id	sid	tid	token	lemma	pos
cana-945	1	1	communications	communication	NOUN
cana-945	1	2	on	on	ADP
cana-945	1	3	applied	apply	VERB
cana-945	1	4	nonlinear	nonlinear	ADJ
cana-945	1	5	analysis	analysis	NOUN
cana-945	1	6	issn	issn	NOUN
cana-945	1	7	:	:	PUNCT
cana-945	1	8	1074	1074	NUM
cana-945	1	9	-	-	PUNCT
cana-945	1	10	133x	133x	NUM
cana-945	1	11	vol	vol	NOUN
cana-945	1	12	31	31	NUM
cana-945	1	13	no	no	NOUN
cana-945	1	14	.	.	PUNCT
cana-945	2	1	4s	4s	NUM
cana-945	2	2	(	(	PUNCT
cana-945	2	3	2024	2024	NUM
cana-945	2	4	)	)	PUNCT
cana-945	2	5	500	500	NUM
cana-945	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-945	2	7	theoretical	theoretical	ADJ
cana-945	2	8	foundation	foundation	NOUN
cana-945	2	9	,	,	PUNCT
cana-945	2	10	topological	topological	ADJ
cana-945	2	11	technique	technique	NOUN
cana-945	2	12	,	,	PUNCT
cana-945	2	13	and	and	CCONJ
cana-945	2	14	decision	decision	NOUN
cana-945	2	15	-	-	PUNCT
cana-945	2	16	making	make	VERB
cana-945	2	17	application	application	NOUN
cana-945	2	18	of	of	ADP
cana-945	2	19	intuitionistic	intuitionistic	ADJ
cana-945	2	20	fuzzy	fuzzy	ADJ
cana-945	2	21	d	d	NOUN
cana-945	2	22	-	-	ADJ
cana-945	2	23	algebra	algebra	ADJ
cana-945	2	24	m.	m.	NOUN
cana-945	2	25	siva1	siva1	PROPN
cana-945	2	26	,	,	PUNCT
cana-945	2	27	a.jeeva2	a.jeeva2	PROPN
cana-945	2	28	,	,	PUNCT
cana-945	2	29	s.	s.	PROPN
cana-945	2	30	kathirvizhi3	kathirvizhi3	PROPN
cana-945	2	31	,	,	PUNCT
cana-945	2	32	n.	n.	PROPN
cana-945	2	33	kumaran4	kumaran4	PROPN
cana-945	3	1	1assistant	1assistant	NUM
cana-945	3	2	professor	professor	NOUN
cana-945	3	3	,	,	PUNCT
cana-945	3	4	department	department	NOUN
cana-945	3	5	of	of	ADP
cana-945	3	6	mathematics	mathematics	PROPN
cana-945	3	7	,	,	PUNCT
cana-945	3	8	st	st	PROPN
cana-945	3	9	.	.	PROPN
cana-945	3	10	joseph	joseph	PROPN
cana-945	3	11	's	's	PART
cana-945	3	12	institute	institute	PROPN
cana-945	3	13	of	of	ADP
cana-945	3	14	technology	technology	PROPN
cana-945	3	15	,	,	PUNCT
cana-945	3	16	chennai	chennai	PROPN
cana-945	3	17	,	,	PUNCT
cana-945	3	18	tamil	tamil	PROPN
cana-945	3	19	nadu	nadu	PROPN
cana-945	3	20	600119	600119	NUM
cana-945	3	21	,	,	PUNCT
cana-945	3	22	india	india	PROPN
cana-945	3	23	.	.	PUNCT
cana-945	4	1	sivam@stjosephstechnology.ac.in	sivam@stjosephstechnology.ac.in	PROPN
cana-945	4	2	2assistant	2assistant	PROPN
cana-945	4	3	professor	professor	NOUN
cana-945	4	4	,	,	PUNCT
cana-945	4	5	vel	vel	PROPN
cana-945	4	6	tech	tech	NOUN
cana-945	4	7	rangarajan	rangarajan	NOUN
cana-945	4	8	dr.sagunthala	dr.sagunthala	NOUN
cana-945	4	9	r&d	r&d	PROPN
cana-945	4	10	institute	institute	PROPN
cana-945	4	11	of	of	ADP
cana-945	4	12	science	science	NOUN
cana-945	4	13	and	and	CCONJ
cana-945	4	14	technology	technology	NOUN
cana-945	4	15	,	,	PUNCT
cana-945	4	16	avadi	avadi	NOUN
cana-945	4	17	,	,	PUNCT
cana-945	4	18	chennai	chennai	NOUN
cana-945	4	19	600062	600062	NUM
cana-945	4	20	.	.	PUNCT
cana-945	5	1	drjeevaa@veltech.edu.in	drjeevaa@veltech.edu.in	NOUN
cana-945	5	2	3assistant	3assistant	NUM
cana-945	5	3	professor	professor	NOUN
cana-945	5	4	jeppiaar	jeppiaar	PROPN
cana-945	5	5	university	university	PROPN
cana-945	5	6	,	,	PUNCT
cana-945	5	7	omr	omr	NOUN
cana-945	5	8	road	road	NOUN
cana-945	5	9	semmanchery	semmanchery	NOUN
cana-945	5	10	,	,	PUNCT
cana-945	5	11	chennai-600119,tamil	chennai-600119,tamil	ADP
cana-945	5	12	nadu.india	nadu.india	NUM
cana-945	5	13	.	.	PUNCT
cana-945	6	1	kathirvizhi02@gmail.com	kathirvizhi02@gmail.com	X
cana-945	7	1	4assistant	4assistant	NUM
cana-945	7	2	professor	professor	NOUN
cana-945	7	3	,	,	PUNCT
cana-945	7	4	department	department	NOUN
cana-945	7	5	of	of	ADP
cana-945	7	6	mathematics	mathematic	NOUN
cana-945	7	7	,	,	PUNCT
cana-945	7	8	vel	vel	PROPN
cana-945	7	9	tech	tech	PROPN
cana-945	7	10	rangarajan	rangarajan	PROPN
cana-945	7	11	dr	dr	PROPN
cana-945	7	12	.	.	PROPN
cana-945	7	13	sagunthala	sagunthala	PROPN
cana-945	7	14	r&d	r&d	PROPN
cana-945	7	15	institute	institute	PROPN
cana-945	7	16	of	of	ADP
cana-945	7	17	science	science	NOUN
cana-945	7	18	and	and	CCONJ
cana-945	7	19	technology	technology	NOUN
cana-945	7	20	,	,	PUNCT
cana-945	7	21	avadi	avadi	NOUN
cana-945	7	22	,	,	PUNCT
cana-945	7	23	chennai	chennai	NOUN
cana-945	7	24	600062	600062	NUM
cana-945	7	25	.	.	PUNCT
cana-945	8	1	nkumaran@veltech.edu.in	nkumaran@veltech.edu.in	NOUN
cana-945	8	2	article	article	NOUN
cana-945	8	3	history	history	NOUN
cana-945	8	4	:	:	PUNCT
cana-945	8	5	received	receive	VERB
cana-945	8	6	:	:	PUNCT
cana-945	8	7	20	20	NUM
cana-945	8	8	-	-	PUNCT
cana-945	8	9	04	04	NUM
cana-945	8	10	-	-	PUNCT
cana-945	8	11	2024	2024	NUM
cana-945	8	12	revised	revise	VERB
cana-945	8	13	:	:	PUNCT
cana-945	8	14	10	10	NUM
cana-945	8	15	-	-	SYM
cana-945	8	16	06	06	NUM
cana-945	8	17	-	-	PUNCT
cana-945	8	18	2024	2024	NUM
cana-945	8	19	accepted	accept	VERB
cana-945	8	20	:	:	PUNCT
cana-945	8	21	28	28	NUM
cana-945	8	22	-	-	SYM
cana-945	8	23	06	06	NUM
cana-945	8	24	-	-	PUNCT
cana-945	8	25	2024	2024	NUM
cana-945	8	26	abstract	abstract	NOUN
cana-945	8	27	:	:	PUNCT
cana-945	8	28	intuitionistic	intuitionistic	ADJ
cana-945	8	29	fuzzy	fuzzy	ADJ
cana-945	8	30	d	d	NOUN
cana-945	8	31	-	-	PUNCT
cana-945	8	32	algebra	algebra	NOUN
cana-945	8	33	introduces	introduce	VERB
cana-945	8	34	a	a	DET
cana-945	8	35	novel	novel	ADJ
cana-945	8	36	framework	framework	NOUN
cana-945	8	37	extending	extend	VERB
cana-945	8	38	classical	classical	ADJ
cana-945	8	39	fuzzy	fuzzy	ADJ
cana-945	8	40	algebra	algebra	NOUN
cana-945	8	41	by	by	ADP
cana-945	8	42	incorporating	incorporate	VERB
cana-945	8	43	degrees	degree	NOUN
cana-945	8	44	of	of	ADP
cana-945	8	45	membership	membership	NOUN
cana-945	8	46	and	and	CCONJ
cana-945	8	47	non	non	ADJ
cana-945	8	48	-	-	NOUN
cana-945	8	49	membership	membership	NOUN
cana-945	8	50	.	.	PUNCT
cana-945	9	1	this	this	DET
cana-945	9	2	approach	approach	NOUN
cana-945	9	3	addresses	address	VERB
cana-945	9	4	the	the	DET
cana-945	9	5	inherent	inherent	ADJ
cana-945	9	6	uncertainty	uncertainty	NOUN
cana-945	9	7	and	and	CCONJ
cana-945	9	8	imprecision	imprecision	NOUN
cana-945	9	9	in	in	ADP
cana-945	9	10	real	real	ADJ
cana-945	9	11	-	-	PUNCT
cana-945	9	12	world	world	NOUN
cana-945	9	13	systems	system	NOUN
cana-945	9	14	.	.	PUNCT
cana-945	10	1	topological	topological	ADJ
cana-945	10	2	techniques	technique	NOUN
cana-945	10	3	facilitate	facilitate	VERB
cana-945	10	4	the	the	DET
cana-945	10	5	analysis	analysis	NOUN
cana-945	10	6	of	of	ADP
cana-945	10	7	convergence	convergence	NOUN
cana-945	10	8	and	and	CCONJ
cana-945	10	9	continuity	continuity	NOUN
cana-945	10	10	properties	property	NOUN
cana-945	10	11	,	,	PUNCT
cana-945	10	12	ensuring	ensure	VERB
cana-945	10	13	the	the	DET
cana-945	10	14	robustness	robustness	NOUN
cana-945	10	15	of	of	ADP
cana-945	10	16	mathematical	mathematical	ADJ
cana-945	10	17	models	model	NOUN
cana-945	10	18	.	.	PUNCT
cana-945	11	1	the	the	DET
cana-945	11	2	need	need	NOUN
cana-945	11	3	for	for	ADP
cana-945	11	4	such	such	DET
cana-945	11	5	a	a	DET
cana-945	11	6	framework	framework	NOUN
cana-945	11	7	arises	arise	VERB
cana-945	11	8	from	from	ADP
cana-945	11	9	the	the	DET
cana-945	11	10	limitations	limitation	NOUN
cana-945	11	11	of	of	ADP
cana-945	11	12	classical	classical	ADJ
cana-945	11	13	fuzzy	fuzzy	ADJ
cana-945	11	14	algebra	algebra	NOUN
cana-945	11	15	in	in	ADP
cana-945	11	16	capturing	capture	VERB
cana-945	11	17	nuanced	nuanced	ADJ
cana-945	11	18	degrees	degree	NOUN
cana-945	11	19	of	of	ADP
cana-945	11	20	uncertainty	uncertainty	NOUN
cana-945	11	21	.	.	PUNCT
cana-945	12	1	realworld	realworld	PROPN
cana-945	12	2	decision	decision	NOUN
cana-945	12	3	-	-	PUNCT
cana-945	12	4	making	make	VERB
cana-945	12	5	processes	process	NOUN
cana-945	12	6	often	often	ADV
cana-945	12	7	involve	involve	VERB
cana-945	12	8	complex	complex	ADJ
cana-945	12	9	,	,	PUNCT
cana-945	12	10	ambiguous	ambiguous	ADJ
cana-945	12	11	information	information	NOUN
cana-945	12	12	that	that	PRON
cana-945	12	13	can	can	AUX
cana-945	12	14	not	not	PART
cana-945	12	15	be	be	AUX
cana-945	12	16	adequately	adequately	ADV
cana-945	12	17	represented	represent	VERB
cana-945	12	18	by	by	ADP
cana-945	12	19	binary	binary	ADJ
cana-945	12	20	membership	membership	NOUN
cana-945	12	21	functions	function	NOUN
cana-945	12	22	alone	alone	ADV
cana-945	12	23	.	.	PUNCT
cana-945	13	1	intuitionistic	intuitionistic	ADJ
cana-945	13	2	fuzzy	fuzzy	ADJ
cana-945	13	3	d	d	NOUN
cana-945	13	4	-	-	PUNCT
cana-945	13	5	algebra	algebra	NOUN
cana-945	13	6	offers	offer	VERB
cana-945	13	7	a	a	DET
cana-945	13	8	more	more	ADV
cana-945	13	9	nuanced	nuanced	ADJ
cana-945	13	10	representation	representation	NOUN
cana-945	13	11	,	,	PUNCT
cana-945	13	12	expressing	express	VERB
cana-945	13	13	hesitation	hesitation	NOUN
cana-945	13	14	and	and	CCONJ
cana-945	13	15	uncertainty	uncertainty	NOUN
cana-945	13	16	inherent	inherent	ADJ
cana-945	13	17	in	in	ADP
cana-945	13	18	decision	decision	NOUN
cana-945	13	19	-	-	PUNCT
cana-945	13	20	making	make	VERB
cana-945	13	21	contexts	context	NOUN
cana-945	13	22	.	.	PUNCT
cana-945	14	1	the	the	DET
cana-945	14	2	proposed	propose	VERB
cana-945	14	3	work	work	NOUN
cana-945	14	4	comprehensively	comprehensively	ADV
cana-945	14	5	explores	explore	VERB
cana-945	14	6	intuitionistic	intuitionistic	ADJ
cana-945	14	7	fuzzy	fuzzy	ADJ
cana-945	14	8	d	d	NOUN
cana-945	14	9	-	-	NOUN
cana-945	14	10	algebra	algebra	NOUN
cana-945	14	11	,	,	PUNCT
cana-945	14	12	including	include	VERB
cana-945	14	13	the	the	DET
cana-945	14	14	formal	formal	ADJ
cana-945	14	15	definition	definition	NOUN
cana-945	14	16	of	of	ADP
cana-945	14	17	core	core	NOUN
cana-945	14	18	structures	structure	NOUN
cana-945	14	19	,	,	PUNCT
cana-945	14	20	mathematical	mathematical	ADJ
cana-945	14	21	modelling	modelling	NOUN
cana-945	14	22	,	,	PUNCT
cana-945	14	23	validation	validation	NOUN
cana-945	14	24	strategies	strategy	NOUN
cana-945	14	25	through	through	ADP
cana-945	14	26	examples	example	NOUN
cana-945	14	27	and	and	CCONJ
cana-945	14	28	counterexamples	counterexample	NOUN
cana-945	14	29	,	,	PUNCT
cana-945	14	30	and	and	CCONJ
cana-945	14	31	the	the	DET
cana-945	14	32	development	development	NOUN
cana-945	14	33	of	of	ADP
cana-945	14	34	interactive	interactive	ADJ
cana-945	14	35	visualizations	visualization	NOUN
cana-945	14	36	.	.	PUNCT
cana-945	15	1	by	by	ADP
cana-945	15	2	integrating	integrate	VERB
cana-945	15	3	computational	computational	ADJ
cana-945	15	4	tools	tool	NOUN
cana-945	15	5	and	and	CCONJ
cana-945	15	6	theoretical	theoretical	ADJ
cana-945	15	7	insights	insight	NOUN
cana-945	15	8	,	,	PUNCT
cana-945	15	9	this	this	DET
cana-945	15	10	framework	framework	NOUN
cana-945	15	11	provides	provide	VERB
cana-945	15	12	a	a	DET
cana-945	15	13	versatile	versatile	ADJ
cana-945	15	14	platform	platform	NOUN
cana-945	15	15	for	for	ADP
cana-945	15	16	addressing	address	VERB
cana-945	15	17	uncertainty	uncertainty	NOUN
cana-945	15	18	in	in	ADP
cana-945	15	19	various	various	ADJ
cana-945	15	20	domains	domain	NOUN
cana-945	15	21	,	,	PUNCT
cana-945	15	22	from	from	ADP
cana-945	15	23	decision	decision	NOUN
cana-945	15	24	-	-	PUNCT
cana-945	15	25	making	make	VERB
cana-945	15	26	systems	system	NOUN
cana-945	15	27	to	to	ADP
cana-945	15	28	artificial	artificial	ADJ
cana-945	15	29	intelligence	intelligence	NOUN
cana-945	15	30	,	,	PUNCT
cana-945	15	31	thus	thus	ADV
cana-945	15	32	paving	pave	VERB
cana-945	15	33	the	the	DET
cana-945	15	34	way	way	NOUN
cana-945	15	35	for	for	ADP
cana-945	15	36	innovative	innovative	ADJ
cana-945	15	37	solutions	solution	NOUN
cana-945	15	38	and	and	CCONJ
cana-945	15	39	improved	improved	ADJ
cana-945	15	40	decision	decision	NOUN
cana-945	15	41	outcomes	outcome	NOUN
cana-945	15	42	.	.	PUNCT
cana-945	16	1	the	the	DET
cana-945	16	2	results	result	NOUN
cana-945	16	3	provide	provide	VERB
cana-945	16	4	an	an	DET
cana-945	16	5	immersive	immersive	ADJ
cana-945	16	6	exploration	exploration	NOUN
cana-945	16	7	into	into	ADP
cana-945	16	8	the	the	DET
cana-945	16	9	intricacies	intricacy	NOUN
cana-945	16	10	of	of	ADP
cana-945	16	11	intuitionistic	intuitionistic	ADJ
cana-945	16	12	fuzzy	fuzzy	ADJ
cana-945	16	13	d	d	NOUN
cana-945	16	14	-	-	NOUN
cana-945	16	15	algebra	algebra	NOUN
cana-945	16	16	.	.	PUNCT
cana-945	17	1	from	from	ADP
cana-945	17	2	the	the	DET
cana-945	17	3	transformation	transformation	NOUN
cana-945	17	4	of	of	ADP
cana-945	17	5	fuzzy	fuzzy	ADJ
cana-945	17	6	sets	set	NOUN
cana-945	17	7	into	into	ADP
cana-945	17	8	topological	topological	ADJ
cana-945	17	9	spaces	space	NOUN
cana-945	17	10	to	to	ADP
cana-945	17	11	the	the	DET
cana-945	17	12	dynamic	dynamic	ADJ
cana-945	17	13	manipulation	manipulation	NOUN
cana-945	17	14	of	of	ADP
cana-945	17	15	algebraic	algebraic	ADJ
cana-945	17	16	operations	operation	NOUN
cana-945	17	17	,	,	PUNCT
cana-945	17	18	each	each	DET
cana-945	17	19	visualization	visualization	NOUN
cana-945	17	20	offers	offer	VERB
cana-945	17	21	an	an	DET
cana-945	17	22	intense	intense	ADJ
cana-945	17	23	dive	dive	NOUN
cana-945	17	24	into	into	ADP
cana-945	17	25	understanding	understand	VERB
cana-945	17	26	uncertainty	uncertainty	NOUN
cana-945	17	27	and	and	CCONJ
cana-945	17	28	imprecision	imprecision	NOUN
cana-945	17	29	.	.	PUNCT
cana-945	18	1	the	the	DET
cana-945	18	2	visuals	visual	NOUN
cana-945	18	3	serve	serve	VERB
cana-945	18	4	as	as	ADP
cana-945	18	5	powerful	powerful	ADJ
cana-945	18	6	educational	educational	ADJ
cana-945	18	7	tools	tool	NOUN
cana-945	18	8	,	,	PUNCT
cana-945	18	9	enabling	enable	VERB
cana-945	18	10	a	a	DET
cana-945	18	11	profound	profound	ADJ
cana-945	18	12	grasp	grasp	NOUN
cana-945	18	13	of	of	ADP
cana-945	18	14	complex	complex	ADJ
cana-945	18	15	mathematical	mathematical	ADJ
cana-945	18	16	concepts	concept	NOUN
cana-945	18	17	and	and	CCONJ
cana-945	18	18	their	their	PRON
cana-945	18	19	practical	practical	ADJ
cana-945	18	20	implications	implication	NOUN
cana-945	18	21	in	in	ADP
cana-945	18	22	decision	decision	NOUN
cana-945	18	23	-	-	PUNCT
cana-945	18	24	making	make	VERB
cana-945	18	25	systems	system	NOUN
cana-945	18	26	and	and	CCONJ
cana-945	18	27	artificial	artificial	ADJ
cana-945	18	28	intelligence	intelligence	NOUN
cana-945	18	29	.	.	PUNCT
cana-945	19	1	keywords	keyword	NOUN
cana-945	19	2	:	:	PUNCT
cana-945	19	3	intuitionistic	intuitionistic	ADJ
cana-945	19	4	fuzzy	fuzzy	ADJ
cana-945	19	5	d	d	NOUN
cana-945	19	6	-	-	PUNCT
cana-945	19	7	algebra	algebra	ADJ
cana-945	19	8	,	,	PUNCT
cana-945	19	9	topological	topological	ADJ
cana-945	19	10	techniques	technique	NOUN
cana-945	19	11	,	,	PUNCT
cana-945	19	12	classical	classical	ADJ
cana-945	19	13	fuzzy	fuzzy	ADJ
cana-945	19	14	algebra	algebra	NOUN
cana-945	19	15	,	,	PUNCT
cana-945	19	16	mathematical	mathematical	ADJ
cana-945	19	17	modelling	modelling	NOUN
cana-945	19	18	,	,	PUNCT
cana-945	19	19	validation	validation	NOUN
cana-945	19	20	strategies	strategy	NOUN
cana-945	19	21	,	,	PUNCT
cana-945	19	22	decision	decision	NOUN
cana-945	19	23	-	-	PUNCT
cana-945	19	24	making	make	VERB
cana-945	19	25	systems	system	NOUN
cana-945	19	26	,	,	PUNCT
cana-945	19	27	artificial	artificial	ADJ
cana-945	19	28	intelligence	intelligence	NOUN
cana-945	19	29	.	.	PUNCT
cana-945	20	1	1	1	X
cana-945	20	2	.	.	X
cana-945	20	3	introduction	introduction	NOUN
cana-945	20	4	the	the	DET
cana-945	20	5	exploration	exploration	NOUN
cana-945	20	6	of	of	ADP
cana-945	20	7	abstract	abstract	ADJ
cana-945	20	8	algebraic	algebraic	ADJ
cana-945	20	9	structures	structure	NOUN
cana-945	20	10	has	have	AUX
cana-945	20	11	led	lead	VERB
cana-945	20	12	to	to	ADP
cana-945	20	13	the	the	DET
cana-945	20	14	introduction	introduction	NOUN
cana-945	20	15	of	of	ADP
cana-945	20	16	various	various	ADJ
cana-945	20	17	algebras	algebra	NOUN
cana-945	20	18	and	and	CCONJ
cana-945	20	19	their	their	PRON
cana-945	20	20	generalizations	generalization	NOUN
cana-945	20	21	,	,	PUNCT
cana-945	20	22	which	which	PRON
cana-945	20	23	play	play	VERB
cana-945	20	24	a	a	DET
cana-945	20	25	crucial	crucial	ADJ
cana-945	20	26	role	role	NOUN
cana-945	20	27	in	in	ADP
cana-945	20	28	mathematical	mathematical	ADJ
cana-945	20	29	logic	logic	NOUN
cana-945	20	30	and	and	CCONJ
cana-945	20	31	theoretical	theoretical	ADJ
cana-945	20	32	computer	computer	NOUN
cana-945	20	33	science	science	NOUN
cana-945	20	34	.	.	PUNCT
cana-945	21	1	among	among	ADP
cana-945	21	2	these	these	PRON
cana-945	21	3	,	,	PUNCT
cana-945	21	4	bck	bck	VERB
cana-945	21	5	-	-	PUNCT
cana-945	21	6	algebras	algebras	PROPN
cana-945	21	7	and	and	CCONJ
cana-945	21	8	bci	bci	NOUN
cana-945	21	9	-	-	PUNCT
cana-945	21	10	algebras	algebra	NOUN
cana-945	21	11	form	form	VERB
cana-945	21	12	fundamental	fundamental	ADJ
cana-945	21	13	classes	class	NOUN
cana-945	21	14	with	with	ADP
cana-945	21	15	intriguing	intriguing	ADJ
cana-945	21	16	properties	property	NOUN
cana-945	21	17	.	.	PUNCT
cana-945	22	1	bck	bck	VERB
cana-945	22	2	-	-	PUNCT
cana-945	22	3	algebras	algebras	PROPN
cana-945	22	4	are	be	AUX
cana-945	22	5	a	a	DET
cana-945	22	6	subset	subset	NOUN
cana-945	22	7	of	of	ADP
cana-945	22	8	the	the	DET
cana-945	22	9	more	more	ADV
cana-945	22	10	general	general	ADJ
cana-945	22	11	bci	bci	NOUN
cana-945	22	12	-	-	PUNCT
cana-945	22	13	algebras	algebra	NOUN
cana-945	22	14	,	,	PUNCT
cana-945	22	15	distinguished	distinguish	VERB
cana-945	22	16	by	by	ADP
cana-945	22	17	certain	certain	ADJ
cana-945	22	18	communications	communication	NOUN
cana-945	22	19	on	on	ADP
cana-945	22	20	applied	apply	VERB
cana-945	22	21	nonlinear	nonlinear	ADJ
cana-945	22	22	analysis	analysis	NOUN
cana-945	22	23	issn	issn	NOUN
cana-945	22	24	:	:	PUNCT
cana-945	22	25	1074	1074	NUM
cana-945	22	26	-	-	PUNCT
cana-945	22	27	133x	133x	NUM
cana-945	22	28	vol	vol	NOUN
cana-945	22	29	31	31	NUM
cana-945	22	30	no	no	NOUN
cana-945	22	31	.	.	PUNCT
cana-945	23	1	4s	4s	NUM
cana-945	23	2	(	(	PUNCT
cana-945	23	3	2024	2024	NUM
cana-945	23	4	)	)	PUNCT
cana-945	23	5	501	501	NUM
cana-945	23	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-945	23	7	additional	additional	ADJ
cana-945	23	8	axioms	axiom	NOUN
cana-945	23	9	and	and	CCONJ
cana-945	23	10	properties	property	NOUN
cana-945	23	11	,	,	PUNCT
cana-945	23	12	focusing	focus	VERB
cana-945	23	13	on	on	ADP
cana-945	23	14	a	a	DET
cana-945	23	15	binary	binary	ADJ
cana-945	23	16	operation	operation	NOUN
cana-945	23	17	and	and	CCONJ
cana-945	23	18	an	an	DET
cana-945	23	19	inequality	inequality	NOUN
cana-945	23	20	relation	relation	NOUN
cana-945	23	21	[	[	X
cana-945	23	22	1	1	NUM
cana-945	23	23	]	]	PUNCT
cana-945	23	24	.	.	PUNCT
cana-945	24	1	this	this	DET
cana-945	24	2	distinction	distinction	NOUN
cana-945	24	3	allows	allow	VERB
cana-945	24	4	bck	bck	VERB
cana-945	24	5	-	-	PUNCT
cana-945	24	6	algebras	algebras	PROPN
cana-945	24	7	to	to	PART
cana-945	24	8	provide	provide	VERB
cana-945	24	9	a	a	DET
cana-945	24	10	rich	rich	ADJ
cana-945	24	11	structure	structure	NOUN
cana-945	24	12	for	for	ADP
cana-945	24	13	logical	logical	ADJ
cana-945	24	14	deduction	deduction	NOUN
cana-945	24	15	and	and	CCONJ
cana-945	24	16	reasoning	reasoning	NOUN
cana-945	24	17	while	while	SCONJ
cana-945	24	18	maintaining	maintain	VERB
cana-945	24	19	a	a	DET
cana-945	24	20	specific	specific	ADJ
cana-945	24	21	set	set	NOUN
cana-945	24	22	of	of	ADP
cana-945	24	23	constraints	constraint	NOUN
cana-945	24	24	that	that	PRON
cana-945	24	25	differentiate	differentiate	VERB
cana-945	24	26	them	they	PRON
cana-945	24	27	from	from	ADP
cana-945	24	28	the	the	DET
cana-945	24	29	broader	broad	ADJ
cana-945	24	30	category	category	NOUN
cana-945	24	31	of	of	ADP
cana-945	24	32	bcialgebras	bcialgebra	NOUN
cana-945	24	33	.	.	PUNCT
cana-945	25	1	in	in	ADP
cana-945	25	2	the	the	DET
cana-945	25	3	realm	realm	NOUN
cana-945	25	4	of	of	ADP
cana-945	25	5	generalizations	generalization	NOUN
cana-945	25	6	,	,	PUNCT
cana-945	25	7	d	d	X
cana-945	25	8	-	-	PUNCT
cana-945	25	9	algebra	algebra	NOUN
cana-945	25	10	represents	represent	VERB
cana-945	25	11	another	another	DET
cana-945	25	12	important	important	ADJ
cana-945	25	13	advancement	advancement	NOUN
cana-945	25	14	[	[	X
cana-945	25	15	2	2	NUM
cana-945	25	16	]	]	PUNCT
cana-945	25	17	.	.	PUNCT
cana-945	26	1	this	this	DET
cana-945	26	2	structure	structure	NOUN
cana-945	26	3	,	,	PUNCT
cana-945	26	4	characterized	characterize	VERB
cana-945	26	5	by	by	ADP
cana-945	26	6	a	a	DET
cana-945	26	7	binary	binary	ADJ
cana-945	26	8	operation	operation	NOUN
cana-945	26	9	that	that	PRON
cana-945	26	10	adheres	adhere	VERB
cana-945	26	11	to	to	ADP
cana-945	26	12	a	a	DET
cana-945	26	13	set	set	NOUN
cana-945	26	14	of	of	ADP
cana-945	26	15	axioms	axiom	NOUN
cana-945	26	16	,	,	PUNCT
cana-945	26	17	extends	extend	VERB
cana-945	26	18	the	the	DET
cana-945	26	19	applicability	applicability	NOUN
cana-945	26	20	of	of	ADP
cana-945	26	21	bck	bck	PROPN
cana-945	26	22	-	-	PUNCT
cana-945	26	23	algebraic	algebraic	ADJ
cana-945	26	24	concepts	concept	NOUN
cana-945	26	25	.	.	PUNCT
cana-945	27	1	the	the	DET
cana-945	27	2	flexibility	flexibility	NOUN
cana-945	27	3	introduced	introduce	VERB
cana-945	27	4	by	by	ADP
cana-945	27	5	d	d	NOUN
cana-945	27	6	-	-	PUNCT
cana-945	27	7	algebra	algebra	NOUN
cana-945	27	8	allows	allow	VERB
cana-945	27	9	for	for	ADP
cana-945	27	10	a	a	DET
cana-945	27	11	more	more	ADV
cana-945	27	12	comprehensive	comprehensive	ADJ
cana-945	27	13	framework	framework	NOUN
cana-945	27	14	in	in	ADP
cana-945	27	15	which	which	PRON
cana-945	27	16	the	the	DET
cana-945	27	17	properties	property	NOUN
cana-945	27	18	of	of	ADP
cana-945	27	19	bck	bck	PROPN
cana-945	27	20	-	-	PUNCT
cana-945	27	21	algebras	algebras	PROPN
cana-945	27	22	can	can	AUX
cana-945	27	23	be	be	AUX
cana-945	27	24	studied	study	VERB
cana-945	27	25	and	and	CCONJ
cana-945	27	26	applied	apply	VERB
cana-945	27	27	in	in	ADP
cana-945	27	28	broader	broad	ADJ
cana-945	27	29	contexts	contexts	NOUN
cana-945	27	30	,	,	PUNCT
cana-945	27	31	facilitating	facilitate	VERB
cana-945	27	32	new	new	ADJ
cana-945	27	33	lines	line	NOUN
cana-945	27	34	of	of	ADP
cana-945	27	35	inquiry	inquiry	NOUN
cana-945	27	36	and	and	CCONJ
cana-945	27	37	application	application	NOUN
cana-945	27	38	.	.	PUNCT
cana-945	28	1	further	far	ADV
cana-945	28	2	enhancing	enhance	VERB
cana-945	28	3	the	the	DET
cana-945	28	4	study	study	NOUN
cana-945	28	5	of	of	ADP
cana-945	28	6	d	d	PROPN
cana-945	28	7	-	-	PUNCT
cana-945	28	8	algebras	algebras	PROPN
cana-945	28	9	is	be	AUX
cana-945	28	10	the	the	DET
cana-945	28	11	concept	concept	NOUN
cana-945	28	12	of	of	ADP
cana-945	28	13	d	d	NOUN
cana-945	28	14	-	-	PUNCT
cana-945	28	15	filters	filter	NOUN
cana-945	28	16	,	,	PUNCT
cana-945	28	17	which	which	PRON
cana-945	28	18	are	be	AUX
cana-945	28	19	specific	specific	ADJ
cana-945	28	20	subsets	subset	NOUN
cana-945	28	21	of	of	ADP
cana-945	28	22	dalgebras	dalgebras	PROPN
cana-945	28	23	satisfying	satisfy	VERB
cana-945	28	24	certain	certain	ADJ
cana-945	28	25	filtering	filter	VERB
cana-945	28	26	properties	property	NOUN
cana-945	28	27	.	.	PUNCT
cana-945	29	1	these	these	DET
cana-945	29	2	filters	filter	NOUN
cana-945	29	3	are	be	AUX
cana-945	29	4	crucial	crucial	ADJ
cana-945	29	5	for	for	ADP
cana-945	29	6	understanding	understand	VERB
cana-945	29	7	the	the	DET
cana-945	29	8	internal	internal	ADJ
cana-945	29	9	structure	structure	NOUN
cana-945	29	10	of	of	ADP
cana-945	29	11	d	d	NOUN
cana-945	29	12	-	-	PUNCT
cana-945	29	13	algebras	algebras	PROPN
cana-945	29	14	and	and	CCONJ
cana-945	29	15	for	for	ADP
cana-945	29	16	studying	study	VERB
cana-945	29	17	their	their	PRON
cana-945	29	18	substructures	substructure	NOUN
cana-945	29	19	in	in	ADP
cana-945	29	20	detail	detail	NOUN
cana-945	29	21	[	[	X
cana-945	29	22	3	3	NUM
cana-945	29	23	]	]	PUNCT
cana-945	29	24	.	.	PUNCT
cana-945	30	1	the	the	DET
cana-945	30	2	notion	notion	NOUN
cana-945	30	3	of	of	ADP
cana-945	30	4	d	d	NOUN
cana-945	30	5	-	-	PUNCT
cana-945	30	6	filters	filter	NOUN
cana-945	30	7	provides	provide	VERB
cana-945	30	8	a	a	DET
cana-945	30	9	powerful	powerful	ADJ
cana-945	30	10	tool	tool	NOUN
cana-945	30	11	for	for	ADP
cana-945	30	12	analyzing	analyze	VERB
cana-945	30	13	and	and	CCONJ
cana-945	30	14	decomposing	decompose	VERB
cana-945	30	15	d	d	NOUN
cana-945	30	16	-	-	PUNCT
cana-945	30	17	algebras	algebras	ADJ
cana-945	30	18	into	into	ADP
cana-945	30	19	more	more	ADV
cana-945	30	20	manageable	manageable	ADJ
cana-945	30	21	components	component	NOUN
cana-945	30	22	,	,	PUNCT
cana-945	30	23	thereby	thereby	ADV
cana-945	30	24	facilitating	facilitate	VERB
cana-945	30	25	deeper	deep	ADJ
cana-945	30	26	insights	insight	NOUN
cana-945	30	27	into	into	ADP
cana-945	30	28	their	their	PRON
cana-945	30	29	algebraic	algebraic	ADJ
cana-945	30	30	properties	property	NOUN
cana-945	30	31	and	and	CCONJ
cana-945	30	32	enhancing	enhance	VERB
cana-945	30	33	the	the	DET
cana-945	30	34	overall	overall	ADJ
cana-945	30	35	comprehension	comprehension	NOUN
cana-945	30	36	of	of	ADP
cana-945	30	37	these	these	DET
cana-945	30	38	complex	complex	ADJ
cana-945	30	39	structures	structure	NOUN
cana-945	30	40	[	[	X
cana-945	30	41	4	4	NUM
cana-945	30	42	]	]	PUNCT
cana-945	30	43	.	.	PUNCT
cana-945	31	1	the	the	DET
cana-945	31	2	introduction	introduction	NOUN
cana-945	31	3	of	of	ADP
cana-945	31	4	fuzzy	fuzzy	ADJ
cana-945	31	5	sets	set	NOUN
cana-945	31	6	in	in	ADP
cana-945	31	7	1965	1965	NUM
cana-945	31	8	revolutionized	revolutionize	VERB
cana-945	31	9	the	the	DET
cana-945	31	10	way	way	NOUN
cana-945	31	11	uncertainty	uncertainty	NOUN
cana-945	31	12	and	and	CCONJ
cana-945	31	13	imprecision	imprecision	NOUN
cana-945	31	14	are	be	AUX
cana-945	31	15	handled	handle	VERB
cana-945	31	16	in	in	ADP
cana-945	31	17	mathematics	mathematic	NOUN
cana-945	31	18	[	[	X
cana-945	31	19	5	5	NUM
cana-945	31	20	]	]	PUNCT
cana-945	31	21	.	.	PUNCT
cana-945	32	1	by	by	ADP
cana-945	32	2	allowing	allow	VERB
cana-945	32	3	elements	element	NOUN
cana-945	32	4	to	to	PART
cana-945	32	5	have	have	VERB
cana-945	32	6	degrees	degree	NOUN
cana-945	32	7	of	of	ADP
cana-945	32	8	membership	membership	NOUN
cana-945	32	9	,	,	PUNCT
cana-945	32	10	fuzzy	fuzzy	ADJ
cana-945	32	11	sets	set	NOUN
cana-945	32	12	enable	enable	VERB
cana-945	32	13	more	more	ADV
cana-945	32	14	nuanced	nuanced	ADJ
cana-945	32	15	modeling	modeling	NOUN
cana-945	32	16	of	of	ADP
cana-945	32	17	real	real	ADJ
cana-945	32	18	-	-	PUNCT
cana-945	32	19	world	world	NOUN
cana-945	32	20	phenomena	phenomenon	NOUN
cana-945	32	21	,	,	PUNCT
cana-945	32	22	offering	offer	VERB
cana-945	32	23	a	a	DET
cana-945	32	24	flexible	flexible	ADJ
cana-945	32	25	approach	approach	NOUN
cana-945	32	26	to	to	ADP
cana-945	32	27	dealing	deal	VERB
cana-945	32	28	with	with	ADP
cana-945	32	29	ambiguity	ambiguity	NOUN
cana-945	32	30	[	[	X
cana-945	32	31	6	6	NUM
cana-945	32	32	]	]	PUNCT
cana-945	32	33	.	.	PUNCT
cana-945	33	1	this	this	DET
cana-945	33	2	innovation	innovation	NOUN
cana-945	33	3	paved	pave	VERB
cana-945	33	4	the	the	DET
cana-945	33	5	way	way	NOUN
cana-945	33	6	for	for	ADP
cana-945	33	7	further	further	ADJ
cana-945	33	8	advancements	advancement	NOUN
cana-945	33	9	,	,	PUNCT
cana-945	33	10	such	such	ADJ
cana-945	33	11	as	as	ADP
cana-945	33	12	the	the	DET
cana-945	33	13	introduction	introduction	NOUN
cana-945	33	14	of	of	ADP
cana-945	33	15	intuitionistic	intuitionistic	ADJ
cana-945	33	16	fuzzy	fuzzy	ADJ
cana-945	33	17	sets	set	NOUN
cana-945	33	18	in	in	ADP
cana-945	33	19	1986	1986	NUM
cana-945	33	20	.	.	PUNCT
cana-945	34	1	intuitionistic	intuitionistic	ADJ
cana-945	34	2	fuzzy	fuzzy	ADJ
cana-945	34	3	sets	set	NOUN
cana-945	34	4	extend	extend	VERB
cana-945	34	5	the	the	DET
cana-945	34	6	concept	concept	NOUN
cana-945	34	7	of	of	ADP
cana-945	34	8	fuzzy	fuzzy	ADJ
cana-945	34	9	sets	set	NOUN
cana-945	34	10	by	by	ADP
cana-945	34	11	incorporating	incorporate	VERB
cana-945	34	12	a	a	DET
cana-945	34	13	degree	degree	NOUN
cana-945	34	14	of	of	ADP
cana-945	34	15	nonmembership	nonmembership	NOUN
cana-945	34	16	alongside	alongside	ADP
cana-945	34	17	the	the	DET
cana-945	34	18	degree	degree	NOUN
cana-945	34	19	of	of	ADP
cana-945	34	20	membership	membership	NOUN
cana-945	34	21	[	[	X
cana-945	34	22	7	7	NUM
cana-945	34	23	]	]	PUNCT
cana-945	34	24	.	.	PUNCT
cana-945	35	1	this	this	DET
cana-945	35	2	dual	dual	ADJ
cana-945	35	3	-	-	PUNCT
cana-945	35	4	degree	degree	NOUN
cana-945	35	5	system	system	NOUN
cana-945	35	6	provides	provide	VERB
cana-945	35	7	a	a	DET
cana-945	35	8	richer	rich	ADJ
cana-945	35	9	framework	framework	NOUN
cana-945	35	10	for	for	ADP
cana-945	35	11	capturing	capture	VERB
cana-945	35	12	uncertainty	uncertainty	NOUN
cana-945	35	13	and	and	CCONJ
cana-945	35	14	ambiguity	ambiguity	NOUN
cana-945	35	15	,	,	PUNCT
cana-945	35	16	making	make	VERB
cana-945	35	17	it	it	PRON
cana-945	35	18	a	a	DET
cana-945	35	19	valuable	valuable	ADJ
cana-945	35	20	tool	tool	NOUN
cana-945	35	21	for	for	ADP
cana-945	35	22	a	a	DET
cana-945	35	23	wide	wide	ADJ
cana-945	35	24	range	range	NOUN
cana-945	35	25	of	of	ADP
cana-945	35	26	applications	application	NOUN
cana-945	35	27	.	.	PUNCT
cana-945	36	1	the	the	DET
cana-945	36	2	application	application	NOUN
cana-945	36	3	of	of	ADP
cana-945	36	4	intuitionistic	intuitionistic	ADJ
cana-945	36	5	fuzzy	fuzzy	ADJ
cana-945	36	6	sets	set	NOUN
cana-945	36	7	to	to	ADP
cana-945	36	8	d	d	VERB
cana-945	36	9	-	-	PUNCT
cana-945	36	10	algebras	algebras	PROPN
cana-945	36	11	has	have	AUX
cana-945	36	12	led	lead	VERB
cana-945	36	13	to	to	ADP
cana-945	36	14	the	the	DET
cana-945	36	15	concept	concept	NOUN
cana-945	36	16	of	of	ADP
cana-945	36	17	intuitionistic	intuitionistic	ADJ
cana-945	36	18	fuzzy	fuzzy	ADJ
cana-945	36	19	d	d	NOUN
cana-945	36	20	-	-	PUNCT
cana-945	36	21	algebras	algebras	X
cana-945	37	1	[	[	X
cana-945	37	2	8	8	NUM
cana-945	37	3	]	]	PUNCT
cana-945	37	4	.	.	PUNCT
cana-945	38	1	this	this	DET
cana-945	38	2	approach	approach	NOUN
cana-945	38	3	integrates	integrate	VERB
cana-945	38	4	the	the	DET
cana-945	38	5	flexibility	flexibility	NOUN
cana-945	38	6	of	of	ADP
cana-945	38	7	intuitionistic	intuitionistic	ADJ
cana-945	38	8	fuzzy	fuzzy	ADJ
cana-945	38	9	sets	set	NOUN
cana-945	38	10	with	with	ADP
cana-945	38	11	the	the	DET
cana-945	38	12	algebraic	algebraic	ADJ
cana-945	38	13	structure	structure	NOUN
cana-945	38	14	of	of	ADP
cana-945	38	15	d	d	PROPN
cana-945	38	16	-	-	PUNCT
cana-945	38	17	algebras	algebras	X
cana-945	38	18	,	,	PUNCT
cana-945	38	19	creating	create	VERB
cana-945	38	20	a	a	DET
cana-945	38	21	hybrid	hybrid	ADJ
cana-945	38	22	system	system	NOUN
cana-945	38	23	that	that	PRON
cana-945	38	24	benefits	benefit	VERB
cana-945	38	25	from	from	ADP
cana-945	38	26	the	the	DET
cana-945	38	27	strengths	strength	NOUN
cana-945	38	28	of	of	ADP
cana-945	38	29	both	both	DET
cana-945	38	30	frameworks	framework	NOUN
cana-945	38	31	.	.	PUNCT
cana-945	39	1	intuitionistic	intuitionistic	ADJ
cana-945	39	2	fuzzy	fuzzy	ADJ
cana-945	39	3	d	d	NOUN
cana-945	39	4	-	-	PUNCT
cana-945	39	5	filters	filter	NOUN
cana-945	39	6	,	,	PUNCT
cana-945	39	7	introduced	introduce	VERB
cana-945	39	8	as	as	ADP
cana-945	39	9	an	an	DET
cana-945	39	10	extension	extension	NOUN
cana-945	39	11	of	of	ADP
cana-945	39	12	d	d	NOUN
cana-945	39	13	-	-	PUNCT
cana-945	39	14	filters	filter	NOUN
cana-945	39	15	within	within	ADP
cana-945	39	16	this	this	DET
cana-945	39	17	context	context	NOUN
cana-945	39	18	,	,	PUNCT
cana-945	39	19	exhibit	exhibit	VERB
cana-945	39	20	unique	unique	ADJ
cana-945	39	21	properties	property	NOUN
cana-945	39	22	that	that	PRON
cana-945	39	23	blend	blend	VERB
cana-945	39	24	the	the	DET
cana-945	39	25	characteristics	characteristic	NOUN
cana-945	39	26	of	of	ADP
cana-945	39	27	intuitionistic	intuitionistic	ADJ
cana-945	39	28	fuzzy	fuzzy	ADJ
cana-945	39	29	sets	set	NOUN
cana-945	39	30	with	with	ADP
cana-945	39	31	the	the	DET
cana-945	39	32	filtering	filter	VERB
cana-945	39	33	criteria	criterion	NOUN
cana-945	39	34	of	of	ADP
cana-945	39	35	dalgebras	dalgebras	PROPN
cana-945	39	36	.	.	PUNCT
cana-945	40	1	these	these	DET
cana-945	40	2	filters	filter	NOUN
cana-945	40	3	play	play	VERB
cana-945	40	4	a	a	DET
cana-945	40	5	significant	significant	ADJ
cana-945	40	6	role	role	NOUN
cana-945	40	7	in	in	ADP
cana-945	40	8	the	the	DET
cana-945	40	9	analysis	analysis	NOUN
cana-945	40	10	and	and	CCONJ
cana-945	40	11	understanding	understanding	NOUN
cana-945	40	12	of	of	ADP
cana-945	40	13	intuitionistic	intuitionistic	ADJ
cana-945	40	14	fuzzy	fuzzy	ADJ
cana-945	40	15	d	d	NOUN
cana-945	40	16	-	-	PUNCT
cana-945	40	17	algebras	algebras	X
cana-945	40	18	,	,	PUNCT
cana-945	40	19	offering	offer	VERB
cana-945	40	20	new	new	ADJ
cana-945	40	21	perspectives	perspective	NOUN
cana-945	40	22	and	and	CCONJ
cana-945	40	23	methodologies	methodology	NOUN
cana-945	40	24	for	for	ADP
cana-945	40	25	studying	study	VERB
cana-945	40	26	these	these	DET
cana-945	40	27	complex	complex	ADJ
cana-945	40	28	systems	system	NOUN
cana-945	40	29	.	.	PUNCT
cana-945	41	1	studying	study	VERB
cana-945	41	2	relations	relation	NOUN
cana-945	41	3	on	on	ADP
cana-945	41	4	intuitionistic	intuitionistic	ADJ
cana-945	41	5	fuzzy	fuzzy	ADJ
cana-945	41	6	d	d	NOUN
cana-945	41	7	-	-	PUNCT
cana-945	41	8	algebras	algebras	PROPN
cana-945	41	9	involves	involve	VERB
cana-945	41	10	examining	examine	VERB
cana-945	41	11	how	how	SCONJ
cana-945	41	12	these	these	DET
cana-945	41	13	structures	structure	NOUN
cana-945	41	14	interact	interact	VERB
cana-945	41	15	under	under	ADP
cana-945	41	16	various	various	ADJ
cana-945	41	17	operations	operation	NOUN
cana-945	41	18	and	and	CCONJ
cana-945	41	19	mappings	mapping	NOUN
cana-945	41	20	.	.	PUNCT
cana-945	42	1	this	this	DET
cana-945	42	2	examination	examination	NOUN
cana-945	42	3	uncovers	uncover	VERB
cana-945	42	4	new	new	ADJ
cana-945	42	5	properties	property	NOUN
cana-945	42	6	and	and	CCONJ
cana-945	42	7	relationships	relationship	NOUN
cana-945	42	8	,	,	PUNCT
cana-945	42	9	enriching	enrich	VERB
cana-945	42	10	the	the	DET
cana-945	42	11	theoretical	theoretical	ADJ
cana-945	42	12	landscape	landscape	NOUN
cana-945	42	13	of	of	ADP
cana-945	42	14	fuzzy	fuzzy	ADJ
cana-945	42	15	algebraic	algebraic	ADJ
cana-945	42	16	systems	system	NOUN
cana-945	42	17	and	and	CCONJ
cana-945	42	18	providing	provide	VERB
cana-945	42	19	deeper	deep	ADJ
cana-945	42	20	insights	insight	NOUN
cana-945	42	21	into	into	ADP
cana-945	42	22	their	their	PRON
cana-945	42	23	behavior	behavior	NOUN
cana-945	42	24	and	and	CCONJ
cana-945	42	25	characteristics	characteristic	NOUN
cana-945	42	26	.	.	PUNCT
cana-945	43	1	the	the	DET
cana-945	43	2	development	development	NOUN
cana-945	43	3	and	and	CCONJ
cana-945	43	4	study	study	NOUN
cana-945	43	5	of	of	ADP
cana-945	43	6	these	these	DET
cana-945	43	7	abstract	abstract	ADJ
cana-945	43	8	algebraic	algebraic	ADJ
cana-945	43	9	structures	structure	NOUN
cana-945	43	10	,	,	PUNCT
cana-945	43	11	from	from	ADP
cana-945	43	12	bck	bck	NOUN
cana-945	43	13	-	-	PUNCT
cana-945	43	14	algebras	algebras	PROPN
cana-945	43	15	and	and	CCONJ
cana-945	43	16	bci	bci	NOUN
cana-945	43	17	-	-	PUNCT
cana-945	43	18	algebras	algebras	PROPN
cana-945	43	19	to	to	ADP
cana-945	43	20	d	d	NOUN
cana-945	43	21	-	-	PUNCT
cana-945	43	22	algebras	algebra	NOUN
cana-945	43	23	and	and	CCONJ
cana-945	43	24	their	their	PRON
cana-945	43	25	fuzzy	fuzzy	ADJ
cana-945	43	26	extensions	extension	NOUN
cana-945	43	27	,	,	PUNCT
cana-945	43	28	provide	provide	VERB
cana-945	43	29	a	a	DET
cana-945	43	30	versatile	versatile	ADJ
cana-945	43	31	and	and	CCONJ
cana-945	43	32	robust	robust	ADJ
cana-945	43	33	framework	framework	NOUN
cana-945	43	34	for	for	ADP
cana-945	43	35	exploring	explore	VERB
cana-945	43	36	complex	complex	ADJ
cana-945	43	37	algebraic	algebraic	ADJ
cana-945	43	38	structures	structure	NOUN
cana-945	43	39	.	.	PUNCT
cana-945	44	1	this	this	DET
cana-945	44	2	framework	framework	NOUN
cana-945	44	3	not	not	PART
cana-945	44	4	only	only	ADV
cana-945	44	5	enhances	enhance	VERB
cana-945	44	6	our	our	PRON
cana-945	44	7	understanding	understanding	NOUN
cana-945	44	8	of	of	ADP
cana-945	44	9	abstract	abstract	ADJ
cana-945	44	10	algebra	algebra	NOUN
cana-945	44	11	but	but	CCONJ
cana-945	44	12	also	also	ADV
cana-945	44	13	offers	offer	VERB
cana-945	44	14	powerful	powerful	ADJ
cana-945	44	15	tools	tool	NOUN
cana-945	44	16	for	for	ADP
cana-945	44	17	addressing	address	VERB
cana-945	44	18	problems	problem	NOUN
cana-945	44	19	in	in	ADP
cana-945	44	20	logic	logic	NOUN
cana-945	44	21	,	,	PUNCT
cana-945	44	22	computation	computation	NOUN
cana-945	44	23	,	,	PUNCT
cana-945	44	24	and	and	CCONJ
cana-945	44	25	applied	apply	VERB
cana-945	44	26	mathematics	mathematic	NOUN
cana-945	44	27	,	,	PUNCT
cana-945	44	28	thereby	thereby	ADV
cana-945	44	29	contributing	contribute	VERB
cana-945	44	30	significantly	significantly	ADV
cana-945	44	31	to	to	ADP
cana-945	44	32	the	the	DET
cana-945	44	33	advancement	advancement	NOUN
cana-945	44	34	of	of	ADP
cana-945	44	35	these	these	DET
cana-945	44	36	fields	field	NOUN
cana-945	44	37	[	[	X
cana-945	44	38	9	9	NUM
cana-945	44	39	]	]	SYM
cana-945	44	40	.	.	PUNCT
cana-945	45	1	2	2	X
cana-945	45	2	.	.	X
cana-945	45	3	preliminaries	preliminary	NOUN
cana-945	45	4	of	of	ADP
cana-945	45	5	fuzzy	fuzzy	ADJ
cana-945	45	6	d	d	NOUN
cana-945	45	7	-	-	PUNCT
cana-945	45	8	algebra	algebra	ADJ
cana-945	45	9	fuzzy	fuzzy	ADJ
cana-945	45	10	d	d	NOUN
cana-945	45	11	-	-	PUNCT
cana-945	45	12	algebra	algebra	NOUN
cana-945	45	13	,	,	PUNCT
cana-945	45	14	an	an	DET
cana-945	45	15	interdisciplinary	interdisciplinary	ADJ
cana-945	45	16	extension	extension	NOUN
cana-945	45	17	of	of	ADP
cana-945	45	18	classical	classical	ADJ
cana-945	45	19	algebraic	algebraic	ADJ
cana-945	45	20	structures	structure	NOUN
cana-945	45	21	,	,	PUNCT
cana-945	45	22	emerges	emerge	VERB
cana-945	45	23	as	as	ADP
cana-945	45	24	a	a	DET
cana-945	45	25	pivotal	pivotal	ADJ
cana-945	45	26	discipline	discipline	NOUN
cana-945	45	27	in	in	ADP
cana-945	45	28	handling	handle	VERB
cana-945	45	29	uncertain	uncertain	ADJ
cana-945	45	30	or	or	CCONJ
cana-945	45	31	imprecise	imprecise	ADJ
cana-945	45	32	data	datum	NOUN
cana-945	45	33	across	across	ADP
cana-945	45	34	diverse	diverse	ADJ
cana-945	45	35	domains	domain	NOUN
cana-945	45	36	such	such	ADJ
cana-945	45	37	as	as	ADP
cana-945	45	38	decision	decision	NOUN
cana-945	45	39	theory	theory	NOUN
cana-945	45	40	,	,	PUNCT
cana-945	45	41	communications	communication	NOUN
cana-945	45	42	on	on	ADP
cana-945	45	43	applied	apply	VERB
cana-945	45	44	nonlinear	nonlinear	ADJ
cana-945	45	45	analysis	analysis	NOUN
cana-945	45	46	issn	issn	NOUN
cana-945	45	47	:	:	PUNCT
cana-945	45	48	1074	1074	NUM
cana-945	45	49	-	-	PUNCT
cana-945	45	50	133x	133x	NUM
cana-945	45	51	vol	vol	NOUN
cana-945	45	52	31	31	NUM
cana-945	45	53	no	no	NOUN
cana-945	45	54	.	.	PUNCT
cana-945	46	1	4s	4s	NUM
cana-945	46	2	(	(	PUNCT
cana-945	46	3	2024	2024	NUM
cana-945	46	4	)	)	PUNCT
cana-945	46	5	502	502	NUM
cana-945	46	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-945	46	7	pattern	pattern	NOUN
cana-945	46	8	recognition	recognition	NOUN
cana-945	46	9	,	,	PUNCT
cana-945	46	10	and	and	CCONJ
cana-945	46	11	artificial	artificial	ADJ
cana-945	46	12	intelligence	intelligence	NOUN
cana-945	46	13	.	.	PUNCT
cana-945	47	1	rooted	root	VERB
cana-945	47	2	in	in	ADP
cana-945	47	3	foundational	foundational	ADJ
cana-945	47	4	definitions	definition	NOUN
cana-945	47	5	,	,	PUNCT
cana-945	47	6	this	this	DET
cana-945	47	7	field	field	NOUN
cana-945	47	8	provides	provide	VERB
cana-945	47	9	a	a	DET
cana-945	47	10	sophisticated	sophisticated	ADJ
cana-945	47	11	framework	framework	NOUN
cana-945	47	12	to	to	PART
cana-945	47	13	capture	capture	VERB
cana-945	47	14	and	and	CCONJ
cana-945	47	15	manipulate	manipulate	VERB
cana-945	47	16	fuzzy	fuzzy	ADJ
cana-945	47	17	information	information	NOUN
cana-945	47	18	effectively	effectively	ADV
cana-945	47	19	.	.	PUNCT
cana-945	48	1	a	a	DET
cana-945	48	2	fuzzy	fuzzy	ADJ
cana-945	48	3	set	set	VERB
cana-945	48	4	a	a	PRON
cana-945	48	5	within	within	ADP
cana-945	48	6	the	the	DET
cana-945	48	7	universe	universe	NOUN
cana-945	48	8	x	x	PUNCT
cana-945	48	9	is	be	AUX
cana-945	48	10	characterized	characterize	VERB
cana-945	48	11	by	by	ADP
cana-945	48	12	its	its	PRON
cana-945	48	13	membership	membership	NOUN
cana-945	48	14	function	function	NOUN
cana-945	48	15	μa(x	μa(x	NOUN
cana-945	48	16	)	)	PUNCT
cana-945	48	17	,	,	PUNCT
cana-945	48	18	assigning	assign	VERB
cana-945	48	19	each	each	DET
cana-945	48	20	element	element	NOUN
cana-945	48	21	x	x	PUNCT
cana-945	48	22	a	a	DET
cana-945	48	23	degree	degree	NOUN
cana-945	48	24	of	of	ADP
cana-945	48	25	membership	membership	NOUN
cana-945	48	26	in	in	ADP
cana-945	48	27	the	the	DET
cana-945	48	28	range	range	NOUN
cana-945	49	1	[	[	X
cana-945	49	2	0,1	0,1	NUM
cana-945	49	3	]	]	X
cana-945	49	4	[	[	X
cana-945	49	5	10	10	NUM
cana-945	49	6	]	]	PUNCT
cana-945	49	7	.	.	PUNCT
cana-945	50	1	this	this	DET
cana-945	50	2	nuanced	nuanced	ADJ
cana-945	50	3	representation	representation	NOUN
cana-945	50	4	allows	allow	VERB
cana-945	50	5	for	for	ADP
cana-945	50	6	the	the	DET
cana-945	50	7	modeling	modeling	NOUN
cana-945	50	8	of	of	ADP
cana-945	50	9	imprecise	imprecise	ADJ
cana-945	50	10	or	or	CCONJ
cana-945	50	11	uncertain	uncertain	ADJ
cana-945	50	12	elements	element	NOUN
cana-945	50	13	,	,	PUNCT
cana-945	50	14	crucial	crucial	ADJ
cana-945	50	15	for	for	ADP
cana-945	50	16	real	real	ADJ
cana-945	50	17	-	-	PUNCT
cana-945	50	18	world	world	NOUN
cana-945	50	19	applications	application	NOUN
cana-945	50	20	.	.	PUNCT
cana-945	51	1	by	by	ADP
cana-945	51	2	virtue	virtue	NOUN
cana-945	51	3	of	of	ADP
cana-945	51	4	its	its	PRON
cana-945	51	5	membership	membership	NOUN
cana-945	51	6	function	function	NOUN
cana-945	51	7	μr(x	μr(x	PROPN
cana-945	51	8	,	,	PUNCT
cana-945	51	9	y	y	PROPN
cana-945	51	10	)	)	PUNCT
cana-945	51	11	,	,	PUNCT
cana-945	51	12	a	a	DET
cana-945	51	13	fuzzy	fuzzy	ADJ
cana-945	51	14	relation	relation	NOUN
cana-945	51	15	r	r	NOUN
cana-945	51	16	between	between	ADP
cana-945	51	17	sets	set	NOUN
cana-945	51	18	x	x	PUNCT
cana-945	51	19	and	and	CCONJ
cana-945	51	20	y	y	PROPN
cana-945	51	21	quantifies	quantify	VERB
cana-945	51	22	the	the	DET
cana-945	51	23	degree	degree	NOUN
cana-945	51	24	of	of	ADP
cana-945	51	25	association	association	NOUN
cana-945	51	26	between	between	ADP
cana-945	51	27	elements	element	NOUN
cana-945	51	28	x	x	PUNCT
cana-945	51	29	and	and	CCONJ
cana-945	51	30	y	y	PROPN
cana-945	51	31	,	,	PUNCT
cana-945	51	32	providing	provide	VERB
cana-945	51	33	a	a	DET
cana-945	51	34	flexible	flexible	ADJ
cana-945	51	35	framework	framework	NOUN
cana-945	51	36	to	to	PART
cana-945	51	37	capture	capture	VERB
cana-945	51	38	vague	vague	ADJ
cana-945	51	39	or	or	CCONJ
cana-945	51	40	indeterminate	indeterminate	ADJ
cana-945	51	41	relationships	relationship	NOUN
cana-945	51	42	[	[	X
cana-945	51	43	11	11	NUM
cana-945	51	44	]	]	PUNCT
cana-945	51	45	.	.	PUNCT
cana-945	52	1	generalizing	generalize	VERB
cana-945	52	2	traditional	traditional	ADJ
cana-945	52	3	algebraic	algebraic	ADJ
cana-945	52	4	structures	structure	NOUN
cana-945	52	5	,	,	PUNCT
cana-945	52	6	a	a	DET
cana-945	52	7	fuzzy	fuzzy	ADJ
cana-945	52	8	algebraic	algebraic	ADJ
cana-945	52	9	structure	structure	NOUN
cana-945	52	10	defined	define	VERB
cana-945	52	11	on	on	ADP
cana-945	52	12	set	set	NOUN
cana-945	52	13	a	a	PRON
cana-945	52	14	,	,	PUNCT
cana-945	52	15	equipped	equip	VERB
cana-945	52	16	with	with	ADP
cana-945	52	17	fuzzy	fuzzy	ADJ
cana-945	52	18	operations	operation	NOUN
cana-945	52	19	∘	∘	ADV
cana-945	52	20	,	,	PUNCT
cana-945	52	21	encompasses	encompass	VERB
cana-945	52	22	imprecise	imprecise	ADJ
cana-945	52	23	elements	element	NOUN
cana-945	52	24	and	and	CCONJ
cana-945	52	25	operations	operation	NOUN
cana-945	52	26	while	while	SCONJ
cana-945	52	27	adhering	adhere	VERB
cana-945	52	28	to	to	ADP
cana-945	52	29	specific	specific	ADJ
cana-945	52	30	algebraic	algebraic	ADJ
cana-945	52	31	properties	property	NOUN
cana-945	52	32	,	,	PUNCT
cana-945	52	33	thus	thus	ADV
cana-945	52	34	accommodating	accommodate	VERB
cana-945	52	35	the	the	DET
cana-945	52	36	inherent	inherent	ADJ
cana-945	52	37	uncertainty	uncertainty	NOUN
cana-945	52	38	[	[	X
cana-945	52	39	12	12	NUM
cana-945	52	40	]	]	PUNCT
cana-945	52	41	.	.	PUNCT
cana-945	53	1	rigorously	rigorously	ADV
cana-945	53	2	formalized	formalize	VERB
cana-945	53	3	,	,	PUNCT
cana-945	53	4	a	a	DET
cana-945	53	5	fuzzy	fuzzy	ADJ
cana-945	53	6	d	d	NOUN
cana-945	53	7	-	-	PUNCT
cana-945	53	8	algebra	algebra	VERB
cana-945	53	9	a	a	DET
cana-945	53	10	comprises	comprise	NOUN
cana-945	53	11	a	a	DET
cana-945	53	12	non	non	ADJ
cana-945	53	13	-	-	ADJ
cana-945	53	14	empty	empty	ADJ
cana-945	53	15	set	set	NOUN
cana-945	53	16	endowed	endow	VERB
cana-945	53	17	with	with	ADP
cana-945	53	18	fuzzy	fuzzy	ADJ
cana-945	53	19	binary	binary	ADJ
cana-945	53	20	operations	operation	NOUN
cana-945	53	21	⨁	⨁	PROPN
cana-945	53	22	and	and	CCONJ
cana-945	53	23	⨀	⨀	PROPN
cana-945	53	24	,	,	PUNCT
cana-945	53	25	ensuring	ensure	VERB
cana-945	53	26	commutativity	commutativity	NOUN
cana-945	53	27	,	,	PUNCT
cana-945	53	28	associativity	associativity	NOUN
cana-945	53	29	,	,	PUNCT
cana-945	53	30	identity	identity	NOUN
cana-945	53	31	,	,	PUNCT
cana-945	53	32	and	and	CCONJ
cana-945	53	33	distributive	distributive	ADJ
cana-945	53	34	properties	property	NOUN
cana-945	53	35	.	.	PUNCT
cana-945	54	1	this	this	DET
cana-945	54	2	framework	framework	NOUN
cana-945	54	3	enables	enable	VERB
cana-945	54	4	seamless	seamless	ADJ
cana-945	54	5	manipulation	manipulation	NOUN
cana-945	54	6	of	of	ADP
cana-945	54	7	fuzzy	fuzzy	ADJ
cana-945	54	8	data	datum	NOUN
cana-945	54	9	,	,	PUNCT
cana-945	54	10	crucial	crucial	ADJ
cana-945	54	11	for	for	ADP
cana-945	54	12	decision	decision	NOUN
cana-945	54	13	-	-	PUNCT
cana-945	54	14	making	making	NOUN
cana-945	54	15	under	under	ADP
cana-945	54	16	uncertainty	uncertainty	NOUN
cana-945	54	17	.	.	PUNCT
cana-945	55	1	within	within	ADP
cana-945	55	2	the	the	DET
cana-945	55	3	context	context	NOUN
cana-945	55	4	of	of	ADP
cana-945	55	5	a	a	DET
cana-945	55	6	fuzzy	fuzzy	ADJ
cana-945	55	7	d	d	NOUN
cana-945	55	8	-	-	PUNCT
cana-945	55	9	algebra	algebra	NOUN
cana-945	55	10	a	a	PRON
cana-945	55	11	,	,	PUNCT
cana-945	55	12	a	a	DET
cana-945	55	13	fuzzy	fuzzy	ADJ
cana-945	55	14	ideal	ideal	NOUN
cana-945	55	15	i	i	PRON
cana-945	55	16	emerges	emerge	VERB
cana-945	55	17	as	as	ADP
cana-945	55	18	a	a	DET
cana-945	55	19	key	key	ADJ
cana-945	55	20	concept	concept	NOUN
cana-945	55	21	,	,	PUNCT
cana-945	55	22	constituting	constitute	VERB
cana-945	55	23	a	a	DET
cana-945	55	24	fuzzy	fuzzy	ADJ
cana-945	55	25	subset	subset	NOUN
cana-945	55	26	where	where	SCONJ
cana-945	55	27	fuzzy	fuzzy	ADJ
cana-945	55	28	operations	operation	NOUN
cana-945	55	29	maintain	maintain	VERB
cana-945	55	30	elements	element	NOUN
cana-945	55	31	within	within	ADP
cana-945	55	32	the	the	DET
cana-945	55	33	ideal	ideal	NOUN
cana-945	55	34	[	[	X
cana-945	55	35	13	13	NUM
cana-945	55	36	]	]	PUNCT
cana-945	55	37	.	.	PUNCT
cana-945	56	1	this	this	DET
cana-945	56	2	notion	notion	NOUN
cana-945	56	3	facilitates	facilitate	VERB
cana-945	56	4	the	the	DET
cana-945	56	5	exploration	exploration	NOUN
cana-945	56	6	of	of	ADP
cana-945	56	7	fuzzy	fuzzy	ADJ
cana-945	56	8	algebraic	algebraic	ADJ
cana-945	56	9	structures	structure	NOUN
cana-945	56	10	under	under	ADP
cana-945	56	11	specific	specific	ADJ
cana-945	56	12	constraints	constraint	NOUN
cana-945	56	13	.	.	PUNCT
cana-945	57	1	building	build	VERB
cana-945	57	2	upon	upon	SCONJ
cana-945	57	3	the	the	DET
cana-945	57	4	foundation	foundation	NOUN
cana-945	57	5	of	of	ADP
cana-945	57	6	fuzzy	fuzzy	ADJ
cana-945	57	7	d	d	NOUN
cana-945	57	8	-	-	PUNCT
cana-945	57	9	algebra	algebra	NOUN
cana-945	57	10	,	,	PUNCT
cana-945	57	11	the	the	DET
cana-945	57	12	concept	concept	NOUN
cana-945	57	13	of	of	ADP
cana-945	57	14	a	a	DET
cana-945	57	15	fuzzy	fuzzy	ADJ
cana-945	57	16	quotient	quotient	NOUN
cana-945	57	17	d	d	NOUN
cana-945	57	18	-	-	PUNCT
cana-945	57	19	algebra	algebra	VERB
cana-945	57	20	a	a	PRON
cana-945	57	21	/	/	SYM
cana-945	57	22	i	i	PRON
cana-945	57	23	arises	arise	VERB
cana-945	57	24	,	,	PUNCT
cana-945	57	25	representing	represent	VERB
cana-945	57	26	equivalence	equivalence	NOUN
cana-945	57	27	classes	class	NOUN
cana-945	57	28	of	of	ADP
cana-945	57	29	elements	element	NOUN
cana-945	57	30	in	in	ADP
cana-945	57	31	a	a	DET
cana-945	57	32	modulo	modulo	NOUN
cana-945	57	33	the	the	DET
cana-945	57	34	fuzzy	fuzzy	ADJ
cana-945	57	35	ideal	ideal	ADJ
cana-945	57	36	i.	i.	NOUN
cana-945	57	37	this	this	DET
cana-945	57	38	construction	construction	NOUN
cana-945	57	39	provides	provide	VERB
cana-945	57	40	a	a	DET
cana-945	57	41	powerful	powerful	ADJ
cana-945	57	42	tool	tool	NOUN
cana-945	57	43	for	for	ADP
cana-945	57	44	analyzing	analyze	VERB
cana-945	57	45	fuzzy	fuzzy	ADJ
cana-945	57	46	algebraic	algebraic	ADJ
cana-945	57	47	structures	structure	NOUN
cana-945	57	48	in	in	ADP
cana-945	57	49	a	a	DET
cana-945	57	50	quotient	quotient	NOUN
cana-945	57	51	space	space	NOUN
cana-945	57	52	setting	setting	NOUN
cana-945	57	53	.	.	PUNCT
cana-945	58	1	given	give	VERB
cana-945	58	2	fuzzy	fuzzy	ADJ
cana-945	58	3	relations	relation	NOUN
cana-945	58	4	r	r	NOUN
cana-945	58	5	and	and	CCONJ
cana-945	58	6	s	s	NOUN
cana-945	58	7	,	,	PUNCT
cana-945	58	8	their	their	PRON
cana-945	58	9	composition	composition	NOUN
cana-945	58	10	r	r	NOUN
cana-945	58	11	∘	∘	NOUN
cana-945	58	12	s	s	VERB
cana-945	58	13	is	be	AUX
cana-945	58	14	defined	define	VERB
cana-945	58	15	by	by	ADP
cana-945	58	16	the	the	DET
cana-945	58	17	membership	membership	NOUN
cana-945	58	18	function	function	NOUN
cana-945	58	19	μr∘s	μr∘s	NOUN
cana-945	58	20	(	(	PUNCT
cana-945	58	21	x	x	NOUN
cana-945	58	22	,	,	PUNCT
cana-945	58	23	y	y	PROPN
cana-945	58	24	)	)	PUNCT
cana-945	58	25	,	,	PUNCT
cana-945	58	26	capturing	capture	VERB
cana-945	58	27	the	the	DET
cana-945	58	28	degree	degree	NOUN
cana-945	58	29	of	of	ADP
cana-945	58	30	association	association	NOUN
cana-945	58	31	between	between	ADP
cana-945	58	32	elements	element	NOUN
cana-945	58	33	x	x	PUNCT
cana-945	58	34	and	and	CCONJ
cana-945	58	35	z	z	PROPN
cana-945	58	36	through	through	ADP
cana-945	58	37	a	a	DET
cana-945	58	38	series	series	NOUN
cana-945	58	39	of	of	ADP
cana-945	58	40	intermediary	intermediary	ADJ
cana-945	58	41	elements	element	NOUN
cana-945	58	42	y	y	PROPN
cana-945	59	1	[	[	X
cana-945	59	2	14	14	NUM
cana-945	59	3	]	]	PUNCT
cana-945	59	4	.	.	PUNCT
cana-945	60	1	a	a	DET
cana-945	60	2	fuzzy	fuzzy	ADJ
cana-945	60	3	relation	relation	NOUN
cana-945	60	4	r	r	NOUN
cana-945	60	5	on	on	ADP
cana-945	60	6	set	set	NOUN
cana-945	60	7	a	a	PRON
cana-945	60	8	is	be	AUX
cana-945	60	9	termed	term	VERB
cana-945	60	10	as	as	ADP
cana-945	60	11	a	a	DET
cana-945	60	12	fuzzy	fuzzy	ADJ
cana-945	60	13	equivalence	equivalence	NOUN
cana-945	60	14	relation	relation	NOUN
cana-945	60	15	if	if	SCONJ
cana-945	60	16	it	it	PRON
cana-945	60	17	is	be	AUX
cana-945	60	18	reflexive	reflexive	ADJ
cana-945	60	19	,	,	PUNCT
cana-945	60	20	symmetric	symmetric	ADJ
cana-945	60	21	,	,	PUNCT
cana-945	60	22	and	and	CCONJ
cana-945	60	23	transitive	transitive	ADJ
cana-945	60	24	,	,	PUNCT
cana-945	60	25	allowing	allow	VERB
cana-945	60	26	for	for	ADP
cana-945	60	27	the	the	DET
cana-945	60	28	classification	classification	NOUN
cana-945	60	29	of	of	ADP
cana-945	60	30	elements	element	NOUN
cana-945	60	31	into	into	ADP
cana-945	60	32	equivalence	equivalence	NOUN
cana-945	60	33	classes	class	NOUN
cana-945	60	34	based	base	VERB
cana-945	60	35	on	on	ADP
cana-945	60	36	their	their	PRON
cana-945	60	37	fuzzy	fuzzy	ADJ
cana-945	60	38	relationships	relationship	NOUN
cana-945	60	39	[	[	X
cana-945	60	40	15	15	NUM
cana-945	60	41	]	]	PUNCT
cana-945	60	42	.	.	PUNCT
cana-945	61	1	extending	extend	VERB
cana-945	61	2	the	the	DET
cana-945	61	3	concept	concept	NOUN
cana-945	61	4	of	of	ADP
cana-945	61	5	classical	classical	ADJ
cana-945	61	6	lattices	lattice	NOUN
cana-945	61	7	,	,	PUNCT
cana-945	61	8	a	a	DET
cana-945	61	9	fuzzy	fuzzy	ADJ
cana-945	61	10	lattice	lattice	NOUN
cana-945	61	11	l	l	NOUN
cana-945	61	12	is	be	AUX
cana-945	61	13	defined	define	VERB
cana-945	61	14	on	on	ADP
cana-945	61	15	a	a	DET
cana-945	61	16	partially	partially	ADV
cana-945	61	17	ordered	order	VERB
cana-945	61	18	set	set	VERB
cana-945	61	19	p	p	PRON
cana-945	61	20	,	,	PUNCT
cana-945	61	21	equipped	equip	VERB
cana-945	61	22	with	with	ADP
cana-945	61	23	fuzzy	fuzzy	ADJ
cana-945	61	24	operations	operation	NOUN
cana-945	61	25	⋁(join	⋁(join	X
cana-945	61	26	)	)	PUNCT
cana-945	61	27	and	and	CCONJ
cana-945	61	28	⋀(meet	⋀(meet	NOUN
cana-945	61	29	)	)	PUNCT
cana-945	61	30	,	,	PUNCT
cana-945	61	31	enabling	enable	VERB
cana-945	61	32	the	the	DET
cana-945	61	33	modeling	modeling	NOUN
cana-945	61	34	of	of	ADP
cana-945	61	35	imprecise	imprecise	ADV
cana-945	61	36	ordering	order	VERB
cana-945	61	37	relationships	relationship	NOUN
cana-945	61	38	among	among	ADP
cana-945	61	39	elements	element	NOUN
cana-945	61	40	[	[	X
cana-945	61	41	16	16	NUM
cana-945	61	42	]	]	PUNCT
cana-945	61	43	.	.	PUNCT
cana-945	62	1	in	in	ADP
cana-945	62	2	the	the	DET
cana-945	62	3	context	context	NOUN
cana-945	62	4	of	of	ADP
cana-945	62	5	a	a	DET
cana-945	62	6	fuzzy	fuzzy	ADJ
cana-945	62	7	algebraic	algebraic	ADJ
cana-945	62	8	structure	structure	NOUN
cana-945	62	9	,	,	PUNCT
cana-945	62	10	a	a	DET
cana-945	62	11	fuzzy	fuzzy	ADJ
cana-945	62	12	congruence	congruence	NOUN
cana-945	62	13	relation	relation	NOUN
cana-945	62	14	θ	θ	PROPN
cana-945	62	15	is	be	AUX
cana-945	62	16	defined	define	VERB
cana-945	62	17	as	as	ADP
cana-945	62	18	an	an	DET
cana-945	62	19	equivalence	equivalence	NOUN
cana-945	62	20	relation	relation	NOUN
cana-945	62	21	that	that	PRON
cana-945	62	22	preserves	preserve	VERB
cana-945	62	23	fuzzy	fuzzy	ADJ
cana-945	62	24	operations	operation	NOUN
cana-945	62	25	,	,	PUNCT
cana-945	62	26	providing	provide	VERB
cana-945	62	27	a	a	DET
cana-945	62	28	foundation	foundation	NOUN
cana-945	62	29	for	for	ADP
cana-945	62	30	quotient	quotient	NOUN
cana-945	62	31	structures	structure	NOUN
cana-945	62	32	in	in	ADP
cana-945	62	33	fuzzy	fuzzy	ADJ
cana-945	62	34	algebraic	algebraic	ADJ
cana-945	62	35	contexts	contexts	NOUN
cana-945	62	36	.	.	PUNCT
cana-945	63	1	3	3	X
cana-945	63	2	.	.	NUM
cana-945	63	3	proposed	propose	VERB
cana-945	63	4	work	work	NOUN
cana-945	63	5	3.1	3.1	NUM
cana-945	63	6	mathematical	mathematical	ADJ
cana-945	63	7	modeling	modeling	NOUN
cana-945	63	8	of	of	ADP
cana-945	63	9	intuitionistic	intuitionistic	ADJ
cana-945	63	10	fuzzy	fuzzy	ADJ
cana-945	63	11	𝑫	𝑫	NOUN
cana-945	63	12	-algebra	-algebra	VERB
cana-945	63	13	structures	structure	NOUN
cana-945	63	14	advancing	advance	VERB
cana-945	63	15	the	the	DET
cana-945	63	16	theoretical	theoretical	ADJ
cana-945	63	17	foundations	foundation	NOUN
cana-945	63	18	of	of	ADP
cana-945	63	19	intuitionistic	intuitionistic	ADJ
cana-945	63	20	fuzzy	fuzzy	ADJ
cana-945	63	21	d	d	PROPN
cana-945	63	22	-algebra	-algebra	NOUN
cana-945	63	23	begins	begin	VERB
cana-945	63	24	with	with	ADP
cana-945	63	25	defining	define	VERB
cana-945	63	26	the	the	DET
cana-945	63	27	core	core	NOUN
cana-945	63	28	structures	structure	NOUN
cana-945	63	29	of	of	ADP
cana-945	63	30	this	this	DET
cana-945	63	31	innovative	innovative	ADJ
cana-945	63	32	field	field	NOUN
cana-945	63	33	.	.	PUNCT
cana-945	64	1	intuitionistic	intuitionistic	ADJ
cana-945	64	2	fuzzy	fuzzy	ADJ
cana-945	64	3	d	d	PROPN
cana-945	64	4	-algebra	-algebra	PROPN
cana-945	64	5	extends	extend	VERB
cana-945	64	6	classical	classical	ADJ
cana-945	64	7	fuzzy	fuzzy	ADJ
cana-945	64	8	algebra	algebra	NOUN
cana-945	64	9	by	by	ADP
cana-945	64	10	incorporating	incorporate	VERB
cana-945	64	11	degrees	degree	NOUN
cana-945	64	12	of	of	ADP
cana-945	64	13	membership	membership	NOUN
cana-945	64	14	and	and	CCONJ
cana-945	64	15	non	non	ADJ
cana-945	64	16	-	-	NOUN
cana-945	64	17	membership	membership	NOUN
cana-945	64	18	,	,	PUNCT
cana-945	64	19	providing	provide	VERB
cana-945	64	20	a	a	DET
cana-945	64	21	richer	rich	ADJ
cana-945	64	22	framework	framework	NOUN
cana-945	64	23	for	for	ADP
cana-945	64	24	dealing	deal	VERB
cana-945	64	25	with	with	ADP
cana-945	64	26	uncertainty	uncertainty	NOUN
cana-945	64	27	and	and	CCONJ
cana-945	64	28	imprecision	imprecision	NOUN
cana-945	64	29	.	.	PUNCT
cana-945	65	1	formally	formally	ADV
cana-945	65	2	,	,	PUNCT
cana-945	65	3	an	an	DET
cana-945	65	4	intuitionistic	intuitionistic	ADJ
cana-945	65	5	fuzzy	fuzzy	ADJ
cana-945	65	6	set	set	VERB
cana-945	65	7	a	a	PRON
cana-945	65	8	in	in	ADP
cana-945	65	9	a	a	DET
cana-945	65	10	universe	universe	NOUN
cana-945	65	11	x	x	PUNCT
cana-945	65	12	is	be	AUX
cana-945	65	13	characterized	characterize	VERB
cana-945	65	14	by	by	ADP
cana-945	65	15	a	a	DET
cana-945	65	16	membership	membership	NOUN
cana-945	65	17	function	function	NOUN
cana-945	65	18	μa	μa	NOUN
cana-945	65	19	:	:	PUNCT
cana-945	65	20	x	x	X
cana-945	65	21	→	→	PUNCT
cana-945	66	1	[	[	X
cana-945	66	2	0.1	0.1	NUM
cana-945	66	3	]	]	PUNCT
cana-945	66	4	and	and	CCONJ
cana-945	66	5	a	a	DET
cana-945	66	6	non	non	ADJ
cana-945	66	7	-	-	ADJ
cana-945	66	8	membership	membership	ADJ
cana-945	66	9	function	function	NOUN
cana-945	66	10	va	va	PROPN
cana-945	66	11	:	:	PUNCT
cana-945	66	12	x	x	X
cana-945	66	13	→	→	PUNCT
cana-945	66	14	[	[	X
cana-945	66	15	0.1	0.1	NUM
cana-945	66	16	]	]	PUNCT
cana-945	66	17	such	such	ADJ
cana-945	66	18	that	that	SCONJ
cana-945	66	19	0	0	NUM
cana-945	66	20	≤	≤	NUM
cana-945	66	21	μa(x	μa(x	NOUN
cana-945	66	22	)	)	PUNCT
cana-945	67	1	+	+	CCONJ
cana-945	67	2	va(x	va(x	NOUN
cana-945	67	3	)	)	PUNCT
cana-945	67	4	≤	≤	NUM
cana-945	67	5	1	1	NUM
cana-945	67	6	for	for	ADP
cana-945	67	7	all	all	PRON
cana-945	67	8	x	x	SYM
cana-945	67	9	∈	∈	ADJ
cana-945	67	10	x.	x.	NOUN
cana-945	67	11	this	this	DET
cana-945	67	12	dual	dual	ADJ
cana-945	67	13	-	-	PUNCT
cana-945	67	14	function	function	NOUN
cana-945	67	15	approach	approach	NOUN
cana-945	67	16	allows	allow	VERB
cana-945	67	17	for	for	ADP
cana-945	67	18	the	the	DET
cana-945	67	19	expression	expression	NOUN
cana-945	67	20	of	of	ADP
cana-945	67	21	hesitation	hesitation	NOUN
cana-945	67	22	,	,	PUNCT
cana-945	67	23	represented	represent	VERB
cana-945	67	24	by	by	ADP
cana-945	67	25	πa(x	πa(x	NOUN
cana-945	67	26	)	)	PUNCT
cana-945	67	27	=	=	SYM
cana-945	67	28	1	1	NUM
cana-945	67	29	−	−	NUM
cana-945	67	30	μa(x	μa(x	NOUN
cana-945	67	31	)	)	PUNCT
cana-945	67	32	−	−	ADP
cana-945	67	33	va(x	va(x	NOUN
cana-945	67	34	)	)	PUNCT
cana-945	67	35	.	.	PUNCT
cana-945	68	1	building	build	VERB
cana-945	68	2	upon	upon	SCONJ
cana-945	68	3	this	this	DET
cana-945	68	4	foundation	foundation	NOUN
cana-945	68	5	,	,	PUNCT
cana-945	68	6	an	an	DET
cana-945	68	7	intuitionistic	intuitionistic	ADJ
cana-945	68	8	fuzzy	fuzzy	ADJ
cana-945	68	9	d	d	NOUN
cana-945	68	10	algebra	algebra	NOUN
cana-945	68	11	structure	structure	NOUN
cana-945	68	12	is	be	AUX
cana-945	68	13	defined	define	VERB
cana-945	68	14	as	as	ADP
cana-945	68	15	a	a	DET
cana-945	68	16	tuple	tuple	NOUN
cana-945	68	17	(	(	PUNCT
cana-945	68	18	x	x	X
cana-945	68	19	,	,	PUNCT
cana-945	68	20	μa	μa	NOUN
cana-945	68	21	,	,	PUNCT
cana-945	68	22	va	va	NOUN
cana-945	68	23	,	,	PUNCT
cana-945	68	24	d	d	NOUN
cana-945	68	25	)	)	PUNCT
cana-945	68	26	,	,	PUNCT
cana-945	68	27	where	where	SCONJ
cana-945	68	28	d	d	PROPN
cana-945	68	29	denotes	denote	VERB
cana-945	68	30	a	a	DET
cana-945	68	31	communications	communication	NOUN
cana-945	68	32	on	on	ADP
cana-945	68	33	applied	apply	VERB
cana-945	68	34	nonlinear	nonlinear	ADJ
cana-945	68	35	analysis	analysis	NOUN
cana-945	68	36	issn	issn	NOUN
cana-945	68	37	:	:	PUNCT
cana-945	68	38	1074	1074	NUM
cana-945	68	39	-	-	PUNCT
cana-945	68	40	133x	133x	NUM
cana-945	68	41	vol	vol	NOUN
cana-945	68	42	31	31	NUM
cana-945	68	43	no	no	NOUN
cana-945	68	44	.	.	PUNCT
cana-945	69	1	4s	4s	NUM
cana-945	69	2	(	(	PUNCT
cana-945	69	3	2024	2024	NUM
cana-945	69	4	)	)	PUNCT
cana-945	69	5	503	503	NUM
cana-945	69	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-945	69	7	binary	binary	ADJ
cana-945	69	8	operation	operation	NOUN
cana-945	69	9	that	that	PRON
cana-945	69	10	satisfies	satisfy	VERB
cana-945	69	11	the	the	DET
cana-945	69	12	properties	property	NOUN
cana-945	69	13	of	of	ADP
cana-945	69	14	a	a	DET
cana-945	69	15	d	d	NOUN
cana-945	69	16	-algebra	-algebra	PROPN
cana-945	69	17	.	.	PUNCT
cana-945	70	1	the	the	DET
cana-945	70	2	primary	primary	ADJ
cana-945	70	3	operation	operation	NOUN
cana-945	70	4	in	in	ADP
cana-945	70	5	an	an	DET
cana-945	70	6	intuitionistic	intuitionistic	ADJ
cana-945	70	7	fuzzy	fuzzy	ADJ
cana-945	70	8	d	d	NOUN
cana-945	70	9	-	-	PUNCT
cana-945	70	10	algebra	algebra	NOUN
cana-945	70	11	can	can	AUX
cana-945	70	12	be	be	AUX
cana-945	70	13	expressed	express	VERB
cana-945	70	14	as	as	ADP
cana-945	70	15	:	:	PUNCT
cana-945	70	16	da(x	da(x	PROPN
cana-945	70	17	,	,	PUNCT
cana-945	70	18	y	y	NOUN
cana-945	70	19	)	)	PUNCT
cana-945	70	20	=	=	SYM
cana-945	70	21	(	(	PUNCT
cana-945	70	22	μa(x)⋀μa(y	μa(x)⋀μa(y	NOUN
cana-945	70	23	)	)	PUNCT
cana-945	70	24	,	,	PUNCT
cana-945	70	25	va(x)⋁va(y	va(x)⋁va(y	NOUN
cana-945	70	26	)	)	PUNCT
cana-945	70	27	)	)	PUNCT
cana-945	71	1	(	(	PUNCT
cana-945	71	2	1	1	X
cana-945	71	3	)	)	PUNCT
cana-945	71	4	where	where	SCONJ
cana-945	71	5	⋀	⋀	PROPN
cana-945	71	6	and	and	CCONJ
cana-945	71	7	⋁	⋁	PROPN
cana-945	71	8	denote	denote	VERB
cana-945	71	9	the	the	DET
cana-945	71	10	minimum	minimum	ADJ
cana-945	71	11	and	and	CCONJ
cana-945	71	12	maximum	maximum	ADJ
cana-945	71	13	operations	operation	NOUN
cana-945	71	14	,	,	PUNCT
cana-945	71	15	respectively	respectively	ADV
cana-945	71	16	.	.	PUNCT
cana-945	72	1	this	this	DET
cana-945	72	2	definition	definition	NOUN
cana-945	72	3	encapsulates	encapsulate	VERB
cana-945	72	4	the	the	DET
cana-945	72	5	interplay	interplay	NOUN
cana-945	72	6	between	between	ADP
cana-945	72	7	membership	membership	NOUN
cana-945	72	8	and	and	CCONJ
cana-945	72	9	non	non	ADJ
cana-945	72	10	-	-	ADJ
cana-945	72	11	membership	membership	ADJ
cana-945	72	12	degrees	degree	NOUN
cana-945	72	13	under	under	ADP
cana-945	72	14	the	the	DET
cana-945	72	15	operation	operation	NOUN
cana-945	72	16	d.	d.	PROPN
cana-945	72	17	building	building	PROPN
cana-945	72	18	upon	upon	SCONJ
cana-945	72	19	these	these	DET
cana-945	72	20	definitions	definition	NOUN
cana-945	72	21	,	,	PUNCT
cana-945	72	22	mathematical	mathematical	ADJ
cana-945	72	23	models	model	NOUN
cana-945	72	24	are	be	AUX
cana-945	72	25	developed	develop	VERB
cana-945	72	26	to	to	PART
cana-945	72	27	represent	represent	VERB
cana-945	72	28	these	these	DET
cana-945	72	29	structures	structure	NOUN
cana-945	72	30	,	,	PUNCT
cana-945	72	31	leveraging	leverage	VERB
cana-945	72	32	advanced	advanced	ADJ
cana-945	72	33	techniques	technique	NOUN
cana-945	72	34	from	from	ADP
cana-945	72	35	lattice	lattice	NOUN
cana-945	72	36	theory	theory	NOUN
cana-945	72	37	and	and	CCONJ
cana-945	72	38	topology	topology	NOUN
cana-945	72	39	.	.	PUNCT
cana-945	73	1	these	these	DET
cana-945	73	2	models	model	NOUN
cana-945	73	3	are	be	AUX
cana-945	73	4	constructed	construct	VERB
cana-945	73	5	to	to	PART
cana-945	73	6	faithfully	faithfully	ADV
cana-945	73	7	represent	represent	VERB
cana-945	73	8	the	the	DET
cana-945	73	9	interactions	interaction	NOUN
cana-945	73	10	and	and	CCONJ
cana-945	73	11	relationships	relationship	NOUN
cana-945	73	12	inherent	inherent	ADJ
cana-945	73	13	in	in	ADP
cana-945	73	14	intuitionistic	intuitionistic	ADJ
cana-945	73	15	fuzzy	fuzzy	ADJ
cana-945	73	16	d	d	NOUN
cana-945	73	17	-	-	NOUN
cana-945	73	18	algebra	algebra	NOUN
cana-945	73	19	,	,	PUNCT
cana-945	73	20	allowing	allow	VERB
cana-945	73	21	for	for	ADP
cana-945	73	22	the	the	DET
cana-945	73	23	exploration	exploration	NOUN
cana-945	73	24	of	of	ADP
cana-945	73	25	their	their	PRON
cana-945	73	26	properties	property	NOUN
cana-945	73	27	through	through	ADP
cana-945	73	28	rigorous	rigorous	ADJ
cana-945	73	29	analysis	analysis	NOUN
cana-945	73	30	and	and	CCONJ
cana-945	73	31	simulation	simulation	NOUN
cana-945	73	32	.	.	PUNCT
cana-945	74	1	by	by	ADP
cana-945	74	2	integrating	integrate	VERB
cana-945	74	3	these	these	DET
cana-945	74	4	models	model	NOUN
cana-945	74	5	with	with	ADP
cana-945	74	6	computational	computational	ADJ
cana-945	74	7	tools	tool	NOUN
cana-945	74	8	such	such	ADJ
cana-945	74	9	as	as	ADP
cana-945	74	10	matlab	matlab	PROPN
cana-945	74	11	and	and	CCONJ
cana-945	74	12	mathematica	mathematica	PROPN
cana-945	74	13	,	,	PUNCT
cana-945	74	14	a	a	DET
cana-945	74	15	versatile	versatile	ADJ
cana-945	74	16	platform	platform	NOUN
cana-945	74	17	is	be	AUX
cana-945	74	18	created	create	VERB
cana-945	74	19	for	for	ADP
cana-945	74	20	both	both	CCONJ
cana-945	74	21	theoretical	theoretical	ADJ
cana-945	74	22	exploration	exploration	NOUN
cana-945	74	23	and	and	CCONJ
cana-945	74	24	practical	practical	ADJ
cana-945	74	25	application	application	NOUN
cana-945	74	26	,	,	PUNCT
cana-945	74	27	paving	pave	VERB
cana-945	74	28	the	the	DET
cana-945	74	29	way	way	NOUN
cana-945	74	30	for	for	ADP
cana-945	74	31	innovative	innovative	ADJ
cana-945	74	32	solutions	solution	NOUN
cana-945	74	33	in	in	ADP
cana-945	74	34	areas	area	NOUN
cana-945	74	35	ranging	range	VERB
cana-945	74	36	from	from	ADP
cana-945	74	37	decision	decision	NOUN
cana-945	74	38	-	-	PUNCT
cana-945	74	39	making	make	VERB
cana-945	74	40	systems	system	NOUN
cana-945	74	41	to	to	ADP
cana-945	74	42	artificial	artificial	ADJ
cana-945	74	43	intelligence	intelligence	NOUN
cana-945	74	44	.	.	PUNCT
cana-945	75	1	consider	consider	VERB
cana-945	75	2	two	two	NUM
cana-945	75	3	elements	element	NOUN
cana-945	75	4	x	x	X
cana-945	75	5	,	,	PUNCT
cana-945	75	6	y	y	PROPN
cana-945	75	7	∈	∈	PROPN
cana-945	75	8	xwith	xwith	ADP
cana-945	75	9	their	their	PRON
cana-945	75	10	respective	respective	ADJ
cana-945	75	11	membership	membership	NOUN
cana-945	75	12	and	and	CCONJ
cana-945	75	13	non	non	ADJ
cana-945	75	14	-	-	ADJ
cana-945	75	15	membership	membership	ADJ
cana-945	75	16	values	value	NOUN
cana-945	75	17	μa(x	μa(x	NOUN
cana-945	75	18	)	)	PUNCT
cana-945	75	19	,	,	PUNCT
cana-945	75	20	μa(y	μa(y	NUM
cana-945	75	21	)	)	PUNCT
cana-945	75	22	,	,	PUNCT
cana-945	75	23	va(x	va(x	NOUN
cana-945	75	24	)	)	PUNCT
cana-945	75	25	and	and	CCONJ
cana-945	75	26	va(y	va(y	NUM
cana-945	75	27	)	)	PUNCT
cana-945	75	28	.	.	PUNCT
cana-945	76	1	applying	apply	VERB
cana-945	76	2	the	the	DET
cana-945	76	3	operation	operation	NOUN
cana-945	76	4	da	da	NOUN
cana-945	76	5	,	,	PUNCT
cana-945	76	6	we	we	PRON
cana-945	76	7	obtain	obtain	VERB
cana-945	76	8	:	:	PUNCT
cana-945	77	1	μda(x	μda(x	PROPN
cana-945	77	2	,	,	PUNCT
cana-945	77	3	y	y	NOUN
cana-945	77	4	)	)	PUNCT
cana-945	77	5	=	=	SYM
cana-945	77	6	μa(x)⋀μa(y	μa(x)⋀μa(y	PROPN
cana-945	77	7	)	)	PUNCT
cana-945	77	8	(	(	PUNCT
cana-945	77	9	2	2	X
cana-945	77	10	)	)	PUNCT
cana-945	77	11	vda(x	vda(x	PROPN
cana-945	77	12	,	,	PUNCT
cana-945	77	13	y	y	NOUN
cana-945	77	14	)	)	PUNCT
cana-945	77	15	=	=	SYM
cana-945	77	16	va(x)⋁va(y	va(x)⋁va(y	PROPN
cana-945	77	17	)	)	PUNCT
cana-945	77	18	(	(	PUNCT
cana-945	77	19	3	3	X
cana-945	77	20	)	)	PUNCT
cana-945	77	21	to	to	PART
cana-945	77	22	illustrate	illustrate	VERB
cana-945	77	23	,	,	PUNCT
cana-945	77	24	choose	choose	VERB
cana-945	77	25	specific	specific	ADJ
cana-945	77	26	values	value	NOUN
cana-945	77	27	μa(x	μa(x	PUNCT
cana-945	77	28	)	)	PUNCT
cana-945	77	29	=	=	SYM
cana-945	77	30	0.7	0.7	NUM
cana-945	77	31	,	,	PUNCT
cana-945	77	32	μa(y	μa(y	NUM
cana-945	77	33	)	)	PUNCT
cana-945	77	34	=	=	SYM
cana-945	77	35	0.4	0.4	NUM
cana-945	77	36	,	,	PUNCT
cana-945	77	37	va(x	va(x	NOUN
cana-945	77	38	)	)	PUNCT
cana-945	77	39	=	=	SYM
cana-945	77	40	0.3	0.3	NUM
cana-945	77	41	and	and	CCONJ
cana-945	77	42	va(y	va(y	NUM
cana-945	77	43	)	)	PUNCT
cana-945	78	1	=	=	PUNCT
cana-945	78	2	0.2	0.2	NUM
cana-945	78	3	then	then	ADV
cana-945	78	4	,	,	PUNCT
cana-945	78	5	μda(x	μda(x	PROPN
cana-945	78	6	,	,	PUNCT
cana-945	78	7	y	y	PROPN
cana-945	78	8	)	)	PUNCT
cana-945	78	9	=	=	SYM
cana-945	78	10	min(0.7,0.4	min(0.7,0.4	PROPN
cana-945	78	11	)	)	PUNCT
cana-945	78	12	=	=	SYM
cana-945	79	1	0.4	0.4	NUM
cana-945	79	2	(	(	PUNCT
cana-945	79	3	4	4	NUM
cana-945	79	4	)	)	PUNCT
cana-945	79	5	vda(x	vda(x	PROPN
cana-945	79	6	,	,	PUNCT
cana-945	79	7	y	y	NOUN
cana-945	79	8	)	)	PUNCT
cana-945	79	9	=	=	SYM
cana-945	80	1	max(0.2,0.3	max(0.2,0.3	ADJ
cana-945	80	2	)	)	PUNCT
cana-945	80	3	=	=	SYM
cana-945	80	4	0.3	0.3	NUM
cana-945	80	5	(	(	PUNCT
cana-945	80	6	5	5	NUM
cana-945	80	7	)	)	PUNCT
cana-945	80	8	the	the	DET
cana-945	80	9	hesitation	hesitation	NOUN
cana-945	80	10	degree	degree	NOUN
cana-945	80	11	πda(x	πda(x	PROPN
cana-945	80	12	,	,	PUNCT
cana-945	80	13	y	y	NOUN
cana-945	80	14	)	)	PUNCT
cana-945	80	15	is	be	AUX
cana-945	80	16	computed	compute	VERB
cana-945	80	17	as	as	ADP
cana-945	80	18	:	:	PUNCT
cana-945	80	19	πda(x	πda(x	PROPN
cana-945	80	20	,	,	PUNCT
cana-945	80	21	y	y	NOUN
cana-945	80	22	)	)	PUNCT
cana-945	80	23	=	=	SYM
cana-945	81	1	1	1	NUM
cana-945	81	2	−	−	PROPN
cana-945	81	3	μda(x	μda(x	PROPN
cana-945	81	4	,	,	PUNCT
cana-945	81	5	y	y	PROPN
cana-945	81	6	)	)	PUNCT
cana-945	81	7	−	−	PROPN
cana-945	81	8	vda(x	vda(x	PROPN
cana-945	81	9	,	,	PUNCT
cana-945	81	10	y	y	NOUN
cana-945	81	11	)	)	PUNCT
cana-945	81	12	=	=	SYM
cana-945	82	1	1	1	NUM
cana-945	82	2	−	−	NOUN
cana-945	82	3	0.4	0.4	NUM
cana-945	82	4	−	−	NOUN
cana-945	82	5	0.3	0.3	NUM
cana-945	82	6	=	=	SYM
cana-945	82	7	0.3	0.3	NUM
cana-945	82	8	(	(	PUNCT
cana-945	82	9	6	6	NUM
cana-945	82	10	)	)	PUNCT
cana-945	82	11	fig.1	fig.1	PROPN
cana-945	82	12	operation	operation	NOUN
cana-945	82	13	𝐃𝐀	𝐃𝐀	NOUN
cana-945	82	14	for	for	ADP
cana-945	82	15	intuitionistic	intuitionistic	ADJ
cana-945	82	16	fuzzy	fuzzy	ADJ
cana-945	82	17	d	d	NOUN
cana-945	82	18	-	-	PUNCT
cana-945	82	19	algorithm	algorithm	NOUN
cana-945	82	20	fig.1	fig.1	PROPN
cana-945	82	21	visualizes	visualize	VERB
cana-945	82	22	the	the	DET
cana-945	82	23	operation	operation	NOUN
cana-945	82	24	da	da	NOUN
cana-945	82	25	within	within	ADP
cana-945	82	26	an	an	DET
cana-945	82	27	intuitionistic	intuitionistic	ADJ
cana-945	82	28	fuzzy	fuzzy	ADJ
cana-945	82	29	ddd	ddd	NOUN
cana-945	82	30	-	-	PUNCT
cana-945	82	31	algebra	algebra	NOUN
cana-945	82	32	,	,	PUNCT
cana-945	82	33	showcasing	showcase	VERB
cana-945	82	34	how	how	SCONJ
cana-945	82	35	it	it	PRON
cana-945	82	36	combines	combine	VERB
cana-945	82	37	the	the	DET
cana-945	82	38	membership	membership	NOUN
cana-945	82	39	and	and	CCONJ
cana-945	82	40	non	non	ADJ
cana-945	82	41	-	-	ADJ
cana-945	82	42	membership	membership	ADJ
cana-945	82	43	degrees	degree	NOUN
cana-945	82	44	of	of	ADP
cana-945	82	45	two	two	NUM
cana-945	82	46	elements	element	NOUN
cana-945	82	47	x	x	PUNCT
cana-945	82	48	and	and	CCONJ
cana-945	82	49	y	y	PROPN
cana-945	82	50	from	from	ADP
cana-945	82	51	the	the	DET
cana-945	82	52	universe	universe	NOUN
cana-945	82	53	of	of	ADP
cana-945	82	54	discourse	discourse	NOUN
cana-945	82	55	.	.	PUNCT
cana-945	83	1	the	the	DET
cana-945	83	2	blue	blue	ADJ
cana-945	83	3	curve	curve	NOUN
cana-945	83	4	represents	represent	VERB
cana-945	83	5	the	the	DET
cana-945	83	6	resulting	result	VERB
cana-945	83	7	membership	membership	NOUN
cana-945	83	8	degree	degree	NOUN
cana-945	83	9	μda(x	μda(x	PROPN
cana-945	83	10	,	,	PUNCT
cana-945	83	11	y),showing	y),showe	VERB
cana-945	83	12	the	the	DET
cana-945	83	13	degree	degree	NOUN
cana-945	83	14	to	to	PART
cana-945	83	15	which	which	PRON
cana-945	83	16	the	the	DET
cana-945	83	17	pair	pair	NOUN
cana-945	83	18	of	of	ADP
cana-945	83	19	elements	element	NOUN
cana-945	83	20	belong	belong	VERB
cana-945	83	21	to	to	ADP
cana-945	83	22	the	the	DET
cana-945	83	23	resulting	result	VERB
cana-945	83	24	intuitionistic	intuitionistic	ADJ
cana-945	83	25	fuzzy	fuzzy	ADJ
cana-945	83	26	set	set	NOUN
cana-945	83	27	.	.	PUNCT
cana-945	84	1	conversely	conversely	ADV
cana-945	84	2	,	,	PUNCT
cana-945	84	3	the	the	DET
cana-945	84	4	red	red	ADJ
cana-945	84	5	curve	curve	NOUN
cana-945	84	6	illustrates	illustrate	VERB
cana-945	84	7	the	the	DET
cana-945	84	8	non	non	ADJ
cana-945	84	9	-	-	ADJ
cana-945	84	10	membership	membership	ADJ
cana-945	84	11	degree	degree	NOUN
cana-945	84	12	vda(x	vda(x	PROPN
cana-945	84	13	,	,	PUNCT
cana-945	84	14	y	y	PROPN
cana-945	84	15	)	)	PUNCT
cana-945	84	16	,	,	PUNCT
cana-945	84	17	indicating	indicate	VERB
cana-945	84	18	the	the	DET
cana-945	84	19	extent	extent	NOUN
cana-945	84	20	to	to	PART
cana-945	84	21	which	which	PRON
cana-945	84	22	the	the	DET
cana-945	84	23	pair	pair	NOUN
cana-945	84	24	of	of	ADP
cana-945	84	25	elements	element	NOUN
cana-945	84	26	do	do	AUX
cana-945	84	27	not	not	PART
cana-945	84	28	belong	belong	VERB
cana-945	84	29	to	to	ADP
cana-945	84	30	the	the	DET
cana-945	84	31	resulting	result	VERB
cana-945	84	32	set	set	NOUN
cana-945	84	33	.	.	PUNCT
cana-945	85	1	the	the	DET
cana-945	85	2	graph	graph	NOUN
cana-945	85	3	demonstrates	demonstrate	VERB
cana-945	85	4	how	how	SCONJ
cana-945	85	5	da	da	NOUN
cana-945	85	6	integrates	integrate	VERB
cana-945	85	7	the	the	DET
cana-945	85	8	degrees	degree	NOUN
cana-945	85	9	communications	communication	NOUN
cana-945	85	10	on	on	ADP
cana-945	85	11	applied	apply	VERB
cana-945	85	12	nonlinear	nonlinear	ADJ
cana-945	85	13	analysis	analysis	NOUN
cana-945	85	14	issn	issn	NOUN
cana-945	85	15	:	:	PUNCT
cana-945	85	16	1074	1074	NUM
cana-945	85	17	-	-	PUNCT
cana-945	85	18	133x	133x	NUM
cana-945	85	19	vol	vol	NOUN
cana-945	85	20	31	31	NUM
cana-945	85	21	no	no	NOUN
cana-945	85	22	.	.	PUNCT
cana-945	86	1	4s	4s	NUM
cana-945	86	2	(	(	PUNCT
cana-945	86	3	2024	2024	NUM
cana-945	86	4	)	)	PUNCT
cana-945	86	5	504	504	NUM
cana-945	86	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-945	86	7	of	of	ADP
cana-945	86	8	membership	membership	NOUN
cana-945	86	9	and	and	CCONJ
cana-945	86	10	non	non	ADJ
cana-945	86	11	-	-	NOUN
cana-945	86	12	membership	membership	NOUN
cana-945	86	13	to	to	PART
cana-945	86	14	define	define	VERB
cana-945	86	15	the	the	DET
cana-945	86	16	characteristics	characteristic	NOUN
cana-945	86	17	of	of	ADP
cana-945	86	18	the	the	DET
cana-945	86	19	intuitionistic	intuitionistic	ADJ
cana-945	86	20	fuzzy	fuzzy	ADJ
cana-945	86	21	set	set	NOUN
cana-945	86	22	formed	form	VERB
cana-945	86	23	by	by	ADP
cana-945	86	24	the	the	DET
cana-945	86	25	operation	operation	NOUN
cana-945	86	26	.	.	PUNCT
cana-945	87	1	3.2	3.2	NUM
cana-945	87	2	topological	topological	ADJ
cana-945	87	3	techniques	technique	NOUN
cana-945	87	4	in	in	ADP
cana-945	87	5	intuitionistic	intuitionistic	ADJ
cana-945	87	6	fuzzy	fuzzy	ADJ
cana-945	87	7	𝑫-algebra	𝑫-algebra	PROPN
cana-945	87	8	topological	topological	ADJ
cana-945	87	9	techniques	technique	NOUN
cana-945	87	10	,	,	PUNCT
cana-945	87	11	intuitionistic	intuitionistic	ADJ
cana-945	87	12	fuzzy	fuzzy	ADJ
cana-945	87	13	sets	set	NOUN
cana-945	87	14	are	be	AUX
cana-945	87	15	mapped	map	VERB
cana-945	87	16	onto	onto	ADP
cana-945	87	17	topological	topological	ADJ
cana-945	87	18	spaces	space	NOUN
cana-945	87	19	,	,	PUNCT
cana-945	87	20	which	which	PRON
cana-945	87	21	are	be	AUX
cana-945	87	22	mathematical	mathematical	ADJ
cana-945	87	23	structures	structure	NOUN
cana-945	87	24	equipped	equip	VERB
cana-945	87	25	with	with	ADP
cana-945	87	26	a	a	DET
cana-945	87	27	notion	notion	NOUN
cana-945	87	28	of	of	ADP
cana-945	87	29	closeness	closeness	NOUN
cana-945	87	30	or	or	CCONJ
cana-945	87	31	proximity	proximity	NOUN
cana-945	87	32	.	.	PUNCT
cana-945	88	1	let	let	VERB
cana-945	88	2	x	x	PRON
cana-945	88	3	be	be	AUX
cana-945	88	4	the	the	DET
cana-945	88	5	universe	universe	NOUN
cana-945	88	6	of	of	ADP
cana-945	88	7	discourse	discourse	NOUN
cana-945	88	8	,	,	PUNCT
cana-945	88	9	and	and	CCONJ
cana-945	88	10	f(x	f(x	PROPN
cana-945	88	11	)	)	PUNCT
cana-945	88	12	be	be	VERB
cana-945	88	13	the	the	DET
cana-945	88	14	set	set	NOUN
cana-945	88	15	of	of	ADP
cana-945	88	16	all	all	DET
cana-945	88	17	intuitionistic	intuitionistic	ADJ
cana-945	88	18	fuzzy	fuzzy	ADJ
cana-945	88	19	subsets	subset	NOUN
cana-945	88	20	of	of	ADP
cana-945	88	21	x.	x.	NOUN
cana-945	88	22	the	the	DET
cana-945	88	23	mapping	mapping	NOUN
cana-945	88	24	φ	φ	NOUN
cana-945	88	25	:	:	PUNCT
cana-945	88	26	f(x	f(x	PROPN
cana-945	88	27	)	)	PUNCT
cana-945	88	28	→	→	PUNCT
cana-945	89	1	t.	t.	PROPN
cana-945	89	2	where	where	SCONJ
cana-945	89	3	t	t	PROPN
cana-945	89	4	is	be	AUX
cana-945	89	5	a	a	DET
cana-945	89	6	topological	topological	ADJ
cana-945	89	7	space	space	NOUN
cana-945	89	8	,	,	PUNCT
cana-945	89	9	assigns	assign	VERB
cana-945	89	10	each	each	DET
cana-945	89	11	intuitionistic	intuitionistic	ADJ
cana-945	89	12	fuzzy	fuzzy	ADJ
cana-945	89	13	set	set	VERB
cana-945	89	14	a	a	PRON
cana-945	89	15	in	in	ADP
cana-945	89	16	x	x	DET
cana-945	89	17	a	a	DET
cana-945	89	18	corresponding	corresponding	ADJ
cana-945	89	19	subset	subset	NOUN
cana-945	89	20	φ(a	φ(a	ADJ
cana-945	89	21	)	)	PUNCT
cana-945	89	22	in	in	ADP
cana-945	89	23	t	t	PROPN
cana-945	89	24	,	,	PUNCT
cana-945	89	25	preserving	preserve	VERB
cana-945	89	26	certain	certain	ADJ
cana-945	89	27	topological	topological	ADJ
cana-945	89	28	properties	property	NOUN
cana-945	89	29	.	.	PUNCT
cana-945	90	1	topological	topological	ADJ
cana-945	90	2	techniques	technique	NOUN
cana-945	90	3	allows	allow	VERB
cana-945	90	4	to	to	PART
cana-945	90	5	investigate	investigate	VERB
cana-945	90	6	the	the	DET
cana-945	90	7	convergence	convergence	NOUN
cana-945	90	8	behavior	behavior	NOUN
cana-945	90	9	of	of	ADP
cana-945	90	10	sequences	sequence	NOUN
cana-945	90	11	of	of	ADP
cana-945	90	12	intuitionistic	intuitionistic	ADJ
cana-945	90	13	fuzzy	fuzzy	ADJ
cana-945	90	14	sets	set	NOUN
cana-945	90	15	and	and	CCONJ
cana-945	90	16	the	the	DET
cana-945	90	17	compactness	compactness	NOUN
cana-945	90	18	of	of	ADP
cana-945	90	19	sets	set	NOUN
cana-945	90	20	within	within	ADP
cana-945	90	21	intuitionistic	intuitionistic	ADJ
cana-945	90	22	fuzzy	fuzzy	ADJ
cana-945	90	23	d	d	PROPN
cana-945	90	24	-algebra	-algebra	NOUN
cana-945	90	25	structures	structure	NOUN
cana-945	90	26	.	.	PUNCT
cana-945	91	1	a	a	DET
cana-945	91	2	sequence	sequence	NOUN
cana-945	91	3	{	{	PUNCT
cana-945	91	4	an	an	NOUN
cana-945	91	5	}	}	PUNCT
cana-945	91	6	of	of	ADP
cana-945	91	7	intuitionistic	intuitionistic	ADJ
cana-945	91	8	fuzzy	fuzzy	ADJ
cana-945	91	9	sets	set	NOUN
cana-945	91	10	is	be	AUX
cana-945	91	11	said	say	VERB
cana-945	91	12	to	to	PART
cana-945	91	13	converge	converge	VERB
cana-945	91	14	to	to	ADP
cana-945	91	15	a	a	DET
cana-945	91	16	limit	limit	NOUN
cana-945	91	17	set	set	VERB
cana-945	91	18	a	a	DET
cana-945	91	19	if	if	NOUN
cana-945	91	20	,	,	PUNCT
cana-945	91	21	for	for	ADP
cana-945	91	22	every	every	DET
cana-945	91	23	point	point	NOUN
cana-945	91	24	x	x	X
cana-945	91	25	in	in	ADP
cana-945	91	26	the	the	DET
cana-945	91	27	universe	universe	NOUN
cana-945	91	28	of	of	ADP
cana-945	91	29	discourse	discourse	NOUN
cana-945	91	30	xxx	xxx	PROPN
cana-945	91	31	,	,	PUNCT
cana-945	91	32	the	the	DET
cana-945	91	33	membership	membership	NOUN
cana-945	91	34	and	and	CCONJ
cana-945	91	35	non	non	ADJ
cana-945	91	36	-	-	ADJ
cana-945	91	37	membership	membership	ADJ
cana-945	91	38	degrees	degree	NOUN
cana-945	91	39	of	of	ADP
cana-945	91	40	an	an	DET
cana-945	91	41	approach	approach	NOUN
cana-945	91	42	the	the	DET
cana-945	91	43	membership	membership	NOUN
cana-945	91	44	and	and	CCONJ
cana-945	91	45	non	non	ADJ
cana-945	91	46	-	-	ADJ
cana-945	91	47	membership	membership	ADJ
cana-945	91	48	degrees	degree	NOUN
cana-945	91	49	of	of	ADP
cana-945	91	50	a	a	PRON
cana-945	91	51	,	,	PUNCT
cana-945	91	52	respectively	respectively	ADV
cana-945	91	53	,	,	PUNCT
cana-945	91	54	as	as	ADP
cana-945	91	55	n	n	NOUN
cana-945	91	56	approaches	approach	VERB
cana-945	91	57	infinity	infinity	NOUN
cana-945	91	58	.	.	PUNCT
cana-945	92	1	the	the	DET
cana-945	92	2	compactness	compactness	NOUN
cana-945	92	3	of	of	ADP
cana-945	92	4	sets	set	NOUN
cana-945	92	5	in	in	ADP
cana-945	92	6	intuitionistic	intuitionistic	ADJ
cana-945	92	7	fuzzy	fuzzy	ADJ
cana-945	92	8	d	d	NOUN
cana-945	92	9	-	-	PUNCT
cana-945	92	10	algebra	algebra	NOUN
cana-945	92	11	captures	capture	VERB
cana-945	92	12	the	the	DET
cana-945	92	13	notion	notion	NOUN
cana-945	92	14	of	of	ADP
cana-945	92	15	boundedness	boundedness	NOUN
cana-945	92	16	and	and	CCONJ
cana-945	92	17	finite	finite	ADJ
cana-945	92	18	subcoverings	subcovering	NOUN
cana-945	92	19	,	,	PUNCT
cana-945	92	20	providing	provide	VERB
cana-945	92	21	insights	insight	NOUN
cana-945	92	22	into	into	ADP
cana-945	92	23	the	the	DET
cana-945	92	24	structure	structure	NOUN
cana-945	92	25	and	and	CCONJ
cana-945	92	26	behavior	behavior	NOUN
cana-945	92	27	of	of	ADP
cana-945	92	28	intuitionistic	intuitionistic	ADJ
cana-945	92	29	fuzzy	fuzzy	ADJ
cana-945	92	30	sets	set	NOUN
cana-945	92	31	under	under	ADP
cana-945	92	32	algebraic	algebraic	ADJ
cana-945	92	33	operations	operation	NOUN
cana-945	92	34	.	.	PUNCT
cana-945	93	1	topological	topological	ADJ
cana-945	93	2	techniques	technique	NOUN
cana-945	93	3	enable	enable	VERB
cana-945	93	4	to	to	PART
cana-945	93	5	analyze	analyze	VERB
cana-945	93	6	the	the	DET
cana-945	93	7	continuity	continuity	NOUN
cana-945	93	8	properties	property	NOUN
cana-945	93	9	of	of	ADP
cana-945	93	10	operations	operation	NOUN
cana-945	93	11	within	within	ADP
cana-945	93	12	intuitionistic	intuitionistic	ADJ
cana-945	93	13	fuzzy	fuzzy	ADJ
cana-945	93	14	d	d	NOUN
cana-945	93	15	-algebra	-algebra	PROPN
cana-945	93	16	.	.	PUNCT
cana-945	94	1	an	an	DET
cana-945	94	2	operation	operation	NOUN
cana-945	94	3	d	d	NOUN
cana-945	94	4	in	in	ADP
cana-945	94	5	intuitionistic	intuitionistic	ADJ
cana-945	94	6	fuzzy	fuzzy	ADJ
cana-945	94	7	d	d	PROPN
cana-945	94	8	-algebra	-algebra	PROPN
cana-945	94	9	is	be	AUX
cana-945	94	10	said	say	VERB
cana-945	94	11	to	to	PART
cana-945	94	12	be	be	AUX
cana-945	94	13	continuous	continuous	ADJ
cana-945	94	14	if	if	SCONJ
cana-945	94	15	,	,	PUNCT
cana-945	94	16	for	for	ADP
cana-945	94	17	every	every	DET
cana-945	94	18	pair	pair	NOUN
cana-945	94	19	of	of	ADP
cana-945	94	20	intuitionistic	intuitionistic	ADJ
cana-945	94	21	fuzzy	fuzzy	ADJ
cana-945	94	22	sets	set	NOUN
cana-945	94	23	a	a	PRON
cana-945	94	24	and	and	CCONJ
cana-945	94	25	b	b	NOUN
cana-945	94	26	,	,	PUNCT
cana-945	94	27	the	the	DET
cana-945	94	28	operation	operation	NOUN
cana-945	94	29	ddd	ddd	PROPN
cana-945	94	30	preserves	preserve	VERB
cana-945	94	31	limits	limit	NOUN
cana-945	94	32	of	of	ADP
cana-945	94	33	convergent	convergent	ADJ
cana-945	94	34	sequences	sequence	NOUN
cana-945	94	35	.	.	PUNCT
cana-945	95	1	mathematically	mathematically	ADV
cana-945	95	2	,	,	PUNCT
cana-945	95	3	this	this	PRON
cana-945	95	4	can	can	AUX
cana-945	95	5	be	be	AUX
cana-945	95	6	expressed	express	VERB
cana-945	95	7	as	as	ADP
cana-945	95	8	:	:	PUNCT
cana-945	95	9	lim	lim	PROPN
cana-945	95	10	n→∞	n→∞	NUM
cana-945	95	11	→	→	SYM
cana-945	95	12	d(an	d(an	PROPN
cana-945	95	13	,	,	PUNCT
cana-945	95	14	bn	bn	ADJ
cana-945	95	15	)	)	PUNCT
cana-945	95	16	=	=	SYM
cana-945	96	1	d	d	X
cana-945	96	2	(	(	PUNCT
cana-945	96	3	lim	lim	PROPN
cana-945	96	4	n→∞	n→∞	X
cana-945	96	5	an	an	PRON
cana-945	96	6	,	,	PUNCT
cana-945	96	7	lim	lim	PROPN
cana-945	96	8	n→∞	n→∞	NUM
cana-945	96	9	bn	bn	NOUN
cana-945	96	10	)	)	PUNCT
cana-945	96	11	(	(	PUNCT
cana-945	96	12	7	7	X
cana-945	96	13	)	)	PUNCT
cana-945	96	14	where	where	SCONJ
cana-945	96	15	an	an	PRON
cana-945	96	16	and	and	CCONJ
cana-945	96	17	bn	bn	NOUN
cana-945	96	18	are	be	AUX
cana-945	96	19	convergent	convergent	ADJ
cana-945	96	20	sequences	sequence	NOUN
cana-945	96	21	of	of	ADP
cana-945	96	22	intuitionistic	intuitionistic	ADJ
cana-945	96	23	fuzzy	fuzzy	ADJ
cana-945	96	24	sets	set	NOUN
cana-945	96	25	.	.	PUNCT
cana-945	97	1	to	to	PART
cana-945	97	2	illustrate	illustrate	VERB
cana-945	97	3	the	the	DET
cana-945	97	4	convergence	convergence	NOUN
cana-945	97	5	behaviour	behaviour	NOUN
cana-945	97	6	and	and	CCONJ
cana-945	97	7	continuity	continuity	NOUN
cana-945	97	8	properties	property	NOUN
cana-945	97	9	.	.	PUNCT
cana-945	98	1	consider	consider	VERB
cana-945	98	2	an	an	DET
cana-945	98	3	example	example	NOUN
cana-945	98	4	of	of	ADP
cana-945	98	5	an	an	DET
cana-945	98	6	intuitionistic	intuitionistic	ADJ
cana-945	98	7	fuzzy	fuzzy	ADJ
cana-945	98	8	d	d	ADJ
cana-945	98	9	-	-	ADJ
cana-945	98	10	algebraic	algebraic	ADJ
cana-945	98	11	operation	operation	NOUN
cana-945	98	12	d	d	NOUN
cana-945	98	13	defined	define	VERB
cana-945	98	14	as	as	SCONJ
cana-945	98	15	follows	follow	VERB
cana-945	98	16	:	:	PUNCT
cana-945	98	17	d(a	d(a	PROPN
cana-945	98	18	,	,	PUNCT
cana-945	98	19	b	b	NOUN
cana-945	98	20	)	)	PUNCT
cana-945	98	21	=	=	SYM
cana-945	98	22	(	(	PUNCT
cana-945	98	23	μa⋀	μa⋀	PROPN
cana-945	98	24	μb	μb	PART
cana-945	98	25	,	,	PUNCT
cana-945	98	26	va⋁	va⋁	NOUN
cana-945	98	27	vb	vb	NOUN
cana-945	98	28	)	)	PUNCT
cana-945	98	29	(	(	PUNCT
cana-945	98	30	8)	8)	NUM
cana-945	98	31	where	where	SCONJ
cana-945	98	32	μaand	μaand	ADJ
cana-945	98	33	va	va	PROPN
cana-945	98	34	are	be	AUX
cana-945	98	35	the	the	DET
cana-945	98	36	membership	membership	NOUN
cana-945	98	37	and	and	CCONJ
cana-945	98	38	non	non	ADJ
cana-945	98	39	-	-	ADJ
cana-945	98	40	membership	membership	ADJ
cana-945	98	41	functions	function	NOUN
cana-945	98	42	of	of	ADP
cana-945	98	43	intuitionistic	intuitionistic	ADJ
cana-945	98	44	fuzzy	fuzzy	ADJ
cana-945	98	45	set	set	NOUN
cana-945	98	46	a	a	PRON
cana-945	98	47	,	,	PUNCT
cana-945	98	48	and	and	CCONJ
cana-945	98	49	μb	μb	PROPN
cana-945	98	50	and	and	CCONJ
cana-945	98	51	vb	vb	NOUN
cana-945	98	52	are	be	AUX
cana-945	98	53	the	the	DET
cana-945	98	54	membership	membership	NOUN
cana-945	98	55	and	and	CCONJ
cana-945	98	56	non	non	ADJ
cana-945	98	57	-	-	ADJ
cana-945	98	58	membership	membership	ADJ
cana-945	98	59	functions	function	NOUN
cana-945	98	60	of	of	ADP
cana-945	98	61	intuitionistic	intuitionistic	ADJ
cana-945	98	62	fuzzy	fuzzy	ADJ
cana-945	98	63	set	set	NOUN
cana-945	98	64	b.	b.	PROPN
cana-945	99	1	we	we	PRON
cana-945	99	2	aim	aim	VERB
cana-945	99	3	to	to	PART
cana-945	99	4	analyze	analyze	VERB
cana-945	99	5	the	the	DET
cana-945	99	6	convergence	convergence	NOUN
cana-945	99	7	behaviour	behaviour	NOUN
cana-945	99	8	of	of	ADP
cana-945	99	9	sequences	sequence	NOUN
cana-945	99	10	an	an	PRON
cana-945	99	11	and	and	CCONJ
cana-945	99	12	bn	bn	PART
cana-945	99	13	prove	prove	VERB
cana-945	99	14	the	the	DET
cana-945	99	15	continuity	continuity	NOUN
cana-945	99	16	of	of	ADP
cana-945	99	17	operation	operation	NOUN
cana-945	99	18	d.	d.	NOUN
cana-945	99	19	3.3	3.3	NUM
cana-945	99	20	validation	validation	NOUN
cana-945	99	21	strategies	strategy	NOUN
cana-945	99	22	examples	example	NOUN
cana-945	99	23	serve	serve	VERB
cana-945	99	24	as	as	ADP
cana-945	99	25	concrete	concrete	ADJ
cana-945	99	26	instances	instance	NOUN
cana-945	99	27	that	that	PRON
cana-945	99	28	illustrate	illustrate	VERB
cana-945	99	29	the	the	DET
cana-945	99	30	application	application	NOUN
cana-945	99	31	and	and	CCONJ
cana-945	99	32	validity	validity	NOUN
cana-945	99	33	of	of	ADP
cana-945	99	34	mathematical	mathematical	ADJ
cana-945	99	35	models	model	NOUN
cana-945	99	36	.	.	PUNCT
cana-945	100	1	in	in	ADP
cana-945	100	2	the	the	DET
cana-945	100	3	context	context	NOUN
cana-945	100	4	of	of	ADP
cana-945	100	5	intuitionistic	intuitionistic	ADJ
cana-945	100	6	fuzzy	fuzzy	ADJ
cana-945	100	7	d	d	NOUN
cana-945	100	8	-	-	PUNCT
cana-945	100	9	algebra	algebra	NOUN
cana-945	100	10	,	,	PUNCT
cana-945	100	11	examples	example	NOUN
cana-945	100	12	can	can	AUX
cana-945	100	13	be	be	AUX
cana-945	100	14	constructed	construct	VERB
cana-945	100	15	to	to	PART
cana-945	100	16	demonstrate	demonstrate	VERB
cana-945	100	17	the	the	DET
cana-945	100	18	behavior	behavior	NOUN
cana-945	100	19	of	of	ADP
cana-945	100	20	algebraic	algebraic	ADJ
cana-945	100	21	operations	operation	NOUN
cana-945	100	22	,	,	PUNCT
cana-945	100	23	the	the	DET
cana-945	100	24	convergence	convergence	NOUN
cana-945	100	25	of	of	ADP
cana-945	100	26	sequences	sequence	NOUN
cana-945	100	27	,	,	PUNCT
cana-945	100	28	or	or	CCONJ
cana-945	100	29	the	the	DET
cana-945	100	30	satisfaction	satisfaction	NOUN
cana-945	100	31	of	of	ADP
cana-945	100	32	specific	specific	ADJ
cana-945	100	33	properties	property	NOUN
cana-945	100	34	.	.	PUNCT
cana-945	101	1	consider	consider	VERB
cana-945	101	2	the	the	DET
cana-945	101	3	following	follow	VERB
cana-945	101	4	example	example	NOUN
cana-945	101	5	illustrating	illustrate	VERB
cana-945	101	6	the	the	DET
cana-945	101	7	application	application	NOUN
cana-945	101	8	of	of	ADP
cana-945	101	9	an	an	DET
cana-945	101	10	intuitionistic	intuitionistic	ADJ
cana-945	101	11	fuzzy	fuzzy	ADJ
cana-945	101	12	dalgebraic	dalgebraic	ADJ
cana-945	101	13	operation	operation	NOUN
cana-945	101	14	.	.	PUNCT
cana-945	102	1	let	let	VERB
cana-945	102	2	a	a	PRON
cana-945	102	3	and	and	CCONJ
cana-945	102	4	b	b	NOUN
cana-945	102	5	be	be	AUX
cana-945	102	6	two	two	NUM
cana-945	102	7	intuitionistic	intuitionistic	ADJ
cana-945	102	8	fuzzy	fuzzy	ADJ
cana-945	102	9	sets	set	NOUN
cana-945	102	10	defined	define	VERB
cana-945	102	11	over	over	ADP
cana-945	102	12	a	a	DET
cana-945	102	13	universe	universe	NOUN
cana-945	102	14	x.	x.	NOUN
cana-945	102	15	suppose	suppose	VERB
cana-945	102	16	a	a	DET
cana-945	102	17	=	=	X
cana-945	102	18	(	(	PUNCT
cana-945	102	19	0.7,0.3	0.7,0.3	PROPN
cana-945	102	20	)	)	PUNCT
cana-945	102	21	and	and	CCONJ
cana-945	102	22	b	b	X
cana-945	102	23	=	=	SYM
cana-945	102	24	(	(	PUNCT
cana-945	102	25	0.5,0.6	0.5,0.6	PROPN
cana-945	102	26	)	)	PUNCT
cana-945	102	27	.	.	PUNCT
cana-945	103	1	the	the	DET
cana-945	103	2	result	result	NOUN
cana-945	103	3	of	of	ADP
cana-945	103	4	the	the	DET
cana-945	103	5	d	d	ADJ
cana-945	103	6	-	-	ADJ
cana-945	103	7	algebraic	algebraic	ADJ
cana-945	103	8	operation	operation	NOUN
cana-945	103	9	d(a	d(a	PROPN
cana-945	103	10	,	,	PUNCT
cana-945	103	11	b	b	NOUN
cana-945	103	12	)	)	PUNCT
cana-945	103	13	can	can	AUX
cana-945	103	14	be	be	AUX
cana-945	103	15	computed	compute	VERB
cana-945	103	16	of	of	ADP
cana-945	103	17	the	the	PRON
cana-945	103	18	as	as	SCONJ
cana-945	103	19	follows	follow	VERB
cana-945	103	20	:	:	PUNCT
cana-945	103	21	d(a	d(a	PROPN
cana-945	103	22	,	,	PUNCT
cana-945	103	23	b	b	NOUN
cana-945	103	24	)	)	PUNCT
cana-945	103	25	=	=	SYM
cana-945	103	26	(	(	PUNCT
cana-945	103	27	μa⋀	μa⋀	PROPN
cana-945	103	28	μb	μb	PART
cana-945	103	29	,	,	PUNCT
cana-945	103	30	va⋁	va⋁	NOUN
cana-945	103	31	vb	vb	NOUN
cana-945	103	32	)	)	PUNCT
cana-945	103	33	=	=	SYM
cana-945	103	34	(	(	PUNCT
cana-945	103	35	0.5,0.6	0.5,0.6	PROPN
cana-945	103	36	)	)	PUNCT
cana-945	103	37	(	(	PUNCT
cana-945	103	38	9	9	X
cana-945	103	39	)	)	PUNCT
cana-945	103	40	communications	communication	NOUN
cana-945	103	41	on	on	ADP
cana-945	103	42	applied	apply	VERB
cana-945	103	43	nonlinear	nonlinear	ADJ
cana-945	103	44	analysis	analysis	NOUN
cana-945	103	45	issn	issn	NOUN
cana-945	103	46	:	:	PUNCT
cana-945	103	47	1074	1074	NUM
cana-945	103	48	-	-	PUNCT
cana-945	103	49	133x	133x	NUM
cana-945	103	50	vol	vol	NOUN
cana-945	103	51	31	31	NUM
cana-945	103	52	no	no	NOUN
cana-945	103	53	.	.	PUNCT
cana-945	104	1	4s	4s	NUM
cana-945	104	2	(	(	PUNCT
cana-945	104	3	2024	2024	NUM
cana-945	104	4	)	)	PUNCT
cana-945	104	5	505	505	NUM
cana-945	104	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-945	105	1	this	this	DET
cana-945	105	2	example	example	NOUN
cana-945	105	3	demonstrates	demonstrate	VERB
cana-945	105	4	the	the	DET
cana-945	105	5	application	application	NOUN
cana-945	105	6	of	of	ADP
cana-945	105	7	the	the	DET
cana-945	105	8	d	d	ADJ
cana-945	105	9	-	-	ADJ
cana-945	105	10	algebraic	algebraic	ADJ
cana-945	105	11	operation	operation	NOUN
cana-945	105	12	to	to	ADP
cana-945	105	13	two	two	NUM
cana-945	105	14	intuitionistic	intuitionistic	ADJ
cana-945	105	15	fuzzy	fuzzy	ADJ
cana-945	105	16	sets	set	NOUN
cana-945	105	17	,	,	PUNCT
cana-945	105	18	showcasing	showcase	VERB
cana-945	105	19	how	how	SCONJ
cana-945	105	20	the	the	DET
cana-945	105	21	operation	operation	NOUN
cana-945	105	22	combines	combine	VERB
cana-945	105	23	their	their	PRON
cana-945	105	24	membership	membership	NOUN
cana-945	105	25	and	and	CCONJ
cana-945	105	26	non	non	ADJ
cana-945	105	27	-	-	ADJ
cana-945	105	28	membership	membership	ADJ
cana-945	105	29	degrees	degree	NOUN
cana-945	105	30	.	.	PUNCT
cana-945	106	1	counterexamples	counterexample	NOUN
cana-945	106	2	,	,	PUNCT
cana-945	106	3	on	on	ADP
cana-945	106	4	the	the	DET
cana-945	106	5	other	other	ADJ
cana-945	106	6	hand	hand	NOUN
cana-945	106	7	,	,	PUNCT
cana-945	106	8	are	be	AUX
cana-945	106	9	instances	instance	NOUN
cana-945	106	10	that	that	PRON
cana-945	106	11	challenge	challenge	VERB
cana-945	106	12	the	the	DET
cana-945	106	13	validity	validity	NOUN
cana-945	106	14	or	or	CCONJ
cana-945	106	15	applicability	applicability	NOUN
cana-945	106	16	of	of	ADP
cana-945	106	17	a	a	DET
cana-945	106	18	mathematical	mathematical	ADJ
cana-945	106	19	model	model	NOUN
cana-945	106	20	by	by	ADP
cana-945	106	21	demonstrating	demonstrate	VERB
cana-945	106	22	scenarios	scenario	NOUN
cana-945	106	23	where	where	SCONJ
cana-945	106	24	the	the	DET
cana-945	106	25	model	model	NOUN
cana-945	106	26	's	's	PART
cana-945	106	27	predictions	prediction	NOUN
cana-945	106	28	or	or	CCONJ
cana-945	106	29	assumptions	assumption	NOUN
cana-945	106	30	fail	fail	VERB
cana-945	106	31	to	to	PART
cana-945	106	32	hold	hold	VERB
cana-945	106	33	.	.	PUNCT
cana-945	107	1	in	in	ADP
cana-945	107	2	the	the	DET
cana-945	107	3	context	context	NOUN
cana-945	107	4	of	of	ADP
cana-945	107	5	intuitionistic	intuitionistic	ADJ
cana-945	107	6	fuzzy	fuzzy	ADJ
cana-945	107	7	d	d	NOUN
cana-945	107	8	-	-	PUNCT
cana-945	107	9	algebra	algebra	NOUN
cana-945	107	10	,	,	PUNCT
cana-945	107	11	counterexamples	counterexample	NOUN
cana-945	107	12	can	can	AUX
cana-945	107	13	reveal	reveal	VERB
cana-945	107	14	limitations	limitation	NOUN
cana-945	107	15	or	or	CCONJ
cana-945	107	16	unexpected	unexpected	ADJ
cana-945	107	17	behaviors	behavior	NOUN
cana-945	107	18	of	of	ADP
cana-945	107	19	the	the	DET
cana-945	107	20	models	model	NOUN
cana-945	107	21	,	,	PUNCT
cana-945	107	22	prompting	prompt	VERB
cana-945	107	23	to	to	PART
cana-945	107	24	refine	refine	VERB
cana-945	107	25	or	or	CCONJ
cana-945	107	26	reconsider	reconsider	VERB
cana-945	107	27	their	their	PRON
cana-945	107	28	approaches	approach	NOUN
cana-945	107	29	.	.	PUNCT
cana-945	108	1	consider	consider	VERB
cana-945	108	2	the	the	DET
cana-945	108	3	following	follow	VERB
cana-945	108	4	counterexample	counterexample	NOUN
cana-945	108	5	illustrating	illustrate	VERB
cana-945	108	6	a	a	DET
cana-945	108	7	scenario	scenario	NOUN
cana-945	108	8	where	where	SCONJ
cana-945	108	9	an	an	DET
cana-945	108	10	algebraic	algebraic	ADJ
cana-945	108	11	property	property	NOUN
cana-945	108	12	does	do	AUX
cana-945	108	13	not	not	PART
cana-945	108	14	hold	hold	VERB
cana-945	108	15	.	.	PUNCT
cana-945	109	1	let	let	VERB
cana-945	109	2	a	a	PRON
cana-945	109	3	and	and	CCONJ
cana-945	109	4	b	b	NOUN
cana-945	109	5	be	be	AUX
cana-945	109	6	two	two	NUM
cana-945	109	7	intuitionistic	intuitionistic	ADJ
cana-945	109	8	fuzzy	fuzzy	ADJ
cana-945	109	9	sets	set	NOUN
cana-945	109	10	defined	define	VERB
cana-945	109	11	over	over	ADP
cana-945	109	12	a	a	DET
cana-945	109	13	universe	universe	NOUN
cana-945	109	14	x.	x.	NOUN
cana-945	109	15	suppose	suppose	VERB
cana-945	109	16	a	a	DET
cana-945	109	17	=	=	X
cana-945	109	18	(	(	PUNCT
cana-945	109	19	0.9,0.2	0.9,0.2	PROPN
cana-945	109	20	)	)	PUNCT
cana-945	109	21	and	and	CCONJ
cana-945	109	22	a	a	PRON
cana-945	109	23	=	=	X
cana-945	109	24	(	(	PUNCT
cana-945	109	25	0.3,0.8	0.3,0.8	PROPN
cana-945	109	26	)	)	PUNCT
cana-945	109	27	.	.	PUNCT
cana-945	110	1	now	now	ADV
cana-945	110	2	,	,	PUNCT
cana-945	110	3	consider	consider	VERB
cana-945	110	4	the	the	DET
cana-945	110	5	associative	associative	ADJ
cana-945	110	6	property	property	NOUN
cana-945	110	7	of	of	ADP
cana-945	110	8	the	the	DET
cana-945	110	9	d	d	ADJ
cana-945	110	10	-	-	ADJ
cana-945	110	11	algebraic	algebraic	ADJ
cana-945	110	12	operation	operation	NOUN
cana-945	110	13	.	.	PUNCT
cana-945	111	1	d(a	d(a	PROPN
cana-945	111	2	,	,	PUNCT
cana-945	111	3	d(b	d(b	PROPN
cana-945	111	4	,	,	PUNCT
cana-945	111	5	c	c	NOUN
cana-945	111	6	)	)	PUNCT
cana-945	111	7	)	)	PUNCT
cana-945	112	1	≠	≠	PROPN
cana-945	112	2	d(d(a	d(d(a	PROPN
cana-945	112	3	,	,	PUNCT
cana-945	112	4	b	b	NOUN
cana-945	112	5	)	)	PUNCT
cana-945	112	6	,	,	PUNCT
cana-945	112	7	c	c	X
cana-945	112	8	)	)	PUNCT
cana-945	112	9	(	(	PUNCT
cana-945	112	10	10	10	NUM
cana-945	112	11	)	)	PUNCT
cana-945	112	12	this	this	DET
cana-945	112	13	counterexample	counterexample	NOUN
cana-945	112	14	demonstrates	demonstrate	VERB
cana-945	112	15	a	a	DET
cana-945	112	16	violation	violation	NOUN
cana-945	112	17	of	of	ADP
cana-945	112	18	the	the	DET
cana-945	112	19	associative	associative	ADJ
cana-945	112	20	property	property	NOUN
cana-945	112	21	,	,	PUNCT
cana-945	112	22	highlighting	highlight	VERB
cana-945	112	23	a	a	DET
cana-945	112	24	scenario	scenario	NOUN
cana-945	112	25	where	where	SCONJ
cana-945	112	26	the	the	DET
cana-945	112	27	ddd	ddd	PROPN
cana-945	112	28	-	-	PUNCT
cana-945	112	29	algebraic	algebraic	ADJ
cana-945	112	30	operation	operation	NOUN
cana-945	112	31	does	do	AUX
cana-945	112	32	not	not	PART
cana-945	112	33	exhibit	exhibit	VERB
cana-945	112	34	the	the	DET
cana-945	112	35	expected	expect	VERB
cana-945	112	36	behaviour	behaviour	NOUN
cana-945	112	37	.	.	PUNCT
cana-945	113	1	(	(	PUNCT
cana-945	113	2	a	a	X
cana-945	113	3	)	)	PUNCT
cana-945	113	4	(	(	PUNCT
cana-945	113	5	b	b	X
cana-945	113	6	)	)	PUNCT
cana-945	113	7	fig.2	fig.2	PROPN
cana-945	113	8	intuitionistic	intuitionistic	ADJ
cana-945	113	9	fuzzy	fuzzy	ADJ
cana-945	113	10	sets	set	NOUN
cana-945	113	11	decision	decision	NOUN
cana-945	113	12	making	make	VERB
cana-945	113	13	fig.2	fig.2	NOUN
cana-945	113	14	enabling	enable	VERB
cana-945	113	15	users	user	NOUN
cana-945	113	16	to	to	PART
cana-945	113	17	explore	explore	VERB
cana-945	113	18	and	and	CCONJ
cana-945	113	19	understand	understand	VERB
cana-945	113	20	the	the	DET
cana-945	113	21	concept	concept	NOUN
cana-945	113	22	of	of	ADP
cana-945	113	23	intuitionistic	intuitionistic	ADJ
cana-945	113	24	fuzzy	fuzzy	ADJ
cana-945	113	25	sets	set	NOUN
cana-945	113	26	in	in	ADP
cana-945	113	27	decisionmaking	decisionmake	VERB
cana-945	113	28	scenarios	scenario	NOUN
cana-945	113	29	.	.	PUNCT
cana-945	114	1	through	through	ADP
cana-945	114	2	this	this	DET
cana-945	114	3	visualization	visualization	NOUN
cana-945	114	4	,	,	PUNCT
cana-945	114	5	users	user	NOUN
cana-945	114	6	can	can	AUX
cana-945	114	7	dynamically	dynamically	ADV
cana-945	114	8	adjust	adjust	VERB
cana-945	114	9	the	the	DET
cana-945	114	10	membership	membership	NOUN
cana-945	114	11	and	and	CCONJ
cana-945	114	12	nonmembership	nonmembership	NOUN
cana-945	114	13	degrees	degree	NOUN
cana-945	114	14	of	of	ADP
cana-945	114	15	two	two	NUM
cana-945	114	16	candidate	candidate	NOUN
cana-945	114	17	sets	set	NOUN
cana-945	114	18	,	,	PUNCT
cana-945	114	19	visualized	visualize	VERB
cana-945	114	20	as	as	ADP
cana-945	114	21	heatmaps	heatmap	NOUN
cana-945	114	22	,	,	PUNCT
cana-945	114	23	and	and	CCONJ
cana-945	114	24	observe	observe	VERB
cana-945	114	25	the	the	DET
cana-945	114	26	resulting	result	VERB
cana-945	114	27	optimal	optimal	ADJ
cana-945	114	28	candidate	candidate	NOUN
cana-945	114	29	in	in	ADP
cana-945	114	30	real	real	ADJ
cana-945	114	31	-	-	PUNCT
cana-945	114	32	time	time	NOUN
cana-945	114	33	.	.	PUNCT
cana-945	115	1	by	by	ADP
cana-945	115	2	interacting	interact	VERB
cana-945	115	3	with	with	ADP
cana-945	115	4	sliders	slider	NOUN
cana-945	115	5	that	that	PRON
cana-945	115	6	control	control	VERB
cana-945	115	7	the	the	DET
cana-945	115	8	degrees	degree	NOUN
cana-945	115	9	of	of	ADP
cana-945	115	10	membership	membership	NOUN
cana-945	115	11	and	and	CCONJ
cana-945	115	12	nonmembership	nonmembership	NOUN
cana-945	115	13	for	for	ADP
cana-945	115	14	each	each	DET
cana-945	115	15	candidate	candidate	NOUN
cana-945	115	16	,	,	PUNCT
cana-945	115	17	users	user	NOUN
cana-945	115	18	gain	gain	VERB
cana-945	115	19	hands	hand	NOUN
cana-945	115	20	-	-	PUNCT
cana-945	115	21	on	on	ADP
cana-945	115	22	experience	experience	NOUN
cana-945	115	23	in	in	ADP
cana-945	115	24	understanding	understand	VERB
cana-945	115	25	how	how	SCONJ
cana-945	115	26	different	different	ADJ
cana-945	115	27	degrees	degree	NOUN
cana-945	115	28	of	of	ADP
cana-945	115	29	qualification	qualification	NOUN
cana-945	115	30	and	and	CCONJ
cana-945	115	31	experience	experience	NOUN
cana-945	115	32	affect	affect	VERB
cana-945	115	33	the	the	DET
cana-945	115	34	selection	selection	NOUN
cana-945	115	35	of	of	ADP
cana-945	115	36	the	the	DET
cana-945	115	37	optimal	optimal	ADJ
cana-945	115	38	candidate	candidate	NOUN
cana-945	115	39	.	.	PUNCT
cana-945	116	1	this	this	DET
cana-945	116	2	interactive	interactive	ADJ
cana-945	116	3	approach	approach	NOUN
cana-945	116	4	facilitates	facilitate	VERB
cana-945	116	5	intuitive	intuitive	ADJ
cana-945	116	6	comprehension	comprehension	NOUN
cana-945	116	7	of	of	ADP
cana-945	116	8	the	the	DET
cana-945	116	9	complex	complex	ADJ
cana-945	116	10	mathematical	mathematical	ADJ
cana-945	116	11	concepts	concept	NOUN
cana-945	116	12	underlying	underlie	VERB
cana-945	116	13	intuitionistic	intuitionistic	ADJ
cana-945	116	14	fuzzy	fuzzy	ADJ
cana-945	116	15	sets	set	NOUN
cana-945	116	16	and	and	CCONJ
cana-945	116	17	their	their	PRON
cana-945	116	18	application	application	NOUN
cana-945	116	19	in	in	ADP
cana-945	116	20	decision	decision	NOUN
cana-945	116	21	-	-	PUNCT
cana-945	116	22	making	make	VERB
cana-945	116	23	processes	process	NOUN
cana-945	116	24	.	.	PUNCT
cana-945	117	1	additionally	additionally	ADV
cana-945	117	2	,	,	PUNCT
cana-945	117	3	the	the	DET
cana-945	117	4	visualization	visualization	NOUN
cana-945	117	5	enhances	enhance	VERB
cana-945	117	6	user	user	NOUN
cana-945	117	7	engagement	engagement	NOUN
cana-945	117	8	by	by	ADP
cana-945	117	9	providing	provide	VERB
cana-945	117	10	immediate	immediate	ADJ
cana-945	117	11	feedback	feedback	NOUN
cana-945	117	12	on	on	ADP
cana-945	117	13	how	how	SCONJ
cana-945	117	14	changes	change	NOUN
cana-945	117	15	in	in	ADP
cana-945	117	16	the	the	DET
cana-945	117	17	degrees	degree	NOUN
cana-945	117	18	of	of	ADP
cana-945	117	19	membership	membership	NOUN
cana-945	117	20	and	and	CCONJ
cana-945	117	21	non	non	ADJ
cana-945	117	22	-	-	ADJ
cana-945	117	23	membership	membership	ADJ
cana-945	117	24	influence	influence	NOUN
cana-945	117	25	the	the	DET
cana-945	117	26	selection	selection	NOUN
cana-945	117	27	of	of	ADP
cana-945	117	28	the	the	DET
cana-945	117	29	optimal	optimal	ADJ
cana-945	117	30	candidate	candidate	NOUN
cana-945	117	31	.	.	PUNCT
cana-945	118	1	users	user	NOUN
cana-945	118	2	can	can	AUX
cana-945	118	3	experiment	experiment	VERB
cana-945	118	4	with	with	ADP
cana-945	118	5	various	various	ADJ
cana-945	118	6	scenarios	scenario	NOUN
cana-945	118	7	,	,	PUNCT
cana-945	118	8	gaining	gain	VERB
cana-945	118	9	insights	insight	NOUN
cana-945	118	10	into	into	ADP
cana-945	118	11	the	the	DET
cana-945	118	12	trade	trade	NOUN
cana-945	118	13	-	-	PUNCT
cana-945	118	14	offs	off	NOUN
cana-945	118	15	between	between	ADP
cana-945	118	16	different	different	ADJ
cana-945	118	17	criteria	criterion	NOUN
cana-945	118	18	and	and	CCONJ
cana-945	118	19	the	the	DET
cana-945	118	20	decision	decision	NOUN
cana-945	118	21	outcomes	outcome	NOUN
cana-945	118	22	based	base	VERB
cana-945	118	23	on	on	ADP
cana-945	118	24	intuitionistic	intuitionistic	ADJ
cana-945	118	25	fuzzy	fuzzy	ADJ
cana-945	118	26	logic	logic	NOUN
cana-945	118	27	principles	principle	NOUN
cana-945	118	28	.	.	PUNCT
cana-945	119	1	communications	communication	NOUN
cana-945	119	2	on	on	ADP
cana-945	119	3	applied	apply	VERB
cana-945	119	4	nonlinear	nonlinear	ADJ
cana-945	119	5	analysis	analysis	NOUN
cana-945	119	6	issn	issn	NOUN
cana-945	119	7	:	:	PUNCT
cana-945	119	8	1074	1074	NUM
cana-945	119	9	-	-	PUNCT
cana-945	119	10	133x	133x	NUM
cana-945	119	11	vol	vol	NOUN
cana-945	119	12	31	31	NUM
cana-945	119	13	no	no	NOUN
cana-945	119	14	.	.	PUNCT
cana-945	120	1	4s	4s	NUM
cana-945	120	2	(	(	PUNCT
cana-945	120	3	2024	2024	NUM
cana-945	120	4	)	)	PUNCT
cana-945	120	5	506	506	NUM
cana-945	120	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-945	120	7	4	4	NUM
cana-945	120	8	.	.	NOUN
cana-945	120	9	results	result	NOUN
cana-945	120	10	to	to	PART
cana-945	120	11	effectively	effectively	ADV
cana-945	120	12	perform	perform	VERB
cana-945	120	13	the	the	DET
cana-945	120	14	visualizations	visualization	NOUN
cana-945	120	15	and	and	CCONJ
cana-945	120	16	interactive	interactive	ADJ
cana-945	120	17	plots	plot	NOUN
cana-945	120	18	for	for	ADP
cana-945	120	19	intuitionistic	intuitionistic	ADJ
cana-945	120	20	fuzzy	fuzzy	ADJ
cana-945	120	21	d	d	NOUN
cana-945	120	22	-	-	ADJ
cana-945	120	23	algebra	algebra	ADJ
cana-945	120	24	operations	operation	NOUN
cana-945	120	25	,	,	PUNCT
cana-945	120	26	the	the	DET
cana-945	120	27	system	system	NOUN
cana-945	120	28	should	should	AUX
cana-945	120	29	adhere	adhere	VERB
cana-945	120	30	to	to	ADP
cana-945	120	31	specific	specific	ADJ
cana-945	120	32	requirements	requirement	NOUN
cana-945	120	33	.	.	PUNCT
cana-945	121	1	it	it	PRON
cana-945	121	2	should	should	AUX
cana-945	121	3	run	run	VERB
cana-945	121	4	on	on	ADP
cana-945	121	5	windows	window	NOUN
cana-945	121	6	,	,	PUNCT
cana-945	121	7	macos	macos	PROPN
cana-945	121	8	,	,	PUNCT
cana-945	121	9	or	or	CCONJ
cana-945	121	10	linux	linux	PROPN
cana-945	121	11	operating	operating	NOUN
cana-945	121	12	systems	system	NOUN
cana-945	121	13	and	and	CCONJ
cana-945	121	14	be	be	AUX
cana-945	121	15	equipped	equip	VERB
cana-945	121	16	with	with	ADP
cana-945	121	17	a	a	DET
cana-945	121	18	multi	multi	ADJ
cana-945	121	19	-	-	ADJ
cana-945	121	20	core	core	ADJ
cana-945	121	21	processor	processor	NOUN
cana-945	121	22	,	,	PUNCT
cana-945	121	23	ideally	ideally	ADV
cana-945	121	24	intel	intel	PROPN
cana-945	121	25	i5	i5	ADV
cana-945	121	26	or	or	CCONJ
cana-945	121	27	amd	amd	ADJ
cana-945	121	28	ryzen	ryzen	NOUN
cana-945	121	29	5	5	NUM
cana-945	121	30	and	and	CCONJ
cana-945	121	31	above	above	ADV
cana-945	121	32	,	,	PUNCT
cana-945	121	33	to	to	PART
cana-945	121	34	handle	handle	VERB
cana-945	121	35	computational	computational	ADJ
cana-945	121	36	tasks	task	NOUN
cana-945	121	37	efficiently	efficiently	ADV
cana-945	121	38	.	.	PUNCT
cana-945	122	1	a	a	DET
cana-945	122	2	minimum	minimum	NOUN
cana-945	122	3	of	of	ADP
cana-945	122	4	8	8	NUM
cana-945	122	5	gb	gb	NOUN
cana-945	122	6	of	of	ADP
cana-945	122	7	ram	ram	NOUN
cana-945	122	8	is	be	AUX
cana-945	122	9	essential	essential	ADJ
cana-945	122	10	to	to	PART
cana-945	122	11	support	support	VERB
cana-945	122	12	the	the	DET
cana-945	122	13	processing	processing	NOUN
cana-945	122	14	demands	demand	NOUN
cana-945	122	15	of	of	ADP
cana-945	122	16	the	the	DET
cana-945	122	17	plotting	plot	VERB
cana-945	122	18	algorithms	algorithm	NOUN
cana-945	122	19	and	and	CCONJ
cana-945	122	20	ensure	ensure	VERB
cana-945	122	21	smooth	smooth	ADJ
cana-945	122	22	performance	performance	NOUN
cana-945	122	23	.	.	PUNCT
cana-945	123	1	adequate	adequate	ADJ
cana-945	123	2	storage	storage	NOUN
cana-945	123	3	space	space	NOUN
cana-945	123	4	of	of	ADP
cana-945	123	5	at	at	ADV
cana-945	123	6	least	least	ADV
cana-945	123	7	1	1	NUM
cana-945	123	8	gb	gb	NOUN
cana-945	123	9	should	should	AUX
cana-945	123	10	be	be	AUX
cana-945	123	11	available	available	ADJ
cana-945	123	12	for	for	ADP
cana-945	123	13	storing	store	VERB
cana-945	123	14	python	python	NOUN
cana-945	123	15	scripts	script	NOUN
cana-945	123	16	,	,	PUNCT
cana-945	123	17	libraries	library	NOUN
cana-945	123	18	,	,	PUNCT
cana-945	123	19	and	and	CCONJ
cana-945	123	20	generated	generate	VERB
cana-945	123	21	plots	plot	NOUN
cana-945	123	22	.	.	PUNCT
cana-945	124	1	python	python	NOUN
cana-945	124	2	3.6	3.6	NUM
cana-945	124	3	or	or	CCONJ
cana-945	124	4	higher	high	ADJ
cana-945	124	5	is	be	AUX
cana-945	124	6	necessary	necessary	ADJ
cana-945	124	7	,	,	PUNCT
cana-945	124	8	along	along	ADP
cana-945	124	9	with	with	ADP
cana-945	124	10	essential	essential	ADJ
cana-945	124	11	libraries	library	NOUN
cana-945	124	12	like	like	ADP
cana-945	124	13	numpy	numpy	NOUN
cana-945	124	14	,	,	PUNCT
cana-945	124	15	matplotlib	matplotlib	PROPN
cana-945	124	16	,	,	PUNCT
cana-945	124	17	and	and	CCONJ
cana-945	124	18	mpl_toolkits	mpl_toolkit	NOUN
cana-945	124	19	,	,	PUNCT
cana-945	124	20	which	which	PRON
cana-945	124	21	can	can	AUX
cana-945	124	22	be	be	AUX
cana-945	124	23	installed	instal	VERB
cana-945	124	24	using	use	VERB
cana-945	124	25	pip	pip	ADJ
cana-945	124	26	package	package	NOUN
cana-945	124	27	manager	manager	NOUN
cana-945	124	28	.	.	PUNCT
cana-945	125	1	while	while	SCONJ
cana-945	125	2	having	have	VERB
cana-945	125	3	a	a	DET
cana-945	125	4	dedicated	dedicated	ADJ
cana-945	125	5	graphics	graphic	NOUN
cana-945	125	6	card	card	NOUN
cana-945	125	7	would	would	AUX
cana-945	125	8	enhance	enhance	VERB
cana-945	125	9	the	the	DET
cana-945	125	10	rendering	rendering	NOUN
cana-945	125	11	performance	performance	NOUN
cana-945	125	12	,	,	PUNCT
cana-945	125	13	it	it	PRON
cana-945	125	14	is	be	AUX
cana-945	125	15	not	not	PART
cana-945	125	16	mandatory	mandatory	ADJ
cana-945	125	17	.	.	PUNCT
cana-945	126	1	furthermore	furthermore	ADV
cana-945	126	2	,	,	PUNCT
cana-945	126	3	a	a	DET
cana-945	126	4	stable	stable	ADJ
cana-945	126	5	internet	internet	NOUN
cana-945	126	6	connection	connection	NOUN
cana-945	126	7	is	be	AUX
cana-945	126	8	recommended	recommend	VERB
cana-945	126	9	for	for	ADP
cana-945	126	10	downloading	download	VERB
cana-945	126	11	libraries	library	NOUN
cana-945	126	12	and	and	CCONJ
cana-945	126	13	updates	update	NOUN
cana-945	126	14	to	to	PART
cana-945	126	15	maintain	maintain	VERB
cana-945	126	16	compatibility	compatibility	NOUN
cana-945	126	17	and	and	CCONJ
cana-945	126	18	functionality	functionality	NOUN
cana-945	126	19	.	.	PUNCT
cana-945	127	1	fig.3	fig.3	ADJ
cana-945	127	2	mapping	mapping	NOUN
cana-945	127	3	intuitionistic	intuitionistic	ADJ
cana-945	127	4	fuzzy	fuzzy	ADJ
cana-945	127	5	set	set	VERB
cana-945	127	6	a	a	PRON
cana-945	127	7	to	to	ADP
cana-945	127	8	topological	topological	ADJ
cana-945	127	9	space	space	NOUN
cana-945	127	10	fig.3	fig.3	PROPN
cana-945	127	11	achieves	achieve	VERB
cana-945	127	12	its	its	PRON
cana-945	127	13	result	result	NOUN
cana-945	127	14	by	by	ADP
cana-945	127	15	visualizing	visualize	VERB
cana-945	127	16	the	the	DET
cana-945	127	17	mapping	mapping	NOUN
cana-945	127	18	of	of	ADP
cana-945	127	19	an	an	DET
cana-945	127	20	intuitionistic	intuitionistic	ADJ
cana-945	127	21	fuzzy	fuzzy	NOUN
cana-945	127	22	set	set	VERB
cana-945	127	23	a	a	PRON
cana-945	127	24	onto	onto	ADP
cana-945	127	25	a	a	DET
cana-945	127	26	topological	topological	ADJ
cana-945	127	27	space	space	NOUN
cana-945	127	28	through	through	ADP
cana-945	127	29	the	the	DET
cana-945	127	30	application	application	NOUN
cana-945	127	31	of	of	ADP
cana-945	127	32	a	a	DET
cana-945	127	33	mapping	mapping	NOUN
cana-945	127	34	function	function	NOUN
cana-945	127	35	φ	φ	PROPN
cana-945	127	36	.	.	PUNCT
cana-945	128	1	initially	initially	ADV
cana-945	128	2	,	,	PUNCT
cana-945	128	3	the	the	DET
cana-945	128	4	membership	membership	NOUN
cana-945	128	5	and	and	CCONJ
cana-945	128	6	nonmembership	nonmembership	NOUN
cana-945	128	7	functions	function	NOUN
cana-945	128	8	of	of	ADP
cana-945	128	9	the	the	DET
cana-945	128	10	intuitionistic	intuitionistic	ADJ
cana-945	128	11	fuzzy	fuzzy	ADJ
cana-945	128	12	set	set	NOUN
cana-945	128	13	a	a	PRON
cana-945	128	14	are	be	AUX
cana-945	128	15	plotted	plot	VERB
cana-945	128	16	over	over	ADP
cana-945	128	17	the	the	DET
cana-945	128	18	universe	universe	NOUN
cana-945	128	19	of	of	ADP
cana-945	128	20	discourse	discourse	NOUN
cana-945	128	21	x	x	NOUN
cana-945	128	22	,	,	PUNCT
cana-945	128	23	providing	provide	VERB
cana-945	128	24	insights	insight	NOUN
cana-945	128	25	into	into	ADP
cana-945	128	26	the	the	DET
cana-945	128	27	degrees	degree	NOUN
cana-945	128	28	of	of	ADP
cana-945	128	29	membership	membership	NOUN
cana-945	128	30	and	and	CCONJ
cana-945	128	31	non	non	ADJ
cana-945	128	32	-	-	NOUN
cana-945	128	33	membership	membership	NOUN
cana-945	128	34	across	across	ADP
cana-945	128	35	different	different	ADJ
cana-945	128	36	elements	element	NOUN
cana-945	128	37	of	of	ADP
cana-945	128	38	x.	x.	NOUN
cana-945	128	39	subsequently	subsequently	ADV
cana-945	128	40	,	,	PUNCT
cana-945	128	41	the	the	DET
cana-945	128	42	mapping	mapping	NOUN
cana-945	128	43	function	function	NOUN
cana-945	128	44	φ	φ	PROPN
cana-945	128	45	is	be	AUX
cana-945	128	46	applied	apply	VERB
cana-945	128	47	to	to	PART
cana-945	128	48	transform	transform	VERB
cana-945	128	49	these	these	DET
cana-945	128	50	membership	membership	NOUN
cana-945	128	51	and	and	CCONJ
cana-945	128	52	nonmembership	nonmembership	NOUN
cana-945	128	53	degrees	degree	NOUN
cana-945	128	54	into	into	ADP
cana-945	128	55	a	a	DET
cana-945	128	56	new	new	ADJ
cana-945	128	57	set	set	NOUN
cana-945	128	58	of	of	ADP
cana-945	128	59	values	value	NOUN
cana-945	128	60	,	,	PUNCT
cana-945	128	61	which	which	PRON
cana-945	128	62	represent	represent	VERB
cana-945	128	63	the	the	DET
cana-945	128	64	mapped	map	VERB
cana-945	128	65	set	set	NOUN
cana-945	128	66	φ(a	φ(a	ADJ
cana-945	128	67	)	)	PUNCT
cana-945	128	68	in	in	ADP
cana-945	128	69	the	the	DET
cana-945	128	70	topological	topological	ADJ
cana-945	128	71	space	space	NOUN
cana-945	128	72	.	.	PUNCT
cana-945	129	1	this	this	DET
cana-945	129	2	mapping	mapping	NOUN
cana-945	129	3	function	function	NOUN
cana-945	129	4	serves	serve	VERB
cana-945	129	5	to	to	PART
cana-945	129	6	preserve	preserve	VERB
cana-945	129	7	certain	certain	ADJ
cana-945	129	8	topological	topological	ADJ
cana-945	129	9	properties	property	NOUN
cana-945	129	10	while	while	SCONJ
cana-945	129	11	translating	translate	VERB
cana-945	129	12	the	the	DET
cana-945	129	13	intuitionistic	intuitionistic	ADJ
cana-945	129	14	fuzzy	fuzzy	ADJ
cana-945	129	15	set	set	VERB
cana-945	129	16	a	a	PRON
cana-945	129	17	into	into	ADP
cana-945	129	18	the	the	DET
cana-945	129	19	topological	topological	ADJ
cana-945	129	20	realm	realm	NOUN
cana-945	129	21	.	.	PUNCT
cana-945	130	1	the	the	DET
cana-945	130	2	resulting	result	VERB
cana-945	130	3	graph	graph	NOUN
cana-945	130	4	illustrates	illustrate	VERB
cana-945	130	5	how	how	SCONJ
cana-945	130	6	the	the	DET
cana-945	130	7	original	original	ADJ
cana-945	130	8	fuzzy	fuzzy	NOUN
cana-945	130	9	set	set	NOUN
cana-945	130	10	a	a	PRON
cana-945	130	11	is	be	AUX
cana-945	130	12	transformed	transform	VERB
cana-945	130	13	into	into	ADP
cana-945	130	14	a	a	DET
cana-945	130	15	new	new	ADJ
cana-945	130	16	representation	representation	NOUN
cana-945	130	17	within	within	ADP
cana-945	130	18	the	the	DET
cana-945	130	19	topological	topological	ADJ
cana-945	130	20	space	space	NOUN
cana-945	130	21	,	,	PUNCT
cana-945	130	22	thereby	thereby	ADV
cana-945	130	23	demonstrating	demonstrate	VERB
cana-945	130	24	the	the	DET
cana-945	130	25	application	application	NOUN
cana-945	130	26	of	of	ADP
cana-945	130	27	topological	topological	ADJ
cana-945	130	28	techniques	technique	NOUN
cana-945	130	29	in	in	ADP
cana-945	130	30	intuitionistic	intuitionistic	ADJ
cana-945	130	31	fuzzy	fuzzy	ADJ
cana-945	130	32	d	d	NOUN
cana-945	130	33	-	-	NOUN
cana-945	130	34	algebra	algebra	NOUN
cana-945	130	35	.	.	PUNCT
cana-945	131	1	through	through	ADP
cana-945	131	2	this	this	DET
cana-945	131	3	visualization	visualization	NOUN
cana-945	131	4	,	,	PUNCT
cana-945	131	5	the	the	DET
cana-945	131	6	relationship	relationship	NOUN
cana-945	131	7	between	between	ADP
cana-945	131	8	intuitionistic	intuitionistic	ADJ
cana-945	131	9	fuzzy	fuzzy	ADJ
cana-945	131	10	sets	set	NOUN
cana-945	131	11	and	and	CCONJ
cana-945	131	12	their	their	PRON
cana-945	131	13	corresponding	corresponding	ADJ
cana-945	131	14	topological	topological	ADJ
cana-945	131	15	representations	representation	NOUN
cana-945	131	16	could	could	AUX
cana-945	131	17	be	be	AUX
cana-945	131	18	understanding	understand	VERB
cana-945	131	19	,	,	PUNCT
cana-945	131	20	facilitating	facilitate	VERB
cana-945	131	21	the	the	DET
cana-945	131	22	analysis	analysis	NOUN
cana-945	131	23	of	of	ADP
cana-945	131	24	convergence	convergence	NOUN
cana-945	131	25	behaviour	behaviour	NOUN
cana-945	131	26	,	,	PUNCT
cana-945	131	27	continuity	continuity	NOUN
cana-945	131	28	properties	property	NOUN
cana-945	131	29	,	,	PUNCT
cana-945	131	30	and	and	CCONJ
cana-945	131	31	other	other	ADJ
cana-945	131	32	key	key	ADJ
cana-945	131	33	aspects	aspect	NOUN
cana-945	131	34	of	of	ADP
cana-945	131	35	intuitionistic	intuitionistic	ADJ
cana-945	131	36	fuzzy	fuzzy	ADJ
cana-945	131	37	d	d	ADJ
cana-945	131	38	-	-	ADJ
cana-945	131	39	algebra	algebra	ADJ
cana-945	131	40	structures	structure	NOUN
cana-945	131	41	.	.	PUNCT
cana-945	132	1	communications	communication	NOUN
cana-945	132	2	on	on	ADP
cana-945	132	3	applied	apply	VERB
cana-945	132	4	nonlinear	nonlinear	ADJ
cana-945	132	5	analysis	analysis	NOUN
cana-945	132	6	issn	issn	NOUN
cana-945	132	7	:	:	PUNCT
cana-945	132	8	1074	1074	NUM
cana-945	132	9	-	-	PUNCT
cana-945	132	10	133x	133x	NUM
cana-945	132	11	vol	vol	NOUN
cana-945	132	12	31	31	NUM
cana-945	132	13	no	no	NOUN
cana-945	132	14	.	.	PUNCT
cana-945	133	1	4s	4s	NUM
cana-945	133	2	(	(	PUNCT
cana-945	133	3	2024	2024	NUM
cana-945	133	4	)	)	PUNCT
cana-945	133	5	507	507	NUM
cana-945	133	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-945	133	7	fig.4	fig.4	DET
cana-945	133	8	convergence	convergence	NOUN
cana-945	133	9	behaviour	behaviour	NOUN
cana-945	133	10	and	and	CCONJ
cana-945	133	11	operation	operation	NOUN
cana-945	133	12	d	d	PROPN
cana-945	133	13	in	in	ADP
cana-945	133	14	intuitionistic	intuitionistic	ADJ
cana-945	133	15	fuzzy	fuzzy	ADJ
cana-945	133	16	d	d	NOUN
cana-945	133	17	-	-	PUNCT
cana-945	133	18	algebra	algebra	ADJ
cana-945	133	19	fig.5	fig.5	ADP
cana-945	133	20	convergence	convergence	NOUN
cana-945	133	21	behaviour	behaviour	NOUN
cana-945	133	22	of	of	ADP
cana-945	133	23	intuitionistic	intuitionistic	ADJ
cana-945	133	24	fuzzy	fuzzy	ADJ
cana-945	133	25	sets	set	NOUN
cana-945	133	26	fig.5	fig.5	NOUN
cana-945	133	27	illustrates	illustrate	VERB
cana-945	133	28	the	the	DET
cana-945	133	29	convergence	convergence	NOUN
cana-945	133	30	behaviour	behaviour	NOUN
cana-945	133	31	of	of	ADP
cana-945	133	32	sequences	sequence	NOUN
cana-945	133	33	of	of	ADP
cana-945	133	34	intuitionistic	intuitionistic	ADJ
cana-945	133	35	fuzzy	fuzzy	ADJ
cana-945	133	36	sets	set	NOUN
cana-945	133	37	towards	towards	ADP
cana-945	133	38	a	a	DET
cana-945	133	39	limit	limit	NOUN
cana-945	133	40	set	set	VERB
cana-945	133	41	a	a	PRON
cana-945	133	42	,	,	PUNCT
cana-945	133	43	providing	provide	VERB
cana-945	133	44	valuable	valuable	ADJ
cana-945	133	45	insights	insight	NOUN
cana-945	133	46	into	into	ADP
cana-945	133	47	the	the	DET
cana-945	133	48	dynamics	dynamic	NOUN
cana-945	133	49	of	of	ADP
cana-945	133	50	convergence	convergence	NOUN
cana-945	133	51	within	within	ADP
cana-945	133	52	intuitionistic	intuitionistic	ADJ
cana-945	133	53	fuzzy	fuzzy	ADJ
cana-945	133	54	dalgebra	dalgebra	NOUN
cana-945	133	55	structures	structure	NOUN
cana-945	133	56	.	.	PUNCT
cana-945	134	1	each	each	DET
cana-945	134	2	line	line	NOUN
cana-945	134	3	on	on	ADP
cana-945	134	4	the	the	DET
cana-945	134	5	graph	graph	NOUN
cana-945	134	6	represents	represent	VERB
cana-945	134	7	a	a	DET
cana-945	134	8	sequence	sequence	NOUN
cana-945	134	9	of	of	ADP
cana-945	134	10	fuzzy	fuzzy	ADJ
cana-945	134	11	sets	set	NOUN
cana-945	134	12	,	,	PUNCT
cana-945	134	13	with	with	ADP
cana-945	134	14	their	their	PRON
cana-945	134	15	membership	membership	NOUN
cana-945	134	16	and	and	CCONJ
cana-945	134	17	non	non	ADJ
cana-945	134	18	-	-	ADJ
cana-945	134	19	membership	membership	ADJ
cana-945	134	20	degrees	degree	NOUN
cana-945	134	21	gradually	gradually	ADV
cana-945	134	22	approaching	approach	VERB
cana-945	134	23	those	those	PRON
cana-945	134	24	of	of	ADP
cana-945	134	25	the	the	DET
cana-945	134	26	limit	limit	NOUN
cana-945	134	27	set	set	VERB
cana-945	134	28	a	a	PRON
cana-945	134	29	as	as	SCONJ
cana-945	134	30	the	the	DET
cana-945	134	31	sequence	sequence	NOUN
cana-945	134	32	progresses	progress	VERB
cana-945	134	33	.	.	PUNCT
cana-945	135	1	the	the	DET
cana-945	135	2	dashed	dash	VERB
cana-945	135	3	lines	line	NOUN
cana-945	135	4	represent	represent	VERB
cana-945	135	5	the	the	DET
cana-945	135	6	membership	membership	NOUN
cana-945	135	7	and	and	CCONJ
cana-945	135	8	non	non	ADJ
cana-945	135	9	-	-	ADJ
cana-945	135	10	membership	membership	ADJ
cana-945	135	11	functions	function	NOUN
cana-945	135	12	of	of	ADP
cana-945	135	13	the	the	DET
cana-945	135	14	limit	limit	NOUN
cana-945	135	15	set	set	VERB
cana-945	135	16	a	a	PRON
cana-945	135	17	,	,	PUNCT
cana-945	135	18	serving	serve	VERB
cana-945	135	19	as	as	ADP
cana-945	135	20	reference	reference	NOUN
cana-945	135	21	points	point	NOUN
cana-945	135	22	for	for	ADP
cana-945	135	23	convergence	convergence	NOUN
cana-945	135	24	.	.	PUNCT
cana-945	136	1	as	as	SCONJ
cana-945	136	2	the	the	DET
cana-945	136	3	sequences	sequence	NOUN
cana-945	136	4	approach	approach	VERB
cana-945	136	5	the	the	DET
cana-945	136	6	limit	limit	NOUN
cana-945	136	7	,	,	PUNCT
cana-945	136	8	their	their	PRON
cana-945	136	9	curves	curve	NOUN
cana-945	136	10	converge	converge	VERB
cana-945	136	11	towards	towards	ADP
cana-945	136	12	these	these	DET
cana-945	136	13	dashed	dash	VERB
cana-945	136	14	lines	line	NOUN
cana-945	136	15	,	,	PUNCT
cana-945	136	16	indicating	indicate	VERB
cana-945	136	17	the	the	DET
cana-945	136	18	increasing	increase	VERB
cana-945	136	19	similarity	similarity	NOUN
cana-945	136	20	of	of	ADP
cana-945	136	21	their	their	PRON
cana-945	136	22	membership	membership	NOUN
cana-945	136	23	and	and	CCONJ
cana-945	136	24	non	non	ADJ
cana-945	136	25	-	-	ADJ
cana-945	136	26	membership	membership	ADJ
cana-945	136	27	degrees	degree	NOUN
cana-945	136	28	to	to	ADP
cana-945	136	29	those	those	PRON
cana-945	136	30	of	of	ADP
cana-945	136	31	the	the	DET
cana-945	136	32	limit	limit	NOUN
cana-945	136	33	set	set	VERB
cana-945	136	34	a.	a.	NOUN
cana-945	136	35	the	the	DET
cana-945	136	36	graph	graph	NOUN
cana-945	136	37	thus	thus	ADV
cana-945	136	38	visually	visually	ADV
cana-945	136	39	demonstrates	demonstrate	VERB
cana-945	136	40	the	the	DET
cana-945	136	41	convergence	convergence	NOUN
cana-945	136	42	process	process	NOUN
cana-945	136	43	,	,	PUNCT
cana-945	136	44	allowing	allow	VERB
cana-945	136	45	to	to	PART
cana-945	136	46	analyse	analyse	VERB
cana-945	136	47	the	the	DET
cana-945	136	48	convergence	convergence	NOUN
cana-945	136	49	rate	rate	NOUN
cana-945	136	50	and	and	CCONJ
cana-945	136	51	understand	understand	VERB
cana-945	136	52	how	how	SCONJ
cana-945	136	53	intuitionistic	intuitionistic	ADJ
cana-945	136	54	fuzzy	fuzzy	ADJ
cana-945	136	55	sets	set	NOUN
cana-945	136	56	evolve	evolve	VERB
cana-945	136	57	towards	towards	ADP
cana-945	136	58	a	a	DET
cana-945	136	59	specific	specific	ADJ
cana-945	136	60	limit	limit	NOUN
cana-945	136	61	under	under	ADP
cana-945	136	62	defined	define	VERB
cana-945	136	63	sequences	sequence	NOUN
cana-945	136	64	.	.	PUNCT
cana-945	137	1	through	through	ADP
cana-945	137	2	this	this	DET
cana-945	137	3	visualization	visualization	NOUN
cana-945	137	4	,	,	PUNCT
cana-945	137	5	a	a	DET
cana-945	137	6	deeper	deep	ADJ
cana-945	137	7	understanding	understanding	NOUN
cana-945	137	8	of	of	ADP
cana-945	137	9	the	the	DET
cana-945	137	10	convergence	convergence	NOUN
cana-945	137	11	behaviour	behaviour	NOUN
cana-945	137	12	within	within	ADP
cana-945	137	13	intuitionistic	intuitionistic	ADJ
cana-945	137	14	fuzzy	fuzzy	ADJ
cana-945	137	15	d	d	NOUN
cana-945	137	16	-	-	PUNCT
cana-945	137	17	algebra	algebra	NOUN
cana-945	137	18	is	be	AUX
cana-945	137	19	achieved	achieve	VERB
cana-945	137	20	,	,	PUNCT
cana-945	137	21	aiding	aid	VERB
cana-945	137	22	in	in	ADP
cana-945	137	23	the	the	DET
cana-945	137	24	exploration	exploration	NOUN
cana-945	137	25	and	and	CCONJ
cana-945	137	26	analysis	analysis	NOUN
cana-945	137	27	of	of	ADP
cana-945	137	28	uncertainty	uncertainty	NOUN
cana-945	137	29	and	and	CCONJ
cana-945	137	30	imprecision	imprecision	NOUN
cana-945	137	31	in	in	ADP
cana-945	137	32	various	various	ADJ
cana-945	137	33	applications	application	NOUN
cana-945	137	34	.	.	PUNCT
cana-945	138	1	fig.6	fig.6	NOUN
cana-945	138	2	membership	membership	NOUN
cana-945	138	3	degree	degree	NOUN
cana-945	138	4	surface	surface	NOUN
cana-945	138	5	plot	plot	NOUN
cana-945	138	6	fig.6	fig.6	PROPN
cana-945	138	7	visualizes	visualize	VERB
cana-945	138	8	the	the	DET
cana-945	138	9	membership	membership	NOUN
cana-945	138	10	degree	degree	NOUN
cana-945	138	11	μda(x	μda(x	PROPN
cana-945	138	12	,	,	PUNCT
cana-945	138	13	y)resulting	y)resulte	VERB
cana-945	138	14	from	from	ADP
cana-945	138	15	the	the	DET
cana-945	138	16	intuitionistic	intuitionistic	ADJ
cana-945	138	17	fuzzy	fuzzy	ADJ
cana-945	138	18	d	d	NOUN
cana-945	138	19	-	-	ADJ
cana-945	138	20	algebra	algebra	ADJ
cana-945	138	21	operation	operation	NOUN
cana-945	138	22	da	da	NOUN
cana-945	138	23	.	.	PUNCT
cana-945	139	1	in	in	ADP
cana-945	139	2	this	this	DET
cana-945	139	3	plot	plot	NOUN
cana-945	139	4	,	,	PUNCT
cana-945	139	5	the	the	DET
cana-945	139	6	x	x	NOUN
cana-945	139	7	-	-	NOUN
cana-945	139	8	axis	axis	ADJ
cana-945	139	9	and	and	CCONJ
cana-945	139	10	y	y	NOUN
cana-945	139	11	-	-	PUNCT
cana-945	139	12	axis	axis	NOUN
cana-945	139	13	represent	represent	VERB
cana-945	139	14	the	the	DET
cana-945	139	15	membership	membership	NOUN
cana-945	139	16	degrees	degree	NOUN
cana-945	139	17	μa(x)and	μa(x)and	VERB
cana-945	139	18	μa(y)of	μa(y)of	ADV
cana-945	139	19	two	two	NUM
cana-945	139	20	elements	element	NOUN
cana-945	139	21	,	,	PUNCT
cana-945	139	22	while	while	SCONJ
cana-945	139	23	the	the	DET
cana-945	139	24	z	z	NOUN
cana-945	139	25	-	-	PUNCT
cana-945	139	26	axis	axis	NOUN
cana-945	139	27	shows	show	VERB
cana-945	139	28	the	the	DET
cana-945	139	29	resulting	result	VERB
cana-945	139	30	membership	membership	NOUN
cana-945	139	31	degreeμda(x	degreeμda(x	PROPN
cana-945	139	32	,	,	PUNCT
cana-945	139	33	y	y	PROPN
cana-945	139	34	)	)	PUNCT
cana-945	139	35	.	.	PUNCT
cana-945	140	1	the	the	DET
cana-945	140	2	surface	surface	NOUN
cana-945	140	3	plot	plot	NOUN
cana-945	140	4	is	be	AUX
cana-945	140	5	colored	color	VERB
cana-945	140	6	using	use	VERB
cana-945	140	7	the	the	DET
cana-945	140	8	'	'	PUNCT
cana-945	140	9	viridis	viridis	PROPN
cana-945	140	10	'	'	PUNCT
cana-945	140	11	colormap	colormap	NOUN
cana-945	140	12	to	to	PART
cana-945	140	13	highlight	highlight	VERB
cana-945	140	14	the	the	DET
cana-945	140	15	variations	variation	NOUN
cana-945	140	16	in	in	ADP
cana-945	140	17	membership	membership	NOUN
cana-945	140	18	degrees	degree	NOUN
cana-945	140	19	.	.	PUNCT
cana-945	141	1	this	this	DET
cana-945	141	2	visualization	visualization	NOUN
cana-945	141	3	clearly	clearly	ADV
cana-945	141	4	demonstrates	demonstrate	VERB
cana-945	141	5	how	how	SCONJ
cana-945	141	6	the	the	DET
cana-945	141	7	membership	membership	NOUN
cana-945	141	8	degrees	degree	NOUN
cana-945	141	9	are	be	AUX
cana-945	141	10	combined	combine	VERB
cana-945	141	11	using	use	VERB
cana-945	141	12	the	the	DET
cana-945	141	13	minimum	minimum	ADJ
cana-945	141	14	operation	operation	NOUN
cana-945	141	15	⋀	⋀	PROPN
cana-945	141	16	,	,	PUNCT
cana-945	141	17	indicating	indicate	VERB
cana-945	141	18	the	the	DET
cana-945	141	19	degree	degree	NOUN
cana-945	141	20	to	to	PART
cana-945	141	21	which	which	PRON
cana-945	141	22	the	the	DET
cana-945	141	23	resulting	result	VERB
cana-945	141	24	pair	pair	NOUN
cana-945	141	25	of	of	ADP
cana-945	141	26	elements	element	NOUN
cana-945	141	27	belong	belong	VERB
cana-945	141	28	to	to	ADP
cana-945	141	29	the	the	DET
cana-945	141	30	intuitionistic	intuitionistic	ADJ
cana-945	141	31	fuzzy	fuzzy	ADJ
cana-945	141	32	set	set	NOUN
cana-945	141	33	.	.	PUNCT
cana-945	142	1	by	by	ADP
cana-945	142	2	examining	examine	VERB
cana-945	142	3	this	this	DET
cana-945	142	4	plot	plot	NOUN
cana-945	142	5	,	,	PUNCT
cana-945	142	6	one	one	PRON
cana-945	142	7	can	can	AUX
cana-945	142	8	understand	understand	VERB
cana-945	142	9	the	the	DET
cana-945	142	10	behavior	behavior	NOUN
cana-945	142	11	and	and	CCONJ
cana-945	142	12	interaction	interaction	NOUN
cana-945	142	13	of	of	ADP
cana-945	142	14	membership	membership	NOUN
cana-945	142	15	values	value	NOUN
cana-945	142	16	under	under	ADP
cana-945	142	17	the	the	DET
cana-945	142	18	intuitionistic	intuitionistic	ADJ
cana-945	142	19	fuzzy	fuzzy	ADJ
cana-945	142	20	d	d	NOUN
cana-945	142	21	-	-	ADJ
cana-945	142	22	algebra	algebra	ADJ
cana-945	142	23	operation	operation	NOUN
cana-945	142	24	.	.	PUNCT
cana-945	143	1	communications	communication	NOUN
cana-945	143	2	on	on	ADP
cana-945	143	3	applied	apply	VERB
cana-945	143	4	nonlinear	nonlinear	ADJ
cana-945	143	5	analysis	analysis	NOUN
cana-945	143	6	issn	issn	NOUN
cana-945	143	7	:	:	PUNCT
cana-945	143	8	1074	1074	NUM
cana-945	143	9	-	-	PUNCT
cana-945	143	10	133x	133x	NUM
cana-945	143	11	vol	vol	NOUN
cana-945	143	12	31	31	NUM
cana-945	143	13	no	no	NOUN
cana-945	143	14	.	.	PUNCT
cana-945	144	1	4s	4s	NUM
cana-945	144	2	(	(	PUNCT
cana-945	144	3	2024	2024	NUM
cana-945	144	4	)	)	PUNCT
cana-945	144	5	508	508	NUM
cana-945	144	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-945	144	7	fig.7	fig.7	ADJ
cana-945	144	8	non	non	ADJ
cana-945	144	9	-	-	ADJ
cana-945	144	10	membership	membership	ADJ
cana-945	144	11	degree	degree	NOUN
cana-945	144	12	surface	surface	NOUN
cana-945	144	13	plot	plot	NOUN
cana-945	144	14	fig.7	fig.7	ADV
cana-945	144	15	depicts	depict	VERB
cana-945	144	16	the	the	DET
cana-945	144	17	non	non	ADJ
cana-945	144	18	-	-	ADJ
cana-945	144	19	membership	membership	ADJ
cana-945	144	20	degree	degree	NOUN
cana-945	144	21	vda(x	vda(x	PROPN
cana-945	144	22	,	,	PUNCT
cana-945	144	23	y)resulting	y)resulte	VERB
cana-945	144	24	from	from	ADP
cana-945	144	25	the	the	DET
cana-945	144	26	same	same	ADJ
cana-945	144	27	intuitionistic	intuitionistic	ADJ
cana-945	144	28	fuzzy	fuzzy	ADJ
cana-945	144	29	dalgebra	dalgebra	NOUN
cana-945	144	30	operation	operation	NOUN
cana-945	144	31	da	da	NOUN
cana-945	144	32	.	.	PUNCT
cana-945	145	1	here	here	ADV
cana-945	145	2	,	,	PUNCT
cana-945	145	3	the	the	DET
cana-945	145	4	x	x	NOUN
cana-945	145	5	-	-	NOUN
cana-945	145	6	axis	axis	ADJ
cana-945	145	7	and	and	CCONJ
cana-945	145	8	y	y	NOUN
cana-945	145	9	-	-	PUNCT
cana-945	145	10	axis	axis	NOUN
cana-945	145	11	represent	represent	VERB
cana-945	145	12	the	the	DET
cana-945	145	13	non	non	ADJ
cana-945	145	14	-	-	ADJ
cana-945	145	15	membership	membership	ADJ
cana-945	145	16	degrees	degree	NOUN
cana-945	145	17	va(x	va(x	NOUN
cana-945	145	18	)	)	PUNCT
cana-945	145	19	and	and	CCONJ
cana-945	145	20	va(y)of	va(y)of	ADV
cana-945	145	21	the	the	DET
cana-945	145	22	two	two	NUM
cana-945	145	23	elements	element	NOUN
cana-945	145	24	,	,	PUNCT
cana-945	145	25	while	while	SCONJ
cana-945	145	26	the	the	DET
cana-945	145	27	z	z	NOUN
cana-945	145	28	-	-	PUNCT
cana-945	145	29	axis	axis	NOUN
cana-945	145	30	shows	show	VERB
cana-945	145	31	the	the	DET
cana-945	145	32	resulting	result	VERB
cana-945	145	33	non	non	ADJ
cana-945	145	34	-	-	ADJ
cana-945	145	35	membership	membership	ADJ
cana-945	145	36	degree	degree	NOUN
cana-945	145	37	vda(x	vda(x	PROPN
cana-945	145	38	,	,	PUNCT
cana-945	145	39	y	y	NOUN
cana-945	145	40	)	)	PUNCT
cana-945	145	41	.	.	PUNCT
cana-945	146	1	this	this	DET
cana-945	146	2	plot	plot	NOUN
cana-945	146	3	uses	use	VERB
cana-945	146	4	the	the	DET
cana-945	146	5	'	'	PUNCT
cana-945	146	6	plasma	plasma	NOUN
cana-945	146	7	'	'	PUNCT
cana-945	146	8	colormap	colormap	NOUN
cana-945	146	9	to	to	PART
cana-945	146	10	illustrate	illustrate	VERB
cana-945	146	11	the	the	DET
cana-945	146	12	variations	variation	NOUN
cana-945	146	13	in	in	ADP
cana-945	146	14	non	non	ADJ
cana-945	146	15	-	-	ADJ
cana-945	146	16	membership	membership	ADJ
cana-945	146	17	degrees	degree	NOUN
cana-945	146	18	.	.	PUNCT
cana-945	147	1	the	the	DET
cana-945	147	2	visualization	visualization	NOUN
cana-945	147	3	highlights	highlight	VERB
cana-945	147	4	how	how	SCONJ
cana-945	147	5	the	the	DET
cana-945	147	6	non	non	ADJ
cana-945	147	7	-	-	ADJ
cana-945	147	8	membership	membership	ADJ
cana-945	147	9	degrees	degree	NOUN
cana-945	147	10	are	be	AUX
cana-945	147	11	combined	combine	VERB
cana-945	147	12	using	use	VERB
cana-945	147	13	the	the	DET
cana-945	147	14	maximum	maximum	ADJ
cana-945	147	15	operation	operation	NOUN
cana-945	147	16	⋁	⋁	PROPN
cana-945	147	17	,	,	PUNCT
cana-945	147	18	indicating	indicate	VERB
cana-945	147	19	the	the	DET
cana-945	147	20	extent	extent	NOUN
cana-945	147	21	to	to	PART
cana-945	147	22	which	which	PRON
cana-945	147	23	the	the	DET
cana-945	147	24	resulting	result	VERB
cana-945	147	25	pair	pair	NOUN
cana-945	147	26	of	of	ADP
cana-945	147	27	elements	element	NOUN
cana-945	147	28	does	do	AUX
cana-945	147	29	not	not	PART
cana-945	147	30	belong	belong	VERB
cana-945	147	31	to	to	ADP
cana-945	147	32	the	the	DET
cana-945	147	33	intuitionistic	intuitionistic	ADJ
cana-945	147	34	fuzzy	fuzzy	ADJ
cana-945	147	35	set	set	NOUN
cana-945	147	36	.	.	PUNCT
cana-945	148	1	this	this	DET
cana-945	148	2	plot	plot	NOUN
cana-945	148	3	provides	provide	VERB
cana-945	148	4	insights	insight	NOUN
cana-945	148	5	into	into	ADP
cana-945	148	6	the	the	DET
cana-945	148	7	interplay	interplay	NOUN
cana-945	148	8	between	between	ADP
cana-945	148	9	non	non	ADJ
cana-945	148	10	-	-	ADJ
cana-945	148	11	membership	membership	ADJ
cana-945	148	12	values	value	NOUN
cana-945	148	13	and	and	CCONJ
cana-945	148	14	how	how	SCONJ
cana-945	148	15	they	they	PRON
cana-945	148	16	aggregate	aggregate	VERB
cana-945	148	17	under	under	ADP
cana-945	148	18	the	the	DET
cana-945	148	19	d	d	ADJ
cana-945	148	20	-	-	ADJ
cana-945	148	21	algebra	algebra	ADJ
cana-945	148	22	operation	operation	NOUN
cana-945	148	23	,	,	PUNCT
cana-945	148	24	complementing	complement	VERB
cana-945	148	25	the	the	DET
cana-945	148	26	understanding	understanding	NOUN
cana-945	148	27	gained	gain	VERB
cana-945	148	28	from	from	ADP
cana-945	148	29	the	the	DET
cana-945	148	30	membership	membership	NOUN
cana-945	148	31	degree	degree	NOUN
cana-945	148	32	surface	surface	NOUN
cana-945	148	33	.	.	PUNCT
cana-945	149	1	fig.8	fig.8	PROPN
cana-945	149	2	intuitionistic	intuitionistic	ADJ
cana-945	149	3	fuzzy	fuzzy	ADJ
cana-945	149	4	d	d	NOUN
cana-945	149	5	-	-	ADJ
cana-945	149	6	algebra	algebra	ADJ
cana-945	149	7	operation	operation	NOUN
cana-945	149	8	fig.8	fig.8	PROPN
cana-945	149	9	with	with	ADP
cana-945	149	10	sliders	slider	NOUN
cana-945	149	11	allows	allow	VERB
cana-945	149	12	for	for	ADP
cana-945	149	13	a	a	DET
cana-945	149	14	dynamic	dynamic	ADJ
cana-945	149	15	exploration	exploration	NOUN
cana-945	149	16	of	of	ADP
cana-945	149	17	the	the	DET
cana-945	149	18	intuitionistic	intuitionistic	ADJ
cana-945	149	19	fuzzy	fuzzy	ADJ
cana-945	149	20	d	d	NOUN
cana-945	149	21	-	-	ADJ
cana-945	149	22	algebra	algebra	ADJ
cana-945	149	23	operation	operation	NOUN
cana-945	149	24	.	.	PUNCT
cana-945	150	1	users	user	NOUN
cana-945	150	2	can	can	AUX
cana-945	150	3	adjust	adjust	VERB
cana-945	150	4	the	the	DET
cana-945	150	5	membership	membership	NOUN
cana-945	150	6	(	(	PUNCT
cana-945	150	7	μa(x	μa(x	NOUN
cana-945	150	8	)	)	PUNCT
cana-945	150	9	,	,	PUNCT
cana-945	150	10	μa(y	μa(y	NUM
cana-945	150	11	)	)	PUNCT
cana-945	150	12	)	)	PUNCT
cana-945	150	13	and	and	CCONJ
cana-945	150	14	non	non	ADJ
cana-945	150	15	-	-	NOUN
cana-945	150	16	membership	membership	ADJ
cana-945	150	17	(	(	PUNCT
cana-945	150	18	va(x	va(x	NOUN
cana-945	150	19	)	)	PUNCT
cana-945	150	20	,	,	PUNCT
cana-945	150	21	va(y	va(y	NUM
cana-945	150	22	)	)	PUNCT
cana-945	150	23	)	)	PUNCT
cana-945	150	24	degrees	degree	NOUN
cana-945	150	25	of	of	ADP
cana-945	150	26	two	two	NUM
cana-945	150	27	elements	element	NOUN
cana-945	150	28	using	use	VERB
cana-945	150	29	sliders	slider	NOUN
cana-945	150	30	,	,	PUNCT
cana-945	150	31	and	and	CCONJ
cana-945	150	32	the	the	DET
cana-945	150	33	resulting	result	VERB
cana-945	150	34	membership	membership	NOUN
cana-945	150	35	(	(	PUNCT
cana-945	150	36	μda	μda	NOUN
cana-945	150	37	)	)	PUNCT
cana-945	150	38	,	,	PUNCT
cana-945	150	39	non	non	ADJ
cana-945	150	40	-	-	NOUN
cana-945	150	41	membership	membership	ADJ
cana-945	150	42	(	(	PUNCT
cana-945	150	43	vda	vda	PROPN
cana-945	150	44	)	)	PUNCT
cana-945	150	45	,	,	PUNCT
cana-945	150	46	and	and	CCONJ
cana-945	150	47	hesitation	hesitation	NOUN
cana-945	150	48	(	(	PUNCT
cana-945	150	49	πda	πda	ADV
cana-945	150	50	)	)	PUNCT
cana-945	150	51	degrees	degree	NOUN
cana-945	150	52	are	be	AUX
cana-945	150	53	displayed	display	VERB
cana-945	150	54	in	in	ADP
cana-945	150	55	a	a	DET
cana-945	150	56	bar	bar	NOUN
cana-945	150	57	chart	chart	NOUN
cana-945	150	58	.	.	PUNCT
cana-945	151	1	this	this	DET
cana-945	151	2	real	real	ADJ
cana-945	151	3	-	-	PUNCT
cana-945	151	4	time	time	NOUN
cana-945	151	5	updating	updating	NOUN
cana-945	151	6	of	of	ADP
cana-945	151	7	the	the	DET
cana-945	151	8	bar	bar	NOUN
cana-945	151	9	chart	chart	NOUN
cana-945	151	10	as	as	SCONJ
cana-945	151	11	the	the	DET
cana-945	151	12	sliders	slider	NOUN
cana-945	151	13	are	be	AUX
cana-945	151	14	adjusted	adjust	VERB
cana-945	151	15	provides	provide	VERB
cana-945	151	16	an	an	DET
cana-945	151	17	intuitive	intuitive	ADJ
cana-945	151	18	understanding	understanding	NOUN
cana-945	151	19	of	of	ADP
cana-945	151	20	how	how	SCONJ
cana-945	151	21	different	different	ADJ
cana-945	151	22	input	input	NOUN
cana-945	151	23	values	value	NOUN
cana-945	151	24	affect	affect	VERB
cana-945	151	25	the	the	DET
cana-945	151	26	outcome	outcome	NOUN
cana-945	151	27	of	of	ADP
cana-945	151	28	the	the	DET
cana-945	151	29	d	d	ADJ
cana-945	151	30	-	-	ADJ
cana-945	151	31	algebra	algebra	ADJ
cana-945	151	32	operation	operation	NOUN
cana-945	151	33	.	.	PUNCT
cana-945	152	1	the	the	DET
cana-945	152	2	plot	plot	NOUN
cana-945	152	3	enhances	enhance	VERB
cana-945	152	4	engagement	engagement	NOUN
cana-945	152	5	and	and	CCONJ
cana-945	152	6	comprehension	comprehension	NOUN
cana-945	152	7	by	by	ADP
cana-945	152	8	allowing	allow	VERB
cana-945	152	9	users	user	NOUN
cana-945	152	10	to	to	PART
cana-945	152	11	experiment	experiment	VERB
cana-945	152	12	with	with	ADP
cana-945	152	13	various	various	ADJ
cana-945	152	14	scenarios	scenario	NOUN
cana-945	152	15	,	,	PUNCT
cana-945	152	16	seeing	see	VERB
cana-945	152	17	first	first	ADJ
cana-945	152	18	-	-	PUNCT
cana-945	152	19	hand	hand	NOUN
cana-945	152	20	how	how	SCONJ
cana-945	152	21	changes	change	NOUN
cana-945	152	22	in	in	ADP
cana-945	152	23	membership	membership	NOUN
cana-945	152	24	and	and	CCONJ
cana-945	152	25	nonmembership	nonmembership	NOUN
cana-945	152	26	degrees	degree	NOUN
cana-945	152	27	influence	influence	VERB
cana-945	152	28	the	the	DET
cana-945	152	29	resulting	result	VERB
cana-945	152	30	degrees	degree	NOUN
cana-945	152	31	.	.	PUNCT
cana-945	153	1	this	this	DET
cana-945	153	2	interactive	interactive	ADJ
cana-945	153	3	tool	tool	NOUN
cana-945	153	4	is	be	AUX
cana-945	153	5	particularly	particularly	ADV
cana-945	153	6	useful	useful	ADJ
cana-945	153	7	for	for	ADP
cana-945	153	8	demonstrating	demonstrate	VERB
cana-945	153	9	the	the	DET
cana-945	153	10	complex	complex	ADJ
cana-945	153	11	relationships	relationship	NOUN
cana-945	153	12	within	within	ADP
cana-945	153	13	intuitionistic	intuitionistic	ADJ
cana-945	153	14	fuzzy	fuzzy	ADJ
cana-945	153	15	sets	set	NOUN
cana-945	153	16	and	and	CCONJ
cana-945	153	17	for	for	ADP
cana-945	153	18	educational	educational	ADJ
cana-945	153	19	purposes	purpose	NOUN
cana-945	153	20	,	,	PUNCT
cana-945	153	21	helping	help	VERB
cana-945	153	22	users	user	NOUN
cana-945	153	23	to	to	PART
cana-945	153	24	grasp	grasp	VERB
cana-945	153	25	the	the	DET
cana-945	153	26	principles	principle	NOUN
cana-945	153	27	of	of	ADP
cana-945	153	28	intuitionistic	intuitionistic	ADJ
cana-945	153	29	fuzzy	fuzzy	ADJ
cana-945	153	30	d	d	NOUN
cana-945	153	31	-	-	NOUN
cana-945	153	32	algebra	algebra	NOUN
cana-945	153	33	through	through	ADP
cana-945	153	34	direct	direct	ADJ
cana-945	153	35	manipulation	manipulation	NOUN
cana-945	153	36	and	and	CCONJ
cana-945	153	37	observation	observation	NOUN
cana-945	153	38	.	.	PUNCT
cana-945	154	1	communications	communication	NOUN
cana-945	154	2	on	on	ADP
cana-945	154	3	applied	apply	VERB
cana-945	154	4	nonlinear	nonlinear	ADJ
cana-945	154	5	analysis	analysis	NOUN
cana-945	154	6	issn	issn	NOUN
cana-945	154	7	:	:	PUNCT
cana-945	154	8	1074	1074	NUM
cana-945	154	9	-	-	PUNCT
cana-945	154	10	133x	133x	NUM
cana-945	154	11	vol	vol	NOUN
cana-945	154	12	31	31	NUM
cana-945	154	13	no	no	NOUN
cana-945	154	14	.	.	PUNCT
cana-945	155	1	4s	4s	NUM
cana-945	155	2	(	(	PUNCT
cana-945	155	3	2024	2024	NUM
cana-945	155	4	)	)	PUNCT
cana-945	155	5	509	509	NUM
cana-945	155	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-945	155	7	5	5	NUM
cana-945	155	8	.	.	PUNCT
cana-945	155	9	conclusion	conclusion	NOUN
cana-945	155	10	and	and	CCONJ
cana-945	155	11	future	future	ADJ
cana-945	155	12	work	work	NOUN
cana-945	155	13	the	the	DET
cana-945	155	14	advancement	advancement	NOUN
cana-945	155	15	of	of	ADP
cana-945	155	16	intuitionistic	intuitionistic	ADJ
cana-945	155	17	fuzzy	fuzzy	ADJ
cana-945	155	18	d	d	NOUN
cana-945	155	19	-	-	PUNCT
cana-945	155	20	algebra	algebra	NOUN
cana-945	155	21	involves	involve	VERB
cana-945	155	22	defining	define	VERB
cana-945	155	23	core	core	NOUN
cana-945	155	24	structures	structure	NOUN
cana-945	155	25	,	,	PUNCT
cana-945	155	26	utilizing	utilize	VERB
cana-945	155	27	mathematical	mathematical	ADJ
cana-945	155	28	models	model	NOUN
cana-945	155	29	,	,	PUNCT
cana-945	155	30	and	and	CCONJ
cana-945	155	31	validating	validate	VERB
cana-945	155	32	through	through	ADP
cana-945	155	33	examples	example	NOUN
cana-945	155	34	.	.	PUNCT
cana-945	156	1	it	it	PRON
cana-945	156	2	extends	extend	VERB
cana-945	156	3	classical	classical	ADJ
cana-945	156	4	fuzzy	fuzzy	ADJ
cana-945	156	5	algebra	algebra	NOUN
cana-945	156	6	by	by	ADP
cana-945	156	7	incorporating	incorporate	VERB
cana-945	156	8	degrees	degree	NOUN
cana-945	156	9	of	of	ADP
cana-945	156	10	membership	membership	NOUN
cana-945	156	11	and	and	CCONJ
cana-945	156	12	non	non	ADJ
cana-945	156	13	-	-	NOUN
cana-945	156	14	membership	membership	NOUN
cana-945	156	15	,	,	PUNCT
cana-945	156	16	enriching	enrich	VERB
cana-945	156	17	frameworks	framework	NOUN
cana-945	156	18	for	for	ADP
cana-945	156	19	handling	handle	VERB
cana-945	156	20	uncertainty	uncertainty	NOUN
cana-945	156	21	.	.	PUNCT
cana-945	157	1	convergence	convergence	NOUN
cana-945	157	2	behaviour	behaviour	NOUN
cana-945	157	3	and	and	CCONJ
cana-945	157	4	continuity	continuity	NOUN
cana-945	157	5	property	property	NOUN
cana-945	157	6	is	be	AUX
cana-945	157	7	analysed	analyse	VERB
cana-945	157	8	through	through	ADP
cana-945	157	9	topological	topological	ADJ
cana-945	157	10	techniques	technique	NOUN
cana-945	157	11	,	,	PUNCT
cana-945	157	12	providing	provide	VERB
cana-945	157	13	deeper	deep	ADJ
cana-945	157	14	insights	insight	NOUN
cana-945	157	15	.	.	PUNCT
cana-945	158	1	validation	validation	NOUN
cana-945	158	2	strategies	strategy	NOUN
cana-945	158	3	elucidate	elucidate	VERB
cana-945	158	4	the	the	DET
cana-945	158	5	applicability	applicability	NOUN
cana-945	158	6	and	and	CCONJ
cana-945	158	7	limitations	limitation	NOUN
cana-945	158	8	of	of	ADP
cana-945	158	9	theoretical	theoretical	ADJ
cana-945	158	10	models	model	NOUN
cana-945	158	11	.	.	PUNCT
cana-945	159	1	interactive	interactive	ADJ
cana-945	159	2	visualizations	visualization	NOUN
cana-945	159	3	aid	aid	NOUN
cana-945	159	4	in	in	ADP
cana-945	159	5	understanding	understand	VERB
cana-945	159	6	intuitionistic	intuitionistic	ADJ
cana-945	159	7	fuzzy	fuzzy	ADJ
cana-945	159	8	sets	set	NOUN
cana-945	159	9	in	in	ADP
cana-945	159	10	decision	decision	NOUN
cana-945	159	11	-	-	PUNCT
cana-945	159	12	making	make	VERB
cana-945	159	13	contexts	context	NOUN
cana-945	159	14	.	.	PUNCT
cana-945	160	1	this	this	DET
cana-945	160	2	comprehensive	comprehensive	ADJ
cana-945	160	3	approach	approach	NOUN
cana-945	160	4	bridges	bridge	NOUN
cana-945	160	5	theory	theory	NOUN
cana-945	160	6	with	with	ADP
cana-945	160	7	practical	practical	ADJ
cana-945	160	8	applications	application	NOUN
cana-945	160	9	,	,	PUNCT
cana-945	160	10	fostering	foster	VERB
cana-945	160	11	innovative	innovative	ADJ
cana-945	160	12	solutions	solution	NOUN
cana-945	160	13	.	.	PUNCT
cana-945	161	1	visualization	visualization	NOUN
cana-945	161	2	representations	representation	NOUN
cana-945	161	3	help	help	AUX
cana-945	161	4	map	map	VERB
cana-945	161	5	sets	set	NOUN
cana-945	161	6	onto	onto	ADP
cana-945	161	7	topological	topological	ADJ
cana-945	161	8	spaces	space	NOUN
cana-945	161	9	to	to	PART
cana-945	161	10	illustrate	illustrate	VERB
cana-945	161	11	convergence	convergence	NOUN
cana-945	161	12	dynamics	dynamic	NOUN
cana-945	161	13	.	.	PUNCT
cana-945	162	1	the	the	DET
cana-945	162	2	results	result	NOUN
cana-945	162	3	offer	offer	VERB
cana-945	162	4	insights	insight	NOUN
cana-945	162	5	into	into	ADP
cana-945	162	6	transformation	transformation	NOUN
cana-945	162	7	processes	process	NOUN
cana-945	162	8	and	and	CCONJ
cana-945	162	9	operational	operational	ADJ
cana-945	162	10	characteristics	characteristic	NOUN
cana-945	162	11	,	,	PUNCT
cana-945	162	12	enhancing	enhance	VERB
cana-945	162	13	comprehension	comprehension	NOUN
cana-945	162	14	of	of	ADP
cana-945	162	15	complex	complex	ADJ
cana-945	162	16	concepts	concept	NOUN
cana-945	162	17	.	.	PUNCT
cana-945	163	1	future	future	ADJ
cana-945	163	2	research	research	NOUN
cana-945	163	3	may	may	AUX
cana-945	163	4	refine	refine	VERB
cana-945	163	5	visualization	visualization	NOUN
cana-945	163	6	techniques	technique	NOUN
cana-945	163	7	and	and	CCONJ
cana-945	163	8	explore	explore	VERB
cana-945	163	9	machine	machine	NOUN
cana-945	163	10	learning	learning	NOUN
cana-945	163	11	applications	application	NOUN
cana-945	163	12	to	to	PART
cana-945	163	13	further	far	ADV
cana-945	163	14	enhance	enhance	VERB
cana-945	163	15	decision	decision	NOUN
cana-945	163	16	-	-	PUNCT
cana-945	163	17	making	make	VERB
cana-945	163	18	processes	process	NOUN
cana-945	163	19	based	base	VERB
cana-945	163	20	on	on	ADP
cana-945	163	21	intuitionistic	intuitionistic	ADJ
cana-945	163	22	fuzzy	fuzzy	ADJ
cana-945	163	23	logic	logic	NOUN
cana-945	163	24	.	.	PUNCT
cana-945	164	1	integrating	integrate	VERB
cana-945	164	2	computational	computational	ADJ
cana-945	164	3	tools	tool	NOUN
cana-945	164	4	and	and	CCONJ
cana-945	164	5	advanced	advanced	ADJ
cana-945	164	6	methodologies	methodology	NOUN
cana-945	164	7	holds	hold	VERB
cana-945	164	8	promise	promise	NOUN
cana-945	164	9	for	for	ADP
cana-945	164	10	innovative	innovative	ADJ
cana-945	164	11	solutions	solution	NOUN
cana-945	164	12	across	across	ADP
cana-945	164	13	domains	domain	NOUN
cana-945	164	14	,	,	PUNCT
cana-945	164	15	from	from	ADP
cana-945	164	16	ai	ai	VERB
cana-945	164	17	to	to	PART
cana-945	164	18	decision	decision	VERB
cana-945	164	19	support	support	NOUN
cana-945	164	20	systems	system	NOUN
cana-945	164	21	.	.	PUNCT
cana-945	165	1	references	reference	NOUN
cana-945	165	2	[	[	X
cana-945	165	3	1	1	NUM
cana-945	165	4	]	]	PUNCT
cana-945	165	5	van	van	PROPN
cana-945	165	6	oostrom	oostrom	PROPN
cana-945	165	7	,	,	PUNCT
cana-945	165	8	v.	v.	ADP
cana-945	165	9	commutative	commutative	ADJ
cana-945	165	10	residual	residual	ADJ
cana-945	165	11	algebra	algebra	NOUN
cana-945	165	12	motivation	motivation	NOUN
cana-945	165	13	,	,	PUNCT
cana-945	165	14	decision	decision	NOUN
cana-945	165	15	,	,	PUNCT
cana-945	165	16	and	and	CCONJ
cana-945	165	17	applications	application	NOUN
cana-945	165	18	.	.	PUNCT
cana-945	166	1	a	a	X
cana-945	166	2	/	/	SYM
cana-945	166	3	a	a	NOUN
cana-945	166	4	,	,	PUNCT
cana-945	166	5	1	1	NUM
cana-945	166	6	,	,	PUNCT
cana-945	166	7	2	2	NUM
cana-945	166	8	.	.	PUNCT
cana-945	167	1	[	[	X
cana-945	167	2	2	2	NUM
cana-945	167	3	]	]	SYM
cana-945	167	4	öztürk	öztürk	NOUN
cana-945	167	5	,	,	PUNCT
cana-945	167	6	m.	m.	NOUN
cana-945	167	7	a.	a.	NOUN
cana-945	167	8	(	(	PUNCT
cana-945	167	9	2021	2021	NUM
cana-945	167	10	)	)	PUNCT
cana-945	167	11	.	.	PUNCT
cana-945	168	1	nearness	nearness	NOUN
cana-945	168	2	d	d	NOUN
cana-945	168	3	-	-	PUNCT
cana-945	168	4	algebras	algebras	PROPN
cana-945	168	5	.	.	PUNCT
cana-945	169	1	journal	journal	PROPN
cana-945	169	2	of	of	ADP
cana-945	169	3	algebraic	algebraic	PROPN
cana-945	169	4	hyperstructures	hyperstructure	NOUN
cana-945	169	5	and	and	CCONJ
cana-945	169	6	logical	logical	ADJ
cana-945	169	7	algebras	algebra	NOUN
cana-945	169	8	,	,	PUNCT
cana-945	169	9	2(3	2(3	NUM
cana-945	169	10	)	)	PUNCT
cana-945	169	11	,	,	PUNCT
cana-945	169	12	73	73	NUM
cana-945	169	13	-	-	SYM
cana-945	169	14	84	84	NUM
cana-945	169	15	.	.	PUNCT
cana-945	170	1	[	[	X
cana-945	170	2	3	3	NUM
cana-945	170	3	]	]	X
cana-945	170	4	eyssidieux	eyssidieux	PROPN
cana-945	170	5	,	,	PUNCT
cana-945	170	6	p.	p.	PROPN
cana-945	170	7	,	,	PUNCT
cana-945	170	8	hwang	hwang	PROPN
cana-945	170	9	,	,	PUNCT
cana-945	170	10	j.	j.	PROPN
cana-945	170	11	m.	m.	PROPN
cana-945	170	12	,	,	PUNCT
cana-945	170	13	kebekus	kebekus	PROPN
cana-945	170	14	,	,	PUNCT
cana-945	170	15	s.	s.	PROPN
cana-945	170	16	,	,	PUNCT
cana-945	170	17	&	&	CCONJ
cana-945	170	18	păun	păun	PROPN
cana-945	170	19	,	,	PUNCT
cana-945	170	20	m.	m.	NOUN
cana-945	170	21	(	(	PUNCT
cana-945	170	22	2023	2023	NUM
cana-945	170	23	)	)	PUNCT
cana-945	170	24	.	.	PUNCT
cana-945	171	1	komplexe	komplexe	PROPN
cana-945	171	2	analysis	analysis	NOUN
cana-945	171	3	–	–	PUNCT
cana-945	171	4	differential	differential	ADJ
cana-945	171	5	and	and	CCONJ
cana-945	171	6	algebraic	algebraic	ADJ
cana-945	171	7	methods	method	NOUN
cana-945	171	8	in	in	ADP
cana-945	171	9	kähler	kähler	PROPN
cana-945	171	10	spaces	space	NOUN
cana-945	171	11	.	.	PUNCT
cana-945	172	1	oberwolfach	oberwolfach	PROPN
cana-945	172	2	reports	report	NOUN
cana-945	172	3	,	,	PUNCT
cana-945	172	4	20(2	20(2	NUM
cana-945	172	5	)	)	PUNCT
cana-945	172	6	,	,	PUNCT
cana-945	172	7	965	965	NUM
cana-945	172	8	-	-	SYM
cana-945	172	9	1030	1030	NUM
cana-945	172	10	.	.	PUNCT
cana-945	173	1	[	[	X
cana-945	173	2	4	4	NUM
cana-945	173	3	]	]	X
cana-945	173	4	singh	singh	PROPN
cana-945	173	5	,	,	PUNCT
cana-945	173	6	h.	h.	PROPN
cana-945	173	7	k.	k.	PROPN
cana-945	173	8	,	,	PUNCT
cana-945	173	9	&	&	CCONJ
cana-945	173	10	azman	azman	PROPN
cana-945	173	11	,	,	PUNCT
cana-945	173	12	h.	h.	PROPN
cana-945	173	13	h.	h.	PROPN
cana-945	173	14	(	(	PUNCT
cana-945	173	15	2023	2023	NUM
cana-945	173	16	)	)	PUNCT
cana-945	173	17	.	.	PUNCT
cana-945	174	1	visualizing	visualize	VERB
cana-945	174	2	algebra	algebra	PROPN
cana-945	174	3	:	:	PUNCT
cana-945	174	4	exploring	explore	VERB
cana-945	174	5	a	a	DET
cana-945	174	6	gifted	gifted	ADJ
cana-945	174	7	3rd	3rd	ADJ
cana-945	174	8	grader	grader	NOUN
cana-945	174	9	's	's	PART
cana-945	174	10	problem	problem	NOUN
cana-945	174	11	-	-	PUNCT
cana-945	174	12	solving	solve	VERB
cana-945	174	13	techniques	technique	NOUN
cana-945	174	14	for	for	ADP
cana-945	174	15	enhanced	enhanced	ADJ
cana-945	174	16	conceptual	conceptual	ADJ
cana-945	174	17	understanding	understanding	NOUN
cana-945	174	18	in	in	ADP
cana-945	174	19	algebra	algebra	NOUN
cana-945	174	20	education	education	NOUN
cana-945	174	21	.	.	PUNCT
cana-945	175	1	international	international	ADJ
cana-945	175	2	stem	stem	NOUN
cana-945	175	3	journal	journal	NOUN
cana-945	175	4	,	,	PUNCT
cana-945	175	5	4(2	4(2	NUM
cana-945	175	6	)	)	PUNCT
cana-945	175	7	,	,	PUNCT
cana-945	175	8	1	1	NUM
cana-945	175	9	-	-	SYM
cana-945	175	10	11	11	NUM
cana-945	175	11	.	.	PUNCT
cana-945	176	1	[	[	X
cana-945	176	2	5	5	NUM
cana-945	176	3	]	]	SYM
cana-945	176	4	wu	wu	PROPN
cana-945	176	5	,	,	PUNCT
cana-945	176	6	h.	h.	PROPN
cana-945	176	7	c.	c.	PROPN
cana-945	176	8	(	(	PUNCT
cana-945	176	9	2023	2023	NUM
cana-945	176	10	)	)	PUNCT
cana-945	176	11	.	.	PUNCT
cana-945	177	1	mathematical	mathematical	ADJ
cana-945	177	2	foundations	foundation	NOUN
cana-945	177	3	of	of	ADP
cana-945	177	4	fuzzy	fuzzy	ADJ
cana-945	177	5	sets	set	NOUN
cana-945	177	6	.	.	PUNCT
cana-945	178	1	john	john	PROPN
cana-945	178	2	wiley	wiley	PROPN
cana-945	178	3	&	&	CCONJ
cana-945	178	4	sons	son	NOUN
cana-945	178	5	.	.	PUNCT
cana-945	179	1	[	[	X
cana-945	179	2	6	6	NUM
cana-945	179	3	]	]	PUNCT
cana-945	179	4	božić	božić	NOUN
cana-945	179	5	,	,	PUNCT
cana-945	179	6	v.	v.	ADP
cana-945	179	7	fuzzy	fuzzy	ADJ
cana-945	179	8	approach	approach	NOUN
cana-945	179	9	to	to	ADP
cana-945	179	10	risk	risk	NOUN
cana-945	179	11	management	management	NOUN
cana-945	179	12	:	:	PUNCT
cana-945	179	13	enhancing	enhance	VERB
cana-945	179	14	decision	decision	NOUN
cana-945	179	15	-	-	PUNCT
cana-945	179	16	making	making	NOUN
cana-945	179	17	under	under	ADP
cana-945	179	18	uncertainty	uncertainty	NOUN
cana-945	179	19	.	.	PUNCT
cana-945	180	1	[	[	X
cana-945	180	2	7	7	NUM
cana-945	180	3	]	]	X
cana-945	180	4	kahraman	kahraman	NOUN
cana-945	180	5	,	,	PUNCT
cana-945	180	6	c.	c.	PROPN
cana-945	180	7	,	,	PUNCT
cana-945	180	8	cebi	cebi	VERB
cana-945	180	9	,	,	PUNCT
cana-945	180	10	s.	s.	PROPN
cana-945	180	11	,	,	PUNCT
cana-945	180	12	oztaysi	oztaysi	PROPN
cana-945	180	13	,	,	PUNCT
cana-945	180	14	b.	b.	PROPN
cana-945	180	15	,	,	PUNCT
cana-945	180	16	&	&	CCONJ
cana-945	180	17	cevik	cevik	PROPN
cana-945	180	18	onar	onar	PROPN
cana-945	180	19	,	,	PUNCT
cana-945	180	20	s.	s.	PROPN
cana-945	180	21	(	(	PUNCT
cana-945	180	22	2023	2023	NUM
cana-945	180	23	)	)	PUNCT
cana-945	180	24	.	.	PUNCT
cana-945	181	1	intuitionistic	intuitionistic	ADJ
cana-945	181	2	fuzzy	fuzzy	ADJ
cana-945	181	3	sets	set	NOUN
cana-945	181	4	with	with	ADP
cana-945	181	5	ordered	order	VERB
cana-945	181	6	pairs	pair	NOUN
cana-945	181	7	and	and	CCONJ
cana-945	181	8	their	their	PRON
cana-945	181	9	usage	usage	NOUN
cana-945	181	10	in	in	ADP
cana-945	181	11	multi	multi	ADJ
cana-945	181	12	-	-	ADJ
cana-945	181	13	attribute	attribute	NOUN
cana-945	181	14	decision	decision	NOUN
cana-945	181	15	making	making	NOUN
cana-945	181	16	:	:	PUNCT
cana-945	181	17	a	a	DET
cana-945	181	18	novel	novel	ADJ
cana-945	181	19	intuitionistic	intuitionistic	ADJ
cana-945	181	20	fuzzy	fuzzy	ADJ
cana-945	181	21	topsis	topsis	NOUN
cana-945	181	22	method	method	NOUN
cana-945	181	23	with	with	ADP
cana-945	181	24	ordered	order	VERB
cana-945	181	25	pairs	pair	NOUN
cana-945	181	26	.	.	PUNCT
cana-945	182	1	mathematics	mathematic	NOUN
cana-945	182	2	,	,	PUNCT
cana-945	182	3	11(18	11(18	NUM
cana-945	182	4	)	)	PUNCT
cana-945	182	5	,	,	PUNCT
cana-945	182	6	3867	3867	NUM
cana-945	182	7	.	.	PUNCT
cana-945	183	1	[	[	X
cana-945	183	2	8	8	NUM
cana-945	183	3	]	]	PUNCT
cana-945	183	4	muhiuddin	muhiuddin	NOUN
cana-945	183	5	,	,	PUNCT
cana-945	183	6	g.	g.	PROPN
cana-945	183	7	,	,	PUNCT
cana-945	183	8	mahboob	mahboob	PROPN
cana-945	183	9	,	,	PUNCT
cana-945	183	10	a.	a.	PROPN
cana-945	183	11	h.	h.	PROPN
cana-945	183	12	s.	s.	PROPN
cana-945	183	13	a.	a.	PROPN
cana-945	183	14	n.	n.	PROPN
cana-945	183	15	,	,	PUNCT
cana-945	183	16	&	&	CCONJ
cana-945	183	17	balamurugan	balamurugan	VERB
cana-945	183	18	,	,	PUNCT
cana-945	183	19	m.	m.	NOUN
cana-945	183	20	(	(	PUNCT
cana-945	183	21	2020	2020	NUM
cana-945	183	22	)	)	PUNCT
cana-945	183	23	.	.	PUNCT
cana-945	184	1	hesitant	hesitant	ADJ
cana-945	184	2	anti	anti	ADJ
cana-945	184	3	-	-	ADJ
cana-945	184	4	intuitionistic	intuitionistic	ADJ
cana-945	184	5	fuzzy	fuzzy	ADJ
cana-945	184	6	soft	soft	ADJ
cana-945	184	7	commutative	commutative	ADJ
cana-945	184	8	ideals	ideal	NOUN
cana-945	184	9	of	of	ADP
cana-945	184	10	bck	bck	NOUN
cana-945	184	11	-	-	PUNCT
cana-945	184	12	algebras	algebras	PROPN
cana-945	184	13	.	.	PUNCT
cana-945	185	1	annals	annal	NOUN
cana-945	185	2	of	of	ADP
cana-945	185	3	communications	communication	NOUN
cana-945	185	4	in	in	ADP
cana-945	185	5	mathematics	mathematic	NOUN
cana-945	185	6	,	,	PUNCT
cana-945	185	7	3(2	3(2	NUM
cana-945	185	8	)	)	PUNCT
cana-945	185	9	,	,	PUNCT
cana-945	185	10	158	158	NUM
cana-945	185	11	-	-	SYM
cana-945	185	12	170	170	NUM
cana-945	185	13	.	.	PUNCT
cana-945	186	1	[	[	X
cana-945	186	2	9	9	NUM
cana-945	186	3	]	]	SYM
cana-945	186	4	shrivastava	shrivastava	PROPN
cana-945	186	5	,	,	PUNCT
cana-945	186	6	h.	h.	PROPN
cana-945	186	7	,	,	PUNCT
cana-945	186	8	gopalakrishnan	gopalakrishnan	PROPN
cana-945	186	9	,	,	PUNCT
cana-945	186	10	s.	s.	PROPN
cana-945	186	11	,	,	PUNCT
cana-945	186	12	al	al	PROPN
cana-945	186	13	-	-	PUNCT
cana-945	186	14	fatlawy	fatlawy	PROPN
cana-945	186	15	,	,	PUNCT
cana-945	186	16	m.	m.	PROPN
cana-945	186	17	h.	h.	PROPN
cana-945	186	18	,	,	PUNCT
cana-945	186	19	sivasubramanian	sivasubramanian	ADJ
cana-945	186	20	,	,	PUNCT
cana-945	186	21	s.	s.	PROPN
cana-945	186	22	,	,	PUNCT
cana-945	186	23	sheela	sheela	PROPN
cana-945	186	24	,	,	PUNCT
cana-945	186	25	m.	m.	NOUN
cana-945	186	26	s.	s.	PROPN
cana-945	186	27	,	,	PUNCT
cana-945	186	28	&	&	CCONJ
cana-945	186	29	zhu	zhu	PROPN
cana-945	186	30	,	,	PUNCT
cana-945	186	31	k.	k.	PROPN
cana-945	186	32	(	(	PUNCT
cana-945	186	33	2023	2023	NUM
cana-945	186	34	,	,	PUNCT
cana-945	186	35	august	august	PROPN
cana-945	186	36	)	)	PUNCT
cana-945	186	37	.	.	PUNCT
cana-945	187	1	construction	construction	NOUN
cana-945	187	2	of	of	ADP
cana-945	187	3	evaluation	evaluation	NOUN
cana-945	187	4	model	model	NOUN
cana-945	187	5	of	of	ADP
cana-945	187	6	regional	regional	ADJ
cana-945	187	7	economic	economic	ADJ
cana-945	187	8	development	development	NOUN
cana-945	187	9	level	level	NOUN
cana-945	187	10	based	base	VERB
cana-945	187	11	on	on	ADP
cana-945	187	12	fuzzy	fuzzy	ADJ
cana-945	187	13	clustering	clustering	ADJ
cana-945	187	14	algorithm	algorithm	NOUN
cana-945	187	15	.	.	PUNCT
cana-945	188	1	in	in	ADP
cana-945	188	2	2023	2023	NUM
cana-945	188	3	second	second	ADJ
cana-945	188	4	international	international	ADJ
cana-945	188	5	conference	conference	NOUN
cana-945	188	6	on	on	ADP
cana-945	188	7	smart	smart	ADJ
cana-945	188	8	technologies	technology	NOUN
cana-945	188	9	for	for	ADP
cana-945	188	10	smart	smart	ADJ
cana-945	188	11	nation	nation	NOUN
cana-945	188	12	(	(	PUNCT
cana-945	188	13	smarttechcon	smarttechcon	PROPN
cana-945	188	14	)	)	PUNCT
cana-945	188	15	(	(	PUNCT
cana-945	188	16	pp	pp	ADJ
cana-945	188	17	.	.	PUNCT
cana-945	189	1	678	678	NUM
cana-945	189	2	-	-	SYM
cana-945	189	3	682	682	NUM
cana-945	189	4	)	)	PUNCT
cana-945	189	5	.	.	PUNCT
cana-945	190	1	ieee	ieee	NOUN
cana-945	190	2	.	.	PUNCT
cana-945	191	1	[	[	X
cana-945	191	2	10	10	NUM
cana-945	191	3	]	]	PUNCT
cana-945	191	4	bayro	bayro	NOUN
cana-945	191	5	-	-	PUNCT
cana-945	191	6	corrochano	corrochano	NOUN
cana-945	191	7	,	,	PUNCT
cana-945	191	8	e.	e.	PROPN
cana-945	191	9	(	(	PUNCT
cana-945	191	10	2021	2021	NUM
cana-945	191	11	)	)	PUNCT
cana-945	191	12	.	.	PUNCT
cana-945	192	1	a	a	DET
cana-945	192	2	survey	survey	NOUN
cana-945	192	3	on	on	ADP
cana-945	192	4	quaternion	quaternion	NOUN
cana-945	192	5	algebra	algebra	NOUN
cana-945	192	6	and	and	CCONJ
cana-945	192	7	geometric	geometric	ADJ
cana-945	192	8	algebra	algebra	NOUN
cana-945	192	9	applications	application	NOUN
cana-945	192	10	in	in	ADP
cana-945	192	11	engineering	engineering	NOUN
cana-945	192	12	and	and	CCONJ
cana-945	192	13	computer	computer	NOUN
cana-945	192	14	science	science	NOUN
cana-945	192	15	1995–2020	1995–2020	NUM
cana-945	192	16	.	.	PUNCT
cana-945	193	1	ieee	ieee	NOUN
cana-945	193	2	access	access	NOUN
cana-945	193	3	,	,	PUNCT
cana-945	193	4	9	9	NUM
cana-945	193	5	,	,	PUNCT
cana-945	193	6	104326	104326	NUM
cana-945	193	7	-	-	SYM
cana-945	193	8	104355	104355	NUM
cana-945	193	9	.	.	PUNCT
cana-945	194	1	[	[	X
cana-945	194	2	11	11	NUM
cana-945	194	3	]	]	PUNCT
cana-945	194	4	baghini	baghini	NOUN
cana-945	194	5	,	,	PUNCT
cana-945	194	6	a.	a.	PROPN
cana-945	194	7	z.	z.	PROPN
cana-945	194	8	,	,	PUNCT
cana-945	194	9	babaei	babaei	PROPN
cana-945	194	10	,	,	PUNCT
cana-945	194	11	h.	h.	PROPN
cana-945	194	12	,	,	PUNCT
cana-945	194	13	&	&	CCONJ
cana-945	194	14	mirhosseini	mirhosseini	PROPN
cana-945	194	15	,	,	PUNCT
cana-945	194	16	r.	r.	PROPN
cana-945	194	17	t.	t.	PROPN
cana-945	194	18	(	(	PUNCT
cana-945	194	19	2024	2024	NUM
cana-945	194	20	)	)	PUNCT
cana-945	194	21	.	.	PUNCT
cana-945	195	1	determining	determine	VERB
cana-945	195	2	the	the	DET
cana-945	195	3	membership	membership	NOUN
cana-945	195	4	degree	degree	NOUN
cana-945	195	5	by	by	ADP
cana-945	195	6	fuzzy	fuzzy	ADJ
cana-945	195	7	hypergraphs	hypergraph	NOUN
cana-945	195	8	.	.	PUNCT
cana-945	196	1	mathematical	mathematical	ADJ
cana-945	196	2	foundations	foundation	NOUN
cana-945	196	3	of	of	ADP
cana-945	196	4	computing	computing	NOUN
cana-945	196	5	,	,	PUNCT
cana-945	196	6	0	0	NUM
cana-945	196	7	-	-	SYM
cana-945	196	8	0	0	NUM
cana-945	196	9	.	.	PUNCT
cana-945	197	1	[	[	X
cana-945	197	2	12	12	NUM
cana-945	197	3	]	]	PUNCT
cana-945	197	4	rawbone	rawbone	NOUN
cana-945	197	5	,	,	PUNCT
cana-945	197	6	t.	t.	PROPN
cana-945	197	7	(	(	PUNCT
cana-945	197	8	2024	2024	NUM
cana-945	197	9	)	)	PUNCT
cana-945	197	10	.	.	PUNCT
cana-945	198	1	fuzzy	fuzzy	ADJ
cana-945	198	2	relational	relational	ADJ
cana-945	198	3	music	music	NOUN
cana-945	198	4	perception	perception	NOUN
cana-945	198	5	:	:	PUNCT
cana-945	198	6	resemblance	resemblance	NOUN
cana-945	198	7	and	and	CCONJ
cana-945	198	8	implication	implication	NOUN
cana-945	198	9	in	in	ADP
cana-945	198	10	the	the	DET
cana-945	198	11	individuation	individuation	NOUN
cana-945	198	12	and	and	CCONJ
cana-945	198	13	assembly	assembly	NOUN
cana-945	198	14	of	of	ADP
cana-945	198	15	concepts	concept	NOUN
cana-945	198	16	.	.	PUNCT
cana-945	199	1	journal	journal	PROPN
cana-945	199	2	of	of	ADP
cana-945	199	3	creative	creative	ADJ
cana-945	199	4	music	music	NOUN
cana-945	199	5	systems	system	NOUN
cana-945	199	6	,	,	PUNCT
cana-945	199	7	8(1	8(1	NOUN
cana-945	199	8	)	)	PUNCT
cana-945	199	9	,	,	PUNCT
cana-945	199	10	1	1	NUM
cana-945	199	11	-	-	SYM
cana-945	199	12	54	54	NUM
cana-945	199	13	.	.	PUNCT
cana-945	200	1	[	[	X
cana-945	200	2	13	13	NUM
cana-945	200	3	]	]	X
cana-945	200	4	saeed	saeed	PROPN
cana-945	200	5	,	,	PUNCT
cana-945	200	6	m.	m.	NOUN
cana-945	200	7	,	,	PUNCT
cana-945	200	8	saeed	saeed	PROPN
cana-945	200	9	,	,	PUNCT
cana-945	200	10	m.	m.	PROPN
cana-945	200	11	h.	h.	PROPN
cana-945	200	12	,	,	PUNCT
cana-945	200	13	khalid	khalid	PROPN
cana-945	200	14	,	,	PUNCT
cana-945	200	15	m.	m.	NOUN
cana-945	200	16	,	,	PUNCT
cana-945	200	17	&	&	CCONJ
cana-945	200	18	mekawy	mekawy	PROPN
cana-945	200	19	,	,	PUNCT
cana-945	200	20	i.	i.	PROPN
cana-945	200	21	(	(	PUNCT
cana-945	200	22	2023	2023	NUM
cana-945	200	23	)	)	PUNCT
cana-945	200	24	.	.	PUNCT
cana-945	201	1	development	development	NOUN
cana-945	201	2	of	of	ADP
cana-945	201	3	hamming	hamming	NOUN
cana-945	201	4	and	and	CCONJ
cana-945	201	5	hausdorff	hausdorff	NOUN
cana-945	201	6	distance	distance	NOUN
cana-945	201	7	metrics	metric	NOUN
cana-945	201	8	for	for	ADP
cana-945	201	9	cubic	cubic	ADJ
cana-945	201	10	intuitionistic	intuitionistic	ADJ
cana-945	201	11	fuzzy	fuzzy	ADJ
cana-945	201	12	hypersoft	hypersoft	NOUN
cana-945	201	13	set	set	VERB
cana-945	201	14	in	in	ADP
cana-945	201	15	cement	cement	NOUN
cana-945	201	16	storage	storage	NOUN
cana-945	201	17	quality	quality	NOUN
cana-945	201	18	control	control	NOUN
cana-945	201	19	:	:	PUNCT
cana-945	201	20	development	development	NOUN
cana-945	201	21	and	and	CCONJ
cana-945	201	22	evaluation	evaluation	NOUN
cana-945	201	23	.	.	PUNCT
cana-945	202	1	plos	plos	PROPN
cana-945	202	2	one	one	NUM
cana-945	202	3	,	,	PUNCT
cana-945	202	4	18(9	18(9	NOUN
cana-945	202	5	)	)	PUNCT
cana-945	202	6	,	,	PUNCT
cana-945	202	7	e0291817	e0291817	PROPN
cana-945	202	8	.	.	PUNCT
cana-945	203	1	[	[	X
cana-945	203	2	14	14	NUM
cana-945	203	3	]	]	X
cana-945	203	4	fan	fan	NOUN
cana-945	203	5	,	,	PUNCT
cana-945	203	6	x.	x.	NOUN
cana-945	203	7	(	(	PUNCT
cana-945	203	8	2022	2022	NUM
cana-945	203	9	)	)	PUNCT
cana-945	203	10	.	.	PUNCT
cana-945	204	1	access	access	NOUN
cana-945	204	2	control	control	NOUN
cana-945	204	3	on	on	ADP
cana-945	204	4	provenance	provenance	NOUN
cana-945	204	5	(	(	PUNCT
cana-945	204	6	doctoral	doctoral	ADJ
cana-945	204	7	dissertation	dissertation	NOUN
cana-945	204	8	,	,	PUNCT
cana-945	204	9	macquarie	macquarie	PROPN
cana-945	204	10	university	university	PROPN
cana-945	204	11	)	)	PUNCT
cana-945	204	12	.	.	PUNCT
cana-945	205	1	[	[	X
cana-945	205	2	15	15	NUM
cana-945	205	3	]	]	X
cana-945	205	4	ulieru	ulieru	PROPN
cana-945	205	5	,	,	PUNCT
cana-945	205	6	m.	m.	NOUN
cana-945	205	7	electrical	electrical	ADJ
cana-945	205	8	and	and	CCONJ
cana-945	205	9	computer	computer	NOUN
cana-945	205	10	engineering	engineering	NOUN
cana-945	205	11	department	department	PROPN
cana-945	205	12	the	the	DET
cana-945	205	13	university	university	PROPN
cana-945	205	14	of	of	ADP
cana-945	205	15	calgary	calgary	PROPN
cana-945	205	16	2500	2500	NUM
cana-945	205	17	university	university	PROPN
cana-945	205	18	dr	dr	PROPN
cana-945	205	19	.	.	PROPN
cana-945	205	20	nw	nw	PROPN
cana-945	205	21	calgary	calgary	PROPN
cana-945	205	22	,	,	PUNCT
cana-945	205	23	alberta	alberta	PROPN
cana-945	205	24	,	,	PUNCT
cana-945	205	25	t1n	t1n	PROPN
cana-945	205	26	1n4	1n4	NUM
cana-945	205	27	canada	canada	PROPN
cana-945	205	28	.	.	PUNCT
cana-945	206	1	[	[	X
cana-945	206	2	16	16	NUM
cana-945	206	3	]	]	X
cana-945	206	4	syropoulos	syropoulo	NOUN
cana-945	206	5	,	,	PUNCT
cana-945	206	6	a.	a.	NOUN
cana-945	206	7	,	,	PUNCT
cana-945	206	8	&	&	CCONJ
cana-945	206	9	grammenos	grammenos	PROPN
cana-945	206	10	,	,	PUNCT
cana-945	206	11	t.	t.	PROPN
cana-945	206	12	(	(	PUNCT
cana-945	206	13	2020	2020	NUM
cana-945	206	14	)	)	PUNCT
cana-945	206	15	.	.	PUNCT
cana-945	207	1	a	a	DET
cana-945	207	2	modern	modern	ADJ
cana-945	207	3	introduction	introduction	NOUN
cana-945	207	4	to	to	ADP
cana-945	207	5	fuzzy	fuzzy	ADJ
cana-945	207	6	mathematics	mathematic	NOUN
cana-945	207	7	.	.	PUNCT
cana-945	208	1	john	john	PROPN
cana-945	208	2	wiley	wiley	PROPN
cana-945	208	3	&	&	CCONJ
cana-945	208	4	sons	son	NOUN
cana-945	208	5	.	.	PUNCT