id	sid	tid	token	lemma	pos
cana-4548	1	1	communications	communication	NOUN
cana-4548	1	2	on	on	ADP
cana-4548	1	3	applied	apply	VERB
cana-4548	1	4	nonlinear	nonlinear	ADJ
cana-4548	1	5	analysis	analysis	NOUN
cana-4548	1	6	issn	issn	NOUN
cana-4548	1	7	:	:	PUNCT
cana-4548	1	8	1074	1074	NUM
cana-4548	1	9	-	-	PUNCT
cana-4548	1	10	133x	133x	NUM
cana-4548	1	11	vol	vol	NOUN
cana-4548	1	12	32	32	NUM
cana-4548	1	13	no	no	NOUN
cana-4548	1	14	.	.	PUNCT
cana-4548	2	1	9s	9s	NUM
cana-4548	2	2	(	(	PUNCT
cana-4548	2	3	2025	2025	NUM
cana-4548	2	4	)	)	PUNCT
cana-4548	2	5	2678	2678	NUM
cana-4548	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4548	2	7	a	a	DET
cana-4548	2	8	smart	smart	ADJ
cana-4548	2	9	technique	technique	NOUN
cana-4548	2	10	approach	approach	NOUN
cana-4548	2	11	in	in	ADP
cana-4548	2	12	picture	picture	NOUN
cana-4548	2	13	fuzzy	fuzzy	ADJ
cana-4548	2	14	schweizer	schweizer	PROPN
cana-4548	2	15	-	-	PUNCT
cana-4548	2	16	sklar	sklar	ADJ
cana-4548	2	17	power	power	NOUN
cana-4548	2	18	geometric	geometric	ADJ
cana-4548	2	19	aggregation	aggregation	NOUN
cana-4548	2	20	operators	operator	NOUN
cana-4548	2	21	for	for	ADP
cana-4548	2	22	enhancing	enhance	VERB
cana-4548	2	23	road	road	NOUN
cana-4548	2	24	construction	construction	NOUN
cana-4548	2	25	companies	company	NOUN
cana-4548	2	26	through	through	ADP
cana-4548	2	27	group	group	NOUN
cana-4548	2	28	decision	decision	NOUN
cana-4548	2	29	-	-	PUNCT
cana-4548	2	30	making	make	VERB
cana-4548	2	31	t.	t.	NOUN
cana-4548	2	32	yogashanthi1	yogashanthi1	NOUN
cana-4548	2	33	and	and	CCONJ
cana-4548	2	34	k.	k.	PROPN
cana-4548	2	35	deva2	deva2	PROPN
cana-4548	2	36	*	*	PROPN
cana-4548	3	1	1department	1department	NUM
cana-4548	3	2	of	of	ADP
cana-4548	3	3	mathematics	mathematic	NOUN
cana-4548	3	4	,	,	PUNCT
cana-4548	3	5	srm	srm	PROPN
cana-4548	3	6	institute	institute	PROPN
cana-4548	3	7	of	of	ADP
cana-4548	3	8	science	science	NOUN
cana-4548	3	9	and	and	CCONJ
cana-4548	3	10	technology	technology	NOUN
cana-4548	3	11	,	,	PUNCT
cana-4548	3	12	ramauram	ramauram	NOUN
cana-4548	3	13	,	,	PUNCT
cana-4548	3	14	chennai	chennai	NOUN
cana-4548	3	15	,	,	PUNCT
cana-4548	3	16	tamilnadu	tamilnadu	NOUN
cana-4548	3	17	,	,	PUNCT
cana-4548	3	18	india	india	PROPN
cana-4548	3	19	.	.	PUNCT
cana-4548	4	1	2	2	NUM
cana-4548	4	2	*	*	PUNCT
cana-4548	4	3	department	department	NOUN
cana-4548	4	4	of	of	ADP
cana-4548	4	5	mathematics	mathematic	NOUN
cana-4548	4	6	,	,	PUNCT
cana-4548	4	7	vel	vel	ADJ
cana-4548	4	8	tech	tech	NOUN
cana-4548	4	9	high	high	ADJ
cana-4548	4	10	tech	tech	NOUN
cana-4548	4	11	dr.rangarajan	dr.rangarajan	NOUN
cana-4548	4	12	dr.sakunthala	dr.sakunthala	NOUN
cana-4548	4	13	engineering	engineering	NOUN
cana-4548	4	14	college	college	NOUN
cana-4548	4	15	,	,	PUNCT
cana-4548	4	16	avadi-600062	avadi-600062	NOUN
cana-4548	4	17	,	,	PUNCT
cana-4548	4	18	tamilnadu	tamilnadu	ADJ
cana-4548	4	19	,	,	PUNCT
cana-4548	4	20	india	india	PROPN
cana-4548	4	21	.	.	PUNCT
cana-4548	5	1	*	*	PUNCT
cana-4548	5	2	corresponding	correspond	VERB
cana-4548	5	3	author	author	NOUN
cana-4548	5	4	:	:	PUNCT
cana-4548	5	5	devakrishnan92@gmail.com	devakrishnan92@gmail.com	X
cana-4548	5	6	article	article	NOUN
cana-4548	5	7	history	history	NOUN
cana-4548	5	8	:	:	PUNCT
cana-4548	5	9	received	receive	VERB
cana-4548	5	10	:	:	PUNCT
cana-4548	5	11	12	12	NUM
cana-4548	5	12	-	-	SYM
cana-4548	5	13	01	01	NUM
cana-4548	5	14	-	-	PUNCT
cana-4548	5	15	2025	2025	NUM
cana-4548	5	16	revised	revise	VERB
cana-4548	5	17	:	:	PUNCT
cana-4548	5	18	15	15	NUM
cana-4548	5	19	-	-	NUM
cana-4548	5	20	02	02	NUM
cana-4548	5	21	-	-	PUNCT
cana-4548	5	22	2025	2025	NUM
cana-4548	5	23	accepted	accept	VERB
cana-4548	5	24	:	:	PUNCT
cana-4548	5	25	01	01	NUM
cana-4548	5	26	-	-	SYM
cana-4548	5	27	03	03	NUM
cana-4548	5	28	-	-	PUNCT
cana-4548	5	29	2025	2025	NUM
cana-4548	5	30	abstract	abstract	NOUN
cana-4548	5	31	:	:	PUNCT
cana-4548	5	32	the	the	DET
cana-4548	5	33	objective	objective	NOUN
cana-4548	5	34	of	of	ADP
cana-4548	5	35	this	this	DET
cana-4548	5	36	paper	paper	NOUN
cana-4548	5	37	is	be	AUX
cana-4548	5	38	to	to	PART
cana-4548	5	39	develop	develop	VERB
cana-4548	5	40	picture	picture	NOUN
cana-4548	5	41	fuzzy	fuzzy	ADJ
cana-4548	5	42	aggregation	aggregation	NOUN
cana-4548	5	43	operators	operator	NOUN
cana-4548	5	44	by	by	ADP
cana-4548	5	45	utilizing	utilize	VERB
cana-4548	5	46	the	the	DET
cana-4548	5	47	concept	concept	NOUN
cana-4548	5	48	of	of	ADP
cana-4548	5	49	power	power	NOUN
cana-4548	5	50	aggregation	aggregation	NOUN
cana-4548	5	51	operators	operator	NOUN
cana-4548	5	52	through	through	ADP
cana-4548	5	53	schweizer	schweizer	PROPN
cana-4548	5	54	-	-	PUNCT
cana-4548	5	55	sklar	sklar	ADJ
cana-4548	5	56	operations	operation	NOUN
cana-4548	5	57	.	.	PUNCT
cana-4548	6	1	the	the	DET
cana-4548	6	2	schweizer	schweizer	PROPN
cana-4548	6	3	-	-	PUNCT
cana-4548	6	4	sklar	sklar	PROPN
cana-4548	6	5	t	t	PROPN
cana-4548	6	6	-	-	PUNCT
cana-4548	6	7	norm	norm	NOUN
cana-4548	6	8	and	and	CCONJ
cana-4548	6	9	t	t	NOUN
cana-4548	6	10	-	-	PUNCT
cana-4548	6	11	conorm	conorm	NOUN
cana-4548	6	12	enhance	enhance	VERB
cana-4548	6	13	the	the	DET
cana-4548	6	14	flexibility	flexibility	NOUN
cana-4548	6	15	of	of	ADP
cana-4548	6	16	the	the	DET
cana-4548	6	17	data	data	NOUN
cana-4548	6	18	integration	integration	NOUN
cana-4548	6	19	process	process	NOUN
cana-4548	6	20	and	and	CCONJ
cana-4548	6	21	the	the	DET
cana-4548	6	22	power	power	NOUN
cana-4548	6	23	aggregation	aggregation	NOUN
cana-4548	6	24	operator	operator	NOUN
cana-4548	6	25	,	,	PUNCT
cana-4548	6	26	by	by	ADP
cana-4548	6	27	capturing	capture	VERB
cana-4548	6	28	the	the	DET
cana-4548	6	29	interrelationships	interrelationship	NOUN
cana-4548	6	30	between	between	ADP
cana-4548	6	31	various	various	ADJ
cana-4548	6	32	criteria	criterion	NOUN
cana-4548	6	33	during	during	ADP
cana-4548	6	34	decision	decision	NOUN
cana-4548	6	35	-	-	PUNCT
cana-4548	6	36	making	making	NOUN
cana-4548	6	37	.	.	PUNCT
cana-4548	7	1	motivated	motivate	VERB
cana-4548	7	2	by	by	ADP
cana-4548	7	3	schweizer	schweizer	PROPN
cana-4548	7	4	-	-	PUNCT
cana-4548	7	5	sklar	sklar	PROPN
cana-4548	7	6	t	t	PROPN
cana-4548	7	7	-	-	PUNCT
cana-4548	7	8	norm	norm	NOUN
cana-4548	7	9	and	and	CCONJ
cana-4548	7	10	tconorm	tconorm	NOUN
cana-4548	7	11	,	,	PUNCT
cana-4548	7	12	this	this	DET
cana-4548	7	13	paper	paper	NOUN
cana-4548	7	14	aims	aim	VERB
cana-4548	7	15	to	to	PART
cana-4548	7	16	develop	develop	VERB
cana-4548	7	17	the	the	DET
cana-4548	7	18	theory	theory	NOUN
cana-4548	7	19	of	of	ADP
cana-4548	7	20	the	the	DET
cana-4548	7	21	picture	picture	NOUN
cana-4548	7	22	fuzzy	fuzzy	ADJ
cana-4548	7	23	schweizer	schweizer	PROPN
cana-4548	7	24	-	-	PUNCT
cana-4548	7	25	sklar	sklar	ADJ
cana-4548	7	26	power	power	NOUN
cana-4548	7	27	weighted	weight	VERB
cana-4548	7	28	geometric	geometric	ADJ
cana-4548	7	29	operator	operator	NOUN
cana-4548	7	30	and	and	CCONJ
cana-4548	7	31	the	the	DET
cana-4548	7	32	picture	picture	NOUN
cana-4548	7	33	fuzzy	fuzzy	ADJ
cana-4548	7	34	schweizer	schweizer	PROPN
cana-4548	7	35	-	-	PUNCT
cana-4548	7	36	sklar	sklar	ADJ
cana-4548	7	37	power	power	NOUN
cana-4548	7	38	ordered	order	VERB
cana-4548	7	39	weighted	weight	VERB
cana-4548	7	40	geometric	geometric	ADJ
cana-4548	7	41	operator	operator	NOUN
cana-4548	7	42	.	.	PUNCT
cana-4548	8	1	the	the	DET
cana-4548	8	2	paper	paper	NOUN
cana-4548	8	3	also	also	ADV
cana-4548	8	4	explores	explore	VERB
cana-4548	8	5	the	the	DET
cana-4548	8	6	properties	property	NOUN
cana-4548	8	7	and	and	CCONJ
cana-4548	8	8	characteristics	characteristic	NOUN
cana-4548	8	9	of	of	ADP
cana-4548	8	10	these	these	DET
cana-4548	8	11	proposed	propose	VERB
cana-4548	8	12	operators	operator	NOUN
cana-4548	8	13	.	.	PUNCT
cana-4548	9	1	criteria	criterion	NOUN
cana-4548	9	2	weights	weight	NOUN
cana-4548	9	3	play	play	VERB
cana-4548	9	4	a	a	DET
cana-4548	9	5	crucial	crucial	ADJ
cana-4548	9	6	role	role	NOUN
cana-4548	9	7	in	in	ADP
cana-4548	9	8	aggregating	aggregate	VERB
cana-4548	9	9	different	different	ADJ
cana-4548	9	10	criteria	criterion	NOUN
cana-4548	9	11	in	in	ADP
cana-4548	9	12	multiple	multiple	ADJ
cana-4548	9	13	criteria	criterion	NOUN
cana-4548	9	14	decision	decision	NOUN
cana-4548	9	15	-	-	PUNCT
cana-4548	9	16	making	make	VERB
cana-4548	9	17	processes	process	NOUN
cana-4548	9	18	.	.	PUNCT
cana-4548	10	1	this	this	DET
cana-4548	10	2	work	work	NOUN
cana-4548	10	3	adopts	adopt	VERB
cana-4548	10	4	the	the	DET
cana-4548	10	5	simple	simple	ADJ
cana-4548	10	6	multiattribute	multiattribute	NOUN
cana-4548	10	7	rating	rating	NOUN
cana-4548	10	8	technique	technique	NOUN
cana-4548	10	9	to	to	PART
cana-4548	10	10	compute	compute	VERB
cana-4548	10	11	criteria	criterion	NOUN
cana-4548	10	12	weights	weight	NOUN
cana-4548	10	13	for	for	ADP
cana-4548	10	14	solving	solve	VERB
cana-4548	10	15	multi	multi	ADJ
cana-4548	10	16	-	-	ADJ
cana-4548	10	17	criteria	criterion	NOUN
cana-4548	10	18	group	group	NOUN
cana-4548	10	19	decision	decision	NOUN
cana-4548	10	20	-	-	PUNCT
cana-4548	10	21	making	make	VERB
cana-4548	10	22	problems	problem	NOUN
cana-4548	10	23	in	in	ADP
cana-4548	10	24	a	a	DET
cana-4548	10	25	picture	picture	NOUN
cana-4548	10	26	fuzzy	fuzzy	ADJ
cana-4548	10	27	environment	environment	NOUN
cana-4548	10	28	.	.	PUNCT
cana-4548	11	1	finally	finally	ADV
cana-4548	11	2	,	,	PUNCT
cana-4548	11	3	an	an	DET
cana-4548	11	4	illustrative	illustrative	ADJ
cana-4548	11	5	example	example	NOUN
cana-4548	11	6	of	of	ADP
cana-4548	11	7	the	the	DET
cana-4548	11	8	road	road	NOUN
cana-4548	11	9	construction	construction	NOUN
cana-4548	11	10	company	company	NOUN
cana-4548	11	11	is	be	AUX
cana-4548	11	12	provided	provide	VERB
cana-4548	11	13	to	to	PART
cana-4548	11	14	demonstrate	demonstrate	VERB
cana-4548	11	15	the	the	DET
cana-4548	11	16	applicability	applicability	NOUN
cana-4548	11	17	of	of	ADP
cana-4548	11	18	the	the	DET
cana-4548	11	19	proposed	propose	VERB
cana-4548	11	20	operators	operator	NOUN
cana-4548	11	21	.	.	PUNCT
cana-4548	12	1	a	a	DET
cana-4548	12	2	comparison	comparison	NOUN
cana-4548	12	3	with	with	ADP
cana-4548	12	4	existing	exist	VERB
cana-4548	12	5	operators	operator	NOUN
cana-4548	12	6	validates	validate	VERB
cana-4548	12	7	the	the	DET
cana-4548	12	8	effectiveness	effectiveness	NOUN
cana-4548	12	9	of	of	ADP
cana-4548	12	10	the	the	DET
cana-4548	12	11	proposed	propose	VERB
cana-4548	12	12	operators	operator	NOUN
cana-4548	12	13	.	.	PUNCT
cana-4548	13	1	keywords	keyword	NOUN
cana-4548	13	2	:	:	PUNCT
cana-4548	13	3	multi	multi	ADJ
cana-4548	13	4	-	-	ADJ
cana-4548	13	5	criteria	criterion	NOUN
cana-4548	13	6	group	group	NOUN
cana-4548	13	7	decision	decision	NOUN
cana-4548	13	8	-	-	PUNCT
cana-4548	13	9	making	making	NOUN
cana-4548	13	10	,	,	PUNCT
cana-4548	13	11	picture	picture	NOUN
cana-4548	13	12	fuzzy	fuzzy	ADJ
cana-4548	13	13	set	set	NOUN
cana-4548	13	14	,	,	PUNCT
cana-4548	13	15	schweizer	schweizer	PROPN
cana-4548	13	16	-	-	PUNCT
cana-4548	13	17	sklar	sklar	ADJ
cana-4548	13	18	tnorms	tnorm	NOUN
cana-4548	13	19	and	and	CCONJ
cana-4548	13	20	t	t	NOUN
cana-4548	13	21	-	-	PUNCT
cana-4548	13	22	conorms	conorm	NOUN
cana-4548	13	23	,	,	PUNCT
cana-4548	13	24	power	power	NOUN
cana-4548	13	25	aggregation	aggregation	NOUN
cana-4548	13	26	operator	operator	NOUN
cana-4548	13	27	,	,	PUNCT
cana-4548	13	28	road	road	NOUN
cana-4548	13	29	construction	construction	NOUN
cana-4548	13	30	companies	company	NOUN
cana-4548	13	31	.	.	PUNCT
cana-4548	14	1	1	1	X
cana-4548	14	2	.	.	X
cana-4548	14	3	introduction	introduction	NOUN
cana-4548	14	4	multi	multi	ADJ
cana-4548	14	5	-	-	ADJ
cana-4548	14	6	criteria	criterion	NOUN
cana-4548	14	7	group	group	NOUN
cana-4548	14	8	decision	decision	NOUN
cana-4548	14	9	-	-	PUNCT
cana-4548	14	10	making	make	VERB
cana-4548	14	11	(	(	PUNCT
cana-4548	14	12	mcgdm	mcgdm	NOUN
cana-4548	14	13	)	)	PUNCT
cana-4548	14	14	is	be	AUX
cana-4548	14	15	an	an	DET
cana-4548	14	16	important	important	ADJ
cana-4548	14	17	area	area	NOUN
cana-4548	14	18	of	of	ADP
cana-4548	14	19	decision	decision	NOUN
cana-4548	14	20	theory	theory	NOUN
cana-4548	14	21	with	with	ADP
cana-4548	14	22	widespread	widespread	ADJ
cana-4548	14	23	applications	application	NOUN
cana-4548	14	24	across	across	ADP
cana-4548	14	25	various	various	ADJ
cana-4548	14	26	fields	field	NOUN
cana-4548	14	27	.	.	PUNCT
cana-4548	15	1	in	in	ADP
cana-4548	15	2	many	many	ADJ
cana-4548	15	3	cases	case	NOUN
cana-4548	15	4	,	,	PUNCT
cana-4548	15	5	decision	decision	NOUN
cana-4548	15	6	-	-	PUNCT
cana-4548	15	7	makers	maker	NOUN
cana-4548	15	8	encounter	encounter	VERB
cana-4548	15	9	difficulties	difficulty	NOUN
cana-4548	15	10	in	in	ADP
cana-4548	15	11	reaching	reach	VERB
cana-4548	15	12	reasonable	reasonable	ADJ
cana-4548	15	13	conclusions	conclusion	NOUN
cana-4548	15	14	,	,	PUNCT
cana-4548	15	15	as	as	SCONJ
cana-4548	15	16	the	the	DET
cana-4548	15	17	process	process	NOUN
cana-4548	15	18	involves	involve	VERB
cana-4548	15	19	identifying	identify	VERB
cana-4548	15	20	multiple	multiple	ADJ
cana-4548	15	21	criteria	criterion	NOUN
cana-4548	15	22	and	and	CCONJ
cana-4548	15	23	evaluating	evaluate	VERB
cana-4548	15	24	several	several	ADJ
cana-4548	15	25	alternatives	alternative	NOUN
cana-4548	15	26	.	.	PUNCT
cana-4548	16	1	moreover	moreover	ADV
cana-4548	16	2	,	,	PUNCT
cana-4548	16	3	in	in	ADP
cana-4548	16	4	real	real	ADJ
cana-4548	16	5	-	-	PUNCT
cana-4548	16	6	world	world	NOUN
cana-4548	16	7	decision	decision	NOUN
cana-4548	16	8	-	-	PUNCT
cana-4548	16	9	making	making	NOUN
cana-4548	16	10	,	,	PUNCT
cana-4548	16	11	the	the	DET
cana-4548	16	12	ambiguity	ambiguity	NOUN
cana-4548	16	13	and	and	CCONJ
cana-4548	16	14	subjectivity	subjectivity	NOUN
cana-4548	16	15	inherent	inherent	ADJ
cana-4548	16	16	in	in	ADP
cana-4548	16	17	human	human	ADJ
cana-4548	16	18	qualitative	qualitative	ADJ
cana-4548	16	19	judgments	judgment	NOUN
cana-4548	16	20	often	often	ADV
cana-4548	16	21	result	result	VERB
cana-4548	16	22	in	in	ADP
cana-4548	16	23	expert	expert	ADJ
cana-4548	16	24	opinions	opinion	NOUN
cana-4548	16	25	that	that	PRON
cana-4548	16	26	encompass	encompass	VERB
cana-4548	16	27	a	a	DET
cana-4548	16	28	range	range	NOUN
cana-4548	16	29	of	of	ADP
cana-4548	16	30	responses	response	NOUN
cana-4548	16	31	such	such	ADJ
cana-4548	16	32	as	as	ADP
cana-4548	16	33	yes	yes	PROPN
cana-4548	16	34	,	,	PUNCT
cana-4548	16	35	abstain	abstain	NOUN
cana-4548	16	36	,	,	PUNCT
cana-4548	16	37	no	no	INTJ
cana-4548	16	38	,	,	PUNCT
cana-4548	16	39	or	or	CCONJ
cana-4548	16	40	refusal	refusal	NOUN
cana-4548	16	41	-	-	PUNCT
cana-4548	16	42	which	which	PRON
cana-4548	16	43	can	can	AUX
cana-4548	16	44	not	not	PART
cana-4548	16	45	be	be	AUX
cana-4548	16	46	accurately	accurately	ADV
cana-4548	16	47	represented	represent	VERB
cana-4548	16	48	by	by	ADP
cana-4548	16	49	crisp	crisp	ADJ
cana-4548	16	50	values	value	NOUN
cana-4548	16	51	.	.	PUNCT
cana-4548	17	1	in	in	ADP
cana-4548	17	2	1965	1965	NUM
cana-4548	17	3	,	,	PUNCT
cana-4548	17	4	zadeh	zadeh	PROPN
cana-4548	17	5	(	(	PUNCT
cana-4548	17	6	1965	1965	NUM
cana-4548	17	7	)	)	PUNCT
cana-4548	17	8	introduced	introduce	VERB
cana-4548	17	9	the	the	DET
cana-4548	17	10	foundational	foundational	ADJ
cana-4548	17	11	concept	concept	NOUN
cana-4548	17	12	of	of	ADP
cana-4548	17	13	fuzzy	fuzzy	ADJ
cana-4548	17	14	set	set	NOUN
cana-4548	17	15	(	(	PUNCT
cana-4548	17	16	fs	fs	NOUN
cana-4548	17	17	)	)	PUNCT
cana-4548	17	18	theory	theory	NOUN
cana-4548	17	19	,	,	PUNCT
cana-4548	17	20	which	which	PRON
cana-4548	17	21	incorporated	incorporate	VERB
cana-4548	17	22	the	the	DET
cana-4548	17	23	degree	degree	NOUN
cana-4548	17	24	of	of	ADP
cana-4548	17	25	membership	membership	NOUN
cana-4548	17	26	μ	μ	PROPN
cana-4548	17	27	.	.	PUNCT
cana-4548	18	1	this	this	DET
cana-4548	18	2	concept	concept	NOUN
cana-4548	18	3	has	have	AUX
cana-4548	18	4	since	since	ADV
cana-4548	18	5	been	be	AUX
cana-4548	18	6	applied	apply	VERB
cana-4548	18	7	to	to	ADP
cana-4548	18	8	numerous	numerous	ADJ
cana-4548	18	9	real	real	ADJ
cana-4548	18	10	-	-	PUNCT
cana-4548	18	11	world	world	NOUN
cana-4548	18	12	problems	problem	NOUN
cana-4548	18	13	.	.	PUNCT
cana-4548	19	1	later	later	ADV
cana-4548	19	2	,	,	PUNCT
cana-4548	19	3	atanassov	atanassov	PROPN
cana-4548	19	4	(	(	PUNCT
cana-4548	19	5	1986	1986	NUM
cana-4548	19	6	)	)	PUNCT
cana-4548	19	7	expanded	expand	VERB
cana-4548	19	8	on	on	ADP
cana-4548	19	9	fs	fs	ADP
cana-4548	19	10	theory	theory	NOUN
cana-4548	19	11	by	by	ADP
cana-4548	19	12	developing	develop	VERB
cana-4548	19	13	the	the	DET
cana-4548	19	14	intuitionistic	intuitionistic	ADJ
cana-4548	19	15	fuzzy	fuzzy	ADJ
cana-4548	19	16	set	set	NOUN
cana-4548	19	17	(	(	PUNCT
cana-4548	19	18	ifs	ifs	PROPN
cana-4548	19	19	)	)	PUNCT
cana-4548	19	20	theory	theory	NOUN
cana-4548	19	21	,	,	PUNCT
cana-4548	19	22	which	which	PRON
cana-4548	19	23	adds	add	VERB
cana-4548	19	24	the	the	DET
cana-4548	19	25	degree	degree	NOUN
cana-4548	19	26	of	of	ADP
cana-4548	19	27	non	non	ADJ
cana-4548	19	28	-	-	ADJ
cana-4548	19	29	membership	membership	ADJ
cana-4548	19	30	ν	ν	NOUN
cana-4548	19	31	alongside	alongside	ADP
cana-4548	19	32	the	the	DET
cana-4548	19	33	degree	degree	NOUN
cana-4548	19	34	of	of	ADP
cana-4548	19	35	membership	membership	NOUN
cana-4548	19	36	μ	μ	PROPN
cana-4548	19	37	under	under	ADP
cana-4548	19	38	the	the	DET
cana-4548	19	39	condition	condition	NOUN
cana-4548	19	40	that	that	SCONJ
cana-4548	19	41	0≤μ+ν≤1	0≤μ+ν≤1	NOUN
cana-4548	19	42	.	.	PUNCT
cana-4548	20	1	mailto:devakrishnan9@gmail.com	mailto:devakrishnan9@gmail.com	X
cana-4548	20	2	communications	communication	NOUN
cana-4548	20	3	on	on	ADP
cana-4548	20	4	applied	apply	VERB
cana-4548	20	5	nonlinear	nonlinear	ADJ
cana-4548	20	6	analysis	analysis	NOUN
cana-4548	20	7	issn	issn	NOUN
cana-4548	20	8	:	:	PUNCT
cana-4548	20	9	1074	1074	NUM
cana-4548	20	10	-	-	PUNCT
cana-4548	20	11	133x	133x	NUM
cana-4548	20	12	vol	vol	NOUN
cana-4548	20	13	32	32	NUM
cana-4548	20	14	no	no	NOUN
cana-4548	20	15	.	.	PUNCT
cana-4548	21	1	9s	9s	NUM
cana-4548	21	2	(	(	PUNCT
cana-4548	21	3	2025	2025	NUM
cana-4548	21	4	)	)	PUNCT
cana-4548	21	5	2679	2679	NUM
cana-4548	21	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4548	21	7	figure	figure	NOUN
cana-4548	21	8	1	1	NUM
cana-4548	21	9	:	:	PUNCT
cana-4548	21	10	extensions	extension	NOUN
cana-4548	21	11	of	of	ADP
cana-4548	21	12	pfs	pfs	PROPN
cana-4548	21	13	the	the	DET
cana-4548	21	14	ifs	ifs	PROPN
cana-4548	21	15	,	,	PUNCT
cana-4548	21	16	while	while	SCONJ
cana-4548	21	17	demonstrating	demonstrate	VERB
cana-4548	21	18	strong	strong	ADJ
cana-4548	21	19	capabilities	capability	NOUN
cana-4548	21	20	in	in	ADP
cana-4548	21	21	multi	multi	ADJ
cana-4548	21	22	-	-	ADJ
cana-4548	21	23	criteria	criterion	NOUN
cana-4548	21	24	decision	decision	NOUN
cana-4548	21	25	-	-	PUNCT
cana-4548	21	26	making	making	NOUN
cana-4548	21	27	(	(	PUNCT
cana-4548	21	28	madm	madm	NOUN
cana-4548	21	29	)	)	PUNCT
cana-4548	21	30	,	,	PUNCT
cana-4548	21	31	can	can	AUX
cana-4548	21	32	not	not	PART
cana-4548	21	33	adequately	adequately	ADV
cana-4548	21	34	express	express	VERB
cana-4548	21	35	more	more	ADV
cana-4548	21	36	complex	complex	ADJ
cana-4548	21	37	fuzzy	fuzzy	ADJ
cana-4548	21	38	information	information	NOUN
cana-4548	21	39	.	.	PUNCT
cana-4548	22	1	one	one	NUM
cana-4548	22	2	limitation	limitation	NOUN
cana-4548	22	3	is	be	AUX
cana-4548	22	4	its	its	PRON
cana-4548	22	5	inability	inability	NOUN
cana-4548	22	6	to	to	PART
cana-4548	22	7	capture	capture	VERB
cana-4548	22	8	ambiguous	ambiguous	ADJ
cana-4548	22	9	information	information	NOUN
cana-4548	22	10	,	,	PUNCT
cana-4548	22	11	such	such	ADJ
cana-4548	22	12	as	as	ADP
cana-4548	22	13	the	the	DET
cana-4548	22	14	degree	degree	NOUN
cana-4548	22	15	of	of	ADP
cana-4548	22	16	neutrality	neutrality	NOUN
cana-4548	22	17	(	(	PUNCT
cana-4548	22	18	η	η	NOUN
cana-4548	22	19	)	)	PUNCT
cana-4548	22	20	.	.	PUNCT
cana-4548	23	1	to	to	PART
cana-4548	23	2	address	address	VERB
cana-4548	23	3	this	this	DET
cana-4548	23	4	issue	issue	NOUN
cana-4548	23	5	,	,	PUNCT
cana-4548	23	6	cuong	cuong	PROPN
cana-4548	23	7	et	et	PROPN
cana-4548	23	8	al	al	PROPN
cana-4548	23	9	.	.	PROPN
cana-4548	24	1	(	(	PUNCT
cana-4548	24	2	2013	2013	NUM
cana-4548	24	3	)	)	PUNCT
cana-4548	24	4	,	,	PUNCT
cana-4548	24	5	introduced	introduce	VERB
cana-4548	24	6	the	the	DET
cana-4548	24	7	concept	concept	NOUN
cana-4548	24	8	of	of	ADP
cana-4548	24	9	the	the	DET
cana-4548	24	10	picture	picture	NOUN
cana-4548	24	11	fuzzy	fuzzy	ADJ
cana-4548	24	12	set	set	NOUN
cana-4548	24	13	(	(	PUNCT
cana-4548	24	14	pfs	pfs	PROPN
cana-4548	24	15	)	)	PUNCT
cana-4548	24	16	,	,	PUNCT
cana-4548	24	17	which	which	PRON
cana-4548	24	18	extends	extend	VERB
cana-4548	24	19	ifs	ifs	PROPN
cana-4548	24	20	by	by	ADP
cana-4548	24	21	adding	add	VERB
cana-4548	24	22	the	the	DET
cana-4548	24	23	degree	degree	NOUN
cana-4548	24	24	of	of	ADP
cana-4548	24	25	neutrality	neutrality	NOUN
cana-4548	24	26	(	(	PUNCT
cana-4548	24	27	η	η	NOUN
cana-4548	24	28	)	)	PUNCT
cana-4548	24	29	alongside	alongside	ADP
cana-4548	24	30	the	the	DET
cana-4548	24	31	degrees	degree	NOUN
cana-4548	24	32	of	of	ADP
cana-4548	24	33	membership	membership	NOUN
cana-4548	24	34	(	(	PUNCT
cana-4548	24	35	μ	μ	NOUN
cana-4548	24	36	)	)	PUNCT
cana-4548	24	37	and	and	CCONJ
cana-4548	24	38	non	non	ADJ
cana-4548	24	39	-	-	NOUN
cana-4548	24	40	membership	membership	ADJ
cana-4548	24	41	(	(	PUNCT
cana-4548	24	42	ν	ν	NOUN
cana-4548	24	43	)	)	PUNCT
cana-4548	24	44	,	,	PUNCT
cana-4548	24	45	under	under	ADP
cana-4548	24	46	the	the	DET
cana-4548	24	47	condition	condition	NOUN
cana-4548	24	48	0≤μ+η+ν≤1	0≤μ+η+ν≤1	PROPN
cana-4548	24	49	.	.	PUNCT
cana-4548	25	1	pfs	pfs	PROPN
cana-4548	25	2	models	model	NOUN
cana-4548	25	3	are	be	AUX
cana-4548	25	4	particularly	particularly	ADV
cana-4548	25	5	useful	useful	ADJ
cana-4548	25	6	in	in	ADP
cana-4548	25	7	situations	situation	NOUN
cana-4548	25	8	where	where	SCONJ
cana-4548	25	9	human	human	ADJ
cana-4548	25	10	opinions	opinion	NOUN
cana-4548	25	11	involve	involve	VERB
cana-4548	25	12	more	more	ADV
cana-4548	25	13	nuanced	nuanced	ADJ
cana-4548	25	14	responses	response	NOUN
cana-4548	25	15	such	such	ADJ
cana-4548	25	16	as	as	ADP
cana-4548	25	17	"	"	PUNCT
cana-4548	25	18	yes	yes	INTJ
cana-4548	25	19	,	,	PUNCT
cana-4548	25	20	"	"	PUNCT
cana-4548	25	21	"	"	PUNCT
cana-4548	25	22	no	no	INTJ
cana-4548	25	23	,	,	PUNCT
cana-4548	25	24	"	"	PUNCT
cana-4548	25	25	"	"	PUNCT
cana-4548	25	26	abstain	abstain	NOUN
cana-4548	25	27	,	,	PUNCT
cana-4548	25	28	"	"	PUNCT
cana-4548	25	29	and	and	CCONJ
cana-4548	25	30	"	"	PUNCT
cana-4548	25	31	refusal	refusal	NOUN
cana-4548	25	32	.	.	PUNCT
cana-4548	25	33	"	"	PUNCT
cana-4548	25	34	figure	figure	NOUN
cana-4548	25	35	1	1	NUM
cana-4548	25	36	illustrates	illustrate	VERB
cana-4548	25	37	the	the	DET
cana-4548	25	38	extensions	extension	NOUN
cana-4548	25	39	of	of	ADP
cana-4548	25	40	a	a	DET
cana-4548	25	41	pfs	pfs	PROPN
cana-4548	25	42	.	.	PUNCT
cana-4548	26	1	additionally	additionally	ADV
cana-4548	26	2	,	,	PUNCT
cana-4548	26	3	a	a	DET
cana-4548	26	4	few	few	ADJ
cana-4548	26	5	students	student	NOUN
cana-4548	26	6	may	may	AUX
cana-4548	26	7	express	express	VERB
cana-4548	26	8	refusal	refusal	NOUN
cana-4548	26	9	to	to	PART
cana-4548	26	10	visit	visit	VERB
cana-4548	26	11	either	either	DET
cana-4548	26	12	destination	destination	NOUN
cana-4548	26	13	(	(	PUNCT
cana-4548	26	14	π	π	NOUN
cana-4548	26	15	)	)	PUNCT
cana-4548	26	16	.	.	PUNCT
cana-4548	27	1	cuong	cuong	PROPN
cana-4548	27	2	et	et	PROPN
cana-4548	27	3	al	al	PROPN
cana-4548	27	4	.	.	PUNCT
cana-4548	28	1	(	(	PUNCT
cana-4548	28	2	2016	2016	NUM
cana-4548	28	3	)	)	PUNCT
cana-4548	28	4	investigated	investigate	VERB
cana-4548	28	5	the	the	DET
cana-4548	28	6	classification	classification	NOUN
cana-4548	28	7	of	of	ADP
cana-4548	28	8	representable	representable	ADJ
cana-4548	28	9	picture	picture	NOUN
cana-4548	28	10	t	t	NOUN
cana-4548	28	11	-	-	PUNCT
cana-4548	28	12	norms	norm	NOUN
cana-4548	28	13	and	and	CCONJ
cana-4548	28	14	picture	picture	NOUN
cana-4548	28	15	t	t	PROPN
cana-4548	28	16	-	-	PUNCT
cana-4548	28	17	conorms	conorm	NOUN
cana-4548	28	18	along	along	ADV
cana-4548	28	19	with	with	ADP
cana-4548	28	20	their	their	PRON
cana-4548	28	21	properties	property	NOUN
cana-4548	28	22	.	.	PUNCT
cana-4548	29	1	yager	yager	NOUN
cana-4548	29	2	(	(	PUNCT
cana-4548	29	3	1988	1988	NUM
cana-4548	29	4	)	)	PUNCT
cana-4548	29	5	introduced	introduce	VERB
cana-4548	29	6	the	the	DET
cana-4548	29	7	ordered	order	VERB
cana-4548	29	8	weighted	weight	VERB
cana-4548	29	9	aggregation	aggregation	NOUN
cana-4548	29	10	(	(	PUNCT
cana-4548	29	11	owa	owa	ADJ
cana-4548	29	12	)	)	PUNCT
cana-4548	29	13	operator	operator	NOUN
cana-4548	29	14	and	and	CCONJ
cana-4548	29	15	explored	explore	VERB
cana-4548	29	16	its	its	PRON
cana-4548	29	17	properties	property	NOUN
cana-4548	29	18	.	.	PUNCT
cana-4548	30	1	wei	wei	PROPN
cana-4548	30	2	(	(	PUNCT
cana-4548	30	3	2017	2017	NUM
cana-4548	30	4	)	)	PUNCT
cana-4548	30	5	described	describe	VERB
cana-4548	30	6	various	various	ADJ
cana-4548	30	7	pf	pf	PROPN
cana-4548	30	8	arithmetic	arithmetic	ADJ
cana-4548	30	9	and	and	CCONJ
cana-4548	30	10	geometric	geometric	ADJ
cana-4548	30	11	operators	operator	NOUN
cana-4548	30	12	,	,	PUNCT
cana-4548	30	13	as	as	ADV
cana-4548	30	14	well	well	ADV
cana-4548	30	15	as	as	ADP
cana-4548	30	16	pf	pf	PROPN
cana-4548	30	17	hybrid	hybrid	ADJ
cana-4548	30	18	aggregation	aggregation	NOUN
cana-4548	30	19	operators	operator	NOUN
cana-4548	30	20	(	(	PUNCT
cana-4548	30	21	aos	aos	PROPN
cana-4548	30	22	)	)	PUNCT
cana-4548	30	23	and	and	CCONJ
cana-4548	30	24	their	their	PRON
cana-4548	30	25	applications	application	NOUN
cana-4548	30	26	.	.	PUNCT
cana-4548	31	1	garg	garg	NOUN
cana-4548	31	2	(	(	PUNCT
cana-4548	31	3	2017	2017	NUM
cana-4548	31	4	)	)	PUNCT
cana-4548	31	5	presented	present	VERB
cana-4548	31	6	a	a	DET
cana-4548	31	7	series	series	NOUN
cana-4548	31	8	of	of	ADP
cana-4548	31	9	aos	aos	PROPN
cana-4548	31	10	for	for	ADP
cana-4548	31	11	pfss	pfss	NOUN
cana-4548	31	12	that	that	PRON
cana-4548	31	13	were	be	AUX
cana-4548	31	14	applied	apply	VERB
cana-4548	31	15	to	to	PART
cana-4548	31	16	solve	solve	VERB
cana-4548	31	17	multicriteria	multicriteria	NOUN
cana-4548	31	18	decision	decision	NOUN
cana-4548	31	19	-	-	PUNCT
cana-4548	31	20	making	making	NOUN
cana-4548	31	21	(	(	PUNCT
cana-4548	31	22	mcdm	mcdm	ADJ
cana-4548	31	23	)	)	PUNCT
cana-4548	31	24	problems	problem	NOUN
cana-4548	31	25	.	.	PUNCT
cana-4548	32	1	wei	wei	PROPN
cana-4548	32	2	(	(	PUNCT
cana-4548	32	3	2018	2018	NUM
cana-4548	32	4	)	)	PUNCT
cana-4548	32	5	studied	study	VERB
cana-4548	32	6	the	the	DET
cana-4548	32	7	madm	madm	NOUN
cana-4548	32	8	problem	problem	NOUN
cana-4548	32	9	using	use	VERB
cana-4548	32	10	arithmetic	arithmetic	ADJ
cana-4548	32	11	and	and	CCONJ
cana-4548	32	12	geometric	geometric	ADJ
cana-4548	32	13	aos	aos	NOUN
cana-4548	32	14	based	base	VERB
cana-4548	32	15	on	on	ADP
cana-4548	32	16	hamacher	hamacher	NOUN
cana-4548	32	17	operations	operation	NOUN
cana-4548	32	18	in	in	ADP
cana-4548	32	19	the	the	DET
cana-4548	32	20	pf	pf	PROPN
cana-4548	32	21	context	context	NOUN
cana-4548	32	22	.	.	PUNCT
cana-4548	33	1	khan	khan	PROPN
cana-4548	33	2	et	et	PROPN
cana-4548	33	3	al	al	PROPN
cana-4548	33	4	.	.	PROPN
cana-4548	34	1	(	(	PUNCT
cana-4548	34	2	2019	2019	NUM
cana-4548	34	3	)	)	PUNCT
cana-4548	34	4	proposed	propose	VERB
cana-4548	34	5	aos	aos	PROPN
cana-4548	34	6	using	use	VERB
cana-4548	34	7	pf	pf	PROPN
cana-4548	34	8	einstein	einstein	PROPN
cana-4548	34	9	operations	operation	NOUN
cana-4548	34	10	and	and	CCONJ
cana-4548	34	11	discussed	discuss	VERB
cana-4548	34	12	their	their	PRON
cana-4548	34	13	application	application	NOUN
cana-4548	34	14	in	in	ADP
cana-4548	34	15	pf	pf	NOUN
cana-4548	34	16	-	-	PUNCT
cana-4548	34	17	based	base	VERB
cana-4548	34	18	decisionmaking	decisionmaking	NOUN
cana-4548	34	19	.	.	PUNCT
cana-4548	35	1	zhang	zhang	PROPN
cana-4548	35	2	et	et	PROPN
cana-4548	35	3	al	al	PROPN
cana-4548	35	4	.	.	PROPN
cana-4548	36	1	(	(	PUNCT
cana-4548	36	2	2018	2018	NUM
cana-4548	36	3	)	)	PUNCT
cana-4548	36	4	introduced	introduce	VERB
cana-4548	36	5	pf	pf	PROPN
cana-4548	36	6	dombi	dombi	PROPN
cana-4548	36	7	heronian	heronian	PROPN
cana-4548	36	8	mean	mean	PROPN
cana-4548	36	9	operators	operator	NOUN
cana-4548	36	10	for	for	ADP
cana-4548	36	11	the	the	DET
cana-4548	36	12	madm	madm	NOUN
cana-4548	36	13	problem	problem	NOUN
cana-4548	36	14	.	.	PUNCT
cana-4548	37	1	jana	jana	PROPN
cana-4548	37	2	et	et	PROPN
cana-4548	37	3	al	al	PROPN
cana-4548	37	4	.	.	PROPN
cana-4548	38	1	(	(	PUNCT
cana-4548	38	2	2019	2019	NUM
cana-4548	38	3	)	)	PUNCT
cana-4548	38	4	developed	develop	VERB
cana-4548	38	5	pf	pf	PROPN
cana-4548	38	6	dombi	dombi	PROPN
cana-4548	38	7	arithmetic	arithmetic	ADJ
cana-4548	38	8	and	and	CCONJ
cana-4548	38	9	geometric	geometric	ADJ
cana-4548	38	10	aos	aos	PROPN
cana-4548	38	11	to	to	PART
cana-4548	38	12	solve	solve	VERB
cana-4548	38	13	decisionmaking	decisionmake	VERB
cana-4548	38	14	problems	problem	NOUN
cana-4548	38	15	.	.	PUNCT
cana-4548	39	1	additionally	additionally	ADV
cana-4548	39	2	,	,	PUNCT
cana-4548	39	3	jana	jana	PROPN
cana-4548	39	4	et	et	PROPN
cana-4548	39	5	al	al	PROPN
cana-4548	39	6	.	.	PROPN
cana-4548	40	1	(	(	PUNCT
cana-4548	40	2	2019	2019	NUM
cana-4548	40	3	)	)	PUNCT
cana-4548	40	4	employed	employ	VERB
cana-4548	40	5	pf	pf	PROPN
cana-4548	40	6	hamacher	hamacher	PROPN
cana-4548	40	7	aos	aos	PROPN
cana-4548	40	8	to	to	PART
cana-4548	40	9	construct	construct	VERB
cana-4548	40	10	madm	madm	NOUN
cana-4548	40	11	approaches	approach	NOUN
cana-4548	40	12	for	for	ADP
cana-4548	40	13	enterprise	enterprise	NOUN
cana-4548	40	14	performance	performance	NOUN
cana-4548	40	15	evaluation	evaluation	NOUN
cana-4548	40	16	within	within	ADP
cana-4548	40	17	the	the	DET
cana-4548	40	18	pf	pf	PROPN
cana-4548	40	19	context	context	NOUN
cana-4548	40	20	.	.	PUNCT
cana-4548	41	1	ates	ates	PROPN
cana-4548	41	2	et	et	PROPN
cana-4548	41	3	al	al	PROPN
cana-4548	41	4	.	.	PROPN
cana-4548	42	1	(	(	PUNCT
cana-4548	42	2	2020	2020	NUM
cana-4548	42	3	)	)	PUNCT
cana-4548	42	4	proposed	propose	VERB
cana-4548	42	5	novel	novel	NOUN
cana-4548	42	6	pf	pf	NOUN
cana-4548	42	7	aggregation	aggregation	NOUN
cana-4548	42	8	operators	operator	NOUN
cana-4548	42	9	and	and	CCONJ
cana-4548	42	10	extended	extend	VERB
cana-4548	42	11	the	the	DET
cana-4548	42	12	bonferroni	bonferroni	NOUN
cana-4548	42	13	mean	mean	NOUN
cana-4548	42	14	operator	operator	NOUN
cana-4548	42	15	to	to	ADP
cana-4548	42	16	mcdm	mcdm	ADJ
cana-4548	42	17	applications	application	NOUN
cana-4548	42	18	.	.	PUNCT
cana-4548	43	1	wang	wang	PROPN
cana-4548	43	2	et	et	PROPN
cana-4548	43	3	al	al	PROPN
cana-4548	43	4	.	.	PROPN
cana-4548	44	1	(	(	PUNCT
cana-4548	44	2	2018	2018	NUM
cana-4548	44	3	)	)	PUNCT
cana-4548	44	4	proposed	propose	VERB
cana-4548	44	5	pf	pf	NOUN
cana-4548	44	6	muirhead	muirhead	NOUN
cana-4548	44	7	mean	mean	VERB
cana-4548	44	8	operators	operator	NOUN
cana-4548	44	9	and	and	CCONJ
cana-4548	44	10	demonstrated	demonstrate	VERB
cana-4548	44	11	their	their	PRON
cana-4548	44	12	application	application	NOUN
cana-4548	44	13	for	for	ADP
cana-4548	44	14	financial	financial	ADJ
cana-4548	44	15	investment	investment	NOUN
cana-4548	44	16	risk	risk	NOUN
cana-4548	44	17	evaluation	evaluation	NOUN
cana-4548	44	18	.	.	PUNCT
cana-4548	45	1	qiyas	qiyas	NOUN
cana-4548	45	2	et	et	PROPN
cana-4548	45	3	al	al	PROPN
cana-4548	45	4	.	.	PROPN
cana-4548	45	5	(	(	PUNCT
cana-4548	45	6	2020	2020	NUM
cana-4548	45	7	)	)	PUNCT
cana-4548	45	8	introduced	introduce	VERB
cana-4548	45	9	several	several	ADJ
cana-4548	45	10	aos	aos	NOUN
cana-4548	45	11	using	use	VERB
cana-4548	45	12	yager	yager	NOUN
cana-4548	45	13	operators	operator	NOUN
cana-4548	45	14	in	in	ADP
cana-4548	45	15	the	the	DET
cana-4548	45	16	pf	pf	PROPN
cana-4548	45	17	context	context	NOUN
cana-4548	45	18	.	.	PUNCT
cana-4548	46	1	several	several	ADJ
cana-4548	46	2	other	other	ADJ
cana-4548	46	3	madm	madm	NOUN
cana-4548	46	4	approaches	approach	NOUN
cana-4548	46	5	based	base	VERB
cana-4548	46	6	on	on	ADP
cana-4548	46	7	aos	aos	PROPN
cana-4548	46	8	for	for	ADP
cana-4548	46	9	pfns	pfns	NOUN
cana-4548	46	10	have	have	AUX
cana-4548	46	11	been	be	AUX
cana-4548	46	12	proposed	propose	VERB
cana-4548	46	13	,	,	PUNCT
cana-4548	46	14	including	include	VERB
cana-4548	46	15	those	those	PRON
cana-4548	46	16	by	by	ADP
cana-4548	46	17	lin	lin	PROPN
cana-4548	46	18	et	et	PROPN
cana-4548	46	19	al	al	PROPN
cana-4548	46	20	.	.	PROPN
cana-4548	47	1	(	(	PUNCT
cana-4548	47	2	2021	2021	NUM
cana-4548	47	3	)	)	PUNCT
cana-4548	47	4	,	,	PUNCT
cana-4548	47	5	qin	qin	PROPN
cana-4548	47	6	et	et	PROPN
cana-4548	47	7	al	al	PROPN
cana-4548	47	8	.	.	PROPN
cana-4548	48	1	(	(	PUNCT
cana-4548	48	2	2021	2021	NUM
cana-4548	48	3	)	)	PUNCT
cana-4548	48	4	,	,	PUNCT
cana-4548	48	5	seikh	seikh	VERB
cana-4548	48	6	et	et	PROPN
cana-4548	48	7	al	al	PROPN
cana-4548	48	8	.	.	PROPN
cana-4548	49	1	(	(	PUNCT
cana-4548	49	2	2021	2021	NUM
cana-4548	49	3	)	)	PUNCT
cana-4548	49	4	,	,	PUNCT
cana-4548	49	5	ullah	ullah	PROPN
cana-4548	49	6	(	(	PUNCT
cana-4548	49	7	2021	2021	NUM
cana-4548	49	8	)	)	PUNCT
cana-4548	49	9	,	,	PUNCT
cana-4548	49	10	and	and	CCONJ
cana-4548	49	11	senapati	senapati	PROPN
cana-4548	49	12	(	(	PUNCT
cana-4548	49	13	2022	2022	NUM
cana-4548	49	14	)	)	PUNCT
cana-4548	49	15	.	.	PUNCT
cana-4548	50	1	communications	communication	NOUN
cana-4548	50	2	on	on	ADP
cana-4548	50	3	applied	apply	VERB
cana-4548	50	4	nonlinear	nonlinear	ADJ
cana-4548	50	5	analysis	analysis	NOUN
cana-4548	50	6	issn	issn	NOUN
cana-4548	50	7	:	:	PUNCT
cana-4548	50	8	1074	1074	NUM
cana-4548	50	9	-	-	PUNCT
cana-4548	50	10	133x	133x	NUM
cana-4548	50	11	vol	vol	NOUN
cana-4548	50	12	32	32	NUM
cana-4548	50	13	no	no	NOUN
cana-4548	50	14	.	.	PUNCT
cana-4548	51	1	9s	9s	NUM
cana-4548	51	2	(	(	PUNCT
cana-4548	51	3	2025	2025	NUM
cana-4548	51	4	)	)	PUNCT
cana-4548	51	5	2680	2680	NUM
cana-4548	51	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4548	51	7	table	table	NOUN
cana-4548	51	8	1	1	NUM
cana-4548	51	9	:	:	PUNCT
cana-4548	51	10	comparison	comparison	NOUN
cana-4548	51	11	of	of	ADP
cana-4548	51	12	different	different	ADJ
cana-4548	51	13	approaches	approach	NOUN
cana-4548	51	14	for	for	ADP
cana-4548	51	15	picture	picture	NOUN
cana-4548	51	16	fuzzy	fuzzy	ADJ
cana-4548	51	17	aos	aos	PROPN
cana-4548	51	18	authors	author	NOUN
cana-4548	51	19	geometric	geometric	ADJ
cana-4548	51	20	operators	operator	NOUN
cana-4548	51	21	status	status	NOUN
cana-4548	51	22	of	of	ADP
cana-4548	51	23	weight	weight	NOUN
cana-4548	51	24	dm	dm	X
cana-4548	51	25	method	method	VERB
cana-4548	51	26	dm	dm	PROPN
cana-4548	51	27	solution	solution	NOUN
cana-4548	51	28	garg	garg	NOUN
cana-4548	51	29	,	,	PUNCT
cana-4548	51	30	et	et	PROPN
cana-4548	51	31	al	al	PROPN
cana-4548	51	32	.	.	PROPN
cana-4548	52	1	(	(	PUNCT
cana-4548	52	2	2023	2023	NUM
cana-4548	52	3	)	)	PUNCT
cana-4548	53	1	if	if	SCONJ
cana-4548	53	2	schweizer	schweizer	PROPN
cana-4548	53	3	-	-	PUNCT
cana-4548	53	4	sklar	sklar	ADJ
cana-4548	53	5	power	power	NOUN
cana-4548	53	6	if	if	SCONJ
cana-4548	53	7	schweizer	schweizer	PROPN
cana-4548	53	8	-	-	PUNCT
cana-4548	53	9	sklar	sklar	PROPN
cana-4548	53	10	weighted	weight	VERB
cana-4548	53	11	known	know	VERB
cana-4548	53	12	madm	madm	NOUN
cana-4548	53	13	score	score	NOUN
cana-4548	53	14	function	function	NOUN
cana-4548	53	15	khan	khan	PROPN
cana-4548	53	16	et	et	PROPN
cana-4548	53	17	al	al	PROPN
cana-4548	53	18	.	.	PROPN
cana-4548	53	19	(	(	PUNCT
cana-4548	53	20	2022	2022	NUM
cana-4548	53	21	)	)	PUNCT
cana-4548	53	22	if	if	SCONJ
cana-4548	53	23	schweizer	schweizer	PROPN
cana-4548	53	24	-	-	PUNCT
cana-4548	53	25	sklar	sklar	ADJ
cana-4548	53	26	generalized	generalize	VERB
cana-4548	53	27	power	power	NOUN
cana-4548	53	28	weighted	weight	VERB
cana-4548	53	29	if	if	SCONJ
cana-4548	53	30	schweizer	schweizer	PROPN
cana-4548	53	31	-	-	PUNCT
cana-4548	53	32	sklar	sklar	ADJ
cana-4548	53	33	generalized	generalized	ADJ
cana-4548	53	34	power	power	NOUN
cana-4548	53	35	ordered	order	VERB
cana-4548	53	36	weighted	weight	VERB
cana-4548	53	37	known	know	VERB
cana-4548	53	38	magdm	magdm	NOUN
cana-4548	53	39	score	score	NOUN
cana-4548	53	40	function	function	PROPN
cana-4548	53	41	biswas	biswas	PROPN
cana-4548	53	42	,	,	PUNCT
cana-4548	53	43	a	a	PRON
cana-4548	53	44	&	&	CCONJ
cana-4548	53	45	deb	deb	PROPN
cana-4548	53	46	,	,	PUNCT
cana-4548	53	47	n.	n.	NOUN
cana-4548	53	48	(	(	PUNCT
cana-4548	53	49	2021	2021	NUM
cana-4548	53	50	)	)	PUNCT
cana-4548	53	51	pyf	pyf	PROPN
cana-4548	53	52	schweizer	schweizer	PROPN
cana-4548	53	53	-	-	PUNCT
cana-4548	53	54	sklar	sklar	ADJ
cana-4548	53	55	power	power	NOUN
cana-4548	53	56	weighted	weight	VERB
cana-4548	53	57	known	know	VERB
cana-4548	53	58	madm	madm	NOUN
cana-4548	53	59	score	score	NOUN
cana-4548	53	60	function	function	PROPN
cana-4548	53	61	wei	wei	PROPN
cana-4548	53	62	,	,	PUNCT
cana-4548	53	63	et	et	PROPN
cana-4548	53	64	al	al	PROPN
cana-4548	53	65	.	.	PROPN
cana-4548	54	1	(	(	PUNCT
cana-4548	54	2	2022	2022	NUM
cana-4548	54	3	)	)	PUNCT
cana-4548	54	4	ff	ff	PROPN
cana-4548	54	5	schweizer	schweizer	PROPN
cana-4548	54	6	-	-	PUNCT
cana-4548	54	7	sklar	sklar	PROPN
cana-4548	54	8	weighted	weight	VERB
cana-4548	54	9	unknown	unknown	ADJ
cana-4548	54	10	magdm	magdm	NOUN
cana-4548	54	11	bestand	bestand	VERB
cana-4548	54	12	worst	bad	ADJ
cana-4548	54	13	ma	ma	PROPN
cana-4548	54	14	et	et	PROPN
cana-4548	54	15	al	al	PROPN
cana-4548	54	16	.	.	PROPN
cana-4548	55	1	(	(	PUNCT
cana-4548	55	2	2024	2024	NUM
cana-4548	55	3	)	)	PUNCT
cana-4548	55	4	q	q	X
cana-4548	55	5	-	-	PUNCT
cana-4548	55	6	rof	rof	NOUN
cana-4548	55	7	schweizer	schweizer	PROPN
cana-4548	55	8	-	-	PUNCT
cana-4548	55	9	sklar	sklar	ADJ
cana-4548	55	10	power	power	NOUN
cana-4548	55	11	and	and	CCONJ
cana-4548	55	12	q	q	ADJ
cana-4548	55	13	-	-	PUNCT
cana-4548	55	14	rof	rof	NOUN
cana-4548	55	15	schweizer	schweizer	PROPN
cana-4548	55	16	-	-	PUNCT
cana-4548	55	17	sklar	sklar	ADJ
cana-4548	55	18	power	power	NOUN
cana-4548	55	19	weighted	weight	VERB
cana-4548	55	20	known	know	VERB
cana-4548	55	21	madm	madm	NOUN
cana-4548	55	22	score	score	NOUN
cana-4548	55	23	function	function	NOUN
cana-4548	55	24	hussain	hussain	PROPN
cana-4548	55	25	,	,	PUNCT
cana-4548	55	26	et	et	PROPN
cana-4548	55	27	al	al	PROPN
cana-4548	55	28	(	(	PUNCT
cana-4548	55	29	2022	2022	NUM
cana-4548	55	30	)	)	PUNCT
cana-4548	55	31	pf	pf	PROPN
cana-4548	55	32	schweizer	schweizer	PROPN
cana-4548	55	33	-	-	PUNCT
cana-4548	55	34	sklar	sklar	ADJ
cana-4548	55	35	prioritized	prioritized	NOUN
cana-4548	55	36	and	and	CCONJ
cana-4548	55	37	pf	pf	ADP
cana-4548	55	38	schweizer	schweizer	PROPN
cana-4548	55	39	-	-	PUNCT
cana-4548	55	40	sklar	sklar	ADJ
cana-4548	55	41	prioritized	prioritized	NOUN
cana-4548	55	42	weighted	weight	VERB
cana-4548	55	43	known	know	VERB
cana-4548	55	44	madm	madm	NOUN
cana-4548	55	45	score	score	NOUN
cana-4548	55	46	function	function	NOUN
cana-4548	55	47	proposed	propose	VERB
cana-4548	55	48	work	work	NOUN
cana-4548	55	49	pf	pf	PROPN
cana-4548	55	50	schweizer	schweizer	PROPN
cana-4548	55	51	-	-	PUNCT
cana-4548	55	52	sklar	sklar	ADJ
cana-4548	55	53	power	power	NOUN
cana-4548	55	54	weighted	weight	VERB
cana-4548	55	55	and	and	CCONJ
cana-4548	55	56	pf	pf	ADP
cana-4548	55	57	schweizersklar	schweizersklar	ADJ
cana-4548	55	58	power	power	NOUN
cana-4548	55	59	ordered	order	VERB
cana-4548	55	60	weighted	weight	VERB
cana-4548	55	61	unknown	unknown	ADJ
cana-4548	55	62	magdm	magdm	NOUN
cana-4548	55	63	score	score	VERB
cana-4548	55	64	function	function	NOUN
cana-4548	55	65	furthermore	furthermore	ADV
cana-4548	55	66	,	,	PUNCT
cana-4548	55	67	various	various	ADJ
cana-4548	55	68	aos	aos	NOUN
cana-4548	55	69	based	base	VERB
cana-4548	55	70	on	on	ADP
cana-4548	55	71	the	the	DET
cana-4548	55	72	schweizer	schweizer	PROPN
cana-4548	55	73	-	-	PUNCT
cana-4548	55	74	sklar	sklar	ADJ
cana-4548	55	75	(	(	PUNCT
cana-4548	55	76	ss	ss	NOUN
cana-4548	55	77	)	)	PUNCT
cana-4548	55	78	operational	operational	ADJ
cana-4548	55	79	law	law	NOUN
cana-4548	55	80	within	within	ADP
cana-4548	55	81	different	different	ADJ
cana-4548	55	82	fs	f	NOUN
cana-4548	55	83	frameworks	framework	NOUN
cana-4548	55	84	are	be	AUX
cana-4548	55	85	summarized	summarize	VERB
cana-4548	55	86	in	in	ADP
cana-4548	55	87	table	table	NOUN
cana-4548	55	88	1	1	NUM
cana-4548	55	89	harish	harish	NOUN
cana-4548	55	90	garg	garg	NOUN
cana-4548	55	91	,	,	PUNCT
cana-4548	55	92	et	et	PROPN
cana-4548	55	93	al	al	PROPN
cana-4548	55	94	.	.	PROPN
cana-4548	56	1	(	(	PUNCT
cana-4548	56	2	2023	2023	NUM
cana-4548	56	3	)	)	PUNCT
cana-4548	56	4	introduced	introduce	VERB
cana-4548	56	5	the	the	DET
cana-4548	56	6	ifss	ifss	NOUN
cana-4548	56	7	prioritized	prioritize	VERB
cana-4548	56	8	ao	ao	NOUN
cana-4548	56	9	for	for	ADP
cana-4548	56	10	solving	solve	VERB
cana-4548	56	11	mcdm	mcdm	ADJ
cana-4548	56	12	problems	problem	NOUN
cana-4548	56	13	.	.	PUNCT
cana-4548	57	1	khan	khan	PROPN
cana-4548	57	2	et	et	PROPN
cana-4548	57	3	al	al	PROPN
cana-4548	57	4	.	.	PROPN
cana-4548	58	1	(	(	PUNCT
cana-4548	58	2	2022	2022	NUM
cana-4548	58	3	)	)	PUNCT
cana-4548	58	4	explored	explore	VERB
cana-4548	58	5	the	the	DET
cana-4548	58	6	concept	concept	NOUN
cana-4548	58	7	of	of	ADP
cana-4548	58	8	the	the	DET
cana-4548	58	9	ifss	ifss	ADJ
cana-4548	58	10	generalized	generalize	VERB
cana-4548	58	11	power	power	NOUN
cana-4548	58	12	ao	ao	PROPN
cana-4548	58	13	.	.	PROPN
cana-4548	59	1	biswas	biswas	PROPN
cana-4548	59	2	,	,	PUNCT
cana-4548	59	3	a.	a.	PROPN
cana-4548	59	4	&	&	CCONJ
cana-4548	59	5	deb	deb	PROPN
cana-4548	59	6	,	,	PUNCT
cana-4548	59	7	n.	n.	NOUN
cana-4548	59	8	(	(	PUNCT
cana-4548	59	9	2021	2021	NUM
cana-4548	59	10	)	)	PUNCT
cana-4548	59	11	developed	develop	VERB
cana-4548	59	12	the	the	DET
cana-4548	59	13	ss	ss	PROPN
cana-4548	59	14	power	power	NOUN
cana-4548	59	15	ao	ao	PROPN
cana-4548	59	16	in	in	ADP
cana-4548	59	17	a	a	DET
cana-4548	59	18	pythagorean	pythagorean	ADJ
cana-4548	59	19	fuzzy	fuzzy	NOUN
cana-4548	59	20	(	(	PUNCT
cana-4548	59	21	pyf	pyf	PROPN
cana-4548	59	22	)	)	PUNCT
cana-4548	59	23	environment	environment	NOUN
cana-4548	59	24	.	.	PUNCT
cana-4548	60	1	wei	wei	PROPN
cana-4548	60	2	,	,	PUNCT
cana-4548	60	3	d	d	PROPN
cana-4548	60	4	et	et	PROPN
cana-4548	60	5	al	al	PROPN
cana-4548	60	6	.	.	PROPN
cana-4548	60	7	(	(	PUNCT
cana-4548	60	8	2022	2022	NUM
cana-4548	60	9	)	)	PUNCT
cana-4548	60	10	established	establish	VERB
cana-4548	60	11	the	the	DET
cana-4548	60	12	fermatean	fermatean	ADJ
cana-4548	60	13	fuzzy	fuzzy	NOUN
cana-4548	60	14	(	(	PUNCT
cana-4548	60	15	ff	ff	NOUN
cana-4548	60	16	)	)	PUNCT
cana-4548	60	17	ss	ss	NOUN
cana-4548	60	18	in	in	ADP
cana-4548	60	19	green	green	ADJ
cana-4548	60	20	supplier	supplier	NOUN
cana-4548	60	21	selection	selection	NOUN
cana-4548	60	22	.	.	PUNCT
cana-4548	61	1	ma	ma	PROPN
cana-4548	61	2	et	et	PROPN
cana-4548	61	3	al	al	PROPN
cana-4548	61	4	.	.	PROPN
cana-4548	62	1	(	(	PUNCT
cana-4548	62	2	2024	2024	NUM
cana-4548	62	3	)	)	PUNCT
cana-4548	62	4	proposed	propose	VERB
cana-4548	62	5	the	the	DET
cana-4548	62	6	q	q	NOUN
cana-4548	62	7	-	-	PUNCT
cana-4548	62	8	rung	rung	ADJ
cana-4548	62	9	orthopair	orthopair	NOUN
cana-4548	62	10	fuzzy	fuzzy	ADJ
cana-4548	62	11	(	(	PUNCT
cana-4548	62	12	q	q	NOUN
cana-4548	62	13	-	-	PUNCT
cana-4548	62	14	rof	rof	NOUN
cana-4548	62	15	)	)	PUNCT
cana-4548	62	16	ss	ss	NOUN
cana-4548	62	17	prioritized	prioritize	VERB
cana-4548	62	18	operator	operator	NOUN
cana-4548	62	19	for	for	ADP
cana-4548	62	20	madm	madm	NOUN
cana-4548	62	21	problems	problem	NOUN
cana-4548	62	22	.	.	PUNCT
cana-4548	63	1	hussain	hussain	PROPN
cana-4548	63	2	et	et	PROPN
cana-4548	63	3	al	al	PROPN
cana-4548	63	4	(	(	PUNCT
cana-4548	63	5	2022	2022	NUM
cana-4548	63	6	)	)	PUNCT
cana-4548	63	7	developed	develop	VERB
cana-4548	63	8	the	the	DET
cana-4548	63	9	pfss	pfss	ADJ
cana-4548	63	10	prioritized	prioritize	VERB
cana-4548	63	11	operator	operator	NOUN
cana-4548	63	12	for	for	ADP
cana-4548	63	13	solving	solve	VERB
cana-4548	63	14	madm	madm	NOUN
cana-4548	63	15	problems	problem	NOUN
cana-4548	63	16	.	.	PUNCT
cana-4548	64	1	communications	communication	NOUN
cana-4548	64	2	on	on	ADP
cana-4548	64	3	applied	apply	VERB
cana-4548	64	4	nonlinear	nonlinear	ADJ
cana-4548	64	5	analysis	analysis	NOUN
cana-4548	64	6	issn	issn	NOUN
cana-4548	64	7	:	:	PUNCT
cana-4548	64	8	1074	1074	NUM
cana-4548	64	9	-	-	PUNCT
cana-4548	64	10	133x	133x	NUM
cana-4548	64	11	vol	vol	NOUN
cana-4548	64	12	32	32	NUM
cana-4548	64	13	no	no	NOUN
cana-4548	64	14	.	.	PUNCT
cana-4548	65	1	9s	9s	NUM
cana-4548	65	2	(	(	PUNCT
cana-4548	65	3	2025	2025	NUM
cana-4548	65	4	)	)	PUNCT
cana-4548	65	5	2681	2681	NUM
cana-4548	65	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4548	66	1	this	this	DET
cana-4548	66	2	article	article	NOUN
cana-4548	66	3	introduces	introduce	VERB
cana-4548	66	4	a	a	DET
cana-4548	66	5	series	series	NOUN
cana-4548	66	6	of	of	ADP
cana-4548	66	7	efficient	efficient	ADJ
cana-4548	66	8	ao	ao	NOUN
cana-4548	66	9	by	by	ADP
cana-4548	66	10	combining	combine	VERB
cana-4548	66	11	the	the	DET
cana-4548	66	12	power	power	NOUN
cana-4548	66	13	aggregation	aggregation	NOUN
cana-4548	66	14	(	(	PUNCT
cana-4548	66	15	pa	pa	NOUN
cana-4548	66	16	)	)	PUNCT
cana-4548	66	17	operator	operator	NOUN
cana-4548	66	18	with	with	ADP
cana-4548	66	19	ss	ss	NOUN
cana-4548	66	20	operations	operation	NOUN
cana-4548	66	21	to	to	PART
cana-4548	66	22	enhance	enhance	VERB
cana-4548	66	23	the	the	DET
cana-4548	66	24	information	information	NOUN
cana-4548	66	25	aggregation	aggregation	NOUN
cana-4548	66	26	process	process	NOUN
cana-4548	66	27	in	in	ADP
cana-4548	66	28	the	the	DET
cana-4548	66	29	pf	pf	PROPN
cana-4548	66	30	environment	environment	NOUN
cana-4548	66	31	.	.	PUNCT
cana-4548	67	1	a	a	DET
cana-4548	67	2	set	set	NOUN
cana-4548	67	3	of	of	ADP
cana-4548	67	4	pf	pf	PROPN
cana-4548	67	5	ao	ao	PROPN
cana-4548	67	6	is	be	AUX
cana-4548	67	7	proposed	propose	VERB
cana-4548	67	8	,	,	PUNCT
cana-4548	67	9	including	include	VERB
cana-4548	67	10	the	the	DET
cana-4548	67	11	pfss	pfss	ADJ
cana-4548	67	12	power	power	NOUN
cana-4548	67	13	geometric	geometric	ADJ
cana-4548	67	14	(	(	PUNCT
cana-4548	67	15	pfsspg	pfsspg	NOUN
cana-4548	67	16	)	)	PUNCT
cana-4548	67	17	operator	operator	NOUN
cana-4548	67	18	,	,	PUNCT
cana-4548	67	19	pfss	pfss	ADJ
cana-4548	67	20	power	power	NOUN
cana-4548	67	21	weighted	weight	VERB
cana-4548	67	22	geometric	geometric	ADJ
cana-4548	67	23	pfsspwg	pfsspwg	NOUN
cana-4548	67	24	operator	operator	NOUN
cana-4548	67	25	,	,	PUNCT
cana-4548	67	26	and	and	CCONJ
cana-4548	67	27	pfss	pfss	ADJ
cana-4548	67	28	power	power	NOUN
cana-4548	67	29	ordered	order	VERB
cana-4548	67	30	weighted	weight	VERB
cana-4548	67	31	geometric	geometric	ADJ
cana-4548	67	32	(	(	PUNCT
cana-4548	67	33	pfsspowg	pfsspowg	ADJ
cana-4548	67	34	)	)	PUNCT
cana-4548	67	35	operator	operator	NOUN
cana-4548	67	36	.	.	PUNCT
cana-4548	68	1	the	the	DET
cana-4548	68	2	article	article	NOUN
cana-4548	68	3	also	also	ADV
cana-4548	68	4	discusses	discuss	VERB
cana-4548	68	5	special	special	ADJ
cana-4548	68	6	cases	case	NOUN
cana-4548	68	7	and	and	CCONJ
cana-4548	68	8	desirable	desirable	ADJ
cana-4548	68	9	properties	property	NOUN
cana-4548	68	10	of	of	ADP
cana-4548	68	11	these	these	DET
cana-4548	68	12	operators	operator	NOUN
cana-4548	68	13	.	.	PUNCT
cana-4548	69	1	a	a	DET
cana-4548	69	2	simple	simple	ADJ
cana-4548	69	3	multi	multi	ADJ
cana-4548	69	4	-	-	ADJ
cana-4548	69	5	criteria	criterion	NOUN
cana-4548	69	6	rating	rating	NOUN
cana-4548	69	7	technique	technique	NOUN
cana-4548	69	8	(	(	PUNCT
cana-4548	69	9	smart	smart	ADJ
cana-4548	69	10	)	)	PUNCT
cana-4548	69	11	is	be	AUX
cana-4548	69	12	presented	present	VERB
cana-4548	69	13	to	to	PART
cana-4548	69	14	solve	solve	VERB
cana-4548	69	15	mcgdm	mcgdm	ADJ
cana-4548	69	16	problems	problem	NOUN
cana-4548	69	17	in	in	ADP
cana-4548	69	18	the	the	DET
cana-4548	69	19	pf	pf	PROPN
cana-4548	69	20	environment	environment	NOUN
cana-4548	69	21	using	use	VERB
cana-4548	69	22	the	the	DET
cana-4548	69	23	proposed	propose	VERB
cana-4548	69	24	operators	operator	NOUN
cana-4548	69	25	.	.	PUNCT
cana-4548	70	1	to	to	PART
cana-4548	70	2	demonstrate	demonstrate	VERB
cana-4548	70	3	the	the	DET
cana-4548	70	4	practicality	practicality	NOUN
cana-4548	70	5	and	and	CCONJ
cana-4548	70	6	effectiveness	effectiveness	NOUN
cana-4548	70	7	of	of	ADP
cana-4548	70	8	the	the	DET
cana-4548	70	9	approach	approach	NOUN
cana-4548	70	10	,	,	PUNCT
cana-4548	70	11	an	an	DET
cana-4548	70	12	illustrative	illustrative	ADJ
cana-4548	70	13	example	example	NOUN
cana-4548	70	14	,	,	PUNCT
cana-4548	70	15	is	be	AUX
cana-4548	70	16	solved	solve	VERB
cana-4548	70	17	and	and	CCONJ
cana-4548	70	18	compared	compare	VERB
cana-4548	70	19	with	with	ADP
cana-4548	70	20	several	several	ADJ
cana-4548	70	21	existing	exist	VERB
cana-4548	70	22	approaches	approach	NOUN
cana-4548	70	23	.	.	PUNCT
cana-4548	71	1	additionally	additionally	ADV
cana-4548	71	2	,	,	PUNCT
cana-4548	71	3	table	table	NOUN
cana-4548	71	4	1	1	NUM
cana-4548	71	5	provides	provide	VERB
cana-4548	71	6	a	a	DET
cana-4548	71	7	summary	summary	NOUN
cana-4548	71	8	of	of	ADP
cana-4548	71	9	various	various	ADJ
cana-4548	71	10	aos	aos	NOUN
cana-4548	71	11	based	base	VERB
cana-4548	71	12	on	on	ADP
cana-4548	71	13	the	the	DET
cana-4548	71	14	ss	ss	PROPN
cana-4548	71	15	operational	operational	ADJ
cana-4548	71	16	law	law	NOUN
cana-4548	71	17	.	.	PUNCT
cana-4548	72	1	our	our	PRON
cana-4548	72	2	study	study	NOUN
cana-4548	72	3	aims	aim	VERB
cana-4548	72	4	to	to	PART
cana-4548	72	5	address	address	VERB
cana-4548	72	6	this	this	DET
cana-4548	72	7	specific	specific	ADJ
cana-4548	72	8	research	research	NOUN
cana-4548	72	9	gap	gap	NOUN
cana-4548	72	10	.	.	PUNCT
cana-4548	73	1	the	the	DET
cana-4548	73	2	main	main	ADJ
cana-4548	73	3	motivations	motivation	NOUN
cana-4548	73	4	of	of	ADP
cana-4548	73	5	this	this	DET
cana-4548	73	6	article	article	NOUN
cana-4548	73	7	are	be	AUX
cana-4548	73	8	as	as	SCONJ
cana-4548	73	9	follows	follow	VERB
cana-4548	73	10	:	:	PUNCT
cana-4548	73	11	•	•	SCONJ
cana-4548	73	12	the	the	DET
cana-4548	73	13	previous	previous	ADJ
cana-4548	73	14	research	research	NOUN
cana-4548	73	15	focuses	focus	VERB
cana-4548	73	16	on	on	ADP
cana-4548	73	17	the	the	DET
cana-4548	73	18	development	development	NOUN
cana-4548	73	19	of	of	ADP
cana-4548	73	20	ao	ao	PROPN
cana-4548	73	21	,	,	PUNCT
cana-4548	73	22	with	with	ADP
cana-4548	73	23	particular	particular	ADJ
cana-4548	73	24	emphasis	emphasis	NOUN
cana-4548	73	25	on	on	ADP
cana-4548	73	26	the	the	DET
cana-4548	73	27	importance	importance	NOUN
cana-4548	73	28	of	of	ADP
cana-4548	73	29	ss	ss	NOUN
cana-4548	73	30	operations	operation	NOUN
cana-4548	73	31	,	,	PUNCT
cana-4548	73	32	which	which	PRON
cana-4548	73	33	serve	serve	VERB
cana-4548	73	34	as	as	ADP
cana-4548	73	35	a	a	DET
cana-4548	73	36	generalization	generalization	NOUN
cana-4548	73	37	of	of	ADP
cana-4548	73	38	algebraic	algebraic	ADJ
cana-4548	73	39	operations	operation	NOUN
cana-4548	73	40	.	.	PUNCT
cana-4548	74	1	•	•	NUM
cana-4548	74	2	to	to	PART
cana-4548	74	3	combine	combine	VERB
cana-4548	74	4	decision	decision	NOUN
cana-4548	74	5	information	information	NOUN
cana-4548	74	6	from	from	ADP
cana-4548	74	7	multiple	multiple	ADJ
cana-4548	74	8	experts	expert	NOUN
cana-4548	74	9	using	use	VERB
cana-4548	74	10	an	an	DET
cana-4548	74	11	pg	pg	NOUN
cana-4548	74	12	operator	operator	NOUN
cana-4548	74	13	that	that	PRON
cana-4548	74	14	accounts	account	VERB
cana-4548	74	15	for	for	ADP
cana-4548	74	16	the	the	DET
cana-4548	74	17	interrelationships	interrelationship	NOUN
cana-4548	74	18	between	between	ADP
cana-4548	74	19	criteria	criterion	NOUN
cana-4548	74	20	.	.	PUNCT
cana-4548	75	1	•	•	ADP
cana-4548	75	2	to	to	PART
cana-4548	75	3	develop	develop	VERB
cana-4548	75	4	an	an	DET
cana-4548	75	5	mcgdm	mcgdm	ADJ
cana-4548	75	6	method	method	NOUN
cana-4548	75	7	incorporating	incorporate	VERB
cana-4548	75	8	the	the	DET
cana-4548	75	9	proposed	propose	VERB
cana-4548	75	10	operators	operator	NOUN
cana-4548	75	11	for	for	ADP
cana-4548	75	12	efficiently	efficiently	ADV
cana-4548	75	13	managing	manage	VERB
cana-4548	75	14	conflicting	conflict	VERB
cana-4548	75	15	criteria	criterion	NOUN
cana-4548	75	16	.	.	PUNCT
cana-4548	76	1	•	•	NUM
cana-4548	76	2	to	to	PART
cana-4548	76	3	showcase	showcase	VERB
cana-4548	76	4	the	the	DET
cana-4548	76	5	practicality	practicality	NOUN
cana-4548	76	6	of	of	ADP
cana-4548	76	7	the	the	DET
cana-4548	76	8	proposed	propose	VERB
cana-4548	76	9	operators	operator	NOUN
cana-4548	76	10	through	through	ADP
cana-4548	76	11	solving	solve	VERB
cana-4548	76	12	a	a	DET
cana-4548	76	13	numerical	numerical	ADJ
cana-4548	76	14	mcgdm	mcgdm	NOUN
cana-4548	76	15	application	application	NOUN
cana-4548	76	16	.	.	PUNCT
cana-4548	77	1	•	•	NUM
cana-4548	77	2	to	to	PART
cana-4548	77	3	validate	validate	VERB
cana-4548	77	4	the	the	DET
cana-4548	77	5	feasibility	feasibility	NOUN
cana-4548	77	6	of	of	ADP
cana-4548	77	7	the	the	DET
cana-4548	77	8	method	method	NOUN
cana-4548	77	9	by	by	ADP
cana-4548	77	10	examining	examine	VERB
cana-4548	77	11	the	the	DET
cana-4548	77	12	parameters	parameter	NOUN
cana-4548	77	13	of	of	ADP
cana-4548	77	14	the	the	DET
cana-4548	77	15	defined	define	VERB
cana-4548	77	16	operators	operator	NOUN
cana-4548	77	17	across	across	ADP
cana-4548	77	18	different	different	ADJ
cana-4548	77	19	values	value	NOUN
cana-4548	77	20	and	and	CCONJ
cana-4548	77	21	comparing	compare	VERB
cana-4548	77	22	them	they	PRON
cana-4548	77	23	with	with	ADP
cana-4548	77	24	existing	exist	VERB
cana-4548	77	25	operators	operator	NOUN
cana-4548	77	26	.	.	PUNCT
cana-4548	78	1	the	the	DET
cana-4548	78	2	main	main	ADJ
cana-4548	78	3	contributions	contribution	NOUN
cana-4548	78	4	of	of	ADP
cana-4548	78	5	this	this	DET
cana-4548	78	6	article	article	NOUN
cana-4548	78	7	are	be	AUX
cana-4548	78	8	as	as	SCONJ
cana-4548	78	9	follows	follow	VERB
cana-4548	78	10	:	:	PUNCT
cana-4548	78	11	•	•	ADP
cana-4548	78	12	this	this	DET
cana-4548	78	13	article	article	NOUN
cana-4548	78	14	introduces	introduce	VERB
cana-4548	78	15	innovative	innovative	ADJ
cana-4548	78	16	ss	ss	NOUN
cana-4548	78	17	operation	operation	NOUN
cana-4548	78	18	laws	law	NOUN
cana-4548	78	19	and	and	CCONJ
cana-4548	78	20	pa	pa	PROPN
cana-4548	78	21	operator	operator	NOUN
cana-4548	78	22	,	,	PUNCT
cana-4548	78	23	namely	namely	ADV
cana-4548	78	24	pfsspg	pfsspg	NOUN
cana-4548	78	25	,	,	PUNCT
cana-4548	78	26	pfsspwg	pfsspwg	NOUN
cana-4548	78	27	and	and	CCONJ
cana-4548	78	28	pfsspowg	pfsspowg	ADJ
cana-4548	78	29	operators	operator	NOUN
cana-4548	78	30	under	under	ADP
cana-4548	78	31	pf	pf	PROPN
cana-4548	78	32	environment	environment	NOUN
cana-4548	78	33	.	.	PUNCT
cana-4548	79	1	•	•	ADP
cana-4548	79	2	these	these	DET
cana-4548	79	3	operators	operator	NOUN
cana-4548	79	4	are	be	AUX
cana-4548	79	5	utilized	utilize	VERB
cana-4548	79	6	to	to	PART
cana-4548	79	7	develop	develop	VERB
cana-4548	79	8	a	a	DET
cana-4548	79	9	novel	novel	ADJ
cana-4548	79	10	pfmcgdm	pfmcgdm	NOUN
cana-4548	79	11	method	method	NOUN
cana-4548	79	12	with	with	ADP
cana-4548	79	13	smart	smart	ADJ
cana-4548	79	14	.	.	PUNCT
cana-4548	80	1	•	•	NUM
cana-4548	80	2	the	the	DET
cana-4548	80	3	effectiveness	effectiveness	NOUN
cana-4548	80	4	and	and	CCONJ
cana-4548	80	5	reliability	reliability	NOUN
cana-4548	80	6	of	of	ADP
cana-4548	80	7	the	the	DET
cana-4548	80	8	proposed	propose	VERB
cana-4548	80	9	pfmcgdm	pfmcgdm	NOUN
cana-4548	80	10	method	method	VERB
cana-4548	80	11	with	with	ADP
cana-4548	80	12	smart	smart	ADJ
cana-4548	80	13	approach	approach	NOUN
cana-4548	80	14	are	be	AUX
cana-4548	80	15	demonstrated	demonstrate	VERB
cana-4548	80	16	by	by	ADP
cana-4548	80	17	applying	apply	VERB
cana-4548	80	18	it	it	PRON
cana-4548	80	19	to	to	PART
cana-4548	80	20	solve	solve	VERB
cana-4548	80	21	a	a	DET
cana-4548	80	22	practical	practical	ADJ
cana-4548	80	23	road	road	NOUN
cana-4548	80	24	construction	construction	NOUN
cana-4548	80	25	company	company	NOUN
cana-4548	80	26	.	.	PUNCT
cana-4548	81	1	•	•	NUM
cana-4548	81	2	furthermore	furthermore	ADV
cana-4548	81	3	,	,	PUNCT
cana-4548	81	4	the	the	DET
cana-4548	81	5	feasibility	feasibility	NOUN
cana-4548	81	6	of	of	ADP
cana-4548	81	7	the	the	DET
cana-4548	81	8	developed	develop	VERB
cana-4548	81	9	method	method	NOUN
cana-4548	81	10	is	be	AUX
cana-4548	81	11	illustrated	illustrate	VERB
cana-4548	81	12	through	through	ADP
cana-4548	81	13	a	a	DET
cana-4548	81	14	comparative	comparative	ADJ
cana-4548	81	15	evaluation	evaluation	NOUN
cana-4548	81	16	against	against	ADP
cana-4548	81	17	existing	exist	VERB
cana-4548	81	18	operators	operator	NOUN
cana-4548	81	19	.	.	PUNCT
cana-4548	82	1	•	•	NUM
cana-4548	82	2	the	the	DET
cana-4548	82	3	contributions	contribution	NOUN
cana-4548	82	4	of	of	ADP
cana-4548	82	5	this	this	DET
cana-4548	82	6	research	research	NOUN
cana-4548	82	7	are	be	AUX
cana-4548	82	8	illustrated	illustrate	VERB
cana-4548	82	9	in	in	ADP
cana-4548	82	10	figure	figure	NOUN
cana-4548	82	11	2	2	NUM
cana-4548	82	12	to	to	PART
cana-4548	82	13	provide	provide	VERB
cana-4548	82	14	readers	reader	NOUN
cana-4548	82	15	with	with	ADP
cana-4548	82	16	a	a	DET
cana-4548	82	17	clear	clear	ADJ
cana-4548	82	18	visual	visual	ADJ
cana-4548	82	19	understanding	understanding	NOUN
cana-4548	82	20	.	.	PUNCT
cana-4548	83	1	this	this	DET
cana-4548	83	2	research	research	NOUN
cana-4548	83	3	work	work	NOUN
cana-4548	83	4	is	be	AUX
cana-4548	83	5	organized	organize	VERB
cana-4548	83	6	into	into	ADP
cana-4548	83	7	eight	eight	NUM
cana-4548	83	8	detailed	detailed	ADJ
cana-4548	83	9	sections	section	NOUN
cana-4548	83	10	as	as	SCONJ
cana-4548	83	11	outlined	outline	VERB
cana-4548	83	12	below	below	ADV
cana-4548	83	13	.	.	PUNCT
cana-4548	84	1	section	section	NOUN
cana-4548	84	2	2	2	NUM
cana-4548	84	3	introduces	introduce	VERB
cana-4548	84	4	the	the	DET
cana-4548	84	5	fundamental	fundamental	ADJ
cana-4548	84	6	concept	concept	NOUN
cana-4548	84	7	of	of	ADP
cana-4548	84	8	pfss	pfss	NOUN
cana-4548	84	9	and	and	CCONJ
cana-4548	84	10	their	their	PRON
cana-4548	84	11	related	related	ADJ
cana-4548	84	12	operations	operation	NOUN
cana-4548	84	13	.	.	PUNCT
cana-4548	85	1	in	in	ADP
cana-4548	85	2	section	section	NOUN
cana-4548	85	3	3	3	NUM
cana-4548	85	4	,	,	PUNCT
cana-4548	85	5	the	the	DET
cana-4548	85	6	proposed	propose	VERB
cana-4548	85	7	picture	picture	NOUN
cana-4548	85	8	fuzzy	fuzzy	ADJ
cana-4548	85	9	schweizer	schweizer	PROPN
cana-4548	85	10	-	-	PUNCT
cana-4548	85	11	sklar	sklar	ADJ
cana-4548	85	12	power	power	NOUN
cana-4548	85	13	geometric	geometric	ADJ
cana-4548	85	14	aggregation	aggregation	NOUN
cana-4548	85	15	operators	operator	NOUN
cana-4548	85	16	,	,	PUNCT
cana-4548	85	17	along	along	ADP
cana-4548	85	18	with	with	ADP
cana-4548	85	19	their	their	PRON
cana-4548	85	20	properties	property	NOUN
cana-4548	85	21	,	,	PUNCT
cana-4548	85	22	are	be	AUX
cana-4548	85	23	discussed	discuss	VERB
cana-4548	85	24	.	.	PUNCT
cana-4548	86	1	section	section	NOUN
cana-4548	86	2	4	4	NUM
cana-4548	86	3	continues	continue	VERB
cana-4548	86	4	this	this	DET
cana-4548	86	5	discussion	discussion	NOUN
cana-4548	86	6	by	by	ADP
cana-4548	86	7	presenting	present	VERB
cana-4548	86	8	the	the	DET
cana-4548	86	9	properties	property	NOUN
cana-4548	86	10	of	of	ADP
cana-4548	86	11	these	these	DET
cana-4548	86	12	aggregation	aggregation	NOUN
cana-4548	86	13	operators	operator	NOUN
cana-4548	86	14	.	.	PUNCT
cana-4548	87	1	communications	communication	NOUN
cana-4548	87	2	on	on	ADP
cana-4548	87	3	applied	apply	VERB
cana-4548	87	4	nonlinear	nonlinear	ADJ
cana-4548	87	5	analysis	analysis	NOUN
cana-4548	87	6	issn	issn	NOUN
cana-4548	87	7	:	:	PUNCT
cana-4548	87	8	1074	1074	NUM
cana-4548	87	9	-	-	PUNCT
cana-4548	87	10	133x	133x	NUM
cana-4548	87	11	vol	vol	NOUN
cana-4548	87	12	32	32	NUM
cana-4548	87	13	no	no	NOUN
cana-4548	87	14	.	.	PUNCT
cana-4548	88	1	9s	9s	NUM
cana-4548	88	2	(	(	PUNCT
cana-4548	88	3	2025	2025	NUM
cana-4548	88	4	)	)	PUNCT
cana-4548	88	5	2682	2682	NUM
cana-4548	89	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-4548	89	2	figure	figure	NOUN
cana-4548	89	3	2	2	NUM
cana-4548	89	4	:	:	PUNCT
cana-4548	89	5	contribution	contribution	NOUN
cana-4548	89	6	of	of	ADP
cana-4548	89	7	the	the	DET
cana-4548	89	8	proposed	propose	VERB
cana-4548	89	9	work	work	NOUN
cana-4548	89	10	to	to	PART
cana-4548	89	11	illustrate	illustrate	VERB
cana-4548	89	12	the	the	DET
cana-4548	89	13	practical	practical	ADJ
cana-4548	89	14	application	application	NOUN
cana-4548	89	15	of	of	ADP
cana-4548	89	16	this	this	DET
cana-4548	89	17	approach	approach	NOUN
cana-4548	89	18	,	,	PUNCT
cana-4548	89	19	a	a	DET
cana-4548	89	20	numerical	numerical	ADJ
cana-4548	89	21	example	example	NOUN
cana-4548	89	22	in	in	ADP
cana-4548	89	23	the	the	DET
cana-4548	89	24	picture	picture	NOUN
cana-4548	89	25	fuzzy	fuzzy	ADJ
cana-4548	89	26	context	context	NOUN
cana-4548	89	27	is	be	AUX
cana-4548	89	28	provided	provide	VERB
cana-4548	89	29	in	in	ADP
cana-4548	89	30	section	section	NOUN
cana-4548	89	31	6	6	NUM
cana-4548	89	32	.	.	PUNCT
cana-4548	90	1	section	section	NOUN
cana-4548	90	2	7	7	NUM
cana-4548	90	3	offers	offer	VERB
cana-4548	90	4	a	a	DET
cana-4548	90	5	comparative	comparative	ADJ
cana-4548	90	6	analysis	analysis	NOUN
cana-4548	90	7	to	to	PART
cana-4548	90	8	demonstrate	demonstrate	VERB
cana-4548	90	9	the	the	DET
cana-4548	90	10	advantages	advantage	NOUN
cana-4548	90	11	of	of	ADP
cana-4548	90	12	the	the	DET
cana-4548	90	13	proposed	propose	VERB
cana-4548	90	14	method	method	NOUN
cana-4548	90	15	over	over	ADP
cana-4548	90	16	existing	exist	VERB
cana-4548	90	17	aggregation	aggregation	NOUN
cana-4548	90	18	operators	operator	NOUN
cana-4548	90	19	.	.	PUNCT
cana-4548	91	1	finally	finally	ADV
cana-4548	91	2	,	,	PUNCT
cana-4548	91	3	section	section	VERB
cana-4548	91	4	8presents	8presents	NUM
cana-4548	91	5	the	the	DET
cana-4548	91	6	conclusions	conclusion	NOUN
cana-4548	91	7	drawn	draw	VERB
cana-4548	91	8	from	from	ADP
cana-4548	91	9	the	the	DET
cana-4548	91	10	study	study	NOUN
cana-4548	91	11	.	.	PUNCT
cana-4548	92	1	2	2	X
cana-4548	92	2	.	.	X
cana-4548	92	3	preliminaries	preliminary	NOUN
cana-4548	92	4	in	in	ADP
cana-4548	92	5	this	this	DET
cana-4548	92	6	section	section	NOUN
cana-4548	92	7	,	,	PUNCT
cana-4548	92	8	some	some	DET
cana-4548	92	9	basic	basic	ADJ
cana-4548	92	10	concepts	concept	NOUN
cana-4548	92	11	have	have	AUX
cana-4548	92	12	been	be	AUX
cana-4548	92	13	reviewed	review	VERB
cana-4548	92	14	related	relate	VERB
cana-4548	92	15	to	to	ADP
cana-4548	92	16	pfs	pfs	PROPN
cana-4548	92	17	.	.	PROPN
cana-4548	92	18	2.1	2.1	NUM
cana-4548	92	19	picture	picture	NOUN
cana-4548	92	20	fuzzy	fuzzy	ADJ
cana-4548	92	21	set	set	VERB
cana-4548	92	22	the	the	DET
cana-4548	92	23	pfs	pfs	PROPN
cana-4548	92	24	(	(	PUNCT
cana-4548	92	25	cuong	cuong	X
cana-4548	92	26	et	et	PROPN
cana-4548	92	27	al	al	PROPN
cana-4548	92	28	.	.	PROPN
cana-4548	93	1	(	(	PUNCT
cana-4548	93	2	2013,2014	2013,2014	NUM
cana-4548	93	3	)	)	PUNCT
cana-4548	93	4	)	)	PUNCT
cana-4548	93	5	is	be	AUX
cana-4548	93	6	an	an	DET
cana-4548	93	7	extension	extension	NOUN
cana-4548	93	8	of	of	ADP
cana-4548	93	9	ifs	ifs	PROPN
cana-4548	93	10	.	.	PUNCT
cana-4548	94	1	the	the	DET
cana-4548	94	2	mathematical	mathematical	ADJ
cana-4548	94	3	form	form	NOUN
cana-4548	94	4	of	of	ADP
cana-4548	94	5	pfs	pfs	PROPN
cana-4548	94	6	is	be	AUX
cana-4548	94	7	expressed	express	VERB
cana-4548	94	8	as	as	SCONJ
cana-4548	94	9	follows	follow	VERB
cana-4548	94	10	:	:	PUNCT
cana-4548	94	11	definition	definition	NOUN
cana-4548	94	12	1	1	NUM
cana-4548	94	13	.	.	PUNCT
cana-4548	95	1	a	a	DET
cana-4548	95	2	picture	picture	NOUN
cana-4548	95	3	fuzzy	fuzzy	ADJ
cana-4548	95	4	set	set	VERB
cana-4548	95	5	𝐴	𝐴	PROPN
cana-4548	95	6	on	on	ADP
cana-4548	95	7	universal	universal	ADJ
cana-4548	95	8	set	set	NOUN
cana-4548	95	9	𝑋	𝑋	PROPN
cana-4548	95	10	is	be	AUX
cana-4548	95	11	defined	define	VERB
cana-4548	95	12	by	by	ADP
cana-4548	95	13	,	,	PUNCT
cana-4548	95	14	𝐴	𝐴	PROPN
cana-4548	95	15	=	=	SYM
cana-4548	95	16	{	{	PUNCT
cana-4548	95	17	⟨𝑥	⟨𝑥	NOUN
cana-4548	95	18	,	,	PUNCT
cana-4548	95	19	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-4548	95	20	)	)	PUNCT
cana-4548	95	21	,	,	PUNCT
cana-4548	95	22	𝜂𝐴(𝑥	𝜂𝐴(𝑥	PROPN
cana-4548	95	23	)	)	PUNCT
cana-4548	95	24	,	,	PUNCT
cana-4548	95	25	𝜈𝐴(𝑥)⟩/𝑥	𝜈𝐴(𝑥)⟩/𝑥	PROPN
cana-4548	95	26	∈	∈	PROPN
cana-4548	95	27	𝑋	𝑋	PROPN
cana-4548	95	28	}	}	PUNCT
cana-4548	95	29	where	where	SCONJ
cana-4548	95	30	,	,	PUNCT
cana-4548	95	31	𝜇a(𝑥	𝜇a(𝑥	ADJ
cana-4548	95	32	)	)	PUNCT
cana-4548	95	33	,	,	PUNCT
cana-4548	95	34	𝜂a(𝑥	𝜂a(𝑥	X
cana-4548	95	35	)	)	PUNCT
cana-4548	95	36	and	and	CCONJ
cana-4548	95	37	𝜈a(𝑥	𝜈a(𝑥	NUM
cana-4548	95	38	)	)	PUNCT
cana-4548	96	1	∈	∈	NOUN
cana-4548	97	1	[	[	X
cana-4548	97	2	0,1	0,1	NUM
cana-4548	97	3	]	]	PUNCT
cana-4548	97	4	are	be	AUX
cana-4548	97	5	the	the	DET
cana-4548	97	6	degree	degree	NOUN
cana-4548	97	7	of	of	ADP
cana-4548	97	8	membership	membership	NOUN
cana-4548	97	9	,	,	PUNCT
cana-4548	97	10	the	the	DET
cana-4548	97	11	degree	degree	NOUN
cana-4548	97	12	of	of	ADP
cana-4548	97	13	neutral	neutral	ADJ
cana-4548	97	14	membership	membership	NOUN
cana-4548	97	15	and	and	CCONJ
cana-4548	97	16	the	the	DET
cana-4548	97	17	degree	degree	NOUN
cana-4548	97	18	of	of	ADP
cana-4548	97	19	non	non	ADJ
cana-4548	97	20	-	-	NOUN
cana-4548	97	21	membership	membership	NOUN
cana-4548	97	22	of	of	ADP
cana-4548	97	23	𝑥	𝑥	PRON
cana-4548	97	24	∈	∈	PROPN
cana-4548	97	25	a	a	DET
cana-4548	97	26	respectively	respectively	ADV
cana-4548	97	27	,	,	PUNCT
cana-4548	97	28	with	with	ADP
cana-4548	97	29	the	the	DET
cana-4548	97	30	following	follow	VERB
cana-4548	97	31	condition	condition	NOUN
cana-4548	97	32	:	:	PUNCT
cana-4548	97	33	0	0	NUM
cana-4548	97	34	≤	≤	NUM
cana-4548	97	35	𝜇a(𝑥	𝜇a(𝑥	PUNCT
cana-4548	97	36	)	)	PUNCT
cana-4548	97	37	+	+	CCONJ
cana-4548	97	38	𝜂a(𝑥	𝜂a(𝑥	X
cana-4548	97	39	)	)	PUNCT
cana-4548	97	40	+	+	CCONJ
cana-4548	97	41	𝜈a(𝑥	𝜈a(𝑥	NUM
cana-4548	97	42	)	)	PUNCT
cana-4548	97	43	≤	≤	NUM
cana-4548	97	44	1∀𝑥	1∀𝑥	NUM
cana-4548	97	45	∈	∈	PROPN
cana-4548	97	46	𝑋.	𝑋.	PROPN
cana-4548	97	47	then	then	ADV
cana-4548	97	48	,	,	PUNCT
cana-4548	97	49	for	for	ADP
cana-4548	97	50	𝑥	𝑥	DET
cana-4548	97	51	∈	∈	PROPN
cana-4548	97	52	𝑋	𝑋	PROPN
cana-4548	97	53	,	,	PUNCT
cana-4548	97	54	𝜋a(𝑥	𝜋a(𝑥	NUM
cana-4548	97	55	)	)	PUNCT
cana-4548	97	56	=	=	SYM
cana-4548	97	57	1	1	NUM
cana-4548	97	58	−	−	NUM
cana-4548	97	59	𝜇a(𝑥	𝜇a(𝑥	NUM
cana-4548	97	60	)	)	PUNCT
cana-4548	97	61	−	−	PRON
cana-4548	97	62	𝜂a(𝑥	𝜂a(𝑥	SYM
cana-4548	97	63	)	)	PUNCT
cana-4548	97	64	−	−	NOUN
cana-4548	97	65	𝜈a(𝑥	𝜈a(𝑥	NUM
cana-4548	97	66	)	)	PUNCT
cana-4548	97	67	could	could	AUX
cana-4548	97	68	be	be	AUX
cana-4548	97	69	called	call	VERB
cana-4548	97	70	the	the	DET
cana-4548	97	71	degree	degree	NOUN
cana-4548	97	72	of	of	ADP
cana-4548	97	73	refusal	refusal	NOUN
cana-4548	97	74	membership	membership	NOUN
cana-4548	97	75	of	of	ADP
cana-4548	97	76	𝑥	𝑥	PROPN
cana-4548	97	77	in	in	ADP
cana-4548	97	78	a.	a.	NOUN
cana-4548	97	79	geometrical	geometrical	ADJ
cana-4548	97	80	representation	representation	NOUN
cana-4548	97	81	of	of	ADP
cana-4548	97	82	pfs	pfs	PROPN
cana-4548	97	83	is	be	AUX
cana-4548	97	84	shown	show	VERB
cana-4548	97	85	in	in	ADP
cana-4548	97	86	figure	figure	NOUN
cana-4548	97	87	3	3	NUM
cana-4548	97	88	.	.	PUNCT
cana-4548	98	1	for	for	ADP
cana-4548	98	2	convenience	convenience	NOUN
cana-4548	98	3	,	,	PUNCT
cana-4548	98	4	𝛼	𝛼	NOUN
cana-4548	98	5	=	=	SYM
cana-4548	98	6	(	(	PUNCT
cana-4548	98	7	𝜇𝛼	𝜇𝛼	NOUN
cana-4548	98	8	,	,	PUNCT
cana-4548	98	9	𝜂𝛼	𝜂𝛼	NOUN
cana-4548	98	10	,	,	PUNCT
cana-4548	98	11	𝜈𝛼	𝜈𝛼	NOUN
cana-4548	98	12	)	)	PUNCT
cana-4548	98	13	is	be	AUX
cana-4548	98	14	called	call	VERB
cana-4548	98	15	a	a	DET
cana-4548	98	16	picture	picture	NOUN
cana-4548	98	17	fuzzy	fuzzy	ADJ
cana-4548	98	18	number	number	NOUN
cana-4548	98	19	(	(	PUNCT
cana-4548	98	20	pfn	pfn	PROPN
cana-4548	98	21	)	)	PUNCT
cana-4548	98	22	.	.	PUNCT
cana-4548	99	1	figure	figure	VERB
cana-4548	99	2	3	3	NUM
cana-4548	99	3	:	:	PUNCT
cana-4548	99	4	geometrical	geometrical	ADJ
cana-4548	99	5	representation	representation	NOUN
cana-4548	99	6	of	of	ADP
cana-4548	99	7	picture	picture	NOUN
cana-4548	99	8	fuzzy	fuzzy	ADJ
cana-4548	99	9	set	set	VERB
cana-4548	99	10	communications	communication	NOUN
cana-4548	99	11	on	on	ADP
cana-4548	99	12	applied	apply	VERB
cana-4548	99	13	nonlinear	nonlinear	ADJ
cana-4548	99	14	analysis	analysis	NOUN
cana-4548	99	15	issn	issn	NOUN
cana-4548	99	16	:	:	PUNCT
cana-4548	99	17	1074	1074	NUM
cana-4548	99	18	-	-	PUNCT
cana-4548	99	19	133x	133x	NUM
cana-4548	99	20	vol	vol	NOUN
cana-4548	99	21	32	32	NUM
cana-4548	100	1	no	no	NOUN
cana-4548	100	2	.	.	PUNCT
cana-4548	101	1	9s	9s	NUM
cana-4548	101	2	(	(	PUNCT
cana-4548	101	3	2025	2025	NUM
cana-4548	101	4	)	)	PUNCT
cana-4548	101	5	2683	2683	NUM
cana-4548	101	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4548	101	7	2.2	2.2	NUM
cana-4548	101	8	comparison	comparison	NOUN
cana-4548	101	9	for	for	ADP
cana-4548	101	10	pfns	pfns	NOUN
cana-4548	101	11	according	accord	VERB
cana-4548	101	12	to	to	ADP
cana-4548	101	13	garg	garg	NOUN
cana-4548	101	14	(	(	PUNCT
cana-4548	101	15	2017	2017	NUM
cana-4548	101	16	)	)	PUNCT
cana-4548	101	17	the	the	DET
cana-4548	101	18	score	score	NOUN
cana-4548	101	19	and	and	CCONJ
cana-4548	101	20	accuracy	accuracy	NOUN
cana-4548	101	21	functions	function	NOUN
cana-4548	101	22	of	of	ADP
cana-4548	101	23	pfns	pfns	NOUN
cana-4548	101	24	are	be	AUX
cana-4548	101	25	as	as	SCONJ
cana-4548	101	26	follows	follow	VERB
cana-4548	101	27	:	:	PUNCT
cana-4548	101	28	definition	definition	NOUN
cana-4548	101	29	2	2	NUM
cana-4548	101	30	.	.	PUNCT
cana-4548	102	1	let	let	VERB
cana-4548	102	2	𝛼	𝛼	VERB
cana-4548	102	3	=	=	SYM
cana-4548	102	4	(	(	PUNCT
cana-4548	102	5	𝜇𝛼	𝜇𝛼	NOUN
cana-4548	102	6	,	,	PUNCT
cana-4548	102	7	𝜂𝛼	𝜂𝛼	PROPN
cana-4548	102	8	,	,	PUNCT
cana-4548	102	9	𝜈𝛼	𝜈𝛼	NOUN
cana-4548	102	10	)	)	PUNCT
cana-4548	102	11	be	be	VERB
cana-4548	102	12	a	a	DET
cana-4548	102	13	pfn	pfn	NOUN
cana-4548	102	14	,	,	PUNCT
cana-4548	102	15	its	its	PRON
cana-4548	102	16	score	score	NOUN
cana-4548	102	17	function	function	NOUN
cana-4548	102	18	𝑆(𝛼	𝑆(𝛼	NOUN
cana-4548	102	19	)	)	PUNCT
cana-4548	102	20	and	and	CCONJ
cana-4548	102	21	its	its	PRON
cana-4548	102	22	accuracy	accuracy	NOUN
cana-4548	102	23	function	function	NOUN
cana-4548	102	24	𝐴(𝛼	𝐴(𝛼	PRON
cana-4548	102	25	)	)	PUNCT
cana-4548	102	26	is	be	AUX
cana-4548	102	27	defined	define	VERB
cana-4548	102	28	by	by	ADP
cana-4548	102	29	𝑆(𝛼	𝑆(𝛼	NOUN
cana-4548	102	30	)	)	PUNCT
cana-4548	102	31	=	=	NOUN
cana-4548	102	32	𝜇𝛼	𝜇𝛼	PRON
cana-4548	102	33	−	−	PROPN
cana-4548	102	34	𝜂𝛼	𝜂𝛼	NOUN
cana-4548	102	35	−	−	PROPN
cana-4548	102	36	𝜈𝛼	𝜈𝛼	NOUN
cana-4548	102	37	;	;	PUNCT
cana-4548	102	38	𝑆(𝛼	𝑆(𝛼	NUM
cana-4548	102	39	)	)	PUNCT
cana-4548	102	40	∈	∈	NOUN
cana-4548	103	1	[	[	X
cana-4548	103	2	−1,1	−1,1	X
cana-4548	103	3	]	]	X
cana-4548	103	4	,	,	PUNCT
cana-4548	103	5	𝐴(𝛼	𝐴(𝛼	X
cana-4548	103	6	)	)	PUNCT
cana-4548	103	7	=	=	SYM
cana-4548	103	8	𝜇𝛼	𝜇𝛼	NOUN
cana-4548	103	9	+	+	NUM
cana-4548	103	10	𝜂𝛼	𝜂𝛼	NOUN
cana-4548	103	11	+	+	CCONJ
cana-4548	103	12	𝜈𝛼	𝜈𝛼	NOUN
cana-4548	103	13	;	;	PUNCT
cana-4548	103	14	𝐴(𝛼	𝐴(𝛼	X
cana-4548	103	15	)	)	PUNCT
cana-4548	103	16	∈	∈	NOUN
cana-4548	104	1	[	[	X
cana-4548	104	2	0,1	0,1	NUM
cana-4548	104	3	]	]	PUNCT
cana-4548	104	4	.	.	PUNCT
cana-4548	105	1	based	base	VERB
cana-4548	105	2	on	on	ADP
cana-4548	105	3	the	the	DET
cana-4548	105	4	𝑆(𝛼	𝑆(𝛼	NOUN
cana-4548	105	5	)	)	PUNCT
cana-4548	105	6	and𝐴(𝛼	and𝐴(𝛼	PART
cana-4548	105	7	)	)	PUNCT
cana-4548	105	8	an	an	DET
cana-4548	105	9	order	order	NOUN
cana-4548	105	10	relationship	relationship	NOUN
cana-4548	105	11	between	between	ADP
cana-4548	105	12	two	two	NUM
cana-4548	105	13	pfns	pfns	NOUN
cana-4548	105	14	is	be	AUX
cana-4548	105	15	defined	define	VERB
cana-4548	105	16	as	as	ADP
cana-4548	105	17	follows	follow	VERB
cana-4548	105	18	.	.	PUNCT
cana-4548	106	1	definition	definition	NOUN
cana-4548	106	2	3	3	NUM
cana-4548	106	3	.	.	PUNCT
cana-4548	107	1	let	let	VERB
cana-4548	107	2	𝛼1	𝛼1	NOUN
cana-4548	107	3	=	=	SYM
cana-4548	107	4	(	(	PUNCT
cana-4548	107	5	𝜇𝛼1	𝜇𝛼1	NOUN
cana-4548	107	6	,	,	PUNCT
cana-4548	107	7	𝜂𝛼1	𝜂𝛼1	NOUN
cana-4548	107	8	,	,	PUNCT
cana-4548	107	9	𝜈𝛼1	𝜈𝛼1	X
cana-4548	107	10	)	)	PUNCT
cana-4548	107	11	and	and	CCONJ
cana-4548	107	12	𝛼2	𝛼2	PROPN
cana-4548	107	13	=	=	PUNCT
cana-4548	107	14	(	(	PUNCT
cana-4548	107	15	𝜇𝛼2	𝜇𝛼2	NOUN
cana-4548	107	16	,	,	PUNCT
cana-4548	107	17	𝜂𝛼2	𝜂𝛼2	PROPN
cana-4548	107	18	,	,	PUNCT
cana-4548	107	19	𝜈𝛼2	𝜈𝛼2	PROPN
cana-4548	107	20	)	)	PUNCT
cana-4548	107	21	be	be	AUX
cana-4548	107	22	two	two	NUM
cana-4548	107	23	pfns	pfns	NOUN
cana-4548	107	24	.	.	PUNCT
cana-4548	108	1	then	then	ADV
cana-4548	108	2	the	the	DET
cana-4548	108	3	following	follow	VERB
cana-4548	108	4	comparison	comparison	NOUN
cana-4548	108	5	rules	rule	NOUN
cana-4548	108	6	can	can	AUX
cana-4548	108	7	be	be	AUX
cana-4548	108	8	used	use	VERB
cana-4548	108	9	:	:	PUNCT
cana-4548	108	10	(	(	PUNCT
cana-4548	108	11	i	i	NOUN
cana-4548	108	12	)	)	PUNCT
cana-4548	108	13	if	if	SCONJ
cana-4548	108	14	𝑆(𝛼1	𝑆(𝛼1	NOUN
cana-4548	108	15	)	)	PUNCT
cana-4548	108	16	<	<	X
cana-4548	108	17	𝑆(𝛼2	𝑆(𝛼2	PROPN
cana-4548	108	18	)	)	PUNCT
cana-4548	108	19	then	then	ADV
cana-4548	108	20	𝛼1	𝛼1	VERB
cana-4548	108	21	≺	≺	NOUN
cana-4548	108	22	𝛼2	𝛼2	PROPN
cana-4548	108	23	(	(	PUNCT
cana-4548	108	24	ii	ii	NOUN
cana-4548	108	25	)	)	PUNCT
cana-4548	108	26	if	if	SCONJ
cana-4548	108	27	𝑆(𝛼1	𝑆(𝛼1	NOUN
cana-4548	108	28	)	)	PUNCT
cana-4548	108	29	=	=	SYM
cana-4548	108	30	𝑆(𝛼2	𝑆(𝛼2	PROPN
cana-4548	108	31	)	)	PUNCT
cana-4548	108	32	then	then	ADV
cana-4548	108	33	(	(	PUNCT
cana-4548	108	34	a	a	X
cana-4548	108	35	)	)	PUNCT
cana-4548	108	36	if	if	SCONJ
cana-4548	108	37	𝐴(𝛼1	𝐴(𝛼1	PROPN
cana-4548	108	38	)	)	PUNCT
cana-4548	108	39	<	<	X
cana-4548	108	40	𝐴(𝛼2	𝐴(𝛼2	PROPN
cana-4548	108	41	)	)	PUNCT
cana-4548	108	42	then	then	ADV
cana-4548	108	43	𝛼1	𝛼1	VERB
cana-4548	108	44	≺	≺	NOUN
cana-4548	108	45	𝛼2	𝛼2	PROPN
cana-4548	108	46	(	(	PUNCT
cana-4548	108	47	b	b	NOUN
cana-4548	108	48	)	)	PUNCT
cana-4548	108	49	if	if	SCONJ
cana-4548	108	50	𝐴(𝛼1	𝐴(𝛼1	PROPN
cana-4548	108	51	)	)	PUNCT
cana-4548	108	52	=	=	PUNCT
cana-4548	109	1	𝐴(𝛼2)then	𝐴(𝛼2)then	PRON
cana-4548	109	2	𝛼1	𝛼1	PROPN
cana-4548	109	3	≈	≈	PROPN
cana-4548	109	4	𝛼2	𝛼2	PROPN
cana-4548	109	5	.	.	PUNCT
cana-4548	110	1	2.3	2.3	NUM
cana-4548	110	2	operation	operation	NOUN
cana-4548	110	3	laws	law	NOUN
cana-4548	110	4	of	of	ADP
cana-4548	110	5	picture	picture	NOUN
cana-4548	110	6	fuzzy	fuzzy	ADJ
cana-4548	110	7	numbers	number	NOUN
cana-4548	110	8	schweizer	schweizer	PROPN
cana-4548	110	9	-	-	PUNCT
cana-4548	110	10	sklar	sklar	PROPN
cana-4548	110	11	(	(	PUNCT
cana-4548	110	12	hussain	hussain	PROPN
cana-4548	110	13	,	,	PUNCT
cana-4548	110	14	a.	a.	PROPN
cana-4548	110	15	et	et	PROPN
cana-4548	110	16	al	al	PROPN
cana-4548	110	17	.	.	PROPN
cana-4548	110	18	(	(	PUNCT
cana-4548	110	19	2022	2022	NUM
cana-4548	110	20	)	)	PUNCT
cana-4548	110	21	)	)	PUNCT
cana-4548	110	22	operations	operation	NOUN
cana-4548	110	23	laws	law	NOUN
cana-4548	110	24	and	and	CCONJ
cana-4548	110	25	power	power	NOUN
cana-4548	110	26	geometric	geometric	ADJ
cana-4548	110	27	aggregation	aggregation	NOUN
cana-4548	110	28	operator	operator	NOUN
cana-4548	110	29	(	(	PUNCT
cana-4548	110	30	ullah	ullah	PROPN
cana-4548	110	31	,	,	PUNCT
cana-4548	110	32	k.	k.	PROPN
cana-4548	110	33	et	et	PROPN
cana-4548	110	34	all	all	PRON
cana-4548	110	35	(	(	PUNCT
cana-4548	110	36	2023	2023	NUM
cana-4548	110	37	)	)	PUNCT
cana-4548	110	38	)	)	PUNCT
cana-4548	110	39	are	be	AUX
cana-4548	110	40	defined	define	VERB
cana-4548	110	41	for	for	ADP
cana-4548	110	42	pfns	pfns	NOUN
cana-4548	110	43	as	as	SCONJ
cana-4548	110	44	follows	follow	VERB
cana-4548	110	45	.	.	PUNCT
cana-4548	111	1	definition	definition	NOUN
cana-4548	111	2	4	4	NUM
cana-4548	111	3	.	.	PUNCT
cana-4548	112	1	the	the	DET
cana-4548	112	2	𝑃𝐺	𝑃𝐺	NOUN
cana-4548	112	3	operator	operator	NOUN
cana-4548	112	4	are	be	AUX
cana-4548	112	5	defined	define	VERB
cana-4548	112	6	as	as	ADP
cana-4548	112	7	:	:	PUNCT
cana-4548	112	8	𝑃𝐺(	𝑃𝐺(	NOUN
cana-4548	112	9	�	�	PROPN
cana-4548	112	10	̆	̆	PROPN
cana-4548	112	11	�	�	PROPN
cana-4548	112	12	1	1	NUM
cana-4548	112	13	,	,	PUNCT
cana-4548	112	14	�	�	PROPN
cana-4548	112	15	̆	̆	NOUN
cana-4548	112	16	�	�	PROPN
cana-4548	112	17	2	2	NUM
cana-4548	112	18	,	,	PUNCT
cana-4548	112	19	…	…	PUNCT
cana-4548	112	20	,	,	PUNCT
cana-4548	112	21	�	�	PROPN
cana-4548	112	22	̆	̆	NOUN
cana-4548	112	23	�	�	PROPN
cana-4548	112	24	𝑟	𝑟	NOUN
cana-4548	112	25	)	)	PUNCT
cana-4548	112	26	=	=	SYM
cana-4548	113	1	∏	∏	NUM
cana-4548	113	2	  	  	SPACE
cana-4548	113	3	𝑟	𝑟	NOUN
cana-4548	113	4	𝑘=1	𝑘=1	PROPN
cana-4548	113	5	  	  	SPACE
cana-4548	113	6	�	�	PROPN
cana-4548	113	7	̆	̆	NOUN
cana-4548	113	8	�	�	PROPN
cana-4548	113	9	𝑘	𝑘	PROPN
cana-4548	113	10	(	(	PUNCT
cana-4548	113	11	1+	1+	NUM
cana-4548	113	12	�	�	PROPN
cana-4548	113	13	̈	̈	SYM
cana-4548	113	14	�	�	PROPN
cana-4548	113	15	(	(	PUNCT
cana-4548	113	16	�	�	PROPN
cana-4548	113	17	̆	̆	PROPN
cana-4548	113	18	�	�	PROPN
cana-4548	113	19	𝑘	𝑘	NOUN
cana-4548	113	20	)	)	PUNCT
cana-4548	113	21	)	)	PUNCT
cana-4548	114	1	∑	∑	ADP
cana-4548	114	2	  	  	SPACE
cana-4548	114	3	𝑟++	𝑟++	NOUN
cana-4548	114	4	�	�	NOUN
cana-4548	114	5	̈	̈	SYM
cana-4548	114	6	�	�	PROPN
cana-4548	114	7	(	(	PUNCT
cana-4548	114	8	�	�	PROPN
cana-4548	114	9	̆	̆	PROPN
cana-4548	114	10	�	�	PROPN
cana-4548	114	11	𝑘	𝑘	NOUN
cana-4548	114	12	)	)	PUNCT
cana-4548	114	13	𝑘=1	𝑘=1	NOUN
cana-4548	114	14	(	(	PUNCT
cana-4548	114	15	1	1	X
cana-4548	114	16	)	)	PUNCT
cana-4548	114	17	where	where	SCONJ
cana-4548	114	18	�	�	PROPN
cana-4548	114	19	̈	̈	SYM
cana-4548	114	20	�	�	PROPN
cana-4548	114	21	(	(	PUNCT
cana-4548	114	22	�	�	PROPN
cana-4548	114	23	̆	̆	PROPN
cana-4548	114	24	�	�	PROPN
cana-4548	114	25	𝑘	𝑘	NOUN
cana-4548	114	26	)	)	PUNCT
cana-4548	114	27	=	=	PUNCT
cana-4548	114	28	∑	∑	PUNCT
cana-4548	114	29	 	 	SPACE
cana-4548	114	30	𝑟	𝑟	NOUN
cana-4548	114	31	𝑘=1,𝑘≠ℎ	𝑘=1,𝑘≠ℎ	PROPN
cana-4548	114	32	sup(	sup(	NOUN
cana-4548	114	33	�	�	PROPN
cana-4548	114	34	̆	̆	NOUN
cana-4548	114	35	�	�	PROPN
cana-4548	114	36	ℎ	ℎ	PROPN
cana-4548	114	37	,	,	PUNCT
cana-4548	114	38	�	�	PROPN
cana-4548	114	39	̆	̆	PROPN
cana-4548	114	40	�	�	PROPN
cana-4548	114	41	𝑘	𝑘	NOUN
cana-4548	114	42	)	)	PUNCT
cana-4548	114	43	,	,	PUNCT
cana-4548	114	44	sup(	sup(	PROPN
cana-4548	114	45	�	�	PROPN
cana-4548	114	46	̆	̆	NOUN
cana-4548	114	47	�	�	PROPN
cana-4548	114	48	ℎ	ℎ	PROPN
cana-4548	114	49	,	,	PUNCT
cana-4548	114	50	�	�	PROPN
cana-4548	114	51	̆	̆	PROPN
cana-4548	114	52	�	�	PROPN
cana-4548	114	53	𝑘	𝑘	NOUN
cana-4548	114	54	)	)	PUNCT
cana-4548	114	55	=	=	SYM
cana-4548	115	1	1	1	NUM
cana-4548	115	2	−	−	PROPN
cana-4548	115	3	𝔇(	𝔇(	PROPN
cana-4548	115	4	�	�	PROPN
cana-4548	115	5	̆	̆	PROPN
cana-4548	115	6	�	�	PROPN
cana-4548	115	7	ℎ	ℎ	PROPN
cana-4548	115	8	,	,	PUNCT
cana-4548	115	9	�	�	PROPN
cana-4548	115	10	̆	̆	PROPN
cana-4548	115	11	�	�	PROPN
cana-4548	115	12	𝑘	𝑘	NOUN
cana-4548	115	13	)	)	PUNCT
cana-4548	115	14	and	and	CCONJ
cana-4548	115	15	the	the	DET
cana-4548	115	16	weight	weight	NOUN
cana-4548	115	17	(	(	PUNCT
cana-4548	115	18	1+	1+	NUM
cana-4548	115	19	�	�	PROPN
cana-4548	115	20	̈	̈	SYM
cana-4548	115	21	�	�	PROPN
cana-4548	115	22	(	(	PUNCT
cana-4548	115	23	�	�	PROPN
cana-4548	115	24	̆	̆	PROPN
cana-4548	115	25	�	�	PROPN
cana-4548	115	26	𝑘	𝑘	NOUN
cana-4548	115	27	)	)	PUNCT
cana-4548	115	28	)	)	PUNCT
cana-4548	115	29	∑	∑	ADP
cana-4548	115	30	 	 	SPACE
cana-4548	115	31	𝑟	𝑟	PRON
cana-4548	115	32	𝑘=1	𝑘=1	X
cana-4548	115	33	 	 	SPACE
cana-4548	115	34	1+	1+	NUM
cana-4548	115	35	�	�	PROPN
cana-4548	115	36	̈	̈	SYM
cana-4548	115	37	�	�	PROPN
cana-4548	115	38	(	(	PUNCT
cana-4548	115	39	�	�	PROPN
cana-4548	115	40	̆	̆	PROPN
cana-4548	115	41	�	�	PROPN
cana-4548	115	42	𝑘	𝑘	NOUN
cana-4548	115	43	)	)	PUNCT
cana-4548	115	44	of	of	ADP
cana-4548	115	45	the	the	DET
cana-4548	115	46	argument	argument	NOUN
cana-4548	115	47	�	�	PROPN
cana-4548	115	48	̆	̆	NOUN
cana-4548	115	49	�	�	NOUN
cana-4548	115	50	ℎ	ℎ	NOUN
cana-4548	115	51	depends	depend	VERB
cana-4548	115	52	on	on	ADP
cana-4548	115	53	all	all	DET
cana-4548	115	54	the	the	DET
cana-4548	115	55	input	input	NOUN
cana-4548	115	56	arguments	argument	NOUN
cana-4548	115	57	�	�	PROPN
cana-4548	115	58	̆	̆	PROPN
cana-4548	115	59	�	�	PROPN
cana-4548	115	60	𝑘(𝑘	𝑘(𝑘	PROPN
cana-4548	115	61	=	=	SYM
cana-4548	115	62	1,2	1,2	NUM
cana-4548	115	63	,	,	PUNCT
cana-4548	115	64	…	…	PUNCT
cana-4548	115	65	,	,	PUNCT
cana-4548	115	66	𝑟	𝑟	X
cana-4548	115	67	)	)	PUNCT
cana-4548	115	68	,	,	PUNCT
cana-4548	115	69	which	which	PRON
cana-4548	115	70	enables	enable	VERB
cana-4548	115	71	the	the	DET
cana-4548	115	72	argument	argument	NOUN
cana-4548	115	73	values	value	NOUN
cana-4548	115	74	to	to	PART
cana-4548	115	75	support	support	VERB
cana-4548	115	76	each	each	DET
cana-4548	115	77	other	other	ADJ
cana-4548	115	78	in	in	ADP
cana-4548	115	79	the	the	DET
cana-4548	115	80	geometric	geometric	ADJ
cana-4548	115	81	aggregation	aggregation	NOUN
cana-4548	115	82	process	process	NOUN
cana-4548	115	83	.	.	PUNCT
cana-4548	116	1	definition	definition	NOUN
cana-4548	116	2	5	5	NUM
cana-4548	116	3	.	.	PUNCT
cana-4548	116	4	let	let	VERB
cana-4548	116	5	𝛼1	𝛼1	NOUN
cana-4548	116	6	=	=	PUNCT
cana-4548	116	7	⟨𝜇𝛼1	⟨𝜇𝛼1	NOUN
cana-4548	116	8	,	,	PUNCT
cana-4548	116	9	𝜂𝛼1	𝜂𝛼1	NOUN
cana-4548	116	10	,	,	PUNCT
cana-4548	116	11	𝜈𝛼1	𝜈𝛼1	CCONJ
cana-4548	116	12	⟩	⟩	NOUN
cana-4548	116	13	and	and	CCONJ
cana-4548	116	14	𝛼2	𝛼2	NOUN
cana-4548	116	15	=	=	PUNCT
cana-4548	116	16	⟨𝜇𝛼2	⟨𝜇𝛼2	NOUN
cana-4548	116	17	,	,	PUNCT
cana-4548	116	18	𝜂𝛼2	𝜂𝛼2	PROPN
cana-4548	116	19	,	,	PUNCT
cana-4548	116	20	𝜈𝛼2	𝜈𝛼2	PROPN
cana-4548	116	21	⟩	⟩	PROPN
cana-4548	116	22	be	be	AUX
cana-4548	116	23	any	any	DET
cana-4548	116	24	two	two	NUM
cana-4548	116	25	pfns	pfns	NOUN
cana-4548	116	26	,	,	PUNCT
cana-4548	116	27	then	then	ADV
cana-4548	116	28	the	the	DET
cana-4548	116	29	euclidean	euclidean	ADJ
cana-4548	116	30	distance	distance	NOUN
cana-4548	116	31	between	between	ADP
cana-4548	116	32	them	they	PRON
cana-4548	116	33	is	be	AUX
cana-4548	116	34	defined	define	VERB
cana-4548	116	35	as	as	SCONJ
cana-4548	116	36	follows	follow	VERB
cana-4548	116	37	:	:	PUNCT
cana-4548	116	38	𝔇(𝛼1	𝔇(𝛼1	NOUN
cana-4548	116	39	,	,	PUNCT
cana-4548	116	40	𝛼2	𝛼2	ADJ
cana-4548	116	41	)	)	PUNCT
cana-4548	116	42	=	=	SYM
cana-4548	117	1	1	1	NUM
cana-4548	117	2	3	3	NUM
cana-4548	117	3	{	{	PUNCT
cana-4548	117	4	|𝜇𝛼1	|𝜇𝛼1	ADP
cana-4548	117	5	−	−	NOUN
cana-4548	118	1	𝜇𝛼2	𝜇𝛼2	NOUN
cana-4548	119	1	|	|	ADV
cana-4548	120	1	+	+	CCONJ
cana-4548	120	2	|𝜂𝛼1	|𝜂𝛼1	VERB
cana-4548	120	3	−	−	NUM
cana-4548	120	4	𝜂𝛼2	𝜂𝛼2	NOUN
cana-4548	121	1	|	|	ADV
cana-4548	122	1	+	+	CCONJ
cana-4548	122	2	|𝜈𝛼1	|𝜈𝛼1	ADV
cana-4548	122	3	−	−	NOUN
cana-4548	122	4	𝜈𝛼2	𝜈𝛼2	NOUN
cana-4548	122	5	|	|	ADV
cana-4548	122	6	}	}	PUNCT
cana-4548	122	7	(	(	PUNCT
cana-4548	122	8	2	2	X
cana-4548	122	9	)	)	PUNCT
cana-4548	122	10	definition	definition	NOUN
cana-4548	122	11	6	6	NUM
cana-4548	122	12	.	.	PUNCT
cana-4548	123	1	let	let	VERB
cana-4548	123	2	𝛼1	𝛼1	NOUN
cana-4548	123	3	=	=	PUNCT
cana-4548	123	4	⟨𝜇𝛼1	⟨𝜇𝛼1	NOUN
cana-4548	123	5	,	,	PUNCT
cana-4548	123	6	𝜂𝛼1	𝜂𝛼1	NOUN
cana-4548	123	7	,	,	PUNCT
cana-4548	123	8	𝜈𝛼1	𝜈𝛼1	CCONJ
cana-4548	123	9	⟩	⟩	NOUN
cana-4548	123	10	and	and	CCONJ
cana-4548	123	11	𝛼2	𝛼2	NOUN
cana-4548	123	12	=	=	PUNCT
cana-4548	123	13	⟨𝜇𝛼2	⟨𝜇𝛼2	NOUN
cana-4548	123	14	,	,	PUNCT
cana-4548	123	15	𝜂𝛼2	𝜂𝛼2	PROPN
cana-4548	123	16	,	,	PUNCT
cana-4548	123	17	𝜈𝛼2	𝜈𝛼2	PROPN
cana-4548	123	18	⟩	⟩	PROPN
cana-4548	123	19	be	be	AUX
cana-4548	123	20	any	any	DET
cana-4548	123	21	two	two	NUM
cana-4548	123	22	pfn	pfn	NOUN
cana-4548	123	23	.	.	PUNCT
cana-4548	124	1	then	then	ADV
cana-4548	124	2	the	the	DET
cana-4548	124	3	generalized	generalized	ADJ
cana-4548	124	4	union	union	NOUN
cana-4548	124	5	and	and	CCONJ
cana-4548	124	6	intersection	intersection	NOUN
cana-4548	124	7	are	be	AUX
cana-4548	124	8	defined	define	VERB
cana-4548	124	9	as	as	SCONJ
cana-4548	124	10	follows	follow	VERB
cana-4548	124	11	:	:	PUNCT
cana-4548	124	12	𝛼1	𝛼1	NOUN
cana-4548	124	13	∪	∪	VERB
cana-4548	124	14	𝛼2	𝛼2	PROPN
cana-4548	124	15	=	=	SYM
cana-4548	124	16	{	{	PUNCT
cana-4548	124	17	⟨𝑥	⟨𝑥	NOUN
cana-4548	124	18	,	,	PUNCT
cana-4548	124	19	{	{	PUNCT
cana-4548	124	20	𝔗∗{𝜇𝛼1	𝔗∗{𝜇𝛼1	X
cana-4548	124	21	(	(	PUNCT
cana-4548	124	22	𝑥	𝑥	NOUN
cana-4548	124	23	)	)	PUNCT
cana-4548	124	24	,	,	PUNCT
cana-4548	124	25	𝜇𝛼2	𝜇𝛼2	NOUN
cana-4548	124	26	(	(	PUNCT
cana-4548	124	27	𝑥	𝑥	NOUN
cana-4548	124	28	)	)	PUNCT
cana-4548	124	29	}	}	PUNCT
cana-4548	124	30	}	}	PUNCT
cana-4548	124	31	,	,	PUNCT
cana-4548	124	32	{	{	PUNCT
cana-4548	124	33	𝔗{𝜂𝛼1	𝔗{𝜂𝛼1	X
cana-4548	124	34	(	(	PUNCT
cana-4548	124	35	𝑥	𝑥	NOUN
cana-4548	124	36	)	)	PUNCT
cana-4548	124	37	,	,	PUNCT
cana-4548	124	38	𝜂𝛼2	𝜂𝛼2	PROPN
cana-4548	124	39	(	(	PUNCT
cana-4548	124	40	𝑥	𝑥	NOUN
cana-4548	124	41	)	)	PUNCT
cana-4548	124	42	}	}	PUNCT
cana-4548	124	43	}	}	PUNCT
cana-4548	124	44	,	,	PUNCT
cana-4548	124	45	{	{	PUNCT
cana-4548	124	46	𝔗{𝜈𝛼1	𝔗{𝜈𝛼1	X
cana-4548	124	47	(	(	PUNCT
cana-4548	124	48	𝑥	𝑥	NOUN
cana-4548	124	49	)	)	PUNCT
cana-4548	124	50	,	,	PUNCT
cana-4548	124	51	𝜈𝛼2	𝜈𝛼2	PROPN
cana-4548	124	52	}	}	PUNCT
cana-4548	124	53	(	(	PUNCT
cana-4548	124	54	𝑥	𝑥	NOUN
cana-4548	124	55	)	)	PUNCT
cana-4548	124	56	}	}	PUNCT
cana-4548	124	57	∣	∣	VERB
cana-4548	124	58	𝑥	𝑥	DET
cana-4548	124	59	∈	∈	PROPN
cana-4548	124	60	𝑋⟩	𝑋⟩	PROPN
cana-4548	124	61	}	}	PUNCT
cana-4548	124	62	;	;	PUNCT
cana-4548	124	63	𝛼1	𝛼1	NOUN
cana-4548	124	64	∩	∩	NOUN
cana-4548	124	65	𝛼2	𝛼2	NOUN
cana-4548	124	66	=	=	SYM
cana-4548	124	67	{	{	PUNCT
cana-4548	124	68	⟨𝑥	⟨𝑥	NOUN
cana-4548	124	69	,	,	PUNCT
cana-4548	124	70	{	{	PUNCT
cana-4548	124	71	𝔗{𝜇𝛼1	𝔗{𝜇𝛼1	X
cana-4548	124	72	(	(	PUNCT
cana-4548	124	73	𝑥	𝑥	NOUN
cana-4548	124	74	)	)	PUNCT
cana-4548	124	75	,	,	PUNCT
cana-4548	124	76	𝜇𝛼2	𝜇𝛼2	NOUN
cana-4548	124	77	(	(	PUNCT
cana-4548	124	78	𝑥	𝑥	NOUN
cana-4548	124	79	)	)	PUNCT
cana-4548	124	80	}	}	PUNCT
cana-4548	124	81	}	}	PUNCT
cana-4548	124	82	,	,	PUNCT
cana-4548	124	83	{	{	PUNCT
cana-4548	124	84	𝔗∗{𝜂𝛼1	𝔗∗{𝜂𝛼1	X
cana-4548	124	85	(	(	PUNCT
cana-4548	124	86	𝑥	𝑥	NOUN
cana-4548	124	87	)	)	PUNCT
cana-4548	124	88	,	,	PUNCT
cana-4548	124	89	𝜂𝛼2	𝜂𝛼2	PROPN
cana-4548	124	90	(	(	PUNCT
cana-4548	124	91	𝑥	𝑥	NOUN
cana-4548	124	92	)	)	PUNCT
cana-4548	124	93	}	}	PUNCT
cana-4548	124	94	}	}	PUNCT
cana-4548	124	95	,	,	PUNCT
cana-4548	124	96	{	{	PUNCT
cana-4548	124	97	𝔗∗{𝜈𝛼1	𝔗∗{𝜈𝛼1	X
cana-4548	124	98	(	(	PUNCT
cana-4548	124	99	𝑥	𝑥	NOUN
cana-4548	124	100	)	)	PUNCT
cana-4548	124	101	,	,	PUNCT
cana-4548	124	102	𝜈𝛼2	𝜈𝛼2	PROPN
cana-4548	124	103	(	(	PUNCT
cana-4548	124	104	𝑥)}}|	𝑥)}}|	PUNCT
cana-4548	124	105	𝑥	𝑥	PRON
cana-4548	124	106	∈	∈	NOUN
cana-4548	124	107	𝑋}⟩	𝑋}⟩	X
cana-4548	124	108	}	}	PUNCT
cana-4548	124	109	;	;	PUNCT
cana-4548	124	110	where𝔗	where𝔗	PROPN
cana-4548	124	111	and	and	CCONJ
cana-4548	124	112	𝔗∗	𝔗∗	NOUN
cana-4548	124	113	respectively	respectively	ADV
cana-4548	124	114	,	,	PUNCT
cana-4548	124	115	express	express	VERB
cana-4548	124	116	tn	tn	NOUN
cana-4548	124	117	and	and	CCONJ
cana-4548	124	118	tcn	tcn	PROPN
cana-4548	124	119	.	.	PUNCT
cana-4548	125	1	the	the	DET
cana-4548	125	2	sstn	sstn	NOUN
cana-4548	125	3	and	and	CCONJ
cana-4548	125	4	sstcn	sstcn	NOUN
cana-4548	125	5	are	be	AUX
cana-4548	125	6	defined	define	VERB
cana-4548	125	7	as	as	ADP
cana-4548	125	8	follow	follow	NOUN
cana-4548	125	9	.	.	PUNCT
cana-4548	126	1	communications	communication	NOUN
cana-4548	126	2	on	on	ADP
cana-4548	126	3	applied	apply	VERB
cana-4548	126	4	nonlinear	nonlinear	ADJ
cana-4548	126	5	analysis	analysis	NOUN
cana-4548	126	6	issn	issn	NOUN
cana-4548	126	7	:	:	PUNCT
cana-4548	126	8	1074	1074	NUM
cana-4548	126	9	-	-	PUNCT
cana-4548	126	10	133x	133x	NUM
cana-4548	126	11	vol	vol	NOUN
cana-4548	126	12	32	32	NUM
cana-4548	126	13	no	no	NOUN
cana-4548	126	14	.	.	PUNCT
cana-4548	127	1	9s	9s	NUM
cana-4548	127	2	(	(	PUNCT
cana-4548	127	3	2025	2025	NUM
cana-4548	127	4	)	)	PUNCT
cana-4548	127	5	2684	2684	NUM
cana-4548	127	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4548	128	1	𝔗(𝑥1	𝔗(𝑥1	PROPN
cana-4548	128	2	,	,	PUNCT
cana-4548	128	3	𝑥2	𝑥2	NOUN
cana-4548	128	4	)	)	PUNCT
cana-4548	128	5	=	=	SYM
cana-4548	129	1	(	(	PUNCT
cana-4548	129	2	𝑥1	𝑥1	NOUN
cana-4548	129	3	𝛽	𝛽	NOUN
cana-4548	129	4	+	+	CCONJ
cana-4548	129	5	𝑥2	𝑥2	PROPN
cana-4548	129	6	𝛽	𝛽	NOUN
cana-4548	129	7	−	−	PROPN
cana-4548	129	8	1	1	NUM
cana-4548	129	9	)	)	SYM
cana-4548	129	10	1	1	NUM
cana-4548	129	11	𝛽	𝛽	NOUN
cana-4548	129	12	𝔗∗(𝑥1	𝔗∗(𝑥1	ADJ
cana-4548	129	13	,	,	PUNCT
cana-4548	129	14	𝑥2	𝑥2	NOUN
cana-4548	129	15	)	)	PUNCT
cana-4548	129	16	=	=	SYM
cana-4548	130	1	1	1	NUM
cana-4548	130	2	−	−	NOUN
cana-4548	130	3	(	(	PUNCT
cana-4548	130	4	1	1	NUM
cana-4548	130	5	−	−	PROPN
cana-4548	130	6	𝑥1	𝑥1	PROPN
cana-4548	130	7	𝛽	𝛽	PROPN
cana-4548	130	8	+	+	CCONJ
cana-4548	130	9	(	(	PUNCT
cana-4548	130	10	1	1	NUM
cana-4548	130	11	−	−	PROPN
cana-4548	130	12	𝑥2	𝑥2	PROPN
cana-4548	130	13	𝛽	𝛽	NOUN
cana-4548	130	14	−	−	PROPN
cana-4548	130	15	1	1	NUM
cana-4548	130	16	)	)	SYM
cana-4548	130	17	1	1	NUM
cana-4548	130	18	𝛽	𝛽	NOUN
cana-4548	130	19	)	)	PUNCT
cana-4548	130	20	additionally	additionally	ADV
cana-4548	130	21	,	,	PUNCT
cana-4548	130	22	when	when	SCONJ
cana-4548	130	23	𝛽	𝛽	NOUN
cana-4548	130	24	=	=	SYM
cana-4548	130	25	0	0	NUM
cana-4548	130	26	,	,	PUNCT
cana-4548	130	27	we	we	PRON
cana-4548	130	28	have	have	VERB
cana-4548	130	29	𝔗(𝑥1	𝔗(𝑥1	ADJ
cana-4548	130	30	,	,	PUNCT
cana-4548	130	31	𝑥2	𝑥2	NOUN
cana-4548	130	32	)	)	PUNCT
cana-4548	130	33	=	=	SYM
cana-4548	130	34	𝑥1𝑥2	𝑥1𝑥2	PROPN
cana-4548	130	35	and	and	CCONJ
cana-4548	130	36	𝔗∗(𝑥1	𝔗∗(𝑥1	ADJ
cana-4548	130	37	,	,	PUNCT
cana-4548	130	38	𝑥2	𝑥2	NOUN
cana-4548	130	39	)	)	PUNCT
cana-4548	130	40	=	=	SYM
cana-4548	130	41	𝑥1	𝑥1	NOUN
cana-4548	130	42	+	+	CCONJ
cana-4548	130	43	𝑥2	𝑥2	PROPN
cana-4548	130	44	−	−	PROPN
cana-4548	130	45	𝑥1𝑥2	𝑥1𝑥2	NOUN
cana-4548	130	46	.	.	PUNCT
cana-4548	131	1	that	that	PRON
cana-4548	131	2	is	be	AUX
cana-4548	131	3	,	,	PUNCT
cana-4548	131	4	sstn	sstn	NOUN
cana-4548	131	5	and	and	CCONJ
cana-4548	131	6	sstcn	sstcn	NOUN
cana-4548	131	7	reduce	reduce	VERB
cana-4548	131	8	to	to	ADP
cana-4548	131	9	algebraic	algebraic	PROPN
cana-4548	131	10	tn	tn	PROPN
cana-4548	131	11	and	and	CCONJ
cana-4548	131	12	tcn	tcn	PROPN
cana-4548	131	13	.	.	PUNCT
cana-4548	132	1	definition	definition	NOUN
cana-4548	132	2	7	7	NUM
cana-4548	132	3	.	.	PUNCT
cana-4548	132	4	let	let	VERB
cana-4548	132	5	𝛼1	𝛼1	NOUN
cana-4548	132	6	=	=	PUNCT
cana-4548	132	7	⟨𝜇𝛼1	⟨𝜇𝛼1	NOUN
cana-4548	132	8	,	,	PUNCT
cana-4548	132	9	𝜂𝛼1	𝜂𝛼1	NOUN
cana-4548	132	10	,	,	PUNCT
cana-4548	132	11	𝜈𝛼1	𝜈𝛼1	CCONJ
cana-4548	132	12	⟩	⟩	NOUN
cana-4548	132	13	and	and	CCONJ
cana-4548	132	14	𝛼2	𝛼2	NOUN
cana-4548	132	15	=	=	PUNCT
cana-4548	132	16	⟨𝜇𝛼2	⟨𝜇𝛼2	NOUN
cana-4548	132	17	,	,	PUNCT
cana-4548	132	18	𝜂𝛼2	𝜂𝛼2	PROPN
cana-4548	132	19	,	,	PUNCT
cana-4548	132	20	𝜈𝛼2	𝜈𝛼2	PROPN
cana-4548	132	21	⟩	⟩	PROPN
cana-4548	132	22	be	be	AUX
cana-4548	132	23	any	any	DET
cana-4548	132	24	two	two	NUM
cana-4548	132	25	pfn	pfn	NOUN
cana-4548	132	26	.	.	PUNCT
cana-4548	133	1	then	then	ADV
cana-4548	133	2	based	base	VERB
cana-4548	133	3	on	on	ADP
cana-4548	133	4	ss	ss	PROPN
cana-4548	133	5	operations	operation	NOUN
cana-4548	133	6	,	,	PUNCT
cana-4548	133	7	the	the	DET
cana-4548	133	8	generalized	generalized	ADJ
cana-4548	133	9	union	union	NOUN
cana-4548	133	10	and	and	CCONJ
cana-4548	133	11	intersection	intersection	NOUN
cana-4548	133	12	are	be	AUX
cana-4548	133	13	introduced	introduce	VERB
cana-4548	133	14	as	as	SCONJ
cana-4548	133	15	follows	follow	VERB
cana-4548	133	16	:	:	PUNCT
cana-4548	133	17	𝛼1	𝛼1	PROPN
cana-4548	133	18	⊕	⊕	PROPN
cana-4548	133	19	𝛼2	𝛼2	PROPN
cana-4548	133	20	=	=	SYM
cana-4548	133	21	⟨𝔗∗(𝜇𝛼1	⟨𝔗∗(𝜇𝛼1	PROPN
cana-4548	133	22	,	,	PUNCT
cana-4548	133	23	𝜇𝛼2	𝜇𝛼2	NOUN
cana-4548	133	24	)	)	PUNCT
cana-4548	133	25	,	,	PUNCT
cana-4548	133	26	𝔗(𝜂𝛼1	𝔗(𝜂𝛼1	NOUN
cana-4548	133	27	,	,	PUNCT
cana-4548	133	28	𝜂𝛼2	𝜂𝛼2	PROPN
cana-4548	133	29	)	)	PUNCT
cana-4548	133	30	,	,	PUNCT
cana-4548	133	31	𝔗(𝜈𝛼1	𝔗(𝜈𝛼1	NOUN
cana-4548	133	32	,	,	PUNCT
cana-4548	133	33	𝜈𝛼2	𝜈𝛼2	PROPN
cana-4548	133	34	)	)	PUNCT
cana-4548	133	35	⟩(3	⟩(3	NOUN
cana-4548	133	36	)	)	PUNCT
cana-4548	133	37	𝛼1	𝛼1	PROPN
cana-4548	133	38	⊗	⊗	PROPN
cana-4548	133	39	𝛼2	𝛼2	PROPN
cana-4548	133	40	=	=	PROPN
cana-4548	133	41	⟨𝔗(𝜇𝛼1	⟨𝔗(𝜇𝛼1	PROPN
cana-4548	133	42	,	,	PUNCT
cana-4548	133	43	𝜇𝛼2	𝜇𝛼2	NOUN
cana-4548	133	44	)	)	PUNCT
cana-4548	133	45	,	,	PUNCT
cana-4548	133	46	𝔗∗(𝜂𝛼1	𝔗∗(𝜂𝛼1	PRON
cana-4548	133	47	,	,	PUNCT
cana-4548	133	48	𝜂𝛼2	𝜂𝛼2	PROPN
cana-4548	133	49	)	)	PUNCT
cana-4548	133	50	,	,	PUNCT
cana-4548	133	51	𝔗∗(𝜈𝛼1	𝔗∗(𝜈𝛼1	ADP
cana-4548	133	52	,	,	PUNCT
cana-4548	133	53	𝜈𝛼2	𝜈𝛼2	PROPN
cana-4548	133	54	)	)	PUNCT
cana-4548	133	55	⟩	⟩	PROPN
cana-4548	133	56	(	(	PUNCT
cana-4548	133	57	4	4	NUM
cana-4548	133	58	)	)	PUNCT
cana-4548	133	59	definition	definition	NOUN
cana-4548	133	60	8	8	NUM
cana-4548	133	61	.	.	PUNCT
cana-4548	134	1	let	let	VERB
cana-4548	134	2	𝛼	𝛼	VERB
cana-4548	134	3	=	=	SYM
cana-4548	134	4	(	(	PUNCT
cana-4548	134	5	𝜇𝛼	𝜇𝛼	NOUN
cana-4548	134	6	,	,	PUNCT
cana-4548	134	7	𝜂𝛼	𝜂𝛼	NOUN
cana-4548	134	8	,	,	PUNCT
cana-4548	134	9	𝜈𝛼	𝜈𝛼	NOUN
cana-4548	134	10	)	)	PUNCT
cana-4548	134	11	,	,	PUNCT
cana-4548	134	12	𝛼1	𝛼1	NOUN
cana-4548	134	13	=	=	SYM
cana-4548	134	14	(	(	PUNCT
cana-4548	134	15	𝜇𝛼1	𝜇𝛼1	NOUN
cana-4548	134	16	,	,	PUNCT
cana-4548	134	17	𝜂𝛼1	𝜂𝛼1	NOUN
cana-4548	134	18	,	,	PUNCT
cana-4548	134	19	𝜈𝛼1	𝜈𝛼1	X
cana-4548	134	20	)	)	PUNCT
cana-4548	134	21	and	and	CCONJ
cana-4548	134	22	𝛼2	𝛼2	PROPN
cana-4548	134	23	=	=	PUNCT
cana-4548	134	24	(	(	PUNCT
cana-4548	134	25	𝜇𝛼2	𝜇𝛼2	NOUN
cana-4548	134	26	,	,	PUNCT
cana-4548	134	27	𝜂𝛼2	𝜂𝛼2	PROPN
cana-4548	134	28	,	,	PUNCT
cana-4548	134	29	𝜈𝛼2	𝜈𝛼2	PROPN
cana-4548	134	30	)	)	PUNCT
cana-4548	134	31	be	be	VERB
cana-4548	134	32	three	three	NUM
cana-4548	134	33	pfns	pfns	NOUN
cana-4548	134	34	and	and	CCONJ
cana-4548	134	35	some	some	DET
cana-4548	134	36	basic	basic	ADJ
cana-4548	134	37	algebraic	algebraic	ADJ
cana-4548	134	38	operations	operation	NOUN
cana-4548	134	39	of	of	ADP
cana-4548	134	40	pfns	pfns	NOUN
cana-4548	134	41	are	be	AUX
cana-4548	134	42	defined	define	VERB
cana-4548	134	43	as	as	ADP
cana-4548	134	44	follow	follow	NOUN
cana-4548	134	45	:	:	PUNCT
cana-4548	135	1	𝛼1	𝛼1	PROPN
cana-4548	135	2	⊕	⊕	PROPN
cana-4548	135	3	𝛼2	𝛼2	ADJ
cana-4548	135	4	=	=	PUNCT
cana-4548	135	5	⟨𝜇𝛼1	⟨𝜇𝛼1	X
cana-4548	135	6	+	+	NUM
cana-4548	135	7	𝜇𝛼2	𝜇𝛼2	NOUN
cana-4548	135	8	−	−	NOUN
cana-4548	135	9	𝜇𝛼1	𝜇𝛼1	NOUN
cana-4548	135	10	𝜇𝛼2	𝜇𝛼2	NOUN
cana-4548	135	11	,	,	PUNCT
cana-4548	135	12	𝜂𝛼1	𝜂𝛼1	NOUN
cana-4548	135	13	𝜂𝛼2	𝜂𝛼2	NOUN
cana-4548	135	14	,	,	PUNCT
cana-4548	135	15	𝜈𝛼1	𝜈𝛼1	ADP
cana-4548	135	16	𝜈𝛼2	𝜈𝛼2	PROPN
cana-4548	135	17	⟩	⟩	PROPN
cana-4548	135	18	𝛼1	𝛼1	PROPN
cana-4548	135	19	⊗	⊗	PROPN
cana-4548	135	20	𝛼2	𝛼2	PROPN
cana-4548	135	21	=	=	PUNCT
cana-4548	135	22	⟨	⟨	VERB
cana-4548	135	23	𝜇𝛼1	𝜇𝛼1	NOUN
cana-4548	135	24	𝜇𝛼2	𝜇𝛼2	NOUN
cana-4548	135	25	,	,	PUNCT
cana-4548	135	26	𝜂𝛼1	𝜂𝛼1	NOUN
cana-4548	135	27	+	+	CCONJ
cana-4548	135	28	𝜂𝛼2	𝜂𝛼2	NOUN
cana-4548	135	29	−	−	NOUN
cana-4548	135	30	𝜂𝛼1	𝜂𝛼1	NOUN
cana-4548	135	31	𝜂𝛼2	𝜂𝛼2	NOUN
cana-4548	135	32	𝜈𝛼1	𝜈𝛼1	NOUN
cana-4548	135	33	+	+	CCONJ
cana-4548	135	34	𝜈𝛼2	𝜈𝛼2	PROPN
cana-4548	135	35	−	−	PROPN
cana-4548	135	36	𝜈𝛼1	𝜈𝛼1	PROPN
cana-4548	135	37	𝜈𝛼2	𝜈𝛼2	PROPN
cana-4548	135	38	⟩	⟩	PROPN
cana-4548	135	39	𝜆𝛼	𝜆𝛼	PROPN
cana-4548	136	1	=	=	PROPN
cana-4548	136	2	⟨1	⟨1	PROPN
cana-4548	136	3	−	−	PROPN
cana-4548	136	4	(	(	PUNCT
cana-4548	136	5	1	1	NUM
cana-4548	136	6	−	−	NOUN
cana-4548	136	7	𝜇𝛼)𝜆	𝜇𝛼)𝜆	PROPN
cana-4548	136	8	,	,	PUNCT
cana-4548	136	9	(	(	PUNCT
cana-4548	136	10	𝜂𝛼)𝜆	𝜂𝛼)𝜆	PROPN
cana-4548	136	11	,	,	PUNCT
cana-4548	136	12	(	(	PUNCT
cana-4548	136	13	𝜈𝛼)𝜆⟩	𝜈𝛼)𝜆⟩	X
cana-4548	136	14	𝛼𝜆	𝛼𝜆	X
cana-4548	136	15	=	=	PUNCT
cana-4548	137	1	⟨(𝜇𝛼)𝜆	⟨(𝜇𝛼)𝜆	ADV
cana-4548	137	2	,	,	PUNCT
cana-4548	137	3	1	1	NUM
cana-4548	137	4	−	−	PROPN
cana-4548	137	5	(	(	PUNCT
cana-4548	137	6	1	1	NUM
cana-4548	137	7	−	−	PROPN
cana-4548	137	8	𝜂𝛼)𝜆	𝜂𝛼)𝜆	PROPN
cana-4548	137	9	,	,	PUNCT
cana-4548	137	10	1	1	NUM
cana-4548	137	11	−	−	PROPN
cana-4548	137	12	(	(	PUNCT
cana-4548	137	13	1	1	NUM
cana-4548	137	14	−	−	NOUN
cana-4548	137	15	𝜈𝛼)𝜆⟩	𝜈𝛼)𝜆⟩	NOUN
cana-4548	137	16	:	:	PUNCT
cana-4548	137	17	𝜆	𝜆	X
cana-4548	137	18	>	>	X
cana-4548	137	19	0	0	X
cana-4548	137	20	.	.	PUNCT
cana-4548	137	21	definition	definition	NOUN
cana-4548	137	22	9	9	NUM
cana-4548	137	23	.	.	PUNCT
cana-4548	138	1	let	let	VERB
cana-4548	138	2	𝛼	𝛼	VERB
cana-4548	138	3	=	=	SYM
cana-4548	138	4	(	(	PUNCT
cana-4548	138	5	𝜇𝛼	𝜇𝛼	NOUN
cana-4548	138	6	,	,	PUNCT
cana-4548	138	7	𝜂𝛼	𝜂𝛼	NOUN
cana-4548	138	8	,	,	PUNCT
cana-4548	138	9	𝜈𝛼	𝜈𝛼	NOUN
cana-4548	138	10	)	)	PUNCT
cana-4548	138	11	,	,	PUNCT
cana-4548	138	12	𝛼1	𝛼1	NOUN
cana-4548	138	13	=	=	SYM
cana-4548	138	14	(	(	PUNCT
cana-4548	138	15	𝜇𝛼1	𝜇𝛼1	NOUN
cana-4548	138	16	,	,	PUNCT
cana-4548	138	17	𝜂𝛼1	𝜂𝛼1	NOUN
cana-4548	138	18	,	,	PUNCT
cana-4548	138	19	𝜈𝛼1	𝜈𝛼1	X
cana-4548	138	20	)	)	PUNCT
cana-4548	138	21	and	and	CCONJ
cana-4548	138	22	𝛼2	𝛼2	PROPN
cana-4548	138	23	=	=	PUNCT
cana-4548	138	24	(	(	PUNCT
cana-4548	138	25	𝜇𝛼2	𝜇𝛼2	NOUN
cana-4548	138	26	,	,	PUNCT
cana-4548	138	27	𝜂𝛼2	𝜂𝛼2	PROPN
cana-4548	138	28	,	,	PUNCT
cana-4548	138	29	𝜈𝛼2	𝜈𝛼2	PROPN
cana-4548	138	30	)	)	PUNCT
cana-4548	138	31	be	be	VERB
cana-4548	138	32	three	three	NUM
cana-4548	138	33	pfns	pfns	NOUN
cana-4548	138	34	and	and	CCONJ
cana-4548	138	35	some	some	DET
cana-4548	138	36	basic	basic	ADJ
cana-4548	138	37	𝑆𝑆	𝑆𝑆	PROPN
cana-4548	138	38	operations	operation	NOUN
cana-4548	138	39	of	of	ADP
cana-4548	138	40	pfns	pfns	NOUN
cana-4548	138	41	are	be	AUX
cana-4548	138	42	defined	define	VERB
cana-4548	138	43	as	as	SCONJ
cana-4548	138	44	follows	follow	VERB
cana-4548	138	45	(	(	PUNCT
cana-4548	138	46	𝛽	𝛽	NOUN
cana-4548	138	47	<	<	X
cana-4548	138	48	0	0	NUM
cana-4548	138	49	)	)	PUNCT
cana-4548	138	50	:	:	PUNCT
cana-4548	139	1	𝛼1	𝛼1	NOUN
cana-4548	139	2	⊕	⊕	PROPN
cana-4548	139	3	𝛼2	𝛼2	PROPN
cana-4548	139	4	=	=	PUNCT
cana-4548	139	5	⟨(1	⟨(1	VERB
cana-4548	139	6	−	−	NOUN
cana-4548	139	7	𝜇𝛼1	𝜇𝛼1	NOUN
cana-4548	139	8	)	)	PUNCT
cana-4548	139	9	𝛽	𝛽	NOUN
cana-4548	139	10	+	+	CCONJ
cana-4548	139	11	(	(	PUNCT
cana-4548	139	12	1	1	NUM
cana-4548	139	13	−	−	NOUN
cana-4548	139	14	𝜇𝛼2	𝜇𝛼2	NOUN
cana-4548	139	15	)	)	PUNCT
cana-4548	139	16	𝛽	𝛽	NOUN
cana-4548	139	17	−	−	PROPN
cana-4548	139	18	1	1	NUM
cana-4548	139	19	)	)	SYM
cana-4548	139	20	1	1	NUM
cana-4548	139	21	𝛽	𝛽	NOUN
cana-4548	139	22	,	,	PUNCT
cana-4548	139	23	(	(	PUNCT
cana-4548	139	24	𝜂	𝜂	PROPN
cana-4548	139	25	𝛼1	𝛼1	PROPN
cana-4548	139	26	𝛽	𝛽	PROPN
cana-4548	139	27	+	+	NOUN
cana-4548	139	28	𝜂	𝜂	PROPN
cana-4548	139	29	𝛼2	𝛼2	PROPN
cana-4548	139	30	𝛽	𝛽	NOUN
cana-4548	139	31	−	−	PROPN
cana-4548	139	32	1	1	NUM
cana-4548	139	33	)	)	SYM
cana-4548	139	34	1	1	NUM
cana-4548	139	35	𝛽	𝛽	NOUN
cana-4548	139	36	,	,	PUNCT
cana-4548	139	37	(	(	PUNCT
cana-4548	139	38	𝜈	𝜈	PROPN
cana-4548	139	39	𝛼1	𝛼1	PROPN
cana-4548	139	40	𝛽	𝛽	PROPN
cana-4548	139	41	+	+	CCONJ
cana-4548	139	42	𝜈	𝜈	PRON
cana-4548	139	43	𝛼2	𝛼2	PROPN
cana-4548	139	44	𝛽	𝛽	PROPN
cana-4548	139	45	−	−	PROPN
cana-4548	139	46	1	1	NUM
cana-4548	139	47	)	)	SYM
cana-4548	139	48	1	1	NUM
cana-4548	139	49	𝛽	𝛽	NOUN
cana-4548	139	50	)	)	PUNCT
cana-4548	139	51	⟩	⟩	NOUN
cana-4548	139	52	𝛼1	𝛼1	PROPN
cana-4548	139	53	⊗	⊗	PROPN
cana-4548	139	54	𝛼2	𝛼2	PROPN
cana-4548	139	55	=	=	PROPN
cana-4548	139	56	⟨(𝜇	⟨(𝜇	PROPN
cana-4548	139	57	𝛼1	𝛼1	PROPN
cana-4548	139	58	𝛽	𝛽	PROPN
cana-4548	139	59	+	+	ADP
cana-4548	139	60	𝜇	𝜇	ADP
cana-4548	139	61	𝛼2	𝛼2	PROPN
cana-4548	139	62	𝛽	𝛽	NOUN
cana-4548	139	63	−	−	PROPN
cana-4548	139	64	1	1	NUM
cana-4548	139	65	)	)	SYM
cana-4548	139	66	1	1	NUM
cana-4548	139	67	𝛽	𝛽	NOUN
cana-4548	139	68	,	,	PUNCT
cana-4548	139	69	1	1	NUM
cana-4548	139	70	−	−	PROPN
cana-4548	139	71	(	(	PUNCT
cana-4548	139	72	(	(	PUNCT
cana-4548	139	73	1	1	NUM
cana-4548	139	74	−	−	NOUN
cana-4548	139	75	𝜂𝛼1	𝜂𝛼1	NOUN
cana-4548	139	76	)	)	PUNCT
cana-4548	140	1	𝛽	𝛽	NOUN
cana-4548	140	2	+	+	CCONJ
cana-4548	140	3	(	(	PUNCT
cana-4548	140	4	1	1	NUM
cana-4548	140	5	−	−	NOUN
cana-4548	140	6	𝜂𝛼2	𝜂𝛼2	NOUN
cana-4548	140	7	)	)	PUNCT
cana-4548	141	1	𝛽	𝛽	NOUN
cana-4548	141	2	−	−	PROPN
cana-4548	141	3	1	1	NUM
cana-4548	141	4	)	)	SYM
cana-4548	141	5	1	1	NUM
cana-4548	141	6	𝛽	𝛽	NOUN
cana-4548	141	7	,	,	PUNCT
cana-4548	141	8	1	1	NUM
cana-4548	141	9	−	−	PROPN
cana-4548	141	10	(	(	PUNCT
cana-4548	141	11	(	(	PUNCT
cana-4548	141	12	1	1	NUM
cana-4548	141	13	−	−	NOUN
cana-4548	141	14	𝜈𝛼1	𝜈𝛼1	NOUN
cana-4548	141	15	)	)	PUNCT
cana-4548	141	16	𝛽	𝛽	NOUN
cana-4548	141	17	+	+	CCONJ
cana-4548	141	18	(	(	PUNCT
cana-4548	141	19	1	1	NUM
cana-4548	141	20	−	−	NOUN
cana-4548	141	21	𝜈𝛼2	𝜈𝛼2	NOUN
cana-4548	141	22	)	)	PUNCT
cana-4548	142	1	𝛽	𝛽	NOUN
cana-4548	142	2	−	−	PROPN
cana-4548	142	3	1	1	NUM
cana-4548	142	4	)	)	SYM
cana-4548	142	5	1	1	NUM
cana-4548	142	6	𝛽	𝛽	NOUN
cana-4548	142	7	⟩	⟩	NOUN
cana-4548	142	8	𝛼1	𝛼1	NOUN
cana-4548	142	9	𝜆	𝜆	NOUN
cana-4548	142	10	=	=	PUNCT
cana-4548	142	11	⟨(𝜆𝜇	⟨(𝜆𝜇	PROPN
cana-4548	142	12	𝛼1	𝛼1	PROPN
cana-4548	142	13	𝛽	𝛽	PROPN
cana-4548	142	14	−	−	PROPN
cana-4548	143	1	(	(	PUNCT
cana-4548	143	2	𝜆	𝜆	PROPN
cana-4548	143	3	−	−	PROPN
cana-4548	143	4	1	1	NUM
cana-4548	143	5	)	)	PUNCT
cana-4548	143	6	)	)	PUNCT
cana-4548	143	7	1	1	NUM
cana-4548	143	8	𝛽	𝛽	NOUN
cana-4548	143	9	,	,	PUNCT
cana-4548	143	10	1	1	NUM
cana-4548	143	11	−	−	PROPN
cana-4548	143	12	(	(	PUNCT
cana-4548	143	13	𝜆(1	𝜆(1	NOUN
cana-4548	143	14	−	−	PROPN
cana-4548	143	15	𝜂𝛼1	𝜂𝛼1	NOUN
cana-4548	143	16	)	)	PUNCT
cana-4548	144	1	𝜆	𝜆	DET
cana-4548	144	2	−	−	PROPN
cana-4548	144	3	(	(	PUNCT
cana-4548	144	4	𝜆	𝜆	PROPN
cana-4548	144	5	−	−	PROPN
cana-4548	144	6	1	1	NUM
cana-4548	144	7	)	)	PUNCT
cana-4548	144	8	)	)	PUNCT
cana-4548	144	9	1	1	NUM
cana-4548	144	10	𝛽	𝛽	NOUN
cana-4548	144	11	,	,	PUNCT
cana-4548	144	12	1	1	NUM
cana-4548	144	13	−	−	PROPN
cana-4548	144	14	(	(	PUNCT
cana-4548	144	15	𝜆(1	𝜆(1	NOUN
cana-4548	144	16	−	−	PROPN
cana-4548	144	17	𝜈𝛼1	𝜈𝛼1	NOUN
cana-4548	144	18	)	)	PUNCT
cana-4548	145	1	𝜆	𝜆	ADV
cana-4548	145	2	−	−	PROPN
cana-4548	145	3	(	(	PUNCT
cana-4548	145	4	𝜆	𝜆	PROPN
cana-4548	145	5	−	−	PROPN
cana-4548	145	6	1	1	NUM
cana-4548	145	7	)	)	PUNCT
cana-4548	145	8	)	)	PUNCT
cana-4548	146	1	1	1	NUM
cana-4548	146	2	𝛽	𝛽	NOUN
cana-4548	146	3	⟩	⟩	NOUN
cana-4548	146	4	,	,	PUNCT
cana-4548	146	5	𝜆	𝜆	PROPN
cana-4548	146	6	>	>	X
cana-4548	146	7	0	0	NUM
cana-4548	146	8	𝜆𝛼1	𝜆𝛼1	PROPN
cana-4548	147	1	=	=	SYM
cana-4548	147	2	⟨1	⟨1	PROPN
cana-4548	147	3	−	−	PROPN
cana-4548	148	1	(	(	PUNCT
cana-4548	149	1	𝜆(1	𝜆(1	NOUN
cana-4548	149	2	−	−	ADP
cana-4548	149	3	𝜇𝛼1	𝜇𝛼1	NOUN
cana-4548	149	4	)	)	PUNCT
cana-4548	150	1	𝜆	𝜆	ADV
cana-4548	150	2	−	−	PROPN
cana-4548	150	3	(	(	PUNCT
cana-4548	150	4	𝜆	𝜆	PROPN
cana-4548	150	5	−	−	PROPN
cana-4548	150	6	1	1	NUM
cana-4548	150	7	)	)	PUNCT
cana-4548	150	8	)	)	PUNCT
cana-4548	150	9	1	1	NUM
cana-4548	150	10	𝛽	𝛽	NOUN
cana-4548	150	11	,	,	PUNCT
cana-4548	150	12	(	(	PUNCT
cana-4548	150	13	𝜆𝜂	𝜆𝜂	ADP
cana-4548	150	14	𝛼1	𝛼1	PROPN
cana-4548	150	15	𝛽	𝛽	NOUN
cana-4548	150	16	−	−	PROPN
cana-4548	151	1	(	(	PUNCT
cana-4548	151	2	𝜆	𝜆	PROPN
cana-4548	151	3	−	−	PROPN
cana-4548	151	4	1	1	NUM
cana-4548	151	5	)	)	PUNCT
cana-4548	151	6	)	)	PUNCT
cana-4548	152	1	1	1	NUM
cana-4548	152	2	𝛽	𝛽	NOUN
cana-4548	152	3	,	,	PUNCT
cana-4548	152	4	(	(	PUNCT
cana-4548	152	5	𝜆𝜈	𝜆𝜈	PROPN
cana-4548	152	6	𝛼1	𝛼1	PROPN
cana-4548	152	7	𝛽	𝛽	PROPN
cana-4548	152	8	−	−	PROPN
cana-4548	152	9	(	(	PUNCT
cana-4548	152	10	𝜆	𝜆	PROPN
cana-4548	152	11	−	−	PROPN
cana-4548	152	12	1	1	NUM
cana-4548	152	13	)	)	PUNCT
cana-4548	152	14	)	)	PUNCT
cana-4548	153	1	1	1	NUM
cana-4548	153	2	𝛽	𝛽	NOUN
cana-4548	153	3	⟩	⟩	NOUN
cana-4548	153	4	,	,	PUNCT
cana-4548	153	5	𝜆	𝜆	PROPN
cana-4548	153	6	>	>	X
cana-4548	153	7	0	0	NUM
cana-4548	153	8	.	.	NOUN
cana-4548	154	1	3	3	X
cana-4548	154	2	.	.	X
cana-4548	154	3	picture	picture	NOUN
cana-4548	154	4	fuzzy	fuzzy	ADJ
cana-4548	154	5	schweizer	schweizer	PROPN
cana-4548	154	6	-	-	PUNCT
cana-4548	154	7	sklar	sklar	ADJ
cana-4548	154	8	power	power	NOUN
cana-4548	154	9	geometric	geometric	ADJ
cana-4548	154	10	aggregation	aggregation	NOUN
cana-4548	154	11	operators	operator	NOUN
cana-4548	154	12	in	in	ADP
cana-4548	154	13	this	this	DET
cana-4548	154	14	section	section	NOUN
cana-4548	154	15	,	,	PUNCT
cana-4548	154	16	we	we	PRON
cana-4548	154	17	presented	present	VERB
cana-4548	154	18	the	the	DET
cana-4548	154	19	schweizer	schweizer	PROPN
cana-4548	154	20	-	-	PUNCT
cana-4548	154	21	sklar	sklar	ADJ
cana-4548	154	22	power	power	NOUN
cana-4548	154	23	geometric	geometric	ADJ
cana-4548	154	24	aos	aos	PROPN
cana-4548	154	25	and	and	CCONJ
cana-4548	154	26	discussed	discuss	VERB
cana-4548	154	27	the	the	DET
cana-4548	154	28	fundamental	fundamental	ADJ
cana-4548	154	29	properties	property	NOUN
cana-4548	154	30	of	of	ADP
cana-4548	154	31	these	these	DET
cana-4548	154	32	proposed	propose	VERB
cana-4548	154	33	operators	operator	NOUN
cana-4548	154	34	within	within	ADP
cana-4548	154	35	the	the	DET
cana-4548	154	36	framework	framework	NOUN
cana-4548	154	37	of	of	ADP
cana-4548	154	38	pfns	pfns	NOUN
cana-4548	154	39	.	.	PUNCT
cana-4548	155	1	3.1	3.1	NUM
cana-4548	155	2	picture	picture	NOUN
cana-4548	155	3	fuzzy	fuzzy	ADJ
cana-4548	155	4	schweizer	schweizer	PROPN
cana-4548	155	5	-	-	PUNCT
cana-4548	155	6	sklar	sklar	ADJ
cana-4548	155	7	power	power	NOUN
cana-4548	155	8	weighted	weight	VERB
cana-4548	155	9	geometric	geometric	ADJ
cana-4548	155	10	aggregation	aggregation	NOUN
cana-4548	155	11	operators	operator	NOUN
cana-4548	155	12	in	in	ADP
cana-4548	155	13	the	the	DET
cana-4548	155	14	next	next	ADJ
cana-4548	155	15	section	section	NOUN
cana-4548	155	16	,	,	PUNCT
cana-4548	155	17	we	we	PRON
cana-4548	155	18	introduce	introduce	VERB
cana-4548	155	19	the	the	DET
cana-4548	155	20	confidence	confidence	NOUN
cana-4548	155	21	picture	picture	NOUN
cana-4548	155	22	fuzzy	fuzzy	ADJ
cana-4548	155	23	schweizer	schweizer	PROPN
cana-4548	155	24	-	-	PUNCT
cana-4548	155	25	sklar	sklar	ADJ
cana-4548	155	26	power	power	NOUN
cana-4548	155	27	weighted	weight	VERB
cana-4548	155	28	geometric	geometric	ADJ
cana-4548	155	29	operator	operator	NOUN
cana-4548	155	30	within	within	ADP
cana-4548	155	31	the	the	DET
cana-4548	155	32	context	context	NOUN
cana-4548	155	33	of	of	ADP
cana-4548	155	34	pf	pf	NOUN
cana-4548	155	35	,	,	PUNCT
cana-4548	155	36	and	and	CCONJ
cana-4548	155	37	we	we	PRON
cana-4548	155	38	examine	examine	VERB
cana-4548	155	39	the	the	DET
cana-4548	155	40	desirable	desirable	ADJ
cana-4548	155	41	properties	property	NOUN
cana-4548	155	42	of	of	ADP
cana-4548	155	43	this	this	DET
cana-4548	155	44	proposed	propose	VERB
cana-4548	155	45	operator	operator	NOUN
cana-4548	155	46	.	.	PUNCT
cana-4548	156	1	additionally	additionally	ADV
cana-4548	156	2	,	,	PUNCT
cana-4548	156	3	we	we	PRON
cana-4548	156	4	applied	apply	VERB
cana-4548	156	5	a	a	DET
cana-4548	156	6	weighted	weight	VERB
cana-4548	156	7	support	support	NOUN
cana-4548	156	8	degree	degree	NOUN
cana-4548	156	9	throughout	throughout	ADP
cana-4548	156	10	our	our	PRON
cana-4548	156	11	article	article	NOUN
cana-4548	156	12	,	,	PUNCT
cana-4548	156	13	using	use	VERB
cana-4548	156	14	the	the	DET
cana-4548	156	15	following	follow	VERB
cana-4548	156	16	equation	equation	NOUN
cana-4548	156	17	:	:	PUNCT
cana-4548	156	18	communications	communication	NOUN
cana-4548	156	19	on	on	ADP
cana-4548	156	20	applied	apply	VERB
cana-4548	156	21	nonlinear	nonlinear	ADJ
cana-4548	156	22	analysis	analysis	NOUN
cana-4548	156	23	issn	issn	NOUN
cana-4548	156	24	:	:	PUNCT
cana-4548	156	25	1074	1074	NUM
cana-4548	156	26	-	-	PUNCT
cana-4548	156	27	133x	133x	NUM
cana-4548	156	28	vol	vol	NOUN
cana-4548	156	29	32	32	NUM
cana-4548	157	1	no	no	NOUN
cana-4548	157	2	.	.	PUNCT
cana-4548	158	1	9s	9s	NUM
cana-4548	158	2	(	(	PUNCT
cana-4548	158	3	2025	2025	NUM
cana-4548	158	4	)	)	PUNCT
cana-4548	158	5	2685	2685	NUM
cana-4548	158	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4548	158	7	�	�	PROPN
cana-4548	158	8	̆	̆	NOUN
cana-4548	158	9	�	�	PROPN
cana-4548	158	10	𝑗(𝑗	𝑗(𝑗	PROPN
cana-4548	158	11	=	=	SYM
cana-4548	158	12	1,2	1,2	NUM
cana-4548	158	13	,	,	PUNCT
cana-4548	158	14	…	…	PUNCT
cana-4548	158	15	,	,	PUNCT
cana-4548	158	16	𝑛	𝑛	X
cana-4548	158	17	)	)	PUNCT
cana-4548	158	18	is	be	AUX
cana-4548	158	19	a	a	DET
cana-4548	158	20	set	set	NOUN
cana-4548	158	21	of	of	ADP
cana-4548	158	22	integrated	integrate	VERB
cana-4548	158	23	weights	weight	NOUN
cana-4548	158	24	,	,	PUNCT
cana-4548	158	25	�	�	PROPN
cana-4548	158	26	̆	̆	NOUN
cana-4548	158	27	�	�	PROPN
cana-4548	158	28	𝑗	𝑗	NOUN
cana-4548	158	29	=	=	SYM
cana-4548	158	30	𝑤𝑗(1+𝔑𝔶(𝛼𝑗	𝑤𝑗(1+𝔑𝔶(𝛼𝑗	PROPN
cana-4548	158	31	)	)	PUNCT
cana-4548	158	32	)	)	PUNCT
cana-4548	159	1	∑	∑	ADV
cana-4548	159	2	 	 	SPACE
cana-4548	159	3	𝑛	𝑛	DET
cana-4548	159	4	𝑗=1	𝑗=1	PROPN
cana-4548	159	5	 	 	SPACE
cana-4548	159	6	𝑤𝑗(1+𝔑𝔶(𝛼𝑗	𝑤𝑗(1+𝔑𝔶(𝛼𝑗	PROPN
cana-4548	159	7	)	)	PUNCT
cana-4548	159	8	)	)	PUNCT
cana-4548	159	9	⋅	⋅	PROPN
cana-4548	159	10	𝔑𝔶(𝛼𝑗	𝔑𝔶(𝛼𝑗	PROPN
cana-4548	159	11	)	)	PUNCT
cana-4548	159	12	=	=	PUNCT
cana-4548	160	1	∑	∑	PUNCT
cana-4548	160	2	 	 	SPACE
cana-4548	160	3	𝑛	𝑛	PRON
cana-4548	160	4	ℎ=1,ℎ≠𝑗	ℎ=1,ℎ≠𝑗	PROPN
cana-4548	160	5	sup(𝛼𝑗	sup(𝛼𝑗	PROPN
cana-4548	160	6	,	,	PUNCT
cana-4548	160	7	𝛼ℎ	𝛼ℎ	NOUN
cana-4548	160	8	)	)	PUNCT
cana-4548	160	9	and	and	CCONJ
cana-4548	160	10	𝑤	𝑤	X
cana-4548	160	11	=	=	SYM
cana-4548	160	12	(	(	PUNCT
cana-4548	160	13	𝑤1	𝑤1	VERB
cana-4548	160	14	,	,	PUNCT
cana-4548	160	15	𝑤2	𝑤2	NOUN
cana-4548	160	16	,	,	PUNCT
cana-4548	160	17	…	…	PUNCT
cana-4548	160	18	,	,	PUNCT
cana-4548	160	19	𝑤𝑛)𝑇	𝑤𝑛)𝑇	PROPN
cana-4548	160	20	is	be	AUX
cana-4548	160	21	the	the	DET
cana-4548	160	22	weight	weight	NOUN
cana-4548	160	23	vector	vector	NOUN
cana-4548	160	24	of	of	ADP
cana-4548	160	25	𝛼𝑗(𝑗	𝛼𝑗(𝑗	NOUN
cana-4548	160	26	=	=	SYM
cana-4548	160	27	1,2	1,2	NUM
cana-4548	160	28	,	,	PUNCT
cana-4548	160	29	…	…	PUNCT
cana-4548	160	30	,	,	PUNCT
cana-4548	160	31	𝑛)𝑤	𝑛)𝑤	X
cana-4548	160	32	∈	∈	PROPN
cana-4548	161	1	[	[	X
cana-4548	161	2	0,1	0,1	NUM
cana-4548	161	3	]	]	PUNCT
cana-4548	161	4	,	,	PUNCT
cana-4548	161	5	∑	∑	ADP
cana-4548	161	6	 	 	SPACE
cana-4548	161	7	𝑛	𝑛	PRON
cana-4548	161	8	𝑗=1	𝑗=1	PROPN
cana-4548	161	9	𝑤𝑗	𝑤𝑗	ADP
cana-4548	161	10	=	=	SYM
cana-4548	161	11	1	1	X
cana-4548	161	12	.	.	PUNCT
cana-4548	162	1	definition	definition	NOUN
cana-4548	162	2	10	10	NUM
cana-4548	162	3	.	.	PUNCT
cana-4548	163	1	let	let	VERB
cana-4548	163	2	𝛼𝑗	𝛼𝑗	PROPN
cana-4548	163	3	=	=	SYM
cana-4548	163	4	⟨𝜇𝛼𝑗	⟨𝜇𝛼𝑗	PROPN
cana-4548	163	5	,	,	PUNCT
cana-4548	163	6	𝜂𝛼𝑗	𝜂𝛼𝑗	VERB
cana-4548	163	7	,	,	PUNCT
cana-4548	163	8	𝜈𝛼𝑗	𝜈𝛼𝑗	VERB
cana-4548	163	9	⟩	⟩	NOUN
cana-4548	163	10	(	(	PUNCT
cana-4548	163	11	𝑗	𝑗	NOUN
cana-4548	163	12	=	=	SYM
cana-4548	163	13	1,2	1,2	NUM
cana-4548	163	14	,	,	PUNCT
cana-4548	163	15	…	…	PUNCT
cana-4548	163	16	,	,	PUNCT
cana-4548	163	17	𝑛	𝑛	X
cana-4548	163	18	)	)	PUNCT
cana-4548	163	19	be	be	VERB
cana-4548	163	20	a	a	DET
cana-4548	163	21	set	set	NOUN
cana-4548	163	22	of	of	ADP
cana-4548	163	23	pfn	pfn	PROPN
cana-4548	163	24	.	.	PUNCT
cana-4548	164	1	then	then	ADV
cana-4548	164	2	the	the	DET
cana-4548	164	3	pfsspwg	pfsspwg	NOUN
cana-4548	164	4	operator	operator	NOUN
cana-4548	164	5	of	of	ADP
cana-4548	164	6	dimension	dimension	NOUN
cana-4548	164	7	𝑛	𝑛	PROPN
cana-4548	164	8	is	be	AUX
cana-4548	164	9	a	a	DET
cana-4548	164	10	mapping	mapping	NOUN
cana-4548	164	11	pfsspwg	pfsspwg	NOUN
cana-4548	164	12	:	:	PUNCT
cana-4548	164	13	𝛼𝑛	𝛼𝑛	PROPN
cana-4548	164	14	→	→	SYM
cana-4548	164	15	𝛼	𝛼	NOUN
cana-4548	164	16	such	such	ADJ
cana-4548	164	17	that	that	DET
cana-4548	164	18	pfsspwg(𝛼1	pfsspwg(𝛼1	NOUN
cana-4548	164	19	,	,	PUNCT
cana-4548	164	20	𝛼2	𝛼2	PROPN
cana-4548	164	21	,	,	PUNCT
cana-4548	164	22	…	…	PUNCT
cana-4548	164	23	,	,	PUNCT
cana-4548	164	24	𝛼𝑛	𝛼𝑛	PROPN
cana-4548	164	25	)	)	PUNCT
cana-4548	164	26	=	=	NOUN
cana-4548	164	27	⊕𝑗=1	⊕𝑗=1	NUM
cana-4548	164	28	𝑛	𝑛	VERB
cana-4548	164	29	𝛼	𝛼	PRON
cana-4548	164	30	𝑗	𝑗	PROPN
cana-4548	164	31	(	(	PUNCT
cana-4548	164	32	𝑤𝑗(1+𝔫𝔶(𝛼𝑗	𝑤𝑗(1+𝔫𝔶(𝛼𝑗	PROPN
cana-4548	164	33	)	)	PUNCT
cana-4548	164	34	)	)	PUNCT
cana-4548	165	1	∑	∑	PUNCT
cana-4548	165	2	 	 	SPACE
cana-4548	165	3	𝑛	𝑛	PRON
cana-4548	165	4	𝑗=1	𝑗=1	PROPN
cana-4548	165	5	 	 	SPACE
cana-4548	165	6	𝑤𝑗(1+𝔫𝔶(𝛼𝑗	𝑤𝑗(1+𝔫𝔶(𝛼𝑗	PROPN
cana-4548	165	7	)	)	PUNCT
cana-4548	165	8	)	)	PUNCT
cana-4548	165	9	)	)	PUNCT
cana-4548	166	1	(	(	PUNCT
cana-4548	166	2	5	5	X
cana-4548	166	3	)	)	PUNCT
cana-4548	166	4	where𝛼	where𝛼	PROPN
cana-4548	166	5	is	be	AUX
cana-4548	166	6	the	the	DET
cana-4548	166	7	set	set	NOUN
cana-4548	166	8	of	of	ADP
cana-4548	166	9	all	all	DET
cana-4548	166	10	pfn	pfn	NOUN
cana-4548	166	11	and	and	CCONJ
cana-4548	166	12	𝔑𝔶(𝛼𝑗	𝔑𝔶(𝛼𝑗	ADJ
cana-4548	166	13	)	)	PUNCT
cana-4548	166	14	=	=	PUNCT
cana-4548	167	1	∑	∑	PUNCT
cana-4548	167	2	 	 	SPACE
cana-4548	167	3	𝑛	𝑛	PRON
cana-4548	167	4	ℎ=1,ℎ≠𝑗	ℎ=1,ℎ≠𝑗	PROPN
cana-4548	167	5	sup(𝛼𝑗	sup(𝛼𝑗	PROPN
cana-4548	167	6	,	,	PUNCT
cana-4548	167	7	𝛼ℎ	𝛼ℎ	NOUN
cana-4548	167	8	)	)	PUNCT
cana-4548	167	9	and	and	CCONJ
cana-4548	167	10	𝑤	𝑤	X
cana-4548	167	11	=	=	SYM
cana-4548	167	12	(	(	PUNCT
cana-4548	167	13	𝑤1	𝑤1	VERB
cana-4548	167	14	,	,	PUNCT
cana-4548	167	15	𝑤2	𝑤2	NOUN
cana-4548	167	16	,	,	PUNCT
cana-4548	167	17	…	…	PUNCT
cana-4548	167	18	,	,	PUNCT
cana-4548	167	19	𝑤𝑛)𝑇	𝑤𝑛)𝑇	PROPN
cana-4548	167	20	is	be	AUX
cana-4548	167	21	the	the	DET
cana-4548	167	22	weight	weight	NOUN
cana-4548	167	23	vector	vector	NOUN
cana-4548	167	24	of	of	ADP
cana-4548	167	25	𝛼𝑗(𝑗	𝛼𝑗(𝑗	NOUN
cana-4548	167	26	=	=	SYM
cana-4548	167	27	1,2	1,2	NUM
cana-4548	167	28	,	,	PUNCT
cana-4548	167	29	…	…	PUNCT
cana-4548	167	30	,	,	PUNCT
cana-4548	167	31	𝑛)𝑤	𝑛)𝑤	X
cana-4548	167	32	∈	∈	PROPN
cana-4548	168	1	[	[	X
cana-4548	168	2	0,1	0,1	NUM
cana-4548	168	3	]	]	PUNCT
cana-4548	168	4	,	,	PUNCT
cana-4548	168	5	∑	∑	ADP
cana-4548	168	6	 	 	SPACE
cana-4548	168	7	𝑛	𝑛	PRON
cana-4548	168	8	𝑗=1	𝑗=1	PROPN
cana-4548	168	9	𝑤𝑗	𝑤𝑗	ADP
cana-4548	168	10	=	=	SYM
cana-4548	168	11	1	1	X
cana-4548	168	12	.	.	PUNCT
cana-4548	168	13	theorem	theorem	NOUN
cana-4548	168	14	1	1	NUM
cana-4548	168	15	.	.	PUNCT
cana-4548	169	1	let	let	VERB
cana-4548	169	2	𝛼𝑗	𝛼𝑗	PROPN
cana-4548	169	3	=	=	SYM
cana-4548	169	4	⟨𝜇𝛼𝑗	⟨𝜇𝛼𝑗	PROPN
cana-4548	169	5	,	,	PUNCT
cana-4548	169	6	𝜂𝛼𝑗	𝜂𝛼𝑗	VERB
cana-4548	169	7	,	,	PUNCT
cana-4548	169	8	𝜈𝛼𝑗	𝜈𝛼𝑗	VERB
cana-4548	169	9	⟩	⟩	NOUN
cana-4548	169	10	(	(	PUNCT
cana-4548	169	11	𝑗	𝑗	NOUN
cana-4548	169	12	=	=	SYM
cana-4548	169	13	1,2	1,2	NUM
cana-4548	169	14	,	,	PUNCT
cana-4548	169	15	…	…	PUNCT
cana-4548	169	16	,	,	PUNCT
cana-4548	169	17	𝑛	𝑛	X
cana-4548	169	18	)	)	PUNCT
cana-4548	169	19	be	be	VERB
cana-4548	169	20	a	a	DET
cana-4548	169	21	set	set	NOUN
cana-4548	169	22	of	of	ADP
cana-4548	169	23	pfn	pfn	NOUN
cana-4548	169	24	and	and	CCONJ
cana-4548	169	25	𝛽	𝛽	NOUN
cana-4548	169	26	<	<	X
cana-4548	169	27	0	0	NUM
cana-4548	169	28	,	,	PUNCT
cana-4548	169	29	then	then	ADV
cana-4548	169	30	the	the	DET
cana-4548	169	31	aggregated	aggregate	VERB
cana-4548	169	32	value	value	NOUN
cana-4548	169	33	obtained	obtain	VERB
cana-4548	169	34	using	use	VERB
cana-4548	169	35	pfsspwg	pfsspwg	NOUN
cana-4548	169	36	operator	operator	NOUN
cana-4548	169	37	is	be	AUX
cana-4548	169	38	also	also	ADV
cana-4548	169	39	a	a	DET
cana-4548	169	40	pfn	pfn	NOUN
cana-4548	169	41	and	and	CCONJ
cana-4548	169	42	can	can	AUX
cana-4548	169	43	be	be	AUX
cana-4548	169	44	expressed	express	VERB
cana-4548	169	45	as	as	SCONJ
cana-4548	169	46	follows	follow	VERB
cana-4548	169	47	:	:	PUNCT
cana-4548	169	48	pfsspwg(𝛼1	pfsspwg(𝛼1	NOUN
cana-4548	169	49	,	,	PUNCT
cana-4548	169	50	𝛼2	𝛼2	PROPN
cana-4548	169	51	,	,	PUNCT
cana-4548	169	52	…	…	PUNCT
cana-4548	169	53	,	,	PUNCT
cana-4548	169	54	𝛼𝑛	𝛼𝑛	PROPN
cana-4548	169	55	)	)	PUNCT
cana-4548	169	56	=	=	PUNCT
cana-4548	170	1	⟨(∑	⟨(∑	X
cana-4548	170	2	  	  	SPACE
cana-4548	170	3	𝑛	𝑛	PRON
cana-4548	170	4	𝑗=1	𝑗=1	PROPN
cana-4548	170	5	  	  	SPACE
cana-4548	170	6	�	�	PROPN
cana-4548	170	7	̆	̆	NOUN
cana-4548	170	8	�	�	PROPN
cana-4548	170	9	𝑗𝜇𝑗	𝑗𝜇𝑗	PROPN
cana-4548	170	10	𝛽	𝛽	PROPN
cana-4548	170	11	)	)	PUNCT
cana-4548	170	12	1	1	NUM
cana-4548	170	13	𝛽	𝛽	NOUN
cana-4548	170	14	,	,	PUNCT
cana-4548	170	15	1	1	NUM
cana-4548	170	16	−	−	PROPN
cana-4548	170	17	(	(	PUNCT
cana-4548	170	18	∑	∑	INTJ
cana-4548	170	19	  	  	SPACE
cana-4548	170	20	𝑛	𝑛	DET
cana-4548	170	21	𝑗=1	𝑗=1	PROPN
cana-4548	170	22	  	  	SPACE
cana-4548	170	23	�	�	PROPN
cana-4548	170	24	̆	̆	NOUN
cana-4548	170	25	�	�	PROPN
cana-4548	170	26	𝑗(1	𝑗(1	PROPN
cana-4548	170	27	−	−	PROPN
cana-4548	170	28	𝜂𝑗	𝜂𝑗	NOUN
cana-4548	170	29	)	)	PUNCT
cana-4548	170	30	𝛽	𝛽	NOUN
cana-4548	170	31	)	)	PUNCT
cana-4548	170	32	1	1	NUM
cana-4548	170	33	𝛽	𝛽	NOUN
cana-4548	170	34	,	,	PUNCT
cana-4548	170	35	1	1	NUM
cana-4548	170	36	−	−	PROPN
cana-4548	170	37	(	(	PUNCT
cana-4548	170	38	∑	∑	INTJ
cana-4548	170	39	  	  	SPACE
cana-4548	170	40	𝑛	𝑛	PRON
cana-4548	170	41	𝑗=1	𝑗=1	PROPN
cana-4548	170	42	  	  	SPACE
cana-4548	170	43	�	�	PROPN
cana-4548	170	44	̆	̆	NOUN
cana-4548	170	45	�	�	PROPN
cana-4548	170	46	𝑗(1	𝑗(1	PROPN
cana-4548	170	47	−	−	PROPN
cana-4548	170	48	𝜈𝑗	𝜈𝑗	PROPN
cana-4548	170	49	)	)	PUNCT
cana-4548	170	50	𝛽	𝛽	NOUN
cana-4548	170	51	)	)	PUNCT
cana-4548	171	1	1	1	NUM
cana-4548	171	2	𝛽	𝛽	NOUN
cana-4548	171	3	⟩	⟩	NOUN
cana-4548	171	4	(	(	PUNCT
cana-4548	171	5	6	6	NUM
cana-4548	171	6	)	)	PUNCT
cana-4548	171	7	where	where	SCONJ
cana-4548	171	8	�	�	NOUN
cana-4548	171	9	̆	̆	NOUN
cana-4548	171	10	�	�	PROPN
cana-4548	171	11	𝑗(𝑗	𝑗(𝑗	PROPN
cana-4548	171	12	=	=	SYM
cana-4548	171	13	1,2	1,2	NUM
cana-4548	171	14	,	,	PUNCT
cana-4548	171	15	…	…	PUNCT
cana-4548	171	16	,	,	PUNCT
cana-4548	171	17	𝑛	𝑛	X
cana-4548	171	18	)	)	PUNCT
cana-4548	171	19	is	be	AUX
cana-4548	171	20	a	a	DET
cana-4548	171	21	set	set	NOUN
cana-4548	171	22	of	of	ADP
cana-4548	171	23	integrated	integrate	VERB
cana-4548	171	24	weights	weight	NOUN
cana-4548	171	25	,	,	PUNCT
cana-4548	171	26	�	�	PROPN
cana-4548	171	27	̆	̆	NOUN
cana-4548	171	28	�	�	PROPN
cana-4548	171	29	𝑗	𝑗	NOUN
cana-4548	171	30	=	=	SYM
cana-4548	171	31	1+𝔑𝔶(𝛼𝑗	1+𝔑𝔶(𝛼𝑗	NUM
cana-4548	171	32	)	)	PUNCT
cana-4548	171	33	∑	∑	ADP
cana-4548	171	34	 	 	SPACE
cana-4548	171	35	𝑛	𝑛	PRON
cana-4548	171	36	𝑗=1	𝑗=1	PROPN
cana-4548	171	37	 	 	SPACE
cana-4548	171	38	(	(	PUNCT
cana-4548	171	39	1+𝔑𝔶(𝛼𝑗	1+𝔑𝔶(𝛼𝑗	NUM
cana-4548	171	40	)	)	PUNCT
cana-4548	171	41	)	)	PUNCT
cana-4548	171	42	.	.	PUNCT
cana-4548	172	1	in	in	ADP
cana-4548	172	2	order	order	NOUN
cana-4548	172	3	to	to	PART
cana-4548	172	4	prove	prove	VERB
cana-4548	172	5	equation	equation	NOUN
cana-4548	172	6	6	6	NUM
cana-4548	172	7	,	,	PUNCT
cana-4548	172	8	we	we	PRON
cana-4548	172	9	first	first	ADV
cana-4548	172	10	prove	prove	VERB
cana-4548	172	11	that	that	SCONJ
cana-4548	172	12	when	when	SCONJ
cana-4548	172	13	�	�	PROPN
cana-4548	172	14	̆	̆	NOUN
cana-4548	172	15	�	�	PROPN
cana-4548	172	16	=	=	SYM
cana-4548	172	17	(	(	PUNCT
cana-4548	172	18	�	�	PROPN
cana-4548	172	19	̆	̆	NOUN
cana-4548	172	20	�	�	PROPN
cana-4548	172	21	1	1	NUM
cana-4548	172	22	,	,	PUNCT
cana-4548	172	23	�	�	PROPN
cana-4548	172	24	̆	̆	NOUN
cana-4548	172	25	�	�	PROPN
cana-4548	172	26	2	2	NUM
cana-4548	172	27	,	,	PUNCT
cana-4548	172	28	…	…	PUNCT
cana-4548	172	29	,	,	PUNCT
cana-4548	172	30	�	�	PROPN
cana-4548	172	31	̆	̆	NOUN
cana-4548	172	32	�	�	PROPN
cana-4548	172	33	𝑛)𝑇	𝑛)𝑇	NOUN
cana-4548	172	34	is	be	AUX
cana-4548	172	35	any	any	DET
cana-4548	172	36	value	value	NOUN
cana-4548	172	37	,	,	PUNCT
cana-4548	172	38	i.e.	i.e.	X
cana-4548	172	39	without	without	ADP
cana-4548	172	40	any	any	DET
cana-4548	172	41	constraint	constraint	NOUN
cana-4548	172	42	for	for	ADP
cana-4548	172	43	�	�	PROPN
cana-4548	172	44	̆	̆	PROPN
cana-4548	172	45	�	�	PROPN
cana-4548	172	46	,	,	PUNCT
cana-4548	172	47	the	the	DET
cana-4548	172	48	following	follow	VERB
cana-4548	172	49	equation	equation	NOUN
cana-4548	172	50	is	be	AUX
cana-4548	172	51	right	right	ADJ
cana-4548	172	52	:	:	PUNCT
cana-4548	172	53	pfsspwg(𝛼1	pfsspwg(𝛼1	NOUN
cana-4548	172	54	,	,	PUNCT
cana-4548	172	55	𝛼2	𝛼2	PROPN
cana-4548	172	56	,	,	PUNCT
cana-4548	172	57	…	…	PUNCT
cana-4548	172	58	,	,	PUNCT
cana-4548	172	59	𝛼𝑛	𝛼𝑛	PROPN
cana-4548	172	60	)	)	PUNCT
cana-4548	172	61	=	=	PROPN
cana-4548	172	62	⟨1	⟨1	PROPN
cana-4548	172	63	−	−	PROPN
cana-4548	173	1	(	(	PUNCT
cana-4548	173	2	∑	∑	INTJ
cana-4548	173	3	  	  	SPACE
cana-4548	173	4	𝑛	𝑛	PRON
cana-4548	173	5	𝑗=1	𝑗=1	PROPN
cana-4548	173	6	  	  	SPACE
cana-4548	173	7	�	�	PROPN
cana-4548	173	8	̆	̆	NOUN
cana-4548	173	9	�	�	PROPN
cana-4548	173	10	𝑗(1	𝑗(1	PROPN
cana-4548	173	11	−	−	PROPN
cana-4548	173	12	𝜇𝑗	𝜇𝑗	PROPN
cana-4548	173	13	)	)	PUNCT
cana-4548	173	14	𝛽	𝛽	NOUN
cana-4548	173	15	−	−	NOUN
cana-4548	173	16	∑	∑	ADP
cana-4548	173	17	  	  	SPACE
cana-4548	173	18	𝑛	𝑛	DET
cana-4548	173	19	𝑗=1	𝑗=1	PROPN
cana-4548	173	20	  	  	SPACE
cana-4548	173	21	�	�	PROPN
cana-4548	173	22	̆	̆	NOUN
cana-4548	173	23	�	�	PROPN
cana-4548	173	24	𝑗	𝑗	PROPN
cana-4548	173	25	+	+	NOUN
cana-4548	173	26	1	1	NUM
cana-4548	173	27	)	)	SYM
cana-4548	173	28	1	1	NUM
cana-4548	173	29	𝛽	𝛽	NOUN
cana-4548	173	30	,	,	PUNCT
cana-4548	173	31	(	(	PUNCT
cana-4548	173	32	∑	∑	ADV
cana-4548	173	33	  	  	SPACE
cana-4548	173	34	𝑛	𝑛	PRON
cana-4548	173	35	𝑗=1	𝑗=1	PROPN
cana-4548	173	36	  	  	SPACE
cana-4548	173	37	�	�	PROPN
cana-4548	173	38	̆	̆	NOUN
cana-4548	173	39	�	�	PROPN
cana-4548	173	40	𝑗𝜂𝑗	𝑗𝜂𝑗	PROPN
cana-4548	173	41	𝛽	𝛽	NOUN
cana-4548	173	42	−	−	PROPN
cana-4548	173	43	∑	∑	ADP
cana-4548	173	44	  	  	SPACE
cana-4548	173	45	𝑛	𝑛	PRON
cana-4548	173	46	𝑗=1	𝑗=1	PROPN
cana-4548	173	47	  	  	SPACE
cana-4548	173	48	�	�	PROPN
cana-4548	173	49	̆	̆	NOUN
cana-4548	173	50	�	�	PROPN
cana-4548	173	51	𝑗	𝑗	PROPN
cana-4548	173	52	+	+	NOUN
cana-4548	173	53	1	1	NUM
cana-4548	173	54	)	)	SYM
cana-4548	173	55	1	1	NUM
cana-4548	173	56	𝛽	𝛽	NOUN
cana-4548	173	57	,	,	PUNCT
cana-4548	173	58	(	(	PUNCT
cana-4548	173	59	∑	∑	ADV
cana-4548	173	60	  	  	SPACE
cana-4548	173	61	𝑛	𝑛	DET
cana-4548	173	62	𝑗=1	𝑗=1	PROPN
cana-4548	173	63	  	  	SPACE
cana-4548	173	64	�	�	PROPN
cana-4548	173	65	̆	̆	NOUN
cana-4548	173	66	�	�	PROPN
cana-4548	173	67	𝑗𝜈𝑗	𝑗𝜈𝑗	PROPN
cana-4548	173	68	𝛽	𝛽	NOUN
cana-4548	173	69	−	−	PROPN
cana-4548	173	70	∑	∑	ADP
cana-4548	173	71	  	  	SPACE
cana-4548	173	72	𝑛	𝑛	DET
cana-4548	173	73	𝑗=1	𝑗=1	PROPN
cana-4548	173	74	  	  	SPACE
cana-4548	173	75	�	�	PROPN
cana-4548	173	76	̆	̆	NOUN
cana-4548	173	77	�	�	PROPN
cana-4548	173	78	𝑗	𝑗	PROPN
cana-4548	173	79	+	+	NOUN
cana-4548	173	80	1	1	NUM
cana-4548	173	81	)	)	PUNCT
cana-4548	173	82	1	1	NUM
cana-4548	173	83	𝛽	𝛽	NOUN
cana-4548	173	84	⟩	⟩	NOUN
cana-4548	173	85	(	(	PUNCT
cana-4548	173	86	7	7	NUM
cana-4548	173	87	)	)	PUNCT
cana-4548	173	88	by	by	ADP
cana-4548	173	89	the	the	DET
cana-4548	173	90	mathematical	mathematical	ADJ
cana-4548	173	91	induction	induction	NOUN
cana-4548	173	92	method	method	NOUN
cana-4548	173	93	,	,	PUNCT
cana-4548	173	94	the	the	DET
cana-4548	173	95	equation	equation	NOUN
cana-4548	173	96	7	7	NUM
cana-4548	173	97	can	can	AUX
cana-4548	173	98	be	be	AUX
cana-4548	173	99	proved	prove	VERB
cana-4548	173	100	as	as	SCONJ
cana-4548	173	101	follows	follow	VERB
cana-4548	173	102	:	:	PUNCT
cana-4548	173	103	proof	proof	NOUN
cana-4548	173	104	.	.	PUNCT
cana-4548	174	1	according	accord	VERB
cana-4548	174	2	to	to	ADP
cana-4548	174	3	the	the	DET
cana-4548	174	4	operational	operational	ADJ
cana-4548	174	5	rules	rule	NOUN
cana-4548	174	6	of	of	ADP
cana-4548	174	7	pfs	pfs	PROPN
cana-4548	174	8	based	base	VERB
cana-4548	174	9	on	on	ADP
cana-4548	174	10	ss	ss	NOUN
cana-4548	174	11	operations	operation	NOUN
cana-4548	174	12	,	,	PUNCT
cana-4548	174	13	we	we	PRON
cana-4548	174	14	have	have	VERB
cana-4548	174	15	�	�	NOUN
cana-4548	174	16	̆	̆	NOUN
cana-4548	174	17	�	�	PROPN
cana-4548	174	18	𝑗𝛼𝑗	𝑗𝛼𝑗	NOUN
cana-4548	174	19	=	=	SYM
cana-4548	174	20	⟨(	⟨(	NUM
cana-4548	174	21	�	�	NOUN
cana-4548	174	22	̆	̆	NOUN
cana-4548	174	23	�	�	PROPN
cana-4548	174	24	𝑗𝜇𝑗	𝑗𝜇𝑗	PROPN
cana-4548	174	25	𝛽	𝛽	PROPN
cana-4548	174	26	−	−	PROPN
cana-4548	174	27	�	�	PROPN
cana-4548	174	28	̆	̆	NOUN
cana-4548	174	29	�	�	PROPN
cana-4548	174	30	𝑗	𝑗	PROPN
cana-4548	174	31	+	+	NOUN
cana-4548	174	32	1	1	NUM
cana-4548	174	33	)	)	SYM
cana-4548	174	34	1	1	NUM
cana-4548	174	35	𝛽	𝛽	NOUN
cana-4548	174	36	1	1	NUM
cana-4548	174	37	−	−	PROPN
cana-4548	174	38	(	(	PUNCT
cana-4548	174	39	�	�	NOUN
cana-4548	174	40	̆	̆	NOUN
cana-4548	174	41	�	�	PROPN
cana-4548	174	42	𝑗(1	𝑗(1	PROPN
cana-4548	174	43	−	−	PROPN
cana-4548	174	44	𝜂𝑗	𝜂𝑗	NOUN
cana-4548	174	45	)	)	PUNCT
cana-4548	174	46	𝛽	𝛽	NOUN
cana-4548	174	47	−	−	PROPN
cana-4548	174	48	�	�	PROPN
cana-4548	174	49	̆	̆	NOUN
cana-4548	174	50	�	�	PROPN
cana-4548	174	51	𝑗	𝑗	PROPN
cana-4548	174	52	+	+	NOUN
cana-4548	174	53	1	1	NUM
cana-4548	174	54	)	)	SYM
cana-4548	174	55	1	1	NUM
cana-4548	174	56	𝛽	𝛽	NOUN
cana-4548	174	57	,	,	PUNCT
cana-4548	174	58	1	1	NUM
cana-4548	174	59	−	−	PROPN
cana-4548	174	60	(	(	PUNCT
cana-4548	174	61	�	�	NOUN
cana-4548	174	62	̆	̆	NOUN
cana-4548	174	63	�	�	PROPN
cana-4548	174	64	𝑗(1	𝑗(1	PROPN
cana-4548	174	65	−	−	PROPN
cana-4548	174	66	𝜈𝑗	𝜈𝑗	PROPN
cana-4548	174	67	)	)	PUNCT
cana-4548	174	68	𝛽	𝛽	PROPN
cana-4548	174	69	−	−	PROPN
cana-4548	174	70	�	�	PROPN
cana-4548	174	71	̆	̆	NOUN
cana-4548	174	72	�	�	PROPN
cana-4548	174	73	𝑗	𝑗	PROPN
cana-4548	174	74	+	+	NOUN
cana-4548	174	75	1	1	NUM
cana-4548	174	76	)	)	PUNCT
cana-4548	174	77	1	1	NUM
cana-4548	174	78	𝛽	𝛽	NOUN
cana-4548	174	79	⟩	⟩	NOUN
cana-4548	174	80	1	1	NUM
cana-4548	174	81	.	.	PUNCT
cana-4548	175	1	when	when	SCONJ
cana-4548	175	2	n	n	X
cana-4548	175	3	=	=	SYM
cana-4548	175	4	2	2	NUM
cana-4548	175	5	,	,	PUNCT
cana-4548	175	6	we	we	PRON
cana-4548	175	7	have	have	VERB
cana-4548	175	8	�	�	PROPN
cana-4548	175	9	̆	̆	PROPN
cana-4548	175	10	�	�	PROPN
cana-4548	175	11	1𝛼1	1𝛼1	NUM
cana-4548	175	12	=	=	SYM
cana-4548	175	13	⟨(	⟨(	NUM
cana-4548	175	14	�	�	NOUN
cana-4548	175	15	̆	̆	NOUN
cana-4548	175	16	�	�	PROPN
cana-4548	175	17	1𝜇1	1𝜇1	NUM
cana-4548	175	18	𝛽	𝛽	PROPN
cana-4548	175	19	−	−	PROPN
cana-4548	175	20	�	�	PROPN
cana-4548	175	21	̆	̆	NOUN
cana-4548	175	22	�	�	PROPN
cana-4548	175	23	1	1	NUM
cana-4548	175	24	+	+	NUM
cana-4548	175	25	1	1	NUM
cana-4548	175	26	)	)	SYM
cana-4548	176	1	1	1	NUM
cana-4548	176	2	𝛽	𝛽	NOUN
cana-4548	176	3	1	1	NUM
cana-4548	176	4	−	−	PROPN
cana-4548	176	5	(	(	PUNCT
cana-4548	176	6	�	�	PROPN
cana-4548	176	7	̆	̆	PROPN
cana-4548	176	8	�	�	PROPN
cana-4548	176	9	1(1	1(1	NUM
cana-4548	176	10	−	−	PROPN
cana-4548	176	11	𝜂1)𝛽	𝜂1)𝛽	NOUN
cana-4548	176	12	−	−	PROPN
cana-4548	176	13	�	�	PROPN
cana-4548	176	14	̆	̆	NOUN
cana-4548	176	15	�	�	PROPN
cana-4548	176	16	1	1	NUM
cana-4548	176	17	+	+	NUM
cana-4548	176	18	1	1	NUM
cana-4548	176	19	)	)	PUNCT
cana-4548	176	20	1	1	NUM
cana-4548	176	21	𝛽	𝛽	NOUN
cana-4548	176	22	,	,	PUNCT
cana-4548	176	23	1	1	NUM
cana-4548	176	24	−	−	PROPN
cana-4548	176	25	(	(	PUNCT
cana-4548	176	26	�	�	PROPN
cana-4548	176	27	̆	̆	PROPN
cana-4548	176	28	�	�	PROPN
cana-4548	176	29	1(1	1(1	NUM
cana-4548	176	30	−	−	PROPN
cana-4548	176	31	𝜈1)𝛽	𝜈1)𝛽	NOUN
cana-4548	176	32	−	−	PROPN
cana-4548	176	33	�	�	PROPN
cana-4548	176	34	̆	̆	NOUN
cana-4548	176	35	�	�	PROPN
cana-4548	176	36	1	1	NUM
cana-4548	176	37	+	+	NUM
cana-4548	176	38	1	1	NUM
cana-4548	176	39	)	)	PUNCT
cana-4548	176	40	1	1	NUM
cana-4548	176	41	𝛽⟩	𝛽⟩	NUM
cana-4548	176	42	;	;	PUNCT
cana-4548	176	43	�	�	PROPN
cana-4548	176	44	̆	̆	PROPN
cana-4548	176	45	�	�	PROPN
cana-4548	176	46	2𝛼2	2𝛼2	NUM
cana-4548	176	47	=	=	SYM
cana-4548	176	48	⟨(	⟨(	NUM
cana-4548	176	49	�	�	NOUN
cana-4548	176	50	̆	̆	NOUN
cana-4548	176	51	�	�	NOUN
cana-4548	176	52	2𝜇2	2𝜇2	NUM
cana-4548	176	53	𝛽	𝛽	PROPN
cana-4548	176	54	−	−	PROPN
cana-4548	176	55	�	�	PROPN
cana-4548	176	56	̆	̆	NOUN
cana-4548	176	57	�	�	PROPN
cana-4548	176	58	2	2	NUM
cana-4548	176	59	+	+	NUM
cana-4548	176	60	1	1	NUM
cana-4548	176	61	)	)	SYM
cana-4548	176	62	1	1	NUM
cana-4548	176	63	𝛽	𝛽	NOUN
cana-4548	176	64	2	2	NUM
cana-4548	176	65	−	−	PROPN
cana-4548	176	66	(	(	PUNCT
cana-4548	176	67	�	�	NOUN
cana-4548	176	68	̆	̆	NOUN
cana-4548	176	69	�	�	PROPN
cana-4548	176	70	2(1	2(1	NUM
cana-4548	176	71	−	−	NOUN
cana-4548	176	72	𝜂2)𝛽	𝜂2)𝛽	PROPN
cana-4548	176	73	−	−	PROPN
cana-4548	176	74	�	�	PROPN
cana-4548	176	75	̆	̆	NOUN
cana-4548	176	76	�	�	PROPN
cana-4548	176	77	2	2	NUM
cana-4548	176	78	+	+	NUM
cana-4548	176	79	1	1	NUM
cana-4548	176	80	)	)	PUNCT
cana-4548	176	81	1	1	NUM
cana-4548	176	82	𝛽	𝛽	NOUN
cana-4548	176	83	,	,	PUNCT
cana-4548	176	84	1	1	NUM
cana-4548	176	85	−	−	PROPN
cana-4548	176	86	(	(	PUNCT
cana-4548	176	87	�	�	PROPN
cana-4548	176	88	̆	̆	NOUN
cana-4548	176	89	�	�	PROPN
cana-4548	176	90	2(1	2(1	NUM
cana-4548	176	91	−	−	PROPN
cana-4548	176	92	𝜈2)𝛽	𝜈2)𝛽	PROPN
cana-4548	176	93	−	−	PROPN
cana-4548	176	94	�	�	PROPN
cana-4548	176	95	̆	̆	NOUN
cana-4548	176	96	�	�	PROPN
cana-4548	176	97	2	2	NUM
cana-4548	176	98	+	+	NUM
cana-4548	176	99	1	1	NUM
cana-4548	176	100	)	)	PUNCT
cana-4548	176	101	1	1	NUM
cana-4548	176	102	𝛽⟩	𝛽⟩	PUNCT
cana-4548	176	103	then	then	ADV
cana-4548	176	104	pfsspwg(𝛼1	pfsspwg(𝛼1	PROPN
cana-4548	176	105	,	,	PUNCT
cana-4548	176	106	𝛼2	𝛼2	PROPN
cana-4548	176	107	)	)	PUNCT
cana-4548	176	108	=	=	SYM
cana-4548	176	109	�	�	PROPN
cana-4548	176	110	̆	̆	PROPN
cana-4548	176	111	�	�	PROPN
cana-4548	176	112	1𝛼1	1𝛼1	NUM
cana-4548	176	113	+	+	SYM
cana-4548	176	114	�	�	PROPN
cana-4548	176	115	̆	̆	PROPN
cana-4548	176	116	�	�	PROPN
cana-4548	176	117	2𝛼2	2𝛼2	NUM
cana-4548	176	118	=	=	SYM
cana-4548	176	119	⟨(	⟨(	NUM
cana-4548	176	120	�	�	NOUN
cana-4548	176	121	̆	̆	NOUN
cana-4548	176	122	�	�	PROPN
cana-4548	176	123	1𝜇1	1𝜇1	NUM
cana-4548	176	124	𝛽	𝛽	PROPN
cana-4548	176	125	−	−	PROPN
cana-4548	176	126	�	�	PROPN
cana-4548	176	127	̆	̆	NOUN
cana-4548	176	128	�	�	PROPN
cana-4548	176	129	1	1	NUM
cana-4548	176	130	+	+	NUM
cana-4548	176	131	1	1	NUM
cana-4548	176	132	)	)	SYM
cana-4548	176	133	1	1	NUM
cana-4548	176	134	𝛽	𝛽	NOUN
cana-4548	176	135	1	1	NUM
cana-4548	176	136	−	−	PROPN
cana-4548	176	137	(	(	PUNCT
cana-4548	176	138	�	�	PROPN
cana-4548	176	139	̆	̆	PROPN
cana-4548	176	140	�	�	PROPN
cana-4548	176	141	1(1	1(1	NUM
cana-4548	176	142	−	−	PROPN
cana-4548	176	143	𝜂1)𝛽	𝜂1)𝛽	NOUN
cana-4548	176	144	−	−	PROPN
cana-4548	176	145	�	�	PROPN
cana-4548	176	146	̆	̆	NOUN
cana-4548	176	147	�	�	PROPN
cana-4548	176	148	1	1	NUM
cana-4548	176	149	+	+	NUM
cana-4548	176	150	1	1	NUM
cana-4548	176	151	)	)	PUNCT
cana-4548	176	152	1	1	NUM
cana-4548	176	153	𝛽	𝛽	NOUN
cana-4548	176	154	,	,	PUNCT
cana-4548	176	155	1	1	NUM
cana-4548	176	156	−	−	PROPN
cana-4548	176	157	(	(	PUNCT
cana-4548	176	158	�	�	PROPN
cana-4548	176	159	̆	̆	PROPN
cana-4548	176	160	�	�	PROPN
cana-4548	176	161	1(1	1(1	NUM
cana-4548	176	162	−	−	PROPN
cana-4548	176	163	𝜈1)𝛽	𝜈1)𝛽	NOUN
cana-4548	176	164	−	−	PROPN
cana-4548	176	165	�	�	PROPN
cana-4548	176	166	̆	̆	NOUN
cana-4548	176	167	�	�	PROPN
cana-4548	176	168	1	1	NUM
cana-4548	176	169	+	+	NUM
cana-4548	176	170	1	1	NUM
cana-4548	176	171	)	)	SYM
cana-4548	176	172	1	1	NUM
cana-4548	176	173	𝛽	𝛽	NOUN
cana-4548	176	174	+	+	CCONJ
cana-4548	176	175	(	(	PUNCT
cana-4548	176	176	�	�	PROPN
cana-4548	176	177	̆	̆	NOUN
cana-4548	176	178	�	�	PROPN
cana-4548	176	179	2𝜇2	2𝜇2	NUM
cana-4548	176	180	𝛽	𝛽	PROPN
cana-4548	176	181	−	−	PROPN
cana-4548	176	182	�	�	PROPN
cana-4548	176	183	̆	̆	NOUN
cana-4548	176	184	�	�	PROPN
cana-4548	176	185	2	2	NUM
cana-4548	176	186	+	+	NUM
cana-4548	176	187	1	1	NUM
cana-4548	176	188	)	)	SYM
cana-4548	176	189	1	1	NUM
cana-4548	176	190	𝛽	𝛽	NOUN
cana-4548	176	191	2	2	NUM
cana-4548	176	192	−	−	PROPN
cana-4548	176	193	(	(	PUNCT
cana-4548	176	194	�	�	NOUN
cana-4548	176	195	̆	̆	NOUN
cana-4548	176	196	�	�	PROPN
cana-4548	176	197	2(1	2(1	NUM
cana-4548	176	198	−	−	NOUN
cana-4548	176	199	𝜂2)𝛽	𝜂2)𝛽	PROPN
cana-4548	176	200	−	−	PROPN
cana-4548	176	201	�	�	PROPN
cana-4548	176	202	̆	̆	NOUN
cana-4548	176	203	�	�	PROPN
cana-4548	176	204	2	2	NUM
cana-4548	176	205	+	+	NUM
cana-4548	176	206	1	1	NUM
cana-4548	176	207	)	)	PUNCT
cana-4548	176	208	1	1	NUM
cana-4548	176	209	𝛽	𝛽	NOUN
cana-4548	176	210	,	,	PUNCT
cana-4548	176	211	1	1	NUM
cana-4548	176	212	−	−	PROPN
cana-4548	176	213	(	(	PUNCT
cana-4548	176	214	�	�	PROPN
cana-4548	176	215	̆	̆	NOUN
cana-4548	176	216	�	�	PROPN
cana-4548	176	217	2(1	2(1	NUM
cana-4548	176	218	−	−	PROPN
cana-4548	176	219	𝜈2)𝛽	𝜈2)𝛽	PROPN
cana-4548	176	220	−	−	PROPN
cana-4548	176	221	�	�	PROPN
cana-4548	176	222	̆	̆	NOUN
cana-4548	176	223	�	�	PROPN
cana-4548	176	224	2	2	NUM
cana-4548	176	225	+	+	NUM
cana-4548	176	226	1	1	NUM
cana-4548	176	227	)	)	SYM
cana-4548	176	228	1	1	NUM
cana-4548	176	229	𝛽⟩	𝛽⟩	NOUN
cana-4548	176	230	=	=	PUNCT
cana-4548	176	231	⟨(∑𝑗=1	⟨(∑𝑗=1	PROPN
cana-4548	176	232	2	2	NUM
cana-4548	176	233	 	 	SPACE
cana-4548	176	234	�	�	PROPN
cana-4548	176	235	̆	̆	PROPN
cana-4548	176	236	�	�	PROPN
cana-4548	176	237	𝑗𝜇𝑗	𝑗𝜇𝑗	PROPN
cana-4548	176	238	𝛽	𝛽	PROPN
cana-4548	176	239	−	−	PROPN
cana-4548	176	240	∑𝑗=1	∑𝑗=1	PROPN
cana-4548	176	241	2	2	NUM
cana-4548	176	242	 	 	SPACE
cana-4548	176	243	�	�	PROPN
cana-4548	176	244	̆	̆	NOUN
cana-4548	176	245	�	�	PROPN
cana-4548	176	246	𝑗	𝑗	PROPN
cana-4548	176	247	+	+	NOUN
cana-4548	176	248	1	1	NUM
cana-4548	176	249	)	)	SYM
cana-4548	176	250	1	1	NUM
cana-4548	176	251	𝛽	𝛽	NOUN
cana-4548	176	252	,	,	PUNCT
cana-4548	176	253	1	1	NUM
cana-4548	176	254	−	−	PROPN
cana-4548	176	255	(	(	PUNCT
cana-4548	176	256	∑𝑗=1	∑𝑗=1	PROPN
cana-4548	176	257	2	2	NUM
cana-4548	176	258	 	 	SPACE
cana-4548	176	259	�	�	PROPN
cana-4548	176	260	̆	̆	NOUN
cana-4548	176	261	�	�	PROPN
cana-4548	176	262	𝑗(1	𝑗(1	PROPN
cana-4548	176	263	−	−	PROPN
cana-4548	176	264	communications	communication	NOUN
cana-4548	176	265	on	on	ADP
cana-4548	176	266	applied	apply	VERB
cana-4548	176	267	nonlinear	nonlinear	ADJ
cana-4548	176	268	analysis	analysis	NOUN
cana-4548	176	269	issn	issn	NOUN
cana-4548	176	270	:	:	PUNCT
cana-4548	176	271	1074	1074	NUM
cana-4548	176	272	-	-	PUNCT
cana-4548	176	273	133x	133x	NUM
cana-4548	176	274	vol	vol	NOUN
cana-4548	176	275	32	32	NUM
cana-4548	176	276	no	no	NOUN
cana-4548	176	277	.	.	PUNCT
cana-4548	177	1	9s	9s	NUM
cana-4548	177	2	(	(	PUNCT
cana-4548	177	3	2025	2025	NUM
cana-4548	177	4	)	)	PUNCT
cana-4548	177	5	2686	2686	NUM
cana-4548	177	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4548	178	1	𝜂𝑗	𝜂𝑗	NOUN
cana-4548	178	2	)	)	PUNCT
cana-4548	178	3	𝛽	𝛽	NOUN
cana-4548	178	4	−	−	PROPN
cana-4548	178	5	∑𝑗=1	∑𝑗=1	PROPN
cana-4548	178	6	2	2	NUM
cana-4548	178	7	 	 	SPACE
cana-4548	178	8	�	�	PROPN
cana-4548	178	9	̆	̆	NOUN
cana-4548	178	10	�	�	PROPN
cana-4548	178	11	𝑗	𝑗	PROPN
cana-4548	178	12	+	+	NOUN
cana-4548	178	13	1	1	NUM
cana-4548	178	14	)	)	PUNCT
cana-4548	178	15	1	1	NUM
cana-4548	178	16	𝛽	𝛽	NOUN
cana-4548	178	17	,	,	PUNCT
cana-4548	178	18	1	1	NUM
cana-4548	178	19	−	−	NOUN
cana-4548	178	20	(	(	PUNCT
cana-4548	178	21	∑𝑗=1	∑𝑗=1	PROPN
cana-4548	178	22	2	2	NUM
cana-4548	178	23	 	 	SPACE
cana-4548	178	24	�	�	PROPN
cana-4548	178	25	̆	̆	NOUN
cana-4548	178	26	�	�	PROPN
cana-4548	178	27	𝑗(1	𝑗(1	PROPN
cana-4548	178	28	−	−	PROPN
cana-4548	178	29	𝜈𝑗	𝜈𝑗	PROPN
cana-4548	178	30	)	)	PUNCT
cana-4548	178	31	𝛽	𝛽	NOUN
cana-4548	178	32	−	−	PROPN
cana-4548	178	33	∑𝑗=1	∑𝑗=1	PROPN
cana-4548	178	34	2	2	NUM
cana-4548	178	35	 	 	SPACE
cana-4548	178	36	�	�	PROPN
cana-4548	178	37	̆	̆	NOUN
cana-4548	178	38	�	�	PROPN
cana-4548	178	39	𝑗	𝑗	PROPN
cana-4548	178	40	+	+	NOUN
cana-4548	178	41	1	1	NUM
cana-4548	178	42	)	)	PUNCT
cana-4548	178	43	1	1	NUM
cana-4548	178	44	𝛽	𝛽	NOUN
cana-4548	178	45	⟩	⟩	NOUN
cana-4548	178	46	i.e.	i.e.	X
cana-4548	178	47	when	when	SCONJ
cana-4548	178	48	n	n	X
cana-4548	178	49	=	=	SYM
cana-4548	178	50	2	2	NUM
cana-4548	178	51	,	,	PUNCT
cana-4548	178	52	equation	equation	NOUN
cana-4548	178	53	7	7	NUM
cana-4548	178	54	is	be	AUX
cana-4548	178	55	right	right	ADJ
cana-4548	178	56	.	.	PUNCT
cana-4548	179	1	2	2	X
cana-4548	179	2	.	.	X
cana-4548	179	3	suppose	suppose	VERB
cana-4548	179	4	n	n	PROPN
cana-4548	179	5	=	=	PROPN
cana-4548	179	6	m	m	PROPN
cana-4548	179	7	,	,	PUNCT
cana-4548	179	8	equation	equation	NOUN
cana-4548	179	9	7	7	NUM
cana-4548	179	10	is	be	AUX
cana-4548	179	11	right	right	ADJ
cana-4548	179	12	,	,	PUNCT
cana-4548	179	13	i.e.	i.e.	X
cana-4548	179	14	pfsspwg(𝛼1	pfsspwg(𝛼1	ADJ
cana-4548	179	15	,	,	PUNCT
cana-4548	179	16	𝛼2	𝛼2	PROPN
cana-4548	179	17	,	,	PUNCT
cana-4548	179	18	…	…	PUNCT
cana-4548	179	19	,	,	PUNCT
cana-4548	179	20	𝛼𝑚	𝛼𝑚	PROPN
cana-4548	179	21	)	)	PUNCT
cana-4548	180	1	=	=	SYM
cana-4548	180	2	⟨1	⟨1	PROPN
cana-4548	180	3	−	−	PROPN
cana-4548	180	4	(	(	PUNCT
cana-4548	180	5	∑𝑗=1	∑𝑗=1	PROPN
cana-4548	180	6	𝑚	𝑚	PROPN
cana-4548	180	7	 	 	SPACE
cana-4548	180	8	�	�	PROPN
cana-4548	180	9	̆	̆	NOUN
cana-4548	180	10	�	�	PROPN
cana-4548	180	11	𝑗(1	𝑗(1	PROPN
cana-4548	180	12	−	−	PROPN
cana-4548	180	13	𝜇𝑗	𝜇𝑗	PROPN
cana-4548	180	14	)	)	PUNCT
cana-4548	180	15	𝛽	𝛽	NOUN
cana-4548	180	16	−	−	PROPN
cana-4548	180	17	∑𝑗=1	∑𝑗=1	PROPN
cana-4548	180	18	𝑚	𝑚	ADP
cana-4548	180	19	 	 	SPACE
cana-4548	180	20	�	�	PROPN
cana-4548	180	21	̆	̆	NOUN
cana-4548	180	22	�	�	PROPN
cana-4548	180	23	𝑗	𝑗	PROPN
cana-4548	180	24	+	+	NOUN
cana-4548	180	25	1	1	NUM
cana-4548	180	26	)	)	PUNCT
cana-4548	180	27	1	1	NUM
cana-4548	180	28	𝛽	𝛽	NOUN
cana-4548	180	29	,	,	PUNCT
cana-4548	180	30	(	(	PUNCT
cana-4548	180	31	∑𝑗=1	∑𝑗=1	PROPN
cana-4548	180	32	𝑚	𝑚	PROPN
cana-4548	180	33	 	 	SPACE
cana-4548	180	34	�	�	PROPN
cana-4548	180	35	̆	̆	PROPN
cana-4548	180	36	�	�	PROPN
cana-4548	180	37	𝑗𝜂𝑗	𝑗𝜂𝑗	PROPN
cana-4548	180	38	𝛽	𝛽	NOUN
cana-4548	180	39	−	−	PROPN
cana-4548	180	40	∑𝑗=1	∑𝑗=1	PROPN
cana-4548	180	41	𝑚	𝑚	ADP
cana-4548	180	42	 	 	SPACE
cana-4548	180	43	�	�	PROPN
cana-4548	180	44	̆	̆	NOUN
cana-4548	180	45	�	�	PROPN
cana-4548	180	46	𝑗	𝑗	PROPN
cana-4548	180	47	+	+	NOUN
cana-4548	180	48	1	1	NUM
cana-4548	180	49	)	)	SYM
cana-4548	180	50	1	1	NUM
cana-4548	180	51	𝛽	𝛽	NOUN
cana-4548	180	52	,	,	PUNCT
cana-4548	180	53	(	(	PUNCT
cana-4548	180	54	∑𝑗=1	∑𝑗=1	PROPN
cana-4548	180	55	𝑚	𝑚	PROPN
cana-4548	180	56	 	 	SPACE
cana-4548	180	57	�	�	PROPN
cana-4548	180	58	̆	̆	NOUN
cana-4548	180	59	�	�	PROPN
cana-4548	180	60	𝑗𝜈𝑗	𝑗𝜈𝑗	PROPN
cana-4548	181	1	𝛽	𝛽	PROPN
cana-4548	181	2	−	−	PROPN
cana-4548	181	3	∑𝑗=1	∑𝑗=1	PROPN
cana-4548	181	4	𝑚	𝑚	ADP
cana-4548	181	5	 	 	SPACE
cana-4548	181	6	�	�	PROPN
cana-4548	181	7	̆	̆	NOUN
cana-4548	181	8	�	�	PROPN
cana-4548	181	9	𝑗	𝑗	PROPN
cana-4548	181	10	+	+	NOUN
cana-4548	181	11	1	1	NUM
cana-4548	181	12	)	)	SYM
cana-4548	181	13	1	1	NUM
cana-4548	181	14	𝛽	𝛽	NOUN
cana-4548	181	15	⟩	⟩	NOUN
cana-4548	181	16	then	then	ADV
cana-4548	181	17	when	when	SCONJ
cana-4548	181	18	n	n	X
cana-4548	181	19	=	=	VERB
cana-4548	181	20	m	m	VERB
cana-4548	181	21	+	+	ADJ
cana-4548	181	22	1	1	NUM
cana-4548	181	23	,	,	PUNCT
cana-4548	181	24	according	accord	VERB
cana-4548	181	25	to	to	ADP
cana-4548	181	26	the	the	DET
cana-4548	181	27	operational	operational	ADJ
cana-4548	181	28	rules	rule	NOUN
cana-4548	181	29	of	of	ADP
cana-4548	181	30	pfns	pfns	NOUN
cana-4548	181	31	,	,	PUNCT
cana-4548	181	32	we	we	PRON
cana-4548	181	33	have	have	VERB
cana-4548	181	34	�	�	PROPN
cana-4548	181	35	̆	̆	NOUN
cana-4548	181	36	�	�	PROPN
cana-4548	181	37	𝑚+1𝛼𝑚+1	𝑚+1𝛼𝑚+1	VERB
cana-4548	181	38	=	=	SYM
cana-4548	181	39	⟨(	⟨(	NUM
cana-4548	181	40	�	�	NOUN
cana-4548	181	41	̆	̆	NOUN
cana-4548	181	42	�	�	NOUN
cana-4548	181	43	𝑚+1𝜇𝑚+1	𝑚+1𝜇𝑚+1	NUM
cana-4548	181	44	𝛽	𝛽	DET
cana-4548	181	45	−	−	PROPN
cana-4548	181	46	�	�	PROPN
cana-4548	181	47	̆	̆	NOUN
cana-4548	181	48	�	�	PROPN
cana-4548	181	49	𝑚+1	𝑚+1	SYM
cana-4548	181	50	+	+	CCONJ
cana-4548	181	51	1	1	X
cana-4548	181	52	)	)	SYM
cana-4548	181	53	1	1	NUM
cana-4548	181	54	𝛽	𝛽	NOUN
cana-4548	181	55	,	,	PUNCT
cana-4548	181	56	1	1	NUM
cana-4548	181	57	−	−	PROPN
cana-4548	181	58	(	(	PUNCT
cana-4548	181	59	�	�	PROPN
cana-4548	181	60	̆	̆	PROPN
cana-4548	181	61	�	�	PROPN
cana-4548	181	62	𝑚+1(1	𝑚+1(1	NOUN
cana-4548	181	63	−	−	PROPN
cana-4548	181	64	𝜂𝑚+1)𝛽	𝜂𝑚+1)𝛽	NOUN
cana-4548	181	65	−	−	PROPN
cana-4548	181	66	�	�	PROPN
cana-4548	181	67	̆	̆	NOUN
cana-4548	181	68	�	�	PROPN
cana-4548	181	69	𝑚+1	𝑚+1	SYM
cana-4548	181	70	+	+	CCONJ
cana-4548	181	71	1	1	X
cana-4548	181	72	)	)	PUNCT
cana-4548	181	73	1	1	NUM
cana-4548	181	74	𝛽	𝛽	NOUN
cana-4548	181	75	,	,	PUNCT
cana-4548	181	76	1	1	NUM
cana-4548	181	77	−	−	PROPN
cana-4548	181	78	(	(	PUNCT
cana-4548	181	79	�	�	PROPN
cana-4548	181	80	̆	̆	PROPN
cana-4548	181	81	�	�	PROPN
cana-4548	181	82	𝑚+1(1	𝑚+1(1	PART
cana-4548	181	83	−	−	PROPN
cana-4548	181	84	𝜈𝑚+1)𝛽	𝜈𝑚+1)𝛽	PROPN
cana-4548	181	85	−	−	PROPN
cana-4548	181	86	�	�	PROPN
cana-4548	181	87	̆	̆	NOUN
cana-4548	181	88	�	�	PROPN
cana-4548	181	89	𝑚+1	𝑚+1	SYM
cana-4548	181	90	+	+	CCONJ
cana-4548	181	91	1	1	X
cana-4548	181	92	)	)	PUNCT
cana-4548	181	93	1	1	NUM
cana-4548	181	94	𝛽⟩	𝛽⟩	PUNCT
cana-4548	181	95	and	and	CCONJ
cana-4548	181	96	pfsspwg(𝛼1	pfsspwg(𝛼1	PROPN
cana-4548	181	97	,	,	PUNCT
cana-4548	181	98	𝛼2	𝛼2	PROPN
cana-4548	181	99	,	,	PUNCT
cana-4548	181	100	…	…	PUNCT
cana-4548	181	101	,	,	PUNCT
cana-4548	181	102	𝛼𝑚	𝛼𝑚	PROPN
cana-4548	181	103	,	,	PUNCT
cana-4548	181	104	𝛼𝑚+1	𝛼𝑚+1	PROPN
cana-4548	181	105	)	)	PUNCT
cana-4548	181	106	=	=	SYM
cana-4548	181	107	pfsspwg(𝛼1	pfsspwg(𝛼1	PROPN
cana-4548	181	108	,	,	PUNCT
cana-4548	181	109	𝛼2	𝛼2	PROPN
cana-4548	181	110	,	,	PUNCT
cana-4548	181	111	…	…	PUNCT
cana-4548	181	112	,	,	PUNCT
cana-4548	181	113	𝛼𝑚	𝛼𝑚	NOUN
cana-4548	181	114	)	)	PUNCT
cana-4548	181	115	⊕	⊕	PROPN
cana-4548	181	116	(	(	PUNCT
cana-4548	181	117	�	�	PROPN
cana-4548	181	118	̆	̆	PROPN
cana-4548	181	119	�	�	PROPN
cana-4548	181	120	𝑚+1𝛼𝑚+1	𝑚+1𝛼𝑚+1	ADJ
cana-4548	181	121	)	)	PUNCT
cana-4548	182	1	=	=	PUNCT
cana-4548	182	2	⟨1	⟨1	PROPN
cana-4548	182	3	−	−	PROPN
cana-4548	182	4	(	(	PUNCT
cana-4548	182	5	∑𝑗=1	∑𝑗=1	PROPN
cana-4548	182	6	𝑚	𝑚	PROPN
cana-4548	182	7	 	 	SPACE
cana-4548	182	8	�	�	PROPN
cana-4548	182	9	̆	̆	NOUN
cana-4548	182	10	�	�	PROPN
cana-4548	182	11	𝑗(1	𝑗(1	PROPN
cana-4548	182	12	−	−	PROPN
cana-4548	182	13	𝜇𝑗	𝜇𝑗	PROPN
cana-4548	182	14	)	)	PUNCT
cana-4548	182	15	𝛽	𝛽	NOUN
cana-4548	182	16	−	−	PROPN
cana-4548	182	17	∑𝑗=1	∑𝑗=1	PROPN
cana-4548	182	18	𝑚	𝑚	ADP
cana-4548	182	19	 	 	SPACE
cana-4548	182	20	�	�	PROPN
cana-4548	182	21	̆	̆	NOUN
cana-4548	182	22	�	�	PROPN
cana-4548	182	23	𝑗	𝑗	PROPN
cana-4548	182	24	+	+	NOUN
cana-4548	182	25	1	1	NUM
cana-4548	182	26	)	)	SYM
cana-4548	182	27	1	1	NUM
cana-4548	182	28	𝛽	𝛽	NOUN
cana-4548	182	29	,	,	PUNCT
cana-4548	182	30	(	(	PUNCT
cana-4548	182	31	∑𝑗=1	∑𝑗=1	PROPN
cana-4548	182	32	𝑚	𝑚	PROPN
cana-4548	182	33	 	 	SPACE
cana-4548	182	34	�	�	PROPN
cana-4548	182	35	̆	̆	PROPN
cana-4548	182	36	�	�	PROPN
cana-4548	182	37	𝑗𝜂𝑗	𝑗𝜂𝑗	PROPN
cana-4548	182	38	𝛽	𝛽	NOUN
cana-4548	182	39	−	−	PROPN
cana-4548	182	40	∑𝑗=1	∑𝑗=1	PROPN
cana-4548	182	41	𝑚	𝑚	ADP
cana-4548	182	42	 	 	SPACE
cana-4548	182	43	�	�	PROPN
cana-4548	182	44	̆	̆	NOUN
cana-4548	182	45	�	�	PROPN
cana-4548	182	46	𝑗	𝑗	PROPN
cana-4548	182	47	+	+	NOUN
cana-4548	182	48	1	1	NUM
cana-4548	182	49	)	)	SYM
cana-4548	182	50	1	1	NUM
cana-4548	182	51	𝛽	𝛽	NOUN
cana-4548	182	52	,	,	PUNCT
cana-4548	182	53	(	(	PUNCT
cana-4548	182	54	∑𝑗=1	∑𝑗=1	PROPN
cana-4548	182	55	𝑚	𝑚	PROPN
cana-4548	182	56	 	 	SPACE
cana-4548	182	57	�	�	PROPN
cana-4548	182	58	̆	̆	NOUN
cana-4548	182	59	�	�	PROPN
cana-4548	182	60	𝑗𝜈𝑗	𝑗𝜈𝑗	PROPN
cana-4548	183	1	𝛽	𝛽	PROPN
cana-4548	183	2	−	−	PROPN
cana-4548	183	3	∑𝑗=1	∑𝑗=1	PROPN
cana-4548	183	4	𝑚	𝑚	ADP
cana-4548	183	5	 	 	SPACE
cana-4548	183	6	�	�	PROPN
cana-4548	183	7	̆	̆	NOUN
cana-4548	183	8	�	�	PROPN
cana-4548	183	9	𝑗	𝑗	PROPN
cana-4548	183	10	+	+	NOUN
cana-4548	183	11	1	1	NUM
cana-4548	183	12	)	)	PUNCT
cana-4548	183	13	1	1	NUM
cana-4548	183	14	𝛽	𝛽	NOUN
cana-4548	183	15	+	+	CCONJ
cana-4548	183	16	(	(	PUNCT
cana-4548	183	17	�	�	PROPN
cana-4548	183	18	̆	̆	NOUN
cana-4548	183	19	�	�	NOUN
cana-4548	183	20	𝑚+1𝜇𝑚+1	𝑚+1𝜇𝑚+1	NUM
cana-4548	183	21	𝛽	𝛽	DET
cana-4548	183	22	−	−	PROPN
cana-4548	183	23	�	�	PROPN
cana-4548	183	24	̆	̆	NOUN
cana-4548	183	25	�	�	PROPN
cana-4548	183	26	𝑚+1	𝑚+1	SYM
cana-4548	183	27	+	+	CCONJ
cana-4548	183	28	1	1	X
cana-4548	183	29	)	)	PUNCT
cana-4548	183	30	1	1	NUM
cana-4548	183	31	𝛽	𝛽	NOUN
cana-4548	183	32	,	,	PUNCT
cana-4548	183	33	1	1	NUM
cana-4548	183	34	−	−	PROPN
cana-4548	183	35	(	(	PUNCT
cana-4548	183	36	�	�	PROPN
cana-4548	183	37	̆	̆	PROPN
cana-4548	183	38	�	�	PROPN
cana-4548	183	39	𝑚+1(1	𝑚+1(1	NOUN
cana-4548	183	40	−	−	PROPN
cana-4548	183	41	𝜂𝑚+1)𝛽	𝜂𝑚+1)𝛽	NOUN
cana-4548	183	42	−	−	PROPN
cana-4548	183	43	�	�	PROPN
cana-4548	183	44	̆	̆	NOUN
cana-4548	183	45	�	�	PROPN
cana-4548	183	46	𝑚+1	𝑚+1	SYM
cana-4548	183	47	+	+	CCONJ
cana-4548	183	48	1	1	X
cana-4548	183	49	)	)	PUNCT
cana-4548	183	50	1	1	NUM
cana-4548	183	51	𝛽	𝛽	NOUN
cana-4548	183	52	,	,	PUNCT
cana-4548	183	53	1	1	NUM
cana-4548	183	54	−	−	PROPN
cana-4548	183	55	(	(	PUNCT
cana-4548	183	56	�	�	PROPN
cana-4548	183	57	̆	̆	PROPN
cana-4548	183	58	�	�	PROPN
cana-4548	183	59	𝑚+1(1	𝑚+1(1	PART
cana-4548	183	60	−	−	PROPN
cana-4548	183	61	𝜈𝑚+1)𝛽	𝜈𝑚+1)𝛽	PROPN
cana-4548	183	62	−	−	PROPN
cana-4548	183	63	�	�	PROPN
cana-4548	183	64	̆	̆	NOUN
cana-4548	183	65	�	�	PROPN
cana-4548	183	66	𝑚+1	𝑚+1	SYM
cana-4548	183	67	+	+	CCONJ
cana-4548	183	68	1	1	X
cana-4548	183	69	)	)	SYM
cana-4548	183	70	1	1	NUM
cana-4548	183	71	𝛽⟩	𝛽⟩	NOUN
cana-4548	183	72	=	=	PUNCT
cana-4548	183	73	⟨(∑𝑗=1	⟨(∑𝑗=1	PROPN
cana-4548	183	74	𝑚+1	𝑚+1	NUM
cana-4548	183	75	 	 	SPACE
cana-4548	183	76	�	�	PROPN
cana-4548	183	77	̆	̆	NOUN
cana-4548	183	78	�	�	PROPN
cana-4548	183	79	𝑗𝜇𝑗	𝑗𝜇𝑗	PROPN
cana-4548	183	80	𝛽	𝛽	PROPN
cana-4548	183	81	−	−	PROPN
cana-4548	183	82	∑𝑗=1	∑𝑗=1	PROPN
cana-4548	183	83	𝑚+1	𝑚+1	NUM
cana-4548	183	84	 	 	SPACE
cana-4548	183	85	�	�	PROPN
cana-4548	183	86	̆	̆	NOUN
cana-4548	183	87	�	�	PROPN
cana-4548	183	88	𝑗	𝑗	PROPN
cana-4548	183	89	+	+	NOUN
cana-4548	183	90	1	1	NUM
cana-4548	183	91	)	)	SYM
cana-4548	183	92	1	1	NUM
cana-4548	183	93	𝛽1	𝛽1	NOUN
cana-4548	183	94	−	−	PROPN
cana-4548	183	95	(	(	PUNCT
cana-4548	183	96	∑𝑗=1	∑𝑗=1	PROPN
cana-4548	183	97	𝑚+1	𝑚+1	NUM
cana-4548	183	98	 	 	SPACE
cana-4548	183	99	�	�	PROPN
cana-4548	183	100	̆	̆	NOUN
cana-4548	183	101	�	�	PROPN
cana-4548	183	102	𝑗(1	𝑗(1	PROPN
cana-4548	183	103	−	−	PROPN
cana-4548	183	104	𝜂𝑗	𝜂𝑗	NOUN
cana-4548	183	105	)	)	PUNCT
cana-4548	183	106	𝛽	𝛽	NOUN
cana-4548	183	107	−	−	PROPN
cana-4548	183	108	∑𝑗=1	∑𝑗=1	PROPN
cana-4548	183	109	𝑚+1	𝑚+1	NUM
cana-4548	183	110	 	 	SPACE
cana-4548	183	111	�	�	PROPN
cana-4548	183	112	̆	̆	NOUN
cana-4548	183	113	�	�	PROPN
cana-4548	183	114	𝑗	𝑗	PROPN
cana-4548	183	115	+	+	NOUN
cana-4548	183	116	1	1	NUM
cana-4548	183	117	)	)	SYM
cana-4548	183	118	1	1	NUM
cana-4548	183	119	𝛽	𝛽	NOUN
cana-4548	183	120	,	,	PUNCT
cana-4548	183	121	1	1	NUM
cana-4548	183	122	−	−	PROPN
cana-4548	183	123	(	(	PUNCT
cana-4548	183	124	∑𝑗=1	∑𝑗=1	PROPN
cana-4548	183	125	𝑚+1	𝑚+1	NUM
cana-4548	183	126	 	 	SPACE
cana-4548	183	127	�	�	PROPN
cana-4548	183	128	̆	̆	NOUN
cana-4548	183	129	�	�	PROPN
cana-4548	183	130	𝑗(1	𝑗(1	PROPN
cana-4548	183	131	−	−	PROPN
cana-4548	183	132	𝜈𝑗	𝜈𝑗	PROPN
cana-4548	183	133	)	)	PUNCT
cana-4548	184	1	𝛽	𝛽	NOUN
cana-4548	184	2	−	−	PROPN
cana-4548	184	3	∑𝑗=1	∑𝑗=1	PROPN
cana-4548	184	4	𝑚+1	𝑚+1	NUM
cana-4548	184	5	 	 	SPACE
cana-4548	184	6	�	�	PROPN
cana-4548	184	7	̆	̆	NOUN
cana-4548	184	8	�	�	PROPN
cana-4548	184	9	𝑗	𝑗	PROPN
cana-4548	184	10	+	+	NOUN
cana-4548	184	11	1	1	NUM
cana-4548	184	12	)	)	PUNCT
cana-4548	184	13	1	1	NUM
cana-4548	184	14	𝛽	𝛽	NOUN
cana-4548	184	15	⟩	⟩	NOUN
cana-4548	184	16	so	so	ADV
cana-4548	184	17	,	,	PUNCT
cana-4548	184	18	when	when	SCONJ
cana-4548	184	19	n	n	X
cana-4548	184	20	=	=	SYM
cana-4548	184	21	m	m	VERB
cana-4548	184	22	+	+	ADJ
cana-4548	184	23	1	1	NUM
cana-4548	184	24	,	,	PUNCT
cana-4548	184	25	equation	equation	NOUN
cana-4548	184	26	7	7	NUM
cana-4548	184	27	is	be	AUX
cana-4548	184	28	right	right	ADJ
cana-4548	184	29	.	.	PUNCT
cana-4548	185	1	3	3	X
cana-4548	185	2	.	.	X
cana-4548	185	3	according	accord	VERB
cana-4548	185	4	to	to	ADP
cana-4548	185	5	steps	step	NOUN
cana-4548	185	6	(	(	PUNCT
cana-4548	185	7	1	1	NUM
cana-4548	185	8	)	)	PUNCT
cana-4548	185	9	and	and	CCONJ
cana-4548	185	10	(	(	PUNCT
cana-4548	185	11	2	2	NUM
cana-4548	185	12	)	)	PUNCT
cana-4548	185	13	,	,	PUNCT
cana-4548	185	14	equation	equation	NOUN
cana-4548	185	15	7	7	NUM
cana-4548	185	16	is	be	AUX
cana-4548	185	17	established	establish	VERB
cana-4548	185	18	for	for	ADP
cana-4548	185	19	any	any	DET
cana-4548	185	20	j.	j.	NOUN
cana-4548	185	21	because	because	SCONJ
cana-4548	185	22	equation	equation	NOUN
cana-4548	185	23	7	7	NUM
cana-4548	185	24	is	be	AUX
cana-4548	185	25	right	right	ADJ
cana-4548	185	26	without	without	ADP
cana-4548	185	27	any	any	DET
cana-4548	185	28	constraint	constraint	NOUN
cana-4548	185	29	for	for	ADP
cana-4548	185	30	�	�	PROPN
cana-4548	185	31	̆	̆	PROPN
cana-4548	185	32	�	�	PROPN
cana-4548	185	33	,	,	PUNCT
cana-4548	185	34	equation	equation	NOUN
cana-4548	185	35	6	6	NUM
cana-4548	185	36	is	be	AUX
cana-4548	185	37	also	also	ADV
cana-4548	185	38	right	right	ADJ
cana-4548	185	39	when	when	SCONJ
cana-4548	185	40	�	�	PROPN
cana-4548	185	41	̆	̆	PROPN
cana-4548	185	42	�	�	PROPN
cana-4548	185	43	𝑗	𝑗	PROPN
cana-4548	185	44	≥	≥	NOUN
cana-4548	185	45	0	0	NUM
cana-4548	185	46	and	and	CCONJ
cana-4548	185	47	∑𝑗=1	∑𝑗=1	PROPN
cana-4548	185	48	𝑛	𝑛	PRON
cana-4548	185	49	 	 	SPACE
cana-4548	185	50	�	�	PROPN
cana-4548	185	51	̆	̆	NOUN
cana-4548	185	52	�	�	PROPN
cana-4548	185	53	𝑗	𝑗	NOUN
cana-4548	185	54	=	=	ADJ
cana-4548	185	55	1	1	NUM
cana-4548	185	56	.	.	NOUN
cana-4548	185	57	example	example	NOUN
cana-4548	185	58	1	1	NUM
cana-4548	185	59	.	.	PUNCT
cana-4548	185	60	suppose	suppose	VERB
cana-4548	185	61	𝛼1	𝛼1	NOUN
cana-4548	185	62	=	=	SYM
cana-4548	185	63	⟨0.8,0.1,0.05⟩	⟨0.8,0.1,0.05⟩	NUM
cana-4548	185	64	,	,	PUNCT
cana-4548	185	65	𝛼2	𝛼2	PROPN
cana-4548	185	66	=	=	SYM
cana-4548	185	67	⟨0.52,0.3,0.1⟩	⟨0.52,0.3,0.1⟩	NOUN
cana-4548	185	68	,	,	PUNCT
cana-4548	185	69	𝛼3	𝛼3	NOUN
cana-4548	185	70	=	=	SYM
cana-4548	186	1	⟨0.45,0.4,0.01⟩	⟨0.45,0.4,0.01⟩	NOUN
cana-4548	186	2	and	and	CCONJ
cana-4548	186	3	𝛼4	𝛼4	NOUN
cana-4548	186	4	=	=	SYM
cana-4548	186	5	⟨0.79,0.156,0.05⟩	⟨0.79,0.156,0.05⟩	NOUN
cana-4548	186	6	are	be	AUX
cana-4548	186	7	four	four	NUM
cana-4548	186	8	pfns	pfns	NOUN
cana-4548	186	9	,	,	PUNCT
cana-4548	186	10	𝑤	𝑤	ADP
cana-4548	186	11	=	=	SYM
cana-4548	186	12	(	(	PUNCT
cana-4548	186	13	𝑤1	𝑤1	PROPN
cana-4548	186	14	,	,	PUNCT
cana-4548	186	15	𝑤2	𝑤2	NOUN
cana-4548	186	16	,	,	PUNCT
cana-4548	186	17	𝑤3	𝑤3	PROPN
cana-4548	186	18	,	,	PUNCT
cana-4548	186	19	𝑤4	𝑤4	NOUN
cana-4548	186	20	)	)	PUNCT
cana-4548	186	21	=	=	PUNCT
cana-4548	187	1	⟨0.2,0.1,0.3,0.4⟩𝑇	⟨0.2,0.1,0.3,0.4⟩𝑇	X
cana-4548	187	2	be	be	AUX
cana-4548	187	3	the	the	DET
cana-4548	187	4	weight	weight	NOUN
cana-4548	187	5	vector	vector	NOUN
cana-4548	187	6	of	of	ADP
cana-4548	187	7	𝛼𝑗(𝑗	𝛼𝑗(𝑗	NUM
cana-4548	187	8	=	=	NOUN
cana-4548	187	9	1,2,3,4	1,2,3,4	NUM
cana-4548	187	10	)	)	PUNCT
cana-4548	187	11	then	then	ADV
cana-4548	187	12	we	we	PRON
cana-4548	187	13	adopt	adopt	VERB
cana-4548	187	14	the	the	DET
cana-4548	187	15	pfsspwg	pfsspwg	NOUN
cana-4548	187	16	to	to	PART
cana-4548	187	17	aggregate	aggregate	VERB
cana-4548	187	18	the	the	DET
cana-4548	187	19	four	four	NUM
cana-4548	187	20	pfns	pfns	NOUN
cana-4548	187	21	and	and	CCONJ
cana-4548	187	22	generate	generate	VERB
cana-4548	187	23	a	a	DET
cana-4548	187	24	comprehensive	comprehensive	ADJ
cana-4548	187	25	value	value	NOUN
cana-4548	187	26	.	.	PUNCT
cana-4548	188	1	the	the	DET
cana-4548	188	2	steps	step	NOUN
cana-4548	188	3	are	be	AUX
cana-4548	188	4	shown	show	VERB
cana-4548	188	5	as	as	SCONJ
cana-4548	188	6	follows	follow	VERB
cana-4548	188	7	:	:	PUNCT
cana-4548	188	8	(	(	PUNCT
cana-4548	188	9	𝛽	𝛽	NOUN
cana-4548	188	10	=	=	SYM
cana-4548	188	11	−2	−2	NOUN
cana-4548	188	12	)	)	PUNCT
cana-4548	188	13	.	.	PUNCT
cana-4548	189	1	sup(𝛼_1	sup(𝛼_1	PROPN
cana-4548	189	2	,	,	PUNCT
cana-4548	189	3	𝛼_2	𝛼_2	NOUN
cana-4548	189	4	)	)	PUNCT
cana-4548	189	5	=	=	PUNCT
cana-4548	189	6	0.823	0.823	NUM
cana-4548	189	7	,	,	PUNCT
cana-4548	189	8	sup(𝛼_1	sup(𝛼_1	PROPN
cana-4548	189	9	,	,	PUNCT
cana-4548	189	10	𝛼_3	𝛼_3	PROPN
cana-4548	189	11	)	)	PUNCT
cana-4548	189	12	=	=	SYM
cana-4548	189	13	0.77	0.77	NUM
cana-4548	189	14	,	,	PUNCT
cana-4548	189	15	sup(𝛼_1	sup(𝛼_1	PROPN
cana-4548	189	16	,	,	PUNCT
cana-4548	189	17	𝛼_4	𝛼_4	NOUN
cana-4548	189	18	)	)	PUNCT
cana-4548	189	19	=	=	SYM
cana-4548	189	20	0.978	0.978	NUM
cana-4548	189	21	,	,	PUNCT
cana-4548	189	22	sup(𝛼_2	sup(𝛼_2	PROPN
cana-4548	189	23	,	,	PUNCT
cana-4548	189	24	𝛼_3	𝛼_3	PROPN
cana-4548	189	25	)	)	PUNCT
cana-4548	189	26	=	=	SYM
cana-4548	189	27	0.913	0.913	NUM
cana-4548	189	28	,	,	PUNCT
cana-4548	189	29	sup(𝛼_2	sup(𝛼_2	PROPN
cana-4548	189	30	,	,	PUNCT
cana-4548	189	31	𝛼_4	𝛼_4	NOUN
cana-4548	189	32	)	)	PUNCT
cana-4548	189	33	=	=	SYM
cana-4548	189	34	0.845	0.845	NUM
cana-4548	189	35	and	and	CCONJ
cana-4548	189	36	sup(𝛼_3	sup(𝛼_3	PROPN
cana-4548	189	37	,	,	PUNCT
cana-4548	189	38	𝛼_4	𝛼_4	NOUN
cana-4548	189	39	)	)	PUNCT
cana-4548	189	40	=	=	PUNCT
cana-4548	189	41	0.792	0.792	NUM
cana-4548	189	42	.	.	PUNCT
cana-4548	189	43	𝔑𝔶(𝛼_1	𝔑𝔶(𝛼_1	NOUN
cana-4548	189	44	)	)	PUNCT
cana-4548	190	1	=	=	SYM
cana-4548	190	2	sup(𝛼_1	sup(𝛼_1	PROPN
cana-4548	190	3	,	,	PUNCT
cana-4548	190	4	𝛼_2	𝛼_2	NOUN
cana-4548	190	5	)	)	PUNCT
cana-4548	191	1	+	+	CCONJ
cana-4548	191	2	sup(𝛼_3	sup(𝛼_3	PROPN
cana-4548	191	3	,	,	PUNCT
cana-4548	191	4	𝛼_1	𝛼_1	NOUN
cana-4548	191	5	)	)	PUNCT
cana-4548	191	6	=	=	PUNCT
cana-4548	192	1	2.571	2.571	NUM
cana-4548	192	2	,	,	PUNCT
cana-4548	192	3	𝔑𝔶(𝛼_2	𝔑𝔶(𝛼_2	ADJ
cana-4548	192	4	)	)	PUNCT
cana-4548	192	5	=	=	SYM
cana-4548	192	6	2.582	2.582	NUM
cana-4548	192	7	,	,	PUNCT
cana-4548	192	8	𝔑𝔶(𝛼_3	𝔑𝔶(𝛼_3	NOUN
cana-4548	192	9	)	)	PUNCT
cana-4548	192	10	=	=	SYM
cana-4548	192	11	2.475	2.475	NUM
cana-4548	192	12	and	and	CCONJ
cana-4548	192	13	𝔑𝔶(𝛼4	𝔑𝔶(𝛼4	NOUN
cana-4548	192	14	)	)	PUNCT
cana-4548	193	1	=	=	SYM
cana-4548	193	2	2.615	2.615	NUM
cana-4548	193	3	.	.	PUNCT
cana-4548	194	1	�	�	PROPN
cana-4548	194	2	̆	̆	NOUN
cana-4548	194	3	�	�	PROPN
cana-4548	194	4	1	1	NUM
cana-4548	194	5	=	=	SYM
cana-4548	194	6	0.201	0.201	NUM
cana-4548	194	7	,	,	PUNCT
cana-4548	194	8	�	�	PROPN
cana-4548	194	9	̆	̆	NOUN
cana-4548	194	10	�	�	PROPN
cana-4548	194	11	2	2	NUM
cana-4548	194	12	=	=	SYM
cana-4548	194	13	0.101	0.101	NUM
cana-4548	194	14	,	,	PUNCT
cana-4548	194	15	�	�	PROPN
cana-4548	194	16	̆	̆	NOUN
cana-4548	194	17	�	�	PROPN
cana-4548	194	18	3	3	NUM
cana-4548	194	19	=	=	SYM
cana-4548	194	20	0.293and	0.293and	NOUN
cana-4548	194	21	�	�	PROPN
cana-4548	194	22	̆	̆	NOUN
cana-4548	194	23	�	�	PROPN
cana-4548	194	24	4	4	NUM
cana-4548	194	25	=	=	SYM
cana-4548	194	26	0.406	0.406	NUM
cana-4548	194	27	.	.	PUNCT
cana-4548	195	1	pfsspwg(𝛼1	pfsspwg(𝛼1	PROPN
cana-4548	195	2	,	,	PUNCT
cana-4548	195	3	𝛼2	𝛼2	PROPN
cana-4548	195	4	,	,	PUNCT
cana-4548	195	5	…	…	PUNCT
cana-4548	195	6	,	,	PUNCT
cana-4548	195	7	𝛼4	𝛼4	NOUN
cana-4548	195	8	)	)	PUNCT
cana-4548	196	1	=	=	PUNCT
cana-4548	196	2	⟨1	⟨1	PROPN
cana-4548	196	3	−	−	PROPN
cana-4548	197	1	(	(	PUNCT
cana-4548	197	2	∑j=1	∑j=1	PROPN
cana-4548	197	3	4	4	NUM
cana-4548	197	4	 	 	SPACE
cana-4548	197	5	�	�	PROPN
cana-4548	197	6	̆	̆	NOUN
cana-4548	197	7	�	�	PROPN
cana-4548	197	8	j(1	j(1	NOUN
cana-4548	197	9	−	−	NOUN
cana-4548	197	10	𝜇j	𝜇j	NOUN
cana-4548	197	11	)	)	PUNCT
cana-4548	197	12	𝛽	𝛽	NOUN
cana-4548	197	13	)	)	PUNCT
cana-4548	197	14	1	1	NUM
cana-4548	197	15	𝛽	𝛽	NOUN
cana-4548	197	16	,	,	PUNCT
cana-4548	197	17	(	(	PUNCT
cana-4548	197	18	∑j=1	∑j=1	PROPN
cana-4548	197	19	4	4	NUM
cana-4548	197	20	 	 	SPACE
cana-4548	197	21	�	�	PROPN
cana-4548	197	22	̆	̆	NOUN
cana-4548	197	23	�	�	PROPN
cana-4548	197	24	j𝜂j	j𝜂j	PROPN
cana-4548	197	25	𝛽	𝛽	PROPN
cana-4548	197	26	)	)	PUNCT
cana-4548	197	27	1	1	NUM
cana-4548	197	28	𝛽	𝛽	NOUN
cana-4548	197	29	,	,	PUNCT
cana-4548	197	30	(	(	PUNCT
cana-4548	197	31	∑j=1	∑j=1	PROPN
cana-4548	197	32	4	4	NUM
cana-4548	197	33	 	 	SPACE
cana-4548	197	34	�	�	PROPN
cana-4548	197	35	̆	̆	NOUN
cana-4548	197	36	�	�	PROPN
cana-4548	197	37	j𝜈	j𝜈	PROPN
cana-4548	197	38	,	,	PUNCT
cana-4548	197	39	⟨0.253,0.262,0.04⟩.	⟨0.253,0.262,0.04⟩.	X
cana-4548	197	40	for	for	ADP
cana-4548	197	41	a	a	DET
cana-4548	197	42	collection	collection	NOUN
cana-4548	197	43	of	of	ADP
cana-4548	197	44	pfn	pfn	PROPN
cana-4548	197	45	,	,	PUNCT
cana-4548	197	46	we	we	PRON
cana-4548	197	47	can	can	AUX
cana-4548	197	48	easily	easily	ADV
cana-4548	197	49	prove	prove	VERB
cana-4548	197	50	the	the	DET
cana-4548	197	51	proposed	propose	VERB
cana-4548	197	52	pfsspwg	pfsspwg	NOUN
cana-4548	197	53	operator	operator	NOUN
cana-4548	197	54	satisfying	satisfy	VERB
cana-4548	197	55	the	the	DET
cana-4548	197	56	idempotency	idempotency	NOUN
cana-4548	197	57	,	,	PUNCT
cana-4548	197	58	monotonicity	monotonicity	NOUN
cana-4548	197	59	and	and	CCONJ
cana-4548	197	60	boundedness	boundedness	NOUN
cana-4548	197	61	properties	property	NOUN
cana-4548	197	62	as	as	SCONJ
cana-4548	197	63	follows	follow	VERB
cana-4548	197	64	:	:	PUNCT
cana-4548	197	65	property	property	NOUN
cana-4548	197	66	1	1	NUM
cana-4548	197	67	.	.	PUNCT
cana-4548	198	1	(	(	PUNCT
cana-4548	198	2	idempotency	idempotency	NOUN
cana-4548	198	3	)	)	PUNCT
cana-4548	198	4	let	let	VERB
cana-4548	198	5	𝛼𝑗	𝛼𝑗	PROPN
cana-4548	198	6	=	=	SYM
cana-4548	198	7	⟨𝜇𝛼𝑗	⟨𝜇𝛼𝑗	PROPN
cana-4548	198	8	,	,	PUNCT
cana-4548	198	9	𝜂𝛼𝑗	𝜂𝛼𝑗	VERB
cana-4548	198	10	,	,	PUNCT
cana-4548	198	11	𝜈𝛼𝑗	𝜈𝛼𝑗	VERB
cana-4548	198	12	⟩	⟩	NOUN
cana-4548	198	13	(	(	PUNCT
cana-4548	198	14	𝑗	𝑗	NOUN
cana-4548	198	15	=	=	SYM
cana-4548	198	16	1,2	1,2	NUM
cana-4548	198	17	,	,	PUNCT
cana-4548	198	18	…	…	PUNCT
cana-4548	198	19	,	,	PUNCT
cana-4548	198	20	𝑛	𝑛	X
cana-4548	198	21	)	)	PUNCT
cana-4548	198	22	be	be	VERB
cana-4548	198	23	a	a	DET
cana-4548	198	24	set	set	NOUN
cana-4548	198	25	of	of	ADP
cana-4548	198	26	pfn	pfn	NOUN
cana-4548	198	27	,	,	PUNCT
cana-4548	198	28	if	if	SCONJ
cana-4548	198	29	𝛼𝑗	𝛼𝑗	PROPN
cana-4548	198	30	=	=	PUNCT
cana-4548	198	31	𝛼	𝛼	X
cana-4548	198	32	=	=	SYM
cana-4548	198	33	(	(	PUNCT
cana-4548	198	34	𝜇	𝜇	ADP
cana-4548	198	35	,	,	PUNCT
cana-4548	198	36	𝜂	𝜂	PROPN
cana-4548	198	37	,	,	PUNCT
cana-4548	198	38	𝜈	𝜈	X
cana-4548	198	39	)	)	PUNCT
cana-4548	198	40	then	then	ADV
cana-4548	198	41	pfsspwg(𝛼1	pfsspwg(𝛼1	PROPN
cana-4548	198	42	,	,	PUNCT
cana-4548	198	43	𝛼2	𝛼2	PROPN
cana-4548	198	44	,	,	PUNCT
cana-4548	198	45	…	…	PUNCT
cana-4548	198	46	,	,	PUNCT
cana-4548	198	47	𝛼𝑛	𝛼𝑛	PROPN
cana-4548	198	48	)	)	PUNCT
cana-4548	198	49	=	=	SYM
cana-4548	198	50	𝛼	𝛼	NOUN
cana-4548	198	51	property	property	NOUN
cana-4548	198	52	2	2	NUM
cana-4548	198	53	.	.	PUNCT
cana-4548	199	1	(	(	PUNCT
cana-4548	199	2	monotonicity	monotonicity	NOUN
cana-4548	199	3	)	)	PUNCT
cana-4548	199	4	let	let	VERB
cana-4548	199	5	𝛼𝑗	𝛼𝑗	PROPN
cana-4548	199	6	=	=	SYM
cana-4548	199	7	⟨𝜇𝛼𝑗	⟨𝜇𝛼𝑗	PROPN
cana-4548	199	8	,	,	PUNCT
cana-4548	199	9	𝜂𝛼𝑗	𝜂𝛼𝑗	VERB
cana-4548	199	10	,	,	PUNCT
cana-4548	199	11	𝜈𝛼𝑗	𝜈𝛼𝑗	VERB
cana-4548	199	12	⟩	⟩	NOUN
cana-4548	199	13	and	and	CCONJ
cana-4548	199	14	𝛼𝑗	𝛼𝑗	PROPN
cana-4548	200	1	′	′	NUM
cana-4548	201	1	=	=	PUNCT
cana-4548	201	2	⟨𝜇𝛼𝑗	⟨𝜇𝛼𝑗	PROPN
cana-4548	201	3	′	′	NOUN
cana-4548	201	4	,	,	PUNCT
cana-4548	201	5	𝜂𝛼𝑗	𝜂𝛼𝑗	ADP
cana-4548	201	6	′	′	NOUN
cana-4548	201	7	,	,	PUNCT
cana-4548	201	8	𝜈𝛼𝑗	𝜈𝛼𝑗	VERB
cana-4548	201	9	′	′	NUM
cana-4548	201	10	⟩	⟩	PROPN
cana-4548	201	11	𝛼𝑗	𝛼𝑗	PROPN
cana-4548	201	12	′(𝑗	′(𝑗	NOUN
cana-4548	201	13	=	=	NOUN
cana-4548	201	14	1,2	1,2	NUM
cana-4548	201	15	,	,	PUNCT
cana-4548	201	16	…	…	PUNCT
cana-4548	201	17	,	,	PUNCT
cana-4548	201	18	𝑛	𝑛	NOUN
cana-4548	201	19	)	)	PUNCT
cana-4548	201	20	as	as	ADP
cana-4548	201	21	two	two	NUM
cana-4548	201	22	sets	set	NOUN
cana-4548	201	23	of	of	ADP
cana-4548	201	24	pfn	pfn	NOUN
cana-4548	201	25	;	;	PUNCT
cana-4548	201	26	and	and	CCONJ
cana-4548	201	27	𝜇𝑗	𝜇𝑗	X
cana-4548	201	28	≤	≤	NUM
cana-4548	201	29	𝜇𝑗	𝜇𝑗	NOUN
cana-4548	201	30	′	′	NUM
cana-4548	201	31	,	,	PUNCT
cana-4548	201	32	𝜂𝑗	𝜂𝑗	NOUN
cana-4548	201	33	′	′	NOUN
cana-4548	201	34	≤	≤	NOUN
cana-4548	201	35	𝜂𝑗	𝜂𝑗	ADP
cana-4548	201	36	and	and	CCONJ
cana-4548	201	37	𝜈𝑗	𝜈𝑗	PROPN
cana-4548	201	38	′	′	NOUN
cana-4548	201	39	≤	≤	PROPN
cana-4548	202	1	𝜈𝑗	𝜈𝑗	ADP
cana-4548	202	2	then	then	ADV
cana-4548	202	3	pfsspwg(𝛼1	pfsspwg(𝛼1	PROPN
cana-4548	202	4	,	,	PUNCT
cana-4548	202	5	𝛼2	𝛼2	PROPN
cana-4548	202	6	,	,	PUNCT
cana-4548	202	7	…	…	PUNCT
cana-4548	202	8	,	,	PUNCT
cana-4548	202	9	𝛼𝑛	𝛼𝑛	PROPN
cana-4548	202	10	)	)	PUNCT
cana-4548	202	11	≤	≤	NUM
cana-4548	202	12	pfsspwg(𝛼1	pfsspwg(𝛼1	NOUN
cana-4548	203	1	′	′	NOUN
cana-4548	203	2	,	,	PUNCT
cana-4548	203	3	𝛼2	𝛼2	PROPN
cana-4548	203	4	′	′	NUM
cana-4548	203	5	,	,	PUNCT
cana-4548	203	6	…	…	PUNCT
cana-4548	203	7	,	,	PUNCT
cana-4548	203	8	𝛼𝑛	𝛼𝑛	ADP
cana-4548	203	9	′	′	NUM
cana-4548	203	10	)	)	PUNCT
cana-4548	204	1	communications	communication	NOUN
cana-4548	204	2	on	on	ADP
cana-4548	204	3	applied	apply	VERB
cana-4548	204	4	nonlinear	nonlinear	ADJ
cana-4548	204	5	analysis	analysis	NOUN
cana-4548	204	6	issn	issn	NOUN
cana-4548	204	7	:	:	PUNCT
cana-4548	204	8	1074	1074	NUM
cana-4548	204	9	-	-	PUNCT
cana-4548	204	10	133x	133x	NUM
cana-4548	204	11	vol	vol	NOUN
cana-4548	204	12	32	32	NUM
cana-4548	204	13	no	no	NOUN
cana-4548	204	14	.	.	PUNCT
cana-4548	205	1	9s	9s	NUM
cana-4548	205	2	(	(	PUNCT
cana-4548	205	3	2025	2025	NUM
cana-4548	205	4	)	)	PUNCT
cana-4548	205	5	2687	2687	NUM
cana-4548	205	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4548	205	7	property	property	NOUN
cana-4548	205	8	3	3	NUM
cana-4548	205	9	.	.	PUNCT
cana-4548	205	10	(	(	PUNCT
cana-4548	205	11	boundedness	boundedness	NOUN
cana-4548	205	12	)	)	PUNCT
cana-4548	205	13	let	let	VERB
cana-4548	205	14	𝛼𝑗	𝛼𝑗	PROPN
cana-4548	205	15	=	=	SYM
cana-4548	205	16	⟨𝜇𝛼𝑗	⟨𝜇𝛼𝑗	PROPN
cana-4548	205	17	,	,	PUNCT
cana-4548	205	18	𝜂𝛼𝑗	𝜂𝛼𝑗	VERB
cana-4548	205	19	,	,	PUNCT
cana-4548	205	20	𝜈𝛼𝑗	𝜈𝛼𝑗	VERB
cana-4548	205	21	⟩	⟩	NOUN
cana-4548	205	22	(	(	PUNCT
cana-4548	205	23	𝑗	𝑗	NOUN
cana-4548	205	24	=	=	SYM
cana-4548	205	25	1,2	1,2	NUM
cana-4548	205	26	,	,	PUNCT
cana-4548	205	27	…	…	PUNCT
cana-4548	205	28	,	,	PUNCT
cana-4548	205	29	𝑛	𝑛	X
cana-4548	205	30	)	)	PUNCT
cana-4548	205	31	be	be	VERB
cana-4548	205	32	a	a	DET
cana-4548	205	33	set	set	NOUN
cana-4548	205	34	of	of	ADP
cana-4548	205	35	pfn	pfn	PROPN
cana-4548	205	36	,	,	PUNCT
cana-4548	205	37	and	and	CCONJ
cana-4548	205	38	𝛼+	𝛼+	ADJ
cana-4548	206	1	=	=	SYM
cana-4548	206	2	(	(	PUNCT
cana-4548	206	3	max	max	PROPN
cana-4548	206	4	𝑛	𝑛	PROPN
cana-4548	206	5	𝑗𝑗=1	𝑗𝑗=1	NOUN
cana-4548	206	6	 	 	SPACE
cana-4548	206	7	,	,	PUNCT
cana-4548	206	8	min	min	NOUN
cana-4548	206	9	𝑛	𝑛	PROPN
cana-4548	206	10	𝑗𝑗=1	𝑗𝑗=1	NOUN
cana-4548	206	11	 	 	SPACE
cana-4548	206	12	,	,	PUNCT
cana-4548	206	13	min𝜈𝑗𝑗=1	min𝜈𝑗𝑗=1	PROPN
cana-4548	206	14	𝑛	𝑛	PROPN
cana-4548	206	15	)	)	PUNCT
cana-4548	206	16	,	,	PUNCT
cana-4548	206	17	𝛼−	𝛼−	PROPN
cana-4548	206	18	=	=	PUNCT
cana-4548	206	19	(	(	PUNCT
cana-4548	206	20	min	min	NOUN
cana-4548	206	21	𝑛	𝑛	PROPN
cana-4548	206	22	𝑗𝑗=1	𝑗𝑗=1	NOUN
cana-4548	206	23	 	 	SPACE
cana-4548	206	24	,	,	PUNCT
cana-4548	206	25	max	max	PROPN
cana-4548	206	26	𝑛	𝑛	PROPN
cana-4548	206	27	𝑗𝑗=1	𝑗𝑗=1	NOUN
cana-4548	206	28	 	 	SPACE
cana-4548	206	29	,	,	PUNCT
cana-4548	206	30	max𝜈𝑗𝑗=1	max𝜈𝑗𝑗=1	ADJ
cana-4548	206	31	𝑛	𝑛	X
cana-4548	206	32	)	)	PUNCT
cana-4548	206	33	then	then	ADV
cana-4548	206	34	𝛼−	𝛼−	PROPN
cana-4548	206	35	≤	≤	ADJ
cana-4548	206	36	𝑃𝐹𝑆𝑆𝑃𝑊𝐺(𝛼1	𝑃𝐹𝑆𝑆𝑃𝑊𝐺(𝛼1	PROPN
cana-4548	206	37	,	,	PUNCT
cana-4548	206	38	𝛼2	𝛼2	ADJ
cana-4548	206	39	,	,	PUNCT
cana-4548	206	40	…	…	PUNCT
cana-4548	206	41	,	,	PUNCT
cana-4548	206	42	𝛼𝑛	𝛼𝑛	PROPN
cana-4548	206	43	)	)	PUNCT
cana-4548	206	44	≤	≤	NOUN
cana-4548	206	45	𝛼+	𝛼+	VERB
cana-4548	206	46	3.2	3.2	NUM
cana-4548	206	47	picture	picture	NOUN
cana-4548	206	48	fuzzy	fuzzy	ADJ
cana-4548	206	49	schweizer	schweizer	PROPN
cana-4548	206	50	-	-	PUNCT
cana-4548	206	51	sklar	sklar	ADJ
cana-4548	206	52	power	power	NOUN
cana-4548	206	53	ordered	order	VERB
cana-4548	206	54	weighted	weight	VERB
cana-4548	206	55	geometric	geometric	ADJ
cana-4548	206	56	aggregation	aggregation	NOUN
cana-4548	206	57	operators	operator	NOUN
cana-4548	206	58	in	in	ADP
cana-4548	206	59	the	the	DET
cana-4548	206	60	following	follow	VERB
cana-4548	206	61	section	section	NOUN
cana-4548	206	62	,	,	PUNCT
cana-4548	206	63	we	we	PRON
cana-4548	206	64	propose	propose	VERB
cana-4548	206	65	the	the	DET
cana-4548	206	66	confidence	confidence	NOUN
cana-4548	206	67	picture	picture	NOUN
cana-4548	206	68	fuzzy	fuzzy	ADJ
cana-4548	206	69	schweizer	schweizer	PROPN
cana-4548	206	70	-	-	PUNCT
cana-4548	206	71	sklar	sklar	ADJ
cana-4548	206	72	power	power	NOUN
cana-4548	206	73	ordered	order	VERB
cana-4548	206	74	weighted	weight	VERB
cana-4548	206	75	geometric	geometric	ADJ
cana-4548	206	76	operator	operator	NOUN
cana-4548	206	77	with	with	ADP
cana-4548	206	78	the	the	DET
cana-4548	206	79	pf	pf	PROPN
cana-4548	206	80	context	context	NOUN
cana-4548	206	81	and	and	CCONJ
cana-4548	206	82	the	the	DET
cana-4548	206	83	desirable	desirable	ADJ
cana-4548	206	84	properties	property	NOUN
cana-4548	206	85	of	of	ADP
cana-4548	206	86	the	the	DET
cana-4548	206	87	proposed	propose	VERB
cana-4548	206	88	operator	operator	NOUN
cana-4548	206	89	are	be	AUX
cana-4548	206	90	investigated	investigate	VERB
cana-4548	206	91	.	.	PUNCT
cana-4548	207	1	definition	definition	NOUN
cana-4548	207	2	11	11	NUM
cana-4548	207	3	.	.	PUNCT
cana-4548	208	1	let	let	VERB
cana-4548	208	2	𝛼𝑗	𝛼𝑗	PROPN
cana-4548	208	3	=	=	SYM
cana-4548	208	4	⟨𝜇𝛼𝑗	⟨𝜇𝛼𝑗	PROPN
cana-4548	208	5	,	,	PUNCT
cana-4548	208	6	𝜂𝛼𝑗	𝜂𝛼𝑗	VERB
cana-4548	208	7	,	,	PUNCT
cana-4548	208	8	𝜈𝛼𝑗	𝜈𝛼𝑗	VERB
cana-4548	208	9	⟩	⟩	NOUN
cana-4548	208	10	(	(	PUNCT
cana-4548	208	11	𝑗	𝑗	NOUN
cana-4548	208	12	=	=	SYM
cana-4548	208	13	1,2	1,2	NUM
cana-4548	208	14	,	,	PUNCT
cana-4548	208	15	…	…	PUNCT
cana-4548	208	16	,	,	PUNCT
cana-4548	208	17	𝑛	𝑛	X
cana-4548	208	18	)	)	PUNCT
cana-4548	208	19	be	be	VERB
cana-4548	208	20	a	a	DET
cana-4548	208	21	set	set	NOUN
cana-4548	208	22	of	of	ADP
cana-4548	208	23	svnn	svnn	NOUN
cana-4548	208	24	.	.	PUNCT
cana-4548	209	1	then	then	ADV
cana-4548	209	2	the	the	DET
cana-4548	209	3	pfsspowg	pfsspowg	ADJ
cana-4548	209	4	operator	operator	NOUN
cana-4548	209	5	of	of	ADP
cana-4548	209	6	dimension	dimension	NOUN
cana-4548	209	7	𝑛	𝑛	PROPN
cana-4548	209	8	is	be	AUX
cana-4548	209	9	a	a	DET
cana-4548	209	10	mapping	mapping	NOUN
cana-4548	209	11	pfsspowg	pfsspowg	ADJ
cana-4548	209	12	:	:	PUNCT
cana-4548	209	13	𝛼𝑛	𝛼𝑛	INTJ
cana-4548	209	14	→	→	SYM
cana-4548	209	15	𝛼	𝛼	NOUN
cana-4548	209	16	such	such	ADJ
cana-4548	209	17	that	that	DET
cana-4548	209	18	pfsspowg(𝛼1	pfsspowg(𝛼1	PROPN
cana-4548	209	19	,	,	PUNCT
cana-4548	209	20	𝛼2	𝛼2	VERB
cana-4548	209	21	,	,	PUNCT
cana-4548	209	22	…	…	PUNCT
cana-4548	209	23	,	,	PUNCT
cana-4548	209	24	𝛼𝑛	𝛼𝑛	PROPN
cana-4548	209	25	)	)	PUNCT
cana-4548	209	26	=	=	NOUN
cana-4548	209	27	⊕𝑗=1	⊕𝑗=1	NUM
cana-4548	209	28	𝑛	𝑛	VERB
cana-4548	209	29	𝛼	𝛼	PRON
cana-4548	209	30	𝜎(𝑗	𝜎(𝑗	NOUN
cana-4548	209	31	)	)	PUNCT
cana-4548	209	32	(	(	PUNCT
cana-4548	209	33	𝑤𝑗(1+𝔑𝔶(𝛼𝜎(𝑗	𝑤𝑗(1+𝔑𝔶(𝛼𝜎(𝑗	NOUN
cana-4548	209	34	)	)	PUNCT
cana-4548	209	35	)	)	PUNCT
cana-4548	209	36	)	)	PUNCT
cana-4548	210	1	∑	∑	PUNCT
cana-4548	210	2	 	 	SPACE
cana-4548	210	3	𝑛	𝑛	PRON
cana-4548	210	4	𝑗=1	𝑗=1	PROPN
cana-4548	210	5	 	 	SPACE
cana-4548	210	6	𝑤𝑗(1+𝔫𝔶(𝛼𝜎(𝑗	𝑤𝑗(1+𝔫𝔶(𝛼𝜎(𝑗	PROPN
cana-4548	210	7	)	)	PUNCT
cana-4548	210	8	)	)	PUNCT
cana-4548	210	9	)	)	PUNCT
cana-4548	210	10	)	)	PUNCT
cana-4548	211	1	(	(	PUNCT
cana-4548	211	2	8)	8)	NUM
cana-4548	211	3	where𝜎(𝑗	where𝜎(𝑗	NOUN
cana-4548	211	4	)	)	PUNCT
cana-4548	211	5	is	be	AUX
cana-4548	211	6	the	the	DET
cana-4548	211	7	permutation	permutation	NOUN
cana-4548	211	8	such	such	ADJ
cana-4548	211	9	that	that	SCONJ
cana-4548	211	10	𝛼𝜎(𝑗−1	𝛼𝜎(𝑗−1	PROPN
cana-4548	211	11	)	)	PUNCT
cana-4548	211	12	≥	≥	NOUN
cana-4548	211	13	𝛼𝜎(𝑗	𝛼𝜎(𝑗	NUM
cana-4548	211	14	)	)	PUNCT
cana-4548	211	15	for	for	ADP
cana-4548	211	16	any	any	DET
cana-4548	211	17	𝑗	𝑗	NOUN
cana-4548	211	18	=	=	SYM
cana-4548	211	19	1,2	1,2	NUM
cana-4548	211	20	,	,	PUNCT
cana-4548	211	21	…	…	PUNCT
cana-4548	211	22	𝑛	𝑛	NOUN
cana-4548	211	23	and	and	CCONJ
cana-4548	211	24	𝔑𝔶(𝛼𝜎(𝑗	𝔑𝔶(𝛼𝜎(𝑗	ADJ
cana-4548	211	25	)	)	PUNCT
cana-4548	211	26	)	)	PUNCT
cana-4548	212	1	=	=	PUNCT
cana-4548	212	2	∑	∑	PUNCT
cana-4548	212	3	 	 	SPACE
cana-4548	212	4	𝑛	𝑛	DET
cana-4548	212	5	ℎ=1,ℎ≠𝑗	ℎ=1,ℎ≠𝑗	PROPN
cana-4548	212	6	sup(𝛼𝜎(𝑗	sup(𝛼𝜎(𝑗	PROPN
cana-4548	212	7	)	)	PUNCT
cana-4548	212	8	,	,	PUNCT
cana-4548	212	9	𝛼𝜎(ℎ	𝛼𝜎(ℎ	NUM
cana-4548	212	10	)	)	PUNCT
cana-4548	212	11	)	)	PUNCT
cana-4548	212	12	and	and	CCONJ
cana-4548	212	13	𝑤	𝑤	X
cana-4548	212	14	=	=	SYM
cana-4548	212	15	(	(	PUNCT
cana-4548	212	16	𝑤1	𝑤1	VERB
cana-4548	212	17	,	,	PUNCT
cana-4548	212	18	𝑤2	𝑤2	NOUN
cana-4548	212	19	,	,	PUNCT
cana-4548	212	20	…	…	PUNCT
cana-4548	212	21	,	,	PUNCT
cana-4548	212	22	𝑤𝑛)𝑇	𝑤𝑛)𝑇	PROPN
cana-4548	212	23	is	be	AUX
cana-4548	212	24	the	the	DET
cana-4548	212	25	weight	weight	NOUN
cana-4548	212	26	vector	vector	NOUN
cana-4548	212	27	of	of	ADP
cana-4548	212	28	𝛼𝜎(𝑗)(𝑗	𝛼𝜎(𝑗)(𝑗	NOUN
cana-4548	212	29	=	=	SYM
cana-4548	212	30	1,2	1,2	NUM
cana-4548	212	31	,	,	PUNCT
cana-4548	212	32	…	…	PUNCT
cana-4548	212	33	,	,	PUNCT
cana-4548	212	34	𝑛	𝑛	NOUN
cana-4548	212	35	)	)	PUNCT
cana-4548	212	36	,	,	PUNCT
cana-4548	212	37	𝑤	𝑤	ADP
cana-4548	212	38	∈	∈	PROPN
cana-4548	213	1	[	[	X
cana-4548	213	2	0,1	0,1	NUM
cana-4548	213	3	]	]	PUNCT
cana-4548	213	4	,	,	PUNCT
cana-4548	213	5	∑	∑	ADP
cana-4548	213	6	 	 	SPACE
cana-4548	213	7	𝑛	𝑛	PRON
cana-4548	213	8	𝑗=1	𝑗=1	PROPN
cana-4548	213	9	𝑤𝑗	𝑤𝑗	ADP
cana-4548	213	10	=	=	SYM
cana-4548	213	11	1	1	X
cana-4548	213	12	.	.	PUNCT
cana-4548	213	13	theorem	theorem	NOUN
cana-4548	213	14	2	2	NUM
cana-4548	213	15	.	.	PUNCT
cana-4548	214	1	let	let	VERB
cana-4548	214	2	𝛼𝑗	𝛼𝑗	PROPN
cana-4548	214	3	=	=	SYM
cana-4548	214	4	⟨𝜇𝛼𝑗	⟨𝜇𝛼𝑗	PROPN
cana-4548	214	5	,	,	PUNCT
cana-4548	214	6	𝜂𝛼𝑗	𝜂𝛼𝑗	VERB
cana-4548	214	7	,	,	PUNCT
cana-4548	214	8	𝜈𝛼𝑗	𝜈𝛼𝑗	VERB
cana-4548	214	9	⟩	⟩	NOUN
cana-4548	214	10	(	(	PUNCT
cana-4548	214	11	𝑗	𝑗	NOUN
cana-4548	214	12	=	=	SYM
cana-4548	214	13	1,2	1,2	NUM
cana-4548	214	14	,	,	PUNCT
cana-4548	214	15	…	…	PUNCT
cana-4548	214	16	,	,	PUNCT
cana-4548	214	17	𝑛	𝑛	X
cana-4548	214	18	)	)	PUNCT
cana-4548	214	19	be	be	VERB
cana-4548	214	20	a	a	DET
cana-4548	214	21	set	set	NOUN
cana-4548	214	22	of	of	ADP
cana-4548	214	23	pfn	pfn	NOUN
cana-4548	214	24	and	and	CCONJ
cana-4548	214	25	𝛽	𝛽	NOUN
cana-4548	214	26	<	<	X
cana-4548	214	27	0	0	NUM
cana-4548	214	28	,	,	PUNCT
cana-4548	214	29	then	then	ADV
cana-4548	214	30	the	the	DET
cana-4548	214	31	aggregated	aggregate	VERB
cana-4548	214	32	value	value	NOUN
cana-4548	214	33	obtained	obtain	VERB
cana-4548	214	34	using	use	VERB
cana-4548	214	35	pfsspowg	pfsspowg	ADJ
cana-4548	214	36	operator	operator	NOUN
cana-4548	214	37	is	be	AUX
cana-4548	214	38	also	also	ADV
cana-4548	214	39	a	a	DET
cana-4548	214	40	pfn	pfn	NOUN
cana-4548	214	41	and	and	CCONJ
cana-4548	214	42	can	can	AUX
cana-4548	214	43	be	be	AUX
cana-4548	214	44	expressed	express	VERB
cana-4548	214	45	as	as	SCONJ
cana-4548	214	46	follows	follow	VERB
cana-4548	214	47	:	:	PUNCT
cana-4548	214	48	pfsspowg(𝛼1	pfsspowg(𝛼1	PROPN
cana-4548	214	49	,	,	PUNCT
cana-4548	214	50	𝛼2	𝛼2	VERB
cana-4548	214	51	,	,	PUNCT
cana-4548	214	52	…	…	PUNCT
cana-4548	214	53	,	,	PUNCT
cana-4548	214	54	𝛼𝑛	𝛼𝑛	PROPN
cana-4548	214	55	)	)	PUNCT
cana-4548	214	56	=	=	PUNCT
cana-4548	215	1	⟨(∑	⟨(∑	X
cana-4548	215	2	  	  	SPACE
cana-4548	215	3	𝑛	𝑛	PRON
cana-4548	215	4	𝑗=1	𝑗=1	PROPN
cana-4548	215	5	  	  	SPACE
cana-4548	215	6	�	�	PROPN
cana-4548	215	7	̆	̆	NOUN
cana-4548	215	8	�	�	PROPN
cana-4548	215	9	𝑗𝜇𝑗	𝑗𝜇𝑗	PROPN
cana-4548	215	10	𝛽	𝛽	PROPN
cana-4548	215	11	)	)	PUNCT
cana-4548	215	12	1	1	NUM
cana-4548	215	13	𝛽	𝛽	NOUN
cana-4548	215	14	,	,	PUNCT
cana-4548	215	15	1	1	NUM
cana-4548	215	16	−	−	PROPN
cana-4548	215	17	(	(	PUNCT
cana-4548	215	18	∑	∑	INTJ
cana-4548	215	19	  	  	SPACE
cana-4548	215	20	𝑛	𝑛	DET
cana-4548	215	21	𝑗=1	𝑗=1	PROPN
cana-4548	215	22	  	  	SPACE
cana-4548	215	23	�	�	PROPN
cana-4548	215	24	̆	̆	NOUN
cana-4548	215	25	�	�	PROPN
cana-4548	215	26	𝑗(1	𝑗(1	PROPN
cana-4548	215	27	−	−	PROPN
cana-4548	215	28	𝜂𝑗	𝜂𝑗	NOUN
cana-4548	215	29	)	)	PUNCT
cana-4548	215	30	𝛽	𝛽	NOUN
cana-4548	215	31	)	)	PUNCT
cana-4548	215	32	1	1	NUM
cana-4548	215	33	𝛽	𝛽	NOUN
cana-4548	215	34	,	,	PUNCT
cana-4548	215	35	1	1	NUM
cana-4548	215	36	−	−	PROPN
cana-4548	215	37	(	(	PUNCT
cana-4548	215	38	∑	∑	INTJ
cana-4548	215	39	  	  	SPACE
cana-4548	215	40	𝑛	𝑛	PRON
cana-4548	215	41	𝑗=1	𝑗=1	PROPN
cana-4548	215	42	  	  	SPACE
cana-4548	215	43	�	�	PROPN
cana-4548	215	44	̆	̆	NOUN
cana-4548	215	45	�	�	PROPN
cana-4548	215	46	𝑗(1	𝑗(1	PROPN
cana-4548	215	47	−	−	PROPN
cana-4548	215	48	𝜈𝑗	𝜈𝑗	PROPN
cana-4548	215	49	)	)	PUNCT
cana-4548	215	50	𝛽	𝛽	NOUN
cana-4548	215	51	)	)	PUNCT
cana-4548	216	1	1	1	NUM
cana-4548	216	2	𝛽	𝛽	NOUN
cana-4548	216	3	⟩	⟩	NOUN
cana-4548	216	4	(	(	PUNCT
cana-4548	216	5	9	9	NUM
cana-4548	216	6	)	)	PUNCT
cana-4548	216	7	proof	proof	NOUN
cana-4548	216	8	.	.	PUNCT
cana-4548	217	1	proof	proof	NOUN
cana-4548	217	2	of	of	ADP
cana-4548	217	3	this	this	DET
cana-4548	217	4	theorem	theorem	NOUN
cana-4548	217	5	is	be	AUX
cana-4548	217	6	similar	similar	ADJ
cana-4548	217	7	to	to	AUX
cana-4548	217	8	theorem	theorem	VERB
cana-4548	217	9	1	1	NUM
cana-4548	217	10	so	so	SCONJ
cana-4548	217	11	we	we	PRON
cana-4548	217	12	omit	omit	VERB
cana-4548	217	13	here	here	ADV
cana-4548	217	14	.	.	PUNCT
cana-4548	218	1	example	example	NOUN
cana-4548	219	1	2	2	NUM
cana-4548	219	2	.	.	PUNCT
cana-4548	219	3	suppose	suppose	VERB
cana-4548	219	4	𝛼1	𝛼1	NOUN
cana-4548	219	5	=	=	SYM
cana-4548	219	6	⟨0.8,0.1,0.05⟩	⟨0.8,0.1,0.05⟩	NUM
cana-4548	219	7	,	,	PUNCT
cana-4548	219	8	𝛼2	𝛼2	ADJ
cana-4548	219	9	=	=	SYM
cana-4548	219	10	⟨0.79,0.159,0.05⟩	⟨0.79,0.159,0.05⟩	NOUN
cana-4548	219	11	,	,	PUNCT
cana-4548	219	12	𝛼3	𝛼3	NOUN
cana-4548	219	13	=	=	SYM
cana-4548	219	14	⟨0.52,0.23,0.1⟩	⟨0.52,0.23,0.1⟩	NOUN
cana-4548	219	15	and	and	CCONJ
cana-4548	219	16	𝛼4	𝛼4	NOUN
cana-4548	219	17	=	=	SYM
cana-4548	219	18	⟨0.45,0.4,0.01⟩	⟨0.45,0.4,0.01⟩	NOUN
cana-4548	219	19	are	be	AUX
cana-4548	219	20	four	four	NUM
cana-4548	219	21	pfns	pfns	NOUN
cana-4548	219	22	,	,	PUNCT
cana-4548	219	23	𝑤	𝑤	ADP
cana-4548	219	24	=	=	SYM
cana-4548	219	25	(	(	PUNCT
cana-4548	219	26	𝑤1	𝑤1	PROPN
cana-4548	219	27	,	,	PUNCT
cana-4548	219	28	𝑤2	𝑤2	NOUN
cana-4548	219	29	,	,	PUNCT
cana-4548	219	30	𝑤3	𝑤3	PROPN
cana-4548	219	31	,	,	PUNCT
cana-4548	219	32	𝑤4	𝑤4	NOUN
cana-4548	219	33	)	)	PUNCT
cana-4548	219	34	=	=	PUNCT
cana-4548	220	1	⟨0.2,0.1,0.3,0.4⟩𝑇	⟨0.2,0.1,0.3,0.4⟩𝑇	X
cana-4548	220	2	be	be	AUX
cana-4548	220	3	the	the	DET
cana-4548	220	4	weight	weight	NOUN
cana-4548	220	5	vector	vector	NOUN
cana-4548	220	6	of	of	ADP
cana-4548	220	7	𝛼𝑗(𝑗	𝛼𝑗(𝑗	NUM
cana-4548	220	8	=	=	NOUN
cana-4548	220	9	1,2,3,4	1,2,3,4	NUM
cana-4548	220	10	)	)	PUNCT
cana-4548	220	11	then	then	ADV
cana-4548	220	12	we	we	PRON
cana-4548	220	13	need	need	VERB
cana-4548	220	14	to	to	PART
cana-4548	220	15	permute	permute	VERB
cana-4548	220	16	the	the	DET
cana-4548	220	17	pfs	pfs	PROPN
cana-4548	220	18	in	in	ADP
cana-4548	220	19	order	order	NOUN
cana-4548	220	20	to	to	PART
cana-4548	220	21	aggregate	aggregate	VERB
cana-4548	220	22	then	then	ADV
cana-4548	220	23	using	use	VERB
cana-4548	220	24	equation	equation	NOUN
cana-4548	220	25	9	9	NUM
cana-4548	220	26	,	,	PUNCT
cana-4548	220	27	we	we	PRON
cana-4548	220	28	first	first	ADV
cana-4548	220	29	calculate	calculate	VERB
cana-4548	220	30	the	the	DET
cana-4548	220	31	score	score	NOUN
cana-4548	220	32	value	value	NOUN
cana-4548	220	33	of	of	ADP
cana-4548	220	34	𝛼𝑗	𝛼𝑗	PROPN
cana-4548	220	35	for	for	ADP
cana-4548	220	36	𝑗	𝑗	NOUN
cana-4548	220	37	=	=	ADJ
cana-4548	220	38	1,2,3,4	1,2,3,4	NUM
cana-4548	220	39	.	.	PUNCT
cana-4548	221	1	sup(𝛼_1	sup(𝛼_1	PROPN
cana-4548	221	2	,	,	PUNCT
cana-4548	221	3	𝛼_2	𝛼_2	NOUN
cana-4548	221	4	)	)	PUNCT
cana-4548	221	5	=	=	SYM
cana-4548	222	1	1	1	NUM
cana-4548	222	2	−	−	PROPN
cana-4548	222	3	𝔇(𝛼_1	𝔇(𝛼_1	PROPN
cana-4548	222	4	,	,	PUNCT
cana-4548	222	5	𝛼_2	𝛼_2	NOUN
cana-4548	222	6	)	)	PUNCT
cana-4548	223	1	=	=	SYM
cana-4548	223	2	0.978	0.978	NUM
cana-4548	223	3	,	,	PUNCT
cana-4548	223	4	sup(𝛼_1	sup(𝛼_1	PROPN
cana-4548	223	5	,	,	PUNCT
cana-4548	223	6	𝛼_3	𝛼_3	PROPN
cana-4548	223	7	)	)	PUNCT
cana-4548	223	8	=	=	SYM
cana-4548	223	9	0.823	0.823	NUM
cana-4548	223	10	,	,	PUNCT
cana-4548	223	11	sup(𝛼_1	sup(𝛼_1	PROPN
cana-4548	223	12	,	,	PUNCT
cana-4548	223	13	𝛼_4	𝛼_4	NOUN
cana-4548	223	14	)	)	PUNCT
cana-4548	223	15	=	=	PUNCT
cana-4548	224	1	0.77	0.77	NUM
cana-4548	224	2	,	,	PUNCT
cana-4548	224	3	sup(𝛼_2	sup(𝛼_2	PROPN
cana-4548	224	4	,	,	PUNCT
cana-4548	224	5	𝛼_3	𝛼_3	PROPN
cana-4548	224	6	)	)	PUNCT
cana-4548	225	1	=	=	SYM
cana-4548	225	2	0.845	0.845	NUM
cana-4548	225	3	,	,	PUNCT
cana-4548	225	4	sup(𝛼_2	sup(𝛼_2	PROPN
cana-4548	225	5	,	,	PUNCT
cana-4548	225	6	𝛼_4	𝛼_4	NOUN
cana-4548	225	7	)	)	PUNCT
cana-4548	225	8	=	=	SYM
cana-4548	225	9	0.792andsup(𝛼3	0.792andsup(𝛼3	NOUN
cana-4548	225	10	,	,	PUNCT
cana-4548	225	11	𝛼4	𝛼4	NOUN
cana-4548	225	12	)	)	PUNCT
cana-4548	225	13	=	=	SYM
cana-4548	225	14	0.913	0.913	NUM
cana-4548	225	15	⋅	⋅	PROPN
cana-4548	225	16	𝔑𝔶(𝛼1	𝔑𝔶(𝛼1	PROPN
cana-4548	225	17	)	)	PUNCT
cana-4548	225	18	=	=	PUNCT
cana-4548	226	1	sup(𝛼1	sup(𝛼1	PROPN
cana-4548	226	2	,	,	PUNCT
cana-4548	226	3	𝛼2	𝛼2	ADJ
cana-4548	226	4	)	)	PUNCT
cana-4548	226	5	+	+	CCONJ
cana-4548	226	6	sup(𝛼3	sup(𝛼3	NOUN
cana-4548	226	7	,	,	PUNCT
cana-4548	226	8	𝛼1	𝛼1	NOUN
cana-4548	226	9	)	)	PUNCT
cana-4548	226	10	=	=	SYM
cana-4548	226	11	2.571	2.571	NUM
cana-4548	226	12	,	,	PUNCT
cana-4548	226	13	𝔑𝔶(𝛼2	𝔑𝔶(𝛼2	VERB
cana-4548	226	14	)	)	PUNCT
cana-4548	226	15	=	=	SYM
cana-4548	226	16	2.615	2.615	NUM
cana-4548	226	17	,	,	PUNCT
cana-4548	226	18	𝔑𝔶(𝛼3	𝔑𝔶(𝛼3	ADJ
cana-4548	226	19	)	)	PUNCT
cana-4548	226	20	=	=	NUM
cana-4548	226	21	2.582	2.582	NUM
cana-4548	226	22	and	and	CCONJ
cana-4548	226	23	𝔑𝔶(𝛼4	𝔑𝔶(𝛼4	NOUN
cana-4548	226	24	)	)	PUNCT
cana-4548	226	25	=	=	SYM
cana-4548	227	1	2.475	2.475	NUM
cana-4548	227	2	.	.	PUNCT
cana-4548	228	1	�	�	PROPN
cana-4548	228	2	̆	̆	NOUN
cana-4548	228	3	�	�	PROPN
cana-4548	228	4	1	1	NUM
cana-4548	228	5	=	=	SYM
cana-4548	228	6	0.201	0.201	NUM
cana-4548	228	7	,	,	PUNCT
cana-4548	228	8	�	�	PROPN
cana-4548	228	9	̆	̆	NOUN
cana-4548	228	10	�	�	PROPN
cana-4548	228	11	2	2	NUM
cana-4548	228	12	=	=	SYM
cana-4548	228	13	0.102	0.102	NUM
cana-4548	228	14	,	,	PUNCT
cana-4548	228	15	�	�	PROPN
cana-4548	228	16	̆	̆	NOUN
cana-4548	228	17	�	�	PROPN
cana-4548	228	18	3	3	NUM
cana-4548	228	19	=	=	SYM
cana-4548	228	20	0.304and	0.304and	NOUN
cana-4548	228	21	�	�	NOUN
cana-4548	228	22	̆	̆	NOUN
cana-4548	228	23	�	�	PROPN
cana-4548	228	24	4	4	NUM
cana-4548	228	25	=	=	SYM
cana-4548	228	26	0.393	0.393	NUM
cana-4548	228	27	.	.	PUNCT
cana-4548	229	1	the	the	DET
cana-4548	229	2	pfsspowg	pfsspowg	NOUN
cana-4548	229	3	to	to	PART
cana-4548	229	4	aggregate	aggregate	VERB
cana-4548	229	5	the	the	DET
cana-4548	229	6	four	four	NUM
cana-4548	229	7	pfns	pfns	NOUN
cana-4548	229	8	and	and	CCONJ
cana-4548	229	9	generate	generate	VERB
cana-4548	229	10	a	a	DET
cana-4548	229	11	comprehensive	comprehensive	ADJ
cana-4548	229	12	value	value	NOUN
cana-4548	229	13	.	.	PUNCT
cana-4548	230	1	the	the	DET
cana-4548	230	2	steps	step	NOUN
cana-4548	230	3	are	be	AUX
cana-4548	230	4	shown	show	VERB
cana-4548	230	5	as	as	SCONJ
cana-4548	230	6	follows	follow	VERB
cana-4548	230	7	:	:	PUNCT
cana-4548	230	8	(	(	PUNCT
cana-4548	230	9	𝛽	𝛽	NOUN
cana-4548	230	10	=	=	SYM
cana-4548	230	11	−2)pfsspowg(𝛼1	−2)pfsspowg(𝛼1	PROPN
cana-4548	230	12	,	,	PUNCT
cana-4548	230	13	𝛼2	𝛼2	VERB
cana-4548	230	14	,	,	PUNCT
cana-4548	230	15	…	…	PUNCT
cana-4548	230	16	,	,	PUNCT
cana-4548	230	17	𝛼4	𝛼4	NOUN
cana-4548	230	18	)	)	PUNCT
cana-4548	231	1	=	=	PUNCT
cana-4548	231	2	⟨1	⟨1	PROPN
cana-4548	231	3	−	−	PROPN
cana-4548	231	4	(	(	PUNCT
cana-4548	231	5	∑	∑	PART
cana-4548	231	6	 	 	SPACE
cana-4548	231	7	4	4	NUM
cana-4548	231	8	𝑗=1	𝑗=1	PROPN
cana-4548	231	9	  	  	SPACE
cana-4548	231	10	�	�	PROPN
cana-4548	231	11	̆	̆	NOUN
cana-4548	231	12	�	�	PROPN
cana-4548	231	13	𝑗(1	𝑗(1	PROPN
cana-4548	231	14	−	−	PROPN
cana-4548	231	15	𝜇𝑗	𝜇𝑗	PROPN
cana-4548	231	16	)	)	PUNCT
cana-4548	231	17	𝛽	𝛽	NOUN
cana-4548	231	18	)	)	PUNCT
cana-4548	231	19	1	1	NUM
cana-4548	231	20	𝛽	𝛽	NOUN
cana-4548	231	21	,	,	PUNCT
cana-4548	231	22	(	(	PUNCT
cana-4548	231	23	∑	∑	ADV
cana-4548	231	24	 	 	SPACE
cana-4548	231	25	4	4	NUM
cana-4548	231	26	𝑗=1	𝑗=1	PROPN
cana-4548	231	27	  	  	SPACE
cana-4548	231	28	�	�	PROPN
cana-4548	231	29	̆	̆	NOUN
cana-4548	231	30	�	�	PROPN
cana-4548	231	31	𝑗𝜂𝑗	𝑗𝜂𝑗	PROPN
cana-4548	231	32	𝛽	𝛽	NOUN
cana-4548	231	33	)	)	PUNCT
cana-4548	231	34	1	1	NUM
cana-4548	231	35	𝛽	𝛽	NOUN
cana-4548	231	36	,	,	PUNCT
cana-4548	231	37	(	(	PUNCT
cana-4548	231	38	∑	∑	ADV
cana-4548	231	39	 	 	SPACE
cana-4548	231	40	4	4	NUM
cana-4548	231	41	𝑗=1	𝑗=1	PROPN
cana-4548	231	42	  	  	SPACE
cana-4548	231	43	�	�	PROPN
cana-4548	231	44	̆	̆	NOUN
cana-4548	231	45	�	�	PROPN
cana-4548	231	46	𝑗𝜈𝑗	𝑗𝜈𝑗	PROPN
cana-4548	231	47	𝛽	𝛽	PROPN
cana-4548	231	48	)	)	PUNCT
cana-4548	231	49	1	1	NUM
cana-4548	231	50	𝛽	𝛽	NOUN
cana-4548	231	51	⟩	⟩	NOUN
cana-4548	231	52	=	=	SYM
cana-4548	231	53	⟨0.317,0.310,0.052⟩.	⟨0.317,0.310,0.052⟩.	NOUN
cana-4548	231	54	for	for	ADP
cana-4548	231	55	a	a	DET
cana-4548	231	56	collection	collection	NOUN
cana-4548	231	57	of	of	ADP
cana-4548	231	58	pfn	pfn	PROPN
cana-4548	231	59	,	,	PUNCT
cana-4548	231	60	we	we	PRON
cana-4548	231	61	can	can	AUX
cana-4548	231	62	easily	easily	ADV
cana-4548	231	63	prove	prove	VERB
cana-4548	231	64	the	the	DET
cana-4548	231	65	proposed	propose	VERB
cana-4548	231	66	pfsspowg	pfsspowg	ADJ
cana-4548	231	67	operator	operator	NOUN
cana-4548	231	68	satisfying	satisfy	VERB
cana-4548	231	69	the	the	DET
cana-4548	231	70	idempotency	idempotency	NOUN
cana-4548	231	71	,	,	PUNCT
cana-4548	231	72	monotonicity	monotonicity	NOUN
cana-4548	231	73	and	and	CCONJ
cana-4548	231	74	boundedness	boundedness	NOUN
cana-4548	231	75	properties	property	NOUN
cana-4548	231	76	as	as	SCONJ
cana-4548	231	77	follows	follow	VERB
cana-4548	231	78	:	:	PUNCT
cana-4548	231	79	communications	communication	NOUN
cana-4548	231	80	on	on	ADP
cana-4548	231	81	applied	apply	VERB
cana-4548	231	82	nonlinear	nonlinear	ADJ
cana-4548	231	83	analysis	analysis	NOUN
cana-4548	231	84	issn	issn	NOUN
cana-4548	231	85	:	:	PUNCT
cana-4548	231	86	1074	1074	NUM
cana-4548	231	87	-	-	PUNCT
cana-4548	231	88	133x	133x	NUM
cana-4548	231	89	vol	vol	NOUN
cana-4548	231	90	32	32	NUM
cana-4548	232	1	no	no	NOUN
cana-4548	232	2	.	.	PUNCT
cana-4548	233	1	9s	9s	NUM
cana-4548	233	2	(	(	PUNCT
cana-4548	233	3	2025	2025	NUM
cana-4548	233	4	)	)	PUNCT
cana-4548	233	5	2688	2688	NUM
cana-4548	233	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4548	233	7	property	property	NOUN
cana-4548	233	8	4	4	NUM
cana-4548	233	9	.	.	PUNCT
cana-4548	234	1	(	(	PUNCT
cana-4548	234	2	idempotency	idempotency	NOUN
cana-4548	234	3	)	)	PUNCT
cana-4548	234	4	let	let	VERB
cana-4548	234	5	𝛼𝑗	𝛼𝑗	PROPN
cana-4548	234	6	=	=	SYM
cana-4548	234	7	⟨𝜇𝛼𝑗	⟨𝜇𝛼𝑗	PROPN
cana-4548	234	8	,	,	PUNCT
cana-4548	234	9	𝜂𝛼𝑗	𝜂𝛼𝑗	VERB
cana-4548	234	10	,	,	PUNCT
cana-4548	234	11	𝜈𝛼𝑗	𝜈𝛼𝑗	VERB
cana-4548	234	12	⟩	⟩	NOUN
cana-4548	234	13	(	(	PUNCT
cana-4548	234	14	𝑗	𝑗	NOUN
cana-4548	234	15	=	=	SYM
cana-4548	234	16	1,2	1,2	NUM
cana-4548	234	17	,	,	PUNCT
cana-4548	234	18	…	…	PUNCT
cana-4548	234	19	,	,	PUNCT
cana-4548	234	20	𝑛	𝑛	X
cana-4548	234	21	)	)	PUNCT
cana-4548	234	22	be	be	VERB
cana-4548	234	23	a	a	DET
cana-4548	234	24	set	set	NOUN
cana-4548	234	25	of	of	ADP
cana-4548	234	26	pfn	pfn	NOUN
cana-4548	234	27	,	,	PUNCT
cana-4548	234	28	if	if	SCONJ
cana-4548	234	29	𝛼𝑗	𝛼𝑗	PROPN
cana-4548	234	30	=	=	PUNCT
cana-4548	234	31	𝛼	𝛼	X
cana-4548	234	32	=	=	SYM
cana-4548	234	33	(	(	PUNCT
cana-4548	234	34	𝜇	𝜇	ADP
cana-4548	234	35	,	,	PUNCT
cana-4548	234	36	𝜂	𝜂	PROPN
cana-4548	234	37	,	,	PUNCT
cana-4548	234	38	𝜈	𝜈	X
cana-4548	234	39	)	)	PUNCT
cana-4548	234	40	then	then	ADV
cana-4548	234	41	pfsspowg(𝛼1	pfsspowg(𝛼1	PROPN
cana-4548	234	42	,	,	PUNCT
cana-4548	234	43	𝛼2	𝛼2	VERB
cana-4548	234	44	,	,	PUNCT
cana-4548	234	45	…	…	PUNCT
cana-4548	234	46	,	,	PUNCT
cana-4548	234	47	𝛼𝑛	𝛼𝑛	PROPN
cana-4548	234	48	)	)	PUNCT
cana-4548	234	49	=	=	PUNCT
cana-4548	234	50	𝛼	𝛼	NOUN
cana-4548	234	51	property	property	NOUN
cana-4548	234	52	5	5	NUM
cana-4548	234	53	.	.	PUNCT
cana-4548	235	1	(	(	PUNCT
cana-4548	235	2	monotonicity	monotonicity	NOUN
cana-4548	235	3	)	)	PUNCT
cana-4548	235	4	let	let	VERB
cana-4548	235	5	𝛼𝑗	𝛼𝑗	PROPN
cana-4548	235	6	=	=	SYM
cana-4548	235	7	⟨𝜇𝛼𝑗	⟨𝜇𝛼𝑗	PROPN
cana-4548	235	8	,	,	PUNCT
cana-4548	235	9	𝜂𝛼𝑗	𝜂𝛼𝑗	VERB
cana-4548	235	10	,	,	PUNCT
cana-4548	235	11	𝜈𝛼𝑗	𝜈𝛼𝑗	VERB
cana-4548	235	12	⟩	⟩	NOUN
cana-4548	235	13	and	and	CCONJ
cana-4548	235	14	𝛼𝑗	𝛼𝑗	PROPN
cana-4548	236	1	′	′	NUM
cana-4548	237	1	=	=	PUNCT
cana-4548	237	2	⟨𝜇𝛼𝑗	⟨𝜇𝛼𝑗	PROPN
cana-4548	237	3	′	′	NOUN
cana-4548	237	4	,	,	PUNCT
cana-4548	237	5	𝜂𝛼𝑗	𝜂𝛼𝑗	ADP
cana-4548	237	6	′	′	NOUN
cana-4548	237	7	,	,	PUNCT
cana-4548	237	8	𝜈𝛼𝑗	𝜈𝛼𝑗	VERB
cana-4548	237	9	′	′	NUM
cana-4548	237	10	⟩	⟩	PROPN
cana-4548	237	11	𝛼𝑗	𝛼𝑗	PROPN
cana-4548	237	12	′(𝑗	′(𝑗	NOUN
cana-4548	237	13	=	=	NOUN
cana-4548	237	14	1,2	1,2	NUM
cana-4548	237	15	,	,	PUNCT
cana-4548	237	16	…	…	PUNCT
cana-4548	237	17	,	,	PUNCT
cana-4548	237	18	𝑛	𝑛	NOUN
cana-4548	237	19	)	)	PUNCT
cana-4548	237	20	as	as	ADP
cana-4548	237	21	two	two	NUM
cana-4548	237	22	sets	set	NOUN
cana-4548	237	23	of	of	ADP
cana-4548	237	24	pfn	pfn	NOUN
cana-4548	237	25	;	;	PUNCT
cana-4548	237	26	and	and	CCONJ
cana-4548	237	27	𝜇𝑗	𝜇𝑗	X
cana-4548	237	28	≤	≤	NUM
cana-4548	237	29	𝜇𝑗	𝜇𝑗	NOUN
cana-4548	237	30	′	′	NUM
cana-4548	237	31	,	,	PUNCT
cana-4548	237	32	𝜂𝑗	𝜂𝑗	NOUN
cana-4548	237	33	′	′	NOUN
cana-4548	237	34	≤	≤	NOUN
cana-4548	237	35	𝜂𝑗	𝜂𝑗	ADP
cana-4548	237	36	and	and	CCONJ
cana-4548	237	37	𝜈𝑗	𝜈𝑗	PROPN
cana-4548	237	38	′	′	NOUN
cana-4548	237	39	≤	≤	PROPN
cana-4548	238	1	𝜈𝑗	𝜈𝑗	ADP
cana-4548	238	2	then	then	ADV
cana-4548	238	3	pfsspowg(𝛼1	pfsspowg(𝛼1	PROPN
cana-4548	238	4	,	,	PUNCT
cana-4548	238	5	𝛼2	𝛼2	VERB
cana-4548	238	6	,	,	PUNCT
cana-4548	238	7	…	…	PUNCT
cana-4548	238	8	,	,	PUNCT
cana-4548	238	9	𝛼𝑛	𝛼𝑛	PROPN
cana-4548	238	10	)	)	PUNCT
cana-4548	238	11	≤	≤	NUM
cana-4548	238	12	pfsspowg(𝛼1	pfsspowg(𝛼1	NOUN
cana-4548	238	13	′	′	NUM
cana-4548	238	14	,	,	PUNCT
cana-4548	238	15	𝛼2	𝛼2	PROPN
cana-4548	238	16	′	′	NUM
cana-4548	238	17	,	,	PUNCT
cana-4548	238	18	…	…	PUNCT
cana-4548	238	19	,	,	PUNCT
cana-4548	238	20	𝛼𝑛	𝛼𝑛	ADP
cana-4548	238	21	′	′	NUM
cana-4548	238	22	)	)	PUNCT
cana-4548	239	1	property	property	NOUN
cana-4548	239	2	6	6	NUM
cana-4548	239	3	.	.	PUNCT
cana-4548	240	1	(	(	PUNCT
cana-4548	240	2	boundedness	boundedness	NOUN
cana-4548	240	3	)	)	PUNCT
cana-4548	240	4	let	let	VERB
cana-4548	240	5	𝛼𝑗	𝛼𝑗	PROPN
cana-4548	240	6	=	=	SYM
cana-4548	240	7	⟨𝜇𝛼𝑗	⟨𝜇𝛼𝑗	PROPN
cana-4548	240	8	,	,	PUNCT
cana-4548	240	9	𝜂𝛼𝑗	𝜂𝛼𝑗	VERB
cana-4548	240	10	,	,	PUNCT
cana-4548	240	11	𝜈𝛼𝑗	𝜈𝛼𝑗	VERB
cana-4548	240	12	⟩	⟩	NOUN
cana-4548	240	13	(	(	PUNCT
cana-4548	240	14	𝑗	𝑗	NOUN
cana-4548	240	15	=	=	SYM
cana-4548	240	16	1,2	1,2	NUM
cana-4548	240	17	,	,	PUNCT
cana-4548	240	18	…	…	PUNCT
cana-4548	240	19	,	,	PUNCT
cana-4548	240	20	𝑛	𝑛	X
cana-4548	240	21	)	)	PUNCT
cana-4548	240	22	be	be	VERB
cana-4548	240	23	a	a	DET
cana-4548	240	24	set	set	NOUN
cana-4548	240	25	of	of	ADP
cana-4548	240	26	pfn	pfn	PROPN
cana-4548	240	27	,	,	PUNCT
cana-4548	240	28	and	and	CCONJ
cana-4548	240	29	𝛼+	𝛼+	ADJ
cana-4548	240	30	=	=	PUNCT
cana-4548	240	31	(	(	PUNCT
cana-4548	240	32	max𝜇𝑗𝑗=1	max𝜇𝑗𝑗=1	NOUN
cana-4548	240	33	𝑛	𝑛	PROPN
cana-4548	240	34	,	,	PUNCT
cana-4548	240	35	min𝜂𝑗𝑗=1	min𝜂𝑗𝑗=1	PROPN
cana-4548	240	36	𝑛	𝑛	VERB
cana-4548	240	37	,	,	PUNCT
cana-4548	240	38	min𝜈𝑗𝑗=1	min𝜈𝑗𝑗=1	PROPN
cana-4548	240	39	𝑛	𝑛	PROPN
cana-4548	240	40	)	)	PUNCT
cana-4548	240	41	,	,	PUNCT
cana-4548	240	42	𝛼−	𝛼−	NOUN
cana-4548	240	43	=	=	PUNCT
cana-4548	240	44	(	(	PUNCT
cana-4548	240	45	min𝜇𝑗𝑗=1	min𝜇𝑗𝑗=1	NOUN
cana-4548	240	46	𝑛	𝑛	PROPN
cana-4548	240	47	,	,	PUNCT
cana-4548	240	48	max𝜂𝑗𝑗=1	max𝜂𝑗𝑗=1	NOUN
cana-4548	240	49	𝑛	𝑛	ADJ
cana-4548	240	50	,	,	PUNCT
cana-4548	240	51	max𝜈𝑗𝑗=1	max𝜈𝑗𝑗=1	ADJ
cana-4548	240	52	𝑛	𝑛	NOUN
cana-4548	240	53	)	)	PUNCT
cana-4548	240	54	then	then	ADV
cana-4548	240	55	𝛼−	𝛼−	PROPN
cana-4548	240	56	≤	≤	PUNCT
cana-4548	240	57	𝑃𝐹𝑆𝑆𝑃𝑂𝑊𝐺(𝛼1	𝑃𝐹𝑆𝑆𝑃𝑂𝑊𝐺(𝛼1	PROPN
cana-4548	240	58	,	,	PUNCT
cana-4548	240	59	𝛼2	𝛼2	ADJ
cana-4548	240	60	,	,	PUNCT
cana-4548	240	61	…	…	PUNCT
cana-4548	240	62	,	,	PUNCT
cana-4548	240	63	𝛼𝑛	𝛼𝑛	PROPN
cana-4548	240	64	)	)	PUNCT
cana-4548	240	65	≤	≤	NOUN
cana-4548	240	66	𝛼+	𝛼+	VERB
cana-4548	240	67	4	4	NUM
cana-4548	240	68	.	.	PUNCT
cana-4548	241	1	an	an	DET
cana-4548	241	2	approach	approach	NOUN
cana-4548	241	3	to	to	ADP
cana-4548	241	4	solving	solve	VERB
cana-4548	241	5	a	a	DET
cana-4548	241	6	multi	multi	ADJ
cana-4548	241	7	criteria	criterion	NOUN
cana-4548	241	8	group	group	NOUN
cana-4548	241	9	decision	decision	NOUN
cana-4548	241	10	-	-	PUNCT
cana-4548	241	11	making	make	VERB
cana-4548	241	12	problem	problem	NOUN
cana-4548	241	13	with	with	ADP
cana-4548	241	14	the	the	DET
cana-4548	241	15	proposed	propose	VERB
cana-4548	241	16	operators	operator	NOUN
cana-4548	241	17	let	let	VERB
cana-4548	241	18	𝐴	𝐴	PROPN
cana-4548	241	19	=	=	SYM
cana-4548	241	20	{	{	PUNCT
cana-4548	241	21	𝐴𝑖	𝐴𝑖	PROPN
cana-4548	241	22	}	}	PUNCT
cana-4548	241	23	;	;	PUNCT
cana-4548	241	24	𝑖	𝑖	SYM
cana-4548	241	25	=	=	SYM
cana-4548	241	26	1,2	1,2	NUM
cana-4548	241	27	,	,	PUNCT
cana-4548	241	28	⋯	⋯	PROPN
cana-4548	241	29	,	,	PUNCT
cana-4548	241	30	𝑚	𝑚	PROPN
cana-4548	241	31	be	be	VERB
cana-4548	241	32	a	a	DET
cana-4548	241	33	finite	finite	ADJ
cana-4548	241	34	set	set	NOUN
cana-4548	241	35	of	of	ADP
cana-4548	241	36	alternatives	alternative	NOUN
cana-4548	241	37	and	and	CCONJ
cana-4548	241	38	𝐵	𝐵	NOUN
cana-4548	241	39	=	=	SYM
cana-4548	241	40	{	{	PUNCT
cana-4548	241	41	𝐵𝑗	𝐵𝑗	PROPN
cana-4548	241	42	}	}	PUNCT
cana-4548	241	43	;	;	PUNCT
cana-4548	241	44	𝑗	𝑗	NOUN
cana-4548	241	45	=	=	SYM
cana-4548	241	46	1,2	1,2	NUM
cana-4548	241	47	,	,	PUNCT
cana-4548	241	48	⋯	⋯	PROPN
cana-4548	241	49	,	,	PUNCT
cana-4548	241	50	𝑛	𝑛	PROPN
cana-4548	241	51	be	be	AUX
cana-4548	241	52	a	a	DET
cana-4548	241	53	finite	finite	ADJ
cana-4548	241	54	set	set	NOUN
cana-4548	241	55	of	of	ADP
cana-4548	241	56	criteria	criterion	NOUN
cana-4548	241	57	which	which	PRON
cana-4548	241	58	are	be	AUX
cana-4548	241	59	represented	represent	VERB
cana-4548	241	60	by	by	ADP
cana-4548	241	61	pfns	pfns	NOUN
cana-4548	241	62	.	.	PUNCT
cana-4548	242	1	let	let	VERB
cana-4548	242	2	𝑤	𝑤	VERB
cana-4548	242	3	=	=	SYM
cana-4548	242	4	(	(	PUNCT
cana-4548	242	5	𝑤1	𝑤1	VERB
cana-4548	242	6	,	,	PUNCT
cana-4548	242	7	𝑤2	𝑤2	NOUN
cana-4548	242	8	,	,	PUNCT
cana-4548	242	9	⋯	⋯	PROPN
cana-4548	242	10	,	,	PUNCT
cana-4548	242	11	𝑤𝑛)𝑇	𝑤𝑛)𝑇	PROPN
cana-4548	242	12	be	be	VERB
cana-4548	242	13	the	the	DET
cana-4548	242	14	weighting	weight	VERB
cana-4548	242	15	vector	vector	NOUN
cana-4548	242	16	of	of	ADP
cana-4548	242	17	the	the	DET
cana-4548	242	18	criteria	criterion	NOUN
cana-4548	242	19	𝐵	𝐵	NOUN
cana-4548	242	20	=	=	PUNCT
cana-4548	242	21	{	{	PUNCT
cana-4548	242	22	𝐵𝑗	𝐵𝑗	PROPN
cana-4548	242	23	}	}	PUNCT
cana-4548	242	24	;	;	PUNCT
cana-4548	242	25	𝑗	𝑗	NOUN
cana-4548	242	26	=	=	SYM
cana-4548	242	27	1,2	1,2	NUM
cana-4548	242	28	,	,	PUNCT
cana-4548	242	29	…	…	PUNCT
cana-4548	242	30	,	,	PUNCT
cana-4548	243	1	𝑛	𝑛	X
cana-4548	243	2	with	with	ADP
cana-4548	243	3	𝑤	𝑤	ADP
cana-4548	243	4	∈	∈	PROPN
cana-4548	244	1	[	[	X
cana-4548	244	2	0,1]and	0,1]and	X
cana-4548	244	3	∑	∑	PART
cana-4548	244	4	 	 	SPACE
cana-4548	244	5	𝑛	𝑛	PROPN
cana-4548	244	6	𝑗=1	𝑗=1	PROPN
cana-4548	244	7	𝑤𝑗	𝑤𝑗	ADP
cana-4548	244	8	=	=	SYM
cana-4548	244	9	1	1	X
cana-4548	244	10	.	.	PUNCT
cana-4548	245	1	let	let	VERB
cana-4548	245	2	𝜑	𝜑	NOUN
cana-4548	245	3	=	=	PUNCT
cana-4548	245	4	(	(	PUNCT
cana-4548	245	5	𝜑1	𝜑1	VERB
cana-4548	245	6	,	,	PUNCT
cana-4548	245	7	𝜑2	𝜑2	NOUN
cana-4548	245	8	,	,	PUNCT
cana-4548	245	9	⋯	⋯	PROPN
cana-4548	245	10	,	,	PUNCT
cana-4548	245	11	𝜑𝑟)𝑇	𝜑𝑟)𝑇	VERB
cana-4548	245	12	be	be	VERB
cana-4548	245	13	the	the	DET
cana-4548	245	14	weighting	weight	VERB
cana-4548	245	15	vector	vector	NOUN
cana-4548	245	16	of	of	ADP
cana-4548	245	17	the	the	DET
cana-4548	245	18	decision	decision	NOUN
cana-4548	245	19	-	-	PUNCT
cana-4548	245	20	makers	maker	NOUN
cana-4548	245	21	𝐶	𝐶	NOUN
cana-4548	245	22	=	=	SYM
cana-4548	245	23	{	{	PUNCT
cana-4548	245	24	𝐶𝑠	𝐶𝑠	PROPN
cana-4548	245	25	}	}	PUNCT
cana-4548	245	26	;	;	PUNCT
cana-4548	245	27	𝑠	𝑠	PROPN
cana-4548	245	28	=	=	SYM
cana-4548	245	29	1,2	1,2	NUM
cana-4548	245	30	,	,	PUNCT
cana-4548	245	31	…	…	PUNCT
cana-4548	245	32	,	,	PUNCT
cana-4548	245	33	𝑟	𝑟	X
cana-4548	245	34	with	with	ADP
cana-4548	245	35	𝜑	𝜑	PROPN
cana-4548	245	36	∈	∈	PROPN
cana-4548	246	1	[	[	X
cana-4548	246	2	0,1	0,1	NUM
cana-4548	246	3	]	]	PUNCT
cana-4548	246	4	and	and	CCONJ
cana-4548	246	5	∑	∑	ADP
cana-4548	246	6	 	 	SPACE
cana-4548	246	7	𝑛	𝑛	PROPN
cana-4548	246	8	𝑠=1	𝑠=1	PUNCT
cana-4548	246	9	𝜑𝑠	𝜑𝑠	X
cana-4548	246	10	=	=	SYM
cana-4548	246	11	1	1	NUM
cana-4548	246	12	.	.	PUNCT
cana-4548	247	1	now	now	ADV
cana-4548	247	2	,	,	PUNCT
cana-4548	247	3	the	the	DET
cana-4548	247	4	procedure	procedure	NOUN
cana-4548	247	5	for	for	ADP
cana-4548	247	6	selecting	select	VERB
cana-4548	247	7	the	the	DET
cana-4548	247	8	best	good	ADJ
cana-4548	247	9	alternative	alternative	NOUN
cana-4548	247	10	using	use	VERB
cana-4548	247	11	the	the	DET
cana-4548	247	12	proposed	propose	VERB
cana-4548	247	13	operators	operator	NOUN
cana-4548	247	14	is	be	AUX
cana-4548	247	15	explained	explain	VERB
cana-4548	247	16	step	step	NOUN
cana-4548	247	17	by	by	ADP
cana-4548	247	18	step	step	NOUN
cana-4548	247	19	.	.	PUNCT
cana-4548	248	1	decision	decision	NOUN
cana-4548	248	2	matrix	matrix	NOUN
cana-4548	249	1	𝐶𝑠	𝐶𝑠	PROPN
cana-4548	249	2	=	=	PUNCT
cana-4548	250	1	[	[	X
cana-4548	250	2	𝛼𝑖𝑗	𝛼𝑖𝑗	X
cana-4548	250	3	]	]	X
cana-4548	250	4	𝑚×𝑛	𝑚×𝑛	PROPN
cana-4548	251	1	𝐶𝑠	𝐶𝑠	PROPN
cana-4548	251	2	=	=	PUNCT
cana-4548	251	3	[	[	PUNCT
cana-4548	251	4	⟨𝛼11⟩	⟨𝛼11⟩	NOUN
cana-4548	251	5	⟨𝛼12⟩	⟨𝛼12⟩	PROPN
cana-4548	251	6	⋯	⋯	PROPN
cana-4548	251	7	⟨𝛼1𝑛⟩	⟨𝛼1𝑛⟩	PROPN
cana-4548	251	8	⟨𝛼21⟩	⟨𝛼21⟩	VERB
cana-4548	251	9	⟨𝛼22⟩	⟨𝛼22⟩	PROPN
cana-4548	251	10	⋯	⋯	ADP
cana-4548	251	11	⟨𝛼2𝑛⟩	⟨𝛼2𝑛⟩	NOUN
cana-4548	251	12	⋮	⋮	NOUN
cana-4548	251	13	⋮	⋮	PROPN
cana-4548	251	14	⋱	⋱	PUNCT
cana-4548	251	15	⋮	⋮	NOUN
cana-4548	251	16	⟨𝛼𝑚1⟩	⟨𝛼𝑚1⟩	NOUN
cana-4548	251	17	⟨𝛼𝑚2⟩	⟨𝛼𝑚2⟩	NOUN
cana-4548	251	18	⋯	⋯	PROPN
cana-4548	251	19	⟨𝛼𝑚𝑛⟩	⟨𝛼𝑚𝑛⟩	PROPN
cana-4548	251	20	]	]	PUNCT
cana-4548	251	21	step	step	NOUN
cana-4548	251	22	1	1	NUM
cana-4548	251	23	:	:	PUNCT
cana-4548	251	24	usually	usually	ADV
cana-4548	251	25	,	,	PUNCT
cana-4548	251	26	every	every	DET
cana-4548	251	27	decision	decision	NOUN
cana-4548	251	28	matrix	matrix	NOUN
cana-4548	251	29	contained	contain	VERB
cana-4548	251	30	two	two	NUM
cana-4548	251	31	types	type	NOUN
cana-4548	251	32	of	of	ADP
cana-4548	251	33	data	datum	NOUN
cana-4548	251	34	,	,	PUNCT
cana-4548	251	35	like	like	ADP
cana-4548	251	36	benefit	benefit	NOUN
cana-4548	251	37	𝐵1	𝐵1	NOUN
cana-4548	251	38	and	and	CCONJ
cana-4548	251	39	cost	cost	VERB
cana-4548	251	40	𝐵2	𝐵2	NOUN
cana-4548	251	41	type	type	NOUN
cana-4548	251	42	criterias	criteria	NOUN
cana-4548	251	43	,	,	PUNCT
cana-4548	251	44	if	if	SCONJ
cana-4548	251	45	the	the	DET
cana-4548	251	46	data	data	NOUN
cana-4548	251	47	is	be	AUX
cana-4548	251	48	cost	cost	NOUN
cana-4548	251	49	type	type	NOUN
cana-4548	251	50	criteria	criterion	NOUN
cana-4548	251	51	,	,	PUNCT
cana-4548	251	52	then	then	ADV
cana-4548	251	53	normalize	normalize	VERB
cana-4548	251	54	the	the	DET
cana-4548	251	55	svn	svn	NOUN
cana-4548	251	56	decision	decision	NOUN
cana-4548	251	57	matrix	matrix	NOUN
cana-4548	251	58	using	use	VERB
cana-4548	251	59	the	the	DET
cana-4548	251	60	following	follow	VERB
cana-4548	251	61	equation	equation	NOUN
cana-4548	251	62	10	10	NUM
cana-4548	251	63	.	.	PUNCT
cana-4548	252	1	𝑟𝑖𝑗	𝑟𝑖𝑗	PROPN
cana-4548	252	2	=	=	SYM
cana-4548	252	3	{	{	PUNCT
cana-4548	252	4	𝛼𝑖𝑗	𝛼𝑖𝑗	NOUN
cana-4548	252	5	;	;	PUNCT
cana-4548	252	6	𝑗	𝑗	PROPN
cana-4548	252	7	∈	∈	PROPN
cana-4548	252	8	𝐵1	𝐵1	NOUN
cana-4548	252	9	𝛼𝑖𝑗	𝛼𝑖𝑗	PROPN
cana-4548	252	10	𝑐	𝑐	NOUN
cana-4548	252	11	;	;	PUNCT
cana-4548	252	12	𝑗	𝑗	PRON
cana-4548	252	13	∈	∈	PROPN
cana-4548	252	14	𝐵2	𝐵2	NOUN
cana-4548	252	15	(	(	PUNCT
cana-4548	252	16	10	10	NUM
cana-4548	252	17	)	)	PUNCT
cana-4548	252	18	where	where	SCONJ
cana-4548	252	19	𝛼𝑖𝑗	𝛼𝑖𝑗	PROPN
cana-4548	252	20	𝑐	𝑐	PROPN
cana-4548	252	21	is	be	AUX
cana-4548	252	22	the	the	DET
cana-4548	252	23	complement	complement	NOUN
cana-4548	252	24	𝛼𝑖𝑗.	𝛼𝑖𝑗.	NUM
cana-4548	252	25	step	step	NOUN
cana-4548	252	26	2	2	NUM
cana-4548	252	27	:	:	PUNCT
cana-4548	252	28	aggregate	aggregate	VERB
cana-4548	252	29	all	all	DET
cana-4548	252	30	𝑠	𝑠	PRON
cana-4548	252	31	decision	decision	NOUN
cana-4548	252	32	matrixs	matrixs	NOUN
cana-4548	253	1	𝐶𝑠	𝐶𝑠	PROPN
cana-4548	253	2	,	,	PUNCT
cana-4548	253	3	𝑠	𝑠	NOUN
cana-4548	253	4	=	=	SYM
cana-4548	253	5	1,2	1,2	NUM
cana-4548	253	6	,	,	PUNCT
cana-4548	253	7	⋯	⋯	PROPN
cana-4548	253	8	,	,	PUNCT
cana-4548	253	9	𝑟	𝑟	NOUN
cana-4548	253	10	as	as	SCONJ
cana-4548	253	11	provided	provide	VERB
cana-4548	253	12	by	by	ADP
cana-4548	253	13	𝑟	𝑟	NOUN
cana-4548	253	14	experts	expert	NOUN
cana-4548	253	15	into	into	ADP
cana-4548	253	16	a	a	DET
cana-4548	253	17	collective	collective	ADJ
cana-4548	253	18	decision	decision	NOUN
cana-4548	253	19	matrix	matrix	NOUN
cana-4548	253	20	by	by	ADP
cana-4548	253	21	employing	employ	VERB
cana-4548	253	22	proposed	propose	VERB
cana-4548	253	23	operators	operator	NOUN
cana-4548	253	24	.	.	PUNCT
cana-4548	254	1	step	step	VERB
cana-4548	254	2	3	3	NUM
cana-4548	254	3	:	:	PUNCT
cana-4548	254	4	determine	determine	VERB
cana-4548	254	5	the	the	DET
cana-4548	254	6	weight	weight	NOUN
cana-4548	254	7	𝑤𝑗	𝑤𝑗	PRON
cana-4548	254	8	for	for	ADP
cana-4548	254	9	each	each	DET
cana-4548	254	10	criteria	criterion	NOUN
cana-4548	255	1	𝐶𝑗.	𝐶𝑗.	PROPN
cana-4548	255	2	in	in	ADP
cana-4548	255	3	this	this	DET
cana-4548	255	4	step	step	NOUN
cana-4548	255	5	,	,	PUNCT
cana-4548	255	6	the	the	DET
cana-4548	255	7	smart	smart	ADJ
cana-4548	255	8	is	be	AUX
cana-4548	255	9	used	use	VERB
cana-4548	255	10	to	to	PART
cana-4548	255	11	establish	establish	VERB
cana-4548	255	12	the	the	DET
cana-4548	255	13	criteria	criterion	NOUN
cana-4548	255	14	weights	weight	NOUN
cana-4548	255	15	,	,	PUNCT
cana-4548	255	16	relying	rely	VERB
cana-4548	255	17	on	on	ADP
cana-4548	255	18	the	the	DET
cana-4548	255	19	subjective	subjective	ADJ
cana-4548	255	20	judgment	judgment	NOUN
cana-4548	255	21	of	of	ADP
cana-4548	255	22	decision	decision	NOUN
cana-4548	255	23	experts	expert	NOUN
cana-4548	255	24	.	.	PUNCT
cana-4548	256	1	the	the	DET
cana-4548	256	2	decision	decision	NOUN
cana-4548	256	3	maker	maker	NOUN
cana-4548	256	4	ranks	rank	VERB
cana-4548	256	5	the	the	DET
cana-4548	256	6	criteria	criterion	NOUN
cana-4548	256	7	according	accord	VERB
cana-4548	256	8	to	to	ADP
cana-4548	256	9	their	their	PRON
cana-4548	256	10	importance	importance	NOUN
cana-4548	256	11	,	,	PUNCT
cana-4548	256	12	from	from	ADP
cana-4548	256	13	least	least	ADJ
cana-4548	256	14	to	to	ADP
cana-4548	256	15	most	most	ADV
cana-4548	256	16	significant	significant	ADJ
cana-4548	256	17	.	.	PUNCT
cana-4548	257	1	the	the	DET
cana-4548	257	2	criteria	criterion	NOUN
cana-4548	257	3	deemed	deem	VERB
cana-4548	257	4	least	least	ADV
cana-4548	257	5	important	important	ADJ
cana-4548	257	6	is	be	AUX
cana-4548	257	7	given	give	VERB
cana-4548	257	8	10	10	NUM
cana-4548	257	9	points	point	NOUN
cana-4548	257	10	,	,	PUNCT
cana-4548	257	11	while	while	SCONJ
cana-4548	257	12	the	the	DET
cana-4548	257	13	most	most	ADV
cana-4548	257	14	important	important	ADJ
cana-4548	257	15	criteria	criterion	NOUN
cana-4548	257	16	are	be	AUX
cana-4548	257	17	assigned	assign	VERB
cana-4548	257	18	100	100	NUM
cana-4548	257	19	points	point	NOUN
cana-4548	257	20	.	.	PUNCT
cana-4548	258	1	the	the	DET
cana-4548	258	2	communications	communication	NOUN
cana-4548	258	3	on	on	ADP
cana-4548	258	4	applied	apply	VERB
cana-4548	258	5	nonlinear	nonlinear	ADJ
cana-4548	258	6	analysis	analysis	NOUN
cana-4548	258	7	issn	issn	NOUN
cana-4548	258	8	:	:	PUNCT
cana-4548	258	9	1074	1074	NUM
cana-4548	258	10	-	-	PUNCT
cana-4548	258	11	133x	133x	NUM
cana-4548	258	12	vol	vol	NOUN
cana-4548	258	13	32	32	NUM
cana-4548	258	14	no	no	NOUN
cana-4548	258	15	.	.	PUNCT
cana-4548	259	1	9s	9s	NUM
cana-4548	259	2	(	(	PUNCT
cana-4548	259	3	2025	2025	NUM
cana-4548	259	4	)	)	PUNCT
cana-4548	259	5	2689	2689	NUM
cana-4548	259	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4548	259	7	remaining	remain	VERB
cana-4548	259	8	criteria	criterion	NOUN
cana-4548	259	9	receive	receive	VERB
cana-4548	259	10	points	point	NOUN
cana-4548	259	11	in	in	ADP
cana-4548	259	12	ascending	ascend	VERB
cana-4548	259	13	order	order	NOUN
cana-4548	259	14	based	base	VERB
cana-4548	259	15	on	on	ADP
cana-4548	259	16	their	their	PRON
cana-4548	259	17	relative	relative	ADJ
cana-4548	259	18	importance	importance	NOUN
cana-4548	259	19	.	.	PUNCT
cana-4548	260	1	finally	finally	ADV
cana-4548	260	2	,	,	PUNCT
cana-4548	260	3	the	the	DET
cana-4548	260	4	weight	weight	NOUN
cana-4548	260	5	of	of	ADP
cana-4548	260	6	each	each	DET
cana-4548	260	7	criteria	criterion	NOUN
cana-4548	260	8	is	be	AUX
cana-4548	260	9	calculated	calculate	VERB
cana-4548	260	10	by	by	ADP
cana-4548	260	11	normalizing	normalize	VERB
cana-4548	260	12	the	the	DET
cana-4548	260	13	total	total	ADJ
cana-4548	260	14	points	point	NOUN
cana-4548	260	15	so	so	SCONJ
cana-4548	260	16	that	that	SCONJ
cana-4548	260	17	they	they	PRON
cana-4548	260	18	sum	sum	VERB
cana-4548	260	19	to	to	ADP
cana-4548	260	20	one	one	NUM
cana-4548	260	21	.	.	PUNCT
cana-4548	261	1	step	step	NOUN
cana-4548	261	2	4	4	NUM
cana-4548	261	3	:	:	PUNCT
cana-4548	261	4	aggregate	aggregate	ADJ
cana-4548	261	5	pfns	pfns	NOUN
cana-4548	261	6	by	by	ADP
cana-4548	261	7	using	use	VERB
cana-4548	261	8	proposed	propose	VERB
cana-4548	261	9	operators	operator	NOUN
cana-4548	261	10	.	.	PUNCT
cana-4548	262	1	step	step	NOUN
cana-4548	262	2	5	5	NUM
cana-4548	262	3	:	:	PUNCT
cana-4548	262	4	calculate	calculate	VERB
cana-4548	262	5	the	the	DET
cana-4548	262	6	score	score	NOUN
cana-4548	262	7	value	value	NOUN
cana-4548	262	8	for	for	ADP
cana-4548	262	9	each	each	DET
cana-4548	262	10	{	{	PUNCT
cana-4548	262	11	𝐴𝑖	𝐴𝑖	PROPN
cana-4548	262	12	}	}	PUNCT
cana-4548	262	13	.	.	PUNCT
cana-4548	263	1	if	if	SCONJ
cana-4548	263	2	𝑆(𝐴𝑖	𝑆(𝐴𝑖	NUM
cana-4548	263	3	)	)	PUNCT
cana-4548	264	1	=	=	SYM
cana-4548	264	2	𝑆(𝐴𝑗	𝑆(𝐴𝑗	NOUN
cana-4548	264	3	)	)	PUNCT
cana-4548	264	4	then	then	ADV
cana-4548	264	5	calculate	calculate	VERB
cana-4548	264	6	the	the	DET
cana-4548	264	7	accuracy	accuracy	NOUN
cana-4548	264	8	value	value	NOUN
cana-4548	264	9	.	.	PUNCT
cana-4548	265	1	step	step	NOUN
cana-4548	265	2	6	6	NUM
cana-4548	265	3	:	:	PUNCT
cana-4548	265	4	the	the	DET
cana-4548	265	5	best	good	ADJ
cana-4548	265	6	alternative	alternative	NOUN
cana-4548	265	7	is	be	AUX
cana-4548	265	8	selected	select	VERB
cana-4548	265	9	by	by	ADP
cana-4548	265	10	ranking	rank	VERB
cana-4548	265	11	the	the	DET
cana-4548	265	12	alternatives	alternative	NOUN
cana-4548	265	13	based	base	VERB
cana-4548	265	14	on	on	ADP
cana-4548	265	15	their	their	PRON
cana-4548	265	16	score	score	NOUN
cana-4548	265	17	and	and	CCONJ
cana-4548	265	18	accuracy	accuracy	NOUN
cana-4548	265	19	values	value	NOUN
cana-4548	265	20	of	of	ADP
cana-4548	265	21	𝐴𝑖.	𝐴𝑖.	PROPN
cana-4548	265	22	the	the	DET
cana-4548	265	23	proposed	propose	VERB
cana-4548	265	24	framework	framework	NOUN
cana-4548	265	25	's	's	PART
cana-4548	265	26	workflow	workflow	NOUN
cana-4548	265	27	is	be	AUX
cana-4548	265	28	illustrated	illustrate	VERB
cana-4548	265	29	in	in	ADP
cana-4548	265	30	figure	figure	NOUN
cana-4548	265	31	4	4	NUM
cana-4548	265	32	5	5	NUM
cana-4548	265	33	numerical	numerical	ADJ
cana-4548	265	34	example	example	NOUN
cana-4548	265	35	the	the	DET
cana-4548	265	36	proposed	propose	VERB
cana-4548	265	37	operators	operator	NOUN
cana-4548	265	38	are	be	AUX
cana-4548	265	39	examined	examine	VERB
cana-4548	265	40	through	through	ADP
cana-4548	265	41	a	a	DET
cana-4548	265	42	numerical	numerical	ADJ
cana-4548	265	43	example	example	NOUN
cana-4548	265	44	from	from	ADP
cana-4548	265	45	the	the	DET
cana-4548	265	46	decision	decision	NOUN
cana-4548	265	47	-	-	PUNCT
cana-4548	265	48	making	make	VERB
cana-4548	265	49	field	field	NOUN
cana-4548	265	50	,	,	PUNCT
cana-4548	265	51	as	as	SCONJ
cana-4548	265	52	outlined	outline	VERB
cana-4548	265	53	below	below	ADV
cana-4548	265	54	:	:	PUNCT
cana-4548	265	55	this	this	DET
cana-4548	265	56	section	section	NOUN
cana-4548	265	57	illustrates	illustrate	VERB
cana-4548	265	58	the	the	DET
cana-4548	265	59	selection	selection	NOUN
cana-4548	265	60	of	of	ADP
cana-4548	265	61	a	a	DET
cana-4548	265	62	road	road	NOUN
cana-4548	265	63	construction	construction	NOUN
cana-4548	265	64	companies	company	NOUN
cana-4548	265	65	to	to	PART
cana-4548	265	66	show	show	VERB
cana-4548	265	67	the	the	DET
cana-4548	265	68	applicability	applicability	NOUN
cana-4548	265	69	of	of	ADP
cana-4548	265	70	magdm	magdm	NOUN
cana-4548	265	71	based	base	VERB
cana-4548	265	72	on	on	ADP
cana-4548	265	73	the	the	DET
cana-4548	265	74	proposed	propose	VERB
cana-4548	265	75	operators	operator	NOUN
cana-4548	265	76	.	.	PUNCT
cana-4548	266	1	selecting	select	VERB
cana-4548	266	2	the	the	DET
cana-4548	266	3	right	right	ADJ
cana-4548	266	4	road	road	NOUN
cana-4548	266	5	construction	construction	NOUN
cana-4548	266	6	company	company	NOUN
cana-4548	266	7	is	be	AUX
cana-4548	266	8	a	a	DET
cana-4548	266	9	crucial	crucial	ADJ
cana-4548	266	10	step	step	NOUN
cana-4548	266	11	for	for	ADP
cana-4548	266	12	governments	government	NOUN
cana-4548	266	13	and	and	CCONJ
cana-4548	266	14	enterprises	enterprise	NOUN
cana-4548	266	15	to	to	PART
cana-4548	266	16	ensure	ensure	VERB
cana-4548	266	17	infrastructure	infrastructure	NOUN
cana-4548	266	18	projects	project	NOUN
cana-4548	266	19	are	be	AUX
cana-4548	266	20	completed	complete	VERB
cana-4548	266	21	efficiently	efficiently	ADV
cana-4548	266	22	and	and	CCONJ
cana-4548	266	23	to	to	ADP
cana-4548	266	24	high	high	ADJ
cana-4548	266	25	standards	standard	NOUN
cana-4548	266	26	.	.	PUNCT
cana-4548	267	1	suppose	suppose	VERB
cana-4548	267	2	a	a	DET
cana-4548	267	3	government	government	NOUN
cana-4548	267	4	agency	agency	NOUN
cana-4548	267	5	is	be	AUX
cana-4548	267	6	responsible	responsible	ADJ
cana-4548	267	7	for	for	ADP
cana-4548	267	8	developing	develop	VERB
cana-4548	267	9	new	new	ADJ
cana-4548	267	10	roads	road	NOUN
cana-4548	267	11	in	in	ADP
cana-4548	267	12	an	an	DET
cana-4548	267	13	urban	urban	ADJ
cana-4548	267	14	area	area	NOUN
cana-4548	267	15	.	.	PUNCT
cana-4548	268	1	these	these	DET
cana-4548	268	2	projects	project	NOUN
cana-4548	268	3	often	often	ADV
cana-4548	268	4	require	require	VERB
cana-4548	268	5	careful	careful	ADJ
cana-4548	268	6	consideration	consideration	NOUN
cana-4548	268	7	of	of	ADP
cana-4548	268	8	multiple	multiple	ADJ
cana-4548	268	9	factors	factor	NOUN
cana-4548	268	10	,	,	PUNCT
cana-4548	268	11	including	include	VERB
cana-4548	268	12	cost	cost	NOUN
cana-4548	268	13	𝐵1	𝐵1	NOUN
cana-4548	268	14	,	,	PUNCT
cana-4548	268	15	quality	quality	NOUN
cana-4548	268	16	𝐵2	𝐵2	NOUN
cana-4548	268	17	,	,	PUNCT
cana-4548	268	18	time	time	NOUN
cana-4548	268	19	𝐵3	𝐵3	PROPN
cana-4548	268	20	,	,	PUNCT
cana-4548	268	21	flexibility	flexibility	NOUN
cana-4548	268	22	𝐵4	𝐵4	NOUN
cana-4548	268	23	,	,	PUNCT
cana-4548	268	24	and	and	CCONJ
cana-4548	268	25	environmental	environmental	ADJ
cana-4548	268	26	impact	impact	NOUN
cana-4548	268	27	𝐵5	𝐵5	NOUN
cana-4548	268	28	.	.	PUNCT
cana-4548	269	1	to	to	PART
cana-4548	269	2	evaluate	evaluate	VERB
cana-4548	269	3	the	the	DET
cana-4548	269	4	five	five	NUM
cana-4548	269	5	companies	company	NOUN
cana-4548	269	6	,	,	PUNCT
cana-4548	269	7	𝐴2	𝐴2	PROPN
cana-4548	269	8	,	,	PUNCT
cana-4548	269	9	𝐴2	𝐴2	PROPN
cana-4548	269	10	,	,	PUNCT
cana-4548	269	11	𝐴3	𝐴3	PROPN
cana-4548	269	12	,	,	PUNCT
cana-4548	269	13	𝐴4	𝐴4	PROPN
cana-4548	269	14	,	,	PUNCT
cana-4548	269	15	and	and	CCONJ
cana-4548	269	16	𝐴5	𝐴5	PROPN
cana-4548	269	17	.	.	PUNCT
cana-4548	270	1	by	by	ADP
cana-4548	270	2	applying	apply	VERB
cana-4548	270	3	the	the	DET
cana-4548	270	4	developed	develop	VERB
cana-4548	270	5	algorithm	algorithm	NOUN
cana-4548	270	6	for	for	ADP
cana-4548	270	7	the	the	DET
cana-4548	270	8	best	good	ADJ
cana-4548	270	9	road	road	NOUN
cana-4548	270	10	construction	construction	NOUN
cana-4548	270	11	companies	company	NOUN
cana-4548	270	12	,	,	PUNCT
cana-4548	270	13	the	the	DET
cana-4548	270	14	group	group	NOUN
cana-4548	270	15	decision	decision	NOUN
cana-4548	270	16	makers	maker	NOUN
cana-4548	270	17	process	process	NOUN
cana-4548	270	18	ensures	ensure	VERB
cana-4548	270	19	that	that	SCONJ
cana-4548	270	20	all	all	DET
cana-4548	270	21	necessary	necessary	ADJ
cana-4548	270	22	steps	step	NOUN
cana-4548	270	23	are	be	AUX
cana-4548	270	24	followed	follow	VERB
cana-4548	270	25	to	to	PART
cana-4548	270	26	choose	choose	VERB
cana-4548	270	27	the	the	DET
cana-4548	270	28	most	most	ADJ
cana-4548	270	29	companies	company	NOUN
cana-4548	270	30	.	.	PUNCT
cana-4548	271	1	the	the	DET
cana-4548	271	2	weights	weight	NOUN
cana-4548	271	3	assigned	assign	VERB
cana-4548	271	4	by	by	ADP
cana-4548	271	5	the	the	DET
cana-4548	271	6	decision	decision	NOUN
cana-4548	271	7	makers	maker	NOUN
cana-4548	271	8	are	be	AUX
cana-4548	271	9	specified	specify	VERB
cana-4548	271	10	as	as	ADP
cana-4548	271	11	𝜑	𝜑	X
cana-4548	271	12	=	=	SYM
cana-4548	271	13	(	(	PUNCT
cana-4548	271	14	0.25,0.45,0.3	0.25,0.45,0.3	NUM
cana-4548	271	15	)	)	PUNCT
cana-4548	271	16	.	.	PUNCT
cana-4548	272	1	gather	gather	VERB
cana-4548	272	2	the	the	DET
cana-4548	272	3	decision	decision	NOUN
cana-4548	272	4	makers	maker	NOUN
cana-4548	272	5	'	'	PART
cana-4548	272	6	opinions	opinion	NOUN
cana-4548	272	7	under	under	ADP
cana-4548	272	8	pf	pf	PROPN
cana-4548	272	9	environment	environment	NOUN
cana-4548	272	10	are	be	AUX
cana-4548	272	11	listed	list	VERB
cana-4548	272	12	in	in	ADP
cana-4548	272	13	table	table	NOUN
cana-4548	272	14	2,3	2,3	NUM
cana-4548	272	15	and	and	CCONJ
cana-4548	272	16	4	4	NUM
cana-4548	272	17	shows	show	VERB
cana-4548	272	18	the	the	DET
cana-4548	272	19	decision	decision	NOUN
cana-4548	272	20	matrices	matrix	NOUN
cana-4548	272	21	.	.	PUNCT
cana-4548	273	1	figure	figure	VERB
cana-4548	273	2	4	4	NUM
cana-4548	273	3	:	:	PUNCT
cana-4548	273	4	flowchart	flowchart	NOUN
cana-4548	273	5	for	for	ADP
cana-4548	273	6	pfmcgdm	pfmcgdm	NOUN
cana-4548	273	7	communications	communication	NOUN
cana-4548	273	8	on	on	ADP
cana-4548	273	9	applied	apply	VERB
cana-4548	273	10	nonlinear	nonlinear	ADJ
cana-4548	273	11	analysis	analysis	NOUN
cana-4548	273	12	issn	issn	NOUN
cana-4548	273	13	:	:	PUNCT
cana-4548	273	14	1074	1074	NUM
cana-4548	273	15	-	-	PUNCT
cana-4548	273	16	133x	133x	NUM
cana-4548	273	17	vol	vol	NOUN
cana-4548	273	18	32	32	NUM
cana-4548	274	1	no	no	NOUN
cana-4548	274	2	.	.	PUNCT
cana-4548	275	1	9s	9s	NUM
cana-4548	275	2	(	(	PUNCT
cana-4548	275	3	2025	2025	NUM
cana-4548	275	4	)	)	PUNCT
cana-4548	275	5	2690	2690	NUM
cana-4548	276	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-4548	276	2	table	table	NOUN
cana-4548	276	3	2	2	NUM
cana-4548	276	4	:	:	PUNCT
cana-4548	276	5	decision	decision	NOUN
cana-4548	276	6	matrix	matrix	NOUN
cana-4548	276	7	derived	derive	VERB
cana-4548	276	8	from	from	ADP
cana-4548	276	9	the	the	DET
cana-4548	276	10	decision	decision	NOUN
cana-4548	276	11	maker	maker	NOUN
cana-4548	276	12	𝑪𝟏	𝑪𝟏	NOUN
cana-4548	276	13	𝐵1	𝐵1	PROPN
cana-4548	276	14	𝐵2	𝐵2	PROPN
cana-4548	276	15	𝐵3	𝐵3	PROPN
cana-4548	276	16	𝐵4	𝐵4	PROPN
cana-4548	276	17	𝐵5	𝐵5	VERB
cana-4548	276	18	𝐴1	𝐴1	PROPN
cana-4548	277	1	⟨0.10,0.20,0.40⟩	⟨0.10,0.20,0.40⟩	PROPN
cana-4548	277	2	⟨0.60,0.05,0.10⟩	⟨0.60,0.05,0.10⟩	PROPN
cana-4548	277	3	⟨0.50,0.10,0.33⟩	⟨0.50,0.10,0.33⟩	PROPN
cana-4548	277	4	⟨0.54,0.23,0.14⟩	⟨0.54,0.23,0.14⟩	PROPN
cana-4548	277	5	⟨0.60,0.20,0.10⟩	⟨0.60,0.20,0.10⟩	PROPN
cana-4548	277	6	𝐴2	𝐴2	PROPN
cana-4548	277	7	⟨0.10,0.20,0.40⟩	⟨0.10,0.20,0.40⟩	PROPN
cana-4548	277	8	⟨0.50,0.10,0.10⟩	⟨0.50,0.10,0.10⟩	PROPN
cana-4548	278	1	⟨0.80,0.04,0.10⟩	⟨0.80,0.04,0.10⟩	PROPN
cana-4548	278	2	⟨0.55,0.20,0.15⟩	⟨0.55,0.20,0.15⟩	PROPN
cana-4548	278	3	⟨0.70,0.10,0.05⟩	⟨0.70,0.10,0.05⟩	PROPN
cana-4548	278	4	𝐴3	𝐴3	PROPN
cana-4548	278	5	⟨040,0.10,0.10⟩	⟨040,0.10,0.10⟩	PROPN
cana-4548	278	6	⟨0.10,0.20,0.40⟩	⟨0.10,0.20,0.40⟩	PROPN
cana-4548	278	7	⟨0.70,0.10,0.02⟩	⟨0.70,0.10,0.02⟩	ADJ
cana-4548	278	8	⟨0.50,0.10,0.30⟩	⟨0.50,0.10,0.30⟩	X
cana-4548	279	1	⟨0.30,0.40,0.20⟩	⟨0.30,0.40,0.20⟩	PROPN
cana-4548	279	2	𝐴4	𝐴4	NOUN
cana-4548	279	3	⟨0.40,0.20,0.30⟩	⟨0.40,0.20,0.30⟩	PROPN
cana-4548	279	4	⟨0.50,0.10,0.15⟩	⟨0.50,0.10,0.15⟩	X
cana-4548	279	5	⟨0.10,0.20,0.40⟩	⟨0.10,0.20,0.40⟩	PROPN
cana-4548	279	6	⟨0.10,0.20,0.40⟩	⟨0.10,0.20,0.40⟩	PROPN
cana-4548	279	7	⟨0.50,0.20,0.05⟩	⟨0.50,0.20,0.05⟩	PROPN
cana-4548	279	8	𝐴5	𝐴5	NOUN
cana-4548	279	9	⟨0.10,0.20,0.40⟩	⟨0.10,0.20,0.40⟩	PROPN
cana-4548	279	10	⟨0.20,0.04,0.06⟩	⟨0.20,0.04,0.06⟩	PROPN
cana-4548	279	11	⟨0.60,0.04,0.05⟩	⟨0.60,0.04,0.05⟩	NOUN
cana-4548	279	12	⟨0.80,0.03,0.06⟩	⟨0.80,0.03,0.06⟩	NOUN
cana-4548	279	13	⟨0.25,0.04,0.50⟩	⟨0.25,0.04,0.50⟩	NOUN
cana-4548	279	14	table	table	NOUN
cana-4548	279	15	3	3	NUM
cana-4548	279	16	:	:	PUNCT
cana-4548	279	17	decision	decision	NOUN
cana-4548	279	18	matrix	matrix	NOUN
cana-4548	279	19	derived	derive	VERB
cana-4548	279	20	from	from	ADP
cana-4548	279	21	the	the	DET
cana-4548	279	22	decision	decision	NOUN
cana-4548	279	23	maker	maker	NOUN
cana-4548	279	24	𝑪𝟐	𝑪𝟐	PROPN
cana-4548	279	25	𝐵1	𝐵1	PROPN
cana-4548	279	26	𝐵2	𝐵2	PROPN
cana-4548	279	27	𝐵3	𝐵3	PROPN
cana-4548	279	28	𝐵4	𝐵4	PROPN
cana-4548	279	29	𝐵5	𝐵5	VERB
cana-4548	279	30	𝐴1	𝐴1	PROPN
cana-4548	279	31	⟨0.10,0.20,0.40⟩	⟨0.10,0.20,0.40⟩	PROPN
cana-4548	279	32	⟨0.20,0.04,0.06⟩	⟨0.20,0.04,0.06⟩	PROPN
cana-4548	279	33	⟨0.60,0.04,0.05⟩	⟨0.60,0.04,0.05⟩	NOUN
cana-4548	279	34	⟨0.80,0.03,0.06⟩	⟨0.80,0.03,0.06⟩	NOUN
cana-4548	279	35	⟨0.25,0.04,0.50⟩	⟨0.25,0.04,0.50⟩	NOUN
cana-4548	279	36	𝐴2	𝐴2	PROPN
cana-4548	279	37	⟨0.40,0.20,0.30⟩	⟨0.40,0.20,0.30⟩	NUM
cana-4548	279	38	⟨0.50,0.10,0.15⟩	⟨0.50,0.10,0.15⟩	X
cana-4548	279	39	⟨0.10,0.20,0.40⟩	⟨0.10,0.20,0.40⟩	PROPN
cana-4548	279	40	⟨0.10,0.20,0.40⟩	⟨0.10,0.20,0.40⟩	PROPN
cana-4548	279	41	⟨0.50,0.20,0.05⟩	⟨0.50,0.20,0.05⟩	PROPN
cana-4548	279	42	𝐴3	𝐴3	PROPN
cana-4548	279	43	⟨040,0.10,0.10⟩	⟨040,0.10,0.10⟩	NOUN
cana-4548	279	44	⟨0.10,0.20,0.40⟩	⟨0.10,0.20,0.40⟩	PROPN
cana-4548	279	45	⟨0.70,0.10,0.02⟩	⟨0.70,0.10,0.02⟩	ADJ
cana-4548	279	46	⟨0.50,0.10,0.30⟩	⟨0.50,0.10,0.30⟩	X
cana-4548	279	47	⟨0.30,0.40,0.20⟩	⟨0.30,0.40,0.20⟩	PROPN
cana-4548	279	48	𝐴4	𝐴4	VERB
cana-4548	279	49	⟨0.10,0.20,0.40⟩	⟨0.10,0.20,0.40⟩	PROPN
cana-4548	279	50	⟨0.50,0.10,0.10⟩	⟨0.50,0.10,0.10⟩	PROPN
cana-4548	280	1	⟨0.80,0.04,0.10⟩	⟨0.80,0.04,0.10⟩	PROPN
cana-4548	280	2	⟨0.55,0.20,0.15⟩	⟨0.55,0.20,0.15⟩	PROPN
cana-4548	281	1	⟨0.70,0.10,0.05⟩	⟨0.70,0.10,0.05⟩	PROPN
cana-4548	281	2	𝐴5	𝐴5	PROPN
cana-4548	281	3	⟨0.10,0.20,0.40⟩	⟨0.10,0.20,0.40⟩	PROPN
cana-4548	281	4	⟨0.60,0.05,0.10⟩	⟨0.60,0.05,0.10⟩	PROPN
cana-4548	281	5	⟨0.50,0.10,0.33⟩	⟨0.50,0.10,0.33⟩	PROPN
cana-4548	281	6	⟨0.54,0.23,0.14⟩	⟨0.54,0.23,0.14⟩	PROPN
cana-4548	281	7	⟨0.60,0.20,0.10⟩	⟨0.60,0.20,0.10⟩	PROPN
cana-4548	281	8	table	table	NOUN
cana-4548	281	9	4	4	NUM
cana-4548	281	10	:	:	PUNCT
cana-4548	281	11	decision	decision	NOUN
cana-4548	281	12	matrix	matrix	NOUN
cana-4548	281	13	derived	derive	VERB
cana-4548	281	14	from	from	ADP
cana-4548	281	15	the	the	DET
cana-4548	281	16	decision	decision	NOUN
cana-4548	281	17	maker	maker	NOUN
cana-4548	281	18	𝑪𝟑	𝑪𝟑	PROPN
cana-4548	281	19	𝐵1	𝐵1	PROPN
cana-4548	281	20	𝐵2	𝐵2	PROPN
cana-4548	281	21	𝐵3	𝐵3	PROPN
cana-4548	281	22	𝐵4	𝐵4	PROPN
cana-4548	281	23	𝐵5	𝐵5	PROPN
cana-4548	281	24	𝐴1	𝐴1	PROPN
cana-4548	281	25	⟨0.40,0.20,0.30⟩	⟨0.40,0.20,0.30⟩	X
cana-4548	282	1	⟨0.50,0.10,0.15⟩	⟨0.50,0.10,0.15⟩	X
cana-4548	282	2	⟨0.10,0.20,0.40⟩	⟨0.10,0.20,0.40⟩	PROPN
cana-4548	282	3	⟨0.10,0.20,0.40⟩	⟨0.10,0.20,0.40⟩	PROPN
cana-4548	282	4	⟨0.50,0.20,0.05⟩	⟨0.50,0.20,0.05⟩	PROPN
cana-4548	282	5	𝐴2	𝐴2	PROPN
cana-4548	282	6	⟨0.10,0.20,0.40⟩	⟨0.10,0.20,0.40⟩	PROPN
cana-4548	282	7	⟨0.20,0.04,0.06⟩	⟨0.20,0.04,0.06⟩	PROPN
cana-4548	282	8	⟨0.60,0.04,0.05⟩	⟨0.60,0.04,0.05⟩	NOUN
cana-4548	282	9	⟨0.80,0.03,0.06⟩	⟨0.80,0.03,0.06⟩	PROPN
cana-4548	282	10	⟨0.25,0.04,0.50⟩	⟨0.25,0.04,0.50⟩	PROPN
cana-4548	282	11	𝐴3	𝐴3	PROPN
cana-4548	282	12	⟨040,0.10,0.10⟩	⟨040,0.10,0.10⟩	PROPN
cana-4548	282	13	⟨0.10,0.20,0.40⟩	⟨0.10,0.20,0.40⟩	PROPN
cana-4548	282	14	⟨0.70,0.10,0.02⟩	⟨0.70,0.10,0.02⟩	ADJ
cana-4548	282	15	⟨0.50,0.10,0.30⟩	⟨0.50,0.10,0.30⟩	X
cana-4548	282	16	⟨0.30,0.40,0.20⟩	⟨0.30,0.40,0.20⟩	PROPN
cana-4548	282	17	𝐴4	𝐴4	VERB
cana-4548	282	18	⟨0.10,0.20,0.40⟩	⟨0.10,0.20,0.40⟩	PROPN
cana-4548	282	19	⟨0.50,0.10,0.10⟩	⟨0.50,0.10,0.10⟩	PROPN
cana-4548	282	20	⟨0.80,0.04,0.10⟩	⟨0.80,0.04,0.10⟩	PROPN
cana-4548	282	21	⟨0.55,0.20,0.15⟩	⟨0.55,0.20,0.15⟩	PROPN
cana-4548	282	22	⟨0.70,0.10,0.05⟩	⟨0.70,0.10,0.05⟩	PROPN
cana-4548	282	23	𝐴5	𝐴5	PROPN
cana-4548	282	24	⟨0.10,0.20,0.40⟩	⟨0.10,0.20,0.40⟩	PROPN
cana-4548	282	25	⟨0.60,0.05,0.10⟩	⟨0.60,0.05,0.10⟩	PROPN
cana-4548	282	26	⟨0.50,0.10,0.33⟩	⟨0.50,0.10,0.33⟩	PROPN
cana-4548	282	27	⟨0.54,0.23,0.14⟩	⟨0.54,0.23,0.14⟩	PROPN
cana-4548	282	28	⟨0.60,0.20,0.10⟩	⟨0.60,0.20,0.10⟩	PROPN
cana-4548	282	29	communications	communication	NOUN
cana-4548	282	30	on	on	ADP
cana-4548	282	31	applied	apply	VERB
cana-4548	282	32	nonlinear	nonlinear	ADJ
cana-4548	282	33	analysis	analysis	NOUN
cana-4548	282	34	issn	issn	NOUN
cana-4548	282	35	:	:	PUNCT
cana-4548	282	36	1074	1074	NUM
cana-4548	282	37	-	-	PUNCT
cana-4548	282	38	133x	133x	NUM
cana-4548	282	39	vol	vol	NOUN
cana-4548	282	40	32	32	NUM
cana-4548	282	41	no	no	NOUN
cana-4548	282	42	.	.	PUNCT
cana-4548	283	1	9s	9s	NUM
cana-4548	283	2	(	(	PUNCT
cana-4548	283	3	2025	2025	NUM
cana-4548	283	4	)	)	PUNCT
cana-4548	283	5	2691	2691	NUM
cana-4548	283	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4548	283	7	5.1	5.1	NUM
cana-4548	283	8	procedure	procedure	NOUN
cana-4548	283	9	steps	step	NOUN
cana-4548	283	10	for	for	ADP
cana-4548	283	11	group	group	NOUN
cana-4548	283	12	decision	decision	NOUN
cana-4548	283	13	-	-	PUNCT
cana-4548	283	14	making	make	VERB
cana-4548	283	15	step	step	NOUN
cana-4548	283	16	1	1	NUM
cana-4548	283	17	:	:	PUNCT
cana-4548	283	18	given	give	VERB
cana-4548	283	19	that	that	SCONJ
cana-4548	283	20	the	the	DET
cana-4548	283	21	criteria	criterion	NOUN
cana-4548	283	22	are	be	AUX
cana-4548	283	23	all	all	PRON
cana-4548	283	24	benefit	benefit	NOUN
cana-4548	283	25	criteria	criterion	NOUN
cana-4548	283	26	,	,	PUNCT
cana-4548	283	27	there	there	PRON
cana-4548	283	28	is	be	VERB
cana-4548	283	29	no	no	DET
cana-4548	283	30	need	need	NOUN
cana-4548	283	31	to	to	PART
cana-4548	283	32	normalise	normalise	VERB
cana-4548	283	33	them	they	PRON
cana-4548	283	34	.	.	PUNCT
cana-4548	284	1	step	step	NOUN
cana-4548	284	2	2	2	NUM
cana-4548	284	3	:	:	PUNCT
cana-4548	284	4	to	to	PART
cana-4548	284	5	combine	combine	VERB
cana-4548	284	6	decision	decision	NOUN
cana-4548	284	7	matrices	matrix	NOUN
cana-4548	284	8	𝐶𝑠	𝐶𝑠	PROPN
cana-4548	284	9	,	,	PUNCT
cana-4548	284	10	𝑠	𝑠	PROPN
cana-4548	284	11	=	=	NOUN
cana-4548	284	12	1,2,3	1,2,3	NOUN
cana-4548	284	13	into	into	ADP
cana-4548	284	14	a	a	DET
cana-4548	284	15	collective	collective	ADJ
cana-4548	284	16	decision	decision	NOUN
cana-4548	284	17	matrix	matrix	NOUN
cana-4548	284	18	,	,	PUNCT
cana-4548	284	19	the	the	DET
cana-4548	284	20	pfsspwg	pfsspwg	NOUN
cana-4548	284	21	operator	operator	NOUN
cana-4548	284	22	is	be	AUX
cana-4548	284	23	applied	apply	VERB
cana-4548	284	24	,	,	PUNCT
cana-4548	284	25	as	as	SCONJ
cana-4548	284	26	shown	show	VERB
cana-4548	284	27	in	in	ADP
cana-4548	284	28	table	table	NOUN
cana-4548	284	29	5	5	NUM
cana-4548	284	30	,	,	PUNCT
cana-4548	284	31	with	with	ADP
cana-4548	284	32	the	the	DET
cana-4548	284	33	decision	decision	NOUN
cana-4548	284	34	maker	maker	NOUN
cana-4548	284	35	's	's	PART
cana-4548	284	36	weighting	weighting	NOUN
cana-4548	284	37	vector	vector	NOUN
cana-4548	284	38	,	,	PUNCT
cana-4548	284	39	𝜑	𝜑	X
cana-4548	284	40	=	=	SYM
cana-4548	284	41	(	(	PUNCT
cana-4548	284	42	0.25,0.45,0.43	0.25,0.45,0.43	NOUN
cana-4548	284	43	)	)	PUNCT
cana-4548	284	44	.	.	PUNCT
cana-4548	285	1	table	table	NOUN
cana-4548	285	2	5	5	NUM
cana-4548	285	3	:	:	PUNCT
cana-4548	285	4	comprehensive	comprehensive	ADJ
cana-4548	285	5	decision	decision	NOUN
cana-4548	285	6	matrix	matrix	NOUN
cana-4548	285	7	𝑪	𝑪	NOUN
cana-4548	285	8	using	use	VERB
cana-4548	285	9	pfsspwg	pfsspwg	NOUN
cana-4548	285	10	operator	operator	NOUN
cana-4548	285	11	𝐵1	𝐵1	PROPN
cana-4548	285	12	𝐵2	𝐵2	PROPN
cana-4548	285	13	𝐵3	𝐵3	PROPN
cana-4548	285	14	𝐵4	𝐵4	PROPN
cana-4548	285	15	𝐵5	𝐵5	PROPN
cana-4548	285	16	𝐴1	𝐴1	PROPN
cana-4548	285	17	⟨0.117,0.200,0.375⟩	⟨0.117,0.200,0.375⟩	PROPN
cana-4548	285	18	⟨0.130,0.200,0.362⟩	⟨0.130,0.200,0.362⟩	PROPN
cana-4548	285	19	⟨0.400	⟨0.400	PROPN
cana-4548	285	20	,	,	PUNCT
cana-4548	285	21	.100,0.100⟩	.100,0.100⟩	PROPN
cana-4548	285	22	⟨0.114,0.200,0.380⟩	⟨0.114,0.200,0.380⟩	NOUN
cana-4548	285	23	⟨0.100,0.200,0.400⟩	⟨0.100,0.200,0.400⟩	NOUN
cana-4548	285	24	𝐴2	𝐴2	NOUN
cana-4548	285	25	⟨0.278,0.062,0.099⟩	⟨0.278,0.062,0.099⟩	NOUN
cana-4548	285	26	⟨0.315,0.084,0.114⟩	⟨0.315,0.084,0.114⟩	PROPN
cana-4548	285	27	⟨0.100,0.200,0.400⟩	⟨0.100,0.200,0.400⟩	NOUN
cana-4548	285	28	⟨0.500,0.100,0.113⟩	⟨0.500,0.100,0.113⟩	NOUN
cana-4548	285	29	⟨0.351,0.048,0.091⟩	⟨0.351,0.048,0.091⟩	VERB
cana-4548	285	30	𝐴3	𝐴3	PROPN
cana-4548	285	31	⟨0.178,0.110,0.272⟩	⟨0.178,0.110,0.272⟩	PROPN
cana-4548	285	32	⟨0.152,0.118,0.264⟩	⟨0.152,0.118,0.264⟩	PROPN
cana-4548	285	33	⟨0.700,0.100,0.020⟩	⟨0.700,0.100,0.020⟩	ADJ
cana-4548	285	34	⟨0.207,0.084,0.203⟩	⟨0.207,0.084,0.203⟩	PROPN
cana-4548	285	35	⟨0.519,0.087,0.285⟩	⟨0.519,0.087,0.285⟩	PROPN
cana-4548	285	36	𝐴4	𝐴4	NOUN
cana-4548	285	37	⟨0.181,0.146,0.225⟩	⟨0.181,0.146,0.225⟩	PROPN
cana-4548	285	38	⟨0.149,0.159,0.278⟩	⟨0.149,0.159,0.278⟩	PROPN
cana-4548	285	39	⟨0.500,0.100,0.300⟩	⟨0.500,0.100,0.300⟩	VERB
cana-4548	285	40	⟨0.196,0.200,0.235⟩	⟨0.196,0.200,0.235⟩	PROPN
cana-4548	285	41	⟨0.579,0.194,0.123⟩	⟨0.579,0.194,0.123⟩	PROPN
cana-4548	285	42	𝐴5	𝐴5	NOUN
cana-4548	285	43	⟨0.337,0.142,0.351⟩	⟨0.337,0.142,0.351⟩	VERB
cana-4548	285	44	⟨0.381,0.137,0.279⟩	⟨0.381,0.137,0.279⟩	NOUN
cana-4548	285	45	⟨0.300,0.400,0.200⟩	⟨0.300,0.400,0.200⟩	NOUN
cana-4548	285	46	⟨0.630,0.128,0.050⟩	⟨0.630,0.128,0.050⟩	VERB
cana-4548	285	47	⟨0.415,0.171,0.268⟩	⟨0.415,0.171,0.268⟩	NOUN
cana-4548	285	48	step	step	NOUN
cana-4548	285	49	3	3	NUM
cana-4548	285	50	:	:	PUNCT
cana-4548	285	51	this	this	DET
cana-4548	285	52	step	step	NOUN
cana-4548	285	53	,	,	PUNCT
cana-4548	285	54	we	we	PRON
cana-4548	285	55	calculate	calculate	VERB
cana-4548	285	56	the	the	DET
cana-4548	285	57	criteria	criterion	NOUN
cana-4548	285	58	weights	weight	NOUN
cana-4548	285	59	using	use	VERB
cana-4548	285	60	smart	smart	ADJ
cana-4548	285	61	.	.	PUNCT
cana-4548	286	1	experts	expert	NOUN
cana-4548	286	2	assign	assign	VERB
cana-4548	286	3	scores	score	NOUN
cana-4548	286	4	ranging	range	VERB
cana-4548	286	5	from	from	ADP
cana-4548	286	6	10	10	NUM
cana-4548	286	7	to	to	PART
cana-4548	286	8	100	100	NUM
cana-4548	286	9	to	to	ADP
cana-4548	286	10	each	each	DET
cana-4548	286	11	criteria	criterion	NOUN
cana-4548	286	12	.	.	PUNCT
cana-4548	287	1	the	the	DET
cana-4548	287	2	normalized	normalize	VERB
cana-4548	287	3	criteria	criterion	NOUN
cana-4548	287	4	weights	weight	NOUN
cana-4548	287	5	are	be	AUX
cana-4548	287	6	then	then	ADV
cana-4548	287	7	determined	determine	VERB
cana-4548	287	8	by	by	ADP
cana-4548	287	9	dividing	divide	VERB
cana-4548	287	10	the	the	DET
cana-4548	287	11	points	point	NOUN
cana-4548	287	12	assigned	assign	VERB
cana-4548	287	13	to	to	ADP
cana-4548	287	14	each	each	DET
cana-4548	287	15	criteria	criterion	NOUN
cana-4548	287	16	by	by	ADP
cana-4548	287	17	the	the	DET
cana-4548	287	18	total	total	ADJ
cana-4548	287	19	sum	sum	NOUN
cana-4548	287	20	of	of	ADP
cana-4548	287	21	points	point	NOUN
cana-4548	287	22	.	.	PUNCT
cana-4548	288	1	table	table	NOUN
cana-4548	288	2	6	6	NUM
cana-4548	288	3	displays	display	VERB
cana-4548	288	4	the	the	DET
cana-4548	288	5	points	point	NOUN
cana-4548	288	6	allocated	allocate	VERB
cana-4548	288	7	by	by	ADP
cana-4548	288	8	each	each	DET
cana-4548	288	9	expert	expert	NOUN
cana-4548	288	10	and	and	CCONJ
cana-4548	288	11	the	the	DET
cana-4548	288	12	corresponding	corresponding	ADJ
cana-4548	288	13	normalized	normalize	VERB
cana-4548	288	14	criteria	criterion	NOUN
cana-4548	288	15	weights	weight	NOUN
cana-4548	288	16	.	.	PUNCT
cana-4548	288	17	table	table	NOUN
cana-4548	288	18	6	6	NUM
cana-4548	288	19	:	:	PUNCT
cana-4548	288	20	criteria	criterion	NOUN
cana-4548	288	21	weights	weight	NOUN
cana-4548	288	22	determined	determine	VERB
cana-4548	288	23	by	by	ADP
cana-4548	288	24	the	the	DET
cana-4548	288	25	expert	expert	NOUN
cana-4548	288	26	sussing	susse	VERB
cana-4548	288	27	smart	smart	ADJ
cana-4548	288	28	technique	technique	NOUN
cana-4548	288	29	.	.	PUNCT
cana-4548	289	1	criteria	criterion	NOUN
cana-4548	289	2	points	point	NOUN
cana-4548	289	3	assigned	assign	VERB
cana-4548	289	4	by	by	ADP
cana-4548	289	5	sum	sum	NOUN
cana-4548	289	6	of	of	ADP
cana-4548	289	7	normalized	normalize	VERB
cana-4548	289	8	𝐶1	𝐶1	PROPN
cana-4548	289	9	𝐶2	𝐶2	PROPN
cana-4548	289	10	𝐶3	𝐶3	PROPN
cana-4548	289	11	points	point	NOUN
cana-4548	289	12	weights	weight	NOUN
cana-4548	289	13	𝑤𝑗	𝑤𝑗	ADP
cana-4548	289	14	𝐵1	𝐵1	NOUN
cana-4548	289	15	80	80	NUM
cana-4548	289	16	80	80	NUM
cana-4548	289	17	80	80	NUM
cana-4548	289	18	240	240	NUM
cana-4548	289	19	0.255319	0.255319	NUM
cana-4548	289	20	𝐵2	𝐵2	NOUN
cana-4548	289	21	90	90	NUM
cana-4548	289	22	90	90	NUM
cana-4548	289	23	90	90	NUM
cana-4548	289	24	270	270	NUM
cana-4548	289	25	0.287234	0.287234	NUM
cana-4548	289	26	𝐵3	𝐵3	NOUN
cana-4548	289	27	70	70	NUM
cana-4548	289	28	70	70	NUM
cana-4548	289	29	70	70	NUM
cana-4548	289	30	210	210	NUM
cana-4548	289	31	0.223404	0.223404	NUM
cana-4548	289	32	𝐵4	𝐵4	NOUN
cana-4548	289	33	40	40	NUM
cana-4548	289	34	30	30	NUM
cana-4548	289	35	40	40	NUM
cana-4548	289	36	110	110	NUM
cana-4548	289	37	0.117021	0.117021	NUM
cana-4548	289	38	𝐵4	𝐵4	NOUN
cana-4548	289	39	40	40	NUM
cana-4548	289	40	40	40	NUM
cana-4548	289	41	30	30	NUM
cana-4548	289	42	110	110	NUM
cana-4548	289	43	0.117021	0.117021	NUM
cana-4548	289	44	total	total	NOUN
cana-4548	289	45	940	940	NUM
cana-4548	289	46	step	step	NOUN
cana-4548	289	47	4	4	NUM
cana-4548	289	48	:	:	PUNCT
cana-4548	289	49	apply	apply	VERB
cana-4548	289	50	the	the	DET
cana-4548	289	51	pfsspwg	pfsspwg	NOUN
cana-4548	289	52	operator	operator	NOUN
cana-4548	289	53	to	to	PART
cana-4548	289	54	aggregate	aggregate	VERB
cana-4548	289	55	all	all	DET
cana-4548	289	56	preference	preference	NOUN
cana-4548	289	57	values	value	NOUN
cana-4548	289	58	in	in	ADP
cana-4548	289	59	table	table	NOUN
cana-4548	289	60	7	7	NUM
cana-4548	289	61	communications	communication	NOUN
cana-4548	289	62	on	on	ADP
cana-4548	289	63	applied	apply	VERB
cana-4548	289	64	nonlinear	nonlinear	ADJ
cana-4548	289	65	analysis	analysis	NOUN
cana-4548	289	66	issn	issn	NOUN
cana-4548	289	67	:	:	PUNCT
cana-4548	289	68	1074	1074	NUM
cana-4548	289	69	-	-	PUNCT
cana-4548	289	70	133x	133x	NUM
cana-4548	289	71	vol	vol	NOUN
cana-4548	289	72	32	32	NUM
cana-4548	289	73	no	no	NOUN
cana-4548	289	74	.	.	PUNCT
cana-4548	290	1	9s	9s	NUM
cana-4548	290	2	(	(	PUNCT
cana-4548	290	3	2025	2025	NUM
cana-4548	290	4	)	)	PUNCT
cana-4548	290	5	2692	2692	NUM
cana-4548	290	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4548	290	7	table	table	NOUN
cana-4548	290	8	7	7	NUM
cana-4548	290	9	:	:	PUNCT
cana-4548	290	10	the	the	DET
cana-4548	290	11	overall	overall	ADJ
cana-4548	290	12	preference	preference	NOUN
cana-4548	290	13	value	value	NOUN
cana-4548	290	14	is	be	AUX
cana-4548	290	15	calculated	calculate	VERB
cana-4548	290	16	using	use	VERB
cana-4548	290	17	the	the	DET
cana-4548	290	18	pfsspwg	pfsspwg	NOUN
cana-4548	290	19	operator	operator	NOUN
cana-4548	290	20	pfewg	pfewg	PROPN
cana-4548	290	21	𝐴1⟨0.131,0.234,0.234⟩	𝐴1⟨0.131,0.234,0.234⟩	PROPN
cana-4548	290	22	𝐴2⟨0.184,0.233,0.233⟩	𝐴2⟨0.184,0.233,0.233⟩	ADP
cana-4548	290	23	𝐴3⟨0.204,0.228,0.228⟩	𝐴3⟨0.204,0.228,0.228⟩	PROPN
cana-4548	290	24	𝐴4⟨0.199,0.234,0.235⟩	𝐴4⟨0.199,0.234,0.235⟩	INTJ
cana-4548	290	25	𝐴5⟨0.360,0.235,0.235⟩	𝐴5⟨0.360,0.235,0.235⟩	NOUN
cana-4548	290	26	step	step	NOUN
cana-4548	290	27	5	5	NUM
cana-4548	290	28	:	:	PUNCT
cana-4548	290	29	since	since	SCONJ
cana-4548	290	30	𝑆(𝐴1	𝑆(𝐴1	NOUN
cana-4548	290	31	)	)	PUNCT
cana-4548	290	32	=	=	SYM
cana-4548	290	33	−0.336	−0.336	PROPN
cana-4548	290	34	,	,	PUNCT
cana-4548	290	35	𝑆(𝐴2	𝑆(𝐴2	NOUN
cana-4548	290	36	)	)	PUNCT
cana-4548	290	37	=	=	SYM
cana-4548	290	38	−0.282	−0.282	PROPN
cana-4548	290	39	,	,	PUNCT
cana-4548	290	40	𝑆(𝐴3	𝑆(𝐴3	NUM
cana-4548	290	41	)	)	PUNCT
cana-4548	290	42	=	=	SYM
cana-4548	291	1	−0.252	−0.252	ADJ
cana-4548	291	2	,	,	PUNCT
cana-4548	291	3	𝑆(𝐴4	𝑆(𝐴4	X
cana-4548	291	4	)	)	PUNCT
cana-4548	291	5	=	=	PUNCT
cana-4548	291	6	−0.269and	−0.269and	NUM
cana-4548	291	7	𝑆(𝐴5	𝑆(𝐴5	ADV
cana-4548	291	8	)	)	PUNCT
cana-4548	292	1	=	=	SYM
cana-4548	292	2	−0.110	−0.110	PROPN
cana-4548	292	3	.	.	PUNCT
cana-4548	293	1	step	step	VERB
cana-4548	293	2	6	6	NUM
cana-4548	293	3	:	:	PUNCT
cana-4548	293	4	the	the	DET
cana-4548	293	5	alternatives	alternative	NOUN
cana-4548	293	6	are	be	AUX
cana-4548	293	7	ranked	rank	VERB
cana-4548	293	8	according	accord	VERB
cana-4548	293	9	to	to	ADP
cana-4548	293	10	preference	preference	NOUN
cana-4548	293	11	.	.	PUNCT
cana-4548	294	1	the	the	DET
cana-4548	294	2	ranking	ranking	NOUN
cana-4548	294	3	of	of	ADP
cana-4548	294	4	the	the	DET
cana-4548	294	5	alternatives	alternative	NOUN
cana-4548	294	6	is	be	AUX
cana-4548	294	7	as	as	SCONJ
cana-4548	294	8	follows	follow	VERB
cana-4548	294	9	:	:	PUNCT
cana-4548	294	10	𝐴5	𝐴5	PROPN
cana-4548	294	11	>	>	X
cana-4548	294	12	𝐴3	𝐴3	PROPN
cana-4548	294	13	>	>	X
cana-4548	294	14	𝐴4	𝐴4	PROPN
cana-4548	294	15	>	>	X
cana-4548	294	16	𝐴2	𝐴2	PROPN
cana-4548	294	17	>	>	X
cana-4548	294	18	𝐴1	𝐴1	PROPN
cana-4548	294	19	.	.	PUNCT
cana-4548	295	1	6	6	NUM
cana-4548	295	2	comparative	comparative	ADJ
cana-4548	295	3	analysis	analysis	NOUN
cana-4548	295	4	to	to	PART
cana-4548	295	5	illustrate	illustrate	VERB
cana-4548	295	6	the	the	DET
cana-4548	295	7	significance	significance	NOUN
cana-4548	295	8	and	and	CCONJ
cana-4548	295	9	applicability	applicability	NOUN
cana-4548	295	10	of	of	ADP
cana-4548	295	11	the	the	DET
cana-4548	295	12	results	result	NOUN
cana-4548	295	13	,	,	PUNCT
cana-4548	295	14	we	we	PRON
cana-4548	295	15	compared	compare	VERB
cana-4548	295	16	the	the	DET
cana-4548	295	17	proposed	propose	VERB
cana-4548	295	18	mcgdm	mcgdm	NOUN
cana-4548	295	19	approach	approach	VERB
cana-4548	295	20	with	with	ADP
cana-4548	295	21	existing	exist	VERB
cana-4548	295	22	aos	aos	PROPN
cana-4548	295	23	.	.	PROPN
cana-4548	296	1	6.1	6.1	NUM
cana-4548	296	2	comparison	comparison	NOUN
cana-4548	296	3	with	with	ADP
cana-4548	296	4	existing	exist	VERB
cana-4548	296	5	approaches	approach	NOUN
cana-4548	296	6	table	table	NOUN
cana-4548	296	7	8	8	NUM
cana-4548	296	8	below	below	ADV
cana-4548	296	9	compares	compare	VERB
cana-4548	296	10	the	the	DET
cana-4548	296	11	proposed	propose	VERB
cana-4548	296	12	operators	operator	NOUN
cana-4548	296	13	with	with	ADP
cana-4548	296	14	various	various	ADJ
cana-4548	296	15	existing	exist	VERB
cana-4548	296	16	aos	aos	PROPN
cana-4548	296	17	.	.	PROPN
cana-4548	296	18	table	table	PROPN
cana-4548	296	19	8	8	NUM
cana-4548	296	20	:	:	PUNCT
cana-4548	296	21	a	a	DET
cana-4548	296	22	comparison	comparison	NOUN
cana-4548	296	23	of	of	ADP
cana-4548	296	24	the	the	DET
cana-4548	296	25	proposed	propose	VERB
cana-4548	296	26	operators	operator	NOUN
cana-4548	296	27	with	with	ADP
cana-4548	296	28	several	several	ADJ
cana-4548	296	29	existing	exist	VERB
cana-4548	296	30	approaches	approach	NOUN
cana-4548	296	31	operators	operator	NOUN
cana-4548	296	32	parameter	parameter	NOUN
cana-4548	296	33	ranking	rank	VERB
cana-4548	296	34	order	order	NOUN
cana-4548	296	35	pfwg	pfwg	NOUN
cana-4548	296	36	(	(	PUNCT
cana-4548	296	37	wei	wei	X
cana-4548	296	38	(	(	PUNCT
cana-4548	296	39	2017	2017	NUM
cana-4548	296	40	)	)	PUNCT
cana-4548	296	41	)	)	PUNCT
cana-4548	296	42	not	not	PART
cana-4548	296	43	considered	consider	VERB
cana-4548	296	44	𝐴3	𝐴3	PROPN
cana-4548	296	45	>	>	X
cana-4548	296	46	𝐴5	𝐴5	PROPN
cana-4548	296	47	>	>	X
cana-4548	296	48	𝐴4	𝐴4	PROPN
cana-4548	296	49	>	>	X
cana-4548	296	50	𝐴2	𝐴2	PROPN
cana-4548	296	51	>	>	X
cana-4548	296	52	𝐴1	𝐴1	PROPN
cana-4548	296	53	pfowg	pfowg	PROPN
cana-4548	296	54	(	(	PUNCT
cana-4548	296	55	wei	wei	PROPN
cana-4548	296	56	(	(	PUNCT
cana-4548	296	57	2017	2017	NUM
cana-4548	296	58	)	)	PUNCT
cana-4548	296	59	)	)	PUNCT
cana-4548	296	60	not	not	PART
cana-4548	296	61	considered	consider	VERB
cana-4548	296	62	𝐴1	𝐴1	PROPN
cana-4548	296	63	>	>	X
cana-4548	296	64	𝐴2	𝐴2	PROPN
cana-4548	296	65	>	>	X
cana-4548	296	66	𝐴3	𝐴3	PROPN
cana-4548	296	67	>	>	X
cana-4548	296	68	𝐴4	𝐴4	PROPN
cana-4548	296	69	>	>	PUNCT
cana-4548	296	70	𝐴5	𝐴5	PROPN
cana-4548	296	71	the	the	DET
cana-4548	296	72	proposed	propose	VERB
cana-4548	296	73	aos	aos	NOUN
cana-4548	296	74	pfsspwg	pfsspwg	NOUN
cana-4548	296	75	considered	consider	VERB
cana-4548	296	76	(	(	PUNCT
cana-4548	296	77	𝛽	𝛽	NOUN
cana-4548	296	78	=	=	PUNCT
cana-4548	296	79	−2	−2	PROPN
cana-4548	296	80	)	)	PUNCT
cana-4548	296	81	𝐴5	𝐴5	PROPN
cana-4548	296	82	>	>	PUNCT
cana-4548	296	83	𝐴3	𝐴3	PROPN
cana-4548	296	84	>	>	X
cana-4548	296	85	𝐴4	𝐴4	PROPN
cana-4548	296	86	>	>	X
cana-4548	296	87	𝐴2	𝐴2	PROPN
cana-4548	296	88	>	>	X
cana-4548	296	89	𝐴1	𝐴1	PROPN
cana-4548	297	1	pfsspowg	pfsspowg	VERB
cana-4548	297	2	considered	consider	VERB
cana-4548	297	3	(	(	PUNCT
cana-4548	297	4	𝛽	𝛽	NOUN
cana-4548	297	5	=	=	SYM
cana-4548	297	6	−2	−2	NOUN
cana-4548	297	7	)	)	PUNCT
cana-4548	298	1	𝐴1	𝐴1	PROPN
cana-4548	298	2	>	>	X
cana-4548	299	1	𝐴2	𝐴2	PROPN
cana-4548	299	2	>	>	X
cana-4548	299	3	𝐴3	𝐴3	PROPN
cana-4548	299	4	>	>	X
cana-4548	299	5	𝐴4	𝐴4	PROPN
cana-4548	299	6	>	>	PUNCT
cana-4548	299	7	𝐴5	𝐴5	PROPN
cana-4548	299	8	table	table	NOUN
cana-4548	299	9	8	8	NUM
cana-4548	299	10	compares	compare	VERB
cana-4548	299	11	the	the	DET
cana-4548	299	12	proposed	propose	VERB
cana-4548	299	13	operators	operator	NOUN
cana-4548	299	14	with	with	ADP
cana-4548	299	15	existing	exist	VERB
cana-4548	299	16	aggregation	aggregation	NOUN
cana-4548	299	17	operators	operator	NOUN
cana-4548	299	18	.	.	PUNCT
cana-4548	300	1	the	the	DET
cana-4548	300	2	suggested	suggest	VERB
cana-4548	300	3	operators	operator	NOUN
cana-4548	300	4	yield	yield	VERB
cana-4548	300	5	different	different	ADJ
cana-4548	300	6	ranking	ranking	ADJ
cana-4548	300	7	outcomes	outcome	NOUN
cana-4548	300	8	compared	compare	VERB
cana-4548	300	9	to	to	ADP
cana-4548	300	10	the	the	DET
cana-4548	300	11	existing	exist	VERB
cana-4548	300	12	ones	one	NOUN
cana-4548	300	13	.	.	PUNCT
cana-4548	301	1	therefore	therefore	ADV
cana-4548	301	2	,	,	PUNCT
cana-4548	301	3	the	the	DET
cana-4548	301	4	proposed	propose	VERB
cana-4548	301	5	operators	operator	NOUN
cana-4548	301	6	can	can	AUX
cana-4548	301	7	serve	serve	VERB
cana-4548	301	8	as	as	ADP
cana-4548	301	9	a	a	DET
cana-4548	301	10	more	more	ADV
cana-4548	301	11	effective	effective	ADJ
cana-4548	301	12	alternative	alternative	NOUN
cana-4548	301	13	to	to	ADP
cana-4548	301	14	the	the	DET
cana-4548	301	15	existing	exist	VERB
cana-4548	301	16	operators.based	operators.base	VERB
cana-4548	301	17	on	on	ADP
cana-4548	301	18	the	the	DET
cana-4548	301	19	communications	communication	NOUN
cana-4548	301	20	on	on	ADP
cana-4548	301	21	applied	apply	VERB
cana-4548	301	22	nonlinear	nonlinear	ADJ
cana-4548	301	23	analysis	analysis	NOUN
cana-4548	301	24	issn	issn	NOUN
cana-4548	301	25	:	:	PUNCT
cana-4548	301	26	1074	1074	NUM
cana-4548	301	27	-	-	PUNCT
cana-4548	301	28	133x	133x	NUM
cana-4548	301	29	vol	vol	NOUN
cana-4548	301	30	32	32	NUM
cana-4548	301	31	no	no	NOUN
cana-4548	301	32	.	.	PUNCT
cana-4548	302	1	9s	9s	NUM
cana-4548	302	2	(	(	PUNCT
cana-4548	302	3	2025	2025	NUM
cana-4548	302	4	)	)	PUNCT
cana-4548	302	5	2693	2693	NUM
cana-4548	302	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4548	302	7	comparative	comparative	ADJ
cana-4548	302	8	study	study	NOUN
cana-4548	302	9	above	above	ADV
cana-4548	302	10	,	,	PUNCT
cana-4548	302	11	the	the	DET
cana-4548	302	12	proposed	propose	VERB
cana-4548	302	13	approach	approach	NOUN
cana-4548	302	14	for	for	ADP
cana-4548	302	15	tackling	tackle	VERB
cana-4548	302	16	decision	decision	NOUN
cana-4548	302	17	-	-	PUNCT
cana-4548	302	18	making	make	VERB
cana-4548	302	19	challenges	challenge	NOUN
cana-4548	302	20	offers	offer	VERB
cana-4548	302	21	several	several	ADJ
cana-4548	302	22	advantages	advantage	NOUN
cana-4548	302	23	over	over	ADP
cana-4548	302	24	the	the	DET
cana-4548	302	25	existing	exist	VERB
cana-4548	302	26	operators	operator	NOUN
cana-4548	302	27	.	.	PUNCT
cana-4548	303	1	•	•	INTJ
cana-4548	303	2	as	as	SCONJ
cana-4548	303	3	observed	observe	VERB
cana-4548	303	4	in	in	ADP
cana-4548	303	5	table	table	NOUN
cana-4548	303	6	8	8	NUM
cana-4548	303	7	the	the	DET
cana-4548	303	8	results	result	NOUN
cana-4548	303	9	obtained	obtain	VERB
cana-4548	303	10	from	from	ADP
cana-4548	303	11	various	various	ADJ
cana-4548	303	12	existing	exist	VERB
cana-4548	303	13	approaches	approach	NOUN
cana-4548	303	14	are	be	AUX
cana-4548	303	15	derived	derive	VERB
cana-4548	303	16	in	in	ADP
cana-4548	303	17	an	an	DET
cana-4548	303	18	environment	environment	NOUN
cana-4548	303	19	that	that	PRON
cana-4548	303	20	does	do	AUX
cana-4548	303	21	not	not	PART
cana-4548	303	22	take	take	VERB
cana-4548	303	23	into	into	ADP
cana-4548	303	24	account	account	NOUN
cana-4548	303	25	the	the	DET
cana-4548	303	26	ss	ss	NOUN
cana-4548	303	27	power	power	NOUN
cana-4548	303	28	of	of	ADP
cana-4548	303	29	the	the	DET
cana-4548	303	30	criteria	criterion	NOUN
cana-4548	303	31	during	during	ADP
cana-4548	303	32	evaluation	evaluation	NOUN
cana-4548	303	33	.	.	PUNCT
cana-4548	304	1	in	in	ADP
cana-4548	304	2	other	other	ADJ
cana-4548	304	3	words	word	NOUN
cana-4548	304	4	,	,	PUNCT
cana-4548	304	5	these	these	DET
cana-4548	304	6	approaches	approach	NOUN
cana-4548	304	7	assume	assume	VERB
cana-4548	304	8	that	that	SCONJ
cana-4548	304	9	decision	decision	NOUN
cana-4548	304	10	-	-	PUNCT
cana-4548	304	11	makers	maker	NOUN
cana-4548	304	12	consider	consider	VERB
cana-4548	304	13	the	the	DET
cana-4548	304	14	alternatives	alternative	NOUN
cana-4548	304	15	being	be	AUX
cana-4548	304	16	assessed	assess	VERB
cana-4548	304	17	.	.	PUNCT
cana-4548	305	1	however	however	ADV
cana-4548	305	2	,	,	PUNCT
cana-4548	305	3	in	in	ADP
cana-4548	305	4	real	real	ADJ
cana-4548	305	5	-	-	PUNCT
cana-4548	305	6	life	life	NOUN
cana-4548	305	7	situations	situation	NOUN
cana-4548	305	8	,	,	PUNCT
cana-4548	305	9	such	such	ADJ
cana-4548	305	10	conditions	condition	NOUN
cana-4548	305	11	are	be	AUX
cana-4548	305	12	only	only	ADV
cana-4548	305	13	partially	partially	ADV
cana-4548	305	14	met	meet	VERB
cana-4548	305	15	.	.	PUNCT
cana-4548	306	1	•	•	NUM
cana-4548	306	2	additionally	additionally	ADV
cana-4548	306	3	,	,	PUNCT
cana-4548	306	4	some	some	DET
cana-4548	306	5	existing	exist	VERB
cana-4548	306	6	operators	operator	NOUN
cana-4548	306	7	for	for	ADP
cana-4548	306	8	pfs	pf	NOUN
cana-4548	306	9	are	be	AUX
cana-4548	306	10	specific	specific	ADJ
cana-4548	306	11	cases	case	NOUN
cana-4548	306	12	of	of	ADP
cana-4548	306	13	the	the	DET
cana-4548	306	14	proposed	propose	VERB
cana-4548	306	15	operators	operator	NOUN
cana-4548	306	16	.	.	PUNCT
cana-4548	307	1	consequently	consequently	ADV
cana-4548	307	2	,	,	PUNCT
cana-4548	307	3	it	it	PRON
cana-4548	307	4	can	can	AUX
cana-4548	307	5	be	be	AUX
cana-4548	307	6	concluded	conclude	VERB
cana-4548	307	7	that	that	SCONJ
cana-4548	307	8	the	the	DET
cana-4548	307	9	proposed	propose	VERB
cana-4548	307	10	aggregation	aggregation	NOUN
cana-4548	307	11	operators	operator	NOUN
cana-4548	307	12	are	be	AUX
cana-4548	307	13	more	more	ADV
cana-4548	307	14	suitable	suitable	ADJ
cana-4548	307	15	for	for	ADP
cana-4548	307	16	accurately	accurately	ADV
cana-4548	307	17	addressing	address	VERB
cana-4548	307	18	real	real	ADJ
cana-4548	307	19	-	-	PUNCT
cana-4548	307	20	life	life	NOUN
cana-4548	307	21	problems	problem	NOUN
cana-4548	307	22	compared	compare	VERB
cana-4548	307	23	to	to	ADP
cana-4548	307	24	the	the	DET
cana-4548	307	25	existing	exist	VERB
cana-4548	307	26	ones	one	NOUN
cana-4548	307	27	.	.	PUNCT
cana-4548	308	1	7	7	X
cana-4548	308	2	.	.	X
cana-4548	308	3	conclusions	conclusion	NOUN
cana-4548	308	4	this	this	DET
cana-4548	308	5	study	study	NOUN
cana-4548	308	6	presents	present	VERB
cana-4548	308	7	the	the	DET
cana-4548	308	8	smart	smart	ADJ
cana-4548	308	9	for	for	ADP
cana-4548	308	10	addressing	address	VERB
cana-4548	308	11	magdm	magdm	NOUN
cana-4548	308	12	problems	problem	NOUN
cana-4548	308	13	involving	involve	VERB
cana-4548	308	14	pf	pf	PROPN
cana-4548	308	15	decision	decision	NOUN
cana-4548	308	16	values	value	NOUN
cana-4548	308	17	.	.	PUNCT
cana-4548	309	1	aggregating	aggregate	VERB
cana-4548	309	2	decision	decision	NOUN
cana-4548	309	3	values	value	NOUN
cana-4548	309	4	is	be	AUX
cana-4548	309	5	a	a	DET
cana-4548	309	6	critical	critical	ADJ
cana-4548	309	7	initial	initial	ADJ
cana-4548	309	8	step	step	NOUN
cana-4548	309	9	in	in	ADP
cana-4548	309	10	pfmcgdm	pfmcgdm	NOUN
cana-4548	309	11	.	.	PUNCT
cana-4548	310	1	we	we	PRON
cana-4548	310	2	introduce	introduce	VERB
cana-4548	310	3	a	a	DET
cana-4548	310	4	series	series	NOUN
cana-4548	310	5	of	of	ADP
cana-4548	310	6	pfsspg	pfsspg	NOUN
cana-4548	310	7	operators	operator	NOUN
cana-4548	310	8	,	,	PUNCT
cana-4548	310	9	starting	start	VERB
cana-4548	310	10	with	with	ADP
cana-4548	310	11	the	the	DET
cana-4548	310	12	pfsspg	pfsspg	NOUN
cana-4548	310	13	operator	operator	NOUN
cana-4548	310	14	and	and	CCONJ
cana-4548	310	15	its	its	PRON
cana-4548	310	16	desirable	desirable	ADJ
cana-4548	310	17	properties	property	NOUN
cana-4548	310	18	.	.	PUNCT
cana-4548	311	1	we	we	PRON
cana-4548	311	2	also	also	ADV
cana-4548	311	3	develop	develop	VERB
cana-4548	311	4	weighted	weighted	ADJ
cana-4548	311	5	variants	variant	NOUN
cana-4548	311	6	,	,	PUNCT
cana-4548	311	7	including	include	VERB
cana-4548	311	8	pfsspwg	pfsspwg	NOUN
cana-4548	311	9	and	and	CCONJ
cana-4548	311	10	pfsspowg	pfsspowg	ADJ
cana-4548	311	11	operators	operator	NOUN
cana-4548	311	12	and	and	CCONJ
cana-4548	311	13	examine	examine	VERB
cana-4548	311	14	their	their	PRON
cana-4548	311	15	fundamental	fundamental	ADJ
cana-4548	311	16	properties	property	NOUN
cana-4548	311	17	.	.	PUNCT
cana-4548	312	1	the	the	DET
cana-4548	312	2	smart	smart	ADJ
cana-4548	312	3	is	be	AUX
cana-4548	312	4	employed	employ	VERB
cana-4548	312	5	to	to	PART
cana-4548	312	6	determine	determine	VERB
cana-4548	312	7	criteria	criterion	NOUN
cana-4548	312	8	weights	weight	NOUN
cana-4548	312	9	based	base	VERB
cana-4548	312	10	on	on	ADP
cana-4548	312	11	decision	decision	NOUN
cana-4548	312	12	experts	expert	NOUN
cana-4548	312	13	'	'	PART
cana-4548	312	14	subjective	subjective	ADJ
cana-4548	312	15	knowledge	knowledge	NOUN
cana-4548	312	16	.	.	PUNCT
cana-4548	313	1	a	a	DET
cana-4548	313	2	real	real	ADJ
cana-4548	313	3	-	-	PUNCT
cana-4548	313	4	life	life	NOUN
cana-4548	313	5	supplier	supplier	NOUN
cana-4548	313	6	selection	selection	NOUN
cana-4548	313	7	application	application	NOUN
cana-4548	313	8	in	in	ADP
cana-4548	313	9	the	the	DET
cana-4548	313	10	chemical	chemical	NOUN
cana-4548	313	11	industry	industry	NOUN
cana-4548	313	12	demonstrates	demonstrate	VERB
cana-4548	313	13	the	the	DET
cana-4548	313	14	practical	practical	ADJ
cana-4548	313	15	applicability	applicability	NOUN
cana-4548	313	16	of	of	ADP
cana-4548	313	17	the	the	DET
cana-4548	313	18	proposed	propose	VERB
cana-4548	313	19	work	work	NOUN
cana-4548	313	20	.	.	PUNCT
cana-4548	314	1	a	a	DET
cana-4548	314	2	comparative	comparative	ADJ
cana-4548	314	3	study	study	NOUN
cana-4548	314	4	with	with	ADP
cana-4548	314	5	existing	exist	VERB
cana-4548	314	6	operators	operator	NOUN
cana-4548	314	7	highlights	highlight	VERB
cana-4548	314	8	the	the	DET
cana-4548	314	9	feasibility	feasibility	NOUN
cana-4548	314	10	and	and	CCONJ
cana-4548	314	11	flexibility	flexibility	NOUN
cana-4548	314	12	of	of	ADP
cana-4548	314	13	our	our	PRON
cana-4548	314	14	solution	solution	NOUN
cana-4548	314	15	methodology	methodology	NOUN
cana-4548	314	16	.	.	PUNCT
cana-4548	315	1	future	future	ADJ
cana-4548	315	2	research	research	NOUN
cana-4548	315	3	will	will	AUX
cana-4548	315	4	focus	focus	VERB
cana-4548	315	5	on	on	ADP
cana-4548	315	6	applying	apply	VERB
cana-4548	315	7	the	the	DET
cana-4548	315	8	developed	developed	ADJ
cana-4548	315	9	ao	ao	NOUN
cana-4548	315	10	to	to	PART
cana-4548	315	11	average	average	VERB
cana-4548	315	12	,	,	PUNCT
cana-4548	315	13	linguistic	linguistic	ADJ
cana-4548	315	14	and	and	CCONJ
cana-4548	315	15	complex	complex	ADJ
cana-4548	315	16	uncertain	uncertain	ADJ
cana-4548	315	17	environments	environment	NOUN
cana-4548	315	18	,	,	PUNCT
cana-4548	315	19	exploring	explore	VERB
cana-4548	315	20	various	various	ADJ
cana-4548	315	21	pf	pf	PROPN
cana-4548	315	22	aos	aos	PROPN
cana-4548	315	23	,	,	PUNCT
cana-4548	315	24	and	and	CCONJ
cana-4548	315	25	applying	apply	VERB
cana-4548	315	26	them	they	PRON
cana-4548	315	27	to	to	ADP
cana-4548	315	28	practical	practical	ADJ
cana-4548	315	29	decision	decision	NOUN
cana-4548	315	30	scenarios	scenario	NOUN
cana-4548	315	31	to	to	PART
cana-4548	315	32	enhance	enhance	VERB
cana-4548	315	33	our	our	PRON
cana-4548	315	34	understanding	understanding	NOUN
cana-4548	315	35	and	and	CCONJ
cana-4548	315	36	effectiveness	effectiveness	NOUN
cana-4548	315	37	in	in	ADP
cana-4548	315	38	handling	handle	VERB
cana-4548	315	39	diverse	diverse	ADJ
cana-4548	315	40	fuzzy	fuzzy	ADJ
cana-4548	315	41	dm	dm	NOUN
cana-4548	315	42	situations	situation	NOUN
cana-4548	315	43	.	.	PUNCT
cana-4548	316	1	references	reference	NOUN
cana-4548	316	2	[	[	X
cana-4548	316	3	1	1	NUM
cana-4548	316	4	]	]	PUNCT
cana-4548	316	5	atanassov	atanassov	NOUN
cana-4548	316	6	,	,	PUNCT
cana-4548	316	7	k.	k.	PROPN
cana-4548	316	8	t.	t.	PROPN
cana-4548	316	9	(	(	PUNCT
cana-4548	316	10	1986	1986	NUM
cana-4548	316	11	)	)	PUNCT
cana-4548	316	12	.	.	PUNCT
cana-4548	317	1	intuitionistic	intuitionistic	ADJ
cana-4548	317	2	fuzzy	fuzzy	ADJ
cana-4548	317	3	sets	set	NOUN
cana-4548	317	4	,	,	PUNCT
cana-4548	317	5	fuzzy	fuzzy	ADJ
cana-4548	317	6	sets	set	NOUN
cana-4548	317	7	and	and	CCONJ
cana-4548	317	8	systems	system	NOUN
cana-4548	317	9	,	,	PUNCT
cana-4548	317	10	20(1	20(1	NUM
cana-4548	317	11	)	)	PUNCT
cana-4548	317	12	,	,	PUNCT
cana-4548	317	13	87	87	NUM
cana-4548	317	14	-	-	SYM
cana-4548	317	15	96	96	NUM
cana-4548	317	16	.	.	PUNCT
cana-4548	318	1	[	[	X
cana-4548	318	2	2	2	NUM
cana-4548	318	3	]	]	X
cana-4548	318	4	ates	ates	PROPN
cana-4548	318	5	,	,	PUNCT
cana-4548	318	6	f.	f.	PROPN
cana-4548	318	7	,	,	PUNCT
cana-4548	318	8	&	&	CCONJ
cana-4548	318	9	akay	akay	PROPN
cana-4548	318	10	,	,	PUNCT
cana-4548	318	11	d.	d.	PROPN
cana-4548	318	12	(	(	PUNCT
cana-4548	318	13	2020	2020	NUM
cana-4548	318	14	)	)	PUNCT
cana-4548	318	15	.	.	PUNCT
cana-4548	319	1	some	some	DET
cana-4548	319	2	picture	picture	NOUN
cana-4548	319	3	fuzzy	fuzzy	ADJ
cana-4548	319	4	bonferroni	bonferroni	NOUN
cana-4548	319	5	mean	mean	VERB
cana-4548	319	6	operators	operator	NOUN
cana-4548	319	7	with	with	ADP
cana-4548	319	8	their	their	PRON
cana-4548	319	9	application	application	NOUN
cana-4548	319	10	to	to	ADP
cana-4548	319	11	multicriteria	multicriteria	PROPN
cana-4548	319	12	decision	decision	NOUN
cana-4548	319	13	making	making	NOUN
cana-4548	319	14	,	,	PUNCT
cana-4548	319	15	international	international	ADJ
cana-4548	319	16	journal	journal	NOUN
cana-4548	319	17	of	of	ADP
cana-4548	319	18	intelligent	intelligent	ADJ
cana-4548	319	19	systems	system	NOUN
cana-4548	319	20	,	,	PUNCT
cana-4548	319	21	35(4	35(4	NUM
cana-4548	319	22	)	)	PUNCT
cana-4548	319	23	,	,	PUNCT
cana-4548	319	24	625	625	NUM
cana-4548	319	25	-	-	SYM
cana-4548	319	26	649	649	NUM
cana-4548	319	27	.	.	PUNCT
cana-4548	320	1	[	[	X
cana-4548	320	2	3	3	NUM
cana-4548	320	3	]	]	X
cana-4548	320	4	biswas	biswas	PROPN
cana-4548	320	5	,	,	PUNCT
cana-4548	320	6	a.	a.	PROPN
cana-4548	320	7	,	,	PUNCT
cana-4548	320	8	&	&	CCONJ
cana-4548	320	9	deb	deb	PROPN
cana-4548	320	10	,	,	PUNCT
cana-4548	320	11	n.	n.	NOUN
cana-4548	320	12	(	(	PUNCT
cana-4548	320	13	2021	2021	NUM
cana-4548	320	14	)	)	PUNCT
cana-4548	320	15	.	.	PUNCT
cana-4548	321	1	pythagorean	pythagorean	PROPN
cana-4548	321	2	fuzzy	fuzzy	PROPN
cana-4548	321	3	schweizer	schweizer	PROPN
cana-4548	321	4	-	-	PUNCT
cana-4548	321	5	sklar	sklar	ADJ
cana-4548	321	6	power	power	NOUN
cana-4548	321	7	aggregation	aggregation	NOUN
cana-4548	321	8	operators	operator	NOUN
cana-4548	321	9	for	for	ADP
cana-4548	321	10	solving	solve	VERB
cana-4548	321	11	multi	multi	ADJ
cana-4548	321	12	-	-	ADJ
cana-4548	321	13	attribute	attribute	NOUN
cana-4548	321	14	decision	decision	NOUN
cana-4548	321	15	making	make	VERB
cana-4548	321	16	problems	problem	NOUN
cana-4548	321	17	,	,	PUNCT
cana-4548	321	18	granular	granular	ADJ
cana-4548	321	19	computing	computing	NOUN
cana-4548	321	20	,	,	PUNCT
cana-4548	321	21	6	6	NUM
cana-4548	321	22	,	,	PUNCT
cana-4548	321	23	991	991	NUM
cana-4548	321	24	-	-	SYM
cana-4548	321	25	1007	1007	NUM
cana-4548	321	26	.	.	PUNCT
cana-4548	322	1	[	[	X
cana-4548	322	2	4	4	NUM
cana-4548	322	3	]	]	X
cana-4548	322	4	cuong	cuong	PROPN
cana-4548	322	5	,	,	PUNCT
cana-4548	322	6	b.	b.	PROPN
cana-4548	322	7	c.	c.	PROPN
cana-4548	322	8	,	,	PUNCT
cana-4548	322	9	&	&	CCONJ
cana-4548	322	10	kreinovich	kreinovich	PROPN
cana-4548	322	11	,	,	PUNCT
cana-4548	322	12	v.	v.	PROPN
cana-4548	322	13	(	(	PUNCT
cana-4548	322	14	2013	2013	NUM
cana-4548	322	15	)	)	PUNCT
cana-4548	322	16	.	.	PUNCT
cana-4548	323	1	picture	picture	NOUN
cana-4548	323	2	fuzzy	fuzzy	ADJ
cana-4548	323	3	sets	set	NOUN
cana-4548	323	4	-	-	PUNCT
cana-4548	323	5	a	a	DET
cana-4548	323	6	new	new	ADJ
cana-4548	323	7	concept	concept	NOUN
cana-4548	323	8	for	for	ADP
cana-4548	323	9	computational	computational	ADJ
cana-4548	323	10	intelligence	intelligence	NOUN
cana-4548	323	11	problems	problem	NOUN
cana-4548	323	12	.	.	PUNCT
cana-4548	324	1	in	in	ADP
cana-4548	324	2	2013	2013	NUM
cana-4548	324	3	third	third	ADJ
cana-4548	324	4	world	world	NOUN
cana-4548	324	5	congress	congress	PROPN
cana-4548	324	6	on	on	ADP
cana-4548	324	7	information	information	NOUN
cana-4548	324	8	and	and	CCONJ
cana-4548	324	9	communication	communication	NOUN
cana-4548	324	10	technologies	technology	NOUN
cana-4548	324	11	(	(	PUNCT
cana-4548	324	12	wict	wict	NOUN
cana-4548	324	13	2013	2013	NUM
cana-4548	324	14	)	)	PUNCT
cana-4548	324	15	,	,	PUNCT
cana-4548	324	16	1	1	NUM
cana-4548	324	17	-	-	SYM
cana-4548	324	18	6	6	NUM
cana-4548	324	19	.	.	PUNCT
cana-4548	324	20	ieee	ieee	NOUN
cana-4548	324	21	.	.	PUNCT
cana-4548	325	1	[	[	X
cana-4548	325	2	5	5	NUM
cana-4548	325	3	]	]	X
cana-4548	325	4	cuong	cuong	PROPN
cana-4548	325	5	,	,	PUNCT
cana-4548	325	6	b.	b.	PROPN
cana-4548	325	7	c.	c.	PROPN
cana-4548	325	8	,	,	PUNCT
cana-4548	325	9	&	&	CCONJ
cana-4548	325	10	kreinovich	kreinovich	PROPN
cana-4548	325	11	,	,	PUNCT
cana-4548	325	12	v.	v.	PROPN
cana-4548	325	13	(	(	PUNCT
cana-4548	325	14	2014	2014	NUM
cana-4548	325	15	)	)	PUNCT
cana-4548	325	16	.	.	PUNCT
cana-4548	326	1	picture	picture	NOUN
cana-4548	326	2	fuzzy	fuzzy	ADJ
cana-4548	326	3	sets	set	NOUN
cana-4548	326	4	.	.	PUNCT
cana-4548	327	1	journal	journal	NOUN
cana-4548	327	2	of	of	ADP
cana-4548	327	3	computer	computer	NOUN
cana-4548	327	4	science	science	NOUN
cana-4548	327	5	and	and	CCONJ
cana-4548	327	6	cybernetics	cybernetic	NOUN
cana-4548	327	7	,	,	PUNCT
cana-4548	327	8	30(4	30(4	NUM
cana-4548	327	9	)	)	PUNCT
cana-4548	327	10	,	,	PUNCT
cana-4548	327	11	409	409	NUM
cana-4548	327	12	-	-	SYM
cana-4548	327	13	420	420	NUM
cana-4548	327	14	.	.	PUNCT
cana-4548	328	1	[	[	X
cana-4548	328	2	6	6	NUM
cana-4548	328	3	]	]	X
cana-4548	328	4	cuong	cuong	PROPN
cana-4548	328	5	,	,	PUNCT
cana-4548	328	6	b.	b.	PROPN
cana-4548	328	7	c.	c.	PROPN
cana-4548	328	8	,	,	PUNCT
cana-4548	328	9	kreinovitch	kreinovitch	NOUN
cana-4548	328	10	,	,	PUNCT
cana-4548	328	11	v.	v.	PROPN
cana-4548	328	12	,	,	PUNCT
cana-4548	328	13	&	&	CCONJ
cana-4548	328	14	ngan	ngan	PROPN
cana-4548	328	15	,	,	PUNCT
cana-4548	328	16	r.	r.	PROPN
cana-4548	328	17	t.	t.	PROPN
cana-4548	328	18	(	(	PUNCT
cana-4548	328	19	2016	2016	NUM
cana-4548	328	20	,	,	PUNCT
cana-4548	328	21	october	october	PROPN
cana-4548	328	22	)	)	PUNCT
cana-4548	328	23	.	.	PUNCT
cana-4548	329	1	a	a	DET
cana-4548	329	2	classification	classification	NOUN
cana-4548	329	3	of	of	ADP
cana-4548	329	4	representable	representable	ADJ
cana-4548	329	5	t	t	PROPN
cana-4548	329	6	-	-	PUNCT
cana-4548	329	7	norm	norm	NOUN
cana-4548	329	8	operators	operator	NOUN
cana-4548	329	9	for	for	ADP
cana-4548	329	10	picture	picture	NOUN
cana-4548	329	11	fuzzy	fuzzy	ADJ
cana-4548	329	12	sets	set	NOUN
cana-4548	329	13	.	.	PUNCT
cana-4548	330	1	in	in	ADP
cana-4548	330	2	2016	2016	NUM
cana-4548	330	3	eighth	eighth	ADJ
cana-4548	330	4	international	international	ADJ
cana-4548	330	5	conference	conference	NOUN
cana-4548	330	6	on	on	ADP
cana-4548	330	7	knowledge	knowledge	NOUN
cana-4548	330	8	and	and	CCONJ
cana-4548	330	9	systems	system	NOUN
cana-4548	330	10	engineering	engineering	NOUN
cana-4548	330	11	(	(	PUNCT
cana-4548	330	12	kse	kse	PROPN
cana-4548	330	13	)	)	PUNCT
cana-4548	330	14	,	,	PUNCT
cana-4548	330	15	19	19	NUM
cana-4548	330	16	-	-	SYM
cana-4548	330	17	24	24	NUM
cana-4548	330	18	.	.	PUNCT
cana-4548	330	19	ieee	ieee	NOUN
cana-4548	330	20	.	.	PUNCT
cana-4548	331	1	[	[	X
cana-4548	331	2	7	7	NUM
cana-4548	331	3	]	]	X
cana-4548	331	4	deva	deva	PROPN
cana-4548	331	5	,	,	PUNCT
cana-4548	331	6	k.	k.	PROPN
cana-4548	331	7	,	,	PUNCT
cana-4548	331	8	&	&	CCONJ
cana-4548	331	9	mohanaselvi	mohanaselvi	PROPN
cana-4548	331	10	,	,	PUNCT
cana-4548	331	11	s.	s.	PROPN
cana-4548	331	12	(	(	PUNCT
cana-4548	331	13	2022	2022	NUM
cana-4548	331	14	)	)	PUNCT
cana-4548	331	15	.	.	PUNCT
cana-4548	332	1	deva	deva	PROPN
cana-4548	332	2	,	,	PUNCT
cana-4548	332	3	k.	k.	PROPN
cana-4548	332	4	,	,	PUNCT
cana-4548	332	5	&	&	CCONJ
cana-4548	332	6	mohanaselvi	mohanaselvi	PROPN
cana-4548	332	7	,	,	PUNCT
cana-4548	332	8	s.	s.	PROPN
cana-4548	332	9	(	(	PUNCT
cana-4548	332	10	2022	2022	NUM
cana-4548	332	11	,	,	PUNCT
cana-4548	332	12	february	february	PROPN
cana-4548	332	13	)	)	PUNCT
cana-4548	332	14	.	.	PUNCT
cana-4548	333	1	picture	picture	NOUN
cana-4548	333	2	fuzzy	fuzzy	ADJ
cana-4548	333	3	einstein	einstein	PROPN
cana-4548	333	4	geometric	geometric	ADJ
cana-4548	333	5	aggregate	aggregate	NOUN
cana-4548	333	6	operators	operator	NOUN
cana-4548	333	7	and	and	CCONJ
cana-4548	333	8	their	their	PRON
cana-4548	333	9	application	application	NOUN
cana-4548	333	10	to	to	ADP
cana-4548	333	11	multiple	multiple	ADJ
cana-4548	333	12	communications	communication	NOUN
cana-4548	333	13	on	on	ADP
cana-4548	333	14	applied	apply	VERB
cana-4548	333	15	nonlinear	nonlinear	ADJ
cana-4548	333	16	analysis	analysis	NOUN
cana-4548	333	17	issn	issn	NOUN
cana-4548	333	18	:	:	PUNCT
cana-4548	333	19	1074	1074	NUM
cana-4548	333	20	-	-	PUNCT
cana-4548	333	21	133x	133x	NUM
cana-4548	333	22	vol	vol	NOUN
cana-4548	333	23	32	32	NUM
cana-4548	333	24	no	no	NOUN
cana-4548	333	25	.	.	PUNCT
cana-4548	334	1	9s	9s	NUM
cana-4548	334	2	(	(	PUNCT
cana-4548	334	3	2025	2025	NUM
cana-4548	334	4	)	)	PUNCT
cana-4548	334	5	2694	2694	NUM
cana-4548	334	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4548	334	7	attribute	attribute	NOUN
cana-4548	334	8	decision	decision	NOUN
cana-4548	334	9	making	making	NOUN
cana-4548	334	10	,	,	PUNCT
cana-4548	334	11	in	in	ADP
cana-4548	334	12	2022	2022	NUM
cana-4548	334	13	first	first	ADJ
cana-4548	334	14	international	international	ADJ
cana-4548	334	15	conference	conference	NOUN
cana-4548	334	16	on	on	ADP
cana-4548	334	17	electrical	electrical	ADJ
cana-4548	334	18	,	,	PUNCT
cana-4548	334	19	electronics	electronic	NOUN
cana-4548	334	20	,	,	PUNCT
cana-4548	334	21	information	information	NOUN
cana-4548	334	22	and	and	CCONJ
cana-4548	334	23	communication	communication	NOUN
cana-4548	334	24	technologies	technology	NOUN
cana-4548	334	25	(	(	PUNCT
cana-4548	334	26	iceeict	iceeict	ADJ
cana-4548	334	27	)	)	PUNCT
cana-4548	334	28	,	,	PUNCT
cana-4548	334	29	(	(	PUNCT
cana-4548	334	30	pp	pp	ADJ
cana-4548	334	31	.	.	PUNCT
cana-4548	335	1	1	1	NUM
cana-4548	335	2	-	-	SYM
cana-4548	335	3	7	7	NUM
cana-4548	335	4	)	)	PUNCT
cana-4548	335	5	.	.	PUNCT
cana-4548	336	1	ieee	ieee	NOUN
cana-4548	336	2	.	.	PUNCT
cana-4548	337	1	[	[	X
cana-4548	337	2	8	8	NUM
cana-4548	337	3	]	]	X
cana-4548	337	4	garg	garg	NOUN
cana-4548	337	5	,	,	PUNCT
cana-4548	337	6	h.	h.	PROPN
cana-4548	337	7	(	(	PUNCT
cana-4548	337	8	2017	2017	NUM
cana-4548	337	9	)	)	PUNCT
cana-4548	337	10	.	.	PUNCT
cana-4548	338	1	some	some	DET
cana-4548	338	2	picture	picture	NOUN
cana-4548	338	3	fuzzy	fuzzy	ADJ
cana-4548	338	4	aggregation	aggregation	NOUN
cana-4548	338	5	operators	operator	NOUN
cana-4548	338	6	and	and	CCONJ
cana-4548	338	7	their	their	PRON
cana-4548	338	8	applications	application	NOUN
cana-4548	338	9	to	to	ADP
cana-4548	338	10	multicriteria	multicriteria	PROPN
cana-4548	338	11	decision	decision	NOUN
cana-4548	338	12	-	-	PUNCT
cana-4548	338	13	making	making	NOUN
cana-4548	338	14	.	.	PUNCT
cana-4548	339	1	,	,	PUNCT
cana-4548	339	2	arabian	arabian	ADJ
cana-4548	339	3	journal	journal	NOUN
cana-4548	339	4	for	for	ADP
cana-4548	339	5	science	science	NOUN
cana-4548	339	6	and	and	CCONJ
cana-4548	339	7	engineering	engineering	NOUN
cana-4548	339	8	,	,	PUNCT
cana-4548	339	9	42(12	42(12	NUM
cana-4548	339	10	)	)	PUNCT
cana-4548	339	11	,	,	PUNCT
cana-4548	339	12	52755290	52755290	NUM
cana-4548	339	13	.	.	PUNCT
cana-4548	340	1	[	[	X
cana-4548	340	2	9	9	NUM
cana-4548	340	3	]	]	X
cana-4548	340	4	garg	garg	NOUN
cana-4548	340	5	,	,	PUNCT
cana-4548	340	6	h.	h.	PROPN
cana-4548	340	7	(	(	PUNCT
cana-4548	340	8	2017	2017	NUM
cana-4548	340	9	)	)	PUNCT
cana-4548	340	10	.	.	PUNCT
cana-4548	341	1	confidence	confidence	NOUN
cana-4548	341	2	levels	level	NOUN
cana-4548	341	3	based	base	VERB
cana-4548	341	4	pythagorean	pythagorean	PROPN
cana-4548	341	5	fuzzy	fuzzy	ADJ
cana-4548	341	6	aggregation	aggregation	NOUN
cana-4548	341	7	operators	operator	NOUN
cana-4548	341	8	and	and	CCONJ
cana-4548	341	9	its	its	PRON
cana-4548	341	10	application	application	NOUN
cana-4548	341	11	to	to	ADP
cana-4548	341	12	decision	decision	NOUN
cana-4548	341	13	-	-	PUNCT
cana-4548	341	14	making	make	VERB
cana-4548	341	15	process	process	NOUN
cana-4548	341	16	.	.	PUNCT
cana-4548	342	1	computational	computational	ADJ
cana-4548	342	2	and	and	CCONJ
cana-4548	342	3	mathematical	mathematical	ADJ
cana-4548	342	4	organization	organization	NOUN
cana-4548	342	5	theory	theory	NOUN
cana-4548	342	6	,	,	PUNCT
cana-4548	342	7	23(4	23(4	NOUN
cana-4548	342	8	)	)	PUNCT
cana-4548	342	9	,	,	PUNCT
cana-4548	342	10	546	546	NUM
cana-4548	342	11	-	-	SYM
cana-4548	342	12	571	571	NUM
cana-4548	342	13	.	.	PUNCT
cana-4548	343	1	[	[	X
cana-4548	343	2	10	10	NUM
cana-4548	343	3	]	]	X
cana-4548	343	4	garg	garg	NOUN
cana-4548	343	5	,	,	PUNCT
cana-4548	343	6	h.	h.	PROPN
cana-4548	343	7	,	,	PUNCT
cana-4548	343	8	tiwari	tiwari	PROPN
cana-4548	343	9	,	,	PUNCT
cana-4548	343	10	p.	p.	NOUN
cana-4548	343	11	,	,	PUNCT
cana-4548	343	12	&	&	CCONJ
cana-4548	343	13	prasad	prasad	PROPN
cana-4548	343	14	,	,	PUNCT
cana-4548	343	15	v.	v.	PROPN
cana-4548	343	16	(	(	PUNCT
cana-4548	343	17	2023	2023	NUM
cana-4548	343	18	)	)	PUNCT
cana-4548	343	19	.	.	PUNCT
cana-4548	344	1	schweizer	schweizer	PROPN
cana-4548	344	2	-	-	PUNCT
cana-4548	344	3	sklar	sklar	ADJ
cana-4548	344	4	prioritized	prioritize	VERB
cana-4548	344	5	aggregation	aggregation	NOUN
cana-4548	344	6	operators	operator	NOUN
cana-4548	344	7	for	for	ADP
cana-4548	344	8	intuitionistic	intuitionistic	ADJ
cana-4548	344	9	fuzzy	fuzzy	ADJ
cana-4548	344	10	information	information	NOUN
cana-4548	344	11	and	and	CCONJ
cana-4548	344	12	their	their	PRON
cana-4548	344	13	application	application	NOUN
cana-4548	344	14	in	in	ADP
cana-4548	344	15	multi	multi	ADJ
cana-4548	344	16	-	-	ADJ
cana-4548	344	17	attribute	attribute	NOUN
cana-4548	344	18	decision	decision	NOUN
cana-4548	344	19	making	making	NOUN
cana-4548	344	20	,	,	PUNCT
cana-4548	344	21	alexandria	alexandria	PROPN
cana-4548	344	22	engineering	engineering	PROPN
cana-4548	344	23	journal	journal	PROPN
cana-4548	344	24	,	,	PUNCT
cana-4548	344	25	67	67	NUM
cana-4548	344	26	,	,	PUNCT
cana-4548	344	27	229	229	NUM
cana-4548	344	28	-	-	SYM
cana-4548	344	29	240	240	NUM
cana-4548	344	30	.	.	PUNCT
cana-4548	345	1	[	[	X
cana-4548	345	2	11	11	NUM
cana-4548	345	3	]	]	X
cana-4548	345	4	jana	jana	PROPN
cana-4548	345	5	,	,	PUNCT
cana-4548	345	6	c.	c.	PROPN
cana-4548	345	7	,	,	PUNCT
cana-4548	345	8	senapati	senapati	NOUN
cana-4548	345	9	,	,	PUNCT
cana-4548	345	10	t.	t.	PROPN
cana-4548	345	11	,	,	PUNCT
cana-4548	345	12	pal	pal	NOUN
cana-4548	345	13	,	,	PUNCT
cana-4548	345	14	m.	m.	NOUN
cana-4548	345	15	,	,	PUNCT
cana-4548	345	16	&	&	CCONJ
cana-4548	345	17	yager	yager	PROPN
cana-4548	345	18	,	,	PUNCT
cana-4548	345	19	r.	r.	PROPN
cana-4548	345	20	r.	r.	PROPN
cana-4548	345	21	(	(	PUNCT
cana-4548	345	22	2019	2019	NUM
cana-4548	345	23	)	)	PUNCT
cana-4548	345	24	.	.	PUNCT
cana-4548	346	1	picture	picture	NOUN
cana-4548	346	2	fuzzy	fuzzy	ADJ
cana-4548	346	3	dombi	dombi	NOUN
cana-4548	346	4	aggregation	aggregation	NOUN
cana-4548	346	5	operators	operator	NOUN
cana-4548	346	6	:	:	PUNCT
cana-4548	346	7	application	application	NOUN
cana-4548	346	8	to	to	ADP
cana-4548	346	9	madm	madm	NOUN
cana-4548	346	10	process	process	NOUN
cana-4548	346	11	,	,	PUNCT
cana-4548	346	12	applied	apply	VERB
cana-4548	346	13	soft	soft	ADJ
cana-4548	346	14	computing	computing	NOUN
cana-4548	346	15	,	,	PUNCT
cana-4548	346	16	74	74	NUM
cana-4548	346	17	,	,	PUNCT
cana-4548	346	18	99	99	NUM
cana-4548	346	19	-	-	SYM
cana-4548	346	20	109	109	NUM
cana-4548	346	21	.	.	PUNCT
cana-4548	347	1	[	[	X
cana-4548	347	2	12	12	NUM
cana-4548	347	3	]	]	X
cana-4548	347	4	jana	jana	PROPN
cana-4548	347	5	,	,	PUNCT
cana-4548	347	6	c.	c.	PROPN
cana-4548	347	7	,	,	PUNCT
cana-4548	347	8	&	&	CCONJ
cana-4548	347	9	pal	pal	NOUN
cana-4548	347	10	,	,	PUNCT
cana-4548	347	11	m.	m.	NOUN
cana-4548	347	12	(	(	PUNCT
cana-4548	347	13	2019	2019	NUM
cana-4548	347	14	)	)	PUNCT
cana-4548	347	15	.	.	PUNCT
cana-4548	348	1	assessment	assessment	NOUN
cana-4548	348	2	of	of	ADP
cana-4548	348	3	enterprise	enterprise	NOUN
cana-4548	348	4	performance	performance	NOUN
cana-4548	348	5	based	base	VERB
cana-4548	348	6	on	on	ADP
cana-4548	348	7	picture	picture	NOUN
cana-4548	348	8	fuzzy	fuzzy	ADJ
cana-4548	348	9	hamacher	hamacher	NOUN
cana-4548	348	10	aggregation	aggregation	NOUN
cana-4548	348	11	operators	operator	NOUN
cana-4548	348	12	,	,	PUNCT
cana-4548	348	13	symmetry	symmetry	NOUN
cana-4548	348	14	,	,	PUNCT
cana-4548	348	15	11(1	11(1	NUM
cana-4548	348	16	)	)	PUNCT
cana-4548	348	17	,	,	PUNCT
cana-4548	348	18	75	75	NUM
cana-4548	348	19	.	.	PUNCT
cana-4548	349	1	[	[	X
cana-4548	349	2	13	13	NUM
cana-4548	349	3	]	]	X
cana-4548	349	4	khan	khan	PROPN
cana-4548	349	5	,	,	PUNCT
cana-4548	349	6	s.	s.	PROPN
cana-4548	349	7	,	,	PUNCT
cana-4548	349	8	abdullah	abdullah	PROPN
cana-4548	349	9	,	,	PUNCT
cana-4548	349	10	s.	s.	PROPN
cana-4548	349	11	,	,	PUNCT
cana-4548	349	12	&	&	CCONJ
cana-4548	349	13	ashraf	ashraf	PROPN
cana-4548	349	14	,	,	PUNCT
cana-4548	349	15	s.	s.	PROPN
cana-4548	349	16	(	(	PUNCT
cana-4548	349	17	2019	2019	NUM
cana-4548	349	18	)	)	PUNCT
cana-4548	349	19	.	.	PUNCT
cana-4548	350	1	picture	picture	NOUN
cana-4548	350	2	fuzzy	fuzzy	ADJ
cana-4548	350	3	aggregation	aggregation	NOUN
cana-4548	350	4	information	information	NOUN
cana-4548	350	5	based	base	VERB
cana-4548	350	6	on	on	ADP
cana-4548	350	7	einstein	einstein	ADJ
cana-4548	350	8	operations	operation	NOUN
cana-4548	350	9	and	and	CCONJ
cana-4548	350	10	their	their	PRON
cana-4548	350	11	application	application	NOUN
cana-4548	350	12	in	in	ADP
cana-4548	350	13	decision	decision	NOUN
cana-4548	350	14	making	making	NOUN
cana-4548	350	15	,	,	PUNCT
cana-4548	350	16	mathematical	mathematical	ADJ
cana-4548	350	17	sciences	science	NOUN
cana-4548	350	18	,	,	PUNCT
cana-4548	350	19	13(3	13(3	NUM
cana-4548	350	20	)	)	PUNCT
cana-4548	350	21	,	,	PUNCT
cana-4548	350	22	213	213	NUM
cana-4548	350	23	-	-	SYM
cana-4548	350	24	229	229	NUM
cana-4548	350	25	.	.	PUNCT
cana-4548	351	1	[	[	X
cana-4548	351	2	14	14	NUM
cana-4548	351	3	]	]	X
cana-4548	351	4	khan	khan	PROPN
cana-4548	351	5	,	,	PUNCT
cana-4548	351	6	q.	q.	PROPN
cana-4548	351	7	,	,	PUNCT
cana-4548	351	8	riaz	riaz	PROPN
cana-4548	351	9	,	,	PUNCT
cana-4548	351	10	m.	m.	NOUN
cana-4548	351	11	,	,	PUNCT
cana-4548	351	12	&	&	CCONJ
cana-4548	351	13	latif	latif	PROPN
cana-4548	351	14	,	,	PUNCT
cana-4548	351	15	s.	s.	PROPN
cana-4548	351	16	(	(	PUNCT
cana-4548	351	17	2022	2022	NUM
cana-4548	351	18	)	)	PUNCT
cana-4548	351	19	.	.	PUNCT
cana-4548	352	1	multiple	multiple	ADJ
cana-4548	352	2	attribute	attribute	NOUN
cana-4548	352	3	group	group	NOUN
cana-4548	352	4	decision	decision	NOUN
cana-4548	352	5	making	making	NOUN
cana-4548	352	6	based	base	VERB
cana-4548	352	7	on	on	ADP
cana-4548	352	8	intuitionistic	intuitionistic	ADJ
cana-4548	352	9	fuzzy	fuzzy	ADJ
cana-4548	352	10	schweizersklar	schweizersklar	ADJ
cana-4548	352	11	generalized	generalized	ADJ
cana-4548	352	12	power	power	NOUN
cana-4548	352	13	aggregation	aggregation	NOUN
cana-4548	352	14	operators	operator	NOUN
cana-4548	352	15	,	,	PUNCT
cana-4548	352	16	mathematical	mathematical	ADJ
cana-4548	352	17	problems	problem	NOUN
cana-4548	352	18	in	in	ADP
cana-4548	352	19	engineering	engineering	NOUN
cana-4548	352	20	,	,	PUNCT
cana-4548	352	21	2022(1	2022(1	NUM
cana-4548	352	22	)	)	PUNCT
cana-4548	352	23	,	,	PUNCT
cana-4548	352	24	4634411	4634411	NUM
cana-4548	352	25	.	.	PUNCT
cana-4548	353	1	[	[	X
cana-4548	353	2	15	15	NUM
cana-4548	353	3	]	]	X
cana-4548	353	4	lin	lin	PROPN
cana-4548	353	5	,	,	PUNCT
cana-4548	353	6	m.	m.	NOUN
cana-4548	353	7	,	,	PUNCT
cana-4548	353	8	li	li	PROPN
cana-4548	353	9	,	,	PUNCT
cana-4548	353	10	x.	x.	PROPN
cana-4548	353	11	,	,	PUNCT
cana-4548	353	12	chen	chen	PROPN
cana-4548	353	13	,	,	PUNCT
cana-4548	353	14	r.	r.	PROPN
cana-4548	353	15	,	,	PUNCT
cana-4548	353	16	fujita	fujita	PROPN
cana-4548	353	17	,	,	PUNCT
cana-4548	353	18	h.	h.	PROPN
cana-4548	353	19	,	,	PUNCT
cana-4548	353	20	&	&	CCONJ
cana-4548	353	21	lin	lin	PROPN
cana-4548	353	22	,	,	PUNCT
cana-4548	353	23	j.	j.	PROPN
cana-4548	353	24	(	(	PUNCT
cana-4548	353	25	2022	2022	NUM
cana-4548	353	26	)	)	PUNCT
cana-4548	353	27	.	.	PUNCT
cana-4548	354	1	picture	picture	NOUN
cana-4548	354	2	fuzzy	fuzzy	ADJ
cana-4548	354	3	interactional	interactional	ADJ
cana-4548	354	4	partitioned	partition	VERB
cana-4548	354	5	heronian	heronian	ADJ
cana-4548	354	6	mean	mean	NOUN
cana-4548	354	7	aggregation	aggregation	NOUN
cana-4548	354	8	operators	operator	NOUN
cana-4548	354	9	:	:	PUNCT
cana-4548	354	10	an	an	DET
cana-4548	354	11	application	application	NOUN
cana-4548	354	12	to	to	ADP
cana-4548	354	13	madm	madm	NOUN
cana-4548	354	14	process	process	NOUN
cana-4548	354	15	.	.	PUNCT
cana-4548	355	1	artificial	artificial	ADJ
cana-4548	355	2	intelligence	intelligence	NOUN
cana-4548	355	3	review	review	NOUN
cana-4548	355	4	,	,	PUNCT
cana-4548	355	5	1	1	NUM
cana-4548	355	6	-	-	SYM
cana-4548	355	7	38	38	NUM
cana-4548	355	8	.	.	PUNCT
cana-4548	356	1	[	[	X
cana-4548	356	2	16	16	NUM
cana-4548	356	3	]	]	X
cana-4548	356	4	ma	ma	PROPN
cana-4548	356	5	,	,	PUNCT
cana-4548	356	6	l.	l.	PROPN
cana-4548	356	7	,	,	PUNCT
cana-4548	356	8	zhang	zhang	PROPN
cana-4548	356	9	,	,	PUNCT
cana-4548	356	10	t.	t.	PROPN
cana-4548	356	11	,	,	PUNCT
cana-4548	356	12	&	&	CCONJ
cana-4548	356	13	wang	wang	PROPN
cana-4548	356	14	,	,	PUNCT
cana-4548	356	15	y.	y.	PROPN
cana-4548	356	16	(	(	PUNCT
cana-4548	356	17	2024	2024	NUM
cana-4548	356	18	)	)	PUNCT
cana-4548	356	19	.	.	PUNCT
cana-4548	357	1	decision	decision	NOUN
cana-4548	357	2	algorithm	algorithm	NOUN
cana-4548	357	3	for	for	ADP
cana-4548	357	4	q	q	ADJ
cana-4548	357	5	-	-	PUNCT
cana-4548	357	6	rung	rung	ADJ
cana-4548	357	7	orthopair	orthopair	ADJ
cana-4548	357	8	fuzzy	fuzzy	ADJ
cana-4548	357	9	information	information	NOUN
cana-4548	357	10	based	base	VERB
cana-4548	357	11	on	on	ADP
cana-4548	357	12	schweizer	schweizer	PROPN
cana-4548	357	13	-	-	PUNCT
cana-4548	357	14	sklar	sklar	ADJ
cana-4548	357	15	aggregation	aggregation	NOUN
cana-4548	357	16	operators	operator	NOUN
cana-4548	357	17	with	with	ADP
cana-4548	357	18	applications	application	NOUN
cana-4548	357	19	in	in	ADP
cana-4548	357	20	agricultural	agricultural	ADJ
cana-4548	357	21	systems	system	NOUN
cana-4548	357	22	,	,	PUNCT
cana-4548	357	23	ieee	ieee	NOUN
cana-4548	357	24	access	access	NOUN
cana-4548	357	25	,	,	PUNCT
cana-4548	357	26	12	12	NUM
cana-4548	357	27	,	,	PUNCT
cana-4548	357	28	25762	25762	NUM
cana-4548	357	29	-	-	SYM
cana-4548	357	30	25778	25778	NUM
cana-4548	357	31	.	.	PUNCT
cana-4548	358	1	[	[	X
cana-4548	358	2	17	17	NUM
cana-4548	358	3	]	]	PUNCT
cana-4548	358	4	qiyas	qiyas	NOUN
cana-4548	358	5	,	,	PUNCT
cana-4548	358	6	m.	m.	NOUN
cana-4548	358	7	,	,	PUNCT
cana-4548	358	8	khan	khan	PROPN
cana-4548	358	9	,	,	PUNCT
cana-4548	358	10	m.	m.	NOUN
cana-4548	358	11	a.	a.	PROPN
cana-4548	358	12	,	,	PUNCT
cana-4548	358	13	khan	khan	PROPN
cana-4548	358	14	,	,	PUNCT
cana-4548	358	15	s.	s.	PROPN
cana-4548	358	16	,	,	PUNCT
cana-4548	358	17	&	&	CCONJ
cana-4548	358	18	abdullah	abdullah	PROPN
cana-4548	358	19	,	,	PUNCT
cana-4548	358	20	s.	s.	PROPN
cana-4548	358	21	(	(	PUNCT
cana-4548	358	22	2020	2020	NUM
cana-4548	358	23	)	)	PUNCT
cana-4548	358	24	.	.	PUNCT
cana-4548	359	1	concept	concept	NOUN
cana-4548	359	2	of	of	ADP
cana-4548	359	3	yager	yager	NOUN
cana-4548	359	4	operators	operator	NOUN
cana-4548	359	5	with	with	ADP
cana-4548	359	6	the	the	DET
cana-4548	359	7	picture	picture	NOUN
cana-4548	359	8	fuzzy	fuzzy	ADJ
cana-4548	359	9	set	set	VERB
cana-4548	359	10	environment	environment	NOUN
cana-4548	359	11	and	and	CCONJ
cana-4548	359	12	its	its	PRON
cana-4548	359	13	application	application	NOUN
cana-4548	359	14	to	to	ADP
cana-4548	359	15	emergency	emergency	NOUN
cana-4548	359	16	program	program	NOUN
cana-4548	359	17	selection	selection	NOUN
cana-4548	359	18	.	.	PUNCT
cana-4548	360	1	international	international	ADJ
cana-4548	360	2	journal	journal	NOUN
cana-4548	360	3	of	of	ADP
cana-4548	360	4	intelligent	intelligent	ADJ
cana-4548	360	5	computing	computing	NOUN
cana-4548	360	6	and	and	CCONJ
cana-4548	360	7	cybernetics	cybernetic	NOUN
cana-4548	360	8	,	,	PUNCT
cana-4548	360	9	13(4	13(4	NUM
cana-4548	360	10	)	)	PUNCT
cana-4548	360	11	,	,	PUNCT
cana-4548	360	12	455	455	NUM
cana-4548	360	13	-	-	SYM
cana-4548	360	14	483	483	NUM
cana-4548	360	15	..	..	PUNCT
cana-4548	361	1	[	[	X
cana-4548	361	2	18	18	NUM
cana-4548	361	3	]	]	X
cana-4548	361	4	qin	qin	PROPN
cana-4548	361	5	,	,	PUNCT
cana-4548	361	6	y.	y.	PROPN
cana-4548	361	7	,	,	PUNCT
cana-4548	361	8	cui	cui	PROPN
cana-4548	361	9	,	,	PUNCT
cana-4548	361	10	x.	x.	PROPN
cana-4548	361	11	,	,	PUNCT
cana-4548	361	12	huang	huang	PROPN
cana-4548	361	13	,	,	PUNCT
cana-4548	361	14	m.	m.	NOUN
cana-4548	361	15	,	,	PUNCT
cana-4548	361	16	zhong	zhong	PROPN
cana-4548	361	17	,	,	PUNCT
cana-4548	361	18	y.	y.	PROPN
cana-4548	361	19	,	,	PUNCT
cana-4548	361	20	tang	tang	PROPN
cana-4548	361	21	,	,	PUNCT
cana-4548	361	22	z.	z.	PROPN
cana-4548	361	23	,	,	PUNCT
cana-4548	361	24	&	&	CCONJ
cana-4548	361	25	shi	shi	PROPN
cana-4548	361	26	,	,	PUNCT
cana-4548	361	27	p.	p.	NOUN
cana-4548	361	28	(	(	PUNCT
cana-4548	361	29	2021	2021	NUM
cana-4548	361	30	)	)	PUNCT
cana-4548	361	31	.	.	PUNCT
cana-4548	362	1	multiple	multiple	ADJ
cana-4548	362	2	-	-	PUNCT
cana-4548	362	3	attribute	attribute	NOUN
cana-4548	362	4	decision	decision	NOUN
cana-4548	362	5	-	-	PUNCT
cana-4548	362	6	making	making	NOUN
cana-4548	362	7	based	base	VERB
cana-4548	362	8	on	on	ADP
cana-4548	362	9	picture	picture	NOUN
cana-4548	362	10	fuzzy	fuzzy	ADJ
cana-4548	362	11	archimedean	archimedean	ADJ
cana-4548	362	12	power	power	NOUN
cana-4548	362	13	maclaurin	maclaurin	NOUN
cana-4548	362	14	symmetric	symmetric	ADJ
cana-4548	362	15	mean	mean	NOUN
cana-4548	362	16	operators	operator	NOUN
cana-4548	362	17	.	.	PUNCT
cana-4548	363	1	granular	granular	ADJ
cana-4548	363	2	computing	computing	NOUN
cana-4548	363	3	,	,	PUNCT
cana-4548	363	4	6(3	6(3	NUM
cana-4548	363	5	)	)	PUNCT
cana-4548	363	6	,	,	PUNCT
cana-4548	363	7	737	737	NUM
cana-4548	363	8	-	-	SYM
cana-4548	363	9	761	761	NUM
cana-4548	363	10	.	.	PUNCT
cana-4548	364	1	[	[	X
cana-4548	364	2	19	19	NUM
cana-4548	364	3	]	]	PUNCT
cana-4548	364	4	seikh	seikh	PROPN
cana-4548	364	5	,	,	PUNCT
cana-4548	364	6	m.	m.	PROPN
cana-4548	364	7	r.	r.	PROPN
cana-4548	364	8	,	,	PUNCT
cana-4548	364	9	&	&	CCONJ
cana-4548	364	10	mandal	mandal	PROPN
cana-4548	364	11	,	,	PUNCT
cana-4548	364	12	u.	u.	PROPN
cana-4548	364	13	(	(	PUNCT
cana-4548	364	14	2021	2021	NUM
cana-4548	364	15	)	)	PUNCT
cana-4548	364	16	.	.	PUNCT
cana-4548	365	1	some	some	DET
cana-4548	365	2	picture	picture	NOUN
cana-4548	365	3	fuzzy	fuzzy	ADJ
cana-4548	365	4	aggregation	aggregation	NOUN
cana-4548	365	5	operators	operator	NOUN
cana-4548	365	6	based	base	VERB
cana-4548	365	7	on	on	ADP
cana-4548	365	8	frank	frank	PROPN
cana-4548	365	9	t	t	PROPN
cana-4548	365	10	-	-	PUNCT
cana-4548	365	11	norm	norm	NOUN
cana-4548	365	12	and	and	CCONJ
cana-4548	365	13	t	t	NOUN
cana-4548	365	14	-	-	PUNCT
cana-4548	365	15	conorm	conorm	NOUN
cana-4548	365	16	:	:	PUNCT
cana-4548	365	17	application	application	NOUN
cana-4548	365	18	to	to	ADP
cana-4548	365	19	madm	madm	NOUN
cana-4548	365	20	process	process	NOUN
cana-4548	365	21	.	.	PUNCT
cana-4548	366	1	informatica	informatica	PROPN
cana-4548	366	2	,	,	PUNCT
cana-4548	366	3	45(3	45(3	NUM
cana-4548	366	4	)	)	PUNCT
cana-4548	366	5	.	.	PUNCT
cana-4548	367	1	[	[	X
cana-4548	367	2	20	20	NUM
cana-4548	367	3	]	]	PUNCT
cana-4548	367	4	senapati	senapati	NOUN
cana-4548	367	5	,	,	PUNCT
cana-4548	367	6	t.	t.	NOUN
cana-4548	367	7	(	(	PUNCT
cana-4548	367	8	2022	2022	NUM
cana-4548	367	9	)	)	PUNCT
cana-4548	367	10	.	.	PUNCT
cana-4548	368	1	approaches	approach	NOUN
cana-4548	368	2	to	to	ADP
cana-4548	368	3	multi	multi	ADJ
cana-4548	368	4	-	-	ADJ
cana-4548	368	5	attribute	attribute	NOUN
cana-4548	368	6	decision	decision	NOUN
cana-4548	368	7	-	-	PUNCT
cana-4548	368	8	making	making	NOUN
cana-4548	368	9	based	base	VERB
cana-4548	368	10	on	on	ADP
cana-4548	368	11	picture	picture	NOUN
cana-4548	368	12	fuzzy	fuzzy	ADJ
cana-4548	368	13	aczel	aczel	NOUN
cana-4548	368	14	-	-	PUNCT
cana-4548	368	15	alsina	alsina	NOUN
cana-4548	368	16	average	average	ADJ
cana-4548	368	17	aggregation	aggregation	NOUN
cana-4548	368	18	operators	operator	NOUN
cana-4548	368	19	.	.	PUNCT
cana-4548	369	1	computational	computational	ADJ
cana-4548	369	2	and	and	CCONJ
cana-4548	369	3	applied	applied	ADJ
cana-4548	369	4	mathematics	mathematic	NOUN
cana-4548	369	5	,	,	PUNCT
cana-4548	369	6	41(1	41(1	NUM
cana-4548	369	7	)	)	PUNCT
cana-4548	369	8	,	,	PUNCT
cana-4548	369	9	40	40	NUM
cana-4548	369	10	.	.	PUNCT
cana-4548	370	1	[	[	X
cana-4548	370	2	21	21	NUM
cana-4548	370	3	]	]	X
cana-4548	370	4	hussain	hussain	PROPN
cana-4548	370	5	,	,	PUNCT
cana-4548	370	6	a.	a.	PROPN
cana-4548	370	7	,	,	PUNCT
cana-4548	370	8	latif	latif	PROPN
cana-4548	370	9	,	,	PUNCT
cana-4548	370	10	s.	s.	PROPN
cana-4548	370	11	,	,	PUNCT
cana-4548	370	12	&	&	CCONJ
cana-4548	370	13	ullah	ullah	PROPN
cana-4548	370	14	,	,	PUNCT
cana-4548	370	15	k.	k.	PROPN
cana-4548	370	16	(	(	PUNCT
cana-4548	370	17	2022	2022	NUM
cana-4548	370	18	)	)	PUNCT
cana-4548	370	19	.	.	PUNCT
cana-4548	371	1	a	a	DET
cana-4548	371	2	novel	novel	ADJ
cana-4548	371	3	approach	approach	NOUN
cana-4548	371	4	of	of	ADP
cana-4548	371	5	picture	picture	NOUN
cana-4548	371	6	fuzzy	fuzzy	ADJ
cana-4548	371	7	sets	set	NOUN
cana-4548	371	8	with	with	ADP
cana-4548	371	9	unknown	unknown	ADJ
cana-4548	371	10	degree	degree	NOUN
cana-4548	371	11	of	of	ADP
cana-4548	371	12	weights	weight	NOUN
cana-4548	371	13	based	base	VERB
cana-4548	371	14	on	on	ADP
cana-4548	371	15	schweizer	schweizer	PROPN
cana-4548	371	16	-	-	PUNCT
cana-4548	371	17	sklar	sklar	ADJ
cana-4548	371	18	aggregation	aggregation	NOUN
cana-4548	371	19	operators	operator	NOUN
cana-4548	371	20	,	,	PUNCT
cana-4548	371	21	journal	journal	NOUN
cana-4548	371	22	of	of	ADP
cana-4548	371	23	innovative	innovative	ADJ
cana-4548	371	24	research	research	NOUN
cana-4548	371	25	in	in	ADP
cana-4548	371	26	mathematical	mathematical	ADJ
cana-4548	371	27	and	and	CCONJ
cana-4548	371	28	computational	computational	ADJ
cana-4548	371	29	sciences	science	NOUN
cana-4548	371	30	,	,	PUNCT
cana-4548	371	31	1(2	1(2	NUM
cana-4548	371	32	)	)	PUNCT
cana-4548	371	33	,	,	PUNCT
cana-4548	371	34	18	18	NUM
cana-4548	371	35	-	-	SYM
cana-4548	371	36	39	39	NUM
cana-4548	371	37	.	.	PUNCT
cana-4548	372	1	communications	communication	NOUN
cana-4548	372	2	on	on	ADP
cana-4548	372	3	applied	apply	VERB
cana-4548	372	4	nonlinear	nonlinear	ADJ
cana-4548	372	5	analysis	analysis	NOUN
cana-4548	372	6	issn	issn	NOUN
cana-4548	372	7	:	:	PUNCT
cana-4548	372	8	1074	1074	NUM
cana-4548	372	9	-	-	PUNCT
cana-4548	372	10	133x	133x	NUM
cana-4548	372	11	vol	vol	NOUN
cana-4548	372	12	32	32	NUM
cana-4548	372	13	no	no	NOUN
cana-4548	372	14	.	.	PUNCT
cana-4548	373	1	9s	9s	NUM
cana-4548	373	2	(	(	PUNCT
cana-4548	373	3	2025	2025	NUM
cana-4548	373	4	)	)	PUNCT
cana-4548	373	5	2695	2695	NUM
cana-4548	373	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4548	374	1	[	[	X
cana-4548	374	2	22	22	NUM
cana-4548	374	3	]	]	PUNCT
cana-4548	374	4	tanuja	tanuja	NOUN
cana-4548	374	5	,	,	PUNCT
cana-4548	374	6	p.	p.	NOUN
cana-4548	374	7	,	,	PUNCT
cana-4548	374	8	&	&	CCONJ
cana-4548	374	9	komal	komal	PROPN
cana-4548	374	10	.	.	PUNCT
cana-4548	375	1	(	(	PUNCT
cana-4548	375	2	2022	2022	NUM
cana-4548	375	3	)	)	PUNCT
cana-4548	375	4	.	.	PUNCT
cana-4548	376	1	picture	picture	NOUN
cana-4548	376	2	fuzzy	fuzzy	ADJ
cana-4548	376	3	einstein	einstein	NOUN
cana-4548	376	4	confidence	confidence	NOUN
cana-4548	376	5	hybrid	hybrid	ADJ
cana-4548	376	6	aggregation	aggregation	NOUN
cana-4548	376	7	operators	operator	NOUN
cana-4548	376	8	and	and	CCONJ
cana-4548	376	9	its	its	PRON
cana-4548	376	10	applications	application	NOUN
cana-4548	376	11	in	in	ADP
cana-4548	376	12	mcgdm	mcgdm	ADJ
cana-4548	376	13	problems	problem	NOUN
cana-4548	376	14	,	,	PUNCT
cana-4548	376	15	applied	apply	VERB
cana-4548	376	16	innovative	innovative	ADJ
cana-4548	376	17	research	research	NOUN
cana-4548	376	18	,	,	PUNCT
cana-4548	376	19	3(1	3(1	NUM
cana-4548	376	20	-	-	SYM
cana-4548	376	21	4	4	NUM
cana-4548	376	22	)	)	PUNCT
cana-4548	376	23	,	,	PUNCT
cana-4548	376	24	11	11	NUM
cana-4548	376	25	-	-	SYM
cana-4548	376	26	24	24	NUM
cana-4548	376	27	.	.	PUNCT
cana-4548	377	1	[	[	X
cana-4548	377	2	23	23	NUM
cana-4548	377	3	]	]	PUNCT
cana-4548	377	4	ullah	ullah	PROPN
cana-4548	377	5	,	,	PUNCT
cana-4548	377	6	k.	k.	PROPN
cana-4548	377	7	(	(	PUNCT
cana-4548	377	8	2021	2021	NUM
cana-4548	377	9	)	)	PUNCT
cana-4548	377	10	.	.	PUNCT
cana-4548	378	1	picture	picture	NOUN
cana-4548	378	2	fuzzy	fuzzy	ADJ
cana-4548	378	3	maclaurin	maclaurin	NOUN
cana-4548	378	4	symmetric	symmetric	ADJ
cana-4548	378	5	mean	mean	NOUN
cana-4548	378	6	operators	operator	NOUN
cana-4548	378	7	and	and	CCONJ
cana-4548	378	8	their	their	PRON
cana-4548	378	9	applications	application	NOUN
cana-4548	378	10	in	in	ADP
cana-4548	378	11	solving	solve	VERB
cana-4548	378	12	multiattribute	multiattribute	NOUN
cana-4548	378	13	decision	decision	NOUN
cana-4548	378	14	-	-	PUNCT
cana-4548	378	15	making	make	VERB
cana-4548	378	16	problems	problem	NOUN
cana-4548	378	17	.	.	PUNCT
cana-4548	379	1	mathematical	mathematical	ADJ
cana-4548	379	2	problems	problem	NOUN
cana-4548	379	3	in	in	ADP
cana-4548	379	4	engineering	engineering	NOUN
cana-4548	379	5	,	,	PUNCT
cana-4548	379	6	1	1	NUM
cana-4548	379	7	-	-	SYM
cana-4548	379	8	13	13	NUM
cana-4548	379	9	.	.	PUNCT
cana-4548	380	1	[	[	X
cana-4548	380	2	24	24	NUM
cana-4548	380	3	]	]	PUNCT
cana-4548	380	4	ullah	ullah	PROPN
cana-4548	380	5	,	,	PUNCT
cana-4548	380	6	k.	k.	PROPN
cana-4548	380	7	,	,	PUNCT
cana-4548	380	8	naeem	naeem	PROPN
cana-4548	380	9	,	,	PUNCT
cana-4548	380	10	m.	m.	NOUN
cana-4548	380	11	,	,	PUNCT
cana-4548	380	12	hussain	hussain	PROPN
cana-4548	380	13	,	,	PUNCT
cana-4548	380	14	a.	a.	NOUN
cana-4548	380	15	,	,	PUNCT
cana-4548	380	16	waqas	waqas	ADJ
cana-4548	380	17	,	,	PUNCT
cana-4548	380	18	m.	m.	NOUN
cana-4548	380	19	,	,	PUNCT
cana-4548	380	20	&	&	CCONJ
cana-4548	380	21	haleemzai	haleemzai	PROPN
cana-4548	380	22	,	,	PUNCT
cana-4548	380	23	i.	i.	PROPN
cana-4548	380	24	(	(	PUNCT
cana-4548	380	25	2023	2023	NUM
cana-4548	380	26	)	)	PUNCT
cana-4548	380	27	.	.	PUNCT
cana-4548	381	1	evaluation	evaluation	NOUN
cana-4548	381	2	of	of	ADP
cana-4548	381	3	electric	electric	ADJ
cana-4548	381	4	motor	motor	NOUN
cana-4548	381	5	cars	car	NOUN
cana-4548	381	6	based	base	VERB
cana-4548	381	7	frank	frank	PROPN
cana-4548	381	8	power	power	NOUN
cana-4548	381	9	aggregation	aggregation	NOUN
cana-4548	381	10	operators	operator	NOUN
cana-4548	381	11	under	under	ADP
cana-4548	381	12	picture	picture	NOUN
cana-4548	381	13	fuzzy	fuzzy	ADJ
cana-4548	381	14	information	information	NOUN
cana-4548	381	15	and	and	CCONJ
cana-4548	381	16	a	a	DET
cana-4548	381	17	multi	multi	ADJ
cana-4548	381	18	-	-	ADJ
cana-4548	381	19	attribute	attribute	NOUN
cana-4548	381	20	group	group	NOUN
cana-4548	381	21	decision	decision	NOUN
cana-4548	381	22	-	-	PUNCT
cana-4548	381	23	making	make	VERB
cana-4548	381	24	process	process	NOUN
cana-4548	381	25	.	.	PUNCT
cana-4548	382	1	ieee	ieee	NOUN
cana-4548	382	2	access	access	NOUN
cana-4548	382	3	,	,	PUNCT
cana-4548	382	4	11	11	NUM
cana-4548	382	5	,	,	PUNCT
cana-4548	382	6	6720167219	6720167219	NUM
cana-4548	382	7	.	.	PUNCT
cana-4548	383	1	[	[	X
cana-4548	383	2	25	25	NUM
cana-4548	383	3	]	]	X
cana-4548	383	4	wang	wang	PROPN
cana-4548	383	5	,	,	PUNCT
cana-4548	383	6	r.	r.	PROPN
cana-4548	383	7	,	,	PUNCT
cana-4548	383	8	wang	wang	PROPN
cana-4548	383	9	,	,	PUNCT
cana-4548	383	10	j.	j.	PROPN
cana-4548	383	11	,	,	PUNCT
cana-4548	383	12	gao	gao	PROPN
cana-4548	383	13	,	,	PUNCT
cana-4548	383	14	h.	h.	PROPN
cana-4548	383	15	,	,	PUNCT
cana-4548	383	16	&	&	CCONJ
cana-4548	383	17	wei	wei	PROPN
cana-4548	383	18	,	,	PUNCT
cana-4548	383	19	g.	g.	PROPN
cana-4548	383	20	(	(	PUNCT
cana-4548	383	21	2018	2018	NUM
cana-4548	383	22	)	)	PUNCT
cana-4548	383	23	.	.	PUNCT
cana-4548	384	1	methods	method	NOUN
cana-4548	384	2	for	for	ADP
cana-4548	384	3	madm	madm	NOUN
cana-4548	384	4	with	with	ADP
cana-4548	384	5	picture	picture	NOUN
cana-4548	384	6	fuzzy	fuzzy	ADJ
cana-4548	384	7	muirhead	muirhead	NOUN
cana-4548	384	8	mean	mean	NOUN
cana-4548	384	9	operators	operator	NOUN
cana-4548	384	10	and	and	CCONJ
cana-4548	384	11	their	their	PRON
cana-4548	384	12	application	application	NOUN
cana-4548	384	13	for	for	ADP
cana-4548	384	14	evaluating	evaluate	VERB
cana-4548	384	15	the	the	DET
cana-4548	384	16	financial	financial	ADJ
cana-4548	384	17	investment	investment	NOUN
cana-4548	384	18	risk	risk	NOUN
cana-4548	384	19	,	,	PUNCT
cana-4548	384	20	symmetry	symmetry	NOUN
cana-4548	384	21	,	,	PUNCT
cana-4548	384	22	11(1	11(1	NUM
cana-4548	384	23	)	)	PUNCT
cana-4548	384	24	,	,	PUNCT
cana-4548	384	25	6	6	NUM
cana-4548	384	26	.	.	PUNCT
cana-4548	385	1	[	[	X
cana-4548	385	2	26	26	NUM
cana-4548	385	3	]	]	X
cana-4548	385	4	wei	wei	PROPN
cana-4548	385	5	,	,	PUNCT
cana-4548	385	6	g.	g.	PROPN
cana-4548	385	7	(	(	PUNCT
cana-4548	385	8	2017	2017	NUM
cana-4548	385	9	)	)	PUNCT
cana-4548	385	10	.	.	PUNCT
cana-4548	386	1	picture	picture	NOUN
cana-4548	386	2	fuzzy	fuzzy	ADJ
cana-4548	386	3	aggregation	aggregation	NOUN
cana-4548	386	4	operators	operator	NOUN
cana-4548	386	5	and	and	CCONJ
cana-4548	386	6	their	their	PRON
cana-4548	386	7	application	application	NOUN
cana-4548	386	8	to	to	ADP
cana-4548	386	9	multiple	multiple	ADJ
cana-4548	386	10	attribute	attribute	NOUN
cana-4548	386	11	decision	decision	NOUN
cana-4548	386	12	making	making	NOUN
cana-4548	386	13	,	,	PUNCT
cana-4548	386	14	journal	journal	NOUN
cana-4548	386	15	of	of	ADP
cana-4548	386	16	intelligent	intelligent	ADJ
cana-4548	386	17	&	&	CCONJ
cana-4548	386	18	fuzzy	fuzzy	ADJ
cana-4548	386	19	systems	system	NOUN
cana-4548	386	20	,	,	PUNCT
cana-4548	386	21	33(2	33(2	NUM
cana-4548	386	22	)	)	PUNCT
cana-4548	386	23	,	,	PUNCT
cana-4548	386	24	713	713	NUM
cana-4548	386	25	-	-	SYM
cana-4548	386	26	724	724	NUM
cana-4548	386	27	.	.	PUNCT
cana-4548	387	1	[	[	X
cana-4548	387	2	27	27	NUM
cana-4548	387	3	]	]	X
cana-4548	387	4	wei	wei	PROPN
cana-4548	387	5	,	,	PUNCT
cana-4548	387	6	g.	g.	PROPN
cana-4548	387	7	(	(	PUNCT
cana-4548	387	8	2018	2018	NUM
cana-4548	387	9	)	)	PUNCT
cana-4548	387	10	.	.	PUNCT
cana-4548	388	1	picture	picture	NOUN
cana-4548	388	2	fuzzy	fuzzy	ADJ
cana-4548	388	3	hamacher	hamacher	NOUN
cana-4548	388	4	aggregation	aggregation	NOUN
cana-4548	388	5	operators	operator	NOUN
cana-4548	388	6	and	and	CCONJ
cana-4548	388	7	their	their	PRON
cana-4548	388	8	application	application	NOUN
cana-4548	388	9	to	to	ADP
cana-4548	388	10	multiple	multiple	ADJ
cana-4548	388	11	attribute	attribute	NOUN
cana-4548	388	12	decision	decision	NOUN
cana-4548	388	13	making	making	NOUN
cana-4548	388	14	.	.	PUNCT
cana-4548	389	1	,	,	PUNCT
cana-4548	389	2	fundamenta	fundamenta	PROPN
cana-4548	389	3	informaticae	informaticae	PROPN
cana-4548	389	4	,	,	PUNCT
cana-4548	389	5	157(3	157(3	NUM
cana-4548	389	6	)	)	PUNCT
cana-4548	389	7	,	,	PUNCT
cana-4548	389	8	271	271	NUM
cana-4548	389	9	-	-	SYM
cana-4548	389	10	320	320	NUM
cana-4548	389	11	.	.	PUNCT
cana-4548	390	1	[	[	X
cana-4548	390	2	28	28	NUM
cana-4548	390	3	]	]	X
cana-4548	390	4	wei	wei	PROPN
cana-4548	390	5	,	,	PUNCT
cana-4548	390	6	d.	d.	PROPN
cana-4548	390	7	,	,	PUNCT
cana-4548	390	8	liu	liu	PROPN
cana-4548	390	9	,	,	PUNCT
cana-4548	390	10	x.	x.	PROPN
cana-4548	390	11	,	,	PUNCT
cana-4548	390	12	&	&	CCONJ
cana-4548	390	13	ma	ma	PROPN
cana-4548	390	14	,	,	PUNCT
cana-4548	390	15	z.	z.	PROPN
cana-4548	390	16	(	(	PUNCT
cana-4548	390	17	2022	2022	NUM
cana-4548	390	18	)	)	PUNCT
cana-4548	390	19	.	.	PUNCT
cana-4548	391	1	fermatean	fermatean	PROPN
cana-4548	391	2	fuzzy	fuzzy	ADJ
cana-4548	391	3	schweizer	schweizer	PROPN
cana-4548	391	4	-	-	PUNCT
cana-4548	391	5	sklar	sklar	ADJ
cana-4548	391	6	operators	operator	NOUN
cana-4548	391	7	and	and	CCONJ
cana-4548	391	8	bwmentropy	bwmentropy	NOUN
cana-4548	391	9	-	-	PUNCT
cana-4548	391	10	based	base	VERB
cana-4548	391	11	combined	combined	ADJ
cana-4548	391	12	compromise	compromise	NOUN
cana-4548	391	13	solution	solution	NOUN
cana-4548	391	14	approach	approach	NOUN
cana-4548	391	15	:	:	PUNCT
cana-4548	391	16	an	an	DET
cana-4548	391	17	application	application	NOUN
cana-4548	391	18	to	to	ADP
cana-4548	391	19	green	green	ADJ
cana-4548	391	20	supplier	supplier	NOUN
cana-4548	391	21	selection	selection	NOUN
cana-4548	391	22	,	,	PUNCT
cana-4548	391	23	entropy	entropy	NOUN
cana-4548	391	24	,	,	PUNCT
cana-4548	391	25	24(6	24(6	NUM
cana-4548	391	26	)	)	PUNCT
cana-4548	391	27	,	,	PUNCT
cana-4548	391	28	776	776	NUM
cana-4548	391	29	.	.	PUNCT
cana-4548	392	1	[	[	X
cana-4548	392	2	29	29	NUM
cana-4548	392	3	]	]	X
cana-4548	392	4	yager	yager	NOUN
cana-4548	392	5	,	,	PUNCT
cana-4548	392	6	r.	r.	PROPN
cana-4548	392	7	r.	r.	PROPN
cana-4548	392	8	(	(	PUNCT
cana-4548	392	9	1988	1988	NUM
cana-4548	392	10	)	)	PUNCT
cana-4548	392	11	.	.	PUNCT
cana-4548	393	1	on	on	ADP
cana-4548	393	2	ordered	order	VERB
cana-4548	393	3	weighted	weight	VERB
cana-4548	393	4	averaging	average	VERB
cana-4548	393	5	aggregation	aggregation	NOUN
cana-4548	393	6	operators	operator	NOUN
cana-4548	393	7	in	in	ADP
cana-4548	393	8	multi	multi	ADJ
cana-4548	393	9	criteria	criterion	NOUN
cana-4548	393	10	decision	decision	NOUN
cana-4548	393	11	making	making	NOUN
cana-4548	393	12	.	.	PUNCT
cana-4548	394	1	ieee	ieee	NOUN
cana-4548	394	2	transactions	transaction	NOUN
cana-4548	394	3	on	on	ADP
cana-4548	394	4	systems	system	NOUN
cana-4548	394	5	man	man	NOUN
cana-4548	394	6	and	and	CCONJ
cana-4548	394	7	cybernetics	cybernetic	NOUN
cana-4548	394	8	,	,	PUNCT
cana-4548	394	9	18(1)(1	18(1)(1	NOUN
cana-4548	394	10	)	)	PUNCT
cana-4548	394	11	,	,	PUNCT
cana-4548	394	12	183	183	NUM
cana-4548	394	13	-	-	SYM
cana-4548	394	14	190	190	NUM
cana-4548	394	15	.	.	PUNCT
cana-4548	395	1	[	[	X
cana-4548	395	2	30	30	NUM
cana-4548	395	3	]	]	X
cana-4548	395	4	yager	yager	NOUN
cana-4548	395	5	,	,	PUNCT
cana-4548	395	6	r.	r.	PROPN
cana-4548	395	7	r	r	PROPN
cana-4548	395	8	(	(	PUNCT
cana-4548	395	9	2001	2001	NUM
cana-4548	395	10	)	)	PUNCT
cana-4548	395	11	.	.	PUNCT
cana-4548	396	1	the	the	DET
cana-4548	396	2	power	power	NOUN
cana-4548	396	3	average	average	NOUN
cana-4548	396	4	operator	operator	NOUN
cana-4548	396	5	.	.	PUNCT
cana-4548	397	1	ieee	ieee	NOUN
cana-4548	397	2	transactions	transaction	NOUN
cana-4548	397	3	on	on	ADP
cana-4548	397	4	systems	system	NOUN
cana-4548	397	5	,	,	PUNCT
cana-4548	397	6	man	man	NOUN
cana-4548	397	7	,	,	PUNCT
cana-4548	397	8	and	and	CCONJ
cana-4548	397	9	cybernetics	cybernetic	NOUN
cana-4548	397	10	-	-	PUNCT
cana-4548	397	11	part	part	NOUN
cana-4548	397	12	a	a	DET
cana-4548	397	13	:	:	PUNCT
cana-4548	397	14	systems	system	NOUN
cana-4548	397	15	and	and	CCONJ
cana-4548	397	16	humans	human	NOUN
cana-4548	397	17	,	,	PUNCT
cana-4548	397	18	31	31	NUM
cana-4548	397	19	(	(	PUNCT
cana-4548	397	20	6	6	NUM
cana-4548	397	21	)	)	PUNCT
cana-4548	397	22	,	,	PUNCT
cana-4548	397	23	724	724	NUM
cana-4548	397	24	-	-	SYM
cana-4548	397	25	731	731	NUM
cana-4548	397	26	.	.	PUNCT
cana-4548	398	1	[	[	X
cana-4548	398	2	31	31	NUM
cana-4548	398	3	]	]	SYM
cana-4548	398	4	zadeh	zadeh	PROPN
cana-4548	398	5	,	,	PUNCT
cana-4548	398	6	l.	l.	PROPN
cana-4548	398	7	a.	a.	PROPN
cana-4548	398	8	(	(	PUNCT
cana-4548	398	9	1965	1965	NUM
cana-4548	398	10	)	)	PUNCT
cana-4548	398	11	.	.	PUNCT
cana-4548	398	12	fuzzy	fuzzy	ADJ
cana-4548	398	13	sets	set	NOUN
cana-4548	398	14	.	.	PUNCT
cana-4548	399	1	information	information	NOUN
cana-4548	399	2	and	and	CCONJ
cana-4548	399	3	control	control	NOUN
cana-4548	399	4	,	,	PUNCT
cana-4548	399	5	8(3	8(3	NUM
cana-4548	399	6	)	)	PUNCT
cana-4548	399	7	,	,	PUNCT
cana-4548	399	8	338	338	NUM
cana-4548	399	9	-	-	SYM
cana-4548	399	10	353	353	NUM
cana-4548	399	11	.	.	PUNCT
cana-4548	400	1	zhang	zhang	PROPN
cana-4548	400	2	,	,	PUNCT
cana-4548	400	3	h.	h.	PROPN
cana-4548	400	4	,	,	PUNCT
cana-4548	400	5	zhang	zhang	PROPN
cana-4548	400	6	,	,	PUNCT
cana-4548	400	7	r.	r.	PROPN
cana-4548	400	8	,	,	PUNCT
cana-4548	400	9	huang	huang	PROPN
cana-4548	400	10	,	,	PUNCT
cana-4548	400	11	h.	h.	PROPN
cana-4548	400	12	,	,	PUNCT
cana-4548	400	13	&	&	CCONJ
cana-4548	400	14	wang	wang	PROPN
cana-4548	400	15	,	,	PUNCT
cana-4548	400	16	j.	j.	PROPN
cana-4548	400	17	(	(	PUNCT
cana-4548	400	18	2018	2018	NUM
cana-4548	400	19	)	)	PUNCT
cana-4548	400	20	.	.	PUNCT
cana-4548	401	1	some	some	DET
cana-4548	401	2	picture	picture	NOUN
cana-4548	401	3	fuzzy	fuzzy	ADJ
cana-4548	401	4	dombi	dombi	NOUN
cana-4548	401	5	heronian	heronian	ADJ
cana-4548	401	6	mean	mean	PROPN
cana-4548	401	7	operators	operator	NOUN
cana-4548	401	8	with	with	ADP
cana-4548	401	9	their	their	PRON
cana-4548	401	10	application	application	NOUN
cana-4548	401	11	to	to	ADP
cana-4548	401	12	multi	multi	ADJ
cana-4548	401	13	-	-	ADJ
cana-4548	401	14	attribute	attribute	NOUN
cana-4548	401	15	decision	decision	NOUN
cana-4548	401	16	-	-	PUNCT
cana-4548	401	17	making	making	NOUN
cana-4548	401	18	,	,	PUNCT
cana-4548	401	19	symmetry	symmetry	NOUN
cana-4548	401	20	,	,	PUNCT
cana-4548	401	21	10(11	10(11	NUM
cana-4548	401	22	)	)	PUNCT
cana-4548	401	23	,	,	PUNCT
cana-4548	401	24	593	593	NUM
cana-4548	401	25	.	.	PUNCT