id	sid	tid	token	lemma	pos
ejpam-5627	1	1	european	european	PROPN
ejpam-5627	1	2	journal	journal	PROPN
ejpam-5627	1	3	of	of	ADP
ejpam-5627	1	4	pure	pure	ADJ
ejpam-5627	1	5	and	and	CCONJ
ejpam-5627	1	6	applied	applied	ADJ
ejpam-5627	1	7	mathematics	mathematic	NOUN
ejpam-5627	1	8	2025	2025	NUM
ejpam-5627	1	9	,	,	PUNCT
ejpam-5627	1	10	vol	vol	NOUN
ejpam-5627	1	11	.	.	PROPN
ejpam-5627	1	12	18	18	NUM
ejpam-5627	1	13	,	,	PUNCT
ejpam-5627	1	14	issue	issue	NOUN
ejpam-5627	1	15	1	1	NUM
ejpam-5627	1	16	,	,	PUNCT
ejpam-5627	1	17	article	article	NOUN
ejpam-5627	1	18	number	number	NOUN
ejpam-5627	1	19	5627	5627	NUM
ejpam-5627	1	20	issn	issn	VERB
ejpam-5627	1	21	1307	1307	NUM
ejpam-5627	1	22	-	-	SYM
ejpam-5627	1	23	5543	5543	NUM
ejpam-5627	1	24	–	–	PUNCT
ejpam-5627	1	25	ejpam.com	ejpam.com	X
ejpam-5627	1	26	published	publish	VERB
ejpam-5627	1	27	by	by	ADP
ejpam-5627	1	28	new	new	PROPN
ejpam-5627	1	29	york	york	PROPN
ejpam-5627	1	30	business	business	PROPN
ejpam-5627	1	31	global	global	ADJ
ejpam-5627	1	32	intuitionistic	intuitionistic	ADJ
ejpam-5627	1	33	fuzzy	fuzzy	ADJ
ejpam-5627	1	34	structures	structure	NOUN
ejpam-5627	1	35	on	on	ADP
ejpam-5627	1	36	sheffer	sheffer	NOUN
ejpam-5627	1	37	stroke	stroke	NOUN
ejpam-5627	1	38	up	up	ADP
ejpam-5627	1	39	-	-	PUNCT
ejpam-5627	1	40	algebras	algebras	NOUN
ejpam-5627	1	41	neelamegarajan	neelamegarajan	PROPN
ejpam-5627	1	42	rajesh1	rajesh1	PROPN
ejpam-5627	1	43	,	,	PUNCT
ejpam-5627	1	44	tahsin	tahsin	PROPN
ejpam-5627	1	45	oner2	oner2	VERB
ejpam-5627	1	46	,	,	PUNCT
ejpam-5627	1	47	aiyared	aiyare	VERB
ejpam-5627	1	48	iampan3,∗	iampan3,∗	NOUN
ejpam-5627	1	49	,	,	PUNCT
ejpam-5627	1	50	ibrahim	ibrahim	PROPN
ejpam-5627	1	51	senturk2	senturk2	PROPN
ejpam-5627	2	1	1	1	NUM
ejpam-5627	2	2	department	department	NOUN
ejpam-5627	2	3	of	of	ADP
ejpam-5627	2	4	mathematics	mathematic	NOUN
ejpam-5627	2	5	,	,	PUNCT
ejpam-5627	2	6	rajah	rajah	NOUN
ejpam-5627	2	7	serfoji	serfoji	ADJ
ejpam-5627	2	8	government	government	NOUN
ejpam-5627	2	9	college	college	NOUN
ejpam-5627	2	10	,	,	PUNCT
ejpam-5627	2	11	thanjavur-613005	thanjavur-613005	NOUN
ejpam-5627	2	12	,	,	PUNCT
ejpam-5627	2	13	tamil	tamil	PROPN
ejpam-5627	2	14	nadu	nadu	NOUN
ejpam-5627	2	15	,	,	PUNCT
ejpam-5627	2	16	india	india	PROPN
ejpam-5627	2	17	2	2	NUM
ejpam-5627	2	18	department	department	NOUN
ejpam-5627	2	19	of	of	ADP
ejpam-5627	2	20	mathematics	mathematic	NOUN
ejpam-5627	2	21	,	,	PUNCT
ejpam-5627	2	22	faculty	faculty	NOUN
ejpam-5627	2	23	of	of	ADP
ejpam-5627	2	24	science	science	NOUN
ejpam-5627	2	25	,	,	PUNCT
ejpam-5627	2	26	ege	ege	PROPN
ejpam-5627	2	27	university	university	NOUN
ejpam-5627	2	28	,	,	PUNCT
ejpam-5627	2	29	35100	35100	NUM
ejpam-5627	2	30	izmir	izmir	PROPN
ejpam-5627	2	31	,	,	PUNCT
ejpam-5627	2	32	turkey	turkey	PROPN
ejpam-5627	2	33	3	3	NUM
ejpam-5627	2	34	department	department	NOUN
ejpam-5627	2	35	of	of	ADP
ejpam-5627	2	36	mathematics	mathematic	NOUN
ejpam-5627	2	37	,	,	PUNCT
ejpam-5627	2	38	school	school	NOUN
ejpam-5627	2	39	of	of	ADP
ejpam-5627	2	40	science	science	NOUN
ejpam-5627	2	41	,	,	PUNCT
ejpam-5627	2	42	university	university	NOUN
ejpam-5627	2	43	of	of	ADP
ejpam-5627	2	44	phayao	phayao	NOUN
ejpam-5627	2	45	,	,	PUNCT
ejpam-5627	2	46	mae	mae	PROPN
ejpam-5627	2	47	ka	ka	PROPN
ejpam-5627	2	48	,	,	PUNCT
ejpam-5627	2	49	mueang	mueang	PROPN
ejpam-5627	2	50	,	,	PUNCT
ejpam-5627	2	51	phayao	phayao	NOUN
ejpam-5627	2	52	56000	56000	NUM
ejpam-5627	2	53	,	,	PUNCT
ejpam-5627	2	54	thailand	thailand	PROPN
ejpam-5627	2	55	abstract	abstract	NOUN
ejpam-5627	2	56	.	.	PUNCT
ejpam-5627	3	1	the	the	DET
ejpam-5627	3	2	study	study	NOUN
ejpam-5627	3	3	defines	define	VERB
ejpam-5627	3	4	an	an	DET
ejpam-5627	3	5	intuitionistic	intuitionistic	ADJ
ejpam-5627	3	6	fuzzy	fuzzy	ADJ
ejpam-5627	3	7	sup	sup	NOUN
ejpam-5627	3	8	-	-	PUNCT
ejpam-5627	3	9	subalgebra	subalgebra	NOUN
ejpam-5627	3	10	and	and	CCONJ
ejpam-5627	3	11	a	a	DET
ejpam-5627	3	12	level	level	NOUN
ejpam-5627	3	13	set	set	NOUN
ejpam-5627	3	14	of	of	ADP
ejpam-5627	3	15	an	an	DET
ejpam-5627	3	16	intuitionistic	intuitionistic	ADJ
ejpam-5627	3	17	fuzzy	fuzzy	ADJ
ejpam-5627	3	18	up	up	NOUN
ejpam-5627	3	19	-	-	PUNCT
ejpam-5627	3	20	structure	structure	NOUN
ejpam-5627	3	21	on	on	ADP
ejpam-5627	3	22	sheffer	sheffer	PROPN
ejpam-5627	3	23	stroke	stroke	PROPN
ejpam-5627	3	24	up	up	ADP
ejpam-5627	3	25	-	-	PUNCT
ejpam-5627	3	26	algebras	algebras	X
ejpam-5627	3	27	.	.	PUNCT
ejpam-5627	4	1	it	it	PRON
ejpam-5627	4	2	appears	appear	VERB
ejpam-5627	4	3	that	that	SCONJ
ejpam-5627	4	4	these	these	DET
ejpam-5627	4	5	concepts	concept	NOUN
ejpam-5627	4	6	are	be	AUX
ejpam-5627	4	7	integral	integral	ADJ
ejpam-5627	4	8	to	to	ADP
ejpam-5627	4	9	understanding	understand	VERB
ejpam-5627	4	10	the	the	DET
ejpam-5627	4	11	behavior	behavior	NOUN
ejpam-5627	4	12	of	of	ADP
ejpam-5627	4	13	neutrosophic	neutrosophic	ADJ
ejpam-5627	4	14	logic	logic	NOUN
ejpam-5627	4	15	within	within	ADP
ejpam-5627	4	16	the	the	DET
ejpam-5627	4	17	framework	framework	NOUN
ejpam-5627	4	18	of	of	ADP
ejpam-5627	4	19	sheffer	sheffer	PROPN
ejpam-5627	4	20	stroke	stroke	NOUN
ejpam-5627	4	21	upalgebras	upalgebra	NOUN
ejpam-5627	4	22	.	.	PUNCT
ejpam-5627	5	1	the	the	DET
ejpam-5627	5	2	study	study	NOUN
ejpam-5627	5	3	establishes	establish	VERB
ejpam-5627	5	4	a	a	DET
ejpam-5627	5	5	relationship	relationship	NOUN
ejpam-5627	5	6	between	between	ADP
ejpam-5627	5	7	up	up	ADV
ejpam-5627	5	8	-	-	PUNCT
ejpam-5627	5	9	subalgebras	subalgebra	NOUN
ejpam-5627	5	10	and	and	CCONJ
ejpam-5627	5	11	level	level	NOUN
ejpam-5627	5	12	sets	set	NOUN
ejpam-5627	5	13	on	on	ADP
ejpam-5627	5	14	sheffer	sheffer	PROPN
ejpam-5627	5	15	stroke	stroke	NOUN
ejpam-5627	5	16	up	up	ADP
ejpam-5627	5	17	-	-	PUNCT
ejpam-5627	5	18	algebras	algebras	X
ejpam-5627	5	19	.	.	PUNCT
ejpam-5627	6	1	specifically	specifically	ADV
ejpam-5627	6	2	,	,	PUNCT
ejpam-5627	6	3	it	it	PRON
ejpam-5627	6	4	proves	prove	VERB
ejpam-5627	6	5	that	that	SCONJ
ejpam-5627	6	6	the	the	DET
ejpam-5627	6	7	level	level	NOUN
ejpam-5627	6	8	set	set	NOUN
ejpam-5627	6	9	of	of	ADP
ejpam-5627	6	10	intuitionistic	intuitionistic	ADJ
ejpam-5627	6	11	fuzzy	fuzzy	ADJ
ejpam-5627	6	12	sup	sup	NOUN
ejpam-5627	6	13	-	-	PUNCT
ejpam-5627	6	14	subalgebras	subalgebras	NOUN
ejpam-5627	6	15	on	on	ADP
ejpam-5627	6	16	this	this	DET
ejpam-5627	6	17	algebra	algebra	NOUN
ejpam-5627	6	18	is	be	AUX
ejpam-5627	6	19	its	its	PRON
ejpam-5627	6	20	subalgebra	subalgebra	NOUN
ejpam-5627	6	21	,	,	PUNCT
ejpam-5627	6	22	and	and	CCONJ
ejpam-5627	6	23	vice	vice	ADV
ejpam-5627	6	24	versa	versa	ADV
ejpam-5627	6	25	.	.	PUNCT
ejpam-5627	7	1	it	it	PRON
ejpam-5627	7	2	is	be	AUX
ejpam-5627	7	3	stated	state	VERB
ejpam-5627	7	4	that	that	SCONJ
ejpam-5627	7	5	the	the	DET
ejpam-5627	7	6	family	family	NOUN
ejpam-5627	7	7	of	of	ADP
ejpam-5627	7	8	all	all	DET
ejpam-5627	7	9	intuitionistic	intuitionistic	ADJ
ejpam-5627	7	10	fuzzy	fuzzy	ADJ
ejpam-5627	7	11	sup	sup	NOUN
ejpam-5627	7	12	-	-	PUNCT
ejpam-5627	7	13	subalgebras	subalgebras	NOUN
ejpam-5627	7	14	of	of	ADP
ejpam-5627	7	15	a	a	DET
ejpam-5627	7	16	sheffer	sheffer	NOUN
ejpam-5627	7	17	stroke	stroke	NOUN
ejpam-5627	7	18	up	up	ADP
ejpam-5627	7	19	-	-	PUNCT
ejpam-5627	7	20	algebra	algebra	NOUN
ejpam-5627	7	21	forms	form	VERB
ejpam-5627	7	22	a	a	DET
ejpam-5627	7	23	complete	complete	ADJ
ejpam-5627	7	24	distributive	distributive	ADJ
ejpam-5627	7	25	lattice	lattice	NOUN
ejpam-5627	7	26	.	.	PUNCT
ejpam-5627	8	1	additionally	additionally	ADV
ejpam-5627	8	2	,	,	PUNCT
ejpam-5627	8	3	it	it	PRON
ejpam-5627	8	4	is	be	AUX
ejpam-5627	8	5	shown	show	VERB
ejpam-5627	8	6	that	that	SCONJ
ejpam-5627	8	7	every	every	DET
ejpam-5627	8	8	intuitionistic	intuitionistic	ADJ
ejpam-5627	8	9	fuzzy	fuzzy	ADJ
ejpam-5627	8	10	sup	sup	NOUN
ejpam-5627	8	11	-	-	PUNCT
ejpam-5627	8	12	ideal	ideal	NOUN
ejpam-5627	8	13	of	of	ADP
ejpam-5627	8	14	a	a	DET
ejpam-5627	8	15	sheffer	sheffer	NOUN
ejpam-5627	8	16	stroke	stroke	NOUN
ejpam-5627	8	17	up	up	ADP
ejpam-5627	8	18	-	-	PUNCT
ejpam-5627	8	19	algebra	algebra	NOUN
ejpam-5627	8	20	is	be	AUX
ejpam-5627	8	21	also	also	ADV
ejpam-5627	8	22	its	its	PRON
ejpam-5627	8	23	intuitionistic	intuitionistic	ADJ
ejpam-5627	8	24	fuzzy	fuzzy	ADJ
ejpam-5627	8	25	sup	sup	NOUN
ejpam-5627	8	26	-	-	PUNCT
ejpam-5627	8	27	subalgebra	subalgebra	NOUN
ejpam-5627	8	28	,	,	PUNCT
ejpam-5627	8	29	though	though	SCONJ
ejpam-5627	8	30	the	the	DET
ejpam-5627	8	31	inverse	inverse	NOUN
ejpam-5627	8	32	is	be	AUX
ejpam-5627	8	33	generally	generally	ADV
ejpam-5627	8	34	not	not	PART
ejpam-5627	8	35	true	true	ADJ
ejpam-5627	8	36	.	.	PUNCT
ejpam-5627	9	1	this	this	DET
ejpam-5627	9	2	highlights	highlight	VERB
ejpam-5627	9	3	the	the	DET
ejpam-5627	9	4	specific	specific	ADJ
ejpam-5627	9	5	characteristics	characteristic	NOUN
ejpam-5627	9	6	and	and	CCONJ
ejpam-5627	9	7	behavior	behavior	NOUN
ejpam-5627	9	8	of	of	ADP
ejpam-5627	9	9	intuitionistic	intuitionistic	ADJ
ejpam-5627	9	10	fuzzy	fuzzy	ADJ
ejpam-5627	9	11	sup	sup	NOUN
ejpam-5627	9	12	-	-	PUNCT
ejpam-5627	9	13	ideals	ideal	NOUN
ejpam-5627	9	14	within	within	ADP
ejpam-5627	9	15	the	the	DET
ejpam-5627	9	16	given	give	VERB
ejpam-5627	9	17	algebraic	algebraic	ADJ
ejpam-5627	9	18	context	context	NOUN
ejpam-5627	9	19	.	.	PUNCT
ejpam-5627	10	1	2020	2020	NUM
ejpam-5627	10	2	mathematics	mathematic	NOUN
ejpam-5627	10	3	subject	subject	NOUN
ejpam-5627	10	4	classifications	classification	NOUN
ejpam-5627	10	5	:	:	PUNCT
ejpam-5627	10	6	06f05	06f05	NUM
ejpam-5627	10	7	;	;	PUNCT
ejpam-5627	10	8	03g25	03g25	NUM
ejpam-5627	10	9	;	;	PUNCT
ejpam-5627	10	10	03g10	03g10	NUM
ejpam-5627	10	11	key	key	ADJ
ejpam-5627	10	12	words	word	NOUN
ejpam-5627	10	13	and	and	CCONJ
ejpam-5627	10	14	phrases	phrase	NOUN
ejpam-5627	10	15	:	:	PUNCT
ejpam-5627	10	16	sheffer	sheffer	VERB
ejpam-5627	10	17	stroke	stroke	NOUN
ejpam-5627	10	18	up	up	ADP
ejpam-5627	10	19	-	-	PUNCT
ejpam-5627	10	20	algebra	algebra	NOUN
ejpam-5627	10	21	(	(	PUNCT
ejpam-5627	10	22	sup	sup	NOUN
ejpam-5627	10	23	-	-	PUNCT
ejpam-5627	10	24	algebra	algebra	NOUN
ejpam-5627	10	25	)	)	PUNCT
ejpam-5627	10	26	,	,	PUNCT
ejpam-5627	10	27	subalgebra	subalgebra	NOUN
ejpam-5627	10	28	,	,	PUNCT
ejpam-5627	10	29	ideal	ideal	ADJ
ejpam-5627	10	30	,	,	PUNCT
ejpam-5627	10	31	intuitionistic	intuitionistic	ADJ
ejpam-5627	10	32	fuzzy	fuzzy	ADJ
ejpam-5627	10	33	sup	sup	NOUN
ejpam-5627	10	34	-	-	PUNCT
ejpam-5627	10	35	subalgebra	subalgebra	NOUN
ejpam-5627	10	36	,	,	PUNCT
ejpam-5627	10	37	intuitionistic	intuitionistic	ADJ
ejpam-5627	10	38	fuzzy	fuzzy	ADJ
ejpam-5627	10	39	sup	sup	NOUN
ejpam-5627	10	40	-	-	PUNCT
ejpam-5627	10	41	ideal	ideal	NOUN
ejpam-5627	10	42	.	.	PUNCT
ejpam-5627	11	1	1	1	X
ejpam-5627	11	2	.	.	X
ejpam-5627	11	3	introduction	introduction	NOUN
ejpam-5627	11	4	the	the	DET
ejpam-5627	11	5	sheffer	sheffer	NOUN
ejpam-5627	11	6	operation	operation	NOUN
ejpam-5627	11	7	,	,	PUNCT
ejpam-5627	11	8	also	also	ADV
ejpam-5627	11	9	known	know	VERB
ejpam-5627	11	10	as	as	ADP
ejpam-5627	11	11	the	the	DET
ejpam-5627	11	12	sheffer	sheffer	NOUN
ejpam-5627	11	13	stroke	stroke	NOUN
ejpam-5627	11	14	or	or	CCONJ
ejpam-5627	11	15	nand	nand	NOUN
ejpam-5627	11	16	operator	operator	NOUN
ejpam-5627	11	17	,	,	PUNCT
ejpam-5627	11	18	was	be	AUX
ejpam-5627	11	19	first	first	ADV
ejpam-5627	11	20	introduced	introduce	VERB
ejpam-5627	11	21	by	by	ADP
ejpam-5627	11	22	sheffer	sheffer	NOUN
ejpam-5627	11	23	[	[	X
ejpam-5627	11	24	12	12	NUM
ejpam-5627	11	25	]	]	PUNCT
ejpam-5627	11	26	.	.	PUNCT
ejpam-5627	12	1	this	this	DET
ejpam-5627	12	2	operation	operation	NOUN
ejpam-5627	12	3	holds	hold	VERB
ejpam-5627	12	4	significance	significance	NOUN
ejpam-5627	12	5	because	because	SCONJ
ejpam-5627	12	6	it	it	PRON
ejpam-5627	12	7	can	can	AUX
ejpam-5627	12	8	be	be	AUX
ejpam-5627	12	9	used	use	VERB
ejpam-5627	12	10	on	on	ADP
ejpam-5627	12	11	its	its	PRON
ejpam-5627	12	12	own	own	ADJ
ejpam-5627	12	13	,	,	PUNCT
ejpam-5627	12	14	without	without	ADP
ejpam-5627	12	15	any	any	DET
ejpam-5627	12	16	other	other	ADJ
ejpam-5627	12	17	logical	logical	ADJ
ejpam-5627	12	18	operators	operator	NOUN
ejpam-5627	12	19	,	,	PUNCT
ejpam-5627	12	20	to	to	PART
ejpam-5627	12	21	construct	construct	VERB
ejpam-5627	12	22	a	a	DET
ejpam-5627	12	23	logical	logical	ADJ
ejpam-5627	12	24	system	system	NOUN
ejpam-5627	12	25	.	.	PUNCT
ejpam-5627	13	1	this	this	PRON
ejpam-5627	13	2	means	mean	VERB
ejpam-5627	13	3	that	that	SCONJ
ejpam-5627	13	4	any	any	DET
ejpam-5627	13	5	axiom	axiom	NOUN
ejpam-5627	13	6	of	of	ADP
ejpam-5627	13	7	a	a	DET
ejpam-5627	13	8	logical	logical	ADJ
ejpam-5627	13	9	system	system	NOUN
ejpam-5627	13	10	can	can	AUX
ejpam-5627	13	11	be	be	AUX
ejpam-5627	13	12	restated	restate	VERB
ejpam-5627	13	13	using	use	VERB
ejpam-5627	13	14	only	only	ADV
ejpam-5627	13	15	the	the	DET
ejpam-5627	13	16	sheffer	sheffer	NOUN
ejpam-5627	13	17	operation	operation	NOUN
ejpam-5627	13	18	.	.	PUNCT
ejpam-5627	14	1	because	because	SCONJ
ejpam-5627	14	2	of	of	ADP
ejpam-5627	14	3	this	this	DET
ejpam-5627	14	4	property	property	NOUN
ejpam-5627	14	5	,	,	PUNCT
ejpam-5627	14	6	it	it	PRON
ejpam-5627	14	7	becomes	become	VERB
ejpam-5627	14	8	easier	easy	ADJ
ejpam-5627	14	9	to	to	PART
ejpam-5627	14	10	control	control	VERB
ejpam-5627	14	11	specific	specific	ADJ
ejpam-5627	14	12	properties	property	NOUN
ejpam-5627	14	13	of	of	ADP
ejpam-5627	14	14	the	the	DET
ejpam-5627	14	15	newly	newly	ADV
ejpam-5627	14	16	constructed	construct	VERB
ejpam-5627	14	17	logical	logical	ADJ
ejpam-5627	14	18	system	system	NOUN
ejpam-5627	14	19	.	.	PUNCT
ejpam-5627	15	1	additionally	additionally	ADV
ejpam-5627	15	2	,	,	PUNCT
ejpam-5627	15	3	it	it	PRON
ejpam-5627	15	4	’s	’	VERB
ejpam-5627	15	5	worth	worth	ADJ
ejpam-5627	15	6	noting	note	VERB
ejpam-5627	15	7	that	that	SCONJ
ejpam-5627	15	8	the	the	DET
ejpam-5627	15	9	axioms	axiom	NOUN
ejpam-5627	15	10	of	of	ADP
ejpam-5627	15	11	boolean	boolean	ADJ
ejpam-5627	15	12	algebra	algebra	NOUN
ejpam-5627	15	13	,	,	PUNCT
ejpam-5627	15	14	which	which	PRON
ejpam-5627	15	15	is	be	AUX
ejpam-5627	15	16	the	the	DET
ejpam-5627	15	17	algebraic	algebraic	ADJ
ejpam-5627	15	18	counterpart	counterpart	NOUN
ejpam-5627	15	19	of	of	ADP
ejpam-5627	15	20	classical	classical	ADJ
ejpam-5627	15	21	propositional	propositional	ADJ
ejpam-5627	15	22	calculus	calculus	NOUN
ejpam-5627	15	23	,	,	PUNCT
ejpam-5627	15	24	can	can	AUX
ejpam-5627	15	25	be	be	AUX
ejpam-5627	15	26	expressed	express	VERB
ejpam-5627	15	27	solely	solely	ADV
ejpam-5627	15	28	∗corresponding	∗corresponde	VERB
ejpam-5627	15	29	author	author	NOUN
ejpam-5627	15	30	.	.	PUNCT
ejpam-5627	16	1	doi	doi	NOUN
ejpam-5627	16	2	:	:	PUNCT
ejpam-5627	16	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5627	https://doi.org/10.29020/nybg.ejpam.v18i1.5627	PRON
ejpam-5627	16	4	email	email	NOUN
ejpam-5627	16	5	addresses	address	NOUN
ejpam-5627	16	6	:	:	PUNCT
ejpam-5627	16	7	nrajesh	nrajesh	PROPN
ejpam-5627	16	8	topology@yahoo.co.in	topology@yahoo.co.in	PROPN
ejpam-5627	16	9	(	(	PUNCT
ejpam-5627	16	10	n.	n.	PROPN
ejpam-5627	16	11	rajesh	rajesh	PROPN
ejpam-5627	16	12	)	)	PUNCT
ejpam-5627	16	13	,	,	PUNCT
ejpam-5627	16	14	tahsin.oner@ege.edu.tr	tahsin.oner@ege.edu.tr	NOUN
ejpam-5627	16	15	(	(	PUNCT
ejpam-5627	16	16	t.	t.	NOUN
ejpam-5627	16	17	oner	oner	PROPN
ejpam-5627	16	18	)	)	PUNCT
ejpam-5627	16	19	,	,	PUNCT
ejpam-5627	16	20	aiyared.ia@up.ac.th	aiyared.ia@up.ac.th	NOUN
ejpam-5627	16	21	(	(	PUNCT
ejpam-5627	16	22	a.	a.	NOUN
ejpam-5627	16	23	iampan	iampan	PROPN
ejpam-5627	16	24	)	)	PUNCT
ejpam-5627	16	25	,	,	PUNCT
ejpam-5627	16	26	ibrahim.senturk@ege.edu.tr	ibrahim.senturk@ege.edu.tr	PROPN
ejpam-5627	16	27	(	(	PUNCT
ejpam-5627	16	28	i.	i.	PROPN
ejpam-5627	16	29	senturk	senturk	PROPN
ejpam-5627	16	30	)	)	PUNCT
ejpam-5627	16	31	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5627	17	1	1	1	NUM
ejpam-5627	17	2	copyright	copyright	NOUN
ejpam-5627	17	3	:	:	PUNCT
ejpam-5627	17	4	©	©	PROPN
ejpam-5627	17	5	2025	2025	NUM
ejpam-5627	17	6	the	the	DET
ejpam-5627	17	7	author(s	author(s	NOUN
ejpam-5627	17	8	)	)	PUNCT
ejpam-5627	17	9	.	.	PUNCT
ejpam-5627	18	1	(	(	PUNCT
ejpam-5627	18	2	cc	cc	NOUN
ejpam-5627	18	3	by	by	ADP
ejpam-5627	18	4	-	-	PUNCT
ejpam-5627	18	5	nc	nc	PROPN
ejpam-5627	18	6	4.0	4.0	NUM
ejpam-5627	18	7	)	)	PUNCT
ejpam-5627	18	8	n.	n.	PROPN
ejpam-5627	18	9	rajesh	rajesh	PROPN
ejpam-5627	18	10	,	,	PUNCT
ejpam-5627	18	11	t.	t.	PROPN
ejpam-5627	18	12	oner	oner	NOUN
ejpam-5627	18	13	,	,	PUNCT
ejpam-5627	18	14	a.	a.	NOUN
ejpam-5627	18	15	iampan	iampan	PROPN
ejpam-5627	18	16	,	,	PUNCT
ejpam-5627	18	17	i.	i.	PROPN
ejpam-5627	18	18	senturk	senturk	PROPN
ejpam-5627	18	19	/	/	SYM
ejpam-5627	18	20	eur	eur	PROPN
ejpam-5627	18	21	.	.	PUNCT
ejpam-5627	19	1	j.	j.	PROPN
ejpam-5627	19	2	pure	pure	PROPN
ejpam-5627	19	3	appl	appl	PROPN
ejpam-5627	19	4	.	.	PROPN
ejpam-5627	19	5	math	math	PROPN
ejpam-5627	19	6	,	,	PUNCT
ejpam-5627	19	7	18	18	NUM
ejpam-5627	19	8	(	(	PUNCT
ejpam-5627	19	9	1	1	NUM
ejpam-5627	19	10	)	)	PUNCT
ejpam-5627	19	11	(	(	PUNCT
ejpam-5627	19	12	2025	2025	NUM
ejpam-5627	19	13	)	)	PUNCT
ejpam-5627	19	14	,	,	PUNCT
ejpam-5627	19	15	5627	5627	NUM
ejpam-5627	19	16	2	2	NUM
ejpam-5627	19	17	of	of	ADP
ejpam-5627	19	18	15	15	NUM
ejpam-5627	19	19	using	use	VERB
ejpam-5627	19	20	the	the	DET
ejpam-5627	19	21	sheffer	sheffer	NOUN
ejpam-5627	19	22	operation	operation	NOUN
ejpam-5627	19	23	.	.	PUNCT
ejpam-5627	20	1	this	this	DET
ejpam-5627	20	2	highlights	highlight	VERB
ejpam-5627	20	3	the	the	DET
ejpam-5627	20	4	fundamental	fundamental	ADJ
ejpam-5627	20	5	nature	nature	NOUN
ejpam-5627	20	6	and	and	CCONJ
ejpam-5627	20	7	versatility	versatility	NOUN
ejpam-5627	20	8	of	of	ADP
ejpam-5627	20	9	the	the	DET
ejpam-5627	20	10	sheffer	sheffer	NOUN
ejpam-5627	20	11	operation	operation	NOUN
ejpam-5627	20	12	in	in	ADP
ejpam-5627	20	13	logical	logical	ADJ
ejpam-5627	20	14	and	and	CCONJ
ejpam-5627	20	15	algebraic	algebraic	ADJ
ejpam-5627	20	16	systems	system	NOUN
ejpam-5627	20	17	.	.	PUNCT
ejpam-5627	21	1	building	build	VERB
ejpam-5627	21	2	on	on	ADP
ejpam-5627	21	3	this	this	DET
ejpam-5627	21	4	foundation	foundation	NOUN
ejpam-5627	21	5	,	,	PUNCT
ejpam-5627	21	6	sheffer	sheffer	VERB
ejpam-5627	21	7	stroke	stroke	NOUN
ejpam-5627	21	8	up	up	ADP
ejpam-5627	21	9	-	-	PUNCT
ejpam-5627	21	10	algebras	algebras	NOUN
ejpam-5627	21	11	introduce	introduce	VERB
ejpam-5627	21	12	a	a	DET
ejpam-5627	21	13	unique	unique	ADJ
ejpam-5627	21	14	algebraic	algebraic	ADJ
ejpam-5627	21	15	structure	structure	NOUN
ejpam-5627	21	16	that	that	PRON
ejpam-5627	21	17	merges	merge	VERB
ejpam-5627	21	18	logical	logical	ADJ
ejpam-5627	21	19	and	and	CCONJ
ejpam-5627	21	20	algebraic	algebraic	ADJ
ejpam-5627	21	21	principles	principle	NOUN
ejpam-5627	21	22	.	.	PUNCT
ejpam-5627	22	1	as	as	SCONJ
ejpam-5627	22	2	detailed	detail	VERB
ejpam-5627	22	3	by	by	ADP
ejpam-5627	22	4	iampan	iampan	NOUN
ejpam-5627	22	5	[	[	X
ejpam-5627	22	6	5	5	X
ejpam-5627	22	7	]	]	PUNCT
ejpam-5627	22	8	in	in	ADP
ejpam-5627	22	9	2017	2017	NUM
ejpam-5627	22	10	,	,	PUNCT
ejpam-5627	22	11	up	up	ADP
ejpam-5627	22	12	-	-	PUNCT
ejpam-5627	22	13	algebras	algebras	PROPN
ejpam-5627	22	14	represent	represent	VERB
ejpam-5627	22	15	a	a	DET
ejpam-5627	22	16	new	new	ADJ
ejpam-5627	22	17	branch	branch	NOUN
ejpam-5627	22	18	of	of	ADP
ejpam-5627	22	19	logical	logical	ADJ
ejpam-5627	22	20	algebra	algebra	NOUN
ejpam-5627	22	21	,	,	PUNCT
ejpam-5627	22	22	providing	provide	VERB
ejpam-5627	22	23	a	a	DET
ejpam-5627	22	24	versatile	versatile	ADJ
ejpam-5627	22	25	framework	framework	NOUN
ejpam-5627	22	26	for	for	ADP
ejpam-5627	22	27	studying	study	VERB
ejpam-5627	22	28	algebraic	algebraic	ADJ
ejpam-5627	22	29	systems	system	NOUN
ejpam-5627	22	30	with	with	ADP
ejpam-5627	22	31	advanced	advanced	ADJ
ejpam-5627	22	32	logical	logical	ADJ
ejpam-5627	22	33	constructs	construct	NOUN
ejpam-5627	22	34	.	.	PUNCT
ejpam-5627	23	1	this	this	DET
ejpam-5627	23	2	innovation	innovation	NOUN
ejpam-5627	23	3	facilitates	facilitate	VERB
ejpam-5627	23	4	a	a	DET
ejpam-5627	23	5	deeper	deep	ADJ
ejpam-5627	23	6	understanding	understanding	NOUN
ejpam-5627	23	7	of	of	ADP
ejpam-5627	23	8	logical	logical	ADJ
ejpam-5627	23	9	operations	operation	NOUN
ejpam-5627	23	10	and	and	CCONJ
ejpam-5627	23	11	their	their	PRON
ejpam-5627	23	12	algebraic	algebraic	ADJ
ejpam-5627	23	13	counterparts	counterpart	NOUN
ejpam-5627	23	14	,	,	PUNCT
ejpam-5627	23	15	paving	pave	VERB
ejpam-5627	23	16	the	the	DET
ejpam-5627	23	17	way	way	NOUN
ejpam-5627	23	18	for	for	ADP
ejpam-5627	23	19	applications	application	NOUN
ejpam-5627	23	20	in	in	ADP
ejpam-5627	23	21	fields	field	NOUN
ejpam-5627	23	22	such	such	ADJ
ejpam-5627	23	23	as	as	ADP
ejpam-5627	23	24	decision	decision	NOUN
ejpam-5627	23	25	theory	theory	NOUN
ejpam-5627	23	26	.	.	PUNCT
ejpam-5627	24	1	the	the	DET
ejpam-5627	24	2	concept	concept	NOUN
ejpam-5627	24	3	of	of	ADP
ejpam-5627	24	4	fuzzy	fuzzy	ADJ
ejpam-5627	24	5	sets	set	NOUN
ejpam-5627	24	6	[	[	X
ejpam-5627	24	7	13	13	NUM
ejpam-5627	24	8	]	]	PUNCT
ejpam-5627	24	9	and	and	CCONJ
ejpam-5627	24	10	their	their	PRON
ejpam-5627	24	11	extensions	extension	NOUN
ejpam-5627	24	12	has	have	AUX
ejpam-5627	24	13	been	be	AUX
ejpam-5627	24	14	pivotal	pivotal	ADJ
ejpam-5627	24	15	in	in	ADP
ejpam-5627	24	16	exploring	explore	VERB
ejpam-5627	24	17	algebraic	algebraic	ADJ
ejpam-5627	24	18	structures	structure	NOUN
ejpam-5627	24	19	under	under	ADP
ejpam-5627	24	20	uncertainty	uncertainty	NOUN
ejpam-5627	24	21	.	.	PUNCT
ejpam-5627	25	1	platil	platil	NOUN
ejpam-5627	25	2	and	and	CCONJ
ejpam-5627	25	3	vilela	vilela	VERB
ejpam-5627	26	1	[	[	X
ejpam-5627	26	2	11	11	NUM
ejpam-5627	26	3	]	]	PUNCT
ejpam-5627	26	4	introduced	introduce	VERB
ejpam-5627	26	5	anti	anti	ADJ
ejpam-5627	26	6	fuzzy	fuzzy	ADJ
ejpam-5627	26	7	substructures	substructure	NOUN
ejpam-5627	26	8	in	in	ADP
ejpam-5627	26	9	ks	ks	NOUN
ejpam-5627	26	10	-	-	PUNCT
ejpam-5627	26	11	semigroups	semigroup	NOUN
ejpam-5627	26	12	,	,	PUNCT
ejpam-5627	26	13	which	which	PRON
ejpam-5627	26	14	provide	provide	VERB
ejpam-5627	26	15	a	a	DET
ejpam-5627	26	16	foundation	foundation	NOUN
ejpam-5627	26	17	for	for	ADP
ejpam-5627	26	18	examining	examine	VERB
ejpam-5627	26	19	fuzzy	fuzzy	ADJ
ejpam-5627	26	20	properties	property	NOUN
ejpam-5627	26	21	in	in	ADP
ejpam-5627	26	22	specialized	specialized	ADJ
ejpam-5627	26	23	algebraic	algebraic	ADJ
ejpam-5627	26	24	systems	system	NOUN
ejpam-5627	26	25	.	.	PUNCT
ejpam-5627	27	1	their	their	PRON
ejpam-5627	27	2	approach	approach	NOUN
ejpam-5627	27	3	offers	offer	VERB
ejpam-5627	27	4	valuable	valuable	ADJ
ejpam-5627	27	5	insights	insight	NOUN
ejpam-5627	27	6	into	into	ADP
ejpam-5627	27	7	how	how	SCONJ
ejpam-5627	27	8	dual	dual	ADJ
ejpam-5627	27	9	properties	property	NOUN
ejpam-5627	27	10	(	(	PUNCT
ejpam-5627	27	11	such	such	ADJ
ejpam-5627	27	12	as	as	ADP
ejpam-5627	27	13	anti	anti	ADJ
ejpam-5627	27	14	-	-	ADJ
ejpam-5627	27	15	fuzziness	fuzziness	NOUN
ejpam-5627	27	16	)	)	PUNCT
ejpam-5627	27	17	can	can	AUX
ejpam-5627	27	18	coexist	coexist	VERB
ejpam-5627	27	19	with	with	ADP
ejpam-5627	27	20	standard	standard	ADJ
ejpam-5627	27	21	fuzzy	fuzzy	ADJ
ejpam-5627	27	22	frameworks	framework	NOUN
ejpam-5627	27	23	,	,	PUNCT
ejpam-5627	27	24	laying	lay	VERB
ejpam-5627	27	25	a	a	DET
ejpam-5627	27	26	conceptual	conceptual	ADJ
ejpam-5627	27	27	groundwork	groundwork	NOUN
ejpam-5627	27	28	for	for	ADP
ejpam-5627	27	29	integrating	integrate	VERB
ejpam-5627	27	30	intuitionistic	intuitionistic	ADJ
ejpam-5627	27	31	fuzzy	fuzzy	ADJ
ejpam-5627	27	32	sets	set	NOUN
ejpam-5627	27	33	into	into	ADP
ejpam-5627	27	34	sheffer	sheffer	PROPN
ejpam-5627	27	35	stroke	stroke	NOUN
ejpam-5627	27	36	up	up	ADP
ejpam-5627	27	37	-	-	PUNCT
ejpam-5627	27	38	algebras	algebras	X
ejpam-5627	27	39	.	.	PUNCT
ejpam-5627	28	1	additionally	additionally	ADV
ejpam-5627	28	2	,	,	PUNCT
ejpam-5627	28	3	platil	platil	NOUN
ejpam-5627	28	4	and	and	CCONJ
ejpam-5627	28	5	petalcorin	petalcorin	NOUN
ejpam-5627	28	6	[	[	X
ejpam-5627	28	7	9	9	NUM
ejpam-5627	28	8	]	]	X
ejpam-5627	28	9	extended	extend	VERB
ejpam-5627	28	10	fuzzy	fuzzy	ADJ
ejpam-5627	28	11	set	set	NOUN
ejpam-5627	28	12	theory	theory	NOUN
ejpam-5627	28	13	to	to	ADP
ejpam-5627	28	14	γ	γ	NOUN
ejpam-5627	28	15	-	-	PUNCT
ejpam-5627	28	16	semimodules	semimodule	NOUN
ejpam-5627	28	17	over	over	ADP
ejpam-5627	28	18	γ	γ	NOUN
ejpam-5627	28	19	-	-	NOUN
ejpam-5627	28	20	semirings	semiring	NOUN
ejpam-5627	28	21	,	,	PUNCT
ejpam-5627	28	22	showcasing	showcase	VERB
ejpam-5627	28	23	the	the	DET
ejpam-5627	28	24	adaptability	adaptability	NOUN
ejpam-5627	28	25	of	of	ADP
ejpam-5627	28	26	fuzzy	fuzzy	ADJ
ejpam-5627	28	27	structures	structure	NOUN
ejpam-5627	28	28	in	in	ADP
ejpam-5627	28	29	modular	modular	ADJ
ejpam-5627	28	30	algebraic	algebraic	ADJ
ejpam-5627	28	31	frameworks	framework	NOUN
ejpam-5627	28	32	.	.	PUNCT
ejpam-5627	29	1	these	these	DET
ejpam-5627	29	2	studies	study	NOUN
ejpam-5627	29	3	underscore	underscore	VERB
ejpam-5627	29	4	the	the	DET
ejpam-5627	29	5	importance	importance	NOUN
ejpam-5627	29	6	of	of	ADP
ejpam-5627	29	7	developing	develop	VERB
ejpam-5627	29	8	fuzzy	fuzzy	ADV
ejpam-5627	29	9	-	-	PUNCT
ejpam-5627	29	10	based	base	VERB
ejpam-5627	29	11	generalizations	generalization	NOUN
ejpam-5627	29	12	in	in	ADP
ejpam-5627	29	13	algebra	algebra	NOUN
ejpam-5627	29	14	,	,	PUNCT
ejpam-5627	29	15	a	a	DET
ejpam-5627	29	16	direction	direction	NOUN
ejpam-5627	29	17	closely	closely	ADV
ejpam-5627	29	18	aligned	align	VERB
ejpam-5627	29	19	with	with	ADP
ejpam-5627	29	20	the	the	DET
ejpam-5627	29	21	intuitionistic	intuitionistic	ADJ
ejpam-5627	29	22	fuzzy	fuzzy	ADJ
ejpam-5627	29	23	structures	structure	NOUN
ejpam-5627	29	24	in	in	ADP
ejpam-5627	29	25	sheffer	sheffer	PROPN
ejpam-5627	29	26	stroke	stroke	NOUN
ejpam-5627	29	27	up	up	ADP
ejpam-5627	29	28	-	-	PUNCT
ejpam-5627	29	29	algebras	algebras	X
ejpam-5627	29	30	.	.	PUNCT
ejpam-5627	30	1	by	by	ADP
ejpam-5627	30	2	building	build	VERB
ejpam-5627	30	3	on	on	ADP
ejpam-5627	30	4	these	these	DET
ejpam-5627	30	5	foundational	foundational	ADJ
ejpam-5627	30	6	works	work	NOUN
ejpam-5627	30	7	,	,	PUNCT
ejpam-5627	30	8	our	our	PRON
ejpam-5627	30	9	study	study	NOUN
ejpam-5627	30	10	aims	aim	VERB
ejpam-5627	30	11	to	to	PART
ejpam-5627	30	12	further	far	ADV
ejpam-5627	30	13	generalize	generalize	VERB
ejpam-5627	30	14	and	and	CCONJ
ejpam-5627	30	15	apply	apply	VERB
ejpam-5627	30	16	intuitionistic	intuitionistic	ADJ
ejpam-5627	30	17	fuzzy	fuzzy	ADJ
ejpam-5627	30	18	concepts	concept	NOUN
ejpam-5627	30	19	,	,	PUNCT
ejpam-5627	30	20	offering	offer	VERB
ejpam-5627	30	21	a	a	DET
ejpam-5627	30	22	deeper	deep	ADJ
ejpam-5627	30	23	understanding	understanding	NOUN
ejpam-5627	30	24	of	of	ADP
ejpam-5627	30	25	their	their	PRON
ejpam-5627	30	26	behavior	behavior	NOUN
ejpam-5627	30	27	and	and	CCONJ
ejpam-5627	30	28	applications	application	NOUN
ejpam-5627	30	29	in	in	ADP
ejpam-5627	30	30	novel	novel	ADJ
ejpam-5627	30	31	algebraic	algebraic	ADJ
ejpam-5627	30	32	contexts	contexts	NOUN
ejpam-5627	30	33	.	.	PUNCT
ejpam-5627	31	1	intuitionistic	intuitionistic	ADJ
ejpam-5627	31	2	fuzzy	fuzzy	ADJ
ejpam-5627	31	3	sets	set	NOUN
ejpam-5627	31	4	(	(	PUNCT
ejpam-5627	31	5	ifss	ifss	NOUN
ejpam-5627	31	6	)	)	PUNCT
ejpam-5627	31	7	,	,	PUNCT
ejpam-5627	31	8	introduced	introduce	VERB
ejpam-5627	31	9	by	by	ADP
ejpam-5627	31	10	atanassov	atanassov	NOUN
ejpam-5627	31	11	[	[	X
ejpam-5627	31	12	3	3	X
ejpam-5627	31	13	]	]	PUNCT
ejpam-5627	31	14	in	in	ADP
ejpam-5627	31	15	1986	1986	NUM
ejpam-5627	31	16	,	,	PUNCT
ejpam-5627	31	17	extend	extend	VERB
ejpam-5627	31	18	classical	classical	ADJ
ejpam-5627	31	19	fuzzy	fuzzy	ADJ
ejpam-5627	31	20	sets	set	NOUN
ejpam-5627	31	21	by	by	ADP
ejpam-5627	31	22	incorporating	incorporate	VERB
ejpam-5627	31	23	a	a	DET
ejpam-5627	31	24	membership	membership	NOUN
ejpam-5627	31	25	function	function	NOUN
ejpam-5627	31	26	,	,	PUNCT
ejpam-5627	31	27	a	a	DET
ejpam-5627	31	28	non	non	ADJ
ejpam-5627	31	29	-	-	ADJ
ejpam-5627	31	30	membership	membership	ADJ
ejpam-5627	31	31	function	function	NOUN
ejpam-5627	31	32	,	,	PUNCT
ejpam-5627	31	33	and	and	CCONJ
ejpam-5627	31	34	a	a	DET
ejpam-5627	31	35	degree	degree	NOUN
ejpam-5627	31	36	of	of	ADP
ejpam-5627	31	37	hesitation	hesitation	NOUN
ejpam-5627	31	38	,	,	PUNCT
ejpam-5627	31	39	offering	offer	VERB
ejpam-5627	31	40	a	a	DET
ejpam-5627	31	41	robust	robust	ADJ
ejpam-5627	31	42	framework	framework	NOUN
ejpam-5627	31	43	for	for	ADP
ejpam-5627	31	44	modeling	model	VERB
ejpam-5627	31	45	uncertainty	uncertainty	NOUN
ejpam-5627	31	46	.	.	PUNCT
ejpam-5627	32	1	satisfying	satisfy	VERB
ejpam-5627	32	2	the	the	DET
ejpam-5627	32	3	condition	condition	NOUN
ejpam-5627	32	4	0	0	NUM
ejpam-5627	32	5	≤	≤	NOUN
ejpam-5627	32	6	µ(x)+	µ(x)+	ADP
ejpam-5627	32	7	ν(x	ν(x	PROPN
ejpam-5627	32	8	)	)	PUNCT
ejpam-5627	32	9	≤	≤	NUM
ejpam-5627	32	10	1	1	NUM
ejpam-5627	32	11	,	,	PUNCT
ejpam-5627	32	12	ifss	ifss	NOUN
ejpam-5627	32	13	have	have	AUX
ejpam-5627	32	14	proven	prove	VERB
ejpam-5627	32	15	to	to	PART
ejpam-5627	32	16	be	be	AUX
ejpam-5627	32	17	highly	highly	ADV
ejpam-5627	32	18	adaptable	adaptable	ADJ
ejpam-5627	32	19	for	for	ADP
ejpam-5627	32	20	analyzing	analyze	VERB
ejpam-5627	32	21	imprecise	imprecise	ADJ
ejpam-5627	32	22	information	information	NOUN
ejpam-5627	32	23	and	and	CCONJ
ejpam-5627	32	24	complex	complex	ADJ
ejpam-5627	32	25	systems	system	NOUN
ejpam-5627	32	26	.	.	PUNCT
ejpam-5627	33	1	their	their	PRON
ejpam-5627	33	2	mathematical	mathematical	ADJ
ejpam-5627	33	3	flexibility	flexibility	NOUN
ejpam-5627	33	4	has	have	AUX
ejpam-5627	33	5	spurred	spur	VERB
ejpam-5627	33	6	extensive	extensive	ADJ
ejpam-5627	33	7	research	research	NOUN
ejpam-5627	33	8	in	in	ADP
ejpam-5627	33	9	various	various	ADJ
ejpam-5627	33	10	algebraic	algebraic	ADJ
ejpam-5627	33	11	systems	system	NOUN
ejpam-5627	33	12	,	,	PUNCT
ejpam-5627	33	13	such	such	ADJ
ejpam-5627	33	14	as	as	ADP
ejpam-5627	33	15	groups	group	NOUN
ejpam-5627	33	16	,	,	PUNCT
ejpam-5627	33	17	rings	ring	NOUN
ejpam-5627	33	18	,	,	PUNCT
ejpam-5627	33	19	semirings	semiring	NOUN
ejpam-5627	33	20	,	,	PUNCT
ejpam-5627	33	21	lattices	lattice	NOUN
ejpam-5627	33	22	,	,	PUNCT
ejpam-5627	33	23	and	and	CCONJ
ejpam-5627	33	24	up	up	ADP
ejpam-5627	33	25	-	-	PUNCT
ejpam-5627	33	26	algebras	algebras	X
ejpam-5627	33	27	,	,	PUNCT
ejpam-5627	33	28	where	where	SCONJ
ejpam-5627	33	29	ifss	ifss	NOUN
ejpam-5627	33	30	facilitate	facilitate	NOUN
ejpam-5627	33	31	the	the	DET
ejpam-5627	33	32	study	study	NOUN
ejpam-5627	33	33	of	of	ADP
ejpam-5627	33	34	generalized	generalized	ADJ
ejpam-5627	33	35	structures	structure	NOUN
ejpam-5627	33	36	,	,	PUNCT
ejpam-5627	33	37	ideals	ideal	NOUN
ejpam-5627	33	38	,	,	PUNCT
ejpam-5627	33	39	and	and	CCONJ
ejpam-5627	33	40	filters	filter	VERB
ejpam-5627	33	41	under	under	ADP
ejpam-5627	33	42	uncertain	uncertain	ADJ
ejpam-5627	33	43	conditions	condition	NOUN
ejpam-5627	33	44	.	.	PUNCT
ejpam-5627	34	1	for	for	ADP
ejpam-5627	34	2	example	example	NOUN
ejpam-5627	34	3	,	,	PUNCT
ejpam-5627	34	4	platil	platil	NOUN
ejpam-5627	34	5	and	and	CCONJ
ejpam-5627	34	6	tanaka	tanaka	PROPN
ejpam-5627	35	1	[	[	X
ejpam-5627	35	2	10	10	NUM
ejpam-5627	35	3	]	]	PUNCT
ejpam-5627	35	4	applied	apply	VERB
ejpam-5627	35	5	ifss	ifss	NOUN
ejpam-5627	35	6	in	in	ADP
ejpam-5627	35	7	multi	multi	ADJ
ejpam-5627	35	8	-	-	ADJ
ejpam-5627	35	9	criteria	criterion	NOUN
ejpam-5627	35	10	evaluation	evaluation	NOUN
ejpam-5627	35	11	based	base	VERB
ejpam-5627	35	12	on	on	ADP
ejpam-5627	35	13	set	set	NOUN
ejpam-5627	35	14	-	-	PUNCT
ejpam-5627	35	15	relations	relation	NOUN
ejpam-5627	35	16	,	,	PUNCT
ejpam-5627	35	17	demonstrating	demonstrate	VERB
ejpam-5627	35	18	their	their	PRON
ejpam-5627	35	19	relevance	relevance	NOUN
ejpam-5627	35	20	in	in	ADP
ejpam-5627	35	21	decision	decision	NOUN
ejpam-5627	35	22	-	-	PUNCT
ejpam-5627	35	23	making	make	VERB
ejpam-5627	35	24	frameworks	framework	NOUN
ejpam-5627	35	25	.	.	PUNCT
ejpam-5627	36	1	kesorn	kesorn	PROPN
ejpam-5627	36	2	et	et	PROPN
ejpam-5627	36	3	al	al	PROPN
ejpam-5627	36	4	.	.	PUNCT
ejpam-5627	37	1	[	[	X
ejpam-5627	37	2	6	6	NUM
ejpam-5627	37	3	]	]	PUNCT
ejpam-5627	37	4	specifically	specifically	ADV
ejpam-5627	37	5	investigated	investigate	VERB
ejpam-5627	37	6	intuitionistic	intuitionistic	ADJ
ejpam-5627	37	7	fuzzy	fuzzy	ADJ
ejpam-5627	37	8	sets	set	NOUN
ejpam-5627	37	9	in	in	ADP
ejpam-5627	37	10	up	up	ADP
ejpam-5627	37	11	-	-	PUNCT
ejpam-5627	37	12	algebras	algebras	X
ejpam-5627	37	13	,	,	PUNCT
ejpam-5627	37	14	offering	offer	VERB
ejpam-5627	37	15	a	a	DET
ejpam-5627	37	16	direct	direct	ADJ
ejpam-5627	37	17	connection	connection	NOUN
ejpam-5627	37	18	to	to	ADP
ejpam-5627	37	19	the	the	DET
ejpam-5627	37	20	present	present	ADJ
ejpam-5627	37	21	study	study	NOUN
ejpam-5627	37	22	.	.	PUNCT
ejpam-5627	38	1	their	their	PRON
ejpam-5627	38	2	analysis	analysis	NOUN
ejpam-5627	38	3	of	of	ADP
ejpam-5627	38	4	intuitionistic	intuitionistic	ADJ
ejpam-5627	38	5	fuzzy	fuzzy	ADJ
ejpam-5627	38	6	filters	filter	NOUN
ejpam-5627	38	7	and	and	CCONJ
ejpam-5627	38	8	ideals	ideal	NOUN
ejpam-5627	38	9	in	in	ADP
ejpam-5627	38	10	up	up	ADV
ejpam-5627	38	11	-	-	PUNCT
ejpam-5627	38	12	algebras	algebras	NOUN
ejpam-5627	38	13	highlights	highlight	VERB
ejpam-5627	38	14	the	the	DET
ejpam-5627	38	15	potential	potential	NOUN
ejpam-5627	38	16	for	for	ADP
ejpam-5627	38	17	applying	apply	VERB
ejpam-5627	38	18	intuitionistic	intuitionistic	ADJ
ejpam-5627	38	19	fuzzy	fuzzy	ADJ
ejpam-5627	38	20	logic	logic	NOUN
ejpam-5627	38	21	to	to	ADP
ejpam-5627	38	22	broader	broad	ADJ
ejpam-5627	38	23	classes	class	NOUN
ejpam-5627	38	24	of	of	ADP
ejpam-5627	38	25	algebraic	algebraic	ADJ
ejpam-5627	38	26	operations	operation	NOUN
ejpam-5627	38	27	.	.	PUNCT
ejpam-5627	39	1	adak	adak	NOUN
ejpam-5627	39	2	et	et	PROPN
ejpam-5627	39	3	al	al	PROPN
ejpam-5627	39	4	.	.	PUNCT
ejpam-5627	40	1	[	[	X
ejpam-5627	40	2	1	1	X
ejpam-5627	40	3	]	]	PUNCT
ejpam-5627	40	4	explored	explore	VERB
ejpam-5627	40	5	the	the	DET
ejpam-5627	40	6	properties	property	NOUN
ejpam-5627	40	7	of	of	ADP
ejpam-5627	40	8	generalized	generalized	ADJ
ejpam-5627	40	9	intuitionistic	intuitionistic	ADJ
ejpam-5627	40	10	fuzzy	fuzzy	ADJ
ejpam-5627	40	11	nilpotent	nilpotent	ADJ
ejpam-5627	40	12	matrices	matrix	NOUN
ejpam-5627	40	13	over	over	ADP
ejpam-5627	40	14	distributive	distributive	ADJ
ejpam-5627	40	15	lattices	lattice	NOUN
ejpam-5627	40	16	,	,	PUNCT
ejpam-5627	40	17	while	while	SCONJ
ejpam-5627	40	18	ebrahimnejad	ebrahimnejad	PROPN
ejpam-5627	40	19	et	et	PROPN
ejpam-5627	40	20	al	al	PROPN
ejpam-5627	40	21	.	.	PUNCT
ejpam-5627	41	1	[	[	X
ejpam-5627	41	2	4	4	NUM
ejpam-5627	41	3	]	]	PUNCT
ejpam-5627	41	4	investigated	investigate	VERB
ejpam-5627	41	5	eigenvalues	eigenvalue	NOUN
ejpam-5627	41	6	of	of	ADP
ejpam-5627	41	7	intuitionistic	intuitionistic	ADJ
ejpam-5627	41	8	fuzzy	fuzzy	ADJ
ejpam-5627	41	9	matrices	matrix	NOUN
ejpam-5627	41	10	,	,	PUNCT
ejpam-5627	41	11	extending	extend	VERB
ejpam-5627	41	12	matrix	matrix	NOUN
ejpam-5627	41	13	theory	theory	NOUN
ejpam-5627	41	14	within	within	ADP
ejpam-5627	41	15	a	a	DET
ejpam-5627	41	16	fuzzy	fuzzy	ADJ
ejpam-5627	41	17	context	context	NOUN
ejpam-5627	41	18	.	.	PUNCT
ejpam-5627	42	1	additionally	additionally	ADV
ejpam-5627	42	2	,	,	PUNCT
ejpam-5627	42	3	adak	adak	PROPN
ejpam-5627	42	4	et	et	PROPN
ejpam-5627	42	5	al	al	PROPN
ejpam-5627	42	6	.	.	PUNCT
ejpam-5627	43	1	[	[	X
ejpam-5627	43	2	2	2	NUM
ejpam-5627	43	3	]	]	PUNCT
ejpam-5627	43	4	developed	develop	VERB
ejpam-5627	43	5	a	a	DET
ejpam-5627	43	6	ranking	ranking	NOUN
ejpam-5627	43	7	method	method	NOUN
ejpam-5627	43	8	for	for	ADP
ejpam-5627	43	9	multi	multi	ADJ
ejpam-5627	43	10	-	-	ADJ
ejpam-5627	43	11	criteria	criterion	NOUN
ejpam-5627	43	12	decision	decision	NOUN
ejpam-5627	43	13	-	-	PUNCT
ejpam-5627	43	14	making	make	VERB
ejpam-5627	43	15	problems	problem	NOUN
ejpam-5627	43	16	utilizing	utilize	VERB
ejpam-5627	43	17	generalized	generalized	ADJ
ejpam-5627	43	18	intuitionistic	intuitionistic	ADJ
ejpam-5627	43	19	fuzzy	fuzzy	ADJ
ejpam-5627	43	20	information	information	NOUN
ejpam-5627	43	21	,	,	PUNCT
ejpam-5627	43	22	highlighting	highlight	VERB
ejpam-5627	43	23	real	real	ADJ
ejpam-5627	43	24	-	-	PUNCT
ejpam-5627	43	25	world	world	NOUN
ejpam-5627	43	26	applications	application	NOUN
ejpam-5627	43	27	of	of	ADP
ejpam-5627	43	28	ifss	ifss	NOUN
ejpam-5627	43	29	in	in	ADP
ejpam-5627	43	30	areas	area	NOUN
ejpam-5627	43	31	such	such	ADJ
ejpam-5627	43	32	as	as	ADP
ejpam-5627	43	33	engineering	engineering	NOUN
ejpam-5627	43	34	and	and	CCONJ
ejpam-5627	43	35	operations	operation	NOUN
ejpam-5627	43	36	research	research	NOUN
ejpam-5627	43	37	.	.	PUNCT
ejpam-5627	44	1	furthermore	furthermore	ADV
ejpam-5627	44	2	,	,	PUNCT
ejpam-5627	44	3	the	the	DET
ejpam-5627	44	4	integration	integration	NOUN
ejpam-5627	44	5	of	of	ADP
ejpam-5627	44	6	ifss	ifss	NOUN
ejpam-5627	44	7	into	into	ADP
ejpam-5627	44	8	algebraic	algebraic	ADJ
ejpam-5627	44	9	frameworks	framework	NOUN
ejpam-5627	44	10	like	like	ADP
ejpam-5627	44	11	sheffer	sheffer	NOUN
ejpam-5627	44	12	stroke	stroke	NOUN
ejpam-5627	44	13	up	up	ADP
ejpam-5627	44	14	-	-	PUNCT
ejpam-5627	44	15	algebras	algebras	PROPN
ejpam-5627	44	16	has	have	AUX
ejpam-5627	44	17	unveiled	unveil	VERB
ejpam-5627	44	18	deeper	deep	ADJ
ejpam-5627	44	19	connections	connection	NOUN
ejpam-5627	44	20	between	between	ADP
ejpam-5627	44	21	fuzzy	fuzzy	ADJ
ejpam-5627	44	22	logic	logic	NOUN
ejpam-5627	44	23	principles	principle	NOUN
ejpam-5627	44	24	and	and	CCONJ
ejpam-5627	44	25	algebraic	algebraic	ADJ
ejpam-5627	44	26	operations	operation	NOUN
ejpam-5627	44	27	,	,	PUNCT
ejpam-5627	44	28	underscoring	underscore	VERB
ejpam-5627	44	29	their	their	PRON
ejpam-5627	44	30	transformative	transformative	ADJ
ejpam-5627	44	31	potential	potential	NOUN
ejpam-5627	44	32	.	.	PUNCT
ejpam-5627	45	1	these	these	DET
ejpam-5627	45	2	advancements	advancement	NOUN
ejpam-5627	45	3	confirm	confirm	VERB
ejpam-5627	45	4	the	the	DET
ejpam-5627	45	5	enduring	endure	VERB
ejpam-5627	45	6	significance	significance	NOUN
ejpam-5627	45	7	of	of	ADP
ejpam-5627	45	8	ifss	ifss	NOUN
ejpam-5627	45	9	in	in	ADP
ejpam-5627	45	10	both	both	CCONJ
ejpam-5627	45	11	theoretical	theoretical	ADJ
ejpam-5627	45	12	explorations	exploration	NOUN
ejpam-5627	45	13	and	and	CCONJ
ejpam-5627	45	14	practical	practical	ADJ
ejpam-5627	45	15	n.	n.	PROPN
ejpam-5627	45	16	rajesh	rajesh	PROPN
ejpam-5627	45	17	,	,	PUNCT
ejpam-5627	45	18	t.	t.	PROPN
ejpam-5627	45	19	oner	oner	NOUN
ejpam-5627	45	20	,	,	PUNCT
ejpam-5627	45	21	a.	a.	NOUN
ejpam-5627	45	22	iampan	iampan	PROPN
ejpam-5627	45	23	,	,	PUNCT
ejpam-5627	45	24	i.	i.	PROPN
ejpam-5627	45	25	senturk	senturk	PROPN
ejpam-5627	45	26	/	/	SYM
ejpam-5627	45	27	eur	eur	PROPN
ejpam-5627	45	28	.	.	PUNCT
ejpam-5627	46	1	j.	j.	PROPN
ejpam-5627	46	2	pure	pure	PROPN
ejpam-5627	46	3	appl	appl	PROPN
ejpam-5627	46	4	.	.	PROPN
ejpam-5627	46	5	math	math	PROPN
ejpam-5627	46	6	,	,	PUNCT
ejpam-5627	46	7	18	18	NUM
ejpam-5627	46	8	(	(	PUNCT
ejpam-5627	46	9	1	1	NUM
ejpam-5627	46	10	)	)	PUNCT
ejpam-5627	46	11	(	(	PUNCT
ejpam-5627	46	12	2025	2025	NUM
ejpam-5627	46	13	)	)	PUNCT
ejpam-5627	46	14	,	,	PUNCT
ejpam-5627	46	15	5627	5627	NUM
ejpam-5627	46	16	3	3	NUM
ejpam-5627	46	17	of	of	ADP
ejpam-5627	46	18	15	15	NUM
ejpam-5627	46	19	problem	problem	NOUN
ejpam-5627	46	20	-	-	PUNCT
ejpam-5627	46	21	solving	solving	NOUN
ejpam-5627	46	22	,	,	PUNCT
ejpam-5627	46	23	ensuring	ensure	VERB
ejpam-5627	46	24	their	their	PRON
ejpam-5627	46	25	continued	continue	VERB
ejpam-5627	46	26	relevance	relevance	NOUN
ejpam-5627	46	27	in	in	ADP
ejpam-5627	46	28	modern	modern	ADJ
ejpam-5627	46	29	mathematical	mathematical	ADJ
ejpam-5627	46	30	and	and	CCONJ
ejpam-5627	46	31	computational	computational	ADJ
ejpam-5627	46	32	studies	study	NOUN
ejpam-5627	46	33	.	.	PUNCT
ejpam-5627	47	1	in	in	ADP
ejpam-5627	47	2	this	this	DET
ejpam-5627	47	3	paper	paper	NOUN
ejpam-5627	47	4	,	,	PUNCT
ejpam-5627	47	5	we	we	PRON
ejpam-5627	47	6	define	define	VERB
ejpam-5627	47	7	an	an	DET
ejpam-5627	47	8	intuitionistic	intuitionistic	ADJ
ejpam-5627	47	9	fuzzy	fuzzy	ADJ
ejpam-5627	47	10	sup	sup	ADJ
ejpam-5627	47	11	-	-	PUNCT
ejpam-5627	47	12	subalgebra	subalgebra	NOUN
ejpam-5627	47	13	and	and	CCONJ
ejpam-5627	47	14	a	a	DET
ejpam-5627	47	15	level	level	NOUN
ejpam-5627	47	16	set	set	NOUN
ejpam-5627	47	17	of	of	ADP
ejpam-5627	47	18	an	an	DET
ejpam-5627	47	19	intuitionistic	intuitionistic	ADJ
ejpam-5627	47	20	fuzzy	fuzzy	ADJ
ejpam-5627	47	21	up	up	NOUN
ejpam-5627	47	22	-	-	PUNCT
ejpam-5627	47	23	structure	structure	NOUN
ejpam-5627	47	24	on	on	ADP
ejpam-5627	47	25	sheffer	sheffer	PROPN
ejpam-5627	47	26	stroke	stroke	PROPN
ejpam-5627	47	27	up	up	ADP
ejpam-5627	47	28	-	-	PUNCT
ejpam-5627	47	29	algebras	algebras	X
ejpam-5627	47	30	.	.	PUNCT
ejpam-5627	48	1	it	it	PRON
ejpam-5627	48	2	appears	appear	VERB
ejpam-5627	48	3	that	that	SCONJ
ejpam-5627	48	4	these	these	DET
ejpam-5627	48	5	concepts	concept	NOUN
ejpam-5627	48	6	are	be	AUX
ejpam-5627	48	7	integral	integral	ADJ
ejpam-5627	48	8	to	to	ADP
ejpam-5627	48	9	understanding	understand	VERB
ejpam-5627	48	10	the	the	DET
ejpam-5627	48	11	behavior	behavior	NOUN
ejpam-5627	48	12	of	of	ADP
ejpam-5627	48	13	neutrosophic	neutrosophic	ADJ
ejpam-5627	48	14	logic	logic	NOUN
ejpam-5627	48	15	within	within	ADP
ejpam-5627	48	16	the	the	DET
ejpam-5627	48	17	framework	framework	NOUN
ejpam-5627	48	18	of	of	ADP
ejpam-5627	48	19	sheffer	sheffer	PROPN
ejpam-5627	48	20	stroke	stroke	PROPN
ejpam-5627	48	21	up	up	ADP
ejpam-5627	48	22	-	-	PUNCT
ejpam-5627	48	23	algebras	algebras	X
ejpam-5627	48	24	.	.	PUNCT
ejpam-5627	49	1	the	the	DET
ejpam-5627	49	2	study	study	NOUN
ejpam-5627	49	3	establishes	establish	VERB
ejpam-5627	49	4	a	a	DET
ejpam-5627	49	5	relationship	relationship	NOUN
ejpam-5627	49	6	between	between	ADP
ejpam-5627	49	7	subalgebras	subalgebra	NOUN
ejpam-5627	49	8	and	and	CCONJ
ejpam-5627	49	9	level	level	NOUN
ejpam-5627	49	10	sets	set	NOUN
ejpam-5627	49	11	on	on	ADP
ejpam-5627	49	12	sheffer	sheffer	PROPN
ejpam-5627	49	13	stroke	stroke	NOUN
ejpam-5627	49	14	up	up	ADP
ejpam-5627	49	15	-	-	PUNCT
ejpam-5627	49	16	algebras	algebras	X
ejpam-5627	49	17	.	.	PUNCT
ejpam-5627	50	1	specifically	specifically	ADV
ejpam-5627	50	2	,	,	PUNCT
ejpam-5627	50	3	it	it	PRON
ejpam-5627	50	4	proves	prove	VERB
ejpam-5627	50	5	that	that	SCONJ
ejpam-5627	50	6	the	the	DET
ejpam-5627	50	7	level	level	NOUN
ejpam-5627	50	8	set	set	NOUN
ejpam-5627	50	9	of	of	ADP
ejpam-5627	50	10	intuitionistic	intuitionistic	ADJ
ejpam-5627	50	11	fuzzy	fuzzy	ADJ
ejpam-5627	50	12	sup	sup	NOUN
ejpam-5627	50	13	-	-	PUNCT
ejpam-5627	50	14	subalgebras	subalgebras	NOUN
ejpam-5627	50	15	on	on	ADP
ejpam-5627	50	16	this	this	DET
ejpam-5627	50	17	algebra	algebra	NOUN
ejpam-5627	50	18	is	be	AUX
ejpam-5627	50	19	its	its	PRON
ejpam-5627	50	20	subalgebra	subalgebra	NOUN
ejpam-5627	50	21	,	,	PUNCT
ejpam-5627	50	22	and	and	CCONJ
ejpam-5627	50	23	vice	vice	ADV
ejpam-5627	50	24	versa	versa	ADV
ejpam-5627	50	25	.	.	PUNCT
ejpam-5627	51	1	this	this	PRON
ejpam-5627	51	2	indicates	indicate	VERB
ejpam-5627	51	3	a	a	DET
ejpam-5627	51	4	tight	tight	ADJ
ejpam-5627	51	5	connection	connection	NOUN
ejpam-5627	51	6	between	between	ADP
ejpam-5627	51	7	two	two	NUM
ejpam-5627	51	8	concepts	concept	NOUN
ejpam-5627	51	9	within	within	ADP
ejpam-5627	51	10	the	the	DET
ejpam-5627	51	11	given	give	VERB
ejpam-5627	51	12	algebraic	algebraic	ADJ
ejpam-5627	51	13	structure	structure	NOUN
ejpam-5627	51	14	.	.	PUNCT
ejpam-5627	52	1	it	it	PRON
ejpam-5627	52	2	is	be	AUX
ejpam-5627	52	3	stated	state	VERB
ejpam-5627	52	4	that	that	SCONJ
ejpam-5627	52	5	the	the	DET
ejpam-5627	52	6	family	family	NOUN
ejpam-5627	52	7	of	of	ADP
ejpam-5627	52	8	all	all	DET
ejpam-5627	52	9	intuitionistic	intuitionistic	ADJ
ejpam-5627	52	10	fuzzy	fuzzy	ADJ
ejpam-5627	52	11	sup	sup	NOUN
ejpam-5627	52	12	-	-	PUNCT
ejpam-5627	52	13	subalgebras	subalgebras	NOUN
ejpam-5627	52	14	of	of	ADP
ejpam-5627	52	15	a	a	DET
ejpam-5627	52	16	sheffer	sheffer	NOUN
ejpam-5627	52	17	stroke	stroke	NOUN
ejpam-5627	52	18	up	up	ADP
ejpam-5627	52	19	-	-	PUNCT
ejpam-5627	52	20	algebra	algebra	NOUN
ejpam-5627	52	21	forms	form	VERB
ejpam-5627	52	22	a	a	DET
ejpam-5627	52	23	complete	complete	ADJ
ejpam-5627	52	24	distributive	distributive	ADJ
ejpam-5627	52	25	lattice	lattice	NOUN
ejpam-5627	52	26	.	.	PUNCT
ejpam-5627	53	1	this	this	PRON
ejpam-5627	53	2	suggests	suggest	VERB
ejpam-5627	53	3	that	that	SCONJ
ejpam-5627	53	4	there	there	PRON
ejpam-5627	53	5	is	be	VERB
ejpam-5627	53	6	a	a	DET
ejpam-5627	53	7	well	well	ADV
ejpam-5627	53	8	-	-	PUNCT
ejpam-5627	53	9	defined	define	VERB
ejpam-5627	53	10	structure	structure	NOUN
ejpam-5627	53	11	and	and	CCONJ
ejpam-5627	53	12	order	order	NOUN
ejpam-5627	53	13	among	among	ADP
ejpam-5627	53	14	these	these	DET
ejpam-5627	53	15	subalgebras	subalgebra	NOUN
ejpam-5627	53	16	,	,	PUNCT
ejpam-5627	53	17	allowing	allow	VERB
ejpam-5627	53	18	for	for	ADP
ejpam-5627	53	19	systematic	systematic	ADJ
ejpam-5627	53	20	analysis	analysis	NOUN
ejpam-5627	53	21	.	.	PUNCT
ejpam-5627	54	1	the	the	DET
ejpam-5627	54	2	study	study	NOUN
ejpam-5627	54	3	describes	describe	VERB
ejpam-5627	54	4	an	an	DET
ejpam-5627	54	5	intuitionistic	intuitionistic	ADJ
ejpam-5627	54	6	fuzzy	fuzzy	ADJ
ejpam-5627	54	7	sup	sup	NOUN
ejpam-5627	54	8	-	-	PUNCT
ejpam-5627	54	9	ideal	ideal	NOUN
ejpam-5627	54	10	of	of	ADP
ejpam-5627	54	11	a	a	DET
ejpam-5627	54	12	sheffer	sheffer	NOUN
ejpam-5627	54	13	stroke	stroke	NOUN
ejpam-5627	54	14	up	up	ADP
ejpam-5627	54	15	-	-	PUNCT
ejpam-5627	54	16	algebra	algebra	NOUN
ejpam-5627	54	17	and	and	CCONJ
ejpam-5627	54	18	provides	provide	VERB
ejpam-5627	54	19	some	some	DET
ejpam-5627	54	20	properties	property	NOUN
ejpam-5627	54	21	.	.	PUNCT
ejpam-5627	55	1	additionally	additionally	ADV
ejpam-5627	55	2	,	,	PUNCT
ejpam-5627	55	3	it	it	PRON
ejpam-5627	55	4	is	be	AUX
ejpam-5627	55	5	shown	show	VERB
ejpam-5627	55	6	that	that	SCONJ
ejpam-5627	55	7	every	every	DET
ejpam-5627	55	8	intuitionistic	intuitionistic	ADJ
ejpam-5627	55	9	fuzzy	fuzzy	ADJ
ejpam-5627	55	10	sup	sup	NOUN
ejpam-5627	55	11	-	-	PUNCT
ejpam-5627	55	12	ideal	ideal	NOUN
ejpam-5627	55	13	of	of	ADP
ejpam-5627	55	14	a	a	DET
ejpam-5627	55	15	sheffer	sheffer	NOUN
ejpam-5627	55	16	stroke	stroke	NOUN
ejpam-5627	55	17	up	up	ADP
ejpam-5627	55	18	-	-	PUNCT
ejpam-5627	55	19	algebra	algebra	NOUN
ejpam-5627	55	20	is	be	AUX
ejpam-5627	55	21	also	also	ADV
ejpam-5627	55	22	its	its	PRON
ejpam-5627	55	23	intuitionistic	intuitionistic	ADJ
ejpam-5627	55	24	fuzzy	fuzzy	ADJ
ejpam-5627	55	25	sup	sup	NOUN
ejpam-5627	55	26	-	-	PUNCT
ejpam-5627	55	27	subalgebra	subalgebra	NOUN
ejpam-5627	55	28	,	,	PUNCT
ejpam-5627	55	29	though	though	SCONJ
ejpam-5627	55	30	the	the	DET
ejpam-5627	55	31	inverse	inverse	NOUN
ejpam-5627	55	32	is	be	AUX
ejpam-5627	55	33	generally	generally	ADV
ejpam-5627	55	34	not	not	PART
ejpam-5627	55	35	true	true	ADJ
ejpam-5627	55	36	.	.	PUNCT
ejpam-5627	56	1	this	this	DET
ejpam-5627	56	2	highlights	highlight	VERB
ejpam-5627	56	3	the	the	DET
ejpam-5627	56	4	specific	specific	ADJ
ejpam-5627	56	5	characteristics	characteristic	NOUN
ejpam-5627	56	6	and	and	CCONJ
ejpam-5627	56	7	behavior	behavior	NOUN
ejpam-5627	56	8	of	of	ADP
ejpam-5627	56	9	intuitionistic	intuitionistic	ADJ
ejpam-5627	56	10	fuzzy	fuzzy	ADJ
ejpam-5627	56	11	sup	sup	NOUN
ejpam-5627	56	12	-	-	PUNCT
ejpam-5627	56	13	ideals	ideal	NOUN
ejpam-5627	56	14	within	within	ADP
ejpam-5627	56	15	the	the	DET
ejpam-5627	56	16	given	give	VERB
ejpam-5627	56	17	algebraic	algebraic	ADJ
ejpam-5627	56	18	context	context	NOUN
ejpam-5627	56	19	.	.	PUNCT
ejpam-5627	57	1	2	2	X
ejpam-5627	57	2	.	.	X
ejpam-5627	57	3	preliminaries	preliminary	NOUN
ejpam-5627	57	4	sheffer	sheffer	VERB
ejpam-5627	57	5	stroke	stroke	NOUN
ejpam-5627	57	6	up	up	ADP
ejpam-5627	57	7	-	-	PUNCT
ejpam-5627	57	8	algebras	algebras	PROPN
ejpam-5627	57	9	represent	represent	VERB
ejpam-5627	57	10	a	a	DET
ejpam-5627	57	11	compelling	compelling	ADJ
ejpam-5627	57	12	intersection	intersection	NOUN
ejpam-5627	57	13	of	of	ADP
ejpam-5627	57	14	algebra	algebra	NOUN
ejpam-5627	57	15	and	and	CCONJ
ejpam-5627	57	16	logic	logic	NOUN
ejpam-5627	57	17	,	,	PUNCT
ejpam-5627	57	18	characterized	characterize	VERB
ejpam-5627	57	19	by	by	ADP
ejpam-5627	57	20	the	the	DET
ejpam-5627	57	21	sheffer	sheffer	PROPN
ejpam-5627	57	22	stroke	stroke	NOUN
ejpam-5627	57	23	operation	operation	NOUN
ejpam-5627	57	24	,	,	PUNCT
ejpam-5627	57	25	a	a	DET
ejpam-5627	57	26	key	key	ADJ
ejpam-5627	57	27	connective	connective	NOUN
ejpam-5627	57	28	in	in	ADP
ejpam-5627	57	29	propositional	propositional	ADJ
ejpam-5627	57	30	calculus	calculus	NOUN
ejpam-5627	57	31	.	.	PUNCT
ejpam-5627	58	1	this	this	DET
ejpam-5627	58	2	algebraic	algebraic	ADJ
ejpam-5627	58	3	structure	structure	NOUN
ejpam-5627	58	4	not	not	PART
ejpam-5627	58	5	only	only	ADV
ejpam-5627	58	6	enhances	enhance	VERB
ejpam-5627	58	7	our	our	PRON
ejpam-5627	58	8	understanding	understanding	NOUN
ejpam-5627	58	9	of	of	ADP
ejpam-5627	58	10	logical	logical	ADJ
ejpam-5627	58	11	operations	operation	NOUN
ejpam-5627	58	12	but	but	CCONJ
ejpam-5627	58	13	also	also	ADV
ejpam-5627	58	14	has	have	VERB
ejpam-5627	58	15	significant	significant	ADJ
ejpam-5627	58	16	implications	implication	NOUN
ejpam-5627	58	17	in	in	ADP
ejpam-5627	58	18	fields	field	NOUN
ejpam-5627	58	19	like	like	ADP
ejpam-5627	58	20	computer	computer	NOUN
ejpam-5627	58	21	science	science	NOUN
ejpam-5627	58	22	and	and	CCONJ
ejpam-5627	58	23	decision	decision	NOUN
ejpam-5627	58	24	theory	theory	NOUN
ejpam-5627	58	25	.	.	PUNCT
ejpam-5627	59	1	this	this	DET
ejpam-5627	59	2	article	article	NOUN
ejpam-5627	59	3	will	will	AUX
ejpam-5627	59	4	delve	delve	VERB
ejpam-5627	59	5	into	into	ADP
ejpam-5627	59	6	the	the	DET
ejpam-5627	59	7	definitions	definition	NOUN
ejpam-5627	59	8	and	and	CCONJ
ejpam-5627	59	9	foundational	foundational	ADJ
ejpam-5627	59	10	aspects	aspect	NOUN
ejpam-5627	59	11	of	of	ADP
ejpam-5627	59	12	sheffer	sheffer	PROPN
ejpam-5627	59	13	stroke	stroke	PROPN
ejpam-5627	59	14	up	up	ADP
ejpam-5627	59	15	-	-	PUNCT
ejpam-5627	59	16	algebras	algebras	X
ejpam-5627	59	17	,	,	PUNCT
ejpam-5627	59	18	highlighting	highlight	VERB
ejpam-5627	59	19	their	their	PRON
ejpam-5627	59	20	relevance	relevance	NOUN
ejpam-5627	59	21	within	within	ADP
ejpam-5627	59	22	algebraic	algebraic	ADJ
ejpam-5627	59	23	theory	theory	NOUN
ejpam-5627	59	24	.	.	PUNCT
ejpam-5627	60	1	definition	definition	NOUN
ejpam-5627	60	2	1	1	NUM
ejpam-5627	60	3	.	.	PUNCT
ejpam-5627	61	1	[	[	X
ejpam-5627	61	2	12	12	NUM
ejpam-5627	61	3	]	]	PUNCT
ejpam-5627	61	4	let	let	VERB
ejpam-5627	61	5	h	h	NOUN
ejpam-5627	61	6	=	=	SYM
ejpam-5627	61	7	⟨h	⟨h	PROPN
ejpam-5627	61	8	,	,	PUNCT
ejpam-5627	61	9	|⟩	|⟩	PROPN
ejpam-5627	61	10	be	be	VERB
ejpam-5627	61	11	a	a	DET
ejpam-5627	61	12	groupoid	groupoid	NOUN
ejpam-5627	61	13	.	.	PUNCT
ejpam-5627	62	1	the	the	DET
ejpam-5627	62	2	operation	operation	NOUN
ejpam-5627	62	3	|	|	ADV
ejpam-5627	62	4	is	be	AUX
ejpam-5627	62	5	said	say	VERB
ejpam-5627	62	6	to	to	PART
ejpam-5627	62	7	be	be	AUX
ejpam-5627	62	8	a	a	DET
ejpam-5627	62	9	sheffer	sheffer	NOUN
ejpam-5627	62	10	stroke	stroke	NOUN
ejpam-5627	62	11	operation	operation	NOUN
ejpam-5627	62	12	if	if	SCONJ
ejpam-5627	62	13	it	it	PRON
ejpam-5627	62	14	satisfies	satisfy	VERB
ejpam-5627	62	15	the	the	DET
ejpam-5627	62	16	following	follow	VERB
ejpam-5627	62	17	conditions	condition	NOUN
ejpam-5627	62	18	:	:	PUNCT
ejpam-5627	62	19	for	for	ADP
ejpam-5627	62	20	all	all	DET
ejpam-5627	62	21	x	x	NOUN
ejpam-5627	62	22	,	,	PUNCT
ejpam-5627	62	23	y	y	PROPN
ejpam-5627	62	24	,	,	PUNCT
ejpam-5627	62	25	z	z	PROPN
ejpam-5627	62	26	∈	∈	PROPN
ejpam-5627	62	27	h	h	NOUN
ejpam-5627	62	28	,	,	PUNCT
ejpam-5627	62	29	(	(	PUNCT
ejpam-5627	62	30	s-1	s-1	PROPN
ejpam-5627	62	31	)	)	PUNCT
ejpam-5627	62	32	x|y	x|y	PUNCT
ejpam-5627	63	1	=	=	PUNCT
ejpam-5627	63	2	y|x	y|x	PROPN
ejpam-5627	63	3	(	(	PUNCT
ejpam-5627	63	4	s-2	s-2	PROPN
ejpam-5627	63	5	)	)	PUNCT
ejpam-5627	63	6	(	(	PUNCT
ejpam-5627	63	7	x|x)|(x|y	x|x)|(x|y	PROPN
ejpam-5627	63	8	)	)	PUNCT
ejpam-5627	64	1	=	=	SYM
ejpam-5627	64	2	x	x	X
ejpam-5627	64	3	(	(	PUNCT
ejpam-5627	64	4	s-3	s-3	NUM
ejpam-5627	64	5	)	)	PUNCT
ejpam-5627	64	6	x|((y|z)|(y|z	x|((y|z)|(y|z	NUM
ejpam-5627	64	7	)	)	PUNCT
ejpam-5627	64	8	)	)	PUNCT
ejpam-5627	65	1	=	=	SYM
ejpam-5627	65	2	(	(	PUNCT
ejpam-5627	65	3	(	(	PUNCT
ejpam-5627	65	4	x|y)|(x|y))|z	x|y)|(x|y))|z	X
ejpam-5627	65	5	(	(	PUNCT
ejpam-5627	65	6	s-4	s-4	PROPN
ejpam-5627	65	7	)	)	PUNCT
ejpam-5627	65	8	(	(	PUNCT
ejpam-5627	65	9	x|((x|x)|(y|y)))|(x|((x|x)|(y|y	x|((x|x)|(y|y)))|(x|((x|x)|(y|y	NUM
ejpam-5627	65	10	)	)	PUNCT
ejpam-5627	65	11	)	)	PUNCT
ejpam-5627	65	12	)	)	PUNCT
ejpam-5627	65	13	=	=	PUNCT
ejpam-5627	66	1	x.	x.	NOUN
ejpam-5627	66	2	definition	definition	NOUN
ejpam-5627	66	3	2	2	NUM
ejpam-5627	66	4	.	.	PUNCT
ejpam-5627	67	1	[	[	X
ejpam-5627	67	2	7	7	X
ejpam-5627	67	3	]	]	X
ejpam-5627	67	4	a	a	DET
ejpam-5627	67	5	sheffer	sheffer	NOUN
ejpam-5627	67	6	stroke	stroke	NOUN
ejpam-5627	67	7	up	up	ADP
ejpam-5627	67	8	-	-	PUNCT
ejpam-5627	67	9	algebra	algebra	NOUN
ejpam-5627	67	10	(	(	PUNCT
ejpam-5627	67	11	briefly	briefly	ADV
ejpam-5627	67	12	,	,	PUNCT
ejpam-5627	67	13	sup	sup	NOUN
ejpam-5627	67	14	-	-	PUNCT
ejpam-5627	67	15	algebra	algebra	NOUN
ejpam-5627	67	16	)	)	PUNCT
ejpam-5627	67	17	is	be	AUX
ejpam-5627	67	18	a	a	DET
ejpam-5627	67	19	structure	structure	NOUN
ejpam-5627	67	20	⟨h	⟨h	NUM
ejpam-5627	67	21	,	,	PUNCT
ejpam-5627	67	22	|	|	ADV
ejpam-5627	67	23	,	,	PUNCT
ejpam-5627	67	24	0⟩	0⟩	PROPN
ejpam-5627	67	25	of	of	ADP
ejpam-5627	67	26	type	type	NOUN
ejpam-5627	67	27	(	(	PUNCT
ejpam-5627	67	28	2	2	NUM
ejpam-5627	67	29	,	,	PUNCT
ejpam-5627	67	30	0	0	NUM
ejpam-5627	67	31	)	)	PUNCT
ejpam-5627	67	32	such	such	ADJ
ejpam-5627	67	33	that	that	DET
ejpam-5627	67	34	0	0	NUM
ejpam-5627	67	35	is	be	AUX
ejpam-5627	67	36	the	the	DET
ejpam-5627	67	37	fixed	fix	VERB
ejpam-5627	67	38	element	element	NOUN
ejpam-5627	67	39	in	in	ADP
ejpam-5627	67	40	h	h	NOUN
ejpam-5627	67	41	and	and	CCONJ
ejpam-5627	67	42	the	the	DET
ejpam-5627	67	43	following	follow	VERB
ejpam-5627	67	44	conditions	condition	NOUN
ejpam-5627	67	45	are	be	AUX
ejpam-5627	67	46	satisfied	satisfied	ADJ
ejpam-5627	67	47	for	for	ADP
ejpam-5627	67	48	all	all	DET
ejpam-5627	67	49	x	x	NOUN
ejpam-5627	67	50	,	,	PUNCT
ejpam-5627	67	51	y	y	PROPN
ejpam-5627	67	52	,	,	PUNCT
ejpam-5627	67	53	z	z	PROPN
ejpam-5627	67	54	∈	∈	PROPN
ejpam-5627	67	55	h	h	NOUN
ejpam-5627	67	56	,	,	PUNCT
ejpam-5627	67	57	(	(	PUNCT
ejpam-5627	67	58	sup-1	sup-1	NOUN
ejpam-5627	67	59	)	)	PUNCT
ejpam-5627	67	60	(	(	PUNCT
ejpam-5627	67	61	(	(	PUNCT
ejpam-5627	67	62	(	(	PUNCT
ejpam-5627	67	63	z|(x|x))|(z|(x|x)))|(((y|(x|x))|(z|(y|y)))|((y|(x|x))|	z|(x|x))|(z|(x|x)))|(((y|(x|x))|(z|(y|y)))|((y|(x|x))|	X
ejpam-5627	67	64	(	(	PUNCT
ejpam-5627	67	65	z|(y|y)))))|(((z|(x|x))|(z|(x|x)))|(((y|(x|x))|(z|(y|y)))|	z|(y|y)))))|(((z|(x|x))|(z|(x|x)))|(((y|(x|x))|(z|(y|y)))|	X
ejpam-5627	67	66	(	(	PUNCT
ejpam-5627	67	67	(	(	PUNCT
ejpam-5627	67	68	y|(x|x))|(z|(y|y	y|(x|x))|(z|(y|y	PROPN
ejpam-5627	67	69	)	)	PUNCT
ejpam-5627	67	70	)	)	PUNCT
ejpam-5627	67	71	)	)	PUNCT
ejpam-5627	67	72	)	)	PUNCT
ejpam-5627	67	73	)	)	PUNCT
ejpam-5627	68	1	=	=	SYM
ejpam-5627	68	2	0	0	PUNCT
ejpam-5627	68	3	(	(	PUNCT
ejpam-5627	68	4	sup-2	sup-2	NOUN
ejpam-5627	68	5	)	)	PUNCT
ejpam-5627	68	6	x|x	x|x	PUNCT
ejpam-5627	69	1	=	=	PUNCT
ejpam-5627	69	2	x|(0|0	x|(0|0	NUM
ejpam-5627	69	3	)	)	PUNCT
ejpam-5627	69	4	(	(	PUNCT
ejpam-5627	69	5	sup-3	sup-3	NOUN
ejpam-5627	69	6	)	)	PUNCT
ejpam-5627	69	7	(	(	PUNCT
ejpam-5627	69	8	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	PROPN
ejpam-5627	69	9	)	)	PUNCT
ejpam-5627	69	10	)	)	PUNCT
ejpam-5627	70	1	=	=	SYM
ejpam-5627	70	2	0	0	NUM
ejpam-5627	71	1	and	and	CCONJ
ejpam-5627	71	2	(	(	PUNCT
ejpam-5627	71	3	y|(x|x))|(y|(x|x	y|(x|x))|(y|(x|x	PROPN
ejpam-5627	71	4	)	)	PUNCT
ejpam-5627	71	5	)	)	PUNCT
ejpam-5627	72	1	=	=	SYM
ejpam-5627	72	2	0	0	NUM
ejpam-5627	72	3	⇒	⇒	NOUN
ejpam-5627	72	4	x	x	PUNCT
ejpam-5627	72	5	=	=	PUNCT
ejpam-5627	72	6	y.	y.	PROPN
ejpam-5627	72	7	n.	n.	PROPN
ejpam-5627	72	8	rajesh	rajesh	PROPN
ejpam-5627	72	9	,	,	PUNCT
ejpam-5627	72	10	t.	t.	PROPN
ejpam-5627	72	11	oner	oner	NOUN
ejpam-5627	72	12	,	,	PUNCT
ejpam-5627	72	13	a.	a.	NOUN
ejpam-5627	72	14	iampan	iampan	PROPN
ejpam-5627	72	15	,	,	PUNCT
ejpam-5627	72	16	i.	i.	PROPN
ejpam-5627	72	17	senturk	senturk	PROPN
ejpam-5627	72	18	/	/	SYM
ejpam-5627	72	19	eur	eur	PROPN
ejpam-5627	72	20	.	.	PUNCT
ejpam-5627	73	1	j.	j.	PROPN
ejpam-5627	73	2	pure	pure	PROPN
ejpam-5627	73	3	appl	appl	PROPN
ejpam-5627	73	4	.	.	PROPN
ejpam-5627	73	5	math	math	PROPN
ejpam-5627	73	6	,	,	PUNCT
ejpam-5627	73	7	18	18	NUM
ejpam-5627	73	8	(	(	PUNCT
ejpam-5627	73	9	1	1	NUM
ejpam-5627	73	10	)	)	PUNCT
ejpam-5627	73	11	(	(	PUNCT
ejpam-5627	73	12	2025	2025	NUM
ejpam-5627	73	13	)	)	PUNCT
ejpam-5627	73	14	,	,	PUNCT
ejpam-5627	73	15	5627	5627	NUM
ejpam-5627	73	16	4	4	NUM
ejpam-5627	73	17	of	of	ADP
ejpam-5627	73	18	15	15	NUM
ejpam-5627	73	19	proposition	proposition	NOUN
ejpam-5627	73	20	1	1	NUM
ejpam-5627	73	21	.	.	PUNCT
ejpam-5627	74	1	[	[	X
ejpam-5627	74	2	7	7	X
ejpam-5627	74	3	]	]	X
ejpam-5627	74	4	let	let	VERB
ejpam-5627	74	5	⟨h	⟨h	PRON
ejpam-5627	74	6	,	,	PUNCT
ejpam-5627	74	7	|	|	ADV
ejpam-5627	74	8	,	,	PUNCT
ejpam-5627	74	9	0⟩	0⟩	PROPN
ejpam-5627	74	10	be	be	VERB
ejpam-5627	74	11	an	an	DET
ejpam-5627	74	12	sup	sup	NOUN
ejpam-5627	74	13	-	-	PUNCT
ejpam-5627	74	14	algebra	algebra	NOUN
ejpam-5627	74	15	.	.	PUNCT
ejpam-5627	75	1	then	then	ADV
ejpam-5627	75	2	the	the	DET
ejpam-5627	75	3	binary	binary	PROPN
ejpam-5627	75	4	relation	relation	PROPN
ejpam-5627	75	5	x	x	SYM
ejpam-5627	75	6	≤	≤	ADJ
ejpam-5627	75	7	y	y	NOUN
ejpam-5627	75	8	if	if	SCONJ
ejpam-5627	76	1	and	and	CCONJ
ejpam-5627	76	2	only	only	ADV
ejpam-5627	76	3	if	if	SCONJ
ejpam-5627	76	4	(	(	PUNCT
ejpam-5627	76	5	y|(x|x))|(y|(x|x	y|(x|x))|(y|(x|x	NOUN
ejpam-5627	76	6	)	)	PUNCT
ejpam-5627	76	7	)	)	PUNCT
ejpam-5627	77	1	=	=	SYM
ejpam-5627	77	2	0	0	NUM
ejpam-5627	77	3	is	be	AUX
ejpam-5627	77	4	a	a	DET
ejpam-5627	77	5	partial	partial	ADJ
ejpam-5627	77	6	order	order	NOUN
ejpam-5627	77	7	on	on	ADP
ejpam-5627	77	8	h.	h.	PROPN
ejpam-5627	77	9	lemma	lemma	PROPN
ejpam-5627	78	1	1	1	X
ejpam-5627	78	2	.	.	PUNCT
ejpam-5627	79	1	[	[	X
ejpam-5627	79	2	7	7	X
ejpam-5627	79	3	]	]	X
ejpam-5627	79	4	let	let	VERB
ejpam-5627	79	5	⟨h	⟨h	PRON
ejpam-5627	79	6	,	,	PUNCT
ejpam-5627	79	7	|	|	ADV
ejpam-5627	79	8	,	,	PUNCT
ejpam-5627	79	9	0⟩	0⟩	PROPN
ejpam-5627	79	10	be	be	VERB
ejpam-5627	79	11	an	an	DET
ejpam-5627	79	12	sup	sup	NOUN
ejpam-5627	79	13	-	-	PUNCT
ejpam-5627	79	14	algebra	algebra	NOUN
ejpam-5627	79	15	.	.	PUNCT
ejpam-5627	80	1	then	then	ADV
ejpam-5627	80	2	for	for	ADP
ejpam-5627	80	3	all	all	DET
ejpam-5627	80	4	x	x	NOUN
ejpam-5627	80	5	,	,	PUNCT
ejpam-5627	80	6	y	y	PROPN
ejpam-5627	80	7	,	,	PUNCT
ejpam-5627	80	8	z	z	PROPN
ejpam-5627	80	9	∈	∈	PROPN
ejpam-5627	80	10	h	h	NOUN
ejpam-5627	80	11	,	,	PUNCT
ejpam-5627	80	12	we	we	PRON
ejpam-5627	80	13	have	have	VERB
ejpam-5627	80	14	(	(	PUNCT
ejpam-5627	80	15	1	1	X
ejpam-5627	80	16	)	)	PUNCT
ejpam-5627	80	17	x	x	PUNCT
ejpam-5627	80	18	≤	≤	X
ejpam-5627	80	19	y	y	PROPN
ejpam-5627	80	20	⇒	⇒	NOUN
ejpam-5627	80	21	y|(z|z	y|(z|z	PROPN
ejpam-5627	80	22	)	)	PUNCT
ejpam-5627	80	23	≤	≤	NOUN
ejpam-5627	80	24	x|(z|z	x|(z|z	PROPN
ejpam-5627	80	25	)	)	PUNCT
ejpam-5627	80	26	and	and	CCONJ
ejpam-5627	80	27	z|(x|x	z|(x|x	PROPN
ejpam-5627	80	28	)	)	PUNCT
ejpam-5627	80	29	≤	≤	NOUN
ejpam-5627	81	1	z|(y|y	z|(y|y	PROPN
ejpam-5627	81	2	)	)	PUNCT
ejpam-5627	81	3	(	(	PUNCT
ejpam-5627	81	4	2	2	X
ejpam-5627	81	5	)	)	PUNCT
ejpam-5627	81	6	x	x	PUNCT
ejpam-5627	81	7	≤	≤	PROPN
ejpam-5627	81	8	y	y	PROPN
ejpam-5627	81	9	⇔	⇔	PROPN
ejpam-5627	81	10	y|y	y|y	PROPN
ejpam-5627	81	11	≤	≤	PROPN
ejpam-5627	81	12	x|x	x|x	PUNCT
ejpam-5627	82	1	(	(	PUNCT
ejpam-5627	82	2	3	3	X
ejpam-5627	82	3	)	)	PUNCT
ejpam-5627	82	4	y|(x|x	y|(x|x	PROPN
ejpam-5627	82	5	)	)	PUNCT
ejpam-5627	82	6	≤	≤	NUM
ejpam-5627	82	7	x	x	SYM
ejpam-5627	82	8	(	(	PUNCT
ejpam-5627	82	9	4	4	X
ejpam-5627	82	10	)	)	PUNCT
ejpam-5627	82	11	y	y	PROPN
ejpam-5627	82	12	≤	≤	PROPN
ejpam-5627	82	13	(	(	PUNCT
ejpam-5627	82	14	y|(x|x))|(y|(x|x	y|(x|x))|(y|(x|x	PROPN
ejpam-5627	82	15	)	)	PUNCT
ejpam-5627	82	16	)	)	PUNCT
ejpam-5627	83	1	(	(	PUNCT
ejpam-5627	83	2	5	5	X
ejpam-5627	83	3	)	)	PUNCT
ejpam-5627	83	4	x	x	PUNCT
ejpam-5627	83	5	≤	≤	X
ejpam-5627	83	6	y	y	PROPN
ejpam-5627	83	7	⇒	⇒	NOUN
ejpam-5627	83	8	x	x	X
ejpam-5627	83	9	≤	≤	X
ejpam-5627	83	10	(	(	PUNCT
ejpam-5627	83	11	y|(z|z))|(y|(z|z	y|(z|z))|(y|(z|z	NOUN
ejpam-5627	83	12	)	)	PUNCT
ejpam-5627	83	13	)	)	PUNCT
ejpam-5627	83	14	(	(	PUNCT
ejpam-5627	83	15	6	6	NUM
ejpam-5627	83	16	)	)	PUNCT
ejpam-5627	83	17	z|(y|y	z|(y|y	NUM
ejpam-5627	83	18	)	)	PUNCT
ejpam-5627	83	19	≤	≤	NOUN
ejpam-5627	83	20	z|(y|(x|x	z|(y|(x|x	NOUN
ejpam-5627	83	21	)	)	PUNCT
ejpam-5627	83	22	)	)	PUNCT
ejpam-5627	84	1	(	(	PUNCT
ejpam-5627	84	2	7	7	X
ejpam-5627	84	3	)	)	PUNCT
ejpam-5627	84	4	(	(	PUNCT
ejpam-5627	84	5	(	(	PUNCT
ejpam-5627	84	6	z|(y|y))|(z|(y|y)))|(x|x	z|(y|y))|(z|(y|y)))|(x|x	NOUN
ejpam-5627	84	7	)	)	PUNCT
ejpam-5627	84	8	≤	≤	NOUN
ejpam-5627	84	9	z|(y|(x|x	z|(y|(x|x	NOUN
ejpam-5627	84	10	)	)	PUNCT
ejpam-5627	84	11	)	)	PUNCT
ejpam-5627	85	1	(	(	PUNCT
ejpam-5627	85	2	8)	8)	NUM
ejpam-5627	85	3	x|((y|(z|z))|(y|(z|z	x|((y|(z|z))|(y|(z|z	NUM
ejpam-5627	85	4	)	)	PUNCT
ejpam-5627	85	5	)	)	PUNCT
ejpam-5627	85	6	)	)	PUNCT
ejpam-5627	86	1	≤	≤	NUM
ejpam-5627	86	2	(	(	PUNCT
ejpam-5627	86	3	x|(y|y))|((x|(z|z))|(x|(z|z	x|(y|y))|((x|(z|z))|(x|(z|z	PROPN
ejpam-5627	86	4	)	)	PUNCT
ejpam-5627	86	5	)	)	PUNCT
ejpam-5627	86	6	)	)	PUNCT
ejpam-5627	86	7	.	.	PUNCT
ejpam-5627	87	1	definition	definition	NOUN
ejpam-5627	87	2	3	3	NUM
ejpam-5627	87	3	.	.	PUNCT
ejpam-5627	88	1	[	[	X
ejpam-5627	88	2	7	7	X
ejpam-5627	88	3	]	]	X
ejpam-5627	88	4	a	a	DET
ejpam-5627	88	5	nonempty	nonempty	NOUN
ejpam-5627	88	6	subset	subset	VERB
ejpam-5627	88	7	g	g	NOUN
ejpam-5627	88	8	of	of	ADP
ejpam-5627	88	9	an	an	DET
ejpam-5627	88	10	sup	sup	ADJ
ejpam-5627	88	11	-	-	PUNCT
ejpam-5627	88	12	algebra	algebra	NOUN
ejpam-5627	88	13	h	h	NOUN
ejpam-5627	88	14	is	be	AUX
ejpam-5627	88	15	called	call	VERB
ejpam-5627	88	16	a	a	DET
ejpam-5627	88	17	subalgebra	subalgebra	NOUN
ejpam-5627	88	18	of	of	ADP
ejpam-5627	88	19	h	h	NOUN
ejpam-5627	88	20	if	if	SCONJ
ejpam-5627	88	21	(	(	PUNCT
ejpam-5627	88	22	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-5627	88	23	)	)	PUNCT
ejpam-5627	88	24	)	)	PUNCT
ejpam-5627	89	1	∈	∈	PROPN
ejpam-5627	89	2	g	g	NOUN
ejpam-5627	89	3	for	for	ADP
ejpam-5627	89	4	all	all	DET
ejpam-5627	89	5	x	x	NOUN
ejpam-5627	89	6	,	,	PUNCT
ejpam-5627	89	7	y	y	PROPN
ejpam-5627	89	8	∈	∈	PROPN
ejpam-5627	89	9	g.	g.	NOUN
ejpam-5627	89	10	definition	definition	NOUN
ejpam-5627	89	11	4	4	NUM
ejpam-5627	89	12	.	.	PUNCT
ejpam-5627	90	1	[	[	X
ejpam-5627	90	2	7	7	NUM
ejpam-5627	90	3	,	,	PUNCT
ejpam-5627	90	4	8	8	NUM
ejpam-5627	90	5	]	]	PUNCT
ejpam-5627	90	6	a	a	DET
ejpam-5627	90	7	nonempty	nonempty	NOUN
ejpam-5627	90	8	subset	subset	VERB
ejpam-5627	90	9	g	g	NOUN
ejpam-5627	90	10	of	of	ADP
ejpam-5627	90	11	an	an	DET
ejpam-5627	90	12	sup	sup	ADJ
ejpam-5627	90	13	-	-	PUNCT
ejpam-5627	90	14	algebra	algebra	NOUN
ejpam-5627	90	15	h	h	NOUN
ejpam-5627	90	16	is	be	AUX
ejpam-5627	90	17	called	call	VERB
ejpam-5627	90	18	an	an	DET
ejpam-5627	90	19	ideal	ideal	NOUN
ejpam-5627	90	20	of	of	ADP
ejpam-5627	90	21	h	h	NOUN
ejpam-5627	90	22	if	if	SCONJ
ejpam-5627	90	23	for	for	ADP
ejpam-5627	90	24	all	all	DET
ejpam-5627	90	25	x	x	NOUN
ejpam-5627	90	26	,	,	PUNCT
ejpam-5627	90	27	y	y	PROPN
ejpam-5627	90	28	∈	∈	PROPN
ejpam-5627	90	29	h	h	NOUN
ejpam-5627	90	30	,	,	PUNCT
ejpam-5627	90	31	(	(	PUNCT
ejpam-5627	90	32	1	1	X
ejpam-5627	90	33	)	)	PUNCT
ejpam-5627	90	34	y	y	PROPN
ejpam-5627	90	35	∈	∈	PROPN
ejpam-5627	90	36	g	g	PROPN
ejpam-5627	90	37	⇒	⇒	NOUN
ejpam-5627	90	38	(	(	PUNCT
ejpam-5627	90	39	y|(x|x))|(y|(x|x	y|(x|x))|(y|(x|x	PROPN
ejpam-5627	90	40	)	)	PUNCT
ejpam-5627	90	41	)	)	PUNCT
ejpam-5627	91	1	∈	∈	PROPN
ejpam-5627	91	2	g	g	PROPN
ejpam-5627	91	3	(	(	PUNCT
ejpam-5627	91	4	2	2	NUM
ejpam-5627	91	5	)	)	PUNCT
ejpam-5627	91	6	(	(	PUNCT
ejpam-5627	91	7	y|(x|x))|(y|(x|x	y|(x|x))|(y|(x|x	NOUN
ejpam-5627	91	8	)	)	PUNCT
ejpam-5627	91	9	)	)	PUNCT
ejpam-5627	92	1	∈	∈	PROPN
ejpam-5627	92	2	g	g	PROPN
ejpam-5627	92	3	and	and	CCONJ
ejpam-5627	92	4	x	x	SYM
ejpam-5627	92	5	∈	∈	PROPN
ejpam-5627	92	6	g	g	PROPN
ejpam-5627	92	7	⇒	⇒	X
ejpam-5627	92	8	y	y	PROPN
ejpam-5627	92	9	∈	∈	PROPN
ejpam-5627	92	10	g.	g.	NOUN
ejpam-5627	92	11	definition	definition	NOUN
ejpam-5627	92	12	5	5	NUM
ejpam-5627	92	13	.	.	PUNCT
ejpam-5627	93	1	[	[	X
ejpam-5627	93	2	3	3	X
ejpam-5627	93	3	]	]	PUNCT
ejpam-5627	93	4	let	let	VERB
ejpam-5627	93	5	h	h	NOUN
ejpam-5627	93	6	be	be	AUX
ejpam-5627	93	7	a	a	DET
ejpam-5627	93	8	nonempty	nonempty	ADV
ejpam-5627	93	9	set	set	VERB
ejpam-5627	93	10	.	.	PUNCT
ejpam-5627	94	1	the	the	DET
ejpam-5627	94	2	intuitionistic	intuitionistic	ADJ
ejpam-5627	94	3	fuzzy	fuzzy	ADJ
ejpam-5627	94	4	set	set	NOUN
ejpam-5627	94	5	(	(	PUNCT
ejpam-5627	94	6	ifs	ifs	PROPN
ejpam-5627	94	7	)	)	PUNCT
ejpam-5627	94	8	h	h	NOUN
ejpam-5627	94	9	=	=	PRON
ejpam-5627	94	10	(	(	PUNCT
ejpam-5627	94	11	h,µ	h,µ	PROPN
ejpam-5627	94	12	,	,	PUNCT
ejpam-5627	94	13	γ	γ	NOUN
ejpam-5627	94	14	)	)	PUNCT
ejpam-5627	94	15	is	be	AUX
ejpam-5627	94	16	defined	define	VERB
ejpam-5627	94	17	to	to	PART
ejpam-5627	94	18	be	be	AUX
ejpam-5627	94	19	a	a	DET
ejpam-5627	94	20	structure	structure	NOUN
ejpam-5627	94	21	h	h	NOUN
ejpam-5627	94	22	:	:	PUNCT
ejpam-5627	94	23	=	=	X
ejpam-5627	94	24	{	{	PUNCT
ejpam-5627	94	25	⟨x	⟨x	VERB
ejpam-5627	94	26	,	,	PUNCT
ejpam-5627	94	27	µ(x	µ(x	NOUN
ejpam-5627	94	28	)	)	PUNCT
ejpam-5627	94	29	,	,	PUNCT
ejpam-5627	94	30	γ(x)⟩	γ(x)⟩	NOUN
ejpam-5627	95	1	|	|	ADV
ejpam-5627	95	2	x	x	SYM
ejpam-5627	95	3	∈	∈	PROPN
ejpam-5627	95	4	h	h	NOUN
ejpam-5627	95	5	}	}	PUNCT
ejpam-5627	95	6	,	,	PUNCT
ejpam-5627	95	7	(	(	PUNCT
ejpam-5627	95	8	1	1	X
ejpam-5627	95	9	)	)	PUNCT
ejpam-5627	95	10	where	where	SCONJ
ejpam-5627	95	11	µ	µ	X
ejpam-5627	95	12	:	:	PUNCT
ejpam-5627	95	13	h	h	NOUN
ejpam-5627	95	14	→	→	PUNCT
ejpam-5627	96	1	[	[	X
ejpam-5627	96	2	0	0	NUM
ejpam-5627	96	3	,	,	PUNCT
ejpam-5627	96	4	1	1	NUM
ejpam-5627	96	5	]	]	PUNCT
ejpam-5627	96	6	is	be	AUX
ejpam-5627	96	7	the	the	DET
ejpam-5627	96	8	degree	degree	NOUN
ejpam-5627	96	9	of	of	ADP
ejpam-5627	96	10	membership	membership	NOUN
ejpam-5627	96	11	of	of	ADP
ejpam-5627	96	12	x	x	PUNCT
ejpam-5627	96	13	to	to	ADP
ejpam-5627	96	14	h	h	NOUN
ejpam-5627	96	15	and	and	CCONJ
ejpam-5627	96	16	γ	γ	X
ejpam-5627	96	17	:	:	PUNCT
ejpam-5627	96	18	h	h	NOUN
ejpam-5627	96	19	→	→	PUNCT
ejpam-5627	97	1	[	[	X
ejpam-5627	97	2	0	0	NUM
ejpam-5627	97	3	,	,	PUNCT
ejpam-5627	97	4	1	1	NUM
ejpam-5627	97	5	]	]	PUNCT
ejpam-5627	97	6	is	be	AUX
ejpam-5627	97	7	the	the	DET
ejpam-5627	97	8	degree	degree	NOUN
ejpam-5627	97	9	of	of	ADP
ejpam-5627	97	10	non	non	ADJ
ejpam-5627	97	11	-	-	NOUN
ejpam-5627	97	12	membership	membership	NOUN
ejpam-5627	97	13	of	of	ADP
ejpam-5627	97	14	x	x	PUNCT
ejpam-5627	97	15	to	to	ADP
ejpam-5627	97	16	h	h	NOUN
ejpam-5627	97	17	such	such	ADJ
ejpam-5627	97	18	that	that	SCONJ
ejpam-5627	97	19	0	0	NUM
ejpam-5627	97	20	≤	≤	NOUN
ejpam-5627	97	21	µ(x	µ(x	NOUN
ejpam-5627	97	22	)	)	PUNCT
ejpam-5627	97	23	+	+	NUM
ejpam-5627	97	24	γ(x	γ(x	NOUN
ejpam-5627	97	25	)	)	PUNCT
ejpam-5627	97	26	≤	≤	NUM
ejpam-5627	97	27	1	1	NUM
ejpam-5627	97	28	.	.	X
ejpam-5627	98	1	3	3	X
ejpam-5627	98	2	.	.	X
ejpam-5627	98	3	intuitionistic	intuitionistic	ADJ
ejpam-5627	98	4	fuzzy	fuzzy	ADJ
ejpam-5627	98	5	sup	sup	NOUN
ejpam-5627	98	6	-	-	PUNCT
ejpam-5627	98	7	algebras	algebras	NOUN
ejpam-5627	98	8	in	in	ADP
ejpam-5627	98	9	this	this	DET
ejpam-5627	98	10	section	section	NOUN
ejpam-5627	99	1	,	,	PUNCT
ejpam-5627	99	2	the	the	DET
ejpam-5627	99	3	study	study	NOUN
ejpam-5627	99	4	introduces	introduce	VERB
ejpam-5627	99	5	the	the	DET
ejpam-5627	99	6	concepts	concept	NOUN
ejpam-5627	99	7	of	of	ADP
ejpam-5627	99	8	intuitionistic	intuitionistic	ADJ
ejpam-5627	99	9	fuzzy	fuzzy	ADJ
ejpam-5627	99	10	sup	sup	NOUN
ejpam-5627	99	11	-	-	PUNCT
ejpam-5627	99	12	subalgebras	subalgebras	PROPN
ejpam-5627	99	13	and	and	CCONJ
ejpam-5627	99	14	intuitionistic	intuitionistic	ADJ
ejpam-5627	99	15	fuzzy	fuzzy	ADJ
ejpam-5627	99	16	sup	sup	NOUN
ejpam-5627	99	17	-	-	PUNCT
ejpam-5627	99	18	ideals	ideal	NOUN
ejpam-5627	99	19	within	within	ADP
ejpam-5627	99	20	the	the	DET
ejpam-5627	99	21	context	context	NOUN
ejpam-5627	99	22	of	of	ADP
ejpam-5627	99	23	sup	sup	NOUN
ejpam-5627	99	24	-	-	PUNCT
ejpam-5627	99	25	algebras	algebras	NOUN
ejpam-5627	99	26	.	.	PUNCT
ejpam-5627	100	1	it	it	PRON
ejpam-5627	100	2	’s	’	VERB
ejpam-5627	100	3	worth	worth	ADJ
ejpam-5627	100	4	noting	note	VERB
ejpam-5627	100	5	that	that	SCONJ
ejpam-5627	100	6	unless	unless	SCONJ
ejpam-5627	100	7	explicitly	explicitly	ADV
ejpam-5627	100	8	stated	state	VERB
ejpam-5627	100	9	otherwise	otherwise	ADV
ejpam-5627	100	10	,	,	PUNCT
ejpam-5627	100	11	h	h	PROPN
ejpam-5627	100	12	refers	refer	VERB
ejpam-5627	100	13	to	to	ADP
ejpam-5627	100	14	an	an	DET
ejpam-5627	100	15	sup	sup	NOUN
ejpam-5627	100	16	-	-	PUNCT
ejpam-5627	100	17	algebra	algebra	NOUN
ejpam-5627	100	18	.	.	PUNCT
ejpam-5627	101	1	definition	definition	NOUN
ejpam-5627	101	2	6	6	NUM
ejpam-5627	101	3	.	.	PUNCT
ejpam-5627	102	1	an	an	DET
ejpam-5627	102	2	ifs	ifs	PROPN
ejpam-5627	102	3	h	h	NOUN
ejpam-5627	102	4	=	=	PUNCT
ejpam-5627	102	5	(	(	PUNCT
ejpam-5627	102	6	h,µ	h,µ	PROPN
ejpam-5627	102	7	,	,	PUNCT
ejpam-5627	102	8	γ	γ	NOUN
ejpam-5627	102	9	)	)	PUNCT
ejpam-5627	102	10	of	of	ADP
ejpam-5627	102	11	h	h	NOUN
ejpam-5627	102	12	is	be	AUX
ejpam-5627	102	13	called	call	VERB
ejpam-5627	102	14	an	an	DET
ejpam-5627	102	15	intuitionistic	intuitionistic	ADJ
ejpam-5627	102	16	fuzzy	fuzzy	ADJ
ejpam-5627	102	17	sup	sup	NOUN
ejpam-5627	102	18	-	-	PUNCT
ejpam-5627	102	19	subalgebra	subalgebra	NOUN
ejpam-5627	102	20	of	of	ADP
ejpam-5627	102	21	h	h	NOUN
ejpam-5627	102	22	if	if	SCONJ
ejpam-5627	102	23	(	(	PUNCT
ejpam-5627	102	24	∀x	∀x	X
ejpam-5627	102	25	,	,	PUNCT
ejpam-5627	102	26	y	y	PROPN
ejpam-5627	102	27	∈	∈	PROPN
ejpam-5627	102	28	h	h	PROPN
ejpam-5627	102	29	)	)	PUNCT
ejpam-5627	102	30	(	(	PUNCT
ejpam-5627	102	31	µ((x|(y|y))|(x|(y|y	µ((x|(y|y))|(x|(y|y	ADJ
ejpam-5627	102	32	)	)	PUNCT
ejpam-5627	102	33	)	)	PUNCT
ejpam-5627	102	34	)	)	PUNCT
ejpam-5627	102	35	≥	≥	NOUN
ejpam-5627	102	36	min{µ(x	min{µ(x	NOUN
ejpam-5627	102	37	)	)	PUNCT
ejpam-5627	102	38	,	,	PUNCT
ejpam-5627	102	39	µ(y	µ(y	PROPN
ejpam-5627	102	40	)	)	PUNCT
ejpam-5627	102	41	}	}	PUNCT
ejpam-5627	102	42	γ((x|(y|y))|(x|(y|y	γ((x|(y|y))|(x|(y|y	ADJ
ejpam-5627	102	43	)	)	PUNCT
ejpam-5627	102	44	)	)	PUNCT
ejpam-5627	102	45	)	)	PUNCT
ejpam-5627	102	46	≤	≤	PUNCT
ejpam-5627	102	47	max{γ(x	max{γ(x	PROPN
ejpam-5627	102	48	)	)	PUNCT
ejpam-5627	102	49	,	,	PUNCT
ejpam-5627	102	50	γ(y	γ(y	PROPN
ejpam-5627	102	51	)	)	PUNCT
ejpam-5627	102	52	}	}	PUNCT
ejpam-5627	102	53	)	)	PUNCT
ejpam-5627	102	54	.	.	PUNCT
ejpam-5627	103	1	(	(	PUNCT
ejpam-5627	103	2	2	2	X
ejpam-5627	103	3	)	)	PUNCT
ejpam-5627	103	4	n.	n.	PROPN
ejpam-5627	103	5	rajesh	rajesh	PROPN
ejpam-5627	103	6	,	,	PUNCT
ejpam-5627	103	7	t.	t.	PROPN
ejpam-5627	103	8	oner	oner	NOUN
ejpam-5627	103	9	,	,	PUNCT
ejpam-5627	103	10	a.	a.	NOUN
ejpam-5627	103	11	iampan	iampan	PROPN
ejpam-5627	103	12	,	,	PUNCT
ejpam-5627	103	13	i.	i.	PROPN
ejpam-5627	103	14	senturk	senturk	PROPN
ejpam-5627	103	15	/	/	SYM
ejpam-5627	103	16	eur	eur	PROPN
ejpam-5627	103	17	.	.	PUNCT
ejpam-5627	104	1	j.	j.	PROPN
ejpam-5627	104	2	pure	pure	PROPN
ejpam-5627	104	3	appl	appl	PROPN
ejpam-5627	104	4	.	.	PROPN
ejpam-5627	104	5	math	math	PROPN
ejpam-5627	104	6	,	,	PUNCT
ejpam-5627	104	7	18	18	NUM
ejpam-5627	104	8	(	(	PUNCT
ejpam-5627	104	9	1	1	NUM
ejpam-5627	104	10	)	)	PUNCT
ejpam-5627	104	11	(	(	PUNCT
ejpam-5627	104	12	2025	2025	NUM
ejpam-5627	104	13	)	)	PUNCT
ejpam-5627	104	14	,	,	PUNCT
ejpam-5627	104	15	5627	5627	NUM
ejpam-5627	104	16	5	5	NUM
ejpam-5627	104	17	of	of	ADP
ejpam-5627	104	18	15	15	NUM
ejpam-5627	104	19	theorem	theorem	NOUN
ejpam-5627	104	20	1	1	NUM
ejpam-5627	104	21	.	.	PUNCT
ejpam-5627	105	1	if	if	SCONJ
ejpam-5627	105	2	h	h	PRON
ejpam-5627	105	3	=	=	SYM
ejpam-5627	105	4	(	(	PUNCT
ejpam-5627	105	5	h,µ	h,µ	PROPN
ejpam-5627	105	6	,	,	PUNCT
ejpam-5627	105	7	γ	γ	NOUN
ejpam-5627	105	8	)	)	PUNCT
ejpam-5627	105	9	is	be	AUX
ejpam-5627	105	10	an	an	DET
ejpam-5627	105	11	intuitionistic	intuitionistic	ADJ
ejpam-5627	105	12	fuzzy	fuzzy	ADJ
ejpam-5627	105	13	sup	sup	NOUN
ejpam-5627	105	14	-	-	PUNCT
ejpam-5627	105	15	subalgebra	subalgebra	NOUN
ejpam-5627	105	16	of	of	ADP
ejpam-5627	105	17	h	h	NOUN
ejpam-5627	105	18	,	,	PUNCT
ejpam-5627	105	19	then	then	ADV
ejpam-5627	105	20	µ(0	µ(0	PROPN
ejpam-5627	105	21	)	)	PUNCT
ejpam-5627	105	22	≥	≥	NOUN
ejpam-5627	105	23	µ(x	µ(x	VERB
ejpam-5627	105	24	)	)	PUNCT
ejpam-5627	105	25	and	and	CCONJ
ejpam-5627	105	26	γ(0	γ(0	PROPN
ejpam-5627	105	27	)	)	PUNCT
ejpam-5627	105	28	≤	≤	NOUN
ejpam-5627	105	29	γ(x	γ(x	NOUN
ejpam-5627	105	30	)	)	PUNCT
ejpam-5627	105	31	for	for	ADP
ejpam-5627	105	32	all	all	DET
ejpam-5627	105	33	x	x	SYM
ejpam-5627	105	34	∈	∈	PROPN
ejpam-5627	105	35	h.	h.	NOUN
ejpam-5627	105	36	proof	proof	NOUN
ejpam-5627	105	37	.	.	PUNCT
ejpam-5627	106	1	for	for	ADP
ejpam-5627	106	2	any	any	DET
ejpam-5627	106	3	x	x	SYM
ejpam-5627	106	4	∈	∈	PROPN
ejpam-5627	106	5	h	h	NOUN
ejpam-5627	106	6	,	,	PUNCT
ejpam-5627	106	7	µ(0	µ(0	NOUN
ejpam-5627	106	8	)	)	PUNCT
ejpam-5627	106	9	=	=	SYM
ejpam-5627	106	10	µ((x|(x|x))|(x|(x|x	µ((x|(x|x))|(x|(x|x	NOUN
ejpam-5627	106	11	)	)	PUNCT
ejpam-5627	106	12	)	)	PUNCT
ejpam-5627	106	13	)	)	PUNCT
ejpam-5627	106	14	≥	≥	NOUN
ejpam-5627	106	15	min{µ(x	min{µ(x	NOUN
ejpam-5627	106	16	)	)	PUNCT
ejpam-5627	106	17	,	,	PUNCT
ejpam-5627	106	18	µ(x	µ(x	NOUN
ejpam-5627	106	19	)	)	PUNCT
ejpam-5627	106	20	}	}	PUNCT
ejpam-5627	106	21	=	=	SYM
ejpam-5627	106	22	µ(x	µ(x	NUM
ejpam-5627	106	23	)	)	PUNCT
ejpam-5627	106	24	,	,	PUNCT
ejpam-5627	106	25	γ(0	γ(0	PROPN
ejpam-5627	106	26	)	)	PUNCT
ejpam-5627	106	27	=	=	SYM
ejpam-5627	106	28	γ((x|(x|x))|(x|(x|x	γ((x|(x|x))|(x|(x|x	NOUN
ejpam-5627	106	29	)	)	PUNCT
ejpam-5627	106	30	)	)	PUNCT
ejpam-5627	106	31	)	)	PUNCT
ejpam-5627	106	32	≤	≤	PUNCT
ejpam-5627	106	33	max{γ(x	max{γ(x	PROPN
ejpam-5627	106	34	)	)	PUNCT
ejpam-5627	106	35	,	,	PUNCT
ejpam-5627	106	36	γ(x	γ(x	NOUN
ejpam-5627	106	37	)	)	PUNCT
ejpam-5627	106	38	}	}	PUNCT
ejpam-5627	106	39	=	=	SYM
ejpam-5627	106	40	γ(x	γ(x	NOUN
ejpam-5627	106	41	)	)	PUNCT
ejpam-5627	106	42	.	.	PUNCT
ejpam-5627	107	1	definition	definition	NOUN
ejpam-5627	107	2	7	7	NUM
ejpam-5627	107	3	.	.	PUNCT
ejpam-5627	108	1	let	let	VERB
ejpam-5627	108	2	µ	µ	X
ejpam-5627	108	3	be	be	AUX
ejpam-5627	108	4	a	a	DET
ejpam-5627	108	5	fuzzy	fuzzy	ADJ
ejpam-5627	108	6	set	set	NOUN
ejpam-5627	108	7	on	on	ADP
ejpam-5627	108	8	an	an	DET
ejpam-5627	108	9	sup	sup	ADJ
ejpam-5627	108	10	-	-	PUNCT
ejpam-5627	108	11	algebra	algebra	NOUN
ejpam-5627	108	12	h	h	NOUN
ejpam-5627	108	13	and	and	CCONJ
ejpam-5627	108	14	α	α	NOUN
ejpam-5627	108	15	∈	∈	PROPN
ejpam-5627	109	1	[	[	X
ejpam-5627	109	2	0	0	NUM
ejpam-5627	109	3	,	,	PUNCT
ejpam-5627	109	4	1	1	NUM
ejpam-5627	109	5	]	]	PUNCT
ejpam-5627	109	6	.	.	PUNCT
ejpam-5627	110	1	we	we	PRON
ejpam-5627	110	2	define	define	VERB
ejpam-5627	110	3	the	the	DET
ejpam-5627	110	4	subsets	subset	NOUN
ejpam-5627	110	5	u(µ	u(µ	PROPN
ejpam-5627	110	6	,	,	PUNCT
ejpam-5627	110	7	t	t	PROPN
ejpam-5627	110	8	)	)	PUNCT
ejpam-5627	110	9	=	=	PRON
ejpam-5627	111	1	{	{	PUNCT
ejpam-5627	111	2	x	x	PUNCT
ejpam-5627	111	3	∈	∈	PROPN
ejpam-5627	111	4	h	h	NOUN
ejpam-5627	111	5	:	:	PUNCT
ejpam-5627	111	6	µ(x	µ(x	X
ejpam-5627	111	7	)	)	PUNCT
ejpam-5627	111	8	≥	≥	NOUN
ejpam-5627	111	9	t	t	NOUN
ejpam-5627	111	10	}	}	PUNCT
ejpam-5627	111	11	and	and	CCONJ
ejpam-5627	111	12	l(µ	l(µ	PROPN
ejpam-5627	111	13	,	,	PUNCT
ejpam-5627	111	14	t	t	PROPN
ejpam-5627	111	15	)	)	PUNCT
ejpam-5627	111	16	=	=	PRON
ejpam-5627	112	1	{	{	PUNCT
ejpam-5627	112	2	x	x	PUNCT
ejpam-5627	112	3	∈	∈	PROPN
ejpam-5627	112	4	h	h	NOUN
ejpam-5627	112	5	:	:	PUNCT
ejpam-5627	112	6	µ(x	µ(x	X
ejpam-5627	112	7	)	)	PUNCT
ejpam-5627	112	8	≤	≤	NOUN
ejpam-5627	112	9	t	t	PROPN
ejpam-5627	112	10	}	}	PUNCT
ejpam-5627	112	11	of	of	ADP
ejpam-5627	112	12	h.	h.	PROPN
ejpam-5627	112	13	theorem	theorem	PROPN
ejpam-5627	112	14	2	2	NUM
ejpam-5627	112	15	.	.	PUNCT
ejpam-5627	112	16	an	an	DET
ejpam-5627	112	17	ifs	ifs	PROPN
ejpam-5627	112	18	h	h	NOUN
ejpam-5627	112	19	=	=	PUNCT
ejpam-5627	112	20	(	(	PUNCT
ejpam-5627	112	21	h	h	NOUN
ejpam-5627	112	22	,	,	PUNCT
ejpam-5627	112	23	α	α	NOUN
ejpam-5627	112	24	,	,	PUNCT
ejpam-5627	112	25	β	β	NOUN
ejpam-5627	112	26	)	)	PUNCT
ejpam-5627	112	27	in	in	ADP
ejpam-5627	112	28	h	h	NOUN
ejpam-5627	112	29	is	be	AUX
ejpam-5627	112	30	an	an	DET
ejpam-5627	112	31	intuitionistic	intuitionistic	ADJ
ejpam-5627	112	32	fuzzy	fuzzy	ADJ
ejpam-5627	112	33	sup	sup	NOUN
ejpam-5627	112	34	-	-	PUNCT
ejpam-5627	112	35	subalgebra	subalgebra	NOUN
ejpam-5627	112	36	of	of	ADP
ejpam-5627	112	37	h	h	NOUN
ejpam-5627	112	38	if	if	SCONJ
ejpam-5627	113	1	and	and	CCONJ
ejpam-5627	113	2	only	only	ADV
ejpam-5627	113	3	if	if	SCONJ
ejpam-5627	113	4	the	the	DET
ejpam-5627	113	5	sets	set	NOUN
ejpam-5627	113	6	l(β	l(β	PROPN
ejpam-5627	113	7	,	,	PUNCT
ejpam-5627	113	8	s	s	NOUN
ejpam-5627	113	9	)	)	PUNCT
ejpam-5627	113	10	and	and	CCONJ
ejpam-5627	113	11	u(α	u(α	PROPN
ejpam-5627	113	12	,	,	PUNCT
ejpam-5627	113	13	t	t	PROPN
ejpam-5627	113	14	)	)	PUNCT
ejpam-5627	113	15	are	be	AUX
ejpam-5627	113	16	subalgebras	subalgebra	NOUN
ejpam-5627	113	17	of	of	ADP
ejpam-5627	113	18	h	h	NOUN
ejpam-5627	113	19	whenever	whenever	SCONJ
ejpam-5627	113	20	they	they	PRON
ejpam-5627	113	21	are	be	AUX
ejpam-5627	113	22	nonempty	nonempty	ADJ
ejpam-5627	113	23	for	for	ADP
ejpam-5627	113	24	all	all	DET
ejpam-5627	113	25	s	s	PROPN
ejpam-5627	113	26	,	,	PUNCT
ejpam-5627	113	27	t	t	PROPN
ejpam-5627	113	28	∈	∈	PROPN
ejpam-5627	114	1	[	[	X
ejpam-5627	114	2	0	0	NUM
ejpam-5627	114	3	,	,	PUNCT
ejpam-5627	114	4	1	1	NUM
ejpam-5627	114	5	]	]	PUNCT
ejpam-5627	114	6	.	.	PUNCT
ejpam-5627	115	1	proof	proof	NOUN
ejpam-5627	115	2	.	.	PUNCT
ejpam-5627	116	1	assume	assume	VERB
ejpam-5627	116	2	that	that	SCONJ
ejpam-5627	116	3	h	h	NOUN
ejpam-5627	116	4	=	=	PUNCT
ejpam-5627	116	5	(	(	PUNCT
ejpam-5627	116	6	h	h	NOUN
ejpam-5627	116	7	,	,	PUNCT
ejpam-5627	116	8	α	α	NOUN
ejpam-5627	116	9	,	,	PUNCT
ejpam-5627	116	10	β	β	NOUN
ejpam-5627	116	11	)	)	PUNCT
ejpam-5627	116	12	is	be	AUX
ejpam-5627	116	13	an	an	DET
ejpam-5627	116	14	intuitionistic	intuitionistic	ADJ
ejpam-5627	116	15	fuzzy	fuzzy	ADJ
ejpam-5627	116	16	sup	sup	NOUN
ejpam-5627	116	17	-	-	PUNCT
ejpam-5627	116	18	subalgebra	subalgebra	NOUN
ejpam-5627	116	19	of	of	ADP
ejpam-5627	116	20	h	h	NOUN
ejpam-5627	116	21	and	and	CCONJ
ejpam-5627	116	22	l(β	l(β	PROPN
ejpam-5627	116	23	,	,	PUNCT
ejpam-5627	116	24	s	s	X
ejpam-5627	116	25	)	)	PUNCT
ejpam-5627	116	26	̸=	̸=	PROPN
ejpam-5627	116	27	∅	∅	NOUN
ejpam-5627	116	28	=	=	NOUN
ejpam-5627	116	29	̸	̸	PUNCT
ejpam-5627	116	30	u(α	u(α	NOUN
ejpam-5627	116	31	,	,	PUNCT
ejpam-5627	116	32	t	t	PROPN
ejpam-5627	116	33	)	)	PUNCT
ejpam-5627	116	34	for	for	ADP
ejpam-5627	116	35	all	all	DET
ejpam-5627	116	36	s	s	PROPN
ejpam-5627	116	37	,	,	PUNCT
ejpam-5627	116	38	t	t	PROPN
ejpam-5627	116	39	∈	∈	PROPN
ejpam-5627	117	1	[	[	X
ejpam-5627	117	2	0	0	NUM
ejpam-5627	117	3	,	,	PUNCT
ejpam-5627	117	4	1	1	NUM
ejpam-5627	117	5	]	]	PUNCT
ejpam-5627	117	6	.	.	PUNCT
ejpam-5627	118	1	let	let	VERB
ejpam-5627	118	2	x	x	PRON
ejpam-5627	118	3	,	,	PUNCT
ejpam-5627	118	4	y	y	PROPN
ejpam-5627	118	5	,	,	PUNCT
ejpam-5627	118	6	a	a	PRON
ejpam-5627	118	7	,	,	PUNCT
ejpam-5627	118	8	b	b	X
ejpam-5627	118	9	∈	∈	PROPN
ejpam-5627	118	10	h	h	NOUN
ejpam-5627	118	11	be	be	AUX
ejpam-5627	118	12	such	such	ADJ
ejpam-5627	118	13	that	that	SCONJ
ejpam-5627	118	14	(	(	PUNCT
ejpam-5627	118	15	x	x	NOUN
ejpam-5627	118	16	,	,	PUNCT
ejpam-5627	118	17	a	a	PRON
ejpam-5627	118	18	)	)	PUNCT
ejpam-5627	118	19	∈	∈	PROPN
ejpam-5627	118	20	l(β	l(β	PROPN
ejpam-5627	118	21	,	,	PUNCT
ejpam-5627	118	22	s	s	X
ejpam-5627	118	23	)	)	PUNCT
ejpam-5627	118	24	×	×	PROPN
ejpam-5627	118	25	u(α	u(α	PROPN
ejpam-5627	118	26	,	,	PUNCT
ejpam-5627	118	27	t	t	PROPN
ejpam-5627	118	28	)	)	PUNCT
ejpam-5627	118	29	and	and	CCONJ
ejpam-5627	118	30	(	(	PUNCT
ejpam-5627	118	31	y	y	PROPN
ejpam-5627	118	32	,	,	PUNCT
ejpam-5627	118	33	b	b	NOUN
ejpam-5627	118	34	)	)	PUNCT
ejpam-5627	118	35	∈	∈	PROPN
ejpam-5627	118	36	l(β	l(β	PROPN
ejpam-5627	118	37	,	,	PUNCT
ejpam-5627	118	38	s	s	X
ejpam-5627	118	39	)	)	PUNCT
ejpam-5627	118	40	×	×	PROPN
ejpam-5627	118	41	u(α	u(α	PROPN
ejpam-5627	118	42	,	,	PUNCT
ejpam-5627	118	43	t	t	PROPN
ejpam-5627	118	44	)	)	PUNCT
ejpam-5627	118	45	.	.	PUNCT
ejpam-5627	119	1	then	then	ADV
ejpam-5627	119	2	β(x	β(x	NOUN
ejpam-5627	119	3	)	)	PUNCT
ejpam-5627	119	4	≤	≤	NOUN
ejpam-5627	119	5	s	s	NOUN
ejpam-5627	119	6	,	,	PUNCT
ejpam-5627	119	7	β(y	β(y	NOUN
ejpam-5627	119	8	)	)	PUNCT
ejpam-5627	119	9	≤	≤	NUM
ejpam-5627	119	10	s	s	PROPN
ejpam-5627	119	11	,	,	PUNCT
ejpam-5627	119	12	α(a	α(a	NOUN
ejpam-5627	119	13	)	)	PUNCT
ejpam-5627	119	14	≥	≥	NOUN
ejpam-5627	119	15	t	t	NOUN
ejpam-5627	119	16	and	and	CCONJ
ejpam-5627	119	17	α(b	α(b	NOUN
ejpam-5627	119	18	)	)	PUNCT
ejpam-5627	119	19	≥	≥	NOUN
ejpam-5627	119	20	t.	t.	NOUN
ejpam-5627	119	21	then	then	ADV
ejpam-5627	119	22	β((x|(y|y))|(x|(y|y	β((x|(y|y))|(x|(y|y	ADJ
ejpam-5627	119	23	)	)	PUNCT
ejpam-5627	119	24	)	)	PUNCT
ejpam-5627	119	25	)	)	PUNCT
ejpam-5627	120	1	≤	≤	NUM
ejpam-5627	120	2	max{β(x	max{β(x	NOUN
ejpam-5627	120	3	)	)	PUNCT
ejpam-5627	120	4	,	,	PUNCT
ejpam-5627	120	5	β(y	β(y	PROPN
ejpam-5627	120	6	)	)	PUNCT
ejpam-5627	120	7	}	}	PUNCT
ejpam-5627	120	8	≤	≤	PROPN
ejpam-5627	120	9	s	s	X
ejpam-5627	120	10	and	and	CCONJ
ejpam-5627	120	11	α((a|(b|b))|(a|(b|b	α((a|(b|b))|(a|(b|b	NOUN
ejpam-5627	120	12	)	)	PUNCT
ejpam-5627	120	13	)	)	PUNCT
ejpam-5627	120	14	)	)	PUNCT
ejpam-5627	120	15	≥	≥	PROPN
ejpam-5627	120	16	min{α(a	min{α(a	NOUN
ejpam-5627	120	17	)	)	PUNCT
ejpam-5627	120	18	,	,	PUNCT
ejpam-5627	120	19	α(b	α(b	NOUN
ejpam-5627	120	20	)	)	PUNCT
ejpam-5627	120	21	}	}	PUNCT
ejpam-5627	120	22	≥	≥	PROPN
ejpam-5627	120	23	t	t	NOUN
ejpam-5627	120	24	and	and	CCONJ
ejpam-5627	120	25	so	so	ADV
ejpam-5627	120	26	(	(	PUNCT
ejpam-5627	120	27	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	PROPN
ejpam-5627	120	28	)	)	PUNCT
ejpam-5627	120	29	)	)	PUNCT
ejpam-5627	120	30	,	,	PUNCT
ejpam-5627	120	31	(	(	PUNCT
ejpam-5627	120	32	a|(b|b))|(a|(b|b	a|(b|b))|(a|(b|b	NOUN
ejpam-5627	120	33	)	)	PUNCT
ejpam-5627	120	34	)	)	PUNCT
ejpam-5627	121	1	∈	∈	PROPN
ejpam-5627	121	2	l(β	l(β	PROPN
ejpam-5627	121	3	,	,	PUNCT
ejpam-5627	121	4	s)×u(α	s)×u(α	PROPN
ejpam-5627	121	5	,	,	PUNCT
ejpam-5627	121	6	t	t	PROPN
ejpam-5627	121	7	)	)	PUNCT
ejpam-5627	121	8	.	.	PUNCT
ejpam-5627	122	1	therefore	therefore	ADV
ejpam-5627	122	2	,	,	PUNCT
ejpam-5627	122	3	l(β	l(β	PROPN
ejpam-5627	122	4	,	,	PUNCT
ejpam-5627	122	5	s	s	AUX
ejpam-5627	122	6	)	)	PUNCT
ejpam-5627	122	7	and	and	CCONJ
ejpam-5627	122	8	u(α	u(α	PROPN
ejpam-5627	122	9	,	,	PUNCT
ejpam-5627	122	10	t	t	PROPN
ejpam-5627	122	11	)	)	PUNCT
ejpam-5627	122	12	are	be	AUX
ejpam-5627	122	13	sup	sup	NOUN
ejpam-5627	122	14	-	-	PUNCT
ejpam-5627	122	15	subalgebras	subalgebras	NOUN
ejpam-5627	122	16	of	of	ADP
ejpam-5627	122	17	h.	h.	PROPN
ejpam-5627	122	18	conversely	conversely	ADV
ejpam-5627	122	19	,	,	PUNCT
ejpam-5627	122	20	let	let	VERB
ejpam-5627	122	21	h	h	NOUN
ejpam-5627	122	22	=	=	PUNCT
ejpam-5627	122	23	(	(	PUNCT
ejpam-5627	122	24	h	h	NOUN
ejpam-5627	122	25	,	,	PUNCT
ejpam-5627	122	26	α	α	NOUN
ejpam-5627	122	27	,	,	PUNCT
ejpam-5627	122	28	β	β	NOUN
ejpam-5627	122	29	)	)	PUNCT
ejpam-5627	122	30	be	be	VERB
ejpam-5627	122	31	an	an	DET
ejpam-5627	122	32	ifs	ifs	PROPN
ejpam-5627	122	33	in	in	ADP
ejpam-5627	122	34	h	h	NOUN
ejpam-5627	122	35	for	for	ADP
ejpam-5627	122	36	which	which	PRON
ejpam-5627	122	37	l(β	l(β	PROPN
ejpam-5627	122	38	,	,	PUNCT
ejpam-5627	122	39	s	s	PART
ejpam-5627	122	40	)	)	PUNCT
ejpam-5627	122	41	and	and	CCONJ
ejpam-5627	122	42	u(α	u(α	PROPN
ejpam-5627	122	43	,	,	PUNCT
ejpam-5627	122	44	t	t	PROPN
ejpam-5627	122	45	)	)	PUNCT
ejpam-5627	122	46	are	be	AUX
ejpam-5627	122	47	sup	sup	NOUN
ejpam-5627	122	48	-	-	PUNCT
ejpam-5627	122	49	subalgebras	subalgebras	NOUN
ejpam-5627	122	50	of	of	ADP
ejpam-5627	122	51	h	h	NOUN
ejpam-5627	122	52	whenever	whenever	SCONJ
ejpam-5627	122	53	they	they	PRON
ejpam-5627	122	54	are	be	AUX
ejpam-5627	122	55	nonempty	nonempty	ADJ
ejpam-5627	122	56	for	for	ADP
ejpam-5627	122	57	all	all	DET
ejpam-5627	122	58	s	s	PROPN
ejpam-5627	122	59	,	,	PUNCT
ejpam-5627	122	60	t	t	PROPN
ejpam-5627	122	61	∈	∈	PROPN
ejpam-5627	123	1	[	[	X
ejpam-5627	123	2	0	0	NUM
ejpam-5627	123	3	,	,	PUNCT
ejpam-5627	123	4	1	1	NUM
ejpam-5627	123	5	]	]	PUNCT
ejpam-5627	123	6	.	.	PUNCT
ejpam-5627	124	1	suppose	suppose	VERB
ejpam-5627	124	2	that	that	SCONJ
ejpam-5627	124	3	β((a|(b|b))|(a|(b|b	β((a|(b|b))|(a|(b|b	NOUN
ejpam-5627	124	4	)	)	PUNCT
ejpam-5627	124	5	)	)	PUNCT
ejpam-5627	124	6	)	)	PUNCT
ejpam-5627	125	1	>	>	PUNCT
ejpam-5627	125	2	max{β(a	max{β(a	PROPN
ejpam-5627	125	3	)	)	PUNCT
ejpam-5627	125	4	,	,	PUNCT
ejpam-5627	125	5	β(b	β(b	PUNCT
ejpam-5627	125	6	)	)	PUNCT
ejpam-5627	125	7	}	}	PUNCT
ejpam-5627	125	8	or	or	CCONJ
ejpam-5627	125	9	α((x|(y|y))|(x|(y|y	α((x|(y|y))|(x|(y|y	VERB
ejpam-5627	125	10	)	)	PUNCT
ejpam-5627	125	11	)	)	PUNCT
ejpam-5627	125	12	)	)	PUNCT
ejpam-5627	126	1	<	<	X
ejpam-5627	126	2	min{α(x	min{α(x	NOUN
ejpam-5627	126	3	)	)	PUNCT
ejpam-5627	126	4	,	,	PUNCT
ejpam-5627	126	5	α(y	α(y	NOUN
ejpam-5627	126	6	)	)	PUNCT
ejpam-5627	126	7	}	}	PUNCT
ejpam-5627	126	8	for	for	ADP
ejpam-5627	126	9	some	some	DET
ejpam-5627	126	10	a	a	DET
ejpam-5627	126	11	,	,	PUNCT
ejpam-5627	126	12	b	b	NOUN
ejpam-5627	126	13	,	,	PUNCT
ejpam-5627	126	14	x	x	X
ejpam-5627	126	15	,	,	PUNCT
ejpam-5627	126	16	y	y	PROPN
ejpam-5627	126	17	∈	∈	PROPN
ejpam-5627	126	18	h.	h.	PROPN
ejpam-5627	126	19	then	then	ADV
ejpam-5627	126	20	a	a	DET
ejpam-5627	126	21	,	,	PUNCT
ejpam-5627	126	22	b	b	X
ejpam-5627	126	23	∈	∈	PROPN
ejpam-5627	126	24	l(β	l(β	PROPN
ejpam-5627	126	25	,	,	PUNCT
ejpam-5627	126	26	s	s	NOUN
ejpam-5627	126	27	)	)	PUNCT
ejpam-5627	126	28	or	or	CCONJ
ejpam-5627	126	29	x	x	SYM
ejpam-5627	126	30	,	,	PUNCT
ejpam-5627	126	31	y	y	PROPN
ejpam-5627	126	32	∈	∈	PROPN
ejpam-5627	126	33	u(α	u(α	PROPN
ejpam-5627	126	34	,	,	PUNCT
ejpam-5627	126	35	t	t	PROPN
ejpam-5627	126	36	)	)	PUNCT
ejpam-5627	126	37	where	where	SCONJ
ejpam-5627	126	38	s	s	VERB
ejpam-5627	126	39	=	=	PUNCT
ejpam-5627	126	40	max{β(a	max{β(a	PROPN
ejpam-5627	126	41	)	)	PUNCT
ejpam-5627	126	42	,	,	PUNCT
ejpam-5627	126	43	β(b	β(b	PUNCT
ejpam-5627	126	44	)	)	PUNCT
ejpam-5627	126	45	}	}	PUNCT
ejpam-5627	126	46	and	and	CCONJ
ejpam-5627	126	47	t	t	X
ejpam-5627	126	48	=	=	SYM
ejpam-5627	126	49	min{α(x	min{α(x	PROPN
ejpam-5627	126	50	)	)	PUNCT
ejpam-5627	126	51	,	,	PUNCT
ejpam-5627	126	52	α(y	α(y	NOUN
ejpam-5627	126	53	)	)	PUNCT
ejpam-5627	126	54	}	}	PUNCT
ejpam-5627	126	55	.	.	PUNCT
ejpam-5627	127	1	but	but	CCONJ
ejpam-5627	127	2	(	(	PUNCT
ejpam-5627	127	3	a|(b|b))|(a|(b|b	a|(b|b))|(a|(b|b	NOUN
ejpam-5627	127	4	)	)	PUNCT
ejpam-5627	127	5	)	)	PUNCT
ejpam-5627	127	6	/∈	/∈	PUNCT
ejpam-5627	128	1	l(β	l(β	PROPN
ejpam-5627	128	2	,	,	PUNCT
ejpam-5627	128	3	s	s	NOUN
ejpam-5627	128	4	)	)	PUNCT
ejpam-5627	128	5	or	or	CCONJ
ejpam-5627	128	6	(	(	PUNCT
ejpam-5627	128	7	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	NUM
ejpam-5627	128	8	)	)	PUNCT
ejpam-5627	128	9	)	)	PUNCT
ejpam-5627	128	10	/∈	/∈	PUNCT
ejpam-5627	129	1	u(α	u(α	NOUN
ejpam-5627	129	2	,	,	PUNCT
ejpam-5627	129	3	t	t	PROPN
ejpam-5627	129	4	)	)	PUNCT
ejpam-5627	129	5	,	,	PUNCT
ejpam-5627	129	6	a	a	DET
ejpam-5627	129	7	contradiction	contradiction	NOUN
ejpam-5627	129	8	.	.	PUNCT
ejpam-5627	130	1	therefore	therefore	ADV
ejpam-5627	130	2	,	,	PUNCT
ejpam-5627	130	3	β((a|(b|b))|(a|(b|b	β((a|(b|b))|(a|(b|b	NOUN
ejpam-5627	130	4	)	)	PUNCT
ejpam-5627	130	5	)	)	PUNCT
ejpam-5627	130	6	)	)	PUNCT
ejpam-5627	130	7	≤	≤	PUNCT
ejpam-5627	131	1	max{β(a	max{β(a	PROPN
ejpam-5627	131	2	)	)	PUNCT
ejpam-5627	131	3	,	,	PUNCT
ejpam-5627	131	4	β(b	β(b	PUNCT
ejpam-5627	131	5	)	)	PUNCT
ejpam-5627	131	6	}	}	PUNCT
ejpam-5627	131	7	,	,	PUNCT
ejpam-5627	131	8	α((x|(y|y))|(x|(y|y	α((x|(y|y))|(x|(y|y	NOUN
ejpam-5627	131	9	)	)	PUNCT
ejpam-5627	131	10	)	)	PUNCT
ejpam-5627	131	11	)	)	PUNCT
ejpam-5627	131	12	≥	≥	X
ejpam-5627	131	13	min{α(x	min{α(x	NOUN
ejpam-5627	131	14	)	)	PUNCT
ejpam-5627	131	15	,	,	PUNCT
ejpam-5627	131	16	α(y	α(y	NOUN
ejpam-5627	131	17	)	)	PUNCT
ejpam-5627	131	18	}	}	PUNCT
ejpam-5627	131	19	for	for	ADP
ejpam-5627	131	20	all	all	DET
ejpam-5627	131	21	a	a	DET
ejpam-5627	131	22	,	,	PUNCT
ejpam-5627	131	23	b	b	NOUN
ejpam-5627	131	24	,	,	PUNCT
ejpam-5627	131	25	x	x	X
ejpam-5627	131	26	,	,	PUNCT
ejpam-5627	131	27	y	y	PROPN
ejpam-5627	131	28	∈	∈	PROPN
ejpam-5627	131	29	h.	h.	PROPN
ejpam-5627	131	30	consequently	consequently	ADV
ejpam-5627	131	31	,	,	PUNCT
ejpam-5627	131	32	h	h	NOUN
ejpam-5627	131	33	=	=	PRON
ejpam-5627	131	34	(	(	PUNCT
ejpam-5627	131	35	h	h	NOUN
ejpam-5627	131	36	,	,	PUNCT
ejpam-5627	131	37	α	α	NOUN
ejpam-5627	131	38	,	,	PUNCT
ejpam-5627	131	39	β	β	NOUN
ejpam-5627	131	40	)	)	PUNCT
ejpam-5627	131	41	is	be	AUX
ejpam-5627	131	42	an	an	DET
ejpam-5627	131	43	intuitionistic	intuitionistic	ADJ
ejpam-5627	131	44	fuzzy	fuzzy	ADJ
ejpam-5627	131	45	sup	sup	NOUN
ejpam-5627	131	46	-	-	PUNCT
ejpam-5627	131	47	subalgebra	subalgebra	NOUN
ejpam-5627	131	48	of	of	ADP
ejpam-5627	131	49	h.	h.	PROPN
ejpam-5627	131	50	theorem	theorem	PROPN
ejpam-5627	131	51	3	3	NUM
ejpam-5627	131	52	.	.	PUNCT
ejpam-5627	131	53	an	an	DET
ejpam-5627	131	54	ifs	ifs	PROPN
ejpam-5627	131	55	h	h	NOUN
ejpam-5627	131	56	=	=	PUNCT
ejpam-5627	131	57	(	(	PUNCT
ejpam-5627	131	58	h	h	NOUN
ejpam-5627	131	59	,	,	PUNCT
ejpam-5627	131	60	α	α	NOUN
ejpam-5627	131	61	,	,	PUNCT
ejpam-5627	131	62	β	β	NOUN
ejpam-5627	131	63	)	)	PUNCT
ejpam-5627	131	64	in	in	ADP
ejpam-5627	131	65	h	h	NOUN
ejpam-5627	131	66	is	be	AUX
ejpam-5627	131	67	an	an	DET
ejpam-5627	131	68	intuitionistic	intuitionistic	ADJ
ejpam-5627	131	69	fuzzy	fuzzy	ADJ
ejpam-5627	131	70	sup	sup	NOUN
ejpam-5627	131	71	-	-	PUNCT
ejpam-5627	131	72	subalgebra	subalgebra	NOUN
ejpam-5627	131	73	of	of	ADP
ejpam-5627	131	74	h	h	NOUN
ejpam-5627	131	75	if	if	SCONJ
ejpam-5627	132	1	and	and	CCONJ
ejpam-5627	132	2	only	only	ADV
ejpam-5627	132	3	if	if	SCONJ
ejpam-5627	132	4	the	the	DET
ejpam-5627	132	5	fuzzy	fuzzy	ADJ
ejpam-5627	132	6	sets	set	VERB
ejpam-5627	132	7	βc	βc	INTJ
ejpam-5627	132	8	and	and	CCONJ
ejpam-5627	132	9	α	α	NOUN
ejpam-5627	132	10	are	be	AUX
ejpam-5627	132	11	fuzzy	fuzzy	ADJ
ejpam-5627	132	12	sup	sup	NOUN
ejpam-5627	132	13	-	-	PUNCT
ejpam-5627	132	14	subalgebras	subalgebras	NOUN
ejpam-5627	132	15	of	of	ADP
ejpam-5627	132	16	h	h	NOUN
ejpam-5627	132	17	,	,	PUNCT
ejpam-5627	132	18	where	where	SCONJ
ejpam-5627	132	19	βc	βc	INTJ
ejpam-5627	132	20	:	:	PUNCT
ejpam-5627	132	21	l	l	X
ejpam-5627	132	22	→	→	PUNCT
ejpam-5627	133	1	[	[	X
ejpam-5627	133	2	0	0	NUM
ejpam-5627	133	3	,	,	PUNCT
ejpam-5627	133	4	1	1	NUM
ejpam-5627	133	5	]	]	PUNCT
ejpam-5627	133	6	,	,	PUNCT
ejpam-5627	133	7	x	x	SYM
ejpam-5627	133	8	7→	7→	NOUN
ejpam-5627	133	9	1−	1−	NUM
ejpam-5627	133	10	β(x	β(x	NOUN
ejpam-5627	133	11	)	)	PUNCT
ejpam-5627	133	12	.	.	PUNCT
ejpam-5627	134	1	proof	proof	NOUN
ejpam-5627	134	2	.	.	PUNCT
ejpam-5627	135	1	assume	assume	VERB
ejpam-5627	135	2	that	that	SCONJ
ejpam-5627	135	3	h	h	NOUN
ejpam-5627	135	4	=	=	PUNCT
ejpam-5627	135	5	(	(	PUNCT
ejpam-5627	135	6	h	h	NOUN
ejpam-5627	135	7	,	,	PUNCT
ejpam-5627	135	8	α	α	NOUN
ejpam-5627	135	9	,	,	PUNCT
ejpam-5627	135	10	β	β	NOUN
ejpam-5627	135	11	)	)	PUNCT
ejpam-5627	135	12	is	be	AUX
ejpam-5627	135	13	an	an	DET
ejpam-5627	135	14	intuitionistic	intuitionistic	ADJ
ejpam-5627	135	15	fuzzy	fuzzy	ADJ
ejpam-5627	135	16	sup	sup	NOUN
ejpam-5627	135	17	-	-	PUNCT
ejpam-5627	135	18	subalgebra	subalgebra	NOUN
ejpam-5627	135	19	of	of	ADP
ejpam-5627	135	20	h.	h.	NOUN
ejpam-5627	135	21	it	it	PRON
ejpam-5627	135	22	is	be	AUX
ejpam-5627	135	23	clear	clear	ADJ
ejpam-5627	135	24	that	that	SCONJ
ejpam-5627	135	25	α	α	PRON
ejpam-5627	135	26	is	be	AUX
ejpam-5627	135	27	a	a	DET
ejpam-5627	135	28	fuzzy	fuzzy	ADJ
ejpam-5627	135	29	sup	sup	ADJ
ejpam-5627	135	30	-	-	PUNCT
ejpam-5627	135	31	subalgebra	subalgebra	NOUN
ejpam-5627	135	32	of	of	ADP
ejpam-5627	135	33	h.	h.	NOUN
ejpam-5627	135	34	for	for	ADP
ejpam-5627	135	35	every	every	DET
ejpam-5627	135	36	x	x	NOUN
ejpam-5627	135	37	,	,	PUNCT
ejpam-5627	135	38	y	y	PROPN
ejpam-5627	135	39	∈	∈	PROPN
ejpam-5627	135	40	h	h	NOUN
ejpam-5627	135	41	,	,	PUNCT
ejpam-5627	135	42	βc((x|(y|y))|(x|(y|y	βc((x|(y|y))|(x|(y|y	NUM
ejpam-5627	135	43	)	)	PUNCT
ejpam-5627	135	44	)	)	PUNCT
ejpam-5627	135	45	)	)	PUNCT
ejpam-5627	136	1	=	=	SYM
ejpam-5627	136	2	1−	1−	NUM
ejpam-5627	136	3	β((x|(y|y))|(x|(y|y	β((x|(y|y))|(x|(y|y	ADJ
ejpam-5627	136	4	)	)	PUNCT
ejpam-5627	136	5	)	)	PUNCT
ejpam-5627	136	6	)	)	PUNCT
ejpam-5627	136	7	≥	≥	NOUN
ejpam-5627	136	8	1−max{β(x	1−max{β(x	NUM
ejpam-5627	136	9	)	)	PUNCT
ejpam-5627	136	10	,	,	PUNCT
ejpam-5627	136	11	β(y	β(y	PROPN
ejpam-5627	136	12	)	)	PUNCT
ejpam-5627	136	13	}	}	PUNCT
ejpam-5627	136	14	=	=	SYM
ejpam-5627	136	15	min{1−	min{1−	VERB
ejpam-5627	136	16	β(x	β(x	NOUN
ejpam-5627	136	17	)	)	PUNCT
ejpam-5627	136	18	,	,	PUNCT
ejpam-5627	136	19	1−	1−	NUM
ejpam-5627	136	20	β(y	β(y	NOUN
ejpam-5627	136	21	)	)	PUNCT
ejpam-5627	136	22	}	}	PUNCT
ejpam-5627	136	23	=	=	SYM
ejpam-5627	136	24	min{βc(x	min{βc(x	NOUN
ejpam-5627	136	25	)	)	PUNCT
ejpam-5627	136	26	,	,	PUNCT
ejpam-5627	136	27	βc(y	βc(y	NUM
ejpam-5627	136	28	)	)	PUNCT
ejpam-5627	136	29	}	}	PUNCT
ejpam-5627	136	30	.	.	PUNCT
ejpam-5627	137	1	n.	n.	PROPN
ejpam-5627	137	2	rajesh	rajesh	PROPN
ejpam-5627	137	3	,	,	PUNCT
ejpam-5627	137	4	t.	t.	PROPN
ejpam-5627	137	5	oner	oner	NOUN
ejpam-5627	137	6	,	,	PUNCT
ejpam-5627	137	7	a.	a.	NOUN
ejpam-5627	137	8	iampan	iampan	PROPN
ejpam-5627	137	9	,	,	PUNCT
ejpam-5627	137	10	i.	i.	PROPN
ejpam-5627	137	11	senturk	senturk	PROPN
ejpam-5627	137	12	/	/	SYM
ejpam-5627	137	13	eur	eur	PROPN
ejpam-5627	137	14	.	.	PUNCT
ejpam-5627	138	1	j.	j.	PROPN
ejpam-5627	138	2	pure	pure	PROPN
ejpam-5627	138	3	appl	appl	PROPN
ejpam-5627	138	4	.	.	PROPN
ejpam-5627	138	5	math	math	PROPN
ejpam-5627	138	6	,	,	PUNCT
ejpam-5627	138	7	18	18	NUM
ejpam-5627	138	8	(	(	PUNCT
ejpam-5627	138	9	1	1	NUM
ejpam-5627	138	10	)	)	PUNCT
ejpam-5627	138	11	(	(	PUNCT
ejpam-5627	138	12	2025	2025	NUM
ejpam-5627	138	13	)	)	PUNCT
ejpam-5627	138	14	,	,	PUNCT
ejpam-5627	138	15	5627	5627	NUM
ejpam-5627	138	16	6	6	NUM
ejpam-5627	138	17	of	of	ADP
ejpam-5627	138	18	15	15	NUM
ejpam-5627	138	19	hence	hence	ADV
ejpam-5627	138	20	,	,	PUNCT
ejpam-5627	138	21	βc	βc	INTJ
ejpam-5627	138	22	is	be	AUX
ejpam-5627	138	23	a	a	DET
ejpam-5627	138	24	fuzzy	fuzzy	ADJ
ejpam-5627	138	25	sup	sup	ADJ
ejpam-5627	138	26	-	-	PUNCT
ejpam-5627	138	27	subalgebra	subalgebra	NOUN
ejpam-5627	138	28	of	of	ADP
ejpam-5627	138	29	h.	h.	NOUN
ejpam-5627	138	30	conversely	conversely	ADV
ejpam-5627	138	31	,	,	PUNCT
ejpam-5627	138	32	let	let	VERB
ejpam-5627	138	33	h	h	NOUN
ejpam-5627	138	34	=	=	PUNCT
ejpam-5627	138	35	(	(	PUNCT
ejpam-5627	138	36	h	h	NOUN
ejpam-5627	138	37	,	,	PUNCT
ejpam-5627	138	38	α	α	NOUN
ejpam-5627	138	39	,	,	PUNCT
ejpam-5627	138	40	β	β	NOUN
ejpam-5627	138	41	)	)	PUNCT
ejpam-5627	138	42	be	be	VERB
ejpam-5627	138	43	an	an	DET
ejpam-5627	138	44	ifs	ifs	PROPN
ejpam-5627	138	45	of	of	ADP
ejpam-5627	138	46	h	h	NOUN
ejpam-5627	138	47	for	for	ADP
ejpam-5627	138	48	which	which	PRON
ejpam-5627	138	49	βc	βc	INTJ
ejpam-5627	138	50	and	and	CCONJ
ejpam-5627	138	51	α	α	PROPN
ejpam-5627	138	52	are	be	AUX
ejpam-5627	138	53	fuzzy	fuzzy	ADJ
ejpam-5627	138	54	supsubalgebras	supsubalgebra	NOUN
ejpam-5627	138	55	of	of	ADP
ejpam-5627	138	56	h.	h.	PROPN
ejpam-5627	138	57	let	let	VERB
ejpam-5627	138	58	x	x	PRON
ejpam-5627	138	59	,	,	PUNCT
ejpam-5627	138	60	y	y	PROPN
ejpam-5627	138	61	∈	∈	PROPN
ejpam-5627	138	62	h.	h.	PROPN
ejpam-5627	138	63	then	then	ADV
ejpam-5627	138	64	1−	1−	NUM
ejpam-5627	138	65	β((x|(y|y))|(x|(y|y	β((x|(y|y))|(x|(y|y	ADJ
ejpam-5627	138	66	)	)	PUNCT
ejpam-5627	138	67	)	)	PUNCT
ejpam-5627	138	68	)	)	PUNCT
ejpam-5627	139	1	=	=	SYM
ejpam-5627	139	2	βc((x|(y|y))|(x|(y|y	βc((x|(y|y))|(x|(y|y	X
ejpam-5627	139	3	)	)	PUNCT
ejpam-5627	139	4	)	)	PUNCT
ejpam-5627	139	5	)	)	PUNCT
ejpam-5627	139	6	≥	≥	PROPN
ejpam-5627	139	7	min{βc(x	min{βc(x	NOUN
ejpam-5627	139	8	)	)	PUNCT
ejpam-5627	139	9	,	,	PUNCT
ejpam-5627	139	10	βc(y	βc(y	NUM
ejpam-5627	139	11	)	)	PUNCT
ejpam-5627	139	12	}	}	PUNCT
ejpam-5627	139	13	=	=	SYM
ejpam-5627	140	1	min{1−	min{1−	VERB
ejpam-5627	140	2	β(x	β(x	NOUN
ejpam-5627	140	3	)	)	PUNCT
ejpam-5627	140	4	,	,	PUNCT
ejpam-5627	140	5	1−	1−	NUM
ejpam-5627	140	6	β(y	β(y	NOUN
ejpam-5627	140	7	)	)	PUNCT
ejpam-5627	140	8	}	}	PUNCT
ejpam-5627	141	1	=	=	SYM
ejpam-5627	141	2	1−max{β(x	1−max{β(x	NUM
ejpam-5627	141	3	)	)	PUNCT
ejpam-5627	141	4	,	,	PUNCT
ejpam-5627	141	5	β(y	β(y	PROPN
ejpam-5627	141	6	)	)	PUNCT
ejpam-5627	141	7	}	}	PUNCT
ejpam-5627	141	8	,	,	PUNCT
ejpam-5627	141	9	β((x|(y|y))|(x|(y|y	β((x|(y|y))|(x|(y|y	ADJ
ejpam-5627	141	10	)	)	PUNCT
ejpam-5627	141	11	)	)	PUNCT
ejpam-5627	141	12	)	)	PUNCT
ejpam-5627	142	1	≤	≤	NUM
ejpam-5627	142	2	max{β(x	max{β(x	NOUN
ejpam-5627	142	3	)	)	PUNCT
ejpam-5627	142	4	,	,	PUNCT
ejpam-5627	142	5	β(y	β(y	PROPN
ejpam-5627	142	6	)	)	PUNCT
ejpam-5627	142	7	}	}	PUNCT
ejpam-5627	142	8	.	.	PUNCT
ejpam-5627	143	1	hence	hence	ADV
ejpam-5627	143	2	,	,	PUNCT
ejpam-5627	143	3	h	h	NOUN
ejpam-5627	143	4	=	=	PRON
ejpam-5627	143	5	(	(	PUNCT
ejpam-5627	143	6	h	h	NOUN
ejpam-5627	143	7	,	,	PUNCT
ejpam-5627	143	8	α	α	NOUN
ejpam-5627	143	9	,	,	PUNCT
ejpam-5627	143	10	β	β	NOUN
ejpam-5627	143	11	)	)	PUNCT
ejpam-5627	143	12	is	be	AUX
ejpam-5627	143	13	an	an	DET
ejpam-5627	143	14	intuitionistic	intuitionistic	ADJ
ejpam-5627	143	15	fuzzy	fuzzy	ADJ
ejpam-5627	143	16	sup	sup	NOUN
ejpam-5627	143	17	-	-	PUNCT
ejpam-5627	143	18	subalgebra	subalgebra	NOUN
ejpam-5627	143	19	of	of	ADP
ejpam-5627	143	20	h.	h.	PROPN
ejpam-5627	143	21	theorem	theorem	PROPN
ejpam-5627	143	22	4	4	NUM
ejpam-5627	143	23	.	.	PUNCT
ejpam-5627	143	24	given	give	VERB
ejpam-5627	143	25	a	a	DET
ejpam-5627	143	26	nonempty	nonempty	ADJ
ejpam-5627	143	27	subset	subset	VERB
ejpam-5627	143	28	f	f	PROPN
ejpam-5627	143	29	of	of	ADP
ejpam-5627	143	30	h	h	NOUN
ejpam-5627	143	31	,	,	PUNCT
ejpam-5627	143	32	let	let	VERB
ejpam-5627	143	33	hf	hf	VERB
ejpam-5627	143	34	=	=	PUNCT
ejpam-5627	143	35	(	(	PUNCT
ejpam-5627	143	36	h	h	NOUN
ejpam-5627	143	37	,	,	PUNCT
ejpam-5627	143	38	αf	αf	VERB
ejpam-5627	143	39	,	,	PUNCT
ejpam-5627	143	40	βf	βf	CCONJ
ejpam-5627	143	41	)	)	PUNCT
ejpam-5627	143	42	be	be	AUX
ejpam-5627	143	43	an	an	DET
ejpam-5627	143	44	ifs	ifs	PROPN
ejpam-5627	143	45	in	in	ADP
ejpam-5627	143	46	h	h	PROPN
ejpam-5627	143	47	defined	define	VERB
ejpam-5627	143	48	as	as	SCONJ
ejpam-5627	143	49	follows	follow	VERB
ejpam-5627	143	50	:	:	PUNCT
ejpam-5627	143	51	α(x	α(x	NUM
ejpam-5627	143	52	)	)	PUNCT
ejpam-5627	143	53	=	=	PRON
ejpam-5627	144	1	{	{	PUNCT
ejpam-5627	144	2	α0	α0	ADJ
ejpam-5627	144	3	if	if	SCONJ
ejpam-5627	144	4	x	x	SYM
ejpam-5627	144	5	∈	∈	PROPN
ejpam-5627	144	6	f	f	PROPN
ejpam-5627	144	7	α1	α1	PROPN
ejpam-5627	144	8	otherwise	otherwise	ADV
ejpam-5627	144	9	,	,	PUNCT
ejpam-5627	144	10	β(x	β(x	NOUN
ejpam-5627	144	11	)	)	PUNCT
ejpam-5627	144	12	=	=	PRON
ejpam-5627	145	1	{	{	PUNCT
ejpam-5627	145	2	β0	β0	ADV
ejpam-5627	145	3	if	if	SCONJ
ejpam-5627	145	4	x	x	SYM
ejpam-5627	145	5	∈	∈	PROPN
ejpam-5627	145	6	f	f	PROPN
ejpam-5627	145	7	β1	β1	PROPN
ejpam-5627	145	8	otherwise	otherwise	ADV
ejpam-5627	145	9	for	for	ADP
ejpam-5627	145	10	all	all	DET
ejpam-5627	145	11	x	x	SYM
ejpam-5627	145	12	∈	∈	PROPN
ejpam-5627	145	13	h	h	NOUN
ejpam-5627	145	14	and	and	CCONJ
ejpam-5627	145	15	αi	αi	PROPN
ejpam-5627	145	16	,	,	PUNCT
ejpam-5627	145	17	βi	βi	PROPN
ejpam-5627	145	18	∈	∈	PROPN
ejpam-5627	146	1	[	[	X
ejpam-5627	146	2	0	0	NUM
ejpam-5627	146	3	,	,	PUNCT
ejpam-5627	146	4	1	1	NUM
ejpam-5627	146	5	]	]	PUNCT
ejpam-5627	146	6	such	such	ADJ
ejpam-5627	146	7	that	that	SCONJ
ejpam-5627	146	8	α0	α0	ADJ
ejpam-5627	146	9	>	>	X
ejpam-5627	146	10	α1	α1	PROPN
ejpam-5627	146	11	,	,	PUNCT
ejpam-5627	146	12	β0	β0	NOUN
ejpam-5627	146	13	<	<	X
ejpam-5627	146	14	β1	β1	PROPN
ejpam-5627	146	15	,	,	PUNCT
ejpam-5627	146	16	and	and	CCONJ
ejpam-5627	146	17	αi	αi	VERB
ejpam-5627	147	1	+	+	CCONJ
ejpam-5627	147	2	βi	βi	VERB
ejpam-5627	147	3	≤	≤	NUM
ejpam-5627	147	4	1	1	NUM
ejpam-5627	147	5	for	for	ADP
ejpam-5627	147	6	i	i	PRON
ejpam-5627	147	7	=	=	SYM
ejpam-5627	147	8	0	0	NUM
ejpam-5627	147	9	,	,	PUNCT
ejpam-5627	147	10	1	1	NUM
ejpam-5627	147	11	.	.	PUNCT
ejpam-5627	148	1	then	then	ADV
ejpam-5627	148	2	hf	hf	PROPN
ejpam-5627	148	3	=	=	PUNCT
ejpam-5627	149	1	(	(	PUNCT
ejpam-5627	149	2	h	h	NOUN
ejpam-5627	149	3	,	,	PUNCT
ejpam-5627	149	4	αf	αf	VERB
ejpam-5627	149	5	,	,	PUNCT
ejpam-5627	149	6	βf	βf	CCONJ
ejpam-5627	149	7	)	)	PUNCT
ejpam-5627	149	8	be	be	AUX
ejpam-5627	149	9	an	an	DET
ejpam-5627	149	10	intuitionistic	intuitionistic	ADJ
ejpam-5627	149	11	fuzzy	fuzzy	ADJ
ejpam-5627	149	12	sup	sup	NOUN
ejpam-5627	149	13	-	-	PUNCT
ejpam-5627	149	14	subalgebra	subalgebra	NOUN
ejpam-5627	149	15	of	of	ADP
ejpam-5627	149	16	h	h	NOUN
ejpam-5627	149	17	if	if	SCONJ
ejpam-5627	150	1	and	and	CCONJ
ejpam-5627	150	2	only	only	ADV
ejpam-5627	150	3	if	if	SCONJ
ejpam-5627	150	4	f	f	PROPN
ejpam-5627	150	5	is	be	AUX
ejpam-5627	150	6	an	an	DET
ejpam-5627	150	7	sup	sup	ADJ
ejpam-5627	150	8	-	-	PUNCT
ejpam-5627	150	9	subalgebra	subalgebra	NOUN
ejpam-5627	150	10	of	of	ADP
ejpam-5627	150	11	h.	h.	NOUN
ejpam-5627	150	12	proof	proof	NOUN
ejpam-5627	150	13	.	.	PUNCT
ejpam-5627	151	1	assume	assume	VERB
ejpam-5627	151	2	that	that	SCONJ
ejpam-5627	151	3	hf	hf	PROPN
ejpam-5627	151	4	=	=	PUNCT
ejpam-5627	151	5	(	(	PUNCT
ejpam-5627	151	6	h	h	NOUN
ejpam-5627	151	7	,	,	PUNCT
ejpam-5627	151	8	αf	αf	VERB
ejpam-5627	151	9	,	,	PUNCT
ejpam-5627	151	10	βf	βf	CCONJ
ejpam-5627	151	11	)	)	PUNCT
ejpam-5627	151	12	is	be	AUX
ejpam-5627	151	13	an	an	DET
ejpam-5627	151	14	intuitionistic	intuitionistic	ADJ
ejpam-5627	151	15	fuzzy	fuzzy	ADJ
ejpam-5627	151	16	sup	sup	NOUN
ejpam-5627	151	17	-	-	PUNCT
ejpam-5627	151	18	subalgebra	subalgebra	NOUN
ejpam-5627	151	19	of	of	ADP
ejpam-5627	151	20	h.	h.	PROPN
ejpam-5627	151	21	let	let	VERB
ejpam-5627	151	22	x	x	PRON
ejpam-5627	151	23	,	,	PUNCT
ejpam-5627	151	24	y	y	PROPN
ejpam-5627	151	25	∈	∈	PROPN
ejpam-5627	151	26	h	h	NOUN
ejpam-5627	151	27	be	be	AUX
ejpam-5627	151	28	such	such	ADJ
ejpam-5627	151	29	that	that	SCONJ
ejpam-5627	151	30	x	x	NOUN
ejpam-5627	151	31	,	,	PUNCT
ejpam-5627	151	32	y	y	PROPN
ejpam-5627	151	33	∈	∈	PROPN
ejpam-5627	151	34	f	f	PROPN
ejpam-5627	151	35	.	.	PUNCT
ejpam-5627	152	1	then	then	ADV
ejpam-5627	152	2	α((x|(y|y))|(x|(y|y	α((x|(y|y))|(x|(y|y	PROPN
ejpam-5627	152	3	)	)	PUNCT
ejpam-5627	152	4	)	)	PUNCT
ejpam-5627	152	5	)	)	PUNCT
ejpam-5627	152	6	≥	≥	X
ejpam-5627	152	7	min{α(x	min{α(x	NOUN
ejpam-5627	152	8	)	)	PUNCT
ejpam-5627	152	9	,	,	PUNCT
ejpam-5627	152	10	α(y	α(y	NOUN
ejpam-5627	152	11	)	)	PUNCT
ejpam-5627	152	12	}	}	PUNCT
ejpam-5627	152	13	=	=	SYM
ejpam-5627	152	14	α0	α0	ADJ
ejpam-5627	152	15	,	,	PUNCT
ejpam-5627	152	16	β((x|(y|y))|(x|(y|y	β((x|(y|y))|(x|(y|y	ADJ
ejpam-5627	152	17	)	)	PUNCT
ejpam-5627	152	18	)	)	PUNCT
ejpam-5627	152	19	)	)	PUNCT
ejpam-5627	152	20	≤	≤	NUM
ejpam-5627	152	21	max{β(x	max{β(x	NOUN
ejpam-5627	152	22	)	)	PUNCT
ejpam-5627	152	23	,	,	PUNCT
ejpam-5627	152	24	β(y	β(y	PROPN
ejpam-5627	152	25	)	)	PUNCT
ejpam-5627	152	26	}	}	PUNCT
ejpam-5627	152	27	=	=	SYM
ejpam-5627	152	28	β0	β0	NOUN
ejpam-5627	152	29	,	,	PUNCT
ejpam-5627	152	30	and	and	CCONJ
ejpam-5627	152	31	so	so	ADV
ejpam-5627	152	32	α((x|(y|y))|(x|(y|y	α((x|(y|y))|(x|(y|y	ADJ
ejpam-5627	152	33	)	)	PUNCT
ejpam-5627	152	34	)	)	PUNCT
ejpam-5627	152	35	)	)	PUNCT
ejpam-5627	153	1	=	=	SYM
ejpam-5627	154	1	α0	α0	ADJ
ejpam-5627	154	2	and	and	CCONJ
ejpam-5627	154	3	β((x|(y|y))|(x|(y|y	β((x|(y|y))|(x|(y|y	ADJ
ejpam-5627	154	4	)	)	PUNCT
ejpam-5627	154	5	)	)	PUNCT
ejpam-5627	154	6	)	)	PUNCT
ejpam-5627	155	1	=	=	SYM
ejpam-5627	155	2	β0	β0	NOUN
ejpam-5627	155	3	.	.	PUNCT
ejpam-5627	156	1	this	this	PRON
ejpam-5627	156	2	shows	show	VERB
ejpam-5627	156	3	that	that	SCONJ
ejpam-5627	156	4	(	(	PUNCT
ejpam-5627	156	5	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-5627	156	6	)	)	PUNCT
ejpam-5627	156	7	)	)	PUNCT
ejpam-5627	157	1	∈	∈	PROPN
ejpam-5627	157	2	f	f	INTJ
ejpam-5627	157	3	.	.	PUNCT
ejpam-5627	158	1	therefore	therefore	ADV
ejpam-5627	158	2	,	,	PUNCT
ejpam-5627	158	3	f	f	PROPN
ejpam-5627	158	4	is	be	AUX
ejpam-5627	158	5	an	an	DET
ejpam-5627	158	6	sup	sup	ADJ
ejpam-5627	158	7	-	-	PUNCT
ejpam-5627	158	8	subalgebra	subalgebra	NOUN
ejpam-5627	158	9	of	of	ADP
ejpam-5627	158	10	h.	h.	NOUN
ejpam-5627	158	11	conversely	conversely	ADV
ejpam-5627	158	12	,	,	PUNCT
ejpam-5627	158	13	let	let	VERB
ejpam-5627	158	14	f	f	PRON
ejpam-5627	158	15	be	be	AUX
ejpam-5627	158	16	an	an	DET
ejpam-5627	158	17	sup	sup	ADJ
ejpam-5627	158	18	-	-	PUNCT
ejpam-5627	158	19	subalgebra	subalgebra	NOUN
ejpam-5627	158	20	of	of	ADP
ejpam-5627	158	21	h.	h.	NOUN
ejpam-5627	158	22	for	for	ADP
ejpam-5627	158	23	every	every	DET
ejpam-5627	158	24	x	x	NOUN
ejpam-5627	158	25	,	,	PUNCT
ejpam-5627	158	26	y	y	PROPN
ejpam-5627	158	27	∈	∈	PROPN
ejpam-5627	158	28	h	h	NOUN
ejpam-5627	158	29	,	,	PUNCT
ejpam-5627	158	30	if	if	SCONJ
ejpam-5627	158	31	x	x	X
ejpam-5627	158	32	,	,	PUNCT
ejpam-5627	158	33	y	y	PROPN
ejpam-5627	158	34	∈	∈	PROPN
ejpam-5627	158	35	f	f	PROPN
ejpam-5627	158	36	,	,	PUNCT
ejpam-5627	158	37	then	then	ADV
ejpam-5627	158	38	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	NUM
ejpam-5627	158	39	)	)	PUNCT
ejpam-5627	158	40	∈	∈	PROPN
ejpam-5627	158	41	f	f	PROPN
ejpam-5627	158	42	which	which	PRON
ejpam-5627	158	43	implies	imply	VERB
ejpam-5627	158	44	that	that	SCONJ
ejpam-5627	158	45	α((x|(y|y))|(x|(y|y	α((x|(y|y))|(x|(y|y	PROPN
ejpam-5627	158	46	)	)	PUNCT
ejpam-5627	158	47	)	)	PUNCT
ejpam-5627	158	48	)	)	PUNCT
ejpam-5627	159	1	=	=	SYM
ejpam-5627	159	2	α0	α0	ADJ
ejpam-5627	159	3	=	=	SYM
ejpam-5627	159	4	min{β(x	min{β(x	NOUN
ejpam-5627	159	5	)	)	PUNCT
ejpam-5627	159	6	,	,	PUNCT
ejpam-5627	159	7	β(y	β(y	PROPN
ejpam-5627	159	8	)	)	PUNCT
ejpam-5627	159	9	}	}	PUNCT
ejpam-5627	159	10	,	,	PUNCT
ejpam-5627	159	11	β((x|(y|y))|(x|(y|y	β((x|(y|y))|(x|(y|y	ADJ
ejpam-5627	159	12	)	)	PUNCT
ejpam-5627	159	13	)	)	PUNCT
ejpam-5627	159	14	)	)	PUNCT
ejpam-5627	160	1	=	=	SYM
ejpam-5627	160	2	β0	β0	PROPN
ejpam-5627	160	3	=	=	SYM
ejpam-5627	160	4	max{β(x	max{β(x	NOUN
ejpam-5627	160	5	)	)	PUNCT
ejpam-5627	160	6	,	,	PUNCT
ejpam-5627	160	7	β(y	β(y	PROPN
ejpam-5627	160	8	)	)	PUNCT
ejpam-5627	160	9	}	}	PUNCT
ejpam-5627	160	10	.	.	PUNCT
ejpam-5627	161	1	if	if	SCONJ
ejpam-5627	161	2	x	x	PROPN
ejpam-5627	161	3	/∈	/∈	PROPN
ejpam-5627	162	1	f	f	PROPN
ejpam-5627	162	2	of	of	ADP
ejpam-5627	162	3	y	y	PROPN
ejpam-5627	162	4	/∈	/∈	PUNCT
ejpam-5627	163	1	f	f	PROPN
ejpam-5627	163	2	,	,	PUNCT
ejpam-5627	163	3	then	then	ADV
ejpam-5627	163	4	α((x|(y|y))|(x|(y|y	α((x|(y|y))|(x|(y|y	PROPN
ejpam-5627	163	5	)	)	PUNCT
ejpam-5627	163	6	)	)	PUNCT
ejpam-5627	163	7	)	)	PUNCT
ejpam-5627	164	1	≥	≥	PROPN
ejpam-5627	164	2	α1	α1	PROPN
ejpam-5627	164	3	=	=	SYM
ejpam-5627	164	4	min{α(x	min{α(x	NOUN
ejpam-5627	164	5	)	)	PUNCT
ejpam-5627	164	6	,	,	PUNCT
ejpam-5627	164	7	α(y	α(y	NOUN
ejpam-5627	164	8	)	)	PUNCT
ejpam-5627	164	9	}	}	PUNCT
ejpam-5627	164	10	,	,	PUNCT
ejpam-5627	164	11	β((x|(y|y))|(x|(y|y	β((x|(y|y))|(x|(y|y	ADJ
ejpam-5627	164	12	)	)	PUNCT
ejpam-5627	164	13	)	)	PUNCT
ejpam-5627	164	14	)	)	PUNCT
ejpam-5627	165	1	≤	≤	NUM
ejpam-5627	166	1	β1	β1	NOUN
ejpam-5627	166	2	=	=	PUNCT
ejpam-5627	166	3	max{β(x	max{β(x	NOUN
ejpam-5627	166	4	)	)	PUNCT
ejpam-5627	166	5	,	,	PUNCT
ejpam-5627	166	6	β(y	β(y	PROPN
ejpam-5627	166	7	)	)	PUNCT
ejpam-5627	166	8	}	}	PUNCT
ejpam-5627	166	9	.	.	PUNCT
ejpam-5627	167	1	therefore	therefore	ADV
ejpam-5627	167	2	,	,	PUNCT
ejpam-5627	167	3	hf	hf	NOUN
ejpam-5627	167	4	=	=	PUNCT
ejpam-5627	167	5	(	(	PUNCT
ejpam-5627	167	6	h	h	NOUN
ejpam-5627	167	7	,	,	PUNCT
ejpam-5627	167	8	αf	αf	VERB
ejpam-5627	167	9	,	,	PUNCT
ejpam-5627	167	10	βf	βf	CCONJ
ejpam-5627	167	11	)	)	PUNCT
ejpam-5627	167	12	is	be	AUX
ejpam-5627	167	13	an	an	DET
ejpam-5627	167	14	intuitionistic	intuitionistic	ADJ
ejpam-5627	167	15	fuzzy	fuzzy	ADJ
ejpam-5627	167	16	sup	sup	NOUN
ejpam-5627	167	17	-	-	PUNCT
ejpam-5627	167	18	subalgebra	subalgebra	NOUN
ejpam-5627	167	19	of	of	ADP
ejpam-5627	167	20	h.	h.	PROPN
ejpam-5627	167	21	definition	definition	NOUN
ejpam-5627	167	22	8	8	NUM
ejpam-5627	167	23	.	.	PUNCT
ejpam-5627	168	1	an	an	DET
ejpam-5627	168	2	ifs	ifs	PROPN
ejpam-5627	168	3	h	h	NOUN
ejpam-5627	168	4	=	=	PUNCT
ejpam-5627	168	5	(	(	PUNCT
ejpam-5627	168	6	h,µ	h,µ	PROPN
ejpam-5627	168	7	,	,	PUNCT
ejpam-5627	168	8	γ	γ	NOUN
ejpam-5627	168	9	)	)	PUNCT
ejpam-5627	168	10	of	of	ADP
ejpam-5627	168	11	h	h	NOUN
ejpam-5627	168	12	is	be	AUX
ejpam-5627	168	13	called	call	VERB
ejpam-5627	168	14	an	an	DET
ejpam-5627	168	15	intuitionistic	intuitionistic	ADJ
ejpam-5627	168	16	fuzzy	fuzzy	ADJ
ejpam-5627	168	17	sup	sup	NOUN
ejpam-5627	168	18	-	-	PUNCT
ejpam-5627	168	19	ideal	ideal	NOUN
ejpam-5627	168	20	of	of	ADP
ejpam-5627	168	21	h	h	NOUN
ejpam-5627	168	22	if	if	SCONJ
ejpam-5627	168	23	(	(	PUNCT
ejpam-5627	168	24	∀x	∀x	X
ejpam-5627	168	25	,	,	PUNCT
ejpam-5627	168	26	y	y	PROPN
ejpam-5627	168	27	∈	∈	PROPN
ejpam-5627	168	28	h	h	PROPN
ejpam-5627	168	29	)	)	PUNCT
ejpam-5627	168	30	(	(	PUNCT
ejpam-5627	168	31	µ((y|(x|x))|(y|(x|x	µ((y|(x|x))|(y|(x|x	NOUN
ejpam-5627	168	32	)	)	PUNCT
ejpam-5627	168	33	)	)	PUNCT
ejpam-5627	168	34	)	)	PUNCT
ejpam-5627	168	35	≥	≥	PROPN
ejpam-5627	168	36	µ(y	µ(y	PROPN
ejpam-5627	168	37	)	)	PUNCT
ejpam-5627	168	38	≥	≥	NOUN
ejpam-5627	168	39	min{µ((y|(x|x))|(y|(x|x	min{µ((y|(x|x))|(y|(x|x	NOUN
ejpam-5627	168	40	)	)	PUNCT
ejpam-5627	168	41	)	)	PUNCT
ejpam-5627	168	42	)	)	PUNCT
ejpam-5627	168	43	,	,	PUNCT
ejpam-5627	168	44	µ(x	µ(x	NOUN
ejpam-5627	168	45	)	)	PUNCT
ejpam-5627	168	46	}	}	PUNCT
ejpam-5627	168	47	γ((y|(x|x))|(y|(x|x	γ((y|(x|x))|(y|(x|x	NOUN
ejpam-5627	168	48	)	)	PUNCT
ejpam-5627	168	49	)	)	PUNCT
ejpam-5627	168	50	)	)	PUNCT
ejpam-5627	168	51	≤	≤	NUM
ejpam-5627	169	1	γ(y	γ(y	PROPN
ejpam-5627	169	2	)	)	PUNCT
ejpam-5627	169	3	≤	≤	NUM
ejpam-5627	169	4	max{γ((y|(x|x))|(y|(x|x	max{γ((y|(x|x))|(y|(x|x	NOUN
ejpam-5627	169	5	)	)	PUNCT
ejpam-5627	169	6	)	)	PUNCT
ejpam-5627	169	7	)	)	PUNCT
ejpam-5627	169	8	,	,	PUNCT
ejpam-5627	169	9	γ(x	γ(x	NOUN
ejpam-5627	169	10	)	)	PUNCT
ejpam-5627	169	11	}	}	PUNCT
ejpam-5627	169	12	)	)	PUNCT
ejpam-5627	169	13	.	.	PUNCT
ejpam-5627	170	1	(	(	PUNCT
ejpam-5627	170	2	3	3	X
ejpam-5627	170	3	)	)	PUNCT
ejpam-5627	170	4	n.	n.	PROPN
ejpam-5627	170	5	rajesh	rajesh	PROPN
ejpam-5627	170	6	,	,	PUNCT
ejpam-5627	170	7	t.	t.	PROPN
ejpam-5627	170	8	oner	oner	NOUN
ejpam-5627	170	9	,	,	PUNCT
ejpam-5627	170	10	a.	a.	NOUN
ejpam-5627	170	11	iampan	iampan	PROPN
ejpam-5627	170	12	,	,	PUNCT
ejpam-5627	170	13	i.	i.	PROPN
ejpam-5627	170	14	senturk	senturk	PROPN
ejpam-5627	170	15	/	/	SYM
ejpam-5627	170	16	eur	eur	PROPN
ejpam-5627	170	17	.	.	PUNCT
ejpam-5627	171	1	j.	j.	PROPN
ejpam-5627	171	2	pure	pure	PROPN
ejpam-5627	171	3	appl	appl	PROPN
ejpam-5627	171	4	.	.	PROPN
ejpam-5627	171	5	math	math	PROPN
ejpam-5627	171	6	,	,	PUNCT
ejpam-5627	171	7	18	18	NUM
ejpam-5627	171	8	(	(	PUNCT
ejpam-5627	171	9	1	1	NUM
ejpam-5627	171	10	)	)	PUNCT
ejpam-5627	171	11	(	(	PUNCT
ejpam-5627	171	12	2025	2025	NUM
ejpam-5627	171	13	)	)	PUNCT
ejpam-5627	171	14	,	,	PUNCT
ejpam-5627	171	15	5627	5627	NUM
ejpam-5627	171	16	7	7	NUM
ejpam-5627	171	17	of	of	ADP
ejpam-5627	171	18	15	15	NUM
ejpam-5627	171	19	theorem	theorem	NOUN
ejpam-5627	171	20	5	5	NUM
ejpam-5627	171	21	.	.	PUNCT
ejpam-5627	172	1	every	every	DET
ejpam-5627	172	2	intuitionistic	intuitionistic	ADJ
ejpam-5627	172	3	fuzzy	fuzzy	ADJ
ejpam-5627	172	4	sup	sup	NOUN
ejpam-5627	172	5	-	-	PUNCT
ejpam-5627	172	6	ideal	ideal	NOUN
ejpam-5627	172	7	of	of	ADP
ejpam-5627	172	8	h	h	NOUN
ejpam-5627	172	9	is	be	AUX
ejpam-5627	172	10	an	an	DET
ejpam-5627	172	11	intuitionistic	intuitionistic	ADJ
ejpam-5627	172	12	fuzzy	fuzzy	ADJ
ejpam-5627	172	13	supsubalgebra	supsubalgebra	NOUN
ejpam-5627	172	14	of	of	ADP
ejpam-5627	172	15	h.	h.	PROPN
ejpam-5627	172	16	lemma	lemma	PROPN
ejpam-5627	173	1	2	2	X
ejpam-5627	173	2	.	.	PUNCT
ejpam-5627	174	1	if	if	SCONJ
ejpam-5627	174	2	h	h	PRON
ejpam-5627	174	3	=	=	SYM
ejpam-5627	174	4	(	(	PUNCT
ejpam-5627	174	5	h,µ	h,µ	PROPN
ejpam-5627	174	6	,	,	PUNCT
ejpam-5627	174	7	γ	γ	NOUN
ejpam-5627	174	8	)	)	PUNCT
ejpam-5627	174	9	is	be	AUX
ejpam-5627	174	10	an	an	DET
ejpam-5627	174	11	intuitionistic	intuitionistic	ADJ
ejpam-5627	174	12	fuzzy	fuzzy	ADJ
ejpam-5627	174	13	sup	sup	NOUN
ejpam-5627	174	14	-	-	PUNCT
ejpam-5627	174	15	ideal	ideal	NOUN
ejpam-5627	174	16	of	of	ADP
ejpam-5627	174	17	h	h	NOUN
ejpam-5627	174	18	,	,	PUNCT
ejpam-5627	174	19	then	then	ADV
ejpam-5627	174	20	(	(	PUNCT
ejpam-5627	174	21	∀	∀	X
ejpam-5627	174	22	x	x	NOUN
ejpam-5627	174	23	,	,	PUNCT
ejpam-5627	174	24	y	y	PROPN
ejpam-5627	174	25	∈	∈	PROPN
ejpam-5627	174	26	h	h	NOUN
ejpam-5627	174	27	)	)	PUNCT
ejpam-5627	174	28	(	(	PUNCT
ejpam-5627	174	29	x	x	SYM
ejpam-5627	174	30	≤	≤	NOUN
ejpam-5627	174	31	y	y	PROPN
ejpam-5627	174	32	⇒	⇒	NOUN
ejpam-5627	174	33	{	{	PUNCT
ejpam-5627	174	34	µ(y	µ(y	PROPN
ejpam-5627	174	35	)	)	PUNCT
ejpam-5627	174	36	≥	≥	NOUN
ejpam-5627	174	37	µ(x	µ(x	NOUN
ejpam-5627	174	38	)	)	PUNCT
ejpam-5627	174	39	γ(y	γ(y	PROPN
ejpam-5627	174	40	)	)	PUNCT
ejpam-5627	174	41	≤	≤	NUM
ejpam-5627	174	42	γ(x	γ(x	NOUN
ejpam-5627	174	43	)	)	PUNCT
ejpam-5627	174	44	)	)	PUNCT
ejpam-5627	174	45	.	.	PUNCT
ejpam-5627	175	1	(	(	PUNCT
ejpam-5627	175	2	4	4	X
ejpam-5627	175	3	)	)	PUNCT
ejpam-5627	175	4	proof	proof	NOUN
ejpam-5627	175	5	.	.	PUNCT
ejpam-5627	176	1	let	let	VERB
ejpam-5627	176	2	h	h	NOUN
ejpam-5627	176	3	=	=	PUNCT
ejpam-5627	176	4	(	(	PUNCT
ejpam-5627	176	5	h,µ	h,µ	PROPN
ejpam-5627	176	6	,	,	PUNCT
ejpam-5627	176	7	γ	γ	NOUN
ejpam-5627	176	8	)	)	PUNCT
ejpam-5627	176	9	be	be	VERB
ejpam-5627	176	10	an	an	DET
ejpam-5627	176	11	intuitionistic	intuitionistic	ADJ
ejpam-5627	176	12	fuzzy	fuzzy	ADJ
ejpam-5627	176	13	sup	sup	NOUN
ejpam-5627	176	14	-	-	PUNCT
ejpam-5627	176	15	ideal	ideal	NOUN
ejpam-5627	176	16	of	of	ADP
ejpam-5627	176	17	h	h	NOUN
ejpam-5627	176	18	and	and	CCONJ
ejpam-5627	176	19	x	x	SYM
ejpam-5627	176	20	≤	≤	PROPN
ejpam-5627	176	21	y.	y.	NOUN
ejpam-5627	176	22	then	then	ADV
ejpam-5627	176	23	µ(y	µ(y	PROPN
ejpam-5627	176	24	)	)	PUNCT
ejpam-5627	176	25	≥	≥	NOUN
ejpam-5627	176	26	min{µ(x	min{µ(x	NOUN
ejpam-5627	176	27	)	)	PUNCT
ejpam-5627	176	28	,	,	PUNCT
ejpam-5627	176	29	µ(0	µ(0	NOUN
ejpam-5627	176	30	)	)	PUNCT
ejpam-5627	176	31	}	}	PUNCT
ejpam-5627	176	32	=	=	PUNCT
ejpam-5627	176	33	µ(0	µ(0	NOUN
ejpam-5627	176	34	)	)	PUNCT
ejpam-5627	176	35	,	,	PUNCT
ejpam-5627	176	36	γ(y	γ(y	PROPN
ejpam-5627	176	37	)	)	PUNCT
ejpam-5627	176	38	≤	≤	PUNCT
ejpam-5627	176	39	max{γ(x	max{γ(x	PROPN
ejpam-5627	176	40	)	)	PUNCT
ejpam-5627	176	41	,	,	PUNCT
ejpam-5627	176	42	γ(0	γ(0	PROPN
ejpam-5627	176	43	)	)	PUNCT
ejpam-5627	176	44	}	}	PUNCT
ejpam-5627	176	45	=	=	SYM
ejpam-5627	176	46	γ(x	γ(x	NOUN
ejpam-5627	176	47	)	)	PUNCT
ejpam-5627	176	48	for	for	ADP
ejpam-5627	176	49	all	all	DET
ejpam-5627	176	50	x	x	NOUN
ejpam-5627	176	51	,	,	PUNCT
ejpam-5627	176	52	y	y	PROPN
ejpam-5627	176	53	∈	∈	PROPN
ejpam-5627	176	54	h.	h.	PROPN
ejpam-5627	176	55	theorem	theorem	VERB
ejpam-5627	176	56	6	6	NUM
ejpam-5627	176	57	.	.	PUNCT
ejpam-5627	177	1	an	an	DET
ejpam-5627	177	2	ifs	ifs	PROPN
ejpam-5627	177	3	h	h	NOUN
ejpam-5627	177	4	=	=	PUNCT
ejpam-5627	177	5	(	(	PUNCT
ejpam-5627	177	6	h	h	NOUN
ejpam-5627	177	7	,	,	PUNCT
ejpam-5627	177	8	α	α	NOUN
ejpam-5627	177	9	,	,	PUNCT
ejpam-5627	177	10	β	β	NOUN
ejpam-5627	177	11	)	)	PUNCT
ejpam-5627	177	12	in	in	ADP
ejpam-5627	177	13	h	h	NOUN
ejpam-5627	177	14	is	be	AUX
ejpam-5627	177	15	an	an	DET
ejpam-5627	177	16	intuitionistic	intuitionistic	ADJ
ejpam-5627	177	17	fuzzy	fuzzy	ADJ
ejpam-5627	177	18	sup	sup	NOUN
ejpam-5627	177	19	-	-	PUNCT
ejpam-5627	177	20	ideal	ideal	NOUN
ejpam-5627	177	21	of	of	ADP
ejpam-5627	177	22	h	h	NOUN
ejpam-5627	177	23	if	if	SCONJ
ejpam-5627	178	1	and	and	CCONJ
ejpam-5627	178	2	only	only	ADV
ejpam-5627	178	3	if	if	SCONJ
ejpam-5627	178	4	the	the	DET
ejpam-5627	178	5	sets	set	NOUN
ejpam-5627	178	6	l(β	l(β	PROPN
ejpam-5627	178	7	,	,	PUNCT
ejpam-5627	178	8	s	s	NOUN
ejpam-5627	178	9	)	)	PUNCT
ejpam-5627	178	10	and	and	CCONJ
ejpam-5627	178	11	u(α	u(α	PROPN
ejpam-5627	178	12	,	,	PUNCT
ejpam-5627	178	13	t	t	PROPN
ejpam-5627	178	14	)	)	PUNCT
ejpam-5627	178	15	are	be	AUX
ejpam-5627	178	16	sup	sup	ADJ
ejpam-5627	178	17	-	-	PUNCT
ejpam-5627	178	18	ideals	ideal	NOUN
ejpam-5627	178	19	of	of	ADP
ejpam-5627	178	20	h	h	NOUN
ejpam-5627	178	21	whenever	whenever	SCONJ
ejpam-5627	178	22	they	they	PRON
ejpam-5627	178	23	are	be	AUX
ejpam-5627	178	24	nonempty	nonempty	ADJ
ejpam-5627	178	25	for	for	ADP
ejpam-5627	178	26	all	all	DET
ejpam-5627	178	27	s	s	PROPN
ejpam-5627	178	28	,	,	PUNCT
ejpam-5627	178	29	t	t	PROPN
ejpam-5627	178	30	∈	∈	PROPN
ejpam-5627	179	1	[	[	X
ejpam-5627	179	2	0	0	NUM
ejpam-5627	179	3	,	,	PUNCT
ejpam-5627	179	4	1	1	NUM
ejpam-5627	179	5	]	]	PUNCT
ejpam-5627	179	6	.	.	PUNCT
ejpam-5627	180	1	proof	proof	NOUN
ejpam-5627	180	2	.	.	PUNCT
ejpam-5627	181	1	assume	assume	VERB
ejpam-5627	181	2	that	that	SCONJ
ejpam-5627	181	3	h	h	NOUN
ejpam-5627	181	4	=	=	PUNCT
ejpam-5627	181	5	(	(	PUNCT
ejpam-5627	181	6	h	h	NOUN
ejpam-5627	181	7	,	,	PUNCT
ejpam-5627	181	8	α	α	NOUN
ejpam-5627	181	9	,	,	PUNCT
ejpam-5627	181	10	β	β	NOUN
ejpam-5627	181	11	)	)	PUNCT
ejpam-5627	181	12	is	be	AUX
ejpam-5627	181	13	an	an	DET
ejpam-5627	181	14	intuitionistic	intuitionistic	ADJ
ejpam-5627	181	15	fuzzy	fuzzy	ADJ
ejpam-5627	181	16	sup	sup	NOUN
ejpam-5627	181	17	-	-	PUNCT
ejpam-5627	181	18	ideal	ideal	NOUN
ejpam-5627	181	19	of	of	ADP
ejpam-5627	181	20	h	h	NOUN
ejpam-5627	181	21	and	and	CCONJ
ejpam-5627	181	22	l(β	l(β	PROPN
ejpam-5627	181	23	,	,	PUNCT
ejpam-5627	181	24	s	s	X
ejpam-5627	181	25	)	)	PUNCT
ejpam-5627	181	26	̸=	̸=	PROPN
ejpam-5627	181	27	∅	∅	NOUN
ejpam-5627	181	28	=	=	NOUN
ejpam-5627	181	29	̸	̸	PUNCT
ejpam-5627	181	30	u(α	u(α	NOUN
ejpam-5627	181	31	,	,	PUNCT
ejpam-5627	181	32	t	t	PROPN
ejpam-5627	181	33	)	)	PUNCT
ejpam-5627	181	34	for	for	ADP
ejpam-5627	181	35	all	all	DET
ejpam-5627	181	36	s	s	PROPN
ejpam-5627	181	37	,	,	PUNCT
ejpam-5627	181	38	t	t	PROPN
ejpam-5627	181	39	∈	∈	PROPN
ejpam-5627	182	1	[	[	X
ejpam-5627	182	2	0	0	NUM
ejpam-5627	182	3	,	,	PUNCT
ejpam-5627	182	4	1	1	NUM
ejpam-5627	182	5	]	]	PUNCT
ejpam-5627	182	6	.	.	PUNCT
ejpam-5627	183	1	let	let	VERB
ejpam-5627	183	2	x	x	PRON
ejpam-5627	183	3	,	,	PUNCT
ejpam-5627	183	4	y	y	PROPN
ejpam-5627	183	5	,	,	PUNCT
ejpam-5627	183	6	a	a	PRON
ejpam-5627	183	7	,	,	PUNCT
ejpam-5627	183	8	b	b	X
ejpam-5627	183	9	∈	∈	PROPN
ejpam-5627	183	10	h	h	NOUN
ejpam-5627	183	11	be	be	AUX
ejpam-5627	183	12	such	such	ADJ
ejpam-5627	184	1	that	that	SCONJ
ejpam-5627	184	2	(	(	PUNCT
ejpam-5627	184	3	y	y	PROPN
ejpam-5627	184	4	,	,	PUNCT
ejpam-5627	184	5	b	b	NOUN
ejpam-5627	184	6	)	)	PUNCT
ejpam-5627	184	7	∈	∈	PROPN
ejpam-5627	184	8	l(β	l(β	PROPN
ejpam-5627	184	9	,	,	PUNCT
ejpam-5627	184	10	s	s	X
ejpam-5627	184	11	)	)	PUNCT
ejpam-5627	184	12	×	×	PROPN
ejpam-5627	184	13	u(α	u(α	PROPN
ejpam-5627	184	14	,	,	PUNCT
ejpam-5627	184	15	t	t	PROPN
ejpam-5627	184	16	)	)	PUNCT
ejpam-5627	184	17	.	.	PUNCT
ejpam-5627	185	1	then	then	ADV
ejpam-5627	185	2	β(y	β(y	NOUN
ejpam-5627	185	3	)	)	PUNCT
ejpam-5627	185	4	≤	≤	PROPN
ejpam-5627	185	5	s	s	X
ejpam-5627	185	6	and	and	CCONJ
ejpam-5627	185	7	α(b	α(b	NOUN
ejpam-5627	185	8	)	)	PUNCT
ejpam-5627	185	9	≥	≥	NOUN
ejpam-5627	185	10	t.	t.	NOUN
ejpam-5627	185	11	then	then	ADV
ejpam-5627	185	12	β((y|(x|x))|(y|(x|x	β((y|(x|x))|(y|(x|x	NOUN
ejpam-5627	185	13	)	)	PUNCT
ejpam-5627	185	14	)	)	PUNCT
ejpam-5627	185	15	)	)	PUNCT
ejpam-5627	186	1	≤	≤	NUM
ejpam-5627	186	2	β(y	β(y	NOUN
ejpam-5627	186	3	)	)	PUNCT
ejpam-5627	186	4	≤	≤	PROPN
ejpam-5627	186	5	s	s	PART
ejpam-5627	186	6	and	and	CCONJ
ejpam-5627	186	7	α((a|(b|b))|(a|(b|b	α((a|(b|b))|(a|(b|b	NOUN
ejpam-5627	186	8	)	)	PUNCT
ejpam-5627	186	9	)	)	PUNCT
ejpam-5627	186	10	)	)	PUNCT
ejpam-5627	186	11	≥	≥	X
ejpam-5627	186	12	α(b	α(b	NOUN
ejpam-5627	186	13	)	)	PUNCT
ejpam-5627	186	14	≥	≥	NOUN
ejpam-5627	186	15	t	t	NOUN
ejpam-5627	187	1	and	and	CCONJ
ejpam-5627	187	2	so	so	ADV
ejpam-5627	187	3	(	(	PUNCT
ejpam-5627	187	4	y|(x|x))|(y|(x|x	y|(x|x))|(y|(x|x	PROPN
ejpam-5627	187	5	)	)	PUNCT
ejpam-5627	187	6	)	)	PUNCT
ejpam-5627	187	7	,	,	PUNCT
ejpam-5627	187	8	(	(	PUNCT
ejpam-5627	187	9	a|(b|b))|(a|(b|b	a|(b|b))|(a|(b|b	NOUN
ejpam-5627	187	10	)	)	PUNCT
ejpam-5627	187	11	)	)	PUNCT
ejpam-5627	188	1	∈	∈	PROPN
ejpam-5627	188	2	l(β	l(β	PROPN
ejpam-5627	188	3	,	,	PUNCT
ejpam-5627	188	4	s	s	X
ejpam-5627	188	5	)	)	PUNCT
ejpam-5627	188	6	×	×	PROPN
ejpam-5627	188	7	u(α	u(α	PROPN
ejpam-5627	188	8	,	,	PUNCT
ejpam-5627	188	9	t	t	PROPN
ejpam-5627	188	10	)	)	PUNCT
ejpam-5627	188	11	.	.	PUNCT
ejpam-5627	189	1	let	let	VERB
ejpam-5627	189	2	x	x	PRON
ejpam-5627	189	3	,	,	PUNCT
ejpam-5627	189	4	y	y	PROPN
ejpam-5627	189	5	,	,	PUNCT
ejpam-5627	189	6	a	a	PRON
ejpam-5627	189	7	,	,	PUNCT
ejpam-5627	189	8	b	b	X
ejpam-5627	189	9	∈	∈	PROPN
ejpam-5627	189	10	h	h	NOUN
ejpam-5627	189	11	be	be	AUX
ejpam-5627	189	12	such	such	ADJ
ejpam-5627	189	13	that	that	SCONJ
ejpam-5627	189	14	(	(	PUNCT
ejpam-5627	189	15	(	(	PUNCT
ejpam-5627	189	16	y|(x|x))|(y|(x|x	y|(x|x))|(y|(x|x	NOUN
ejpam-5627	189	17	)	)	PUNCT
ejpam-5627	189	18	)	)	PUNCT
ejpam-5627	189	19	,	,	PUNCT
ejpam-5627	189	20	(	(	PUNCT
ejpam-5627	189	21	a|(b|b))|(a|(b|b	a|(b|b))|(a|(b|b	NOUN
ejpam-5627	189	22	)	)	PUNCT
ejpam-5627	189	23	)	)	PUNCT
ejpam-5627	189	24	)	)	PUNCT
ejpam-5627	190	1	∈	∈	PROPN
ejpam-5627	190	2	l(β	l(β	PROPN
ejpam-5627	190	3	,	,	PUNCT
ejpam-5627	190	4	s)×u(α	s)×u(α	PROPN
ejpam-5627	190	5	,	,	PUNCT
ejpam-5627	190	6	t	t	PROPN
ejpam-5627	190	7	)	)	PUNCT
ejpam-5627	190	8	and	and	CCONJ
ejpam-5627	190	9	(	(	PUNCT
ejpam-5627	190	10	x	x	NOUN
ejpam-5627	190	11	,	,	PUNCT
ejpam-5627	190	12	a	a	PRON
ejpam-5627	190	13	)	)	PUNCT
ejpam-5627	190	14	∈	∈	PROPN
ejpam-5627	190	15	l(β	l(β	PROPN
ejpam-5627	190	16	,	,	PUNCT
ejpam-5627	190	17	s)×u(α	s)×u(α	PROPN
ejpam-5627	190	18	,	,	PUNCT
ejpam-5627	190	19	t	t	PROPN
ejpam-5627	190	20	)	)	PUNCT
ejpam-5627	190	21	.	.	PUNCT
ejpam-5627	191	1	then	then	ADV
ejpam-5627	191	2	β((y|(x|x))|(y|(x|x	β((y|(x|x))|(y|(x|x	NOUN
ejpam-5627	191	3	)	)	PUNCT
ejpam-5627	191	4	)	)	PUNCT
ejpam-5627	191	5	)	)	PUNCT
ejpam-5627	192	1	≤	≤	PROPN
ejpam-5627	192	2	s	s	X
ejpam-5627	192	3	,	,	PUNCT
ejpam-5627	192	4	β(x	β(x	NOUN
ejpam-5627	192	5	)	)	PUNCT
ejpam-5627	192	6	≤	≤	NUM
ejpam-5627	192	7	s	s	PROPN
ejpam-5627	192	8	,	,	PUNCT
ejpam-5627	192	9	α((a|(b|b))|(a|(b|b	α((a|(b|b))|(a|(b|b	NOUN
ejpam-5627	192	10	)	)	PUNCT
ejpam-5627	192	11	)	)	PUNCT
ejpam-5627	192	12	)	)	PUNCT
ejpam-5627	192	13	)	)	PUNCT
ejpam-5627	192	14	≥	≥	PROPN
ejpam-5627	192	15	t	t	NOUN
ejpam-5627	192	16	and	and	CCONJ
ejpam-5627	192	17	α(a	α(a	PROPN
ejpam-5627	192	18	)	)	PUNCT
ejpam-5627	192	19	≥	≥	NOUN
ejpam-5627	192	20	t.	t.	NOUN
ejpam-5627	192	21	then	then	ADV
ejpam-5627	192	22	β(y	β(y	NOUN
ejpam-5627	192	23	)	)	PUNCT
ejpam-5627	192	24	≤	≤	NUM
ejpam-5627	192	25	max{β(((y|(x|x))|(y|(x|x	max{β(((y|(x|x))|(y|(x|x	NOUN
ejpam-5627	192	26	)	)	PUNCT
ejpam-5627	192	27	)	)	PUNCT
ejpam-5627	192	28	)	)	PUNCT
ejpam-5627	192	29	,	,	PUNCT
ejpam-5627	192	30	β(x	β(x	NOUN
ejpam-5627	192	31	)	)	PUNCT
ejpam-5627	192	32	}	}	PUNCT
ejpam-5627	192	33	≤	≤	NUM
ejpam-5627	192	34	s	s	X
ejpam-5627	192	35	and	and	CCONJ
ejpam-5627	192	36	α(b	α(b	NOUN
ejpam-5627	192	37	)	)	PUNCT
ejpam-5627	192	38	≥	≥	PROPN
ejpam-5627	192	39	min{α((a|(b|b))|(a|(b|b	min{α((a|(b|b))|(a|(b|b	NOUN
ejpam-5627	192	40	)	)	PUNCT
ejpam-5627	192	41	)	)	PUNCT
ejpam-5627	192	42	)	)	PUNCT
ejpam-5627	192	43	,	,	PUNCT
ejpam-5627	192	44	α(a	α(a	NOUN
ejpam-5627	192	45	)	)	PUNCT
ejpam-5627	192	46	}	}	PUNCT
ejpam-5627	192	47	≥	≥	PROPN
ejpam-5627	192	48	t	t	NOUN
ejpam-5627	192	49	and	and	CCONJ
ejpam-5627	192	50	so	so	ADV
ejpam-5627	192	51	(	(	PUNCT
ejpam-5627	192	52	y	y	PROPN
ejpam-5627	192	53	,	,	PUNCT
ejpam-5627	192	54	b	b	NOUN
ejpam-5627	192	55	)	)	PUNCT
ejpam-5627	192	56	∈	∈	PROPN
ejpam-5627	192	57	l(β	l(β	PROPN
ejpam-5627	192	58	,	,	PUNCT
ejpam-5627	192	59	s)×u(α	s)×u(α	PROPN
ejpam-5627	192	60	,	,	PUNCT
ejpam-5627	192	61	t	t	PROPN
ejpam-5627	192	62	)	)	PUNCT
ejpam-5627	192	63	.	.	PUNCT
ejpam-5627	193	1	therefore	therefore	ADV
ejpam-5627	193	2	,	,	PUNCT
ejpam-5627	193	3	l(β	l(β	PROPN
ejpam-5627	193	4	,	,	PUNCT
ejpam-5627	193	5	s	s	AUX
ejpam-5627	193	6	)	)	PUNCT
ejpam-5627	193	7	and	and	CCONJ
ejpam-5627	193	8	u(α	u(α	PROPN
ejpam-5627	193	9	,	,	PUNCT
ejpam-5627	193	10	t	t	PROPN
ejpam-5627	193	11	)	)	PUNCT
ejpam-5627	193	12	are	be	AUX
ejpam-5627	193	13	sup	sup	ADJ
ejpam-5627	193	14	-	-	PUNCT
ejpam-5627	193	15	ideals	ideal	NOUN
ejpam-5627	193	16	of	of	ADP
ejpam-5627	193	17	h.	h.	NOUN
ejpam-5627	193	18	conversely	conversely	ADV
ejpam-5627	193	19	,	,	PUNCT
ejpam-5627	193	20	let	let	VERB
ejpam-5627	193	21	h	h	NOUN
ejpam-5627	193	22	=	=	PUNCT
ejpam-5627	193	23	(	(	PUNCT
ejpam-5627	193	24	h	h	NOUN
ejpam-5627	193	25	,	,	PUNCT
ejpam-5627	193	26	α	α	NOUN
ejpam-5627	193	27	,	,	PUNCT
ejpam-5627	193	28	β	β	NOUN
ejpam-5627	193	29	)	)	PUNCT
ejpam-5627	193	30	be	be	VERB
ejpam-5627	193	31	an	an	DET
ejpam-5627	193	32	ifs	ifs	PROPN
ejpam-5627	193	33	in	in	ADP
ejpam-5627	193	34	h	h	NOUN
ejpam-5627	193	35	for	for	ADP
ejpam-5627	193	36	which	which	PRON
ejpam-5627	193	37	its	its	PRON
ejpam-5627	193	38	negative	negative	ADJ
ejpam-5627	193	39	s	s	NOUN
ejpam-5627	193	40	-	-	PUNCT
ejpam-5627	193	41	cut	cut	VERB
ejpam-5627	193	42	and	and	CCONJ
ejpam-5627	193	43	positive	positive	ADJ
ejpam-5627	193	44	t	t	NOUN
ejpam-5627	193	45	-	-	PUNCT
ejpam-5627	193	46	cut	cut	NOUN
ejpam-5627	193	47	are	be	AUX
ejpam-5627	193	48	sup	sup	ADJ
ejpam-5627	193	49	-	-	PUNCT
ejpam-5627	193	50	ideals	ideal	NOUN
ejpam-5627	193	51	of	of	ADP
ejpam-5627	193	52	h	h	NOUN
ejpam-5627	193	53	whenever	whenever	SCONJ
ejpam-5627	193	54	they	they	PRON
ejpam-5627	193	55	are	be	AUX
ejpam-5627	193	56	nonempty	nonempty	ADJ
ejpam-5627	193	57	for	for	ADP
ejpam-5627	193	58	all	all	DET
ejpam-5627	193	59	s	s	PROPN
ejpam-5627	193	60	,	,	PUNCT
ejpam-5627	193	61	t	t	PROPN
ejpam-5627	193	62	∈	∈	PROPN
ejpam-5627	194	1	[	[	X
ejpam-5627	194	2	0	0	NUM
ejpam-5627	194	3	,	,	PUNCT
ejpam-5627	194	4	1	1	NUM
ejpam-5627	194	5	]	]	PUNCT
ejpam-5627	194	6	.	.	PUNCT
ejpam-5627	195	1	suppose	suppose	VERB
ejpam-5627	195	2	that	that	SCONJ
ejpam-5627	195	3	β((a|(b|b))|(a|(b|b	β((a|(b|b))|(a|(b|b	NOUN
ejpam-5627	195	4	)	)	PUNCT
ejpam-5627	195	5	)	)	PUNCT
ejpam-5627	195	6	)	)	PUNCT
ejpam-5627	195	7	>	>	X
ejpam-5627	195	8	β(b	β(b	PUNCT
ejpam-5627	195	9	)	)	PUNCT
ejpam-5627	195	10	for	for	ADP
ejpam-5627	195	11	some	some	PRON
ejpam-5627	195	12	a	a	PRON
ejpam-5627	195	13	,	,	PUNCT
ejpam-5627	195	14	b	b	PROPN
ejpam-5627	195	15	∈	∈	PROPN
ejpam-5627	195	16	h.	h.	NOUN
ejpam-5627	195	17	then	then	ADV
ejpam-5627	195	18	b	b	X
ejpam-5627	195	19	∈	∈	PROPN
ejpam-5627	195	20	l(β	l(β	PROPN
ejpam-5627	195	21	,	,	PUNCT
ejpam-5627	195	22	β(b	β(b	PUNCT
ejpam-5627	195	23	)	)	PUNCT
ejpam-5627	195	24	)	)	PUNCT
ejpam-5627	196	1	but	but	CCONJ
ejpam-5627	196	2	(	(	PUNCT
ejpam-5627	196	3	a|(b|b))|(a|(b|b	a|(b|b))|(a|(b|b	NOUN
ejpam-5627	196	4	)	)	PUNCT
ejpam-5627	196	5	)	)	PUNCT
ejpam-5627	196	6	/∈	/∈	PUNCT
ejpam-5627	197	1	l(β	l(β	PROPN
ejpam-5627	197	2	,	,	PUNCT
ejpam-5627	197	3	β(b	β(b	NUM
ejpam-5627	197	4	)	)	PUNCT
ejpam-5627	197	5	)	)	PUNCT
ejpam-5627	197	6	,	,	PUNCT
ejpam-5627	197	7	a	a	DET
ejpam-5627	197	8	contradiction	contradiction	NOUN
ejpam-5627	197	9	.	.	PUNCT
ejpam-5627	198	1	hence	hence	ADV
ejpam-5627	198	2	,	,	PUNCT
ejpam-5627	198	3	β((y|(x|x))|(y|(x|x	β((y|(x|x))|(y|(x|x	NOUN
ejpam-5627	198	4	)	)	PUNCT
ejpam-5627	198	5	)	)	PUNCT
ejpam-5627	198	6	)	)	PUNCT
ejpam-5627	199	1	≤	≤	NUM
ejpam-5627	199	2	β(y	β(y	NOUN
ejpam-5627	199	3	)	)	PUNCT
ejpam-5627	199	4	for	for	ADP
ejpam-5627	199	5	all	all	DET
ejpam-5627	199	6	x	x	NOUN
ejpam-5627	199	7	,	,	PUNCT
ejpam-5627	199	8	y	y	PROPN
ejpam-5627	199	9	∈	∈	PROPN
ejpam-5627	199	10	h.	h.	PROPN
ejpam-5627	199	11	suppose	suppose	VERB
ejpam-5627	199	12	that	that	SCONJ
ejpam-5627	199	13	α((x|(y|y))|(x|(y|y	α((x|(y|y))|(x|(y|y	PROPN
ejpam-5627	199	14	)	)	PUNCT
ejpam-5627	199	15	)	)	PUNCT
ejpam-5627	199	16	)	)	PUNCT
ejpam-5627	200	1	<	<	X
ejpam-5627	200	2	α(y	α(y	NOUN
ejpam-5627	200	3	)	)	PUNCT
ejpam-5627	200	4	for	for	ADP
ejpam-5627	200	5	some	some	DET
ejpam-5627	200	6	x	x	NOUN
ejpam-5627	200	7	,	,	PUNCT
ejpam-5627	200	8	y	y	PROPN
ejpam-5627	200	9	∈	∈	PROPN
ejpam-5627	200	10	h.	h.	NOUN
ejpam-5627	200	11	then	then	ADV
ejpam-5627	200	12	y	y	PROPN
ejpam-5627	200	13	∈	∈	PROPN
ejpam-5627	200	14	u(α	u(α	PROPN
ejpam-5627	200	15	,	,	PUNCT
ejpam-5627	200	16	α(y	α(y	NOUN
ejpam-5627	200	17	)	)	PUNCT
ejpam-5627	200	18	)	)	PUNCT
ejpam-5627	201	1	but	but	CCONJ
ejpam-5627	201	2	(	(	PUNCT
ejpam-5627	201	3	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	NUM
ejpam-5627	201	4	)	)	PUNCT
ejpam-5627	201	5	)	)	PUNCT
ejpam-5627	201	6	/∈	/∈	PUNCT
ejpam-5627	202	1	u(α	u(α	NOUN
ejpam-5627	202	2	,	,	PUNCT
ejpam-5627	202	3	α(y	α(y	NOUN
ejpam-5627	202	4	)	)	PUNCT
ejpam-5627	202	5	)	)	PUNCT
ejpam-5627	202	6	,	,	PUNCT
ejpam-5627	202	7	a	a	DET
ejpam-5627	202	8	contradiction	contradiction	NOUN
ejpam-5627	202	9	.	.	PUNCT
ejpam-5627	203	1	hence	hence	ADV
ejpam-5627	203	2	,	,	PUNCT
ejpam-5627	203	3	β((a|(b|b))|(a|(b|b	β((a|(b|b))|(a|(b|b	NOUN
ejpam-5627	203	4	)	)	PUNCT
ejpam-5627	203	5	)	)	PUNCT
ejpam-5627	203	6	)	)	PUNCT
ejpam-5627	203	7	≥	≥	NOUN
ejpam-5627	203	8	β(b	β(b	PUNCT
ejpam-5627	203	9	)	)	PUNCT
ejpam-5627	203	10	for	for	ADP
ejpam-5627	203	11	all	all	DET
ejpam-5627	203	12	a	a	PRON
ejpam-5627	203	13	,	,	PUNCT
ejpam-5627	203	14	b	b	X
ejpam-5627	203	15	∈	∈	PROPN
ejpam-5627	203	16	h.	h.	PROPN
ejpam-5627	203	17	suppose	suppose	VERB
ejpam-5627	203	18	that	that	SCONJ
ejpam-5627	203	19	β(b	β(b	PROPN
ejpam-5627	203	20	)	)	PUNCT
ejpam-5627	203	21	>	>	X
ejpam-5627	203	22	max{β((a|(b|b))|(a|(b|b	max{β((a|(b|b))|(a|(b|b	PROPN
ejpam-5627	203	23	)	)	PUNCT
ejpam-5627	203	24	)	)	PUNCT
ejpam-5627	203	25	)	)	PUNCT
ejpam-5627	203	26	,	,	PUNCT
ejpam-5627	203	27	β(a	β(a	PROPN
ejpam-5627	203	28	)	)	PUNCT
ejpam-5627	203	29	}	}	PUNCT
ejpam-5627	203	30	or	or	CCONJ
ejpam-5627	203	31	α(y	α(y	NOUN
ejpam-5627	203	32	)	)	PUNCT
ejpam-5627	203	33	<	<	X
ejpam-5627	203	34	min{α((x|(y|y))|(x|(y|y	min{α((x|(y|y))|(x|(y|y	NOUN
ejpam-5627	203	35	)	)	PUNCT
ejpam-5627	203	36	)	)	PUNCT
ejpam-5627	203	37	)	)	PUNCT
ejpam-5627	203	38	,	,	PUNCT
ejpam-5627	203	39	α(x	α(x	NOUN
ejpam-5627	203	40	)	)	PUNCT
ejpam-5627	203	41	}	}	PUNCT
ejpam-5627	203	42	for	for	ADP
ejpam-5627	203	43	some	some	DET
ejpam-5627	203	44	a	a	DET
ejpam-5627	203	45	,	,	PUNCT
ejpam-5627	203	46	b	b	NOUN
ejpam-5627	203	47	,	,	PUNCT
ejpam-5627	203	48	x	x	X
ejpam-5627	203	49	,	,	PUNCT
ejpam-5627	203	50	y	y	PROPN
ejpam-5627	203	51	∈	∈	PROPN
ejpam-5627	203	52	h.	h.	PROPN
ejpam-5627	203	53	then	then	ADV
ejpam-5627	203	54	(	(	PUNCT
ejpam-5627	203	55	a|(b|b))|(a|(b|b	a|(b|b))|(a|(b|b	NOUN
ejpam-5627	203	56	)	)	PUNCT
ejpam-5627	203	57	)	)	PUNCT
ejpam-5627	203	58	,	,	PUNCT
ejpam-5627	203	59	a	a	DET
ejpam-5627	203	60	∈	∈	NOUN
ejpam-5627	203	61	l(β	l(β	PROPN
ejpam-5627	203	62	,	,	PUNCT
ejpam-5627	203	63	s	s	NOUN
ejpam-5627	203	64	)	)	PUNCT
ejpam-5627	203	65	or	or	CCONJ
ejpam-5627	203	66	(	(	PUNCT
ejpam-5627	203	67	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	PROPN
ejpam-5627	203	68	)	)	PUNCT
ejpam-5627	203	69	)	)	PUNCT
ejpam-5627	203	70	,	,	PUNCT
ejpam-5627	203	71	x	x	PUNCT
ejpam-5627	203	72	∈	∈	PROPN
ejpam-5627	203	73	u(α	u(α	PROPN
ejpam-5627	203	74	,	,	PUNCT
ejpam-5627	203	75	t	t	PROPN
ejpam-5627	203	76	)	)	PUNCT
ejpam-5627	203	77	where	where	SCONJ
ejpam-5627	203	78	s	s	NOUN
ejpam-5627	203	79	=	=	NOUN
ejpam-5627	203	80	max{β((a|(b|b))|(a|(b|b	max{β((a|(b|b))|(a|(b|b	NOUN
ejpam-5627	203	81	)	)	PUNCT
ejpam-5627	203	82	)	)	PUNCT
ejpam-5627	203	83	)	)	PUNCT
ejpam-5627	203	84	,	,	PUNCT
ejpam-5627	203	85	β(a	β(a	PROPN
ejpam-5627	203	86	)	)	PUNCT
ejpam-5627	203	87	}	}	PUNCT
ejpam-5627	203	88	and	and	CCONJ
ejpam-5627	203	89	t	t	X
ejpam-5627	203	90	=	=	SYM
ejpam-5627	203	91	min{α((x|(y|y))|(x|(y|y	min{α((x|(y|y))|(x|(y|y	NUM
ejpam-5627	203	92	)	)	PUNCT
ejpam-5627	203	93	)	)	PUNCT
ejpam-5627	203	94	)	)	PUNCT
ejpam-5627	203	95	,	,	PUNCT
ejpam-5627	203	96	α(x	α(x	NOUN
ejpam-5627	203	97	)	)	PUNCT
ejpam-5627	203	98	}	}	PUNCT
ejpam-5627	203	99	.	.	PUNCT
ejpam-5627	204	1	but	but	CCONJ
ejpam-5627	204	2	b	b	X
ejpam-5627	204	3	/∈	/∈	PUNCT
ejpam-5627	205	1	l(β	l(β	PROPN
ejpam-5627	205	2	,	,	PUNCT
ejpam-5627	205	3	s	s	NOUN
ejpam-5627	205	4	)	)	PUNCT
ejpam-5627	205	5	or	or	CCONJ
ejpam-5627	205	6	y	y	PROPN
ejpam-5627	205	7	/∈	/∈	PUNCT
ejpam-5627	206	1	u(α	u(α	PROPN
ejpam-5627	206	2	,	,	PUNCT
ejpam-5627	206	3	t	t	PROPN
ejpam-5627	206	4	)	)	PUNCT
ejpam-5627	206	5	,	,	PUNCT
ejpam-5627	206	6	a	a	DET
ejpam-5627	206	7	contradiction	contradiction	NOUN
ejpam-5627	206	8	.	.	PUNCT
ejpam-5627	207	1	therefore	therefore	ADV
ejpam-5627	207	2	,	,	PUNCT
ejpam-5627	207	3	β(y	β(y	NOUN
ejpam-5627	207	4	)	)	PUNCT
ejpam-5627	207	5	≤	≤	NOUN
ejpam-5627	207	6	max{β((x|(y|y))|(x|(y|y	max{β((x|(y|y))|(x|(y|y	PROPN
ejpam-5627	207	7	)	)	PUNCT
ejpam-5627	207	8	)	)	PUNCT
ejpam-5627	207	9	)	)	PUNCT
ejpam-5627	207	10	,	,	PUNCT
ejpam-5627	207	11	β(x	β(x	NOUN
ejpam-5627	207	12	)	)	PUNCT
ejpam-5627	207	13	}	}	PUNCT
ejpam-5627	207	14	,	,	PUNCT
ejpam-5627	207	15	α((x|(y|y))|(x|(y|y	α((x|(y|y))|(x|(y|y	NOUN
ejpam-5627	207	16	)	)	PUNCT
ejpam-5627	207	17	)	)	PUNCT
ejpam-5627	207	18	)	)	PUNCT
ejpam-5627	207	19	≥	≥	X
ejpam-5627	207	20	min{α(x	min{α(x	NOUN
ejpam-5627	207	21	)	)	PUNCT
ejpam-5627	207	22	,	,	PUNCT
ejpam-5627	207	23	α(y	α(y	NOUN
ejpam-5627	207	24	)	)	PUNCT
ejpam-5627	207	25	}	}	PUNCT
ejpam-5627	207	26	for	for	ADP
ejpam-5627	207	27	all	all	DET
ejpam-5627	207	28	x	x	NOUN
ejpam-5627	207	29	,	,	PUNCT
ejpam-5627	207	30	y	y	PROPN
ejpam-5627	207	31	∈	∈	PROPN
ejpam-5627	207	32	h.	h.	PROPN
ejpam-5627	207	33	consequently	consequently	ADV
ejpam-5627	207	34	,	,	PUNCT
ejpam-5627	207	35	h	h	NOUN
ejpam-5627	207	36	=	=	PRON
ejpam-5627	207	37	(	(	PUNCT
ejpam-5627	207	38	h	h	NOUN
ejpam-5627	207	39	,	,	PUNCT
ejpam-5627	207	40	α	α	NOUN
ejpam-5627	207	41	,	,	PUNCT
ejpam-5627	207	42	β	β	NOUN
ejpam-5627	207	43	)	)	PUNCT
ejpam-5627	207	44	is	be	AUX
ejpam-5627	207	45	an	an	DET
ejpam-5627	207	46	intuitionistic	intuitionistic	ADJ
ejpam-5627	207	47	fuzzy	fuzzy	ADJ
ejpam-5627	207	48	sup	sup	NOUN
ejpam-5627	207	49	-	-	PUNCT
ejpam-5627	207	50	ideal	ideal	NOUN
ejpam-5627	207	51	of	of	ADP
ejpam-5627	207	52	h.	h.	PROPN
ejpam-5627	207	53	n.	n.	PROPN
ejpam-5627	207	54	rajesh	rajesh	PROPN
ejpam-5627	207	55	,	,	PUNCT
ejpam-5627	207	56	t.	t.	PROPN
ejpam-5627	207	57	oner	oner	NOUN
ejpam-5627	207	58	,	,	PUNCT
ejpam-5627	207	59	a.	a.	NOUN
ejpam-5627	207	60	iampan	iampan	PROPN
ejpam-5627	207	61	,	,	PUNCT
ejpam-5627	207	62	i.	i.	PROPN
ejpam-5627	207	63	senturk	senturk	PROPN
ejpam-5627	207	64	/	/	SYM
ejpam-5627	207	65	eur	eur	PROPN
ejpam-5627	207	66	.	.	PUNCT
ejpam-5627	208	1	j.	j.	PROPN
ejpam-5627	208	2	pure	pure	PROPN
ejpam-5627	208	3	appl	appl	PROPN
ejpam-5627	208	4	.	.	PROPN
ejpam-5627	208	5	math	math	PROPN
ejpam-5627	208	6	,	,	PUNCT
ejpam-5627	208	7	18	18	NUM
ejpam-5627	208	8	(	(	PUNCT
ejpam-5627	208	9	1	1	NUM
ejpam-5627	208	10	)	)	PUNCT
ejpam-5627	208	11	(	(	PUNCT
ejpam-5627	208	12	2025	2025	NUM
ejpam-5627	208	13	)	)	PUNCT
ejpam-5627	208	14	,	,	PUNCT
ejpam-5627	208	15	5627	5627	NUM
ejpam-5627	208	16	8	8	NUM
ejpam-5627	208	17	of	of	ADP
ejpam-5627	208	18	15	15	NUM
ejpam-5627	208	19	theorem	theorem	NOUN
ejpam-5627	208	20	7	7	NUM
ejpam-5627	208	21	.	.	PUNCT
ejpam-5627	209	1	an	an	DET
ejpam-5627	209	2	ifs	ifs	PROPN
ejpam-5627	209	3	h	h	NOUN
ejpam-5627	209	4	=	=	PUNCT
ejpam-5627	209	5	(	(	PUNCT
ejpam-5627	209	6	h	h	NOUN
ejpam-5627	209	7	,	,	PUNCT
ejpam-5627	209	8	α	α	NOUN
ejpam-5627	209	9	,	,	PUNCT
ejpam-5627	209	10	β	β	NOUN
ejpam-5627	209	11	)	)	PUNCT
ejpam-5627	209	12	in	in	ADP
ejpam-5627	209	13	h	h	NOUN
ejpam-5627	209	14	is	be	AUX
ejpam-5627	209	15	an	an	DET
ejpam-5627	209	16	intuitionistic	intuitionistic	ADJ
ejpam-5627	209	17	fuzzy	fuzzy	ADJ
ejpam-5627	209	18	sup	sup	NOUN
ejpam-5627	209	19	-	-	PUNCT
ejpam-5627	209	20	ideal	ideal	NOUN
ejpam-5627	209	21	of	of	ADP
ejpam-5627	209	22	h	h	NOUN
ejpam-5627	209	23	if	if	SCONJ
ejpam-5627	210	1	and	and	CCONJ
ejpam-5627	210	2	only	only	ADV
ejpam-5627	210	3	if	if	SCONJ
ejpam-5627	210	4	the	the	DET
ejpam-5627	210	5	fuzzy	fuzzy	ADJ
ejpam-5627	210	6	sets	set	VERB
ejpam-5627	210	7	βc	βc	INTJ
ejpam-5627	210	8	and	and	CCONJ
ejpam-5627	210	9	α	α	NOUN
ejpam-5627	210	10	are	be	AUX
ejpam-5627	210	11	fuzzy	fuzzy	ADJ
ejpam-5627	210	12	sup	sup	ADJ
ejpam-5627	210	13	-	-	PUNCT
ejpam-5627	210	14	ideals	ideal	NOUN
ejpam-5627	210	15	of	of	ADP
ejpam-5627	210	16	h	h	NOUN
ejpam-5627	210	17	,	,	PUNCT
ejpam-5627	210	18	where	where	SCONJ
ejpam-5627	210	19	βc	βc	INTJ
ejpam-5627	210	20	:	:	PUNCT
ejpam-5627	210	21	l	l	X
ejpam-5627	210	22	→	→	PUNCT
ejpam-5627	211	1	[	[	X
ejpam-5627	211	2	0	0	NUM
ejpam-5627	211	3	,	,	PUNCT
ejpam-5627	211	4	1	1	NUM
ejpam-5627	211	5	]	]	PUNCT
ejpam-5627	211	6	,	,	PUNCT
ejpam-5627	211	7	x	x	SYM
ejpam-5627	211	8	7→	7→	NOUN
ejpam-5627	211	9	1−	1−	NUM
ejpam-5627	211	10	β(x	β(x	NOUN
ejpam-5627	211	11	)	)	PUNCT
ejpam-5627	211	12	.	.	PUNCT
ejpam-5627	212	1	proof	proof	NOUN
ejpam-5627	212	2	.	.	PUNCT
ejpam-5627	213	1	assume	assume	VERB
ejpam-5627	213	2	that	that	SCONJ
ejpam-5627	213	3	h	h	NOUN
ejpam-5627	213	4	=	=	PUNCT
ejpam-5627	213	5	(	(	PUNCT
ejpam-5627	213	6	h	h	NOUN
ejpam-5627	213	7	,	,	PUNCT
ejpam-5627	213	8	α	α	NOUN
ejpam-5627	213	9	,	,	PUNCT
ejpam-5627	213	10	β	β	NOUN
ejpam-5627	213	11	)	)	PUNCT
ejpam-5627	213	12	is	be	AUX
ejpam-5627	213	13	an	an	DET
ejpam-5627	213	14	intuitionistic	intuitionistic	ADJ
ejpam-5627	213	15	fuzzy	fuzzy	ADJ
ejpam-5627	213	16	sup	sup	NOUN
ejpam-5627	213	17	-	-	PUNCT
ejpam-5627	213	18	ideal	ideal	NOUN
ejpam-5627	213	19	of	of	ADP
ejpam-5627	213	20	h.	h.	PROPN
ejpam-5627	213	21	it	it	PRON
ejpam-5627	213	22	is	be	AUX
ejpam-5627	213	23	clear	clear	ADJ
ejpam-5627	213	24	that	that	SCONJ
ejpam-5627	213	25	α	α	PRON
ejpam-5627	213	26	is	be	AUX
ejpam-5627	213	27	a	a	DET
ejpam-5627	213	28	fuzzy	fuzzy	ADJ
ejpam-5627	213	29	sup	sup	ADJ
ejpam-5627	213	30	-	-	PUNCT
ejpam-5627	213	31	ideal	ideal	NOUN
ejpam-5627	213	32	of	of	ADP
ejpam-5627	213	33	h.	h.	NOUN
ejpam-5627	213	34	for	for	ADP
ejpam-5627	213	35	every	every	DET
ejpam-5627	213	36	x	x	NOUN
ejpam-5627	213	37	,	,	PUNCT
ejpam-5627	213	38	y	y	PROPN
ejpam-5627	213	39	∈	∈	PROPN
ejpam-5627	213	40	h	h	NOUN
ejpam-5627	213	41	,	,	PUNCT
ejpam-5627	213	42	βc((x|(y|y))|(x|(y|y	βc((x|(y|y))|(x|(y|y	NUM
ejpam-5627	213	43	)	)	PUNCT
ejpam-5627	213	44	)	)	PUNCT
ejpam-5627	213	45	)	)	PUNCT
ejpam-5627	214	1	=	=	SYM
ejpam-5627	214	2	1−	1−	NUM
ejpam-5627	214	3	β((x|(y|y))|(x|(y|y	β((x|(y|y))|(x|(y|y	ADJ
ejpam-5627	214	4	)	)	PUNCT
ejpam-5627	214	5	)	)	PUNCT
ejpam-5627	214	6	)	)	PUNCT
ejpam-5627	215	1	≥	≥	NOUN
ejpam-5627	215	2	1−	1−	NUM
ejpam-5627	215	3	β(y	β(y	NOUN
ejpam-5627	215	4	)	)	PUNCT
ejpam-5627	215	5	=	=	SYM
ejpam-5627	215	6	1−	1−	NUM
ejpam-5627	215	7	β(y	β(y	NUM
ejpam-5627	215	8	)	)	PUNCT
ejpam-5627	215	9	=	=	PUNCT
ejpam-5627	215	10	βc(y	βc(y	NUM
ejpam-5627	215	11	)	)	PUNCT
ejpam-5627	215	12	,	,	PUNCT
ejpam-5627	215	13	βc(y	βc(y	NUM
ejpam-5627	215	14	)	)	PUNCT
ejpam-5627	215	15	=	=	SYM
ejpam-5627	215	16	1−	1−	NUM
ejpam-5627	215	17	β(y	β(y	NOUN
ejpam-5627	215	18	)	)	PUNCT
ejpam-5627	215	19	≥	≥	NOUN
ejpam-5627	215	20	1−max{β(x	1−max{β(x	NUM
ejpam-5627	215	21	)	)	PUNCT
ejpam-5627	215	22	,	,	PUNCT
ejpam-5627	215	23	β(y	β(y	PROPN
ejpam-5627	215	24	)	)	PUNCT
ejpam-5627	215	25	}	}	PUNCT
ejpam-5627	215	26	=	=	PUNCT
ejpam-5627	216	1	min{1−	min{1−	VERB
ejpam-5627	216	2	β((x|(y|y))|(x|(y|y	β((x|(y|y))|(x|(y|y	ADJ
ejpam-5627	216	3	)	)	PUNCT
ejpam-5627	216	4	)	)	PUNCT
ejpam-5627	216	5	)	)	PUNCT
ejpam-5627	216	6	,	,	PUNCT
ejpam-5627	216	7	1−	1−	NUM
ejpam-5627	216	8	β(x	β(x	NOUN
ejpam-5627	216	9	)	)	PUNCT
ejpam-5627	216	10	}	}	PUNCT
ejpam-5627	216	11	=	=	SYM
ejpam-5627	216	12	min{βc((x|(y|y))|(x|(y|y	min{βc((x|(y|y))|(x|(y|y	X
ejpam-5627	216	13	)	)	PUNCT
ejpam-5627	216	14	)	)	PUNCT
ejpam-5627	216	15	)	)	PUNCT
ejpam-5627	216	16	,	,	PUNCT
ejpam-5627	216	17	βc(x	βc(x	NUM
ejpam-5627	216	18	)	)	PUNCT
ejpam-5627	216	19	}	}	PUNCT
ejpam-5627	216	20	.	.	PUNCT
ejpam-5627	217	1	hence	hence	ADV
ejpam-5627	217	2	,	,	PUNCT
ejpam-5627	217	3	βc	βc	INTJ
ejpam-5627	217	4	is	be	AUX
ejpam-5627	217	5	a	a	DET
ejpam-5627	217	6	fuzzy	fuzzy	ADJ
ejpam-5627	217	7	sup	sup	ADJ
ejpam-5627	217	8	-	-	PUNCT
ejpam-5627	217	9	ideal	ideal	NOUN
ejpam-5627	217	10	of	of	ADP
ejpam-5627	217	11	h.	h.	NOUN
ejpam-5627	217	12	conversely	conversely	ADV
ejpam-5627	217	13	,	,	PUNCT
ejpam-5627	217	14	let	let	VERB
ejpam-5627	217	15	h	h	NOUN
ejpam-5627	217	16	=	=	PUNCT
ejpam-5627	217	17	(	(	PUNCT
ejpam-5627	217	18	h	h	NOUN
ejpam-5627	217	19	,	,	PUNCT
ejpam-5627	217	20	α	α	NOUN
ejpam-5627	217	21	,	,	PUNCT
ejpam-5627	217	22	β	β	NOUN
ejpam-5627	217	23	)	)	PUNCT
ejpam-5627	217	24	be	be	VERB
ejpam-5627	217	25	an	an	DET
ejpam-5627	217	26	ifs	ifs	PROPN
ejpam-5627	217	27	of	of	ADP
ejpam-5627	217	28	h	h	NOUN
ejpam-5627	217	29	for	for	ADP
ejpam-5627	217	30	which	which	PRON
ejpam-5627	217	31	βc	βc	INTJ
ejpam-5627	217	32	and	and	CCONJ
ejpam-5627	217	33	α	α	NOUN
ejpam-5627	217	34	are	be	AUX
ejpam-5627	217	35	fuzzy	fuzzy	ADJ
ejpam-5627	217	36	sup	sup	ADJ
ejpam-5627	217	37	-	-	PUNCT
ejpam-5627	217	38	ideals	ideal	NOUN
ejpam-5627	217	39	of	of	ADP
ejpam-5627	217	40	h.	h.	PROPN
ejpam-5627	217	41	let	let	VERB
ejpam-5627	217	42	x	x	PRON
ejpam-5627	217	43	,	,	PUNCT
ejpam-5627	217	44	y	y	PROPN
ejpam-5627	217	45	∈	∈	PROPN
ejpam-5627	217	46	h.	h.	PROPN
ejpam-5627	217	47	then	then	ADV
ejpam-5627	217	48	1−	1−	NUM
ejpam-5627	217	49	β((x|(y|y))|(x|(y|y	β((x|(y|y))|(x|(y|y	ADJ
ejpam-5627	217	50	)	)	PUNCT
ejpam-5627	217	51	)	)	PUNCT
ejpam-5627	217	52	)	)	PUNCT
ejpam-5627	218	1	=	=	SYM
ejpam-5627	218	2	βc((x|(y|y))|(x|(y|y	βc((x|(y|y))|(x|(y|y	X
ejpam-5627	218	3	)	)	PUNCT
ejpam-5627	218	4	)	)	PUNCT
ejpam-5627	218	5	)	)	PUNCT
ejpam-5627	219	1	≥	≥	NOUN
ejpam-5627	219	2	βc(y	βc(y	PUNCT
ejpam-5627	219	3	)	)	PUNCT
ejpam-5627	219	4	=	=	SYM
ejpam-5627	219	5	1−	1−	NUM
ejpam-5627	219	6	β(y	β(y	NUM
ejpam-5627	219	7	)	)	PUNCT
ejpam-5627	219	8	,	,	PUNCT
ejpam-5627	219	9	β((x|(y|y))|(x|(y|y	β((x|(y|y))|(x|(y|y	ADJ
ejpam-5627	219	10	)	)	PUNCT
ejpam-5627	219	11	)	)	PUNCT
ejpam-5627	219	12	)	)	PUNCT
ejpam-5627	220	1	≤	≤	NUM
ejpam-5627	220	2	β(y	β(y	NOUN
ejpam-5627	220	3	)	)	PUNCT
ejpam-5627	220	4	,	,	PUNCT
ejpam-5627	220	5	1−	1−	NUM
ejpam-5627	220	6	β(y	β(y	NUM
ejpam-5627	220	7	)	)	PUNCT
ejpam-5627	220	8	=	=	PUNCT
ejpam-5627	220	9	βc(y	βc(y	X
ejpam-5627	220	10	)	)	PUNCT
ejpam-5627	220	11	≥	≥	NOUN
ejpam-5627	220	12	min{βc(x	min{βc(x	NOUN
ejpam-5627	220	13	)	)	PUNCT
ejpam-5627	220	14	,	,	PUNCT
ejpam-5627	220	15	βc(y	βc(y	NUM
ejpam-5627	220	16	)	)	PUNCT
ejpam-5627	220	17	}	}	PUNCT
ejpam-5627	220	18	=	=	PUNCT
ejpam-5627	220	19	min{1−	min{1−	VERB
ejpam-5627	220	20	β((x|(y|y))|(x|(y|y	β((x|(y|y))|(x|(y|y	ADJ
ejpam-5627	220	21	)	)	PUNCT
ejpam-5627	220	22	)	)	PUNCT
ejpam-5627	220	23	)	)	PUNCT
ejpam-5627	220	24	,	,	PUNCT
ejpam-5627	220	25	1−	1−	NUM
ejpam-5627	220	26	β(x	β(x	NOUN
ejpam-5627	220	27	)	)	PUNCT
ejpam-5627	220	28	}	}	PUNCT
ejpam-5627	220	29	=	=	SYM
ejpam-5627	220	30	1−max{β((x|(y|y))|(x|(y|y	1−max{β((x|(y|y))|(x|(y|y	NUM
ejpam-5627	220	31	)	)	PUNCT
ejpam-5627	220	32	)	)	PUNCT
ejpam-5627	220	33	)	)	PUNCT
ejpam-5627	220	34	,	,	PUNCT
ejpam-5627	220	35	β(x	β(x	NOUN
ejpam-5627	220	36	)	)	PUNCT
ejpam-5627	220	37	}	}	PUNCT
ejpam-5627	220	38	,	,	PUNCT
ejpam-5627	220	39	β(y	β(y	NOUN
ejpam-5627	220	40	)	)	PUNCT
ejpam-5627	220	41	≤	≤	NOUN
ejpam-5627	220	42	max{β((x|(y|y))|(x|(y|y	max{β((x|(y|y))|(x|(y|y	PROPN
ejpam-5627	220	43	)	)	PUNCT
ejpam-5627	220	44	)	)	PUNCT
ejpam-5627	220	45	)	)	PUNCT
ejpam-5627	220	46	,	,	PUNCT
ejpam-5627	220	47	β(x	β(x	NOUN
ejpam-5627	220	48	)	)	PUNCT
ejpam-5627	220	49	}	}	PUNCT
ejpam-5627	220	50	.	.	PUNCT
ejpam-5627	221	1	hence	hence	ADV
ejpam-5627	221	2	,	,	PUNCT
ejpam-5627	221	3	h	h	NOUN
ejpam-5627	221	4	=	=	PRON
ejpam-5627	221	5	(	(	PUNCT
ejpam-5627	221	6	h	h	NOUN
ejpam-5627	221	7	,	,	PUNCT
ejpam-5627	221	8	α	α	NOUN
ejpam-5627	221	9	,	,	PUNCT
ejpam-5627	221	10	β	β	NOUN
ejpam-5627	221	11	)	)	PUNCT
ejpam-5627	221	12	is	be	AUX
ejpam-5627	221	13	an	an	DET
ejpam-5627	221	14	intuitionistic	intuitionistic	ADJ
ejpam-5627	221	15	fuzzy	fuzzy	ADJ
ejpam-5627	221	16	sup	sup	NOUN
ejpam-5627	221	17	-	-	PUNCT
ejpam-5627	221	18	ideal	ideal	NOUN
ejpam-5627	221	19	of	of	ADP
ejpam-5627	221	20	h.	h.	PROPN
ejpam-5627	221	21	theorem	theorem	PROPN
ejpam-5627	221	22	8	8	NUM
ejpam-5627	221	23	.	.	PUNCT
ejpam-5627	221	24	given	give	VERB
ejpam-5627	221	25	a	a	DET
ejpam-5627	221	26	nonempty	nonempty	ADJ
ejpam-5627	221	27	subset	subset	VERB
ejpam-5627	221	28	f	f	PROPN
ejpam-5627	221	29	of	of	ADP
ejpam-5627	221	30	h	h	NOUN
ejpam-5627	221	31	,	,	PUNCT
ejpam-5627	221	32	let	let	VERB
ejpam-5627	221	33	hf	hf	VERB
ejpam-5627	221	34	=	=	PUNCT
ejpam-5627	221	35	(	(	PUNCT
ejpam-5627	221	36	h	h	NOUN
ejpam-5627	221	37	,	,	PUNCT
ejpam-5627	221	38	αf	αf	VERB
ejpam-5627	221	39	,	,	PUNCT
ejpam-5627	221	40	βf	βf	CCONJ
ejpam-5627	221	41	)	)	PUNCT
ejpam-5627	221	42	be	be	AUX
ejpam-5627	221	43	an	an	DET
ejpam-5627	221	44	ifs	ifs	PROPN
ejpam-5627	221	45	in	in	ADP
ejpam-5627	221	46	h	h	PROPN
ejpam-5627	221	47	defined	define	VERB
ejpam-5627	221	48	as	as	SCONJ
ejpam-5627	221	49	follows	follow	VERB
ejpam-5627	221	50	:	:	PUNCT
ejpam-5627	221	51	αf	αf	ADP
ejpam-5627	221	52	:	:	PUNCT
ejpam-5627	222	1	l	l	X
ejpam-5627	222	2	→	→	PUNCT
ejpam-5627	223	1	[	[	X
ejpam-5627	223	2	0	0	NUM
ejpam-5627	223	3	,	,	PUNCT
ejpam-5627	223	4	1	1	NUM
ejpam-5627	223	5	]	]	PUNCT
ejpam-5627	223	6	,	,	PUNCT
ejpam-5627	223	7	x	x	SYM
ejpam-5627	223	8	7→	7→	NUM
ejpam-5627	223	9	{	{	PUNCT
ejpam-5627	223	10	α0	α0	ADJ
ejpam-5627	223	11	if	if	SCONJ
ejpam-5627	223	12	x	x	SYM
ejpam-5627	223	13	∈	∈	PROPN
ejpam-5627	223	14	f	f	PROPN
ejpam-5627	223	15	,	,	PUNCT
ejpam-5627	223	16	α1	α1	PROPN
ejpam-5627	223	17	otherwise	otherwise	ADV
ejpam-5627	223	18	βf	βf	PRON
ejpam-5627	223	19	:	:	PUNCT
ejpam-5627	223	20	l	l	X
ejpam-5627	223	21	→	→	PUNCT
ejpam-5627	223	22	[	[	X
ejpam-5627	223	23	0	0	NUM
ejpam-5627	223	24	,	,	PUNCT
ejpam-5627	223	25	1	1	NUM
ejpam-5627	223	26	]	]	PUNCT
ejpam-5627	223	27	,	,	PUNCT
ejpam-5627	223	28	a	a	DET
ejpam-5627	223	29	7→	7→	NUM
ejpam-5627	223	30	{	{	PUNCT
ejpam-5627	223	31	β0	β0	ADV
ejpam-5627	223	32	if	if	SCONJ
ejpam-5627	223	33	a	a	DET
ejpam-5627	223	34	∈	∈	ADJ
ejpam-5627	223	35	f	f	X
ejpam-5627	223	36	,	,	PUNCT
ejpam-5627	223	37	β1	β1	PROPN
ejpam-5627	223	38	otherwise	otherwise	ADV
ejpam-5627	223	39	,	,	PUNCT
ejpam-5627	223	40	where	where	SCONJ
ejpam-5627	223	41	β0	β0	NOUN
ejpam-5627	223	42	<	<	X
ejpam-5627	223	43	β1	β1	PROPN
ejpam-5627	223	44	in	in	ADP
ejpam-5627	223	45	[	[	X
ejpam-5627	223	46	0	0	NUM
ejpam-5627	223	47	,	,	PUNCT
ejpam-5627	223	48	1	1	NUM
ejpam-5627	223	49	]	]	PUNCT
ejpam-5627	223	50	and	and	CCONJ
ejpam-5627	223	51	α0	α0	ADJ
ejpam-5627	223	52	>	>	X
ejpam-5627	223	53	α1	α1	PROPN
ejpam-5627	223	54	in	in	ADP
ejpam-5627	223	55	[	[	X
ejpam-5627	223	56	0	0	NUM
ejpam-5627	223	57	,	,	PUNCT
ejpam-5627	223	58	1	1	NUM
ejpam-5627	223	59	]	]	PUNCT
ejpam-5627	223	60	.	.	PUNCT
ejpam-5627	224	1	then	then	ADV
ejpam-5627	224	2	hf	hf	PROPN
ejpam-5627	224	3	=	=	PUNCT
ejpam-5627	224	4	(	(	PUNCT
ejpam-5627	224	5	h	h	NOUN
ejpam-5627	224	6	,	,	PUNCT
ejpam-5627	224	7	αf	αf	VERB
ejpam-5627	224	8	,	,	PUNCT
ejpam-5627	224	9	βf	βf	CCONJ
ejpam-5627	224	10	)	)	PUNCT
ejpam-5627	224	11	is	be	AUX
ejpam-5627	224	12	an	an	DET
ejpam-5627	224	13	intuitionistic	intuitionistic	ADJ
ejpam-5627	224	14	fuzzy	fuzzy	ADJ
ejpam-5627	224	15	sup	sup	NOUN
ejpam-5627	224	16	-	-	PUNCT
ejpam-5627	224	17	ideal	ideal	NOUN
ejpam-5627	224	18	of	of	ADP
ejpam-5627	224	19	h	h	NOUN
ejpam-5627	224	20	if	if	SCONJ
ejpam-5627	225	1	and	and	CCONJ
ejpam-5627	225	2	only	only	ADV
ejpam-5627	225	3	if	if	SCONJ
ejpam-5627	225	4	f	f	PROPN
ejpam-5627	225	5	is	be	AUX
ejpam-5627	225	6	an	an	DET
ejpam-5627	225	7	sup	sup	ADJ
ejpam-5627	225	8	-	-	PUNCT
ejpam-5627	225	9	ideal	ideal	NOUN
ejpam-5627	225	10	of	of	ADP
ejpam-5627	225	11	h.	h.	NOUN
ejpam-5627	225	12	proof	proof	PROPN
ejpam-5627	225	13	.	.	PUNCT
ejpam-5627	226	1	assume	assume	VERB
ejpam-5627	226	2	that	that	SCONJ
ejpam-5627	226	3	hf	hf	PROPN
ejpam-5627	226	4	=	=	PUNCT
ejpam-5627	226	5	(	(	PUNCT
ejpam-5627	226	6	h	h	NOUN
ejpam-5627	226	7	,	,	PUNCT
ejpam-5627	226	8	αf	αf	VERB
ejpam-5627	226	9	,	,	PUNCT
ejpam-5627	226	10	βf	βf	CCONJ
ejpam-5627	226	11	)	)	PUNCT
ejpam-5627	226	12	is	be	AUX
ejpam-5627	226	13	an	an	DET
ejpam-5627	226	14	intuitionistic	intuitionistic	ADJ
ejpam-5627	226	15	fuzzy	fuzzy	ADJ
ejpam-5627	226	16	sup	sup	NOUN
ejpam-5627	226	17	-	-	PUNCT
ejpam-5627	226	18	ideal	ideal	NOUN
ejpam-5627	226	19	of	of	ADP
ejpam-5627	226	20	h.	h.	PROPN
ejpam-5627	226	21	let	let	VERB
ejpam-5627	226	22	x	x	PRON
ejpam-5627	226	23	,	,	PUNCT
ejpam-5627	226	24	y	y	PROPN
ejpam-5627	226	25	∈	∈	PROPN
ejpam-5627	226	26	h	h	NOUN
ejpam-5627	226	27	be	be	AUX
ejpam-5627	226	28	such	such	ADJ
ejpam-5627	226	29	that	that	SCONJ
ejpam-5627	226	30	x	x	NOUN
ejpam-5627	226	31	,	,	PUNCT
ejpam-5627	226	32	y	y	PROPN
ejpam-5627	226	33	∈	∈	PROPN
ejpam-5627	226	34	f	f	PROPN
ejpam-5627	226	35	.	.	PUNCT
ejpam-5627	227	1	then	then	ADV
ejpam-5627	227	2	α((x|(y|y))|(x|(y|y	α((x|(y|y))|(x|(y|y	PROPN
ejpam-5627	227	3	)	)	PUNCT
ejpam-5627	227	4	)	)	PUNCT
ejpam-5627	227	5	)	)	PUNCT
ejpam-5627	228	1	≥	≥	NOUN
ejpam-5627	228	2	α(y	α(y	NOUN
ejpam-5627	228	3	)	)	PUNCT
ejpam-5627	229	1	=	=	SYM
ejpam-5627	229	2	α0	α0	ADJ
ejpam-5627	229	3	,	,	PUNCT
ejpam-5627	229	4	n.	n.	PROPN
ejpam-5627	229	5	rajesh	rajesh	PROPN
ejpam-5627	229	6	,	,	PUNCT
ejpam-5627	229	7	t.	t.	PROPN
ejpam-5627	229	8	oner	oner	NOUN
ejpam-5627	229	9	,	,	PUNCT
ejpam-5627	229	10	a.	a.	NOUN
ejpam-5627	229	11	iampan	iampan	PROPN
ejpam-5627	229	12	,	,	PUNCT
ejpam-5627	229	13	i.	i.	PROPN
ejpam-5627	229	14	senturk	senturk	PROPN
ejpam-5627	229	15	/	/	SYM
ejpam-5627	229	16	eur	eur	PROPN
ejpam-5627	229	17	.	.	PUNCT
ejpam-5627	230	1	j.	j.	PROPN
ejpam-5627	230	2	pure	pure	PROPN
ejpam-5627	230	3	appl	appl	PROPN
ejpam-5627	230	4	.	.	PROPN
ejpam-5627	230	5	math	math	PROPN
ejpam-5627	230	6	,	,	PUNCT
ejpam-5627	230	7	18	18	NUM
ejpam-5627	230	8	(	(	PUNCT
ejpam-5627	230	9	1	1	NUM
ejpam-5627	230	10	)	)	PUNCT
ejpam-5627	230	11	(	(	PUNCT
ejpam-5627	230	12	2025	2025	NUM
ejpam-5627	230	13	)	)	PUNCT
ejpam-5627	230	14	,	,	PUNCT
ejpam-5627	230	15	5627	5627	NUM
ejpam-5627	230	16	9	9	NUM
ejpam-5627	230	17	of	of	ADP
ejpam-5627	230	18	15	15	NUM
ejpam-5627	230	19	β((x|(y|y))|(x|(y|y	β((x|(y|y))|(x|(y|y	ADJ
ejpam-5627	230	20	)	)	PUNCT
ejpam-5627	230	21	)	)	PUNCT
ejpam-5627	230	22	)	)	PUNCT
ejpam-5627	231	1	≤	≤	NUM
ejpam-5627	231	2	β(y	β(y	NOUN
ejpam-5627	231	3	)	)	PUNCT
ejpam-5627	231	4	=	=	SYM
ejpam-5627	231	5	β0	β0	NOUN
ejpam-5627	231	6	,	,	PUNCT
ejpam-5627	231	7	and	and	CCONJ
ejpam-5627	231	8	so	so	ADV
ejpam-5627	231	9	α((x|(y|y))|(x|(y|y	α((x|(y|y))|(x|(y|y	ADJ
ejpam-5627	231	10	)	)	PUNCT
ejpam-5627	231	11	)	)	PUNCT
ejpam-5627	231	12	)	)	PUNCT
ejpam-5627	232	1	=	=	SYM
ejpam-5627	233	1	α0	α0	ADJ
ejpam-5627	233	2	and	and	CCONJ
ejpam-5627	233	3	β((x|(y|y))|(x|(y|y	β((x|(y|y))|(x|(y|y	ADJ
ejpam-5627	233	4	)	)	PUNCT
ejpam-5627	233	5	)	)	PUNCT
ejpam-5627	233	6	)	)	PUNCT
ejpam-5627	234	1	=	=	SYM
ejpam-5627	234	2	β0	β0	NOUN
ejpam-5627	234	3	.	.	PUNCT
ejpam-5627	235	1	this	this	PRON
ejpam-5627	235	2	shows	show	VERB
ejpam-5627	235	3	that	that	SCONJ
ejpam-5627	235	4	(	(	PUNCT
ejpam-5627	235	5	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-5627	235	6	)	)	PUNCT
ejpam-5627	235	7	)	)	PUNCT
ejpam-5627	236	1	∈	∈	PROPN
ejpam-5627	236	2	f	f	INTJ
ejpam-5627	236	3	.	.	PUNCT
ejpam-5627	237	1	then	then	ADV
ejpam-5627	237	2	α(y	α(y	NOUN
ejpam-5627	237	3	)	)	PUNCT
ejpam-5627	237	4	≥	≥	NOUN
ejpam-5627	237	5	min{α((x|(y|y))|(x|(y|y	min{α((x|(y|y))|(x|(y|y	NUM
ejpam-5627	237	6	)	)	PUNCT
ejpam-5627	237	7	)	)	PUNCT
ejpam-5627	237	8	)	)	PUNCT
ejpam-5627	237	9	,	,	PUNCT
ejpam-5627	237	10	α(x	α(x	NOUN
ejpam-5627	237	11	)	)	PUNCT
ejpam-5627	237	12	}	}	PUNCT
ejpam-5627	237	13	=	=	SYM
ejpam-5627	237	14	α0	α0	ADJ
ejpam-5627	237	15	,	,	PUNCT
ejpam-5627	237	16	β(y	β(y	NUM
ejpam-5627	237	17	)	)	PUNCT
ejpam-5627	237	18	≤	≤	NOUN
ejpam-5627	237	19	max{β((x|(y|y))|(x|(y|y	max{β((x|(y|y))|(x|(y|y	PROPN
ejpam-5627	237	20	)	)	PUNCT
ejpam-5627	237	21	)	)	PUNCT
ejpam-5627	237	22	)	)	PUNCT
ejpam-5627	237	23	,	,	PUNCT
ejpam-5627	237	24	β(x	β(x	NOUN
ejpam-5627	237	25	)	)	PUNCT
ejpam-5627	237	26	}	}	PUNCT
ejpam-5627	238	1	=	=	SYM
ejpam-5627	238	2	β0	β0	NOUN
ejpam-5627	238	3	,	,	PUNCT
ejpam-5627	238	4	and	and	CCONJ
ejpam-5627	238	5	so	so	ADV
ejpam-5627	238	6	α(y	α(y	NOUN
ejpam-5627	238	7	)	)	PUNCT
ejpam-5627	238	8	=	=	SYM
ejpam-5627	239	1	α0	α0	ADJ
ejpam-5627	239	2	and	and	CCONJ
ejpam-5627	239	3	β(y	β(y	NUM
ejpam-5627	239	4	)	)	PUNCT
ejpam-5627	240	1	=	=	SYM
ejpam-5627	240	2	β0	β0	NOUN
ejpam-5627	240	3	.	.	PUNCT
ejpam-5627	241	1	this	this	PRON
ejpam-5627	241	2	shows	show	VERB
ejpam-5627	241	3	that	that	SCONJ
ejpam-5627	241	4	y	y	PROPN
ejpam-5627	241	5	∈	∈	PROPN
ejpam-5627	241	6	f	f	PROPN
ejpam-5627	241	7	.	.	PUNCT
ejpam-5627	242	1	therefore	therefore	ADV
ejpam-5627	242	2	,	,	PUNCT
ejpam-5627	242	3	f	f	PROPN
ejpam-5627	242	4	is	be	AUX
ejpam-5627	242	5	an	an	DET
ejpam-5627	242	6	sup	sup	ADJ
ejpam-5627	242	7	-	-	PUNCT
ejpam-5627	242	8	ideal	ideal	NOUN
ejpam-5627	242	9	of	of	ADP
ejpam-5627	242	10	h.	h.	NOUN
ejpam-5627	242	11	conversely	conversely	ADV
ejpam-5627	242	12	,	,	PUNCT
ejpam-5627	242	13	let	let	VERB
ejpam-5627	242	14	f	f	PRON
ejpam-5627	242	15	be	be	AUX
ejpam-5627	242	16	an	an	DET
ejpam-5627	242	17	sup	sup	ADJ
ejpam-5627	242	18	-	-	PUNCT
ejpam-5627	242	19	ideal	ideal	NOUN
ejpam-5627	242	20	of	of	ADP
ejpam-5627	242	21	h.	h.	NOUN
ejpam-5627	242	22	for	for	ADP
ejpam-5627	242	23	every	every	DET
ejpam-5627	242	24	x	x	NOUN
ejpam-5627	242	25	,	,	PUNCT
ejpam-5627	242	26	y	y	PROPN
ejpam-5627	242	27	∈	∈	PROPN
ejpam-5627	242	28	h	h	NOUN
ejpam-5627	242	29	,	,	PUNCT
ejpam-5627	242	30	if	if	SCONJ
ejpam-5627	242	31	(	(	PUNCT
ejpam-5627	242	32	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	ADJ
ejpam-5627	242	33	)	)	PUNCT
ejpam-5627	242	34	)	)	PUNCT
ejpam-5627	243	1	∈	∈	PROPN
ejpam-5627	243	2	f	f	PROPN
ejpam-5627	243	3	,	,	PUNCT
ejpam-5627	243	4	then	then	ADV
ejpam-5627	243	5	y	y	PROPN
ejpam-5627	243	6	∈	∈	PROPN
ejpam-5627	243	7	f	f	PROPN
ejpam-5627	243	8	which	which	PRON
ejpam-5627	243	9	implies	imply	VERB
ejpam-5627	243	10	that	that	SCONJ
ejpam-5627	243	11	α(y	α(y	NOUN
ejpam-5627	243	12	)	)	PUNCT
ejpam-5627	243	13	=	=	SYM
ejpam-5627	244	1	α0	α0	VERB
ejpam-5627	244	2	=	=	SYM
ejpam-5627	244	3	β((x|(y|y))|(x|(y|y	β((x|(y|y))|(x|(y|y	ADJ
ejpam-5627	244	4	)	)	PUNCT
ejpam-5627	244	5	)	)	PUNCT
ejpam-5627	244	6	)	)	PUNCT
ejpam-5627	244	7	,	,	PUNCT
ejpam-5627	244	8	β(y	β(y	NOUN
ejpam-5627	244	9	)	)	PUNCT
ejpam-5627	245	1	=	=	SYM
ejpam-5627	245	2	β0	β0	NOUN
ejpam-5627	245	3	=	=	PUNCT
ejpam-5627	245	4	β((x|(y|y))|(x|(y|y	β((x|(y|y))|(x|(y|y	ADJ
ejpam-5627	245	5	)	)	PUNCT
ejpam-5627	245	6	)	)	PUNCT
ejpam-5627	245	7	)	)	PUNCT
ejpam-5627	245	8	.	.	PUNCT
ejpam-5627	246	1	if	if	SCONJ
ejpam-5627	246	2	(	(	PUNCT
ejpam-5627	246	3	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	NUM
ejpam-5627	246	4	)	)	PUNCT
ejpam-5627	246	5	)	)	PUNCT
ejpam-5627	246	6	/∈	/∈	PUNCT
ejpam-5627	247	1	f	f	PROPN
ejpam-5627	247	2	,	,	PUNCT
ejpam-5627	247	3	then	then	ADV
ejpam-5627	247	4	α((x|(y|y))|(x|(y|y	α((x|(y|y))|(x|(y|y	PROPN
ejpam-5627	247	5	)	)	PUNCT
ejpam-5627	247	6	)	)	PUNCT
ejpam-5627	247	7	)	)	PUNCT
ejpam-5627	248	1	=	=	SYM
ejpam-5627	248	2	α1	α1	PROPN
ejpam-5627	248	3	<	<	X
ejpam-5627	248	4	β(y	β(y	PROPN
ejpam-5627	248	5	)	)	PUNCT
ejpam-5627	248	6	,	,	PUNCT
ejpam-5627	248	7	β((x|(y|y))|(x|(y|y	β((x|(y|y))|(x|(y|y	ADJ
ejpam-5627	248	8	)	)	PUNCT
ejpam-5627	248	9	)	)	PUNCT
ejpam-5627	248	10	)	)	PUNCT
ejpam-5627	249	1	=	=	PUNCT
ejpam-5627	249	2	β1	β1	PROPN
ejpam-5627	249	3	>	>	X
ejpam-5627	249	4	β(y	β(y	PROPN
ejpam-5627	249	5	)	)	PUNCT
ejpam-5627	249	6	.	.	PUNCT
ejpam-5627	250	1	for	for	ADP
ejpam-5627	250	2	every	every	DET
ejpam-5627	250	3	x	x	PROPN
ejpam-5627	250	4	,	,	PUNCT
ejpam-5627	250	5	y	y	PROPN
ejpam-5627	250	6	∈	∈	PROPN
ejpam-5627	250	7	h	h	NOUN
ejpam-5627	250	8	,	,	PUNCT
ejpam-5627	250	9	if	if	SCONJ
ejpam-5627	250	10	x	x	X
ejpam-5627	250	11	,	,	PUNCT
ejpam-5627	250	12	y	y	PROPN
ejpam-5627	250	13	∈	∈	PROPN
ejpam-5627	250	14	f	f	PROPN
ejpam-5627	250	15	,	,	PUNCT
ejpam-5627	250	16	then	then	ADV
ejpam-5627	250	17	x|(y|y))|(x|(y|y	x|(y|y))|(x|(y|y	NUM
ejpam-5627	250	18	)	)	PUNCT
ejpam-5627	250	19	∈	∈	PROPN
ejpam-5627	250	20	f	f	PROPN
ejpam-5627	250	21	which	which	PRON
ejpam-5627	250	22	implies	imply	VERB
ejpam-5627	250	23	that	that	SCONJ
ejpam-5627	250	24	α((x|(y|y))|(x|(y|y	α((x|(y|y))|(x|(y|y	PROPN
ejpam-5627	250	25	)	)	PUNCT
ejpam-5627	250	26	)	)	PUNCT
ejpam-5627	250	27	)	)	PUNCT
ejpam-5627	251	1	=	=	SYM
ejpam-5627	251	2	α0	α0	ADJ
ejpam-5627	251	3	=	=	SYM
ejpam-5627	251	4	min{α(x	min{α(x	PROPN
ejpam-5627	251	5	)	)	PUNCT
ejpam-5627	251	6	,	,	PUNCT
ejpam-5627	251	7	α(y	α(y	NOUN
ejpam-5627	251	8	)	)	PUNCT
ejpam-5627	251	9	}	}	PUNCT
ejpam-5627	251	10	,	,	PUNCT
ejpam-5627	251	11	β((x|(y|y))|(x|(y|y	β((x|(y|y))|(x|(y|y	ADJ
ejpam-5627	251	12	)	)	PUNCT
ejpam-5627	251	13	)	)	PUNCT
ejpam-5627	251	14	)	)	PUNCT
ejpam-5627	252	1	=	=	SYM
ejpam-5627	252	2	β0	β0	PROPN
ejpam-5627	252	3	=	=	SYM
ejpam-5627	252	4	max{β(x	max{β(x	NOUN
ejpam-5627	252	5	)	)	PUNCT
ejpam-5627	252	6	,	,	PUNCT
ejpam-5627	252	7	β(y	β(y	PROPN
ejpam-5627	252	8	)	)	PUNCT
ejpam-5627	252	9	}	}	PUNCT
ejpam-5627	252	10	.	.	PUNCT
ejpam-5627	253	1	if	if	SCONJ
ejpam-5627	253	2	x	x	PROPN
ejpam-5627	253	3	/∈	/∈	PROPN
ejpam-5627	254	1	f	f	PROPN
ejpam-5627	254	2	of	of	ADP
ejpam-5627	254	3	y	y	PROPN
ejpam-5627	254	4	/∈	/∈	PUNCT
ejpam-5627	255	1	f	f	PROPN
ejpam-5627	255	2	,	,	PUNCT
ejpam-5627	255	3	then	then	ADV
ejpam-5627	255	4	α((x|(y|y))|(x|(y|y	α((x|(y|y))|(x|(y|y	PROPN
ejpam-5627	255	5	)	)	PUNCT
ejpam-5627	255	6	)	)	PUNCT
ejpam-5627	255	7	)	)	PUNCT
ejpam-5627	256	1	≥	≥	PROPN
ejpam-5627	256	2	α1	α1	PROPN
ejpam-5627	256	3	=	=	SYM
ejpam-5627	256	4	min{α(x	min{α(x	NOUN
ejpam-5627	256	5	)	)	PUNCT
ejpam-5627	256	6	,	,	PUNCT
ejpam-5627	256	7	α(y	α(y	NOUN
ejpam-5627	256	8	)	)	PUNCT
ejpam-5627	256	9	}	}	PUNCT
ejpam-5627	256	10	,	,	PUNCT
ejpam-5627	256	11	β((x|(y|y))|(x|(y|y	β((x|(y|y))|(x|(y|y	ADJ
ejpam-5627	256	12	)	)	PUNCT
ejpam-5627	256	13	)	)	PUNCT
ejpam-5627	256	14	)	)	PUNCT
ejpam-5627	257	1	≤	≤	NUM
ejpam-5627	258	1	β1	β1	NOUN
ejpam-5627	258	2	=	=	PUNCT
ejpam-5627	258	3	max{β(x	max{β(x	NOUN
ejpam-5627	258	4	)	)	PUNCT
ejpam-5627	258	5	,	,	PUNCT
ejpam-5627	258	6	β(y	β(y	PROPN
ejpam-5627	258	7	)	)	PUNCT
ejpam-5627	258	8	}	}	PUNCT
ejpam-5627	258	9	.	.	PUNCT
ejpam-5627	259	1	therefore	therefore	ADV
ejpam-5627	259	2	,	,	PUNCT
ejpam-5627	259	3	hf	hf	NOUN
ejpam-5627	259	4	=	=	PUNCT
ejpam-5627	259	5	(	(	PUNCT
ejpam-5627	259	6	h	h	NOUN
ejpam-5627	259	7	,	,	PUNCT
ejpam-5627	259	8	αf	αf	VERB
ejpam-5627	259	9	,	,	PUNCT
ejpam-5627	259	10	βf	βf	CCONJ
ejpam-5627	259	11	)	)	PUNCT
ejpam-5627	259	12	is	be	AUX
ejpam-5627	259	13	an	an	DET
ejpam-5627	259	14	intuitionistic	intuitionistic	ADJ
ejpam-5627	259	15	fuzzy	fuzzy	ADJ
ejpam-5627	259	16	sup	sup	NOUN
ejpam-5627	259	17	-	-	PUNCT
ejpam-5627	259	18	ideal	ideal	NOUN
ejpam-5627	259	19	of	of	ADP
ejpam-5627	259	20	h.	h.	NOUN
ejpam-5627	259	21	proposition	proposition	PROPN
ejpam-5627	259	22	2	2	X
ejpam-5627	259	23	.	.	PUNCT
ejpam-5627	260	1	if	if	SCONJ
ejpam-5627	260	2	hi	hi	ADJ
ejpam-5627	260	3	=	=	SYM
ejpam-5627	260	4	{	{	PUNCT
ejpam-5627	260	5	(	(	PUNCT
ejpam-5627	260	6	h	h	NOUN
ejpam-5627	260	7	,	,	PUNCT
ejpam-5627	260	8	αi	αi	PROPN
ejpam-5627	260	9	,	,	PUNCT
ejpam-5627	260	10	βi	βi	PROPN
ejpam-5627	260	11	)	)	PUNCT
ejpam-5627	260	12	:	:	PUNCT
ejpam-5627	260	13	i	i	PRON
ejpam-5627	260	14	∈	∈	PROPN
ejpam-5627	260	15	∆	∆	PROPN
ejpam-5627	260	16	}	}	PUNCT
ejpam-5627	260	17	is	be	AUX
ejpam-5627	260	18	a	a	DET
ejpam-5627	260	19	family	family	NOUN
ejpam-5627	260	20	of	of	ADP
ejpam-5627	260	21	intuitionistic	intuitionistic	ADJ
ejpam-5627	260	22	fuzzy	fuzzy	ADJ
ejpam-5627	260	23	sup	sup	NOUN
ejpam-5627	260	24	-	-	PUNCT
ejpam-5627	260	25	ideals	ideal	NOUN
ejpam-5627	260	26	of	of	ADP
ejpam-5627	260	27	h	h	NOUN
ejpam-5627	260	28	,	,	PUNCT
ejpam-5627	260	29	then	then	ADV
ejpam-5627	260	30	∧	∧	PROPN
ejpam-5627	260	31	i∈∆	i∈∆	PROPN
ejpam-5627	260	32	xi	xi	PROPN
ejpam-5627	260	33	is	be	AUX
ejpam-5627	260	34	an	an	DET
ejpam-5627	260	35	intuitionistic	intuitionistic	ADJ
ejpam-5627	260	36	fuzzy	fuzzy	ADJ
ejpam-5627	260	37	sup	sup	NOUN
ejpam-5627	260	38	-	-	PUNCT
ejpam-5627	260	39	ideal	ideal	NOUN
ejpam-5627	260	40	of	of	ADP
ejpam-5627	260	41	h.	h.	NOUN
ejpam-5627	260	42	proof	proof	NOUN
ejpam-5627	260	43	.	.	PUNCT
ejpam-5627	261	1	let	let	VERB
ejpam-5627	261	2	hi	hi	INTJ
ejpam-5627	261	3	=	=	VERB
ejpam-5627	261	4	{	{	PUNCT
ejpam-5627	261	5	(	(	PUNCT
ejpam-5627	261	6	h	h	NOUN
ejpam-5627	261	7	,	,	PUNCT
ejpam-5627	261	8	αi	αi	PROPN
ejpam-5627	261	9	,	,	PUNCT
ejpam-5627	261	10	βi	βi	PROPN
ejpam-5627	261	11	)	)	PUNCT
ejpam-5627	261	12	:	:	PUNCT
ejpam-5627	261	13	i	i	PRON
ejpam-5627	261	14	∈	∈	PROPN
ejpam-5627	261	15	∆	∆	PROPN
ejpam-5627	261	16	}	}	PUNCT
ejpam-5627	261	17	be	be	AUX
ejpam-5627	261	18	a	a	DET
ejpam-5627	261	19	family	family	NOUN
ejpam-5627	261	20	of	of	ADP
ejpam-5627	261	21	intuitionistic	intuitionistic	ADJ
ejpam-5627	261	22	fuzzy	fuzzy	ADJ
ejpam-5627	261	23	sup	sup	NOUN
ejpam-5627	261	24	-	-	PUNCT
ejpam-5627	261	25	ideals	ideal	NOUN
ejpam-5627	261	26	of	of	ADP
ejpam-5627	261	27	h.	h.	PROPN
ejpam-5627	261	28	let	let	VERB
ejpam-5627	261	29	x	x	PRON
ejpam-5627	261	30	,	,	PUNCT
ejpam-5627	261	31	y	y	PROPN
ejpam-5627	261	32	∈	∈	PROPN
ejpam-5627	261	33	h.	h.	NOUN
ejpam-5627	262	1	then	then	ADV
ejpam-5627	262	2	(	(	PUNCT
ejpam-5627	262	3	∧	∧	PROPN
ejpam-5627	262	4	i∈∆	i∈∆	PROPN
ejpam-5627	262	5	αi)((x|(y|y))|(x|(y|y	αi)((x|(y|y))|(x|(y|y	NOUN
ejpam-5627	262	6	)	)	PUNCT
ejpam-5627	262	7	)	)	PUNCT
ejpam-5627	262	8	)	)	PUNCT
ejpam-5627	263	1	=	=	PRON
ejpam-5627	263	2	inf	inf	PROPN
ejpam-5627	263	3	i∈∆	i∈∆	PROPN
ejpam-5627	263	4	{	{	PUNCT
ejpam-5627	263	5	αi((x|(y|y))|(x|(y|y	αi((x|(y|y))|(x|(y|y	ADJ
ejpam-5627	263	6	)	)	PUNCT
ejpam-5627	263	7	)	)	PUNCT
ejpam-5627	263	8	)	)	PUNCT
ejpam-5627	263	9	}	}	PUNCT
ejpam-5627	263	10	≥	≥	PROPN
ejpam-5627	263	11	inf	inf	NOUN
ejpam-5627	263	12	i∈∆	i∈∆	PROPN
ejpam-5627	263	13	{	{	PUNCT
ejpam-5627	263	14	αi(y	αi(y	NOUN
ejpam-5627	263	15	)	)	PUNCT
ejpam-5627	263	16	}	}	PUNCT
ejpam-5627	263	17	=	=	SYM
ejpam-5627	263	18	(	(	PUNCT
ejpam-5627	263	19	∧	∧	PROPN
ejpam-5627	263	20	i∈∆	i∈∆	PROPN
ejpam-5627	263	21	αi)(y	αi)(y	PROPN
ejpam-5627	263	22	)	)	PUNCT
ejpam-5627	263	23	,	,	PUNCT
ejpam-5627	263	24	(	(	PUNCT
ejpam-5627	263	25	∧	∧	NOUN
ejpam-5627	263	26	i∈∆	i∈∆	PROPN
ejpam-5627	263	27	βi)((x|(y|y))|(x|(y|y	βi)((x|(y|y))|(x|(y|y	ADJ
ejpam-5627	263	28	)	)	PUNCT
ejpam-5627	263	29	)	)	PUNCT
ejpam-5627	263	30	)	)	PUNCT
ejpam-5627	264	1	=	=	PUNCT
ejpam-5627	264	2	sup	sup	NOUN
ejpam-5627	264	3	i∈∆	i∈∆	PROPN
ejpam-5627	264	4	{	{	PUNCT
ejpam-5627	264	5	βi((x|(y|y))|(x|(y|y	βi((x|(y|y))|(x|(y|y	PROPN
ejpam-5627	264	6	)	)	PUNCT
ejpam-5627	264	7	)	)	PUNCT
ejpam-5627	264	8	)	)	PUNCT
ejpam-5627	264	9	}	}	PUNCT
ejpam-5627	264	10	≤	≤	NUM
ejpam-5627	264	11	sup	sup	NOUN
ejpam-5627	264	12	i∈∆	i∈∆	NOUN
ejpam-5627	264	13	{	{	PUNCT
ejpam-5627	264	14	βi(y	βi(y	NUM
ejpam-5627	264	15	)	)	PUNCT
ejpam-5627	264	16	}	}	PUNCT
ejpam-5627	264	17	=	=	SYM
ejpam-5627	265	1	(	(	PUNCT
ejpam-5627	265	2	∧	∧	NOUN
ejpam-5627	265	3	i∈∆	i∈∆	PROPN
ejpam-5627	265	4	βi)(y	βi)(y	PROPN
ejpam-5627	265	5	)	)	PUNCT
ejpam-5627	265	6	.	.	PUNCT
ejpam-5627	266	1	n.	n.	PROPN
ejpam-5627	266	2	rajesh	rajesh	PROPN
ejpam-5627	266	3	,	,	PUNCT
ejpam-5627	266	4	t.	t.	PROPN
ejpam-5627	266	5	oner	oner	NOUN
ejpam-5627	266	6	,	,	PUNCT
ejpam-5627	266	7	a.	a.	NOUN
ejpam-5627	266	8	iampan	iampan	PROPN
ejpam-5627	266	9	,	,	PUNCT
ejpam-5627	266	10	i.	i.	PROPN
ejpam-5627	266	11	senturk	senturk	PROPN
ejpam-5627	266	12	/	/	SYM
ejpam-5627	266	13	eur	eur	PROPN
ejpam-5627	266	14	.	.	PUNCT
ejpam-5627	267	1	j.	j.	PROPN
ejpam-5627	267	2	pure	pure	PROPN
ejpam-5627	267	3	appl	appl	PROPN
ejpam-5627	267	4	.	.	PROPN
ejpam-5627	267	5	math	math	PROPN
ejpam-5627	267	6	,	,	PUNCT
ejpam-5627	267	7	18	18	NUM
ejpam-5627	267	8	(	(	PUNCT
ejpam-5627	267	9	1	1	NUM
ejpam-5627	267	10	)	)	PUNCT
ejpam-5627	267	11	(	(	PUNCT
ejpam-5627	267	12	2025	2025	NUM
ejpam-5627	267	13	)	)	PUNCT
ejpam-5627	267	14	,	,	PUNCT
ejpam-5627	267	15	5627	5627	NUM
ejpam-5627	267	16	10	10	NUM
ejpam-5627	267	17	of	of	ADP
ejpam-5627	267	18	15	15	NUM
ejpam-5627	267	19	let	let	VERB
ejpam-5627	267	20	x	x	PRON
ejpam-5627	267	21	,	,	PUNCT
ejpam-5627	267	22	y	y	PROPN
ejpam-5627	267	23	∈	∈	PROPN
ejpam-5627	267	24	h.	h.	NOUN
ejpam-5627	268	1	then	then	ADV
ejpam-5627	268	2	(	(	PUNCT
ejpam-5627	268	3	∧	∧	NOUN
ejpam-5627	268	4	i∈∆	i∈∆	NOUN
ejpam-5627	268	5	αi)(y	αi)(y	PROPN
ejpam-5627	268	6	)	)	PUNCT
ejpam-5627	268	7	=	=	SYM
ejpam-5627	268	8	inf	inf	NOUN
ejpam-5627	268	9	i∈∆	i∈∆	NOUN
ejpam-5627	268	10	{	{	PUNCT
ejpam-5627	268	11	αi(y	αi(y	NOUN
ejpam-5627	268	12	)	)	PUNCT
ejpam-5627	268	13	}	}	PUNCT
ejpam-5627	268	14	≥	≥	PROPN
ejpam-5627	268	15	inf	inf	PROPN
ejpam-5627	268	16	i∈∆	i∈∆	PROPN
ejpam-5627	268	17	{	{	PUNCT
ejpam-5627	268	18	min{αi((x|(y|y))|(x|(y|y	min{αi((x|(y|y))|(x|(y|y	ADJ
ejpam-5627	268	19	)	)	PUNCT
ejpam-5627	268	20	)	)	PUNCT
ejpam-5627	268	21	)	)	PUNCT
ejpam-5627	268	22	,	,	PUNCT
ejpam-5627	268	23	αi(x	αi(x	NUM
ejpam-5627	268	24	)	)	PUNCT
ejpam-5627	268	25	}	}	PUNCT
ejpam-5627	268	26	}	}	PUNCT
ejpam-5627	268	27	=	=	SYM
ejpam-5627	268	28	min	min	X
ejpam-5627	268	29	{	{	PUNCT
ejpam-5627	268	30	inf	inf	NOUN
ejpam-5627	268	31	i∈∆	i∈∆	PROPN
ejpam-5627	268	32	αi((x|(y|y))|(x|(y|y	αi((x|(y|y))|(x|(y|y	ADJ
ejpam-5627	268	33	)	)	PUNCT
ejpam-5627	268	34	)	)	PUNCT
ejpam-5627	268	35	)	)	PUNCT
ejpam-5627	268	36	,	,	PUNCT
ejpam-5627	268	37	inf	inf	NOUN
ejpam-5627	268	38	i∈∆	i∈∆	NOUN
ejpam-5627	268	39	αi(x	αi(x	NUM
ejpam-5627	268	40	)	)	PUNCT
ejpam-5627	268	41	}	}	PUNCT
ejpam-5627	268	42	=	=	SYM
ejpam-5627	268	43	min	min	X
ejpam-5627	268	44	{	{	PUNCT
ejpam-5627	268	45	(	(	PUNCT
ejpam-5627	268	46	∧	∧	PROPN
ejpam-5627	268	47	i∈∆	i∈∆	PROPN
ejpam-5627	268	48	αi)((x|(y|y))|(x|(y|y	αi)((x|(y|y))|(x|(y|y	NOUN
ejpam-5627	268	49	)	)	PUNCT
ejpam-5627	268	50	)	)	PUNCT
ejpam-5627	268	51	)	)	PUNCT
ejpam-5627	268	52	,	,	PUNCT
ejpam-5627	268	53	(	(	PUNCT
ejpam-5627	268	54	∧	∧	NOUN
ejpam-5627	268	55	i∈∆	i∈∆	PROPN
ejpam-5627	268	56	αi)(x	αi)(x	PROPN
ejpam-5627	268	57	)	)	PUNCT
ejpam-5627	268	58	}	}	PUNCT
ejpam-5627	268	59	,	,	PUNCT
ejpam-5627	268	60	(	(	PUNCT
ejpam-5627	268	61	∧	∧	NOUN
ejpam-5627	268	62	i∈∆	i∈∆	PROPN
ejpam-5627	268	63	βi)(y	βi)(y	PROPN
ejpam-5627	268	64	)	)	PUNCT
ejpam-5627	269	1	=	=	PUNCT
ejpam-5627	269	2	sup	sup	NOUN
ejpam-5627	269	3	i∈∆	i∈∆	NOUN
ejpam-5627	269	4	{	{	PUNCT
ejpam-5627	269	5	βi(y	βi(y	NUM
ejpam-5627	269	6	)	)	PUNCT
ejpam-5627	269	7	}	}	PUNCT
ejpam-5627	269	8	≤	≤	NUM
ejpam-5627	269	9	sup	sup	NOUN
ejpam-5627	269	10	i∈∆	i∈∆	NOUN
ejpam-5627	269	11	{	{	PUNCT
ejpam-5627	269	12	max{βi((x|(y|y))|(x|(y|y	max{βi((x|(y|y))|(x|(y|y	NOUN
ejpam-5627	269	13	)	)	PUNCT
ejpam-5627	269	14	)	)	PUNCT
ejpam-5627	269	15	)	)	PUNCT
ejpam-5627	269	16	,	,	PUNCT
ejpam-5627	269	17	βi(x	βi(x	NUM
ejpam-5627	269	18	)	)	PUNCT
ejpam-5627	269	19	}	}	PUNCT
ejpam-5627	269	20	}	}	PUNCT
ejpam-5627	269	21	=	=	PUNCT
ejpam-5627	269	22	max{sup	max{sup	ADJ
ejpam-5627	269	23	i∈∆	i∈∆	PROPN
ejpam-5627	269	24	βi((x|(y|y))|(x|(y|y	βi((x|(y|y))|(x|(y|y	PROPN
ejpam-5627	269	25	)	)	PUNCT
ejpam-5627	269	26	)	)	PUNCT
ejpam-5627	269	27	)	)	PUNCT
ejpam-5627	269	28	,	,	PUNCT
ejpam-5627	269	29	sup	sup	NOUN
ejpam-5627	269	30	i∈∆	i∈∆	ADV
ejpam-5627	269	31	βi(x	βi(x	PUNCT
ejpam-5627	269	32	)	)	PUNCT
ejpam-5627	269	33	}	}	PUNCT
ejpam-5627	269	34	=	=	SYM
ejpam-5627	269	35	max	max	X
ejpam-5627	269	36	{	{	PUNCT
ejpam-5627	269	37	(	(	PUNCT
ejpam-5627	269	38	∧	∧	PROPN
ejpam-5627	269	39	i∈∆	i∈∆	PROPN
ejpam-5627	269	40	βi)((x|(y|y))|(x|(y|y	βi)((x|(y|y))|(x|(y|y	ADJ
ejpam-5627	269	41	)	)	PUNCT
ejpam-5627	269	42	)	)	PUNCT
ejpam-5627	269	43	)	)	PUNCT
ejpam-5627	269	44	,	,	PUNCT
ejpam-5627	269	45	(	(	PUNCT
ejpam-5627	269	46	∧	∧	NOUN
ejpam-5627	269	47	i∈∆	i∈∆	PROPN
ejpam-5627	269	48	βi)(x	βi)(x	PROPN
ejpam-5627	269	49	)	)	PUNCT
ejpam-5627	269	50	}	}	PUNCT
ejpam-5627	269	51	.	.	PUNCT
ejpam-5627	270	1	hence	hence	ADV
ejpam-5627	270	2	,	,	PUNCT
ejpam-5627	270	3	∧	∧	PROPN
ejpam-5627	270	4	i∈∆	i∈∆	NOUN
ejpam-5627	270	5	xi	xi	PROPN
ejpam-5627	270	6	is	be	AUX
ejpam-5627	270	7	an	an	DET
ejpam-5627	270	8	intuitionistic	intuitionistic	ADJ
ejpam-5627	270	9	fuzzy	fuzzy	ADJ
ejpam-5627	270	10	sup	sup	NOUN
ejpam-5627	270	11	-	-	PUNCT
ejpam-5627	270	12	ideal	ideal	NOUN
ejpam-5627	270	13	of	of	ADP
ejpam-5627	270	14	an	an	DET
ejpam-5627	270	15	sup	sup	ADJ
ejpam-5627	270	16	-	-	PUNCT
ejpam-5627	270	17	algebra	algebra	NOUN
ejpam-5627	270	18	h.	h.	NOUN
ejpam-5627	270	19	theorem	theorem	VERB
ejpam-5627	270	20	9	9	NUM
ejpam-5627	270	21	.	.	PUNCT
ejpam-5627	271	1	[	[	X
ejpam-5627	271	2	7	7	X
ejpam-5627	271	3	]	]	X
ejpam-5627	271	4	let	let	VERB
ejpam-5627	271	5	⟨a	⟨a	NOUN
ejpam-5627	271	6	,	,	PUNCT
ejpam-5627	271	7	|a	|a	NOUN
ejpam-5627	271	8	,	,	PUNCT
ejpam-5627	271	9	0a⟩	0a⟩	NUM
ejpam-5627	271	10	and	and	CCONJ
ejpam-5627	271	11	⟨b	⟨b	PROPN
ejpam-5627	271	12	,	,	PUNCT
ejpam-5627	271	13	|b	|b	PROPN
ejpam-5627	271	14	,	,	PUNCT
ejpam-5627	271	15	0b⟩	0b⟩	NUM
ejpam-5627	271	16	be	be	VERB
ejpam-5627	271	17	sup	sup	NOUN
ejpam-5627	271	18	-	-	PUNCT
ejpam-5627	271	19	algebras	algebras	NOUN
ejpam-5627	271	20	.	.	PUNCT
ejpam-5627	272	1	then	then	ADV
ejpam-5627	272	2	⟨a×b	⟨a×b	NUM
ejpam-5627	272	3	,	,	PUNCT
ejpam-5627	272	4	|a×b	|a×b	PROPN
ejpam-5627	272	5	,	,	PUNCT
ejpam-5627	272	6	0a×b⟩	0a×b⟩	PROPN
ejpam-5627	272	7	is	be	AUX
ejpam-5627	272	8	an	an	DET
ejpam-5627	272	9	sup	sup	NOUN
ejpam-5627	272	10	-	-	PUNCT
ejpam-5627	272	11	algebra	algebra	NOUN
ejpam-5627	272	12	where	where	SCONJ
ejpam-5627	272	13	the	the	DET
ejpam-5627	272	14	set	set	NOUN
ejpam-5627	272	15	a	a	DET
ejpam-5627	272	16	×	×	PROPN
ejpam-5627	272	17	b	b	PROPN
ejpam-5627	272	18	is	be	AUX
ejpam-5627	272	19	the	the	DET
ejpam-5627	272	20	cartesian	cartesian	ADJ
ejpam-5627	272	21	product	product	NOUN
ejpam-5627	272	22	of	of	ADP
ejpam-5627	272	23	a	a	PRON
ejpam-5627	272	24	and	and	CCONJ
ejpam-5627	272	25	b	b	NOUN
ejpam-5627	272	26	and	and	CCONJ
ejpam-5627	272	27	the	the	DET
ejpam-5627	272	28	operation	operation	NOUN
ejpam-5627	272	29	|a×b	|a×b	PROPN
ejpam-5627	272	30	on	on	ADP
ejpam-5627	272	31	this	this	DET
ejpam-5627	272	32	set	set	NOUN
ejpam-5627	272	33	is	be	AUX
ejpam-5627	272	34	defined	define	VERB
ejpam-5627	272	35	by	by	ADP
ejpam-5627	272	36	(	(	PUNCT
ejpam-5627	272	37	a1	a1	NOUN
ejpam-5627	272	38	,	,	PUNCT
ejpam-5627	272	39	b1)|a×b(a2	b1)|a×b(a2	NUM
ejpam-5627	272	40	,	,	PUNCT
ejpam-5627	272	41	b2	b2	NOUN
ejpam-5627	272	42	)	)	PUNCT
ejpam-5627	272	43	=	=	SYM
ejpam-5627	272	44	(	(	PUNCT
ejpam-5627	272	45	a1|aa2	a1|aa2	PROPN
ejpam-5627	272	46	,	,	PUNCT
ejpam-5627	272	47	b1|bb2	b1|bb2	NOUN
ejpam-5627	272	48	)	)	PUNCT
ejpam-5627	272	49	,	,	PUNCT
ejpam-5627	272	50	and	and	CCONJ
ejpam-5627	272	51	the	the	DET
ejpam-5627	272	52	fixed	fix	VERB
ejpam-5627	272	53	element	element	NOUN
ejpam-5627	272	54	is	be	AUX
ejpam-5627	272	55	0a×b	0a×b	PUNCT
ejpam-5627	273	1	=	=	PUNCT
ejpam-5627	273	2	(	(	PUNCT
ejpam-5627	273	3	0a	0a	PROPN
ejpam-5627	273	4	,	,	PUNCT
ejpam-5627	273	5	0b	0b	NUM
ejpam-5627	273	6	)	)	PUNCT
ejpam-5627	273	7	.	.	PUNCT
ejpam-5627	274	1	theorem	theorem	ADJ
ejpam-5627	274	2	10	10	NUM
ejpam-5627	274	3	.	.	PUNCT
ejpam-5627	275	1	let	let	VERB
ejpam-5627	275	2	⟨a	⟨a	NOUN
ejpam-5627	275	3	,	,	PUNCT
ejpam-5627	275	4	|a	|a	NOUN
ejpam-5627	275	5	,	,	PUNCT
ejpam-5627	275	6	0a⟩	0a⟩	NUM
ejpam-5627	275	7	and	and	CCONJ
ejpam-5627	275	8	⟨b	⟨b	PROPN
ejpam-5627	275	9	,	,	PUNCT
ejpam-5627	275	10	|b	|b	PROPN
ejpam-5627	275	11	,	,	PUNCT
ejpam-5627	275	12	0b⟩	0b⟩	NUM
ejpam-5627	275	13	be	be	VERB
ejpam-5627	275	14	sup	sup	NOUN
ejpam-5627	275	15	-	-	PUNCT
ejpam-5627	275	16	algebras	algebras	NOUN
ejpam-5627	275	17	.	.	PUNCT
ejpam-5627	276	1	if	if	SCONJ
ejpam-5627	276	2	ha	ha	X
ejpam-5627	276	3	=	=	X
ejpam-5627	276	4	(	(	PUNCT
ejpam-5627	276	5	a,µa	a,µa	PROPN
ejpam-5627	276	6	,	,	PUNCT
ejpam-5627	276	7	γa	γa	PROPN
ejpam-5627	276	8	)	)	PUNCT
ejpam-5627	276	9	and	and	CCONJ
ejpam-5627	276	10	hb	hb	X
ejpam-5627	276	11	=	=	SYM
ejpam-5627	276	12	(	(	PUNCT
ejpam-5627	276	13	b,µb	b,µb	NUM
ejpam-5627	276	14	,	,	PUNCT
ejpam-5627	276	15	γb	γb	NOUN
ejpam-5627	276	16	)	)	PUNCT
ejpam-5627	276	17	are	be	AUX
ejpam-5627	276	18	intuitionistic	intuitionistic	ADJ
ejpam-5627	276	19	fuzzy	fuzzy	ADJ
ejpam-5627	276	20	sup	sup	NOUN
ejpam-5627	276	21	-	-	PUNCT
ejpam-5627	276	22	subalgebras	subalgebras	NOUN
ejpam-5627	276	23	of	of	ADP
ejpam-5627	276	24	⟨a	⟨a	PROPN
ejpam-5627	276	25	,	,	PUNCT
ejpam-5627	276	26	|a	|a	NOUN
ejpam-5627	276	27	,	,	PUNCT
ejpam-5627	276	28	0a⟩	0a⟩	NUM
ejpam-5627	276	29	and	and	CCONJ
ejpam-5627	276	30	⟨b	⟨b	PROPN
ejpam-5627	276	31	,	,	PUNCT
ejpam-5627	276	32	|b	|b	ADJ
ejpam-5627	276	33	,	,	PUNCT
ejpam-5627	276	34	0b⟩	0b⟩	NUM
ejpam-5627	276	35	,	,	PUNCT
ejpam-5627	276	36	respectively	respectively	ADV
ejpam-5627	276	37	,	,	PUNCT
ejpam-5627	276	38	then	then	ADV
ejpam-5627	276	39	ha×b	ha×b	PROPN
ejpam-5627	276	40	=	=	SYM
ejpam-5627	276	41	(	(	PUNCT
ejpam-5627	276	42	a×b,µa×b	a×b,µa×b	PROPN
ejpam-5627	276	43	,	,	PUNCT
ejpam-5627	276	44	γa×b	γa×b	NOUN
ejpam-5627	276	45	)	)	PUNCT
ejpam-5627	276	46	is	be	AUX
ejpam-5627	276	47	an	an	DET
ejpam-5627	276	48	intuitionistic	intuitionistic	ADJ
ejpam-5627	276	49	fuzzy	fuzzy	ADJ
ejpam-5627	276	50	sup	sup	NOUN
ejpam-5627	276	51	-	-	PUNCT
ejpam-5627	276	52	subalgebra	subalgebra	NOUN
ejpam-5627	276	53	of	of	ADP
ejpam-5627	276	54	⟨a×b	⟨a×b	NOUN
ejpam-5627	276	55	,	,	PUNCT
ejpam-5627	276	56	|a×b	|a×b	PROPN
ejpam-5627	276	57	,	,	PUNCT
ejpam-5627	276	58	0a×b⟩.	0a×b⟩.	NOUN
ejpam-5627	276	59	proof	proof	NOUN
ejpam-5627	276	60	.	.	PUNCT
ejpam-5627	277	1	let	let	VERB
ejpam-5627	277	2	⟨a	⟨a	NOUN
ejpam-5627	277	3	,	,	PUNCT
ejpam-5627	277	4	|a	|a	NOUN
ejpam-5627	277	5	,	,	PUNCT
ejpam-5627	277	6	0a⟩	0a⟩	NUM
ejpam-5627	277	7	and	and	CCONJ
ejpam-5627	277	8	⟨b	⟨b	PROPN
ejpam-5627	277	9	,	,	PUNCT
ejpam-5627	277	10	|b	|b	PROPN
ejpam-5627	277	11	,	,	PUNCT
ejpam-5627	277	12	0b⟩	0b⟩	NUM
ejpam-5627	277	13	be	be	VERB
ejpam-5627	277	14	sup	sup	NOUN
ejpam-5627	277	15	-	-	PUNCT
ejpam-5627	277	16	algebras	algebras	NOUN
ejpam-5627	277	17	.	.	PUNCT
ejpam-5627	278	1	if	if	SCONJ
ejpam-5627	278	2	ha	ha	X
ejpam-5627	278	3	=	=	X
ejpam-5627	278	4	(	(	PUNCT
ejpam-5627	278	5	a,µa	a,µa	PROPN
ejpam-5627	278	6	,	,	PUNCT
ejpam-5627	278	7	γa	γa	PROPN
ejpam-5627	278	8	)	)	PUNCT
ejpam-5627	278	9	and	and	CCONJ
ejpam-5627	278	10	hb	hb	X
ejpam-5627	278	11	=	=	SYM
ejpam-5627	278	12	(	(	PUNCT
ejpam-5627	278	13	b,µb	b,µb	NUM
ejpam-5627	278	14	,	,	PUNCT
ejpam-5627	278	15	γb	γb	NOUN
ejpam-5627	278	16	)	)	PUNCT
ejpam-5627	278	17	are	be	AUX
ejpam-5627	278	18	intuitionistic	intuitionistic	ADJ
ejpam-5627	278	19	fuzzy	fuzzy	ADJ
ejpam-5627	278	20	sup	sup	NOUN
ejpam-5627	278	21	-	-	PUNCT
ejpam-5627	278	22	subalgebras	subalgebras	NOUN
ejpam-5627	278	23	of	of	ADP
ejpam-5627	278	24	⟨a	⟨a	PROPN
ejpam-5627	278	25	,	,	PUNCT
ejpam-5627	278	26	|a	|a	NOUN
ejpam-5627	278	27	,	,	PUNCT
ejpam-5627	278	28	0a⟩	0a⟩	NUM
ejpam-5627	278	29	and	and	CCONJ
ejpam-5627	278	30	⟨b	⟨b	PROPN
ejpam-5627	278	31	,	,	PUNCT
ejpam-5627	278	32	|b	|b	ADJ
ejpam-5627	278	33	,	,	PUNCT
ejpam-5627	278	34	0b⟩	0b⟩	NUM
ejpam-5627	278	35	,	,	PUNCT
ejpam-5627	278	36	respectively	respectively	ADV
ejpam-5627	278	37	.	.	PUNCT
ejpam-5627	279	1	let	let	VERB
ejpam-5627	279	2	(	(	PUNCT
ejpam-5627	279	3	a1	a1	NOUN
ejpam-5627	279	4	,	,	PUNCT
ejpam-5627	279	5	b1	b1	NOUN
ejpam-5627	279	6	)	)	PUNCT
ejpam-5627	279	7	,	,	PUNCT
ejpam-5627	279	8	(	(	PUNCT
ejpam-5627	279	9	a2	a2	PROPN
ejpam-5627	279	10	,	,	PUNCT
ejpam-5627	279	11	b2	b2	NOUN
ejpam-5627	279	12	)	)	PUNCT
ejpam-5627	279	13	∈	∈	PROPN
ejpam-5627	279	14	a×b	a×b	PROPN
ejpam-5627	279	15	.	.	PUNCT
ejpam-5627	280	1	then	then	ADV
ejpam-5627	280	2	µa×b(((a1	µa×b(((a1	NUM
ejpam-5627	280	3	,	,	PUNCT
ejpam-5627	280	4	b1)|a×b((a2	b1)|a×b((a2	NOUN
ejpam-5627	280	5	,	,	PUNCT
ejpam-5627	280	6	b2)|a×b(a2	b2)|a×b(a2	NUM
ejpam-5627	280	7	,	,	PUNCT
ejpam-5627	280	8	b2)))|a×b((a1	b2)))|a×b((a1	NOUN
ejpam-5627	280	9	,	,	PUNCT
ejpam-5627	280	10	b1)|a×b((a2	b1)|a×b((a2	NOUN
ejpam-5627	280	11	,	,	PUNCT
ejpam-5627	280	12	b2)|a×b(a2	b2)|a×b(a2	NUM
ejpam-5627	280	13	,	,	PUNCT
ejpam-5627	280	14	b2	b2	NOUN
ejpam-5627	280	15	)	)	PUNCT
ejpam-5627	280	16	)	)	PUNCT
ejpam-5627	280	17	)	)	PUNCT
ejpam-5627	280	18	)	)	PUNCT
ejpam-5627	281	1	=	=	PUNCT
ejpam-5627	281	2	µa×b((a1|a(a2|aa2))|a(a1|a(a2|aa2	µa×b((a1|a(a2|aa2))|a(a1|a(a2|aa2	NUM
ejpam-5627	281	3	)	)	PUNCT
ejpam-5627	281	4	)	)	PUNCT
ejpam-5627	281	5	,	,	PUNCT
ejpam-5627	281	6	(	(	PUNCT
ejpam-5627	281	7	b1|b(b2|bb2))|b(b1|b(b2|bb2	b1|b(b2|bb2))|b(b1|b(b2|bb2	PROPN
ejpam-5627	281	8	)	)	PUNCT
ejpam-5627	281	9	)	)	PUNCT
ejpam-5627	281	10	)	)	PUNCT
ejpam-5627	282	1	=	=	SYM
ejpam-5627	282	2	max{µa((a1|a(a2|aa2))|a(a1|a(a2|aa2	max{µa((a1|a(a2|aa2))|a(a1|a(a2|aa2	NUM
ejpam-5627	282	3	)	)	PUNCT
ejpam-5627	282	4	)	)	PUNCT
ejpam-5627	282	5	,	,	PUNCT
ejpam-5627	282	6	tb(b1|b(b2|bb2))|b(b1|b(b2|bb2	tb(b1|b(b2|bb2))|b(b1|b(b2|bb2	PROPN
ejpam-5627	282	7	)	)	PUNCT
ejpam-5627	282	8	)	)	PUNCT
ejpam-5627	282	9	)	)	PUNCT
ejpam-5627	282	10	}	}	PUNCT
ejpam-5627	282	11	≥	≥	X
ejpam-5627	282	12	max{min{µa(a1	max{min{µa(a1	NOUN
ejpam-5627	282	13	)	)	PUNCT
ejpam-5627	282	14	,	,	PUNCT
ejpam-5627	282	15	µa(a2)},min{µb(b1	µa(a2)},min{µb(b1	NOUN
ejpam-5627	282	16	)	)	PUNCT
ejpam-5627	282	17	,	,	PUNCT
ejpam-5627	282	18	µb(b2	µb(b2	NOUN
ejpam-5627	282	19	)	)	PUNCT
ejpam-5627	282	20	}	}	PUNCT
ejpam-5627	282	21	}	}	PUNCT
ejpam-5627	282	22	=	=	SYM
ejpam-5627	282	23	max{min{µa(a1	max{min{µa(a1	NOUN
ejpam-5627	282	24	)	)	PUNCT
ejpam-5627	282	25	,	,	PUNCT
ejpam-5627	282	26	µb(b1)},min{µa(a2	µb(b1)},min{µa(a2	PROPN
ejpam-5627	282	27	)	)	PUNCT
ejpam-5627	282	28	,	,	PUNCT
ejpam-5627	282	29	ib(b2	ib(b2	NOUN
ejpam-5627	282	30	)	)	PUNCT
ejpam-5627	282	31	}	}	PUNCT
ejpam-5627	282	32	}	}	PUNCT
ejpam-5627	282	33	=	=	SYM
ejpam-5627	282	34	max{µa×b(a1	max{µa×b(a1	NOUN
ejpam-5627	282	35	,	,	PUNCT
ejpam-5627	282	36	b1	b1	NOUN
ejpam-5627	282	37	)	)	PUNCT
ejpam-5627	282	38	,	,	PUNCT
ejpam-5627	282	39	ia×b(a2	ia×b(a2	NOUN
ejpam-5627	282	40	,	,	PUNCT
ejpam-5627	282	41	b2	b2	NOUN
ejpam-5627	282	42	)	)	PUNCT
ejpam-5627	282	43	}	}	PUNCT
ejpam-5627	282	44	,	,	PUNCT
ejpam-5627	282	45	γa×b(((a1	γa×b(((a1	NOUN
ejpam-5627	282	46	,	,	PUNCT
ejpam-5627	282	47	b1)|a×b((a2	b1)|a×b((a2	NOUN
ejpam-5627	282	48	,	,	PUNCT
ejpam-5627	282	49	b2)|a×b(a2	b2)|a×b(a2	NUM
ejpam-5627	282	50	,	,	PUNCT
ejpam-5627	282	51	b2)))|a×b((a1	b2)))|a×b((a1	NOUN
ejpam-5627	282	52	,	,	PUNCT
ejpam-5627	282	53	b1)|a×b((a2	b1)|a×b((a2	NOUN
ejpam-5627	282	54	,	,	PUNCT
ejpam-5627	282	55	b2)|a×b(a2	b2)|a×b(a2	NUM
ejpam-5627	282	56	,	,	PUNCT
ejpam-5627	282	57	b2	b2	NOUN
ejpam-5627	282	58	)	)	PUNCT
ejpam-5627	282	59	)	)	PUNCT
ejpam-5627	282	60	)	)	PUNCT
ejpam-5627	282	61	)	)	PUNCT
ejpam-5627	283	1	=	=	PUNCT
ejpam-5627	283	2	γa×b((a1|a(a2|aa2))|a(a1|a(a2|aa2	γa×b((a1|a(a2|aa2))|a(a1|a(a2|aa2	PUNCT
ejpam-5627	283	3	)	)	PUNCT
ejpam-5627	283	4	)	)	PUNCT
ejpam-5627	283	5	,	,	PUNCT
ejpam-5627	283	6	(	(	PUNCT
ejpam-5627	283	7	b1|b(b2|bb2))|b(b1|b(b2|bb2	b1|b(b2|bb2))|b(b1|b(b2|bb2	PROPN
ejpam-5627	283	8	)	)	PUNCT
ejpam-5627	283	9	)	)	PUNCT
ejpam-5627	283	10	)	)	PUNCT
ejpam-5627	284	1	=	=	SYM
ejpam-5627	284	2	max{γa((a1|a(a2|aa2))|a(a1|a(a2|aa2	max{γa((a1|a(a2|aa2))|a(a1|a(a2|aa2	PROPN
ejpam-5627	284	3	)	)	PUNCT
ejpam-5627	284	4	)	)	PUNCT
ejpam-5627	284	5	,	,	PUNCT
ejpam-5627	284	6	γb(b1|b(b2|bb2))|b(b1|b(b2|bb2	γb(b1|b(b2|bb2))|b(b1|b(b2|bb2	PROPN
ejpam-5627	284	7	)	)	PUNCT
ejpam-5627	284	8	)	)	PUNCT
ejpam-5627	284	9	)	)	PUNCT
ejpam-5627	284	10	}	}	PUNCT
ejpam-5627	284	11	≤	≤	NUM
ejpam-5627	284	12	max{max{γa(a1	max{max{γa(a1	NOUN
ejpam-5627	284	13	)	)	PUNCT
ejpam-5627	284	14	,	,	PUNCT
ejpam-5627	284	15	γa(a2)},max{γb(b1	γa(a2)},max{γb(b1	NOUN
ejpam-5627	284	16	)	)	PUNCT
ejpam-5627	284	17	,	,	PUNCT
ejpam-5627	284	18	γb(b2	γb(b2	NOUN
ejpam-5627	284	19	)	)	PUNCT
ejpam-5627	284	20	}	}	PUNCT
ejpam-5627	284	21	}	}	PUNCT
ejpam-5627	284	22	=	=	SYM
ejpam-5627	284	23	max{max{γa(a1	max{max{γa(a1	PROPN
ejpam-5627	284	24	)	)	PUNCT
ejpam-5627	284	25	,	,	PUNCT
ejpam-5627	284	26	γb(b1)},max{γa(a2	γb(b1)},max{γa(a2	PROPN
ejpam-5627	284	27	)	)	PUNCT
ejpam-5627	284	28	,	,	PUNCT
ejpam-5627	284	29	γb(b2	γb(b2	NOUN
ejpam-5627	284	30	)	)	PUNCT
ejpam-5627	284	31	}	}	PUNCT
ejpam-5627	284	32	}	}	PUNCT
ejpam-5627	284	33	=	=	SYM
ejpam-5627	284	34	max{γa×b(a1	max{γa×b(a1	NUM
ejpam-5627	284	35	,	,	PUNCT
ejpam-5627	284	36	b1	b1	NOUN
ejpam-5627	284	37	)	)	PUNCT
ejpam-5627	284	38	,	,	PUNCT
ejpam-5627	284	39	γa×b(a2	γa×b(a2	NOUN
ejpam-5627	284	40	,	,	PUNCT
ejpam-5627	284	41	b2	b2	NOUN
ejpam-5627	284	42	)	)	PUNCT
ejpam-5627	284	43	}	}	PUNCT
ejpam-5627	284	44	.	.	PUNCT
ejpam-5627	285	1	n.	n.	PROPN
ejpam-5627	285	2	rajesh	rajesh	PROPN
ejpam-5627	285	3	,	,	PUNCT
ejpam-5627	285	4	t.	t.	PROPN
ejpam-5627	285	5	oner	oner	NOUN
ejpam-5627	285	6	,	,	PUNCT
ejpam-5627	285	7	a.	a.	NOUN
ejpam-5627	285	8	iampan	iampan	PROPN
ejpam-5627	285	9	,	,	PUNCT
ejpam-5627	285	10	i.	i.	PROPN
ejpam-5627	285	11	senturk	senturk	PROPN
ejpam-5627	285	12	/	/	SYM
ejpam-5627	285	13	eur	eur	PROPN
ejpam-5627	285	14	.	.	PUNCT
ejpam-5627	286	1	j.	j.	PROPN
ejpam-5627	286	2	pure	pure	PROPN
ejpam-5627	286	3	appl	appl	PROPN
ejpam-5627	286	4	.	.	PROPN
ejpam-5627	286	5	math	math	PROPN
ejpam-5627	286	6	,	,	PUNCT
ejpam-5627	286	7	18	18	NUM
ejpam-5627	286	8	(	(	PUNCT
ejpam-5627	286	9	1	1	NUM
ejpam-5627	286	10	)	)	PUNCT
ejpam-5627	286	11	(	(	PUNCT
ejpam-5627	286	12	2025	2025	NUM
ejpam-5627	286	13	)	)	PUNCT
ejpam-5627	286	14	,	,	PUNCT
ejpam-5627	286	15	5627	5627	NUM
ejpam-5627	286	16	11	11	NUM
ejpam-5627	286	17	of	of	ADP
ejpam-5627	286	18	15	15	NUM
ejpam-5627	286	19	hence	hence	ADV
ejpam-5627	286	20	,	,	PUNCT
ejpam-5627	286	21	ha×b	ha×b	PROPN
ejpam-5627	286	22	=	=	PUNCT
ejpam-5627	286	23	(	(	PUNCT
ejpam-5627	286	24	a	a	DET
ejpam-5627	286	25	×	×	NOUN
ejpam-5627	286	26	b,µa×b	b,µa×b	NOUN
ejpam-5627	286	27	,	,	PUNCT
ejpam-5627	286	28	γa×b	γa×b	NOUN
ejpam-5627	286	29	)	)	PUNCT
ejpam-5627	286	30	is	be	AUX
ejpam-5627	286	31	an	an	DET
ejpam-5627	286	32	intuitionistic	intuitionistic	ADJ
ejpam-5627	286	33	fuzzy	fuzzy	ADJ
ejpam-5627	286	34	sup	sup	NOUN
ejpam-5627	286	35	-	-	PUNCT
ejpam-5627	286	36	subalgebra	subalgebra	NOUN
ejpam-5627	286	37	of	of	ADP
ejpam-5627	286	38	⟨a	⟨a	X
ejpam-5627	286	39	×	×	PROPN
ejpam-5627	286	40	b	b	PROPN
ejpam-5627	286	41	,	,	PUNCT
ejpam-5627	286	42	|a×b	|a×b	PROPN
ejpam-5627	286	43	,	,	PUNCT
ejpam-5627	286	44	0a×b⟩.	0a×b⟩.	PROPN
ejpam-5627	286	45	theorem	theorem	VERB
ejpam-5627	286	46	11	11	NUM
ejpam-5627	286	47	.	.	PUNCT
ejpam-5627	287	1	let	let	VERB
ejpam-5627	287	2	⟨a	⟨a	NOUN
ejpam-5627	287	3	,	,	PUNCT
ejpam-5627	287	4	|a	|a	NOUN
ejpam-5627	287	5	,	,	PUNCT
ejpam-5627	287	6	0a⟩	0a⟩	NUM
ejpam-5627	287	7	and	and	CCONJ
ejpam-5627	287	8	⟨b	⟨b	PROPN
ejpam-5627	287	9	,	,	PUNCT
ejpam-5627	287	10	|b	|b	PROPN
ejpam-5627	287	11	,	,	PUNCT
ejpam-5627	287	12	0b⟩	0b⟩	NUM
ejpam-5627	287	13	be	be	VERB
ejpam-5627	287	14	sup	sup	NOUN
ejpam-5627	287	15	-	-	PUNCT
ejpam-5627	287	16	algebras	algebras	NOUN
ejpam-5627	287	17	.	.	PUNCT
ejpam-5627	288	1	if	if	SCONJ
ejpam-5627	288	2	ha	ha	X
ejpam-5627	288	3	=	=	X
ejpam-5627	288	4	(	(	PUNCT
ejpam-5627	288	5	a,µa	a,µa	PROPN
ejpam-5627	288	6	,	,	PUNCT
ejpam-5627	288	7	γa	γa	PROPN
ejpam-5627	288	8	)	)	PUNCT
ejpam-5627	288	9	and	and	CCONJ
ejpam-5627	288	10	hb	hb	X
ejpam-5627	288	11	=	=	SYM
ejpam-5627	288	12	(	(	PUNCT
ejpam-5627	288	13	b,µb	b,µb	NUM
ejpam-5627	288	14	,	,	PUNCT
ejpam-5627	288	15	γb	γb	NOUN
ejpam-5627	288	16	)	)	PUNCT
ejpam-5627	288	17	are	be	AUX
ejpam-5627	288	18	intuitionistic	intuitionistic	ADJ
ejpam-5627	288	19	fuzzy	fuzzy	ADJ
ejpam-5627	288	20	sup	sup	ADJ
ejpam-5627	288	21	-	-	PUNCT
ejpam-5627	288	22	ideal	ideal	NOUN
ejpam-5627	288	23	of	of	ADP
ejpam-5627	288	24	⟨a	⟨a	PROPN
ejpam-5627	288	25	,	,	PUNCT
ejpam-5627	288	26	|a	|a	NOUN
ejpam-5627	288	27	,	,	PUNCT
ejpam-5627	288	28	0a⟩	0a⟩	NUM
ejpam-5627	288	29	and	and	CCONJ
ejpam-5627	288	30	⟨b	⟨b	PROPN
ejpam-5627	288	31	,	,	PUNCT
ejpam-5627	288	32	|b	|b	ADJ
ejpam-5627	288	33	,	,	PUNCT
ejpam-5627	288	34	0b⟩	0b⟩	NUM
ejpam-5627	288	35	,	,	PUNCT
ejpam-5627	288	36	respectively	respectively	ADV
ejpam-5627	288	37	,	,	PUNCT
ejpam-5627	288	38	then	then	ADV
ejpam-5627	288	39	ha×b	ha×b	PROPN
ejpam-5627	288	40	=	=	SYM
ejpam-5627	288	41	(	(	PUNCT
ejpam-5627	288	42	a	a	DET
ejpam-5627	288	43	×	×	NOUN
ejpam-5627	288	44	b,µa×b	b,µa×b	NOUN
ejpam-5627	288	45	,	,	PUNCT
ejpam-5627	288	46	γa×b	γa×b	NOUN
ejpam-5627	288	47	)	)	PUNCT
ejpam-5627	288	48	is	be	AUX
ejpam-5627	288	49	an	an	DET
ejpam-5627	288	50	intuitionistic	intuitionistic	ADJ
ejpam-5627	288	51	fuzzy	fuzzy	ADJ
ejpam-5627	288	52	sup	sup	ADJ
ejpam-5627	288	53	-	-	PUNCT
ejpam-5627	288	54	ideal	ideal	NOUN
ejpam-5627	288	55	of	of	ADP
ejpam-5627	288	56	⟨a×b	⟨a×b	NOUN
ejpam-5627	288	57	,	,	PUNCT
ejpam-5627	288	58	|a×b	|a×b	PROPN
ejpam-5627	288	59	,	,	PUNCT
ejpam-5627	288	60	0a×b⟩.	0a×b⟩.	NOUN
ejpam-5627	288	61	proof	proof	NOUN
ejpam-5627	288	62	.	.	PUNCT
ejpam-5627	289	1	let	let	VERB
ejpam-5627	289	2	⟨a	⟨a	NOUN
ejpam-5627	289	3	,	,	PUNCT
ejpam-5627	289	4	|a	|a	NOUN
ejpam-5627	289	5	,	,	PUNCT
ejpam-5627	289	6	0a⟩	0a⟩	NUM
ejpam-5627	289	7	and	and	CCONJ
ejpam-5627	289	8	⟨b	⟨b	PROPN
ejpam-5627	289	9	,	,	PUNCT
ejpam-5627	289	10	|b	|b	PROPN
ejpam-5627	289	11	,	,	PUNCT
ejpam-5627	289	12	0b⟩	0b⟩	NUM
ejpam-5627	289	13	be	be	VERB
ejpam-5627	289	14	sup	sup	NOUN
ejpam-5627	289	15	-	-	PUNCT
ejpam-5627	289	16	algebras	algebra	NOUN
ejpam-5627	289	17	and	and	CCONJ
ejpam-5627	289	18	ha	ha	INTJ
ejpam-5627	289	19	=	=	SYM
ejpam-5627	289	20	(	(	PUNCT
ejpam-5627	289	21	a,µa	a,µa	PROPN
ejpam-5627	289	22	,	,	PUNCT
ejpam-5627	289	23	γa	γa	PROPN
ejpam-5627	289	24	)	)	PUNCT
ejpam-5627	289	25	and	and	CCONJ
ejpam-5627	289	26	hb	hb	X
ejpam-5627	289	27	=	=	SYM
ejpam-5627	289	28	(	(	PUNCT
ejpam-5627	289	29	b,µb	b,µb	NUM
ejpam-5627	289	30	,	,	PUNCT
ejpam-5627	289	31	γb	γb	NOUN
ejpam-5627	289	32	)	)	PUNCT
ejpam-5627	289	33	be	be	AUX
ejpam-5627	289	34	intuitionistic	intuitionistic	ADJ
ejpam-5627	289	35	fuzzy	fuzzy	ADJ
ejpam-5627	289	36	sup	sup	ADJ
ejpam-5627	289	37	-	-	PUNCT
ejpam-5627	289	38	ideal	ideal	NOUN
ejpam-5627	289	39	of	of	ADP
ejpam-5627	289	40	⟨a	⟨a	PROPN
ejpam-5627	289	41	,	,	PUNCT
ejpam-5627	289	42	|a	|a	NOUN
ejpam-5627	289	43	,	,	PUNCT
ejpam-5627	289	44	0a⟩	0a⟩	NUM
ejpam-5627	289	45	and	and	CCONJ
ejpam-5627	289	46	⟨b	⟨b	PROPN
ejpam-5627	289	47	,	,	PUNCT
ejpam-5627	289	48	|b	|b	ADJ
ejpam-5627	289	49	,	,	PUNCT
ejpam-5627	289	50	0b⟩	0b⟩	NUM
ejpam-5627	289	51	,	,	PUNCT
ejpam-5627	289	52	respectively	respectively	ADV
ejpam-5627	289	53	.	.	PUNCT
ejpam-5627	290	1	let	let	VERB
ejpam-5627	290	2	(	(	PUNCT
ejpam-5627	290	3	a1	a1	NOUN
ejpam-5627	290	4	,	,	PUNCT
ejpam-5627	290	5	b1	b1	NOUN
ejpam-5627	290	6	)	)	PUNCT
ejpam-5627	290	7	,	,	PUNCT
ejpam-5627	290	8	(	(	PUNCT
ejpam-5627	290	9	a2	a2	PROPN
ejpam-5627	290	10	,	,	PUNCT
ejpam-5627	290	11	b2	b2	NOUN
ejpam-5627	290	12	)	)	PUNCT
ejpam-5627	290	13	∈	∈	PROPN
ejpam-5627	290	14	a×b	a×b	PROPN
ejpam-5627	290	15	.	.	PUNCT
ejpam-5627	290	16	then	then	ADV
ejpam-5627	290	17	µa×b(((a2	µa×b(((a2	NOUN
ejpam-5627	290	18	,	,	PUNCT
ejpam-5627	290	19	b2)|a×b((a1	b2)|a×b((a1	X
ejpam-5627	290	20	,	,	PUNCT
ejpam-5627	290	21	b1)|a×b(a1	b1)|a×b(a1	NOUN
ejpam-5627	290	22	,	,	PUNCT
ejpam-5627	290	23	b1)))|a×b((a2	b1)))|a×b((a2	PROPN
ejpam-5627	290	24	,	,	PUNCT
ejpam-5627	290	25	b2)|a×b((a1	b2)|a×b((a1	NOUN
ejpam-5627	290	26	,	,	PUNCT
ejpam-5627	290	27	b1)|a×b(a1	b1)|a×b(a1	NOUN
ejpam-5627	290	28	,	,	PUNCT
ejpam-5627	290	29	b1	b1	NOUN
ejpam-5627	290	30	)	)	PUNCT
ejpam-5627	290	31	)	)	PUNCT
ejpam-5627	290	32	)	)	PUNCT
ejpam-5627	290	33	)	)	PUNCT
ejpam-5627	291	1	=	=	SYM
ejpam-5627	291	2	max{µa((a2|a(a1|aa1))|a(a2|a(a1|aa1	max{µa((a2|a(a1|aa1))|a(a2|a(a1|aa1	PROPN
ejpam-5627	291	3	)	)	PUNCT
ejpam-5627	291	4	)	)	PUNCT
ejpam-5627	291	5	)	)	PUNCT
ejpam-5627	291	6	,	,	PUNCT
ejpam-5627	291	7	µb((b2|b(b1|bb1))|b(b2|b(b1|bb1	µb((b2|b(b1|bb1))|b(b2|b(b1|bb1	NOUN
ejpam-5627	291	8	)	)	PUNCT
ejpam-5627	291	9	)	)	PUNCT
ejpam-5627	291	10	)	)	PUNCT
ejpam-5627	291	11	}	}	PUNCT
ejpam-5627	291	12	≥	≥	X
ejpam-5627	291	13	max{µa(a2	max{µa(a2	PROPN
ejpam-5627	291	14	)	)	PUNCT
ejpam-5627	291	15	,	,	PUNCT
ejpam-5627	291	16	µb(b2	µb(b2	NOUN
ejpam-5627	291	17	)	)	PUNCT
ejpam-5627	291	18	}	}	PUNCT
ejpam-5627	291	19	=	=	SYM
ejpam-5627	291	20	µa×b(a2	µa×b(a2	ADP
ejpam-5627	291	21	,	,	PUNCT
ejpam-5627	291	22	b2	b2	NOUN
ejpam-5627	291	23	)	)	PUNCT
ejpam-5627	291	24	,	,	PUNCT
ejpam-5627	291	25	γa×b(((a2	γa×b(((a2	PROPN
ejpam-5627	291	26	,	,	PUNCT
ejpam-5627	291	27	b2)|a×b((a1	b2)|a×b((a1	NOUN
ejpam-5627	291	28	,	,	PUNCT
ejpam-5627	291	29	b1)|a×b(a1	b1)|a×b(a1	NOUN
ejpam-5627	291	30	,	,	PUNCT
ejpam-5627	291	31	b1)))|a×b((a2	b1)))|a×b((a2	PROPN
ejpam-5627	291	32	,	,	PUNCT
ejpam-5627	291	33	b2)|a×b((a1	b2)|a×b((a1	NOUN
ejpam-5627	291	34	,	,	PUNCT
ejpam-5627	291	35	b1)|a×b(a1	b1)|a×b(a1	NOUN
ejpam-5627	291	36	,	,	PUNCT
ejpam-5627	291	37	b1	b1	NOUN
ejpam-5627	291	38	)	)	PUNCT
ejpam-5627	291	39	)	)	PUNCT
ejpam-5627	291	40	)	)	PUNCT
ejpam-5627	291	41	)	)	PUNCT
ejpam-5627	292	1	=	=	SYM
ejpam-5627	292	2	max{γa((a2|a(a1|aa1))|a(a2|a(a1|aa1	max{γa((a2|a(a1|aa1))|a(a2|a(a1|aa1	NOUN
ejpam-5627	292	3	)	)	PUNCT
ejpam-5627	292	4	)	)	PUNCT
ejpam-5627	292	5	)	)	PUNCT
ejpam-5627	292	6	,	,	PUNCT
ejpam-5627	292	7	fb((b2|b(b1|bb1))|b(b2|b(b1|bb1	fb((b2|b(b1|bb1))|b(b2|b(b1|bb1	NOUN
ejpam-5627	292	8	)	)	PUNCT
ejpam-5627	292	9	)	)	PUNCT
ejpam-5627	292	10	)	)	PUNCT
ejpam-5627	292	11	}	}	PUNCT
ejpam-5627	293	1	≤	≤	NUM
ejpam-5627	293	2	max{γa(a2	max{γa(a2	NOUN
ejpam-5627	293	3	)	)	PUNCT
ejpam-5627	293	4	,	,	PUNCT
ejpam-5627	293	5	γb(b2	γb(b2	NOUN
ejpam-5627	293	6	)	)	PUNCT
ejpam-5627	293	7	}	}	PUNCT
ejpam-5627	293	8	=	=	SYM
ejpam-5627	293	9	γa×b(a2	γa×b(a2	NOUN
ejpam-5627	293	10	,	,	PUNCT
ejpam-5627	293	11	b2	b2	NOUN
ejpam-5627	293	12	)	)	PUNCT
ejpam-5627	293	13	,	,	PUNCT
ejpam-5627	293	14	µa×b(a2	µa×b(a2	NUM
ejpam-5627	293	15	,	,	PUNCT
ejpam-5627	293	16	b2	b2	NOUN
ejpam-5627	293	17	)	)	PUNCT
ejpam-5627	293	18	=	=	SYM
ejpam-5627	293	19	max{µa(a2	max{µa(a2	PROPN
ejpam-5627	293	20	)	)	PUNCT
ejpam-5627	293	21	,	,	PUNCT
ejpam-5627	293	22	µb(b2	µb(b2	NOUN
ejpam-5627	293	23	)	)	PUNCT
ejpam-5627	293	24	}	}	PUNCT
ejpam-5627	293	25	≥	≥	NOUN
ejpam-5627	293	26	max{min{µa(a1	max{min{µa(a1	NOUN
ejpam-5627	293	27	)	)	PUNCT
ejpam-5627	293	28	,	,	PUNCT
ejpam-5627	293	29	µa((a2|a(a1|aa1))|a(a2|a(a1|aa1	µa((a2|a(a1|aa1))|a(a2|a(a1|aa1	X
ejpam-5627	293	30	)	)	PUNCT
ejpam-5627	293	31	)	)	PUNCT
ejpam-5627	293	32	)	)	PUNCT
ejpam-5627	293	33	}	}	PUNCT
ejpam-5627	293	34	,	,	PUNCT
ejpam-5627	293	35	min{µb(b1	min{µb(b1	PROPN
ejpam-5627	293	36	)	)	PUNCT
ejpam-5627	293	37	,	,	PUNCT
ejpam-5627	293	38	µb((b2|b(b1|bb1))|b(b2|b(b1|bb1	µb((b2|b(b1|bb1))|b(b2|b(b1|bb1	NOUN
ejpam-5627	293	39	)	)	PUNCT
ejpam-5627	293	40	)	)	PUNCT
ejpam-5627	293	41	)	)	PUNCT
ejpam-5627	293	42	}	}	PUNCT
ejpam-5627	293	43	}	}	PUNCT
ejpam-5627	293	44	=	=	SYM
ejpam-5627	293	45	max{min{µa(a1	max{min{µa(a1	NOUN
ejpam-5627	293	46	)	)	PUNCT
ejpam-5627	293	47	,	,	PUNCT
ejpam-5627	293	48	µb(b1)},min{µa((a2|a(a1|aa1))|a(a2|a(a1|aa1	µb(b1)},min{µa((a2|a(a1|aa1))|a(a2|a(a1|aa1	PROPN
ejpam-5627	293	49	)	)	PUNCT
ejpam-5627	293	50	)	)	PUNCT
ejpam-5627	293	51	)	)	PUNCT
ejpam-5627	293	52	,	,	PUNCT
ejpam-5627	293	53	µb((b2|b(b1|bb1))|b(b2|b(b1|bb1	µb((b2|b(b1|bb1))|b(b2|b(b1|bb1	NOUN
ejpam-5627	293	54	)	)	PUNCT
ejpam-5627	293	55	)	)	PUNCT
ejpam-5627	293	56	)	)	PUNCT
ejpam-5627	293	57	}	}	PUNCT
ejpam-5627	293	58	}	}	PUNCT
ejpam-5627	293	59	=	=	SYM
ejpam-5627	293	60	max{µa×b(a1	max{µa×b(a1	NOUN
ejpam-5627	293	61	,	,	PUNCT
ejpam-5627	293	62	b1	b1	NOUN
ejpam-5627	293	63	)	)	PUNCT
ejpam-5627	293	64	,	,	PUNCT
ejpam-5627	293	65	µa×b(((a2	µa×b(((a2	NOUN
ejpam-5627	293	66	,	,	PUNCT
ejpam-5627	293	67	b2)|a×b	b2)|a×b	NOUN
ejpam-5627	293	68	(	(	PUNCT
ejpam-5627	293	69	(	(	PUNCT
ejpam-5627	293	70	a1	a1	NOUN
ejpam-5627	293	71	,	,	PUNCT
ejpam-5627	293	72	b1)|a×b(a1	b1)|a×b(a1	NOUN
ejpam-5627	293	73	,	,	PUNCT
ejpam-5627	293	74	b1)))|a×b((a2	b1)))|a×b((a2	PROPN
ejpam-5627	293	75	,	,	PUNCT
ejpam-5627	293	76	b2)|a×b((a1	b2)|a×b((a1	NOUN
ejpam-5627	293	77	,	,	PUNCT
ejpam-5627	293	78	b1)|a×b(a1	b1)|a×b(a1	NOUN
ejpam-5627	293	79	,	,	PUNCT
ejpam-5627	293	80	b1	b1	NOUN
ejpam-5627	293	81	)	)	PUNCT
ejpam-5627	293	82	)	)	PUNCT
ejpam-5627	293	83	)	)	PUNCT
ejpam-5627	293	84	)	)	PUNCT
ejpam-5627	293	85	}	}	PUNCT
ejpam-5627	293	86	,	,	PUNCT
ejpam-5627	293	87	γa×b(a2	γa×b(a2	NOUN
ejpam-5627	293	88	,	,	PUNCT
ejpam-5627	293	89	b2	b2	NOUN
ejpam-5627	293	90	)	)	PUNCT
ejpam-5627	293	91	=	=	SYM
ejpam-5627	293	92	max{γa(a2	max{γa(a2	NOUN
ejpam-5627	293	93	)	)	PUNCT
ejpam-5627	293	94	,	,	PUNCT
ejpam-5627	293	95	γb(b2	γb(b2	NOUN
ejpam-5627	293	96	)	)	PUNCT
ejpam-5627	293	97	}	}	PUNCT
ejpam-5627	293	98	≤	≤	NUM
ejpam-5627	293	99	max{max{γa(a1	max{max{γa(a1	NOUN
ejpam-5627	293	100	)	)	PUNCT
ejpam-5627	293	101	,	,	PUNCT
ejpam-5627	293	102	γa((a2|a(a1|aa1))|a(a2|a(a1|aa1	γa((a2|a(a1|aa1))|a(a2|a(a1|aa1	NOUN
ejpam-5627	293	103	)	)	PUNCT
ejpam-5627	293	104	)	)	PUNCT
ejpam-5627	293	105	)	)	PUNCT
ejpam-5627	293	106	}	}	PUNCT
ejpam-5627	293	107	,	,	PUNCT
ejpam-5627	293	108	max{γb(b1	max{γb(b1	NOUN
ejpam-5627	293	109	)	)	PUNCT
ejpam-5627	293	110	,	,	PUNCT
ejpam-5627	293	111	γb((b2|b(b1|bb1))|b(b2|b(b1|bb1	γb((b2|b(b1|bb1))|b(b2|b(b1|bb1	NOUN
ejpam-5627	293	112	)	)	PUNCT
ejpam-5627	293	113	)	)	PUNCT
ejpam-5627	293	114	)	)	PUNCT
ejpam-5627	293	115	}	}	PUNCT
ejpam-5627	293	116	}	}	PUNCT
ejpam-5627	293	117	=	=	SYM
ejpam-5627	293	118	max{max{γa(a1	max{max{γa(a1	PROPN
ejpam-5627	293	119	)	)	PUNCT
ejpam-5627	293	120	,	,	PUNCT
ejpam-5627	293	121	γb(b1)},max{γa((a2|a(a1|aa1))|a(a2|a(a1|aa1	γb(b1)},max{γa((a2|a(a1|aa1))|a(a2|a(a1|aa1	PROPN
ejpam-5627	293	122	)	)	PUNCT
ejpam-5627	293	123	)	)	PUNCT
ejpam-5627	293	124	)	)	PUNCT
ejpam-5627	293	125	,	,	PUNCT
ejpam-5627	293	126	γb((b2|b(b1|bb1))|b(b2|b(b1|bb1	γb((b2|b(b1|bb1))|b(b2|b(b1|bb1	NOUN
ejpam-5627	293	127	)	)	PUNCT
ejpam-5627	293	128	)	)	PUNCT
ejpam-5627	293	129	)	)	PUNCT
ejpam-5627	293	130	}	}	PUNCT
ejpam-5627	293	131	}	}	PUNCT
ejpam-5627	293	132	=	=	SYM
ejpam-5627	293	133	max{γa×b(a1	max{γa×b(a1	NUM
ejpam-5627	293	134	,	,	PUNCT
ejpam-5627	293	135	b1	b1	NOUN
ejpam-5627	293	136	)	)	PUNCT
ejpam-5627	293	137	,	,	PUNCT
ejpam-5627	293	138	γa×b(((a2	γa×b(((a2	PROPN
ejpam-5627	293	139	,	,	PUNCT
ejpam-5627	293	140	b2)|a×b	b2)|a×b	NOUN
ejpam-5627	293	141	(	(	PUNCT
ejpam-5627	293	142	(	(	PUNCT
ejpam-5627	293	143	a1	a1	NOUN
ejpam-5627	293	144	,	,	PUNCT
ejpam-5627	293	145	b1)|a×b(a1	b1)|a×b(a1	NOUN
ejpam-5627	293	146	,	,	PUNCT
ejpam-5627	293	147	b1)))|a×b((a2	b1)))|a×b((a2	PROPN
ejpam-5627	293	148	,	,	PUNCT
ejpam-5627	293	149	b2)|a×b((a1	b2)|a×b((a1	NOUN
ejpam-5627	293	150	,	,	PUNCT
ejpam-5627	293	151	b1)|a×b(a1	b1)|a×b(a1	NOUN
ejpam-5627	293	152	,	,	PUNCT
ejpam-5627	293	153	b1	b1	NOUN
ejpam-5627	293	154	)	)	PUNCT
ejpam-5627	293	155	)	)	PUNCT
ejpam-5627	293	156	)	)	PUNCT
ejpam-5627	293	157	)	)	PUNCT
ejpam-5627	293	158	}	}	PUNCT
ejpam-5627	293	159	.	.	PUNCT
ejpam-5627	294	1	hence	hence	ADV
ejpam-5627	294	2	,	,	PUNCT
ejpam-5627	294	3	ha×b	ha×b	PROPN
ejpam-5627	294	4	=	=	SYM
ejpam-5627	294	5	(	(	PUNCT
ejpam-5627	294	6	a×b,µa×b	a×b,µa×b	PROPN
ejpam-5627	294	7	,	,	PUNCT
ejpam-5627	294	8	γa×b	γa×b	NOUN
ejpam-5627	294	9	)	)	PUNCT
ejpam-5627	294	10	is	be	AUX
ejpam-5627	294	11	an	an	DET
ejpam-5627	294	12	intuitionistic	intuitionistic	ADJ
ejpam-5627	294	13	fuzzy	fuzzy	ADJ
ejpam-5627	294	14	sup	sup	ADJ
ejpam-5627	294	15	-	-	PUNCT
ejpam-5627	294	16	ideal	ideal	NOUN
ejpam-5627	294	17	of	of	ADP
ejpam-5627	294	18	⟨a×b	⟨a×b	NOUN
ejpam-5627	294	19	,	,	PUNCT
ejpam-5627	294	20	|a×b	|a×b	PROPN
ejpam-5627	294	21	,	,	PUNCT
ejpam-5627	294	22	0a×b⟩.	0a×b⟩.	NUM
ejpam-5627	294	23	definition	definition	NOUN
ejpam-5627	294	24	9	9	NUM
ejpam-5627	294	25	.	.	PUNCT
ejpam-5627	295	1	[	[	X
ejpam-5627	295	2	7	7	X
ejpam-5627	295	3	]	]	X
ejpam-5627	295	4	let	let	VERB
ejpam-5627	295	5	⟨a	⟨a	NOUN
ejpam-5627	295	6	,	,	PUNCT
ejpam-5627	295	7	|a	|a	NOUN
ejpam-5627	295	8	,	,	PUNCT
ejpam-5627	295	9	0a⟩	0a⟩	NUM
ejpam-5627	295	10	and	and	CCONJ
ejpam-5627	295	11	⟨b	⟨b	PROPN
ejpam-5627	295	12	,	,	PUNCT
ejpam-5627	295	13	|b	|b	PROPN
ejpam-5627	295	14	,	,	PUNCT
ejpam-5627	295	15	0b⟩	0b⟩	NUM
ejpam-5627	295	16	be	be	VERB
ejpam-5627	295	17	sup	sup	NOUN
ejpam-5627	295	18	-	-	PUNCT
ejpam-5627	295	19	algebras	algebras	NOUN
ejpam-5627	295	20	.	.	PUNCT
ejpam-5627	296	1	then	then	ADV
ejpam-5627	296	2	a	a	DET
ejpam-5627	296	3	mapping	mapping	NOUN
ejpam-5627	296	4	f	f	NOUN
ejpam-5627	296	5	:	:	PUNCT
ejpam-5627	296	6	a	a	DET
ejpam-5627	296	7	→	→	SYM
ejpam-5627	296	8	b	b	PROPN
ejpam-5627	296	9	is	be	AUX
ejpam-5627	296	10	called	call	VERB
ejpam-5627	296	11	a	a	DET
ejpam-5627	296	12	homomorphism	homomorphism	NOUN
ejpam-5627	296	13	if	if	SCONJ
ejpam-5627	296	14	f(x|ay	f(x|ay	ADJ
ejpam-5627	296	15	)	)	PUNCT
ejpam-5627	296	16	=	=	SYM
ejpam-5627	296	17	f(x)|bf(y	f(x)|bf(y	NOUN
ejpam-5627	296	18	)	)	PUNCT
ejpam-5627	296	19	for	for	ADP
ejpam-5627	296	20	all	all	DET
ejpam-5627	296	21	x	x	NOUN
ejpam-5627	296	22	,	,	PUNCT
ejpam-5627	296	23	y	y	PROPN
ejpam-5627	296	24	∈	∈	PROPN
ejpam-5627	296	25	h	h	NOUN
ejpam-5627	296	26	and	and	CCONJ
ejpam-5627	296	27	f(0a	f(0a	NOUN
ejpam-5627	296	28	)	)	PUNCT
ejpam-5627	296	29	=	=	NOUN
ejpam-5627	296	30	0b	0b	NOUN
ejpam-5627	296	31	.	.	PUNCT
ejpam-5627	297	1	n.	n.	PROPN
ejpam-5627	297	2	rajesh	rajesh	PROPN
ejpam-5627	297	3	,	,	PUNCT
ejpam-5627	297	4	t.	t.	PROPN
ejpam-5627	297	5	oner	oner	NOUN
ejpam-5627	297	6	,	,	PUNCT
ejpam-5627	297	7	a.	a.	NOUN
ejpam-5627	297	8	iampan	iampan	PROPN
ejpam-5627	297	9	,	,	PUNCT
ejpam-5627	297	10	i.	i.	PROPN
ejpam-5627	297	11	senturk	senturk	PROPN
ejpam-5627	297	12	/	/	SYM
ejpam-5627	297	13	eur	eur	PROPN
ejpam-5627	297	14	.	.	PUNCT
ejpam-5627	298	1	j.	j.	PROPN
ejpam-5627	298	2	pure	pure	PROPN
ejpam-5627	298	3	appl	appl	PROPN
ejpam-5627	298	4	.	.	PROPN
ejpam-5627	298	5	math	math	PROPN
ejpam-5627	298	6	,	,	PUNCT
ejpam-5627	298	7	18	18	NUM
ejpam-5627	298	8	(	(	PUNCT
ejpam-5627	298	9	1	1	NUM
ejpam-5627	298	10	)	)	PUNCT
ejpam-5627	298	11	(	(	PUNCT
ejpam-5627	298	12	2025	2025	NUM
ejpam-5627	298	13	)	)	PUNCT
ejpam-5627	298	14	,	,	PUNCT
ejpam-5627	298	15	5627	5627	NUM
ejpam-5627	298	16	12	12	NUM
ejpam-5627	298	17	of	of	ADP
ejpam-5627	298	18	15	15	NUM
ejpam-5627	298	19	theorem	theorem	NOUN
ejpam-5627	298	20	12	12	NUM
ejpam-5627	298	21	.	.	PUNCT
ejpam-5627	299	1	let	let	VERB
ejpam-5627	299	2	⟨a	⟨a	NOUN
ejpam-5627	299	3	,	,	PUNCT
ejpam-5627	299	4	|a	|a	NOUN
ejpam-5627	299	5	,	,	PUNCT
ejpam-5627	299	6	0a⟩	0a⟩	NUM
ejpam-5627	299	7	and	and	CCONJ
ejpam-5627	299	8	⟨b	⟨b	PROPN
ejpam-5627	299	9	,	,	PUNCT
ejpam-5627	299	10	|b	|b	PROPN
ejpam-5627	299	11	,	,	PUNCT
ejpam-5627	299	12	0b⟩	0b⟩	NUM
ejpam-5627	299	13	be	be	VERB
ejpam-5627	299	14	sup	sup	NOUN
ejpam-5627	299	15	-	-	PUNCT
ejpam-5627	299	16	algebras	algebra	NOUN
ejpam-5627	299	17	,	,	PUNCT
ejpam-5627	299	18	f	f	X
ejpam-5627	299	19	:	:	PUNCT
ejpam-5627	299	20	a	a	DET
ejpam-5627	299	21	→	→	SYM
ejpam-5627	299	22	b	b	X
ejpam-5627	299	23	be	be	AUX
ejpam-5627	299	24	a	a	DET
ejpam-5627	299	25	surjective	surjective	ADJ
ejpam-5627	299	26	homomorphism	homomorphism	NOUN
ejpam-5627	299	27	,	,	PUNCT
ejpam-5627	299	28	and	and	CCONJ
ejpam-5627	299	29	b	b	X
ejpam-5627	299	30	=	=	SYM
ejpam-5627	299	31	(	(	PUNCT
ejpam-5627	299	32	b,µ	b,µ	PROPN
ejpam-5627	299	33	,	,	PUNCT
ejpam-5627	299	34	γ	γ	PROPN
ejpam-5627	299	35	)	)	PUNCT
ejpam-5627	299	36	be	be	VERB
ejpam-5627	299	37	an	an	DET
ejpam-5627	299	38	intuitionistic	intuitionistic	ADJ
ejpam-5627	299	39	fuzzy	fuzzy	ADJ
ejpam-5627	299	40	up	up	NOUN
ejpam-5627	299	41	-	-	PUNCT
ejpam-5627	299	42	structure	structure	NOUN
ejpam-5627	299	43	on	on	ADP
ejpam-5627	299	44	b.	b.	PROPN
ejpam-5627	300	1	then	then	ADV
ejpam-5627	300	2	b	b	X
ejpam-5627	300	3	=	=	SYM
ejpam-5627	300	4	(	(	PUNCT
ejpam-5627	300	5	b,µ	b,µ	PROPN
ejpam-5627	300	6	,	,	PUNCT
ejpam-5627	300	7	γ	γ	PROPN
ejpam-5627	300	8	)	)	PUNCT
ejpam-5627	300	9	is	be	AUX
ejpam-5627	300	10	an	an	DET
ejpam-5627	300	11	intuitionistic	intuitionistic	ADJ
ejpam-5627	300	12	fuzzy	fuzzy	ADJ
ejpam-5627	300	13	sup	sup	NOUN
ejpam-5627	300	14	-	-	PUNCT
ejpam-5627	300	15	ideal	ideal	NOUN
ejpam-5627	300	16	of	of	ADP
ejpam-5627	300	17	b	b	NOUN
ejpam-5627	300	18	if	if	NOUN
ejpam-5627	300	19	and	and	CCONJ
ejpam-5627	300	20	only	only	ADV
ejpam-5627	300	21	if	if	SCONJ
ejpam-5627	300	22	bf	bf	NOUN
ejpam-5627	300	23	=	=	SYM
ejpam-5627	300	24	(	(	PUNCT
ejpam-5627	300	25	b,µf	b,µf	NUM
ejpam-5627	300	26	,	,	PUNCT
ejpam-5627	300	27	γf	γf	PROPN
ejpam-5627	300	28	)	)	PUNCT
ejpam-5627	300	29	is	be	AUX
ejpam-5627	300	30	an	an	DET
ejpam-5627	300	31	intuitionistic	intuitionistic	ADJ
ejpam-5627	300	32	fuzzy	fuzzy	ADJ
ejpam-5627	300	33	sup	sup	NOUN
ejpam-5627	300	34	-	-	PUNCT
ejpam-5627	300	35	ideal	ideal	NOUN
ejpam-5627	300	36	of	of	ADP
ejpam-5627	300	37	a.	a.	NOUN
ejpam-5627	300	38	proof	proof	NOUN
ejpam-5627	300	39	.	.	PUNCT
ejpam-5627	301	1	let	let	VERB
ejpam-5627	301	2	⟨a	⟨a	NOUN
ejpam-5627	301	3	,	,	PUNCT
ejpam-5627	301	4	|a	|a	NOUN
ejpam-5627	301	5	,	,	PUNCT
ejpam-5627	301	6	0a⟩	0a⟩	NUM
ejpam-5627	301	7	and	and	CCONJ
ejpam-5627	301	8	⟨b	⟨b	PROPN
ejpam-5627	301	9	,	,	PUNCT
ejpam-5627	301	10	|b	|b	PROPN
ejpam-5627	301	11	,	,	PUNCT
ejpam-5627	301	12	0b⟩	0b⟩	NUM
ejpam-5627	301	13	be	be	VERB
ejpam-5627	301	14	sup	sup	NOUN
ejpam-5627	301	15	-	-	PUNCT
ejpam-5627	301	16	algebras	algebra	NOUN
ejpam-5627	301	17	,	,	PUNCT
ejpam-5627	301	18	f	f	X
ejpam-5627	301	19	:	:	PUNCT
ejpam-5627	301	20	a	a	DET
ejpam-5627	301	21	→	→	SYM
ejpam-5627	301	22	b	b	X
ejpam-5627	301	23	be	be	AUX
ejpam-5627	301	24	a	a	DET
ejpam-5627	301	25	surjective	surjective	ADJ
ejpam-5627	301	26	homomorphism	homomorphism	NOUN
ejpam-5627	301	27	,	,	PUNCT
ejpam-5627	301	28	and	and	CCONJ
ejpam-5627	301	29	b	b	X
ejpam-5627	301	30	=	=	SYM
ejpam-5627	301	31	(	(	PUNCT
ejpam-5627	301	32	b,µ	b,µ	PROPN
ejpam-5627	301	33	,	,	PUNCT
ejpam-5627	301	34	γ	γ	PROPN
ejpam-5627	301	35	)	)	PUNCT
ejpam-5627	301	36	be	be	VERB
ejpam-5627	301	37	an	an	DET
ejpam-5627	301	38	intuitionistic	intuitionistic	ADJ
ejpam-5627	301	39	fuzzy	fuzzy	ADJ
ejpam-5627	301	40	sup	sup	NOUN
ejpam-5627	301	41	-	-	PUNCT
ejpam-5627	301	42	ideal	ideal	NOUN
ejpam-5627	301	43	of	of	ADP
ejpam-5627	301	44	b.	b.	PROPN
ejpam-5627	301	45	let	let	VERB
ejpam-5627	301	46	x1	x1	PROPN
ejpam-5627	301	47	,	,	PUNCT
ejpam-5627	301	48	x2	x2	PROPN
ejpam-5627	301	49	∈	∈	PROPN
ejpam-5627	301	50	a.	a.	NOUN
ejpam-5627	301	51	then	then	ADV
ejpam-5627	301	52	µf	µf	X
ejpam-5627	301	53	(	(	PUNCT
ejpam-5627	301	54	(	(	PUNCT
ejpam-5627	301	55	x2|a(x1|ax1))|a(x2|a(x1|ax1	x2|a(x1|ax1))|a(x2|a(x1|ax1	NOUN
ejpam-5627	301	56	)	)	PUNCT
ejpam-5627	301	57	)	)	PUNCT
ejpam-5627	301	58	)	)	PUNCT
ejpam-5627	302	1	=	=	SYM
ejpam-5627	302	2	µ(f((x2|a(x1|ax1))|a(x2|a(x1|ax1	µ(f((x2|a(x1|ax1))|a(x2|a(x1|ax1	NOUN
ejpam-5627	302	3	)	)	PUNCT
ejpam-5627	302	4	)	)	PUNCT
ejpam-5627	302	5	)	)	PUNCT
ejpam-5627	302	6	)	)	PUNCT
ejpam-5627	303	1	=	=	SYM
ejpam-5627	303	2	µ((f(x2)|b(f(x1)|bf(x1)))|b(f(x2)|b(f(x1)|bf(x1	µ((f(x2)|b(f(x1)|bf(x1)))|b(f(x2)|b(f(x1)|bf(x1	NOUN
ejpam-5627	303	3	)	)	PUNCT
ejpam-5627	303	4	)	)	PUNCT
ejpam-5627	303	5	)	)	PUNCT
ejpam-5627	303	6	)	)	PUNCT
ejpam-5627	303	7	≥	≥	NOUN
ejpam-5627	303	8	µ(f(x2	µ(f(x2	NOUN
ejpam-5627	303	9	)	)	PUNCT
ejpam-5627	303	10	)	)	PUNCT
ejpam-5627	304	1	=	=	SYM
ejpam-5627	304	2	µf	µf	X
ejpam-5627	304	3	(	(	PUNCT
ejpam-5627	304	4	x2	x2	PROPN
ejpam-5627	304	5	)	)	PUNCT
ejpam-5627	304	6	,	,	PUNCT
ejpam-5627	304	7	γf	γf	PROPN
ejpam-5627	304	8	(	(	PUNCT
ejpam-5627	304	9	(	(	PUNCT
ejpam-5627	304	10	x2|a(x1|ax1))|a(x2|a(x1|ax1	x2|a(x1|ax1))|a(x2|a(x1|ax1	NOUN
ejpam-5627	304	11	)	)	PUNCT
ejpam-5627	304	12	)	)	PUNCT
ejpam-5627	304	13	)	)	PUNCT
ejpam-5627	305	1	=	=	SYM
ejpam-5627	305	2	γ(f((x2|a(x1|ax1))|a(x2|a(x1|ax1	γ(f((x2|a(x1|ax1))|a(x2|a(x1|ax1	NOUN
ejpam-5627	305	3	)	)	PUNCT
ejpam-5627	305	4	)	)	PUNCT
ejpam-5627	305	5	)	)	PUNCT
ejpam-5627	305	6	)	)	PUNCT
ejpam-5627	306	1	=	=	SYM
ejpam-5627	306	2	γ((f(x2)|b(f(x1)|bf(x1)))|b(f(x2)|b(f(x1)|bf(x1	γ((f(x2)|b(f(x1)|bf(x1)))|b(f(x2)|b(f(x1)|bf(x1	NUM
ejpam-5627	306	3	)	)	PUNCT
ejpam-5627	306	4	)	)	PUNCT
ejpam-5627	306	5	)	)	PUNCT
ejpam-5627	306	6	)	)	PUNCT
ejpam-5627	307	1	≤	≤	NUM
ejpam-5627	307	2	γ(f(x2	γ(f(x2	NOUN
ejpam-5627	307	3	)	)	PUNCT
ejpam-5627	307	4	)	)	PUNCT
ejpam-5627	308	1	=	=	SYM
ejpam-5627	308	2	γf	γf	INTJ
ejpam-5627	308	3	(	(	PUNCT
ejpam-5627	308	4	x2	x2	PROPN
ejpam-5627	308	5	)	)	PUNCT
ejpam-5627	308	6	,	,	PUNCT
ejpam-5627	308	7	µf	µf	X
ejpam-5627	308	8	(	(	PUNCT
ejpam-5627	308	9	x2	x2	PROPN
ejpam-5627	308	10	)	)	PUNCT
ejpam-5627	308	11	=	=	SYM
ejpam-5627	308	12	µ(f(x2	µ(f(x2	NOUN
ejpam-5627	308	13	)	)	PUNCT
ejpam-5627	308	14	)	)	PUNCT
ejpam-5627	308	15	≥	≥	NOUN
ejpam-5627	308	16	min{µ(f(x1	min{µ(f(x1	PROPN
ejpam-5627	308	17	)	)	PUNCT
ejpam-5627	308	18	)	)	PUNCT
ejpam-5627	308	19	,	,	PUNCT
ejpam-5627	308	20	µ((f(x2)|b(f(x1)|bf(x1)))|b(f(x2)|b(f(x1)|bf(x1	µ((f(x2)|b(f(x1)|bf(x1)))|b(f(x2)|b(f(x1)|bf(x1	NOUN
ejpam-5627	308	21	)	)	PUNCT
ejpam-5627	308	22	)	)	PUNCT
ejpam-5627	308	23	)	)	PUNCT
ejpam-5627	308	24	)	)	PUNCT
ejpam-5627	308	25	}	}	PUNCT
ejpam-5627	308	26	=	=	SYM
ejpam-5627	308	27	min{µ(f(x1	min{µ(f(x1	ADJ
ejpam-5627	308	28	)	)	PUNCT
ejpam-5627	308	29	)	)	PUNCT
ejpam-5627	308	30	,	,	PUNCT
ejpam-5627	308	31	µ(f((x2|a(x1|ax1))|a(x2|a(x1|ax1	µ(f((x2|a(x1|ax1))|a(x2|a(x1|ax1	NUM
ejpam-5627	308	32	)	)	PUNCT
ejpam-5627	308	33	)	)	PUNCT
ejpam-5627	308	34	)	)	PUNCT
ejpam-5627	308	35	)	)	PUNCT
ejpam-5627	308	36	}	}	PUNCT
ejpam-5627	308	37	=	=	SYM
ejpam-5627	308	38	min{µf	min{µf	NOUN
ejpam-5627	308	39	(	(	PUNCT
ejpam-5627	308	40	x1	x1	NUM
ejpam-5627	308	41	)	)	PUNCT
ejpam-5627	308	42	,	,	PUNCT
ejpam-5627	308	43	µ	µ	PROPN
ejpam-5627	308	44	f	f	X
ejpam-5627	308	45	(	(	PUNCT
ejpam-5627	308	46	(	(	PUNCT
ejpam-5627	308	47	x2|a(x1|ax1))|a(x2|a(x1|ax1	x2|a(x1|ax1))|a(x2|a(x1|ax1	NOUN
ejpam-5627	308	48	)	)	PUNCT
ejpam-5627	308	49	)	)	PUNCT
ejpam-5627	308	50	)	)	PUNCT
ejpam-5627	308	51	}	}	PUNCT
ejpam-5627	308	52	,	,	PUNCT
ejpam-5627	308	53	γf	γf	PROPN
ejpam-5627	308	54	(	(	PUNCT
ejpam-5627	308	55	x2	x2	PROPN
ejpam-5627	308	56	)	)	PUNCT
ejpam-5627	308	57	=	=	SYM
ejpam-5627	308	58	γ(f(x2	γ(f(x2	NOUN
ejpam-5627	308	59	)	)	PUNCT
ejpam-5627	308	60	)	)	PUNCT
ejpam-5627	308	61	≤	≤	PROPN
ejpam-5627	309	1	max{γ(f(x1	max{γ(f(x1	PROPN
ejpam-5627	309	2	)	)	PUNCT
ejpam-5627	309	3	)	)	PUNCT
ejpam-5627	309	4	,	,	PUNCT
ejpam-5627	309	5	γ((f(x2)|b(f(x1)|bf(x1)))|b(f(x2)|b(f(x1)|bf(x1	γ((f(x2)|b(f(x1)|bf(x1)))|b(f(x2)|b(f(x1)|bf(x1	NUM
ejpam-5627	309	6	)	)	PUNCT
ejpam-5627	309	7	)	)	PUNCT
ejpam-5627	309	8	)	)	PUNCT
ejpam-5627	309	9	)	)	PUNCT
ejpam-5627	309	10	}	}	PUNCT
ejpam-5627	309	11	=	=	SYM
ejpam-5627	309	12	max{γ(f(x1	max{γ(f(x1	PROPN
ejpam-5627	309	13	)	)	PUNCT
ejpam-5627	309	14	)	)	PUNCT
ejpam-5627	309	15	,	,	PUNCT
ejpam-5627	309	16	γ(f((x2|a(x1|ax1))|a(x2|a(x1|ax1	γ(f((x2|a(x1|ax1))|a(x2|a(x1|ax1	NOUN
ejpam-5627	309	17	)	)	PUNCT
ejpam-5627	309	18	)	)	PUNCT
ejpam-5627	309	19	)	)	PUNCT
ejpam-5627	309	20	)	)	PUNCT
ejpam-5627	309	21	}	}	PUNCT
ejpam-5627	310	1	=	=	SYM
ejpam-5627	310	2	max{γf	max{γf	NOUN
ejpam-5627	310	3	(	(	PUNCT
ejpam-5627	310	4	x1	x1	PROPN
ejpam-5627	310	5	)	)	PUNCT
ejpam-5627	310	6	,	,	PUNCT
ejpam-5627	310	7	γf	γf	PROPN
ejpam-5627	310	8	(	(	PUNCT
ejpam-5627	310	9	(	(	PUNCT
ejpam-5627	310	10	x2|a(x1|ax1))|a(x2|a(x1|ax1	x2|a(x1|ax1))|a(x2|a(x1|ax1	NOUN
ejpam-5627	310	11	)	)	PUNCT
ejpam-5627	310	12	)	)	PUNCT
ejpam-5627	310	13	)	)	PUNCT
ejpam-5627	310	14	}	}	PUNCT
ejpam-5627	310	15	.	.	PUNCT
ejpam-5627	311	1	hence	hence	ADV
ejpam-5627	311	2	,	,	PUNCT
ejpam-5627	311	3	bf	bf	NOUN
ejpam-5627	311	4	=	=	SYM
ejpam-5627	311	5	(	(	PUNCT
ejpam-5627	311	6	b,µf	b,µf	NUM
ejpam-5627	311	7	,	,	PUNCT
ejpam-5627	311	8	γf	γf	PROPN
ejpam-5627	311	9	)	)	PUNCT
ejpam-5627	311	10	is	be	AUX
ejpam-5627	311	11	an	an	DET
ejpam-5627	311	12	intuitionistic	intuitionistic	ADJ
ejpam-5627	311	13	fuzzy	fuzzy	ADJ
ejpam-5627	311	14	sup	sup	NOUN
ejpam-5627	311	15	-	-	PUNCT
ejpam-5627	311	16	ideal	ideal	NOUN
ejpam-5627	311	17	of	of	ADP
ejpam-5627	311	18	a.	a.	NOUN
ejpam-5627	311	19	conversely	conversely	ADV
ejpam-5627	311	20	,	,	PUNCT
ejpam-5627	311	21	let	let	VERB
ejpam-5627	311	22	bf	bf	NOUN
ejpam-5627	311	23	=	=	PUNCT
ejpam-5627	311	24	(	(	PUNCT
ejpam-5627	311	25	b,µf	b,µf	NUM
ejpam-5627	311	26	,	,	PUNCT
ejpam-5627	311	27	γf	γf	PROPN
ejpam-5627	311	28	)	)	PUNCT
ejpam-5627	311	29	be	be	AUX
ejpam-5627	311	30	an	an	DET
ejpam-5627	311	31	intuitionistic	intuitionistic	ADJ
ejpam-5627	311	32	fuzzy	fuzzy	ADJ
ejpam-5627	311	33	sup	sup	NOUN
ejpam-5627	311	34	-	-	PUNCT
ejpam-5627	311	35	ideal	ideal	NOUN
ejpam-5627	311	36	of	of	ADP
ejpam-5627	311	37	a.	a.	NOUN
ejpam-5627	311	38	let	let	VERB
ejpam-5627	311	39	y1	y1	PROPN
ejpam-5627	311	40	,	,	PUNCT
ejpam-5627	312	1	y2	y2	PROPN
ejpam-5627	312	2	∈	∈	PROPN
ejpam-5627	312	3	b	b	PROPN
ejpam-5627	312	4	such	such	ADJ
ejpam-5627	312	5	that	that	DET
ejpam-5627	312	6	f(x1	f(x1	NOUN
ejpam-5627	312	7	)	)	PUNCT
ejpam-5627	312	8	=	=	SYM
ejpam-5627	312	9	y1	y1	NOUN
ejpam-5627	312	10	and	and	CCONJ
ejpam-5627	312	11	f(x2	f(x2	NOUN
ejpam-5627	312	12	)	)	PUNCT
ejpam-5627	313	1	=	=	VERB
ejpam-5627	313	2	y2	y2	PROPN
ejpam-5627	313	3	for	for	ADP
ejpam-5627	313	4	x1	x1	PROPN
ejpam-5627	313	5	,	,	PUNCT
ejpam-5627	313	6	x2	x2	PROPN
ejpam-5627	313	7	∈	∈	PROPN
ejpam-5627	313	8	a.	a.	NOUN
ejpam-5627	313	9	then	then	ADV
ejpam-5627	313	10	µ((y2|b(y1|by1))|b(y2|b(y1|by1	µ((y2|b(y1|by1))|b(y2|b(y1|by1	NOUN
ejpam-5627	313	11	)	)	PUNCT
ejpam-5627	313	12	)	)	PUNCT
ejpam-5627	313	13	)	)	PUNCT
ejpam-5627	314	1	=	=	SYM
ejpam-5627	314	2	µ((f(x2)|b(f(x1)|bf(x1)))|b(f(x2)|b(f(x1)|bf(x1	µ((f(x2)|b(f(x1)|bf(x1)))|b(f(x2)|b(f(x1)|bf(x1	NOUN
ejpam-5627	314	3	)	)	PUNCT
ejpam-5627	314	4	)	)	PUNCT
ejpam-5627	314	5	)	)	PUNCT
ejpam-5627	314	6	)	)	PUNCT
ejpam-5627	315	1	=	=	PRON
ejpam-5627	315	2	µf	µf	X
ejpam-5627	315	3	(	(	PUNCT
ejpam-5627	315	4	(	(	PUNCT
ejpam-5627	315	5	x2|a(x1|ax1))|a(x2|a(x1|ax1	x2|a(x1|ax1))|a(x2|a(x1|ax1	NOUN
ejpam-5627	315	6	)	)	PUNCT
ejpam-5627	315	7	)	)	PUNCT
ejpam-5627	315	8	)	)	PUNCT
ejpam-5627	315	9	≥	≥	PRON
ejpam-5627	315	10	µf	µf	X
ejpam-5627	315	11	(	(	PUNCT
ejpam-5627	315	12	x2	x2	PROPN
ejpam-5627	315	13	)	)	PUNCT
ejpam-5627	315	14	=	=	SYM
ejpam-5627	315	15	µ(f(x2	µ(f(x2	NOUN
ejpam-5627	315	16	)	)	PUNCT
ejpam-5627	315	17	)	)	PUNCT
ejpam-5627	315	18	=	=	PUNCT
ejpam-5627	315	19	µ(y2	µ(y2	NOUN
ejpam-5627	315	20	)	)	PUNCT
ejpam-5627	315	21	,	,	PUNCT
ejpam-5627	315	22	γ((y2|b(y1|by1))|b(y2|b(y1|by1	γ((y2|b(y1|by1))|b(y2|b(y1|by1	NOUN
ejpam-5627	315	23	)	)	PUNCT
ejpam-5627	315	24	)	)	PUNCT
ejpam-5627	315	25	)	)	PUNCT
ejpam-5627	316	1	=	=	SYM
ejpam-5627	316	2	γ((f(x2)|b(f(x1)|bf(x1)))|b(f(x2)|b(f(x1)|bf(x1	γ((f(x2)|b(f(x1)|bf(x1)))|b(f(x2)|b(f(x1)|bf(x1	NUM
ejpam-5627	316	3	)	)	PUNCT
ejpam-5627	316	4	)	)	PUNCT
ejpam-5627	316	5	)	)	PUNCT
ejpam-5627	316	6	)	)	PUNCT
ejpam-5627	317	1	=	=	SYM
ejpam-5627	317	2	γf	γf	INTJ
ejpam-5627	317	3	(	(	PUNCT
ejpam-5627	317	4	(	(	PUNCT
ejpam-5627	317	5	x2|a(x1|ax1))|a(x2|a(x1|ax1	x2|a(x1|ax1))|a(x2|a(x1|ax1	NOUN
ejpam-5627	317	6	)	)	PUNCT
ejpam-5627	317	7	)	)	PUNCT
ejpam-5627	317	8	)	)	PUNCT
ejpam-5627	317	9	≤	≤	NUM
ejpam-5627	318	1	γf	γf	NOUN
ejpam-5627	318	2	(	(	PUNCT
ejpam-5627	318	3	x2	x2	PROPN
ejpam-5627	318	4	)	)	PUNCT
ejpam-5627	318	5	=	=	SYM
ejpam-5627	318	6	γ(f(x2	γ(f(x2	NOUN
ejpam-5627	318	7	)	)	PUNCT
ejpam-5627	318	8	)	)	PUNCT
ejpam-5627	319	1	=	=	SYM
ejpam-5627	319	2	γ(y2	γ(y2	PROPN
ejpam-5627	319	3	)	)	PUNCT
ejpam-5627	319	4	,	,	PUNCT
ejpam-5627	319	5	n.	n.	PROPN
ejpam-5627	319	6	rajesh	rajesh	PROPN
ejpam-5627	319	7	,	,	PUNCT
ejpam-5627	319	8	t.	t.	PROPN
ejpam-5627	319	9	oner	oner	NOUN
ejpam-5627	319	10	,	,	PUNCT
ejpam-5627	319	11	a.	a.	NOUN
ejpam-5627	319	12	iampan	iampan	PROPN
ejpam-5627	319	13	,	,	PUNCT
ejpam-5627	319	14	i.	i.	PROPN
ejpam-5627	319	15	senturk	senturk	PROPN
ejpam-5627	319	16	/	/	SYM
ejpam-5627	319	17	eur	eur	PROPN
ejpam-5627	319	18	.	.	PUNCT
ejpam-5627	320	1	j.	j.	PROPN
ejpam-5627	320	2	pure	pure	PROPN
ejpam-5627	320	3	appl	appl	PROPN
ejpam-5627	320	4	.	.	PROPN
ejpam-5627	320	5	math	math	PROPN
ejpam-5627	320	6	,	,	PUNCT
ejpam-5627	320	7	18	18	NUM
ejpam-5627	320	8	(	(	PUNCT
ejpam-5627	320	9	1	1	NUM
ejpam-5627	320	10	)	)	PUNCT
ejpam-5627	320	11	(	(	PUNCT
ejpam-5627	320	12	2025	2025	NUM
ejpam-5627	320	13	)	)	PUNCT
ejpam-5627	320	14	,	,	PUNCT
ejpam-5627	320	15	5627	5627	NUM
ejpam-5627	320	16	13	13	NUM
ejpam-5627	320	17	of	of	ADP
ejpam-5627	320	18	15	15	NUM
ejpam-5627	320	19	µ(y2	µ(y2	ADJ
ejpam-5627	320	20	)	)	PUNCT
ejpam-5627	320	21	=	=	SYM
ejpam-5627	320	22	µ(f(x2	µ(f(x2	NOUN
ejpam-5627	320	23	)	)	PUNCT
ejpam-5627	320	24	)	)	PUNCT
ejpam-5627	321	1	=	=	SYM
ejpam-5627	321	2	µf	µf	X
ejpam-5627	321	3	(	(	PUNCT
ejpam-5627	321	4	x2	x2	PROPN
ejpam-5627	321	5	)	)	PUNCT
ejpam-5627	321	6	≥	≥	NUM
ejpam-5627	321	7	min{µf	min{µf	ADP
ejpam-5627	321	8	(	(	PUNCT
ejpam-5627	321	9	x1	x1	PROPN
ejpam-5627	321	10	)	)	PUNCT
ejpam-5627	321	11	,	,	PUNCT
ejpam-5627	321	12	µ	µ	PROPN
ejpam-5627	321	13	f	f	X
ejpam-5627	321	14	(	(	PUNCT
ejpam-5627	321	15	(	(	PUNCT
ejpam-5627	321	16	x2|a(x1|ax1))|a(x2|a(x1|ax1	x2|a(x1|ax1))|a(x2|a(x1|ax1	NOUN
ejpam-5627	321	17	)	)	PUNCT
ejpam-5627	321	18	)	)	PUNCT
ejpam-5627	321	19	)	)	PUNCT
ejpam-5627	321	20	}	}	PUNCT
ejpam-5627	321	21	=	=	SYM
ejpam-5627	321	22	min{µ(f(x1	min{µ(f(x1	ADJ
ejpam-5627	321	23	)	)	PUNCT
ejpam-5627	321	24	)	)	PUNCT
ejpam-5627	321	25	,	,	PUNCT
ejpam-5627	321	26	µ(f((x2|a(x1|ax1))|a(x2|a(x1|ax1	µ(f((x2|a(x1|ax1))|a(x2|a(x1|ax1	NUM
ejpam-5627	321	27	)	)	PUNCT
ejpam-5627	321	28	)	)	PUNCT
ejpam-5627	321	29	)	)	PUNCT
ejpam-5627	321	30	)	)	PUNCT
ejpam-5627	321	31	}	}	PUNCT
ejpam-5627	321	32	=	=	SYM
ejpam-5627	321	33	min{µ(f(x1	min{µ(f(x1	ADJ
ejpam-5627	321	34	)	)	PUNCT
ejpam-5627	321	35	)	)	PUNCT
ejpam-5627	321	36	,	,	PUNCT
ejpam-5627	321	37	µ((f(x2)|b(f(x1)|bf(x1)))|b(f(x2)|b(f(x1)|bf(x1	µ((f(x2)|b(f(x1)|bf(x1)))|b(f(x2)|b(f(x1)|bf(x1	NOUN
ejpam-5627	321	38	)	)	PUNCT
ejpam-5627	321	39	)	)	PUNCT
ejpam-5627	321	40	)	)	PUNCT
ejpam-5627	321	41	)	)	PUNCT
ejpam-5627	321	42	}	}	PUNCT
ejpam-5627	321	43	=	=	SYM
ejpam-5627	321	44	min{µ(y1	min{µ(y1	NOUN
ejpam-5627	321	45	)	)	PUNCT
ejpam-5627	321	46	,	,	PUNCT
ejpam-5627	321	47	µ((y2|b(y1|by1))|b(y2|b(y1|by1	µ((y2|b(y1|by1))|b(y2|b(y1|by1	NOUN
ejpam-5627	321	48	)	)	PUNCT
ejpam-5627	321	49	)	)	PUNCT
ejpam-5627	321	50	)	)	PUNCT
ejpam-5627	321	51	}	}	PUNCT
ejpam-5627	321	52	,	,	PUNCT
ejpam-5627	321	53	γ(y2	γ(y2	PROPN
ejpam-5627	321	54	)	)	PUNCT
ejpam-5627	321	55	=	=	SYM
ejpam-5627	321	56	γ(f(x2	γ(f(x2	NOUN
ejpam-5627	321	57	)	)	PUNCT
ejpam-5627	321	58	)	)	PUNCT
ejpam-5627	322	1	=	=	SYM
ejpam-5627	322	2	γf	γf	ADJ
ejpam-5627	322	3	(	(	PUNCT
ejpam-5627	322	4	x2	x2	NOUN
ejpam-5627	322	5	)	)	PUNCT
ejpam-5627	322	6	≤	≤	NOUN
ejpam-5627	322	7	max{γf	max{γf	PUNCT
ejpam-5627	322	8	(	(	PUNCT
ejpam-5627	322	9	x1	x1	PROPN
ejpam-5627	322	10	)	)	PUNCT
ejpam-5627	322	11	,	,	PUNCT
ejpam-5627	322	12	γf	γf	PROPN
ejpam-5627	322	13	(	(	PUNCT
ejpam-5627	322	14	(	(	PUNCT
ejpam-5627	322	15	x2|a(x1|ax1))|a(x2|a(x1|ax1	x2|a(x1|ax1))|a(x2|a(x1|ax1	NOUN
ejpam-5627	322	16	)	)	PUNCT
ejpam-5627	322	17	)	)	PUNCT
ejpam-5627	322	18	)	)	PUNCT
ejpam-5627	322	19	}	}	PUNCT
ejpam-5627	322	20	=	=	SYM
ejpam-5627	322	21	max{γ(f(x1	max{γ(f(x1	PROPN
ejpam-5627	322	22	)	)	PUNCT
ejpam-5627	322	23	)	)	PUNCT
ejpam-5627	322	24	,	,	PUNCT
ejpam-5627	322	25	γ(f((x2|a(x1|ax1))|a(x2|a(x1|ax1	γ(f((x2|a(x1|ax1))|a(x2|a(x1|ax1	NOUN
ejpam-5627	322	26	)	)	PUNCT
ejpam-5627	322	27	)	)	PUNCT
ejpam-5627	322	28	)	)	PUNCT
ejpam-5627	322	29	)	)	PUNCT
ejpam-5627	322	30	}	}	PUNCT
ejpam-5627	322	31	=	=	SYM
ejpam-5627	322	32	max{γ(f(x1	max{γ(f(x1	PROPN
ejpam-5627	322	33	)	)	PUNCT
ejpam-5627	322	34	)	)	PUNCT
ejpam-5627	322	35	,	,	PUNCT
ejpam-5627	322	36	γ((f(x2)|b(f(x1)|bf(x1)))|b(f(x2)|b(f(x1)|bf(x1	γ((f(x2)|b(f(x1)|bf(x1)))|b(f(x2)|b(f(x1)|bf(x1	NUM
ejpam-5627	322	37	)	)	PUNCT
ejpam-5627	322	38	)	)	PUNCT
ejpam-5627	322	39	)	)	PUNCT
ejpam-5627	322	40	)	)	PUNCT
ejpam-5627	322	41	}	}	PUNCT
ejpam-5627	322	42	=	=	SYM
ejpam-5627	322	43	max{γ(y1	max{γ(y1	NOUN
ejpam-5627	322	44	)	)	PUNCT
ejpam-5627	322	45	,	,	PUNCT
ejpam-5627	322	46	γ((y2|b(y1|by1))|b(y2|b(y1|by1	γ((y2|b(y1|by1))|b(y2|b(y1|by1	NOUN
ejpam-5627	322	47	)	)	PUNCT
ejpam-5627	322	48	)	)	PUNCT
ejpam-5627	322	49	)	)	PUNCT
ejpam-5627	322	50	}	}	PUNCT
ejpam-5627	322	51	.	.	PUNCT
ejpam-5627	323	1	hence	hence	ADV
ejpam-5627	323	2	,	,	PUNCT
ejpam-5627	323	3	b	b	X
ejpam-5627	323	4	=	=	SYM
ejpam-5627	323	5	(	(	PUNCT
ejpam-5627	323	6	b,µ	b,µ	PROPN
ejpam-5627	323	7	,	,	PUNCT
ejpam-5627	323	8	γ	γ	PROPN
ejpam-5627	323	9	)	)	PUNCT
ejpam-5627	323	10	is	be	AUX
ejpam-5627	323	11	an	an	DET
ejpam-5627	323	12	intuitionistic	intuitionistic	ADJ
ejpam-5627	323	13	fuzzy	fuzzy	ADJ
ejpam-5627	323	14	sup	sup	NOUN
ejpam-5627	323	15	-	-	PUNCT
ejpam-5627	323	16	ideal	ideal	NOUN
ejpam-5627	323	17	of	of	ADP
ejpam-5627	323	18	b.	b.	PROPN
ejpam-5627	323	19	theorem	theorem	PROPN
ejpam-5627	323	20	13	13	NUM
ejpam-5627	323	21	.	.	PUNCT
ejpam-5627	324	1	let	let	VERB
ejpam-5627	324	2	⟨a	⟨a	NOUN
ejpam-5627	324	3	,	,	PUNCT
ejpam-5627	324	4	|a	|a	NOUN
ejpam-5627	324	5	,	,	PUNCT
ejpam-5627	324	6	0a⟩	0a⟩	NUM
ejpam-5627	324	7	and	and	CCONJ
ejpam-5627	324	8	⟨b	⟨b	PROPN
ejpam-5627	324	9	,	,	PUNCT
ejpam-5627	324	10	|b	|b	PROPN
ejpam-5627	324	11	,	,	PUNCT
ejpam-5627	324	12	0b⟩	0b⟩	NUM
ejpam-5627	324	13	be	be	VERB
ejpam-5627	324	14	sup	sup	NOUN
ejpam-5627	324	15	-	-	PUNCT
ejpam-5627	324	16	algebras	algebra	NOUN
ejpam-5627	324	17	,	,	PUNCT
ejpam-5627	324	18	f	f	X
ejpam-5627	324	19	:	:	PUNCT
ejpam-5627	324	20	a	a	DET
ejpam-5627	324	21	→	→	SYM
ejpam-5627	324	22	b	b	X
ejpam-5627	324	23	be	be	AUX
ejpam-5627	324	24	a	a	DET
ejpam-5627	324	25	surjective	surjective	ADJ
ejpam-5627	324	26	homomorphism	homomorphism	NOUN
ejpam-5627	324	27	,	,	PUNCT
ejpam-5627	324	28	and	and	CCONJ
ejpam-5627	324	29	b	b	X
ejpam-5627	324	30	=	=	SYM
ejpam-5627	324	31	(	(	PUNCT
ejpam-5627	324	32	b,µ	b,µ	PROPN
ejpam-5627	324	33	,	,	PUNCT
ejpam-5627	324	34	γ	γ	PROPN
ejpam-5627	324	35	)	)	PUNCT
ejpam-5627	324	36	be	be	VERB
ejpam-5627	324	37	an	an	DET
ejpam-5627	324	38	intuitionistic	intuitionistic	ADJ
ejpam-5627	324	39	fuzzy	fuzzy	ADJ
ejpam-5627	324	40	up	up	NOUN
ejpam-5627	324	41	-	-	PUNCT
ejpam-5627	324	42	structure	structure	NOUN
ejpam-5627	324	43	on	on	ADP
ejpam-5627	324	44	b.	b.	PROPN
ejpam-5627	325	1	then	then	ADV
ejpam-5627	325	2	b	b	X
ejpam-5627	325	3	=	=	SYM
ejpam-5627	325	4	(	(	PUNCT
ejpam-5627	325	5	b,µ	b,µ	PROPN
ejpam-5627	325	6	,	,	PUNCT
ejpam-5627	325	7	γ	γ	PROPN
ejpam-5627	325	8	)	)	PUNCT
ejpam-5627	325	9	is	be	AUX
ejpam-5627	325	10	an	an	DET
ejpam-5627	325	11	intuitionistic	intuitionistic	ADJ
ejpam-5627	325	12	fuzzy	fuzzy	ADJ
ejpam-5627	325	13	sup	sup	NOUN
ejpam-5627	325	14	-	-	PUNCT
ejpam-5627	325	15	subalgebra	subalgebra	NOUN
ejpam-5627	325	16	of	of	ADP
ejpam-5627	325	17	b	b	NOUN
ejpam-5627	325	18	if	if	NOUN
ejpam-5627	325	19	and	and	CCONJ
ejpam-5627	325	20	only	only	ADV
ejpam-5627	325	21	if	if	SCONJ
ejpam-5627	325	22	bf	bf	NOUN
ejpam-5627	325	23	=	=	SYM
ejpam-5627	325	24	(	(	PUNCT
ejpam-5627	325	25	b,µf	b,µf	NUM
ejpam-5627	325	26	,	,	PUNCT
ejpam-5627	325	27	γf	γf	PROPN
ejpam-5627	325	28	)	)	PUNCT
ejpam-5627	325	29	is	be	AUX
ejpam-5627	325	30	an	an	DET
ejpam-5627	325	31	intuitionistic	intuitionistic	ADJ
ejpam-5627	325	32	fuzzy	fuzzy	ADJ
ejpam-5627	325	33	sup	sup	NOUN
ejpam-5627	325	34	-	-	PUNCT
ejpam-5627	325	35	subalgebra	subalgebra	NOUN
ejpam-5627	325	36	of	of	ADP
ejpam-5627	325	37	a.	a.	NOUN
ejpam-5627	325	38	proof	proof	NOUN
ejpam-5627	325	39	.	.	PUNCT
ejpam-5627	326	1	let	let	VERB
ejpam-5627	326	2	⟨a	⟨a	NOUN
ejpam-5627	326	3	,	,	PUNCT
ejpam-5627	326	4	|a	|a	NOUN
ejpam-5627	326	5	,	,	PUNCT
ejpam-5627	326	6	0a⟩	0a⟩	NUM
ejpam-5627	326	7	and	and	CCONJ
ejpam-5627	326	8	⟨b	⟨b	PROPN
ejpam-5627	326	9	,	,	PUNCT
ejpam-5627	326	10	|b	|b	PROPN
ejpam-5627	326	11	,	,	PUNCT
ejpam-5627	326	12	0b⟩	0b⟩	NUM
ejpam-5627	326	13	be	be	VERB
ejpam-5627	326	14	sup	sup	NOUN
ejpam-5627	326	15	-	-	PUNCT
ejpam-5627	326	16	algebras	algebra	NOUN
ejpam-5627	326	17	,	,	PUNCT
ejpam-5627	326	18	f	f	X
ejpam-5627	326	19	:	:	PUNCT
ejpam-5627	326	20	a	a	DET
ejpam-5627	326	21	→	→	SYM
ejpam-5627	326	22	b	b	X
ejpam-5627	326	23	be	be	AUX
ejpam-5627	326	24	a	a	DET
ejpam-5627	326	25	surjective	surjective	ADJ
ejpam-5627	326	26	homomorphism	homomorphism	NOUN
ejpam-5627	326	27	,	,	PUNCT
ejpam-5627	326	28	and	and	CCONJ
ejpam-5627	326	29	b	b	X
ejpam-5627	326	30	=	=	SYM
ejpam-5627	326	31	(	(	PUNCT
ejpam-5627	326	32	b,µ	b,µ	PROPN
ejpam-5627	326	33	,	,	PUNCT
ejpam-5627	326	34	γ	γ	PROPN
ejpam-5627	326	35	)	)	PUNCT
ejpam-5627	326	36	be	be	VERB
ejpam-5627	326	37	an	an	DET
ejpam-5627	326	38	intuitionistic	intuitionistic	ADJ
ejpam-5627	326	39	fuzzy	fuzzy	ADJ
ejpam-5627	326	40	sup	sup	NOUN
ejpam-5627	326	41	-	-	PUNCT
ejpam-5627	326	42	subalgebra	subalgebra	NOUN
ejpam-5627	326	43	of	of	ADP
ejpam-5627	326	44	b.	b.	PROPN
ejpam-5627	326	45	let	let	VERB
ejpam-5627	326	46	x1	x1	PROPN
ejpam-5627	326	47	,	,	PUNCT
ejpam-5627	326	48	x2	x2	PROPN
ejpam-5627	326	49	∈	∈	PROPN
ejpam-5627	326	50	a.	a.	NOUN
ejpam-5627	326	51	then	then	ADV
ejpam-5627	326	52	µf	µf	X
ejpam-5627	326	53	(	(	PUNCT
ejpam-5627	326	54	(	(	PUNCT
ejpam-5627	326	55	x1|a(x2|ax2))|a(x1|a(x2|ax2	x1|a(x2|ax2))|a(x1|a(x2|ax2	NOUN
ejpam-5627	326	56	)	)	PUNCT
ejpam-5627	326	57	)	)	PUNCT
ejpam-5627	326	58	)	)	PUNCT
ejpam-5627	327	1	=	=	PUNCT
ejpam-5627	327	2	µ(f((x1|a(x2|ax2))|a(x1|a(x2|ax2	µ(f((x1|a(x2|ax2))|a(x1|a(x2|ax2	VERB
ejpam-5627	327	3	)	)	PUNCT
ejpam-5627	327	4	)	)	PUNCT
ejpam-5627	327	5	)	)	PUNCT
ejpam-5627	327	6	)	)	PUNCT
ejpam-5627	328	1	=	=	SYM
ejpam-5627	328	2	µ(f(x1)|b(f(x2)|bf(x2))|b(f(x1)|b(f(x2)|bf(x2	µ(f(x1)|b(f(x2)|bf(x2))|b(f(x1)|b(f(x2)|bf(x2	NOUN
ejpam-5627	328	3	)	)	PUNCT
ejpam-5627	328	4	)	)	PUNCT
ejpam-5627	328	5	)	)	PUNCT
ejpam-5627	328	6	)	)	PUNCT
ejpam-5627	328	7	≥	≥	NOUN
ejpam-5627	328	8	min{µ(f(x1	min{µ(f(x1	PROPN
ejpam-5627	328	9	)	)	PUNCT
ejpam-5627	328	10	)	)	PUNCT
ejpam-5627	328	11	,	,	PUNCT
ejpam-5627	328	12	µ(f(x2	µ(f(x2	NOUN
ejpam-5627	328	13	)	)	PUNCT
ejpam-5627	328	14	)	)	PUNCT
ejpam-5627	328	15	}	}	PUNCT
ejpam-5627	328	16	=	=	SYM
ejpam-5627	328	17	min{µf	min{µf	NOUN
ejpam-5627	328	18	(	(	PUNCT
ejpam-5627	328	19	x1	x1	NUM
ejpam-5627	328	20	)	)	PUNCT
ejpam-5627	328	21	,	,	PUNCT
ejpam-5627	328	22	µ	µ	PROPN
ejpam-5627	328	23	f	f	X
ejpam-5627	328	24	(	(	PUNCT
ejpam-5627	328	25	x2	x2	PROPN
ejpam-5627	328	26	)	)	PUNCT
ejpam-5627	328	27	}	}	PUNCT
ejpam-5627	328	28	,	,	PUNCT
ejpam-5627	328	29	γf	γf	INTJ
ejpam-5627	328	30	(	(	PUNCT
ejpam-5627	328	31	(	(	PUNCT
ejpam-5627	328	32	x1|a(x2|ax2))|a(x1|a(x2|ax2	x1|a(x2|ax2))|a(x1|a(x2|ax2	NOUN
ejpam-5627	328	33	)	)	PUNCT
ejpam-5627	328	34	)	)	PUNCT
ejpam-5627	328	35	)	)	PUNCT
ejpam-5627	329	1	=	=	SYM
ejpam-5627	329	2	γ(f((x1|a(x2|ax2))|a(x1|a(x2|ax2	γ(f((x1|a(x2|ax2))|a(x1|a(x2|ax2	NOUN
ejpam-5627	329	3	)	)	PUNCT
ejpam-5627	329	4	)	)	PUNCT
ejpam-5627	329	5	)	)	PUNCT
ejpam-5627	329	6	)	)	PUNCT
ejpam-5627	330	1	=	=	SYM
ejpam-5627	330	2	γ(f(x1)|b(f(x2)|bf(x2))|b(f(x1)|b(f(x2)|bf(x2	γ(f(x1)|b(f(x2)|bf(x2))|b(f(x1)|b(f(x2)|bf(x2	NOUN
ejpam-5627	330	3	)	)	PUNCT
ejpam-5627	330	4	)	)	PUNCT
ejpam-5627	330	5	)	)	PUNCT
ejpam-5627	330	6	)	)	PUNCT
ejpam-5627	331	1	≤	≤	PROPN
ejpam-5627	331	2	max{γ(f(x1	max{γ(f(x1	PROPN
ejpam-5627	331	3	)	)	PUNCT
ejpam-5627	331	4	)	)	PUNCT
ejpam-5627	331	5	,	,	PUNCT
ejpam-5627	331	6	γ(f(x2	γ(f(x2	NOUN
ejpam-5627	331	7	)	)	PUNCT
ejpam-5627	331	8	)	)	PUNCT
ejpam-5627	331	9	}	}	PUNCT
ejpam-5627	332	1	=	=	SYM
ejpam-5627	332	2	max{γf	max{γf	NOUN
ejpam-5627	332	3	(	(	PUNCT
ejpam-5627	332	4	x1	x1	PROPN
ejpam-5627	332	5	)	)	PUNCT
ejpam-5627	332	6	,	,	PUNCT
ejpam-5627	332	7	γf	γf	PROPN
ejpam-5627	332	8	(	(	PUNCT
ejpam-5627	332	9	x2	x2	PROPN
ejpam-5627	332	10	)	)	PUNCT
ejpam-5627	332	11	}	}	PUNCT
ejpam-5627	332	12	.	.	PUNCT
ejpam-5627	333	1	hence	hence	ADV
ejpam-5627	333	2	,	,	PUNCT
ejpam-5627	333	3	bf	bf	NOUN
ejpam-5627	333	4	=	=	SYM
ejpam-5627	333	5	(	(	PUNCT
ejpam-5627	333	6	a,µf	a,µf	X
ejpam-5627	333	7	,	,	PUNCT
ejpam-5627	333	8	γf	γf	PROPN
ejpam-5627	333	9	)	)	PUNCT
ejpam-5627	333	10	is	be	AUX
ejpam-5627	333	11	an	an	DET
ejpam-5627	333	12	intuitionistic	intuitionistic	ADJ
ejpam-5627	333	13	fuzzy	fuzzy	ADJ
ejpam-5627	333	14	sup	sup	NOUN
ejpam-5627	333	15	-	-	PUNCT
ejpam-5627	333	16	subalgebra	subalgebra	NOUN
ejpam-5627	333	17	of	of	ADP
ejpam-5627	333	18	a.	a.	NOUN
ejpam-5627	333	19	conversely	conversely	ADV
ejpam-5627	333	20	,	,	PUNCT
ejpam-5627	333	21	let	let	VERB
ejpam-5627	333	22	bf	bf	NOUN
ejpam-5627	333	23	=	=	SYM
ejpam-5627	333	24	(	(	PUNCT
ejpam-5627	333	25	a,µf	a,µf	X
ejpam-5627	333	26	,	,	PUNCT
ejpam-5627	333	27	γf	γf	PROPN
ejpam-5627	333	28	)	)	PUNCT
ejpam-5627	333	29	be	be	AUX
ejpam-5627	333	30	an	an	DET
ejpam-5627	333	31	intuitionistic	intuitionistic	ADJ
ejpam-5627	333	32	fuzzy	fuzzy	ADJ
ejpam-5627	333	33	sup	sup	NOUN
ejpam-5627	333	34	-	-	PUNCT
ejpam-5627	333	35	subalgebra	subalgebra	NOUN
ejpam-5627	333	36	of	of	ADP
ejpam-5627	333	37	a.	a.	NOUN
ejpam-5627	333	38	let	let	VERB
ejpam-5627	333	39	y1	y1	PROPN
ejpam-5627	333	40	,	,	PUNCT
ejpam-5627	334	1	y2	y2	PROPN
ejpam-5627	334	2	∈	∈	PROPN
ejpam-5627	334	3	b	b	NOUN
ejpam-5627	334	4	be	be	AUX
ejpam-5627	334	5	such	such	ADJ
ejpam-5627	334	6	that	that	SCONJ
ejpam-5627	334	7	f(x1	f(x1	NOUN
ejpam-5627	334	8	)	)	PUNCT
ejpam-5627	335	1	=	=	SYM
ejpam-5627	335	2	y1	y1	NOUN
ejpam-5627	335	3	and	and	CCONJ
ejpam-5627	335	4	f(x2	f(x2	NOUN
ejpam-5627	335	5	)	)	PUNCT
ejpam-5627	335	6	=	=	VERB
ejpam-5627	336	1	y2	y2	PROPN
ejpam-5627	336	2	for	for	ADP
ejpam-5627	336	3	x1	x1	PROPN
ejpam-5627	336	4	,	,	PUNCT
ejpam-5627	336	5	x2	x2	PROPN
ejpam-5627	336	6	∈	∈	PROPN
ejpam-5627	336	7	a.	a.	NOUN
ejpam-5627	336	8	then	then	ADV
ejpam-5627	336	9	µ((y1|b(y2|by2))|b(y1|b(y2|by2	µ((y1|b(y2|by2))|b(y1|b(y2|by2	NOUN
ejpam-5627	336	10	)	)	PUNCT
ejpam-5627	336	11	)	)	PUNCT
ejpam-5627	336	12	)	)	PUNCT
ejpam-5627	337	1	=	=	SYM
ejpam-5627	337	2	µ((f(x1)|b(f(x2)|bf(x2)))|b(f(x1)|b(f(x2)|bf(x2	µ((f(x1)|b(f(x2)|bf(x2)))|b(f(x1)|b(f(x2)|bf(x2	X
ejpam-5627	337	3	)	)	PUNCT
ejpam-5627	337	4	)	)	PUNCT
ejpam-5627	337	5	)	)	PUNCT
ejpam-5627	337	6	)	)	PUNCT
ejpam-5627	338	1	=	=	PUNCT
ejpam-5627	338	2	µ(f((x1|a(x2|ax2))|a(x1|a(x2|ax2	µ(f((x1|a(x2|ax2))|a(x1|a(x2|ax2	VERB
ejpam-5627	338	3	)	)	PUNCT
ejpam-5627	338	4	)	)	PUNCT
ejpam-5627	338	5	)	)	PUNCT
ejpam-5627	338	6	)	)	PUNCT
ejpam-5627	339	1	=	=	PRON
ejpam-5627	339	2	µf	µf	X
ejpam-5627	339	3	(	(	PUNCT
ejpam-5627	339	4	(	(	PUNCT
ejpam-5627	339	5	x1|a(x2|ax2))|a(x1|a(x2|ax2	x1|a(x2|ax2))|a(x1|a(x2|ax2	NOUN
ejpam-5627	339	6	)	)	PUNCT
ejpam-5627	339	7	)	)	PUNCT
ejpam-5627	339	8	)	)	PUNCT
ejpam-5627	339	9	≥	≥	X
ejpam-5627	339	10	min{µf	min{µf	ADV
ejpam-5627	339	11	(	(	PUNCT
ejpam-5627	339	12	x1	x1	PROPN
ejpam-5627	339	13	)	)	PUNCT
ejpam-5627	339	14	,	,	PUNCT
ejpam-5627	339	15	µ	µ	PROPN
ejpam-5627	339	16	f	f	X
ejpam-5627	339	17	(	(	PUNCT
ejpam-5627	339	18	x2	x2	PROPN
ejpam-5627	339	19	)	)	PUNCT
ejpam-5627	339	20	}	}	PUNCT
ejpam-5627	339	21	=	=	SYM
ejpam-5627	339	22	min{µ(f(x1	min{µ(f(x1	ADJ
ejpam-5627	339	23	)	)	PUNCT
ejpam-5627	339	24	)	)	PUNCT
ejpam-5627	339	25	,	,	PUNCT
ejpam-5627	339	26	µ(f(x2	µ(f(x2	NOUN
ejpam-5627	339	27	)	)	PUNCT
ejpam-5627	339	28	)	)	PUNCT
ejpam-5627	339	29	}	}	PUNCT
ejpam-5627	339	30	=	=	SYM
ejpam-5627	339	31	min{µ(y1	min{µ(y1	NOUN
ejpam-5627	339	32	)	)	PUNCT
ejpam-5627	339	33	,	,	PUNCT
ejpam-5627	339	34	µ(y2	µ(y2	NOUN
ejpam-5627	339	35	)	)	PUNCT
ejpam-5627	339	36	}	}	PUNCT
ejpam-5627	339	37	,	,	PUNCT
ejpam-5627	339	38	n.	n.	PROPN
ejpam-5627	339	39	rajesh	rajesh	PROPN
ejpam-5627	339	40	,	,	PUNCT
ejpam-5627	339	41	t.	t.	PROPN
ejpam-5627	339	42	oner	oner	NOUN
ejpam-5627	339	43	,	,	PUNCT
ejpam-5627	339	44	a.	a.	NOUN
ejpam-5627	339	45	iampan	iampan	PROPN
ejpam-5627	339	46	,	,	PUNCT
ejpam-5627	339	47	i.	i.	PROPN
ejpam-5627	339	48	senturk	senturk	PROPN
ejpam-5627	339	49	/	/	SYM
ejpam-5627	339	50	eur	eur	PROPN
ejpam-5627	339	51	.	.	PUNCT
ejpam-5627	340	1	j.	j.	PROPN
ejpam-5627	340	2	pure	pure	PROPN
ejpam-5627	340	3	appl	appl	PROPN
ejpam-5627	340	4	.	.	PROPN
ejpam-5627	340	5	math	math	PROPN
ejpam-5627	340	6	,	,	PUNCT
ejpam-5627	340	7	18	18	NUM
ejpam-5627	340	8	(	(	PUNCT
ejpam-5627	340	9	1	1	NUM
ejpam-5627	340	10	)	)	PUNCT
ejpam-5627	340	11	(	(	PUNCT
ejpam-5627	340	12	2025	2025	NUM
ejpam-5627	340	13	)	)	PUNCT
ejpam-5627	340	14	,	,	PUNCT
ejpam-5627	340	15	5627	5627	NUM
ejpam-5627	340	16	14	14	NUM
ejpam-5627	340	17	of	of	ADP
ejpam-5627	340	18	15	15	NUM
ejpam-5627	340	19	γ((y1|b(y2|by2))|b(y1|b(y2|by2	γ((y1|b(y2|by2))|b(y1|b(y2|by2	NOUN
ejpam-5627	340	20	)	)	PUNCT
ejpam-5627	340	21	)	)	PUNCT
ejpam-5627	340	22	)	)	PUNCT
ejpam-5627	341	1	=	=	SYM
ejpam-5627	341	2	γ((f(x1)|b(f(x2)|bf(x2)))|b(f(x1)|b(f(x2)|bf(x2	γ((f(x1)|b(f(x2)|bf(x2)))|b(f(x1)|b(f(x2)|bf(x2	NOUN
ejpam-5627	341	3	)	)	PUNCT
ejpam-5627	341	4	)	)	PUNCT
ejpam-5627	341	5	)	)	PUNCT
ejpam-5627	341	6	)	)	PUNCT
ejpam-5627	342	1	=	=	SYM
ejpam-5627	342	2	γ(f((x1|a(x2|ax2))|a(x1|a(x2|ax2	γ(f((x1|a(x2|ax2))|a(x1|a(x2|ax2	NOUN
ejpam-5627	342	3	)	)	PUNCT
ejpam-5627	342	4	)	)	PUNCT
ejpam-5627	342	5	)	)	PUNCT
ejpam-5627	342	6	)	)	PUNCT
ejpam-5627	343	1	=	=	SYM
ejpam-5627	343	2	γf	γf	INTJ
ejpam-5627	343	3	(	(	PUNCT
ejpam-5627	343	4	(	(	PUNCT
ejpam-5627	343	5	x1|a(x2|ax2))|a(x1|a(x2|ax2	x1|a(x2|ax2))|a(x1|a(x2|ax2	NOUN
ejpam-5627	343	6	)	)	PUNCT
ejpam-5627	343	7	)	)	PUNCT
ejpam-5627	343	8	)	)	PUNCT
ejpam-5627	344	1	≤	≤	NUM
ejpam-5627	344	2	max{γf	max{γf	NOUN
ejpam-5627	344	3	(	(	PUNCT
ejpam-5627	344	4	x1	x1	PROPN
ejpam-5627	344	5	)	)	PUNCT
ejpam-5627	344	6	,	,	PUNCT
ejpam-5627	344	7	γf	γf	PROPN
ejpam-5627	344	8	(	(	PUNCT
ejpam-5627	344	9	x2	x2	NOUN
ejpam-5627	344	10	)	)	PUNCT
ejpam-5627	344	11	}	}	PUNCT
ejpam-5627	344	12	=	=	SYM
ejpam-5627	344	13	max{γ(f(x1	max{γ(f(x1	PROPN
ejpam-5627	344	14	)	)	PUNCT
ejpam-5627	344	15	)	)	PUNCT
ejpam-5627	344	16	,	,	PUNCT
ejpam-5627	344	17	γ(f(x2	γ(f(x2	NOUN
ejpam-5627	344	18	)	)	PUNCT
ejpam-5627	344	19	)	)	PUNCT
ejpam-5627	344	20	}	}	PUNCT
ejpam-5627	344	21	=	=	SYM
ejpam-5627	345	1	max{γ(y1	max{γ(y1	NOUN
ejpam-5627	345	2	)	)	PUNCT
ejpam-5627	345	3	,	,	PUNCT
ejpam-5627	345	4	γ(y2	γ(y2	NOUN
ejpam-5627	345	5	)	)	PUNCT
ejpam-5627	345	6	}	}	PUNCT
ejpam-5627	345	7	.	.	PUNCT
ejpam-5627	346	1	hence	hence	ADV
ejpam-5627	346	2	,	,	PUNCT
ejpam-5627	346	3	b	b	X
ejpam-5627	346	4	=	=	SYM
ejpam-5627	346	5	(	(	PUNCT
ejpam-5627	346	6	b,µ	b,µ	PROPN
ejpam-5627	346	7	,	,	PUNCT
ejpam-5627	346	8	γ	γ	PROPN
ejpam-5627	346	9	)	)	PUNCT
ejpam-5627	346	10	is	be	AUX
ejpam-5627	346	11	an	an	DET
ejpam-5627	346	12	intuitionistic	intuitionistic	ADJ
ejpam-5627	346	13	fuzzy	fuzzy	ADJ
ejpam-5627	346	14	sup	sup	NOUN
ejpam-5627	346	15	-	-	PUNCT
ejpam-5627	346	16	subalgebra	subalgebra	NOUN
ejpam-5627	346	17	of	of	ADP
ejpam-5627	346	18	b.	b.	PROPN
ejpam-5627	346	19	4	4	NUM
ejpam-5627	346	20	.	.	PUNCT
ejpam-5627	346	21	conclusion	conclusion	NOUN
ejpam-5627	346	22	this	this	DET
ejpam-5627	346	23	study	study	NOUN
ejpam-5627	346	24	introduces	introduce	VERB
ejpam-5627	346	25	the	the	DET
ejpam-5627	346	26	concepts	concept	NOUN
ejpam-5627	346	27	of	of	ADP
ejpam-5627	346	28	intuitionistic	intuitionistic	ADJ
ejpam-5627	346	29	fuzzy	fuzzy	ADJ
ejpam-5627	346	30	sup	sup	NOUN
ejpam-5627	346	31	-	-	PUNCT
ejpam-5627	346	32	subalgebras	subalgebra	NOUN
ejpam-5627	346	33	and	and	CCONJ
ejpam-5627	346	34	level	level	NOUN
ejpam-5627	346	35	sets	set	NOUN
ejpam-5627	346	36	within	within	ADP
ejpam-5627	346	37	sup	sup	NOUN
ejpam-5627	346	38	-	-	PUNCT
ejpam-5627	346	39	algebras	algebra	NOUN
ejpam-5627	346	40	,	,	PUNCT
ejpam-5627	346	41	emphasizing	emphasize	VERB
ejpam-5627	346	42	their	their	PRON
ejpam-5627	346	43	significance	significance	NOUN
ejpam-5627	346	44	in	in	ADP
ejpam-5627	346	45	understanding	understand	VERB
ejpam-5627	346	46	neutrosophic	neutrosophic	ADJ
ejpam-5627	346	47	logic	logic	NOUN
ejpam-5627	346	48	in	in	ADP
ejpam-5627	346	49	this	this	DET
ejpam-5627	346	50	context	context	NOUN
ejpam-5627	346	51	.	.	PUNCT
ejpam-5627	347	1	we	we	PRON
ejpam-5627	347	2	establish	establish	VERB
ejpam-5627	347	3	a	a	DET
ejpam-5627	347	4	crucial	crucial	ADJ
ejpam-5627	347	5	relationship	relationship	NOUN
ejpam-5627	347	6	between	between	ADP
ejpam-5627	347	7	subalgebras	subalgebra	NOUN
ejpam-5627	347	8	and	and	CCONJ
ejpam-5627	347	9	level	level	NOUN
ejpam-5627	347	10	sets	set	NOUN
ejpam-5627	347	11	,	,	PUNCT
ejpam-5627	347	12	demonstrating	demonstrate	VERB
ejpam-5627	347	13	that	that	SCONJ
ejpam-5627	347	14	the	the	DET
ejpam-5627	347	15	level	level	NOUN
ejpam-5627	347	16	set	set	NOUN
ejpam-5627	347	17	of	of	ADP
ejpam-5627	347	18	an	an	DET
ejpam-5627	347	19	intuitionistic	intuitionistic	ADJ
ejpam-5627	347	20	fuzzy	fuzzy	ADJ
ejpam-5627	347	21	sup	sup	NOUN
ejpam-5627	347	22	-	-	PUNCT
ejpam-5627	347	23	subalgebra	subalgebra	NOUN
ejpam-5627	347	24	is	be	AUX
ejpam-5627	347	25	also	also	ADV
ejpam-5627	347	26	a	a	DET
ejpam-5627	347	27	subalgebra	subalgebra	NOUN
ejpam-5627	347	28	,	,	PUNCT
ejpam-5627	347	29	and	and	CCONJ
ejpam-5627	347	30	vice	vice	ADV
ejpam-5627	347	31	versa	versa	ADV
ejpam-5627	347	32	.	.	PUNCT
ejpam-5627	348	1	furthermore	furthermore	ADV
ejpam-5627	348	2	,	,	PUNCT
ejpam-5627	348	3	we	we	PRON
ejpam-5627	348	4	show	show	VERB
ejpam-5627	348	5	that	that	SCONJ
ejpam-5627	348	6	the	the	DET
ejpam-5627	348	7	collection	collection	NOUN
ejpam-5627	348	8	of	of	ADP
ejpam-5627	348	9	all	all	DET
ejpam-5627	348	10	intuitionistic	intuitionistic	ADJ
ejpam-5627	348	11	fuzzy	fuzzy	ADJ
ejpam-5627	348	12	sup	sup	NOUN
ejpam-5627	348	13	-	-	PUNCT
ejpam-5627	348	14	subalgebras	subalgebras	NOUN
ejpam-5627	348	15	in	in	ADP
ejpam-5627	348	16	an	an	DET
ejpam-5627	348	17	sup	sup	ADJ
ejpam-5627	348	18	-	-	PUNCT
ejpam-5627	348	19	algebra	algebra	NOUN
ejpam-5627	348	20	forms	form	VERB
ejpam-5627	348	21	a	a	DET
ejpam-5627	348	22	complete	complete	ADJ
ejpam-5627	348	23	distributive	distributive	ADJ
ejpam-5627	348	24	lattice	lattice	NOUN
ejpam-5627	348	25	.	.	PUNCT
ejpam-5627	349	1	additionally	additionally	ADV
ejpam-5627	349	2	,	,	PUNCT
ejpam-5627	349	3	we	we	PRON
ejpam-5627	349	4	highlight	highlight	VERB
ejpam-5627	349	5	that	that	SCONJ
ejpam-5627	349	6	while	while	SCONJ
ejpam-5627	349	7	every	every	DET
ejpam-5627	349	8	intuitionistic	intuitionistic	ADJ
ejpam-5627	349	9	fuzzy	fuzzy	ADJ
ejpam-5627	349	10	sup	sup	NOUN
ejpam-5627	349	11	-	-	PUNCT
ejpam-5627	349	12	ideal	ideal	NOUN
ejpam-5627	349	13	is	be	AUX
ejpam-5627	349	14	an	an	DET
ejpam-5627	349	15	intuitionistic	intuitionistic	ADJ
ejpam-5627	349	16	fuzzy	fuzzy	ADJ
ejpam-5627	349	17	sup	sup	NOUN
ejpam-5627	349	18	-	-	PUNCT
ejpam-5627	349	19	subalgebra	subalgebra	NOUN
ejpam-5627	349	20	,	,	PUNCT
ejpam-5627	349	21	the	the	DET
ejpam-5627	349	22	reverse	reverse	NOUN
ejpam-5627	349	23	does	do	AUX
ejpam-5627	349	24	not	not	PART
ejpam-5627	349	25	hold	hold	VERB
ejpam-5627	349	26	true	true	ADJ
ejpam-5627	349	27	,	,	PUNCT
ejpam-5627	349	28	thereby	thereby	ADV
ejpam-5627	349	29	illustrating	illustrate	VERB
ejpam-5627	349	30	the	the	DET
ejpam-5627	349	31	unique	unique	ADJ
ejpam-5627	349	32	characteristics	characteristic	NOUN
ejpam-5627	349	33	of	of	ADP
ejpam-5627	349	34	intuitionistic	intuitionistic	ADJ
ejpam-5627	349	35	fuzzy	fuzzy	ADJ
ejpam-5627	349	36	sup	sup	NOUN
ejpam-5627	349	37	-	-	PUNCT
ejpam-5627	349	38	ideals	ideal	NOUN
ejpam-5627	349	39	within	within	ADP
ejpam-5627	349	40	this	this	DET
ejpam-5627	349	41	algebraic	algebraic	ADJ
ejpam-5627	349	42	structure	structure	NOUN
ejpam-5627	349	43	.	.	PUNCT
ejpam-5627	350	1	acknowledgements	acknowledgement	NOUN
ejpam-5627	350	2	this	this	DET
ejpam-5627	350	3	research	research	NOUN
ejpam-5627	350	4	was	be	AUX
ejpam-5627	350	5	supported	support	VERB
ejpam-5627	350	6	by	by	ADP
ejpam-5627	350	7	university	university	NOUN
ejpam-5627	350	8	of	of	ADP
ejpam-5627	350	9	phayao	phayao	NOUN
ejpam-5627	350	10	and	and	CCONJ
ejpam-5627	350	11	thailand	thailand	PROPN
ejpam-5627	350	12	science	science	PROPN
ejpam-5627	350	13	research	research	PROPN
ejpam-5627	350	14	and	and	CCONJ
ejpam-5627	350	15	innovation	innovation	NOUN
ejpam-5627	350	16	fund	fund	NOUN
ejpam-5627	350	17	(	(	PUNCT
ejpam-5627	350	18	fundamental	fundamental	ADJ
ejpam-5627	350	19	fund	fund	NOUN
ejpam-5627	350	20	2025	2025	NUM
ejpam-5627	350	21	,	,	PUNCT
ejpam-5627	350	22	grant	grant	VERB
ejpam-5627	350	23	no	no	NOUN
ejpam-5627	350	24	.	.	PROPN
ejpam-5627	351	1	5027/2567	5027/2567	NUM
ejpam-5627	351	2	)	)	PUNCT
ejpam-5627	351	3	.	.	PUNCT
ejpam-5627	352	1	references	reference	NOUN
ejpam-5627	352	2	[	[	X
ejpam-5627	352	3	1	1	NUM
ejpam-5627	352	4	]	]	PUNCT
ejpam-5627	352	5	a.	a.	NOUN
ejpam-5627	352	6	k.	k.	PROPN
ejpam-5627	352	7	adak	adak	PROPN
ejpam-5627	352	8	,	,	PUNCT
ejpam-5627	352	9	m.	m.	NOUN
ejpam-5627	352	10	bhowmik	bhowmik	ADJ
ejpam-5627	352	11	,	,	PUNCT
ejpam-5627	352	12	and	and	CCONJ
ejpam-5627	352	13	m.	m.	NOUN
ejpam-5627	352	14	pal	pal	NOUN
ejpam-5627	352	15	.	.	PUNCT
ejpam-5627	353	1	some	some	DET
ejpam-5627	353	2	properties	property	NOUN
ejpam-5627	353	3	of	of	ADP
ejpam-5627	353	4	generalized	generalized	ADJ
ejpam-5627	353	5	intuitionistic	intuitionistic	ADJ
ejpam-5627	353	6	fuzzy	fuzzy	ADJ
ejpam-5627	353	7	nilpotent	nilpotent	ADJ
ejpam-5627	353	8	matrices	matrix	NOUN
ejpam-5627	353	9	over	over	ADP
ejpam-5627	353	10	distributive	distributive	ADJ
ejpam-5627	353	11	lattice	lattice	NOUN
ejpam-5627	353	12	.	.	PUNCT
ejpam-5627	354	1	fuzzy	fuzzy	PROPN
ejpam-5627	354	2	inf	inf	PROPN
ejpam-5627	354	3	.	.	PUNCT
ejpam-5627	355	1	eng	eng	PROPN
ejpam-5627	355	2	.	.	PROPN
ejpam-5627	355	3	,	,	PUNCT
ejpam-5627	355	4	4(4):371–387	4(4):371–387	NOUN
ejpam-5627	355	5	,	,	PUNCT
ejpam-5627	355	6	2012	2012	NUM
ejpam-5627	355	7	.	.	PUNCT
ejpam-5627	356	1	[	[	X
ejpam-5627	356	2	2	2	NUM
ejpam-5627	356	3	]	]	PUNCT
ejpam-5627	356	4	a.	a.	NOUN
ejpam-5627	356	5	k.	k.	PROPN
ejpam-5627	356	6	adak	adak	PROPN
ejpam-5627	356	7	,	,	PUNCT
ejpam-5627	356	8	nilkamal	nilkamal	NOUN
ejpam-5627	356	9	,	,	PUNCT
ejpam-5627	356	10	and	and	CCONJ
ejpam-5627	356	11	k.	k.	PROPN
ejpam-5627	356	12	n.	n.	PROPN
ejpam-5627	356	13	srivastava	srivastava	PROPN
ejpam-5627	356	14	.	.	PUNCT
ejpam-5627	357	1	new	new	ADJ
ejpam-5627	357	2	ranking	ranking	NOUN
ejpam-5627	357	3	approach	approach	NOUN
ejpam-5627	357	4	to	to	PART
ejpam-5627	357	5	solve	solve	VERB
ejpam-5627	357	6	mcdm	mcdm	ADJ
ejpam-5627	357	7	problems	problem	NOUN
ejpam-5627	357	8	with	with	ADP
ejpam-5627	357	9	generalized	generalized	ADJ
ejpam-5627	357	10	intuitionistic	intuitionistic	ADJ
ejpam-5627	357	11	fuzzy	fuzzy	ADJ
ejpam-5627	357	12	information	information	NOUN
ejpam-5627	357	13	,	,	PUNCT
ejpam-5627	357	14	real	real	ADJ
ejpam-5627	357	15	life	life	NOUN
ejpam-5627	357	16	applications	application	NOUN
ejpam-5627	357	17	of	of	ADP
ejpam-5627	357	18	multiple	multiple	ADJ
ejpam-5627	357	19	criteria	criterion	NOUN
ejpam-5627	357	20	decision	decision	NOUN
ejpam-5627	357	21	making	make	VERB
ejpam-5627	357	22	techniques	technique	NOUN
ejpam-5627	357	23	in	in	ADP
ejpam-5627	357	24	fuzzy	fuzzy	ADJ
ejpam-5627	357	25	domain	domain	NOUN
ejpam-5627	357	26	,	,	PUNCT
ejpam-5627	357	27	studies	study	NOUN
ejpam-5627	357	28	in	in	ADP
ejpam-5627	357	29	fuzziness	fuzziness	NOUN
ejpam-5627	357	30	and	and	CCONJ
ejpam-5627	357	31	soft	soft	ADJ
ejpam-5627	357	32	computing	computing	NOUN
ejpam-5627	357	33	,	,	PUNCT
ejpam-5627	357	34	volume	volume	NOUN
ejpam-5627	357	35	420	420	NUM
ejpam-5627	357	36	.	.	PUNCT
ejpam-5627	358	1	springer	springer	NOUN
ejpam-5627	358	2	,	,	PUNCT
ejpam-5627	358	3	singapore	singapore	PROPN
ejpam-5627	358	4	,	,	PUNCT
ejpam-5627	358	5	2022	2022	NUM
ejpam-5627	358	6	.	.	PUNCT
ejpam-5627	359	1	[	[	X
ejpam-5627	359	2	3	3	X
ejpam-5627	359	3	]	]	PUNCT
ejpam-5627	359	4	k.	k.	PROPN
ejpam-5627	359	5	t.	t.	PROPN
ejpam-5627	359	6	atanassov	atanassov	PROPN
ejpam-5627	359	7	.	.	PUNCT
ejpam-5627	360	1	intuitionistic	intuitionistic	ADJ
ejpam-5627	360	2	fuzzy	fuzzy	ADJ
ejpam-5627	360	3	sets	set	NOUN
ejpam-5627	360	4	.	.	PUNCT
ejpam-5627	361	1	fuzzy	fuzzy	ADJ
ejpam-5627	361	2	sets	set	NOUN
ejpam-5627	361	3	syst	syst	PROPN
ejpam-5627	361	4	.	.	PUNCT
ejpam-5627	361	5	,	,	PUNCT
ejpam-5627	361	6	20(1):87–96	20(1):87–96	NUM
ejpam-5627	361	7	,	,	PUNCT
ejpam-5627	361	8	1986	1986	NUM
ejpam-5627	361	9	.	.	PUNCT
ejpam-5627	362	1	[	[	X
ejpam-5627	362	2	4	4	NUM
ejpam-5627	362	3	]	]	PUNCT
ejpam-5627	362	4	a.	a.	NOUN
ejpam-5627	362	5	ebrahimnejad	ebrahimnejad	PROPN
ejpam-5627	362	6	,	,	PUNCT
ejpam-5627	362	7	a.	a.	PROPN
ejpam-5627	362	8	k.	k.	PROPN
ejpam-5627	362	9	adak	adak	PROPN
ejpam-5627	362	10	,	,	PUNCT
ejpam-5627	362	11	and	and	CCONJ
ejpam-5627	362	12	e.	e.	PROPN
ejpam-5627	362	13	b.	b.	PROPN
ejpam-5627	362	14	jamkhaneh	jamkhaneh	PROPN
ejpam-5627	362	15	.	.	PUNCT
ejpam-5627	363	1	eigenvalue	eigenvalue	PROPN
ejpam-5627	363	2	of	of	ADP
ejpam-5627	363	3	intuitionistic	intuitionistic	ADJ
ejpam-5627	363	4	fuzzy	fuzzy	ADJ
ejpam-5627	363	5	matrices	matrix	NOUN
ejpam-5627	363	6	over	over	ADP
ejpam-5627	363	7	distributive	distributive	ADJ
ejpam-5627	363	8	lattice	lattice	NOUN
ejpam-5627	363	9	.	.	PUNCT
ejpam-5627	364	1	int	int	NOUN
ejpam-5627	364	2	.	.	PUNCT
ejpam-5627	365	1	j.	j.	PROPN
ejpam-5627	365	2	fuzzy	fuzzy	PROPN
ejpam-5627	365	3	syst	syst	PROPN
ejpam-5627	365	4	.	.	PUNCT
ejpam-5627	366	1	appl	appl	PROPN
ejpam-5627	366	2	.	.	PROPN
ejpam-5627	366	3	,	,	PUNCT
ejpam-5627	366	4	8(1):1–18	8(1):1–18	NUM
ejpam-5627	366	5	,	,	PUNCT
ejpam-5627	366	6	2019	2019	NUM
ejpam-5627	366	7	.	.	PUNCT
ejpam-5627	367	1	[	[	X
ejpam-5627	367	2	5	5	NUM
ejpam-5627	367	3	]	]	PUNCT
ejpam-5627	367	4	a.	a.	NOUN
ejpam-5627	367	5	iampan	iampan	PROPN
ejpam-5627	367	6	.	.	PUNCT
ejpam-5627	368	1	a	a	DET
ejpam-5627	368	2	new	new	ADJ
ejpam-5627	368	3	branch	branch	NOUN
ejpam-5627	368	4	of	of	ADP
ejpam-5627	368	5	the	the	DET
ejpam-5627	368	6	logical	logical	ADJ
ejpam-5627	368	7	algebra	algebra	NOUN
ejpam-5627	368	8	:	:	PUNCT
ejpam-5627	368	9	up	up	ADP
ejpam-5627	368	10	-	-	PUNCT
ejpam-5627	368	11	algebras	algebras	X
ejpam-5627	368	12	.	.	PUNCT
ejpam-5627	369	1	j.	j.	PROPN
ejpam-5627	369	2	algebra	algebra	PROPN
ejpam-5627	369	3	relat	relat	PROPN
ejpam-5627	369	4	.	.	PUNCT
ejpam-5627	370	1	top	top	PROPN
ejpam-5627	370	2	.	.	PROPN
ejpam-5627	370	3	,	,	PUNCT
ejpam-5627	370	4	5(1):35–54	5(1):35–54	NUM
ejpam-5627	370	5	,	,	PUNCT
ejpam-5627	370	6	2017	2017	NUM
ejpam-5627	370	7	.	.	PUNCT
ejpam-5627	371	1	[	[	X
ejpam-5627	371	2	6	6	NUM
ejpam-5627	371	3	]	]	X
ejpam-5627	371	4	b.	b.	PROPN
ejpam-5627	371	5	kesorn	kesorn	PROPN
ejpam-5627	371	6	,	,	PUNCT
ejpam-5627	371	7	k.	k.	PROPN
ejpam-5627	371	8	maimun	maimun	PROPN
ejpam-5627	371	9	,	,	PUNCT
ejpam-5627	371	10	w.	w.	PROPN
ejpam-5627	371	11	ratbandan	ratbandan	PROPN
ejpam-5627	371	12	,	,	PUNCT
ejpam-5627	371	13	and	and	CCONJ
ejpam-5627	371	14	a.	a.	NOUN
ejpam-5627	371	15	iampan	iampan	PROPN
ejpam-5627	371	16	.	.	PUNCT
ejpam-5627	372	1	intuitionistic	intuitionistic	ADJ
ejpam-5627	372	2	fuzzy	fuzzy	ADJ
ejpam-5627	372	3	sets	set	NOUN
ejpam-5627	372	4	in	in	ADP
ejpam-5627	372	5	up	up	ADP
ejpam-5627	372	6	-	-	PUNCT
ejpam-5627	372	7	algebras	algebras	X
ejpam-5627	372	8	.	.	PUNCT
ejpam-5627	373	1	ital	ital	PROPN
ejpam-5627	373	2	.	.	PUNCT
ejpam-5627	374	1	j.	j.	PROPN
ejpam-5627	374	2	pure	pure	PROPN
ejpam-5627	374	3	appl	appl	PROPN
ejpam-5627	374	4	.	.	PUNCT
ejpam-5627	374	5	math	math	PROPN
ejpam-5627	374	6	.	.	PUNCT
ejpam-5627	374	7	,	,	PUNCT
ejpam-5627	374	8	34(1):339–364	34(1):339–364	NUM
ejpam-5627	374	9	,	,	PUNCT
ejpam-5627	374	10	2015	2015	NUM
ejpam-5627	374	11	.	.	PUNCT
ejpam-5627	375	1	n.	n.	PROPN
ejpam-5627	375	2	rajesh	rajesh	PROPN
ejpam-5627	375	3	,	,	PUNCT
ejpam-5627	375	4	t.	t.	PROPN
ejpam-5627	375	5	oner	oner	NOUN
ejpam-5627	375	6	,	,	PUNCT
ejpam-5627	375	7	a.	a.	NOUN
ejpam-5627	375	8	iampan	iampan	PROPN
ejpam-5627	375	9	,	,	PUNCT
ejpam-5627	375	10	i.	i.	PROPN
ejpam-5627	375	11	senturk	senturk	PROPN
ejpam-5627	375	12	/	/	SYM
ejpam-5627	375	13	eur	eur	PROPN
ejpam-5627	375	14	.	.	PUNCT
ejpam-5627	376	1	j.	j.	PROPN
ejpam-5627	376	2	pure	pure	PROPN
ejpam-5627	376	3	appl	appl	PROPN
ejpam-5627	376	4	.	.	PROPN
ejpam-5627	376	5	math	math	PROPN
ejpam-5627	376	6	,	,	PUNCT
ejpam-5627	376	7	18	18	NUM
ejpam-5627	376	8	(	(	PUNCT
ejpam-5627	376	9	1	1	NUM
ejpam-5627	376	10	)	)	PUNCT
ejpam-5627	376	11	(	(	PUNCT
ejpam-5627	376	12	2025	2025	NUM
ejpam-5627	376	13	)	)	PUNCT
ejpam-5627	376	14	,	,	PUNCT
ejpam-5627	376	15	5627	5627	NUM
ejpam-5627	376	16	15	15	NUM
ejpam-5627	376	17	of	of	ADP
ejpam-5627	376	18	15	15	NUM
ejpam-5627	376	19	[	[	X
ejpam-5627	376	20	7	7	NUM
ejpam-5627	376	21	]	]	PUNCT
ejpam-5627	376	22	t.	t.	NOUN
ejpam-5627	376	23	oner	oner	NOUN
ejpam-5627	376	24	and	and	CCONJ
ejpam-5627	376	25	t.	t.	PROPN
ejpam-5627	376	26	katican	katican	PROPN
ejpam-5627	376	27	.	.	PUNCT
ejpam-5627	377	1	on	on	ADP
ejpam-5627	377	2	sheffer	sheffer	PROPN
ejpam-5627	377	3	stroke	stroke	PROPN
ejpam-5627	377	4	up	up	ADP
ejpam-5627	377	5	-	-	PUNCT
ejpam-5627	377	6	algebras	algebras	X
ejpam-5627	377	7	.	.	PUNCT
ejpam-5627	378	1	discuss	discuss	PROPN
ejpam-5627	378	2	.	.	PUNCT
ejpam-5627	378	3	math	math	PROPN
ejpam-5627	378	4	.	.	PUNCT
ejpam-5627	378	5	,	,	PUNCT
ejpam-5627	379	1	gen	gen	PROPN
ejpam-5627	379	2	.	.	PROPN
ejpam-5627	379	3	algebra	algebra	PROPN
ejpam-5627	379	4	appl	appl	PROPN
ejpam-5627	379	5	.	.	PROPN
ejpam-5627	379	6	,	,	PUNCT
ejpam-5627	379	7	41:381–394	41:381–394	NUM
ejpam-5627	379	8	,	,	PUNCT
ejpam-5627	379	9	2021	2021	NUM
ejpam-5627	379	10	.	.	PUNCT
ejpam-5627	380	1	[	[	X
ejpam-5627	380	2	8	8	NUM
ejpam-5627	380	3	]	]	PUNCT
ejpam-5627	380	4	t.	t.	NOUN
ejpam-5627	380	5	oner	oner	NOUN
ejpam-5627	380	6	and	and	CCONJ
ejpam-5627	380	7	t.	t.	PROPN
ejpam-5627	380	8	katican	katican	PROPN
ejpam-5627	380	9	.	.	PUNCT
ejpam-5627	381	1	on	on	ADP
ejpam-5627	381	2	ideals	ideal	NOUN
ejpam-5627	381	3	of	of	ADP
ejpam-5627	381	4	sheffer	sheffer	NOUN
ejpam-5627	381	5	stroke	stroke	NOUN
ejpam-5627	381	6	up	up	ADP
ejpam-5627	381	7	-	-	PUNCT
ejpam-5627	381	8	algebras	algebras	X
ejpam-5627	381	9	.	.	PUNCT
ejpam-5627	382	1	j.	j.	PROPN
ejpam-5627	382	2	discrete	discrete	PROPN
ejpam-5627	382	3	math	math	PROPN
ejpam-5627	382	4	.	.	PUNCT
ejpam-5627	383	1	sci	sci	PROPN
ejpam-5627	383	2	.	.	PROPN
ejpam-5627	383	3	cryptogr	cryptogr	PROPN
ejpam-5627	383	4	.	.	PUNCT
ejpam-5627	383	5	,	,	PUNCT
ejpam-5627	383	6	26(8):2257–2271	26(8):2257–2271	NUM
ejpam-5627	383	7	,	,	PUNCT
ejpam-5627	383	8	2023	2023	NUM
ejpam-5627	383	9	.	.	PUNCT
ejpam-5627	384	1	[	[	X
ejpam-5627	384	2	9	9	NUM
ejpam-5627	384	3	]	]	SYM
ejpam-5627	384	4	l.	l.	PROPN
ejpam-5627	384	5	c.	c.	PROPN
ejpam-5627	384	6	platil	platil	PROPN
ejpam-5627	384	7	and	and	CCONJ
ejpam-5627	384	8	g.	g.	PROPN
ejpam-5627	384	9	c.	c.	PROPN
ejpam-5627	384	10	petalcorin	petalcorin	PROPN
ejpam-5627	384	11	.	.	PUNCT
ejpam-5627	385	1	fuzzy	fuzzy	ADJ
ejpam-5627	385	2	γ	γ	NOUN
ejpam-5627	385	3	-	-	NOUN
ejpam-5627	385	4	semimodules	semimodule	NOUN
ejpam-5627	385	5	over	over	ADP
ejpam-5627	385	6	γ	γ	NOUN
ejpam-5627	385	7	-	-	NOUN
ejpam-5627	385	8	semirings	semiring	NOUN
ejpam-5627	385	9	.	.	PUNCT
ejpam-5627	386	1	j.	j.	PROPN
ejpam-5627	386	2	anal	anal	PROPN
ejpam-5627	386	3	.	.	PUNCT
ejpam-5627	387	1	appl	appl	PROPN
ejpam-5627	387	2	.	.	PROPN
ejpam-5627	387	3	,	,	PUNCT
ejpam-5627	387	4	15:71–83	15:71–83	NUM
ejpam-5627	387	5	,	,	PUNCT
ejpam-5627	387	6	2017	2017	NUM
ejpam-5627	387	7	.	.	PUNCT
ejpam-5627	388	1	[	[	X
ejpam-5627	388	2	10	10	NUM
ejpam-5627	388	3	]	]	X
ejpam-5627	388	4	l.	l.	PROPN
ejpam-5627	388	5	c.	c.	PROPN
ejpam-5627	388	6	platil	platil	PROPN
ejpam-5627	388	7	and	and	CCONJ
ejpam-5627	388	8	t.	t.	PROPN
ejpam-5627	388	9	tanaka	tanaka	PROPN
ejpam-5627	388	10	.	.	PUNCT
ejpam-5627	389	1	multi	multi	ADJ
ejpam-5627	389	2	-	-	ADJ
ejpam-5627	389	3	criteria	criteria	ADJ
ejpam-5627	389	4	evaluation	evaluation	NOUN
ejpam-5627	389	5	for	for	ADP
ejpam-5627	389	6	intuitionistic	intuitionistic	ADJ
ejpam-5627	389	7	fuzzy	fuzzy	ADJ
ejpam-5627	389	8	sets	set	NOUN
ejpam-5627	389	9	based	base	VERB
ejpam-5627	389	10	on	on	ADP
ejpam-5627	389	11	set	set	NOUN
ejpam-5627	389	12	-	-	PUNCT
ejpam-5627	389	13	relations	relation	NOUN
ejpam-5627	389	14	.	.	PUNCT
ejpam-5627	390	1	nihonkai	nihonkai	PROPN
ejpam-5627	390	2	math	math	PROPN
ejpam-5627	390	3	.	.	PUNCT
ejpam-5627	391	1	j.	j.	PROPN
ejpam-5627	391	2	,	,	PUNCT
ejpam-5627	391	3	34(1):1–18	34(1):1–18	NUM
ejpam-5627	391	4	,	,	PUNCT
ejpam-5627	391	5	2023	2023	NUM
ejpam-5627	391	6	.	.	PUNCT
ejpam-5627	392	1	[	[	X
ejpam-5627	392	2	11	11	NUM
ejpam-5627	392	3	]	]	X
ejpam-5627	392	4	l.	l.	PROPN
ejpam-5627	392	5	c.	c.	PROPN
ejpam-5627	392	6	platil	platil	PROPN
ejpam-5627	392	7	and	and	CCONJ
ejpam-5627	392	8	j.	j.	PROPN
ejpam-5627	392	9	p.	p.	PROPN
ejpam-5627	392	10	vilela	vilela	PROPN
ejpam-5627	392	11	.	.	PUNCT
ejpam-5627	393	1	on	on	ADP
ejpam-5627	393	2	anti	anti	X
ejpam-5627	393	3	fuzzy	fuzzy	ADJ
ejpam-5627	393	4	sub	sub	NOUN
ejpam-5627	393	5	ks	k	NOUN
ejpam-5627	393	6	-	-	PUNCT
ejpam-5627	393	7	semigroups	semigroup	NOUN
ejpam-5627	393	8	.	.	PUNCT
ejpam-5627	394	1	asia	asia	PROPN
ejpam-5627	394	2	-	-	PUNCT
ejpam-5627	394	3	pac	pac	PROPN
ejpam-5627	394	4	.	.	PUNCT
ejpam-5627	394	5	j.	j.	PROPN
ejpam-5627	394	6	sci	sci	PROPN
ejpam-5627	394	7	.	.	PROPN
ejpam-5627	394	8	math	math	PROPN
ejpam-5627	394	9	.	.	PUNCT
ejpam-5627	395	1	eng	eng	PROPN
ejpam-5627	395	2	.	.	PROPN
ejpam-5627	395	3	,	,	PUNCT
ejpam-5627	395	4	3(1):7–10	3(1):7–10	NUM
ejpam-5627	395	5	,	,	PUNCT
ejpam-5627	395	6	2015	2015	NUM
ejpam-5627	395	7	.	.	PUNCT
ejpam-5627	396	1	[	[	X
ejpam-5627	396	2	12	12	NUM
ejpam-5627	396	3	]	]	X
ejpam-5627	396	4	h.	h.	PROPN
ejpam-5627	396	5	m.	m.	PROPN
ejpam-5627	396	6	sheffer	sheffer	PROPN
ejpam-5627	396	7	.	.	PUNCT
ejpam-5627	397	1	a	a	DET
ejpam-5627	397	2	set	set	NOUN
ejpam-5627	397	3	of	of	ADP
ejpam-5627	397	4	five	five	NUM
ejpam-5627	397	5	independent	independent	ADJ
ejpam-5627	397	6	postulates	postulate	NOUN
ejpam-5627	397	7	for	for	ADP
ejpam-5627	397	8	boolean	boolean	ADJ
ejpam-5627	397	9	algebras	algebra	NOUN
ejpam-5627	397	10	,	,	PUNCT
ejpam-5627	397	11	with	with	ADP
ejpam-5627	397	12	application	application	NOUN
ejpam-5627	397	13	to	to	ADP
ejpam-5627	397	14	logical	logical	ADJ
ejpam-5627	397	15	constants	constant	NOUN
ejpam-5627	397	16	.	.	PUNCT
ejpam-5627	398	1	trans	trans	AUX
ejpam-5627	398	2	.	.	PUNCT
ejpam-5627	398	3	am	be	AUX
ejpam-5627	398	4	.	.	PUNCT
ejpam-5627	399	1	math	math	NOUN
ejpam-5627	399	2	.	.	PUNCT
ejpam-5627	400	1	soc	soc	PROPN
ejpam-5627	400	2	.	.	PUNCT
ejpam-5627	400	3	,	,	PUNCT
ejpam-5627	400	4	14(4):481–488	14(4):481–488	NUM
ejpam-5627	400	5	,	,	PUNCT
ejpam-5627	400	6	1913	1913	NUM
ejpam-5627	400	7	.	.	PUNCT
ejpam-5627	401	1	[	[	X
ejpam-5627	401	2	13	13	NUM
ejpam-5627	401	3	]	]	PUNCT
ejpam-5627	401	4	l.	l.	PROPN
ejpam-5627	401	5	a.	a.	PROPN
ejpam-5627	401	6	zadeh	zadeh	PROPN
ejpam-5627	401	7	.	.	PUNCT
ejpam-5627	401	8	fuzzy	fuzzy	ADJ
ejpam-5627	401	9	sets	set	NOUN
ejpam-5627	401	10	.	.	PUNCT
ejpam-5627	402	1	inf	inf	PROPN
ejpam-5627	402	2	.	.	PUNCT
ejpam-5627	402	3	control	control	PROPN
ejpam-5627	402	4	,	,	PUNCT
ejpam-5627	402	5	8(3):338–353	8(3):338–353	NUM
ejpam-5627	402	6	,	,	PUNCT
ejpam-5627	402	7	1965	1965	NUM
ejpam-5627	402	8	.	.	PUNCT