id	sid	tid	token	lemma	pos
cana-2175	1	1	communications	communication	NOUN
cana-2175	1	2	on	on	ADP
cana-2175	1	3	applied	apply	VERB
cana-2175	1	4	nonlinear	nonlinear	ADJ
cana-2175	1	5	analysis	analysis	NOUN
cana-2175	1	6	issn	issn	NOUN
cana-2175	1	7	:	:	PUNCT
cana-2175	1	8	1074	1074	NUM
cana-2175	1	9	-	-	PUNCT
cana-2175	1	10	133x	133x	NUM
cana-2175	1	11	vol	vol	NOUN
cana-2175	1	12	32	32	NUM
cana-2175	1	13	no	no	NOUN
cana-2175	1	14	.	.	PUNCT
cana-2175	2	1	1s	1s	NUM
cana-2175	2	2	(	(	PUNCT
cana-2175	2	3	2025	2025	NUM
cana-2175	2	4	)	)	PUNCT
cana-2175	2	5	324	324	NUM
cana-2175	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2175	2	7	advancing	advance	VERB
cana-2175	2	8	disc	disc	NOUN
cana-2175	2	9	-	-	PUNCT
cana-2175	2	10	based	base	VERB
cana-2175	2	11	pythagorean	pythagorean	ADJ
cana-2175	2	12	fuzzy	fuzzy	ADJ
cana-2175	2	13	sets	set	NOUN
cana-2175	2	14	with	with	ADP
cana-2175	2	15	distinct	distinct	ADJ
cana-2175	2	16	radii	radius	NOUN
cana-2175	2	17	vinoth	vinoth	NOUN
cana-2175	2	18	kumar	kumar	PROPN
cana-2175	2	19	v1	v1	PROPN
cana-2175	2	20	*	*	PROPN
cana-2175	2	21	,	,	PUNCT
cana-2175	2	22	p.yashaswinii2	p.yashaswinii2	INTJ
cana-2175	2	23	,	,	PUNCT
cana-2175	2	24	r.	r.	PROPN
cana-2175	2	25	rajalakshmi3	rajalakshmi3	PROPN
cana-2175	2	26	,	,	PUNCT
cana-2175	2	27	r.	r.	PROPN
cana-2175	2	28	priyanka	priyanka	PROPN
cana-2175	2	29	pramila4	pramila4	PROPN
cana-2175	2	30	,	,	PUNCT
cana-2175	2	31	m.	m.	PROPN
cana-2175	2	32	siva5	siva5	PROPN
cana-2175	2	33	,	,	PUNCT
cana-2175	2	34	s.	s.	PROPN
cana-2175	2	35	arun	arun	PROPN
cana-2175	2	36	kumar6	kumar6	PROPN
cana-2175	2	37	1assistant	1assistant	NUM
cana-2175	2	38	professor	professor	NOUN
cana-2175	2	39	,	,	PUNCT
cana-2175	2	40	department	department	NOUN
cana-2175	2	41	of	of	ADP
cana-2175	2	42	electronics	electronic	NOUN
cana-2175	2	43	and	and	CCONJ
cana-2175	2	44	communication	communication	NOUN
cana-2175	2	45	engineering	engineering	NOUN
cana-2175	2	46	,	,	PUNCT
cana-2175	2	47	vel	vel	PROPN
cana-2175	2	48	tech	tech	PROPN
cana-2175	2	49	rangarajan	rangarajan	PROPN
cana-2175	2	50	dr	dr	PROPN
cana-2175	2	51	sagunthala	sagunthala	PROPN
cana-2175	2	52	r&d	r&d	PROPN
cana-2175	2	53	institute	institute	PROPN
cana-2175	2	54	of	of	ADP
cana-2175	2	55	science	science	NOUN
cana-2175	2	56	and	and	CCONJ
cana-2175	2	57	technology	technology	NOUN
cana-2175	2	58	,	,	PUNCT
cana-2175	2	59	chennai	chennai	PROPN
cana-2175	2	60	,	,	PUNCT
cana-2175	2	61	tamil	tamil	PROPN
cana-2175	2	62	nadu	nadu	PROPN
cana-2175	2	63	600062	600062	NUM
cana-2175	2	64	,	,	PUNCT
cana-2175	3	1	india	india	PROPN
cana-2175	3	2	.	.	PUNCT
cana-2175	3	3	email	email	NOUN
cana-2175	3	4	:	:	PUNCT
cana-2175	3	5	icevinoth@gmail.com	icevinoth@gmail.com	X
cana-2175	3	6	(	(	PUNCT
cana-2175	3	7	corresponding	corresponding	ADJ
cana-2175	3	8	author	author	NOUN
cana-2175	3	9	)	)	PUNCT
cana-2175	3	10	2pg	2pg	ADJ
cana-2175	3	11	resident	resident	NOUN
cana-2175	3	12	,	,	PUNCT
cana-2175	3	13	department	department	NOUN
cana-2175	3	14	of	of	ADP
cana-2175	3	15	radio	radio	NOUN
cana-2175	3	16	-	-	PUNCT
cana-2175	3	17	diagnosis	diagnosis	NOUN
cana-2175	3	18	,	,	PUNCT
cana-2175	3	19	saveetha	saveetha	PROPN
cana-2175	3	20	medical	medical	PROPN
cana-2175	3	21	college	college	PROPN
cana-2175	3	22	and	and	CCONJ
cana-2175	3	23	hospital	hospital	NOUN
cana-2175	3	24	,	,	PUNCT
cana-2175	3	25	saveetha	saveetha	PROPN
cana-2175	3	26	institute	institute	PROPN
cana-2175	3	27	of	of	ADP
cana-2175	3	28	medical	medical	ADJ
cana-2175	3	29	and	and	CCONJ
cana-2175	3	30	technical	technical	ADJ
cana-2175	3	31	sciences	science	NOUN
cana-2175	3	32	,	,	PUNCT
cana-2175	3	33	chennai	chennai	PROPN
cana-2175	3	34	,	,	PUNCT
cana-2175	3	35	tamil	tamil	PROPN
cana-2175	3	36	nadu	nadu	PROPN
cana-2175	3	37	602105	602105	NUM
cana-2175	3	38	,	,	PUNCT
cana-2175	4	1	india	india	PROPN
cana-2175	4	2	.	.	PUNCT
cana-2175	4	3	email	email	NOUN
cana-2175	4	4	:	:	PUNCT
cana-2175	4	5	yashireddy2606@gmail.com	yashireddy2606@gmail.com	NOUN
cana-2175	4	6	3assistant	3assistant	NUM
cana-2175	4	7	professor	professor	NOUN
cana-2175	4	8	,	,	PUNCT
cana-2175	4	9	department	department	NOUN
cana-2175	4	10	of	of	ADP
cana-2175	4	11	mathematics	mathematic	NOUN
cana-2175	4	12	,	,	PUNCT
cana-2175	4	13	panimalar	panimalar	ADJ
cana-2175	4	14	engineering	engineering	NOUN
cana-2175	4	15	college	college	NOUN
cana-2175	4	16	,	,	PUNCT
cana-2175	4	17	chennai	chennai	PROPN
cana-2175	4	18	,	,	PUNCT
cana-2175	4	19	tamil	tamil	PROPN
cana-2175	4	20	nadu	nadu	PROPN
cana-2175	4	21	600123	600123	NUM
cana-2175	4	22	,	,	PUNCT
cana-2175	4	23	india	india	PROPN
cana-2175	4	24	.	.	PUNCT
cana-2175	5	1	email:rajimat2020@gmail.com	email:rajimat2020@gmail.com	PROPN
cana-2175	5	2	4assistant	4assistant	NUM
cana-2175	5	3	professor	professor	NOUN
cana-2175	5	4	,	,	PUNCT
cana-2175	5	5	department	department	NOUN
cana-2175	5	6	of	of	ADP
cana-2175	5	7	artificial	artificial	ADJ
cana-2175	5	8	intelligence	intelligence	NOUN
cana-2175	5	9	and	and	CCONJ
cana-2175	5	10	data	datum	NOUN
cana-2175	5	11	science	science	NOUN
cana-2175	5	12	,	,	PUNCT
cana-2175	5	13	r.m.k	r.m.k	NOUN
cana-2175	5	14	.	.	PUNCT
cana-2175	6	1	engineering	engineering	PROPN
cana-2175	6	2	college	college	PROPN
cana-2175	6	3	,	,	PUNCT
cana-2175	6	4	kavaraipettai	kavaraipettai	PROPN
cana-2175	6	5	,	,	PUNCT
cana-2175	6	6	tamil	tamil	PROPN
cana-2175	6	7	nadu	nadu	PROPN
cana-2175	6	8	601206	601206	NUM
cana-2175	6	9	,	,	PUNCT
cana-2175	6	10	india	india	PROPN
cana-2175	6	11	.	.	PUNCT
cana-2175	6	12	email	email	NOUN
cana-2175	6	13	:	:	PUNCT
cana-2175	6	14	pp.ad@rmkec.ac.in	pp.ad@rmkec.ac.in	PUNCT
cana-2175	6	15	5assistant	5assistant	NUM
cana-2175	6	16	professor	professor	NOUN
cana-2175	6	17	,	,	PUNCT
cana-2175	6	18	department	department	NOUN
cana-2175	6	19	of	of	ADP
cana-2175	6	20	mathematics	mathematics	PROPN
cana-2175	6	21	,	,	PUNCT
cana-2175	6	22	st	st	PROPN
cana-2175	6	23	.	.	PROPN
cana-2175	6	24	joseph	joseph	PROPN
cana-2175	6	25	's	's	PART
cana-2175	6	26	institute	institute	PROPN
cana-2175	6	27	of	of	ADP
cana-2175	6	28	technology	technology	PROPN
cana-2175	6	29	,	,	PUNCT
cana-2175	6	30	chennai	chennai	PROPN
cana-2175	6	31	,	,	PUNCT
cana-2175	6	32	tamil	tamil	PROPN
cana-2175	6	33	nadu	nadu	PROPN
cana-2175	6	34	600119	600119	NUM
cana-2175	6	35	,	,	PUNCT
cana-2175	6	36	india	india	PROPN
cana-2175	6	37	.	.	PUNCT
cana-2175	6	38	email	email	NOUN
cana-2175	6	39	:	:	PUNCT
cana-2175	6	40	sivam@stjosephstechnology.ac.in	sivam@stjosephstechnology.ac.in	PROPN
cana-2175	6	41	6assistant	6assistant	NUM
cana-2175	6	42	professor	professor	NOUN
cana-2175	6	43	,	,	PUNCT
cana-2175	6	44	department	department	NOUN
cana-2175	6	45	of	of	ADP
cana-2175	6	46	electronics	electronic	NOUN
cana-2175	6	47	and	and	CCONJ
cana-2175	6	48	communication	communication	NOUN
cana-2175	6	49	engineering	engineering	NOUN
cana-2175	6	50	,	,	PUNCT
cana-2175	6	51	psna	psna	PROPN
cana-2175	6	52	college	college	PROPN
cana-2175	6	53	of	of	ADP
cana-2175	6	54	engineering	engineering	NOUN
cana-2175	6	55	and	and	CCONJ
cana-2175	6	56	technology	technology	NOUN
cana-2175	6	57	,	,	PUNCT
cana-2175	6	58	dindigul	dindigul	ADV
cana-2175	6	59	624	624	NUM
cana-2175	6	60	622	622	NUM
cana-2175	6	61	,	,	PUNCT
cana-2175	6	62	tamil	tamil	PROPN
cana-2175	6	63	nadu	nadu	PROPN
cana-2175	6	64	,	,	PUNCT
cana-2175	6	65	india	india	PROPN
cana-2175	6	66	.	.	PUNCT
cana-2175	6	67	email	email	NOUN
cana-2175	6	68	:	:	PUNCT
cana-2175	6	69	murphy_arun@psnacet.edu.in	murphy_arun@psnacet.edu.in	ADJ
cana-2175	6	70	article	article	NOUN
cana-2175	6	71	history	history	NOUN
cana-2175	6	72	:	:	PUNCT
cana-2175	6	73	received	receive	VERB
cana-2175	6	74	:	:	PUNCT
cana-2175	6	75	18	18	NUM
cana-2175	6	76	-	-	SYM
cana-2175	6	77	08	08	NUM
cana-2175	6	78	-	-	PUNCT
cana-2175	6	79	2024	2024	NUM
cana-2175	6	80	revised	revise	VERB
cana-2175	6	81	:	:	PUNCT
cana-2175	6	82	29	29	NUM
cana-2175	6	83	-	-	SYM
cana-2175	6	84	09	09	NUM
cana-2175	6	85	-	-	PUNCT
cana-2175	6	86	2024	2024	NUM
cana-2175	6	87	accepted	accept	VERB
cana-2175	6	88	:	:	PUNCT
cana-2175	6	89	18	18	NUM
cana-2175	6	90	-	-	SYM
cana-2175	6	91	10	10	NUM
cana-2175	6	92	-	-	PUNCT
cana-2175	6	93	2024	2024	NUM
cana-2175	6	94	abstract	abstract	NOUN
cana-2175	6	95	:	:	PUNCT
cana-2175	6	96	disc	disc	NOUN
cana-2175	6	97	-	-	PUNCT
cana-2175	6	98	based	base	VERB
cana-2175	6	99	pythagorean	pythagorean	PROPN
cana-2175	6	100	fuzzy	fuzzy	ADJ
cana-2175	6	101	sets	set	NOUN
cana-2175	6	102	(	(	PUNCT
cana-2175	6	103	d	d	NOUN
cana-2175	6	104	-	-	NOUN
cana-2175	6	105	pfss	pfss	ADJ
cana-2175	6	106	)	)	PUNCT
cana-2175	6	107	extend	extend	VERB
cana-2175	6	108	traditional	traditional	ADJ
cana-2175	6	109	fuzzy	fuzzy	ADJ
cana-2175	6	110	sets	set	NOUN
cana-2175	6	111	by	by	ADP
cana-2175	6	112	incorporating	incorporate	VERB
cana-2175	6	113	the	the	DET
cana-2175	6	114	concept	concept	NOUN
cana-2175	6	115	of	of	ADP
cana-2175	6	116	distinct	distinct	ADJ
cana-2175	6	117	radii	radius	NOUN
cana-2175	6	118	to	to	AUX
cana-2175	6	119	model	model	VERB
cana-2175	6	120	uncertainty	uncertainty	NOUN
cana-2175	6	121	more	more	ADV
cana-2175	6	122	flexibly	flexibly	ADV
cana-2175	6	123	.	.	PUNCT
cana-2175	7	1	unlike	unlike	ADP
cana-2175	7	2	classical	classical	ADJ
cana-2175	7	3	fuzzy	fuzzy	ADJ
cana-2175	7	4	sets	set	NOUN
cana-2175	7	5	that	that	PRON
cana-2175	7	6	use	use	VERB
cana-2175	7	7	fixed	fix	VERB
cana-2175	7	8	radii	radius	NOUN
cana-2175	7	9	,	,	PUNCT
cana-2175	7	10	d	d	X
cana-2175	7	11	-	-	PUNCT
cana-2175	7	12	pfss	pfss	ADV
cana-2175	7	13	allow	allow	VERB
cana-2175	7	14	each	each	DET
cana-2175	7	15	element	element	NOUN
cana-2175	7	16	to	to	PART
cana-2175	7	17	have	have	VERB
cana-2175	7	18	its	its	PRON
cana-2175	7	19	own	own	ADJ
cana-2175	7	20	radius	radius	NOUN
cana-2175	7	21	,	,	PUNCT
cana-2175	7	22	which	which	PRON
cana-2175	7	23	enhances	enhance	VERB
cana-2175	7	24	the	the	DET
cana-2175	7	25	representation	representation	NOUN
cana-2175	7	26	of	of	ADP
cana-2175	7	27	varying	vary	VERB
cana-2175	7	28	degrees	degree	NOUN
cana-2175	7	29	of	of	ADP
cana-2175	7	30	uncertainty	uncertainty	NOUN
cana-2175	7	31	.	.	PUNCT
cana-2175	8	1	in	in	ADP
cana-2175	8	2	implementing	implement	VERB
cana-2175	8	3	dpfss	dpfss	NOUN
cana-2175	8	4	,	,	PUNCT
cana-2175	8	5	a	a	DET
cana-2175	8	6	systematic	systematic	ADJ
cana-2175	8	7	approach	approach	NOUN
cana-2175	8	8	is	be	AUX
cana-2175	8	9	crucial	crucial	ADJ
cana-2175	8	10	for	for	ADP
cana-2175	8	11	effective	effective	ADJ
cana-2175	8	12	uncertainty	uncertainty	NOUN
cana-2175	8	13	modeling	modeling	NOUN
cana-2175	8	14	.	.	PUNCT
cana-2175	9	1	each	each	DET
cana-2175	9	2	d	d	ADJ
cana-2175	9	3	-	-	PUNCT
cana-2175	9	4	pfs	pf	VERB
cana-2175	9	5	element	element	NOUN
cana-2175	9	6	is	be	AUX
cana-2175	9	7	defined	define	VERB
cana-2175	9	8	by	by	ADP
cana-2175	9	9	membership	membership	NOUN
cana-2175	9	10	and	and	CCONJ
cana-2175	9	11	non	non	ADJ
cana-2175	9	12	-	-	ADJ
cana-2175	9	13	membership	membership	ADJ
cana-2175	9	14	degrees	degree	NOUN
cana-2175	9	15	,	,	PUNCT
cana-2175	9	16	and	and	CCONJ
cana-2175	9	17	a	a	DET
cana-2175	9	18	distinct	distinct	ADJ
cana-2175	9	19	radius	radius	NOUN
cana-2175	9	20	.	.	PUNCT
cana-2175	10	1	the	the	DET
cana-2175	10	2	pythagorean	pythagorean	PROPN
cana-2175	10	3	condition	condition	NOUN
cana-2175	10	4	ensures	ensure	VERB
cana-2175	10	5	that	that	SCONJ
cana-2175	10	6	the	the	DET
cana-2175	10	7	sum	sum	NOUN
cana-2175	10	8	of	of	ADP
cana-2175	10	9	the	the	DET
cana-2175	10	10	squares	square	NOUN
cana-2175	10	11	of	of	ADP
cana-2175	10	12	membership	membership	NOUN
cana-2175	10	13	and	and	CCONJ
cana-2175	10	14	nonmembership	nonmembership	NOUN
cana-2175	10	15	degrees	degree	NOUN
cana-2175	10	16	does	do	AUX
cana-2175	10	17	not	not	PART
cana-2175	10	18	exceed	exceed	VERB
cana-2175	10	19	the	the	DET
cana-2175	10	20	element	element	NOUN
cana-2175	10	21	's	's	PART
cana-2175	10	22	radius	radius	NOUN
cana-2175	10	23	squared	square	VERB
cana-2175	10	24	.	.	PUNCT
cana-2175	11	1	union	union	NOUN
cana-2175	11	2	and	and	CCONJ
cana-2175	11	3	intersection	intersection	NOUN
cana-2175	11	4	operations	operation	NOUN
cana-2175	11	5	involve	involve	VERB
cana-2175	11	6	combining	combine	VERB
cana-2175	11	7	degrees	degree	NOUN
cana-2175	11	8	with	with	ADP
cana-2175	11	9	specific	specific	ADJ
cana-2175	11	10	formulas	formula	NOUN
cana-2175	11	11	,	,	PUNCT
cana-2175	11	12	where	where	SCONJ
cana-2175	11	13	the	the	DET
cana-2175	11	14	union	union	NOUN
cana-2175	11	15	uses	use	VERB
cana-2175	11	16	the	the	DET
cana-2175	11	17	minimum	minimum	ADJ
cana-2175	11	18	radius	radius	NOUN
cana-2175	11	19	and	and	CCONJ
cana-2175	11	20	the	the	DET
cana-2175	11	21	intersection	intersection	NOUN
cana-2175	11	22	uses	use	VERB
cana-2175	11	23	the	the	DET
cana-2175	11	24	maximum	maximum	ADJ
cana-2175	11	25	radius	radius	NOUN
cana-2175	11	26	of	of	ADP
cana-2175	11	27	the	the	DET
cana-2175	11	28	involved	involve	VERB
cana-2175	11	29	sets	set	NOUN
cana-2175	11	30	.	.	PUNCT
cana-2175	12	1	the	the	DET
cana-2175	12	2	complement	complement	NOUN
cana-2175	12	3	operation	operation	NOUN
cana-2175	12	4	swaps	swap	VERB
cana-2175	12	5	the	the	DET
cana-2175	12	6	membership	membership	NOUN
cana-2175	12	7	and	and	CCONJ
cana-2175	12	8	non	non	ADJ
cana-2175	12	9	-	-	ADJ
cana-2175	12	10	membership	membership	ADJ
cana-2175	12	11	degrees	degree	NOUN
cana-2175	12	12	while	while	SCONJ
cana-2175	12	13	retaining	retain	VERB
cana-2175	12	14	the	the	DET
cana-2175	12	15	radius	radius	NOUN
cana-2175	12	16	.	.	PUNCT
cana-2175	13	1	integrating	integrate	VERB
cana-2175	13	2	d	d	X
cana-2175	13	3	-	-	NOUN
cana-2175	13	4	pfss	pfss	ADJ
cana-2175	13	5	into	into	ADP
cana-2175	13	6	the	the	DET
cana-2175	13	7	topsis	topsis	NOUN
cana-2175	13	8	method	method	NOUN
cana-2175	13	9	for	for	ADP
cana-2175	13	10	multi	multi	ADJ
cana-2175	13	11	-	-	ADJ
cana-2175	13	12	criteria	criterion	NOUN
cana-2175	13	13	decision	decision	NOUN
cana-2175	13	14	-	-	PUNCT
cana-2175	13	15	making	making	NOUN
cana-2175	13	16	involves	involve	NOUN
cana-2175	13	17	replacing	replace	VERB
cana-2175	13	18	decision	decision	NOUN
cana-2175	13	19	matrix	matrix	NOUN
cana-2175	13	20	elements	element	NOUN
cana-2175	13	21	with	with	ADP
cana-2175	13	22	pythagorean	pythagorean	ADJ
cana-2175	13	23	fuzzy	fuzzy	ADJ
cana-2175	13	24	numbers	number	NOUN
cana-2175	13	25	,	,	PUNCT
cana-2175	13	26	normalizing	normalize	VERB
cana-2175	13	27	these	these	DET
cana-2175	13	28	numbers	number	NOUN
cana-2175	13	29	,	,	PUNCT
cana-2175	13	30	and	and	CCONJ
cana-2175	13	31	calculating	calculate	VERB
cana-2175	13	32	ideal	ideal	ADJ
cana-2175	13	33	solutions	solution	NOUN
cana-2175	13	34	and	and	CCONJ
cana-2175	13	35	distances	distance	NOUN
cana-2175	13	36	using	use	VERB
cana-2175	13	37	euclidean	euclidean	ADJ
cana-2175	13	38	measures	measure	NOUN
cana-2175	13	39	.	.	PUNCT
cana-2175	14	1	alternatives	alternative	NOUN
cana-2175	14	2	are	be	AUX
cana-2175	14	3	then	then	ADV
cana-2175	14	4	ranked	rank	VERB
cana-2175	14	5	based	base	VERB
cana-2175	14	6	on	on	ADP
cana-2175	14	7	their	their	PRON
cana-2175	14	8	proximity	proximity	NOUN
cana-2175	14	9	to	to	ADP
cana-2175	14	10	ideal	ideal	ADJ
cana-2175	14	11	solutions	solution	NOUN
cana-2175	14	12	.	.	PUNCT
cana-2175	15	1	the	the	DET
cana-2175	15	2	results	result	NOUN
cana-2175	15	3	demonstrate	demonstrate	VERB
cana-2175	15	4	that	that	SCONJ
cana-2175	15	5	d	d	X
cana-2175	15	6	-	-	PUNCT
cana-2175	15	7	pfss	pfss	ADJ
cana-2175	15	8	provide	provide	VERB
cana-2175	15	9	enhanced	enhance	VERB
cana-2175	15	10	flexibility	flexibility	NOUN
cana-2175	15	11	by	by	ADP
cana-2175	15	12	accommodating	accommodate	VERB
cana-2175	15	13	distinct	distinct	ADJ
cana-2175	15	14	radii	radius	NOUN
cana-2175	15	15	,	,	PUNCT
cana-2175	15	16	allowing	allow	VERB
cana-2175	15	17	for	for	ADP
cana-2175	15	18	a	a	DET
cana-2175	15	19	nuanced	nuanced	ADJ
cana-2175	15	20	representation	representation	NOUN
cana-2175	15	21	of	of	ADP
cana-2175	15	22	uncertainty	uncertainty	NOUN
cana-2175	15	23	.	.	PUNCT
cana-2175	16	1	validation	validation	NOUN
cana-2175	16	2	confirms	confirm	VERB
cana-2175	16	3	adherence	adherence	NOUN
cana-2175	16	4	to	to	ADP
cana-2175	16	5	the	the	DET
cana-2175	16	6	pythagorean	pythagorean	PROPN
cana-2175	16	7	condition	condition	NOUN
cana-2175	16	8	,	,	PUNCT
cana-2175	16	9	and	and	CCONJ
cana-2175	16	10	the	the	DET
cana-2175	16	11	varying	vary	VERB
cana-2175	16	12	radii	radius	NOUN
cana-2175	16	13	effectively	effectively	ADV
cana-2175	16	14	influence	influence	VERB
cana-2175	16	15	the	the	DET
cana-2175	16	16	degrees	degree	NOUN
cana-2175	16	17	.	.	PUNCT
cana-2175	17	1	the	the	DET
cana-2175	17	2	comparison	comparison	NOUN
cana-2175	17	3	of	of	ADP
cana-2175	17	4	union	union	NOUN
cana-2175	17	5	and	and	CCONJ
cana-2175	17	6	intersection	intersection	NOUN
cana-2175	17	7	operations	operation	NOUN
cana-2175	17	8	further	far	ADV
cana-2175	17	9	showcases	showcase	VERB
cana-2175	17	10	d	d	PROPN
cana-2175	17	11	-	-	ADJ
cana-2175	17	12	pfss	pfss	ADJ
cana-2175	17	13	'	'	PUNCT
cana-2175	17	14	superior	superior	ADJ
cana-2175	17	15	capability	capability	NOUN
cana-2175	17	16	in	in	ADP
cana-2175	17	17	managing	manage	VERB
cana-2175	17	18	complex	complex	ADJ
cana-2175	17	19	uncertainties	uncertainty	NOUN
cana-2175	17	20	.	.	PUNCT
cana-2175	18	1	keywords	keyword	NOUN
cana-2175	18	2	:	:	PUNCT
cana-2175	18	3	disc	disc	NOUN
cana-2175	18	4	-	-	PUNCT
cana-2175	18	5	based	base	VERB
cana-2175	18	6	pythagorean	pythagorean	PROPN
cana-2175	18	7	fuzzy	fuzzy	ADJ
cana-2175	18	8	sets	set	NOUN
cana-2175	18	9	,	,	PUNCT
cana-2175	18	10	classical	classical	ADJ
cana-2175	18	11	fuzzy	fuzzy	ADJ
cana-2175	18	12	sets	set	NOUN
cana-2175	18	13	,	,	PUNCT
cana-2175	18	14	distinct	distinct	ADJ
cana-2175	18	15	radius	radius	NOUN
cana-2175	18	16	,	,	PUNCT
cana-2175	18	17	union	union	NOUN
cana-2175	18	18	,	,	PUNCT
cana-2175	18	19	intersection	intersection	NOUN
cana-2175	18	20	,	,	PUNCT
cana-2175	18	21	topsis	topsis	NOUN
cana-2175	18	22	,	,	PUNCT
cana-2175	18	23	decision	decision	NOUN
cana-2175	18	24	-	-	PUNCT
cana-2175	18	25	making	making	NOUN
cana-2175	18	26	,	,	PUNCT
cana-2175	18	27	pythagorean	pythagorean	PROPN
cana-2175	18	28	condition	condition	NOUN
cana-2175	18	29	.	.	PUNCT
cana-2175	19	1	1	1	X
cana-2175	19	2	.	.	X
cana-2175	19	3	introduction	introduction	NOUN
cana-2175	19	4	in	in	ADP
cana-2175	19	5	the	the	DET
cana-2175	19	6	realm	realm	NOUN
cana-2175	19	7	of	of	ADP
cana-2175	19	8	fuzzy	fuzzy	ADJ
cana-2175	19	9	logic	logic	NOUN
cana-2175	19	10	,	,	PUNCT
cana-2175	19	11	disc	disc	NOUN
cana-2175	19	12	-	-	PUNCT
cana-2175	19	13	based	base	VERB
cana-2175	19	14	pythagorean	pythagorean	PROPN
cana-2175	19	15	fuzzy	fuzzy	ADJ
cana-2175	19	16	sets	set	NOUN
cana-2175	19	17	(	(	PUNCT
cana-2175	19	18	dbpfs	dbpfs	PROPN
cana-2175	19	19	)	)	PUNCT
cana-2175	19	20	represent	represent	VERB
cana-2175	19	21	a	a	DET
cana-2175	19	22	significant	significant	ADJ
cana-2175	19	23	evolution	evolution	NOUN
cana-2175	19	24	of	of	ADP
cana-2175	19	25	traditional	traditional	ADJ
cana-2175	19	26	fuzzy	fuzzy	ADJ
cana-2175	19	27	sets	set	NOUN
cana-2175	19	28	,	,	PUNCT
cana-2175	19	29	offering	offer	VERB
cana-2175	19	30	a	a	DET
cana-2175	19	31	sophisticated	sophisticated	ADJ
cana-2175	19	32	framework	framework	NOUN
cana-2175	19	33	for	for	ADP
cana-2175	19	34	managing	manage	VERB
cana-2175	19	35	uncertainty	uncertainty	NOUN
cana-2175	19	36	and	and	CCONJ
cana-2175	19	37	mailto:icevinoth@gmail.com	mailto:icevinoth@gmail.com	PROPN
cana-2175	19	38	mailto:pp.ad@rmkec.ac.in	mailto:pp.ad@rmkec.ac.in	PART
cana-2175	19	39	communications	communication	NOUN
cana-2175	19	40	on	on	ADP
cana-2175	19	41	applied	apply	VERB
cana-2175	19	42	nonlinear	nonlinear	ADJ
cana-2175	19	43	analysis	analysis	NOUN
cana-2175	19	44	issn	issn	NOUN
cana-2175	19	45	:	:	PUNCT
cana-2175	19	46	1074	1074	NUM
cana-2175	19	47	-	-	PUNCT
cana-2175	19	48	133x	133x	NUM
cana-2175	19	49	vol	vol	NOUN
cana-2175	19	50	32	32	NUM
cana-2175	20	1	no	no	NOUN
cana-2175	20	2	.	.	PUNCT
cana-2175	21	1	1s	1s	NUM
cana-2175	21	2	(	(	PUNCT
cana-2175	21	3	2025	2025	NUM
cana-2175	21	4	)	)	PUNCT
cana-2175	21	5	325	325	NUM
cana-2175	21	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2175	21	7	imprecision	imprecision	NOUN
cana-2175	21	8	in	in	ADP
cana-2175	21	9	data	datum	NOUN
cana-2175	21	10	representation	representation	NOUN
cana-2175	21	11	.	.	PUNCT
cana-2175	22	1	classical	classical	ADJ
cana-2175	22	2	fuzzy	fuzzy	ADJ
cana-2175	22	3	sets	set	NOUN
cana-2175	22	4	,	,	PUNCT
cana-2175	22	5	while	while	SCONJ
cana-2175	22	6	effective	effective	ADJ
cana-2175	22	7	in	in	ADP
cana-2175	22	8	many	many	ADJ
cana-2175	22	9	scenarios	scenario	NOUN
cana-2175	22	10	,	,	PUNCT
cana-2175	22	11	are	be	AUX
cana-2175	22	12	often	often	ADV
cana-2175	22	13	constrained	constrain	VERB
cana-2175	22	14	by	by	ADP
cana-2175	22	15	their	their	PRON
cana-2175	22	16	simplicity	simplicity	NOUN
cana-2175	22	17	,	,	PUNCT
cana-2175	22	18	which	which	PRON
cana-2175	22	19	limits	limit	VERB
cana-2175	22	20	their	their	PRON
cana-2175	22	21	capacity	capacity	NOUN
cana-2175	22	22	to	to	PART
cana-2175	22	23	model	model	VERB
cana-2175	22	24	complex	complex	ADJ
cana-2175	22	25	and	and	CCONJ
cana-2175	22	26	nuanced	nuanced	ADJ
cana-2175	22	27	information	information	NOUN
cana-2175	22	28	accurately	accurately	ADV
cana-2175	22	29	[	[	X
cana-2175	22	30	1	1	NUM
cana-2175	22	31	]	]	PUNCT
cana-2175	22	32	.	.	PUNCT
cana-2175	23	1	to	to	PART
cana-2175	23	2	overcome	overcome	VERB
cana-2175	23	3	these	these	DET
cana-2175	23	4	limitations	limitation	NOUN
cana-2175	23	5	,	,	PUNCT
cana-2175	23	6	pythagorean	pythagorean	PROPN
cana-2175	23	7	fuzzy	fuzzy	ADJ
cana-2175	23	8	sets	set	NOUN
cana-2175	23	9	were	be	AUX
cana-2175	23	10	introduced	introduce	VERB
cana-2175	23	11	,	,	PUNCT
cana-2175	23	12	extending	extend	VERB
cana-2175	23	13	the	the	DET
cana-2175	23	14	classical	classical	ADJ
cana-2175	23	15	model	model	NOUN
cana-2175	23	16	by	by	ADP
cana-2175	23	17	incorporating	incorporate	VERB
cana-2175	23	18	both	both	CCONJ
cana-2175	23	19	a	a	DET
cana-2175	23	20	degree	degree	NOUN
cana-2175	23	21	of	of	ADP
cana-2175	23	22	membership	membership	NOUN
cana-2175	23	23	and	and	CCONJ
cana-2175	23	24	a	a	DET
cana-2175	23	25	degree	degree	NOUN
cana-2175	23	26	of	of	ADP
cana-2175	23	27	non	non	ADJ
cana-2175	23	28	-	-	NOUN
cana-2175	23	29	membership	membership	ADJ
cana-2175	23	30	[	[	X
cana-2175	23	31	2	2	NUM
cana-2175	23	32	]	]	PUNCT
cana-2175	23	33	.	.	PUNCT
cana-2175	24	1	this	this	DET
cana-2175	24	2	extension	extension	NOUN
cana-2175	24	3	adheres	adhere	VERB
cana-2175	24	4	to	to	ADP
cana-2175	24	5	the	the	DET
cana-2175	24	6	pythagorean	pythagorean	PROPN
cana-2175	24	7	theorem	theorem	PROPN
cana-2175	24	8	,	,	PUNCT
cana-2175	24	9	which	which	PRON
cana-2175	24	10	asserts	assert	VERB
cana-2175	24	11	that	that	SCONJ
cana-2175	24	12	the	the	DET
cana-2175	24	13	sum	sum	NOUN
cana-2175	24	14	of	of	ADP
cana-2175	24	15	the	the	DET
cana-2175	24	16	squares	square	NOUN
cana-2175	24	17	of	of	ADP
cana-2175	24	18	the	the	DET
cana-2175	24	19	membership	membership	NOUN
cana-2175	24	20	and	and	CCONJ
cana-2175	24	21	non	non	ADJ
cana-2175	24	22	-	-	ADJ
cana-2175	24	23	membership	membership	ADJ
cana-2175	24	24	degrees	degree	NOUN
cana-2175	24	25	must	must	AUX
cana-2175	24	26	be	be	AUX
cana-2175	24	27	less	less	ADJ
cana-2175	24	28	than	than	ADP
cana-2175	24	29	or	or	CCONJ
cana-2175	24	30	equal	equal	ADJ
cana-2175	24	31	to	to	ADP
cana-2175	24	32	one	one	NUM
cana-2175	24	33	[	[	X
cana-2175	24	34	3	3	NUM
cana-2175	24	35	]	]	PUNCT
cana-2175	24	36	.	.	PUNCT
cana-2175	25	1	this	this	DET
cana-2175	25	2	formulation	formulation	NOUN
cana-2175	25	3	enhances	enhance	VERB
cana-2175	25	4	the	the	DET
cana-2175	25	5	ability	ability	NOUN
cana-2175	25	6	to	to	PART
cana-2175	25	7	represent	represent	VERB
cana-2175	25	8	and	and	CCONJ
cana-2175	25	9	process	process	VERB
cana-2175	25	10	uncertain	uncertain	ADJ
cana-2175	25	11	information	information	NOUN
cana-2175	25	12	by	by	ADP
cana-2175	25	13	allowing	allow	VERB
cana-2175	25	14	for	for	ADP
cana-2175	25	15	a	a	DET
cana-2175	25	16	more	more	ADV
cana-2175	25	17	comprehensive	comprehensive	ADJ
cana-2175	25	18	characterization	characterization	NOUN
cana-2175	25	19	of	of	ADP
cana-2175	25	20	ambiguity	ambiguity	NOUN
cana-2175	25	21	.	.	PUNCT
cana-2175	26	1	the	the	DET
cana-2175	26	2	advancement	advancement	NOUN
cana-2175	26	3	of	of	ADP
cana-2175	26	4	disc	disc	NOUN
cana-2175	26	5	-	-	PUNCT
cana-2175	26	6	based	base	VERB
cana-2175	26	7	pythagorean	pythagorean	PROPN
cana-2175	26	8	fuzzy	fuzzy	ADJ
cana-2175	26	9	sets	set	NOUN
cana-2175	26	10	introduces	introduce	VERB
cana-2175	26	11	the	the	DET
cana-2175	26	12	concept	concept	NOUN
cana-2175	26	13	of	of	ADP
cana-2175	26	14	distinct	distinct	ADJ
cana-2175	26	15	radii	radius	NOUN
cana-2175	26	16	to	to	PART
cana-2175	26	17	represent	represent	VERB
cana-2175	26	18	the	the	DET
cana-2175	26	19	membership	membership	NOUN
cana-2175	26	20	and	and	CCONJ
cana-2175	26	21	non	non	ADJ
cana-2175	26	22	-	-	ADJ
cana-2175	26	23	membership	membership	ADJ
cana-2175	26	24	values	value	NOUN
cana-2175	26	25	.	.	PUNCT
cana-2175	27	1	in	in	ADP
cana-2175	27	2	traditional	traditional	ADJ
cana-2175	27	3	pythagorean	pythagorean	ADJ
cana-2175	27	4	fuzzy	fuzzy	ADJ
cana-2175	27	5	sets	set	NOUN
cana-2175	27	6	,	,	PUNCT
cana-2175	27	7	the	the	DET
cana-2175	27	8	representation	representation	NOUN
cana-2175	27	9	is	be	AUX
cana-2175	27	10	typically	typically	ADV
cana-2175	27	11	constrained	constrain	VERB
cana-2175	27	12	to	to	ADP
cana-2175	27	13	a	a	DET
cana-2175	27	14	single	single	ADJ
cana-2175	27	15	radius	radius	NOUN
cana-2175	27	16	,	,	PUNCT
cana-2175	27	17	which	which	PRON
cana-2175	27	18	can	can	AUX
cana-2175	27	19	limit	limit	VERB
cana-2175	27	20	the	the	DET
cana-2175	27	21	granularity	granularity	NOUN
cana-2175	27	22	and	and	CCONJ
cana-2175	27	23	precision	precision	NOUN
cana-2175	27	24	of	of	ADP
cana-2175	27	25	uncertainty	uncertainty	NOUN
cana-2175	27	26	modelling	model	VERB
cana-2175	27	27	[	[	X
cana-2175	27	28	4	4	NUM
cana-2175	27	29	]	]	PUNCT
cana-2175	27	30	.	.	PUNCT
cana-2175	28	1	by	by	ADP
cana-2175	28	2	using	use	VERB
cana-2175	28	3	distinct	distinct	ADJ
cana-2175	28	4	radii	radius	NOUN
cana-2175	28	5	for	for	ADP
cana-2175	28	6	membership	membership	NOUN
cana-2175	28	7	and	and	CCONJ
cana-2175	28	8	non	non	ADJ
cana-2175	28	9	-	-	NOUN
cana-2175	28	10	membership	membership	NOUN
cana-2175	28	11	,	,	PUNCT
cana-2175	28	12	dbpfs	dbpf	NOUN
cana-2175	28	13	can	can	AUX
cana-2175	28	14	more	more	ADV
cana-2175	28	15	accurately	accurately	ADV
cana-2175	28	16	capture	capture	VERB
cana-2175	28	17	the	the	DET
cana-2175	28	18	variability	variability	NOUN
cana-2175	28	19	and	and	CCONJ
cana-2175	28	20	intricacies	intricacy	NOUN
cana-2175	28	21	of	of	ADP
cana-2175	28	22	real	real	ADJ
cana-2175	28	23	-	-	PUNCT
cana-2175	28	24	world	world	NOUN
cana-2175	28	25	situations	situation	NOUN
cana-2175	28	26	.	.	PUNCT
cana-2175	29	1	this	this	DET
cana-2175	29	2	distinction	distinction	NOUN
cana-2175	29	3	allows	allow	VERB
cana-2175	29	4	for	for	ADP
cana-2175	29	5	a	a	DET
cana-2175	29	6	more	more	ADV
cana-2175	29	7	flexible	flexible	ADJ
cana-2175	29	8	and	and	CCONJ
cana-2175	29	9	detailed	detailed	ADJ
cana-2175	29	10	representation	representation	NOUN
cana-2175	29	11	of	of	ADP
cana-2175	29	12	uncertainty	uncertainty	NOUN
cana-2175	29	13	,	,	PUNCT
cana-2175	29	14	making	make	VERB
cana-2175	29	15	dbpfs	dbpf	NOUN
cana-2175	29	16	particularly	particularly	ADV
cana-2175	29	17	useful	useful	ADJ
cana-2175	29	18	in	in	ADP
cana-2175	29	19	scenarios	scenario	NOUN
cana-2175	29	20	where	where	SCONJ
cana-2175	29	21	different	different	ADJ
cana-2175	29	22	aspects	aspect	NOUN
cana-2175	29	23	of	of	ADP
cana-2175	29	24	uncertainty	uncertainty	NOUN
cana-2175	29	25	need	need	VERB
cana-2175	29	26	to	to	PART
cana-2175	29	27	be	be	AUX
cana-2175	29	28	considered	consider	VERB
cana-2175	29	29	separately	separately	ADV
cana-2175	29	30	.	.	PUNCT
cana-2175	30	1	in	in	ADP
cana-2175	30	2	the	the	DET
cana-2175	30	3	medical	medical	ADJ
cana-2175	30	4	field	field	NOUN
cana-2175	30	5	,	,	PUNCT
cana-2175	30	6	accurate	accurate	ADJ
cana-2175	30	7	diagnosis	diagnosis	NOUN
cana-2175	30	8	often	often	ADV
cana-2175	30	9	relies	rely	VERB
cana-2175	30	10	on	on	ADP
cana-2175	30	11	interpreting	interpret	VERB
cana-2175	30	12	symptoms	symptom	NOUN
cana-2175	30	13	,	,	PUNCT
cana-2175	30	14	test	test	NOUN
cana-2175	30	15	results	result	NOUN
cana-2175	30	16	,	,	PUNCT
cana-2175	30	17	and	and	CCONJ
cana-2175	30	18	patient	patient	ADJ
cana-2175	30	19	history	history	NOUN
cana-2175	30	20	,	,	PUNCT
cana-2175	30	21	which	which	PRON
cana-2175	30	22	are	be	AUX
cana-2175	30	23	inherently	inherently	ADV
cana-2175	30	24	uncertain	uncertain	ADJ
cana-2175	30	25	.	.	PUNCT
cana-2175	31	1	traditional	traditional	ADJ
cana-2175	31	2	methods	method	NOUN
cana-2175	31	3	might	might	AUX
cana-2175	31	4	struggle	struggle	VERB
cana-2175	31	5	to	to	PART
cana-2175	31	6	handle	handle	VERB
cana-2175	31	7	the	the	DET
cana-2175	31	8	complexity	complexity	NOUN
cana-2175	31	9	of	of	ADP
cana-2175	31	10	overlapping	overlap	VERB
cana-2175	31	11	and	and	CCONJ
cana-2175	31	12	ambiguous	ambiguous	ADJ
cana-2175	31	13	data	datum	NOUN
cana-2175	31	14	[	[	X
cana-2175	31	15	5	5	NUM
cana-2175	31	16	]	]	PUNCT
cana-2175	31	17	.	.	PUNCT
cana-2175	32	1	dbpfs	dbpf	NOUN
cana-2175	32	2	can	can	AUX
cana-2175	32	3	enhance	enhance	VERB
cana-2175	32	4	diagnostic	diagnostic	ADJ
cana-2175	32	5	accuracy	accuracy	NOUN
cana-2175	32	6	by	by	ADP
cana-2175	32	7	providing	provide	VERB
cana-2175	32	8	a	a	DET
cana-2175	32	9	more	more	ADV
cana-2175	32	10	refined	refined	ADJ
cana-2175	32	11	model	model	NOUN
cana-2175	32	12	of	of	ADP
cana-2175	32	13	uncertainty	uncertainty	NOUN
cana-2175	32	14	.	.	PUNCT
cana-2175	33	1	for	for	ADP
cana-2175	33	2	example	example	NOUN
cana-2175	33	3	,	,	PUNCT
cana-2175	33	4	in	in	ADP
cana-2175	33	5	assessing	assess	VERB
cana-2175	33	6	the	the	DET
cana-2175	33	7	likelihood	likelihood	NOUN
cana-2175	33	8	of	of	ADP
cana-2175	33	9	a	a	DET
cana-2175	33	10	disease	disease	NOUN
cana-2175	33	11	,	,	PUNCT
cana-2175	33	12	dbpfs	dbpf	NOUN
cana-2175	33	13	can	can	AUX
cana-2175	33	14	separately	separately	ADV
cana-2175	33	15	represent	represent	VERB
cana-2175	33	16	the	the	DET
cana-2175	33	17	degree	degree	NOUN
cana-2175	33	18	to	to	PART
cana-2175	33	19	which	which	PRON
cana-2175	33	20	a	a	DET
cana-2175	33	21	patient	patient	NOUN
cana-2175	33	22	exhibits	exhibit	VERB
cana-2175	33	23	symptoms	symptom	NOUN
cana-2175	33	24	and	and	CCONJ
cana-2175	33	25	the	the	DET
cana-2175	33	26	degree	degree	NOUN
cana-2175	33	27	to	to	PART
cana-2175	33	28	which	which	PRON
cana-2175	33	29	those	those	DET
cana-2175	33	30	symptoms	symptom	NOUN
cana-2175	33	31	are	be	AUX
cana-2175	33	32	not	not	PART
cana-2175	33	33	present	present	ADJ
cana-2175	33	34	,	,	PUNCT
cana-2175	33	35	leading	lead	VERB
cana-2175	33	36	to	to	ADP
cana-2175	33	37	more	more	ADV
cana-2175	33	38	precise	precise	ADJ
cana-2175	33	39	diagnostic	diagnostic	ADJ
cana-2175	33	40	criteria	criterion	NOUN
cana-2175	33	41	and	and	CCONJ
cana-2175	33	42	better	well	ADJ
cana-2175	33	43	patient	patient	ADJ
cana-2175	33	44	outcomes	outcome	NOUN
cana-2175	33	45	.	.	PUNCT
cana-2175	34	1	financial	financial	ADJ
cana-2175	34	2	markets	market	NOUN
cana-2175	34	3	are	be	AUX
cana-2175	34	4	characterized	characterize	VERB
cana-2175	34	5	by	by	ADP
cana-2175	34	6	high	high	ADJ
cana-2175	34	7	levels	level	NOUN
cana-2175	34	8	of	of	ADP
cana-2175	34	9	uncertainty	uncertainty	NOUN
cana-2175	34	10	and	and	CCONJ
cana-2175	34	11	volatility	volatility	NOUN
cana-2175	34	12	.	.	PUNCT
cana-2175	35	1	dbpfs	dbpf	NOUN
cana-2175	35	2	can	can	AUX
cana-2175	35	3	improve	improve	VERB
cana-2175	35	4	risk	risk	NOUN
cana-2175	35	5	assessment	assessment	NOUN
cana-2175	35	6	and	and	CCONJ
cana-2175	35	7	forecasting	forecasting	NOUN
cana-2175	35	8	by	by	ADP
cana-2175	35	9	modeling	model	VERB
cana-2175	35	10	the	the	DET
cana-2175	35	11	inherent	inherent	ADJ
cana-2175	35	12	uncertainty	uncertainty	NOUN
cana-2175	35	13	in	in	ADP
cana-2175	35	14	market	market	NOUN
cana-2175	35	15	conditions	condition	NOUN
cana-2175	35	16	.	.	PUNCT
cana-2175	36	1	for	for	ADP
cana-2175	36	2	instance	instance	NOUN
cana-2175	36	3	,	,	PUNCT
cana-2175	36	4	in	in	ADP
cana-2175	36	5	portfolio	portfolio	NOUN
cana-2175	36	6	management	management	NOUN
cana-2175	36	7	,	,	PUNCT
cana-2175	36	8	dbpfs	dbpf	NOUN
cana-2175	36	9	can	can	AUX
cana-2175	36	10	be	be	AUX
cana-2175	36	11	used	use	VERB
cana-2175	36	12	to	to	PART
cana-2175	36	13	evaluate	evaluate	VERB
cana-2175	36	14	the	the	DET
cana-2175	36	15	risk	risk	NOUN
cana-2175	36	16	associated	associate	VERB
cana-2175	36	17	with	with	ADP
cana-2175	36	18	different	different	ADJ
cana-2175	36	19	investment	investment	NOUN
cana-2175	36	20	options	option	NOUN
cana-2175	36	21	by	by	ADP
cana-2175	36	22	separately	separately	ADV
cana-2175	36	23	modeling	model	VERB
cana-2175	36	24	the	the	DET
cana-2175	36	25	potential	potential	ADJ
cana-2175	36	26	gains	gain	NOUN
cana-2175	36	27	and	and	CCONJ
cana-2175	36	28	losses	loss	NOUN
cana-2175	36	29	[	[	X
cana-2175	36	30	6	6	NUM
cana-2175	36	31	]	]	PUNCT
cana-2175	36	32	.	.	PUNCT
cana-2175	37	1	this	this	PRON
cana-2175	37	2	allows	allow	VERB
cana-2175	37	3	for	for	ADP
cana-2175	37	4	more	more	ADV
cana-2175	37	5	robust	robust	ADJ
cana-2175	37	6	decision	decision	NOUN
cana-2175	37	7	-	-	PUNCT
cana-2175	37	8	making	making	NOUN
cana-2175	37	9	and	and	CCONJ
cana-2175	37	10	strategic	strategic	ADJ
cana-2175	37	11	planning	planning	NOUN
cana-2175	37	12	,	,	PUNCT
cana-2175	37	13	ultimately	ultimately	ADV
cana-2175	37	14	leading	lead	VERB
cana-2175	37	15	to	to	ADP
cana-2175	37	16	more	more	ADV
cana-2175	37	17	effective	effective	ADJ
cana-2175	37	18	financial	financial	ADJ
cana-2175	37	19	management	management	NOUN
cana-2175	37	20	.	.	PUNCT
cana-2175	38	1	in	in	ADP
cana-2175	38	2	engineering	engineering	NOUN
cana-2175	38	3	and	and	CCONJ
cana-2175	38	4	manufacturing	manufacturing	NOUN
cana-2175	38	5	,	,	PUNCT
cana-2175	38	6	quality	quality	NOUN
cana-2175	38	7	control	control	NOUN
cana-2175	38	8	processes	process	NOUN
cana-2175	38	9	often	often	ADV
cana-2175	38	10	deal	deal	VERB
cana-2175	38	11	with	with	ADP
cana-2175	38	12	variations	variation	NOUN
cana-2175	38	13	and	and	CCONJ
cana-2175	38	14	imperfections	imperfection	NOUN
cana-2175	38	15	in	in	ADP
cana-2175	38	16	production	production	NOUN
cana-2175	38	17	data	datum	NOUN
cana-2175	38	18	[	[	X
cana-2175	38	19	7	7	NUM
cana-2175	38	20	]	]	PUNCT
cana-2175	38	21	.	.	PUNCT
cana-2175	39	1	dbpfs	dbpf	NOUN
cana-2175	39	2	can	can	AUX
cana-2175	39	3	optimize	optimize	VERB
cana-2175	39	4	these	these	DET
cana-2175	39	5	processes	process	NOUN
cana-2175	39	6	by	by	ADP
cana-2175	39	7	providing	provide	VERB
cana-2175	39	8	a	a	DET
cana-2175	39	9	detailed	detailed	ADJ
cana-2175	39	10	representation	representation	NOUN
cana-2175	39	11	of	of	ADP
cana-2175	39	12	the	the	DET
cana-2175	39	13	uncertainties	uncertainty	NOUN
cana-2175	39	14	involved	involve	VERB
cana-2175	39	15	.	.	PUNCT
cana-2175	40	1	for	for	ADP
cana-2175	40	2	example	example	NOUN
cana-2175	40	3	,	,	PUNCT
cana-2175	40	4	in	in	ADP
cana-2175	40	5	the	the	DET
cana-2175	40	6	manufacturing	manufacturing	NOUN
cana-2175	40	7	of	of	ADP
cana-2175	40	8	precision	precision	NOUN
cana-2175	40	9	components	component	NOUN
cana-2175	40	10	,	,	PUNCT
cana-2175	40	11	dbpfs	dbpf	NOUN
cana-2175	40	12	can	can	AUX
cana-2175	40	13	model	model	VERB
cana-2175	40	14	the	the	DET
cana-2175	40	15	variability	variability	NOUN
cana-2175	40	16	in	in	ADP
cana-2175	40	17	dimensions	dimension	NOUN
cana-2175	40	18	and	and	CCONJ
cana-2175	40	19	tolerances	tolerance	NOUN
cana-2175	40	20	,	,	PUNCT
cana-2175	40	21	enabling	enable	VERB
cana-2175	40	22	better	well	ADJ
cana-2175	40	23	control	control	NOUN
cana-2175	40	24	of	of	ADP
cana-2175	40	25	product	product	NOUN
cana-2175	40	26	quality	quality	NOUN
cana-2175	40	27	and	and	CCONJ
cana-2175	40	28	more	more	ADV
cana-2175	40	29	effective	effective	ADJ
cana-2175	40	30	corrective	corrective	ADJ
cana-2175	40	31	actions	action	NOUN
cana-2175	40	32	.	.	PUNCT
cana-2175	41	1	environmental	environmental	ADJ
cana-2175	41	2	data	datum	NOUN
cana-2175	41	3	,	,	PUNCT
cana-2175	41	4	such	such	ADJ
cana-2175	41	5	as	as	ADP
cana-2175	41	6	measurements	measurement	NOUN
cana-2175	41	7	of	of	ADP
cana-2175	41	8	pollution	pollution	NOUN
cana-2175	41	9	levels	level	NOUN
cana-2175	41	10	or	or	CCONJ
cana-2175	41	11	biodiversity	biodiversity	NOUN
cana-2175	41	12	indices	index	NOUN
cana-2175	41	13	,	,	PUNCT
cana-2175	41	14	often	often	ADV
cana-2175	41	15	come	come	VERB
cana-2175	41	16	with	with	ADP
cana-2175	41	17	uncertainties	uncertainty	NOUN
cana-2175	41	18	due	due	ADJ
cana-2175	41	19	to	to	ADP
cana-2175	41	20	varying	vary	VERB
cana-2175	41	21	measurement	measurement	NOUN
cana-2175	41	22	techniques	technique	NOUN
cana-2175	41	23	and	and	CCONJ
cana-2175	41	24	natural	natural	ADJ
cana-2175	41	25	variability	variability	NOUN
cana-2175	41	26	[	[	X
cana-2175	41	27	8	8	NUM
cana-2175	41	28	]	]	PUNCT
cana-2175	41	29	.	.	PUNCT
cana-2175	42	1	dbpfs	dbpf	NOUN
cana-2175	42	2	can	can	AUX
cana-2175	42	3	enhance	enhance	VERB
cana-2175	42	4	the	the	DET
cana-2175	42	5	analysis	analysis	NOUN
cana-2175	42	6	of	of	ADP
cana-2175	42	7	such	such	ADJ
cana-2175	42	8	data	datum	NOUN
cana-2175	42	9	by	by	ADP
cana-2175	42	10	separately	separately	ADV
cana-2175	42	11	modeling	model	VERB
cana-2175	42	12	the	the	DET
cana-2175	42	13	degree	degree	NOUN
cana-2175	42	14	of	of	ADP
cana-2175	42	15	environmental	environmental	ADJ
cana-2175	42	16	impact	impact	NOUN
cana-2175	42	17	and	and	CCONJ
cana-2175	42	18	the	the	DET
cana-2175	42	19	degree	degree	NOUN
cana-2175	42	20	of	of	ADP
cana-2175	42	21	non	non	NOUN
cana-2175	42	22	-	-	NOUN
cana-2175	42	23	impact	impact	NOUN
cana-2175	42	24	.	.	PUNCT
cana-2175	43	1	this	this	DET
cana-2175	43	2	improved	improve	VERB
cana-2175	43	3	representation	representation	NOUN
cana-2175	43	4	can	can	AUX
cana-2175	43	5	lead	lead	VERB
cana-2175	43	6	to	to	ADP
cana-2175	43	7	more	more	ADV
cana-2175	43	8	accurate	accurate	ADJ
cana-2175	43	9	assessments	assessment	NOUN
cana-2175	43	10	of	of	ADP
cana-2175	43	11	environmental	environmental	ADJ
cana-2175	43	12	conditions	condition	NOUN
cana-2175	43	13	and	and	CCONJ
cana-2175	43	14	more	more	ADV
cana-2175	43	15	informed	informed	ADJ
cana-2175	43	16	conservation	conservation	NOUN
cana-2175	43	17	strategies	strategy	NOUN
cana-2175	43	18	.	.	PUNCT
cana-2175	44	1	in	in	ADP
cana-2175	44	2	complex	complex	ADJ
cana-2175	44	3	decision	decision	NOUN
cana-2175	44	4	-	-	PUNCT
cana-2175	44	5	making	make	VERB
cana-2175	44	6	scenarios	scenario	NOUN
cana-2175	44	7	,	,	PUNCT
cana-2175	44	8	where	where	SCONJ
cana-2175	44	9	multiple	multiple	ADJ
cana-2175	44	10	factors	factor	NOUN
cana-2175	44	11	and	and	CCONJ
cana-2175	44	12	their	their	PRON
cana-2175	44	13	uncertainties	uncertainty	NOUN
cana-2175	44	14	need	need	VERB
cana-2175	44	15	to	to	PART
cana-2175	44	16	be	be	AUX
cana-2175	44	17	considered	consider	VERB
cana-2175	44	18	,	,	PUNCT
cana-2175	44	19	dbpfs	dbpf	NOUN
cana-2175	44	20	offer	offer	VERB
cana-2175	44	21	a	a	DET
cana-2175	44	22	valuable	valuable	ADJ
cana-2175	44	23	tool	tool	NOUN
cana-2175	44	24	.	.	PUNCT
cana-2175	45	1	for	for	ADP
cana-2175	45	2	example	example	NOUN
cana-2175	45	3	,	,	PUNCT
cana-2175	45	4	in	in	ADP
cana-2175	45	5	multi	multi	ADJ
cana-2175	45	6	-	-	ADJ
cana-2175	45	7	criteria	criteria	ADJ
cana-2175	45	8	decision	decision	NOUN
cana-2175	45	9	analysis	analysis	NOUN
cana-2175	45	10	,	,	PUNCT
cana-2175	45	11	dbpfs	dbpf	NOUN
cana-2175	45	12	can	can	AUX
cana-2175	45	13	separately	separately	ADV
cana-2175	45	14	evaluate	evaluate	VERB
cana-2175	45	15	different	different	ADJ
cana-2175	45	16	criteria	criterion	NOUN
cana-2175	45	17	's	's	PART
cana-2175	45	18	importance	importance	NOUN
cana-2175	45	19	and	and	CCONJ
cana-2175	45	20	the	the	DET
cana-2175	45	21	degree	degree	NOUN
cana-2175	45	22	of	of	ADP
cana-2175	45	23	uncertainty	uncertainty	NOUN
cana-2175	45	24	associated	associate	VERB
cana-2175	45	25	with	with	ADP
cana-2175	45	26	each	each	DET
cana-2175	45	27	criterion	criterion	NOUN
cana-2175	45	28	.	.	PUNCT
cana-2175	46	1	this	this	PRON
cana-2175	46	2	allows	allow	VERB
cana-2175	46	3	for	for	ADP
cana-2175	46	4	a	a	DET
cana-2175	46	5	more	more	ADV
cana-2175	46	6	nuanced	nuanced	ADJ
cana-2175	46	7	and	and	CCONJ
cana-2175	46	8	balanced	balanced	ADJ
cana-2175	46	9	decisionmaking	decisionmaking	NOUN
cana-2175	46	10	process	process	NOUN
cana-2175	46	11	,	,	PUNCT
cana-2175	46	12	accommodating	accommodate	VERB
cana-2175	46	13	a	a	DET
cana-2175	46	14	wider	wide	ADJ
cana-2175	46	15	range	range	NOUN
cana-2175	46	16	of	of	ADP
cana-2175	46	17	possibilities	possibility	NOUN
cana-2175	46	18	and	and	CCONJ
cana-2175	46	19	uncertainties	uncertainty	NOUN
cana-2175	46	20	.	.	PUNCT
cana-2175	47	1	communications	communication	NOUN
cana-2175	47	2	on	on	ADP
cana-2175	47	3	applied	apply	VERB
cana-2175	47	4	nonlinear	nonlinear	ADJ
cana-2175	47	5	analysis	analysis	NOUN
cana-2175	47	6	issn	issn	NOUN
cana-2175	47	7	:	:	PUNCT
cana-2175	47	8	1074	1074	NUM
cana-2175	47	9	-	-	PUNCT
cana-2175	47	10	133x	133x	NUM
cana-2175	47	11	vol	vol	NOUN
cana-2175	47	12	32	32	NUM
cana-2175	47	13	no	no	NOUN
cana-2175	47	14	.	.	PUNCT
cana-2175	48	1	1s	1s	NUM
cana-2175	48	2	(	(	PUNCT
cana-2175	48	3	2025	2025	NUM
cana-2175	48	4	)	)	PUNCT
cana-2175	48	5	326	326	NUM
cana-2175	48	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2175	48	7	2	2	NUM
cana-2175	48	8	.	.	PUNCT
cana-2175	48	9	preliminaries	preliminary	NOUN
cana-2175	48	10	pythagorean	pythagorean	VERB
cana-2175	48	11	fuzzy	fuzzy	ADJ
cana-2175	48	12	sets	set	NOUN
cana-2175	48	13	(	(	PUNCT
cana-2175	48	14	pfs	pfs	PROPN
cana-2175	48	15	)	)	PUNCT
cana-2175	48	16	represent	represent	VERB
cana-2175	48	17	a	a	DET
cana-2175	48	18	significant	significant	ADJ
cana-2175	48	19	advancement	advancement	NOUN
cana-2175	48	20	in	in	ADP
cana-2175	48	21	handling	handle	VERB
cana-2175	48	22	uncertainty	uncertainty	NOUN
cana-2175	48	23	and	and	CCONJ
cana-2175	48	24	vagueness	vagueness	NOUN
cana-2175	48	25	compared	compare	VERB
cana-2175	48	26	to	to	ADP
cana-2175	48	27	traditional	traditional	ADJ
cana-2175	48	28	fuzzy	fuzzy	ADJ
cana-2175	48	29	and	and	CCONJ
cana-2175	48	30	intuitionistic	intuitionistic	ADJ
cana-2175	48	31	fuzzy	fuzzy	ADJ
cana-2175	48	32	sets	set	NOUN
cana-2175	48	33	.	.	PUNCT
cana-2175	49	1	pfs	pfs	PROPN
cana-2175	49	2	relax	relax	VERB
cana-2175	49	3	the	the	DET
cana-2175	49	4	constraint	constraint	NOUN
cana-2175	49	5	on	on	ADP
cana-2175	49	6	the	the	DET
cana-2175	49	7	sum	sum	NOUN
cana-2175	49	8	of	of	ADP
cana-2175	49	9	the	the	DET
cana-2175	49	10	membership	membership	NOUN
cana-2175	49	11	and	and	CCONJ
cana-2175	49	12	non	non	ADJ
cana-2175	49	13	-	-	ADJ
cana-2175	49	14	membership	membership	ADJ
cana-2175	49	15	degrees	degree	NOUN
cana-2175	49	16	,	,	PUNCT
cana-2175	49	17	allowing	allow	VERB
cana-2175	49	18	for	for	ADP
cana-2175	49	19	a	a	DET
cana-2175	49	20	broader	broad	ADJ
cana-2175	49	21	range	range	NOUN
cana-2175	49	22	of	of	ADP
cana-2175	49	23	values	value	NOUN
cana-2175	49	24	[	[	X
cana-2175	49	25	9	9	NUM
cana-2175	49	26	]	]	PUNCT
cana-2175	49	27	.	.	PUNCT
cana-2175	50	1	specifically	specifically	ADV
cana-2175	50	2	,	,	PUNCT
cana-2175	50	3	in	in	ADP
cana-2175	50	4	a	a	DET
cana-2175	50	5	pfs	pfs	PROPN
cana-2175	50	6	,	,	PUNCT
cana-2175	50	7	each	each	DET
cana-2175	50	8	element	element	NOUN
cana-2175	50	9	x	x	PUNCT
cana-2175	50	10	in	in	ADP
cana-2175	50	11	the	the	DET
cana-2175	50	12	universe	universe	NOUN
cana-2175	50	13	of	of	ADP
cana-2175	50	14	discourse	discourse	NOUN
cana-2175	50	15	x	x	SYM
cana-2175	50	16	is	be	AUX
cana-2175	50	17	characterized	characterize	VERB
cana-2175	50	18	by	by	ADP
cana-2175	50	19	a	a	DET
cana-2175	50	20	membership	membership	NOUN
cana-2175	50	21	degree	degree	NOUN
cana-2175	50	22	μ	μ	PROPN
cana-2175	50	23	a	a	DET
cana-2175	50	24	(	(	PUNCT
cana-2175	50	25	x	x	NOUN
cana-2175	50	26	)	)	PUNCT
cana-2175	50	27	and	and	CCONJ
cana-2175	50	28	a	a	DET
cana-2175	50	29	non	non	ADJ
cana-2175	50	30	-	-	ADJ
cana-2175	50	31	membership	membership	ADJ
cana-2175	50	32	degree	degree	NOUN
cana-2175	50	33	va(x	va(x	NOUN
cana-2175	50	34	)	)	PUNCT
cana-2175	50	35	such	such	ADJ
cana-2175	50	36	that	that	SCONJ
cana-2175	50	37	the	the	DET
cana-2175	50	38	sum	sum	NOUN
cana-2175	50	39	of	of	ADP
cana-2175	50	40	their	their	PRON
cana-2175	50	41	squares	square	NOUN
cana-2175	50	42	does	do	AUX
cana-2175	50	43	not	not	PART
cana-2175	50	44	exceed	exceed	VERB
cana-2175	50	45	one	one	NUM
cana-2175	50	46	:	:	PUNCT
cana-2175	50	47	0	0	NUM
cana-2175	50	48	≤	≤	NUM
cana-2175	50	49	μ	μ	NUM
cana-2175	50	50	a	a	PRON
cana-2175	50	51	(	(	PUNCT
cana-2175	50	52	x)2	x)2	NOUN
cana-2175	50	53	+	+	CCONJ
cana-2175	50	54	va(x)2	va(x)2	NOUN
cana-2175	50	55	≤	≤	NUM
cana-2175	50	56	1	1	NUM
cana-2175	50	57	(	(	PUNCT
cana-2175	50	58	1	1	NUM
cana-2175	50	59	)	)	PUNCT
cana-2175	50	60	πa(x	πa(x	NOUN
cana-2175	50	61	)	)	PUNCT
cana-2175	50	62	=	=	PUNCT
cana-2175	51	1	√1	√1	ADV
cana-2175	51	2	−	−	PROPN
cana-2175	51	3	μ	μ	PROPN
cana-2175	51	4	a	a	PRON
cana-2175	51	5	(	(	PUNCT
cana-2175	51	6	x)2	x)2	NOUN
cana-2175	51	7	−	−	NOUN
cana-2175	51	8	va(x)2	va(x)2	NOUN
cana-2175	51	9	(	(	PUNCT
cana-2175	51	10	2	2	NUM
cana-2175	51	11	)	)	PUNCT
cana-2175	51	12	an	an	DET
cana-2175	51	13	extension	extension	NOUN
cana-2175	51	14	of	of	ADP
cana-2175	51	15	pfs	pfs	PROPN
cana-2175	51	16	,	,	PUNCT
cana-2175	51	17	known	know	VERB
cana-2175	51	18	as	as	ADP
cana-2175	51	19	dpfs	dpfs	PROPN
cana-2175	51	20	,	,	PUNCT
cana-2175	51	21	incorporates	incorporate	VERB
cana-2175	51	22	a	a	DET
cana-2175	51	23	geometric	geometric	ADJ
cana-2175	51	24	representation	representation	NOUN
cana-2175	51	25	of	of	ADP
cana-2175	51	26	membership	membership	NOUN
cana-2175	51	27	and	and	CCONJ
cana-2175	51	28	non	non	ADJ
cana-2175	51	29	-	-	ADJ
cana-2175	51	30	membership	membership	ADJ
cana-2175	51	31	degrees	degree	NOUN
cana-2175	51	32	within	within	ADP
cana-2175	51	33	a	a	DET
cana-2175	51	34	unit	unit	NOUN
cana-2175	51	35	disc	disc	NOUN
cana-2175	51	36	.	.	PUNCT
cana-2175	52	1	this	this	DET
cana-2175	52	2	disc	disc	NOUN
cana-2175	52	3	-	-	PUNCT
cana-2175	52	4	based	base	VERB
cana-2175	52	5	approach	approach	NOUN
cana-2175	52	6	provides	provide	VERB
cana-2175	52	7	a	a	DET
cana-2175	52	8	more	more	ADV
cana-2175	52	9	intuitive	intuitive	ADJ
cana-2175	52	10	visualization	visualization	NOUN
cana-2175	52	11	of	of	ADP
cana-2175	52	12	the	the	DET
cana-2175	52	13	fuzzy	fuzzy	ADJ
cana-2175	52	14	set	set	NOUN
cana-2175	52	15	’s	’s	PART
cana-2175	52	16	characteristics	characteristic	NOUN
cana-2175	52	17	and	and	CCONJ
cana-2175	52	18	relationships	relationship	NOUN
cana-2175	52	19	between	between	ADP
cana-2175	52	20	different	different	ADJ
cana-2175	52	21	degrees	degree	NOUN
cana-2175	52	22	of	of	ADP
cana-2175	52	23	membership	membership	NOUN
cana-2175	52	24	,	,	PUNCT
cana-2175	52	25	non	non	ADJ
cana-2175	52	26	-	-	NOUN
cana-2175	52	27	membership	membership	NOUN
cana-2175	52	28	,	,	PUNCT
cana-2175	52	29	and	and	CCONJ
cana-2175	52	30	hesitation	hesitation	NOUN
cana-2175	52	31	.	.	PUNCT
cana-2175	53	1	a	a	DET
cana-2175	53	2	further	further	ADJ
cana-2175	53	3	refinement	refinement	NOUN
cana-2175	53	4	in	in	ADP
cana-2175	53	5	dpfs	dpfs	PROPN
cana-2175	53	6	involves	involve	VERB
cana-2175	53	7	the	the	DET
cana-2175	53	8	concept	concept	NOUN
cana-2175	53	9	of	of	ADP
cana-2175	53	10	distinct	distinct	ADJ
cana-2175	53	11	radii	radius	NOUN
cana-2175	53	12	[	[	X
cana-2175	53	13	10	10	NUM
cana-2175	53	14	]	]	PUNCT
cana-2175	53	15	.	.	PUNCT
cana-2175	54	1	by	by	ADP
cana-2175	54	2	varying	vary	VERB
cana-2175	54	3	the	the	DET
cana-2175	54	4	radius	radius	NOUN
cana-2175	54	5	of	of	ADP
cana-2175	54	6	the	the	DET
cana-2175	54	7	disc	disc	NOUN
cana-2175	54	8	,	,	PUNCT
cana-2175	54	9	researchers	researcher	NOUN
cana-2175	54	10	can	can	AUX
cana-2175	54	11	capture	capture	VERB
cana-2175	54	12	and	and	CCONJ
cana-2175	54	13	represent	represent	VERB
cana-2175	54	14	different	different	ADJ
cana-2175	54	15	levels	level	NOUN
cana-2175	54	16	of	of	ADP
cana-2175	54	17	uncertainty	uncertainty	NOUN
cana-2175	54	18	with	with	ADP
cana-2175	54	19	greater	great	ADJ
cana-2175	54	20	flexibility	flexibility	NOUN
cana-2175	54	21	.	.	PUNCT
cana-2175	55	1	this	this	DET
cana-2175	55	2	modification	modification	NOUN
cana-2175	55	3	enhances	enhance	VERB
cana-2175	55	4	the	the	DET
cana-2175	55	5	expressiveness	expressiveness	NOUN
cana-2175	55	6	of	of	ADP
cana-2175	55	7	dpfs	dpfs	PROPN
cana-2175	55	8	,	,	PUNCT
cana-2175	55	9	allowing	allow	VERB
cana-2175	55	10	for	for	ADP
cana-2175	55	11	a	a	DET
cana-2175	55	12	more	more	ADV
cana-2175	55	13	nuanced	nuanced	ADJ
cana-2175	55	14	representation	representation	NOUN
cana-2175	55	15	of	of	ADP
cana-2175	55	16	fuzzy	fuzzy	ADJ
cana-2175	55	17	information	information	NOUN
cana-2175	55	18	[	[	X
cana-2175	55	19	11	11	NUM
cana-2175	55	20	]	]	PUNCT
cana-2175	55	21	.	.	PUNCT
cana-2175	56	1	for	for	ADP
cana-2175	56	2	instance	instance	NOUN
cana-2175	56	3	,	,	PUNCT
cana-2175	56	4	adjusting	adjust	VERB
cana-2175	56	5	the	the	DET
cana-2175	56	6	radii	radius	NOUN
cana-2175	56	7	can	can	AUX
cana-2175	56	8	model	model	VERB
cana-2175	56	9	various	various	ADJ
cana-2175	56	10	degrees	degree	NOUN
cana-2175	56	11	of	of	ADP
cana-2175	56	12	uncertainty	uncertainty	NOUN
cana-2175	56	13	and	and	CCONJ
cana-2175	56	14	hesitation	hesitation	NOUN
cana-2175	56	15	,	,	PUNCT
cana-2175	56	16	thereby	thereby	ADV
cana-2175	56	17	providing	provide	VERB
cana-2175	56	18	a	a	DET
cana-2175	56	19	more	more	ADV
cana-2175	56	20	comprehensive	comprehensive	ADJ
cana-2175	56	21	framework	framework	NOUN
cana-2175	56	22	for	for	ADP
cana-2175	56	23	handling	handle	VERB
cana-2175	56	24	complex	complex	ADJ
cana-2175	56	25	scenarios	scenario	NOUN
cana-2175	56	26	.	.	PUNCT
cana-2175	57	1	recent	recent	ADJ
cana-2175	57	2	advancements	advancement	NOUN
cana-2175	57	3	in	in	ADP
cana-2175	57	4	pfs	pfs	PROPN
cana-2175	57	5	and	and	CCONJ
cana-2175	57	6	the	the	DET
cana-2175	57	7	development	development	NOUN
cana-2175	57	8	of	of	ADP
cana-2175	57	9	dpfs	dpfs	PROPN
cana-2175	57	10	with	with	ADP
cana-2175	57	11	distinct	distinct	ADJ
cana-2175	57	12	radii	radius	NOUN
cana-2175	57	13	have	have	AUX
cana-2175	57	14	shown	show	VERB
cana-2175	57	15	promising	promising	ADJ
cana-2175	57	16	results	result	NOUN
cana-2175	57	17	in	in	ADP
cana-2175	57	18	several	several	ADJ
cana-2175	57	19	applications	application	NOUN
cana-2175	57	20	[	[	X
cana-2175	57	21	12	12	NUM
cana-2175	57	22	]	]	PUNCT
cana-2175	57	23	.	.	PUNCT
cana-2175	58	1	for	for	ADP
cana-2175	58	2	example	example	NOUN
cana-2175	58	3	,	,	PUNCT
cana-2175	58	4	in	in	ADP
cana-2175	58	5	multi	multi	ADJ
cana-2175	58	6	-	-	ADJ
cana-2175	58	7	criteria	criterion	NOUN
cana-2175	58	8	decision	decision	NOUN
cana-2175	58	9	-	-	PUNCT
cana-2175	58	10	making	making	NOUN
cana-2175	58	11	,	,	PUNCT
cana-2175	58	12	new	new	ADJ
cana-2175	58	13	aggregation	aggregation	NOUN
cana-2175	58	14	operators	operator	NOUN
cana-2175	58	15	have	have	AUX
cana-2175	58	16	been	be	AUX
cana-2175	58	17	introduced	introduce	VERB
cana-2175	58	18	to	to	PART
cana-2175	58	19	manage	manage	VERB
cana-2175	58	20	complex	complex	ADJ
cana-2175	58	21	decision	decision	NOUN
cana-2175	58	22	scenarios	scenario	NOUN
cana-2175	58	23	more	more	ADV
cana-2175	58	24	effectively	effectively	ADV
cana-2175	58	25	[	[	X
cana-2175	58	26	13	13	NUM
cana-2175	58	27	]	]	PUNCT
cana-2175	58	28	.	.	PUNCT
cana-2175	59	1	similarly	similarly	ADV
cana-2175	59	2	,	,	PUNCT
cana-2175	59	3	novel	novel	ADJ
cana-2175	59	4	similarity	similarity	NOUN
cana-2175	59	5	measures	measure	NOUN
cana-2175	59	6	for	for	ADP
cana-2175	59	7	pfs	pf	NOUN
cana-2175	59	8	have	have	AUX
cana-2175	59	9	improved	improve	VERB
cana-2175	59	10	pattern	pattern	NOUN
cana-2175	59	11	recognition	recognition	NOUN
cana-2175	59	12	tasks	task	NOUN
cana-2175	59	13	.	.	PUNCT
cana-2175	60	1	the	the	DET
cana-2175	60	2	geometric	geometric	ADJ
cana-2175	60	3	approach	approach	NOUN
cana-2175	60	4	of	of	ADP
cana-2175	60	5	dpfs	dpfs	PROPN
cana-2175	60	6	has	have	AUX
cana-2175	60	7	proven	prove	VERB
cana-2175	60	8	effective	effective	ADJ
cana-2175	60	9	in	in	ADP
cana-2175	60	10	fields	field	NOUN
cana-2175	60	11	such	such	ADJ
cana-2175	60	12	as	as	ADP
cana-2175	60	13	medical	medical	ADJ
cana-2175	60	14	diagnosis	diagnosis	NOUN
cana-2175	60	15	and	and	CCONJ
cana-2175	60	16	risk	risk	NOUN
cana-2175	60	17	assessment	assessment	NOUN
cana-2175	60	18	,	,	PUNCT
cana-2175	60	19	where	where	SCONJ
cana-2175	60	20	the	the	DET
cana-2175	60	21	visual	visual	ADJ
cana-2175	60	22	representation	representation	NOUN
cana-2175	60	23	aids	aid	NOUN
cana-2175	60	24	in	in	ADP
cana-2175	60	25	understanding	understanding	NOUN
cana-2175	60	26	and	and	CCONJ
cana-2175	60	27	manipulating	manipulate	VERB
cana-2175	60	28	fuzzy	fuzzy	ADJ
cana-2175	60	29	information	information	NOUN
cana-2175	60	30	[	[	X
cana-2175	60	31	14	14	NUM
cana-2175	60	32	]	]	PUNCT
cana-2175	60	33	.	.	PUNCT
cana-2175	61	1	the	the	DET
cana-2175	61	2	application	application	NOUN
cana-2175	61	3	of	of	ADP
cana-2175	61	4	distinct	distinct	ADJ
cana-2175	61	5	radii	radius	NOUN
cana-2175	61	6	within	within	ADP
cana-2175	61	7	dpfs	dpfs	PROPN
cana-2175	61	8	is	be	AUX
cana-2175	61	9	a	a	DET
cana-2175	61	10	relatively	relatively	ADV
cana-2175	61	11	recent	recent	ADJ
cana-2175	61	12	development	development	NOUN
cana-2175	61	13	that	that	PRON
cana-2175	61	14	aims	aim	VERB
cana-2175	61	15	to	to	PART
cana-2175	61	16	further	far	ADV
cana-2175	61	17	enhance	enhance	VERB
cana-2175	61	18	the	the	DET
cana-2175	61	19	flexibility	flexibility	NOUN
cana-2175	61	20	and	and	CCONJ
cana-2175	61	21	accuracy	accuracy	NOUN
cana-2175	61	22	of	of	ADP
cana-2175	61	23	pythagorean	pythagorean	PROPN
cana-2175	61	24	fuzzy	fuzzy	ADJ
cana-2175	61	25	sets	set	NOUN
cana-2175	61	26	.	.	PUNCT
cana-2175	62	1	by	by	ADP
cana-2175	62	2	varying	vary	VERB
cana-2175	62	3	the	the	DET
cana-2175	62	4	radii	radius	NOUN
cana-2175	62	5	,	,	PUNCT
cana-2175	62	6	researchers	researcher	NOUN
cana-2175	62	7	can	can	AUX
cana-2175	62	8	better	well	ADV
cana-2175	62	9	model	model	VERB
cana-2175	62	10	uncertainty	uncertainty	NOUN
cana-2175	62	11	and	and	CCONJ
cana-2175	62	12	hesitation	hesitation	NOUN
cana-2175	62	13	,	,	PUNCT
cana-2175	62	14	which	which	PRON
cana-2175	62	15	has	have	VERB
cana-2175	62	16	significant	significant	ADJ
cana-2175	62	17	implications	implication	NOUN
cana-2175	62	18	for	for	ADP
cana-2175	62	19	fields	field	NOUN
cana-2175	62	20	such	such	ADJ
cana-2175	62	21	as	as	ADP
cana-2175	62	22	financial	financial	ADJ
cana-2175	62	23	forecasting	forecasting	NOUN
cana-2175	62	24	and	and	CCONJ
cana-2175	62	25	environmental	environmental	ADJ
cana-2175	62	26	monitoring	monitoring	NOUN
cana-2175	62	27	.	.	PUNCT
cana-2175	63	1	these	these	DET
cana-2175	63	2	advancements	advancement	NOUN
cana-2175	63	3	reflect	reflect	VERB
cana-2175	63	4	a	a	DET
cana-2175	63	5	substantial	substantial	ADJ
cana-2175	63	6	progress	progress	NOUN
cana-2175	63	7	in	in	ADP
cana-2175	63	8	the	the	DET
cana-2175	63	9	field	field	NOUN
cana-2175	63	10	of	of	ADP
cana-2175	63	11	fuzzy	fuzzy	ADJ
cana-2175	63	12	logic	logic	NOUN
cana-2175	63	13	,	,	PUNCT
cana-2175	63	14	offering	offer	VERB
cana-2175	63	15	more	more	ADJ
cana-2175	63	16	powerful	powerful	ADJ
cana-2175	63	17	tools	tool	NOUN
cana-2175	63	18	for	for	ADP
cana-2175	63	19	managing	manage	VERB
cana-2175	63	20	uncertainty	uncertainty	NOUN
cana-2175	63	21	and	and	CCONJ
cana-2175	63	22	improving	improve	VERB
cana-2175	63	23	decision	decision	NOUN
cana-2175	63	24	-	-	PUNCT
cana-2175	63	25	making	make	VERB
cana-2175	63	26	processes	process	NOUN
cana-2175	63	27	[	[	X
cana-2175	63	28	15	15	NUM
cana-2175	63	29	]	]	PUNCT
cana-2175	63	30	.	.	PUNCT
cana-2175	64	1	3	3	X
cana-2175	64	2	.	.	X
cana-2175	64	3	balance	balance	NOUN
cana-2175	64	4	equations	equation	NOUN
cana-2175	64	5	circular	circular	ADJ
cana-2175	64	6	pythagorean	pythagorean	NOUN
cana-2175	64	7	fuzzy	fuzzy	ADJ
cana-2175	64	8	sets	set	NOUN
cana-2175	64	9	(	(	PUNCT
cana-2175	64	10	c	c	NOUN
cana-2175	64	11	-	-	NOUN
cana-2175	64	12	pfss	pfss	NOUN
cana-2175	64	13	)	)	PUNCT
cana-2175	64	14	represent	represent	VERB
cana-2175	64	15	membership	membership	NOUN
cana-2175	64	16	and	and	CCONJ
cana-2175	64	17	non	non	ADJ
cana-2175	64	18	-	-	ADJ
cana-2175	64	19	membership	membership	ADJ
cana-2175	64	20	degrees	degree	NOUN
cana-2175	64	21	within	within	ADP
cana-2175	64	22	a	a	DET
cana-2175	64	23	fixed	fix	VERB
cana-2175	64	24	-	-	PUNCT
cana-2175	64	25	radius	radius	NOUN
cana-2175	64	26	circle	circle	NOUN
cana-2175	64	27	on	on	ADP
cana-2175	64	28	a	a	DET
cana-2175	64	29	two	two	NUM
cana-2175	64	30	-	-	PUNCT
cana-2175	64	31	dimensional	dimensional	ADJ
cana-2175	64	32	plane	plane	NOUN
cana-2175	64	33	.	.	PUNCT
cana-2175	65	1	for	for	ADP
cana-2175	65	2	any	any	DET
cana-2175	65	3	element	element	NOUN
cana-2175	65	4	x	x	NOUN
cana-2175	65	5	,	,	PUNCT
cana-2175	65	6	the	the	DET
cana-2175	65	7	membership	membership	NOUN
cana-2175	65	8	degree	degree	NOUN
cana-2175	65	9	μ	μ	PROPN
cana-2175	65	10	x	x	X
cana-2175	65	11	and	and	CCONJ
cana-2175	65	12	non	non	ADJ
cana-2175	65	13	-	-	ADJ
cana-2175	65	14	membership	membership	ADJ
cana-2175	65	15	degree	degree	NOUN
cana-2175	65	16	vx	vx	PROPN
cana-2175	65	17	must	must	AUX
cana-2175	65	18	satisfy	satisfy	VERB
cana-2175	65	19	the	the	DET
cana-2175	65	20	condition	condition	NOUN
cana-2175	65	21	μ	μ	NOUN
cana-2175	65	22	x	x	SYM
cana-2175	65	23	2	2	NUM
cana-2175	65	24	+	+	CCONJ
cana-2175	65	25	vx	vx	PROPN
cana-2175	65	26	2	2	NUM
cana-2175	65	27	≤	≤	NUM
cana-2175	65	28	1	1	NUM
cana-2175	65	29	(	(	PUNCT
cana-2175	65	30	3	3	X
cana-2175	65	31	)	)	PUNCT
cana-2175	65	32	this	this	PRON
cana-2175	65	33	ensures	ensure	VERB
cana-2175	65	34	that	that	SCONJ
cana-2175	65	35	the	the	DET
cana-2175	65	36	sum	sum	NOUN
cana-2175	65	37	of	of	ADP
cana-2175	65	38	the	the	DET
cana-2175	65	39	squares	square	NOUN
cana-2175	65	40	of	of	ADP
cana-2175	65	41	the	the	DET
cana-2175	65	42	membership	membership	NOUN
cana-2175	65	43	and	and	CCONJ
cana-2175	65	44	non	non	ADJ
cana-2175	65	45	-	-	ADJ
cana-2175	65	46	membership	membership	ADJ
cana-2175	65	47	degrees	degree	NOUN
cana-2175	65	48	does	do	AUX
cana-2175	65	49	not	not	PART
cana-2175	65	50	exceed	exceed	VERB
cana-2175	65	51	the	the	DET
cana-2175	65	52	radius	radius	NOUN
cana-2175	65	53	of	of	ADP
cana-2175	65	54	the	the	DET
cana-2175	65	55	circle	circle	NOUN
cana-2175	65	56	,	,	PUNCT
cana-2175	65	57	which	which	PRON
cana-2175	65	58	is	be	AUX
cana-2175	65	59	1	1	NUM
cana-2175	65	60	in	in	ADP
cana-2175	65	61	this	this	DET
cana-2175	65	62	case	case	NOUN
cana-2175	65	63	.	.	PUNCT
cana-2175	66	1	disc	disc	NOUN
cana-2175	66	2	pythagorean	pythagorean	PROPN
cana-2175	66	3	fuzzy	fuzzy	ADJ
cana-2175	66	4	sets	set	NOUN
cana-2175	66	5	(	(	PUNCT
cana-2175	66	6	d	d	NOUN
cana-2175	66	7	-	-	ADJ
cana-2175	66	8	pfss	pfss	ADJ
cana-2175	66	9	)	)	PUNCT
cana-2175	66	10	extend	extend	VERB
cana-2175	66	11	communications	communication	NOUN
cana-2175	66	12	on	on	ADP
cana-2175	66	13	applied	apply	VERB
cana-2175	66	14	nonlinear	nonlinear	ADJ
cana-2175	66	15	analysis	analysis	NOUN
cana-2175	66	16	issn	issn	NOUN
cana-2175	66	17	:	:	PUNCT
cana-2175	66	18	1074	1074	NUM
cana-2175	66	19	-	-	PUNCT
cana-2175	66	20	133x	133x	NUM
cana-2175	66	21	vol	vol	NOUN
cana-2175	66	22	32	32	NUM
cana-2175	67	1	no	no	NOUN
cana-2175	67	2	.	.	PUNCT
cana-2175	68	1	1s	1s	NUM
cana-2175	68	2	(	(	PUNCT
cana-2175	68	3	2025	2025	NUM
cana-2175	68	4	)	)	PUNCT
cana-2175	68	5	327	327	NUM
cana-2175	68	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2175	69	1	c	c	X
cana-2175	69	2	-	-	VERB
cana-2175	69	3	pfss	pfss	ADJ
cana-2175	69	4	by	by	ADP
cana-2175	69	5	introducing	introduce	VERB
cana-2175	69	6	distinct	distinct	ADJ
cana-2175	69	7	radii	radius	NOUN
cana-2175	69	8	for	for	ADP
cana-2175	69	9	each	each	DET
cana-2175	69	10	element	element	NOUN
cana-2175	69	11	,	,	PUNCT
cana-2175	69	12	providing	provide	VERB
cana-2175	69	13	a	a	DET
cana-2175	69	14	more	more	ADV
cana-2175	69	15	flexible	flexible	ADJ
cana-2175	69	16	representation	representation	NOUN
cana-2175	69	17	of	of	ADP
cana-2175	69	18	uncertainty	uncertainty	NOUN
cana-2175	69	19	.	.	PUNCT
cana-2175	70	1	in	in	ADP
cana-2175	70	2	d	d	PROPN
cana-2175	70	3	-	-	NOUN
cana-2175	70	4	pfss	pfss	ADJ
cana-2175	70	5	,	,	PUNCT
cana-2175	70	6	each	each	DET
cana-2175	70	7	element	element	NOUN
cana-2175	70	8	xxx	xxx	NOUN
cana-2175	70	9	is	be	AUX
cana-2175	70	10	defined	define	VERB
cana-2175	70	11	by	by	ADP
cana-2175	70	12	a	a	DET
cana-2175	70	13	triplet	triplet	NOUN
cana-2175	70	14	(	(	PUNCT
cana-2175	70	15	x	x	PROPN
cana-2175	70	16	,	,	PUNCT
cana-2175	70	17	μ	μ	PROPN
cana-2175	70	18	x	x	X
cana-2175	70	19	,	,	PUNCT
cana-2175	70	20	vx	vx	PROPN
cana-2175	70	21	,	,	PUNCT
cana-2175	70	22	rx	rx	ADJ
cana-2175	70	23	)	)	PUNCT
cana-2175	70	24	,	,	PUNCT
cana-2175	70	25	where	where	SCONJ
cana-2175	70	26	μ	μ	NOUN
cana-2175	70	27	x	x	X
cana-2175	70	28	and	and	CCONJ
cana-2175	70	29	vx	vx	PROPN
cana-2175	70	30	are	be	AUX
cana-2175	70	31	the	the	DET
cana-2175	70	32	membership	membership	NOUN
cana-2175	70	33	and	and	CCONJ
cana-2175	70	34	non	non	ADJ
cana-2175	70	35	-	-	ADJ
cana-2175	70	36	membership	membership	ADJ
cana-2175	70	37	degrees	degree	NOUN
cana-2175	70	38	,	,	PUNCT
cana-2175	70	39	respectively	respectively	ADV
cana-2175	70	40	,	,	PUNCT
cana-2175	70	41	and	and	CCONJ
cana-2175	70	42	rx	rx	NOUN
cana-2175	70	43	is	be	AUX
cana-2175	70	44	the	the	DET
cana-2175	70	45	distinct	distinct	ADJ
cana-2175	70	46	radius	radius	NOUN
cana-2175	70	47	.	.	PUNCT
cana-2175	71	1	the	the	DET
cana-2175	71	2	pythagorean	pythagorean	PROPN
cana-2175	71	3	condition	condition	NOUN
cana-2175	71	4	for	for	ADP
cana-2175	71	5	d	d	X
cana-2175	71	6	-	-	ADJ
cana-2175	71	7	pfss	pfss	NOUN
cana-2175	71	8	is	be	AUX
cana-2175	71	9	given	give	VERB
cana-2175	71	10	by	by	ADP
cana-2175	71	11	μ	μ	PROPN
cana-2175	71	12	x	x	SYM
cana-2175	71	13	2	2	NUM
cana-2175	71	14	+	+	CCONJ
cana-2175	71	15	vx	vx	PROPN
cana-2175	71	16	2	2	NUM
cana-2175	71	17	≤	≤	NUM
cana-2175	71	18	rx	rx	VERB
cana-2175	71	19	2	2	NUM
cana-2175	71	20	(	(	PUNCT
cana-2175	71	21	4	4	NUM
cana-2175	71	22	)	)	PUNCT
cana-2175	71	23	this	this	DET
cana-2175	71	24	condition	condition	NOUN
cana-2175	71	25	allows	allow	VERB
cana-2175	71	26	each	each	DET
cana-2175	71	27	element	element	NOUN
cana-2175	71	28	to	to	PART
cana-2175	71	29	have	have	VERB
cana-2175	71	30	its	its	PRON
cana-2175	71	31	own	own	ADJ
cana-2175	71	32	radius	radius	NOUN
cana-2175	71	33	,	,	PUNCT
cana-2175	71	34	offering	offer	VERB
cana-2175	71	35	greater	great	ADJ
cana-2175	71	36	flexibility	flexibility	NOUN
cana-2175	71	37	in	in	ADP
cana-2175	71	38	modeling	model	VERB
cana-2175	71	39	varying	vary	VERB
cana-2175	71	40	degrees	degree	NOUN
cana-2175	71	41	of	of	ADP
cana-2175	71	42	uncertainty	uncertainty	NOUN
cana-2175	71	43	.	.	PUNCT
cana-2175	72	1	the	the	DET
cana-2175	72	2	mathematical	mathematical	ADJ
cana-2175	72	3	formulation	formulation	NOUN
cana-2175	72	4	and	and	CCONJ
cana-2175	72	5	operations	operation	NOUN
cana-2175	72	6	for	for	ADP
cana-2175	72	7	d	d	X
cana-2175	72	8	-	-	PUNCT
cana-2175	72	9	pfss	pfss	ADJ
cana-2175	72	10	involve	involve	VERB
cana-2175	72	11	several	several	ADJ
cana-2175	72	12	steps	step	NOUN
cana-2175	72	13	.	.	PUNCT
cana-2175	73	1	first	first	ADV
cana-2175	73	2	,	,	PUNCT
cana-2175	73	3	the	the	DET
cana-2175	73	4	validation	validation	NOUN
cana-2175	73	5	of	of	ADP
cana-2175	73	6	the	the	DET
cana-2175	73	7	pythagorean	pythagorean	PROPN
cana-2175	73	8	condition	condition	NOUN
cana-2175	73	9	for	for	ADP
cana-2175	73	10	any	any	DET
cana-2175	73	11	element	element	NOUN
cana-2175	73	12	x	x	PRON
cana-2175	73	13	ensures	ensure	VERB
cana-2175	73	14	the	the	DET
cana-2175	73	15	integrity	integrity	NOUN
cana-2175	73	16	of	of	ADP
cana-2175	73	17	the	the	DET
cana-2175	73	18	fuzzy	fuzzy	ADJ
cana-2175	73	19	set	set	NOUN
cana-2175	73	20	.	.	PUNCT
cana-2175	74	1	the	the	DET
cana-2175	74	2	union	union	PROPN
cana-2175	74	3	operation	operation	NOUN
cana-2175	74	4	of	of	ADP
cana-2175	74	5	two	two	NUM
cana-2175	74	6	d	d	NOUN
cana-2175	74	7	-	-	NOUN
cana-2175	74	8	pfss	pfss	ADJ
cana-2175	74	9	,	,	PUNCT
cana-2175	74	10	a	a	PRON
cana-2175	74	11	and	and	CCONJ
cana-2175	74	12	b	b	NOUN
cana-2175	74	13	,	,	PUNCT
cana-2175	74	14	for	for	ADP
cana-2175	74	15	an	an	DET
cana-2175	74	16	element	element	NOUN
cana-2175	74	17	x	x	NOUN
cana-2175	74	18	,	,	PUNCT
cana-2175	74	19	is	be	AUX
cana-2175	74	20	defined	define	VERB
cana-2175	74	21	by	by	ADP
cana-2175	74	22	new	new	ADJ
cana-2175	74	23	membership	membership	NOUN
cana-2175	74	24	and	and	CCONJ
cana-2175	74	25	non	non	ADJ
cana-2175	74	26	-	-	ADJ
cana-2175	74	27	membership	membership	ADJ
cana-2175	74	28	degrees	degree	NOUN
cana-2175	74	29	calculated	calculate	VERB
cana-2175	74	30	as	as	ADP
cana-2175	74	31	μ	μ	PROPN
cana-2175	74	32	a∪b	a∪b	NOUN
cana-2175	74	33	(	(	PUNCT
cana-2175	74	34	x	x	NOUN
cana-2175	74	35	)	)	PUNCT
cana-2175	74	36	=	=	SYM
cana-2175	74	37	min(1	min(1	X
cana-2175	74	38	,	,	PUNCT
cana-2175	74	39	√μ	√μ	X
cana-2175	74	40	a	a	DET
cana-2175	74	41	(	(	PUNCT
cana-2175	74	42	x)2	x)2	PROPN
cana-2175	74	43	+	+	CCONJ
cana-2175	74	44	μ	μ	PROPN
cana-2175	74	45	b	b	PROPN
cana-2175	74	46	(	(	PUNCT
cana-2175	74	47	x)2	x)2	X
cana-2175	74	48	(	(	PUNCT
cana-2175	74	49	5	5	NUM
cana-2175	74	50	)	)	PUNCT
cana-2175	74	51	va∪b(x	va∪b(x	ADJ
cana-2175	74	52	)	)	PUNCT
cana-2175	74	53	=	=	SYM
cana-2175	74	54	min(1	min(1	NOUN
cana-2175	74	55	,	,	PUNCT
cana-2175	74	56	√va(x)2	√va(x)2	VERB
cana-2175	74	57	+	+	PRON
cana-2175	74	58	vb(x)2	vb(x)2	NOUN
cana-2175	74	59	(	(	PUNCT
cana-2175	74	60	6	6	NUM
cana-2175	74	61	)	)	PUNCT
cana-2175	74	62	the	the	DET
cana-2175	74	63	radius	radius	NOUN
cana-2175	74	64	for	for	ADP
cana-2175	74	65	the	the	DET
cana-2175	74	66	union	union	NOUN
cana-2175	74	67	is	be	AUX
cana-2175	74	68	typically	typically	ADV
cana-2175	74	69	taken	take	VERB
cana-2175	74	70	as	as	ADP
cana-2175	74	71	the	the	DET
cana-2175	74	72	minimum	minimum	ADJ
cana-2175	74	73	radius	radius	NOUN
cana-2175	74	74	of	of	ADP
cana-2175	74	75	the	the	DET
cana-2175	74	76	corresponding	corresponding	ADJ
cana-2175	74	77	elements	element	NOUN
cana-2175	74	78	in	in	ADP
cana-2175	74	79	a	a	PRON
cana-2175	74	80	and	and	CCONJ
cana-2175	74	81	b	b	NOUN
cana-2175	74	82	:	:	PUNCT
cana-2175	74	83	ra∪b(x	ra∪b(x	ADJ
cana-2175	74	84	)	)	PUNCT
cana-2175	74	85	=	=	SYM
cana-2175	74	86	min	min	PROPN
cana-2175	74	87	(	(	PUNCT
cana-2175	74	88	ra(x	ra(x	NOUN
cana-2175	74	89	)	)	PUNCT
cana-2175	74	90	,	,	PUNCT
cana-2175	74	91	rb(x	rb(x	NOUN
cana-2175	74	92	)	)	PUNCT
cana-2175	74	93	)	)	PUNCT
cana-2175	75	1	(	(	PUNCT
cana-2175	75	2	7	7	X
cana-2175	75	3	)	)	PUNCT
cana-2175	75	4	the	the	DET
cana-2175	75	5	intersection	intersection	NOUN
cana-2175	75	6	operation	operation	NOUN
cana-2175	75	7	of	of	ADP
cana-2175	75	8	two	two	NUM
cana-2175	75	9	d	d	NOUN
cana-2175	75	10	-	-	NOUN
cana-2175	75	11	pfss	pfss	ADJ
cana-2175	75	12	,	,	PUNCT
cana-2175	75	13	a	a	PRON
cana-2175	75	14	and	and	CCONJ
cana-2175	75	15	b	b	NOUN
cana-2175	75	16	,	,	PUNCT
cana-2175	75	17	for	for	ADP
cana-2175	75	18	an	an	DET
cana-2175	75	19	element	element	NOUN
cana-2175	75	20	x	x	NOUN
cana-2175	75	21	,	,	PUNCT
cana-2175	75	22	is	be	AUX
cana-2175	75	23	defined	define	VERB
cana-2175	75	24	by	by	ADP
cana-2175	75	25	μ	μ	PROPN
cana-2175	75	26	a∪b	a∪b	NOUN
cana-2175	75	27	(	(	PUNCT
cana-2175	75	28	x	x	X
cana-2175	75	29	)	)	PUNCT
cana-2175	75	30	=	=	SYM
cana-2175	75	31	max	max	PROPN
cana-2175	75	32	(	(	PUNCT
cana-2175	75	33	0	0	NUM
cana-2175	75	34	,	,	PUNCT
cana-2175	75	35	√μ	√μ	X
cana-2175	75	36	a	a	PRON
cana-2175	75	37	(	(	PUNCT
cana-2175	75	38	x)2	x)2	PROPN
cana-2175	76	1	+	+	CCONJ
cana-2175	76	2	μ	μ	PROPN
cana-2175	76	3	b	b	PROPN
cana-2175	76	4	(	(	PUNCT
cana-2175	76	5	x)2	x)2	VERB
cana-2175	76	6	−	−	PROPN
cana-2175	76	7	1	1	NUM
cana-2175	76	8	(	(	PUNCT
cana-2175	76	9	8)	8)	NUM
cana-2175	76	10	va∪b(x	va∪b(x	NOUN
cana-2175	76	11	)	)	PUNCT
cana-2175	76	12	=	=	SYM
cana-2175	76	13	max	max	PROPN
cana-2175	76	14	(	(	PUNCT
cana-2175	76	15	0	0	NUM
cana-2175	76	16	,	,	PUNCT
cana-2175	76	17	√va(x)2	√va(x)2	NOUN
cana-2175	76	18	+	+	PRON
cana-2175	76	19	vb(x)2	vb(x)2	NOUN
cana-2175	76	20	−	−	NOUN
cana-2175	76	21	1	1	NUM
cana-2175	76	22	(	(	PUNCT
cana-2175	76	23	9	9	NUM
cana-2175	76	24	)	)	PUNCT
cana-2175	76	25	the	the	DET
cana-2175	76	26	radius	radius	NOUN
cana-2175	76	27	for	for	ADP
cana-2175	76	28	the	the	DET
cana-2175	76	29	intersection	intersection	NOUN
cana-2175	76	30	is	be	AUX
cana-2175	76	31	typically	typically	ADV
cana-2175	76	32	taken	take	VERB
cana-2175	76	33	as	as	ADP
cana-2175	76	34	the	the	DET
cana-2175	76	35	maximum	maximum	ADJ
cana-2175	76	36	radius	radius	NOUN
cana-2175	76	37	of	of	ADP
cana-2175	76	38	the	the	DET
cana-2175	76	39	corresponding	corresponding	ADJ
cana-2175	76	40	elements	element	NOUN
cana-2175	76	41	in	in	ADP
cana-2175	76	42	a	a	DET
cana-2175	76	43	and	and	CCONJ
cana-2175	76	44	b	b	NOUN
cana-2175	76	45	:	:	PUNCT
cana-2175	76	46	ra∩b(x	ra∩b(x	ADJ
cana-2175	76	47	)	)	PUNCT
cana-2175	76	48	=	=	SYM
cana-2175	76	49	max	max	PROPN
cana-2175	76	50	(	(	PUNCT
cana-2175	76	51	ra(x	ra(x	NOUN
cana-2175	76	52	)	)	PUNCT
cana-2175	76	53	,	,	PUNCT
cana-2175	76	54	rb(x	rb(x	NOUN
cana-2175	76	55	)	)	PUNCT
cana-2175	76	56	)	)	PUNCT
cana-2175	76	57	(	(	PUNCT
cana-2175	76	58	10	10	NUM
cana-2175	76	59	)	)	PUNCT
cana-2175	76	60	the	the	DET
cana-2175	76	61	complement	complement	NOUN
cana-2175	76	62	of	of	ADP
cana-2175	76	63	a	a	DET
cana-2175	76	64	d	d	NOUN
cana-2175	76	65	-	-	PUNCT
cana-2175	76	66	pfs	pfs	ADJ
cana-2175	76	67	a	a	PRON
cana-2175	76	68	,	,	PUNCT
cana-2175	76	69	for	for	ADP
cana-2175	76	70	an	an	DET
cana-2175	76	71	element	element	NOUN
cana-2175	76	72	x	x	NOUN
cana-2175	76	73	,	,	PUNCT
cana-2175	76	74	is	be	AUX
cana-2175	76	75	defined	define	VERB
cana-2175	76	76	by	by	ADP
cana-2175	76	77	swapping	swap	VERB
cana-2175	76	78	the	the	DET
cana-2175	76	79	membership	membership	NOUN
cana-2175	76	80	and	and	CCONJ
cana-2175	76	81	nonmembership	nonmembership	NOUN
cana-2175	76	82	degrees	degree	NOUN
cana-2175	76	83	:	:	PUNCT
cana-2175	76	84	μ¬a(x	μ¬a(x	X
cana-2175	76	85	)	)	PUNCT
cana-2175	76	86	=	=	SYM
cana-2175	76	87	va(x	va(x	NOUN
cana-2175	76	88	)	)	PUNCT
cana-2175	76	89	(	(	PUNCT
cana-2175	76	90	11	11	NUM
cana-2175	76	91	)	)	PUNCT
cana-2175	76	92	v¬a(x	v¬a(x	NOUN
cana-2175	76	93	)	)	PUNCT
cana-2175	76	94	=	=	SYM
cana-2175	76	95	μ	μ	PROPN
cana-2175	76	96	a	a	DET
cana-2175	76	97	(	(	PUNCT
cana-2175	76	98	x	x	NOUN
cana-2175	76	99	)	)	PUNCT
cana-2175	76	100	(	(	PUNCT
cana-2175	76	101	12	12	NUM
cana-2175	76	102	)	)	PUNCT
cana-2175	76	103	the	the	DET
cana-2175	76	104	radius	radius	NOUN
cana-2175	76	105	remains	remain	VERB
cana-2175	76	106	unchanged	unchanged	ADJ
cana-2175	76	107	:	:	PUNCT
cana-2175	76	108	r¬a(x	r¬a(x	NOUN
cana-2175	76	109	)	)	PUNCT
cana-2175	77	1	=	=	SYM
cana-2175	77	2	ra(x	ra(x	NOUN
cana-2175	77	3	)	)	PUNCT
cana-2175	77	4	(	(	PUNCT
cana-2175	77	5	13	13	NUM
cana-2175	77	6	)	)	PUNCT
cana-2175	77	7	implementing	implement	VERB
cana-2175	77	8	d	d	X
cana-2175	77	9	-	-	ADJ
cana-2175	77	10	pfss	pfss	ADJ
cana-2175	77	11	required	require	VERB
cana-2175	77	12	careful	careful	ADJ
cana-2175	77	13	attention	attention	NOUN
cana-2175	77	14	to	to	ADP
cana-2175	77	15	practical	practical	ADJ
cana-2175	77	16	details	detail	NOUN
cana-2175	77	17	.	.	PUNCT
cana-2175	78	1	the	the	DET
cana-2175	78	2	elements	element	NOUN
cana-2175	78	3	of	of	ADP
cana-2175	78	4	the	the	DET
cana-2175	78	5	d	d	PROPN
cana-2175	78	6	-	-	PUNCT
cana-2175	78	7	pfs	pfs	PROPN
cana-2175	78	8	were	be	AUX
cana-2175	78	9	defined	define	VERB
cana-2175	78	10	,	,	PUNCT
cana-2175	78	11	with	with	ADP
cana-2175	78	12	each	each	DET
cana-2175	78	13	element	element	NOUN
cana-2175	78	14	characterized	characterize	VERB
cana-2175	78	15	by	by	ADP
cana-2175	78	16	its	its	PRON
cana-2175	78	17	membership	membership	NOUN
cana-2175	78	18	degree	degree	NOUN
cana-2175	78	19	μ	μ	PROPN
cana-2175	78	20	x	x	SYM
cana-2175	78	21	,	,	PUNCT
cana-2175	78	22	non	non	ADJ
cana-2175	78	23	-	-	ADJ
cana-2175	78	24	membership	membership	ADJ
cana-2175	78	25	degree	degree	NOUN
cana-2175	78	26	vx	vx	PROPN
cana-2175	78	27	,	,	PUNCT
cana-2175	78	28	and	and	CCONJ
cana-2175	78	29	distinct	distinct	ADJ
cana-2175	78	30	radius	radius	NOUN
cana-2175	78	31	rx	rx	VERB
cana-2175	78	32	.	.	PUNCT
cana-2175	79	1	an	an	DET
cana-2175	79	2	efficient	efficient	ADJ
cana-2175	79	3	data	data	NOUN
cana-2175	79	4	structure	structure	NOUN
cana-2175	79	5	,	,	PUNCT
cana-2175	79	6	such	such	ADJ
cana-2175	79	7	as	as	ADP
cana-2175	79	8	a	a	DET
cana-2175	79	9	hash	hash	NOUN
cana-2175	79	10	map	map	NOUN
cana-2175	79	11	,	,	PUNCT
cana-2175	79	12	was	be	AUX
cana-2175	79	13	chosen	choose	VERB
cana-2175	79	14	to	to	PART
cana-2175	79	15	store	store	VERB
cana-2175	79	16	these	these	DET
cana-2175	79	17	parameters	parameter	NOUN
cana-2175	79	18	,	,	PUNCT
cana-2175	79	19	facilitating	facilitate	VERB
cana-2175	79	20	easy	easy	ADJ
cana-2175	79	21	access	access	NOUN
cana-2175	79	22	and	and	CCONJ
cana-2175	79	23	manipulation	manipulation	NOUN
cana-2175	79	24	.	.	PUNCT
cana-2175	80	1	mechanisms	mechanism	NOUN
cana-2175	80	2	were	be	AUX
cana-2175	80	3	developed	develop	VERB
cana-2175	80	4	and	and	CCONJ
cana-2175	80	5	applied	apply	VERB
cana-2175	80	6	to	to	PART
cana-2175	80	7	verify	verify	VERB
cana-2175	80	8	that	that	SCONJ
cana-2175	80	9	the	the	DET
cana-2175	80	10	pythagorean	pythagorean	PROPN
cana-2175	80	11	condition	condition	NOUN
cana-2175	80	12	(	(	PUNCT
cana-2175	80	13	2	2	X
cana-2175	80	14	)	)	PUNCT
cana-2175	80	15	held	hold	VERB
cana-2175	80	16	true	true	ADJ
cana-2175	80	17	for	for	ADP
cana-2175	80	18	each	each	DET
cana-2175	80	19	element	element	NOUN
cana-2175	80	20	,	,	PUNCT
cana-2175	80	21	ensuring	ensure	VERB
cana-2175	80	22	the	the	DET
cana-2175	80	23	integrity	integrity	NOUN
cana-2175	80	24	of	of	ADP
cana-2175	80	25	the	the	DET
cana-2175	80	26	fuzzy	fuzzy	ADJ
cana-2175	80	27	communications	communication	NOUN
cana-2175	80	28	on	on	ADP
cana-2175	80	29	applied	apply	VERB
cana-2175	80	30	nonlinear	nonlinear	ADJ
cana-2175	80	31	analysis	analysis	NOUN
cana-2175	80	32	issn	issn	NOUN
cana-2175	80	33	:	:	PUNCT
cana-2175	80	34	1074	1074	NUM
cana-2175	80	35	-	-	PUNCT
cana-2175	80	36	133x	133x	NUM
cana-2175	80	37	vol	vol	NOUN
cana-2175	80	38	32	32	NUM
cana-2175	80	39	no	no	NOUN
cana-2175	80	40	.	.	PUNCT
cana-2175	81	1	1s	1s	NUM
cana-2175	81	2	(	(	PUNCT
cana-2175	81	3	2025	2025	NUM
cana-2175	81	4	)	)	PUNCT
cana-2175	81	5	328	328	NUM
cana-2175	81	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2175	81	7	set	set	NOUN
cana-2175	81	8	.	.	PUNCT
cana-2175	82	1	the	the	DET
cana-2175	82	2	operations	operation	NOUN
cana-2175	82	3	of	of	ADP
cana-2175	82	4	union	union	NOUN
cana-2175	82	5	,	,	PUNCT
cana-2175	82	6	intersection	intersection	NOUN
cana-2175	82	7	,	,	PUNCT
cana-2175	82	8	and	and	CCONJ
cana-2175	82	9	complement	complement	NOUN
cana-2175	82	10	were	be	AUX
cana-2175	82	11	implemented	implement	VERB
cana-2175	82	12	while	while	SCONJ
cana-2175	82	13	respecting	respect	VERB
cana-2175	82	14	the	the	DET
cana-2175	82	15	distinct	distinct	ADJ
cana-2175	82	16	radii	radii	NOUN
cana-2175	82	17	.	.	PUNCT
cana-2175	83	1	for	for	ADP
cana-2175	83	2	the	the	DET
cana-2175	83	3	union	union	NOUN
cana-2175	83	4	operation	operation	NOUN
cana-2175	83	5	,	,	PUNCT
cana-2175	83	6	the	the	DET
cana-2175	83	7	new	new	ADJ
cana-2175	83	8	membership	membership	NOUN
cana-2175	83	9	and	and	CCONJ
cana-2175	83	10	non	non	ADJ
cana-2175	83	11	-	-	ADJ
cana-2175	83	12	membership	membership	ADJ
cana-2175	83	13	degrees	degree	NOUN
cana-2175	83	14	were	be	AUX
cana-2175	83	15	computed	compute	VERB
cana-2175	83	16	,	,	PUNCT
cana-2175	83	17	and	and	CCONJ
cana-2175	83	18	the	the	DET
cana-2175	83	19	radius	radius	NOUN
cana-2175	83	20	was	be	AUX
cana-2175	83	21	set	set	VERB
cana-2175	83	22	as	as	ADP
cana-2175	83	23	the	the	DET
cana-2175	83	24	minimum	minimum	NOUN
cana-2175	83	25	of	of	ADP
cana-2175	83	26	the	the	DET
cana-2175	83	27	radii	radius	NOUN
cana-2175	83	28	involved	involve	VERB
cana-2175	83	29	.	.	PUNCT
cana-2175	84	1	for	for	ADP
cana-2175	84	2	the	the	DET
cana-2175	84	3	intersection	intersection	NOUN
cana-2175	84	4	,	,	PUNCT
cana-2175	84	5	the	the	DET
cana-2175	84	6	degrees	degree	NOUN
cana-2175	84	7	were	be	AUX
cana-2175	84	8	calculated	calculate	VERB
cana-2175	84	9	,	,	PUNCT
cana-2175	84	10	and	and	CCONJ
cana-2175	84	11	the	the	DET
cana-2175	84	12	radius	radius	NOUN
cana-2175	84	13	was	be	AUX
cana-2175	84	14	set	set	VERB
cana-2175	84	15	as	as	ADP
cana-2175	84	16	the	the	DET
cana-2175	84	17	maximum	maximum	NOUN
cana-2175	84	18	of	of	ADP
cana-2175	84	19	the	the	DET
cana-2175	84	20	radii	radii	NOUN
cana-2175	84	21	.	.	PUNCT
cana-2175	85	1	for	for	ADP
cana-2175	85	2	the	the	DET
cana-2175	85	3	complement	complement	NOUN
cana-2175	85	4	,	,	PUNCT
cana-2175	85	5	the	the	DET
cana-2175	85	6	membership	membership	NOUN
cana-2175	85	7	and	and	CCONJ
cana-2175	85	8	non	non	ADJ
cana-2175	85	9	-	-	ADJ
cana-2175	85	10	membership	membership	ADJ
cana-2175	85	11	degrees	degree	NOUN
cana-2175	85	12	were	be	AUX
cana-2175	85	13	swapped	swap	VERB
cana-2175	85	14	while	while	SCONJ
cana-2175	85	15	keeping	keep	VERB
cana-2175	85	16	the	the	DET
cana-2175	85	17	radius	radius	NOUN
cana-2175	85	18	unchanged	unchanged	ADJ
cana-2175	85	19	.	.	PUNCT
cana-2175	86	1	adhering	adhere	VERB
cana-2175	86	2	to	to	ADP
cana-2175	86	3	these	these	DET
cana-2175	86	4	steps	step	NOUN
cana-2175	86	5	ensured	ensure	VERB
cana-2175	86	6	that	that	SCONJ
cana-2175	86	7	d	d	X
cana-2175	86	8	-	-	PUNCT
cana-2175	86	9	pfss	pfss	ADJ
cana-2175	86	10	were	be	AUX
cana-2175	86	11	robust	robust	ADJ
cana-2175	86	12	and	and	CCONJ
cana-2175	86	13	effective	effective	ADJ
cana-2175	86	14	in	in	ADP
cana-2175	86	15	modeling	modeling	NOUN
cana-2175	86	16	and	and	CCONJ
cana-2175	86	17	managing	manage	VERB
cana-2175	86	18	uncertainty	uncertainty	NOUN
cana-2175	86	19	.	.	PUNCT
cana-2175	87	1	fig	fig	NOUN
cana-2175	87	2	.	.	PUNCT
cana-2175	88	1	1	1	NUM
cana-2175	88	2	circular	circular	ADJ
cana-2175	88	3	pythagorean	pythagorean	NOUN
cana-2175	88	4	fuzzy	fuzzy	ADJ
cana-2175	88	5	sets	set	NOUN
cana-2175	88	6	(	(	PUNCT
cana-2175	88	7	c	c	NOUN
cana-2175	88	8	-	-	PUNCT
cana-2175	88	9	pfss	pfss	NOUN
cana-2175	88	10	)	)	PUNCT
cana-2175	88	11	fig.1	fig.1	PROPN
cana-2175	88	12	visualizes	visualize	VERB
cana-2175	88	13	c	c	NOUN
cana-2175	88	14	-	-	PUNCT
cana-2175	88	15	pfs	pfs	ADJ
cana-2175	88	16	elements	element	NOUN
cana-2175	88	17	by	by	ADP
cana-2175	88	18	plotting	plot	VERB
cana-2175	88	19	them	they	PRON
cana-2175	88	20	within	within	ADP
cana-2175	88	21	a	a	DET
cana-2175	88	22	unit	unit	NOUN
cana-2175	88	23	circle	circle	NOUN
cana-2175	88	24	.	.	PUNCT
cana-2175	89	1	each	each	DET
cana-2175	89	2	element	element	NOUN
cana-2175	89	3	is	be	AUX
cana-2175	89	4	represented	represent	VERB
cana-2175	89	5	by	by	ADP
cana-2175	89	6	a	a	DET
cana-2175	89	7	line	line	NOUN
cana-2175	89	8	from	from	ADP
cana-2175	89	9	the	the	DET
cana-2175	89	10	origin	origin	NOUN
cana-2175	89	11	to	to	ADP
cana-2175	89	12	its	its	PRON
cana-2175	89	13	membership	membership	NOUN
cana-2175	89	14	and	and	CCONJ
cana-2175	89	15	non	non	ADJ
cana-2175	89	16	-	-	ADJ
cana-2175	89	17	membership	membership	ADJ
cana-2175	89	18	degrees	degree	NOUN
cana-2175	89	19	,	,	PUNCT
cana-2175	89	20	marked	mark	VERB
cana-2175	89	21	with	with	ADP
cana-2175	89	22	a	a	DET
cana-2175	89	23	point	point	NOUN
cana-2175	89	24	.	.	PUNCT
cana-2175	90	1	the	the	DET
cana-2175	90	2	plot	plot	NOUN
cana-2175	90	3	helps	help	VERB
cana-2175	90	4	illustrate	illustrate	VERB
cana-2175	90	5	the	the	DET
cana-2175	90	6	relationship	relationship	NOUN
cana-2175	90	7	between	between	ADP
cana-2175	90	8	the	the	DET
cana-2175	90	9	degrees	degree	NOUN
cana-2175	90	10	and	and	CCONJ
cana-2175	90	11	their	their	PRON
cana-2175	90	12	compliance	compliance	NOUN
cana-2175	90	13	with	with	ADP
cana-2175	90	14	the	the	DET
cana-2175	90	15	pythagorean	pythagorean	PROPN
cana-2175	90	16	condition	condition	NOUN
cana-2175	90	17	.	.	PUNCT
cana-2175	91	1	the	the	DET
cana-2175	91	2	circle	circle	NOUN
cana-2175	91	3	boundary	boundary	NOUN
cana-2175	91	4	visually	visually	ADV
cana-2175	91	5	enforces	enforce	VERB
cana-2175	91	6	the	the	DET
cana-2175	91	7	constraint	constraint	NOUN
cana-2175	91	8	that	that	SCONJ
cana-2175	91	9	(	(	PUNCT
cana-2175	91	10	1	1	NUM
cana-2175	91	11	)	)	PUNCT
cana-2175	91	12	,	,	PUNCT
cana-2175	91	13	providing	provide	VERB
cana-2175	91	14	a	a	DET
cana-2175	91	15	clear	clear	ADJ
cana-2175	91	16	and	and	CCONJ
cana-2175	91	17	intuitive	intuitive	ADJ
cana-2175	91	18	representation	representation	NOUN
cana-2175	91	19	of	of	ADP
cana-2175	91	20	the	the	DET
cana-2175	91	21	elements	element	NOUN
cana-2175	91	22	within	within	ADP
cana-2175	91	23	the	the	DET
cana-2175	91	24	fixed	fix	VERB
cana-2175	91	25	-	-	PUNCT
cana-2175	91	26	radius	radius	NOUN
cana-2175	91	27	framework	framework	NOUN
cana-2175	91	28	.	.	PUNCT
cana-2175	92	1	fig.2	fig.2	PROPN
cana-2175	92	2	shows	show	VERB
cana-2175	92	3	elements	element	NOUN
cana-2175	92	4	represented	represent	VERB
cana-2175	92	5	within	within	ADP
cana-2175	92	6	circles	circle	NOUN
cana-2175	92	7	of	of	ADP
cana-2175	92	8	their	their	PRON
cana-2175	92	9	respective	respective	ADJ
cana-2175	92	10	radii	radius	NOUN
cana-2175	92	11	on	on	ADP
cana-2175	92	12	a	a	DET
cana-2175	92	13	two	two	NUM
cana-2175	92	14	-	-	PUNCT
cana-2175	92	15	dimensional	dimensional	ADJ
cana-2175	92	16	plane	plane	NOUN
cana-2175	92	17	.	.	PUNCT
cana-2175	93	1	each	each	DET
cana-2175	93	2	element	element	NOUN
cana-2175	93	3	xxx	xxx	NOUN
cana-2175	93	4	is	be	AUX
cana-2175	93	5	defined	define	VERB
cana-2175	93	6	by	by	ADP
cana-2175	93	7	its	its	PRON
cana-2175	93	8	membership	membership	NOUN
cana-2175	93	9	degree	degree	NOUN
cana-2175	93	10	μ	μ	PROPN
cana-2175	93	11	x	x	SYM
cana-2175	93	12	,	,	PUNCT
cana-2175	93	13	non	non	ADJ
cana-2175	93	14	-	-	ADJ
cana-2175	93	15	membership	membership	ADJ
cana-2175	93	16	degree	degree	NOUN
cana-2175	93	17	vx	vx	PROPN
cana-2175	93	18	,	,	PUNCT
cana-2175	93	19	and	and	CCONJ
cana-2175	93	20	distinct	distinct	ADJ
cana-2175	93	21	radius	radius	NOUN
cana-2175	93	22	rx	rx	VERB
cana-2175	93	23	.	.	PUNCT
cana-2175	94	1	the	the	DET
cana-2175	94	2	pythagorean	pythagorean	PROPN
cana-2175	94	3	condition	condition	NOUN
cana-2175	94	4	(	(	PUNCT
cana-2175	94	5	2	2	X
cana-2175	94	6	)	)	PUNCT
cana-2175	94	7	is	be	AUX
cana-2175	94	8	visually	visually	ADV
cana-2175	94	9	enforced	enforce	VERB
cana-2175	94	10	by	by	ADP
cana-2175	94	11	the	the	DET
cana-2175	94	12	circles	circle	NOUN
cana-2175	94	13	.	.	PUNCT
cana-2175	95	1	each	each	DET
cana-2175	95	2	element	element	NOUN
cana-2175	95	3	is	be	AUX
cana-2175	95	4	plotted	plot	VERB
cana-2175	95	5	with	with	ADP
cana-2175	95	6	a	a	DET
cana-2175	95	7	line	line	NOUN
cana-2175	95	8	from	from	ADP
cana-2175	95	9	the	the	DET
cana-2175	95	10	origin	origin	NOUN
cana-2175	95	11	to	to	ADP
cana-2175	95	12	its	its	PRON
cana-2175	95	13	membership	membership	NOUN
cana-2175	95	14	and	and	CCONJ
cana-2175	95	15	non	non	ADJ
cana-2175	95	16	-	-	ADJ
cana-2175	95	17	membership	membership	ADJ
cana-2175	95	18	degrees	degree	NOUN
cana-2175	95	19	,	,	PUNCT
cana-2175	95	20	marked	mark	VERB
cana-2175	95	21	with	with	ADP
cana-2175	95	22	a	a	DET
cana-2175	95	23	point	point	NOUN
cana-2175	95	24	.	.	PUNCT
cana-2175	96	1	this	this	DET
cana-2175	96	2	visualization	visualization	NOUN
cana-2175	96	3	demonstrates	demonstrate	VERB
cana-2175	96	4	how	how	SCONJ
cana-2175	96	5	each	each	DET
cana-2175	96	6	element	element	NOUN
cana-2175	96	7	's	's	PART
cana-2175	96	8	degrees	degree	NOUN
cana-2175	96	9	comply	comply	VERB
cana-2175	96	10	with	with	ADP
cana-2175	96	11	the	the	DET
cana-2175	96	12	pythagorean	pythagorean	PROPN
cana-2175	96	13	condition	condition	NOUN
cana-2175	96	14	within	within	ADP
cana-2175	96	15	its	its	PRON
cana-2175	96	16	unique	unique	ADJ
cana-2175	96	17	radius	radius	NOUN
cana-2175	96	18	,	,	PUNCT
cana-2175	96	19	providing	provide	VERB
cana-2175	96	20	a	a	DET
cana-2175	96	21	dynamic	dynamic	ADJ
cana-2175	96	22	representation	representation	NOUN
cana-2175	96	23	of	of	ADP
cana-2175	96	24	uncertainty	uncertainty	NOUN
cana-2175	96	25	.	.	PUNCT
cana-2175	97	1	the	the	DET
cana-2175	97	2	union	union	NOUN
cana-2175	97	3	and	and	CCONJ
cana-2175	97	4	intersection	intersection	NOUN
cana-2175	97	5	operations	operation	NOUN
cana-2175	97	6	for	for	ADP
cana-2175	97	7	d	d	NOUN
cana-2175	97	8	-	-	NOUN
cana-2175	97	9	pfss	pfss	ADJ
cana-2175	97	10	with	with	ADP
cana-2175	97	11	distinct	distinct	ADJ
cana-2175	97	12	radii	radius	NOUN
cana-2175	97	13	are	be	AUX
cana-2175	97	14	essential	essential	ADJ
cana-2175	97	15	for	for	ADP
cana-2175	97	16	combining	combine	VERB
cana-2175	97	17	and	and	CCONJ
cana-2175	97	18	comparing	compare	VERB
cana-2175	97	19	fuzzy	fuzzy	ADJ
cana-2175	97	20	sets	set	NOUN
cana-2175	97	21	.	.	PUNCT
cana-2175	98	1	these	these	DET
cana-2175	98	2	operations	operation	NOUN
cana-2175	98	3	consider	consider	VERB
cana-2175	98	4	the	the	DET
cana-2175	98	5	distinct	distinct	ADJ
cana-2175	98	6	radii	radii	NOUN
cana-2175	98	7	,	,	PUNCT
cana-2175	98	8	enhancing	enhance	VERB
cana-2175	98	9	the	the	DET
cana-2175	98	10	representation	representation	NOUN
cana-2175	98	11	of	of	ADP
cana-2175	98	12	uncertainty	uncertainty	NOUN
cana-2175	98	13	.	.	PUNCT
cana-2175	99	1	communications	communication	NOUN
cana-2175	99	2	on	on	ADP
cana-2175	99	3	applied	apply	VERB
cana-2175	99	4	nonlinear	nonlinear	ADJ
cana-2175	99	5	analysis	analysis	NOUN
cana-2175	99	6	issn	issn	NOUN
cana-2175	99	7	:	:	PUNCT
cana-2175	99	8	1074	1074	NUM
cana-2175	99	9	-	-	PUNCT
cana-2175	99	10	133x	133x	NUM
cana-2175	99	11	vol	vol	NOUN
cana-2175	99	12	32	32	NUM
cana-2175	99	13	no	no	NOUN
cana-2175	99	14	.	.	PUNCT
cana-2175	100	1	1s	1s	NUM
cana-2175	100	2	(	(	PUNCT
cana-2175	100	3	2025	2025	NUM
cana-2175	100	4	)	)	PUNCT
cana-2175	100	5	329	329	NUM
cana-2175	100	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2175	100	7	fig	fig	NOUN
cana-2175	100	8	.	.	PUNCT
cana-2175	101	1	2	2	NUM
cana-2175	101	2	disc	disc	NOUN
cana-2175	101	3	pythagorean	pythagorean	NOUN
cana-2175	101	4	fuzzy	fuzzy	ADJ
cana-2175	101	5	sets	set	NOUN
cana-2175	101	6	(	(	PUNCT
cana-2175	101	7	d	d	NOUN
cana-2175	101	8	-	-	NOUN
cana-2175	101	9	pfss	pfss	NOUN
cana-2175	101	10	)	)	PUNCT
cana-2175	101	11	for	for	ADP
cana-2175	101	12	two	two	NUM
cana-2175	101	13	d	d	NOUN
cana-2175	101	14	-	-	NOUN
cana-2175	101	15	pfss	pfss	NOUN
cana-2175	101	16	a	a	PRON
cana-2175	101	17	and	and	CCONJ
cana-2175	101	18	b	b	NOUN
cana-2175	101	19	with	with	ADP
cana-2175	101	20	distinct	distinct	ADJ
cana-2175	101	21	radii	radius	NOUN
cana-2175	101	22	ra	ra	PROPN
cana-2175	101	23	and	and	CCONJ
cana-2175	101	24	rb	rb	PROPN
cana-2175	101	25	,	,	PUNCT
cana-2175	101	26	the	the	DET
cana-2175	101	27	union	union	NOUN
cana-2175	101	28	operation	operation	NOUN
cana-2175	101	29	combines	combine	VERB
cana-2175	101	30	the	the	DET
cana-2175	101	31	membership	membership	NOUN
cana-2175	101	32	degrees	degree	NOUN
cana-2175	101	33	by	by	ADP
cana-2175	101	34	taking	take	VERB
cana-2175	101	35	the	the	DET
cana-2175	101	36	highest	high	ADJ
cana-2175	101	37	degree	degree	NOUN
cana-2175	101	38	of	of	ADP
cana-2175	101	39	membership	membership	NOUN
cana-2175	101	40	for	for	ADP
cana-2175	101	41	each	each	DET
cana-2175	101	42	element	element	NOUN
cana-2175	101	43	across	across	ADP
cana-2175	101	44	both	both	DET
cana-2175	101	45	sets	set	NOUN
cana-2175	101	46	.	.	PUNCT
cana-2175	102	1	mathematically	mathematically	ADV
cana-2175	102	2	,	,	PUNCT
cana-2175	102	3	the	the	DET
cana-2175	102	4	union	union	NOUN
cana-2175	102	5	a	a	DET
cana-2175	102	6	∪	∪	X
cana-2175	102	7	b	b	NOUN
cana-2175	102	8	is	be	AUX
cana-2175	102	9	expressed	express	VERB
cana-2175	102	10	as	as	ADP
cana-2175	102	11	:	:	PUNCT
cana-2175	102	12	μ	μ	NUM
cana-2175	102	13	a∪b	a∪b	NOUN
cana-2175	102	14	(	(	PUNCT
cana-2175	102	15	x	x	X
cana-2175	102	16	)	)	PUNCT
cana-2175	103	1	=	=	SYM
cana-2175	103	2	max	max	PROPN
cana-2175	103	3	(	(	PUNCT
cana-2175	103	4	μ	μ	PROPN
cana-2175	103	5	a	a	PROPN
cana-2175	103	6	(	(	PUNCT
cana-2175	103	7	x	x	NOUN
cana-2175	103	8	)	)	PUNCT
cana-2175	103	9	.	.	PUNCT
cana-2175	104	1	ra	ra	PROPN
cana-2175	104	2	,	,	PUNCT
cana-2175	104	3	μ	μ	PROPN
cana-2175	104	4	b	b	PROPN
cana-2175	104	5	(	(	PUNCT
cana-2175	104	6	x	x	NOUN
cana-2175	104	7	)	)	PUNCT
cana-2175	104	8	.	.	PUNCT
cana-2175	105	1	rb	rb	X
cana-2175	105	2	)	)	PUNCT
cana-2175	105	3	(	(	PUNCT
cana-2175	105	4	14	14	NUM
cana-2175	105	5	)	)	PUNCT
cana-2175	105	6	here	here	ADV
cana-2175	105	7	,	,	PUNCT
cana-2175	105	8	the	the	DET
cana-2175	105	9	distinct	distinct	ADJ
cana-2175	105	10	radii	radius	NOUN
cana-2175	105	11	ra	ra	PROPN
cana-2175	105	12	and	and	CCONJ
cana-2175	105	13	rb	rb	PROPN
cana-2175	105	14	adjust	adjust	VERB
cana-2175	105	15	the	the	DET
cana-2175	105	16	membership	membership	NOUN
cana-2175	105	17	degrees	degree	NOUN
cana-2175	105	18	,	,	PUNCT
cana-2175	105	19	providing	provide	VERB
cana-2175	105	20	a	a	DET
cana-2175	105	21	more	more	ADV
cana-2175	105	22	nuanced	nuanced	ADJ
cana-2175	105	23	combination	combination	NOUN
cana-2175	105	24	.	.	PUNCT
cana-2175	106	1	similarly	similarly	ADV
cana-2175	106	2	,	,	PUNCT
cana-2175	106	3	the	the	DET
cana-2175	106	4	intersection	intersection	NOUN
cana-2175	106	5	of	of	ADP
cana-2175	106	6	two	two	NUM
cana-2175	106	7	d	d	NOUN
cana-2175	106	8	-	-	NOUN
cana-2175	106	9	pfss	pfss	NOUN
cana-2175	106	10	a	a	PRON
cana-2175	106	11	and	and	CCONJ
cana-2175	106	12	b	b	NOUN
cana-2175	106	13	with	with	ADP
cana-2175	106	14	distinct	distinct	ADJ
cana-2175	106	15	radii	radius	NOUN
cana-2175	106	16	ra	ra	PROPN
cana-2175	106	17	and	and	CCONJ
cana-2175	106	18	rb	rb	NOUN
cana-2175	106	19	is	be	AUX
cana-2175	106	20	defined	define	VERB
cana-2175	106	21	by	by	ADP
cana-2175	106	22	taking	take	VERB
cana-2175	106	23	the	the	DET
cana-2175	106	24	lowest	low	ADJ
cana-2175	106	25	degree	degree	NOUN
cana-2175	106	26	of	of	ADP
cana-2175	106	27	membership	membership	NOUN
cana-2175	106	28	for	for	ADP
cana-2175	106	29	each	each	DET
cana-2175	106	30	element	element	NOUN
cana-2175	106	31	in	in	ADP
cana-2175	106	32	both	both	DET
cana-2175	106	33	sets	set	NOUN
cana-2175	106	34	:	:	PUNCT
cana-2175	106	35	μ	μ	PROPN
cana-2175	106	36	a∩b	a∩b	PROPN
cana-2175	106	37	(	(	PUNCT
cana-2175	106	38	x	x	X
cana-2175	106	39	)	)	PUNCT
cana-2175	106	40	=	=	SYM
cana-2175	106	41	min	min	PROPN
cana-2175	106	42	(	(	PUNCT
cana-2175	106	43	μ	μ	PROPN
cana-2175	106	44	a	a	PROPN
cana-2175	106	45	(	(	PUNCT
cana-2175	106	46	x	x	NOUN
cana-2175	106	47	)	)	PUNCT
cana-2175	106	48	.	.	PUNCT
cana-2175	107	1	ra	ra	PROPN
cana-2175	107	2	,	,	PUNCT
cana-2175	107	3	μ	μ	PROPN
cana-2175	107	4	b	b	PROPN
cana-2175	107	5	(	(	PUNCT
cana-2175	107	6	x	x	NOUN
cana-2175	107	7	)	)	PUNCT
cana-2175	107	8	.	.	PUNCT
cana-2175	108	1	rb	rb	X
cana-2175	108	2	)	)	PUNCT
cana-2175	108	3	(	(	PUNCT
cana-2175	108	4	15	15	NUM
cana-2175	108	5	)	)	PUNCT
cana-2175	108	6	scalar	scalar	ADJ
cana-2175	108	7	multiplication	multiplication	NOUN
cana-2175	108	8	for	for	ADP
cana-2175	108	9	d	d	NOUN
cana-2175	108	10	-	-	NOUN
cana-2175	108	11	pfss	pfss	ADJ
cana-2175	108	12	with	with	ADP
cana-2175	108	13	distinct	distinct	ADJ
cana-2175	108	14	radii	radius	NOUN
cana-2175	108	15	involves	involve	VERB
cana-2175	108	16	multiplying	multiply	VERB
cana-2175	108	17	each	each	DET
cana-2175	108	18	element	element	NOUN
cana-2175	108	19	of	of	ADP
cana-2175	108	20	a	a	DET
cana-2175	108	21	fuzzy	fuzzy	ADJ
cana-2175	108	22	set	set	VERB
cana-2175	108	23	by	by	ADP
cana-2175	108	24	a	a	DET
cana-2175	108	25	scalar	scalar	ADJ
cana-2175	108	26	value	value	NOUN
cana-2175	108	27	,	,	PUNCT
cana-2175	108	28	adjusting	adjust	VERB
cana-2175	108	29	the	the	DET
cana-2175	108	30	membership	membership	NOUN
cana-2175	108	31	degree	degree	NOUN
cana-2175	108	32	and	and	CCONJ
cana-2175	108	33	radius	radius	NOUN
cana-2175	108	34	accordingly	accordingly	ADV
cana-2175	108	35	.	.	PUNCT
cana-2175	109	1	for	for	ADP
cana-2175	109	2	a	a	DET
cana-2175	109	3	d	d	NOUN
cana-2175	109	4	-	-	PUNCT
cana-2175	109	5	pfs	pf	VERB
cana-2175	109	6	a	a	PRON
cana-2175	109	7	with	with	ADP
cana-2175	109	8	radius	radius	PROPN
cana-2175	109	9	ra	ra	PROPN
cana-2175	109	10	and	and	CCONJ
cana-2175	109	11	a	a	DET
cana-2175	109	12	scalar	scalar	ADJ
cana-2175	109	13	λ	λ	NOUN
cana-2175	109	14	,	,	PUNCT
cana-2175	109	15	the	the	DET
cana-2175	109	16	resulting	result	VERB
cana-2175	109	17	fuzzy	fuzzy	ADJ
cana-2175	109	18	set	set	VERB
cana-2175	109	19	bbb	bbb	PROPN
cana-2175	109	20	with	with	ADP
cana-2175	109	21	radiusrb	radiusrb	NOUN
cana-2175	109	22	is	be	AUX
cana-2175	109	23	given	give	VERB
cana-2175	109	24	by	by	ADP
cana-2175	109	25	:	:	PUNCT
cana-2175	109	26	μ	μ	PROPN
cana-2175	109	27	b	b	PROPN
cana-2175	109	28	(	(	PUNCT
cana-2175	109	29	x	x	NOUN
cana-2175	109	30	)	)	PUNCT
cana-2175	109	31	=	=	SYM
cana-2175	109	32	μ	μ	PROPN
cana-2175	109	33	a	a	DET
cana-2175	109	34	(	(	PUNCT
cana-2175	109	35	x	x	SYM
cana-2175	109	36	λ	λ	NOUN
cana-2175	109	37	)	)	PUNCT
cana-2175	109	38	(	(	PUNCT
cana-2175	109	39	16	16	NUM
cana-2175	109	40	)	)	PUNCT
cana-2175	109	41	where	where	SCONJ
cana-2175	109	42	rb	rb	NOUN
cana-2175	109	43	is	be	AUX
cana-2175	109	44	the	the	DET
cana-2175	109	45	adjusted	adjusted	ADJ
cana-2175	109	46	radius	radius	NOUN
cana-2175	109	47	.	.	PUNCT
cana-2175	110	1	scalar	scalar	ADJ
cana-2175	110	2	multiplication	multiplication	NOUN
cana-2175	110	3	allows	allow	VERB
cana-2175	110	4	for	for	ADP
cana-2175	110	5	scaling	scale	VERB
cana-2175	110	6	the	the	DET
cana-2175	110	7	elements	element	NOUN
cana-2175	110	8	of	of	ADP
cana-2175	110	9	a	a	DET
cana-2175	110	10	fuzzy	fuzzy	ADJ
cana-2175	110	11	set	set	NOUN
cana-2175	110	12	,	,	PUNCT
cana-2175	110	13	making	make	VERB
cana-2175	110	14	it	it	PRON
cana-2175	110	15	useful	useful	ADJ
cana-2175	110	16	in	in	ADP
cana-2175	110	17	applications	application	NOUN
cana-2175	110	18	like	like	ADP
cana-2175	110	19	adjusting	adjust	VERB
cana-2175	110	20	the	the	DET
cana-2175	110	21	intensity	intensity	NOUN
cana-2175	110	22	of	of	ADP
cana-2175	110	23	membership	membership	NOUN
cana-2175	110	24	functions	function	NOUN
cana-2175	110	25	in	in	ADP
cana-2175	110	26	fuzzy	fuzzy	ADJ
cana-2175	110	27	control	control	NOUN
cana-2175	110	28	systems	system	NOUN
cana-2175	110	29	.	.	PUNCT
cana-2175	111	1	3.1	3.1	NUM
cana-2175	111	2	technique	technique	NOUN
cana-2175	111	3	for	for	ADP
cana-2175	111	4	order	order	NOUN
cana-2175	111	5	of	of	ADP
cana-2175	111	6	preference	preference	NOUN
cana-2175	111	7	by	by	ADP
cana-2175	111	8	similarity	similarity	NOUN
cana-2175	111	9	to	to	ADP
cana-2175	111	10	ideal	ideal	ADJ
cana-2175	111	11	solution	solution	NOUN
cana-2175	111	12	(	(	PUNCT
cana-2175	111	13	topsis	topsis	NOUN
cana-2175	111	14	)	)	PUNCT
cana-2175	111	15	to	to	PART
cana-2175	111	16	adapt	adapt	VERB
cana-2175	111	17	the	the	DET
cana-2175	111	18	topsis	topsis	NOUN
cana-2175	111	19	method	method	NOUN
cana-2175	111	20	to	to	ADP
cana-2175	111	21	the	the	DET
cana-2175	111	22	d	d	ADJ
cana-2175	111	23	-	-	ADJ
cana-2175	111	24	pfss	pfss	ADJ
cana-2175	111	25	framework	framework	NOUN
cana-2175	111	26	,	,	PUNCT
cana-2175	111	27	we	we	PRON
cana-2175	111	28	incorporate	incorporate	VERB
cana-2175	111	29	pythagorean	pythagorean	ADJ
cana-2175	111	30	fuzzy	fuzzy	ADJ
cana-2175	111	31	values	value	NOUN
cana-2175	111	32	into	into	ADP
cana-2175	111	33	the	the	DET
cana-2175	111	34	decision	decision	NOUN
cana-2175	111	35	-	-	PUNCT
cana-2175	111	36	making	make	VERB
cana-2175	111	37	process	process	NOUN
cana-2175	111	38	.	.	PUNCT
cana-2175	112	1	pythagorean	pythagorean	PROPN
cana-2175	112	2	fuzzy	fuzzy	ADJ
cana-2175	112	3	sets	set	NOUN
cana-2175	112	4	extend	extend	VERB
cana-2175	112	5	traditional	traditional	ADJ
cana-2175	112	6	fuzzy	fuzzy	ADJ
cana-2175	112	7	sets	set	NOUN
cana-2175	112	8	by	by	ADP
cana-2175	112	9	allowing	allow	VERB
cana-2175	112	10	membership	membership	NOUN
cana-2175	112	11	and	and	CCONJ
cana-2175	112	12	non	non	ADJ
cana-2175	112	13	-	-	ADJ
cana-2175	112	14	membership	membership	ADJ
cana-2175	112	15	degrees	degree	NOUN
cana-2175	112	16	to	to	PART
cana-2175	112	17	form	form	VERB
cana-2175	112	18	a	a	DET
cana-2175	112	19	pythagorean	pythagorean	PROPN
cana-2175	112	20	relationship	relationship	NOUN
cana-2175	112	21	,	,	PUNCT
cana-2175	112	22	where	where	SCONJ
cana-2175	112	23	the	the	DET
cana-2175	112	24	sum	sum	NOUN
cana-2175	112	25	of	of	ADP
cana-2175	112	26	their	their	PRON
cana-2175	112	27	squares	square	NOUN
cana-2175	112	28	is	be	AUX
cana-2175	112	29	less	less	ADJ
cana-2175	112	30	than	than	ADP
cana-2175	112	31	or	or	CCONJ
cana-2175	112	32	equal	equal	ADJ
cana-2175	112	33	to	to	ADP
cana-2175	112	34	one	one	NUM
cana-2175	112	35	.	.	PUNCT
cana-2175	113	1	the	the	DET
cana-2175	113	2	steps	step	NOUN
cana-2175	113	3	involved	involve	VERB
cana-2175	113	4	in	in	ADP
cana-2175	113	5	incorporating	incorporate	VERB
cana-2175	113	6	pythagorean	pythagorean	PROPN
cana-2175	113	7	fuzzy	fuzzy	ADJ
cana-2175	113	8	values	value	NOUN
cana-2175	113	9	are	be	AUX
cana-2175	113	10	,	,	PUNCT
cana-2175	113	11	define	define	VERB
cana-2175	113	12	pythagorean	pythagorean	ADJ
cana-2175	113	13	fuzzy	fuzzy	ADJ
cana-2175	113	14	decision	decision	NOUN
cana-2175	113	15	matrix	matrix	NOUN
cana-2175	113	16	,	,	PUNCT
cana-2175	113	17	each	each	DET
cana-2175	113	18	element	element	NOUN
cana-2175	113	19	dij	dij	INTJ
cana-2175	113	20	in	in	ADP
cana-2175	113	21	the	the	DET
cana-2175	113	22	decision	decision	NOUN
cana-2175	113	23	matrix	matrix	NOUN
cana-2175	113	24	is	be	AUX
cana-2175	113	25	replaced	replace	VERB
cana-2175	113	26	by	by	ADP
cana-2175	113	27	a	a	DET
cana-2175	113	28	pythagorean	pythagorean	ADJ
cana-2175	113	29	fuzzy	fuzzy	ADJ
cana-2175	113	30	number	number	NOUN
cana-2175	114	1	dij	dij	NOUN
cana-2175	115	1	=	=	SYM
cana-2175	116	1	(	(	PUNCT
cana-2175	116	2	μ	μ	NUM
cana-2175	116	3	ij	ij	INTJ
cana-2175	116	4	,	,	PUNCT
cana-2175	116	5	vij	vij	PROPN
cana-2175	116	6	)	)	PUNCT
cana-2175	116	7	(	(	PUNCT
cana-2175	116	8	17	17	NUM
cana-2175	116	9	)	)	PUNCT
cana-2175	116	10	communications	communication	NOUN
cana-2175	116	11	on	on	ADP
cana-2175	116	12	applied	apply	VERB
cana-2175	116	13	nonlinear	nonlinear	ADJ
cana-2175	116	14	analysis	analysis	NOUN
cana-2175	116	15	issn	issn	NOUN
cana-2175	116	16	:	:	PUNCT
cana-2175	116	17	1074	1074	NUM
cana-2175	116	18	-	-	PUNCT
cana-2175	116	19	133x	133x	NUM
cana-2175	116	20	vol	vol	NOUN
cana-2175	116	21	32	32	NUM
cana-2175	116	22	no	no	NOUN
cana-2175	116	23	.	.	PUNCT
cana-2175	117	1	1s	1s	NUM
cana-2175	117	2	(	(	PUNCT
cana-2175	117	3	2025	2025	NUM
cana-2175	117	4	)	)	PUNCT
cana-2175	117	5	330	330	NUM
cana-2175	117	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2175	117	7	where	where	SCONJ
cana-2175	117	8	μ	μ	PROPN
cana-2175	117	9	ij	ij	NOUN
cana-2175	117	10	and	and	CCONJ
cana-2175	117	11	vij	vij	PROPN
cana-2175	117	12	are	be	AUX
cana-2175	117	13	the	the	DET
cana-2175	117	14	membership	membership	NOUN
cana-2175	117	15	and	and	CCONJ
cana-2175	117	16	non	non	ADJ
cana-2175	117	17	-	-	ADJ
cana-2175	117	18	membership	membership	ADJ
cana-2175	117	19	degrees	degree	NOUN
cana-2175	117	20	,	,	PUNCT
cana-2175	117	21	respectively	respectively	ADV
cana-2175	117	22	,	,	PUNCT
cana-2175	117	23	satisfying	satisfy	VERB
cana-2175	117	24	(	(	PUNCT
cana-2175	117	25	1	1	NUM
cana-2175	117	26	)	)	PUNCT
cana-2175	117	27	.	.	PUNCT
cana-2175	118	1	normalize	normalize	VERB
cana-2175	118	2	the	the	DET
cana-2175	118	3	pythagorean	pythagorean	PROPN
cana-2175	118	4	fuzzy	fuzzy	ADJ
cana-2175	118	5	numbers	number	NOUN
cana-2175	118	6	using	use	VERB
cana-2175	118	7	the	the	DET
cana-2175	118	8	normalization	normalization	NOUN
cana-2175	118	9	formula	formula	NOUN
cana-2175	118	10	for	for	ADP
cana-2175	118	11	pythagorean	pythagorean	ADJ
cana-2175	118	12	fuzzy	fuzzy	ADJ
cana-2175	118	13	sets	set	NOUN
cana-2175	118	14	.	.	PUNCT
cana-2175	119	1	the	the	DET
cana-2175	119	2	mathematical	mathematical	ADJ
cana-2175	119	3	formulation	formulation	NOUN
cana-2175	119	4	of	of	ADP
cana-2175	119	5	the	the	DET
cana-2175	119	6	topsis	topsis	NOUN
cana-2175	119	7	approach	approach	NOUN
cana-2175	119	8	in	in	ADP
cana-2175	119	9	the	the	DET
cana-2175	119	10	context	context	NOUN
cana-2175	119	11	of	of	ADP
cana-2175	119	12	d	d	NOUN
cana-2175	119	13	-	-	ADJ
cana-2175	119	14	pfss	pfss	ADJ
cana-2175	119	15	includes	include	VERB
cana-2175	119	16	the	the	DET
cana-2175	119	17	calculation	calculation	NOUN
cana-2175	119	18	of	of	ADP
cana-2175	119	19	positive	positive	ADJ
cana-2175	119	20	and	and	CCONJ
cana-2175	119	21	negative	negative	ADJ
cana-2175	119	22	ideal	ideal	ADJ
cana-2175	119	23	solutions	solution	NOUN
cana-2175	119	24	,	,	PUNCT
cana-2175	119	25	the	the	DET
cana-2175	119	26	distance	distance	NOUN
cana-2175	119	27	of	of	ADP
cana-2175	119	28	each	each	DET
cana-2175	119	29	alternative	alternative	NOUN
cana-2175	119	30	from	from	ADP
cana-2175	119	31	these	these	DET
cana-2175	119	32	ideal	ideal	ADJ
cana-2175	119	33	solutions	solution	NOUN
cana-2175	119	34	,	,	PUNCT
cana-2175	119	35	and	and	CCONJ
cana-2175	119	36	the	the	DET
cana-2175	119	37	ranking	ranking	NOUN
cana-2175	119	38	process	process	NOUN
cana-2175	119	39	.	.	PUNCT
cana-2175	120	1	the	the	DET
cana-2175	120	2	positive	positive	ADJ
cana-2175	120	3	ideal	ideal	ADJ
cana-2175	120	4	solution	solution	NOUN
cana-2175	120	5	(	(	PUNCT
cana-2175	120	6	pis	pis	NOUN
cana-2175	120	7	)	)	PUNCT
cana-2175	120	8	and	and	CCONJ
cana-2175	120	9	negative	negative	ADJ
cana-2175	120	10	ideal	ideal	ADJ
cana-2175	120	11	solution	solution	NOUN
cana-2175	120	12	(	(	PUNCT
cana-2175	120	13	nis	nis	NOUN
cana-2175	120	14	)	)	PUNCT
cana-2175	120	15	of	of	ADP
cana-2175	120	16	pythagorean	pythagorean	PROPN
cana-2175	120	17	fuzzy	fuzzy	ADJ
cana-2175	120	18	sets	set	NOUN
cana-2175	120	19	are	be	AUX
cana-2175	120	20	defined	define	VERB
cana-2175	120	21	as	as	ADP
cana-2175	120	22	:	:	PUNCT
cana-2175	120	23	ã	ã	PROPN
cana-2175	120	24	+	+	NUM
cana-2175	120	25	=	=	SYM
cana-2175	120	26	(	(	PUNCT
cana-2175	120	27	μ	μ	PROPN
cana-2175	120	28	j	j	PROPN
cana-2175	121	1	+	+	PROPN
cana-2175	121	2	,	,	PUNCT
cana-2175	121	3	vj	vj	INTJ
cana-2175	121	4	+	+	NOUN
cana-2175	121	5	)	)	PUNCT
cana-2175	121	6	(	(	PUNCT
cana-2175	121	7	18	18	NUM
cana-2175	121	8	)	)	PUNCT
cana-2175	121	9	where	where	SCONJ
cana-2175	121	10	μ	μ	PROPN
cana-2175	121	11	j	j	PROPN
cana-2175	121	12	+	+	CCONJ
cana-2175	121	13	=	=	NOUN
cana-2175	121	14	maxiμij	maxiμij	NOUN
cana-2175	121	15	(	(	PUNCT
cana-2175	121	16	19	19	NUM
cana-2175	121	17	)	)	PUNCT
cana-2175	121	18	vj	vj	NOUN
cana-2175	121	19	+	+	CCONJ
cana-2175	121	20	=	=	NOUN
cana-2175	121	21	minivij	minivij	ADJ
cana-2175	121	22	(	(	PUNCT
cana-2175	121	23	20	20	NUM
cana-2175	121	24	)	)	PUNCT
cana-2175	121	25	ã	ã	PROPN
cana-2175	121	26	−	−	PROPN
cana-2175	122	1	=	=	SYM
cana-2175	122	2	(	(	PUNCT
cana-2175	122	3	μ	μ	PROPN
cana-2175	122	4	j	j	PROPN
cana-2175	122	5	−	−	PROPN
cana-2175	122	6	,	,	PUNCT
cana-2175	122	7	vj	vj	PROPN
cana-2175	122	8	−	−	NOUN
cana-2175	122	9	)	)	PUNCT
cana-2175	122	10	(	(	PUNCT
cana-2175	122	11	21	21	NUM
cana-2175	122	12	)	)	PUNCT
cana-2175	123	1	where	where	SCONJ
cana-2175	123	2	μ	μ	PROPN
cana-2175	123	3	j	j	PROPN
cana-2175	123	4	−	−	PROPN
cana-2175	123	5	=	=	SYM
cana-2175	123	6	miniμij	miniμij	PROPN
cana-2175	123	7	(	(	PUNCT
cana-2175	123	8	22	22	NUM
cana-2175	123	9	)	)	PUNCT
cana-2175	123	10	vj	vj	INTJ
cana-2175	123	11	−	−	PROPN
cana-2175	123	12	=	=	SYM
cana-2175	123	13	maxivij	maxivij	ADJ
cana-2175	123	14	(	(	PUNCT
cana-2175	123	15	23	23	NUM
cana-2175	123	16	)	)	PUNCT
cana-2175	123	17	calculate	calculate	VERB
cana-2175	123	18	the	the	DET
cana-2175	123	19	distance	distance	NOUN
cana-2175	123	20	of	of	ADP
cana-2175	123	21	each	each	DET
cana-2175	123	22	alternative	alternative	NOUN
cana-2175	123	23	from	from	ADP
cana-2175	123	24	the	the	DET
cana-2175	123	25	pis	pis	NOUN
cana-2175	123	26	and	and	CCONJ
cana-2175	123	27	nis	nis	PROPN
cana-2175	123	28	using	use	VERB
cana-2175	123	29	a	a	DET
cana-2175	123	30	suitable	suitable	ADJ
cana-2175	123	31	distance	distance	NOUN
cana-2175	123	32	measure	measure	NOUN
cana-2175	123	33	for	for	ADP
cana-2175	123	34	pythagorean	pythagorean	ADJ
cana-2175	123	35	fuzzy	fuzzy	ADJ
cana-2175	123	36	sets	set	NOUN
cana-2175	123	37	,	,	PUNCT
cana-2175	123	38	such	such	ADJ
cana-2175	123	39	as	as	ADP
cana-2175	123	40	the	the	DET
cana-2175	123	41	euclidean	euclidean	ADJ
cana-2175	123	42	distance	distance	NOUN
cana-2175	123	43	:	:	PUNCT
cana-2175	123	44	di	di	NOUN
cana-2175	124	1	+	+	NOUN
cana-2175	125	1	=	=	SYM
cana-2175	125	2	∑((μ	∑((μ	PROPN
cana-2175	125	3	ij	ij	INTJ
cana-2175	125	4	−	−	PROPN
cana-2175	125	5	μ	μ	PROPN
cana-2175	125	6	j	j	PROPN
cana-2175	126	1	+	+	NOUN
cana-2175	126	2	)	)	PUNCT
cana-2175	126	3	2	2	NUM
cana-2175	127	1	+	+	CCONJ
cana-2175	127	2	(	(	PUNCT
cana-2175	127	3	vij	vij	PROPN
cana-2175	127	4	−	−	PROPN
cana-2175	127	5	vj	vj	PROPN
cana-2175	128	1	+	+	NOUN
cana-2175	128	2	)	)	PUNCT
cana-2175	128	3	2	2	NUM
cana-2175	128	4	)	)	PUNCT
cana-2175	128	5	n	n	CCONJ
cana-2175	128	6	j=1	j=1	NOUN
cana-2175	128	7	(	(	PUNCT
cana-2175	128	8	24	24	NUM
cana-2175	128	9	)	)	PUNCT
cana-2175	128	10	di	di	NOUN
cana-2175	128	11	−	−	NOUN
cana-2175	129	1	=	=	PUNCT
cana-2175	129	2	∑((μ	∑((μ	PROPN
cana-2175	129	3	ij	ij	INTJ
cana-2175	129	4	−	−	PROPN
cana-2175	130	1	μ	μ	PROPN
cana-2175	130	2	j	j	PROPN
cana-2175	130	3	−	−	NOUN
cana-2175	130	4	)	)	PUNCT
cana-2175	130	5	2	2	NUM
cana-2175	131	1	+	+	CCONJ
cana-2175	131	2	(	(	PUNCT
cana-2175	131	3	vij	vij	PROPN
cana-2175	131	4	−	−	PROPN
cana-2175	131	5	vj	vj	PROPN
cana-2175	131	6	−	−	NOUN
cana-2175	131	7	)	)	PUNCT
cana-2175	131	8	2	2	NUM
cana-2175	131	9	)	)	PUNCT
cana-2175	131	10	n	n	CCONJ
cana-2175	131	11	j=1	j=1	NOUN
cana-2175	131	12	(	(	PUNCT
cana-2175	131	13	25	25	NUM
cana-2175	131	14	)	)	PUNCT
cana-2175	131	15	calculate	calculate	VERB
cana-2175	131	16	the	the	DET
cana-2175	131	17	relative	relative	ADJ
cana-2175	131	18	closeness	closeness	NOUN
cana-2175	131	19	ci	ci	PROPN
cana-2175	131	20	of	of	ADP
cana-2175	131	21	each	each	DET
cana-2175	131	22	alternative	alternative	NOUN
cana-2175	131	23	to	to	ADP
cana-2175	131	24	the	the	DET
cana-2175	131	25	ideal	ideal	ADJ
cana-2175	131	26	solution	solution	NOUN
cana-2175	131	27	:	:	PUNCT
cana-2175	131	28	ci	ci	PROPN
cana-2175	131	29	=	=	PUNCT
cana-2175	131	30	di	di	NOUN
cana-2175	131	31	−	−	PROPN
cana-2175	131	32	di	di	NOUN
cana-2175	131	33	+	+	CCONJ
cana-2175	131	34	+	+	CCONJ
cana-2175	131	35	di	di	INTJ
cana-2175	131	36	−	−	PROPN
cana-2175	131	37	(	(	PUNCT
cana-2175	131	38	26	26	NUM
cana-2175	131	39	)	)	PUNCT
cana-2175	131	40	alternatives	alternative	NOUN
cana-2175	131	41	are	be	AUX
cana-2175	131	42	then	then	ADV
cana-2175	131	43	ranked	rank	VERB
cana-2175	131	44	based	base	VERB
cana-2175	131	45	on	on	ADP
cana-2175	131	46	the	the	DET
cana-2175	131	47	values	value	NOUN
cana-2175	131	48	of	of	ADP
cana-2175	131	49	ci	ci	NOUN
cana-2175	131	50	,	,	PUNCT
cana-2175	131	51	with	with	ADP
cana-2175	131	52	higher	high	ADJ
cana-2175	131	53	values	value	NOUN
cana-2175	131	54	indicating	indicate	VERB
cana-2175	131	55	closer	close	ADJ
cana-2175	131	56	proximity	proximity	NOUN
cana-2175	131	57	to	to	ADP
cana-2175	131	58	the	the	DET
cana-2175	131	59	ideal	ideal	ADJ
cana-2175	131	60	solution	solution	NOUN
cana-2175	131	61	.	.	PUNCT
cana-2175	132	1	this	this	DET
cana-2175	132	2	approach	approach	NOUN
cana-2175	132	3	allows	allow	VERB
cana-2175	132	4	for	for	ADP
cana-2175	132	5	an	an	DET
cana-2175	132	6	effective	effective	ADJ
cana-2175	132	7	multi	multi	ADJ
cana-2175	132	8	-	-	ADJ
cana-2175	132	9	criteria	criterion	NOUN
cana-2175	132	10	decision	decision	NOUN
cana-2175	132	11	-	-	PUNCT
cana-2175	132	12	making	make	VERB
cana-2175	132	13	process	process	NOUN
cana-2175	132	14	that	that	PRON
cana-2175	132	15	incorporates	incorporate	VERB
cana-2175	132	16	the	the	DET
cana-2175	132	17	flexibility	flexibility	NOUN
cana-2175	132	18	and	and	CCONJ
cana-2175	132	19	robustness	robustness	NOUN
cana-2175	132	20	of	of	ADP
cana-2175	132	21	pythagorean	pythagorean	ADJ
cana-2175	132	22	fuzzy	fuzzy	ADJ
cana-2175	132	23	sets	set	NOUN
cana-2175	132	24	.	.	PUNCT
cana-2175	133	1	4	4	X
cana-2175	133	2	.	.	NOUN
cana-2175	133	3	results	result	NOUN
cana-2175	133	4	to	to	PART
cana-2175	133	5	perform	perform	VERB
cana-2175	133	6	the	the	DET
cana-2175	133	7	experiment	experiment	NOUN
cana-2175	133	8	on	on	ADP
cana-2175	133	9	d	d	NOUN
cana-2175	133	10	-	-	NOUN
cana-2175	133	11	pfss	pfss	ADJ
cana-2175	133	12	,	,	PUNCT
cana-2175	133	13	several	several	ADJ
cana-2175	133	14	key	key	ADJ
cana-2175	133	15	resources	resource	NOUN
cana-2175	133	16	and	and	CCONJ
cana-2175	133	17	tools	tool	NOUN
cana-2175	133	18	are	be	AUX
cana-2175	133	19	needed	need	VERB
cana-2175	133	20	.	.	PUNCT
cana-2175	134	1	first	first	ADV
cana-2175	134	2	,	,	PUNCT
cana-2175	134	3	access	access	NOUN
cana-2175	134	4	to	to	ADP
cana-2175	134	5	data	datum	NOUN
cana-2175	134	6	representation	representation	NOUN
cana-2175	134	7	and	and	CCONJ
cana-2175	134	8	visualization	visualization	NOUN
cana-2175	134	9	software	software	NOUN
cana-2175	134	10	is	be	AUX
cana-2175	134	11	essential	essential	ADJ
cana-2175	134	12	,	,	PUNCT
cana-2175	134	13	such	such	ADJ
cana-2175	134	14	as	as	ADP
cana-2175	134	15	python	python	NOUN
cana-2175	134	16	with	with	ADP
cana-2175	134	17	libraries	library	NOUN
cana-2175	134	18	like	like	VERB
cana-2175	134	19	,	,	PUNCT
cana-2175	134	20	for	for	ADP
cana-2175	134	21	plotting	plot	VERB
cana-2175	134	22	membership	membership	NOUN
cana-2175	134	23	and	and	CCONJ
cana-2175	134	24	non	non	ADJ
cana-2175	134	25	-	-	ADJ
cana-2175	134	26	membership	membership	ADJ
cana-2175	134	27	degrees	degree	NOUN
cana-2175	134	28	along	along	ADP
cana-2175	134	29	with	with	ADP
cana-2175	134	30	distinct	distinct	ADJ
cana-2175	134	31	radii	radius	NOUN
cana-2175	134	32	.	.	PUNCT
cana-2175	135	1	these	these	DET
cana-2175	135	2	tools	tool	NOUN
cana-2175	135	3	will	will	AUX
cana-2175	135	4	facilitate	facilitate	VERB
cana-2175	135	5	the	the	DET
cana-2175	135	6	creation	creation	NOUN
cana-2175	135	7	of	of	ADP
cana-2175	135	8	detailed	detailed	ADJ
cana-2175	135	9	visualizations	visualization	NOUN
cana-2175	135	10	,	,	PUNCT
cana-2175	135	11	including	include	VERB
cana-2175	135	12	2d	2d	NUM
cana-2175	135	13	and	and	CCONJ
cana-2175	135	14	3d	3d	NUM
cana-2175	135	15	plots	plot	NOUN
cana-2175	135	16	,	,	PUNCT
cana-2175	135	17	to	to	PART
cana-2175	135	18	illustrate	illustrate	VERB
cana-2175	135	19	how	how	SCONJ
cana-2175	135	20	elements	element	NOUN
cana-2175	135	21	of	of	ADP
cana-2175	135	22	d	d	ADJ
cana-2175	135	23	-	-	ADJ
cana-2175	135	24	pfss	pfss	ADJ
cana-2175	135	25	interact	interact	NOUN
cana-2175	135	26	and	and	CCONJ
cana-2175	135	27	satisfy	satisfy	VERB
cana-2175	135	28	the	the	DET
cana-2175	135	29	pythagorean	pythagorean	PROPN
cana-2175	135	30	conditions	condition	NOUN
cana-2175	135	31	.	.	PUNCT
cana-2175	136	1	second	second	ADJ
cana-2175	136	2	,	,	PUNCT
cana-2175	136	3	a	a	DET
cana-2175	136	4	solid	solid	ADJ
cana-2175	136	5	understanding	understanding	NOUN
cana-2175	136	6	of	of	ADP
cana-2175	136	7	the	the	DET
cana-2175	136	8	mathematical	mathematical	ADJ
cana-2175	136	9	formulations	formulation	NOUN
cana-2175	136	10	governing	govern	VERB
cana-2175	136	11	d	d	X
cana-2175	136	12	-	-	NOUN
cana-2175	136	13	pfss	pfss	PROPN
cana-2175	136	14	is	be	AUX
cana-2175	136	15	necessary	necessary	ADJ
cana-2175	136	16	,	,	PUNCT
cana-2175	136	17	including	include	VERB
cana-2175	136	18	the	the	DET
cana-2175	136	19	pythagorean	pythagorean	PROPN
cana-2175	136	20	condition	condition	NOUN
cana-2175	136	21	and	and	CCONJ
cana-2175	136	22	operations	operation	NOUN
cana-2175	136	23	like	like	ADP
cana-2175	136	24	communications	communication	NOUN
cana-2175	136	25	on	on	ADP
cana-2175	136	26	applied	apply	VERB
cana-2175	136	27	nonlinear	nonlinear	ADJ
cana-2175	136	28	analysis	analysis	NOUN
cana-2175	136	29	issn	issn	NOUN
cana-2175	136	30	:	:	PUNCT
cana-2175	136	31	1074	1074	NUM
cana-2175	136	32	-	-	PUNCT
cana-2175	136	33	133x	133x	NUM
cana-2175	136	34	vol	vol	NOUN
cana-2175	136	35	32	32	NUM
cana-2175	136	36	no	no	NOUN
cana-2175	136	37	.	.	PUNCT
cana-2175	137	1	1s	1s	NUM
cana-2175	137	2	(	(	PUNCT
cana-2175	137	3	2025	2025	NUM
cana-2175	137	4	)	)	PUNCT
cana-2175	137	5	331	331	NUM
cana-2175	137	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2175	137	7	union	union	NOUN
cana-2175	137	8	,	,	PUNCT
cana-2175	137	9	intersection	intersection	NOUN
cana-2175	137	10	,	,	PUNCT
cana-2175	137	11	and	and	CCONJ
cana-2175	137	12	complement	complement	NOUN
cana-2175	137	13	.	.	PUNCT
cana-2175	138	1	this	this	DET
cana-2175	138	2	knowledge	knowledge	NOUN
cana-2175	138	3	ensures	ensure	VERB
cana-2175	138	4	accurate	accurate	ADJ
cana-2175	138	5	implementation	implementation	NOUN
cana-2175	138	6	and	and	CCONJ
cana-2175	138	7	analysis	analysis	NOUN
cana-2175	138	8	of	of	ADP
cana-2175	138	9	fuzzy	fuzzy	ADJ
cana-2175	138	10	set	set	VERB
cana-2175	138	11	operations	operation	NOUN
cana-2175	138	12	.	.	PUNCT
cana-2175	139	1	these	these	DET
cana-2175	139	2	resources	resource	NOUN
cana-2175	139	3	will	will	AUX
cana-2175	139	4	support	support	VERB
cana-2175	139	5	the	the	DET
cana-2175	139	6	calculations	calculation	NOUN
cana-2175	139	7	needed	need	VERB
cana-2175	139	8	to	to	PART
cana-2175	139	9	validate	validate	VERB
cana-2175	139	10	the	the	DET
cana-2175	139	11	pythagorean	pythagorean	ADJ
cana-2175	139	12	condition	condition	NOUN
cana-2175	139	13	and	and	CCONJ
cana-2175	139	14	perform	perform	VERB
cana-2175	139	15	the	the	DET
cana-2175	139	16	various	various	ADJ
cana-2175	139	17	operations	operation	NOUN
cana-2175	139	18	on	on	ADP
cana-2175	139	19	the	the	DET
cana-2175	139	20	fuzzy	fuzzy	ADJ
cana-2175	139	21	sets	set	NOUN
cana-2175	139	22	.	.	PUNCT
cana-2175	140	1	together	together	ADV
cana-2175	140	2	,	,	PUNCT
cana-2175	140	3	these	these	DET
cana-2175	140	4	requirements	requirement	NOUN
cana-2175	140	5	will	will	AUX
cana-2175	140	6	enable	enable	VERB
cana-2175	140	7	a	a	DET
cana-2175	140	8	comprehensive	comprehensive	ADJ
cana-2175	140	9	examination	examination	NOUN
cana-2175	140	10	of	of	ADP
cana-2175	140	11	d	d	PROPN
cana-2175	140	12	-	-	ADJ
cana-2175	140	13	pfss	pfss	ADJ
cana-2175	140	14	,	,	PUNCT
cana-2175	140	15	highlighting	highlight	VERB
cana-2175	140	16	their	their	PRON
cana-2175	140	17	flexibility	flexibility	NOUN
cana-2175	140	18	and	and	CCONJ
cana-2175	140	19	robustness	robustness	NOUN
cana-2175	140	20	in	in	ADP
cana-2175	140	21	modeling	modeling	NOUN
cana-2175	140	22	and	and	CCONJ
cana-2175	140	23	managing	manage	VERB
cana-2175	140	24	uncertainty	uncertainty	NOUN
cana-2175	140	25	.	.	PUNCT
cana-2175	141	1	fig	fig	NOUN
cana-2175	141	2	.	.	PUNCT
cana-2175	142	1	3	3	NUM
cana-2175	142	2	membership	membership	NOUN
cana-2175	142	3	and	and	CCONJ
cana-2175	142	4	non	non	ADJ
cana-2175	142	5	-	-	ADJ
cana-2175	142	6	membership	membership	ADJ
cana-2175	142	7	degrees	degree	NOUN
cana-2175	142	8	for	for	ADP
cana-2175	142	9	multiple	multiple	ADJ
cana-2175	142	10	elements	element	NOUN
cana-2175	142	11	with	with	ADP
cana-2175	142	12	distinct	distinct	ADJ
cana-2175	142	13	radii	radius	NOUN
cana-2175	142	14	fig.3	fig.3	PROPN
cana-2175	142	15	visualizes	visualize	VERB
cana-2175	142	16	the	the	DET
cana-2175	142	17	membership	membership	NOUN
cana-2175	142	18	and	and	CCONJ
cana-2175	142	19	non	non	ADJ
cana-2175	142	20	-	-	ADJ
cana-2175	142	21	membership	membership	ADJ
cana-2175	142	22	degrees	degree	NOUN
cana-2175	142	23	for	for	ADP
cana-2175	142	24	multiple	multiple	ADJ
cana-2175	142	25	elements	element	NOUN
cana-2175	142	26	within	within	ADP
cana-2175	142	27	distinct	distinct	ADJ
cana-2175	142	28	radii	radius	NOUN
cana-2175	142	29	,	,	PUNCT
cana-2175	142	30	emphasizing	emphasize	VERB
cana-2175	142	31	the	the	DET
cana-2175	142	32	flexibility	flexibility	NOUN
cana-2175	142	33	of	of	ADP
cana-2175	142	34	d	d	NOUN
cana-2175	142	35	-	-	NOUN
cana-2175	142	36	pfss	pfss	NOUN
cana-2175	142	37	.	.	PUNCT
cana-2175	143	1	each	each	DET
cana-2175	143	2	point	point	NOUN
cana-2175	143	3	represents	represent	VERB
cana-2175	143	4	an	an	DET
cana-2175	143	5	element	element	NOUN
cana-2175	143	6	,	,	PUNCT
cana-2175	143	7	with	with	ADP
cana-2175	143	8	the	the	DET
cana-2175	143	9	circle	circle	NOUN
cana-2175	143	10	's	's	PART
cana-2175	143	11	size	size	NOUN
cana-2175	143	12	proportional	proportional	NOUN
cana-2175	143	13	to	to	ADP
cana-2175	143	14	its	its	PRON
cana-2175	143	15	unique	unique	ADJ
cana-2175	143	16	radius	radius	NOUN
cana-2175	143	17	.	.	PUNCT
cana-2175	144	1	fig.3	fig.3	PROPN
cana-2175	144	2	showcases	showcase	VERB
cana-2175	144	3	how	how	SCONJ
cana-2175	144	4	d	d	X
cana-2175	144	5	-	-	ADJ
cana-2175	144	6	pfss	pfss	ADJ
cana-2175	144	7	extend	extend	VERB
cana-2175	144	8	traditional	traditional	ADJ
cana-2175	144	9	fuzzy	fuzzy	ADJ
cana-2175	144	10	sets	set	NOUN
cana-2175	144	11	by	by	ADP
cana-2175	144	12	allowing	allow	VERB
cana-2175	144	13	each	each	DET
cana-2175	144	14	element	element	NOUN
cana-2175	144	15	to	to	PART
cana-2175	144	16	have	have	VERB
cana-2175	144	17	a	a	DET
cana-2175	144	18	distinct	distinct	ADJ
cana-2175	144	19	radius	radius	NOUN
cana-2175	144	20	,	,	PUNCT
cana-2175	144	21	providing	provide	VERB
cana-2175	144	22	a	a	DET
cana-2175	144	23	more	more	ADV
cana-2175	144	24	nuanced	nuanced	ADJ
cana-2175	144	25	representation	representation	NOUN
cana-2175	144	26	of	of	ADP
cana-2175	144	27	uncertainty	uncertainty	NOUN
cana-2175	144	28	.	.	PUNCT
cana-2175	145	1	by	by	ADP
cana-2175	145	2	illustrating	illustrate	VERB
cana-2175	145	3	the	the	DET
cana-2175	145	4	relationship	relationship	NOUN
cana-2175	145	5	between	between	ADP
cana-2175	145	6	the	the	DET
cana-2175	145	7	membership	membership	NOUN
cana-2175	145	8	and	and	CCONJ
cana-2175	145	9	non	non	ADJ
cana-2175	145	10	-	-	ADJ
cana-2175	145	11	membership	membership	ADJ
cana-2175	145	12	degrees	degree	NOUN
cana-2175	145	13	,	,	PUNCT
cana-2175	145	14	the	the	DET
cana-2175	145	15	graph	graph	NOUN
cana-2175	145	16	demonstrates	demonstrate	VERB
cana-2175	145	17	the	the	DET
cana-2175	145	18	capability	capability	NOUN
cana-2175	145	19	of	of	ADP
cana-2175	145	20	d	d	NOUN
cana-2175	145	21	-	-	ADJ
cana-2175	145	22	pfss	pfss	ADJ
cana-2175	145	23	to	to	PART
cana-2175	145	24	model	model	VERB
cana-2175	145	25	complex	complex	ADJ
cana-2175	145	26	scenarios	scenario	NOUN
cana-2175	145	27	with	with	ADP
cana-2175	145	28	varying	vary	VERB
cana-2175	145	29	levels	level	NOUN
cana-2175	145	30	of	of	ADP
cana-2175	145	31	uncertainty	uncertainty	NOUN
cana-2175	145	32	for	for	ADP
cana-2175	145	33	different	different	ADJ
cana-2175	145	34	elements	element	NOUN
cana-2175	145	35	.	.	PUNCT
cana-2175	146	1	fig.4	fig.4	PROPN
cana-2175	146	2	validates	validate	VERB
cana-2175	146	3	the	the	DET
cana-2175	146	4	pythagorean	pythagorean	PROPN
cana-2175	146	5	condition	condition	NOUN
cana-2175	146	6	for	for	ADP
cana-2175	146	7	d	d	NOUN
cana-2175	146	8	-	-	NOUN
cana-2175	146	9	pfss	pfss	ADJ
cana-2175	146	10	by	by	ADP
cana-2175	146	11	plotting	plot	VERB
cana-2175	146	12	circles	circle	NOUN
cana-2175	146	13	representing	represent	VERB
cana-2175	146	14	each	each	DET
cana-2175	146	15	element	element	NOUN
cana-2175	146	16	's	's	PART
cana-2175	146	17	radius	radius	NOUN
cana-2175	146	18	.	.	PUNCT
cana-2175	147	1	this	this	PRON
cana-2175	147	2	ensures	ensure	VERB
cana-2175	147	3	that	that	SCONJ
cana-2175	147	4	the	the	DET
cana-2175	147	5	membership	membership	NOUN
cana-2175	147	6	and	and	CCONJ
cana-2175	147	7	non	non	ADJ
cana-2175	147	8	-	-	ADJ
cana-2175	147	9	membership	membership	ADJ
cana-2175	147	10	degrees	degree	NOUN
cana-2175	147	11	lie	lie	VERB
cana-2175	147	12	within	within	ADP
cana-2175	147	13	their	their	PRON
cana-2175	147	14	respective	respective	ADJ
cana-2175	147	15	radii	radii	NOUN
cana-2175	147	16	,	,	PUNCT
cana-2175	147	17	demonstrating	demonstrate	VERB
cana-2175	147	18	compliance	compliance	NOUN
cana-2175	147	19	with	with	ADP
cana-2175	147	20	the	the	DET
cana-2175	147	21	pythagorean	pythagorean	PROPN
cana-2175	147	22	condition	condition	NOUN
cana-2175	147	23	.	.	PUNCT
cana-2175	148	1	this	this	DET
cana-2175	148	2	validation	validation	NOUN
cana-2175	148	3	is	be	AUX
cana-2175	148	4	crucial	crucial	ADJ
cana-2175	148	5	for	for	ADP
cana-2175	148	6	maintaining	maintain	VERB
cana-2175	148	7	the	the	DET
cana-2175	148	8	integrity	integrity	NOUN
cana-2175	148	9	of	of	ADP
cana-2175	148	10	d	d	NOUN
cana-2175	148	11	-	-	NOUN
cana-2175	148	12	pfss	pfss	ADJ
cana-2175	148	13	in	in	ADP
cana-2175	148	14	modeling	model	VERB
cana-2175	148	15	uncertainty	uncertainty	NOUN
cana-2175	148	16	.	.	PUNCT
cana-2175	149	1	by	by	ADP
cana-2175	149	2	visually	visually	ADV
cana-2175	149	3	enforcing	enforce	VERB
cana-2175	149	4	the	the	DET
cana-2175	149	5	constraint	constraint	NOUN
cana-2175	149	6	that	that	SCONJ
cana-2175	149	7	(	(	PUNCT
cana-2175	149	8	2	2	NUM
cana-2175	149	9	)	)	PUNCT
cana-2175	149	10	,	,	PUNCT
cana-2175	149	11	fig.4	fig.4	PROPN
cana-2175	149	12	underscores	underscore	VERB
cana-2175	149	13	the	the	DET
cana-2175	149	14	mathematical	mathematical	ADJ
cana-2175	149	15	robustness	robustness	NOUN
cana-2175	149	16	of	of	ADP
cana-2175	149	17	d	d	NOUN
cana-2175	149	18	-	-	NOUN
cana-2175	149	19	pfss	pfss	ADJ
cana-2175	149	20	.	.	PUNCT
cana-2175	150	1	it	it	PRON
cana-2175	150	2	illustrates	illustrate	VERB
cana-2175	150	3	that	that	SCONJ
cana-2175	150	4	each	each	DET
cana-2175	150	5	element	element	NOUN
cana-2175	150	6	adheres	adhere	VERB
cana-2175	150	7	to	to	ADP
cana-2175	150	8	the	the	DET
cana-2175	150	9	fundamental	fundamental	ADJ
cana-2175	150	10	pythagorean	pythagorean	PROPN
cana-2175	150	11	relationship	relationship	NOUN
cana-2175	150	12	,	,	PUNCT
cana-2175	150	13	which	which	PRON
cana-2175	150	14	is	be	AUX
cana-2175	150	15	vital	vital	ADJ
cana-2175	150	16	for	for	ADP
cana-2175	150	17	the	the	DET
cana-2175	150	18	accurate	accurate	ADJ
cana-2175	150	19	representation	representation	NOUN
cana-2175	150	20	of	of	ADP
cana-2175	150	21	uncertainty	uncertainty	NOUN
cana-2175	150	22	in	in	ADP
cana-2175	150	23	diverse	diverse	ADJ
cana-2175	150	24	applications	application	NOUN
cana-2175	150	25	.	.	PUNCT
cana-2175	151	1	fig	fig	NOUN
cana-2175	151	2	.	.	PUNCT
cana-2175	152	1	4	4	NUM
cana-2175	152	2	validation	validation	NOUN
cana-2175	152	3	of	of	ADP
cana-2175	152	4	pythagorean	pythagorean	ADJ
cana-2175	152	5	condition	condition	NOUN
cana-2175	152	6	for	for	ADP
cana-2175	152	7	d	d	ADJ
cana-2175	152	8	-	-	ADJ
cana-2175	152	9	pfss	pfss	ADJ
cana-2175	152	10	communications	communication	NOUN
cana-2175	152	11	on	on	ADP
cana-2175	152	12	applied	apply	VERB
cana-2175	152	13	nonlinear	nonlinear	ADJ
cana-2175	152	14	analysis	analysis	NOUN
cana-2175	152	15	issn	issn	NOUN
cana-2175	152	16	:	:	PUNCT
cana-2175	152	17	1074	1074	NUM
cana-2175	152	18	-	-	PUNCT
cana-2175	152	19	133x	133x	NUM
cana-2175	152	20	vol	vol	NOUN
cana-2175	152	21	32	32	NUM
cana-2175	152	22	no	no	NOUN
cana-2175	152	23	.	.	PUNCT
cana-2175	153	1	1s	1s	NUM
cana-2175	153	2	(	(	PUNCT
cana-2175	153	3	2025	2025	NUM
cana-2175	153	4	)	)	PUNCT
cana-2175	153	5	332	332	NUM
cana-2175	153	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2175	153	7	fig	fig	NOUN
cana-2175	153	8	.	.	PUNCT
cana-2175	154	1	5	5	NUM
cana-2175	154	2	membership	membership	NOUN
cana-2175	154	3	and	and	CCONJ
cana-2175	154	4	non	non	ADJ
cana-2175	154	5	-	-	ADJ
cana-2175	154	6	membership	membership	ADJ
cana-2175	154	7	degrees	degree	NOUN
cana-2175	154	8	with	with	ADP
cana-2175	154	9	distinct	distinct	ADJ
cana-2175	154	10	radii	radius	NOUN
cana-2175	154	11	fig.5	fig.5	PROPN
cana-2175	154	12	illustrates	illustrate	VERB
cana-2175	154	13	how	how	SCONJ
cana-2175	154	14	membership	membership	NOUN
cana-2175	154	15	(	(	PUNCT
cana-2175	154	16	μ	μ	NOUN
cana-2175	154	17	)	)	PUNCT
cana-2175	154	18	and	and	CCONJ
cana-2175	154	19	non	non	ADJ
cana-2175	154	20	-	-	ADJ
cana-2175	154	21	membership	membership	ADJ
cana-2175	154	22	(	(	PUNCT
cana-2175	154	23	v	v	NOUN
cana-2175	154	24	)	)	PUNCT
cana-2175	154	25	degrees	degree	NOUN
cana-2175	154	26	vary	vary	VERB
cana-2175	154	27	as	as	ADP
cana-2175	154	28	the	the	DET
cana-2175	154	29	radius	radius	NOUN
cana-2175	154	30	(	(	PUNCT
cana-2175	154	31	r	r	NOUN
cana-2175	154	32	)	)	PUNCT
cana-2175	154	33	changes	change	NOUN
cana-2175	154	34	for	for	ADP
cana-2175	154	35	different	different	ADJ
cana-2175	154	36	elements	element	NOUN
cana-2175	154	37	.	.	PUNCT
cana-2175	155	1	each	each	DET
cana-2175	155	2	element	element	NOUN
cana-2175	155	3	's	's	PART
cana-2175	155	4	μ	μ	NOUN
cana-2175	155	5	and	and	CCONJ
cana-2175	155	6	v	v	NUM
cana-2175	155	7	degrees	degree	NOUN
cana-2175	155	8	are	be	AUX
cana-2175	155	9	plotted	plot	VERB
cana-2175	155	10	against	against	ADP
cana-2175	155	11	a	a	DET
cana-2175	155	12	range	range	NOUN
cana-2175	155	13	of	of	ADP
cana-2175	155	14	radii	radius	NOUN
cana-2175	155	15	,	,	PUNCT
cana-2175	155	16	showing	show	VERB
cana-2175	155	17	how	how	SCONJ
cana-2175	155	18	these	these	DET
cana-2175	155	19	values	value	NOUN
cana-2175	155	20	scale	scale	VERB
cana-2175	155	21	proportionally	proportionally	ADV
cana-2175	155	22	.	.	PUNCT
cana-2175	156	1	this	this	DET
cana-2175	156	2	visualization	visualization	NOUN
cana-2175	156	3	underscores	underscore	VERB
cana-2175	156	4	the	the	DET
cana-2175	156	5	flexibility	flexibility	NOUN
cana-2175	156	6	of	of	ADP
cana-2175	156	7	d	d	NOUN
cana-2175	156	8	-	-	NOUN
cana-2175	156	9	pfss	pfss	NOUN
cana-2175	156	10	,	,	PUNCT
cana-2175	156	11	which	which	PRON
cana-2175	156	12	allow	allow	VERB
cana-2175	156	13	elements	element	NOUN
cana-2175	156	14	to	to	PART
cana-2175	156	15	adapt	adapt	VERB
cana-2175	156	16	their	their	PRON
cana-2175	156	17	degrees	degree	NOUN
cana-2175	156	18	dynamically	dynamically	ADV
cana-2175	156	19	with	with	ADP
cana-2175	156	20	varying	vary	VERB
cana-2175	156	21	radii	radius	NOUN
cana-2175	156	22	.	.	PUNCT
cana-2175	157	1	by	by	ADP
cana-2175	157	2	demonstrating	demonstrate	VERB
cana-2175	157	3	this	this	DET
cana-2175	157	4	variation	variation	NOUN
cana-2175	157	5	,	,	PUNCT
cana-2175	157	6	the	the	DET
cana-2175	157	7	graph	graph	NOUN
cana-2175	157	8	highlights	highlight	VERB
cana-2175	157	9	d	d	ADJ
cana-2175	157	10	-	-	ADJ
cana-2175	157	11	pfss	pfss	NOUN
cana-2175	157	12	'	'	PUNCT
cana-2175	157	13	ability	ability	NOUN
cana-2175	157	14	to	to	PART
cana-2175	157	15	model	model	VERB
cana-2175	157	16	uncertainty	uncertainty	NOUN
cana-2175	157	17	more	more	ADV
cana-2175	157	18	accurately	accurately	ADV
cana-2175	157	19	compared	compare	VERB
cana-2175	157	20	to	to	ADP
cana-2175	157	21	traditional	traditional	ADJ
cana-2175	157	22	fuzzy	fuzzy	ADJ
cana-2175	157	23	sets	set	NOUN
cana-2175	157	24	,	,	PUNCT
cana-2175	157	25	where	where	SCONJ
cana-2175	157	26	the	the	DET
cana-2175	157	27	radius	radius	NOUN
cana-2175	157	28	is	be	AUX
cana-2175	157	29	fixed	fix	VERB
cana-2175	157	30	.	.	PUNCT
cana-2175	158	1	this	this	DET
cana-2175	158	2	dynamic	dynamic	ADJ
cana-2175	158	3	adaptation	adaptation	NOUN
cana-2175	158	4	is	be	AUX
cana-2175	158	5	crucial	crucial	ADJ
cana-2175	158	6	for	for	ADP
cana-2175	158	7	applications	application	NOUN
cana-2175	158	8	requiring	require	VERB
cana-2175	158	9	nuanced	nuanced	ADJ
cana-2175	158	10	and	and	CCONJ
cana-2175	158	11	flexible	flexible	ADJ
cana-2175	158	12	uncertainty	uncertainty	NOUN
cana-2175	158	13	representation	representation	NOUN
cana-2175	158	14	,	,	PUNCT
cana-2175	158	15	such	such	ADJ
cana-2175	158	16	as	as	ADP
cana-2175	158	17	decision	decision	NOUN
cana-2175	158	18	-	-	PUNCT
cana-2175	158	19	making	make	VERB
cana-2175	158	20	and	and	CCONJ
cana-2175	158	21	control	control	NOUN
cana-2175	158	22	systems	system	NOUN
cana-2175	158	23	.	.	PUNCT
cana-2175	159	1	fig	fig	NOUN
cana-2175	159	2	.	.	PUNCT
cana-2175	160	1	6	6	NUM
cana-2175	160	2	visualization	visualization	NOUN
cana-2175	160	3	of	of	ADP
cana-2175	160	4	pythagorean	pythagorean	ADJ
cana-2175	160	5	condition	condition	NOUN
cana-2175	160	6	in	in	ADP
cana-2175	160	7	3d	3d	PROPN
cana-2175	160	8	fig.6	fig.6	PROPN
cana-2175	160	9	provides	provide	VERB
cana-2175	160	10	a	a	DET
cana-2175	160	11	3d	3d	NOUN
cana-2175	160	12	visualization	visualization	NOUN
cana-2175	160	13	of	of	ADP
cana-2175	160	14	the	the	DET
cana-2175	160	15	pythagorean	pythagorean	PROPN
cana-2175	160	16	condition	condition	NOUN
cana-2175	160	17	for	for	ADP
cana-2175	160	18	d	d	NOUN
cana-2175	160	19	-	-	ADJ
cana-2175	160	20	pfss	pfss	ADJ
cana-2175	160	21	,	,	PUNCT
cana-2175	160	22	plotting	plot	VERB
cana-2175	160	23	membership	membership	NOUN
cana-2175	160	24	degree	degree	NOUN
cana-2175	160	25	(	(	PUNCT
cana-2175	160	26	μ	μ	NOUN
cana-2175	160	27	)	)	PUNCT
cana-2175	160	28	,	,	PUNCT
cana-2175	160	29	non	non	ADJ
cana-2175	160	30	-	-	ADJ
cana-2175	160	31	membership	membership	ADJ
cana-2175	160	32	degree	degree	NOUN
cana-2175	160	33	(	(	PUNCT
cana-2175	160	34	v	v	NOUN
cana-2175	160	35	)	)	PUNCT
cana-2175	160	36	,	,	PUNCT
cana-2175	160	37	and	and	CCONJ
cana-2175	160	38	radius	radius	NOUN
cana-2175	160	39	(	(	PUNCT
cana-2175	160	40	r	r	NOUN
cana-2175	160	41	)	)	PUNCT
cana-2175	160	42	for	for	ADP
cana-2175	160	43	multiple	multiple	ADJ
cana-2175	160	44	elements	element	NOUN
cana-2175	160	45	.	.	PUNCT
cana-2175	161	1	this	this	DET
cana-2175	161	2	comprehensive	comprehensive	ADJ
cana-2175	161	3	view	view	NOUN
cana-2175	161	4	reveals	reveal	VERB
cana-2175	161	5	the	the	DET
cana-2175	161	6	intricate	intricate	ADJ
cana-2175	161	7	relationship	relationship	NOUN
cana-2175	161	8	between	between	ADP
cana-2175	161	9	these	these	DET
cana-2175	161	10	parameters	parameter	NOUN
cana-2175	161	11	,	,	PUNCT
cana-2175	161	12	ensuring	ensure	VERB
cana-2175	161	13	each	each	DET
cana-2175	161	14	element	element	ADJ
cana-2175	161	15	satisfies	satisfie	NOUN
cana-2175	161	16	(	(	PUNCT
cana-2175	161	17	2	2	NUM
cana-2175	161	18	)	)	PUNCT
cana-2175	161	19	.	.	PUNCT
cana-2175	162	1	by	by	ADP
cana-2175	162	2	visualizing	visualize	VERB
cana-2175	162	3	the	the	DET
cana-2175	162	4	elements	element	NOUN
cana-2175	162	5	in	in	ADP
cana-2175	162	6	three	three	NUM
cana-2175	162	7	dimensions	dimension	NOUN
cana-2175	162	8	,	,	PUNCT
cana-2175	162	9	the	the	DET
cana-2175	162	10	graph	graph	NOUN
cana-2175	162	11	emphasizes	emphasize	VERB
cana-2175	162	12	the	the	DET
cana-2175	162	13	robustness	robustness	NOUN
cana-2175	162	14	of	of	ADP
cana-2175	162	15	d	d	NOUN
cana-2175	162	16	-	-	NOUN
cana-2175	162	17	pfss	pfss	ADJ
cana-2175	162	18	in	in	ADP
cana-2175	162	19	maintaining	maintain	VERB
cana-2175	162	20	the	the	DET
cana-2175	162	21	pythagorean	pythagorean	PROPN
cana-2175	162	22	condition	condition	NOUN
cana-2175	162	23	across	across	ADP
cana-2175	162	24	varying	vary	VERB
cana-2175	162	25	radii	radius	NOUN
cana-2175	162	26	.	.	PUNCT
cana-2175	163	1	this	this	DET
cana-2175	163	2	3d	3d	NUM
cana-2175	163	3	representation	representation	NOUN
cana-2175	163	4	is	be	AUX
cana-2175	163	5	particularly	particularly	ADV
cana-2175	163	6	effective	effective	ADJ
cana-2175	163	7	in	in	ADP
cana-2175	163	8	illustrating	illustrate	VERB
cana-2175	163	9	the	the	DET
cana-2175	163	10	complex	complex	ADJ
cana-2175	163	11	interplay	interplay	NOUN
cana-2175	163	12	between	between	ADP
cana-2175	163	13	μ	μ	PROPN
cana-2175	163	14	,	,	PUNCT
cana-2175	163	15	v	v	NOUN
cana-2175	163	16	,	,	PUNCT
cana-2175	163	17	and	and	CCONJ
cana-2175	163	18	r	r	NOUN
cana-2175	163	19	,	,	PUNCT
cana-2175	163	20	reinforcing	reinforce	VERB
cana-2175	163	21	the	the	DET
cana-2175	163	22	enhanced	enhanced	ADJ
cana-2175	163	23	modeling	modeling	NOUN
cana-2175	163	24	capabilities	capability	NOUN
cana-2175	163	25	of	of	ADP
cana-2175	163	26	d	d	NOUN
cana-2175	163	27	-	-	NOUN
cana-2175	163	28	pfss	pfss	ADJ
cana-2175	163	29	in	in	ADP
cana-2175	163	30	capturing	capture	VERB
cana-2175	163	31	diverse	diverse	ADJ
cana-2175	163	32	degrees	degree	NOUN
cana-2175	163	33	of	of	ADP
cana-2175	163	34	uncertainty	uncertainty	NOUN
cana-2175	163	35	.	.	PUNCT
cana-2175	164	1	communications	communication	NOUN
cana-2175	164	2	on	on	ADP
cana-2175	164	3	applied	apply	VERB
cana-2175	164	4	nonlinear	nonlinear	ADJ
cana-2175	164	5	analysis	analysis	NOUN
cana-2175	164	6	issn	issn	NOUN
cana-2175	164	7	:	:	PUNCT
cana-2175	164	8	1074	1074	NUM
cana-2175	164	9	-	-	PUNCT
cana-2175	164	10	133x	133x	NUM
cana-2175	164	11	vol	vol	NOUN
cana-2175	164	12	32	32	NUM
cana-2175	164	13	no	no	NOUN
cana-2175	164	14	.	.	PUNCT
cana-2175	165	1	1s	1s	NUM
cana-2175	165	2	(	(	PUNCT
cana-2175	165	3	2025	2025	NUM
cana-2175	165	4	)	)	PUNCT
cana-2175	165	5	333	333	NUM
cana-2175	165	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2175	165	7	fig	fig	NOUN
cana-2175	165	8	.	.	PUNCT
cana-2175	166	1	7	7	NUM
cana-2175	166	2	comparison	comparison	NOUN
cana-2175	166	3	of	of	ADP
cana-2175	166	4	union	union	NOUN
cana-2175	166	5	and	and	CCONJ
cana-2175	166	6	intersection	intersection	NOUN
cana-2175	166	7	operations	operation	NOUN
cana-2175	166	8	for	for	ADP
cana-2175	166	9	d	d	NOUN
cana-2175	166	10	-	-	ADJ
cana-2175	166	11	pfss	pfss	ADJ
cana-2175	166	12	fig.7	fig.7	ADJ
cana-2175	166	13	illustrates	illustrate	VERB
cana-2175	166	14	the	the	DET
cana-2175	166	15	union	union	NOUN
cana-2175	166	16	and	and	CCONJ
cana-2175	166	17	intersection	intersection	NOUN
cana-2175	166	18	operations	operation	NOUN
cana-2175	166	19	for	for	ADP
cana-2175	166	20	d	d	NOUN
cana-2175	166	21	-	-	NOUN
cana-2175	166	22	pfss	pfss	ADJ
cana-2175	166	23	.	.	PUNCT
cana-2175	167	1	it	it	PRON
cana-2175	167	2	plots	plot	VERB
cana-2175	167	3	the	the	DET
cana-2175	167	4	membership	membership	NOUN
cana-2175	167	5	(	(	PUNCT
cana-2175	167	6	μ	μ	NOUN
cana-2175	167	7	)	)	PUNCT
cana-2175	167	8	and	and	CCONJ
cana-2175	167	9	nonmembership	nonmembership	NOUN
cana-2175	167	10	(	(	PUNCT
cana-2175	167	11	v	v	NOUN
cana-2175	167	12	)	)	PUNCT
cana-2175	167	13	degrees	degree	NOUN
cana-2175	167	14	of	of	ADP
cana-2175	167	15	two	two	NUM
cana-2175	167	16	elements	element	NOUN
cana-2175	167	17	,	,	PUNCT
cana-2175	167	18	a	a	PRON
cana-2175	167	19	and	and	CCONJ
cana-2175	167	20	b	b	NOUN
cana-2175	167	21	,	,	PUNCT
cana-2175	167	22	along	along	ADP
cana-2175	167	23	with	with	ADP
cana-2175	167	24	their	their	PRON
cana-2175	167	25	respective	respective	ADJ
cana-2175	167	26	radii	radii	NOUN
cana-2175	167	27	.	.	PUNCT
cana-2175	168	1	the	the	DET
cana-2175	168	2	union	union	PROPN
cana-2175	168	3	operation	operation	NOUN
cana-2175	168	4	combines	combine	VERB
cana-2175	168	5	these	these	DET
cana-2175	168	6	elements	element	NOUN
cana-2175	168	7	by	by	ADP
cana-2175	168	8	taking	take	VERB
cana-2175	168	9	the	the	DET
cana-2175	168	10	minimum	minimum	NOUN
cana-2175	168	11	of	of	ADP
cana-2175	168	12	their	their	PRON
cana-2175	168	13	radii	radius	NOUN
cana-2175	168	14	and	and	CCONJ
cana-2175	168	15	calculating	calculate	VERB
cana-2175	168	16	the	the	DET
cana-2175	168	17	new	new	ADJ
cana-2175	168	18	μ	μ	PROPN
cana-2175	168	19	and	and	CCONJ
cana-2175	168	20	v	v	NUM
cana-2175	168	21	degrees	degree	NOUN
cana-2175	168	22	,	,	PUNCT
cana-2175	168	23	resulting	result	VERB
cana-2175	168	24	in	in	ADP
cana-2175	168	25	a	a	DET
cana-2175	168	26	point	point	NOUN
cana-2175	168	27	that	that	PRON
cana-2175	168	28	represents	represent	VERB
cana-2175	168	29	the	the	DET
cana-2175	168	30	union	union	NOUN
cana-2175	168	31	set	set	NOUN
cana-2175	168	32	.	.	PUNCT
cana-2175	169	1	conversely	conversely	ADV
cana-2175	169	2	,	,	PUNCT
cana-2175	169	3	the	the	DET
cana-2175	169	4	intersection	intersection	NOUN
cana-2175	169	5	operation	operation	NOUN
cana-2175	169	6	takes	take	VERB
cana-2175	169	7	the	the	DET
cana-2175	169	8	maximum	maximum	NOUN
cana-2175	169	9	of	of	ADP
cana-2175	169	10	the	the	DET
cana-2175	169	11	radii	radius	NOUN
cana-2175	169	12	and	and	CCONJ
cana-2175	169	13	calculates	calculate	VERB
cana-2175	169	14	the	the	DET
cana-2175	169	15	new	new	ADJ
cana-2175	169	16	μ	μ	PROPN
cana-2175	169	17	and	and	CCONJ
cana-2175	169	18	v	v	NUM
cana-2175	169	19	degrees	degree	NOUN
cana-2175	169	20	,	,	PUNCT
cana-2175	169	21	producing	produce	VERB
cana-2175	169	22	a	a	DET
cana-2175	169	23	point	point	NOUN
cana-2175	169	24	that	that	PRON
cana-2175	169	25	represents	represent	VERB
cana-2175	169	26	the	the	DET
cana-2175	169	27	intersection	intersection	NOUN
cana-2175	169	28	set	set	NOUN
cana-2175	169	29	.	.	PUNCT
cana-2175	170	1	this	this	DET
cana-2175	170	2	graph	graph	NOUN
cana-2175	170	3	effectively	effectively	ADV
cana-2175	170	4	demonstrates	demonstrate	VERB
cana-2175	170	5	the	the	DET
cana-2175	170	6	flexibility	flexibility	NOUN
cana-2175	170	7	and	and	CCONJ
cana-2175	170	8	robustness	robustness	NOUN
cana-2175	170	9	of	of	ADP
cana-2175	170	10	d	d	NOUN
cana-2175	170	11	-	-	NOUN
cana-2175	170	12	pfss	pfss	ADJ
cana-2175	170	13	in	in	ADP
cana-2175	170	14	handling	handle	VERB
cana-2175	170	15	fuzzy	fuzzy	ADJ
cana-2175	170	16	set	set	VERB
cana-2175	170	17	operations	operation	NOUN
cana-2175	170	18	,	,	PUNCT
cana-2175	170	19	highlighting	highlight	VERB
cana-2175	170	20	how	how	SCONJ
cana-2175	170	21	distinct	distinct	ADJ
cana-2175	170	22	radii	radii	NOUN
cana-2175	170	23	influence	influence	NOUN
cana-2175	170	24	the	the	DET
cana-2175	170	25	resulting	result	VERB
cana-2175	170	26	degrees	degree	NOUN
cana-2175	170	27	in	in	ADP
cana-2175	170	28	union	union	NOUN
cana-2175	170	29	and	and	CCONJ
cana-2175	170	30	intersection	intersection	NOUN
cana-2175	170	31	operations	operation	NOUN
cana-2175	170	32	.	.	PUNCT
cana-2175	171	1	this	this	DET
cana-2175	171	2	dynamic	dynamic	ADJ
cana-2175	171	3	handling	handling	NOUN
cana-2175	171	4	of	of	ADP
cana-2175	171	5	elements	element	NOUN
cana-2175	171	6	with	with	ADP
cana-2175	171	7	varying	vary	VERB
cana-2175	171	8	degrees	degree	NOUN
cana-2175	171	9	and	and	CCONJ
cana-2175	171	10	radii	radius	NOUN
cana-2175	171	11	proves	prove	VERB
cana-2175	171	12	the	the	DET
cana-2175	171	13	superior	superior	ADJ
cana-2175	171	14	modeling	modeling	NOUN
cana-2175	171	15	capabilities	capability	NOUN
cana-2175	171	16	of	of	ADP
cana-2175	171	17	d	d	NOUN
cana-2175	171	18	-	-	NOUN
cana-2175	171	19	pfss	pfss	ADJ
cana-2175	171	20	in	in	ADP
cana-2175	171	21	representing	represent	VERB
cana-2175	171	22	complex	complex	ADJ
cana-2175	171	23	uncertainties	uncertainty	NOUN
cana-2175	171	24	.	.	PUNCT
cana-2175	172	1	4	4	X
cana-2175	172	2	.	.	X
cana-2175	172	3	conclusion	conclusion	VERB
cana-2175	172	4	the	the	DET
cana-2175	172	5	integration	integration	NOUN
cana-2175	172	6	of	of	ADP
cana-2175	172	7	d	d	NOUN
cana-2175	172	8	-	-	NOUN
cana-2175	172	9	pfss	pfss	ADJ
cana-2175	172	10	into	into	ADP
cana-2175	172	11	the	the	DET
cana-2175	172	12	topsis	topsis	NOUN
cana-2175	172	13	method	method	NOUN
cana-2175	172	14	significantly	significantly	ADV
cana-2175	172	15	enhances	enhance	VERB
cana-2175	172	16	decision	decision	NOUN
cana-2175	172	17	-	-	PUNCT
cana-2175	172	18	making	making	NOUN
cana-2175	172	19	by	by	ADP
cana-2175	172	20	offering	offer	VERB
cana-2175	172	21	a	a	DET
cana-2175	172	22	nuanced	nuanced	ADJ
cana-2175	172	23	representation	representation	NOUN
cana-2175	172	24	of	of	ADP
cana-2175	172	25	uncertainty	uncertainty	NOUN
cana-2175	172	26	through	through	ADP
cana-2175	172	27	distinct	distinct	ADJ
cana-2175	172	28	radii	radius	NOUN
cana-2175	172	29	for	for	ADP
cana-2175	172	30	each	each	DET
cana-2175	172	31	element	element	NOUN
cana-2175	172	32	.	.	PUNCT
cana-2175	173	1	this	this	DET
cana-2175	173	2	flexibility	flexibility	NOUN
cana-2175	173	3	allows	allow	VERB
cana-2175	173	4	for	for	ADP
cana-2175	173	5	more	more	ADV
cana-2175	173	6	accurate	accurate	ADJ
cana-2175	173	7	modeling	modeling	NOUN
cana-2175	173	8	of	of	ADP
cana-2175	173	9	complex	complex	ADJ
cana-2175	173	10	uncertainties	uncertainty	NOUN
cana-2175	173	11	.	.	PUNCT
cana-2175	174	1	the	the	DET
cana-2175	174	2	results	result	NOUN
cana-2175	174	3	validate	validate	VERB
cana-2175	174	4	that	that	SCONJ
cana-2175	174	5	d	d	X
cana-2175	174	6	-	-	PUNCT
cana-2175	174	7	pfss	pfss	ADJ
cana-2175	174	8	adhere	adhere	NOUN
cana-2175	174	9	to	to	ADP
cana-2175	174	10	the	the	DET
cana-2175	174	11	pythagorean	pythagorean	PROPN
cana-2175	174	12	condition	condition	NOUN
cana-2175	174	13	,	,	PUNCT
cana-2175	174	14	with	with	ADP
cana-2175	174	15	union	union	NOUN
cana-2175	174	16	and	and	CCONJ
cana-2175	174	17	intersection	intersection	NOUN
cana-2175	174	18	operations	operation	NOUN
cana-2175	174	19	effectively	effectively	ADV
cana-2175	174	20	accommodating	accommodate	VERB
cana-2175	174	21	varying	vary	VERB
cana-2175	174	22	degrees	degree	NOUN
cana-2175	174	23	of	of	ADP
cana-2175	174	24	uncertainty	uncertainty	NOUN
cana-2175	174	25	,	,	PUNCT
cana-2175	174	26	thereby	thereby	ADV
cana-2175	174	27	improving	improve	VERB
cana-2175	174	28	the	the	DET
cana-2175	174	29	precision	precision	NOUN
cana-2175	174	30	of	of	ADP
cana-2175	174	31	multi	multi	ADJ
cana-2175	174	32	-	-	ADJ
cana-2175	174	33	criteria	criterion	NOUN
cana-2175	174	34	evaluations	evaluation	NOUN
cana-2175	174	35	.	.	PUNCT
cana-2175	175	1	future	future	ADJ
cana-2175	175	2	research	research	NOUN
cana-2175	175	3	should	should	AUX
cana-2175	175	4	explore	explore	VERB
cana-2175	175	5	d	d	NOUN
cana-2175	175	6	-	-	NOUN
cana-2175	175	7	pfss	pfss	ADJ
cana-2175	175	8	in	in	ADP
cana-2175	175	9	dynamic	dynamic	ADJ
cana-2175	175	10	decision	decision	NOUN
cana-2175	175	11	-	-	PUNCT
cana-2175	175	12	making	make	VERB
cana-2175	175	13	environments	environment	NOUN
cana-2175	175	14	and	and	CCONJ
cana-2175	175	15	real	real	ADJ
cana-2175	175	16	-	-	PUNCT
cana-2175	175	17	time	time	NOUN
cana-2175	175	18	applications	application	NOUN
cana-2175	175	19	.	.	PUNCT
cana-2175	176	1	investigating	investigate	VERB
cana-2175	176	2	their	their	PRON
cana-2175	176	3	scalability	scalability	NOUN
cana-2175	176	4	and	and	CCONJ
cana-2175	176	5	efficiency	efficiency	NOUN
cana-2175	176	6	in	in	ADP
cana-2175	176	7	larger	large	ADJ
cana-2175	176	8	datasets	dataset	NOUN
cana-2175	176	9	and	and	CCONJ
cana-2175	176	10	integrating	integrate	VERB
cana-2175	176	11	them	they	PRON
cana-2175	176	12	with	with	ADP
cana-2175	176	13	other	other	ADJ
cana-2175	176	14	advanced	advanced	ADJ
cana-2175	176	15	decision	decision	NOUN
cana-2175	176	16	-	-	PUNCT
cana-2175	176	17	making	make	VERB
cana-2175	176	18	frameworks	framework	NOUN
cana-2175	176	19	could	could	AUX
cana-2175	176	20	further	far	ADV
cana-2175	176	21	enhance	enhance	VERB
cana-2175	176	22	their	their	PRON
cana-2175	176	23	applicability	applicability	NOUN
cana-2175	176	24	and	and	CCONJ
cana-2175	176	25	performance	performance	NOUN
cana-2175	176	26	.	.	PUNCT
cana-2175	177	1	references	reference	NOUN
cana-2175	177	2	[	[	X
cana-2175	177	3	1	1	NUM
cana-2175	177	4	]	]	X
cana-2175	177	5	herrera	herrera	ADJ
cana-2175	177	6	-	-	PUNCT
cana-2175	177	7	viedma	viedma	NOUN
cana-2175	177	8	,	,	PUNCT
cana-2175	177	9	e.	e.	PROPN
cana-2175	177	10	,	,	PUNCT
cana-2175	177	11	palomares	palomares	PROPN
cana-2175	177	12	,	,	PUNCT
cana-2175	177	13	i.	i.	PROPN
cana-2175	177	14	,	,	PUNCT
cana-2175	177	15	li	li	PROPN
cana-2175	177	16	,	,	PUNCT
cana-2175	177	17	c.	c.	PROPN
cana-2175	177	18	c.	c.	PROPN
cana-2175	177	19	,	,	PUNCT
cana-2175	177	20	cabrerizo	cabrerizo	PROPN
cana-2175	177	21	,	,	PUNCT
cana-2175	177	22	f.	f.	PROPN
cana-2175	177	23	j.	j.	PROPN
cana-2175	177	24	,	,	PUNCT
cana-2175	177	25	dong	dong	PROPN
cana-2175	177	26	,	,	PUNCT
cana-2175	177	27	y.	y.	PROPN
cana-2175	177	28	,	,	PUNCT
cana-2175	177	29	chiclana	chiclana	PROPN
cana-2175	177	30	,	,	PUNCT
cana-2175	177	31	f.	f.	PROPN
cana-2175	177	32	,	,	PUNCT
cana-2175	177	33	&	&	CCONJ
cana-2175	177	34	herrera	herrera	PROPN
cana-2175	177	35	,	,	PUNCT
cana-2175	177	36	f.	f.	PROPN
cana-2175	177	37	(	(	PUNCT
cana-2175	177	38	2020	2020	NUM
cana-2175	177	39	)	)	PUNCT
cana-2175	177	40	.	.	PUNCT
cana-2175	178	1	revisiting	revisit	VERB
cana-2175	178	2	fuzzy	fuzzy	ADJ
cana-2175	178	3	and	and	CCONJ
cana-2175	178	4	linguistic	linguistic	ADJ
cana-2175	178	5	decision	decision	NOUN
cana-2175	178	6	making	making	NOUN
cana-2175	178	7	:	:	PUNCT
cana-2175	178	8	scenarios	scenario	NOUN
cana-2175	178	9	and	and	CCONJ
cana-2175	178	10	challenges	challenge	NOUN
cana-2175	178	11	for	for	ADP
cana-2175	178	12	making	make	VERB
cana-2175	178	13	wiser	wise	ADJ
cana-2175	178	14	decisions	decision	NOUN
cana-2175	178	15	in	in	ADP
cana-2175	178	16	a	a	DET
cana-2175	178	17	better	well	ADJ
cana-2175	178	18	way	way	NOUN
cana-2175	178	19	.	.	PUNCT
cana-2175	179	1	ieee	ieee	NOUN
cana-2175	179	2	transactions	transaction	NOUN
cana-2175	179	3	on	on	ADP
cana-2175	179	4	systems	system	NOUN
cana-2175	179	5	,	,	PUNCT
cana-2175	179	6	man	man	NOUN
cana-2175	179	7	,	,	PUNCT
cana-2175	179	8	and	and	CCONJ
cana-2175	179	9	cybernetics	cybernetic	NOUN
cana-2175	179	10	:	:	PUNCT
cana-2175	179	11	systems	system	NOUN
cana-2175	179	12	,	,	PUNCT
cana-2175	179	13	51(1	51(1	NUM
cana-2175	179	14	)	)	PUNCT
cana-2175	179	15	,	,	PUNCT
cana-2175	179	16	191	191	NUM
cana-2175	179	17	-	-	SYM
cana-2175	179	18	208	208	NUM
cana-2175	179	19	.	.	PUNCT
cana-2175	180	1	[	[	X
cana-2175	180	2	2	2	NUM
cana-2175	180	3	]	]	PUNCT
cana-2175	180	4	deveci	deveci	NOUN
cana-2175	180	5	,	,	PUNCT
cana-2175	180	6	m.	m.	NOUN
cana-2175	180	7	,	,	PUNCT
cana-2175	180	8	eriskin	eriskin	X
cana-2175	180	9	,	,	PUNCT
cana-2175	180	10	l.	l.	PROPN
cana-2175	180	11	,	,	PUNCT
cana-2175	180	12	&	&	CCONJ
cana-2175	180	13	karatas	karata	NOUN
cana-2175	180	14	,	,	PUNCT
cana-2175	180	15	m.	m.	NOUN
cana-2175	180	16	(	(	PUNCT
cana-2175	180	17	2021	2021	NUM
cana-2175	180	18	)	)	PUNCT
cana-2175	180	19	.	.	PUNCT
cana-2175	181	1	a	a	DET
cana-2175	181	2	survey	survey	NOUN
cana-2175	181	3	on	on	ADP
cana-2175	181	4	recent	recent	ADJ
cana-2175	181	5	applications	application	NOUN
cana-2175	181	6	of	of	ADP
cana-2175	181	7	pythagorean	pythagorean	PROPN
cana-2175	181	8	fuzzy	fuzzy	ADJ
cana-2175	181	9	sets	set	NOUN
cana-2175	181	10	:	:	PUNCT
cana-2175	181	11	a	a	DET
cana-2175	181	12	state	state	NOUN
cana-2175	181	13	-	-	PUNCT
cana-2175	181	14	ofthe	ofthe	NOUN
cana-2175	181	15	-	-	PUNCT
cana-2175	181	16	art	art	NOUN
cana-2175	181	17	between	between	ADP
cana-2175	181	18	2013	2013	NUM
cana-2175	181	19	and	and	CCONJ
cana-2175	181	20	2020	2020	NUM
cana-2175	181	21	.	.	PUNCT
cana-2175	182	1	pythagorean	pythagorean	PROPN
cana-2175	182	2	fuzzy	fuzzy	ADJ
cana-2175	182	3	sets	set	NOUN
cana-2175	182	4	:	:	PUNCT
cana-2175	182	5	theory	theory	NOUN
cana-2175	182	6	and	and	CCONJ
cana-2175	182	7	applications	application	NOUN
cana-2175	182	8	,	,	PUNCT
cana-2175	182	9	3	3	NUM
cana-2175	182	10	-	-	SYM
cana-2175	182	11	38	38	NUM
cana-2175	182	12	.	.	PUNCT
cana-2175	183	1	[	[	X
cana-2175	183	2	3	3	NUM
cana-2175	183	3	]	]	X
cana-2175	183	4	khan	khan	PROPN
cana-2175	183	5	,	,	PUNCT
cana-2175	183	6	m.	m.	NOUN
cana-2175	183	7	,	,	PUNCT
cana-2175	183	8	rahim	rahim	PROPN
cana-2175	183	9	,	,	PUNCT
cana-2175	183	10	m.	m.	NOUN
cana-2175	183	11	,	,	PUNCT
cana-2175	183	12	alanzi	alanzi	NOUN
cana-2175	183	13	,	,	PUNCT
cana-2175	183	14	a.	a.	NOUN
cana-2175	183	15	m.	m.	NOUN
cana-2175	183	16	,	,	PUNCT
cana-2175	183	17	ahmad	ahmad	PROPN
cana-2175	183	18	,	,	PUNCT
cana-2175	183	19	s.	s.	PROPN
cana-2175	183	20	,	,	PUNCT
cana-2175	183	21	fatlane	fatlane	ADJ
cana-2175	183	22	,	,	PUNCT
cana-2175	183	23	j.	j.	PROPN
cana-2175	183	24	m.	m.	PROPN
cana-2175	183	25	,	,	PUNCT
cana-2175	183	26	aphane	aphane	ADJ
cana-2175	183	27	,	,	PUNCT
cana-2175	183	28	m.	m.	NOUN
cana-2175	183	29	,	,	PUNCT
cana-2175	183	30	&	&	CCONJ
cana-2175	183	31	khalifa	khalifa	PROPN
cana-2175	183	32	,	,	PUNCT
cana-2175	183	33	h.	h.	PROPN
cana-2175	183	34	a.	a.	PROPN
cana-2175	183	35	e.	e.	PROPN
cana-2175	183	36	w.	w.	PROPN
cana-2175	183	37	(	(	PUNCT
cana-2175	183	38	2023	2023	NUM
cana-2175	183	39	)	)	PUNCT
cana-2175	183	40	.	.	PUNCT
cana-2175	184	1	dombi	dombi	PROPN
cana-2175	184	2	aggregation	aggregation	NOUN
cana-2175	184	3	operators	operator	NOUN
cana-2175	184	4	for	for	ADP
cana-2175	184	5	p	p	PRON
cana-2175	184	6	,	,	PUNCT
cana-2175	184	7	q	q	ADJ
cana-2175	184	8	,	,	PUNCT
cana-2175	184	9	r	r	NOUN
cana-2175	184	10	–	–	PUNCT
cana-2175	184	11	spherical	spherical	ADJ
cana-2175	184	12	fuzzy	fuzzy	ADJ
cana-2175	184	13	sets	set	NOUN
cana-2175	184	14	:	:	PUNCT
cana-2175	184	15	application	application	NOUN
cana-2175	184	16	in	in	ADP
cana-2175	184	17	the	the	DET
cana-2175	184	18	stability	stability	NOUN
cana-2175	184	19	assessment	assessment	NOUN
cana-2175	184	20	of	of	ADP
cana-2175	184	21	cryptocurrencies	cryptocurrencie	NOUN
cana-2175	184	22	.	.	PUNCT
cana-2175	185	1	ieee	ieee	NOUN
cana-2175	185	2	access	access	NOUN
cana-2175	185	3	.	.	PUNCT
cana-2175	186	1	[	[	X
cana-2175	186	2	4	4	NUM
cana-2175	186	3	]	]	X
cana-2175	186	4	fatima	fatima	PROPN
cana-2175	186	5	,	,	PUNCT
cana-2175	186	6	s.	s.	PROPN
cana-2175	186	7	,	,	PUNCT
cana-2175	186	8	sarwar	sarwar	PROPN
cana-2175	186	9	,	,	PUNCT
cana-2175	186	10	m.	m.	NOUN
cana-2175	186	11	,	,	PUNCT
cana-2175	186	12	&	&	CCONJ
cana-2175	186	13	zafar	zafar	PROPN
cana-2175	186	14	,	,	PUNCT
cana-2175	186	15	f.	f.	PROPN
cana-2175	186	16	(	(	PUNCT
cana-2175	186	17	2023	2023	NUM
cana-2175	186	18	)	)	PUNCT
cana-2175	186	19	.	.	PUNCT
cana-2175	187	1	rough	rough	ADJ
cana-2175	187	2	approximations	approximation	NOUN
cana-2175	187	3	of	of	ADP
cana-2175	187	4	similarity	similarity	NOUN
cana-2175	187	5	measures	measure	NOUN
cana-2175	187	6	under	under	ADP
cana-2175	187	7	pythagorean	pythagorean	PROPN
cana-2175	187	8	fuzzy	fuzzy	ADJ
cana-2175	187	9	information	information	NOUN
cana-2175	187	10	:	:	PUNCT
cana-2175	187	11	a	a	DET
cana-2175	187	12	novel	novel	ADJ
cana-2175	187	13	approach	approach	NOUN
cana-2175	187	14	to	to	ADP
cana-2175	187	15	decision	decision	NOUN
cana-2175	187	16	-	-	PUNCT
cana-2175	187	17	making	making	NOUN
cana-2175	187	18	.	.	PUNCT
cana-2175	188	1	soft	soft	ADJ
cana-2175	188	2	computing	computing	NOUN
cana-2175	188	3	,	,	PUNCT
cana-2175	188	4	1	1	NUM
cana-2175	188	5	-	-	SYM
cana-2175	188	6	25	25	NUM
cana-2175	188	7	.	.	PUNCT
cana-2175	189	1	[	[	X
cana-2175	189	2	5	5	NUM
cana-2175	189	3	]	]	X
cana-2175	189	4	de	de	PROPN
cana-2175	189	5	juan	juan	PROPN
cana-2175	189	6	,	,	PUNCT
cana-2175	189	7	a.	a.	PROPN
cana-2175	189	8	,	,	PUNCT
cana-2175	189	9	&	&	CCONJ
cana-2175	189	10	tauler	tauler	NOUN
cana-2175	189	11	,	,	PUNCT
cana-2175	189	12	r.	r.	PROPN
cana-2175	189	13	(	(	PUNCT
cana-2175	189	14	2021	2021	NUM
cana-2175	189	15	)	)	PUNCT
cana-2175	189	16	.	.	PUNCT
cana-2175	189	17	multivariate	multivariate	NOUN
cana-2175	189	18	curve	curve	NOUN
cana-2175	189	19	resolution	resolution	NOUN
cana-2175	189	20	:	:	PUNCT
cana-2175	189	21	50	50	NUM
cana-2175	189	22	years	year	NOUN
cana-2175	189	23	addressing	address	VERB
cana-2175	189	24	the	the	DET
cana-2175	189	25	mixture	mixture	NOUN
cana-2175	189	26	analysis	analysis	NOUN
cana-2175	189	27	problem	problem	NOUN
cana-2175	189	28	–	–	PUNCT
cana-2175	189	29	a	a	DET
cana-2175	189	30	review	review	NOUN
cana-2175	189	31	.	.	PUNCT
cana-2175	190	1	analytica	analytica	PROPN
cana-2175	190	2	chimica	chimica	PROPN
cana-2175	190	3	acta	acta	PROPN
cana-2175	190	4	,	,	PUNCT
cana-2175	190	5	1145	1145	NUM
cana-2175	190	6	,	,	PUNCT
cana-2175	190	7	59	59	NUM
cana-2175	190	8	-	-	SYM
cana-2175	190	9	78	78	NUM
cana-2175	190	10	.	.	PUNCT
cana-2175	191	1	communications	communication	NOUN
cana-2175	191	2	on	on	ADP
cana-2175	191	3	applied	apply	VERB
cana-2175	191	4	nonlinear	nonlinear	ADJ
cana-2175	191	5	analysis	analysis	NOUN
cana-2175	191	6	issn	issn	NOUN
cana-2175	191	7	:	:	PUNCT
cana-2175	191	8	1074	1074	NUM
cana-2175	191	9	-	-	PUNCT
cana-2175	191	10	133x	133x	NUM
cana-2175	191	11	vol	vol	NOUN
cana-2175	191	12	32	32	NUM
cana-2175	191	13	no	no	NOUN
cana-2175	191	14	.	.	PUNCT
cana-2175	192	1	1s	1s	NUM
cana-2175	192	2	(	(	PUNCT
cana-2175	192	3	2025	2025	NUM
cana-2175	192	4	)	)	PUNCT
cana-2175	192	5	334	334	NUM
cana-2175	192	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2175	193	1	[	[	X
cana-2175	193	2	6	6	NUM
cana-2175	193	3	]	]	X
cana-2175	193	4	coimbra	coimbra	NOUN
cana-2175	193	5	,	,	PUNCT
cana-2175	193	6	n.	n.	NOUN
cana-2175	193	7	,	,	PUNCT
cana-2175	193	8	gomes	gomes	PROPN
cana-2175	193	9	,	,	PUNCT
cana-2175	193	10	f.	f.	PROPN
cana-2175	193	11	,	,	PUNCT
cana-2175	193	12	michaelides	michaelide	NOUN
cana-2175	193	13	,	,	PUNCT
cana-2175	193	14	a.	a.	NOUN
cana-2175	193	15	,	,	PUNCT
cana-2175	193	16	&	&	CCONJ
cana-2175	193	17	shen	shen	PROPN
cana-2175	193	18	,	,	PUNCT
cana-2175	193	19	j.	j.	PROPN
cana-2175	193	20	(	(	PUNCT
cana-2175	193	21	2023	2023	NUM
cana-2175	193	22	)	)	PUNCT
cana-2175	193	23	.	.	PUNCT
cana-2175	194	1	asset	asset	NOUN
cana-2175	194	2	pricing	pricing	NOUN
cana-2175	194	3	and	and	CCONJ
cana-2175	194	4	risk	risk	NOUN
cana-2175	194	5	sharing	sharing	NOUN
cana-2175	194	6	implications	implication	NOUN
cana-2175	194	7	of	of	ADP
cana-2175	194	8	alternative	alternative	ADJ
cana-2175	194	9	pension	pension	NOUN
cana-2175	194	10	plan	plan	NOUN
cana-2175	194	11	systems	system	NOUN
cana-2175	194	12	.	.	PUNCT
cana-2175	195	1	available	available	ADJ
cana-2175	195	2	at	at	ADP
cana-2175	195	3	ssrn	ssrn	NOUN
cana-2175	195	4	4406011	4406011	NUM
cana-2175	195	5	.	.	PUNCT
cana-2175	196	1	[	[	X
cana-2175	196	2	7	7	NUM
cana-2175	196	3	]	]	X
cana-2175	196	4	escobar	escobar	PROPN
cana-2175	196	5	,	,	PUNCT
cana-2175	196	6	c.	c.	PROPN
cana-2175	196	7	a.	a.	PROPN
cana-2175	196	8	,	,	PUNCT
cana-2175	196	9	mcgovern	mcgovern	PROPN
cana-2175	196	10	,	,	PUNCT
cana-2175	196	11	m.	m.	PROPN
cana-2175	196	12	e.	e.	PROPN
cana-2175	196	13	,	,	PUNCT
cana-2175	196	14	&	&	CCONJ
cana-2175	196	15	morales	morales	PROPN
cana-2175	196	16	-	-	PUNCT
cana-2175	196	17	menendez	menendez	PROPN
cana-2175	196	18	,	,	PUNCT
cana-2175	196	19	r.	r.	PROPN
cana-2175	196	20	(	(	PUNCT
cana-2175	196	21	2021	2021	NUM
cana-2175	196	22	)	)	PUNCT
cana-2175	196	23	.	.	PUNCT
cana-2175	197	1	quality	quality	NOUN
cana-2175	197	2	4.0	4.0	NUM
cana-2175	197	3	:	:	PUNCT
cana-2175	197	4	a	a	DET
cana-2175	197	5	review	review	NOUN
cana-2175	197	6	of	of	ADP
cana-2175	197	7	big	big	ADJ
cana-2175	197	8	data	datum	NOUN
cana-2175	197	9	challenges	challenge	NOUN
cana-2175	197	10	in	in	ADP
cana-2175	197	11	manufacturing	manufacturing	NOUN
cana-2175	197	12	.	.	PUNCT
cana-2175	198	1	journal	journal	NOUN
cana-2175	198	2	of	of	ADP
cana-2175	198	3	intelligent	intelligent	ADJ
cana-2175	198	4	manufacturing	manufacturing	NOUN
cana-2175	198	5	,	,	PUNCT
cana-2175	198	6	32(8	32(8	NUM
cana-2175	198	7	)	)	PUNCT
cana-2175	198	8	,	,	PUNCT
cana-2175	198	9	2319	2319	NUM
cana-2175	198	10	-	-	SYM
cana-2175	198	11	2334	2334	NUM
cana-2175	198	12	.	.	PUNCT
cana-2175	199	1	[	[	X
cana-2175	199	2	8	8	NUM
cana-2175	199	3	]	]	X
cana-2175	199	4	chapman	chapman	PROPN
cana-2175	199	5	,	,	PUNCT
cana-2175	199	6	j.	j.	PROPN
cana-2175	199	7	,	,	PUNCT
cana-2175	199	8	truong	truong	PROPN
cana-2175	199	9	,	,	PUNCT
cana-2175	199	10	v.	v.	PROPN
cana-2175	199	11	k.	k.	PROPN
cana-2175	199	12	,	,	PUNCT
cana-2175	199	13	elbourne	elbourne	PROPN
cana-2175	199	14	,	,	PUNCT
cana-2175	199	15	a.	a.	NOUN
cana-2175	199	16	,	,	PUNCT
cana-2175	199	17	gangadoo	gangadoo	PROPN
cana-2175	199	18	,	,	PUNCT
cana-2175	199	19	s.	s.	PROPN
cana-2175	199	20	,	,	PUNCT
cana-2175	199	21	cheeseman	cheeseman	PROPN
cana-2175	199	22	,	,	PUNCT
cana-2175	199	23	s.	s.	PROPN
cana-2175	199	24	,	,	PUNCT
cana-2175	199	25	rajapaksha	rajapaksha	PROPN
cana-2175	199	26	,	,	PUNCT
cana-2175	199	27	p.	p.	PROPN
cana-2175	199	28	,	,	PUNCT
cana-2175	199	29	...	...	PUNCT
cana-2175	199	30	&	&	CCONJ
cana-2175	199	31	cozzolino	cozzolino	PROPN
cana-2175	199	32	,	,	PUNCT
cana-2175	199	33	d.	d.	PROPN
cana-2175	199	34	(	(	PUNCT
cana-2175	199	35	2020	2020	NUM
cana-2175	199	36	)	)	PUNCT
cana-2175	199	37	.	.	PUNCT
cana-2175	200	1	combining	combine	VERB
cana-2175	200	2	chemometrics	chemometric	NOUN
cana-2175	200	3	and	and	CCONJ
cana-2175	200	4	sensors	sensor	NOUN
cana-2175	200	5	:	:	PUNCT
cana-2175	200	6	toward	toward	ADP
cana-2175	200	7	new	new	ADJ
cana-2175	200	8	applications	application	NOUN
cana-2175	200	9	in	in	ADP
cana-2175	200	10	monitoring	monitoring	NOUN
cana-2175	200	11	and	and	CCONJ
cana-2175	200	12	environmental	environmental	ADJ
cana-2175	200	13	analysis	analysis	NOUN
cana-2175	200	14	.	.	PUNCT
cana-2175	201	1	chemical	chemical	NOUN
cana-2175	201	2	reviews	review	NOUN
cana-2175	201	3	,	,	PUNCT
cana-2175	201	4	120(13	120(13	NUM
cana-2175	201	5	)	)	PUNCT
cana-2175	201	6	,	,	PUNCT
cana-2175	201	7	6048	6048	NUM
cana-2175	201	8	-	-	SYM
cana-2175	201	9	6069	6069	NUM
cana-2175	201	10	.	.	PUNCT
cana-2175	202	1	[	[	X
cana-2175	202	2	9	9	NUM
cana-2175	202	3	]	]	X
cana-2175	202	4	akram	akram	NOUN
cana-2175	202	5	,	,	PUNCT
cana-2175	202	6	m.	m.	NOUN
cana-2175	202	7	,	,	PUNCT
cana-2175	202	8	ullah	ullah	PROPN
cana-2175	202	9	,	,	PUNCT
cana-2175	202	10	i.	i.	PROPN
cana-2175	202	11	,	,	PUNCT
cana-2175	202	12	allahviranloo	allahviranloo	NOUN
cana-2175	202	13	,	,	PUNCT
cana-2175	202	14	t.	t.	PROPN
cana-2175	202	15	,	,	PUNCT
cana-2175	202	16	&	&	CCONJ
cana-2175	202	17	edalatpanah	edalatpanah	PROPN
cana-2175	202	18	,	,	PUNCT
cana-2175	202	19	s.	s.	PROPN
cana-2175	202	20	a.	a.	PROPN
cana-2175	202	21	(	(	PUNCT
cana-2175	202	22	2021	2021	NUM
cana-2175	202	23	)	)	PUNCT
cana-2175	202	24	.	.	PUNCT
cana-2175	203	1	fully	fully	ADV
cana-2175	203	2	pythagorean	pythagorean	VERB
cana-2175	203	3	fuzzy	fuzzy	ADJ
cana-2175	203	4	linear	linear	ADJ
cana-2175	203	5	programming	programming	NOUN
cana-2175	203	6	problems	problem	NOUN
cana-2175	203	7	with	with	ADP
cana-2175	203	8	equality	equality	NOUN
cana-2175	203	9	constraints	constraint	NOUN
cana-2175	203	10	.	.	PUNCT
cana-2175	204	1	computational	computational	ADJ
cana-2175	204	2	and	and	CCONJ
cana-2175	204	3	applied	applied	ADJ
cana-2175	204	4	mathematics	mathematic	NOUN
cana-2175	204	5	,	,	PUNCT
cana-2175	204	6	40(4	40(4	NUM
cana-2175	204	7	)	)	PUNCT
cana-2175	204	8	,	,	PUNCT
cana-2175	204	9	120	120	NUM
cana-2175	204	10	.	.	PUNCT
cana-2175	205	1	[	[	X
cana-2175	205	2	10	10	NUM
cana-2175	205	3	]	]	X
cana-2175	205	4	thompson	thompson	PROPN
cana-2175	205	5	,	,	PUNCT
cana-2175	205	6	n.	n.	PROPN
cana-2175	205	7	b.	b.	PROPN
cana-2175	205	8	,	,	PUNCT
cana-2175	205	9	mulfort	mulfort	PROPN
cana-2175	205	10	,	,	PUNCT
cana-2175	205	11	k.	k.	PROPN
cana-2175	205	12	l.	l.	PROPN
cana-2175	205	13	,	,	PUNCT
cana-2175	205	14	&	&	CCONJ
cana-2175	205	15	tiede	tiede	PROPN
cana-2175	205	16	,	,	PUNCT
cana-2175	205	17	d.	d.	PROPN
cana-2175	205	18	m.	m.	PROPN
cana-2175	205	19	(	(	PUNCT
cana-2175	205	20	2024	2024	NUM
cana-2175	205	21	)	)	PUNCT
cana-2175	205	22	.	.	PUNCT
cana-2175	206	1	toward	toward	ADP
cana-2175	206	2	a	a	DET
cana-2175	206	3	quantitative	quantitative	ADJ
cana-2175	206	4	description	description	NOUN
cana-2175	206	5	of	of	ADP
cana-2175	206	6	solvation	solvation	NOUN
cana-2175	206	7	structure	structure	NOUN
cana-2175	206	8	:	:	PUNCT
cana-2175	206	9	a	a	DET
cana-2175	206	10	framework	framework	NOUN
cana-2175	206	11	for	for	ADP
cana-2175	206	12	differential	differential	ADJ
cana-2175	206	13	solution	solution	NOUN
cana-2175	206	14	scattering	scatter	VERB
cana-2175	206	15	measurements	measurement	NOUN
cana-2175	206	16	.	.	PUNCT
cana-2175	207	1	iucrj	iucrj	NOUN
cana-2175	207	2	,	,	PUNCT
cana-2175	207	3	11(pt	11(pt	NUM
cana-2175	207	4	3	3	NUM
cana-2175	207	5	)	)	PUNCT
cana-2175	207	6	,	,	PUNCT
cana-2175	207	7	423	423	NUM
cana-2175	207	8	.	.	PUNCT
cana-2175	208	1	[	[	X
cana-2175	208	2	11	11	NUM
cana-2175	208	3	]	]	PUNCT
cana-2175	208	4	gonnade	gonnade	NOUN
cana-2175	208	5	,	,	PUNCT
cana-2175	208	6	p.	p.	NOUN
cana-2175	208	7	,	,	PUNCT
cana-2175	208	8	&	&	CCONJ
cana-2175	208	9	ridhorkar	ridhorkar	NOUN
cana-2175	208	10	,	,	PUNCT
cana-2175	208	11	s.	s.	PROPN
cana-2175	208	12	(	(	PUNCT
cana-2175	208	13	2023	2023	NUM
cana-2175	208	14	)	)	PUNCT
cana-2175	208	15	.	.	PUNCT
cana-2175	209	1	empirical	empirical	ADJ
cana-2175	209	2	analysis	analysis	NOUN
cana-2175	209	3	of	of	ADP
cana-2175	209	4	decision	decision	NOUN
cana-2175	209	5	recommendation	recommendation	NOUN
cana-2175	209	6	models	model	NOUN
cana-2175	209	7	for	for	ADP
cana-2175	209	8	various	various	ADJ
cana-2175	209	9	processes	process	NOUN
cana-2175	209	10	from	from	ADP
cana-2175	209	11	a	a	DET
cana-2175	209	12	pragmatic	pragmatic	ADJ
cana-2175	209	13	perspective	perspective	NOUN
cana-2175	209	14	.	.	PUNCT
cana-2175	210	1	british	british	ADJ
cana-2175	210	2	journal	journal	PROPN
cana-2175	210	3	of	of	ADP
cana-2175	210	4	multidisciplinary	multidisciplinary	ADJ
cana-2175	210	5	and	and	CCONJ
cana-2175	210	6	advanced	advanced	ADJ
cana-2175	210	7	studies	study	NOUN
cana-2175	210	8	,	,	PUNCT
cana-2175	210	9	4(6	4(6	NUM
cana-2175	210	10	)	)	PUNCT
cana-2175	210	11	,	,	PUNCT
cana-2175	210	12	20	20	NUM
cana-2175	210	13	-	-	SYM
cana-2175	210	14	49	49	NUM
cana-2175	210	15	.	.	PUNCT
cana-2175	211	1	[	[	X
cana-2175	211	2	12	12	NUM
cana-2175	211	3	]	]	PUNCT
cana-2175	211	4	auluck	auluck	NOUN
cana-2175	211	5	,	,	PUNCT
cana-2175	211	6	s.	s.	PROPN
cana-2175	211	7	,	,	PUNCT
cana-2175	211	8	kubes	kube	NOUN
cana-2175	211	9	,	,	PUNCT
cana-2175	211	10	p.	p.	NOUN
cana-2175	211	11	,	,	PUNCT
cana-2175	211	12	paduch	paduch	NOUN
cana-2175	211	13	,	,	PUNCT
cana-2175	211	14	m.	m.	NOUN
cana-2175	211	15	,	,	PUNCT
cana-2175	211	16	sadowski	sadowski	PROPN
cana-2175	211	17	,	,	PUNCT
cana-2175	211	18	m.	m.	PROPN
cana-2175	211	19	j.	j.	PROPN
cana-2175	211	20	,	,	PUNCT
cana-2175	211	21	krauz	krauz	PROPN
cana-2175	211	22	,	,	PUNCT
cana-2175	211	23	v.	v.	PROPN
cana-2175	211	24	i.	i.	PROPN
cana-2175	211	25	,	,	PUNCT
cana-2175	211	26	lee	lee	PROPN
cana-2175	211	27	,	,	PUNCT
cana-2175	211	28	s.	s.	PROPN
cana-2175	211	29	,	,	PUNCT
cana-2175	211	30	...	...	PUNCT
cana-2175	211	31	&	&	CCONJ
cana-2175	211	32	laas	laas	PROPN
cana-2175	211	33	,	,	PUNCT
cana-2175	211	34	t.	t.	NOUN
cana-2175	211	35	(	(	PUNCT
cana-2175	211	36	2021	2021	NUM
cana-2175	211	37	)	)	PUNCT
cana-2175	211	38	.	.	PUNCT
cana-2175	212	1	update	update	NOUN
cana-2175	212	2	on	on	ADP
cana-2175	212	3	the	the	DET
cana-2175	212	4	scientific	scientific	ADJ
cana-2175	212	5	status	status	NOUN
cana-2175	212	6	of	of	ADP
cana-2175	212	7	the	the	DET
cana-2175	212	8	plasma	plasma	NOUN
cana-2175	212	9	focus	focus	NOUN
cana-2175	212	10	.	.	PUNCT
cana-2175	213	1	plasma	plasma	NOUN
cana-2175	213	2	,	,	PUNCT
cana-2175	213	3	4(3	4(3	NUM
cana-2175	213	4	)	)	PUNCT
cana-2175	213	5	,	,	PUNCT
cana-2175	213	6	450	450	NUM
cana-2175	213	7	-	-	SYM
cana-2175	213	8	669	669	NUM
cana-2175	213	9	.	.	PUNCT
cana-2175	214	1	[	[	X
cana-2175	214	2	13	13	NUM
cana-2175	214	3	]	]	SYM
cana-2175	214	4	thakkar	thakkar	NOUN
cana-2175	214	5	,	,	PUNCT
cana-2175	214	6	j.	j.	PROPN
cana-2175	214	7	j.	j.	PROPN
cana-2175	214	8	(	(	PUNCT
cana-2175	214	9	2021	2021	NUM
cana-2175	214	10	)	)	PUNCT
cana-2175	214	11	.	.	PUNCT
cana-2175	215	1	multi	multi	ADJ
cana-2175	215	2	-	-	ADJ
cana-2175	215	3	criteria	criterion	NOUN
cana-2175	215	4	decision	decision	NOUN
cana-2175	215	5	making	making	NOUN
cana-2175	215	6	(	(	PUNCT
cana-2175	215	7	vol	vol	NOUN
cana-2175	215	8	.	.	NOUN
cana-2175	215	9	336	336	NUM
cana-2175	215	10	,	,	PUNCT
cana-2175	215	11	pp	pp	ADJ
cana-2175	215	12	.	.	PUNCT
cana-2175	216	1	1	1	NUM
cana-2175	216	2	-	-	SYM
cana-2175	216	3	365	365	NUM
cana-2175	216	4	)	)	PUNCT
cana-2175	216	5	.	.	PUNCT
cana-2175	217	1	singapore	singapore	PROPN
cana-2175	217	2	:	:	PUNCT
cana-2175	217	3	springer	springer	NOUN
cana-2175	217	4	.	.	PUNCT
cana-2175	218	1	[	[	X
cana-2175	218	2	14	14	NUM
cana-2175	218	3	]	]	X
cana-2175	218	4	çelik	çelik	NOUN
cana-2175	218	5	,	,	PUNCT
cana-2175	218	6	m.	m.	NOUN
cana-2175	218	7	(	(	PUNCT
cana-2175	218	8	2021	2021	NUM
cana-2175	218	9	)	)	PUNCT
cana-2175	218	10	.	.	PUNCT
cana-2175	219	1	26	26	NUM
cana-2175	219	2	use	use	NOUN
cana-2175	219	3	of	of	ADP
cana-2175	219	4	artificial	artificial	ADJ
cana-2175	219	5	intelligence	intelligence	NOUN
cana-2175	219	6	and	and	CCONJ
cana-2175	219	7	expert	expert	NOUN
cana-2175	219	8	systems	system	NOUN
cana-2175	219	9	in	in	ADP
cana-2175	219	10	pharmaceutical	pharmaceutical	ADJ
cana-2175	219	11	applications	application	NOUN
cana-2175	219	12	.	.	PUNCT
cana-2175	220	1	in	in	ADP
cana-2175	220	2	handbook	handbook	NOUN
cana-2175	220	3	of	of	ADP
cana-2175	220	4	pharmaceutical	pharmaceutical	NOUN
cana-2175	220	5	granulation	granulation	NOUN
cana-2175	220	6	technology	technology	NOUN
cana-2175	220	7	:	:	PUNCT
cana-2175	220	8	fourth	fourth	ADJ
cana-2175	220	9	edition	edition	NOUN
cana-2175	220	10	(	(	PUNCT
cana-2175	220	11	pp	pp	ADJ
cana-2175	220	12	.	.	PUNCT
cana-2175	220	13	765	765	NUM
cana-2175	220	14	-	-	SYM
cana-2175	220	15	800	800	NUM
cana-2175	220	16	)	)	PUNCT
cana-2175	220	17	.	.	PUNCT
cana-2175	221	1	crc	crc	PROPN
cana-2175	221	2	press	press	PROPN
cana-2175	221	3	.	.	PUNCT
cana-2175	222	1	[	[	X
cana-2175	222	2	15	15	NUM
cana-2175	222	3	]	]	X
cana-2175	222	4	sahoo	sahoo	PROPN
cana-2175	222	5	,	,	PUNCT
cana-2175	222	6	s.	s.	PROPN
cana-2175	222	7	k.	k.	PROPN
cana-2175	222	8	,	,	PUNCT
cana-2175	222	9	&	&	CCONJ
cana-2175	222	10	goswami	goswami	PROPN
cana-2175	222	11	,	,	PUNCT
cana-2175	222	12	s.	s.	PROPN
cana-2175	222	13	s.	s.	PROPN
cana-2175	222	14	(	(	PUNCT
cana-2175	222	15	2023	2023	NUM
cana-2175	222	16	)	)	PUNCT
cana-2175	222	17	.	.	PUNCT
cana-2175	223	1	a	a	DET
cana-2175	223	2	comprehensive	comprehensive	ADJ
cana-2175	223	3	review	review	NOUN
cana-2175	223	4	of	of	ADP
cana-2175	223	5	multiple	multiple	ADJ
cana-2175	223	6	criteria	criterion	NOUN
cana-2175	223	7	decision	decision	NOUN
cana-2175	223	8	-	-	PUNCT
cana-2175	223	9	making	making	NOUN
cana-2175	223	10	(	(	PUNCT
cana-2175	223	11	mcdm	mcdm	ADJ
cana-2175	223	12	)	)	PUNCT
cana-2175	223	13	methods	method	NOUN
cana-2175	223	14	:	:	PUNCT
cana-2175	223	15	advancements	advancement	NOUN
cana-2175	223	16	,	,	PUNCT
cana-2175	223	17	applications	application	NOUN
cana-2175	223	18	,	,	PUNCT
cana-2175	223	19	and	and	CCONJ
cana-2175	223	20	future	future	ADJ
cana-2175	223	21	directions	direction	NOUN
cana-2175	223	22	.	.	PUNCT
cana-2175	224	1	decision	decision	NOUN
cana-2175	224	2	making	make	VERB
cana-2175	224	3	advances	advance	NOUN
cana-2175	224	4	,	,	PUNCT
cana-2175	224	5	1(1	1(1	NUM
cana-2175	224	6	)	)	PUNCT
cana-2175	224	7	,	,	PUNCT
cana-2175	224	8	25	25	NUM
cana-2175	224	9	-	-	SYM
cana-2175	224	10	48	48	NUM
cana-2175	224	11	.	.	PUNCT