id	sid	tid	token	lemma	pos
cana-1323	1	1	communications	communication	NOUN
cana-1323	1	2	on	on	ADP
cana-1323	1	3	applied	apply	VERB
cana-1323	1	4	nonlinear	nonlinear	ADJ
cana-1323	1	5	analysis	analysis	NOUN
cana-1323	1	6	issn	issn	NOUN
cana-1323	1	7	:	:	PUNCT
cana-1323	1	8	1074	1074	NUM
cana-1323	1	9	-	-	PUNCT
cana-1323	1	10	133x	133x	NUM
cana-1323	1	11	vol	vol	NOUN
cana-1323	1	12	31	31	NUM
cana-1323	1	13	no	no	NOUN
cana-1323	1	14	.	.	PUNCT
cana-1323	2	1	7s	7	NOUN
cana-1323	2	2	(	(	PUNCT
cana-1323	2	3	2024	2024	NUM
cana-1323	2	4	)	)	PUNCT
cana-1323	2	5	444	444	NUM
cana-1323	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1323	2	7	homomorphism	homomorphism	NOUN
cana-1323	2	8	of	of	ADP
cana-1323	2	9	tripolar	tripolar	ADJ
cana-1323	2	10	fuzzy	fuzzy	ADJ
cana-1323	2	11	soft	soft	ADJ
cana-1323	2	12	ternary	ternary	ADJ
cana-1323	2	13	γ	γ	X
cana-1323	2	14	-	-	PUNCT
cana-1323	2	15	semiring	semire	VERB
cana-1323	2	16	e.	e.	PROPN
cana-1323	2	17	meera	meera	PROPN
cana-1323	2	18	prasad	prasad	PROPN
cana-1323	2	19	1,2	1,2	NUM
cana-1323	2	20	,	,	PUNCT
cana-1323	2	21	d.	d.	PROPN
cana-1323	2	22	madhusudhana	madhusudhana	PROPN
cana-1323	2	23	rao	rao	PROPN
cana-1323	2	24	3	3	NUM
cana-1323	2	25	,	,	PUNCT
cana-1323	2	26	4	4	NUM
cana-1323	2	27	g.	g.	PROPN
cana-1323	2	28	srinivasa	srinivasa	PROPN
cana-1323	2	29	rao	rao	PROPN
cana-1323	2	30	,	,	PUNCT
cana-1323	2	31	g.	g.	PROPN
cana-1323	2	32	suresh	suresh	PROPN
cana-1323	2	33	kumar	kumar	PROPN
cana-1323	2	34	4	4	PROPN
cana-1323	2	35	.	.	PUNCT
cana-1323	3	1	m.	m.	NOUN
cana-1323	3	2	vasantha	vasantha	NOUN
cana-1323	3	3	5	5	NUM
cana-1323	3	4	1	1	NUM
cana-1323	3	5	research	research	NOUN
cana-1323	3	6	scholar	scholar	NOUN
cana-1323	3	7	,	,	PUNCT
cana-1323	3	8	department	department	NOUN
cana-1323	3	9	of	of	ADP
cana-1323	3	10	mathematics	mathematic	NOUN
cana-1323	3	11	,	,	PUNCT
cana-1323	3	12	konerulakshmaiah	konerulakshmaiah	PROPN
cana-1323	3	13	education	education	PROPN
cana-1323	3	14	foundation	foundation	PROPN
cana-1323	3	15	,	,	PUNCT
cana-1323	3	16	vaddeswaram	vaddeswaram	PROPN
cana-1323	3	17	,	,	PUNCT
cana-1323	3	18	guntur	guntur	PROPN
cana-1323	3	19	,	,	PUNCT
cana-1323	3	20	a.p	a.p	PROPN
cana-1323	3	21	.	.	PROPN
cana-1323	3	22	india	india	PROPN
cana-1323	3	23	.	.	PUNCT
cana-1323	4	1	emai:meeraprasad.6499@gmail.com	emai:meeraprasad.6499@gmail.com	PROPN
cana-1323	4	2	2	2	NUM
cana-1323	4	3	deputy	deputy	NOUN
cana-1323	4	4	transport	transport	NOUN
cana-1323	4	5	commissioner	commissioner	NOUN
cana-1323	4	6	,	,	PUNCT
cana-1323	4	7	guntur(dt	guntur(dt	PROPN
cana-1323	4	8	)	)	PUNCT
cana-1323	4	9	,	,	PUNCT
cana-1323	4	10	guntur	guntur	PROPN
cana-1323	4	11	,	,	PUNCT
cana-1323	4	12	a.p	a.p	PROPN
cana-1323	4	13	.	.	PROPN
cana-1323	4	14	,	,	PUNCT
cana-1323	4	15	india	india	PROPN
cana-1323	4	16	.	.	PROPN
cana-1323	5	1	3	3	NUM
cana-1323	5	2	department	department	NOUN
cana-1323	5	3	of	of	ADP
cana-1323	5	4	mathematics	mathematic	NOUN
cana-1323	5	5	,	,	PUNCT
cana-1323	5	6	government	government	NOUN
cana-1323	5	7	degree	degree	NOUN
cana-1323	5	8	college	college	NOUN
cana-1323	5	9	for	for	ADP
cana-1323	5	10	women(a	women(a	PROPN
cana-1323	5	11	)	)	PUNCT
cana-1323	5	12	,	,	PUNCT
cana-1323	5	13	guntur	guntur	PROPN
cana-1323	5	14	,	,	PUNCT
cana-1323	5	15	a.p	a.p	PROPN
cana-1323	5	16	.	.	PROPN
cana-1323	5	17	india	india	PROPN
cana-1323	5	18	.	.	PUNCT
cana-1323	6	1	email:dmrmaths@gmail.com	email:dmrmaths@gmail.com	X
cana-1323	6	2	4	4	NUM
cana-1323	6	3	department	department	NOUN
cana-1323	6	4	of	of	ADP
cana-1323	6	5	mathematics	mathematics	PROPN
cana-1323	6	6	&	&	CCONJ
cana-1323	6	7	statistics	statistic	NOUN
cana-1323	6	8	,	,	PUNCT
cana-1323	6	9	vfstr	vfstr	NOUN
cana-1323	6	10	deemed	deem	VERB
cana-1323	6	11	to	to	PART
cana-1323	6	12	be	be	AUX
cana-1323	6	13	university	university	NOUN
cana-1323	6	14	,	,	PUNCT
cana-1323	6	15	vadlamudi	vadlamudi	NOUN
cana-1323	6	16	,	,	PUNCT
cana-1323	6	17	guntur	guntur	PROPN
cana-1323	6	18	,	,	PUNCT
cana-1323	6	19	a.p	a.p	PROPN
cana-1323	6	20	.	.	PROPN
cana-1323	6	21	,	,	PUNCT
cana-1323	6	22	india.email:gsrinulakshmi77@gmail.com	india.email:gsrinulakshmi77@gmail.com	X
cana-1323	6	23	4	4	NUM
cana-1323	6	24	department	department	NOUN
cana-1323	6	25	of	of	ADP
cana-1323	6	26	mathematics	mathematic	NOUN
cana-1323	6	27	,	,	PUNCT
cana-1323	6	28	konerulakshmaiah	konerulakshmaiah	PROPN
cana-1323	6	29	education	education	PROPN
cana-1323	6	30	foundation	foundation	PROPN
cana-1323	6	31	,	,	PUNCT
cana-1323	6	32	vaddeswaram	vaddeswaram	PROPN
cana-1323	6	33	,	,	PUNCT
cana-1323	6	34	guntur	guntur	PROPN
cana-1323	6	35	,	,	PUNCT
cana-1323	6	36	a.p	a.p	PROPN
cana-1323	6	37	.	.	PROPN
cana-1323	6	38	india	india	PROPN
cana-1323	6	39	.	.	PUNCT
cana-1323	7	1	email	email	NOUN
cana-1323	7	2	:	:	PUNCT
cana-1323	7	3	drgsk006@kluniversity.in	drgsk006@kluniversity.in	PROPN
cana-1323	7	4	5	5	NUM
cana-1323	7	5	department	department	NOUN
cana-1323	7	6	of	of	ADP
cana-1323	7	7	h&s	h&s	PROPN
cana-1323	7	8	,	,	PUNCT
cana-1323	7	9	mallareddy	mallareddy	ADJ
cana-1323	7	10	engineering	engineering	NOUN
cana-1323	7	11	college	college	NOUN
cana-1323	7	12	for	for	ADP
cana-1323	7	13	women	woman	NOUN
cana-1323	7	14	,	,	PUNCT
cana-1323	7	15	hyderabad	hyderabad	PROPN
cana-1323	7	16	,	,	PUNCT
cana-1323	7	17	telangana	telangana	PROPN
cana-1323	7	18	,	,	PUNCT
cana-1323	7	19	india	india	PROPN
cana-1323	7	20	.	.	PUNCT
cana-1323	7	21	email	email	NOUN
cana-1323	7	22	:	:	PUNCT
cana-1323	8	1	bezawadavasantha@gmail.com	bezawadavasantha@gmail.com	X
cana-1323	8	2	article	article	NOUN
cana-1323	8	3	history	history	NOUN
cana-1323	8	4	:	:	PUNCT
cana-1323	8	5	received	receive	VERB
cana-1323	8	6	:	:	PUNCT
cana-1323	8	7	01	01	NUM
cana-1323	8	8	-	-	PUNCT
cana-1323	8	9	06	06	NUM
cana-1323	8	10	-	-	PUNCT
cana-1323	8	11	2024	2024	NUM
cana-1323	8	12	revised	revise	VERB
cana-1323	8	13	:	:	PUNCT
cana-1323	8	14	03	03	NUM
cana-1323	8	15	-	-	PUNCT
cana-1323	8	16	07	07	NUM
cana-1323	8	17	-	-	PUNCT
cana-1323	8	18	2024	2024	NUM
cana-1323	8	19	accepted	accept	VERB
cana-1323	8	20	:	:	PUNCT
cana-1323	8	21	29	29	NUM
cana-1323	8	22	-	-	SYM
cana-1323	8	23	07	07	NUM
cana-1323	8	24	-	-	PUNCT
cana-1323	8	25	2024	2024	NUM
cana-1323	8	26	abstract	abstract	NOUN
cana-1323	8	27	:	:	PUNCT
cana-1323	8	28	the	the	DET
cana-1323	8	29	notions	notion	NOUN
cana-1323	8	30	of	of	ADP
cana-1323	8	31	a	a	DET
cana-1323	8	32	tripolar	tripolar	ADJ
cana-1323	8	33	fuzzy	fuzzy	ADJ
cana-1323	8	34	soft	soft	ADJ
cana-1323	8	35	ternary	ternary	ADJ
cana-1323	8	36	γ−semirings	γ−semiring	NOUN
cana-1323	8	37	,	,	PUNCT
cana-1323	8	38	a	a	DET
cana-1323	8	39	tripolar	tripolar	ADJ
cana-1323	8	40	fuzzy	fuzzy	ADJ
cana-1323	8	41	soft	soft	ADJ
cana-1323	8	42	ternary	ternary	NOUN
cana-1323	8	43	γ−semiring	γ−semire	VERB
cana-1323	8	44	homomorphism	homomorphism	NOUN
cana-1323	8	45	and	and	CCONJ
cana-1323	8	46	a	a	DET
cana-1323	8	47	tripolar	tripolar	ADJ
cana-1323	8	48	fuzzy	fuzzy	ADJ
cana-1323	8	49	soft	soft	ADJ
cana-1323	8	50	ideal	ideal	NOUN
cana-1323	8	51	in	in	ADP
cana-1323	8	52	ternary	ternary	ADJ
cana-1323	8	53	γ−semirings	γ−semiring	NOUN
cana-1323	8	54	are	be	AUX
cana-1323	8	55	discussed	discuss	VERB
cana-1323	8	56	,	,	PUNCT
cana-1323	8	57	and	and	CCONJ
cana-1323	8	58	related	related	ADJ
cana-1323	8	59	properties	property	NOUN
cana-1323	8	60	are	be	AUX
cana-1323	8	61	investigated	investigate	VERB
cana-1323	8	62	.	.	PUNCT
cana-1323	9	1	on	on	ADP
cana-1323	9	2	the	the	DET
cana-1323	9	3	other	other	ADJ
cana-1323	9	4	hand	hand	NOUN
cana-1323	9	5	,	,	PUNCT
cana-1323	9	6	in	in	ADP
cana-1323	9	7	this	this	DET
cana-1323	9	8	paper	paper	NOUN
cana-1323	9	9	,	,	PUNCT
cana-1323	9	10	we	we	PRON
cana-1323	9	11	also	also	ADV
cana-1323	9	12	define	define	VERB
cana-1323	9	13	the	the	DET
cana-1323	9	14	image	image	NOUN
cana-1323	9	15	and	and	CCONJ
cana-1323	9	16	pre	pre	NOUN
cana-1323	9	17	-	-	NOUN
cana-1323	9	18	image	image	NOUN
cana-1323	9	19	of	of	ADP
cana-1323	9	20	tripolar	tripolar	ADJ
cana-1323	9	21	fuzzy	fuzzy	ADJ
cana-1323	9	22	soft	soft	ADJ
cana-1323	9	23	ternary	ternary	ADJ
cana-1323	9	24	γ−semirings	γ−semiring	NOUN
cana-1323	9	25	.	.	PUNCT
cana-1323	10	1	some	some	DET
cana-1323	10	2	properties	property	NOUN
cana-1323	10	3	and	and	CCONJ
cana-1323	10	4	results	result	NOUN
cana-1323	10	5	involving	involve	VERB
cana-1323	10	6	these	these	DET
cana-1323	10	7	concepts	concept	NOUN
cana-1323	10	8	are	be	AUX
cana-1323	10	9	stated	state	VERB
cana-1323	10	10	and	and	CCONJ
cana-1323	10	11	proved	prove	VERB
cana-1323	10	12	.	.	PUNCT
cana-1323	11	1	keywords	keyword	NOUN
cana-1323	11	2	:	:	PUNCT
cana-1323	11	3	soft	soft	ADJ
cana-1323	11	4	set	set	NOUN
cana-1323	11	5	,	,	PUNCT
cana-1323	11	6	fuzzy	fuzzy	ADJ
cana-1323	11	7	soft	soft	ADJ
cana-1323	11	8	set	set	NOUN
cana-1323	11	9	,	,	PUNCT
cana-1323	11	10	tripolar	tripolar	ADJ
cana-1323	11	11	fuzzy	fuzzy	ADJ
cana-1323	11	12	soft	soft	ADJ
cana-1323	11	13	set	set	NOUN
cana-1323	11	14	,	,	PUNCT
cana-1323	11	15	tripolar	tripolar	ADJ
cana-1323	11	16	fuzzy	fuzzy	ADJ
cana-1323	11	17	soft	soft	ADJ
cana-1323	11	18	ternary	ternary	ADJ
cana-1323	11	19	γ−semiring	γ−semiring	NOUN
cana-1323	11	20	,	,	PUNCT
cana-1323	11	21	tripolar	tripolar	ADJ
cana-1323	11	22	fuzzy	fuzzy	ADJ
cana-1323	11	23	soft	soft	ADJ
cana-1323	11	24	ideal	ideal	NOUN
cana-1323	11	25	,	,	PUNCT
cana-1323	11	26	tripolar	tripolar	ADJ
cana-1323	11	27	fuzzy	fuzzy	ADJ
cana-1323	11	28	soft	soft	ADJ
cana-1323	11	29	ternary	ternary	NOUN
cana-1323	11	30	γ−semiring	γ−semire	VERB
cana-1323	11	31	homomorphism	homomorphism	NOUN
cana-1323	11	32	.	.	PUNCT
cana-1323	12	1	1	1	X
cana-1323	12	2	.	.	X
cana-1323	12	3	introduction	introduction	NOUN
cana-1323	12	4	in	in	ADP
cana-1323	12	5	the	the	DET
cana-1323	12	6	year	year	NOUN
cana-1323	12	7	2017	2017	NUM
cana-1323	12	8	revathi	revathi	PROPN
cana-1323	12	9	et.al	et.al	PROPN
cana-1323	13	1	[	[	X
cana-1323	13	2	7	7	NUM
cana-1323	13	3	,	,	PUNCT
cana-1323	13	4	8	8	NUM
cana-1323	13	5	]	]	PUNCT
cana-1323	13	6	introduced	introduce	VERB
cana-1323	13	7	the	the	DET
cana-1323	13	8	concept	concept	NOUN
cana-1323	13	9	of	of	ADP
cana-1323	13	10	“	"	PUNCT
cana-1323	13	11	fuzzy	fuzzy	ADJ
cana-1323	13	12	ideals	ideal	NOUN
cana-1323	13	13	”	"	PUNCT
cana-1323	13	14	in	in	ADP
cana-1323	13	15	“	"	PUNCT
cana-1323	13	16	ternary	ternary	ADJ
cana-1323	13	17	gamma	gamma	NOUN
cana-1323	13	18	semirings	semiring	NOUN
cana-1323	13	19	”	"	PUNCT
cana-1323	13	20	.	.	PUNCT
cana-1323	14	1	in	in	ADP
cana-1323	14	2	the	the	DET
cana-1323	14	3	year	year	NOUN
cana-1323	14	4	2018	2018	NUM
cana-1323	14	5	,	,	PUNCT
cana-1323	14	6	they	they	PRON
cana-1323	14	7	[	[	X
cana-1323	14	8	9,10,11	9,10,11	X
cana-1323	14	9	]	]	PUNCT
cana-1323	14	10	studied	study	VERB
cana-1323	14	11	“	"	PUNCT
cana-1323	14	12	fuzzy	fuzzy	ADJ
cana-1323	14	13	regular	regular	ADJ
cana-1323	14	14	ternary	ternary	ADJ
cana-1323	14	15	gamma	gamma	NOUN
cana-1323	14	16	semirings	semiring	NOUN
cana-1323	14	17	”	"	PUNCT
cana-1323	14	18	,	,	PUNCT
cana-1323	14	19	“	"	PUNCT
cana-1323	14	20	completely	completely	ADV
cana-1323	14	21	prime	prime	ADJ
cana-1323	14	22	fuzzy	fuzzy	ADJ
cana-1323	14	23	ideals	ideal	NOUN
cana-1323	14	24	”	"	PUNCT
cana-1323	14	25	and	and	CCONJ
cana-1323	14	26	“	"	PUNCT
cana-1323	14	27	prime	prime	ADJ
cana-1323	14	28	fuzzy	fuzzy	ADJ
cana-1323	14	29	ideals	ideal	NOUN
cana-1323	14	30	in	in	ADP
cana-1323	14	31	ternary	ternary	ADJ
cana-1323	14	32	gamma	gamma	NOUN
cana-1323	14	33	semirings	semiring	NOUN
cana-1323	14	34	”	"	PUNCT
cana-1323	14	35	.	.	PUNCT
cana-1323	15	1	in	in	ADP
cana-1323	15	2	the	the	DET
cana-1323	15	3	year	year	NOUN
cana-1323	15	4	2020	2020	NUM
cana-1323	15	5	e.	e.	PROPN
cana-1323	15	6	meera	meera	PROPN
cana-1323	15	7	prasad	prasad	PROPN
cana-1323	15	8	et.al	et.al	PROPN
cana-1323	16	1	[	[	X
cana-1323	16	2	6	6	NUM
cana-1323	16	3	]	]	PUNCT
cana-1323	16	4	introduced	introduce	VERB
cana-1323	16	5	the	the	DET
cana-1323	16	6	notion	notion	NOUN
cana-1323	16	7	of	of	ADP
cana-1323	16	8	“	"	PUNCT
cana-1323	16	9	fuzzy	fuzzy	ADJ
cana-1323	16	10	soft	soft	ADJ
cana-1323	16	11	bi	bi	NOUN
cana-1323	16	12	-	-	NOUN
cana-1323	16	13	ideals	ideal	NOUN
cana-1323	16	14	”	"	PUNCT
cana-1323	16	15	over	over	ADP
cana-1323	16	16	“	"	PUNCT
cana-1323	16	17	ternary	ternary	ADJ
cana-1323	16	18	gamma	gamma	NOUN
cana-1323	16	19	semirings	semiring	NOUN
cana-1323	16	20	”	"	PUNCT
cana-1323	16	21	.	.	PUNCT
cana-1323	17	1	satish	satish	PROPN
cana-1323	17	2	.	.	PUNCT
cana-1323	18	1	t	t	PROPN
cana-1323	18	2	et	et	PROPN
cana-1323	18	3	.	.	PUNCT
cana-1323	19	1	al	al	PROPN
cana-1323	20	1	[	[	X
cana-1323	20	2	14	14	NUM
cana-1323	20	3	]	]	PUNCT
cana-1323	20	4	studied	study	VERB
cana-1323	20	5	about	about	ADP
cana-1323	20	6	“	"	PUNCT
cana-1323	20	7	fuzzy	fuzzy	ADJ
cana-1323	20	8	soft	soft	ADJ
cana-1323	20	9	ideals	ideal	NOUN
cana-1323	20	10	in	in	ADP
cana-1323	20	11	ternary	ternary	ADJ
cana-1323	20	12	gamma	gamma	NOUN
cana-1323	20	13	semirings	semiring	NOUN
cana-1323	20	14	”	"	PUNCT
cana-1323	20	15	.	.	PUNCT
cana-1323	21	1	g.	g.	PROPN
cana-1323	21	2	srinivasa	srinivasa	PROPN
cana-1323	21	3	rao	rao	PROPN
cana-1323	21	4	et.al	et.al	PROPN
cana-1323	21	5	[	[	PUNCT
cana-1323	21	6	]	]	X
cana-1323	21	7	studies	study	NOUN
cana-1323	21	8	about	about	ADP
cana-1323	21	9	ternary	ternary	ADJ
cana-1323	21	10	gamma	gamma	NOUN
cana-1323	21	11	semirings	semiring	NOUN
cana-1323	21	12	extensively	extensively	ADV
cana-1323	21	13	.	.	PUNCT
cana-1323	22	1	in	in	ADP
cana-1323	22	2	this	this	DET
cana-1323	22	3	paper	paper	NOUN
cana-1323	22	4	we	we	PRON
cana-1323	22	5	introduce	introduce	VERB
cana-1323	22	6	the	the	DET
cana-1323	22	7	notion	notion	NOUN
cana-1323	22	8	“	"	PUNCT
cana-1323	22	9	tripolar	tripolar	ADJ
cana-1323	22	10	fuzzy	fuzzy	ADJ
cana-1323	22	11	soft	soft	ADJ
cana-1323	22	12	ternary	ternary	ADJ
cana-1323	22	13	γ	γ	X
cana-1323	22	14	-	-	ADJ
cana-1323	22	15	semiring	semiring	ADJ
cana-1323	22	16	homomorphism	homomorphism	NOUN
cana-1323	22	17	”	"	PUNCT
cana-1323	22	18	.	.	PUNCT
cana-1323	23	1	throughout	throughout	ADP
cana-1323	23	2	this	this	DET
cana-1323	23	3	paper	paper	NOUN
cana-1323	23	4	we	we	PRON
cana-1323	23	5	indicate	indicate	VERB
cana-1323	23	6	“	"	PUNCT
cana-1323	23	7	ternary	ternary	ADJ
cana-1323	23	8	gamma	gamma	NOUN
cana-1323	23	9	semiring	semiring	NOUN
cana-1323	23	10	”	"	PUNCT
cana-1323	23	11	as	as	ADP
cana-1323	23	12	tgsr	tgsr	ADJ
cana-1323	23	13	,	,	PUNCT
cana-1323	23	14	“	"	PUNCT
cana-1323	23	15	fuzzy	fuzzy	ADJ
cana-1323	23	16	soft	soft	ADJ
cana-1323	23	17	ternary	ternary	ADJ
cana-1323	23	18	gamma	gamma	NOUN
cana-1323	23	19	semiring	semiring	NOUN
cana-1323	23	20	”	"	PUNCT
cana-1323	23	21	as	as	SCONJ
cana-1323	23	22	fstgsr	fstgsr	ADJ
cana-1323	23	23	,	,	PUNCT
cana-1323	23	24	“	"	PUNCT
cana-1323	23	25	tripolar	tripolar	ADJ
cana-1323	23	26	fuzzy	fuzzy	ADJ
cana-1323	23	27	soft	soft	ADJ
cana-1323	23	28	set	set	NOUN
cana-1323	23	29	”	"	PUNCT
cana-1323	23	30	as	as	ADP
cana-1323	23	31	tfss	tfss	NOUN
cana-1323	23	32	,	,	PUNCT
cana-1323	23	33	“	"	PUNCT
cana-1323	23	34	tripolar	tripolar	ADJ
cana-1323	23	35	fuzzy	fuzzy	ADJ
cana-1323	23	36	soft	soft	ADJ
cana-1323	23	37	ternary	ternary	ADJ
cana-1323	23	38	gamma	gamma	NOUN
cana-1323	23	39	semiring	semiring	NOUN
cana-1323	23	40	”	"	PUNCT
cana-1323	23	41	as	as	ADP
cana-1323	23	42	tfstgsr	tfstgsr	NOUN
cana-1323	23	43	,	,	PUNCT
cana-1323	23	44	“	"	PUNCT
cana-1323	23	45	tripolar	tripolar	ADJ
cana-1323	23	46	fuzzy	fuzzy	ADJ
cana-1323	23	47	soft	soft	ADJ
cana-1323	23	48	gamma	gamma	NOUN
cana-1323	23	49	ideal	ideal	NOUN
cana-1323	23	50	”	"	PUNCT
cana-1323	23	51	as	as	ADP
cana-1323	23	52	tfsi	tfsi	PROPN
cana-1323	23	53	and	and	CCONJ
cana-1323	23	54	“	"	PUNCT
cana-1323	23	55	tripolar	tripolar	ADJ
cana-1323	23	56	fuzzy	fuzzy	ADJ
cana-1323	23	57	soft	soft	ADJ
cana-1323	23	58	ternary	ternary	ADJ
cana-1323	23	59	γ	γ	X
cana-1323	23	60	-	-	ADJ
cana-1323	23	61	semiring	semiring	ADJ
cana-1323	23	62	homomorphism	homomorphism	NOUN
cana-1323	23	63	”	"	PUNCT
cana-1323	23	64	as	as	ADP
cana-1323	23	65	tfstgsrh	tfstgsrh	ADJ
cana-1323	23	66	,	,	PUNCT
cana-1323	23	67	unless	unless	SCONJ
cana-1323	23	68	otherwise	otherwise	ADV
cana-1323	23	69	stated	state	VERB
cana-1323	23	70	.	.	PUNCT
cana-1323	24	1	2	2	X
cana-1323	24	2	.	.	X
cana-1323	24	3	preliminaries	preliminary	NOUN
cana-1323	24	4	:	:	PUNCT
cana-1323	24	5	definition	definition	NOUN
cana-1323	24	6	2.1	2.1	NUM
cana-1323	24	7	:	:	PUNCT
cana-1323	24	8	a	a	DET
cana-1323	24	9	“	"	PUNCT
cana-1323	24	10	tripolar	tripolar	ADJ
cana-1323	24	11	fuzzy	fuzzy	ADJ
cana-1323	24	12	set	set	NOUN
cana-1323	24	13	”	"	PUNCT
cana-1323	24	14	t	t	PROPN
cana-1323	24	15	in	in	ADP
cana-1323	24	16	a	a	DET
cana-1323	24	17	universe	universe	NOUN
cana-1323	24	18	set	set	NOUN
cana-1323	24	19	m	m	VERB
cana-1323	24	20	is	be	AUX
cana-1323	24	21	an	an	DET
cana-1323	24	22	object	object	NOUN
cana-1323	24	23	having	have	VERB
cana-1323	24	24	the	the	DET
cana-1323	24	25	form	form	NOUN
cana-1323	24	26	t	t	NOUN
cana-1323	24	27	=	=	SYM
cana-1323	24	28	{	{	PUNCT
cana-1323	24	29	(	(	PUNCT
cana-1323	24	30	a	a	PRON
cana-1323	24	31	,	,	PUNCT
cana-1323	24	32	νt(a	νt(a	NOUN
cana-1323	24	33	)	)	PUNCT
cana-1323	24	34	,	,	PUNCT
cana-1323	24	35	γt(a	γt(a	NUM
cana-1323	24	36	)	)	PUNCT
cana-1323	24	37	,	,	PUNCT
cana-1323	24	38	βt(a	βt(a	NUM
cana-1323	24	39	)	)	PUNCT
cana-1323	24	40	)	)	PUNCT
cana-1323	25	1	|	|	ADV
cana-1323	25	2	a	a	DET
cana-1323	25	3	∈	∈	PROPN
cana-1323	25	4	m	m	NOUN
cana-1323	25	5	,	,	PUNCT
cana-1323	25	6	0	0	NUM
cana-1323	25	7	≤	≤	NUM
cana-1323	25	8	νt(a	νt(a	NOUN
cana-1323	25	9	)	)	PUNCT
cana-1323	25	10	+	+	NUM
cana-1323	25	11	γt(a	γt(a	NOUN
cana-1323	25	12	)	)	PUNCT
cana-1323	25	13	≤	≤	NUM
cana-1323	25	14	1	1	NUM
cana-1323	25	15	}	}	PUNCT
cana-1323	25	16	,	,	PUNCT
cana-1323	25	17	where	where	SCONJ
cana-1323	25	18	νt	νt	ADJ
cana-1323	25	19	:	:	PUNCT
cana-1323	25	20	m	m	VERB
cana-1323	25	21	⟶	⟶	ADJ
cana-1323	25	22	[	[	X
cana-1323	25	23	0	0	NUM
cana-1323	25	24	,	,	PUNCT
cana-1323	25	25	1	1	NUM
cana-1323	25	26	]	]	PUNCT
cana-1323	25	27	,	,	PUNCT
cana-1323	25	28	γt	γt	NOUN
cana-1323	25	29	:	:	PUNCT
cana-1323	25	30	m	m	NOUN
cana-1323	25	31	⟶	⟶	ADJ
cana-1323	25	32	[	[	X
cana-1323	25	33	0	0	NUM
cana-1323	25	34	,	,	PUNCT
cana-1323	25	35	1	1	NUM
cana-1323	25	36	]	]	PUNCT
cana-1323	25	37	and	and	CCONJ
cana-1323	25	38	βt	βt	ADP
cana-1323	25	39	:	:	PUNCT
cana-1323	26	1	m	m	VERB
cana-1323	26	2	⟶	⟶	ADJ
cana-1323	26	3	[	[	X
cana-1323	26	4	-1	-1	X
cana-1323	26	5	,	,	PUNCT
cana-1323	26	6	0	0	NUM
cana-1323	26	7	]	]	PUNCT
cana-1323	26	8	such	such	ADJ
cana-1323	26	9	that	that	SCONJ
cana-1323	26	10	0	0	NUM
cana-1323	26	11	≤	≤	NUM
cana-1323	26	12	νt(a	νt(a	NOUN
cana-1323	26	13	)	)	PUNCT
cana-1323	26	14	+	+	NUM
cana-1323	26	15	γt(a	γt(a	NOUN
cana-1323	26	16	)	)	PUNCT
cana-1323	26	17	≤	≤	NUM
cana-1323	26	18	1	1	NUM
cana-1323	26	19	.	.	PUNCT
cana-1323	27	1	since	since	SCONJ
cana-1323	27	2	νt	νt	NOUN
cana-1323	27	3	characterises	characterise	VERB
cana-1323	27	4	the	the	DET
cana-1323	27	5	extent	extent	NOUN
cana-1323	27	6	that	that	SCONJ
cana-1323	27	7	the	the	DET
cana-1323	27	8	mailto:meeraprasad.6499@gmail.com	mailto:meeraprasad.6499@gmail.com	PROPN
cana-1323	27	9	mailto:dmrmaths@gmail.com	mailto:dmrmaths@gmail.com	PROPN
cana-1323	27	10	mailto:drgsk006@kluniversity.in	mailto:drgsk006@kluniversity.in	PROPN
cana-1323	27	11	mailto:bezawadavasantha@gmail.com	mailto:bezawadavasantha@gmail.com	X
cana-1323	27	12	communications	communication	NOUN
cana-1323	27	13	on	on	ADP
cana-1323	27	14	applied	apply	VERB
cana-1323	27	15	nonlinear	nonlinear	ADJ
cana-1323	27	16	analysis	analysis	NOUN
cana-1323	27	17	issn	issn	NOUN
cana-1323	27	18	:	:	PUNCT
cana-1323	27	19	1074	1074	NUM
cana-1323	27	20	-	-	PUNCT
cana-1323	27	21	133x	133x	NUM
cana-1323	27	22	vol	vol	NOUN
cana-1323	27	23	31	31	NUM
cana-1323	27	24	no	no	NOUN
cana-1323	27	25	.	.	PUNCT
cana-1323	28	1	7s	7	NOUN
cana-1323	28	2	(	(	PUNCT
cana-1323	28	3	2024	2024	NUM
cana-1323	28	4	)	)	PUNCT
cana-1323	28	5	445	445	NUM
cana-1323	29	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-1323	29	2	element	element	NOUN
cana-1323	29	3	a	a	DET
cana-1323	29	4	satisfies	satisfie	NOUN
cana-1323	29	5	the	the	DET
cana-1323	29	6	property	property	NOUN
cana-1323	29	7	corresponding	correspond	VERB
cana-1323	29	8	the	the	DET
cana-1323	29	9	tripolar	tripolar	ADJ
cana-1323	29	10	fuzzy	fuzzy	NOUN
cana-1323	29	11	set	set	VERB
cana-1323	29	12	t	t	PROPN
cana-1323	29	13	,	,	PUNCT
cana-1323	29	14	γt	γt	PROPN
cana-1323	29	15	characterises	characterise	VERB
cana-1323	29	16	the	the	DET
cana-1323	29	17	extent	extent	NOUN
cana-1323	29	18	that	that	SCONJ
cana-1323	29	19	the	the	DET
cana-1323	29	20	element	element	NOUN
cana-1323	29	21	a	a	DET
cana-1323	29	22	satisfies	satisfie	NOUN
cana-1323	29	23	the	the	DET
cana-1323	29	24	irrelevant	irrelevant	ADJ
cana-1323	29	25	(	(	PUNCT
cana-1323	29	26	non	non	X
cana-1323	29	27	property	property	NOUN
cana-1323	29	28	)	)	PUNCT
cana-1323	29	29	corresponding	correspond	VERB
cana-1323	29	30	the	the	DET
cana-1323	29	31	tripolar	tripolar	ADJ
cana-1323	29	32	fuzzy	fuzzy	NOUN
cana-1323	29	33	set	set	VERB
cana-1323	29	34	t	t	NOUN
cana-1323	29	35	and	and	CCONJ
cana-1323	29	36	βt	βt	VERB
cana-1323	29	37	characterises	characterise	VERB
cana-1323	29	38	the	the	DET
cana-1323	29	39	extent	extent	NOUN
cana-1323	29	40	that	that	SCONJ
cana-1323	29	41	the	the	DET
cana-1323	29	42	element	element	NOUN
cana-1323	29	43	a	a	DET
cana-1323	29	44	satisfies	satisfie	NOUN
cana-1323	29	45	to	to	ADP
cana-1323	29	46	the	the	DET
cana-1323	29	47	implicit	implicit	ADJ
cana-1323	29	48	counter	counter	ADJ
cana-1323	29	49	property	property	NOUN
cana-1323	29	50	of	of	ADP
cana-1323	29	51	the	the	DET
cana-1323	29	52	tripolar	tripolar	ADJ
cana-1323	29	53	fuzzy	fuzzy	ADJ
cana-1323	29	54	set	set	NOUN
cana-1323	29	55	t.	t.	NOUN
cana-1323	29	56	we	we	PRON
cana-1323	29	57	use	use	VERB
cana-1323	29	58	the	the	DET
cana-1323	29	59	notion	notion	NOUN
cana-1323	29	60	t	t	PROPN
cana-1323	29	61	=	=	SYM
cana-1323	29	62	{	{	PUNCT
cana-1323	29	63	νt	νt	PROPN
cana-1323	29	64	,	,	PUNCT
cana-1323	29	65	γt	γt	NOUN
cana-1323	29	66	,	,	PUNCT
cana-1323	29	67	βt	βt	VERB
cana-1323	29	68	}	}	PUNCT
cana-1323	29	69	instead	instead	ADV
cana-1323	29	70	of	of	ADP
cana-1323	29	71	t	t	NOUN
cana-1323	29	72	=	=	SYM
cana-1323	29	73	{	{	PUNCT
cana-1323	29	74	(	(	PUNCT
cana-1323	29	75	a	a	PRON
cana-1323	29	76	,	,	PUNCT
cana-1323	29	77	νt(a	νt(a	NOUN
cana-1323	29	78	)	)	PUNCT
cana-1323	29	79	,	,	PUNCT
cana-1323	29	80	γt(a	γt(a	NUM
cana-1323	29	81	)	)	PUNCT
cana-1323	29	82	,	,	PUNCT
cana-1323	29	83	βt(a	βt(a	NUM
cana-1323	29	84	)	)	PUNCT
cana-1323	29	85	)	)	PUNCT
cana-1323	29	86	|	|	ADV
cana-1323	29	87	a	a	DET
cana-1323	29	88	∈	∈	PROPN
cana-1323	29	89	m	m	NOUN
cana-1323	29	90	,	,	PUNCT
cana-1323	29	91	0	0	NUM
cana-1323	29	92	≤	≤	NUM
cana-1323	29	93	νt(a	νt(a	NOUN
cana-1323	29	94	)	)	PUNCT
cana-1323	29	95	+	+	NUM
cana-1323	29	96	γt(a	γt(a	NOUN
cana-1323	29	97	)	)	PUNCT
cana-1323	29	98	≤	≤	NUM
cana-1323	29	99	1	1	NUM
cana-1323	29	100	}	}	PUNCT
cana-1323	29	101	.	.	PUNCT
cana-1323	30	1	definition	definition	NOUN
cana-1323	30	2	2.2	2.2	NUM
cana-1323	30	3	:	:	PUNCT
cana-1323	30	4	a	a	DET
cana-1323	30	5	tfss	tfss	NOUN
cana-1323	30	6	(	(	PUNCT
cana-1323	30	7	δ	δ	PROPN
cana-1323	30	8	,	,	PUNCT
cana-1323	30	9	v	v	PROPN
cana-1323	30	10	,	,	PUNCT
cana-1323	30	11	γ	γ	NOUN
cana-1323	30	12	)	)	PUNCT
cana-1323	30	13	over	over	ADP
cana-1323	30	14	tgsr	tgsr	PROPN
cana-1323	30	15	m	m	NOUN
cana-1323	30	16	is	be	AUX
cana-1323	30	17	nothing	nothing	PRON
cana-1323	30	18	but	but	SCONJ
cana-1323	30	19	tfstgsr	tfstgsr	NOUN
cana-1323	30	20	over	over	ADP
cana-1323	30	21	tgsr	tgsr	PROPN
cana-1323	30	22	m	m	PROPN
cana-1323	30	23	if	if	SCONJ
cana-1323	30	24	ν(a	ν(a	PROPN
cana-1323	30	25	)	)	PUNCT
cana-1323	30	26	=	=	PRON
cana-1323	30	27	{	{	PUNCT
cana-1323	30	28	(	(	PUNCT
cana-1323	30	29	p	p	NOUN
cana-1323	30	30	,	,	PUNCT
cana-1323	30	31	νδ(a	νδ(a	NUM
cana-1323	30	32	)	)	PUNCT
cana-1323	30	33	(	(	PUNCT
cana-1323	30	34	p	p	NOUN
cana-1323	30	35	)	)	PUNCT
cana-1323	30	36	,	,	PUNCT
cana-1323	30	37	γ	γ	X
cana-1323	30	38	δ(a)(p	δ(a)(p	NOUN
cana-1323	30	39	)	)	PUNCT
cana-1323	30	40	,	,	PUNCT
cana-1323	30	41	β	β	X
cana-1323	30	42	δ(a)(p	δ(a)(p	X
cana-1323	30	43	)	)	PUNCT
cana-1323	30	44	/	/	PUNCT
cana-1323	30	45	p	p	NOUN
cana-1323	30	46	∈	∈	PROPN
cana-1323	30	47	m	m	PROPN
cana-1323	30	48	,	,	PUNCT
cana-1323	30	49	a	a	DET
cana-1323	30	50	∈	∈	PROPN
cana-1323	30	51	v	v	NOUN
cana-1323	30	52	}	}	PUNCT
cana-1323	30	53	,	,	PUNCT
cana-1323	30	54	where	where	SCONJ
cana-1323	30	55	νδ(a	νδ(a	NUM
cana-1323	30	56	):	):	PUNCT
cana-1323	30	57	m	m	VERB
cana-1323	30	58	→	→	SYM
cana-1323	31	1	[	[	X
cana-1323	31	2	0	0	NUM
cana-1323	31	3	,	,	PUNCT
cana-1323	31	4	1	1	NUM
cana-1323	31	5	]	]	PUNCT
cana-1323	31	6	,	,	PUNCT
cana-1323	31	7	γ	γ	PROPN
cana-1323	31	8	δ(a	δ(a	PROPN
cana-1323	31	9	):	):	PUNCT
cana-1323	31	10	m	m	VERB
cana-1323	31	11	→	→	SYM
cana-1323	32	1	[	[	X
cana-1323	32	2	0	0	NUM
cana-1323	32	3	,	,	PUNCT
cana-1323	32	4	1	1	NUM
cana-1323	32	5	]	]	PUNCT
cana-1323	32	6	and	and	CCONJ
cana-1323	32	7	β	β	X
cana-1323	32	8	δ(a	δ(a	PROPN
cana-1323	32	9	):	):	PUNCT
cana-1323	32	10	m	m	VERB
cana-1323	32	11	→	→	SYM
cana-1323	32	12	[	[	X
cana-1323	32	13	-1	-1	X
cana-1323	32	14	,	,	PUNCT
cana-1323	32	15	0	0	NUM
cana-1323	32	16	]	]	PUNCT
cana-1323	32	17	,	,	PUNCT
cana-1323	32	18	∋	∋	NOUN
cana-1323	32	19	0	0	NUM
cana-1323	32	20	≤	≤	NUM
cana-1323	32	21	νδ(a	νδ(a	NOUN
cana-1323	32	22	)	)	PUNCT
cana-1323	33	1	+	+	CCONJ
cana-1323	33	2	γ	γ	X
cana-1323	33	3	δ(a	δ(a	PROPN
cana-1323	33	4	)	)	PUNCT
cana-1323	33	5	≤	≤	NUM
cana-1323	33	6	1	1	NUM
cana-1323	33	7	and	and	CCONJ
cana-1323	33	8	∀	∀	NOUN
cana-1323	33	9	p	p	X
cana-1323	33	10	∈	∈	PROPN
cana-1323	33	11	m	m	AUX
cana-1323	33	12	satisfying	satisfy	VERB
cana-1323	33	13	the	the	DET
cana-1323	33	14	following	follow	VERB
cana-1323	33	15	conditions	condition	NOUN
cana-1323	33	16	:	:	PUNCT
cana-1323	33	17	(	(	PUNCT
cana-1323	33	18	1	1	X
cana-1323	33	19	)	)	PUNCT
cana-1323	33	20	νδ(a)(j	νδ(a)(j	PROPN
cana-1323	34	1	+	+	NUM
cana-1323	34	2	m	m	X
cana-1323	34	3	)	)	PUNCT
cana-1323	34	4	≥	≥	PROPN
cana-1323	34	5	min	min	PROPN
cana-1323	34	6	{	{	PUNCT
cana-1323	34	7	νδ(a)(j	νδ(a)(j	PROPN
cana-1323	34	8	)	)	PUNCT
cana-1323	34	9	,	,	PUNCT
cana-1323	34	10	νδ(a)(m	νδ(a)(m	NUM
cana-1323	34	11	)	)	PUNCT
cana-1323	34	12	}	}	PUNCT
cana-1323	34	13	(	(	PUNCT
cana-1323	34	14	2	2	X
cana-1323	34	15	)	)	PUNCT
cana-1323	34	16	γ	γ	NOUN
cana-1323	34	17	δ(a)(j	δ(a)(j	PUNCT
cana-1323	34	18	+	+	NUM
cana-1323	34	19	m	m	NOUN
cana-1323	34	20	)	)	PUNCT
cana-1323	34	21	≤	≤	NUM
cana-1323	34	22	max	max	PROPN
cana-1323	34	23	{	{	PUNCT
cana-1323	34	24	γ	γ	X
cana-1323	34	25	δ(a)(j	δ(a)(j	NOUN
cana-1323	34	26	)	)	PUNCT
cana-1323	34	27	,	,	PUNCT
cana-1323	34	28	γ	γ	X
cana-1323	34	29	δ(a)(m	δ(a)(m	VERB
cana-1323	34	30	)	)	PUNCT
cana-1323	34	31	}	}	PUNCT
cana-1323	34	32	(	(	PUNCT
cana-1323	34	33	3	3	X
cana-1323	34	34	)	)	PUNCT
cana-1323	34	35	β	β	X
cana-1323	34	36	δ(a)(j	δ(a)(j	PUNCT
cana-1323	34	37	+	+	NUM
cana-1323	34	38	m	m	NOUN
cana-1323	34	39	)	)	PUNCT
cana-1323	34	40	≤	≤	NUM
cana-1323	34	41	max	max	PROPN
cana-1323	34	42	{	{	PUNCT
cana-1323	34	43	β	β	X
cana-1323	34	44	δ(a)(j	δ(a)(j	NOUN
cana-1323	34	45	)	)	PUNCT
cana-1323	34	46	,	,	PUNCT
cana-1323	34	47	β	β	X
cana-1323	34	48	δ(a)(m	δ(a)(m	VERB
cana-1323	34	49	)	)	PUNCT
cana-1323	34	50	}	}	PUNCT
cana-1323	34	51	(	(	PUNCT
cana-1323	34	52	4	4	NUM
cana-1323	34	53	)	)	PUNCT
cana-1323	34	54	νδ(a)(j𝛼m𝜃k	νδ(a)(j𝛼m𝜃k	ADV
cana-1323	34	55	)	)	PUNCT
cana-1323	34	56	≥	≥	PROPN
cana-1323	34	57	min	min	PROPN
cana-1323	34	58	{	{	PUNCT
cana-1323	34	59	νδ(a)(j	νδ(a)(j	PROPN
cana-1323	34	60	)	)	PUNCT
cana-1323	34	61	,	,	PUNCT
cana-1323	34	62	νδ(a)(m	νδ(a)(m	NUM
cana-1323	34	63	)	)	PUNCT
cana-1323	34	64	,	,	PUNCT
cana-1323	34	65	νδ(a)(k	νδ(a)(k	NOUN
cana-1323	34	66	)	)	PUNCT
cana-1323	34	67	}	}	PUNCT
cana-1323	34	68	(	(	PUNCT
cana-1323	34	69	5	5	X
cana-1323	34	70	)	)	PUNCT
cana-1323	34	71	γ	γ	NOUN
cana-1323	34	72	δ(a)(j𝛼m𝜃k	δ(a)(j𝛼m𝜃k	X
cana-1323	34	73	)	)	PUNCT
cana-1323	34	74	≤	≤	NUM
cana-1323	34	75	max	max	PROPN
cana-1323	34	76	{	{	PUNCT
cana-1323	34	77	γ	γ	X
cana-1323	34	78	δ(a)(j	δ(a)(j	NOUN
cana-1323	34	79	)	)	PUNCT
cana-1323	34	80	,	,	PUNCT
cana-1323	34	81	γ	γ	X
cana-1323	34	82	δ(a)(m	δ(a)(m	NUM
cana-1323	34	83	)	)	PUNCT
cana-1323	34	84	,	,	PUNCT
cana-1323	34	85	γ	γ	NOUN
cana-1323	34	86	δ(a)(k	δ(a)(k	NOUN
cana-1323	34	87	)	)	PUNCT
cana-1323	34	88	}	}	PUNCT
cana-1323	34	89	(	(	PUNCT
cana-1323	34	90	6	6	NUM
cana-1323	34	91	)	)	PUNCT
cana-1323	34	92	β	β	NOUN
cana-1323	34	93	δ(a)(j𝛼m𝜃k	δ(a)(j𝛼m𝜃k	X
cana-1323	34	94	)	)	PUNCT
cana-1323	34	95	≤	≤	NUM
cana-1323	34	96	max	max	PROPN
cana-1323	34	97	{	{	PUNCT
cana-1323	34	98	β	β	X
cana-1323	34	99	δ(a)(j	δ(a)(j	NOUN
cana-1323	34	100	)	)	PUNCT
cana-1323	34	101	,	,	PUNCT
cana-1323	34	102	β	β	X
cana-1323	34	103	δ(a)(m	δ(a)(m	VERB
cana-1323	34	104	)	)	PUNCT
cana-1323	34	105	,	,	PUNCT
cana-1323	34	106	β	β	X
cana-1323	34	107	δ(a)(k	δ(a)(k	NOUN
cana-1323	34	108	)	)	PUNCT
cana-1323	34	109	}	}	PUNCT
cana-1323	34	110	∀	∀	X
cana-1323	34	111	j	j	PROPN
cana-1323	34	112	,	,	PUNCT
cana-1323	34	113	m	m	PROPN
cana-1323	34	114	,	,	PUNCT
cana-1323	34	115	k	k	PROPN
cana-1323	34	116	∈	∈	PROPN
cana-1323	34	117	m	m	PROPN
cana-1323	34	118	,	,	PUNCT
cana-1323	34	119	a	a	DET
cana-1323	34	120	∈	∈	PROPN
cana-1323	34	121	v	v	NOUN
cana-1323	34	122	,	,	PUNCT
cana-1323	34	123	α	α	X
cana-1323	34	124	,	,	PUNCT
cana-1323	34	125	ζ	ζ	PROPN
cana-1323	34	126	∈	∈	PROPN
cana-1323	34	127	γ	γ	PROPN
cana-1323	34	128	.	.	PROPN
cana-1323	34	129	definition	definition	NOUN
cana-1323	34	130	2.3	2.3	NUM
cana-1323	34	131	:	:	PUNCT
cana-1323	34	132	a	a	DET
cana-1323	34	133	tfss	tfss	NOUN
cana-1323	34	134	(	(	PUNCT
cana-1323	34	135	δ	δ	PROPN
cana-1323	34	136	,	,	PUNCT
cana-1323	34	137	v	v	PROPN
cana-1323	34	138	,	,	PUNCT
cana-1323	34	139	γ	γ	NOUN
cana-1323	34	140	)	)	PUNCT
cana-1323	34	141	over	over	ADP
cana-1323	34	142	tgsr	tgsr	PROPN
cana-1323	34	143	m	m	NOUN
cana-1323	34	144	is	be	AUX
cana-1323	34	145	nothing	nothing	PRON
cana-1323	34	146	but	but	CCONJ
cana-1323	34	147	tfsi	tfsi	PROPN
cana-1323	34	148	over	over	ADP
cana-1323	34	149	tgsr	tgsr	PROPN
cana-1323	34	150	m	m	NOUN
cana-1323	34	151	if	if	SCONJ
cana-1323	34	152	(	(	PUNCT
cana-1323	34	153	1	1	NUM
cana-1323	34	154	)	)	PUNCT
cana-1323	34	155	νδ(a)(j	νδ(a)(j	PROPN
cana-1323	35	1	+	+	NUM
cana-1323	35	2	m	m	X
cana-1323	35	3	)	)	PUNCT
cana-1323	35	4	≥	≥	PROPN
cana-1323	35	5	min	min	PROPN
cana-1323	35	6	{	{	PUNCT
cana-1323	35	7	νδ(a)(j	νδ(a)(j	PROPN
cana-1323	35	8	)	)	PUNCT
cana-1323	35	9	,	,	PUNCT
cana-1323	35	10	νδ(a)(m	νδ(a)(m	NUM
cana-1323	35	11	)	)	PUNCT
cana-1323	35	12	}	}	PUNCT
cana-1323	35	13	(	(	PUNCT
cana-1323	35	14	2	2	X
cana-1323	35	15	)	)	PUNCT
cana-1323	35	16	γ	γ	NOUN
cana-1323	35	17	δ(a)(j	δ(a)(j	PUNCT
cana-1323	35	18	+	+	NUM
cana-1323	35	19	m	m	NOUN
cana-1323	35	20	)	)	PUNCT
cana-1323	35	21	≤	≤	NUM
cana-1323	35	22	max	max	PROPN
cana-1323	35	23	{	{	PUNCT
cana-1323	35	24	γ	γ	X
cana-1323	35	25	δ(a)(j	δ(a)(j	NOUN
cana-1323	35	26	)	)	PUNCT
cana-1323	35	27	,	,	PUNCT
cana-1323	35	28	γ	γ	X
cana-1323	35	29	δ(a)(m	δ(a)(m	VERB
cana-1323	35	30	)	)	PUNCT
cana-1323	35	31	}	}	PUNCT
cana-1323	35	32	(	(	PUNCT
cana-1323	35	33	3	3	X
cana-1323	35	34	)	)	PUNCT
cana-1323	35	35	β	β	X
cana-1323	35	36	δ(a)(j	δ(a)(j	PUNCT
cana-1323	35	37	+	+	NUM
cana-1323	35	38	m	m	NOUN
cana-1323	35	39	)	)	PUNCT
cana-1323	35	40	≤	≤	NUM
cana-1323	35	41	max	max	PROPN
cana-1323	35	42	{	{	PUNCT
cana-1323	35	43	β	β	X
cana-1323	35	44	δ(a)(j	δ(a)(j	NOUN
cana-1323	35	45	)	)	PUNCT
cana-1323	35	46	,	,	PUNCT
cana-1323	35	47	β	β	X
cana-1323	35	48	δ(a)(m	δ(a)(m	VERB
cana-1323	35	49	)	)	PUNCT
cana-1323	35	50	}	}	PUNCT
cana-1323	35	51	(	(	PUNCT
cana-1323	35	52	4	4	NUM
cana-1323	35	53	)	)	PUNCT
cana-1323	35	54	νδ(a)(j𝛼m𝜃k	νδ(a)(j𝛼m𝜃k	ADV
cana-1323	35	55	)	)	PUNCT
cana-1323	35	56	≥	≥	PROPN
cana-1323	35	57	max	max	PROPN
cana-1323	35	58	{	{	PUNCT
cana-1323	35	59	νδ(a)(j	νδ(a)(j	PROPN
cana-1323	35	60	)	)	PUNCT
cana-1323	35	61	,	,	PUNCT
cana-1323	35	62	νδ(a)(m	νδ(a)(m	NUM
cana-1323	35	63	)	)	PUNCT
cana-1323	35	64	,	,	PUNCT
cana-1323	35	65	νδ(a)(k	νδ(a)(k	NOUN
cana-1323	35	66	)	)	PUNCT
cana-1323	35	67	}	}	PUNCT
cana-1323	35	68	(	(	PUNCT
cana-1323	35	69	5	5	X
cana-1323	35	70	)	)	PUNCT
cana-1323	35	71	γ	γ	NOUN
cana-1323	35	72	δ(a)(j𝛼m𝜃k	δ(a)(j𝛼m𝜃k	X
cana-1323	35	73	)	)	PUNCT
cana-1323	35	74	≤	≤	NUM
cana-1323	35	75	min	min	NOUN
cana-1323	35	76	{	{	PUNCT
cana-1323	35	77	γ	γ	X
cana-1323	35	78	δ(a)(j	δ(a)(j	NOUN
cana-1323	35	79	)	)	PUNCT
cana-1323	35	80	,	,	PUNCT
cana-1323	35	81	γ	γ	X
cana-1323	35	82	δ(a)(m	δ(a)(m	NUM
cana-1323	35	83	)	)	PUNCT
cana-1323	35	84	,	,	PUNCT
cana-1323	35	85	γ	γ	NOUN
cana-1323	35	86	δ(a)(k	δ(a)(k	NOUN
cana-1323	35	87	)	)	PUNCT
cana-1323	35	88	}	}	PUNCT
cana-1323	35	89	(	(	PUNCT
cana-1323	35	90	6	6	NUM
cana-1323	35	91	)	)	PUNCT
cana-1323	35	92	β	β	NOUN
cana-1323	35	93	δ(a)(j𝛼m𝜃k	δ(a)(j𝛼m𝜃k	X
cana-1323	35	94	)	)	PUNCT
cana-1323	35	95	≤	≤	NUM
cana-1323	35	96	min	min	NOUN
cana-1323	35	97	{	{	PUNCT
cana-1323	35	98	β	β	X
cana-1323	35	99	δ(a)(j	δ(a)(j	NOUN
cana-1323	35	100	)	)	PUNCT
cana-1323	35	101	,	,	PUNCT
cana-1323	35	102	β	β	X
cana-1323	35	103	δ(a)(m	δ(a)(m	VERB
cana-1323	35	104	)	)	PUNCT
cana-1323	35	105	,	,	PUNCT
cana-1323	35	106	β	β	X
cana-1323	35	107	δ(a)(k	δ(a)(k	NOUN
cana-1323	35	108	)	)	PUNCT
cana-1323	35	109	}	}	PUNCT
cana-1323	35	110	∀	∀	X
cana-1323	35	111	j	j	PROPN
cana-1323	35	112	,	,	PUNCT
cana-1323	35	113	m	m	PROPN
cana-1323	35	114	,	,	PUNCT
cana-1323	35	115	k	k	PROPN
cana-1323	35	116	∈	∈	PROPN
cana-1323	35	117	m	m	PROPN
cana-1323	35	118	,	,	PUNCT
cana-1323	35	119	a	a	DET
cana-1323	35	120	∈	∈	PROPN
cana-1323	35	121	v	v	NOUN
cana-1323	35	122	,	,	PUNCT
cana-1323	35	123	α	α	X
cana-1323	35	124	,	,	PUNCT
cana-1323	35	125	ζ	ζ	PROPN
cana-1323	35	126	∈	∈	PROPN
cana-1323	35	127	γ	γ	X
cana-1323	35	128	.	.	PROPN
cana-1323	35	129	definition	definition	NOUN
cana-1323	35	130	2.4	2.4	NUM
cana-1323	35	131	:	:	PUNCT
cana-1323	35	132	if	if	SCONJ
cana-1323	35	133	m1	m1	PROPN
cana-1323	35	134	and	and	CCONJ
cana-1323	35	135	m2	m2	PROPN
cana-1323	35	136	are	be	AUX
cana-1323	35	137	two	two	NUM
cana-1323	35	138	tgsrs	tgsrs	ADJ
cana-1323	35	139	,	,	PUNCT
cana-1323	35	140	a	a	DET
cana-1323	35	141	function	function	NOUN
cana-1323	35	142	π	π	NOUN
cana-1323	35	143	:	:	PUNCT
cana-1323	35	144	m1	m1	PROPN
cana-1323	35	145	→	→	SYM
cana-1323	35	146	m2	m2	PROPN
cana-1323	35	147	is	be	AUX
cana-1323	35	148	called	call	VERB
cana-1323	35	149	a	a	DET
cana-1323	35	150	homomorphism	homomorphism	NOUN
cana-1323	35	151	tgsr	tgsr	NOUN
cana-1323	35	152	if	if	SCONJ
cana-1323	35	153	π(j	π(j	PROPN
cana-1323	35	154	+	+	NUM
cana-1323	35	155	m	m	VERB
cana-1323	35	156	)	)	PUNCT
cana-1323	35	157	=	=	SYM
cana-1323	35	158	π(j	π(j	PROPN
cana-1323	35	159	)	)	PUNCT
cana-1323	36	1	+	+	NUM
cana-1323	36	2	π(m	π(m	NOUN
cana-1323	36	3	)	)	PUNCT
cana-1323	36	4	and	and	CCONJ
cana-1323	36	5	π(j𝛼m𝜃k	π(j𝛼m𝜃k	ADJ
cana-1323	36	6	)	)	PUNCT
cana-1323	36	7	=	=	SYM
cana-1323	37	1	π(j)απ(m)ζπ(k	π(j)απ(m)ζπ(k	ADJ
cana-1323	37	2	)	)	PUNCT
cana-1323	37	3	,	,	PUNCT
cana-1323	37	4	∀	∀	X
cana-1323	37	5	j	j	PROPN
cana-1323	37	6	,	,	PUNCT
cana-1323	37	7	m	m	PROPN
cana-1323	37	8	,	,	PUNCT
cana-1323	37	9	k	k	PROPN
cana-1323	37	10	∈	∈	PROPN
cana-1323	37	11	m1	m1	NOUN
cana-1323	37	12	,	,	PUNCT
cana-1323	37	13	α	α	X
cana-1323	37	14	,	,	PUNCT
cana-1323	37	15	𝜃	𝜃	PROPN
cana-1323	37	16	∈	∈	PROPN
cana-1323	37	17	γ	γ	AUX
cana-1323	37	18	.	.	PUNCT
cana-1323	37	19	let	let	VERB
cana-1323	37	20	m1	m1	PROPN
cana-1323	37	21	and	and	CCONJ
cana-1323	37	22	m2	m2	PROPN
cana-1323	37	23	two	two	NUM
cana-1323	37	24	sets	set	NOUN
cana-1323	37	25	and	and	CCONJ
cana-1323	37	26	ψ	ψ	NOUN
cana-1323	37	27	:	:	PUNCT
cana-1323	37	28	m1	m1	PROPN
cana-1323	37	29	⟶	⟶	NOUN
cana-1323	37	30	m2	m2	PROPN
cana-1323	37	31	is	be	AUX
cana-1323	37	32	any	any	DET
cana-1323	37	33	function	function	NOUN
cana-1323	37	34	.	.	PUNCT
cana-1323	38	1	a	a	DET
cana-1323	38	2	bipolar	bipolar	ADJ
cana-1323	38	3	fuzzy	fuzzy	ADJ
cana-1323	38	4	subset	subset	VERB
cana-1323	38	5	ε	ε	PROPN
cana-1323	38	6	of	of	ADP
cana-1323	38	7	m1	m1	PROPN
cana-1323	38	8	is	be	AUX
cana-1323	38	9	nothing	nothing	PRON
cana-1323	38	10	but	but	SCONJ
cana-1323	38	11	a	a	DET
cana-1323	38	12	ε	ε	PROPN
cana-1323	38	13	-	-	PUNCT
cana-1323	38	14	invariant	invariant	ADJ
cana-1323	38	15	ψ(p	ψ(p	NOUN
cana-1323	38	16	)	)	PUNCT
cana-1323	38	17	=	=	SYM
cana-1323	39	1	ψ(q	ψ(q	PROPN
cana-1323	39	2	)	)	PUNCT
cana-1323	39	3	⟹	⟹	PUNCT
cana-1323	40	1	ε(p	ε(p	NOUN
cana-1323	40	2	)	)	PUNCT
cana-1323	40	3	=	=	SYM
cana-1323	40	4	ε(q	ε(q	PROPN
cana-1323	40	5	)	)	PUNCT
cana-1323	40	6	.	.	PUNCT
cana-1323	41	1	let	let	VERB
cana-1323	41	2	ψ	ψ	NOUN
cana-1323	41	3	:	:	PUNCT
cana-1323	41	4	m1	m1	PROPN
cana-1323	41	5	⟶	⟶	NOUN
cana-1323	41	6	m2	m2	PROPN
cana-1323	41	7	is	be	AUX
cana-1323	41	8	any	any	DET
cana-1323	41	9	function	function	NOUN
cana-1323	41	10	,	,	PUNCT
cana-1323	41	11	ε	ε	PROPN
cana-1323	41	12	=	=	PUNCT
cana-1323	41	13	(	(	PUNCT
cana-1323	41	14	ε	ε	PROPN
cana-1323	41	15	+	+	NUM
cana-1323	41	16	,	,	PUNCT
cana-1323	41	17	ε	ε	PROPN
cana-1323	41	18	)	)	PUNCT
cana-1323	41	19	and	and	CCONJ
cana-1323	41	20	ε	ε	PROPN
cana-1323	41	21	=	=	SYM
cana-1323	41	22	(	(	PUNCT
cana-1323	41	23	ε	ε	PROPN
cana-1323	41	24	+	+	PROPN
cana-1323	41	25	,	,	PUNCT
cana-1323	41	26	ε	ε	PROPN
cana-1323	41	27	)	)	PUNCT
cana-1323	41	28	are	be	AUX
cana-1323	41	29	bipolar	bipolar	ADJ
cana-1323	41	30	fuzzy	fuzzy	ADJ
cana-1323	41	31	subsets	subset	NOUN
cana-1323	41	32	in	in	ADP
cana-1323	41	33	m1	m1	PROPN
cana-1323	41	34	,	,	PUNCT
cana-1323	41	35	m2	m2	PROPN
cana-1323	41	36	respectively	respectively	ADV
cana-1323	41	37	.	.	PUNCT
cana-1323	42	1	then	then	ADV
cana-1323	42	2	the	the	DET
cana-1323	42	3	image	image	NOUN
cana-1323	42	4	ψ(𝜀	ψ(𝜀	ADV
cana-1323	42	5	)	)	PUNCT
cana-1323	42	6	of	of	ADP
cana-1323	42	7	ε	ε	PROPN
cana-1323	42	8	is	be	AUX
cana-1323	42	9	the	the	DET
cana-1323	42	10	bipolar	bipolar	ADJ
cana-1323	42	11	fuzzy	fuzzy	ADJ
cana-1323	42	12	subset	subset	NOUN
cana-1323	42	13	ψ(ε	ψ(ε	PROPN
cana-1323	42	14	)	)	PUNCT
cana-1323	43	1	=	=	PRON
cana-1323	43	2	(	(	PUNCT
cana-1323	43	3	(	(	PUNCT
cana-1323	43	4	ψ(ε	ψ(ε	PROPN
cana-1323	43	5	)	)	PUNCT
cana-1323	43	6	)	)	PUNCT
cana-1323	44	1	+	+	CCONJ
cana-1323	44	2	,	,	PUNCT
cana-1323	44	3	(	(	PUNCT
cana-1323	44	4	ψ(ε	ψ(ε	PROPN
cana-1323	44	5	)	)	PUNCT
cana-1323	44	6	)	)	PUNCT
cana-1323	44	7	)	)	PUNCT
cana-1323	44	8	of	of	ADP
cana-1323	44	9	m2	m2	PROPN
cana-1323	44	10	defined	define	VERB
cana-1323	44	11	as	as	ADP
cana-1323	44	12			PROPN
cana-1323	44	13			PROPN
cana-1323	44	14			PROPN
cana-1323	44	15			NOUN
cana-1323	44	16			PROPN
cana-1323	44	17	max	max	PROPN
cana-1323	44	18	{	{	PUNCT
cana-1323	44	19	(	(	PUNCT
cana-1323	44	20	)	)	PUNCT
cana-1323	44	21	(	(	PUNCT
cana-1323	44	22	):	):	PUNCT
cana-1323	44	23	(	(	PUNCT
cana-1323	44	24	):	):	PUNCT
cana-1323	44	25	(	(	PUNCT
cana-1323	44	26	)	)	PUNCT
cana-1323	44	27	}	}	PUNCT
cana-1323	44	28	0	0	NUM
cana-1323	45	1	otherwise	otherwise	ADV
cana-1323	45	2	p	p	X
cana-1323	45	3	p	p	X
cana-1323	46	1	p	p	NOUN
cana-1323	47	1	if	if	SCONJ
cana-1323	47	2	pp	pp	PROPN
cana-1323	47	3			PROPN
cana-1323	47	4			PRON
cana-1323	47	5			NOUN
cana-1323	47	6			PROPN
cana-1323	47	7			PUNCT
cana-1323	47	8			PROPN
cana-1323	47	9			PROPN
cana-1323	47	10			PROPN
cana-1323	47	11			PUNCT
cana-1323	47	12			PROPN
cana-1323	47	13			NOUN
cana-1323	47	14			PROPN
cana-1323	47	15			NOUN
cana-1323	47	16			PROPN
cana-1323	47	17	max	max	PROPN
cana-1323	47	18	{	{	PUNCT
cana-1323	47	19	(	(	PUNCT
cana-1323	47	20	)	)	PUNCT
cana-1323	47	21	(	(	PUNCT
cana-1323	47	22	):	):	PUNCT
cana-1323	47	23	(	(	PUNCT
cana-1323	47	24	):	):	PUNCT
cana-1323	47	25	(	(	PUNCT
cana-1323	47	26	)	)	PUNCT
cana-1323	47	27	}	}	PUNCT
cana-1323	47	28	0	0	NUM
cana-1323	48	1	otherwise	otherwise	ADV
cana-1323	48	2	p	p	X
cana-1323	48	3	p	p	X
cana-1323	49	1	p	p	NOUN
cana-1323	50	1	if	if	SCONJ
cana-1323	50	2	pp	pp	PROPN
cana-1323	50	3			PROPN
cana-1323	50	4			PRON
cana-1323	50	5			NOUN
cana-1323	50	6			PROPN
cana-1323	50	7			PROPN
cana-1323	50	8			PROPN
cana-1323	50	9			PUNCT
cana-1323	50	10			NOUN
cana-1323	50	11			PUNCT
cana-1323	50	12	and	and	CCONJ
cana-1323	50	13	the	the	DET
cana-1323	50	14	pre	pre	ADJ
cana-1323	50	15	-	-	NOUN
cana-1323	50	16	image	image	ADJ
cana-1323	50	17	ψ	ψ	X
cana-1323	50	18	(	(	PUNCT
cana-1323	50	19	ε	ε	PROPN
cana-1323	50	20	)	)	PUNCT
cana-1323	50	21	of	of	ADP
cana-1323	50	22	ε	ε	PROPN
cana-1323	50	23	under	under	ADP
cana-1323	50	24	ψ	ψ	NOUN
cana-1323	50	25	is	be	AUX
cana-1323	50	26	the	the	DET
cana-1323	50	27	bipolar	bipolar	ADJ
cana-1323	50	28	fuzzy	fuzzy	ADJ
cana-1323	50	29	subset	subset	NOUN
cana-1323	50	30	of	of	ADP
cana-1323	50	31	m1	m1	PROPN
cana-1323	50	32	defined	define	VERB
cana-1323	50	33	by	by	ADP
cana-1323	50	34	for	for	ADP
cana-1323	50	35	p	p	PROPN
cana-1323	50	36	∈	∈	PROPN
cana-1323	50	37	m1	m1	NOUN
cana-1323	50	38	(	(	PUNCT
cana-1323	50	39	(	(	PUNCT
cana-1323	50	40	ψ	ψ	SYM
cana-1323	50	41	1	1	NUM
cana-1323	50	42	(	(	PUNCT
cana-1323	50	43	ε	ε	PROPN
cana-1323	50	44	)	)	PUNCT
cana-1323	50	45	)	)	PUNCT
cana-1323	51	1	+	+	CCONJ
cana-1323	51	2	(	(	PUNCT
cana-1323	51	3	p	p	X
cana-1323	51	4	)	)	PUNCT
cana-1323	51	5	=	=	PUNCT
cana-1323	51	6	ε	ε	PROPN
cana-1323	51	7	+	+	CCONJ
cana-1323	51	8	(	(	PUNCT
cana-1323	51	9	ψ(a	ψ(a	PROPN
cana-1323	51	10	)	)	PUNCT
cana-1323	51	11	)	)	PUNCT
cana-1323	51	12	and	and	CCONJ
cana-1323	51	13	(	(	PUNCT
cana-1323	51	14	(	(	PUNCT
cana-1323	51	15	ψ	ψ	X
cana-1323	51	16	-1	-1	PUNCT
cana-1323	51	17	(	(	PUNCT
cana-1323	51	18	ε	ε	PROPN
cana-1323	51	19	)	)	PUNCT
cana-1323	51	20	)	)	PUNCT
cana-1323	51	21	-1	-1	PUNCT
cana-1323	52	1	(	(	PUNCT
cana-1323	52	2	p	p	X
cana-1323	52	3	)	)	PUNCT
cana-1323	52	4	=	=	SYM
cana-1323	52	5	ε	ε	PROPN
cana-1323	52	6	-1	-1	PUNCT
cana-1323	52	7	(	(	PUNCT
cana-1323	52	8	ψ(a	ψ(a	PROPN
cana-1323	52	9	)	)	PUNCT
cana-1323	52	10	)	)	PUNCT
cana-1323	52	11	.	.	PUNCT
cana-1323	53	1	for	for	ADP
cana-1323	53	2	more	more	ADJ
cana-1323	53	3	preliminaries	preliminary	NOUN
cana-1323	53	4	refer	refer	VERB
cana-1323	53	5	the	the	DET
cana-1323	53	6	references	reference	NOUN
cana-1323	53	7	and	and	CCONJ
cana-1323	53	8	their	their	PRON
cana-1323	53	9	references	reference	NOUN
cana-1323	53	10	.	.	PUNCT
cana-1323	54	1	for	for	ADP
cana-1323	54	2	more	more	ADJ
cana-1323	54	3	preliminaries	preliminary	NOUN
cana-1323	54	4	consider	consider	VERB
cana-1323	54	5	the	the	DET
cana-1323	54	6	references	reference	NOUN
cana-1323	54	7	and	and	CCONJ
cana-1323	54	8	their	their	PRON
cana-1323	54	9	references	reference	NOUN
cana-1323	54	10	.	.	PUNCT
cana-1323	55	1	communications	communication	NOUN
cana-1323	55	2	on	on	ADP
cana-1323	55	3	applied	apply	VERB
cana-1323	55	4	nonlinear	nonlinear	ADJ
cana-1323	55	5	analysis	analysis	NOUN
cana-1323	55	6	issn	issn	NOUN
cana-1323	55	7	:	:	PUNCT
cana-1323	55	8	1074	1074	NUM
cana-1323	55	9	-	-	PUNCT
cana-1323	55	10	133x	133x	NUM
cana-1323	55	11	vol	vol	NOUN
cana-1323	55	12	31	31	NUM
cana-1323	55	13	no	no	NOUN
cana-1323	55	14	.	.	PUNCT
cana-1323	56	1	7s	7	NOUN
cana-1323	56	2	(	(	PUNCT
cana-1323	56	3	2024	2024	NUM
cana-1323	56	4	)	)	PUNCT
cana-1323	56	5	446	446	NUM
cana-1323	56	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1323	56	7	3	3	NUM
cana-1323	56	8	:	:	PUNCT
cana-1323	56	9	homomorphism	homomorphism	NOUN
cana-1323	56	10	in	in	ADP
cana-1323	56	11	tripolar	tripolar	ADJ
cana-1323	56	12	fuzzy	fuzzy	ADJ
cana-1323	56	13	soft	soft	ADJ
cana-1323	56	14	ternary	ternary	ADJ
cana-1323	56	15	γ−semiring	γ−semiring	NOUN
cana-1323	56	16	:	:	PUNCT
cana-1323	56	17	in	in	ADP
cana-1323	56	18	this	this	DET
cana-1323	56	19	section	section	NOUN
cana-1323	56	20	the	the	DET
cana-1323	56	21	homomorphism	homomorphism	NOUN
cana-1323	56	22	concept	concept	NOUN
cana-1323	56	23	over	over	ADP
cana-1323	56	24	tfstgsr	tfstgsr	PROPN
cana-1323	56	25	is	be	AUX
cana-1323	56	26	introduced	introduce	VERB
cana-1323	56	27	and	and	CCONJ
cana-1323	56	28	studied	study	VERB
cana-1323	56	29	their	their	PRON
cana-1323	56	30	properties	property	NOUN
cana-1323	56	31	.	.	PUNCT
cana-1323	57	1	definition	definition	NOUN
cana-1323	57	2	3.1	3.1	NUM
cana-1323	57	3	:	:	PUNCT
cana-1323	57	4	let	let	VERB
cana-1323	57	5	(	(	PUNCT
cana-1323	57	6	δ	δ	PROPN
cana-1323	57	7	,	,	PUNCT
cana-1323	57	8	v	v	PROPN
cana-1323	57	9	,	,	PUNCT
cana-1323	57	10	γ	γ	NOUN
cana-1323	57	11	)	)	PUNCT
cana-1323	57	12	and	and	CCONJ
cana-1323	57	13	(	(	PUNCT
cana-1323	57	14	ε	ε	PROPN
cana-1323	57	15	,	,	PUNCT
cana-1323	57	16	w	w	PROPN
cana-1323	57	17	,	,	PUNCT
cana-1323	57	18	γ	γ	NOUN
cana-1323	57	19	)	)	PUNCT
cana-1323	57	20	tfss	tfss	NOUN
cana-1323	57	21	over	over	ADP
cana-1323	57	22	tgsr	tgsr	ADJ
cana-1323	57	23	m1	m1	PROPN
cana-1323	57	24	and	and	CCONJ
cana-1323	57	25	m2	m2	PROPN
cana-1323	57	26	and	and	CCONJ
cana-1323	57	27	ψ1	ψ1	PROPN
cana-1323	57	28	:	:	PUNCT
cana-1323	57	29	m1	m1	PROPN
cana-1323	57	30	⟶	⟶	NOUN
cana-1323	57	31	m2	m2	PROPN
cana-1323	57	32	,	,	PUNCT
cana-1323	57	33	ψ2	ψ2	NOUN
cana-1323	57	34	:	:	PUNCT
cana-1323	57	35	v	v	NUM
cana-1323	57	36	⟶	⟶	NOUN
cana-1323	57	37	w	w	PROPN
cana-1323	57	38	ware	ware	NOUN
cana-1323	57	39	two	two	NUM
cana-1323	57	40	functions	function	NOUN
cana-1323	57	41	such	such	ADJ
cana-1323	57	42	that	that	DET
cana-1323	57	43	v	v	NOUN
cana-1323	57	44	,	,	PUNCT
cana-1323	57	45	w	w	PROPN
cana-1323	57	46	ware	ware	NOUN
cana-1323	57	47	parameter	parameter	NOUN
cana-1323	57	48	sets	set	NOUN
cana-1323	57	49	for	for	ADP
cana-1323	57	50	the	the	DET
cana-1323	57	51	crisp	crisp	ADJ
cana-1323	57	52	sets	set	NOUN
cana-1323	57	53	m1	m1	PROPN
cana-1323	57	54	and	and	CCONJ
cana-1323	57	55	m2	m2	PROPN
cana-1323	57	56	,	,	PUNCT
cana-1323	57	57	then	then	ADV
cana-1323	57	58	(	(	PUNCT
cana-1323	57	59	ψ1	ψ1	NOUN
cana-1323	57	60	,	,	PUNCT
cana-1323	57	61	ψ2	ψ2	NOUN
cana-1323	57	62	)	)	PUNCT
cana-1323	57	63	is	be	AUX
cana-1323	57	64	nothing	nothing	PRON
cana-1323	57	65	but	but	SCONJ
cana-1323	57	66	tripolar	tripolar	ADJ
cana-1323	57	67	fuzzy	fuzzy	ADJ
cana-1323	57	68	soft	soft	ADJ
cana-1323	57	69	function	function	NOUN
cana-1323	57	70	from	from	ADP
cana-1323	57	71	m1	m1	PROPN
cana-1323	57	72	to	to	ADP
cana-1323	57	73	m2	m2	PROPN
cana-1323	57	74	.	.	PUNCT
cana-1323	58	1	definition	definition	NOUN
cana-1323	58	2	3.2	3.2	NUM
cana-1323	58	3	:	:	PUNCT
cana-1323	58	4	let	let	VERB
cana-1323	58	5	(	(	PUNCT
cana-1323	58	6	δ	δ	PROPN
cana-1323	58	7	,	,	PUNCT
cana-1323	58	8	v	v	PROPN
cana-1323	58	9	,	,	PUNCT
cana-1323	58	10	γ	γ	NOUN
cana-1323	58	11	)	)	PUNCT
cana-1323	58	12	and	and	CCONJ
cana-1323	58	13	(	(	PUNCT
cana-1323	58	14	ε	ε	PROPN
cana-1323	58	15	,	,	PUNCT
cana-1323	58	16	w	w	PROPN
cana-1323	58	17	,	,	PUNCT
cana-1323	58	18	γ	γ	NOUN
cana-1323	58	19	)	)	PUNCT
cana-1323	58	20	tfss	tfss	NOUN
cana-1323	58	21	over	over	ADP
cana-1323	58	22	tgsr	tgsr	ADJ
cana-1323	58	23	m1	m1	PROPN
cana-1323	58	24	and	and	CCONJ
cana-1323	58	25	m2	m2	PROPN
cana-1323	58	26	and	and	CCONJ
cana-1323	58	27	(	(	PUNCT
cana-1323	58	28	ψ1	ψ1	NOUN
cana-1323	58	29	,	,	PUNCT
cana-1323	58	30	ψ2	ψ2	NOUN
cana-1323	58	31	)	)	PUNCT
cana-1323	58	32	is	be	AUX
cana-1323	58	33	tripolar	tripolar	VERB
cana-1323	58	34	fuzzy	fuzzy	ADJ
cana-1323	58	35	soft	soft	ADJ
cana-1323	58	36	function	function	NOUN
cana-1323	58	37	from	from	ADP
cana-1323	58	38	m1	m1	PROPN
cana-1323	58	39	to	to	ADP
cana-1323	58	40	m2	m2	PROPN
cana-1323	58	41	.	.	PUNCT
cana-1323	59	1	then	then	ADV
cana-1323	59	2	(	(	PUNCT
cana-1323	59	3	ψ1	ψ1	NOUN
cana-1323	59	4	,	,	PUNCT
cana-1323	59	5	ψ2	ψ2	NOUN
cana-1323	59	6	)	)	PUNCT
cana-1323	59	7	is	be	AUX
cana-1323	59	8	called	call	VERB
cana-1323	59	9	tripolar	tripolar	ADJ
cana-1323	59	10	fuzzy	fuzzy	ADJ
cana-1323	59	11	soft	soft	ADJ
cana-1323	59	12	ternary	ternary	ADJ
cana-1323	59	13	γ	γ	X
cana-1323	59	14	-	-	PUNCT
cana-1323	59	15	semiring	semire	VERB
cana-1323	59	16	homomorphism	homomorphism	NOUN
cana-1323	59	17	if	if	SCONJ
cana-1323	59	18	satisfying	satisfy	VERB
cana-1323	59	19	the	the	DET
cana-1323	59	20	following	follow	VERB
cana-1323	59	21	laws	law	NOUN
cana-1323	59	22	:	:	PUNCT
cana-1323	59	23	1	1	X
cana-1323	59	24	)	)	PUNCT
cana-1323	59	25	ψ1	ψ1	NOUN
cana-1323	59	26	is	be	AUX
cana-1323	59	27	a	a	DET
cana-1323	59	28	ternary	ternary	ADJ
cana-1323	59	29	γ	γ	X
cana-1323	59	30	-	-	PUNCT
cana-1323	59	31	semiring	semire	VERB
cana-1323	59	32	homomorphism	homomorphism	NOUN
cana-1323	59	33	from	from	ADP
cana-1323	59	34	m1	m1	PROPN
cana-1323	59	35	onto	onto	ADP
cana-1323	59	36	m2	m2	PROPN
cana-1323	59	37	.	.	PROPN
cana-1323	59	38	2	2	NUM
cana-1323	59	39	)	)	PUNCT
cana-1323	59	40	ψ2	ψ2	NOUN
cana-1323	59	41	is	be	AUX
cana-1323	59	42	a	a	DET
cana-1323	59	43	mapping	mapping	NOUN
cana-1323	59	44	from	from	ADP
cana-1323	59	45	v	v	NOUN
cana-1323	59	46	onto	onto	ADP
cana-1323	59	47	w.	w.	NOUN
cana-1323	59	48	3	3	NUM
cana-1323	59	49	)	)	PUNCT
cana-1323	59	50	21	21	NUM
cana-1323	59	51	(	(	PUNCT
cana-1323	59	52	)	)	PUNCT
cana-1323	59	53	(	(	PUNCT
cana-1323	59	54	)	)	PUNCT
cana-1323	59	55	(	(	PUNCT
cana-1323	59	56	)	)	PUNCT
cana-1323	59	57	x	x	SYM
cana-1323	59	58	x	x	PROPN
cana-1323	59	59			NOUN
cana-1323	59	60			PUNCT
cana-1323	60	1			PROPN
cana-1323	60	2	,	,	PUNCT
cana-1323	60	3	21	21	NUM
cana-1323	60	4	(	(	PUNCT
cana-1323	60	5	)	)	PUNCT
cana-1323	60	6	(	(	PUNCT
cana-1323	60	7	)	)	PUNCT
cana-1323	60	8	(	(	PUNCT
cana-1323	60	9	)	)	PUNCT
cana-1323	60	10	x	x	SYM
cana-1323	60	11	x	x	PROPN
cana-1323	60	12			NOUN
cana-1323	60	13			NUM
cana-1323	61	1			PROPN
cana-1323	61	2	and	and	CCONJ
cana-1323	61	3	21	21	NUM
cana-1323	61	4	(	(	PUNCT
cana-1323	61	5	)	)	PUNCT
cana-1323	61	6	(	(	PUNCT
cana-1323	61	7	)	)	PUNCT
cana-1323	61	8	(	(	PUNCT
cana-1323	61	9	)	)	PUNCT
cana-1323	61	10	x	x	SYM
cana-1323	61	11	x	x	PROPN
cana-1323	61	12			NOUN
cana-1323	61	13			PROPN
cana-1323	61	14			PROPN
cana-1323	61	15	note	note	VERB
cana-1323	61	16	3.3	3.3	NUM
cana-1323	61	17	:	:	PUNCT
cana-1323	61	18	if	if	SCONJ
cana-1323	61	19	there	there	PRON
cana-1323	61	20	exist	exist	VERB
cana-1323	61	21	a	a	DET
cana-1323	61	22	tfstgsrh	tfstgsrh	NOUN
cana-1323	61	23	between	between	ADP
cana-1323	61	24	(	(	PUNCT
cana-1323	61	25	δ	δ	PROPN
cana-1323	61	26	,	,	PUNCT
cana-1323	61	27	v	v	PROPN
cana-1323	61	28	,	,	PUNCT
cana-1323	61	29	γ	γ	NOUN
cana-1323	61	30	)	)	PUNCT
cana-1323	61	31	and	and	CCONJ
cana-1323	61	32	(	(	PUNCT
cana-1323	61	33	ε	ε	PROPN
cana-1323	61	34	,	,	PUNCT
cana-1323	61	35	w	w	PROPN
cana-1323	61	36	,	,	PUNCT
cana-1323	61	37	γ	γ	NOUN
cana-1323	61	38	)	)	PUNCT
cana-1323	61	39	,	,	PUNCT
cana-1323	61	40	then	then	ADV
cana-1323	61	41	we	we	PRON
cana-1323	61	42	say	say	VERB
cana-1323	61	43	that	that	SCONJ
cana-1323	61	44	(	(	PUNCT
cana-1323	61	45	δ	δ	PROPN
cana-1323	61	46	,	,	PUNCT
cana-1323	61	47	v	v	PROPN
cana-1323	61	48	,	,	PUNCT
cana-1323	61	49	γ	γ	NOUN
cana-1323	61	50	)	)	PUNCT
cana-1323	61	51	is	be	AUX
cana-1323	61	52	soft	soft	ADJ
cana-1323	61	53	homomorphic	homomorphic	ADJ
cana-1323	61	54	to	to	ADP
cana-1323	61	55	(	(	PUNCT
cana-1323	61	56	ε	ε	PROPN
cana-1323	61	57	,	,	PUNCT
cana-1323	61	58	w	w	PROPN
cana-1323	61	59	,	,	PUNCT
cana-1323	61	60	γ	γ	NOUN
cana-1323	61	61	)	)	PUNCT
cana-1323	61	62	.	.	PUNCT
cana-1323	62	1	definition	definition	NOUN
cana-1323	62	2	3.4	3.4	NUM
cana-1323	62	3	:	:	PUNCT
cana-1323	62	4	if	if	SCONJ
cana-1323	62	5	(	(	PUNCT
cana-1323	62	6	ψ1	ψ1	NOUN
cana-1323	62	7	,	,	PUNCT
cana-1323	62	8	ψ2	ψ2	NOUN
cana-1323	62	9	)	)	PUNCT
cana-1323	62	10	is	be	AUX
cana-1323	62	11	a	a	DET
cana-1323	62	12	tripolar	tripolar	ADJ
cana-1323	62	13	fuzzy	fuzzy	ADJ
cana-1323	62	14	soft	soft	ADJ
cana-1323	62	15	function	function	NOUN
cana-1323	62	16	from	from	ADP
cana-1323	62	17	m1	m1	PROPN
cana-1323	62	18	to	to	ADP
cana-1323	62	19	m2	m2	PROPN
cana-1323	62	20	.	.	PUNCT
cana-1323	63	1	the	the	DET
cana-1323	63	2	pre	pre	ADJ
cana-1323	63	3	image	image	NOUN
cana-1323	63	4	of	of	ADP
cana-1323	63	5	(	(	PUNCT
cana-1323	63	6	ε	ε	PROPN
cana-1323	63	7	,	,	PUNCT
cana-1323	63	8	w	w	PROPN
cana-1323	63	9	,	,	PUNCT
cana-1323	63	10	γ	γ	NOUN
cana-1323	63	11	)	)	PUNCT
cana-1323	63	12	under	under	ADP
cana-1323	63	13	the	the	DET
cana-1323	63	14	tripolar	tripolar	ADJ
cana-1323	63	15	fuzzy	fuzzy	ADJ
cana-1323	63	16	soft	soft	ADJ
cana-1323	63	17	function	function	NOUN
cana-1323	63	18	(	(	PUNCT
cana-1323	63	19	ψ1	ψ1	NOUN
cana-1323	63	20	,	,	PUNCT
cana-1323	63	21	ψ2	ψ2	NOUN
cana-1323	63	22	)	)	PUNCT
cana-1323	63	23	devoted	devote	VERB
cana-1323	63	24	by	by	ADP
cana-1323	63	25	(	(	PUNCT
cana-1323	63	26	ψ1	ψ1	NOUN
cana-1323	63	27	,	,	PUNCT
cana-1323	63	28	ψ2	ψ2	NOUN
cana-1323	63	29	)	)	PUNCT
cana-1323	63	30	-1	-1	PUNCT
cana-1323	63	31	(	(	PUNCT
cana-1323	63	32	ε	ε	PROPN
cana-1323	63	33	,	,	PUNCT
cana-1323	63	34	w	w	PROPN
cana-1323	63	35	,	,	PUNCT
cana-1323	63	36	γ	γ	NOUN
cana-1323	63	37	)	)	PUNCT
cana-1323	63	38	defined	define	VERB
cana-1323	63	39	as	as	ADP
cana-1323	63	40	(	(	PUNCT
cana-1323	63	41	ψ1	ψ1	NOUN
cana-1323	63	42	,	,	PUNCT
cana-1323	63	43	ψ2	ψ2	NOUN
cana-1323	63	44	)	)	PUNCT
cana-1323	63	45	-1	-1	PUNCT
cana-1323	63	46	(	(	PUNCT
cana-1323	63	47	ε	ε	PROPN
cana-1323	63	48	,	,	PUNCT
cana-1323	63	49	w	w	PROPN
cana-1323	63	50	,	,	PUNCT
cana-1323	63	51	γ	γ	NOUN
cana-1323	63	52	)	)	PUNCT
cana-1323	63	53	=	=	SYM
cana-1323	63	54	1	1	NUM
cana-1323	63	55	1	1	NUM
cana-1323	63	56	1	1	NUM
cana-1323	63	57	2	2	NUM
cana-1323	63	58	(	(	PUNCT
cana-1323	63	59	(	(	PUNCT
cana-1323	63	60	)	)	PUNCT
cana-1323	63	61	,	,	PUNCT
cana-1323	63	62	(	(	PUNCT
cana-1323	63	63	)	)	PUNCT
cana-1323	63	64	)	)	PUNCT
cana-1323	63	65	w	w	PROPN
cana-1323	64	1			PROPN
cana-1323	64	2			PROPN
cana-1323	64	3			PROPN
cana-1323	64	4	is	be	AUX
cana-1323	64	5	a	a	DET
cana-1323	64	6	tfss	tfss	NOUN
cana-1323	64	7	.	.	PUNCT
cana-1323	65	1	theorem	theorem	VERB
cana-1323	65	2	3.5	3.5	NUM
cana-1323	65	3	:	:	PUNCT
cana-1323	65	4	if	if	SCONJ
cana-1323	65	5	(	(	PUNCT
cana-1323	65	6	ε	ε	PROPN
cana-1323	65	7	,	,	PUNCT
cana-1323	65	8	w	w	PROPN
cana-1323	65	9	,	,	PUNCT
cana-1323	65	10	γ	γ	NOUN
cana-1323	65	11	)	)	PUNCT
cana-1323	65	12	is	be	AUX
cana-1323	65	13	a	a	DET
cana-1323	65	14	tfstgsr	tfstgsr	NOUN
cana-1323	65	15	over	over	ADP
cana-1323	65	16	tgsr	tgsr	PROPN
cana-1323	65	17	m2	m2	PROPN
cana-1323	65	18	,	,	PUNCT
cana-1323	65	19	ψ	ψ	ADP
cana-1323	65	20	:	:	PUNCT
cana-1323	65	21	m1	m1	PROPN
cana-1323	65	22	⟶	⟶	NOUN
cana-1323	65	23	m2	m2	PROPN
cana-1323	65	24	is	be	AUX
cana-1323	65	25	a	a	DET
cana-1323	65	26	monomorphism	monomorphism	NOUN
cana-1323	65	27	and	and	CCONJ
cana-1323	65	28	for	for	ADP
cana-1323	65	29	each	each	DET
cana-1323	65	30	w	w	NOUN
cana-1323	65	31	∈w	∈w	NOUN
cana-1323	65	32	,	,	PUNCT
cana-1323	65	33	define	define	NOUN
cana-1323	65	34	(	(	PUNCT
cana-1323	65	35	ψε)w(m	ψε)w(m	NOUN
cana-1323	65	36	)	)	PUNCT
cana-1323	66	1	=	=	SYM
cana-1323	66	2	ψw	ψw	X
cana-1323	66	3	(	(	PUNCT
cana-1323	66	4	ε(m	ε(m	NOUN
cana-1323	66	5	)	)	PUNCT
cana-1323	66	6	)	)	PUNCT
cana-1323	66	7	for	for	ADP
cana-1323	66	8	all	all	DET
cana-1323	66	9	m	m	PROPN
cana-1323	66	10	∈	∈	PROPN
cana-1323	66	11	m1	m1	NOUN
cana-1323	66	12	.	.	PUNCT
cana-1323	67	1	then	then	ADV
cana-1323	67	2	(	(	PUNCT
cana-1323	67	3	ψε	ψε	PROPN
cana-1323	67	4	,	,	PUNCT
cana-1323	67	5	w	w	PROPN
cana-1323	67	6	,	,	PUNCT
cana-1323	67	7	γ	γ	NOUN
cana-1323	67	8	)	)	PUNCT
cana-1323	67	9	is	be	AUX
cana-1323	67	10	a	a	DET
cana-1323	67	11	tfstgsr	tfstgsr	NOUN
cana-1323	67	12	over	over	ADP
cana-1323	67	13	tgsr	tgsr	PROPN
cana-1323	67	14	m2	m2	PROPN
cana-1323	67	15	.	.	PUNCT
cana-1323	68	1	proof	proof	NOUN
cana-1323	68	2	:	:	PUNCT
cana-1323	68	3	suppose	suppose	VERB
cana-1323	68	4	j	j	PROPN
cana-1323	68	5	,	,	PUNCT
cana-1323	68	6	m	m	PROPN
cana-1323	68	7	,	,	PUNCT
cana-1323	68	8	k	k	PROPN
cana-1323	68	9	∈	∈	PROPN
cana-1323	68	10	m	m	PROPN
cana-1323	68	11	,	,	PUNCT
cana-1323	68	12	w	w	PROPN
cana-1323	68	13	∈	∈	PROPN
cana-1323	68	14	w	w	NOUN
cana-1323	68	15	and	and	CCONJ
cana-1323	68	16	α	α	NOUN
cana-1323	68	17	,	,	PUNCT
cana-1323	68	18	𝜃	𝜃	PROPN
cana-1323	68	19	∈	∈	PROPN
cana-1323	68	20	γ	γ	X
cana-1323	68	21	.	.	PROPN
cana-1323	69	1	then	then	ADV
cana-1323	69	2	1	1	X
cana-1323	69	3	.	.	PUNCT
cana-1323	69	4	(	(	PUNCT
cana-1323	69	5	ψε)w(j	ψε)w(j	X
cana-1323	69	6	+	+	NUM
cana-1323	69	7	m	m	X
cana-1323	69	8	)	)	PUNCT
cana-1323	69	9	=	=	SYM
cana-1323	69	10	ψw(ε(j	ψw(ε(j	X
cana-1323	69	11	+	+	NOUN
cana-1323	69	12	m	m	VERB
cana-1323	69	13	)	)	PUNCT
cana-1323	69	14	)	)	PUNCT
cana-1323	70	1	=	=	SYM
cana-1323	70	2	νψw(ε(j	νψw(ε(j	NOUN
cana-1323	70	3	)	)	PUNCT
cana-1323	70	4	+	+	ADJ
cana-1323	70	5	ε(m	ε(m	NOUN
cana-1323	70	6	)	)	PUNCT
cana-1323	70	7	)	)	PUNCT
cana-1323	70	8	≥min	≥min	NOUN
cana-1323	70	9	{	{	PUNCT
cana-1323	70	10	νψw(ε(j	νψw(ε(j	NOUN
cana-1323	70	11	)	)	PUNCT
cana-1323	70	12	)	)	PUNCT
cana-1323	70	13	,	,	PUNCT
cana-1323	70	14	νψw(ε(m	νψw(ε(m	PROPN
cana-1323	70	15	)	)	PUNCT
cana-1323	70	16	)	)	PUNCT
cana-1323	70	17	}	}	PUNCT
cana-1323	70	18	=	=	SYM
cana-1323	70	19	min	min	NOUN
cana-1323	70	20	{	{	PUNCT
cana-1323	70	21	(	(	PUNCT
cana-1323	70	22	ψε)w(j	ψε)w(j	X
cana-1323	70	23	)	)	PUNCT
cana-1323	70	24	,	,	PUNCT
cana-1323	70	25	(	(	PUNCT
cana-1323	70	26	ψε)w(m	ψε)w(m	NOUN
cana-1323	70	27	)	)	PUNCT
cana-1323	70	28	}	}	PUNCT
cana-1323	70	29	2	2	NUM
cana-1323	70	30	.	.	PUNCT
cana-1323	70	31	(	(	PUNCT
cana-1323	70	32	ψε)w(j	ψε)w(j	X
cana-1323	70	33	+	+	NUM
cana-1323	70	34	m	m	X
cana-1323	70	35	)	)	PUNCT
cana-1323	70	36	=	=	SYM
cana-1323	70	37	ψw(ε(j	ψw(ε(j	X
cana-1323	70	38	+	+	NOUN
cana-1323	70	39	m	m	VERB
cana-1323	70	40	)	)	PUNCT
cana-1323	70	41	)	)	PUNCT
cana-1323	71	1	=	=	SYM
cana-1323	71	2	γψw(ε(j	γψw(ε(j	X
cana-1323	71	3	)	)	PUNCT
cana-1323	72	1	+	+	ADJ
cana-1323	72	2	ε(m	ε(m	NOUN
cana-1323	72	3	)	)	PUNCT
cana-1323	72	4	)	)	PUNCT
cana-1323	72	5	≤	≤	NUM
cana-1323	72	6	max	max	PROPN
cana-1323	72	7	{	{	PUNCT
cana-1323	72	8	γψw(ε(j	γψw(ε(j	PROPN
cana-1323	72	9	)	)	PUNCT
cana-1323	72	10	)	)	PUNCT
cana-1323	72	11	,	,	PUNCT
cana-1323	72	12	γψw	γψw	NOUN
cana-1323	72	13	(	(	PUNCT
cana-1323	72	14	ε(m	ε(m	PROPN
cana-1323	72	15	)	)	PUNCT
cana-1323	72	16	)	)	PUNCT
cana-1323	72	17	}	}	PUNCT
cana-1323	72	18	=	=	SYM
cana-1323	72	19	max	max	X
cana-1323	72	20	{	{	PUNCT
cana-1323	72	21	(	(	PUNCT
cana-1323	72	22	ψε)w(j	ψε)w(j	X
cana-1323	72	23	)	)	PUNCT
cana-1323	72	24	,	,	PUNCT
cana-1323	72	25	(	(	PUNCT
cana-1323	72	26	ψε)w(m	ψε)w(m	NOUN
cana-1323	72	27	)	)	PUNCT
cana-1323	72	28	}	}	PUNCT
cana-1323	72	29	.	.	PUNCT
cana-1323	73	1	3	3	X
cana-1323	73	2	.	.	X
cana-1323	73	3	(	(	PUNCT
cana-1323	73	4	ψε)w(j	ψε)w(j	X
cana-1323	73	5	+	+	NUM
cana-1323	73	6	m	m	X
cana-1323	73	7	)	)	PUNCT
cana-1323	74	1	=	=	SYM
cana-1323	74	2	ψw(ε(j	ψw(ε(j	X
cana-1323	74	3	+	+	NOUN
cana-1323	74	4	m	m	VERB
cana-1323	74	5	)	)	PUNCT
cana-1323	74	6	)	)	PUNCT
cana-1323	75	1	=	=	SYM
cana-1323	75	2	𝛽ψw(ε(j	𝛽ψw(ε(j	NOUN
cana-1323	75	3	)	)	PUNCT
cana-1323	76	1	+	+	ADJ
cana-1323	76	2	ε(m	ε(m	NOUN
cana-1323	76	3	)	)	PUNCT
cana-1323	76	4	)	)	PUNCT
cana-1323	77	1	≤	≤	NUM
cana-1323	77	2	max	max	PROPN
cana-1323	77	3	{	{	PUNCT
cana-1323	77	4	βψw(ε(j	βψw(ε(j	PROPN
cana-1323	77	5	)	)	PUNCT
cana-1323	77	6	)	)	PUNCT
cana-1323	77	7	,	,	PUNCT
cana-1323	77	8	βψw	βψw	NOUN
cana-1323	77	9	(	(	PUNCT
cana-1323	77	10	ε(m	ε(m	PROPN
cana-1323	77	11	)	)	PUNCT
cana-1323	77	12	)	)	PUNCT
cana-1323	77	13	}	}	PUNCT
cana-1323	77	14	=	=	SYM
cana-1323	77	15	max	max	X
cana-1323	77	16	{	{	PUNCT
cana-1323	77	17	(	(	PUNCT
cana-1323	77	18	ψε)w(j	ψε)w(j	X
cana-1323	77	19	)	)	PUNCT
cana-1323	77	20	,	,	PUNCT
cana-1323	77	21	(	(	PUNCT
cana-1323	77	22	ψε)w(m	ψε)w(m	NOUN
cana-1323	77	23	)	)	PUNCT
cana-1323	77	24	}	}	PUNCT
cana-1323	77	25	.	.	PUNCT
cana-1323	78	1	4	4	X
cana-1323	78	2	.	.	X
cana-1323	78	3	(	(	PUNCT
cana-1323	78	4	ψε)w(j𝛼m𝜃k	ψε)w(j𝛼m𝜃k	PROPN
cana-1323	78	5	)	)	PUNCT
cana-1323	78	6	=	=	SYM
cana-1323	78	7	ψw(ε(j𝛼m𝜃k	ψw(ε(j𝛼m𝜃k	X
cana-1323	78	8	)	)	PUNCT
cana-1323	78	9	)	)	PUNCT
cana-1323	78	10	=	=	SYM
cana-1323	78	11	νψw(ε(j	νψw(ε(j	NOUN
cana-1323	78	12	)	)	PUNCT
cana-1323	78	13	𝛼ε(m)𝜃𝜀(k	𝛼ε(m)𝜃𝜀(k	NOUN
cana-1323	78	14	)	)	PUNCT
cana-1323	78	15	)	)	PUNCT
cana-1323	79	1	≥min	≥min	NOUN
cana-1323	79	2	{	{	PUNCT
cana-1323	79	3	νψw(ε(j	νψw(ε(j	NOUN
cana-1323	79	4	)	)	PUNCT
cana-1323	79	5	)	)	PUNCT
cana-1323	79	6	,	,	PUNCT
cana-1323	79	7	νψw(ε(m	νψw(ε(m	PROPN
cana-1323	79	8	)	)	PUNCT
cana-1323	79	9	)	)	PUNCT
cana-1323	79	10	,	,	PUNCT
cana-1323	79	11	νψw(ε(k	νψw(ε(k	PROPN
cana-1323	79	12	)	)	PUNCT
cana-1323	79	13	)	)	PUNCT
cana-1323	79	14	}	}	PUNCT
cana-1323	79	15	=	=	SYM
cana-1323	79	16	min	min	NOUN
cana-1323	79	17	{	{	PUNCT
cana-1323	79	18	(	(	PUNCT
cana-1323	79	19	ψε)w(j	ψε)w(j	X
cana-1323	79	20	)	)	PUNCT
cana-1323	79	21	,	,	PUNCT
cana-1323	79	22	(	(	PUNCT
cana-1323	79	23	ψε)w(m	ψε)w(m	NOUN
cana-1323	79	24	)	)	PUNCT
cana-1323	79	25	,	,	PUNCT
cana-1323	79	26	(	(	PUNCT
cana-1323	79	27	ψε)w(k	ψε)w(k	VERB
cana-1323	79	28	)	)	PUNCT
cana-1323	79	29	}	}	PUNCT
cana-1323	79	30	.	.	PUNCT
cana-1323	80	1	5	5	X
cana-1323	80	2	.	.	X
cana-1323	80	3	(	(	PUNCT
cana-1323	80	4	ψε)w(j𝛼m𝜃k	ψε)w(j𝛼m𝜃k	PROPN
cana-1323	80	5	)	)	PUNCT
cana-1323	80	6	=	=	SYM
cana-1323	80	7	ψw(ε(j𝛼m𝜃k	ψw(ε(j𝛼m𝜃k	X
cana-1323	80	8	)	)	PUNCT
cana-1323	80	9	)	)	PUNCT
cana-1323	81	1	=	=	SYM
cana-1323	81	2	γψw(ε(j	γψw(ε(j	X
cana-1323	81	3	)	)	PUNCT
cana-1323	81	4	𝛼ε(m)𝜃𝜀(k	𝛼ε(m)𝜃𝜀(k	PROPN
cana-1323	81	5	)	)	PUNCT
cana-1323	81	6	)	)	PUNCT
cana-1323	81	7	≤max	≤max	PUNCT
cana-1323	81	8	{	{	PUNCT
cana-1323	81	9	γψw(ε(j	γψw(ε(j	NOUN
cana-1323	81	10	)	)	PUNCT
cana-1323	81	11	)	)	PUNCT
cana-1323	81	12	,	,	PUNCT
cana-1323	81	13	γψw(ε(m	γψw(ε(m	PROPN
cana-1323	81	14	)	)	PUNCT
cana-1323	81	15	)	)	PUNCT
cana-1323	81	16	,	,	PUNCT
cana-1323	81	17	γψw(ε(k	γψw(ε(k	NOUN
cana-1323	81	18	)	)	PUNCT
cana-1323	81	19	)	)	PUNCT
cana-1323	81	20	}	}	PUNCT
cana-1323	81	21	=	=	SYM
cana-1323	81	22	max	max	X
cana-1323	81	23	{	{	PUNCT
cana-1323	81	24	(	(	PUNCT
cana-1323	81	25	ψε)w(j	ψε)w(j	X
cana-1323	81	26	)	)	PUNCT
cana-1323	81	27	,	,	PUNCT
cana-1323	81	28	(	(	PUNCT
cana-1323	81	29	ψε)w(m	ψε)w(m	NOUN
cana-1323	81	30	)	)	PUNCT
cana-1323	81	31	,	,	PUNCT
cana-1323	81	32	(	(	PUNCT
cana-1323	81	33	ψε)w(k	ψε)w(k	VERB
cana-1323	81	34	)	)	PUNCT
cana-1323	81	35	}	}	PUNCT
cana-1323	81	36	.	.	PUNCT
cana-1323	82	1	6	6	NUM
cana-1323	82	2	.	.	X
cana-1323	82	3	(	(	PUNCT
cana-1323	82	4	ψε)w(j𝛼m𝜃k	ψε)w(j𝛼m𝜃k	PROPN
cana-1323	82	5	)	)	PUNCT
cana-1323	82	6	=	=	SYM
cana-1323	82	7	ψw(ε(j𝛼m𝜃k	ψw(ε(j𝛼m𝜃k	X
cana-1323	82	8	)	)	PUNCT
cana-1323	82	9	)	)	PUNCT
cana-1323	83	1	=	=	SYM
cana-1323	83	2	βψw(ε(j	βψw(ε(j	NOUN
cana-1323	83	3	)	)	PUNCT
cana-1323	83	4	𝛼ε(m)𝜃𝜀(k	𝛼ε(m)𝜃𝜀(k	PROPN
cana-1323	83	5	)	)	PUNCT
cana-1323	83	6	)	)	PUNCT
cana-1323	83	7	≤max	≤max	PUNCT
cana-1323	83	8	{	{	PUNCT
cana-1323	83	9	βψw(ε(j	βψw(ε(j	NOUN
cana-1323	83	10	)	)	PUNCT
cana-1323	83	11	)	)	PUNCT
cana-1323	83	12	,	,	PUNCT
cana-1323	83	13	βψw(ε(m	βψw(ε(m	NOUN
cana-1323	83	14	)	)	PUNCT
cana-1323	83	15	)	)	PUNCT
cana-1323	83	16	,	,	PUNCT
cana-1323	83	17	βψw(ε(k	βψw(ε(k	PROPN
cana-1323	83	18	)	)	PUNCT
cana-1323	83	19	)	)	PUNCT
cana-1323	83	20	}	}	PUNCT
cana-1323	84	1	=	=	SYM
cana-1323	84	2	max	max	X
cana-1323	84	3	{	{	PUNCT
cana-1323	84	4	(	(	PUNCT
cana-1323	84	5	ψε)w(j	ψε)w(j	X
cana-1323	84	6	)	)	PUNCT
cana-1323	84	7	,	,	PUNCT
cana-1323	84	8	(	(	PUNCT
cana-1323	84	9	ψε)w(m	ψε)w(m	NOUN
cana-1323	84	10	)	)	PUNCT
cana-1323	84	11	,	,	PUNCT
cana-1323	84	12	(	(	PUNCT
cana-1323	84	13	ψε)w(k	ψε)w(k	VERB
cana-1323	84	14	)	)	PUNCT
cana-1323	84	15	}	}	PUNCT
cana-1323	84	16	.	.	PUNCT
cana-1323	85	1	therefore	therefore	ADV
cana-1323	85	2	(	(	PUNCT
cana-1323	85	3	ψε)w(m	ψε)w(m	NOUN
cana-1323	85	4	)	)	PUNCT
cana-1323	85	5	is	be	AUX
cana-1323	85	6	a	a	DET
cana-1323	85	7	tripolar	tripolar	ADJ
cana-1323	85	8	fuzzy	fuzzy	ADJ
cana-1323	85	9	soft	soft	ADJ
cana-1323	85	10	γ−subsemiring	γ−subsemiring	NOUN
cana-1323	85	11	of	of	ADP
cana-1323	85	12	m.	m.	NOUN
cana-1323	85	13	thus	thus	ADV
cana-1323	85	14	(	(	PUNCT
cana-1323	85	15	ψε	ψε	NOUN
cana-1323	85	16	,	,	PUNCT
cana-1323	85	17	w	w	PROPN
cana-1323	85	18	,	,	PUNCT
cana-1323	85	19	γ	γ	NOUN
cana-1323	85	20	)	)	PUNCT
cana-1323	85	21	is	be	AUX
cana-1323	85	22	a	a	DET
cana-1323	85	23	tripolar	tripolar	ADJ
cana-1323	85	24	fuzzy	fuzzy	ADJ
cana-1323	85	25	soft	soft	ADJ
cana-1323	85	26	ternary	ternary	NOUN
cana-1323	85	27	γ−semiring	γ−semire	VERB
cana-1323	85	28	over	over	ADP
cana-1323	85	29	m2	m2	PROPN
cana-1323	85	30	.	.	PUNCT
cana-1323	86	1	communications	communication	NOUN
cana-1323	86	2	on	on	ADP
cana-1323	86	3	applied	apply	VERB
cana-1323	86	4	nonlinear	nonlinear	ADJ
cana-1323	86	5	analysis	analysis	NOUN
cana-1323	86	6	issn	issn	NOUN
cana-1323	86	7	:	:	PUNCT
cana-1323	86	8	1074	1074	NUM
cana-1323	86	9	-	-	PUNCT
cana-1323	86	10	133x	133x	NUM
cana-1323	86	11	vol	vol	NOUN
cana-1323	86	12	31	31	NUM
cana-1323	86	13	no	no	NOUN
cana-1323	86	14	.	.	PUNCT
cana-1323	87	1	7s	7	NOUN
cana-1323	87	2	(	(	PUNCT
cana-1323	87	3	2024	2024	NUM
cana-1323	87	4	)	)	PUNCT
cana-1323	87	5	447	447	NUM
cana-1323	87	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1323	87	7	theorem	theorem	VERB
cana-1323	87	8	3.6	3.6	NUM
cana-1323	87	9	:	:	PUNCT
cana-1323	87	10	if	if	SCONJ
cana-1323	87	11	(	(	PUNCT
cana-1323	87	12	𝛗	𝛗	X
cana-1323	87	13	,	,	PUNCT
cana-1323	87	14	w	w	PROPN
cana-1323	87	15	,	,	PUNCT
cana-1323	87	16	𝚪	𝚪	NOUN
cana-1323	87	17	)	)	PUNCT
cana-1323	87	18	tftsr	tftsr	NOUN
cana-1323	87	19	over	over	ADP
cana-1323	87	20	tgsr	tgsr	PROPN
cana-1323	87	21	m	m	PROPN
cana-1323	87	22	,	,	PUNCT
cana-1323	87	23	𝛘	𝛘	PROPN
cana-1323	87	24	is	be	AUX
cana-1323	87	25	an	an	DET
cana-1323	87	26	endomorphism	endomorphism	NOUN
cana-1323	87	27	of	of	ADP
cana-1323	87	28	m	m	PRON
cana-1323	87	29	and	and	CCONJ
cana-1323	87	30	defined	define	VERB
cana-1323	87	31	(	(	PUNCT
cana-1323	87	32	𝛗𝛘)w	𝛗𝛘)w	PROPN
cana-1323	87	33	=	=	PUNCT
cana-1323	87	34	𝛗w𝛘	𝛗w𝛘	PROPN
cana-1323	87	35	for	for	ADP
cana-1323	87	36	each	each	DET
cana-1323	87	37	w	w	NOUN
cana-1323	87	38	∈w	∈w	NOUN
cana-1323	87	39	.	.	PUNCT
cana-1323	88	1	then	then	ADV
cana-1323	88	2	(	(	PUNCT
cana-1323	88	3	𝛗𝛘	𝛗𝛘	PROPN
cana-1323	88	4	,	,	PUNCT
cana-1323	88	5	w	w	PROPN
cana-1323	88	6	,	,	PUNCT
cana-1323	88	7	𝚪	𝚪	NOUN
cana-1323	88	8	)	)	PUNCT
cana-1323	88	9	is	be	AUX
cana-1323	88	10	a	a	DET
cana-1323	88	11	tfstgsr	tfstgsr	NOUN
cana-1323	88	12	over	over	ADP
cana-1323	88	13	m.	m.	NOUN
cana-1323	88	14	proof	proof	NOUN
cana-1323	88	15	:	:	PUNCT
cana-1323	88	16	suppose	suppose	VERB
cana-1323	88	17	j	j	PROPN
cana-1323	88	18	,	,	PUNCT
cana-1323	88	19	m	m	PROPN
cana-1323	88	20	,	,	PUNCT
cana-1323	88	21	k	k	PROPN
cana-1323	88	22	∈	∈	PROPN
cana-1323	88	23	m	m	PROPN
cana-1323	88	24	,	,	PUNCT
cana-1323	88	25	w	w	PROPN
cana-1323	88	26	∈	∈	PROPN
cana-1323	88	27	w	w	NOUN
cana-1323	88	28	and	and	CCONJ
cana-1323	88	29	α	α	NOUN
cana-1323	88	30	,	,	PUNCT
cana-1323	88	31	𝜃	𝜃	PROPN
cana-1323	88	32	∈	∈	PROPN
cana-1323	88	33	γ	γ	X
cana-1323	88	34	.	.	PROPN
cana-1323	89	1	then	then	ADV
cana-1323	89	2	1	1	X
cana-1323	89	3	.	.	PUNCT
cana-1323	89	4	(	(	PUNCT
cana-1323	89	5	ν𝛘)w(j	ν𝛘)w(j	VERB
cana-1323	89	6	+	+	X
cana-1323	89	7	m	m	X
cana-1323	89	8	)	)	PUNCT
cana-1323	89	9	=	=	SYM
cana-1323	89	10	νφ(w)(χ(j	νφ(w)(χ(j	X
cana-1323	89	11	+	+	X
cana-1323	89	12	m))=	m))=	PROPN
cana-1323	89	13	νφ(w)(χ(j	νφ(w)(χ(j	NOUN
cana-1323	89	14	)	)	PUNCT
cana-1323	89	15	+	+	CCONJ
cana-1323	89	16	χ(m	χ(m	PROPN
cana-1323	89	17	)	)	PUNCT
cana-1323	89	18	)	)	PUNCT
cana-1323	90	1	≥min	≥min	PROPN
cana-1323	90	2	{	{	PUNCT
cana-1323	90	3	νφ(w)(χ(j	νφ(w)(χ(j	NOUN
cana-1323	90	4	)	)	PUNCT
cana-1323	90	5	,	,	PUNCT
cana-1323	90	6	νφ(w)(χ(m	νφ(w)(χ(m	NOUN
cana-1323	90	7	)	)	PUNCT
cana-1323	90	8	}	}	PUNCT
cana-1323	90	9	=	=	SYM
cana-1323	90	10	min	min	NOUN
cana-1323	90	11	{	{	PUNCT
cana-1323	90	12	(	(	PUNCT
cana-1323	90	13	(	(	PUNCT
cana-1323	90	14	νχ)w(j	νχ)w(j	ADJ
cana-1323	90	15	)	)	PUNCT
cana-1323	90	16	)	)	PUNCT
cana-1323	90	17	,	,	PUNCT
cana-1323	90	18	(	(	PUNCT
cana-1323	90	19	(	(	PUNCT
cana-1323	90	20	νχ)w(m	νχ)w(m	NOUN
cana-1323	90	21	)	)	PUNCT
cana-1323	90	22	)	)	PUNCT
cana-1323	90	23	}	}	PUNCT
cana-1323	90	24	2	2	X
cana-1323	90	25	.	.	PUNCT
cana-1323	90	26	(	(	PUNCT
cana-1323	90	27	γ𝛘)w(j	γ𝛘)w(j	X
cana-1323	90	28	+	+	NOUN
cana-1323	90	29	m	m	X
cana-1323	90	30	)	)	PUNCT
cana-1323	90	31	=	=	PUNCT
cana-1323	90	32	γφ(w)(χ(j	γφ(w)(χ(j	ADJ
cana-1323	90	33	+	+	CCONJ
cana-1323	90	34	m))=	m))=	PROPN
cana-1323	90	35	γφ(w)(χ(j	γφ(w)(χ(j	NOUN
cana-1323	90	36	)	)	PUNCT
cana-1323	90	37	+	+	CCONJ
cana-1323	90	38	χ(m	χ(m	PROPN
cana-1323	90	39	)	)	PUNCT
cana-1323	90	40	)	)	PUNCT
cana-1323	91	1	≤	≤	NUM
cana-1323	91	2	max	max	PROPN
cana-1323	91	3	{	{	PUNCT
cana-1323	91	4	γφ(w)(χ(j	γφ(w)(χ(j	PROPN
cana-1323	91	5	)	)	PUNCT
cana-1323	91	6	,	,	PUNCT
cana-1323	91	7	γφ(w)(χ(m	γφ(w)(χ(m	ADJ
cana-1323	91	8	)	)	PUNCT
cana-1323	91	9	}	}	PUNCT
cana-1323	91	10	=	=	SYM
cana-1323	91	11	max	max	X
cana-1323	91	12	{	{	PUNCT
cana-1323	91	13	(	(	PUNCT
cana-1323	91	14	(	(	PUNCT
cana-1323	91	15	γχ)w(j	γχ)w(j	ADJ
cana-1323	91	16	)	)	PUNCT
cana-1323	91	17	)	)	PUNCT
cana-1323	91	18	,	,	PUNCT
cana-1323	91	19	(	(	PUNCT
cana-1323	91	20	(	(	PUNCT
cana-1323	91	21	γχ)w(m	γχ)w(m	NOUN
cana-1323	91	22	)	)	PUNCT
cana-1323	91	23	)	)	PUNCT
cana-1323	91	24	}	}	PUNCT
cana-1323	91	25	3	3	X
cana-1323	91	26	.	.	PUNCT
cana-1323	91	27	(	(	PUNCT
cana-1323	91	28	𝛽𝛘)w(j	𝛽𝛘)w(j	X
cana-1323	91	29	+	+	NUM
cana-1323	91	30	m	m	X
cana-1323	91	31	)	)	PUNCT
cana-1323	91	32	=	=	PUNCT
cana-1323	91	33	𝛽φ(w)(χ(j	𝛽φ(w)(χ(j	VERB
cana-1323	91	34	+	+	CCONJ
cana-1323	91	35	m))=	m))=	NOUN
cana-1323	91	36	𝛽φ(w)(χ(j	𝛽φ(w)(χ(j	ADJ
cana-1323	91	37	)	)	PUNCT
cana-1323	91	38	+	+	CCONJ
cana-1323	91	39	χ(m	χ(m	PROPN
cana-1323	91	40	)	)	PUNCT
cana-1323	91	41	)	)	PUNCT
cana-1323	91	42	≤	≤	NUM
cana-1323	91	43	max	max	PROPN
cana-1323	91	44	{	{	PUNCT
cana-1323	91	45	𝛽φ(w)(χ(j	𝛽φ(w)(χ(j	ADJ
cana-1323	91	46	)	)	PUNCT
cana-1323	91	47	,	,	PUNCT
cana-1323	91	48	𝛽φ(w)(χ(m	𝛽φ(w)(χ(m	NOUN
cana-1323	91	49	)	)	PUNCT
cana-1323	91	50	}	}	PUNCT
cana-1323	91	51	=	=	SYM
cana-1323	91	52	max	max	X
cana-1323	91	53	{	{	PUNCT
cana-1323	91	54	(	(	PUNCT
cana-1323	91	55	(	(	PUNCT
cana-1323	91	56	𝛽χ)w(j	𝛽χ)w(j	NOUN
cana-1323	91	57	)	)	PUNCT
cana-1323	91	58	)	)	PUNCT
cana-1323	91	59	,	,	PUNCT
cana-1323	91	60	(	(	PUNCT
cana-1323	91	61	(	(	PUNCT
cana-1323	91	62	𝛽χ)w(m	𝛽χ)w(m	NOUN
cana-1323	91	63	)	)	PUNCT
cana-1323	91	64	)	)	PUNCT
cana-1323	91	65	}	}	PUNCT
cana-1323	91	66	4	4	NUM
cana-1323	91	67	.	.	PUNCT
cana-1323	91	68	(	(	PUNCT
cana-1323	91	69	ν𝛘)w(j𝛼m𝜃k)=	ν𝛘)w(j𝛼m𝜃k)=	PUNCT
cana-1323	91	70	νφ(w)(χ(j𝛼m𝜃k))=	νφ(w)(χ(j𝛼m𝜃k))=	PROPN
cana-1323	91	71	νφ(w)(χ(j)𝛼χ(m)𝜃	νφ(w)(χ(j)𝛼χ(m)𝜃	NUM
cana-1323	91	72	χ(k	χ(k	NOUN
cana-1323	91	73	)	)	PUNCT
cana-1323	91	74	)	)	PUNCT
cana-1323	91	75	≥	≥	PROPN
cana-1323	91	76	min	min	PROPN
cana-1323	91	77	{	{	PUNCT
cana-1323	91	78	νφ(w)(χ(j	νφ(w)(χ(j	NOUN
cana-1323	91	79	)	)	PUNCT
cana-1323	91	80	,	,	PUNCT
cana-1323	91	81	νφ(w)(χ(m	νφ(w)(χ(m	NOUN
cana-1323	91	82	)	)	PUNCT
cana-1323	91	83	,	,	PUNCT
cana-1323	91	84	νφ(w)(χ(k	νφ(w)(χ(k	NOUN
cana-1323	91	85	)	)	PUNCT
cana-1323	91	86	}	}	PUNCT
cana-1323	91	87	=	=	SYM
cana-1323	91	88	min	min	NOUN
cana-1323	91	89	{	{	PUNCT
cana-1323	91	90	(	(	PUNCT
cana-1323	91	91	ν𝛘)w(j	ν𝛘)w(j	NOUN
cana-1323	91	92	)	)	PUNCT
cana-1323	91	93	,	,	PUNCT
cana-1323	91	94	(	(	PUNCT
cana-1323	91	95	ν𝛘)w(m	ν𝛘)w(m	NOUN
cana-1323	91	96	)	)	PUNCT
cana-1323	91	97	,	,	PUNCT
cana-1323	91	98	(	(	PUNCT
cana-1323	91	99	ν𝛘)w(k	ν𝛘)w(k	NOUN
cana-1323	91	100	)	)	PUNCT
cana-1323	91	101	}	}	PUNCT
cana-1323	91	102	5	5	NUM
cana-1323	91	103	.	.	PUNCT
cana-1323	91	104	(	(	PUNCT
cana-1323	91	105	γ𝛘)w(j𝛼m𝜃k)=	γ𝛘)w(j𝛼m𝜃k)=	PROPN
cana-1323	91	106	γφ(w)(χ(j𝛼m𝜃k))=	γφ(w)(χ(j𝛼m𝜃k))=	PROPN
cana-1323	91	107	γφ(w)(χ(j)𝛼χ(m)𝜃	γφ(w)(χ(j)𝛼χ(m)𝜃	NOUN
cana-1323	91	108	χ(k	χ(k	NOUN
cana-1323	91	109	)	)	PUNCT
cana-1323	91	110	)	)	PUNCT
cana-1323	92	1	≤	≤	NUM
cana-1323	92	2	max	max	PROPN
cana-1323	92	3	{	{	PUNCT
cana-1323	92	4	γφ(w)(χ(j	γφ(w)(χ(j	PROPN
cana-1323	92	5	)	)	PUNCT
cana-1323	92	6	,	,	PUNCT
cana-1323	92	7	γφ(w)(χ(m	γφ(w)(χ(m	ADJ
cana-1323	92	8	)	)	PUNCT
cana-1323	92	9	,	,	PUNCT
cana-1323	92	10	γφ(w)(χ(k	γφ(w)(χ(k	ADV
cana-1323	92	11	)	)	PUNCT
cana-1323	92	12	}	}	PUNCT
cana-1323	92	13	=	=	SYM
cana-1323	92	14	max	max	X
cana-1323	92	15	{	{	PUNCT
cana-1323	92	16	(	(	PUNCT
cana-1323	92	17	γ𝛘)w(j	γ𝛘)w(j	NOUN
cana-1323	92	18	)	)	PUNCT
cana-1323	92	19	,	,	PUNCT
cana-1323	92	20	(	(	PUNCT
cana-1323	92	21	γ𝛘)w(m	γ𝛘)w(m	NOUN
cana-1323	92	22	)	)	PUNCT
cana-1323	92	23	,	,	PUNCT
cana-1323	92	24	(	(	PUNCT
cana-1323	92	25	γ𝛘)w(k	γ𝛘)w(k	NUM
cana-1323	92	26	)	)	PUNCT
cana-1323	92	27	}	}	PUNCT
cana-1323	92	28	.	.	PUNCT
cana-1323	93	1	6	6	NUM
cana-1323	93	2	.	.	X
cana-1323	93	3	(	(	PUNCT
cana-1323	93	4	𝛽𝛘)w(j𝛼m𝜃k)=	𝛽𝛘)w(j𝛼m𝜃k)=	PUNCT
cana-1323	93	5	𝛽φ(w)(χ(j𝛼m𝜃k))=	𝛽φ(w)(χ(j𝛼m𝜃k))=	PROPN
cana-1323	93	6	𝛽φ(w)(χ(j)𝛼χ(m)𝜃	𝛽φ(w)(χ(j)𝛼χ(m)𝜃	VERB
cana-1323	93	7	χ(k	χ(k	NOUN
cana-1323	93	8	)	)	PUNCT
cana-1323	93	9	)	)	PUNCT
cana-1323	94	1	≤	≤	NUM
cana-1323	94	2	max	max	PROPN
cana-1323	94	3	{	{	PUNCT
cana-1323	94	4	𝛽φ(w)(χ(j	𝛽φ(w)(χ(j	ADJ
cana-1323	94	5	)	)	PUNCT
cana-1323	94	6	,	,	PUNCT
cana-1323	94	7	𝛽φ(w)(χ(m	𝛽φ(w)(χ(m	NOUN
cana-1323	94	8	)	)	PUNCT
cana-1323	94	9	,	,	PUNCT
cana-1323	94	10	𝛽φ(w)(χ(k	𝛽φ(w)(χ(k	NOUN
cana-1323	94	11	)	)	PUNCT
cana-1323	94	12	}	}	PUNCT
cana-1323	94	13	=	=	SYM
cana-1323	94	14	max	max	X
cana-1323	94	15	{	{	PUNCT
cana-1323	94	16	(	(	PUNCT
cana-1323	94	17	𝛽𝛘)w(j	𝛽𝛘)w(j	NOUN
cana-1323	94	18	)	)	PUNCT
cana-1323	94	19	,	,	PUNCT
cana-1323	94	20	(	(	PUNCT
cana-1323	94	21	𝛽𝛘)w(m	𝛽𝛘)w(m	NOUN
cana-1323	94	22	)	)	PUNCT
cana-1323	94	23	,	,	PUNCT
cana-1323	94	24	(	(	PUNCT
cana-1323	94	25	𝛽𝛘)w(k	𝛽𝛘)w(k	NOUN
cana-1323	94	26	)	)	PUNCT
cana-1323	94	27	}	}	PUNCT
cana-1323	94	28	.	.	PUNCT
cana-1323	95	1	thus	thus	ADV
cana-1323	95	2	(	(	PUNCT
cana-1323	95	3	𝛗𝛘)w	𝛗𝛘)w	NOUN
cana-1323	95	4	is	be	AUX
cana-1323	95	5	a	a	DET
cana-1323	95	6	tfgsr	tfgsr	NOUN
cana-1323	95	7	of	of	ADP
cana-1323	95	8	m.	m.	NOUN
cana-1323	95	9	then	then	ADV
cana-1323	95	10	(	(	PUNCT
cana-1323	95	11	𝛗𝛘	𝛗𝛘	PROPN
cana-1323	95	12	,	,	PUNCT
cana-1323	95	13	w	w	PROPN
cana-1323	95	14	,	,	PUNCT
cana-1323	95	15	𝚪	𝚪	NOUN
cana-1323	95	16	)	)	PUNCT
cana-1323	95	17	is	be	AUX
cana-1323	95	18	a	a	DET
cana-1323	95	19	tfstgsr	tfstgsr	NOUN
cana-1323	95	20	over	over	ADP
cana-1323	95	21	m.	m.	NOUN
cana-1323	95	22	theorem	theorem	VERB
cana-1323	95	23	3.7	3.7	NUM
cana-1323	95	24	:	:	PUNCT
cana-1323	95	25	if	if	SCONJ
cana-1323	95	26	φ	φ	PROPN
cana-1323	95	27	:	:	PUNCT
cana-1323	95	28	m1→	m1→	NUM
cana-1323	95	29	m2	m2	PROPN
cana-1323	95	30	is	be	AUX
cana-1323	95	31	an	an	DET
cana-1323	95	32	epimorphism	epimorphism	NOUN
cana-1323	95	33	of	of	ADP
cana-1323	95	34	tgsr	tgsr	ADJ
cana-1323	95	35	and	and	CCONJ
cana-1323	95	36	(	(	PUNCT
cana-1323	95	37	ρ	ρ	PROPN
cana-1323	95	38	,	,	PUNCT
cana-1323	95	39	w	w	PROPN
cana-1323	95	40	,	,	PUNCT
cana-1323	95	41	γ	γ	NOUN
cana-1323	95	42	)	)	PUNCT
cana-1323	95	43	is	be	AUX
cana-1323	95	44	a	a	DET
cana-1323	95	45	“	"	PUNCT
cana-1323	95	46	tripolar	tripolar	ADJ
cana-1323	95	47	fuzzy	fuzzy	ADJ
cana-1323	95	48	soft	soft	ADJ
cana-1323	95	49	right	right	ADJ
cana-1323	95	50	ideal	ideal	NOUN
cana-1323	95	51	”	"	PUNCT
cana-1323	95	52	over	over	ADP
cana-1323	95	53	m2	m2	PROPN
cana-1323	95	54	.	.	PUNCT
cana-1323	96	1	if	if	SCONJ
cana-1323	96	2	for	for	ADP
cana-1323	96	3	each	each	DET
cana-1323	96	4	w	w	PROPN
cana-1323	96	5	∈	∈	PROPN
cana-1323	96	6	w	w	PROPN
cana-1323	96	7	,	,	PUNCT
cana-1323	96	8	w	w	PROPN
cana-1323	96	9	=	=	SYM
cana-1323	96	10	1	1	NUM
cana-1323	96	11	(	(	PUNCT
cana-1323	96	12	)	)	PUNCT
cana-1323	96	13	w	w	X
cana-1323	96	14			ADJ
cana-1323	96	15	then	then	ADV
cana-1323	96	16	(	(	PUNCT
cana-1323	96	17	ζ	ζ	NOUN
cana-1323	96	18	,	,	PUNCT
cana-1323	96	19	w	w	PROPN
cana-1323	96	20	,	,	PUNCT
cana-1323	96	21	γ	γ	NOUN
cana-1323	96	22	)	)	PUNCT
cana-1323	96	23	is	be	AUX
cana-1323	96	24	a	a	DET
cana-1323	96	25	“	"	PUNCT
cana-1323	96	26	tripolar	tripolar	ADJ
cana-1323	96	27	fuzzy	fuzzy	ADJ
cana-1323	96	28	soft	soft	ADJ
cana-1323	96	29	right	right	ADJ
cana-1323	96	30	ideal	ideal	NOUN
cana-1323	96	31	”	"	PUNCT
cana-1323	96	32	over	over	ADP
cana-1323	96	33	m1	m1	NOUN
cana-1323	96	34	.	.	PUNCT
cana-1323	97	1	proof	proof	NOUN
cana-1323	97	2	:	:	PUNCT
cana-1323	97	3	if	if	SCONJ
cana-1323	97	4	w	w	PROPN
cana-1323	97	5	∈	∈	PROPN
cana-1323	97	6	w	w	PROPN
cana-1323	97	7	and	and	CCONJ
cana-1323	97	8	α	α	NOUN
cana-1323	97	9	,	,	PUNCT
cana-1323	97	10	ζ	ζ	PROPN
cana-1323	97	11	∈	∈	PROPN
cana-1323	97	12	γ	γ	X
cana-1323	97	13	.	.	PROPN
cana-1323	97	14	then	then	ADV
cana-1323	97	15	ρx	ρx	PROPN
cana-1323	97	16	is	be	AUX
cana-1323	97	17	a	a	DET
cana-1323	97	18	“	"	PUNCT
cana-1323	97	19	tripolar	tripolar	ADJ
cana-1323	97	20	fuzzy	fuzzy	ADJ
cana-1323	97	21	soft	soft	ADJ
cana-1323	97	22	right	right	ADJ
cana-1323	97	23	ideal	ideal	NOUN
cana-1323	97	24	”	"	PUNCT
cana-1323	97	25	over	over	ADP
cana-1323	97	26	m2	m2	PROPN
cana-1323	97	27	.	.	PUNCT
cana-1323	98	1	if	if	SCONJ
cana-1323	98	2	j	j	PROPN
cana-1323	98	3	,	,	PUNCT
cana-1323	98	4	m	m	PROPN
cana-1323	98	5	,	,	PUNCT
cana-1323	98	6	k	k	PROPN
cana-1323	98	7	∈	∈	PROPN
cana-1323	98	8	m1	m1	PROPN
cana-1323	98	9	and	and	CCONJ
cana-1323	98	10	α	α	NOUN
cana-1323	98	11	,	,	PUNCT
cana-1323	98	12	ζ	ζ	PROPN
cana-1323	98	13	∈	∈	PROPN
cana-1323	98	14	γ	γ	NOUN
cana-1323	98	15	,	,	PUNCT
cana-1323	98	16	then	then	ADV
cana-1323	98	17	:	:	PUNCT
cana-1323	98	18	1	1	X
cana-1323	98	19	.	.	X
cana-1323	98	20	1	1	NUM
cana-1323	98	21			NOUN
cana-1323	98	22	(	(	PUNCT
cana-1323	98	23	νw(j	νw(j	PUNCT
cana-1323	98	24	+	+	CCONJ
cana-1323	98	25	m	m	NOUN
cana-1323	98	26	)	)	PUNCT
cana-1323	98	27	)	)	PUNCT
cana-1323	99	1	=	=	SYM
cana-1323	99	2	ν𝜌(w	ν𝜌(w	NOUN
cana-1323	99	3	)	)	PUNCT
cana-1323	99	4	(	(	PUNCT
cana-1323	99	5	φ(j	φ(j	PROPN
cana-1323	99	6	+	+	NOUN
cana-1323	99	7	m	m	NOUN
cana-1323	99	8	)	)	PUNCT
cana-1323	99	9	)	)	PUNCT
cana-1323	100	1	=	=	SYM
cana-1323	100	2	ν𝜌(w	ν𝜌(w	NOUN
cana-1323	100	3	)	)	PUNCT
cana-1323	100	4	(	(	PUNCT
cana-1323	100	5	φ(j	φ(j	PROPN
cana-1323	100	6	)	)	PUNCT
cana-1323	100	7	+	+	NUM
cana-1323	100	8	φ(m	φ(m	NOUN
cana-1323	100	9	)	)	PUNCT
cana-1323	100	10	)	)	PUNCT
cana-1323	100	11	≥	≥	PROPN
cana-1323	100	12	min	min	PROPN
cana-1323	100	13	{	{	PUNCT
cana-1323	100	14	ν𝜌(w	ν𝜌(w	NOUN
cana-1323	100	15	)	)	PUNCT
cana-1323	100	16	(	(	PUNCT
cana-1323	100	17	φ(j	φ(j	PROPN
cana-1323	100	18	)	)	PUNCT
cana-1323	100	19	,	,	PUNCT
cana-1323	100	20	ν𝜌(w	ν𝜌(w	NOUN
cana-1323	100	21	)	)	PUNCT
cana-1323	100	22	(	(	PUNCT
cana-1323	100	23	φ(m	φ(m	ADJ
cana-1323	100	24	)	)	PUNCT
cana-1323	100	25	)	)	PUNCT
cana-1323	100	26	}	}	PUNCT
cana-1323	100	27	=	=	SYM
cana-1323	100	28	min	min	X
cana-1323	100	29	{	{	PUNCT
cana-1323	100	30	1	1	NUM
cana-1323	100	31			NOUN
cana-1323	100	32	(	(	PUNCT
cana-1323	100	33	νw(j	νw(j	NOUN
cana-1323	100	34	)	)	PUNCT
cana-1323	100	35	)	)	PUNCT
cana-1323	100	36	,	,	PUNCT
cana-1323	100	37	1	1	NUM
cana-1323	100	38			NOUN
cana-1323	100	39	(	(	PUNCT
cana-1323	100	40	νw(m	νw(m	NUM
cana-1323	100	41	)	)	PUNCT
cana-1323	100	42	)	)	PUNCT
cana-1323	100	43	}	}	PUNCT
cana-1323	101	1	2	2	NUM
cana-1323	101	2	.	.	X
cana-1323	101	3	1	1	NUM
cana-1323	101	4			NOUN
cana-1323	101	5	(	(	PUNCT
cana-1323	101	6	γw	γw	PROPN
cana-1323	101	7	)	)	PUNCT
cana-1323	101	8	(	(	PUNCT
cana-1323	101	9	j	j	PROPN
cana-1323	101	10	+	+	CCONJ
cana-1323	101	11	m	m	VERB
cana-1323	101	12	)	)	PUNCT
cana-1323	101	13	=	=	SYM
cana-1323	101	14	γ𝜌(w	γ𝜌(w	X
cana-1323	101	15	)	)	PUNCT
cana-1323	101	16	(	(	PUNCT
cana-1323	101	17	φ(j	φ(j	PROPN
cana-1323	101	18	+	+	NOUN
cana-1323	101	19	m	m	NOUN
cana-1323	101	20	)	)	PUNCT
cana-1323	101	21	)	)	PUNCT
cana-1323	102	1	=	=	SYM
cana-1323	102	2	γ𝜌(w	γ𝜌(w	NOUN
cana-1323	102	3	)	)	PUNCT
cana-1323	102	4	(	(	PUNCT
cana-1323	102	5	φ(j	φ(j	PROPN
cana-1323	102	6	)	)	PUNCT
cana-1323	102	7	+	+	NUM
cana-1323	102	8	φ(m	φ(m	NOUN
cana-1323	102	9	)	)	PUNCT
cana-1323	102	10	)	)	PUNCT
cana-1323	102	11	≤	≤	NUM
cana-1323	102	12	max	max	PROPN
cana-1323	102	13	{	{	PUNCT
cana-1323	102	14	γ𝜌(w	γ𝜌(w	NOUN
cana-1323	102	15	)	)	PUNCT
cana-1323	102	16	(	(	PUNCT
cana-1323	102	17	φ(j	φ(j	PROPN
cana-1323	102	18	)	)	PUNCT
cana-1323	102	19	)	)	PUNCT
cana-1323	102	20	,	,	PUNCT
cana-1323	102	21	γ𝜌(w	γ𝜌(w	NOUN
cana-1323	102	22	)	)	PUNCT
cana-1323	102	23	(	(	PUNCT
cana-1323	102	24	φ(m	φ(m	ADV
cana-1323	102	25	)	)	PUNCT
cana-1323	102	26	)	)	PUNCT
cana-1323	102	27	}	}	PUNCT
cana-1323	102	28	=	=	SYM
cana-1323	102	29	max	max	X
cana-1323	102	30	{	{	PUNCT
cana-1323	102	31	1	1	NUM
cana-1323	102	32			X
cana-1323	102	33	(	(	PUNCT
cana-1323	102	34	γw	γw	PROPN
cana-1323	102	35	)	)	PUNCT
cana-1323	102	36	(	(	PUNCT
cana-1323	102	37	j	j	PROPN
cana-1323	102	38	)	)	PUNCT
cana-1323	102	39	,	,	PUNCT
cana-1323	102	40	1	1	NUM
cana-1323	102	41			X
cana-1323	102	42	(	(	PUNCT
cana-1323	102	43	γw	γw	NOUN
cana-1323	102	44	)	)	PUNCT
cana-1323	102	45	(	(	PUNCT
cana-1323	102	46	m	m	NOUN
cana-1323	102	47	)	)	PUNCT
cana-1323	102	48	}	}	PUNCT
cana-1323	102	49	.	.	PUNCT
cana-1323	103	1	3	3	X
cana-1323	103	2	.	.	X
cana-1323	103	3	1	1	NUM
cana-1323	103	4			NOUN
cana-1323	103	5	(	(	PUNCT
cana-1323	103	6	βw	βw	ADV
cana-1323	103	7	)	)	PUNCT
cana-1323	103	8	(	(	PUNCT
cana-1323	103	9	j	j	PROPN
cana-1323	103	10	+	+	CCONJ
cana-1323	103	11	m	m	VERB
cana-1323	103	12	)	)	PUNCT
cana-1323	103	13	=	=	PUNCT
cana-1323	103	14	β𝜌(w	β𝜌(w	X
cana-1323	103	15	)	)	PUNCT
cana-1323	103	16	(	(	PUNCT
cana-1323	103	17	φ(j	φ(j	PROPN
cana-1323	103	18	+	+	NOUN
cana-1323	103	19	m	m	NOUN
cana-1323	103	20	)	)	PUNCT
cana-1323	103	21	)	)	PUNCT
cana-1323	104	1	=	=	PUNCT
cana-1323	104	2	β𝜌(w	β𝜌(w	NOUN
cana-1323	104	3	)	)	PUNCT
cana-1323	104	4	(	(	PUNCT
cana-1323	104	5	φ(j	φ(j	PROPN
cana-1323	104	6	)	)	PUNCT
cana-1323	104	7	+	+	NUM
cana-1323	104	8	φ(m	φ(m	NOUN
cana-1323	104	9	)	)	PUNCT
cana-1323	104	10	)	)	PUNCT
cana-1323	104	11	≤	≤	NUM
cana-1323	104	12	max	max	PROPN
cana-1323	104	13	{	{	PUNCT
cana-1323	104	14	β𝜌(w	β𝜌(w	ADP
cana-1323	104	15	)	)	PUNCT
cana-1323	104	16	(	(	PUNCT
cana-1323	104	17	φ(j	φ(j	PROPN
cana-1323	104	18	)	)	PUNCT
cana-1323	104	19	)	)	PUNCT
cana-1323	104	20	,	,	PUNCT
cana-1323	104	21	β𝜌(w	β𝜌(w	NOUN
cana-1323	104	22	)	)	PUNCT
cana-1323	104	23	(	(	PUNCT
cana-1323	104	24	φ(m	φ(m	NOUN
cana-1323	104	25	)	)	PUNCT
cana-1323	104	26	)	)	PUNCT
cana-1323	104	27	}	}	PUNCT
cana-1323	104	28	communications	communication	NOUN
cana-1323	104	29	on	on	ADP
cana-1323	104	30	applied	apply	VERB
cana-1323	104	31	nonlinear	nonlinear	ADJ
cana-1323	104	32	analysis	analysis	NOUN
cana-1323	104	33	issn	issn	NOUN
cana-1323	104	34	:	:	PUNCT
cana-1323	104	35	1074	1074	NUM
cana-1323	104	36	-	-	PUNCT
cana-1323	104	37	133x	133x	NUM
cana-1323	104	38	vol	vol	NOUN
cana-1323	104	39	31	31	NUM
cana-1323	104	40	no	no	NOUN
cana-1323	104	41	.	.	PUNCT
cana-1323	105	1	7s	7	NOUN
cana-1323	105	2	(	(	PUNCT
cana-1323	105	3	2024	2024	NUM
cana-1323	105	4	)	)	PUNCT
cana-1323	105	5	448	448	NUM
cana-1323	105	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1323	105	7	=	=	SYM
cana-1323	105	8	max	max	PROPN
cana-1323	105	9	{	{	PUNCT
cana-1323	105	10	1	1	NUM
cana-1323	105	11			NOUN
cana-1323	105	12	(	(	PUNCT
cana-1323	105	13	βw	βw	ADV
cana-1323	105	14	)	)	PUNCT
cana-1323	105	15	(	(	PUNCT
cana-1323	105	16	j	j	PROPN
cana-1323	105	17	)	)	PUNCT
cana-1323	105	18	,	,	PUNCT
cana-1323	105	19	1	1	NUM
cana-1323	105	20			NOUN
cana-1323	105	21	(	(	PUNCT
cana-1323	105	22	βw	βw	ADV
cana-1323	105	23	)	)	PUNCT
cana-1323	105	24	(	(	PUNCT
cana-1323	105	25	m	m	NOUN
cana-1323	105	26	)	)	PUNCT
cana-1323	105	27	}	}	PUNCT
cana-1323	105	28	.	.	PUNCT
cana-1323	106	1	4	4	NUM
cana-1323	106	2	.	.	X
cana-1323	106	3	1	1	NUM
cana-1323	106	4			NOUN
cana-1323	106	5	(	(	PUNCT
cana-1323	106	6	νw(j𝛼m𝜃k	νw(j𝛼m𝜃k	ADJ
cana-1323	106	7	)	)	PUNCT
cana-1323	106	8	)	)	PUNCT
cana-1323	107	1	=	=	SYM
cana-1323	107	2	ν𝜌(w	ν𝜌(w	NOUN
cana-1323	107	3	)	)	PUNCT
cana-1323	107	4	(	(	PUNCT
cana-1323	107	5	φ(j𝛼m𝜃k	φ(j𝛼m𝜃k	ADV
cana-1323	107	6	)	)	PUNCT
cana-1323	107	7	)	)	PUNCT
cana-1323	108	1	=	=	SYM
cana-1323	108	2	ν𝜌(w	ν𝜌(w	NOUN
cana-1323	108	3	)	)	PUNCT
cana-1323	108	4	(	(	PUNCT
cana-1323	108	5	φ(j)𝛼φ(m)𝜃	φ(j)𝛼φ(m)𝜃	PUNCT
cana-1323	108	6	φ(k	φ(k	PROPN
cana-1323	108	7	)	)	PUNCT
cana-1323	108	8	)	)	PUNCT
cana-1323	108	9	≥	≥	NOUN
cana-1323	108	10	ν𝜌(w	ν𝜌(w	NOUN
cana-1323	108	11	)	)	PUNCT
cana-1323	108	12	(	(	PUNCT
cana-1323	108	13	φ(j	φ(j	PROPN
cana-1323	108	14	)	)	PUNCT
cana-1323	108	15	=	=	SYM
cana-1323	108	16	1	1	NUM
cana-1323	108	17			NOUN
cana-1323	108	18	(	(	PUNCT
cana-1323	108	19	νw(j	νw(j	NOUN
cana-1323	108	20	)	)	PUNCT
cana-1323	108	21	)	)	PUNCT
cana-1323	108	22	.	.	PUNCT
cana-1323	109	1	5	5	X
cana-1323	109	2	.	.	X
cana-1323	109	3	1	1	NUM
cana-1323	109	4			NOUN
cana-1323	109	5	(	(	PUNCT
cana-1323	109	6	γw(j𝛼m𝜃k	γw(j𝛼m𝜃k	PROPN
cana-1323	109	7	)	)	PUNCT
cana-1323	109	8	)	)	PUNCT
cana-1323	110	1	=	=	SYM
cana-1323	110	2	γ𝜌(w)(φ(j𝛼m𝜃k	γ𝜌(w)(φ(j𝛼m𝜃k	NUM
cana-1323	110	3	)	)	PUNCT
cana-1323	110	4	)	)	PUNCT
cana-1323	111	1	=	=	NOUN
cana-1323	111	2	γ𝜌(w	γ𝜌(w	NOUN
cana-1323	111	3	)	)	PUNCT
cana-1323	111	4	(	(	PUNCT
cana-1323	111	5	φ(j)𝛼φ(m)𝜃	φ(j)𝛼φ(m)𝜃	PUNCT
cana-1323	111	6	φ(k	φ(k	PROPN
cana-1323	111	7	)	)	PUNCT
cana-1323	111	8	)	)	PUNCT
cana-1323	111	9	≤	≤	NOUN
cana-1323	111	10	γ𝜌(w	γ𝜌(w	NOUN
cana-1323	111	11	)	)	PUNCT
cana-1323	111	12	(	(	PUNCT
cana-1323	111	13	φ(j	φ(j	PROPN
cana-1323	111	14	)	)	PUNCT
cana-1323	111	15	=	=	PUNCT
cana-1323	111	16	1	1	NUM
cana-1323	111	17			NOUN
cana-1323	111	18	(	(	PUNCT
cana-1323	111	19	γw(j	γw(j	NOUN
cana-1323	111	20	)	)	PUNCT
cana-1323	111	21	)	)	PUNCT
cana-1323	111	22	.	.	PUNCT
cana-1323	112	1	6	6	NUM
cana-1323	112	2	.	.	X
cana-1323	112	3	1	1	NUM
cana-1323	112	4			NOUN
cana-1323	112	5	(	(	PUNCT
cana-1323	112	6	βw(j𝛼m𝜃k	βw(j𝛼m𝜃k	ADJ
cana-1323	112	7	)	)	PUNCT
cana-1323	112	8	)	)	PUNCT
cana-1323	113	1	=	=	PUNCT
cana-1323	113	2	β𝜌(w	β𝜌(w	X
cana-1323	113	3	)	)	PUNCT
cana-1323	113	4	(	(	PUNCT
cana-1323	113	5	φ(j𝛼m𝜃k	φ(j𝛼m𝜃k	ADV
cana-1323	113	6	)	)	PUNCT
cana-1323	113	7	)	)	PUNCT
cana-1323	114	1	=	=	PUNCT
cana-1323	114	2	β𝜌(w	β𝜌(w	X
cana-1323	114	3	)	)	PUNCT
cana-1323	114	4	(	(	PUNCT
cana-1323	114	5	φ(j)𝛼φ(m)𝜃	φ(j)𝛼φ(m)𝜃	PUNCT
cana-1323	114	6	φ(k	φ(k	PROPN
cana-1323	114	7	)	)	PUNCT
cana-1323	114	8	)	)	PUNCT
cana-1323	114	9	≤	≤	NOUN
cana-1323	114	10	β𝜌(w	β𝜌(w	ADP
cana-1323	114	11	)	)	PUNCT
cana-1323	114	12	(	(	PUNCT
cana-1323	114	13	φ(j	φ(j	PROPN
cana-1323	114	14	)	)	PUNCT
cana-1323	114	15	=	=	PUNCT
cana-1323	114	16	1	1	NUM
cana-1323	114	17			NOUN
cana-1323	114	18	(	(	PUNCT
cana-1323	114	19	βw(j	βw(j	PUNCT
cana-1323	114	20	)	)	PUNCT
cana-1323	114	21	)	)	PUNCT
cana-1323	114	22	.	.	PUNCT
cana-1323	115	1	therefore	therefore	ADV
cana-1323	115	2	w	w	X
cana-1323	115	3	=	=	SYM
cana-1323	115	4	1	1	NUM
cana-1323	115	5	(	(	PUNCT
cana-1323	115	6	)	)	PUNCT
cana-1323	115	7	w	w	X
cana-1323	115	8			X
cana-1323	115	9	is	be	AUX
cana-1323	115	10	a	a	DET
cana-1323	115	11	“	"	PUNCT
cana-1323	115	12	tripolar	tripolar	ADJ
cana-1323	115	13	fuzzy	fuzzy	ADJ
cana-1323	115	14	right	right	ADJ
cana-1323	115	15	rideal	rideal	NOUN
cana-1323	115	16	”	"	PUNCT
cana-1323	115	17	of	of	ADP
cana-1323	115	18	m1	m1	PROPN
cana-1323	115	19	.	.	PUNCT
cana-1323	116	1	thus	thus	ADV
cana-1323	116	2	(	(	PUNCT
cana-1323	116	3	δ	δ	PROPN
cana-1323	116	4	,	,	PUNCT
cana-1323	116	5	w	w	PROPN
cana-1323	116	6	,	,	PUNCT
cana-1323	116	7	γ	γ	NOUN
cana-1323	116	8	)	)	PUNCT
cana-1323	116	9	is	be	AUX
cana-1323	116	10	a	a	DET
cana-1323	116	11	“	"	PUNCT
cana-1323	116	12	tripolar	tripolar	ADJ
cana-1323	116	13	fuzzy	fuzzy	ADJ
cana-1323	116	14	soft	soft	ADJ
cana-1323	116	15	right	right	ADJ
cana-1323	116	16	ideal	ideal	NOUN
cana-1323	116	17	”	"	PUNCT
cana-1323	116	18	over	over	ADP
cana-1323	116	19	m1	m1	PROPN
cana-1323	116	20	.	.	PUNCT
cana-1323	117	1	theorem	theorem	VERB
cana-1323	117	2	3.7	3.7	NUM
cana-1323	117	3	is	be	AUX
cana-1323	117	4	also	also	ADV
cana-1323	117	5	true	true	ADJ
cana-1323	117	6	for	for	SCONJ
cana-1323	117	7	tripolar	tripolar	ADJ
cana-1323	117	8	fuzzy	fuzzy	ADJ
cana-1323	117	9	left	leave	VERB
cana-1323	117	10	ideal	ideal	NOUN
cana-1323	117	11	.	.	PUNCT
cana-1323	118	1	proposition	proposition	NOUN
cana-1323	118	2	3.8	3.8	NUM
cana-1323	118	3	.	.	PUNCT
cana-1323	119	1	if	if	SCONJ
cana-1323	119	2	m1	m1	PROPN
cana-1323	119	3	and	and	CCONJ
cana-1323	119	4	m2	m2	PROPN
cana-1323	119	5	are	be	AUX
cana-1323	119	6	tgsrs	tgsrs	ADJ
cana-1323	119	7	,	,	PUNCT
cana-1323	119	8	𝛘	𝛘	X
cana-1323	119	9	:	:	PUNCT
cana-1323	119	10	m1	m1	PROPN
cana-1323	119	11	→	→	SYM
cana-1323	119	12	m2	m2	PROPN
cana-1323	119	13	is	be	AUX
cana-1323	119	14	a	a	DET
cana-1323	119	15	tgsrh	tgsrh	NOUN
cana-1323	119	16	and	and	CCONJ
cana-1323	119	17	φ	φ	PROPN
cana-1323	119	18	is	be	AUX
cana-1323	119	19	a	a	DET
cana-1323	119	20	𝛘−invariant	𝛘−invariant	ADJ
cana-1323	119	21	bipolar	bipolar	ADJ
cana-1323	119	22	fuzzy	fuzzy	ADJ
cana-1323	119	23	subset	subset	NOUN
cana-1323	119	24	of	of	ADP
cana-1323	119	25	m1	m1	NOUN
cana-1323	119	26	,	,	PUNCT
cana-1323	119	27	if	if	SCONJ
cana-1323	119	28	w	w	PROPN
cana-1323	119	29	=	=	SYM
cana-1323	119	30	𝛘(u	𝛘(u	NOUN
cana-1323	119	31	)	)	PUNCT
cana-1323	119	32	then	then	ADV
cana-1323	119	33	𝛘(φ)(w	𝛘(φ)(w	NOUN
cana-1323	119	34	)	)	PUNCT
cana-1323	119	35	=	=	SYM
cana-1323	119	36	φ(u	φ(u	NOUN
cana-1323	119	37	)	)	PUNCT
cana-1323	119	38	;	;	PUNCT
cana-1323	119	39	u	u	PROPN
cana-1323	119	40	∈	∈	PROPN
cana-1323	119	41	m1	m1	NOUN
cana-1323	119	42	.	.	PUNCT
cana-1323	120	1	proof	proof	NOUN
cana-1323	120	2	:	:	PUNCT
cana-1323	120	3	straight	straight	ADV
cana-1323	120	4	forward	forward	ADV
cana-1323	120	5	.	.	PUNCT
cana-1323	121	1	theorem	theorem	VERB
cana-1323	121	2	3.9	3.9	NUM
cana-1323	121	3	:	:	PUNCT
cana-1323	121	4	if	if	SCONJ
cana-1323	121	5	(	(	PUNCT
cana-1323	121	6	𝛗	𝛗	X
cana-1323	121	7	,	,	PUNCT
cana-1323	121	8	w	w	PROPN
cana-1323	121	9	,	,	PUNCT
cana-1323	121	10	𝚪	𝚪	NOUN
cana-1323	121	11	)	)	PUNCT
cana-1323	121	12	is	be	AUX
cana-1323	121	13	a	a	DET
cana-1323	121	14	tripolar	tripolar	ADJ
cana-1323	121	15	fuzzy	fuzzy	ADJ
cana-1323	121	16	soft	soft	ADJ
cana-1323	121	17	right	right	ADJ
cana-1323	121	18	ideal	ideal	NOUN
cana-1323	121	19	over	over	ADP
cana-1323	121	20	tgsr	tgsr	ADJ
cana-1323	121	21	m1	m1	PROPN
cana-1323	121	22	and	and	CCONJ
cana-1323	121	23	𝛘	𝛘	PROPN
cana-1323	121	24	is	be	AUX
cana-1323	121	25	a	a	DET
cana-1323	121	26	homomorphism	homomorphism	NOUN
cana-1323	121	27	from	from	ADP
cana-1323	121	28	m1	m1	PROPN
cana-1323	121	29	onto	onto	ADP
cana-1323	121	30	m2	m2	PROPN
cana-1323	121	31	.	.	PROPN
cana-1323	122	1	for	for	ADP
cana-1323	122	2	each	each	DET
cana-1323	122	3	w	w	PROPN
cana-1323	122	4	∈	∈	PROPN
cana-1323	122	5	w	w	PROPN
cana-1323	122	6	,	,	PUNCT
cana-1323	122	7	𝛗w	𝛗w	INTJ
cana-1323	122	8	is	be	AUX
cana-1323	122	9	a	a	DET
cana-1323	122	10	𝝌−invariant	𝝌−invariant	ADJ
cana-1323	122	11	bipolar	bipolar	ADJ
cana-1323	122	12	fuzzy	fuzzy	ADJ
cana-1323	122	13	right	right	ADJ
cana-1323	122	14	rideal	rideal	NOUN
cana-1323	122	15	of	of	ADP
cana-1323	122	16	m1	m1	NOUN
cana-1323	122	17	,	,	PUNCT
cana-1323	122	18	if	if	SCONJ
cana-1323	122	19	ζw	ζw	ADP
cana-1323	122	20	=	=	NOUN
cana-1323	122	21	𝛘(𝛗w	𝛘(𝛗w	PROPN
cana-1323	122	22	)	)	PUNCT
cana-1323	122	23	then	then	ADV
cana-1323	122	24	(	(	PUNCT
cana-1323	122	25	ζ	ζ	NOUN
cana-1323	122	26	,	,	PUNCT
cana-1323	122	27	w	w	PROPN
cana-1323	122	28	,	,	PUNCT
cana-1323	122	29	𝚪	𝚪	NOUN
cana-1323	122	30	)	)	PUNCT
cana-1323	122	31	is	be	AUX
cana-1323	122	32	a	a	DET
cana-1323	122	33	tripolar	tripolar	ADJ
cana-1323	122	34	fuzzy	fuzzy	ADJ
cana-1323	122	35	soft	soft	ADJ
cana-1323	122	36	right	right	ADJ
cana-1323	122	37	ideal	ideal	NOUN
cana-1323	122	38	over	over	ADP
cana-1323	122	39	m2	m2	PROPN
cana-1323	122	40	.	.	PUNCT
cana-1323	123	1	proof	proof	NOUN
cana-1323	123	2	:	:	PUNCT
cana-1323	123	3	let	let	VERB
cana-1323	123	4	m1	m1	PROPN
cana-1323	123	5	,	,	PUNCT
cana-1323	123	6	m2	m2	PROPN
cana-1323	123	7	,	,	PUNCT
cana-1323	123	8	m3	m3	PROPN
cana-1323	123	9	∈	∈	PROPN
cana-1323	123	10	m2	m2	PROPN
cana-1323	123	11	,	,	PUNCT
cana-1323	123	12	w	w	PROPN
cana-1323	123	13	∈	∈	PROPN
cana-1323	123	14	w	w	PROPN
cana-1323	123	15	,	,	PUNCT
cana-1323	123	16	α	α	PROPN
cana-1323	123	17	,	,	PUNCT
cana-1323	123	18	𝛽	𝛽	PROPN
cana-1323	123	19	∈	∈	PROPN
cana-1323	123	20	γ	γ	PROPN
cana-1323	123	21	.	.	PROPN
cana-1323	123	22	then	then	PROPN
cana-1323	123	23	∃	∃	PROPN
cana-1323	123	24	m4	m4	PROPN
cana-1323	123	25	,	,	PUNCT
cana-1323	123	26	m5	m5	PROPN
cana-1323	123	27	,	,	PUNCT
cana-1323	123	28	m6	m6	PROPN
cana-1323	123	29	∈	∈	PROPN
cana-1323	123	30	m1	m1	PROPN
cana-1323	123	31	∋	∋	NOUN
cana-1323	123	32	χ(m4	χ(m4	NOUN
cana-1323	123	33	)	)	PUNCT
cana-1323	124	1	=	=	SYM
cana-1323	124	2	m1	m1	NOUN
cana-1323	124	3	,	,	PUNCT
cana-1323	124	4	χ(m5	χ(m5	NOUN
cana-1323	124	5	)	)	PUNCT
cana-1323	125	1	=	=	SYM
cana-1323	125	2	m2	m2	PROPN
cana-1323	125	3	,	,	PUNCT
cana-1323	125	4	χ(m6	χ(m6	ADV
cana-1323	125	5	)	)	PUNCT
cana-1323	125	6	=	=	SYM
cana-1323	125	7	m3	m3	PROPN
cana-1323	125	8	,	,	PUNCT
cana-1323	125	9	m1	m1	PROPN
cana-1323	125	10	+	+	NUM
cana-1323	125	11	m2	m2	PROPN
cana-1323	125	12	=	=	PUNCT
cana-1323	125	13	χ(m4	χ(m4	NOUN
cana-1323	125	14	+	+	SYM
cana-1323	125	15	m5	m5	NOUN
cana-1323	125	16	)	)	PUNCT
cana-1323	125	17	&	&	CCONJ
cana-1323	125	18	m1𝛼m2𝛽m3	m1𝛼m2𝛽m3	NOUN
cana-1323	125	19	=	=	SYM
cana-1323	125	20	χ(m4𝛼m5𝛽m6	χ(m4𝛼m5𝛽m6	PROPN
cana-1323	125	21	)	)	PUNCT
cana-1323	125	22	.	.	PUNCT
cana-1323	126	1	𝛗w	𝛗w	PROPN
cana-1323	126	2	is	be	AUX
cana-1323	126	3	a	a	DET
cana-1323	126	4	𝝌−invariant	𝝌−invariant	NOUN
cana-1323	126	5	.	.	PUNCT
cana-1323	127	1	thus	thus	ADV
cana-1323	127	2	,	,	PUNCT
cana-1323	127	3	by	by	ADP
cana-1323	127	4	proposition	proposition	NOUN
cana-1323	127	5	3.8	3.8	NUM
cana-1323	127	6	,	,	PUNCT
cana-1323	127	7	we	we	PRON
cana-1323	127	8	have	have	VERB
cana-1323	127	9	:	:	PUNCT
cana-1323	127	10	1	1	NUM
cana-1323	127	11	.	.	NUM
cana-1323	127	12	νς(w)(m1	νς(w)(m1	NOUN
cana-1323	127	13	+	+	CCONJ
cana-1323	127	14	m2	m2	PROPN
cana-1323	127	15	)	)	PUNCT
cana-1323	128	1	=	=	PUNCT
cana-1323	128	2	𝛘(ν𝛗w)(m1	𝛘(ν𝛗w)(m1	NOUN
cana-1323	128	3	+	+	CCONJ
cana-1323	128	4	m2	m2	PROPN
cana-1323	128	5	)	)	PUNCT
cana-1323	128	6	=	=	SYM
cana-1323	128	7	ν𝛗w	ν𝛗w	PROPN
cana-1323	128	8	(	(	PUNCT
cana-1323	128	9	m4	m4	PROPN
cana-1323	128	10	+	+	CCONJ
cana-1323	128	11	m5	m5	NOUN
cana-1323	128	12	)	)	PUNCT
cana-1323	128	13	≥	≥	NOUN
cana-1323	128	14	min	min	PROPN
cana-1323	128	15	{	{	PUNCT
cana-1323	128	16	ν𝛗w(m4	ν𝛗w(m4	PROPN
cana-1323	128	17	)	)	PUNCT
cana-1323	128	18	,	,	PUNCT
cana-1323	128	19	ν𝛗w(m5	ν𝛗w(m5	PROPN
cana-1323	128	20	)	)	PUNCT
cana-1323	128	21	}	}	PUNCT
cana-1323	128	22	=	=	SYM
cana-1323	128	23	min	min	NOUN
cana-1323	128	24	{	{	PUNCT
cana-1323	128	25	𝛘(ν𝛗w)(m1	𝛘(ν𝛗w)(m1	PROPN
cana-1323	128	26	)	)	PUNCT
cana-1323	128	27	,	,	PUNCT
cana-1323	128	28	𝛘(ν𝛗w)(m2	𝛘(ν𝛗w)(m2	NUM
cana-1323	128	29	)	)	PUNCT
cana-1323	128	30	}	}	PUNCT
cana-1323	128	31	=	=	SYM
cana-1323	128	32	min	min	NOUN
cana-1323	128	33	{	{	PUNCT
cana-1323	128	34	νς(w	νς(w	NOUN
cana-1323	128	35	)	)	PUNCT
cana-1323	128	36	(	(	PUNCT
cana-1323	128	37	m1	m1	NOUN
cana-1323	128	38	)	)	PUNCT
cana-1323	128	39	,	,	PUNCT
cana-1323	128	40	νς(w	νς(w	VERB
cana-1323	128	41	)	)	PUNCT
cana-1323	128	42	(	(	PUNCT
cana-1323	128	43	m1	m1	NOUN
cana-1323	128	44	)	)	PUNCT
cana-1323	128	45	}	}	PUNCT
cana-1323	128	46	2	2	NUM
cana-1323	128	47	.	.	NUM
cana-1323	128	48	γς(w)(m1	γς(w)(m1	NOUN
cana-1323	128	49	+	+	CCONJ
cana-1323	128	50	m2	m2	NOUN
cana-1323	128	51	)	)	PUNCT
cana-1323	128	52	=	=	PUNCT
cana-1323	128	53	𝛘(γ𝛗w)(m1	𝛘(γ𝛗w)(m1	NOUN
cana-1323	128	54	+	+	CCONJ
cana-1323	128	55	m2	m2	PROPN
cana-1323	128	56	)	)	PUNCT
cana-1323	128	57	=	=	SYM
cana-1323	128	58	γ𝛗w	γ𝛗w	NOUN
cana-1323	128	59	(	(	PUNCT
cana-1323	128	60	m4	m4	PROPN
cana-1323	128	61	+	+	CCONJ
cana-1323	128	62	m5	m5	NOUN
cana-1323	128	63	)	)	PUNCT
cana-1323	128	64	≤	≤	NUM
cana-1323	128	65	max{γ𝛗w	max{γ𝛗w	NOUN
cana-1323	128	66	(	(	PUNCT
cana-1323	128	67	m4	m4	PROPN
cana-1323	128	68	)	)	PUNCT
cana-1323	128	69	,	,	PUNCT
cana-1323	128	70	γ𝛗w	γ𝛗w	NOUN
cana-1323	128	71	(	(	PUNCT
cana-1323	128	72	m5	m5	NOUN
cana-1323	128	73	)	)	PUNCT
cana-1323	128	74	}	}	PUNCT
cana-1323	128	75	=	=	SYM
cana-1323	128	76	max{𝛘(γ𝛗w)(m1	max{𝛘(γ𝛗w)(m1	NOUN
cana-1323	128	77	)	)	PUNCT
cana-1323	128	78	,	,	PUNCT
cana-1323	128	79	𝛘(γ𝛗w)(m2	𝛘(γ𝛗w)(m2	NOUN
cana-1323	128	80	)	)	PUNCT
cana-1323	128	81	}	}	PUNCT
cana-1323	128	82	=	=	SYM
cana-1323	128	83	max{γς(w)(m1	max{γς(w)(m1	NOUN
cana-1323	128	84	)	)	PUNCT
cana-1323	128	85	,	,	PUNCT
cana-1323	128	86	γς(w)(m2	γς(w)(m2	NUM
cana-1323	128	87	)	)	PUNCT
cana-1323	128	88	}	}	PUNCT
cana-1323	128	89	3	3	NUM
cana-1323	128	90	.	.	NOUN
cana-1323	128	91	βς(w)(m1	βς(w)(m1	NOUN
cana-1323	129	1	+	+	CCONJ
cana-1323	129	2	m2	m2	NOUN
cana-1323	129	3	)	)	PUNCT
cana-1323	129	4	=	=	PUNCT
cana-1323	129	5	𝛘(β𝛗w)(m1	𝛘(β𝛗w)(m1	PROPN
cana-1323	129	6	+	+	CCONJ
cana-1323	129	7	m2	m2	PROPN
cana-1323	129	8	)	)	PUNCT
cana-1323	129	9	=	=	SYM
cana-1323	129	10	β𝛗w	β𝛗w	PROPN
cana-1323	129	11	(	(	PUNCT
cana-1323	129	12	m4	m4	PROPN
cana-1323	129	13	+	+	CCONJ
cana-1323	129	14	m5	m5	NOUN
cana-1323	129	15	)	)	PUNCT
cana-1323	129	16	≤	≤	NUM
cana-1323	129	17	max{β𝛗w	max{β𝛗w	NOUN
cana-1323	129	18	(	(	PUNCT
cana-1323	129	19	m4	m4	PROPN
cana-1323	129	20	)	)	PUNCT
cana-1323	129	21	,	,	PUNCT
cana-1323	129	22	β𝛗w	β𝛗w	PROPN
cana-1323	129	23	(	(	PUNCT
cana-1323	129	24	m5	m5	PROPN
cana-1323	129	25	)	)	PUNCT
cana-1323	129	26	}	}	PUNCT
cana-1323	129	27	=	=	SYM
cana-1323	129	28	max{𝛘(β𝛗w)(m1	max{𝛘(β𝛗w)(m1	NOUN
cana-1323	129	29	)	)	PUNCT
cana-1323	129	30	,	,	PUNCT
cana-1323	129	31	𝛘(β𝛗w)(m2	𝛘(β𝛗w)(m2	NOUN
cana-1323	129	32	)	)	PUNCT
cana-1323	129	33	}	}	PUNCT
cana-1323	129	34	=	=	SYM
cana-1323	129	35	max{βς(w)(m1	max{βς(w)(m1	NOUN
cana-1323	129	36	)	)	PUNCT
cana-1323	129	37	,	,	PUNCT
cana-1323	129	38	βς(w)(m2	βς(w)(m2	NUM
cana-1323	129	39	)	)	PUNCT
cana-1323	129	40	}	}	PUNCT
cana-1323	129	41	4	4	NUM
cana-1323	129	42	.	.	PUNCT
cana-1323	130	1	νς(w)(m1𝛼m2𝛽m3	νς(w)(m1𝛼m2𝛽m3	PROPN
cana-1323	130	2	)	)	PUNCT
cana-1323	131	1	=	=	SYM
cana-1323	131	2	𝛘(ν𝛗w)(m1𝛼m2𝛽m3	𝛘(ν𝛗w)(m1𝛼m2𝛽m3	PROPN
cana-1323	131	3	)	)	PUNCT
cana-1323	131	4	=	=	SYM
cana-1323	131	5	ν𝛗w(𝜒(m4𝛼m5𝛽m6	ν𝛗w(𝜒(m4𝛼m5𝛽m6	ADJ
cana-1323	131	6	)	)	PUNCT
cana-1323	131	7	)	)	PUNCT
cana-1323	132	1	=	=	PUNCT
cana-1323	132	2	ν𝛗w(𝜒(m4)𝛼𝜒(m5)𝛽	ν𝛗w(𝜒(m4)𝛼𝜒(m5)𝛽	NUM
cana-1323	132	3	𝜒(m6	𝜒(m6	NOUN
cana-1323	132	4	)	)	PUNCT
cana-1323	132	5	)	)	PUNCT
cana-1323	132	6	≥	≥	NUM
cana-1323	133	1	ν𝛗w(𝜒(m4	ν𝛗w(𝜒(m4	PROPN
cana-1323	133	2	)	)	PUNCT
cana-1323	133	3	=	=	SYM
cana-1323	133	4	𝛘(ν𝛗w)(m1	𝛘(ν𝛗w)(m1	PROPN
cana-1323	133	5	)	)	PUNCT
cana-1323	133	6	=	=	PUNCT
cana-1323	133	7	νς(w	νς(w	NOUN
cana-1323	133	8	)	)	PUNCT
cana-1323	133	9	(	(	PUNCT
cana-1323	133	10	m1	m1	NOUN
cana-1323	133	11	)	)	PUNCT
cana-1323	133	12	.	.	PUNCT
cana-1323	134	1	5	5	X
cana-1323	134	2	.	.	X
cana-1323	134	3	γς(w)(m1𝛼m2𝛽m3	γς(w)(m1𝛼m2𝛽m3	PROPN
cana-1323	134	4	)	)	PUNCT
cana-1323	134	5	=	=	SYM
cana-1323	134	6	𝛘(γ𝛗w)(m1𝛼m2𝛽m3	𝛘(γ𝛗w)(m1𝛼m2𝛽m3	NOUN
cana-1323	134	7	)	)	PUNCT
cana-1323	134	8	=	=	SYM
cana-1323	134	9	γ𝛗w(𝜒(m4𝛼m5𝛽m6	γ𝛗w(𝜒(m4𝛼m5𝛽m6	NUM
cana-1323	134	10	)	)	PUNCT
cana-1323	134	11	)	)	PUNCT
cana-1323	134	12	communications	communication	NOUN
cana-1323	134	13	on	on	ADP
cana-1323	134	14	applied	apply	VERB
cana-1323	134	15	nonlinear	nonlinear	ADJ
cana-1323	134	16	analysis	analysis	NOUN
cana-1323	134	17	issn	issn	NOUN
cana-1323	134	18	:	:	PUNCT
cana-1323	134	19	1074	1074	NUM
cana-1323	134	20	-	-	PUNCT
cana-1323	134	21	133x	133x	NUM
cana-1323	134	22	vol	vol	NOUN
cana-1323	134	23	31	31	NUM
cana-1323	134	24	no	no	NOUN
cana-1323	134	25	.	.	PUNCT
cana-1323	135	1	7s	7	NOUN
cana-1323	135	2	(	(	PUNCT
cana-1323	135	3	2024	2024	NUM
cana-1323	135	4	)	)	PUNCT
cana-1323	135	5	449	449	NUM
cana-1323	135	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1323	135	7	=	=	PUNCT
cana-1323	135	8	γ𝛗w(𝜒(m4)𝛼𝜒(m5)𝛽	γ𝛗w(𝜒(m4)𝛼𝜒(m5)𝛽	X
cana-1323	135	9	𝜒(m6	𝜒(m6	NOUN
cana-1323	135	10	)	)	PUNCT
cana-1323	135	11	)	)	PUNCT
cana-1323	136	1	≤	≤	NUM
cana-1323	136	2	γ𝛗w(𝜒(m4	γ𝛗w(𝜒(m4	NOUN
cana-1323	136	3	)	)	PUNCT
cana-1323	136	4	=	=	SYM
cana-1323	136	5	𝛘(γ𝛗w)(m1	𝛘(γ𝛗w)(m1	NOUN
cana-1323	136	6	)	)	PUNCT
cana-1323	136	7	=	=	PUNCT
cana-1323	136	8	γς(w	γς(w	X
cana-1323	136	9	)	)	PUNCT
cana-1323	136	10	(	(	PUNCT
cana-1323	136	11	m1	m1	NOUN
cana-1323	136	12	)	)	PUNCT
cana-1323	136	13	.	.	PUNCT
cana-1323	137	1	6	6	X
cana-1323	137	2	.	.	X
cana-1323	137	3	βς(w)(m1𝛼m2𝛽m3	βς(w)(m1𝛼m2𝛽m3	NOUN
cana-1323	137	4	)	)	PUNCT
cana-1323	137	5	=	=	SYM
cana-1323	137	6	𝛘(β𝛗w)(m1𝛼m2𝛽m3	𝛘(β𝛗w)(m1𝛼m2𝛽m3	NUM
cana-1323	137	7	)	)	PUNCT
cana-1323	137	8	=	=	SYM
cana-1323	138	1	β𝛗w(𝜒(m4𝛼m5𝛽m6	β𝛗w(𝜒(m4𝛼m5𝛽m6	PROPN
cana-1323	138	2	)	)	PUNCT
cana-1323	138	3	)	)	PUNCT
cana-1323	139	1	=	=	SYM
cana-1323	139	2	β𝛗w(𝜒(m4)𝛼𝜒(m5)𝛽𝜒(m6	β𝛗w(𝜒(m4)𝛼𝜒(m5)𝛽𝜒(m6	NUM
cana-1323	139	3	)	)	PUNCT
cana-1323	139	4	)	)	PUNCT
cana-1323	139	5	≤	≤	NOUN
cana-1323	140	1	β𝛗w(𝜒(m4	β𝛗w(𝜒(m4	PROPN
cana-1323	140	2	)	)	PUNCT
cana-1323	140	3	=	=	SYM
cana-1323	140	4	𝛘(β𝛗w)(m1	𝛘(β𝛗w)(m1	PROPN
cana-1323	140	5	)	)	PUNCT
cana-1323	140	6	=	=	NOUN
cana-1323	140	7	βς(w	βς(w	NOUN
cana-1323	140	8	)	)	PUNCT
cana-1323	140	9	(	(	PUNCT
cana-1323	140	10	m1	m1	NOUN
cana-1323	140	11	)	)	PUNCT
cana-1323	140	12	.	.	PUNCT
cana-1323	141	1	then	then	ADV
cana-1323	141	2	δw	δw	INTJ
cana-1323	141	3	is	be	AUX
cana-1323	141	4	a	a	DET
cana-1323	141	5	tripolar	tripolar	ADJ
cana-1323	141	6	fuzzy	fuzzy	ADJ
cana-1323	141	7	ideal	ideal	NOUN
cana-1323	141	8	of	of	ADP
cana-1323	141	9	m2	m2	PROPN
cana-1323	141	10	.	.	PUNCT
cana-1323	142	1	hence	hence	ADV
cana-1323	142	2	(	(	PUNCT
cana-1323	142	3	δ	δ	PROPN
cana-1323	142	4	,	,	PUNCT
cana-1323	142	5	w	w	PROPN
cana-1323	142	6	,	,	PUNCT
cana-1323	142	7	𝚪	𝚪	NOUN
cana-1323	142	8	)	)	PUNCT
cana-1323	142	9	is	be	AUX
cana-1323	142	10	a	a	DET
cana-1323	142	11	tripolar	tripolar	ADJ
cana-1323	142	12	fuzzy	fuzzy	ADJ
cana-1323	142	13	soft	soft	ADJ
cana-1323	142	14	right	right	ADJ
cana-1323	142	15	ideal	ideal	NOUN
cana-1323	142	16	over	over	ADP
cana-1323	142	17	m2	m2	PROPN
cana-1323	142	18	.	.	PUNCT
cana-1323	142	19	theorem	theorem	VERB
cana-1323	142	20	3.10	3.10	NUM
cana-1323	142	21	:	:	PUNCT
cana-1323	142	22	if	if	SCONJ
cana-1323	142	23	(	(	PUNCT
cana-1323	142	24	𝛗1	𝛗1	NOUN
cana-1323	142	25	,	,	PUNCT
cana-1323	142	26	w1	w1	NOUN
cana-1323	142	27	,	,	PUNCT
cana-1323	142	28	𝚪	𝚪	PROPN
cana-1323	142	29	)	)	PUNCT
cana-1323	142	30	and	and	CCONJ
cana-1323	142	31	(	(	PUNCT
cana-1323	142	32	𝛗2	𝛗2	NOUN
cana-1323	142	33	,	,	PUNCT
cana-1323	142	34	w2	w2	NOUN
cana-1323	142	35	,	,	PUNCT
cana-1323	142	36	𝚪	𝚪	PROPN
cana-1323	142	37	)	)	PUNCT
cana-1323	142	38	are	be	AUX
cana-1323	142	39	two	two	NUM
cana-1323	142	40	bipolar	bipolar	ADJ
cana-1323	142	41	fstgsr	fstgsr	ADJ
cana-1323	142	42	over	over	ADP
cana-1323	142	43	m1	m1	PROPN
cana-1323	142	44	and	and	CCONJ
cana-1323	142	45	m2	m2	PROPN
cana-1323	142	46	respectively	respectively	ADV
cana-1323	142	47	,	,	PUNCT
cana-1323	142	48	and	and	CCONJ
cana-1323	142	49	(	(	PUNCT
cana-1323	142	50	𝛘	𝛘	X
cana-1323	142	51	,	,	PUNCT
cana-1323	142	52	ψ	ψ	NOUN
cana-1323	142	53	)	)	PUNCT
cana-1323	142	54	is	be	AUX
cana-1323	142	55	a	a	DET
cana-1323	142	56	tfstgsrh	tfstgsrh	NOUN
cana-1323	142	57	from	from	ADP
cana-1323	142	58	(	(	PUNCT
cana-1323	142	59	𝛗1	𝛗1	NOUN
cana-1323	142	60	,	,	PUNCT
cana-1323	142	61	w1	w1	NOUN
cana-1323	142	62	,	,	PUNCT
cana-1323	142	63	𝚪	𝚪	PROPN
cana-1323	142	64	)	)	PUNCT
cana-1323	142	65	onto	onto	ADP
cana-1323	142	66	(	(	PUNCT
cana-1323	142	67	𝛗2	𝛗2	NOUN
cana-1323	142	68	,	,	PUNCT
cana-1323	142	69	w2	w2	NOUN
cana-1323	142	70	,	,	PUNCT
cana-1323	142	71	𝚪	𝚪	PROPN
cana-1323	142	72	)	)	PUNCT
cana-1323	142	73	.	.	PUNCT
cana-1323	143	1	then	then	ADV
cana-1323	143	2	(	(	PUNCT
cana-1323	143	3	𝛘(𝛗1	𝛘(𝛗1	NOUN
cana-1323	143	4	)	)	PUNCT
cana-1323	143	5	,	,	PUNCT
cana-1323	143	6	m2	m2	PROPN
cana-1323	143	7	,	,	PUNCT
cana-1323	143	8	𝚪	𝚪	PROPN
cana-1323	143	9	)	)	PUNCT
cana-1323	143	10	is	be	AUX
cana-1323	143	11	a	a	DET
cana-1323	143	12	tfstgsr	tfstgsr	NOUN
cana-1323	143	13	over	over	ADP
cana-1323	143	14	m2	m2	PROPN
cana-1323	143	15	.	.	PUNCT
cana-1323	144	1	proof	proof	NOUN
cana-1323	144	2	:	:	PUNCT
cana-1323	144	3	by	by	ADP
cana-1323	144	4	definition	definition	NOUN
cana-1323	144	5	3.2	3.2	NUM
cana-1323	144	6	.	.	PUNCT
cana-1323	144	7	,	,	PUNCT
cana-1323	144	8	𝛘	𝛘	PROPN
cana-1323	144	9	is	be	AUX
cana-1323	144	10	a	a	DET
cana-1323	144	11	tgsrh	tgsrh	NOUN
cana-1323	144	12	from	from	ADP
cana-1323	144	13	m1	m1	PROPN
cana-1323	144	14	into	into	ADP
cana-1323	144	15	m2	m2	PROPN
cana-1323	144	16	and	and	CCONJ
cana-1323	144	17	ψ	ψ	PROPN
cana-1323	144	18	is	be	AUX
cana-1323	144	19	a	a	DET
cana-1323	144	20	mapping	mapping	NOUN
cana-1323	144	21	from	from	ADP
cana-1323	144	22	w1	w1	NOUN
cana-1323	144	23	into	into	ADP
cana-1323	144	24	w2	w2	NOUN
cana-1323	144	25	.	.	PUNCT
cana-1323	145	1	for	for	ADP
cana-1323	145	2	each	each	DET
cana-1323	145	3	w2	w2	NOUN
cana-1323	145	4	∈w2	∈w2	PROPN
cana-1323	145	5	∃	∃	PROPN
cana-1323	145	6	w1	w1	PROPN
cana-1323	145	7	∈w1	∈w1	PROPN
cana-1323	145	8	∋	∋	NOUN
cana-1323	145	9	ψ(w1	ψ(w1	PROPN
cana-1323	145	10	)	)	PUNCT
cana-1323	145	11	=	=	SYM
cana-1323	145	12	w2	w2	NOUN
cana-1323	145	13	.	.	PUNCT
cana-1323	146	1	define	define	VERB
cana-1323	146	2	2	2	NUM
cana-1323	146	3	(	(	PUNCT
cana-1323	146	4	(	(	PUNCT
cana-1323	146	5	)	)	PUNCT
cana-1323	146	6	)	)	PUNCT
cana-1323	146	7	w	w	VERB
cana-1323	146	8			NOUN
cana-1323	146	9	=	=	SYM
cana-1323	146	10	1	1	NUM
cana-1323	146	11	(	(	PUNCT
cana-1323	146	12	)	)	PUNCT
cana-1323	146	13	w	w	VERB
cana-1323	146	14			PROPN
cana-1323	146	15	.	.	PUNCT
cana-1323	147	1	if	if	SCONJ
cana-1323	147	2	m4	m4	PROPN
cana-1323	147	3	,	,	PUNCT
cana-1323	147	4	m5	m5	PROPN
cana-1323	147	5	,	,	PUNCT
cana-1323	147	6	m6	m6	PROPN
cana-1323	147	7	∈m2	∈m2	PROPN
cana-1323	147	8	,	,	PUNCT
cana-1323	147	9	𝛼	𝛼	X
cana-1323	147	10	,	,	PUNCT
cana-1323	147	11	𝜃	𝜃	X
cana-1323	147	12	∈γ	∈γ	NOUN
cana-1323	147	13	.	.	PUNCT
cana-1323	148	1	then	then	ADV
cana-1323	148	2	∃	∃	PROPN
cana-1323	148	3	m1	m1	PROPN
cana-1323	148	4	,	,	PUNCT
cana-1323	148	5	m2	m2	PROPN
cana-1323	148	6	,	,	PUNCT
cana-1323	148	7	m3	m3	PROPN
cana-1323	148	8	∈m1	∈m1	ADJ
cana-1323	148	9	∋	∋	NOUN
cana-1323	148	10	χ(m1	χ(m1	NOUN
cana-1323	148	11	)	)	PUNCT
cana-1323	148	12	=	=	SYM
cana-1323	148	13	m4	m4	PROPN
cana-1323	148	14	,	,	PUNCT
cana-1323	148	15	χ(m2	χ(m2	NOUN
cana-1323	148	16	)	)	PUNCT
cana-1323	148	17	=	=	SYM
cana-1323	148	18	m5	m5	NOUN
cana-1323	148	19	,	,	PUNCT
cana-1323	148	20	χ(m3	χ(m3	NOUN
cana-1323	148	21	)	)	PUNCT
cana-1323	148	22	=	=	SYM
cana-1323	148	23	m6	m6	PROPN
cana-1323	148	24	,	,	PUNCT
cana-1323	148	25	χ(m1	χ(m1	VERB
cana-1323	148	26	+	+	NUM
cana-1323	148	27	m2	m2	PROPN
cana-1323	148	28	)	)	PUNCT
cana-1323	148	29	=	=	PUNCT
cana-1323	148	30	m4	m4	PROPN
cana-1323	148	31	+	+	CCONJ
cana-1323	148	32	m5	m5	PROPN
cana-1323	148	33	&	&	CCONJ
cana-1323	148	34	χ(m1𝛼m2𝜃m3	χ(m1𝛼m2𝜃m3	PROPN
cana-1323	148	35	)	)	PUNCT
cana-1323	148	36	=	=	SYM
cana-1323	149	1	m4𝛼m5𝜃m6	m4𝛼m5𝜃m6	PROPN
cana-1323	149	2	.	.	PUNCT
cana-1323	150	1	thus	thus	ADV
cana-1323	150	2	,	,	PUNCT
cana-1323	150	3	we	we	PRON
cana-1323	150	4	get	get	VERB
cana-1323	150	5	1	1	NUM
cana-1323	150	6	.	.	NOUN
cana-1323	150	7	1	1	NUM
cana-1323	150	8	1	1	NUM
cana-1323	150	9	(	(	PUNCT
cana-1323	150	10	)	)	PUNCT
cana-1323	150	11	(	(	PUNCT
cana-1323	150	12	)	)	PUNCT
cana-1323	150	13	(	(	PUNCT
cana-1323	150	14	(	(	PUNCT
cana-1323	150	15	)	)	PUNCT
cana-1323	150	16	)	)	PUNCT
cana-1323	150	17	w	w	PUNCT
cana-1323	151	1			X
cana-1323	151	2			INTJ
cana-1323	151	3	(	(	PUNCT
cana-1323	151	4	m1	m1	PROPN
cana-1323	151	5	+	+	CCONJ
cana-1323	151	6	m2	m2	PROPN
cana-1323	151	7	)	)	PUNCT
cana-1323	151	8	=	=	SYM
cana-1323	151	9	1	1	NUM
cana-1323	151	10	(	(	PUNCT
cana-1323	151	11	)	)	PUNCT
cana-1323	151	12	1	1	NUM
cana-1323	151	13	(	(	PUNCT
cana-1323	151	14	(	(	PUNCT
cana-1323	151	15	(	(	PUNCT
cana-1323	151	16	)	)	PUNCT
cana-1323	151	17	)	)	PUNCT
cana-1323	151	18	w	w	PROPN
cana-1323	151	19			INTJ
cana-1323	151	20	(	(	PUNCT
cana-1323	151	21	m1	m1	PROPN
cana-1323	151	22	+	+	CCONJ
cana-1323	151	23	m2	m2	PROPN
cana-1323	151	24	)	)	PUNCT
cana-1323	151	25	=	=	SYM
cana-1323	151	26	1	1	NUM
cana-1323	151	27	(	(	PUNCT
cana-1323	151	28	)	)	PUNCT
cana-1323	151	29	1	1	NUM
cana-1323	151	30	(	(	PUNCT
cana-1323	151	31	)	)	PUNCT
cana-1323	151	32	w	w	PROPN
cana-1323	151	33	(	(	PUNCT
cana-1323	151	34	m4	m4	PROPN
cana-1323	151	35	+	+	CCONJ
cana-1323	151	36	m5	m5	NOUN
cana-1323	151	37	)	)	PUNCT
cana-1323	151	38	≥	≥	NOUN
cana-1323	151	39	min	min	NOUN
cana-1323	151	40	{	{	PUNCT
cana-1323	151	41	1	1	NUM
cana-1323	151	42	(	(	PUNCT
cana-1323	151	43	)	)	PUNCT
cana-1323	151	44	1	1	NUM
cana-1323	151	45	(	(	PUNCT
cana-1323	151	46	)	)	PUNCT
cana-1323	151	47	w	w	PROPN
cana-1323	151	48	(	(	PUNCT
cana-1323	151	49	m4	m4	PROPN
cana-1323	151	50	)	)	PUNCT
cana-1323	151	51	,	,	PUNCT
cana-1323	151	52	1	1	NUM
cana-1323	151	53	(	(	PUNCT
cana-1323	151	54	)	)	PUNCT
cana-1323	151	55	1	1	NUM
cana-1323	151	56	(	(	PUNCT
cana-1323	151	57	)	)	PUNCT
cana-1323	151	58	w	w	PROPN
cana-1323	151	59	(	(	PUNCT
cana-1323	151	60	m5	m5	NOUN
cana-1323	151	61	)	)	PUNCT
cana-1323	151	62	}	}	PUNCT
cana-1323	151	63	=	=	SYM
cana-1323	151	64	min	min	NOUN
cana-1323	151	65	{	{	PUNCT
cana-1323	151	66	1	1	NUM
cana-1323	151	67	(	(	PUNCT
cana-1323	151	68	)	)	PUNCT
cana-1323	151	69	1	1	NUM
cana-1323	151	70	(	(	PUNCT
cana-1323	151	71	(	(	PUNCT
cana-1323	151	72	(	(	PUNCT
cana-1323	151	73	)	)	PUNCT
cana-1323	151	74	)	)	PUNCT
cana-1323	151	75	w	w	PROPN
cana-1323	151	76			INTJ
cana-1323	151	77	(	(	PUNCT
cana-1323	151	78	m1	m1	NOUN
cana-1323	151	79	)	)	PUNCT
cana-1323	151	80	,	,	PUNCT
cana-1323	151	81	1	1	NUM
cana-1323	151	82	(	(	PUNCT
cana-1323	151	83	)	)	PUNCT
cana-1323	151	84	1	1	NUM
cana-1323	151	85	(	(	PUNCT
cana-1323	151	86	(	(	PUNCT
cana-1323	151	87	(	(	PUNCT
cana-1323	151	88	)	)	PUNCT
cana-1323	151	89	)	)	PUNCT
cana-1323	151	90	w	w	PROPN
cana-1323	151	91			NOUN
cana-1323	151	92	(	(	PUNCT
cana-1323	151	93	m2	m2	PROPN
cana-1323	151	94	)	)	PUNCT
cana-1323	151	95	}	}	PUNCT
cana-1323	151	96	=	=	SYM
cana-1323	151	97	min	min	NOUN
cana-1323	151	98	{	{	PUNCT
cana-1323	151	99	1	1	NUM
cana-1323	151	100	1	1	NUM
cana-1323	151	101	(	(	PUNCT
cana-1323	151	102	)	)	PUNCT
cana-1323	151	103	(	(	PUNCT
cana-1323	151	104	)	)	PUNCT
cana-1323	151	105	(	(	PUNCT
cana-1323	151	106	(	(	PUNCT
cana-1323	151	107	)	)	PUNCT
cana-1323	151	108	)	)	PUNCT
cana-1323	151	109	w	w	PUNCT
cana-1323	152	1			X
cana-1323	152	2			INTJ
cana-1323	152	3	(	(	PUNCT
cana-1323	152	4	m1	m1	NOUN
cana-1323	152	5	)	)	PUNCT
cana-1323	152	6	,	,	PUNCT
cana-1323	152	7	1	1	NUM
cana-1323	152	8	1	1	NUM
cana-1323	152	9	(	(	PUNCT
cana-1323	152	10	)	)	PUNCT
cana-1323	152	11	(	(	PUNCT
cana-1323	152	12	)	)	PUNCT
cana-1323	152	13	(	(	PUNCT
cana-1323	152	14	(	(	PUNCT
cana-1323	152	15	)	)	PUNCT
cana-1323	152	16	)	)	PUNCT
cana-1323	152	17	w	w	PUNCT
cana-1323	153	1			X
cana-1323	153	2			INTJ
cana-1323	153	3	(	(	PUNCT
cana-1323	153	4	m2	m2	PROPN
cana-1323	153	5	)	)	PUNCT
cana-1323	153	6	}	}	PUNCT
cana-1323	153	7	2	2	NUM
cana-1323	153	8	.	.	SYM
cana-1323	153	9	1	1	NUM
cana-1323	153	10	1	1	NUM
cana-1323	153	11	(	(	PUNCT
cana-1323	153	12	)	)	PUNCT
cana-1323	153	13	(	(	PUNCT
cana-1323	153	14	)	)	PUNCT
cana-1323	153	15	(	(	PUNCT
cana-1323	153	16	(	(	PUNCT
cana-1323	153	17	)	)	PUNCT
cana-1323	153	18	)	)	PUNCT
cana-1323	153	19	w	w	PROPN
cana-1323	154	1			PROPN
cana-1323	154	2	(	(	PUNCT
cana-1323	154	3	m1	m1	PROPN
cana-1323	154	4	+	+	CCONJ
cana-1323	154	5	m2	m2	PROPN
cana-1323	154	6	)	)	PUNCT
cana-1323	154	7	=	=	SYM
cana-1323	154	8	1	1	NUM
cana-1323	154	9	(	(	PUNCT
cana-1323	154	10	)	)	PUNCT
cana-1323	154	11	1	1	NUM
cana-1323	154	12	(	(	PUNCT
cana-1323	154	13	(	(	PUNCT
cana-1323	154	14	(	(	PUNCT
cana-1323	154	15	)	)	PUNCT
cana-1323	154	16	)	)	PUNCT
cana-1323	154	17	w	w	PROPN
cana-1323	154	18			NUM
cana-1323	154	19	(	(	PUNCT
cana-1323	154	20	m1	m1	PROPN
cana-1323	154	21	+	+	CCONJ
cana-1323	154	22	m2	m2	PROPN
cana-1323	154	23	)	)	PUNCT
cana-1323	154	24	=	=	SYM
cana-1323	154	25	1	1	NUM
cana-1323	154	26	(	(	PUNCT
cana-1323	154	27	)	)	PUNCT
cana-1323	154	28	1	1	NUM
cana-1323	154	29	(	(	PUNCT
cana-1323	154	30	)	)	PUNCT
cana-1323	154	31	w	w	NOUN
cana-1323	154	32	(	(	PUNCT
cana-1323	154	33	m4	m4	PROPN
cana-1323	154	34	+	+	CCONJ
cana-1323	154	35	m5	m5	NOUN
cana-1323	154	36	)	)	PUNCT
cana-1323	154	37	≤	≤	NUM
cana-1323	154	38	max	max	NOUN
cana-1323	154	39	{	{	PUNCT
cana-1323	154	40	1	1	NUM
cana-1323	154	41	(	(	PUNCT
cana-1323	154	42	)	)	PUNCT
cana-1323	154	43	1	1	NUM
cana-1323	154	44	(	(	PUNCT
cana-1323	154	45	)	)	PUNCT
cana-1323	154	46	w	w	NOUN
cana-1323	154	47	(	(	PUNCT
cana-1323	154	48	m4	m4	PROPN
cana-1323	154	49	)	)	PUNCT
cana-1323	154	50	,	,	PUNCT
cana-1323	154	51	1	1	NUM
cana-1323	154	52	(	(	PUNCT
cana-1323	154	53	)	)	PUNCT
cana-1323	154	54	1	1	NUM
cana-1323	154	55	(	(	PUNCT
cana-1323	154	56	)	)	PUNCT
cana-1323	154	57	w	w	NOUN
cana-1323	154	58	(	(	PUNCT
cana-1323	154	59	m5	m5	NOUN
cana-1323	154	60	)	)	PUNCT
cana-1323	154	61	}	}	PUNCT
cana-1323	154	62	=	=	SYM
cana-1323	154	63	max	max	X
cana-1323	154	64	{	{	PUNCT
cana-1323	154	65	1	1	NUM
cana-1323	154	66	(	(	PUNCT
cana-1323	154	67	)	)	PUNCT
cana-1323	154	68	1	1	NUM
cana-1323	154	69	(	(	PUNCT
cana-1323	154	70	(	(	PUNCT
cana-1323	154	71	(	(	PUNCT
cana-1323	154	72	)	)	PUNCT
cana-1323	154	73	)	)	PUNCT
cana-1323	154	74	w	w	PROPN
cana-1323	154	75			NUM
cana-1323	154	76	(	(	PUNCT
cana-1323	154	77	m1	m1	PROPN
cana-1323	154	78	)	)	PUNCT
cana-1323	154	79	,	,	PUNCT
cana-1323	154	80	1	1	NUM
cana-1323	154	81	(	(	PUNCT
cana-1323	154	82	)	)	PUNCT
cana-1323	154	83	1	1	NUM
cana-1323	154	84	(	(	PUNCT
cana-1323	154	85	(	(	PUNCT
cana-1323	154	86	(	(	PUNCT
cana-1323	154	87	)	)	PUNCT
cana-1323	154	88	)	)	PUNCT
cana-1323	154	89	w	w	PROPN
cana-1323	154	90			NUM
cana-1323	154	91	(	(	PUNCT
cana-1323	154	92	m2	m2	PROPN
cana-1323	154	93	)	)	PUNCT
cana-1323	154	94	}	}	PUNCT
cana-1323	154	95	=	=	SYM
cana-1323	154	96	max	max	X
cana-1323	154	97	{	{	PUNCT
cana-1323	154	98	1	1	NUM
cana-1323	154	99	1	1	NUM
cana-1323	154	100	(	(	PUNCT
cana-1323	154	101	)	)	PUNCT
cana-1323	154	102	(	(	PUNCT
cana-1323	154	103	)	)	PUNCT
cana-1323	154	104	(	(	PUNCT
cana-1323	154	105	(	(	PUNCT
cana-1323	154	106	)	)	PUNCT
cana-1323	154	107	)	)	PUNCT
cana-1323	154	108	w	w	PROPN
cana-1323	155	1			PROPN
cana-1323	155	2	(	(	PUNCT
cana-1323	155	3	m1	m1	PROPN
cana-1323	155	4	)	)	PUNCT
cana-1323	155	5	,	,	PUNCT
cana-1323	155	6	1	1	NUM
cana-1323	155	7	1	1	NUM
cana-1323	155	8	(	(	PUNCT
cana-1323	155	9	)	)	PUNCT
cana-1323	155	10	(	(	PUNCT
cana-1323	155	11	)	)	PUNCT
cana-1323	155	12	(	(	PUNCT
cana-1323	155	13	(	(	PUNCT
cana-1323	155	14	)	)	PUNCT
cana-1323	155	15	)	)	PUNCT
cana-1323	155	16	w	w	PROPN
cana-1323	156	1			PROPN
cana-1323	156	2	(	(	PUNCT
cana-1323	156	3	m2	m2	PROPN
cana-1323	156	4	)	)	PUNCT
cana-1323	156	5	}	}	PUNCT
cana-1323	156	6	3	3	NUM
cana-1323	156	7	.	.	NOUN
cana-1323	156	8	1	1	NUM
cana-1323	156	9	1	1	NUM
cana-1323	156	10	(	(	PUNCT
cana-1323	156	11	)	)	PUNCT
cana-1323	156	12	(	(	PUNCT
cana-1323	156	13	)	)	PUNCT
cana-1323	156	14	(	(	PUNCT
cana-1323	156	15	(	(	PUNCT
cana-1323	156	16	)	)	PUNCT
cana-1323	156	17	)	)	PUNCT
cana-1323	156	18	w	w	X
cana-1323	157	1			PROPN
cana-1323	157	2	(	(	PUNCT
cana-1323	157	3	m1	m1	PROPN
cana-1323	157	4	+	+	CCONJ
cana-1323	157	5	m2	m2	PROPN
cana-1323	157	6	)	)	PUNCT
cana-1323	157	7	=	=	SYM
cana-1323	157	8	1	1	NUM
cana-1323	157	9	(	(	PUNCT
cana-1323	157	10	)	)	PUNCT
cana-1323	157	11	1	1	NUM
cana-1323	157	12	(	(	PUNCT
cana-1323	157	13	(	(	PUNCT
cana-1323	157	14	(	(	PUNCT
cana-1323	157	15	)	)	PUNCT
cana-1323	157	16	)	)	PUNCT
cana-1323	157	17	w	w	PROPN
cana-1323	157	18			PROPN
cana-1323	157	19	(	(	PUNCT
cana-1323	157	20	m1	m1	PROPN
cana-1323	157	21	+	+	CCONJ
cana-1323	157	22	m2	m2	PROPN
cana-1323	157	23	)	)	PUNCT
cana-1323	157	24	=	=	SYM
cana-1323	157	25	1	1	NUM
cana-1323	157	26	(	(	PUNCT
cana-1323	157	27	)	)	PUNCT
cana-1323	157	28	1	1	NUM
cana-1323	157	29	(	(	PUNCT
cana-1323	157	30	)	)	PUNCT
cana-1323	157	31	w	w	X
cana-1323	157	32	(	(	PUNCT
cana-1323	157	33	m4	m4	PROPN
cana-1323	157	34	+	+	CCONJ
cana-1323	157	35	m5	m5	NOUN
cana-1323	157	36	)	)	PUNCT
cana-1323	157	37	≤	≤	NUM
cana-1323	157	38	max	max	NOUN
cana-1323	157	39	{	{	PUNCT
cana-1323	157	40	1	1	NUM
cana-1323	157	41	(	(	PUNCT
cana-1323	157	42	)	)	PUNCT
cana-1323	157	43	1	1	NUM
cana-1323	157	44	(	(	PUNCT
cana-1323	157	45	)	)	PUNCT
cana-1323	157	46	w	w	X
cana-1323	157	47	(	(	PUNCT
cana-1323	157	48	m4	m4	PROPN
cana-1323	157	49	)	)	PUNCT
cana-1323	157	50	,	,	PUNCT
cana-1323	157	51	1	1	NUM
cana-1323	157	52	(	(	PUNCT
cana-1323	157	53	)	)	PUNCT
cana-1323	157	54	1	1	NUM
cana-1323	157	55	(	(	PUNCT
cana-1323	157	56	)	)	PUNCT
cana-1323	157	57	w	w	X
cana-1323	157	58	(	(	PUNCT
cana-1323	157	59	m5	m5	PROPN
cana-1323	157	60	)	)	PUNCT
cana-1323	157	61	}	}	PUNCT
cana-1323	157	62	=	=	SYM
cana-1323	157	63	max	max	X
cana-1323	157	64	{	{	PUNCT
cana-1323	157	65	1	1	NUM
cana-1323	157	66	(	(	PUNCT
cana-1323	157	67	)	)	PUNCT
cana-1323	157	68	1	1	NUM
cana-1323	157	69	(	(	PUNCT
cana-1323	157	70	(	(	PUNCT
cana-1323	157	71	(	(	PUNCT
cana-1323	157	72	)	)	PUNCT
cana-1323	157	73	)	)	PUNCT
cana-1323	157	74	w	w	PROPN
cana-1323	157	75			PROPN
cana-1323	157	76	(	(	PUNCT
cana-1323	157	77	m1	m1	PROPN
cana-1323	157	78	)	)	PUNCT
cana-1323	157	79	,	,	PUNCT
cana-1323	157	80	1	1	NUM
cana-1323	157	81	(	(	PUNCT
cana-1323	157	82	)	)	PUNCT
cana-1323	157	83	1	1	NUM
cana-1323	157	84	(	(	PUNCT
cana-1323	157	85	(	(	PUNCT
cana-1323	157	86	(	(	PUNCT
cana-1323	157	87	)	)	PUNCT
cana-1323	157	88	)	)	PUNCT
cana-1323	157	89	w	w	PROPN
cana-1323	157	90			PROPN
cana-1323	157	91	(	(	PUNCT
cana-1323	157	92	m2	m2	PROPN
cana-1323	157	93	)	)	PUNCT
cana-1323	157	94	}	}	PUNCT
cana-1323	157	95	=	=	SYM
cana-1323	157	96	max	max	X
cana-1323	157	97	{	{	PUNCT
cana-1323	157	98	1	1	NUM
cana-1323	157	99	1	1	NUM
cana-1323	157	100	(	(	PUNCT
cana-1323	157	101	)	)	PUNCT
cana-1323	157	102	(	(	PUNCT
cana-1323	157	103	)	)	PUNCT
cana-1323	157	104	(	(	PUNCT
cana-1323	157	105	(	(	PUNCT
cana-1323	157	106	)	)	PUNCT
cana-1323	157	107	)	)	PUNCT
cana-1323	157	108	w	w	PUNCT
cana-1323	158	1			PRON
cana-1323	158	2			PROPN
cana-1323	158	3	(	(	PUNCT
cana-1323	158	4	m1	m1	PROPN
cana-1323	158	5	)	)	PUNCT
cana-1323	158	6	,	,	PUNCT
cana-1323	158	7	1	1	NUM
cana-1323	158	8	1	1	NUM
cana-1323	158	9	(	(	PUNCT
cana-1323	158	10	)	)	PUNCT
cana-1323	158	11	(	(	PUNCT
cana-1323	158	12	)	)	PUNCT
cana-1323	158	13	(	(	PUNCT
cana-1323	158	14	(	(	PUNCT
cana-1323	158	15	)	)	PUNCT
cana-1323	158	16	)	)	PUNCT
cana-1323	158	17	w	w	PUNCT
cana-1323	159	1			PRON
cana-1323	159	2			PROPN
cana-1323	159	3	(	(	PUNCT
cana-1323	159	4	m2	m2	PROPN
cana-1323	159	5	)	)	PUNCT
cana-1323	159	6	}	}	PUNCT
cana-1323	159	7	4	4	NUM
cana-1323	159	8	.	.	NOUN
cana-1323	159	9	1	1	NUM
cana-1323	159	10	1	1	NUM
cana-1323	159	11	(	(	PUNCT
cana-1323	159	12	)	)	PUNCT
cana-1323	159	13	(	(	PUNCT
cana-1323	159	14	)	)	PUNCT
cana-1323	159	15	(	(	PUNCT
cana-1323	159	16	(	(	PUNCT
cana-1323	159	17	)	)	PUNCT
cana-1323	159	18	)	)	PUNCT
cana-1323	159	19	w	w	PUNCT
cana-1323	160	1			INTJ
cana-1323	160	2			INTJ
cana-1323	160	3	(	(	PUNCT
cana-1323	160	4	m1𝛼m2𝜃m3	m1𝛼m2𝜃m3	NOUN
cana-1323	160	5	)	)	PUNCT
cana-1323	160	6	=	=	SYM
cana-1323	160	7	1	1	NUM
cana-1323	160	8	(	(	PUNCT
cana-1323	160	9	)	)	PUNCT
cana-1323	160	10	1	1	NUM
cana-1323	160	11	(	(	PUNCT
cana-1323	160	12	(	(	PUNCT
cana-1323	160	13	(	(	PUNCT
cana-1323	160	14	)	)	PUNCT
cana-1323	160	15	)	)	PUNCT
cana-1323	160	16	w	w	NOUN
cana-1323	160	17			INTJ
cana-1323	160	18	(	(	PUNCT
cana-1323	160	19	m1𝛼m2𝜃m3	m1𝛼m2𝜃m3	NOUN
cana-1323	160	20	)	)	PUNCT
cana-1323	160	21	=	=	SYM
cana-1323	160	22	1	1	NUM
cana-1323	160	23	(	(	PUNCT
cana-1323	160	24	)	)	PUNCT
cana-1323	160	25	1	1	NUM
cana-1323	160	26	(	(	PUNCT
cana-1323	160	27	)	)	PUNCT
cana-1323	160	28	w	w	PROPN
cana-1323	160	29	(	(	PUNCT
cana-1323	160	30	m4𝛼m5𝜃m6	m4𝛼m5𝜃m6	PROPN
cana-1323	160	31	)	)	PUNCT
cana-1323	160	32	≥	≥	PROPN
cana-1323	160	33	min	min	PROPN
cana-1323	160	34	{	{	PUNCT
cana-1323	160	35	1	1	NUM
cana-1323	160	36	(	(	PUNCT
cana-1323	160	37	)	)	PUNCT
cana-1323	160	38	1	1	NUM
cana-1323	160	39	(	(	PUNCT
cana-1323	160	40	)	)	PUNCT
cana-1323	160	41	w	w	PROPN
cana-1323	160	42	(	(	PUNCT
cana-1323	160	43	m4	m4	PROPN
cana-1323	160	44	)	)	PUNCT
cana-1323	160	45	,	,	PUNCT
cana-1323	160	46	1	1	NUM
cana-1323	160	47	(	(	PUNCT
cana-1323	160	48	)	)	PUNCT
cana-1323	160	49	1	1	NUM
cana-1323	160	50	(	(	PUNCT
cana-1323	160	51	)	)	PUNCT
cana-1323	160	52	w	w	PROPN
cana-1323	160	53	(	(	PUNCT
cana-1323	160	54	m5	m5	PROPN
cana-1323	160	55	)	)	PUNCT
cana-1323	160	56	,	,	PUNCT
cana-1323	160	57	1	1	NUM
cana-1323	160	58	(	(	PUNCT
cana-1323	160	59	)	)	PUNCT
cana-1323	160	60	1	1	NUM
cana-1323	160	61	(	(	PUNCT
cana-1323	160	62	)	)	PUNCT
cana-1323	160	63	w	w	PROPN
cana-1323	160	64	(	(	PUNCT
cana-1323	160	65	m6	m6	ADJ
cana-1323	160	66	)	)	PUNCT
cana-1323	160	67	}	}	PUNCT
cana-1323	160	68	=	=	SYM
cana-1323	160	69	min	min	NOUN
cana-1323	160	70	{	{	PUNCT
cana-1323	160	71	1	1	NUM
cana-1323	160	72	(	(	PUNCT
cana-1323	160	73	)	)	PUNCT
cana-1323	160	74	1	1	NUM
cana-1323	160	75	(	(	PUNCT
cana-1323	160	76	(	(	PUNCT
cana-1323	160	77	(	(	PUNCT
cana-1323	160	78	)	)	PUNCT
cana-1323	160	79	)	)	PUNCT
cana-1323	160	80	w	w	PROPN
cana-1323	160	81			INTJ
cana-1323	160	82	(	(	PUNCT
cana-1323	160	83	m1	m1	NOUN
cana-1323	160	84	)	)	PUNCT
cana-1323	160	85	,	,	PUNCT
cana-1323	160	86	1	1	NUM
cana-1323	160	87	(	(	PUNCT
cana-1323	160	88	)	)	PUNCT
cana-1323	160	89	1	1	NUM
cana-1323	160	90	(	(	PUNCT
cana-1323	160	91	(	(	PUNCT
cana-1323	160	92	(	(	PUNCT
cana-1323	160	93	)	)	PUNCT
cana-1323	160	94	)	)	PUNCT
cana-1323	160	95	w	w	PROPN
cana-1323	160	96			NOUN
cana-1323	160	97	(	(	PUNCT
cana-1323	160	98	m2	m2	PROPN
cana-1323	160	99	)	)	PUNCT
cana-1323	160	100	,	,	PUNCT
cana-1323	160	101	1	1	NUM
cana-1323	160	102	(	(	PUNCT
cana-1323	160	103	)	)	PUNCT
cana-1323	160	104	1	1	NUM
cana-1323	160	105	(	(	PUNCT
cana-1323	160	106	(	(	PUNCT
cana-1323	160	107	(	(	PUNCT
cana-1323	160	108	)	)	PUNCT
cana-1323	160	109	)	)	PUNCT
cana-1323	160	110	w	w	NOUN
cana-1323	160	111			NOUN
cana-1323	160	112	(	(	PUNCT
cana-1323	160	113	m3	m3	PROPN
cana-1323	160	114	)	)	PUNCT
cana-1323	160	115	}	}	PUNCT
cana-1323	160	116	=	=	SYM
cana-1323	160	117	min	min	NOUN
cana-1323	160	118	{	{	PUNCT
cana-1323	160	119	1	1	NUM
cana-1323	160	120	1	1	NUM
cana-1323	160	121	(	(	PUNCT
cana-1323	160	122	)	)	PUNCT
cana-1323	160	123	(	(	PUNCT
cana-1323	160	124	)	)	PUNCT
cana-1323	160	125	(	(	PUNCT
cana-1323	160	126	(	(	PUNCT
cana-1323	160	127	)	)	PUNCT
cana-1323	160	128	)	)	PUNCT
cana-1323	160	129	w	w	PUNCT
cana-1323	161	1			X
cana-1323	161	2			INTJ
cana-1323	161	3	(	(	PUNCT
cana-1323	161	4	m1	m1	NOUN
cana-1323	161	5	)	)	PUNCT
cana-1323	161	6	,	,	PUNCT
cana-1323	161	7	1	1	NUM
cana-1323	161	8	1	1	NUM
cana-1323	161	9	(	(	PUNCT
cana-1323	161	10	)	)	PUNCT
cana-1323	161	11	(	(	PUNCT
cana-1323	161	12	)	)	PUNCT
cana-1323	161	13	(	(	PUNCT
cana-1323	161	14	(	(	PUNCT
cana-1323	161	15	)	)	PUNCT
cana-1323	161	16	)	)	PUNCT
cana-1323	161	17	w	w	PUNCT
cana-1323	162	1			X
cana-1323	162	2			INTJ
cana-1323	162	3	(	(	PUNCT
cana-1323	162	4	m2	m2	PROPN
cana-1323	162	5	)	)	PUNCT
cana-1323	162	6	,	,	PUNCT
cana-1323	162	7	1	1	NUM
cana-1323	162	8	1	1	NUM
cana-1323	162	9	(	(	PUNCT
cana-1323	162	10	)	)	PUNCT
cana-1323	162	11	(	(	PUNCT
cana-1323	162	12	)	)	PUNCT
cana-1323	162	13	(	(	PUNCT
cana-1323	162	14	(	(	PUNCT
cana-1323	162	15	)	)	PUNCT
cana-1323	162	16	)	)	PUNCT
cana-1323	162	17	w	w	PUNCT
cana-1323	163	1			X
cana-1323	163	2			INTJ
cana-1323	163	3	(	(	PUNCT
cana-1323	163	4	m2	m2	PROPN
cana-1323	163	5	)	)	PUNCT
cana-1323	163	6	}	}	PUNCT
cana-1323	163	7	5	5	NUM
cana-1323	163	8	.	.	SYM
cana-1323	163	9	1	1	NUM
cana-1323	163	10	1	1	NUM
cana-1323	163	11	(	(	PUNCT
cana-1323	163	12	)	)	PUNCT
cana-1323	163	13	(	(	PUNCT
cana-1323	163	14	)	)	PUNCT
cana-1323	163	15	(	(	PUNCT
cana-1323	163	16	(	(	PUNCT
cana-1323	163	17	)	)	PUNCT
cana-1323	163	18	)	)	PUNCT
cana-1323	163	19	w	w	PROPN
cana-1323	164	1			PROPN
cana-1323	164	2	(	(	PUNCT
cana-1323	164	3	m1𝛼m2𝜃m3	m1𝛼m2𝜃m3	NOUN
cana-1323	164	4	)	)	PUNCT
cana-1323	164	5	=	=	SYM
cana-1323	164	6	1	1	NUM
cana-1323	164	7	(	(	PUNCT
cana-1323	164	8	)	)	PUNCT
cana-1323	164	9	1	1	NUM
cana-1323	164	10	(	(	PUNCT
cana-1323	164	11	(	(	PUNCT
cana-1323	164	12	(	(	PUNCT
cana-1323	164	13	)	)	PUNCT
cana-1323	164	14	)	)	PUNCT
cana-1323	164	15	w	w	PROPN
cana-1323	164	16			NUM
cana-1323	164	17	(	(	PUNCT
cana-1323	164	18	m1𝛼m2𝜃m3	m1𝛼m2𝜃m3	NOUN
cana-1323	164	19	)	)	PUNCT
cana-1323	164	20	=	=	SYM
cana-1323	164	21	1	1	NUM
cana-1323	164	22	(	(	PUNCT
cana-1323	164	23	)	)	PUNCT
cana-1323	164	24	1	1	NUM
cana-1323	164	25	(	(	PUNCT
cana-1323	164	26	)	)	PUNCT
cana-1323	164	27	w	w	NOUN
cana-1323	164	28	(	(	PUNCT
cana-1323	164	29	m4𝛼m5𝜃m6	m4𝛼m5𝜃m6	NUM
cana-1323	164	30	)	)	PUNCT
cana-1323	164	31	≤	≤	NOUN
cana-1323	164	32	max	max	NOUN
cana-1323	164	33	{	{	PUNCT
cana-1323	164	34	1	1	NUM
cana-1323	164	35	(	(	PUNCT
cana-1323	164	36	)	)	PUNCT
cana-1323	164	37	1	1	NUM
cana-1323	164	38	(	(	PUNCT
cana-1323	164	39	)	)	PUNCT
cana-1323	164	40	w	w	NOUN
cana-1323	164	41	(	(	PUNCT
cana-1323	164	42	m4	m4	PROPN
cana-1323	164	43	)	)	PUNCT
cana-1323	164	44	,	,	PUNCT
cana-1323	164	45	1	1	NUM
cana-1323	164	46	(	(	PUNCT
cana-1323	164	47	)	)	PUNCT
cana-1323	164	48	1	1	NUM
cana-1323	164	49	(	(	PUNCT
cana-1323	164	50	)	)	PUNCT
cana-1323	164	51	w	w	NOUN
cana-1323	164	52	(	(	PUNCT
cana-1323	164	53	m5	m5	PROPN
cana-1323	164	54	)	)	PUNCT
cana-1323	164	55	,	,	PUNCT
cana-1323	164	56	1	1	NUM
cana-1323	164	57	(	(	PUNCT
cana-1323	164	58	)	)	PUNCT
cana-1323	164	59	1	1	NUM
cana-1323	164	60	(	(	PUNCT
cana-1323	164	61	)	)	PUNCT
cana-1323	164	62	w	w	NOUN
cana-1323	164	63	(	(	PUNCT
cana-1323	164	64	m6	m6	ADJ
cana-1323	164	65	)	)	PUNCT
cana-1323	164	66	}	}	PUNCT
cana-1323	164	67	=	=	SYM
cana-1323	164	68	max	max	X
cana-1323	164	69	{	{	PUNCT
cana-1323	164	70	1	1	NUM
cana-1323	164	71	(	(	PUNCT
cana-1323	164	72	)	)	PUNCT
cana-1323	164	73	1	1	NUM
cana-1323	164	74	(	(	PUNCT
cana-1323	164	75	(	(	PUNCT
cana-1323	164	76	(	(	PUNCT
cana-1323	164	77	)	)	PUNCT
cana-1323	164	78	)	)	PUNCT
cana-1323	164	79	w	w	PROPN
cana-1323	164	80			NUM
cana-1323	164	81	(	(	PUNCT
cana-1323	164	82	m1	m1	PROPN
cana-1323	164	83	)	)	PUNCT
cana-1323	164	84	,	,	PUNCT
cana-1323	164	85	1	1	NUM
cana-1323	164	86	(	(	PUNCT
cana-1323	164	87	)	)	PUNCT
cana-1323	164	88	1	1	NUM
cana-1323	164	89	(	(	PUNCT
cana-1323	164	90	(	(	PUNCT
cana-1323	164	91	(	(	PUNCT
cana-1323	164	92	)	)	PUNCT
cana-1323	164	93	)	)	PUNCT
cana-1323	164	94	w	w	PROPN
cana-1323	164	95			NUM
cana-1323	164	96	(	(	PUNCT
cana-1323	164	97	m2	m2	PROPN
cana-1323	164	98	)	)	PUNCT
cana-1323	164	99	,	,	PUNCT
cana-1323	164	100	1	1	NUM
cana-1323	164	101	(	(	PUNCT
cana-1323	164	102	)	)	PUNCT
cana-1323	164	103	1	1	NUM
cana-1323	164	104	(	(	PUNCT
cana-1323	164	105	(	(	PUNCT
cana-1323	164	106	(	(	PUNCT
cana-1323	164	107	)	)	PUNCT
cana-1323	164	108	)	)	PUNCT
cana-1323	164	109	w	w	PROPN
cana-1323	164	110			NUM
cana-1323	164	111	(	(	PUNCT
cana-1323	164	112	m3	m3	PROPN
cana-1323	164	113	)	)	PUNCT
cana-1323	164	114	}	}	PUNCT
cana-1323	164	115	communications	communication	NOUN
cana-1323	164	116	on	on	ADP
cana-1323	164	117	applied	apply	VERB
cana-1323	164	118	nonlinear	nonlinear	ADJ
cana-1323	164	119	analysis	analysis	NOUN
cana-1323	164	120	issn	issn	NOUN
cana-1323	164	121	:	:	PUNCT
cana-1323	164	122	1074	1074	NUM
cana-1323	164	123	-	-	PUNCT
cana-1323	164	124	133x	133x	NUM
cana-1323	164	125	vol	vol	NOUN
cana-1323	164	126	31	31	NUM
cana-1323	164	127	no	no	NOUN
cana-1323	164	128	.	.	PUNCT
cana-1323	165	1	7s	7	NOUN
cana-1323	165	2	(	(	PUNCT
cana-1323	165	3	2024	2024	NUM
cana-1323	165	4	)	)	PUNCT
cana-1323	165	5	450	450	NUM
cana-1323	165	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1323	165	7	=	=	SYM
cana-1323	165	8	max	max	PROPN
cana-1323	165	9	{	{	PUNCT
cana-1323	165	10	1	1	NUM
cana-1323	165	11	1	1	NUM
cana-1323	165	12	(	(	PUNCT
cana-1323	165	13	)	)	PUNCT
cana-1323	165	14	(	(	PUNCT
cana-1323	165	15	)	)	PUNCT
cana-1323	165	16	(	(	PUNCT
cana-1323	165	17	(	(	PUNCT
cana-1323	165	18	)	)	PUNCT
cana-1323	165	19	)	)	PUNCT
cana-1323	165	20	w	w	PROPN
cana-1323	166	1			PROPN
cana-1323	166	2	(	(	PUNCT
cana-1323	166	3	m1	m1	PROPN
cana-1323	166	4	)	)	PUNCT
cana-1323	166	5	,	,	PUNCT
cana-1323	166	6	1	1	NUM
cana-1323	166	7	1	1	NUM
cana-1323	166	8	(	(	PUNCT
cana-1323	166	9	)	)	PUNCT
cana-1323	166	10	(	(	PUNCT
cana-1323	166	11	)	)	PUNCT
cana-1323	166	12	(	(	PUNCT
cana-1323	166	13	(	(	PUNCT
cana-1323	166	14	)	)	PUNCT
cana-1323	166	15	)	)	PUNCT
cana-1323	166	16	w	w	PROPN
cana-1323	167	1			PROPN
cana-1323	167	2	(	(	PUNCT
cana-1323	167	3	m2	m2	PROPN
cana-1323	167	4	)	)	PUNCT
cana-1323	167	5	,	,	PUNCT
cana-1323	167	6	1	1	NUM
cana-1323	167	7	1	1	NUM
cana-1323	167	8	(	(	PUNCT
cana-1323	167	9	)	)	PUNCT
cana-1323	167	10	(	(	PUNCT
cana-1323	167	11	)	)	PUNCT
cana-1323	167	12	(	(	PUNCT
cana-1323	167	13	(	(	PUNCT
cana-1323	167	14	)	)	PUNCT
cana-1323	167	15	)	)	PUNCT
cana-1323	167	16	w	w	PROPN
cana-1323	168	1			PROPN
cana-1323	168	2	(	(	PUNCT
cana-1323	168	3	m3	m3	PROPN
cana-1323	168	4	)	)	PUNCT
cana-1323	168	5	}	}	PUNCT
cana-1323	168	6	6	6	NUM
cana-1323	168	7	.	.	SYM
cana-1323	168	8	1	1	NUM
cana-1323	168	9	1	1	NUM
cana-1323	168	10	(	(	PUNCT
cana-1323	168	11	)	)	PUNCT
cana-1323	168	12	(	(	PUNCT
cana-1323	168	13	)	)	PUNCT
cana-1323	168	14	(	(	PUNCT
cana-1323	168	15	(	(	PUNCT
cana-1323	168	16	)	)	PUNCT
cana-1323	168	17	)	)	PUNCT
cana-1323	168	18	w	w	X
cana-1323	169	1			VERB
cana-1323	169	2	(	(	PUNCT
cana-1323	169	3	m1𝛼m2𝜃m3	m1𝛼m2𝜃m3	NOUN
cana-1323	169	4	)	)	PUNCT
cana-1323	169	5	=	=	SYM
cana-1323	169	6	1	1	NUM
cana-1323	169	7	(	(	PUNCT
cana-1323	169	8	)	)	PUNCT
cana-1323	169	9	1	1	NUM
cana-1323	169	10	(	(	PUNCT
cana-1323	169	11	(	(	PUNCT
cana-1323	169	12	(	(	PUNCT
cana-1323	169	13	)	)	PUNCT
cana-1323	169	14	)	)	PUNCT
cana-1323	170	1	w	w	PROPN
cana-1323	170	2			PROPN
cana-1323	170	3	(	(	PUNCT
cana-1323	170	4	m1𝛼m2𝜃m3	m1𝛼m2𝜃m3	NOUN
cana-1323	170	5	)	)	PUNCT
cana-1323	170	6	=	=	SYM
cana-1323	170	7	1	1	NUM
cana-1323	170	8	(	(	PUNCT
cana-1323	170	9	)	)	PUNCT
cana-1323	170	10	1	1	NUM
cana-1323	170	11	(	(	PUNCT
cana-1323	170	12	)	)	PUNCT
cana-1323	170	13	w	w	X
cana-1323	170	14	(	(	PUNCT
cana-1323	170	15	m4𝛼m5𝜃m6	m4𝛼m5𝜃m6	PROPN
cana-1323	170	16	)	)	PUNCT
cana-1323	170	17	≤	≤	NOUN
cana-1323	170	18	max	max	NOUN
cana-1323	170	19	{	{	PUNCT
cana-1323	170	20	1	1	NUM
cana-1323	170	21	(	(	PUNCT
cana-1323	170	22	)	)	PUNCT
cana-1323	170	23	1	1	NUM
cana-1323	170	24	(	(	PUNCT
cana-1323	170	25	)	)	PUNCT
cana-1323	170	26	w	w	X
cana-1323	170	27	(	(	PUNCT
cana-1323	170	28	m4	m4	PROPN
cana-1323	170	29	)	)	PUNCT
cana-1323	170	30	,	,	PUNCT
cana-1323	170	31	1	1	NUM
cana-1323	170	32	(	(	PUNCT
cana-1323	170	33	)	)	PUNCT
cana-1323	170	34	1	1	NUM
cana-1323	170	35	(	(	PUNCT
cana-1323	170	36	)	)	PUNCT
cana-1323	170	37	w	w	X
cana-1323	170	38	(	(	PUNCT
cana-1323	170	39	m5	m5	PROPN
cana-1323	170	40	)	)	PUNCT
cana-1323	170	41	,	,	PUNCT
cana-1323	170	42	1	1	NUM
cana-1323	170	43	(	(	PUNCT
cana-1323	170	44	)	)	PUNCT
cana-1323	170	45	1	1	NUM
cana-1323	170	46	(	(	PUNCT
cana-1323	170	47	)	)	PUNCT
cana-1323	170	48	w	w	X
cana-1323	170	49	(	(	PUNCT
cana-1323	170	50	m6	m6	ADJ
cana-1323	170	51	)	)	PUNCT
cana-1323	170	52	}	}	PUNCT
cana-1323	170	53	=	=	SYM
cana-1323	170	54	max	max	X
cana-1323	170	55	{	{	PUNCT
cana-1323	170	56	1	1	NUM
cana-1323	170	57	(	(	PUNCT
cana-1323	170	58	)	)	PUNCT
cana-1323	170	59	1	1	NUM
cana-1323	170	60	(	(	PUNCT
cana-1323	170	61	(	(	PUNCT
cana-1323	170	62	(	(	PUNCT
cana-1323	170	63	)	)	PUNCT
cana-1323	170	64	)	)	PUNCT
cana-1323	170	65	w	w	PROPN
cana-1323	170	66			PROPN
cana-1323	170	67	(	(	PUNCT
cana-1323	170	68	m1	m1	PROPN
cana-1323	170	69	)	)	PUNCT
cana-1323	170	70	,	,	PUNCT
cana-1323	170	71	1	1	NUM
cana-1323	170	72	(	(	PUNCT
cana-1323	170	73	)	)	PUNCT
cana-1323	170	74	1	1	NUM
cana-1323	170	75	(	(	PUNCT
cana-1323	170	76	(	(	PUNCT
cana-1323	170	77	(	(	PUNCT
cana-1323	170	78	)	)	PUNCT
cana-1323	170	79	)	)	PUNCT
cana-1323	170	80	w	w	PROPN
cana-1323	170	81			PROPN
cana-1323	170	82	(	(	PUNCT
cana-1323	170	83	m2	m2	PROPN
cana-1323	170	84	)	)	PUNCT
cana-1323	170	85	,	,	PUNCT
cana-1323	170	86	1	1	NUM
cana-1323	170	87	(	(	PUNCT
cana-1323	170	88	)	)	PUNCT
cana-1323	170	89	1	1	NUM
cana-1323	170	90	(	(	PUNCT
cana-1323	170	91	(	(	PUNCT
cana-1323	170	92	(	(	PUNCT
cana-1323	170	93	)	)	PUNCT
cana-1323	170	94	)	)	PUNCT
cana-1323	170	95	w	w	PROPN
cana-1323	170	96			PROPN
cana-1323	170	97	(	(	PUNCT
cana-1323	170	98	m6	m6	ADJ
cana-1323	170	99	)	)	PUNCT
cana-1323	170	100	}	}	PUNCT
cana-1323	170	101	=	=	SYM
cana-1323	170	102	max	max	X
cana-1323	170	103	{	{	PUNCT
cana-1323	170	104	1	1	NUM
cana-1323	170	105	1	1	NUM
cana-1323	170	106	(	(	PUNCT
cana-1323	170	107	)	)	PUNCT
cana-1323	170	108	(	(	PUNCT
cana-1323	170	109	)	)	PUNCT
cana-1323	170	110	(	(	PUNCT
cana-1323	170	111	(	(	PUNCT
cana-1323	170	112	)	)	PUNCT
cana-1323	170	113	)	)	PUNCT
cana-1323	170	114	w	w	PUNCT
cana-1323	171	1			PRON
cana-1323	171	2			PROPN
cana-1323	171	3	(	(	PUNCT
cana-1323	171	4	m1	m1	PROPN
cana-1323	171	5	)	)	PUNCT
cana-1323	171	6	,	,	PUNCT
cana-1323	171	7	1	1	NUM
cana-1323	171	8	1	1	NUM
cana-1323	171	9	(	(	PUNCT
cana-1323	171	10	)	)	PUNCT
cana-1323	171	11	(	(	PUNCT
cana-1323	171	12	)	)	PUNCT
cana-1323	171	13	(	(	PUNCT
cana-1323	171	14	(	(	PUNCT
cana-1323	171	15	)	)	PUNCT
cana-1323	171	16	)	)	PUNCT
cana-1323	171	17	w	w	PUNCT
cana-1323	172	1			PRON
cana-1323	172	2			PROPN
cana-1323	172	3	(	(	PUNCT
cana-1323	172	4	m2	m2	PROPN
cana-1323	172	5	)	)	PUNCT
cana-1323	172	6	,	,	PUNCT
cana-1323	172	7	1	1	NUM
cana-1323	172	8	1	1	NUM
cana-1323	172	9	(	(	PUNCT
cana-1323	172	10	)	)	PUNCT
cana-1323	172	11	(	(	PUNCT
cana-1323	172	12	)	)	PUNCT
cana-1323	172	13	(	(	PUNCT
cana-1323	172	14	(	(	PUNCT
cana-1323	172	15	)	)	PUNCT
cana-1323	172	16	)	)	PUNCT
cana-1323	172	17	w	w	PUNCT
cana-1323	173	1			PRON
cana-1323	173	2			PROPN
cana-1323	173	3	(	(	PUNCT
cana-1323	173	4	m3	m3	PROPN
cana-1323	173	5	)	)	PUNCT
cana-1323	173	6	}	}	PUNCT
cana-1323	173	7	then	then	ADV
cana-1323	173	8	2	2	NUM
cana-1323	173	9	(	(	PUNCT
cana-1323	173	10	(	(	PUNCT
cana-1323	173	11	)	)	PUNCT
cana-1323	173	12	)	)	PUNCT
cana-1323	173	13	w	w	NOUN
cana-1323	173	14			PROPN
cana-1323	173	15	is	be	AUX
cana-1323	173	16	a	a	DET
cana-1323	173	17	“	"	PUNCT
cana-1323	173	18	tripolar	tripolar	ADJ
cana-1323	173	19	fuzzy	fuzzy	ADJ
cana-1323	173	20	ternary	ternary	ADJ
cana-1323	173	21	γ−sub	γ−sub	NOUN
cana-1323	173	22	semiring	semire	VERB
cana-1323	173	23	”	"	PUNCT
cana-1323	173	24	of	of	ADP
cana-1323	173	25	m2	m2	PROPN
cana-1323	173	26	.	.	PUNCT
cana-1323	174	1	hence	hence	ADV
cana-1323	174	2	(	(	PUNCT
cana-1323	174	3	𝛘(𝛗1	𝛘(𝛗1	ADJ
cana-1323	174	4	)	)	PUNCT
cana-1323	174	5	,	,	PUNCT
cana-1323	174	6	m2	m2	PROPN
cana-1323	174	7	,	,	PUNCT
cana-1323	174	8	𝚪	𝚪	PROPN
cana-1323	174	9	)	)	PUNCT
cana-1323	174	10	is	be	AUX
cana-1323	174	11	a	a	DET
cana-1323	174	12	“	"	PUNCT
cana-1323	174	13	tripolar	tripolar	ADJ
cana-1323	174	14	fuzzy	fuzzy	ADJ
cana-1323	174	15	soft	soft	ADJ
cana-1323	174	16	ternary	ternary	ADJ
cana-1323	174	17	γ−semiring	γ−semiring	NOUN
cana-1323	174	18	”	"	PUNCT
cana-1323	174	19	over	over	ADP
cana-1323	174	20	m2	m2	PROPN
cana-1323	174	21	.	.	PUNCT
cana-1323	175	1	theorem	theorem	VERB
cana-1323	175	2	3.11	3.11	NUM
cana-1323	175	3	:	:	PUNCT
cana-1323	175	4	if	if	SCONJ
cana-1323	175	5	m1	m1	PROPN
cana-1323	175	6	and	and	CCONJ
cana-1323	175	7	m2	m2	PROPN
cana-1323	175	8	are	be	AUX
cana-1323	175	9	tgsrs	tgsrs	ADJ
cana-1323	175	10	,	,	PUNCT
cana-1323	175	11	𝛘	𝛘	X
cana-1323	175	12	:	:	PUNCT
cana-1323	175	13	m1	m1	PROPN
cana-1323	175	14	→	→	SYM
cana-1323	175	15	m2	m2	PROPN
cana-1323	175	16	is	be	AUX
cana-1323	175	17	a	a	DET
cana-1323	175	18	tgsrh	tgsrh	NOUN
cana-1323	175	19	,	,	PUNCT
cana-1323	175	20	(	(	PUNCT
cana-1323	175	21	𝛗1	𝛗1	NOUN
cana-1323	175	22	,	,	PUNCT
cana-1323	175	23	w1	w1	NOUN
cana-1323	175	24	,	,	PUNCT
cana-1323	175	25	𝚪	𝚪	PROPN
cana-1323	175	26	)	)	PUNCT
cana-1323	175	27	and	and	CCONJ
cana-1323	175	28	(	(	PUNCT
cana-1323	175	29	𝛗2	𝛗2	NOUN
cana-1323	175	30	,	,	PUNCT
cana-1323	175	31	w2	w2	NOUN
cana-1323	175	32	,	,	PUNCT
cana-1323	175	33	𝚪	𝚪	PROPN
cana-1323	175	34	)	)	PUNCT
cana-1323	175	35	are	be	AUX
cana-1323	175	36	tfstgsr	tfstgsr	VERB
cana-1323	175	37	over	over	ADP
cana-1323	175	38	m1	m1	PROPN
cana-1323	175	39	and	and	CCONJ
cana-1323	176	1	(	(	PUNCT
cana-1323	176	2	𝛗1	𝛗1	NOUN
cana-1323	176	3	,	,	PUNCT
cana-1323	176	4	w1	w1	NOUN
cana-1323	176	5	,	,	PUNCT
cana-1323	176	6	𝚪	𝚪	PROPN
cana-1323	176	7	)	)	PUNCT
cana-1323	176	8	is	be	AUX
cana-1323	176	9	a	a	DET
cana-1323	176	10	“	"	PUNCT
cana-1323	176	11	tripolar	tripolar	ADJ
cana-1323	176	12	fuzzy	fuzzy	ADJ
cana-1323	176	13	soft	soft	ADJ
cana-1323	176	14	ternary	ternary	ADJ
cana-1323	176	15	γ−sub	γ−sub	NOUN
cana-1323	176	16	semiring	semire	VERB
cana-1323	176	17	”	"	PUNCT
cana-1323	176	18	of	of	ADP
cana-1323	176	19	(	(	PUNCT
cana-1323	176	20	𝛗2	𝛗2	NOUN
cana-1323	176	21	,	,	PUNCT
cana-1323	176	22	w2	w2	NOUN
cana-1323	176	23	,	,	PUNCT
cana-1323	176	24	𝚪	𝚪	PROPN
cana-1323	176	25	)	)	PUNCT
cana-1323	176	26	.	.	PUNCT
cana-1323	177	1	then	then	ADV
cana-1323	177	2	(	(	PUNCT
cana-1323	177	3	𝛘(𝛗1	𝛘(𝛗1	ADJ
cana-1323	177	4	)	)	PUNCT
cana-1323	177	5	,	,	PUNCT
cana-1323	177	6	w1	w1	NOUN
cana-1323	177	7	,	,	PUNCT
cana-1323	177	8	𝚪	𝚪	PROPN
cana-1323	177	9	)	)	PUNCT
cana-1323	177	10	and	and	CCONJ
cana-1323	177	11	(	(	PUNCT
cana-1323	177	12	𝛘(𝛗2	𝛘(𝛗2	NOUN
cana-1323	177	13	)	)	PUNCT
cana-1323	177	14	,	,	PUNCT
cana-1323	177	15	w2	w2	NOUN
cana-1323	177	16	,	,	PUNCT
cana-1323	177	17	𝚪	𝚪	PROPN
cana-1323	177	18	)	)	PUNCT
cana-1323	177	19	are	be	AUX
cana-1323	177	20	“	"	PUNCT
cana-1323	177	21	tripolar	tripolar	ADJ
cana-1323	177	22	fuzzy	fuzzy	ADJ
cana-1323	177	23	soft	soft	ADJ
cana-1323	177	24	ternary	ternary	ADJ
cana-1323	177	25	γ−sub	γ−sub	NOUN
cana-1323	177	26	semirings	semiring	NOUN
cana-1323	177	27	”	"	PUNCT
cana-1323	177	28	over	over	ADP
cana-1323	177	29	m2	m2	PROPN
cana-1323	177	30	and	and	CCONJ
cana-1323	177	31	(	(	PUNCT
cana-1323	177	32	𝛘(𝛗1	𝛘(𝛗1	ADJ
cana-1323	177	33	)	)	PUNCT
cana-1323	177	34	,	,	PUNCT
cana-1323	177	35	w1	w1	NOUN
cana-1323	177	36	,	,	PUNCT
cana-1323	177	37	𝚪	𝚪	PROPN
cana-1323	177	38	)	)	PUNCT
cana-1323	177	39	is	be	AUX
cana-1323	177	40	a	a	DET
cana-1323	177	41	“	"	PUNCT
cana-1323	177	42	tripolar	tripolar	ADJ
cana-1323	177	43	fuzzy	fuzzy	ADJ
cana-1323	177	44	soft	soft	ADJ
cana-1323	177	45	ternary	ternary	ADJ
cana-1323	177	46	γ−sub	γ−sub	NOUN
cana-1323	177	47	semiring	semire	VERB
cana-1323	177	48	”	"	PUNCT
cana-1323	177	49	of	of	ADP
cana-1323	177	50	(	(	PUNCT
cana-1323	177	51	𝛘(𝛗2	𝛘(𝛗2	NOUN
cana-1323	177	52	)	)	PUNCT
cana-1323	177	53	,	,	PUNCT
cana-1323	177	54	w2	w2	NOUN
cana-1323	177	55	,	,	PUNCT
cana-1323	177	56	𝚪	𝚪	PROPN
cana-1323	177	57	)	)	PUNCT
cana-1323	177	58	.	.	PUNCT
cana-1323	178	1	proof	proof	NOUN
cana-1323	178	2	:	:	PUNCT
cana-1323	178	3	since	since	SCONJ
cana-1323	178	4	11	11	NUM
cana-1323	178	5	(	(	PUNCT
cana-1323	178	6	(	(	PUNCT
cana-1323	178	7	)	)	PUNCT
cana-1323	178	8	)	)	PUNCT
cana-1323	178	9	w	w	VERB
cana-1323	178	10			NOUN
cana-1323	178	11	=	=	SYM
cana-1323	178	12	1	1	NUM
cana-1323	178	13	1	1	NUM
cana-1323	178	14	(	(	PUNCT
cana-1323	178	15	(	(	PUNCT
cana-1323	178	16	(	(	PUNCT
cana-1323	178	17	)	)	PUNCT
cana-1323	178	18	)	)	PUNCT
cana-1323	178	19	w	w	NOUN
cana-1323	178	20			PROPN
cana-1323	178	21	is	be	AUX
cana-1323	178	22	a	a	DET
cana-1323	178	23	tripolar	tripolar	ADJ
cana-1323	178	24	fuzzy	fuzzy	ADJ
cana-1323	178	25	ternary	ternary	ADJ
cana-1323	178	26	γ	γ	X
cana-1323	178	27	-	-	PUNCT
cana-1323	178	28	sub	sub	ADJ
cana-1323	178	29	semiring	semiring	NOUN
cana-1323	178	30	of	of	ADP
cana-1323	178	31	m2	m2	PROPN
cana-1323	178	32	∀	∀	NOUN
cana-1323	178	33	w1	w1	PROPN
cana-1323	178	34	∈	∈	PROPN
cana-1323	178	35	w1	w1	NOUN
cana-1323	178	36	and	and	CCONJ
cana-1323	178	37	22	22	NUM
cana-1323	178	38	(	(	PUNCT
cana-1323	178	39	(	(	PUNCT
cana-1323	178	40	)	)	PUNCT
cana-1323	178	41	)	)	PUNCT
cana-1323	178	42	w	w	VERB
cana-1323	178	43			NOUN
cana-1323	178	44	=	=	SYM
cana-1323	178	45	2	2	NUM
cana-1323	178	46	2	2	NUM
cana-1323	178	47	(	(	PUNCT
cana-1323	178	48	(	(	PUNCT
cana-1323	178	49	(	(	PUNCT
cana-1323	178	50	)	)	PUNCT
cana-1323	178	51	)	)	PUNCT
cana-1323	179	1	w	w	NOUN
cana-1323	179	2			PROPN
cana-1323	179	3	is	be	AUX
cana-1323	179	4	a	a	DET
cana-1323	179	5	tripolar	tripolar	ADJ
cana-1323	179	6	fuzzy	fuzzy	ADJ
cana-1323	179	7	ternary	ternary	ADJ
cana-1323	179	8	γ−sub	γ−sub	NOUN
cana-1323	179	9	semiring	semire	VERB
cana-1323	179	10	of	of	ADP
cana-1323	179	11	m2	m2	PROPN
cana-1323	179	12	∀	∀	PROPN
cana-1323	179	13	w2	w2	PROPN
cana-1323	179	14	∈	∈	PROPN
cana-1323	179	15	w2	w2	NOUN
cana-1323	179	16	.	.	PUNCT
cana-1323	180	1	hence	hence	ADV
cana-1323	180	2	(	(	PUNCT
cana-1323	180	3	𝛘(𝛗1	𝛘(𝛗1	ADJ
cana-1323	180	4	)	)	PUNCT
cana-1323	180	5	,	,	PUNCT
cana-1323	180	6	w1	w1	NOUN
cana-1323	180	7	,	,	PUNCT
cana-1323	180	8	𝚪	𝚪	PROPN
cana-1323	180	9	)	)	PUNCT
cana-1323	180	10	and	and	CCONJ
cana-1323	180	11	(	(	PUNCT
cana-1323	180	12	𝛘(𝛗2	𝛘(𝛗2	NOUN
cana-1323	180	13	)	)	PUNCT
cana-1323	180	14	,	,	PUNCT
cana-1323	180	15	w2	w2	NOUN
cana-1323	180	16	,	,	PUNCT
cana-1323	180	17	𝚪	𝚪	PROPN
cana-1323	180	18	)	)	PUNCT
cana-1323	180	19	are	be	AUX
cana-1323	180	20	tripolar	tripolar	ADJ
cana-1323	180	21	fuzzy	fuzzy	ADJ
cana-1323	180	22	soft	soft	ADJ
cana-1323	180	23	ternary	ternary	NOUN
cana-1323	180	24	γ−semiring	γ−semire	VERB
cana-1323	180	25	over	over	ADP
cana-1323	180	26	m2	m2	PROPN
cana-1323	180	27	.	.	PUNCT
cana-1323	181	1	since	since	SCONJ
cana-1323	181	2	(	(	PUNCT
cana-1323	181	3	𝛗1	𝛗1	NOUN
cana-1323	181	4	,	,	PUNCT
cana-1323	181	5	w1	w1	NOUN
cana-1323	181	6	,	,	PUNCT
cana-1323	181	7	𝚪	𝚪	PROPN
cana-1323	181	8	)	)	PUNCT
cana-1323	181	9	is	be	AUX
cana-1323	181	10	a	a	DET
cana-1323	181	11	tripolar	tripolar	ADJ
cana-1323	181	12	fuzzy	fuzzy	ADJ
cana-1323	181	13	soft	soft	ADJ
cana-1323	181	14	ternary	ternary	ADJ
cana-1323	181	15	γ−sub	γ−sub	NOUN
cana-1323	181	16	semiring	semire	VERB
cana-1323	181	17	of	of	ADP
cana-1323	181	18	(	(	PUNCT
cana-1323	181	19	𝛗2	𝛗2	NOUN
cana-1323	181	20	,	,	PUNCT
cana-1323	181	21	w2	w2	NOUN
cana-1323	181	22	,	,	PUNCT
cana-1323	181	23	𝚪	𝚪	PROPN
cana-1323	181	24	)	)	PUNCT
cana-1323	181	25	.	.	PUNCT
cana-1323	182	1	11	11	NUM
cana-1323	182	2	(	(	PUNCT
cana-1323	182	3	)	)	PUNCT
cana-1323	182	4	w	w	PROPN
cana-1323	182	5	is	be	AUX
cana-1323	182	6	a	a	DET
cana-1323	182	7	tripolar	tripolar	ADJ
cana-1323	182	8	fuzzy	fuzzy	ADJ
cana-1323	182	9	ternary	ternary	ADJ
cana-1323	182	10	sub	sub	NOUN
cana-1323	182	11	semiring	semiring	NOUN
cana-1323	182	12	of	of	ADP
cana-1323	182	13	2	2	NUM
cana-1323	182	14	2	2	NUM
cana-1323	182	15	(	(	PUNCT
cana-1323	182	16	)	)	PUNCT
cana-1323	182	17	w	w	PROPN
cana-1323	182	18	.	.	PUNCT
cana-1323	183	1	hence	hence	ADV
cana-1323	183	2	1	1	NUM
cana-1323	183	3	1	1	NUM
cana-1323	183	4	(	(	PUNCT
cana-1323	183	5	(	(	PUNCT
cana-1323	183	6	(	(	PUNCT
cana-1323	183	7	)	)	PUNCT
cana-1323	183	8	)	)	PUNCT
cana-1323	183	9	w	w	NOUN
cana-1323	183	10			PROPN
cana-1323	183	11	is	be	AUX
cana-1323	183	12	a	a	DET
cana-1323	183	13	tripolar	tripolar	ADJ
cana-1323	183	14	fuzzy	fuzzy	ADJ
cana-1323	183	15	ternary	ternary	ADJ
cana-1323	183	16	γ−sub	γ−sub	NOUN
cana-1323	183	17	semiring	semire	VERB
cana-1323	183	18	of	of	ADP
cana-1323	183	19	2	2	NUM
cana-1323	183	20	2	2	NUM
cana-1323	183	21	(	(	PUNCT
cana-1323	183	22	(	(	PUNCT
cana-1323	183	23	(	(	PUNCT
cana-1323	183	24	)	)	PUNCT
cana-1323	183	25	)	)	PUNCT
cana-1323	183	26	w	w	VERB
cana-1323	183	27			PROPN
cana-1323	183	28	∀	∀	NOUN
cana-1323	183	29	w1	w1	NOUN
cana-1323	183	30	∈	∈	PROPN
cana-1323	183	31	w1	w1	NOUN
cana-1323	183	32	.	.	PUNCT
cana-1323	184	1	therefore	therefore	ADV
cana-1323	184	2	(	(	PUNCT
cana-1323	184	3	𝛘(𝛗1	𝛘(𝛗1	ADJ
cana-1323	184	4	)	)	PUNCT
cana-1323	184	5	,	,	PUNCT
cana-1323	184	6	w1	w1	NOUN
cana-1323	184	7	,	,	PUNCT
cana-1323	184	8	𝚪	𝚪	PROPN
cana-1323	184	9	)	)	PUNCT
cana-1323	184	10	is	be	AUX
cana-1323	184	11	a	a	DET
cana-1323	184	12	tripolar	tripolar	ADJ
cana-1323	184	13	fuzzy	fuzzy	ADJ
cana-1323	184	14	soft	soft	ADJ
cana-1323	184	15	ternary	ternary	ADJ
cana-1323	184	16	γ−sub	γ−sub	NOUN
cana-1323	184	17	semiring	semire	VERB
cana-1323	184	18	of	of	ADP
cana-1323	184	19	(	(	PUNCT
cana-1323	184	20	𝛘(𝛗2	𝛘(𝛗2	NOUN
cana-1323	184	21	)	)	PUNCT
cana-1323	184	22	,	,	PUNCT
cana-1323	184	23	w2	w2	NOUN
cana-1323	184	24	,	,	PUNCT
cana-1323	184	25	𝚪	𝚪	PROPN
cana-1323	184	26	)	)	PUNCT
cana-1323	184	27	.	.	PUNCT
cana-1323	185	1	theorem	theorem	VERB
cana-1323	185	2	3.12	3.12	NUM
cana-1323	185	3	:	:	PUNCT
cana-1323	185	4	if	if	SCONJ
cana-1323	185	5	(	(	PUNCT
cana-1323	185	6	𝛗1	𝛗1	NOUN
cana-1323	185	7	,	,	PUNCT
cana-1323	185	8	w1	w1	NOUN
cana-1323	185	9	,	,	PUNCT
cana-1323	185	10	𝚪	𝚪	PROPN
cana-1323	185	11	)	)	PUNCT
cana-1323	185	12	and	and	CCONJ
cana-1323	185	13	(	(	PUNCT
cana-1323	185	14	𝛗2	𝛗2	NOUN
cana-1323	185	15	,	,	PUNCT
cana-1323	185	16	w2	w2	NOUN
cana-1323	185	17	,	,	PUNCT
cana-1323	185	18	𝚪	𝚪	PROPN
cana-1323	185	19	)	)	PUNCT
cana-1323	185	20	are	be	AUX
cana-1323	185	21	tfstgsrs	tfstgsrs	ADJ
cana-1323	185	22	over	over	ADP
cana-1323	185	23	m1	m1	PROPN
cana-1323	185	24	and	and	CCONJ
cana-1323	185	25	m2	m2	PROPN
cana-1323	185	26	respectively	respectively	ADV
cana-1323	185	27	and	and	CCONJ
cana-1323	185	28	(	(	PUNCT
cana-1323	185	29	𝛘	𝛘	X
cana-1323	185	30	,	,	PUNCT
cana-1323	185	31	ψ	ψ	NOUN
cana-1323	185	32	)	)	PUNCT
cana-1323	185	33	is	be	AUX
cana-1323	185	34	a	a	DET
cana-1323	185	35	tfsh	tfsh	NOUN
cana-1323	185	36	from	from	ADP
cana-1323	185	37	(	(	PUNCT
cana-1323	185	38	𝛗1	𝛗1	NOUN
cana-1323	185	39	,	,	PUNCT
cana-1323	185	40	w1	w1	NOUN
cana-1323	185	41	,	,	PUNCT
cana-1323	185	42	𝚪	𝚪	PROPN
cana-1323	185	43	)	)	PUNCT
cana-1323	185	44	onto	onto	ADP
cana-1323	185	45	(	(	PUNCT
cana-1323	185	46	𝛗2	𝛗2	NOUN
cana-1323	185	47	,	,	PUNCT
cana-1323	185	48	w2	w2	NOUN
cana-1323	185	49	,	,	PUNCT
cana-1323	185	50	𝚪	𝚪	PROPN
cana-1323	185	51	)	)	PUNCT
cana-1323	185	52	.	.	PUNCT
cana-1323	186	1	then	then	ADV
cana-1323	186	2	the	the	DET
cana-1323	186	3	pre	pre	NOUN
cana-1323	186	4	-	-	NOUN
cana-1323	186	5	image	image	NOUN
cana-1323	186	6	of	of	ADP
cana-1323	186	7	(	(	PUNCT
cana-1323	186	8	𝛗2	𝛗2	NOUN
cana-1323	186	9	,	,	PUNCT
cana-1323	186	10	w2	w2	NOUN
cana-1323	186	11	,	,	PUNCT
cana-1323	186	12	𝚪	𝚪	PROPN
cana-1323	186	13	)	)	PUNCT
cana-1323	186	14	under	under	ADP
cana-1323	186	15	tfstgsrh	tfstgsrh	NOUN
cana-1323	186	16	is	be	AUX
cana-1323	186	17	a	a	DET
cana-1323	186	18	“	"	PUNCT
cana-1323	186	19	tripolar	tripolar	ADJ
cana-1323	186	20	fuzzy	fuzzy	ADJ
cana-1323	186	21	soft	soft	ADJ
cana-1323	186	22	ternary	ternary	ADJ
cana-1323	186	23	γ−sub	γ−sub	NOUN
cana-1323	186	24	semiring	semire	VERB
cana-1323	186	25	”	"	PUNCT
cana-1323	186	26	of	of	ADP
cana-1323	186	27	(	(	PUNCT
cana-1323	186	28	𝛗1	𝛗1	NOUN
cana-1323	186	29	,	,	PUNCT
cana-1323	186	30	w1	w1	NOUN
cana-1323	186	31	,	,	PUNCT
cana-1323	186	32	𝚪	𝚪	PROPN
cana-1323	186	33	)	)	PUNCT
cana-1323	186	34	over	over	ADP
cana-1323	186	35	m1	m1	NOUN
cana-1323	186	36	.	.	PUNCT
cana-1323	187	1	proof	proof	NOUN
cana-1323	187	2	:	:	PUNCT
cana-1323	187	3	by	by	ADP
cana-1323	187	4	definition	definition	NOUN
cana-1323	187	5	3.4	3.4	NUM
cana-1323	187	6	.	.	PUNCT
cana-1323	187	7	,	,	PUNCT
cana-1323	187	8	(	(	PUNCT
cana-1323	187	9	χ	χ	X
cana-1323	187	10	,	,	PUNCT
cana-1323	187	11	ψ	ψ	NOUN
cana-1323	187	12	)	)	PUNCT
cana-1323	187	13	-1	-1	PRON
cana-1323	187	14	(	(	PUNCT
cana-1323	187	15	φ2	φ2	PROPN
cana-1323	187	16	,	,	PUNCT
cana-1323	187	17	w2	w2	NOUN
cana-1323	187	18	,	,	PUNCT
cana-1323	187	19	γ	γ	NOUN
cana-1323	187	20	)	)	PUNCT
cana-1323	187	21	=	=	SYM
cana-1323	187	22	1	1	NUM
cana-1323	187	23	1	1	NUM
cana-1323	187	24	2	2	NUM
cana-1323	187	25	2	2	NUM
cana-1323	187	26	(	(	PUNCT
cana-1323	187	27	(	(	PUNCT
cana-1323	187	28	)	)	PUNCT
cana-1323	187	29	,	,	PUNCT
cana-1323	187	30	(	(	PUNCT
cana-1323	187	31	)	)	PUNCT
cana-1323	187	32	)	)	PUNCT
cana-1323	187	33	w	w	VERB
cana-1323	187	34			PROPN
cana-1323	187	35			PROPN
cana-1323	187	36			NOUN
cana-1323	187	37	.	.	PUNCT
cana-1323	188	1	define	define	VERB
cana-1323	188	2	1	1	NUM
cana-1323	188	3	1	1	NUM
cana-1323	188	4	2	2	NUM
cana-1323	188	5	1	1	NUM
cana-1323	188	6	(	(	PUNCT
cana-1323	188	7	(	(	PUNCT
cana-1323	188	8	)	)	PUNCT
cana-1323	188	9	)	)	PUNCT
cana-1323	189	1	(	(	PUNCT
cana-1323	189	2	)	)	PUNCT
cana-1323	189	3	w	w	NOUN
cana-1323	189	4	m	m	NOUN
cana-1323	189	5			NOUN
cana-1323	189	6	=	=	SYM
cana-1323	189	7	(	(	PUNCT
cana-1323	189	8	)	)	SYM
cana-1323	189	9	1	1	NUM
cana-1323	189	10	2	2	NUM
cana-1323	189	11	1	1	NUM
cana-1323	189	12	(	(	PUNCT
cana-1323	189	13	(	(	PUNCT
cana-1323	189	14	)	)	PUNCT
cana-1323	189	15	)	)	PUNCT
cana-1323	190	1	w	w	NOUN
cana-1323	190	2	m	m	VERB
cana-1323	190	3			NOUN
cana-1323	190	4			ADJ
cana-1323	190	5			NOUN
cana-1323	190	6	∀	∀	X
cana-1323	190	7	m1	m1	PROPN
cana-1323	190	8	∈m1	∈m1	PROPN
cana-1323	190	9	&	&	CCONJ
cana-1323	190	10	w1	w1	PROPN
cana-1323	190	11	∈	∈	PROPN
cana-1323	190	12	1	1	NUM
cana-1323	190	13	2	2	NUM
cana-1323	190	14	(	(	PUNCT
cana-1323	190	15	)	)	PUNCT
cana-1323	190	16	w	w	PROPN
cana-1323	191	1			NOUN
cana-1323	191	2	.	.	PUNCT
cana-1323	192	1	if	if	SCONJ
cana-1323	192	2	m1	m1	PROPN
cana-1323	192	3	,	,	PUNCT
cana-1323	192	4	m2	m2	PROPN
cana-1323	192	5	,	,	PUNCT
cana-1323	192	6	m3	m3	PROPN
cana-1323	192	7	∈m1	∈m1	PROPN
cana-1323	192	8	&	&	CCONJ
cana-1323	192	9	𝛼	𝛼	X
cana-1323	192	10	,	,	PUNCT
cana-1323	192	11	𝜃	𝜃	X
cana-1323	192	12	∈γ	∈γ	NOUN
cana-1323	192	13	.	.	PUNCT
cana-1323	193	1	then	then	ADV
cana-1323	193	2	1	1	NUM
cana-1323	193	3	.	.	SYM
cana-1323	193	4	2	2	NUM
cana-1323	193	5	1	1	NUM
cana-1323	193	6	1	1	NUM
cana-1323	193	7	1	1	NUM
cana-1323	193	8	2	2	NUM
cana-1323	193	9	(	(	PUNCT
cana-1323	193	10	(	(	PUNCT
cana-1323	193	11	)	)	PUNCT
cana-1323	193	12	)	)	PUNCT
cana-1323	193	13	(	(	PUNCT
cana-1323	193	14	)	)	PUNCT
cana-1323	193	15	w	w	NOUN
cana-1323	193	16	m	m	PROPN
cana-1323	193	17	m	m	NOUN
cana-1323	193	18			NOUN
cana-1323	193	19			PUNCT
cana-1323	193	20	=	=	SYM
cana-1323	193	21	2	2	NUM
cana-1323	193	22	1	1	NUM
cana-1323	193	23	(	(	PUNCT
cana-1323	193	24	)	)	PUNCT
cana-1323	193	25	1	1	NUM
cana-1323	193	26	2	2	NUM
cana-1323	193	27	(	(	PUNCT
cana-1323	193	28	(	(	PUNCT
cana-1323	193	29	)	)	PUNCT
cana-1323	193	30	)	)	PUNCT
cana-1323	193	31	w	w	PROPN
cana-1323	193	32	m	m	PROPN
cana-1323	193	33	m	m	NUM
cana-1323	194	1			PROPN
cana-1323	194	2			VERB
cana-1323	194	3			ADV
cana-1323	194	4	=	=	PUNCT
cana-1323	194	5	2	2	NUM
cana-1323	194	6	1	1	NUM
cana-1323	194	7	(	(	PUNCT
cana-1323	194	8	)	)	PUNCT
cana-1323	194	9	1	1	NUM
cana-1323	194	10	2	2	NUM
cana-1323	194	11	(	(	PUNCT
cana-1323	194	12	(	(	PUNCT
cana-1323	194	13	)	)	PUNCT
cana-1323	194	14	(	(	PUNCT
cana-1323	194	15	)	)	PUNCT
cana-1323	194	16	)	)	PUNCT
cana-1323	194	17	w	w	PROPN
cana-1323	194	18	m	m	PROPN
cana-1323	194	19	m	m	NOUN
cana-1323	194	20			PROPN
cana-1323	194	21			AUX
cana-1323	194	22			PROPN
cana-1323	194	23	≥	≥	NUM
cana-1323	194	24	min	min	PROPN
cana-1323	194	25	{	{	PUNCT
cana-1323	194	26	2	2	NUM
cana-1323	194	27	1	1	NUM
cana-1323	194	28	2	2	NUM
cana-1323	194	29	1	1	NUM
cana-1323	194	30	(	(	PUNCT
cana-1323	194	31	)	)	PUNCT
cana-1323	194	32	1	1	NUM
cana-1323	194	33	(	(	PUNCT
cana-1323	194	34	)	)	PUNCT
cana-1323	194	35	2	2	NUM
cana-1323	194	36	(	(	PUNCT
cana-1323	194	37	(	(	PUNCT
cana-1323	194	38	)	)	PUNCT
cana-1323	194	39	)	)	PUNCT
cana-1323	194	40	,	,	PUNCT
cana-1323	194	41	(	(	PUNCT
cana-1323	194	42	(	(	PUNCT
cana-1323	194	43	)	)	PUNCT
cana-1323	194	44	)	)	PUNCT
cana-1323	194	45	w	w	PROPN
cana-1323	194	46	wm	wm	PROPN
cana-1323	194	47	m	m	NUM
cana-1323	194	48			NOUN
cana-1323	194	49			PROPN
cana-1323	194	50			PROPN
cana-1323	194	51			VERB
cana-1323	194	52			ADJ
cana-1323	194	53			NOUN
cana-1323	194	54	}	}	PUNCT
cana-1323	194	55	=	=	SYM
cana-1323	194	56	min	min	NOUN
cana-1323	194	57	{	{	PUNCT
cana-1323	194	58	2	2	NUM
cana-1323	194	59	1	1	NUM
cana-1323	194	60	(	(	PUNCT
cana-1323	194	61	)	)	PUNCT
cana-1323	194	62			NOUN
cana-1323	194	63			NOUN
cana-1323	194	64	(	(	PUNCT
cana-1323	194	65	m1	m1	NOUN
cana-1323	194	66	)	)	PUNCT
cana-1323	194	67	,	,	PUNCT
cana-1323	194	68	2	2	NUM
cana-1323	194	69	1	1	NUM
cana-1323	194	70	(	(	PUNCT
cana-1323	194	71	)	)	PUNCT
cana-1323	194	72			NOUN
cana-1323	194	73			NOUN
cana-1323	194	74	(	(	PUNCT
cana-1323	194	75	m2	m2	PROPN
cana-1323	194	76	)	)	PUNCT
cana-1323	194	77	}	}	PUNCT
cana-1323	194	78	2	2	NUM
cana-1323	194	79	.	.	SYM
cana-1323	194	80	2	2	NUM
cana-1323	194	81	1	1	NUM
cana-1323	194	82	1	1	NUM
cana-1323	194	83	1	1	NUM
cana-1323	194	84	2	2	NUM
cana-1323	194	85	(	(	PUNCT
cana-1323	194	86	(	(	PUNCT
cana-1323	194	87	)	)	PUNCT
cana-1323	194	88	)	)	PUNCT
cana-1323	195	1	(	(	PUNCT
cana-1323	195	2	)	)	PUNCT
cana-1323	195	3	w	w	NOUN
cana-1323	195	4	m	m	PROPN
cana-1323	195	5	m	m	PROPN
cana-1323	195	6			PROPN
cana-1323	195	7			NOUN
cana-1323	195	8	=	=	PUNCT
cana-1323	195	9	2	2	NUM
cana-1323	195	10	1	1	NUM
cana-1323	195	11	(	(	PUNCT
cana-1323	195	12	)	)	PUNCT
cana-1323	195	13	1	1	NUM
cana-1323	195	14	2	2	NUM
cana-1323	195	15	(	(	PUNCT
cana-1323	195	16	(	(	PUNCT
cana-1323	195	17	)	)	PUNCT
cana-1323	195	18	)	)	PUNCT
cana-1323	195	19	w	w	PROPN
cana-1323	195	20	m	m	VERB
cana-1323	195	21	m	m	PRON
cana-1323	195	22			NOUN
cana-1323	195	23			VERB
cana-1323	195	24			ADV
cana-1323	196	1	=	=	PUNCT
cana-1323	197	1	2	2	NUM
cana-1323	197	2	1	1	NUM
cana-1323	197	3	(	(	PUNCT
cana-1323	197	4	)	)	PUNCT
cana-1323	197	5	1	1	NUM
cana-1323	197	6	2	2	NUM
cana-1323	197	7	(	(	PUNCT
cana-1323	197	8	(	(	PUNCT
cana-1323	197	9	)	)	PUNCT
cana-1323	197	10	(	(	PUNCT
cana-1323	197	11	)	)	PUNCT
cana-1323	197	12	)	)	PUNCT
cana-1323	197	13	w	w	PROPN
cana-1323	197	14	m	m	VERB
cana-1323	197	15	m	m	PRON
cana-1323	197	16			NOUN
cana-1323	197	17			AUX
cana-1323	197	18			PROPN
cana-1323	197	19	≤	≤	NUM
cana-1323	197	20	max	max	PROPN
cana-1323	197	21	{	{	PUNCT
cana-1323	197	22	2	2	NUM
cana-1323	197	23	1	1	NUM
cana-1323	197	24	2	2	NUM
cana-1323	197	25	1	1	NUM
cana-1323	197	26	(	(	PUNCT
cana-1323	197	27	)	)	PUNCT
cana-1323	197	28	1	1	NUM
cana-1323	197	29	(	(	PUNCT
cana-1323	197	30	)	)	PUNCT
cana-1323	197	31	2	2	NUM
cana-1323	197	32	(	(	PUNCT
cana-1323	197	33	(	(	PUNCT
cana-1323	197	34	)	)	PUNCT
cana-1323	197	35	)	)	PUNCT
cana-1323	197	36	,	,	PUNCT
cana-1323	197	37	(	(	PUNCT
cana-1323	197	38	(	(	PUNCT
cana-1323	197	39	)	)	PUNCT
cana-1323	197	40	)	)	PUNCT
cana-1323	198	1	w	w	PROPN
cana-1323	198	2	wm	wm	PROPN
cana-1323	198	3	m	m	NUM
cana-1323	198	4			NOUN
cana-1323	198	5			ADJ
cana-1323	198	6			NOUN
cana-1323	198	7			NOUN
cana-1323	198	8			NUM
cana-1323	198	9			VERB
cana-1323	198	10	}	}	PUNCT
cana-1323	198	11	=	=	SYM
cana-1323	198	12	max	max	X
cana-1323	198	13	{	{	PUNCT
cana-1323	198	14	2	2	NUM
cana-1323	198	15	1	1	NUM
cana-1323	198	16	(	(	PUNCT
cana-1323	198	17	)	)	PUNCT
cana-1323	198	18			PROPN
cana-1323	198	19			PROPN
cana-1323	198	20	(	(	PUNCT
cana-1323	198	21	m1	m1	PROPN
cana-1323	198	22	)	)	PUNCT
cana-1323	198	23	,	,	PUNCT
cana-1323	198	24	2	2	NUM
cana-1323	198	25	1	1	NUM
cana-1323	198	26	(	(	PUNCT
cana-1323	198	27	)	)	PUNCT
cana-1323	198	28			PROPN
cana-1323	198	29			PROPN
cana-1323	198	30	(	(	PUNCT
cana-1323	198	31	m2	m2	PROPN
cana-1323	198	32	)	)	PUNCT
cana-1323	198	33	}	}	PUNCT
cana-1323	198	34	3	3	NUM
cana-1323	198	35	.	.	SYM
cana-1323	198	36	2	2	NUM
cana-1323	198	37	1	1	NUM
cana-1323	198	38	1	1	NUM
cana-1323	198	39	1	1	NUM
cana-1323	198	40	2	2	NUM
cana-1323	198	41	(	(	PUNCT
cana-1323	198	42	(	(	PUNCT
cana-1323	198	43	)	)	PUNCT
cana-1323	198	44	)	)	PUNCT
cana-1323	198	45	(	(	PUNCT
cana-1323	198	46	)	)	PUNCT
cana-1323	198	47	w	w	NOUN
cana-1323	198	48	m	m	PROPN
cana-1323	198	49	m	m	PROPN
cana-1323	198	50			PROPN
cana-1323	198	51			ADV
cana-1323	198	52	=	=	PUNCT
cana-1323	198	53	2	2	NUM
cana-1323	198	54	1	1	NUM
cana-1323	198	55	(	(	PUNCT
cana-1323	198	56	)	)	PUNCT
cana-1323	198	57	1	1	NUM
cana-1323	198	58	2	2	NUM
cana-1323	198	59	(	(	PUNCT
cana-1323	198	60	(	(	PUNCT
cana-1323	198	61	)	)	PUNCT
cana-1323	198	62	)	)	PUNCT
cana-1323	198	63	w	w	PROPN
cana-1323	198	64	m	m	VERB
cana-1323	198	65	m	m	DET
cana-1323	199	1			ADJ
cana-1323	199	2			VERB
cana-1323	199	3			ADV
cana-1323	199	4	=	=	PUNCT
cana-1323	199	5	2	2	NUM
cana-1323	199	6	1	1	NUM
cana-1323	199	7	(	(	PUNCT
cana-1323	199	8	)	)	PUNCT
cana-1323	199	9	1	1	NUM
cana-1323	199	10	2	2	NUM
cana-1323	199	11	(	(	PUNCT
cana-1323	199	12	(	(	PUNCT
cana-1323	199	13	)	)	PUNCT
cana-1323	199	14	(	(	PUNCT
cana-1323	199	15	)	)	PUNCT
cana-1323	199	16	)	)	PUNCT
cana-1323	199	17	w	w	PROPN
cana-1323	199	18	m	m	VERB
cana-1323	199	19	m	m	PRON
cana-1323	199	20			ADJ
cana-1323	199	21			VERB
cana-1323	199	22			PROPN
cana-1323	199	23	≤	≤	NUM
cana-1323	199	24	max	max	PROPN
cana-1323	199	25	{	{	PUNCT
cana-1323	199	26	2	2	NUM
cana-1323	199	27	1	1	NUM
cana-1323	199	28	2	2	NUM
cana-1323	199	29	1	1	NUM
cana-1323	199	30	(	(	PUNCT
cana-1323	199	31	)	)	PUNCT
cana-1323	199	32	1	1	NUM
cana-1323	199	33	(	(	PUNCT
cana-1323	199	34	)	)	PUNCT
cana-1323	199	35	2	2	NUM
cana-1323	199	36	(	(	PUNCT
cana-1323	199	37	(	(	PUNCT
cana-1323	199	38	)	)	PUNCT
cana-1323	199	39	)	)	PUNCT
cana-1323	199	40	,	,	PUNCT
cana-1323	199	41	(	(	PUNCT
cana-1323	199	42	(	(	PUNCT
cana-1323	199	43	)	)	PUNCT
cana-1323	199	44	)	)	PUNCT
cana-1323	199	45	w	w	PROPN
cana-1323	199	46	wm	wm	PROPN
cana-1323	199	47	m	m	NUM
cana-1323	199	48			NOUN
cana-1323	199	49			PROPN
cana-1323	199	50			PROPN
cana-1323	199	51			NOUN
cana-1323	199	52			NOUN
cana-1323	199	53			NOUN
cana-1323	199	54	}	}	PUNCT
cana-1323	199	55	=	=	SYM
cana-1323	199	56	max	max	X
cana-1323	199	57	{	{	PUNCT
cana-1323	199	58	2	2	NUM
cana-1323	199	59	1	1	NUM
cana-1323	199	60	(	(	PUNCT
cana-1323	199	61	)	)	PUNCT
cana-1323	199	62			PROPN
cana-1323	199	63			PROPN
cana-1323	199	64	(	(	PUNCT
cana-1323	199	65	m1	m1	PROPN
cana-1323	199	66	)	)	PUNCT
cana-1323	199	67	,	,	PUNCT
cana-1323	199	68	2	2	NUM
cana-1323	199	69	1	1	NUM
cana-1323	199	70	(	(	PUNCT
cana-1323	199	71	)	)	PUNCT
cana-1323	199	72			PROPN
cana-1323	199	73			PROPN
cana-1323	199	74	(	(	PUNCT
cana-1323	199	75	m2	m2	PROPN
cana-1323	199	76	)	)	PUNCT
cana-1323	199	77	}	}	PUNCT
cana-1323	199	78	communications	communication	NOUN
cana-1323	199	79	on	on	ADP
cana-1323	199	80	applied	apply	VERB
cana-1323	199	81	nonlinear	nonlinear	ADJ
cana-1323	199	82	analysis	analysis	NOUN
cana-1323	199	83	issn	issn	NOUN
cana-1323	199	84	:	:	PUNCT
cana-1323	199	85	1074	1074	NUM
cana-1323	199	86	-	-	PUNCT
cana-1323	199	87	133x	133x	NUM
cana-1323	199	88	vol	vol	NOUN
cana-1323	199	89	31	31	NUM
cana-1323	199	90	no	no	NOUN
cana-1323	199	91	.	.	PUNCT
cana-1323	200	1	7s	7	NOUN
cana-1323	200	2	(	(	PUNCT
cana-1323	200	3	2024	2024	NUM
cana-1323	200	4	)	)	PUNCT
cana-1323	200	5	451	451	NUM
cana-1323	200	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1323	200	7	4	4	NUM
cana-1323	200	8	.	.	NOUN
cana-1323	200	9	2	2	NUM
cana-1323	200	10	1	1	NUM
cana-1323	200	11	2	2	NUM
cana-1323	200	12	1	1	NUM
cana-1323	200	13	1	1	NUM
cana-1323	200	14	3	3	NUM
cana-1323	200	15	(	(	PUNCT
cana-1323	200	16	(	(	PUNCT
cana-1323	200	17	)	)	PUNCT
cana-1323	200	18	)	)	PUNCT
cana-1323	201	1	(	(	PUNCT
cana-1323	201	2	)	)	PUNCT
cana-1323	201	3	w	w	NOUN
cana-1323	201	4	m	m	VERB
cana-1323	201	5	m	m	VERB
cana-1323	201	6	m	m	PROPN
cana-1323	201	7			ADJ
cana-1323	201	8			NOUN
cana-1323	201	9			NOUN
cana-1323	201	10	=	=	SYM
cana-1323	201	11	2	2	NUM
cana-1323	201	12	1	1	NUM
cana-1323	201	13	)	)	PUNCT
cana-1323	201	14	2	2	NUM
cana-1323	201	15	3	3	NUM
cana-1323	201	16	(	(	PUNCT
cana-1323	201	17	1	1	NUM
cana-1323	201	18	(	(	PUNCT
cana-1323	201	19	(	(	PUNCT
cana-1323	201	20	)	)	PUNCT
cana-1323	201	21	)	)	PUNCT
cana-1323	201	22	w	w	PROPN
cana-1323	202	1	m	m	VERB
cana-1323	202	2	m	m	VERB
cana-1323	202	3	m	m	NUM
cana-1323	202	4			PROPN
cana-1323	202	5			VERB
cana-1323	202	6			NOUN
cana-1323	202	7			X
cana-1323	202	8	=	=	SYM
cana-1323	202	9	2	2	NUM
cana-1323	202	10	1	1	NUM
cana-1323	202	11	(	(	PUNCT
cana-1323	202	12	)	)	PUNCT
cana-1323	202	13	1	1	NUM
cana-1323	202	14	2	2	NUM
cana-1323	202	15	3	3	NUM
cana-1323	202	16	(	(	PUNCT
cana-1323	202	17	(	(	PUNCT
cana-1323	202	18	)	)	PUNCT
cana-1323	202	19	(	(	PUNCT
cana-1323	202	20	)	)	PUNCT
cana-1323	202	21	(	(	PUNCT
cana-1323	202	22	)	)	PUNCT
cana-1323	202	23	)	)	PUNCT
cana-1323	203	1	w	w	PROPN
cana-1323	203	2	m	m	VERB
cana-1323	203	3	m	m	VERB
cana-1323	203	4	m	m	NOUN
cana-1323	203	5			PROPN
cana-1323	203	6			VERB
cana-1323	203	7			PROPN
cana-1323	203	8			PROPN
cana-1323	203	9	≥	≥	NUM
cana-1323	203	10	min	min	NOUN
cana-1323	203	11	{	{	PUNCT
cana-1323	203	12	2	2	NUM
cana-1323	203	13	1	1	NUM
cana-1323	203	14	2	2	NUM
cana-1323	203	15	1	1	NUM
cana-1323	203	16	2	2	NUM
cana-1323	203	17	1	1	NUM
cana-1323	203	18	(	(	PUNCT
cana-1323	203	19	)	)	PUNCT
cana-1323	203	20	1	1	NUM
cana-1323	203	21	(	(	PUNCT
cana-1323	203	22	)	)	PUNCT
cana-1323	203	23	2	2	NUM
cana-1323	203	24	(	(	PUNCT
cana-1323	203	25	)	)	PUNCT
cana-1323	203	26	3	3	NUM
cana-1323	203	27	(	(	PUNCT
cana-1323	203	28	(	(	PUNCT
cana-1323	203	29	)	)	PUNCT
cana-1323	203	30	)	)	PUNCT
cana-1323	203	31	,	,	PUNCT
cana-1323	203	32	(	(	PUNCT
cana-1323	203	33	(	(	PUNCT
cana-1323	203	34	)	)	PUNCT
cana-1323	203	35	,	,	PUNCT
cana-1323	203	36	(	(	PUNCT
cana-1323	203	37	(	(	PUNCT
cana-1323	203	38	)	)	PUNCT
cana-1323	203	39	)	)	PUNCT
cana-1323	204	1	w	w	PROPN
cana-1323	204	2	w	w	PROPN
cana-1323	204	3	wm	wm	PROPN
cana-1323	204	4	m	m	PROPN
cana-1323	204	5	m	m	NOUN
cana-1323	204	6			ADJ
cana-1323	204	7			ADJ
cana-1323	204	8			NOUN
cana-1323	204	9			PROPN
cana-1323	204	10			PROPN
cana-1323	204	11			VERB
cana-1323	204	12			ADJ
cana-1323	204	13			NOUN
cana-1323	204	14			ADJ
cana-1323	204	15			NOUN
cana-1323	204	16	}	}	PUNCT
cana-1323	204	17	=	=	SYM
cana-1323	204	18	min	min	NOUN
cana-1323	204	19	{	{	PUNCT
cana-1323	204	20	2	2	NUM
cana-1323	204	21	1	1	NUM
cana-1323	204	22	(	(	PUNCT
cana-1323	204	23	)	)	PUNCT
cana-1323	204	24			NOUN
cana-1323	204	25			NOUN
cana-1323	204	26	(	(	PUNCT
cana-1323	204	27	m1	m1	NOUN
cana-1323	204	28	)	)	PUNCT
cana-1323	204	29	,	,	PUNCT
cana-1323	204	30	2	2	NUM
cana-1323	204	31	1	1	NUM
cana-1323	204	32	(	(	PUNCT
cana-1323	204	33	)	)	PUNCT
cana-1323	204	34			NOUN
cana-1323	204	35			NOUN
cana-1323	204	36	(	(	PUNCT
cana-1323	204	37	m2	m2	PROPN
cana-1323	204	38	)	)	PUNCT
cana-1323	204	39	2	2	NUM
cana-1323	204	40	1	1	NUM
cana-1323	204	41	(	(	PUNCT
cana-1323	204	42	)	)	PUNCT
cana-1323	204	43			NOUN
cana-1323	204	44			NOUN
cana-1323	204	45	(	(	PUNCT
cana-1323	204	46	m3	m3	PROPN
cana-1323	204	47	)	)	PUNCT
cana-1323	204	48	}	}	PUNCT
cana-1323	204	49	5	5	NUM
cana-1323	204	50	.	.	SYM
cana-1323	204	51	2	2	NUM
cana-1323	204	52	1	1	NUM
cana-1323	204	53	2	2	NUM
cana-1323	204	54	1	1	NUM
cana-1323	204	55	1	1	NUM
cana-1323	204	56	3	3	NUM
cana-1323	204	57	(	(	PUNCT
cana-1323	204	58	(	(	PUNCT
cana-1323	204	59	)	)	PUNCT
cana-1323	204	60	)	)	PUNCT
cana-1323	205	1	(	(	PUNCT
cana-1323	205	2	)	)	PUNCT
cana-1323	205	3	w	w	NOUN
cana-1323	205	4	m	m	VERB
cana-1323	205	5	m	m	VERB
cana-1323	205	6	m	m	PROPN
cana-1323	205	7			NUM
cana-1323	205	8			NOUN
cana-1323	205	9			NOUN
cana-1323	205	10	=	=	SYM
cana-1323	205	11	2	2	NUM
cana-1323	205	12	1	1	NUM
cana-1323	205	13	)	)	PUNCT
cana-1323	205	14	2	2	NUM
cana-1323	205	15	3	3	NUM
cana-1323	205	16	(	(	PUNCT
cana-1323	205	17	1	1	NUM
cana-1323	205	18	(	(	PUNCT
cana-1323	205	19	(	(	PUNCT
cana-1323	205	20	)	)	PUNCT
cana-1323	205	21	)	)	PUNCT
cana-1323	206	1	w	w	PROPN
cana-1323	206	2	m	m	VERB
cana-1323	206	3	m	m	VERB
cana-1323	206	4	m	m	PRON
cana-1323	206	5			NOUN
cana-1323	206	6			VERB
cana-1323	206	7			NOUN
cana-1323	206	8			X
cana-1323	206	9	=	=	SYM
cana-1323	206	10	2	2	NUM
cana-1323	206	11	1	1	NUM
cana-1323	206	12	(	(	PUNCT
cana-1323	206	13	)	)	PUNCT
cana-1323	206	14	1	1	NUM
cana-1323	206	15	2	2	NUM
cana-1323	206	16	3	3	NUM
cana-1323	206	17	(	(	PUNCT
cana-1323	206	18	(	(	PUNCT
cana-1323	206	19	)	)	PUNCT
cana-1323	206	20	(	(	PUNCT
cana-1323	206	21	)	)	PUNCT
cana-1323	206	22	(	(	PUNCT
cana-1323	206	23	)	)	PUNCT
cana-1323	206	24	)	)	PUNCT
cana-1323	207	1	w	w	PROPN
cana-1323	207	2	m	m	VERB
cana-1323	207	3	m	m	VERB
cana-1323	207	4	m	m	PRON
cana-1323	207	5			NOUN
cana-1323	207	6			NOUN
cana-1323	207	7			PROPN
cana-1323	207	8			PROPN
cana-1323	207	9	≤	≤	NUM
cana-1323	207	10	max	max	PROPN
cana-1323	207	11	{	{	PUNCT
cana-1323	207	12	2	2	NUM
cana-1323	207	13	1	1	NUM
cana-1323	207	14	2	2	NUM
cana-1323	207	15	1	1	NUM
cana-1323	207	16	2	2	NUM
cana-1323	207	17	1	1	NUM
cana-1323	207	18	(	(	PUNCT
cana-1323	207	19	)	)	PUNCT
cana-1323	207	20	1	1	NUM
cana-1323	207	21	(	(	PUNCT
cana-1323	207	22	)	)	PUNCT
cana-1323	207	23	2	2	NUM
cana-1323	207	24	(	(	PUNCT
cana-1323	207	25	)	)	PUNCT
cana-1323	207	26	3	3	NUM
cana-1323	207	27	(	(	PUNCT
cana-1323	207	28	(	(	PUNCT
cana-1323	207	29	)	)	PUNCT
cana-1323	207	30	)	)	PUNCT
cana-1323	207	31	,	,	PUNCT
cana-1323	207	32	(	(	PUNCT
cana-1323	207	33	(	(	PUNCT
cana-1323	207	34	)	)	PUNCT
cana-1323	207	35	,	,	PUNCT
cana-1323	207	36	(	(	PUNCT
cana-1323	207	37	(	(	PUNCT
cana-1323	207	38	)	)	PUNCT
cana-1323	207	39	)	)	PUNCT
cana-1323	208	1	w	w	PROPN
cana-1323	208	2	w	w	PROPN
cana-1323	208	3	wm	wm	PROPN
cana-1323	208	4	m	m	PROPN
cana-1323	208	5	m	m	NOUN
cana-1323	208	6			NOUN
cana-1323	208	7			ADJ
cana-1323	208	8			ADJ
cana-1323	208	9			ADJ
cana-1323	208	10			NOUN
cana-1323	208	11			NOUN
cana-1323	208	12			NUM
cana-1323	208	13			VERB
cana-1323	208	14			NUM
cana-1323	208	15			VERB
cana-1323	208	16	}	}	PUNCT
cana-1323	208	17	=	=	SYM
cana-1323	208	18	max	max	X
cana-1323	208	19	{	{	PUNCT
cana-1323	208	20	2	2	NUM
cana-1323	208	21	1	1	NUM
cana-1323	208	22	(	(	PUNCT
cana-1323	208	23	)	)	PUNCT
cana-1323	208	24			PROPN
cana-1323	208	25			PROPN
cana-1323	208	26	(	(	PUNCT
cana-1323	208	27	m1	m1	PROPN
cana-1323	208	28	)	)	PUNCT
cana-1323	208	29	,	,	PUNCT
cana-1323	208	30	2	2	NUM
cana-1323	208	31	1	1	NUM
cana-1323	208	32	(	(	PUNCT
cana-1323	208	33	)	)	PUNCT
cana-1323	208	34			PROPN
cana-1323	208	35			PROPN
cana-1323	208	36	(	(	PUNCT
cana-1323	208	37	m2	m2	PROPN
cana-1323	208	38	)	)	PUNCT
cana-1323	208	39	2	2	NUM
cana-1323	208	40	1	1	NUM
cana-1323	208	41	(	(	PUNCT
cana-1323	208	42	)	)	PUNCT
cana-1323	208	43			PROPN
cana-1323	208	44			PROPN
cana-1323	208	45	(	(	PUNCT
cana-1323	208	46	m3	m3	PROPN
cana-1323	208	47	)	)	PUNCT
cana-1323	208	48	}	}	PUNCT
cana-1323	208	49	6	6	NUM
cana-1323	208	50	.	.	SYM
cana-1323	208	51	2	2	NUM
cana-1323	208	52	1	1	NUM
cana-1323	208	53	2	2	NUM
cana-1323	208	54	1	1	NUM
cana-1323	208	55	1	1	NUM
cana-1323	208	56	3	3	NUM
cana-1323	208	57	(	(	PUNCT
cana-1323	208	58	(	(	PUNCT
cana-1323	208	59	)	)	PUNCT
cana-1323	208	60	)	)	PUNCT
cana-1323	208	61	(	(	PUNCT
cana-1323	208	62	)	)	PUNCT
cana-1323	208	63	w	w	NOUN
cana-1323	208	64	m	m	VERB
cana-1323	208	65	m	m	VERB
cana-1323	208	66	m	m	PROPN
cana-1323	208	67			PROPN
cana-1323	208	68			NOUN
cana-1323	208	69			NOUN
cana-1323	208	70	=	=	SYM
cana-1323	208	71	2	2	NUM
cana-1323	208	72	1	1	NUM
cana-1323	208	73	)	)	PUNCT
cana-1323	208	74	2	2	NUM
cana-1323	208	75	3	3	NUM
cana-1323	208	76	(	(	PUNCT
cana-1323	208	77	1	1	NUM
cana-1323	208	78	(	(	PUNCT
cana-1323	208	79	(	(	PUNCT
cana-1323	208	80	)	)	PUNCT
cana-1323	208	81	)	)	PUNCT
cana-1323	209	1	w	w	PROPN
cana-1323	209	2	m	m	VERB
cana-1323	209	3	m	m	VERB
cana-1323	209	4	m	m	PRON
cana-1323	209	5			ADJ
cana-1323	209	6			VERB
cana-1323	209	7			NOUN
cana-1323	209	8			X
cana-1323	209	9	=	=	SYM
cana-1323	209	10	2	2	NUM
cana-1323	209	11	1	1	NUM
cana-1323	209	12	(	(	PUNCT
cana-1323	209	13	)	)	PUNCT
cana-1323	209	14	1	1	NUM
cana-1323	209	15	2	2	NUM
cana-1323	209	16	3	3	NUM
cana-1323	209	17	(	(	PUNCT
cana-1323	209	18	(	(	PUNCT
cana-1323	209	19	)	)	PUNCT
cana-1323	209	20	(	(	PUNCT
cana-1323	209	21	)	)	PUNCT
cana-1323	209	22	(	(	PUNCT
cana-1323	209	23	)	)	PUNCT
cana-1323	209	24	)	)	PUNCT
cana-1323	210	1	w	w	PROPN
cana-1323	210	2	m	m	VERB
cana-1323	210	3	m	m	VERB
cana-1323	210	4	m	m	PRON
cana-1323	210	5			ADJ
cana-1323	210	6			NOUN
cana-1323	210	7			PROPN
cana-1323	210	8			PROPN
cana-1323	210	9	≤	≤	NUM
cana-1323	210	10	max	max	PROPN
cana-1323	210	11	{	{	PUNCT
cana-1323	210	12	2	2	NUM
cana-1323	210	13	1	1	NUM
cana-1323	210	14	2	2	NUM
cana-1323	210	15	1	1	NUM
cana-1323	210	16	2	2	NUM
cana-1323	210	17	1	1	NUM
cana-1323	210	18	(	(	PUNCT
cana-1323	210	19	)	)	PUNCT
cana-1323	210	20	1	1	NUM
cana-1323	210	21	(	(	PUNCT
cana-1323	210	22	)	)	PUNCT
cana-1323	210	23	2	2	NUM
cana-1323	210	24	(	(	PUNCT
cana-1323	210	25	)	)	PUNCT
cana-1323	210	26	3	3	NUM
cana-1323	210	27	(	(	PUNCT
cana-1323	210	28	(	(	PUNCT
cana-1323	210	29	)	)	PUNCT
cana-1323	210	30	)	)	PUNCT
cana-1323	210	31	,	,	PUNCT
cana-1323	210	32	(	(	PUNCT
cana-1323	210	33	(	(	PUNCT
cana-1323	210	34	)	)	PUNCT
cana-1323	210	35	,	,	PUNCT
cana-1323	210	36	(	(	PUNCT
cana-1323	210	37	(	(	PUNCT
cana-1323	210	38	)	)	PUNCT
cana-1323	210	39	)	)	PUNCT
cana-1323	211	1	w	w	PROPN
cana-1323	211	2	w	w	PROPN
cana-1323	211	3	wm	wm	PROPN
cana-1323	211	4	m	m	PROPN
cana-1323	211	5	m	m	NOUN
cana-1323	211	6			ADJ
cana-1323	211	7			ADJ
cana-1323	211	8			NOUN
cana-1323	211	9			PROPN
cana-1323	211	10			PROPN
cana-1323	211	11			NOUN
cana-1323	211	12			NOUN
cana-1323	211	13			NOUN
cana-1323	211	14			NOUN
cana-1323	211	15			NOUN
cana-1323	211	16	}	}	PUNCT
cana-1323	211	17	=	=	SYM
cana-1323	211	18	max	max	X
cana-1323	211	19	{	{	PUNCT
cana-1323	211	20	2	2	NUM
cana-1323	211	21	1	1	NUM
cana-1323	211	22	(	(	PUNCT
cana-1323	211	23	)	)	PUNCT
cana-1323	211	24			PROPN
cana-1323	211	25			PROPN
cana-1323	211	26	(	(	PUNCT
cana-1323	211	27	m1	m1	PROPN
cana-1323	211	28	)	)	PUNCT
cana-1323	211	29	,	,	PUNCT
cana-1323	211	30	2	2	NUM
cana-1323	211	31	1	1	NUM
cana-1323	211	32	(	(	PUNCT
cana-1323	211	33	)	)	PUNCT
cana-1323	211	34			PROPN
cana-1323	211	35			PROPN
cana-1323	211	36	(	(	PUNCT
cana-1323	211	37	m2	m2	PROPN
cana-1323	211	38	)	)	PUNCT
cana-1323	211	39	2	2	NUM
cana-1323	211	40	1	1	NUM
cana-1323	211	41	(	(	PUNCT
cana-1323	211	42	)	)	PUNCT
cana-1323	211	43			PROPN
cana-1323	211	44			PROPN
cana-1323	211	45	(	(	PUNCT
cana-1323	211	46	m3	m3	PROPN
cana-1323	211	47	)	)	PUNCT
cana-1323	211	48	}	}	PUNCT
cana-1323	211	49	thus	thus	ADV
cana-1323	211	50	1	1	NUM
cana-1323	211	51	1	1	NUM
cana-1323	211	52	2	2	NUM
cana-1323	211	53	(	(	PUNCT
cana-1323	211	54	(	(	PUNCT
cana-1323	211	55	)	)	PUNCT
cana-1323	211	56	)	)	PUNCT
cana-1323	211	57	w	w	NOUN
cana-1323	211	58			NOUN
cana-1323	211	59	is	be	AUX
cana-1323	211	60	a	a	DET
cana-1323	211	61	“	"	PUNCT
cana-1323	211	62	tripolar	tripolar	ADJ
cana-1323	211	63	fuzzy	fuzzy	ADJ
cana-1323	211	64	ternary	ternary	ADJ
cana-1323	211	65	γ−sub	γ−sub	NOUN
cana-1323	211	66	semiring	semire	VERB
cana-1323	211	67	”	"	PUNCT
cana-1323	211	68	of	of	ADP
cana-1323	211	69	m1	m1	PROPN
cana-1323	211	70	∀	∀	X
cana-1323	211	71	w1	w1	NOUN
cana-1323	211	72	∈	∈	PROPN
cana-1323	211	73	1	1	NUM
cana-1323	211	74	2	2	NUM
cana-1323	211	75	(	(	PUNCT
cana-1323	211	76	)	)	PUNCT
cana-1323	211	77	w	w	PROPN
cana-1323	211	78			NOUN
cana-1323	211	79	.	.	PUNCT
cana-1323	212	1	∴	∴	NOUN
cana-1323	212	2	1	1	NUM
cana-1323	212	3	1	1	NUM
cana-1323	212	4	2	2	NUM
cana-1323	212	5	2	2	NUM
cana-1323	212	6	(	(	PUNCT
cana-1323	212	7	(	(	PUNCT
cana-1323	212	8	)	)	PUNCT
cana-1323	212	9	,	,	PUNCT
cana-1323	212	10	(	(	PUNCT
cana-1323	212	11	)	)	PUNCT
cana-1323	212	12	)	)	PUNCT
cana-1323	212	13	w	w	VERB
cana-1323	212	14			PROPN
cana-1323	212	15			PROPN
cana-1323	212	16			NOUN
cana-1323	212	17	is	be	AUX
cana-1323	212	18	a	a	DET
cana-1323	212	19	“	"	PUNCT
cana-1323	212	20	tripolar	tripolar	ADJ
cana-1323	212	21	fuzzy	fuzzy	ADJ
cana-1323	212	22	soft	soft	ADJ
cana-1323	212	23	ternary	ternary	ADJ
cana-1323	212	24	γ−sub	γ−sub	NOUN
cana-1323	212	25	semiring	semire	VERB
cana-1323	212	26	”	"	PUNCT
cana-1323	212	27	of	of	ADP
cana-1323	212	28	(	(	PUNCT
cana-1323	212	29	𝛗1	𝛗1	NOUN
cana-1323	212	30	,	,	PUNCT
cana-1323	212	31	w1	w1	NOUN
cana-1323	212	32	,	,	PUNCT
cana-1323	212	33	𝚪	𝚪	PROPN
cana-1323	212	34	)	)	PUNCT
cana-1323	212	35	over	over	ADP
cana-1323	212	36	m1	m1	PROPN
cana-1323	212	37	.	.	PUNCT
cana-1323	213	1	4	4	X
cana-1323	213	2	.	.	X
cana-1323	213	3	conclusion	conclusion	NOUN
cana-1323	213	4	:	:	PUNCT
cana-1323	213	5	here	here	ADV
cana-1323	213	6	,	,	PUNCT
cana-1323	213	7	we	we	PRON
cana-1323	213	8	investigate	investigate	VERB
cana-1323	213	9	the	the	DET
cana-1323	213	10	notion	notion	NOUN
cana-1323	213	11	of	of	ADP
cana-1323	213	12	tfstgsrh	tfstgsrh	NOUN
cana-1323	213	13	and	and	CCONJ
cana-1323	213	14	studied	study	VERB
cana-1323	213	15	some	some	DET
cana-1323	213	16	properties	property	NOUN
cana-1323	213	17	of	of	ADP
cana-1323	213	18	homomorphic	homomorphic	ADJ
cana-1323	213	19	image	image	NOUN
cana-1323	213	20	and	and	CCONJ
cana-1323	213	21	pre	pre	ADJ
cana-1323	213	22	image	image	NOUN
cana-1323	213	23	of	of	ADP
cana-1323	213	24	tfstgsr	tfstgsr	NOUN
cana-1323	213	25	.	.	PUNCT
cana-1323	214	1	these	these	DET
cana-1323	214	2	notions	notion	NOUN
cana-1323	214	3	are	be	AUX
cana-1323	214	4	basic	basic	ADJ
cana-1323	214	5	supporting	support	VERB
cana-1323	214	6	structures	structure	NOUN
cana-1323	214	7	for	for	ADP
cana-1323	214	8	development	development	NOUN
cana-1323	214	9	the	the	DET
cana-1323	214	10	structure	structure	NOUN
cana-1323	214	11	of	of	ADP
cana-1323	214	12	soft	soft	ADJ
cana-1323	214	13	set	set	NOUN
cana-1323	214	14	.	.	PUNCT
cana-1323	215	1	this	this	DET
cana-1323	215	2	work	work	NOUN
cana-1323	215	3	can	can	AUX
cana-1323	215	4	be	be	AUX
cana-1323	215	5	extended	extend	VERB
cana-1323	215	6	to	to	ADP
cana-1323	215	7	the	the	DET
cana-1323	215	8	properties	property	NOUN
cana-1323	215	9	of	of	ADP
cana-1323	215	10	different	different	ADJ
cana-1323	215	11	concepts	concept	NOUN
cana-1323	215	12	of	of	ADP
cana-1323	215	13	kernel	kernel	PROPN
cana-1323	215	14	of	of	ADP
cana-1323	215	15	tfstgsrh	tfstgsrh	PROPN
cana-1323	215	16	,	,	PUNCT
cana-1323	215	17	“	"	PUNCT
cana-1323	215	18	tripolar	tripolar	ADJ
cana-1323	215	19	fuzzy	fuzzy	ADJ
cana-1323	215	20	soft	soft	ADJ
cana-1323	215	21	filters	filter	NOUN
cana-1323	215	22	over	over	ADP
cana-1323	215	23	ternary	ternary	ADJ
cana-1323	215	24	γ	γ	PROPN
cana-1323	215	25	-	-	PUNCT
cana-1323	215	26	semirings	semiring	NOUN
cana-1323	215	27	”	"	PUNCT
cana-1323	215	28	.	.	PUNCT
cana-1323	216	1	acknowledgement	acknowledgement	NOUN
cana-1323	216	2	:	:	PUNCT
cana-1323	216	3	the	the	DET
cana-1323	216	4	authors	author	NOUN
cana-1323	216	5	are	be	AUX
cana-1323	216	6	very	very	ADV
cana-1323	216	7	thank	thank	VERB
cana-1323	216	8	full	full	ADJ
cana-1323	216	9	to	to	ADP
cana-1323	216	10	supporters	supporter	NOUN
cana-1323	216	11	to	to	PART
cana-1323	216	12	prepare	prepare	VERB
cana-1323	216	13	this	this	DET
cana-1323	216	14	paper	paper	NOUN
cana-1323	216	15	in	in	ADP
cana-1323	216	16	this	this	DET
cana-1323	216	17	manner	manner	NOUN
cana-1323	216	18	.	.	PUNCT
cana-1323	217	1	references	reference	NOUN
cana-1323	217	2	:	:	PUNCT
cana-1323	218	1	[	[	X
cana-1323	218	2	1	1	X
cana-1323	218	3	]	]	PUNCT
cana-1323	218	4	p.	p.	NOUN
cana-1323	218	5	k.	k.	PROPN
cana-1323	219	1	maji	maji	PROPN
cana-1323	219	2	.	.	PROPN
cana-1323	219	3	,	,	PUNCT
cana-1323	219	4	r.	r.	PROPN
cana-1323	219	5	biswas	biswas	PROPN
cana-1323	219	6	and	and	CCONJ
cana-1323	219	7	a.	a.	PROPN
cana-1323	219	8	r.	r.	PROPN
cana-1323	219	9	roy	roy	PROPN
cana-1323	219	10	.	.	PROPN
cana-1323	219	11	,	,	PUNCT
cana-1323	219	12	fuzzy	fuzzy	ADJ
cana-1323	219	13	soft	soft	ADJ
cana-1323	219	14	sets	set	NOUN
cana-1323	219	15	,	,	PUNCT
cana-1323	219	16	j.	j.	PROPN
cana-1323	219	17	of	of	ADP
cana-1323	219	18	fuzzy	fuzzy	ADJ
cana-1323	219	19	math	math	NOUN
cana-1323	219	20	.	.	PUNCT
cana-1323	219	21	,	,	PUNCT
cana-1323	219	22	9(2001	9(2001	X
cana-1323	219	23	)	)	PUNCT
cana-1323	220	1	pp	pp	ADJ
cana-1323	220	2	.	.	PUNCT
cana-1323	221	1	589	589	NUM
cana-1323	221	2	602	602	NUM
cana-1323	221	3	.	.	PUNCT
cana-1323	222	1	[	[	X
cana-1323	222	2	2	2	NUM
cana-1323	222	3	]	]	X
cana-1323	222	4	m.o	m.o	PROPN
cana-1323	222	5	.	.	PROPN
cana-1323	222	6	massa’deh	massa’deh	PROPN
cana-1323	222	7	.	.	PUNCT
cana-1323	222	8	,	,	PUNCT
cana-1323	222	9	on	on	ADP
cana-1323	222	10	bipolar	bipolar	ADJ
cana-1323	222	11	fuzzy	fuzzy	ADJ
cana-1323	222	12	cosets	coset	NOUN
cana-1323	222	13	,	,	PUNCT
cana-1323	222	14	bipolar	bipolar	ADJ
cana-1323	222	15	fuzzy	fuzzy	ADJ
cana-1323	222	16	ideals	ideal	NOUN
cana-1323	222	17	and	and	CCONJ
cana-1323	222	18	homomorphism	homomorphism	NOUN
cana-1323	222	19	of	of	ADP
cana-1323	222	20	γ−nearrings	γ−nearrings	PROPN
cana-1323	222	21	,	,	PUNCT
cana-1323	222	22	far	far	PROPN
cana-1323	222	23	east	east	PROPN
cana-1323	222	24	journal	journal	PROPN
cana-1323	222	25	of	of	ADP
cana-1323	222	26	mathematical	mathematical	ADJ
cana-1323	222	27	of	of	ADP
cana-1323	222	28	science	science	NOUN
cana-1323	222	29	,	,	PUNCT
cana-1323	222	30	102(4	102(4	NUM
cana-1323	222	31	)	)	PUNCT
cana-1323	222	32	,	,	PUNCT
cana-1323	222	33	(	(	PUNCT
cana-1323	222	34	2017	2017	NUM
cana-1323	222	35	)	)	PUNCT
cana-1323	222	36	,	,	PUNCT
cana-1323	222	37	163	163	NUM
cana-1323	222	38	-	-	SYM
cana-1323	222	39	178	178	NUM
cana-1323	222	40	.	.	PUNCT
cana-1323	223	1	[	[	X
cana-1323	223	2	3	3	X
cana-1323	223	3	]	]	PUNCT
cana-1323	223	4	m.	m.	NOUN
cana-1323	223	5	murali	murali	PROPN
cana-1323	223	6	krishna	krishna	PROPN
cana-1323	223	7	rao	rao	PROPN
cana-1323	223	8	.	.	PUNCT
cana-1323	223	9	,	,	PUNCT
cana-1323	223	10	fuzzy	fuzzy	ADJ
cana-1323	223	11	soft	soft	ADJ
cana-1323	223	12	ideal	ideal	ADJ
cana-1323	223	13	,	,	PUNCT
cana-1323	223	14	fuzzy	fuzzy	ADJ
cana-1323	223	15	soft	soft	ADJ
cana-1323	223	16	bi	bi	NOUN
cana-1323	223	17	-	-	ADJ
cana-1323	223	18	ideal	ideal	ADJ
cana-1323	223	19	,	,	PUNCT
cana-1323	223	20	fuzzy	fuzzy	ADJ
cana-1323	223	21	soft	soft	ADJ
cana-1323	223	22	quasi	quasi	ADJ
cana-1323	223	23	-	-	ADJ
cana-1323	223	24	ideal	ideal	ADJ
cana-1323	223	25	and	and	CCONJ
cana-1323	223	26	fuzzy	fuzzy	ADJ
cana-1323	223	27	soft	soft	ADJ
cana-1323	223	28	interior	interior	ADJ
cana-1323	223	29	ideal	ideal	NOUN
cana-1323	223	30	over	over	ADP
cana-1323	223	31	ordered	order	VERB
cana-1323	223	32	γ−semiring	γ−semiring	PROPN
cana-1323	223	33	,	,	PUNCT
cana-1323	223	34	asia	asia	PROPN
cana-1323	223	35	.	.	PUNCT
cana-1323	224	1	pac	pac	PROPN
cana-1323	224	2	.	.	PUNCT
cana-1323	225	1	j.	j.	PROPN
cana-1323	225	2	math	math	PROPN
cana-1323	225	3	.	.	PUNCT
cana-1323	225	4	,	,	PUNCT
cana-1323	225	5	5(2018	5(2018	NUM
cana-1323	225	6	)	)	PUNCT
cana-1323	226	1	pp	pp	ADV
cana-1323	226	2	.	.	PUNCT
cana-1323	227	1	60	60	NUM
cana-1323	227	2	-	-	SYM
cana-1323	227	3	81	81	NUM
cana-1323	227	4	.	.	PUNCT
cana-1323	228	1	[	[	X
cana-1323	228	2	4	4	NUM
cana-1323	228	3	]	]	PUNCT
cana-1323	228	4	m.	m.	NOUN
cana-1323	228	5	murali	murali	PROPN
cana-1323	228	6	krishna	krishna	PROPN
cana-1323	228	7	rao	rao	PROPN
cana-1323	228	8	.	.	PROPN
cana-1323	228	9	,	,	PUNCT
cana-1323	228	10	γ−semirings	γ−semirings	X
cana-1323	228	11	-	-	PUNCT
cana-1323	228	12	i	i	PRON
cana-1323	228	13	,	,	PUNCT
cana-1323	228	14	southeast	southeast	ADJ
cana-1323	228	15	asian	asian	ADJ
cana-1323	228	16	bull	bull	NOUN
cana-1323	228	17	.	.	PUNCT
cana-1323	229	1	math	math	NOUN
cana-1323	229	2	,	,	PUNCT
cana-1323	229	3	19(1	19(1	NUM
cana-1323	229	4	)	)	PUNCT
cana-1323	229	5	(	(	PUNCT
cana-1323	229	6	1995	1995	NUM
cana-1323	229	7	)	)	PUNCT
cana-1323	229	8	49	49	NUM
cana-1323	229	9	–	–	PUNCT
cana-1323	229	10	54	54	NUM
cana-1323	229	11	.	.	PUNCT
cana-1323	230	1	[	[	X
cana-1323	230	2	5	5	NUM
cana-1323	230	3	]	]	PUNCT
cana-1323	230	4	m.	m.	NOUN
cana-1323	230	5	murali	murali	PROPN
cana-1323	230	6	krishna	krishna	PROPN
cana-1323	230	7	rao	rao	PROPN
cana-1323	230	8	,	,	PUNCT
cana-1323	230	9	b.venkateswarulu	b.venkateswarulu	PROPN
cana-1323	230	10	.	.	PUNCT
cana-1323	231	1	and	and	CCONJ
cana-1323	231	2	y.	y.	PROPN
cana-1323	231	3	adi	adi	PROPN
cana-1323	231	4	narayana	narayana	PROPN
cana-1323	231	5	,	,	PUNCT
cana-1323	231	6	tripolar	tripolar	ADJ
cana-1323	231	7	fuzzy	fuzzy	ADJ
cana-1323	231	8	soft	soft	ADJ
cana-1323	231	9	ideals	ideal	NOUN
cana-1323	231	10	and	and	CCONJ
cana-1323	231	11	tripolar	tripolar	ADJ
cana-1323	231	12	fuzzy	fuzzy	ADJ
cana-1323	231	13	soft	soft	ADJ
cana-1323	231	14	interior	interior	ADJ
cana-1323	231	15	ideals	ideal	NOUN
cana-1323	231	16	over	over	ADP
cana-1323	231	17	semiring	semiring	NOUN
cana-1323	231	18	,	,	PUNCT
cana-1323	231	19	italian	italian	ADJ
cana-1323	231	20	journal	journal	NOUN
cana-1323	231	21	of	of	ADP
cana-1323	231	22	pure	pure	ADJ
cana-1323	231	23	and	and	CCONJ
cana-1323	231	24	applied	applied	ADJ
cana-1323	231	25	mathematics	mathematic	NOUN
cana-1323	231	26	,	,	PUNCT
cana-1323	231	27	42	42	NUM
cana-1323	231	28	,	,	PUNCT
cana-1323	231	29	(	(	PUNCT
cana-1323	231	30	2019	2019	NUM
cana-1323	231	31	)	)	PUNCT
cana-1323	231	32	,	,	PUNCT
cana-1323	231	33	731	731	NUM
cana-1323	231	34	-	-	SYM
cana-1323	231	35	743	743	NUM
cana-1323	231	36	.	.	PUNCT
cana-1323	232	1	[	[	X
cana-1323	232	2	6	6	NUM
cana-1323	232	3	]	]	X
cana-1323	232	4	meera	meera	PROPN
cana-1323	232	5	prasad	prasad	PROPN
cana-1323	232	6	.	.	PUNCT
cana-1323	233	1	e	e	X
cana-1323	233	2	,	,	PUNCT
cana-1323	233	3	madhusudhana	madhusudhana	PROPN
cana-1323	233	4	rao	rao	PROPN
cana-1323	233	5	.	.	PUNCT
cana-1323	234	1	d	d	X
cana-1323	234	2	,	,	PUNCT
cana-1323	234	3	suresh	suresh	PROPN
cana-1323	234	4	kumar	kumar	PROPN
cana-1323	234	5	.	.	PUNCT
cana-1323	235	1	g	g	PROPN
cana-1323	235	2	,	,	PUNCT
cana-1323	235	3	vasantha	vasantha	NOUN
cana-1323	235	4	.	.	PUNCT
cana-1323	236	1	m	m	PROPN
cana-1323	236	2	,	,	PUNCT
cana-1323	236	3	fuzzy	fuzzy	ADJ
cana-1323	236	4	soft	soft	ADJ
cana-1323	236	5	bi	bi	NOUN
cana-1323	236	6	-	-	NOUN
cana-1323	236	7	ideals	ideal	NOUN
cana-1323	236	8	over	over	ADP
cana-1323	236	9	ternary	ternary	ADJ
cana-1323	236	10	γsemirings	γsemiring	NOUN
cana-1323	236	11	-	-	PUNCT
cana-1323	236	12	advances	advance	NOUN
cana-1323	236	13	in	in	ADP
cana-1323	236	14	mathematics	mathematic	NOUN
cana-1323	236	15	scientific	scientific	ADJ
cana-1323	236	16	journal	journal	NOUN
cana-1323	236	17	9(2020	9(2020	NOUN
cana-1323	236	18	)	)	PUNCT
cana-1323	236	19	,	,	PUNCT
cana-1323	236	20	no.12	no.12	VERB
cana-1323	236	21	,	,	PUNCT
cana-1323	236	22	10145	10145	NUM
cana-1323	236	23	-	-	SYM
cana-1323	236	24	10154	10154	NUM
cana-1323	236	25	.	.	PUNCT
cana-1323	237	1	[	[	X
cana-1323	237	2	7	7	NUM
cana-1323	237	3	]	]	X
cana-1323	237	4	revathi	revathi	PROPN
cana-1323	237	5	.	.	PUNCT
cana-1323	238	1	k	k	X
cana-1323	238	2	,	,	PUNCT
cana-1323	238	3	sundarayya	sundarayya	ADJ
cana-1323	238	4	.	.	PUNCT
cana-1323	239	1	p	p	X
cana-1323	239	2	,	,	PUNCT
cana-1323	239	3	madhusudhanarao	madhusudhanarao	PROPN
cana-1323	239	4	.	.	PUNCT
cana-1323	240	1	d	d	X
cana-1323	240	2	,	,	PUNCT
cana-1323	240	3	siva	siva	PROPN
cana-1323	240	4	prasad	prasad	PROPN
cana-1323	240	5	.	.	PUNCT
cana-1323	241	1	pcompositions	pcomposition	NOUN
cana-1323	241	2	of	of	ADP
cana-1323	241	3	fuzzy	fuzzy	ADJ
cana-1323	241	4	tγ	tγ	NOUN
cana-1323	241	5	-	-	PUNCT
cana-1323	241	6	ideals	ideal	NOUN
cana-1323	241	7	in	in	ADP
cana-1323	241	8	ternary	ternary	ADJ
cana-1323	241	9	γsemi	γsemi	ADP
cana-1323	241	10	ring	ring	NOUN
cana-1323	241	11	,	,	PUNCT
cana-1323	241	12	international	international	ADJ
cana-1323	241	13	journal	journal	NOUN
cana-1323	241	14	of	of	ADP
cana-1323	241	15	advanced	advanced	ADJ
cana-1323	241	16	in	in	ADP
cana-1323	241	17	management	management	NOUN
cana-1323	241	18	,	,	PUNCT
cana-1323	241	19	technology	technology	NOUN
cana-1323	241	20	and	and	CCONJ
cana-1323	241	21	engineering	engineering	NOUN
cana-1323	241	22	sciences	science	NOUN
cana-1323	241	23	,	,	PUNCT
cana-1323	241	24	issn	issn	VERB
cana-1323	241	25	no	no	PRON
cana-1323	241	26	:	:	PUNCT
cana-1323	241	27	2249	2249	NUM
cana-1323	241	28	-	-	SYM
cana-1323	241	29	7455	7455	NUM
cana-1323	241	30	,	,	PUNCT
cana-1323	241	31	volume	volume	NOUN
cana-1323	241	32	07	07	NUM
cana-1323	241	33	,	,	PUNCT
cana-1323	241	34	issue	issue	NOUN
cana-1323	241	35	12	12	NUM
cana-1323	241	36	,	,	PUNCT
cana-1323	241	37	december	december	PROPN
cana-1323	241	38	,	,	PUNCT
cana-1323	241	39	2017	2017	NUM
cana-1323	241	40	,	,	PUNCT
cana-1323	241	41	pp	pp	CCONJ
cana-1323	241	42	:	:	PUNCT
cana-1323	241	43	135	135	NUM
cana-1323	241	44	-	-	SYM
cana-1323	241	45	145	145	NUM
cana-1323	241	46	.	.	PUNCT
cana-1323	242	1	[	[	X
cana-1323	242	2	8	8	NUM
cana-1323	242	3	]	]	X
cana-1323	242	4	revathi	revathi	PROPN
cana-1323	242	5	.	.	PUNCT
cana-1323	243	1	k	k	X
cana-1323	243	2	,	,	PUNCT
cana-1323	243	3	sundarayya	sundarayya	ADJ
cana-1323	243	4	.	.	PUNCT
cana-1323	244	1	p	p	X
cana-1323	244	2	,	,	PUNCT
cana-1323	244	3	madhusudhanarao	madhusudhanarao	PROPN
cana-1323	244	4	.	.	PUNCT
cana-1323	245	1	d	d	X
cana-1323	245	2	,	,	PUNCT
cana-1323	245	3	siva	siva	PROPN
cana-1323	245	4	prasad	prasad	PROPN
cana-1323	245	5	.	.	PUNCT
cana-1323	246	1	p-“a	p-“a	NOUN
cana-1323	246	2	study	study	NOUN
cana-1323	246	3	on	on	ADP
cana-1323	246	4	fuzzy	fuzzy	ADJ
cana-1323	246	5	t𝚪-ideals	t𝚪-ideal	NOUN
cana-1323	246	6	in	in	ADP
cana-1323	246	7	ternary	ternary	ADJ
cana-1323	246	8	𝚪semiring”,international	𝚪semiring”,international	PROPN
cana-1323	246	9	journal	journal	NOUN
cana-1323	246	10	of	of	ADP
cana-1323	246	11	engineering	engineering	PROPN
cana-1323	246	12	&	&	CCONJ
cana-1323	246	13	technology	technology	PROPN
cana-1323	246	14	volume	volume	NOUN
cana-1323	246	15	7	7	NUM
cana-1323	246	16	,	,	PUNCT
cana-1323	246	17	issue	issue	NOUN
cana-1323	246	18	3.31	3.31	NUM
cana-1323	246	19	(	(	PUNCT
cana-1323	246	20	2018	2018	NUM
cana-1323	246	21	)	)	PUNCT
cana-1323	246	22	.	.	PUNCT
cana-1323	247	1	communications	communication	NOUN
cana-1323	247	2	on	on	ADP
cana-1323	247	3	applied	apply	VERB
cana-1323	247	4	nonlinear	nonlinear	ADJ
cana-1323	247	5	analysis	analysis	NOUN
cana-1323	247	6	issn	issn	NOUN
cana-1323	247	7	:	:	PUNCT
cana-1323	247	8	1074	1074	NUM
cana-1323	247	9	-	-	PUNCT
cana-1323	247	10	133x	133x	NUM
cana-1323	247	11	vol	vol	NOUN
cana-1323	247	12	31	31	NUM
cana-1323	247	13	no	no	NOUN
cana-1323	247	14	.	.	PUNCT
cana-1323	248	1	7s	7	NOUN
cana-1323	248	2	(	(	PUNCT
cana-1323	248	3	2024	2024	NUM
cana-1323	248	4	)	)	PUNCT
cana-1323	248	5	452	452	NUM
cana-1323	248	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1323	249	1	[	[	X
cana-1323	249	2	9	9	NUM
cana-1323	249	3	]	]	X
cana-1323	249	4	revathi	revathi	PROPN
cana-1323	249	5	.	.	PUNCT
cana-1323	250	1	k	k	X
cana-1323	250	2	,	,	PUNCT
cana-1323	250	3	sundarayya	sundarayya	ADJ
cana-1323	250	4	.	.	PUNCT
cana-1323	251	1	p	p	X
cana-1323	251	2	,	,	PUNCT
cana-1323	251	3	madhusudhanarao	madhusudhanarao	PROPN
cana-1323	251	4	.	.	PUNCT
cana-1323	252	1	d	d	X
cana-1323	252	2	,	,	PUNCT
cana-1323	252	3	siva	siva	PROPN
cana-1323	252	4	prasad	prasad	PROPN
cana-1323	252	5	.	.	PUNCT
cana-1323	253	1	p	p	X
cana-1323	253	2	-	-	PUNCT
cana-1323	253	3	on	on	ADV
cana-1323	253	4	fuzzy	fuzzy	ADJ
cana-1323	253	5	regular	regular	ADJ
cana-1323	253	6	t	t	PROPN
cana-1323	253	7	-	-	PUNCT
cana-1323	253	8	γsr	γsr	PROPN
cana-1323	253	9	,	,	PUNCT
cana-1323	253	10	“	"	PUNCT
cana-1323	253	11	journal	journal	NOUN
cana-1323	253	12	of	of	ADP
cana-1323	253	13	physics	physics	PROPN
cana-1323	253	14	:	:	PUNCT
cana-1323	253	15	conferences	conference	NOUN
cana-1323	253	16	series	series	NOUN
cana-1323	253	17	”	"	PUNCT
cana-1323	253	18	1000	1000	NUM
cana-1323	253	19	(	(	PUNCT
cana-1323	253	20	2018	2018	NUM
cana-1323	253	21	)	)	PUNCT
cana-1323	253	22	012060	012060	NUM
cana-1323	253	23	.	.	PUNCT
cana-1323	254	1	[	[	X
cana-1323	254	2	10	10	NUM
cana-1323	254	3	]	]	X
cana-1323	254	4	revathi	revathi	PROPN
cana-1323	254	5	.	.	PUNCT
cana-1323	255	1	k	k	X
cana-1323	255	2	,	,	PUNCT
cana-1323	255	3	sundarayya	sundarayya	ADJ
cana-1323	255	4	.	.	PUNCT
cana-1323	256	1	p	p	X
cana-1323	256	2	,	,	PUNCT
cana-1323	256	3	madhusudhanarao	madhusudhanarao	PROPN
cana-1323	256	4	.	.	PUNCT
cana-1323	257	1	d	d	X
cana-1323	257	2	,	,	PUNCT
cana-1323	257	3	siva	siva	PROPN
cana-1323	257	4	prasad	prasad	PROPN
cana-1323	257	5	.	.	PUNCT
cana-1323	258	1	p	p	X
cana-1323	258	2	-	-	PUNCT
cana-1323	258	3	normal	normal	ADJ
cana-1323	258	4	fuzzy	fuzzy	ADJ
cana-1323	258	5	𝚪-ideals	𝚪-ideals	PROPN
cana-1323	258	6	in	in	ADP
cana-1323	258	7	ternary	ternary	ADJ
cana-1323	258	8	𝚪-semirings	𝚪-semiring	NOUN
cana-1323	258	9	,	,	PUNCT
cana-1323	258	10	“	"	PUNCT
cana-1323	258	11	global	global	ADJ
cana-1323	258	12	journal	journal	NOUN
cana-1323	258	13	of	of	ADP
cana-1323	258	14	pure	pure	ADJ
cana-1323	258	15	and	and	CCONJ
cana-1323	258	16	applied	applied	ADJ
cana-1323	258	17	mathematics	mathematic	NOUN
cana-1323	258	18	,	,	PUNCT
cana-1323	258	19	volume	volume	NOUN
cana-1323	258	20	13	13	NUM
cana-1323	258	21	,	,	PUNCT
cana-1323	258	22	number	number	NOUN
cana-1323	258	23	4	4	NUM
cana-1323	258	24	(	(	PUNCT
cana-1323	258	25	2017	2017	NUM
cana-1323	258	26	)	)	PUNCT
cana-1323	258	27	,	,	PUNCT
cana-1323	258	28	pp	pp	ADP
cana-1323	258	29	58	58	NUM
cana-1323	258	30	-	-	SYM
cana-1323	258	31	62	62	NUM
cana-1323	258	32	.	.	PUNCT
cana-1323	259	1	[	[	X
cana-1323	259	2	11	11	NUM
cana-1323	259	3	]	]	X
cana-1323	259	4	revathi	revathi	PROPN
cana-1323	259	5	.	.	PUNCT
cana-1323	260	1	k	k	X
cana-1323	260	2	,	,	PUNCT
cana-1323	260	3	sundarayya	sundarayya	ADJ
cana-1323	260	4	.	.	PUNCT
cana-1323	261	1	p	p	X
cana-1323	261	2	,	,	PUNCT
cana-1323	261	3	madhusudhanarao	madhusudhanarao	PROPN
cana-1323	261	4	.	.	PUNCT
cana-1323	262	1	d	d	X
cana-1323	262	2	,	,	PUNCT
cana-1323	262	3	siva	siva	PROPN
cana-1323	262	4	prasad	prasad	PROPN
cana-1323	262	5	.	.	PUNCT
cana-1323	263	1	p	p	X
cana-1323	263	2	-	-	PUNCT
cana-1323	263	3	completely	completely	ADV
cana-1323	263	4	prime	prime	ADJ
cana-1323	263	5	and	and	CCONJ
cana-1323	263	6	prime	prime	ADJ
cana-1323	263	7	fuzzy	fuzzy	ADJ
cana-1323	263	8	t𝚪-ideals	t𝚪-ideal	NOUN
cana-1323	263	9	in	in	ADP
cana-1323	263	10	t𝚪-semi	t𝚪-semi	X
cana-1323	263	11	rings	ring	NOUN
cana-1323	263	12	.	.	PUNCT
cana-1323	264	1	,	,	PUNCT
cana-1323	264	2	“	"	PUNCT
cana-1323	264	3	international	international	ADJ
cana-1323	264	4	journal	journal	NOUN
cana-1323	264	5	of	of	ADP
cana-1323	264	6	engineering	engineering	PROPN
cana-1323	264	7	&	&	CCONJ
cana-1323	264	8	technology	technology	NOUN
cana-1323	264	9	,	,	PUNCT
cana-1323	264	10	volume	volume	NOUN
cana-1323	264	11	7	7	NUM
cana-1323	264	12	,	,	PUNCT
cana-1323	264	13	issue	issue	NOUN
cana-1323	264	14	3.31	3.31	NUM
cana-1323	264	15	(	(	PUNCT
cana-1323	264	16	2018	2018	NUM
cana-1323	264	17	)	)	PUNCT
cana-1323	264	18	,	,	PUNCT
cana-1323	264	19	pp	pp	ADP
cana-1323	264	20	:	:	PUNCT
cana-1323	264	21	163	163	NUM
cana-1323	264	22	-	-	SYM
cana-1323	264	23	167	167	NUM
cana-1323	264	24	.	.	PUNCT
cana-1323	265	1	[	[	X
cana-1323	265	2	12	12	NUM
cana-1323	265	3	]	]	PUNCT
cana-1323	265	4	ravi	ravi	PROPN
cana-1323	265	5	kumar	kumar	PROPN
cana-1323	265	6	.	.	PROPN
cana-1323	266	1	b	b	PROPN
cana-1323	266	2	,	,	PUNCT
cana-1323	266	3	madhusudhana	madhusudhana	PROPN
cana-1323	266	4	rao	rao	PROPN
cana-1323	266	5	.	.	PUNCT
cana-1323	267	1	d	d	X
cana-1323	267	2	,	,	PUNCT
cana-1323	267	3	satish	satish	PROPN
cana-1323	267	4	.	.	PUNCT
cana-1323	267	5	t	t	PROPN
cana-1323	267	6	,	,	PUNCT
cana-1323	267	7	sankar	sankar	NOUN
cana-1323	267	8	rao	rao	PROPN
cana-1323	267	9	.	.	PUNCT
cana-1323	268	1	b	b	X
cana-1323	268	2	,	,	PUNCT
cana-1323	268	3	vasantha	vasantha	NOUN
cana-1323	268	4	.	.	PUNCT
cana-1323	269	1	m	m	PROPN
cana-1323	269	2	,	,	PUNCT
cana-1323	269	3	soft	soft	ADJ
cana-1323	269	4	ternary	ternary	ADJ
cana-1323	269	5	𝚪-semiring	𝚪-semiring	PROPN
cana-1323	269	6	-	-	PUNCT
cana-1323	269	7	ii	ii	NOUN
cana-1323	269	8	,	,	PUNCT
cana-1323	269	9	international	international	ADJ
cana-1323	269	10	journal	journal	NOUN
cana-1323	269	11	of	of	ADP
cana-1323	269	12	recent	recent	ADJ
cana-1323	269	13	technology	technology	NOUN
cana-1323	269	14	and	and	CCONJ
cana-1323	269	15	engineering	engineering	NOUN
cana-1323	269	16	(	(	PUNCT
cana-1323	269	17	ijrte	ijrte	NOUN
cana-1323	269	18	)	)	PUNCT
cana-1323	269	19	issn	issn	PROPN
cana-1323	269	20	:	:	PUNCT
cana-1323	269	21	2277	2277	NUM
cana-1323	269	22	-	-	SYM
cana-1323	269	23	3878	3878	NUM
cana-1323	269	24	,	,	PUNCT
cana-1323	269	25	volume-8	volume-8	NUM
cana-1323	269	26	issue-1s3	issue-1s3	NOUN
cana-1323	269	27	,	,	PUNCT
cana-1323	269	28	june	june	PROPN
cana-1323	269	29	2019	2019	NUM
cana-1323	269	30	.	.	PUNCT
cana-1323	270	1	[	[	X
cana-1323	270	2	13	13	NUM
cana-1323	270	3	]	]	PUNCT
cana-1323	270	4	ravi	ravi	PROPN
cana-1323	270	5	kumar	kumar	PROPN
cana-1323	270	6	.	.	PROPN
cana-1323	271	1	b	b	PROPN
cana-1323	271	2	,	,	PUNCT
cana-1323	271	3	sankar	sankar	NOUN
cana-1323	271	4	rao	rao	PROPN
cana-1323	271	5	.	.	PUNCT
cana-1323	272	1	b	b	X
cana-1323	272	2	,	,	PUNCT
cana-1323	272	3	madhusudhana	madhusudhana	PROPN
cana-1323	272	4	rao	rao	PROPN
cana-1323	272	5	.	.	PUNCT
cana-1323	273	1	d	d	X
cana-1323	273	2	,	,	PUNCT
cana-1323	273	3	siva	siva	PROPN
cana-1323	273	4	prasad	prasad	PROPN
cana-1323	273	5	.	.	PUNCT
cana-1323	274	1	p	p	X
cana-1323	274	2	,	,	PUNCT
cana-1323	274	3	vasantha	vasantha	NOUN
cana-1323	274	4	.	.	PUNCT
cana-1323	275	1	m	m	PROPN
cana-1323	275	2	,	,	PUNCT
cana-1323	275	3	soft	soft	ADJ
cana-1323	275	4	ternary	ternary	ADJ
cana-1323	275	5	𝚪-semiring	𝚪-semiring	NOUN
cana-1323	275	6	-	-	PUNCT
cana-1323	275	7	i	i	PROPN
cana-1323	275	8	,	,	PUNCT
cana-1323	275	9	iop	iop	PROPN
cana-1323	275	10	conf	conf	NOUN
cana-1323	275	11	.	.	PUNCT
cana-1323	276	1	series	series	PROPN
cana-1323	276	2	:	:	PUNCT
cana-1323	276	3	journal	journal	PROPN
cana-1323	276	4	of	of	ADP
cana-1323	276	5	physics	physics	PROPN
cana-1323	276	6	:	:	PUNCT
cana-1323	276	7	conf	conf	PROPN
cana-1323	276	8	.	.	PUNCT
cana-1323	277	1	series	series	PROPN
cana-1323	277	2	1344	1344	NUM
cana-1323	277	3	(	(	PUNCT
cana-1323	277	4	2019	2019	NUM
cana-1323	277	5	)	)	PUNCT
cana-1323	277	6	012023	012023	NUM
cana-1323	277	7	.	.	PUNCT
cana-1323	278	1	[	[	X
cana-1323	278	2	14	14	NUM
cana-1323	278	3	]	]	SYM
cana-1323	278	4	satish	satish	PROPN
cana-1323	278	5	.	.	PUNCT
cana-1323	279	1	t	t	PROPN
cana-1323	279	2	,	,	PUNCT
cana-1323	279	3	madhusudhana	madhusudhana	PROPN
cana-1323	279	4	rao	rao	PROPN
cana-1323	279	5	.	.	PUNCT
cana-1323	280	1	d	d	X
cana-1323	280	2	,	,	PUNCT
cana-1323	280	3	vasantha	vasantha	NOUN
cana-1323	280	4	.	.	PUNCT
cana-1323	281	1	m	m	PROPN
cana-1323	281	2	,	,	PUNCT
cana-1323	281	3	praveen	praveen	PROPN
cana-1323	281	4	kumar	kumar	PROPN
cana-1323	281	5	.	.	PUNCT
cana-1323	282	1	k	k	ADJ
cana-1323	282	2	-	-	ADJ
cana-1323	282	3	fuzzy	fuzzy	ADJ
cana-1323	282	4	soft	soft	ADJ
cana-1323	282	5	ternary	ternary	ADJ
cana-1323	282	6	𝚪-semiring	𝚪-semiring	NOUN
cana-1323	282	7	-	-	PUNCT
cana-1323	282	8	iii	iii	NOUN
cana-1323	282	9	,	,	PUNCT
cana-1323	282	10	mukt	mukt	PROPN
cana-1323	282	11	shabd	shabd	PROPN
cana-1323	282	12	journal	journal	PROPN
cana-1323	282	13	,	,	PUNCT
cana-1323	282	14	volume	volume	NOUN
cana-1323	282	15	ix	ix	ADV
cana-1323	282	16	,	,	PUNCT
cana-1323	282	17	issue	issue	NOUN
cana-1323	282	18	iv	iv	SYM
cana-1323	282	19	,	,	PUNCT
cana-1323	282	20	april-2020	april-2020	VERB
cana-1323	282	21	,	,	PUNCT
cana-1323	282	22	pp	pp	CCONJ
cana-1323	282	23	:	:	PUNCT
cana-1323	282	24	2396	2396	NUM
cana-1323	282	25	-	-	SYM
cana-1323	282	26	2406	2406	NUM
cana-1323	282	27	.	.	PUNCT
cana-1323	283	1	[	[	X
cana-1323	283	2	15	15	NUM
cana-1323	283	3	]	]	X
cana-1323	283	4	g.	g.	PROPN
cana-1323	283	5	srinivasa	srinivasa	PROPN
cana-1323	283	6	rao	rao	PROPN
cana-1323	283	7	,	,	PUNCT
cana-1323	283	8	d.	d.	PROPN
cana-1323	283	9	madhusudhanarao	madhusudhanarao	PROPN
cana-1323	283	10	and	and	CCONJ
cana-1323	283	11	p.	p.	PROPN
cana-1323	283	12	siva	siva	PROPN
cana-1323	283	13	prasad	prasad	PROPN
cana-1323	283	14	,	,	PUNCT
cana-1323	283	15	simple	simple	ADJ
cana-1323	283	16	ternary	ternary	ADJ
cana-1323	283	17	semi	semi	NOUN
cana-1323	283	18	-	-	NOUN
cana-1323	283	19	rings	ring	NOUN
cana-1323	283	20	,	,	PUNCT
cana-1323	283	21	the	the	DET
cana-1323	283	22	global	global	ADJ
cana-1323	283	23	journal	journal	NOUN
cana-1323	283	24	of	of	ADP
cana-1323	283	25	mathematics	mathematics	PROPN
cana-1323	283	26	&	&	CCONJ
cana-1323	283	27	mathematical	mathematical	PROPN
cana-1323	283	28	sciences	sciences	PROPN
cana-1323	283	29	,	,	PUNCT
cana-1323	283	30	9(2	9(2	NUM
cana-1323	283	31	)	)	PUNCT
cana-1323	283	32	(	(	PUNCT
cana-1323	283	33	2016	2016	NUM
cana-1323	283	34	)	)	PUNCT
cana-1323	283	35	,	,	PUNCT
cana-1323	283	36	185	185	NUM
cana-1323	283	37	-	-	SYM
cana-1323	283	38	196	196	NUM
cana-1323	283	39	.	.	PUNCT
cana-1323	284	1	[	[	X
cana-1323	284	2	16	16	NUM
cana-1323	284	3	]	]	X
cana-1323	284	4	d.	d.	PROPN
cana-1323	284	5	madhusudhana	madhusudhana	PROPN
cana-1323	284	6	rao	rao	PROPN
cana-1323	284	7	,	,	PUNCT
cana-1323	284	8	g.	g.	PROPN
cana-1323	284	9	srinivasa	srinivasa	PROPN
cana-1323	284	10	rao	rao	PROPN
cana-1323	284	11	,	,	PUNCT
cana-1323	284	12	special	special	ADJ
cana-1323	284	13	elements	element	NOUN
cana-1323	284	14	in	in	ADP
cana-1323	284	15	ternary	ternary	ADJ
cana-1323	284	16	semi	semi	ADJ
cana-1323	284	17	rings	ring	NOUN
cana-1323	284	18	,	,	PUNCT
cana-1323	284	19	international	international	ADJ
cana-1323	284	20	journal	journal	NOUN
cana-1323	284	21	of	of	ADP
cana-1323	284	22	engineering	engineering	NOUN
cana-1323	284	23	research	research	NOUN
cana-1323	284	24	and	and	CCONJ
cana-1323	284	25	applications	application	NOUN
cana-1323	284	26	,	,	PUNCT
cana-1323	284	27	4(11	4(11	NUM
cana-1323	284	28	)	)	PUNCT
cana-1323	284	29	(	(	PUNCT
cana-1323	284	30	2014	2014	NUM
cana-1323	284	31	)	)	PUNCT
cana-1323	284	32	,	,	PUNCT
cana-1323	284	33	123	123	NUM
cana-1323	284	34	-	-	SYM
cana-1323	284	35	130	130	NUM
cana-1323	284	36	.	.	PUNCT
cana-1323	285	1	[	[	X
cana-1323	285	2	17	17	NUM
cana-1323	285	3	]	]	X
cana-1323	285	4	g.	g.	PROPN
cana-1323	285	5	srinivasa	srinivasa	PROPN
cana-1323	285	6	rao	rao	PROPN
cana-1323	285	7	,	,	PUNCT
cana-1323	285	8	d.	d.	PROPN
cana-1323	285	9	madhusudhana	madhusudhana	PROPN
cana-1323	285	10	rao	rao	PROPN
cana-1323	285	11	,	,	PUNCT
cana-1323	285	12	structure	structure	NOUN
cana-1323	285	13	of	of	ADP
cana-1323	285	14	certain	certain	ADJ
cana-1323	285	15	ideals	ideal	NOUN
cana-1323	285	16	in	in	ADP
cana-1323	285	17	ternary	ternary	ADJ
cana-1323	285	18	semi	semi	ADJ
cana-1323	285	19	rings	ring	NOUN
cana-1323	285	20	,	,	PUNCT
cana-1323	285	21	int	int	NOUN
cana-1323	285	22	.	.	PUNCT
cana-1323	286	1	j.	j.	PROPN
cana-1323	286	2	of	of	ADP
cana-1323	286	3	innovative	innovative	ADJ
cana-1323	286	4	science	science	NOUN
cana-1323	286	5	and	and	CCONJ
cana-1323	286	6	modern	modern	ADJ
cana-1323	286	7	engg	engg	PROPN
cana-1323	286	8	.	.	PUNCT
cana-1323	286	9	,	,	PUNCT
cana-1323	286	10	3(3	3(3	NUM
cana-1323	286	11	)	)	PUNCT
cana-1323	286	12	(	(	PUNCT
cana-1323	286	13	2015	2015	NUM
cana-1323	286	14	)	)	PUNCT
cana-1323	286	15	,	,	PUNCT
cana-1323	286	16	49	49	NUM
cana-1323	286	17	-	-	SYM
cana-1323	286	18	56	56	NUM
cana-1323	286	19	.	.	PUNCT
cana-1323	287	1	[	[	X
cana-1323	287	2	18	18	NUM
cana-1323	287	3	]	]	X
cana-1323	287	4	g.	g.	PROPN
cana-1323	287	5	srinivasa	srinivasa	PROPN
cana-1323	287	6	rao	rao	PROPN
cana-1323	287	7	,	,	PUNCT
cana-1323	287	8	d.	d.	PROPN
cana-1323	287	9	madhusudhana	madhusudhana	PROPN
cana-1323	287	10	rao	rao	PROPN
cana-1323	287	11	,	,	PUNCT
cana-1323	287	12	a	a	DET
cana-1323	287	13	study	study	NOUN
cana-1323	287	14	on	on	ADP
cana-1323	287	15	ternary	ternary	ADJ
cana-1323	287	16	semi	semi	ADJ
cana-1323	287	17	rings	ring	NOUN
cana-1323	287	18	,	,	PUNCT
cana-1323	287	19	int	int	NOUN
cana-1323	287	20	.	.	PUNCT
cana-1323	288	1	j.	j.	PROPN
cana-1323	288	2	of	of	ADP
cana-1323	288	3	math	math	PROPN
cana-1323	288	4	.	.	PUNCT
cana-1323	289	1	archive	archive	NOUN
cana-1323	289	2	,	,	PUNCT
cana-1323	289	3	5(12	5(12	NUM
cana-1323	289	4	)	)	PUNCT
cana-1323	289	5	(	(	PUNCT
cana-1323	289	6	2014	2014	NUM
cana-1323	289	7	)	)	PUNCT
cana-1323	289	8	,	,	PUNCT
cana-1323	289	9	24	24	NUM
cana-1323	289	10	-	-	SYM
cana-1323	289	11	30	30	NUM
cana-1323	289	12	.	.	PUNCT
cana-1323	290	1	[	[	X
cana-1323	290	2	19	19	NUM
cana-1323	290	3	]	]	PUNCT
cana-1323	290	4	g.	g.	PROPN
cana-1323	290	5	srinivasa	srinivasa	PROPN
cana-1323	290	6	rao	rao	PROPN
cana-1323	290	7	,	,	PUNCT
cana-1323	290	8	d.	d.	PROPN
cana-1323	290	9	madhusudhana	madhusudhana	PROPN
cana-1323	290	10	rao	rao	PROPN
cana-1323	290	11	,	,	PUNCT
cana-1323	290	12	characteristics	characteristic	NOUN
cana-1323	290	13	of	of	ADP
cana-1323	290	14	ternary	ternary	ADJ
cana-1323	290	15	semi	semi	ADJ
cana-1323	290	16	rings	ring	NOUN
cana-1323	290	17	,	,	PUNCT
cana-1323	290	18	int.j	int.j	PROPN
cana-1323	290	19	.	.	PROPN
cana-1323	290	20	of	of	ADP
cana-1323	290	21	engg	engg	PROPN
cana-1323	290	22	.	.	PUNCT
cana-1323	291	1	res	re	NOUN
cana-1323	291	2	.	.	PUNCT
cana-1323	291	3	and	and	CCONJ
cana-1323	291	4	mgt	mgt	PROPN
cana-1323	291	5	.	.	PUNCT
cana-1323	291	6	,	,	PUNCT
cana-1323	291	7	2(1	2(1	NUM
cana-1323	291	8	)	)	PUNCT
cana-1323	291	9	(	(	PUNCT
cana-1323	291	10	2015	2015	NUM
cana-1323	291	11	)	)	PUNCT
cana-1323	291	12	,	,	PUNCT
cana-1323	291	13	3	3	NUM
cana-1323	291	14	-	-	SYM
cana-1323	291	15	6	6	NUM
cana-1323	291	16	.	.	PUNCT
cana-1323	292	1	[	[	X
cana-1323	292	2	20	20	NUM
cana-1323	292	3	]	]	PUNCT
cana-1323	292	4	g.	g.	PROPN
cana-1323	292	5	srinivasa	srinivasa	PROPN
cana-1323	292	6	rao	rao	PROPN
cana-1323	292	7	,	,	PUNCT
cana-1323	292	8	a.	a.	PROPN
cana-1323	292	9	nagamalleswara	nagamalleswara	PROPN
cana-1323	292	10	rao	rao	PROPN
cana-1323	292	11	,	,	PUNCT
cana-1323	292	12	p.l.n	p.l.n	PROPN
cana-1323	292	13	.	.	PROPN
cana-1323	292	14	varma	varma	PROPN
cana-1323	292	15	,	,	PUNCT
cana-1323	292	16	d.madhusudhana	d.madhusudhana	PROPN
cana-1323	292	17	rao	rao	PROPN
cana-1323	292	18	,	,	PUNCT
cana-1323	292	19	ch	ch	NOUN
cana-1323	292	20	.	.	PROPN
cana-1323	292	21	ramprasad	ramprasad	ADJ
cana-1323	292	22	,	,	PUNCT
cana-1323	292	23	prime	prime	ADJ
cana-1323	292	24	biinterior	biinterior	PROPN
cana-1323	292	25	ideals	ideal	NOUN
cana-1323	292	26	in	in	ADP
cana-1323	292	27	tgsr	tgsr	ADJ
cana-1323	292	28	,	,	PUNCT
cana-1323	292	29	malaya	malaya	PROPN
cana-1323	292	30	journal	journal	PROPN
cana-1323	292	31	of	of	ADP
cana-1323	292	32	mathematika	mathematika	NOUN
cana-1323	292	33	,	,	PUNCT
cana-1323	292	34	vol.9	vol.9	PROPN
cana-1323	292	35	,	,	PUNCT
cana-1323	292	36	no.1	no.1	NUM
cana-1323	292	37	,	,	PUNCT
cana-1323	292	38	pp:542	pp:542	ADV
cana-1323	292	39	-	-	PUNCT
cana-1323	292	40	546	546	NUM
cana-1323	292	41	,	,	PUNCT
cana-1323	292	42	2021	2021	NUM
cana-1323	292	43	.	.	PUNCT
cana-1323	293	1	[	[	X
cana-1323	293	2	21	21	NUM
cana-1323	293	3	]	]	X
cana-1323	293	4	g.	g.	PROPN
cana-1323	293	5	srinivasa	srinivasa	PROPN
cana-1323	293	6	rao	rao	PROPN
cana-1323	293	7	,	,	PUNCT
cana-1323	293	8	a.	a.	PROPN
cana-1323	293	9	nagamalleswara	nagamalleswara	PROPN
cana-1323	293	10	rao	rao	PROPN
cana-1323	293	11	,	,	PUNCT
cana-1323	293	12	p.l.n	p.l.n	PROPN
cana-1323	293	13	.	.	PROPN
cana-1323	293	14	varma	varma	PROPN
cana-1323	293	15	,	,	PUNCT
cana-1323	293	16	d.	d.	PROPN
cana-1323	293	17	madhusudhana	madhusudhana	PROPN
cana-1323	293	18	rao	rao	PROPN
cana-1323	293	19	,	,	PUNCT
cana-1323	293	20	ch	ch	NOUN
cana-1323	293	21	.	.	PROPN
cana-1323	293	22	ramprasad	ramprasad	ADJ
cana-1323	293	23	,	,	PUNCT
cana-1323	293	24	bi	bi	ADJ
cana-1323	293	25	-	-	ADJ
cana-1323	293	26	interior	interior	ADJ
cana-1323	293	27	ideals	ideal	NOUN
cana-1323	293	28	in	in	ADP
cana-1323	293	29	tgsr	tgsr	ADJ
cana-1323	293	30	,	,	PUNCT
cana-1323	293	31	advances	advance	NOUN
cana-1323	293	32	in	in	ADP
cana-1323	293	33	mathematics	mathematics	NOUN
cana-1323	293	34	scientific	scientific	ADJ
cana-1323	293	35	journal	journal	NOUN
cana-1323	293	36	,	,	PUNCT
cana-1323	293	37	10	10	NUM
cana-1323	293	38	(	(	PUNCT
cana-1323	293	39	2021	2021	NUM
cana-1323	293	40	)	)	PUNCT
cana-1323	293	41	,	,	PUNCT
cana-1323	293	42	no.3	no.3	VERB
cana-1323	293	43	,	,	PUNCT
cana-1323	293	44	pp	pp	CCONJ
cana-1323	293	45	:	:	PUNCT
cana-1323	293	46	1183	1183	NUM
cana-1323	293	47	-	-	SYM
cana-1323	293	48	1195	1195	NUM
cana-1323	293	49	.	.	PUNCT