id	sid	tid	token	lemma	pos
cana-735	1	1	communications	communication	NOUN
cana-735	1	2	on	on	ADP
cana-735	1	3	applied	apply	VERB
cana-735	1	4	nonlinear	nonlinear	ADJ
cana-735	1	5	analysis	analysis	NOUN
cana-735	1	6	issn	issn	NOUN
cana-735	1	7	:	:	PUNCT
cana-735	1	8	1074	1074	NUM
cana-735	1	9	-	-	PUNCT
cana-735	1	10	133x	133x	NUM
cana-735	1	11	vol	vol	NOUN
cana-735	1	12	31	31	NUM
cana-735	1	13	no	no	NOUN
cana-735	1	14	.	.	PUNCT
cana-735	2	1	3s	3s	NUM
cana-735	2	2	(	(	PUNCT
cana-735	2	3	2024	2024	NUM
cana-735	2	4	)	)	PUNCT
cana-735	2	5	105	105	NUM
cana-735	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-735	2	7	comparative	comparative	ADJ
cana-735	2	8	analysis	analysis	NOUN
cana-735	2	9	of	of	ADP
cana-735	2	10	fuzzy	fuzzy	ADJ
cana-735	2	11	dagum	dagum	NOUN
cana-735	2	12	hazard	hazard	NOUN
cana-735	2	13	function	function	NOUN
cana-735	2	14	approaches	approach	NOUN
cana-735	2	15	for	for	ADP
cana-735	2	16	estimating	estimate	VERB
cana-735	2	17	failure	failure	NOUN
cana-735	2	18	rates	rate	NOUN
cana-735	2	19	1*vidya	1*vidya	PROPN
cana-735	2	20	p	p	NOUN
cana-735	2	21	,	,	PUNCT
cana-735	2	22	2parthiban	2parthiban	PROPN
cana-735	2	23	s	s	PART
cana-735	2	24	1*,2	1*,2	NUM
cana-735	2	25	department	department	NOUN
cana-735	2	26	of	of	ADP
cana-735	2	27	mathematics	mathematics	PROPN
cana-735	2	28	and	and	CCONJ
cana-735	2	29	statistics	statistic	NOUN
cana-735	2	30	,	,	PUNCT
cana-735	2	31	school	school	NOUN
cana-735	2	32	of	of	ADP
cana-735	2	33	applied	apply	VERB
cana-735	2	34	sciences	science	NOUN
cana-735	2	35	and	and	CCONJ
cana-735	2	36	humanities	humanity	NOUN
cana-735	2	37	,	,	PUNCT
cana-735	2	38	vignan	vignan	NOUN
cana-735	2	39	’s	’s	PART
cana-735	2	40	foundation	foundation	PROPN
cana-735	2	41	for	for	ADP
cana-735	2	42	science	science	NOUN
cana-735	2	43	,	,	PUNCT
cana-735	2	44	technology	technology	NOUN
cana-735	2	45	,	,	PUNCT
cana-735	2	46	and	and	CCONJ
cana-735	2	47	research	research	NOUN
cana-735	2	48	,	,	PUNCT
cana-735	2	49	vadlamudi	vadlamudi	NOUN
cana-735	2	50	,	,	PUNCT
cana-735	2	51	guntur	guntur	PROPN
cana-735	2	52	district	district	PROPN
cana-735	2	53	,	,	PUNCT
cana-735	2	54	andhra	andhra	PROPN
cana-735	2	55	pradesh	pradesh	PROPN
cana-735	2	56	,	,	PUNCT
cana-735	2	57	india	india	PROPN
cana-735	2	58	,	,	PUNCT
cana-735	2	59	pin	pin	NOUN
cana-735	2	60	:	:	PUNCT
cana-735	2	61	522	522	NUM
cana-735	2	62	213	213	NUM
cana-735	2	63	.	.	PUNCT
cana-735	3	1	e	e	X
cana-735	3	2	-	-	NOUN
cana-735	3	3	mail	mail	NOUN
cana-735	3	4	:	:	PUNCT
cana-735	3	5	vidyap	vidyap	NOUN
cana-735	3	6	.	.	PUNCT
cana-735	4	1	p387@gmail	p387@gmail	NOUN
cana-735	4	2	.	.	PUNCT
cana-735	5	1	com1∗	com1∗	X
cana-735	5	2	,	,	PUNCT
cana-735	5	3	selvamparthiban1979@gmail	selvamparthiban1979@gmail	NOUN
cana-735	5	4	.	.	PUNCT
cana-735	5	5	com	com	NOUN
cana-735	5	6	2	2	NUM
cana-735	5	7	article	article	NOUN
cana-735	5	8	history	history	NOUN
cana-735	5	9	:	:	PUNCT
cana-735	5	10	received	receive	VERB
cana-735	5	11	:	:	PUNCT
cana-735	5	12	10	10	NUM
cana-735	5	13	-	-	PUNCT
cana-735	5	14	04	04	NUM
cana-735	5	15	-	-	PUNCT
cana-735	5	16	2024	2024	NUM
cana-735	5	17	revised	revise	VERB
cana-735	5	18	:	:	PUNCT
cana-735	5	19	18	18	NUM
cana-735	5	20	-	-	SYM
cana-735	5	21	05	05	NUM
cana-735	5	22	-	-	PUNCT
cana-735	5	23	2024	2024	NUM
cana-735	5	24	accepted	accept	VERB
cana-735	5	25	:	:	PUNCT
cana-735	5	26	04	04	NUM
cana-735	5	27	-	-	PUNCT
cana-735	5	28	06	06	NUM
cana-735	5	29	-	-	PUNCT
cana-735	5	30	2024	2024	NUM
cana-735	5	31	abstract	abstract	NOUN
cana-735	5	32	when	when	SCONJ
cana-735	5	33	analysing	analyse	VERB
cana-735	5	34	the	the	DET
cana-735	5	35	maintenance	maintenance	NOUN
cana-735	5	36	plan	plan	NOUN
cana-735	5	37	for	for	ADP
cana-735	5	38	a	a	DET
cana-735	5	39	manufacturing	manufacturing	NOUN
cana-735	5	40	system	system	NOUN
cana-735	5	41	,	,	PUNCT
cana-735	5	42	the	the	DET
cana-735	5	43	number	number	NOUN
cana-735	5	44	of	of	ADP
cana-735	5	45	failures	failure	NOUN
cana-735	5	46	is	be	AUX
cana-735	5	47	a	a	DET
cana-735	5	48	crucial	crucial	ADJ
cana-735	5	49	consideration	consideration	NOUN
cana-735	5	50	.	.	PUNCT
cana-735	6	1	there	there	PRON
cana-735	6	2	are	be	VERB
cana-735	6	3	frequently	frequently	ADV
cana-735	6	4	some	some	DET
cana-735	6	5	uncertainties	uncertainty	NOUN
cana-735	6	6	that	that	PRON
cana-735	6	7	have	have	VERB
cana-735	6	8	an	an	DET
cana-735	6	9	impact	impact	NOUN
cana-735	6	10	on	on	ADP
cana-735	6	11	this	this	DET
cana-735	6	12	number	number	NOUN
cana-735	6	13	.	.	PUNCT
cana-735	7	1	the	the	DET
cana-735	7	2	category	category	NOUN
cana-735	7	3	of	of	ADP
cana-735	7	4	probabilistic	probabilistic	ADJ
cana-735	7	5	uncertainty	uncertainty	NOUN
cana-735	7	6	is	be	AUX
cana-735	7	7	distinct	distinct	ADJ
cana-735	7	8	from	from	ADP
cana-735	7	9	probabilistic	probabilistic	ADJ
cana-735	7	10	uncertainty	uncertainty	NOUN
cana-735	7	11	,	,	PUNCT
cana-735	7	12	which	which	PRON
cana-735	7	13	encompasses	encompass	VERB
cana-735	7	14	most	most	ADJ
cana-735	7	15	uncertainties	uncertainty	NOUN
cana-735	7	16	.	.	PUNCT
cana-735	8	1	by	by	ADP
cana-735	8	2	using	use	VERB
cana-735	8	3	the	the	DET
cana-735	8	4	fuzzy	fuzzy	ADJ
cana-735	8	5	theoretical	theoretical	ADJ
cana-735	8	6	framework	framework	NOUN
cana-735	8	7	,	,	PUNCT
cana-735	8	8	this	this	DET
cana-735	8	9	uncertainty	uncertainty	NOUN
cana-735	8	10	is	be	AUX
cana-735	8	11	frequently	frequently	ADV
cana-735	8	12	modelled	model	VERB
cana-735	8	13	.	.	PUNCT
cana-735	9	1	with	with	ADP
cana-735	9	2	a	a	DET
cana-735	9	3	fuzzy	fuzzy	ADJ
cana-735	9	4	shape	shape	NOUN
cana-735	9	5	parameter	parameter	NOUN
cana-735	9	6	,	,	PUNCT
cana-735	9	7	the	the	DET
cana-735	9	8	failure	failure	NOUN
cana-735	9	9	numbers	number	NOUN
cana-735	9	10	of	of	ADP
cana-735	9	11	the	the	DET
cana-735	9	12	dagum	dagum	NOUN
cana-735	9	13	system	system	NOUN
cana-735	9	14	under	under	ADP
cana-735	9	15	study	study	NOUN
cana-735	9	16	in	in	ADP
cana-735	9	17	this	this	DET
cana-735	9	18	paper	paper	NOUN
cana-735	9	19	is	be	AUX
cana-735	9	20	exhausted	exhaust	VERB
cana-735	9	21	to	to	PART
cana-735	9	22	calculate	calculate	VERB
cana-735	9	23	several	several	ADJ
cana-735	9	24	failures	failure	NOUN
cana-735	9	25	.	.	PUNCT
cana-735	10	1	here	here	ADV
cana-735	10	2	,	,	PUNCT
cana-735	10	3	the	the	DET
cana-735	10	4	figure	figure	NOUN
cana-735	10	5	is	be	AUX
cana-735	10	6	computed	compute	VERB
cana-735	10	7	via	via	ADP
cana-735	10	8	two	two	NUM
cana-735	10	9	distinct	distinct	ADJ
cana-735	10	10	approaches	approach	NOUN
cana-735	10	11	.	.	PUNCT
cana-735	11	1	with	with	ADP
cana-735	11	2	the	the	DET
cana-735	11	3	first	first	ADJ
cana-735	11	4	approach	approach	NOUN
cana-735	11	5	,	,	PUNCT
cana-735	11	6	the	the	DET
cana-735	11	7	quality	quality	NOUN
cana-735	11	8	of	of	ADP
cana-735	11	9	failure	failure	NOUN
cana-735	11	10	receives	receive	VERB
cana-735	11	11	the	the	DET
cana-735	11	12	exact	exact	ADJ
cana-735	11	13	same	same	ADJ
cana-735	11	14	membership	membership	NOUN
cana-735	11	15	values	value	NOUN
cana-735	11	16	based	base	VERB
cana-735	11	17	on	on	ADP
cana-735	11	18	fuzziness	fuzziness	NOUN
cana-735	11	19	of	of	ADP
cana-735	11	20	dgm	dgm	PROPN
cana-735	11	21	shape	shape	PROPN
cana-735	11	22	parameter	parameter	NOUN
cana-735	11	23	.	.	PUNCT
cana-735	12	1	to	to	PART
cana-735	12	2	determine	determine	VERB
cana-735	12	3	membership	membership	NOUN
cana-735	12	4	,	,	PUNCT
cana-735	12	5	using	use	VERB
cana-735	12	6	level	level	NOUN
cana-735	12	7	of	of	ADP
cana-735	12	8	α	α	NOUN
cana-735	12	9	-	-	NOUN
cana-735	12	10	cut	cut	NOUN
cana-735	12	11	of	of	ADP
cana-735	12	12	the	the	DET
cana-735	12	13	shape	shape	NOUN
cana-735	12	14	parameter	parameter	NOUN
cana-735	12	15	approach	approach	NOUN
cana-735	12	16	and	and	CCONJ
cana-735	12	17	estimate	estimate	VERB
cana-735	12	18	formula	formula	NOUN
cana-735	12	19	for	for	ADP
cana-735	12	20	failure	failure	NOUN
cana-735	12	21	number	number	NOUN
cana-735	12	22	from	from	ADP
cana-735	12	23	the	the	DET
cana-735	12	24	second	second	ADJ
cana-735	12	25	method	method	NOUN
cana-735	12	26	.	.	PUNCT
cana-735	13	1	for	for	ADP
cana-735	13	2	the	the	DET
cana-735	13	3	dagum	dagum	NOUN
cana-735	13	4	shape	shape	NOUN
cana-735	13	5	parameter	parameter	NOUN
cana-735	13	6	,	,	PUNCT
cana-735	13	7	we	we	PRON
cana-735	13	8	employ	employ	VERB
cana-735	13	9	the	the	DET
cana-735	13	10	triangular	triangular	NOUN
cana-735	13	11	fuzzy	fuzzy	ADJ
cana-735	13	12	number	number	NOUN
cana-735	13	13	(	(	PUNCT
cana-735	13	14	trfn	trfn	PROPN
cana-735	13	15	)	)	PUNCT
cana-735	13	16	without	without	ADP
cana-735	13	17	losing	lose	VERB
cana-735	13	18	generality	generality	NOUN
cana-735	13	19	.	.	PUNCT
cana-735	14	1	we	we	PRON
cana-735	14	2	demonstrate	demonstrate	VERB
cana-735	14	3	that	that	SCONJ
cana-735	14	4	both	both	DET
cana-735	14	5	approaches	approach	NOUN
cana-735	14	6	were	be	AUX
cana-735	14	7	successful	successful	ADJ
cana-735	14	8	in	in	ADP
cana-735	14	9	calculating	calculate	VERB
cana-735	14	10	the	the	DET
cana-735	14	11	failure	failure	NOUN
cana-735	14	12	rate	rate	NOUN
cana-735	14	13	.	.	PUNCT
cana-735	15	1	when	when	SCONJ
cana-735	15	2	we	we	PRON
cana-735	15	3	deliberate	deliberate	VERB
cana-735	15	4	failures	failure	NOUN
cana-735	15	5	as	as	ADP
cana-735	15	6	an	an	DET
cana-735	15	7	operating	operating	NOUN
cana-735	15	8	time	time	NOUN
cana-735	15	9	,	,	PUNCT
cana-735	15	10	both	both	DET
cana-735	15	11	methodologies	methodology	NOUN
cana-735	15	12	show	show	VERB
cana-735	15	13	that	that	SCONJ
cana-735	15	14	as	as	ADP
cana-735	15	15	time	time	NOUN
cana-735	15	16	increases	increase	NOUN
cana-735	15	17	,	,	PUNCT
cana-735	15	18	the	the	DET
cana-735	15	19	ambiguity	ambiguity	NOUN
cana-735	15	20	(	(	PUNCT
cana-735	15	21	or	or	CCONJ
cana-735	15	22	fuzziness	fuzziness	NOUN
cana-735	15	23	)	)	PUNCT
cana-735	15	24	of	of	ADP
cana-735	15	25	the	the	DET
cana-735	15	26	various	various	ADJ
cana-735	15	27	failures	failure	NOUN
cana-735	15	28	that	that	PRON
cana-735	15	29	arise	arise	VERB
cana-735	15	30	rises	rise	VERB
cana-735	15	31	.	.	PUNCT
cana-735	16	1	the	the	DET
cana-735	16	2	failure	failure	NOUN
cana-735	16	3	numbers	number	NOUN
cana-735	16	4	that	that	PRON
cana-735	16	5	result	result	VERB
cana-735	16	6	as	as	ADP
cana-735	16	7	using	use	VERB
cana-735	16	8	the	the	DET
cana-735	16	9	first	first	ADJ
cana-735	16	10	method	method	NOUN
cana-735	16	11	has	have	VERB
cana-735	16	12	a	a	DET
cana-735	16	13	trfn	trfn	NOUN
cana-735	16	14	form	form	NOUN
cana-735	16	15	.	.	PUNCT
cana-735	17	1	the	the	DET
cana-735	17	2	second	second	ADJ
cana-735	17	3	method	method	NOUN
cana-735	17	4	's	's	PART
cana-735	17	5	output	output	NOUN
cana-735	17	6	failure	failure	NOUN
cana-735	17	7	rate	rate	NOUN
cana-735	17	8	,	,	PUNCT
cana-735	17	9	however	however	ADV
cana-735	17	10	,	,	PUNCT
cana-735	17	11	has	have	VERB
cana-735	17	12	a	a	DET
cana-735	17	13	trfn	trfn	NOUN
cana-735	17	14	-	-	PUNCT
cana-735	17	15	like	like	ADJ
cana-735	17	16	form	form	NOUN
cana-735	17	17	rather	rather	ADV
cana-735	17	18	than	than	ADP
cana-735	17	19	necessarily	necessarily	ADV
cana-735	17	20	having	have	VERB
cana-735	17	21	a	a	DET
cana-735	17	22	trfn	trfn	NOUN
cana-735	17	23	form	form	NOUN
cana-735	17	24	.	.	PUNCT
cana-735	18	1	the	the	DET
cana-735	18	2	generalised	generalise	VERB
cana-735	18	3	mean	mean	NOUN
cana-735	18	4	value	value	NOUN
cana-735	18	5	defuzzification	defuzzification	NOUN
cana-735	18	6	(	(	PUNCT
cana-735	18	7	gmdf	gmdf	NOUN
cana-735	18	8	)	)	PUNCT
cana-735	18	9	method	method	NOUN
cana-735	18	10	is	be	AUX
cana-735	18	11	used	use	VERB
cana-735	18	12	to	to	PART
cana-735	18	13	compare	compare	VERB
cana-735	18	14	some	some	DET
cana-735	18	15	aspects	aspect	NOUN
cana-735	18	16	of	of	ADP
cana-735	18	17	these	these	DET
cana-735	18	18	two	two	NUM
cana-735	18	19	approaches	approach	NOUN
cana-735	18	20	.	.	PUNCT
cana-735	19	1	the	the	DET
cana-735	19	2	results	result	NOUN
cana-735	19	3	reveal	reveal	VERB
cana-735	19	4	that	that	SCONJ
cana-735	19	5	the	the	DET
cana-735	19	6	focal	focal	ADJ
cana-735	19	7	point	point	NOUN
cana-735	19	8	of	of	ADP
cana-735	19	9	these	these	DET
cana-735	19	10	fuzzy	fuzzy	ADJ
cana-735	19	11	numbers	number	NOUN
cana-735	19	12	of	of	ADP
cana-735	19	13	failures	failure	NOUN
cana-735	19	14	of	of	ADP
cana-735	19	15	corresponding	correspond	VERB
cana-735	19	16	dgm	dgm	PROPN
cana-735	19	17	(	(	PUNCT
cana-735	19	18	dagum	dagum	NOUN
cana-735	19	19	distribution	distribution	NOUN
cana-735	19	20	)	)	PUNCT
cana-735	19	21	are	be	AUX
cana-735	19	22	the	the	DET
cana-735	19	23	same	same	ADJ
cana-735	19	24	for	for	ADP
cana-735	19	25	any	any	DET
cana-735	19	26	given	give	VERB
cana-735	19	27	gmdf	gmdf	NOUN
cana-735	19	28	weighting	weighting	NOUN
cana-735	19	29	factor	factor	NOUN
cana-735	19	30	.	.	PUNCT
cana-735	20	1	keywords	keyword	NOUN
cana-735	20	2	:	:	PUNCT
cana-735	20	3	dagum	dagum	NOUN
cana-735	20	4	hazard	hazard	NOUN
cana-735	20	5	function	function	NOUN
cana-735	20	6	;	;	PUNCT
cana-735	20	7	trfn	trfn	NOUN
cana-735	20	8	;	;	PUNCT
cana-735	20	9	failure	failure	NOUN
cana-735	20	10	number	number	NOUN
cana-735	20	11	;	;	PUNCT
cana-735	20	12	gmdf	gmdf	PROPN
cana-735	20	13	;	;	PUNCT
cana-735	20	14	α	α	X
cana-735	20	15	-	-	PUNCT
cana-735	20	16	cut	cut	NOUN
cana-735	20	17	of	of	ADP
cana-735	20	18	fn	fn	NOUN
cana-735	20	19	.	.	PUNCT
cana-735	21	1	ams	am	NOUN
cana-735	21	2	classification	classification	NOUN
cana-735	21	3	:	:	PUNCT
cana-735	21	4	62e15	62e15	NUM
cana-735	21	5	,	,	PUNCT
cana-735	22	1	62f30,62e86,62e17,62h10,62a86	62f30,62e86,62e17,62h10,62a86	NUM
cana-735	22	2	1	1	NUM
cana-735	22	3	.	.	PUNCT
cana-735	22	4	introduction	introduction	NOUN
cana-735	22	5	almost	almost	ADV
cana-735	22	6	all	all	PRON
cana-735	22	7	decision	decision	NOUN
cana-735	22	8	-	-	PUNCT
cana-735	22	9	making	make	VERB
cana-735	22	10	situations	situation	NOUN
cana-735	22	11	involve	involve	VERB
cana-735	22	12	some	some	DET
cana-735	22	13	level	level	NOUN
cana-735	22	14	of	of	ADP
cana-735	22	15	uncertainty	uncertainty	NOUN
cana-735	22	16	,	,	PUNCT
cana-735	22	17	and	and	CCONJ
cana-735	22	18	reliability	reliability	NOUN
cana-735	22	19	and	and	CCONJ
cana-735	22	20	maintenance	maintenance	NOUN
cana-735	22	21	issues	issue	NOUN
cana-735	22	22	are	be	AUX
cana-735	22	23	no	no	DET
cana-735	22	24	exception	exception	NOUN
cana-735	22	25	.	.	PUNCT
cana-735	23	1	this	this	PRON
cana-735	23	2	is	be	AUX
cana-735	23	3	a	a	DET
cana-735	23	4	result	result	NOUN
cana-735	23	5	of	of	ADP
cana-735	23	6	social	social	ADJ
cana-735	23	7	subjectivity	subjectivity	NOUN
cana-735	23	8	in	in	ADP
cana-735	23	9	a	a	DET
cana-735	23	10	decision	decision	NOUN
cana-735	23	11	-	-	PUNCT
cana-735	23	12	making	make	VERB
cana-735	23	13	process	process	NOUN
cana-735	23	14	,	,	PUNCT
cana-735	23	15	uncertain	uncertain	ADJ
cana-735	23	16	future	future	ADJ
cana-735	23	17	events	event	NOUN
cana-735	23	18	,	,	PUNCT
cana-735	23	19	and	and	CCONJ
cana-735	23	20	imprecision	imprecision	NOUN
cana-735	23	21	[	[	X
cana-735	23	22	7	7	NUM
cana-735	23	23	]	]	PUNCT
cana-735	23	24	.	.	PUNCT
cana-735	24	1	in	in	ADP
cana-735	24	2	every	every	DET
cana-735	24	3	field	field	NOUN
cana-735	24	4	,	,	PUNCT
cana-735	24	5	there	there	PRON
cana-735	24	6	are	be	VERB
cana-735	24	7	some	some	DET
cana-735	24	8	significant	significant	ADJ
cana-735	24	9	variables	variable	NOUN
cana-735	24	10	that	that	PRON
cana-735	24	11	have	have	VERB
cana-735	24	12	a	a	DET
cana-735	24	13	big	big	ADJ
cana-735	24	14	impact	impact	NOUN
cana-735	24	15	on	on	ADP
cana-735	24	16	how	how	SCONJ
cana-735	24	17	decisions	decision	NOUN
cana-735	24	18	are	be	AUX
cana-735	24	19	made	make	VERB
cana-735	24	20	.	.	PUNCT
cana-735	25	1	the	the	DET
cana-735	25	2	number	number	NOUN
cana-735	25	3	of	of	ADP
cana-735	25	4	failures	failure	NOUN
cana-735	25	5	has	have	VERB
cana-735	25	6	a	a	DET
cana-735	25	7	significant	significant	ADJ
cana-735	25	8	impact	impact	NOUN
cana-735	25	9	on	on	ADP
cana-735	25	10	the	the	DET
cana-735	25	11	analysis	analysis	NOUN
cana-735	25	12	of	of	ADP
cana-735	25	13	a	a	DET
cana-735	25	14	manufacturing	manufacturing	NOUN
cana-735	25	15	system	system	NOUN
cana-735	25	16	's	's	PART
cana-735	25	17	maintenance	maintenance	NOUN
cana-735	25	18	strategy	strategy	NOUN
cana-735	25	19	in	in	ADP
cana-735	25	20	the	the	DET
cana-735	25	21	field	field	NOUN
cana-735	25	22	of	of	ADP
cana-735	25	23	reliability	reliability	NOUN
cana-735	25	24	and	and	CCONJ
cana-735	25	25	preservation	preservation	NOUN
cana-735	25	26	.	.	PUNCT
cana-735	26	1	numerous	numerous	ADJ
cana-735	26	2	uncertainties	uncertainty	NOUN
cana-735	26	3	fall	fall	VERB
cana-735	26	4	under	under	ADP
cana-735	26	5	probabilistic	probabilistic	ADJ
cana-735	26	6	uncertainty	uncertainty	NOUN
cana-735	26	7	rather	rather	ADV
cana-735	26	8	than	than	ADP
cana-735	26	9	possibility	possibility	NOUN
cana-735	26	10	of	of	ADP
cana-735	26	11	uncertainty	uncertainty	NOUN
cana-735	26	12	,	,	PUNCT
cana-735	26	13	which	which	PRON
cana-735	26	14	is	be	AUX
cana-735	26	15	a	a	DET
cana-735	26	16	different	different	ADJ
cana-735	26	17	category	category	NOUN
cana-735	26	18	.	.	PUNCT
cana-735	27	1	many	many	ADJ
cana-735	27	2	times	time	NOUN
cana-735	27	3	,	,	PUNCT
cana-735	27	4	at	at	ADP
cana-735	27	5	least	least	ADJ
cana-735	27	6	one	one	NUM
cana-735	27	7	of	of	ADP
cana-735	27	8	the	the	DET
cana-735	27	9	decision	decision	NOUN
cana-735	27	10	function	function	NOUN
cana-735	27	11	's	's	PART
cana-735	27	12	parameters	parameter	NOUN
cana-735	27	13	or	or	CCONJ
cana-735	27	14	variables	variable	NOUN
cana-735	27	15	have	have	VERB
cana-735	27	16	a	a	DET
cana-735	27	17	fuzzy	fuzzy	ADJ
cana-735	27	18	value	value	NOUN
cana-735	27	19	rather	rather	ADV
cana-735	27	20	than	than	ADP
cana-735	27	21	a	a	DET
cana-735	27	22	crisp	crisp	ADJ
cana-735	27	23	value	value	NOUN
cana-735	27	24	.	.	PUNCT
cana-735	28	1	communications	communication	NOUN
cana-735	28	2	on	on	ADP
cana-735	28	3	applied	apply	VERB
cana-735	28	4	nonlinear	nonlinear	ADJ
cana-735	28	5	analysis	analysis	NOUN
cana-735	28	6	issn	issn	NOUN
cana-735	28	7	:	:	PUNCT
cana-735	28	8	1074	1074	NUM
cana-735	28	9	-	-	PUNCT
cana-735	28	10	133x	133x	NUM
cana-735	28	11	vol	vol	NOUN
cana-735	28	12	31	31	NUM
cana-735	28	13	no	no	NOUN
cana-735	28	14	.	.	PUNCT
cana-735	29	1	3s	3s	NUM
cana-735	29	2	(	(	PUNCT
cana-735	29	3	2024	2024	NUM
cana-735	29	4	)	)	PUNCT
cana-735	29	5	106	106	NUM
cana-735	29	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-735	29	7	the	the	DET
cana-735	29	8	number	number	NOUN
cana-735	29	9	of	of	ADP
cana-735	29	10	failures	failure	NOUN
cana-735	29	11	is	be	AUX
cana-735	29	12	a	a	DET
cana-735	29	13	crucial	crucial	ADJ
cana-735	29	14	factor	factor	NOUN
cana-735	29	15	that	that	PRON
cana-735	29	16	must	must	AUX
cana-735	29	17	be	be	AUX
cana-735	29	18	ascertained	ascertain	VERB
cana-735	29	19	because	because	SCONJ
cana-735	29	20	it	it	PRON
cana-735	29	21	serves	serve	VERB
cana-735	29	22	as	as	ADP
cana-735	29	23	the	the	DET
cana-735	29	24	basis	basis	NOUN
cana-735	29	25	for	for	ADP
cana-735	29	26	additional	additional	ADJ
cana-735	29	27	decisionmaking	decisionmaking	NOUN
cana-735	29	28	in	in	ADP
cana-735	29	29	maintenance	maintenance	NOUN
cana-735	29	30	and	and	CCONJ
cana-735	29	31	reliability	reliability	NOUN
cana-735	29	32	analysis	analysis	NOUN
cana-735	29	33	.	.	PUNCT
cana-735	30	1	for	for	ADP
cana-735	30	2	example	example	NOUN
cana-735	30	3	,	,	PUNCT
cana-735	30	4	this	this	DET
cana-735	30	5	number	number	NOUN
cana-735	30	6	is	be	AUX
cana-735	30	7	exhausted	exhaust	VERB
cana-735	30	8	when	when	SCONJ
cana-735	30	9	creating	create	VERB
cana-735	30	10	the	the	DET
cana-735	30	11	best	good	ADJ
cana-735	30	12	maintenance	maintenance	NOUN
cana-735	30	13	plan	plan	NOUN
cana-735	30	14	to	to	PART
cana-735	30	15	reduce	reduce	VERB
cana-735	30	16	multiple	multiple	ADJ
cana-735	30	17	failures	failure	NOUN
cana-735	30	18	and	and	CCONJ
cana-735	30	19	maintenance	maintenance	NOUN
cana-735	30	20	costs	cost	NOUN
cana-735	30	21	[	[	X
cana-735	30	22	9,10	9,10	NUM
cana-735	30	23	]	]	PUNCT
cana-735	30	24	.	.	PUNCT
cana-735	31	1	it	it	PRON
cana-735	31	2	is	be	AUX
cana-735	31	3	therefore	therefore	ADV
cana-735	31	4	essential	essential	ADJ
cana-735	31	5	to	to	PART
cana-735	31	6	understand	understand	VERB
cana-735	31	7	how	how	SCONJ
cana-735	31	8	to	to	PART
cana-735	31	9	estimate	estimate	VERB
cana-735	31	10	the	the	DET
cana-735	31	11	failures	failure	NOUN
cana-735	31	12	.	.	PUNCT
cana-735	32	1	failure	failure	NOUN
cana-735	32	2	data	datum	NOUN
cana-735	32	3	are	be	AUX
cana-735	32	4	often	often	ADV
cana-735	32	5	difficult	difficult	ADJ
cana-735	32	6	to	to	PART
cana-735	32	7	obtain	obtain	VERB
cana-735	32	8	due	due	ADP
cana-735	32	9	to	to	ADP
cana-735	32	10	uncertainty	uncertainty	NOUN
cana-735	32	11	,	,	PUNCT
cana-735	32	12	inaccuracy	inaccuracy	NOUN
cana-735	32	13	and	and	CCONJ
cana-735	32	14	complexity	complexity	NOUN
cana-735	32	15	of	of	ADP
cana-735	32	16	the	the	DET
cana-735	32	17	model	model	NOUN
cana-735	32	18	under	under	ADP
cana-735	32	19	survey	survey	NOUN
cana-735	32	20	.	.	PUNCT
cana-735	33	1	in	in	ADP
cana-735	33	2	this	this	DET
cana-735	33	3	context	context	NOUN
cana-735	33	4	idea	idea	NOUN
cana-735	33	5	of	of	ADP
cana-735	33	6	fuzzy	fuzzy	ADJ
cana-735	33	7	set	set	NOUN
cana-735	33	8	is	be	AUX
cana-735	33	9	often	often	ADV
cana-735	33	10	used	use	VERB
cana-735	33	11	to	to	PART
cana-735	33	12	provide	provide	VERB
cana-735	33	13	a	a	DET
cana-735	33	14	framework	framework	NOUN
cana-735	33	15	for	for	ADP
cana-735	33	16	controlling	control	VERB
cana-735	33	17	uncertainty	uncertainty	NOUN
cana-735	33	18	and	and	CCONJ
cana-735	33	19	error	error	NOUN
cana-735	33	20	[	[	X
cana-735	33	21	11	11	NUM
cana-735	33	22	]	]	PUNCT
cana-735	33	23	.	.	PUNCT
cana-735	34	1	one	one	NUM
cana-735	34	2	of	of	ADP
cana-735	34	3	the	the	DET
cana-735	34	4	most	most	ADJ
cana-735	34	5	difficulties	difficulty	NOUN
cana-735	34	6	in	in	ADP
cana-735	34	7	calculating	calculate	VERB
cana-735	34	8	the	the	DET
cana-735	34	9	number	number	NOUN
cana-735	34	10	of	of	ADP
cana-735	34	11	failures	failure	NOUN
cana-735	34	12	with	with	ADP
cana-735	34	13	probabilistic	probabilistic	ADJ
cana-735	34	14	uncertainty	uncertainty	NOUN
cana-735	34	15	is	be	AUX
cana-735	34	16	determining	determine	VERB
cana-735	34	17	the	the	DET
cana-735	34	18	computation	computation	NOUN
cana-735	34	19	of	of	ADP
cana-735	34	20	this	this	DET
cana-735	34	21	failure	failure	NOUN
cana-735	34	22	numbers	number	NOUN
cana-735	34	23	for	for	ADP
cana-735	34	24	a	a	DET
cana-735	34	25	specified	specify	VERB
cana-735	34	26	probability	probability	NOUN
cana-735	34	27	distribution	distribution	NOUN
cana-735	34	28	with	with	ADP
cana-735	34	29	fuzzy	fuzzy	ADJ
cana-735	34	30	parameters	parameter	NOUN
cana-735	34	31	.	.	PUNCT
cana-735	35	1	fuzzy	fuzzy	ADJ
cana-735	35	2	number	number	NOUN
cana-735	35	3	calculators	calculator	NOUN
cana-735	35	4	are	be	AUX
cana-735	35	5	now	now	ADV
cana-735	35	6	commonly	commonly	ADV
cana-735	35	7	available	available	ADJ
cana-735	35	8	[	[	X
cana-735	35	9	13	13	NUM
cana-735	35	10	]	]	PUNCT
cana-735	35	11	.	.	PUNCT
cana-735	36	1	second	second	ADJ
cana-735	36	2	,	,	PUNCT
cana-735	36	3	understanding	understand	VERB
cana-735	36	4	how	how	SCONJ
cana-735	36	5	the	the	DET
cana-735	36	6	parameters	parameter	NOUN
cana-735	36	7	'	'	PART
cana-735	36	8	level	level	NOUN
cana-735	36	9	of	of	ADP
cana-735	36	10	uncertainty	uncertainty	NOUN
cana-735	36	11	affects	affect	VERB
cana-735	36	12	the	the	DET
cana-735	36	13	failure	failure	NOUN
cana-735	36	14	rates	rate	NOUN
cana-735	36	15	that	that	PRON
cana-735	36	16	result	result	VERB
cana-735	36	17	is	be	AUX
cana-735	36	18	crucial	crucial	ADJ
cana-735	36	19	.	.	PUNCT
cana-735	37	1	this	this	PRON
cana-735	37	2	is	be	AUX
cana-735	37	3	generally	generally	ADV
cana-735	37	4	referred	refer	VERB
cana-735	37	5	to	to	ADP
cana-735	37	6	the	the	DET
cana-735	37	7	dissemination	dissemination	NOUN
cana-735	37	8	of	of	ADP
cana-735	37	9	fuzziness	fuzziness	NOUN
cana-735	37	10	,	,	PUNCT
cana-735	37	11	that	that	PRON
cana-735	37	12	described	describe	VERB
cana-735	37	13	as	as	ADP
cana-735	37	14	"	"	PUNCT
cana-735	37	15	the	the	DET
cana-735	37	16	way	way	NOUN
cana-735	37	17	in	in	ADP
cana-735	37	18	which	which	PRON
cana-735	37	19	the	the	DET
cana-735	37	20	amount	amount	NOUN
cana-735	37	21	of	of	ADP
cana-735	37	22	imprecision	imprecision	NOUN
cana-735	37	23	in	in	ADP
cana-735	37	24	the	the	DET
cana-735	37	25	model	model	NOUN
cana-735	37	26	's	's	PART
cana-735	37	27	inputs	input	NOUN
cana-735	37	28	affects	affect	VERB
cana-735	37	29	the	the	DET
cana-735	37	30	changes	change	NOUN
cana-735	37	31	in	in	ADP
cana-735	37	32	the	the	DET
cana-735	37	33	model	model	NOUN
cana-735	37	34	's	's	PART
cana-735	37	35	output	output	NOUN
cana-735	37	36	"	"	PUNCT
cana-735	38	1	[	[	X
cana-735	38	2	12	12	NUM
cana-735	38	3	]	]	PUNCT
cana-735	38	4	.	.	PUNCT
cana-735	39	1	in	in	ADP
cana-735	39	2	theory	theory	NOUN
cana-735	39	3	,	,	PUNCT
cana-735	39	4	model	model	NOUN
cana-735	39	5	and	and	CCONJ
cana-735	39	6	computations	computation	NOUN
cana-735	39	7	use	use	NOUN
cana-735	39	8	of	of	ADP
cana-735	39	9	mathematical	mathematical	ADJ
cana-735	39	10	operations	operation	NOUN
cana-735	39	11	leads	lead	VERB
cana-735	39	12	to	to	ADP
cana-735	39	13	the	the	DET
cana-735	39	14	spread	spread	NOUN
cana-735	39	15	of	of	ADP
cana-735	39	16	uncertainty	uncertainty	NOUN
cana-735	39	17	.	.	PUNCT
cana-735	40	1	the	the	DET
cana-735	40	2	decision	decision	NOUN
cana-735	40	3	-	-	PUNCT
cana-735	40	4	making	make	VERB
cana-735	40	5	process	process	NOUN
cana-735	40	6	will	will	AUX
cana-735	40	7	be	be	AUX
cana-735	40	8	significantly	significantly	ADV
cana-735	40	9	improved	improve	VERB
cana-735	40	10	by	by	ADP
cana-735	40	11	understanding	understand	VERB
cana-735	40	12	the	the	DET
cana-735	40	13	number	number	NOUN
cana-735	40	14	's	's	PART
cana-735	40	15	calculation	calculation	NOUN
cana-735	40	16	process	process	NOUN
cana-735	40	17	and	and	CCONJ
cana-735	40	18	degree	degree	NOUN
cana-735	40	19	of	of	ADP
cana-735	40	20	uncertainty	uncertainty	NOUN
cana-735	40	21	(	(	PUNCT
cana-735	40	22	see	see	VERB
cana-735	40	23	also	also	ADV
cana-735	40	24	[	[	X
cana-735	40	25	13,14	13,14	X
cana-735	40	26	]	]	X
cana-735	40	27	for	for	ADP
cana-735	40	28	examples	example	NOUN
cana-735	40	29	of	of	ADP
cana-735	40	30	this	this	PRON
cana-735	40	31	in	in	ADP
cana-735	40	32	other	other	ADJ
cana-735	40	33	fields	field	NOUN
cana-735	40	34	)	)	PUNCT
cana-735	40	35	.	.	PUNCT
cana-735	41	1	in	in	ADP
cana-735	41	2	complex	complex	ADJ
cana-735	41	3	engineering	engineering	NOUN
cana-735	41	4	systems	system	NOUN
cana-735	41	5	in	in	ADP
cana-735	41	6	general	general	ADJ
cana-735	41	7	,	,	PUNCT
cana-735	41	8	fuzziness	fuzziness	NOUN
cana-735	41	9	propagation	propagation	NOUN
cana-735	41	10	can	can	AUX
cana-735	41	11	be	be	AUX
cana-735	41	12	very	very	ADV
cana-735	41	13	difficult	difficult	ADJ
cana-735	41	14	[	[	X
cana-735	41	15	15	15	NUM
cana-735	41	16	]	]	PUNCT
cana-735	41	17	.	.	PUNCT
cana-735	42	1	the	the	DET
cana-735	42	2	paper	paper	NOUN
cana-735	42	3	has	have	VERB
cana-735	42	4	two	two	NUM
cana-735	42	5	objectives	objective	NOUN
cana-735	42	6	:	:	PUNCT
cana-735	42	7	•	•	ADP
cana-735	42	8	the	the	DET
cana-735	42	9	first	first	ADJ
cana-735	42	10	,	,	PUNCT
cana-735	42	11	step	step	NOUN
cana-735	42	12	is	be	AUX
cana-735	42	13	to	to	PART
cana-735	42	14	figure	figure	VERB
cana-735	42	15	out	out	ADP
cana-735	42	16	number	number	NOUN
cana-735	42	17	of	of	ADP
cana-735	42	18	failures	failure	NOUN
cana-735	42	19	a	a	DET
cana-735	42	20	system	system	NOUN
cana-735	42	21	with	with	ADP
cana-735	42	22	fuzzy	fuzzy	ADJ
cana-735	42	23	shape	shape	NOUN
cana-735	42	24	parameter	parameter	NOUN
cana-735	42	25	and	and	CCONJ
cana-735	42	26	failure	failure	NOUN
cana-735	42	27	number	number	NOUN
cana-735	42	28	of	of	ADP
cana-735	42	29	dgm	dgm	PROPN
cana-735	42	30	distribution	distribution	NOUN
cana-735	42	31	will	will	AUX
cana-735	42	32	have	have	VERB
cana-735	42	33	,	,	PUNCT
cana-735	42	34	and	and	CCONJ
cana-735	42	35	•	•	ADV
cana-735	42	36	secondly	secondly	ADV
cana-735	42	37	to	to	PART
cana-735	42	38	understand	understand	VERB
cana-735	42	39	how	how	SCONJ
cana-735	42	40	the	the	DET
cana-735	42	41	number	number	NOUN
cana-735	42	42	of	of	ADP
cana-735	42	43	failures	failure	NOUN
cana-735	42	44	that	that	PRON
cana-735	42	45	results	result	VERB
cana-735	42	46	from	from	ADP
cana-735	42	47	this	this	DET
cana-735	42	48	shape	shape	NOUN
cana-735	42	49	parameters	parameter	NOUN
cana-735	42	50	with	with	ADP
cana-735	42	51	fuzziness	fuzziness	NOUN
cana-735	42	52	.	.	PUNCT
cana-735	43	1	the	the	DET
cana-735	43	2	significance	significance	NOUN
cana-735	43	3	and	and	CCONJ
cana-735	43	4	impacts	impact	NOUN
cana-735	43	5	of	of	ADP
cana-735	43	6	the	the	DET
cana-735	43	7	work	work	NOUN
cana-735	43	8	performed	perform	VERB
cana-735	43	9	in	in	ADP
cana-735	43	10	this	this	DET
cana-735	43	11	paper	paper	NOUN
cana-735	43	12	are	be	AUX
cana-735	43	13	comprised	comprise	VERB
cana-735	43	14	of	of	ADP
cana-735	43	15	these	these	DET
cana-735	43	16	two	two	NUM
cana-735	43	17	objectives	objective	NOUN
cana-735	43	18	.	.	PUNCT
cana-735	44	1	additionally	additionally	ADV
cana-735	44	2	,	,	PUNCT
cana-735	44	3	two	two	NUM
cana-735	44	4	different	different	ADJ
cana-735	44	5	approaches	approach	NOUN
cana-735	44	6	are	be	AUX
cana-735	44	7	used	use	VERB
cana-735	44	8	in	in	ADP
cana-735	44	9	this	this	DET
cana-735	44	10	paper	paper	NOUN
cana-735	44	11	to	to	PART
cana-735	44	12	determine	determine	VERB
cana-735	44	13	the	the	DET
cana-735	44	14	failure	failure	NOUN
cana-735	44	15	rate	rate	NOUN
cana-735	44	16	using	use	VERB
cana-735	44	17	two	two	NUM
cana-735	44	18	different	different	ADJ
cana-735	44	19	metrics	metric	NOUN
cana-735	44	20	.	.	PUNCT
cana-735	45	1	the	the	DET
cana-735	45	2	first	first	ADJ
cana-735	45	3	method	method	NOUN
cana-735	45	4	propagates	propagate	VERB
cana-735	45	5	the	the	DET
cana-735	45	6	membership	membership	NOUN
cana-735	45	7	function	function	NOUN
cana-735	45	8	to	to	ADP
cana-735	45	9	failure	failure	NOUN
cana-735	45	10	numbers	number	NOUN
cana-735	45	11	to	to	ADP
cana-735	45	12	dgm	dgm	PROPN
cana-735	45	13	of	of	ADP
cana-735	45	14	fuzziness	fuzziness	NOUN
cana-735	45	15	shape	shape	NOUN
cana-735	45	16	parameters	parameter	NOUN
cana-735	45	17	giving	give	VERB
cana-735	45	18	them	they	PRON
cana-735	45	19	the	the	DET
cana-735	45	20	same	same	ADJ
cana-735	45	21	membership	membership	NOUN
cana-735	45	22	values	value	NOUN
cana-735	45	23	.	.	PUNCT
cana-735	46	1	in	in	ADP
cana-735	46	2	contrast	contrast	NOUN
cana-735	46	3	,	,	PUNCT
cana-735	46	4	in	in	ADP
cana-735	46	5	the	the	DET
cana-735	46	6	method	method	NOUN
cana-735	46	7	two	two	NUM
cana-735	46	8	,	,	PUNCT
cana-735	46	9	the	the	DET
cana-735	46	10	shape	shape	NOUN
cana-735	46	11	parameter	parameter	NOUN
cana-735	46	12	's	's	PART
cana-735	46	13	α	α	NOUN
cana-735	46	14	-	-	PUNCT
cana-735	46	15	cut	cut	VERB
cana-735	46	16	,	,	PUNCT
cana-735	46	17	or	or	CCONJ
cana-735	46	18	level	level	NOUN
cana-735	46	19	is	be	AUX
cana-735	46	20	used	use	VERB
cana-735	46	21	to	to	PART
cana-735	46	22	compute	compute	VERB
cana-735	46	23	the	the	DET
cana-735	46	24	membership	membership	NOUN
cana-735	46	25	.	.	PUNCT
cana-735	47	1	2	2	X
cana-735	47	2	.	.	X
cana-735	47	3	methods	method	NOUN
cana-735	47	4	the	the	DET
cana-735	47	5	mathematical	mathematical	ADJ
cana-735	47	6	model	model	NOUN
cana-735	47	7	for	for	ADP
cana-735	47	8	describing	describe	VERB
cana-735	47	9	the	the	DET
cana-735	47	10	decline	decline	NOUN
cana-735	47	11	of	of	ADP
cana-735	47	12	an	an	DET
cana-735	47	13	industrial	industrial	ADJ
cana-735	47	14	system	system	NOUN
cana-735	47	15	or	or	CCONJ
cana-735	47	16	piece	piece	NOUN
cana-735	47	17	of	of	ADP
cana-735	47	18	equipment	equipment	NOUN
cana-735	47	19	is	be	AUX
cana-735	47	20	called	call	VERB
cana-735	47	21	the	the	DET
cana-735	47	22	dgm	dgm	PROPN
cana-735	47	23	distribution	distribution	NOUN
cana-735	47	24	function	function	NOUN
cana-735	47	25	,	,	PUNCT
cana-735	47	26	and	and	CCONJ
cana-735	47	27	it	it	PRON
cana-735	47	28	is	be	AUX
cana-735	47	29	the	the	DET
cana-735	47	30	focus	focus	NOUN
cana-735	47	31	of	of	ADP
cana-735	47	32	this	this	DET
cana-735	47	33	paper	paper	NOUN
cana-735	47	34	.	.	PUNCT
cana-735	48	1	dgm	dgm	PROPN
cana-735	48	2	distribution	distribution	NOUN
cana-735	48	3	functions	function	NOUN
cana-735	48	4	,	,	PUNCT
cana-735	48	5	such	such	ADJ
cana-735	48	6	as	as	ADP
cana-735	48	7	those	those	PRON
cana-735	48	8	found	find	VERB
cana-735	48	9	in	in	ADP
cana-735	48	10	[	[	X
cana-735	48	11	18	18	NUM
cana-735	48	12	]	]	PUNCT
cana-735	48	13	,	,	PUNCT
cana-735	48	14	are	be	AUX
cana-735	48	15	frequently	frequently	ADV
cana-735	48	16	used	use	VERB
cana-735	48	17	to	to	PART
cana-735	48	18	model	model	VERB
cana-735	48	19	the	the	DET
cana-735	48	20	deterioration	deterioration	NOUN
cana-735	48	21	or	or	CCONJ
cana-735	48	22	failure	failure	NOUN
cana-735	48	23	data	datum	NOUN
cana-735	48	24	.	.	PUNCT
cana-735	49	1	because	because	SCONJ
cana-735	49	2	of	of	ADP
cana-735	49	3	its	its	PRON
cana-735	49	4	adaptability	adaptability	NOUN
cana-735	49	5	,	,	PUNCT
cana-735	49	6	the	the	DET
cana-735	49	7	dgm	dgm	PROPN
cana-735	49	8	function	function	PROPN
cana-735	49	9	has	have	AUX
cana-735	49	10	gained	gain	VERB
cana-735	49	11	popularity	popularity	NOUN
cana-735	49	12	and	and	CCONJ
cana-735	49	13	can	can	AUX
cana-735	49	14	be	be	AUX
cana-735	49	15	considered	consider	VERB
cana-735	49	16	as	as	ADP
cana-735	49	17	a	a	DET
cana-735	49	18	generalisation	generalisation	NOUN
cana-735	49	19	of	of	ADP
cana-735	49	20	the	the	DET
cana-735	49	21	rayleigh	rayleigh	PROPN
cana-735	49	22	and	and	CCONJ
cana-735	49	23	exponential	exponential	ADJ
cana-735	49	24	distributions	distribution	NOUN
cana-735	49	25	,	,	PUNCT
cana-735	49	26	which	which	PRON
cana-735	49	27	are	be	AUX
cana-735	49	28	widely	widely	ADV
cana-735	49	29	applied	apply	VERB
cana-735	49	30	in	in	ADP
cana-735	49	31	the	the	DET
cana-735	49	32	reliability	reliability	NOUN
cana-735	49	33	studies	study	NOUN
cana-735	49	34	[	[	X
cana-735	49	35	19	19	NUM
cana-735	49	36	]	]	PUNCT
cana-735	49	37	.	.	PUNCT
cana-735	50	1	the	the	DET
cana-735	50	2	continuous	continuous	ADJ
cana-735	50	3	probability	probability	NOUN
cana-735	50	4	density	density	NOUN
cana-735	50	5	function	function	NOUN
cana-735	50	6	of	of	ADP
cana-735	50	7	dgm	dgm	PROPN
cana-735	50	8	distribution	distribution	NOUN
cana-735	50	9	having	have	VERB
cana-735	50	10	the	the	DET
cana-735	50	11	form	form	NOUN
cana-735	50	12	.	.	PUNCT
cana-735	51	1	f(x	f(x	NOUN
cana-735	51	2	)	)	PUNCT
cana-735	52	1	=	=	PRON
cana-735	52	2	{	{	PUNCT
cana-735	52	3	βδ	βδ	NOUN
cana-735	52	4	x−(δ+1	x−(δ+1	NUM
cana-735	52	5	)	)	PUNCT
cana-735	52	6	(	(	PUNCT
cana-735	52	7	1	1	NUM
cana-735	52	8	+	+	CCONJ
cana-735	52	9	x−δ)−(β+1	x−δ)−(β+1	PROPN
cana-735	52	10	)	)	PUNCT
cana-735	52	11	,	,	PUNCT
cana-735	52	12	for	for	ADP
cana-735	52	13	x>0	x>0	PROPN
cana-735	52	14	,	,	PUNCT
cana-735	52	15	β	β	X
cana-735	52	16	,	,	PUNCT
cana-735	52	17	δ>0	δ>0	PROPN
cana-735	52	18	0	0	NUM
cana-735	52	19	otherwise	otherwise	ADV
cana-735	52	20	.	.	PUNCT
cana-735	53	1	(	(	PUNCT
cana-735	53	2	1	1	X
cana-735	53	3	)	)	PUNCT
cana-735	53	4	communications	communication	NOUN
cana-735	53	5	on	on	ADP
cana-735	53	6	applied	apply	VERB
cana-735	53	7	nonlinear	nonlinear	ADJ
cana-735	53	8	analysis	analysis	NOUN
cana-735	53	9	issn	issn	NOUN
cana-735	53	10	:	:	PUNCT
cana-735	53	11	1074	1074	NUM
cana-735	53	12	-	-	PUNCT
cana-735	53	13	133x	133x	NUM
cana-735	53	14	vol	vol	NOUN
cana-735	53	15	31	31	NUM
cana-735	53	16	no	no	NOUN
cana-735	53	17	.	.	PUNCT
cana-735	54	1	3s	3s	NUM
cana-735	54	2	(	(	PUNCT
cana-735	54	3	2024	2024	NUM
cana-735	54	4	)	)	PUNCT
cana-735	54	5	107	107	NUM
cana-735	54	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-735	54	7	where	where	SCONJ
cana-735	54	8	γ	γ	PROPN
cana-735	54	9	,	,	PUNCT
cana-735	54	10	δ	δ	PROPN
cana-735	54	11	,	,	PUNCT
cana-735	54	12	β	β	X
cana-735	54	13	are	be	AUX
cana-735	54	14	scale	scale	NOUN
cana-735	54	15	and	and	CCONJ
cana-735	54	16	shape	shape	NOUN
cana-735	54	17	parameters	parameter	NOUN
cana-735	54	18	respectively	respectively	ADV
cana-735	54	19	.	.	PUNCT
cana-735	55	1	to	to	PART
cana-735	55	2	model	model	VERB
cana-735	55	3	wealth	wealth	NOUN
cana-735	55	4	and	and	CCONJ
cana-735	55	5	income	income	NOUN
cana-735	55	6	,	,	PUNCT
cana-735	55	7	camilo	camilo	PROPN
cana-735	55	8	dagum	dagum	PROPN
cana-735	55	9	proposed	propose	VERB
cana-735	55	10	the	the	DET
cana-735	55	11	dagum	dagum	NOUN
cana-735	55	12	distribution	distribution	NOUN
cana-735	55	13	(	(	PUNCT
cana-735	55	14	dgm	dgm	PROPN
cana-735	55	15	)	)	PUNCT
cana-735	55	16	in	in	ADP
cana-735	55	17	1970	1970	NUM
cana-735	55	18	.	.	PUNCT
cana-735	56	1	it	it	PRON
cana-735	56	2	is	be	AUX
cana-735	56	3	also	also	ADV
cana-735	56	4	known	know	VERB
cana-735	56	5	as	as	ADP
cana-735	56	6	the	the	DET
cana-735	56	7	inverse	inverse	NOUN
cana-735	56	8	burr	burr	NOUN
cana-735	56	9	distribution	distribution	NOUN
cana-735	56	10	,	,	PUNCT
cana-735	56	11	or	or	CCONJ
cana-735	56	12	the	the	DET
cana-735	56	13	generalised	generalise	VERB
cana-735	56	14	logistic	logistic	ADJ
cana-735	56	15	burr	burr	NOUN
cana-735	56	16	distribution	distribution	NOUN
cana-735	56	17	.	.	PUNCT
cana-735	57	1	by	by	ADP
cana-735	57	2	varying	vary	VERB
cana-735	57	3	the	the	DET
cana-735	57	4	parameter	parameter	NOUN
cana-735	57	5	in	in	ADP
cana-735	57	6	shape	shape	NOUN
cana-735	57	7	,	,	PUNCT
cana-735	57	8	the	the	DET
cana-735	57	9	dgm	dgm	PROPN
cana-735	57	10	distribution	distribution	NOUN
cana-735	57	11	can	can	AUX
cana-735	57	12	be	be	AUX
cana-735	57	13	exhausted	exhaust	VERB
cana-735	57	14	a	a	DET
cana-735	57	15	variety	variety	NOUN
cana-735	57	16	of	of	ADP
cana-735	57	17	real	real	ADJ
cana-735	57	18	-	-	PUNCT
cana-735	57	19	life	life	NOUN
cana-735	57	20	data	datum	NOUN
cana-735	57	21	,	,	PUNCT
cana-735	57	22	for	for	ADP
cana-735	57	23	example	example	NOUN
cana-735	57	24	,	,	PUNCT
cana-735	57	25	rayleigh	rayleigh	ADJ
cana-735	57	26	distribution	distribution	NOUN
cana-735	57	27	function	function	NOUN
cana-735	57	28	can	can	AUX
cana-735	57	29	be	be	AUX
cana-735	57	30	obtained	obtain	VERB
cana-735	57	31	if	if	SCONJ
cana-735	57	32	β	β	X
cana-735	57	33	=	=	SYM
cana-735	57	34	2	2	NUM
cana-735	57	35	and	and	CCONJ
cana-735	57	36	an	an	DET
cana-735	57	37	exponential	exponential	ADJ
cana-735	57	38	distribution	distribution	NOUN
cana-735	57	39	can	can	AUX
cana-735	57	40	be	be	AUX
cana-735	57	41	obtained	obtain	VERB
cana-735	57	42	if	if	SCONJ
cana-735	57	43	β	β	X
cana-735	57	44	=	=	SYM
cana-735	57	45	2	2	NUM
cana-735	58	1	[	[	X
cana-735	58	2	19	19	NUM
cana-735	58	3	]	]	PUNCT
cana-735	58	4	.	.	PUNCT
cana-735	59	1	we	we	PRON
cana-735	59	2	will	will	AUX
cana-735	59	3	make	make	VERB
cana-735	59	4	the	the	DET
cana-735	59	5	scale	scale	NOUN
cana-735	59	6	parameter	parameter	NOUN
cana-735	59	7	δ	δ	PROPN
cana-735	59	8	=	=	PUNCT
cana-735	59	9	1	1	NUM
cana-735	59	10	our	our	PRON
cana-735	59	11	starting	start	VERB
cana-735	59	12	point	point	NOUN
cana-735	59	13	throughout	throughout	ADP
cana-735	59	14	the	the	DET
cana-735	59	15	paper	paper	NOUN
cana-735	59	16	for	for	ADP
cana-735	59	17	a	a	DET
cana-735	59	18	few	few	ADJ
cana-735	59	19	different	different	ADJ
cana-735	59	20	reasons	reason	NOUN
cana-735	59	21	.	.	PUNCT
cana-735	60	1	for	for	ADP
cana-735	60	2	example	example	NOUN
cana-735	60	3	,	,	PUNCT
cana-735	60	4	maintenance	maintenance	NOUN
cana-735	60	5	modelling	modelling	NOUN
cana-735	60	6	,	,	PUNCT
cana-735	60	7	this	this	DET
cana-735	60	8	choice	choice	NOUN
cana-735	60	9	is	be	AUX
cana-735	60	10	sufficient	sufficient	ADJ
cana-735	60	11	if	if	SCONJ
cana-735	60	12	assume	assume	VERB
cana-735	60	13	that	that	SCONJ
cana-735	60	14	the	the	DET
cana-735	60	15	equipment	equipment	NOUN
cana-735	60	16	or	or	CCONJ
cana-735	60	17	system	system	NOUN
cana-735	60	18	that	that	PRON
cana-735	60	19	the	the	DET
cana-735	60	20	equipment	equipment	NOUN
cana-735	60	21	or	or	CCONJ
cana-735	60	22	system	system	NOUN
cana-735	60	23	under	under	ADP
cana-735	60	24	investigation	investigation	NOUN
cana-735	60	25	,	,	PUNCT
cana-735	60	26	as	as	ADP
cana-735	60	27	of	of	ADP
cana-735	60	28	guarantee	guarantee	NOUN
cana-735	60	29	and	and	CCONJ
cana-735	60	30	heigh	heigh	ADJ
cana-735	60	31	level	level	NOUN
cana-735	60	32	eminence	eminence	NOUN
cana-735	60	33	control	control	NOUN
cana-735	60	34	,	,	PUNCT
cana-735	60	35	experiences	experience	VERB
cana-735	60	36	its	its	PRON
cana-735	60	37	first	first	ADJ
cana-735	60	38	failure	failure	NOUN
cana-735	60	39	on	on	ADP
cana-735	60	40	average	average	ADJ
cana-735	60	41	within	within	ADP
cana-735	60	42	a	a	DET
cana-735	60	43	unit	unit	NOUN
cana-735	60	44	of	of	ADP
cana-735	60	45	time	time	NOUN
cana-735	60	46	,	,	PUNCT
cana-735	60	47	such	such	ADJ
cana-735	60	48	as	as	ADP
cana-735	60	49	a	a	DET
cana-735	60	50	month	month	NOUN
cana-735	60	51	or	or	CCONJ
cana-735	60	52	a	a	DET
cana-735	60	53	year	year	NOUN
cana-735	60	54	.	.	PUNCT
cana-735	61	1	it	it	PRON
cana-735	61	2	is	be	AUX
cana-735	61	3	possible	possible	ADJ
cana-735	61	4	to	to	PART
cana-735	61	5	compute	compute	VERB
cana-735	61	6	failure	failure	NOUN
cana-735	61	7	numbers	number	NOUN
cana-735	61	8	,	,	PUNCT
cana-735	61	9	hazard	hazard	NOUN
cana-735	61	10	function	function	NOUN
cana-735	61	11	,	,	PUNCT
cana-735	61	12	preventative	preventative	ADJ
cana-735	61	13	maintenance	maintenance	NOUN
cana-735	61	14	time	time	NOUN
cana-735	61	15	and	and	CCONJ
cana-735	61	16	auxiliary	auxiliary	ADJ
cana-735	61	17	time	time	NOUN
cana-735	61	18	using	use	VERB
cana-735	61	19	the	the	DET
cana-735	61	20	dgm	dgm	PROPN
cana-735	61	21	distribution	distribution	NOUN
cana-735	61	22	function	function	NOUN
cana-735	61	23	.	.	PUNCT
cana-735	62	1	among	among	ADP
cana-735	62	2	other	other	ADJ
cana-735	62	3	places	place	NOUN
cana-735	62	4	,	,	PUNCT
cana-735	62	5	[	[	X
cana-735	62	6	20,21	20,21	NUM
cana-735	62	7	]	]	PUNCT
cana-735	62	8	contains	contain	VERB
cana-735	62	9	the	the	DET
cana-735	62	10	conventional	conventional	ADJ
cana-735	62	11	approaches	approach	NOUN
cana-735	62	12	for	for	ADP
cana-735	62	13	calculating	calculate	VERB
cana-735	62	14	these	these	DET
cana-735	62	15	indices	index	NOUN
cana-735	62	16	for	for	ADP
cana-735	62	17	both	both	CCONJ
cana-735	62	18	simple	simple	ADJ
cana-735	62	19	and	and	CCONJ
cana-735	62	20	complex	complex	ADJ
cana-735	62	21	systems	system	NOUN
cana-735	62	22	.	.	PUNCT
cana-735	63	1	in	in	ADP
cana-735	63	2	[	[	X
cana-735	63	3	22,23	22,23	NOUN
cana-735	63	4	]	]	PUNCT
cana-735	63	5	,	,	PUNCT
cana-735	63	6	the	the	DET
cana-735	63	7	dgm	dgm	PROPN
cana-735	63	8	distribution	distribution	NOUN
cana-735	63	9	function	function	NOUN
cana-735	63	10	's	's	PART
cana-735	63	11	theory	theory	NOUN
cana-735	63	12	and	and	CCONJ
cana-735	63	13	applications	application	NOUN
cana-735	63	14	are	be	AUX
cana-735	63	15	covered	cover	VERB
cana-735	63	16	in	in	ADP
cana-735	63	17	detail	detail	NOUN
cana-735	63	18	.	.	PUNCT
cana-735	64	1	the	the	DET
cana-735	64	2	fn	fn	NOUN
cana-735	64	3	and	and	CCONJ
cana-735	64	4	its	its	PRON
cana-735	64	5	membership	membership	NOUN
cana-735	64	6	function	function	NOUN
cana-735	64	7	,	,	PUNCT
cana-735	64	8	the	the	DET
cana-735	64	9	α	α	NOUN
cana-735	64	10	-	-	PUNCT
cana-735	64	11	cut	cut	NOUN
cana-735	64	12	of	of	ADP
cana-735	64	13	fn	fn	NOUN
cana-735	64	14	and	and	CCONJ
cana-735	64	15	the	the	DET
cana-735	64	16	generalised	generalise	VERB
cana-735	64	17	mean	mean	NOUN
cana-735	64	18	value	value	NOUN
cana-735	64	19	de	de	NOUN
cana-735	64	20	-	-	NOUN
cana-735	64	21	fuzzification	fuzzification	NOUN
cana-735	64	22	(	(	PUNCT
cana-735	64	23	dfuz	dfuz	NOUN
cana-735	64	24	)	)	PUNCT
cana-735	64	25	process	process	NOUN
cana-735	64	26	are	be	AUX
cana-735	64	27	some	some	DET
cana-735	64	28	concepts	concept	NOUN
cana-735	64	29	from	from	ADP
cana-735	64	30	the	the	DET
cana-735	64	31	fuzzy	fuzzy	ADJ
cana-735	64	32	theoretical	theoretical	ADJ
cana-735	64	33	framework	framework	NOUN
cana-735	64	34	that	that	PRON
cana-735	64	35	are	be	AUX
cana-735	64	36	presented	present	VERB
cana-735	64	37	and	and	CCONJ
cana-735	64	38	extended	extend	VERB
cana-735	64	39	in	in	ADP
cana-735	64	40	the	the	DET
cana-735	64	41	technique	technique	NOUN
cana-735	64	42	and	and	CCONJ
cana-735	64	43	investigation	investigation	NOUN
cana-735	64	44	that	that	PRON
cana-735	64	45	follow	follow	VERB
cana-735	64	46	.	.	PUNCT
cana-735	65	1	2.1	2.1	NUM
cana-735	65	2	defining	define	VERB
cana-735	65	3	of	of	ADP
cana-735	65	4	fn	fn	NOUN
cana-735	65	5	and	and	CCONJ
cana-735	65	6	its	its	PRON
cana-735	65	7	membership	membership	NOUN
cana-735	65	8	function	function	NOUN
cana-735	65	9	in	in	ADP
cana-735	65	10	this	this	DET
cana-735	65	11	section	section	NOUN
cana-735	65	12	,	,	PUNCT
cana-735	65	13	define	define	VERB
cana-735	65	14	some	some	DET
cana-735	65	15	terms	term	NOUN
cana-735	65	16	related	relate	VERB
cana-735	65	17	to	to	ADP
cana-735	65	18	fn	fn	PROPN
cana-735	65	19	theory	theory	NOUN
cana-735	65	20	that	that	PRON
cana-735	65	21	will	will	AUX
cana-735	65	22	be	be	AUX
cana-735	65	23	use	use	VERB
cana-735	65	24	innovative	innovative	ADJ
cana-735	65	25	.	.	PUNCT
cana-735	66	1	one	one	NUM
cana-735	66	2	way	way	NOUN
cana-735	66	3	to	to	PART
cana-735	66	4	conceptualize	conceptualize	VERB
cana-735	66	5	fn	fn	NOUN
cana-735	66	6	is	be	AUX
cana-735	66	7	as	as	ADP
cana-735	66	8	generalisation	generalisation	NOUN
cana-735	66	9	of	of	ADP
cana-735	66	10	a	a	DET
cana-735	66	11	real	real	ADJ
cana-735	66	12	number	number	NOUN
cana-735	66	13	because	because	SCONJ
cana-735	66	14	it	it	PRON
cana-735	66	15	represents	represent	VERB
cana-735	66	16	uncertainty	uncertainty	NOUN
cana-735	66	17	using	use	VERB
cana-735	66	18	a	a	DET
cana-735	66	19	membership	membership	NOUN
cana-735	66	20	function	function	NOUN
cana-735	66	21	.	.	PUNCT
cana-735	67	1	membership	membership	NOUN
cana-735	67	2	has	have	VERB
cana-735	67	3	a	a	DET
cana-735	67	4	defined	define	VERB
cana-735	67	5	value	value	NOUN
cana-735	67	6	when	when	SCONJ
cana-735	67	7	it	it	PRON
cana-735	67	8	is	be	AUX
cana-735	67	9	binary	binary	ADJ
cana-735	67	10	.	.	PUNCT
cana-735	68	1	when	when	SCONJ
cana-735	68	2	fn	fn	PROPN
cana-735	68	3	is	be	AUX
cana-735	68	4	zero	zero	NUM
cana-735	68	5	,	,	PUNCT
cana-735	68	6	it	it	PRON
cana-735	68	7	is	be	AUX
cana-735	68	8	obviously	obviously	ADV
cana-735	68	9	not	not	PART
cana-735	68	10	a	a	DET
cana-735	68	11	member	member	NOUN
cana-735	68	12	of	of	ADP
cana-735	68	13	a	a	DET
cana-735	68	14	set	set	NOUN
cana-735	68	15	μ	μ	NOUN
cana-735	68	16	and	and	CCONJ
cana-735	68	17	when	when	SCONJ
cana-735	68	18	it	it	PRON
cana-735	68	19	is	be	AUX
cana-735	68	20	one	one	NUM
cana-735	68	21	,	,	PUNCT
cana-735	68	22	it	it	PRON
cana-735	68	23	is	be	AUX
cana-735	68	24	obviously	obviously	ADV
cana-735	68	25	a	a	DET
cana-735	68	26	set	set	NOUN
cana-735	68	27	μ	μ	NOUN
cana-735	68	28	.	.	PUNCT
cana-735	69	1	fn	fn	PROPN
cana-735	69	2	ã	ã	PROPN
cana-735	69	3	is	be	AUX
cana-735	69	4	defined	define	VERB
cana-735	69	5	mathematically	mathematically	ADV
cana-735	69	6	associated	associate	VERB
cana-735	69	7	with	with	ADP
cana-735	69	8	feasible	feasible	ADJ
cana-735	69	9	values	value	NOUN
cana-735	69	10	,	,	PUNCT
cana-735	69	11	for	for	ADP
cana-735	69	12	all	all	DET
cana-735	69	13	values	value	NOUN
cana-735	69	14	of	of	ADP
cana-735	69	15	ã	ã	PROPN
cana-735	69	16	is	be	AUX
cana-735	69	17	possible	possible	ADJ
cana-735	69	18	.	.	PUNCT
cana-735	70	1	suppose	suppose	VERB
cana-735	70	2	that	that	SCONJ
cana-735	70	3	a	a	DET
cana-735	70	4	distinct	distinct	ADJ
cana-735	70	5	membership	membership	NOUN
cana-735	70	6	in	in	ADP
cana-735	70	7	[	[	X
cana-735	70	8	0,1	0,1	NUM
cana-735	70	9	]	]	PUNCT
cana-735	70	10	,	,	PUNCT
cana-735	70	11	the	the	DET
cana-735	70	12	term	term	NOUN
cana-735	70	13	"	"	PUNCT
cana-735	70	14	membership	membership	NOUN
cana-735	70	15	function	function	NOUN
cana-735	70	16	"	"	PUNCT
cana-735	70	17	refers	refer	VERB
cana-735	70	18	to	to	ADP
cana-735	70	19	this	this	DET
cana-735	70	20	number	number	NOUN
cana-735	70	21	,	,	PUNCT
cana-735	70	22	which	which	PRON
cana-735	70	23	is	be	AUX
cana-735	70	24	typically	typically	ADV
cana-735	70	25	written	write	VERB
cana-735	70	26	as	as	ADP
cana-735	70	27	"	"	PUNCT
cana-735	70	28	ξ	ξ	X
cana-735	70	29	:	:	PUNCT
cana-735	70	30	a	a	DET
cana-735	70	31	∈	∈	PROPN
cana-735	70	32	a	a	DET
cana-735	70	33	→x	→x	PROPN
cana-735	70	34	∈	∈	PROPN
cana-735	71	1	[	[	X
cana-735	71	2	0	0	NUM
cana-735	71	3	,	,	PUNCT
cana-735	71	4	1	1	NUM
cana-735	71	5	]	]	PUNCT
cana-735	71	6	,	,	PUNCT
cana-735	71	7	"	"	PUNCT
cana-735	71	8	and	and	CCONJ
cana-735	71	9	measures	measure	NOUN
cana-735	71	10	how	how	SCONJ
cana-735	71	11	likely	likely	ADJ
cana-735	71	12	it	it	PRON
cana-735	71	13	is	be	AUX
cana-735	71	14	for	for	SCONJ
cana-735	71	15	a	a	PRON
cana-735	71	16	to	to	PART
cana-735	71	17	belong	belong	VERB
cana-735	71	18	to	to	ADP
cana-735	71	19	ã	ã	PROPN
cana-735	71	20	=	=	SYM
cana-735	71	21	(	(	PUNCT
cana-735	71	22	a	a	PRON
cana-735	71	23	,	,	PUNCT
cana-735	71	24	ξ(a	ξ(a	NUM
cana-735	71	25	)	)	PUNCT
cana-735	71	26	)	)	PUNCT
cana-735	71	27	or	or	CCONJ
cana-735	71	28	ã	ã	PROPN
cana-735	71	29	=	=	SYM
cana-735	71	30	(	(	PUNCT
cana-735	71	31	x	x	NOUN
cana-735	71	32	,	,	PUNCT
cana-735	71	33	ξa̅(x	ξa̅(x	NOUN
cana-735	71	34	)	)	PUNCT
cana-735	71	35	|x∈	|x∈	ADV
cana-735	71	36	x	x	VERB
cana-735	71	37	are	be	AUX
cana-735	71	38	two	two	NUM
cana-735	71	39	other	other	ADJ
cana-735	71	40	common	common	ADJ
cana-735	71	41	ways	way	NOUN
cana-735	71	42	to	to	PART
cana-735	71	43	represent	represent	VERB
cana-735	71	44	this	this	DET
cana-735	71	45	fuzzy	fuzzy	ADJ
cana-735	71	46	number	number	NOUN
cana-735	71	47	.	.	PUNCT
cana-735	72	1	the	the	DET
cana-735	72	2	fuzzy	fuzzy	ADJ
cana-735	72	3	number	number	NOUN
cana-735	72	4	can	can	AUX
cana-735	72	5	be	be	AUX
cana-735	72	6	thought	think	VERB
cana-735	72	7	of	of	ADP
cana-735	72	8	in	in	ADP
cana-735	72	9	this	this	DET
cana-735	72	10	way	way	NOUN
cana-735	72	11	as	as	ADP
cana-735	72	12	a	a	DET
cana-735	72	13	pair	pair	NOUN
cana-735	72	14	of	of	ADP
cana-735	72	15	mathematical	mathematical	ADJ
cana-735	72	16	objects	object	NOUN
cana-735	72	17	that	that	PRON
cana-735	72	18	are	be	AUX
cana-735	72	19	made	make	VERB
cana-735	72	20	up	up	ADP
cana-735	72	21	of	of	ADP
cana-735	72	22	a	a	DET
cana-735	72	23	set	set	NOUN
cana-735	72	24	and	and	CCONJ
cana-735	72	25	its	its	PRON
cana-735	72	26	membership	membership	NOUN
cana-735	72	27	function	function	NOUN
cana-735	72	28	or	or	CCONJ
cana-735	72	29	grade	grade	NOUN
cana-735	72	30	.	.	PUNCT
cana-735	73	1	the	the	DET
cana-735	73	2	fuzzy	fuzzy	ADJ
cana-735	73	3	number	number	NOUN
cana-735	73	4	is	be	AUX
cana-735	73	5	supposedly	supposedly	ADV
cana-735	73	6	meant	mean	VERB
cana-735	73	7	to	to	PART
cana-735	73	8	quantify	quantify	VERB
cana-735	73	9	the	the	DET
cana-735	73	10	ambiguity	ambiguity	NOUN
cana-735	73	11	and	and	CCONJ
cana-735	73	12	inaccuracy	inaccuracy	NOUN
cana-735	73	13	of	of	ADP
cana-735	73	14	too	too	ADV
cana-735	73	15	much	much	ADJ
cana-735	73	16	information	information	NOUN
cana-735	73	17	as	as	ADV
cana-735	73	18	well	well	ADV
cana-735	73	19	as	as	ADP
cana-735	73	20	to	to	PART
cana-735	73	21	show	show	VERB
cana-735	73	22	probabilistic	probabilistic	ADJ
cana-735	73	23	uncertainty	uncertainty	NOUN
cana-735	73	24	.	.	PUNCT
cana-735	74	1	numerous	numerous	ADJ
cana-735	74	2	functional	functional	ADJ
cana-735	74	3	approaches	approach	NOUN
cana-735	74	4	may	may	AUX
cana-735	74	5	be	be	AUX
cana-735	74	6	used	use	VERB
cana-735	74	7	to	to	PART
cana-735	74	8	identify	identify	VERB
cana-735	74	9	the	the	DET
cana-735	74	10	fn	fn	NOUN
cana-735	74	11	membership	membership	NOUN
cana-735	74	12	,	,	PUNCT
cana-735	74	13	that	that	PRON
cana-735	74	14	can	can	AUX
cana-735	74	15	divide	divide	VERB
cana-735	74	16	into	into	ADP
cana-735	74	17	two	two	NUM
cana-735	74	18	functional	functional	ADJ
cana-735	74	19	forms	form	NOUN
cana-735	74	20	,	,	PUNCT
cana-735	74	21	linear	linear	ADJ
cana-735	74	22	and	and	CCONJ
cana-735	74	23	non	non	ADJ
cana-735	74	24	-	-	ADJ
cana-735	74	25	linear	linear	ADJ
cana-735	74	26	respectively	respectively	ADV
cana-735	74	27	[	[	X
cana-735	74	28	16	16	NUM
cana-735	74	29	]	]	PUNCT
cana-735	74	30	.	.	PUNCT
cana-735	75	1	the	the	DET
cana-735	75	2	fuzzy	fuzzy	ADJ
cana-735	75	3	numbers	number	NOUN
cana-735	75	4	are	be	AUX
cana-735	75	5	represented	represent	VERB
cana-735	75	6	graphically	graphically	ADV
cana-735	75	7	in	in	ADP
cana-735	75	8	figures	figure	NOUN
cana-735	75	9	1	1	NUM
cana-735	75	10	and	and	CCONJ
cana-735	75	11	2	2	NUM
cana-735	75	12	and	and	CCONJ
cana-735	75	13	their	their	PRON
cana-735	75	14	functional	functional	ADJ
cana-735	75	15	forms	form	NOUN
cana-735	75	16	and	and	CCONJ
cana-735	75	17	membership	membership	NOUN
cana-735	75	18	functions	function	NOUN
cana-735	75	19	are	be	AUX
cana-735	75	20	obtained	obtain	VERB
cana-735	75	21	by	by	ADP
cana-735	75	22	equations	equation	NOUN
cana-735	75	23	(	(	PUNCT
cana-735	75	24	2	2	NUM
cana-735	75	25	)	)	PUNCT
cana-735	75	26	and	and	CCONJ
cana-735	75	27	(	(	PUNCT
cana-735	75	28	3	3	NUM
cana-735	75	29	)	)	PUNCT
cana-735	75	30	.	.	PUNCT
cana-735	76	1	observe	observe	VERB
cana-735	76	2	that	that	SCONJ
cana-735	76	3	the	the	DET
cana-735	76	4	tpfn	tpfn	NOUN
cana-735	76	5	in	in	ADP
cana-735	76	6	(	(	PUNCT
cana-735	76	7	3	3	X
cana-735	76	8	)	)	PUNCT
cana-735	76	9	is	be	AUX
cana-735	76	10	provided	provide	VERB
cana-735	76	11	an	an	DET
cana-735	76	12	increase	increase	NOUN
cana-735	76	13	or	or	CCONJ
cana-735	76	14	decrease	decrease	VERB
cana-735	76	15	linear	linear	ADJ
cana-735	76	16	curve	curve	NOUN
cana-735	76	17	that	that	PRON
cana-735	76	18	provides	provide	VERB
cana-735	76	19	the	the	DET
cana-735	76	20	membership	membership	NOUN
cana-735	76	21	function	function	NOUN
cana-735	76	22	in	in	ADP
cana-735	76	23	[	[	X
cana-735	76	24	a	a	DET
cana-735	76	25	,	,	PUNCT
cana-735	76	26	b	b	NOUN
cana-735	76	27	]	]	PUNCT
cana-735	76	28	and	and	CCONJ
cana-735	76	29	[	[	X
cana-735	76	30	c	c	X
cana-735	76	31	,	,	PUNCT
cana-735	76	32	d	d	NOUN
cana-735	76	33	]	]	X
cana-735	76	34	.	.	PUNCT
cana-735	77	1	this	this	DET
cana-735	77	2	notion	notion	NOUN
cana-735	77	3	is	be	AUX
cana-735	77	4	generalised	generalise	VERB
cana-735	77	5	from	from	ADP
cana-735	77	6	linear	linear	ADJ
cana-735	77	7	-	-	PUNCT
cana-735	77	8	flat	flat	ADJ
cana-735	77	9	fuzzy	fuzzy	ADJ
cana-735	77	10	number	number	NOUN
cana-735	77	11	and	and	CCONJ
cana-735	77	12	used	use	VERB
cana-735	77	13	as	as	ADP
cana-735	77	14	a	a	DET
cana-735	77	15	new	new	ADJ
cana-735	77	16	strategy	strategy	NOUN
cana-735	77	17	in	in	ADP
cana-735	77	18	[	[	X
cana-735	77	19	8,24,25	8,24,25	NUM
cana-735	77	20	]	]	PUNCT
cana-735	77	21	.	.	PUNCT
cana-735	78	1	trfn	trfn	PROPN
cana-735	78	2	membership	membership	NOUN
cana-735	78	3	function	function	NOUN
cana-735	78	4	is	be	AUX
cana-735	78	5	as	as	SCONJ
cana-735	78	6	follows	follow	VERB
cana-735	78	7	.	.	PUNCT
cana-735	79	1	communications	communication	NOUN
cana-735	79	2	on	on	ADP
cana-735	79	3	applied	apply	VERB
cana-735	79	4	nonlinear	nonlinear	ADJ
cana-735	79	5	analysis	analysis	NOUN
cana-735	79	6	issn	issn	NOUN
cana-735	79	7	:	:	PUNCT
cana-735	79	8	1074	1074	NUM
cana-735	79	9	-	-	PUNCT
cana-735	79	10	133x	133x	NUM
cana-735	79	11	vol	vol	NOUN
cana-735	79	12	31	31	NUM
cana-735	79	13	no	no	NOUN
cana-735	79	14	.	.	PUNCT
cana-735	80	1	3s	3s	NUM
cana-735	80	2	(	(	PUNCT
cana-735	80	3	2024	2024	NUM
cana-735	80	4	)	)	PUNCT
cana-735	80	5	108	108	NUM
cana-735	80	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-735	80	7	ξa̅(x	ξa̅(x	NOUN
cana-735	80	8	)	)	PUNCT
cana-735	80	9	=	=	PUNCT
cana-735	80	10	{	{	PUNCT
cana-735	80	11	0	0	NUM
cana-735	80	12	,	,	PUNCT
cana-735	80	13	x≤a	x≤a	PROPN
cana-735	80	14	x	x	PART
cana-735	80	15	−a	−a	VERB
cana-735	80	16	a	a	DET
cana-735	80	17	−a	−a	NOUN
cana-735	80	18	,	,	PUNCT
cana-735	80	19	a≤x≤b	a≤x≤b	X
cana-735	80	20	x	x	PART
cana-735	80	21	−c	−c	NOUN
cana-735	80	22	b	b	PROPN
cana-735	80	23	−c	−c	NOUN
cana-735	80	24	,	,	PUNCT
cana-735	80	25	b≤x≤c	b≤x≤c	ADP
cana-735	80	26	0	0	NUM
cana-735	80	27	,	,	PUNCT
cana-735	80	28	x≥c	x≥c	PROPN
cana-735	80	29	(	(	PUNCT
cana-735	80	30	2	2	NUM
cana-735	80	31	)	)	PUNCT
cana-735	80	32	tpfn	tpfn	NOUN
cana-735	80	33	membership	membership	NOUN
cana-735	80	34	function	function	NOUN
cana-735	80	35	is	be	AUX
cana-735	80	36	as	as	SCONJ
cana-735	80	37	follows	follow	VERB
cana-735	80	38	.	.	PUNCT
cana-735	81	1	ξa̅(x	ξa̅(x	NOUN
cana-735	81	2	)	)	PUNCT
cana-735	81	3	=	=	PUNCT
cana-735	81	4	{	{	PUNCT
cana-735	81	5	0	0	NUM
cana-735	81	6	,	,	PUNCT
cana-735	81	7	x≤a	x≤a	PROPN
cana-735	82	1	x	x	SYM
cana-735	82	2	−a	−a	NOUN
cana-735	82	3	b	b	PROPN
cana-735	82	4	−a	−a	NOUN
cana-735	82	5	,	,	PUNCT
cana-735	82	6	a≤x≤b	a≤x≤b	X
cana-735	82	7	x	x	PART
cana-735	82	8	−c	−c	VERB
cana-735	82	9	c−d	c−d	NOUN
cana-735	82	10	,	,	PUNCT
cana-735	82	11	b≤x≤c	b≤x≤c	ADP
cana-735	82	12	0	0	NUM
cana-735	82	13	,	,	PUNCT
cana-735	82	14	x≥d	x≥d	PROPN
cana-735	82	15	1	1	NUM
cana-735	82	16	,	,	PUNCT
cana-735	82	17	b	b	NOUN
cana-735	82	18	≤	≤	NUM
cana-735	82	19	x	x	PUNCT
cana-735	82	20	≤	≤	NUM
cana-735	82	21	c	c	X
cana-735	82	22	(	(	PUNCT
cana-735	82	23	3	3	NUM
cana-735	82	24	)	)	PUNCT
cana-735	82	25	figure1	figure1	X
cana-735	82	26	.	.	PUNCT
cana-735	83	1	graphical	graphical	ADJ
cana-735	83	2	representation	representation	NOUN
cana-735	83	3	of	of	ADP
cana-735	83	4	trfn	trfn	NOUN
cana-735	83	5	and	and	CCONJ
cana-735	83	6	tpfn	tpfn	NOUN
cana-735	83	7	with	with	ADP
cana-735	83	8	parameters	parameter	NOUN
cana-735	83	9	(	(	PUNCT
cana-735	83	10	a	a	DET
cana-735	83	11	,	,	PUNCT
cana-735	83	12	b	b	NOUN
cana-735	83	13	,	,	PUNCT
cana-735	83	14	c	c	NOUN
cana-735	83	15	)	)	PUNCT
cana-735	83	16	and	and	CCONJ
cana-735	83	17	(	(	PUNCT
cana-735	83	18	a	a	PRON
cana-735	83	19	,	,	PUNCT
cana-735	83	20	b	b	NOUN
cana-735	83	21	,	,	PUNCT
cana-735	83	22	c	c	NOUN
cana-735	83	23	,	,	PUNCT
cana-735	83	24	d	d	NOUN
cana-735	83	25	)	)	PUNCT
cana-735	83	26	respectively	respectively	ADV
cana-735	83	27	.	.	PUNCT
cana-735	84	1	in	in	ADP
cana-735	84	2	this	this	DET
cana-735	84	3	scenario	scenario	NOUN
cana-735	84	4	,	,	PUNCT
cana-735	84	5	b	b	PROPN
cana-735	84	6	is	be	AUX
cana-735	84	7	referred	refer	VERB
cana-735	84	8	to	to	ADP
cana-735	84	9	as	as	ADP
cana-735	84	10	the	the	DET
cana-735	84	11	fuzzy	fuzzy	ADJ
cana-735	84	12	number	number	NOUN
cana-735	84	13	's	's	PART
cana-735	84	14	core	core	NOUN
cana-735	84	15	group	group	NOUN
cana-735	84	16	,	,	PUNCT
cana-735	84	17	while	while	SCONJ
cana-735	84	18	the	the	DET
cana-735	84	19	sets	set	NOUN
cana-735	84	20	[	[	X
cana-735	84	21	a	a	DET
cana-735	84	22	,	,	PUNCT
cana-735	84	23	b	b	NOUN
cana-735	84	24	)	)	PUNCT
cana-735	84	25	and	and	CCONJ
cana-735	84	26	(	(	PUNCT
cana-735	84	27	b	b	NOUN
cana-735	84	28	,	,	PUNCT
cana-735	84	29	c	c	NOUN
cana-735	84	30	)	)	PUNCT
cana-735	84	31	are	be	AUX
cana-735	84	32	referred	refer	VERB
cana-735	84	33	to	to	ADP
cana-735	84	34	as	as	ADP
cana-735	84	35	fn	fn	NOUN
cana-735	84	36	’s	’s	NOUN
cana-735	84	37	.	.	PUNCT
cana-735	85	1	similarly	similarly	ADV
cana-735	85	2	,	,	PUNCT
cana-735	85	3	in	in	ADP
cana-735	85	4	tpfn	tpfn	NOUN
cana-735	85	5	(	(	PUNCT
cana-735	85	6	3	3	NUM
cana-735	85	7	)	)	PUNCT
cana-735	85	8	,	,	PUNCT
cana-735	85	9	the	the	DET
cana-735	85	10	core	core	NOUN
cana-735	85	11	of	of	ADP
cana-735	85	12	the	the	DET
cana-735	85	13	fn	fn	NOUN
cana-735	85	14	provided	provide	VERB
cana-735	85	15	with	with	ADP
cana-735	85	16	[	[	X
cana-735	85	17	b	b	X
cana-735	85	18	,	,	PUNCT
cana-735	85	19	c	c	NOUN
cana-735	85	20	]	]	X
cana-735	85	21	,	,	PUNCT
cana-735	85	22	while	while	SCONJ
cana-735	85	23	supporting	support	VERB
cana-735	85	24	by	by	ADP
cana-735	85	25	the	the	DET
cana-735	85	26	sets	set	NOUN
cana-735	85	27	[	[	X
cana-735	85	28	a	a	DET
cana-735	85	29	,	,	PUNCT
cana-735	85	30	b	b	NOUN
cana-735	85	31	)	)	PUNCT
cana-735	85	32	and	and	CCONJ
cana-735	85	33	(	(	PUNCT
cana-735	85	34	c	c	X
cana-735	85	35	,	,	PUNCT
cana-735	85	36	d	d	NOUN
cana-735	85	37	)	)	PUNCT
cana-735	85	38	where	where	SCONJ
cana-735	85	39	a	a	DET
cana-735	85	40	,	,	PUNCT
cana-735	85	41	b	b	NOUN
cana-735	85	42	,	,	PUNCT
cana-735	85	43	c	c	NOUN
cana-735	85	44	,	,	PUNCT
cana-735	85	45	d	d	PROPN
cana-735	85	46	∈	∈	PROPN
cana-735	85	47	r.	r.	NOUN
cana-735	85	48	there	there	PRON
cana-735	85	49	are	be	VERB
cana-735	85	50	many	many	ADJ
cana-735	85	51	different	different	ADJ
cana-735	85	52	types	type	NOUN
cana-735	85	53	of	of	ADP
cana-735	85	54	fuzzy	fuzzy	ADJ
cana-735	85	55	numbers	number	NOUN
cana-735	85	56	[	[	X
cana-735	85	57	24	24	NUM
cana-735	85	58	]	]	X
cana-735	85	59	,	,	PUNCT
cana-735	85	60	such	such	ADJ
cana-735	85	61	as	as	ADP
cana-735	85	62	piecewise	piecewise	NOUN
cana-735	85	63	quadratic	quadratic	ADJ
cana-735	85	64	[	[	X
cana-735	85	65	26	26	NUM
cana-735	85	66	]	]	X
cana-735	85	67	,	,	PUNCT
cana-735	85	68	pentagonal	pentagonal	ADJ
cana-735	85	69	[	[	X
cana-735	85	70	27	27	NUM
cana-735	85	71	]	]	PUNCT
cana-735	85	72	,	,	PUNCT
cana-735	85	73	bell	bell	PROPN
cana-735	85	74	designed	design	VERB
cana-735	85	75	[	[	X
cana-735	85	76	28	28	NUM
cana-735	85	77	]	]	PUNCT
cana-735	85	78	,	,	PUNCT
cana-735	85	79	parabolic	parabolic	PROPN
cana-735	85	80	trapezoidal	trapezoidal	NOUN
cana-735	86	1	[	[	X
cana-735	86	2	29	29	NUM
cana-735	86	3	]	]	PUNCT
cana-735	86	4	,	,	PUNCT
cana-735	86	5	new	new	PROPN
cana-735	86	6	bellshaped	bellshape	VERB
cana-735	86	7	[	[	X
cana-735	86	8	30	30	NUM
cana-735	86	9	]	]	PUNCT
cana-735	86	10	,	,	PUNCT
cana-735	86	11	and	and	CCONJ
cana-735	86	12	numerous	numerous	ADJ
cana-735	86	13	others	other	NOUN
cana-735	86	14	are	be	AUX
cana-735	86	15	an	an	DET
cana-735	86	16	excellent	excellent	ADJ
cana-735	86	17	reference	reference	NOUN
cana-735	86	18	for	for	ADP
cana-735	86	19	how	how	SCONJ
cana-735	86	20	certain	certain	ADJ
cana-735	86	21	new	new	ADJ
cana-735	86	22	methodologies	methodology	NOUN
cana-735	86	23	and	and	CCONJ
cana-735	86	24	strategies	strategy	NOUN
cana-735	86	25	are	be	AUX
cana-735	86	26	established	establish	VERB
cana-735	86	27	to	to	PART
cana-735	86	28	expand	expand	VERB
cana-735	86	29	fuzzy	fuzzy	ADJ
cana-735	86	30	number	number	NOUN
cana-735	86	31	notions	notion	NOUN
cana-735	86	32	for	for	ADP
cana-735	86	33	current	current	ADJ
cana-735	86	34	analytics	analytic	NOUN
cana-735	86	35	.	.	PUNCT
cana-735	87	1	for	for	ADP
cana-735	87	2	the	the	DET
cana-735	87	3	sake	sake	NOUN
cana-735	87	4	of	of	ADP
cana-735	87	5	simplicity	simplicity	NOUN
cana-735	87	6	,	,	PUNCT
cana-735	87	7	in	in	ADP
cana-735	87	8	this	this	DET
cana-735	87	9	work	work	NOUN
cana-735	87	10	assume	assume	VERB
cana-735	87	11	trfn	trfn	NOUN
cana-735	87	12	to	to	PART
cana-735	87	13	highlight	highlight	VERB
cana-735	87	14	the	the	DET
cana-735	87	15	methodological	methodological	ADJ
cana-735	87	16	component	component	NOUN
cana-735	87	17	.	.	PUNCT
cana-735	88	1	we	we	PRON
cana-735	88	2	will	will	AUX
cana-735	88	3	briefly	briefly	ADV
cana-735	88	4	cover	cover	VERB
cana-735	88	5	the	the	DET
cana-735	88	6	α	α	NOUN
cana-735	88	7	-	-	NOUN
cana-735	88	8	cut	cut	NOUN
cana-735	88	9	of	of	ADP
cana-735	88	10	trfn	trfn	NOUN
cana-735	88	11	.	.	PUNCT
cana-735	89	1	2.2	2.2	NUM
cana-735	89	2	the	the	DET
cana-735	89	3	α	α	NOUN
cana-735	89	4	-	-	PUNCT
cana-735	89	5	cut	cut	NOUN
cana-735	89	6	of	of	ADP
cana-735	89	7	fn	fn	NOUN
cana-735	89	8	each	each	DET
cana-735	89	9	fn	fn	NOUN
cana-735	89	10	connected	connect	VERB
cana-735	89	11	with	with	ADP
cana-735	89	12	fuzzy	fuzzy	ADJ
cana-735	89	13	set	set	NOUN
cana-735	89	14	that	that	PRON
cana-735	89	15	have	have	VERB
cana-735	89	16	membership	membership	NOUN
cana-735	89	17	values	value	NOUN
cana-735	89	18	,	,	PUNCT
cana-735	89	19	this	this	PRON
cana-735	89	20	is	be	AUX
cana-735	89	21	a	a	DET
cana-735	89	22	fuzzy	fuzzy	ADJ
cana-735	89	23	integer	integer	NOUN
cana-735	89	24	represented	represent	VERB
cana-735	89	25	by	by	ADP
cana-735	89	26	a	a	DET
cana-735	89	27	clear	clear	ADJ
cana-735	89	28	set	set	NOUN
cana-735	89	29	.	.	PUNCT
cana-735	90	1	by	by	ADP
cana-735	90	2	applying	apply	VERB
cana-735	90	3	this	this	DET
cana-735	90	4	idea	idea	NOUN
cana-735	90	5	,	,	PUNCT
cana-735	90	6	it	it	PRON
cana-735	90	7	is	be	AUX
cana-735	90	8	possible	possible	ADJ
cana-735	90	9	to	to	PART
cana-735	90	10	show	show	VERB
cana-735	90	11	that	that	SCONJ
cana-735	90	12	the	the	DET
cana-735	90	13	trfn	trfn	NOUN
cana-735	90	14	α	α	NOUN
cana-735	90	15	-	-	NOUN
cana-735	90	16	cut	cut	VERB
cana-735	90	17	(	(	PUNCT
cana-735	90	18	1	1	NUM
cana-735	90	19	)	)	PUNCT
cana-735	90	20	is	be	AUX
cana-735	90	21	provided	provide	VERB
cana-735	90	22	by	by	ADP
cana-735	90	23	𝒜α	𝒜α	PROPN
cana-735	90	24	=[	=[	PROPN
cana-735	90	25	𝒶1	𝒶1	PROPN
cana-735	90	26	α	α	NOUN
cana-735	90	27	,	,	PUNCT
cana-735	90	28	𝒶2	𝒶2	NOUN
cana-735	90	29	α	α	NOUN
cana-735	90	30	]	]	X
cana-735	90	31	=	=	PUNCT
cana-735	91	1	[	[	X
cana-735	91	2	(	(	PUNCT
cana-735	91	3	b	b	NOUN
cana-735	91	4	a	a	NOUN
cana-735	91	5	)	)	PUNCT
cana-735	91	6	α	α	NOUN
cana-735	91	7	+	+	X
cana-735	91	8	a	a	X
cana-735	91	9	,	,	PUNCT
cana-735	91	10	(	(	PUNCT
cana-735	91	11	b	b	NOUN
cana-735	91	12	c	c	NOUN
cana-735	91	13	)	)	PUNCT
cana-735	91	14	α	α	NOUN
cana-735	92	1	+	+	X
cana-735	92	2	c	c	X
cana-735	92	3	]	]	X
cana-735	92	4	,	,	PUNCT
cana-735	92	5	for	for	ADP
cana-735	92	6	all	all	DET
cana-735	92	7	α	α	PRON
cana-735	92	8	∈	∈	PROPN
cana-735	92	9	[	[	X
cana-735	92	10	0,1	0,1	NUM
cana-735	92	11	]	]	PUNCT
cana-735	92	12	(	(	PUNCT
cana-735	92	13	4	4	X
cana-735	92	14	)	)	PUNCT
cana-735	92	15	gmdf	gmdf	NOUN
cana-735	92	16	(	(	PUNCT
cana-735	92	17	generalised	generalise	VERB
cana-735	92	18	mean	mean	NOUN
cana-735	92	19	value	value	NOUN
cana-735	92	20	de	de	NOUN
cana-735	92	21	-	-	NOUN
cana-735	92	22	fuzzification	fuzzification	NOUN
cana-735	92	23	)	)	PUNCT
cana-735	92	24	information	information	NOUN
cana-735	92	25	regarding	regard	VERB
cana-735	92	26	suitable	suitable	ADJ
cana-735	92	27	way	way	NOUN
cana-735	92	28	to	to	PART
cana-735	92	29	represent	represent	VERB
cana-735	92	30	a	a	DET
cana-735	92	31	crisp	crisp	ADJ
cana-735	92	32	number	number	NOUN
cana-735	92	33	as	as	SCONJ
cana-735	92	34	fn	fn	NOUN
cana-735	92	35	is	be	AUX
cana-735	92	36	desired	desire	VERB
cana-735	92	37	for	for	ADP
cana-735	92	38	a	a	DET
cana-735	92	39	variety	variety	NOUN
cana-735	92	40	of	of	ADP
cana-735	92	41	reasons	reason	NOUN
cana-735	92	42	.	.	PUNCT
cana-735	93	1	the	the	DET
cana-735	93	2	fuzzy	fuzzy	ADJ
cana-735	93	3	number	number	NOUN
cana-735	93	4	is	be	AUX
cana-735	93	5	de	de	ADJ
cana-735	93	6	-	-	ADJ
cana-735	93	7	fuzzified	fuzzified	ADJ
cana-735	93	8	in	in	ADP
cana-735	93	9	this	this	DET
cana-735	93	10	situation	situation	NOUN
cana-735	93	11	.	.	PUNCT
cana-735	94	1	regarding	regard	VERB
cana-735	94	2	a	a	DET
cana-735	94	3	fuzzy	fuzzy	ADJ
cana-735	94	4	set	set	NOUN
cana-735	94	5	,	,	PUNCT
cana-735	94	6	it	it	PRON
cana-735	94	7	is	be	AUX
cana-735	94	8	arithmetical	arithmetical	ADJ
cana-735	94	9	estimation	estimation	NOUN
cana-735	94	10	that	that	PRON
cana-735	94	11	translates	translate	VERB
cana-735	94	12	a	a	DET
cana-735	94	13	fn	fn	NOUN
cana-735	94	14	into	into	ADP
cana-735	94	15	a	a	DET
cana-735	94	16	single	single	ADJ
cana-735	94	17	crisp	crisp	ADJ
cana-735	94	18	value	value	NOUN
cana-735	94	19	.	.	PUNCT
cana-735	95	1	the	the	DET
cana-735	95	2	literature	literature	NOUN
cana-735	95	3	contains	contain	VERB
cana-735	95	4	a	a	DET
cana-735	95	5	few	few	ADJ
cana-735	95	6	dfuz	dfuz	NOUN
cana-735	95	7	,	,	PUNCT
cana-735	95	8	including	include	VERB
cana-735	95	9	weighted	weight	VERB
cana-735	95	10	fuzzy	fuzzy	ADJ
cana-735	95	11	mean	mean	NOUN
cana-735	95	12	,	,	PUNCT
cana-735	95	13	last	last	ADJ
cana-735	95	14	of	of	ADP
cana-735	95	15	maxima	maxima	NOUN
cana-735	95	16	,	,	PUNCT
cana-735	95	17	centre	centre	NOUN
cana-735	95	18	of	of	ADP
cana-735	95	19	gravity	gravity	NOUN
cana-735	95	20	and	and	CCONJ
cana-735	95	21	basic	basic	ADJ
cana-735	95	22	dfuz	dfuz	NOUN
cana-735	95	23	of	of	ADP
cana-735	95	24	distributions	distribution	NOUN
cana-735	95	25	[	[	X
cana-735	95	26	31	31	NUM
cana-735	95	27	-	-	SYM
cana-735	95	28	33	33	NUM
cana-735	95	29	]	]	PUNCT
cana-735	95	30	.	.	PUNCT
cana-735	96	1	the	the	DET
cana-735	96	2	gmdf	gmdf	PROPN
cana-735	96	3	technique	technique	NOUN
cana-735	96	4	in	in	ADP
cana-735	96	5	this	this	DET
cana-735	96	6	work	work	NOUN
cana-735	96	7	is	be	AUX
cana-735	96	8	described	describe	VERB
cana-735	96	9	as	as	ADP
cana-735	96	10	communications	communication	NOUN
cana-735	96	11	on	on	ADP
cana-735	96	12	applied	apply	VERB
cana-735	96	13	nonlinear	nonlinear	ADJ
cana-735	96	14	analysis	analysis	NOUN
cana-735	96	15	issn	issn	NOUN
cana-735	96	16	:	:	PUNCT
cana-735	96	17	1074	1074	NUM
cana-735	96	18	-	-	PUNCT
cana-735	96	19	133x	133x	NUM
cana-735	96	20	vol	vol	NOUN
cana-735	96	21	31	31	NUM
cana-735	96	22	no	no	NOUN
cana-735	96	23	.	.	PUNCT
cana-735	97	1	3s	3s	NUM
cana-735	97	2	(	(	PUNCT
cana-735	97	3	2024	2024	NUM
cana-735	97	4	)	)	PUNCT
cana-735	97	5	109	109	NUM
cana-735	97	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-735	97	7	μ(𝒜	μ(𝒜	NUM
cana-735	97	8	)	)	PUNCT
cana-735	97	9	=	=	PUNCT
cana-735	98	1	a+t	a+t	PUNCT
cana-735	98	2	b+c	b+c	PROPN
cana-735	98	3	t+2	t+2	X
cana-735	98	4	,	,	PUNCT
cana-735	98	5	where	where	SCONJ
cana-735	98	6	𝒜	𝒜	NOUN
cana-735	98	7	=	=	SYM
cana-735	98	8	(	(	PUNCT
cana-735	98	9	a	a	PRON
cana-735	98	10	;	;	PUNCT
cana-735	98	11	b	b	NOUN
cana-735	98	12	;	;	PUNCT
cana-735	98	13	c	c	X
cana-735	98	14	)	)	PUNCT
cana-735	98	15	is	be	AUX
cana-735	98	16	a	a	DET
cana-735	98	17	trfn	trfn	NOUN
cana-735	98	18	and	and	CCONJ
cana-735	98	19	t	t	PROPN
cana-735	98	20	be	be	AUX
cana-735	98	21	the	the	DET
cana-735	98	22	weight	weight	NOUN
cana-735	98	23	of	of	ADP
cana-735	98	24	the	the	DET
cana-735	98	25	fn	fn	NOUN
cana-735	98	26	(	(	PUNCT
cana-735	98	27	5	5	NUM
cana-735	98	28	)	)	PUNCT
cana-735	98	29	features	feature	NOUN
cana-735	98	30	of	of	ADP
cana-735	98	31	gmdf	gmdf	PROPN
cana-735	98	32	will	will	AUX
cana-735	98	33	be	be	AUX
cana-735	98	34	explored	explore	VERB
cana-735	98	35	future	future	ADJ
cana-735	98	36	and	and	CCONJ
cana-735	98	37	utilised	utilise	VERB
cana-735	98	38	to	to	PART
cana-735	98	39	compare	compare	VERB
cana-735	98	40	failures	failure	NOUN
cana-735	98	41	arise	arise	VERB
cana-735	98	42	.	.	PUNCT
cana-735	99	1	3	3	X
cana-735	99	2	.	.	X
cana-735	99	3	results	result	VERB
cana-735	99	4	3.1	3.1	NUM
cana-735	99	5	.	.	PUNCT
cana-735	100	1	dgmhf	dgmhf	NOUN
cana-735	100	2	(	(	PUNCT
cana-735	100	3	dgm	dgm	PROPN
cana-735	100	4	hazard	hazard	PROPN
cana-735	100	5	function	function	PROPN
cana-735	100	6	)	)	PUNCT
cana-735	100	7	failure	failure	NOUN
cana-735	100	8	numbers	number	NOUN
cana-735	100	9	with	with	ADP
cana-735	100	10	fuzzy	fuzzy	ADJ
cana-735	100	11	parameter	parameter	NOUN
cana-735	100	12	one	one	NUM
cana-735	100	13	parameter	parameter	NOUN
cana-735	100	14	dgm	dgm	PROPN
cana-735	100	15	distribution	distribution	NOUN
cana-735	100	16	function	function	NOUN
cana-735	100	17	as	as	SCONJ
cana-735	100	18	mentioned	mention	VERB
cana-735	100	19	in	in	ADP
cana-735	100	20	the	the	DET
cana-735	100	21	section	section	NOUN
cana-735	100	22	above	above	ADV
cana-735	100	23	is	be	AUX
cana-735	100	24	adequate	adequate	ADJ
cana-735	100	25	for	for	ADP
cana-735	100	26	our	our	PRON
cana-735	100	27	purposes	purpose	NOUN
cana-735	100	28	of	of	ADP
cana-735	100	29	maintenance	maintenance	NOUN
cana-735	100	30	modelling	modelling	NOUN
cana-735	100	31	if	if	SCONJ
cana-735	100	32	we	we	PRON
cana-735	100	33	assume	assume	VERB
cana-735	100	34	that	that	SCONJ
cana-735	100	35	because	because	SCONJ
cana-735	100	36	of	of	ADP
cana-735	100	37	the	the	DET
cana-735	100	38	system	system	NOUN
cana-735	100	39	under	under	ADP
cana-735	100	40	investigation	investigation	NOUN
cana-735	100	41	’s	’s	PART
cana-735	100	42	warranty	warranty	NOUN
cana-735	100	43	and	and	CCONJ
cana-735	100	44	good	good	ADJ
cana-735	100	45	quality	quality	NOUN
cana-735	100	46	control	control	NOUN
cana-735	100	47	,	,	PUNCT
cana-735	100	48	the	the	DET
cana-735	100	49	average	average	ADJ
cana-735	100	50	first	first	ADJ
cana-735	100	51	failure	failure	NOUN
cana-735	100	52	will	will	AUX
cana-735	100	53	happen	happen	VERB
cana-735	100	54	within	within	ADP
cana-735	100	55	a	a	DET
cana-735	100	56	given	give	VERB
cana-735	100	57	time	time	NOUN
cana-735	100	58	frame	frame	NOUN
cana-735	100	59	,	,	PUNCT
cana-735	100	60	such	such	ADJ
cana-735	100	61	as	as	ADP
cana-735	100	62	a	a	DET
cana-735	100	63	month	month	NOUN
cana-735	100	64	or	or	CCONJ
cana-735	100	65	a	a	DET
cana-735	100	66	year	year	NOUN
cana-735	100	67	.	.	PUNCT
cana-735	101	1	the	the	DET
cana-735	101	2	first	first	ADJ
cana-735	101	3	technique	technique	NOUN
cana-735	101	4	estimates	estimate	VERB
cana-735	101	5	the	the	DET
cana-735	101	6	number	number	NOUN
cana-735	101	7	of	of	ADP
cana-735	101	8	failures	failure	NOUN
cana-735	101	9	based	base	VERB
cana-735	101	10	on	on	ADP
cana-735	101	11	the	the	DET
cana-735	101	12	assumption	assumption	NOUN
cana-735	101	13	(	(	PUNCT
cana-735	101	14	δ	δ	NOUN
cana-735	101	15	=	=	SYM
cana-735	101	16	1	1	NUM
cana-735	101	17	)	)	PUNCT
cana-735	101	18	.	.	PUNCT
cana-735	102	1	to	to	PART
cana-735	102	2	calculate	calculate	VERB
cana-735	102	3	fn	fn	PROPN
cana-735	102	4	,	,	PUNCT
cana-735	102	5	point	point	VERB
cana-735	102	6	wise	wise	ADJ
cana-735	102	7	,	,	PUNCT
cana-735	102	8	we	we	PRON
cana-735	102	9	simply	simply	ADV
cana-735	102	10	need	need	VERB
cana-735	102	11	the	the	DET
cana-735	102	12	crisp	crisp	ADJ
cana-735	102	13	function	function	NOUN
cana-735	102	14	.	.	PUNCT
cana-735	103	1	the	the	DET
cana-735	103	2	probability	probability	NOUN
cana-735	103	3	density	density	NOUN
cana-735	103	4	function	function	NOUN
cana-735	103	5	f	f	PROPN
cana-735	103	6	and	and	CCONJ
cana-735	103	7	cdf	cdf	PROPN
cana-735	103	8	,	,	PUNCT
cana-735	103	9	f	f	PROPN
cana-735	103	10	using	use	VERB
cana-735	103	11	equation	equation	NOUN
cana-735	103	12	(	(	PUNCT
cana-735	103	13	1	1	NUM
cana-735	103	14	)	)	PUNCT
cana-735	103	15	and	and	CCONJ
cana-735	103	16	its	its	PRON
cana-735	103	17	hazard	hazard	NOUN
cana-735	103	18	function	function	NOUN
cana-735	103	19	h	h	NOUN
cana-735	103	20	derived	derive	VERB
cana-735	103	21	by	by	ADP
cana-735	103	22	f(x	f(x	PROPN
cana-735	103	23	)	)	PUNCT
cana-735	103	24	=	=	SYM
cana-735	103	25	δ	δ	PROPN
cana-735	103	26	(	(	PUNCT
cana-735	103	27	1+x−1)−1−δ	1+x−1)−1−δ	NUM
cana-735	103	28	x2	x2	PROPN
cana-735	103	29	f(x	f(x	PROPN
cana-735	103	30	)	)	PUNCT
cana-735	103	31	=	=	PUNCT
cana-735	104	1	(	(	PUNCT
cana-735	104	2	1	1	NUM
cana-735	104	3	+	+	NUM
cana-735	104	4	x−1)−δ	x−1)−δ	PROPN
cana-735	104	5	(	(	PUNCT
cana-735	104	6	6	6	NUM
cana-735	104	7	)	)	PUNCT
cana-735	104	8	and	and	CCONJ
cana-735	104	9	h(x	h(x	PROPN
cana-735	104	10	)	)	PUNCT
cana-735	105	1	=	=	SYM
cana-735	105	2	δ	δ	PROPN
cana-735	105	3	(	(	PUNCT
cana-735	105	4	1+x−1	1+x−1	NUM
cana-735	105	5	)	)	PUNCT
cana-735	105	6	−(1+δ	−(1+δ	PROPN
cana-735	105	7	)	)	PUNCT
cana-735	106	1	x2	x2	NOUN
cana-735	107	1	[	[	X
cana-735	107	2	1−(1+x−1)−δ	1−(1+x−1)−δ	NUM
cana-735	107	3	]	]	X
cana-735	107	4	(	(	PUNCT
cana-735	107	5	7	7	X
cana-735	107	6	)	)	PUNCT
cana-735	107	7	the	the	DET
cana-735	107	8	failure	failure	NOUN
cana-735	107	9	number	number	NOUN
cana-735	107	10	of	of	ADP
cana-735	107	11	dgm	dgm	PROPN
cana-735	107	12	is	be	AUX
cana-735	107	13	obtained	obtain	VERB
cana-735	107	14	by	by	ADP
cana-735	107	15	n(x	n(x	NOUN
cana-735	107	16	)	)	PUNCT
cana-735	107	17	=	=	VERB
cana-735	108	1	x2δ	x2δ	PROPN
cana-735	108	2	(	(	PUNCT
cana-735	108	3	8)	8)	NUM
cana-735	108	4	the	the	DET
cana-735	108	5	fuzzy	fuzzy	ADJ
cana-735	108	6	integer	integer	NOUN
cana-735	108	7	that	that	PRON
cana-735	108	8	corresponds	correspond	VERB
cana-735	108	9	δ	δ	PROPN
cana-735	108	10	the	the	DET
cana-735	108	11	shape	shape	NOUN
cana-735	108	12	parameter	parameter	NOUN
cana-735	108	13	of	of	ADP
cana-735	108	14	dgm	dgm	PROPN
cana-735	108	15	distribution	distribution	NOUN
cana-735	108	16	function	function	NOUN
cana-735	108	17	is	be	AUX
cana-735	108	18	called	call	VERB
cana-735	108	19	as	as	ADP
cana-735	108	20	the	the	DET
cana-735	108	21	fuzziness	fuzziness	NOUN
cana-735	108	22	of	of	ADP
cana-735	108	23	dgm	dgm	PROPN
cana-735	108	24	.	.	PUNCT
cana-735	109	1	two	two	NUM
cana-735	109	2	approaches	approach	NOUN
cana-735	109	3	will	will	AUX
cana-735	109	4	be	be	AUX
cana-735	109	5	used	use	VERB
cana-735	109	6	to	to	PART
cana-735	109	7	deal	deal	VERB
cana-735	109	8	with	with	ADP
cana-735	109	9	the	the	DET
cana-735	109	10	shape	shape	NOUN
cana-735	109	11	parameter	parameter	NOUN
cana-735	109	12	’s	’s	PART
cana-735	109	13	fuzziness	fuzziness	NOUN
cana-735	109	14	:	:	PUNCT
cana-735	109	15	(	(	PUNCT
cana-735	109	16	i	i	NOUN
cana-735	109	17	)	)	PUNCT
cana-735	109	18	a	a	DET
cana-735	109	19	crisp	crisp	ADJ
cana-735	109	20	function	function	NOUN
cana-735	109	21	that	that	PRON
cana-735	109	22	conducts	conduct	VERB
cana-735	109	23	the	the	DET
cana-735	109	24	computation	computation	NOUN
cana-735	109	25	pointwise	pointwise	VERB
cana-735	109	26	and	and	CCONJ
cana-735	109	27	generates	generate	VERB
cana-735	109	28	the	the	DET
cana-735	109	29	fuzziness	fuzziness	NOUN
cana-735	109	30	of	of	ADP
cana-735	109	31	the	the	DET
cana-735	109	32	independent	independent	ADJ
cana-735	109	33	and	and	CCONJ
cana-735	109	34	dependent	dependent	ADJ
cana-735	109	35	variable	variable	NOUN
cana-735	109	36	correspondingly	correspondingly	ADV
cana-735	109	37	.	.	PUNCT
cana-735	110	1	(	(	PUNCT
cana-735	110	2	ii	ii	NOUN
cana-735	110	3	)	)	PUNCT
cana-735	110	4	a	a	DET
cana-735	110	5	crisp	crisp	ADJ
cana-735	110	6	function	function	NOUN
cana-735	110	7	with	with	ADP
cana-735	110	8	fuzzy	fuzzy	ADJ
cana-735	110	9	limitations	limitation	NOUN
cana-735	110	10	by	by	ADP
cana-735	110	11	computing	compute	VERB
cana-735	110	12	using	use	VERB
cana-735	110	13	level	level	NOUN
cana-735	110	14	set	set	NOUN
cana-735	110	15	.	.	PUNCT
cana-735	111	1	3.2	3.2	NUM
cana-735	111	2	method	method	NOUN
cana-735	111	3	one	one	NUM
cana-735	111	4	(	(	PUNCT
cana-735	111	5	point	point	NOUN
cana-735	111	6	-	-	PUNCT
cana-735	111	7	by	by	ADP
cana-735	111	8	-	-	PUNCT
cana-735	111	9	point	point	NOUN
cana-735	111	10	):	):	PUNCT
cana-735	111	11	assume	assume	VERB
cana-735	111	12	that	that	SCONJ
cana-735	111	13	there	there	PRON
cana-735	111	14	is	be	VERB
cana-735	111	15	a	a	DET
cana-735	111	16	trfn	trfn	NOUN
cana-735	111	17	α	α	NOUN
cana-735	111	18	;	;	PUNCT
cana-735	111	19	β	β	X
cana-735	111	20	;	;	PUNCT
cana-735	111	21	and	and	CCONJ
cana-735	111	22	γ	γ	NOUN
cana-735	111	23	which	which	PRON
cana-735	111	24	can	can	AUX
cana-735	111	25	be	be	AUX
cana-735	111	26	identified	identify	VERB
cana-735	111	27	by	by	ADP
cana-735	111	28	three	three	NUM
cana-735	111	29	unique	unique	ADJ
cana-735	111	30	numbers	number	NOUN
cana-735	111	31	.	.	PUNCT
cana-735	112	1	equation	equation	NOUN
cana-735	112	2	(	(	PUNCT
cana-735	112	3	2	2	X
cana-735	112	4	)	)	PUNCT
cana-735	112	5	is	be	AUX
cana-735	112	6	satisfied	satisfied	ADJ
cana-735	112	7	by	by	ADP
cana-735	112	8	𝛿	𝛿	ADJ
cana-735	112	9	=	=	SYM
cana-735	112	10	(	(	PUNCT
cana-735	112	11	α	α	NOUN
cana-735	112	12	;	;	PUNCT
cana-735	112	13	β	β	X
cana-735	112	14	;	;	PUNCT
cana-735	112	15	γ	γ	X
cana-735	112	16	)	)	PUNCT
cana-735	112	17	.	.	PUNCT
cana-735	113	1	estimate	estimate	VERB
cana-735	113	2	the	the	DET
cana-735	113	3	failure	failure	NOUN
cana-735	113	4	numbers	number	NOUN
cana-735	113	5	,	,	PUNCT
cana-735	113	6	point	point	NOUN
cana-735	113	7	by	by	ADP
cana-735	113	8	point	point	NOUN
cana-735	113	9	to	to	PART
cana-735	113	10	get	get	VERB
cana-735	113	11	the	the	DET
cana-735	113	12	crisp	crisp	ADJ
cana-735	113	13	integers	integer	NOUN
cana-735	113	14	one	one	NUM
cana-735	113	15	at	at	ADP
cana-735	113	16	a	a	DET
cana-735	113	17	time	time	NOUN
cana-735	113	18	to	to	PART
cana-735	113	19	.	.	PUNCT
cana-735	114	1	we	we	PRON
cana-735	114	2	get	get	VERB
cana-735	114	3	μ	μ	NOUN
cana-735	114	4	(	(	PUNCT
cana-735	114	5	α	α	NOUN
cana-735	114	6	)	)	PUNCT
cana-735	114	7	=	=	SYM
cana-735	114	8	μ	μ	PROPN
cana-735	114	9	(	(	PUNCT
cana-735	114	10	α	α	NOUN
cana-735	114	11	'	'	NOUN
cana-735	114	12	)	)	PUNCT
cana-735	114	13	,	,	PUNCT
cana-735	114	14	μ	μ	PROPN
cana-735	114	15	(	(	PUNCT
cana-735	114	16	β	β	X
cana-735	114	17	)	)	PUNCT
cana-735	114	18	=	=	SYM
cana-735	114	19	μ	μ	PROPN
cana-735	114	20	(	(	PUNCT
cana-735	114	21	β	β	NOUN
cana-735	114	22	'	'	NUM
cana-735	114	23	)	)	PUNCT
cana-735	114	24	,	,	PUNCT
cana-735	114	25	and	and	CCONJ
cana-735	114	26	μ	μ	PROPN
cana-735	114	27	(	(	PUNCT
cana-735	114	28	γ	γ	NOUN
cana-735	114	29	)	)	PUNCT
cana-735	114	30	=	=	SYM
cana-735	114	31	μ	μ	PROPN
cana-735	114	32	(	(	PUNCT
cana-735	114	33	γ	γ	X
cana-735	114	34	'	'	PUNCT
cana-735	114	35	)	)	PUNCT
cana-735	114	36	giving	give	VERB
cana-735	114	37	a	a	DET
cana-735	114	38	trfn	trfn	NOUN
cana-735	114	39	(	(	PUNCT
cana-735	114	40	α	α	NOUN
cana-735	114	41	'	'	PUNCT
cana-735	114	42	;	;	PUNCT
cana-735	114	43	β	β	X
cana-735	114	44	'	'	NUM
cana-735	114	45	;	;	PUNCT
cana-735	114	46	γ	γ	X
cana-735	114	47	'	'	PUNCT
cana-735	114	48	)	)	PUNCT
cana-735	114	49	for	for	ADP
cana-735	114	50	functions	function	NOUN
cana-735	114	51	g(x	g(x	NOUN
cana-735	114	52	)	)	PUNCT
cana-735	114	53	,	,	PUNCT
cana-735	114	54	h(x	h(x	PROPN
cana-735	114	55	)	)	PUNCT
cana-735	114	56	,	,	PUNCT
cana-735	114	57	and	and	CCONJ
cana-735	114	58	n(x	n(x	NOUN
cana-735	114	59	)	)	PUNCT
cana-735	115	1	[	[	X
cana-735	115	2	17	17	NUM
cana-735	115	3	]	]	PUNCT
cana-735	115	4	respectively	respectively	ADV
cana-735	115	5	.	.	PUNCT
cana-735	116	1	3.3	3.3	NUM
cana-735	116	2	second	second	ADJ
cana-735	116	3	method	method	NOUN
cana-735	116	4	(	(	PUNCT
cana-735	116	5	𝛂cut	𝛂cut	ADJ
cana-735	116	6	method	method	NOUN
cana-735	116	7	):	):	PUNCT
cana-735	116	8	fn	fn	PROPN
cana-735	116	9	δ	δ	PROPN
cana-735	116	10	is	be	AUX
cana-735	116	11	recognized	recognize	VERB
cana-735	116	12	as	as	ADP
cana-735	116	13	α	α	NOUN
cana-735	116	14	-	-	PUNCT
cana-735	116	15	cut	cut	VERB
cana-735	116	16	meeting	meeting	NOUN
cana-735	116	17	equation	equation	NOUN
cana-735	116	18	(	(	PUNCT
cana-735	116	19	4	4	NUM
cana-735	116	20	)	)	PUNCT
cana-735	116	21	in	in	ADP
cana-735	116	22	the	the	DET
cana-735	116	23	second	second	ADJ
cana-735	116	24	method	method	NOUN
cana-735	116	25	.	.	PUNCT
cana-735	117	1	a	a	DET
cana-735	117	2	series	series	NOUN
cana-735	117	3	of	of	ADP
cana-735	117	4	intervals	interval	NOUN
cana-735	117	5	connected	connect	VERB
cana-735	117	6	to	to	ADP
cana-735	117	7	the	the	DET
cana-735	117	8	number	number	NOUN
cana-735	117	9	in	in	ADP
cana-735	117	10	[	[	X
cana-735	117	11	0,1	0,1	NUM
cana-735	117	12	]	]	PUNCT
cana-735	117	13	can	can	AUX
cana-735	117	14	be	be	AUX
cana-735	117	15	used	use	VERB
cana-735	117	16	parameter	parameter	NOUN
cana-735	117	17	[	[	X
cana-735	117	18	17	17	NUM
cana-735	117	19	]	]	PUNCT
cana-735	117	20	.	.	PUNCT
cana-735	118	1	at	at	ADP
cana-735	118	2	the	the	DET
cana-735	118	3	interval	interval	NOUN
cana-735	118	4	's	's	PART
cana-735	118	5	end	end	NOUN
cana-735	118	6	points	point	NOUN
cana-735	118	7	,	,	PUNCT
cana-735	118	8	the	the	DET
cana-735	118	9	failure	failure	NOUN
cana-735	118	10	’s	’s	PART
cana-735	118	11	number	number	NOUN
cana-735	118	12	is	be	AUX
cana-735	118	13	computed	compute	VERB
cana-735	118	14	.	.	PUNCT
cana-735	119	1	the	the	DET
cana-735	119	2	stack	stack	NOUN
cana-735	119	3	of	of	ADP
cana-735	119	4	the	the	DET
cana-735	119	5	end	end	NOUN
cana-735	119	6	points	point	VERB
cana-735	119	7	the	the	DET
cana-735	119	8	intervals	interval	NOUN
cana-735	119	9	does	do	AUX
cana-735	119	10	n’t	not	PART
cana-735	119	11	have	have	VERB
cana-735	119	12	trfn	trfn	NOUN
cana-735	119	13	in	in	ADP
cana-735	119	14	this	this	DET
cana-735	119	15	case	case	NOUN
cana-735	119	16	,	,	PUNCT
cana-735	119	17	although	although	SCONJ
cana-735	119	18	it	it	PRON
cana-735	119	19	is	be	AUX
cana-735	119	20	frequently	frequently	ADV
cana-735	119	21	(	(	PUNCT
cana-735	119	22	see	see	VERB
cana-735	119	23	numerical	numerical	ADJ
cana-735	119	24	examples	example	NOUN
cana-735	119	25	for	for	ADP
cana-735	119	26	details	detail	NOUN
cana-735	119	27	)	)	PUNCT
cana-735	119	28	.	.	PUNCT
cana-735	120	1	we	we	PRON
cana-735	120	2	utilise	utilise	VERB
cana-735	120	3	the	the	DET
cana-735	120	4	gmdf	gmdf	NOUN
cana-735	120	5	specified	specify	VERB
cana-735	120	6	in	in	ADP
cana-735	120	7	equation	equation	NOUN
cana-735	120	8	(	(	PUNCT
cana-735	120	9	5	5	NUM
cana-735	120	10	)	)	PUNCT
cana-735	120	11	to	to	PART
cana-735	120	12	make	make	VERB
cana-735	120	13	it	it	PRON
cana-735	120	14	easier	easy	ADJ
cana-735	120	15	to	to	PART
cana-735	120	16	compare	compare	VERB
cana-735	120	17	the	the	DET
cana-735	120	18	outcomes	outcome	NOUN
cana-735	120	19	of	of	ADP
cana-735	120	20	two	two	NUM
cana-735	120	21	techniques	technique	NOUN
cana-735	120	22	.	.	PUNCT
cana-735	121	1	if	if	SCONJ
cana-735	121	2	(	(	PUNCT
cana-735	121	3	α	α	NOUN
cana-735	121	4	;	;	PUNCT
cana-735	121	5	β	β	X
cana-735	121	6	;	;	PUNCT
cana-735	121	7	γ	γ	X
cana-735	121	8	)	)	PUNCT
cana-735	121	9	is	be	AUX
cana-735	121	10	a	a	DET
cana-735	121	11	trfn	trfn	NOUN
cana-735	121	12	,	,	PUNCT
cana-735	121	13	gmdf	gmdf	PROPN
cana-735	121	14	specified	specify	VERB
cana-735	121	15	by	by	ADP
cana-735	121	16	equation	equation	NOUN
cana-735	121	17	(	(	PUNCT
cana-735	121	18	5	5	X
cana-735	121	19	)	)	PUNCT
cana-735	121	20	hold	hold	VERB
cana-735	121	21	the	the	DET
cana-735	121	22	following	follow	VERB
cana-735	121	23	features	feature	NOUN
cana-735	121	24	.	.	PUNCT
cana-735	122	1	communications	communication	NOUN
cana-735	122	2	on	on	ADP
cana-735	122	3	applied	apply	VERB
cana-735	122	4	nonlinear	nonlinear	ADJ
cana-735	122	5	analysis	analysis	NOUN
cana-735	122	6	issn	issn	NOUN
cana-735	122	7	:	:	PUNCT
cana-735	122	8	1074	1074	NUM
cana-735	122	9	-	-	PUNCT
cana-735	122	10	133x	133x	NUM
cana-735	122	11	vol	vol	NOUN
cana-735	122	12	31	31	NUM
cana-735	122	13	no	no	NOUN
cana-735	122	14	.	.	PUNCT
cana-735	123	1	3s	3s	NUM
cana-735	123	2	(	(	PUNCT
cana-735	123	3	2024	2024	NUM
cana-735	123	4	)	)	PUNCT
cana-735	123	5	110	110	NUM
cana-735	123	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-735	123	7	theorem1	theorem1	X
cana-735	123	8	.	.	PUNCT
cana-735	124	1	let	let	VERB
cana-735	124	2	a	a	DET
cana-735	124	3	trfn	trfn	NOUN
cana-735	124	4	is	be	AUX
cana-735	124	5	given	give	VERB
cana-735	124	6	by	by	ADP
cana-735	124	7	(	(	PUNCT
cana-735	124	8	α	α	NOUN
cana-735	124	9	;	;	PUNCT
cana-735	124	10	β	β	X
cana-735	124	11	;	;	PUNCT
cana-735	124	12	γ	γ	X
cana-735	124	13	)	)	PUNCT
cana-735	124	14	,	,	PUNCT
cana-735	124	15	then	then	ADV
cana-735	124	16	the	the	DET
cana-735	124	17	gmdf	gmdf	NOUN
cana-735	124	18	obtained	obtain	VERB
cana-735	124	19	by	by	ADP
cana-735	124	20	(	(	PUNCT
cana-735	124	21	5	5	NUM
cana-735	124	22	)	)	PUNCT
cana-735	124	23	holds	hold	VERB
cana-735	124	24	given	give	VERB
cana-735	124	25	:	:	PUNCT
cana-735	124	26	1	1	X
cana-735	124	27	.	.	X
cana-735	125	1	in	in	ADP
cana-735	125	2	a	a	DET
cana-735	125	3	symmetrical	symmetrical	ADJ
cana-735	125	4	case	case	NOUN
cana-735	125	5	,	,	PUNCT
cana-735	125	6	β	β	X
cana-735	125	7	−	−	NOUN
cana-735	125	8	α	α	NOUN
cana-735	125	9	=	=	SYM
cana-735	125	10	γ	γ	X
cana-735	125	11	−	−	NOUN
cana-735	125	12	λ	λ	PROPN
cana-735	125	13	=	=	SYM
cana-735	125	14	∆	∆	PROPN
cana-735	125	15	then	then	ADV
cana-735	125	16	μ(𝒜	μ(𝒜	NUM
cana-735	125	17	)	)	PUNCT
cana-735	126	1	=	=	PUNCT
cana-735	126	2	β	β	X
cana-735	126	3	2	2	NUM
cana-735	126	4	.	.	X
cana-735	127	1	for	for	ADP
cana-735	127	2	an	an	DET
cana-735	127	3	asymmetrical	asymmetrical	ADJ
cana-735	127	4	case	case	NOUN
cana-735	127	5	β	β	NOUN
cana-735	127	6	−	−	PROPN
cana-735	127	7	α	α	PROPN
cana-735	127	8	=	=	PUNCT
cana-735	127	9	∆α≠	∆α≠	PROPN
cana-735	127	10	γ	γ	NOUN
cana-735	127	11	−	−	PROPN
cana-735	127	12	λ	λ	PROPN
cana-735	127	13	=	=	SYM
cana-735	127	14	∆γ	∆γ	PROPN
cana-735	127	15	,	,	PUNCT
cana-735	127	16	a.	a.	NOUN
cana-735	127	17	if	if	SCONJ
cana-735	127	18	∆α	∆α	PROPN
cana-735	127	19	<	<	X
cana-735	127	20	∆γthen	∆γthen	ADJ
cana-735	127	21	μ(𝒜	μ(𝒜	NUM
cana-735	127	22	)	)	PUNCT
cana-735	127	23	>	>	X
cana-735	127	24	β	β	PROPN
cana-735	127	25	b.	b.	PROPN
cana-735	128	1	if	if	SCONJ
cana-735	128	2	∆α	∆α	PROPN
cana-735	128	3	>	>	X
cana-735	128	4	∆γ	∆γ	PROPN
cana-735	128	5	then	then	ADV
cana-735	128	6	μ(𝒜	μ(𝒜	NUM
cana-735	128	7	)	)	PUNCT
cana-735	128	8	<	<	X
cana-735	128	9	β	β	X
cana-735	128	10	3	3	X
cana-735	128	11	.	.	PUNCT
cana-735	129	1	if	if	SCONJ
cana-735	129	2	μ(𝒜	μ(𝒜	NUM
cana-735	129	3	)	)	PUNCT
cana-735	130	1	=	=	SYM
cana-735	130	2	β	β	NOUN
cana-735	130	3	,	,	PUNCT
cana-735	130	4	where	where	SCONJ
cana-735	130	5	k→	k→	ADJ
cana-735	130	6	∞	∞	PROPN
cana-735	130	7	however	however	ADV
cana-735	130	8	,	,	PUNCT
cana-735	130	9	value	value	NOUN
cana-735	130	10	α	α	NOUN
cana-735	130	11	and	and	CCONJ
cana-735	130	12	β	β	X
cana-735	130	13	proof	proof	NOUN
cana-735	130	14	:	:	PUNCT
cana-735	130	15	symmetrical	symmetrical	ADJ
cana-735	130	16	case	case	NOUN
cana-735	130	17	:	:	PUNCT
cana-735	130	18	β	β	X
cana-735	130	19	−	−	NOUN
cana-735	130	20	α	α	NOUN
cana-735	130	21	=	=	SYM
cana-735	130	22	γ	γ	X
cana-735	130	23	−	−	NOUN
cana-735	130	24	λ	λ	PROPN
cana-735	130	25	=	=	SYM
cana-735	130	26	∆	∆	PROPN
cana-735	130	27	then	then	ADV
cana-735	130	28	μ(𝒜	μ(𝒜	NUM
cana-735	130	29	)	)	PUNCT
cana-735	131	1	=	=	SYM
cana-735	131	2	α+kβ+α+2δ	α+kβ+α+2δ	NOUN
cana-735	131	3	k+2	k+2	PROPN
cana-735	131	4	=	=	SYM
cana-735	131	5	2α+kβ+2δ	2α+kβ+2δ	NUM
cana-735	131	6	k+2	k+2	NUM
cana-735	131	7	=	=	SYM
cana-735	131	8	2(α+δ)+kβ	2(α+δ)+kβ	NUM
cana-735	131	9	k+2	k+2	NOUN
cana-735	131	10	=	=	SYM
cana-735	131	11	2(β)+kβ	2(β)+kβ	NUM
cana-735	131	12	k+2	k+2	NOUN
cana-735	131	13	=	=	SYM
cana-735	131	14	(	(	PUNCT
cana-735	131	15	2+k)β	2+k)β	NUM
cana-735	131	16	k+2	k+2	PROPN
cana-735	131	17	=	=	SYM
cana-735	131	18	β	β	X
cana-735	131	19	hence	hence	ADV
cana-735	131	20	μ(𝒜	μ(𝒜	NUM
cana-735	131	21	)	)	PUNCT
cana-735	132	1	=	=	PUNCT
cana-735	132	2	β	β	X
cana-735	132	3	1	1	NUM
cana-735	132	4	.	.	PUNCT
cana-735	132	5	asymmetrical	asymmetrical	ADJ
cana-735	132	6	case	case	NOUN
cana-735	132	7	:	:	PUNCT
cana-735	132	8	β	β	X
cana-735	132	9	−	−	NOUN
cana-735	132	10	α	α	X
cana-735	132	11	=	=	PUNCT
cana-735	132	12	∆αis	∆αi	NOUN
cana-735	132	13	not	not	PART
cana-735	132	14	equal	equal	ADJ
cana-735	132	15	to	to	ADP
cana-735	132	16	γ	γ	PROPN
cana-735	132	17	−	−	PROPN
cana-735	132	18	λ	λ	NOUN
cana-735	132	19	=	=	SYM
cana-735	132	20	∆γ	∆γ	PROPN
cana-735	132	21	then	then	ADV
cana-735	132	22	a.	a.	NOUN
cana-735	132	23	μ(𝒜	μ(𝒜	NUM
cana-735	132	24	)	)	PUNCT
cana-735	132	25	>	>	X
cana-735	133	1	β	β	X
cana-735	133	2	if	if	SCONJ
cana-735	133	3	∆α	∆α	PROPN
cana-735	133	4	<	<	X
cana-735	133	5	∆γ	∆γ	NOUN
cana-735	133	6	μ(𝒜	μ(𝒜	PUNCT
cana-735	133	7	)	)	PUNCT
cana-735	134	1	=	=	SYM
cana-735	134	2	α+kβ+α+∆α+∆r	α+kβ+α+∆α+∆r	NOUN
cana-735	135	1	k+2	k+2	NUM
cana-735	135	2	>	>	PUNCT
cana-735	135	3	α+kβ+(α+2∆α	α+kβ+(α+2∆α	PROPN
cana-735	135	4	)	)	PUNCT
cana-735	135	5	k+2	k+2	PROPN
cana-735	135	6	=	=	NOUN
cana-735	135	7	2(α	2(α	NUM
cana-735	135	8	)	)	PUNCT
cana-735	136	1	+	+	CCONJ
cana-735	136	2	kβ	kβ	PRON
cana-735	136	3	+	+	NOUN
cana-735	136	4	2∆α	2∆α	NUM
cana-735	136	5	k	k	NOUN
cana-735	137	1	+	+	CCONJ
cana-735	137	2	2	2	NUM
cana-735	137	3	hence	hence	ADV
cana-735	137	4	μ(𝒜	μ(𝒜	NUM
cana-735	137	5	)	)	PUNCT
cana-735	137	6	>	>	PUNCT
cana-735	138	1	β	β	X
cana-735	138	2	b.	b.	PROPN
cana-735	138	3	μ(𝒜	μ(𝒜	NUM
cana-735	138	4	)	)	PUNCT
cana-735	139	1	<	<	X
cana-735	139	2	β	β	X
cana-735	139	3	if	if	SCONJ
cana-735	139	4	∆α	∆α	PROPN
cana-735	139	5	>	>	X
cana-735	139	6	∆r	∆r	NOUN
cana-735	139	7	μ(𝒜	μ(𝒜	NUM
cana-735	139	8	)	)	PUNCT
cana-735	139	9	=	=	SYM
cana-735	139	10	α+kβ+α+∆α+∆r	α+kβ+α+∆α+∆r	NOUN
cana-735	139	11	k+2	k+2	NUM
cana-735	139	12	<	<	X
cana-735	139	13	α+kβ+(α+2∆α	α+kβ+(α+2∆α	PROPN
cana-735	139	14	)	)	PUNCT
cana-735	139	15	k+2	k+2	PROPN
cana-735	139	16	=	=	NOUN
cana-735	139	17	2(α	2(α	NUM
cana-735	139	18	)	)	PUNCT
cana-735	139	19	+	+	CCONJ
cana-735	139	20	kβ	kβ	PRON
cana-735	139	21	+	+	NOUN
cana-735	139	22	2∆α	2∆α	NUM
cana-735	139	23	k	k	NOUN
cana-735	140	1	+	+	CCONJ
cana-735	140	2	2	2	NUM
cana-735	140	3	hence	hence	ADV
cana-735	140	4	μ(𝒜	μ(𝒜	NUM
cana-735	140	5	)	)	PUNCT
cana-735	140	6	<	<	X
cana-735	140	7	β	β	X
cana-735	140	8	.	.	NOUN
cana-735	141	1	2	2	X
cana-735	141	2	.	.	X
cana-735	142	1	if	if	SCONJ
cana-735	142	2	k	k	PROPN
cana-735	142	3	tends	tend	VERB
cana-735	142	4	to	to	ADP
cana-735	142	5	∞	∞	PROPN
cana-735	142	6	then	then	ADV
cana-735	142	7	lim	lim	PROPN
cana-735	142	8	k→∞	k→∞	NOUN
cana-735	142	9	μ(𝒜	μ(𝒜	NUM
cana-735	142	10	)	)	PUNCT
cana-735	143	1	=	=	SYM
cana-735	143	2	lim	lim	PROPN
cana-735	143	3	k→∞	k→∞	PROPN
cana-735	143	4	μ	μ	PROPN
cana-735	143	5	(	(	PUNCT
cana-735	143	6	kβ+α+γ	kβ+α+γ	PROPN
cana-735	143	7	k+2	k+2	PROPN
cana-735	143	8	)	)	PUNCT
cana-735	143	9	=	=	NOUN
cana-735	143	10	β	β	NOUN
cana-735	143	11	figure	figure	NOUN
cana-735	143	12	2	2	NUM
cana-735	143	13	.	.	PUNCT
cana-735	143	14	fuzzy	fuzzy	ADJ
cana-735	143	15	membership	membership	NOUN
cana-735	143	16	for	for	ADP
cana-735	143	17	triangular	triangular	NOUN
cana-735	143	18	function	function	NOUN
cana-735	143	19	with	with	ADP
cana-735	143	20	dgm	dgm	PROPN
cana-735	143	21	shape	shape	PROPN
cana-735	143	22	parameter	parameter	NOUN
cana-735	143	23	communications	communication	NOUN
cana-735	143	24	on	on	ADP
cana-735	143	25	applied	apply	VERB
cana-735	143	26	nonlinear	nonlinear	ADJ
cana-735	143	27	analysis	analysis	NOUN
cana-735	143	28	issn	issn	NOUN
cana-735	143	29	:	:	PUNCT
cana-735	143	30	1074	1074	NUM
cana-735	143	31	-	-	PUNCT
cana-735	143	32	133x	133x	NUM
cana-735	143	33	vol	vol	NOUN
cana-735	143	34	31	31	NUM
cana-735	143	35	no	no	NOUN
cana-735	143	36	.	.	PUNCT
cana-735	144	1	3s	3s	NUM
cana-735	144	2	(	(	PUNCT
cana-735	144	3	2024	2024	NUM
cana-735	144	4	)	)	PUNCT
cana-735	144	5	111	111	NUM
cana-735	144	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-735	144	7	figure	figure	NOUN
cana-735	144	8	3	3	NUM
cana-735	144	9	.	.	PUNCT
cana-735	144	10	fuzzy	fuzzy	ADJ
cana-735	144	11	membership	membership	NOUN
cana-735	144	12	for	for	ADP
cana-735	144	13	trapezoidal	trapezoidal	ADJ
cana-735	144	14	function	function	NOUN
cana-735	144	15	with	with	ADP
cana-735	144	16	dgm	dgm	PROPN
cana-735	144	17	shape	shape	NOUN
cana-735	144	18	parameter	parameter	NOUN
cana-735	144	19	as	as	SCONJ
cana-735	144	20	demonstrated	demonstrate	VERB
cana-735	144	21	by	by	ADP
cana-735	144	22	the	the	DET
cana-735	144	23	theorem	theorem	NOUN
cana-735	144	24	,	,	PUNCT
cana-735	144	25	the	the	DET
cana-735	144	26	gmdf	gmdf	NOUN
cana-735	144	27	has	have	VERB
cana-735	144	28	a	a	DET
cana-735	144	29	unique	unique	ADJ
cana-735	144	30	property	property	NOUN
cana-735	144	31	in	in	SCONJ
cana-735	144	32	that	that	SCONJ
cana-735	144	33	it	it	PRON
cana-735	144	34	can	can	AUX
cana-735	144	35	discover	discover	VERB
cana-735	144	36	a	a	DET
cana-735	144	37	crisp	crisp	ADJ
cana-735	144	38	number	number	NOUN
cana-735	144	39	that	that	PRON
cana-735	144	40	is	be	AUX
cana-735	144	41	near	near	ADJ
cana-735	144	42	to	to	ADP
cana-735	144	43	the	the	DET
cana-735	144	44	group	group	NOUN
cana-735	144	45	of	of	ADP
cana-735	144	46	a	a	DET
cana-735	144	47	trfn	trfn	NOUN
cana-735	144	48	.	.	PUNCT
cana-735	145	1	a	a	DET
cana-735	145	2	symmetric	symmetric	ADJ
cana-735	145	3	trfn	trfn	NOUN
cana-735	145	4	is	be	AUX
cana-735	145	5	denoted	denote	VERB
cana-735	145	6	by	by	ADP
cana-735	145	7	the	the	DET
cana-735	145	8	equation	equation	NOUN
cana-735	145	9	δ̅	δ̅	VERB
cana-735	145	10	=	=	PUNCT
cana-735	145	11	(	(	PUNCT
cana-735	145	12	α	α	X
cana-735	145	13	=	=	SYM
cana-735	145	14	1.35	1.35	NUM
cana-735	145	15	;	;	PUNCT
cana-735	145	16	β	β	X
cana-735	145	17	=	=	SYM
cana-735	145	18	1.55	1.55	NUM
cana-735	145	19	;	;	PUNCT
cana-735	145	20	γ	γ	X
cana-735	145	21	=	=	PROPN
cana-735	145	22	1.75	1.75	NUM
cana-735	145	23	)	)	PUNCT
cana-735	145	24	.	.	PUNCT
cana-735	146	1	if	if	SCONJ
cana-735	146	2	k=1	k=1	PROPN
cana-735	146	3	then	then	ADV
cana-735	146	4	gmdf	gmdf	VERB
cana-735	146	5	=	=	NOUN
cana-735	146	6	1.55	1.55	NUM
cana-735	146	7	;	;	PUNCT
cana-735	146	8	if	if	SCONJ
cana-735	146	9	k	k	PROPN
cana-735	146	10	=	=	NOUN
cana-735	146	11	1000	1000	NUM
cana-735	146	12	then	then	ADV
cana-735	146	13	gmdf	gmdf	VERB
cana-735	146	14	=	=	NOUN
cana-735	146	15	1.55	1.55	NUM
cana-735	146	16	.	.	PUNCT
cana-735	147	1	gmdf	gmdf	PROPN
cana-735	147	2	are	be	AUX
cana-735	147	3	the	the	DET
cana-735	147	4	same	same	ADJ
cana-735	147	5	trfn	trfn	NOUN
cana-735	147	6	core	core	NOUN
cana-735	147	7	for	for	ADP
cana-735	147	8	all	all	DET
cana-735	147	9	k	k	NOUN
cana-735	147	10	since	since	SCONJ
cana-735	147	11	it	it	PRON
cana-735	147	12	is	be	AUX
cana-735	147	13	symmetrical	symmetrical	ADJ
cana-735	147	14	.	.	PUNCT
cana-735	148	1	on	on	ADP
cana-735	148	2	the	the	DET
cana-735	148	3	other	other	ADJ
cana-735	148	4	hand	hand	NOUN
cana-735	148	5	,	,	PUNCT
cana-735	148	6	with	with	ADP
cana-735	148	7	nonsymmetrical	nonsymmetrical	ADJ
cana-735	148	8	trfn	trfn	NOUN
cana-735	148	9	,	,	PUNCT
cana-735	148	10	skewed	skew	VERB
cana-735	148	11	such	such	ADJ
cana-735	148	12	as	as	ADP
cana-735	148	13	left	leave	VERB
cana-735	148	14	trfn	trfn	NOUN
cana-735	149	1	δ̅	δ̅	VERB
cana-735	149	2	=	=	PUNCT
cana-735	149	3	(	(	PUNCT
cana-735	149	4	α	α	X
cana-735	149	5	=	=	SYM
cana-735	149	6	2.55	2.55	NUM
cana-735	149	7	;	;	PUNCT
cana-735	149	8	β	β	X
cana-735	149	9	=	=	SYM
cana-735	149	10	2.70	2.70	NUM
cana-735	149	11	;	;	PUNCT
cana-735	149	12	γ	γ	X
cana-735	149	13	=	=	PROPN
cana-735	149	14	2.85	2.85	NUM
cana-735	149	15	)	)	PUNCT
cana-735	149	16	,	,	PUNCT
cana-735	149	17	if	if	SCONJ
cana-735	149	18	k=1	k=1	PROPN
cana-735	149	19	and	and	CCONJ
cana-735	149	20	k=	k=	INTJ
cana-735	149	21	1000	1000	NUM
cana-735	149	22	then	then	ADV
cana-735	149	23	gmdf	gmdf	X
cana-735	149	24	=	=	PROPN
cana-735	149	25	2.6833	2.6833	NUM
cana-735	149	26	and	and	CCONJ
cana-735	149	27	2.7498	2.7498	NUM
cana-735	149	28	respectively	respectively	ADV
cana-735	149	29	.	.	PUNCT
cana-735	150	1	in	in	ADP
cana-735	150	2	this	this	DET
cana-735	150	3	case	case	NOUN
cana-735	150	4	,	,	PUNCT
cana-735	150	5	k	k	PROPN
cana-735	150	6	is	be	AUX
cana-735	150	7	closer	close	ADJ
cana-735	150	8	to	to	ADP
cana-735	150	9	the	the	DET
cana-735	150	10	tfn	tfn	NOUN
cana-735	150	11	's	's	PART
cana-735	150	12	core	core	NOUN
cana-735	150	13	,	,	PUNCT
cana-735	150	14	or	or	CCONJ
cana-735	150	15	2.75	2.75	NUM
cana-735	150	16	,	,	PUNCT
cana-735	150	17	the	the	DET
cana-735	150	18	larger	large	ADJ
cana-735	150	19	k.	k.	NOUN
cana-735	150	20	the	the	DET
cana-735	150	21	comparatively	comparatively	ADV
cana-735	150	22	small	small	ADJ
cana-735	150	23	shape	shape	NOUN
cana-735	150	24	parameter	parameter	NOUN
cana-735	150	25	δ̅	δ̅	PROPN
cana-735	150	26	=	=	PUNCT
cana-735	150	27	(	(	PUNCT
cana-735	150	28	α	α	X
cana-735	150	29	=	=	SYM
cana-735	150	30	1.35	1.35	NUM
cana-735	150	31	;	;	PUNCT
cana-735	150	32	β	β	X
cana-735	150	33	=	=	SYM
cana-735	150	34	1.55	1.55	NUM
cana-735	150	35	;	;	PUNCT
cana-735	150	36	γ	γ	X
cana-735	150	37	=	=	SYM
cana-735	150	38	1.75	1.75	NUM
cana-735	150	39	,	,	PUNCT
cana-735	150	40	while	while	SCONJ
cana-735	150	41	the	the	DET
cana-735	150	42	quite	quite	ADV
cana-735	150	43	big	big	ADJ
cana-735	150	44	shape	shape	NOUN
cana-735	150	45	parameter	parameter	NOUN
cana-735	150	46	δ̅	δ̅	PROPN
cana-735	150	47	=	=	PUNCT
cana-735	150	48	(	(	PUNCT
cana-735	150	49	α	α	X
cana-735	150	50	=	=	SYM
cana-735	150	51	1.55	1.55	NUM
cana-735	150	52	;	;	PUNCT
cana-735	150	53	β	β	X
cana-735	150	54	=	=	SYM
cana-735	150	55	2.70	2.70	NUM
cana-735	150	56	;	;	PUNCT
cana-735	150	57	γ	γ	X
cana-735	150	58	=	=	SYM
cana-735	150	59	2.85	2.85	NUM
cana-735	150	60	)	)	PUNCT
cana-735	150	61	is	be	AUX
cana-735	150	62	presented	present	VERB
cana-735	150	63	on	on	ADP
cana-735	150	64	the	the	DET
cana-735	150	65	right	right	ADJ
cana-735	150	66	figure	figure	NOUN
cana-735	150	67	.	.	PUNCT
cana-735	151	1	the	the	DET
cana-735	151	2	fuzzy	fuzzy	ADJ
cana-735	151	3	failure	failure	NOUN
cana-735	151	4	numbers	number	NOUN
cana-735	151	5	generated	generate	VERB
cana-735	151	6	by	by	ADP
cana-735	151	7	the	the	DET
cana-735	151	8	dgm	dgm	PROPN
cana-735	151	9	distribution	distribution	NOUN
cana-735	151	10	is	be	AUX
cana-735	151	11	then	then	ADV
cana-735	151	12	examined	examine	VERB
cana-735	151	13	using	use	VERB
cana-735	151	14	α	α	X
cana-735	151	15	-cut	-cut	ADJ
cana-735	151	16	technique	technique	NOUN
cana-735	151	17	.	.	PUNCT
cana-735	152	1	let	let	VERB
cana-735	152	2	us	we	PRON
cana-735	152	3	evoke	evoke	VERB
cana-735	152	4	that	that	SCONJ
cana-735	152	5	α	α	X
cana-735	152	6	-cut	-cut	VERB
cana-735	152	7	of	of	ADP
cana-735	152	8	trfn	trfn	NOUN
cana-735	152	9	μ(𝒜	μ(𝒜	NUM
cana-735	152	10	)	)	PUNCT
cana-735	153	1	=	=	PRON
cana-735	153	2	(	(	PUNCT
cana-735	153	3	α	α	NOUN
cana-735	153	4	;	;	PUNCT
cana-735	153	5	β	β	X
cana-735	153	6	;	;	PUNCT
cana-735	153	7	γ	γ	X
cana-735	153	8	)	)	PUNCT
cana-735	153	9	is	be	AUX
cana-735	153	10	μ(𝒜)=	μ(𝒜)=	NOUN
cana-735	154	1	[	[	X
cana-735	154	2	a	a	DET
cana-735	154	3	1	1	NUM
cana-735	154	4	,	,	PUNCT
cana-735	154	5	a	a	DET
cana-735	154	6	2	2	NUM
cana-735	154	7	]	]	PUNCT
cana-735	154	8	=	=	SYM
cana-735	155	1	[	[	X
cana-735	155	2	(	(	PUNCT
cana-735	155	3	β	β	X
cana-735	155	4	α	α	NOUN
cana-735	155	5	)	)	PUNCT
cana-735	155	6	+	+	CCONJ
cana-735	155	7	α	α	X
cana-735	155	8	,	,	PUNCT
cana-735	155	9	(	(	PUNCT
cana-735	155	10	β	β	X
cana-735	155	11	γ	γ	X
cana-735	155	12	)	)	PUNCT
cana-735	155	13	+	+	CCONJ
cana-735	155	14	γ	γ	X
cana-735	155	15	]	]	X
cana-735	155	16	.	.	PUNCT
cana-735	156	1	the	the	DET
cana-735	156	2	pdf	pdf	NOUN
cana-735	156	3	,	,	PUNCT
cana-735	156	4	cdf	cdf	PROPN
cana-735	156	5	and	and	CCONJ
cana-735	156	6	hazard	hazard	NOUN
cana-735	156	7	function	function	NOUN
cana-735	156	8	for	for	ADP
cana-735	156	9	dgm	dgm	PROPN
cana-735	156	10	distribution	distribution	NOUN
cana-735	156	11	with	with	ADP
cana-735	156	12	shape	shape	NOUN
cana-735	156	13	parameter	parameter	NOUN
cana-735	156	14	represented	represent	VERB
cana-735	156	15	in	in	ADP
cana-735	156	16	α	α	NOUN
cana-735	156	17	-	-	PUNCT
cana-735	156	18	cut	cut	NOUN
cana-735	156	19	obtained	obtain	VERB
cana-735	156	20	by	by	ADP
cana-735	156	21	,	,	PUNCT
cana-735	156	22	δα	δα	PROPN
cana-735	156	23	=	=	PUNCT
cana-735	157	1	[	[	X
cana-735	157	2	t1	t1	NOUN
cana-735	157	3	+	+	CCONJ
cana-735	157	4	t3	t3	PROPN
cana-735	157	5	α	α	NOUN
cana-735	157	6	,	,	PUNCT
cana-735	157	7	t2	t2	NOUN
cana-735	157	8	−	−	PROPN
cana-735	157	9	t3	t3	PROPN
cana-735	157	10	α	α	PROPN
cana-735	157	11	,	,	PUNCT
cana-735	157	12	]	]	X
cana-735	157	13	(	(	PUNCT
cana-735	157	14	9	9	X
cana-735	157	15	)	)	PUNCT
cana-735	157	16	r	r	NOUN
cana-735	157	17	for	for	ADP
cana-735	157	18	some	some	DET
cana-735	157	19	t1	t1	NOUN
cana-735	157	20	,	,	PUNCT
cana-735	157	21	t2	t2	NOUN
cana-735	157	22	,	,	PUNCT
cana-735	157	23	t3	t3	PROPN
cana-735	157	24	.	.	PUNCT
cana-735	158	1	by	by	ADP
cana-735	158	2	analysing	analyse	VERB
cana-735	158	3	the	the	DET
cana-735	158	4	α	α	PROPN
cana-735	158	5	-cut	-cut	PUNCT
cana-735	158	6	in	in	ADP
cana-735	158	7	equation	equation	NOUN
cana-735	158	8	(	(	PUNCT
cana-735	158	9	9	9	NUM
cana-735	158	10	)	)	PUNCT
cana-735	158	11	and	and	CCONJ
cana-735	158	12	applying	apply	VERB
cana-735	158	13	fuzzy	fuzzy	ADJ
cana-735	158	14	arithmetic	arithmetic	ADJ
cana-735	158	15	to	to	PART
cana-735	158	16	replace	replace	VERB
cana-735	158	17	it	it	PRON
cana-735	158	18	in	in	ADP
cana-735	158	19	equations	equation	NOUN
cana-735	158	20	(	(	PUNCT
cana-735	158	21	6	6	NUM
cana-735	158	22	)	)	PUNCT
cana-735	158	23	and	and	CCONJ
cana-735	158	24	(	(	PUNCT
cana-735	158	25	7	7	NUM
cana-735	158	26	)	)	PUNCT
cana-735	158	27	,	,	PUNCT
cana-735	158	28	the	the	DET
cana-735	158	29	cumulative	cumulative	ADJ
cana-735	158	30	distribution	distribution	NOUN
cana-735	158	31	may	may	AUX
cana-735	158	32	be	be	AUX
cana-735	158	33	determined	determine	VERB
cana-735	158	34	.	.	PUNCT
cana-735	159	1	f(t)α	f(t)α	PROPN
cana-735	159	2	=	=	PUNCT
cana-735	160	1	[	[	PUNCT
cana-735	160	2	(	(	PUNCT
cana-735	160	3	t1	t1	NOUN
cana-735	160	4	+	+	CCONJ
cana-735	160	5	t3	t3	PROPN
cana-735	160	6	α	α	NOUN
cana-735	160	7	)	)	PUNCT
cana-735	160	8	x−2	x−2	PROPN
cana-735	160	9	(	(	PUNCT
cana-735	160	10	1	1	NUM
cana-735	160	11	+	+	NUM
cana-735	160	12	x−1)−(1+(t1+t3	x−1)−(1+(t1+t3	PROPN
cana-735	160	13	α	α	X
cana-735	160	14	)	)	PUNCT
cana-735	160	15	)	)	PUNCT
cana-735	160	16	,	,	PUNCT
cana-735	160	17	(	(	PUNCT
cana-735	160	18	t2	t2	NOUN
cana-735	160	19	+	+	CCONJ
cana-735	160	20	t3	t3	PROPN
cana-735	160	21	α	α	NOUN
cana-735	160	22	)	)	PUNCT
cana-735	160	23	x−2	x−2	PROPN
cana-735	160	24	(	(	PUNCT
cana-735	160	25	1	1	NUM
cana-735	160	26	+	+	CCONJ
cana-735	160	27	x−1)−(1+t2+t3	x−1)−(1+t2+t3	PROPN
cana-735	160	28	α	α	X
cana-735	160	29	)	)	PUNCT
cana-735	160	30	f(t)α	f(t)α	NOUN
cana-735	160	31	=	=	PUNCT
cana-735	160	32	[	[	PUNCT
cana-735	160	33	(	(	PUNCT
cana-735	160	34	1	1	NUM
cana-735	160	35	+	+	X
cana-735	160	36	x−1)−(t1+t3	x−1)−(t1+t3	PROPN
cana-735	160	37	α	α	NUM
cana-735	160	38	)	)	PUNCT
cana-735	160	39	,	,	PUNCT
cana-735	160	40	(	(	PUNCT
cana-735	160	41	1	1	NUM
cana-735	160	42	+	+	NUM
cana-735	160	43	x−1)−(t2−t3	x−1)−(t2−t3	PROPN
cana-735	160	44	α	α	NUM
cana-735	160	45	)	)	PUNCT
cana-735	160	46	]	]	PUNCT
cana-735	160	47	,	,	PUNCT
cana-735	160	48	where	where	SCONJ
cana-735	160	49	t1	t1	NOUN
cana-735	160	50	,	,	PUNCT
cana-735	160	51	t2	t2	NOUN
cana-735	160	52	,	,	PUNCT
cana-735	160	53	t3	t3	PROPN
cana-735	160	54	∈	∈	PROPN
cana-735	160	55	r	r	NOUN
cana-735	160	56	(	(	PUNCT
cana-735	160	57	10	10	NUM
cana-735	160	58	)	)	PUNCT
cana-735	160	59	h(t	h(t	PROPN
cana-735	160	60	)	)	PUNCT
cana-735	161	1	=	=	PRON
cana-735	161	2	[	[	PUNCT
cana-735	161	3	(	(	PUNCT
cana-735	161	4	y1	y1	INTJ
cana-735	161	5	+	+	X
cana-735	161	6	𝑦3	𝑦3	PROPN
cana-735	161	7	α)x−(2)(1	α)x−(2)(1	NOUN
cana-735	161	8	+	+	CCONJ
cana-735	161	9	x−1)−(1+(y1+y3	x−1)−(1+(y1+y3	PUNCT
cana-735	161	10	α))[1	α))[1	PRON
cana-735	162	1	−	−	PROPN
cana-735	162	2	(	(	PUNCT
cana-735	162	3	1	1	NUM
cana-735	162	4	+	+	NUM
cana-735	162	5	x−1)−(y1+y3	x−1)−(y1+y3	PROPN
cana-735	162	6	α	α	NOUN
cana-735	162	7	)	)	PUNCT
cana-735	162	8	]	]	PUNCT
cana-735	162	9	−1	−1	NOUN
cana-735	162	10	,	,	PUNCT
cana-735	162	11	(	(	PUNCT
cana-735	162	12	y2	y2	INTJ
cana-735	162	13	−	−	PROPN
cana-735	162	14	y3	y3	NOUN
cana-735	162	15	α)x−(2)(1	α)x−(2)(1	NOUN
cana-735	162	16	+	+	CCONJ
cana-735	162	17	x−1)−(1+(y2−yα))[1	x−1)−(1+(y2−yα))[1	PROPN
cana-735	162	18	−	−	PROPN
cana-735	163	1	(	(	PUNCT
cana-735	163	2	1	1	NUM
cana-735	163	3	+	+	CCONJ
cana-735	163	4	x−1)−(y2−𝑦α)]−1	x−1)−(y2−𝑦α)]−1	X
cana-735	163	5	(	(	PUNCT
cana-735	163	6	11	11	NUM
cana-735	163	7	)	)	PUNCT
cana-735	163	8	r.	r.	NOUN
cana-735	163	9	for	for	ADP
cana-735	163	10	some	some	DET
cana-735	163	11	y1	y1	NOUN
cana-735	163	12	,	,	PUNCT
cana-735	163	13	y2	y2	PROPN
cana-735	163	14	,	,	PUNCT
cana-735	163	15	y3	y3	PROPN
cana-735	163	16	,	,	PUNCT
cana-735	163	17	y4	y4	PROPN
cana-735	163	18	,	,	PUNCT
cana-735	163	19	y5	y5	NOUN
cana-735	163	20	,	,	PUNCT
cana-735	163	21	y6	y6	PROPN
cana-735	163	22	∈	∈	PROPN
cana-735	163	23	r.	r.	PROPN
cana-735	163	24	so	so	ADV
cana-735	163	25	,	,	PUNCT
cana-735	163	26	integrate	integrate	VERB
cana-735	163	27	equation	equation	NOUN
cana-735	163	28	(	(	PUNCT
cana-735	163	29	11	11	NUM
cana-735	163	30	)	)	PUNCT
cana-735	163	31	on	on	ADP
cana-735	163	32	both	both	DET
cana-735	163	33	sides	side	NOUN
cana-735	163	34	we	we	PRON
cana-735	163	35	get	get	VERB
cana-735	163	36	the	the	DET
cana-735	163	37	number	number	NOUN
cana-735	163	38	of	of	ADP
cana-735	163	39	failures	failure	NOUN
cana-735	163	40	,	,	PUNCT
cana-735	163	41	which	which	PRON
cana-735	163	42	is	be	AUX
cana-735	163	43	provided	provide	VERB
cana-735	163	44	by	by	ADP
cana-735	163	45	.	.	PUNCT
cana-735	164	1	the	the	DET
cana-735	164	2	failure	failure	NOUN
cana-735	164	3	’s	’s	PART
cana-735	164	4	number	number	NOUN
cana-735	164	5	given	give	VERB
cana-735	164	6	by	by	ADP
cana-735	164	7	n(𝑡	n(𝑡	NOUN
cana-735	164	8	)	)	PUNCT
cana-735	164	9	=	=	PUNCT
cana-735	165	1	[	[	X
cana-735	165	2	t2(s1+s3	t2(s1+s3	X
cana-735	165	3	α	α	PROPN
cana-735	165	4	)	)	PUNCT
cana-735	165	5	,	,	PUNCT
cana-735	165	6	t2(s2	t2(s2	PRON
cana-735	165	7	−s3	−s3	ADJ
cana-735	165	8	α	α	PROPN
cana-735	165	9	)	)	PUNCT
cana-735	165	10	]	]	X
cana-735	165	11	,	,	PUNCT
cana-735	165	12	s1	s1	NOUN
cana-735	165	13	,	,	PUNCT
cana-735	165	14	s2	s2	PROPN
cana-735	165	15	,	,	PUNCT
cana-735	165	16	s3	s3	PROPN
cana-735	165	17	∈	∈	PROPN
cana-735	165	18	r	r	NOUN
cana-735	165	19	(	(	PUNCT
cana-735	165	20	12	12	NUM
cana-735	165	21	)	)	PUNCT
cana-735	165	22	theorem	theorem	ADJ
cana-735	165	23	2	2	NUM
cana-735	165	24	proves	prove	VERB
cana-735	165	25	gmdf	gmdf	NOUN
cana-735	165	26	of	of	ADP
cana-735	165	27	failures	failure	NOUN
cana-735	165	28	raises	raise	VERB
cana-735	165	29	and	and	CCONJ
cana-735	165	30	supports	support	VERB
cana-735	165	31	to	to	PART
cana-735	165	32	expand	expand	VERB
cana-735	165	33	.	.	PUNCT
cana-735	166	1	as	as	ADP
cana-735	166	2	a	a	DET
cana-735	166	3	result	result	NOUN
cana-735	166	4	,	,	PUNCT
cana-735	166	5	the	the	DET
cana-735	166	6	level	level	NOUN
cana-735	166	7	of	of	ADP
cana-735	166	8	uncertainty	uncertainty	NOUN
cana-735	166	9	rises	rise	VERB
cana-735	166	10	.	.	PUNCT
cana-735	167	1	communications	communication	NOUN
cana-735	167	2	on	on	ADP
cana-735	167	3	applied	apply	VERB
cana-735	167	4	nonlinear	nonlinear	ADJ
cana-735	167	5	analysis	analysis	NOUN
cana-735	167	6	issn	issn	NOUN
cana-735	167	7	:	:	PUNCT
cana-735	167	8	1074	1074	NUM
cana-735	167	9	-	-	PUNCT
cana-735	167	10	133x	133x	NUM
cana-735	167	11	vol	vol	NOUN
cana-735	167	12	31	31	NUM
cana-735	167	13	no	no	NOUN
cana-735	167	14	.	.	PUNCT
cana-735	168	1	3s	3s	NUM
cana-735	168	2	(	(	PUNCT
cana-735	168	3	2024	2024	NUM
cana-735	168	4	)	)	PUNCT
cana-735	168	5	112	112	NUM
cana-735	168	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-735	168	7	theorem2	theorem2	NOUN
cana-735	168	8	.	.	PROPN
cana-735	169	1	for	for	ADP
cana-735	169	2	∆λ	∆λ	PROPN
cana-735	169	3	>	>	X
cana-735	169	4	0	0	PUNCT
cana-735	169	5	let	let	VERB
cana-735	169	6	n(λ)α	n(λ)α	ADJ
cana-735	169	7	and	and	CCONJ
cana-735	169	8	n(λ	n(λ	PROPN
cana-735	169	9	+	+	CCONJ
cana-735	169	10	∆λ)α	∆λ)α	NOUN
cana-735	169	11	be	be	VERB
cana-735	169	12	the	the	DET
cana-735	169	13	fuzzy	fuzzy	ADJ
cana-735	169	14	failures	failure	NOUN
cana-735	169	15	at	at	ADP
cana-735	169	16	time	time	NOUN
cana-735	169	17	λ	λ	PROPN
cana-735	169	18	and	and	CCONJ
cana-735	169	19	λ	λ	X
cana-735	170	1	+	+	CCONJ
cana-735	170	2	∆λ	∆λ	PROPN
cana-735	170	3	respectively	respectively	ADV
cana-735	170	4	then	then	ADV
cana-735	170	5	:	:	PUNCT
cana-735	170	6	(	(	PUNCT
cana-735	170	7	a	a	X
cana-735	170	8	)	)	PUNCT
cana-735	170	9	n(λ)α	n(λ)α	NOUN
cana-735	170	10	=	=	SYM
cana-735	170	11	(	(	PUNCT
cana-735	170	12	λcα	λcα	PROPN
cana-735	170	13	,	,	PUNCT
cana-735	170	14	λdα	λdα	ADJ
cana-735	170	15	)	)	PUNCT
cana-735	170	16	and	and	CCONJ
cana-735	170	17	n(λ	n(λ	PROPN
cana-735	170	18	+	+	CCONJ
cana-735	170	19	∆λ)α	∆λ)α	NOUN
cana-735	170	20	=	=	SYM
cana-735	170	21	(	(	PUNCT
cana-735	170	22	λ	λ	X
cana-735	170	23	+	+	SYM
cana-735	170	24	∆λ)cα	∆λ)cα	PROPN
cana-735	170	25	,	,	PUNCT
cana-735	170	26	(	(	PUNCT
cana-735	170	27	λ	λ	X
cana-735	170	28	+	+	CCONJ
cana-735	170	29	∆λ)dα	∆λ)dα	PROPN
cana-735	170	30	)	)	PUNCT
cana-735	170	31	(	(	PUNCT
cana-735	170	32	b	b	X
cana-735	170	33	)	)	PUNCT
cana-735	170	34	gmdf	gmdf	NOUN
cana-735	170	35	n(λ	n(λ	PROPN
cana-735	170	36	+	+	CCONJ
cana-735	170	37	∆λ)α	∆λ)α	PROPN
cana-735	170	38	≥	≥	NOUN
cana-735	170	39	gmdf	gmdf	PROPN
cana-735	171	1	n(λ)α	n(λ)α	NUM
cana-735	171	2	∀	∀	PUNCT
cana-735	171	3	λ	λ	X
cana-735	171	4	∈	∈	NOUN
cana-735	171	5	r+	r+	NOUN
cana-735	171	6	(	(	PUNCT
cana-735	171	7	c	c	X
cana-735	171	8	)	)	PUNCT
cana-735	172	1	[	[	X
cana-735	172	2	(	(	PUNCT
cana-735	172	3	λ	λ	X
cana-735	172	4	+	+	PROPN
cana-735	172	5	∆λ)cα	∆λ)cα	NUM
cana-735	172	6	−	−	PROPN
cana-735	172	7	(	(	PUNCT
cana-735	172	8	λ	λ	X
cana-735	172	9	+	+	CCONJ
cana-735	172	10	∆λ)dα	∆λ)dα	PROPN
cana-735	172	11	]	]	X
cana-735	172	12	−	−	PUNCT
cana-735	173	1	[	[	X
cana-735	173	2	(	(	PUNCT
cana-735	173	3	λcα	λcα	X
cana-735	173	4	−	−	X
cana-735	173	5	λdα	λdα	ADJ
cana-735	173	6	)	)	PUNCT
cana-735	173	7	]	]	PUNCT
cana-735	173	8	≥	≥	NOUN
cana-735	173	9	0	0	NUM
cana-735	173	10	∀	∀	PUNCT
cana-735	173	11	λ	λ	X
cana-735	173	12	∈	∈	PROPN
cana-735	173	13	z+	z+	NUM
cana-735	173	14	.	.	PUNCT
cana-735	174	1	(	(	PUNCT
cana-735	174	2	i	i	NOUN
cana-735	174	3	)	)	PUNCT
cana-735	174	4	by	by	ADP
cana-735	174	5	using	use	VERB
cana-735	174	6	theorem	theorem	NOUN
cana-735	174	7	1	1	NUM
cana-735	174	8	,	,	PUNCT
cana-735	174	9	proof	proof	NOUN
cana-735	174	10	has	have	AUX
cana-735	174	11	done	do	VERB
cana-735	174	12	very	very	ADV
cana-735	174	13	clearly	clearly	ADV
cana-735	174	14	.	.	PUNCT
cana-735	175	1	(	(	PUNCT
cana-735	175	2	ii	ii	NOUN
cana-735	175	3	)	)	PUNCT
cana-735	175	4	equation	equation	NOUN
cana-735	175	5	(	(	PUNCT
cana-735	175	6	12	12	NUM
cana-735	175	7	)	)	PUNCT
cana-735	175	8	expressed	express	VERB
cana-735	175	9	for	for	ADP
cana-735	175	10	any	any	DET
cana-735	175	11	α	α	NOUN
cana-735	175	12	∈	∈	PROPN
cana-735	176	1	[	[	X
cana-735	176	2	0,1	0,1	NUM
cana-735	176	3	]	]	PUNCT
cana-735	176	4	,	,	PUNCT
cana-735	176	5	then	then	ADV
cana-735	176	6	interval	interval	NOUN
cana-735	176	7	has	have	AUX
cana-735	176	8	defined	define	VERB
cana-735	176	9	(	(	PUNCT
cana-735	176	10	𝑡cα	𝑡cα	NOUN
cana-735	176	11	,	,	PUNCT
cana-735	176	12	tdα	tdα	PROPN
cana-735	176	13	)	)	PUNCT
cana-735	176	14	where	where	SCONJ
cana-735	176	15	cα	cα	NOUN
cana-735	176	16	,	,	PUNCT
cana-735	176	17	dα	dα	PROPN
cana-735	176	18	∈	∈	PROPN
cana-735	176	19	r.	r.	PROPN
cana-735	176	20	without	without	ADP
cana-735	176	21	loss	loss	NOUN
cana-735	176	22	of	of	ADP
cana-735	176	23	generality	generality	NOUN
cana-735	176	24	need	need	VERB
cana-735	176	25	to	to	PART
cana-735	176	26	prove	prove	VERB
cana-735	176	27	theorem	theorem	VERB
cana-735	176	28	.	.	PUNCT
cana-735	177	1	[	[	X
cana-735	177	2	(	(	PUNCT
cana-735	177	3	t	t	NOUN
cana-735	177	4	+	+	NUM
cana-735	177	5	∆t)c	∆t)c	PROPN
cana-735	177	6	−	−	PROPN
cana-735	177	7	(	(	PUNCT
cana-735	177	8	t	t	PROPN
cana-735	177	9	+	+	CCONJ
cana-735	177	10	∆t)d	∆t)d	VERB
cana-735	177	11	]	]	X
cana-735	177	12	−	−	PROPN
cana-735	178	1	[	[	X
cana-735	178	2	(	(	PUNCT
cana-735	178	3	λc	λc	INTJ
cana-735	178	4	−	−	PROPN
cana-735	178	5	λd	λd	NOUN
cana-735	178	6	)	)	PUNCT
cana-735	178	7	]	]	PUNCT
cana-735	178	8	≥	≥	NOUN
cana-735	178	9	0	0	NUM
cana-735	178	10	.	.	PUNCT
cana-735	179	1	let	let	AUX
cana-735	179	2	consider	consider	VERB
cana-735	179	3	the	the	DET
cana-735	179	4	binomial	binomial	ADJ
cana-735	179	5	expansion	expansion	NOUN
cana-735	179	6	rule	rule	NOUN
cana-735	179	7	,	,	PUNCT
cana-735	179	8	(	(	PUNCT
cana-735	179	9	t	t	NOUN
cana-735	179	10	+	+	CCONJ
cana-735	179	11	∆t)c	∆t)c	NOUN
cana-735	179	12	=	=	PUNCT
cana-735	179	13	∑	∑	PUNCT
cana-735	179	14	c	c	X
cana-735	179	15	!	!	PUNCT
cana-735	180	1	(	(	PUNCT
cana-735	180	2	c	c	NOUN
cana-735	180	3	−	−	PROPN
cana-735	180	4	n	n	CCONJ
cana-735	180	5	)	)	PUNCT
cana-735	180	6	!	!	PUNCT
cana-735	181	1	n	n	X
cana-735	181	2	!	!	PUNCT
cana-735	182	1	∆𝑡(c−1)−n	∆𝑡(c−1)−n	ADP
cana-735	182	2	c	c	PROPN
cana-735	182	3	n=0	n=0	SYM
cana-735	182	4	tn	tn	PROPN
cana-735	182	5	(	(	PUNCT
cana-735	182	6	t	t	NOUN
cana-735	182	7	+	+	CCONJ
cana-735	182	8	∆t)c	∆t)c	NOUN
cana-735	182	9	=	=	PUNCT
cana-735	182	10	∑	∑	PUNCT
cana-735	182	11	(	(	PUNCT
cana-735	182	12	c	c	NOUN
cana-735	182	13	−	−	PROPN
cana-735	182	14	1	1	NUM
cana-735	182	15	)	)	PUNCT
cana-735	182	16	!	!	PUNCT
cana-735	183	1	(	(	PUNCT
cana-735	183	2	(	(	PUNCT
cana-735	183	3	c	c	NOUN
cana-735	183	4	−	−	NOUN
cana-735	183	5	1	1	NUM
cana-735	183	6	)	)	PUNCT
cana-735	183	7	−	−	NOUN
cana-735	183	8	n	n	CCONJ
cana-735	183	9	)	)	PUNCT
cana-735	183	10	!	!	PUNCT
cana-735	184	1	n	n	X
cana-735	184	2	!	!	PUNCT
cana-735	185	1	∆t(c−1)−n	∆t(c−1)−n	PROPN
cana-735	185	2	c−1	c−1	PROPN
cana-735	185	3	n=0	n=0	PUNCT
cana-735	185	4	tc	tc	NOUN
cana-735	185	5	+	+	CCONJ
cana-735	185	6	𝑡c	𝑡c	VERB
cana-735	185	7	then	then	ADV
cana-735	185	8	for	for	ADP
cana-735	185	9	cα	cα	ADP
cana-735	185	10	,	,	PUNCT
cana-735	185	11	dα	dα	PROPN
cana-735	185	12	∈	∈	PROPN
cana-735	185	13	z+	z+	NUM
cana-735	185	14	we	we	PRON
cana-735	185	15	have	have	VERB
cana-735	185	16	(	(	PUNCT
cana-735	185	17	t	t	NOUN
cana-735	185	18	+	+	CCONJ
cana-735	185	19	∆t)c	∆t)c	NOUN
cana-735	185	20	=	=	PUNCT
cana-735	185	21	∑	∑	PUNCT
cana-735	185	22	(	(	PUNCT
cana-735	185	23	c	c	NOUN
cana-735	185	24	−	−	PROPN
cana-735	185	25	1	1	NUM
cana-735	185	26	)	)	PUNCT
cana-735	185	27	!	!	PUNCT
cana-735	186	1	(	(	PUNCT
cana-735	186	2	(	(	PUNCT
cana-735	186	3	c	c	NOUN
cana-735	186	4	−	−	NOUN
cana-735	186	5	1	1	NUM
cana-735	186	6	)	)	PUNCT
cana-735	186	7	−	−	NOUN
cana-735	186	8	n	n	CCONJ
cana-735	186	9	)	)	PUNCT
cana-735	186	10	!	!	PUNCT
cana-735	187	1	n	n	X
cana-735	187	2	!	!	PUNCT
cana-735	188	1	∆t(c−1)−n	∆t(c−1)−n	PROPN
cana-735	188	2	c−1	c−1	PROPN
cana-735	188	3	n=0	n=0	PUNCT
cana-735	188	4	tc	tc	NOUN
cana-735	188	5	+	+	CCONJ
cana-735	188	6	𝑡c	𝑡c	PROPN
cana-735	188	7	(	(	PUNCT
cana-735	188	8	t	t	NOUN
cana-735	188	9	+	+	CCONJ
cana-735	188	10	∆t)d	∆t)d	ADJ
cana-735	188	11	=	=	PUNCT
cana-735	188	12	∑	∑	PUNCT
cana-735	188	13	(	(	PUNCT
cana-735	188	14	d	d	NOUN
cana-735	188	15	−	−	PROPN
cana-735	188	16	1	1	NUM
cana-735	188	17	)	)	PUNCT
cana-735	188	18	!	!	PUNCT
cana-735	189	1	(	(	PUNCT
cana-735	189	2	(	(	PUNCT
cana-735	189	3	d	d	NOUN
cana-735	189	4	−	−	PROPN
cana-735	189	5	1	1	NUM
cana-735	189	6	)	)	PUNCT
cana-735	189	7	−	−	NOUN
cana-735	189	8	n	n	CCONJ
cana-735	189	9	)	)	PUNCT
cana-735	189	10	!	!	PUNCT
cana-735	190	1	n	n	X
cana-735	190	2	!	!	PUNCT
cana-735	191	1	∆t(d−1)−n	∆t(d−1)−n	PROPN
cana-735	191	2	d−1	d−1	PROPN
cana-735	191	3	n=0	n=0	PROPN
cana-735	191	4	td	td	NOUN
cana-735	191	5	+	+	CCONJ
cana-735	191	6	𝑡d	𝑡d	ADP
cana-735	191	7	then	then	ADV
cana-735	191	8	[	[	X
cana-735	191	9	(	(	PUNCT
cana-735	191	10	t	t	NOUN
cana-735	191	11	+	+	NUM
cana-735	191	12	∆t)c	∆t)c	PROPN
cana-735	191	13	−	−	PROPN
cana-735	191	14	(	(	PUNCT
cana-735	191	15	t	t	PROPN
cana-735	191	16	+	+	CCONJ
cana-735	191	17	∆t)d	∆t)d	VERB
cana-735	191	18	]	]	X
cana-735	191	19	−	−	PROPN
cana-735	192	1	[	[	X
cana-735	192	2	(	(	PUNCT
cana-735	192	3	tc	tc	NOUN
cana-735	192	4	−	−	NOUN
cana-735	192	5	td	td	NOUN
cana-735	192	6	)	)	PUNCT
cana-735	192	7	]	]	PUNCT
cana-735	193	1	=	=	PUNCT
cana-735	193	2	∑	∑	PUNCT
cana-735	193	3	(	(	PUNCT
cana-735	193	4	c	c	NOUN
cana-735	193	5	−	−	PROPN
cana-735	193	6	1	1	NUM
cana-735	193	7	)	)	PUNCT
cana-735	193	8	!	!	PUNCT
cana-735	194	1	(	(	PUNCT
cana-735	194	2	(	(	PUNCT
cana-735	194	3	c	c	NOUN
cana-735	194	4	−	−	NOUN
cana-735	194	5	1	1	NUM
cana-735	194	6	)	)	PUNCT
cana-735	194	7	−	−	NOUN
cana-735	194	8	n	n	CCONJ
cana-735	194	9	)	)	PUNCT
cana-735	194	10	!	!	PUNCT
cana-735	195	1	n	n	X
cana-735	195	2	!	!	PUNCT
cana-735	196	1	∆t(c−1)−n	∆t(c−1)−n	PROPN
cana-735	196	2	c−1	c−1	PROPN
cana-735	196	3	n=0	n=0	PUNCT
cana-735	196	4	tc	tc	ADP
cana-735	196	5	−	−	NOUN
cana-735	196	6	∑	∑	PUNCT
cana-735	196	7	(	(	PUNCT
cana-735	196	8	d	d	NOUN
cana-735	196	9	−	−	PROPN
cana-735	196	10	1	1	NUM
cana-735	196	11	)	)	PUNCT
cana-735	196	12	!	!	PUNCT
cana-735	197	1	(	(	PUNCT
cana-735	197	2	(	(	PUNCT
cana-735	197	3	d	d	NOUN
cana-735	197	4	−	−	PROPN
cana-735	197	5	1	1	NUM
cana-735	197	6	)	)	PUNCT
cana-735	197	7	−	−	NOUN
cana-735	197	8	n	n	CCONJ
cana-735	197	9	)	)	PUNCT
cana-735	197	10	!	!	PUNCT
cana-735	198	1	n	n	X
cana-735	198	2	!	!	PUNCT
cana-735	199	1	∆t(d−1)−n	∆t(d−1)−n	PROPN
cana-735	199	2	d−1	d−1	PROPN
cana-735	199	3	n=0	n=0	PROPN
cana-735	199	4	td	td	NOUN
cana-735	199	5	=	=	PUNCT
cana-735	199	6	∑	∑	PROPN
cana-735	199	7	(	(	PUNCT
cana-735	199	8	c−1	c−1	PROPN
cana-735	199	9	)	)	PUNCT
cana-735	199	10	!	!	PUNCT
cana-735	200	1	(	(	PUNCT
cana-735	200	2	(	(	PUNCT
cana-735	200	3	c−1)−n)!n	c−1)−n)!n	VERB
cana-735	200	4	!	!	PUNCT
cana-735	201	1	∆t(c−1)−nc−1	∆t(c−1)−nc−1	PROPN
cana-735	201	2	n	n	CCONJ
cana-735	201	3	=	=	PROPN
cana-735	201	4	d	d	PROPN
cana-735	201	5	tc	tc	NUM
cana-735	201	6	≥	≥	NOUN
cana-735	201	7	0	0	NUM
cana-735	201	8	,	,	PUNCT
cana-735	201	9	hence	hence	ADV
cana-735	201	10	,	,	PUNCT
cana-735	201	11	[	[	X
cana-735	201	12	(	(	PUNCT
cana-735	201	13	t	t	NOUN
cana-735	201	14	+	+	NUM
cana-735	201	15	∆t)c	∆t)c	PROPN
cana-735	201	16	−	−	PROPN
cana-735	201	17	(	(	PUNCT
cana-735	201	18	t	t	PROPN
cana-735	201	19	+	+	CCONJ
cana-735	201	20	∆t)d	∆t)d	VERB
cana-735	201	21	]	]	X
cana-735	201	22	−	−	PROPN
cana-735	202	1	[	[	X
cana-735	202	2	(	(	PUNCT
cana-735	202	3	tc	tc	NOUN
cana-735	202	4	−	−	NOUN
cana-735	202	5	td	td	NOUN
cana-735	202	6	)	)	PUNCT
cana-735	202	7	]	]	PUNCT
cana-735	202	8	≥	≥	NOUN
cana-735	202	9	0	0	NUM
cana-735	202	10	∀t	∀t	PROPN
cana-735	202	11	∈	∈	PROPN
cana-735	202	12	z+	z+	PUNCT
cana-735	202	13	.	.	PUNCT
cana-735	203	1	it	it	PRON
cana-735	203	2	can	can	AUX
cana-735	203	3	be	be	AUX
cana-735	203	4	extended	extend	VERB
cana-735	203	5	to	to	ADP
cana-735	203	6	cα	cα	ADP
cana-735	203	7	,	,	PUNCT
cana-735	203	8	dα	dα	PROPN
cana-735	203	9	∈	∈	PROPN
cana-735	203	10	r+	r+	X
cana-735	203	11	.	.	PUNCT
cana-735	204	1	another	another	DET
cana-735	204	2	way	way	NOUN
cana-735	204	3	can	can	AUX
cana-735	204	4	be	be	AUX
cana-735	204	5	proved	prove	VERB
cana-735	204	6	by	by	ADP
cana-735	204	7	using	use	VERB
cana-735	204	8	newton	newton	PROPN
cana-735	204	9	’s	’s	PART
cana-735	204	10	generalised	generalise	VERB
cana-735	204	11	binomial	binomial	NOUN
cana-735	204	12	[	[	X
cana-735	204	13	34,35	34,35	NOUN
cana-735	204	14	]	]	X
cana-735	204	15	form	form	NOUN
cana-735	204	16	of	of	ADP
cana-735	204	17	infinite	infinite	ADJ
cana-735	204	18	series	series	NOUN
cana-735	204	19	instead	instead	ADV
cana-735	204	20	of	of	ADP
cana-735	204	21	series	series	PROPN
cana-735	204	22	λ	λ	PROPN
cana-735	204	23	∈	∈	PROPN
cana-735	204	24	z+	z+	NUM
cana-735	204	25	.	.	NOUN
cana-735	204	26	4	4	NUM
cana-735	204	27	.	.	X
cana-735	204	28	illustration	illustration	NOUN
cana-735	204	29	to	to	PART
cana-735	204	30	have	have	AUX
cana-735	204	31	a	a	DET
cana-735	204	32	better	well	ADJ
cana-735	204	33	understanding	understanding	NOUN
cana-735	204	34	of	of	ADP
cana-735	204	35	the	the	DET
cana-735	204	36	preceding	precede	VERB
cana-735	204	37	section	section	NOUN
cana-735	204	38	's	's	PART
cana-735	204	39	conclusions	conclusion	NOUN
cana-735	204	40	,	,	PUNCT
cana-735	204	41	we	we	PRON
cana-735	204	42	demonstrate	demonstrate	VERB
cana-735	204	43	by	by	ADP
cana-735	204	44	utilizing	utilize	VERB
cana-735	204	45	two	two	NUM
cana-735	204	46	distinct	distinct	ADJ
cana-735	204	47	values	value	NOUN
cana-735	204	48	for	for	ADP
cana-735	204	49	different	different	ADJ
cana-735	204	50	shape	shape	NOUN
cana-735	204	51	parameters	parameter	NOUN
cana-735	204	52	comparatively	comparatively	ADV
cana-735	204	53	small	small	ADJ
cana-735	204	54	value	value	NOUN
cana-735	204	55	δ	δ	NOUN
cana-735	204	56	=	=	SYM
cana-735	204	57	(	(	PUNCT
cana-735	204	58	α	α	X
cana-735	204	59	=	=	SYM
cana-735	204	60	1.35	1.35	NUM
cana-735	204	61	;	;	PUNCT
cana-735	204	62	β	β	X
cana-735	204	63	=	=	SYM
cana-735	204	64	1.45	1.45	NUM
cana-735	204	65	;	;	PUNCT
cana-735	204	66	γ	γ	X
cana-735	204	67	=	=	PROPN
cana-735	204	68	1.75	1.75	NUM
cana-735	204	69	)	)	PUNCT
cana-735	204	70	,	,	PUNCT
cana-735	204	71	bigger	big	ADJ
cana-735	204	72	value	value	NOUN
cana-735	204	73	δ	δ	NOUN
cana-735	204	74	=	=	SYM
cana-735	204	75	(	(	PUNCT
cana-735	204	76	α	α	X
cana-735	204	77	=	=	SYM
cana-735	204	78	2.55	2.55	NUM
cana-735	204	79	;	;	PUNCT
cana-735	204	80	β	β	X
cana-735	204	81	=	=	SYM
cana-735	204	82	2.70	2.70	NUM
cana-735	204	83	;	;	PUNCT
cana-735	204	84	γ	γ	X
cana-735	204	85	=	=	PROPN
cana-735	204	86	2.85	2.85	NUM
cana-735	204	87	)	)	PUNCT
cana-735	204	88	.	.	PUNCT
cana-735	205	1	here	here	ADV
cana-735	205	2	,	,	PUNCT
cana-735	205	3	α	α	X
cana-735	205	4	,	,	PUNCT
cana-735	205	5	β	β	NOUN
cana-735	205	6	,	,	PUNCT
cana-735	205	7	and	and	CCONJ
cana-735	205	8	λ	λ	NOUN
cana-735	205	9	are	be	AUX
cana-735	205	10	the	the	DET
cana-735	205	11	trfn	trfn	NOUN
cana-735	205	12	components	component	NOUN
cana-735	205	13	that	that	PRON
cana-735	205	14	make	make	VERB
cana-735	205	15	up	up	ADP
cana-735	205	16	the	the	DET
cana-735	205	17	trfn	trfn	NOUN
cana-735	205	18	,	,	PUNCT
cana-735	205	19	which	which	PRON
cana-735	205	20	are	be	AUX
cana-735	205	21	defined	define	VERB
cana-735	205	22	similarly	similarly	ADV
cana-735	205	23	to	to	ADP
cana-735	205	24	α	α	PRON
cana-735	205	25	,	,	PUNCT
cana-735	205	26	β	β	NOUN
cana-735	205	27	,	,	PUNCT
cana-735	205	28	and	and	CCONJ
cana-735	205	29	γ	γ	X
cana-735	205	30	in	in	ADP
cana-735	205	31	equation	equation	NOUN
cana-735	205	32	(	(	PUNCT
cana-735	205	33	2	2	NUM
cana-735	205	34	)	)	PUNCT
cana-735	205	35	.	.	PUNCT
cana-735	206	1	communications	communication	NOUN
cana-735	206	2	on	on	ADP
cana-735	206	3	applied	apply	VERB
cana-735	206	4	nonlinear	nonlinear	ADJ
cana-735	206	5	analysis	analysis	NOUN
cana-735	206	6	issn	issn	NOUN
cana-735	206	7	:	:	PUNCT
cana-735	206	8	1074	1074	NUM
cana-735	206	9	-	-	PUNCT
cana-735	206	10	133x	133x	NUM
cana-735	206	11	vol	vol	NOUN
cana-735	206	12	31	31	NUM
cana-735	206	13	no	no	NOUN
cana-735	206	14	.	.	PUNCT
cana-735	207	1	3s	3s	NUM
cana-735	207	2	(	(	PUNCT
cana-735	207	3	2024	2024	NUM
cana-735	207	4	)	)	PUNCT
cana-735	207	5	113	113	NUM
cana-735	207	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-735	207	7	(	(	PUNCT
cana-735	207	8	i	i	NOUN
cana-735	207	9	)	)	PUNCT
cana-735	207	10	in	in	ADP
cana-735	207	11	contrast	contrast	NOUN
cana-735	207	12	to	to	PART
cana-735	207	13	method	method	VERB
cana-735	207	14	one	one	NUM
cana-735	207	15	,	,	PUNCT
cana-735	207	16	shape	shape	NOUN
cana-735	207	17	parameter	parameter	NOUN
cana-735	207	18	in	in	ADP
cana-735	207	19	fuzziness	fuzziness	NOUN
cana-735	207	20	reflected	reflect	VERB
cana-735	207	21	number	number	NOUN
cana-735	207	22	of	of	ADP
cana-735	207	23	failure	failure	NOUN
cana-735	207	24	same	same	ADJ
cana-735	207	25	form	form	NOUN
cana-735	207	26	of	of	ADP
cana-735	207	27	fuzzy	fuzzy	ADJ
cana-735	207	28	numbers	number	NOUN
cana-735	207	29	,	,	PUNCT
cana-735	207	30	when	when	SCONJ
cana-735	207	31	the	the	DET
cana-735	207	32	number	number	NOUN
cana-735	207	33	of	of	ADP
cana-735	207	34	failures	failure	NOUN
cana-735	207	35	is	be	AUX
cana-735	207	36	plotted	plot	VERB
cana-735	207	37	against	against	ADP
cana-735	207	38	time	time	NOUN
cana-735	207	39	,	,	PUNCT
cana-735	207	40	the	the	DET
cana-735	207	41	curves	curve	NOUN
cana-735	207	42	are	be	AUX
cana-735	207	43	"	"	PUNCT
cana-735	207	44	exponentially	exponentially	ADV
cana-735	207	45	"	"	PUNCT
cana-735	207	46	spread	spread	VERB
cana-735	207	47	in	in	ADP
cana-735	207	48	place	place	NOUN
cana-735	207	49	predicted	predict	VERB
cana-735	207	50	by	by	ADP
cana-735	207	51	theory	theory	NOUN
cana-735	207	52	.	.	PUNCT
cana-735	208	1	(	(	PUNCT
cana-735	208	2	ii	ii	NOUN
cana-735	208	3	)	)	PUNCT
cana-735	208	4	second	second	ADJ
cana-735	208	5	method	method	NOUN
cana-735	208	6	is	be	AUX
cana-735	208	7	displayed	display	VERB
cana-735	208	8	.	.	PUNCT
cana-735	209	1	figure	figure	VERB
cana-735	209	2	3	3	NUM
cana-735	209	3	graph	graph	NOUN
cana-735	209	4	effectively	effectively	ADV
cana-735	209	5	depict	depict	VERB
cana-735	209	6	the	the	DET
cana-735	209	7	failure	failure	NOUN
cana-735	209	8	numbers	number	NOUN
cana-735	209	9	with	with	ADP
cana-735	209	10	the	the	DET
cana-735	209	11	parameter	parameter	NOUN
cana-735	209	12	's	's	PART
cana-735	209	13	end	end	NOUN
cana-735	209	14	points	point	NOUN
cana-735	209	15	and	and	CCONJ
cana-735	209	16	core	core	NOUN
cana-735	209	17	,	,	PUNCT
cana-735	209	18	trfns	trfns	NOUN
cana-735	209	19	mathematics	mathematic	NOUN
cana-735	209	20	2021	2021	NUM
cana-735	209	21	,	,	PUNCT
cana-735	209	22	9	9	NUM
cana-735	209	23	,	,	PUNCT
cana-735	209	24	2858	2858	NUM
cana-735	209	25	10	10	NUM
cana-735	209	26	of	of	ADP
cana-735	209	27	19	19	NUM
cana-735	209	28	.	.	PUNCT
cana-735	210	1	more	more	ADV
cana-735	210	2	precisely	precisely	ADV
cana-735	210	3	,	,	PUNCT
cana-735	210	4	these	these	DET
cana-735	210	5	plots	plot	NOUN
cana-735	210	6	show	show	VERB
cana-735	210	7	the	the	DET
cana-735	210	8	number	number	NOUN
cana-735	210	9	of	of	ADP
cana-735	210	10	failure	failure	NOUN
cana-735	210	11	bands	band	NOUN
cana-735	210	12	for	for	ADP
cana-735	210	13	dgm	dgm	PROPN
cana-735	210	14	,	,	PUNCT
cana-735	210	15	which	which	PRON
cana-735	210	16	can	can	AUX
cana-735	210	17	be	be	AUX
cana-735	210	18	obtained	obtain	VERB
cana-735	210	19	analytically	analytically	ADV
cana-735	210	20	from	from	ADP
cana-735	210	21	equation	equation	NOUN
cana-735	210	22	(	(	PUNCT
cana-735	210	23	8)	8)	NUM
cana-735	210	24	and	and	CCONJ
cana-735	210	25	is	be	AUX
cana-735	210	26	like	like	ADP
cana-735	210	27	the	the	DET
cana-735	210	28	α	α	PROPN
cana-735	210	29	cut	cut	NOUN
cana-735	210	30	's	's	PART
cana-735	210	31	equations	equation	NOUN
cana-735	210	32	(	(	PUNCT
cana-735	210	33	10	10	NUM
cana-735	210	34	)	)	PUNCT
cana-735	210	35	and	and	CCONJ
cana-735	210	36	(	(	PUNCT
cana-735	210	37	14	14	NUM
cana-735	210	38	)	)	PUNCT
cana-735	210	39	in	in	ADP
cana-735	210	40	that	that	SCONJ
cana-735	210	41	it	it	PRON
cana-735	210	42	has	have	AUX
cana-735	210	43	a	a	DET
cana-735	210	44	power	power	NOUN
cana-735	210	45	curve	curve	NOUN
cana-735	210	46	.	.	PUNCT
cana-735	211	1	this	this	PRON
cana-735	211	2	corresponds	correspond	VERB
cana-735	211	3	sharply	sharply	ADV
cana-735	211	4	parameterized	parameterized	ADJ
cana-735	211	5	curve	curve	NOUN
cana-735	211	6	for	for	ADP
cana-735	211	7	dgm	dgm	PROPN
cana-735	211	8	's	's	PART
cana-735	211	9	failure	failure	NOUN
cana-735	211	10	numbers	number	NOUN
cana-735	211	11	[	[	X
cana-735	211	12	36	36	NUM
cana-735	211	13	]	]	PUNCT
cana-735	211	14	.	.	PUNCT
cana-735	212	1	the	the	DET
cana-735	212	2	αcut	αcut	PROPN
cana-735	212	3	approach	approach	NOUN
cana-735	212	4	,	,	PUNCT
cana-735	212	5	which	which	PRON
cana-735	212	6	is	be	AUX
cana-735	212	7	the	the	DET
cana-735	212	8	second	second	ADJ
cana-735	212	9	choice	choice	NOUN
cana-735	212	10	,	,	PUNCT
cana-735	212	11	likewise	likewise	ADV
cana-735	212	12	follows	follow	VERB
cana-735	212	13	same	same	ADJ
cana-735	212	14	logic	logic	NOUN
cana-735	212	15	,	,	PUNCT
cana-735	212	16	even	even	ADV
cana-735	212	17	though	though	SCONJ
cana-735	212	18	the	the	DET
cana-735	212	19	graphs	graph	NOUN
cana-735	212	20	are	be	AUX
cana-735	212	21	not	not	PART
cana-735	212	22	displayed	display	VERB
cana-735	212	23	here	here	ADV
cana-735	212	24	.	.	PUNCT
cana-735	213	1	5	5	X
cana-735	213	2	.	.	X
cana-735	213	3	results	result	NOUN
cana-735	213	4	of	of	ADP
cana-735	213	5	dgm	dgm	PROPN
cana-735	213	6	distribution	distribution	NOUN
cana-735	213	7	by	by	ADP
cana-735	213	8	𝛂	𝛂	PROPN
cana-735	213	9	-cut	-cut	ADJ
cana-735	213	10	method	method	NOUN
cana-735	213	11	plotting	plot	VERB
cana-735	213	12	results	result	NOUN
cana-735	213	13	of	of	ADP
cana-735	213	14	the	the	DET
cana-735	213	15	α	α	PROPN
cana-735	213	16	−cut	−cut	ADJ
cana-735	213	17	method	method	NOUN
cana-735	213	18	,	,	PUNCT
cana-735	213	19	the	the	DET
cana-735	213	20	number	number	NOUN
cana-735	213	21	of	of	ADP
cana-735	213	22	failures	failure	NOUN
cana-735	213	23	yields	yield	NOUN
cana-735	213	24	following	follow	VERB
cana-735	213	25	results	result	NOUN
cana-735	213	26	.	.	PUNCT
cana-735	214	1	remember	remember	VERB
cana-735	214	2	that	that	SCONJ
cana-735	214	3	α	α	PROPN
cana-735	214	4	−cut	−cut	VERB
cana-735	214	5	of	of	ADP
cana-735	214	6	the	the	DET
cana-735	214	7	trfn	trfn	NOUN
cana-735	214	8	=	=	PUNCT
cana-735	215	1	𝒜α	𝒜α	PROPN
cana-735	215	2	=[	=[	NOUN
cana-735	215	3	𝒶1	𝒶1	NOUN
cana-735	215	4	α	α	NOUN
cana-735	215	5	,	,	PUNCT
cana-735	215	6	𝒶2	𝒶2	PROPN
cana-735	215	7	α]=	α]=	PROPN
cana-735	216	1	[	[	X
cana-735	216	2	(	(	PUNCT
cana-735	216	3	q	q	ADJ
cana-735	216	4	-	-	PUNCT
cana-735	216	5	p	p	ADJ
cana-735	216	6	)	)	PUNCT
cana-735	216	7	α	α	NOUN
cana-735	217	1	+	+	X
cana-735	217	2	p	p	X
cana-735	217	3	,	,	PUNCT
cana-735	217	4	(	(	PUNCT
cana-735	217	5	q	q	NOUN
cana-735	217	6	-	-	PUNCT
cana-735	217	7	r	r	NOUN
cana-735	217	8	)	)	PUNCT
cana-735	217	9	α	α	NOUN
cana-735	218	1	+	+	NOUN
cana-735	218	2	r	r	NOUN
cana-735	218	3	]	]	X
cana-735	218	4	.	.	PUNCT
cana-735	219	1	consequently	consequently	ADV
cana-735	219	2	,	,	PUNCT
cana-735	219	3	we	we	PRON
cana-735	219	4	obtain	obtain	VERB
cana-735	219	5	the	the	DET
cana-735	219	6	α	α	NOUN
cana-735	219	7	−cut	−cut	VERB
cana-735	219	8	as	as	ADP
cana-735	219	9	δ̅	δ̅	PROPN
cana-735	219	10	=	=	SYM
cana-735	219	11	(	(	PUNCT
cana-735	219	12	α	α	X
cana-735	219	13	=	=	SYM
cana-735	219	14	1.35	1.35	NUM
cana-735	219	15	;	;	PUNCT
cana-735	219	16	β	β	X
cana-735	219	17	=	=	SYM
cana-735	219	18	1.45	1.45	NUM
cana-735	219	19	;	;	PUNCT
cana-735	219	20	γ	γ	X
cana-735	219	21	=	=	PROPN
cana-735	219	22	1.75	1.75	NUM
cana-735	219	23	)	)	PUNCT
cana-735	219	24	as	as	ADP
cana-735	219	25	the	the	DET
cana-735	219	26	fn	fn	NOUN
cana-735	219	27	shape	shape	NOUN
cana-735	219	28	parameter	parameter	NOUN
cana-735	219	29	.	.	PUNCT
cana-735	220	1	then	then	ADV
cana-735	220	2	α	α	PRON
cana-735	220	3	−cut	−cut	VERB
cana-735	220	4	δα	δα	X
cana-735	220	5	=	=	PUNCT
cana-735	221	1	[	[	X
cana-735	221	2	1.25	1.25	NUM
cana-735	221	3	+	+	CCONJ
cana-735	221	4	0.30α	0.30α	NOUN
cana-735	221	5	,	,	PUNCT
cana-735	221	6	1.85	1.85	NUM
cana-735	221	7	−	−	NOUN
cana-735	221	8	0.30α	0.30α	NUM
cana-735	221	9	]	]	PUNCT
cana-735	221	10	(	(	PUNCT
cana-735	221	11	13	13	NUM
cana-735	221	12	)	)	PUNCT
cana-735	221	13	ddf	ddf	NOUN
cana-735	221	14	(	(	PUNCT
cana-735	221	15	dagum	dagum	NOUN
cana-735	221	16	density	density	NOUN
cana-735	221	17	function	function	NOUN
cana-735	221	18	)	)	PUNCT
cana-735	221	19	f(t)α	f(t)α	PROPN
cana-735	221	20	,	,	PUNCT
cana-735	221	21	dcf	dcf	X
cana-735	221	22	(	(	PUNCT
cana-735	221	23	dagum	dagum	NOUN
cana-735	221	24	cumulative	cumulative	ADJ
cana-735	221	25	distribution	distribution	NOUN
cana-735	221	26	)	)	PUNCT
cana-735	221	27	f(t)α	f(t)α	PROPN
cana-735	221	28	is	be	AUX
cana-735	221	29	obtained	obtain	VERB
cana-735	221	30	by	by	ADP
cana-735	221	31	taking	take	VERB
cana-735	221	32	α	α	PROPN
cana-735	221	33	−cut	−cut	ADJ
cana-735	221	34	from	from	ADP
cana-735	221	35	equation	equation	NOUN
cana-735	221	36	,	,	PUNCT
cana-735	221	37	(	(	PUNCT
cana-735	221	38	7	7	NUM
cana-735	221	39	)	)	PUNCT
cana-735	221	40	and	and	CCONJ
cana-735	221	41	using	use	VERB
cana-735	221	42	fuzzy	fuzzy	ADJ
cana-735	221	43	arithmetic	arithmetic	ADJ
cana-735	221	44	to	to	PART
cana-735	221	45	substitute	substitute	VERB
cana-735	221	46	it	it	PRON
cana-735	221	47	into	into	ADP
cana-735	221	48	equations	equation	NOUN
cana-735	221	49	(	(	PUNCT
cana-735	221	50	5	5	NUM
cana-735	221	51	)	)	PUNCT
cana-735	221	52	and	and	CCONJ
cana-735	221	53	(	(	PUNCT
cana-735	221	54	6	6	NUM
cana-735	221	55	)	)	PUNCT
cana-735	221	56	.	.	PUNCT
cana-735	222	1	f(x)α	f(x)α	PROPN
cana-735	223	1	=	=	PRON
cana-735	223	2	[	[	PUNCT
cana-735	223	3	(	(	PUNCT
cana-735	223	4	1.35	1.35	NUM
cana-735	223	5	+	+	NUM
cana-735	223	6	0.30α	0.30α	NOUN
cana-735	223	7	)	)	PUNCT
cana-735	223	8	x−2	x−2	PROPN
cana-735	224	1	(	(	PUNCT
cana-735	224	2	1	1	NUM
cana-735	224	3	+	+	CCONJ
cana-735	224	4	x−1)−(1	x−1)−(1	PROPN
cana-735	224	5	+	+	PROPN
cana-735	224	6	1.25	1.25	NUM
cana-735	224	7	+	+	NOUN
cana-735	224	8	0.30α	0.30α	NOUN
cana-735	224	9	)	)	PUNCT
cana-735	224	10	,	,	PUNCT
cana-735	224	11	(	(	PUNCT
cana-735	224	12	1.85	1.85	NUM
cana-735	224	13	−	−	NUM
cana-735	224	14	0.30	0.30	NUM
cana-735	224	15	α	α	NOUN
cana-735	224	16	)	)	PUNCT
cana-735	225	1	x−2	x−2	PROPN
cana-735	225	2	(	(	PUNCT
cana-735	225	3	1	1	NUM
cana-735	226	1	+	+	CCONJ
cana-735	226	2	x−1)−(1	x−1)−(1	PROPN
cana-735	226	3	+	+	PROPN
cana-735	226	4	1.85−0.30	1.85−0.30	PROPN
cana-735	226	5	α	α	NOUN
cana-735	226	6	)	)	PUNCT
cana-735	226	7	f(x)α	f(x)α	PROPN
cana-735	227	1	=	=	X
cana-735	227	2	[	[	PUNCT
cana-735	227	3	(	(	PUNCT
cana-735	227	4	1	1	NUM
cana-735	227	5	+	+	NUM
cana-735	227	6	x−1)−(1.25	x−1)−(1.25	NUM
cana-735	227	7	+	+	NOUN
cana-735	227	8	0.30α	0.30α	NOUN
cana-735	227	9	)	)	PUNCT
cana-735	227	10	,	,	PUNCT
cana-735	227	11	(	(	PUNCT
cana-735	227	12	1	1	NUM
cana-735	227	13	+	+	NUM
cana-735	227	14	x−1)−(1.25	x−1)−(1.25	NUM
cana-735	227	15	+	+	NOUN
cana-735	227	16	0.30α	0.30α	NOUN
cana-735	227	17	)	)	PUNCT
cana-735	227	18	]	]	PUNCT
cana-735	227	19	(	(	PUNCT
cana-735	227	20	14	14	NUM
cana-735	227	21	)	)	PUNCT
cana-735	227	22	and	and	CCONJ
cana-735	227	23	the	the	DET
cana-735	227	24	hazard	hazard	NOUN
cana-735	227	25	function	function	NOUN
cana-735	227	26	h(t)α	h(t)α	PROPN
cana-735	227	27	is	be	AUX
cana-735	227	28	obtained	obtain	VERB
cana-735	227	29	by	by	ADP
cana-735	227	30	,	,	PUNCT
cana-735	227	31	h(x	h(x	PROPN
cana-735	227	32	)	)	PUNCT
cana-735	228	1	=	=	PUNCT
cana-735	229	1	[	[	PUNCT
cana-735	229	2	(	(	PUNCT
cana-735	229	3	1.25	1.25	NUM
cana-735	229	4	+	+	NOUN
cana-735	229	5	0.30	0.30	NUM
cana-735	229	6	α)x−(2)(1	α)x−(2)(1	NOUN
cana-735	229	7	+	+	CCONJ
cana-735	229	8	x−1)−(1+(1.25	x−1)−(1+(1.25	PROPN
cana-735	229	9	+	+	PROPN
cana-735	229	10	0.30	0.30	NUM
cana-735	229	11	α))[1	α))[1	PRON
cana-735	229	12	−	−	PROPN
cana-735	229	13	(	(	PUNCT
cana-735	229	14	1	1	NUM
cana-735	229	15	+	+	CCONJ
cana-735	229	16	x−1)−(1.25	x−1)−(1.25	NUM
cana-735	229	17	+	+	NOUN
cana-735	229	18	0.30	0.30	NUM
cana-735	229	19	α	α	NOUN
cana-735	229	20	)	)	PUNCT
cana-735	229	21	]	]	PUNCT
cana-735	229	22	−1	−1	NOUN
cana-735	229	23	,	,	PUNCT
cana-735	229	24	(	(	PUNCT
cana-735	229	25	1.85	1.85	NUM
cana-735	229	26	−	−	NUM
cana-735	229	27	0.30α	0.30α	NUM
cana-735	229	28	)	)	PUNCT
cana-735	229	29	x−(2)(1	x−(2)(1	ADP
cana-735	229	30	+	+	CCONJ
cana-735	229	31	x−1)−(1	x−1)−(1	PROPN
cana-735	229	32	+	+	PROPN
cana-735	229	33	1.85−0.30α	1.85−0.30α	NUM
cana-735	229	34	)	)	PUNCT
cana-735	230	1	[	[	X
cana-735	230	2	1	1	NUM
cana-735	230	3	−	−	NOUN
cana-735	230	4	(	(	PUNCT
cana-735	230	5	1	1	NUM
cana-735	230	6	+	+	NUM
cana-735	230	7	x−1)−(1.85−0.30α	x−1)−(1.85−0.30α	NUM
cana-735	230	8	)	)	PUNCT
cana-735	231	1	]	]	X
cana-735	231	2	−1	−1	NOUN
cana-735	231	3	(	(	PUNCT
cana-735	231	4	15	15	NUM
cana-735	231	5	)	)	PUNCT
cana-735	231	6	from	from	ADP
cana-735	231	7	the	the	DET
cana-735	231	8	equation	equation	NOUN
cana-735	231	9	(	(	PUNCT
cana-735	231	10	9	9	X
cana-735	231	11	)	)	PUNCT
cana-735	231	12	integrating	integrate	VERB
cana-735	231	13	both	both	DET
cana-735	231	14	sides	side	NOUN
cana-735	231	15	we	we	PRON
cana-735	231	16	get	get	VERB
cana-735	231	17	,	,	PUNCT
cana-735	231	18	n(x	n(x	PROPN
cana-735	231	19	)	)	PUNCT
cana-735	231	20	=	=	PUNCT
cana-735	232	1	[	[	X
cana-735	232	2	x2(1.25	x2(1.25	X
cana-735	232	3	+	+	PROPN
cana-735	232	4	1.30	1.30	NUM
cana-735	232	5	α	α	NOUN
cana-735	232	6	)	)	PUNCT
cana-735	232	7	,	,	PUNCT
cana-735	232	8	x2(1.85−0.30)α	x2(1.85−0.30)α	NUM
cana-735	232	9	]	]	X
cana-735	232	10	(	(	PUNCT
cana-735	232	11	16	16	NUM
cana-735	232	12	)	)	PUNCT
cana-735	232	13	hence	hence	ADV
cana-735	232	14	by	by	ADP
cana-735	232	15	using	use	VERB
cana-735	232	16	α	α	PROPN
cana-735	232	17	−cut	−cut	PROPN
cana-735	232	18	,	,	PUNCT
cana-735	232	19	we	we	PRON
cana-735	232	20	obtain	obtain	VERB
cana-735	232	21	the	the	DET
cana-735	232	22	trfn	trfn	NOUN
cana-735	232	23	which	which	PRON
cana-735	232	24	is	be	AUX
cana-735	232	25	comparable	comparable	ADJ
cana-735	232	26	to	to	ADP
cana-735	232	27	the	the	DET
cana-735	232	28	fn	fn	NOUN
cana-735	232	29	(	(	PUNCT
cana-735	232	30	p	p	X
cana-735	232	31	;	;	PUNCT
cana-735	232	32	q	q	ADJ
cana-735	232	33	;	;	PUNCT
cana-735	232	34	r	r	X
cana-735	232	35	)	)	PUNCT
cana-735	232	36	obtained	obtain	VERB
cana-735	232	37	by	by	ADP
cana-735	232	38	α	α	PROPN
cana-735	232	39	=	=	SYM
cana-735	232	40	min	min	NOUN
cana-735	232	41	n(x)α=0	n(x)α=0	NOUN
cana-735	233	1	=	=	PUNCT
cana-735	234	1	[	[	X
cana-735	234	2	x(1.25	x(1.25	PROPN
cana-735	234	3	+	+	PROPN
cana-735	234	4	1.30	1.30	NUM
cana-735	234	5	α	α	NOUN
cana-735	234	6	)	)	PUNCT
cana-735	234	7	,	,	PUNCT
cana-735	234	8	x(1.85−0.30	x(1.85−0.30	PROPN
cana-735	234	9	α	α	PROPN
cana-735	234	10	)	)	PUNCT
cana-735	234	11	]	]	PUNCT
cana-735	235	1	=	=	PUNCT
cana-735	235	2	x	x	SYM
cana-735	235	3	5	5	NUM
cana-735	235	4	4⁄	4⁄	NUM
cana-735	235	5	β	β	NOUN
cana-735	235	6	=	=	PUNCT
cana-735	235	7	min	min	NOUN
cana-735	235	8	n(x)α=1	n(x)α=1	X
cana-735	235	9	=	=	PUNCT
cana-735	236	1	[	[	X
cana-735	236	2	x(1.25	x(1.25	PROPN
cana-735	236	3	+	+	PROPN
cana-735	236	4	1.30	1.30	NUM
cana-735	236	5	α	α	NOUN
cana-735	236	6	)	)	PUNCT
cana-735	236	7	,	,	PUNCT
cana-735	236	8	x(1.85−0.30	x(1.85−0.30	PROPN
cana-735	236	9	α	α	PROPN
cana-735	236	10	)	)	PUNCT
cana-735	236	11	]	]	PUNCT
cana-735	237	1	=	=	PUNCT
cana-735	237	2	x	x	SYM
cana-735	237	3	31	31	NUM
cana-735	237	4	20⁄	20⁄	PROPN
cana-735	237	5	γ	γ	X
cana-735	237	6	=	=	SYM
cana-735	237	7	min	min	NOUN
cana-735	237	8	n(x)α=0	n(x)α=0	NOUN
cana-735	238	1	=	=	PUNCT
cana-735	239	1	[	[	X
cana-735	239	2	x(1.25	x(1.25	PROPN
cana-735	239	3	+	+	PROPN
cana-735	239	4	1.30	1.30	NUM
cana-735	239	5	α	α	NOUN
cana-735	239	6	)	)	PUNCT
cana-735	239	7	,	,	PUNCT
cana-735	239	8	x(1.85−0.30	x(1.85−0.30	PROPN
cana-735	239	9	α	α	PROPN
cana-735	239	10	)	)	PUNCT
cana-735	239	11	]	]	PUNCT
cana-735	240	1	=	=	PUNCT
cana-735	240	2	x	x	SYM
cana-735	240	3	37	37	NUM
cana-735	240	4	20⁄	20⁄	PROPN
cana-735	240	5	communications	communication	NOUN
cana-735	240	6	on	on	ADP
cana-735	240	7	applied	apply	VERB
cana-735	240	8	nonlinear	nonlinear	ADJ
cana-735	240	9	analysis	analysis	NOUN
cana-735	240	10	issn	issn	NOUN
cana-735	240	11	:	:	PUNCT
cana-735	240	12	1074	1074	NUM
cana-735	240	13	-	-	PUNCT
cana-735	240	14	133x	133x	NUM
cana-735	240	15	vol	vol	NOUN
cana-735	240	16	31	31	NUM
cana-735	240	17	no	no	NOUN
cana-735	240	18	.	.	PUNCT
cana-735	241	1	3s	3s	NUM
cana-735	241	2	(	(	PUNCT
cana-735	241	3	2024	2024	NUM
cana-735	241	4	)	)	PUNCT
cana-735	241	5	114	114	NUM
cana-735	241	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-735	241	7	figure	figure	NOUN
cana-735	241	8	3	3	NUM
cana-735	241	9	density	density	NOUN
cana-735	241	10	function	function	NOUN
cana-735	241	11	in	in	ADP
cana-735	241	12	time	time	NOUN
cana-735	241	13	series	series	PROPN
cana-735	241	14	δ̅	δ̅	PROPN
cana-735	241	15	=	=	PUNCT
cana-735	241	16	(	(	PUNCT
cana-735	241	17	α	α	X
cana-735	241	18	=	=	SYM
cana-735	241	19	1.35	1.35	NUM
cana-735	241	20	;	;	PUNCT
cana-735	241	21	β	β	X
cana-735	241	22	=	=	SYM
cana-735	241	23	1.45	1.45	NUM
cana-735	241	24	;	;	PUNCT
cana-735	241	25	γ	γ	X
cana-735	241	26	=	=	SYM
cana-735	241	27	1.75	1.75	NUM
cana-735	241	28	)	)	PUNCT
cana-735	241	29	and	and	CCONJ
cana-735	241	30	δ	δ	PROPN
cana-735	241	31	=	=	PRON
cana-735	241	32	(	(	PUNCT
cana-735	241	33	α	α	X
cana-735	241	34	=	=	SYM
cana-735	241	35	2.55	2.55	NUM
cana-735	241	36	;	;	PUNCT
cana-735	241	37	β	β	X
cana-735	241	38	=	=	SYM
cana-735	241	39	2.70	2.70	NUM
cana-735	241	40	;	;	PUNCT
cana-735	241	41	γ	γ	X
cana-735	241	42	=	=	SYM
cana-735	241	43	2.85	2.85	NUM
cana-735	241	44	)	)	PUNCT
cana-735	241	45	figure	figure	NOUN
cana-735	241	46	4	4	NUM
cana-735	241	47	cumulative	cumulative	ADJ
cana-735	241	48	distribution	distribution	NOUN
cana-735	241	49	function	function	NOUN
cana-735	241	50	in	in	ADP
cana-735	241	51	time	time	NOUN
cana-735	241	52	series	series	PROPN
cana-735	241	53	δ̅	δ̅	PROPN
cana-735	241	54	=	=	PUNCT
cana-735	241	55	(	(	PUNCT
cana-735	241	56	α	α	X
cana-735	241	57	=	=	SYM
cana-735	241	58	1.35	1.35	NUM
cana-735	241	59	;	;	PUNCT
cana-735	241	60	β	β	X
cana-735	241	61	=	=	SYM
cana-735	241	62	1.45	1.45	NUM
cana-735	241	63	;	;	PUNCT
cana-735	241	64	γ	γ	X
cana-735	241	65	=	=	SYM
cana-735	241	66	1.75	1.75	NUM
cana-735	241	67	)	)	PUNCT
cana-735	241	68	and	and	CCONJ
cana-735	241	69	δ	δ	PROPN
cana-735	241	70	=	=	PRON
cana-735	241	71	(	(	PUNCT
cana-735	241	72	α	α	X
cana-735	241	73	=	=	SYM
cana-735	241	74	2.55	2.55	NUM
cana-735	241	75	;	;	PUNCT
cana-735	241	76	β	β	X
cana-735	241	77	=	=	SYM
cana-735	241	78	2.70	2.70	NUM
cana-735	241	79	;	;	PUNCT
cana-735	241	80	γ	γ	X
cana-735	241	81	=	=	NOUN
cana-735	241	82	2.85	2.85	NUM
cana-735	241	83	)	)	PUNCT
cana-735	241	84	.	.	PUNCT
cana-735	242	1	figure	figure	VERB
cana-735	242	2	5	5	NUM
cana-735	242	3	hazard	hazard	NOUN
cana-735	242	4	function	function	NOUN
cana-735	242	5	and	and	CCONJ
cana-735	242	6	the	the	DET
cana-735	242	7	number	number	NOUN
cana-735	242	8	of	of	ADP
cana-735	242	9	failures	failure	NOUN
cana-735	242	10	δ̅	δ̅	ADJ
cana-735	242	11	=	=	PUNCT
cana-735	242	12	(	(	PUNCT
cana-735	242	13	α	α	X
cana-735	242	14	=	=	SYM
cana-735	242	15	1.35	1.35	NUM
cana-735	242	16	;	;	PUNCT
cana-735	242	17	β	β	X
cana-735	242	18	=	=	SYM
cana-735	242	19	1.45	1.45	NUM
cana-735	242	20	;	;	PUNCT
cana-735	242	21	γ	γ	X
cana-735	242	22	=	=	SYM
cana-735	242	23	1.75	1.75	NUM
cana-735	242	24	)	)	PUNCT
cana-735	242	25	and	and	CCONJ
cana-735	242	26	δ	δ	PROPN
cana-735	242	27	=	=	PRON
cana-735	242	28	(	(	PUNCT
cana-735	242	29	α	α	X
cana-735	242	30	=	=	SYM
cana-735	242	31	2.55	2.55	NUM
cana-735	242	32	;	;	PUNCT
cana-735	242	33	β	β	X
cana-735	242	34	=	=	SYM
cana-735	242	35	2.70	2.70	NUM
cana-735	242	36	;	;	PUNCT
cana-735	242	37	γ	γ	X
cana-735	242	38	=	=	NOUN
cana-735	242	39	2.85	2.85	NUM
cana-735	242	40	)	)	PUNCT
cana-735	242	41	0	0	NUM
cana-735	242	42	0.2	0.2	NUM
cana-735	242	43	0.4	0.4	NUM
cana-735	242	44	0.6	0.6	NUM
cana-735	242	45	0.8	0.8	NUM
cana-735	242	46	1	1	NUM
cana-735	242	47	1.2	1.2	NUM
cana-735	242	48	1.4	1.4	NUM
cana-735	242	49	1.6	1.6	NUM
cana-735	242	50	0	0	NUM
cana-735	242	51	0.5	0.5	NUM
cana-735	242	52	1	1	NUM
cana-735	242	53	1.5	1.5	NUM
cana-735	242	54	2	2	NUM
cana-735	242	55	2.5	2.5	NUM
cana-735	242	56	pdf	pdf	NOUN
cana-735	242	57	with	with	ADP
cana-735	242	58	shape	shape	NOUN
cana-735	242	59	parameter	parameter	NOUN
cana-735	242	60	0	0	NUM
cana-735	242	61	0.2	0.2	NUM
cana-735	242	62	0.4	0.4	NUM
cana-735	242	63	0.6	0.6	NUM
cana-735	242	64	0.8	0.8	NUM
cana-735	242	65	1	1	NUM
cana-735	242	66	1.2	1.2	NUM
cana-735	242	67	0	0	NUM
cana-735	242	68	0.5	0.5	NUM
cana-735	242	69	1	1	NUM
cana-735	242	70	1.5	1.5	NUM
cana-735	242	71	2	2	NUM
cana-735	242	72	2.5	2.5	NUM
cana-735	242	73	cumulative	cumulative	ADJ
cana-735	242	74	distribution	distribution	NOUN
cana-735	242	75	with	with	ADP
cana-735	242	76	shape	shape	NOUN
cana-735	242	77	parameter	parameter	NOUN
cana-735	242	78	0	0	NUM
cana-735	242	79	0.2	0.2	NUM
cana-735	242	80	0.4	0.4	NUM
cana-735	242	81	0.6	0.6	NUM
cana-735	242	82	0.8	0.8	NUM
cana-735	242	83	1	1	NUM
cana-735	242	84	1.2	1.2	NUM
cana-735	242	85	1.4	1.4	NUM
cana-735	242	86	1.6	1.6	NUM
cana-735	242	87	1.8	1.8	NUM
cana-735	242	88	2	2	NUM
cana-735	242	89	0	0	NUM
cana-735	242	90	0.5	0.5	NUM
cana-735	242	91	1	1	NUM
cana-735	242	92	1.5	1.5	NUM
cana-735	242	93	2	2	NUM
cana-735	242	94	2.5	2.5	NUM
cana-735	242	95	hazard	hazard	NOUN
cana-735	242	96	rate	rate	NOUN
cana-735	242	97	function	function	NOUN
cana-735	242	98	with	with	ADP
cana-735	242	99	various	various	ADJ
cana-735	242	100	shape	shape	NOUN
cana-735	242	101	parameter	parameter	NOUN
cana-735	242	102	communications	communication	NOUN
cana-735	242	103	on	on	ADP
cana-735	242	104	applied	apply	VERB
cana-735	242	105	nonlinear	nonlinear	ADJ
cana-735	242	106	analysis	analysis	NOUN
cana-735	242	107	issn	issn	NOUN
cana-735	242	108	:	:	PUNCT
cana-735	242	109	1074	1074	NUM
cana-735	242	110	-	-	PUNCT
cana-735	242	111	133x	133x	NUM
cana-735	242	112	vol	vol	NOUN
cana-735	242	113	31	31	NUM
cana-735	242	114	no	no	NOUN
cana-735	242	115	.	.	PUNCT
cana-735	243	1	3s	3s	NUM
cana-735	243	2	(	(	PUNCT
cana-735	243	3	2024	2024	NUM
cana-735	243	4	)	)	PUNCT
cana-735	243	5	115	115	NUM
cana-735	243	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-735	243	7	6	6	NUM
cana-735	243	8	.	.	PUNCT
cana-735	243	9	results	result	VERB
cana-735	243	10	discussions	discussion	NOUN
cana-735	243	11	the	the	DET
cana-735	243	12	results	result	NOUN
cana-735	243	13	are	be	AUX
cana-735	243	14	numerically	numerically	ADV
cana-735	243	15	demonstrated	demonstrate	VERB
cana-735	243	16	to	to	PART
cana-735	243	17	increase	increase	VERB
cana-735	243	18	the	the	DET
cana-735	243	19	understanding	understanding	NOUN
cana-735	243	20	of	of	ADP
cana-735	243	21	the	the	DET
cana-735	243	22	above	above	ADJ
cana-735	243	23	conclusion	conclusion	NOUN
cana-735	243	24	by	by	ADP
cana-735	243	25	using	use	VERB
cana-735	243	26	as	as	ADP
cana-735	243	27	δ̅	δ̅	PROPN
cana-735	243	28	=	=	PUNCT
cana-735	243	29	(	(	PUNCT
cana-735	243	30	α	α	X
cana-735	243	31	=	=	SYM
cana-735	243	32	1.35	1.35	NUM
cana-735	243	33	;	;	PUNCT
cana-735	243	34	β	β	X
cana-735	243	35	=	=	SYM
cana-735	243	36	1.45	1.45	NUM
cana-735	243	37	;	;	PUNCT
cana-735	243	38	γ	γ	X
cana-735	243	39	=	=	SYM
cana-735	243	40	1.75	1.75	NUM
cana-735	243	41	)	)	PUNCT
cana-735	243	42	and	and	CCONJ
cana-735	243	43	δ	δ	PROPN
cana-735	243	44	=	=	PRON
cana-735	243	45	(	(	PUNCT
cana-735	243	46	α	α	X
cana-735	243	47	=	=	SYM
cana-735	243	48	2.55	2.55	NUM
cana-735	243	49	;	;	PUNCT
cana-735	243	50	β	β	X
cana-735	243	51	=	=	SYM
cana-735	243	52	2.70	2.70	NUM
cana-735	243	53	;	;	PUNCT
cana-735	243	54	γ	γ	X
cana-735	243	55	=	=	PROPN
cana-735	243	56	2.85	2.85	NUM
cana-735	243	57	)	)	PUNCT
cana-735	243	58	,	,	PUNCT
cana-735	243	59	which	which	PRON
cana-735	243	60	reflect	reflect	VERB
cana-735	243	61	a	a	DET
cana-735	243	62	comparatively	comparatively	ADV
cana-735	243	63	small	small	ADJ
cana-735	243	64	and	and	CCONJ
cana-735	243	65	also	also	ADV
cana-735	243	66	large	large	ADJ
cana-735	243	67	shape	shape	NOUN
cana-735	243	68	parameter	parameter	NOUN
cana-735	243	69	respectively	respectively	ADV
cana-735	243	70	.	.	PUNCT
cana-735	244	1	the	the	DET
cana-735	244	2	trfn	trfn	NOUN
cana-735	244	3	is	be	AUX
cana-735	244	4	composed	compose	VERB
cana-735	244	5	α	α	X
cana-735	244	6	,	,	PUNCT
cana-735	244	7	β	β	NOUN
cana-735	244	8	,	,	PUNCT
cana-735	244	9	and	and	CCONJ
cana-735	244	10	γ	γ	X
cana-735	244	11	,	,	PUNCT
cana-735	244	12	the	the	DET
cana-735	244	13	tpfn	tpfn	NOUN
cana-735	244	14	parameters	parameter	NOUN
cana-735	244	15	that	that	PRON
cana-735	244	16	are	be	AUX
cana-735	244	17	defined	define	VERB
cana-735	244	18	in	in	ADP
cana-735	244	19	the	the	DET
cana-735	244	20	similar	similar	ADJ
cana-735	244	21	way	way	NOUN
cana-735	244	22	as	as	ADP
cana-735	244	23	α	α	NOUN
cana-735	244	24	,	,	PUNCT
cana-735	244	25	β	β	NOUN
cana-735	244	26	,	,	PUNCT
cana-735	244	27	and	and	CCONJ
cana-735	244	28	γ	γ	X
cana-735	244	29	in	in	ADP
cana-735	244	30	equation	equation	NOUN
cana-735	244	31	(	(	PUNCT
cana-735	244	32	1	1	NUM
cana-735	244	33	)	)	PUNCT
cana-735	244	34	.	.	PUNCT
cana-735	245	1	the	the	DET
cana-735	245	2	plots	plot	NOUN
cana-735	245	3	of	of	ADP
cana-735	245	4	these	these	DET
cana-735	245	5	trfns	trfns	NOUN
cana-735	245	6	displayed	display	VERB
cana-735	245	7	figures	figure	NOUN
cana-735	245	8	2	2	NUM
cana-735	245	9	and	and	CCONJ
cana-735	245	10	3	3	NUM
cana-735	245	11	,	,	PUNCT
cana-735	245	12	respectively	respectively	ADV
cana-735	245	13	.	.	PUNCT
cana-735	246	1	we	we	PRON
cana-735	246	2	suggested	suggest	VERB
cana-735	246	3	two	two	NUM
cana-735	246	4	methods	method	NOUN
cana-735	246	5	to	to	PART
cana-735	246	6	calculate	calculate	VERB
cana-735	246	7	failure	failure	NOUN
cana-735	246	8	numbers	number	NOUN
cana-735	246	9	:	:	PUNCT
cana-735	246	10	the	the	DET
cana-735	246	11	first	first	ADJ
cana-735	246	12	method	method	NOUN
cana-735	246	13	is	be	AUX
cana-735	246	14	straightforward	straightforward	ADJ
cana-735	246	15	and	and	CCONJ
cana-735	246	16	assumes	assume	VERB
cana-735	246	17	that	that	SCONJ
cana-735	246	18	the	the	DET
cana-735	246	19	shape	shape	NOUN
cana-735	246	20	parameter	parameter	NOUN
cana-735	246	21	's	's	PART
cana-735	246	22	fuzziness	fuzziness	NOUN
cana-735	246	23	extends	extend	VERB
cana-735	246	24	to	to	ADP
cana-735	246	25	failure	failure	NOUN
cana-735	246	26	numbers	number	NOUN
cana-735	246	27	with	with	ADP
cana-735	246	28	same	same	ADJ
cana-735	246	29	fuzzy	fuzzy	ADJ
cana-735	246	30	number	number	NOUN
cana-735	246	31	membership	membership	NOUN
cana-735	246	32	form	form	NOUN
cana-735	246	33	.	.	PUNCT
cana-735	247	1	method	method	PROPN
cana-735	247	2	two	two	NUM
cana-735	247	3	uses	use	VERB
cana-735	247	4	the	the	DET
cana-735	247	5	α	α	NOUN
cana-735	247	6	-	-	PUNCT
cana-735	247	7	cut	cut	VERB
cana-735	247	8	method	method	NOUN
cana-735	247	9	to	to	PART
cana-735	247	10	calculate	calculate	VERB
cana-735	247	11	the	the	DET
cana-735	247	12	number	number	NOUN
cana-735	247	13	of	of	ADP
cana-735	247	14	failures	failure	NOUN
cana-735	247	15	.	.	PUNCT
cana-735	248	1	to	to	PART
cana-735	248	2	broaden	broaden	VERB
cana-735	248	3	its	its	PRON
cana-735	248	4	application	application	NOUN
cana-735	248	5	to	to	ADP
cana-735	248	6	other	other	ADJ
cana-735	248	7	areas	area	NOUN
cana-735	248	8	,	,	PUNCT
cana-735	248	9	this	this	DET
cana-735	248	10	approach	approach	NOUN
cana-735	248	11	might	might	AUX
cana-735	248	12	be	be	AUX
cana-735	248	13	expanded	expand	VERB
cana-735	248	14	to	to	ADP
cana-735	248	15	the	the	DET
cana-735	248	16	dgm	dgm	PROPN
cana-735	248	17	distribution	distribution	NOUN
cana-735	248	18	with	with	ADP
cana-735	248	19	more	more	ADJ
cana-735	248	20	parameters	parameter	NOUN
cana-735	248	21	[	[	X
cana-735	248	22	37	37	NUM
cana-735	248	23	]	]	PUNCT
cana-735	248	24	.	.	PUNCT
cana-735	249	1	7	7	X
cana-735	249	2	.	.	X
cana-735	249	3	conclusions	conclusion	NOUN
cana-735	249	4	we	we	PRON
cana-735	249	5	examined	examine	VERB
cana-735	249	6	the	the	DET
cana-735	249	7	dgm	dgm	PROPN
cana-735	249	8	hazard	hazard	PROPN
cana-735	249	9	function	function	NOUN
cana-735	249	10	in	in	ADP
cana-735	249	11	this	this	DET
cana-735	249	12	study	study	NOUN
cana-735	249	13	to	to	PART
cana-735	249	14	calculate	calculate	VERB
cana-735	249	15	the	the	DET
cana-735	249	16	fuzzy	fuzzy	ADJ
cana-735	249	17	failure	failure	NOUN
cana-735	249	18	’s	’s	PART
cana-735	249	19	numbers	number	NOUN
cana-735	249	20	,	,	PUNCT
cana-735	249	21	a	a	DET
cana-735	249	22	fuzzy	fuzzy	ADJ
cana-735	249	23	shape	shape	NOUN
cana-735	249	24	parameter	parameter	NOUN
cana-735	249	25	is	be	AUX
cana-735	249	26	assumed	assume	VERB
cana-735	249	27	.	.	PUNCT
cana-735	250	1	in	in	ADP
cana-735	250	2	this	this	DET
cana-735	250	3	research	research	NOUN
cana-735	250	4	,	,	PUNCT
cana-735	250	5	we	we	PRON
cana-735	250	6	suggested	suggest	VERB
cana-735	250	7	two	two	NUM
cana-735	250	8	techniques	technique	NOUN
cana-735	250	9	to	to	PART
cana-735	250	10	work	work	VERB
cana-735	250	11	out	out	ADP
cana-735	250	12	the	the	DET
cana-735	250	13	number	number	NOUN
cana-735	250	14	of	of	ADP
cana-735	250	15	failures	failure	NOUN
cana-735	250	16	,	,	PUNCT
cana-735	250	17	(	(	PUNCT
cana-735	250	18	i	i	NOUN
cana-735	250	19	)	)	PUNCT
cana-735	250	20	the	the	DET
cana-735	250	21	first	first	ADJ
cana-735	250	22	approach	approach	NOUN
cana-735	250	23	is	be	AUX
cana-735	250	24	simple	simple	ADJ
cana-735	250	25	and	and	CCONJ
cana-735	250	26	assumes	assume	VERB
cana-735	250	27	that	that	SCONJ
cana-735	250	28	failure	failure	NOUN
cana-735	250	29	numbers	number	NOUN
cana-735	250	30	with	with	ADP
cana-735	250	31	the	the	DET
cana-735	250	32	same	same	ADJ
cana-735	250	33	fuzzy	fuzzy	ADJ
cana-735	250	34	number	number	NOUN
cana-735	250	35	membership	membership	NOUN
cana-735	250	36	form	form	NOUN
cana-735	250	37	is	be	AUX
cana-735	250	38	propagated	propagate	VERB
cana-735	250	39	by	by	ADP
cana-735	250	40	the	the	DET
cana-735	250	41	shape	shape	NOUN
cana-735	250	42	parameter	parameter	NOUN
cana-735	250	43	's	's	PART
cana-735	250	44	fuzziness	fuzziness	NOUN
cana-735	250	45	.	.	PUNCT
cana-735	251	1	(	(	PUNCT
cana-735	251	2	ii	ii	X
cana-735	251	3	)	)	PUNCT
cana-735	251	4	the	the	DET
cana-735	251	5	second	second	ADJ
cana-735	251	6	approach	approach	NOUN
cana-735	251	7	determines	determine	VERB
cana-735	251	8	failure	failure	NOUN
cana-735	251	9	numbers	number	NOUN
cana-735	251	10	by	by	ADP
cana-735	251	11	applying	apply	VERB
cana-735	251	12	the	the	DET
cana-735	251	13	α	α	NOUN
cana-735	251	14	-	-	PUNCT
cana-735	251	15	cut	cut	VERB
cana-735	251	16	technique	technique	NOUN
cana-735	251	17	.	.	PUNCT
cana-735	252	1	we	we	PRON
cana-735	252	2	showed	show	VERB
cana-735	252	3	that	that	SCONJ
cana-735	252	4	both	both	DET
cana-735	252	5	approaches	approach	NOUN
cana-735	252	6	worked	work	VERB
cana-735	252	7	well	well	ADV
cana-735	252	8	for	for	ADP
cana-735	252	9	figuring	figure	VERB
cana-735	252	10	out	out	ADP
cana-735	252	11	how	how	SCONJ
cana-735	252	12	many	many	ADJ
cana-735	252	13	times	time	NOUN
cana-735	252	14	the	the	DET
cana-735	252	15	system	system	NOUN
cana-735	252	16	in	in	ADP
cana-735	252	17	question	question	NOUN
cana-735	252	18	failed	fail	VERB
cana-735	252	19	.	.	PUNCT
cana-735	253	1	both	both	DET
cana-735	253	2	methods	method	NOUN
cana-735	253	3	show	show	VERB
cana-735	253	4	that	that	SCONJ
cana-735	253	5	the	the	DET
cana-735	253	6	ambiguity	ambiguity	NOUN
cana-735	253	7	(	(	PUNCT
cana-735	253	8	fuzziness	fuzziness	NOUN
cana-735	253	9	)	)	PUNCT
cana-735	253	10	of	of	ADP
cana-735	253	11	the	the	DET
cana-735	253	12	total	total	ADJ
cana-735	253	13	failure	failure	NOUN
cana-735	253	14	numbers	number	NOUN
cana-735	253	15	increased	increase	VERB
cana-735	253	16	when	when	SCONJ
cana-735	253	17	the	the	DET
cana-735	253	18	failures	failure	NOUN
cana-735	253	19	’	'	PUNCT
cana-735	253	20	function	function	NOUN
cana-735	253	21	is	be	AUX
cana-735	253	22	examined	examine	VERB
cana-735	253	23	as	as	ADP
cana-735	253	24	a	a	DET
cana-735	253	25	function	function	NOUN
cana-735	253	26	of	of	ADP
cana-735	253	27	time	time	NOUN
cana-735	253	28	.	.	PUNCT
cana-735	254	1	this	this	PRON
cana-735	254	2	demonstrates	demonstrate	VERB
cana-735	254	3	how	how	SCONJ
cana-735	254	4	form	form	NOUN
cana-735	254	5	parameter	parameter	NOUN
cana-735	254	6	uncertainty	uncertainty	NOUN
cana-735	254	7	affects	affect	VERB
cana-735	254	8	the	the	DET
cana-735	254	9	total	total	ADJ
cana-735	254	10	number	number	NOUN
cana-735	254	11	of	of	ADP
cana-735	254	12	failures	failure	NOUN
cana-735	254	13	;	;	PUNCT
cana-735	254	14	at	at	ADP
cana-735	254	15	large	large	ADJ
cana-735	254	16	x	x	ADJ
cana-735	254	17	values	value	NOUN
cana-735	254	18	,	,	PUNCT
cana-735	254	19	even	even	ADV
cana-735	254	20	a	a	DET
cana-735	254	21	little	little	ADJ
cana-735	254	22	amount	amount	NOUN
cana-735	254	23	of	of	ADP
cana-735	254	24	shape	shape	NOUN
cana-735	254	25	parameter	parameter	NOUN
cana-735	254	26	uncertainty	uncertainty	NOUN
cana-735	254	27	greatly	greatly	ADV
cana-735	254	28	supports	support	VERB
cana-735	254	29	the	the	DET
cana-735	254	30	fuzzy	fuzzy	ADJ
cana-735	254	31	failure	failure	NOUN
cana-735	254	32	numbers	number	NOUN
cana-735	254	33	.	.	PUNCT
cana-735	255	1	in	in	ADP
cana-735	255	2	the	the	DET
cana-735	255	3	real	real	ADJ
cana-735	255	4	world	world	NOUN
cana-735	255	5	,	,	PUNCT
cana-735	255	6	these	these	DET
cana-735	255	7	features	feature	NOUN
cana-735	255	8	are	be	AUX
cana-735	255	9	crucial	crucial	ADJ
cana-735	255	10	to	to	PART
cana-735	255	11	consider	consider	VERB
cana-735	255	12	when	when	SCONJ
cana-735	255	13	utilising	utilise	VERB
cana-735	255	14	the	the	DET
cana-735	255	15	total	total	ADJ
cana-735	255	16	failure	failure	NOUN
cana-735	255	17	numbers	number	NOUN
cana-735	255	18	as	as	ADP
cana-735	255	19	a	a	DET
cana-735	255	20	basis	basis	NOUN
cana-735	255	21	for	for	ADP
cana-735	255	22	subsequent	subsequent	ADJ
cana-735	255	23	decision	decision	NOUN
cana-735	255	24	-	-	PUNCT
cana-735	255	25	making	make	VERB
cana-735	255	26	process	process	NOUN
cana-735	255	27	.	.	PUNCT
cana-735	256	1	in	in	ADP
cana-735	256	2	this	this	DET
cana-735	256	3	paper	paper	NOUN
cana-735	256	4	the	the	DET
cana-735	256	5	trfn	trfn	NOUN
cana-735	256	6	shape	shape	NOUN
cana-735	256	7	parameter	parameter	NOUN
cana-735	256	8	from	from	ADP
cana-735	256	9	the	the	DET
cana-735	256	10	first	first	ADJ
cana-735	256	11	method	method	NOUN
cana-735	256	12	the	the	DET
cana-735	256	13	resultant	resultant	NOUN
cana-735	256	14	failure	failure	NOUN
cana-735	256	15	number	number	NOUN
cana-735	256	16	has	have	VERB
cana-735	256	17	trfn	trfn	NOUN
cana-735	256	18	form	form	NOUN
cana-735	256	19	.	.	PUNCT
cana-735	257	1	further	far	ADV
cana-735	257	2	in	in	ADP
cana-735	257	3	method	method	NOUN
cana-735	257	4	two	two	NUM
cana-735	257	5	does	do	AUX
cana-735	257	6	not	not	PART
cana-735	257	7	have	have	VERB
cana-735	257	8	trfn	trfn	NOUN
cana-735	257	9	form	form	NOUN
cana-735	257	10	.	.	PUNCT
cana-735	258	1	from	from	ADP
cana-735	258	2	the	the	DET
cana-735	258	3	comparisons	comparison	NOUN
cana-735	258	4	between	between	ADP
cana-735	258	5	two	two	NUM
cana-735	258	6	methods	method	NOUN
cana-735	258	7	using	use	VERB
cana-735	258	8	gmdv	gmdv	NOUN
cana-735	258	9	,	,	PUNCT
cana-735	258	10	it	it	PRON
cana-735	258	11	gives	give	VERB
cana-735	258	12	some	some	DET
cana-735	258	13	weighting	weighting	NOUN
cana-735	258	14	factor	factor	NOUN
cana-735	258	15	of	of	ADP
cana-735	258	16	gmdv	gmdv	NOUN
cana-735	258	17	.	.	PUNCT
cana-735	259	1	further	further	ADJ
cana-735	259	2	research	research	NOUN
cana-735	259	3	can	can	AUX
cana-735	259	4	be	be	AUX
cana-735	259	5	conducted	conduct	VERB
cana-735	259	6	by	by	ADP
cana-735	259	7	seeing	see	VERB
cana-735	259	8	a	a	DET
cana-735	259	9	comparison	comparison	NOUN
cana-735	259	10	with	with	ADP
cana-735	259	11	a	a	DET
cana-735	259	12	technique	technique	NOUN
cana-735	259	13	that	that	PRON
cana-735	259	14	retains	retain	VERB
cana-735	259	15	uncertainty	uncertainty	NOUN
cana-735	259	16	.	.	PUNCT
cana-735	260	1	the	the	DET
cana-735	260	2	trfn	trfn	NOUN
cana-735	260	3	and	and	CCONJ
cana-735	260	4	shape	shape	NOUN
cana-735	260	5	parameter	parameter	NOUN
cana-735	260	6	value	value	NOUN
cana-735	260	7	utilised	utilise	VERB
cana-735	260	8	in	in	ADP
cana-735	260	9	the	the	DET
cana-735	260	10	dgm	dgm	PROPN
cana-735	260	11	distribution	distribution	NOUN
cana-735	260	12	function	function	NOUN
cana-735	260	13	were	be	AUX
cana-735	260	14	assumed	assume	VERB
cana-735	260	15	.	.	PUNCT
cana-735	261	1	this	this	PRON
cana-735	261	2	would	would	AUX
cana-735	261	3	be	be	AUX
cana-735	261	4	difficult	difficult	ADJ
cana-735	261	5	to	to	PART
cana-735	261	6	implement	implement	VERB
cana-735	261	7	in	in	ADP
cana-735	261	8	practise	practise	NOUN
cana-735	261	9	.	.	PUNCT
cana-735	262	1	accurately	accurately	ADV
cana-735	262	2	determining	determine	VERB
cana-735	262	3	the	the	DET
cana-735	262	4	fuzzy	fuzzy	ADJ
cana-735	262	5	number	number	NOUN
cana-735	262	6	's	's	PART
cana-735	262	7	true	true	ADJ
cana-735	262	8	shape	shape	NOUN
cana-735	262	9	and	and	CCONJ
cana-735	262	10	approximating	approximate	VERB
cana-735	262	11	its	its	PRON
cana-735	262	12	value	value	NOUN
cana-735	262	13	should	should	AUX
cana-735	262	14	be	be	AUX
cana-735	262	15	done	do	VERB
cana-735	262	16	with	with	ADP
cana-735	262	17	readily	readily	ADV
cana-735	262	18	available	available	ADJ
cana-735	262	19	real	real	ADJ
cana-735	262	20	facts	fact	NOUN
cana-735	262	21	.	.	PUNCT
cana-735	263	1	these	these	DET
cana-735	263	2	concerns	concern	NOUN
cana-735	263	3	are	be	AUX
cana-735	263	4	between	between	ADP
cana-735	263	5	the	the	DET
cana-735	263	6	limits	limit	NOUN
cana-735	263	7	of	of	ADP
cana-735	263	8	the	the	DET
cana-735	263	9	approaches	approach	NOUN
cana-735	263	10	provided	provide	VERB
cana-735	263	11	here	here	ADV
cana-735	263	12	,	,	PUNCT
cana-735	263	13	and	and	CCONJ
cana-735	263	14	they	they	PRON
cana-735	263	15	may	may	AUX
cana-735	263	16	potentially	potentially	ADV
cana-735	263	17	lead	lead	VERB
cana-735	263	18	to	to	ADP
cana-735	263	19	future	future	ADJ
cana-735	263	20	study	study	NOUN
cana-735	263	21	directions	direction	NOUN
cana-735	263	22	.	.	PUNCT
cana-735	264	1	additionally	additionally	ADV
cana-735	264	2	,	,	PUNCT
cana-735	264	3	this	this	PRON
cana-735	264	4	will	will	AUX
cana-735	264	5	open	open	VERB
cana-735	264	6	a	a	DET
cana-735	264	7	significant	significant	ADJ
cana-735	264	8	study	study	NOUN
cana-735	264	9	avenue	avenue	NOUN
cana-735	264	10	in	in	ADP
cana-735	264	11	the	the	DET
cana-735	264	12	future	future	NOUN
cana-735	264	13	(	(	PUNCT
cana-735	264	14	now	now	ADV
cana-735	264	15	crisp	crisp	ADJ
cana-735	264	16	value	value	NOUN
cana-735	264	17	application	application	NOUN
cana-735	264	18	refuses	refuse	VERB
cana-735	264	19	the	the	DET
cana-735	264	20	four	four	NUM
cana-735	264	21	-	-	PUNCT
cana-735	264	22	parameter	parameter	NOUN
cana-735	264	23	dgm	dgm	PROPN
cana-735	264	24	distribution	distribution	NOUN
cana-735	264	25	)	)	PUNCT
cana-735	264	26	.	.	PUNCT
cana-735	265	1	since	since	SCONJ
cana-735	265	2	the	the	DET
cana-735	265	3	scale	scale	NOUN
cana-735	265	4	parameter	parameter	NOUN
cana-735	265	5	is	be	AUX
cana-735	265	6	taken	take	VERB
cana-735	265	7	to	to	PART
cana-735	265	8	be	be	AUX
cana-735	265	9	one	one	NUM
cana-735	265	10	,	,	PUNCT
cana-735	265	11	we	we	PRON
cana-735	265	12	only	only	ADV
cana-735	265	13	study	study	VERB
cana-735	265	14	oneparameter	oneparameter	NOUN
cana-735	265	15	dgm	dgm	PROPN
cana-735	265	16	distributions	distribution	NOUN
cana-735	265	17	in	in	ADP
cana-735	265	18	this	this	DET
cana-735	265	19	section	section	NOUN
cana-735	265	20	.	.	PUNCT
cana-735	266	1	this	this	PRON
cana-735	266	2	is	be	AUX
cana-735	266	3	enough	enough	ADJ
cana-735	266	4	in	in	ADP
cana-735	266	5	the	the	DET
cana-735	266	6	context	context	NOUN
cana-735	266	7	of	of	ADP
cana-735	266	8	maintenance	maintenance	NOUN
cana-735	266	9	modelling	modelling	NOUN
cana-735	266	10	if	if	SCONJ
cana-735	266	11	we	we	PRON
cana-735	266	12	suppose	suppose	VERB
cana-735	266	13	that	that	SCONJ
cana-735	266	14	the	the	DET
cana-735	266	15	equipment	equipment	NOUN
cana-735	266	16	system	system	NOUN
cana-735	266	17	under	under	ADP
cana-735	266	18	investigation	investigation	NOUN
cana-735	266	19	has	have	VERB
cana-735	266	20	its	its	PRON
cana-735	266	21	average	average	ADJ
cana-735	266	22	initial	initial	ADJ
cana-735	266	23	failure	failure	NOUN
cana-735	266	24	in	in	ADP
cana-735	266	25	a	a	DET
cana-735	266	26	single	single	ADJ
cana-735	266	27	communications	communication	NOUN
cana-735	266	28	on	on	ADP
cana-735	266	29	applied	apply	VERB
cana-735	266	30	nonlinear	nonlinear	ADJ
cana-735	266	31	analysis	analysis	NOUN
cana-735	266	32	issn	issn	NOUN
cana-735	266	33	:	:	PUNCT
cana-735	266	34	1074	1074	NUM
cana-735	266	35	-	-	PUNCT
cana-735	266	36	133x	133x	NUM
cana-735	266	37	vol	vol	NOUN
cana-735	266	38	31	31	NUM
cana-735	266	39	no	no	NOUN
cana-735	266	40	.	.	PUNCT
cana-735	267	1	3s	3s	NUM
cana-735	267	2	(	(	PUNCT
cana-735	267	3	2024	2024	NUM
cana-735	267	4	)	)	PUNCT
cana-735	267	5	116	116	NUM
cana-735	267	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-735	267	7	unit	unit	NOUN
cana-735	267	8	of	of	ADP
cana-735	267	9	time	time	NOUN
cana-735	267	10	.	.	PUNCT
cana-735	268	1	this	this	PRON
cana-735	268	2	might	might	AUX
cana-735	268	3	not	not	PART
cana-735	268	4	always	always	ADV
cana-735	268	5	be	be	AUX
cana-735	268	6	the	the	DET
cana-735	268	7	case	case	NOUN
cana-735	268	8	in	in	ADP
cana-735	268	9	practice	practice	NOUN
cana-735	268	10	;	;	PUNCT
cana-735	268	11	thus	thus	ADV
cana-735	268	12	,	,	PUNCT
cana-735	268	13	we	we	PRON
cana-735	268	14	need	need	VERB
cana-735	268	15	to	to	PART
cana-735	268	16	expand	expand	VERB
cana-735	268	17	the	the	DET
cana-735	268	18	study	study	NOUN
cana-735	268	19	to	to	PART
cana-735	268	20	include	include	VERB
cana-735	268	21	dgm	dgm	PROPN
cana-735	268	22	distributions	distribution	NOUN
cana-735	268	23	with	with	ADP
cana-735	268	24	other	other	ADJ
cana-735	268	25	scale	scale	NOUN
cana-735	268	26	parameter	parameter	NOUN
cana-735	268	27	values	value	NOUN
cana-735	268	28	.	.	PUNCT
cana-735	269	1	additional	additional	ADJ
cana-735	269	2	investigation	investigation	NOUN
cana-735	269	3	may	may	AUX
cana-735	269	4	be	be	AUX
cana-735	269	5	conducted	conduct	VERB
cana-735	269	6	into	into	ADP
cana-735	269	7	many	many	ADJ
cana-735	269	8	techniques	technique	NOUN
cana-735	269	9	using	use	VERB
cana-735	269	10	various	various	ADJ
cana-735	269	11	kinds	kind	NOUN
cana-735	269	12	of	of	ADP
cana-735	269	13	fuzzy	fuzzy	ADJ
cana-735	269	14	numbers	number	NOUN
cana-735	269	15	,	,	PUNCT
cana-735	269	16	various	various	ADJ
cana-735	269	17	applications	application	NOUN
cana-735	269	18	of	of	ADP
cana-735	269	19	de	de	ADJ
cana-735	269	20	-	-	NOUN
cana-735	269	21	fuzzification	fuzzification	NOUN
cana-735	269	22	techniques	technique	NOUN
cana-735	269	23	,	,	PUNCT
cana-735	269	24	and	and	CCONJ
cana-735	269	25	investigating	investigate	VERB
cana-735	269	26	the	the	DET
cana-735	269	27	theory	theory	NOUN
cana-735	269	28	's	's	PART
cana-735	269	29	applicability	applicability	NOUN
cana-735	269	30	in	in	ADP
cana-735	269	31	several	several	ADJ
cana-735	269	32	related	relate	VERB
cana-735	269	33	domains	domain	NOUN
cana-735	269	34	,	,	PUNCT
cana-735	269	35	such	such	DET
cana-735	269	36	the	the	DET
cana-735	269	37	failure	failure	NOUN
cana-735	269	38	numbers	number	NOUN
cana-735	269	39	in	in	ADP
cana-735	269	40	biological	biological	ADJ
cana-735	269	41	processes	process	NOUN
cana-735	269	42	.	.	PUNCT
cana-735	270	1	data	datum	NOUN
cana-735	270	2	availability	availability	NOUN
cana-735	270	3	data	datum	NOUN
cana-735	270	4	sharing	sharing	NOUN
cana-735	270	5	is	be	AUX
cana-735	270	6	not	not	PART
cana-735	270	7	applicable	applicable	ADJ
cana-735	270	8	to	to	ADP
cana-735	270	9	this	this	DET
cana-735	270	10	article	article	NOUN
cana-735	270	11	as	as	SCONJ
cana-735	270	12	no	no	DET
cana-735	270	13	datasets	dataset	NOUN
cana-735	270	14	were	be	AUX
cana-735	270	15	generated	generate	VERB
cana-735	270	16	or	or	CCONJ
cana-735	270	17	analysed	analyse	VERB
cana-735	270	18	during	during	ADP
cana-735	270	19	the	the	DET
cana-735	270	20	current	current	ADJ
cana-735	270	21	study	study	NOUN
cana-735	270	22	.	.	PUNCT
cana-735	271	1	competing	compete	VERB
cana-735	271	2	interests	interest	NOUN
cana-735	271	3	the	the	DET
cana-735	271	4	authors	author	NOUN
cana-735	271	5	have	have	AUX
cana-735	271	6	not	not	PART
cana-735	271	7	disclosed	disclose	VERB
cana-735	271	8	any	any	DET
cana-735	271	9	competing	compete	VERB
cana-735	271	10	interests	interest	NOUN
cana-735	271	11	.	.	PUNCT
cana-735	272	1	references	reference	NOUN
cana-735	272	2	[	[	X
cana-735	272	3	1	1	NUM
cana-735	272	4	]	]	X
cana-735	272	5	zadeh	zadeh	PROPN
cana-735	272	6	,	,	PUNCT
cana-735	272	7	l.	l.	PROPN
cana-735	272	8	the	the	DET
cana-735	272	9	concept	concept	NOUN
cana-735	272	10	of	of	ADP
cana-735	272	11	a	a	DET
cana-735	272	12	linguistic	linguistic	ADJ
cana-735	272	13	variable	variable	NOUN
cana-735	272	14	and	and	CCONJ
cana-735	272	15	its	its	PRON
cana-735	272	16	application	application	NOUN
cana-735	272	17	to	to	PART
cana-735	272	18	approximate	approximate	ADJ
cana-735	272	19	reasoning	reasoning	NOUN
cana-735	272	20	–	–	PUNCT
cana-735	272	21	i.	i.	PROPN
cana-735	272	22	inf	inf	PROPN
cana-735	272	23	.	.	PUNCT
cana-735	273	1	sci	sci	PROPN
cana-735	273	2	.	.	PROPN
cana-735	273	3	1975	1975	NUM
cana-735	273	4	,	,	PUNCT
cana-735	273	5	8	8	NUM
cana-735	273	6	,	,	PUNCT
cana-735	273	7	199	199	NUM
cana-735	273	8	–	–	PUNCT
cana-735	273	9	249	249	NUM
cana-735	273	10	.	.	PUNCT
cana-735	274	1	[	[	X
cana-735	274	2	2	2	NUM
cana-735	274	3	]	]	SYM
cana-735	274	4	zadeh	zadeh	PROPN
cana-735	274	5	,	,	PUNCT
cana-735	274	6	l.	l.	PROPN
cana-735	274	7	fuzzy	fuzzy	PROPN
cana-735	274	8	sets	set	NOUN
cana-735	274	9	as	as	ADP
cana-735	274	10	a	a	DET
cana-735	274	11	basis	basis	NOUN
cana-735	274	12	for	for	ADP
cana-735	274	13	a	a	DET
cana-735	274	14	theory	theory	NOUN
cana-735	274	15	of	of	ADP
cana-735	274	16	possibility	possibility	NOUN
cana-735	274	17	.	.	PUNCT
cana-735	275	1	fuzzy	fuzzy	ADJ
cana-735	275	2	sets	set	NOUN
cana-735	275	3	syst	syst	PROPN
cana-735	275	4	.	.	PUNCT
cana-735	276	1	1999	1999	NUM
cana-735	276	2	,	,	PUNCT
cana-735	276	3	100	100	NUM
cana-735	276	4	,	,	PUNCT
cana-735	276	5	9–34	9–34	NOUN
cana-735	276	6	.	.	PUNCT
cana-735	277	1	aljarrah	aljarrah	PROPN
cana-735	277	2	m.	m.	PROPN
cana-735	277	3	a.	a.	PROPN
cana-735	277	4	,	,	PUNCT
cana-735	277	5	lee	lee	PROPN
cana-735	277	6	c.	c.	PROPN
cana-735	277	7	,	,	PUNCT
cana-735	277	8	and	and	CCONJ
cana-735	277	9	famoye	famoye	PROPN
cana-735	277	10	f	f	PROPN
cana-735	277	11	2014	2014	NUM
cana-735	277	12	journal	journal	NOUN
cana-735	277	13	of	of	ADP
cana-735	277	14	statistical	statistical	ADJ
cana-735	277	15	distributions	distribution	NOUN
cana-735	277	16	and	and	CCONJ
cana-735	277	17	applications	application	NOUN
cana-735	277	18	,	,	PUNCT
cana-735	277	19	1	1	NUM
cana-735	277	20	,	,	PUNCT
cana-735	277	21	2	2	NUM
cana-735	277	22	[	[	SYM
cana-735	277	23	3	3	NUM
cana-735	277	24	]	]	X
cana-735	277	25	butt	butt	NOUN
cana-735	277	26	m.	m.	NOUN
cana-735	277	27	,	,	PUNCT
cana-735	277	28	alzaatreh	alzaatreh	PROPN
cana-735	277	29	a.	a.	NOUN
cana-735	277	30	,	,	PUNCT
cana-735	277	31	cordeiro	cordeiro	PROPN
cana-735	277	32	g.	g.	PROPN
cana-735	277	33	,	,	PUNCT
cana-735	277	34	tahir	tahir	PROPN
cana-735	277	35	m.	m.	PROPN
cana-735	277	36	h.	h.	PROPN
cana-735	277	37	,	,	PUNCT
cana-735	277	38	and	and	CCONJ
cana-735	277	39	mansoor	mansoor	PROPN
cana-735	277	40	m.	m.	PROPN
cana-735	277	41	,	,	PUNCT
cana-735	277	42	filomat	filomat	NOUN
cana-735	277	43	,	,	PUNCT
cana-735	277	44	2018	2018	NUM
cana-735	277	45	,	,	PUNCT
cana-735	277	46	32	32	NUM
cana-735	277	47	,	,	PUNCT
cana-735	277	48	4,1259–1272	4,1259–1272	NOUN
cana-735	278	1	[	[	X
cana-735	278	2	4	4	NUM
cana-735	278	3	]	]	X
cana-735	278	4	famoye	famoye	PROPN
cana-735	278	5	f.	f.	PROPN
cana-735	278	6	,	,	PUNCT
cana-735	278	7	akarawak	akarawak	PROPN
cana-735	278	8	e.	e.	PROPN
cana-735	278	9	,	,	PUNCT
cana-735	278	10	and	and	CCONJ
cana-735	278	11	ekum	ekum	ADJ
cana-735	278	12	m.	m.	NOUN
cana-735	278	13	,	,	PUNCT
cana-735	278	14	2018	2018	NUM
cana-735	278	15	journal	journal	NOUN
cana-735	278	16	of	of	ADP
cana-735	278	17	statistical	statistical	ADJ
cana-735	278	18	theory	theory	NOUN
cana-735	278	19	and	and	CCONJ
cana-735	278	20	applications	application	NOUN
cana-735	278	21	,	,	PUNCT
cana-735	278	22	17	17	NUM
cana-735	278	23	,	,	PUNCT
cana-735	278	24	4	4	NUM
cana-735	278	25	,	,	PUNCT
cana-735	278	26	719–727	719–727	NUM
cana-735	278	27	[	[	SYM
cana-735	278	28	5	5	NUM
cana-735	278	29	]	]	PUNCT
cana-735	278	30	eugene	eugene	PROPN
cana-735	278	31	n.	n.	PROPN
cana-735	278	32	,	,	PUNCT
cana-735	278	33	lee	lee	PROPN
cana-735	278	34	c.	c.	PROPN
cana-735	278	35	,	,	PUNCT
cana-735	278	36	and	and	CCONJ
cana-735	278	37	f.	f.	PROPN
cana-735	278	38	famoye	famoye	PROPN
cana-735	278	39	2002	2002	NUM
cana-735	278	40	communications	communication	NOUN
cana-735	278	41	in	in	ADP
cana-735	278	42	statistics	statistic	NOUN
cana-735	278	43	-	-	PUNCT
cana-735	278	44	theory	theory	NOUN
cana-735	278	45	and	and	CCONJ
cana-735	278	46	methods	method	NOUN
cana-735	278	47	,	,	PUNCT
cana-735	278	48	31,4	31,4	ADV
cana-735	278	49	,	,	PUNCT
cana-735	278	50	497–512	497–512	NUM
cana-735	278	51	[	[	X
cana-735	278	52	6	6	NUM
cana-735	278	53	]	]	PUNCT
cana-735	278	54	alzaatreh	alzaatreh	PROPN
cana-735	278	55	a.	a.	PROPN
cana-735	278	56	,	,	PUNCT
cana-735	278	57	lee	lee	PROPN
cana-735	278	58	c.	c.	PROPN
cana-735	278	59	,	,	PUNCT
cana-735	278	60	famoye	famoye	PROPN
cana-735	278	61	f.	f.	PROPN
cana-735	278	62	,	,	PUNCT
cana-735	278	63	2013	2013	NUM
cana-735	278	64	metron	metron	NOUN
cana-735	278	65	,	,	PUNCT
cana-735	278	66	71,1,63–79	71,1,63–79	ADV
cana-735	278	67	[	[	X
cana-735	278	68	7	7	NUM
cana-735	278	69	]	]	X
cana-735	278	70	esogbue	esogbue	NOUN
cana-735	278	71	,	,	PUNCT
cana-735	278	72	a.o	a.o	PROPN
cana-735	278	73	.	.	PROPN
cana-735	278	74	hearnes	hearnes	PROPN
cana-735	278	75	,	,	PUNCT
cana-735	278	76	w.e	w.e	PROPN
cana-735	278	77	.	.	PROPN
cana-735	278	78	on	on	ADP
cana-735	278	79	replacement	replacement	NOUN
cana-735	278	80	models	model	NOUN
cana-735	278	81	via	via	ADP
cana-735	278	82	a	a	DET
cana-735	278	83	fuzzy	fuzzy	ADJ
cana-735	278	84	set	set	NOUN
cana-735	278	85	theory	theory	NOUN
cana-735	278	86	framework	framework	NOUN
cana-735	278	87	.	.	PUNCT
cana-735	279	1	ieee	ieee	PROPN
cana-735	279	2	trans	trans	PROPN
cana-735	279	3	.	.	PUNCT
cana-735	280	1	syst	syst	PROPN
cana-735	280	2	.	.	PUNCT
cana-735	281	1	man	man	PROPN
cana-735	281	2	cybern	cybern	PROPN
cana-735	281	3	.	.	PUNCT
cana-735	282	1	part	part	NOUN
cana-735	282	2	c	c	PROPN
cana-735	282	3	appl	appl	PROPN
cana-735	282	4	.	.	PUNCT
cana-735	283	1	rev	rev	PROPN
cana-735	283	2	.	.	PROPN
cana-735	283	3	1998	1998	NUM
cana-735	283	4	,	,	PUNCT
cana-735	283	5	28	28	NUM
cana-735	283	6	,	,	PUNCT
cana-735	283	7	549	549	NUM
cana-735	283	8	-	-	SYM
cana-735	283	9	560	560	NUM
cana-735	283	10	.	.	PUNCT
cana-735	284	1	[	[	X
cana-735	284	2	8	8	NUM
cana-735	284	3	]	]	X
cana-735	284	4	parchami	parchami	NOUN
cana-735	284	5	,	,	PUNCT
cana-735	284	6	a.	a.	NOUN
cana-735	284	7	calculator	calculator	NOUN
cana-735	284	8	for	for	ADP
cana-735	284	9	fuzzy	fuzzy	ADJ
cana-735	284	10	numbers	number	NOUN
cana-735	284	11	.	.	PUNCT
cana-735	285	1	complex	complex	ADJ
cana-735	285	2	.	.	PUNCT
cana-735	285	3	intell	intell	PROPN
cana-735	285	4	.	.	PUNCT
cana-735	286	1	syst,5,331	syst,5,331	VERB
cana-735	286	2	-	-	SYM
cana-735	286	3	342	342	NUM
cana-735	286	4	.	.	PUNCT
cana-735	287	1	[	[	X
cana-735	287	2	9	9	NUM
cana-735	287	3	]	]	X
cana-735	287	4	husniah	husniah	PROPN
cana-735	287	5	,	,	PUNCT
cana-735	287	6	h.	h.	NOUN
cana-735	287	7	supriatna	supriatna	PROPN
cana-735	287	8	,	,	PUNCT
cana-735	287	9	a.k	a.k	PROPN
cana-735	287	10	.	.	PROPN
cana-735	287	11	iskandar	iskandar	PROPN
cana-735	287	12	,	,	PUNCT
cana-735	287	13	b.p	b.p	PROPN
cana-735	287	14	.	.	PROPN
cana-735	287	15	lease	lease	NOUN
cana-735	287	16	contract	contract	NOUN
cana-735	287	17	with	with	ADP
cana-735	287	18	servicing	servicing	NOUN
cana-735	287	19	strategy	strategy	NOUN
cana-735	287	20	model	model	NOUN
cana-735	287	21	for	for	ADP
cana-735	287	22	used	use	VERB
cana-735	287	23	product	product	NOUN
cana-735	287	24	considering	consider	VERB
cana-735	287	25	crisp	crisp	ADJ
cana-735	287	26	and	and	CCONJ
cana-735	287	27	fuzzy	fuzzy	ADJ
cana-735	287	28	usage	usage	NOUN
cana-735	287	29	rate	rate	NOUN
cana-735	287	30	.	.	PUNCT
cana-735	288	1	int.j	int.j	PROPN
cana-735	288	2	.	.	PUNCT
cana-735	288	3	artif	artif	PROPN
cana-735	288	4	.	.	PUNCT
cana-735	289	1	intell.2018,18,177	intell.2018,18,177	PROPN
cana-735	289	2	-	-	SYM
cana-735	289	3	192	192	NUM
cana-735	289	4	.	.	PUNCT
cana-735	290	1	[	[	X
cana-735	290	2	10	10	NUM
cana-735	290	3	]	]	X
cana-735	290	4	husniah	husniah	PROPN
cana-735	290	5	,	,	PUNCT
cana-735	290	6	h.	h.	PROPN
cana-735	290	7	pasaribu	pasaribu	PROPN
cana-735	290	8	,	,	PUNCT
cana-735	290	9	u.s	u.s	PROPN
cana-735	290	10	.	.	PROPN
cana-735	290	11	wangsaputra	wangsaputra	PROPN
cana-735	290	12	,	,	PUNCT
cana-735	290	13	r.	r.	PROPN
cana-735	290	14	iskandar	iskandar	PROPN
cana-735	290	15	,	,	PUNCT
cana-735	290	16	b.p	b.p	PROPN
cana-735	290	17	.	.	PROPN
cana-735	290	18	condition	condition	NOUN
cana-735	290	19	based	base	VERB
cana-735	290	20	maintenance	maintenance	NOUN
cana-735	290	21	policy	policy	NOUN
cana-735	290	22	for	for	ADP
cana-735	290	23	a	a	DET
cana-735	290	24	leased	lease	VERB
cana-735	290	25	reman	reman	NOUN
cana-735	290	26	product	product	NOUN
cana-735	290	27	.	.	PUNCT
cana-735	291	1	heliyon	heliyon	NOUN
cana-735	291	2	2021	2021	NUM
cana-735	291	3	,	,	PUNCT
cana-735	291	4	7	7	NUM
cana-735	291	5	,	,	PUNCT
cana-735	291	6	e06494	e06494	NUM
cana-735	291	7	.	.	PUNCT
cana-735	292	1	[	[	X
cana-735	292	2	11	11	NUM
cana-735	292	3	]	]	PUNCT
cana-735	292	4	verma	verma	PROPN
cana-735	292	5	,	,	PUNCT
cana-735	292	6	a.k	a.k	PROPN
cana-735	292	7	.	.	PUNCT
cana-735	293	1	the	the	DET
cana-735	293	2	use	use	NOUN
cana-735	293	3	of	of	ADP
cana-735	293	4	fuzzy	fuzzy	ADJ
cana-735	293	5	numbers	number	NOUN
cana-735	293	6	in	in	ADP
cana-735	293	7	reliability	reliability	NOUN
cana-735	293	8	calculations	calculation	NOUN
cana-735	293	9	.	.	PUNCT
cana-735	294	1	iete	iete	ADJ
cana-735	294	2	tech	tech	PROPN
cana-735	294	3	.	.	PUNCT
cana-735	295	1	rev	rev	PROPN
cana-735	295	2	.	.	PROPN
cana-735	295	3	2001	2001	NUM
cana-735	295	4	,	,	PUNCT
cana-735	295	5	18	18	NUM
cana-735	295	6	,	,	PUNCT
cana-735	295	7	27	27	NUM
cana-735	295	8	-	-	SYM
cana-735	295	9	31	31	NUM
cana-735	295	10	.	.	PUNCT
cana-735	296	1	[	[	X
cana-735	296	2	12	12	NUM
cana-735	296	3	]	]	X
cana-735	296	4	glockner	glockner	NOUN
cana-735	296	5	,	,	PUNCT
cana-735	296	6	i.	i.	NOUN
cana-735	296	7	fuzzy	fuzzy	PROPN
cana-735	296	8	quantifiers	quantifier	VERB
cana-735	296	9	:	:	PUNCT
cana-735	296	10	a	a	DET
cana-735	296	11	computational	computational	ADJ
cana-735	296	12	theory	theory	NOUN
cana-735	296	13	;	;	PUNCT
cana-735	296	14	springer	springer	NOUN
cana-735	296	15	;	;	PUNCT
cana-735	296	16	berlin	berlin	PROPN
cana-735	296	17	/	/	SYM
cana-735	296	18	heidelberg	heidelberg	PROPN
cana-735	296	19	,	,	PUNCT
cana-735	296	20	germany,2006	germany,2006	NOUN
cana-735	296	21	.	.	PUNCT
cana-735	297	1	[	[	X
cana-735	297	2	13	13	NUM
cana-735	297	3	]	]	X
cana-735	297	4	husniah	husniah	PROPN
cana-735	297	5	,	,	PUNCT
cana-735	297	6	h.	h.	PROPN
cana-735	297	7	;	;	PUNCT
cana-735	297	8	pasaribu	pasaribu	PROPN
cana-735	297	9	,	,	PUNCT
cana-735	297	10	u.s	u.s	PROPN
cana-735	297	11	.	.	PROPN
cana-735	297	12	;	;	PUNCT
cana-735	297	13	iskandar	iskandar	PROPN
cana-735	297	14	,	,	PUNCT
cana-735	297	15	b.p	b.p	PROPN
cana-735	297	16	.	.	PROPN
cana-735	297	17	multi	multi	ADJ
cana-735	297	18	-	-	ADJ
cana-735	297	19	period	period	ADJ
cana-735	297	20	lease	lease	NOUN
cana-735	297	21	contract	contract	NOUN
cana-735	297	22	for	for	ADP
cana-735	297	23	glöckner	glöckner	PROPN
cana-735	297	24	,	,	PUNCT
cana-735	297	25	i.	i.	NOUN
cana-735	297	26	fuzzy	fuzzy	PROPN
cana-735	297	27	quantifiers	quantifier	VERB
cana-735	297	28	:	:	PUNCT
cana-735	297	29	a	a	DET
cana-735	297	30	computational	computational	ADJ
cana-735	297	31	theory	theory	NOUN
cana-735	297	32	;	;	PUNCT
cana-735	297	33	springer	springer	NOUN
cana-735	297	34	:	:	PUNCT
cana-735	297	35	berlin	berlin	PROPN
cana-735	297	36	/	/	SYM
cana-735	297	37	heidelberg	heidelberg	PROPN
cana-735	297	38	,	,	PUNCT
cana-735	297	39	germany	germany	PROPN
cana-735	297	40	,	,	PUNCT
cana-735	297	41	2006	2006	NUM
cana-735	297	42	.	.	PUNCT
cana-735	298	1	[	[	X
cana-735	298	2	14	14	NUM
cana-735	298	3	]	]	X
cana-735	298	4	venkatesh	venkatesh	PROPN
cana-735	298	5	,	,	PUNCT
cana-735	298	6	a.	a.	NOUN
cana-735	298	7	;	;	PUNCT
cana-735	298	8	elango	elango	PROPN
cana-735	298	9	,	,	PUNCT
cana-735	298	10	s.	s.	PROPN
cana-735	298	11	a	a	DET
cana-735	298	12	mathematical	mathematical	ADJ
cana-735	298	13	model	model	NOUN
cana-735	298	14	for	for	ADP
cana-735	298	15	the	the	DET
cana-735	298	16	effect	effect	NOUN
cana-735	298	17	of	of	ADP
cana-735	298	18	trh	trh	NOUN
cana-735	298	19	using	use	VERB
cana-735	298	20	fuzzy	fuzzy	ADJ
cana-735	298	21	reliability	reliability	NOUN
cana-735	298	22	analysis	analysis	NOUN
cana-735	298	23	.	.	PUNCT
cana-735	299	1	glob	glob	PROPN
cana-735	299	2	.	.	PUNCT
cana-735	300	1	j.	j.	PROPN
cana-735	300	2	pure	pure	PROPN
cana-735	300	3	appl	appl	PROPN
cana-735	300	4	.	.	PUNCT
cana-735	300	5	math	math	PROPN
cana-735	300	6	.	.	PUNCT
cana-735	301	1	2017	2017	NUM
cana-735	301	2	,	,	PUNCT
cana-735	301	3	13	13	NUM
cana-735	301	4	,	,	PUNCT
cana-735	301	5	5673–5686	5673–5686	NUM
cana-735	301	6	.	.	PUNCT
cana-735	302	1	[	[	X
cana-735	302	2	15	15	NUM
cana-735	302	3	]	]	X
cana-735	302	4	venkatesh	venkatesh	NOUN
cana-735	302	5	,	,	PUNCT
cana-735	302	6	a.	a.	NOUN
cana-735	302	7	;	;	PUNCT
cana-735	302	8	subramani	subramani	PROPN
cana-735	302	9	,	,	PUNCT
cana-735	302	10	g.	g.	PROPN
cana-735	302	11	;	;	PUNCT
cana-735	302	12	elango	elango	PROPN
cana-735	302	13	,	,	PUNCT
cana-735	302	14	s.	s.	PROPN
cana-735	302	15	a	a	DET
cana-735	302	16	mathematical	mathematical	ADJ
cana-735	302	17	model	model	NOUN
cana-735	302	18	for	for	ADP
cana-735	302	19	the	the	DET
cana-735	302	20	effect	effect	NOUN
cana-735	302	21	of	of	ADP
cana-735	302	22	gastrin	gastrin	NOUN
cana-735	302	23	in	in	ADP
cana-735	302	24	humans	human	NOUN
cana-735	302	25	using	use	VERB
cana-735	302	26	fuzzy	fuzzy	ADJ
cana-735	302	27	weibull	weibull	NOUN
cana-735	302	28	distribution	distribution	NOUN
cana-735	302	29	.	.	PUNCT
cana-735	303	1	int	int	NOUN
cana-735	303	2	.	.	PUNCT
cana-735	304	1	j.	j.	PROPN
cana-735	304	2	pure	pure	PROPN
cana-735	304	3	appl	appl	PROPN
cana-735	304	4	.	.	PUNCT
cana-735	304	5	math	math	PROPN
cana-735	304	6	.	.	PUNCT
cana-735	305	1	2017	2017	NUM
cana-735	305	2	,	,	PUNCT
cana-735	305	3	117	117	NUM
cana-735	305	4	,	,	PUNCT
cana-735	305	5	155–164	155–164	NUM
cana-735	305	6	.	.	PUNCT
cana-735	306	1	[	[	X
cana-735	306	2	16	16	NUM
cana-735	306	3	]	]	X
cana-735	306	4	husniah	husniah	PROPN
cana-735	306	5	,	,	PUNCT
cana-735	306	6	h.	h.	PROPN
cana-735	306	7	;	;	PUNCT
cana-735	306	8	pasaribu	pasaribu	PROPN
cana-735	306	9	,	,	PUNCT
cana-735	306	10	u.s	u.s	PROPN
cana-735	306	11	.	.	PROPN
cana-735	306	12	;	;	PUNCT
cana-735	306	13	supriatna	supriatna	PROPN
cana-735	306	14	,	,	PUNCT
cana-735	306	15	a.k	a.k	PROPN
cana-735	306	16	.	.	PROPN
cana-735	306	17	;	;	PUNCT
cana-735	306	18	iskandar	iskandar	PROPN
cana-735	306	19	,	,	PUNCT
cana-735	306	20	b.p	b.p	PROPN
cana-735	306	21	.	.	PROPN
cana-735	306	22	optimal	optimal	ADJ
cana-735	306	23	number	number	NOUN
cana-735	306	24	of	of	ADP
cana-735	306	25	fleet	fleet	NOUN
cana-735	306	26	maintenance	maintenance	NOUN
cana-735	306	27	contract	contract	NOUN
cana-735	306	28	with	with	ADP
cana-735	306	29	policy	policy	NOUN
cana-735	306	30	limit	limit	NOUN
cana-735	306	31	cost	cost	NOUN
cana-735	306	32	.	.	PUNCT
cana-735	307	1	in	in	ADP
cana-735	307	2	proceedings	proceeding	NOUN
cana-735	307	3	of	of	ADP
cana-735	307	4	the	the	DET
cana-735	307	5	4th	4th	ADJ
cana-735	307	6	international	international	ADJ
cana-735	307	7	conference	conference	NOUN
cana-735	307	8	on	on	ADP
cana-735	307	9	control	control	NOUN
cana-735	307	10	,	,	PUNCT
cana-735	307	11	decision	decision	NOUN
cana-735	307	12	and	and	CCONJ
cana-735	307	13	information	information	NOUN
cana-735	307	14	technologies	technology	NOUN
cana-735	307	15	(	(	PUNCT
cana-735	307	16	codit	codit	NOUN
cana-735	307	17	)	)	PUNCT
cana-735	307	18	,	,	PUNCT
cana-735	307	19	bandung	bandung	PROPN
cana-735	307	20	,	,	PUNCT
cana-735	307	21	indonesia	indonesia	PROPN
cana-735	307	22	,	,	PUNCT
cana-735	307	23	5–7	5–7	PROPN
cana-735	307	24	april	april	PROPN
cana-735	307	25	2017	2017	NUM
cana-735	307	26	.	.	PUNCT
cana-735	308	1	[	[	X
cana-735	308	2	17	17	NUM
cana-735	308	3	]	]	X
cana-735	308	4	lee	lee	PROPN
cana-735	308	5	,	,	PUNCT
cana-735	308	6	k.h	k.h	PROPN
cana-735	308	7	.	.	PUNCT
cana-735	309	1	first	first	ADJ
cana-735	309	2	course	course	NOUN
cana-735	309	3	on	on	ADP
cana-735	309	4	fuzzy	fuzzy	ADJ
cana-735	309	5	theory	theory	NOUN
cana-735	309	6	and	and	CCONJ
cana-735	309	7	applications	application	NOUN
cana-735	309	8	;	;	PUNCT
cana-735	309	9	springer	springer	NOUN
cana-735	309	10	:	:	PUNCT
cana-735	309	11	berlin	berlin	PROPN
cana-735	309	12	/	/	SYM
cana-735	309	13	heidelberg	heidelberg	PROPN
cana-735	309	14	,	,	PUNCT
cana-735	309	15	germany	germany	PROPN
cana-735	309	16	,	,	PUNCT
cana-735	309	17	2005	2005	NUM
cana-735	309	18	.	.	PUNCT
cana-735	310	1	[	[	X
cana-735	310	2	18	18	NUM
cana-735	310	3	]	]	X
cana-735	310	4	lai	lai	PROPN
cana-735	310	5	,	,	PUNCT
cana-735	310	6	c.d	c.d	PROPN
cana-735	310	7	.	.	PROPN
cana-735	310	8	;	;	PUNCT
cana-735	310	9	murthy	murthy	PROPN
cana-735	310	10	,	,	PUNCT
cana-735	310	11	d.n	d.n	PROPN
cana-735	310	12	.	.	PROPN
cana-735	310	13	;	;	PUNCT
cana-735	310	14	xie	xie	PROPN
cana-735	310	15	,	,	PUNCT
cana-735	310	16	m.	m.	NOUN
cana-735	310	17	weibull	weibull	PROPN
cana-735	310	18	distributions	distribution	NOUN
cana-735	310	19	and	and	CCONJ
cana-735	310	20	their	their	PRON
cana-735	310	21	applications	application	NOUN
cana-735	310	22	.	.	PUNCT
cana-735	311	1	in	in	ADP
cana-735	311	2	springer	springer	NOUN
cana-735	311	3	handbook	handbook	NOUN
cana-735	311	4	of	of	ADP
cana-735	311	5	engineering	engineering	NOUN
cana-735	311	6	statistics	statistic	NOUN
cana-735	311	7	;	;	PUNCT
cana-735	311	8	pham	pham	PROPN
cana-735	311	9	,	,	PUNCT
cana-735	311	10	h.	h.	PROPN
cana-735	311	11	,	,	PUNCT
cana-735	311	12	ed	ed	NOUN
cana-735	311	13	.	.	PUNCT
cana-735	311	14	;	;	PUNCT
cana-735	311	15	springer	springer	NOUN
cana-735	311	16	:	:	PUNCT
cana-735	311	17	new	new	PROPN
cana-735	311	18	york	york	PROPN
cana-735	311	19	,	,	PUNCT
cana-735	311	20	ny	ny	PROPN
cana-735	311	21	,	,	PUNCT
cana-735	311	22	usa	usa	PROPN
cana-735	311	23	,	,	PUNCT
cana-735	311	24	2006	2006	NUM
cana-735	311	25	;	;	PUNCT
cana-735	311	26	pp	pp	NUM
cana-735	311	27	.	.	PUNCT
cana-735	311	28	63–78	63–78	X
cana-735	311	29	.	.	PUNCT
cana-735	312	1	[	[	X
cana-735	312	2	19	19	NUM
cana-735	312	3	]	]	X
cana-735	312	4	kumar	kumar	PROPN
cana-735	312	5	,	,	PUNCT
cana-735	312	6	p.	p.	PROPN
cana-735	312	7	;	;	PUNCT
cana-735	312	8	singh	singh	PROPN
cana-735	312	9	,	,	PUNCT
cana-735	312	10	s.b	s.b	PROPN
cana-735	312	11	.	.	PROPN
cana-735	312	12	fuzzy	fuzzy	ADJ
cana-735	312	13	system	system	NOUN
cana-735	312	14	reliability	reliability	NOUN
cana-735	312	15	using	use	VERB
cana-735	312	16	intuitionistic	intuitionistic	ADJ
cana-735	312	17	fuzzy	fuzzy	ADJ
cana-735	312	18	weibull	weibull	NOUN
cana-735	312	19	lifetime	lifetime	NOUN
cana-735	312	20	distribution	distribution	NOUN
cana-735	312	21	.	.	PUNCT
cana-735	313	1	int	int	NOUN
cana-735	313	2	.	.	PUNCT
cana-735	314	1	j.	j.	PROPN
cana-735	314	2	reliab	reliab	PROPN
cana-735	314	3	.	.	PUNCT
cana-735	315	1	appl	appl	PROPN
cana-735	315	2	.	.	PROPN
cana-735	316	1	2015	2015	NUM
cana-735	316	2	,	,	PUNCT
cana-735	316	3	16	16	NUM
cana-735	316	4	,	,	PUNCT
cana-735	316	5	15–26	15–26	NUM
cana-735	316	6	.	.	PUNCT
cana-735	317	1	[	[	X
cana-735	317	2	20	20	NUM
cana-735	317	3	]	]	PUNCT
cana-735	317	4	nakagawa	nakagawa	PROPN
cana-735	317	5	,	,	PUNCT
cana-735	317	6	t.	t.	NOUN
cana-735	317	7	maintenance	maintenance	NOUN
cana-735	317	8	theory	theory	NOUN
cana-735	317	9	of	of	ADP
cana-735	317	10	reliability	reliability	NOUN
cana-735	317	11	;	;	PUNCT
cana-735	317	12	springer	springer	NOUN
cana-735	317	13	-	-	PUNCT
cana-735	317	14	verlag	verlag	PROPN
cana-735	317	15	:	:	PUNCT
cana-735	317	16	london	london	PROPN
cana-735	317	17	,	,	PUNCT
cana-735	317	18	uk	uk	PROPN
cana-735	317	19	,	,	PUNCT
cana-735	317	20	2005	2005	NUM
cana-735	317	21	.	.	PUNCT
cana-735	318	1	[	[	X
cana-735	318	2	21	21	NUM
cana-735	318	3	]	]	X
cana-735	318	4	kobbacy	kobbacy	NOUN
cana-735	318	5	,	,	PUNCT
cana-735	318	6	k.a.h	k.a.h	PROPN
cana-735	318	7	.	.	PROPN
cana-735	318	8	;	;	PUNCT
cana-735	318	9	murthy	murthy	ADJ
cana-735	318	10	,	,	PUNCT
cana-735	318	11	d.n.p	d.n.p	ADJ
cana-735	318	12	.	.	PUNCT
cana-735	318	13	complex	complex	ADJ
cana-735	318	14	system	system	NOUN
cana-735	318	15	maintenance	maintenance	NOUN
cana-735	318	16	handbook	handbook	NOUN
cana-735	318	17	;	;	PUNCT
cana-735	318	18	springer	springer	NOUN
cana-735	318	19	nature	nature	NOUN
cana-735	318	20	:	:	PUNCT
cana-735	318	21	cham	cham	PROPN
cana-735	318	22	,	,	PUNCT
cana-735	318	23	switzerland	switzerland	PROPN
cana-735	318	24	,	,	PUNCT
cana-735	318	25	2008	2008	NUM
cana-735	318	26	.	.	PUNCT
cana-735	319	1	communications	communication	NOUN
cana-735	319	2	on	on	ADP
cana-735	319	3	applied	apply	VERB
cana-735	319	4	nonlinear	nonlinear	ADJ
cana-735	319	5	analysis	analysis	NOUN
cana-735	319	6	issn	issn	NOUN
cana-735	319	7	:	:	PUNCT
cana-735	319	8	1074	1074	NUM
cana-735	319	9	-	-	PUNCT
cana-735	319	10	133x	133x	NUM
cana-735	319	11	vol	vol	NOUN
cana-735	319	12	31	31	NUM
cana-735	319	13	no	no	NOUN
cana-735	319	14	.	.	PUNCT
cana-735	320	1	3s	3s	NUM
cana-735	320	2	(	(	PUNCT
cana-735	320	3	2024	2024	NUM
cana-735	320	4	)	)	PUNCT
cana-735	320	5	117	117	NUM
cana-735	320	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-735	321	1	[	[	X
cana-735	321	2	22	22	NUM
cana-735	321	3	]	]	X
cana-735	321	4	rinne	rinne	PROPN
cana-735	321	5	,	,	PUNCT
cana-735	321	6	h.	h.	PROPN
cana-735	322	1	the	the	DET
cana-735	322	2	weibull	weibull	PROPN
cana-735	322	3	distribution	distribution	NOUN
cana-735	322	4	a	a	DET
cana-735	322	5	handbook	handbook	NOUN
cana-735	322	6	,	,	PUNCT
cana-735	322	7	1st	1st	ADJ
cana-735	322	8	ed	ed	NOUN
cana-735	322	9	.	.	PUNCT
cana-735	322	10	;	;	PUNCT
cana-735	322	11	chapman	chapman	NOUN
cana-735	322	12	and	and	CCONJ
cana-735	322	13	hall	hall	PROPN
cana-735	322	14	/	/	SYM
cana-735	322	15	crc	crc	PROPN
cana-735	322	16	:	:	PUNCT
cana-735	322	17	new	new	PROPN
cana-735	322	18	york	york	PROPN
cana-735	322	19	,	,	PUNCT
cana-735	322	20	ny	ny	PROPN
cana-735	322	21	,	,	PUNCT
cana-735	322	22	usa	usa	PROPN
cana-735	322	23	,	,	PUNCT
cana-735	322	24	2008	2008	NUM
cana-735	322	25	.	.	PUNCT
cana-735	323	1	[	[	X
cana-735	323	2	23	23	NUM
cana-735	323	3	]	]	X
cana-735	323	4	mccool	mccool	PROPN
cana-735	323	5	,	,	PUNCT
cana-735	323	6	j.i	j.i	PROPN
cana-735	323	7	.	.	PROPN
cana-735	323	8	using	use	VERB
cana-735	323	9	the	the	DET
cana-735	323	10	weibull	weibull	NOUN
cana-735	323	11	distribution	distribution	NOUN
cana-735	323	12	:	:	PUNCT
cana-735	323	13	reliability	reliability	NOUN
cana-735	323	14	,	,	PUNCT
cana-735	323	15	modeling	modeling	NOUN
cana-735	323	16	,	,	PUNCT
cana-735	323	17	and	and	CCONJ
cana-735	323	18	inference	inference	NOUN
cana-735	323	19	;	;	PUNCT
cana-735	323	20	john	john	PROPN
cana-735	323	21	wiley	wiley	PROPN
cana-735	323	22	&	&	CCONJ
cana-735	323	23	sons	sons	PROPN
cana-735	323	24	:	:	PUNCT
cana-735	323	25	hoboken	hoboken	PROPN
cana-735	323	26	,	,	PUNCT
cana-735	323	27	nj	nj	PROPN
cana-735	323	28	,	,	PUNCT
cana-735	323	29	usa	usa	PROPN
cana-735	323	30	,	,	PUNCT
cana-735	323	31	2012	2012	NUM
cana-735	323	32	.	.	PUNCT
cana-735	324	1	[	[	X
cana-735	324	2	24	24	NUM
cana-735	324	3	]	]	X
cana-735	324	4	ebrahimnejad	ebrahimnejad	PROPN
cana-735	324	5	,	,	PUNCT
cana-735	324	6	a.	a.	NOUN
cana-735	324	7	;	;	PUNCT
cana-735	324	8	verdegay	verdegay	NOUN
cana-735	324	9	,	,	PUNCT
cana-735	324	10	j.l	j.l	PROPN
cana-735	324	11	.	.	PROPN
cana-735	324	12	fuzzy	fuzzy	ADJ
cana-735	324	13	sets	set	NOUN
cana-735	324	14	-	-	PUNCT
cana-735	324	15	based	base	VERB
cana-735	324	16	methods	method	NOUN
cana-735	324	17	and	and	CCONJ
cana-735	324	18	techniques	technique	NOUN
cana-735	324	19	for	for	ADP
cana-735	324	20	modern	modern	ADJ
cana-735	324	21	analytics	analytic	NOUN
cana-735	324	22	;	;	PUNCT
cana-735	324	23	springer	springer	NOUN
cana-735	324	24	international	international	ADJ
cana-735	324	25	publishing	publishing	NOUN
cana-735	324	26	:	:	PUNCT
cana-735	324	27	cham	cham	PROPN
cana-735	324	28	,	,	PUNCT
cana-735	324	29	switzerland	switzerland	PROPN
cana-735	324	30	,	,	PUNCT
cana-735	324	31	2018	2018	NUM
cana-735	324	32	.	.	PUNCT
cana-735	325	1	[	[	X
cana-735	325	2	25	25	NUM
cana-735	325	3	]	]	X
cana-735	325	4	ebrahimnejad	ebrahimnejad	PROPN
cana-735	325	5	,	,	PUNCT
cana-735	325	6	a.	a.	NOUN
cana-735	325	7	new	new	ADJ
cana-735	325	8	method	method	NOUN
cana-735	325	9	for	for	ADP
cana-735	325	10	solving	solve	VERB
cana-735	325	11	fuzzy	fuzzy	ADJ
cana-735	325	12	transportation	transportation	NOUN
cana-735	325	13	problems	problem	NOUN
cana-735	325	14	with	with	ADP
cana-735	325	15	lr	lr	NOUN
cana-735	325	16	flat	flat	ADJ
cana-735	325	17	fuzzy	fuzzy	ADJ
cana-735	325	18	numbers	number	NOUN
cana-735	325	19	.	.	PUNCT
cana-735	326	1	inf	inf	PROPN
cana-735	326	2	.	.	PUNCT
cana-735	327	1	sci	sci	PROPN
cana-735	327	2	.	.	PROPN
cana-735	327	3	2016	2016	NUM
cana-735	327	4	,	,	PUNCT
cana-735	327	5	357	357	NUM
cana-735	327	6	,	,	PUNCT
cana-735	327	7	108–124	108–124	NUM
cana-735	327	8	.	.	PUNCT
cana-735	328	1	[	[	X
cana-735	328	2	26	26	NUM
cana-735	328	3	]	]	PUNCT
cana-735	328	4	jain	jain	PROPN
cana-735	328	5	,	,	PUNCT
cana-735	328	6	s.	s.	PROPN
cana-735	328	7	close	close	ADJ
cana-735	328	8	interval	interval	NOUN
cana-735	328	9	approximation	approximation	NOUN
cana-735	328	10	of	of	ADP
cana-735	328	11	piecewise	piecewise	NOUN
cana-735	328	12	quadratic	quadratic	ADJ
cana-735	328	13	fuzzy	fuzzy	ADJ
cana-735	328	14	numbers	number	NOUN
cana-735	328	15	for	for	ADP
cana-735	328	16	fuzzy	fuzzy	ADJ
cana-735	328	17	fractional	fractional	ADJ
cana-735	328	18	program	program	NOUN
cana-735	328	19	.	.	PUNCT
cana-735	329	1	iran	iran	PROPN
cana-735	329	2	.	.	PUNCT
cana-735	330	1	j.	j.	PROPN
cana-735	330	2	oper	oper	PROPN
cana-735	330	3	.	.	PUNCT
cana-735	331	1	res	res	PROPN
cana-735	331	2	.	.	PUNCT
cana-735	331	3	2010	2010	NUM
cana-735	331	4	,	,	PUNCT
cana-735	331	5	2	2	NUM
cana-735	331	6	,	,	PUNCT
cana-735	331	7	77–88	77–88	NUM
cana-735	331	8	.	.	PUNCT
cana-735	332	1	[	[	X
cana-735	332	2	27	27	NUM
cana-735	332	3	]	]	PUNCT
cana-735	332	4	panda	panda	NOUN
cana-735	332	5	,	,	PUNCT
cana-735	332	6	a.	a.	NOUN
cana-735	332	7	;	;	PUNCT
cana-735	332	8	pal	pal	NOUN
cana-735	332	9	,	,	PUNCT
cana-735	332	10	m.	m.	NOUN
cana-735	332	11	a	a	DET
cana-735	332	12	study	study	NOUN
cana-735	332	13	on	on	ADP
cana-735	332	14	pentagonal	pentagonal	ADJ
cana-735	332	15	fuzzy	fuzzy	ADJ
cana-735	332	16	number	number	NOUN
cana-735	332	17	and	and	CCONJ
cana-735	332	18	its	its	PRON
cana-735	332	19	corresponding	corresponding	ADJ
cana-735	332	20	matrices	matrix	NOUN
cana-735	332	21	.	.	PUNCT
cana-735	333	1	pac	pac	PROPN
cana-735	333	2	.	.	PUNCT
cana-735	333	3	sci	sci	PROPN
cana-735	333	4	.	.	PROPN
cana-735	333	5	rev	rev	PROPN
cana-735	333	6	.	.	PROPN
cana-735	333	7	b.	b.	PROPN
cana-735	333	8	humanit	humanit	PROPN
cana-735	333	9	.	.	PUNCT
cana-735	334	1	soc	soc	PROPN
cana-735	334	2	.	.	PUNCT
cana-735	335	1	sci	sci	PROPN
cana-735	335	2	.	.	PROPN
cana-735	335	3	2015	2015	NUM
cana-735	335	4	,	,	PUNCT
cana-735	335	5	1	1	NUM
cana-735	335	6	,	,	PUNCT
cana-735	335	7	131–139	131–139	NUM
cana-735	335	8	.	.	PUNCT
cana-735	336	1	[	[	X
cana-735	336	2	28	28	NUM
cana-735	336	3	]	]	X
cana-735	336	4	maturo	maturo	PROPN
cana-735	336	5	,	,	PUNCT
cana-735	336	6	f.	f.	PROPN
cana-735	336	7	;	;	PUNCT
cana-735	336	8	fortuna	fortuna	PROPN
cana-735	336	9	,	,	PUNCT
cana-735	336	10	f.	f.	PROPN
cana-735	336	11	bell	bell	PROPN
cana-735	336	12	-	-	PUNCT
cana-735	336	13	shaped	shape	VERB
cana-735	336	14	fuzzy	fuzzy	ADJ
cana-735	336	15	numbers	number	NOUN
cana-735	336	16	associated	associate	VERB
cana-735	336	17	with	with	ADP
cana-735	336	18	the	the	DET
cana-735	336	19	normal	normal	ADJ
cana-735	336	20	curve	curve	NOUN
cana-735	336	21	.	.	PUNCT
cana-735	337	1	in	in	ADP
cana-735	337	2	topics	topic	NOUN
cana-735	337	3	on	on	ADP
cana-735	337	4	methodological	methodological	ADJ
cana-735	337	5	and	and	CCONJ
cana-735	337	6	applied	apply	VERB
cana-735	337	7	statistical	statistical	ADJ
cana-735	337	8	inference	inference	NOUN
cana-735	337	9	;	;	PUNCT
cana-735	337	10	di	di	X
cana-735	337	11	battista	battista	PROPN
cana-735	337	12	,	,	PUNCT
cana-735	337	13	t.	t.	PROPN
cana-735	337	14	,	,	PUNCT
cana-735	337	15	moreno	moreno	PROPN
cana-735	337	16	,	,	PUNCT
cana-735	337	17	e.	e.	PROPN
cana-735	337	18	,	,	PUNCT
cana-735	337	19	racugno	racugno	PROPN
cana-735	337	20	,	,	PUNCT
cana-735	337	21	w.	w.	PROPN
cana-735	337	22	,	,	PUNCT
cana-735	337	23	eds	eds	PROPN
cana-735	337	24	.	.	PUNCT
cana-735	337	25	;	;	PUNCT
cana-735	337	26	springer	springer	NOUN
cana-735	337	27	nature	nature	NOUN
cana-735	337	28	:	:	PUNCT
cana-735	337	29	cham	cham	PROPN
cana-735	337	30	,	,	PUNCT
cana-735	337	31	switzerland	switzerland	PROPN
cana-735	337	32	,	,	PUNCT
cana-735	337	33	2016	2016	NUM
cana-735	337	34	;	;	PUNCT
cana-735	337	35	pp	pp	ADP
cana-735	337	36	.	.	PUNCT
cana-735	338	1	131–144	131–144	NUM
cana-735	338	2	.	.	PUNCT
cana-735	339	1	[	[	X
cana-735	339	2	29	29	NUM
cana-735	339	3	]	]	PUNCT
cana-735	339	4	thangavelu	thangavelu	NOUN
cana-735	339	5	,	,	PUNCT
cana-735	339	6	k.	k.	PROPN
cana-735	339	7	;	;	PUNCT
cana-735	339	8	uthra	uthra	PROPN
cana-735	339	9	,	,	PUNCT
cana-735	339	10	g.	g.	PROPN
cana-735	339	11	;	;	PUNCT
cana-735	339	12	shanmugapriya	shanmugapriya	PROPN
cana-735	339	13	,	,	PUNCT
cana-735	339	14	s.	s.	PROPN
cana-735	339	15	a	a	DET
cana-735	339	16	new	new	ADJ
cana-735	339	17	approach	approach	NOUN
cana-735	339	18	on	on	ADP
cana-735	339	19	the	the	DET
cana-735	339	20	membership	membership	NOUN
cana-735	339	21	functions	function	NOUN
cana-735	339	22	of	of	ADP
cana-735	339	23	fuzzy	fuzzy	ADJ
cana-735	339	24	numbers	number	NOUN
cana-735	339	25	.	.	PUNCT
cana-735	340	1	int	int	NOUN
cana-735	340	2	.	.	PUNCT
cana-735	341	1	j.	j.	PROPN
cana-735	341	2	pure	pure	PROPN
cana-735	341	3	appl	appl	PROPN
cana-735	341	4	.	.	PUNCT
cana-735	341	5	math	math	PROPN
cana-735	341	6	.	.	PUNCT
cana-735	342	1	2017	2017	NUM
cana-735	342	2	,	,	PUNCT
cana-735	342	3	114	114	NUM
cana-735	342	4	,	,	PUNCT
cana-735	342	5	145–152	145–152	NUM
cana-735	342	6	.	.	PUNCT
cana-735	343	1	[	[	X
cana-735	343	2	30	30	NUM
cana-735	343	3	]	]	X
cana-735	343	4	bagheri	bagheri	PROPN
cana-735	343	5	,	,	PUNCT
cana-735	343	6	n.	n.	NOUN
cana-735	343	7	;	;	PUNCT
cana-735	343	8	hashemin	hashemin	PROPN
cana-735	343	9	,	,	PUNCT
cana-735	343	10	s.s	s.s	PROPN
cana-735	343	11	.	.	PUNCT
cana-735	344	1	a	a	DET
cana-735	344	2	new	new	ADJ
cana-735	344	3	bell	bell	NOUN
cana-735	344	4	shape	shape	NOUN
cana-735	344	5	fuzzy	fuzzy	ADJ
cana-735	344	6	number	number	NOUN
cana-735	344	7	.	.	PUNCT
cana-735	345	1	int	int	NOUN
cana-735	345	2	.	.	PUNCT
cana-735	346	1	j.	j.	PROPN
cana-735	346	2	math	math	PROPN
cana-735	346	3	.	.	PUNCT
cana-735	347	1	trends	trend	NOUN
cana-735	347	2	technol	technol	ADJ
cana-735	347	3	.	.	PROPN
cana-735	347	4	2018	2018	NUM
cana-735	347	5	,	,	PUNCT
cana-735	347	6	54	54	NUM
cana-735	347	7	,	,	PUNCT
cana-735	347	8	377–382	377–382	NUM
cana-735	347	9	.	.	PUNCT
cana-735	348	1	[	[	X
cana-735	348	2	31	31	NUM
cana-735	348	3	]	]	PUNCT
cana-735	348	4	van	van	PROPN
cana-735	348	5	leekwijck	leekwijck	PROPN
cana-735	348	6	,	,	PUNCT
cana-735	348	7	w.	w.	PROPN
cana-735	348	8	;	;	PUNCT
cana-735	348	9	kerre	kerre	PROPN
cana-735	348	10	,	,	PUNCT
cana-735	348	11	e.e	e.e	PROPN
cana-735	348	12	.	.	PROPN
cana-735	348	13	defuzzification	defuzzification	NOUN
cana-735	348	14	:	:	PUNCT
cana-735	348	15	criteria	criterion	NOUN
cana-735	348	16	and	and	CCONJ
cana-735	348	17	classification	classification	NOUN
cana-735	348	18	.	.	PUNCT
cana-735	349	1	fuzzy	fuzzy	ADJ
cana-735	349	2	sets	set	VERB
cana-735	349	3	syst	syst	PROPN
cana-735	349	4	.	.	PUNCT
cana-735	349	5	1999	1999	NUM
cana-735	349	6	,	,	PUNCT
cana-735	349	7	108	108	NUM
cana-735	349	8	,	,	PUNCT
cana-735	349	9	159–178	159–178	NUM
cana-735	349	10	.	.	PUNCT
cana-735	350	1	[	[	X
cana-735	350	2	32	32	NUM
cana-735	350	3	]	]	PUNCT
cana-735	350	4	madau	madau	NOUN
cana-735	350	5	,	,	PUNCT
cana-735	350	6	d.p	d.p	PROPN
cana-735	350	7	.	.	PROPN
cana-735	350	8	;	;	PUNCT
cana-735	350	9	feldkamp	feldkamp	PROPN
cana-735	350	10	,	,	PUNCT
cana-735	350	11	l.a	l.a	PROPN
cana-735	350	12	.	.	PROPN
cana-735	350	13	influence	influence	NOUN
cana-735	350	14	value	value	NOUN
cana-735	350	15	defuzzification	defuzzification	NOUN
cana-735	350	16	method	method	NOUN
cana-735	350	17	.	.	PUNCT
cana-735	351	1	in	in	ADP
cana-735	351	2	proceedings	proceeding	NOUN
cana-735	351	3	of	of	ADP
cana-735	351	4	the	the	DET
cana-735	351	5	ieee	ieee	NOUN
cana-735	351	6	5th	5th	ADJ
cana-735	351	7	international	international	ADJ
cana-735	351	8	fuzzy	fuzzy	ADJ
cana-735	351	9	systems	system	NOUN
cana-735	351	10	,	,	PUNCT
cana-735	351	11	new	new	PROPN
cana-735	351	12	orleans	orleans	PROPN
cana-735	351	13	,	,	PUNCT
cana-735	351	14	la	la	PROPN
cana-735	351	15	,	,	PUNCT
cana-735	351	16	usa	usa	PROPN
cana-735	351	17	,	,	PUNCT
cana-735	351	18	11	11	NUM
cana-735	351	19	september	september	PROPN
cana-735	351	20	1996	1996	NUM
cana-735	351	21	;	;	PUNCT
cana-735	351	22	pp	pp	X
cana-735	351	23	.	.	PUNCT
cana-735	351	24	1819–1824	1819–1824	X
cana-735	351	25	.	.	PUNCT
cana-735	352	1	[	[	X
cana-735	352	2	33	33	NUM
cana-735	352	3	]	]	X
cana-735	352	4	jager	jager	PROPN
cana-735	352	5	,	,	PUNCT
cana-735	352	6	b.	b.	PROPN
cana-735	352	7	;	;	PUNCT
cana-735	352	8	verbruggen	verbruggen	PROPN
cana-735	352	9	,	,	PUNCT
cana-735	352	10	h.b	h.b	PROPN
cana-735	352	11	.	.	PROPN
cana-735	352	12	;	;	PUNCT
cana-735	352	13	bruijn	bruijn	PROPN
cana-735	352	14	,	,	PUNCT
cana-735	352	15	p.m.	p.m.	NOUN
cana-735	353	1	the	the	DET
cana-735	353	2	role	role	NOUN
cana-735	353	3	of	of	ADP
cana-735	353	4	defuzzification	defuzzification	NOUN
cana-735	353	5	methods	method	NOUN
cana-735	353	6	in	in	ADP
cana-735	353	7	the	the	DET
cana-735	353	8	application	application	NOUN
cana-735	353	9	of	of	ADP
cana-735	353	10	fuzzy	fuzzy	ADJ
cana-735	353	11	control	control	NOUN
cana-735	353	12	.	.	PUNCT
cana-735	354	1	ifac	ifac	NOUN
cana-735	354	2	proc	proc	NOUN
cana-735	354	3	.	.	PUNCT
cana-735	355	1	umes	ume	NOUN
cana-735	355	2	1992	1992	NUM
cana-735	355	3	,	,	PUNCT
cana-735	355	4	25	25	NUM
cana-735	355	5	,	,	PUNCT
cana-735	355	6	75–80	75–80	PROPN
cana-735	355	7	.	.	PUNCT
cana-735	356	1	[	[	X
cana-735	356	2	34	34	NUM
cana-735	356	3	]	]	X
cana-735	356	4	koh	koh	PROPN
cana-735	356	5	,	,	PUNCT
cana-735	356	6	y.	y.	PROPN
cana-735	356	7	;	;	PUNCT
cana-735	356	8	ree	ree	NOUN
cana-735	356	9	,	,	PUNCT
cana-735	356	10	s.	s.	PROPN
cana-735	356	11	the	the	DET
cana-735	356	12	origin	origin	NOUN
cana-735	356	13	of	of	ADP
cana-735	356	14	newton	newton	PROPN
cana-735	356	15	’s	’s	PART
cana-735	356	16	generalized	generalize	VERB
cana-735	356	17	binomial	binomial	ADJ
cana-735	356	18	theorem	theorem	NOUN
cana-735	356	19	.	.	PUNCT
cana-735	356	20	j.	j.	PROPN
cana-735	356	21	hist	hist	PROPN
cana-735	356	22	.	.	PUNCT
cana-735	356	23	math	math	PROPN
cana-735	356	24	.	.	PUNCT
cana-735	357	1	2014	2014	NUM
cana-735	357	2	,	,	PUNCT
cana-735	357	3	27	27	NUM
cana-735	357	4	,	,	PUNCT
cana-735	357	5	127–138	127–138	NUM
cana-735	357	6	.	.	PUNCT
cana-735	358	1	[	[	X
cana-735	358	2	35	35	NUM
cana-735	358	3	]	]	PUNCT
cana-735	358	4	scheideggera	scheideggera	NOUN
cana-735	358	5	,	,	PUNCT
cana-735	358	6	a.	a.	NOUN
cana-735	358	7	;	;	PUNCT
cana-735	358	8	scholtena	scholtena	PROPN
cana-735	358	9	,	,	PUNCT
cana-735	358	10	l.	l.	PROPN
cana-735	358	11	;	;	PUNCT
cana-735	358	12	maurera	maurera	NOUN
cana-735	358	13	,	,	PUNCT
cana-735	358	14	m.	m.	NOUN
cana-735	358	15	;	;	PUNCT
cana-735	358	16	reichert	reichert	PROPN
cana-735	358	17	,	,	PUNCT
cana-735	358	18	p.	p.	NOUN
cana-735	358	19	extension	extension	NOUN
cana-735	358	20	of	of	ADP
cana-735	358	21	pipe	pipe	NOUN
cana-735	358	22	failure	failure	NOUN
cana-735	358	23	models	model	NOUN
cana-735	358	24	to	to	PART
cana-735	358	25	consider	consider	VERB
cana-735	358	26	the	the	DET
cana-735	358	27	absence	absence	NOUN
cana-735	358	28	of	of	ADP
cana-735	358	29	data	datum	NOUN
cana-735	358	30	from	from	ADP
cana-735	358	31	replaced	replace	VERB
cana-735	358	32	pipes	pipe	NOUN
cana-735	358	33	.	.	PUNCT
cana-735	359	1	water	water	NOUN
cana-735	359	2	res	re	NOUN
cana-735	359	3	.	.	PUNCT
cana-735	360	1	2013	2013	NUM
cana-735	360	2	,	,	PUNCT
cana-735	360	3	47	47	NUM
cana-735	360	4	,	,	PUNCT
cana-735	360	5	3696–3705	3696–3705	NUM
cana-735	360	6	.	.	PUNCT
cana-735	361	1	[	[	X
cana-735	361	2	36	36	NUM
cana-735	361	3	]	]	X
cana-735	361	4	izadparast	izadparast	NOUN
cana-735	361	5	,	,	PUNCT
cana-735	361	6	h.a	h.a	PROPN
cana-735	361	7	.	.	PROPN
cana-735	361	8	;	;	PUNCT
cana-735	361	9	niedzwecki	niedzwecki	PROPN
cana-735	361	10	,	,	PUNCT
cana-735	361	11	j.m	j.m	PROPN
cana-735	361	12	.	.	PROPN
cana-735	361	13	four	four	NUM
cana-735	361	14	-	-	PUNCT
cana-735	361	15	parameter	parameter	NOUN
cana-735	361	16	weibull	weibull	PROPN
cana-735	361	17	probability	probability	NOUN
cana-735	361	18	distribution	distribution	NOUN
cana-735	361	19	model	model	NOUN
cana-735	361	20	for	for	ADP
cana-735	361	21	weakly	weakly	ADJ
cana-735	361	22	non	non	ADJ
cana-735	361	23	-	-	ADJ
cana-735	361	24	linear	linear	ADJ
cana-735	361	25	random	random	ADJ
cana-735	361	26	variables	variable	NOUN
cana-735	361	27	.	.	PUNCT
cana-735	362	1	probabilistic	probabilistic	PROPN
cana-735	362	2	eng	eng	PROPN
cana-735	362	3	.	.	PROPN
cana-735	362	4	mech	mech	PROPN
cana-735	362	5	.	.	PUNCT
cana-735	363	1	2013	2013	NUM
cana-735	363	2	,	,	PUNCT
cana-735	363	3	32	32	NUM
cana-735	363	4	,	,	PUNCT
cana-735	363	5	31–38	31–38	NUM
cana-735	363	6	.	.	PUNCT
cana-735	364	1	[	[	X
cana-735	364	2	37	37	NUM
cana-735	364	3	]	]	X
cana-735	364	4	gupta	gupta	PROPN
cana-735	364	5	r.d	r.d	PROPN
cana-735	364	6	and	and	CCONJ
cana-735	364	7	kundu	kundu	NOUN
cana-735	364	8	d	d	PROPN
cana-735	364	9	,	,	PUNCT
cana-735	364	10	2001	2001	NUM
cana-735	364	11	.	.	PUNCT
cana-735	365	1	“	"	PUNCT
cana-735	365	2	exponentiated	exponentiate	VERB
cana-735	365	3	exponential	exponential	ADJ
cana-735	365	4	family	family	NOUN
cana-735	365	5	:	:	PUNCT
cana-735	365	6	an	an	DET
cana-735	365	7	alternative	alternative	NOUN
cana-735	365	8	to	to	ADP
cana-735	365	9	gamma	gamma	NOUN
cana-735	365	10	and	and	CCONJ
cana-735	365	11	weibull	weibull	PROPN
cana-735	365	12	distributions	distribution	NOUN
cana-735	365	13	,	,	PUNCT
cana-735	365	14	”	"	PUNCT
cana-735	365	15	biometrical	biometrical	ADJ
cana-735	365	16	journal	journal	NOUN
cana-735	365	17	.	.	PUNCT
cana-735	366	1	117–130	117–130	NUM
cana-735	366	2	.	.	PUNCT
cana-735	367	1	https://doi.org/10.1002/1521-4036(200102)43:1<117::aidbimj117>3.0.co;2-r	https://doi.org/10.1002/1521-4036(200102)43:1<117::aidbimj117>3.0.co;2-r	X
cana-735	367	2	.	.	PUNCT
cana-735	368	1	[	[	X
cana-735	368	2	38	38	NUM
cana-735	368	3	]	]	PUNCT
cana-735	368	4	gajivaradhan	gajivaradhan	NOUN
cana-735	368	5	p	p	NOUN
cana-735	368	6	,	,	PUNCT
cana-735	368	7	parthiban	parthiban	NOUN
cana-735	368	8	s	s	NOUN
cana-735	368	9	,	,	PUNCT
cana-735	368	10	2015	2015	NUM
cana-735	368	11	.	.	PUNCT
cana-735	369	1	“	"	PUNCT
cana-735	369	2	statical	statical	ADJ
cana-735	369	3	hypothesis	hypothesis	NOUN
cana-735	369	4	testing	test	VERB
cana-735	369	5	through	through	ADP
cana-735	369	6	trapezoidal	trapezoidal	ADJ
cana-735	369	7	fuzzy	fuzzy	ADJ
cana-735	369	8	interval	interval	NOUN
cana-735	369	9	data	datum	NOUN
cana-735	369	10	.	.	PUNCT
cana-735	369	11	”	"	PUNCT
cana-735	370	1	international	international	ADJ
cana-735	370	2	research	research	NOUN
cana-735	370	3	journal	journal	NOUN
cana-735	370	4	of	of	ADP
cana-735	370	5	engineering	engineering	NOUN
cana-735	370	6	and	and	CCONJ
cana-735	370	7	technology.252	technology.252	NOUN
cana-735	370	8	-	-	PUNCT
cana-735	370	9	258	258	NUM
cana-735	370	10	.	.	PUNCT
cana-735	371	1	[	[	X
cana-735	371	2	39	39	NUM
cana-735	371	3	]	]	PUNCT
cana-735	371	4	gajivaradhan	gajivaradhan	NOUN
cana-735	371	5	p	p	X
cana-735	371	6	,	,	PUNCT
cana-735	371	7	parthiban	parthiban	ADJ
cana-735	371	8	s.	s.	PROPN
cana-735	371	9	2016	2016	NUM
cana-735	371	10	.	.	PUNCT
cana-735	372	1	“	"	PUNCT
cana-735	372	2	statical	statical	ADJ
cana-735	372	3	hypothesis	hypothesis	NOUN
cana-735	372	4	test	test	NOUN
cana-735	372	5	in	in	ADP
cana-735	372	6	three	three	NUM
cana-735	372	7	factor	factor	NOUN
cana-735	372	8	anova	anova	PROPN
cana-735	372	9	model	model	PROPN
cana-735	372	10	under	under	ADP
cana-735	372	11	fuzzy	fuzzy	ADJ
cana-735	372	12	environments	environment	NOUN
cana-735	372	13	using	use	VERB
cana-735	372	14	trapezoidal	trapezoidal	ADJ
cana-735	372	15	fuzzy	fuzzy	ADJ
cana-735	372	16	numbers	number	NOUN
cana-735	372	17	.	.	PUNCT
cana-735	372	18	”	"	PUNCT
cana-735	373	1	bulletin	bulletin	NOUN
cana-735	373	2	of	of	ADP
cana-735	373	3	mathematical	mathematical	ADJ
cana-735	373	4	sciences	science	NOUN
cana-735	373	5	and	and	CCONJ
cana-735	373	6	applications	application	NOUN
cana-735	373	7	.	.	PUNCT
cana-735	374	1	23	23	NUM
cana-735	374	2	-	-	SYM
cana-735	374	3	42	42	NUM
cana-735	374	4	.	.	PUNCT
cana-735	375	1	https://doi.org/10.18052/www.scipress.com/bmsa.14.23	https://doi.org/10.18052/www.scipress.com/bmsa.14.23	X
cana-735	375	2	.	.	PUNCT