id	sid	tid	token	lemma	pos
cana-766	1	1	communications	communication	NOUN
cana-766	1	2	on	on	ADP
cana-766	1	3	applied	apply	VERB
cana-766	1	4	nonlinear	nonlinear	ADJ
cana-766	1	5	analysis	analysis	NOUN
cana-766	1	6	issn	issn	NOUN
cana-766	1	7	:	:	PUNCT
cana-766	1	8	1074	1074	NUM
cana-766	1	9	-	-	PUNCT
cana-766	1	10	133x	133x	NUM
cana-766	1	11	vol	vol	NOUN
cana-766	1	12	31	31	NUM
cana-766	1	13	no	no	NOUN
cana-766	1	14	.	.	PUNCT
cana-766	2	1	3s	3s	NUM
cana-766	2	2	(	(	PUNCT
cana-766	2	3	2024	2024	NUM
cana-766	2	4	)	)	PUNCT
cana-766	2	5	294	294	NUM
cana-766	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-766	2	7	vague	vague	ADJ
cana-766	2	8	strong	strong	ADJ
cana-766	2	9	implicative	implicative	ADJ
cana-766	2	10	filters	filter	NOUN
cana-766	2	11	of	of	ADP
cana-766	2	12	lattice	lattice	PROPN
cana-766	2	13	wajsberg	wajsberg	PROPN
cana-766	2	14	algebras	algebras	PROPN
cana-766	2	15	1.praveen	1.praveen	NUM
cana-766	2	16	vardhan	vardhan	PROPN
cana-766	2	17	kuppili	kuppili	PROPN
cana-766	2	18	,	,	PUNCT
cana-766	2	19	2.v.b.v.n.prasad	2.v.b.v.n.prasad	PROPN
cana-766	2	20	,	,	PUNCT
cana-766	2	21	3.rama	3.rama	NUM
cana-766	2	22	devi	devi	PROPN
cana-766	2	23	burri	burri	PROPN
cana-766	2	24	1research	1research	NUM
cana-766	2	25	scholar	scholar	NOUN
cana-766	2	26	,	,	PUNCT
cana-766	2	27	department	department	NOUN
cana-766	2	28	of	of	ADP
cana-766	2	29	engineering	engineering	NOUN
cana-766	2	30	mathematics	mathematic	NOUN
cana-766	2	31	,	,	PUNCT
cana-766	2	32	koneru	koneru	PROPN
cana-766	2	33	lakshmaiah	lakshmaiah	PROPN
cana-766	2	34	education	education	PROPN
cana-766	2	35	foundation	foundation	PROPN
cana-766	2	36	,	,	PUNCT
cana-766	2	37	vaddeswaram	vaddeswaram	PROPN
cana-766	2	38	,	,	PUNCT
cana-766	2	39	guntur	guntur	PROPN
cana-766	2	40	,	,	PUNCT
cana-766	2	41	a.p	a.p	PROPN
cana-766	2	42	,	,	PUNCT
cana-766	2	43	india	india	PROPN
cana-766	2	44	.	.	PUNCT
cana-766	3	1	pvkuppili@yahoo.co.in	pvkuppili@yahoo.co.in	CCONJ
cana-766	3	2	2.v.b.v.n.prasad	2.v.b.v.n.prasad	NOUN
cana-766	3	3	,	,	PUNCT
cana-766	3	4	professor	professor	NOUN
cana-766	3	5	,	,	PUNCT
cana-766	3	6	department	department	NOUN
cana-766	3	7	of	of	ADP
cana-766	3	8	engineering	engineering	NOUN
cana-766	3	9	mathematics	mathematic	NOUN
cana-766	3	10	,	,	PUNCT
cana-766	3	11	koneru	koneru	PROPN
cana-766	3	12	lakshmaiah	lakshmaiah	PROPN
cana-766	3	13	education	education	PROPN
cana-766	3	14	foundation	foundation	PROPN
cana-766	3	15	,	,	PUNCT
cana-766	3	16	vaddeswaram	vaddeswaram	PROPN
cana-766	3	17	,	,	PUNCT
cana-766	3	18	guntur	guntur	PROPN
cana-766	3	19	,	,	PUNCT
cana-766	3	20	a.p	a.p	PROPN
cana-766	3	21	,	,	PUNCT
cana-766	3	22	india	india	PROPN
cana-766	3	23	.	.	PUNCT
cana-766	4	1	vbvnprasad@kluniversity.in	vbvnprasad@kluniversity.in	PROPN
cana-766	4	2	3professor	3professor	NUM
cana-766	4	3	,	,	PUNCT
cana-766	4	4	department	department	NOUN
cana-766	4	5	of	of	ADP
cana-766	4	6	information	information	NOUN
cana-766	4	7	technology	technology	PROPN
cana-766	4	8	,	,	PUNCT
cana-766	4	9	institute	institute	NOUN
cana-766	4	10	of	of	ADP
cana-766	4	11	aeronautical	aeronautical	PROPN
cana-766	4	12	engineering	engineering	PROPN
cana-766	4	13	,	,	PUNCT
cana-766	4	14	dundigal	dundigal	PROPN
cana-766	4	15	,	,	PUNCT
cana-766	4	16	hyderabad	hyderabad	PROPN
cana-766	4	17	,	,	PUNCT
cana-766	4	18	telangana	telangana	PROPN
cana-766	4	19	,	,	PUNCT
cana-766	4	20	india	india	PROPN
cana-766	4	21	ramaburri5@gmail.com	ramaburri5@gmail.com	PROPN
cana-766	4	22	article	article	NOUN
cana-766	4	23	history	history	NOUN
cana-766	4	24	:	:	PUNCT
cana-766	4	25	received	receive	VERB
cana-766	4	26	:	:	PUNCT
cana-766	4	27	10	10	NUM
cana-766	4	28	-	-	PUNCT
cana-766	4	29	04	04	NUM
cana-766	4	30	-	-	PUNCT
cana-766	4	31	2024	2024	NUM
cana-766	4	32	revised	revise	VERB
cana-766	4	33	:	:	PUNCT
cana-766	4	34	24	24	NUM
cana-766	4	35	-	-	PUNCT
cana-766	4	36	05	05	NUM
cana-766	4	37	-	-	PUNCT
cana-766	4	38	2024	2024	NUM
cana-766	4	39	accepted	accept	VERB
cana-766	4	40	:	:	PUNCT
cana-766	4	41	12	12	NUM
cana-766	4	42	-	-	PUNCT
cana-766	4	43	06	06	NUM
cana-766	4	44	-	-	PUNCT
cana-766	4	45	2024	2024	NUM
cana-766	4	46	abstract	abstract	NOUN
cana-766	4	47	:	:	PUNCT
cana-766	4	48	in	in	ADP
cana-766	4	49	this	this	DET
cana-766	4	50	paper	paper	NOUN
cana-766	4	51	,	,	PUNCT
cana-766	4	52	we	we	PRON
cana-766	4	53	introduce	introduce	VERB
cana-766	4	54	the	the	DET
cana-766	4	55	notation	notation	NOUN
cana-766	4	56	of	of	ADP
cana-766	4	57	a	a	DET
cana-766	4	58	vague	vague	ADJ
cana-766	4	59	strong	strong	ADJ
cana-766	4	60	implicative	implicative	ADJ
cana-766	4	61	filter	filter	NOUN
cana-766	4	62	of	of	ADP
cana-766	4	63	lattice	lattice	PROPN
cana-766	4	64	wajsberg	wajsberg	PROPN
cana-766	4	65	algebra	algebra	PROPN
cana-766	4	66	.	.	PUNCT
cana-766	5	1	also	also	ADV
cana-766	5	2	,	,	PUNCT
cana-766	5	3	we	we	PRON
cana-766	5	4	investigate	investigate	VERB
cana-766	5	5	some	some	PRON
cana-766	5	6	of	of	ADP
cana-766	5	7	its	its	PRON
cana-766	5	8	properties	property	NOUN
cana-766	5	9	with	with	ADP
cana-766	5	10	illustrations	illustration	NOUN
cana-766	5	11	.	.	PUNCT
cana-766	6	1	further	far	ADV
cana-766	6	2	,	,	PUNCT
cana-766	6	3	we	we	PRON
cana-766	6	4	obtain	obtain	VERB
cana-766	6	5	the	the	DET
cana-766	6	6	relation	relation	NOUN
cana-766	6	7	between	between	ADP
cana-766	6	8	vague	vague	ADJ
cana-766	6	9	implicative	implicative	ADJ
cana-766	6	10	filter	filter	NOUN
cana-766	6	11	and	and	CCONJ
cana-766	6	12	anti	anti	ADJ
cana-766	6	13	vague	vague	ADJ
cana-766	6	14	strong	strong	ADJ
cana-766	6	15	implicative	implicative	ADJ
cana-766	6	16	filter	filter	NOUN
cana-766	6	17	in	in	ADP
cana-766	6	18	lattice	lattice	PROPN
cana-766	6	19	wajssberg	wajssberg	PROPN
cana-766	6	20	algebra	algebra	PROPN
cana-766	6	21	.	.	PUNCT
cana-766	7	1	finally	finally	ADV
cana-766	7	2	,	,	PUNCT
cana-766	7	3	we	we	PRON
cana-766	7	4	establish	establish	VERB
cana-766	7	5	the	the	DET
cana-766	7	6	equivalent	equivalent	ADJ
cana-766	7	7	condition	condition	NOUN
cana-766	7	8	of	of	ADP
cana-766	7	9	a	a	DET
cana-766	7	10	vague	vague	ADJ
cana-766	7	11	strong	strong	ADJ
cana-766	7	12	implicative	implicative	ADJ
cana-766	7	13	filter	filter	NOUN
cana-766	7	14	.	.	PUNCT
cana-766	8	1	keywords	keyword	NOUN
cana-766	8	2	:	:	PUNCT
cana-766	8	3	wajsberg	wajsberg	ADJ
cana-766	8	4	algebra	algebra	NOUN
cana-766	8	5	;	;	PUNCT
cana-766	8	6	lattice	lattice	VERB
cana-766	8	7	wajsberg	wajsberg	PROPN
cana-766	8	8	algebra	algebra	PROPN
cana-766	8	9	;	;	PUNCT
cana-766	8	10	implicative	implicative	ADJ
cana-766	8	11	filter	filter	NOUN
cana-766	8	12	;	;	PUNCT
cana-766	9	1	strong	strong	ADJ
cana-766	9	2	implicative	implicative	ADJ
cana-766	9	3	filter	filter	NOUN
cana-766	9	4	,	,	PUNCT
cana-766	9	5	vague	vague	ADJ
cana-766	9	6	implicative	implicative	ADJ
cana-766	9	7	strong	strong	ADJ
cana-766	9	8	filter	filter	NOUN
cana-766	9	9	;	;	PUNCT
cana-766	9	10	vague	vague	ADJ
cana-766	9	11	strong	strong	ADJ
cana-766	9	12	implicative	implicative	ADJ
cana-766	9	13	filter	filter	NOUN
cana-766	9	14	;	;	PUNCT
cana-766	9	15	vague	vague	ADJ
cana-766	9	16	implicative	implicative	ADJ
cana-766	9	17	filter	filter	NOUN
cana-766	9	18	,	,	PUNCT
cana-766	9	19	vague	vague	ADJ
cana-766	9	20	strong	strong	ADJ
cana-766	9	21	implicative	implicative	ADJ
cana-766	9	22	filter	filter	NOUN
cana-766	9	23	.	.	PUNCT
cana-766	10	1	1	1	X
cana-766	10	2	.	.	X
cana-766	10	3	introduction	introduction	NOUN
cana-766	10	4	:	:	PUNCT
cana-766	10	5	the	the	DET
cana-766	10	6	concept	concept	NOUN
cana-766	10	7	of	of	ADP
cana-766	10	8	lattice	lattice	NOUN
cana-766	10	9	was	be	AUX
cana-766	10	10	first	first	ADV
cana-766	10	11	defined	define	VERB
cana-766	10	12	by	by	ADP
cana-766	10	13	dedekind	dedekind	NOUN
cana-766	10	14	in	in	ADP
cana-766	10	15	1897	1897	NUM
cana-766	10	16	and	and	CCONJ
cana-766	10	17	then	then	ADV
cana-766	10	18	developed	develop	VERB
cana-766	10	19	by	by	ADP
cana-766	10	20	birkhoft.g	birkhoft.g	PROPN
cana-766	10	21	,	,	PUNCT
cana-766	10	22	imposed	impose	VERB
cana-766	10	23	an	an	DET
cana-766	10	24	operation	operation	NOUN
cana-766	10	25	an	an	DET
cana-766	10	26	open	open	ADJ
cana-766	10	27	problem	problem	NOUN
cana-766	10	28	"	"	PUNCT
cana-766	10	29	is	be	AUX
cana-766	10	30	there	there	PRON
cana-766	10	31	a	a	DET
cana-766	10	32	common	common	ADJ
cana-766	10	33	abstraction	abstraction	NOUN
cana-766	10	34	which	which	PRON
cana-766	10	35	includes	include	VERB
cana-766	10	36	boolean	boolean	ADJ
cana-766	10	37	algebra	algebra	NOUN
cana-766	10	38	,	,	PUNCT
cana-766	10	39	boolean	boolean	ADJ
cana-766	10	40	rings	ring	NOUN
cana-766	10	41	and	and	CCONJ
cana-766	10	42	lattice	lattice	PROPN
cana-766	10	43	ordered	order	VERB
cana-766	10	44	group	group	NOUN
cana-766	10	45	or	or	CCONJ
cana-766	10	46	l	l	NOUN
cana-766	10	47	-	-	NOUN
cana-766	10	48	group	group	NOUN
cana-766	10	49	is	be	AUX
cana-766	10	50	an	an	DET
cana-766	10	51	algebraic	algebraic	ADJ
cana-766	10	52	structure	structure	NOUN
cana-766	10	53	connecting	connect	VERB
cana-766	10	54	lattice	lattice	NOUN
cana-766	10	55	and	and	CCONJ
cana-766	10	56	group	group	NOUN
cana-766	10	57	.	.	PUNCT
cana-766	11	1	to	to	PART
cana-766	11	2	answer	answer	VERB
cana-766	11	3	this	this	DET
cana-766	11	4	problem	problem	NOUN
cana-766	11	5	many	many	ADJ
cana-766	11	6	common	common	ADJ
cana-766	11	7	abstractions	abstraction	NOUN
cana-766	11	8	,	,	PUNCT
cana-766	11	9	namely	namely	ADV
cana-766	11	10	dually	dually	ADV
cana-766	11	11	residuated	residuate	VERB
cana-766	11	12	lattice	lattice	NOUN
cana-766	11	13	ordered	order	VERB
cana-766	11	14	semigroups	semigroup	NOUN
cana-766	11	15	,	,	PUNCT
cana-766	11	16	commutative	commutative	ADJ
cana-766	11	17	lattice	lattice	NOUN
cana-766	11	18	ordered	order	VERB
cana-766	11	19	groups	group	NOUN
cana-766	11	20	.	.	PUNCT
cana-766	12	1	lattice	lattice	PROPN
cana-766	12	2	ordered	order	VERB
cana-766	12	3	rings	ring	NOUN
cana-766	12	4	,	,	PUNCT
cana-766	12	5	latice	latice	PROPN
cana-766	12	6	ordered	order	VERB
cana-766	12	7	near	near	ADP
cana-766	12	8	rings	ring	NOUN
cana-766	12	9	and	and	CCONJ
cana-766	12	10	lattice	lattice	PROPN
cana-766	12	11	ordered	order	VERB
cana-766	12	12	semirings	semiring	NOUN
cana-766	12	13	are	be	AUX
cana-766	12	14	presented.amoung	presented.amoung	VERB
cana-766	12	15	them	they	PRON
cana-766	12	16	the	the	DET
cana-766	12	17	algebraic	algebraic	ADJ
cana-766	12	18	structure	structure	NOUN
cana-766	12	19	lattice	lattice	PROPN
cana-766	12	20	ordered	order	VERB
cana-766	12	21	semirings	semiring	NOUN
cana-766	12	22	or	or	CCONJ
cana-766	12	23	l	l	NOUN
cana-766	12	24	-	-	ADJ
cana-766	12	25	semiring	semiring	NOUN
cana-766	12	26	was	be	AUX
cana-766	12	27	introduced	introduce	VERB
cana-766	12	28	by	by	ADP
cana-766	12	29	rangarao.p	rangarao.p	NOUN
cana-766	12	30	.	.	PUNCT
cana-766	12	31	,[9].also	,[9].also	PUNCT
cana-766	12	32	the	the	DET
cana-766	12	33	concept	concept	NOUN
cana-766	12	34	proposed	propose	VERB
cana-766	12	35	by	by	ADP
cana-766	12	36	zadeh.l.a.[13	zadeh.l.a.[13	PROPN
cana-766	12	37	]	]	PUNCT
cana-766	12	38	defining	define	VERB
cana-766	12	39	a	a	DET
cana-766	12	40	fuzzy	fuzzy	ADJ
cana-766	12	41	subset	subset	NOUN
cana-766	12	42	a	a	PRON
cana-766	12	43	of	of	ADP
cana-766	12	44	a	a	DET
cana-766	12	45	given	give	VERB
cana-766	12	46	universe	universe	NOUN
cana-766	12	47	x	x	PUNCT
cana-766	12	48	characterizing	characterize	VERB
cana-766	12	49	the	the	DET
cana-766	12	50	membership	membership	NOUN
cana-766	12	51	of	of	ADP
cana-766	12	52	an	an	DET
cana-766	12	53	element	element	NOUN
cana-766	12	54	x	x	PUNCT
cana-766	12	55	of	of	ADP
cana-766	12	56	x	x	PUNCT
cana-766	12	57	belonging	belong	VERB
cana-766	12	58	to	to	ADP
cana-766	12	59	a	a	PRON
cana-766	12	60	by	by	ADP
cana-766	12	61	means	mean	NOUN
cana-766	12	62	of	of	ADP
cana-766	12	63	a	a	DET
cana-766	12	64	membership	membership	NOUN
cana-766	12	65	function	function	NOUN
cana-766	12	66	µa(x	µa(x	ADV
cana-766	12	67	)	)	PUNCT
cana-766	12	68	defined	define	VERB
cana-766	12	69	from	from	ADP
cana-766	12	70	x	x	PRON
cana-766	12	71	in	in	ADP
cana-766	12	72	to	to	ADP
cana-766	12	73	[	[	X
cana-766	12	74	0	0	NUM
cana-766	12	75	1	1	NUM
cana-766	12	76	]	]	PUNCT
cana-766	12	77	has	have	AUX
cana-766	12	78	revolutionized	revolutionize	VERB
cana-766	12	79	the	the	DET
cana-766	12	80	theory	theory	NOUN
cana-766	12	81	of	of	ADP
cana-766	12	82	mathematical	mathematical	ADJ
cana-766	12	83	modeling	modeling	NOUN
cana-766	12	84	.	.	PUNCT
cana-766	13	1	decision	decision	NOUN
cana-766	13	2	making	make	VERB
cana-766	13	3	etc	etc	X
cana-766	13	4	.	.	X
cana-766	13	5	,in	,in	PUNCT
cana-766	13	6	handling	handle	VERB
cana-766	13	7	the	the	DET
cana-766	13	8	imprecise	imprecise	ADJ
cana-766	13	9	real	real	ADJ
cana-766	13	10	life	life	NOUN
cana-766	13	11	situations	situation	NOUN
cana-766	13	12	mathematically	mathematically	ADV
cana-766	13	13	.	.	PUNCT
cana-766	14	1	now	now	ADV
cana-766	14	2	several	several	ADJ
cana-766	14	3	branches	branch	NOUN
cana-766	14	4	of	of	ADP
cana-766	14	5	fuzzy	fuzzy	ADJ
cana-766	14	6	mathematics	mathematic	NOUN
cana-766	14	7	like	like	ADP
cana-766	14	8	fuzzy	fuzzy	ADJ
cana-766	14	9	algebra	algebra	NOUN
cana-766	14	10	,	,	PUNCT
cana-766	14	11	fuzzy	fuzzy	ADJ
cana-766	14	12	topology	topology	NOUN
cana-766	14	13	,	,	PUNCT
cana-766	14	14	fuzzy	fuzzy	ADJ
cana-766	14	15	control	control	NOUN
cana-766	14	16	theory	theory	NOUN
cana-766	14	17	,	,	PUNCT
cana-766	14	18	fuzzy	fuzzy	ADJ
cana-766	14	19	measure	measure	NOUN
cana-766	14	20	theory	theory	NOUN
cana-766	14	21	etc	etc	X
cana-766	14	22	.	.	X
cana-766	14	23	,haveemerged.but	,haveemerged.but	NOUN
cana-766	14	24	in	in	ADP
cana-766	14	25	the	the	DET
cana-766	14	26	decision	decision	NOUN
cana-766	14	27	making	making	NOUN
cana-766	14	28	,	,	PUNCT
cana-766	14	29	the	the	DET
cana-766	14	30	fuzzy	fuzzy	ADJ
cana-766	14	31	theory	theory	NOUN
cana-766	14	32	takes	take	VERB
cana-766	14	33	care	care	NOUN
cana-766	14	34	of	of	ADP
cana-766	14	35	membership	membership	NOUN
cana-766	14	36	of	of	ADP
cana-766	14	37	an	an	DET
cana-766	14	38	element	element	NOUN
cana-766	14	39	x	x	PUNCT
cana-766	14	40	only	only	ADV
cana-766	14	41	,	,	PUNCT
cana-766	14	42	that	that	PRON
cana-766	14	43	is	be	AUX
cana-766	14	44	the	the	DET
cana-766	14	45	evidence	evidence	NOUN
cana-766	14	46	against	against	ADP
cana-766	14	47	x	x	SYM
cana-766	14	48	belonging	belong	VERB
cana-766	14	49	to	to	ADP
cana-766	14	50	a	a	PRON
cana-766	14	51	.	.	PUNCT
cana-766	15	1	gau	gau	NOUN
cana-766	15	2	and	and	CCONJ
cana-766	15	3	buehrer.d.j	buehrer.d.j	NOUN
cana-766	15	4	and	and	CCONJ
cana-766	15	5	some	some	DET
cana-766	15	6	other	other	ADJ
cana-766	15	7	areas	area	NOUN
cana-766	15	8	of	of	ADP
cana-766	15	9	mathematical	mathematical	ADJ
cana-766	15	10	modeling.since	modeling.since	NOUN
cana-766	15	11	then	then	ADV
cana-766	15	12	the	the	DET
cana-766	15	13	theory	theory	NOUN
cana-766	15	14	of	of	ADP
cana-766	15	15	fuzzy	fuzzy	ADJ
cana-766	15	16	sets	set	NOUN
cana-766	15	17	developed	develop	VERB
cana-766	15	18	extensively	extensively	ADV
cana-766	15	19	and	and	CCONJ
cana-766	15	20	embraced	embrace	VERB
cana-766	15	21	almost	almost	ADV
cana-766	15	22	all	all	PRON
cana-766	15	23	subjects	subject	NOUN
cana-766	15	24	like	like	ADP
cana-766	15	25	engineering	engineering	NOUN
cana-766	15	26	science	science	NOUN
cana-766	15	27	and	and	CCONJ
cana-766	15	28	technology	technology	NOUN
cana-766	15	29	.	.	PUNCT
cana-766	16	1	but	but	CCONJ
cana-766	16	2	the	the	DET
cana-766	16	3	membership	membership	NOUN
cana-766	16	4	function	function	VERB
cana-766	16	5	µa	µa	PROPN
cana-766	16	6	(	(	PUNCT
cana-766	16	7	x	x	X
cana-766	16	8	)	)	PUNCT
cana-766	16	9	gives	give	VERB
cana-766	16	10	only	only	ADV
cana-766	16	11	a	a	DET
cana-766	16	12	approximation	approximation	NOUN
cana-766	16	13	belong	belong	VERB
cana-766	16	14	to	to	ADP
cana-766	16	15	a	a	DET
cana-766	16	16	.to	.to	PUNCT
cana-766	16	17	avid	avid	NOUN
cana-766	16	18	this	this	PRON
cana-766	16	19	and	and	CCONJ
cana-766	16	20	obtain	obtain	VERB
cana-766	16	21	a	a	DET
cana-766	16	22	communications	communication	NOUN
cana-766	16	23	on	on	ADP
cana-766	16	24	applied	apply	VERB
cana-766	16	25	nonlinear	nonlinear	ADJ
cana-766	16	26	analysis	analysis	NOUN
cana-766	16	27	issn	issn	NOUN
cana-766	16	28	:	:	PUNCT
cana-766	16	29	1074	1074	NUM
cana-766	16	30	-	-	PUNCT
cana-766	16	31	133x	133x	NUM
cana-766	16	32	vol	vol	NOUN
cana-766	16	33	31	31	NUM
cana-766	16	34	no	no	NOUN
cana-766	16	35	.	.	PUNCT
cana-766	17	1	3s	3s	NUM
cana-766	17	2	(	(	PUNCT
cana-766	17	3	2024	2024	NUM
cana-766	17	4	)	)	PUNCT
cana-766	17	5	295	295	NUM
cana-766	17	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-766	17	7	better	well	ADJ
cana-766	17	8	estimation	estimation	NOUN
cana-766	17	9	and	and	CCONJ
cana-766	17	10	analysis	analysis	NOUN
cana-766	17	11	of	of	ADP
cana-766	17	12	data	datum	NOUN
cana-766	17	13	decision	decision	NOUN
cana-766	17	14	making	making	NOUN
cana-766	17	15	.	.	PUNCT
cana-766	18	1	gau.w.l	gau.w.l	NOUN
cana-766	18	2	and	and	CCONJ
cana-766	18	3	bueher	bueher	NOUN
cana-766	18	4	d.j	d.j	PROPN
cana-766	18	5	.	.	PUNCT
cana-766	19	1	[	[	X
cana-766	19	2	3	3	X
cana-766	19	3	]	]	PUNCT
cana-766	19	4	have	have	AUX
cana-766	19	5	initiated	initiate	VERB
cana-766	19	6	the	the	DET
cana-766	19	7	study	study	NOUN
cana-766	19	8	of	of	ADP
cana-766	19	9	vague	vague	ADJ
cana-766	19	10	sets	set	NOUN
cana-766	19	11	with	with	ADP
cana-766	19	12	the	the	DET
cana-766	19	13	hope	hope	NOUN
cana-766	19	14	that	that	SCONJ
cana-766	19	15	they	they	PRON
cana-766	19	16	form	form	VERB
cana-766	19	17	a	a	DET
cana-766	19	18	better	well	ADJ
cana-766	19	19	tool	tool	NOUN
cana-766	19	20	to	to	PART
cana-766	19	21	understand	understand	VERB
cana-766	19	22	,	,	PUNCT
cana-766	19	23	interpret	interpret	VERB
cana-766	19	24	and	and	CCONJ
cana-766	19	25	solve	solve	VERB
cana-766	19	26	real	real	ADJ
cana-766	19	27	life	life	NOUN
cana-766	19	28	problems	problem	NOUN
cana-766	19	29	which	which	PRON
cana-766	19	30	are	be	AUX
cana-766	19	31	in	in	ADP
cana-766	19	32	general	general	ADJ
cana-766	19	33	vague	vague	NOUN
cana-766	19	34	,	,	PUNCT
cana-766	19	35	than	than	SCONJ
cana-766	19	36	the	the	DET
cana-766	19	37	theory	theory	NOUN
cana-766	19	38	of	of	ADP
cana-766	19	39	vague	vague	ADJ
cana-766	19	40	sets	set	NOUN
cana-766	19	41	do	do	VERB
cana-766	19	42	.	.	PUNCT
cana-766	20	1	ranjit	ranjit	VERB
cana-766	20	2	biswas[6	biswas[6	PROPN
cana-766	20	3	]	]	PUNCT
cana-766	20	4	initiated	initiate	VERB
cana-766	20	5	the	the	DET
cana-766	20	6	study	study	NOUN
cana-766	20	7	of	of	ADP
cana-766	20	8	vague	vague	ADJ
cana-766	20	9	groups	group	NOUN
cana-766	20	10	by	by	ADP
cana-766	20	11	ramakrishna.n	ramakrishna.n	NOUN
cana-766	21	1	[	[	X
cana-766	21	2	4	4	NUM
cana-766	21	3	]	]	PUNCT
cana-766	21	4	,	,	PUNCT
cana-766	21	5	[	[	X
cana-766	21	6	5	5	NUM
cana-766	21	7	]	]	PUNCT
cana-766	21	8	,	,	PUNCT
cana-766	21	9	[	[	X
cana-766	21	10	7	7	NUM
cana-766	21	11	]	]	PUNCT
cana-766	21	12	are	be	AUX
cana-766	21	13	grate	grate	NOUN
cana-766	21	14	extended	extend	VERB
cana-766	21	15	the	the	DET
cana-766	21	16	study	study	NOUN
cana-766	21	17	of	of	ADP
cana-766	21	18	vague	vague	ADJ
cana-766	21	19	algebra	algebra	NOUN
cana-766	21	20	.	.	PUNCT
cana-766	22	1	the	the	DET
cana-766	22	2	objective	objective	NOUN
cana-766	22	3	of	of	ADP
cana-766	22	4	this	this	DET
cana-766	22	5	paper	paper	NOUN
cana-766	22	6	is	be	AUX
cana-766	22	7	to	to	PART
cana-766	22	8	contribute	contribute	VERB
cana-766	22	9	further	far	ADV
cana-766	22	10	to	to	ADP
cana-766	22	11	the	the	DET
cana-766	22	12	study	study	NOUN
cana-766	22	13	of	of	ADP
cana-766	22	14	vague	vague	ADJ
cana-766	22	15	algebra	algebra	NOUN
cana-766	22	16	by	by	ADP
cana-766	22	17	in	in	ADP
cana-766	22	18	this	this	DET
cana-766	22	19	section	section	NOUN
cana-766	22	20	,	,	PUNCT
cana-766	22	21	we	we	PRON
cana-766	22	22	introduce	introduce	VERB
cana-766	22	23	vague	vague	ADJ
cana-766	22	24	strong	strong	ADJ
cana-766	22	25	implicative	implicative	ADJ
cana-766	22	26	filter	filter	NOUN
cana-766	22	27	of	of	ADP
cana-766	22	28	lattice	lattice	NOUN
cana-766	22	29	of	of	ADP
cana-766	22	30	wajsberg	wajsberg	PROPN
cana-766	22	31	algebra	algebra	NOUN
cana-766	22	32	and	and	CCONJ
cana-766	22	33	vague	vague	ADJ
cana-766	22	34	strong	strong	ADJ
cana-766	22	35	implicative	implicative	ADJ
cana-766	22	36	filter	filter	NOUN
cana-766	22	37	of	of	ADP
cana-766	22	38	lattice	lattice	NOUN
cana-766	22	39	of	of	ADP
cana-766	22	40	wajsberg	wajsberg	PROPN
cana-766	22	41	algebra	algebra	PROPN
cana-766	22	42	a	a	PRON
cana-766	22	43	with	with	ADP
cana-766	22	44	illustrations	illustration	NOUN
cana-766	22	45	and	and	CCONJ
cana-766	22	46	investigate	investigate	VERB
cana-766	22	47	some	some	DET
cana-766	22	48	properties	property	NOUN
cana-766	22	49	with	with	ADP
cana-766	22	50	suitable	suitable	ADJ
cana-766	22	51	examples	example	NOUN
cana-766	22	52	.	.	PUNCT
cana-766	23	1	2	2	X
cana-766	23	2	.	.	X
cana-766	23	3	preliminaries	preliminary	NOUN
cana-766	23	4	in	in	ADP
cana-766	23	5	this	this	DET
cana-766	23	6	section	section	NOUN
cana-766	23	7	,	,	PUNCT
cana-766	23	8	we	we	PRON
cana-766	23	9	recall	recall	VERB
cana-766	23	10	some	some	DET
cana-766	23	11	basic	basic	ADJ
cana-766	23	12	definitions	definition	NOUN
cana-766	23	13	and	and	CCONJ
cana-766	23	14	properties	property	NOUN
cana-766	23	15	which	which	PRON
cana-766	23	16	are	be	AUX
cana-766	23	17	useful	useful	ADJ
cana-766	23	18	to	to	PART
cana-766	23	19	develop	develop	VERB
cana-766	23	20	the	the	DET
cana-766	23	21	main	main	ADJ
cana-766	23	22	results	result	NOUN
cana-766	23	23	.	.	PUNCT
cana-766	24	1	definition	definition	NOUN
cana-766	24	2	2.1	2.1	NUM
cana-766	24	3	[	[	X
cana-766	24	4	2	2	NUM
cana-766	24	5	]	]	PUNCT
cana-766	24	6	let	let	VERB
cana-766	24	7	(	(	PUNCT
cana-766	24	8	a	a	DET
cana-766	24	9	,	,	PUNCT
cana-766	24	10	→	→	ADP
cana-766	24	11	,	,	PUNCT
cana-766	24	12	*	*	SYM
cana-766	24	13	,	,	PUNCT
cana-766	24	14	1	1	NUM
cana-766	24	15	)	)	PUNCT
cana-766	24	16	be	be	AUX
cana-766	24	17	an	an	DET
cana-766	24	18	algebra	algebra	NOUN
cana-766	24	19	with	with	ADP
cana-766	24	20	a	a	DET
cana-766	24	21	binary	binary	ADJ
cana-766	24	22	operation	operation	NOUN
cana-766	24	23	“	"	PUNCT
cana-766	24	24	→”and	→”and	PROPN
cana-766	24	25	a	a	DET
cana-766	24	26	quasi	quasi	ADJ
cana-766	24	27	complement	complement	NOUN
cana-766	24	28	“	"	PUNCT
cana-766	24	29	*	*	PUNCT
cana-766	24	30	”	"	PUNCT
cana-766	24	31	is	be	AUX
cana-766	24	32	called	call	VERB
cana-766	24	33	a	a	DET
cana-766	24	34	wajsberg	wajsberg	ADJ
cana-766	24	35	algebra	algebra	NOUN
cana-766	24	36	if	if	SCONJ
cana-766	24	37	and	and	CCONJ
cana-766	24	38	only	only	ADV
cana-766	24	39	if	if	SCONJ
cana-766	24	40	it	it	PRON
cana-766	24	41	satisfies	satisfy	VERB
cana-766	24	42	the	the	DET
cana-766	24	43	following	following	ADJ
cana-766	24	44	axioms	axiom	NOUN
cana-766	24	45	for	for	ADP
cana-766	24	46	all	all	DET
cana-766	24	47	x	x	NOUN
cana-766	24	48	,	,	PUNCT
cana-766	24	49	y	y	PROPN
cana-766	24	50	,	,	PUNCT
cana-766	24	51	z	z	PROPN
cana-766	24	52	∈	∈	PROPN
cana-766	24	53	a	a	DET
cana-766	24	54	,	,	PUNCT
cana-766	24	55	1	1	NUM
cana-766	24	56	.	.	X
cana-766	25	1	1→x	1→x	NUM
cana-766	25	2	=	=	NOUN
cana-766	25	3	x	x	SYM
cana-766	25	4	2	2	NUM
cana-766	25	5	.	.	PUNCT
cana-766	25	6	(	(	PUNCT
cana-766	25	7	x→	x→	PUNCT
cana-766	25	8	𝑦	𝑦	X
cana-766	25	9	)	)	PUNCT
cana-766	25	10	→	→	SYM
cana-766	25	11	(	(	PUNCT
cana-766	25	12	(	(	PUNCT
cana-766	25	13	𝑦	𝑦	NOUN
cana-766	25	14	→	→	SYM
cana-766	25	15	𝑧	𝑧	NOUN
cana-766	25	16	)	)	PUNCT
cana-766	25	17	→	→	SYM
cana-766	25	18	(	(	PUNCT
cana-766	25	19	𝑥	𝑥	X
cana-766	25	20	→	→	SYM
cana-766	25	21	𝑧))=1	𝑧))=1	PROPN
cana-766	25	22	3	3	NUM
cana-766	25	23	.	.	PUNCT
cana-766	25	24	(	(	PUNCT
cana-766	25	25	x→	x→	PUNCT
cana-766	25	26	𝑦	𝑦	X
cana-766	25	27	)	)	PUNCT
cana-766	25	28	→	→	SYM
cana-766	25	29	𝑦	𝑦	SYM
cana-766	25	30	=	=	SYM
cana-766	25	31	(	(	PUNCT
cana-766	25	32	y→	y→	NOUN
cana-766	25	33	𝑥	𝑥	NOUN
cana-766	25	34	)	)	PUNCT
cana-766	25	35	→	→	SYM
cana-766	25	36	𝑥	𝑥	PROPN
cana-766	25	37	4	4	NUM
cana-766	25	38	.	.	PUNCT
cana-766	26	1	(	(	PUNCT
cana-766	26	2	x	x	X
cana-766	26	3	*	*	PUNCT
cana-766	26	4	→	→	SYM
cana-766	26	5	y∗	y∗	ADV
cana-766	26	6	)	)	PUNCT
cana-766	26	7	→	→	SYM
cana-766	26	8	(	(	PUNCT
cana-766	26	9	y→	y→	INTJ
cana-766	26	10	𝑥)=1	𝑥)=1	NOUN
cana-766	26	11	.	.	PUNCT
cana-766	26	12	definition	definition	NOUN
cana-766	26	13	2.2[2	2.2[2	NUM
cana-766	26	14	]	]	PUNCT
cana-766	26	15	the	the	DET
cana-766	26	16	wajsberg	wajsberg	PROPN
cana-766	26	17	algebra	algebra	PROPN
cana-766	26	18	(	(	PUNCT
cana-766	26	19	a	a	PRON
cana-766	26	20	,	,	PUNCT
cana-766	26	21	→	→	SYM
cana-766	26	22	,	,	PUNCT
cana-766	26	23	*	*	SYM
cana-766	26	24	,	,	PUNCT
cana-766	26	25	1	1	X
cana-766	26	26	)	)	PUNCT
cana-766	26	27	satisfies	satisfy	VERB
cana-766	26	28	the	the	DET
cana-766	26	29	following	follow	VERB
cana-766	26	30	properties	property	NOUN
cana-766	26	31	for	for	ADP
cana-766	26	32	all	all	DET
cana-766	26	33	x	x	NOUN
cana-766	26	34	,	,	PUNCT
cana-766	26	35	y	y	PROPN
cana-766	26	36	,	,	PUNCT
cana-766	26	37	z	z	PROPN
cana-766	26	38	∈	∈	PROPN
cana-766	26	39	a	a	PRON
cana-766	26	40	,	,	PUNCT
cana-766	26	41	(	(	PUNCT
cana-766	26	42	i).x	i).x	X
cana-766	26	43	→x	→x	PROPN
cana-766	26	44	=	=	NOUN
cana-766	26	45	x	x	X
cana-766	26	46	(	(	PUNCT
cana-766	26	47	ii	ii	NOUN
cana-766	26	48	)	)	PUNCT
cana-766	26	49	.	.	PUNCT
cana-766	27	1	if	if	SCONJ
cana-766	27	2	(	(	PUNCT
cana-766	27	3	𝑥	𝑥	NOUN
cana-766	27	4	→y)=	→y)=	NUM
cana-766	27	5	𝑦	𝑦	NOUN
cana-766	27	6	→x=1	→x=1	NOUN
cana-766	27	7	then	then	ADV
cana-766	27	8	x	x	X
cana-766	27	9	=	=	NOUN
cana-766	27	10	y	y	PROPN
cana-766	27	11	(	(	PUNCT
cana-766	27	12	iii).x→	iii).x→	NOUN
cana-766	27	13	1	1	NUM
cana-766	27	14	=	=	SYM
cana-766	27	15	1	1	NUM
cana-766	27	16	(	(	PUNCT
cana-766	27	17	iv).x→	iv).x→	NOUN
cana-766	27	18	(	(	PUNCT
cana-766	27	19	𝑦	𝑦	NOUN
cana-766	27	20	→x)=1	→x)=1	PROPN
cana-766	27	21	(	(	PUNCT
cana-766	27	22	v).if	v).if	PROPN
cana-766	27	23	x→	x→	PUNCT
cana-766	28	1	𝑦	𝑦	NOUN
cana-766	28	2	=	=	X
cana-766	28	3	y→	y→	X
cana-766	28	4	𝑧=1	𝑧=1	X
cana-766	28	5	then	then	ADV
cana-766	28	6	x→	x→	PUNCT
cana-766	28	7	𝑧	𝑧	NOUN
cana-766	28	8	=	=	SYM
cana-766	28	9	1	1	NUM
cana-766	28	10	(	(	PUNCT
cana-766	28	11	vi	vi	NOUN
cana-766	28	12	)	)	PUNCT
cana-766	28	13	.	.	PUNCT
cana-766	29	1	if	if	SCONJ
cana-766	29	2	(	(	PUNCT
cana-766	29	3	𝑥	𝑥	PROPN
cana-766	29	4	→	→	SYM
cana-766	29	5	y	y	NOUN
cana-766	29	6	)	)	PUNCT
cana-766	29	7	→	→	X
cana-766	29	8	(	(	PUNCT
cana-766	29	9	(	(	PUNCT
cana-766	29	10	𝑧	𝑧	PROPN
cana-766	29	11	→	→	SYM
cana-766	29	12	𝑥	𝑥	NOUN
cana-766	29	13	)	)	PUNCT
cana-766	29	14	→	→	SYM
cana-766	29	15	(	(	PUNCT
cana-766	29	16	𝑧	𝑧	PROPN
cana-766	29	17	→	→	SYM
cana-766	29	18	𝑦	𝑦	NOUN
cana-766	29	19	)	)	PUNCT
cana-766	29	20	)	)	PUNCT
cana-766	30	1	=	=	SYM
cana-766	30	2	1	1	NUM
cana-766	30	3	(	(	PUNCT
cana-766	30	4	vii).x	vii).x	NOUN
cana-766	30	5	→	→	PUNCT
cana-766	30	6	(	(	PUNCT
cana-766	30	7	𝑦	𝑦	PROPN
cana-766	30	8	→	→	SYM
cana-766	30	9	𝑧	𝑧	NOUN
cana-766	30	10	)	)	PUNCT
cana-766	30	11	=	=	SYM
cana-766	30	12	𝑦	𝑦	NOUN
cana-766	30	13	→	→	SYM
cana-766	30	14	(	(	PUNCT
cana-766	30	15	𝑥	𝑥	X
cana-766	30	16	→	→	SYM
cana-766	30	17	𝑧	𝑧	NOUN
cana-766	30	18	)	)	PUNCT
cana-766	30	19	(	(	PUNCT
cana-766	30	20	viii).x→	viii).x→	NOUN
cana-766	30	21	0	0	NUM
cana-766	31	1	=	=	SYM
cana-766	31	2	𝑥	𝑥	PROPN
cana-766	31	3	→	→	SYM
cana-766	31	4	1	1	NUM
cana-766	31	5	*	*	SYM
cana-766	31	6	=	=	NOUN
cana-766	31	7	x	x	X
cana-766	31	8	*	*	PUNCT
cana-766	31	9	(	(	PUNCT
cana-766	31	10	ix).(x	ix).(x	X
cana-766	31	11	*	*	NOUN
cana-766	31	12	)	)	PUNCT
cana-766	31	13	*	*	PUNCT
cana-766	32	1	=	=	PUNCT
cana-766	32	2	x	x	SYM
cana-766	32	3	(	(	PUNCT
cana-766	32	4	x	x	NOUN
cana-766	32	5	)	)	PUNCT
cana-766	32	6	.x	.x	PROPN
cana-766	32	7	*	*	PUNCT
cana-766	32	8	→y	→y	PROPN
cana-766	32	9	*	*	PUNCT
cana-766	32	10	=	=	PUNCT
cana-766	32	11	y→	y→	X
cana-766	32	12	𝑥.	𝑥.	ADJ
cana-766	32	13	definition	definition	NOUN
cana-766	32	14	2.3	2.3	NUM
cana-766	32	15	[	[	X
cana-766	32	16	2	2	X
cana-766	32	17	]	]	PUNCT
cana-766	32	18	the	the	DET
cana-766	32	19	wajsberg	wajsberg	PROPN
cana-766	32	20	algebra	algebra	PROPN
cana-766	32	21	(	(	PUNCT
cana-766	32	22	a	a	PRON
cana-766	32	23	,	,	PUNCT
cana-766	32	24	→,*,1	→,*,1	PUNCT
cana-766	32	25	)	)	PUNCT
cana-766	32	26	is	be	AUX
cana-766	32	27	called	call	VERB
cana-766	32	28	a	a	DET
cana-766	32	29	lattice	lattice	NOUN
cana-766	32	30	wajsberg	wajsberg	PROPN
cana-766	32	31	algebra	algebra	NOUN
cana-766	32	32	if	if	SCONJ
cana-766	32	33	it	it	PRON
cana-766	32	34	satisfies	satisfy	VERB
cana-766	32	35	the	the	DET
cana-766	32	36	following	follow	VERB
cana-766	32	37	properties	property	NOUN
cana-766	32	38	for	for	ADP
cana-766	32	39	all	all	DET
cana-766	32	40	x	x	NOUN
cana-766	32	41	,	,	PUNCT
cana-766	32	42	y	y	PROPN
cana-766	32	43	∈	∈	PROPN
cana-766	32	44	a	a	DET
cana-766	32	45	,	,	PUNCT
cana-766	32	46	(	(	PUNCT
cana-766	32	47	1	1	X
cana-766	32	48	)	)	PUNCT
cana-766	32	49	a	a	DET
cana-766	32	50	partial	partial	ADJ
cana-766	32	51	ordering	ordering	NOUN
cana-766	32	52	“	"	PUNCT
cana-766	32	53	≤	≤	NOUN
cana-766	32	54	”	"	PUNCT
cana-766	32	55	on	on	ADP
cana-766	32	56	a	a	DET
cana-766	32	57	lattice	lattice	NOUN
cana-766	32	58	wajsberg	wajsberg	PROPN
cana-766	32	59	algebra	algebra	PROPN
cana-766	32	60	a	a	PRON
cana-766	32	61	,	,	PUNCT
cana-766	32	62	such	such	ADJ
cana-766	32	63	that	that	SCONJ
cana-766	32	64	x≤y	x≤y	ADV
cana-766	32	65	if	if	SCONJ
cana-766	32	66	and	and	CCONJ
cana-766	32	67	only	only	ADV
cana-766	32	68	if	if	SCONJ
cana-766	32	69	x→	x→	PROPN
cana-766	32	70	𝑦	𝑦	NOUN
cana-766	32	71	=	=	SYM
cana-766	32	72	1	1	NUM
cana-766	32	73	(	(	PUNCT
cana-766	32	74	2	2	NUM
cana-766	32	75	)	)	PUNCT
cana-766	32	76	(	(	PUNCT
cana-766	32	77	xꓦy)=(x→	xꓦy)=(x→	PROPN
cana-766	32	78	𝑦	𝑦	X
cana-766	32	79	)	)	PUNCT
cana-766	32	80	→	→	SYM
cana-766	32	81	𝑦	𝑦	NOUN
cana-766	32	82	communications	communication	NOUN
cana-766	32	83	on	on	ADP
cana-766	32	84	applied	apply	VERB
cana-766	32	85	nonlinear	nonlinear	ADJ
cana-766	32	86	analysis	analysis	NOUN
cana-766	32	87	issn	issn	NOUN
cana-766	32	88	:	:	PUNCT
cana-766	32	89	1074	1074	NUM
cana-766	32	90	-	-	PUNCT
cana-766	32	91	133x	133x	NUM
cana-766	32	92	vol	vol	NOUN
cana-766	32	93	31	31	NUM
cana-766	32	94	no	no	NOUN
cana-766	32	95	.	.	PUNCT
cana-766	33	1	3s	3s	NUM
cana-766	33	2	(	(	PUNCT
cana-766	33	3	2024	2024	NUM
cana-766	33	4	)	)	PUNCT
cana-766	33	5	296	296	NUM
cana-766	33	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-766	33	7	(	(	PUNCT
cana-766	33	8	3	3	NUM
cana-766	33	9	)	)	PUNCT
cana-766	33	10	(	(	PUNCT
cana-766	33	11	xꓥy)=	xꓥy)=	X
cana-766	33	12	(	(	PUNCT
cana-766	33	13	(	(	PUNCT
cana-766	33	14	x*→	x*→	X
cana-766	33	15	𝑦*)→	𝑦*)→	PROPN
cana-766	33	16	𝑦	𝑦	PROPN
cana-766	33	17	*	*	NOUN
cana-766	33	18	)	)	PUNCT
cana-766	33	19	*	*	PUNCT
cana-766	33	20	thus	thus	ADV
cana-766	33	21	,	,	PUNCT
cana-766	33	22	we	we	PRON
cana-766	33	23	have	have	AUX
cana-766	33	24	(	(	PUNCT
cana-766	33	25	a,ꓦ,ꓥ,*0,1	a,ꓦ,ꓥ,*0,1	NOUN
cana-766	33	26	)	)	PUNCT
cana-766	33	27	is	be	AUX
cana-766	33	28	a	a	DET
cana-766	33	29	lattice	lattice	NOUN
cana-766	33	30	wajsberg	wajsberg	ADJ
cana-766	33	31	algebra	algebra	NOUN
cana-766	33	32	with	with	ADP
cana-766	33	33	lower	low	ADJ
cana-766	33	34	bound	bind	VERB
cana-766	33	35	0	0	NUM
cana-766	33	36	and	and	CCONJ
cana-766	33	37	upper	upper	ADJ
cana-766	33	38	bound	bind	VERB
cana-766	33	39	1	1	NUM
cana-766	33	40	.	.	PUNCT
cana-766	34	1	theorem	theorem	VERB
cana-766	34	2	2.4	2.4	NUM
cana-766	34	3	[	[	SYM
cana-766	34	4	2	2	NUM
cana-766	34	5	]	]	PUNCT
cana-766	34	6	the	the	DET
cana-766	34	7	wajsberg	wajsberg	PROPN
cana-766	34	8	algebra	algebra	PROPN
cana-766	34	9	(	(	PUNCT
cana-766	34	10	a	a	PRON
cana-766	34	11	,	,	PUNCT
cana-766	34	12	→,*,1	→,*,1	PUNCT
cana-766	34	13	)	)	PUNCT
cana-766	34	14	satisfies	satisfy	VERB
cana-766	34	15	the	the	DET
cana-766	34	16	following	follow	VERB
cana-766	34	17	properties	property	NOUN
cana-766	34	18	for	for	ADP
cana-766	34	19	all	all	DET
cana-766	34	20	x	x	NOUN
cana-766	34	21	,	,	PUNCT
cana-766	34	22	y	y	PROPN
cana-766	34	23	,	,	PUNCT
cana-766	34	24	𝑧	𝑧	PROPN
cana-766	34	25	∈	∈	PROPN
cana-766	34	26	a	a	DET
cana-766	34	27	,	,	PUNCT
cana-766	34	28	1	1	NUM
cana-766	34	29	.	.	PUNCT
cana-766	35	1	if	if	SCONJ
cana-766	35	2	x≤y	x≤y	PROPN
cana-766	35	3	then	then	ADV
cana-766	35	4	x	x	PART
cana-766	35	5	→z	→z	VERB
cana-766	35	6	≥	≥	NOUN
cana-766	35	7	y→	y→	X
cana-766	35	8	𝑧	𝑧	PROPN
cana-766	35	9	2	2	NUM
cana-766	35	10	.	.	PUNCT
cana-766	36	1	if	if	SCONJ
cana-766	36	2	x≤y	x≤y	PROPN
cana-766	36	3	then	then	ADV
cana-766	36	4	z	z	NOUN
cana-766	36	5	→x	→x	PROPN
cana-766	36	6	≤	≤	NUM
cana-766	36	7	z→	z→	NUM
cana-766	36	8	𝑦	𝑦	NOUN
cana-766	36	9	3	3	NUM
cana-766	36	10	.	.	PUNCT
cana-766	37	1	if	if	SCONJ
cana-766	37	2	x≤y→z	x≤y→z	PROPN
cana-766	37	3	if	if	SCONJ
cana-766	37	4	and	and	CCONJ
cana-766	37	5	only	only	ADV
cana-766	37	6	if	if	SCONJ
cana-766	37	7	y	y	PROPN
cana-766	37	8	≤	≤	X
cana-766	37	9	x→	x→	PUNCT
cana-766	38	1	𝑧	𝑧	PROPN
cana-766	38	2	4.(xꓦy	4.(xꓦy	PROPN
cana-766	38	3	)	)	PUNCT
cana-766	38	4	*	*	PUNCT
cana-766	39	1	=(	=(	PROPN
cana-766	39	2	x	x	X
cana-766	39	3	*	*	PUNCT
cana-766	39	4	ꓦy	ꓦy	PROPN
cana-766	39	5	*	*	PROPN
cana-766	39	6	)	)	PUNCT
cana-766	39	7	5.(xꓥy	5.(xꓥy	NUM
cana-766	39	8	)	)	PUNCT
cana-766	39	9	*	*	PUNCT
cana-766	40	1	=(	=(	NOUN
cana-766	40	2	x	x	X
cana-766	40	3	*	*	PUNCT
cana-766	40	4	ꓥ	ꓥ	X
cana-766	40	5	y	y	PROPN
cana-766	40	6	*	*	NOUN
cana-766	40	7	)	)	PUNCT
cana-766	40	8	6	6	NUM
cana-766	40	9	.	.	PUNCT
cana-766	41	1	(	(	PUNCT
cana-766	41	2	xꓦy)→z=(x→	xꓦy)→z=(x→	X
cana-766	41	3	𝑧)ꓥ(y→	𝑧)ꓥ(y→	PROPN
cana-766	42	1	𝑧	𝑧	PRON
cana-766	42	2	7.x→(yꓥz)=(x→	7.x→(yꓥz)=(x→	NUM
cana-766	42	3	𝑦)ꓥ(x→	𝑦)ꓥ(x→	PROPN
cana-766	42	4	𝑧	𝑧	NOUN
cana-766	42	5	)	)	PUNCT
cana-766	42	6	8.(x→	8.(x→	NUM
cana-766	42	7	𝑦)ꓦ(y→x)=1	𝑦)ꓦ(y→x)=1	PROPN
cana-766	42	8	9.x→	9.x→	NOUN
cana-766	42	9	(	(	PUNCT
cana-766	42	10	𝑦	𝑦	NUM
cana-766	42	11	ꓦz)=(x→	ꓦz)=(x→	NOUN
cana-766	42	12	𝑦)ꓦ(x→	𝑦)ꓦ(x→	PROPN
cana-766	42	13	𝑧	𝑧	NOUN
cana-766	42	14	)	)	PUNCT
cana-766	42	15	10.(xꓥy	10.(xꓥy	NUM
cana-766	42	16	)	)	PUNCT
cana-766	42	17	→	→	PUNCT
cana-766	42	18	𝑧	𝑧	DET
cana-766	42	19	=(	=(	X
cana-766	42	20	x→	x→	SYM
cana-766	42	21	𝑦)ꓦ(x→	𝑦)ꓦ(x→	PROPN
cana-766	42	22	𝑧	𝑧	PART
cana-766	42	23	)	)	PUNCT
cana-766	42	24	11.(xꓥy	11.(xꓥy	NUM
cana-766	42	25	)	)	PUNCT
cana-766	42	26	ꓦz	ꓦz	VERB
cana-766	42	27	=(	=(	PROPN
cana-766	42	28	xꓦ𝑧)ꓥ(yꓦz	xꓦ𝑧)ꓥ(yꓦz	PROPN
cana-766	42	29	)	)	PUNCT
cana-766	42	30	12.(xꓥy	12.(xꓥy	NUM
cana-766	42	31	)	)	PUNCT
cana-766	42	32	→z	→z	PUNCT
cana-766	42	33	=(	=(	X
cana-766	42	34	x→	x→	SYM
cana-766	42	35	𝑦	𝑦	X
cana-766	42	36	)	)	PUNCT
cana-766	42	37	→(x→	→(x→	PROPN
cana-766	43	1	z	z	X
cana-766	43	2	)	)	PUNCT
cana-766	43	3	for	for	ADP
cana-766	43	4	all	all	DET
cana-766	43	5	x	x	PROPN
cana-766	43	6	,	,	PUNCT
cana-766	43	7	y	y	PROPN
cana-766	43	8	,	,	PUNCT
cana-766	43	9	z	z	NOUN
cana-766	43	10	in	in	ADP
cana-766	43	11	a.	a.	NOUN
cana-766	43	12	definition	definition	NOUN
cana-766	43	13	2.5[2	2.5[2	NUM
cana-766	43	14	]	]	X
cana-766	43	15	a	a	DET
cana-766	43	16	lattice	lattice	NOUN
cana-766	43	17	wajsberg	wajsberg	PROPN
cana-766	43	18	algebra	algebra	PROPN
cana-766	43	19	(	(	PUNCT
cana-766	43	20	a	a	PRON
cana-766	43	21	,	,	PUNCT
cana-766	43	22	→	→	SYM
cana-766	43	23	,	,	PUNCT
cana-766	43	24	*	*	SYM
cana-766	43	25	,	,	PUNCT
cana-766	43	26	1	1	NUM
cana-766	43	27	)	)	PUNCT
cana-766	43	28	is	be	AUX
cana-766	43	29	called	call	VERB
cana-766	43	30	a	a	DET
cana-766	43	31	lattice	lattice	ADJ
cana-766	43	32	h	h	ADJ
cana-766	43	33	-	-	PUNCT
cana-766	43	34	wajsberg	wajsberg	ADJ
cana-766	43	35	algebra	algebra	NOUN
cana-766	43	36	,	,	PUNCT
cana-766	43	37	if	if	SCONJ
cana-766	43	38	it	it	PRON
cana-766	43	39	satisfies	satisfy	VERB
cana-766	43	40	xꓦyꓦ((xꓥy)→z)=1	xꓦyꓦ((xꓥy)→z)=1	PROPN
cana-766	43	41	for	for	ADP
cana-766	43	42	all	all	DET
cana-766	43	43	x	x	PROPN
cana-766	43	44	,	,	PUNCT
cana-766	43	45	y.z	y.z	PROPN
cana-766	43	46	∈	∈	PROPN
cana-766	43	47	a.	a.	NOUN
cana-766	43	48	in	in	ADP
cana-766	43	49	a	a	DET
cana-766	43	50	lattice	lattice	ADJ
cana-766	43	51	h	h	NOUN
cana-766	43	52	-	-	PUNCT
cana-766	43	53	wajsberg	wajsberg	ADJ
cana-766	43	54	algebra	algebra	PROPN
cana-766	43	55	a	a	DET
cana-766	43	56	,	,	PUNCT
cana-766	43	57	the	the	DET
cana-766	43	58	following	follow	VERB
cana-766	43	59	hold	hold	NOUN
cana-766	43	60	.	.	PUNCT
cana-766	44	1	1.x→(x→	1.x→(x→	NUM
cana-766	44	2	𝑦)=(x→	𝑦)=(x→	PROPN
cana-766	44	3	𝑦	𝑦	NOUN
cana-766	44	4	)	)	PUNCT
cana-766	44	5	2.x→	2.x→	NOUN
cana-766	44	6	(	(	PUNCT
cana-766	44	7	𝑦	𝑦	NOUN
cana-766	44	8	→	→	SYM
cana-766	44	9	𝑧	𝑧	NOUN
cana-766	44	10	)	)	PUNCT
cana-766	44	11	=(	=(	NOUN
cana-766	44	12	x→	x→	SYM
cana-766	44	13	𝑦	𝑦	X
cana-766	44	14	)	)	PUNCT
cana-766	44	15	→(x→	→(x→	PROPN
cana-766	44	16	𝑧	𝑧	PART
cana-766	44	17	)	)	PUNCT
cana-766	44	18	foa	foa	NOUN
cana-766	44	19	all	all	DET
cana-766	44	20	x	x	PROPN
cana-766	44	21	,	,	PUNCT
cana-766	44	22	y	y	PROPN
cana-766	44	23	,	,	PUNCT
cana-766	44	24	z	z	NOUN
cana-766	44	25	in	in	ADP
cana-766	44	26	a.	a.	NOUN
cana-766	44	27	definition	definition	NOUN
cana-766	44	28	2.6[2	2.6[2	NUM
cana-766	44	29	]	]	X
cana-766	44	30	let	let	NOUN
cana-766	44	31	(	(	PUNCT
cana-766	44	32	a1	a1	VERB
cana-766	44	33	,	,	PUNCT
cana-766	44	34	→	→	SYM
cana-766	44	35	,	,	PUNCT
cana-766	44	36	*	*	SYM
cana-766	44	37	,	,	PUNCT
cana-766	44	38	1	1	NUM
cana-766	44	39	)	)	PUNCT
cana-766	44	40	and	and	CCONJ
cana-766	44	41	(	(	PUNCT
cana-766	44	42	a2	a2	PROPN
cana-766	44	43	,	,	PUNCT
cana-766	44	44	→	→	SYM
cana-766	44	45	,	,	PUNCT
cana-766	44	46	*	*	SYM
cana-766	44	47	,	,	PUNCT
cana-766	44	48	1	1	X
cana-766	44	49	)	)	PUNCT
cana-766	44	50	be	be	AUX
cana-766	44	51	lattice	lattice	PROPN
cana-766	44	52	wajsberg	wajsberg	PROPN
cana-766	44	53	algebras	algebras	PROPN
cana-766	44	54	,	,	PUNCT
cana-766	44	55	a	a	DET
cana-766	44	56	maping	maping	NOUN
cana-766	44	57	f	f	NOUN
cana-766	44	58	:	:	PUNCT
cana-766	44	59	a1→	a1→	NOUN
cana-766	44	60	a2	a2	PROPN
cana-766	44	61	is	be	AUX
cana-766	44	62	called	call	VERB
cana-766	44	63	implication	implication	NOUN
cana-766	44	64	homomorphism	homomorphism	NOUN
cana-766	44	65	if	if	SCONJ
cana-766	44	66	f(x	f(x	PROPN
cana-766	44	67	→	→	SYM
cana-766	44	68	y	y	PROPN
cana-766	44	69	)	)	PUNCT
cana-766	44	70	=	=	SYM
cana-766	44	71	f(x	f(x	PROPN
cana-766	44	72	)	)	PUNCT
cana-766	44	73	→f(y	→f(y	NUM
cana-766	44	74	)	)	PUNCT
cana-766	44	75	holds	hold	VERB
cana-766	44	76	,	,	PUNCT
cana-766	44	77	definition	definition	NOUN
cana-766	44	78	2.7[2	2.7[2	NUM
cana-766	44	79	]	]	X
cana-766	45	1	let	let	NOUN
cana-766	45	2	(	(	PUNCT
cana-766	45	3	a1	a1	VERB
cana-766	45	4	,	,	PUNCT
cana-766	45	5	→	→	SYM
cana-766	45	6	,	,	PUNCT
cana-766	45	7	*	*	SYM
cana-766	45	8	,	,	PUNCT
cana-766	45	9	1	1	NUM
cana-766	45	10	)	)	PUNCT
cana-766	45	11	and	and	CCONJ
cana-766	45	12	(	(	PUNCT
cana-766	45	13	a2	a2	PROPN
cana-766	45	14	,	,	PUNCT
cana-766	45	15	→	→	SYM
cana-766	45	16	,	,	PUNCT
cana-766	45	17	*	*	SYM
cana-766	45	18	,	,	PUNCT
cana-766	45	19	1	1	X
cana-766	45	20	)	)	PUNCT
cana-766	45	21	be	be	AUX
cana-766	45	22	lattice	lattice	PROPN
cana-766	45	23	wajsberg	wajsberg	PROPN
cana-766	45	24	algebras	algebra	NOUN
cana-766	45	25	,	,	PUNCT
cana-766	45	26	f	f	X
cana-766	45	27	:	:	PUNCT
cana-766	45	28	a1→	a1→	NOUN
cana-766	45	29	a2	a2	PROPN
cana-766	45	30	is	be	AUX
cana-766	45	31	implication	implication	NOUN
cana-766	45	32	homomorphism	homomorphism	NOUN
cana-766	45	33	from	from	ADP
cana-766	45	34	a1	a1	NOUN
cana-766	45	35	to	to	ADP
cana-766	45	36	a2	a2	PROPN
cana-766	45	37	satisfies	satisfy	VERB
cana-766	45	38	the	the	DET
cana-766	45	39	following	follow	VERB
cana-766	45	40	properties	property	NOUN
cana-766	45	41	.	.	PUNCT
cana-766	46	1	1	1	X
cana-766	46	2	.	.	X
cana-766	47	1	f(x	f(x	PROPN
cana-766	47	2	ꓥ	ꓥ	PROPN
cana-766	47	3	y	y	PROPN
cana-766	47	4	)	)	PUNCT
cana-766	47	5	=	=	NOUN
cana-766	47	6	f(x)ꓥf(y	f(x)ꓥf(y	X
cana-766	47	7	)	)	PUNCT
cana-766	47	8	2	2	NUM
cana-766	47	9	.	.	PUNCT
cana-766	48	1	f(x	f(x	PROPN
cana-766	48	2	ꓦ	ꓦ	NUM
cana-766	48	3	y	y	NOUN
cana-766	48	4	)	)	PUNCT
cana-766	48	5	=	=	SYM
cana-766	48	6	f(x)ꓦf(y	f(x)ꓦf(y	NOUN
cana-766	48	7	)	)	PUNCT
cana-766	48	8	3.f(x	3.f(x	NUM
cana-766	48	9	*	*	SYM
cana-766	48	10	)	)	PUNCT
cana-766	49	1	=[	=[	NOUN
cana-766	49	2	f(x	f(x	PROPN
cana-766	49	3	)	)	PUNCT
cana-766	49	4	]	]	PUNCT
cana-766	50	1	*	*	PUNCT
cana-766	50	2	definition	definition	NOUN
cana-766	50	3	2.8[2	2.8[2	NUM
cana-766	50	4	]	]	X
cana-766	50	5	let	let	ADJ
cana-766	50	6	(	(	PUNCT
cana-766	50	7	a1	a1	VERB
cana-766	50	8	,	,	PUNCT
cana-766	50	9	→	→	SYM
cana-766	50	10	,	,	PUNCT
cana-766	50	11	*	*	SYM
cana-766	50	12	,	,	PUNCT
cana-766	50	13	1	1	X
cana-766	50	14	)	)	PUNCT
cana-766	50	15	be	be	AUX
cana-766	50	16	a	a	DET
cana-766	50	17	lattice	lattice	NOUN
cana-766	50	18	wajsberg	wajsberg	ADJ
cana-766	50	19	algebra	algebra	PROPN
cana-766	50	20	.	.	PUNCT
cana-766	51	1	a	a	DET
cana-766	51	2	subset	subset	NOUN
cana-766	51	3	f	f	NOUN
cana-766	51	4	of	of	ADP
cana-766	51	5	a	a	PRON
cana-766	51	6	is	be	AUX
cana-766	51	7	called	call	VERB
cana-766	51	8	an	an	DET
cana-766	51	9	implicative	implicative	ADJ
cana-766	51	10	filter	filter	NOUN
cana-766	51	11	of	of	ADP
cana-766	51	12	a	a	PRON
cana-766	51	13	if	if	SCONJ
cana-766	51	14	it	it	PRON
cana-766	51	15	satisfies	satisfy	VERB
cana-766	51	16	the	the	DET
cana-766	51	17	following	follow	VERB
cana-766	51	18	properties	property	NOUN
cana-766	51	19	for	for	ADP
cana-766	51	20	all	all	DET
cana-766	51	21	x	x	NOUN
cana-766	51	22	,	,	PUNCT
cana-766	51	23	y	y	PROPN
cana-766	51	24	∈	∈	PROPN
cana-766	51	25	𝐴.	𝐴.	PROPN
cana-766	51	26	1.1∈	1.1∈	NUM
cana-766	51	27	f	f	NOUN
cana-766	51	28	2	2	NUM
cana-766	51	29	.	.	NOUN
cana-766	51	30	x∈f	x∈f	NOUN
cana-766	51	31	and	and	CCONJ
cana-766	51	32	x→y	x→y	NUM
cana-766	51	33	∈	∈	PROPN
cana-766	51	34	f	f	PROPN
cana-766	51	35	implies	imply	VERB
cana-766	51	36	x	x	X
cana-766	51	37	,	,	PUNCT
cana-766	51	38	y	y	PROPN
cana-766	51	39	∈	∈	PROPN
cana-766	51	40	𝐹.	𝐹.	PROPN
cana-766	51	41	definition	definition	NOUN
cana-766	51	42	2.9[1	2.9[1	NUM
cana-766	51	43	]	]	PUNCT
cana-766	51	44	let	let	VERB
cana-766	51	45	x	x	PRON
cana-766	51	46	be	be	AUX
cana-766	51	47	a	a	DET
cana-766	51	48	set	set	NOUN
cana-766	51	49	.	.	PUNCT
cana-766	52	1	a	a	DET
cana-766	52	2	function	function	NOUN
cana-766	52	3	μ	μ	NOUN
cana-766	52	4	:	:	PUNCT
cana-766	52	5	x→[0,1	x→[0,1	X
cana-766	52	6	]	]	PUNCT
cana-766	52	7	is	be	AUX
cana-766	52	8	called	call	VERB
cana-766	52	9	a	a	DET
cana-766	52	10	fuzzy	fuzzy	ADJ
cana-766	52	11	subset	subset	NOUN
cana-766	52	12	on	on	ADP
cana-766	52	13	x	x	PRON
cana-766	52	14	,	,	PUNCT
cana-766	52	15	for	for	ADP
cana-766	52	16	all	all	DET
cana-766	52	17	x	x	SYM
cana-766	52	18	∈	∈	NOUN
cana-766	52	19	x	x	X
cana-766	52	20	the	the	DET
cana-766	52	21	value	value	NOUN
cana-766	52	22	of	of	ADP
cana-766	52	23	μ(x	μ(x	NOUN
cana-766	52	24	)	)	PUNCT
cana-766	52	25	describes	describe	VERB
cana-766	52	26	a	a	DET
cana-766	52	27	degree	degree	NOUN
cana-766	52	28	of	of	ADP
cana-766	52	29	membership	membership	NOUN
cana-766	52	30	of	of	ADP
cana-766	52	31	x	x	PROPN
cana-766	52	32	in	in	ADP
cana-766	52	33	μ	μ	NUM
cana-766	52	34	.	.	PUNCT
cana-766	53	1	communications	communication	NOUN
cana-766	53	2	on	on	ADP
cana-766	53	3	applied	apply	VERB
cana-766	53	4	nonlinear	nonlinear	ADJ
cana-766	53	5	analysis	analysis	NOUN
cana-766	53	6	issn	issn	NOUN
cana-766	53	7	:	:	PUNCT
cana-766	53	8	1074	1074	NUM
cana-766	53	9	-	-	PUNCT
cana-766	53	10	133x	133x	NUM
cana-766	53	11	vol	vol	NOUN
cana-766	53	12	31	31	NUM
cana-766	53	13	no	no	NOUN
cana-766	53	14	.	.	PUNCT
cana-766	54	1	3s	3s	NUM
cana-766	54	2	(	(	PUNCT
cana-766	54	3	2024	2024	NUM
cana-766	54	4	)	)	PUNCT
cana-766	54	5	297	297	NUM
cana-766	54	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-766	54	7	definition	definition	NOUN
cana-766	54	8	2.10[11	2.10[11	NUM
cana-766	54	9	]	]	PUNCT
cana-766	54	10	let	let	VERB
cana-766	54	11	μ	μ	NOUN
cana-766	54	12	be	be	AUX
cana-766	54	13	a	a	DET
cana-766	54	14	fuzzy	fuzzy	ADJ
cana-766	54	15	subset	subset	NOUN
cana-766	54	16	in	in	ADP
cana-766	54	17	set	set	ADJ
cana-766	54	18	a.	a.	NOUN
cana-766	54	19	then	then	ADV
cana-766	54	20	for	for	ADP
cana-766	54	21	t	t	PROPN
cana-766	54	22	∈	∈	PROPN
cana-766	55	1	[	[	X
cana-766	55	2	0	0	NUM
cana-766	55	3	,	,	PUNCT
cana-766	55	4	1],the	1],the	DET
cana-766	55	5	st	st	PROPN
cana-766	55	6	μt	μt	PROPN
cana-766	55	7	=	=	PROPN
cana-766	55	8	{	{	PUNCT
cana-766	55	9	x	x	SYM
cana-766	55	10	∈a	∈a	ADJ
cana-766	55	11	:	:	PUNCT
cana-766	55	12	μ(x	μ(x	NUM
cana-766	55	13	)	)	PUNCT
cana-766	55	14	≥	≥	PROPN
cana-766	55	15	t	t	PROPN
cana-766	55	16	}	}	PUNCT
cana-766	55	17	is	be	AUX
cana-766	55	18	called	call	VERB
cana-766	55	19	a	a	DET
cana-766	55	20	level	level	NOUN
cana-766	55	21	subset	subset	NOUN
cana-766	55	22	of	of	ADP
cana-766	55	23	μ	μ	PROPN
cana-766	55	24	.	.	PUNCT
cana-766	56	1	definition	definition	NOUN
cana-766	56	2	2.11	2.11	NUM
cana-766	56	3	[	[	X
cana-766	56	4	11]let	11]let	NUM
cana-766	56	5	(	(	PUNCT
cana-766	56	6	a1	a1	PROPN
cana-766	56	7	,	,	PUNCT
cana-766	56	8	→	→	SYM
cana-766	56	9	,	,	PUNCT
cana-766	56	10	*	*	SYM
cana-766	56	11	,	,	PUNCT
cana-766	56	12	1	1	X
cana-766	56	13	)	)	PUNCT
cana-766	56	14	be	be	AUX
cana-766	56	15	a	a	DET
cana-766	56	16	lattice	lattice	NOUN
cana-766	56	17	wajsberg	wajsberg	ADJ
cana-766	56	18	algebra	algebra	PROPN
cana-766	56	19	.	.	PUNCT
cana-766	57	1	a	a	DET
cana-766	57	2	fuzzy	fuzzy	ADJ
cana-766	57	3	subset	subset	VERB
cana-766	57	4	μ	μ	NOUN
cana-766	57	5	of	of	ADP
cana-766	57	6	a	a	PRON
cana-766	57	7	is	be	AUX
cana-766	57	8	called	call	VERB
cana-766	57	9	a	a	DET
cana-766	57	10	fuzzy	fuzzy	ADJ
cana-766	57	11	implicative	implicative	ADJ
cana-766	57	12	filter	filter	NOUN
cana-766	57	13	of	of	ADP
cana-766	57	14	a	a	PRON
cana-766	57	15	if	if	SCONJ
cana-766	57	16	it	it	PRON
cana-766	57	17	satisfies	satisfy	VERB
cana-766	57	18	the	the	DET
cana-766	57	19	following	follow	VERB
cana-766	57	20	properties	property	NOUN
cana-766	57	21	for	for	ADP
cana-766	57	22	all	all	DET
cana-766	57	23	x	x	NOUN
cana-766	57	24	,	,	PUNCT
cana-766	57	25	y	y	PROPN
cana-766	57	26	in	in	ADP
cana-766	57	27	a.	a.	NOUN
cana-766	57	28	1	1	NUM
cana-766	57	29	.	.	PUNCT
cana-766	58	1	μ(1)≥	μ(1)≥	PROPN
cana-766	58	2	μ(x	μ(x	NOUN
cana-766	58	3	)	)	PUNCT
cana-766	59	1	2	2	NUM
cana-766	59	2	.	.	X
cana-766	59	3	μ(𝑧)≥min	μ(𝑧)≥min	NOUN
cana-766	59	4	{	{	PUNCT
cana-766	59	5	μ(𝑦	μ(𝑦	ADJ
cana-766	59	6	)	)	PUNCT
cana-766	59	7	,	,	PUNCT
cana-766	59	8	μ((y→z	μ((y→z	NOUN
cana-766	59	9	)	)	PUNCT
cana-766	59	10	}	}	PUNCT
cana-766	59	11	.	.	PUNCT
cana-766	60	1	definition	definition	NOUN
cana-766	60	2	2.12	2.12	NUM
cana-766	61	1	[	[	X
cana-766	61	2	12]let	12]let	NUM
cana-766	61	3	μ	μ	NOUN
cana-766	61	4	be	be	AUX
cana-766	61	5	a	a	DET
cana-766	61	6	fuzzy	fuzzy	ADJ
cana-766	61	7	implicative	implicative	ADJ
cana-766	61	8	filter	filter	NOUN
cana-766	61	9	of	of	ADP
cana-766	61	10	a	a	DET
cana-766	61	11	lattice	lattice	NOUN
cana-766	61	12	wajsberg	wajsberg	PROPN
cana-766	61	13	algebra	algebra	PROPN
cana-766	62	1	a	a	PRON
cana-766	62	2	,	,	PUNCT
cana-766	62	3	then	then	ADV
cana-766	62	4	a	a	PRON
cana-766	62	5	is	be	AUX
cana-766	62	6	called	call	VERB
cana-766	62	7	x≤y	x≤y	ADV
cana-766	62	8	implies	imply	VERB
cana-766	62	9	μ(x)≤	μ(x)≤	NOUN
cana-766	62	10	μ(y	μ(y	NOUN
cana-766	62	11	)	)	PUNCT
cana-766	62	12	for	for	ADP
cana-766	62	13	all	all	DET
cana-766	62	14	x	x	NOUN
cana-766	62	15	,	,	PUNCT
cana-766	62	16	y	y	PROPN
cana-766	62	17	in	in	ADP
cana-766	62	18	a	a	DET
cana-766	62	19	definition	definition	NOUN
cana-766	62	20	2.13	2.13	NUM
cana-766	62	21	[	[	X
cana-766	62	22	11]let	11]let	NUM
cana-766	62	23	(	(	PUNCT
cana-766	62	24	a1	a1	PROPN
cana-766	62	25	,	,	PUNCT
cana-766	62	26	→	→	SYM
cana-766	62	27	,	,	PUNCT
cana-766	62	28	*	*	SYM
cana-766	62	29	,	,	PUNCT
cana-766	62	30	1	1	X
cana-766	62	31	)	)	PUNCT
cana-766	62	32	be	be	AUX
cana-766	62	33	a	a	DET
cana-766	62	34	lattice	lattice	NOUN
cana-766	62	35	wajsberg	wajsberg	ADJ
cana-766	62	36	algebra	algebra	PROPN
cana-766	62	37	.	.	PUNCT
cana-766	63	1	a	a	DET
cana-766	63	2	fuzzy	fuzzy	ADJ
cana-766	63	3	subset	subset	VERB
cana-766	63	4	μ	μ	NOUN
cana-766	63	5	of	of	ADP
cana-766	63	6	a	a	PRON
cana-766	63	7	is	be	AUX
cana-766	63	8	called	call	VERB
cana-766	63	9	a	a	DET
cana-766	63	10	strong	strong	ADJ
cana-766	63	11	implicative	implicative	ADJ
cana-766	63	12	filter	filter	NOUN
cana-766	63	13	if	if	SCONJ
cana-766	63	14	it	it	PRON
cana-766	63	15	satisfies	satisfy	VERB
cana-766	63	16	1	1	NUM
cana-766	63	17	.	.	PUNCT
cana-766	64	1	1∈	1∈	PROPN
cana-766	64	2	𝐹	𝐹	PROPN
cana-766	64	3	2	2	NUM
cana-766	64	4	.	.	NUM
cana-766	64	5	x→	x→	PUNCT
cana-766	65	1	(	(	PUNCT
cana-766	65	2	𝑦	𝑦	NOUN
cana-766	65	3	→	→	SYM
cana-766	65	4	z	z	NOUN
cana-766	65	5	)	)	PUNCT
cana-766	65	6	∈	∈	PROPN
cana-766	65	7	𝐹	𝐹	PROPN
cana-766	65	8	and	and	CCONJ
cana-766	65	9	x	x	X
cana-766	65	10	→	→	SYM
cana-766	65	11	𝑦	𝑦	NUM
cana-766	65	12	∈	∈	X
cana-766	65	13	f	f	PROPN
cana-766	65	14	implies	imply	VERB
cana-766	65	15	x→	x→	PUNCT
cana-766	65	16	𝑧	𝑧	PROPN
cana-766	65	17	∈	∈	PROPN
cana-766	65	18	f.	f.	PROPN
cana-766	65	19	definition	definition	NOUN
cana-766	65	20	2.14[2	2.14[2	NUM
cana-766	65	21	]	]	PUNCT
cana-766	65	22	let	let	VERB
cana-766	65	23	μ	μ	NOUN
cana-766	65	24	be	be	AUX
cana-766	65	25	a	a	DET
cana-766	65	26	fuzzy	fuzzy	ADJ
cana-766	65	27	implicative	implicative	ADJ
cana-766	65	28	filter	filter	NOUN
cana-766	65	29	of	of	ADP
cana-766	65	30	a	a	DET
cana-766	65	31	lattice	lattice	NOUN
cana-766	65	32	wajsberg	wajsberg	PROPN
cana-766	65	33	algebra.a	algebra.a	PROPN
cana-766	65	34	fuzzy	fuzzy	ADJ
cana-766	65	35	sub	sub	NOUN
cana-766	65	36	set	set	VERB
cana-766	65	37	μ	μ	PROPN
cana-766	65	38	of	of	ADP
cana-766	65	39	a	a	PRON
cana-766	65	40	is	be	AUX
cana-766	65	41	called	call	VERB
cana-766	65	42	fuzzy	fuzzy	ADJ
cana-766	65	43	strong	strong	ADJ
cana-766	65	44	implicative	implicative	ADJ
cana-766	65	45	filter	filter	NOUN
cana-766	65	46	of	of	ADP
cana-766	65	47	a	a	PRON
cana-766	65	48	if	if	SCONJ
cana-766	65	49	it	it	PRON
cana-766	65	50	satisfies	satisfy	VERB
cana-766	65	51	the	the	DET
cana-766	65	52	properties	property	NOUN
cana-766	65	53	.	.	PUNCT
cana-766	66	1	1.μ(1)≥	1.μ(1)≥	NUM
cana-766	66	2	μ(x	μ(x	NOUN
cana-766	66	3	)	)	PUNCT
cana-766	66	4	2.μ(𝑥	2.μ(𝑥	PROPN
cana-766	66	5	→	→	SYM
cana-766	66	6	𝑧)≥min	𝑧)≥min	X
cana-766	66	7	{	{	PUNCT
cana-766	66	8	μ(𝑥	μ(𝑥	PROPN
cana-766	66	9	→	→	SYM
cana-766	66	10	𝑦	𝑦	NOUN
cana-766	66	11	)	)	PUNCT
cana-766	66	12	,	,	PUNCT
cana-766	66	13	μ((x→y→z	μ((x→y→z	PROPN
cana-766	66	14	)	)	PUNCT
cana-766	66	15	}	}	PUNCT
cana-766	66	16	.	.	PUNCT
cana-766	67	1	definition	definition	NOUN
cana-766	67	2	2.15	2.15	NUM
cana-766	67	3	[	[	X
cana-766	67	4	3	3	NUM
cana-766	67	5	]	]	X
cana-766	67	6	:	:	PUNCT
cana-766	67	7	a	a	DET
cana-766	67	8	vague	vague	NOUN
cana-766	67	9	set	set	VERB
cana-766	67	10	a	a	PRON
cana-766	67	11	in	in	ADP
cana-766	67	12	the	the	DET
cana-766	67	13	universe	universe	NOUN
cana-766	67	14	of	of	ADP
cana-766	67	15	discourse	discourse	NOUN
cana-766	67	16	x	x	VERB
cana-766	67	17	is	be	AUX
cana-766	67	18	a	a	DET
cana-766	67	19	pair	pair	NOUN
cana-766	67	20	(	(	PUNCT
cana-766	67	21	ta	ta	X
cana-766	67	22	,	,	PUNCT
cana-766	67	23	fa	fa	PROPN
cana-766	67	24	)	)	PUNCT
cana-766	67	25	where	where	SCONJ
cana-766	67	26	ta	ta	X
cana-766	67	27	:	:	PUNCT
cana-766	67	28	x→[0	x→[0	PROPN
cana-766	67	29	,	,	PUNCT
cana-766	67	30	1	1	X
cana-766	67	31	]	]	PUNCT
cana-766	67	32	,	,	PUNCT
cana-766	67	33	fa	fa	PROPN
cana-766	67	34	:	:	PUNCT
cana-766	67	35	x→	x→	PUNCT
cana-766	68	1	[	[	X
cana-766	68	2	0,1	0,1	NUM
cana-766	68	3	]	]	PUNCT
cana-766	68	4	with	with	ADP
cana-766	68	5	ta(x)+fa(x	ta(x)+fa(x	NOUN
cana-766	68	6	)	)	PUNCT
cana-766	68	7	≤	≤	NOUN
cana-766	68	8	1	1	NUM
cana-766	68	9	for	for	ADP
cana-766	68	10	all	all	DET
cana-766	68	11	x	x	NOUN
cana-766	68	12	in	in	ADP
cana-766	68	13	x.	x.	NOUN
cana-766	68	14	here	here	ADV
cana-766	68	15	ta	ta	PROPN
cana-766	68	16	is	be	AUX
cana-766	68	17	called	call	VERB
cana-766	68	18	the	the	DET
cana-766	68	19	membership	membership	NOUN
cana-766	68	20	function	function	NOUN
cana-766	68	21	and	and	CCONJ
cana-766	68	22	fa	fa	PROPN
cana-766	68	23	is	be	AUX
cana-766	68	24	called	call	VERB
cana-766	68	25	non	non	ADJ
cana-766	68	26	-	-	ADJ
cana-766	68	27	membership	membership	ADJ
cana-766	68	28	function	function	NOUN
cana-766	68	29	and	and	CCONJ
cana-766	68	30	also	also	ADV
cana-766	68	31	called	call	VERB
cana-766	68	32	true	true	ADJ
cana-766	68	33	membership	membership	NOUN
cana-766	68	34	function	function	NOUN
cana-766	68	35	,	,	PUNCT
cana-766	68	36	false	false	ADJ
cana-766	68	37	membership	membership	NOUN
cana-766	68	38	function	function	NOUN
cana-766	68	39	respectively	respectively	ADV
cana-766	68	40	.	.	PUNCT
cana-766	69	1	3	3	X
cana-766	69	2	.	.	X
cana-766	69	3	conclusions	conclusion	NOUN
cana-766	69	4	:	:	PUNCT
cana-766	69	5	in	in	ADP
cana-766	69	6	this	this	DET
cana-766	69	7	paper	paper	NOUN
cana-766	69	8	,	,	PUNCT
cana-766	69	9	we	we	PRON
cana-766	69	10	have	have	AUX
cana-766	69	11	introduced	introduce	VERB
cana-766	69	12	the	the	DET
cana-766	69	13	definitions	definition	NOUN
cana-766	69	14	of	of	ADP
cana-766	69	15	vague	vague	ADJ
cana-766	69	16	wi	wi	PROPN
cana-766	69	17	-	-	PUNCT
cana-766	69	18	ideal	ideal	PROPN
cana-766	69	19	lattice	lattice	PROPN
cana-766	69	20	ideal	ideal	NOUN
cana-766	69	21	of	of	ADP
cana-766	69	22	lattice	lattice	PROPN
cana-766	69	23	wajsberg	wajsberg	PROPN
cana-766	69	24	algebra	algebra	PROPN
cana-766	69	25	.	.	PUNCT
cana-766	70	1	we	we	PRON
cana-766	70	2	have	have	AUX
cana-766	70	3	discussed	discuss	VERB
cana-766	70	4	some	some	PRON
cana-766	70	5	of	of	ADP
cana-766	70	6	their	their	PRON
cana-766	70	7	properties	property	NOUN
cana-766	70	8	with	with	ADP
cana-766	70	9	illustrations	illustration	NOUN
cana-766	70	10	.	.	PUNCT
cana-766	71	1	also	also	ADV
cana-766	71	2	,	,	PUNCT
cana-766	71	3	we	we	PRON
cana-766	71	4	have	have	AUX
cana-766	71	5	shown	show	VERB
cana-766	71	6	that	that	SCONJ
cana-766	71	7	every	every	DET
cana-766	71	8	vague	vague	ADJ
cana-766	71	9	wi	wi	PROPN
cana-766	71	10	-	-	PUNCT
cana-766	71	11	ideal	ideal	NOUN
cana-766	71	12	of	of	ADP
cana-766	71	13	lattice	lattice	PROPN
cana-766	71	14	wajsberg	wajsberg	PROPN
cana-766	71	15	algebra	algebra	PROPN
cana-766	71	16	is	be	AUX
cana-766	71	17	an	an	DET
cana-766	71	18	finally	finally	ADV
cana-766	71	19	,	,	PUNCT
cana-766	71	20	we	we	PRON
cana-766	71	21	have	have	AUX
cana-766	71	22	shown	show	VERB
cana-766	71	23	that	that	DET
cana-766	71	24	collection	collection	NOUN
cana-766	71	25	of	of	ADP
cana-766	71	26	wi	wi	PROPN
cana-766	71	27	-	-	PUNCT
cana-766	71	28	ideals	ideal	NOUN
cana-766	71	29	of	of	ADP
cana-766	71	30	lattice	lattice	PROPN
cana-766	71	31	wajsberg	wajsberg	PROPN
cana-766	71	32	algebras	algebras	PROPN
cana-766	71	33	is	be	AUX
cana-766	71	34	an	an	DET
cana-766	71	35	lattice	lattice	ADJ
cana-766	71	36	ideal	ideal	NOUN
cana-766	71	37	of	of	ADP
cana-766	71	38	lattice	lattice	PROPN
cana-766	71	39	wajsberg	wajsberg	PROPN
cana-766	71	40	algebra	algebra	PROPN
cana-766	71	41	.	.	PUNCT
cana-766	72	1	but	but	CCONJ
cana-766	72	2	,	,	PUNCT
cana-766	72	3	the	the	DET
cana-766	72	4	converse	converse	NOUN
cana-766	72	5	part	part	NOUN
cana-766	72	6	is	be	AUX
cana-766	72	7	true	true	ADJ
cana-766	72	8	only	only	ADV
cana-766	72	9	in	in	ADP
cana-766	72	10	the	the	DET
cana-766	72	11	lattice	lattice	NOUN
cana-766	72	12	h	h	PROPN
cana-766	72	13	-	-	PUNCT
cana-766	72	14	wajsberg	wajsberg	ADJ
cana-766	72	15	algebras	algebra	NOUN
cana-766	72	16	.	.	PUNCT
cana-766	73	1	finally	finally	ADV
cana-766	73	2	,	,	PUNCT
cana-766	73	3	we	we	PRON
cana-766	73	4	have	have	AUX
cana-766	73	5	shown	show	VERB
cana-766	73	6	that	that	DET
cana-766	73	7	collection	collection	NOUN
cana-766	73	8	of	of	ADP
cana-766	73	9	wi	wi	PROPN
cana-766	73	10	-	-	PUNCT
cana-766	73	11	ideals	ideal	NOUN
cana-766	73	12	of	of	ADP
cana-766	73	13	lattice	lattice	PROPN
cana-766	73	14	wajsberg	wajsberg	PROPN
cana-766	73	15	algebras	algebras	PROPN
cana-766	73	16	is	be	AUX
cana-766	73	17	an	an	DET
cana-766	73	18	results	result	NOUN
cana-766	73	19	:	:	PUNCT
cana-766	73	20	3	3	X
cana-766	73	21	.	.	X
cana-766	73	22	vague	vague	ADJ
cana-766	73	23	strong	strong	ADJ
cana-766	73	24	implicative	implicative	ADJ
cana-766	73	25	filters	filter	NOUN
cana-766	73	26	in	in	ADP
cana-766	73	27	this	this	DET
cana-766	73	28	section	section	NOUN
cana-766	73	29	,	,	PUNCT
cana-766	73	30	we	we	PRON
cana-766	73	31	introduce	introduce	VERB
cana-766	73	32	vague	vague	ADJ
cana-766	73	33	implicative	implicative	ADJ
cana-766	73	34	filter	filter	NOUN
cana-766	73	35	of	of	ADP
cana-766	73	36	lattice	lattice	NOUN
cana-766	73	37	of	of	ADP
cana-766	73	38	wajsberg	wajsberg	PROPN
cana-766	73	39	algebra	algebra	NOUN
cana-766	73	40	and	and	CCONJ
cana-766	73	41	vague	vague	ADJ
cana-766	73	42	strong	strong	ADJ
cana-766	73	43	implicative	implicative	ADJ
cana-766	73	44	filter	filter	NOUN
cana-766	73	45	of	of	ADP
cana-766	73	46	lattice	lattice	NOUN
cana-766	73	47	of	of	ADP
cana-766	73	48	wajsberg	wajsberg	PROPN
cana-766	73	49	algebra	algebra	PROPN
cana-766	73	50	a	a	PRON
cana-766	73	51	with	with	ADP
cana-766	73	52	illustrations	illustration	NOUN
cana-766	73	53	and	and	CCONJ
cana-766	73	54	investigate	investigate	VERB
cana-766	73	55	some	some	DET
cana-766	73	56	properties	property	NOUN
cana-766	73	57	.	.	PUNCT
cana-766	74	1	definition	definition	NOUN
cana-766	74	2	3.1	3.1	NUM
cana-766	74	3	let	let	VERB
cana-766	74	4	w	w	PROPN
cana-766	74	5	=(	=(	PROPN
cana-766	74	6	a	a	PRON
cana-766	74	7	,	,	PUNCT
cana-766	74	8	→	→	SYM
cana-766	74	9	,	,	PUNCT
cana-766	74	10	*	*	SYM
cana-766	74	11	,	,	PUNCT
cana-766	74	12	1	1	X
cana-766	74	13	)	)	PUNCT
cana-766	74	14	be	be	AUX
cana-766	74	15	a	a	DET
cana-766	74	16	lattice	lattice	NOUN
cana-766	74	17	wajsberg	wajsberg	ADJ
cana-766	74	18	algebra	algebra	PROPN
cana-766	74	19	.	.	PUNCT
cana-766	75	1	an	an	DET
cana-766	75	2	vague	vague	ADJ
cana-766	75	3	set	set	NOUN
cana-766	75	4	a=	a=	PROPN
cana-766	75	5	(	(	PUNCT
cana-766	75	6	ta	ta	X
cana-766	75	7	,	,	PUNCT
cana-766	75	8	fa	fa	PROPN
cana-766	75	9	)	)	PUNCT
cana-766	75	10	of	of	ADP
cana-766	75	11	w	w	PROPN
cana-766	75	12	is	be	AUX
cana-766	75	13	called	call	VERB
cana-766	75	14	vague	vague	ADJ
cana-766	75	15	implicative	implicative	ADJ
cana-766	75	16	filter	filter	NOUN
cana-766	75	17	of	of	ADP
cana-766	75	18	a	a	PRON
cana-766	75	19	if	if	SCONJ
cana-766	75	20	it	it	PRON
cana-766	75	21	satisfies	satisfy	VERB
cana-766	75	22	the	the	DET
cana-766	75	23	properties	property	NOUN
cana-766	75	24	.	.	PUNCT
cana-766	76	1	1	1	X
cana-766	76	2	.	.	X
cana-766	76	3	ma	ma	PROPN
cana-766	76	4	(	(	PUNCT
cana-766	76	5	1	1	NUM
cana-766	76	6	)	)	PUNCT
cana-766	76	7	≥	≥	NOUN
cana-766	76	8	ma	ma	PROPN
cana-766	76	9	(	(	PUNCT
cana-766	76	10	x	x	NOUN
cana-766	76	11	)	)	PUNCT
cana-766	76	12	and	and	CCONJ
cana-766	76	13	na	na	INTJ
cana-766	76	14	(	(	PUNCT
cana-766	76	15	1	1	X
cana-766	76	16	)	)	PUNCT
cana-766	76	17	≤	≤	NOUN
cana-766	76	18	na	na	PART
cana-766	76	19	(	(	PUNCT
cana-766	76	20	x	x	X
cana-766	76	21	)	)	PUNCT
cana-766	76	22	2	2	NUM
cana-766	76	23	.	.	X
cana-766	76	24	ma	ma	PROPN
cana-766	76	25	(	(	PUNCT
cana-766	76	26	𝑦	𝑦	NOUN
cana-766	76	27	)	)	PUNCT
cana-766	76	28	≥	≥	NOUN
cana-766	76	29	min	min	PROPN
cana-766	76	30	{	{	PUNCT
cana-766	76	31	m(𝑥	m(𝑥	PROPN
cana-766	76	32	)	)	PUNCT
cana-766	76	33	,	,	PUNCT
cana-766	76	34	m(𝑥→𝑦	m(𝑥→𝑦	PROPN
cana-766	76	35	)	)	PUNCT
cana-766	76	36	}	}	PUNCT
cana-766	76	37	n(𝑦	n(𝑦	NOUN
cana-766	76	38	)	)	PUNCT
cana-766	76	39	≤	≤	NUM
cana-766	76	40	max	max	PROPN
cana-766	76	41	{	{	PUNCT
cana-766	76	42	na	na	X
cana-766	76	43	(	(	PUNCT
cana-766	76	44	𝑥	𝑥	NOUN
cana-766	76	45	)	)	PUNCT
cana-766	76	46	,	,	PUNCT
cana-766	76	47	na	na	X
cana-766	76	48	(	(	PUNCT
cana-766	76	49	𝑥→𝑦	𝑥→𝑦	NUM
cana-766	76	50	)	)	PUNCT
cana-766	76	51	}	}	PUNCT
cana-766	76	52	for	for	SCONJ
cana-766	76	53	all	all	DET
cana-766	76	54	x	x	NOUN
cana-766	76	55	,	,	PUNCT
cana-766	76	56	y	y	PROPN
cana-766	76	57	,	,	PUNCT
cana-766	76	58	z	z	PROPN
cana-766	76	59	∈	∈	PROPN
cana-766	76	60	a.	a.	NOUN
cana-766	76	61	communications	communication	NOUN
cana-766	76	62	on	on	ADP
cana-766	76	63	applied	apply	VERB
cana-766	76	64	nonlinear	nonlinear	ADJ
cana-766	76	65	analysis	analysis	NOUN
cana-766	76	66	issn	issn	NOUN
cana-766	76	67	:	:	PUNCT
cana-766	76	68	1074	1074	NUM
cana-766	76	69	-	-	PUNCT
cana-766	76	70	133x	133x	NUM
cana-766	76	71	vol	vol	NOUN
cana-766	76	72	31	31	NUM
cana-766	76	73	no	no	NOUN
cana-766	76	74	.	.	PUNCT
cana-766	77	1	3s	3s	NUM
cana-766	77	2	(	(	PUNCT
cana-766	77	3	2024	2024	NUM
cana-766	77	4	)	)	PUNCT
cana-766	77	5	298	298	NUM
cana-766	77	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-766	77	7	definition	definition	NOUN
cana-766	77	8	3.2	3.2	NUM
cana-766	77	9	let	let	VERB
cana-766	77	10	w=	w=	NOUN
cana-766	77	11	(	(	PUNCT
cana-766	77	12	a	a	PRON
cana-766	77	13	,	,	PUNCT
cana-766	77	14	→	→	SYM
cana-766	77	15	,	,	PUNCT
cana-766	77	16	*	*	PUNCT
cana-766	77	17	,	,	PUNCT
cana-766	77	18	1)be	1)be	VERB
cana-766	77	19	a	a	DET
cana-766	77	20	lattice	lattice	NOUN
cana-766	77	21	wajsberg	wajsberg	PROPN
cana-766	77	22	algebra	algebra	PROPN
cana-766	77	23	.	.	PUNCT
cana-766	78	1	an	an	DET
cana-766	78	2	vague	vague	ADJ
cana-766	78	3	set	set	NOUN
cana-766	78	4	a=	a=	PROPN
cana-766	78	5	(	(	PUNCT
cana-766	78	6	ma	ma	PROPN
cana-766	78	7	,	,	PUNCT
cana-766	78	8	na	na	NOUN
cana-766	78	9	)	)	PUNCT
cana-766	78	10	of	of	ADP
cana-766	78	11	w	w	PROPN
cana-766	78	12	is	be	AUX
cana-766	78	13	called	call	VERB
cana-766	78	14	vague	vague	ADJ
cana-766	78	15	strong	strong	ADJ
cana-766	78	16	implicative	implicative	ADJ
cana-766	78	17	filter	filter	NOUN
cana-766	78	18	of	of	ADP
cana-766	78	19	a	a	PRON
cana-766	78	20	if	if	SCONJ
cana-766	78	21	it	it	PRON
cana-766	78	22	satisfies	satisfy	VERB
cana-766	78	23	the	the	DET
cana-766	78	24	properties	property	NOUN
cana-766	78	25	.	.	PUNCT
cana-766	79	1	1	1	X
cana-766	79	2	.	.	X
cana-766	79	3	ma	ma	PROPN
cana-766	79	4	(	(	PUNCT
cana-766	79	5	1	1	NUM
cana-766	79	6	)	)	PUNCT
cana-766	79	7	≥	≥	NOUN
cana-766	79	8	ma	ma	PROPN
cana-766	79	9	(	(	PUNCT
cana-766	79	10	x	x	NOUN
cana-766	79	11	)	)	PUNCT
cana-766	79	12	and	and	CCONJ
cana-766	79	13	na	na	INTJ
cana-766	79	14	(	(	PUNCT
cana-766	79	15	1	1	X
cana-766	79	16	)	)	PUNCT
cana-766	79	17	≤	≤	NOUN
cana-766	79	18	na	na	PART
cana-766	79	19	(	(	PUNCT
cana-766	79	20	x	x	X
cana-766	79	21	)	)	PUNCT
cana-766	79	22	𝑚𝐴	𝑚𝐴	PROPN
cana-766	79	23	(	(	PUNCT
cana-766	79	24	𝑥→𝑧	𝑥→𝑧	NUM
cana-766	79	25	)	)	PUNCT
cana-766	79	26	≥	≥	PROPN
cana-766	79	27	min	min	PROPN
cana-766	79	28	{	{	PUNCT
cana-766	79	29	ma	ma	PROPN
cana-766	79	30	(	(	PUNCT
cana-766	79	31	𝑥→𝑦	𝑥→𝑦	NUM
cana-766	79	32	)	)	PUNCT
cana-766	79	33	,	,	PUNCT
cana-766	79	34	ma	ma	PROPN
cana-766	79	35	(	(	PUNCT
cana-766	79	36	𝑥→(𝑦→𝑧	𝑥→(𝑦→𝑧	PROPN
cana-766	79	37	)	)	PUNCT
cana-766	79	38	)	)	PUNCT
cana-766	79	39	}	}	PUNCT
cana-766	79	40	3	3	X
cana-766	79	41	.	.	PUNCT
cana-766	79	42	na	na	PART
cana-766	79	43	(	(	PUNCT
cana-766	79	44	𝑥→𝑧	𝑥→𝑧	NOUN
cana-766	79	45	)	)	PUNCT
cana-766	79	46	≤	≤	NUM
cana-766	79	47	max	max	PROPN
cana-766	79	48	{	{	PUNCT
cana-766	79	49	na	na	X
cana-766	79	50	(	(	PUNCT
cana-766	79	51	𝑥→𝑦	𝑥→𝑦	NUM
cana-766	79	52	)	)	PUNCT
cana-766	79	53	,	,	PUNCT
cana-766	79	54	na	na	X
cana-766	79	55	(	(	PUNCT
cana-766	79	56	𝑥→(𝑦→𝑧	𝑥→(𝑦→𝑧	NOUN
cana-766	79	57	)	)	PUNCT
cana-766	79	58	)	)	PUNCT
cana-766	79	59	}	}	PUNCT
cana-766	79	60	.	.	PUNCT
cana-766	80	1	example	example	NOUN
cana-766	80	2	3.2	3.2	NUM
cana-766	80	3	let	let	VERB
cana-766	80	4	a	a	DET
cana-766	80	5	set	set	NOUN
cana-766	80	6	a={0,a	a={0,a	NOUN
cana-766	80	7	,	,	PUNCT
cana-766	80	8	b	b	NOUN
cana-766	80	9	,	,	PUNCT
cana-766	80	10	c	c	NOUN
cana-766	80	11	,	,	PUNCT
cana-766	80	12	d,1	d,1	NUM
cana-766	80	13	}	}	PUNCT
cana-766	80	14	with	with	ADP
cana-766	80	15	the	the	DET
cana-766	80	16	following	follow	VERB
cana-766	80	17	figures	figure	NOUN
cana-766	80	18	3.2.1,3.2.2	3.2.1,3.2.2	NUM
cana-766	80	19	and	and	CCONJ
cana-766	80	20	3.2.3	3.2.3	NUM
cana-766	80	21	as	as	ADP
cana-766	80	22	a	a	DET
cana-766	80	23	partial	partial	ADJ
cana-766	80	24	ordering	ordering	NOUN
cana-766	80	25	.define	.define	PRON
cana-766	80	26	a	a	DET
cana-766	80	27	quasi	quasi	ADJ
cana-766	80	28	complement	complement	NOUN
cana-766	80	29	“	"	PUNCT
cana-766	80	30	*	*	PUNCT
cana-766	80	31	”	"	PUNCT
cana-766	80	32	and	and	CCONJ
cana-766	80	33	a	a	DET
cana-766	80	34	binary	binary	ADJ
cana-766	80	35	operation	operation	NOUN
cana-766	80	36	→	→	PUNCT
cana-766	80	37	on	on	ADP
cana-766	80	38	a	a	DET
cana-766	80	39	as	as	ADP
cana-766	80	40	in	in	ADP
cana-766	80	41	the	the	DET
cana-766	80	42	tables	table	NOUN
cana-766	80	43	3.2.1	3.2.1	NUM
cana-766	80	44	and	and	CCONJ
cana-766	80	45	3.2.2	3.2.2	NUM
cana-766	80	46	.	.	PUNCT
cana-766	80	47	table	table	NOUN
cana-766	80	48	3.2.1	3.2.1	NUM
cana-766	80	49	(	(	PUNCT
cana-766	80	50	implication	implication	NOUN
cana-766	80	51	)	)	PUNCT
cana-766	80	52	→	→	SYM
cana-766	80	53	0	0	NUM
cana-766	80	54	a	a	DET
cana-766	80	55	b	b	NOUN
cana-766	80	56	c	c	NOUN
cana-766	80	57	d	d	SYM
cana-766	80	58	1	1	NUM
cana-766	80	59	0	0	NUM
cana-766	80	60	1	1	NUM
cana-766	80	61	1	1	NUM
cana-766	80	62	1	1	NUM
cana-766	80	63	1	1	NUM
cana-766	80	64	1	1	NUM
cana-766	80	65	1	1	NUM
cana-766	80	66	a	a	DET
cana-766	80	67	d	d	PROPN
cana-766	80	68	1	1	NUM
cana-766	80	69	a	a	DET
cana-766	80	70	c	c	NOUN
cana-766	80	71	c	c	NOUN
cana-766	80	72	1	1	NUM
cana-766	80	73	b	b	SYM
cana-766	80	74	c	c	NOUN
cana-766	80	75	1	1	NUM
cana-766	81	1	1	1	NUM
cana-766	81	2	c	c	NOUN
cana-766	81	3	c	c	NOUN
cana-766	81	4	1	1	NUM
cana-766	81	5	c	c	NOUN
cana-766	81	6	b	b	PROPN
cana-766	81	7	a	a	PRON
cana-766	81	8	b	b	NOUN
cana-766	81	9	1	1	NUM
cana-766	81	10	a	a	DET
cana-766	81	11	1	1	NUM
cana-766	81	12	d	d	NOUN
cana-766	81	13	a	a	DET
cana-766	81	14	1	1	NUM
cana-766	81	15	a	a	DET
cana-766	81	16	1	1	NUM
cana-766	81	17	1	1	NUM
cana-766	81	18	1	1	NUM
cana-766	81	19	1	1	NUM
cana-766	81	20	0	0	NUM
cana-766	81	21	a	a	DET
cana-766	81	22	b	b	NOUN
cana-766	81	23	c	c	NOUN
cana-766	81	24	d	d	SYM
cana-766	81	25	1	1	NUM
cana-766	81	26	table:3.2	table:3.2	NOUN
cana-766	81	27	.2	.2	NUM
cana-766	81	28	(	(	PUNCT
cana-766	81	29	complement	complement	NOUN
cana-766	81	30	)	)	PUNCT
cana-766	81	31	x	x	PUNCT
cana-766	82	1	x	x	X
cana-766	82	2	*	*	NOUN
cana-766	82	3	0	0	NUM
cana-766	82	4	1	1	NUM
cana-766	82	5	a	a	DET
cana-766	82	6	c	c	NOUN
cana-766	82	7	b	b	PROPN
cana-766	82	8	d	d	PROPN
cana-766	82	9	c	c	PROPN
cana-766	82	10	a	a	DET
cana-766	82	11	d	d	X
cana-766	82	12	b	b	X
cana-766	82	13	1	1	NUM
cana-766	82	14	0	0	NUM
cana-766	82	15	define	define	VERB
cana-766	82	16	‘	'	PUNCT
cana-766	82	17	ꓦ	ꓦ	NOUN
cana-766	82	18	’	'	PUNCT
cana-766	82	19	and	and	CCONJ
cana-766	82	20	‘	'	PUNCT
cana-766	82	21	ꓥ	ꓥ	NOUN
cana-766	82	22	’	'	PUNCT
cana-766	82	23	operations	operation	NOUN
cana-766	82	24	on	on	ADP
cana-766	82	25	a	a	PRON
cana-766	82	26	as	as	SCONJ
cana-766	82	27	follows	follow	VERB
cana-766	82	28	:	:	PUNCT
cana-766	82	29	a	a	X
cana-766	82	30	)	)	PUNCT
cana-766	82	31	(	(	PUNCT
cana-766	82	32	xꓦy)=(x→y)→	xꓦy)=(x→y)→	PROPN
cana-766	82	33	𝑦	𝑦	PROPN
cana-766	82	34	b	b	PROPN
cana-766	82	35	)	)	PUNCT
cana-766	82	36	(	(	PUNCT
cana-766	82	37	xꓥy)=	xꓥy)=	X
cana-766	82	38	(	(	PUNCT
cana-766	82	39	(	(	PUNCT
cana-766	82	40	x	x	X
cana-766	82	41	*	*	PUNCT
cana-766	82	42	→y	→y	PROPN
cana-766	82	43	*	*	NUM
cana-766	82	44	)	)	PUNCT
cana-766	82	45	→y	→y	PROPN
cana-766	82	46	*	*	NUM
cana-766	82	47	)	)	PUNCT
cana-766	82	48	)	)	PUNCT
cana-766	82	49	*	*	PUNCT
cana-766	82	50	for	for	ADP
cana-766	82	51	all	all	DET
cana-766	82	52	x	x	NOUN
cana-766	82	53	,	,	PUNCT
cana-766	82	54	y	y	PROPN
cana-766	82	55	in	in	ADP
cana-766	82	56	a	a	PRON
cana-766	82	57	,	,	PUNCT
cana-766	82	58	then	then	ADV
cana-766	82	59	a	a	PRON
cana-766	82	60	is	be	AUX
cana-766	82	61	a	a	DET
cana-766	82	62	lattice	lattice	NOUN
cana-766	82	63	wajsberg	wajsberg	ADJ
cana-766	82	64	algebra	algebra	PROPN
cana-766	82	65	.	.	PUNCT
cana-766	83	1	let	let	AUX
cana-766	83	2	a={(0,0.4,0.1)(a,0.7,0.2)(b,0.4,0.2)(c,0.6,0.3)(d	a={(0,0.4,0.1)(a,0.7,0.2)(b,0.4,0.2)(c,0.6,0.3)(d	PROPN
cana-766	83	3	0.5,0.1),(1,0.7,0.3	0.5,0.1),(1,0.7,0.3	PRON
cana-766	83	4	}	}	PUNCT
cana-766	83	5	be	be	AUX
cana-766	83	6	a	a	DET
cana-766	83	7	vague	vague	ADJ
cana-766	83	8	strong	strong	ADJ
cana-766	83	9	implicative	implicative	ADJ
cana-766	83	10	filter	filter	NOUN
cana-766	83	11	of	of	ADP
cana-766	83	12	a	a	DET
cana-766	83	13	but	but	CCONJ
cana-766	83	14	not	not	PART
cana-766	83	15	an	an	DET
cana-766	83	16	vague	vague	ADJ
cana-766	83	17	strong	strong	ADJ
cana-766	83	18	implicative	implicative	ADJ
cana-766	83	19	filter	filter	NOUN
cana-766	83	20	of	of	ADP
cana-766	83	21	lattice	lattice	PROPN
cana-766	83	22	wajsberg	wajsberg	PROPN
cana-766	83	23	algebra	algebra	PROPN
cana-766	83	24	w.	w.	PROPN
cana-766	83	25	sol	sol	PROPN
cana-766	83	26	:	:	PUNCT
cana-766	83	27	(	(	PUNCT
cana-766	83	28	i	i	NOUN
cana-766	83	29	)	)	PUNCT
cana-766	83	30	ma	ma	PROPN
cana-766	83	31	(	(	PUNCT
cana-766	83	32	1	1	NUM
cana-766	83	33	)	)	PUNCT
cana-766	83	34	≥	≥	NOUN
cana-766	83	35	ma	ma	PROPN
cana-766	83	36	(	(	PUNCT
cana-766	83	37	x	x	NOUN
cana-766	83	38	)	)	PUNCT
cana-766	83	39	and	and	CCONJ
cana-766	83	40	na	na	INTJ
cana-766	83	41	(	(	PUNCT
cana-766	83	42	1	1	X
cana-766	83	43	)	)	PUNCT
cana-766	83	44	≤	≤	NOUN
cana-766	83	45	na	na	PART
cana-766	83	46	(	(	PUNCT
cana-766	83	47	x	x	X
cana-766	83	48	)	)	PUNCT
cana-766	83	49	(	(	PUNCT
cana-766	83	50	ii	ii	PROPN
cana-766	83	51	)	)	PUNCT
cana-766	83	52	ma	ma	PROPN
cana-766	83	53	(	(	PUNCT
cana-766	83	54	𝑦	𝑦	NOUN
cana-766	83	55	)	)	PUNCT
cana-766	83	56	≥	≥	PROPN
cana-766	83	57	min	min	PROPN
cana-766	83	58	{	{	PUNCT
cana-766	83	59	ma	ma	PROPN
cana-766	83	60	(	(	PUNCT
cana-766	83	61	𝑦	𝑦	NOUN
cana-766	83	62	)	)	PUNCT
cana-766	83	63	,	,	PUNCT
cana-766	83	64	ma	ma	PROPN
cana-766	83	65	(	(	PUNCT
cana-766	83	66	𝑥→𝑦	𝑥→𝑦	NUM
cana-766	83	67	)	)	PUNCT
cana-766	83	68	}	}	PUNCT
cana-766	83	69	and	and	CCONJ
cana-766	83	70	(	(	PUNCT
cana-766	83	71	iii	iii	NOUN
cana-766	83	72	)	)	PUNCT
cana-766	83	73	.	.	PUNCT
cana-766	84	1	na	na	X
cana-766	84	2	(	(	PUNCT
cana-766	84	3	𝑦	𝑦	NOUN
cana-766	84	4	)	)	PUNCT
cana-766	84	5	≤	≤	NUM
cana-766	84	6	max	max	PROPN
cana-766	84	7	{	{	PUNCT
cana-766	84	8	na	na	X
cana-766	84	9	(	(	PUNCT
cana-766	84	10	𝑥	𝑥	NOUN
cana-766	84	11	)	)	PUNCT
cana-766	84	12	,	,	PUNCT
cana-766	84	13	na	na	X
cana-766	84	14	(	(	PUNCT
cana-766	84	15	𝑥→𝑦	𝑥→𝑦	NUM
cana-766	84	16	)	)	PUNCT
cana-766	84	17	}	}	PUNCT
cana-766	84	18	for	for	ADP
cana-766	84	19	all	all	DET
cana-766	84	20	x	x	NOUN
cana-766	84	21	,	,	PUNCT
cana-766	84	22	y	y	PROPN
cana-766	84	23	,	,	PUNCT
cana-766	84	24	z	z	PROPN
cana-766	84	25	∈	∈	PROPN
cana-766	84	26	a.	a.	NOUN
cana-766	84	27	clearly	clearly	ADV
cana-766	84	28	(	(	PUNCT
cana-766	84	29	1	1	X
cana-766	84	30	)	)	PUNCT
cana-766	84	31	ma	ma	NOUN
cana-766	84	32	(	(	PUNCT
cana-766	84	33	1	1	NUM
cana-766	84	34	)	)	PUNCT
cana-766	84	35	≥	≥	NOUN
cana-766	84	36	ma	ma	PROPN
cana-766	84	37	(	(	PUNCT
cana-766	84	38	x	x	NOUN
cana-766	84	39	)	)	PUNCT
cana-766	84	40	and	and	CCONJ
cana-766	84	41	na	na	INTJ
cana-766	84	42	(	(	PUNCT
cana-766	84	43	1	1	X
cana-766	84	44	)	)	PUNCT
cana-766	84	45	≤	≤	NOUN
cana-766	84	46	na	na	PART
cana-766	84	47	(	(	PUNCT
cana-766	84	48	x	x	X
cana-766	84	49	)	)	PUNCT
cana-766	84	50	for	for	ADP
cana-766	84	51	all	all	DET
cana-766	84	52	x	x	NOUN
cana-766	84	53	in	in	ADP
cana-766	84	54	a	a	DET
cana-766	84	55	(	(	PUNCT
cana-766	84	56	ii	ii	NOUN
cana-766	84	57	)	)	PUNCT
cana-766	84	58	ma	ma	PROPN
cana-766	84	59	(	(	PUNCT
cana-766	84	60	𝑦)=	𝑦)=	NOUN
cana-766	84	61	ma	ma	PROPN
cana-766	84	62	(	(	PUNCT
cana-766	84	63	𝑏)=0.4	𝑏)=0.4	NUM
cana-766	84	64	ma	ma	PROPN
cana-766	84	65	(	(	PUNCT
cana-766	84	66	𝑎→𝑏)=ma	𝑎→𝑏)=ma	X
cana-766	84	67	(	(	PUNCT
cana-766	84	68	𝑎)=0.7	𝑎)=0.7	ADJ
cana-766	84	69	and	and	CCONJ
cana-766	84	70	min{ma	min{ma	X
cana-766	84	71	(	(	PUNCT
cana-766	84	72	𝑏	𝑏	NOUN
cana-766	84	73	)	)	PUNCT
cana-766	84	74	,	,	PUNCT
cana-766	84	75	ma	ma	PROPN
cana-766	84	76	(	(	PUNCT
cana-766	84	77	𝑎)}=min{0.4,0.7}=0.4	𝑎)}=min{0.4,0.7}=0.4	PROPN
cana-766	84	78	(	(	PUNCT
cana-766	84	79	iii)na	iii)na	NOUN
cana-766	84	80	(	(	PUNCT
cana-766	84	81	𝑎→𝑏)=na	𝑎→𝑏)=na	X
cana-766	84	82	(	(	PUNCT
cana-766	84	83	𝑎)=0.2	𝑎)=0.2	NOUN
cana-766	84	84	max{na	max{na	X
cana-766	84	85	(	(	PUNCT
cana-766	84	86	𝑥→𝑦	𝑥→𝑦	NUM
cana-766	84	87	)	)	PUNCT
cana-766	84	88	,	,	PUNCT
cana-766	84	89	na	na	X
cana-766	84	90	(	(	PUNCT
cana-766	84	91	𝑥→(𝑦→𝑧	𝑥→(𝑦→𝑧	NOUN
cana-766	84	92	)	)	PUNCT
cana-766	84	93	}	}	PUNCT
cana-766	84	94	communications	communication	NOUN
cana-766	84	95	on	on	ADP
cana-766	84	96	applied	apply	VERB
cana-766	84	97	nonlinear	nonlinear	ADJ
cana-766	84	98	analysis	analysis	NOUN
cana-766	84	99	issn	issn	NOUN
cana-766	84	100	:	:	PUNCT
cana-766	84	101	1074	1074	NUM
cana-766	84	102	-	-	PUNCT
cana-766	84	103	133x	133x	NUM
cana-766	84	104	vol	vol	NOUN
cana-766	84	105	31	31	NUM
cana-766	84	106	no	no	NOUN
cana-766	84	107	.	.	PUNCT
cana-766	85	1	3s	3s	NUM
cana-766	85	2	(	(	PUNCT
cana-766	85	3	2024	2024	NUM
cana-766	85	4	)	)	PUNCT
cana-766	85	5	299	299	NUM
cana-766	85	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-766	85	7	=	=	PUNCT
cana-766	85	8	max	max	X
cana-766	85	9	{	{	PUNCT
cana-766	85	10	na	na	X
cana-766	85	11	(	(	PUNCT
cana-766	85	12	𝑎	𝑎	NOUN
cana-766	85	13	)	)	PUNCT
cana-766	85	14	,	,	PUNCT
cana-766	85	15	na	na	X
cana-766	85	16	(	(	PUNCT
cana-766	85	17	𝑎→𝑐)}=max{na	𝑎→𝑐)}=max{na	PROPN
cana-766	85	18	(	(	PUNCT
cana-766	85	19	𝑎	𝑎	NOUN
cana-766	85	20	)	)	PUNCT
cana-766	85	21	,	,	PUNCT
cana-766	85	22	na	na	X
cana-766	85	23	(	(	PUNCT
cana-766	85	24	𝑐)}=0.7	𝑐)}=0.7	VERB
cana-766	85	25	therefore	therefore	ADV
cana-766	85	26	na	na	X
cana-766	85	27	(	(	PUNCT
cana-766	85	28	𝑥→𝑧	𝑥→𝑧	NOUN
cana-766	85	29	)	)	PUNCT
cana-766	85	30	≤	≤	NUM
cana-766	85	31	max	max	PROPN
cana-766	85	32	{	{	PUNCT
cana-766	85	33	na	na	X
cana-766	85	34	(	(	PUNCT
cana-766	85	35	𝑥→𝑦	𝑥→𝑦	NUM
cana-766	85	36	)	)	PUNCT
cana-766	85	37	,	,	PUNCT
cana-766	85	38	na	na	X
cana-766	85	39	(	(	PUNCT
cana-766	85	40	𝑥→(𝑦→𝑧	𝑥→(𝑦→𝑧	NOUN
cana-766	85	41	)	)	PUNCT
cana-766	85	42	}	}	PUNCT
cana-766	85	43	hence	hence	ADV
cana-766	85	44	a={(0,0.4,0.1)(a,0.7,0.2)(b,0.4,0.2)(c,0.6,0.4)(d	a={(0,0.4,0.1)(a,0.7,0.2)(b,0.4,0.2)(c,0.6,0.4)(d	VERB
cana-766	85	45	0.5,0.1),(1,0.7,0.3	0.5,0.1),(1,0.7,0.3	PRON
cana-766	85	46	}	}	PUNCT
cana-766	85	47	be	be	AUX
cana-766	85	48	a	a	DET
cana-766	85	49	vague	vague	ADJ
cana-766	85	50	implicative	implicative	ADJ
cana-766	85	51	filter	filter	NOUN
cana-766	85	52	of	of	ADP
cana-766	85	53	a	a	DET
cana-766	85	54	but	but	CCONJ
cana-766	85	55	not	not	PART
cana-766	85	56	an	an	DET
cana-766	85	57	vague	vague	ADJ
cana-766	85	58	strong	strong	ADJ
cana-766	85	59	implicative	implicative	ADJ
cana-766	85	60	filter	filter	NOUN
cana-766	85	61	of	of	ADP
cana-766	85	62	lattice	lattice	PROPN
cana-766	85	63	wajsberg	wajsberg	PROPN
cana-766	85	64	algebra	algebra	PROPN
cana-766	85	65	w.	w.	PROPN
cana-766	85	66	theorem	theorem	VERB
cana-766	85	67	3.3	3.3	NUM
cana-766	85	68	let	let	VERB
cana-766	85	69	w	w	NOUN
cana-766	85	70	be	be	AUX
cana-766	85	71	a	a	DET
cana-766	85	72	lattice	lattice	NOUN
cana-766	85	73	wajsberg	wajsberg	ADJ
cana-766	85	74	algebra	algebra	NOUN
cana-766	85	75	,	,	PUNCT
cana-766	85	76	and	and	CCONJ
cana-766	85	77	let	let	VERB
cana-766	85	78	a=	a=	VERB
cana-766	85	79	(	(	PUNCT
cana-766	85	80	ma	ma	PROPN
cana-766	85	81	,	,	PUNCT
cana-766	85	82	na	na	PART
cana-766	85	83	)	)	PUNCT
cana-766	85	84	be	be	AUX
cana-766	85	85	a	a	DET
cana-766	85	86	vague	vague	ADJ
cana-766	85	87	strong	strong	ADJ
cana-766	85	88	implicative	implicative	ADJ
cana-766	85	89	filter	filter	NOUN
cana-766	85	90	of	of	ADP
cana-766	85	91	w	w	PROPN
cana-766	85	92	,	,	PUNCT
cana-766	85	93	then	then	ADV
cana-766	85	94	a=	a=	PROPN
cana-766	85	95	(	(	PUNCT
cana-766	85	96	ma	ma	PROPN
cana-766	85	97	,	,	PUNCT
cana-766	85	98	na	na	INTJ
cana-766	85	99	)	)	PUNCT
cana-766	85	100	is	be	AUX
cana-766	85	101	an	an	DET
cana-766	85	102	vague	vague	ADJ
cana-766	85	103	implicative	implicative	ADJ
cana-766	85	104	filter	filter	NOUN
cana-766	85	105	of	of	ADP
cana-766	85	106	w.	w.	NOUN
cana-766	85	107	proof	proof	NOUN
cana-766	85	108	:	:	PUNCT
cana-766	85	109	let	let	VERB
cana-766	85	110	w	w	PROPN
cana-766	85	111	=(	=(	PROPN
cana-766	85	112	a	a	PRON
cana-766	85	113	,	,	PUNCT
cana-766	85	114	→	→	SYM
cana-766	85	115	,	,	PUNCT
cana-766	85	116	*	*	SYM
cana-766	85	117	,	,	PUNCT
cana-766	85	118	1	1	X
cana-766	85	119	)	)	PUNCT
cana-766	85	120	be	be	AUX
cana-766	85	121	a	a	DET
cana-766	85	122	lattice	lattice	NOUN
cana-766	85	123	wajsberg	wajsberg	PROPN
cana-766	85	124	algebra	algebra	NOUN
cana-766	85	125	,	,	PUNCT
cana-766	85	126	by	by	ADP
cana-766	85	127	the	the	DET
cana-766	85	128	definition	definition	NOUN
cana-766	85	129	of	of	ADP
cana-766	85	130	w	w	PROPN
cana-766	85	131	1	1	NUM
cana-766	85	132	.	.	PUNCT
cana-766	85	133	ma	ma	PROPN
cana-766	85	134	(	(	PUNCT
cana-766	85	135	1	1	NUM
cana-766	85	136	)	)	PUNCT
cana-766	85	137	≥	≥	NOUN
cana-766	85	138	ma	ma	PROPN
cana-766	85	139	(	(	PUNCT
cana-766	85	140	x	x	NOUN
cana-766	85	141	)	)	PUNCT
cana-766	85	142	and	and	CCONJ
cana-766	85	143	na	na	INTJ
cana-766	85	144	(	(	PUNCT
cana-766	85	145	1	1	X
cana-766	85	146	)	)	PUNCT
cana-766	85	147	≤	≤	NOUN
cana-766	85	148	na	na	PART
cana-766	85	149	(	(	PUNCT
cana-766	85	150	x	x	X
cana-766	85	151	)	)	PUNCT
cana-766	85	152	2	2	NUM
cana-766	85	153	.	.	X
cana-766	85	154	ma	ma	PROPN
cana-766	85	155	(	(	PUNCT
cana-766	85	156	𝑥→𝑧	𝑥→𝑧	PROPN
cana-766	85	157	)	)	PUNCT
cana-766	85	158	≥	≥	PROPN
cana-766	85	159	min	min	PROPN
cana-766	85	160	{	{	PUNCT
cana-766	85	161	ma	ma	PROPN
cana-766	85	162	(	(	PUNCT
cana-766	85	163	𝑥→𝑦	𝑥→𝑦	NUM
cana-766	85	164	)	)	PUNCT
cana-766	85	165	,	,	PUNCT
cana-766	85	166	ma	ma	PROPN
cana-766	85	167	(	(	PUNCT
cana-766	85	168	𝑥→(𝑦→𝑧	𝑥→(𝑦→𝑧	PROPN
cana-766	85	169	)	)	PUNCT
cana-766	85	170	)	)	PUNCT
cana-766	85	171	}	}	PUNCT
cana-766	86	1	3	3	X
cana-766	86	2	.	.	PUNCT
cana-766	86	3	na	na	PART
cana-766	86	4	(	(	PUNCT
cana-766	86	5	𝑥→𝑧	𝑥→𝑧	NOUN
cana-766	86	6	)	)	PUNCT
cana-766	86	7	≤	≤	NUM
cana-766	86	8	max	max	PROPN
cana-766	86	9	{	{	PUNCT
cana-766	86	10	na	na	X
cana-766	86	11	(	(	PUNCT
cana-766	86	12	𝑥→𝑦	𝑥→𝑦	NUM
cana-766	86	13	)	)	PUNCT
cana-766	86	14	,	,	PUNCT
cana-766	86	15	na	na	X
cana-766	86	16	(	(	PUNCT
cana-766	86	17	𝑥→(𝑦→𝑧	𝑥→(𝑦→𝑧	NOUN
cana-766	86	18	)	)	PUNCT
cana-766	86	19	)	)	PUNCT
cana-766	86	20	}	}	PUNCT
cana-766	86	21	put	put	VERB
cana-766	86	22	x=1	x=1	PUNCT
cana-766	86	23	in	in	ADP
cana-766	86	24	above	above	ADV
cana-766	86	25	(	(	PUNCT
cana-766	86	26	2	2	NUM
cana-766	86	27	)	)	PUNCT
cana-766	86	28	and	and	CCONJ
cana-766	86	29	(	(	PUNCT
cana-766	86	30	3	3	X
cana-766	86	31	)	)	PUNCT
cana-766	86	32	then	then	ADV
cana-766	86	33	we	we	PRON
cana-766	86	34	get	get	VERB
cana-766	86	35	2	2	NUM
cana-766	86	36	.	.	PUNCT
cana-766	87	1	ma	ma	PROPN
cana-766	88	1	(	(	PUNCT
cana-766	88	2	1→𝑧	1→𝑧	NUM
cana-766	88	3	)	)	PUNCT
cana-766	88	4	≥	≥	PROPN
cana-766	88	5	min	min	PROPN
cana-766	88	6	{	{	PUNCT
cana-766	88	7	ma	ma	PROPN
cana-766	88	8	(	(	PUNCT
cana-766	88	9	1→𝑦	1→𝑦	NUM
cana-766	88	10	)	)	PUNCT
cana-766	88	11	,	,	PUNCT
cana-766	88	12	m(1→(𝑦→𝑧	m(1→(𝑦→𝑧	NOUN
cana-766	88	13	)	)	PUNCT
cana-766	88	14	)	)	PUNCT
cana-766	88	15	}	}	PUNCT
cana-766	88	16	implies	imply	VERB
cana-766	88	17	ma	ma	PROPN
cana-766	88	18	(	(	PUNCT
cana-766	88	19	𝑧	𝑧	NOUN
cana-766	88	20	)	)	PUNCT
cana-766	88	21	≥	≥	PROPN
cana-766	88	22	min	min	PROPN
cana-766	88	23	{	{	PUNCT
cana-766	88	24	ma	ma	PROPN
cana-766	88	25	(	(	PUNCT
cana-766	88	26	𝑦	𝑦	NOUN
cana-766	88	27	)	)	PUNCT
cana-766	88	28	,	,	PUNCT
cana-766	88	29	ma	ma	PROPN
cana-766	88	30	(	(	PUNCT
cana-766	88	31	𝑦→𝑧	𝑦→𝑧	NUM
cana-766	88	32	)	)	PUNCT
cana-766	88	33	}	}	PUNCT
cana-766	88	34	and	and	CCONJ
cana-766	88	35	na	na	INTJ
cana-766	88	36	(	(	PUNCT
cana-766	88	37	1→𝑧	1→𝑧	NUM
cana-766	88	38	)	)	PUNCT
cana-766	88	39	≤	≤	NUM
cana-766	88	40	max	max	PROPN
cana-766	88	41	{	{	PUNCT
cana-766	88	42	na	na	X
cana-766	88	43	(	(	PUNCT
cana-766	88	44	1→𝑦	1→𝑦	NUM
cana-766	88	45	)	)	PUNCT
cana-766	88	46	,	,	PUNCT
cana-766	88	47	na	na	X
cana-766	88	48	(	(	PUNCT
cana-766	88	49	1→(𝑦→𝑧	1→(𝑦→𝑧	NUM
cana-766	88	50	)	)	PUNCT
cana-766	88	51	)	)	PUNCT
cana-766	88	52	}	}	PUNCT
cana-766	88	53	implies	imply	VERB
cana-766	88	54	that	that	SCONJ
cana-766	88	55	na	na	INTJ
cana-766	88	56	(	(	PUNCT
cana-766	88	57	𝑧	𝑧	NOUN
cana-766	88	58	)	)	PUNCT
cana-766	88	59	≤	≤	NUM
cana-766	88	60	max	max	PROPN
cana-766	88	61	{	{	PUNCT
cana-766	88	62	na	na	PROPN
cana-766	88	63	(	(	PUNCT
cana-766	88	64	𝑦	𝑦	NOUN
cana-766	88	65	)	)	PUNCT
cana-766	88	66	,	,	PUNCT
cana-766	88	67	na	na	X
cana-766	88	68	(	(	PUNCT
cana-766	88	69	𝑦→𝑧	𝑦→𝑧	NUM
cana-766	88	70	)	)	PUNCT
cana-766	88	71	}	}	PUNCT
cana-766	88	72	hence	hence	ADV
cana-766	88	73	a=	a=	VERB
cana-766	88	74	(	(	PUNCT
cana-766	88	75	ma	ma	PROPN
cana-766	88	76	,	,	PUNCT
cana-766	88	77	na	na	INTJ
cana-766	88	78	)	)	PUNCT
cana-766	88	79	is	be	AUX
cana-766	88	80	an	an	DET
cana-766	88	81	vague	vague	ADJ
cana-766	88	82	implicative	implicative	ADJ
cana-766	88	83	filter	filter	NOUN
cana-766	88	84	of	of	ADP
cana-766	88	85	w.	w.	PROPN
cana-766	88	86	theorem	theorem	VERB
cana-766	88	87	3.4	3.4	NUM
cana-766	88	88	let	let	VERB
cana-766	88	89	w	w	NOUN
cana-766	88	90	be	be	AUX
cana-766	88	91	a	a	DET
cana-766	88	92	lattice	lattice	NOUN
cana-766	88	93	wajsberg	wajsberg	ADJ
cana-766	88	94	algebra	algebra	PROPN
cana-766	88	95	.	.	PUNCT
cana-766	89	1	then	then	ADV
cana-766	89	2	w	w	PROPN
cana-766	89	3	is	be	AUX
cana-766	89	4	a	a	DET
cana-766	89	5	h	h	NOUN
cana-766	89	6	-	-	PUNCT
cana-766	89	7	wajsberj	wajsberj	NOUN
cana-766	89	8	algebra	algebra	NOUN
cana-766	89	9	if	if	SCONJ
cana-766	89	10	and	and	CCONJ
cana-766	89	11	only	only	ADV
cana-766	89	12	if	if	SCONJ
cana-766	89	13	each	each	DET
cana-766	89	14	a	a	DET
cana-766	89	15	vague	vague	ADJ
cana-766	89	16	implicative	implicative	ADJ
cana-766	89	17	filter	filter	NOUN
cana-766	89	18	of	of	ADP
cana-766	89	19	w	w	PROPN
cana-766	89	20	is	be	AUX
cana-766	89	21	an	an	DET
cana-766	89	22	vague	vague	ADJ
cana-766	89	23	strong	strong	ADJ
cana-766	89	24	implicative	implicative	ADJ
cana-766	89	25	filter	filter	NOUN
cana-766	89	26	.	.	PUNCT
cana-766	90	1	proof	proof	NOUN
cana-766	90	2	:	:	PUNCT
cana-766	90	3	let	let	VERB
cana-766	90	4	w	w	PROPN
cana-766	90	5	=(	=(	PROPN
cana-766	90	6	a	a	PRON
cana-766	90	7	,	,	PUNCT
cana-766	90	8	→	→	SYM
cana-766	90	9	,	,	PUNCT
cana-766	90	10	*	*	SYM
cana-766	90	11	,	,	PUNCT
cana-766	90	12	1	1	X
cana-766	90	13	)	)	PUNCT
cana-766	90	14	be	be	AUX
cana-766	90	15	a	a	DET
cana-766	90	16	lattice	lattice	NOUN
cana-766	90	17	wajsberg	wajsberg	ADJ
cana-766	90	18	algebra	algebra	NOUN
cana-766	90	19	and	and	CCONJ
cana-766	90	20	let	let	VERB
cana-766	90	21	a=	a=	VERB
cana-766	90	22	(	(	PUNCT
cana-766	90	23	ma	ma	PROPN
cana-766	90	24	,	,	PUNCT
cana-766	90	25	na	na	PART
cana-766	90	26	)	)	PUNCT
cana-766	90	27	be	be	AUX
cana-766	90	28	a	a	DET
cana-766	90	29	vague	vague	ADJ
cana-766	90	30	strong	strong	ADJ
cana-766	90	31	implicative	implicative	ADJ
cana-766	90	32	filter	filter	NOUN
cana-766	90	33	of	of	ADP
cana-766	90	34	w	w	PROPN
cana-766	90	35	,	,	PUNCT
cana-766	90	36	we	we	PRON
cana-766	90	37	have	have	VERB
cana-766	90	38	1	1	NUM
cana-766	90	39	.	.	PUNCT
cana-766	91	1	ma	ma	PROPN
cana-766	91	2	(	(	PUNCT
cana-766	91	3	1	1	NUM
cana-766	91	4	)	)	PUNCT
cana-766	91	5	≥	≥	NOUN
cana-766	91	6	ma	ma	PROPN
cana-766	91	7	(	(	PUNCT
cana-766	91	8	x	x	NOUN
cana-766	91	9	)	)	PUNCT
cana-766	91	10	and	and	CCONJ
cana-766	91	11	na	na	INTJ
cana-766	91	12	(	(	PUNCT
cana-766	91	13	1	1	X
cana-766	91	14	)	)	PUNCT
cana-766	91	15	≤	≤	NOUN
cana-766	91	16	na	na	PART
cana-766	91	17	(	(	PUNCT
cana-766	91	18	x	x	X
cana-766	91	19	)	)	PUNCT
cana-766	91	20	2	2	NUM
cana-766	91	21	.	.	X
cana-766	91	22	ma	ma	PROPN
cana-766	91	23	(	(	PUNCT
cana-766	91	24	𝑦	𝑦	NOUN
cana-766	91	25	)	)	PUNCT
cana-766	91	26	≥	≥	PROPN
cana-766	91	27	min	min	PROPN
cana-766	91	28	{	{	PUNCT
cana-766	91	29	ma	ma	PROPN
cana-766	91	30	(	(	PUNCT
cana-766	91	31	𝑦	𝑦	NOUN
cana-766	91	32	)	)	PUNCT
cana-766	91	33	,	,	PUNCT
cana-766	91	34	ma	ma	PROPN
cana-766	91	35	(	(	PUNCT
cana-766	91	36	𝑥→𝑦	𝑥→𝑦	NUM
cana-766	91	37	)	)	PUNCT
cana-766	91	38	}	}	PUNCT
cana-766	91	39	3	3	X
cana-766	91	40	.	.	PUNCT
cana-766	91	41	na	na	PART
cana-766	91	42	(	(	PUNCT
cana-766	91	43	𝑥→𝑧	𝑥→𝑧	NOUN
cana-766	91	44	)	)	PUNCT
cana-766	91	45	≤	≤	NUM
cana-766	91	46	max	max	PROPN
cana-766	91	47	{	{	PUNCT
cana-766	91	48	na	na	X
cana-766	91	49	(	(	PUNCT
cana-766	91	50	𝑥→𝑦	𝑥→𝑦	NUM
cana-766	91	51	)	)	PUNCT
cana-766	91	52	,	,	PUNCT
cana-766	91	53	na	na	X
cana-766	91	54	(	(	PUNCT
cana-766	91	55	𝑥→(𝑦→𝑧	𝑥→(𝑦→𝑧	NOUN
cana-766	91	56	)	)	PUNCT
cana-766	91	57	}	}	PUNCT
cana-766	91	58	also	also	ADV
cana-766	91	59	we	we	PRON
cana-766	91	60	have	have	VERB
cana-766	91	61	by	by	ADP
cana-766	91	62	the	the	DET
cana-766	91	63	definition	definition	NOUN
cana-766	91	64	of	of	ADP
cana-766	91	65	h	h	NOUN
cana-766	91	66	-	-	PUNCT
cana-766	91	67	wajsberj	wajsberj	NOUN
cana-766	91	68	algebra	algebra	NOUN
cana-766	91	69	x→	x→	PUNCT
cana-766	92	1	(	(	PUNCT
cana-766	92	2	𝑦	𝑦	NOUN
cana-766	92	3	→	→	SYM
cana-766	92	4	𝑧	𝑧	NOUN
cana-766	92	5	)	)	PUNCT
cana-766	92	6	=(	=(	NOUN
cana-766	92	7	x→	x→	SYM
cana-766	92	8	𝑦	𝑦	X
cana-766	92	9	)	)	PUNCT
cana-766	92	10	→(x→	→(x→	PROPN
cana-766	92	11	𝑧	𝑧	PART
cana-766	92	12	)	)	PUNCT
cana-766	92	13	foa	foa	NOUN
cana-766	92	14	all	all	DET
cana-766	92	15	x	x	PROPN
cana-766	92	16	,	,	PUNCT
cana-766	92	17	y	y	PROPN
cana-766	92	18	,	,	PUNCT
cana-766	92	19	z	z	PROPN
cana-766	92	20	in	in	ADP
cana-766	92	21	w.	w.	PROPN
cana-766	92	22	implies	imply	VERB
cana-766	92	23	min	min	PROPN
cana-766	92	24	{	{	PUNCT
cana-766	92	25	ma	ma	PROPN
cana-766	92	26	(	(	PUNCT
cana-766	92	27	𝑥→𝑦	𝑥→𝑦	NUM
cana-766	92	28	)	)	PUNCT
cana-766	92	29	,	,	PUNCT
cana-766	92	30	ma	ma	PROPN
cana-766	92	31	(	(	PUNCT
cana-766	92	32	𝑥→(𝑦→𝑧	𝑥→(𝑦→𝑧	PROPN
cana-766	92	33	)	)	PUNCT
cana-766	92	34	)	)	PUNCT
cana-766	92	35	}	}	PUNCT
cana-766	93	1	=	=	SYM
cana-766	93	2	min{ma	min{ma	X
cana-766	93	3	(	(	PUNCT
cana-766	93	4	𝑥→𝑦	𝑥→𝑦	NUM
cana-766	93	5	)	)	PUNCT
cana-766	93	6	,	,	PUNCT
cana-766	93	7	ma	ma	PROPN
cana-766	93	8	(	(	PUNCT
cana-766	93	9	𝑥→𝑦)→(𝑥→𝑧)}≤	𝑥→𝑦)→(𝑥→𝑧)}≤	X
cana-766	93	10	ma	ma	PROPN
cana-766	93	11	(	(	PUNCT
cana-766	93	12	𝑥→𝑧	𝑥→𝑧	NOUN
cana-766	93	13	)	)	PUNCT
cana-766	93	14	.	.	PUNCT
cana-766	94	1	therefore	therefore	ADV
cana-766	94	2	ma	ma	PROPN
cana-766	94	3	(	(	PUNCT
cana-766	94	4	𝑥→𝑧).≥	𝑥→𝑧).≥	PROPN
cana-766	94	5	min{ma	min{ma	X
cana-766	94	6	(	(	PUNCT
cana-766	94	7	𝑥→𝑦	𝑥→𝑦	NUM
cana-766	94	8	)	)	PUNCT
cana-766	94	9	,	,	PUNCT
cana-766	94	10	ma	ma	PROPN
cana-766	94	11	(	(	PUNCT
cana-766	94	12	𝑥→𝑦)→(𝑥→𝑧)}	𝑥→𝑦)→(𝑥→𝑧)}	PROPN
cana-766	94	13	…	…	PUNCT
cana-766	94	14	…	…	PUNCT
cana-766	94	15	.(3.4.1	.(3.4.1	NUM
cana-766	94	16	)	)	PUNCT
cana-766	94	17	and	and	CCONJ
cana-766	94	18	max	max	PROPN
cana-766	94	19	{	{	PUNCT
cana-766	94	20	na	na	X
cana-766	94	21	(	(	PUNCT
cana-766	94	22	𝑥→𝑦	𝑥→𝑦	NUM
cana-766	94	23	)	)	PUNCT
cana-766	94	24	,	,	PUNCT
cana-766	94	25	na	na	X
cana-766	94	26	(	(	PUNCT
cana-766	94	27	𝑥→(𝑦→𝑧	𝑥→(𝑦→𝑧	NOUN
cana-766	94	28	)	)	PUNCT
cana-766	94	29	)	)	PUNCT
cana-766	94	30	}	}	PUNCT
cana-766	94	31	=	=	SYM
cana-766	94	32	max{na	max{na	X
cana-766	94	33	(	(	PUNCT
cana-766	94	34	𝑥→𝑦	𝑥→𝑦	NUM
cana-766	94	35	)	)	PUNCT
cana-766	94	36	,	,	PUNCT
cana-766	94	37	na	na	X
cana-766	94	38	(	(	PUNCT
cana-766	94	39	𝑥→𝑦)→(𝑥→𝑧)}≥na	𝑥→𝑦)→(𝑥→𝑧)}≥na	PROPN
cana-766	94	40	(	(	PUNCT
cana-766	94	41	𝑥→𝑧	𝑥→𝑧	NOUN
cana-766	94	42	)	)	PUNCT
cana-766	94	43	.	.	PUNCT
cana-766	95	1	therefore	therefore	ADV
cana-766	95	2	na	na	INTJ
cana-766	95	3	(	(	PUNCT
cana-766	95	4	𝑥→𝑧)≤	𝑥→𝑧)≤	PRON
cana-766	95	5	max{na	max{na	ADJ
cana-766	95	6	(	(	PUNCT
cana-766	95	7	𝑥→𝑦	𝑥→𝑦	NUM
cana-766	95	8	)	)	PUNCT
cana-766	95	9	,	,	PUNCT
cana-766	95	10	na	na	X
cana-766	95	11	(	(	PUNCT
cana-766	95	12	𝑥→𝑦)→(𝑥→𝑧	𝑥→𝑦)→(𝑥→𝑧	PROPN
cana-766	95	13	)	)	PUNCT
cana-766	95	14	}	}	PUNCT
cana-766	95	15	for	for	ADP
cana-766	95	16	all	all	DET
cana-766	95	17	x	x	NOUN
cana-766	95	18	,	,	PUNCT
cana-766	95	19	y	y	PROPN
cana-766	95	20	,	,	PUNCT
cana-766	95	21	z	z	NOUN
cana-766	95	22	in	in	ADP
cana-766	95	23	w	w	PROPN
cana-766	95	24	…	…	PUNCT
cana-766	95	25	…	…	PUNCT
cana-766	95	26	.(3.4.2	.(3.4.2	NOUN
cana-766	95	27	)	)	PUNCT
cana-766	95	28	from	from	ADP
cana-766	95	29	(	(	PUNCT
cana-766	95	30	3.4.1	3.4.1	NUM
cana-766	95	31	)	)	PUNCT
cana-766	95	32	and	and	CCONJ
cana-766	95	33	(	(	PUNCT
cana-766	95	34	3.4.2	3.4.2	NUM
cana-766	95	35	)	)	PUNCT
cana-766	95	36	”	"	PUNCT
cana-766	95	37	w	w	PROPN
cana-766	95	38	”	"	PUNCT
cana-766	95	39	is	be	AUX
cana-766	95	40	an	an	DET
cana-766	95	41	vague	vague	ADJ
cana-766	95	42	strong	strong	ADJ
cana-766	95	43	implicative	implicative	ADJ
cana-766	95	44	filter	filter	NOUN
cana-766	95	45	.	.	PUNCT
cana-766	96	1	conversely	conversely	ADV
cana-766	96	2	,	,	PUNCT
cana-766	96	3	we	we	PRON
cana-766	96	4	consider	consider	VERB
cana-766	96	5	an	an	DET
cana-766	96	6	vague	vague	ADJ
cana-766	96	7	strong	strong	ADJ
cana-766	96	8	implicative	implicative	ADJ
cana-766	96	9	filter	filter	NOUN
cana-766	96	10	a=	a=	X
cana-766	96	11	{	{	PUNCT
cana-766	96	12	(	(	PUNCT
cana-766	96	13	0,0,0.7)(a,0,0.7)(b,0,0.7),(c,0,0.7)(d,0,0.7)(1,0.8,0	0,0,0.7)(a,0,0.7)(b,0,0.7),(c,0,0.7)(d,0,0.7)(1,0.8,0	ADV
cana-766	96	14	)	)	PUNCT
cana-766	96	15	}	}	PUNCT
cana-766	96	16	of	of	ADP
cana-766	96	17	w	w	NOUN
cana-766	96	18	is	be	AUX
cana-766	96	19	vague	vague	ADV
cana-766	96	20	strong	strong	ADJ
cana-766	96	21	implicative	implicative	ADJ
cana-766	96	22	filter	filter	NOUN
cana-766	96	23	.	.	PUNCT
cana-766	97	1	then	then	ADV
cana-766	97	2	a	a	PRON
cana-766	97	3	is	be	AUX
cana-766	97	4	implicative	implicative	ADJ
cana-766	97	5	filter	filter	NOUN
cana-766	97	6	,	,	PUNCT
cana-766	97	7	and	and	CCONJ
cana-766	97	8	then	then	ADV
cana-766	97	9	implies	imply	VERB
cana-766	97	10	that	that	SCONJ
cana-766	97	11	a	a	PRON
cana-766	97	12	is	be	AUX
cana-766	97	13	lattice	lattice	ADJ
cana-766	97	14	hwajsberg	hwajsberg	PROPN
cana-766	97	15	algebra	algebra	PROPN
cana-766	97	16	.	.	PUNCT
cana-766	98	1	theorem	theorem	VERB
cana-766	98	2	3.5	3.5	NUM
cana-766	98	3	let	let	VERB
cana-766	98	4	w	w	NOUN
cana-766	98	5	be	be	AUX
cana-766	98	6	a	a	DET
cana-766	98	7	lattice	lattice	NOUN
cana-766	98	8	wajsberg	wajsberg	PROPN
cana-766	98	9	algebra	algebra	NOUN
cana-766	98	10	and	and	CCONJ
cana-766	98	11	a=	a=	PROPN
cana-766	98	12	(	(	PUNCT
cana-766	98	13	ma	ma	PROPN
cana-766	98	14	,	,	PUNCT
cana-766	98	15	na	na	INTJ
cana-766	98	16	)	)	PUNCT
cana-766	98	17	be	be	AUX
cana-766	98	18	a	a	DET
cana-766	98	19	vague	vague	ADJ
cana-766	98	20	set	set	NOUN
cana-766	98	21	of	of	ADP
cana-766	98	22	a	a	DET
cana-766	98	23	,	,	PUNCT
cana-766	98	24	if	if	SCONJ
cana-766	98	25	a=(ma	a=(ma	PROPN
cana-766	98	26	,	,	PUNCT
cana-766	98	27	na	na	PART
cana-766	98	28	)	)	PUNCT
cana-766	98	29	vague	vague	VERB
cana-766	98	30	strong	strong	ADJ
cana-766	98	31	implicative	implicative	ADJ
cana-766	98	32	filter	filter	NOUN
cana-766	98	33	,	,	PUNCT
cana-766	98	34	then	then	ADV
cana-766	98	35	the	the	DET
cana-766	98	36	following	following	NOUN
cana-766	98	37	are	be	AUX
cana-766	98	38	satisfied	satisfied	ADJ
cana-766	98	39	and	and	CCONJ
cana-766	98	40	equivalent	equivalent	ADJ
cana-766	98	41	.	.	PUNCT
cana-766	99	1	communications	communication	NOUN
cana-766	99	2	on	on	ADP
cana-766	99	3	applied	apply	VERB
cana-766	99	4	nonlinear	nonlinear	ADJ
cana-766	99	5	analysis	analysis	NOUN
cana-766	99	6	issn	issn	NOUN
cana-766	99	7	:	:	PUNCT
cana-766	99	8	1074	1074	NUM
cana-766	99	9	-	-	PUNCT
cana-766	99	10	133x	133x	NUM
cana-766	99	11	vol	vol	NOUN
cana-766	99	12	31	31	NUM
cana-766	99	13	no	no	NOUN
cana-766	99	14	.	.	PUNCT
cana-766	100	1	3s	3s	NUM
cana-766	100	2	(	(	PUNCT
cana-766	100	3	2024	2024	NUM
cana-766	100	4	)	)	PUNCT
cana-766	100	5	300	300	NUM
cana-766	100	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-766	100	7	(	(	PUNCT
cana-766	100	8	i	i	NOUN
cana-766	100	9	)	)	PUNCT
cana-766	100	10	if	if	SCONJ
cana-766	100	11	a=	a=	PROPN
cana-766	100	12	(	(	PUNCT
cana-766	100	13	ma	ma	PROPN
cana-766	100	14	,	,	PUNCT
cana-766	100	15	na	na	PROPN
cana-766	100	16	)	)	PUNCT
cana-766	100	17	is	be	AUX
cana-766	100	18	an	an	DET
cana-766	100	19	vague	vague	ADJ
cana-766	100	20	implicative	implicative	ADJ
cana-766	100	21	filter	filter	NOUN
cana-766	100	22	and	and	CCONJ
cana-766	100	23	for	for	ADP
cana-766	100	24	all	all	DET
cana-766	100	25	x	x	NOUN
cana-766	100	26	,	,	PUNCT
cana-766	100	27	y	y	PROPN
cana-766	100	28	∈	∈	PROPN
cana-766	100	29	𝐴	𝐴	PROPN
cana-766	100	30	,	,	PUNCT
cana-766	100	31	ma	ma	PROPN
cana-766	100	32	(	(	PUNCT
cana-766	100	33	𝑥→𝑦	𝑥→𝑦	NUM
cana-766	100	34	)	)	PUNCT
cana-766	100	35	≥	≥	PROPN
cana-766	100	36	min	min	PROPN
cana-766	100	37	{	{	PUNCT
cana-766	100	38	ma	ma	PROPN
cana-766	100	39	(	(	PUNCT
cana-766	100	40	𝑥→(𝑥→𝑦	𝑥→(𝑥→𝑦	PROPN
cana-766	100	41	)	)	PUNCT
cana-766	100	42	and	and	CCONJ
cana-766	100	43	na	na	INTJ
cana-766	100	44	(	(	PUNCT
cana-766	100	45	𝑥→𝑦	𝑥→𝑦	NUM
cana-766	100	46	)	)	PUNCT
cana-766	100	47	≤	≤	NUM
cana-766	100	48	min	min	NOUN
cana-766	100	49	{	{	PUNCT
cana-766	100	50	na	na	X
cana-766	100	51	(	(	PUNCT
cana-766	100	52	𝑥→(𝑥→𝑦	𝑥→(𝑥→𝑦	PROPN
cana-766	100	53	)	)	PUNCT
cana-766	100	54	}	}	PUNCT
cana-766	100	55	(	(	PUNCT
cana-766	100	56	ii)if	ii)if	NOUN
cana-766	100	57	a=	a=	PROPN
cana-766	100	58	(	(	PUNCT
cana-766	100	59	ma	ma	PROPN
cana-766	100	60	,	,	PUNCT
cana-766	100	61	na	na	PROPN
cana-766	100	62	)	)	PUNCT
cana-766	100	63	is	be	AUX
cana-766	100	64	an	an	DET
cana-766	100	65	vague	vague	ADJ
cana-766	100	66	implicative	implicative	ADJ
cana-766	100	67	filter	filter	NOUN
cana-766	100	68	and	and	CCONJ
cana-766	100	69	for	for	ADP
cana-766	100	70	all	all	DET
cana-766	100	71	x	x	NOUN
cana-766	100	72	,	,	PUNCT
cana-766	100	73	y	y	PROPN
cana-766	100	74	,	,	PUNCT
cana-766	100	75	z	z	PROPN
cana-766	100	76	∈	∈	PROPN
cana-766	100	77	𝐴	𝐴	PROPN
cana-766	100	78	,	,	PUNCT
cana-766	100	79	ma	ma	PROPN
cana-766	100	80	(	(	PUNCT
cana-766	100	81	𝑥→𝑦)→(𝑥→𝑧)≥	𝑥→𝑦)→(𝑥→𝑧)≥	PROPN
cana-766	100	82	ma	ma	PROPN
cana-766	100	83	(	(	PUNCT
cana-766	100	84	𝑥→(𝑦→𝑧	𝑥→(𝑦→𝑧	PROPN
cana-766	100	85	)	)	PUNCT
cana-766	100	86	)	)	PUNCT
cana-766	100	87	and	and	CCONJ
cana-766	100	88	na	na	INTJ
cana-766	100	89	(	(	PUNCT
cana-766	100	90	𝑥→𝑦)→(𝑥→𝑧	𝑥→𝑦)→(𝑥→𝑧	PROPN
cana-766	100	91	)	)	PUNCT
cana-766	100	92	≤	≤	NOUN
cana-766	100	93	na	na	PART
cana-766	100	94	(	(	PUNCT
cana-766	100	95	𝑥→(𝑦→𝑧	𝑥→(𝑦→𝑧	NOUN
cana-766	100	96	)	)	PUNCT
cana-766	100	97	)	)	PUNCT
cana-766	100	98	.	.	PUNCT
cana-766	101	1	(	(	PUNCT
cana-766	101	2	iii	iii	X
cana-766	101	3	)	)	PUNCT
cana-766	101	4	ma	ma	PROPN
cana-766	101	5	(	(	PUNCT
cana-766	101	6	1)≥	1)≥	NUM
cana-766	101	7	ma	ma	PROPN
cana-766	101	8	(	(	PUNCT
cana-766	101	9	𝑥	𝑥	NOUN
cana-766	101	10	)	)	PUNCT
cana-766	101	11	and	and	CCONJ
cana-766	101	12	na	na	INTJ
cana-766	101	13	(	(	PUNCT
cana-766	101	14	1)≤	1)≤	INTJ
cana-766	101	15	na	na	INTJ
cana-766	101	16	(	(	PUNCT
cana-766	101	17	𝑥	𝑥	NOUN
cana-766	101	18	)	)	PUNCT
cana-766	101	19	for	for	ADP
cana-766	101	20	all	all	DET
cana-766	101	21	x	x	PROPN
cana-766	101	22	,	,	PUNCT
cana-766	101	23	y	y	PROPN
cana-766	101	24	,	,	PUNCT
cana-766	101	25	z	z	NOUN
cana-766	101	26	in	in	ADP
cana-766	101	27	a.	a.	NOUN
cana-766	101	28	(	(	PUNCT
cana-766	101	29	iv	iv	X
cana-766	101	30	)	)	PUNCT
cana-766	101	31	ma	ma	PROPN
cana-766	101	32	(	(	PUNCT
cana-766	101	33	𝑥→𝑦	𝑥→𝑦	NOUN
cana-766	101	34	)	)	PUNCT
cana-766	101	35	≥min	≥min	PROPN
cana-766	101	36	{	{	PUNCT
cana-766	101	37	ma	ma	PROPN
cana-766	101	38	(	(	PUNCT
cana-766	101	39	𝑧→(𝑥→(𝑥→𝑦	𝑧→(𝑥→(𝑥→𝑦	PROPN
cana-766	101	40	)	)	PUNCT
cana-766	101	41	)	)	PUNCT
cana-766	101	42	)	)	PUNCT
cana-766	101	43	,	,	PUNCT
cana-766	101	44	ma	ma	PROPN
cana-766	101	45	(	(	PUNCT
cana-766	101	46	𝑧	𝑧	PROPN
cana-766	101	47	)	)	PUNCT
cana-766	101	48	}	}	PUNCT
cana-766	101	49	and	and	CCONJ
cana-766	101	50	na	na	INTJ
cana-766	101	51	(	(	PUNCT
cana-766	101	52	𝑥→𝑦	𝑥→𝑦	NUM
cana-766	101	53	)	)	PUNCT
cana-766	101	54	≤max	≤max	NUM
cana-766	101	55	{	{	PUNCT
cana-766	101	56	na	na	X
cana-766	101	57	(	(	PUNCT
cana-766	101	58	𝑧→(𝑥→(𝑥→𝑦	𝑧→(𝑥→(𝑥→𝑦	PROPN
cana-766	101	59	)	)	PUNCT
cana-766	101	60	)	)	PUNCT
cana-766	101	61	)	)	PUNCT
cana-766	101	62	,	,	PUNCT
cana-766	101	63	na	na	X
cana-766	101	64	(	(	PUNCT
cana-766	101	65	𝑧	𝑧	NOUN
cana-766	101	66	)	)	PUNCT
cana-766	101	67	}	}	PUNCT
cana-766	101	68	,	,	PUNCT
cana-766	101	69	for	for	ADP
cana-766	101	70	all	all	DET
cana-766	101	71	x	x	NOUN
cana-766	101	72	,	,	PUNCT
cana-766	101	73	y	y	PROPN
cana-766	101	74	,	,	PUNCT
cana-766	101	75	z	z	NOUN
cana-766	101	76	in	in	ADP
cana-766	101	77	a.	a.	NOUN
cana-766	101	78	proof:(i	proof:(i	PROPN
cana-766	101	79	)	)	PUNCT
cana-766	101	80	implies	imply	VERB
cana-766	101	81	(	(	PUNCT
cana-766	101	82	ii	ii	NOUN
cana-766	101	83	):	):	PUNCT
cana-766	101	84	let	let	VERB
cana-766	101	85	a=	a=	ADV
cana-766	101	86	(	(	PUNCT
cana-766	101	87	ma	ma	PROPN
cana-766	101	88	,	,	PUNCT
cana-766	101	89	na	na	PROPN
cana-766	101	90	)	)	PUNCT
cana-766	101	91	is	be	AUX
cana-766	101	92	an	an	DET
cana-766	101	93	vague	vague	ADJ
cana-766	101	94	strong	strong	ADJ
cana-766	101	95	implicative	implicative	ADJ
cana-766	101	96	filter	filter	NOUN
cana-766	101	97	and	and	CCONJ
cana-766	101	98	for	for	ADP
cana-766	101	99	all	all	DET
cana-766	101	100	x	x	NOUN
cana-766	101	101	,	,	PUNCT
cana-766	101	102	y	y	PROPN
cana-766	101	103	∈	∈	PROPN
cana-766	101	104	𝐴	𝐴	PROPN
cana-766	101	105	,	,	PUNCT
cana-766	101	106	we	we	PRON
cana-766	101	107	have	have	VERB
cana-766	101	108	ma	ma	PROPN
cana-766	101	109	(	(	PUNCT
cana-766	101	110	1	1	NUM
cana-766	101	111	)	)	PUNCT
cana-766	101	112	≥	≥	NOUN
cana-766	101	113	ma	ma	PROPN
cana-766	101	114	(	(	PUNCT
cana-766	101	115	x	x	NOUN
cana-766	101	116	)	)	PUNCT
cana-766	101	117	and	and	CCONJ
cana-766	101	118	na	na	INTJ
cana-766	101	119	(	(	PUNCT
cana-766	101	120	1	1	X
cana-766	101	121	)	)	PUNCT
cana-766	101	122	≤	≤	NOUN
cana-766	101	123	na	na	PART
cana-766	101	124	(	(	PUNCT
cana-766	101	125	x	x	X
cana-766	101	126	)	)	PUNCT
cana-766	101	127	ma	ma	PROPN
cana-766	101	128	(	(	PUNCT
cana-766	101	129	𝑥→𝑧	𝑥→𝑧	NOUN
cana-766	101	130	)	)	PUNCT
cana-766	101	131	≥	≥	PROPN
cana-766	101	132	min	min	PROPN
cana-766	101	133	{	{	PUNCT
cana-766	101	134	ma	ma	PROPN
cana-766	101	135	(	(	PUNCT
cana-766	101	136	𝑥→𝑦	𝑥→𝑦	NUM
cana-766	101	137	)	)	PUNCT
cana-766	101	138	,	,	PUNCT
cana-766	101	139	ma	ma	PROPN
cana-766	101	140	(	(	PUNCT
cana-766	101	141	𝑥→(𝑦→𝑧	𝑥→(𝑦→𝑧	PROPN
cana-766	101	142	)	)	PUNCT
cana-766	101	143	}	}	PUNCT
cana-766	101	144	and	and	CCONJ
cana-766	101	145	na	na	INTJ
cana-766	101	146	(	(	PUNCT
cana-766	101	147	𝑥→𝑧	𝑥→𝑧	NOUN
cana-766	101	148	)	)	PUNCT
cana-766	101	149	≤	≤	NUM
cana-766	101	150	max	max	PROPN
cana-766	101	151	{	{	PUNCT
cana-766	101	152	na	na	X
cana-766	101	153	(	(	PUNCT
cana-766	101	154	𝑥→𝑦	𝑥→𝑦	NUM
cana-766	101	155	)	)	PUNCT
cana-766	101	156	,	,	PUNCT
cana-766	101	157	na	na	INTJ
cana-766	101	158	(	(	PUNCT
cana-766	101	159	𝑥→(𝑦→𝑧	𝑥→(𝑦→𝑧	NOUN
cana-766	101	160	)	)	PUNCT
cana-766	101	161	}	}	PUNCT
cana-766	101	162	we	we	PRON
cana-766	101	163	have	have	VERB
cana-766	101	164	1	1	NUM
cana-766	101	165	.	.	PUNCT
cana-766	102	1	ma	ma	PROPN
cana-766	103	1	(	(	PUNCT
cana-766	103	2	1	1	NUM
cana-766	103	3	)	)	PUNCT
cana-766	103	4	≥	≥	NOUN
cana-766	103	5	ma	ma	PROPN
cana-766	103	6	(	(	PUNCT
cana-766	103	7	x	x	NOUN
cana-766	103	8	)	)	PUNCT
cana-766	103	9	and	and	CCONJ
cana-766	103	10	na	na	INTJ
cana-766	103	11	(	(	PUNCT
cana-766	103	12	1	1	X
cana-766	103	13	)	)	PUNCT
cana-766	103	14	≤	≤	NOUN
cana-766	103	15	na	na	PART
cana-766	103	16	(	(	PUNCT
cana-766	103	17	x	x	X
cana-766	103	18	)	)	PUNCT
cana-766	103	19	ma	ma	PROPN
cana-766	103	20	(	(	PUNCT
cana-766	103	21	𝑥→𝑧	𝑥→𝑧	NOUN
cana-766	103	22	)	)	PUNCT
cana-766	103	23	≥	≥	PROPN
cana-766	103	24	min	min	PROPN
cana-766	103	25	{	{	PUNCT
cana-766	103	26	ma	ma	PROPN
cana-766	103	27	(	(	PUNCT
cana-766	103	28	𝑥→𝑦	𝑥→𝑦	NUM
cana-766	103	29	)	)	PUNCT
cana-766	103	30	,	,	PUNCT
cana-766	103	31	ma	ma	PROPN
cana-766	103	32	(	(	PUNCT
cana-766	103	33	𝑥→(𝑦→𝑧	𝑥→(𝑦→𝑧	PROPN
cana-766	103	34	)	)	PUNCT
cana-766	103	35	)	)	PUNCT
cana-766	103	36	}	}	PUNCT
cana-766	104	1	and	and	CCONJ
cana-766	104	2	na	na	INTJ
cana-766	104	3	(	(	PUNCT
cana-766	104	4	𝑥→𝑧	𝑥→𝑧	NOUN
cana-766	104	5	)	)	PUNCT
cana-766	104	6	≤	≤	NUM
cana-766	104	7	max	max	PROPN
cana-766	104	8	{	{	PUNCT
cana-766	104	9	na	na	X
cana-766	104	10	(	(	PUNCT
cana-766	104	11	𝑥→𝑦	𝑥→𝑦	NUM
cana-766	104	12	)	)	PUNCT
cana-766	104	13	,	,	PUNCT
cana-766	104	14	na	na	X
cana-766	104	15	(	(	PUNCT
cana-766	104	16	𝑥→(𝑦→𝑧	𝑥→(𝑦→𝑧	NOUN
cana-766	104	17	)	)	PUNCT
cana-766	104	18	)	)	PUNCT
cana-766	104	19	}	}	PUNCT
cana-766	104	20	put	put	VERB
cana-766	104	21	x=	x=	NOUN
cana-766	104	22	1	1	NUM
cana-766	105	1	then	then	ADV
cana-766	105	2	ma	ma	PROPN
cana-766	105	3	(	(	PUNCT
cana-766	105	4	𝑧	𝑧	PROPN
cana-766	105	5	)	)	PUNCT
cana-766	105	6	≥	≥	PROPN
cana-766	105	7	min	min	PROPN
cana-766	105	8	{	{	PUNCT
cana-766	105	9	ma	ma	PROPN
cana-766	105	10	(	(	PUNCT
cana-766	105	11	𝑦	𝑦	NOUN
cana-766	105	12	)	)	PUNCT
cana-766	105	13	,	,	PUNCT
cana-766	105	14	ma	ma	PROPN
cana-766	105	15	(	(	PUNCT
cana-766	105	16	𝑦→𝑧	𝑦→𝑧	NUM
cana-766	105	17	)	)	PUNCT
cana-766	105	18	)	)	PUNCT
cana-766	105	19	}	}	PUNCT
cana-766	105	20	and	and	CCONJ
cana-766	105	21	na	na	INTJ
cana-766	105	22	(	(	PUNCT
cana-766	105	23	𝑧	𝑧	NOUN
cana-766	105	24	)	)	PUNCT
cana-766	105	25	≤	≤	NUM
cana-766	105	26	max	max	PROPN
cana-766	105	27	{	{	PUNCT
cana-766	105	28	na	na	PROPN
cana-766	105	29	(	(	PUNCT
cana-766	105	30	𝑦	𝑦	NOUN
cana-766	105	31	)	)	PUNCT
cana-766	105	32	,	,	PUNCT
cana-766	105	33	na	na	X
cana-766	105	34	(	(	PUNCT
cana-766	105	35	𝑦→𝑧	𝑦→𝑧	NUM
cana-766	105	36	)	)	PUNCT
cana-766	105	37	)	)	PUNCT
cana-766	105	38	}	}	PUNCT
cana-766	105	39	for	for	ADP
cana-766	105	40	all	all	DET
cana-766	105	41	x	x	NOUN
cana-766	105	42	,	,	PUNCT
cana-766	105	43	y	y	PROPN
cana-766	105	44	z	z	PROPN
cana-766	105	45	∈	∈	PROPN
cana-766	105	46	𝐴.	𝐴.	PROPN
cana-766	105	47	therefore	therefore	ADV
cana-766	105	48	a=	a=	PROPN
cana-766	105	49	(	(	PUNCT
cana-766	105	50	ma	ma	PROPN
cana-766	105	51	,	,	PUNCT
cana-766	105	52	na	na	PROPN
cana-766	105	53	)	)	PUNCT
cana-766	105	54	is	be	AUX
cana-766	105	55	an	an	DET
cana-766	105	56	vague	vague	ADJ
cana-766	105	57	implicative	implicative	ADJ
cana-766	105	58	filter	filter	NOUN
cana-766	105	59	and	and	CCONJ
cana-766	105	60	for	for	ADP
cana-766	105	61	all	all	DET
cana-766	105	62	x	x	NOUN
cana-766	105	63	,	,	PUNCT
cana-766	105	64	y	y	PROPN
cana-766	105	65	,	,	PUNCT
cana-766	105	66	z	z	PROPN
cana-766	105	67	∈	∈	PROPN
cana-766	105	68	𝐴.	𝐴.	PROPN
cana-766	105	69	from	from	ADP
cana-766	105	70	ma	ma	PROPN
cana-766	105	71	(	(	PUNCT
cana-766	105	72	𝑥→𝑧	𝑥→𝑧	NOUN
cana-766	105	73	)	)	PUNCT
cana-766	105	74	≥	≥	PROPN
cana-766	105	75	min	min	PROPN
cana-766	105	76	{	{	PUNCT
cana-766	105	77	ma	ma	PROPN
cana-766	105	78	(	(	PUNCT
cana-766	105	79	𝑥→𝑦	𝑥→𝑦	NUM
cana-766	105	80	)	)	PUNCT
cana-766	105	81	,	,	PUNCT
cana-766	105	82	ma	ma	PROPN
cana-766	105	83	(	(	PUNCT
cana-766	105	84	𝑥→(𝑦→𝑧	𝑥→(𝑦→𝑧	PROPN
cana-766	105	85	)	)	PUNCT
cana-766	105	86	)	)	PUNCT
cana-766	105	87	}	}	PUNCT
cana-766	105	88	and	and	CCONJ
cana-766	105	89	na	na	INTJ
cana-766	105	90	(	(	PUNCT
cana-766	105	91	𝑥→𝑧	𝑥→𝑧	NOUN
cana-766	105	92	)	)	PUNCT
cana-766	105	93	≤	≤	NUM
cana-766	105	94	max	max	PROPN
cana-766	105	95	{	{	PUNCT
cana-766	105	96	na	na	X
cana-766	105	97	(	(	PUNCT
cana-766	105	98	𝑥→𝑦	𝑥→𝑦	NUM
cana-766	105	99	)	)	PUNCT
cana-766	105	100	,	,	PUNCT
cana-766	105	101	na	na	X
cana-766	105	102	(	(	PUNCT
cana-766	105	103	𝑥→(𝑦→𝑧	𝑥→(𝑦→𝑧	NOUN
cana-766	105	104	)	)	PUNCT
cana-766	105	105	)	)	PUNCT
cana-766	105	106	}	}	PUNCT
cana-766	105	107	put	put	VERB
cana-766	105	108	z	z	NOUN
cana-766	105	109	=	=	NOUN
cana-766	105	110	y	y	PROPN
cana-766	105	111	in	in	ADP
cana-766	105	112	the	the	DET
cana-766	105	113	above	above	ADJ
cana-766	105	114	condition	condition	NOUN
cana-766	105	115	then	then	ADV
cana-766	105	116	ma	ma	PROPN
cana-766	105	117	(	(	PUNCT
cana-766	105	118	𝑥→𝑦	𝑥→𝑦	NUM
cana-766	105	119	)	)	PUNCT
cana-766	105	120	≥	≥	NOUN
cana-766	105	121	ma	ma	PROPN
cana-766	105	122	(	(	PUNCT
cana-766	105	123	𝑥→(𝑥→𝑦	𝑥→(𝑥→𝑦	PROPN
cana-766	105	124	)	)	PUNCT
cana-766	105	125	)	)	PUNCT
cana-766	105	126	and	and	CCONJ
cana-766	105	127	na	na	AUX
cana-766	105	128	(	(	PUNCT
cana-766	105	129	𝑥→𝑦	𝑥→𝑦	NUM
cana-766	105	130	)	)	PUNCT
cana-766	105	131	≤	≤	NOUN
cana-766	105	132	na	na	PART
cana-766	105	133	(	(	PUNCT
cana-766	105	134	𝑥→(𝑦→𝑧	𝑥→(𝑦→𝑧	NOUN
cana-766	105	135	)	)	PUNCT
cana-766	105	136	)	)	PUNCT
cana-766	106	1	if	if	SCONJ
cana-766	106	2	for	for	ADP
cana-766	106	3	any	any	DET
cana-766	106	4	x	x	NOUN
cana-766	106	5	,	,	PUNCT
cana-766	106	6	y	y	PROPN
cana-766	106	7	,	,	PUNCT
cana-766	106	8	z	z	PROPN
cana-766	106	9	∈	∈	PROPN
cana-766	106	10	𝐴	𝐴	PROPN
cana-766	106	11	ma	ma	PROPN
cana-766	106	12	(	(	PUNCT
cana-766	106	13	𝑥→𝑦	𝑥→𝑦	NUM
cana-766	106	14	)	)	PUNCT
cana-766	106	15	≥	≥	NOUN
cana-766	106	16	ma	ma	PROPN
cana-766	106	17	(	(	PUNCT
cana-766	106	18	𝑥→(𝑥→𝑦	𝑥→(𝑥→𝑦	PROPN
cana-766	106	19	)	)	PUNCT
cana-766	106	20	,	,	PUNCT
cana-766	106	21	and	and	CCONJ
cana-766	106	22	na	na	INTJ
cana-766	106	23	(	(	PUNCT
cana-766	106	24	𝑥→𝑦	𝑥→𝑦	NUM
cana-766	106	25	)	)	PUNCT
cana-766	106	26	≤	≤	NOUN
cana-766	106	27	na	na	PART
cana-766	106	28	(	(	PUNCT
cana-766	106	29	𝑥→𝑦	𝑥→𝑦	NUM
cana-766	106	30	)	)	PUNCT
cana-766	106	31	,	,	PUNCT
cana-766	106	32	na	na	X
cana-766	106	33	(	(	PUNCT
cana-766	106	34	𝑥→(𝑥→𝑦	𝑥→(𝑥→𝑦	PROPN
cana-766	106	35	)	)	PUNCT
cana-766	106	36	)	)	PUNCT
cana-766	106	37	}	}	PUNCT
cana-766	106	38	.	.	PUNCT
cana-766	107	1	implies	imply	VERB
cana-766	107	2	ma	ma	PROPN
cana-766	107	3	(	(	PUNCT
cana-766	107	4	𝑥→𝑦)→(𝑥→𝑧	𝑥→𝑦)→(𝑥→𝑧	PROPN
cana-766	107	5	)	)	PUNCT
cana-766	107	6	=	=	PROPN
cana-766	107	7	ma	ma	PROPN
cana-766	107	8	(	(	PUNCT
cana-766	107	9	𝑥→((𝑥→𝑦)→𝑧	𝑥→((𝑥→𝑦)→𝑧	NOUN
cana-766	107	10	)	)	PUNCT
cana-766	107	11	)	)	PUNCT
cana-766	107	12	≥	≥	PROPN
cana-766	107	13	ma	ma	PROPN
cana-766	107	14	(	(	PUNCT
cana-766	107	15	(	(	PUNCT
cana-766	107	16	𝑥→𝑥→((𝑥→𝑦)→𝑧	𝑥→𝑥→((𝑥→𝑦)→𝑧	PROPN
cana-766	107	17	)	)	PUNCT
cana-766	107	18	)	)	PUNCT
cana-766	107	19	)	)	PUNCT
cana-766	107	20	.	.	PUNCT
cana-766	108	1	therefore	therefore	ADV
cana-766	108	2	a=	a=	PROPN
cana-766	108	3	(	(	PUNCT
cana-766	108	4	ma	ma	PROPN
cana-766	108	5	,	,	PUNCT
cana-766	108	6	na	na	PROPN
cana-766	108	7	)	)	PUNCT
cana-766	108	8	is	be	AUX
cana-766	108	9	an	an	DET
cana-766	108	10	vague	vague	ADJ
cana-766	108	11	implicative	implicative	ADJ
cana-766	108	12	filter	filter	NOUN
cana-766	108	13	and	and	CCONJ
cana-766	108	14	for	for	ADP
cana-766	108	15	all	all	DET
cana-766	108	16	x	x	NOUN
cana-766	108	17	,	,	PUNCT
cana-766	108	18	y	y	PROPN
cana-766	108	19	,	,	PUNCT
cana-766	108	20	z	z	PROPN
cana-766	108	21	∈	∈	PROPN
cana-766	108	22	𝐴	𝐴	PROPN
cana-766	108	23	,	,	PUNCT
cana-766	108	24	ma	ma	PROPN
cana-766	108	25	(	(	PUNCT
cana-766	108	26	𝑥→𝑦)→(𝑥→𝑧)≥	𝑥→𝑦)→(𝑥→𝑧)≥	PROPN
cana-766	108	27	ma	ma	PROPN
cana-766	108	28	(	(	PUNCT
cana-766	108	29	𝑥→(𝑦→𝑧	𝑥→(𝑦→𝑧	PROPN
cana-766	108	30	)	)	PUNCT
cana-766	108	31	)	)	PUNCT
cana-766	108	32	and	and	CCONJ
cana-766	108	33	na	na	INTJ
cana-766	108	34	(	(	PUNCT
cana-766	108	35	𝑥→𝑦)→(𝑥→𝑧	𝑥→𝑦)→(𝑥→𝑧	PROPN
cana-766	108	36	)	)	PUNCT
cana-766	108	37	≤	≤	NOUN
cana-766	108	38	na	na	PART
cana-766	108	39	(	(	PUNCT
cana-766	108	40	𝑥→(𝑦→𝑧	𝑥→(𝑦→𝑧	NOUN
cana-766	108	41	)	)	PUNCT
cana-766	108	42	)	)	PUNCT
cana-766	108	43	.	.	PUNCT
cana-766	109	1	(	(	PUNCT
cana-766	109	2	ii	ii	NOUN
cana-766	109	3	)	)	PUNCT
cana-766	109	4	implies	imply	VERB
cana-766	109	5	(	(	PUNCT
cana-766	109	6	iii):let	iii):let	PROPN
cana-766	109	7	(	(	PUNCT
cana-766	109	8	ii	ii	NOUN
cana-766	109	9	)	)	PUNCT
cana-766	109	10	be	be	AUX
cana-766	109	11	hold	hold	NOUN
cana-766	109	12	.then	.then	ADP
cana-766	109	13	,	,	PUNCT
cana-766	109	14	it	it	PRON
cana-766	109	15	is	be	AUX
cana-766	109	16	clear	clear	ADJ
cana-766	109	17	ma	ma	PROPN
cana-766	109	18	(	(	PUNCT
cana-766	109	19	1)≥	1)≥	NUM
cana-766	109	20	ma	ma	PROPN
cana-766	109	21	(	(	PUNCT
cana-766	109	22	𝑥	𝑥	NOUN
cana-766	109	23	)	)	PUNCT
cana-766	109	24	and	and	CCONJ
cana-766	109	25	na	na	INTJ
cana-766	109	26	(	(	PUNCT
cana-766	109	27	1)≤	1)≤	INTJ
cana-766	109	28	na	na	INTJ
cana-766	109	29	(	(	PUNCT
cana-766	109	30	𝑥	𝑥	NOUN
cana-766	109	31	)	)	PUNCT
cana-766	109	32	.	.	PUNCT
cana-766	110	1	if	if	SCONJ
cana-766	110	2	any	any	DET
cana-766	110	3	x	x	NOUN
cana-766	110	4	,	,	PUNCT
cana-766	110	5	y	y	PROPN
cana-766	110	6	∈	∈	PROPN
cana-766	110	7	a	a	PRON
cana-766	110	8	,	,	PUNCT
cana-766	110	9	we	we	PRON
cana-766	110	10	have	have	VERB
cana-766	110	11	ma	ma	PROPN
cana-766	110	12	(	(	PUNCT
cana-766	110	13	𝑥→𝑦)→(𝑥→𝑧)≥	𝑥→𝑦)→(𝑥→𝑧)≥	PROPN
cana-766	110	14	ma	ma	PROPN
cana-766	110	15	(	(	PUNCT
cana-766	110	16	𝑥→(𝑦→𝑧	𝑥→(𝑦→𝑧	PROPN
cana-766	110	17	)	)	PUNCT
cana-766	110	18	and	and	CCONJ
cana-766	110	19	na	na	INTJ
cana-766	110	20	(	(	PUNCT
cana-766	110	21	𝑥→𝑦)→(𝑥→𝑧	𝑥→𝑦)→(𝑥→𝑧	PROPN
cana-766	110	22	)	)	PUNCT
cana-766	110	23	≤	≤	NOUN
cana-766	110	24	na	na	ADP
cana-766	110	25	(	(	PUNCT
cana-766	110	26	𝑥→(𝑦→𝑧)).put	𝑥→(𝑦→𝑧)).put	VERB
cana-766	110	27	y	y	PROPN
cana-766	110	28	=	=	NOUN
cana-766	110	29	x	x	NOUN
cana-766	110	30	,	,	PUNCT
cana-766	110	31	then	then	ADV
cana-766	110	32	,	,	PUNCT
cana-766	110	33	we	we	PRON
cana-766	110	34	get	get	VERB
cana-766	110	35	𝑚	𝑚	ADP
cana-766	110	36	a	a	PRON
cana-766	110	37	(	(	PUNCT
cana-766	110	38	𝑥→𝑥)→(𝑥→𝑧)≥	𝑥→𝑥)→(𝑥→𝑧)≥	PROPN
cana-766	110	39	ma	ma	PROPN
cana-766	110	40	(	(	PUNCT
cana-766	110	41	𝑥→(𝑥→𝑧	𝑥→(𝑥→𝑧	PROPN
cana-766	110	42	)	)	PUNCT
cana-766	110	43	implies	imply	VERB
cana-766	110	44	ma	ma	PROPN
cana-766	110	45	(	(	PUNCT
cana-766	110	46	𝑥→𝑧)≥	𝑥→𝑧)≥	X
cana-766	110	47	ma	ma	PROPN
cana-766	110	48	(	(	PUNCT
cana-766	110	49	𝑥→(𝑥→𝑧	𝑥→(𝑥→𝑧	PROPN
cana-766	110	50	)	)	PUNCT
cana-766	110	51	and	and	CCONJ
cana-766	110	52	we	we	PRON
cana-766	110	53	have	have	VERB
cana-766	110	54	for	for	ADP
cana-766	110	55	any	any	DET
cana-766	110	56	x	x	NOUN
cana-766	110	57	,	,	PUNCT
cana-766	110	58	y	y	PROPN
cana-766	110	59	in	in	ADP
cana-766	110	60	a	a	DET
cana-766	110	61	ma	ma	PROPN
cana-766	110	62	(	(	PUNCT
cana-766	110	63	𝑥→𝑦)≥	𝑥→𝑦)≥	X
cana-766	110	64	ma	ma	PROPN
cana-766	110	65	(	(	PUNCT
cana-766	110	66	𝑥→(𝑥→𝑦	𝑥→(𝑥→𝑦	PROPN
cana-766	110	67	)	)	PUNCT
cana-766	110	68	since	since	SCONJ
cana-766	110	69	ma	ma	PROPN
cana-766	110	70	(	(	PUNCT
cana-766	110	71	𝑥	𝑥	NOUN
cana-766	110	72	)	)	PUNCT
cana-766	110	73	is	be	AUX
cana-766	110	74	an	an	DET
cana-766	110	75	implicative	implicative	ADJ
cana-766	110	76	filter	filter	NOUN
cana-766	110	77	and	and	CCONJ
cana-766	110	78	t	t	NOUN
cana-766	110	79	hen	hen	NOUN
cana-766	110	80	,	,	PUNCT
cana-766	110	81	we	we	PRON
cana-766	110	82	have	have	VERB
cana-766	110	83	ma	ma	PROPN
cana-766	110	84	(	(	PUNCT
cana-766	110	85	𝑥→(𝑥→𝑦)≥	𝑥→(𝑥→𝑦)≥	PUNCT
cana-766	110	86	min	min	PROPN
cana-766	110	87	{	{	PUNCT
cana-766	110	88	ma	ma	PROPN
cana-766	110	89	(	(	PUNCT
cana-766	110	90	𝑧→(𝑥→(𝑥→𝑦	𝑧→(𝑥→(𝑥→𝑦	PROPN
cana-766	110	91	)	)	PUNCT
cana-766	110	92	)	)	PUNCT
cana-766	110	93	,	,	PUNCT
cana-766	110	94	ma	ma	PROPN
cana-766	110	95	(	(	PUNCT
cana-766	110	96	𝑧	𝑧	PROPN
cana-766	110	97	)	)	PUNCT
cana-766	110	98	}	}	PUNCT
cana-766	110	99	.	.	PUNCT
cana-766	111	1	hence	hence	ADV
cana-766	111	2	ma	ma	PROPN
cana-766	111	3	(	(	PUNCT
cana-766	111	4	𝑥→𝑧)≥	𝑥→𝑧)≥	NOUN
cana-766	111	5	min	min	PROPN
cana-766	111	6	{	{	PUNCT
cana-766	111	7	ma	ma	PROPN
cana-766	111	8	(	(	PUNCT
cana-766	111	9	𝑧→(𝑥→(𝑥→𝑦	𝑧→(𝑥→(𝑥→𝑦	PROPN
cana-766	111	10	)	)	PUNCT
cana-766	111	11	)	)	PUNCT
cana-766	111	12	,	,	PUNCT
cana-766	111	13	ma	ma	PROPN
cana-766	111	14	(	(	PUNCT
cana-766	111	15	𝑧	𝑧	PROPN
cana-766	111	16	)	)	PUNCT
cana-766	111	17	}	}	PUNCT
cana-766	111	18	.	.	PUNCT
cana-766	112	1	similarly	similarly	ADV
cana-766	112	2	na	na	INTJ
cana-766	112	3	(	(	PUNCT
cana-766	112	4	𝑥→𝑧)≤	𝑥→𝑧)≤	PROPN
cana-766	112	5	max	max	PROPN
cana-766	112	6	{	{	PUNCT
cana-766	112	7	na	na	PROPN
cana-766	112	8	(	(	PUNCT
cana-766	112	9	𝑧→(𝑥→(𝑥→𝑦	𝑧→(𝑥→(𝑥→𝑦	PROPN
cana-766	112	10	)	)	PUNCT
cana-766	112	11	)	)	PUNCT
cana-766	112	12	,	,	PUNCT
cana-766	112	13	na	na	X
cana-766	112	14	(	(	PUNCT
cana-766	112	15	𝑧	𝑧	NOUN
cana-766	112	16	)	)	PUNCT
cana-766	112	17	}	}	PUNCT
cana-766	112	18	.	.	PUNCT
cana-766	113	1	communications	communication	NOUN
cana-766	113	2	on	on	ADP
cana-766	113	3	applied	apply	VERB
cana-766	113	4	nonlinear	nonlinear	ADJ
cana-766	113	5	analysis	analysis	NOUN
cana-766	113	6	issn	issn	NOUN
cana-766	113	7	:	:	PUNCT
cana-766	113	8	1074	1074	NUM
cana-766	113	9	-	-	PUNCT
cana-766	113	10	133x	133x	NUM
cana-766	113	11	vol	vol	NOUN
cana-766	113	12	31	31	NUM
cana-766	113	13	no	no	NOUN
cana-766	113	14	.	.	PUNCT
cana-766	114	1	3s	3s	NUM
cana-766	114	2	(	(	PUNCT
cana-766	114	3	2024	2024	NUM
cana-766	114	4	)	)	PUNCT
cana-766	114	5	301	301	NUM
cana-766	114	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-766	114	7	(	(	PUNCT
cana-766	114	8	iii	iii	NOUN
cana-766	114	9	)	)	PUNCT
cana-766	114	10	implies	imply	VERB
cana-766	114	11	(	(	PUNCT
cana-766	114	12	i	i	NOUN
cana-766	114	13	):	):	PUNCT
cana-766	114	14	let	let	VERB
cana-766	114	15	(	(	PUNCT
cana-766	114	16	iii	iii	X
cana-766	114	17	)	)	PUNCT
cana-766	114	18	be	be	AUX
cana-766	114	19	hold	hold	VERB
cana-766	114	20	.	.	PUNCT
cana-766	115	1	put	put	VERB
cana-766	115	2	x=1then	x=1then	PUNCT
cana-766	115	3	,	,	PUNCT
cana-766	115	4	we	we	PRON
cana-766	115	5	get	get	VERB
cana-766	115	6	ma	ma	PROPN
cana-766	115	7	(	(	PUNCT
cana-766	115	8	𝑦)≥min	𝑦)≥min	PROPN
cana-766	115	9	{	{	PUNCT
cana-766	115	10	ma	ma	PROPN
cana-766	115	11	(	(	PUNCT
cana-766	115	12	𝑧→𝑦	𝑧→𝑦	NUM
cana-766	115	13	)	)	PUNCT
cana-766	115	14	,	,	PUNCT
cana-766	115	15	ma	ma	PROPN
cana-766	115	16	(	(	PUNCT
cana-766	115	17	𝑧	𝑧	PROPN
cana-766	115	18	)	)	PUNCT
cana-766	115	19	}	}	PUNCT
cana-766	115	20	and	and	CCONJ
cana-766	115	21	na	na	INTJ
cana-766	115	22	(	(	PUNCT
cana-766	115	23	𝑥→𝑦)≤	𝑥→𝑦)≤	ADV
cana-766	115	24	na	na	INTJ
cana-766	115	25	(	(	PUNCT
cana-766	115	26	𝑥→(𝑥→𝑦	𝑥→(𝑥→𝑦	PROPN
cana-766	115	27	)	)	PUNCT
cana-766	115	28	implies	imply	VERB
cana-766	115	29	ma	ma	PROPN
cana-766	115	30	(	(	PUNCT
cana-766	115	31	1)≥	1)≥	NUM
cana-766	115	32	ma	ma	PROPN
cana-766	115	33	(	(	PUNCT
cana-766	115	34	𝑥	𝑥	NOUN
cana-766	115	35	)	)	PUNCT
cana-766	115	36	and	and	CCONJ
cana-766	115	37	n(1)≤	n(1)≤	ADP
cana-766	115	38	na	na	INTJ
cana-766	115	39	(	(	PUNCT
cana-766	115	40	𝑥	𝑥	NOUN
cana-766	115	41	)	)	PUNCT
cana-766	115	42	for	for	ADP
cana-766	115	43	all	all	DET
cana-766	115	44	x	x	NOUN
cana-766	115	45	,	,	PUNCT
cana-766	115	46	y	y	PROPN
cana-766	115	47	,	,	PUNCT
cana-766	115	48	z	z	NOUN
cana-766	115	49	in	in	ADP
cana-766	115	50	a.	a.	NOUN
cana-766	115	51	theorem	theorem	VERB
cana-766	115	52	3.5	3.5	NUM
cana-766	115	53	a=	a=	NOUN
cana-766	115	54	(	(	PUNCT
cana-766	115	55	ma	ma	PROPN
cana-766	115	56	,	,	PUNCT
cana-766	115	57	na	na	PART
cana-766	115	58	)	)	PUNCT
cana-766	115	59	be	be	AUX
cana-766	115	60	a	a	DET
cana-766	115	61	vague	vague	ADJ
cana-766	115	62	strong	strong	ADJ
cana-766	115	63	implicative	implicative	ADJ
cana-766	115	64	filter	filter	NOUN
cana-766	115	65	of	of	ADP
cana-766	115	66	lattice	lattice	PROPN
cana-766	115	67	wajsberg	wajsberg	PROPN
cana-766	115	68	algebra	algebra	PROPN
cana-766	115	69	a	a	DET
cana-766	115	70	if	if	NOUN
cana-766	115	71	and	and	CCONJ
cana-766	116	1	only	only	ADV
cana-766	116	2	if	if	SCONJ
cana-766	116	3	and	and	CCONJ
cana-766	116	4	the	the	DET
cana-766	116	5	fuzzy	fuzzy	ADJ
cana-766	116	6	sets	set	VERB
cana-766	116	7	ma	ma	PROPN
cana-766	116	8	,	,	PUNCT
cana-766	116	9	𝑛𝐴	𝑛𝐴	PROPN
cana-766	116	10	𝑐	𝑐	ADP
cana-766	116	11	strong	strong	ADJ
cana-766	116	12	implicative	implicative	ADJ
cana-766	116	13	filter	filter	NOUN
cana-766	116	14	a	a	DET
cana-766	116	15	where	where	SCONJ
cana-766	116	16	𝑛𝐴	𝑛𝐴	ADJ
cana-766	116	17	𝑐(𝑥)=1na	𝑐(𝑥)=1na	ADJ
cana-766	116	18	(	(	PUNCT
cana-766	116	19	x	x	NOUN
cana-766	116	20	)	)	PUNCT
cana-766	116	21	for	for	ADP
cana-766	116	22	all	all	DET
cana-766	116	23	x	x	SYM
cana-766	116	24	∈	∈	NOUN
cana-766	116	25	𝐴.	𝐴.	NOUN
cana-766	116	26	proof	proof	NOUN
cana-766	116	27	:	:	PUNCT
cana-766	116	28	let	let	VERB
cana-766	116	29	a=	a=	ADV
cana-766	116	30	(	(	PUNCT
cana-766	116	31	ma	ma	PROPN
cana-766	116	32	,	,	PUNCT
cana-766	116	33	na	na	PART
cana-766	116	34	)	)	PUNCT
cana-766	116	35	be	be	AUX
cana-766	116	36	a	a	DET
cana-766	116	37	vague	vague	ADJ
cana-766	116	38	strong	strong	ADJ
cana-766	116	39	implicative	implicative	ADJ
cana-766	116	40	filter	filter	NOUN
cana-766	116	41	of	of	ADP
cana-766	116	42	lattice	lattice	PROPN
cana-766	116	43	wajsberg	wajsberg	PROPN
cana-766	116	44	algebra	algebra	PROPN
cana-766	116	45	a.	a.	NOUN
cana-766	116	46	from	from	ADP
cana-766	116	47	the	the	DET
cana-766	116	48	definition	definition	NOUN
cana-766	116	49	we	we	PRON
cana-766	116	50	have	have	VERB
cana-766	116	51	the	the	DET
cana-766	116	52	fuzzy	fuzzy	ADJ
cana-766	116	53	subset	subset	VERB
cana-766	116	54	ma	ma	PROPN
cana-766	116	55	(	(	PUNCT
cana-766	116	56	membership	membership	NOUN
cana-766	116	57	function	function	NOUN
cana-766	116	58	)	)	PUNCT
cana-766	116	59	is	be	AUX
cana-766	116	60	strong	strong	ADJ
cana-766	116	61	implicative	implicative	ADJ
cana-766	116	62	filter	filter	NOUN
cana-766	116	63	of	of	ADP
cana-766	116	64	a.	a.	NOUN
cana-766	116	65	now	now	ADV
cana-766	116	66	𝑛𝐴	𝑛𝐴	ADV
cana-766	116	67	𝐶(1	𝐶(1	NUM
cana-766	116	68	)	)	PUNCT
cana-766	117	1	=	=	NOUN
cana-766	117	2	1-𝑛𝐴	1-𝑛𝐴	NOUN
cana-766	117	3	(	(	PUNCT
cana-766	117	4	1)≥1-𝑛𝐴	1)≥1-𝑛𝐴	PROPN
cana-766	117	5	(	(	PUNCT
cana-766	117	6	x	x	NOUN
cana-766	117	7	)	)	PUNCT
cana-766	117	8	=	=	PROPN
cana-766	117	9	𝑛𝐴	𝑛𝐴	PROPN
cana-766	117	10	𝐶	𝐶	PROPN
cana-766	117	11	(	(	PUNCT
cana-766	117	12	x	x	NOUN
cana-766	117	13	)	)	PUNCT
cana-766	117	14	and	and	CCONJ
cana-766	117	15	𝑛𝐴	𝑛𝐴	ADV
cana-766	117	16	𝐶(x→	𝐶(x→	ADP
cana-766	117	17	𝑧	𝑧	NOUN
cana-766	117	18	)	)	PUNCT
cana-766	118	1	=	=	SYM
cana-766	118	2	1-𝑛𝐴(x→	1-𝑛𝐴(x→	PROPN
cana-766	118	3	𝑧)≥1-𝑛𝐴(x→	𝑧)≥1-𝑛𝐴(x→	NUM
cana-766	118	4	𝑧	𝑧	NOUN
cana-766	118	5	)	)	PUNCT
cana-766	118	6	=	=	PROPN
cana-766	118	7	𝑛𝐴	𝑛𝐴	PROPN
cana-766	118	8	𝐶	𝐶	PROPN
cana-766	118	9	(	(	PUNCT
cana-766	118	10	x→	x→	PROPN
cana-766	118	11	𝑧)≥1	𝑧)≥1	PROPN
cana-766	118	12	-	-	PUNCT
cana-766	118	13	max	max	PROPN
cana-766	118	14	{	{	PUNCT
cana-766	118	15	𝑛𝐴(x→	𝑛𝐴(x→	NOUN
cana-766	118	16	𝑦	𝑦	NOUN
cana-766	118	17	)	)	PUNCT
cana-766	118	18	,	,	PUNCT
cana-766	118	19	𝑛𝐴(x→	𝑛𝐴(x→	X
cana-766	118	20	(	(	PUNCT
cana-766	118	21	𝑦	𝑦	NOUN
cana-766	118	22	→	→	SYM
cana-766	118	23	𝑧	𝑧	NOUN
cana-766	118	24	)	)	PUNCT
cana-766	118	25	)	)	PUNCT
cana-766	118	26	}	}	PUNCT
cana-766	119	1	=	=	X
cana-766	119	2	min	min	NOUN
cana-766	119	3	{	{	PUNCT
cana-766	119	4	1	1	NUM
cana-766	119	5	−	−	PROPN
cana-766	119	6	𝑛𝐴(x→	𝑛𝐴(x→	NOUN
cana-766	119	7	𝑦	𝑦	NOUN
cana-766	119	8	)	)	PUNCT
cana-766	119	9	,	,	PUNCT
cana-766	119	10	1	1	NUM
cana-766	119	11	−	−	NOUN
cana-766	119	12	𝑛𝐴(x→	𝑛𝐴(x→	NOUN
cana-766	119	13	(	(	PUNCT
cana-766	119	14	𝑦	𝑦	NOUN
cana-766	119	15	→	→	SYM
cana-766	119	16	𝑧	𝑧	NOUN
cana-766	119	17	)	)	PUNCT
cana-766	119	18	)	)	PUNCT
cana-766	119	19	}	}	PUNCT
cana-766	119	20	=	=	SYM
cana-766	119	21	min	min	X
cana-766	119	22	{	{	PUNCT
cana-766	119	23	𝑛𝐴	𝑛𝐴	ADV
cana-766	119	24	𝐶(x→	𝐶(x→	NOUN
cana-766	119	25	𝑧	𝑧	NOUN
cana-766	119	26	)	)	PUNCT
cana-766	119	27	,	,	PUNCT
cana-766	119	28	𝑛𝐴	𝑛𝐴	ADJ
cana-766	119	29	𝐶(x→	𝐶(x→	NOUN
cana-766	119	30	(	(	PUNCT
cana-766	119	31	𝑦	𝑦	NOUN
cana-766	119	32	→	→	SYM
cana-766	119	33	𝑧	𝑧	NOUN
cana-766	119	34	)	)	PUNCT
cana-766	119	35	)	)	PUNCT
cana-766	119	36	}	}	PUNCT
cana-766	119	37	𝑛𝐴	𝑛𝐴	ADV
cana-766	119	38	𝐶(x→	𝐶(x→	NUM
cana-766	119	39	𝑧)≥	𝑧)≥	ADP
cana-766	119	40	min	min	PROPN
cana-766	119	41	{	{	PUNCT
cana-766	119	42	𝑛𝐴	𝑛𝐴	ADV
cana-766	119	43	𝐶(x→	𝐶(x→	NOUN
cana-766	119	44	𝑧	𝑧	NOUN
cana-766	119	45	)	)	PUNCT
cana-766	119	46	,	,	PUNCT
cana-766	119	47	𝑛𝐴	𝑛𝐴	ADJ
cana-766	119	48	𝐶(x→	𝐶(x→	NOUN
cana-766	119	49	(	(	PUNCT
cana-766	119	50	𝑦	𝑦	NOUN
cana-766	119	51	→	→	SYM
cana-766	119	52	𝑧	𝑧	NOUN
cana-766	119	53	)	)	PUNCT
cana-766	119	54	)	)	PUNCT
cana-766	119	55	}	}	PUNCT
cana-766	119	56	therefore	therefore	ADV
cana-766	119	57	𝑛𝐴	𝑛𝐴	ADV
cana-766	119	58	𝑐	𝑐	ADP
cana-766	119	59	strong	strong	ADJ
cana-766	119	60	implicative	implicative	ADJ
cana-766	119	61	filter	filter	NOUN
cana-766	119	62	a.	a.	NOUN
cana-766	119	63	conversely	conversely	ADV
cana-766	119	64	,	,	PUNCT
cana-766	119	65	if	if	SCONJ
cana-766	119	66	ma	ma	PROPN
cana-766	119	67	,	,	PUNCT
cana-766	119	68	𝑛𝐴	𝑛𝐴	PROPN
cana-766	119	69	𝑐	𝑐	SYM
cana-766	119	70	fuzzy	fuzzy	ADJ
cana-766	119	71	strong	strong	ADJ
cana-766	119	72	implicative	implicative	ADJ
cana-766	119	73	filter	filter	NOUN
cana-766	119	74	a.	a.	NOUN
cana-766	119	75	then	then	ADV
cana-766	119	76	we	we	PRON
cana-766	119	77	have	have	VERB
cana-766	119	78	ma	ma	PROPN
cana-766	119	79	(	(	PUNCT
cana-766	119	80	1)≥	1)≥	NUM
cana-766	119	81	ma	ma	PROPN
cana-766	119	82	(	(	PUNCT
cana-766	119	83	x	x	NOUN
cana-766	119	84	)	)	PUNCT
cana-766	119	85	and	and	CCONJ
cana-766	119	86	1	1	NUM
cana-766	119	87	-	-	PUNCT
cana-766	119	88	na	na	INTJ
cana-766	119	89	(	(	PUNCT
cana-766	119	90	1)=	1)=	NUM
cana-766	119	91	𝑛𝐴	𝑛𝐴	PROPN
cana-766	119	92	𝑐(1)≥𝑛𝐴	𝑐(1)≥𝑛𝐴	X
cana-766	119	93	𝑐(𝑥)=1na	𝑐(𝑥)=1na	NUM
cana-766	119	94	(	(	PUNCT
cana-766	119	95	x	x	NOUN
cana-766	119	96	)	)	PUNCT
cana-766	119	97	implies	imply	VERB
cana-766	119	98	that	that	SCONJ
cana-766	120	1	na	na	INTJ
cana-766	120	2	(	(	PUNCT
cana-766	120	3	x)≥	x)≥	PROPN
cana-766	120	4	na	na	PART
cana-766	120	5	(	(	PUNCT
cana-766	120	6	1	1	X
cana-766	120	7	)	)	PUNCT
cana-766	120	8	also	also	ADV
cana-766	120	9	we	we	PRON
cana-766	120	10	have	have	AUX
cana-766	120	11	ma	ma	PROPN
cana-766	120	12	(	(	PUNCT
cana-766	120	13	𝑥→𝑧	𝑥→𝑧	NOUN
cana-766	120	14	)	)	PUNCT
cana-766	120	15	≥	≥	PROPN
cana-766	120	16	min	min	PROPN
cana-766	120	17	{	{	PUNCT
cana-766	120	18	ma	ma	PROPN
cana-766	120	19	(	(	PUNCT
cana-766	120	20	𝑥→𝑦	𝑥→𝑦	NUM
cana-766	120	21	)	)	PUNCT
cana-766	120	22	,	,	PUNCT
cana-766	120	23	ma	ma	PROPN
cana-766	120	24	(	(	PUNCT
cana-766	120	25	𝑥→(𝑦→𝑧	𝑥→(𝑦→𝑧	PROPN
cana-766	120	26	)	)	PUNCT
cana-766	120	27	)	)	PUNCT
cana-766	120	28	}	}	PUNCT
cana-766	120	29	and	and	CCONJ
cana-766	120	30	𝑛𝐴	𝑛𝐴	ADJ
cana-766	120	31	𝐶(x→	𝐶(x→	PROPN
cana-766	120	32	𝑧)≥	𝑧)≥	ADP
cana-766	120	33	min	min	PROPN
cana-766	120	34	{	{	PUNCT
cana-766	120	35	𝑛𝐴	𝑛𝐴	ADV
cana-766	120	36	𝐶(x→	𝐶(x→	NOUN
cana-766	120	37	𝑧	𝑧	NOUN
cana-766	120	38	)	)	PUNCT
cana-766	120	39	,	,	PUNCT
cana-766	120	40	𝑛𝐴	𝑛𝐴	ADJ
cana-766	120	41	𝐶(x→	𝐶(x→	NOUN
cana-766	120	42	(	(	PUNCT
cana-766	120	43	𝑦	𝑦	NOUN
cana-766	120	44	→	→	SYM
cana-766	120	45	𝑧	𝑧	NOUN
cana-766	120	46	)	)	PUNCT
cana-766	120	47	)	)	PUNCT
cana-766	120	48	}	}	PUNCT
cana-766	120	49	implies	imply	VERB
cana-766	120	50	that	that	SCONJ
cana-766	120	51	1	1	NUM
cana-766	120	52	−	−	NOUN
cana-766	120	53	𝑛𝐴(x→	𝑛𝐴(x→	NOUN
cana-766	120	54	𝑧)≥min{1	𝑧)≥min{1	NOUN
cana-766	120	55	−	−	PROPN
cana-766	120	56	𝑛𝐴(x→	𝑛𝐴(x→	NOUN
cana-766	120	57	𝑦	𝑦	NOUN
cana-766	120	58	)	)	PUNCT
cana-766	120	59	,	,	PUNCT
cana-766	120	60	1	1	NUM
cana-766	120	61	−	−	NOUN
cana-766	120	62	𝑛𝐴(x→	𝑛𝐴(x→	NOUN
cana-766	120	63	(	(	PUNCT
cana-766	120	64	𝑦	𝑦	NOUN
cana-766	120	65	→	→	SYM
cana-766	120	66	𝑧	𝑧	NOUN
cana-766	120	67	)	)	PUNCT
cana-766	120	68	)	)	PUNCT
cana-766	120	69	}	}	PUNCT
cana-766	121	1	=	=	NUM
cana-766	121	2	1max{𝑛𝐴(x→	1max{𝑛𝐴(x→	NUM
cana-766	121	3	𝑦	𝑦	NOUN
cana-766	121	4	)	)	PUNCT
cana-766	121	5	,	,	PUNCT
cana-766	121	6	𝑛𝐴(x→	𝑛𝐴(x→	X
cana-766	121	7	(	(	PUNCT
cana-766	121	8	𝑦	𝑦	NOUN
cana-766	121	9	→	→	SYM
cana-766	121	10	𝑧	𝑧	NOUN
cana-766	121	11	)	)	PUNCT
cana-766	121	12	)	)	PUNCT
cana-766	121	13	}	}	PUNCT
cana-766	121	14	.	.	PUNCT
cana-766	122	1	therefore	therefore	ADV
cana-766	122	2	𝑛𝐴(x→	𝑛𝐴(x→	AUX
cana-766	122	3	𝑧)≤	𝑧)≤	ADV
cana-766	122	4	max{𝑛𝐴(x→	max{𝑛𝐴(x→	PROPN
cana-766	122	5	𝑦	𝑦	NUM
cana-766	122	6	)	)	PUNCT
cana-766	122	7	,	,	PUNCT
cana-766	122	8	𝑛𝐴(x→	𝑛𝐴(x→	X
cana-766	122	9	(	(	PUNCT
cana-766	122	10	𝑦	𝑦	NOUN
cana-766	122	11	→	→	SYM
cana-766	122	12	𝑧	𝑧	NOUN
cana-766	122	13	)	)	PUNCT
cana-766	122	14	)	)	PUNCT
cana-766	122	15	}	}	PUNCT
cana-766	122	16	.	.	PUNCT
cana-766	123	1	discussion	discussion	NOUN
cana-766	123	2	(	(	PUNCT
cana-766	123	3	acknowledgements	acknowledgement	NOUN
cana-766	123	4	):	):	PUNCT
cana-766	123	5	the	the	DET
cana-766	123	6	authors	author	NOUN
cana-766	123	7	are	be	AUX
cana-766	123	8	grateful	grateful	ADJ
cana-766	123	9	to	to	ADP
cana-766	123	10	prof.t.eswarlal	prof.t.eswarlal	PROPN
cana-766	123	11	for	for	ADP
cana-766	123	12	his	his	PRON
cana-766	123	13	valuable	valuable	ADJ
cana-766	123	14	suggestions	suggestion	NOUN
cana-766	123	15	and	and	CCONJ
cana-766	123	16	discussions	discussion	NOUN
cana-766	123	17	on	on	ADP
cana-766	123	18	this	this	DET
cana-766	123	19	work	work	NOUN
cana-766	123	20	.	.	PUNCT
cana-766	124	1	refrences	refrence	VERB
cana-766	124	2	:	:	PUNCT
cana-766	125	1	[	[	X
cana-766	125	2	1	1	NUM
cana-766	125	3	]	]	PUNCT
cana-766	125	4	atanassov.k.t	atanassov.k.t	ADV
cana-766	125	5	,	,	PUNCT
cana-766	125	6	intuitionisticfuzzy	intuitionisticfuzzy	ADJ
cana-766	125	7	sets	set	NOUN
cana-766	125	8	,	,	PUNCT
cana-766	125	9	fuzzy	fuzzy	ADJ
cana-766	125	10	sets	set	NOUN
cana-766	125	11	and	and	CCONJ
cana-766	125	12	systems,33(1989),37	systems,33(1989),37	NOUN
cana-766	125	13	-	-	PUNCT
cana-766	125	14	45	45	NUM
cana-766	125	15	.	.	PUNCT
cana-766	126	1	[	[	X
cana-766	126	2	2	2	X
cana-766	126	3	]	]	PUNCT
cana-766	126	4	basheer	basheer	NOUN
cana-766	126	5	ahamed	ahamed	PROPN
cana-766	126	6	and	and	CCONJ
cana-766	126	7	a.ibrahim	a.ibrahim	PRON
cana-766	126	8	,	,	PUNCT
cana-766	126	9	fuzzy	fuzzy	ADJ
cana-766	126	10	implicative	implicative	ADJ
cana-766	126	11	filters	filter	NOUN
cana-766	126	12	of	of	ADP
cana-766	126	13	lattice	lattice	PROPN
cana-766	126	14	wajsberg	wajsberg	PROPN
cana-766	126	15	algebras	algebras	PROPN
cana-766	126	16	,	,	PUNCT
cana-766	126	17	advances	advance	NOUN
cana-766	126	18	in	in	ADP
cana-766	126	19	fuzzy	fuzzy	ADJ
cana-766	126	20	mathematics,6(2),(2011),235	mathematics,6(2),(2011),235	NOUN
cana-766	126	21	-	-	NOUN
cana-766	126	22	243	243	NUM
cana-766	126	23	.	.	PUNCT
cana-766	127	1	[	[	X
cana-766	127	2	3	3	NUM
cana-766	127	3	]	]	X
cana-766	127	4	gahu.w.l.buehrer.d.j	gahu.w.l.buehrer.d.j	NOUN
cana-766	127	5	.	.	PUNCT
cana-766	127	6	,vague	,vague	PUNCT
cana-766	127	7	sets	set	VERB
cana-766	127	8	ieeetransactions	ieeetransaction	NOUN
cana-766	127	9	on	on	ADP
cana-766	127	10	systems	system	NOUN
cana-766	127	11	,	,	PUNCT
cana-766	127	12	man	man	NOUN
cana-766	127	13	and	and	CCONJ
cana-766	127	14	cybernetics	cybernetic	NOUN
cana-766	127	15	vol.23(1993),610	vol.23(1993),610	PROPN
cana-766	127	16	-	-	SYM
cana-766	127	17	614	614	NUM
cana-766	127	18	[	[	SYM
cana-766	127	19	4	4	NUM
cana-766	127	20	]	]	SYM
cana-766	127	21	ramakrishana.n	ramakrishana.n	NUM
cana-766	127	22	,	,	PUNCT
cana-766	127	23	nageswararao.b	nageswararao.b	NOUN
cana-766	127	24	,	,	PUNCT
cana-766	127	25	eswarlal.tandsatyanarayana.ch	eswarlal.tandsatyanarayana.ch	PROPN
cana-766	127	26	,	,	PUNCT
cana-766	127	27	anti	anti	ADJ
cana-766	127	28	-	-	ADJ
cana-766	127	29	homomorphisms	homomorphism	NOUN
cana-766	127	30	in	in	ADP
cana-766	127	31	vague	vague	ADJ
cana-766	127	32	groups	group	NOUN
cana-766	127	33	(	(	PUNCT
cana-766	127	34	ijmsea	ijmsea	NOUN
cana-766	127	35	)	)	PUNCT
cana-766	127	36	issn	issn	PROPN
cana-766	127	37	0973	0973	NUM
cana-766	127	38	-	-	SYM
cana-766	127	39	9424,vol.6	9424,vol.6	NUM
cana-766	127	40	,	,	PUNCT
cana-766	127	41	no.2.(march,2012),pp.449	no.2.(march,2012),pp.449	NOUN
cana-766	127	42	-	-	PUNCT
cana-766	127	43	459	459	NUM
cana-766	127	44	.	.	PUNCT
cana-766	128	1	[	[	X
cana-766	128	2	5	5	NUM
cana-766	128	3	]	]	SYM
cana-766	128	4	ramakrishana.n	ramakrishana.n	NUM
cana-766	128	5	,	,	PUNCT
cana-766	128	6	satyanarayana.ch	satyanarayana.ch	NOUN
cana-766	128	7	and	and	CCONJ
cana-766	128	8	nageswararao	nageswararao	NOUN
cana-766	128	9	.	.	PUNCT
cana-766	129	1	b	b	X
cana-766	130	1	some	some	DET
cana-766	130	2	characterizations	characterization	NOUN
cana-766	130	3	vague	vague	ADJ
cana-766	130	4	groups	group	NOUN
cana-766	130	5	vague	vague	VERB
cana-766	130	6	normal	normal	ADJ
cana-766	130	7	groups	group	NOUN
cana-766	130	8	(	(	PUNCT
cana-766	130	9	ijmsea),vol.6,no:3(may,2012	ijmsea),vol.6,no:3(may,2012	NOUN
cana-766	130	10	)	)	PUNCT
cana-766	130	11	,	,	PUNCT
cana-766	130	12	pp.387	pp.387	NOUN
cana-766	130	13	-	-	SYM
cana-766	130	14	397	397	NUM
cana-766	130	15	.	.	PUNCT
cana-766	131	1	[	[	X
cana-766	131	2	6	6	NUM
cana-766	131	3	]	]	PUNCT
cana-766	131	4	ranjit	ranjit	PROPN
cana-766	131	5	biswas	biswas	PROPN
cana-766	131	6	,	,	PUNCT
cana-766	131	7	vaguegroups	vaguegroup	NOUN
cana-766	131	8	,	,	PUNCT
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cana-766	131	10	of	of	ADP
cana-766	131	11	computational	computational	ADJ
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cana-766	131	13	,	,	PUNCT
cana-766	131	14	vol.4	vol.4	PROPN
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cana-766	131	16	2006	2006	NUM
cana-766	131	17	.	.	PUNCT
cana-766	132	1	[	[	X
cana-766	132	2	7	7	NUM
cana-766	132	3	]	]	X
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cana-766	132	8	boolean	boolean	ADJ
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cana-766	132	11	,	,	PUNCT
cana-766	132	12	int.journal	int.journal	ADJ
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cana-766	132	15	,	,	PUNCT
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cana-766	132	17	(	(	PUNCT
cana-766	132	18	2007),50	2007),50	NUM
cana-766	132	19	-	-	SYM
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cana-766	132	21	.	.	PUNCT
cana-766	133	1	[	[	X
cana-766	133	2	8	8	NUM
cana-766	133	3	]	]	SYM
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cana-766	133	5	,	,	PUNCT
cana-766	133	6	achatracterization	achatracterization	NOUN
cana-766	133	7	of	of	ADP
cana-766	133	8	cyclic	cyclic	ADJ
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cana-766	133	10	of	of	ADP
cana-766	133	11	vague	vague	ADJ
cana-766	133	12	groups	group	NOUN
cana-766	133	13	,	,	PUNCT
cana-766	133	14	int.journal	int.journal	ADJ
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cana-766	133	16	computational	computational	ADJ
cana-766	133	17	congnition	congnition	NOUN
cana-766	133	18	,	,	PUNCT
cana-766	133	19	vol.6	vol.6	PROPN
cana-766	133	20	no.2(2008),17	no.2(2008),17	PROPN
cana-766	133	21	-	-	SYM
cana-766	133	22	20	20	NUM
cana-766	133	23	.	.	PUNCT
cana-766	134	1	[	[	X
cana-766	134	2	9	9	NUM
cana-766	134	3	]	]	X
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cana-766	134	7	,	,	PUNCT
cana-766	134	8	"	"	PUNCT
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cana-766	134	11	semirings	semiring	NOUN
cana-766	134	12	"	"	PUNCT
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cana-766	134	14	seminar	seminar	NOUN
cana-766	134	15	notes	note	NOUN
cana-766	134	16	,	,	PUNCT
cana-766	134	17	kob	kob	PROPN
cana-766	134	18	univ	univ	PROPN
cana-766	134	19	,	,	PUNCT
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cana-766	134	21	-	-	PUNCT
cana-766	134	22	149	149	NUM
cana-766	134	23	.	.	PUNCT
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cana-766	135	2	10	10	NUM
cana-766	135	3	]	]	X
cana-766	135	4	rosenfeld	rosenfeld	PROPN
cana-766	135	5	a.	a.	NOUN
cana-766	135	6	fuzzy	fuzzy	ADJ
cana-766	135	7	groups	group	NOUN
cana-766	135	8	.	.	PUNCT
cana-766	136	1	jon.maths	jon.math	NOUN
cana-766	136	2	.	.	PUNCT
cana-766	137	1	anal	anal	PROPN
cana-766	137	2	.	.	PUNCT
cana-766	138	1	appli.35(1971)512	appli.35(1971)512	PROPN
cana-766	138	2	-	-	PUNCT
cana-766	138	3	517	517	PROPN
cana-766	138	4	.	.	PUNCT
cana-766	139	1	[	[	X
cana-766	139	2	11	11	NUM
cana-766	139	3	]	]	PUNCT
cana-766	139	4	vimala.j	vimala.j	NUM
cana-766	139	5	,	,	PUNCT
cana-766	139	6	fuzzy	fuzzy	ADJ
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cana-766	139	8	orderdgroup	orderdgroup	ADV
cana-766	139	9	,	,	PUNCT
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cana-766	139	14	and	and	CCONJ
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cana-766	139	16	research	research	NOUN
cana-766	139	17	volume	volume	NOUN
cana-766	139	18	5,issue	5,issue	NUM
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cana-766	139	20	2	2	NUM
cana-766	139	21	.	.	PUNCT
cana-766	139	22	communications	communication	NOUN
cana-766	139	23	on	on	ADP
cana-766	139	24	applied	apply	VERB
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cana-766	139	26	analysis	analysis	NOUN
cana-766	139	27	issn	issn	NOUN
cana-766	139	28	:	:	PUNCT
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cana-766	139	30	-	-	PUNCT
cana-766	139	31	133x	133x	NUM
cana-766	139	32	vol	vol	NOUN
cana-766	139	33	31	31	NUM
cana-766	139	34	no	no	NOUN
cana-766	139	35	.	.	PUNCT
cana-766	140	1	3s	3s	NUM
cana-766	140	2	(	(	PUNCT
cana-766	140	3	2024	2024	NUM
cana-766	140	4	)	)	PUNCT
cana-766	140	5	302	302	NUM
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cana-766	141	1	[	[	X
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cana-766	141	3	]	]	PUNCT
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cana-766	141	5	,	,	PUNCT
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cana-766	141	8	,	,	PUNCT
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cana-766	141	12	.	.	PUNCT
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cana-766	142	2	13	13	NUM
cana-766	142	3	]	]	SYM
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cana-766	142	5	,	,	PUNCT
cana-766	142	6	l.a	l.a	PROPN
cana-766	142	7	.	.	PROPN
cana-766	142	8	,	,	PUNCT
cana-766	142	9	fuzzy	fuzzy	ADJ
cana-766	142	10	sets	set	NOUN
cana-766	142	11	,	,	PUNCT
cana-766	142	12	infor	infor	NOUN
cana-766	142	13	and	and	CCONJ
cana-766	142	14	control	control	NOUN
cana-766	142	15	,	,	PUNCT
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cana-766	142	17	8	8	NUM
cana-766	142	18	(	(	PUNCT
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cana-766	142	20	)	)	PUNCT
cana-766	142	21	338	338	NUM
cana-766	142	22	-	-	SYM
cana-766	142	23	353	353	NUM
cana-766	142	24	.	.	PUNCT