49	1	1	NUM
cana-5829	398	50	,	,	PUNCT
cana-5829	398	51	∣ν11∣=	∣ν11∣=	X
cana-5829	398	52	(	(	PUNCT
cana-5829	398	53	normµe22	normµe22	X
cana-5829	398	54	(	(	PUNCT
cana-5829	398	55	𝛾22))2	𝛾22))2	X
cana-5829	398	56	+	+	CCONJ
cana-5829	398	57	(	(	PUNCT
cana-5829	398	58	normγe22	normγe22	X
cana-5829	398	59	(	(	PUNCT
cana-5829	398	60	𝛿22	𝛿22	NOUN
cana-5829	398	61	)	)	PUNCT
cana-5829	398	62	)	)	PUNCT
cana-5829	398	63	2	2	NUM
cana-5829	398	64	<	<	X
cana-5829	398	65	1	1	NUM
cana-5829	398	66	,	,	PUNCT
cana-5829	398	67	∣μ22∣+∣ν22∣	∣μ22∣+∣ν22∣	ADV
cana-5829	398	68	≤	≤	NUM
cana-5829	398	69	1	1	NUM
cana-5829	398	70	.	.	PUNCT
cana-5829	398	71	x11	x11	PROPN
cana-5829	398	72	=(	=(	PROPN
cana-5829	398	73	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	398	74	(	(	PUNCT
cana-5829	398	75	max	max	PROPN
cana-5829	398	76	(	(	PUNCT
cana-5829	398	77	𝛼11	𝛼11	PROPN
cana-5829	398	78	,	,	PUNCT
cana-5829	398	79	𝑥11	𝑥11	ADV
cana-5829	398	80	)	)	PUNCT
cana-5829	398	81	+	+	CCONJ
cana-5829	398	82	𝑖	𝑖	SYM
cana-5829	398	83	max	max	PROPN
cana-5829	398	84	(	(	PUNCT
cana-5829	398	85	𝛽11	𝛽11	PROPN
cana-5829	398	86	,	,	PUNCT
cana-5829	398	87	𝑦11	𝑦11	NOUN
cana-5829	398	88	)	)	PUNCT
cana-5829	398	89	)	)	PUNCT
cana-5829	398	90	)	)	PUNCT
cana-5829	398	91	,	,	PUNCT
cana-5829	398	92	normµe11	normµe11	NOUN
cana-5829	398	93	(	(	PUNCT
cana-5829	398	94	min	min	NOUN
cana-5829	398	95	(	(	PUNCT
cana-5829	398	96	𝛾11	𝛾11	VERB
cana-5829	398	97	,	,	PUNCT
cana-5829	398	98	𝜇11	𝜇11	ADJ
cana-5829	398	99	)	)	PUNCT
cana-5829	398	100	+	+	CCONJ
cana-5829	399	1	𝑖min	𝑖min	NOUN
cana-5829	399	2	(	(	PUNCT
cana-5829	399	3	𝛿11	𝛿11	NOUN
cana-5829	399	4	,	,	PUNCT
cana-5829	399	5	𝜃11	𝜃11	NOUN
cana-5829	399	6	)	)	PUNCT
cana-5829	399	7	)	)	PUNCT
cana-5829	400	1	where	where	SCONJ
cana-5829	400	2	∣μ11∣=	∣μ11∣=	NOUN
cana-5829	400	3	(	(	PUNCT
cana-5829	400	4	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	400	5	(	(	PUNCT
cana-5829	400	6	max(𝛼11	max(𝛼11	NUM
cana-5829	400	7	,	,	PUNCT
cana-5829	400	8	𝑥11))2	𝑥11))2	X
cana-5829	400	9	+	+	CCONJ
cana-5829	400	10	(	(	PUNCT
cana-5829	400	11	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	400	12	max(𝛽11	max(𝛽11	PROPN
cana-5829	400	13	,	,	PUNCT
cana-5829	400	14	𝑦11))2	𝑦11))2	X
cana-5829	400	15	+	+	ADJ
cana-5829	400	16	(	(	PUNCT
cana-5829	400	17	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	400	18	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
cana-5829	400	19	(	(	PUNCT
cana-5829	400	20	𝛾11	𝛾11	VERB
cana-5829	400	21	,	,	PUNCT
cana-5829	400	22	𝜇11))2	𝜇11))2	ADJ
cana-5829	400	23	+	+	ADJ
cana-5829	400	24	(	(	PUNCT
cana-5829	400	25	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	400	26	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
cana-5829	400	27	(	(	PUNCT
cana-5829	400	28	𝛾11	𝛾11	VERB
cana-5829	400	29	,	,	PUNCT
cana-5829	400	30	𝜇11))2	𝜇11))2	PRON
cana-5829	400	31	<	<	X
cana-5829	400	32	1	1	NUM
cana-5829	400	33	,	,	PUNCT
cana-5829	400	34	∣ν11∣=	∣ν11∣=	PROPN
cana-5829	400	35	(	(	PUNCT
cana-5829	400	36	normµe11	normµe11	NOUN
cana-5829	400	37	𝑚𝑖𝑛(𝛾11	𝑚𝑖𝑛(𝛾11	PROPN
cana-5829	400	38	,	,	PUNCT
cana-5829	400	39	𝜇11))2	𝜇11))2	X
cana-5829	400	40	+	+	ADJ
cana-5829	400	41	(	(	PUNCT
cana-5829	400	42	𝑁𝑜𝑟𝑚𝛾𝐸11	𝑁𝑜𝑟𝑚𝛾𝐸11	X
cana-5829	400	43	𝑚𝑖𝑛(𝛿11	𝑚𝑖𝑛(𝛿11	PROPN
cana-5829	400	44	,	,	PUNCT
cana-5829	400	45	𝜃11))2	𝜃11))2	X
cana-5829	400	46	<	<	X
cana-5829	400	47	1	1	NUM
cana-5829	400	48	,	,	PUNCT
cana-5829	400	49	∣μ11∣+∣ν11∣	∣μ11∣+∣ν11∣	VERB
cana-5829	400	50	≤	≤	NUM
cana-5829	400	51	1	1	NUM
cana-5829	400	52	.	.	PUNCT
cana-5829	401	1	x12	x12	NUM
cana-5829	401	2	=(	=(	NOUN
cana-5829	401	3	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	NOUN
cana-5829	401	4	(	(	PUNCT
cana-5829	401	5	max	max	PROPN
cana-5829	401	6	(	(	PUNCT
cana-5829	401	7	𝛼12	𝛼12	PROPN
cana-5829	401	8	,	,	PUNCT
cana-5829	401	9	𝑥12	𝑥12	VERB
cana-5829	401	10	)	)	PUNCT
cana-5829	401	11	+	+	CCONJ
cana-5829	401	12	𝑖	𝑖	SYM
cana-5829	401	13	max	max	PROPN
cana-5829	401	14	(	(	PUNCT
cana-5829	401	15	𝛽12	𝛽12	PROPN
cana-5829	401	16	,	,	PUNCT
cana-5829	401	17	𝑦12	𝑦12	NOUN
cana-5829	401	18	)	)	PUNCT
cana-5829	401	19	)	)	PUNCT
cana-5829	401	20	,	,	PUNCT
cana-5829	401	21	normµe12	normµe12	NOUN
cana-5829	401	22	(	(	PUNCT
cana-5829	401	23	min	min	PROPN
cana-5829	401	24	(	(	PUNCT
cana-5829	401	25	𝛾12	𝛾12	PROPN
cana-5829	401	26	,	,	PUNCT
cana-5829	401	27	𝜇12	𝜇12	NOUN
cana-5829	401	28	)	)	PUNCT
cana-5829	402	1	+	+	CCONJ
cana-5829	403	1	𝑖min	𝑖min	NOUN
cana-5829	403	2	(	(	PUNCT
cana-5829	403	3	𝛿12	𝛿12	PROPN
cana-5829	403	4	,	,	PUNCT
cana-5829	403	5	𝜃12	𝜃12	NUM
cana-5829	403	6	)	)	PUNCT
cana-5829	403	7	)	)	PUNCT
cana-5829	403	8	where	where	SCONJ
cana-5829	403	9	∣μ12∣=(𝑁𝑜𝑟𝑚𝜗𝐸12	∣μ12∣=(𝑁𝑜𝑟𝑚𝜗𝐸12	X
cana-5829	403	10	𝑚𝑎𝑥	𝑚𝑎𝑥	NOUN
cana-5829	403	11	(	(	PUNCT
cana-5829	403	12	𝛼12	𝛼12	NUM
cana-5829	403	13	,	,	PUNCT
cana-5829	403	14	𝑥12))2	𝑥12))2	X
cana-5829	404	1	+	+	ADJ
cana-5829	404	2	(	(	PUNCT
cana-5829	404	3	𝑁𝑜𝑟𝑚𝛿𝐹12	𝑁𝑜𝑟𝑚𝛿𝐹12	ADV
cana-5829	404	4	𝑚𝑎𝑥	𝑚𝑎𝑥	ADJ
cana-5829	404	5	(	(	PUNCT
cana-5829	404	6	𝛽12	𝛽12	PROPN
cana-5829	404	7	,	,	PUNCT
cana-5829	404	8	𝑦12))2	𝑦12))2	X
cana-5829	404	9	<	<	X
cana-5829	404	10	1	1	NUM
cana-5829	404	11	,	,	PUNCT
cana-5829	404	12	∣ν12∣=	∣ν12∣=	NOUN
cana-5829	404	13	(	(	PUNCT
cana-5829	404	14	normµe12	normµe12	NOUN
cana-5829	404	15	𝑚𝑖𝑛(𝛾12	𝑚𝑖𝑛(𝛾12	NUM
cana-5829	404	16	,	,	PUNCT
cana-5829	404	17	𝜇12))2	𝜇12))2	X
cana-5829	404	18	+	+	ADJ
cana-5829	404	19	(	(	PUNCT
cana-5829	404	20	𝑁𝑜𝑟𝑚𝛾𝐸12	𝑁𝑜𝑟𝑚𝛾𝐸12	NOUN
cana-5829	404	21	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
cana-5829	404	22	(	(	PUNCT
cana-5829	404	23	(	(	PUNCT
cana-5829	404	24	𝛿12	𝛿12	PROPN
cana-5829	404	25	,	,	PUNCT
cana-5829	404	26	𝜃12))2	𝜃12))2	X
cana-5829	404	27	<	<	X
cana-5829	404	28	1	1	NUM
cana-5829	404	29	,	,	PUNCT
cana-5829	404	30	∣μ12∣+∣ν12∣	∣μ12∣+∣ν12∣	ADJ
cana-5829	404	31	≤	≤	NUM
cana-5829	404	32	1	1	NUM
cana-5829	404	33	.	.	PUNCT
cana-5829	405	1	communications	communication	NOUN
cana-5829	405	2	on	on	ADP
cana-5829	405	3	applied	apply	VERB
cana-5829	405	4	nonlinear	nonlinear	ADJ
cana-5829	405	5	analysis	analysis	NOUN
cana-5829	405	6	issn	issn	NOUN
cana-5829	405	7	:	:	PUNCT
cana-5829	405	8	1074	1074	NUM
cana-5829	405	9	-	-	PUNCT
cana-5829	405	10	133x	133x	NUM
cana-5829	405	11	vol	vol	VERB
cana-5829	405	12	32	32	NUM
cana-5829	405	13	no	no	NOUN
cana-5829	405	14	.	.	PUNCT
cana-5829	406	1	10s	10	NOUN
cana-5829	406	2	(	(	PUNCT
cana-5829	406	3	2025	2025	NUM
cana-5829	406	4	)	)	PUNCT
cana-5829	406	5	2940	2940	NUM
cana-5829	406	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5829	407	1	x21	x21	NUM
cana-5829	407	2	=	=	PRON
cana-5829	407	3	{	{	PUNCT
cana-5829	407	4	(	(	PUNCT
cana-5829	407	5	normϑe21	normϑe21	ADJ
cana-5829	407	6	𝑚𝑎𝑥	𝑚𝑎𝑥	NOUN
cana-5829	407	7	(	(	PUNCT
cana-5829	407	8	𝛼21	𝛼21	NOUN
cana-5829	407	9	,	,	PUNCT
cana-5829	407	10	𝑥21	𝑥21	NOUN
cana-5829	407	11	)	)	PUNCT
cana-5829	407	12	+	+	NUM
cana-5829	407	13	inormδf21	inormδf21	NOUN
cana-5829	407	14	𝑚𝑎𝑥(𝛽21	𝑚𝑎𝑥(𝛽21	NOUN
cana-5829	407	15	,	,	PUNCT
cana-5829	407	16	𝑦21	𝑦21	NOUN
cana-5829	407	17	)	)	PUNCT
cana-5829	407	18	,	,	PUNCT
cana-5829	407	19	(	(	PUNCT
cana-5829	407	20	normµe21	normµe21	X
cana-5829	407	21	𝑚𝑖𝑛(𝛾21	𝑚𝑖𝑛(𝛾21	NOUN
cana-5829	407	22	,	,	PUNCT
cana-5829	407	23	𝜇21	𝜇21	NOUN
cana-5829	407	24	)	)	PUNCT
cana-5829	408	1	+	+	CCONJ
cana-5829	408	2	inormγe21	inormγe21	ADV
cana-5829	408	3	𝑚𝑖𝑛(𝛿21	𝑚𝑖𝑛(𝛿21	PROPN
cana-5829	408	4	,	,	PUNCT
cana-5829	408	5	𝜃21	𝜃21	NOUN
cana-5829	408	6	)	)	PUNCT
cana-5829	408	7	}	}	PUNCT
cana-5829	409	1	where	where	SCONJ
cana-5829	409	2	∣μ21∣=(𝑁𝑜𝑟𝑚𝜗𝐸21	∣μ21∣=(𝑁𝑜𝑟𝑚𝜗𝐸21	NOUN
cana-5829	409	3	𝑚𝑎𝑥	𝑚𝑎𝑥	NOUN
cana-5829	409	4	(	(	PUNCT
cana-5829	409	5	𝛼21	𝛼21	NOUN
cana-5829	409	6	,	,	PUNCT
cana-5829	409	7	𝑥21))2	𝑥21))2	X
cana-5829	410	1	+	+	ADV
cana-5829	410	2	(	(	PUNCT
cana-5829	410	3	𝑁𝑜𝑟𝑚𝛿𝐹21	𝑁𝑜𝑟𝑚𝛿𝐹21	ADP
cana-5829	410	4	𝑚𝑎𝑥	𝑚𝑎𝑥	PROPN
cana-5829	410	5	(	(	PUNCT
cana-5829	410	6	𝛽21	𝛽21	PROPN
cana-5829	410	7	,	,	PUNCT
cana-5829	410	8	𝑦21))2	𝑦21))2	PROPN
cana-5829	410	9	<	<	X
cana-5829	410	10	1	1	NUM
cana-5829	410	11	,	,	PUNCT
cana-5829	410	12	∣ν21∣=	∣ν21∣=	PRON
cana-5829	410	13	(	(	PUNCT
cana-5829	410	14	normµe21	normµe21	NOUN
cana-5829	410	15	𝑚𝑖𝑛(𝛾21	𝑚𝑖𝑛(𝛾21	NOUN
cana-5829	410	16	,	,	PUNCT
cana-5829	410	17	𝜇21))2	𝜇21))2	X
cana-5829	410	18	+	+	ADJ
cana-5829	410	19	(	(	PUNCT
cana-5829	410	20	𝑁𝑜𝑟𝑚𝛾𝐸21	𝑁𝑜𝑟𝑚𝛾𝐸21	PROPN
cana-5829	410	21	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
cana-5829	410	22	(	(	PUNCT
cana-5829	410	23	(	(	PUNCT
cana-5829	410	24	𝛿21	𝛿21	PROPN
cana-5829	410	25	,	,	PUNCT
cana-5829	410	26	𝜃21))2	𝜃21))2	X
cana-5829	410	27	<	<	X
cana-5829	410	28	1	1	NUM
cana-5829	410	29	,	,	PUNCT
cana-5829	410	30	∣μ21∣+∣ν21∣	∣μ21∣+∣ν21∣	VERB
cana-5829	410	31	≤	≤	NUM
cana-5829	410	32	1	1	NUM
cana-5829	410	33	.	.	PUNCT
cana-5829	410	34	x22	x22	NOUN
cana-5829	411	1	=	=	SYM
cana-5829	411	2	{	{	PUNCT
cana-5829	411	3	max	max	PROPN
cana-5829	411	4	(	(	PUNCT
cana-5829	411	5	normϑe22	normϑe22	NOUN
cana-5829	411	6	(	(	PUNCT
cana-5829	411	7	𝛼22	𝛼22	NOUN
cana-5829	411	8	,	,	PUNCT
cana-5829	411	9	𝑥22	𝑥22	NOUN
cana-5829	411	10	)	)	PUNCT
cana-5829	411	11	)	)	PUNCT
cana-5829	411	12	,	,	PUNCT
cana-5829	411	13	inormδf22	inormδf22	NOUN
cana-5829	411	14	𝑚𝑎𝑥	𝑚𝑎𝑥	NOUN
cana-5829	411	15	(	(	PUNCT
cana-5829	411	16	𝛽22	𝛽22	NOUN
cana-5829	411	17	,	,	PUNCT
cana-5829	411	18	𝑦22	𝑦22	NUM
cana-5829	411	19	)	)	PUNCT
cana-5829	411	20	,	,	PUNCT
cana-5829	411	21	min	min	NOUN
cana-5829	411	22	(	(	PUNCT
cana-5829	411	23	normµe22	normµe22	X
cana-5829	411	24	(	(	PUNCT
cana-5829	411	25	𝛾22	𝛾22	ADJ
cana-5829	411	26	,	,	PUNCT
cana-5829	411	27	𝜇21	𝜇21	NOUN
cana-5829	411	28	)	)	PUNCT
cana-5829	411	29	,	,	PUNCT
cana-5829	411	30	normγe22	normγe22	NOUN
cana-5829	411	31	(	(	PUNCT
cana-5829	411	32	𝛿22	𝛿22	NOUN
cana-5829	411	33	,	,	PUNCT
cana-5829	411	34	𝜃22	𝜃22	NOUN
cana-5829	411	35	)	)	PUNCT
cana-5829	411	36	}	}	PUNCT
cana-5829	411	37	where	where	SCONJ
cana-5829	411	38	∣μ22∣=(𝑁𝑜𝑟𝑚𝜗𝐸22	∣μ22∣=(𝑁𝑜𝑟𝑚𝜗𝐸22	ADJ
cana-5829	411	39	𝑚𝑎𝑥	𝑚𝑎𝑥	X
cana-5829	411	40	(	(	PUNCT
cana-5829	411	41	𝛼22	𝛼22	NOUN
cana-5829	411	42	,	,	PUNCT
cana-5829	411	43	𝑥22))2	𝑥22))2	VERB
cana-5829	412	1	+	+	ADV
cana-5829	412	2	(	(	PUNCT
cana-5829	412	3	𝑁𝑜𝑟𝑚𝛿𝐹22	𝑁𝑜𝑟𝑚𝛿𝐹22	X
cana-5829	412	4	𝑚𝑎𝑥	𝑚𝑎𝑥	NOUN
cana-5829	412	5	(	(	PUNCT
cana-5829	412	6	𝛽22	𝛽22	VERB
cana-5829	412	7	,	,	PUNCT
cana-5829	412	8	𝑦22))2	𝑦22))2	X
cana-5829	412	9	<	<	X
cana-5829	412	10	1	1	NUM
cana-5829	412	11	,	,	PUNCT
cana-5829	412	12	∣ν21∣=	∣ν21∣=	PRON
cana-5829	412	13	(	(	PUNCT
cana-5829	412	14	normµe22	normµe22	X
cana-5829	412	15	𝑚𝑖𝑛(𝛾22	𝑚𝑖𝑛(𝛾22	ADJ
cana-5829	412	16	,	,	PUNCT
cana-5829	412	17	𝜇22))2	𝜇22))2	VERB
cana-5829	412	18	+	+	ADJ
cana-5829	412	19	(	(	PUNCT
cana-5829	412	20	𝑁𝑜𝑟𝑚𝛾𝐸22	𝑁𝑜𝑟𝑚𝛾𝐸22	INTJ
cana-5829	412	21	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
cana-5829	412	22	(	(	PUNCT
cana-5829	412	23	(	(	PUNCT
cana-5829	412	24	𝛿22	𝛿22	NOUN
cana-5829	412	25	,	,	PUNCT
cana-5829	412	26	𝜃22))2	𝜃22))2	PUNCT
cana-5829	412	27	<	<	X
cana-5829	412	28	1	1	NUM
cana-5829	412	29	,	,	PUNCT
cana-5829	412	30	∣μ22∣+∣ν22∣	∣μ22∣+∣ν22∣	ADV
cana-5829	412	31	≤	≤	NUM
cana-5829	412	32	1	1	NUM
cana-5829	412	33	.	.	PUNCT
cana-5829	413	1	we	we	PRON
cana-5829	413	2	have	have	VERB
cana-5829	413	3	norm𝐴𝐸	norm𝐴𝐸	PROPN
cana-5829	413	4	∪	∪	ADJ
cana-5829	413	5	𝑁𝑜𝑟𝑚𝐵𝐹=	𝑁𝑜𝑟𝑚𝐵𝐹=	PROPN
cana-5829	413	6	(	(	PUNCT
cana-5829	413	7	𝑋11	𝑋11	PROPN
cana-5829	413	8	𝑋12	𝑋12	PROPN
cana-5829	413	9	𝑋21	𝑋21	NOUN
cana-5829	413	10	𝑋22	𝑋22	ADJ
cana-5829	413	11	)	)	PUNCT
cana-5829	413	12	is	be	AUX
cana-5829	413	13	normalization	normalization	NOUN
cana-5829	413	14	of	of	ADP
cana-5829	413	15	complex	complex	ADJ
cana-5829	413	16	intuitionistic	intuitionistic	ADJ
cana-5829	413	17	fuzzy	fuzzy	ADJ
cana-5829	413	18	matrix	matrix	NOUN
cana-5829	413	19	.	.	PUNCT
cana-5829	414	1	example5.2.4	example5.2.4	NOUN
cana-5829	414	2	:	:	PUNCT
cana-5829	414	3	if	if	SCONJ
cana-5829	414	4	𝐴𝐸=	𝐴𝐸=	NOUN
cana-5829	414	5	(	(	PUNCT
cana-5829	414	6	(	(	PUNCT
cana-5829	414	7	0.6	0.6	NUM
cana-5829	414	8	+	+	CCONJ
cana-5829	414	9	0.2i	0.2i	ADJ
cana-5829	414	10	,	,	PUNCT
cana-5829	414	11	0.3	0.3	NUM
cana-5829	414	12	+	+	NOUN
cana-5829	414	13	0.1i)(0.4	0.1i)(0.4	X
cana-5829	415	1	+	+	CCONJ
cana-5829	415	2	0.1i	0.1i	NOUN
cana-5829	415	3	,	,	PUNCT
cana-5829	415	4	0.5	0.5	NUM
cana-5829	415	5	+	+	NUM
cana-5829	415	6	0.2i	0.2i	NUM
cana-5829	415	7	)	)	PUNCT
cana-5829	415	8	(	(	PUNCT
cana-5829	415	9	0.5	0.5	NUM
cana-5829	415	10	+	+	CCONJ
cana-5829	415	11	0.3i	0.3i	NOUN
cana-5829	415	12	,	,	PUNCT
cana-5829	415	13	0.2	0.2	NUM
cana-5829	415	14	+	+	CCONJ
cana-5829	415	15	0.1i)(0.3	0.1i)(0.3	PRON
cana-5829	415	16	+	+	CCONJ
cana-5829	415	17	0.2i	0.2i	ADJ
cana-5829	415	18	,	,	PUNCT
cana-5829	415	19	0.6	0.6	NUM
cana-5829	415	20	+	+	NUM
cana-5829	415	21	0.1i	0.1i	NOUN
cana-5829	415	22	)	)	PUNCT
cana-5829	415	23	)	)	PUNCT
cana-5829	415	24	and	and	CCONJ
cana-5829	415	25	bf	bf	NOUN
cana-5829	415	26	=	=	SYM
cana-5829	415	27	(	(	PUNCT
cana-5829	415	28	(	(	PUNCT
cana-5829	415	29	0.4	0.4	NUM
cana-5829	415	30	+	+	CCONJ
cana-5829	415	31	0.3i	0.3i	NOUN
cana-5829	415	32	,	,	PUNCT
cana-5829	415	33	0.5	0.5	NUM
cana-5829	415	34	+	+	CCONJ
cana-5829	415	35	0.1i)(0.3	0.1i)(0.3	PRON
cana-5829	415	36	+	+	CCONJ
cana-5829	415	37	0.4i	0.4i	NOUN
cana-5829	415	38	,	,	PUNCT
cana-5829	415	39	0.4	0.4	NUM
cana-5829	415	40	+	+	CCONJ
cana-5829	415	41	0.2i	0.2i	NUM
cana-5829	415	42	)	)	PUNCT
cana-5829	415	43	(	(	PUNCT
cana-5829	415	44	0.6	0.6	NUM
cana-5829	415	45	+	+	CCONJ
cana-5829	415	46	0.2i	0.2i	ADJ
cana-5829	415	47	,	,	PUNCT
cana-5829	415	48	0.2	0.2	NUM
cana-5829	415	49	+	+	CCONJ
cana-5829	415	50	0.2i)(0.5	0.2i)(0.5	X
cana-5829	416	1	+	+	CCONJ
cana-5829	416	2	0.1i	0.1i	NOUN
cana-5829	416	3	,	,	PUNCT
cana-5829	416	4	0.4	0.4	NUM
cana-5829	416	5	+	+	CCONJ
cana-5829	416	6	0.3i	0.3i	NOUN
cana-5829	416	7	)	)	PUNCT
cana-5829	416	8	)	)	PUNCT
cana-5829	416	9	are	be	AUX
cana-5829	416	10	normalization	normalization	NOUN
cana-5829	416	11	of	of	ADP
cana-5829	416	12	complex	complex	ADJ
cana-5829	416	13	intuitionistic	intuitionistic	ADJ
cana-5829	416	14	fuzzy	fuzzy	ADJ
cana-5829	416	15	matrix	matrix	NOUN
cana-5829	416	16	two	two	NUM
cana-5829	416	17	intuitionistic	intuitionistic	ADJ
cana-5829	416	18	fuzzy	fuzzy	ADJ
cana-5829	416	19	matrices	matrix	NOUN
cana-5829	416	20	over	over	ADP
cana-5829	416	21	different	different	ADJ
cana-5829	416	22	universe	universe	NOUN
cana-5829	416	23	e	e	NOUN
cana-5829	416	24	and	and	CCONJ
cana-5829	416	25	f	f	PROPN
cana-5829	416	26	then	then	ADV
cana-5829	416	27	norm	norm	VERB
cana-5829	416	28	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	416	29			NOUN
cana-5829	416	30	𝑁𝑜𝑟𝑚	𝑁𝑜𝑟𝑚	PROPN
cana-5829	416	31	𝐵𝐹	𝐵𝐹	PROPN
cana-5829	416	32	is	be	AUX
cana-5829	416	33	also	also	ADV
cana-5829	416	34	normalization	normalization	NOUN
cana-5829	416	35	of	of	ADP
cana-5829	416	36	complex	complex	ADJ
cana-5829	416	37	intuitionistic	intuitionistic	ADJ
cana-5829	416	38	fuzzy	fuzzy	ADJ
cana-5829	416	39	matrix	matrix	NOUN
cana-5829	416	40	.	.	PUNCT
cana-5829	417	1	proof	proof	NOUN
cana-5829	417	2	:	:	PUNCT
cana-5829	417	3	given	give	VERB
cana-5829	417	4	𝑨𝑬=	𝑨𝑬=	PROPN
cana-5829	417	5	(	(	PUNCT
cana-5829	417	6	(	(	PUNCT
cana-5829	417	7	0.6	0.6	NUM
cana-5829	417	8	+	+	CCONJ
cana-5829	417	9	0.2i	0.2i	ADJ
cana-5829	417	10	,	,	PUNCT
cana-5829	417	11	0.3	0.3	NUM
cana-5829	417	12	+	+	NOUN
cana-5829	417	13	0.1i)(0.4	0.1i)(0.4	X
cana-5829	418	1	+	+	CCONJ
cana-5829	418	2	0.1i	0.1i	NOUN
cana-5829	418	3	,	,	PUNCT
cana-5829	418	4	0.5	0.5	NUM
cana-5829	418	5	+	+	NUM
cana-5829	418	6	0.2i	0.2i	NUM
cana-5829	418	7	)	)	PUNCT
cana-5829	418	8	(	(	PUNCT
cana-5829	418	9	0.5	0.5	NUM
cana-5829	418	10	+	+	CCONJ
cana-5829	418	11	0.3i	0.3i	NOUN
cana-5829	418	12	,	,	PUNCT
cana-5829	418	13	0.2	0.2	NUM
cana-5829	418	14	+	+	CCONJ
cana-5829	418	15	0.1i)(0.3	0.1i)(0.3	PRON
cana-5829	418	16	+	+	CCONJ
cana-5829	418	17	0.2i	0.2i	ADJ
cana-5829	418	18	,	,	PUNCT
cana-5829	418	19	0.6	0.6	NUM
cana-5829	418	20	+	+	NUM
cana-5829	418	21	0.1i	0.1i	NOUN
cana-5829	418	22	)	)	PUNCT
cana-5829	418	23	)	)	PUNCT
cana-5829	418	24	and	and	CCONJ
cana-5829	418	25	𝑩𝑭	𝑩𝑭	PROPN
cana-5829	418	26	=	=	SYM
cana-5829	418	27	(	(	PUNCT
cana-5829	418	28	(	(	PUNCT
cana-5829	418	29	0.4	0.4	NUM
cana-5829	418	30	+	+	CCONJ
cana-5829	418	31	0.3i	0.3i	NOUN
cana-5829	418	32	,	,	PUNCT
cana-5829	418	33	0.5	0.5	NUM
cana-5829	418	34	+	+	CCONJ
cana-5829	418	35	0.1i)(0.3	0.1i)(0.3	PRON
cana-5829	418	36	+	+	CCONJ
cana-5829	418	37	0.4i	0.4i	NOUN
cana-5829	418	38	,	,	PUNCT
cana-5829	418	39	0.4	0.4	NUM
cana-5829	418	40	+	+	CCONJ
cana-5829	418	41	0.2i	0.2i	NUM
cana-5829	418	42	)	)	PUNCT
cana-5829	418	43	(	(	PUNCT
cana-5829	418	44	0.6	0.6	NUM
cana-5829	418	45	+	+	CCONJ
cana-5829	418	46	0.2i	0.2i	ADJ
cana-5829	418	47	,	,	PUNCT
cana-5829	418	48	0.2	0.2	NUM
cana-5829	418	49	+	+	CCONJ
cana-5829	418	50	0.2i)(0.5	0.2i)(0.5	X
cana-5829	419	1	+	+	CCONJ
cana-5829	419	2	0.1i	0.1i	NOUN
cana-5829	419	3	,	,	PUNCT
cana-5829	419	4	0.4	0.4	NUM
cana-5829	419	5	+	+	CCONJ
cana-5829	419	6	0.3i	0.3i	NOUN
cana-5829	419	7	)	)	PUNCT
cana-5829	419	8	)	)	PUNCT
cana-5829	419	9	norm	norm	VERB
cana-5829	419	10	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	419	11	=	=	SYM
cana-5829	420	1	(	(	PUNCT
cana-5829	420	2	(	(	PUNCT
cana-5829	420	3	1	1	NUM
cana-5829	420	4	+	+	NUM
cana-5829	420	5	0.67𝑖	0.67𝑖	NUM
cana-5829	420	6	0.125	0.125	NUM
cana-5829	420	7	+	+	NUM
cana-5829	420	8	0𝑖	0𝑖	NOUN
cana-5829	420	9	)	)	PUNCT
cana-5829	420	10	(	(	PUNCT
cana-5829	420	11	0.67	0.67	NUM
cana-5829	420	12	+	+	CCONJ
cana-5829	420	13	0.33𝑖	0.33𝑖	NUM
cana-5829	420	14	0.30	0.30	NUM
cana-5829	420	15	+	+	CCONJ
cana-5829	420	16	0.10𝑖	0.10𝑖	NOUN
cana-5829	420	17	)	)	PUNCT
cana-5829	420	18	(	(	PUNCT
cana-5829	420	19	0.83	0.83	NUM
cana-5829	420	20	+	+	NUM
cana-5829	420	21	1𝑖	1𝑖	NOUN
cana-5829	420	22	0	0	NUM
cana-5829	421	1	+	+	NUM
cana-5829	421	2	0𝑖	0𝑖	NOUN
cana-5829	421	3	)	)	PUNCT
cana-5829	421	4	(	(	PUNCT
cana-5829	421	5	0.5	0.5	NUM
cana-5829	421	6	+	+	NUM
cana-5829	421	7	0.67𝑖	0.67𝑖	NUM
cana-5829	421	8	0.5	0.5	NUM
cana-5829	421	9	+	+	NUM
cana-5829	421	10	0𝑖	0𝑖	NOUN
cana-5829	421	11	)	)	PUNCT
cana-5829	421	12	)	)	PUNCT
cana-5829	422	1	𝑁𝑜𝑟𝑚	𝑁𝑜𝑟𝑚	NOUN
cana-5829	422	2	𝐵𝐹=	𝐵𝐹=	ADP
cana-5829	422	3	(	(	PUNCT
cana-5829	422	4	(	(	PUNCT
cana-5829	422	5	0.67	0.67	NUM
cana-5829	422	6	+	+	CCONJ
cana-5829	422	7	0.75𝑖	0.75𝑖	PROPN
cana-5829	422	8	0.375	0.375	NUM
cana-5829	422	9	+	+	NUM
cana-5829	422	10	0𝑖	0𝑖	NOUN
cana-5829	422	11	)	)	PUNCT
cana-5829	422	12	(	(	PUNCT
cana-5829	422	13	0.5	0.5	NUM
cana-5829	422	14	+	+	NUM
cana-5829	422	15	1𝑖	1𝑖	NUM
cana-5829	422	16	0.25	0.25	NUM
cana-5829	422	17	+	+	CCONJ
cana-5829	422	18	0.11𝑖	0.11𝑖	NUM
cana-5829	422	19	)	)	PUNCT
cana-5829	422	20	(	(	PUNCT
cana-5829	422	21	1	1	NUM
cana-5829	422	22	+	+	NUM
cana-5829	422	23	0.5𝑖	0.5𝑖	NOUN
cana-5829	422	24	0	0	NUM
cana-5829	423	1	+	+	CCONJ
cana-5829	423	2	0.11𝑖	0.11𝑖	NUM
cana-5829	423	3	)	)	PUNCT
cana-5829	423	4	(	(	PUNCT
cana-5829	423	5	0.83	0.83	NUM
cana-5829	423	6	+	+	NUM
cana-5829	423	7	0.25𝑖	0.25𝑖	NOUN
cana-5829	423	8	0.25	0.25	NUM
cana-5829	423	9	+	+	PUNCT
cana-5829	423	10	0.22𝑖	0.22𝑖	NUM
cana-5829	423	11	)	)	PUNCT
cana-5829	423	12	)	)	PUNCT
cana-5829	424	1	norm𝐴𝐸	norm𝐴𝐸	NOUN
cana-5829	424	2	∪	∪	VERB
cana-5829	424	3	𝑁𝑜𝑟𝑚𝐵𝐹	𝑁𝑜𝑟𝑚𝐵𝐹	PROPN
cana-5829	424	4	=	=	PUNCT
cana-5829	424	5	(	(	PUNCT
cana-5829	424	6	(	(	PUNCT
cana-5829	424	7	1	1	NUM
cana-5829	424	8	+	+	NUM
cana-5829	424	9	0.67𝑖	0.67𝑖	NUM
cana-5829	424	10	0.125	0.125	NUM
cana-5829	424	11	+	+	NUM
cana-5829	424	12	0𝑖	0𝑖	NOUN
cana-5829	424	13	)	)	PUNCT
cana-5829	424	14	(	(	PUNCT
cana-5829	424	15	0.67	0.67	NUM
cana-5829	424	16	+	+	CCONJ
cana-5829	424	17	0.33𝑖	0.33𝑖	NUM
cana-5829	424	18	0.30	0.30	NUM
cana-5829	424	19	+	+	CCONJ
cana-5829	424	20	0.10𝑖	0.10𝑖	NOUN
cana-5829	424	21	)	)	PUNCT
cana-5829	424	22	(	(	PUNCT
cana-5829	424	23	0.83	0.83	NUM
cana-5829	424	24	+	+	NUM
cana-5829	424	25	1𝑖	1𝑖	NOUN
cana-5829	424	26	0	0	NUM
cana-5829	425	1	+	+	NUM
cana-5829	425	2	0𝑖	0𝑖	NOUN
cana-5829	425	3	)	)	PUNCT
cana-5829	425	4	(	(	PUNCT
cana-5829	425	5	0.5	0.5	NUM
cana-5829	425	6	+	+	NUM
cana-5829	425	7	0.67𝑖	0.67𝑖	NUM
cana-5829	425	8	0.5	0.5	NUM
cana-5829	425	9	+	+	NUM
cana-5829	425	10	0𝑖	0𝑖	NOUN
cana-5829	425	11	)	)	PUNCT
cana-5829	425	12	)	)	PUNCT
cana-5829	425	13	∪	∪	ADP
cana-5829	425	14	(	(	PUNCT
cana-5829	425	15	(	(	PUNCT
cana-5829	425	16	0.67	0.67	NUM
cana-5829	425	17	+	+	CCONJ
cana-5829	425	18	0.75𝑖	0.75𝑖	PROPN
cana-5829	425	19	0.375	0.375	NUM
cana-5829	425	20	+	+	NUM
cana-5829	425	21	0𝑖	0𝑖	NOUN
cana-5829	425	22	)	)	PUNCT
cana-5829	425	23	(	(	PUNCT
cana-5829	425	24	0.5	0.5	NUM
cana-5829	425	25	+	+	NUM
cana-5829	425	26	1𝑖	1𝑖	NUM
cana-5829	425	27	0.25	0.25	NUM
cana-5829	425	28	+	+	CCONJ
cana-5829	425	29	0.11𝑖	0.11𝑖	NUM
cana-5829	425	30	)	)	PUNCT
cana-5829	425	31	(	(	PUNCT
cana-5829	425	32	1	1	NUM
cana-5829	425	33	+	+	NUM
cana-5829	425	34	0.5𝑖	0.5𝑖	NOUN
cana-5829	425	35	0	0	NUM
cana-5829	426	1	+	+	CCONJ
cana-5829	426	2	0.11𝑖	0.11𝑖	NUM
cana-5829	426	3	)	)	PUNCT
cana-5829	426	4	(	(	PUNCT
cana-5829	427	1	0.83	0.83	NUM
cana-5829	427	2	+	+	NUM
cana-5829	427	3	0.25𝑖	0.25𝑖	NOUN
cana-5829	427	4	0.25	0.25	NUM
cana-5829	427	5	+	+	PUNCT
cana-5829	427	6	0.22𝑖	0.22𝑖	NUM
cana-5829	427	7	)	)	PUNCT
cana-5829	427	8	)	)	PUNCT
cana-5829	428	1	𝑋11	𝑋11	PROPN
cana-5829	428	2	=	=	PUNCT
cana-5829	428	3	(	(	PUNCT
cana-5829	428	4	1	1	NUM
cana-5829	428	5	+	+	NUM
cana-5829	428	6	0.67𝑖	0.67𝑖	NUM
cana-5829	428	7	0.125	0.125	NUM
cana-5829	428	8	+	+	NUM
cana-5829	428	9	0𝑖	0𝑖	NOUN
cana-5829	428	10	)	)	PUNCT
cana-5829	428	11	∪	∪	NOUN
cana-5829	428	12	(	(	PUNCT
cana-5829	428	13	0.67	0.67	NUM
cana-5829	428	14	+	+	CCONJ
cana-5829	428	15	0.75𝑖	0.75𝑖	PROPN
cana-5829	428	16	0.375	0.375	NUM
cana-5829	428	17	+	+	NUM
cana-5829	428	18	0𝑖	0𝑖	NOUN
cana-5829	428	19	)	)	PUNCT
cana-5829	428	20	𝑋12	𝑋12	PROPN
cana-5829	428	21	=	=	PUNCT
cana-5829	428	22	(	(	PUNCT
cana-5829	428	23	0.67	0.67	NUM
cana-5829	428	24	+	+	CCONJ
cana-5829	428	25	0.33𝑖	0.33𝑖	NUM
cana-5829	428	26	0.30	0.30	NUM
cana-5829	428	27	+	+	CCONJ
cana-5829	428	28	0.10𝑖	0.10𝑖	NOUN
cana-5829	428	29	)	)	PUNCT
cana-5829	428	30	∪	∪	NOUN
cana-5829	428	31	(	(	PUNCT
cana-5829	428	32	0.5	0.5	NUM
cana-5829	428	33	+	+	NUM
cana-5829	428	34	1𝑖	1𝑖	NUM
cana-5829	428	35	0.25	0.25	NUM
cana-5829	428	36	+	+	CCONJ
cana-5829	428	37	0.11𝑖	0.11𝑖	NUM
cana-5829	428	38	)	)	PUNCT
cana-5829	428	39	𝑋21	𝑋21	NOUN
cana-5829	428	40	=	=	SYM
cana-5829	428	41	(	(	PUNCT
cana-5829	428	42	0.83	0.83	NUM
cana-5829	428	43	+	+	NUM
cana-5829	428	44	1𝑖	1𝑖	NOUN
cana-5829	428	45	0	0	NUM
cana-5829	429	1	+	+	NUM
cana-5829	429	2	0𝑖	0𝑖	NOUN
cana-5829	429	3	)	)	PUNCT
cana-5829	429	4	∪	∪	NOUN
cana-5829	429	5	(	(	PUNCT
cana-5829	429	6	1	1	NUM
cana-5829	429	7	+	+	NUM
cana-5829	429	8	0.5𝑖	0.5𝑖	NOUN
cana-5829	429	9	0	0	NUM
cana-5829	430	1	+	+	CCONJ
cana-5829	430	2	0.11𝑖	0.11𝑖	NUM
cana-5829	430	3	)	)	PUNCT
cana-5829	431	1	𝑋22	𝑋22	ADJ
cana-5829	431	2	=	=	PUNCT
cana-5829	431	3	(	(	PUNCT
cana-5829	431	4	0.5	0.5	NUM
cana-5829	431	5	+	+	NUM
cana-5829	431	6	0.67𝑖	0.67𝑖	NUM
cana-5829	431	7	0.5	0.5	NUM
cana-5829	431	8	+	+	NUM
cana-5829	431	9	0𝑖	0𝑖	NOUN
cana-5829	431	10	)	)	PUNCT
cana-5829	431	11	∪	∪	NOUN
cana-5829	431	12	(	(	PUNCT
cana-5829	431	13	0.83	0.83	NUM
cana-5829	431	14	+	+	NOUN
cana-5829	431	15	0.25𝑖	0.25𝑖	NOUN
cana-5829	431	16	0.25	0.25	NUM
cana-5829	431	17	+	+	CCONJ
cana-5829	431	18	0.22𝑖	0.22𝑖	NOUN
cana-5829	431	19	)	)	PUNCT
cana-5829	431	20	𝐴𝑝𝑝𝑙𝑦𝑖𝑛𝑔	𝐴𝑝𝑝𝑙𝑦𝑖𝑛𝑔	PROPN
cana-5829	431	21	𝑓𝑜𝑟𝑚𝑢𝑙𝑎	𝑓𝑜𝑟𝑚𝑢𝑙𝑎	VERB
cana-5829	431	22	aebf	aebf	X
cana-5829	431	23	=	=	SYM
cana-5829	431	24	{	{	PUNCT
cana-5829	431	25	(	(	PUNCT
cana-5829	431	26	x	x	NOUN
cana-5829	431	27	,	,	PUNCT
cana-5829	431	28	y	y	PROPN
cana-5829	431	29	)	)	PUNCT
cana-5829	431	30	,	,	PUNCT
cana-5829	431	31	max	max	PROPN
cana-5829	431	32	(	(	PUNCT
cana-5829	431	33	μa(x	μa(x	NOUN
cana-5829	431	34	)	)	PUNCT
cana-5829	431	35	,	,	PUNCT
cana-5829	431	36	μb(y	μb(y	NUM
cana-5829	431	37	)	)	PUNCT
cana-5829	431	38	)	)	PUNCT
cana-5829	431	39	,	,	PUNCT
cana-5829	431	40	min	min	PROPN
cana-5829	431	41	(	(	PUNCT
cana-5829	431	42	ϑa(x	ϑa(x	NOUN
cana-5829	431	43	)	)	PUNCT
cana-5829	431	44	,	,	PUNCT
cana-5829	431	45	ϑb(x	ϑb(x	NUM
cana-5829	431	46	)	)	PUNCT
cana-5829	431	47	):	):	PUNCT
cana-5829	431	48	xe	xe	PROPN
cana-5829	431	49	,	,	PUNCT
cana-5829	431	50	yf	yf	NUM
cana-5829	431	51	}	}	PUNCT
cana-5829	431	52	𝑋11	𝑋11	PROPN
cana-5829	431	53	=	=	PRON
cana-5829	431	54	{	{	PUNCT
cana-5829	431	55	max(1	max(1	NOUN
cana-5829	431	56	+	+	CCONJ
cana-5829	431	57	0.67𝑖	0.67𝑖	NUM
cana-5829	431	58	,	,	PUNCT
cana-5829	431	59	0.67	0.67	NUM
cana-5829	431	60	+	+	CCONJ
cana-5829	431	61	0.75𝑖	0.75𝑖	PROPN
cana-5829	431	62	)	)	PUNCT
cana-5829	431	63	,	,	PUNCT
cana-5829	431	64	min(0.125	min(0.125	PROPN
cana-5829	431	65	+	+	NUM
cana-5829	431	66	0𝑖	0𝑖	NOUN
cana-5829	431	67	,	,	PUNCT
cana-5829	431	68	0.375	0.375	NUM
cana-5829	431	69	+	+	NUM
cana-5829	431	70	0𝑖	0𝑖	NOUN
cana-5829	431	71	)	)	PUNCT
cana-5829	431	72	}	}	PUNCT
cana-5829	431	73	𝑋12	𝑋12	PROPN
cana-5829	432	1	=	=	PRON
cana-5829	432	2	{	{	PUNCT
cana-5829	432	3	max(0.67	max(0.67	NOUN
cana-5829	432	4	+	+	CCONJ
cana-5829	432	5	0.33𝑖	0.33𝑖	ADJ
cana-5829	432	6	,	,	PUNCT
cana-5829	432	7	0.5	0.5	NUM
cana-5829	432	8	+	+	NUM
cana-5829	432	9	1𝑖	1𝑖	NUM
cana-5829	432	10	)	)	PUNCT
cana-5829	432	11	,	,	PUNCT
cana-5829	432	12	min(0.30	min(0.30	VERB
cana-5829	432	13	+	+	CCONJ
cana-5829	432	14	0.10𝑖	0.10𝑖	NOUN
cana-5829	432	15	,	,	PUNCT
cana-5829	432	16	0.25	0.25	NUM
cana-5829	432	17	+	+	X
cana-5829	432	18	0.11𝑖	0.11𝑖	NUM
cana-5829	432	19	)	)	PUNCT
cana-5829	432	20	}	}	PUNCT
cana-5829	433	1	𝑋21	𝑋21	VERB
cana-5829	433	2	=	=	PRON
cana-5829	433	3	{	{	PUNCT
cana-5829	433	4	max(0.83	max(0.83	X
cana-5829	433	5	+	+	NUM
cana-5829	433	6	1𝑖	1𝑖	NOUN
cana-5829	433	7	,	,	PUNCT
cana-5829	433	8	1	1	NUM
cana-5829	433	9	+	+	SYM
cana-5829	433	10	0.5𝑖	0.5𝑖	NUM
cana-5829	433	11	)	)	PUNCT
cana-5829	433	12	,	,	PUNCT
cana-5829	433	13	min(0	min(0	NOUN
cana-5829	433	14	+	+	CCONJ
cana-5829	433	15	0𝑖	0𝑖	NOUN
cana-5829	433	16	,	,	PUNCT
cana-5829	433	17	0	0	NUM
cana-5829	434	1	+	+	CCONJ
cana-5829	434	2	0.11𝑖	0.11𝑖	NUM
cana-5829	434	3	)	)	PUNCT
cana-5829	434	4	}	}	PUNCT
cana-5829	434	5	communications	communication	NOUN
cana-5829	434	6	on	on	ADP
cana-5829	434	7	applied	apply	VERB
cana-5829	434	8	nonlinear	nonlinear	ADJ
cana-5829	434	9	analysis	analysis	NOUN
cana-5829	434	10	issn	issn	NOUN
cana-5829	434	11	:	:	PUNCT
cana-5829	434	12	1074	1074	NUM
cana-5829	434	13	-	-	PUNCT
cana-5829	434	14	133x	133x	NUM
cana-5829	434	15	vol	vol	VERB
cana-5829	434	16	32	32	NUM
cana-5829	434	17	no	no	NOUN
cana-5829	434	18	.	.	PUNCT
cana-5829	435	1	10s	10	NOUN
cana-5829	435	2	(	(	PUNCT
cana-5829	435	3	2025	2025	NUM
cana-5829	435	4	)	)	PUNCT
cana-5829	435	5	2941	2941	NUM
cana-5829	435	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5829	436	1	𝑋22	𝑋22	VERB
cana-5829	436	2	=	=	PRON
cana-5829	436	3	{	{	PUNCT
cana-5829	436	4	max(0.5	max(0.5	NUM
cana-5829	436	5	+	+	NOUN
cana-5829	436	6	0.67𝑖	0.67𝑖	ADJ
cana-5829	436	7	,	,	PUNCT
cana-5829	436	8	0.83	0.83	NUM
cana-5829	436	9	+	+	NUM
cana-5829	436	10	0.25𝑖	0.25𝑖	NUM
cana-5829	436	11	)	)	PUNCT
cana-5829	436	12	,	,	PUNCT
cana-5829	436	13	min(0.5	min(0.5	NUM
cana-5829	436	14	+	+	NUM
cana-5829	436	15	0𝑖	0𝑖	NOUN
cana-5829	436	16	,	,	PUNCT
cana-5829	436	17	0.25	0.25	NUM
cana-5829	436	18	+	+	CCONJ
cana-5829	436	19	0.22𝑖	0.22𝑖	NUM
cana-5829	436	20	)	)	PUNCT
cana-5829	436	21	}	}	PUNCT
cana-5829	437	1	𝑋11	𝑋11	PROPN
cana-5829	437	2	=	=	PRON
cana-5829	437	3	{	{	PUNCT
cana-5829	437	4	1	1	NUM
cana-5829	437	5	+	+	NOUN
cana-5829	437	6	0.75i	0.75i	NUM
cana-5829	437	7	,	,	PUNCT
cana-5829	437	8	0.125	0.125	NUM
cana-5829	437	9	+	+	NOUN
cana-5829	437	10	0i	0i	X
cana-5829	437	11	}	}	PUNCT
cana-5829	437	12	𝑋12	𝑋12	VERB
cana-5829	437	13	=	=	PRON
cana-5829	437	14	{	{	PUNCT
cana-5829	437	15	0.67	0.67	NUM
cana-5829	437	16	+	+	NOUN
cana-5829	437	17	1i	1i	NOUN
cana-5829	437	18	,	,	PUNCT
cana-5829	437	19	0.25	0.25	NUM
cana-5829	437	20	+	+	NOUN
cana-5829	437	21	0.10i	0.10i	NOUN
cana-5829	437	22	}	}	PUNCT
cana-5829	437	23	𝑋21	𝑋21	VERB
cana-5829	437	24	=	=	NUM
cana-5829	437	25	{	{	PUNCT
cana-5829	437	26	1	1	NUM
cana-5829	437	27	+	+	NOUN
cana-5829	437	28	1i	1i	NOUN
cana-5829	437	29	,	,	PUNCT
cana-5829	437	30	0	0	PUNCT
cana-5829	437	31	+	+	NOUN
cana-5829	437	32	0i	0i	X
cana-5829	437	33	}	}	PUNCT
cana-5829	437	34	𝑋22	𝑋22	VERB
cana-5829	437	35	=	=	PRON
cana-5829	437	36	{	{	PUNCT
cana-5829	437	37	0.83	0.83	NUM
cana-5829	437	38	+	+	NOUN
cana-5829	437	39	0.67i	0.67i	NUM
cana-5829	437	40	,	,	PUNCT
cana-5829	437	41	0.25	0.25	NUM
cana-5829	437	42	+	+	NOUN
cana-5829	437	43	0i	0i	X
cana-5829	437	44	}	}	PUNCT
cana-5829	437	45	we	we	PRON
cana-5829	437	46	have	have	VERB
cana-5829	437	47	norm𝐴𝐸	norm𝐴𝐸	PROPN
cana-5829	437	48	∪	∪	ADJ
cana-5829	437	49	𝑁𝑜𝑟𝑚𝐵𝐹	𝑁𝑜𝑟𝑚𝐵𝐹	PROPN
cana-5829	437	50	=	=	PUNCT
cana-5829	437	51	(	(	PUNCT
cana-5829	437	52	(	(	PUNCT
cana-5829	437	53	1	1	NUM
cana-5829	437	54	+	+	NUM
cana-5829	437	55	0.75i	0.75i	NUM
cana-5829	437	56	,	,	PUNCT
cana-5829	437	57	0.125	0.125	NUM
cana-5829	437	58	+	+	NUM
cana-5829	437	59	0i	0i	NOUN
cana-5829	437	60	)	)	PUNCT
cana-5829	437	61	(	(	PUNCT
cana-5829	437	62	0.67	0.67	NUM
cana-5829	437	63	+	+	NUM
cana-5829	437	64	1i	1i	NOUN
cana-5829	437	65	,	,	PUNCT
cana-5829	437	66	0.25	0.25	NUM
cana-5829	437	67	+	+	CCONJ
cana-5829	437	68	0.10i	0.10i	NUM
cana-5829	437	69	)	)	PUNCT
cana-5829	437	70	(	(	PUNCT
cana-5829	437	71	1	1	NUM
cana-5829	437	72	+	+	NUM
cana-5829	437	73	1i	1i	NOUN
cana-5829	437	74	,	,	PUNCT
cana-5829	437	75	0	0	PUNCT
cana-5829	438	1	+	+	NUM
cana-5829	438	2	0i	0i	NOUN
cana-5829	438	3	)	)	PUNCT
cana-5829	438	4	(	(	PUNCT
cana-5829	438	5	0.83	0.83	NUM
cana-5829	438	6	+	+	CCONJ
cana-5829	438	7	0.67i	0.67i	NUM
cana-5829	438	8	,	,	PUNCT
cana-5829	438	9	0.25	0.25	NUM
cana-5829	438	10	+	+	NUM
cana-5829	438	11	0i	0i	NOUN
cana-5829	438	12	)	)	PUNCT
cana-5829	438	13	)	)	PUNCT
cana-5829	438	14	is	be	AUX
cana-5829	438	15	also	also	ADV
cana-5829	438	16	normalization	normalization	NOUN
cana-5829	438	17	of	of	ADP
cana-5829	438	18	complex	complex	ADJ
cana-5829	438	19	intuitionistic	intuitionistic	ADJ
cana-5829	438	20	fuzzy	fuzzy	ADJ
cana-5829	438	21	matrix	matrix	NOUN
cana-5829	438	22	.	.	PUNCT
cana-5829	439	1	theorem	theorem	VERB
cana-5829	439	2	5.2.5	5.2.5	NUM
cana-5829	439	3	:	:	PUNCT
cana-5829	439	4	if	if	SCONJ
cana-5829	439	5	e	e	PROPN
cana-5829	439	6	and	and	CCONJ
cana-5829	439	7	f	f	PROPN
cana-5829	439	8	be	be	AUX
cana-5829	439	9	two	two	NUM
cana-5829	439	10	universal	universal	ADJ
cana-5829	439	11	sets	set	NOUN
cana-5829	439	12	.	.	PUNCT
cana-5829	440	1	for	for	ADP
cana-5829	440	2	every	every	DET
cana-5829	440	3	normalization	normalization	NOUN
cana-5829	440	4	of	of	ADP
cana-5829	440	5	complex	complex	ADJ
cana-5829	440	6	intuitionistic	intuitionistic	ADJ
cana-5829	440	7	fuzzy	fuzzy	ADJ
cana-5829	440	8	matrices	matrix	NOUN
cana-5829	440	9	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	440	10	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-5829	440	11	𝐵𝐹	𝐵𝐹	PROPN
cana-5829	440	12	are	be	AUX
cana-5829	440	13	in	in	ADP
cana-5829	440	14	e	e	PROPN
cana-5829	440	15	and	and	CCONJ
cana-5829	440	16	f	f	PROPN
cana-5829	440	17	then	then	ADV
cana-5829	440	18	norm𝐴𝐸𝑁𝑜𝑟𝑚𝐵𝐹	norm𝐴𝐸𝑁𝑜𝑟𝑚𝐵𝐹	PROPN
cana-5829	440	19	is	be	AUX
cana-5829	440	20	also	also	ADV
cana-5829	440	21	normalization	normalization	NOUN
cana-5829	440	22	of	of	ADP
cana-5829	440	23	complex	complex	ADJ
cana-5829	440	24	intuitionistic	intuitionistic	ADJ
cana-5829	440	25	fuzzy	fuzzy	ADJ
cana-5829	440	26	matrix	matrix	NOUN
cana-5829	440	27	.	.	PUNCT
cana-5829	441	1	proof	proof	NOUN
cana-5829	441	2	:	:	PUNCT
cana-5829	441	3	if	if	SCONJ
cana-5829	441	4	norm	norm	NOUN
cana-5829	441	5	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	441	6	and	and	CCONJ
cana-5829	441	7	𝑁𝑜𝑟𝑚	𝑁𝑜𝑟𝑚	PROPN
cana-5829	441	8	𝐵𝐹	𝐵𝐹	PROPN
cana-5829	441	9	are	be	AUX
cana-5829	441	10	two	two	NUM
cana-5829	441	11	normalization	normalization	NOUN
cana-5829	441	12	intuitionistic	intuitionistic	ADJ
cana-5829	441	13	fuzzy	fuzzy	ADJ
cana-5829	441	14	matrices	matrix	NOUN
cana-5829	441	15	over	over	ADP
cana-5829	441	16	different	different	ADJ
cana-5829	441	17	unive𝑟𝑠𝑒𝑠	unive𝑟𝑠𝑒𝑠	ADJ
cana-5829	441	18	𝑠𝑒𝑡𝑠	𝑠𝑒𝑡𝑠	PROPN
cana-5829	441	19	𝐸	𝐸	PROPN
cana-5829	441	20	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-5829	441	21	𝐹.	𝐹.	PROPN
cana-5829	441	22	if	if	SCONJ
cana-5829	441	23	we	we	PRON
cana-5829	441	24	consider	consider	VERB
cana-5829	441	25	two	two	NUM
cana-5829	441	26	2	2	NUM
cana-5829	441	27	×	×	NOUN
cana-5829	441	28	2	2	NUM
cana-5829	441	29	normalization	normalization	NOUN
cana-5829	441	30	intuitionistic	intuitionistic	ADJ
cana-5829	441	31	fuzzy	fuzzy	ADJ
cana-5829	441	32	matrices	matrix	NOUN
cana-5829	441	33	,	,	PUNCT
cana-5829	441	34	norm	norm	NOUN
cana-5829	441	35	𝐴𝐸𝑎𝑛𝑑	𝐴𝐸𝑎𝑛𝑑	PROPN
cana-5829	441	36	𝑁𝑜𝑟𝑚	𝑁𝑜𝑟𝑚	PROPN
cana-5829	441	37	𝐵𝐹.	𝐵𝐹.	NOUN
cana-5829	441	38	let	let	VERB
cana-5829	441	39	norm	norm	VERB
cana-5829	441	40	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	441	41	=	=	SYM
cana-5829	441	42	(	(	PUNCT
cana-5829	441	43	(	(	PUNCT
cana-5829	441	44	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	441	45	(	(	PUNCT
cana-5829	441	46	𝛼11	𝛼11	NOUN
cana-5829	441	47	+	+	PROPN
cana-5829	441	48	𝑖𝛽11	𝑖𝛽11	PROPN
cana-5829	441	49	)	)	PUNCT
cana-5829	441	50	𝑁𝑜𝑟𝑚µ𝐸11	𝑁𝑜𝑟𝑚µ𝐸11	NOUN
cana-5829	441	51	(	(	PUNCT
cana-5829	441	52	𝛾11	𝛾11	VERB
cana-5829	441	53	+	+	CCONJ
cana-5829	441	54	𝑖𝛿11	𝑖𝛿11	PROPN
cana-5829	441	55	)	)	PUNCT
cana-5829	441	56	)	)	PUNCT
cana-5829	441	57	(	(	PUNCT
cana-5829	441	58	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	NOUN
cana-5829	441	59	(	(	PUNCT
cana-5829	441	60	𝛼12	𝛼12	NOUN
cana-5829	441	61	+	+	CCONJ
cana-5829	441	62	𝑖𝛽12	𝑖𝛽12	PROPN
cana-5829	441	63	)	)	PUNCT
cana-5829	441	64	𝑁𝑜𝑟𝑚µ𝐸12	𝑁𝑜𝑟𝑚µ𝐸12	NOUN
cana-5829	441	65	(	(	PUNCT
cana-5829	441	66	𝛾12	𝛾12	VERB
cana-5829	441	67	+	+	CCONJ
cana-5829	441	68	𝑖𝛿12	𝑖𝛿12	PROPN
cana-5829	441	69	)	)	PUNCT
cana-5829	441	70	)	)	PUNCT
cana-5829	442	1	(	(	PUNCT
cana-5829	442	2	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	X
cana-5829	442	3	(	(	PUNCT
cana-5829	442	4	𝛼21	𝛼21	NOUN
cana-5829	442	5	+	+	X
cana-5829	442	6	𝑖𝛽21	𝑖𝛽21	PROPN
cana-5829	442	7	)	)	PUNCT
cana-5829	442	8	𝑁𝑜𝑟𝑚µ𝐸21	𝑁𝑜𝑟𝑚µ𝐸21	NOUN
cana-5829	442	9	(	(	PUNCT
cana-5829	442	10	𝛾21	𝛾21	NOUN
cana-5829	442	11	+	+	CCONJ
cana-5829	443	1	𝑖𝛿21	𝑖𝛿21	PROPN
cana-5829	443	2	)	)	PUNCT
cana-5829	443	3	)	)	PUNCT
cana-5829	444	1	(	(	PUNCT
cana-5829	444	2	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	X
cana-5829	444	3	(	(	PUNCT
cana-5829	444	4	𝛼22	𝛼22	NOUN
cana-5829	444	5	+	+	CCONJ
cana-5829	444	6	𝑖𝛽22	𝑖𝛽22	PROPN
cana-5829	444	7	)	)	PUNCT
cana-5829	444	8	𝑁𝑜𝑟𝑚µ𝐸22	𝑁𝑜𝑟𝑚µ𝐸22	NOUN
cana-5829	444	9	(	(	PUNCT
cana-5829	444	10	𝛾22	𝛾22	PROPN
cana-5829	444	11	+	+	PROPN
cana-5829	444	12	𝑖𝛿22	𝑖𝛿22	PROPN
cana-5829	444	13	)	)	PUNCT
cana-5829	444	14	)	)	PUNCT
cana-5829	444	15	)	)	PUNCT
cana-5829	445	1	and	and	CCONJ
cana-5829	445	2	𝑁𝑜𝑟𝑚	𝑁𝑜𝑟𝑚	PROPN
cana-5829	445	3	𝐵𝐹	𝐵𝐹	NOUN
cana-5829	445	4	=	=	SYM
cana-5829	445	5	(	(	PUNCT
cana-5829	445	6	(	(	PUNCT
cana-5829	445	7	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	445	8	(	(	PUNCT
cana-5829	445	9	𝑥11	𝑥11	ADV
cana-5829	445	10	+	+	CCONJ
cana-5829	445	11	𝑖𝑦11	𝑖𝑦11	NOUN
cana-5829	445	12	)	)	PUNCT
cana-5829	445	13	𝑁𝑜𝑟𝑚𝛾𝐹11	𝑁𝑜𝑟𝑚𝛾𝐹11	X
cana-5829	445	14	(	(	PUNCT
cana-5829	445	15	𝜇11	𝜇11	PROPN
cana-5829	445	16	+	+	PROPN
cana-5829	445	17	𝑖𝜃11	𝑖𝜃11	PROPN
cana-5829	445	18	)	)	PUNCT
cana-5829	445	19	)	)	PUNCT
cana-5829	446	1	(	(	PUNCT
cana-5829	446	2	𝑁𝑜𝑟𝑚𝛿𝐹12	𝑁𝑜𝑟𝑚𝛿𝐹12	X
cana-5829	446	3	(	(	PUNCT
cana-5829	446	4	𝑥12	𝑥12	VERB
cana-5829	446	5	+	+	CCONJ
cana-5829	446	6	𝑖𝑦12	𝑖𝑦12	PROPN
cana-5829	446	7	)	)	PUNCT
cana-5829	446	8	𝑁𝑜𝑟𝑚𝛾𝐹12	𝑁𝑜𝑟𝑚𝛾𝐹12	NOUN
cana-5829	446	9	(	(	PUNCT
cana-5829	446	10	𝜇12	𝜇12	NOUN
cana-5829	446	11	+	+	CCONJ
cana-5829	447	1	𝑖𝜃12	𝑖𝜃12	PROPN
cana-5829	447	2	)	)	PUNCT
cana-5829	447	3	)	)	PUNCT
cana-5829	448	1	(	(	PUNCT
cana-5829	448	2	𝑁𝑜𝑟𝑚𝛿𝐹21	𝑁𝑜𝑟𝑚𝛿𝐹21	X
cana-5829	448	3	(	(	PUNCT
cana-5829	448	4	𝑥21	𝑥21	PROPN
cana-5829	448	5	+	+	CCONJ
cana-5829	448	6	𝑖𝑦21	𝑖𝑦21	PROPN
cana-5829	448	7	)	)	PUNCT
cana-5829	448	8	𝑁𝑜𝑟𝑚𝛾𝐹21	𝑁𝑜𝑟𝑚𝛾𝐹21	ADV
cana-5829	448	9	(	(	PUNCT
cana-5829	448	10	𝜇21	𝜇21	VERB
cana-5829	448	11	+	+	CCONJ
cana-5829	448	12	𝑖𝜃21	𝑖𝜃21	PROPN
cana-5829	448	13	)	)	PUNCT
cana-5829	448	14	)	)	PUNCT
cana-5829	448	15	(	(	PUNCT
cana-5829	448	16	𝑁𝑜𝑟𝑚𝛿𝐹22	𝑁𝑜𝑟𝑚𝛿𝐹22	X
cana-5829	448	17	(	(	PUNCT
cana-5829	448	18	𝑥22	𝑥22	NOUN
cana-5829	448	19	+	+	X
cana-5829	448	20	𝑖𝑦22	𝑖𝑦22	PROPN
cana-5829	448	21	)	)	PUNCT
cana-5829	448	22	𝑁𝑜𝑟𝑚𝛾𝐹22	𝑁𝑜𝑟𝑚𝛾𝐹22	NOUN
cana-5829	448	23	(	(	PUNCT
cana-5829	448	24	𝜇22	𝜇22	NOUN
cana-5829	448	25	+	+	CCONJ
cana-5829	448	26	𝑖𝜃22	𝑖𝜃22	PROPN
cana-5829	448	27	)	)	PUNCT
cana-5829	448	28	)	)	PUNCT
cana-5829	448	29	)	)	PUNCT
cana-5829	448	30	are	be	AUX
cana-5829	448	31	two	two	NUM
cana-5829	448	32	normalization	normalization	NOUN
cana-5829	448	33	intuitionistic	intuitionistic	ADJ
cana-5829	448	34	fuzzy	fuzzy	ADJ
cana-5829	448	35	matrices	matrix	NOUN
cana-5829	448	36	.	.	PUNCT
cana-5829	449	1	norm𝐴𝐸𝑁𝑜𝑟𝑚𝐵𝐹	norm𝐴𝐸𝑁𝑜𝑟𝑚𝐵𝐹	PROPN
cana-5829	449	2	=	=	PUNCT
cana-5829	449	3	(	(	PUNCT
cana-5829	449	4	(	(	PUNCT
cana-5829	449	5	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	449	6	(	(	PUNCT
cana-5829	449	7	𝛼11	𝛼11	NOUN
cana-5829	449	8	+	+	PROPN
cana-5829	449	9	𝑖𝛽11	𝑖𝛽11	PROPN
cana-5829	449	10	)	)	PUNCT
cana-5829	449	11	𝑁𝑜𝑟𝑚µ𝐸11	𝑁𝑜𝑟𝑚µ𝐸11	NOUN
cana-5829	449	12	(	(	PUNCT
cana-5829	449	13	𝛾11	𝛾11	VERB
cana-5829	449	14	+	+	CCONJ
cana-5829	449	15	𝑖𝛿11	𝑖𝛿11	PROPN
cana-5829	449	16	)	)	PUNCT
cana-5829	449	17	)	)	PUNCT
cana-5829	449	18	(	(	PUNCT
cana-5829	449	19	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	NOUN
cana-5829	449	20	(	(	PUNCT
cana-5829	449	21	𝛼12	𝛼12	NOUN
cana-5829	449	22	+	+	CCONJ
cana-5829	449	23	𝑖𝛽12	𝑖𝛽12	PROPN
cana-5829	449	24	)	)	PUNCT
cana-5829	449	25	𝑁𝑜𝑟𝑚µ𝐸12	𝑁𝑜𝑟𝑚µ𝐸12	NOUN
cana-5829	449	26	(	(	PUNCT
cana-5829	449	27	𝛾12	𝛾12	VERB
cana-5829	449	28	+	+	CCONJ
cana-5829	449	29	𝑖𝛿12	𝑖𝛿12	PROPN
cana-5829	449	30	)	)	PUNCT
cana-5829	449	31	)	)	PUNCT
cana-5829	449	32	(	(	PUNCT
cana-5829	449	33	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	X
cana-5829	449	34	(	(	PUNCT
cana-5829	449	35	𝛼21	𝛼21	NOUN
cana-5829	449	36	+	+	X
cana-5829	449	37	𝑖𝛽21	𝑖𝛽21	PROPN
cana-5829	449	38	)	)	PUNCT
cana-5829	449	39	𝑁𝑜𝑟𝑚µ𝐸21	𝑁𝑜𝑟𝑚µ𝐸21	NOUN
cana-5829	449	40	(	(	PUNCT
cana-5829	449	41	𝛾21	𝛾21	NOUN
cana-5829	449	42	+	+	CCONJ
cana-5829	450	1	𝑖𝛿21	𝑖𝛿21	PROPN
cana-5829	450	2	)	)	PUNCT
cana-5829	450	3	)	)	PUNCT
cana-5829	451	1	(	(	PUNCT
cana-5829	451	2	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	X
cana-5829	451	3	(	(	PUNCT
cana-5829	451	4	𝛼22	𝛼22	NOUN
cana-5829	451	5	+	+	CCONJ
cana-5829	451	6	𝑖𝛽22	𝑖𝛽22	PROPN
cana-5829	451	7	)	)	PUNCT
cana-5829	451	8	𝑁𝑜𝑟𝑚µ𝐸22	𝑁𝑜𝑟𝑚µ𝐸22	NOUN
cana-5829	451	9	(	(	PUNCT
cana-5829	451	10	𝛾22	𝛾22	PROPN
cana-5829	451	11	+	+	PROPN
cana-5829	451	12	𝑖𝛿22	𝑖𝛿22	PROPN
cana-5829	451	13	)	)	PUNCT
cana-5829	451	14	)	)	PUNCT
cana-5829	451	15	)	)	PUNCT
cana-5829	451	16			INTJ
cana-5829	451	17	(	(	PUNCT
cana-5829	451	18	(	(	PUNCT
cana-5829	451	19	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	451	20	(	(	PUNCT
cana-5829	451	21	𝑥11	𝑥11	ADV
cana-5829	451	22	+	+	CCONJ
cana-5829	451	23	𝑖𝑦11	𝑖𝑦11	NOUN
cana-5829	451	24	)	)	PUNCT
cana-5829	451	25	𝑁𝑜𝑟𝑚𝛾𝐹11	𝑁𝑜𝑟𝑚𝛾𝐹11	X
cana-5829	451	26	(	(	PUNCT
cana-5829	451	27	𝜇11	𝜇11	PROPN
cana-5829	451	28	+	+	PROPN
cana-5829	451	29	𝑖𝜃11	𝑖𝜃11	PROPN
cana-5829	451	30	)	)	PUNCT
cana-5829	451	31	)	)	PUNCT
cana-5829	451	32	(	(	PUNCT
cana-5829	451	33	𝑁𝑜𝑟𝑚𝛿𝐹12	𝑁𝑜𝑟𝑚𝛿𝐹12	X
cana-5829	451	34	(	(	PUNCT
cana-5829	451	35	𝑥12	𝑥12	VERB
cana-5829	451	36	+	+	CCONJ
cana-5829	451	37	𝑖𝑦12	𝑖𝑦12	PROPN
cana-5829	451	38	)	)	PUNCT
cana-5829	451	39	𝑁𝑜𝑟𝑚𝛾𝐹12	𝑁𝑜𝑟𝑚𝛾𝐹12	NOUN
cana-5829	452	1	(	(	PUNCT
cana-5829	452	2	𝜇12	𝜇12	NOUN
cana-5829	452	3	+	+	CCONJ
cana-5829	452	4	𝑖𝜃12	𝑖𝜃12	PROPN
cana-5829	452	5	)	)	PUNCT
cana-5829	452	6	)	)	PUNCT
cana-5829	453	1	(	(	PUNCT
cana-5829	453	2	𝑁𝑜𝑟𝑚𝛿𝐹21	𝑁𝑜𝑟𝑚𝛿𝐹21	X
cana-5829	453	3	(	(	PUNCT
cana-5829	453	4	𝑥21	𝑥21	PROPN
cana-5829	453	5	+	+	CCONJ
cana-5829	453	6	𝑖𝑦21	𝑖𝑦21	PROPN
cana-5829	453	7	)	)	PUNCT
cana-5829	453	8	𝑁𝑜𝑟𝑚𝛾𝐹21	𝑁𝑜𝑟𝑚𝛾𝐹21	ADV
cana-5829	453	9	(	(	PUNCT
cana-5829	453	10	𝜇21	𝜇21	VERB
cana-5829	453	11	+	+	CCONJ
cana-5829	453	12	𝑖𝜃21	𝑖𝜃21	PROPN
cana-5829	453	13	)	)	PUNCT
cana-5829	453	14	)	)	PUNCT
cana-5829	453	15	(	(	PUNCT
cana-5829	453	16	𝑁𝑜𝑟𝑚𝛿𝐹22	𝑁𝑜𝑟𝑚𝛿𝐹22	X
cana-5829	453	17	(	(	PUNCT
cana-5829	453	18	𝑥22	𝑥22	NOUN
cana-5829	453	19	+	+	X
cana-5829	453	20	𝑖𝑦22	𝑖𝑦22	PROPN
cana-5829	453	21	)	)	PUNCT
cana-5829	453	22	𝑁𝑜𝑟𝑚𝛾𝐹22	𝑁𝑜𝑟𝑚𝛾𝐹22	NOUN
cana-5829	453	23	(	(	PUNCT
cana-5829	453	24	𝜇22	𝜇22	NOUN
cana-5829	453	25	+	+	CCONJ
cana-5829	453	26	𝑖𝜃22	𝑖𝜃22	PROPN
cana-5829	453	27	)	)	PUNCT
cana-5829	453	28	)	)	PUNCT
cana-5829	453	29	)	)	PUNCT
cana-5829	453	30	calculate	calculate	NOUN
cana-5829	453	31	,	,	PUNCT
cana-5829	453	32	𝑋11	𝑋11	PROPN
cana-5829	453	33	,	,	PUNCT
cana-5829	453	34	𝑋12	𝑋12	PROPN
cana-5829	453	35	,	,	PUNCT
cana-5829	453	36	𝑋21and	𝑋21and	PROPN
cana-5829	453	37	𝑋22	𝑋22	PROPN
cana-5829	453	38	,	,	PUNCT
cana-5829	453	39	we	we	PRON
cana-5829	453	40	have	have	VERB
cana-5829	453	41	.	.	PUNCT
cana-5829	454	1	now	now	ADV
cana-5829	454	2	applying	apply	VERB
cana-5829	454	3	both	both	DET
cana-5829	454	4	side	side	NOUN
cana-5829	454	5	on	on	ADP
cana-5829	454	6	aebf	aebf	X
cana-5829	454	7	=	=	PRON
cana-5829	454	8	{	{	PUNCT
cana-5829	454	9	(	(	PUNCT
cana-5829	454	10	x	x	NOUN
cana-5829	454	11	,	,	PUNCT
cana-5829	454	12	y	y	PROPN
cana-5829	454	13	)	)	PUNCT
cana-5829	454	14	,	,	PUNCT
cana-5829	454	15	(	(	PUNCT
cana-5829	454	16	μa(x	μa(x	X
cana-5829	454	17	)	)	PUNCT
cana-5829	454	18	+	+	CCONJ
cana-5829	454	19	μb(y	μb(y	NUM
cana-5829	454	20	)	)	PUNCT
cana-5829	454	21	)	)	PUNCT
cana-5829	454	22	μa(x	μa(x	NOUN
cana-5829	454	23	)	)	PUNCT
cana-5829	454	24	.	.	PUNCT
cana-5829	455	1	μb(y	μb(y	NUM
cana-5829	455	2	)	)	PUNCT
cana-5829	456	1	,	,	PUNCT
cana-5829	456	2	ϑa(x).ϑb(y	ϑa(x).ϑb(y	ADJ
cana-5829	456	3	):	):	PUNCT
cana-5829	456	4	xe	xe	PROPN
cana-5829	456	5	,	,	PUNCT
cana-5829	456	6	yf	yf	NUM
cana-5829	456	7	}	}	PUNCT
cana-5829	456	8	,	,	PUNCT
cana-5829	456	9	we	we	PRON
cana-5829	456	10	have	have	VERB
cana-5829	456	11	norm𝐴𝐸𝑁𝑜𝑟𝑚𝐵𝐹	norm𝐴𝐸𝑁𝑜𝑟𝑚𝐵𝐹	PROPN
cana-5829	456	12	=	=	SYM
cana-5829	456	13	(	(	PUNCT
cana-5829	456	14	(	(	PUNCT
cana-5829	456	15	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	456	16	(	(	PUNCT
cana-5829	456	17	𝛼11	𝛼11	NOUN
cana-5829	456	18	+	+	PROPN
cana-5829	456	19	𝑖𝛽11	𝑖𝛽11	PROPN
cana-5829	456	20	)	)	PUNCT
cana-5829	456	21	𝑁𝑜𝑟𝑚µ𝐸11	𝑁𝑜𝑟𝑚µ𝐸11	NOUN
cana-5829	456	22	(	(	PUNCT
cana-5829	456	23	𝛾11	𝛾11	VERB
cana-5829	456	24	+	+	CCONJ
cana-5829	457	1	𝑖𝛿11	𝑖𝛿11	PROPN
cana-5829	457	2	)	)	PUNCT
cana-5829	457	3	)	)	PUNCT
cana-5829	457	4	(	(	PUNCT
cana-5829	457	5	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	NOUN
cana-5829	457	6	(	(	PUNCT
cana-5829	457	7	𝛼12	𝛼12	NOUN
cana-5829	457	8	+	+	CCONJ
cana-5829	457	9	𝑖𝛽12	𝑖𝛽12	PROPN
cana-5829	457	10	)	)	PUNCT
cana-5829	457	11	𝑁𝑜𝑟𝑚µ𝐸12	𝑁𝑜𝑟𝑚µ𝐸12	NOUN
cana-5829	457	12	(	(	PUNCT
cana-5829	457	13	𝛾12	𝛾12	VERB
cana-5829	457	14	+	+	CCONJ
cana-5829	457	15	𝑖𝛿12	𝑖𝛿12	PROPN
cana-5829	457	16	)	)	PUNCT
cana-5829	457	17	)	)	PUNCT
cana-5829	458	1	(	(	PUNCT
cana-5829	458	2	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	X
cana-5829	458	3	(	(	PUNCT
cana-5829	458	4	𝛼21	𝛼21	NOUN
cana-5829	458	5	+	+	X
cana-5829	458	6	𝑖𝛽21	𝑖𝛽21	PROPN
cana-5829	458	7	)	)	PUNCT
cana-5829	458	8	𝑁𝑜𝑟𝑚µ𝐸21	𝑁𝑜𝑟𝑚µ𝐸21	NOUN
cana-5829	458	9	(	(	PUNCT
cana-5829	458	10	𝛾21	𝛾21	NOUN
cana-5829	458	11	+	+	CCONJ
cana-5829	459	1	𝑖𝛿21	𝑖𝛿21	PROPN
cana-5829	459	2	)	)	PUNCT
cana-5829	459	3	)	)	PUNCT
cana-5829	460	1	(	(	PUNCT
cana-5829	460	2	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	X
cana-5829	460	3	(	(	PUNCT
cana-5829	460	4	𝛼22	𝛼22	NOUN
cana-5829	460	5	+	+	CCONJ
cana-5829	460	6	𝑖𝛽22	𝑖𝛽22	PROPN
cana-5829	460	7	)	)	PUNCT
cana-5829	460	8	𝑁𝑜𝑟𝑚µ𝐸22	𝑁𝑜𝑟𝑚µ𝐸22	NOUN
cana-5829	460	9	(	(	PUNCT
cana-5829	460	10	𝛾22	𝛾22	PROPN
cana-5829	460	11	+	+	PROPN
cana-5829	460	12	𝑖𝛿22	𝑖𝛿22	PROPN
cana-5829	460	13	)	)	PUNCT
cana-5829	460	14	)	)	PUNCT
cana-5829	460	15	)	)	PUNCT
cana-5829	460	16			INTJ
cana-5829	460	17	(	(	PUNCT
cana-5829	460	18	(	(	PUNCT
cana-5829	460	19	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	460	20	(	(	PUNCT
cana-5829	460	21	𝑥11	𝑥11	ADV
cana-5829	460	22	+	+	CCONJ
cana-5829	460	23	𝑖𝑦11	𝑖𝑦11	NOUN
cana-5829	460	24	)	)	PUNCT
cana-5829	460	25	𝑁𝑜𝑟𝑚𝛾𝐹11	𝑁𝑜𝑟𝑚𝛾𝐹11	X
cana-5829	460	26	(	(	PUNCT
cana-5829	460	27	𝜇11	𝜇11	PROPN
cana-5829	460	28	+	+	PROPN
cana-5829	460	29	𝑖𝜃11	𝑖𝜃11	PROPN
cana-5829	460	30	)	)	PUNCT
cana-5829	460	31	)	)	PUNCT
cana-5829	460	32	(	(	PUNCT
cana-5829	460	33	𝑁𝑜𝑟𝑚𝛿𝐹12	𝑁𝑜𝑟𝑚𝛿𝐹12	X
cana-5829	460	34	(	(	PUNCT
cana-5829	460	35	𝑥12	𝑥12	VERB
cana-5829	460	36	+	+	CCONJ
cana-5829	460	37	𝑖𝑦12	𝑖𝑦12	PROPN
cana-5829	460	38	)	)	PUNCT
cana-5829	460	39	𝑁𝑜𝑟𝑚𝛾𝐹12	𝑁𝑜𝑟𝑚𝛾𝐹12	NOUN
cana-5829	461	1	(	(	PUNCT
cana-5829	461	2	𝜇12	𝜇12	NOUN
cana-5829	461	3	+	+	CCONJ
cana-5829	461	4	𝑖𝜃12	𝑖𝜃12	PROPN
cana-5829	461	5	)	)	PUNCT
cana-5829	461	6	)	)	PUNCT
cana-5829	462	1	(	(	PUNCT
cana-5829	462	2	𝑁𝑜𝑟𝑚𝛿𝐹21	𝑁𝑜𝑟𝑚𝛿𝐹21	X
cana-5829	462	3	(	(	PUNCT
cana-5829	462	4	𝑥21	𝑥21	PROPN
cana-5829	462	5	+	+	CCONJ
cana-5829	462	6	𝑖𝑦21	𝑖𝑦21	PROPN
cana-5829	462	7	)	)	PUNCT
cana-5829	462	8	𝑁𝑜𝑟𝑚𝛾𝐹21	𝑁𝑜𝑟𝑚𝛾𝐹21	ADV
cana-5829	462	9	(	(	PUNCT
cana-5829	462	10	𝜇21	𝜇21	VERB
cana-5829	462	11	+	+	CCONJ
cana-5829	462	12	𝑖𝜃21	𝑖𝜃21	PROPN
cana-5829	462	13	)	)	PUNCT
cana-5829	462	14	)	)	PUNCT
cana-5829	462	15	(	(	PUNCT
cana-5829	462	16	𝑁𝑜𝑟𝑚𝛿𝐹22	𝑁𝑜𝑟𝑚𝛿𝐹22	X
cana-5829	462	17	(	(	PUNCT
cana-5829	462	18	𝑥22	𝑥22	NOUN
cana-5829	462	19	+	+	X
cana-5829	462	20	𝑖𝑦22	𝑖𝑦22	PROPN
cana-5829	462	21	)	)	PUNCT
cana-5829	462	22	𝑁𝑜𝑟𝑚𝛾𝐹22	𝑁𝑜𝑟𝑚𝛾𝐹22	NOUN
cana-5829	462	23	(	(	PUNCT
cana-5829	462	24	𝜇22	𝜇22	NOUN
cana-5829	462	25	+	+	CCONJ
cana-5829	462	26	𝑖𝜃22	𝑖𝜃22	PROPN
cana-5829	462	27	)	)	PUNCT
cana-5829	462	28	)	)	PUNCT
cana-5829	462	29	)	)	PUNCT
cana-5829	462	30	calculate	calculate	NOUN
cana-5829	462	31	,	,	PUNCT
cana-5829	462	32	𝑋11	𝑋11	PROPN
cana-5829	462	33	,	,	PUNCT
cana-5829	462	34	𝑋12	𝑋12	PROPN
cana-5829	462	35	,	,	PUNCT
cana-5829	462	36	𝑋21and	𝑋21and	PROPN
cana-5829	462	37	𝑋22	𝑋22	PROPN
cana-5829	462	38	,	,	PUNCT
cana-5829	462	39	we	we	PRON
cana-5829	462	40	have	have	VERB
cana-5829	462	41	x11	x11	PROPN
cana-5829	462	42	=(	=(	NOUN
cana-5829	462	43	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	462	44	(	(	PUNCT
cana-5829	462	45	𝛼11	𝛼11	NOUN
cana-5829	462	46	+	+	PROPN
cana-5829	462	47	𝑖𝛽11	𝑖𝛽11	PROPN
cana-5829	462	48	)	)	PUNCT
cana-5829	462	49	𝑁𝑜𝑟𝑚µ𝐸11	𝑁𝑜𝑟𝑚µ𝐸11	NOUN
cana-5829	462	50	(	(	PUNCT
cana-5829	462	51	𝛾11	𝛾11	VERB
cana-5829	462	52	+	+	CCONJ
cana-5829	462	53	𝑖𝛿11	𝑖𝛿11	PROPN
cana-5829	462	54	)	)	PUNCT
cana-5829	462	55	)	)	PUNCT
cana-5829	463	1	+	+	ADV
cana-5829	463	2	(	(	PUNCT
cana-5829	463	3	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	463	4	(	(	PUNCT
cana-5829	463	5	𝑥11	𝑥11	ADV
cana-5829	463	6	+	+	CCONJ
cana-5829	463	7	𝑖𝑦11	𝑖𝑦11	NOUN
cana-5829	463	8	)	)	PUNCT
cana-5829	463	9	𝑁𝑜𝑟𝑚𝛾𝐹11	𝑁𝑜𝑟𝑚𝛾𝐹11	X
cana-5829	463	10	(	(	PUNCT
cana-5829	463	11	𝜇11	𝜇11	PROPN
cana-5829	463	12	+	+	PROPN
cana-5829	463	13	𝑖𝜃11	𝑖𝜃11	PROPN
cana-5829	463	14	)	)	PUNCT
cana-5829	463	15	)	)	PUNCT
cana-5829	463	16	communications	communication	NOUN
cana-5829	463	17	on	on	ADP
cana-5829	463	18	applied	apply	VERB
cana-5829	463	19	nonlinear	nonlinear	ADJ
cana-5829	463	20	analysis	analysis	NOUN
cana-5829	463	21	issn	issn	NOUN
cana-5829	463	22	:	:	PUNCT
cana-5829	463	23	1074	1074	NUM
cana-5829	463	24	-	-	PUNCT
cana-5829	463	25	133x	133x	NUM
cana-5829	463	26	vol	vol	VERB
cana-5829	463	27	32	32	NUM
cana-5829	463	28	no	no	NOUN
cana-5829	463	29	.	.	PUNCT
cana-5829	464	1	10s	10	NOUN
cana-5829	464	2	(	(	PUNCT
cana-5829	464	3	2025	2025	NUM
cana-5829	464	4	)	)	PUNCT
cana-5829	464	5	2942	2942	NUM
cana-5829	464	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5829	465	1	where	where	SCONJ
cana-5829	465	2	∣μ11∣=	∣μ11∣=	X
cana-5829	465	3	(	(	PUNCT
cana-5829	465	4	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	465	5	(	(	PUNCT
cana-5829	465	6	max(𝛼11	max(𝛼11	NUM
cana-5829	465	7	,	,	PUNCT
cana-5829	465	8	𝑥11))2	𝑥11))2	X
cana-5829	465	9	+	+	CCONJ
cana-5829	465	10	(	(	PUNCT
cana-5829	465	11	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	465	12	max(𝛽11	max(𝛽11	PROPN
cana-5829	465	13	,	,	PUNCT
cana-5829	465	14	𝑦11))2	𝑦11))2	X
cana-5829	466	1	+	+	ADJ
cana-5829	466	2	(	(	PUNCT
cana-5829	466	3	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	466	4	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
cana-5829	466	5	(	(	PUNCT
cana-5829	466	6	𝛾11	𝛾11	VERB
cana-5829	466	7	,	,	PUNCT
cana-5829	466	8	𝜇11))2	𝜇11))2	ADJ
cana-5829	466	9	+	+	ADJ
cana-5829	466	10	(	(	PUNCT
cana-5829	466	11	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	466	12	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
cana-5829	466	13	(	(	PUNCT
cana-5829	466	14	𝛾11	𝛾11	VERB
cana-5829	466	15	,	,	PUNCT
cana-5829	466	16	𝜇11))2	𝜇11))2	PRON
cana-5829	466	17	<	<	X
cana-5829	466	18	1	1	NUM
cana-5829	466	19	,	,	PUNCT
cana-5829	466	20	∣ν11∣=	∣ν11∣=	PROPN
cana-5829	466	21	(	(	PUNCT
cana-5829	466	22	normµe11	normµe11	NOUN
cana-5829	466	23	𝑚𝑖𝑛(𝛾11	𝑚𝑖𝑛(𝛾11	PROPN
cana-5829	466	24	,	,	PUNCT
cana-5829	466	25	𝜇11))2	𝜇11))2	X
cana-5829	466	26	+	+	ADJ
cana-5829	466	27	(	(	PUNCT
cana-5829	466	28	𝑁𝑜𝑟𝑚𝛾𝐸11	𝑁𝑜𝑟𝑚𝛾𝐸11	X
cana-5829	466	29	𝑚𝑖𝑛(𝛿11	𝑚𝑖𝑛(𝛿11	PROPN
cana-5829	466	30	,	,	PUNCT
cana-5829	466	31	𝜃11))2	𝜃11))2	X
cana-5829	466	32	<	<	X
cana-5829	466	33	1	1	NUM
cana-5829	466	34	,	,	PUNCT
cana-5829	466	35	∣μ11∣+∣ν11∣	∣μ11∣+∣ν11∣	VERB
cana-5829	466	36	≤	≤	NUM
cana-5829	466	37	1	1	NUM
cana-5829	466	38	.	.	PUNCT
cana-5829	467	1	x12	x12	NUM
cana-5829	467	2	=(	=(	NOUN
cana-5829	467	3	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	NOUN
cana-5829	467	4	(	(	PUNCT
cana-5829	467	5	𝛼12	𝛼12	NOUN
cana-5829	467	6	+	+	CCONJ
cana-5829	467	7	𝑖𝛽12	𝑖𝛽12	PROPN
cana-5829	467	8	)	)	PUNCT
cana-5829	467	9	𝑁𝑜𝑟𝑚µ𝐸12	𝑁𝑜𝑟𝑚µ𝐸12	NOUN
cana-5829	467	10	(	(	PUNCT
cana-5829	467	11	𝛾12	𝛾12	VERB
cana-5829	467	12	+	+	CCONJ
cana-5829	467	13	𝑖𝛿12	𝑖𝛿12	PROPN
cana-5829	467	14	)	)	PUNCT
cana-5829	467	15	)	)	PUNCT
cana-5829	468	1	+	+	CCONJ
cana-5829	468	2	(	(	PUNCT
cana-5829	468	3	𝑁𝑜𝑟𝑚𝛿𝐹12	𝑁𝑜𝑟𝑚𝛿𝐹12	X
cana-5829	468	4	(	(	PUNCT
cana-5829	468	5	𝑥12	𝑥12	VERB
cana-5829	468	6	+	+	CCONJ
cana-5829	468	7	𝑖𝑦12	𝑖𝑦12	PROPN
cana-5829	468	8	)	)	PUNCT
cana-5829	468	9	𝑁𝑜𝑟𝑚𝛾𝐹12	𝑁𝑜𝑟𝑚𝛾𝐹12	NOUN
cana-5829	468	10	(	(	PUNCT
cana-5829	468	11	𝜇12	𝜇12	NOUN
cana-5829	468	12	+	+	CCONJ
cana-5829	468	13	𝑖𝜃12	𝑖𝜃12	PROPN
cana-5829	468	14	)	)	PUNCT
cana-5829	468	15	)	)	PUNCT
cana-5829	469	1	x21	x21	NUM
cana-5829	469	2	=(	=(	NOUN
cana-5829	469	3	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	PROPN
cana-5829	469	4	(	(	PUNCT
cana-5829	469	5	𝛼21	𝛼21	NOUN
cana-5829	469	6	+	+	X
cana-5829	469	7	𝑖𝛽21	𝑖𝛽21	PROPN
cana-5829	469	8	)	)	PUNCT
cana-5829	469	9	𝑁𝑜𝑟𝑚µ𝐸21	𝑁𝑜𝑟𝑚µ𝐸21	NOUN
cana-5829	469	10	(	(	PUNCT
cana-5829	469	11	𝛾21	𝛾21	NOUN
cana-5829	469	12	+	+	CCONJ
cana-5829	470	1	𝑖𝛿21	𝑖𝛿21	PROPN
cana-5829	470	2	)	)	PUNCT
cana-5829	470	3	)	)	PUNCT
cana-5829	471	1	+	+	CCONJ
cana-5829	471	2	(	(	PUNCT
cana-5829	471	3	𝑁𝑜𝑟𝑚𝛿𝐹21	𝑁𝑜𝑟𝑚𝛿𝐹21	ADP
cana-5829	471	4	(	(	PUNCT
cana-5829	471	5	𝑥21	𝑥21	PROPN
cana-5829	471	6	+	+	CCONJ
cana-5829	471	7	𝑖𝑦21	𝑖𝑦21	PROPN
cana-5829	471	8	)	)	PUNCT
cana-5829	471	9	𝑁𝑜𝑟𝑚𝛾𝐹21	𝑁𝑜𝑟𝑚𝛾𝐹21	ADV
cana-5829	471	10	(	(	PUNCT
cana-5829	471	11	𝜇21	𝜇21	VERB
cana-5829	471	12	+	+	CCONJ
cana-5829	471	13	𝑖𝜃21	𝑖𝜃21	PROPN
cana-5829	471	14	)	)	PUNCT
cana-5829	471	15	)	)	PUNCT
cana-5829	471	16	x22	x22	NUM
cana-5829	471	17	=(	=(	NOUN
cana-5829	471	18	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	PROPN
cana-5829	471	19	(	(	PUNCT
cana-5829	471	20	𝛼22	𝛼22	NOUN
cana-5829	471	21	+	+	CCONJ
cana-5829	471	22	𝑖𝛽22	𝑖𝛽22	PROPN
cana-5829	471	23	)	)	PUNCT
cana-5829	471	24	𝑁𝑜𝑟𝑚µ𝐸22	𝑁𝑜𝑟𝑚µ𝐸22	NOUN
cana-5829	471	25	(	(	PUNCT
cana-5829	471	26	𝛾22	𝛾22	PROPN
cana-5829	471	27	+	+	PROPN
cana-5829	471	28	𝑖𝛿22	𝑖𝛿22	PROPN
cana-5829	471	29	)	)	PUNCT
cana-5829	471	30	)	)	PUNCT
cana-5829	472	1	+	+	CCONJ
cana-5829	472	2	(	(	PUNCT
cana-5829	472	3	𝑁𝑜𝑟𝑚𝛿𝐹22	𝑁𝑜𝑟𝑚𝛿𝐹22	X
cana-5829	472	4	(	(	PUNCT
cana-5829	472	5	𝑥22	𝑥22	NOUN
cana-5829	472	6	+	+	X
cana-5829	472	7	𝑖𝑦22	𝑖𝑦22	PROPN
cana-5829	472	8	)	)	PUNCT
cana-5829	472	9	𝑁𝑜𝑟𝑚𝛾𝐹22	𝑁𝑜𝑟𝑚𝛾𝐹22	NOUN
cana-5829	472	10	(	(	PUNCT
cana-5829	472	11	𝜇22	𝜇22	NOUN
cana-5829	472	12	+	+	CCONJ
cana-5829	472	13	𝑖𝜃22	𝑖𝜃22	PROPN
cana-5829	472	14	)	)	PUNCT
cana-5829	472	15	)	)	PUNCT
cana-5829	473	1	𝐴𝑝𝑝𝑙𝑦𝑖𝑛𝑔	𝐴𝑝𝑝𝑙𝑦𝑖𝑛𝑔	PROPN
cana-5829	473	2	𝑓𝑜𝑟𝑚𝑢𝑙𝑎	𝑓𝑜𝑟𝑚𝑢𝑙𝑎	VERB
cana-5829	473	3	aebf	aebf	X
cana-5829	474	1	=	=	PRON
cana-5829	474	2	{	{	PUNCT
cana-5829	474	3	(	(	PUNCT
cana-5829	474	4	x	x	NOUN
cana-5829	474	5	,	,	PUNCT
cana-5829	474	6	y	y	PROPN
cana-5829	474	7	)	)	PUNCT
cana-5829	474	8	,	,	PUNCT
cana-5829	474	9	(	(	PUNCT
cana-5829	474	10	μa(x	μa(x	X
cana-5829	474	11	)	)	PUNCT
cana-5829	475	1	+	+	CCONJ
cana-5829	475	2	μb(y	μb(y	NUM
cana-5829	475	3	)	)	PUNCT
cana-5829	475	4	)	)	PUNCT
cana-5829	475	5	μa(x	μa(x	NOUN
cana-5829	475	6	)	)	PUNCT
cana-5829	475	7	.	.	PUNCT
cana-5829	476	1	μb(y	μb(y	NUM
cana-5829	476	2	)	)	PUNCT
cana-5829	476	3	,	,	PUNCT
cana-5829	477	1	ϑa(x).ϑb(y	ϑa(x).ϑb(y	ADJ
cana-5829	477	2	):	):	PUNCT
cana-5829	477	3	xe	xe	PROPN
cana-5829	477	4	,	,	PUNCT
cana-5829	477	5	yf	yf	NUM
cana-5829	477	6	}	}	PUNCT
cana-5829	477	7	x11	x11	NOUN
cana-5829	478	1	=	=	NOUN
cana-5829	478	2	{	{	PUNCT
cana-5829	478	3	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	478	4	(	(	PUNCT
cana-5829	478	5	𝛼11	𝛼11	NOUN
cana-5829	478	6	+	+	X
cana-5829	478	7	𝑖𝛽11	𝑖𝛽11	PUNCT
cana-5829	478	8	)	)	PUNCT
cana-5829	479	1	+	+	CCONJ
cana-5829	479	2	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	479	3	(	(	PUNCT
cana-5829	479	4	𝑥11	𝑥11	ADV
cana-5829	479	5	+	+	CCONJ
cana-5829	479	6	𝑖𝑦11	𝑖𝑦11	PROPN
cana-5829	479	7	)	)	PUNCT
cana-5829	479	8	−	−	NOUN
cana-5829	479	9	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	SYM
cana-5829	479	10	(	(	PUNCT
cana-5829	479	11	𝛼11	𝛼11	NOUN
cana-5829	479	12	+	+	PROPN
cana-5829	479	13	𝑖𝛽11	𝑖𝛽11	PROPN
cana-5829	479	14	)	)	PUNCT
cana-5829	479	15	.	.	PUNCT
cana-5829	480	1	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	480	2	(	(	PUNCT
cana-5829	480	3	𝑥11	𝑥11	ADV
cana-5829	480	4	+	+	CCONJ
cana-5829	480	5	𝑖𝑦11	𝑖𝑦11	PROPN
cana-5829	480	6	)	)	PUNCT
cana-5829	480	7	,	,	PUNCT
cana-5829	480	8	𝑁𝑜𝑟𝑚µ𝐸11	𝑁𝑜𝑟𝑚µ𝐸11	NOUN
cana-5829	480	9	(	(	PUNCT
cana-5829	480	10	𝛾11	𝛾11	VERB
cana-5829	480	11	+	+	CCONJ
cana-5829	480	12	𝑖𝛿11	𝑖𝛿11	PROPN
cana-5829	480	13	)	)	PUNCT
cana-5829	480	14	.	.	PUNCT
cana-5829	481	1	𝑁𝑜𝑟𝑚𝛾𝐹11	𝑁𝑜𝑟𝑚𝛾𝐹11	PROPN
cana-5829	481	2	(	(	PUNCT
cana-5829	481	3	𝜇11	𝜇11	PROPN
cana-5829	481	4	+	+	PROPN
cana-5829	481	5	𝑖𝜃11	𝑖𝜃11	PROPN
cana-5829	481	6	)	)	PUNCT
cana-5829	481	7	}	}	PUNCT
cana-5829	481	8	x12	x12	NUM
cana-5829	482	1	=	=	SYM
cana-5829	482	2	{	{	PUNCT
cana-5829	482	3	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	NOUN
cana-5829	482	4	(	(	PUNCT
cana-5829	482	5	𝛼12	𝛼12	NOUN
cana-5829	482	6	+	+	X
cana-5829	482	7	𝑖𝛽12	𝑖𝛽12	PROPN
cana-5829	482	8	)	)	PUNCT
cana-5829	483	1	+	+	CCONJ
cana-5829	483	2	𝑁𝑜𝑟𝑚𝛿𝐹12	𝑁𝑜𝑟𝑚𝛿𝐹12	X
cana-5829	483	3	(	(	PUNCT
cana-5829	483	4	𝑥12	𝑥12	VERB
cana-5829	483	5	+	+	CCONJ
cana-5829	483	6	𝑖𝑦12	𝑖𝑦12	PROPN
cana-5829	483	7	)	)	PUNCT
cana-5829	483	8	−	−	NOUN
cana-5829	483	9	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	NOUN
cana-5829	483	10	(	(	PUNCT
cana-5829	483	11	𝛼12	𝛼12	NOUN
cana-5829	483	12	+	+	X
cana-5829	483	13	𝑖𝛽12	𝑖𝛽12	PROPN
cana-5829	483	14	)	)	PUNCT
cana-5829	483	15	.	.	PUNCT
cana-5829	484	1	𝑁𝑜𝑟𝑚𝛿𝐹12	𝑁𝑜𝑟𝑚𝛿𝐹12	PROPN
cana-5829	485	1	(	(	PUNCT
cana-5829	485	2	𝑥12	𝑥12	VERB
cana-5829	485	3	+	+	CCONJ
cana-5829	485	4	𝑖𝑦12	𝑖𝑦12	PROPN
cana-5829	485	5	)	)	PUNCT
cana-5829	485	6	,	,	PUNCT
cana-5829	485	7	𝑁𝑜𝑟𝑚µ𝐸12	𝑁𝑜𝑟𝑚µ𝐸12	NOUN
cana-5829	485	8	(	(	PUNCT
cana-5829	485	9	𝛾12	𝛾12	VERB
cana-5829	485	10	+	+	CCONJ
cana-5829	485	11	𝑖𝛿12	𝑖𝛿12	PROPN
cana-5829	485	12	)	)	PUNCT
cana-5829	485	13	.	.	PUNCT
cana-5829	486	1	𝑁𝑜𝑟𝑚𝛾𝐹12	𝑁𝑜𝑟𝑚𝛾𝐹12	NOUN
cana-5829	487	1	(	(	PUNCT
cana-5829	487	2	𝜇12	𝜇12	NOUN
cana-5829	487	3	+	+	CCONJ
cana-5829	487	4	𝑖𝜃12	𝑖𝜃12	PROPN
cana-5829	487	5	)	)	PUNCT
cana-5829	487	6	}	}	PUNCT
cana-5829	487	7	x21	x21	PROPN
cana-5829	488	1	=	=	SYM
cana-5829	488	2	{	{	PUNCT
cana-5829	488	3	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	X
cana-5829	488	4	(	(	PUNCT
cana-5829	488	5	𝛼21	𝛼21	NOUN
cana-5829	488	6	+	+	X
cana-5829	488	7	𝑖𝛽21	𝑖𝛽21	PROPN
cana-5829	488	8	)	)	PUNCT
cana-5829	488	9	+	+	NUM
cana-5829	488	10	𝑁𝑜𝑟𝑚𝛿𝐹21	𝑁𝑜𝑟𝑚𝛿𝐹21	PRON
cana-5829	488	11	(	(	PUNCT
cana-5829	488	12	𝑥21	𝑥21	NOUN
cana-5829	488	13	+	+	CCONJ
cana-5829	488	14	𝑖𝑦21	𝑖𝑦21	PROPN
cana-5829	488	15	)	)	PUNCT
cana-5829	488	16	−	−	PRON
cana-5829	489	1	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	X
cana-5829	489	2	(	(	PUNCT
cana-5829	489	3	𝛼21	𝛼21	NOUN
cana-5829	489	4	+	+	X
cana-5829	489	5	𝑖𝛽21	𝑖𝛽21	PROPN
cana-5829	489	6	)	)	PUNCT
cana-5829	489	7	.	.	PUNCT
cana-5829	490	1	𝑁𝑜𝑟𝑚𝛿𝐹21	𝑁𝑜𝑟𝑚𝛿𝐹21	PUNCT
cana-5829	490	2	(	(	PUNCT
cana-5829	490	3	𝑥21	𝑥21	NOUN
cana-5829	490	4	+	+	CCONJ
cana-5829	490	5	𝑦21	𝑦21	NOUN
cana-5829	490	6	)	)	PUNCT
cana-5829	490	7	,	,	PUNCT
cana-5829	490	8	𝑁𝑜𝑟𝑚µ𝐸21	𝑁𝑜𝑟𝑚µ𝐸21	INTJ
cana-5829	490	9	(	(	PUNCT
cana-5829	490	10	𝛾21	𝛾21	NOUN
cana-5829	490	11	+	+	CCONJ
cana-5829	490	12	𝑖𝛿21	𝑖𝛿21	PROPN
cana-5829	490	13	)	)	PUNCT
cana-5829	490	14	.	.	PUNCT
cana-5829	491	1	𝑁𝑜𝑟𝑚𝛾𝐹21	𝑁𝑜𝑟𝑚𝛾𝐹21	ADV
cana-5829	491	2	(	(	PUNCT
cana-5829	491	3	𝜇21	𝜇21	VERB
cana-5829	491	4	+	+	CCONJ
cana-5829	491	5	𝑖𝜃21	𝑖𝜃21	PROPN
cana-5829	491	6	)	)	PUNCT
cana-5829	491	7	}	}	PUNCT
cana-5829	491	8	x22	x22	NOUN
cana-5829	492	1	=	=	SYM
cana-5829	492	2	{	{	PUNCT
cana-5829	492	3	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	X
cana-5829	492	4	(	(	PUNCT
cana-5829	492	5	𝛼22	𝛼22	NOUN
cana-5829	492	6	+	+	PUNCT
cana-5829	492	7	𝑖𝛽22	𝑖𝛽22	PROPN
cana-5829	492	8	)	)	PUNCT
cana-5829	493	1	+	+	CCONJ
cana-5829	494	1	𝑁𝑜𝑟𝑚𝛿𝐹22	𝑁𝑜𝑟𝑚𝛿𝐹22	X
cana-5829	494	2	(	(	PUNCT
cana-5829	494	3	𝑥22	𝑥22	NOUN
cana-5829	494	4	+	+	X
cana-5829	494	5	𝑖𝑦22	𝑖𝑦22	PROPN
cana-5829	494	6	)	)	PUNCT
cana-5829	494	7	−	−	PROPN
cana-5829	494	8	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	NOUN
cana-5829	495	1	(	(	PUNCT
cana-5829	495	2	𝛼22	𝛼22	NOUN
cana-5829	495	3	+	+	PUNCT
cana-5829	495	4	𝑖𝛽22	𝑖𝛽22	PROPN
cana-5829	495	5	)	)	PUNCT
cana-5829	495	6	.	.	PUNCT
cana-5829	496	1	𝑁𝑜𝑟𝑚𝛿𝐹22	𝑁𝑜𝑟𝑚𝛿𝐹22	PUNCT
cana-5829	496	2	(	(	PUNCT
cana-5829	496	3	𝑥22	𝑥22	NOUN
cana-5829	496	4	+	+	CCONJ
cana-5829	496	5	𝑦22	𝑦22	NUM
cana-5829	496	6	)	)	PUNCT
cana-5829	496	7	,	,	PUNCT
cana-5829	496	8	𝑁𝑜𝑟𝑚µ𝐸22	𝑁𝑜𝑟𝑚µ𝐸22	CCONJ
cana-5829	496	9	(	(	PUNCT
cana-5829	496	10	𝛾22	𝛾22	PROPN
cana-5829	496	11	+	+	PROPN
cana-5829	496	12	𝑖𝛿22	𝑖𝛿22	PROPN
cana-5829	496	13	)	)	PUNCT
cana-5829	496	14	.	.	PUNCT
cana-5829	496	15	𝑁𝑜𝑟𝑚𝛾𝐹22	𝑁𝑜𝑟𝑚𝛾𝐹22	X
cana-5829	497	1	(	(	PUNCT
cana-5829	497	2	𝜇22	𝜇22	NOUN
cana-5829	497	3	+	+	CCONJ
cana-5829	497	4	𝑖𝜃22	𝑖𝜃22	PROPN
cana-5829	497	5	)	)	PUNCT
cana-5829	497	6	}	}	PUNCT
cana-5829	497	7	x11	x11	NOUN
cana-5829	498	1	=	=	NOUN
cana-5829	498	2	{	{	PUNCT
cana-5829	498	3	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	VERB
cana-5829	498	4	+	+	PUNCT
cana-5829	498	5	𝛿𝐹11	𝛿𝐹11	X
cana-5829	498	6	(	(	PUNCT
cana-5829	498	7	(	(	PUNCT
cana-5829	498	8	𝛼11	𝛼11	NOUN
cana-5829	498	9	+	+	CCONJ
cana-5829	498	10	𝑥11	𝑥11	ADV
cana-5829	498	11	−	−	PROPN
cana-5829	498	12	𝛼11	𝛼11	PROPN
cana-5829	498	13	.	.	PUNCT
cana-5829	498	14	𝑥11	𝑥11	ADV
cana-5829	498	15	)	)	PUNCT
cana-5829	499	1	+	+	CCONJ
cana-5829	499	2	𝑖(𝛽11+𝑦11	𝑖(𝛽11+𝑦11	PRON
cana-5829	499	3	−	−	NOUN
cana-5829	499	4	𝛽11.𝑦11	𝛽11.𝑦11	PROPN
cana-5829	499	5	)	)	PUNCT
cana-5829	499	6	)	)	PUNCT
cana-5829	499	7	,	,	PUNCT
cana-5829	499	8	𝑁𝑜𝑟𝑚µ𝐸11+𝛾𝐹11	𝑁𝑜𝑟𝑚µ𝐸11+𝛾𝐹11	X
cana-5829	499	9	(	(	PUNCT
cana-5829	499	10	𝛾11	𝛾11	VERB
cana-5829	499	11	.	.	PUNCT
cana-5829	500	1	𝜇11	𝜇11	PROPN
cana-5829	500	2	+	+	PUNCT
cana-5829	500	3	𝑖𝛿11	𝑖𝛿11	PROPN
cana-5829	500	4	.	.	PROPN
cana-5829	500	5	𝜃11	𝜃11	NOUN
cana-5829	500	6	)	)	PUNCT
cana-5829	500	7	}	}	PUNCT
cana-5829	500	8	where	where	SCONJ
cana-5829	500	9	∣μ11∣=	∣μ11∣=	NOUN
cana-5829	500	10	(	(	PUNCT
cana-5829	500	11	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	VERB
cana-5829	500	12	+	+	CCONJ
cana-5829	500	13	𝛿𝐹11	𝛿𝐹11	X
cana-5829	500	14	(	(	PUNCT
cana-5829	500	15	(	(	PUNCT
cana-5829	500	16	𝛼11	𝛼11	NOUN
cana-5829	500	17	+	+	CCONJ
cana-5829	500	18	𝑥11	𝑥11	ADV
cana-5829	500	19	−	−	PROPN
cana-5829	500	20	𝛼11	𝛼11	ADJ
cana-5829	500	21	.	.	PUNCT
cana-5829	501	1	𝑥11))2	𝑥11))2	X
cana-5829	502	1	+	+	CCONJ
cana-5829	502	2	(	(	PUNCT
cana-5829	502	3	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	502	4	+	+	PUNCT
cana-5829	502	5	𝛿𝐹11	𝛿𝐹11	NUM
cana-5829	502	6	(	(	PUNCT
cana-5829	502	7	𝛽11	𝛽11	NOUN
cana-5829	502	8	+	+	CCONJ
cana-5829	502	9	𝑦11	𝑦11	ADJ
cana-5829	502	10	−	−	PROPN
cana-5829	502	11	𝛽11	𝛽11	NOUN
cana-5829	502	12	.	.	PUNCT
cana-5829	503	1	𝑦11))2	𝑦11))2	X
cana-5829	504	1	<	<	X
cana-5829	504	2	1	1	NUM
cana-5829	504	3	∣	∣	PROPN
cana-5829	504	4	ν11	ν11	NOUN
cana-5829	504	5	∣=	∣=	PROPN
cana-5829	504	6	(	(	PUNCT
cana-5829	504	7	𝑁𝑜𝑟𝑚µ𝐸11+𝛾𝐹11	𝑁𝑜𝑟𝑚µ𝐸11+𝛾𝐹11	X
cana-5829	504	8	(	(	PUNCT
cana-5829	504	9	𝛾11	𝛾11	VERB
cana-5829	504	10	.	.	PUNCT
cana-5829	505	1	𝜇11)2	𝜇11)2	AUX
cana-5829	505	2	+	+	CCONJ
cana-5829	505	3	𝑁𝑜𝑟𝑚µ𝐸11+𝛾𝐹11	𝑁𝑜𝑟𝑚µ𝐸11+𝛾𝐹11	X
cana-5829	505	4	(	(	PUNCT
cana-5829	505	5	𝛿11	𝛿11	PROPN
cana-5829	505	6	.	.	PUNCT
cana-5829	505	7	𝜃11)2	𝜃11)2	VERB
cana-5829	505	8	<	<	X
cana-5829	505	9	1	1	NUM
cana-5829	505	10	,	,	PUNCT
cana-5829	505	11	∣μ11∣+∣ν11∣	∣μ11∣+∣ν11∣	VERB
cana-5829	505	12	≤	≤	NUM
cana-5829	505	13	1	1	NUM
cana-5829	505	14	.	.	PUNCT
cana-5829	505	15	x12	x12	NUM
cana-5829	506	1	=	=	SYM
cana-5829	506	2	{	{	PUNCT
cana-5829	506	3	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	X
cana-5829	506	4	+	+	CCONJ
cana-5829	506	5	𝛿𝐹12	𝛿𝐹12	X
cana-5829	506	6	(	(	PUNCT
cana-5829	506	7	(	(	PUNCT
cana-5829	506	8	𝛼12	𝛼12	NOUN
cana-5829	506	9	+	+	CCONJ
cana-5829	506	10	𝑥12	𝑥12	VERB
cana-5829	506	11	−	−	PROPN
cana-5829	506	12	𝛼12	𝛼12	NOUN
cana-5829	506	13	.	.	PUNCT
cana-5829	507	1	𝑥12	𝑥12	VERB
cana-5829	507	2	)	)	PUNCT
cana-5829	508	1	+	+	NUM
cana-5829	508	2	𝑖(𝛽12+𝑦12	𝑖(𝛽12+𝑦12	NOUN
cana-5829	508	3	−	−	PROPN
cana-5829	508	4	𝛽12.𝑦12	𝛽12.𝑦12	PROPN
cana-5829	508	5	)	)	PUNCT
cana-5829	508	6	)	)	PUNCT
cana-5829	508	7	,	,	PUNCT
cana-5829	508	8	𝑁𝑜𝑟𝑚µ𝐸12+𝛾𝐹12	𝑁𝑜𝑟𝑚µ𝐸12+𝛾𝐹12	PROPN
cana-5829	508	9	(	(	PUNCT
cana-5829	508	10	𝛾12	𝛾12	PROPN
cana-5829	508	11	.	.	PUNCT
cana-5829	508	12	𝜇12	𝜇12	PROPN
cana-5829	508	13	+	+	CCONJ
cana-5829	508	14	𝑖𝛿12	𝑖𝛿12	PROPN
cana-5829	508	15	.	.	PUNCT
cana-5829	508	16	𝜃12	𝜃12	ADJ
cana-5829	508	17	)	)	PUNCT
cana-5829	508	18	}	}	PUNCT
cana-5829	508	19	where	where	SCONJ
cana-5829	508	20	∣μ12∣=	∣μ12∣=	X
cana-5829	508	21	(	(	PUNCT
cana-5829	508	22	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	NOUN
cana-5829	508	23	+	+	CCONJ
cana-5829	508	24	𝛿𝐹12	𝛿𝐹12	X
cana-5829	508	25	(	(	PUNCT
cana-5829	508	26	(	(	PUNCT
cana-5829	508	27	𝛼12	𝛼12	NOUN
cana-5829	508	28	+	+	CCONJ
cana-5829	508	29	𝑥12	𝑥12	VERB
cana-5829	508	30	−	−	PROPN
cana-5829	508	31	𝛼12	𝛼12	NUM
cana-5829	508	32	.	.	PUNCT
cana-5829	509	1	𝑥12))2	𝑥12))2	X
cana-5829	510	1	+	+	CCONJ
cana-5829	510	2	(	(	PUNCT
cana-5829	510	3	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	X
cana-5829	510	4	+	+	CCONJ
cana-5829	510	5	𝛿𝐹12	𝛿𝐹12	X
cana-5829	510	6	(	(	PUNCT
cana-5829	510	7	𝛽12	𝛽12	PROPN
cana-5829	510	8	+	+	NUM
cana-5829	510	9	𝑦12	𝑦12	NOUN
cana-5829	510	10	−	−	PROPN
cana-5829	510	11	𝛽12	𝛽12	ADJ
cana-5829	510	12	.	.	PUNCT
cana-5829	510	13	𝑦12))2	𝑦12))2	X
cana-5829	511	1	<	<	X
cana-5829	511	2	1	1	NUM
cana-5829	511	3	∣	∣	PROPN
cana-5829	511	4	ν12	ν12	NOUN
cana-5829	511	5	∣=	∣=	PROPN
cana-5829	511	6	(	(	PUNCT
cana-5829	511	7	𝑁𝑜𝑟𝑚µ𝐸12+𝛾𝐹12	𝑁𝑜𝑟𝑚µ𝐸12+𝛾𝐹12	PROPN
cana-5829	511	8	(	(	PUNCT
cana-5829	511	9	𝛾12	𝛾12	PROPN
cana-5829	511	10	.	.	PUNCT
cana-5829	511	11	𝜇12)2	𝜇12)2	PROPN
cana-5829	511	12	+	+	CCONJ
cana-5829	511	13	𝑁𝑜𝑟𝑚µ𝐸12+𝛾𝐹12	𝑁𝑜𝑟𝑚µ𝐸12+𝛾𝐹12	PROPN
cana-5829	511	14	(	(	PUNCT
cana-5829	511	15	𝛿12	𝛿12	NOUN
cana-5829	511	16	.	.	PROPN
cana-5829	511	17	𝜃12)2	𝜃12)2	VERB
cana-5829	511	18	<	<	X
cana-5829	511	19	1	1	NUM
cana-5829	511	20	,	,	PUNCT
cana-5829	511	21	∣μ12∣+∣ν12∣	∣μ12∣+∣ν12∣	ADJ
cana-5829	511	22	≤	≤	NUM
cana-5829	511	23	1	1	NUM
cana-5829	511	24	.	.	PUNCT
cana-5829	512	1	x21	x21	NUM
cana-5829	512	2	=	=	SYM
cana-5829	512	3	{	{	PUNCT
cana-5829	512	4	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	ADV
cana-5829	512	5	+	+	NUM
cana-5829	512	6	𝛿𝐹21	𝛿𝐹21	X
cana-5829	512	7	(	(	PUNCT
cana-5829	512	8	(	(	PUNCT
cana-5829	512	9	𝛼21	𝛼21	NOUN
cana-5829	512	10	+	+	CCONJ
cana-5829	512	11	𝑥21	𝑥21	NOUN
cana-5829	512	12	−	−	PROPN
cana-5829	512	13	𝛼21	𝛼21	NOUN
cana-5829	512	14	.	.	PUNCT
cana-5829	513	1	𝑥21	𝑥21	NOUN
cana-5829	513	2	)	)	PUNCT
cana-5829	514	1	+	+	CCONJ
cana-5829	514	2	𝑖(𝛽21+𝑦21	𝑖(𝛽21+𝑦21	NUM
cana-5829	514	3	−	−	X
cana-5829	514	4	𝛽21.𝑦21	𝛽21.𝑦21	NOUN
cana-5829	514	5	)	)	PUNCT
cana-5829	514	6	)	)	PUNCT
cana-5829	514	7	,	,	PUNCT
cana-5829	514	8	𝑁𝑜𝑟𝑚µ𝐸21+𝛾𝐹21	𝑁𝑜𝑟𝑚µ𝐸21+𝛾𝐹21	NUM
cana-5829	514	9	(	(	PUNCT
cana-5829	514	10	𝛾21	𝛾21	PROPN
cana-5829	514	11	.	.	PUNCT
cana-5829	515	1	𝜇21	𝜇21	PROPN
cana-5829	516	1	+	+	PROPN
cana-5829	516	2	𝑖𝛿21	𝑖𝛿21	PROPN
cana-5829	516	3	.	.	PUNCT
cana-5829	516	4	𝜃21	𝜃21	NOUN
cana-5829	516	5	)	)	PUNCT
cana-5829	516	6	}	}	PUNCT
cana-5829	516	7	where	where	SCONJ
cana-5829	516	8	∣μ21∣=	∣μ21∣=	X
cana-5829	516	9	(	(	PUNCT
cana-5829	516	10	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	X
cana-5829	516	11	+	+	NUM
cana-5829	516	12	𝛿𝐹21	𝛿𝐹21	X
cana-5829	516	13	(	(	PUNCT
cana-5829	516	14	(	(	PUNCT
cana-5829	516	15	𝛼21	𝛼21	NOUN
cana-5829	516	16	+	+	CCONJ
cana-5829	516	17	𝑥21	𝑥21	NOUN
cana-5829	516	18	−	−	PROPN
cana-5829	516	19	𝛼21	𝛼21	NOUN
cana-5829	516	20	.	.	PUNCT
cana-5829	517	1	𝑥21))2	𝑥21))2	X
cana-5829	518	1	+	+	CCONJ
cana-5829	518	2	(	(	PUNCT
cana-5829	518	3	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	X
cana-5829	518	4	+	+	NUM
cana-5829	518	5	𝛿𝐹21	𝛿𝐹21	X
cana-5829	518	6	(	(	PUNCT
cana-5829	518	7	𝛽21	𝛽21	NOUN
cana-5829	518	8	+	+	CCONJ
cana-5829	518	9	𝑦21	𝑦21	PROPN
cana-5829	518	10	−	−	PROPN
cana-5829	518	11	𝛽21	𝛽21	PROPN
cana-5829	518	12	.	.	PUNCT
cana-5829	519	1	𝑦21))2	𝑦21))2	PRON
cana-5829	520	1	<	<	X
cana-5829	520	2	1	1	NUM
cana-5829	520	3	∣	∣	ADJ
cana-5829	520	4	ν21	ν21	NOUN
cana-5829	520	5	∣=	∣=	PROPN
cana-5829	520	6	(	(	PUNCT
cana-5829	520	7	𝑁𝑜𝑟𝑚µ𝐸21+𝛾𝐹21	𝑁𝑜𝑟𝑚µ𝐸21+𝛾𝐹21	X
cana-5829	520	8	(	(	PUNCT
cana-5829	520	9	𝛾21	𝛾21	PROPN
cana-5829	520	10	.	.	PUNCT
cana-5829	521	1	𝜇21)2	𝜇21)2	VERB
cana-5829	521	2	+	+	NUM
cana-5829	521	3	𝑁𝑜𝑟𝑚µ𝐸21+𝛾𝐹21	𝑁𝑜𝑟𝑚µ𝐸21+𝛾𝐹21	PROPN
cana-5829	521	4	(	(	PUNCT
cana-5829	521	5	𝛿21	𝛿21	PROPN
cana-5829	521	6	.	.	PUNCT
cana-5829	522	1	𝜃21)2	𝜃21)2	VERB
cana-5829	523	1	<	<	X
cana-5829	524	1	1	1	NUM
cana-5829	524	2	,	,	PUNCT
cana-5829	524	3	∣μ21∣+∣ν21∣	∣μ21∣+∣ν21∣	VERB
cana-5829	524	4	≤	≤	NUM
cana-5829	524	5	1	1	NUM
cana-5829	524	6	.	.	PUNCT
cana-5829	524	7	x22	x22	NOUN
cana-5829	525	1	=	=	SYM
cana-5829	525	2	{	{	PUNCT
cana-5829	525	3	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	X
cana-5829	525	4	+	+	SYM
cana-5829	525	5	𝛿𝐹22	𝛿𝐹22	X
cana-5829	525	6	(	(	PUNCT
cana-5829	525	7	(	(	PUNCT
cana-5829	525	8	𝛼22	𝛼22	NOUN
cana-5829	525	9	+	+	CCONJ
cana-5829	525	10	𝑥22	𝑥22	NOUN
cana-5829	525	11	−	−	PROPN
cana-5829	525	12	𝛼22	𝛼22	NOUN
cana-5829	525	13	.	.	PUNCT
cana-5829	526	1	𝑥22	𝑥22	NOUN
cana-5829	526	2	)	)	PUNCT
cana-5829	527	1	+	+	CCONJ
cana-5829	527	2	𝑖(𝛽22+𝑦22	𝑖(𝛽22+𝑦22	ADP
cana-5829	527	3	−	−	PROPN
cana-5829	527	4	𝛽22.𝑦22	𝛽22.𝑦22	PROPN
cana-5829	527	5	)	)	PUNCT
cana-5829	527	6	)	)	PUNCT
cana-5829	527	7	,	,	PUNCT
cana-5829	528	1	𝑁𝑜𝑟𝑚µ𝐸22+𝛾𝐹22	𝑁𝑜𝑟𝑚µ𝐸22+𝛾𝐹22	X
cana-5829	528	2	(	(	PUNCT
cana-5829	528	3	𝛾22	𝛾22	PROPN
cana-5829	528	4	.	.	PUNCT
cana-5829	528	5	𝜇22	𝜇22	PROPN
cana-5829	528	6	+	+	CCONJ
cana-5829	529	1	𝑖𝛿22	𝑖𝛿22	PROPN
cana-5829	529	2	.	.	PUNCT
cana-5829	529	3	𝜃22	𝜃22	NOUN
cana-5829	529	4	)	)	PUNCT
cana-5829	529	5	}	}	PUNCT
cana-5829	529	6	communications	communication	NOUN
cana-5829	529	7	on	on	ADP
cana-5829	529	8	applied	apply	VERB
cana-5829	529	9	nonlinear	nonlinear	ADJ
cana-5829	529	10	analysis	analysis	NOUN
cana-5829	529	11	issn	issn	NOUN
cana-5829	529	12	:	:	PUNCT
cana-5829	529	13	1074	1074	NUM
cana-5829	529	14	-	-	PUNCT
cana-5829	529	15	133x	133x	NUM
cana-5829	529	16	vol	vol	VERB
cana-5829	529	17	32	32	NUM
cana-5829	529	18	no	no	NOUN
cana-5829	529	19	.	.	PUNCT
cana-5829	530	1	10s	10	NOUN
cana-5829	530	2	(	(	PUNCT
cana-5829	530	3	2025	2025	NUM
cana-5829	530	4	)	)	PUNCT
cana-5829	530	5	2943	2943	NUM
cana-5829	530	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5829	530	7	where	where	SCONJ
cana-5829	530	8	∣μ22∣=	∣μ22∣=	PROPN
cana-5829	530	9	(	(	PUNCT
cana-5829	530	10	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	ADJ
cana-5829	530	11	+	+	CCONJ
cana-5829	530	12	𝛿𝐹22	𝛿𝐹22	X
cana-5829	530	13	(	(	PUNCT
cana-5829	530	14	(	(	PUNCT
cana-5829	530	15	𝛼22	𝛼22	NOUN
cana-5829	530	16	+	+	CCONJ
cana-5829	530	17	𝑥22	𝑥22	NOUN
cana-5829	530	18	−	−	PROPN
cana-5829	530	19	𝛼22	𝛼22	NOUN
cana-5829	530	20	.	.	PUNCT
cana-5829	531	1	𝑥22))2	𝑥22))2	X
cana-5829	532	1	+	+	CCONJ
cana-5829	532	2	(	(	PUNCT
cana-5829	532	3	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	X
cana-5829	532	4	+	+	X
cana-5829	532	5	𝛿𝐹22	𝛿𝐹22	X
cana-5829	532	6	(	(	PUNCT
cana-5829	532	7	𝛽22	𝛽22	VERB
cana-5829	532	8	+	+	CCONJ
cana-5829	532	9	𝑦22	𝑦22	NOUN
cana-5829	532	10	−	−	NOUN
cana-5829	532	11	𝛽22	𝛽22	NOUN
cana-5829	532	12	.	.	PUNCT
cana-5829	533	1	𝑦22))2	𝑦22))2	X
cana-5829	534	1	<	<	X
cana-5829	534	2	1	1	NUM
cana-5829	534	3	∣	∣	PROPN
cana-5829	534	4	ν22	ν22	NOUN
cana-5829	534	5	∣=	∣=	PROPN
cana-5829	534	6	(	(	PUNCT
cana-5829	534	7	𝑁𝑜𝑟𝑚µ𝐸22+𝛾𝐹22	𝑁𝑜𝑟𝑚µ𝐸22+𝛾𝐹22	X
cana-5829	534	8	(	(	PUNCT
cana-5829	534	9	𝛾22	𝛾22	ADJ
cana-5829	534	10	.	.	PUNCT
cana-5829	535	1	𝜇22)2	𝜇22)2	NOUN
cana-5829	535	2	+	+	CCONJ
cana-5829	535	3	𝑁𝑜𝑟𝑚µ𝐸22+𝛾𝐹22	𝑁𝑜𝑟𝑚µ𝐸22+𝛾𝐹22	X
cana-5829	535	4	(	(	PUNCT
cana-5829	535	5	𝛿22	𝛿22	NOUN
cana-5829	535	6	.	.	PUNCT
cana-5829	535	7	𝜃22)2	𝜃22)2	NOUN
cana-5829	535	8	<	<	X
cana-5829	535	9	1	1	NUM
cana-5829	535	10	,	,	PUNCT
cana-5829	535	11	∣μ22∣+∣ν22∣	∣μ22∣+∣ν22∣	ADV
cana-5829	535	12	≤	≤	NUM
cana-5829	535	13	1	1	NUM
cana-5829	535	14	.	.	PUNCT
cana-5829	536	1	we	we	PRON
cana-5829	536	2	have	have	VERB
cana-5829	536	3	norm𝐴𝐸𝑁𝑜𝑟𝑚𝐵𝐹	norm𝐴𝐸𝑁𝑜𝑟𝑚𝐵𝐹	PROPN
cana-5829	536	4	=	=	SYM
cana-5829	536	5	(	(	PUNCT
cana-5829	536	6	𝑋11	𝑋11	PROPN
cana-5829	536	7	𝑋12	𝑋12	PROPN
cana-5829	536	8	𝑋21	𝑋21	NOUN
cana-5829	536	9	𝑋22	𝑋22	ADJ
cana-5829	536	10	)	)	PUNCT
cana-5829	536	11	is	be	AUX
cana-5829	536	12	also	also	ADV
cana-5829	536	13	intuitionistic	intuitionistic	ADJ
cana-5829	536	14	fuzzy	fuzzy	ADJ
cana-5829	536	15	matrix	matrix	NOUN
cana-5829	536	16	.	.	PUNCT
cana-5829	537	1	example5.2.6	example5.2.6	PRON
cana-5829	537	2	:	:	PUNCT
cana-5829	537	3	:	:	PUNCT
cana-5829	537	4	if	if	SCONJ
cana-5829	537	5	𝐴𝐸=	𝐴𝐸=	NOUN
cana-5829	537	6	(	(	PUNCT
cana-5829	537	7	(	(	PUNCT
cana-5829	537	8	0.6	0.6	NUM
cana-5829	537	9	+	+	CCONJ
cana-5829	537	10	0.2i	0.2i	ADJ
cana-5829	537	11	,	,	PUNCT
cana-5829	537	12	0.3	0.3	NUM
cana-5829	537	13	+	+	NOUN
cana-5829	537	14	0.1i)(0.4	0.1i)(0.4	X
cana-5829	538	1	+	+	CCONJ
cana-5829	538	2	0.1i	0.1i	NOUN
cana-5829	538	3	,	,	PUNCT
cana-5829	538	4	0.5	0.5	NUM
cana-5829	538	5	+	+	NUM
cana-5829	538	6	0.2i	0.2i	NUM
cana-5829	538	7	)	)	PUNCT
cana-5829	538	8	(	(	PUNCT
cana-5829	538	9	0.5	0.5	NUM
cana-5829	538	10	+	+	CCONJ
cana-5829	538	11	0.3i	0.3i	NOUN
cana-5829	538	12	,	,	PUNCT
cana-5829	538	13	0.2	0.2	NUM
cana-5829	538	14	+	+	CCONJ
cana-5829	538	15	0.1i)(0.3	0.1i)(0.3	PRON
cana-5829	538	16	+	+	CCONJ
cana-5829	538	17	0.2i	0.2i	ADJ
cana-5829	538	18	,	,	PUNCT
cana-5829	538	19	0.6	0.6	NUM
cana-5829	538	20	+	+	NUM
cana-5829	538	21	0.1i	0.1i	NOUN
cana-5829	538	22	)	)	PUNCT
cana-5829	538	23	)	)	PUNCT
cana-5829	538	24	and	and	CCONJ
cana-5829	538	25	bf	bf	NOUN
cana-5829	538	26	=	=	SYM
cana-5829	538	27	(	(	PUNCT
cana-5829	538	28	(	(	PUNCT
cana-5829	538	29	0.4	0.4	NUM
cana-5829	538	30	+	+	CCONJ
cana-5829	538	31	0.3i	0.3i	NOUN
cana-5829	538	32	,	,	PUNCT
cana-5829	538	33	0.5	0.5	NUM
cana-5829	538	34	+	+	CCONJ
cana-5829	538	35	0.1i)(0.3	0.1i)(0.3	PRON
cana-5829	538	36	+	+	CCONJ
cana-5829	538	37	0.4i	0.4i	NOUN
cana-5829	538	38	,	,	PUNCT
cana-5829	538	39	0.4	0.4	NUM
cana-5829	538	40	+	+	CCONJ
cana-5829	538	41	0.2i	0.2i	NUM
cana-5829	538	42	)	)	PUNCT
cana-5829	538	43	(	(	PUNCT
cana-5829	538	44	0.6	0.6	NUM
cana-5829	538	45	+	+	CCONJ
cana-5829	538	46	0.2i	0.2i	ADJ
cana-5829	538	47	,	,	PUNCT
cana-5829	538	48	0.2	0.2	NUM
cana-5829	538	49	+	+	CCONJ
cana-5829	538	50	0.2i)(0.5	0.2i)(0.5	X
cana-5829	539	1	+	+	CCONJ
cana-5829	539	2	0.1i	0.1i	NOUN
cana-5829	539	3	,	,	PUNCT
cana-5829	539	4	0.4	0.4	NUM
cana-5829	539	5	+	+	CCONJ
cana-5829	539	6	0.3i	0.3i	NOUN
cana-5829	539	7	)	)	PUNCT
cana-5829	539	8	)	)	PUNCT
cana-5829	539	9	are	be	AUX
cana-5829	539	10	normalization	normalization	NOUN
cana-5829	539	11	of	of	ADP
cana-5829	539	12	complex	complex	ADJ
cana-5829	539	13	intuitionistic	intuitionistic	ADJ
cana-5829	539	14	fuzzy	fuzzy	ADJ
cana-5829	539	15	matrix	matrix	NOUN
cana-5829	539	16	two	two	NUM
cana-5829	539	17	intuitionistic	intuitionistic	ADJ
cana-5829	539	18	fuzzy	fuzzy	ADJ
cana-5829	539	19	matrices	matrix	NOUN
cana-5829	539	20	over	over	ADP
cana-5829	539	21	different	different	ADJ
cana-5829	539	22	universe	universe	NOUN
cana-5829	539	23	e	e	NOUN
cana-5829	539	24	and	and	CCONJ
cana-5829	539	25	f	f	PROPN
cana-5829	539	26	then	then	ADV
cana-5829	539	27	norm𝐴𝐸𝑁𝑜𝑟𝑚𝐵𝐹	norm𝐴𝐸𝑁𝑜𝑟𝑚𝐵𝐹	PROPN
cana-5829	539	28	is	be	AUX
cana-5829	539	29	also	also	ADV
cana-5829	539	30	normalization	normalization	NOUN
cana-5829	539	31	of	of	ADP
cana-5829	539	32	complex	complex	ADJ
cana-5829	539	33	intuitionistic	intuitionistic	ADJ
cana-5829	539	34	fuzzy	fuzzy	ADJ
cana-5829	539	35	matrix	matrix	NOUN
cana-5829	539	36	.	.	PUNCT
cana-5829	540	1	proof	proof	NOUN
cana-5829	540	2	:	:	PUNCT
cana-5829	540	3	given	give	VERB
cana-5829	540	4	𝑨𝑬=	𝑨𝑬=	PROPN
cana-5829	540	5	(	(	PUNCT
cana-5829	540	6	(	(	PUNCT
cana-5829	540	7	0.6	0.6	NUM
cana-5829	540	8	+	+	CCONJ
cana-5829	540	9	0.2i	0.2i	ADJ
cana-5829	540	10	,	,	PUNCT
cana-5829	540	11	0.3	0.3	NUM
cana-5829	540	12	+	+	NOUN
cana-5829	540	13	0.1i)(0.4	0.1i)(0.4	X
cana-5829	541	1	+	+	CCONJ
cana-5829	541	2	0.1i	0.1i	NOUN
cana-5829	541	3	,	,	PUNCT
cana-5829	541	4	0.5	0.5	NUM
cana-5829	541	5	+	+	NUM
cana-5829	541	6	0.2i	0.2i	NUM
cana-5829	541	7	)	)	PUNCT
cana-5829	541	8	(	(	PUNCT
cana-5829	541	9	0.5	0.5	NUM
cana-5829	541	10	+	+	CCONJ
cana-5829	541	11	0.3i	0.3i	NOUN
cana-5829	541	12	,	,	PUNCT
cana-5829	541	13	0.2	0.2	NUM
cana-5829	541	14	+	+	CCONJ
cana-5829	541	15	0.1i)(0.3	0.1i)(0.3	PRON
cana-5829	541	16	+	+	CCONJ
cana-5829	541	17	0.2i	0.2i	ADJ
cana-5829	541	18	,	,	PUNCT
cana-5829	541	19	0.6	0.6	NUM
cana-5829	541	20	+	+	NUM
cana-5829	541	21	0.1i	0.1i	NOUN
cana-5829	541	22	)	)	PUNCT
cana-5829	541	23	)	)	PUNCT
cana-5829	541	24	and	and	CCONJ
cana-5829	541	25	𝑩𝑭	𝑩𝑭	PROPN
cana-5829	541	26	=	=	SYM
cana-5829	541	27	(	(	PUNCT
cana-5829	541	28	(	(	PUNCT
cana-5829	541	29	0.4	0.4	NUM
cana-5829	541	30	+	+	CCONJ
cana-5829	541	31	0.3i	0.3i	NOUN
cana-5829	541	32	,	,	PUNCT
cana-5829	541	33	0.5	0.5	NUM
cana-5829	541	34	+	+	CCONJ
cana-5829	541	35	0.1i)(0.3	0.1i)(0.3	PRON
cana-5829	541	36	+	+	CCONJ
cana-5829	541	37	0.4i	0.4i	NOUN
cana-5829	541	38	,	,	PUNCT
cana-5829	541	39	0.4	0.4	NUM
cana-5829	541	40	+	+	CCONJ
cana-5829	541	41	0.2i	0.2i	NUM
cana-5829	541	42	)	)	PUNCT
cana-5829	541	43	(	(	PUNCT
cana-5829	541	44	0.6	0.6	NUM
cana-5829	541	45	+	+	CCONJ
cana-5829	541	46	0.2i	0.2i	ADJ
cana-5829	541	47	,	,	PUNCT
cana-5829	541	48	0.2	0.2	NUM
cana-5829	541	49	+	+	CCONJ
cana-5829	541	50	0.2i)(0.5	0.2i)(0.5	X
cana-5829	542	1	+	+	CCONJ
cana-5829	542	2	0.1i	0.1i	NOUN
cana-5829	542	3	,	,	PUNCT
cana-5829	542	4	0.4	0.4	NUM
cana-5829	542	5	+	+	CCONJ
cana-5829	542	6	0.3i	0.3i	NOUN
cana-5829	542	7	)	)	PUNCT
cana-5829	542	8	)	)	PUNCT
cana-5829	542	9	norm	norm	VERB
cana-5829	542	10	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	542	11	=	=	SYM
cana-5829	543	1	(	(	PUNCT
cana-5829	543	2	(	(	PUNCT
cana-5829	543	3	1	1	NUM
cana-5829	543	4	+	+	NUM
cana-5829	543	5	0.67𝑖	0.67𝑖	NUM
cana-5829	543	6	0.125	0.125	NUM
cana-5829	543	7	+	+	NUM
cana-5829	543	8	0𝑖	0𝑖	NOUN
cana-5829	543	9	)	)	PUNCT
cana-5829	543	10	(	(	PUNCT
cana-5829	543	11	0.67	0.67	NUM
cana-5829	543	12	+	+	CCONJ
cana-5829	543	13	0.33𝑖	0.33𝑖	NUM
cana-5829	543	14	0.30	0.30	NUM
cana-5829	543	15	+	+	CCONJ
cana-5829	543	16	0.10𝑖	0.10𝑖	NOUN
cana-5829	543	17	)	)	PUNCT
cana-5829	543	18	(	(	PUNCT
cana-5829	543	19	0.83	0.83	NUM
cana-5829	543	20	+	+	NUM
cana-5829	543	21	1𝑖	1𝑖	NOUN
cana-5829	543	22	0	0	NUM
cana-5829	544	1	+	+	NUM
cana-5829	544	2	0𝑖	0𝑖	NOUN
cana-5829	544	3	)	)	PUNCT
cana-5829	544	4	(	(	PUNCT
cana-5829	544	5	0.5	0.5	NUM
cana-5829	544	6	+	+	NUM
cana-5829	544	7	0.67𝑖	0.67𝑖	NUM
cana-5829	544	8	0.5	0.5	NUM
cana-5829	544	9	+	+	NUM
cana-5829	544	10	0𝑖	0𝑖	NOUN
cana-5829	544	11	)	)	PUNCT
cana-5829	544	12	)	)	PUNCT
cana-5829	545	1	𝑁𝑜𝑟𝑚	𝑁𝑜𝑟𝑚	NOUN
cana-5829	545	2	𝐵𝐹=	𝐵𝐹=	ADP
cana-5829	545	3	(	(	PUNCT
cana-5829	545	4	(	(	PUNCT
cana-5829	545	5	0.67	0.67	NUM
cana-5829	545	6	+	+	CCONJ
cana-5829	545	7	0.75𝑖	0.75𝑖	PROPN
cana-5829	545	8	0.375	0.375	NUM
cana-5829	545	9	+	+	NUM
cana-5829	545	10	0𝑖	0𝑖	NOUN
cana-5829	545	11	)	)	PUNCT
cana-5829	545	12	(	(	PUNCT
cana-5829	545	13	0.5	0.5	NUM
cana-5829	545	14	+	+	NUM
cana-5829	545	15	1𝑖	1𝑖	NUM
cana-5829	545	16	0.25	0.25	NUM
cana-5829	545	17	+	+	CCONJ
cana-5829	545	18	0.11𝑖	0.11𝑖	NUM
cana-5829	545	19	)	)	PUNCT
cana-5829	545	20	(	(	PUNCT
cana-5829	545	21	1	1	NUM
cana-5829	545	22	+	+	NUM
cana-5829	545	23	0.5𝑖	0.5𝑖	NOUN
cana-5829	545	24	0	0	NUM
cana-5829	546	1	+	+	CCONJ
cana-5829	546	2	0.11𝑖	0.11𝑖	NUM
cana-5829	546	3	)	)	PUNCT
cana-5829	546	4	(	(	PUNCT
cana-5829	546	5	0.83	0.83	NUM
cana-5829	546	6	+	+	NUM
cana-5829	546	7	0.25𝑖	0.25𝑖	NOUN
cana-5829	546	8	0.25	0.25	NUM
cana-5829	546	9	+	+	PUNCT
cana-5829	546	10	0.22𝑖	0.22𝑖	NUM
cana-5829	546	11	)	)	PUNCT
cana-5829	546	12	)	)	PUNCT
cana-5829	547	1	norm𝐴𝐸𝑁𝑜𝑟𝑚𝐵𝐹	norm𝐴𝐸𝑁𝑜𝑟𝑚𝐵𝐹	PROPN
cana-5829	547	2	=	=	PUNCT
cana-5829	547	3	(	(	PUNCT
cana-5829	547	4	(	(	PUNCT
cana-5829	547	5	1	1	NUM
cana-5829	547	6	+	+	NUM
cana-5829	547	7	0.67𝑖	0.67𝑖	NUM
cana-5829	547	8	0.125	0.125	NUM
cana-5829	547	9	+	+	NUM
cana-5829	547	10	0𝑖	0𝑖	NOUN
cana-5829	547	11	)	)	PUNCT
cana-5829	547	12	(	(	PUNCT
cana-5829	547	13	0.67	0.67	NUM
cana-5829	547	14	+	+	CCONJ
cana-5829	547	15	0.33𝑖	0.33𝑖	NUM
cana-5829	547	16	0.30	0.30	NUM
cana-5829	547	17	+	+	CCONJ
cana-5829	547	18	0.10𝑖	0.10𝑖	NOUN
cana-5829	547	19	)	)	PUNCT
cana-5829	547	20	(	(	PUNCT
cana-5829	547	21	0.83	0.83	NUM
cana-5829	547	22	+	+	NUM
cana-5829	547	23	1𝑖	1𝑖	NOUN
cana-5829	547	24	0	0	NUM
cana-5829	548	1	+	+	NUM
cana-5829	548	2	0𝑖	0𝑖	NOUN
cana-5829	548	3	)	)	PUNCT
cana-5829	548	4	(	(	PUNCT
cana-5829	548	5	0.5	0.5	NUM
cana-5829	548	6	+	+	NUM
cana-5829	548	7	0.67𝑖	0.67𝑖	NUM
cana-5829	548	8	0.5	0.5	NUM
cana-5829	548	9	+	+	NUM
cana-5829	548	10	0𝑖	0𝑖	NOUN
cana-5829	548	11	)	)	PUNCT
cana-5829	548	12	)	)	PUNCT
cana-5829	549	1			INTJ
cana-5829	549	2	(	(	PUNCT
cana-5829	549	3	(	(	PUNCT
cana-5829	549	4	0.67	0.67	NUM
cana-5829	550	1	+	+	CCONJ
cana-5829	550	2	0.75𝑖	0.75𝑖	PROPN
cana-5829	550	3	0.375	0.375	NUM
cana-5829	550	4	+	+	NUM
cana-5829	550	5	0𝑖	0𝑖	NOUN
cana-5829	550	6	)	)	PUNCT
cana-5829	550	7	(	(	PUNCT
cana-5829	550	8	0.5	0.5	NUM
cana-5829	550	9	+	+	NUM
cana-5829	550	10	1𝑖	1𝑖	NUM
cana-5829	550	11	0.25	0.25	NUM
cana-5829	550	12	+	+	CCONJ
cana-5829	550	13	0.11𝑖	0.11𝑖	NUM
cana-5829	550	14	)	)	PUNCT
cana-5829	550	15	(	(	PUNCT
cana-5829	550	16	1	1	NUM
cana-5829	551	1	+	+	NUM
cana-5829	551	2	0.5𝑖	0.5𝑖	NOUN
cana-5829	551	3	0	0	NUM
cana-5829	552	1	+	+	CCONJ
cana-5829	552	2	0.11𝑖	0.11𝑖	NUM
cana-5829	552	3	)	)	PUNCT
cana-5829	552	4	(	(	PUNCT
cana-5829	553	1	0.83	0.83	NUM
cana-5829	553	2	+	+	NUM
cana-5829	553	3	0.25𝑖	0.25𝑖	NOUN
cana-5829	553	4	0.25	0.25	NUM
cana-5829	553	5	+	+	PUNCT
cana-5829	553	6	0.22𝑖	0.22𝑖	NUM
cana-5829	553	7	)	)	PUNCT
cana-5829	553	8	)	)	PUNCT
cana-5829	554	1	𝑋11	𝑋11	PROPN
cana-5829	554	2	=	=	PUNCT
cana-5829	554	3	(	(	PUNCT
cana-5829	554	4	1	1	NUM
cana-5829	554	5	+	+	NUM
cana-5829	554	6	0.67𝑖	0.67𝑖	NUM
cana-5829	554	7	0.125	0.125	NUM
cana-5829	554	8	+	+	NUM
cana-5829	554	9	0𝑖)(0.67	0𝑖)(0.67	NOUN
cana-5829	554	10	+	+	CCONJ
cana-5829	554	11	0.75𝑖	0.75𝑖	PROPN
cana-5829	554	12	0.375	0.375	NUM
cana-5829	554	13	+	+	NUM
cana-5829	554	14	0𝑖	0𝑖	NOUN
cana-5829	554	15	)	)	PUNCT
cana-5829	555	1	𝑋12	𝑋12	PROPN
cana-5829	555	2	=	=	PUNCT
cana-5829	555	3	(	(	PUNCT
cana-5829	555	4	0.67	0.67	NUM
cana-5829	555	5	+	+	CCONJ
cana-5829	555	6	0.33𝑖	0.33𝑖	NUM
cana-5829	555	7	0.30	0.30	NUM
cana-5829	555	8	+	+	CCONJ
cana-5829	555	9	0.10𝑖	0.10𝑖	NOUN
cana-5829	555	10	)	)	PUNCT
cana-5829	555	11	(0.5	(0.5	NOUN
cana-5829	556	1	+	+	CCONJ
cana-5829	556	2	1𝑖	1𝑖	NUM
cana-5829	556	3	0.25	0.25	NUM
cana-5829	556	4	+	+	CCONJ
cana-5829	556	5	0.11𝑖	0.11𝑖	NUM
cana-5829	556	6	)	)	PUNCT
cana-5829	556	7	𝑋21	𝑋21	NOUN
cana-5829	556	8	=	=	SYM
cana-5829	556	9	(	(	PUNCT
cana-5829	556	10	0.83	0.83	NUM
cana-5829	556	11	+	+	NUM
cana-5829	556	12	1𝑖	1𝑖	NOUN
cana-5829	556	13	0	0	NUM
cana-5829	557	1	+	+	NUM
cana-5829	557	2	0𝑖	0𝑖	NOUN
cana-5829	557	3	)	)	PUNCT
cana-5829	557	4			PROPN
cana-5829	557	5	(	(	PUNCT
cana-5829	557	6	1	1	NUM
cana-5829	557	7	+	+	NUM
cana-5829	557	8	0.5𝑖	0.5𝑖	NOUN
cana-5829	557	9	0	0	NUM
cana-5829	558	1	+	+	CCONJ
cana-5829	558	2	0.11𝑖	0.11𝑖	NUM
cana-5829	558	3	)	)	PUNCT
cana-5829	559	1	𝑋22	𝑋22	ADJ
cana-5829	559	2	=	=	PUNCT
cana-5829	559	3	(	(	PUNCT
cana-5829	559	4	0.5	0.5	NUM
cana-5829	559	5	+	+	NUM
cana-5829	559	6	0.67𝑖	0.67𝑖	NUM
cana-5829	559	7	0.5	0.5	NUM
cana-5829	559	8	+	+	CCONJ
cana-5829	559	9	0𝑖)(0.83	0𝑖)(0.83	ADJ
cana-5829	559	10	+	+	CCONJ
cana-5829	559	11	0.25𝑖	0.25𝑖	NOUN
cana-5829	559	12	0.25	0.25	NUM
cana-5829	559	13	+	+	CCONJ
cana-5829	559	14	0.22𝑖	0.22𝑖	NOUN
cana-5829	559	15	)	)	PUNCT
cana-5829	559	16	𝐴𝑝𝑝𝑙𝑦𝑖𝑛𝑔	𝐴𝑝𝑝𝑙𝑦𝑖𝑛𝑔	PROPN
cana-5829	559	17	𝑓𝑜𝑟𝑚𝑢𝑙𝑎	𝑓𝑜𝑟𝑚𝑢𝑙𝑎	VERB
cana-5829	559	18	aebf	aebf	X
cana-5829	560	1	=	=	PRON
cana-5829	560	2	{	{	PUNCT
cana-5829	560	3	(	(	PUNCT
cana-5829	560	4	x	x	NOUN
cana-5829	560	5	,	,	PUNCT
cana-5829	560	6	y	y	PROPN
cana-5829	560	7	)	)	PUNCT
cana-5829	560	8	,	,	PUNCT
cana-5829	560	9	(	(	PUNCT
cana-5829	560	10	μa(x	μa(x	X
cana-5829	560	11	)	)	PUNCT
cana-5829	561	1	+	+	CCONJ
cana-5829	561	2	μb(y	μb(y	NUM
cana-5829	561	3	)	)	PUNCT
cana-5829	561	4	)	)	PUNCT
cana-5829	561	5	μa(x	μa(x	NOUN
cana-5829	561	6	)	)	PUNCT
cana-5829	561	7	.	.	PUNCT
cana-5829	562	1	μb(y	μb(y	NUM
cana-5829	562	2	)	)	PUNCT
cana-5829	562	3	,	,	PUNCT
cana-5829	562	4	ϑa(x).ϑb(y	ϑa(x).ϑb(y	ADJ
cana-5829	562	5	):	):	PUNCT
cana-5829	562	6	xe	xe	PROPN
cana-5829	562	7	,	,	PUNCT
cana-5829	562	8	yf	yf	ADJ
cana-5829	562	9	}	}	PUNCT
cana-5829	562	10	aebf	aebf	NOUN
cana-5829	563	1	=	=	PUNCT
cana-5829	563	2	(	(	PUNCT
cana-5829	563	3	1	1	NUM
cana-5829	563	4	+	+	CCONJ
cana-5829	563	5	0.9175𝑖	0.9175𝑖	NUM
cana-5829	563	6	,	,	PUNCT
cana-5829	563	7	0.046	0.046	NUM
cana-5829	563	8	+	+	NUM
cana-5829	563	9	0𝑖	0𝑖	NOUN
cana-5829	563	10	0.835	0.835	NUM
cana-5829	563	11	+	+	CCONJ
cana-5829	563	12	1𝑖	1𝑖	NUM
cana-5829	563	13	,	,	PUNCT
cana-5829	563	14	0.075	0.075	NUM
cana-5829	563	15	+	+	CCONJ
cana-5829	564	1	0.011𝑖	0.011𝑖	NUM
cana-5829	564	2	1	1	NUM
cana-5829	564	3	+	+	NUM
cana-5829	564	4	1𝑖	1𝑖	NUM
cana-5829	564	5	,	,	PUNCT
cana-5829	564	6	0	0	NUM
cana-5829	565	1	+	+	NUM
cana-5829	565	2	0𝑖	0𝑖	NOUN
cana-5829	565	3	0.915	0.915	NUM
cana-5829	565	4	+	+	SYM
cana-5829	565	5	0.752𝑖	0.752𝑖	NOUN
cana-5829	565	6	,	,	PUNCT
cana-5829	565	7	0.125	0.125	NUM
cana-5829	565	8	+	+	NUM
cana-5829	565	9	0𝑖	0𝑖	NOUN
cana-5829	565	10	)	)	PUNCT
cana-5829	566	1	𝑋11	𝑋11	PROPN
cana-5829	566	2	=	=	PRON
cana-5829	566	3	{	{	PUNCT
cana-5829	566	4	1	1	NUM
cana-5829	566	5	+	+	NOUN
cana-5829	566	6	0.9175i	0.9175i	NOUN
cana-5829	566	7	,	,	PUNCT
cana-5829	566	8	0.046	0.046	NUM
cana-5829	566	9	+	+	ADJ
cana-5829	566	10	0i	0i	X
cana-5829	566	11	}	}	PUNCT
cana-5829	566	12	𝑋12	𝑋12	VERB
cana-5829	566	13	=	=	PRON
cana-5829	566	14	{	{	PUNCT
cana-5829	566	15	0.835	0.835	NUM
cana-5829	566	16	+	+	NOUN
cana-5829	566	17	1i	1i	NOUN
cana-5829	566	18	,	,	PUNCT
cana-5829	566	19	0.075	0.075	NUM
cana-5829	566	20	+	+	NOUN
cana-5829	566	21	0.011i	0.011i	ADJ
cana-5829	566	22	}	}	PUNCT
cana-5829	566	23	𝑋21	𝑋21	NOUN
cana-5829	566	24	=	=	NUM
cana-5829	566	25	{	{	PUNCT
cana-5829	566	26	1	1	NUM
cana-5829	566	27	+	+	NOUN
cana-5829	566	28	1i	1i	NOUN
cana-5829	566	29	,	,	PUNCT
cana-5829	566	30	0	0	PUNCT
cana-5829	567	1	+	+	NOUN
cana-5829	567	2	0i	0i	X
cana-5829	567	3	}	}	PUNCT
cana-5829	567	4	𝑋22	𝑋22	VERB
cana-5829	567	5	=	=	PRON
cana-5829	567	6	{	{	PUNCT
cana-5829	567	7	0.915	0.915	NUM
cana-5829	567	8	+	+	NOUN
cana-5829	567	9	0.752i	0.752i	ADJ
cana-5829	567	10	,	,	PUNCT
cana-5829	567	11	0.125	0.125	NUM
cana-5829	567	12	+	+	NOUN
cana-5829	567	13	0i	0i	NOUN
cana-5829	567	14	}	}	PUNCT
cana-5829	567	15	communications	communication	NOUN
cana-5829	567	16	on	on	ADP
cana-5829	567	17	applied	apply	VERB
cana-5829	567	18	nonlinear	nonlinear	ADJ
cana-5829	567	19	analysis	analysis	NOUN
cana-5829	567	20	issn	issn	NOUN
cana-5829	567	21	:	:	PUNCT
cana-5829	567	22	1074	1074	NUM
cana-5829	567	23	-	-	PUNCT
cana-5829	567	24	133x	133x	NUM
cana-5829	567	25	vol	vol	VERB
cana-5829	567	26	32	32	NUM
cana-5829	567	27	no	no	NOUN
cana-5829	567	28	.	.	PUNCT
cana-5829	568	1	10s	10	NOUN
cana-5829	568	2	(	(	PUNCT
cana-5829	568	3	2025	2025	NUM
cana-5829	568	4	)	)	PUNCT
cana-5829	568	5	2944	2944	NUM
cana-5829	568	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5829	569	1	we	we	PRON
cana-5829	569	2	have	have	VERB
cana-5829	569	3	norm𝐴𝐸𝑁𝑜𝑟𝑚𝐵𝐹	norm𝐴𝐸𝑁𝑜𝑟𝑚𝐵𝐹	PROPN
cana-5829	569	4	=	=	SYM
cana-5829	569	5	(	(	PUNCT
cana-5829	569	6	(	(	PUNCT
cana-5829	569	7	1	1	NUM
cana-5829	569	8	+	+	NUM
cana-5829	569	9	0.9175i	0.9175i	NOUN
cana-5829	569	10	,	,	PUNCT
cana-5829	569	11	0.046	0.046	NUM
cana-5829	569	12	+	+	NUM
cana-5829	569	13	0i	0i	NOUN
cana-5829	569	14	)	)	PUNCT
cana-5829	569	15	(	(	PUNCT
cana-5829	569	16	0.835	0.835	NUM
cana-5829	569	17	+	+	CCONJ
cana-5829	569	18	1i	1i	NOUN
cana-5829	569	19	,	,	PUNCT
cana-5829	569	20	0.075	0.075	NUM
cana-5829	569	21	+	+	CCONJ
cana-5829	569	22	0.011i	0.011i	NUM
cana-5829	569	23	)	)	PUNCT
cana-5829	569	24	(	(	PUNCT
cana-5829	569	25	1	1	NUM
cana-5829	569	26	+	+	NUM
cana-5829	569	27	1i	1i	NOUN
cana-5829	569	28	,	,	PUNCT
cana-5829	569	29	0	0	PUNCT
cana-5829	570	1	+	+	NUM
cana-5829	570	2	0i	0i	NOUN
cana-5829	570	3	)	)	PUNCT
cana-5829	570	4	(	(	PUNCT
cana-5829	570	5	0.915	0.915	NUM
cana-5829	570	6	+	+	CCONJ
cana-5829	570	7	0.752i	0.752i	ADJ
cana-5829	570	8	,	,	PUNCT
cana-5829	570	9	0.125	0.125	NUM
cana-5829	570	10	+	+	NUM
cana-5829	570	11	0i	0i	NOUN
cana-5829	570	12	)	)	PUNCT
cana-5829	570	13	)	)	PUNCT
cana-5829	570	14	is	be	AUX
cana-5829	570	15	also	also	ADV
cana-5829	570	16	normalization	normalization	NOUN
cana-5829	570	17	of	of	ADP
cana-5829	570	18	complex	complex	ADJ
cana-5829	570	19	intuitionistic	intuitionistic	ADJ
cana-5829	570	20	fuzzy	fuzzy	ADJ
cana-5829	570	21	matrix	matrix	NOUN
cana-5829	570	22	.	.	PUNCT
cana-5829	571	1	theorem5.2.7	theorem5.2.7	PRON
cana-5829	571	2	:	:	PUNCT
cana-5829	571	3	if	if	SCONJ
cana-5829	571	4	e	e	PROPN
cana-5829	571	5	and	and	CCONJ
cana-5829	571	6	f	f	PROPN
cana-5829	571	7	be	be	AUX
cana-5829	571	8	two	two	NUM
cana-5829	571	9	universal	universal	ADJ
cana-5829	571	10	sets	set	NOUN
cana-5829	571	11	.	.	PUNCT
cana-5829	572	1	for	for	ADP
cana-5829	572	2	every	every	DET
cana-5829	572	3	normalization	normalization	NOUN
cana-5829	572	4	of	of	ADP
cana-5829	572	5	complex	complex	ADJ
cana-5829	572	6	intuitionistic	intuitionistic	ADJ
cana-5829	572	7	fuzzy	fuzzy	ADJ
cana-5829	572	8	matrices	matrix	NOUN
cana-5829	572	9	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	572	10	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-5829	572	11	𝐵𝐹	𝐵𝐹	PROPN
cana-5829	572	12	are	be	AUX
cana-5829	572	13	in	in	ADP
cana-5829	572	14	e	e	PROPN
cana-5829	572	15	and	and	CCONJ
cana-5829	572	16	f	f	PROPN
cana-5829	572	17	then	then	ADV
cana-5829	572	18	norm𝐴𝐸𝑁𝑜𝑟𝑚𝐵𝐹	norm𝐴𝐸𝑁𝑜𝑟𝑚𝐵𝐹	PROPN
cana-5829	572	19	is	be	AUX
cana-5829	572	20	also	also	ADV
cana-5829	572	21	normalization	normalization	NOUN
cana-5829	572	22	of	of	ADP
cana-5829	572	23	complex	complex	ADJ
cana-5829	572	24	intuitionistic	intuitionistic	ADJ
cana-5829	572	25	fuzzy	fuzzy	ADJ
cana-5829	572	26	matrix	matrix	NOUN
cana-5829	572	27	.	.	PUNCT
cana-5829	573	1	proof	proof	NOUN
cana-5829	573	2	:	:	PUNCT
cana-5829	573	3	if	if	SCONJ
cana-5829	573	4	norm	norm	NOUN
cana-5829	573	5	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	573	6	and	and	CCONJ
cana-5829	573	7	𝑁𝑜𝑟𝑚	𝑁𝑜𝑟𝑚	PROPN
cana-5829	573	8	𝐵𝐹	𝐵𝐹	PROPN
cana-5829	573	9	are	be	AUX
cana-5829	573	10	two	two	NUM
cana-5829	573	11	normalization	normalization	NOUN
cana-5829	573	12	intuitionistic	intuitionistic	ADJ
cana-5829	573	13	fuzzy	fuzzy	ADJ
cana-5829	573	14	matrices	matrix	NOUN
cana-5829	573	15	over	over	ADP
cana-5829	573	16	different	different	ADJ
cana-5829	573	17	unive𝑟𝑠𝑒𝑠	unive𝑟𝑠𝑒𝑠	ADJ
cana-5829	573	18	𝑠𝑒𝑡𝑠	𝑠𝑒𝑡𝑠	PROPN
cana-5829	573	19	𝐸	𝐸	PROPN
cana-5829	573	20	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-5829	573	21	𝐹.	𝐹.	PROPN
cana-5829	573	22	if	if	SCONJ
cana-5829	573	23	we	we	PRON
cana-5829	573	24	consider	consider	VERB
cana-5829	573	25	two	two	NUM
cana-5829	573	26	2	2	NUM
cana-5829	573	27	×	×	NOUN
cana-5829	573	28	2	2	NUM
cana-5829	573	29	normalization	normalization	NOUN
cana-5829	573	30	intuitionistic	intuitionistic	ADJ
cana-5829	573	31	fuzzy	fuzzy	ADJ
cana-5829	573	32	matrices	matrix	NOUN
cana-5829	573	33	,	,	PUNCT
cana-5829	573	34	norm	norm	NOUN
cana-5829	573	35	𝐴𝐸𝑎𝑛𝑑	𝐴𝐸𝑎𝑛𝑑	PROPN
cana-5829	573	36	𝑁𝑜𝑟𝑚	𝑁𝑜𝑟𝑚	PROPN
cana-5829	573	37	𝐵𝐹.	𝐵𝐹.	NOUN
cana-5829	573	38	let	let	VERB
cana-5829	573	39	norm	norm	VERB
cana-5829	573	40	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	573	41	=	=	SYM
cana-5829	573	42	(	(	PUNCT
cana-5829	573	43	(	(	PUNCT
cana-5829	573	44	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	573	45	(	(	PUNCT
cana-5829	573	46	𝛼11	𝛼11	NOUN
cana-5829	573	47	+	+	PROPN
cana-5829	573	48	𝑖𝛽11	𝑖𝛽11	PROPN
cana-5829	573	49	)	)	PUNCT
cana-5829	573	50	𝑁𝑜𝑟𝑚µ𝐸11	𝑁𝑜𝑟𝑚µ𝐸11	NOUN
cana-5829	573	51	(	(	PUNCT
cana-5829	573	52	𝛾11	𝛾11	VERB
cana-5829	573	53	+	+	CCONJ
cana-5829	573	54	𝑖𝛿11	𝑖𝛿11	PROPN
cana-5829	573	55	)	)	PUNCT
cana-5829	573	56	)	)	PUNCT
cana-5829	573	57	(	(	PUNCT
cana-5829	573	58	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	NOUN
cana-5829	573	59	(	(	PUNCT
cana-5829	573	60	𝛼12	𝛼12	NOUN
cana-5829	573	61	+	+	CCONJ
cana-5829	573	62	𝑖𝛽12	𝑖𝛽12	PROPN
cana-5829	573	63	)	)	PUNCT
cana-5829	573	64	𝑁𝑜𝑟𝑚µ𝐸12	𝑁𝑜𝑟𝑚µ𝐸12	NOUN
cana-5829	573	65	(	(	PUNCT
cana-5829	573	66	𝛾12	𝛾12	VERB
cana-5829	573	67	+	+	CCONJ
cana-5829	573	68	𝑖𝛿12	𝑖𝛿12	PROPN
cana-5829	573	69	)	)	PUNCT
cana-5829	573	70	)	)	PUNCT
cana-5829	574	1	(	(	PUNCT
cana-5829	574	2	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	X
cana-5829	574	3	(	(	PUNCT
cana-5829	574	4	𝛼21	𝛼21	NOUN
cana-5829	574	5	+	+	X
cana-5829	574	6	𝑖𝛽21	𝑖𝛽21	PROPN
cana-5829	574	7	)	)	PUNCT
cana-5829	574	8	𝑁𝑜𝑟𝑚µ𝐸21	𝑁𝑜𝑟𝑚µ𝐸21	NOUN
cana-5829	574	9	(	(	PUNCT
cana-5829	574	10	𝛾21	𝛾21	NOUN
cana-5829	574	11	+	+	CCONJ
cana-5829	575	1	𝑖𝛿21	𝑖𝛿21	PROPN
cana-5829	575	2	)	)	PUNCT
cana-5829	575	3	)	)	PUNCT
cana-5829	576	1	(	(	PUNCT
cana-5829	576	2	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	X
cana-5829	576	3	(	(	PUNCT
cana-5829	576	4	𝛼22	𝛼22	NOUN
cana-5829	576	5	+	+	CCONJ
cana-5829	576	6	𝑖𝛽22	𝑖𝛽22	PROPN
cana-5829	576	7	)	)	PUNCT
cana-5829	576	8	𝑁𝑜𝑟𝑚µ𝐸22	𝑁𝑜𝑟𝑚µ𝐸22	NOUN
cana-5829	576	9	(	(	PUNCT
cana-5829	576	10	𝛾22	𝛾22	PROPN
cana-5829	576	11	+	+	PROPN
cana-5829	576	12	𝑖𝛿22	𝑖𝛿22	PROPN
cana-5829	576	13	)	)	PUNCT
cana-5829	576	14	)	)	PUNCT
cana-5829	576	15	)	)	PUNCT
cana-5829	577	1	and	and	CCONJ
cana-5829	577	2	𝑁𝑜𝑟𝑚	𝑁𝑜𝑟𝑚	PROPN
cana-5829	577	3	𝐵𝐹	𝐵𝐹	NOUN
cana-5829	577	4	=	=	SYM
cana-5829	577	5	(	(	PUNCT
cana-5829	577	6	(	(	PUNCT
cana-5829	577	7	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	577	8	(	(	PUNCT
cana-5829	577	9	𝑥11	𝑥11	ADV
cana-5829	577	10	+	+	CCONJ
cana-5829	577	11	𝑖𝑦11	𝑖𝑦11	NOUN
cana-5829	577	12	)	)	PUNCT
cana-5829	577	13	𝑁𝑜𝑟𝑚𝛾𝐹11	𝑁𝑜𝑟𝑚𝛾𝐹11	X
cana-5829	577	14	(	(	PUNCT
cana-5829	577	15	𝜇11	𝜇11	PROPN
cana-5829	577	16	+	+	PROPN
cana-5829	577	17	𝑖𝜃11	𝑖𝜃11	PROPN
cana-5829	577	18	)	)	PUNCT
cana-5829	577	19	)	)	PUNCT
cana-5829	578	1	(	(	PUNCT
cana-5829	578	2	𝑁𝑜𝑟𝑚𝛿𝐹12	𝑁𝑜𝑟𝑚𝛿𝐹12	X
cana-5829	578	3	(	(	PUNCT
cana-5829	578	4	𝑥12	𝑥12	VERB
cana-5829	578	5	+	+	CCONJ
cana-5829	578	6	𝑖𝑦12	𝑖𝑦12	PROPN
cana-5829	578	7	)	)	PUNCT
cana-5829	578	8	𝑁𝑜𝑟𝑚𝛾𝐹12	𝑁𝑜𝑟𝑚𝛾𝐹12	NOUN
cana-5829	578	9	(	(	PUNCT
cana-5829	578	10	𝜇12	𝜇12	NOUN
cana-5829	578	11	+	+	CCONJ
cana-5829	579	1	𝑖𝜃12	𝑖𝜃12	PROPN
cana-5829	579	2	)	)	PUNCT
cana-5829	579	3	)	)	PUNCT
cana-5829	580	1	(	(	PUNCT
cana-5829	580	2	𝑁𝑜𝑟𝑚𝛿𝐹21	𝑁𝑜𝑟𝑚𝛿𝐹21	X
cana-5829	580	3	(	(	PUNCT
cana-5829	580	4	𝑥21	𝑥21	PROPN
cana-5829	580	5	+	+	CCONJ
cana-5829	580	6	𝑖𝑦21	𝑖𝑦21	PROPN
cana-5829	580	7	)	)	PUNCT
cana-5829	580	8	𝑁𝑜𝑟𝑚𝛾𝐹21	𝑁𝑜𝑟𝑚𝛾𝐹21	ADV
cana-5829	580	9	(	(	PUNCT
cana-5829	580	10	𝜇21	𝜇21	VERB
cana-5829	580	11	+	+	CCONJ
cana-5829	580	12	𝑖𝜃21	𝑖𝜃21	PROPN
cana-5829	580	13	)	)	PUNCT
cana-5829	580	14	)	)	PUNCT
cana-5829	580	15	(	(	PUNCT
cana-5829	580	16	𝑁𝑜𝑟𝑚𝛿𝐹22	𝑁𝑜𝑟𝑚𝛿𝐹22	X
cana-5829	580	17	(	(	PUNCT
cana-5829	580	18	𝑥22	𝑥22	NOUN
cana-5829	580	19	+	+	X
cana-5829	580	20	𝑖𝑦22	𝑖𝑦22	PROPN
cana-5829	580	21	)	)	PUNCT
cana-5829	580	22	𝑁𝑜𝑟𝑚𝛾𝐹22	𝑁𝑜𝑟𝑚𝛾𝐹22	NOUN
cana-5829	580	23	(	(	PUNCT
cana-5829	580	24	𝜇22	𝜇22	NOUN
cana-5829	580	25	+	+	CCONJ
cana-5829	580	26	𝑖𝜃22	𝑖𝜃22	PROPN
cana-5829	580	27	)	)	PUNCT
cana-5829	580	28	)	)	PUNCT
cana-5829	580	29	)	)	PUNCT
cana-5829	580	30	are	be	AUX
cana-5829	580	31	two	two	NUM
cana-5829	580	32	normalization	normalization	NOUN
cana-5829	580	33	intuitionistic	intuitionistic	ADJ
cana-5829	580	34	fuzzy	fuzzy	ADJ
cana-5829	580	35	matrices	matrix	NOUN
cana-5829	580	36	.	.	PUNCT
cana-5829	580	37	norm𝐴𝐸𝑁𝑜𝑟𝑚𝐵𝐹	norm𝐴𝐸𝑁𝑜𝑟𝑚𝐵𝐹	PUNCT
cana-5829	581	1	=	=	PUNCT
cana-5829	581	2	(	(	PUNCT
cana-5829	581	3	(	(	PUNCT
cana-5829	581	4	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	581	5	(	(	PUNCT
cana-5829	581	6	𝛼11	𝛼11	NOUN
cana-5829	581	7	+	+	PROPN
cana-5829	581	8	𝑖𝛽11	𝑖𝛽11	PROPN
cana-5829	581	9	)	)	PUNCT
cana-5829	581	10	𝑁𝑜𝑟𝑚µ𝐸11	𝑁𝑜𝑟𝑚µ𝐸11	NOUN
cana-5829	581	11	(	(	PUNCT
cana-5829	581	12	𝛾11	𝛾11	VERB
cana-5829	581	13	+	+	CCONJ
cana-5829	581	14	𝑖𝛿11	𝑖𝛿11	PROPN
cana-5829	581	15	)	)	PUNCT
cana-5829	581	16	)	)	PUNCT
cana-5829	581	17	(	(	PUNCT
cana-5829	581	18	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	NOUN
cana-5829	581	19	(	(	PUNCT
cana-5829	581	20	𝛼12	𝛼12	NOUN
cana-5829	581	21	+	+	CCONJ
cana-5829	581	22	𝑖𝛽12	𝑖𝛽12	PROPN
cana-5829	581	23	)	)	PUNCT
cana-5829	581	24	𝑁𝑜𝑟𝑚µ𝐸12	𝑁𝑜𝑟𝑚µ𝐸12	NOUN
cana-5829	581	25	(	(	PUNCT
cana-5829	581	26	𝛾12	𝛾12	VERB
cana-5829	581	27	+	+	CCONJ
cana-5829	581	28	𝑖𝛿12	𝑖𝛿12	PROPN
cana-5829	581	29	)	)	PUNCT
cana-5829	581	30	)	)	PUNCT
cana-5829	581	31	(	(	PUNCT
cana-5829	581	32	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	X
cana-5829	581	33	(	(	PUNCT
cana-5829	581	34	𝛼21	𝛼21	NOUN
cana-5829	581	35	+	+	X
cana-5829	581	36	𝑖𝛽21	𝑖𝛽21	PROPN
cana-5829	581	37	)	)	PUNCT
cana-5829	581	38	𝑁𝑜𝑟𝑚µ𝐸21	𝑁𝑜𝑟𝑚µ𝐸21	NOUN
cana-5829	581	39	(	(	PUNCT
cana-5829	581	40	𝛾21	𝛾21	NOUN
cana-5829	581	41	+	+	CCONJ
cana-5829	582	1	𝑖𝛿21	𝑖𝛿21	PROPN
cana-5829	582	2	)	)	PUNCT
cana-5829	582	3	)	)	PUNCT
cana-5829	583	1	(	(	PUNCT
cana-5829	583	2	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	X
cana-5829	583	3	(	(	PUNCT
cana-5829	583	4	𝛼22	𝛼22	NOUN
cana-5829	583	5	+	+	CCONJ
cana-5829	583	6	𝑖𝛽22	𝑖𝛽22	PROPN
cana-5829	583	7	)	)	PUNCT
cana-5829	583	8	𝑁𝑜𝑟𝑚µ𝐸22	𝑁𝑜𝑟𝑚µ𝐸22	NOUN
cana-5829	583	9	(	(	PUNCT
cana-5829	583	10	𝛾22	𝛾22	PROPN
cana-5829	583	11	+	+	PROPN
cana-5829	583	12	𝑖𝛿22	𝑖𝛿22	PROPN
cana-5829	583	13	)	)	PUNCT
cana-5829	583	14	)	)	PUNCT
cana-5829	583	15	)	)	PUNCT
cana-5829	583	16			X
cana-5829	583	17	(	(	PUNCT
cana-5829	583	18	(	(	PUNCT
cana-5829	583	19	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	583	20	(	(	PUNCT
cana-5829	583	21	𝑥11	𝑥11	ADV
cana-5829	583	22	+	+	CCONJ
cana-5829	583	23	𝑖𝑦11	𝑖𝑦11	NOUN
cana-5829	583	24	)	)	PUNCT
cana-5829	583	25	𝑁𝑜𝑟𝑚𝛾𝐹11	𝑁𝑜𝑟𝑚𝛾𝐹11	X
cana-5829	583	26	(	(	PUNCT
cana-5829	583	27	𝜇11	𝜇11	PROPN
cana-5829	583	28	+	+	PROPN
cana-5829	583	29	𝑖𝜃11	𝑖𝜃11	PROPN
cana-5829	583	30	)	)	PUNCT
cana-5829	583	31	)	)	PUNCT
cana-5829	584	1	(	(	PUNCT
cana-5829	584	2	𝑁𝑜𝑟𝑚𝛿𝐹12	𝑁𝑜𝑟𝑚𝛿𝐹12	X
cana-5829	584	3	(	(	PUNCT
cana-5829	584	4	𝑥12	𝑥12	VERB
cana-5829	584	5	+	+	CCONJ
cana-5829	584	6	𝑖𝑦12	𝑖𝑦12	PROPN
cana-5829	584	7	)	)	PUNCT
cana-5829	584	8	𝑁𝑜𝑟𝑚𝛾𝐹12	𝑁𝑜𝑟𝑚𝛾𝐹12	NOUN
cana-5829	584	9	(	(	PUNCT
cana-5829	584	10	𝜇12	𝜇12	NOUN
cana-5829	584	11	+	+	CCONJ
cana-5829	585	1	𝑖𝜃12	𝑖𝜃12	PROPN
cana-5829	585	2	)	)	PUNCT
cana-5829	585	3	)	)	PUNCT
cana-5829	586	1	(	(	PUNCT
cana-5829	586	2	𝑁𝑜𝑟𝑚𝛿𝐹21	𝑁𝑜𝑟𝑚𝛿𝐹21	X
cana-5829	586	3	(	(	PUNCT
cana-5829	586	4	𝑥21	𝑥21	PROPN
cana-5829	586	5	+	+	CCONJ
cana-5829	586	6	𝑖𝑦21	𝑖𝑦21	PROPN
cana-5829	586	7	)	)	PUNCT
cana-5829	586	8	𝑁𝑜𝑟𝑚𝛾𝐹21	𝑁𝑜𝑟𝑚𝛾𝐹21	ADV
cana-5829	586	9	(	(	PUNCT
cana-5829	586	10	𝜇21	𝜇21	VERB
cana-5829	586	11	+	+	CCONJ
cana-5829	586	12	𝑖𝜃21	𝑖𝜃21	PROPN
cana-5829	586	13	)	)	PUNCT
cana-5829	586	14	)	)	PUNCT
cana-5829	586	15	(	(	PUNCT
cana-5829	586	16	𝑁𝑜𝑟𝑚𝛿𝐹22	𝑁𝑜𝑟𝑚𝛿𝐹22	X
cana-5829	586	17	(	(	PUNCT
cana-5829	586	18	𝑥22	𝑥22	NOUN
cana-5829	586	19	+	+	X
cana-5829	586	20	𝑖𝑦22	𝑖𝑦22	PROPN
cana-5829	586	21	)	)	PUNCT
cana-5829	586	22	𝑁𝑜𝑟𝑚𝛾𝐹22	𝑁𝑜𝑟𝑚𝛾𝐹22	NOUN
cana-5829	586	23	(	(	PUNCT
cana-5829	586	24	𝜇22	𝜇22	NOUN
cana-5829	586	25	+	+	CCONJ
cana-5829	586	26	𝑖𝜃22	𝑖𝜃22	PROPN
cana-5829	586	27	)	)	PUNCT
cana-5829	586	28	)	)	PUNCT
cana-5829	586	29	)	)	PUNCT
cana-5829	586	30	calculate	calculate	NOUN
cana-5829	586	31	,	,	PUNCT
cana-5829	586	32	𝑋11	𝑋11	PROPN
cana-5829	586	33	,	,	PUNCT
cana-5829	586	34	𝑋12	𝑋12	PROPN
cana-5829	586	35	,	,	PUNCT
cana-5829	586	36	𝑋21and	𝑋21and	PROPN
cana-5829	586	37	𝑋22	𝑋22	PROPN
cana-5829	586	38	,	,	PUNCT
cana-5829	586	39	we	we	PRON
cana-5829	586	40	have	have	VERB
cana-5829	586	41	x11	x11	PROPN
cana-5829	586	42	=(	=(	NOUN
cana-5829	586	43	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	586	44	(	(	PUNCT
cana-5829	586	45	𝛼11	𝛼11	NOUN
cana-5829	586	46	+	+	PROPN
cana-5829	586	47	𝑖𝛽11	𝑖𝛽11	PROPN
cana-5829	586	48	)	)	PUNCT
cana-5829	586	49	𝑁𝑜𝑟𝑚µ𝐸11	𝑁𝑜𝑟𝑚µ𝐸11	NOUN
cana-5829	586	50	(	(	PUNCT
cana-5829	586	51	𝛾11	𝛾11	VERB
cana-5829	586	52	+	+	CCONJ
cana-5829	586	53	𝑖𝛿11	𝑖𝛿11	PROPN
cana-5829	586	54	)	)	PUNCT
cana-5829	586	55	)	)	PUNCT
cana-5829	587	1	(𝑁𝑜𝑟𝑚𝛿𝐹11	(𝑁𝑜𝑟𝑚𝛿𝐹11	NOUN
cana-5829	587	2	(	(	PUNCT
cana-5829	587	3	𝑥11	𝑥11	ADV
cana-5829	587	4	+	+	CCONJ
cana-5829	587	5	𝑖𝑦11	𝑖𝑦11	NOUN
cana-5829	587	6	)	)	PUNCT
cana-5829	587	7	𝑁𝑜𝑟𝑚𝛾𝐹11	𝑁𝑜𝑟𝑚𝛾𝐹11	X
cana-5829	587	8	(	(	PUNCT
cana-5829	587	9	𝜇11	𝜇11	PROPN
cana-5829	587	10	+	+	PROPN
cana-5829	587	11	𝑖𝜃11	𝑖𝜃11	PROPN
cana-5829	587	12	)	)	PUNCT
cana-5829	587	13	)	)	PUNCT
cana-5829	588	1	where	where	SCONJ
cana-5829	588	2	∣μ11∣=	∣μ11∣=	NOUN
cana-5829	588	3	(	(	PUNCT
cana-5829	588	4	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	588	5	(	(	PUNCT
cana-5829	588	6	max(𝛼11	max(𝛼11	NUM
cana-5829	588	7	,	,	PUNCT
cana-5829	588	8	𝑥11))2	𝑥11))2	X
cana-5829	588	9	+	+	CCONJ
cana-5829	588	10	(	(	PUNCT
cana-5829	588	11	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	588	12	max(𝛽11	max(𝛽11	PROPN
cana-5829	588	13	,	,	PUNCT
cana-5829	588	14	𝑦11))2	𝑦11))2	X
cana-5829	589	1	+	+	ADJ
cana-5829	589	2	(	(	PUNCT
cana-5829	589	3	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	589	4	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
cana-5829	589	5	(	(	PUNCT
cana-5829	589	6	𝛾11	𝛾11	VERB
cana-5829	589	7	,	,	PUNCT
cana-5829	589	8	𝜇11))2	𝜇11))2	ADJ
cana-5829	589	9	+	+	ADJ
cana-5829	589	10	(	(	PUNCT
cana-5829	589	11	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	589	12	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
cana-5829	589	13	(	(	PUNCT
cana-5829	589	14	𝛾11	𝛾11	VERB
cana-5829	589	15	,	,	PUNCT
cana-5829	589	16	𝜇11))2	𝜇11))2	PRON
cana-5829	589	17	<	<	X
cana-5829	589	18	1	1	NUM
cana-5829	589	19	,	,	PUNCT
cana-5829	589	20	∣ν11∣=	∣ν11∣=	PROPN
cana-5829	589	21	(	(	PUNCT
cana-5829	589	22	normµe11	normµe11	NOUN
cana-5829	589	23	𝑚𝑖𝑛(𝛾11	𝑚𝑖𝑛(𝛾11	PROPN
cana-5829	589	24	,	,	PUNCT
cana-5829	589	25	𝜇11))2	𝜇11))2	X
cana-5829	589	26	+	+	ADJ
cana-5829	589	27	(	(	PUNCT
cana-5829	589	28	𝑁𝑜𝑟𝑚𝛾𝐸11	𝑁𝑜𝑟𝑚𝛾𝐸11	X
cana-5829	589	29	𝑚𝑖𝑛(𝛿11	𝑚𝑖𝑛(𝛿11	PROPN
cana-5829	589	30	,	,	PUNCT
cana-5829	589	31	𝜃11))2	𝜃11))2	X
cana-5829	589	32	<	<	X
cana-5829	589	33	1	1	NUM
cana-5829	589	34	,	,	PUNCT
cana-5829	589	35	∣μ11∣+∣ν11∣	∣μ11∣+∣ν11∣	VERB
cana-5829	589	36	≤	≤	NUM
cana-5829	589	37	1	1	NUM
cana-5829	589	38	.	.	PUNCT
cana-5829	590	1	x12	x12	NUM
cana-5829	590	2	=(	=(	NOUN
cana-5829	590	3	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	NOUN
cana-5829	590	4	(	(	PUNCT
cana-5829	590	5	𝛼12	𝛼12	NOUN
cana-5829	590	6	+	+	CCONJ
cana-5829	590	7	𝑖𝛽12	𝑖𝛽12	PROPN
cana-5829	590	8	)	)	PUNCT
cana-5829	590	9	𝑁𝑜𝑟𝑚µ𝐸12	𝑁𝑜𝑟𝑚µ𝐸12	NOUN
cana-5829	590	10	(	(	PUNCT
cana-5829	590	11	𝛾12	𝛾12	VERB
cana-5829	590	12	+	+	CCONJ
cana-5829	590	13	𝑖𝛿12	𝑖𝛿12	PROPN
cana-5829	590	14	)	)	PUNCT
cana-5829	590	15	)	)	PUNCT
cana-5829	591	1			X
cana-5829	591	2	(	(	PUNCT
cana-5829	591	3	𝑁𝑜𝑟𝑚𝛿𝐹12	𝑁𝑜𝑟𝑚𝛿𝐹12	X
cana-5829	591	4	(	(	PUNCT
cana-5829	591	5	𝑥12	𝑥12	VERB
cana-5829	591	6	+	+	CCONJ
cana-5829	591	7	𝑖𝑦12	𝑖𝑦12	PROPN
cana-5829	591	8	)	)	PUNCT
cana-5829	591	9	𝑁𝑜𝑟𝑚𝛾𝐹12	𝑁𝑜𝑟𝑚𝛾𝐹12	NOUN
cana-5829	592	1	(	(	PUNCT
cana-5829	592	2	𝜇12	𝜇12	NOUN
cana-5829	592	3	+	+	CCONJ
cana-5829	592	4	𝑖𝜃12	𝑖𝜃12	PROPN
cana-5829	592	5	)	)	PUNCT
cana-5829	592	6	)	)	PUNCT
cana-5829	593	1	x21	x21	NUM
cana-5829	593	2	=(	=(	NOUN
cana-5829	593	3	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	PROPN
cana-5829	593	4	(	(	PUNCT
cana-5829	593	5	𝛼21	𝛼21	NOUN
cana-5829	593	6	+	+	X
cana-5829	593	7	𝑖𝛽21	𝑖𝛽21	PROPN
cana-5829	593	8	)	)	PUNCT
cana-5829	593	9	𝑁𝑜𝑟𝑚µ𝐸21	𝑁𝑜𝑟𝑚µ𝐸21	NOUN
cana-5829	593	10	(	(	PUNCT
cana-5829	593	11	𝛾21	𝛾21	NOUN
cana-5829	593	12	+	+	CCONJ
cana-5829	594	1	𝑖𝛿21	𝑖𝛿21	PROPN
cana-5829	594	2	)	)	PUNCT
cana-5829	594	3	)	)	PUNCT
cana-5829	595	1			X
cana-5829	595	2	(	(	PUNCT
cana-5829	595	3	𝑁𝑜𝑟𝑚𝛿𝐹21	𝑁𝑜𝑟𝑚𝛿𝐹21	ADP
cana-5829	595	4	(	(	PUNCT
cana-5829	595	5	𝑥21	𝑥21	PROPN
cana-5829	595	6	+	+	CCONJ
cana-5829	595	7	𝑖𝑦21	𝑖𝑦21	PROPN
cana-5829	595	8	)	)	PUNCT
cana-5829	595	9	𝑁𝑜𝑟𝑚𝛾𝐹21	𝑁𝑜𝑟𝑚𝛾𝐹21	ADV
cana-5829	595	10	(	(	PUNCT
cana-5829	595	11	𝜇21	𝜇21	VERB
cana-5829	595	12	+	+	CCONJ
cana-5829	595	13	𝑖𝜃21	𝑖𝜃21	PROPN
cana-5829	595	14	)	)	PUNCT
cana-5829	595	15	)	)	PUNCT
cana-5829	596	1	x22	x22	NUM
cana-5829	597	1	=(	=(	NOUN
cana-5829	597	2	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	PROPN
cana-5829	597	3	(	(	PUNCT
cana-5829	597	4	𝛼22	𝛼22	NOUN
cana-5829	597	5	+	+	CCONJ
cana-5829	597	6	𝑖𝛽22	𝑖𝛽22	PROPN
cana-5829	597	7	)	)	PUNCT
cana-5829	597	8	𝑁𝑜𝑟𝑚µ𝐸22	𝑁𝑜𝑟𝑚µ𝐸22	NOUN
cana-5829	597	9	(	(	PUNCT
cana-5829	597	10	𝛾22	𝛾22	PROPN
cana-5829	597	11	+	+	PROPN
cana-5829	597	12	𝑖𝛿22	𝑖𝛿22	PROPN
cana-5829	597	13	)	)	PUNCT
cana-5829	597	14	)	)	PUNCT
cana-5829	597	15			X
cana-5829	597	16	(	(	PUNCT
cana-5829	597	17	𝑁𝑜𝑟𝑚𝛿𝐹22	𝑁𝑜𝑟𝑚𝛿𝐹22	X
cana-5829	597	18	(	(	PUNCT
cana-5829	597	19	𝑥22	𝑥22	NOUN
cana-5829	597	20	+	+	X
cana-5829	597	21	𝑖𝑦22	𝑖𝑦22	PROPN
cana-5829	597	22	)	)	PUNCT
cana-5829	597	23	𝑁𝑜𝑟𝑚𝛾𝐹22	𝑁𝑜𝑟𝑚𝛾𝐹22	NOUN
cana-5829	597	24	(	(	PUNCT
cana-5829	597	25	𝜇22	𝜇22	NOUN
cana-5829	597	26	+	+	CCONJ
cana-5829	597	27	𝑖𝜃22	𝑖𝜃22	PROPN
cana-5829	597	28	)	)	PUNCT
cana-5829	597	29	)	)	PUNCT
cana-5829	598	1	𝐴𝑝𝑝𝑙𝑦𝑖𝑛𝑔	𝐴𝑝𝑝𝑙𝑦𝑖𝑛𝑔	PROPN
cana-5829	598	2	𝑓𝑜𝑟𝑚𝑢𝑙𝑎	𝑓𝑜𝑟𝑚𝑢𝑙𝑎	VERB
cana-5829	598	3	aebf	aebf	PROPN
cana-5829	599	1	=	=	PRON
cana-5829	599	2	{	{	PUNCT
cana-5829	599	3	(	(	PUNCT
cana-5829	599	4	x	x	NOUN
cana-5829	599	5	,	,	PUNCT
cana-5829	599	6	y	y	PROPN
cana-5829	599	7	)	)	PUNCT
cana-5829	599	8	,	,	PUNCT
cana-5829	599	9	μa(x	μa(x	NOUN
cana-5829	599	10	)	)	PUNCT
cana-5829	599	11	.	.	PUNCT
cana-5829	600	1	μb(y	μb(y	NUM
cana-5829	600	2	)	)	PUNCT
cana-5829	600	3	,	,	PUNCT
cana-5829	600	4	ϑa(x	ϑa(x	NOUN
cana-5829	600	5	)	)	PUNCT
cana-5829	601	1	+	+	ADJ
cana-5829	601	2	ϑb(y	ϑb(y	X
cana-5829	601	3	)	)	PUNCT
cana-5829	601	4	ϑa(x).ϑb(y	ϑa(x).ϑb(y	ADJ
cana-5829	601	5	):	):	PUNCT
cana-5829	601	6	xe	xe	PROPN
cana-5829	601	7	,	,	PUNCT
cana-5829	601	8	yf	yf	NUM
cana-5829	601	9	}	}	PUNCT
cana-5829	601	10	x11	x11	NOUN
cana-5829	602	1	=	=	NOUN
cana-5829	602	2	{	{	PUNCT
cana-5829	602	3	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	602	4	(	(	PUNCT
cana-5829	602	5	𝛼11	𝛼11	NOUN
cana-5829	602	6	+	+	PROPN
cana-5829	602	7	𝑖𝛽11	𝑖𝛽11	PROPN
cana-5829	602	8	)	)	PUNCT
cana-5829	602	9	.	.	PUNCT
cana-5829	603	1	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	603	2	(	(	PUNCT
cana-5829	603	3	𝑥11	𝑥11	ADV
cana-5829	603	4	+	+	CCONJ
cana-5829	603	5	𝑖𝑦11	𝑖𝑦11	PROPN
cana-5829	603	6	)	)	PUNCT
cana-5829	603	7	,	,	PUNCT
cana-5829	603	8	𝑁𝑜𝑟𝑚µ𝐸11	𝑁𝑜𝑟𝑚µ𝐸11	NOUN
cana-5829	603	9	(	(	PUNCT
cana-5829	603	10	𝛾11	𝛾11	VERB
cana-5829	603	11	+	+	CCONJ
cana-5829	603	12	𝑖𝛿11	𝑖𝛿11	PROPN
cana-5829	603	13	)	)	PUNCT
cana-5829	604	1	+	+	CCONJ
cana-5829	604	2	𝑁𝑜𝑟𝑚𝛾𝐹11	𝑁𝑜𝑟𝑚𝛾𝐹11	X
cana-5829	604	3	(	(	PUNCT
cana-5829	604	4	𝜇11	𝜇11	PROPN
cana-5829	604	5	+	+	NOUN
cana-5829	604	6	𝑖𝜃11	𝑖𝜃11	PROPN
cana-5829	604	7	)	)	PUNCT
cana-5829	604	8	−	−	NOUN
cana-5829	604	9	𝑁𝑜𝑟𝑚µ𝐸11	𝑁𝑜𝑟𝑚µ𝐸11	NOUN
cana-5829	604	10	(	(	PUNCT
cana-5829	604	11	𝛾11	𝛾11	VERB
cana-5829	604	12	+	+	CCONJ
cana-5829	604	13	𝑖𝛿11	𝑖𝛿11	PROPN
cana-5829	604	14	)	)	PUNCT
cana-5829	604	15	.	.	PUNCT
cana-5829	605	1	𝑁𝑜𝑟𝑚𝛾𝐹11	𝑁𝑜𝑟𝑚𝛾𝐹11	PROPN
cana-5829	605	2	(	(	PUNCT
cana-5829	605	3	𝜇11	𝜇11	PROPN
cana-5829	605	4	+	+	PROPN
cana-5829	605	5	𝑖𝜃11	𝑖𝜃11	PROPN
cana-5829	605	6	)	)	PUNCT
cana-5829	605	7	}	}	PUNCT
cana-5829	605	8	communications	communication	NOUN
cana-5829	605	9	on	on	ADP
cana-5829	605	10	applied	apply	VERB
cana-5829	605	11	nonlinear	nonlinear	ADJ
cana-5829	605	12	analysis	analysis	NOUN
cana-5829	605	13	issn	issn	NOUN
cana-5829	605	14	:	:	PUNCT
cana-5829	605	15	1074	1074	NUM
cana-5829	605	16	-	-	PUNCT
cana-5829	605	17	133x	133x	NUM
cana-5829	605	18	vol	vol	VERB
cana-5829	605	19	32	32	NUM
cana-5829	605	20	no	no	NOUN
cana-5829	605	21	.	.	PUNCT
cana-5829	606	1	10s	10	NOUN
cana-5829	606	2	(	(	PUNCT
cana-5829	606	3	2025	2025	NUM
cana-5829	606	4	)	)	PUNCT
cana-5829	606	5	2945	2945	NUM
cana-5829	606	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5829	606	7	x12	x12	NUM
cana-5829	606	8	=	=	SYM
cana-5829	606	9	{	{	PUNCT
cana-5829	606	10	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	NOUN
cana-5829	606	11	(	(	PUNCT
cana-5829	606	12	𝛼12	𝛼12	NOUN
cana-5829	606	13	+	+	X
cana-5829	606	14	𝑖𝛽12	𝑖𝛽12	PROPN
cana-5829	606	15	)	)	PUNCT
cana-5829	606	16	.	.	PUNCT
cana-5829	607	1	𝑁𝑜𝑟𝑚𝛿𝐹12	𝑁𝑜𝑟𝑚𝛿𝐹12	PROPN
cana-5829	608	1	(	(	PUNCT
cana-5829	608	2	𝑥12	𝑥12	VERB
cana-5829	608	3	+	+	CCONJ
cana-5829	608	4	𝑖𝑦12	𝑖𝑦12	PROPN
cana-5829	608	5	)	)	PUNCT
cana-5829	608	6	,	,	PUNCT
cana-5829	608	7	𝑁𝑜𝑟𝑚µ𝐸12	𝑁𝑜𝑟𝑚µ𝐸12	NOUN
cana-5829	608	8	(	(	PUNCT
cana-5829	608	9	𝛾12	𝛾12	VERB
cana-5829	608	10	+	+	CCONJ
cana-5829	608	11	𝑖𝛿12	𝑖𝛿12	PROPN
cana-5829	608	12	)	)	PUNCT
cana-5829	609	1	+	+	CCONJ
cana-5829	609	2	𝑁𝑜𝑟𝑚𝛾𝐹12	𝑁𝑜𝑟𝑚𝛾𝐹12	NOUN
cana-5829	609	3	(	(	PUNCT
cana-5829	609	4	𝜇12	𝜇12	NOUN
cana-5829	609	5	+	+	CCONJ
cana-5829	609	6	𝑖𝜃12	𝑖𝜃12	PROPN
cana-5829	609	7	)	)	PUNCT
cana-5829	609	8	−	−	ADP
cana-5829	609	9	𝑁𝑜𝑟𝑚µ𝐸12	𝑁𝑜𝑟𝑚µ𝐸12	NOUN
cana-5829	609	10	(	(	PUNCT
cana-5829	609	11	𝛾12	𝛾12	VERB
cana-5829	609	12	+	+	CCONJ
cana-5829	609	13	𝑖𝛿12	𝑖𝛿12	PROPN
cana-5829	609	14	)	)	PUNCT
cana-5829	609	15	.	.	PUNCT
cana-5829	610	1	𝑁𝑜𝑟𝑚𝛾𝐹12	𝑁𝑜𝑟𝑚𝛾𝐹12	NOUN
cana-5829	611	1	(	(	PUNCT
cana-5829	611	2	𝜇12	𝜇12	NOUN
cana-5829	611	3	+	+	CCONJ
cana-5829	611	4	𝑖𝜃12	𝑖𝜃12	PROPN
cana-5829	611	5	)	)	PUNCT
cana-5829	611	6	}	}	PUNCT
cana-5829	611	7	x21	x21	NOUN
cana-5829	612	1	=	=	SYM
cana-5829	612	2	{	{	PUNCT
cana-5829	612	3	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	X
cana-5829	612	4	(	(	PUNCT
cana-5829	612	5	𝛼21	𝛼21	NOUN
cana-5829	612	6	+	+	X
cana-5829	612	7	𝑖𝛽21	𝑖𝛽21	PROPN
cana-5829	612	8	)	)	PUNCT
cana-5829	612	9	.	.	PUNCT
cana-5829	613	1	𝑁𝑜𝑟𝑚𝛿𝐹21	𝑁𝑜𝑟𝑚𝛿𝐹21	PUNCT
cana-5829	613	2	(	(	PUNCT
cana-5829	613	3	𝑥21	𝑥21	NOUN
cana-5829	613	4	+	+	CCONJ
cana-5829	613	5	𝑦21	𝑦21	NOUN
cana-5829	613	6	)	)	PUNCT
cana-5829	613	7	,	,	PUNCT
cana-5829	613	8	𝑁𝑜𝑟𝑚µ𝐸21	𝑁𝑜𝑟𝑚µ𝐸21	INTJ
cana-5829	613	9	(	(	PUNCT
cana-5829	613	10	𝛾21	𝛾21	NOUN
cana-5829	613	11	+	+	CCONJ
cana-5829	613	12	𝑖𝛿21	𝑖𝛿21	PROPN
cana-5829	613	13	)	)	PUNCT
cana-5829	613	14	+	+	CCONJ
cana-5829	613	15	𝑁𝑜𝑟𝑚𝛾𝐹21	𝑁𝑜𝑟𝑚𝛾𝐹21	ADV
cana-5829	613	16	(	(	PUNCT
cana-5829	613	17	𝜇21	𝜇21	X
cana-5829	613	18	+	+	CCONJ
cana-5829	613	19	𝑖𝜃21	𝑖𝜃21	PROPN
cana-5829	613	20	)	)	PUNCT
cana-5829	613	21	−	−	NOUN
cana-5829	614	1	𝑁𝑜𝑟𝑚µ𝐸21	𝑁𝑜𝑟𝑚µ𝐸21	INTJ
cana-5829	614	2	(	(	PUNCT
cana-5829	614	3	𝛾21	𝛾21	NOUN
cana-5829	614	4	+	+	CCONJ
cana-5829	615	1	𝑖𝛿21	𝑖𝛿21	PROPN
cana-5829	615	2	)	)	PUNCT
cana-5829	615	3	.	.	PUNCT
cana-5829	616	1	𝑁𝑜𝑟𝑚𝛾𝐹21	𝑁𝑜𝑟𝑚𝛾𝐹21	ADV
cana-5829	616	2	(	(	PUNCT
cana-5829	616	3	𝜇21	𝜇21	VERB
cana-5829	616	4	+	+	CCONJ
cana-5829	616	5	𝑖𝜃21	𝑖𝜃21	PROPN
cana-5829	616	6	)	)	PUNCT
cana-5829	616	7	}	}	PUNCT
cana-5829	616	8	x22	x22	NOUN
cana-5829	617	1	=	=	SYM
cana-5829	617	2	{	{	PUNCT
cana-5829	617	3	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	X
cana-5829	617	4	(	(	PUNCT
cana-5829	617	5	𝛼22	𝛼22	NOUN
cana-5829	617	6	+	+	PUNCT
cana-5829	617	7	𝑖𝛽22	𝑖𝛽22	PROPN
cana-5829	617	8	)	)	PUNCT
cana-5829	617	9	.	.	PUNCT
cana-5829	618	1	𝑁𝑜𝑟𝑚𝛿𝐹22	𝑁𝑜𝑟𝑚𝛿𝐹22	PUNCT
cana-5829	618	2	(	(	PUNCT
cana-5829	618	3	𝑥22	𝑥22	NOUN
cana-5829	618	4	+	+	CCONJ
cana-5829	618	5	𝑦22	𝑦22	NUM
cana-5829	618	6	)	)	PUNCT
cana-5829	618	7	,	,	PUNCT
cana-5829	618	8	𝑁𝑜𝑟𝑚µ𝐸22	𝑁𝑜𝑟𝑚µ𝐸22	CCONJ
cana-5829	618	9	(	(	PUNCT
cana-5829	618	10	𝛾22	𝛾22	PROPN
cana-5829	618	11	+	+	X
cana-5829	618	12	𝑖𝛿22	𝑖𝛿22	PROPN
cana-5829	618	13	)	)	PUNCT
cana-5829	619	1	+	+	CCONJ
cana-5829	619	2	𝑁𝑜𝑟𝑚𝛾𝐹22	𝑁𝑜𝑟𝑚𝛾𝐹22	X
cana-5829	619	3	(	(	PUNCT
cana-5829	619	4	𝜇22	𝜇22	NOUN
cana-5829	619	5	+	+	CCONJ
cana-5829	619	6	𝑖𝜃22	𝑖𝜃22	PROPN
cana-5829	619	7	)	)	PUNCT
cana-5829	619	8	−	−	PROPN
cana-5829	620	1	𝑁𝑜𝑟𝑚µ𝐸22	𝑁𝑜𝑟𝑚µ𝐸22	NOUN
cana-5829	620	2	(	(	PUNCT
cana-5829	620	3	𝛾22	𝛾22	PROPN
cana-5829	620	4	+	+	PROPN
cana-5829	620	5	𝑖𝛿22	𝑖𝛿22	PROPN
cana-5829	620	6	)	)	PUNCT
cana-5829	620	7	.	.	PUNCT
cana-5829	621	1	𝑁𝑜𝑟𝑚𝛾𝐹22	𝑁𝑜𝑟𝑚𝛾𝐹22	X
cana-5829	621	2	(	(	PUNCT
cana-5829	621	3	𝜇22	𝜇22	NOUN
cana-5829	621	4	+	+	CCONJ
cana-5829	621	5	𝑖𝜃22	𝑖𝜃22	PROPN
cana-5829	621	6	)	)	PUNCT
cana-5829	621	7	}	}	PUNCT
cana-5829	621	8	x11	x11	NOUN
cana-5829	622	1	=	=	NOUN
cana-5829	622	2	{	{	PUNCT
cana-5829	622	3	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	VERB
cana-5829	622	4	+	+	PUNCT
cana-5829	622	5	𝛿𝐹11	𝛿𝐹11	PUNCT
cana-5829	622	6	(	(	PUNCT
cana-5829	622	7	𝛼11	𝛼11	PROPN
cana-5829	622	8	.	.	PUNCT
cana-5829	622	9	𝑥11	𝑥11	ADV
cana-5829	622	10	)	)	PUNCT
cana-5829	623	1	+	+	CCONJ
cana-5829	623	2	𝑖(𝛽11.𝑦11	𝑖(𝛽11.𝑦11	X
cana-5829	623	3	)	)	PUNCT
cana-5829	623	4	,	,	PUNCT
cana-5829	623	5	𝑁𝑜𝑟𝑚µ𝐸11+𝛾𝐹11	𝑁𝑜𝑟𝑚µ𝐸11+𝛾𝐹11	X
cana-5829	623	6	(	(	PUNCT
cana-5829	623	7	𝛾11	𝛾11	VERB
cana-5829	623	8	+	+	CCONJ
cana-5829	623	9	𝜇11	𝜇11	ADJ
cana-5829	623	10	−	−	NOUN
cana-5829	623	11	𝛾11	𝛾11	NOUN
cana-5829	623	12	.	.	PUNCT
cana-5829	624	1	𝜇11	𝜇11	PROPN
cana-5829	624	2	+	+	NUM
cana-5829	624	3	𝑖(𝛿11	𝑖(𝛿11	NOUN
cana-5829	624	4	+	+	CCONJ
cana-5829	624	5	𝜃11	𝜃11	ADJ
cana-5829	624	6	−	−	PROPN
cana-5829	624	7	𝛿11	𝛿11	PROPN
cana-5829	624	8	.	.	PUNCT
cana-5829	624	9	𝜃11	𝜃11	NOUN
cana-5829	624	10	)	)	PUNCT
cana-5829	624	11	}	}	PUNCT
cana-5829	624	12	where	where	SCONJ
cana-5829	624	13	∣μ11∣=	∣μ11∣=	NOUN
cana-5829	624	14	(	(	PUNCT
cana-5829	624	15	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	VERB
cana-5829	624	16	+	+	PUNCT
cana-5829	624	17	𝛿𝐹11	𝛿𝐹11	PUNCT
cana-5829	624	18	(	(	PUNCT
cana-5829	624	19	𝛼11	𝛼11	NOUN
cana-5829	624	20	.	.	PUNCT
cana-5829	624	21	𝑥11))2	𝑥11))2	X
cana-5829	625	1	+	+	CCONJ
cana-5829	625	2	(	(	PUNCT
cana-5829	625	3	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	625	4	+	+	PUNCT
cana-5829	625	5	𝛿𝐹11	𝛿𝐹11	PUNCT
cana-5829	625	6	(	(	PUNCT
cana-5829	625	7	𝛽11	𝛽11	NOUN
cana-5829	625	8	.	.	PUNCT
cana-5829	625	9	𝑦11)2	𝑦11)2	X
cana-5829	625	10	<	<	X
cana-5829	625	11	1	1	NUM
cana-5829	625	12	∣	∣	PROPN
cana-5829	625	13	ν11	ν11	NOUN
cana-5829	625	14	∣=	∣=	PROPN
cana-5829	625	15	(	(	PUNCT
cana-5829	625	16	𝑁𝑜𝑟𝑚µ𝐸11+𝛾𝐹11	𝑁𝑜𝑟𝑚µ𝐸11+𝛾𝐹11	X
cana-5829	625	17	(	(	PUNCT
cana-5829	625	18	𝛾11	𝛾11	VERB
cana-5829	625	19	+	+	CCONJ
cana-5829	625	20	𝜇11	𝜇11	ADJ
cana-5829	625	21	−	−	NOUN
cana-5829	625	22	𝛾11	𝛾11	NOUN
cana-5829	625	23	.	.	PUNCT
cana-5829	626	1	𝜇11)2	𝜇11)2	VERB
cana-5829	626	2	+	+	CCONJ
cana-5829	626	3	𝑁𝑜𝑟𝑚µ𝐸11+𝛾𝐹11	𝑁𝑜𝑟𝑚µ𝐸11+𝛾𝐹11	X
cana-5829	626	4	(	(	PUNCT
cana-5829	626	5	𝛿11	𝛿11	NOUN
cana-5829	626	6	+	+	CCONJ
cana-5829	626	7	𝜃11	𝜃11	NOUN
cana-5829	626	8	−	−	PROPN
cana-5829	626	9	𝛿11	𝛿11	NOUN
cana-5829	626	10	.	.	PUNCT
cana-5829	627	1	𝜃11)2	𝜃11)2	VERB
cana-5829	627	2	<	<	X
cana-5829	627	3	1	1	NUM
cana-5829	627	4	,	,	PUNCT
cana-5829	627	5	∣μ11∣+∣ν11∣	∣μ11∣+∣ν11∣	VERB
cana-5829	627	6	≤	≤	NUM
cana-5829	627	7	1	1	NUM
cana-5829	627	8	.	.	PUNCT
cana-5829	627	9	x12	x12	NUM
cana-5829	628	1	=	=	SYM
cana-5829	628	2	{	{	PUNCT
cana-5829	628	3	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	X
cana-5829	628	4	+	+	CCONJ
cana-5829	628	5	𝛿𝐹12	𝛿𝐹12	X
cana-5829	628	6	(	(	PUNCT
cana-5829	628	7	𝛼12	𝛼12	PROPN
cana-5829	628	8	.	.	PUNCT
cana-5829	629	1	𝑥12	𝑥12	VERB
cana-5829	629	2	)	)	PUNCT
cana-5829	629	3	+	+	NUM
cana-5829	629	4	𝑖(𝛽12.𝑦12	𝑖(𝛽12.𝑦12	NUM
cana-5829	629	5	)	)	PUNCT
cana-5829	629	6	,	,	PUNCT
cana-5829	629	7	𝑁𝑜𝑟𝑚µ𝐸12+𝛾𝐹12	𝑁𝑜𝑟𝑚µ𝐸12+𝛾𝐹12	PROPN
cana-5829	629	8	(	(	PUNCT
cana-5829	629	9	𝛾12	𝛾12	NOUN
cana-5829	629	10	+	+	NUM
cana-5829	629	11	𝜇12	𝜇12	NOUN
cana-5829	629	12	−	−	PROPN
cana-5829	629	13	𝛾12	𝛾12	PROPN
cana-5829	629	14	.	.	PUNCT
cana-5829	629	15	𝜇12	𝜇12	PROPN
cana-5829	629	16	)	)	PUNCT
cana-5829	630	1	+	+	CCONJ
cana-5829	630	2	𝑖(𝛿12	𝑖(𝛿12	NUM
cana-5829	630	3	+	+	CCONJ
cana-5829	630	4	𝜃12	𝜃12	ADJ
cana-5829	630	5	−	−	PROPN
cana-5829	630	6	𝛿12	𝛿12	PROPN
cana-5829	630	7	.	.	PROPN
cana-5829	630	8	𝜃12	𝜃12	PROPN
cana-5829	630	9	)	)	PUNCT
cana-5829	630	10	}	}	PUNCT
cana-5829	630	11	where	where	SCONJ
cana-5829	630	12	∣μ12∣=	∣μ12∣=	X
cana-5829	630	13	(	(	PUNCT
cana-5829	630	14	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	NOUN
cana-5829	630	15	+	+	CCONJ
cana-5829	630	16	𝛿𝐹12	𝛿𝐹12	X
cana-5829	630	17	(	(	PUNCT
cana-5829	630	18	𝛼12	𝛼12	PROPN
cana-5829	630	19	.	.	PUNCT
cana-5829	630	20	𝑥12)2	𝑥12)2	VERB
cana-5829	631	1	+	+	CCONJ
cana-5829	631	2	(	(	PUNCT
cana-5829	631	3	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	X
cana-5829	631	4	+	+	CCONJ
cana-5829	631	5	𝛿𝐹12	𝛿𝐹12	X
cana-5829	631	6	(	(	PUNCT
cana-5829	631	7	𝛽12	𝛽12	PROPN
cana-5829	631	8	.	.	PUNCT
cana-5829	631	9	𝑦12)2	𝑦12)2	NOUN
cana-5829	631	10	<	<	X
cana-5829	631	11	1	1	NUM
cana-5829	631	12	∣	∣	PROPN
cana-5829	631	13	ν12	ν12	NOUN
cana-5829	631	14	∣=	∣=	PROPN
cana-5829	631	15	(	(	PUNCT
cana-5829	631	16	𝑁𝑜𝑟𝑚µ𝐸12+𝛾𝐹12	𝑁𝑜𝑟𝑚µ𝐸12+𝛾𝐹12	PROPN
cana-5829	631	17	(	(	PUNCT
cana-5829	631	18	𝛾12	𝛾12	NOUN
cana-5829	631	19	+	+	NUM
cana-5829	631	20	𝜇12	𝜇12	NOUN
cana-5829	631	21	−	−	PROPN
cana-5829	631	22	𝛾12	𝛾12	PROPN
cana-5829	631	23	.	.	PUNCT
cana-5829	632	1	𝜇12)2	𝜇12)2	PROPN
cana-5829	632	2	+	+	CCONJ
cana-5829	632	3	𝑁𝑜𝑟𝑚µ𝐸12+𝛾𝐹12	𝑁𝑜𝑟𝑚µ𝐸12+𝛾𝐹12	PROPN
cana-5829	633	1	(	(	PUNCT
cana-5829	633	2	𝛿12	𝛿12	NOUN
cana-5829	633	3	+	+	CCONJ
cana-5829	633	4	𝜃12	𝜃12	ADJ
cana-5829	633	5	−	−	PROPN
cana-5829	633	6	𝛿12	𝛿12	NOUN
cana-5829	633	7	.	.	PROPN
cana-5829	633	8	𝜃12)2	𝜃12)2	VERB
cana-5829	633	9	<	<	X
cana-5829	633	10	1	1	NUM
cana-5829	633	11	,	,	PUNCT
cana-5829	633	12	∣μ12∣+∣ν12∣	∣μ12∣+∣ν12∣	ADJ
cana-5829	633	13	≤	≤	NUM
cana-5829	633	14	1	1	NUM
cana-5829	633	15	.	.	PUNCT
cana-5829	634	1	x21	x21	NUM
cana-5829	634	2	=	=	SYM
cana-5829	634	3	{	{	PUNCT
cana-5829	634	4	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	ADV
cana-5829	634	5	+	+	NUM
cana-5829	634	6	𝛿𝐹21	𝛿𝐹21	X
cana-5829	634	7	(	(	PUNCT
cana-5829	634	8	𝛼21	𝛼21	NOUN
cana-5829	634	9	.	.	PUNCT
cana-5829	634	10	𝑥21	𝑥21	NOUN
cana-5829	634	11	)	)	PUNCT
cana-5829	634	12	+	+	PUNCT
cana-5829	634	13	𝑖(𝛽21.𝑦21	𝑖(𝛽21.𝑦21	NOUN
cana-5829	634	14	)	)	PUNCT
cana-5829	634	15	,	,	PUNCT
cana-5829	634	16	𝑁𝑜𝑟𝑚µ𝐸21+𝛾𝐹21	𝑁𝑜𝑟𝑚µ𝐸21+𝛾𝐹21	NUM
cana-5829	634	17	(	(	PUNCT
cana-5829	634	18	𝛾21	𝛾21	NOUN
cana-5829	634	19	+	+	CCONJ
cana-5829	634	20	𝜇21	𝜇21	ADJ
cana-5829	634	21	−	−	NOUN
cana-5829	634	22	𝛾21	𝛾21	NOUN
cana-5829	634	23	.	.	PUNCT
cana-5829	635	1	𝜇21	𝜇21	VERB
cana-5829	635	2	+	+	CCONJ
cana-5829	635	3	𝑖(𝛿21	𝑖(𝛿21	NOUN
cana-5829	635	4	+	+	CCONJ
cana-5829	635	5	𝜃21	𝜃21	NOUN
cana-5829	635	6	−	−	PROPN
cana-5829	635	7	𝛿21	𝛿21	PROPN
cana-5829	635	8	.	.	PUNCT
cana-5829	636	1	𝜃21	𝜃21	PROPN
cana-5829	636	2	}	}	PUNCT
cana-5829	636	3	where	where	SCONJ
cana-5829	636	4	∣μ21∣=	∣μ21∣=	X
cana-5829	636	5	(	(	PUNCT
cana-5829	636	6	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	X
cana-5829	636	7	+	+	NUM
cana-5829	636	8	𝛿𝐹21	𝛿𝐹21	X
cana-5829	636	9	(	(	PUNCT
cana-5829	636	10	𝛼21	𝛼21	NOUN
cana-5829	636	11	.	.	PUNCT
cana-5829	637	1	𝑥21)2	𝑥21)2	PRON
cana-5829	637	2	+	+	CCONJ
cana-5829	637	3	(	(	PUNCT
cana-5829	637	4	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	X
cana-5829	637	5	+	+	NUM
cana-5829	637	6	𝛿𝐹21	𝛿𝐹21	X
cana-5829	637	7	(	(	PUNCT
cana-5829	637	8	𝛽21	𝛽21	PROPN
cana-5829	637	9	.	.	PUNCT
cana-5829	638	1	𝑦21)2	𝑦21)2	VERB
cana-5829	638	2	<	<	X
cana-5829	638	3	1	1	NUM
cana-5829	638	4	∣	∣	ADJ
cana-5829	638	5	ν21	ν21	NOUN
cana-5829	638	6	∣=	∣=	PROPN
cana-5829	638	7	(	(	PUNCT
cana-5829	638	8	𝑁𝑜𝑟𝑚µ𝐸21+𝛾𝐹21	𝑁𝑜𝑟𝑚µ𝐸21+𝛾𝐹21	X
cana-5829	638	9	(	(	PUNCT
cana-5829	638	10	𝛾21	𝛾21	NOUN
cana-5829	638	11	+	+	CCONJ
cana-5829	638	12	𝜇21	𝜇21	ADJ
cana-5829	638	13	−	−	NOUN
cana-5829	638	14	𝛾21	𝛾21	NOUN
cana-5829	638	15	.	.	PUNCT
cana-5829	639	1	𝜇21)2	𝜇21)2	VERB
cana-5829	639	2	+	+	NUM
cana-5829	639	3	𝑁𝑜𝑟𝑚µ𝐸21+𝛾𝐹21	𝑁𝑜𝑟𝑚µ𝐸21+𝛾𝐹21	X
cana-5829	639	4	(	(	PUNCT
cana-5829	639	5	𝛿21	𝛿21	PROPN
cana-5829	639	6	+	+	CCONJ
cana-5829	639	7	𝜃21	𝜃21	NOUN
cana-5829	639	8	−	−	PROPN
cana-5829	639	9	𝛿21	𝛿21	PROPN
cana-5829	639	10	.	.	PUNCT
cana-5829	640	1	𝜃21)2	𝜃21)2	VERB
cana-5829	641	1	<	<	X
cana-5829	642	1	1	1	NUM
cana-5829	642	2	,	,	PUNCT
cana-5829	642	3	∣μ21∣+∣ν21∣	∣μ21∣+∣ν21∣	VERB
cana-5829	642	4	≤	≤	NUM
cana-5829	642	5	1	1	NUM
cana-5829	642	6	.	.	PUNCT
cana-5829	642	7	x22	x22	NOUN
cana-5829	643	1	=	=	SYM
cana-5829	643	2	{	{	PUNCT
cana-5829	643	3	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	X
cana-5829	643	4	+	+	SYM
cana-5829	643	5	𝛿𝐹22	𝛿𝐹22	X
cana-5829	643	6	(	(	PUNCT
cana-5829	643	7	𝛼22	𝛼22	NOUN
cana-5829	643	8	.	.	PUNCT
cana-5829	644	1	𝑥22	𝑥22	NOUN
cana-5829	644	2	)	)	PUNCT
cana-5829	645	1	+	+	CCONJ
cana-5829	645	2	𝑖(𝛽22.𝑦22	𝑖(𝛽22.𝑦22	NOUN
cana-5829	645	3	)	)	PUNCT
cana-5829	645	4	,	,	PUNCT
cana-5829	645	5	𝑁𝑜𝑟𝑚µ𝐸22+𝛾𝐹22	𝑁𝑜𝑟𝑚µ𝐸22+𝛾𝐹22	X
cana-5829	645	6	(	(	PUNCT
cana-5829	645	7	𝛾22	𝛾22	ADJ
cana-5829	645	8	+	+	CCONJ
cana-5829	645	9	𝜇22	𝜇22	NOUN
cana-5829	645	10	−	−	PROPN
cana-5829	645	11	𝛾22	𝛾22	PROPN
cana-5829	645	12	.	.	PUNCT
cana-5829	645	13	𝜇22	𝜇22	PROPN
cana-5829	645	14	)	)	PUNCT
cana-5829	645	15	+	+	CCONJ
cana-5829	645	16	𝑖(𝛿22	𝑖(𝛿22	NOUN
cana-5829	645	17	+	+	CCONJ
cana-5829	645	18	𝜃22	𝜃22	ADV
cana-5829	645	19	−	−	NOUN
cana-5829	645	20	𝛿22	𝛿22	NOUN
cana-5829	645	21	.	.	PUNCT
cana-5829	646	1	𝜃22	𝜃22	NUM
cana-5829	646	2	)	)	PUNCT
cana-5829	646	3	}	}	PUNCT
cana-5829	647	1	where	where	SCONJ
cana-5829	647	2	∣μ22∣=	∣μ22∣=	AUX
cana-5829	647	3	(	(	PUNCT
cana-5829	647	4	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	ADJ
cana-5829	647	5	+	+	NUM
cana-5829	647	6	𝛿𝐹22	𝛿𝐹22	X
cana-5829	647	7	(	(	PUNCT
cana-5829	647	8	𝛼22	𝛼22	NOUN
cana-5829	647	9	.	.	PUNCT
cana-5829	648	1	𝑥22)2	𝑥22)2	ADP
cana-5829	648	2	+	+	CCONJ
cana-5829	648	3	(	(	PUNCT
cana-5829	648	4	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	X
cana-5829	648	5	+	+	X
cana-5829	648	6	𝛿𝐹22	𝛿𝐹22	X
cana-5829	648	7	(	(	PUNCT
cana-5829	648	8	𝛽22	𝛽22	NOUN
cana-5829	648	9	.	.	PUNCT
cana-5829	649	1	𝑦22)2	𝑦22)2	VERB
cana-5829	649	2	<	<	X
cana-5829	649	3	1	1	NUM
cana-5829	649	4	∣	∣	PROPN
cana-5829	649	5	ν22	ν22	NOUN
cana-5829	649	6	∣=	∣=	PROPN
cana-5829	649	7	(	(	PUNCT
cana-5829	649	8	𝑁𝑜𝑟𝑚µ𝐸22+𝛾𝐹22	𝑁𝑜𝑟𝑚µ𝐸22+𝛾𝐹22	X
cana-5829	649	9	(	(	PUNCT
cana-5829	649	10	𝛾22	𝛾22	ADJ
cana-5829	649	11	+	+	CCONJ
cana-5829	649	12	𝜇22	𝜇22	NOUN
cana-5829	649	13	−	−	PROPN
cana-5829	649	14	𝛾22	𝛾22	NOUN
cana-5829	649	15	.	.	PUNCT
cana-5829	650	1	𝜇22)2	𝜇22)2	NOUN
cana-5829	650	2	+	+	CCONJ
cana-5829	650	3	𝑁𝑜𝑟𝑚µ𝐸22+𝛾𝐹22	𝑁𝑜𝑟𝑚µ𝐸22+𝛾𝐹22	X
cana-5829	650	4	(	(	PUNCT
cana-5829	650	5	𝛿22	𝛿22	NOUN
cana-5829	650	6	+	+	CCONJ
cana-5829	650	7	𝜃22	𝜃22	ADJ
cana-5829	650	8	−	−	NOUN
cana-5829	650	9	𝛿22	𝛿22	NOUN
cana-5829	650	10	.	.	PUNCT
cana-5829	650	11	𝜃22)2	𝜃22)2	NOUN
cana-5829	650	12	<	<	X
cana-5829	650	13	1	1	NUM
cana-5829	650	14	,	,	PUNCT
cana-5829	650	15	∣μ22∣+∣ν22∣	∣μ22∣+∣ν22∣	ADV
cana-5829	650	16	≤	≤	NUM
cana-5829	650	17	1	1	NUM
cana-5829	650	18	.	.	PUNCT
cana-5829	651	1	we	we	PRON
cana-5829	651	2	have	have	VERB
cana-5829	651	3	norm𝐴𝐸𝑁𝑜𝑟𝑚𝐵𝐹	norm𝐴𝐸𝑁𝑜𝑟𝑚𝐵𝐹	PUNCT
cana-5829	651	4	=	=	SYM
cana-5829	652	1	(	(	PUNCT
cana-5829	652	2	𝑋11	𝑋11	PROPN
cana-5829	652	3	𝑋12	𝑋12	PROPN
cana-5829	652	4	𝑋21	𝑋21	NOUN
cana-5829	652	5	𝑋22	𝑋22	ADJ
cana-5829	652	6	)	)	PUNCT
cana-5829	652	7	is	be	AUX
cana-5829	652	8	also	also	ADV
cana-5829	652	9	normalization	normalization	NOUN
cana-5829	652	10	of	of	ADP
cana-5829	652	11	complex	complex	ADJ
cana-5829	652	12	intuitionistic	intuitionistic	ADJ
cana-5829	652	13	fuzzy	fuzzy	ADJ
cana-5829	652	14	matrix	matrix	NOUN
cana-5829	653	1	example5.2.8	example5.2.8	ADJ
cana-5829	653	2	:	:	PUNCT
cana-5829	653	3	if	if	SCONJ
cana-5829	653	4	𝐴𝐸=	𝐴𝐸=	NOUN
cana-5829	653	5	(	(	PUNCT
cana-5829	653	6	(	(	PUNCT
cana-5829	653	7	0.6	0.6	NUM
cana-5829	653	8	+	+	CCONJ
cana-5829	653	9	0.2i	0.2i	ADJ
cana-5829	653	10	,	,	PUNCT
cana-5829	653	11	0.3	0.3	NUM
cana-5829	653	12	+	+	NOUN
cana-5829	653	13	0.1i)(0.4	0.1i)(0.4	X
cana-5829	654	1	+	+	CCONJ
cana-5829	654	2	0.1i	0.1i	NOUN
cana-5829	654	3	,	,	PUNCT
cana-5829	654	4	0.5	0.5	NUM
cana-5829	654	5	+	+	NUM
cana-5829	654	6	0.2i	0.2i	NUM
cana-5829	654	7	)	)	PUNCT
cana-5829	654	8	(	(	PUNCT
cana-5829	654	9	0.5	0.5	NUM
cana-5829	654	10	+	+	CCONJ
cana-5829	654	11	0.3i	0.3i	NOUN
cana-5829	654	12	,	,	PUNCT
cana-5829	654	13	0.2	0.2	NUM
cana-5829	654	14	+	+	CCONJ
cana-5829	654	15	0.1i)(0.3	0.1i)(0.3	PRON
cana-5829	654	16	+	+	CCONJ
cana-5829	654	17	0.2i	0.2i	ADJ
cana-5829	654	18	,	,	PUNCT
cana-5829	654	19	0.6	0.6	NUM
cana-5829	654	20	+	+	NUM
cana-5829	654	21	0.1i	0.1i	NOUN
cana-5829	654	22	)	)	PUNCT
cana-5829	654	23	)	)	PUNCT
cana-5829	654	24	and	and	CCONJ
cana-5829	654	25	bf	bf	NOUN
cana-5829	654	26	=	=	SYM
cana-5829	654	27	(	(	PUNCT
cana-5829	654	28	(	(	PUNCT
cana-5829	654	29	0.4	0.4	NUM
cana-5829	654	30	+	+	CCONJ
cana-5829	654	31	0.3i	0.3i	NOUN
cana-5829	654	32	,	,	PUNCT
cana-5829	654	33	0.5	0.5	NUM
cana-5829	654	34	+	+	CCONJ
cana-5829	654	35	0.1i)(0.3	0.1i)(0.3	PRON
cana-5829	654	36	+	+	CCONJ
cana-5829	654	37	0.4i	0.4i	NOUN
cana-5829	654	38	,	,	PUNCT
cana-5829	654	39	0.4	0.4	NUM
cana-5829	654	40	+	+	CCONJ
cana-5829	654	41	0.2i	0.2i	NUM
cana-5829	654	42	)	)	PUNCT
cana-5829	654	43	(	(	PUNCT
cana-5829	654	44	0.6	0.6	NUM
cana-5829	654	45	+	+	CCONJ
cana-5829	654	46	0.2i	0.2i	ADJ
cana-5829	654	47	,	,	PUNCT
cana-5829	654	48	0.2	0.2	NUM
cana-5829	654	49	+	+	CCONJ
cana-5829	654	50	0.2i)(0.5	0.2i)(0.5	X
cana-5829	655	1	+	+	CCONJ
cana-5829	655	2	0.1i	0.1i	NOUN
cana-5829	655	3	,	,	PUNCT
cana-5829	655	4	0.4	0.4	NUM
cana-5829	655	5	+	+	CCONJ
cana-5829	655	6	0.3i	0.3i	NOUN
cana-5829	655	7	)	)	PUNCT
cana-5829	655	8	)	)	PUNCT
cana-5829	655	9	are	be	AUX
cana-5829	655	10	normalization	normalization	NOUN
cana-5829	655	11	of	of	ADP
cana-5829	655	12	complex	complex	ADJ
cana-5829	655	13	intuitionistic	intuitionistic	ADJ
cana-5829	655	14	fuzzy	fuzzy	ADJ
cana-5829	655	15	matrix	matrix	NOUN
cana-5829	655	16	two	two	NUM
cana-5829	655	17	intuitionistic	intuitionistic	ADJ
cana-5829	655	18	fuzzy	fuzzy	ADJ
cana-5829	655	19	matrices	matrix	NOUN
cana-5829	655	20	over	over	ADP
cana-5829	655	21	different	different	ADJ
cana-5829	655	22	universe	universe	NOUN
cana-5829	655	23	e	e	NOUN
cana-5829	655	24	and	and	CCONJ
cana-5829	655	25	f	f	PROPN
cana-5829	655	26	then	then	ADV
cana-5829	655	27	norm𝐴𝐸𝑁𝑜𝑟𝑚𝐵𝐹	norm𝐴𝐸𝑁𝑜𝑟𝑚𝐵𝐹	PROPN
cana-5829	655	28	is	be	AUX
cana-5829	655	29	also	also	ADV
cana-5829	655	30	normalization	normalization	NOUN
cana-5829	655	31	of	of	ADP
cana-5829	655	32	complex	complex	ADJ
cana-5829	655	33	intuitionistic	intuitionistic	ADJ
cana-5829	655	34	fuzzy	fuzzy	ADJ
cana-5829	655	35	matrix	matrix	NOUN
cana-5829	655	36	.	.	PUNCT
cana-5829	656	1	proof	proof	NOUN
cana-5829	656	2	:	:	PUNCT
cana-5829	656	3	communications	communication	NOUN
cana-5829	656	4	on	on	ADP
cana-5829	656	5	applied	apply	VERB
cana-5829	656	6	nonlinear	nonlinear	ADJ
cana-5829	656	7	analysis	analysis	NOUN
cana-5829	656	8	issn	issn	NOUN
cana-5829	656	9	:	:	PUNCT
cana-5829	656	10	1074	1074	NUM
cana-5829	656	11	-	-	PUNCT
cana-5829	656	12	133x	133x	NUM
cana-5829	656	13	vol	vol	VERB
cana-5829	656	14	32	32	NUM
cana-5829	656	15	no	no	NOUN
cana-5829	656	16	.	.	PUNCT
cana-5829	657	1	10s	10	NOUN
cana-5829	657	2	(	(	PUNCT
cana-5829	657	3	2025	2025	NUM
cana-5829	657	4	)	)	PUNCT
cana-5829	657	5	2946	2946	NUM
cana-5829	657	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5829	657	7	given	give	VERB
cana-5829	657	8	𝑨𝑬=	𝑨𝑬=	PROPN
cana-5829	657	9	(	(	PUNCT
cana-5829	657	10	(	(	PUNCT
cana-5829	657	11	0.6	0.6	NUM
cana-5829	657	12	+	+	CCONJ
cana-5829	657	13	0.2i	0.2i	ADJ
cana-5829	657	14	,	,	PUNCT
cana-5829	657	15	0.3	0.3	NUM
cana-5829	657	16	+	+	NOUN
cana-5829	657	17	0.1i)(0.4	0.1i)(0.4	X
cana-5829	658	1	+	+	CCONJ
cana-5829	658	2	0.1i	0.1i	NOUN
cana-5829	658	3	,	,	PUNCT
cana-5829	658	4	0.5	0.5	NUM
cana-5829	658	5	+	+	NUM
cana-5829	658	6	0.2i	0.2i	NUM
cana-5829	658	7	)	)	PUNCT
cana-5829	658	8	(	(	PUNCT
cana-5829	658	9	0.5	0.5	NUM
cana-5829	658	10	+	+	CCONJ
cana-5829	658	11	0.3i	0.3i	NOUN
cana-5829	658	12	,	,	PUNCT
cana-5829	658	13	0.2	0.2	NUM
cana-5829	658	14	+	+	CCONJ
cana-5829	658	15	0.1i)(0.3	0.1i)(0.3	PRON
cana-5829	658	16	+	+	CCONJ
cana-5829	658	17	0.2i	0.2i	ADJ
cana-5829	658	18	,	,	PUNCT
cana-5829	658	19	0.6	0.6	NUM
cana-5829	658	20	+	+	NUM
cana-5829	658	21	0.1i	0.1i	NOUN
cana-5829	658	22	)	)	PUNCT
cana-5829	658	23	)	)	PUNCT
cana-5829	658	24	and	and	CCONJ
cana-5829	658	25	𝑩𝑭	𝑩𝑭	PROPN
cana-5829	658	26	=	=	SYM
cana-5829	658	27	(	(	PUNCT
cana-5829	658	28	(	(	PUNCT
cana-5829	658	29	0.4	0.4	NUM
cana-5829	658	30	+	+	CCONJ
cana-5829	658	31	0.3i	0.3i	NOUN
cana-5829	658	32	,	,	PUNCT
cana-5829	658	33	0.5	0.5	NUM
cana-5829	658	34	+	+	CCONJ
cana-5829	658	35	0.1i)(0.3	0.1i)(0.3	PRON
cana-5829	658	36	+	+	CCONJ
cana-5829	658	37	0.4i	0.4i	NOUN
cana-5829	658	38	,	,	PUNCT
cana-5829	658	39	0.4	0.4	NUM
cana-5829	658	40	+	+	CCONJ
cana-5829	658	41	0.2i	0.2i	NUM
cana-5829	658	42	)	)	PUNCT
cana-5829	658	43	(	(	PUNCT
cana-5829	658	44	0.6	0.6	NUM
cana-5829	658	45	+	+	CCONJ
cana-5829	658	46	0.2i	0.2i	ADJ
cana-5829	658	47	,	,	PUNCT
cana-5829	658	48	0.2	0.2	NUM
cana-5829	658	49	+	+	CCONJ
cana-5829	658	50	0.2i)(0.5	0.2i)(0.5	X
cana-5829	659	1	+	+	CCONJ
cana-5829	659	2	0.1i	0.1i	NOUN
cana-5829	659	3	,	,	PUNCT
cana-5829	659	4	0.4	0.4	NUM
cana-5829	659	5	+	+	CCONJ
cana-5829	659	6	0.3i	0.3i	NOUN
cana-5829	659	7	)	)	PUNCT
cana-5829	659	8	)	)	PUNCT
cana-5829	659	9	norm	norm	VERB
cana-5829	659	10	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	659	11	=	=	SYM
cana-5829	660	1	(	(	PUNCT
cana-5829	660	2	(	(	PUNCT
cana-5829	660	3	1	1	NUM
cana-5829	660	4	+	+	NUM
cana-5829	660	5	0.67𝑖	0.67𝑖	NUM
cana-5829	660	6	0.125	0.125	NUM
cana-5829	660	7	+	+	NUM
cana-5829	660	8	0𝑖	0𝑖	NOUN
cana-5829	660	9	)	)	PUNCT
cana-5829	660	10	(	(	PUNCT
cana-5829	660	11	0.67	0.67	NUM
cana-5829	660	12	+	+	CCONJ
cana-5829	660	13	0.33𝑖	0.33𝑖	NUM
cana-5829	660	14	0.30	0.30	NUM
cana-5829	660	15	+	+	CCONJ
cana-5829	660	16	0.10𝑖	0.10𝑖	NOUN
cana-5829	660	17	)	)	PUNCT
cana-5829	660	18	(	(	PUNCT
cana-5829	660	19	0.83	0.83	NUM
cana-5829	660	20	+	+	NUM
cana-5829	660	21	1𝑖	1𝑖	NOUN
cana-5829	660	22	0	0	NUM
cana-5829	661	1	+	+	NUM
cana-5829	661	2	0𝑖	0𝑖	NOUN
cana-5829	661	3	)	)	PUNCT
cana-5829	661	4	(	(	PUNCT
cana-5829	661	5	0.5	0.5	NUM
cana-5829	661	6	+	+	NUM
cana-5829	661	7	0.67𝑖	0.67𝑖	NUM
cana-5829	661	8	0.5	0.5	NUM
cana-5829	661	9	+	+	NUM
cana-5829	661	10	0𝑖	0𝑖	NOUN
cana-5829	661	11	)	)	PUNCT
cana-5829	661	12	)	)	PUNCT
cana-5829	662	1	𝑁𝑜𝑟𝑚	𝑁𝑜𝑟𝑚	NOUN
cana-5829	662	2	𝐵𝐹=	𝐵𝐹=	ADP
cana-5829	662	3	(	(	PUNCT
cana-5829	662	4	(	(	PUNCT
cana-5829	662	5	0.67	0.67	NUM
cana-5829	662	6	+	+	CCONJ
cana-5829	662	7	0.75𝑖	0.75𝑖	PROPN
cana-5829	662	8	0.375	0.375	NUM
cana-5829	662	9	+	+	NUM
cana-5829	662	10	0𝑖	0𝑖	NOUN
cana-5829	662	11	)	)	PUNCT
cana-5829	662	12	(	(	PUNCT
cana-5829	662	13	0.5	0.5	NUM
cana-5829	662	14	+	+	NUM
cana-5829	662	15	1𝑖	1𝑖	NUM
cana-5829	662	16	0.25	0.25	NUM
cana-5829	662	17	+	+	CCONJ
cana-5829	662	18	0.11𝑖	0.11𝑖	NUM
cana-5829	662	19	)	)	PUNCT
cana-5829	662	20	(	(	PUNCT
cana-5829	662	21	1	1	NUM
cana-5829	662	22	+	+	NUM
cana-5829	662	23	0.5𝑖	0.5𝑖	NOUN
cana-5829	662	24	0	0	NUM
cana-5829	663	1	+	+	CCONJ
cana-5829	663	2	0.11𝑖	0.11𝑖	NUM
cana-5829	663	3	)	)	PUNCT
cana-5829	663	4	(	(	PUNCT
cana-5829	663	5	0.83	0.83	NUM
cana-5829	663	6	+	+	NUM
cana-5829	663	7	0.25𝑖	0.25𝑖	NOUN
cana-5829	663	8	0.25	0.25	NUM
cana-5829	663	9	+	+	PUNCT
cana-5829	663	10	0.22𝑖	0.22𝑖	NOUN
cana-5829	663	11	)	)	PUNCT
cana-5829	663	12	)	)	PUNCT
cana-5829	663	13	apply	apply	VERB
cana-5829	663	14	the	the	DET
cana-5829	663	15	formula	formula	NOUN
cana-5829	663	16	aebf	aebf	X
cana-5829	664	1	=	=	SYM
cana-5829	664	2	{	{	PUNCT
cana-5829	664	3	(	(	PUNCT
cana-5829	664	4	x	x	NOUN
cana-5829	664	5	,	,	PUNCT
cana-5829	664	6	y	y	PROPN
cana-5829	664	7	)	)	PUNCT
cana-5829	664	8	,	,	PUNCT
cana-5829	664	9	μa(x	μa(x	NOUN
cana-5829	664	10	)	)	PUNCT
cana-5829	664	11	.	.	PUNCT
cana-5829	665	1	μb(y	μb(y	NUM
cana-5829	665	2	)	)	PUNCT
cana-5829	665	3	,	,	PUNCT
cana-5829	665	4	ϑa(x	ϑa(x	NOUN
cana-5829	665	5	)	)	PUNCT
cana-5829	666	1	+	+	ADJ
cana-5829	666	2	ϑb(y	ϑb(y	X
cana-5829	666	3	)	)	PUNCT
cana-5829	666	4	ϑa(x).ϑb(y	ϑa(x).ϑb(y	ADJ
cana-5829	666	5	):	):	PUNCT
cana-5829	666	6	xe	xe	PROPN
cana-5829	666	7	,	,	PUNCT
cana-5829	666	8	yf	yf	PROPN
cana-5829	666	9	aebf	aebf	PUNCT
cana-5829	667	1	=	=	PUNCT
cana-5829	667	2	(	(	PUNCT
cana-5829	667	3	(	(	PUNCT
cana-5829	667	4	1	1	NUM
cana-5829	667	5	+	+	NUM
cana-5829	667	6	0.67𝑖	0.67𝑖	NUM
cana-5829	667	7	0.125	0.125	NUM
cana-5829	667	8	+	+	NUM
cana-5829	667	9	0𝑖	0𝑖	NOUN
cana-5829	667	10	)	)	PUNCT
cana-5829	667	11	(	(	PUNCT
cana-5829	667	12	0.67	0.67	NUM
cana-5829	667	13	+	+	CCONJ
cana-5829	667	14	0.33𝑖	0.33𝑖	NUM
cana-5829	667	15	0.30	0.30	NUM
cana-5829	667	16	+	+	CCONJ
cana-5829	667	17	0.10𝑖	0.10𝑖	NOUN
cana-5829	667	18	)	)	PUNCT
cana-5829	667	19	(	(	PUNCT
cana-5829	667	20	0.83	0.83	NUM
cana-5829	667	21	+	+	NUM
cana-5829	667	22	1𝑖	1𝑖	NOUN
cana-5829	667	23	0	0	NUM
cana-5829	668	1	+	+	NUM
cana-5829	668	2	0𝑖	0𝑖	NOUN
cana-5829	668	3	)	)	PUNCT
cana-5829	668	4	(	(	PUNCT
cana-5829	668	5	0.5	0.5	NUM
cana-5829	668	6	+	+	NUM
cana-5829	668	7	0.67𝑖	0.67𝑖	NUM
cana-5829	668	8	0.5	0.5	NUM
cana-5829	668	9	+	+	NUM
cana-5829	668	10	0𝑖	0𝑖	NOUN
cana-5829	668	11	)	)	PUNCT
cana-5829	668	12	)	)	PUNCT
cana-5829	669	1			X
cana-5829	669	2	(	(	PUNCT
cana-5829	669	3	(	(	PUNCT
cana-5829	669	4	0.67	0.67	NUM
cana-5829	669	5	+	+	CCONJ
cana-5829	669	6	0.75𝑖	0.75𝑖	PROPN
cana-5829	669	7	0.375	0.375	NUM
cana-5829	669	8	+	+	NUM
cana-5829	669	9	0𝑖	0𝑖	NOUN
cana-5829	669	10	)	)	PUNCT
cana-5829	669	11	(	(	PUNCT
cana-5829	669	12	0.5	0.5	NUM
cana-5829	669	13	+	+	NUM
cana-5829	669	14	1𝑖	1𝑖	NUM
cana-5829	669	15	0.25	0.25	NUM
cana-5829	669	16	+	+	CCONJ
cana-5829	669	17	0.11𝑖	0.11𝑖	NUM
cana-5829	669	18	)	)	PUNCT
cana-5829	669	19	(	(	PUNCT
cana-5829	669	20	1	1	NUM
cana-5829	670	1	+	+	NUM
cana-5829	670	2	0.5𝑖	0.5𝑖	NOUN
cana-5829	670	3	0	0	NUM
cana-5829	671	1	+	+	CCONJ
cana-5829	671	2	0.11𝑖	0.11𝑖	NUM
cana-5829	671	3	)	)	PUNCT
cana-5829	671	4	(	(	PUNCT
cana-5829	672	1	0.83	0.83	NUM
cana-5829	672	2	+	+	NUM
cana-5829	672	3	0.25𝑖	0.25𝑖	NOUN
cana-5829	672	4	0.25	0.25	NUM
cana-5829	672	5	+	+	PUNCT
cana-5829	672	6	0.22𝑖	0.22𝑖	NUM
cana-5829	672	7	)	)	PUNCT
cana-5829	672	8	)	)	PUNCT
cana-5829	673	1	𝑋11	𝑋11	PROPN
cana-5829	673	2	=	=	PUNCT
cana-5829	673	3	(	(	PUNCT
cana-5829	673	4	1	1	NUM
cana-5829	673	5	+	+	NUM
cana-5829	673	6	0.67𝑖	0.67𝑖	NUM
cana-5829	673	7	0.125	0.125	NUM
cana-5829	673	8	+	+	CCONJ
cana-5829	673	9	0𝑖)(0.67	0𝑖)(0.67	NOUN
cana-5829	673	10	+	+	CCONJ
cana-5829	673	11	0.75𝑖	0.75𝑖	PROPN
cana-5829	673	12	0.375	0.375	NUM
cana-5829	673	13	+	+	NUM
cana-5829	673	14	0𝑖	0𝑖	NOUN
cana-5829	673	15	)	)	PUNCT
cana-5829	673	16	𝑋12	𝑋12	PROPN
cana-5829	674	1	=	=	PUNCT
cana-5829	675	1	(	(	PUNCT
cana-5829	675	2	0.67	0.67	NUM
cana-5829	675	3	+	+	CCONJ
cana-5829	675	4	0.33𝑖	0.33𝑖	NUM
cana-5829	675	5	0.30	0.30	NUM
cana-5829	675	6	+	+	CCONJ
cana-5829	675	7	0.10𝑖	0.10𝑖	NOUN
cana-5829	675	8	)	)	PUNCT
cana-5829	675	9	(0.5	(0.5	NOUN
cana-5829	675	10	+	+	CCONJ
cana-5829	675	11	1𝑖	1𝑖	NUM
cana-5829	675	12	0.25	0.25	NUM
cana-5829	675	13	+	+	CCONJ
cana-5829	675	14	0.11𝑖	0.11𝑖	NUM
cana-5829	675	15	)	)	PUNCT
cana-5829	675	16	𝑋21	𝑋21	NOUN
cana-5829	675	17	=	=	SYM
cana-5829	675	18	(	(	PUNCT
cana-5829	675	19	0.83	0.83	NUM
cana-5829	676	1	+	+	NUM
cana-5829	676	2	1𝑖	1𝑖	NOUN
cana-5829	676	3	0	0	NUM
cana-5829	677	1	+	+	NUM
cana-5829	677	2	0𝑖	0𝑖	NOUN
cana-5829	677	3	)	)	PUNCT
cana-5829	677	4			VERB
cana-5829	677	5	(	(	PUNCT
cana-5829	677	6	1	1	NUM
cana-5829	677	7	+	+	NUM
cana-5829	677	8	0.5𝑖	0.5𝑖	NOUN
cana-5829	677	9	0	0	NUM
cana-5829	678	1	+	+	CCONJ
cana-5829	678	2	0.11𝑖	0.11𝑖	NUM
cana-5829	678	3	)	)	PUNCT
cana-5829	679	1	𝑋22	𝑋22	ADJ
cana-5829	679	2	=	=	PUNCT
cana-5829	679	3	(	(	PUNCT
cana-5829	679	4	0.5	0.5	NUM
cana-5829	679	5	+	+	NUM
cana-5829	679	6	0.67𝑖	0.67𝑖	NUM
cana-5829	679	7	0.5	0.5	NUM
cana-5829	679	8	+	+	CCONJ
cana-5829	679	9	0𝑖)(0.83	0𝑖)(0.83	PRON
cana-5829	680	1	+	+	X
cana-5829	680	2	0.25𝑖	0.25𝑖	NOUN
cana-5829	680	3	0.25	0.25	NUM
cana-5829	680	4	+	+	CCONJ
cana-5829	680	5	0.22𝑖	0.22𝑖	NOUN
cana-5829	680	6	)	)	PUNCT
cana-5829	680	7	𝐴𝑝𝑝𝑙𝑦𝑖𝑛𝑔	𝐴𝑝𝑝𝑙𝑦𝑖𝑛𝑔	PROPN
cana-5829	680	8	𝑓𝑜𝑟𝑚𝑢𝑙𝑎	𝑓𝑜𝑟𝑚𝑢𝑙𝑎	VERB
cana-5829	680	9	aebf	aebf	PROPN
cana-5829	681	1	=	=	PRON
cana-5829	681	2	{	{	PUNCT
cana-5829	681	3	(	(	PUNCT
cana-5829	681	4	x	x	NOUN
cana-5829	681	5	,	,	PUNCT
cana-5829	681	6	y	y	PROPN
cana-5829	681	7	)	)	PUNCT
cana-5829	681	8	,	,	PUNCT
cana-5829	681	9	μa(x	μa(x	NOUN
cana-5829	681	10	)	)	PUNCT
cana-5829	681	11	.	.	PUNCT
cana-5829	682	1	μb(y	μb(y	NUM
cana-5829	682	2	)	)	PUNCT
cana-5829	682	3	,	,	PUNCT
cana-5829	682	4	ϑa(x	ϑa(x	NOUN
cana-5829	682	5	)	)	PUNCT
cana-5829	683	1	+	+	ADJ
cana-5829	683	2	ϑb(y	ϑb(y	X
cana-5829	683	3	)	)	PUNCT
cana-5829	683	4	ϑa(x).ϑb(y	ϑa(x).ϑb(y	ADJ
cana-5829	683	5	):	):	PUNCT
cana-5829	683	6	xe	xe	PROPN
cana-5829	683	7	,	,	PUNCT
cana-5829	683	8	yf	yf	PROPN
cana-5829	683	9	aebf	aebf	PUNCT
cana-5829	684	1	=	=	PUNCT
cana-5829	684	2	(	(	PUNCT
cana-5829	684	3	0.67	0.67	NUM
cana-5829	684	4	+	+	NUM
cana-5829	684	5	0.502𝑖	0.502𝑖	NOUN
cana-5829	684	6	,	,	PUNCT
cana-5829	684	7	0.453	0.453	NUM
cana-5829	684	8	+	+	NUM
cana-5829	684	9	0𝑖	0𝑖	NOUN
cana-5829	684	10	0.335	0.335	NUM
cana-5829	684	11	+	+	CCONJ
cana-5829	684	12	0.33𝑖	0.33𝑖	ADJ
cana-5829	684	13	,	,	PUNCT
cana-5829	684	14	0.65	0.65	NUM
cana-5829	684	15	+	+	CCONJ
cana-5829	684	16	0.199𝑖	0.199𝑖	ADJ
cana-5829	684	17	0.83	0.83	NUM
cana-5829	685	1	+	+	CCONJ
cana-5829	685	2	0.5𝑖	0.5𝑖	NUM
cana-5829	685	3	,	,	PUNCT
cana-5829	685	4	0	0	NUM
cana-5829	686	1	+	+	CCONJ
cana-5829	686	2	0.11𝑖	0.11𝑖	NUM
cana-5829	686	3	0.415	0.415	NUM
cana-5829	686	4	+	+	CCONJ
cana-5829	686	5	0.1678𝑖	0.1678𝑖	PROPN
cana-5829	686	6	,	,	PUNCT
cana-5829	686	7	0.625	0.625	NUM
cana-5829	686	8	+	+	NOUN
cana-5829	686	9	0.22𝑖	0.22𝑖	NUM
cana-5829	686	10	)	)	PUNCT
cana-5829	687	1	𝑋11	𝑋11	PROPN
cana-5829	687	2	=	=	PRON
cana-5829	687	3	{	{	PUNCT
cana-5829	687	4	0.807	0.807	NUM
cana-5829	687	5	+	+	NOUN
cana-5829	687	6	1i	1i	NOUN
cana-5829	687	7	,	,	PUNCT
cana-5829	687	8	0.0.453	0.0.453	NOUN
cana-5829	687	9	+	+	NOUN
cana-5829	687	10	0i	0i	NOUN
cana-5829	687	11	}	}	PUNCT
cana-5829	687	12	𝑋12	𝑋12	VERB
cana-5829	687	13	=	=	SYM
cana-5829	687	14	{	{	PUNCT
cana-5829	687	15	0.403	0.403	NUM
cana-5829	687	16	+	+	NOUN
cana-5829	687	17	0.667i	0.667i	NOUN
cana-5829	687	18	,	,	PUNCT
cana-5829	687	19	0.65	0.65	NUM
cana-5829	687	20	+	+	NOUN
cana-5829	687	21	0.199i	0.199i	NOUN
cana-5829	687	22	}	}	PUNCT
cana-5829	687	23	𝑋21	𝑋21	NOUN
cana-5829	687	24	=	=	PRON
cana-5829	687	25	{	{	PUNCT
cana-5829	687	26	1	1	NUM
cana-5829	687	27	+	+	NOUN
cana-5829	687	28	0.99i	0.99i	NOUN
cana-5829	687	29	,	,	PUNCT
cana-5829	687	30	0	0	PUNCT
cana-5829	688	1	+	+	NUM
cana-5829	688	2	0.11i	0.11i	NOUN
cana-5829	688	3	}	}	PUNCT
cana-5829	688	4	𝑋22	𝑋22	VERB
cana-5829	688	5	=	=	X
cana-5829	688	6	{	{	PUNCT
cana-5829	688	7	0.5	0.5	NUM
cana-5829	688	8	+	+	NOUN
cana-5829	688	9	0.332i	0.332i	NOUN
cana-5829	688	10	,	,	PUNCT
cana-5829	688	11	0.625	0.625	NUM
cana-5829	688	12	+	+	NUM
cana-5829	688	13	022i	022i	NOUN
cana-5829	688	14	}	}	PUNCT
cana-5829	688	15	we	we	PRON
cana-5829	688	16	have	have	VERB
cana-5829	688	17	norm𝐴𝐸𝑁𝑜𝑟𝑚𝐵𝐹	norm𝐴𝐸𝑁𝑜𝑟𝑚𝐵𝐹	PUNCT
cana-5829	689	1	=	=	SYM
cana-5829	689	2	(	(	PUNCT
cana-5829	689	3	(	(	PUNCT
cana-5829	689	4	0.807	0.807	NUM
cana-5829	689	5	+	+	NUM
cana-5829	689	6	1i	1i	NOUN
cana-5829	689	7	,	,	PUNCT
cana-5829	689	8	0.0.453	0.0.453	NUM
cana-5829	689	9	+	+	NUM
cana-5829	689	10	0i	0i	NOUN
cana-5829	689	11	)	)	PUNCT
cana-5829	689	12	(	(	PUNCT
cana-5829	689	13	0.403	0.403	NUM
cana-5829	689	14	+	+	CCONJ
cana-5829	689	15	0.667i	0.667i	NOUN
cana-5829	689	16	,	,	PUNCT
cana-5829	689	17	0.65	0.65	NUM
cana-5829	689	18	+	+	CCONJ
cana-5829	689	19	0.199i	0.199i	NOUN
cana-5829	689	20	)	)	PUNCT
cana-5829	689	21	(	(	PUNCT
cana-5829	689	22	1	1	NUM
cana-5829	689	23	+	+	CCONJ
cana-5829	689	24	0.99i	0.99i	NUM
cana-5829	689	25	,	,	PUNCT
cana-5829	689	26	0	0	NUM
cana-5829	690	1	+	+	NUM
cana-5829	690	2	0.11i	0.11i	NOUN
cana-5829	690	3	)	)	PUNCT
cana-5829	690	4	(	(	PUNCT
cana-5829	690	5	0.5	0.5	NUM
cana-5829	690	6	+	+	CCONJ
cana-5829	690	7	0.332i	0.332i	NOUN
cana-5829	690	8	,	,	PUNCT
cana-5829	690	9	0.625	0.625	NUM
cana-5829	690	10	+	+	NUM
cana-5829	690	11	022i	022i	NOUN
cana-5829	690	12	)	)	PUNCT
cana-5829	690	13	)	)	PUNCT
cana-5829	690	14	is	be	AUX
cana-5829	690	15	also	also	ADV
cana-5829	690	16	normalization	normalization	NOUN
cana-5829	690	17	of	of	ADP
cana-5829	690	18	complex	complex	ADJ
cana-5829	690	19	intuitionistic	intuitionistic	ADJ
cana-5829	690	20	fuzzy	fuzzy	ADJ
cana-5829	690	21	matrix	matrix	NOUN
cana-5829	690	22	.	.	PUNCT
cana-5829	691	1	theorem	theorem	ADJ
cana-5829	691	2	5.2.9	5.2.9	NUM
cana-5829	691	3	:	:	PUNCT
cana-5829	691	4	if	if	SCONJ
cana-5829	691	5	e	e	PROPN
cana-5829	691	6	and	and	CCONJ
cana-5829	691	7	f	f	PROPN
cana-5829	691	8	be	be	AUX
cana-5829	691	9	two	two	NUM
cana-5829	691	10	universal	universal	ADJ
cana-5829	691	11	sets	set	NOUN
cana-5829	691	12	.	.	PUNCT
cana-5829	692	1	for	for	ADP
cana-5829	692	2	every	every	DET
cana-5829	692	3	normalization	normalization	NOUN
cana-5829	692	4	of	of	ADP
cana-5829	692	5	complex	complex	ADJ
cana-5829	692	6	intuitionistic	intuitionistic	ADJ
cana-5829	692	7	fuzzy	fuzzy	ADJ
cana-5829	692	8	matrices	matrix	NOUN
cana-5829	692	9	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	692	10	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-5829	692	11	𝐵𝐹	𝐵𝐹	PROPN
cana-5829	692	12	are	be	AUX
cana-5829	692	13	in	in	ADP
cana-5829	692	14	e	e	PROPN
cana-5829	692	15	and	and	CCONJ
cana-5829	692	16	f	f	PROPN
cana-5829	692	17	then	then	ADV
cana-5829	692	18	norm𝐴𝐸@𝑁𝑜𝑟𝑚𝐵𝐹	norm𝐴𝐸@𝑁𝑜𝑟𝑚𝐵𝐹	PROPN
cana-5829	692	19	is	be	AUX
cana-5829	692	20	also	also	ADV
cana-5829	692	21	normalization	normalization	NOUN
cana-5829	692	22	of	of	ADP
cana-5829	692	23	complex	complex	ADJ
cana-5829	692	24	intuitionistic	intuitionistic	ADJ
cana-5829	692	25	fuzzy	fuzzy	ADJ
cana-5829	692	26	matrix	matrix	NOUN
cana-5829	692	27	.	.	PUNCT
cana-5829	693	1	proof	proof	NOUN
cana-5829	693	2	:	:	PUNCT
cana-5829	693	3	if	if	SCONJ
cana-5829	693	4	norm	norm	NOUN
cana-5829	693	5	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	693	6	and	and	CCONJ
cana-5829	693	7	𝑁𝑜𝑟𝑚	𝑁𝑜𝑟𝑚	PROPN
cana-5829	693	8	𝐵𝐹	𝐵𝐹	PROPN
cana-5829	693	9	are	be	AUX
cana-5829	693	10	two	two	NUM
cana-5829	693	11	normalization	normalization	NOUN
cana-5829	693	12	intuitionistic	intuitionistic	ADJ
cana-5829	693	13	fuzzy	fuzzy	ADJ
cana-5829	693	14	matrices	matrix	NOUN
cana-5829	693	15	over	over	ADP
cana-5829	693	16	different	different	ADJ
cana-5829	693	17	unive𝑟𝑠𝑒𝑠	unive𝑟𝑠𝑒𝑠	ADJ
cana-5829	693	18	𝑠𝑒𝑡𝑠	𝑠𝑒𝑡𝑠	PROPN
cana-5829	693	19	𝐸	𝐸	PROPN
cana-5829	693	20	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-5829	693	21	𝐹.	𝐹.	PROPN
cana-5829	693	22	if	if	SCONJ
cana-5829	693	23	we	we	PRON
cana-5829	693	24	consider	consider	VERB
cana-5829	693	25	two	two	NUM
cana-5829	693	26	2	2	NUM
cana-5829	693	27	×	×	NOUN
cana-5829	693	28	2	2	NUM
cana-5829	693	29	normalization	normalization	NOUN
cana-5829	693	30	intuitionistic	intuitionistic	ADJ
cana-5829	693	31	fuzzy	fuzzy	ADJ
cana-5829	693	32	matrices	matrix	NOUN
cana-5829	693	33	,	,	PUNCT
cana-5829	693	34	norm	norm	NOUN
cana-5829	693	35	𝐴𝐸𝑎𝑛𝑑	𝐴𝐸𝑎𝑛𝑑	PROPN
cana-5829	693	36	𝑁𝑜𝑟𝑚	𝑁𝑜𝑟𝑚	PROPN
cana-5829	693	37	𝐵𝐹.	𝐵𝐹.	NOUN
cana-5829	693	38	let	let	VERB
cana-5829	693	39	norm	norm	VERB
cana-5829	693	40	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	693	41	=	=	SYM
cana-5829	693	42	(	(	PUNCT
cana-5829	693	43	(	(	PUNCT
cana-5829	693	44	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	693	45	(	(	PUNCT
cana-5829	693	46	𝛼11	𝛼11	NOUN
cana-5829	693	47	+	+	PROPN
cana-5829	693	48	𝑖𝛽11	𝑖𝛽11	PROPN
cana-5829	693	49	)	)	PUNCT
cana-5829	693	50	𝑁𝑜𝑟𝑚µ𝐸11	𝑁𝑜𝑟𝑚µ𝐸11	NOUN
cana-5829	693	51	(	(	PUNCT
cana-5829	693	52	𝛾11	𝛾11	VERB
cana-5829	693	53	+	+	CCONJ
cana-5829	693	54	𝑖𝛿11	𝑖𝛿11	PROPN
cana-5829	693	55	)	)	PUNCT
cana-5829	693	56	)	)	PUNCT
cana-5829	693	57	(	(	PUNCT
cana-5829	693	58	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	NOUN
cana-5829	693	59	(	(	PUNCT
cana-5829	693	60	𝛼12	𝛼12	NOUN
cana-5829	693	61	+	+	CCONJ
cana-5829	693	62	𝑖𝛽12	𝑖𝛽12	PROPN
cana-5829	693	63	)	)	PUNCT
cana-5829	693	64	𝑁𝑜𝑟𝑚µ𝐸12	𝑁𝑜𝑟𝑚µ𝐸12	NOUN
cana-5829	693	65	(	(	PUNCT
cana-5829	693	66	𝛾12	𝛾12	VERB
cana-5829	693	67	+	+	CCONJ
cana-5829	693	68	𝑖𝛿12	𝑖𝛿12	PROPN
cana-5829	693	69	)	)	PUNCT
cana-5829	693	70	)	)	PUNCT
cana-5829	694	1	(	(	PUNCT
cana-5829	694	2	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	X
cana-5829	694	3	(	(	PUNCT
cana-5829	694	4	𝛼21	𝛼21	NOUN
cana-5829	694	5	+	+	X
cana-5829	694	6	𝑖𝛽21	𝑖𝛽21	PROPN
cana-5829	694	7	)	)	PUNCT
cana-5829	694	8	𝑁𝑜𝑟𝑚µ𝐸21	𝑁𝑜𝑟𝑚µ𝐸21	NOUN
cana-5829	694	9	(	(	PUNCT
cana-5829	694	10	𝛾21	𝛾21	NOUN
cana-5829	694	11	+	+	CCONJ
cana-5829	695	1	𝑖𝛿21	𝑖𝛿21	PROPN
cana-5829	695	2	)	)	PUNCT
cana-5829	695	3	)	)	PUNCT
cana-5829	696	1	(	(	PUNCT
cana-5829	696	2	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	X
cana-5829	696	3	(	(	PUNCT
cana-5829	696	4	𝛼22	𝛼22	NOUN
cana-5829	696	5	+	+	CCONJ
cana-5829	696	6	𝑖𝛽22	𝑖𝛽22	PROPN
cana-5829	696	7	)	)	PUNCT
cana-5829	696	8	𝑁𝑜𝑟𝑚µ𝐸22	𝑁𝑜𝑟𝑚µ𝐸22	NOUN
cana-5829	696	9	(	(	PUNCT
cana-5829	696	10	𝛾22	𝛾22	PROPN
cana-5829	696	11	+	+	PROPN
cana-5829	696	12	𝑖𝛿22	𝑖𝛿22	PROPN
cana-5829	696	13	)	)	PUNCT
cana-5829	696	14	)	)	PUNCT
cana-5829	696	15	)	)	PUNCT
cana-5829	696	16	communications	communication	NOUN
cana-5829	696	17	on	on	ADP
cana-5829	696	18	applied	apply	VERB
cana-5829	696	19	nonlinear	nonlinear	ADJ
cana-5829	696	20	analysis	analysis	NOUN
cana-5829	696	21	issn	issn	NOUN
cana-5829	696	22	:	:	PUNCT
cana-5829	696	23	1074	1074	NUM
cana-5829	696	24	-	-	PUNCT
cana-5829	696	25	133x	133x	NUM
cana-5829	696	26	vol	vol	VERB
cana-5829	696	27	32	32	NUM
cana-5829	696	28	no	no	NOUN
cana-5829	696	29	.	.	PUNCT
cana-5829	697	1	10s	10	NOUN
cana-5829	697	2	(	(	PUNCT
cana-5829	697	3	2025	2025	NUM
cana-5829	697	4	)	)	PUNCT
cana-5829	697	5	2947	2947	NUM
cana-5829	697	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5829	697	7	and	and	CCONJ
cana-5829	697	8	𝑁𝑜𝑟𝑚	𝑁𝑜𝑟𝑚	PROPN
cana-5829	697	9	𝐵𝐹	𝐵𝐹	PROPN
cana-5829	697	10	=	=	SYM
cana-5829	697	11	(	(	PUNCT
cana-5829	697	12	(	(	PUNCT
cana-5829	697	13	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	697	14	(	(	PUNCT
cana-5829	697	15	𝑥11	𝑥11	ADV
cana-5829	697	16	+	+	CCONJ
cana-5829	697	17	𝑖𝑦11	𝑖𝑦11	NOUN
cana-5829	697	18	)	)	PUNCT
cana-5829	697	19	𝑁𝑜𝑟𝑚𝛾𝐹11	𝑁𝑜𝑟𝑚𝛾𝐹11	X
cana-5829	697	20	(	(	PUNCT
cana-5829	697	21	𝜇11	𝜇11	PROPN
cana-5829	697	22	+	+	PROPN
cana-5829	697	23	𝑖𝜃11	𝑖𝜃11	PROPN
cana-5829	697	24	)	)	PUNCT
cana-5829	697	25	)	)	PUNCT
cana-5829	698	1	(	(	PUNCT
cana-5829	698	2	𝑁𝑜𝑟𝑚𝛿𝐹12	𝑁𝑜𝑟𝑚𝛿𝐹12	X
cana-5829	698	3	(	(	PUNCT
cana-5829	698	4	𝑥12	𝑥12	VERB
cana-5829	698	5	+	+	CCONJ
cana-5829	698	6	𝑖𝑦12	𝑖𝑦12	PROPN
cana-5829	698	7	)	)	PUNCT
cana-5829	698	8	𝑁𝑜𝑟𝑚𝛾𝐹12	𝑁𝑜𝑟𝑚𝛾𝐹12	NOUN
cana-5829	698	9	(	(	PUNCT
cana-5829	698	10	𝜇12	𝜇12	NOUN
cana-5829	698	11	+	+	CCONJ
cana-5829	699	1	𝑖𝜃12	𝑖𝜃12	PROPN
cana-5829	699	2	)	)	PUNCT
cana-5829	699	3	)	)	PUNCT
cana-5829	700	1	(	(	PUNCT
cana-5829	700	2	𝑁𝑜𝑟𝑚𝛿𝐹21	𝑁𝑜𝑟𝑚𝛿𝐹21	X
cana-5829	700	3	(	(	PUNCT
cana-5829	700	4	𝑥21	𝑥21	PROPN
cana-5829	700	5	+	+	CCONJ
cana-5829	700	6	𝑖𝑦21	𝑖𝑦21	PROPN
cana-5829	700	7	)	)	PUNCT
cana-5829	700	8	𝑁𝑜𝑟𝑚𝛾𝐹21	𝑁𝑜𝑟𝑚𝛾𝐹21	ADV
cana-5829	700	9	(	(	PUNCT
cana-5829	700	10	𝜇21	𝜇21	VERB
cana-5829	700	11	+	+	CCONJ
cana-5829	700	12	𝑖𝜃21	𝑖𝜃21	PROPN
cana-5829	700	13	)	)	PUNCT
cana-5829	700	14	)	)	PUNCT
cana-5829	700	15	(	(	PUNCT
cana-5829	700	16	𝑁𝑜𝑟𝑚𝛿𝐹22	𝑁𝑜𝑟𝑚𝛿𝐹22	X
cana-5829	700	17	(	(	PUNCT
cana-5829	700	18	𝑥22	𝑥22	NOUN
cana-5829	700	19	+	+	X
cana-5829	700	20	𝑖𝑦22	𝑖𝑦22	PROPN
cana-5829	700	21	)	)	PUNCT
cana-5829	700	22	𝑁𝑜𝑟𝑚𝛾𝐹22	𝑁𝑜𝑟𝑚𝛾𝐹22	NOUN
cana-5829	700	23	(	(	PUNCT
cana-5829	700	24	𝜇22	𝜇22	NOUN
cana-5829	700	25	+	+	CCONJ
cana-5829	700	26	𝑖𝜃22	𝑖𝜃22	PROPN
cana-5829	700	27	)	)	PUNCT
cana-5829	700	28	)	)	PUNCT
cana-5829	700	29	)	)	PUNCT
cana-5829	700	30	are	be	AUX
cana-5829	700	31	two	two	NUM
cana-5829	700	32	normalization	normalization	NOUN
cana-5829	700	33	intuitionistic	intuitionistic	ADJ
cana-5829	700	34	fuzzy	fuzzy	ADJ
cana-5829	700	35	matrices	matrix	NOUN
cana-5829	700	36	.	.	PUNCT
cana-5829	701	1	norm𝐴𝐸@𝑁𝑜𝑟𝑚𝐵𝐹	norm𝐴𝐸@𝑁𝑜𝑟𝑚𝐵𝐹	X
cana-5829	701	2	=	=	PUNCT
cana-5829	702	1	(	(	PUNCT
cana-5829	702	2	(	(	PUNCT
cana-5829	702	3	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	702	4	(	(	PUNCT
cana-5829	702	5	𝛼11	𝛼11	NOUN
cana-5829	702	6	+	+	PROPN
cana-5829	702	7	𝑖𝛽11	𝑖𝛽11	PROPN
cana-5829	702	8	)	)	PUNCT
cana-5829	702	9	𝑁𝑜𝑟𝑚µ𝐸11	𝑁𝑜𝑟𝑚µ𝐸11	NOUN
cana-5829	702	10	(	(	PUNCT
cana-5829	702	11	𝛾11	𝛾11	VERB
cana-5829	702	12	+	+	CCONJ
cana-5829	702	13	𝑖𝛿11	𝑖𝛿11	PROPN
cana-5829	702	14	)	)	PUNCT
cana-5829	702	15	)	)	PUNCT
cana-5829	702	16	(	(	PUNCT
cana-5829	702	17	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	NOUN
cana-5829	702	18	(	(	PUNCT
cana-5829	702	19	𝛼12	𝛼12	NOUN
cana-5829	702	20	+	+	CCONJ
cana-5829	702	21	𝑖𝛽12	𝑖𝛽12	PROPN
cana-5829	702	22	)	)	PUNCT
cana-5829	702	23	𝑁𝑜𝑟𝑚µ𝐸12	𝑁𝑜𝑟𝑚µ𝐸12	NOUN
cana-5829	702	24	(	(	PUNCT
cana-5829	702	25	𝛾12	𝛾12	VERB
cana-5829	702	26	+	+	CCONJ
cana-5829	702	27	𝑖𝛿12	𝑖𝛿12	PROPN
cana-5829	702	28	)	)	PUNCT
cana-5829	702	29	)	)	PUNCT
cana-5829	702	30	(	(	PUNCT
cana-5829	702	31	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	X
cana-5829	702	32	(	(	PUNCT
cana-5829	702	33	𝛼21	𝛼21	NOUN
cana-5829	702	34	+	+	X
cana-5829	702	35	𝑖𝛽21	𝑖𝛽21	PROPN
cana-5829	702	36	)	)	PUNCT
cana-5829	702	37	𝑁𝑜𝑟𝑚µ𝐸21	𝑁𝑜𝑟𝑚µ𝐸21	NOUN
cana-5829	702	38	(	(	PUNCT
cana-5829	702	39	𝛾21	𝛾21	NOUN
cana-5829	702	40	+	+	CCONJ
cana-5829	703	1	𝑖𝛿21	𝑖𝛿21	PROPN
cana-5829	703	2	)	)	PUNCT
cana-5829	703	3	)	)	PUNCT
cana-5829	704	1	(	(	PUNCT
cana-5829	704	2	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	X
cana-5829	704	3	(	(	PUNCT
cana-5829	704	4	𝛼22	𝛼22	NOUN
cana-5829	704	5	+	+	CCONJ
cana-5829	704	6	𝑖𝛽22	𝑖𝛽22	PROPN
cana-5829	704	7	)	)	PUNCT
cana-5829	704	8	𝑁𝑜𝑟𝑚µ𝐸22	𝑁𝑜𝑟𝑚µ𝐸22	NOUN
cana-5829	704	9	(	(	PUNCT
cana-5829	704	10	𝛾22	𝛾22	PROPN
cana-5829	704	11	+	+	PROPN
cana-5829	704	12	𝑖𝛿22	𝑖𝛿22	PROPN
cana-5829	704	13	)	)	PUNCT
cana-5829	704	14	)	)	PUNCT
cana-5829	704	15	)	)	PUNCT
cana-5829	704	16	@	@	ADP
cana-5829	704	17	(	(	PUNCT
cana-5829	704	18	(	(	PUNCT
cana-5829	704	19	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	704	20	(	(	PUNCT
cana-5829	704	21	𝑥11	𝑥11	ADV
cana-5829	704	22	+	+	CCONJ
cana-5829	704	23	𝑖𝑦11	𝑖𝑦11	NOUN
cana-5829	704	24	)	)	PUNCT
cana-5829	704	25	𝑁𝑜𝑟𝑚𝛾𝐹11	𝑁𝑜𝑟𝑚𝛾𝐹11	X
cana-5829	704	26	(	(	PUNCT
cana-5829	704	27	𝜇11	𝜇11	PROPN
cana-5829	704	28	+	+	PROPN
cana-5829	704	29	𝑖𝜃11	𝑖𝜃11	PROPN
cana-5829	704	30	)	)	PUNCT
cana-5829	704	31	)	)	PUNCT
cana-5829	704	32	(	(	PUNCT
cana-5829	704	33	𝑁𝑜𝑟𝑚𝛿𝐹12	𝑁𝑜𝑟𝑚𝛿𝐹12	X
cana-5829	704	34	(	(	PUNCT
cana-5829	704	35	𝑥12	𝑥12	VERB
cana-5829	704	36	+	+	CCONJ
cana-5829	704	37	𝑖𝑦12	𝑖𝑦12	PROPN
cana-5829	704	38	)	)	PUNCT
cana-5829	704	39	𝑁𝑜𝑟𝑚𝛾𝐹12	𝑁𝑜𝑟𝑚𝛾𝐹12	NOUN
cana-5829	704	40	(	(	PUNCT
cana-5829	704	41	𝜇12	𝜇12	NOUN
cana-5829	704	42	+	+	CCONJ
cana-5829	705	1	𝑖𝜃12	𝑖𝜃12	PROPN
cana-5829	705	2	)	)	PUNCT
cana-5829	705	3	)	)	PUNCT
cana-5829	706	1	(	(	PUNCT
cana-5829	706	2	𝑁𝑜𝑟𝑚𝛿𝐹21	𝑁𝑜𝑟𝑚𝛿𝐹21	X
cana-5829	706	3	(	(	PUNCT
cana-5829	706	4	𝑥21	𝑥21	PROPN
cana-5829	706	5	+	+	CCONJ
cana-5829	706	6	𝑖𝑦21	𝑖𝑦21	PROPN
cana-5829	706	7	)	)	PUNCT
cana-5829	706	8	𝑁𝑜𝑟𝑚𝛾𝐹21	𝑁𝑜𝑟𝑚𝛾𝐹21	ADV
cana-5829	706	9	(	(	PUNCT
cana-5829	706	10	𝜇21	𝜇21	VERB
cana-5829	706	11	+	+	CCONJ
cana-5829	706	12	𝑖𝜃21	𝑖𝜃21	PROPN
cana-5829	706	13	)	)	PUNCT
cana-5829	706	14	)	)	PUNCT
cana-5829	706	15	(	(	PUNCT
cana-5829	706	16	𝑁𝑜𝑟𝑚𝛿𝐹22	𝑁𝑜𝑟𝑚𝛿𝐹22	X
cana-5829	706	17	(	(	PUNCT
cana-5829	706	18	𝑥22	𝑥22	NOUN
cana-5829	706	19	+	+	X
cana-5829	706	20	𝑖𝑦22	𝑖𝑦22	PROPN
cana-5829	706	21	)	)	PUNCT
cana-5829	706	22	𝑁𝑜𝑟𝑚𝛾𝐹22	𝑁𝑜𝑟𝑚𝛾𝐹22	NOUN
cana-5829	706	23	(	(	PUNCT
cana-5829	706	24	𝜇22	𝜇22	NOUN
cana-5829	706	25	+	+	CCONJ
cana-5829	706	26	𝑖𝜃22	𝑖𝜃22	PROPN
cana-5829	706	27	)	)	PUNCT
cana-5829	706	28	)	)	PUNCT
cana-5829	706	29	)	)	PUNCT
cana-5829	706	30	calculate	calculate	NOUN
cana-5829	706	31	,	,	PUNCT
cana-5829	706	32	𝑋11	𝑋11	PROPN
cana-5829	706	33	,	,	PUNCT
cana-5829	706	34	𝑋12	𝑋12	PROPN
cana-5829	706	35	,	,	PUNCT
cana-5829	706	36	𝑋21and	𝑋21and	PROPN
cana-5829	706	37	𝑋22	𝑋22	PROPN
cana-5829	706	38	,	,	PUNCT
cana-5829	706	39	we	we	PRON
cana-5829	706	40	have	have	VERB
cana-5829	706	41	x11	x11	PROPN
cana-5829	706	42	=(	=(	NOUN
cana-5829	706	43	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	706	44	(	(	PUNCT
cana-5829	706	45	𝛼11	𝛼11	NOUN
cana-5829	706	46	+	+	PROPN
cana-5829	706	47	𝑖𝛽11	𝑖𝛽11	PROPN
cana-5829	706	48	)	)	PUNCT
cana-5829	706	49	𝑁𝑜𝑟𝑚µ𝐸11	𝑁𝑜𝑟𝑚µ𝐸11	NOUN
cana-5829	706	50	(	(	PUNCT
cana-5829	706	51	𝛾11	𝛾11	VERB
cana-5829	706	52	+	+	CCONJ
cana-5829	706	53	𝑖𝛿11	𝑖𝛿11	PROPN
cana-5829	706	54	)	)	PUNCT
cana-5829	706	55	)	)	PUNCT
cana-5829	706	56	@(𝑁𝑜𝑟𝑚𝛿𝐹11	@(𝑁𝑜𝑟𝑚𝛿𝐹11	NOUN
cana-5829	707	1	(	(	PUNCT
cana-5829	707	2	𝑥11	𝑥11	ADV
cana-5829	707	3	+	+	CCONJ
cana-5829	707	4	𝑖𝑦11	𝑖𝑦11	NOUN
cana-5829	707	5	)	)	PUNCT
cana-5829	707	6	𝑁𝑜𝑟𝑚𝛾𝐹11	𝑁𝑜𝑟𝑚𝛾𝐹11	X
cana-5829	707	7	(	(	PUNCT
cana-5829	707	8	𝜇11	𝜇11	PROPN
cana-5829	707	9	+	+	PROPN
cana-5829	707	10	𝑖𝜃11	𝑖𝜃11	PROPN
cana-5829	707	11	)	)	PUNCT
cana-5829	707	12	)	)	PUNCT
cana-5829	707	13	where	where	SCONJ
cana-5829	707	14	∣μ11∣=	∣μ11∣=	NOUN
cana-5829	707	15	(	(	PUNCT
cana-5829	707	16	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	707	17	(	(	PUNCT
cana-5829	707	18	max(𝛼11	max(𝛼11	NUM
cana-5829	707	19	,	,	PUNCT
cana-5829	707	20	𝑥11))2	𝑥11))2	X
cana-5829	707	21	+	+	CCONJ
cana-5829	707	22	(	(	PUNCT
cana-5829	707	23	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	707	24	max(𝛽11	max(𝛽11	PROPN
cana-5829	707	25	,	,	PUNCT
cana-5829	707	26	𝑦11))2	𝑦11))2	X
cana-5829	708	1	+	+	ADJ
cana-5829	708	2	(	(	PUNCT
cana-5829	708	3	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	708	4	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
cana-5829	708	5	(	(	PUNCT
cana-5829	708	6	𝛾11	𝛾11	VERB
cana-5829	708	7	,	,	PUNCT
cana-5829	708	8	𝜇11))2	𝜇11))2	ADJ
cana-5829	708	9	+	+	ADJ
cana-5829	708	10	(	(	PUNCT
cana-5829	708	11	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	708	12	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
cana-5829	708	13	(	(	PUNCT
cana-5829	708	14	𝛾11	𝛾11	VERB
cana-5829	708	15	,	,	PUNCT
cana-5829	708	16	𝜇11))2	𝜇11))2	PRON
cana-5829	708	17	<	<	X
cana-5829	708	18	1	1	NUM
cana-5829	708	19	,	,	PUNCT
cana-5829	708	20	∣ν11∣=	∣ν11∣=	PROPN
cana-5829	708	21	(	(	PUNCT
cana-5829	708	22	normµe11	normµe11	NOUN
cana-5829	708	23	𝑚𝑖𝑛(𝛾11	𝑚𝑖𝑛(𝛾11	PROPN
cana-5829	708	24	,	,	PUNCT
cana-5829	708	25	𝜇11))2	𝜇11))2	X
cana-5829	708	26	+	+	ADJ
cana-5829	708	27	(	(	PUNCT
cana-5829	708	28	𝑁𝑜𝑟𝑚𝛾𝐸11	𝑁𝑜𝑟𝑚𝛾𝐸11	X
cana-5829	708	29	𝑚𝑖𝑛(𝛿11	𝑚𝑖𝑛(𝛿11	PROPN
cana-5829	708	30	,	,	PUNCT
cana-5829	708	31	𝜃11))2	𝜃11))2	X
cana-5829	708	32	<	<	X
cana-5829	708	33	1	1	NUM
cana-5829	708	34	,	,	PUNCT
cana-5829	708	35	∣μ11∣+∣ν11∣	∣μ11∣+∣ν11∣	VERB
cana-5829	708	36	≤	≤	NUM
cana-5829	708	37	1	1	NUM
cana-5829	708	38	.	.	PUNCT
cana-5829	709	1	x12	x12	NUM
cana-5829	709	2	=(	=(	NOUN
cana-5829	709	3	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	NOUN
cana-5829	709	4	(	(	PUNCT
cana-5829	709	5	𝛼12	𝛼12	NOUN
cana-5829	709	6	+	+	CCONJ
cana-5829	709	7	𝑖𝛽12	𝑖𝛽12	PROPN
cana-5829	709	8	)	)	PUNCT
cana-5829	709	9	𝑁𝑜𝑟𝑚µ𝐸12	𝑁𝑜𝑟𝑚µ𝐸12	NOUN
cana-5829	709	10	(	(	PUNCT
cana-5829	709	11	𝛾12	𝛾12	VERB
cana-5829	709	12	+	+	CCONJ
cana-5829	709	13	𝑖𝛿12	𝑖𝛿12	PROPN
cana-5829	709	14	)	)	PUNCT
cana-5829	709	15	)	)	PUNCT
cana-5829	709	16	@	@	ADP
cana-5829	710	1	(	(	PUNCT
cana-5829	710	2	𝑁𝑜𝑟𝑚𝛿𝐹12	𝑁𝑜𝑟𝑚𝛿𝐹12	X
cana-5829	710	3	(	(	PUNCT
cana-5829	710	4	𝑥12	𝑥12	VERB
cana-5829	710	5	+	+	CCONJ
cana-5829	710	6	𝑖𝑦12	𝑖𝑦12	PROPN
cana-5829	710	7	)	)	PUNCT
cana-5829	710	8	𝑁𝑜𝑟𝑚𝛾𝐹12	𝑁𝑜𝑟𝑚𝛾𝐹12	NOUN
cana-5829	711	1	(	(	PUNCT
cana-5829	711	2	𝜇12	𝜇12	NOUN
cana-5829	711	3	+	+	CCONJ
cana-5829	711	4	𝑖𝜃12	𝑖𝜃12	PROPN
cana-5829	711	5	)	)	PUNCT
cana-5829	711	6	)	)	PUNCT
cana-5829	712	1	x21	x21	NUM
cana-5829	712	2	=(	=(	NOUN
cana-5829	712	3	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	PROPN
cana-5829	712	4	(	(	PUNCT
cana-5829	712	5	𝛼21	𝛼21	NOUN
cana-5829	712	6	+	+	X
cana-5829	712	7	𝑖𝛽21	𝑖𝛽21	PROPN
cana-5829	712	8	)	)	PUNCT
cana-5829	712	9	𝑁𝑜𝑟𝑚µ𝐸21	𝑁𝑜𝑟𝑚µ𝐸21	NOUN
cana-5829	712	10	(	(	PUNCT
cana-5829	712	11	𝛾21	𝛾21	NOUN
cana-5829	712	12	+	+	CCONJ
cana-5829	713	1	𝑖𝛿21	𝑖𝛿21	PROPN
cana-5829	713	2	)	)	PUNCT
cana-5829	713	3	)	)	PUNCT
cana-5829	714	1	@	@	ADP
cana-5829	714	2	(	(	PUNCT
cana-5829	714	3	𝑁𝑜𝑟𝑚𝛿𝐹21	𝑁𝑜𝑟𝑚𝛿𝐹21	X
cana-5829	714	4	(	(	PUNCT
cana-5829	714	5	𝑥21	𝑥21	PROPN
cana-5829	714	6	+	+	CCONJ
cana-5829	714	7	𝑖𝑦21	𝑖𝑦21	PROPN
cana-5829	714	8	)	)	PUNCT
cana-5829	714	9	𝑁𝑜𝑟𝑚𝛾𝐹21	𝑁𝑜𝑟𝑚𝛾𝐹21	ADV
cana-5829	714	10	(	(	PUNCT
cana-5829	714	11	𝜇21	𝜇21	VERB
cana-5829	714	12	+	+	CCONJ
cana-5829	714	13	𝑖𝜃21	𝑖𝜃21	PROPN
cana-5829	714	14	)	)	PUNCT
cana-5829	714	15	)	)	PUNCT
cana-5829	715	1	x22	x22	NUM
cana-5829	716	1	=(	=(	NOUN
cana-5829	716	2	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	PROPN
cana-5829	716	3	(	(	PUNCT
cana-5829	716	4	𝛼22	𝛼22	NOUN
cana-5829	716	5	+	+	CCONJ
cana-5829	716	6	𝑖𝛽22	𝑖𝛽22	PROPN
cana-5829	716	7	)	)	PUNCT
cana-5829	716	8	𝑁𝑜𝑟𝑚µ𝐸22	𝑁𝑜𝑟𝑚µ𝐸22	NOUN
cana-5829	716	9	(	(	PUNCT
cana-5829	716	10	𝛾22	𝛾22	PROPN
cana-5829	716	11	+	+	PROPN
cana-5829	716	12	𝑖𝛿22	𝑖𝛿22	PROPN
cana-5829	716	13	)	)	PUNCT
cana-5829	716	14	)	)	PUNCT
cana-5829	716	15	@	@	ADP
cana-5829	717	1	(	(	PUNCT
cana-5829	717	2	𝑁𝑜𝑟𝑚𝛿𝐹22	𝑁𝑜𝑟𝑚𝛿𝐹22	X
cana-5829	717	3	(	(	PUNCT
cana-5829	717	4	𝑥22	𝑥22	NOUN
cana-5829	717	5	+	+	X
cana-5829	717	6	𝑖𝑦22	𝑖𝑦22	PROPN
cana-5829	717	7	)	)	PUNCT
cana-5829	717	8	𝑁𝑜𝑟𝑚𝛾𝐹22	𝑁𝑜𝑟𝑚𝛾𝐹22	NOUN
cana-5829	717	9	(	(	PUNCT
cana-5829	717	10	𝜇22	𝜇22	NOUN
cana-5829	717	11	+	+	CCONJ
cana-5829	717	12	𝑖𝜃22	𝑖𝜃22	PROPN
cana-5829	717	13	)	)	PUNCT
cana-5829	717	14	)	)	PUNCT
cana-5829	718	1	𝐴𝑝𝑝𝑙𝑦𝑖𝑛𝑔	𝐴𝑝𝑝𝑙𝑦𝑖𝑛𝑔	PROPN
cana-5829	718	2	𝑓𝑜𝑟𝑚𝑢𝑙𝑎	𝑓𝑜𝑟𝑚𝑢𝑙𝑎	VERB
cana-5829	718	3	ae@bf	ae@bf	PROPN
cana-5829	719	1	=	=	SYM
cana-5829	720	1	{	{	PUNCT
cana-5829	720	2	(	(	PUNCT
cana-5829	720	3	x	x	NOUN
cana-5829	720	4	,	,	PUNCT
cana-5829	720	5	y	y	PROPN
cana-5829	720	6	)	)	PUNCT
cana-5829	720	7	,	,	PUNCT
cana-5829	720	8	μa(x)+	μa(x)+	NOUN
cana-5829	720	9	μb(y	μb(y	NUM
cana-5829	720	10	)	)	PUNCT
cana-5829	720	11	2	2	NUM
cana-5829	720	12	,	,	PUNCT
cana-5829	720	13	ϑa(x)+ϑb(y	ϑa(x)+ϑb(y	ADJ
cana-5829	720	14	)	)	PUNCT
cana-5829	720	15	2	2	NUM
cana-5829	720	16	:	:	PUNCT
cana-5829	720	17	xe	xe	NUM
cana-5829	720	18	,	,	PUNCT
cana-5829	720	19	yf	yf	NUM
cana-5829	720	20	}	}	PUNCT
cana-5829	720	21	x11	x11	NOUN
cana-5829	720	22	=	=	NOUN
cana-5829	720	23	{	{	PUNCT
cana-5829	720	24	𝑁𝑜𝑟𝑚𝜗𝐸11@𝛿𝐹11	𝑁𝑜𝑟𝑚𝜗𝐸11@𝛿𝐹11	X
cana-5829	720	25	(	(	PUNCT
cana-5829	720	26	𝛼11+𝑥11+𝑖(𝛽11+𝑦11	𝛼11+𝑥11+𝑖(𝛽11+𝑦11	NOUN
cana-5829	720	27	)	)	PUNCT
cana-5829	720	28	2	2	NUM
cana-5829	720	29	)	)	PUNCT
cana-5829	720	30	,	,	PUNCT
cana-5829	720	31	𝑁𝑜𝑟𝑚µ𝐸11@𝛾𝐹11	𝑁𝑜𝑟𝑚µ𝐸11@𝛾𝐹11	NOUN
cana-5829	720	32	(	(	PUNCT
cana-5829	720	33	𝛾11+𝜇11+𝑖(𝛿11+𝜃11	𝛾11+𝜇11+𝑖(𝛿11+𝜃11	NOUN
cana-5829	720	34	)	)	PUNCT
cana-5829	720	35	2	2	NUM
cana-5829	720	36	)	)	PUNCT
cana-5829	720	37	}	}	PUNCT
cana-5829	720	38	where	where	SCONJ
cana-5829	720	39	(	(	PUNCT
cana-5829	720	40	(	(	PUNCT
cana-5829	720	41	𝑁𝑜𝑟𝑚𝜗𝐸11@𝛿𝐹11	𝑁𝑜𝑟𝑚𝜗𝐸11@𝛿𝐹11	X
cana-5829	720	42	(	(	PUNCT
cana-5829	720	43	𝛼11+𝑥11	𝛼11+𝑥11	ADV
cana-5829	720	44	2	2	NUM
cana-5829	720	45	)	)	PUNCT
cana-5829	720	46	x12	x12	NOUN
cana-5829	721	1	=	=	SYM
cana-5829	721	2	{	{	PUNCT
cana-5829	721	3	𝑁𝑜𝑟𝑚𝜗𝐸11@𝛿𝐹11	𝑁𝑜𝑟𝑚𝜗𝐸11@𝛿𝐹11	X
cana-5829	721	4	(	(	PUNCT
cana-5829	721	5	𝛼11+𝑥11+𝑖(𝛽11+𝑦11	𝛼11+𝑥11+𝑖(𝛽11+𝑦11	NOUN
cana-5829	721	6	)	)	PUNCT
cana-5829	721	7	2	2	NUM
cana-5829	721	8	)	)	PUNCT
cana-5829	721	9	,	,	PUNCT
cana-5829	721	10	𝑁𝑜𝑟𝑚µ𝐸11@𝛾𝐹11	𝑁𝑜𝑟𝑚µ𝐸11@𝛾𝐹11	NOUN
cana-5829	721	11	(	(	PUNCT
cana-5829	721	12	𝛾11+𝜇11+𝑖(𝛿11+𝜃11	𝛾11+𝜇11+𝑖(𝛿11+𝜃11	NOUN
cana-5829	721	13	)	)	PUNCT
cana-5829	721	14	2	2	NUM
cana-5829	721	15	)	)	PUNCT
cana-5829	721	16	}	}	PUNCT
cana-5829	722	1	x21	x21	PROPN
cana-5829	723	1	=	=	SYM
cana-5829	723	2	{	{	PUNCT
cana-5829	723	3	𝑁𝑜𝑟𝑚𝜗𝐸11@𝛿𝐹11	𝑁𝑜𝑟𝑚𝜗𝐸11@𝛿𝐹11	X
cana-5829	723	4	(	(	PUNCT
cana-5829	723	5	𝛼11+𝑥11+𝑖(𝛽11+𝑦11	𝛼11+𝑥11+𝑖(𝛽11+𝑦11	NOUN
cana-5829	723	6	)	)	PUNCT
cana-5829	723	7	2	2	NUM
cana-5829	723	8	)	)	PUNCT
cana-5829	723	9	,	,	PUNCT
cana-5829	723	10	𝑁𝑜𝑟𝑚µ𝐸11@𝛾𝐹11	𝑁𝑜𝑟𝑚µ𝐸11@𝛾𝐹11	NOUN
cana-5829	723	11	(	(	PUNCT
cana-5829	723	12	𝛾11+𝜇11+𝑖(𝛿11+𝜃11	𝛾11+𝜇11+𝑖(𝛿11+𝜃11	NOUN
cana-5829	723	13	)	)	PUNCT
cana-5829	723	14	2	2	NUM
cana-5829	723	15	)	)	PUNCT
cana-5829	723	16	}	}	PUNCT
cana-5829	723	17	x22	x22	NOUN
cana-5829	724	1	=	=	NOUN
cana-5829	724	2	{	{	PUNCT
cana-5829	724	3	𝑁𝑜𝑟𝑚𝜗𝐸11@𝛿𝐹11	𝑁𝑜𝑟𝑚𝜗𝐸11@𝛿𝐹11	X
cana-5829	724	4	(	(	PUNCT
cana-5829	724	5	𝛼11+𝑥11+𝑖(𝛽11+𝑦11	𝛼11+𝑥11+𝑖(𝛽11+𝑦11	NOUN
cana-5829	724	6	)	)	PUNCT
cana-5829	724	7	2	2	NUM
cana-5829	724	8	)	)	PUNCT
cana-5829	724	9	,	,	PUNCT
cana-5829	724	10	𝑁𝑜𝑟𝑚µ𝐸11@𝛾𝐹11	𝑁𝑜𝑟𝑚µ𝐸11@𝛾𝐹11	NOUN
cana-5829	724	11	(	(	PUNCT
cana-5829	724	12	𝛾11+𝜇11+𝑖(𝛿11+𝜃11	𝛾11+𝜇11+𝑖(𝛿11+𝜃11	NOUN
cana-5829	724	13	)	)	PUNCT
cana-5829	724	14	2	2	NUM
cana-5829	724	15	)	)	PUNCT
cana-5829	724	16	}	}	PUNCT
cana-5829	724	17	x11	x11	NOUN
cana-5829	725	1	=	=	NOUN
cana-5829	725	2	{	{	PUNCT
cana-5829	725	3	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	VERB
cana-5829	725	4	+	+	PUNCT
cana-5829	725	5	𝛿𝐹11	𝛿𝐹11	PUNCT
cana-5829	725	6	(	(	PUNCT
cana-5829	725	7	𝛼11	𝛼11	PROPN
cana-5829	725	8	.	.	PUNCT
cana-5829	725	9	𝑥11	𝑥11	ADV
cana-5829	725	10	)	)	PUNCT
cana-5829	726	1	+	+	CCONJ
cana-5829	726	2	𝑖(𝛽11.𝑦11	𝑖(𝛽11.𝑦11	X
cana-5829	726	3	)	)	PUNCT
cana-5829	726	4	,	,	PUNCT
cana-5829	726	5	𝑁𝑜𝑟𝑚µ𝐸11+𝛾𝐹11	𝑁𝑜𝑟𝑚µ𝐸11+𝛾𝐹11	X
cana-5829	726	6	(	(	PUNCT
cana-5829	726	7	𝛾11	𝛾11	VERB
cana-5829	726	8	+	+	CCONJ
cana-5829	726	9	𝜇11	𝜇11	ADJ
cana-5829	726	10	−	−	NOUN
cana-5829	726	11	𝛾11	𝛾11	NOUN
cana-5829	726	12	.	.	PUNCT
cana-5829	727	1	𝜇11	𝜇11	PROPN
cana-5829	727	2	+	+	NUM
cana-5829	727	3	𝑖(𝛿11	𝑖(𝛿11	NOUN
cana-5829	727	4	+	+	CCONJ
cana-5829	727	5	𝜃11	𝜃11	ADJ
cana-5829	727	6	−	−	PROPN
cana-5829	727	7	𝛿11	𝛿11	PROPN
cana-5829	727	8	.	.	PUNCT
cana-5829	727	9	𝜃11	𝜃11	NOUN
cana-5829	727	10	)	)	PUNCT
cana-5829	727	11	}	}	PUNCT
cana-5829	727	12	where	where	SCONJ
cana-5829	727	13	∣μ11∣=	∣μ11∣=	NOUN
cana-5829	727	14	(	(	PUNCT
cana-5829	727	15	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	VERB
cana-5829	727	16	+	+	PUNCT
cana-5829	727	17	𝛿𝐹11	𝛿𝐹11	PUNCT
cana-5829	727	18	(	(	PUNCT
cana-5829	727	19	𝛼11	𝛼11	NOUN
cana-5829	727	20	.	.	PUNCT
cana-5829	727	21	𝑥11))2	𝑥11))2	X
cana-5829	728	1	+	+	CCONJ
cana-5829	728	2	(	(	PUNCT
cana-5829	728	3	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	728	4	+	+	PUNCT
cana-5829	728	5	𝛿𝐹11	𝛿𝐹11	PUNCT
cana-5829	728	6	(	(	PUNCT
cana-5829	728	7	𝛽11	𝛽11	NOUN
cana-5829	728	8	.	.	PUNCT
cana-5829	728	9	𝑦11)2	𝑦11)2	X
cana-5829	728	10	<	<	X
cana-5829	728	11	1	1	NUM
cana-5829	728	12	∣	∣	PROPN
cana-5829	728	13	ν11	ν11	NOUN
cana-5829	728	14	∣=	∣=	PROPN
cana-5829	728	15	(	(	PUNCT
cana-5829	728	16	𝑁𝑜𝑟𝑚µ𝐸11+𝛾𝐹11	𝑁𝑜𝑟𝑚µ𝐸11+𝛾𝐹11	X
cana-5829	728	17	(	(	PUNCT
cana-5829	728	18	𝛾11	𝛾11	VERB
cana-5829	728	19	+	+	CCONJ
cana-5829	728	20	𝜇11	𝜇11	ADJ
cana-5829	728	21	−	−	NOUN
cana-5829	728	22	𝛾11	𝛾11	NOUN
cana-5829	728	23	.	.	PUNCT
cana-5829	729	1	𝜇11)2	𝜇11)2	VERB
cana-5829	729	2	+	+	CCONJ
cana-5829	729	3	𝑁𝑜𝑟𝑚µ𝐸11+𝛾𝐹11	𝑁𝑜𝑟𝑚µ𝐸11+𝛾𝐹11	X
cana-5829	729	4	(	(	PUNCT
cana-5829	729	5	𝛿11	𝛿11	NOUN
cana-5829	729	6	+	+	CCONJ
cana-5829	729	7	𝜃11	𝜃11	NOUN
cana-5829	729	8	−	−	PROPN
cana-5829	729	9	𝛿11	𝛿11	NOUN
cana-5829	729	10	.	.	PUNCT
cana-5829	730	1	𝜃11)2	𝜃11)2	VERB
cana-5829	730	2	<	<	X
cana-5829	730	3	1	1	NUM
cana-5829	730	4	,	,	PUNCT
cana-5829	730	5	∣μ11∣+∣ν11∣	∣μ11∣+∣ν11∣	VERB
cana-5829	730	6	≤	≤	NUM
cana-5829	730	7	1	1	NUM
cana-5829	730	8	.	.	PUNCT
cana-5829	731	1	communications	communication	NOUN
cana-5829	731	2	on	on	ADP
cana-5829	731	3	applied	apply	VERB
cana-5829	731	4	nonlinear	nonlinear	ADJ
cana-5829	731	5	analysis	analysis	NOUN
cana-5829	731	6	issn	issn	NOUN
cana-5829	731	7	:	:	PUNCT
cana-5829	731	8	1074	1074	NUM
cana-5829	731	9	-	-	PUNCT
cana-5829	731	10	133x	133x	NUM
cana-5829	731	11	vol	vol	VERB
cana-5829	731	12	32	32	NUM
cana-5829	731	13	no	no	NOUN
cana-5829	731	14	.	.	PUNCT
cana-5829	732	1	10s	10	NOUN
cana-5829	732	2	(	(	PUNCT
cana-5829	732	3	2025	2025	NUM
cana-5829	732	4	)	)	PUNCT
cana-5829	732	5	2948	2948	NUM
cana-5829	732	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5829	732	7	x12	x12	NUM
cana-5829	732	8	=	=	SYM
cana-5829	732	9	{	{	PUNCT
cana-5829	732	10	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	X
cana-5829	732	11	+	+	CCONJ
cana-5829	732	12	𝛿𝐹12	𝛿𝐹12	X
cana-5829	732	13	(	(	PUNCT
cana-5829	732	14	𝛼12	𝛼12	PROPN
cana-5829	732	15	.	.	PUNCT
cana-5829	733	1	𝑥12	𝑥12	VERB
cana-5829	733	2	)	)	PUNCT
cana-5829	733	3	+	+	NUM
cana-5829	733	4	𝑖(𝛽12.𝑦12	𝑖(𝛽12.𝑦12	NUM
cana-5829	733	5	)	)	PUNCT
cana-5829	733	6	,	,	PUNCT
cana-5829	733	7	𝑁𝑜𝑟𝑚µ𝐸12+𝛾𝐹12	𝑁𝑜𝑟𝑚µ𝐸12+𝛾𝐹12	PROPN
cana-5829	733	8	(	(	PUNCT
cana-5829	733	9	𝛾12	𝛾12	NOUN
cana-5829	733	10	+	+	NUM
cana-5829	733	11	𝜇12	𝜇12	NOUN
cana-5829	733	12	−	−	PROPN
cana-5829	733	13	𝛾12	𝛾12	PROPN
cana-5829	733	14	.	.	PUNCT
cana-5829	733	15	𝜇12	𝜇12	PROPN
cana-5829	733	16	)	)	PUNCT
cana-5829	734	1	+	+	CCONJ
cana-5829	734	2	𝑖(𝛿12	𝑖(𝛿12	NUM
cana-5829	734	3	+	+	CCONJ
cana-5829	734	4	𝜃12	𝜃12	ADJ
cana-5829	734	5	−	−	PROPN
cana-5829	734	6	𝛿12	𝛿12	PROPN
cana-5829	734	7	.	.	PROPN
cana-5829	734	8	𝜃12	𝜃12	PROPN
cana-5829	734	9	)	)	PUNCT
cana-5829	734	10	}	}	PUNCT
cana-5829	734	11	where	where	SCONJ
cana-5829	734	12	∣μ12∣=	∣μ12∣=	X
cana-5829	734	13	(	(	PUNCT
cana-5829	734	14	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	NOUN
cana-5829	734	15	+	+	CCONJ
cana-5829	734	16	𝛿𝐹12	𝛿𝐹12	X
cana-5829	734	17	(	(	PUNCT
cana-5829	734	18	𝛼12	𝛼12	PROPN
cana-5829	734	19	.	.	PUNCT
cana-5829	734	20	𝑥12)2	𝑥12)2	VERB
cana-5829	735	1	+	+	CCONJ
cana-5829	735	2	(	(	PUNCT
cana-5829	735	3	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	X
cana-5829	735	4	+	+	CCONJ
cana-5829	735	5	𝛿𝐹12	𝛿𝐹12	X
cana-5829	735	6	(	(	PUNCT
cana-5829	735	7	𝛽12	𝛽12	PROPN
cana-5829	735	8	.	.	PUNCT
cana-5829	735	9	𝑦12)2	𝑦12)2	NOUN
cana-5829	735	10	<	<	X
cana-5829	735	11	1	1	NUM
cana-5829	735	12	∣	∣	PROPN
cana-5829	735	13	ν12	ν12	NOUN
cana-5829	735	14	∣=	∣=	PROPN
cana-5829	735	15	(	(	PUNCT
cana-5829	735	16	𝑁𝑜𝑟𝑚µ𝐸12+𝛾𝐹12	𝑁𝑜𝑟𝑚µ𝐸12+𝛾𝐹12	PROPN
cana-5829	735	17	(	(	PUNCT
cana-5829	735	18	𝛾12	𝛾12	NOUN
cana-5829	735	19	+	+	NUM
cana-5829	735	20	𝜇12	𝜇12	NOUN
cana-5829	735	21	−	−	PROPN
cana-5829	735	22	𝛾12	𝛾12	PROPN
cana-5829	735	23	.	.	PUNCT
cana-5829	736	1	𝜇12)2	𝜇12)2	PROPN
cana-5829	736	2	+	+	CCONJ
cana-5829	736	3	𝑁𝑜𝑟𝑚µ𝐸12+𝛾𝐹12	𝑁𝑜𝑟𝑚µ𝐸12+𝛾𝐹12	PROPN
cana-5829	737	1	(	(	PUNCT
cana-5829	737	2	𝛿12	𝛿12	NOUN
cana-5829	737	3	+	+	CCONJ
cana-5829	737	4	𝜃12	𝜃12	ADJ
cana-5829	737	5	−	−	PROPN
cana-5829	737	6	𝛿12	𝛿12	NOUN
cana-5829	737	7	.	.	PROPN
cana-5829	737	8	𝜃12)2	𝜃12)2	VERB
cana-5829	737	9	<	<	X
cana-5829	737	10	1	1	NUM
cana-5829	737	11	,	,	PUNCT
cana-5829	737	12	∣μ12∣+∣ν12∣	∣μ12∣+∣ν12∣	ADJ
cana-5829	737	13	≤	≤	NUM
cana-5829	737	14	1	1	NUM
cana-5829	737	15	.	.	PUNCT
cana-5829	738	1	x21	x21	NUM
cana-5829	738	2	=	=	SYM
cana-5829	738	3	{	{	PUNCT
cana-5829	738	4	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	ADV
cana-5829	738	5	+	+	NUM
cana-5829	738	6	𝛿𝐹21	𝛿𝐹21	X
cana-5829	738	7	(	(	PUNCT
cana-5829	738	8	𝛼21	𝛼21	NOUN
cana-5829	738	9	.	.	PUNCT
cana-5829	738	10	𝑥21	𝑥21	NOUN
cana-5829	738	11	)	)	PUNCT
cana-5829	738	12	+	+	PUNCT
cana-5829	738	13	𝑖(𝛽21.𝑦21	𝑖(𝛽21.𝑦21	NOUN
cana-5829	738	14	)	)	PUNCT
cana-5829	738	15	,	,	PUNCT
cana-5829	738	16	𝑁𝑜𝑟𝑚µ𝐸21+𝛾𝐹21	𝑁𝑜𝑟𝑚µ𝐸21+𝛾𝐹21	NUM
cana-5829	738	17	(	(	PUNCT
cana-5829	738	18	𝛾21	𝛾21	NOUN
cana-5829	738	19	+	+	CCONJ
cana-5829	738	20	𝜇21	𝜇21	ADJ
cana-5829	738	21	−	−	NOUN
cana-5829	738	22	𝛾21	𝛾21	NOUN
cana-5829	738	23	.	.	PUNCT
cana-5829	739	1	𝜇21	𝜇21	VERB
cana-5829	739	2	+	+	CCONJ
cana-5829	739	3	𝑖(𝛿21	𝑖(𝛿21	NOUN
cana-5829	739	4	+	+	CCONJ
cana-5829	739	5	𝜃21	𝜃21	NOUN
cana-5829	739	6	−	−	PROPN
cana-5829	739	7	𝛿21	𝛿21	PROPN
cana-5829	739	8	.	.	PUNCT
cana-5829	740	1	𝜃21	𝜃21	PROPN
cana-5829	740	2	}	}	PUNCT
cana-5829	740	3	where	where	SCONJ
cana-5829	740	4	∣μ21∣=	∣μ21∣=	X
cana-5829	740	5	(	(	PUNCT
cana-5829	740	6	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	X
cana-5829	740	7	+	+	NUM
cana-5829	740	8	𝛿𝐹21	𝛿𝐹21	X
cana-5829	740	9	(	(	PUNCT
cana-5829	740	10	𝛼21	𝛼21	NOUN
cana-5829	740	11	.	.	PUNCT
cana-5829	741	1	𝑥21)2	𝑥21)2	PRON
cana-5829	741	2	+	+	CCONJ
cana-5829	741	3	(	(	PUNCT
cana-5829	741	4	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	X
cana-5829	741	5	+	+	NUM
cana-5829	741	6	𝛿𝐹21	𝛿𝐹21	X
cana-5829	741	7	(	(	PUNCT
cana-5829	741	8	𝛽21	𝛽21	PROPN
cana-5829	741	9	.	.	PUNCT
cana-5829	742	1	𝑦21)2	𝑦21)2	VERB
cana-5829	742	2	<	<	X
cana-5829	742	3	1	1	NUM
cana-5829	742	4	∣	∣	ADJ
cana-5829	742	5	ν21	ν21	NOUN
cana-5829	742	6	∣=	∣=	PROPN
cana-5829	742	7	(	(	PUNCT
cana-5829	742	8	𝑁𝑜𝑟𝑚µ𝐸21+𝛾𝐹21	𝑁𝑜𝑟𝑚µ𝐸21+𝛾𝐹21	X
cana-5829	742	9	(	(	PUNCT
cana-5829	742	10	𝛾21	𝛾21	NOUN
cana-5829	742	11	+	+	CCONJ
cana-5829	742	12	𝜇21	𝜇21	ADJ
cana-5829	742	13	−	−	NOUN
cana-5829	742	14	𝛾21	𝛾21	NOUN
cana-5829	742	15	.	.	PUNCT
cana-5829	743	1	𝜇21)2	𝜇21)2	VERB
cana-5829	743	2	+	+	NUM
cana-5829	743	3	𝑁𝑜𝑟𝑚µ𝐸21+𝛾𝐹21	𝑁𝑜𝑟𝑚µ𝐸21+𝛾𝐹21	X
cana-5829	743	4	(	(	PUNCT
cana-5829	743	5	𝛿21	𝛿21	PROPN
cana-5829	743	6	+	+	CCONJ
cana-5829	743	7	𝜃21	𝜃21	NOUN
cana-5829	743	8	−	−	PROPN
cana-5829	743	9	𝛿21	𝛿21	PROPN
cana-5829	743	10	.	.	PUNCT
cana-5829	744	1	𝜃21)2	𝜃21)2	VERB
cana-5829	745	1	<	<	X
cana-5829	746	1	1	1	NUM
cana-5829	746	2	,	,	PUNCT
cana-5829	746	3	∣μ21∣+∣ν21∣	∣μ21∣+∣ν21∣	VERB
cana-5829	746	4	≤	≤	NUM
cana-5829	746	5	1	1	NUM
cana-5829	746	6	.	.	PUNCT
cana-5829	746	7	x22	x22	NOUN
cana-5829	747	1	=	=	SYM
cana-5829	747	2	{	{	PUNCT
cana-5829	747	3	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	X
cana-5829	747	4	+	+	SYM
cana-5829	747	5	𝛿𝐹22	𝛿𝐹22	X
cana-5829	747	6	(	(	PUNCT
cana-5829	747	7	𝛼22	𝛼22	NOUN
cana-5829	747	8	.	.	PUNCT
cana-5829	748	1	𝑥22	𝑥22	NOUN
cana-5829	748	2	)	)	PUNCT
cana-5829	749	1	+	+	CCONJ
cana-5829	749	2	𝑖(𝛽22.𝑦22	𝑖(𝛽22.𝑦22	NOUN
cana-5829	749	3	)	)	PUNCT
cana-5829	749	4	,	,	PUNCT
cana-5829	749	5	𝑁𝑜𝑟𝑚µ𝐸22+𝛾𝐹22	𝑁𝑜𝑟𝑚µ𝐸22+𝛾𝐹22	X
cana-5829	749	6	(	(	PUNCT
cana-5829	749	7	𝛾22	𝛾22	ADJ
cana-5829	749	8	+	+	CCONJ
cana-5829	749	9	𝜇22	𝜇22	NOUN
cana-5829	749	10	−	−	PROPN
cana-5829	749	11	𝛾22	𝛾22	PROPN
cana-5829	749	12	.	.	PUNCT
cana-5829	749	13	𝜇22	𝜇22	PROPN
cana-5829	749	14	)	)	PUNCT
cana-5829	749	15	+	+	CCONJ
cana-5829	749	16	𝑖(𝛿22	𝑖(𝛿22	NOUN
cana-5829	749	17	+	+	CCONJ
cana-5829	749	18	𝜃22	𝜃22	ADV
cana-5829	749	19	−	−	NOUN
cana-5829	749	20	𝛿22	𝛿22	NOUN
cana-5829	749	21	.	.	PUNCT
cana-5829	750	1	𝜃22	𝜃22	NUM
cana-5829	750	2	)	)	PUNCT
cana-5829	750	3	}	}	PUNCT
cana-5829	751	1	where	where	SCONJ
cana-5829	751	2	∣μ22∣=	∣μ22∣=	AUX
cana-5829	751	3	(	(	PUNCT
cana-5829	751	4	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	ADJ
cana-5829	751	5	+	+	NUM
cana-5829	751	6	𝛿𝐹22	𝛿𝐹22	X
cana-5829	751	7	(	(	PUNCT
cana-5829	751	8	𝛼22	𝛼22	NOUN
cana-5829	751	9	.	.	PUNCT
cana-5829	752	1	𝑥22)2	𝑥22)2	ADP
cana-5829	752	2	+	+	CCONJ
cana-5829	752	3	(	(	PUNCT
cana-5829	752	4	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	X
cana-5829	752	5	+	+	X
cana-5829	752	6	𝛿𝐹22	𝛿𝐹22	X
cana-5829	752	7	(	(	PUNCT
cana-5829	752	8	𝛽22	𝛽22	NOUN
cana-5829	752	9	.	.	PUNCT
cana-5829	753	1	𝑦22)2	𝑦22)2	VERB
cana-5829	753	2	<	<	X
cana-5829	753	3	1	1	NUM
cana-5829	753	4	∣	∣	PROPN
cana-5829	753	5	ν22	ν22	NOUN
cana-5829	753	6	∣=	∣=	PROPN
cana-5829	753	7	(	(	PUNCT
cana-5829	753	8	𝑁𝑜𝑟𝑚µ𝐸22+𝛾𝐹22	𝑁𝑜𝑟𝑚µ𝐸22+𝛾𝐹22	X
cana-5829	753	9	(	(	PUNCT
cana-5829	753	10	𝛾22	𝛾22	ADJ
cana-5829	753	11	+	+	CCONJ
cana-5829	753	12	𝜇22	𝜇22	NOUN
cana-5829	753	13	−	−	PROPN
cana-5829	753	14	𝛾22	𝛾22	NOUN
cana-5829	753	15	.	.	PUNCT
cana-5829	754	1	𝜇22)2	𝜇22)2	NOUN
cana-5829	754	2	+	+	CCONJ
cana-5829	754	3	𝑁𝑜𝑟𝑚µ𝐸22+𝛾𝐹22	𝑁𝑜𝑟𝑚µ𝐸22+𝛾𝐹22	X
cana-5829	754	4	(	(	PUNCT
cana-5829	754	5	𝛿22	𝛿22	NOUN
cana-5829	754	6	+	+	CCONJ
cana-5829	754	7	𝜃22	𝜃22	ADJ
cana-5829	754	8	−	−	NOUN
cana-5829	754	9	𝛿22	𝛿22	NOUN
cana-5829	754	10	.	.	PUNCT
cana-5829	754	11	𝜃22)2	𝜃22)2	NOUN
cana-5829	754	12	<	<	X
cana-5829	754	13	1	1	NUM
cana-5829	754	14	,	,	PUNCT
cana-5829	754	15	∣μ22∣+∣ν22∣	∣μ22∣+∣ν22∣	ADV
cana-5829	754	16	≤	≤	NUM
cana-5829	754	17	1	1	NUM
cana-5829	754	18	.	.	PUNCT
cana-5829	755	1	we	we	PRON
cana-5829	755	2	have	have	VERB
cana-5829	755	3	norm𝐴𝐸𝑁𝑜𝑟𝑚𝐵𝐹	norm𝐴𝐸𝑁𝑜𝑟𝑚𝐵𝐹	PUNCT
cana-5829	755	4	=	=	SYM
cana-5829	756	1	(	(	PUNCT
cana-5829	756	2	𝑋11	𝑋11	PROPN
cana-5829	756	3	𝑋12	𝑋12	PROPN
cana-5829	756	4	𝑋21	𝑋21	NOUN
cana-5829	756	5	𝑋22	𝑋22	ADJ
cana-5829	756	6	)	)	PUNCT
cana-5829	756	7	is	be	AUX
cana-5829	756	8	also	also	ADV
cana-5829	756	9	intuitionistic	intuitionistic	ADJ
cana-5829	756	10	fuzzy	fuzzy	ADJ
cana-5829	756	11	matrix	matrix	NOUN
cana-5829	756	12	example5.2.10	example5.2.10	ADP
cana-5829	756	13	:	:	PUNCT
cana-5829	757	1	if	if	SCONJ
cana-5829	757	2	𝑨𝑬=	𝑨𝑬=	NOUN
cana-5829	757	3	(	(	PUNCT
cana-5829	757	4	(	(	PUNCT
cana-5829	757	5	.9	.9	NUM
cana-5829	757	6	,	,	PUNCT
cana-5829	757	7	.4	.4	NUM
cana-5829	757	8	)	)	PUNCT
cana-5829	757	9	(	(	PUNCT
cana-5829	757	10	.4	.4	PROPN
cana-5829	757	11	,	,	PUNCT
cana-5829	757	12	.1	.1	NUM
cana-5829	757	13	)	)	PUNCT
cana-5829	757	14	(	(	PUNCT
cana-5829	757	15	.5	.5	NUM
cana-5829	757	16	,	,	PUNCT
cana-5829	757	17	.3	.3	NUM
cana-5829	757	18	)	)	PUNCT
cana-5829	757	19	(	(	PUNCT
cana-5829	757	20	.8	.8	NUM
cana-5829	757	21	,	,	PUNCT
cana-5829	757	22	.3	.3	NUM
cana-5829	757	23	)	)	PUNCT
cana-5829	757	24	)	)	PUNCT
cana-5829	757	25	and𝑩𝑭	and𝑩𝑭	NOUN
cana-5829	757	26	=	=	SYM
cana-5829	757	27	(	(	PUNCT
cana-5829	757	28	(	(	PUNCT
cana-5829	757	29	.8	.8	NUM
cana-5829	757	30	,	,	PUNCT
cana-5829	757	31	.6	.6	NUM
cana-5829	757	32	)	)	PUNCT
cana-5829	757	33	(	(	PUNCT
cana-5829	757	34	.6	.6	PROPN
cana-5829	757	35	,	,	PUNCT
cana-5829	757	36	.3	.3	NUM
cana-5829	757	37	)	)	PUNCT
cana-5829	757	38	(	(	PUNCT
cana-5829	757	39	.7	.7	PROPN
cana-5829	757	40	,	,	PUNCT
cana-5829	757	41	.5	.5	NUM
cana-5829	757	42	)	)	PUNCT
cana-5829	757	43	(	(	PUNCT
cana-5829	757	44	.9	.9	NUM
cana-5829	757	45	,	,	PUNCT
cana-5829	757	46	.4	.4	NUM
cana-5829	757	47	)	)	PUNCT
cana-5829	757	48	)	)	PUNCT
cana-5829	757	49	are	be	AUX
cana-5829	757	50	two	two	NUM
cana-5829	757	51	intuitionistic	intuitionistic	ADJ
cana-5829	757	52	fuzzy	fuzzy	ADJ
cana-5829	757	53	matrices	matrix	NOUN
cana-5829	757	54	over	over	ADP
cana-5829	757	55	different	different	ADJ
cana-5829	757	56	universe	universe	NOUN
cana-5829	757	57	e	e	NOUN
cana-5829	757	58	and	and	CCONJ
cana-5829	757	59	f	f	PROPN
cana-5829	757	60	then	then	ADV
cana-5829	757	61	norm𝐴̅	norm𝐴̅	PROPN
cana-5829	757	62	𝐸@𝑁𝑜𝑟𝑚	𝐸@𝑁𝑜𝑟𝑚	NOUN
cana-5829	757	63	�	�	NOUN
cana-5829	757	64	̅	̅	NOUN
cana-5829	757	65	�	�	NOUN
cana-5829	757	66	𝐹is	𝐹i	VERB
cana-5829	757	67	also	also	ADV
cana-5829	757	68	fuzzy	fuzzy	ADJ
cana-5829	757	69	matrix	matrix	NOUN
cana-5829	757	70	set	set	NOUN
cana-5829	757	71	.	.	PUNCT
cana-5829	758	1	proof	proof	NOUN
cana-5829	758	2	:	:	PUNCT
cana-5829	758	3	given	give	VERB
cana-5829	758	4	𝑨𝑬	𝑨𝑬	PROPN
cana-5829	758	5	=(	=(	NOUN
cana-5829	758	6	(	(	PUNCT
cana-5829	758	7	.9	.9	NUM
cana-5829	758	8	,	,	PUNCT
cana-5829	758	9	.4	.4	NUM
cana-5829	758	10	)	)	PUNCT
cana-5829	758	11	(	(	PUNCT
cana-5829	758	12	.4	.4	PROPN
cana-5829	758	13	,	,	PUNCT
cana-5829	758	14	.1	.1	NUM
cana-5829	758	15	)	)	PUNCT
cana-5829	758	16	(	(	PUNCT
cana-5829	758	17	.5	.5	NUM
cana-5829	758	18	,	,	PUNCT
cana-5829	758	19	.3	.3	NUM
cana-5829	758	20	)	)	PUNCT
cana-5829	758	21	(	(	PUNCT
cana-5829	758	22	.8	.8	NUM
cana-5829	758	23	,	,	PUNCT
cana-5829	758	24	.3	.3	NUM
cana-5829	758	25	)	)	PUNCT
cana-5829	758	26	)	)	PUNCT
cana-5829	758	27	and	and	CCONJ
cana-5829	758	28	𝑩𝑭	𝑩𝑭	PROPN
cana-5829	758	29	=	=	SYM
cana-5829	758	30	(	(	PUNCT
cana-5829	758	31	(	(	PUNCT
cana-5829	758	32	.8	.8	NUM
cana-5829	758	33	,	,	PUNCT
cana-5829	758	34	.6	.6	NUM
cana-5829	758	35	)	)	PUNCT
cana-5829	758	36	(	(	PUNCT
cana-5829	758	37	.6	.6	PROPN
cana-5829	758	38	,	,	PUNCT
cana-5829	758	39	.3	.3	NUM
cana-5829	758	40	)	)	PUNCT
cana-5829	758	41	(	(	PUNCT
cana-5829	758	42	.7	.7	PROPN
cana-5829	758	43	,	,	PUNCT
cana-5829	758	44	.5	.5	NUM
cana-5829	758	45	)	)	PUNCT
cana-5829	758	46	(	(	PUNCT
cana-5829	758	47	.9	.9	NUM
cana-5829	758	48	,	,	PUNCT
cana-5829	758	49	.4	.4	NUM
cana-5829	758	50	)	)	PUNCT
cana-5829	758	51	)	)	PUNCT
cana-5829	759	1	𝑁𝑜𝑟𝑚̅̅	𝑁𝑜𝑟𝑚̅̅	NOUN
cana-5829	759	2	̅̅	̅̅	PROPN
cana-5829	759	3	̅̅	̅̅	PROPN
cana-5829	759	4	̅̅	̅̅	PROPN
cana-5829	759	5	𝐴	𝐴	PROPN
cana-5829	759	6	=(	=(	NOUN
cana-5829	759	7	(	(	PUNCT
cana-5829	759	8	.8,1	.8,1	NOUN
cana-5829	759	9	)	)	PUNCT
cana-5829	759	10	(	(	PUNCT
cana-5829	759	11	0	0	NUM
cana-5829	759	12	,	,	PUNCT
cana-5829	759	13	.3	.3	NUM
cana-5829	759	14	)	)	PUNCT
cana-5829	759	15	(	(	PUNCT
cana-5829	759	16	.2	.2	NUM
cana-5829	759	17	,	,	PUNCT
cana-5829	759	18	.8	.8	NUM
cana-5829	759	19	)	)	PUNCT
cana-5829	759	20	(	(	PUNCT
cana-5829	759	21	.7	.7	PROPN
cana-5829	759	22	,	,	PUNCT
cana-5829	759	23	.8	.8	NUM
cana-5829	759	24	)	)	PUNCT
cana-5829	759	25	)	)	PUNCT
cana-5829	759	26	and	and	CCONJ
cana-5829	760	1	𝑁𝑜𝑟𝑚̅̅	𝑁𝑜𝑟𝑚̅̅	PROPN
cana-5829	760	2	̅̅	̅̅	PROPN
cana-5829	760	3	̅̅	̅̅	PROPN
cana-5829	760	4	̅̅	̅̅	PROPN
cana-5829	760	5	𝐵=	𝐵=	PROPN
cana-5829	760	6	(	(	PUNCT
cana-5829	760	7	(	(	PUNCT
cana-5829	760	8	.5	.5	NUM
cana-5829	760	9	,	,	PUNCT
cana-5829	760	10	1	1	NUM
cana-5829	760	11	)	)	PUNCT
cana-5829	760	12	(	(	PUNCT
cana-5829	760	13	0	0	NUM
cana-5829	760	14	,	,	PUNCT
cana-5829	760	15	.5	.5	NUM
cana-5829	760	16	)	)	PUNCT
cana-5829	760	17	(	(	PUNCT
cana-5829	760	18	.3	.3	NUM
cana-5829	760	19	,	,	PUNCT
cana-5829	760	20	.8	.8	NUM
cana-5829	760	21	)	)	PUNCT
cana-5829	760	22	(	(	PUNCT
cana-5829	760	23	.8	.8	PROPN
cana-5829	760	24	,	,	PUNCT
cana-5829	760	25	.7	.7	PROPN
cana-5829	760	26	)	)	PUNCT
cana-5829	760	27	)	)	PUNCT
cana-5829	761	1	𝑁𝑜𝑟𝑚̅̅	𝑁𝑜𝑟𝑚̅̅	NOUN
cana-5829	761	2	̅̅	̅̅	PROPN
cana-5829	761	3	̅̅	̅̅	PROPN
cana-5829	761	4	̅̅	̅̅	PROPN
cana-5829	761	5	𝐴@	𝐴@	PROPN
cana-5829	761	6	𝑁𝑜𝑟𝑚̅̅	𝑁𝑜𝑟𝑚̅̅	PROPN
cana-5829	761	7	̅̅	̅̅	PROPN
cana-5829	761	8	̅̅	̅̅	PROPN
cana-5829	761	9	̅̅	̅̅	PROPN
cana-5829	761	10	̅	̅	PROPN
cana-5829	761	11	𝐵	𝐵	NOUN
cana-5829	761	12	=	=	SYM
cana-5829	761	13	(	(	PUNCT
cana-5829	761	14	(	(	PUNCT
cana-5829	761	15	.8,1	.8,1	NOUN
cana-5829	761	16	)	)	PUNCT
cana-5829	761	17	(	(	PUNCT
cana-5829	761	18	0	0	NUM
cana-5829	761	19	,	,	PUNCT
cana-5829	761	20	.3	.3	NUM
cana-5829	761	21	)	)	PUNCT
cana-5829	761	22	(	(	PUNCT
cana-5829	761	23	.2	.2	NUM
cana-5829	761	24	,	,	PUNCT
cana-5829	761	25	.8	.8	NUM
cana-5829	761	26	)	)	PUNCT
cana-5829	761	27	(	(	PUNCT
cana-5829	761	28	.7	.7	PROPN
cana-5829	761	29	,	,	PUNCT
cana-5829	761	30	.8	.8	NUM
cana-5829	761	31	)	)	PUNCT
cana-5829	761	32	)	)	PUNCT
cana-5829	762	1	@	@	ADP
cana-5829	762	2	(	(	PUNCT
cana-5829	762	3	(	(	PUNCT
cana-5829	762	4	.5	.5	NUM
cana-5829	762	5	,	,	PUNCT
cana-5829	762	6	1	1	NUM
cana-5829	762	7	)	)	PUNCT
cana-5829	762	8	(	(	PUNCT
cana-5829	762	9	0	0	NUM
cana-5829	762	10	,	,	PUNCT
cana-5829	762	11	.5	.5	NUM
cana-5829	762	12	)	)	PUNCT
cana-5829	762	13	(	(	PUNCT
cana-5829	762	14	.3	.3	NUM
cana-5829	762	15	,	,	PUNCT
cana-5829	762	16	.8	.8	NUM
cana-5829	762	17	)	)	PUNCT
cana-5829	762	18	(	(	PUNCT
cana-5829	762	19	.8	.8	PROPN
cana-5829	762	20	,	,	PUNCT
cana-5829	762	21	.7	.7	PROPN
cana-5829	762	22	)	)	PUNCT
cana-5829	762	23	)	)	PUNCT
cana-5829	763	1	𝑋11	𝑋11	PROPN
cana-5829	763	2	=	=	SYM
cana-5829	763	3	(	(	PUNCT
cana-5829	763	4	.8	.8	PROPN
cana-5829	763	5	,	,	PUNCT
cana-5829	763	6	1)@	1)@	NUM
cana-5829	763	7	(	(	PUNCT
cana-5829	763	8	.	.	NOUN
cana-5829	763	9	5	5	NUM
cana-5829	763	10	,	,	PUNCT
cana-5829	763	11	1	1	NUM
cana-5829	763	12	)	)	PUNCT
cana-5829	763	13	𝑋12	𝑋12	NOUN
cana-5829	763	14	=	=	PUNCT
cana-5829	763	15	(	(	PUNCT
cana-5829	763	16	0	0	NUM
cana-5829	763	17	,	,	PUNCT
cana-5829	763	18	.3)@(0	.3)@(0	PROPN
cana-5829	763	19	,	,	PUNCT
cana-5829	763	20	.5	.5	NUM
cana-5829	763	21	)	)	PUNCT
cana-5829	763	22	𝑋21	𝑋21	NOUN
cana-5829	763	23	=	=	SYM
cana-5829	763	24	(	(	PUNCT
cana-5829	763	25	.2	.2	NUM
cana-5829	763	26	,	,	PUNCT
cana-5829	763	27	.8	.8	NUM
cana-5829	763	28	)	)	PUNCT
cana-5829	763	29	@	@	ADP
cana-5829	763	30	(	(	PUNCT
cana-5829	763	31	.3	.3	NUM
cana-5829	763	32	,	,	PUNCT
cana-5829	763	33	.8	.8	NUM
cana-5829	763	34	)	)	PUNCT
cana-5829	764	1	𝑋22	𝑋22	ADJ
cana-5829	764	2	=	=	PUNCT
cana-5829	764	3	(	(	PUNCT
cana-5829	764	4	.	.	NOUN
cana-5829	764	5	7	7	NUM
cana-5829	764	6	,	,	PUNCT
cana-5829	764	7	.8)@(.8	.8)@(.8	PROPN
cana-5829	764	8	,	,	PUNCT
cana-5829	764	9	.7	.7	PROPN
cana-5829	764	10	)	)	PUNCT
cana-5829	765	1	𝐴𝑝𝑝𝑙𝑦𝑖𝑛𝑔	𝐴𝑝𝑝𝑙𝑦𝑖𝑛𝑔	PROPN
cana-5829	765	2	𝑓𝑜𝑟𝑚𝑢𝑙𝑎	𝑓𝑜𝑟𝑚𝑢𝑙𝑎	VERB
cana-5829	765	3	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	765	4	̅̅̅̅	̅̅̅̅	ADJ
cana-5829	765	5	@𝐵𝐹	@𝐵𝐹	PROPN
cana-5829	765	6	̅̅̅̅	̅̅̅̅	NOUN
cana-5829	765	7	=	=	PUNCT
cana-5829	765	8	{	{	PUNCT
cana-5829	765	9	〈	〈	PROPN
cana-5829	765	10	x	x	PROPN
cana-5829	765	11	,	,	PUNCT
cana-5829	765	12	y	y	ADJ
cana-5829	765	13	〉	〉	NOUN
cana-5829	765	14	(	(	PUNCT
cana-5829	765	15	𝜗𝐴(x	𝜗𝐴(x	NUM
cana-5829	765	16	)	)	PUNCT
cana-5829	766	1	+	+	NOUN
cana-5829	766	2	𝜗𝐵(y	𝜗𝐵(y	NUM
cana-5829	766	3	)	)	PUNCT
cana-5829	766	4	)	)	PUNCT
cana-5829	766	5	2	2	NUM
cana-5829	766	6	,	,	PUNCT
cana-5829	766	7	(	(	PUNCT
cana-5829	766	8	µ𝐴(x	µ𝐴(x	NOUN
cana-5829	766	9	)	)	PUNCT
cana-5829	766	10	.	.	PUNCT
cana-5829	767	1	µ𝐵(y	µ𝐵(y	NUM
cana-5829	767	2	)	)	PUNCT
cana-5829	767	3	)	)	PUNCT
cana-5829	768	1	2	2	NUM
cana-5829	768	2	:	:	PUNCT
cana-5829	768	3	xe	xe	PROPN
cana-5829	768	4	,	,	PUNCT
cana-5829	768	5	y𝐹	y𝐹	NOUN
cana-5829	768	6	}	}	PUNCT
cana-5829	769	1	𝑋11	𝑋11	PROPN
cana-5829	769	2	=	=	PUNCT
cana-5829	769	3	(	(	PUNCT
cana-5829	769	4	.	.	NUM
cana-5829	769	5	8	8	NUM
cana-5829	769	6	+	+	NUM
cana-5829	769	7	.5	.5	NUM
cana-5829	769	8	2	2	NUM
cana-5829	769	9	)	)	PUNCT
cana-5829	769	10	,	,	PUNCT
cana-5829	769	11	(	(	PUNCT
cana-5829	769	12	1	1	X
cana-5829	769	13	.	.	SYM
cana-5829	769	14	1	1	NUM
cana-5829	769	15	2	2	NUM
cana-5829	769	16	)	)	PUNCT
cana-5829	770	1	𝑋12	𝑋12	PROPN
cana-5829	770	2	=	=	PUNCT
cana-5829	771	1	(	(	PUNCT
cana-5829	771	2	0	0	NUM
cana-5829	771	3	+	+	CCONJ
cana-5829	771	4	0	0	NUM
cana-5829	771	5	2	2	NUM
cana-5829	771	6	)	)	PUNCT
cana-5829	771	7	,	,	PUNCT
cana-5829	771	8	(	(	PUNCT
cana-5829	771	9	.	.	PUNCT
cana-5829	772	1	3	3	NUM
cana-5829	772	2	.	.	SYM
cana-5829	772	3	5	5	NUM
cana-5829	772	4	2	2	X
cana-5829	772	5	)	)	PUNCT
cana-5829	773	1	𝑋21	𝑋21	NOUN
cana-5829	773	2	=	=	SYM
cana-5829	773	3	(	(	PUNCT
cana-5829	773	4	.	.	NOUN
cana-5829	773	5	2	2	NUM
cana-5829	773	6	+	+	NUM
cana-5829	773	7	.3	.3	NUM
cana-5829	773	8	2	2	NUM
cana-5829	773	9	)	)	PUNCT
cana-5829	773	10	,	,	PUNCT
cana-5829	773	11	(	(	PUNCT
cana-5829	773	12	.	.	X
cana-5829	773	13	8	8	NUM
cana-5829	773	14	.	.	SYM
cana-5829	773	15	8	8	NUM
cana-5829	773	16	2	2	NUM
cana-5829	773	17	)	)	PUNCT
cana-5829	773	18	communications	communication	NOUN
cana-5829	773	19	on	on	ADP
cana-5829	773	20	applied	apply	VERB
cana-5829	773	21	nonlinear	nonlinear	ADJ
cana-5829	773	22	analysis	analysis	NOUN
cana-5829	773	23	issn	issn	NOUN
cana-5829	773	24	:	:	PUNCT
cana-5829	773	25	1074	1074	NUM
cana-5829	773	26	-	-	PUNCT
cana-5829	773	27	133x	133x	NUM
cana-5829	773	28	vol	vol	VERB
cana-5829	773	29	32	32	NUM
cana-5829	773	30	no	no	NOUN
cana-5829	773	31	.	.	PUNCT
cana-5829	774	1	10s	10	NOUN
cana-5829	774	2	(	(	PUNCT
cana-5829	774	3	2025	2025	NUM
cana-5829	774	4	)	)	PUNCT
cana-5829	774	5	2949	2949	NUM
cana-5829	774	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5829	775	1	𝑋22	𝑋22	ADJ
cana-5829	775	2	=	=	PUNCT
cana-5829	775	3	(	(	PUNCT
cana-5829	775	4	.	.	PUNCT
cana-5829	775	5	7	7	NUM
cana-5829	776	1	+	+	CCONJ
cana-5829	776	2	.8	.8	PROPN
cana-5829	776	3	2	2	NUM
cana-5829	776	4	)	)	PUNCT
cana-5829	776	5	,	,	PUNCT
cana-5829	776	6	(	(	PUNCT
cana-5829	776	7	.	.	X
cana-5829	777	1	8	8	NUM
cana-5829	777	2	.	.	NOUN
cana-5829	777	3	7	7	NUM
cana-5829	777	4	2	2	NUM
cana-5829	777	5	)	)	PUNCT
cana-5829	777	6	𝑋11	𝑋11	PROPN
cana-5829	777	7	=	=	SYM
cana-5829	777	8	{	{	PUNCT
cana-5829	777	9	.7	.7	PROPN
cana-5829	777	10	,	,	PUNCT
cana-5829	777	11	.5	.5	NUM
cana-5829	777	12	}	}	PUNCT
cana-5829	777	13	𝑋12	𝑋12	VERB
cana-5829	777	14	=	=	SYM
cana-5829	777	15	{	{	PUNCT
cana-5829	777	16	0	0	NUM
cana-5829	777	17	,	,	PUNCT
cana-5829	777	18	.07	.07	NUM
cana-5829	777	19	}	}	PUNCT
cana-5829	777	20	𝑋21	𝑋21	VERB
cana-5829	777	21	=	=	NUM
cana-5829	777	22	{	{	PUNCT
cana-5829	777	23	.3	.3	NUM
cana-5829	777	24	,	,	PUNCT
cana-5829	777	25	.3	.3	NUM
cana-5829	777	26	}	}	PUNCT
cana-5829	777	27	𝑋22	𝑋22	VERB
cana-5829	777	28	=	=	X
cana-5829	777	29	{	{	PUNCT
cana-5829	777	30	.8	.8	NUM
cana-5829	777	31	,	,	PUNCT
cana-5829	777	32	.3	.3	NUM
cana-5829	777	33	}	}	PUNCT
cana-5829	777	34	we	we	PRON
cana-5829	777	35	have	have	VERB
cana-5829	777	36	norm𝐴̅	norm𝐴̅	PROPN
cana-5829	777	37	𝐸@	𝐸@	ADJ
cana-5829	777	38	𝑁𝑜𝑟𝑚	𝑁𝑜𝑟𝑚	PROPN
cana-5829	777	39	�	�	NOUN
cana-5829	777	40	̅	̅	NOUN
cana-5829	777	41	�	�	NOUN
cana-5829	777	42	𝐹	𝐹	NOUN
cana-5829	777	43	=	=	SYM
cana-5829	777	44	(	(	PUNCT
cana-5829	777	45	(	(	PUNCT
cana-5829	777	46	.7	.7	PROPN
cana-5829	777	47	,	,	PUNCT
cana-5829	777	48	.5	.5	NUM
cana-5829	777	49	)	)	PUNCT
cana-5829	777	50	(	(	PUNCT
cana-5829	777	51	0	0	NUM
cana-5829	777	52	,	,	PUNCT
cana-5829	777	53	.07	.07	NUM
cana-5829	777	54	)	)	PUNCT
cana-5829	777	55	(	(	PUNCT
cana-5829	777	56	.3	.3	NUM
cana-5829	777	57	,	,	PUNCT
cana-5829	777	58	.3	.3	NUM
cana-5829	777	59	)	)	PUNCT
cana-5829	777	60	(	(	PUNCT
cana-5829	777	61	.8	.8	NUM
cana-5829	777	62	,	,	PUNCT
cana-5829	777	63	.3	.3	NUM
cana-5829	777	64	)	)	PUNCT
cana-5829	777	65	)	)	PUNCT
cana-5829	777	66	is	be	AUX
cana-5829	777	67	also	also	ADV
cana-5829	777	68	intuitionistic	intuitionistic	ADJ
cana-5829	777	69	fuzzy	fuzzy	ADJ
cana-5829	777	70	matrix	matrix	NOUN
cana-5829	777	71	theorem	theorem	VERB
cana-5829	777	72	5.2.6	5.2.6	NUM
cana-5829	777	73	:	:	PUNCT
cana-5829	777	74	if	if	SCONJ
cana-5829	777	75	e	e	PROPN
cana-5829	777	76	and	and	CCONJ
cana-5829	777	77	f	f	PROPN
cana-5829	777	78	be	be	AUX
cana-5829	777	79	two	two	NUM
cana-5829	777	80	universal	universal	ADJ
cana-5829	777	81	sets	set	NOUN
cana-5829	777	82	.	.	PUNCT
cana-5829	778	1	for	for	ADP
cana-5829	778	2	every	every	DET
cana-5829	778	3	normalization	normalization	NOUN
cana-5829	778	4	of	of	ADP
cana-5829	778	5	an	an	DET
cana-5829	778	6	intuitionistic	intuitionistic	ADJ
cana-5829	778	7	fuzzy	fuzzy	ADJ
cana-5829	778	8	matrices	matrix	NOUN
cana-5829	778	9	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	778	10	̅̅̅̅	̅̅̅̅	ADJ
cana-5829	778	11	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-5829	778	12	𝐵𝐹	𝐵𝐹	PROPN
cana-5829	778	13	̅̅̅̅	̅̅̅̅	NOUN
cana-5829	778	14	are	be	AUX
cana-5829	778	15	in	in	ADP
cana-5829	778	16	e	e	PROPN
cana-5829	778	17	and	and	CCONJ
cana-5829	778	18	f	f	PROPN
cana-5829	779	1	then	then	ADV
cana-5829	779	2	norm𝐴̅	norm𝐴̅	PROPN
cana-5829	779	3	𝐸	𝐸	PROPN
cana-5829	779	4	$	$	SYM
cana-5829	779	5	𝑁𝑜𝑟𝑚	𝑁𝑜𝑟𝑚	PROPN
cana-5829	779	6	�	�	NOUN
cana-5829	779	7	̅	̅	NOUN
cana-5829	779	8	�	�	NOUN
cana-5829	779	9	𝐹is	𝐹i	VERB
cana-5829	779	10	also	also	ADV
cana-5829	779	11	normalization	normalization	NOUN
cana-5829	779	12	of	of	ADP
cana-5829	779	13	an	an	DET
cana-5829	779	14	intuitionistic	intuitionistic	ADJ
cana-5829	779	15	fuzzy	fuzzy	ADJ
cana-5829	779	16	matrices	matrix	NOUN
cana-5829	779	17	.	.	PUNCT
cana-5829	780	1	proof	proof	NOUN
cana-5829	780	2	:	:	PUNCT
cana-5829	780	3	if	if	SCONJ
cana-5829	780	4	𝑁𝑜𝑟𝑚𝐴	𝑁𝑜𝑟𝑚𝐴	PROPN
cana-5829	780	5	and	and	CCONJ
cana-5829	780	6	𝑁𝑜𝑟𝑚𝐵	𝑁𝑜𝑟𝑚𝐵	PROPN
cana-5829	780	7	are	be	AUX
cana-5829	780	8	two	two	NUM
cana-5829	780	9	normalization	normalization	NOUN
cana-5829	780	10	intuitionistic	intuitionistic	ADJ
cana-5829	780	11	fuzzy	fuzzy	ADJ
cana-5829	780	12	matrices	matrix	NOUN
cana-5829	780	13	over	over	ADP
cana-5829	780	14	different	different	ADJ
cana-5829	780	15	unive𝑟𝑠𝑒𝑠	unive𝑟𝑠𝑒𝑠	ADJ
cana-5829	780	16	𝑠𝑒𝑡𝑠	𝑠𝑒𝑡𝑠	PROPN
cana-5829	780	17	𝐸	𝐸	PROPN
cana-5829	781	1	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-5829	781	2	𝐹.	𝐹.	NOUN
cana-5829	781	3	𝐼𝑓	𝐼𝑓	PROPN
cana-5829	781	4	𝑤𝑒	𝑤𝑒	PROPN
cana-5829	781	5	𝑐𝑜𝑛𝑠𝑖𝑑𝑒𝑟	𝑐𝑜𝑛𝑠𝑖𝑑𝑒𝑟	PROPN
cana-5829	781	6	𝑡𝑤𝑜	𝑡𝑤𝑜	PROPN
cana-5829	781	7	2	2	NUM
cana-5829	781	8	×	×	NOUN
cana-5829	781	9	2	2	NUM
cana-5829	781	10	𝑚𝑎𝑡𝑟𝑖𝑥	𝑚𝑎𝑡𝑟𝑖𝑥	ADJ
cana-5829	781	11	𝑁𝑜𝑟𝑚̅̅	𝑁𝑜𝑟𝑚̅̅	PROPN
cana-5829	781	12	̅̅	̅̅	PROPN
cana-5829	781	13	̅̅	̅̅	PROPN
cana-5829	781	14	̅̅	̅̅	PROPN
cana-5829	781	15	𝐴	𝐴	PROPN
cana-5829	781	16	=(	=(	NOUN
cana-5829	781	17	(	(	PUNCT
cana-5829	781	18	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	781	19	(	(	PUNCT
cana-5829	781	20	𝑥	𝑥	NOUN
cana-5829	781	21	)	)	PUNCT
cana-5829	781	22	𝑁𝑜𝑟𝑚µ𝐸11(𝑥	𝑁𝑜𝑟𝑚µ𝐸11(𝑥	NOUN
cana-5829	781	23	)	)	PUNCT
cana-5829	781	24	)	)	PUNCT
cana-5829	782	1	(	(	PUNCT
cana-5829	782	2	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	X
cana-5829	782	3	(	(	PUNCT
cana-5829	782	4	𝑥	𝑥	NOUN
cana-5829	782	5	)	)	PUNCT
cana-5829	782	6	𝑁𝑜𝑟𝑚µ𝐸12(𝑥	𝑁𝑜𝑟𝑚µ𝐸12(𝑥	NOUN
cana-5829	782	7	)	)	PUNCT
cana-5829	782	8	)	)	PUNCT
cana-5829	782	9	(	(	PUNCT
cana-5829	782	10	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	X
cana-5829	782	11	(	(	PUNCT
cana-5829	782	12	𝑥	𝑥	NOUN
cana-5829	782	13	)	)	PUNCT
cana-5829	782	14	𝑁𝑜𝑟𝑚µ𝐸21	𝑁𝑜𝑟𝑚µ𝐸21	NOUN
cana-5829	782	15	(	(	PUNCT
cana-5829	782	16	𝑥	𝑥	NOUN
cana-5829	782	17	)	)	PUNCT
cana-5829	782	18	)	)	PUNCT
cana-5829	782	19	(	(	PUNCT
cana-5829	782	20	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	X
cana-5829	782	21	(	(	PUNCT
cana-5829	782	22	𝑥	𝑥	NOUN
cana-5829	782	23	)	)	PUNCT
cana-5829	782	24	𝑁𝑜𝑟𝑚µ𝐸22	𝑁𝑜𝑟𝑚µ𝐸22	NOUN
cana-5829	782	25	(	(	PUNCT
cana-5829	782	26	𝑥	𝑥	NOUN
cana-5829	782	27	)	)	PUNCT
cana-5829	782	28	)	)	PUNCT
cana-5829	782	29	)	)	PUNCT
cana-5829	782	30	and	and	CCONJ
cana-5829	783	1	𝑁𝑜𝑟𝑚̅̅	𝑁𝑜𝑟𝑚̅̅	PROPN
cana-5829	783	2	̅̅	̅̅	PROPN
cana-5829	783	3	̅̅	̅̅	PROPN
cana-5829	783	4	̅̅	̅̅	PROPN
cana-5829	783	5	𝐵=	𝐵=	PROPN
cana-5829	783	6	(	(	PUNCT
cana-5829	783	7	(	(	PUNCT
cana-5829	783	8	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	783	9	(	(	PUNCT
cana-5829	783	10	𝑦	𝑦	NOUN
cana-5829	783	11	)	)	PUNCT
cana-5829	783	12	𝑁𝑜𝑟𝑚𝛾𝐹11(𝑦	𝑁𝑜𝑟𝑚𝛾𝐹11(𝑦	NUM
cana-5829	783	13	)	)	PUNCT
cana-5829	783	14	)	)	PUNCT
cana-5829	783	15	(	(	PUNCT
cana-5829	783	16	𝑁𝑜𝑟𝑚𝛿𝐹12	𝑁𝑜𝑟𝑚𝛿𝐹12	X
cana-5829	783	17	(	(	PUNCT
cana-5829	783	18	𝑦	𝑦	NOUN
cana-5829	783	19	)	)	PUNCT
cana-5829	783	20	𝑁𝑜𝑟𝑚𝛾𝐹12(𝑦	𝑁𝑜𝑟𝑚𝛾𝐹12(𝑦	NOUN
cana-5829	783	21	)	)	PUNCT
cana-5829	783	22	)	)	PUNCT
cana-5829	783	23	(	(	PUNCT
cana-5829	783	24	𝑁𝑜𝑟𝑚𝛿𝐹21	𝑁𝑜𝑟𝑚𝛿𝐹21	X
cana-5829	783	25	(	(	PUNCT
cana-5829	783	26	𝑦	𝑦	NOUN
cana-5829	783	27	)	)	PUNCT
cana-5829	783	28	𝑁𝑜𝑟𝑚𝛾𝐹21	𝑁𝑜𝑟𝑚𝛾𝐹21	ADV
cana-5829	783	29	(	(	PUNCT
cana-5829	783	30	𝑦	𝑦	NOUN
cana-5829	783	31	)	)	PUNCT
cana-5829	783	32	)	)	PUNCT
cana-5829	783	33	(	(	PUNCT
cana-5829	783	34	𝑁𝑜𝑟𝑚𝛿𝐹22	𝑁𝑜𝑟𝑚𝛿𝐹22	X
cana-5829	783	35	(	(	PUNCT
cana-5829	783	36	𝑦	𝑦	NOUN
cana-5829	783	37	)	)	PUNCT
cana-5829	783	38	𝑁𝑜𝑟𝑚𝛾𝐹22	𝑁𝑜𝑟𝑚𝛾𝐹22	X
cana-5829	783	39	(	(	PUNCT
cana-5829	783	40	𝑦	𝑦	NOUN
cana-5829	783	41	)	)	PUNCT
cana-5829	783	42	)	)	PUNCT
cana-5829	783	43	)	)	PUNCT
cana-5829	784	1	𝑁𝑜𝑟𝑚̅̅	𝑁𝑜𝑟𝑚̅̅	NOUN
cana-5829	784	2	̅̅	̅̅	PROPN
cana-5829	784	3	̅̅	̅̅	PROPN
cana-5829	784	4	̅̅	̅̅	PROPN
cana-5829	784	5	𝐴	𝐴	PROPN
cana-5829	784	6	$	$	PROPN
cana-5829	784	7	𝑁𝑜𝑟𝑚̅̅	𝑁𝑜𝑟𝑚̅̅	NOUN
cana-5829	784	8	̅̅	̅̅	PROPN
cana-5829	784	9	̅̅	̅̅	PROPN
cana-5829	784	10	̅̅	̅̅	PROPN
cana-5829	784	11	𝐵	𝐵	PROPN
cana-5829	784	12	=	=	PUNCT
cana-5829	784	13	(	(	PUNCT
cana-5829	784	14	(	(	PUNCT
cana-5829	784	15	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	784	16	(	(	PUNCT
cana-5829	784	17	𝑥	𝑥	NOUN
cana-5829	784	18	)	)	PUNCT
cana-5829	784	19	𝑁𝑜𝑟𝑚µ𝐸11	𝑁𝑜𝑟𝑚µ𝐸11	NOUN
cana-5829	784	20	(	(	PUNCT
cana-5829	784	21	𝑥	𝑥	NOUN
cana-5829	784	22	)	)	PUNCT
cana-5829	784	23	)	)	PUNCT
cana-5829	784	24	(	(	PUNCT
cana-5829	784	25	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	X
cana-5829	784	26	(	(	PUNCT
cana-5829	784	27	𝑥	𝑥	NOUN
cana-5829	784	28	)	)	PUNCT
cana-5829	784	29	𝑁𝑜𝑟𝑚µ𝐸12	𝑁𝑜𝑟𝑚µ𝐸12	NOUN
cana-5829	784	30	(	(	PUNCT
cana-5829	784	31	𝑥	𝑥	NOUN
cana-5829	784	32	)	)	PUNCT
cana-5829	784	33	)	)	PUNCT
cana-5829	784	34	(	(	PUNCT
cana-5829	784	35	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	X
cana-5829	784	36	(	(	PUNCT
cana-5829	784	37	𝑥	𝑥	NOUN
cana-5829	784	38	)	)	PUNCT
cana-5829	784	39	𝑁𝑜𝑟𝑚µ𝐸21	𝑁𝑜𝑟𝑚µ𝐸21	NOUN
cana-5829	784	40	(	(	PUNCT
cana-5829	784	41	𝑥	𝑥	NOUN
cana-5829	784	42	)	)	PUNCT
cana-5829	784	43	)	)	PUNCT
cana-5829	784	44	(	(	PUNCT
cana-5829	784	45	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	X
cana-5829	784	46	(	(	PUNCT
cana-5829	784	47	𝑥	𝑥	NOUN
cana-5829	784	48	)	)	PUNCT
cana-5829	784	49	𝑁𝑜𝑟𝑚µ𝐸22	𝑁𝑜𝑟𝑚µ𝐸22	NOUN
cana-5829	784	50	(	(	PUNCT
cana-5829	784	51	𝑥	𝑥	NOUN
cana-5829	784	52	)	)	PUNCT
cana-5829	784	53	)	)	PUNCT
cana-5829	784	54	)	)	PUNCT
cana-5829	784	55	$	$	X
cana-5829	784	56	(	(	PUNCT
cana-5829	784	57	(	(	PUNCT
cana-5829	784	58	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	784	59	(	(	PUNCT
cana-5829	784	60	𝑦	𝑦	NOUN
cana-5829	784	61	)	)	PUNCT
cana-5829	784	62	𝑁𝑜𝑟𝑚𝛾𝐹11(𝑦	𝑁𝑜𝑟𝑚𝛾𝐹11(𝑦	NUM
cana-5829	784	63	)	)	PUNCT
cana-5829	784	64	)	)	PUNCT
cana-5829	784	65	(	(	PUNCT
cana-5829	784	66	𝑁𝑜𝑟𝑚𝛿𝐹12	𝑁𝑜𝑟𝑚𝛿𝐹12	X
cana-5829	784	67	(	(	PUNCT
cana-5829	784	68	𝑦	𝑦	NOUN
cana-5829	784	69	)	)	PUNCT
cana-5829	784	70	𝑁𝑜𝑟𝑚𝛾𝐹12(𝑦	𝑁𝑜𝑟𝑚𝛾𝐹12(𝑦	NOUN
cana-5829	784	71	)	)	PUNCT
cana-5829	784	72	)	)	PUNCT
cana-5829	784	73	(	(	PUNCT
cana-5829	784	74	𝑁𝑜𝑟𝑚𝛿𝐹21	𝑁𝑜𝑟𝑚𝛿𝐹21	X
cana-5829	784	75	(	(	PUNCT
cana-5829	784	76	𝑦	𝑦	NOUN
cana-5829	784	77	)	)	PUNCT
cana-5829	784	78	𝑁𝑜𝑟𝑚𝛾𝐹21	𝑁𝑜𝑟𝑚𝛾𝐹21	ADV
cana-5829	784	79	(	(	PUNCT
cana-5829	784	80	𝑦	𝑦	NOUN
cana-5829	784	81	)	)	PUNCT
cana-5829	784	82	)	)	PUNCT
cana-5829	784	83	(	(	PUNCT
cana-5829	784	84	𝑁𝑜𝑟𝑚𝛿𝐹22	𝑁𝑜𝑟𝑚𝛿𝐹22	X
cana-5829	784	85	(	(	PUNCT
cana-5829	784	86	𝑦	𝑦	NOUN
cana-5829	784	87	)	)	PUNCT
cana-5829	784	88	𝑁𝑜𝑟𝑚𝛾𝐹22	𝑁𝑜𝑟𝑚𝛾𝐹22	X
cana-5829	784	89	(	(	PUNCT
cana-5829	784	90	𝑦	𝑦	NOUN
cana-5829	784	91	)	)	PUNCT
cana-5829	784	92	)	)	PUNCT
cana-5829	784	93	)	)	PUNCT
cana-5829	785	1	𝑋11	𝑋11	PROPN
cana-5829	785	2	=(	=(	NOUN
cana-5829	785	3	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	785	4	(	(	PUNCT
cana-5829	785	5	𝑥	𝑥	NOUN
cana-5829	785	6	)	)	PUNCT
cana-5829	785	7	𝑁𝑜𝑟𝑚µ𝐸11(𝑥	𝑁𝑜𝑟𝑚µ𝐸11(𝑥	NOUN
cana-5829	785	8	)	)	PUNCT
cana-5829	785	9	)	)	PUNCT
cana-5829	785	10	$	$	SYM
cana-5829	785	11	(	(	PUNCT
cana-5829	785	12	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	785	13	(	(	PUNCT
cana-5829	785	14	𝑦	𝑦	NOUN
cana-5829	785	15	)	)	PUNCT
cana-5829	785	16	𝑁𝑜𝑟𝑚𝛾𝐹11(𝑦	𝑁𝑜𝑟𝑚𝛾𝐹11(𝑦	NUM
cana-5829	785	17	)	)	PUNCT
cana-5829	785	18	)	)	PUNCT
cana-5829	786	1	𝑋12	𝑋12	PROPN
cana-5829	786	2	=(	=(	NOUN
cana-5829	786	3	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	NOUN
cana-5829	786	4	(	(	PUNCT
cana-5829	786	5	𝑥	𝑥	NOUN
cana-5829	786	6	)	)	PUNCT
cana-5829	786	7	𝑁𝑜𝑟𝑚µ𝐸12(𝑥	𝑁𝑜𝑟𝑚µ𝐸12(𝑥	NOUN
cana-5829	786	8	)	)	PUNCT
cana-5829	786	9	)	)	PUNCT
cana-5829	786	10	$	$	SYM
cana-5829	786	11	(	(	PUNCT
cana-5829	786	12	𝑁𝑜𝑟𝑚𝛿𝐹12	𝑁𝑜𝑟𝑚𝛿𝐹12	X
cana-5829	786	13	(	(	PUNCT
cana-5829	786	14	𝑦	𝑦	NOUN
cana-5829	786	15	)	)	PUNCT
cana-5829	786	16	𝑁𝑜𝑟𝑚𝛾𝐹12(𝑦	𝑁𝑜𝑟𝑚𝛾𝐹12(𝑦	NOUN
cana-5829	786	17	)	)	PUNCT
cana-5829	786	18	)	)	PUNCT
cana-5829	787	1	𝑋21	𝑋21	VERB
cana-5829	787	2	=(	=(	NOUN
cana-5829	787	3	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	NOUN
cana-5829	787	4	(	(	PUNCT
cana-5829	787	5	𝑥	𝑥	NOUN
cana-5829	787	6	)	)	PUNCT
cana-5829	787	7	𝑁𝑜𝑟𝑚µ𝐸21	𝑁𝑜𝑟𝑚µ𝐸21	NOUN
cana-5829	787	8	(	(	PUNCT
cana-5829	787	9	𝑥	𝑥	NOUN
cana-5829	787	10	)	)	PUNCT
cana-5829	787	11	)	)	PUNCT
cana-5829	787	12	$	$	SYM
cana-5829	787	13	(	(	PUNCT
cana-5829	787	14	𝑁𝑜𝑟𝑚𝛿𝐹21	𝑁𝑜𝑟𝑚𝛿𝐹21	X
cana-5829	787	15	(	(	PUNCT
cana-5829	787	16	𝑦	𝑦	NOUN
cana-5829	787	17	)	)	PUNCT
cana-5829	787	18	𝑁𝑜𝑟𝑚𝛾𝐹21	𝑁𝑜𝑟𝑚𝛾𝐹21	ADV
cana-5829	787	19	(	(	PUNCT
cana-5829	787	20	𝑦	𝑦	NOUN
cana-5829	787	21	)	)	PUNCT
cana-5829	787	22	)	)	PUNCT
cana-5829	788	1	𝑋22	𝑋22	VERB
cana-5829	788	2	=(	=(	PROPN
cana-5829	788	3	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	PROPN
cana-5829	788	4	(	(	PUNCT
cana-5829	788	5	𝑥	𝑥	NOUN
cana-5829	788	6	)	)	PUNCT
cana-5829	788	7	𝑁𝑜𝑟𝑚µ𝐸22	𝑁𝑜𝑟𝑚µ𝐸22	NOUN
cana-5829	788	8	(	(	PUNCT
cana-5829	788	9	𝑥	𝑥	NOUN
cana-5829	788	10	)	)	PUNCT
cana-5829	788	11	)	)	PUNCT
cana-5829	788	12	$	$	SYM
cana-5829	788	13	(	(	PUNCT
cana-5829	788	14	𝑁𝑜𝑟𝑚𝛿𝐹22	𝑁𝑜𝑟𝑚𝛿𝐹22	X
cana-5829	788	15	(	(	PUNCT
cana-5829	788	16	𝑦	𝑦	NOUN
cana-5829	788	17	)	)	PUNCT
cana-5829	788	18	𝑁𝑜𝑟𝑚𝛾𝐹22	𝑁𝑜𝑟𝑚𝛾𝐹22	X
cana-5829	788	19	(	(	PUNCT
cana-5829	788	20	𝑦	𝑦	NOUN
cana-5829	788	21	)	)	PUNCT
cana-5829	788	22	)	)	PUNCT
cana-5829	789	1	𝐴𝑝𝑝𝑙𝑦𝑖𝑛𝑔	𝐴𝑝𝑝𝑙𝑦𝑖𝑛𝑔	PROPN
cana-5829	789	2	𝑓𝑜𝑟𝑚𝑢𝑙𝑎	𝑓𝑜𝑟𝑚𝑢𝑙𝑎	VERB
cana-5829	789	3	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	789	4	̅̅̅̅	̅̅̅̅	ADJ
cana-5829	789	5	$	$	SYM
cana-5829	789	6	𝐵𝐹	𝐵𝐹	PROPN
cana-5829	789	7	̅̅̅̅	̅̅̅̅	NOUN
cana-5829	789	8	=	=	PUNCT
cana-5829	789	9	{	{	PUNCT
cana-5829	789	10	〈	〈	PROPN
cana-5829	789	11	x	x	PROPN
cana-5829	789	12	,	,	PUNCT
cana-5829	789	13	y	y	PROPN
cana-5829	789	14	〉	〉	NOUN
cana-5829	789	15	,	,	PUNCT
cana-5829	789	16	√𝜗𝐴(x	√𝜗𝐴(x	PROPN
cana-5829	789	17	)	)	PUNCT
cana-5829	789	18	.	.	PUNCT
cana-5829	790	1	𝜗𝐵(y	𝜗𝐵(y	X
cana-5829	790	2	)	)	PUNCT
cana-5829	790	3	,	,	PUNCT
cana-5829	790	4	√	√	ADP
cana-5829	790	5	µ𝐴	µ𝐴	PROPN
cana-5829	790	6	(	(	PUNCT
cana-5829	790	7	x	x	X
cana-5829	790	8	)	)	PUNCT
cana-5829	790	9	.	.	PUNCT
cana-5829	791	1	µ𝐵(y	µ𝐵(y	NUM
cana-5829	791	2	)	)	PUNCT
cana-5829	791	3	,	,	PUNCT
cana-5829	791	4	:	:	PUNCT
cana-5829	791	5	xe	xe	PROPN
cana-5829	791	6	,	,	PUNCT
cana-5829	791	7	y𝐹	y𝐹	NOUN
cana-5829	791	8	}	}	PUNCT
cana-5829	792	1	𝑋11	𝑋11	PROPN
cana-5829	792	2	=	=	SYM
cana-5829	792	3	(	(	PUNCT
cana-5829	792	4	√𝑁𝑜𝑟𝑚𝜗𝐸11	√𝑁𝑜𝑟𝑚𝜗𝐸11	NOUN
cana-5829	792	5	(	(	PUNCT
cana-5829	792	6	𝑥	𝑥	NOUN
cana-5829	792	7	)	)	PUNCT
cana-5829	792	8	.	.	PUNCT
cana-5829	793	1	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	793	2	(	(	PUNCT
cana-5829	793	3	𝑦	𝑦	NOUN
cana-5829	793	4	)	)	PUNCT
cana-5829	793	5	,	,	PUNCT
cana-5829	793	6	√𝑁𝑜𝑟𝑚µ𝐸11	√𝑁𝑜𝑟𝑚µ𝐸11	NOUN
cana-5829	793	7	(	(	PUNCT
cana-5829	793	8	𝑥	𝑥	NOUN
cana-5829	793	9	)	)	PUNCT
cana-5829	793	10	.	.	PUNCT
cana-5829	794	1	𝑁𝑜𝑟𝑚𝛾𝐹11	𝑁𝑜𝑟𝑚𝛾𝐹11	PROPN
cana-5829	794	2	(	(	PUNCT
cana-5829	794	3	𝑦	𝑦	NOUN
cana-5829	794	4	)	)	PUNCT
cana-5829	794	5	)	)	PUNCT
cana-5829	795	1	𝑋12	𝑋12	PROPN
cana-5829	795	2	=	=	PUNCT
cana-5829	795	3	(	(	PUNCT
cana-5829	795	4	√𝑁𝑜𝑟𝑚𝜗𝐸12	√𝑁𝑜𝑟𝑚𝜗𝐸12	X
cana-5829	795	5	(	(	PUNCT
cana-5829	795	6	𝑥	𝑥	NOUN
cana-5829	795	7	)	)	PUNCT
cana-5829	795	8	.	.	PUNCT
cana-5829	796	1	𝑁𝑜𝑟𝑚𝛿𝐹12	𝑁𝑜𝑟𝑚𝛿𝐹12	PROPN
cana-5829	796	2	(	(	PUNCT
cana-5829	796	3	𝑦	𝑦	NOUN
cana-5829	796	4	)	)	PUNCT
cana-5829	796	5	,	,	PUNCT
cana-5829	796	6	√𝑁𝑜𝑟𝑚µ𝐸12	√𝑁𝑜𝑟𝑚µ𝐸12	PROPN
cana-5829	796	7	(	(	PUNCT
cana-5829	796	8	𝑥	𝑥	NOUN
cana-5829	796	9	)	)	PUNCT
cana-5829	796	10	.	.	PUNCT
cana-5829	797	1	𝑁𝑜𝑟𝑚𝛾𝐹12	𝑁𝑜𝑟𝑚𝛾𝐹12	X
cana-5829	798	1	(	(	PUNCT
cana-5829	798	2	𝑦	𝑦	NOUN
cana-5829	798	3	)	)	PUNCT
cana-5829	798	4	)	)	PUNCT
cana-5829	799	1	𝑋21	𝑋21	NOUN
cana-5829	799	2	=	=	SYM
cana-5829	799	3	(	(	PUNCT
cana-5829	799	4	√𝑁𝑜𝑟𝑚𝜗21	√𝑁𝑜𝑟𝑚𝜗21	X
cana-5829	799	5	(	(	PUNCT
cana-5829	799	6	𝑥	𝑥	NOUN
cana-5829	799	7	)	)	PUNCT
cana-5829	799	8	.	.	PUNCT
cana-5829	800	1	𝑁𝑜𝑟𝑚𝛿𝐹21	𝑁𝑜𝑟𝑚𝛿𝐹21	PUNCT
cana-5829	800	2	(	(	PUNCT
cana-5829	800	3	𝑦	𝑦	NOUN
cana-5829	800	4	)	)	PUNCT
cana-5829	800	5	,	,	PUNCT
cana-5829	800	6	√𝑁𝑜𝑟𝑚µ𝐸21	√𝑁𝑜𝑟𝑚µ𝐸21	X
cana-5829	800	7	(	(	PUNCT
cana-5829	800	8	𝑥	𝑥	NOUN
cana-5829	800	9	)	)	PUNCT
cana-5829	800	10	.	.	PUNCT
cana-5829	801	1	𝑁𝑜𝑟𝑚𝛾𝐹21	𝑁𝑜𝑟𝑚𝛾𝐹21	ADV
cana-5829	801	2	(	(	PUNCT
cana-5829	801	3	𝑦	𝑦	NOUN
cana-5829	801	4	)	)	PUNCT
cana-5829	801	5	)	)	PUNCT
cana-5829	802	1	𝑋22	𝑋22	VERB
cana-5829	802	2	=	=	PUNCT
cana-5829	802	3	(	(	PUNCT
cana-5829	802	4	√𝑁𝑜𝑟𝑚𝜗𝐸22	√𝑁𝑜𝑟𝑚𝜗𝐸22	PROPN
cana-5829	802	5	(	(	PUNCT
cana-5829	802	6	𝑥	𝑥	NOUN
cana-5829	802	7	)	)	PUNCT
cana-5829	802	8	.	.	PUNCT
cana-5829	803	1	𝑁𝑜𝑟𝑚𝛿𝐹22	𝑁𝑜𝑟𝑚𝛿𝐹22	X
cana-5829	803	2	(	(	PUNCT
cana-5829	803	3	𝑦	𝑦	NOUN
cana-5829	803	4	)	)	PUNCT
cana-5829	803	5	,	,	PUNCT
cana-5829	803	6	√𝑁𝑜𝑟𝑚µ𝐸22	√𝑁𝑜𝑟𝑚µ𝐸22	PROPN
cana-5829	803	7	(	(	PUNCT
cana-5829	803	8	𝑥	𝑥	NOUN
cana-5829	803	9	)	)	PUNCT
cana-5829	803	10	.	.	PUNCT
cana-5829	804	1	𝑁𝑜𝑟𝑚𝛾𝐹22	𝑁𝑜𝑟𝑚𝛾𝐹22	X
cana-5829	804	2	(	(	PUNCT
cana-5829	804	3	𝑦	𝑦	NOUN
cana-5829	804	4	)	)	PUNCT
cana-5829	804	5	)	)	PUNCT
cana-5829	805	1	we	we	PRON
cana-5829	805	2	have	have	VERB
cana-5829	805	3	norm𝐴̅	norm𝐴̅	PROPN
cana-5829	805	4	𝐸$	𝐸$	PROPN
cana-5829	805	5	𝑁𝑜𝑟𝑚	𝑁𝑜𝑟𝑚	PROPN
cana-5829	805	6	�	�	NOUN
cana-5829	805	7	̅	̅	NOUN
cana-5829	805	8	�	�	NOUN
cana-5829	805	9	𝐹	𝐹	NOUN
cana-5829	805	10	=	=	PUNCT
cana-5829	805	11	(	(	PUNCT
cana-5829	805	12	𝑋11	𝑋11	PROPN
cana-5829	805	13	𝑋12	𝑋12	PROPN
cana-5829	805	14	𝑋21	𝑋21	NOUN
cana-5829	805	15	𝑋22	𝑋22	ADJ
cana-5829	805	16	)	)	PUNCT
cana-5829	805	17	is	be	AUX
cana-5829	805	18	also	also	ADV
cana-5829	805	19	intuitionistic	intuitionistic	ADJ
cana-5829	805	20	fuzzy	fuzzy	ADJ
cana-5829	805	21	matrix	matrix	NOUN
cana-5829	805	22	communications	communication	NOUN
cana-5829	805	23	on	on	ADP
cana-5829	805	24	applied	apply	VERB
cana-5829	805	25	nonlinear	nonlinear	ADJ
cana-5829	805	26	analysis	analysis	NOUN
cana-5829	805	27	issn	issn	NOUN
cana-5829	805	28	:	:	PUNCT
cana-5829	805	29	1074	1074	NUM
cana-5829	805	30	-	-	PUNCT
cana-5829	805	31	133x	133x	NUM
cana-5829	805	32	vol	vol	VERB
cana-5829	805	33	32	32	NUM
cana-5829	805	34	no	no	NOUN
cana-5829	805	35	.	.	PUNCT
cana-5829	806	1	10s	10	NOUN
cana-5829	806	2	(	(	PUNCT
cana-5829	806	3	2025	2025	NUM
cana-5829	806	4	)	)	PUNCT
cana-5829	806	5	2950	2950	NUM
cana-5829	806	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5829	806	7	example	example	NOUN
cana-5829	806	8	:	:	PUNCT
cana-5829	807	1	if	if	SCONJ
cana-5829	807	2	𝑨𝑬=	𝑨𝑬=	NOUN
cana-5829	807	3	(	(	PUNCT
cana-5829	807	4	(	(	PUNCT
cana-5829	807	5	.9	.9	NUM
cana-5829	807	6	,	,	PUNCT
cana-5829	807	7	.4	.4	NUM
cana-5829	807	8	)	)	PUNCT
cana-5829	807	9	(	(	PUNCT
cana-5829	807	10	.4	.4	PROPN
cana-5829	807	11	,	,	PUNCT
cana-5829	807	12	.1	.1	NUM
cana-5829	807	13	)	)	PUNCT
cana-5829	807	14	(	(	PUNCT
cana-5829	807	15	.5	.5	NUM
cana-5829	807	16	,	,	PUNCT
cana-5829	807	17	.3	.3	NUM
cana-5829	807	18	)	)	PUNCT
cana-5829	807	19	(	(	PUNCT
cana-5829	807	20	.8	.8	NUM
cana-5829	807	21	,	,	PUNCT
cana-5829	807	22	.3	.3	NUM
cana-5829	807	23	)	)	PUNCT
cana-5829	807	24	)	)	PUNCT
cana-5829	807	25	and𝑩𝑭	and𝑩𝑭	NOUN
cana-5829	807	26	=	=	SYM
cana-5829	807	27	(	(	PUNCT
cana-5829	807	28	(	(	PUNCT
cana-5829	807	29	.8	.8	NUM
cana-5829	807	30	,	,	PUNCT
cana-5829	807	31	.6	.6	NUM
cana-5829	807	32	)	)	PUNCT
cana-5829	807	33	(	(	PUNCT
cana-5829	807	34	.6	.6	PROPN
cana-5829	807	35	,	,	PUNCT
cana-5829	807	36	.3	.3	NUM
cana-5829	807	37	)	)	PUNCT
cana-5829	807	38	(	(	PUNCT
cana-5829	807	39	.7	.7	PROPN
cana-5829	807	40	,	,	PUNCT
cana-5829	807	41	.5	.5	NUM
cana-5829	807	42	)	)	PUNCT
cana-5829	807	43	(	(	PUNCT
cana-5829	807	44	.9	.9	NUM
cana-5829	807	45	,	,	PUNCT
cana-5829	807	46	.4	.4	NUM
cana-5829	807	47	)	)	PUNCT
cana-5829	807	48	)	)	PUNCT
cana-5829	807	49	are	be	AUX
cana-5829	807	50	two	two	NUM
cana-5829	807	51	intuitionistic	intuitionistic	ADJ
cana-5829	807	52	fuzzy	fuzzy	ADJ
cana-5829	807	53	matrices	matrix	NOUN
cana-5829	807	54	over	over	ADP
cana-5829	807	55	different	different	ADJ
cana-5829	807	56	universe	universe	NOUN
cana-5829	807	57	e	e	NOUN
cana-5829	807	58	and	and	CCONJ
cana-5829	807	59	f	f	PROPN
cana-5829	807	60	then	then	ADV
cana-5829	807	61	norm𝐴̅	norm𝐴̅	PROPN
cana-5829	807	62	𝐸$𝑁𝑜𝑟𝑚	𝐸$𝑁𝑜𝑟𝑚	PROPN
cana-5829	807	63	�	�	PROPN
cana-5829	807	64	̅	̅	NOUN
cana-5829	807	65	�	�	NOUN
cana-5829	807	66	𝐹is	𝐹i	VERB
cana-5829	807	67	also	also	ADV
cana-5829	807	68	fuzzy	fuzzy	ADJ
cana-5829	807	69	matrix	matrix	NOUN
cana-5829	807	70	set	set	NOUN
cana-5829	807	71	.	.	PUNCT
cana-5829	808	1	proof	proof	NOUN
cana-5829	808	2	:	:	PUNCT
cana-5829	808	3	given	give	VERB
cana-5829	808	4	𝑨𝑬	𝑨𝑬	PROPN
cana-5829	808	5	=(	=(	NOUN
cana-5829	808	6	(	(	PUNCT
cana-5829	808	7	.9	.9	NUM
cana-5829	808	8	,	,	PUNCT
cana-5829	808	9	.4	.4	NUM
cana-5829	808	10	)	)	PUNCT
cana-5829	808	11	(	(	PUNCT
cana-5829	808	12	.4	.4	PROPN
cana-5829	808	13	,	,	PUNCT
cana-5829	808	14	.1	.1	NUM
cana-5829	808	15	)	)	PUNCT
cana-5829	808	16	(	(	PUNCT
cana-5829	808	17	.5	.5	NUM
cana-5829	808	18	,	,	PUNCT
cana-5829	808	19	.3	.3	NUM
cana-5829	808	20	)	)	PUNCT
cana-5829	808	21	(	(	PUNCT
cana-5829	808	22	.8	.8	NUM
cana-5829	808	23	,	,	PUNCT
cana-5829	808	24	.3	.3	NUM
cana-5829	808	25	)	)	PUNCT
cana-5829	808	26	)	)	PUNCT
cana-5829	808	27	and	and	CCONJ
cana-5829	808	28	𝑩𝑭	𝑩𝑭	PROPN
cana-5829	808	29	=	=	SYM
cana-5829	808	30	(	(	PUNCT
cana-5829	808	31	(	(	PUNCT
cana-5829	808	32	.8	.8	NUM
cana-5829	808	33	,	,	PUNCT
cana-5829	808	34	.6	.6	NUM
cana-5829	808	35	)	)	PUNCT
cana-5829	808	36	(	(	PUNCT
cana-5829	808	37	.6	.6	PROPN
cana-5829	808	38	,	,	PUNCT
cana-5829	808	39	.3	.3	NUM
cana-5829	808	40	)	)	PUNCT
cana-5829	808	41	(	(	PUNCT
cana-5829	808	42	.7	.7	PROPN
cana-5829	808	43	,	,	PUNCT
cana-5829	808	44	.5	.5	NUM
cana-5829	808	45	)	)	PUNCT
cana-5829	808	46	(	(	PUNCT
cana-5829	808	47	.9	.9	NUM
cana-5829	808	48	,	,	PUNCT
cana-5829	808	49	.4	.4	NUM
cana-5829	808	50	)	)	PUNCT
cana-5829	808	51	)	)	PUNCT
cana-5829	809	1	𝑁𝑜𝑟𝑚̅̅	𝑁𝑜𝑟𝑚̅̅	NOUN
cana-5829	809	2	̅̅	̅̅	PROPN
cana-5829	809	3	̅̅	̅̅	PROPN
cana-5829	809	4	̅̅	̅̅	PROPN
cana-5829	809	5	𝐴	𝐴	PROPN
cana-5829	809	6	=(	=(	NOUN
cana-5829	809	7	(	(	PUNCT
cana-5829	809	8	.8,1	.8,1	NOUN
cana-5829	809	9	)	)	PUNCT
cana-5829	809	10	(	(	PUNCT
cana-5829	809	11	0	0	NUM
cana-5829	809	12	,	,	PUNCT
cana-5829	809	13	.3	.3	NUM
cana-5829	809	14	)	)	PUNCT
cana-5829	809	15	(	(	PUNCT
cana-5829	809	16	.2	.2	NUM
cana-5829	809	17	,	,	PUNCT
cana-5829	809	18	.8	.8	NUM
cana-5829	809	19	)	)	PUNCT
cana-5829	809	20	(	(	PUNCT
cana-5829	809	21	.7	.7	PROPN
cana-5829	809	22	,	,	PUNCT
cana-5829	809	23	.8	.8	NUM
cana-5829	809	24	)	)	PUNCT
cana-5829	809	25	)	)	PUNCT
cana-5829	809	26	and	and	CCONJ
cana-5829	810	1	𝑁𝑜𝑟𝑚̅̅	𝑁𝑜𝑟𝑚̅̅	PROPN
cana-5829	810	2	̅̅	̅̅	PROPN
cana-5829	810	3	̅̅	̅̅	PROPN
cana-5829	810	4	̅̅	̅̅	PROPN
cana-5829	810	5	𝐵=	𝐵=	PROPN
cana-5829	810	6	(	(	PUNCT
cana-5829	810	7	(	(	PUNCT
cana-5829	810	8	.5	.5	NUM
cana-5829	810	9	,	,	PUNCT
cana-5829	810	10	1	1	NUM
cana-5829	810	11	)	)	PUNCT
cana-5829	810	12	(	(	PUNCT
cana-5829	810	13	0	0	NUM
cana-5829	810	14	,	,	PUNCT
cana-5829	810	15	.5	.5	NUM
cana-5829	810	16	)	)	PUNCT
cana-5829	810	17	(	(	PUNCT
cana-5829	810	18	.3	.3	NUM
cana-5829	810	19	,	,	PUNCT
cana-5829	810	20	.8	.8	NUM
cana-5829	810	21	)	)	PUNCT
cana-5829	810	22	(	(	PUNCT
cana-5829	810	23	.8	.8	PROPN
cana-5829	810	24	,	,	PUNCT
cana-5829	810	25	.7	.7	PROPN
cana-5829	810	26	)	)	PUNCT
cana-5829	810	27	)	)	PUNCT
cana-5829	811	1	𝑁𝑜𝑟𝑚̅̅	𝑁𝑜𝑟𝑚̅̅	NOUN
cana-5829	811	2	̅̅	̅̅	PROPN
cana-5829	811	3	̅̅	̅̅	PROPN
cana-5829	811	4	̅̅	̅̅	PROPN
cana-5829	811	5	𝐴$	𝐴$	PROPN
cana-5829	811	6	𝑁𝑜𝑟𝑚̅̅	𝑁𝑜𝑟𝑚̅̅	PROPN
cana-5829	811	7	̅̅	̅̅	PROPN
cana-5829	811	8	̅̅	̅̅	PROPN
cana-5829	811	9	̅̅	̅̅	PROPN
cana-5829	811	10	̅	̅	PROPN
cana-5829	811	11	𝐵	𝐵	NOUN
cana-5829	811	12	=	=	SYM
cana-5829	811	13	(	(	PUNCT
cana-5829	811	14	(	(	PUNCT
cana-5829	811	15	.8,1	.8,1	NOUN
cana-5829	811	16	)	)	PUNCT
cana-5829	811	17	(	(	PUNCT
cana-5829	811	18	0	0	NUM
cana-5829	811	19	,	,	PUNCT
cana-5829	811	20	.3	.3	NUM
cana-5829	811	21	)	)	PUNCT
cana-5829	811	22	(	(	PUNCT
cana-5829	811	23	.2	.2	NUM
cana-5829	811	24	,	,	PUNCT
cana-5829	811	25	.8	.8	NUM
cana-5829	811	26	)	)	PUNCT
cana-5829	811	27	(	(	PUNCT
cana-5829	811	28	.7	.7	PROPN
cana-5829	811	29	,	,	PUNCT
cana-5829	811	30	.8	.8	NUM
cana-5829	811	31	)	)	PUNCT
cana-5829	811	32	)	)	PUNCT
cana-5829	812	1	$	$	SYM
cana-5829	812	2	(	(	PUNCT
cana-5829	812	3	(	(	PUNCT
cana-5829	812	4	.5	.5	NUM
cana-5829	812	5	,	,	PUNCT
cana-5829	812	6	1	1	NUM
cana-5829	812	7	)	)	PUNCT
cana-5829	812	8	(	(	PUNCT
cana-5829	812	9	0	0	NUM
cana-5829	812	10	,	,	PUNCT
cana-5829	812	11	.5	.5	NUM
cana-5829	812	12	)	)	PUNCT
cana-5829	812	13	(	(	PUNCT
cana-5829	812	14	.3	.3	NUM
cana-5829	812	15	,	,	PUNCT
cana-5829	812	16	.8	.8	NUM
cana-5829	812	17	)	)	PUNCT
cana-5829	812	18	(	(	PUNCT
cana-5829	812	19	.8	.8	PROPN
cana-5829	812	20	,	,	PUNCT
cana-5829	812	21	.7	.7	PROPN
cana-5829	812	22	)	)	PUNCT
cana-5829	812	23	)	)	PUNCT
cana-5829	813	1	𝑋11	𝑋11	PROPN
cana-5829	813	2	=	=	SYM
cana-5829	813	3	(	(	PUNCT
cana-5829	813	4	.8	.8	PROPN
cana-5829	813	5	,	,	PUNCT
cana-5829	813	6	1)$	1)$	NUM
cana-5829	813	7	(	(	PUNCT
cana-5829	813	8	.	.	PUNCT
cana-5829	813	9	5	5	NUM
cana-5829	813	10	,	,	PUNCT
cana-5829	813	11	1	1	NUM
cana-5829	813	12	)	)	PUNCT
cana-5829	813	13	𝑋12	𝑋12	NOUN
cana-5829	813	14	=	=	PUNCT
cana-5829	813	15	(	(	PUNCT
cana-5829	813	16	0	0	NUM
cana-5829	813	17	,	,	PUNCT
cana-5829	813	18	.3	.3	NUM
cana-5829	813	19	)	)	PUNCT
cana-5829	813	20	$	$	SYM
cana-5829	813	21	(	(	PUNCT
cana-5829	813	22	0	0	NUM
cana-5829	813	23	,	,	PUNCT
cana-5829	813	24	.5	.5	NUM
cana-5829	813	25	)	)	PUNCT
cana-5829	813	26	𝑋21	𝑋21	NOUN
cana-5829	813	27	=	=	SYM
cana-5829	813	28	(	(	PUNCT
cana-5829	813	29	.2	.2	NUM
cana-5829	813	30	,	,	PUNCT
cana-5829	813	31	.8	.8	NUM
cana-5829	813	32	)	)	PUNCT
cana-5829	813	33	$	$	SYM
cana-5829	813	34	(	(	PUNCT
cana-5829	813	35	.3	.3	NUM
cana-5829	813	36	,	,	PUNCT
cana-5829	813	37	.8	.8	NUM
cana-5829	813	38	)	)	PUNCT
cana-5829	814	1	𝑋22	𝑋22	ADJ
cana-5829	814	2	=	=	PUNCT
cana-5829	814	3	(	(	PUNCT
cana-5829	814	4	.	.	NOUN
cana-5829	814	5	7	7	NUM
cana-5829	814	6	,	,	PUNCT
cana-5829	814	7	.8)$(.8	.8)$(.8	PROPN
cana-5829	814	8	,	,	PUNCT
cana-5829	814	9	.7	.7	PROPN
cana-5829	814	10	)	)	PUNCT
cana-5829	815	1	𝐴𝑝𝑝𝑙𝑦𝑖𝑛𝑔	𝐴𝑝𝑝𝑙𝑦𝑖𝑛𝑔	PROPN
cana-5829	815	2	𝑓𝑜𝑟𝑚𝑢𝑙𝑎	𝑓𝑜𝑟𝑚𝑢𝑙𝑎	VERB
cana-5829	815	3	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	815	4	̅̅̅̅	̅̅̅̅	ADJ
cana-5829	815	5	$	$	SYM
cana-5829	815	6	𝐵𝐹	𝐵𝐹	PROPN
cana-5829	815	7	̅̅̅̅	̅̅̅̅	NOUN
cana-5829	815	8	=	=	PUNCT
cana-5829	815	9	{	{	PUNCT
cana-5829	815	10	〈	〈	PROPN
cana-5829	815	11	x	x	PROPN
cana-5829	815	12	,	,	PUNCT
cana-5829	815	13	y	y	PROPN
cana-5829	815	14	〉	〉	NOUN
cana-5829	815	15	,	,	PUNCT
cana-5829	815	16	√𝜗𝐴(x	√𝜗𝐴(x	PROPN
cana-5829	815	17	)	)	PUNCT
cana-5829	815	18	.	.	PUNCT
cana-5829	816	1	𝜗𝐵(y	𝜗𝐵(y	X
cana-5829	816	2	)	)	PUNCT
cana-5829	816	3	,	,	PUNCT
cana-5829	816	4	√	√	ADP
cana-5829	816	5	µ𝐴	µ𝐴	PROPN
cana-5829	816	6	(	(	PUNCT
cana-5829	816	7	x	x	X
cana-5829	816	8	)	)	PUNCT
cana-5829	816	9	.	.	PUNCT
cana-5829	817	1	µ𝐵(y	µ𝐵(y	NUM
cana-5829	817	2	)	)	PUNCT
cana-5829	817	3	,	,	PUNCT
cana-5829	817	4	:	:	PUNCT
cana-5829	817	5	xe	xe	PROPN
cana-5829	817	6	,	,	PUNCT
cana-5829	817	7	y𝐹	y𝐹	NOUN
cana-5829	817	8	}	}	PUNCT
cana-5829	817	9	𝑋11	𝑋11	PROPN
cana-5829	817	10	=	=	SYM
cana-5829	817	11	(	(	PUNCT
cana-5829	817	12	√.	√.	PROPN
cana-5829	817	13	8	8	NUM
cana-5829	817	14	.5	.5	NUM
cana-5829	817	15	,	,	PUNCT
cana-5829	817	16	√1	√1	PROPN
cana-5829	817	17	.	.	PUNCT
cana-5829	818	1	1	1	X
cana-5829	818	2	)	)	PUNCT
cana-5829	818	3	𝑋12	𝑋12	PROPN
cana-5829	818	4	=	=	PUNCT
cana-5829	818	5	(	(	PUNCT
cana-5829	818	6	√0	√0	PROPN
cana-5829	818	7	.	.	PUNCT
cana-5829	818	8	0	0	NUM
cana-5829	818	9	,	,	PUNCT
cana-5829	818	10	√.	√.	PROPN
cana-5829	818	11	3	3	NUM
cana-5829	818	12	.5	.5	NUM
cana-5829	818	13	)	)	PUNCT
cana-5829	819	1	𝑋21	𝑋21	NOUN
cana-5829	819	2	=	=	SYM
cana-5829	819	3	(	(	PUNCT
cana-5829	819	4	√.	√.	NOUN
cana-5829	819	5	2	2	NUM
cana-5829	819	6	.3	.3	NUM
cana-5829	819	7	,	,	PUNCT
cana-5829	819	8	√.	√.	PROPN
cana-5829	819	9	8	8	NUM
cana-5829	819	10	.8	.8	NUM
cana-5829	819	11	)	)	PUNCT
cana-5829	820	1	𝑋22	𝑋22	ADJ
cana-5829	820	2	=	=	PUNCT
cana-5829	820	3	(	(	PUNCT
cana-5829	820	4	√.	√.	NUM
cana-5829	820	5	7	7	NUM
cana-5829	820	6	.8	.8	NUM
cana-5829	820	7	,	,	PUNCT
cana-5829	820	8	√.	√.	PROPN
cana-5829	820	9	8	8	NUM
cana-5829	820	10	.7	.7	NUM
cana-5829	820	11	)	)	PUNCT
cana-5829	821	1	𝑋11	𝑋11	PROPN
cana-5829	821	2	=	=	PRON
cana-5829	821	3	{	{	PUNCT
cana-5829	821	4	.6	.6	PROPN
cana-5829	821	5	,	,	PUNCT
cana-5829	821	6	.1	.1	NUM
cana-5829	821	7	}	}	PUNCT
cana-5829	821	8	𝑋12	𝑋12	VERB
cana-5829	821	9	=	=	SYM
cana-5829	821	10	{	{	PUNCT
cana-5829	821	11	0	0	NUM
cana-5829	821	12	,	,	PUNCT
cana-5829	821	13	.4	.4	NUM
cana-5829	821	14	}	}	PUNCT
cana-5829	821	15	𝑋21	𝑋21	VERB
cana-5829	821	16	=	=	PRON
cana-5829	821	17	{	{	PUNCT
cana-5829	821	18	.2	.2	NUM
cana-5829	821	19	,	,	PUNCT
cana-5829	821	20	.8	.8	NUM
cana-5829	821	21	}	}	PUNCT
cana-5829	821	22	𝑋22	𝑋22	VERB
cana-5829	821	23	=	=	PRON
cana-5829	821	24	{	{	PUNCT
cana-5829	821	25	.7	.7	PROPN
cana-5829	821	26	,	,	PUNCT
cana-5829	821	27	.7	.7	PROPN
cana-5829	821	28	}	}	PUNCT
cana-5829	821	29	we	we	PRON
cana-5829	821	30	have	have	VERB
cana-5829	821	31	norm𝐴̅	norm𝐴̅	PROPN
cana-5829	821	32	𝐸$	𝐸$	PROPN
cana-5829	821	33	𝑁𝑜𝑟𝑚	𝑁𝑜𝑟𝑚	PROPN
cana-5829	821	34	�	�	NOUN
cana-5829	821	35	̅	̅	NOUN
cana-5829	821	36	�	�	NOUN
cana-5829	821	37	𝐹	𝐹	NOUN
cana-5829	821	38	=	=	SYM
cana-5829	821	39	(	(	PUNCT
cana-5829	821	40	(	(	PUNCT
cana-5829	821	41	.6	.6	NUM
cana-5829	821	42	,	,	PUNCT
cana-5829	821	43	.1	.1	NUM
cana-5829	821	44	)	)	PUNCT
cana-5829	821	45	(	(	PUNCT
cana-5829	821	46	0	0	NUM
cana-5829	821	47	,	,	PUNCT
cana-5829	821	48	.4	.4	NUM
cana-5829	821	49	)	)	PUNCT
cana-5829	821	50	(	(	PUNCT
cana-5829	821	51	.2	.2	NUM
cana-5829	821	52	,	,	PUNCT
cana-5829	821	53	.8	.8	NUM
cana-5829	821	54	)	)	PUNCT
cana-5829	821	55	(	(	PUNCT
cana-5829	821	56	.7	.7	PROPN
cana-5829	821	57	,	,	PUNCT
cana-5829	821	58	.7	.7	PROPN
cana-5829	821	59	)	)	PUNCT
cana-5829	821	60	)	)	PUNCT
cana-5829	821	61	is	be	AUX
cana-5829	821	62	also	also	ADV
cana-5829	821	63	intuitionistic	intuitionistic	ADJ
cana-5829	821	64	fuzzy	fuzzy	ADJ
cana-5829	821	65	matrix	matrix	NOUN
cana-5829	821	66	.	.	PUNCT
cana-5829	822	1	theorem	theorem	VERB
cana-5829	822	2	5.2.7	5.2.7	NUM
cana-5829	822	3	:	:	PUNCT
cana-5829	822	4	if	if	SCONJ
cana-5829	822	5	e	e	PROPN
cana-5829	822	6	and	and	CCONJ
cana-5829	822	7	f	f	PROPN
cana-5829	822	8	be	be	AUX
cana-5829	822	9	two	two	NUM
cana-5829	822	10	universal	universal	ADJ
cana-5829	822	11	sets	set	NOUN
cana-5829	822	12	.	.	PUNCT
cana-5829	823	1	for	for	ADP
cana-5829	823	2	every	every	DET
cana-5829	823	3	normalization	normalization	NOUN
cana-5829	823	4	of	of	ADP
cana-5829	823	5	an	an	DET
cana-5829	823	6	intuitionistic	intuitionistic	ADJ
cana-5829	823	7	fuzzy	fuzzy	ADJ
cana-5829	823	8	matrices	matrix	NOUN
cana-5829	823	9	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	823	10	̅̅̅̅	̅̅̅̅	ADJ
cana-5829	823	11	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-5829	823	12	𝐵𝐹	𝐵𝐹	PROPN
cana-5829	823	13	̅̅̅̅	̅̅̅̅	NOUN
cana-5829	823	14	are	be	AUX
cana-5829	823	15	in	in	ADP
cana-5829	823	16	e	e	PROPN
cana-5829	823	17	and	and	CCONJ
cana-5829	823	18	f	f	PROPN
cana-5829	823	19	then	then	ADV
cana-5829	823	20	norm𝐴̅	norm𝐴̅	PROPN
cana-5829	823	21	𝐸	𝐸	PROPN
cana-5829	823	22	#	#	NOUN
cana-5829	823	23	𝑁𝑜𝑟𝑚	𝑁𝑜𝑟𝑚	PROPN
cana-5829	823	24	�	�	NOUN
cana-5829	823	25	̅	̅	NOUN
cana-5829	823	26	�	�	NOUN
cana-5829	823	27	𝐹	𝐹	PROPN
cana-5829	823	28	is	be	AUX
cana-5829	823	29	also	also	ADV
cana-5829	823	30	normalization	normalization	NOUN
cana-5829	823	31	of	of	ADP
cana-5829	823	32	an	an	DET
cana-5829	823	33	intuitionistic	intuitionistic	ADJ
cana-5829	823	34	fuzzy	fuzzy	ADJ
cana-5829	823	35	matrices	matrix	NOUN
cana-5829	823	36	.	.	PUNCT
cana-5829	824	1	proof	proof	NOUN
cana-5829	824	2	:	:	PUNCT
cana-5829	824	3	if	if	SCONJ
cana-5829	824	4	𝑁𝑜𝑟𝑚𝐴	𝑁𝑜𝑟𝑚𝐴	PROPN
cana-5829	824	5	and	and	CCONJ
cana-5829	824	6	𝑁𝑜𝑟𝑚𝐵	𝑁𝑜𝑟𝑚𝐵	PROPN
cana-5829	824	7	are	be	AUX
cana-5829	824	8	two	two	NUM
cana-5829	824	9	normalization	normalization	NOUN
cana-5829	824	10	intuitionistic	intuitionistic	ADJ
cana-5829	824	11	fuzzy	fuzzy	ADJ
cana-5829	824	12	matrices	matrix	NOUN
cana-5829	824	13	over	over	ADP
cana-5829	824	14	different	different	ADJ
cana-5829	824	15	unive𝑟𝑠𝑒𝑠	unive𝑟𝑠𝑒𝑠	ADJ
cana-5829	824	16	𝑠𝑒𝑡𝑠	𝑠𝑒𝑡𝑠	PROPN
cana-5829	824	17	𝐸	𝐸	PROPN
cana-5829	825	1	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-5829	825	2	𝐹.	𝐹.	NOUN
cana-5829	825	3	𝐼𝑓	𝐼𝑓	PROPN
cana-5829	825	4	𝑤𝑒	𝑤𝑒	PROPN
cana-5829	825	5	𝑐𝑜𝑛𝑠𝑖𝑑𝑒𝑟	𝑐𝑜𝑛𝑠𝑖𝑑𝑒𝑟	PROPN
cana-5829	825	6	𝑡𝑤𝑜	𝑡𝑤𝑜	PROPN
cana-5829	825	7	2	2	NUM
cana-5829	825	8	×	×	NOUN
cana-5829	825	9	2	2	NUM
cana-5829	825	10	𝑚𝑎𝑡𝑟𝑖𝑥	𝑚𝑎𝑡𝑟𝑖𝑥	ADJ
cana-5829	825	11	𝑁𝑜𝑟𝑚̅̅	𝑁𝑜𝑟𝑚̅̅	PROPN
cana-5829	825	12	̅̅	̅̅	PROPN
cana-5829	825	13	̅̅	̅̅	PROPN
cana-5829	825	14	̅̅	̅̅	PROPN
cana-5829	825	15	𝐴	𝐴	PROPN
cana-5829	825	16	=(	=(	NOUN
cana-5829	825	17	(	(	PUNCT
cana-5829	825	18	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	825	19	(	(	PUNCT
cana-5829	825	20	𝑥	𝑥	NOUN
cana-5829	825	21	)	)	PUNCT
cana-5829	825	22	𝑁𝑜𝑟𝑚µ𝐸11(𝑥	𝑁𝑜𝑟𝑚µ𝐸11(𝑥	NOUN
cana-5829	825	23	)	)	PUNCT
cana-5829	825	24	)	)	PUNCT
cana-5829	826	1	(	(	PUNCT
cana-5829	826	2	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	X
cana-5829	826	3	(	(	PUNCT
cana-5829	826	4	𝑥	𝑥	NOUN
cana-5829	826	5	)	)	PUNCT
cana-5829	826	6	𝑁𝑜𝑟𝑚µ𝐸12(𝑥	𝑁𝑜𝑟𝑚µ𝐸12(𝑥	NOUN
cana-5829	826	7	)	)	PUNCT
cana-5829	826	8	)	)	PUNCT
cana-5829	826	9	(	(	PUNCT
cana-5829	826	10	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	X
cana-5829	826	11	(	(	PUNCT
cana-5829	826	12	𝑥	𝑥	NOUN
cana-5829	826	13	)	)	PUNCT
cana-5829	826	14	𝑁𝑜𝑟𝑚µ𝐸21	𝑁𝑜𝑟𝑚µ𝐸21	NOUN
cana-5829	826	15	(	(	PUNCT
cana-5829	826	16	𝑥	𝑥	NOUN
cana-5829	826	17	)	)	PUNCT
cana-5829	826	18	)	)	PUNCT
cana-5829	826	19	(	(	PUNCT
cana-5829	826	20	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	X
cana-5829	826	21	(	(	PUNCT
cana-5829	826	22	𝑥	𝑥	NOUN
cana-5829	826	23	)	)	PUNCT
cana-5829	826	24	𝑁𝑜𝑟𝑚µ𝐸22	𝑁𝑜𝑟𝑚µ𝐸22	NOUN
cana-5829	826	25	(	(	PUNCT
cana-5829	826	26	𝑥	𝑥	NOUN
cana-5829	826	27	)	)	PUNCT
cana-5829	826	28	)	)	PUNCT
cana-5829	826	29	)	)	PUNCT
cana-5829	826	30	and	and	CCONJ
cana-5829	827	1	𝑁𝑜𝑟𝑚̅̅	𝑁𝑜𝑟𝑚̅̅	PROPN
cana-5829	827	2	̅̅	̅̅	PROPN
cana-5829	827	3	̅̅	̅̅	PROPN
cana-5829	827	4	̅̅	̅̅	PROPN
cana-5829	827	5	𝐵=	𝐵=	PROPN
cana-5829	827	6	(	(	PUNCT
cana-5829	827	7	(	(	PUNCT
cana-5829	827	8	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	827	9	(	(	PUNCT
cana-5829	827	10	𝑦	𝑦	NOUN
cana-5829	827	11	)	)	PUNCT
cana-5829	827	12	𝑁𝑜𝑟𝑚𝛾𝐹11(𝑦	𝑁𝑜𝑟𝑚𝛾𝐹11(𝑦	NUM
cana-5829	827	13	)	)	PUNCT
cana-5829	827	14	)	)	PUNCT
cana-5829	827	15	(	(	PUNCT
cana-5829	827	16	𝑁𝑜𝑟𝑚𝛿𝐹12	𝑁𝑜𝑟𝑚𝛿𝐹12	X
cana-5829	827	17	(	(	PUNCT
cana-5829	827	18	𝑦	𝑦	NOUN
cana-5829	827	19	)	)	PUNCT
cana-5829	827	20	𝑁𝑜𝑟𝑚𝛾𝐹12(𝑦	𝑁𝑜𝑟𝑚𝛾𝐹12(𝑦	NOUN
cana-5829	827	21	)	)	PUNCT
cana-5829	827	22	)	)	PUNCT
cana-5829	827	23	(	(	PUNCT
cana-5829	827	24	𝑁𝑜𝑟𝑚𝛿𝐹21	𝑁𝑜𝑟𝑚𝛿𝐹21	X
cana-5829	827	25	(	(	PUNCT
cana-5829	827	26	𝑦	𝑦	NOUN
cana-5829	827	27	)	)	PUNCT
cana-5829	827	28	𝑁𝑜𝑟𝑚𝛾𝐹21	𝑁𝑜𝑟𝑚𝛾𝐹21	ADV
cana-5829	827	29	(	(	PUNCT
cana-5829	827	30	𝑦	𝑦	NOUN
cana-5829	827	31	)	)	PUNCT
cana-5829	827	32	)	)	PUNCT
cana-5829	827	33	(	(	PUNCT
cana-5829	827	34	𝑁𝑜𝑟𝑚𝛿𝐹22	𝑁𝑜𝑟𝑚𝛿𝐹22	X
cana-5829	827	35	(	(	PUNCT
cana-5829	827	36	𝑦	𝑦	NOUN
cana-5829	827	37	)	)	PUNCT
cana-5829	827	38	𝑁𝑜𝑟𝑚𝛾𝐹22	𝑁𝑜𝑟𝑚𝛾𝐹22	X
cana-5829	827	39	(	(	PUNCT
cana-5829	827	40	𝑦	𝑦	NOUN
cana-5829	827	41	)	)	PUNCT
cana-5829	827	42	)	)	PUNCT
cana-5829	827	43	)	)	PUNCT
cana-5829	828	1	𝑁𝑜𝑟𝑚̅̅	𝑁𝑜𝑟𝑚̅̅	NOUN
cana-5829	828	2	̅̅	̅̅	PROPN
cana-5829	828	3	̅̅	̅̅	PROPN
cana-5829	828	4	̅̅	̅̅	PROPN
cana-5829	828	5	𝐴	𝐴	PROPN
cana-5829	828	6	#	#	NOUN
cana-5829	828	7	𝑁𝑜𝑟𝑚̅̅	𝑁𝑜𝑟𝑚̅̅	NOUN
cana-5829	828	8	̅̅	̅̅	PROPN
cana-5829	828	9	̅̅	̅̅	PROPN
cana-5829	828	10	̅̅	̅̅	PROPN
cana-5829	828	11	𝐵	𝐵	PROPN
cana-5829	828	12	=	=	PUNCT
cana-5829	828	13	(	(	PUNCT
cana-5829	828	14	(	(	PUNCT
cana-5829	828	15	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	828	16	(	(	PUNCT
cana-5829	828	17	𝑥	𝑥	NOUN
cana-5829	828	18	)	)	PUNCT
cana-5829	828	19	𝑁𝑜𝑟𝑚µ𝐸11	𝑁𝑜𝑟𝑚µ𝐸11	NOUN
cana-5829	828	20	(	(	PUNCT
cana-5829	828	21	𝑥	𝑥	NOUN
cana-5829	828	22	)	)	PUNCT
cana-5829	828	23	)	)	PUNCT
cana-5829	828	24	(	(	PUNCT
cana-5829	828	25	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	X
cana-5829	828	26	(	(	PUNCT
cana-5829	828	27	𝑥	𝑥	NOUN
cana-5829	828	28	)	)	PUNCT
cana-5829	828	29	𝑁𝑜𝑟𝑚µ𝐸12	𝑁𝑜𝑟𝑚µ𝐸12	NOUN
cana-5829	828	30	(	(	PUNCT
cana-5829	828	31	𝑥	𝑥	NOUN
cana-5829	828	32	)	)	PUNCT
cana-5829	828	33	)	)	PUNCT
cana-5829	828	34	(	(	PUNCT
cana-5829	828	35	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	X
cana-5829	828	36	(	(	PUNCT
cana-5829	828	37	𝑥	𝑥	NOUN
cana-5829	828	38	)	)	PUNCT
cana-5829	828	39	𝑁𝑜𝑟𝑚µ𝐸21	𝑁𝑜𝑟𝑚µ𝐸21	NOUN
cana-5829	828	40	(	(	PUNCT
cana-5829	828	41	𝑥	𝑥	NOUN
cana-5829	828	42	)	)	PUNCT
cana-5829	828	43	)	)	PUNCT
cana-5829	828	44	(	(	PUNCT
cana-5829	828	45	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	X
cana-5829	828	46	(	(	PUNCT
cana-5829	828	47	𝑥	𝑥	NOUN
cana-5829	828	48	)	)	PUNCT
cana-5829	828	49	𝑁𝑜𝑟𝑚µ𝐸22	𝑁𝑜𝑟𝑚µ𝐸22	NOUN
cana-5829	828	50	(	(	PUNCT
cana-5829	828	51	𝑥	𝑥	NOUN
cana-5829	828	52	)	)	PUNCT
cana-5829	828	53	)	)	PUNCT
cana-5829	828	54	)	)	PUNCT
cana-5829	828	55	#	#	NOUN
cana-5829	828	56	communications	communication	NOUN
cana-5829	828	57	on	on	ADP
cana-5829	828	58	applied	apply	VERB
cana-5829	828	59	nonlinear	nonlinear	ADJ
cana-5829	828	60	analysis	analysis	NOUN
cana-5829	828	61	issn	issn	NOUN
cana-5829	828	62	:	:	PUNCT
cana-5829	828	63	1074	1074	NUM
cana-5829	828	64	-	-	PUNCT
cana-5829	828	65	133x	133x	NUM
cana-5829	828	66	vol	vol	VERB
cana-5829	828	67	32	32	NUM
cana-5829	828	68	no	no	NOUN
cana-5829	828	69	.	.	PUNCT
cana-5829	829	1	10s	10	NOUN
cana-5829	829	2	(	(	PUNCT
cana-5829	829	3	2025	2025	NUM
cana-5829	829	4	)	)	PUNCT
cana-5829	829	5	2951	2951	NUM
cana-5829	829	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5829	829	7	(	(	PUNCT
cana-5829	829	8	(	(	PUNCT
cana-5829	829	9	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	829	10	(	(	PUNCT
cana-5829	829	11	𝑦	𝑦	NOUN
cana-5829	829	12	)	)	PUNCT
cana-5829	829	13	𝑁𝑜𝑟𝑚𝛾𝐹11(𝑦	𝑁𝑜𝑟𝑚𝛾𝐹11(𝑦	NUM
cana-5829	829	14	)	)	PUNCT
cana-5829	829	15	)	)	PUNCT
cana-5829	830	1	(	(	PUNCT
cana-5829	830	2	𝑁𝑜𝑟𝑚𝛿𝐹12	𝑁𝑜𝑟𝑚𝛿𝐹12	X
cana-5829	830	3	(	(	PUNCT
cana-5829	830	4	𝑦	𝑦	NOUN
cana-5829	830	5	)	)	PUNCT
cana-5829	830	6	𝑁𝑜𝑟𝑚𝛾𝐹12(𝑦	𝑁𝑜𝑟𝑚𝛾𝐹12(𝑦	NOUN
cana-5829	830	7	)	)	PUNCT
cana-5829	830	8	)	)	PUNCT
cana-5829	830	9	(	(	PUNCT
cana-5829	830	10	𝑁𝑜𝑟𝑚𝛿𝐹21	𝑁𝑜𝑟𝑚𝛿𝐹21	X
cana-5829	830	11	(	(	PUNCT
cana-5829	830	12	𝑦	𝑦	NOUN
cana-5829	830	13	)	)	PUNCT
cana-5829	830	14	𝑁𝑜𝑟𝑚𝛾𝐹21	𝑁𝑜𝑟𝑚𝛾𝐹21	ADV
cana-5829	830	15	(	(	PUNCT
cana-5829	830	16	𝑦	𝑦	NOUN
cana-5829	830	17	)	)	PUNCT
cana-5829	830	18	)	)	PUNCT
cana-5829	830	19	(	(	PUNCT
cana-5829	830	20	𝑁𝑜𝑟𝑚𝛿𝐹22	𝑁𝑜𝑟𝑚𝛿𝐹22	X
cana-5829	830	21	(	(	PUNCT
cana-5829	830	22	𝑦	𝑦	NOUN
cana-5829	830	23	)	)	PUNCT
cana-5829	830	24	𝑁𝑜𝑟𝑚𝛾𝐹22	𝑁𝑜𝑟𝑚𝛾𝐹22	X
cana-5829	830	25	(	(	PUNCT
cana-5829	830	26	𝑦	𝑦	NOUN
cana-5829	830	27	)	)	PUNCT
cana-5829	830	28	)	)	PUNCT
cana-5829	830	29	)	)	PUNCT
cana-5829	831	1	𝑋11	𝑋11	PROPN
cana-5829	831	2	=(	=(	NOUN
cana-5829	831	3	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	831	4	(	(	PUNCT
cana-5829	831	5	𝑥	𝑥	NOUN
cana-5829	831	6	)	)	PUNCT
cana-5829	831	7	𝑁𝑜𝑟𝑚µ𝐸11(𝑥	𝑁𝑜𝑟𝑚µ𝐸11(𝑥	NOUN
cana-5829	831	8	)	)	PUNCT
cana-5829	831	9	)	)	PUNCT
cana-5829	831	10	#	#	NOUN
cana-5829	831	11	(	(	PUNCT
cana-5829	831	12	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	831	13	(	(	PUNCT
cana-5829	831	14	𝑦	𝑦	NOUN
cana-5829	831	15	)	)	PUNCT
cana-5829	831	16	𝑁𝑜𝑟𝑚𝛾𝐹11(𝑦	𝑁𝑜𝑟𝑚𝛾𝐹11(𝑦	NUM
cana-5829	831	17	)	)	PUNCT
cana-5829	831	18	)	)	PUNCT
cana-5829	832	1	𝑋12	𝑋12	PROPN
cana-5829	832	2	=(	=(	NOUN
cana-5829	832	3	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	NOUN
cana-5829	832	4	(	(	PUNCT
cana-5829	832	5	𝑥	𝑥	NOUN
cana-5829	832	6	)	)	PUNCT
cana-5829	832	7	𝑁𝑜𝑟𝑚µ𝐸12(𝑥	𝑁𝑜𝑟𝑚µ𝐸12(𝑥	NOUN
cana-5829	832	8	)	)	PUNCT
cana-5829	832	9	)	)	PUNCT
cana-5829	833	1	#	#	NOUN
cana-5829	833	2	(	(	PUNCT
cana-5829	833	3	𝑁𝑜𝑟𝑚𝛿𝐹12	𝑁𝑜𝑟𝑚𝛿𝐹12	X
cana-5829	833	4	(	(	PUNCT
cana-5829	833	5	𝑦	𝑦	NOUN
cana-5829	833	6	)	)	PUNCT
cana-5829	833	7	𝑁𝑜𝑟𝑚𝛾𝐹12(𝑦	𝑁𝑜𝑟𝑚𝛾𝐹12(𝑦	NOUN
cana-5829	833	8	)	)	PUNCT
cana-5829	833	9	)	)	PUNCT
cana-5829	834	1	𝑋21	𝑋21	VERB
cana-5829	834	2	=(	=(	NOUN
cana-5829	834	3	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	NOUN
cana-5829	834	4	(	(	PUNCT
cana-5829	834	5	𝑥	𝑥	NOUN
cana-5829	834	6	)	)	PUNCT
cana-5829	834	7	𝑁𝑜𝑟𝑚µ𝐸21	𝑁𝑜𝑟𝑚µ𝐸21	NOUN
cana-5829	834	8	(	(	PUNCT
cana-5829	834	9	𝑥	𝑥	NOUN
cana-5829	834	10	)	)	PUNCT
cana-5829	834	11	)	)	PUNCT
cana-5829	834	12	#	#	NOUN
cana-5829	834	13	(	(	PUNCT
cana-5829	834	14	𝑁𝑜𝑟𝑚𝛿𝐹21	𝑁𝑜𝑟𝑚𝛿𝐹21	X
cana-5829	834	15	(	(	PUNCT
cana-5829	834	16	𝑦	𝑦	NOUN
cana-5829	834	17	)	)	PUNCT
cana-5829	834	18	𝑁𝑜𝑟𝑚𝛾𝐹21	𝑁𝑜𝑟𝑚𝛾𝐹21	ADV
cana-5829	834	19	(	(	PUNCT
cana-5829	834	20	𝑦	𝑦	NOUN
cana-5829	834	21	)	)	PUNCT
cana-5829	834	22	)	)	PUNCT
cana-5829	835	1	𝑋22	𝑋22	VERB
cana-5829	835	2	=(	=(	PROPN
cana-5829	835	3	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	PROPN
cana-5829	835	4	(	(	PUNCT
cana-5829	835	5	𝑥	𝑥	NOUN
cana-5829	835	6	)	)	PUNCT
cana-5829	835	7	𝑁𝑜𝑟𝑚µ𝐸22	𝑁𝑜𝑟𝑚µ𝐸22	NOUN
cana-5829	835	8	(	(	PUNCT
cana-5829	835	9	𝑥	𝑥	NOUN
cana-5829	835	10	)	)	PUNCT
cana-5829	835	11	)	)	PUNCT
cana-5829	835	12	#	#	NOUN
cana-5829	835	13	(	(	PUNCT
cana-5829	835	14	𝑁𝑜𝑟𝑚𝛿𝐹22	𝑁𝑜𝑟𝑚𝛿𝐹22	X
cana-5829	835	15	(	(	PUNCT
cana-5829	835	16	𝑦	𝑦	NOUN
cana-5829	835	17	)	)	PUNCT
cana-5829	835	18	𝑁𝑜𝑟𝑚𝛾𝐹22	𝑁𝑜𝑟𝑚𝛾𝐹22	X
cana-5829	835	19	(	(	PUNCT
cana-5829	835	20	𝑦	𝑦	NOUN
cana-5829	835	21	)	)	PUNCT
cana-5829	835	22	)	)	PUNCT
cana-5829	836	1	𝐴𝑝𝑝𝑙𝑦𝑖𝑛𝑔	𝐴𝑝𝑝𝑙𝑦𝑖𝑛𝑔	PROPN
cana-5829	836	2	𝑓𝑜𝑟𝑚𝑢𝑙𝑎	𝑓𝑜𝑟𝑚𝑢𝑙𝑎	VERB
cana-5829	836	3	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	836	4	̅̅̅̅	̅̅̅̅	ADJ
cana-5829	836	5	#	#	NOUN
cana-5829	836	6	𝐵𝐹	𝐵𝐹	PROPN
cana-5829	836	7	̅̅̅̅	̅̅̅̅	NOUN
cana-5829	836	8	=	=	PUNCT
cana-5829	836	9	{	{	PUNCT
cana-5829	836	10	〈	〈	PROPN
cana-5829	836	11	x	x	PROPN
cana-5829	836	12	,	,	PUNCT
cana-5829	836	13	y	y	PROPN
cana-5829	836	14	〉	〉	NOUN
cana-5829	836	15	,	,	PUNCT
cana-5829	836	16	2𝜗𝐴(x	2𝜗𝐴(x	NUM
cana-5829	836	17	)	)	PUNCT
cana-5829	836	18	.𝜗𝐵(y	.𝜗𝐵(y	NOUN
cana-5829	836	19	)	)	PUNCT
cana-5829	836	20	𝜗𝐴(x)+𝜗𝐵(y	𝜗𝐴(x)+𝜗𝐵(y	NUM
cana-5829	836	21	)	)	PUNCT
cana-5829	836	22	,	,	PUNCT
cana-5829	836	23	2µ𝐴	2µ𝐴	NUM
cana-5829	836	24	(	(	PUNCT
cana-5829	836	25	x	x	NOUN
cana-5829	836	26	)	)	PUNCT
cana-5829	836	27	.µ𝐵(y	.µ𝐵(y	NUM
cana-5829	836	28	)	)	PUNCT
cana-5829	837	1	µ𝐴	µ𝐴	ADP
cana-5829	837	2	(	(	PUNCT
cana-5829	837	3	x)+	x)+	NUM
cana-5829	837	4	µ𝐵(y	µ𝐵(y	NUM
cana-5829	837	5	)	)	PUNCT
cana-5829	837	6	∶	∶	NOUN
cana-5829	837	7	xe	xe	PROPN
cana-5829	837	8	,	,	PUNCT
cana-5829	837	9	y𝐹	y𝐹	NOUN
cana-5829	837	10	}	}	PUNCT
cana-5829	837	11	𝑋11	𝑋11	PROPN
cana-5829	837	12	=	=	PUNCT
cana-5829	837	13	(	(	PUNCT
cana-5829	837	14	2𝑁𝑜𝑟𝑚𝜗𝐸11	2𝑁𝑜𝑟𝑚𝜗𝐸11	NUM
cana-5829	837	15	(	(	PUNCT
cana-5829	837	16	𝑥	𝑥	NOUN
cana-5829	837	17	)	)	PUNCT
cana-5829	837	18	.	.	PUNCT
cana-5829	838	1	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	838	2	(	(	PUNCT
cana-5829	838	3	𝑦	𝑦	NOUN
cana-5829	838	4	)	)	PUNCT
cana-5829	838	5	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	VERB
cana-5829	838	6	(	(	PUNCT
cana-5829	838	7	𝑥	𝑥	NOUN
cana-5829	838	8	)	)	PUNCT
cana-5829	838	9	+	+	CCONJ
cana-5829	838	10	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	838	11	(	(	PUNCT
cana-5829	838	12	𝑦	𝑦	NOUN
cana-5829	838	13	)	)	PUNCT
cana-5829	838	14	,	,	PUNCT
cana-5829	838	15	2𝑁𝑜𝑟𝑚µ𝐸11	2𝑁𝑜𝑟𝑚µ𝐸11	NUM
cana-5829	838	16	(	(	PUNCT
cana-5829	838	17	𝑥	𝑥	NOUN
cana-5829	838	18	)	)	PUNCT
cana-5829	838	19	.	.	PUNCT
cana-5829	839	1	𝑁𝑜𝑟𝑚𝛾𝐹11	𝑁𝑜𝑟𝑚𝛾𝐹11	PROPN
cana-5829	839	2	(	(	PUNCT
cana-5829	839	3	𝑦	𝑦	NOUN
cana-5829	839	4	)	)	PUNCT
cana-5829	839	5	𝑁𝑜𝑟𝑚µ𝐸11	𝑁𝑜𝑟𝑚µ𝐸11	NOUN
cana-5829	839	6	(	(	PUNCT
cana-5829	839	7	𝑥	𝑥	NOUN
cana-5829	839	8	)	)	PUNCT
cana-5829	840	1	+	+	CCONJ
cana-5829	840	2	𝑁𝑜𝑟𝑚𝛾𝐹11	𝑁𝑜𝑟𝑚𝛾𝐹11	X
cana-5829	840	3	(	(	PUNCT
cana-5829	840	4	𝑦	𝑦	NOUN
cana-5829	840	5	)	)	PUNCT
cana-5829	840	6	)	)	PUNCT
cana-5829	840	7	𝑋12	𝑋12	PROPN
cana-5829	840	8	=	=	PUNCT
cana-5829	841	1	(	(	PUNCT
cana-5829	841	2	2𝑁𝑜𝑟𝑚𝜗𝐸12	2𝑁𝑜𝑟𝑚𝜗𝐸12	NUM
cana-5829	841	3	(	(	PUNCT
cana-5829	841	4	𝑥	𝑥	NOUN
cana-5829	841	5	)	)	PUNCT
cana-5829	841	6	.	.	PUNCT
cana-5829	842	1	𝑁𝑜𝑟𝑚𝛿𝐹12	𝑁𝑜𝑟𝑚𝛿𝐹12	PROPN
cana-5829	842	2	(	(	PUNCT
cana-5829	842	3	𝑦	𝑦	NOUN
cana-5829	842	4	)	)	PUNCT
cana-5829	842	5	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	NOUN
cana-5829	842	6	(	(	PUNCT
cana-5829	842	7	𝑥	𝑥	NOUN
cana-5829	842	8	)	)	PUNCT
cana-5829	843	1	+	+	CCONJ
cana-5829	843	2	𝑁𝑜𝑟𝑚𝛿𝐹12	𝑁𝑜𝑟𝑚𝛿𝐹12	PRON
cana-5829	843	3	(	(	PUNCT
cana-5829	843	4	𝑦	𝑦	NOUN
cana-5829	843	5	)	)	PUNCT
cana-5829	843	6	,	,	PUNCT
cana-5829	843	7	2𝑁𝑜𝑟𝑚µ𝐸12	2𝑁𝑜𝑟𝑚µ𝐸12	NUM
cana-5829	843	8	(	(	PUNCT
cana-5829	843	9	𝑥	𝑥	NOUN
cana-5829	843	10	)	)	PUNCT
cana-5829	843	11	.	.	PUNCT
cana-5829	843	12	𝑁𝑜𝑟𝑚𝛾𝐹12	𝑁𝑜𝑟𝑚𝛾𝐹12	X
cana-5829	844	1	(	(	PUNCT
cana-5829	844	2	𝑦	𝑦	NOUN
cana-5829	844	3	)	)	PUNCT
cana-5829	844	4	𝑁𝑜𝑟𝑚µ𝐸12	𝑁𝑜𝑟𝑚µ𝐸12	NOUN
cana-5829	844	5	(	(	PUNCT
cana-5829	844	6	𝑥	𝑥	NOUN
cana-5829	844	7	)	)	PUNCT
cana-5829	844	8	+	+	CCONJ
cana-5829	844	9	𝑁𝑜𝑟𝑚𝛾𝐹12	𝑁𝑜𝑟𝑚𝛾𝐹12	PRON
cana-5829	844	10	(	(	PUNCT
cana-5829	844	11	𝑦	𝑦	NOUN
cana-5829	844	12	)	)	PUNCT
cana-5829	844	13	)	)	PUNCT
cana-5829	845	1	𝑋21	𝑋21	NOUN
cana-5829	845	2	=	=	SYM
cana-5829	845	3	(	(	PUNCT
cana-5829	845	4	2𝑁𝑜𝑟𝑚𝜗𝐸21	2𝑁𝑜𝑟𝑚𝜗𝐸21	NUM
cana-5829	845	5	(	(	PUNCT
cana-5829	845	6	𝑥	𝑥	NOUN
cana-5829	845	7	)	)	PUNCT
cana-5829	845	8	.	.	PUNCT
cana-5829	846	1	𝑁𝑜𝑟𝑚𝛿𝐹21	𝑁𝑜𝑟𝑚𝛿𝐹21	PUNCT
cana-5829	846	2	(	(	PUNCT
cana-5829	846	3	𝑦	𝑦	NOUN
cana-5829	846	4	)	)	PUNCT
cana-5829	846	5	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	ADP
cana-5829	846	6	(	(	PUNCT
cana-5829	846	7	𝑥	𝑥	NOUN
cana-5829	846	8	)	)	PUNCT
cana-5829	847	1	+	+	NUM
cana-5829	847	2	𝑁𝑜𝑟𝑚𝛿𝐹21	𝑁𝑜𝑟𝑚𝛿𝐹21	ADP
cana-5829	847	3	(	(	PUNCT
cana-5829	847	4	𝑦	𝑦	NOUN
cana-5829	847	5	)	)	PUNCT
cana-5829	847	6	,	,	PUNCT
cana-5829	847	7	2𝑁𝑜𝑟𝑚µ𝐸21	2𝑁𝑜𝑟𝑚µ𝐸21	NUM
cana-5829	847	8	(	(	PUNCT
cana-5829	847	9	𝑥	𝑥	NOUN
cana-5829	847	10	)	)	PUNCT
cana-5829	847	11	.	.	PUNCT
cana-5829	848	1	𝑁𝑜𝑟𝑚𝛾𝐹21	𝑁𝑜𝑟𝑚𝛾𝐹21	ADV
cana-5829	848	2	(	(	PUNCT
cana-5829	848	3	𝑦	𝑦	NOUN
cana-5829	848	4	)	)	PUNCT
cana-5829	848	5	𝑁𝑜𝑟𝑚µ𝐸21	𝑁𝑜𝑟𝑚µ𝐸21	NOUN
cana-5829	848	6	(	(	PUNCT
cana-5829	848	7	𝑥	𝑥	NOUN
cana-5829	848	8	)	)	PUNCT
cana-5829	849	1	+	+	CCONJ
cana-5829	849	2	𝑁𝑜𝑟𝑚𝛾𝐹21	𝑁𝑜𝑟𝑚𝛾𝐹21	ADV
cana-5829	849	3	(	(	PUNCT
cana-5829	849	4	𝑦	𝑦	NOUN
cana-5829	849	5	)	)	PUNCT
cana-5829	849	6	)	)	PUNCT
cana-5829	849	7	𝑋22	𝑋22	VERB
cana-5829	849	8	=	=	PUNCT
cana-5829	849	9	(	(	PUNCT
cana-5829	849	10	2𝑁𝑜𝑟𝑚𝜗𝐸22	2𝑁𝑜𝑟𝑚𝜗𝐸22	NUM
cana-5829	849	11	(	(	PUNCT
cana-5829	849	12	𝑥	𝑥	NOUN
cana-5829	849	13	)	)	PUNCT
cana-5829	849	14	.	.	PUNCT
cana-5829	850	1	𝑁𝑜𝑟𝑚𝛿𝐹22	𝑁𝑜𝑟𝑚𝛿𝐹22	X
cana-5829	850	2	(	(	PUNCT
cana-5829	850	3	𝑦	𝑦	NOUN
cana-5829	850	4	)	)	PUNCT
cana-5829	850	5	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	NOUN
cana-5829	851	1	(	(	PUNCT
cana-5829	851	2	𝑥	𝑥	NOUN
cana-5829	851	3	)	)	PUNCT
cana-5829	852	1	+	+	NUM
cana-5829	852	2	𝑁𝑜𝑟𝑚𝛿𝐹22	𝑁𝑜𝑟𝑚𝛿𝐹22	X
cana-5829	852	3	(	(	PUNCT
cana-5829	852	4	𝑦	𝑦	NOUN
cana-5829	852	5	)	)	PUNCT
cana-5829	852	6	,	,	PUNCT
cana-5829	852	7	2𝑁𝑜𝑟𝑚µ𝐸22	2𝑁𝑜𝑟𝑚µ𝐸22	NUM
cana-5829	852	8	(	(	PUNCT
cana-5829	852	9	𝑥	𝑥	NOUN
cana-5829	852	10	)	)	PUNCT
cana-5829	852	11	.	.	PUNCT
cana-5829	853	1	𝑁𝑜𝑟𝑚𝛾𝐹22	𝑁𝑜𝑟𝑚𝛾𝐹22	X
cana-5829	853	2	(	(	PUNCT
cana-5829	853	3	𝑦	𝑦	NOUN
cana-5829	853	4	)	)	PUNCT
cana-5829	853	5	𝑁𝑜𝑟𝑚µ𝐸22	𝑁𝑜𝑟𝑚µ𝐸22	NOUN
cana-5829	853	6	(	(	PUNCT
cana-5829	853	7	𝑥	𝑥	NOUN
cana-5829	853	8	)	)	PUNCT
cana-5829	854	1	+	+	CCONJ
cana-5829	854	2	𝑁𝑜𝑟𝑚𝛾𝐹22	𝑁𝑜𝑟𝑚𝛾𝐹22	X
cana-5829	854	3	(	(	PUNCT
cana-5829	854	4	𝑦	𝑦	NOUN
cana-5829	854	5	)	)	PUNCT
cana-5829	854	6	)	)	PUNCT
cana-5829	855	1	we	we	PRON
cana-5829	855	2	have	have	VERB
cana-5829	855	3	norm𝐴̅	norm𝐴̅	PROPN
cana-5829	855	4	𝐸	𝐸	PROPN
cana-5829	855	5	#	#	NOUN
cana-5829	855	6	𝑁𝑜𝑟𝑚	𝑁𝑜𝑟𝑚	PROPN
cana-5829	855	7	�	�	NOUN
cana-5829	855	8	̅	̅	NOUN
cana-5829	855	9	�	�	NOUN
cana-5829	855	10	𝐹	𝐹	NOUN
cana-5829	855	11	=	=	PUNCT
cana-5829	856	1	(	(	PUNCT
cana-5829	856	2	𝑋11	𝑋11	PROPN
cana-5829	856	3	𝑋12	𝑋12	PROPN
cana-5829	856	4	𝑋21	𝑋21	NOUN
cana-5829	856	5	𝑋22	𝑋22	ADJ
cana-5829	856	6	)	)	PUNCT
cana-5829	856	7	is	be	AUX
cana-5829	856	8	also	also	ADV
cana-5829	856	9	intuitionistic	intuitionistic	ADJ
cana-5829	856	10	fuzzy	fuzzy	ADJ
cana-5829	856	11	matrix	matrix	NOUN
cana-5829	856	12	example	example	NOUN
cana-5829	856	13	:	:	PUNCT
cana-5829	856	14	if	if	SCONJ
cana-5829	856	15	𝑨𝑬=	𝑨𝑬=	NOUN
cana-5829	856	16	(	(	PUNCT
cana-5829	856	17	(	(	PUNCT
cana-5829	856	18	.9	.9	NUM
cana-5829	856	19	,	,	PUNCT
cana-5829	856	20	.4	.4	NUM
cana-5829	856	21	)	)	PUNCT
cana-5829	856	22	(	(	PUNCT
cana-5829	856	23	.4	.4	PROPN
cana-5829	856	24	,	,	PUNCT
cana-5829	856	25	.1	.1	NUM
cana-5829	856	26	)	)	PUNCT
cana-5829	856	27	(	(	PUNCT
cana-5829	856	28	.5	.5	NUM
cana-5829	856	29	,	,	PUNCT
cana-5829	856	30	.3	.3	NUM
cana-5829	856	31	)	)	PUNCT
cana-5829	856	32	(	(	PUNCT
cana-5829	856	33	.8	.8	NUM
cana-5829	856	34	,	,	PUNCT
cana-5829	856	35	.3	.3	NUM
cana-5829	856	36	)	)	PUNCT
cana-5829	856	37	)	)	PUNCT
cana-5829	857	1	and𝑩𝑭	and𝑩𝑭	NOUN
cana-5829	857	2	=	=	SYM
cana-5829	857	3	(	(	PUNCT
cana-5829	857	4	(	(	PUNCT
cana-5829	857	5	.8	.8	NUM
cana-5829	857	6	,	,	PUNCT
cana-5829	857	7	.6	.6	NUM
cana-5829	857	8	)	)	PUNCT
cana-5829	857	9	(	(	PUNCT
cana-5829	857	10	.6	.6	PROPN
cana-5829	857	11	,	,	PUNCT
cana-5829	857	12	.3	.3	NUM
cana-5829	857	13	)	)	PUNCT
cana-5829	857	14	(	(	PUNCT
cana-5829	857	15	.7	.7	PROPN
cana-5829	857	16	,	,	PUNCT
cana-5829	857	17	.5	.5	NUM
cana-5829	857	18	)	)	PUNCT
cana-5829	857	19	(	(	PUNCT
cana-5829	857	20	.9	.9	NUM
cana-5829	857	21	,	,	PUNCT
cana-5829	857	22	.4	.4	NUM
cana-5829	857	23	)	)	PUNCT
cana-5829	857	24	)	)	PUNCT
cana-5829	857	25	are	be	AUX
cana-5829	857	26	two	two	NUM
cana-5829	857	27	intuitionistic	intuitionistic	ADJ
cana-5829	857	28	fuzzy	fuzzy	ADJ
cana-5829	857	29	matrices	matrix	NOUN
cana-5829	857	30	over	over	ADP
cana-5829	857	31	different	different	ADJ
cana-5829	857	32	universe	universe	NOUN
cana-5829	857	33	e	e	NOUN
cana-5829	857	34	and	and	CCONJ
cana-5829	857	35	f	f	PROPN
cana-5829	857	36	then	then	ADV
cana-5829	857	37	norm𝐴̅	norm𝐴̅	PROPN
cana-5829	857	38	𝐸$𝑁𝑜𝑟𝑚	𝐸$𝑁𝑜𝑟𝑚	PROPN
cana-5829	857	39	�	�	PROPN
cana-5829	857	40	̅	̅	NOUN
cana-5829	857	41	�	�	NOUN
cana-5829	857	42	𝐹is	𝐹i	VERB
cana-5829	857	43	also	also	ADV
cana-5829	857	44	fuzzy	fuzzy	ADJ
cana-5829	857	45	matrix	matrix	NOUN
cana-5829	857	46	set	set	NOUN
cana-5829	857	47	.	.	PUNCT
cana-5829	858	1	proof	proof	NOUN
cana-5829	858	2	:	:	PUNCT
cana-5829	858	3	given	give	VERB
cana-5829	858	4	𝑨𝑬	𝑨𝑬	PROPN
cana-5829	858	5	=(	=(	NOUN
cana-5829	858	6	(	(	PUNCT
cana-5829	858	7	.9	.9	NUM
cana-5829	858	8	,	,	PUNCT
cana-5829	858	9	.4	.4	NUM
cana-5829	858	10	)	)	PUNCT
cana-5829	858	11	(	(	PUNCT
cana-5829	858	12	.4	.4	PROPN
cana-5829	858	13	,	,	PUNCT
cana-5829	858	14	.1	.1	NUM
cana-5829	858	15	)	)	PUNCT
cana-5829	858	16	(	(	PUNCT
cana-5829	858	17	.5	.5	NUM
cana-5829	858	18	,	,	PUNCT
cana-5829	858	19	.3	.3	NUM
cana-5829	858	20	)	)	PUNCT
cana-5829	858	21	(	(	PUNCT
cana-5829	858	22	.8	.8	NUM
cana-5829	858	23	,	,	PUNCT
cana-5829	858	24	.3	.3	NUM
cana-5829	858	25	)	)	PUNCT
cana-5829	858	26	)	)	PUNCT
cana-5829	858	27	and	and	CCONJ
cana-5829	858	28	𝑩𝑭	𝑩𝑭	PROPN
cana-5829	858	29	=	=	SYM
cana-5829	858	30	(	(	PUNCT
cana-5829	858	31	(	(	PUNCT
cana-5829	858	32	.8	.8	NUM
cana-5829	858	33	,	,	PUNCT
cana-5829	858	34	.6	.6	NUM
cana-5829	858	35	)	)	PUNCT
cana-5829	858	36	(	(	PUNCT
cana-5829	858	37	.6	.6	PROPN
cana-5829	858	38	,	,	PUNCT
cana-5829	858	39	.3	.3	NUM
cana-5829	858	40	)	)	PUNCT
cana-5829	858	41	(	(	PUNCT
cana-5829	858	42	.7	.7	PROPN
cana-5829	858	43	,	,	PUNCT
cana-5829	858	44	.5	.5	NUM
cana-5829	858	45	)	)	PUNCT
cana-5829	858	46	(	(	PUNCT
cana-5829	858	47	.9	.9	NUM
cana-5829	858	48	,	,	PUNCT
cana-5829	858	49	.4	.4	NUM
cana-5829	858	50	)	)	PUNCT
cana-5829	858	51	)	)	PUNCT
cana-5829	859	1	𝑁𝑜𝑟𝑚̅̅	𝑁𝑜𝑟𝑚̅̅	NOUN
cana-5829	859	2	̅̅	̅̅	PROPN
cana-5829	859	3	̅̅	̅̅	PROPN
cana-5829	859	4	̅̅	̅̅	PROPN
cana-5829	859	5	𝐴	𝐴	PROPN
cana-5829	859	6	=(	=(	NOUN
cana-5829	859	7	(	(	PUNCT
cana-5829	859	8	.8,1	.8,1	NOUN
cana-5829	859	9	)	)	PUNCT
cana-5829	859	10	(	(	PUNCT
cana-5829	859	11	0	0	NUM
cana-5829	859	12	,	,	PUNCT
cana-5829	859	13	.3	.3	NUM
cana-5829	859	14	)	)	PUNCT
cana-5829	859	15	(	(	PUNCT
cana-5829	859	16	.2	.2	NUM
cana-5829	859	17	,	,	PUNCT
cana-5829	859	18	.8	.8	NUM
cana-5829	859	19	)	)	PUNCT
cana-5829	859	20	(	(	PUNCT
cana-5829	859	21	.7	.7	PROPN
cana-5829	859	22	,	,	PUNCT
cana-5829	859	23	.8	.8	NUM
cana-5829	859	24	)	)	PUNCT
cana-5829	859	25	)	)	PUNCT
cana-5829	859	26	and	and	CCONJ
cana-5829	860	1	𝑁𝑜𝑟𝑚̅̅	𝑁𝑜𝑟𝑚̅̅	PROPN
cana-5829	860	2	̅̅	̅̅	PROPN
cana-5829	860	3	̅̅	̅̅	PROPN
cana-5829	860	4	̅̅	̅̅	PROPN
cana-5829	860	5	𝐵=	𝐵=	PROPN
cana-5829	860	6	(	(	PUNCT
cana-5829	860	7	(	(	PUNCT
cana-5829	860	8	.5	.5	NUM
cana-5829	860	9	,	,	PUNCT
cana-5829	860	10	1	1	NUM
cana-5829	860	11	)	)	PUNCT
cana-5829	860	12	(	(	PUNCT
cana-5829	860	13	0	0	NUM
cana-5829	860	14	,	,	PUNCT
cana-5829	860	15	.5	.5	NUM
cana-5829	860	16	)	)	PUNCT
cana-5829	860	17	(	(	PUNCT
cana-5829	860	18	.3	.3	NUM
cana-5829	860	19	,	,	PUNCT
cana-5829	860	20	.8	.8	NUM
cana-5829	860	21	)	)	PUNCT
cana-5829	860	22	(	(	PUNCT
cana-5829	860	23	.8	.8	PROPN
cana-5829	860	24	,	,	PUNCT
cana-5829	860	25	.7	.7	PROPN
cana-5829	860	26	)	)	PUNCT
cana-5829	860	27	)	)	PUNCT
cana-5829	861	1	𝑁𝑜𝑟𝑚̅̅	𝑁𝑜𝑟𝑚̅̅	NOUN
cana-5829	861	2	̅̅	̅̅	PROPN
cana-5829	861	3	̅̅	̅̅	PROPN
cana-5829	861	4	̅̅	̅̅	PROPN
cana-5829	861	5	𝐴	𝐴	PROPN
cana-5829	861	6	#	#	PROPN
cana-5829	861	7	𝑁𝑜𝑟𝑚̅̅	𝑁𝑜𝑟𝑚̅̅	NOUN
cana-5829	861	8	̅̅	̅̅	PROPN
cana-5829	861	9	̅̅	̅̅	PROPN
cana-5829	861	10	̅̅	̅̅	PROPN
cana-5829	861	11	̅	̅	PROPN
cana-5829	861	12	𝐵	𝐵	NOUN
cana-5829	861	13	=	=	SYM
cana-5829	861	14	(	(	PUNCT
cana-5829	861	15	(	(	PUNCT
cana-5829	861	16	.8,1	.8,1	NOUN
cana-5829	861	17	)	)	PUNCT
cana-5829	861	18	(	(	PUNCT
cana-5829	861	19	0	0	NUM
cana-5829	861	20	,	,	PUNCT
cana-5829	861	21	.3	.3	NUM
cana-5829	861	22	)	)	PUNCT
cana-5829	861	23	(	(	PUNCT
cana-5829	861	24	.2	.2	NUM
cana-5829	861	25	,	,	PUNCT
cana-5829	861	26	.8	.8	NUM
cana-5829	861	27	)	)	PUNCT
cana-5829	861	28	(	(	PUNCT
cana-5829	861	29	.7	.7	PROPN
cana-5829	861	30	,	,	PUNCT
cana-5829	861	31	.8	.8	NUM
cana-5829	861	32	)	)	PUNCT
cana-5829	861	33	)	)	PUNCT
cana-5829	862	1	#	#	NOUN
cana-5829	862	2	(	(	PUNCT
cana-5829	862	3	(	(	PUNCT
cana-5829	862	4	.5	.5	NUM
cana-5829	862	5	,	,	PUNCT
cana-5829	862	6	1	1	NUM
cana-5829	862	7	)	)	PUNCT
cana-5829	862	8	(	(	PUNCT
cana-5829	862	9	0	0	NUM
cana-5829	862	10	,	,	PUNCT
cana-5829	862	11	.5	.5	NUM
cana-5829	862	12	)	)	PUNCT
cana-5829	862	13	(	(	PUNCT
cana-5829	862	14	.3	.3	NUM
cana-5829	862	15	,	,	PUNCT
cana-5829	862	16	.8	.8	NUM
cana-5829	862	17	)	)	PUNCT
cana-5829	862	18	(	(	PUNCT
cana-5829	862	19	.8	.8	PROPN
cana-5829	862	20	,	,	PUNCT
cana-5829	862	21	.7	.7	PROPN
cana-5829	862	22	)	)	PUNCT
cana-5829	862	23	)	)	PUNCT
cana-5829	863	1	𝑋11	𝑋11	PROPN
cana-5829	863	2	=	=	SYM
cana-5829	863	3	(	(	PUNCT
cana-5829	863	4	.8	.8	PROPN
cana-5829	863	5	,	,	PUNCT
cana-5829	863	6	1	1	NUM
cana-5829	863	7	)	)	PUNCT
cana-5829	863	8	#	#	NOUN
cana-5829	863	9	(	(	PUNCT
cana-5829	863	10	.	.	NOUN
cana-5829	863	11	5	5	NUM
cana-5829	863	12	,	,	PUNCT
cana-5829	863	13	1	1	NUM
cana-5829	863	14	)	)	PUNCT
cana-5829	863	15	𝑋12	𝑋12	NOUN
cana-5829	863	16	=	=	PUNCT
cana-5829	863	17	(	(	PUNCT
cana-5829	863	18	0	0	NUM
cana-5829	863	19	,	,	PUNCT
cana-5829	863	20	.3	.3	NUM
cana-5829	863	21	)	)	PUNCT
cana-5829	863	22	#	#	SYM
cana-5829	863	23	(	(	PUNCT
cana-5829	863	24	0	0	NUM
cana-5829	863	25	,	,	PUNCT
cana-5829	863	26	.5	.5	NUM
cana-5829	863	27	)	)	PUNCT
cana-5829	863	28	𝑋21	𝑋21	NOUN
cana-5829	863	29	=	=	SYM
cana-5829	863	30	(	(	PUNCT
cana-5829	863	31	.	.	NOUN
cana-5829	863	32	2	2	NUM
cana-5829	863	33	,	,	PUNCT
cana-5829	863	34	.8	.8	NUM
cana-5829	863	35	)	)	PUNCT
cana-5829	863	36	#	#	NOUN
cana-5829	863	37	(	(	PUNCT
cana-5829	863	38	.3	.3	NUM
cana-5829	863	39	,	,	PUNCT
cana-5829	863	40	.8	.8	NUM
cana-5829	863	41	)	)	PUNCT
cana-5829	864	1	𝑋22	𝑋22	ADJ
cana-5829	864	2	=	=	PUNCT
cana-5829	864	3	(	(	PUNCT
cana-5829	864	4	.	.	NOUN
cana-5829	864	5	7	7	NUM
cana-5829	864	6	,	,	PUNCT
cana-5829	864	7	.8)#(.8	.8)#(.8	PROPN
cana-5829	864	8	,	,	PUNCT
cana-5829	864	9	.7	.7	NUM
cana-5829	864	10	)	)	PUNCT
cana-5829	864	11	𝐴𝑝𝑝𝑙𝑦𝑖𝑛𝑔	𝐴𝑝𝑝𝑙𝑦𝑖𝑛𝑔	PROPN
cana-5829	864	12	𝑓𝑜𝑟𝑚𝑢𝑙𝑎𝐴𝐸	𝑓𝑜𝑟𝑚𝑢𝑙𝑎𝐴𝐸	PROPN
cana-5829	864	13	̅̅̅̅	̅̅̅̅	ADJ
cana-5829	864	14	#	#	NOUN
cana-5829	864	15	𝐵𝐹	𝐵𝐹	PROPN
cana-5829	864	16	̅̅̅̅	̅̅̅̅	NOUN
cana-5829	864	17	=	=	PUNCT
cana-5829	864	18	{	{	PUNCT
cana-5829	864	19	〈	〈	PROPN
cana-5829	864	20	x	x	PROPN
cana-5829	864	21	,	,	PUNCT
cana-5829	864	22	y	y	PROPN
cana-5829	864	23	〉	〉	NOUN
cana-5829	864	24	,	,	PUNCT
cana-5829	864	25	2𝜗𝐴(x	2𝜗𝐴(x	NUM
cana-5829	864	26	)	)	PUNCT
cana-5829	864	27	.𝜗𝐵(y	.𝜗𝐵(y	NOUN
cana-5829	864	28	)	)	PUNCT
cana-5829	864	29	𝜗𝐴(x)+𝜗𝐵(y	𝜗𝐴(x)+𝜗𝐵(y	NUM
cana-5829	864	30	)	)	PUNCT
cana-5829	864	31	,	,	PUNCT
cana-5829	864	32	2µ𝐴	2µ𝐴	NUM
cana-5829	864	33	(	(	PUNCT
cana-5829	864	34	x	x	NOUN
cana-5829	864	35	)	)	PUNCT
cana-5829	864	36	.µ𝐵(y	.µ𝐵(y	NUM
cana-5829	864	37	)	)	PUNCT
cana-5829	865	1	µ𝐴	µ𝐴	ADP
cana-5829	865	2	(	(	PUNCT
cana-5829	865	3	x)+	x)+	NUM
cana-5829	865	4	µ𝐵(y	µ𝐵(y	NUM
cana-5829	865	5	)	)	PUNCT
cana-5829	865	6	∶	∶	NOUN
cana-5829	865	7	xe	xe	PROPN
cana-5829	865	8	,	,	PUNCT
cana-5829	865	9	y𝐹	y𝐹	NOUN
cana-5829	865	10	}	}	PUNCT
cana-5829	865	11	𝑋11	𝑋11	PROPN
cana-5829	865	12	=	=	PUNCT
cana-5829	865	13	(	(	PUNCT
cana-5829	865	14	2	2	NUM
cana-5829	865	15	(	(	PUNCT
cana-5829	865	16	.	.	PUNCT
cana-5829	866	1	8)	8)	NUM
cana-5829	866	2	.	.	PUNCT
cana-5829	867	1	(	(	PUNCT
cana-5829	867	2	.5	.5	NUM
cana-5829	867	3	)	)	PUNCT
cana-5829	867	4	(	(	PUNCT
cana-5829	867	5	.	.	PUNCT
cana-5829	868	1	8)	8)	NUM
cana-5829	868	2	+	+	CCONJ
cana-5829	868	3	(	(	PUNCT
cana-5829	868	4	.5	.5	NUM
cana-5829	868	5	)	)	PUNCT
cana-5829	868	6	,	,	PUNCT
cana-5829	868	7	2(1	2(1	NUM
cana-5829	868	8	)	)	PUNCT
cana-5829	868	9	.	.	PUNCT
cana-5829	869	1	(	(	PUNCT
cana-5829	869	2	1	1	X
cana-5829	869	3	)	)	PUNCT
cana-5829	869	4	1	1	NUM
cana-5829	870	1	+	+	CCONJ
cana-5829	870	2	1	1	NUM
cana-5829	870	3	)	)	PUNCT
cana-5829	870	4	𝑋12	𝑋12	PROPN
cana-5829	870	5	=	=	PUNCT
cana-5829	870	6	(	(	PUNCT
cana-5829	870	7	2(0	2(0	NUM
cana-5829	870	8	)	)	PUNCT
cana-5829	870	9	.	.	PUNCT
cana-5829	871	1	(	(	PUNCT
cana-5829	871	2	0	0	NUM
cana-5829	871	3	)	)	PUNCT
cana-5829	871	4	(	(	PUNCT
cana-5829	871	5	0	0	NUM
cana-5829	871	6	)	)	PUNCT
cana-5829	871	7	+	+	CCONJ
cana-5829	871	8	(	(	PUNCT
cana-5829	871	9	0	0	NUM
cana-5829	871	10	)	)	PUNCT
cana-5829	871	11	,	,	PUNCT
cana-5829	871	12	2(.3	2(.3	NUM
cana-5829	871	13	)	)	PUNCT
cana-5829	871	14	.	.	PUNCT
cana-5829	872	1	(	(	PUNCT
cana-5829	872	2	5	5	NUM
cana-5829	872	3	)	)	PUNCT
cana-5829	872	4	(	(	PUNCT
cana-5829	872	5	.3	.3	NUM
cana-5829	872	6	)	)	PUNCT
cana-5829	873	1	+	+	CCONJ
cana-5829	873	2	(	(	PUNCT
cana-5829	873	3	.5	.5	NUM
cana-5829	873	4	)	)	PUNCT
cana-5829	873	5	)	)	PUNCT
cana-5829	874	1	communications	communication	NOUN
cana-5829	874	2	on	on	ADP
cana-5829	874	3	applied	apply	VERB
cana-5829	874	4	nonlinear	nonlinear	ADJ
cana-5829	874	5	analysis	analysis	NOUN
cana-5829	874	6	issn	issn	NOUN
cana-5829	874	7	:	:	PUNCT
cana-5829	874	8	1074	1074	NUM
cana-5829	874	9	-	-	PUNCT
cana-5829	874	10	133x	133x	NUM
cana-5829	874	11	vol	vol	VERB
cana-5829	874	12	32	32	NUM
cana-5829	874	13	no	no	NOUN
cana-5829	874	14	.	.	PUNCT
cana-5829	875	1	10s	10	NOUN
cana-5829	875	2	(	(	PUNCT
cana-5829	875	3	2025	2025	NUM
cana-5829	875	4	)	)	PUNCT
cana-5829	875	5	2952	2952	NUM
cana-5829	875	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5829	876	1	𝑋21	𝑋21	NOUN
cana-5829	876	2	=	=	SYM
cana-5829	876	3	(	(	PUNCT
cana-5829	876	4	2	2	NUM
cana-5829	876	5	(	(	PUNCT
cana-5829	876	6	.	.	NOUN
cana-5829	876	7	2	2	NUM
cana-5829	876	8	)	)	PUNCT
cana-5829	876	9	.	.	PUNCT
cana-5829	877	1	(	(	PUNCT
cana-5829	877	2	.3	.3	NUM
cana-5829	877	3	)	)	PUNCT
cana-5829	877	4	(	(	PUNCT
cana-5829	877	5	.	.	NOUN
cana-5829	878	1	2	2	X
cana-5829	878	2	)	)	PUNCT
cana-5829	878	3	+	+	CCONJ
cana-5829	878	4	(	(	PUNCT
cana-5829	878	5	.3	.3	NUM
cana-5829	878	6	)	)	PUNCT
cana-5829	878	7	,	,	PUNCT
cana-5829	878	8	2(.8	2(.8	NOUN
cana-5829	878	9	)	)	PUNCT
cana-5829	878	10	.	.	PUNCT
cana-5829	879	1	(	(	PUNCT
cana-5829	879	2	.8	.8	NUM
cana-5829	879	3	)	)	PUNCT
cana-5829	879	4	(	(	PUNCT
cana-5829	879	5	.8	.8	NUM
cana-5829	879	6	)	)	PUNCT
cana-5829	880	1	+	+	CCONJ
cana-5829	880	2	(	(	PUNCT
cana-5829	880	3	.8	.8	NUM
cana-5829	880	4	)	)	PUNCT
cana-5829	880	5	)	)	PUNCT
cana-5829	881	1	𝑋22	𝑋22	VERB
cana-5829	881	2	=	=	PUNCT
cana-5829	881	3	(	(	PUNCT
cana-5829	881	4	2	2	NUM
cana-5829	881	5	(	(	PUNCT
cana-5829	881	6	.	.	NOUN
cana-5829	881	7	7	7	NUM
cana-5829	881	8	)	)	PUNCT
cana-5829	881	9	.	.	PUNCT
cana-5829	882	1	(	(	PUNCT
cana-5829	882	2	.8	.8	NUM
cana-5829	882	3	)	)	PUNCT
cana-5829	882	4	(	(	PUNCT
cana-5829	882	5	.	.	PUNCT
cana-5829	883	1	7	7	X
cana-5829	883	2	)	)	PUNCT
cana-5829	883	3	+	+	CCONJ
cana-5829	883	4	(	(	PUNCT
cana-5829	883	5	.8	.8	NUM
cana-5829	883	6	)	)	PUNCT
cana-5829	883	7	,	,	PUNCT
cana-5829	883	8	2(.8	2(.8	NOUN
cana-5829	883	9	)	)	PUNCT
cana-5829	883	10	.	.	PUNCT
cana-5829	884	1	(	(	PUNCT
cana-5829	884	2	7	7	NUM
cana-5829	884	3	)	)	PUNCT
cana-5829	884	4	(	(	PUNCT
cana-5829	884	5	.8	.8	NUM
cana-5829	884	6	)	)	PUNCT
cana-5829	885	1	+	+	CCONJ
cana-5829	885	2	(	(	PUNCT
cana-5829	885	3	.7	.7	PROPN
cana-5829	885	4	)	)	PUNCT
cana-5829	885	5	)	)	PUNCT
cana-5829	886	1	𝑋11	𝑋11	PROPN
cana-5829	886	2	=	=	PRON
cana-5829	886	3	{	{	PUNCT
cana-5829	886	4	.6	.6	X
cana-5829	886	5	,	,	PUNCT
cana-5829	886	6	1	1	X
cana-5829	886	7	}	}	PUNCT
cana-5829	886	8	𝑋12	𝑋12	VERB
cana-5829	886	9	=	=	SYM
cana-5829	886	10	{	{	PUNCT
cana-5829	886	11	0	0	NUM
cana-5829	886	12	,	,	PUNCT
cana-5829	886	13	.4	.4	NUM
cana-5829	886	14	}	}	PUNCT
cana-5829	886	15	𝑋21	𝑋21	VERB
cana-5829	886	16	=	=	PRON
cana-5829	886	17	{	{	PUNCT
cana-5829	886	18	.2	.2	NUM
cana-5829	886	19	,	,	PUNCT
cana-5829	886	20	.8	.8	NUM
cana-5829	886	21	}	}	PUNCT
cana-5829	886	22	𝑋22	𝑋22	VERB
cana-5829	886	23	=	=	PRON
cana-5829	886	24	{	{	PUNCT
cana-5829	886	25	.7	.7	PROPN
cana-5829	886	26	,	,	PUNCT
cana-5829	886	27	.7	.7	PROPN
cana-5829	886	28	}	}	PUNCT
cana-5829	886	29	we	we	PRON
cana-5829	886	30	have	have	VERB
cana-5829	886	31	norm𝐴̅	norm𝐴̅	PROPN
cana-5829	886	32	𝐸$	𝐸$	PROPN
cana-5829	886	33	𝑁𝑜𝑟𝑚	𝑁𝑜𝑟𝑚	PROPN
cana-5829	886	34	�	�	NOUN
cana-5829	886	35	̅	̅	NOUN
cana-5829	886	36	�	�	NOUN
cana-5829	886	37	𝐹	𝐹	NOUN
cana-5829	886	38	=	=	SYM
cana-5829	886	39	(	(	PUNCT
cana-5829	886	40	(	(	PUNCT
cana-5829	886	41	.6	.6	NUM
cana-5829	886	42	,	,	PUNCT
cana-5829	886	43	.1	.1	NUM
cana-5829	886	44	)	)	PUNCT
cana-5829	886	45	(	(	PUNCT
cana-5829	886	46	0	0	NUM
cana-5829	886	47	,	,	PUNCT
cana-5829	886	48	.4	.4	NUM
cana-5829	886	49	)	)	PUNCT
cana-5829	886	50	(	(	PUNCT
cana-5829	886	51	.2	.2	NUM
cana-5829	886	52	,	,	PUNCT
cana-5829	886	53	.8	.8	NUM
cana-5829	886	54	)	)	PUNCT
cana-5829	886	55	(	(	PUNCT
cana-5829	886	56	.7	.7	PROPN
cana-5829	886	57	,	,	PUNCT
cana-5829	886	58	.7	.7	PROPN
cana-5829	886	59	)	)	PUNCT
cana-5829	886	60	)	)	PUNCT
cana-5829	886	61	is	be	AUX
cana-5829	886	62	also	also	ADV
cana-5829	886	63	intuitionistic	intuitionistic	ADJ
cana-5829	886	64	fuzzy	fuzzy	ADJ
cana-5829	886	65	matrix	matrix	NOUN
cana-5829	886	66	.	.	PUNCT
cana-5829	887	1	theorem5.2.8	theorem5.2.8	ADV
cana-5829	887	2	:	:	PUNCT
cana-5829	887	3	if	if	SCONJ
cana-5829	887	4	e	e	PROPN
cana-5829	887	5	and	and	CCONJ
cana-5829	887	6	f	f	PROPN
cana-5829	887	7	be	be	AUX
cana-5829	887	8	two	two	NUM
cana-5829	887	9	universal	universal	ADJ
cana-5829	887	10	sets	set	NOUN
cana-5829	887	11	.	.	PUNCT
cana-5829	888	1	for	for	ADP
cana-5829	888	2	every	every	DET
cana-5829	888	3	normalization	normalization	NOUN
cana-5829	888	4	of	of	ADP
cana-5829	888	5	an	an	DET
cana-5829	888	6	intuitionistic	intuitionistic	ADJ
cana-5829	888	7	fuzzy	fuzzy	ADJ
cana-5829	888	8	matrices	matrix	NOUN
cana-5829	888	9	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	888	10	̅̅̅̅	̅̅̅̅	ADJ
cana-5829	888	11	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-5829	888	12	𝐵𝐹	𝐵𝐹	PROPN
cana-5829	888	13	̅̅̅̅	̅̅̅̅	NOUN
cana-5829	888	14	are	be	AUX
cana-5829	888	15	in	in	ADP
cana-5829	888	16	e	e	PROPN
cana-5829	888	17	and	and	CCONJ
cana-5829	888	18	f	f	PROPN
cana-5829	889	1	then	then	ADV
cana-5829	889	2	norm𝐴̅	norm𝐴̅	PROPN
cana-5829	889	3	𝐸	𝐸	PROPN
cana-5829	889	4	∗	∗	NOUN
cana-5829	889	5	𝑁𝑜𝑟𝑚	𝑁𝑜𝑟𝑚	PROPN
cana-5829	889	6	�	�	NOUN
cana-5829	889	7	̅	̅	NOUN
cana-5829	889	8	�	�	NOUN
cana-5829	889	9	𝐹is	𝐹i	VERB
cana-5829	889	10	also	also	ADV
cana-5829	889	11	normalization	normalization	NOUN
cana-5829	889	12	of	of	ADP
cana-5829	889	13	an	an	DET
cana-5829	889	14	intuitionistic	intuitionistic	ADJ
cana-5829	889	15	fuzzy	fuzzy	ADJ
cana-5829	889	16	matrices	matrix	NOUN
cana-5829	889	17	.	.	PUNCT
cana-5829	890	1	proof	proof	NOUN
cana-5829	890	2	:	:	PUNCT
cana-5829	890	3	if	if	SCONJ
cana-5829	890	4	𝑁𝑜𝑟𝑚𝐴	𝑁𝑜𝑟𝑚𝐴	PROPN
cana-5829	890	5	and	and	CCONJ
cana-5829	890	6	𝑁𝑜𝑟𝑚𝐵	𝑁𝑜𝑟𝑚𝐵	PROPN
cana-5829	890	7	are	be	AUX
cana-5829	890	8	two	two	NUM
cana-5829	890	9	normalization	normalization	NOUN
cana-5829	890	10	intuitionistic	intuitionistic	ADJ
cana-5829	890	11	fuzzy	fuzzy	ADJ
cana-5829	890	12	matrices	matrix	NOUN
cana-5829	890	13	over	over	ADP
cana-5829	890	14	different	different	ADJ
cana-5829	890	15	unive𝑟𝑠𝑒𝑠	unive𝑟𝑠𝑒𝑠	ADJ
cana-5829	890	16	𝑠𝑒𝑡𝑠	𝑠𝑒𝑡𝑠	PROPN
cana-5829	890	17	𝐸	𝐸	PROPN
cana-5829	891	1	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-5829	891	2	𝐹.	𝐹.	NOUN
cana-5829	891	3	𝐼𝑓	𝐼𝑓	PROPN
cana-5829	891	4	𝑤𝑒	𝑤𝑒	PROPN
cana-5829	891	5	𝑐𝑜𝑛𝑠𝑖𝑑𝑒𝑟	𝑐𝑜𝑛𝑠𝑖𝑑𝑒𝑟	PROPN
cana-5829	891	6	𝑡𝑤𝑜	𝑡𝑤𝑜	PROPN
cana-5829	891	7	2	2	NUM
cana-5829	891	8	×	×	NOUN
cana-5829	891	9	2	2	NUM
cana-5829	891	10	𝑚𝑎𝑡𝑟𝑖𝑥	𝑚𝑎𝑡𝑟𝑖𝑥	ADJ
cana-5829	891	11	𝑁𝑜𝑟𝑚̅̅	𝑁𝑜𝑟𝑚̅̅	PROPN
cana-5829	891	12	̅̅	̅̅	PROPN
cana-5829	891	13	̅̅	̅̅	PROPN
cana-5829	891	14	̅̅	̅̅	PROPN
cana-5829	891	15	𝐴	𝐴	PROPN
cana-5829	891	16	=(	=(	NOUN
cana-5829	891	17	(	(	PUNCT
cana-5829	891	18	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	891	19	(	(	PUNCT
cana-5829	891	20	𝑥	𝑥	NOUN
cana-5829	891	21	)	)	PUNCT
cana-5829	891	22	𝑁𝑜𝑟𝑚µ𝐸11(𝑥	𝑁𝑜𝑟𝑚µ𝐸11(𝑥	NOUN
cana-5829	891	23	)	)	PUNCT
cana-5829	891	24	)	)	PUNCT
cana-5829	892	1	(	(	PUNCT
cana-5829	892	2	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	X
cana-5829	892	3	(	(	PUNCT
cana-5829	892	4	𝑥	𝑥	NOUN
cana-5829	892	5	)	)	PUNCT
cana-5829	892	6	𝑁𝑜𝑟𝑚µ𝐸12(𝑥	𝑁𝑜𝑟𝑚µ𝐸12(𝑥	NOUN
cana-5829	892	7	)	)	PUNCT
cana-5829	892	8	)	)	PUNCT
cana-5829	892	9	(	(	PUNCT
cana-5829	892	10	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	X
cana-5829	892	11	(	(	PUNCT
cana-5829	892	12	𝑥	𝑥	NOUN
cana-5829	892	13	)	)	PUNCT
cana-5829	892	14	𝑁𝑜𝑟𝑚µ𝐸21	𝑁𝑜𝑟𝑚µ𝐸21	NOUN
cana-5829	892	15	(	(	PUNCT
cana-5829	892	16	𝑥	𝑥	NOUN
cana-5829	892	17	)	)	PUNCT
cana-5829	892	18	)	)	PUNCT
cana-5829	892	19	(	(	PUNCT
cana-5829	892	20	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	X
cana-5829	892	21	(	(	PUNCT
cana-5829	892	22	𝑥	𝑥	NOUN
cana-5829	892	23	)	)	PUNCT
cana-5829	892	24	𝑁𝑜𝑟𝑚µ𝐸22	𝑁𝑜𝑟𝑚µ𝐸22	NOUN
cana-5829	892	25	(	(	PUNCT
cana-5829	892	26	𝑥	𝑥	NOUN
cana-5829	892	27	)	)	PUNCT
cana-5829	892	28	)	)	PUNCT
cana-5829	892	29	)	)	PUNCT
cana-5829	892	30	and	and	CCONJ
cana-5829	893	1	𝑁𝑜𝑟𝑚̅̅	𝑁𝑜𝑟𝑚̅̅	PROPN
cana-5829	893	2	̅̅	̅̅	PROPN
cana-5829	893	3	̅̅	̅̅	PROPN
cana-5829	893	4	̅̅	̅̅	PROPN
cana-5829	893	5	𝐵=	𝐵=	PROPN
cana-5829	893	6	(	(	PUNCT
cana-5829	893	7	(	(	PUNCT
cana-5829	893	8	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	893	9	(	(	PUNCT
cana-5829	893	10	𝑦	𝑦	NOUN
cana-5829	893	11	)	)	PUNCT
cana-5829	893	12	𝑁𝑜𝑟𝑚𝛾𝐹11(𝑦	𝑁𝑜𝑟𝑚𝛾𝐹11(𝑦	NUM
cana-5829	893	13	)	)	PUNCT
cana-5829	893	14	)	)	PUNCT
cana-5829	893	15	(	(	PUNCT
cana-5829	893	16	𝑁𝑜𝑟𝑚𝛿𝐹12	𝑁𝑜𝑟𝑚𝛿𝐹12	X
cana-5829	893	17	(	(	PUNCT
cana-5829	893	18	𝑦	𝑦	NOUN
cana-5829	893	19	)	)	PUNCT
cana-5829	893	20	𝑁𝑜𝑟𝑚𝛾𝐹12(𝑦	𝑁𝑜𝑟𝑚𝛾𝐹12(𝑦	NOUN
cana-5829	893	21	)	)	PUNCT
cana-5829	893	22	)	)	PUNCT
cana-5829	893	23	(	(	PUNCT
cana-5829	893	24	𝑁𝑜𝑟𝑚𝛿𝐹21	𝑁𝑜𝑟𝑚𝛿𝐹21	X
cana-5829	893	25	(	(	PUNCT
cana-5829	893	26	𝑦	𝑦	NOUN
cana-5829	893	27	)	)	PUNCT
cana-5829	893	28	𝑁𝑜𝑟𝑚𝛾𝐹21	𝑁𝑜𝑟𝑚𝛾𝐹21	ADV
cana-5829	893	29	(	(	PUNCT
cana-5829	893	30	𝑦	𝑦	NOUN
cana-5829	893	31	)	)	PUNCT
cana-5829	893	32	)	)	PUNCT
cana-5829	893	33	(	(	PUNCT
cana-5829	893	34	𝑁𝑜𝑟𝑚𝛿𝐹22	𝑁𝑜𝑟𝑚𝛿𝐹22	X
cana-5829	893	35	(	(	PUNCT
cana-5829	893	36	𝑦	𝑦	NOUN
cana-5829	893	37	)	)	PUNCT
cana-5829	893	38	𝑁𝑜𝑟𝑚𝛾𝐹22	𝑁𝑜𝑟𝑚𝛾𝐹22	X
cana-5829	893	39	(	(	PUNCT
cana-5829	893	40	𝑦	𝑦	NOUN
cana-5829	893	41	)	)	PUNCT
cana-5829	893	42	)	)	PUNCT
cana-5829	893	43	)	)	PUNCT
cana-5829	894	1	𝑁𝑜𝑟𝑚̅̅	𝑁𝑜𝑟𝑚̅̅	NOUN
cana-5829	894	2	̅̅	̅̅	PROPN
cana-5829	894	3	̅̅	̅̅	PROPN
cana-5829	894	4	̅̅	̅̅	PROPN
cana-5829	894	5	𝐴	𝐴	PROPN
cana-5829	894	6	∗	∗	NOUN
cana-5829	894	7	𝑁𝑜𝑟𝑚̅̅	𝑁𝑜𝑟𝑚̅̅	PROPN
cana-5829	894	8	̅̅	̅̅	PROPN
cana-5829	894	9	̅̅	̅̅	PROPN
cana-5829	894	10	̅̅	̅̅	PROPN
cana-5829	894	11	𝐵	𝐵	PROPN
cana-5829	894	12	=	=	PUNCT
cana-5829	894	13	(	(	PUNCT
cana-5829	894	14	(	(	PUNCT
cana-5829	894	15	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	894	16	(	(	PUNCT
cana-5829	894	17	𝑥	𝑥	NOUN
cana-5829	894	18	)	)	PUNCT
cana-5829	894	19	𝑁𝑜𝑟𝑚µ𝐸11	𝑁𝑜𝑟𝑚µ𝐸11	NOUN
cana-5829	894	20	(	(	PUNCT
cana-5829	894	21	𝑥	𝑥	NOUN
cana-5829	894	22	)	)	PUNCT
cana-5829	894	23	)	)	PUNCT
cana-5829	894	24	(	(	PUNCT
cana-5829	894	25	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	X
cana-5829	894	26	(	(	PUNCT
cana-5829	894	27	𝑥	𝑥	NOUN
cana-5829	894	28	)	)	PUNCT
cana-5829	894	29	𝑁𝑜𝑟𝑚µ𝐸12	𝑁𝑜𝑟𝑚µ𝐸12	NOUN
cana-5829	894	30	(	(	PUNCT
cana-5829	894	31	𝑥	𝑥	NOUN
cana-5829	894	32	)	)	PUNCT
cana-5829	894	33	)	)	PUNCT
cana-5829	894	34	(	(	PUNCT
cana-5829	894	35	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	X
cana-5829	894	36	(	(	PUNCT
cana-5829	894	37	𝑥	𝑥	NOUN
cana-5829	894	38	)	)	PUNCT
cana-5829	894	39	𝑁𝑜𝑟𝑚µ𝐸21	𝑁𝑜𝑟𝑚µ𝐸21	NOUN
cana-5829	894	40	(	(	PUNCT
cana-5829	894	41	𝑥	𝑥	NOUN
cana-5829	894	42	)	)	PUNCT
cana-5829	894	43	)	)	PUNCT
cana-5829	894	44	(	(	PUNCT
cana-5829	894	45	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	X
cana-5829	894	46	(	(	PUNCT
cana-5829	894	47	𝑥	𝑥	NOUN
cana-5829	894	48	)	)	PUNCT
cana-5829	894	49	𝑁𝑜𝑟𝑚µ𝐸22	𝑁𝑜𝑟𝑚µ𝐸22	NOUN
cana-5829	894	50	(	(	PUNCT
cana-5829	894	51	𝑥	𝑥	NOUN
cana-5829	894	52	)	)	PUNCT
cana-5829	894	53	)	)	PUNCT
cana-5829	894	54	)	)	PUNCT
cana-5829	894	55	∗	∗	NOUN
cana-5829	894	56	(	(	PUNCT
cana-5829	894	57	(	(	PUNCT
cana-5829	894	58	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	894	59	(	(	PUNCT
cana-5829	894	60	𝑦	𝑦	NOUN
cana-5829	894	61	)	)	PUNCT
cana-5829	894	62	𝑁𝑜𝑟𝑚𝛾𝐹11(𝑦	𝑁𝑜𝑟𝑚𝛾𝐹11(𝑦	NUM
cana-5829	894	63	)	)	PUNCT
cana-5829	894	64	)	)	PUNCT
cana-5829	894	65	(	(	PUNCT
cana-5829	894	66	𝑁𝑜𝑟𝑚𝛿𝐹12	𝑁𝑜𝑟𝑚𝛿𝐹12	X
cana-5829	894	67	(	(	PUNCT
cana-5829	894	68	𝑦	𝑦	NOUN
cana-5829	894	69	)	)	PUNCT
cana-5829	894	70	𝑁𝑜𝑟𝑚𝛾𝐹12(𝑦	𝑁𝑜𝑟𝑚𝛾𝐹12(𝑦	NOUN
cana-5829	894	71	)	)	PUNCT
cana-5829	894	72	)	)	PUNCT
cana-5829	894	73	(	(	PUNCT
cana-5829	894	74	𝑁𝑜𝑟𝑚𝛿𝐹21	𝑁𝑜𝑟𝑚𝛿𝐹21	X
cana-5829	894	75	(	(	PUNCT
cana-5829	894	76	𝑦	𝑦	NOUN
cana-5829	894	77	)	)	PUNCT
cana-5829	894	78	𝑁𝑜𝑟𝑚𝛾𝐹21	𝑁𝑜𝑟𝑚𝛾𝐹21	ADV
cana-5829	894	79	(	(	PUNCT
cana-5829	894	80	𝑦	𝑦	NOUN
cana-5829	894	81	)	)	PUNCT
cana-5829	894	82	)	)	PUNCT
cana-5829	894	83	(	(	PUNCT
cana-5829	894	84	𝑁𝑜𝑟𝑚𝛿𝐹22	𝑁𝑜𝑟𝑚𝛿𝐹22	X
cana-5829	894	85	(	(	PUNCT
cana-5829	894	86	𝑦	𝑦	NOUN
cana-5829	894	87	)	)	PUNCT
cana-5829	894	88	𝑁𝑜𝑟𝑚𝛾𝐹22	𝑁𝑜𝑟𝑚𝛾𝐹22	X
cana-5829	894	89	(	(	PUNCT
cana-5829	894	90	𝑦	𝑦	NOUN
cana-5829	894	91	)	)	PUNCT
cana-5829	894	92	)	)	PUNCT
cana-5829	894	93	)	)	PUNCT
cana-5829	895	1	𝑋11	𝑋11	PROPN
cana-5829	895	2	=(	=(	NOUN
cana-5829	895	3	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	895	4	(	(	PUNCT
cana-5829	895	5	𝑥	𝑥	NOUN
cana-5829	895	6	)	)	PUNCT
cana-5829	895	7	𝑁𝑜𝑟𝑚µ𝐸11(𝑥	𝑁𝑜𝑟𝑚µ𝐸11(𝑥	NOUN
cana-5829	895	8	)	)	PUNCT
cana-5829	895	9	)	)	PUNCT
cana-5829	895	10	∗	∗	NOUN
cana-5829	895	11	(	(	PUNCT
cana-5829	895	12	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	895	13	(	(	PUNCT
cana-5829	895	14	𝑦	𝑦	NOUN
cana-5829	895	15	)	)	PUNCT
cana-5829	895	16	𝑁𝑜𝑟𝑚𝛾𝐹11(𝑦	𝑁𝑜𝑟𝑚𝛾𝐹11(𝑦	NUM
cana-5829	895	17	)	)	PUNCT
cana-5829	895	18	)	)	PUNCT
cana-5829	896	1	𝑋12	𝑋12	PROPN
cana-5829	896	2	=(	=(	NOUN
cana-5829	896	3	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	NOUN
cana-5829	896	4	(	(	PUNCT
cana-5829	896	5	𝑥	𝑥	NOUN
cana-5829	896	6	)	)	PUNCT
cana-5829	896	7	𝑁𝑜𝑟𝑚µ𝐸12(𝑥	𝑁𝑜𝑟𝑚µ𝐸12(𝑥	NOUN
cana-5829	896	8	)	)	PUNCT
cana-5829	896	9	)	)	PUNCT
cana-5829	897	1	∗	∗	NOUN
cana-5829	897	2	(	(	PUNCT
cana-5829	897	3	𝑁𝑜𝑟𝑚𝛿𝐹12	𝑁𝑜𝑟𝑚𝛿𝐹12	X
cana-5829	897	4	(	(	PUNCT
cana-5829	897	5	𝑦	𝑦	NOUN
cana-5829	897	6	)	)	PUNCT
cana-5829	897	7	𝑁𝑜𝑟𝑚𝛾𝐹12(𝑦	𝑁𝑜𝑟𝑚𝛾𝐹12(𝑦	NOUN
cana-5829	897	8	)	)	PUNCT
cana-5829	897	9	)	)	PUNCT
cana-5829	898	1	𝑋21	𝑋21	VERB
cana-5829	898	2	=(	=(	NOUN
cana-5829	898	3	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	NOUN
cana-5829	898	4	(	(	PUNCT
cana-5829	898	5	𝑥	𝑥	NOUN
cana-5829	898	6	)	)	PUNCT
cana-5829	898	7	𝑁𝑜𝑟𝑚µ𝐸21	𝑁𝑜𝑟𝑚µ𝐸21	NOUN
cana-5829	898	8	(	(	PUNCT
cana-5829	898	9	𝑥	𝑥	NOUN
cana-5829	898	10	)	)	PUNCT
cana-5829	898	11	)	)	PUNCT
cana-5829	898	12	∗	∗	NOUN
cana-5829	898	13	(	(	PUNCT
cana-5829	898	14	𝑁𝑜𝑟𝑚𝛿𝐹21	𝑁𝑜𝑟𝑚𝛿𝐹21	X
cana-5829	898	15	(	(	PUNCT
cana-5829	898	16	𝑦	𝑦	NOUN
cana-5829	898	17	)	)	PUNCT
cana-5829	898	18	𝑁𝑜𝑟𝑚𝛾𝐹21	𝑁𝑜𝑟𝑚𝛾𝐹21	ADV
cana-5829	898	19	(	(	PUNCT
cana-5829	898	20	𝑦	𝑦	NOUN
cana-5829	898	21	)	)	PUNCT
cana-5829	898	22	)	)	PUNCT
cana-5829	899	1	𝑋22	𝑋22	VERB
cana-5829	899	2	=(	=(	PROPN
cana-5829	899	3	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	PROPN
cana-5829	899	4	(	(	PUNCT
cana-5829	899	5	𝑥	𝑥	NOUN
cana-5829	899	6	)	)	PUNCT
cana-5829	899	7	𝑁𝑜𝑟𝑚µ𝐸22	𝑁𝑜𝑟𝑚µ𝐸22	NOUN
cana-5829	899	8	(	(	PUNCT
cana-5829	899	9	𝑥	𝑥	NOUN
cana-5829	899	10	)	)	PUNCT
cana-5829	899	11	)	)	PUNCT
cana-5829	899	12	∗	∗	NOUN
cana-5829	899	13	(	(	PUNCT
cana-5829	899	14	𝑁𝑜𝑟𝑚𝛿𝐹22	𝑁𝑜𝑟𝑚𝛿𝐹22	X
cana-5829	899	15	(	(	PUNCT
cana-5829	899	16	𝑦	𝑦	NOUN
cana-5829	899	17	)	)	PUNCT
cana-5829	899	18	𝑁𝑜𝑟𝑚𝛾𝐹22	𝑁𝑜𝑟𝑚𝛾𝐹22	X
cana-5829	899	19	(	(	PUNCT
cana-5829	899	20	𝑦	𝑦	NOUN
cana-5829	899	21	)	)	PUNCT
cana-5829	899	22	)	)	PUNCT
cana-5829	900	1	𝐴𝑝𝑝𝑙𝑦𝑖𝑛𝑔	𝐴𝑝𝑝𝑙𝑦𝑖𝑛𝑔	PROPN
cana-5829	900	2	𝑓𝑜𝑟𝑚𝑢𝑙𝑎	𝑓𝑜𝑟𝑚𝑢𝑙𝑎	VERB
cana-5829	900	3	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	900	4	̅̅̅̅	̅̅̅̅	ADJ
cana-5829	900	5	∗	∗	NOUN
cana-5829	900	6	𝐵𝐹	𝐵𝐹	PROPN
cana-5829	900	7	̅̅̅̅	̅̅̅̅	NOUN
cana-5829	900	8	=	=	X
cana-5829	900	9	{	{	PUNCT
cana-5829	900	10	〈	〈	PROPN
cana-5829	900	11	x	x	PROPN
cana-5829	900	12	,	,	PUNCT
cana-5829	900	13	y	y	PROPN
cana-5829	900	14	〉	〉	NOUN
cana-5829	900	15	,	,	PUNCT
cana-5829	900	16	𝜗𝐴(x)+𝜗𝐵(y	𝜗𝐴(x)+𝜗𝐵(y	NUM
cana-5829	900	17	)	)	PUNCT
cana-5829	900	18	2(𝜗𝐴(x).𝜗𝐵(y)+1	2(𝜗𝐴(x).𝜗𝐵(y)+1	NUM
cana-5829	900	19	)	)	PUNCT
cana-5829	900	20	,	,	PUNCT
cana-5829	900	21	µ𝐴	µ𝐴	SCONJ
cana-5829	900	22	(	(	PUNCT
cana-5829	900	23	x)+	x)+	NUM
cana-5829	900	24	µ𝐵(y	µ𝐵(y	NUM
cana-5829	900	25	)	)	PUNCT
cana-5829	900	26	2(µ𝐴(x).µ𝐵(y)+1	2(µ𝐴(x).µ𝐵(y)+1	NUM
cana-5829	900	27	)	)	PUNCT
cana-5829	900	28	:	:	PUNCT
cana-5829	901	1	xe	xe	PROPN
cana-5829	901	2	,	,	PUNCT
cana-5829	901	3	y𝐹	y𝐹	NOUN
cana-5829	901	4	}	}	PUNCT
cana-5829	902	1	𝑋11	𝑋11	PROPN
cana-5829	902	2	=	=	PUNCT
cana-5829	902	3	(	(	PUNCT
cana-5829	902	4	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	902	5	(	(	PUNCT
cana-5829	902	6	𝑥	𝑥	NOUN
cana-5829	902	7	)	)	PUNCT
cana-5829	902	8	+	+	CCONJ
cana-5829	902	9	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	902	10	(	(	PUNCT
cana-5829	902	11	𝑦	𝑦	NOUN
cana-5829	902	12	)	)	PUNCT
cana-5829	902	13	2(𝑁𝑜𝑟𝑚𝜗𝐸11	2(𝑁𝑜𝑟𝑚𝜗𝐸11	NUM
cana-5829	902	14	(	(	PUNCT
cana-5829	902	15	𝑥	𝑥	NOUN
cana-5829	902	16	)	)	PUNCT
cana-5829	902	17	.	.	PUNCT
cana-5829	903	1	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	903	2	(	(	PUNCT
cana-5829	903	3	𝑦	𝑦	NOUN
cana-5829	903	4	)	)	PUNCT
cana-5829	903	5	+	+	CCONJ
cana-5829	903	6	1	1	NUM
cana-5829	903	7	)	)	PUNCT
cana-5829	903	8	,	,	PUNCT
cana-5829	903	9	𝑁𝑜𝑟𝑚µ𝐸11	𝑁𝑜𝑟𝑚µ𝐸11	X
cana-5829	903	10	(	(	PUNCT
cana-5829	903	11	𝑥	𝑥	NOUN
cana-5829	903	12	)	)	PUNCT
cana-5829	903	13	+	+	CCONJ
cana-5829	903	14	𝑁𝑜𝑟𝑚𝛾𝐹11	𝑁𝑜𝑟𝑚𝛾𝐹11	X
cana-5829	903	15	(	(	PUNCT
cana-5829	903	16	𝑦	𝑦	NOUN
cana-5829	903	17	)	)	PUNCT
cana-5829	903	18	2(𝑁𝑜𝑟𝑚µ𝐸11	2(𝑁𝑜𝑟𝑚µ𝐸11	NUM
cana-5829	903	19	(	(	PUNCT
cana-5829	903	20	𝑥	𝑥	NOUN
cana-5829	903	21	)	)	PUNCT
cana-5829	903	22	.	.	PUNCT
cana-5829	904	1	𝑁𝑜𝑟𝑚𝛾𝐹11	𝑁𝑜𝑟𝑚𝛾𝐹11	PROPN
cana-5829	904	2	(	(	PUNCT
cana-5829	904	3	𝑦	𝑦	NOUN
cana-5829	904	4	)	)	PUNCT
cana-5829	904	5	+	+	CCONJ
cana-5829	904	6	1	1	NUM
cana-5829	904	7	)	)	PUNCT
cana-5829	904	8	)	)	PUNCT
cana-5829	905	1	𝑋12	𝑋12	PROPN
cana-5829	905	2	=	=	PUNCT
cana-5829	905	3	(	(	PUNCT
cana-5829	905	4	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	X
cana-5829	905	5	(	(	PUNCT
cana-5829	905	6	𝑥	𝑥	NOUN
cana-5829	905	7	)	)	PUNCT
cana-5829	906	1	+	+	CCONJ
cana-5829	906	2	𝑁𝑜𝑟𝑚𝛿𝐹12	𝑁𝑜𝑟𝑚𝛿𝐹12	PRON
cana-5829	906	3	(	(	PUNCT
cana-5829	906	4	𝑦	𝑦	NOUN
cana-5829	906	5	)	)	PUNCT
cana-5829	906	6	2(𝑁𝑜𝑟𝑚𝜗𝐸12	2(𝑁𝑜𝑟𝑚𝜗𝐸12	NUM
cana-5829	906	7	(	(	PUNCT
cana-5829	906	8	𝑥	𝑥	NOUN
cana-5829	906	9	)	)	PUNCT
cana-5829	906	10	.	.	PUNCT
cana-5829	906	11	𝑁𝑜𝑟𝑚𝛿𝐹12	𝑁𝑜𝑟𝑚𝛿𝐹12	PROPN
cana-5829	907	1	(	(	PUNCT
cana-5829	907	2	𝑦	𝑦	NOUN
cana-5829	907	3	)	)	PUNCT
cana-5829	908	1	+	+	CCONJ
cana-5829	908	2	1	1	NUM
cana-5829	908	3	)	)	PUNCT
cana-5829	908	4	,	,	PUNCT
cana-5829	908	5	𝑁𝑜𝑟𝑚µ𝐸12	𝑁𝑜𝑟𝑚µ𝐸12	X
cana-5829	908	6	(	(	PUNCT
cana-5829	908	7	𝑥	𝑥	NOUN
cana-5829	908	8	)	)	PUNCT
cana-5829	908	9	+	+	CCONJ
cana-5829	908	10	𝑁𝑜𝑟𝑚𝛾𝐹12	𝑁𝑜𝑟𝑚𝛾𝐹12	PRON
cana-5829	908	11	(	(	PUNCT
cana-5829	908	12	𝑦	𝑦	NOUN
cana-5829	908	13	)	)	PUNCT
cana-5829	908	14	2(𝑁𝑜𝑟𝑚µ𝐸12	2(𝑁𝑜𝑟𝑚µ𝐸12	NUM
cana-5829	908	15	(	(	PUNCT
cana-5829	908	16	𝑥	𝑥	NOUN
cana-5829	908	17	)	)	PUNCT
cana-5829	908	18	.	.	PUNCT
cana-5829	909	1	𝑁𝑜𝑟𝑚𝛾𝐹12	𝑁𝑜𝑟𝑚𝛾𝐹12	X
cana-5829	910	1	(	(	PUNCT
cana-5829	910	2	𝑦	𝑦	NOUN
cana-5829	910	3	)	)	PUNCT
cana-5829	911	1	+	+	CCONJ
cana-5829	911	2	1	1	NUM
cana-5829	911	3	)	)	PUNCT
cana-5829	911	4	)	)	PUNCT
cana-5829	912	1	communications	communication	NOUN
cana-5829	912	2	on	on	ADP
cana-5829	912	3	applied	apply	VERB
cana-5829	912	4	nonlinear	nonlinear	ADJ
cana-5829	912	5	analysis	analysis	NOUN
cana-5829	912	6	issn	issn	NOUN
cana-5829	912	7	:	:	PUNCT
cana-5829	912	8	1074	1074	NUM
cana-5829	912	9	-	-	PUNCT
cana-5829	912	10	133x	133x	NUM
cana-5829	912	11	vol	vol	VERB
cana-5829	912	12	32	32	NUM
cana-5829	912	13	no	no	NOUN
cana-5829	912	14	.	.	PUNCT
cana-5829	913	1	10s	10	NOUN
cana-5829	913	2	(	(	PUNCT
cana-5829	913	3	2025	2025	NUM
cana-5829	913	4	)	)	PUNCT
cana-5829	913	5	2953	2953	NUM
cana-5829	913	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5829	914	1	𝑋21	𝑋21	NOUN
cana-5829	914	2	=	=	SYM
cana-5829	914	3	(	(	PUNCT
cana-5829	914	4	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	X
cana-5829	914	5	(	(	PUNCT
cana-5829	914	6	𝑥	𝑥	NOUN
cana-5829	914	7	)	)	PUNCT
cana-5829	915	1	+	+	NUM
cana-5829	915	2	𝑁𝑜𝑟𝑚𝛿𝐹21	𝑁𝑜𝑟𝑚𝛿𝐹21	ADP
cana-5829	915	3	(	(	PUNCT
cana-5829	915	4	𝑦	𝑦	NOUN
cana-5829	915	5	)	)	PUNCT
cana-5829	915	6	2(𝑁𝑜𝑟𝑚𝜗𝐸21	2(𝑁𝑜𝑟𝑚𝜗𝐸21	NUM
cana-5829	915	7	(	(	PUNCT
cana-5829	915	8	𝑥	𝑥	NOUN
cana-5829	915	9	)	)	PUNCT
cana-5829	915	10	.	.	PUNCT
cana-5829	915	11	𝑁𝑜𝑟𝑚𝛿𝐹21	𝑁𝑜𝑟𝑚𝛿𝐹21	PUNCT
cana-5829	915	12	(	(	PUNCT
cana-5829	915	13	𝑦	𝑦	NOUN
cana-5829	915	14	)	)	PUNCT
cana-5829	915	15	+	+	CCONJ
cana-5829	915	16	1	1	NUM
cana-5829	915	17	)	)	PUNCT
cana-5829	915	18	,	,	PUNCT
cana-5829	915	19	𝑁𝑜𝑟𝑚µ𝐸21	𝑁𝑜𝑟𝑚µ𝐸21	INTJ
cana-5829	915	20	(	(	PUNCT
cana-5829	915	21	𝑥	𝑥	NOUN
cana-5829	915	22	)	)	PUNCT
cana-5829	915	23	+	+	CCONJ
cana-5829	915	24	𝑁𝑜𝑟𝑚𝛾𝐹21	𝑁𝑜𝑟𝑚𝛾𝐹21	ADV
cana-5829	915	25	(	(	PUNCT
cana-5829	915	26	𝑦	𝑦	NOUN
cana-5829	915	27	)	)	PUNCT
cana-5829	915	28	2(𝑁𝑜𝑟𝑚µ𝐸21	2(𝑁𝑜𝑟𝑚µ𝐸21	NUM
cana-5829	915	29	(	(	PUNCT
cana-5829	915	30	𝑥	𝑥	NOUN
cana-5829	915	31	)	)	PUNCT
cana-5829	915	32	.	.	PUNCT
cana-5829	916	1	𝑁𝑜𝑟𝑚𝛾𝐹21	𝑁𝑜𝑟𝑚𝛾𝐹21	ADV
cana-5829	916	2	(	(	PUNCT
cana-5829	916	3	𝑦	𝑦	NOUN
cana-5829	916	4	)	)	PUNCT
cana-5829	916	5	+	+	CCONJ
cana-5829	916	6	1	1	NUM
cana-5829	916	7	)	)	PUNCT
cana-5829	916	8	)	)	PUNCT
cana-5829	917	1	𝑋22	𝑋22	VERB
cana-5829	917	2	=	=	PUNCT
cana-5829	917	3	(	(	PUNCT
cana-5829	917	4	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	X
cana-5829	917	5	(	(	PUNCT
cana-5829	917	6	𝑥	𝑥	NOUN
cana-5829	917	7	)	)	PUNCT
cana-5829	918	1	+	+	NUM
cana-5829	918	2	𝑁𝑜𝑟𝑚𝛿𝐹22	𝑁𝑜𝑟𝑚𝛿𝐹22	X
cana-5829	918	3	(	(	PUNCT
cana-5829	918	4	𝑦	𝑦	NOUN
cana-5829	918	5	)	)	PUNCT
cana-5829	918	6	2(𝑁𝑜𝑟𝑚𝜗𝐸11	2(𝑁𝑜𝑟𝑚𝜗𝐸11	NUM
cana-5829	918	7	(	(	PUNCT
cana-5829	918	8	𝑥	𝑥	NOUN
cana-5829	918	9	)	)	PUNCT
cana-5829	918	10	.	.	PUNCT
cana-5829	919	1	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	919	2	(	(	PUNCT
cana-5829	919	3	𝑦	𝑦	NOUN
cana-5829	919	4	)	)	PUNCT
cana-5829	919	5	+	+	CCONJ
cana-5829	919	6	1	1	NUM
cana-5829	919	7	)	)	PUNCT
cana-5829	919	8	,	,	PUNCT
cana-5829	919	9	𝑁𝑜𝑟𝑚µ𝐸22	𝑁𝑜𝑟𝑚µ𝐸22	NOUN
cana-5829	919	10	(	(	PUNCT
cana-5829	919	11	𝑥	𝑥	NOUN
cana-5829	919	12	)	)	PUNCT
cana-5829	919	13	+	+	CCONJ
cana-5829	919	14	𝑁𝑜𝑟𝑚𝛾𝐹22	𝑁𝑜𝑟𝑚𝛾𝐹22	X
cana-5829	919	15	(	(	PUNCT
cana-5829	919	16	𝑦	𝑦	NOUN
cana-5829	919	17	)	)	PUNCT
cana-5829	919	18	2(𝑁𝑜𝑟𝑚µ𝐸22	2(𝑁𝑜𝑟𝑚µ𝐸22	NUM
cana-5829	919	19	(	(	PUNCT
cana-5829	919	20	𝑥	𝑥	NOUN
cana-5829	919	21	)	)	PUNCT
cana-5829	919	22	.	.	PUNCT
cana-5829	920	1	𝑁𝑜𝑟𝑚𝛾𝐹22	𝑁𝑜𝑟𝑚𝛾𝐹22	X
cana-5829	920	2	(	(	PUNCT
cana-5829	920	3	𝑦	𝑦	NOUN
cana-5829	920	4	)	)	PUNCT
cana-5829	920	5	+	+	CCONJ
cana-5829	920	6	1	1	NUM
cana-5829	920	7	)	)	PUNCT
cana-5829	920	8	)	)	PUNCT
cana-5829	921	1	we	we	PRON
cana-5829	921	2	have	have	VERB
cana-5829	921	3	norm𝐴̅	norm𝐴̅	PROPN
cana-5829	921	4	𝐸	𝐸	PROPN
cana-5829	921	5	∗	∗	NOUN
cana-5829	921	6	𝑁𝑜𝑟𝑚	𝑁𝑜𝑟𝑚	PROPN
cana-5829	921	7	�	�	NOUN
cana-5829	921	8	̅	̅	NOUN
cana-5829	921	9	�	�	NOUN
cana-5829	921	10	𝐹	𝐹	NOUN
cana-5829	921	11	=	=	PUNCT
cana-5829	921	12	(	(	PUNCT
cana-5829	921	13	𝑋11	𝑋11	PROPN
cana-5829	921	14	𝑋12	𝑋12	PROPN
cana-5829	921	15	𝑋21	𝑋21	NOUN
cana-5829	921	16	𝑋22	𝑋22	ADJ
cana-5829	921	17	)	)	PUNCT
cana-5829	921	18	is	be	AUX
cana-5829	921	19	also	also	ADV
cana-5829	921	20	intuitionistic	intuitionistic	ADJ
cana-5829	921	21	fuzzy	fuzzy	ADJ
cana-5829	921	22	matrix	matrix	NOUN
cana-5829	921	23	example	example	NOUN
cana-5829	921	24	:	:	PUNCT
cana-5829	921	25	if	if	SCONJ
cana-5829	921	26	𝑨𝑬=	𝑨𝑬=	NOUN
cana-5829	921	27	(	(	PUNCT
cana-5829	921	28	(	(	PUNCT
cana-5829	921	29	.9	.9	NUM
cana-5829	921	30	,	,	PUNCT
cana-5829	921	31	.4	.4	NUM
cana-5829	921	32	)	)	PUNCT
cana-5829	921	33	(	(	PUNCT
cana-5829	921	34	.4	.4	PROPN
cana-5829	921	35	,	,	PUNCT
cana-5829	921	36	.1	.1	NUM
cana-5829	921	37	)	)	PUNCT
cana-5829	921	38	(	(	PUNCT
cana-5829	921	39	.5	.5	NUM
cana-5829	921	40	,	,	PUNCT
cana-5829	921	41	.3	.3	NUM
cana-5829	921	42	)	)	PUNCT
cana-5829	921	43	(	(	PUNCT
cana-5829	921	44	.8	.8	NUM
cana-5829	921	45	,	,	PUNCT
cana-5829	921	46	.3	.3	NUM
cana-5829	921	47	)	)	PUNCT
cana-5829	921	48	)	)	PUNCT
cana-5829	922	1	and𝑩𝑭	and𝑩𝑭	NOUN
cana-5829	922	2	=	=	SYM
cana-5829	922	3	(	(	PUNCT
cana-5829	922	4	(	(	PUNCT
cana-5829	922	5	.8	.8	NUM
cana-5829	922	6	,	,	PUNCT
cana-5829	922	7	.6	.6	NUM
cana-5829	922	8	)	)	PUNCT
cana-5829	922	9	(	(	PUNCT
cana-5829	922	10	.6	.6	PROPN
cana-5829	922	11	,	,	PUNCT
cana-5829	922	12	.3	.3	NUM
cana-5829	922	13	)	)	PUNCT
cana-5829	922	14	(	(	PUNCT
cana-5829	922	15	.7	.7	PROPN
cana-5829	922	16	,	,	PUNCT
cana-5829	922	17	.5	.5	NUM
cana-5829	922	18	)	)	PUNCT
cana-5829	922	19	(	(	PUNCT
cana-5829	922	20	.9	.9	NUM
cana-5829	922	21	,	,	PUNCT
cana-5829	922	22	.4	.4	NUM
cana-5829	922	23	)	)	PUNCT
cana-5829	922	24	)	)	PUNCT
cana-5829	922	25	are	be	AUX
cana-5829	922	26	two	two	NUM
cana-5829	922	27	intuitionistic	intuitionistic	ADJ
cana-5829	922	28	fuzzy	fuzzy	ADJ
cana-5829	922	29	matrices	matrix	NOUN
cana-5829	922	30	over	over	ADP
cana-5829	922	31	different	different	ADJ
cana-5829	922	32	universe	universe	NOUN
cana-5829	922	33	e	e	NOUN
cana-5829	922	34	and	and	CCONJ
cana-5829	922	35	f	f	PROPN
cana-5829	923	1	then	then	ADV
cana-5829	923	2	norm𝐴̅	norm𝐴̅	PROPN
cana-5829	923	3	𝐸	𝐸	PROPN
cana-5829	923	4	∗	∗	NOUN
cana-5829	923	5	𝑁𝑜𝑟𝑚	𝑁𝑜𝑟𝑚	PROPN
cana-5829	923	6	�	�	NOUN
cana-5829	923	7	̅	̅	NOUN
cana-5829	923	8	�	�	NOUN
cana-5829	923	9	𝐹is	𝐹i	VERB
cana-5829	923	10	also	also	ADV
cana-5829	923	11	fuzzy	fuzzy	ADJ
cana-5829	923	12	matrix	matrix	NOUN
cana-5829	923	13	set	set	NOUN
cana-5829	923	14	.	.	PUNCT
cana-5829	924	1	proof	proof	NOUN
cana-5829	924	2	:	:	PUNCT
cana-5829	924	3	given	give	VERB
cana-5829	924	4	𝑨𝑬	𝑨𝑬	PROPN
cana-5829	924	5	=(	=(	NOUN
cana-5829	924	6	(	(	PUNCT
cana-5829	924	7	.9	.9	NUM
cana-5829	924	8	,	,	PUNCT
cana-5829	924	9	.4	.4	NUM
cana-5829	924	10	)	)	PUNCT
cana-5829	924	11	(	(	PUNCT
cana-5829	924	12	.4	.4	PROPN
cana-5829	924	13	,	,	PUNCT
cana-5829	924	14	.1	.1	NUM
cana-5829	924	15	)	)	PUNCT
cana-5829	924	16	(	(	PUNCT
cana-5829	924	17	.5	.5	NUM
cana-5829	924	18	,	,	PUNCT
cana-5829	924	19	.3	.3	NUM
cana-5829	924	20	)	)	PUNCT
cana-5829	924	21	(	(	PUNCT
cana-5829	924	22	.8	.8	NUM
cana-5829	924	23	,	,	PUNCT
cana-5829	924	24	.3	.3	NUM
cana-5829	924	25	)	)	PUNCT
cana-5829	924	26	)	)	PUNCT
cana-5829	924	27	and	and	CCONJ
cana-5829	924	28	𝑩𝑭	𝑩𝑭	PROPN
cana-5829	924	29	=	=	SYM
cana-5829	924	30	(	(	PUNCT
cana-5829	924	31	(	(	PUNCT
cana-5829	924	32	.8	.8	NUM
cana-5829	924	33	,	,	PUNCT
cana-5829	924	34	.6	.6	NUM
cana-5829	924	35	)	)	PUNCT
cana-5829	924	36	(	(	PUNCT
cana-5829	924	37	.6	.6	PROPN
cana-5829	924	38	,	,	PUNCT
cana-5829	924	39	.3	.3	NUM
cana-5829	924	40	)	)	PUNCT
cana-5829	924	41	(	(	PUNCT
cana-5829	924	42	.7	.7	PROPN
cana-5829	924	43	,	,	PUNCT
cana-5829	924	44	.5	.5	NUM
cana-5829	924	45	)	)	PUNCT
cana-5829	924	46	(	(	PUNCT
cana-5829	924	47	.9	.9	NUM
cana-5829	924	48	,	,	PUNCT
cana-5829	924	49	.4	.4	NUM
cana-5829	924	50	)	)	PUNCT
cana-5829	924	51	)	)	PUNCT
cana-5829	925	1	𝑁𝑜𝑟𝑚̅̅	𝑁𝑜𝑟𝑚̅̅	NOUN
cana-5829	925	2	̅̅	̅̅	PROPN
cana-5829	925	3	̅̅	̅̅	PROPN
cana-5829	925	4	̅̅	̅̅	PROPN
cana-5829	925	5	𝐴	𝐴	PROPN
cana-5829	925	6	=(	=(	NOUN
cana-5829	925	7	(	(	PUNCT
cana-5829	925	8	.8,1	.8,1	NOUN
cana-5829	925	9	)	)	PUNCT
cana-5829	925	10	(	(	PUNCT
cana-5829	925	11	0	0	NUM
cana-5829	925	12	,	,	PUNCT
cana-5829	925	13	.3	.3	NUM
cana-5829	925	14	)	)	PUNCT
cana-5829	925	15	(	(	PUNCT
cana-5829	925	16	.2	.2	NUM
cana-5829	925	17	,	,	PUNCT
cana-5829	925	18	.8	.8	NUM
cana-5829	925	19	)	)	PUNCT
cana-5829	925	20	(	(	PUNCT
cana-5829	925	21	.7	.7	PROPN
cana-5829	925	22	,	,	PUNCT
cana-5829	925	23	.8	.8	NUM
cana-5829	925	24	)	)	PUNCT
cana-5829	925	25	)	)	PUNCT
cana-5829	925	26	and	and	CCONJ
cana-5829	926	1	𝑁𝑜𝑟𝑚̅̅	𝑁𝑜𝑟𝑚̅̅	PROPN
cana-5829	926	2	̅̅	̅̅	PROPN
cana-5829	926	3	̅̅	̅̅	PROPN
cana-5829	926	4	̅̅	̅̅	PROPN
cana-5829	926	5	𝐵=	𝐵=	PROPN
cana-5829	926	6	(	(	PUNCT
cana-5829	926	7	(	(	PUNCT
cana-5829	926	8	.5	.5	NUM
cana-5829	926	9	,	,	PUNCT
cana-5829	926	10	1	1	NUM
cana-5829	926	11	)	)	PUNCT
cana-5829	926	12	(	(	PUNCT
cana-5829	926	13	0	0	NUM
cana-5829	926	14	,	,	PUNCT
cana-5829	926	15	.5	.5	NUM
cana-5829	926	16	)	)	PUNCT
cana-5829	926	17	(	(	PUNCT
cana-5829	926	18	.3	.3	NUM
cana-5829	926	19	,	,	PUNCT
cana-5829	926	20	.8	.8	NUM
cana-5829	926	21	)	)	PUNCT
cana-5829	926	22	(	(	PUNCT
cana-5829	926	23	.8	.8	PROPN
cana-5829	926	24	,	,	PUNCT
cana-5829	926	25	.7	.7	PROPN
cana-5829	926	26	)	)	PUNCT
cana-5829	926	27	)	)	PUNCT
cana-5829	927	1	𝑁𝑜𝑟𝑚̅̅	𝑁𝑜𝑟𝑚̅̅	NOUN
cana-5829	927	2	̅̅	̅̅	PROPN
cana-5829	927	3	̅̅	̅̅	PROPN
cana-5829	927	4	̅̅	̅̅	PROPN
cana-5829	927	5	𝐴	𝐴	PROPN
cana-5829	927	6	∗	∗	NOUN
cana-5829	927	7	𝑁𝑜𝑟𝑚̅̅	𝑁𝑜𝑟𝑚̅̅	PROPN
cana-5829	927	8	̅̅	̅̅	PROPN
cana-5829	927	9	̅̅	̅̅	PROPN
cana-5829	927	10	̅̅	̅̅	PROPN
cana-5829	927	11	̅	̅	PROPN
cana-5829	927	12	𝐵	𝐵	NOUN
cana-5829	927	13	=	=	SYM
cana-5829	927	14	(	(	PUNCT
cana-5829	927	15	(	(	PUNCT
cana-5829	927	16	.8,1	.8,1	NOUN
cana-5829	927	17	)	)	PUNCT
cana-5829	927	18	(	(	PUNCT
cana-5829	927	19	0	0	NUM
cana-5829	927	20	,	,	PUNCT
cana-5829	927	21	.3	.3	NUM
cana-5829	927	22	)	)	PUNCT
cana-5829	927	23	(	(	PUNCT
cana-5829	927	24	.2	.2	NUM
cana-5829	927	25	,	,	PUNCT
cana-5829	927	26	.8	.8	NUM
cana-5829	927	27	)	)	PUNCT
cana-5829	927	28	(	(	PUNCT
cana-5829	927	29	.7	.7	PROPN
cana-5829	927	30	,	,	PUNCT
cana-5829	927	31	.8	.8	NUM
cana-5829	927	32	)	)	PUNCT
cana-5829	927	33	)	)	PUNCT
cana-5829	928	1	∗	∗	NOUN
cana-5829	928	2	(	(	PUNCT
cana-5829	928	3	(	(	PUNCT
cana-5829	928	4	.5	.5	NUM
cana-5829	928	5	,	,	PUNCT
cana-5829	928	6	1	1	NUM
cana-5829	928	7	)	)	PUNCT
cana-5829	928	8	(	(	PUNCT
cana-5829	928	9	0	0	NUM
cana-5829	928	10	,	,	PUNCT
cana-5829	928	11	.5	.5	NUM
cana-5829	928	12	)	)	PUNCT
cana-5829	928	13	(	(	PUNCT
cana-5829	928	14	.3	.3	NUM
cana-5829	928	15	,	,	PUNCT
cana-5829	928	16	.8	.8	NUM
cana-5829	928	17	)	)	PUNCT
cana-5829	928	18	(	(	PUNCT
cana-5829	928	19	.8	.8	PROPN
cana-5829	928	20	,	,	PUNCT
cana-5829	928	21	.7	.7	PROPN
cana-5829	928	22	)	)	PUNCT
cana-5829	928	23	)	)	PUNCT
cana-5829	929	1	𝑋11	𝑋11	PROPN
cana-5829	929	2	=	=	SYM
cana-5829	929	3	(	(	PUNCT
cana-5829	929	4	.8	.8	PROPN
cana-5829	929	5	,	,	PUNCT
cana-5829	929	6	1	1	NUM
cana-5829	929	7	)	)	PUNCT
cana-5829	929	8	∗	∗	NOUN
cana-5829	929	9	(	(	PUNCT
cana-5829	929	10	.	.	NOUN
cana-5829	929	11	5	5	NUM
cana-5829	929	12	,	,	PUNCT
cana-5829	929	13	1	1	NUM
cana-5829	929	14	)	)	PUNCT
cana-5829	929	15	𝑋12	𝑋12	NOUN
cana-5829	929	16	=	=	PUNCT
cana-5829	929	17	(	(	PUNCT
cana-5829	929	18	0	0	NUM
cana-5829	929	19	,	,	PUNCT
cana-5829	929	20	.3	.3	NUM
cana-5829	929	21	)	)	PUNCT
cana-5829	929	22	∗	∗	NOUN
cana-5829	929	23	(	(	PUNCT
cana-5829	929	24	0	0	NUM
cana-5829	929	25	,	,	PUNCT
cana-5829	929	26	.5	.5	NUM
cana-5829	929	27	)	)	PUNCT
cana-5829	930	1	𝑋21	𝑋21	NOUN
cana-5829	930	2	=	=	SYM
cana-5829	930	3	(	(	PUNCT
cana-5829	930	4	.2	.2	NUM
cana-5829	930	5	,	,	PUNCT
cana-5829	930	6	.8	.8	NUM
cana-5829	930	7	)	)	PUNCT
cana-5829	930	8	∗	∗	NOUN
cana-5829	930	9	(	(	PUNCT
cana-5829	930	10	.3	.3	NUM
cana-5829	930	11	,	,	PUNCT
cana-5829	930	12	.8	.8	NUM
cana-5829	930	13	)	)	PUNCT
cana-5829	931	1	𝑋22	𝑋22	ADJ
cana-5829	931	2	=	=	PUNCT
cana-5829	931	3	(	(	PUNCT
cana-5829	931	4	.	.	NOUN
cana-5829	931	5	7	7	NUM
cana-5829	931	6	,	,	PUNCT
cana-5829	931	7	.8	.8	NUM
cana-5829	931	8	)	)	PUNCT
cana-5829	931	9	∗	∗	NOUN
cana-5829	931	10	(	(	PUNCT
cana-5829	931	11	.8	.8	NUM
cana-5829	931	12	,	,	PUNCT
cana-5829	931	13	.7	.7	PROPN
cana-5829	931	14	)	)	PUNCT
cana-5829	932	1	𝐴𝑝𝑝𝑙𝑦𝑖𝑛𝑔	𝐴𝑝𝑝𝑙𝑦𝑖𝑛𝑔	PROPN
cana-5829	932	2	𝑓𝑜𝑟𝑚𝑢𝑙𝑎	𝑓𝑜𝑟𝑚𝑢𝑙𝑎	VERB
cana-5829	932	3	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	932	4	̅̅̅̅	̅̅̅̅	ADJ
cana-5829	932	5	∗	∗	NOUN
cana-5829	932	6	𝐵𝐹	𝐵𝐹	PROPN
cana-5829	932	7	̅̅̅̅	̅̅̅̅	NOUN
cana-5829	932	8	=	=	X
cana-5829	932	9	{	{	PUNCT
cana-5829	932	10	〈	〈	PROPN
cana-5829	932	11	x	x	PROPN
cana-5829	932	12	,	,	PUNCT
cana-5829	932	13	y	y	PROPN
cana-5829	932	14	〉	〉	NOUN
cana-5829	932	15	,	,	PUNCT
cana-5829	932	16	𝜗𝐴(x)+𝜗𝐵(y	𝜗𝐴(x)+𝜗𝐵(y	NUM
cana-5829	932	17	)	)	PUNCT
cana-5829	932	18	2(𝜗𝐴(x).𝜗𝐵(y)+1	2(𝜗𝐴(x).𝜗𝐵(y)+1	NUM
cana-5829	932	19	)	)	PUNCT
cana-5829	932	20	,	,	PUNCT
cana-5829	932	21	µ𝐴	µ𝐴	SCONJ
cana-5829	932	22	(	(	PUNCT
cana-5829	932	23	x)+	x)+	NUM
cana-5829	932	24	µ𝐵(y	µ𝐵(y	NUM
cana-5829	932	25	)	)	PUNCT
cana-5829	932	26	2(µ𝐴(x).µ𝐵(y)+1	2(µ𝐴(x).µ𝐵(y)+1	NUM
cana-5829	932	27	)	)	PUNCT
cana-5829	932	28	:	:	PUNCT
cana-5829	933	1	xe	xe	PROPN
cana-5829	933	2	,	,	PUNCT
cana-5829	933	3	y𝐹	y𝐹	NOUN
cana-5829	933	4	}	}	PUNCT
cana-5829	934	1	𝑋11	𝑋11	PROPN
cana-5829	934	2	=	=	PUNCT
cana-5829	934	3	(	(	PUNCT
cana-5829	934	4	(	(	PUNCT
cana-5829	934	5	.	.	NUM
cana-5829	934	6	8)	8)	NUM
cana-5829	934	7	+	+	CCONJ
cana-5829	934	8	(	(	PUNCT
cana-5829	934	9	.5	.5	NUM
cana-5829	934	10	)	)	PUNCT
cana-5829	934	11	2	2	NUM
cana-5829	934	12	(	(	PUNCT
cana-5829	934	13	(	(	PUNCT
cana-5829	934	14	.	.	PUNCT
cana-5829	934	15	8)	8)	NUM
cana-5829	934	16	.	.	PUNCT
cana-5829	935	1	(	(	PUNCT
cana-5829	935	2	.	.	NOUN
cana-5829	936	1	5	5	X
cana-5829	936	2	)	)	PUNCT
cana-5829	936	3	+	+	NUM
cana-5829	936	4	1	1	NUM
cana-5829	936	5	)	)	PUNCT
cana-5829	936	6	,	,	PUNCT
cana-5829	936	7	(	(	PUNCT
cana-5829	936	8	1	1	X
cana-5829	936	9	)	)	PUNCT
cana-5829	936	10	+	+	CCONJ
cana-5829	936	11	(	(	PUNCT
cana-5829	936	12	1	1	X
cana-5829	936	13	)	)	PUNCT
cana-5829	936	14	2(1.1	2(1.1	NUM
cana-5829	937	1	+	+	CCONJ
cana-5829	937	2	1	1	NUM
cana-5829	937	3	)	)	PUNCT
cana-5829	937	4	)	)	PUNCT
cana-5829	938	1	𝑋12	𝑋12	PROPN
cana-5829	938	2	=	=	PUNCT
cana-5829	939	1	(	(	PUNCT
cana-5829	939	2	(	(	PUNCT
cana-5829	939	3	0	0	NUM
cana-5829	939	4	)	)	PUNCT
cana-5829	940	1	+	+	CCONJ
cana-5829	940	2	(	(	PUNCT
cana-5829	940	3	0	0	NUM
cana-5829	940	4	)	)	PUNCT
cana-5829	940	5	2((0	2((0	NUM
cana-5829	940	6	)	)	PUNCT
cana-5829	940	7	.	.	PUNCT
cana-5829	941	1	(	(	PUNCT
cana-5829	941	2	0	0	X
cana-5829	941	3	)	)	PUNCT
cana-5829	941	4	+	+	CCONJ
cana-5829	941	5	1	1	NUM
cana-5829	941	6	)	)	PUNCT
cana-5829	941	7	,	,	PUNCT
cana-5829	941	8	(	(	PUNCT
cana-5829	941	9	.	.	PUNCT
cana-5829	942	1	3	3	X
cana-5829	942	2	)	)	PUNCT
cana-5829	942	3	+	+	CCONJ
cana-5829	942	4	(	(	PUNCT
cana-5829	942	5	.5	.5	NUM
cana-5829	942	6	)	)	PUNCT
cana-5829	942	7	2(.3	2(.3	NOUN
cana-5829	942	8	.5	.5	NUM
cana-5829	943	1	+	+	CCONJ
cana-5829	943	2	1	1	NUM
cana-5829	943	3	)	)	PUNCT
cana-5829	943	4	)	)	PUNCT
cana-5829	944	1	𝑋21	𝑋21	NOUN
cana-5829	944	2	=	=	SYM
cana-5829	944	3	(	(	PUNCT
cana-5829	944	4	(	(	PUNCT
cana-5829	944	5	.	.	NOUN
cana-5829	944	6	2	2	X
cana-5829	944	7	)	)	PUNCT
cana-5829	944	8	+	+	CCONJ
cana-5829	944	9	(	(	PUNCT
cana-5829	944	10	.3	.3	NUM
cana-5829	944	11	)	)	PUNCT
cana-5829	944	12	2	2	NUM
cana-5829	944	13	(	(	PUNCT
cana-5829	944	14	(	(	PUNCT
cana-5829	944	15	.	.	NOUN
cana-5829	944	16	2	2	NUM
cana-5829	944	17	)	)	PUNCT
cana-5829	944	18	.	.	PUNCT
cana-5829	945	1	(	(	PUNCT
cana-5829	945	2	.	.	PUNCT
cana-5829	946	1	3	3	X
cana-5829	946	2	)	)	PUNCT
cana-5829	946	3	+	+	NUM
cana-5829	946	4	1	1	NUM
cana-5829	946	5	)	)	PUNCT
cana-5829	946	6	,	,	PUNCT
cana-5829	946	7	(	(	PUNCT
cana-5829	946	8	.	.	PUNCT
cana-5829	946	9	8)	8)	NUM
cana-5829	947	1	+	+	CCONJ
cana-5829	947	2	(	(	PUNCT
cana-5829	947	3	.8	.8	NUM
cana-5829	947	4	)	)	PUNCT
cana-5829	947	5	2(.8	2(.8	NOUN
cana-5829	947	6	.8	.8	PROPN
cana-5829	948	1	+	+	CCONJ
cana-5829	948	2	1	1	NUM
cana-5829	948	3	)	)	PUNCT
cana-5829	948	4	)	)	PUNCT
cana-5829	949	1	𝑋22	𝑋22	VERB
cana-5829	949	2	=	=	PUNCT
cana-5829	949	3	(	(	PUNCT
cana-5829	949	4	(	(	PUNCT
cana-5829	949	5	.	.	PUNCT
cana-5829	950	1	7	7	X
cana-5829	950	2	)	)	PUNCT
cana-5829	950	3	+	+	CCONJ
cana-5829	950	4	(	(	PUNCT
cana-5829	950	5	.8	.8	NUM
cana-5829	950	6	)	)	PUNCT
cana-5829	950	7	2	2	NUM
cana-5829	950	8	(	(	PUNCT
cana-5829	950	9	(	(	PUNCT
cana-5829	950	10	.	.	NOUN
cana-5829	950	11	7	7	NUM
cana-5829	950	12	)	)	PUNCT
cana-5829	950	13	.	.	PUNCT
cana-5829	951	1	(	(	PUNCT
cana-5829	951	2	.	.	NUM
cana-5829	951	3	8)	8)	NUM
cana-5829	952	1	+	+	CCONJ
cana-5829	952	2	1	1	NUM
cana-5829	952	3	)	)	PUNCT
cana-5829	952	4	,	,	PUNCT
cana-5829	952	5	(	(	PUNCT
cana-5829	952	6	.	.	PUNCT
cana-5829	952	7	8)	8)	NUM
cana-5829	952	8	+	+	CCONJ
cana-5829	952	9	(	(	PUNCT
cana-5829	952	10	.7	.7	PROPN
cana-5829	952	11	)	)	PUNCT
cana-5829	952	12	2(.8	2(.8	NOUN
cana-5829	952	13	.7	.7	NOUN
cana-5829	953	1	+	+	CCONJ
cana-5829	953	2	1	1	NUM
cana-5829	953	3	)	)	PUNCT
cana-5829	953	4	)	)	PUNCT
cana-5829	954	1	𝑋11	𝑋11	PROPN
cana-5829	954	2	=	=	PRON
cana-5829	954	3	{	{	PUNCT
cana-5829	954	4	.5	.5	NUM
cana-5829	954	5	,	,	PUNCT
cana-5829	954	6	.5	.5	NUM
cana-5829	954	7	}	}	PUNCT
cana-5829	954	8	𝑋12	𝑋12	PROPN
cana-5829	954	9	=	=	SYM
cana-5829	954	10	{	{	PUNCT
cana-5829	954	11	0	0	NUM
cana-5829	954	12	,	,	PUNCT
cana-5829	954	13	.3	.3	NUM
cana-5829	954	14	}	}	PUNCT
cana-5829	954	15	𝑋21	𝑋21	VERB
cana-5829	954	16	=	=	PRON
cana-5829	954	17	{	{	PUNCT
cana-5829	954	18	.2	.2	NUM
cana-5829	954	19	,	,	PUNCT
cana-5829	954	20	.5	.5	NUM
cana-5829	954	21	}	}	PUNCT
cana-5829	954	22	𝑋22	𝑋22	VERB
cana-5829	954	23	=	=	PRON
cana-5829	954	24	{	{	PUNCT
cana-5829	954	25	.5	.5	NUM
cana-5829	954	26	,	,	PUNCT
cana-5829	954	27	.5	.5	NUM
cana-5829	954	28	}	}	PUNCT
cana-5829	954	29	we	we	PRON
cana-5829	954	30	have	have	VERB
cana-5829	954	31	norm𝐴̅	norm𝐴̅	PROPN
cana-5829	954	32	𝐸	𝐸	PROPN
cana-5829	954	33	∗	∗	NOUN
cana-5829	954	34	𝑁𝑜𝑟𝑚	𝑁𝑜𝑟𝑚	PROPN
cana-5829	954	35	�	�	NOUN
cana-5829	954	36	̅	̅	NOUN
cana-5829	954	37	�	�	NOUN
cana-5829	954	38	𝐹	𝐹	NOUN
cana-5829	954	39	=	=	PUNCT
cana-5829	954	40	(	(	PUNCT
cana-5829	954	41	(	(	PUNCT
cana-5829	954	42	.5	.5	NUM
cana-5829	954	43	,	,	PUNCT
cana-5829	954	44	.5	.5	NUM
cana-5829	954	45	)	)	PUNCT
cana-5829	954	46	(	(	PUNCT
cana-5829	954	47	0	0	NUM
cana-5829	954	48	,	,	PUNCT
cana-5829	954	49	.3	.3	NUM
cana-5829	954	50	)	)	PUNCT
cana-5829	954	51	(	(	PUNCT
cana-5829	954	52	.2	.2	NUM
cana-5829	954	53	,	,	PUNCT
cana-5829	954	54	.5	.5	NUM
cana-5829	954	55	)	)	PUNCT
cana-5829	954	56	(	(	PUNCT
cana-5829	954	57	.5	.5	NUM
cana-5829	954	58	,	,	PUNCT
cana-5829	954	59	.5	.5	NUM
cana-5829	954	60	)	)	PUNCT
cana-5829	954	61	)	)	PUNCT
cana-5829	954	62	is	be	AUX
cana-5829	954	63	also	also	ADV
cana-5829	954	64	intuitionistic	intuitionistic	ADJ
cana-5829	954	65	fuzzy	fuzzy	ADJ
cana-5829	954	66	matrix	matrix	NOUN
cana-5829	954	67	.	.	PUNCT
cana-5829	955	1	communications	communication	NOUN
cana-5829	955	2	on	on	ADP
cana-5829	955	3	applied	apply	VERB
cana-5829	955	4	nonlinear	nonlinear	ADJ
cana-5829	955	5	analysis	analysis	NOUN
cana-5829	955	6	issn	issn	NOUN
cana-5829	955	7	:	:	PUNCT
cana-5829	955	8	1074	1074	NUM
cana-5829	955	9	-	-	PUNCT
cana-5829	955	10	133x	133x	NUM
cana-5829	955	11	vol	vol	VERB
cana-5829	955	12	32	32	NUM
cana-5829	955	13	no	no	NOUN
cana-5829	955	14	.	.	PUNCT
cana-5829	956	1	10s	10	NOUN
cana-5829	956	2	(	(	PUNCT
cana-5829	956	3	2025	2025	NUM
cana-5829	956	4	)	)	PUNCT
cana-5829	956	5	2954	2954	NUM
cana-5829	956	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5829	956	7	theorem	theorem	VERB
cana-5829	956	8	5.2.9	5.2.9	NUM
cana-5829	956	9	:	:	PUNCT
cana-5829	956	10	if	if	SCONJ
cana-5829	956	11	e	e	PROPN
cana-5829	956	12	and	and	CCONJ
cana-5829	956	13	f	f	PROPN
cana-5829	956	14	be	be	AUX
cana-5829	956	15	two	two	NUM
cana-5829	956	16	universal	universal	ADJ
cana-5829	956	17	sets	set	NOUN
cana-5829	956	18	.	.	PUNCT
cana-5829	957	1	for	for	ADP
cana-5829	957	2	every	every	DET
cana-5829	957	3	normalization	normalization	NOUN
cana-5829	957	4	of	of	ADP
cana-5829	957	5	an	an	DET
cana-5829	957	6	intuitionistic	intuitionistic	ADJ
cana-5829	957	7	fuzzy	fuzzy	ADJ
cana-5829	957	8	matrices	matrix	NOUN
cana-5829	957	9	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	957	10	̅̅̅̅	̅̅̅̅	ADJ
cana-5829	957	11	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-5829	957	12	𝐵𝐹	𝐵𝐹	PROPN
cana-5829	957	13	̅̅̅̅	̅̅̅̅	NOUN
cana-5829	957	14	are	be	AUX
cana-5829	957	15	in	in	ADP
cana-5829	957	16	e	e	PROPN
cana-5829	957	17	and	and	CCONJ
cana-5829	957	18	f	f	PROPN
cana-5829	958	1	then	then	ADV
cana-5829	958	2	norm𝐴̅	norm𝐴̅	PROPN
cana-5829	958	3	𝐸∆	𝐸∆	PROPN
cana-5829	958	4	𝑁𝑜𝑟𝑚	𝑁𝑜𝑟𝑚	PROPN
cana-5829	958	5	�	�	NOUN
cana-5829	958	6	̅	̅	NOUN
cana-5829	958	7	�	�	NOUN
cana-5829	958	8	𝐹is	𝐹i	VERB
cana-5829	958	9	also	also	ADV
cana-5829	958	10	normalization	normalization	NOUN
cana-5829	958	11	of	of	ADP
cana-5829	958	12	an	an	DET
cana-5829	958	13	intuitionistic	intuitionistic	ADJ
cana-5829	958	14	fuzzy	fuzzy	ADJ
cana-5829	958	15	matrices	matrix	NOUN
cana-5829	958	16	.	.	PUNCT
cana-5829	959	1	proof	proof	NOUN
cana-5829	959	2	:	:	PUNCT
cana-5829	959	3	if	if	SCONJ
cana-5829	959	4	𝑁𝑜𝑟𝑚𝐴	𝑁𝑜𝑟𝑚𝐴	PROPN
cana-5829	959	5	and	and	CCONJ
cana-5829	959	6	𝑁𝑜𝑟𝑚𝐵	𝑁𝑜𝑟𝑚𝐵	PROPN
cana-5829	959	7	are	be	AUX
cana-5829	959	8	two	two	NUM
cana-5829	959	9	normalization	normalization	NOUN
cana-5829	959	10	intuitionistic	intuitionistic	ADJ
cana-5829	959	11	fuzzy	fuzzy	ADJ
cana-5829	959	12	matrices	matrix	NOUN
cana-5829	959	13	over	over	ADP
cana-5829	959	14	different	different	ADJ
cana-5829	959	15	unive𝑟𝑠𝑒𝑠	unive𝑟𝑠𝑒𝑠	ADJ
cana-5829	959	16	𝑠𝑒𝑡𝑠	𝑠𝑒𝑡𝑠	PROPN
cana-5829	959	17	𝐸	𝐸	PROPN
cana-5829	960	1	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-5829	960	2	𝐹.	𝐹.	NOUN
cana-5829	960	3	𝐼𝑓	𝐼𝑓	PROPN
cana-5829	960	4	𝑤𝑒	𝑤𝑒	PROPN
cana-5829	960	5	𝑐𝑜𝑛𝑠𝑖𝑑𝑒𝑟	𝑐𝑜𝑛𝑠𝑖𝑑𝑒𝑟	PROPN
cana-5829	960	6	𝑡𝑤𝑜	𝑡𝑤𝑜	PROPN
cana-5829	960	7	2	2	NUM
cana-5829	960	8	×	×	NOUN
cana-5829	960	9	2	2	NUM
cana-5829	960	10	𝑚𝑎𝑡𝑟𝑖𝑥	𝑚𝑎𝑡𝑟𝑖𝑥	ADJ
cana-5829	960	11	𝑁𝑜𝑟𝑚̅̅	𝑁𝑜𝑟𝑚̅̅	PROPN
cana-5829	960	12	̅̅	̅̅	PROPN
cana-5829	960	13	̅̅	̅̅	PROPN
cana-5829	960	14	̅̅	̅̅	PROPN
cana-5829	960	15	𝐴	𝐴	PROPN
cana-5829	960	16	=(	=(	NOUN
cana-5829	960	17	(	(	PUNCT
cana-5829	960	18	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	960	19	(	(	PUNCT
cana-5829	960	20	𝑥	𝑥	NOUN
cana-5829	960	21	)	)	PUNCT
cana-5829	960	22	𝑁𝑜𝑟𝑚µ𝐸11(𝑥	𝑁𝑜𝑟𝑚µ𝐸11(𝑥	NOUN
cana-5829	960	23	)	)	PUNCT
cana-5829	960	24	)	)	PUNCT
cana-5829	961	1	(	(	PUNCT
cana-5829	961	2	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	X
cana-5829	961	3	(	(	PUNCT
cana-5829	961	4	𝑥	𝑥	NOUN
cana-5829	961	5	)	)	PUNCT
cana-5829	961	6	𝑁𝑜𝑟𝑚µ𝐸12(𝑥	𝑁𝑜𝑟𝑚µ𝐸12(𝑥	NOUN
cana-5829	961	7	)	)	PUNCT
cana-5829	961	8	)	)	PUNCT
cana-5829	961	9	(	(	PUNCT
cana-5829	961	10	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	X
cana-5829	961	11	(	(	PUNCT
cana-5829	961	12	𝑥	𝑥	NOUN
cana-5829	961	13	)	)	PUNCT
cana-5829	961	14	𝑁𝑜𝑟𝑚µ𝐸21	𝑁𝑜𝑟𝑚µ𝐸21	NOUN
cana-5829	961	15	(	(	PUNCT
cana-5829	961	16	𝑥	𝑥	NOUN
cana-5829	961	17	)	)	PUNCT
cana-5829	961	18	)	)	PUNCT
cana-5829	961	19	(	(	PUNCT
cana-5829	961	20	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	X
cana-5829	961	21	(	(	PUNCT
cana-5829	961	22	𝑥	𝑥	NOUN
cana-5829	961	23	)	)	PUNCT
cana-5829	961	24	𝑁𝑜𝑟𝑚µ𝐸22	𝑁𝑜𝑟𝑚µ𝐸22	NOUN
cana-5829	961	25	(	(	PUNCT
cana-5829	961	26	𝑥	𝑥	NOUN
cana-5829	961	27	)	)	PUNCT
cana-5829	961	28	)	)	PUNCT
cana-5829	961	29	)	)	PUNCT
cana-5829	961	30	and	and	CCONJ
cana-5829	962	1	𝑁𝑜𝑟𝑚̅̅	𝑁𝑜𝑟𝑚̅̅	PROPN
cana-5829	962	2	̅̅	̅̅	PROPN
cana-5829	962	3	̅̅	̅̅	PROPN
cana-5829	962	4	̅̅	̅̅	PROPN
cana-5829	962	5	𝐵=	𝐵=	PROPN
cana-5829	962	6	(	(	PUNCT
cana-5829	962	7	(	(	PUNCT
cana-5829	962	8	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	962	9	(	(	PUNCT
cana-5829	962	10	𝑦	𝑦	NOUN
cana-5829	962	11	)	)	PUNCT
cana-5829	962	12	𝑁𝑜𝑟𝑚𝛾𝐹11(𝑦	𝑁𝑜𝑟𝑚𝛾𝐹11(𝑦	NUM
cana-5829	962	13	)	)	PUNCT
cana-5829	962	14	)	)	PUNCT
cana-5829	962	15	(	(	PUNCT
cana-5829	962	16	𝑁𝑜𝑟𝑚𝛿𝐹12	𝑁𝑜𝑟𝑚𝛿𝐹12	X
cana-5829	962	17	(	(	PUNCT
cana-5829	962	18	𝑦	𝑦	NOUN
cana-5829	962	19	)	)	PUNCT
cana-5829	962	20	𝑁𝑜𝑟𝑚𝛾𝐹12(𝑦	𝑁𝑜𝑟𝑚𝛾𝐹12(𝑦	NOUN
cana-5829	962	21	)	)	PUNCT
cana-5829	962	22	)	)	PUNCT
cana-5829	962	23	(	(	PUNCT
cana-5829	962	24	𝑁𝑜𝑟𝑚𝛿𝐹21	𝑁𝑜𝑟𝑚𝛿𝐹21	X
cana-5829	962	25	(	(	PUNCT
cana-5829	962	26	𝑦	𝑦	NOUN
cana-5829	962	27	)	)	PUNCT
cana-5829	962	28	𝑁𝑜𝑟𝑚𝛾𝐹21	𝑁𝑜𝑟𝑚𝛾𝐹21	ADV
cana-5829	962	29	(	(	PUNCT
cana-5829	962	30	𝑦	𝑦	NOUN
cana-5829	962	31	)	)	PUNCT
cana-5829	962	32	)	)	PUNCT
cana-5829	962	33	(	(	PUNCT
cana-5829	962	34	𝑁𝑜𝑟𝑚𝛿𝐹22	𝑁𝑜𝑟𝑚𝛿𝐹22	X
cana-5829	962	35	(	(	PUNCT
cana-5829	962	36	𝑦	𝑦	NOUN
cana-5829	962	37	)	)	PUNCT
cana-5829	962	38	𝑁𝑜𝑟𝑚𝛾𝐹22	𝑁𝑜𝑟𝑚𝛾𝐹22	X
cana-5829	962	39	(	(	PUNCT
cana-5829	962	40	𝑦	𝑦	NOUN
cana-5829	962	41	)	)	PUNCT
cana-5829	962	42	)	)	PUNCT
cana-5829	962	43	)	)	PUNCT
cana-5829	963	1	𝑁𝑜𝑟𝑚̅̅	𝑁𝑜𝑟𝑚̅̅	NOUN
cana-5829	963	2	̅̅	̅̅	PROPN
cana-5829	963	3	̅̅	̅̅	PROPN
cana-5829	963	4	̅̅	̅̅	PROPN
cana-5829	963	5	𝐴	𝐴	PROPN
cana-5829	963	6	∆	∆	PROPN
cana-5829	963	7	𝑁𝑜𝑟𝑚̅̅	𝑁𝑜𝑟𝑚̅̅	NOUN
cana-5829	963	8	̅̅	̅̅	PROPN
cana-5829	963	9	̅̅	̅̅	PROPN
cana-5829	963	10	̅̅	̅̅	PROPN
cana-5829	963	11	𝐵	𝐵	PROPN
cana-5829	963	12	=	=	PUNCT
cana-5829	963	13	(	(	PUNCT
cana-5829	963	14	(	(	PUNCT
cana-5829	963	15	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	963	16	(	(	PUNCT
cana-5829	963	17	𝑥	𝑥	NOUN
cana-5829	963	18	)	)	PUNCT
cana-5829	963	19	𝑁𝑜𝑟𝑚µ𝐸11	𝑁𝑜𝑟𝑚µ𝐸11	NOUN
cana-5829	963	20	(	(	PUNCT
cana-5829	963	21	𝑥	𝑥	NOUN
cana-5829	963	22	)	)	PUNCT
cana-5829	963	23	)	)	PUNCT
cana-5829	963	24	(	(	PUNCT
cana-5829	963	25	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	X
cana-5829	963	26	(	(	PUNCT
cana-5829	963	27	𝑥	𝑥	NOUN
cana-5829	963	28	)	)	PUNCT
cana-5829	963	29	𝑁𝑜𝑟𝑚µ𝐸12	𝑁𝑜𝑟𝑚µ𝐸12	NOUN
cana-5829	963	30	(	(	PUNCT
cana-5829	963	31	𝑥	𝑥	NOUN
cana-5829	963	32	)	)	PUNCT
cana-5829	963	33	)	)	PUNCT
cana-5829	963	34	(	(	PUNCT
cana-5829	963	35	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	X
cana-5829	963	36	(	(	PUNCT
cana-5829	963	37	𝑥	𝑥	NOUN
cana-5829	963	38	)	)	PUNCT
cana-5829	963	39	𝑁𝑜𝑟𝑚µ𝐸21	𝑁𝑜𝑟𝑚µ𝐸21	NOUN
cana-5829	963	40	(	(	PUNCT
cana-5829	963	41	𝑥	𝑥	NOUN
cana-5829	963	42	)	)	PUNCT
cana-5829	963	43	)	)	PUNCT
cana-5829	963	44	(	(	PUNCT
cana-5829	963	45	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	X
cana-5829	963	46	(	(	PUNCT
cana-5829	963	47	𝑥	𝑥	NOUN
cana-5829	963	48	)	)	PUNCT
cana-5829	963	49	𝑁𝑜𝑟𝑚µ𝐸22	𝑁𝑜𝑟𝑚µ𝐸22	NOUN
cana-5829	963	50	(	(	PUNCT
cana-5829	963	51	𝑥	𝑥	NOUN
cana-5829	963	52	)	)	PUNCT
cana-5829	963	53	)	)	PUNCT
cana-5829	963	54	)	)	PUNCT
cana-5829	963	55	∆	∆	PROPN
cana-5829	964	1	(	(	PUNCT
cana-5829	964	2	(	(	PUNCT
cana-5829	964	3	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	964	4	(	(	PUNCT
cana-5829	964	5	𝑦	𝑦	NOUN
cana-5829	964	6	)	)	PUNCT
cana-5829	964	7	𝑁𝑜𝑟𝑚𝛾𝐹11(𝑦	𝑁𝑜𝑟𝑚𝛾𝐹11(𝑦	NUM
cana-5829	964	8	)	)	PUNCT
cana-5829	964	9	)	)	PUNCT
cana-5829	965	1	(	(	PUNCT
cana-5829	965	2	𝑁𝑜𝑟𝑚𝛿𝐹12	𝑁𝑜𝑟𝑚𝛿𝐹12	X
cana-5829	965	3	(	(	PUNCT
cana-5829	965	4	𝑦	𝑦	NOUN
cana-5829	965	5	)	)	PUNCT
cana-5829	965	6	𝑁𝑜𝑟𝑚𝛾𝐹12(𝑦	𝑁𝑜𝑟𝑚𝛾𝐹12(𝑦	NOUN
cana-5829	965	7	)	)	PUNCT
cana-5829	965	8	)	)	PUNCT
cana-5829	965	9	(	(	PUNCT
cana-5829	965	10	𝑁𝑜𝑟𝑚𝛿𝐹21	𝑁𝑜𝑟𝑚𝛿𝐹21	X
cana-5829	965	11	(	(	PUNCT
cana-5829	965	12	𝑦	𝑦	NOUN
cana-5829	965	13	)	)	PUNCT
cana-5829	965	14	𝑁𝑜𝑟𝑚𝛾𝐹21	𝑁𝑜𝑟𝑚𝛾𝐹21	ADV
cana-5829	965	15	(	(	PUNCT
cana-5829	965	16	𝑦	𝑦	NOUN
cana-5829	965	17	)	)	PUNCT
cana-5829	965	18	)	)	PUNCT
cana-5829	965	19	(	(	PUNCT
cana-5829	965	20	𝑁𝑜𝑟𝑚𝛿𝐹22	𝑁𝑜𝑟𝑚𝛿𝐹22	X
cana-5829	965	21	(	(	PUNCT
cana-5829	965	22	𝑦	𝑦	NOUN
cana-5829	965	23	)	)	PUNCT
cana-5829	965	24	𝑁𝑜𝑟𝑚𝛾𝐹22	𝑁𝑜𝑟𝑚𝛾𝐹22	X
cana-5829	965	25	(	(	PUNCT
cana-5829	965	26	𝑦	𝑦	NOUN
cana-5829	965	27	)	)	PUNCT
cana-5829	965	28	)	)	PUNCT
cana-5829	965	29	)	)	PUNCT
cana-5829	966	1	𝑋11	𝑋11	PROPN
cana-5829	966	2	=(	=(	NOUN
cana-5829	966	3	𝑁𝑜𝑟𝑚𝜗𝐸11	𝑁𝑜𝑟𝑚𝜗𝐸11	X
cana-5829	966	4	(	(	PUNCT
cana-5829	966	5	𝑥	𝑥	NOUN
cana-5829	966	6	)	)	PUNCT
cana-5829	966	7	𝑁𝑜𝑟𝑚µ𝐸11(𝑥	𝑁𝑜𝑟𝑚µ𝐸11(𝑥	NOUN
cana-5829	966	8	)	)	PUNCT
cana-5829	966	9	)	)	PUNCT
cana-5829	966	10	∆	∆	PROPN
cana-5829	966	11	(	(	PUNCT
cana-5829	966	12	𝑁𝑜𝑟𝑚𝛿𝐹11	𝑁𝑜𝑟𝑚𝛿𝐹11	X
cana-5829	966	13	(	(	PUNCT
cana-5829	966	14	𝑦	𝑦	NOUN
cana-5829	966	15	)	)	PUNCT
cana-5829	966	16	𝑁𝑜𝑟𝑚𝛾𝐹11(𝑦	𝑁𝑜𝑟𝑚𝛾𝐹11(𝑦	NUM
cana-5829	966	17	)	)	PUNCT
cana-5829	966	18	)	)	PUNCT
cana-5829	966	19	𝑋12	𝑋12	PROPN
cana-5829	966	20	=(	=(	NOUN
cana-5829	966	21	𝑁𝑜𝑟𝑚𝜗𝐸12	𝑁𝑜𝑟𝑚𝜗𝐸12	NOUN
cana-5829	966	22	(	(	PUNCT
cana-5829	966	23	𝑥	𝑥	NOUN
cana-5829	966	24	)	)	PUNCT
cana-5829	966	25	𝑁𝑜𝑟𝑚µ𝐸12(𝑥	𝑁𝑜𝑟𝑚µ𝐸12(𝑥	NOUN
cana-5829	966	26	)	)	PUNCT
cana-5829	966	27	)	)	PUNCT
cana-5829	967	1	∆	∆	PROPN
cana-5829	967	2	(	(	PUNCT
cana-5829	967	3	𝑁𝑜𝑟𝑚𝛿𝐹12	𝑁𝑜𝑟𝑚𝛿𝐹12	X
cana-5829	967	4	(	(	PUNCT
cana-5829	967	5	𝑦	𝑦	NOUN
cana-5829	967	6	)	)	PUNCT
cana-5829	967	7	𝑁𝑜𝑟𝑚𝛾𝐹12(𝑦	𝑁𝑜𝑟𝑚𝛾𝐹12(𝑦	NOUN
cana-5829	967	8	)	)	PUNCT
cana-5829	967	9	)	)	PUNCT
cana-5829	968	1	𝑋21	𝑋21	VERB
cana-5829	968	2	=(	=(	NOUN
cana-5829	968	3	𝑁𝑜𝑟𝑚𝜗𝐸21	𝑁𝑜𝑟𝑚𝜗𝐸21	NOUN
cana-5829	968	4	(	(	PUNCT
cana-5829	968	5	𝑥	𝑥	NOUN
cana-5829	968	6	)	)	PUNCT
cana-5829	968	7	𝑁𝑜𝑟𝑚µ𝐸21	𝑁𝑜𝑟𝑚µ𝐸21	NOUN
cana-5829	968	8	(	(	PUNCT
cana-5829	968	9	𝑥	𝑥	NOUN
cana-5829	968	10	)	)	PUNCT
cana-5829	968	11	)	)	PUNCT
cana-5829	968	12	∆	∆	PROPN
cana-5829	968	13	(	(	PUNCT
cana-5829	968	14	𝑁𝑜𝑟𝑚𝛿𝐹21	𝑁𝑜𝑟𝑚𝛿𝐹21	X
cana-5829	968	15	(	(	PUNCT
cana-5829	968	16	𝑦	𝑦	NOUN
cana-5829	968	17	)	)	PUNCT
cana-5829	968	18	𝑁𝑜𝑟𝑚𝛾𝐹21	𝑁𝑜𝑟𝑚𝛾𝐹21	ADV
cana-5829	968	19	(	(	PUNCT
cana-5829	968	20	𝑦	𝑦	NOUN
cana-5829	968	21	)	)	PUNCT
cana-5829	968	22	)	)	PUNCT
cana-5829	969	1	𝑋22	𝑋22	VERB
cana-5829	969	2	=(	=(	PROPN
cana-5829	969	3	𝑁𝑜𝑟𝑚𝜗𝐸22	𝑁𝑜𝑟𝑚𝜗𝐸22	PROPN
cana-5829	969	4	(	(	PUNCT
cana-5829	969	5	𝑥	𝑥	NOUN
cana-5829	969	6	)	)	PUNCT
cana-5829	969	7	𝑁𝑜𝑟𝑚µ𝐸22	𝑁𝑜𝑟𝑚µ𝐸22	NOUN
cana-5829	969	8	(	(	PUNCT
cana-5829	969	9	𝑥	𝑥	NOUN
cana-5829	969	10	)	)	PUNCT
cana-5829	969	11	)	)	PUNCT
cana-5829	970	1	∆	∆	PROPN
cana-5829	970	2	(	(	PUNCT
cana-5829	970	3	𝑁𝑜𝑟𝑚𝛿𝐹22	𝑁𝑜𝑟𝑚𝛿𝐹22	X
cana-5829	970	4	(	(	PUNCT
cana-5829	970	5	𝑦	𝑦	NOUN
cana-5829	970	6	)	)	PUNCT
cana-5829	970	7	𝑁𝑜𝑟𝑚𝛾𝐹22	𝑁𝑜𝑟𝑚𝛾𝐹22	X
cana-5829	970	8	(	(	PUNCT
cana-5829	970	9	𝑦	𝑦	NOUN
cana-5829	970	10	)	)	PUNCT
cana-5829	970	11	)	)	PUNCT
cana-5829	971	1	𝐴𝑝𝑝𝑙𝑦𝑖𝑛𝑔	𝐴𝑝𝑝𝑙𝑦𝑖𝑛𝑔	PROPN
cana-5829	971	2	𝑓𝑜𝑟𝑚𝑢𝑙𝑎	𝑓𝑜𝑟𝑚𝑢𝑙𝑎	VERB
cana-5829	971	3	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	971	4	̅̅̅̅	̅̅̅̅	NOUN
cana-5829	971	5			PUNCT
cana-5829	971	6	𝐵𝐹	𝐵𝐹	PROPN
cana-5829	971	7	̅̅̅̅	̅̅̅̅	NOUN
cana-5829	971	8	=	=	X
cana-5829	971	9	{	{	PUNCT
cana-5829	971	10	〈	〈	PROPN
cana-5829	971	11	x	x	PROPN
cana-5829	971	12	,	,	PUNCT
cana-5829	971	13	y	y	PROPN
cana-5829	971	14	〉	〉	NOUN
cana-5829	971	15	,	,	PUNCT
cana-5829	971	16	𝜗𝐴(x)+𝜗𝐵(y	𝜗𝐴(x)+𝜗𝐵(y	NUM
cana-5829	971	17	)	)	PUNCT
cana-5829	972	1	µ𝐴	µ𝐴	ADP
cana-5829	972	2	(	(	PUNCT
cana-5829	972	3	x)+	x)+	NUM
cana-5829	972	4	µ𝐵(y)+𝜗𝐴(x)+𝜗𝐵(y	µ𝐵(y)+𝜗𝐴(x)+𝜗𝐵(y	NOUN
cana-5829	972	5	)	)	PUNCT
cana-5829	972	6	,	,	PUNCT
cana-5829	972	7	µ𝐴	µ𝐴	SCONJ
cana-5829	972	8	(	(	PUNCT
cana-5829	972	9	x)+	x)+	NUM
cana-5829	972	10	µ𝐵(y	µ𝐵(y	NOUN
cana-5829	972	11	)	)	PUNCT
cana-5829	972	12	µ𝐴	µ𝐴	ADP
cana-5829	972	13	(	(	PUNCT
cana-5829	972	14	x)+	x)+	NUM
cana-5829	972	15	µ𝐵(y)+𝜗𝐴(x)+𝜗𝐵(y	µ𝐵(y)+𝜗𝐴(x)+𝜗𝐵(y	NOUN
cana-5829	972	16	)	)	PUNCT
cana-5829	972	17	:	:	PUNCT
cana-5829	972	18	xe	xe	PROPN
cana-5829	972	19	,	,	PUNCT
cana-5829	972	20	y𝐹	y𝐹	PROPN
cana-5829	972	21	}	}	PUNCT
cana-5829	972	22	x11	x11	NOUN
cana-5829	972	23	=	=	SYM
cana-5829	972	24	normϑe11	normϑe11	X
cana-5829	972	25	(	(	PUNCT
cana-5829	972	26	x)+normδf11	x)+normδf11	X
cana-5829	972	27	(	(	PUNCT
cana-5829	972	28	y	y	NOUN
cana-5829	972	29	)	)	PUNCT
cana-5829	972	30	normµe11	normµe11	NOUN
cana-5829	972	31	(	(	PUNCT
cana-5829	972	32	x)+normγf11	x)+normγf11	PROPN
cana-5829	972	33	(	(	PUNCT
cana-5829	972	34	y)+normϑe11	y)+normϑe11	PROPN
cana-5829	972	35	(	(	PUNCT
cana-5829	972	36	x)+normδf11	x)+normδf11	X
cana-5829	972	37	(	(	PUNCT
cana-5829	972	38	y	y	NOUN
cana-5829	972	39	)	)	PUNCT
cana-5829	972	40	,	,	PUNCT
cana-5829	972	41	normµe11	normµe11	NOUN
cana-5829	972	42	(	(	PUNCT
cana-5829	972	43	x)+normγf11	x)+normγf11	PROPN
cana-5829	972	44	(	(	PUNCT
cana-5829	972	45	y	y	NOUN
cana-5829	972	46	)	)	PUNCT
cana-5829	972	47	normµe11	normµe11	NOUN
cana-5829	972	48	(	(	PUNCT
cana-5829	972	49	x)+normγf11	x)+normγf11	PROPN
cana-5829	972	50	(	(	PUNCT
cana-5829	972	51	y)+normϑe11	y)+normϑe11	PROPN
cana-5829	972	52	(	(	PUNCT
cana-5829	972	53	x)+normδf11	x)+normδf11	X
cana-5829	972	54	(	(	PUNCT
cana-5829	972	55	y	y	NOUN
cana-5829	972	56	)	)	PUNCT
cana-5829	972	57	x12	x12	NOUN
cana-5829	972	58	=	=	SYM
cana-5829	972	59	normϑe12	normϑe12	NOUN
cana-5829	972	60	(	(	PUNCT
cana-5829	972	61	x)+normδf12	x)+normδf12	PROPN
cana-5829	972	62	(	(	PUNCT
cana-5829	972	63	y	y	NOUN
cana-5829	972	64	)	)	PUNCT
cana-5829	972	65	normµe12	normµe12	NOUN
cana-5829	972	66	(	(	PUNCT
cana-5829	972	67	x)+normγf12	x)+normγf12	X
cana-5829	972	68	(	(	PUNCT
cana-5829	972	69	y)+normϑe12	y)+normϑe12	NOUN
cana-5829	972	70	(	(	PUNCT
cana-5829	972	71	x)+normδf12	x)+normδf12	PROPN
cana-5829	972	72	(	(	PUNCT
cana-5829	972	73	y	y	NOUN
cana-5829	972	74	)	)	PUNCT
cana-5829	972	75	,	,	PUNCT
cana-5829	972	76	normµe12	normµe12	NOUN
cana-5829	972	77	(	(	PUNCT
cana-5829	972	78	x)+normγf12	x)+normγf12	PROPN
cana-5829	972	79	(	(	PUNCT
cana-5829	972	80	y	y	NOUN
cana-5829	972	81	)	)	PUNCT
cana-5829	972	82	normµe12	normµe12	NOUN
cana-5829	972	83	(	(	PUNCT
cana-5829	972	84	x)+normγf12	x)+normγf12	X
cana-5829	972	85	(	(	PUNCT
cana-5829	972	86	y)+normϑe12	y)+normϑe12	NOUN
cana-5829	972	87	(	(	PUNCT
cana-5829	972	88	x)+normδf12	x)+normδf12	PROPN
cana-5829	972	89	(	(	PUNCT
cana-5829	972	90	y	y	NOUN
cana-5829	972	91	)	)	PUNCT
cana-5829	972	92	x21	x21	PROPN
cana-5829	972	93	=	=	SYM
cana-5829	972	94	normϑ21	normϑ21	NOUN
cana-5829	972	95	(	(	PUNCT
cana-5829	972	96	x)+normδf21	x)+normδf21	PROPN
cana-5829	972	97	(	(	PUNCT
cana-5829	972	98	y	y	NOUN
cana-5829	972	99	)	)	PUNCT
cana-5829	972	100	normµe21	normµe21	NOUN
cana-5829	972	101	(	(	PUNCT
cana-5829	972	102	x)+normγf21	x)+normγf21	X
cana-5829	972	103	(	(	PUNCT
cana-5829	972	104	y)+normϑe21	y)+normϑe21	PROPN
cana-5829	972	105	(	(	PUNCT
cana-5829	972	106	x)+normδf21	x)+normδf21	PROPN
cana-5829	972	107	(	(	PUNCT
cana-5829	972	108	y	y	NOUN
cana-5829	972	109	)	)	PUNCT
cana-5829	972	110	,	,	PUNCT
cana-5829	972	111	normµe21	normµe21	PROPN
cana-5829	972	112	(	(	PUNCT
cana-5829	972	113	x)+normγf21	x)+normγf21	X
cana-5829	972	114	(	(	PUNCT
cana-5829	972	115	y	y	NOUN
cana-5829	972	116	)	)	PUNCT
cana-5829	972	117	normµe21	normµe21	NOUN
cana-5829	972	118	(	(	PUNCT
cana-5829	972	119	x)+normγf21	x)+normγf21	X
cana-5829	972	120	(	(	PUNCT
cana-5829	972	121	y)+normϑe21	y)+normϑe21	PROPN
cana-5829	972	122	(	(	PUNCT
cana-5829	972	123	x)+normδf21	x)+normδf21	PROPN
cana-5829	972	124	(	(	PUNCT
cana-5829	972	125	y	y	NOUN
cana-5829	972	126	)	)	PUNCT
cana-5829	972	127	x22	x22	NOUN
cana-5829	972	128	=	=	SYM
cana-5829	972	129	normϑe22	normϑe22	NOUN
cana-5829	972	130	(	(	PUNCT
cana-5829	972	131	x)+normδf22	x)+normδf22	PROPN
cana-5829	972	132	(	(	PUNCT
cana-5829	972	133	y	y	NOUN
cana-5829	972	134	)	)	PUNCT
cana-5829	972	135	normµe22	normµe22	NOUN
cana-5829	972	136	(	(	PUNCT
cana-5829	972	137	x)+normγf22	x)+normγf22	X
cana-5829	972	138	(	(	PUNCT
cana-5829	972	139	y)+normϑe22	y)+normϑe22	X
cana-5829	972	140	(	(	PUNCT
cana-5829	972	141	x)+normδf22	x)+normδf22	PROPN
cana-5829	972	142	(	(	PUNCT
cana-5829	972	143	y	y	NOUN
cana-5829	972	144	)	)	PUNCT
cana-5829	972	145	,	,	PUNCT
cana-5829	972	146	normµe22	normµe22	NOUN
cana-5829	972	147	(	(	PUNCT
cana-5829	972	148	x)+normγf22	x)+normγf22	X
cana-5829	972	149	(	(	PUNCT
cana-5829	972	150	y	y	NOUN
cana-5829	972	151	)	)	PUNCT
cana-5829	972	152	normµe22	normµe22	NOUN
cana-5829	972	153	(	(	PUNCT
cana-5829	972	154	x)+normγf22	x)+normγf22	X
cana-5829	972	155	(	(	PUNCT
cana-5829	972	156	y)+normϑe22	y)+normϑe22	X
cana-5829	972	157	(	(	PUNCT
cana-5829	972	158	x)+normδf22	x)+normδf22	PROPN
cana-5829	972	159	(	(	PUNCT
cana-5829	972	160	y	y	X
cana-5829	972	161	)	)	PUNCT
cana-5829	972	162	we	we	PRON
cana-5829	972	163	have	have	VERB
cana-5829	972	164	norm𝐴̅	norm𝐴̅	PROPN
cana-5829	972	165	𝐸	𝐸	PROPN
cana-5829	972	166	𝑁𝑜𝑟𝑚	𝑁𝑜𝑟𝑚	PROPN
cana-5829	972	167	�	�	NOUN
cana-5829	972	168	̅	̅	NOUN
cana-5829	972	169	�	�	NOUN
cana-5829	972	170	𝐹	𝐹	NOUN
cana-5829	972	171	=	=	PUNCT
cana-5829	972	172	(	(	PUNCT
cana-5829	972	173	𝑋11	𝑋11	PROPN
cana-5829	972	174	𝑋12	𝑋12	PROPN
cana-5829	972	175	𝑋21	𝑋21	NOUN
cana-5829	972	176	𝑋22	𝑋22	ADJ
cana-5829	972	177	)	)	PUNCT
cana-5829	972	178	is	be	AUX
cana-5829	972	179	also	also	ADV
cana-5829	972	180	intuitionistic	intuitionistic	ADJ
cana-5829	972	181	fuzzy	fuzzy	ADJ
cana-5829	972	182	matrix	matrix	NOUN
cana-5829	972	183	.	.	PUNCT
cana-5829	973	1	communications	communication	NOUN
cana-5829	973	2	on	on	ADP
cana-5829	973	3	applied	apply	VERB
cana-5829	973	4	nonlinear	nonlinear	ADJ
cana-5829	973	5	analysis	analysis	NOUN
cana-5829	973	6	issn	issn	NOUN
cana-5829	973	7	:	:	PUNCT
cana-5829	973	8	1074	1074	NUM
cana-5829	973	9	-	-	PUNCT
cana-5829	973	10	133x	133x	NUM
cana-5829	973	11	vol	vol	VERB
cana-5829	973	12	32	32	NUM
cana-5829	973	13	no	no	NOUN
cana-5829	973	14	.	.	PUNCT
cana-5829	974	1	10s	10	NOUN
cana-5829	974	2	(	(	PUNCT
cana-5829	974	3	2025	2025	NUM
cana-5829	974	4	)	)	PUNCT
cana-5829	974	5	2955	2955	NUM
cana-5829	974	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5829	974	7	example	example	NOUN
cana-5829	974	8	:	:	PUNCT
cana-5829	975	1	if	if	SCONJ
cana-5829	975	2	𝑨𝑬=	𝑨𝑬=	NOUN
cana-5829	975	3	(	(	PUNCT
cana-5829	975	4	(	(	PUNCT
cana-5829	975	5	.9	.9	NUM
cana-5829	975	6	,	,	PUNCT
cana-5829	975	7	.4	.4	NUM
cana-5829	975	8	)	)	PUNCT
cana-5829	975	9	(	(	PUNCT
cana-5829	975	10	.4	.4	PROPN
cana-5829	975	11	,	,	PUNCT
cana-5829	975	12	.1	.1	NUM
cana-5829	975	13	)	)	PUNCT
cana-5829	975	14	(	(	PUNCT
cana-5829	975	15	.5	.5	NUM
cana-5829	975	16	,	,	PUNCT
cana-5829	975	17	.3	.3	NUM
cana-5829	975	18	)	)	PUNCT
cana-5829	975	19	(	(	PUNCT
cana-5829	975	20	.8	.8	NUM
cana-5829	975	21	,	,	PUNCT
cana-5829	975	22	.3	.3	NUM
cana-5829	975	23	)	)	PUNCT
cana-5829	975	24	)	)	PUNCT
cana-5829	975	25	and𝑩𝑭	and𝑩𝑭	NOUN
cana-5829	975	26	=	=	SYM
cana-5829	975	27	(	(	PUNCT
cana-5829	975	28	(	(	PUNCT
cana-5829	975	29	.8	.8	NUM
cana-5829	975	30	,	,	PUNCT
cana-5829	975	31	.6	.6	NUM
cana-5829	975	32	)	)	PUNCT
cana-5829	975	33	(	(	PUNCT
cana-5829	975	34	.6	.6	PROPN
cana-5829	975	35	,	,	PUNCT
cana-5829	975	36	.3	.3	NUM
cana-5829	975	37	)	)	PUNCT
cana-5829	975	38	(	(	PUNCT
cana-5829	975	39	.7	.7	PROPN
cana-5829	975	40	,	,	PUNCT
cana-5829	975	41	.5	.5	NUM
cana-5829	975	42	)	)	PUNCT
cana-5829	975	43	(	(	PUNCT
cana-5829	975	44	.9	.9	NUM
cana-5829	975	45	,	,	PUNCT
cana-5829	975	46	.4	.4	NUM
cana-5829	975	47	)	)	PUNCT
cana-5829	975	48	)	)	PUNCT
cana-5829	975	49	are	be	AUX
cana-5829	975	50	two	two	NUM
cana-5829	975	51	intuitionistic	intuitionistic	ADJ
cana-5829	975	52	fuzzy	fuzzy	ADJ
cana-5829	975	53	matrices	matrix	NOUN
cana-5829	975	54	over	over	ADP
cana-5829	975	55	different	different	ADJ
cana-5829	975	56	universe	universe	NOUN
cana-5829	975	57	e	e	NOUN
cana-5829	975	58	and	and	CCONJ
cana-5829	975	59	f	f	PROPN
cana-5829	975	60	then	then	ADV
cana-5829	975	61	norm𝐴̅	norm𝐴̅	PROPN
cana-5829	975	62	𝐸𝑁𝑜𝑟𝑚	𝐸𝑁𝑜𝑟𝑚	NOUN
cana-5829	975	63	�	�	NOUN
cana-5829	975	64	̅	̅	NOUN
cana-5829	975	65	�	�	NOUN
cana-5829	975	66	𝐹is	𝐹i	VERB
cana-5829	975	67	also	also	ADV
cana-5829	975	68	fuzzy	fuzzy	ADJ
cana-5829	975	69	matrix	matrix	NOUN
cana-5829	975	70	set	set	NOUN
cana-5829	975	71	.	.	PUNCT
cana-5829	976	1	proof	proof	NOUN
cana-5829	976	2	:	:	PUNCT
cana-5829	976	3	given	give	VERB
cana-5829	976	4	𝑨𝑬	𝑨𝑬	PROPN
cana-5829	976	5	=(	=(	NOUN
cana-5829	976	6	(	(	PUNCT
cana-5829	976	7	.9	.9	NUM
cana-5829	976	8	,	,	PUNCT
cana-5829	976	9	.4	.4	NUM
cana-5829	976	10	)	)	PUNCT
cana-5829	976	11	(	(	PUNCT
cana-5829	976	12	.4	.4	PROPN
cana-5829	976	13	,	,	PUNCT
cana-5829	976	14	.1	.1	NUM
cana-5829	976	15	)	)	PUNCT
cana-5829	976	16	(	(	PUNCT
cana-5829	976	17	.5	.5	NUM
cana-5829	976	18	,	,	PUNCT
cana-5829	976	19	.3	.3	NUM
cana-5829	976	20	)	)	PUNCT
cana-5829	976	21	(	(	PUNCT
cana-5829	976	22	.8	.8	NUM
cana-5829	976	23	,	,	PUNCT
cana-5829	976	24	.3	.3	NUM
cana-5829	976	25	)	)	PUNCT
cana-5829	976	26	)	)	PUNCT
cana-5829	976	27	and	and	CCONJ
cana-5829	976	28	𝑩𝑭	𝑩𝑭	PROPN
cana-5829	976	29	=	=	SYM
cana-5829	976	30	(	(	PUNCT
cana-5829	976	31	(	(	PUNCT
cana-5829	976	32	.8	.8	NUM
cana-5829	976	33	,	,	PUNCT
cana-5829	976	34	.6	.6	NUM
cana-5829	976	35	)	)	PUNCT
cana-5829	976	36	(	(	PUNCT
cana-5829	976	37	.6	.6	PROPN
cana-5829	976	38	,	,	PUNCT
cana-5829	976	39	.3	.3	NUM
cana-5829	976	40	)	)	PUNCT
cana-5829	976	41	(	(	PUNCT
cana-5829	976	42	.7	.7	PROPN
cana-5829	976	43	,	,	PUNCT
cana-5829	976	44	.5	.5	NUM
cana-5829	976	45	)	)	PUNCT
cana-5829	976	46	(	(	PUNCT
cana-5829	976	47	.9	.9	NUM
cana-5829	976	48	,	,	PUNCT
cana-5829	976	49	.4	.4	NUM
cana-5829	976	50	)	)	PUNCT
cana-5829	976	51	)	)	PUNCT
cana-5829	977	1	𝑁𝑜𝑟𝑚̅̅	𝑁𝑜𝑟𝑚̅̅	NOUN
cana-5829	977	2	̅̅	̅̅	PROPN
cana-5829	977	3	̅̅	̅̅	PROPN
cana-5829	977	4	̅̅	̅̅	PROPN
cana-5829	977	5	𝐴	𝐴	PROPN
cana-5829	977	6	=(	=(	NOUN
cana-5829	977	7	(	(	PUNCT
cana-5829	977	8	.8,1	.8,1	NOUN
cana-5829	977	9	)	)	PUNCT
cana-5829	977	10	(	(	PUNCT
cana-5829	977	11	0	0	NUM
cana-5829	977	12	,	,	PUNCT
cana-5829	977	13	.3	.3	NUM
cana-5829	977	14	)	)	PUNCT
cana-5829	977	15	(	(	PUNCT
cana-5829	977	16	.2	.2	NUM
cana-5829	977	17	,	,	PUNCT
cana-5829	977	18	.8	.8	NUM
cana-5829	977	19	)	)	PUNCT
cana-5829	977	20	(	(	PUNCT
cana-5829	977	21	.7	.7	PROPN
cana-5829	977	22	,	,	PUNCT
cana-5829	977	23	.8	.8	NUM
cana-5829	977	24	)	)	PUNCT
cana-5829	977	25	)	)	PUNCT
cana-5829	977	26	and	and	CCONJ
cana-5829	978	1	𝑁𝑜𝑟𝑚̅̅	𝑁𝑜𝑟𝑚̅̅	PROPN
cana-5829	978	2	̅̅	̅̅	PROPN
cana-5829	978	3	̅̅	̅̅	PROPN
cana-5829	978	4	̅̅	̅̅	PROPN
cana-5829	978	5	𝐵=	𝐵=	PROPN
cana-5829	978	6	(	(	PUNCT
cana-5829	978	7	(	(	PUNCT
cana-5829	978	8	.5	.5	NUM
cana-5829	978	9	,	,	PUNCT
cana-5829	978	10	1	1	NUM
cana-5829	978	11	)	)	PUNCT
cana-5829	978	12	(	(	PUNCT
cana-5829	978	13	0	0	NUM
cana-5829	978	14	,	,	PUNCT
cana-5829	978	15	.5	.5	NUM
cana-5829	978	16	)	)	PUNCT
cana-5829	978	17	(	(	PUNCT
cana-5829	978	18	.3	.3	NUM
cana-5829	978	19	,	,	PUNCT
cana-5829	978	20	.8	.8	NUM
cana-5829	978	21	)	)	PUNCT
cana-5829	978	22	(	(	PUNCT
cana-5829	978	23	.8	.8	PROPN
cana-5829	978	24	,	,	PUNCT
cana-5829	978	25	.7	.7	PROPN
cana-5829	978	26	)	)	PUNCT
cana-5829	978	27	)	)	PUNCT
cana-5829	979	1	𝑁𝑜𝑟𝑚̅̅	𝑁𝑜𝑟𝑚̅̅	NOUN
cana-5829	979	2	̅̅	̅̅	PROPN
cana-5829	979	3	̅̅	̅̅	PROPN
cana-5829	979	4	̅̅	̅̅	PROPN
cana-5829	979	5	𝐴	𝐴	PROPN
cana-5829	979	6	𝑁𝑜𝑟𝑚̅̅	𝑁𝑜𝑟𝑚̅̅	PROPN
cana-5829	979	7	̅̅	̅̅	PROPN
cana-5829	979	8	̅̅	̅̅	PROPN
cana-5829	979	9	̅̅	̅̅	PROPN
cana-5829	979	10	̅	̅	PROPN
cana-5829	979	11	𝐵	𝐵	NOUN
cana-5829	979	12	=	=	SYM
cana-5829	979	13	(	(	PUNCT
cana-5829	979	14	(	(	PUNCT
cana-5829	979	15	.8,1	.8,1	NOUN
cana-5829	979	16	)	)	PUNCT
cana-5829	979	17	(	(	PUNCT
cana-5829	979	18	0	0	NUM
cana-5829	979	19	,	,	PUNCT
cana-5829	979	20	.3	.3	NUM
cana-5829	979	21	)	)	PUNCT
cana-5829	979	22	(	(	PUNCT
cana-5829	979	23	.2	.2	NUM
cana-5829	979	24	,	,	PUNCT
cana-5829	979	25	.8	.8	NUM
cana-5829	979	26	)	)	PUNCT
cana-5829	979	27	(	(	PUNCT
cana-5829	979	28	.7	.7	PROPN
cana-5829	979	29	,	,	PUNCT
cana-5829	979	30	.8	.8	NUM
cana-5829	979	31	)	)	PUNCT
cana-5829	979	32	)	)	PUNCT
cana-5829	979	33			X
cana-5829	980	1	(	(	PUNCT
cana-5829	980	2	(	(	PUNCT
cana-5829	980	3	.5	.5	NUM
cana-5829	980	4	,	,	PUNCT
cana-5829	980	5	1	1	NUM
cana-5829	980	6	)	)	PUNCT
cana-5829	980	7	(	(	PUNCT
cana-5829	980	8	0	0	NUM
cana-5829	980	9	,	,	PUNCT
cana-5829	980	10	.5	.5	NUM
cana-5829	980	11	)	)	PUNCT
cana-5829	980	12	(	(	PUNCT
cana-5829	980	13	.3	.3	NUM
cana-5829	980	14	,	,	PUNCT
cana-5829	980	15	.8	.8	NUM
cana-5829	980	16	)	)	PUNCT
cana-5829	980	17	(	(	PUNCT
cana-5829	980	18	.8	.8	PROPN
cana-5829	980	19	,	,	PUNCT
cana-5829	980	20	.7	.7	PROPN
cana-5829	980	21	)	)	PUNCT
cana-5829	980	22	)	)	PUNCT
cana-5829	981	1	𝑋11	𝑋11	PROPN
cana-5829	981	2	=	=	SYM
cana-5829	981	3	(	(	PUNCT
cana-5829	981	4	.8	.8	PROPN
cana-5829	981	5	,	,	PUNCT
cana-5829	981	6	1)	1)	NUM
cana-5829	981	7	(	(	PUNCT
cana-5829	981	8	.	.	NOUN
cana-5829	981	9	5	5	NUM
cana-5829	981	10	,	,	PUNCT
cana-5829	981	11	1	1	NUM
cana-5829	981	12	)	)	PUNCT
cana-5829	981	13	𝑋12	𝑋12	NOUN
cana-5829	981	14	=	=	PUNCT
cana-5829	981	15	(	(	PUNCT
cana-5829	981	16	0	0	NUM
cana-5829	981	17	,	,	PUNCT
cana-5829	981	18	.3)(0	.3)(0	PROPN
cana-5829	981	19	,	,	PUNCT
cana-5829	981	20	.5	.5	NUM
cana-5829	981	21	)	)	PUNCT
cana-5829	981	22	𝑋21	𝑋21	NOUN
cana-5829	981	23	=	=	SYM
cana-5829	981	24	(	(	PUNCT
cana-5829	981	25	.2	.2	NUM
cana-5829	981	26	,	,	PUNCT
cana-5829	981	27	.8)	.8)	PROPN
cana-5829	981	28	(	(	PUNCT
cana-5829	981	29	.3	.3	NUM
cana-5829	981	30	,	,	PUNCT
cana-5829	981	31	.8	.8	NUM
cana-5829	981	32	)	)	PUNCT
cana-5829	982	1	𝑋22	𝑋22	ADJ
cana-5829	982	2	=	=	PUNCT
cana-5829	982	3	(	(	PUNCT
cana-5829	982	4	.	.	NOUN
cana-5829	982	5	7	7	NUM
cana-5829	982	6	,	,	PUNCT
cana-5829	982	7	.8)(.8	.8)(.8	PROPN
cana-5829	982	8	,	,	PUNCT
cana-5829	982	9	.7	.7	PROPN
cana-5829	982	10	)	)	PUNCT
cana-5829	983	1	𝐴𝑝𝑝𝑙𝑦𝑖𝑛𝑔	𝐴𝑝𝑝𝑙𝑦𝑖𝑛𝑔	PROPN
cana-5829	983	2	𝑓𝑜𝑟𝑚𝑢𝑙𝑎	𝑓𝑜𝑟𝑚𝑢𝑙𝑎	VERB
cana-5829	983	3	𝐴𝐸	𝐴𝐸	PROPN
cana-5829	983	4	̅̅̅̅	̅̅̅̅	NOUN
cana-5829	983	5			PUNCT
cana-5829	983	6	𝐵𝐹	𝐵𝐹	PROPN
cana-5829	983	7	̅̅̅̅	̅̅̅̅	NOUN
cana-5829	983	8	=	=	X
cana-5829	983	9	{	{	PUNCT
cana-5829	983	10	〈	〈	PROPN
cana-5829	983	11	x	x	PROPN
cana-5829	983	12	,	,	PUNCT
cana-5829	983	13	y	y	PROPN
cana-5829	983	14	〉	〉	NOUN
cana-5829	983	15	,	,	PUNCT
cana-5829	983	16	𝜗𝐴(x)+𝜗𝐵(y	𝜗𝐴(x)+𝜗𝐵(y	NUM
cana-5829	983	17	)	)	PUNCT
cana-5829	984	1	µ𝐴	µ𝐴	ADP
cana-5829	984	2	(	(	PUNCT
cana-5829	984	3	x)+	x)+	NUM
cana-5829	984	4	µ𝐵(y)+𝜗𝐴(x)+𝜗𝐵(y	µ𝐵(y)+𝜗𝐴(x)+𝜗𝐵(y	NOUN
cana-5829	984	5	)	)	PUNCT
cana-5829	984	6	,	,	PUNCT
cana-5829	984	7	µ𝐴	µ𝐴	SCONJ
cana-5829	984	8	(	(	PUNCT
cana-5829	984	9	x)+	x)+	NUM
cana-5829	984	10	µ𝐵(y	µ𝐵(y	NOUN
cana-5829	984	11	)	)	PUNCT
cana-5829	984	12	µ𝐴	µ𝐴	ADP
cana-5829	984	13	(	(	PUNCT
cana-5829	984	14	x)+	x)+	NUM
cana-5829	984	15	µ𝐵(y)+𝜗𝐴(x)+𝜗𝐵(y	µ𝐵(y)+𝜗𝐴(x)+𝜗𝐵(y	NOUN
cana-5829	984	16	)	)	PUNCT
cana-5829	984	17	:	:	PUNCT
cana-5829	984	18	xe	xe	PROPN
cana-5829	984	19	,	,	PUNCT
cana-5829	984	20	y𝐹	y𝐹	NOUN
cana-5829	984	21	}	}	PUNCT
cana-5829	984	22	𝑋11	𝑋11	PROPN
cana-5829	984	23	=	=	SYM
cana-5829	984	24	(	(	PUNCT
cana-5829	984	25	.8)+(.5	.8)+(.5	PROPN
cana-5829	984	26	)	)	PUNCT
cana-5829	984	27	(	(	PUNCT
cana-5829	984	28	1)+(1)+(.8)+(.5	1)+(1)+(.8)+(.5	NUM
cana-5829	984	29	)	)	PUNCT
cana-5829	984	30	,	,	PUNCT
cana-5829	984	31	(	(	PUNCT
cana-5829	984	32	1)+(1	1)+(1	NUM
cana-5829	984	33	)	)	PUNCT
cana-5829	984	34	(	(	PUNCT
cana-5829	984	35	1)+(1)+(.8)+(.5	1)+(1)+(.8)+(.5	NUM
cana-5829	984	36	)	)	PUNCT
cana-5829	984	37	𝑋12	𝑋12	NOUN
cana-5829	984	38	=	=	SYM
cana-5829	984	39	(	(	PUNCT
cana-5829	984	40	0)+(0	0)+(0	NUM
cana-5829	984	41	)	)	PUNCT
cana-5829	984	42	(	(	PUNCT
cana-5829	984	43	.3)+(.5)+(0)+(0	.3)+(.5)+(0)+(0	PROPN
cana-5829	984	44	)	)	PUNCT
cana-5829	984	45	,	,	PUNCT
cana-5829	984	46	(	(	PUNCT
cana-5829	984	47	.3)+(.5	.3)+(.5	PROPN
cana-5829	984	48	)	)	PUNCT
cana-5829	984	49	(	(	PUNCT
cana-5829	984	50	.3)+(.5)+(0)+(0	.3)+(.5)+(0)+(0	PROPN
cana-5829	984	51	)	)	PUNCT
cana-5829	985	1	𝑋21	𝑋21	NOUN
cana-5829	985	2	=	=	SYM
cana-5829	985	3	(	(	PUNCT
cana-5829	985	4	.2)+(.3	.2)+(.3	PROPN
cana-5829	985	5	)	)	PUNCT
cana-5829	985	6	(	(	PUNCT
cana-5829	985	7	.8)+(.8)+(.2)+(.3	.8)+(.8)+(.2)+(.3	PROPN
cana-5829	985	8	)	)	PUNCT
cana-5829	985	9	,	,	PUNCT
cana-5829	985	10	(	(	PUNCT
cana-5829	985	11	.8)+(.8	.8)+(.8	PROPN
cana-5829	985	12	)	)	PUNCT
cana-5829	985	13	(	(	PUNCT
cana-5829	985	14	.8)+(.8)+(.2)+(.3	.8)+(.8)+(.2)+(.3	NOUN
cana-5829	985	15	)	)	PUNCT
cana-5829	986	1	𝑋22	𝑋22	ADJ
cana-5829	986	2	=	=	SYM
cana-5829	986	3	(	(	PUNCT
cana-5829	986	4	.7)+(.8	.7)+(.8	PROPN
cana-5829	986	5	)	)	PUNCT
cana-5829	986	6	(	(	PUNCT
cana-5829	986	7	.8)+(.7)+(.7)+(.8	.8)+(.7)+(.7)+(.8	PROPN
cana-5829	986	8	)	)	PUNCT
cana-5829	986	9	,	,	PUNCT
cana-5829	986	10	(	(	PUNCT
cana-5829	986	11	.8)+(.7	.8)+(.7	PROPN
cana-5829	986	12	)	)	PUNCT
cana-5829	986	13	(	(	PUNCT
cana-5829	986	14	.8)+(.7)+(.7)+(.8	.8)+(.7)+(.7)+(.8	PROPN
cana-5829	986	15	)	)	PUNCT
cana-5829	987	1	𝑋11	𝑋11	PROPN
cana-5829	987	2	=	=	PRON
cana-5829	987	3	{	{	PUNCT
cana-5829	987	4	.4	.4	NUM
cana-5829	987	5	,	,	PUNCT
cana-5829	987	6	.6	.6	NUM
cana-5829	987	7	}	}	PUNCT
cana-5829	987	8	𝑋12	𝑋12	VERB
cana-5829	987	9	=	=	PRON
cana-5829	987	10	{	{	PUNCT
cana-5829	987	11	0	0	NUM
cana-5829	987	12	,	,	PUNCT
cana-5829	987	13	1	1	X
cana-5829	987	14	}	}	PUNCT
cana-5829	987	15	𝑋21	𝑋21	VERB
cana-5829	987	16	=	=	PRON
cana-5829	987	17	{	{	PUNCT
cana-5829	987	18	.2	.2	NUM
cana-5829	987	19	,	,	PUNCT
cana-5829	987	20	.8	.8	NUM
cana-5829	987	21	}	}	PUNCT
cana-5829	987	22	𝑋22	𝑋22	VERB
cana-5829	987	23	=	=	PRON
cana-5829	987	24	{	{	PUNCT
cana-5829	987	25	.5	.5	NUM
cana-5829	987	26	,	,	PUNCT
cana-5829	987	27	.5	.5	NUM
cana-5829	987	28	}	}	PUNCT
cana-5829	987	29	we	we	PRON
cana-5829	987	30	have	have	VERB
cana-5829	987	31	norm𝐴̅	norm𝐴̅	PROPN
cana-5829	987	32	𝐸	𝐸	PROPN
cana-5829	987	33	𝑁𝑜𝑟𝑚	𝑁𝑜𝑟𝑚	PROPN
cana-5829	987	34	�	�	NOUN
cana-5829	987	35	̅	̅	NOUN
cana-5829	987	36	�	�	NOUN
cana-5829	987	37	𝐹	𝐹	NOUN
cana-5829	987	38	=	=	PUNCT
cana-5829	987	39	(	(	PUNCT
cana-5829	987	40	(	(	PUNCT
cana-5829	987	41	.4	.4	NUM
cana-5829	987	42	,	,	PUNCT
cana-5829	987	43	.6	.6	NUM
cana-5829	987	44	)	)	PUNCT
cana-5829	987	45	(	(	PUNCT
cana-5829	987	46	0	0	NUM
cana-5829	987	47	,	,	PUNCT
cana-5829	987	48	.1	.1	NUM
cana-5829	987	49	)	)	PUNCT
cana-5829	987	50	(	(	PUNCT
cana-5829	987	51	.2	.2	NUM
cana-5829	987	52	,	,	PUNCT
cana-5829	987	53	.8	.8	NUM
cana-5829	987	54	)	)	PUNCT
cana-5829	987	55	(	(	PUNCT
cana-5829	987	56	.5	.5	NUM
cana-5829	987	57	,	,	PUNCT
cana-5829	987	58	.5	.5	NUM
cana-5829	987	59	)	)	PUNCT
cana-5829	987	60	)	)	PUNCT
cana-5829	987	61	is	be	AUX
cana-5829	987	62	also	also	ADV
cana-5829	987	63	intuitionistic	intuitionistic	ADJ
cana-5829	987	64	fuzzy	fuzzy	ADJ
cana-5829	987	65	matrix	matrix	NOUN
cana-5829	987	66	.	.	PUNCT
cana-5829	988	1	conclusion	conclusion	NOUN
cana-5829	988	2	:	:	PUNCT
cana-5829	988	3	normalization	normalization	NOUN
cana-5829	988	4	of	of	ADP
cana-5829	988	5	intuitionistic	intuitionistic	ADJ
cana-5829	988	6	fuzzy	fuzzy	ADJ
cana-5829	988	7	matrices	matrix	NOUN
cana-5829	988	8	ensures	ensure	VERB
cana-5829	988	9	that	that	SCONJ
cana-5829	988	10	the	the	DET
cana-5829	988	11	values	value	NOUN
cana-5829	988	12	are	be	AUX
cana-5829	988	13	scaled	scale	VERB
cana-5829	988	14	within	within	ADP
cana-5829	988	15	a	a	DET
cana-5829	988	16	specific	specific	ADJ
cana-5829	988	17	range	range	NOUN
cana-5829	988	18	,	,	PUNCT
cana-5829	988	19	facilitating	facilitate	VERB
cana-5829	988	20	their	their	PRON
cana-5829	988	21	use	use	NOUN
cana-5829	988	22	in	in	ADP
cana-5829	988	23	decision	decision	NOUN
cana-5829	988	24	-	-	PUNCT
cana-5829	988	25	making	make	VERB
cana-5829	988	26	algorithms	algorithm	NOUN
cana-5829	988	27	or	or	CCONJ
cana-5829	988	28	other	other	ADJ
cana-5829	988	29	computational	computational	ADJ
cana-5829	988	30	models	model	NOUN
cana-5829	988	31	.	.	PUNCT
cana-5829	989	1	the	the	DET
cana-5829	989	2	key	key	NOUN
cana-5829	989	3	is	be	AUX
cana-5829	989	4	to	to	PART
cana-5829	989	5	handle	handle	VERB
cana-5829	989	6	the	the	DET
cana-5829	989	7	three	three	NUM
cana-5829	989	8	components	component	NOUN
cana-5829	989	9	—	—	PUNCT
cana-5829	989	10	membership	membership	NOUN
cana-5829	989	11	,	,	PUNCT
cana-5829	989	12	non	non	ADJ
cana-5829	989	13	-	-	NOUN
cana-5829	989	14	membership	membership	NOUN
cana-5829	989	15	,	,	PUNCT
cana-5829	989	16	and	and	CCONJ
cana-5829	989	17	indeterminacy	indeterminacy	NOUN
cana-5829	989	18	—	—	PUNCT
cana-5829	989	19	carefully	carefully	ADV
cana-5829	989	20	to	to	PART
cana-5829	989	21	preserve	preserve	VERB
cana-5829	989	22	their	their	PRON
cana-5829	989	23	relationships	relationship	NOUN
cana-5829	989	24	while	while	SCONJ
cana-5829	989	25	standardizing	standardize	VERB
cana-5829	989	26	the	the	DET
cana-5829	989	27	values	value	NOUN
cana-5829	989	28	across	across	ADP
cana-5829	989	29	the	the	DET
cana-5829	989	30	matrix	matrix	NOUN
cana-5829	989	31	.	.	PUNCT
cana-5829	990	1	reference	reference	NOUN
cana-5829	990	2	[	[	X
cana-5829	990	3	1	1	NUM
cana-5829	990	4	]	]	X
cana-5829	990	5	atanassov	atanassov	NOUN
cana-5829	990	6	,	,	PUNCT
cana-5829	990	7	k.	k.	PROPN
cana-5829	990	8	,	,	PUNCT
cana-5829	990	9	“	"	PUNCT
cana-5829	990	10	intuitionistic	intuitionistic	ADJ
cana-5829	990	11	fuzzy	fuzzy	ADJ
cana-5829	990	12	sets	set	NOUN
cana-5829	990	13	”	"	PUNCT
cana-5829	990	14	,	,	PUNCT
cana-5829	990	15	fuzzy	fuzzy	ADJ
cana-5829	990	16	sets	set	NOUN
cana-5829	990	17	and	and	CCONJ
cana-5829	990	18	systems	system	NOUN
cana-5829	990	19	,	,	PUNCT
cana-5829	990	20	vol	vol	NOUN
cana-5829	990	21	.	.	PROPN
cana-5829	990	22	20	20	NUM
cana-5829	990	23	,	,	PUNCT
cana-5829	990	24	pp	pp	ADJ
cana-5829	990	25	.	.	PUNCT
cana-5829	991	1	87	87	NUM
cana-5829	991	2	-	-	SYM
cana-5829	991	3	96	96	NUM
cana-5829	991	4	,	,	PUNCT
cana-5829	991	5	1986	1986	NUM
cana-5829	991	6	[	[	X
cana-5829	991	7	2	2	NUM
cana-5829	991	8	]	]	X
cana-5829	991	9	b.	b.	PROPN
cana-5829	991	10	ahmad	ahmad	PROPN
cana-5829	991	11	and	and	CCONJ
cana-5829	991	12	a.	a.	PROPN
cana-5829	991	13	kharal	kharal	PROPN
cana-5829	991	14	,	,	PUNCT
cana-5829	991	15	on	on	ADP
cana-5829	991	16	fuzzy	fuzzy	ADJ
cana-5829	991	17	soft	soft	ADJ
cana-5829	991	18	sets	set	NOUN
cana-5829	991	19	,	,	PUNCT
cana-5829	991	20	advances	advance	NOUN
cana-5829	991	21	in	in	ADP
cana-5829	991	22	fuzzy	fuzzy	ADJ
cana-5829	991	23	systems	system	NOUN
cana-5829	991	24	,	,	PUNCT
cana-5829	991	25	(	(	PUNCT
cana-5829	991	26	2009	2009	NUM
cana-5829	991	27	)	)	PUNCT
cana-5829	991	28	,	,	PUNCT
cana-5829	991	29	1	1	NUM
cana-5829	991	30	-	-	SYM
cana-5829	991	31	6	6	NUM
cana-5829	991	32	.	.	PUNCT
cana-5829	992	1	communications	communication	NOUN
cana-5829	992	2	on	on	ADP
cana-5829	992	3	applied	apply	VERB
cana-5829	992	4	nonlinear	nonlinear	ADJ
cana-5829	992	5	analysis	analysis	NOUN
cana-5829	992	6	issn	issn	NOUN
cana-5829	992	7	:	:	PUNCT
cana-5829	992	8	1074	1074	NUM
cana-5829	992	9	-	-	PUNCT
cana-5829	992	10	133x	133x	NUM
cana-5829	992	11	vol	vol	VERB
cana-5829	992	12	32	32	NUM
cana-5829	992	13	no	no	NOUN
cana-5829	992	14	.	.	PUNCT
cana-5829	993	1	10s	10	NOUN
cana-5829	993	2	(	(	PUNCT
cana-5829	993	3	2025	2025	NUM
cana-5829	993	4	)	)	PUNCT
cana-5829	993	5	2956	2956	NUM
cana-5829	993	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5829	994	1	[	[	X
cana-5829	994	2	3	3	NUM
cana-5829	994	3	]	]	X
cana-5829	994	4	bărbăcioru	bărbăcioru	NOUN
cana-5829	994	5	,	,	PUNCT
cana-5829	994	6	i.	i.	PROPN
cana-5829	994	7	c.	c.	PROPN
cana-5829	994	8	,	,	PUNCT
cana-5829	994	9	“	"	PUNCT
cana-5829	994	10	multiplication	multiplication	NOUN
cana-5829	994	11	operation	operation	NOUN
cana-5829	994	12	on	on	ADP
cana-5829	994	13	intuitionistic	intuitionistic	ADJ
cana-5829	994	14	fuzzy	fuzzy	ADJ
cana-5829	994	15	numbers	number	NOUN
cana-5829	994	16	”	"	PUNCT
cana-5829	994	17	,	,	PUNCT
cana-5829	994	18	annals	annal	NOUN
cana-5829	994	19	of	of	ADP
cana-5829	994	20	the	the	DET
cana-5829	994	21	“	"	PUNCT
cana-5829	994	22	constantin	constantin	NOUN
cana-5829	994	23	brancusi	brancusi	NOUN
cana-5829	994	24	”	"	PUNCT
cana-5829	994	25	university	university	PROPN
cana-5829	994	26	of	of	ADP
cana-5829	994	27	targu	targu	PROPN
cana-5829	994	28	jiu	jiu	PROPN
cana-5829	994	29	,	,	PUNCT
cana-5829	994	30	engineering	engineering	NOUN
cana-5829	994	31	series	series	NOUN
cana-5829	994	32	,	,	PUNCT
cana-5829	994	33	vol	vol	NOUN
cana-5829	994	34	.	.	PROPN
cana-5829	994	35	4	4	NUM
cana-5829	994	36	,	,	PUNCT
cana-5829	994	37	pp	pp	ADJ
cana-5829	994	38	.	.	PUNCT
cana-5829	994	39	134	134	NUM
cana-5829	994	40	-	-	SYM
cana-5829	994	41	138	138	NUM
cana-5829	994	42	,	,	PUNCT
cana-5829	994	43	2018	2018	NUM
cana-5829	994	44	[	[	X
cana-5829	994	45	4	4	X
cana-5829	994	46	]	]	PUNCT
cana-5829	994	47	babitha	babitha	PROPN
cana-5829	994	48	k.v	k.v	PROPN
cana-5829	994	49	.	.	PROPN
cana-5829	994	50	and	and	CCONJ
cana-5829	994	51	sunil	sunil	PROPN
cana-5829	994	52	jacob	jacob	PROPN
cana-5829	994	53	john	john	PROPN
cana-5829	994	54	,	,	PUNCT
cana-5829	994	55	generalized	generalize	VERB
cana-5829	994	56	intuitionistic	intuitionistic	ADJ
cana-5829	994	57	fuzzy	fuzzy	ADJ
cana-5829	994	58	soft	soft	ADJ
cana-5829	994	59	sets	set	NOUN
cana-5829	994	60	and	and	CCONJ
cana-5829	994	61	its	its	PRON
cana-5829	994	62	applications	application	NOUN
cana-5829	994	63	,	,	PUNCT
cana-5829	994	64	gen	gen	PROPN
cana-5829	994	65	.	.	PROPN
cana-5829	994	66	math	math	PROPN
cana-5829	994	67	.	.	PUNCT
cana-5829	995	1	notes	note	NOUN
cana-5829	995	2	,	,	PUNCT
cana-5829	995	3	vol	vol	NOUN
cana-5829	995	4	.	.	PROPN
cana-5829	995	5	7	7	NUM
cana-5829	995	6	,	,	PUNCT
cana-5829	995	7	no.2	no.2	PROPN
cana-5829	995	8	.	.	PUNCT
cana-5829	996	1	december	december	PROPN
cana-5829	996	2	2011	2011	NUM
cana-5829	996	3	,	,	PUNCT
cana-5829	996	4	pp.1	pp.1	NOUN
cana-5829	996	5	-	-	PUNCT
cana-5829	996	6	14	14	NUM
cana-5829	996	7	[	[	X
cana-5829	996	8	5	5	NUM
cana-5829	996	9	]	]	PUNCT
cana-5829	996	10	b.chetia	b.chetia	ADV
cana-5829	996	11	and	and	CCONJ
cana-5829	996	12	p.k	p.k	PROPN
cana-5829	996	13	.	.	PUNCT
cana-5829	996	14	das	das	PROPN
cana-5829	996	15	,	,	PUNCT
cana-5829	996	16	some	some	DET
cana-5829	996	17	results	result	NOUN
cana-5829	996	18	of	of	ADP
cana-5829	996	19	intuitionistic	intuitionistic	ADJ
cana-5829	996	20	fuzzy	fuzzy	ADJ
cana-5829	996	21	soft	soft	ADJ
cana-5829	996	22	matrix	matrix	NOUN
cana-5829	996	23	theory	theory	NOUN
cana-5829	996	24	,	,	PUNCT
cana-5829	996	25	advances	advance	NOUN
cana-5829	996	26	in	in	ADP
cana-5829	996	27	applied	apply	VERB
cana-5829	996	28	science	science	NOUN
cana-5829	996	29	research	research	NOUN
cana-5829	996	30	(	(	PUNCT
cana-5829	996	31	2012),3(1	2012),3(1	NUM
cana-5829	996	32	)	)	PUNCT
cana-5829	996	33	,	,	PUNCT
cana-5829	996	34	412	412	NUM
cana-5829	996	35	-	-	SYM
cana-5829	996	36	423	423	NUM
cana-5829	996	37	.	.	PUNCT
cana-5829	997	1	[	[	X
cana-5829	997	2	6	6	NUM
cana-5829	997	3	]	]	PUNCT
cana-5829	997	4	n.cagman	n.cagman	NOUN
cana-5829	997	5	and	and	CCONJ
cana-5829	997	6	s.	s.	PROPN
cana-5829	997	7	enginoglu	enginoglu	PROPN
cana-5829	997	8	,	,	PUNCT
cana-5829	997	9	fuzzy	fuzzy	ADJ
cana-5829	997	10	soft	soft	ADJ
cana-5829	997	11	matrix	matrix	NOUN
cana-5829	997	12	theory	theory	NOUN
cana-5829	997	13	and	and	CCONJ
cana-5829	997	14	its	its	PRON
cana-5829	997	15	application	application	NOUN
cana-5829	997	16	in	in	ADP
cana-5829	997	17	decision	decision	NOUN
cana-5829	997	18	making	making	NOUN
cana-5829	997	19	,	,	PUNCT
cana-5829	997	20	international	international	ADJ
cana-5829	997	21	journal	journal	NOUN
cana-5829	997	22	of	of	ADP
cana-5829	997	23	fuzzy	fuzzy	ADJ
cana-5829	997	24	systems	system	NOUN
cana-5829	997	25	,	,	PUNCT
cana-5829	997	26	vol.9	vol.9	PROPN
cana-5829	997	27	,	,	PUNCT
cana-5829	997	28	(	(	PUNCT
cana-5829	997	29	2012	2012	NUM
cana-5829	997	30	)	)	PUNCT
cana-5829	998	1	pp.109	pp.109	PROPN
cana-5829	998	2	-	-	NOUN
cana-5829	998	3	119	119	NUM
cana-5829	998	4	[	[	X
cana-5829	998	5	7	7	NUM
cana-5829	998	6	]	]	X
cana-5829	998	7	djatna	djatna	NOUN
cana-5829	998	8	,	,	PUNCT
cana-5829	998	9	t.	t.	PROPN
cana-5829	998	10	,kusuma	,kusuma	PUNCT
cana-5829	998	11	,	,	PUNCT
cana-5829	998	12	m.	m.	NOUN
cana-5829	998	13	,	,	PUNCT
cana-5829	998	14	hardhienata	hardhienata	PROPN
cana-5829	998	15	d.	d.	PROPN
cana-5829	998	16	,	,	PUNCT
cana-5829	998	17	masruriyah	masruriyah	PROPN
cana-5829	998	18	,	,	PUNCT
cana-5829	998	19	a.	a.	PROPN
cana-5829	998	20	f.	f.	PROPN
cana-5829	998	21	n.	n.	PROPN
cana-5829	998	22	,	,	PUNCT
cana-5829	998	23	“	"	PUNCT
cana-5829	998	24	an	an	DET
cana-5829	998	25	intuitionistic	intuitionistic	ADJ
cana-5829	998	26	fuzzy	fuzzy	ADJ
cana-5829	998	27	diagnosis	diagnosis	NOUN
cana-5829	998	28	analytics	analytic	NOUN
cana-5829	998	29	for	for	ADP
cana-5829	998	30	stroke	stroke	NOUN
cana-5829	998	31	disease	disease	NOUN
cana-5829	998	32	”	"	PUNCT
cana-5829	998	33	,	,	PUNCT
cana-5829	998	34	journal	journal	NOUN
cana-5829	998	35	of	of	ADP
cana-5829	998	36	big	big	ADJ
cana-5829	998	37	data	datum	NOUN
cana-5829	998	38	,	,	PUNCT
cana-5829	998	39	vol	vol	NOUN
cana-5829	998	40	.	.	PROPN
cana-5829	998	41	5	5	NUM
cana-5829	998	42	,	,	PUNCT
cana-5829	998	43	no	no	INTJ
cana-5829	998	44	.	.	NOUN
cana-5829	998	45	35	35	NUM
cana-5829	998	46	,	,	PUNCT
cana-5829	998	47	pp	pp	ADJ
cana-5829	998	48	.	.	PUNCT
cana-5829	999	1	1	1	NUM
cana-5829	999	2	-	-	SYM
cana-5829	999	3	14	14	NUM
cana-5829	999	4	,	,	PUNCT
cana-5829	999	5	2018	2018	NUM
cana-5829	999	6	.	.	PUNCT
cana-5829	1000	1	[	[	X
cana-5829	1000	2	8	8	NUM
cana-5829	1000	3	]	]	X
cana-5829	1000	4	d.	d.	PROPN
cana-5829	1000	5	dubois	dubois	PROPN
cana-5829	1000	6	and	and	CCONJ
cana-5829	1000	7	h.	h.	PROPN
cana-5829	1000	8	prade	prade	PROPN
cana-5829	1000	9	,	,	PUNCT
cana-5829	1000	10	fuzzy	fuzzy	ADJ
cana-5829	1000	11	sets	set	NOUN
cana-5829	1000	12	and	and	CCONJ
cana-5829	1000	13	systems	system	NOUN
cana-5829	1000	14	:	:	PUNCT
cana-5829	1000	15	theory	theory	NOUN
cana-5829	1000	16	and	and	CCONJ
cana-5829	1000	17	applications	application	NOUN
cana-5829	1000	18	,	,	PUNCT
cana-5829	1000	19	academic	academic	ADJ
cana-5829	1000	20	press	press	NOUN
cana-5829	1000	21	,	,	PUNCT
cana-5829	1000	22	new	new	PROPN
cana-5829	1000	23	york	york	PROPN
cana-5829	1000	24	,	,	PUNCT
cana-5829	1000	25	(	(	PUNCT
cana-5829	1000	26	1980).16	1980).16	NUM
cana-5829	1000	27	.	.	PUNCT
cana-5829	1001	1	p.j.m	p.j.m	PROPN
cana-5829	1001	2	.	.	PUNCT
cana-5829	1002	1	van	van	PROPN
cana-5829	1002	2	,	,	PUNCT
cana-5829	1002	3	[	[	X
cana-5829	1002	4	9	9	NUM
cana-5829	1002	5	]	]	X
cana-5829	1002	6	emam	emam	PROPN
cana-5829	1002	7	,	,	PUNCT
cana-5829	1002	8	e.g.	e.g.	ADV
cana-5829	1002	9	,	,	PUNCT
cana-5829	1002	10	“	"	PUNCT
cana-5829	1002	11	intuitionistic	intuitionistic	ADJ
cana-5829	1002	12	circular	circular	ADJ
cana-5829	1002	13	bifuzzy	bifuzzy	NOUN
cana-5829	1002	14	matrices	matrix	NOUN
cana-5829	1002	15	”	"	PUNCT
cana-5829	1002	16	,	,	PUNCT
cana-5829	1002	17	journal	journal	NOUN
cana-5829	1002	18	of	of	ADP
cana-5829	1002	19	the	the	DET
cana-5829	1002	20	egyptian	egyptian	PROPN
cana-5829	1002	21	mathematical	mathematical	PROPN
cana-5829	1002	22	society	society	NOUN
cana-5829	1002	23	,	,	PUNCT
cana-5829	1002	24	vol	vol	NOUN
cana-5829	1002	25	.	.	PROPN
cana-5829	1002	26	25	25	NUM
cana-5829	1002	27	,	,	PUNCT
cana-5829	1002	28	no	no	INTJ
cana-5829	1002	29	.	.	NOUN
cana-5829	1002	30	3	3	NUM
cana-5829	1002	31	,	,	PUNCT
cana-5829	1002	32	pp	pp	ADJ
cana-5829	1002	33	.	.	PUNCT
cana-5829	1003	1	272	272	NUM
cana-5829	1003	2	-	-	SYM
cana-5829	1003	3	275	275	NUM
cana-5829	1003	4	,	,	PUNCT
cana-5829	1003	5	2017	2017	NUM
cana-5829	1004	1	[	[	SYM
cana-5829	1004	2	10	10	NUM
cana-5829	1004	3	]	]	PUNCT
cana-5829	1004	4	e.g.	e.g.	ADV
cana-5829	1004	5	emam	emam	PROPN
cana-5829	1004	6	and	and	CCONJ
cana-5829	1004	7	m.z	m.z	PROPN
cana-5829	1004	8	.	.	PROPN
cana-5829	1004	9	ragab	ragab	PROPN
cana-5829	1004	10	,	,	PUNCT
cana-5829	1004	11	the	the	DET
cana-5829	1004	12	determinant	determinant	ADJ
cana-5829	1004	13	and	and	CCONJ
cana-5829	1004	14	adjoint	adjoint	NOUN
cana-5829	1004	15	of	of	ADP
cana-5829	1004	16	a	a	DET
cana-5829	1004	17	square	square	ADJ
cana-5829	1004	18	fuzzy	fuzzy	ADJ
cana-5829	1004	19	matrix	matrix	NOUN
cana-5829	1004	20	,	,	PUNCT
cana-5829	1004	21	information	information	NOUN
cana-5829	1004	22	sciences	science	NOUN
cana-5829	1004	23	,	,	PUNCT
cana-5829	1004	24	vol	vol	NOUN
cana-5829	1004	25	.	.	PUNCT
cana-5829	1005	1	84	84	NUM
cana-5829	1005	2	(	(	PUNCT
cana-5829	1005	3	new	new	PROPN
cana-5829	1005	4	york	york	PROPN
cana-5829	1005	5	,	,	PUNCT
cana-5829	1005	6	new	new	PROPN
cana-5829	1005	7	york	york	PROPN
cana-5829	1005	8	,	,	PUNCT
cana-5829	1005	9	1995	1995	NUM
cana-5829	1005	10	)	)	PUNCT
cana-5829	1006	1	pp	pp	ADP
cana-5829	1006	2	.	.	PUNCT
cana-5829	1007	1	209	209	NUM
cana-5829	1007	2	-	-	SYM
cana-5829	1007	3	220	220	NUM
cana-5829	1007	4	[	[	PUNCT
cana-5829	1007	5	11	11	NUM
cana-5829	1007	6	]	]	X
cana-5829	1007	7	enginoǧlu	enginoǧlu	NOUN
cana-5829	1007	8	s.	s.	PROPN
cana-5829	1007	9	,	,	PUNCT
cana-5829	1007	10	arslan	arslan	PROPN
cana-5829	1007	11	b.	b.	PROPN
cana-5829	1007	12	,	,	PUNCT
cana-5829	1007	13	“	"	PUNCT
cana-5829	1007	14	intuitionistic	intuitionistic	ADJ
cana-5829	1007	15	fuzzy	fuzzy	ADJ
cana-5829	1007	16	parameterized	parameterized	ADJ
cana-5829	1007	17	intuitionistic	intuitionistic	ADJ
cana-5829	1007	18	fuzzy	fuzzy	ADJ
cana-5829	1007	19	soft	soft	ADJ
cana-5829	1007	20	matrices	matrix	NOUN
cana-5829	1007	21	and	and	CCONJ
cana-5829	1007	22	their	their	PRON
cana-5829	1007	23	application	application	NOUN
cana-5829	1007	24	in	in	ADP
cana-5829	1007	25	decision	decision	NOUN
cana-5829	1007	26	-	-	PUNCT
cana-5829	1007	27	making	making	NOUN
cana-5829	1007	28	”	"	PUNCT
cana-5829	1007	29	,	,	PUNCT
cana-5829	1007	30	computational	computational	ADJ
cana-5829	1007	31	and	and	CCONJ
cana-5829	1007	32	applied	applied	ADJ
cana-5829	1007	33	mathematics	mathematic	NOUN
cana-5829	1007	34	,	,	PUNCT
cana-5829	1007	35	vol	vol	NOUN
cana-5829	1007	36	.	.	PROPN
cana-5829	1007	37	39	39	NUM
cana-5829	1007	38	,	,	PUNCT
cana-5829	1007	39	article	article	NOUN
cana-5829	1007	40	no	no	NOUN
cana-5829	1007	41	.	.	PROPN
cana-5829	1007	42	325	325	NUM
cana-5829	1007	43	,	,	PUNCT
cana-5829	1007	44	pp	pp	ADJ
cana-5829	1007	45	.	.	PUNCT
cana-5829	1008	1	1	1	NUM
cana-5829	1008	2	-	-	SYM
cana-5829	1008	3	20	20	NUM
cana-5829	1008	4	,	,	PUNCT
cana-5829	1008	5	2020	2020	NUM
cana-5829	1008	6	.	.	PUNCT
cana-5829	1009	1	[	[	X
cana-5829	1009	2	12	12	NUM
cana-5829	1009	3	]	]	X
cana-5829	1009	4	p.w	p.w	PROPN
cana-5829	1009	5	.	.	PROPN
cana-5829	1009	6	eklund	eklund	PROPN
cana-5829	1009	7	,	,	PUNCT
cana-5829	1009	8	x.	x.	PROPN
cana-5829	1009	9	sun	sun	PROPN
cana-5829	1009	10	,	,	PUNCT
cana-5829	1009	11	and	and	CCONJ
cana-5829	1009	12	d.a	d.a	PROPN
cana-5829	1009	13	.	.	PROPN
cana-5829	1009	14	thomas	thomas	PROPN
cana-5829	1009	15	,	,	PUNCT
cana-5829	1009	16	fuzzy	fuzzy	ADJ
cana-5829	1009	17	matrices	matrix	NOUN
cana-5829	1009	18	:	:	PUNCT
cana-5829	1009	19	an	an	DET
cana-5829	1009	20	application	application	NOUN
cana-5829	1009	21	in	in	ADP
cana-5829	1009	22	agriculture	agriculture	NOUN
cana-5829	1009	23	,	,	PUNCT
cana-5829	1009	24	proc	proc	NOUN
cana-5829	1009	25	.	.	PUNCT
cana-5829	1010	1	ipmu	ipmu	PROPN
cana-5829	1010	2	,	,	PUNCT
cana-5829	1010	3	(	(	PUNCT
cana-5829	1010	4	september	september	PROPN
cana-5829	1010	5	1995	1995	NUM
cana-5829	1010	6	)	)	PUNCT
cana-5829	1011	1	pp	pp	ADP
cana-5829	1011	2	.	.	PUNCT
cana-5829	1012	1	765	765	NUM
cana-5829	1012	2	-	-	SYM
cana-5829	1012	3	769	769	NUM
cana-5829	1012	4	.	.	PUNCT
cana-5829	1013	1	[	[	X
cana-5829	1013	2	13	13	NUM
cana-5829	1013	3	]	]	X
cana-5829	1013	4	f.	f.	PROPN
cana-5829	1013	5	feng	feng	PROPN
cana-5829	1013	6	,	,	PUNCT
cana-5829	1013	7	y.	y.	PROPN
cana-5829	1013	8	b.	b.	PROPN
cana-5829	1013	9	jun	jun	PROPN
cana-5829	1013	10	,	,	PUNCT
cana-5829	1013	11	x.	x.	PROPN
cana-5829	1013	12	liu	liu	PROPN
cana-5829	1013	13	and	and	CCONJ
cana-5829	1013	14	l.	l.	PROPN
cana-5829	1013	15	li	li	PROPN
cana-5829	1013	16	,	,	PUNCT
cana-5829	1013	17	an	an	DET
cana-5829	1013	18	adjustable	adjustable	ADJ
cana-5829	1013	19	approach	approach	NOUN
cana-5829	1013	20	to	to	ADP
cana-5829	1013	21	fuzzy	fuzzy	ADJ
cana-5829	1013	22	soft	soft	ADJ
cana-5829	1013	23	set	set	NOUN
cana-5829	1013	24	based	base	VERB
cana-5829	1013	25	decision	decision	NOUN
cana-5829	1013	26	making	making	NOUN
cana-5829	1013	27	,	,	PUNCT
cana-5829	1013	28	journal	journal	NOUN
cana-5829	1013	29	of	of	ADP
cana-5829	1013	30	computational	computational	ADJ
cana-5829	1013	31	and	and	CCONJ
cana-5829	1013	32	applied	applied	ADJ
cana-5829	1013	33	mathematics	mathematic	NOUN
cana-5829	1013	34	,	,	PUNCT
cana-5829	1013	35	234	234	NUM
cana-5829	1013	36	(	(	PUNCT
cana-5829	1013	37	2010	2010	NUM
cana-5829	1013	38	)	)	PUNCT
cana-5829	1013	39	,	,	PUNCT
cana-5829	1013	40	10	10	NUM
cana-5829	1013	41	-	-	SYM
cana-5829	1013	42	20	20	NUM
cana-5829	1013	43	.	.	PUNCT
cana-5829	1014	1	[	[	X
cana-5829	1014	2	14	14	NUM
cana-5829	1014	3	]	]	PUNCT
cana-5829	1014	4	a_gman	a_gman	PROPN
cana-5829	1014	5	,	,	PUNCT
cana-5829	1014	6	f.	f.	PROPN
cana-5829	1014	7	c_tak	c_tak	PROPN
cana-5829	1014	8	and	and	CCONJ
cana-5829	1014	9	s.	s.	PROPN
cana-5829	1014	10	engino_glu	engino_glu	PROPN
cana-5829	1014	11	,	,	PUNCT
cana-5829	1014	12	fuzzy	fuzzy	ADJ
cana-5829	1014	13	parameterized	parameterized	ADJ
cana-5829	1014	14	fuzzy	fuzzy	ADJ
cana-5829	1014	15	soft	soft	ADJ
cana-5829	1014	16	set	set	NOUN
cana-5829	1014	17	theory	theory	NOUN
cana-5829	1014	18	and	and	CCONJ
cana-5829	1014	19	its	its	PRON
cana-5829	1014	20	applications	application	NOUN
cana-5829	1014	21	,	,	PUNCT
cana-5829	1014	22	turkish	turkish	ADJ
cana-5829	1014	23	journal	journal	NOUN
cana-5829	1014	24	of	of	ADP
cana-5829	1014	25	fuzzy	fuzzy	ADJ
cana-5829	1014	26	systems	system	NOUN
cana-5829	1014	27	,	,	PUNCT
cana-5829	1014	28	1(1	1(1	NUM
cana-5829	1014	29	)	)	PUNCT
cana-5829	1014	30	(	(	PUNCT
cana-5829	1014	31	2010	2010	NUM
cana-5829	1014	32	)	)	PUNCT
cana-5829	1014	33	,	,	PUNCT
cana-5829	1014	34	21	21	NUM
cana-5829	1014	35	-	-	SYM
cana-5829	1014	36	35	35	NUM
cana-5829	1014	37	.	.	PUNCT
cana-5829	1015	1	[	[	X
cana-5829	1015	2	15	15	NUM
cana-5829	1015	3	]	]	X
cana-5829	1015	4	a_gman	a_gman	PROPN
cana-5829	1015	5	,	,	PUNCT
cana-5829	1015	6	s.	s.	PROPN
cana-5829	1015	7	engino_glu	engino_glu	PROPN
cana-5829	1015	8	and	and	CCONJ
cana-5829	1015	9	f.	f.	PROPN
cana-5829	1015	10	c_tak	c_tak	PROPN
cana-5829	1015	11	,	,	PUNCT
cana-5829	1015	12	fuzzy	fuzzy	ADJ
cana-5829	1015	13	soft	soft	ADJ
cana-5829	1015	14	set	set	NOUN
cana-5829	1015	15	theory	theory	NOUN
cana-5829	1015	16	and	and	CCONJ
cana-5829	1015	17	its	its	PRON
cana-5829	1015	18	applications	application	NOUN
cana-5829	1015	19	,	,	PUNCT
cana-5829	1015	20	iranian	iranian	NOUN
cana-5829	1015	21	,	,	PUNCT
cana-5829	1015	22	journal	journal	NOUN
cana-5829	1015	23	of	of	ADP
cana-5829	1015	24	fuzzy	fuzzy	ADJ
cana-5829	1015	25	systems	system	NOUN
cana-5829	1015	26	,	,	PUNCT
cana-5829	1015	27	8(3	8(3	NUM
cana-5829	1015	28	)	)	PUNCT
cana-5829	1015	29	(	(	PUNCT
cana-5829	1015	30	2011	2011	NUM
cana-5829	1015	31	)	)	PUNCT
cana-5829	1015	32	,	,	PUNCT
cana-5829	1015	33	137	137	NUM
cana-5829	1015	34	-	-	SYM
cana-5829	1015	35	147	147	NUM
cana-5829	1015	36	.	.	PUNCT
cana-5829	1016	1	[	[	X
cana-5829	1016	2	16	16	NUM
cana-5829	1016	3	]	]	X
cana-5829	1016	4	fuzzy	fuzzy	ADJ
cana-5829	1016	5	set	set	NOUN
cana-5829	1016	6	theory	theory	NOUN
cana-5829	1016	7	and	and	CCONJ
cana-5829	1016	8	its	its	PRON
cana-5829	1016	9	applications	application	NOUN
cana-5829	1016	10	by	by	ADP
cana-5829	1016	11	hans	hans	PROPN
cana-5829	1016	12	-	-	PUNCT
cana-5829	1016	13	jürgen	jürgen	PROPN
cana-5829	1016	14	zimmermann	zimmermann	PROPN
cana-5829	1016	15	kluwer	kluwer	PROPN
cana-5829	1016	16	academic	academic	ADJ
cana-5829	1016	17	publishers	publisher	NOUN
cana-5829	1016	18	(	(	PUNCT
cana-5829	1016	19	1992	1992	NUM
cana-5829	1016	20	)	)	PUNCT
cana-5829	1017	1	[	[	X
cana-5829	1017	2	17	17	NUM
cana-5829	1017	3	]	]	X
cana-5829	1017	4	k.	k.	PROPN
cana-5829	1018	1	ilanthenral	ilanthenral	PROPN
cana-5829	1018	2	,	,	PUNCT
cana-5829	1018	3	f.	f.	PROPN
cana-5829	1018	4	smarandache	smarandache	PROPN
cana-5829	1018	5	,	,	PUNCT
cana-5829	1018	6	and	and	CCONJ
cana-5829	1018	7	w.b	w.b	PROPN
cana-5829	1018	8	.	.	PROPN
cana-5829	1018	9	vasantha	vasantha	PROPN
cana-5829	1018	10	kandasamy	kandasamy	PROPN
cana-5829	1018	11	,	,	PUNCT
cana-5829	1018	12	elementary	elementary	ADJ
cana-5829	1018	13	fuzzy	fuzzy	ADJ
cana-5829	1018	14	matrix	matrix	NOUN
cana-5829	1018	15	theory	theory	NOUN
cana-5829	1018	16	and	and	CCONJ
cana-5829	1018	17	fuzzy	fuzzy	ADJ
cana-5829	1018	18	models	model	NOUN
cana-5829	1018	19	for	for	ADP
cana-5829	1018	20	social	social	ADJ
cana-5829	1018	21	scientists	scientist	NOUN
cana-5829	1018	22	,	,	PUNCT
cana-5829	1018	23	(	(	PUNCT
cana-5829	1018	24	los	los	PROPN
cana-5829	1018	25	angeles	angeles	PROPN
cana-5829	1018	26	,	,	PUNCT
cana-5829	1018	27	california	california	PROPN
cana-5829	1018	28	,	,	PUNCT
cana-5829	1018	29	2007	2007	NUM
cana-5829	1018	30	)	)	PUNCT
cana-5829	1019	1	p.	p.	NOUN
cana-5829	1019	2	33	33	NUM
cana-5829	1019	3	.	.	PUNCT
cana-5829	1020	1	[	[	X
cana-5829	1020	2	18	18	NUM
cana-5829	1020	3	]	]	X
cana-5829	1020	4	irfan	irfan	PROPN
cana-5829	1020	5	deli	deli	PROPN
cana-5829	1020	6	,	,	PUNCT
cana-5829	1020	7	naim	naim	PROPN
cana-5829	1020	8	cagman	cagman	NOUN
cana-5829	1020	9	,	,	PUNCT
cana-5829	1020	10	intuitionistic	intuitionistic	ADJ
cana-5829	1020	11	fuzzy	fuzzy	ADJ
cana-5829	1020	12	parameterized	parameterized	ADJ
cana-5829	1020	13	soft	soft	ADJ
cana-5829	1020	14	set	set	NOUN
cana-5829	1020	15	theory	theory	NOUN
cana-5829	1020	16	and	and	CCONJ
cana-5829	1020	17	its	its	PRON
cana-5829	1020	18	decision	decision	NOUN
cana-5829	1020	19	making_1301.0454v13	making_1301.0454v13	NOUN
cana-5829	1020	20	jan	jan	PROPN
cana-5829	1020	21	2013	2013	NUM
cana-5829	1020	22	.	.	PUNCT
cana-5829	1021	1	[	[	X
cana-5829	1021	2	19	19	NUM
cana-5829	1021	3	]	]	PUNCT
cana-5829	1021	4	kalra	kalra	NOUN
cana-5829	1021	5	,	,	PUNCT
cana-5829	1021	6	n.	n.	PROPN
cana-5829	1021	7	,	,	PUNCT
cana-5829	1021	8	khan	khan	PROPN
cana-5829	1021	9	,	,	PUNCT
cana-5829	1021	10	m.	m.	NOUN
cana-5829	1021	11	a.	a.	PROPN
cana-5829	1021	12	,	,	PUNCT
cana-5829	1021	13	“	"	PUNCT
cana-5829	1021	14	a	a	DET
cana-5829	1021	15	study	study	NOUN
cana-5829	1021	16	of	of	ADP
cana-5829	1021	17	fuzzy	fuzzy	ADJ
cana-5829	1021	18	,	,	PUNCT
cana-5829	1021	19	super	super	ADJ
cana-5829	1021	20	and	and	CCONJ
cana-5829	1021	21	super	super	ADV
cana-5829	1021	22	fuzzy	fuzzy	ADJ
cana-5829	1021	23	matrix	matrix	NOUN
cana-5829	1021	24	theory	theory	NOUN
cana-5829	1021	25	”	"	PUNCT
cana-5829	1021	26	,	,	PUNCT
cana-5829	1021	27	thesis	thesis	NOUN
cana-5829	1021	28	,	,	PUNCT
cana-5829	1021	29	thapar	thapar	PROPN
cana-5829	1021	30	university	university	PROPN
cana-5829	1021	31	,	,	PUNCT
cana-5829	1021	32	patiala	patiala	NOUN
cana-5829	1021	33	,	,	PUNCT
cana-5829	1021	34	punjab	punjab	PROPN
cana-5829	1021	35	,	,	PUNCT
cana-5829	1021	36	india	india	PROPN
cana-5829	1021	37	,	,	PUNCT
cana-5829	1021	38	july	july	PROPN
cana-5829	1021	39	,	,	PUNCT
cana-5829	1021	40	2010	2010	NUM
cana-5829	1021	41	.	.	PUNCT
cana-5829	1022	1	[	[	X
cana-5829	1022	2	20	20	NUM
cana-5829	1022	3	]	]	X
cana-5829	1022	4	k.s	k.s	PROPN
cana-5829	1022	5	.	.	PROPN
cana-5829	1022	6	krishnamohan	krishnamohan	PROPN
cana-5829	1022	7	and	and	CCONJ
cana-5829	1022	8	k.	k.	PROPN
cana-5829	1022	9	muthugurupackiam	muthugurupackiam	PROPN
cana-5829	1022	10	,	,	PUNCT
cana-5829	1022	11	generalisation	generalisation	NOUN
cana-5829	1022	12	of	of	ADP
cana-5829	1022	13	idempotent	idempotent	ADJ
cana-5829	1022	14	fuzzy	fuzzy	ADJ
cana-5829	1022	15	matrices	matrix	NOUN
cana-5829	1022	16	,	,	PUNCT
cana-5829	1022	17	220	220	NUM
cana-5829	1022	18	international	international	ADJ
cana-5829	1022	19	journal	journal	NOUN
cana-5829	1022	20	of	of	ADP
cana-5829	1022	21	applied	apply	VERB
cana-5829	1022	22	engineering	engineering	NOUN
cana-5829	1022	23	research	research	NOUN
cana-5829	1022	24	,	,	PUNCT
cana-5829	1022	25	vol	vol	NOUN
cana-5829	1022	26	.	.	PROPN
cana-5829	1022	27	13	13	NUM
cana-5829	1022	28	,	,	PUNCT
cana-5829	1022	29	no	no	INTJ
cana-5829	1022	30	.	.	NOUN
cana-5829	1022	31	13	13	NUM
cana-5829	1022	32	(	(	PUNCT
cana-5829	1022	33	2018	2018	NUM
cana-5829	1022	34	)	)	PUNCT
cana-5829	1022	35	pp	pp	ADV
cana-5829	1022	36	.	.	PUNCT
cana-5829	1023	1	1108711090	1108711090	NUM
cana-5829	1023	2	.	.	PUNCT
cana-5829	1024	1	[	[	X
cana-5829	1024	2	21	21	NUM
cana-5829	1024	3	]	]	PUNCT
cana-5829	1024	4	m.	m.	NOUN
cana-5829	1024	5	kaliraja	kaliraja	PROPN
cana-5829	1024	6	,	,	PUNCT
cana-5829	1024	7	a.	a.	PROPN
cana-5829	1024	8	r.	r.	PROPN
cana-5829	1024	9	meenakshi	meenakshi	PROPN
cana-5829	1024	10	,	,	PUNCT
cana-5829	1024	11	an	an	DET
cana-5829	1024	12	application	application	NOUN
cana-5829	1024	13	of	of	ADP
cana-5829	1024	14	interval	interval	NOUN
cana-5829	1024	15	valued	value	VERB
cana-5829	1024	16	fuzzy	fuzzy	ADJ
cana-5829	1024	17	matrices	matrix	NOUN
cana-5829	1024	18	in	in	ADP
cana-5829	1024	19	medical	medical	ADJ
cana-5829	1024	20	diagnosis	diagnosis	NOUN
cana-5829	1024	21	,	,	PUNCT
cana-5829	1024	22	international	international	ADJ
cana-5829	1024	23	journal	journal	NOUN
cana-5829	1024	24	of	of	ADP
cana-5829	1024	25	mathematical	mathematical	ADJ
cana-5829	1024	26	analysis	analysis	NOUN
cana-5829	1024	27	,	,	PUNCT
cana-5829	1024	28	vol	vol	NOUN
cana-5829	1024	29	.	.	PROPN
cana-5829	1024	30	5	5	NUM
cana-5829	1024	31	,	,	PUNCT
cana-5829	1024	32	no	no	INTJ
cana-5829	1024	33	.	.	NOUN
cana-5829	1024	34	36	36	NUM
cana-5829	1024	35	(	(	PUNCT
cana-5829	1024	36	2011	2011	NUM
cana-5829	1024	37	)	)	PUNCT
cana-5829	1024	38	pp	pp	ADP
cana-5829	1024	39	.	.	PUNCT
cana-5829	1025	1	1791	1791	NUM
cana-5829	1025	2	-	-	SYM
cana-5829	1025	3	1802	1802	NUM
cana-5829	1025	4	.	.	PUNCT
cana-5829	1026	1	communications	communication	NOUN
cana-5829	1026	2	on	on	ADP
cana-5829	1026	3	applied	apply	VERB
cana-5829	1026	4	nonlinear	nonlinear	ADJ
cana-5829	1026	5	analysis	analysis	NOUN
cana-5829	1026	6	issn	issn	NOUN
cana-5829	1026	7	:	:	PUNCT
cana-5829	1026	8	1074	1074	NUM
cana-5829	1026	9	-	-	PUNCT
cana-5829	1026	10	133x	133x	NUM
cana-5829	1026	11	vol	vol	VERB
cana-5829	1026	12	32	32	NUM
cana-5829	1026	13	no	no	NOUN
cana-5829	1026	14	.	.	PUNCT
cana-5829	1027	1	10s	10	NOUN
cana-5829	1027	2	(	(	PUNCT
cana-5829	1027	3	2025	2025	NUM
cana-5829	1027	4	)	)	PUNCT
cana-5829	1027	5	2957	2957	NUM
cana-5829	1027	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5829	1028	1	[	[	X
cana-5829	1028	2	22	22	NUM
cana-5829	1028	3	]	]	X
cana-5829	1028	4	fuzzy	fuzzy	ADJ
cana-5829	1028	5	sets	set	NOUN
cana-5829	1028	6	,	,	PUNCT
cana-5829	1028	7	fuzzy	fuzzy	ADJ
cana-5829	1028	8	algebra	algebra	NOUN
cana-5829	1028	9	,	,	PUNCT
cana-5829	1028	10	and	and	CCONJ
cana-5829	1028	11	fuzzy	fuzzy	ADJ
cana-5829	1028	12	statistics	statistic	NOUN
cana-5829	1028	13	by	by	ADP
cana-5829	1028	14	a.	a.	NOUN
cana-5829	1028	15	kandle	kandle	PROPN
cana-5829	1028	16	and	and	CCONJ
cana-5829	1028	17	w.	w.	PROPN
cana-5829	1028	18	j.	j.	PROPN
cana-5829	1028	19	byatt	byatt	PROPN
cana-5829	1028	20	(	(	PUNCT
cana-5829	1028	21	1978	1978	NUM
cana-5829	1028	22	)	)	PUNCT
cana-5829	1028	23	,	,	PUNCT
cana-5829	1028	24	ieee	ieee	NOUN
cana-5829	1029	1	[	[	X
cana-5829	1029	2	23	23	NUM
cana-5829	1029	3	]	]	X
cana-5829	1029	4	leon	leon	PROPN
cana-5829	1029	5	-	-	PUNCT
cana-5829	1029	6	castro	castro	PROPN
cana-5829	1029	7	,	,	PUNCT
cana-5829	1029	8	e.	e.	PROPN
cana-5829	1029	9	,	,	PUNCT
cana-5829	1029	10	blanco	blanco	PROPN
cana-5829	1029	11	-	-	PUNCT
cana-5829	1029	12	mesa	mesa	PROPN
cana-5829	1029	13	,	,	PUNCT
cana-5829	1029	14	f.	f.	PROPN
cana-5829	1029	15	,	,	PUNCT
cana-5829	1029	16	alfaro	alfaro	PROPN
cana-5829	1029	17	-	-	PUNCT
cana-5829	1029	18	garcia	garcia	PROPN
cana-5829	1029	19	,	,	PUNCT
cana-5829	1029	20	v.	v.	PROPN
cana-5829	1029	21	,	,	PUNCT
cana-5829	1029	22	gil	gil	PROPN
cana-5829	1029	23	-	-	PUNCT
cana-5829	1029	24	lafuente	lafuente	PROPN
cana-5829	1029	25	a.	a.	NOUN
cana-5829	1029	26	m.	m.	NOUN
cana-5829	1029	27	,	,	PUNCT
cana-5829	1029	28	merigo	merigo	PROPN
cana-5829	1029	29	jose	jose	PROPN
cana-5829	1029	30	m.	m.	NOUN
cana-5829	1029	31	,	,	PUNCT
cana-5829	1029	32	“	"	PUNCT
cana-5829	1029	33	computational	computational	ADJ
cana-5829	1029	34	and	and	CCONJ
cana-5829	1029	35	mathematical	mathematical	ADJ
cana-5829	1029	36	organization	organization	NOUN
cana-5829	1029	37	theory	theory	NOUN
cana-5829	1029	38	”	"	PUNCT
cana-5829	1029	39	,	,	PUNCT
cana-5829	1029	40	fuzzy	fuzzy	ADJ
cana-5829	1029	41	systems	system	NOUN
cana-5829	1029	42	in	in	ADP
cana-5829	1029	43	innovation	innovation	NOUN
cana-5829	1029	44	and	and	CCONJ
cana-5829	1029	45	sustainability	sustainability	NOUN
cana-5829	1029	46	,	,	PUNCT
cana-5829	1029	47	vol	vol	NOUN
cana-5829	1029	48	.	.	PROPN
cana-5829	1029	49	27	27	NUM
cana-5829	1029	50	,	,	PUNCT
cana-5829	1029	51	no	no	INTJ
cana-5829	1029	52	.	.	NOUN
cana-5829	1029	53	4	4	NUM
cana-5829	1029	54	,	,	PUNCT
cana-5829	1029	55	pp	pp	ADJ
cana-5829	1029	56	.	.	PUNCT
cana-5829	1030	1	377	377	NUM
cana-5829	1030	2	-	-	SYM
cana-5829	1030	3	383	383	NUM
cana-5829	1030	4	,	,	PUNCT
cana-5829	1030	5	2021	2021	NUM
cana-5829	1030	6	.	.	PUNCT
cana-5829	1031	1	[	[	X
cana-5829	1031	2	24	24	NUM
cana-5829	1031	3	]	]	PUNCT
cana-5829	1031	4	p.	p.	PROPN
cana-5829	1031	5	k.	k.	PROPN
cana-5829	1032	1	maji	maji	PROPN
cana-5829	1032	2	,	,	PUNCT
cana-5829	1032	3	r.	r.	PROPN
cana-5829	1032	4	biswas	biswas	PROPN
cana-5829	1032	5	and	and	CCONJ
cana-5829	1032	6	a.	a.	PROPN
cana-5829	1032	7	r.	r.	PROPN
cana-5829	1032	8	roy	roy	PROPN
cana-5829	1032	9	,	,	PUNCT
cana-5829	1032	10	“	"	PUNCT
cana-5829	1032	11	fuzzy	fuzzy	ADJ
cana-5829	1032	12	soft	soft	ADJ
cana-5829	1032	13	sets	set	NOUN
cana-5829	1032	14	”	"	PUNCT
cana-5829	1032	15	,	,	PUNCT
cana-5829	1032	16	journal	journal	NOUN
cana-5829	1032	17	of	of	ADP
cana-5829	1032	18	fuzzy	fuzzy	ADJ
cana-5829	1032	19	mathematics	mathematic	NOUN
cana-5829	1032	20	,	,	PUNCT
cana-5829	1032	21	vol	vol	NOUN
cana-5829	1032	22	9	9	NUM
cana-5829	1032	23	,	,	PUNCT
cana-5829	1032	24	no.3	no.3	VERB
cana-5829	1032	25	,	,	PUNCT
cana-5829	1032	26	(	(	PUNCT
cana-5829	1032	27	2001	2001	NUM
cana-5829	1032	28	)	)	PUNCT
cana-5829	1032	29	,	,	PUNCT
cana-5829	1032	30	pp.589	pp.589	NOUN
cana-5829	1032	31	–	–	PUNCT
cana-5829	1032	32	602	602	NUM
cana-5829	1032	33	.	.	PUNCT
cana-5829	1033	1	[	[	X
cana-5829	1033	2	25	25	NUM
cana-5829	1033	3	]	]	X
cana-5829	1033	4	mondal	mondal	PROPN
cana-5829	1033	5	,	,	PUNCT
cana-5829	1033	6	s.	s.	PROPN
cana-5829	1033	7	,	,	PUNCT
cana-5829	1033	8	pal	pal	NOUN
cana-5829	1033	9	,	,	PUNCT
cana-5829	1033	10	m.	m.	NOUN
cana-5829	1033	11	,	,	PUNCT
cana-5829	1033	12	“	"	PUNCT
cana-5829	1033	13	intuitionistic	intuitionistic	ADJ
cana-5829	1033	14	fuzzy	fuzzy	ADJ
cana-5829	1033	15	incline	incline	NOUN
cana-5829	1033	16	matrix	matrix	NOUN
cana-5829	1033	17	and	and	CCONJ
cana-5829	1033	18	determinant	determinant	ADJ
cana-5829	1033	19	”	"	PUNCT
cana-5829	1033	20	,	,	PUNCT
cana-5829	1033	21	annals	annal	NOUN
cana-5829	1033	22	of	of	ADP
cana-5829	1033	23	fuzzy	fuzzy	ADJ
cana-5829	1033	24	mathematics	mathematic	NOUN
cana-5829	1033	25	and	and	CCONJ
cana-5829	1033	26	informatics	informatic	NOUN
cana-5829	1033	27	,	,	PUNCT
cana-5829	1033	28	vol	vol	NOUN
cana-5829	1033	29	.	.	PROPN
cana-5829	1033	30	8	8	NUM
cana-5829	1033	31	,	,	PUNCT
cana-5829	1033	32	no	no	INTJ
cana-5829	1033	33	.	.	NOUN
cana-5829	1033	34	1	1	NUM
cana-5829	1033	35	,	,	PUNCT
cana-5829	1033	36	pp	pp	ADJ
cana-5829	1033	37	.	.	PUNCT
cana-5829	1034	1	14	14	NUM
cana-5829	1034	2	.	.	PUNCT
cana-5829	1035	1	[	[	X
cana-5829	1035	2	26	26	NUM
cana-5829	1035	3	]	]	X
cana-5829	1035	4	muthuraji	muthuraji	X
cana-5829	1035	5	,	,	PUNCT
cana-5829	1035	6	t.	t.	PROPN
cana-5829	1035	7	,	,	PUNCT
cana-5829	1035	8	sriram	sriram	PROPN
cana-5829	1035	9	,	,	PUNCT
cana-5829	1035	10	s.	s.	PROPN
cana-5829	1035	11	,	,	PUNCT
cana-5829	1035	12	murugadas	murugadas	PROPN
cana-5829	1035	13	p.	p.	NOUN
cana-5829	1035	14	,	,	PUNCT
cana-5829	1035	15	“	"	PUNCT
cana-5829	1035	16	decomposition	decomposition	NOUN
cana-5829	1035	17	of	of	ADP
cana-5829	1035	18	intuitionistic	intuitionistic	ADJ
cana-5829	1035	19	fuzzy	fuzzy	ADJ
cana-5829	1035	20	matrices	matrix	NOUN
cana-5829	1035	21	”	"	PUNCT
cana-5829	1035	22	,	,	PUNCT
cana-5829	1035	23	fuzzy	fuzzy	ADJ
cana-5829	1035	24	information	information	NOUN
cana-5829	1035	25	and	and	CCONJ
cana-5829	1035	26	engineering	engineering	NOUN
cana-5829	1035	27	,	,	PUNCT
cana-5829	1035	28	vol	vol	NOUN
cana-5829	1035	29	.	.	PROPN
cana-5829	1035	30	8	8	NUM
cana-5829	1035	31	,	,	PUNCT
cana-5829	1035	32	no	no	INTJ
cana-5829	1035	33	.	.	NOUN
cana-5829	1035	34	3	3	NUM
cana-5829	1035	35	,	,	PUNCT
cana-5829	1035	36	pp	pp	ADJ
cana-5829	1035	37	.	.	PUNCT
cana-5829	1036	1	345	345	NUM
cana-5829	1036	2	-	-	SYM
cana-5829	1036	3	354	354	NUM
cana-5829	1036	4	,	,	PUNCT
cana-5829	1036	5	2016	2016	NUM
cana-5829	1036	6	.	.	PUNCT
cana-5829	1037	1	[	[	X
cana-5829	1037	2	27	27	NUM
cana-5829	1037	3	]	]	SYM
cana-5829	1037	4	otadi	otadi	NOUN
cana-5829	1037	5	,	,	PUNCT
cana-5829	1037	6	m.	m.	NOUN
cana-5829	1037	7	,	,	PUNCT
cana-5829	1037	8	mosleh	mosleh	NOUN
cana-5829	1037	9	,	,	PUNCT
cana-5829	1037	10	m	m	PRON
cana-5829	1037	11	,	,	PUNCT
cana-5829	1037	12	“	"	PUNCT
cana-5829	1037	13	solving	solve	VERB
cana-5829	1037	14	fully	fully	ADV
cana-5829	1037	15	fuzzy	fuzzy	ADJ
cana-5829	1037	16	matrix	matrix	NOUN
cana-5829	1037	17	equations	equation	NOUN
cana-5829	1037	18	”	"	PUNCT
cana-5829	1037	19	,	,	PUNCT
cana-5829	1037	20	applied	apply	VERB
cana-5829	1037	21	mathematical	mathematical	ADJ
cana-5829	1037	22	modelling	modelling	NOUN
cana-5829	1037	23	,	,	PUNCT
cana-5829	1037	24	vol	vol	NOUN
cana-5829	1037	25	.	.	PROPN
cana-5829	1038	1	36	36	NUM
cana-5829	1038	2	,	,	PUNCT
cana-5829	1038	3	no	no	INTJ
cana-5829	1038	4	.	.	NOUN
cana-5829	1038	5	12	12	NUM
cana-5829	1038	6	,	,	PUNCT
cana-5829	1038	7	pp	pp	ADJ
cana-5829	1038	8	.	.	PUNCT
cana-5829	1039	1	6114	6114	NUM
cana-5829	1039	2	-	-	SYM
cana-5829	1039	3	6121	6121	NUM
cana-5829	1039	4	,	,	PUNCT
cana-5829	1039	5	2012	2012	NUM
cana-5829	1039	6	[	[	X
cana-5829	1039	7	28	28	NUM
cana-5829	1039	8	]	]	X
cana-5829	1039	9	fuzzy	fuzzy	ADJ
cana-5829	1039	10	set	set	NOUN
cana-5829	1039	11	theory	theory	NOUN
cana-5829	1039	12	and	and	CCONJ
cana-5829	1039	13	its	its	PRON
cana-5829	1039	14	applications	application	NOUN
cana-5829	1039	15	by	by	ADP
cana-5829	1039	16	by	by	ADP
cana-5829	1039	17	wolkenhauer	wolkenhauer	NOUN
cana-5829	1039	18	and	and	CCONJ
cana-5829	1039	19	olaf	olaf	PROPN
cana-5829	1039	20	,	,	PUNCT
cana-5829	1039	21	international	international	ADJ
cana-5829	1039	22	journal	journal	NOUN
cana-5829	1039	23	of	of	ADP
cana-5829	1039	24	electrical	electrical	ADJ
cana-5829	1039	25	engineering	engineering	NOUN
cana-5829	1039	26	education	education	NOUN
cana-5829	1039	27	(	(	PUNCT
cana-5829	1039	28	1998	1998	NUM
cana-5829	1039	29	)	)	PUNCT
cana-5829	1039	30	.	.	PUNCT
cana-5829	1040	1	[	[	X
cana-5829	1040	2	29	29	NUM
cana-5829	1040	3	]	]	X
cana-5829	1040	4	pal	pal	NOUN
cana-5829	1040	5	,	,	PUNCT
cana-5829	1040	6	m.	m.	NOUN
cana-5829	1040	7	,	,	PUNCT
cana-5829	1040	8	khan	khan	PROPN
cana-5829	1040	9	,	,	PUNCT
cana-5829	1040	10	s.	s.	PROPN
cana-5829	1040	11	k.	k.	PROPN
cana-5829	1040	12	,	,	PUNCT
cana-5829	1040	13	shyamal	shyamal	ADJ
cana-5829	1040	14	a.	a.	NOUN
cana-5829	1040	15	k.	k.	PROPN
cana-5829	1040	16	,	,	PUNCT
cana-5829	1040	17	“	"	PUNCT
cana-5829	1040	18	intuitionistic	intuitionistic	ADJ
cana-5829	1040	19	fuzzy	fuzzy	ADJ
cana-5829	1040	20	matrices	matrix	NOUN
cana-5829	1040	21	”	"	PUNCT
cana-5829	1040	22	,	,	PUNCT
cana-5829	1040	23	notes	note	NOUN
cana-5829	1040	24	on	on	ADP
cana-5829	1040	25	intuitionistic	intuitionistic	ADJ
cana-5829	1040	26	fuzzy	fuzzy	ADJ
cana-5829	1040	27	sets	set	NOUN
cana-5829	1040	28	,	,	PUNCT
cana-5829	1040	29	vol	vol	NOUN
cana-5829	1040	30	.	.	PROPN
cana-5829	1040	31	8	8	NUM
cana-5829	1040	32	,	,	PUNCT
cana-5829	1040	33	no	no	INTJ
cana-5829	1040	34	.	.	NOUN
cana-5829	1040	35	2	2	NUM
cana-5829	1040	36	,	,	PUNCT
cana-5829	1040	37	pp	pp	ADJ
cana-5829	1040	38	.	.	PUNCT
cana-5829	1041	1	51	51	NUM
cana-5829	1041	2	-	-	SYM
cana-5829	1041	3	62	62	NUM
cana-5829	1041	4	,	,	PUNCT
cana-5829	1041	5	2002	2002	NUM
cana-5829	1041	6	.	.	PUNCT
cana-5829	1042	1	[	[	X
cana-5829	1042	2	30	30	NUM
cana-5829	1042	3	]	]	X
cana-5829	1042	4	pradhan	pradhan	PROPN
cana-5829	1042	5	,	,	PUNCT
cana-5829	1042	6	r.	r.	PROPN
cana-5829	1042	7	,	,	PUNCT
cana-5829	1042	8	pal	pal	NOUN
cana-5829	1042	9	,	,	PUNCT
cana-5829	1042	10	m.	m.	NOUN
cana-5829	1042	11	,	,	PUNCT
cana-5829	1042	12	“	"	PUNCT
cana-5829	1042	13	the	the	DET
cana-5829	1042	14	generalized	generalized	ADJ
cana-5829	1042	15	inverse	inverse	NOUN
cana-5829	1042	16	of	of	ADP
cana-5829	1042	17	atanassov	atanassov	PROPN
cana-5829	1042	18	’s	’s	PART
cana-5829	1042	19	intuitionistic	intuitionistic	ADJ
cana-5829	1042	20	fuzzy	fuzzy	ADJ
cana-5829	1042	21	matrices	matrix	NOUN
cana-5829	1042	22	”	"	PUNCT
cana-5829	1042	23	,	,	PUNCT
cana-5829	1042	24	international	international	ADJ
cana-5829	1042	25	journal	journal	NOUN
cana-5829	1042	26	of	of	ADP
cana-5829	1042	27	computational	computational	ADJ
cana-5829	1042	28	intelligence	intelligence	NOUN
cana-5829	1042	29	systems	system	NOUN
cana-5829	1042	30	,	,	PUNCT
cana-5829	1042	31	vol	vol	NOUN
cana-5829	1042	32	.	.	PROPN
cana-5829	1042	33	7	7	NUM
cana-5829	1042	34	,	,	PUNCT
cana-5829	1042	35	no	no	INTJ
cana-5829	1042	36	.	.	NOUN
cana-5829	1042	37	6	6	NUM
cana-5829	1042	38	,	,	PUNCT
cana-5829	1042	39	pp	pp	ADJ
cana-5829	1042	40	.	.	PUNCT
cana-5829	1042	41	1083	1083	NUM
cana-5829	1042	42	-	-	SYM
cana-5829	1042	43	1095	1095	NUM
cana-5829	1042	44	,	,	PUNCT
cana-5829	1042	45	2014	2014	NUM
cana-5829	1042	46	.	.	PUNCT
cana-5829	1043	1	[	[	X
cana-5829	1043	2	31	31	NUM
cana-5829	1043	3	]	]	PUNCT
cana-5829	1043	4	.	.	PUNCT
cana-5829	1044	1	d.	d.	PROPN
cana-5829	1044	2	dubois	dubois	PROPN
cana-5829	1044	3	and	and	CCONJ
cana-5829	1044	4	h.	h.	PROPN
cana-5829	1044	5	prade	prade	PROPN
cana-5829	1044	6	,	,	PUNCT
cana-5829	1044	7	fuzzy	fuzzy	ADJ
cana-5829	1044	8	sets	set	NOUN
cana-5829	1044	9	and	and	CCONJ
cana-5829	1044	10	systems	system	NOUN
cana-5829	1044	11	:	:	PUNCT
cana-5829	1044	12	theory	theory	NOUN
cana-5829	1044	13	and	and	CCONJ
cana-5829	1044	14	applications	application	NOUN
cana-5829	1044	15	,	,	PUNCT
cana-5829	1044	16	academic	academic	ADJ
cana-5829	1044	17	press	press	NOUN
cana-5829	1044	18	,	,	PUNCT
cana-5829	1044	19	new	new	PROPN
cana-5829	1044	20	york	york	PROPN
cana-5829	1044	21	,	,	PUNCT
cana-5829	1044	22	(	(	PUNCT
cana-5829	1044	23	1980	1980	NUM
cana-5829	1044	24	)	)	PUNCT
cana-5829	1044	25	.	.	PUNCT
cana-5829	1045	1	extension	extension	NOUN
cana-5829	1045	2	o	o	NOUN
cana-5829	1046	1	[	[	X
cana-5829	1046	2	32	32	NUM
cana-5829	1046	3	]	]	PUNCT
cana-5829	1046	4	p.rajarajeswari	p.rajarajeswari	NOUN
cana-5829	1046	5	,	,	PUNCT
cana-5829	1046	6	p.dhanalakshmi	p.dhanalakshmi	VERB
cana-5829	1046	7	,	,	PUNCT
cana-5829	1046	8	intuitionistic	intuitionistic	ADJ
cana-5829	1046	9	fuzzy	fuzzy	ADJ
cana-5829	1046	10	soft	soft	ADJ
cana-5829	1046	11	matrix	matrix	NOUN
cana-5829	1046	12	theory	theory	NOUN
cana-5829	1046	13	and	and	CCONJ
cana-5829	1046	14	its	its	PRON
cana-5829	1046	15	application	application	NOUN
cana-5829	1046	16	in	in	ADP
cana-5829	1046	17	decision	decision	NOUN
cana-5829	1046	18	making	making	NOUN
cana-5829	1046	19	,	,	PUNCT
cana-5829	1046	20	international	international	ADJ
cana-5829	1046	21	journal	journal	NOUN
cana-5829	1046	22	of	of	ADP
cana-5829	1046	23	engineering	engineering	PROPN
cana-5829	1046	24	research	research	PROPN
cana-5829	1046	25	&	&	CCONJ
cana-5829	1046	26	technology	technology	NOUN
cana-5829	1046	27	,	,	PUNCT
cana-5829	1046	28	vol	vol	NOUN
cana-5829	1046	29	.	.	NOUN
cana-5829	1046	30	2	2	NUM
cana-5829	1046	31	,	,	PUNCT
cana-5829	1046	32	issue	issue	NOUN
cana-5829	1046	33	4	4	NUM
cana-5829	1046	34	,	,	PUNCT
cana-5829	1046	35	april-2013	april-2013	NOUN
cana-5829	1046	36	.	.	PUNCT
cana-5829	1047	1	[	[	X
cana-5829	1047	2	33	33	NUM
cana-5829	1047	3	]	]	PUNCT
cana-5829	1047	4	sahni	sahni	NOUN
cana-5829	1047	5	,	,	PUNCT
cana-5829	1047	6	m.	m.	NOUN
cana-5829	1047	7	,	,	PUNCT
cana-5829	1047	8	sahni	sahni	PROPN
cana-5829	1047	9	,	,	PUNCT
cana-5829	1047	10	r.	r.	PROPN
cana-5829	1047	11	,	,	PUNCT
cana-5829	1047	12	verma	verma	PROPN
cana-5829	1047	13	,	,	PUNCT
cana-5829	1047	14	r.	r.	PROPN
cana-5829	1047	15	,	,	PUNCT
cana-5829	1047	16	mandaliya	mandaliya	PROPN
cana-5829	1047	17	,	,	PUNCT
cana-5829	1047	18	a.	a.	PROPN
cana-5829	1047	19	,	,	PUNCT
cana-5829	1047	20	shah	shah	PROPN
cana-5829	1047	21	,	,	PUNCT
cana-5829	1047	22	d.	d.	PROPN
cana-5829	1047	23	,	,	PUNCT
cana-5829	1047	24	“	"	PUNCT
cana-5829	1047	25	generalized	generalized	ADJ
cana-5829	1047	26	trapezoidal	trapezoidal	ADJ
cana-5829	1047	27	intuitionistic	intuitionistic	ADJ
cana-5829	1047	28	fuzzy	fuzzy	ADJ
cana-5829	1047	29	number	number	NOUN
cana-5829	1047	30	for	for	ADP
cana-5829	1047	31	finding	find	VERB
cana-5829	1047	32	radial	radial	ADJ
cana-5829	1047	33	displacement	displacement	NOUN
cana-5829	1047	34	of	of	ADP
cana-5829	1047	35	a	a	DET
cana-5829	1047	36	solid	solid	ADJ
cana-5829	1047	37	disk	disk	NOUN
cana-5829	1047	38	”	"	PUNCT
cana-5829	1047	39	,	,	PUNCT
cana-5829	1047	40	wseas	wsea	VERB
cana-5829	1047	41	transactions	transaction	NOUN
cana-5829	1047	42	on	on	ADP
cana-5829	1047	43	mathematics	mathematic	NOUN
cana-5829	1047	44	,	,	PUNCT
cana-5829	1047	45	vol	vol	NOUN
cana-5829	1047	46	.	.	PROPN
cana-5829	1047	47	18	18	NUM
cana-5829	1047	48	,	,	PUNCT
cana-5829	1047	49	pp	pp	ADJ
cana-5829	1047	50	.	.	PUNCT
cana-5829	1048	1	105	105	NUM
cana-5829	1048	2	-	-	SYM
cana-5829	1048	3	111	111	NUM
cana-5829	1048	4	,	,	PUNCT
cana-5829	1048	5	2019	2019	NUM
cana-5829	1048	6	.	.	PUNCT
cana-5829	1049	1	[	[	X
cana-5829	1049	2	34	34	NUM
cana-5829	1049	3	]	]	PUNCT
cana-5829	1049	4	saw	see	VERB
cana-5829	1049	5	b.	b.	PROPN
cana-5829	1049	6	c.	c.	PROPN
cana-5829	1049	7	,	,	PUNCT
cana-5829	1049	8	hazra	hazra	PROPN
cana-5829	1049	9	,	,	PUNCT
cana-5829	1049	10	s.	s.	PROPN
cana-5829	1049	11	b.	b.	PROPN
cana-5829	1049	12	,	,	PUNCT
cana-5829	1049	13	“	"	PUNCT
cana-5829	1049	14	𝛼	𝛼	PROPN
cana-5829	1049	15	,	,	PUNCT
cana-5829	1049	16	𝛽	𝛽	NOUN
cana-5829	1049	17	,	,	PUNCT
cana-5829	1049	18	𝛾	𝛾	PROPN
cana-5829	1049	19	,	,	PUNCT
cana-5829	1049	20	𝛿	𝛿	DET
cana-5829	1049	21	parametric	parametric	ADJ
cana-5829	1049	22	form	form	NOUN
cana-5829	1049	23	for	for	ADP
cana-5829	1049	24	solving	solve	VERB
cana-5829	1049	25	intuitionistic	intuitionistic	ADJ
cana-5829	1049	26	fuzzy	fuzzy	ADJ
cana-5829	1049	27	linear	linear	ADJ
cana-5829	1049	28	system	system	NOUN
cana-5829	1049	29	of	of	ADP
cana-5829	1049	30	equations	equation	NOUN
cana-5829	1049	31	”	"	PUNCT
cana-5829	1049	32	,	,	PUNCT
cana-5829	1049	33	advances	advance	VERB
cana-5829	1049	34	in	in	ADP
cana-5829	1049	35	fuzzy	fuzzy	ADJ
cana-5829	1049	36	mathematics	mathematic	NOUN
cana-5829	1049	37	(	(	PUNCT
cana-5829	1049	38	afm	afm	PROPN
cana-5829	1049	39	)	)	PUNCT
cana-5829	1049	40	.	.	PUNCT
cana-5829	1050	1	issn	issn	PROPN
cana-5829	1050	2	0973	0973	NUM
cana-5829	1050	3	-	-	PUNCT
cana-5829	1050	4	533x	533x	PROPN
cana-5829	1050	5	,	,	PUNCT
cana-5829	1050	6	vol	vol	NOUN
cana-5829	1050	7	.	.	PROPN
cana-5829	1050	8	16	16	NUM
cana-5829	1050	9	,	,	PUNCT
cana-5829	1050	10	no	no	INTJ
cana-5829	1050	11	.	.	NOUN
cana-5829	1050	12	1	1	NUM
cana-5829	1050	13	,	,	PUNCT
cana-5829	1050	14	pp	pp	ADJ
cana-5829	1050	15	.	.	PUNCT
cana-5829	1050	16	115	115	NUM
cana-5829	1050	17	,	,	PUNCT
cana-5829	1050	18	2021	2021	NUM
cana-5829	1050	19	.	.	PUNCT
cana-5829	1051	1	[	[	X
cana-5829	1051	2	35	35	NUM
cana-5829	1051	3	]	]	X
cana-5829	1051	4	smarandache	smarandache	NOUN
cana-5829	1051	5	,	,	PUNCT
cana-5829	1051	6	f.	f.	PROPN
cana-5829	1051	7	,	,	PUNCT
cana-5829	1051	8	“	"	PUNCT
cana-5829	1051	9	neutrosophic	neutrosophic	ADJ
cana-5829	1051	10	set	set	NOUN
cana-5829	1051	11	-	-	PUNCT
cana-5829	1051	12	a	a	DET
cana-5829	1051	13	generalization	generalization	NOUN
cana-5829	1051	14	of	of	ADP
cana-5829	1051	15	intuitionistic	intuitionistic	ADJ
cana-5829	1051	16	fuzzy	fuzzy	ADJ
cana-5829	1051	17	sets	set	NOUN
cana-5829	1051	18	”	"	PUNCT
cana-5829	1051	19	,	,	PUNCT
cana-5829	1051	20	international	international	ADJ
cana-5829	1051	21	journal	journal	NOUN
cana-5829	1051	22	of	of	ADP
cana-5829	1051	23	pure	pure	ADJ
cana-5829	1051	24	and	and	CCONJ
cana-5829	1051	25	applied	applied	ADJ
cana-5829	1051	26	mathematics	mathematic	NOUN
cana-5829	1051	27	,	,	PUNCT
cana-5829	1051	28	vol	vol	NOUN
cana-5829	1051	29	.	.	PROPN
cana-5829	1051	30	24	24	NUM
cana-5829	1051	31	,	,	PUNCT
cana-5829	1051	32	no	no	INTJ
cana-5829	1051	33	.	.	NOUN
cana-5829	1051	34	3	3	NUM
cana-5829	1051	35	,	,	PUNCT
cana-5829	1051	36	pp	pp	ADJ
cana-5829	1051	37	.	.	PUNCT
cana-5829	1052	1	287–297	287–297	NUM
cana-5829	1052	2	,	,	PUNCT
cana-5829	1052	3	2005	2005	NUM
cana-5829	1052	4	.	.	PUNCT
cana-5829	1053	1	[	[	X
cana-5829	1053	2	36	36	NUM
cana-5829	1053	3	]	]	SYM
cana-5829	1053	4	sy	sy	PROPN
cana-5829	1053	5	-	-	PUNCT
cana-5829	1053	6	ming	ming	PROPN
cana-5829	1053	7	guu	guu	PROPN
cana-5829	1053	8	,	,	PUNCT
cana-5829	1053	9	yung	yung	NOUN
cana-5829	1053	10	-	-	PUNCT
cana-5829	1053	11	yih	yih	NOUN
cana-5829	1053	12	lur	lur	PROPN
cana-5829	1053	13	,	,	PUNCT
cana-5829	1053	14	and	and	CCONJ
cana-5829	1053	15	chin	chin	PROPN
cana-5829	1053	16	-	-	PUNCT
cana-5829	1053	17	tzong	tzong	PROPN
cana-5829	1053	18	pang	pang	NOUN
cana-5829	1053	19	,	,	PUNCT
cana-5829	1053	20	“	"	PUNCT
cana-5829	1053	21	on	on	ADP
cana-5829	1053	22	infinite	infinite	ADJ
cana-5829	1053	23	products	product	NOUN
cana-5829	1053	24	of	of	ADP
cana-5829	1053	25	fuzzy	fuzzy	ADJ
cana-5829	1053	26	matrices	matrix	NOUN
cana-5829	1053	27	”	"	PUNCT
cana-5829	1053	28	,	,	PUNCT
cana-5829	1053	29	siam	siam	ADJ
cana-5829	1053	30	j.	j.	PROPN
cana-5829	1053	31	matrix	matrix	PROPN
cana-5829	1053	32	anal	anal	PROPN
cana-5829	1053	33	.	.	PUNCT
cana-5829	1054	1	appl	appl	PROPN
cana-5829	1054	2	.	.	PROPN
cana-5829	1054	3	,	,	PUNCT
cana-5829	1054	4	vol	vol	NOUN
cana-5829	1054	5	.	.	PROPN
cana-5829	1055	1	22	22	NUM
cana-5829	1055	2	,	,	PUNCT
cana-5829	1055	3	no	no	INTJ
cana-5829	1055	4	.	.	NOUN
cana-5829	1055	5	4	4	NUM
cana-5829	1055	6	,	,	PUNCT
cana-5829	1055	7	pp	pp	ADJ
cana-5829	1055	8	.	.	PUNCT
cana-5829	1056	1	1190–1203	1190–1203	NUM
cana-5829	1056	2	,	,	PUNCT
cana-5829	1056	3	2001	2001	NUM
cana-5829	1056	4	.	.	PUNCT
cana-5829	1057	1	[	[	X
cana-5829	1057	2	37	37	NUM
cana-5829	1057	3	]	]	X
cana-5829	1057	4	thomason	thomason	PROPN
cana-5829	1057	5	,	,	PUNCT
cana-5829	1057	6	m.	m.	NOUN
cana-5829	1057	7	g	g	NOUN
cana-5829	1057	8	,	,	PUNCT
cana-5829	1057	9	“	"	PUNCT
cana-5829	1057	10	convergence	convergence	NOUN
cana-5829	1057	11	of	of	ADP
cana-5829	1057	12	powers	power	NOUN
cana-5829	1057	13	of	of	ADP
cana-5829	1057	14	a	a	DET
cana-5829	1057	15	fuzzy	fuzzy	ADJ
cana-5829	1057	16	matrix	matrix	NOUN
cana-5829	1057	17	”	"	PUNCT
cana-5829	1057	18	,	,	PUNCT
cana-5829	1057	19	j	j	PROPN
cana-5829	1057	20	,	,	PUNCT
cana-5829	1057	21	math	math	PROPN
cana-5829	1057	22	anal	anal	PROPN
cana-5829	1057	23	.	.	PUNCT
cana-5829	1058	1	appl	appl	PROPN
cana-5829	1058	2	.	.	PROPN
cana-5829	1058	3	,	,	PUNCT
cana-5829	1058	4	vol	vol	NOUN
cana-5829	1058	5	.	.	PROPN
cana-5829	1058	6	57	57	NUM
cana-5829	1058	7	,	,	PUNCT
cana-5829	1058	8	pp	pp	ADJ
cana-5829	1058	9	.	.	PUNCT
cana-5829	1059	1	476	476	NUM
cana-5829	1059	2	-	-	SYM
cana-5829	1059	3	480	480	NUM
cana-5829	1059	4	,	,	PUNCT
cana-5829	1059	5	1977	1977	NUM
cana-5829	1059	6	.	.	PUNCT
cana-5829	1060	1	[	[	X
cana-5829	1060	2	38	38	NUM
cana-5829	1060	3	]	]	PUNCT
cana-5829	1060	4	venkatesan	venkatesan	NOUN
cana-5829	1060	5	,	,	PUNCT
cana-5829	1060	6	d.	d.	PROPN
cana-5829	1060	7	,	,	PUNCT
cana-5829	1060	8	sriram	sriram	PROPN
cana-5829	1060	9	,	,	PUNCT
cana-5829	1060	10	s.	s.	PROPN
cana-5829	1060	11	,	,	PUNCT
cana-5829	1060	12	“	"	PUNCT
cana-5829	1060	13	remarks	remark	NOUN
cana-5829	1060	14	on	on	ADP
cana-5829	1060	15	the	the	DET
cana-5829	1060	16	multiplicative	multiplicative	ADJ
cana-5829	1060	17	operations	operation	NOUN
cana-5829	1060	18	of	of	ADP
cana-5829	1060	19	intuitionistic	intuitionistic	ADJ
cana-5829	1060	20	fuzzy	fuzzy	ADJ
cana-5829	1060	21	matrices	matrix	NOUN
cana-5829	1060	22	”	"	PUNCT
cana-5829	1060	23	,	,	PUNCT
cana-5829	1060	24	journal	journal	NOUN
cana-5829	1060	25	of	of	ADP
cana-5829	1060	26	applied	apply	VERB
cana-5829	1060	27	and	and	CCONJ
cana-5829	1060	28	engineering	engineering	NOUN
cana-5829	1060	29	mathematics	mathematic	NOUN
cana-5829	1060	30	,	,	PUNCT
cana-5829	1060	31	vol	vol	NOUN
cana-5829	1060	32	.	.	PROPN
cana-5829	1061	1	11	11	NUM
cana-5829	1061	2	,	,	PUNCT
cana-5829	1061	3	no	no	INTJ
cana-5829	1061	4	.	.	NOUN
cana-5829	1061	5	4	4	NUM
cana-5829	1061	6	,	,	PUNCT
cana-5829	1061	7	1116	1116	NUM
cana-5829	1061	8	+	+	ADJ
cana-5829	1061	9	,	,	PUNCT
cana-5829	1061	10	2021	2021	NUM
cana-5829	1061	11	.	.	PUNCT
cana-5829	1062	1	[	[	X
cana-5829	1062	2	39	39	NUM
cana-5829	1062	3	]	]	PUNCT
cana-5829	1062	4	p.j.m	p.j.m	NOUN
cana-5829	1062	5	.	.	PUNCT
cana-5829	1063	1	van	van	PROPN
cana-5829	1063	2	laarhoven	laarhoven	PROPN
cana-5829	1063	3	and	and	CCONJ
cana-5829	1063	4	w.	w.	PROPN
cana-5829	1063	5	pedrycz	pedrycz	NOUN
cana-5829	1063	6	,	,	PUNCT
cana-5829	1063	7	a	a	DET
cana-5829	1063	8	fuzzy	fuzzy	ADJ
cana-5829	1063	9	extension	extension	NOUN
cana-5829	1063	10	of	of	ADP
cana-5829	1063	11	saaty	saaty	NOUN
cana-5829	1063	12	's	's	PART
cana-5829	1063	13	priority	priority	NOUN
cana-5829	1063	14	theory	theory	NOUN
cana-5829	1063	15	,	,	PUNCT
cana-5829	1063	16	fuzzy	fuzzy	ADJ
cana-5829	1063	17	sets	set	NOUN
cana-5829	1063	18	and	and	CCONJ
cana-5829	1063	19	systems11,229	systems11,229	PROPN
cana-5829	1063	20	-	-	PUNCT
cana-5829	1063	21	241	241	PROPN
cana-5829	1063	22	(	(	PUNCT
cana-5829	1063	23	1983	1983	NUM
cana-5829	1063	24	)	)	PUNCT
cana-5829	1063	25	.	.	PUNCT
cana-5829	1064	1	communications	communication	NOUN
cana-5829	1064	2	on	on	ADP
cana-5829	1064	3	applied	apply	VERB
cana-5829	1064	4	nonlinear	nonlinear	ADJ
cana-5829	1064	5	analysis	analysis	NOUN
cana-5829	1064	6	issn	issn	NOUN
cana-5829	1064	7	:	:	PUNCT
cana-5829	1064	8	1074	1074	NUM
cana-5829	1064	9	-	-	PUNCT
cana-5829	1064	10	133x	133x	NUM
cana-5829	1064	11	vol	vol	VERB
cana-5829	1064	12	32	32	NUM
cana-5829	1064	13	no	no	NOUN
cana-5829	1064	14	.	.	PUNCT
cana-5829	1065	1	10s	10	NOUN
cana-5829	1065	2	(	(	PUNCT
cana-5829	1065	3	2025	2025	NUM
cana-5829	1065	4	)	)	PUNCT
cana-5829	1065	5	2958	2958	NUM
cana-5829	1065	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5829	1066	1	[	[	X
cana-5829	1066	2	40	40	NUM
cana-5829	1066	3	]	]	PUNCT
cana-5829	1066	4	verma	verma	PROPN
cana-5829	1066	5	r.	r.	PROPN
cana-5829	1066	6	,	,	PUNCT
cana-5829	1066	7	merigo	merigo	PROPN
cana-5829	1066	8	jose	jose	PROPN
cana-5829	1066	9	m.	m.	NOUN
cana-5829	1066	10	,	,	PUNCT
cana-5829	1066	11	“	"	PUNCT
cana-5829	1066	12	on	on	ADP
cana-5829	1066	13	sharma	sharma	PROPN
cana-5829	1066	14	-	-	PUNCT
cana-5829	1066	15	mittal	mittal	PROPN
cana-5829	1066	16	’s	’s	PART
cana-5829	1066	17	entropy	entropy	NOUN
cana-5829	1066	18	under	under	ADP
cana-5829	1066	19	intuitionistic	intuitionistic	ADJ
cana-5829	1066	20	fuzzy	fuzzy	ADJ
cana-5829	1066	21	environment	environment	NOUN
cana-5829	1066	22	”	"	PUNCT
cana-5829	1066	23	,	,	PUNCT
cana-5829	1066	24	cybernetics	cybernetic	NOUN
cana-5829	1066	25	and	and	CCONJ
cana-5829	1066	26	systems	system	NOUN
cana-5829	1066	27	,	,	PUNCT
cana-5829	1066	28	vol	vol	NOUN
cana-5829	1066	29	.	.	PROPN
cana-5829	1067	1	52	52	NUM
cana-5829	1067	2	,	,	PUNCT
cana-5829	1067	3	no	no	INTJ
cana-5829	1067	4	.	.	NOUN
cana-5829	1067	5	1	1	NUM
cana-5829	1067	6	,	,	PUNCT
cana-5829	1067	7	pp	pp	ADJ
cana-5829	1067	8	.	.	PUNCT
cana-5829	1068	1	1	1	NUM
cana-5829	1068	2	-	-	SYM
cana-5829	1068	3	24	24	NUM
cana-5829	1068	4	,	,	PUNCT
cana-5829	1068	5	2021	2021	NUM
cana-5829	1068	6	.	.	PUNCT
cana-5829	1069	1	[	[	X
cana-5829	1069	2	41	41	NUM
cana-5829	1069	3	]	]	PUNCT
cana-5829	1069	4	m.	m.	NOUN
cana-5829	1069	5	wagenknecht	wagenknecht	PROPN
cana-5829	1069	6	and	and	CCONJ
cana-5829	1069	7	k.	k.	PROPN
cana-5829	1069	8	hartmann	hartmann	PROPN
cana-5829	1069	9	,	,	PUNCT
cana-5829	1069	10	on	on	ADP
cana-5829	1069	11	fuzzy	fuzzy	ADJ
cana-5829	1069	12	rank	rank	NOUN
cana-5829	1069	13	-	-	PUNCT
cana-5829	1069	14	ordering	ordering	NOUN
cana-5829	1069	15	in	in	ADP
cana-5829	1069	16	politicizations	politicization	NOUN
cana-5829	1069	17	,	,	PUNCT
cana-5829	1069	18	fuzzy	fuzzy	ADJ
cana-5829	1069	19	sets	set	NOUN
cana-5829	1069	20	and	and	CCONJ
cana-5829	1069	21	systems11	systems11	NOUN
cana-5829	1069	22	,	,	PUNCT
cana-5829	1069	23	253	253	NUM
cana-5829	1069	24	-	-	SYM
cana-5829	1069	25	264	264	NUM
cana-5829	1069	26	(	(	PUNCT
cana-5829	1069	27	1983	1983	NUM
cana-5829	1069	28	)	)	PUNCT
cana-5829	1069	29	.	.	PUNCT
cana-5829	1070	1	[	[	X
cana-5829	1070	2	42	42	NUM
cana-5829	1070	3	]	]	PUNCT
cana-5829	1070	4	xu	xu	PROPN
cana-5829	1070	5	,	,	PUNCT
cana-5829	1070	6	z.	z.	PROPN
cana-5829	1070	7	,	,	PUNCT
cana-5829	1070	8	“	"	PUNCT
cana-5829	1070	9	multi	multi	ADJ
cana-5829	1070	10	-	-	ADJ
cana-5829	1070	11	person	person	ADJ
cana-5829	1070	12	multi	multi	ADJ
cana-5829	1070	13	-	-	ADJ
cana-5829	1070	14	attribute	attribute	ADJ
cana-5829	1070	15	decision	decision	NOUN
cana-5829	1070	16	making	make	VERB
cana-5829	1070	17	models	model	NOUN
cana-5829	1070	18	under	under	ADP
cana-5829	1070	19	intuitionistic	intuitionistic	ADJ
cana-5829	1070	20	fuzzy	fuzzy	ADJ
cana-5829	1070	21	environment	environment	NOUN
cana-5829	1070	22	”	"	PUNCT
cana-5829	1070	23	,	,	PUNCT
cana-5829	1070	24	fuzzy	fuzzy	ADJ
cana-5829	1070	25	optimization	optimization	NOUN
cana-5829	1070	26	decision	decision	NOUN
cana-5829	1070	27	making	making	NOUN
cana-5829	1070	28	,	,	PUNCT
cana-5829	1070	29	vol	vol	NOUN
cana-5829	1070	30	.	.	PROPN
cana-5829	1070	31	6	6	NUM
cana-5829	1070	32	,	,	PUNCT
cana-5829	1070	33	pp	pp	ADJ
cana-5829	1070	34	.	.	PUNCT
cana-5829	1071	1	221–236	221–236	NUM
cana-5829	1071	2	,	,	PUNCT
cana-5829	1071	3	2007	2007	NUM
cana-5829	1071	4	.	.	PUNCT
cana-5829	1072	1	[	[	X
cana-5829	1072	2	43	43	NUM
cana-5829	1072	3	]	]	X
cana-5829	1072	4	yager	yager	NOUN
cana-5829	1072	5	,	,	PUNCT
cana-5829	1072	6	r.	r.	PROPN
cana-5829	1072	7	r	r	PROPN
cana-5829	1072	8	,	,	PUNCT
cana-5829	1072	9	“	"	PUNCT
cana-5829	1072	10	some	some	DET
cana-5829	1072	11	aspects	aspect	NOUN
cana-5829	1072	12	of	of	ADP
cana-5829	1072	13	intuitionistic	intuitionistic	ADJ
cana-5829	1072	14	fuzzy	fuzzy	ADJ
cana-5829	1072	15	sets	set	NOUN
cana-5829	1072	16	”	"	PUNCT
cana-5829	1072	17	,	,	PUNCT
cana-5829	1072	18	fuzzy	fuzzy	ADJ
cana-5829	1072	19	optimization	optimization	NOUN
cana-5829	1072	20	and	and	CCONJ
cana-5829	1072	21	decision	decision	NOUN
cana-5829	1072	22	making	making	NOUN
cana-5829	1072	23	,	,	PUNCT
cana-5829	1072	24	vol	vol	NOUN
cana-5829	1072	25	.	.	PROPN
cana-5829	1072	26	8	8	NUM
cana-5829	1072	27	,	,	PUNCT
cana-5829	1072	28	no	no	INTJ
cana-5829	1072	29	.	.	NOUN
cana-5829	1072	30	1	1	NUM
cana-5829	1072	31	,	,	PUNCT
cana-5829	1072	32	pp	pp	ADJ
cana-5829	1072	33	.	.	PUNCT
cana-5829	1073	1	67–90	67–90	NUM
cana-5829	1073	2	,	,	PUNCT
cana-5829	1073	3	2009	2009	NUM
cana-5829	1073	4	.	.	PUNCT
cana-5829	1074	1	[	[	X
cana-5829	1074	2	44	44	NUM
cana-5829	1074	3	]	]	X
cana-5829	1074	4	zhou	zhou	PROPN
cana-5829	1074	5	,	,	PUNCT
cana-5829	1074	6	x.	x.	PROPN
cana-5829	1074	7	g.	g.	PROPN
cana-5829	1074	8	,	,	PUNCT
cana-5829	1074	9	ding	ding	NOUN
cana-5829	1074	10	,	,	PUNCT
cana-5829	1074	11	y.	y.	PROPN
cana-5829	1074	12	f.	f.	PROPN
cana-5829	1074	13	,	,	PUNCT
cana-5829	1074	14	lu	lu	PROPN
cana-5829	1074	15	,	,	PUNCT
cana-5829	1074	16	m.	m.	NOUN
cana-5829	1074	17	,	,	PUNCT
cana-5829	1074	18	“	"	PUNCT
cana-5829	1074	19	study	study	NOUN
cana-5829	1074	20	on	on	ADP
cana-5829	1074	21	bond	bond	NOUN
cana-5829	1074	22	selection	selection	NOUN
cana-5829	1074	23	under	under	ADP
cana-5829	1074	24	intuitionistic	intuitionistic	ADJ
cana-5829	1074	25	fuzzy	fuzzy	ADJ
cana-5829	1074	26	conditions	condition	NOUN
cana-5829	1074	27	”	"	PUNCT
cana-5829	1074	28	,	,	PUNCT
cana-5829	1074	29	journal	journal	NOUN
cana-5829	1074	30	of	of	ADP
cana-5829	1074	31	algorithms	algorithms	PROPN
cana-5829	1074	32	computational	computational	ADJ
cana-5829	1074	33	technology	technology	NOUN
cana-5829	1074	34	,	,	PUNCT
cana-5829	1074	35	vol	vol	NOUN
cana-5829	1074	36	.	.	PROPN
cana-5829	1074	37	12	12	NUM
cana-5829	1074	38	,	,	PUNCT
cana-5829	1074	39	no	no	INTJ
cana-5829	1074	40	.	.	NOUN
cana-5829	1074	41	4	4	NUM
cana-5829	1074	42	,	,	PUNCT
cana-5829	1074	43	pp	pp	ADJ
cana-5829	1074	44	.	.	PUNCT
cana-5829	1075	1	376–386	376–386	NUM
cana-5829	1075	2	,	,	PUNCT
cana-5829	1075	3	2018	2018	NUM
cana-5829	1075	4	.	.	PUNCT
cana-5829	1076	1	[	[	X
cana-5829	1076	2	45	45	NUM
cana-5829	1076	3	]	]	X
cana-5829	1076	4	zhang	zhang	PROPN
cana-5829	1076	5	,	,	PUNCT
cana-5829	1076	6	f.	f.	PROPN
cana-5829	1076	7	w.	w.	PROPN
cana-5829	1076	8	,	,	PUNCT
cana-5829	1076	9	huang	huang	PROPN
cana-5829	1076	10	,	,	PUNCT
cana-5829	1076	11	w.	w.	PROPN
cana-5829	1076	12	w.	w.	PROPN
cana-5829	1076	13	,	,	PUNCT
cana-5829	1076	14	sun	sun	PROPN
cana-5829	1076	15	,	,	PUNCT
cana-5829	1076	16	j.	j.	PROPN
cana-5829	1076	17	,	,	PUNCT
cana-5829	1076	18	liu	liu	PROPN
cana-5829	1076	19	,	,	PUNCT
cana-5829	1076	20	z.	z.	PROPN
cana-5829	1076	21	d.	d.	PROPN
cana-5829	1076	22	,	,	PUNCT
cana-5829	1076	23	zhu	zhu	PROPN
cana-5829	1076	24	,	,	PUNCT
cana-5829	1076	25	y.	y.	PROPN
cana-5829	1076	26	h.	h.	PROPN
cana-5829	1076	27	,	,	PUNCT
cana-5829	1076	28	li	li	PROPN
cana-5829	1076	29	,	,	PUNCT
cana-5829	1076	30	k.	k.	PROPN
cana-5829	1076	31	t.	t.	PROPN
cana-5829	1076	32	,	,	PUNCT
cana-5829	1076	33	xu	xu	PROPN
cana-5829	1076	34	,	,	PUNCT
cana-5829	1076	35	s.	s.	PROPN
cana-5829	1076	36	h.	h.	PROPN
cana-5829	1076	37	,	,	PUNCT
cana-5829	1076	38	li	li	PROPN
cana-5829	1076	39	,	,	PUNCT
cana-5829	1076	40	q.	q.	PROPN
cana-5829	1076	41	,	,	PUNCT
cana-5829	1076	42	“	"	PUNCT
cana-5829	1076	43	generalized	generalize	VERB
cana-5829	1076	44	fuzzy	fuzzy	ADJ
cana-5829	1076	45	additive	additive	ADJ
cana-5829	1076	46	operators	operator	NOUN
cana-5829	1076	47	on	on	ADP
cana-5829	1076	48	intuitionistic	intuitionistic	ADJ
cana-5829	1076	49	fuzzy	fuzzy	ADJ
cana-5829	1076	50	sets	set	NOUN
cana-5829	1076	51	and	and	CCONJ
cana-5829	1076	52	interval	interval	NOUN
cana-5829	1076	53	-	-	PUNCT
cana-5829	1076	54	valued	value	VERB
cana-5829	1076	55	intuitionistic	intuitionistic	ADJ
cana-5829	1076	56	fuzzy	fuzzy	ADJ
cana-5829	1076	57	sets	set	NOUN
cana-5829	1076	58	and	and	CCONJ
cana-5829	1076	59	their	their	PRON
cana-5829	1076	60	application	application	NOUN
cana-5829	1076	61	”	"	PUNCT
cana-5829	1076	62	,	,	PUNCT
cana-5829	1076	63	ieee	ieee	NOUN
cana-5829	1076	64	,	,	PUNCT
cana-5829	1076	65	vol	vol	NOUN
cana-5829	1076	66	.	.	PROPN
cana-5829	1076	67	7	7	NUM
cana-5829	1076	68	,	,	PUNCT
cana-5829	1076	69	pp	pp	ADJ
cana-5829	1076	70	.	.	PUNCT
cana-5829	1076	71	45734	45734	NUM
cana-5829	1076	72	–	–	PUNCT
cana-5829	1076	73	45743	45743	NUM
cana-5829	1076	74	,	,	PUNCT
cana-5829	1076	75	2019	2019	NUM
cana-5829	1076	76	.	.	PUNCT
cana-5829	1077	1	[	[	X
cana-5829	1077	2	46	46	NUM
cana-5829	1077	3	]	]	SYM
cana-5829	1077	4	zadeh	zadeh	PROPN
cana-5829	1077	5	,	,	PUNCT
cana-5829	1077	6	l.	l.	PROPN
cana-5829	1077	7	a.	a.	PROPN
cana-5829	1077	8	,	,	PUNCT
cana-5829	1077	9	“	"	PUNCT
cana-5829	1077	10	fuzzy	fuzzy	ADJ
cana-5829	1077	11	sets	set	NOUN
cana-5829	1077	12	”	"	PUNCT
cana-5829	1077	13	,	,	PUNCT
cana-5829	1077	14	information	information	NOUN
cana-5829	1077	15	and	and	CCONJ
cana-5829	1077	16	control	control	NOUN
cana-5829	1077	17	,	,	PUNCT
cana-5829	1077	18	vol	vol	NOUN
cana-5829	1077	19	.	.	PROPN
cana-5829	1077	20	8	8	NUM
cana-5829	1077	21	,	,	PUNCT
cana-5829	1077	22	pp	pp	ADJ
cana-5829	1077	23	.	.	PUNCT
cana-5829	1077	24	338	338	NUM
cana-5829	1077	25	-	-	SYM
cana-5829	1077	26	353	353	NUM
cana-5829	1077	27	,	,	PUNCT
cana-5829	1077	28	1965	1965	NUM
cana-5829	1077	29	.	.	PUNCT
cana-5829	1078	1	[	[	X
cana-5829	1078	2	47	47	NUM
cana-5829	1078	3	]	]	PUNCT
cana-5829	1078	4	l.	l.	PROPN
cana-5829	1078	5	a.	a.	PROPN
cana-5829	1078	6	zadeh	zadeh	PROPN
cana-5829	1078	7	,	,	PUNCT
cana-5829	1078	8	fuzzy	fuzzy	ADJ
cana-5829	1078	9	sets	set	NOUN
cana-5829	1078	10	,	,	PUNCT
cana-5829	1078	11	information	information	NOUN
cana-5829	1078	12	and	and	CCONJ
cana-5829	1078	13	control	control	NOUN
cana-5829	1078	14	,	,	PUNCT
cana-5829	1078	15	8	8	NUM
cana-5829	1078	16	(	(	PUNCT
cana-5829	1078	17	1965	1965	NUM
cana-5829	1078	18	)	)	PUNCT
cana-5829	1078	19	,	,	PUNCT
cana-5829	1078	20	338-353.and	338-353.and	NUM
cana-5829	1078	21	applications	application	NOUN
cana-5829	1078	22	,	,	PUNCT
cana-5829	1078	23	vol	vol	NOUN
cana-5829	1078	24	.	.	PUNCT
cana-5829	1078	25	57(2	57(2	NUM
cana-5829	1078	26	)	)	PUNCT
cana-5829	1078	27	(	(	PUNCT
cana-5829	1078	28	february	february	PROPN
cana-5829	1078	29	1977	1977	NUM
cana-5829	1078	30	)	)	PUNCT
cana-5829	1079	1	pp	pp	ADP
cana-5829	1079	2	.	.	PUNCT
cana-5829	1080	1	476	476	NUM
cana-5829	1080	2	-	-	SYM
cana-5829	1080	3	480	480	NUM
cana-5829	1080	4	.	.	PUNCT
cana-5829	1081	1	[	[	X
cana-5829	1081	2	48	48	NUM
cana-5829	1081	3	]	]	SYM
cana-5829	1081	4	l.a	l.a	PROPN
cana-5829	1081	5	.	.	PROPN
cana-5829	1081	6	zadeh	zadeh	PROPN
cana-5829	1081	7	,	,	PUNCT
cana-5829	1081	8	fuzzy	fuzzy	ADJ
cana-5829	1081	9	sets	set	NOUN
cana-5829	1081	10	,	,	PUNCT
cana-5829	1081	11	information	information	NOUN
cana-5829	1081	12	and	and	CCONJ
cana-5829	1081	13	control	control	NOUN
cana-5829	1081	14	,	,	PUNCT
cana-5829	1081	15	vol	vol	NOUN
cana-5829	1081	16	.	.	PUNCT
cana-5829	1081	17	8(3	8(3	NUM
cana-5829	1081	18	)	)	PUNCT
cana-5829	1081	19	(	(	PUNCT
cana-5829	1081	20	june	june	PROPN
cana-5829	1081	21	1965	1965	NUM
cana-5829	1081	22	)	)	PUNCT
cana-5829	1081	23	pp	pp	ADP
cana-5829	1081	24	.	.	PUNCT
cana-5829	1082	1	338-353.naim	338-353.naim	NUM
cana-5829	1082	2	cagman	cagman	NOUN
cana-5829	1082	3	_	_	PROPN
cana-5829	1082	4	,	,	PUNCT
cana-5829	1082	5	department	department	NOUN
cana-5829	1082	6	of	of	ADP
cana-5829	1082	7	mathematics	mathematic	NOUN
cana-5829	1082	8	,	,	PUNCT
cana-5829	1082	9	faculty	faculty	NOUN
cana-5829	1082	10	of	of	ADP
cana-5829	1082	11	arts	art	NOUN
cana-5829	1082	12	and	and	CCONJ
cana-5829	1082	13	sciences	science	NOUN
cana-5829	1082	14	,	,	PUNCT