id	sid	tid	token	lemma	pos
ejpam-5385	1	1	european	european	PROPN
ejpam-5385	1	2	journal	journal	PROPN
ejpam-5385	1	3	of	of	ADP
ejpam-5385	1	4	pure	pure	ADJ
ejpam-5385	1	5	and	and	CCONJ
ejpam-5385	1	6	applied	apply	VERB
ejpam-5385	1	7	mathematics	mathematic	NOUN
ejpam-5385	1	8	vol	vol	NOUN
ejpam-5385	1	9	.	.	PROPN
ejpam-5385	2	1	17	17	NUM
ejpam-5385	2	2	,	,	PUNCT
ejpam-5385	2	3	no	no	INTJ
ejpam-5385	2	4	.	.	NOUN
ejpam-5385	2	5	4	4	NUM
ejpam-5385	2	6	,	,	PUNCT
ejpam-5385	2	7	2024	2024	NUM
ejpam-5385	2	8	,	,	PUNCT
ejpam-5385	2	9	3291	3291	NUM
ejpam-5385	2	10	-	-	SYM
ejpam-5385	2	11	3303	3303	NUM
ejpam-5385	2	12	issn	issn	PROPN
ejpam-5385	2	13	1307	1307	NUM
ejpam-5385	2	14	-	-	SYM
ejpam-5385	2	15	5543	5543	NUM
ejpam-5385	2	16	–	–	PUNCT
ejpam-5385	3	1	ejpam.com	ejpam.com	X
ejpam-5385	3	2	published	publish	VERB
ejpam-5385	3	3	by	by	ADP
ejpam-5385	3	4	new	new	PROPN
ejpam-5385	3	5	york	york	PROPN
ejpam-5385	3	6	business	business	PROPN
ejpam-5385	3	7	global	global	PROPN
ejpam-5385	3	8	on	on	ADP
ejpam-5385	3	9	lie	lie	NOUN
ejpam-5385	3	10	homomorphisms	homomorphism	NOUN
ejpam-5385	3	11	of	of	ADP
ejpam-5385	3	12	complex	complex	ADJ
ejpam-5385	3	13	intuitionistic	intuitionistic	ADJ
ejpam-5385	3	14	fuzzy	fuzzy	ADJ
ejpam-5385	3	15	lie	lie	NOUN
ejpam-5385	3	16	algebras	algebras	PROPN
ejpam-5385	3	17	shadi	shadi	PROPN
ejpam-5385	3	18	m.	m.	PROPN
ejpam-5385	3	19	shaqaqha1,∗	shaqaqha1,∗	PROPN
ejpam-5385	3	20	,	,	PUNCT
ejpam-5385	3	21	mounther	mounther	NOUN
ejpam-5385	3	22	y.	y.	PROPN
ejpam-5385	3	23	al	al	PROPN
ejpam-5385	3	24	-	-	PUNCT
ejpam-5385	3	25	deiakeh1	deiakeh1	PROPN
ejpam-5385	3	26	1	1	NUM
ejpam-5385	3	27	department	department	NOUN
ejpam-5385	3	28	of	of	ADP
ejpam-5385	3	29	mathematics	mathematic	NOUN
ejpam-5385	3	30	,	,	PUNCT
ejpam-5385	3	31	yarmouk	yarmouk	CCONJ
ejpam-5385	3	32	university	university	NOUN
ejpam-5385	3	33	,	,	PUNCT
ejpam-5385	3	34	shafiq	shafiq	PROPN
ejpam-5385	3	35	irshidat	irshidat	PROPN
ejpam-5385	3	36	street	street	PROPN
ejpam-5385	3	37	,	,	PUNCT
ejpam-5385	3	38	irbid	irbid	VERB
ejpam-5385	3	39	21163	21163	NUM
ejpam-5385	3	40	,	,	PUNCT
ejpam-5385	3	41	jordan	jordan	PROPN
ejpam-5385	3	42	abstract	abstract	PROPN
ejpam-5385	3	43	.	.	PUNCT
ejpam-5385	4	1	in	in	ADP
ejpam-5385	4	2	this	this	DET
ejpam-5385	4	3	paper	paper	NOUN
ejpam-5385	4	4	,	,	PUNCT
ejpam-5385	4	5	we	we	PRON
ejpam-5385	4	6	investigate	investigate	VERB
ejpam-5385	4	7	the	the	DET
ejpam-5385	4	8	properties	property	NOUN
ejpam-5385	4	9	of	of	ADP
ejpam-5385	4	10	complex	complex	ADJ
ejpam-5385	4	11	intuitionistic	intuitionistic	ADJ
ejpam-5385	4	12	fuzzy	fuzzy	ADJ
ejpam-5385	4	13	lie	lie	NOUN
ejpam-5385	4	14	subalgebras	subalgebra	NOUN
ejpam-5385	4	15	and	and	CCONJ
ejpam-5385	4	16	ideals	ideal	NOUN
ejpam-5385	4	17	under	under	ADP
ejpam-5385	4	18	lie	lie	NOUN
ejpam-5385	4	19	algebra	algebra	NOUN
ejpam-5385	4	20	homomorphisms	homomorphism	NOUN
ejpam-5385	4	21	,	,	PUNCT
ejpam-5385	4	22	focusing	focus	VERB
ejpam-5385	4	23	on	on	ADP
ejpam-5385	4	24	both	both	DET
ejpam-5385	4	25	images	image	NOUN
ejpam-5385	4	26	and	and	CCONJ
ejpam-5385	4	27	inverse	inverse	NOUN
ejpam-5385	4	28	images	image	NOUN
ejpam-5385	4	29	.	.	PUNCT
ejpam-5385	5	1	we	we	PRON
ejpam-5385	5	2	provide	provide	VERB
ejpam-5385	5	3	detailed	detailed	ADJ
ejpam-5385	5	4	proofs	proof	NOUN
ejpam-5385	5	5	for	for	ADP
ejpam-5385	5	6	several	several	ADJ
ejpam-5385	5	7	new	new	ADJ
ejpam-5385	5	8	results	result	NOUN
ejpam-5385	5	9	concerning	concern	VERB
ejpam-5385	5	10	the	the	DET
ejpam-5385	5	11	preservation	preservation	NOUN
ejpam-5385	5	12	of	of	ADP
ejpam-5385	5	13	complex	complex	ADJ
ejpam-5385	5	14	intuitionistic	intuitionistic	ADJ
ejpam-5385	5	15	fuzzy	fuzzy	ADJ
ejpam-5385	5	16	structures	structure	NOUN
ejpam-5385	5	17	through	through	ADP
ejpam-5385	5	18	homomorphisms	homomorphism	NOUN
ejpam-5385	5	19	,	,	PUNCT
ejpam-5385	5	20	and	and	CCONJ
ejpam-5385	5	21	we	we	PRON
ejpam-5385	5	22	introduce	introduce	VERB
ejpam-5385	5	23	additional	additional	ADJ
ejpam-5385	5	24	homomorphismrelated	homomorphismrelate	VERB
ejpam-5385	5	25	properties	property	NOUN
ejpam-5385	5	26	for	for	ADP
ejpam-5385	5	27	these	these	DET
ejpam-5385	5	28	structures	structure	NOUN
ejpam-5385	5	29	.	.	PUNCT
ejpam-5385	6	1	this	this	DET
ejpam-5385	6	2	work	work	NOUN
ejpam-5385	6	3	extends	extend	VERB
ejpam-5385	6	4	known	know	VERB
ejpam-5385	6	5	results	result	NOUN
ejpam-5385	6	6	to	to	ADP
ejpam-5385	6	7	the	the	DET
ejpam-5385	6	8	context	context	NOUN
ejpam-5385	6	9	of	of	ADP
ejpam-5385	6	10	complex	complex	ADJ
ejpam-5385	6	11	intuitionistic	intuitionistic	ADJ
ejpam-5385	6	12	fuzzy	fuzzy	ADJ
ejpam-5385	6	13	lie	lie	NOUN
ejpam-5385	6	14	algebras	algebra	NOUN
ejpam-5385	6	15	,	,	PUNCT
ejpam-5385	6	16	contributing	contribute	VERB
ejpam-5385	6	17	new	new	ADJ
ejpam-5385	6	18	insights	insight	NOUN
ejpam-5385	6	19	into	into	ADP
ejpam-5385	6	20	their	their	PRON
ejpam-5385	6	21	behavior	behavior	NOUN
ejpam-5385	6	22	under	under	ADP
ejpam-5385	6	23	algebraic	algebraic	ADJ
ejpam-5385	6	24	mappings	mapping	NOUN
ejpam-5385	6	25	.	.	PUNCT
ejpam-5385	7	1	2020	2020	NUM
ejpam-5385	7	2	mathematics	mathematic	NOUN
ejpam-5385	7	3	subject	subject	NOUN
ejpam-5385	7	4	classifications	classification	NOUN
ejpam-5385	7	5	:	:	PUNCT
ejpam-5385	7	6	17b99	17b99	NUM
ejpam-5385	7	7	,	,	PUNCT
ejpam-5385	7	8	08a72	08a72	NUM
ejpam-5385	7	9	,	,	PUNCT
ejpam-5385	7	10	03e72	03e72	X
ejpam-5385	7	11	key	key	ADJ
ejpam-5385	7	12	words	word	NOUN
ejpam-5385	7	13	and	and	CCONJ
ejpam-5385	7	14	phrases	phrase	NOUN
ejpam-5385	7	15	:	:	PUNCT
ejpam-5385	7	16	lie	lie	VERB
ejpam-5385	7	17	ideal	ideal	ADJ
ejpam-5385	7	18	,	,	PUNCT
ejpam-5385	7	19	lie	lie	VERB
ejpam-5385	7	20	algebra	algebra	PROPN
ejpam-5385	7	21	homomorphism	homomorphism	NOUN
ejpam-5385	7	22	,	,	PUNCT
ejpam-5385	7	23	fuzzy	fuzzy	ADJ
ejpam-5385	7	24	set	set	NOUN
ejpam-5385	7	25	,	,	PUNCT
ejpam-5385	7	26	fuzzy	fuzzy	ADJ
ejpam-5385	7	27	lie	lie	NOUN
ejpam-5385	7	28	subalgebra	subalgebra	NOUN
ejpam-5385	7	29	,	,	PUNCT
ejpam-5385	7	30	intuitionistic	intuitionistic	ADJ
ejpam-5385	7	31	fuzzy	fuzzy	ADJ
ejpam-5385	7	32	set	set	NOUN
ejpam-5385	7	33	,	,	PUNCT
ejpam-5385	7	34	intuitionistic	intuitionistic	ADJ
ejpam-5385	7	35	fuzzy	fuzzy	ADJ
ejpam-5385	7	36	lie	lie	NOUN
ejpam-5385	7	37	subalgebra	subalgebra	NOUN
ejpam-5385	7	38	,	,	PUNCT
ejpam-5385	7	39	homogeneous	homogeneous	ADJ
ejpam-5385	7	40	complex	complex	ADJ
ejpam-5385	7	41	intuitionistic	intuitionistic	ADJ
ejpam-5385	7	42	fuzzy	fuzzy	ADJ
ejpam-5385	7	43	lie	lie	NOUN
ejpam-5385	7	44	subalgebra	subalgebra	NOUN
ejpam-5385	7	45	,	,	PUNCT
ejpam-5385	7	46	complex	complex	ADJ
ejpam-5385	7	47	intuitionistic	intuitionistic	ADJ
ejpam-5385	7	48	fuzzy	fuzzy	ADJ
ejpam-5385	7	49	lie	lie	NOUN
ejpam-5385	7	50	ideal	ideal	ADJ
ejpam-5385	7	51	1	1	NUM
ejpam-5385	7	52	.	.	PUNCT
ejpam-5385	8	1	introduction	introduction	NOUN
ejpam-5385	8	2	introduced	introduce	VERB
ejpam-5385	8	3	by	by	ADP
ejpam-5385	8	4	lotfi	lotfi	PROPN
ejpam-5385	8	5	zadeh	zadeh	PROPN
ejpam-5385	8	6	in	in	ADP
ejpam-5385	8	7	1965	1965	NUM
ejpam-5385	8	8	,	,	PUNCT
ejpam-5385	8	9	fuzzy	fuzzy	ADJ
ejpam-5385	8	10	sets	set	NOUN
ejpam-5385	8	11	provide	provide	VERB
ejpam-5385	8	12	a	a	DET
ejpam-5385	8	13	mathematical	mathematical	ADJ
ejpam-5385	8	14	framework	framework	NOUN
ejpam-5385	8	15	for	for	ADP
ejpam-5385	8	16	representing	represent	VERB
ejpam-5385	8	17	and	and	CCONJ
ejpam-5385	8	18	managing	manage	VERB
ejpam-5385	8	19	imprecise	imprecise	ADV
ejpam-5385	8	20	and	and	CCONJ
ejpam-5385	8	21	uncertain	uncertain	ADJ
ejpam-5385	8	22	information	information	NOUN
ejpam-5385	8	23	[	[	X
ejpam-5385	8	24	22	22	NUM
ejpam-5385	8	25	]	]	PUNCT
ejpam-5385	8	26	.	.	PUNCT
ejpam-5385	9	1	unlike	unlike	ADP
ejpam-5385	9	2	classical	classical	ADJ
ejpam-5385	9	3	crisp	crisp	ADJ
ejpam-5385	9	4	sets	set	NOUN
ejpam-5385	9	5	with	with	ADP
ejpam-5385	9	6	binary	binary	ADJ
ejpam-5385	9	7	membership	membership	NOUN
ejpam-5385	9	8	values	value	NOUN
ejpam-5385	9	9	,	,	PUNCT
ejpam-5385	9	10	fuzzy	fuzzy	ADJ
ejpam-5385	9	11	sets	set	NOUN
ejpam-5385	9	12	allow	allow	VERB
ejpam-5385	9	13	for	for	ADP
ejpam-5385	9	14	gradual	gradual	ADJ
ejpam-5385	9	15	degrees	degree	NOUN
ejpam-5385	9	16	of	of	ADP
ejpam-5385	9	17	membership	membership	NOUN
ejpam-5385	9	18	,	,	PUNCT
ejpam-5385	9	19	offering	offer	VERB
ejpam-5385	9	20	a	a	DET
ejpam-5385	9	21	more	more	ADV
ejpam-5385	9	22	flexible	flexible	ADJ
ejpam-5385	9	23	approach	approach	NOUN
ejpam-5385	9	24	to	to	ADP
ejpam-5385	9	25	dealing	deal	VERB
ejpam-5385	9	26	with	with	ADP
ejpam-5385	9	27	uncertainty	uncertainty	NOUN
ejpam-5385	9	28	.	.	PUNCT
ejpam-5385	10	1	in	in	ADP
ejpam-5385	10	2	1986	1986	NUM
ejpam-5385	10	3	,	,	PUNCT
ejpam-5385	10	4	atanassov	atanassov	PROPN
ejpam-5385	10	5	extended	extend	VERB
ejpam-5385	10	6	the	the	DET
ejpam-5385	10	7	concept	concept	NOUN
ejpam-5385	10	8	of	of	ADP
ejpam-5385	10	9	fuzzy	fuzzy	ADJ
ejpam-5385	10	10	sets	set	NOUN
ejpam-5385	10	11	by	by	ADP
ejpam-5385	10	12	introducing	introduce	VERB
ejpam-5385	10	13	intuitionistic	intuitionistic	ADJ
ejpam-5385	10	14	fuzzy	fuzzy	ADJ
ejpam-5385	10	15	sets	set	NOUN
ejpam-5385	10	16	[	[	X
ejpam-5385	10	17	6	6	NUM
ejpam-5385	10	18	]	]	PUNCT
ejpam-5385	10	19	,	,	PUNCT
ejpam-5385	10	20	which	which	PRON
ejpam-5385	10	21	account	account	VERB
ejpam-5385	10	22	for	for	ADP
ejpam-5385	10	23	both	both	PRON
ejpam-5385	10	24	membership	membership	NOUN
ejpam-5385	10	25	and	and	CCONJ
ejpam-5385	10	26	non	non	ADJ
ejpam-5385	10	27	-	-	ADJ
ejpam-5385	10	28	membership	membership	ADJ
ejpam-5385	10	29	degrees	degree	NOUN
ejpam-5385	10	30	.	.	PUNCT
ejpam-5385	11	1	this	this	DET
ejpam-5385	11	2	concept	concept	NOUN
ejpam-5385	11	3	garnered	garner	VERB
ejpam-5385	11	4	significant	significant	ADJ
ejpam-5385	11	5	attention	attention	NOUN
ejpam-5385	11	6	,	,	PUNCT
ejpam-5385	11	7	such	such	ADJ
ejpam-5385	11	8	as	as	ADP
ejpam-5385	11	9	in	in	ADP
ejpam-5385	11	10	[	[	X
ejpam-5385	11	11	10	10	NUM
ejpam-5385	11	12	,	,	PUNCT
ejpam-5385	11	13	11	11	NUM
ejpam-5385	11	14	]	]	PUNCT
ejpam-5385	11	15	,	,	PUNCT
ejpam-5385	11	16	leading	lead	VERB
ejpam-5385	11	17	to	to	ADP
ejpam-5385	11	18	the	the	DET
ejpam-5385	11	19	evolution	evolution	NOUN
ejpam-5385	11	20	of	of	ADP
ejpam-5385	11	21	intuitionistic	intuitionistic	ADJ
ejpam-5385	11	22	fuzzy	fuzzy	ADJ
ejpam-5385	11	23	set	set	NOUN
ejpam-5385	11	24	theory	theory	NOUN
ejpam-5385	11	25	,	,	PUNCT
ejpam-5385	11	26	which	which	PRON
ejpam-5385	11	27	has	have	AUX
ejpam-5385	11	28	found	find	VERB
ejpam-5385	11	29	utility	utility	NOUN
ejpam-5385	11	30	in	in	ADP
ejpam-5385	11	31	diverse	diverse	ADJ
ejpam-5385	11	32	domains	domain	NOUN
ejpam-5385	11	33	such	such	ADJ
ejpam-5385	11	34	as	as	ADP
ejpam-5385	11	35	decisionmaking	decisionmake	VERB
ejpam-5385	11	36	,	,	PUNCT
ejpam-5385	11	37	control	control	NOUN
ejpam-5385	11	38	systems	system	NOUN
ejpam-5385	11	39	,	,	PUNCT
ejpam-5385	11	40	and	and	CCONJ
ejpam-5385	11	41	pattern	pattern	NOUN
ejpam-5385	11	42	recognition	recognition	NOUN
ejpam-5385	11	43	.	.	PUNCT
ejpam-5385	12	1	building	build	VERB
ejpam-5385	12	2	on	on	ADP
ejpam-5385	12	3	these	these	DET
ejpam-5385	12	4	ideas	idea	NOUN
ejpam-5385	12	5	,	,	PUNCT
ejpam-5385	12	6	complex	complex	ADJ
ejpam-5385	12	7	intuitionistic	intuitionistic	ADJ
ejpam-5385	12	8	fuzzy	fuzzy	ADJ
ejpam-5385	12	9	sets	set	NOUN
ejpam-5385	12	10	(	(	PUNCT
ejpam-5385	12	11	cifs	cifs	PROPN
ejpam-5385	12	12	)	)	PUNCT
ejpam-5385	12	13	were	be	AUX
ejpam-5385	12	14	introduced	introduce	VERB
ejpam-5385	12	15	by	by	ADP
ejpam-5385	12	16	alkouri	alkouri	PROPN
ejpam-5385	12	17	and	and	CCONJ
ejpam-5385	12	18	salleh	salleh	NOUN
ejpam-5385	12	19	in	in	ADP
ejpam-5385	12	20	2012	2012	NUM
ejpam-5385	12	21	[	[	X
ejpam-5385	12	22	5	5	NUM
ejpam-5385	12	23	]	]	PUNCT
ejpam-5385	12	24	.	.	PUNCT
ejpam-5385	13	1	cifs	cif	VERB
ejpam-5385	13	2	extend	extend	VERB
ejpam-5385	13	3	intuitionistic	intuitionistic	ADJ
ejpam-5385	13	4	fuzzy	fuzzy	ADJ
ejpam-5385	13	5	sets	set	NOUN
ejpam-5385	13	6	by	by	ADP
ejpam-5385	13	7	using	use	VERB
ejpam-5385	13	8	complex	complex	ADJ
ejpam-5385	13	9	numbers	number	NOUN
ejpam-5385	13	10	to	to	PART
ejpam-5385	13	11	represent	represent	VERB
ejpam-5385	13	12	membership	membership	NOUN
ejpam-5385	13	13	and	and	CCONJ
ejpam-5385	13	14	non	non	ADJ
ejpam-5385	13	15	-	-	ADJ
ejpam-5385	13	16	membership	membership	ADJ
ejpam-5385	13	17	values	value	NOUN
ejpam-5385	13	18	,	,	PUNCT
ejpam-5385	13	19	offering	offer	VERB
ejpam-5385	13	20	a	a	DET
ejpam-5385	13	21	more	more	ADV
ejpam-5385	13	22	expressive	expressive	ADJ
ejpam-5385	13	23	∗corresponding	∗corresponding	NOUN
ejpam-5385	13	24	author	author	NOUN
ejpam-5385	13	25	.	.	PUNCT
ejpam-5385	14	1	doi	doi	NOUN
ejpam-5385	14	2	:	:	PUNCT
ejpam-5385	14	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5385	https://doi.org/10.29020/nybg.ejpam.v17i4.5385	PROPN
ejpam-5385	14	4	email	email	NOUN
ejpam-5385	14	5	address	address	NOUN
ejpam-5385	14	6	:	:	PUNCT
ejpam-5385	14	7	shadi.s@yu.edu.jo	shadi.s@yu.edu.jo	ADJ
ejpam-5385	14	8	(	(	PUNCT
ejpam-5385	14	9	s.	s.	PROPN
ejpam-5385	14	10	shaqaqha	shaqaqha	PROPN
ejpam-5385	14	11	)	)	PUNCT
ejpam-5385	14	12	,	,	PUNCT
ejpam-5385	14	13	mountheraldeiakeh@gmail.com	mountheraldeiakeh@gmail.com	PROPN
ejpam-5385	14	14	(	(	PUNCT
ejpam-5385	14	15	m.	m.	NOUN
ejpam-5385	14	16	al	al	PROPN
ejpam-5385	14	17	-	-	PUNCT
ejpam-5385	14	18	deiakeh	deiakeh	NOUN
ejpam-5385	14	19	)	)	PUNCT
ejpam-5385	14	20	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5385	15	1	3291	3291	NUM
ejpam-5385	15	2	copyright	copyright	NOUN
ejpam-5385	15	3	:	:	PUNCT
ejpam-5385	15	4	©	©	PROPN
ejpam-5385	15	5	2024	2024	NUM
ejpam-5385	15	6	the	the	DET
ejpam-5385	15	7	author(s	author(s	NOUN
ejpam-5385	15	8	)	)	PUNCT
ejpam-5385	15	9	.	.	PUNCT
ejpam-5385	16	1	(	(	PUNCT
ejpam-5385	16	2	cc	cc	NOUN
ejpam-5385	16	3	by	by	ADP
ejpam-5385	16	4	-	-	PUNCT
ejpam-5385	16	5	nc	nc	PROPN
ejpam-5385	16	6	4.0	4.0	NUM
ejpam-5385	16	7	)	)	PUNCT
ejpam-5385	16	8	s.	s.	PROPN
ejpam-5385	16	9	shaqaqha	shaqaqha	PROPN
ejpam-5385	16	10	,	,	PUNCT
ejpam-5385	16	11	m.	m.	PROPN
ejpam-5385	16	12	y.	y.	PROPN
ejpam-5385	16	13	al	al	PROPN
ejpam-5385	16	14	-	-	PUNCT
ejpam-5385	16	15	deiakeh	deiakeh	PROPN
ejpam-5385	16	16	/	/	SYM
ejpam-5385	16	17	eur	eur	NOUN
ejpam-5385	16	18	.	.	PUNCT
ejpam-5385	17	1	j.	j.	PROPN
ejpam-5385	17	2	pure	pure	PROPN
ejpam-5385	17	3	appl	appl	PROPN
ejpam-5385	17	4	.	.	PROPN
ejpam-5385	17	5	math	math	PROPN
ejpam-5385	17	6	,	,	PUNCT
ejpam-5385	17	7	17	17	NUM
ejpam-5385	17	8	(	(	PUNCT
ejpam-5385	17	9	4	4	NUM
ejpam-5385	17	10	)	)	PUNCT
ejpam-5385	17	11	(	(	PUNCT
ejpam-5385	17	12	2024	2024	NUM
ejpam-5385	17	13	)	)	PUNCT
ejpam-5385	17	14	,	,	PUNCT
ejpam-5385	17	15	3291	3291	NUM
ejpam-5385	17	16	-	-	SYM
ejpam-5385	17	17	3303	3303	NUM
ejpam-5385	17	18	3292	3292	NUM
ejpam-5385	17	19	way	way	NOUN
ejpam-5385	17	20	to	to	PART
ejpam-5385	17	21	handle	handle	VERB
ejpam-5385	17	22	uncertainty	uncertainty	NOUN
ejpam-5385	17	23	and	and	CCONJ
ejpam-5385	17	24	ambiguity	ambiguity	NOUN
ejpam-5385	17	25	.	.	PUNCT
ejpam-5385	18	1	this	this	DET
ejpam-5385	18	2	framework	framework	NOUN
ejpam-5385	18	3	has	have	AUX
ejpam-5385	18	4	proven	prove	VERB
ejpam-5385	18	5	useful	useful	ADJ
ejpam-5385	18	6	in	in	ADP
ejpam-5385	18	7	decisionmaking	decisionmake	VERB
ejpam-5385	18	8	,	,	PUNCT
ejpam-5385	18	9	pattern	pattern	NOUN
ejpam-5385	18	10	recognition	recognition	NOUN
ejpam-5385	18	11	,	,	PUNCT
ejpam-5385	18	12	and	and	CCONJ
ejpam-5385	18	13	image	image	NOUN
ejpam-5385	18	14	processing	processing	NOUN
ejpam-5385	18	15	,	,	PUNCT
ejpam-5385	18	16	where	where	SCONJ
ejpam-5385	18	17	complex	complex	ADJ
ejpam-5385	18	18	and	and	CCONJ
ejpam-5385	18	19	conflicting	conflict	VERB
ejpam-5385	18	20	information	information	NOUN
ejpam-5385	18	21	needs	need	VERB
ejpam-5385	18	22	to	to	PART
ejpam-5385	18	23	be	be	AUX
ejpam-5385	18	24	systematically	systematically	ADV
ejpam-5385	18	25	managed	manage	VERB
ejpam-5385	18	26	.	.	PUNCT
ejpam-5385	19	1	related	relate	VERB
ejpam-5385	19	2	work	work	NOUN
ejpam-5385	19	3	on	on	ADP
ejpam-5385	19	4	fuzzy	fuzzy	ADJ
ejpam-5385	19	5	lie	lie	NOUN
ejpam-5385	19	6	algebras	algebra	NOUN
ejpam-5385	19	7	can	can	AUX
ejpam-5385	19	8	be	be	AUX
ejpam-5385	19	9	found	find	VERB
ejpam-5385	19	10	in	in	ADP
ejpam-5385	19	11	[	[	X
ejpam-5385	19	12	3	3	NUM
ejpam-5385	19	13	]	]	PUNCT
ejpam-5385	19	14	,	,	PUNCT
ejpam-5385	19	15	and	and	CCONJ
ejpam-5385	19	16	studies	study	NOUN
ejpam-5385	19	17	on	on	ADP
ejpam-5385	19	18	bipolar	bipolar	ADJ
ejpam-5385	19	19	fuzzy	fuzzy	ADJ
ejpam-5385	19	20	soft	soft	ADJ
ejpam-5385	19	21	lie	lie	NOUN
ejpam-5385	19	22	algebras	algebra	NOUN
ejpam-5385	19	23	in	in	ADP
ejpam-5385	19	24	[	[	X
ejpam-5385	19	25	2	2	NUM
ejpam-5385	19	26	]	]	PUNCT
ejpam-5385	19	27	.	.	PUNCT
ejpam-5385	20	1	these	these	DET
ejpam-5385	20	2	foundational	foundational	ADJ
ejpam-5385	20	3	studies	study	NOUN
ejpam-5385	20	4	have	have	AUX
ejpam-5385	20	5	contributed	contribute	VERB
ejpam-5385	20	6	significantly	significantly	ADV
ejpam-5385	20	7	to	to	ADP
ejpam-5385	20	8	the	the	DET
ejpam-5385	20	9	extension	extension	NOUN
ejpam-5385	20	10	of	of	ADP
ejpam-5385	20	11	fuzzy	fuzzy	ADJ
ejpam-5385	20	12	algebraic	algebraic	ADJ
ejpam-5385	20	13	structures	structure	NOUN
ejpam-5385	20	14	and	and	CCONJ
ejpam-5385	20	15	motivate	motivate	VERB
ejpam-5385	20	16	further	further	ADJ
ejpam-5385	20	17	research	research	NOUN
ejpam-5385	20	18	in	in	ADP
ejpam-5385	20	19	this	this	DET
ejpam-5385	20	20	area	area	NOUN
ejpam-5385	20	21	.	.	PUNCT
ejpam-5385	21	1	this	this	DET
ejpam-5385	21	2	work	work	NOUN
ejpam-5385	21	3	aligns	align	VERB
ejpam-5385	21	4	with	with	ADP
ejpam-5385	21	5	recent	recent	ADJ
ejpam-5385	21	6	research	research	NOUN
ejpam-5385	21	7	in	in	ADP
ejpam-5385	21	8	the	the	DET
ejpam-5385	21	9	field	field	NOUN
ejpam-5385	21	10	,	,	PUNCT
ejpam-5385	21	11	such	such	ADJ
ejpam-5385	21	12	as	as	ADP
ejpam-5385	21	13	the	the	DET
ejpam-5385	21	14	study	study	NOUN
ejpam-5385	21	15	of	of	ADP
ejpam-5385	21	16	intuitionistic	intuitionistic	ADJ
ejpam-5385	21	17	fuzzy	fuzzy	ADJ
ejpam-5385	21	18	ordered	order	VERB
ejpam-5385	21	19	subalgebras	subalgebras	PROPN
ejpam-5385	21	20	in	in	ADP
ejpam-5385	21	21	ordered	order	VERB
ejpam-5385	21	22	bci	bci	NOUN
ejpam-5385	21	23	-	-	PUNCT
ejpam-5385	21	24	algebras	algebra	VERB
ejpam-5385	21	25	by	by	ADP
ejpam-5385	21	26	roh	roh	PROPN
ejpam-5385	21	27	et	et	PROPN
ejpam-5385	21	28	al	al	PROPN
ejpam-5385	21	29	.	.	PUNCT
ejpam-5385	22	1	[	[	X
ejpam-5385	22	2	12	12	NUM
ejpam-5385	22	3	]	]	PUNCT
ejpam-5385	22	4	.	.	PUNCT
ejpam-5385	23	1	in	in	ADP
ejpam-5385	23	2	a	a	DET
ejpam-5385	23	3	recent	recent	ADJ
ejpam-5385	23	4	work	work	NOUN
ejpam-5385	23	5	[	[	X
ejpam-5385	23	6	18	18	NUM
ejpam-5385	23	7	]	]	PUNCT
ejpam-5385	23	8	,	,	PUNCT
ejpam-5385	23	9	we	we	PRON
ejpam-5385	23	10	introduced	introduce	VERB
ejpam-5385	23	11	the	the	DET
ejpam-5385	23	12	notion	notion	NOUN
ejpam-5385	23	13	of	of	ADP
ejpam-5385	23	14	a	a	DET
ejpam-5385	23	15	complex	complex	ADJ
ejpam-5385	23	16	intuitionistic	intuitionistic	ADJ
ejpam-5385	23	17	fuzzy	fuzzy	ADJ
ejpam-5385	23	18	lie	lie	NOUN
ejpam-5385	23	19	algebra	algebra	NOUN
ejpam-5385	23	20	,	,	PUNCT
ejpam-5385	23	21	which	which	PRON
ejpam-5385	23	22	characterizes	characterize	VERB
ejpam-5385	23	23	a	a	DET
ejpam-5385	23	24	lie	lie	NOUN
ejpam-5385	23	25	algebra	algebra	NOUN
ejpam-5385	23	26	using	use	VERB
ejpam-5385	23	27	elements	element	NOUN
ejpam-5385	23	28	represented	represent	VERB
ejpam-5385	23	29	as	as	ADP
ejpam-5385	23	30	complex	complex	ADJ
ejpam-5385	23	31	intuitionistic	intuitionistic	ADJ
ejpam-5385	23	32	fuzzy	fuzzy	ADJ
ejpam-5385	23	33	sets	set	NOUN
ejpam-5385	23	34	.	.	PUNCT
ejpam-5385	24	1	the	the	DET
ejpam-5385	24	2	lie	lie	NOUN
ejpam-5385	24	3	bracket	bracket	NOUN
ejpam-5385	24	4	operation	operation	NOUN
ejpam-5385	24	5	is	be	AUX
ejpam-5385	24	6	formulated	formulate	VERB
ejpam-5385	24	7	based	base	VERB
ejpam-5385	24	8	on	on	ADP
ejpam-5385	24	9	the	the	DET
ejpam-5385	24	10	principles	principle	NOUN
ejpam-5385	24	11	of	of	ADP
ejpam-5385	24	12	complex	complex	ADJ
ejpam-5385	24	13	intuitionistic	intuitionistic	ADJ
ejpam-5385	24	14	fuzzy	fuzzy	ADJ
ejpam-5385	24	15	logic	logic	NOUN
ejpam-5385	24	16	.	.	PUNCT
ejpam-5385	25	1	these	these	DET
ejpam-5385	25	2	complex	complex	ADJ
ejpam-5385	25	3	intuitionistic	intuitionistic	ADJ
ejpam-5385	25	4	fuzzy	fuzzy	ADJ
ejpam-5385	25	5	lie	lie	NOUN
ejpam-5385	25	6	algebras	algebra	NOUN
ejpam-5385	25	7	can	can	AUX
ejpam-5385	25	8	be	be	AUX
ejpam-5385	25	9	perceived	perceive	VERB
ejpam-5385	25	10	as	as	ADP
ejpam-5385	25	11	a	a	DET
ejpam-5385	25	12	broader	broad	ADJ
ejpam-5385	25	13	generalization	generalization	NOUN
ejpam-5385	25	14	encompassing	encompass	VERB
ejpam-5385	25	15	fuzzy	fuzzy	ADJ
ejpam-5385	25	16	lie	lie	NOUN
ejpam-5385	25	17	algebras	algebra	NOUN
ejpam-5385	25	18	[	[	X
ejpam-5385	25	19	21	21	NUM
ejpam-5385	25	20	]	]	PUNCT
ejpam-5385	25	21	,	,	PUNCT
ejpam-5385	25	22	intuitionistic	intuitionistic	ADJ
ejpam-5385	25	23	fuzzy	fuzzy	ADJ
ejpam-5385	25	24	lie	lie	NOUN
ejpam-5385	25	25	algebras	algebra	NOUN
ejpam-5385	26	1	[	[	X
ejpam-5385	26	2	1	1	NUM
ejpam-5385	26	3	]	]	PUNCT
ejpam-5385	26	4	,	,	PUNCT
ejpam-5385	26	5	and	and	CCONJ
ejpam-5385	26	6	complex	complex	ADJ
ejpam-5385	26	7	fuzzy	fuzzy	ADJ
ejpam-5385	26	8	lie	lie	NOUN
ejpam-5385	26	9	algebras	algebra	NOUN
ejpam-5385	26	10	[	[	X
ejpam-5385	26	11	13	13	NUM
ejpam-5385	26	12	]	]	PUNCT
ejpam-5385	26	13	.	.	PUNCT
ejpam-5385	27	1	2	2	X
ejpam-5385	27	2	.	.	X
ejpam-5385	28	1	some	some	DET
ejpam-5385	28	2	preliminaries	preliminary	NOUN
ejpam-5385	28	3	on	on	ADP
ejpam-5385	28	4	lie	lie	NOUN
ejpam-5385	28	5	algebras	algebra	NOUN
ejpam-5385	28	6	and	and	CCONJ
ejpam-5385	28	7	complex	complex	ADJ
ejpam-5385	28	8	intuitionistic	intuitionistic	ADJ
ejpam-5385	28	9	fuzzy	fuzzy	ADJ
ejpam-5385	28	10	lie	lie	NOUN
ejpam-5385	28	11	ideals	ideal	NOUN
ejpam-5385	28	12	2.1	2.1	NUM
ejpam-5385	28	13	.	.	PUNCT
ejpam-5385	29	1	fundamentals	fundamental	NOUN
ejpam-5385	29	2	of	of	ADP
ejpam-5385	29	3	lie	lie	NOUN
ejpam-5385	29	4	algebras	algebra	NOUN
ejpam-5385	29	5	in	in	ADP
ejpam-5385	29	6	this	this	DET
ejpam-5385	29	7	section	section	NOUN
ejpam-5385	29	8	,	,	PUNCT
ejpam-5385	29	9	we	we	PRON
ejpam-5385	29	10	delve	delve	VERB
ejpam-5385	29	11	into	into	ADP
ejpam-5385	29	12	the	the	DET
ejpam-5385	29	13	core	core	NOUN
ejpam-5385	29	14	concepts	concept	NOUN
ejpam-5385	29	15	surrounding	surround	VERB
ejpam-5385	29	16	lie	lie	NOUN
ejpam-5385	29	17	algebras	algebra	NOUN
ejpam-5385	29	18	,	,	PUNCT
ejpam-5385	29	19	drawing	draw	VERB
ejpam-5385	29	20	insights	insight	NOUN
ejpam-5385	29	21	from	from	ADP
ejpam-5385	29	22	the	the	DET
ejpam-5385	29	23	sources	source	NOUN
ejpam-5385	29	24	[	[	X
ejpam-5385	29	25	7	7	X
ejpam-5385	29	26	]	]	PUNCT
ejpam-5385	29	27	and	and	CCONJ
ejpam-5385	29	28	[	[	X
ejpam-5385	29	29	9	9	NUM
ejpam-5385	29	30	]	]	PUNCT
ejpam-5385	29	31	.	.	PUNCT
ejpam-5385	30	1	we	we	PRON
ejpam-5385	30	2	explore	explore	VERB
ejpam-5385	30	3	the	the	DET
ejpam-5385	30	4	foundational	foundational	ADJ
ejpam-5385	30	5	notion	notion	NOUN
ejpam-5385	30	6	of	of	ADP
ejpam-5385	30	7	lie	lie	NOUN
ejpam-5385	30	8	algebras	algebra	NOUN
ejpam-5385	30	9	,	,	PUNCT
ejpam-5385	30	10	denoted	denote	VERB
ejpam-5385	30	11	as	as	ADP
ejpam-5385	30	12	(	(	PUNCT
ejpam-5385	30	13	m	m	PROPN
ejpam-5385	30	14	,	,	PUNCT
ejpam-5385	30	15	[	[	X
ejpam-5385	30	16	.	.	PUNCT
ejpam-5385	30	17	,	,	PUNCT
ejpam-5385	30	18	.	.	PUNCT
ejpam-5385	31	1	]	]	X
ejpam-5385	31	2	)	)	PUNCT
ejpam-5385	31	3	,	,	PUNCT
ejpam-5385	31	4	wherem	wherem	PROPN
ejpam-5385	31	5	signifies	signify	VERB
ejpam-5385	31	6	a	a	DET
ejpam-5385	31	7	vector	vector	NOUN
ejpam-5385	31	8	space	space	NOUN
ejpam-5385	31	9	over	over	ADP
ejpam-5385	31	10	the	the	DET
ejpam-5385	31	11	fieldk	fieldk	ADJ
ejpam-5385	31	12	,	,	PUNCT
ejpam-5385	31	13	and	and	CCONJ
ejpam-5385	31	14	[	[	X
ejpam-5385	31	15	.	.	PUNCT
ejpam-5385	31	16	,	,	PUNCT
ejpam-5385	31	17	.	.	PUNCT
ejpam-5385	31	18	]	]	PUNCT
ejpam-5385	32	1	:	:	PUNCT
ejpam-5385	32	2	m×m	m×m	ADJ
ejpam-5385	32	3	→	→	SYM
ejpam-5385	32	4	m	m	NOUN
ejpam-5385	32	5	represents	represent	VERB
ejpam-5385	32	6	a	a	DET
ejpam-5385	32	7	bilinear	bilinear	NOUN
ejpam-5385	32	8	mapping	mapping	NOUN
ejpam-5385	32	9	(	(	PUNCT
ejpam-5385	32	10	called	call	VERB
ejpam-5385	32	11	lie	lie	NOUN
ejpam-5385	32	12	product	product	NOUN
ejpam-5385	32	13	)	)	PUNCT
ejpam-5385	32	14	.	.	PUNCT
ejpam-5385	33	1	the	the	DET
ejpam-5385	33	2	lie	lie	NOUN
ejpam-5385	33	3	product	product	NOUN
ejpam-5385	33	4	adheres	adhere	VERB
ejpam-5385	33	5	to	to	ADP
ejpam-5385	33	6	two	two	NUM
ejpam-5385	33	7	key	key	ADJ
ejpam-5385	33	8	axioms	axiom	NOUN
ejpam-5385	33	9	for	for	ADP
ejpam-5385	33	10	any	any	DET
ejpam-5385	33	11	elements	element	NOUN
ejpam-5385	33	12	m1,m2,m3	m1,m2,m3	VERB
ejpam-5385	33	13	∈	∈	PROPN
ejpam-5385	33	14	m	m	NOUN
ejpam-5385	33	15	:	:	PUNCT
ejpam-5385	33	16	(	(	PUNCT
ejpam-5385	33	17	i	i	NOUN
ejpam-5385	33	18	)	)	PUNCT
ejpam-5385	33	19	the	the	DET
ejpam-5385	33	20	condition	condition	NOUN
ejpam-5385	33	21	[	[	X
ejpam-5385	33	22	m1	m1	PROPN
ejpam-5385	33	23	,	,	PUNCT
ejpam-5385	33	24	m2	m2	PROPN
ejpam-5385	33	25	]	]	X
ejpam-5385	33	26	=	=	SYM
ejpam-5385	34	1	0	0	NUM
ejpam-5385	34	2	m	m	NOUN
ejpam-5385	34	3	holds	hold	NOUN
ejpam-5385	34	4	,	,	PUNCT
ejpam-5385	34	5	leading	lead	VERB
ejpam-5385	34	6	to	to	ADP
ejpam-5385	34	7	the	the	DET
ejpam-5385	34	8	implication	implication	NOUN
ejpam-5385	34	9	of	of	ADP
ejpam-5385	34	10	anti	anti	ADJ
ejpam-5385	34	11	-	-	NOUN
ejpam-5385	34	12	symmetry	symmetry	NOUN
ejpam-5385	34	13	:	:	PUNCT
ejpam-5385	35	1	[	[	X
ejpam-5385	35	2	m1	m1	NOUN
ejpam-5385	35	3	,	,	PUNCT
ejpam-5385	35	4	m2	m2	PROPN
ejpam-5385	35	5	]	]	X
ejpam-5385	35	6	=	=	SYM
ejpam-5385	35	7	−[m2	−[m2	PROPN
ejpam-5385	35	8	,	,	PUNCT
ejpam-5385	35	9	m1	m1	PROPN
ejpam-5385	35	10	]	]	PUNCT
ejpam-5385	35	11	.	.	PUNCT
ejpam-5385	35	12	(	(	PUNCT
ejpam-5385	35	13	ii	ii	X
ejpam-5385	35	14	)	)	PUNCT
ejpam-5385	35	15	the	the	DET
ejpam-5385	35	16	jacobi	jacobi	PROPN
ejpam-5385	35	17	identity	identity	NOUN
ejpam-5385	35	18	,	,	PUNCT
ejpam-5385	35	19	denoted	denote	VERB
ejpam-5385	35	20	as	as	ADP
ejpam-5385	35	21	[	[	X
ejpam-5385	35	22	m1	m1	NOUN
ejpam-5385	35	23	,	,	PUNCT
ejpam-5385	35	24	[	[	X
ejpam-5385	35	25	m2,m3	m2,m3	X
ejpam-5385	35	26	]	]	X
ejpam-5385	35	27	]	]	PUNCT
ejpam-5385	36	1	+	+	CCONJ
ejpam-5385	36	2	[	[	X
ejpam-5385	36	3	m2	m2	NOUN
ejpam-5385	36	4	,	,	PUNCT
ejpam-5385	36	5	[	[	X
ejpam-5385	36	6	m3,m1	m3,m1	PROPN
ejpam-5385	36	7	]	]	X
ejpam-5385	36	8	]	]	X
ejpam-5385	37	1	+	+	CCONJ
ejpam-5385	37	2	[	[	X
ejpam-5385	37	3	m3	m3	PROPN
ejpam-5385	37	4	,	,	PUNCT
ejpam-5385	37	5	[	[	X
ejpam-5385	37	6	m1	m1	NOUN
ejpam-5385	37	7	,	,	PUNCT
ejpam-5385	37	8	m2	m2	PROPN
ejpam-5385	37	9	]	]	X
ejpam-5385	37	10	]	]	X
ejpam-5385	37	11	=	=	PUNCT
ejpam-5385	37	12	0	0	NUM
ejpam-5385	37	13	m	m	NOUN
ejpam-5385	37	14	,	,	PUNCT
ejpam-5385	37	15	is	be	AUX
ejpam-5385	37	16	satisfied	satisfied	ADJ
ejpam-5385	37	17	.	.	PUNCT
ejpam-5385	38	1	it	it	PRON
ejpam-5385	38	2	’s	’	VERB
ejpam-5385	38	3	clear	clear	ADJ
ejpam-5385	38	4	that	that	SCONJ
ejpam-5385	39	1	[	[	X
ejpam-5385	39	2	m	m	X
ejpam-5385	39	3	,	,	PUNCT
ejpam-5385	39	4	0	0	NUM
ejpam-5385	39	5	m	m	VERB
ejpam-5385	39	6	]	]	X
ejpam-5385	40	1	=	=	PUNCT
ejpam-5385	41	1	[	[	X
ejpam-5385	41	2	0	0	NUM
ejpam-5385	41	3	m	m	NOUN
ejpam-5385	41	4	,	,	PUNCT
ejpam-5385	41	5	m	m	VERB
ejpam-5385	41	6	]	]	X
ejpam-5385	41	7	=	=	PUNCT
ejpam-5385	41	8	0	0	NUM
ejpam-5385	41	9	m	m	VERB
ejpam-5385	41	10	for	for	ADP
ejpam-5385	41	11	any	any	DET
ejpam-5385	41	12	m	m	PROPN
ejpam-5385	41	13	∈	∈	NOUN
ejpam-5385	41	14	m.	m.	NOUN
ejpam-5385	41	15	additionally	additionally	ADV
ejpam-5385	41	16	,	,	PUNCT
ejpam-5385	41	17	when	when	SCONJ
ejpam-5385	41	18	char(k	char(k	ADJ
ejpam-5385	41	19	)	)	PUNCT
ejpam-5385	41	20	̸=	̸=	PROPN
ejpam-5385	41	21	2	2	NUM
ejpam-5385	41	22	,	,	PUNCT
ejpam-5385	41	23	the	the	DET
ejpam-5385	41	24	identity	identity	NOUN
ejpam-5385	41	25	[	[	X
ejpam-5385	41	26	m1	m1	NOUN
ejpam-5385	41	27	,	,	PUNCT
ejpam-5385	41	28	m2	m2	PROPN
ejpam-5385	41	29	]	]	X
ejpam-5385	41	30	=	=	SYM
ejpam-5385	41	31	−[m2	−[m2	PROPN
ejpam-5385	41	32	,	,	PUNCT
ejpam-5385	41	33	m1	m1	PROPN
ejpam-5385	41	34	]	]	PUNCT
ejpam-5385	41	35	for	for	ADP
ejpam-5385	41	36	all	all	DET
ejpam-5385	41	37	m1	m1	NOUN
ejpam-5385	41	38	,	,	PUNCT
ejpam-5385	41	39	m2	m2	PROPN
ejpam-5385	41	40	∈	∈	PROPN
ejpam-5385	41	41	m	m	VERB
ejpam-5385	41	42	implies	imply	VERB
ejpam-5385	41	43	[	[	X
ejpam-5385	41	44	m	m	X
ejpam-5385	41	45	,	,	PUNCT
ejpam-5385	41	46	m	m	VERB
ejpam-5385	41	47	]	]	X
ejpam-5385	41	48	=	=	PUNCT
ejpam-5385	41	49	0	0	NUM
ejpam-5385	41	50	m	m	VERB
ejpam-5385	41	51	for	for	ADP
ejpam-5385	41	52	each	each	DET
ejpam-5385	41	53	m	m	PROPN
ejpam-5385	41	54	∈	∈	PROPN
ejpam-5385	41	55	m.	m.	NOUN
ejpam-5385	41	56	various	various	ADJ
ejpam-5385	41	57	illustrative	illustrative	ADJ
ejpam-5385	41	58	examples	example	NOUN
ejpam-5385	41	59	highlight	highlight	VERB
ejpam-5385	41	60	diverse	diverse	ADJ
ejpam-5385	41	61	instances	instance	NOUN
ejpam-5385	41	62	of	of	ADP
ejpam-5385	41	63	lie	lie	NOUN
ejpam-5385	41	64	algebras	algebra	NOUN
ejpam-5385	41	65	:	:	PUNCT
ejpam-5385	41	66	(	(	PUNCT
ejpam-5385	41	67	i	i	NOUN
ejpam-5385	41	68	)	)	PUNCT
ejpam-5385	41	69	any	any	DET
ejpam-5385	41	70	vector	vector	NOUN
ejpam-5385	41	71	space	space	NOUN
ejpam-5385	41	72	v	v	NOUN
ejpam-5385	41	73	can	can	AUX
ejpam-5385	41	74	be	be	AUX
ejpam-5385	41	75	viewed	view	VERB
ejpam-5385	41	76	as	as	ADP
ejpam-5385	41	77	an	an	DET
ejpam-5385	41	78	abelian	abelian	ADJ
ejpam-5385	41	79	lie	lie	NOUN
ejpam-5385	41	80	algebra	algebra	NOUN
ejpam-5385	41	81	using	use	VERB
ejpam-5385	41	82	the	the	DET
ejpam-5385	41	83	lie	lie	NOUN
ejpam-5385	41	84	bracket	bracket	NOUN
ejpam-5385	41	85	[	[	X
ejpam-5385	41	86	v1	v1	NOUN
ejpam-5385	41	87	,	,	PUNCT
ejpam-5385	41	88	v2	v2	NOUN
ejpam-5385	41	89	]	]	PUNCT
ejpam-5385	41	90	=	=	SYM
ejpam-5385	41	91	0v	0v	NOUN
ejpam-5385	41	92	for	for	ADP
ejpam-5385	41	93	all	all	DET
ejpam-5385	41	94	elements	element	NOUN
ejpam-5385	41	95	v1	v1	NOUN
ejpam-5385	41	96	,	,	PUNCT
ejpam-5385	41	97	v2	v2	PROPN
ejpam-5385	41	98	∈	∈	PROPN
ejpam-5385	41	99	v	v	NOUN
ejpam-5385	41	100	.	.	PUNCT
ejpam-5385	42	1	(	(	PUNCT
ejpam-5385	42	2	ii	ii	NOUN
ejpam-5385	42	3	)	)	PUNCT
ejpam-5385	42	4	when	when	SCONJ
ejpam-5385	42	5	a	a	DET
ejpam-5385	42	6	vector	vector	NOUN
ejpam-5385	42	7	space	space	NOUN
ejpam-5385	42	8	v	v	NOUN
ejpam-5385	42	9	is	be	AUX
ejpam-5385	42	10	endowed	endow	VERB
ejpam-5385	42	11	with	with	ADP
ejpam-5385	42	12	an	an	DET
ejpam-5385	42	13	associative	associative	ADJ
ejpam-5385	42	14	multiplication	multiplication	NOUN
ejpam-5385	42	15	,	,	PUNCT
ejpam-5385	42	16	it	it	PRON
ejpam-5385	42	17	can	can	AUX
ejpam-5385	42	18	be	be	AUX
ejpam-5385	42	19	transformed	transform	VERB
ejpam-5385	42	20	into	into	ADP
ejpam-5385	42	21	a	a	DET
ejpam-5385	42	22	lie	lie	NOUN
ejpam-5385	42	23	algebra	algebra	NOUN
ejpam-5385	42	24	with	with	ADP
ejpam-5385	42	25	the	the	DET
ejpam-5385	42	26	commutator	commutator	NOUN
ejpam-5385	42	27	operation	operation	NOUN
ejpam-5385	43	1	[	[	X
ejpam-5385	43	2	v1	v1	NOUN
ejpam-5385	43	3	,	,	PUNCT
ejpam-5385	43	4	v2	v2	NOUN
ejpam-5385	43	5	]	]	PUNCT
ejpam-5385	43	6	=	=	SYM
ejpam-5385	43	7	v1v2−v2v1	v1v2−v2v1	PROPN
ejpam-5385	43	8	s.	s.	PROPN
ejpam-5385	43	9	shaqaqha	shaqaqha	PROPN
ejpam-5385	43	10	,	,	PUNCT
ejpam-5385	43	11	m.	m.	PROPN
ejpam-5385	43	12	y.	y.	PROPN
ejpam-5385	43	13	al	al	PROPN
ejpam-5385	43	14	-	-	PUNCT
ejpam-5385	43	15	deiakeh	deiakeh	PROPN
ejpam-5385	43	16	/	/	SYM
ejpam-5385	43	17	eur	eur	NOUN
ejpam-5385	43	18	.	.	PUNCT
ejpam-5385	44	1	j.	j.	PROPN
ejpam-5385	44	2	pure	pure	PROPN
ejpam-5385	44	3	appl	appl	PROPN
ejpam-5385	44	4	.	.	PROPN
ejpam-5385	44	5	math	math	PROPN
ejpam-5385	44	6	,	,	PUNCT
ejpam-5385	44	7	17	17	NUM
ejpam-5385	44	8	(	(	PUNCT
ejpam-5385	44	9	4	4	NUM
ejpam-5385	44	10	)	)	PUNCT
ejpam-5385	44	11	(	(	PUNCT
ejpam-5385	44	12	2024	2024	NUM
ejpam-5385	44	13	)	)	PUNCT
ejpam-5385	44	14	,	,	PUNCT
ejpam-5385	44	15	3291	3291	NUM
ejpam-5385	44	16	-	-	SYM
ejpam-5385	44	17	3303	3303	NUM
ejpam-5385	44	18	3293	3293	NUM
ejpam-5385	44	19	for	for	ADP
ejpam-5385	44	20	all	all	DET
ejpam-5385	44	21	v1	v1	NOUN
ejpam-5385	44	22	,	,	PUNCT
ejpam-5385	44	23	v2	v2	PROPN
ejpam-5385	44	24	∈	∈	PROPN
ejpam-5385	44	25	v	v	NOUN
ejpam-5385	44	26	.	.	PUNCT
ejpam-5385	45	1	in	in	ADP
ejpam-5385	45	2	the	the	DET
ejpam-5385	45	3	realm	realm	NOUN
ejpam-5385	45	4	of	of	ADP
ejpam-5385	45	5	finite	finite	ADJ
ejpam-5385	45	6	-	-	ADJ
ejpam-5385	45	7	dimensional	dimensional	ADJ
ejpam-5385	45	8	vector	vector	NOUN
ejpam-5385	45	9	spaces	space	NOUN
ejpam-5385	45	10	,	,	PUNCT
ejpam-5385	45	11	the	the	DET
ejpam-5385	45	12	set	set	NOUN
ejpam-5385	45	13	of	of	ADP
ejpam-5385	45	14	linear	linear	ADJ
ejpam-5385	45	15	transformations	transformation	NOUN
ejpam-5385	45	16	from	from	ADP
ejpam-5385	45	17	v	v	NUM
ejpam-5385	45	18	to	to	ADP
ejpam-5385	45	19	itself	itself	PRON
ejpam-5385	45	20	,	,	PUNCT
ejpam-5385	45	21	denoted	denote	VERB
ejpam-5385	45	22	gl(v	gl(v	X
ejpam-5385	45	23	)	)	PUNCT
ejpam-5385	45	24	,	,	PUNCT
ejpam-5385	45	25	constitutes	constitute	VERB
ejpam-5385	45	26	a	a	DET
ejpam-5385	45	27	lie	lie	NOUN
ejpam-5385	45	28	algebra	algebra	NOUN
ejpam-5385	45	29	,	,	PUNCT
ejpam-5385	45	30	with	with	ADP
ejpam-5385	45	31	the	the	DET
ejpam-5385	45	32	bracket	bracket	NOUN
ejpam-5385	45	33	defined	define	VERB
ejpam-5385	45	34	as	as	ADP
ejpam-5385	45	35	[	[	X
ejpam-5385	45	36	f1	f1	NOUN
ejpam-5385	45	37	,	,	PUNCT
ejpam-5385	45	38	f2	f2	PROPN
ejpam-5385	45	39	]	]	PUNCT
ejpam-5385	45	40	=	=	SYM
ejpam-5385	45	41	f1	f1	PROPN
ejpam-5385	45	42	◦	◦	NOUN
ejpam-5385	45	43	f2	f2	ADV
ejpam-5385	45	44	−	−	ADP
ejpam-5385	45	45	f2	f2	PROPN
ejpam-5385	45	46	◦	◦	NOUN
ejpam-5385	45	47	f1	f1	NOUN
ejpam-5385	45	48	for	for	ADP
ejpam-5385	45	49	any	any	DET
ejpam-5385	45	50	f1	f1	NOUN
ejpam-5385	45	51	,	,	PUNCT
ejpam-5385	45	52	f2	f2	PROPN
ejpam-5385	45	53	∈	∈	PROPN
ejpam-5385	45	54	gl(v	gl(v	NUM
ejpam-5385	45	55	)	)	PUNCT
ejpam-5385	45	56	.	.	PUNCT
ejpam-5385	46	1	(	(	PUNCT
ejpam-5385	46	2	iii	iii	X
ejpam-5385	46	3	)	)	PUNCT
ejpam-5385	46	4	the	the	DET
ejpam-5385	46	5	lie	lie	NOUN
ejpam-5385	46	6	algebra	algebra	NOUN
ejpam-5385	46	7	structure	structure	NOUN
ejpam-5385	46	8	is	be	AUX
ejpam-5385	46	9	evident	evident	ADJ
ejpam-5385	46	10	in	in	ADP
ejpam-5385	46	11	the	the	DET
ejpam-5385	46	12	vector	vector	NOUN
ejpam-5385	46	13	space	space	NOUN
ejpam-5385	46	14	r3	r3	PROPN
ejpam-5385	46	15	when	when	SCONJ
ejpam-5385	46	16	the	the	DET
ejpam-5385	46	17	cross	cross	NOUN
ejpam-5385	46	18	product	product	NOUN
ejpam-5385	46	19	operation	operation	NOUN
ejpam-5385	46	20	is	be	AUX
ejpam-5385	46	21	employed	employ	VERB
ejpam-5385	46	22	as	as	ADP
ejpam-5385	46	23	[	[	X
ejpam-5385	46	24	a	a	X
ejpam-5385	46	25	,	,	PUNCT
ejpam-5385	46	26	b	b	NOUN
ejpam-5385	46	27	]	]	X
ejpam-5385	46	28	=	=	PUNCT
ejpam-5385	46	29	a×	a×	PROPN
ejpam-5385	46	30	b.	b.	NOUN
ejpam-5385	46	31	these	these	DET
ejpam-5385	46	32	examples	example	NOUN
ejpam-5385	46	33	showcase	showcase	VERB
ejpam-5385	46	34	the	the	DET
ejpam-5385	46	35	wide	wide	ADV
ejpam-5385	46	36	-	-	PUNCT
ejpam-5385	46	37	ranging	range	VERB
ejpam-5385	46	38	applications	application	NOUN
ejpam-5385	46	39	and	and	CCONJ
ejpam-5385	46	40	properties	property	NOUN
ejpam-5385	46	41	of	of	ADP
ejpam-5385	46	42	lie	lie	NOUN
ejpam-5385	46	43	algebras	algebra	NOUN
ejpam-5385	46	44	.	.	PUNCT
ejpam-5385	47	1	in	in	ADP
ejpam-5385	47	2	the	the	DET
ejpam-5385	47	3	context	context	NOUN
ejpam-5385	47	4	of	of	ADP
ejpam-5385	47	5	lie	lie	NOUN
ejpam-5385	47	6	algebras	algebra	NOUN
ejpam-5385	47	7	,	,	PUNCT
ejpam-5385	47	8	a	a	DET
ejpam-5385	47	9	subspace	subspace	NOUN
ejpam-5385	47	10	q	q	PROPN
ejpam-5385	47	11	of	of	ADP
ejpam-5385	47	12	m	m	PROPN
ejpam-5385	47	13	is	be	AUX
ejpam-5385	47	14	referred	refer	VERB
ejpam-5385	47	15	to	to	ADP
ejpam-5385	47	16	as	as	ADP
ejpam-5385	47	17	a	a	DET
ejpam-5385	47	18	lie	lie	NOUN
ejpam-5385	47	19	subalgebra	subalgebra	NOUN
ejpam-5385	47	20	if	if	SCONJ
ejpam-5385	47	21	it	it	PRON
ejpam-5385	47	22	remains	remain	VERB
ejpam-5385	47	23	closed	closed	ADJ
ejpam-5385	47	24	under	under	ADP
ejpam-5385	47	25	the	the	DET
ejpam-5385	47	26	lie	lie	NOUN
ejpam-5385	47	27	product	product	NOUN
ejpam-5385	47	28	operation	operation	NOUN
ejpam-5385	47	29	,	,	PUNCT
ejpam-5385	47	30	implying	imply	VERB
ejpam-5385	47	31	that	that	SCONJ
ejpam-5385	47	32	[	[	X
ejpam-5385	47	33	q1	q1	ADP
ejpam-5385	47	34	,	,	PUNCT
ejpam-5385	47	35	q2	q2	NOUN
ejpam-5385	47	36	]	]	PUNCT
ejpam-5385	47	37	∈	∈	PROPN
ejpam-5385	47	38	q	q	NOUN
ejpam-5385	47	39	for	for	ADP
ejpam-5385	47	40	any	any	DET
ejpam-5385	47	41	q1	q1	NOUN
ejpam-5385	47	42	,	,	PUNCT
ejpam-5385	47	43	q2	q2	PROPN
ejpam-5385	47	44	∈	∈	PROPN
ejpam-5385	47	45	q.	q.	PROPN
ejpam-5385	47	46	also	also	ADV
ejpam-5385	47	47	,	,	PUNCT
ejpam-5385	47	48	q	q	PROPN
ejpam-5385	47	49	is	be	AUX
ejpam-5385	47	50	termed	term	VERB
ejpam-5385	47	51	a	a	DET
ejpam-5385	47	52	lie	lie	NOUN
ejpam-5385	47	53	ideal	ideal	NOUN
ejpam-5385	47	54	of	of	ADP
ejpam-5385	47	55	m	m	PRON
ejpam-5385	47	56	if	if	SCONJ
ejpam-5385	47	57	[	[	X
ejpam-5385	47	58	m	m	X
ejpam-5385	47	59	,	,	PUNCT
ejpam-5385	47	60	n	n	CCONJ
ejpam-5385	47	61	]	]	PUNCT
ejpam-5385	47	62	∈	∈	PROPN
ejpam-5385	47	63	n	n	X
ejpam-5385	47	64	for	for	ADP
ejpam-5385	47	65	any	any	DET
ejpam-5385	47	66	m	m	NOUN
ejpam-5385	47	67	∈	∈	NOUN
ejpam-5385	47	68	m	m	NOUN
ejpam-5385	47	69	and	and	CCONJ
ejpam-5385	47	70	n	n	PRON
ejpam-5385	47	71	∈	∈	PROPN
ejpam-5385	47	72	n	n	X
ejpam-5385	47	73	.	.	PUNCT
ejpam-5385	48	1	notably	notably	ADV
ejpam-5385	48	2	,	,	PUNCT
ejpam-5385	48	3	the	the	DET
ejpam-5385	48	4	subspaces	subspace	NOUN
ejpam-5385	48	5	0	0	NUM
ejpam-5385	48	6	m	m	NOUN
ejpam-5385	48	7	and	and	CCONJ
ejpam-5385	48	8	m	m	VERB
ejpam-5385	48	9	are	be	AUX
ejpam-5385	48	10	considered	consider	VERB
ejpam-5385	48	11	ideals	ideal	NOUN
ejpam-5385	48	12	of	of	ADP
ejpam-5385	48	13	m	m	PRON
ejpam-5385	48	14	,	,	PUNCT
ejpam-5385	48	15	termed	term	VERB
ejpam-5385	48	16	the	the	DET
ejpam-5385	48	17	trivial	trivial	ADJ
ejpam-5385	48	18	ideals	ideal	NOUN
ejpam-5385	48	19	.	.	PUNCT
ejpam-5385	49	1	additionally	additionally	ADV
ejpam-5385	49	2	,	,	PUNCT
ejpam-5385	49	3	the	the	DET
ejpam-5385	49	4	center	center	NOUN
ejpam-5385	49	5	of	of	ADP
ejpam-5385	49	6	m	m	PROPN
ejpam-5385	49	7	,	,	PUNCT
ejpam-5385	49	8	denoted	denote	VERB
ejpam-5385	49	9	z(m	z(m	NOUN
ejpam-5385	49	10	)	)	PUNCT
ejpam-5385	49	11	,	,	PUNCT
ejpam-5385	49	12	consists	consist	VERB
ejpam-5385	49	13	of	of	ADP
ejpam-5385	49	14	elements	element	NOUN
ejpam-5385	49	15	m	m	VERB
ejpam-5385	49	16	in	in	ADP
ejpam-5385	49	17	m	m	PROPN
ejpam-5385	49	18	for	for	ADP
ejpam-5385	49	19	which	which	PRON
ejpam-5385	49	20	[	[	X
ejpam-5385	49	21	m	m	X
ejpam-5385	49	22	,	,	PUNCT
ejpam-5385	49	23	n	n	CCONJ
ejpam-5385	49	24	]	]	PUNCT
ejpam-5385	49	25	=	=	PUNCT
ejpam-5385	50	1	0	0	NUM
ejpam-5385	50	2	m	m	VERB
ejpam-5385	50	3	for	for	ADP
ejpam-5385	50	4	all	all	PRON
ejpam-5385	50	5	n	n	PRON
ejpam-5385	50	6	∈	∈	PROPN
ejpam-5385	50	7	m	m	PRON
ejpam-5385	50	8	,	,	PUNCT
ejpam-5385	50	9	making	make	VERB
ejpam-5385	50	10	it	it	PRON
ejpam-5385	50	11	a	a	DET
ejpam-5385	50	12	lie	lie	NOUN
ejpam-5385	50	13	ideal	ideal	NOUN
ejpam-5385	50	14	of	of	ADP
ejpam-5385	50	15	m.	m.	NOUN
ejpam-5385	50	16	furthermore	furthermore	ADV
ejpam-5385	50	17	,	,	PUNCT
ejpam-5385	50	18	if	if	SCONJ
ejpam-5385	50	19	q	q	X
ejpam-5385	50	20	and	and	CCONJ
ejpam-5385	50	21	s	s	VERB
ejpam-5385	50	22	are	be	AUX
ejpam-5385	50	23	ideals	ideal	NOUN
ejpam-5385	50	24	of	of	ADP
ejpam-5385	50	25	m	m	PRON
ejpam-5385	50	26	,	,	PUNCT
ejpam-5385	50	27	then	then	ADV
ejpam-5385	50	28	q	q	PROPN
ejpam-5385	51	1	+	+	NUM
ejpam-5385	51	2	s	s	NOUN
ejpam-5385	51	3	=	=	PUNCT
ejpam-5385	51	4	{	{	PUNCT
ejpam-5385	51	5	q	q	PROPN
ejpam-5385	51	6	+	+	X
ejpam-5385	51	7	s	s	X
ejpam-5385	51	8	:	:	PUNCT
ejpam-5385	51	9	q	q	PROPN
ejpam-5385	51	10	∈	∈	PROPN
ejpam-5385	51	11	q	q	X
ejpam-5385	51	12	and	and	CCONJ
ejpam-5385	51	13	s	s	PROPN
ejpam-5385	51	14	∈	∈	NOUN
ejpam-5385	51	15	s	s	PART
ejpam-5385	51	16	}	}	PUNCT
ejpam-5385	51	17	,	,	PUNCT
ejpam-5385	52	1	[	[	X
ejpam-5385	52	2	q	q	X
ejpam-5385	52	3	,	,	PUNCT
ejpam-5385	52	4	s	s	PART
ejpam-5385	52	5	]	]	X
ejpam-5385	52	6	=	=	SYM
ejpam-5385	52	7	span{[q	span{[q	NOUN
ejpam-5385	52	8	,	,	PUNCT
ejpam-5385	52	9	s	s	X
ejpam-5385	52	10	]	]	X
ejpam-5385	52	11	:	:	PUNCT
ejpam-5385	52	12	q	q	PUNCT
ejpam-5385	53	1	∈	∈	PROPN
ejpam-5385	53	2	q	q	X
ejpam-5385	53	3	and	and	CCONJ
ejpam-5385	53	4	s	s	PROPN
ejpam-5385	53	5	∈	∈	NOUN
ejpam-5385	53	6	s	s	NOUN
ejpam-5385	53	7	}	}	PUNCT
ejpam-5385	53	8	,	,	PUNCT
ejpam-5385	53	9	and	and	CCONJ
ejpam-5385	53	10	q	q	PROPN
ejpam-5385	53	11	∩	∩	X
ejpam-5385	53	12	s	s	PART
ejpam-5385	53	13	=	=	PUNCT
ejpam-5385	53	14	{	{	PUNCT
ejpam-5385	53	15	m	m	NOUN
ejpam-5385	53	16	:	:	PUNCT
ejpam-5385	53	17	m	m	VERB
ejpam-5385	53	18	∈	∈	PROPN
ejpam-5385	53	19	q	q	NOUN
ejpam-5385	53	20	and	and	CCONJ
ejpam-5385	53	21	m	m	PROPN
ejpam-5385	53	22	∈	∈	NOUN
ejpam-5385	53	23	s	s	PRON
ejpam-5385	53	24	}	}	PUNCT
ejpam-5385	53	25	are	be	AUX
ejpam-5385	53	26	also	also	ADV
ejpam-5385	53	27	considered	consider	VERB
ejpam-5385	53	28	ideals	ideal	NOUN
ejpam-5385	53	29	of	of	ADP
ejpam-5385	53	30	m.	m.	NOUN
ejpam-5385	53	31	considering	consider	VERB
ejpam-5385	53	32	two	two	NUM
ejpam-5385	53	33	lie	lie	NOUN
ejpam-5385	53	34	algebras	algebras	PROPN
ejpam-5385	53	35	m1	m1	PROPN
ejpam-5385	53	36	and	and	CCONJ
ejpam-5385	53	37	m2	m2	PROPN
ejpam-5385	53	38	over	over	ADP
ejpam-5385	53	39	k	k	PROPN
ejpam-5385	53	40	,	,	PUNCT
ejpam-5385	53	41	a	a	DET
ejpam-5385	53	42	linear	linear	ADJ
ejpam-5385	53	43	transformation	transformation	NOUN
ejpam-5385	53	44	t	t	NOUN
ejpam-5385	53	45	:	:	PUNCT
ejpam-5385	53	46	m1	m1	PROPN
ejpam-5385	53	47	→	→	PUNCT
ejpam-5385	53	48	m2	m2	PROPN
ejpam-5385	53	49	is	be	AUX
ejpam-5385	53	50	considered	consider	VERB
ejpam-5385	53	51	a	a	DET
ejpam-5385	53	52	lie	lie	NOUN
ejpam-5385	53	53	algebra	algebra	NOUN
ejpam-5385	53	54	homomorphism	homomorphism	NOUN
ejpam-5385	53	55	if	if	SCONJ
ejpam-5385	53	56	it	it	PRON
ejpam-5385	53	57	satisfies	satisfy	VERB
ejpam-5385	53	58	t	t	X
ejpam-5385	53	59	(	(	PUNCT
ejpam-5385	53	60	[	[	X
ejpam-5385	53	61	m	m	X
ejpam-5385	53	62	,	,	PUNCT
ejpam-5385	53	63	n	n	CCONJ
ejpam-5385	53	64	]	]	PUNCT
ejpam-5385	53	65	)	)	PUNCT
ejpam-5385	54	1	=	=	PUNCT
ejpam-5385	55	1	[	[	X
ejpam-5385	55	2	t	t	X
ejpam-5385	55	3	(	(	PUNCT
ejpam-5385	55	4	m	m	PROPN
ejpam-5385	55	5	)	)	PUNCT
ejpam-5385	55	6	,	,	PUNCT
ejpam-5385	55	7	t	t	PROPN
ejpam-5385	55	8	(	(	PUNCT
ejpam-5385	55	9	n	n	CCONJ
ejpam-5385	55	10	)	)	PUNCT
ejpam-5385	55	11	]	]	PUNCT
ejpam-5385	55	12	for	for	ADP
ejpam-5385	55	13	all	all	DET
ejpam-5385	55	14	m	m	PROPN
ejpam-5385	55	15	,	,	PUNCT
ejpam-5385	55	16	n	n	PROPN
ejpam-5385	55	17	∈	∈	PROPN
ejpam-5385	55	18	m1	m1	NOUN
ejpam-5385	55	19	.	.	PUNCT
ejpam-5385	56	1	furthermore	furthermore	ADV
ejpam-5385	56	2	,	,	PUNCT
ejpam-5385	56	3	if	if	SCONJ
ejpam-5385	56	4	t	t	PROPN
ejpam-5385	56	5	is	be	AUX
ejpam-5385	56	6	both	both	PRON
ejpam-5385	56	7	a	a	DET
ejpam-5385	56	8	lie	lie	NOUN
ejpam-5385	56	9	algebra	algebra	VERB
ejpam-5385	56	10	homomorphism	homomorphism	NOUN
ejpam-5385	56	11	and	and	CCONJ
ejpam-5385	56	12	a	a	DET
ejpam-5385	56	13	bijection	bijection	NOUN
ejpam-5385	56	14	(	(	PUNCT
ejpam-5385	56	15	one	one	NUM
ejpam-5385	56	16	-	-	PUNCT
ejpam-5385	56	17	to	to	ADP
ejpam-5385	56	18	-	-	PUNCT
ejpam-5385	56	19	one	one	NUM
ejpam-5385	56	20	and	and	CCONJ
ejpam-5385	56	21	onto	onto	ADP
ejpam-5385	56	22	)	)	PUNCT
ejpam-5385	56	23	,	,	PUNCT
ejpam-5385	56	24	it	it	PRON
ejpam-5385	56	25	’s	’s	AUX
ejpam-5385	56	26	termed	term	VERB
ejpam-5385	56	27	a	a	DET
ejpam-5385	56	28	lie	lie	NOUN
ejpam-5385	56	29	algebra	algebra	NOUN
ejpam-5385	56	30	isomorphism	isomorphism	NOUN
ejpam-5385	56	31	.	.	PUNCT
ejpam-5385	57	1	an	an	DET
ejpam-5385	57	2	illustrative	illustrative	ADJ
ejpam-5385	57	3	example	example	NOUN
ejpam-5385	57	4	showcases	showcase	VERB
ejpam-5385	57	5	the	the	DET
ejpam-5385	57	6	adjoint	adjoint	NOUN
ejpam-5385	57	7	representation	representation	NOUN
ejpam-5385	57	8	of	of	ADP
ejpam-5385	57	9	a	a	DET
ejpam-5385	57	10	lie	lie	NOUN
ejpam-5385	57	11	algebra	algebra	NOUN
ejpam-5385	57	12	.	.	PUNCT
ejpam-5385	58	1	for	for	ADP
ejpam-5385	58	2	m	m	PROPN
ejpam-5385	58	3	∈	∈	PROPN
ejpam-5385	58	4	m	m	PRON
ejpam-5385	58	5	,	,	PUNCT
ejpam-5385	58	6	the	the	DET
ejpam-5385	58	7	function	function	NOUN
ejpam-5385	58	8	adm	adm	NOUN
ejpam-5385	58	9	:	:	PUNCT
ejpam-5385	58	10	m	m	VERB
ejpam-5385	58	11	→	→	SYM
ejpam-5385	58	12	m	m	PROPN
ejpam-5385	58	13	;	;	PUNCT
ejpam-5385	58	14	n	n	PRON
ejpam-5385	58	15	7→	7→	NUM
ejpam-5385	59	1	[	[	X
ejpam-5385	59	2	m	m	X
ejpam-5385	59	3	,	,	PUNCT
ejpam-5385	59	4	n	n	CCONJ
ejpam-5385	59	5	]	]	PUNCT
ejpam-5385	59	6	is	be	AUX
ejpam-5385	59	7	defined	define	VERB
ejpam-5385	59	8	,	,	PUNCT
ejpam-5385	59	9	and	and	CCONJ
ejpam-5385	59	10	the	the	DET
ejpam-5385	59	11	set	set	NOUN
ejpam-5385	59	12	adm	adm	PROPN
ejpam-5385	59	13	=	=	SYM
ejpam-5385	59	14	{	{	PUNCT
ejpam-5385	59	15	adm	adm	PROPN
ejpam-5385	59	16	:	:	PUNCT
ejpam-5385	59	17	m	m	VERB
ejpam-5385	59	18	∈	∈	PROPN
ejpam-5385	59	19	m	m	AUX
ejpam-5385	59	20	}	}	PUNCT
ejpam-5385	59	21	is	be	AUX
ejpam-5385	59	22	shown	show	VERB
ejpam-5385	59	23	to	to	PART
ejpam-5385	59	24	be	be	AUX
ejpam-5385	59	25	a	a	DET
ejpam-5385	59	26	lie	lie	NOUN
ejpam-5385	59	27	subalgebra	subalgebra	NOUN
ejpam-5385	59	28	of	of	ADP
ejpam-5385	59	29	gl(m	gl(m	PROPN
ejpam-5385	59	30	)	)	PUNCT
ejpam-5385	59	31	.	.	PUNCT
ejpam-5385	60	1	the	the	DET
ejpam-5385	60	2	function	function	NOUN
ejpam-5385	60	3	ad	ad	NOUN
ejpam-5385	60	4	:	:	PUNCT
ejpam-5385	60	5	m	m	VERB
ejpam-5385	60	6	→	→	SYM
ejpam-5385	60	7	adm;m	adm;m	PROPN
ejpam-5385	60	8	7→	7→	NUM
ejpam-5385	60	9	adm	adm	NOUN
ejpam-5385	60	10	is	be	AUX
ejpam-5385	60	11	a	a	DET
ejpam-5385	60	12	lie	lie	NOUN
ejpam-5385	60	13	algebra	algebra	NOUN
ejpam-5385	60	14	homomorphism	homomorphism	PROPN
ejpam-5385	60	15	and	and	CCONJ
ejpam-5385	60	16	is	be	AUX
ejpam-5385	60	17	known	know	VERB
ejpam-5385	60	18	as	as	ADP
ejpam-5385	60	19	the	the	DET
ejpam-5385	60	20	adjoint	adjoint	PROPN
ejpam-5385	60	21	representation	representation	NOUN
ejpam-5385	60	22	of	of	ADP
ejpam-5385	60	23	m.	m.	NOUN
ejpam-5385	60	24	moreover	moreover	ADV
ejpam-5385	60	25	,	,	PUNCT
ejpam-5385	60	26	for	for	SCONJ
ejpam-5385	60	27	a	a	DET
ejpam-5385	60	28	lie	lie	NOUN
ejpam-5385	60	29	algebra	algebra	NOUN
ejpam-5385	60	30	homomorphism	homomorphism	PROPN
ejpam-5385	60	31	f	f	X
ejpam-5385	60	32	:	:	PUNCT
ejpam-5385	60	33	m1	m1	PROPN
ejpam-5385	60	34	→	→	SYM
ejpam-5385	60	35	m2	m2	PROPN
ejpam-5385	60	36	,	,	PUNCT
ejpam-5385	60	37	the	the	DET
ejpam-5385	60	38	image	image	NOUN
ejpam-5385	60	39	of	of	ADP
ejpam-5385	60	40	f	f	PROPN
ejpam-5385	60	41	is	be	AUX
ejpam-5385	60	42	characterized	characterize	VERB
ejpam-5385	60	43	as	as	ADP
ejpam-5385	60	44	im(f	im(f	NOUN
ejpam-5385	60	45	)	)	PUNCT
ejpam-5385	60	46	=	=	PRON
ejpam-5385	60	47	{	{	PUNCT
ejpam-5385	60	48	f(q	f(q	PROPN
ejpam-5385	60	49	)	)	PUNCT
ejpam-5385	60	50	:	:	PUNCT
ejpam-5385	60	51	q	q	PROPN
ejpam-5385	60	52	∈	∈	PROPN
ejpam-5385	60	53	m1	m1	NOUN
ejpam-5385	60	54	}	}	PUNCT
ejpam-5385	60	55	,	,	PUNCT
ejpam-5385	60	56	while	while	SCONJ
ejpam-5385	60	57	the	the	DET
ejpam-5385	60	58	kernel	kernel	NOUN
ejpam-5385	60	59	of	of	ADP
ejpam-5385	60	60	f	f	PROPN
ejpam-5385	60	61	is	be	AUX
ejpam-5385	60	62	denoted	denote	VERB
ejpam-5385	60	63	as	as	ADP
ejpam-5385	60	64	ker(f	ker(f	PROPN
ejpam-5385	60	65	)	)	PUNCT
ejpam-5385	60	66	=	=	PRON
ejpam-5385	61	1	{	{	PUNCT
ejpam-5385	61	2	s	s	NOUN
ejpam-5385	61	3	∈	∈	PROPN
ejpam-5385	61	4	m1	m1	NOUN
ejpam-5385	61	5	:	:	PUNCT
ejpam-5385	61	6	f(s	f(s	X
ejpam-5385	61	7	)	)	PUNCT
ejpam-5385	61	8	=	=	SYM
ejpam-5385	61	9	0m2	0m2	NUM
ejpam-5385	61	10	}	}	PUNCT
ejpam-5385	61	11	.	.	PUNCT
ejpam-5385	62	1	as	as	ADP
ejpam-5385	62	2	a	a	DET
ejpam-5385	62	3	consequence	consequence	NOUN
ejpam-5385	62	4	,	,	PUNCT
ejpam-5385	62	5	im(f	im(f	NOUN
ejpam-5385	62	6	)	)	PUNCT
ejpam-5385	62	7	emerges	emerge	VERB
ejpam-5385	62	8	as	as	ADP
ejpam-5385	62	9	a	a	DET
ejpam-5385	62	10	lie	lie	NOUN
ejpam-5385	62	11	subalgebra	subalgebra	NOUN
ejpam-5385	62	12	within	within	ADP
ejpam-5385	62	13	m2	m2	PROPN
ejpam-5385	62	14	,	,	PUNCT
ejpam-5385	62	15	and	and	CCONJ
ejpam-5385	62	16	ker(f	ker(f	PROPN
ejpam-5385	62	17	)	)	PUNCT
ejpam-5385	62	18	establishes	establish	VERB
ejpam-5385	62	19	itself	itself	PRON
ejpam-5385	62	20	as	as	ADP
ejpam-5385	62	21	an	an	DET
ejpam-5385	62	22	ideal	ideal	NOUN
ejpam-5385	62	23	within	within	ADP
ejpam-5385	62	24	m1	m1	NOUN
ejpam-5385	62	25	.	.	PUNCT
ejpam-5385	63	1	2.2	2.2	NUM
ejpam-5385	63	2	.	.	PUNCT
ejpam-5385	63	3	fundamentals	fundamental	NOUN
ejpam-5385	63	4	of	of	ADP
ejpam-5385	63	5	complex	complex	ADJ
ejpam-5385	63	6	intuitionistic	intuitionistic	ADJ
ejpam-5385	63	7	fuzzy	fuzzy	ADJ
ejpam-5385	63	8	lie	lie	NOUN
ejpam-5385	63	9	ideals	ideal	NOUN
ejpam-5385	63	10	a	a	DET
ejpam-5385	63	11	complex	complex	ADJ
ejpam-5385	63	12	intuitionistic	intuitionistic	ADJ
ejpam-5385	63	13	fuzzy	fuzzy	ADJ
ejpam-5385	63	14	set	set	NOUN
ejpam-5385	63	15	defined	define	VERB
ejpam-5385	63	16	on	on	ADP
ejpam-5385	63	17	a	a	DET
ejpam-5385	63	18	non	non	ADJ
ejpam-5385	63	19	-	-	ADJ
ejpam-5385	63	20	empty	empty	ADJ
ejpam-5385	63	21	set	set	NOUN
ejpam-5385	63	22	x	x	PUNCT
ejpam-5385	63	23	can	can	AUX
ejpam-5385	63	24	be	be	AUX
ejpam-5385	63	25	denoted	denote	VERB
ejpam-5385	63	26	as	as	ADP
ejpam-5385	63	27	e	e	X
ejpam-5385	63	28	=	=	PUNCT
ejpam-5385	63	29	(	(	PUNCT
ejpam-5385	63	30	ϕe	ϕe	INTJ
ejpam-5385	63	31	,	,	PUNCT
ejpam-5385	63	32	ψe	ψe	NOUN
ejpam-5385	63	33	)	)	PUNCT
ejpam-5385	63	34	=	=	SYM
ejpam-5385	63	35	{	{	PUNCT
ejpam-5385	63	36	(	(	PUNCT
ejpam-5385	63	37	x	x	NOUN
ejpam-5385	63	38	,	,	PUNCT
ejpam-5385	63	39	ϕe(x	ϕe(x	NUM
ejpam-5385	63	40	)	)	PUNCT
ejpam-5385	63	41	,	,	PUNCT
ejpam-5385	63	42	ψe(x	ψe(x	PROPN
ejpam-5385	63	43	)	)	PUNCT
ejpam-5385	63	44	)	)	PUNCT
ejpam-5385	63	45	:	:	PUNCT
ejpam-5385	64	1	x	x	X
ejpam-5385	64	2	∈	∈	NOUN
ejpam-5385	64	3	x	x	X
ejpam-5385	64	4	}	}	PUNCT
ejpam-5385	64	5	.	.	PUNCT
ejpam-5385	65	1	in	in	ADP
ejpam-5385	65	2	this	this	DET
ejpam-5385	65	3	representation	representation	NOUN
ejpam-5385	65	4	,	,	PUNCT
ejpam-5385	65	5	ϕe(x	ϕe(x	PROPN
ejpam-5385	65	6	)	)	PUNCT
ejpam-5385	65	7	and	and	CCONJ
ejpam-5385	65	8	ψe(x	ψe(x	NUM
ejpam-5385	65	9	)	)	PUNCT
ejpam-5385	65	10	are	be	AUX
ejpam-5385	65	11	complex	complex	ADJ
ejpam-5385	65	12	numbers	number	NOUN
ejpam-5385	65	13	situated	situate	VERB
ejpam-5385	65	14	within	within	ADP
ejpam-5385	65	15	the	the	DET
ejpam-5385	65	16	unit	unit	NOUN
ejpam-5385	65	17	circle	circle	NOUN
ejpam-5385	65	18	,	,	PUNCT
ejpam-5385	65	19	ensuring	ensure	VERB
ejpam-5385	65	20	that	that	SCONJ
ejpam-5385	65	21	their	their	PRON
ejpam-5385	65	22	absolute	absolute	ADJ
ejpam-5385	65	23	values	value	NOUN
ejpam-5385	65	24	satisfy	satisfy	VERB
ejpam-5385	65	25	the	the	DET
ejpam-5385	65	26	condition	condition	NOUN
ejpam-5385	65	27	|	|	ADV
ejpam-5385	65	28	ϕe(x	ϕe(x	PUNCT
ejpam-5385	65	29	)	)	PUNCT
ejpam-5385	66	1	|	|	ADV
ejpam-5385	66	2	+	+	CCONJ
ejpam-5385	66	3	|	|	ADV
ejpam-5385	66	4	ψe(x	ψe(x	VERB
ejpam-5385	66	5	)	)	PUNCT
ejpam-5385	66	6	|≤	|≤	PROPN
ejpam-5385	66	7	1	1	NUM
ejpam-5385	66	8	.	.	PUNCT
ejpam-5385	67	1	in	in	ADP
ejpam-5385	67	2	this	this	DET
ejpam-5385	67	3	context	context	NOUN
ejpam-5385	67	4	,	,	PUNCT
ejpam-5385	67	5	i	i	PRON
ejpam-5385	67	6	=	=	PUNCT
ejpam-5385	67	7	√	√	NUM
ejpam-5385	67	8	−1	−1	NOUN
ejpam-5385	67	9	,	,	PUNCT
ejpam-5385	67	10	and	and	CCONJ
ejpam-5385	67	11	the	the	DET
ejpam-5385	67	12	expressions	expression	NOUN
ejpam-5385	67	13	for	for	ADP
ejpam-5385	67	14	ϕe(x	ϕe(x	PUNCT
ejpam-5385	67	15	)	)	PUNCT
ejpam-5385	67	16	and	and	CCONJ
ejpam-5385	67	17	ψe(x	ψe(x	X
ejpam-5385	67	18	)	)	PUNCT
ejpam-5385	67	19	take	take	VERB
ejpam-5385	67	20	the	the	DET
ejpam-5385	67	21	form	form	NOUN
ejpam-5385	67	22	ρe(x)e	ρe(x)e	PROPN
ejpam-5385	67	23	iζe(x	iζe(x	PROPN
ejpam-5385	67	24	)	)	PUNCT
ejpam-5385	67	25	and	and	CCONJ
ejpam-5385	67	26	ρ̂e(x)e	ρ̂e(x)e	ADJ
ejpam-5385	67	27	iζ̂e(x	iζ̂e(x	NOUN
ejpam-5385	67	28	)	)	PUNCT
ejpam-5385	67	29	respectively	respectively	ADV
ejpam-5385	67	30	.	.	PUNCT
ejpam-5385	68	1	here	here	ADV
ejpam-5385	68	2	,	,	PUNCT
ejpam-5385	68	3	ρe(x	ρe(x	NUM
ejpam-5385	68	4	)	)	PUNCT
ejpam-5385	68	5	and	and	CCONJ
ejpam-5385	68	6	ρ̂a(x	ρ̂a(x	NOUN
ejpam-5385	68	7	)	)	PUNCT
ejpam-5385	68	8	are	be	AUX
ejpam-5385	68	9	real	real	ADJ
ejpam-5385	68	10	numbers	number	NOUN
ejpam-5385	68	11	ranging	range	VERB
ejpam-5385	68	12	from	from	ADP
ejpam-5385	68	13	0	0	NUM
ejpam-5385	68	14	to	to	ADP
ejpam-5385	68	15	1	1	NUM
ejpam-5385	68	16	,	,	PUNCT
ejpam-5385	68	17	while	while	SCONJ
ejpam-5385	68	18	ζm(x	ζm(x	NUM
ejpam-5385	68	19	)	)	PUNCT
ejpam-5385	68	20	and	and	CCONJ
ejpam-5385	68	21	ζ̂m(x	ζ̂m(x	NOUN
ejpam-5385	68	22	)	)	PUNCT
ejpam-5385	68	23	are	be	AUX
ejpam-5385	68	24	real	real	ADJ
ejpam-5385	68	25	numbers	number	NOUN
ejpam-5385	68	26	within	within	ADP
ejpam-5385	68	27	the	the	DET
ejpam-5385	68	28	interval	interval	NOUN
ejpam-5385	68	29	of	of	ADP
ejpam-5385	68	30	[	[	X
ejpam-5385	68	31	0	0	NUM
ejpam-5385	68	32	,	,	PUNCT
ejpam-5385	68	33	2π	2π	NOUN
ejpam-5385	68	34	]	]	PUNCT
ejpam-5385	68	35	.	.	PUNCT
ejpam-5385	69	1	the	the	DET
ejpam-5385	69	2	notion	notion	NOUN
ejpam-5385	69	3	of	of	ADP
ejpam-5385	69	4	complex	complex	ADJ
ejpam-5385	69	5	intuitionistic	intuitionistic	ADJ
ejpam-5385	69	6	fuzzy	fuzzy	ADJ
ejpam-5385	69	7	sets	set	NOUN
ejpam-5385	69	8	(	(	PUNCT
ejpam-5385	69	9	cifs	cifs	PROPN
ejpam-5385	69	10	)	)	PUNCT
ejpam-5385	69	11	can	can	AUX
ejpam-5385	69	12	be	be	AUX
ejpam-5385	69	13	seen	see	VERB
ejpam-5385	69	14	as	as	ADP
ejpam-5385	69	15	an	an	DET
ejpam-5385	69	16	expansion	expansion	NOUN
ejpam-5385	69	17	of	of	ADP
ejpam-5385	69	18	intuitionistic	intuitionistic	ADJ
ejpam-5385	69	19	fuzzy	fuzzy	ADJ
ejpam-5385	69	20	sets	set	NOUN
ejpam-5385	69	21	.	.	PUNCT
ejpam-5385	70	1	when	when	SCONJ
ejpam-5385	70	2	both	both	DET
ejpam-5385	70	3	ζe(x	ζe(x	NUM
ejpam-5385	70	4	)	)	PUNCT
ejpam-5385	70	5	and	and	CCONJ
ejpam-5385	70	6	ζ̂e(x	ζ̂e(x	PROPN
ejpam-5385	70	7	)	)	PUNCT
ejpam-5385	70	8	are	be	AUX
ejpam-5385	70	9	set	set	VERB
ejpam-5385	70	10	to	to	ADP
ejpam-5385	70	11	0	0	NUM
ejpam-5385	70	12	,	,	PUNCT
ejpam-5385	70	13	it	it	PRON
ejpam-5385	70	14	reverts	revert	VERB
ejpam-5385	70	15	to	to	ADP
ejpam-5385	70	16	the	the	DET
ejpam-5385	70	17	classical	classical	ADJ
ejpam-5385	70	18	s.	s.	PROPN
ejpam-5385	70	19	shaqaqha	shaqaqha	PROPN
ejpam-5385	70	20	,	,	PUNCT
ejpam-5385	70	21	m.	m.	PROPN
ejpam-5385	70	22	y.	y.	PROPN
ejpam-5385	70	23	al	al	PROPN
ejpam-5385	70	24	-	-	PUNCT
ejpam-5385	70	25	deiakeh	deiakeh	PROPN
ejpam-5385	70	26	/	/	SYM
ejpam-5385	70	27	eur	eur	NOUN
ejpam-5385	70	28	.	.	PUNCT
ejpam-5385	71	1	j.	j.	PROPN
ejpam-5385	71	2	pure	pure	PROPN
ejpam-5385	71	3	appl	appl	PROPN
ejpam-5385	71	4	.	.	PROPN
ejpam-5385	71	5	math	math	PROPN
ejpam-5385	71	6	,	,	PUNCT
ejpam-5385	71	7	17	17	NUM
ejpam-5385	71	8	(	(	PUNCT
ejpam-5385	71	9	4	4	NUM
ejpam-5385	71	10	)	)	PUNCT
ejpam-5385	71	11	(	(	PUNCT
ejpam-5385	71	12	2024	2024	NUM
ejpam-5385	71	13	)	)	PUNCT
ejpam-5385	71	14	,	,	PUNCT
ejpam-5385	71	15	3291	3291	NUM
ejpam-5385	71	16	-	-	SYM
ejpam-5385	71	17	3303	3303	NUM
ejpam-5385	71	18	3294	3294	NUM
ejpam-5385	71	19	fuzzy	fuzzy	ADJ
ejpam-5385	71	20	set	set	NOUN
ejpam-5385	71	21	.	.	PUNCT
ejpam-5385	72	1	furthermore	furthermore	ADV
ejpam-5385	72	2	,	,	PUNCT
ejpam-5385	72	3	when	when	SCONJ
ejpam-5385	72	4	ψe(x	ψe(x	VERB
ejpam-5385	72	5	)	)	PUNCT
ejpam-5385	72	6	=	=	SYM
ejpam-5385	72	7	(	(	PUNCT
ejpam-5385	72	8	1−ρe(x))ei(2π−ζe(x	1−ρe(x))ei(2π−ζe(x	NUM
ejpam-5385	72	9	)	)	PUNCT
ejpam-5385	72	10	)	)	PUNCT
ejpam-5385	72	11	,	,	PUNCT
ejpam-5385	72	12	it	it	PRON
ejpam-5385	72	13	produces	produce	VERB
ejpam-5385	72	14	a	a	DET
ejpam-5385	72	15	complex	complex	ADJ
ejpam-5385	72	16	fuzzy	fuzzy	ADJ
ejpam-5385	72	17	set	set	NOUN
ejpam-5385	72	18	.	.	PUNCT
ejpam-5385	73	1	a	a	DET
ejpam-5385	73	2	homogeneous	homogeneous	ADJ
ejpam-5385	73	3	complex	complex	ADJ
ejpam-5385	73	4	intuitionistic	intuitionistic	ADJ
ejpam-5385	73	5	fuzzy	fuzzy	ADJ
ejpam-5385	73	6	set	set	NOUN
ejpam-5385	73	7	is	be	AUX
ejpam-5385	73	8	defined	define	VERB
ejpam-5385	73	9	as	as	ADP
ejpam-5385	73	10	a	a	DET
ejpam-5385	73	11	cifs	cif	NOUN
ejpam-5385	73	12	that	that	PRON
ejpam-5385	73	13	fulfills	fulfill	VERB
ejpam-5385	73	14	two	two	NUM
ejpam-5385	73	15	conditions	condition	NOUN
ejpam-5385	73	16	for	for	ADP
ejpam-5385	73	17	any	any	DET
ejpam-5385	73	18	x	x	NOUN
ejpam-5385	73	19	and	and	CCONJ
ejpam-5385	73	20	y	y	PROPN
ejpam-5385	73	21	belonging	belong	VERB
ejpam-5385	73	22	to	to	ADP
ejpam-5385	73	23	the	the	DET
ejpam-5385	73	24	set	set	NOUN
ejpam-5385	73	25	x	x	NOUN
ejpam-5385	73	26	:	:	PUNCT
ejpam-5385	73	27	(	(	PUNCT
ejpam-5385	73	28	i	i	NOUN
ejpam-5385	73	29	)	)	PUNCT
ejpam-5385	73	30	ρe(x	ρe(x	X
ejpam-5385	73	31	)	)	PUNCT
ejpam-5385	73	32	≤	≤	NOUN
ejpam-5385	73	33	ρe(y	ρe(y	VERB
ejpam-5385	73	34	)	)	PUNCT
ejpam-5385	73	35	if	if	SCONJ
ejpam-5385	73	36	and	and	CCONJ
ejpam-5385	73	37	only	only	ADV
ejpam-5385	73	38	if	if	SCONJ
ejpam-5385	73	39	ζe(x	ζe(x	NUM
ejpam-5385	73	40	)	)	PUNCT
ejpam-5385	73	41	≤	≤	NOUN
ejpam-5385	73	42	ζe(y	ζe(y	NUM
ejpam-5385	73	43	)	)	PUNCT
ejpam-5385	73	44	,	,	PUNCT
ejpam-5385	73	45	and	and	CCONJ
ejpam-5385	73	46	(	(	PUNCT
ejpam-5385	73	47	ii	ii	NOUN
ejpam-5385	73	48	)	)	PUNCT
ejpam-5385	73	49	ρ̂e(x	ρ̂e(x	PROPN
ejpam-5385	73	50	)	)	PUNCT
ejpam-5385	73	51	≤	≤	NOUN
ejpam-5385	74	1	ρ̂e(y	ρ̂e(y	PROPN
ejpam-5385	74	2	)	)	PUNCT
ejpam-5385	75	1	if	if	SCONJ
ejpam-5385	75	2	and	and	CCONJ
ejpam-5385	75	3	only	only	ADV
ejpam-5385	75	4	if	if	SCONJ
ejpam-5385	75	5	ζ̂e(x	ζ̂e(x	PROPN
ejpam-5385	75	6	)	)	PUNCT
ejpam-5385	75	7	≤	≤	NUM
ejpam-5385	75	8	ζ̂e(y	ζ̂e(y	PROPN
ejpam-5385	75	9	)	)	PUNCT
ejpam-5385	75	10	.	.	PUNCT
ejpam-5385	76	1	in	in	ADP
ejpam-5385	76	2	the	the	DET
ejpam-5385	76	3	article	article	NOUN
ejpam-5385	76	4	,	,	PUNCT
ejpam-5385	76	5	it	it	PRON
ejpam-5385	76	6	is	be	AUX
ejpam-5385	76	7	assumed	assume	VERB
ejpam-5385	76	8	that	that	SCONJ
ejpam-5385	76	9	all	all	DET
ejpam-5385	76	10	complex	complex	ADJ
ejpam-5385	76	11	intuitionistic	intuitionistic	ADJ
ejpam-5385	76	12	fuzzy	fuzzy	ADJ
ejpam-5385	76	13	sets	set	NOUN
ejpam-5385	76	14	are	be	AUX
ejpam-5385	76	15	of	of	ADP
ejpam-5385	76	16	this	this	DET
ejpam-5385	76	17	homogeneous	homogeneous	ADJ
ejpam-5385	76	18	type	type	NOUN
ejpam-5385	76	19	.	.	PUNCT
ejpam-5385	77	1	also	also	ADV
ejpam-5385	77	2	,	,	PUNCT
ejpam-5385	77	3	for	for	ADP
ejpam-5385	77	4	z1	z1	NOUN
ejpam-5385	77	5	=	=	SYM
ejpam-5385	77	6	ρ1e	ρ1e	PROPN
ejpam-5385	77	7	iζ1	iζ1	NOUN
ejpam-5385	77	8	and	and	CCONJ
ejpam-5385	77	9	z2ρ2e	z2ρ2e	NUM
ejpam-5385	77	10	iζ2	iζ2	PROPN
ejpam-5385	77	11	(	(	PUNCT
ejpam-5385	77	12	ρ1	ρ1	NOUN
ejpam-5385	77	13	,	,	PUNCT
ejpam-5385	77	14	ρ2	ρ2	PROPN
ejpam-5385	77	15	∈	∈	PROPN
ejpam-5385	78	1	[	[	X
ejpam-5385	78	2	0	0	NUM
ejpam-5385	78	3	,	,	PUNCT
ejpam-5385	78	4	1	1	NUM
ejpam-5385	78	5	]	]	PUNCT
ejpam-5385	78	6	and	and	CCONJ
ejpam-5385	78	7	ζ1	ζ1	NOUN
ejpam-5385	78	8	,	,	PUNCT
ejpam-5385	78	9	ζ2	ζ2	NOUN
ejpam-5385	78	10	∈	∈	PROPN
ejpam-5385	79	1	[	[	X
ejpam-5385	79	2	0	0	NUM
ejpam-5385	79	3	,	,	PUNCT
ejpam-5385	79	4	2π	2π	NOUN
ejpam-5385	79	5	]	]	PUNCT
ejpam-5385	79	6	)	)	PUNCT
ejpam-5385	79	7	are	be	AUX
ejpam-5385	79	8	two	two	NUM
ejpam-5385	79	9	complex	complex	ADJ
ejpam-5385	79	10	numbers	number	NOUN
ejpam-5385	79	11	,	,	PUNCT
ejpam-5385	79	12	we	we	PRON
ejpam-5385	79	13	say	say	VERB
ejpam-5385	79	14	z1	z1	ADJ
ejpam-5385	79	15	≤	≤	PROPN
ejpam-5385	79	16	z2	z2	PROPN
ejpam-5385	79	17	if	if	SCONJ
ejpam-5385	79	18	and	and	CCONJ
ejpam-5385	79	19	only	only	ADV
ejpam-5385	79	20	if	if	SCONJ
ejpam-5385	79	21	ρ1	ρ1	NOUN
ejpam-5385	79	22	≤	≤	NUM
ejpam-5385	79	23	ρ2	ρ2	NOUN
ejpam-5385	79	24	and	and	CCONJ
ejpam-5385	79	25	ζ1	ζ1	NOUN
ejpam-5385	79	26	≤	≤	ADJ
ejpam-5385	79	27	ζ2	ζ2	NOUN
ejpam-5385	79	28	.	.	PUNCT
ejpam-5385	80	1	definition	definition	NOUN
ejpam-5385	80	2	1	1	NUM
ejpam-5385	80	3	.	.	PUNCT
ejpam-5385	81	1	(	(	PUNCT
ejpam-5385	81	2	[	[	X
ejpam-5385	81	3	18	18	NUM
ejpam-5385	81	4	]	]	SYM
ejpam-5385	81	5	)	)	PUNCT
ejpam-5385	81	6	a	a	DET
ejpam-5385	81	7	complex	complex	ADJ
ejpam-5385	81	8	intuitionistic	intuitionistic	ADJ
ejpam-5385	81	9	fuzzy	fuzzy	ADJ
ejpam-5385	81	10	set	set	NOUN
ejpam-5385	81	11	e	e	NOUN
ejpam-5385	81	12	=	=	SYM
ejpam-5385	81	13	(	(	PUNCT
ejpam-5385	81	14	ϕe	ϕe	INTJ
ejpam-5385	81	15	,	,	PUNCT
ejpam-5385	81	16	ψa	ψa	PROPN
ejpam-5385	81	17	)	)	PUNCT
ejpam-5385	81	18	defined	define	VERB
ejpam-5385	81	19	on	on	ADP
ejpam-5385	81	20	a	a	DET
ejpam-5385	81	21	lie	lie	NOUN
ejpam-5385	81	22	algebra	algebra	NOUN
ejpam-5385	81	23	m	m	VERB
ejpam-5385	81	24	is	be	AUX
ejpam-5385	81	25	categorized	categorize	VERB
ejpam-5385	81	26	as	as	ADP
ejpam-5385	81	27	a	a	DET
ejpam-5385	81	28	complex	complex	ADJ
ejpam-5385	81	29	intuitionistic	intuitionistic	ADJ
ejpam-5385	81	30	fuzzy	fuzzy	ADJ
ejpam-5385	81	31	lie	lie	NOUN
ejpam-5385	81	32	subalgebra	subalgebra	NOUN
ejpam-5385	81	33	when	when	SCONJ
ejpam-5385	81	34	it	it	PRON
ejpam-5385	81	35	meets	meet	VERB
ejpam-5385	81	36	three	three	NUM
ejpam-5385	81	37	conditions	condition	NOUN
ejpam-5385	81	38	for	for	ADP
ejpam-5385	81	39	all	all	DET
ejpam-5385	81	40	m1,m2	m1,m2	PROPN
ejpam-5385	81	41	∈	∈	PROPN
ejpam-5385	81	42	m	m	NOUN
ejpam-5385	81	43	,	,	PUNCT
ejpam-5385	81	44	and	and	CCONJ
ejpam-5385	81	45	k	k	PROPN
ejpam-5385	81	46	∈	∈	PROPN
ejpam-5385	82	1	k	k	NOUN
ejpam-5385	82	2	:	:	PUNCT
ejpam-5385	82	3	(	(	PUNCT
ejpam-5385	82	4	i	i	NOUN
ejpam-5385	82	5	)	)	PUNCT
ejpam-5385	82	6	ϕe(m1	ϕe(m1	VERB
ejpam-5385	83	1	+	+	SYM
ejpam-5385	83	2	m2	m2	NOUN
ejpam-5385	83	3	)	)	PUNCT
ejpam-5385	83	4	≥	≥	NOUN
ejpam-5385	83	5	ϕe(m1	ϕe(m1	X
ejpam-5385	83	6	)	)	PUNCT
ejpam-5385	83	7	∧	∧	NOUN
ejpam-5385	83	8	ϕe(m2	ϕe(m2	PRON
ejpam-5385	83	9	)	)	PUNCT
ejpam-5385	83	10	and	and	CCONJ
ejpam-5385	83	11	ψm(m1	ψm(m1	VERB
ejpam-5385	83	12	+	+	ADJ
ejpam-5385	83	13	m2	m2	NOUN
ejpam-5385	83	14	)	)	PUNCT
ejpam-5385	83	15	≤	≤	NUM
ejpam-5385	83	16	ψe(m1	ψe(m1	NOUN
ejpam-5385	83	17	)	)	PUNCT
ejpam-5385	83	18	∨	∨	NUM
ejpam-5385	83	19	ψe(m2	ψe(m2	X
ejpam-5385	83	20	)	)	PUNCT
ejpam-5385	83	21	,	,	PUNCT
ejpam-5385	83	22	(	(	PUNCT
ejpam-5385	83	23	ii	ii	NOUN
ejpam-5385	83	24	)	)	PUNCT
ejpam-5385	83	25	ϕe(km1	ϕe(km1	PROPN
ejpam-5385	83	26	)	)	PUNCT
ejpam-5385	83	27	≥	≥	NOUN
ejpam-5385	83	28	ϕe(x	ϕe(x	PUNCT
ejpam-5385	83	29	)	)	PUNCT
ejpam-5385	83	30	and	and	CCONJ
ejpam-5385	83	31	ψe(km1	ψe(km1	NOUN
ejpam-5385	83	32	)	)	PUNCT
ejpam-5385	83	33	≤	≤	NUM
ejpam-5385	83	34	ψe(m1	ψe(m1	NOUN
ejpam-5385	83	35	)	)	PUNCT
ejpam-5385	83	36	,	,	PUNCT
ejpam-5385	83	37	and	and	CCONJ
ejpam-5385	83	38	(	(	PUNCT
ejpam-5385	83	39	iii	iii	X
ejpam-5385	83	40	)	)	PUNCT
ejpam-5385	83	41	ϕe([m1,m2	ϕe([m1,m2	PROPN
ejpam-5385	83	42	]	]	PUNCT
ejpam-5385	83	43	)	)	PUNCT
ejpam-5385	83	44	≥	≥	NOUN
ejpam-5385	83	45	ϕe(m1	ϕe(m1	X
ejpam-5385	83	46	)	)	PUNCT
ejpam-5385	83	47	∧	∧	NOUN
ejpam-5385	83	48	ϕe(m2	ϕe(m2	PRON
ejpam-5385	83	49	)	)	PUNCT
ejpam-5385	83	50	and	and	CCONJ
ejpam-5385	83	51	ψe([m1,m2	ψe([m1,m2	PROPN
ejpam-5385	83	52	]	]	PUNCT
ejpam-5385	83	53	)	)	PUNCT
ejpam-5385	83	54	≤	≤	NUM
ejpam-5385	83	55	ψe(m1	ψe(m1	NOUN
ejpam-5385	83	56	)	)	PUNCT
ejpam-5385	83	57	∨	∨	NUM
ejpam-5385	83	58	ψe(m2	ψe(m2	X
ejpam-5385	83	59	)	)	PUNCT
ejpam-5385	83	60	.	.	PUNCT
ejpam-5385	84	1	if	if	SCONJ
ejpam-5385	84	2	condition	condition	NOUN
ejpam-5385	84	3	(	(	PUNCT
ejpam-5385	84	4	iii	iii	NOUN
ejpam-5385	84	5	)	)	PUNCT
ejpam-5385	84	6	is	be	AUX
ejpam-5385	84	7	substituted	substitute	VERB
ejpam-5385	84	8	with	with	ADP
ejpam-5385	84	9	ϕe([m1,m2	ϕe([m1,m2	PROPN
ejpam-5385	84	10	]	]	PUNCT
ejpam-5385	84	11	)	)	PUNCT
ejpam-5385	84	12	≥	≥	PROPN
ejpam-5385	84	13	ϕe(m1)∨ϕe(m2	ϕe(m1)∨ϕe(m2	NOUN
ejpam-5385	84	14	)	)	PUNCT
ejpam-5385	84	15	,	,	PUNCT
ejpam-5385	84	16	and	and	CCONJ
ejpam-5385	84	17	ψe([m1,m2	ψe([m1,m2	NOUN
ejpam-5385	84	18	]	]	PUNCT
ejpam-5385	84	19	)	)	PUNCT
ejpam-5385	84	20	≤	≤	NUM
ejpam-5385	84	21	ψe(m1	ψe(m1	NOUN
ejpam-5385	84	22	)	)	PUNCT
ejpam-5385	84	23	∧	∧	PROPN
ejpam-5385	84	24	ψe(m2	ψe(m2	X
ejpam-5385	84	25	)	)	PUNCT
ejpam-5385	84	26	,	,	PUNCT
ejpam-5385	84	27	then	then	ADV
ejpam-5385	84	28	e	e	PROPN
ejpam-5385	84	29	is	be	AUX
ejpam-5385	84	30	denoted	denote	VERB
ejpam-5385	84	31	as	as	ADP
ejpam-5385	84	32	a	a	DET
ejpam-5385	84	33	complex	complex	ADJ
ejpam-5385	84	34	intuitionistic	intuitionistic	ADJ
ejpam-5385	84	35	fuzzy	fuzzy	ADJ
ejpam-5385	84	36	lie	lie	NOUN
ejpam-5385	84	37	ideal	ideal	NOUN
ejpam-5385	84	38	within	within	ADP
ejpam-5385	84	39	the	the	DET
ejpam-5385	84	40	context	context	NOUN
ejpam-5385	84	41	of	of	ADP
ejpam-5385	84	42	m.	m.	NOUN
ejpam-5385	84	43	3	3	NUM
ejpam-5385	84	44	.	.	PUNCT
ejpam-5385	84	45	mappings	mapping	NOUN
ejpam-5385	84	46	and	and	CCONJ
ejpam-5385	84	47	inverse	inverse	NOUN
ejpam-5385	84	48	mappings	mapping	NOUN
ejpam-5385	84	49	of	of	ADP
ejpam-5385	84	50	complex	complex	ADJ
ejpam-5385	84	51	intuitionistic	intuitionistic	ADJ
ejpam-5385	84	52	fuzzy	fuzzy	ADJ
ejpam-5385	84	53	lie	lie	NOUN
ejpam-5385	84	54	subalgebras	subalgebras	PROPN
ejpam-5385	84	55	(	(	PUNCT
ejpam-5385	84	56	ideals	ideal	NOUN
ejpam-5385	84	57	)	)	PUNCT
ejpam-5385	84	58	through	through	ADP
ejpam-5385	84	59	lie	lie	NOUN
ejpam-5385	84	60	morphisms	morphism	NOUN
ejpam-5385	84	61	.	.	PUNCT
ejpam-5385	85	1	consider	consider	VERB
ejpam-5385	85	2	lie	lie	NOUN
ejpam-5385	85	3	algebras	algebras	PROPN
ejpam-5385	85	4	m1	m1	PROPN
ejpam-5385	85	5	and	and	CCONJ
ejpam-5385	85	6	m2	m2	PROPN
ejpam-5385	85	7	,	,	PUNCT
ejpam-5385	85	8	a	a	DET
ejpam-5385	85	9	complex	complex	ADJ
ejpam-5385	85	10	intuitionistic	intuitionistic	ADJ
ejpam-5385	85	11	subset	subset	NOUN
ejpam-5385	85	12	e	e	NOUN
ejpam-5385	85	13	=	=	SYM
ejpam-5385	85	14	(	(	PUNCT
ejpam-5385	85	15	ϕe	ϕe	INTJ
ejpam-5385	85	16	,	,	PUNCT
ejpam-5385	85	17	ψe	ψe	NOUN
ejpam-5385	85	18	)	)	PUNCT
ejpam-5385	85	19	of	of	ADP
ejpam-5385	85	20	m1	m1	PROPN
ejpam-5385	85	21	,	,	PUNCT
ejpam-5385	85	22	and	and	CCONJ
ejpam-5385	85	23	a	a	DET
ejpam-5385	85	24	function	function	NOUN
ejpam-5385	85	25	f	f	NOUN
ejpam-5385	85	26	:	:	PUNCT
ejpam-5385	85	27	m1	m1	PROPN
ejpam-5385	85	28	→	→	SYM
ejpam-5385	85	29	m2	m2	PROPN
ejpam-5385	85	30	.	.	PUNCT
ejpam-5385	86	1	the	the	DET
ejpam-5385	86	2	complex	complex	ADJ
ejpam-5385	86	3	intuitionistic	intuitionistic	ADJ
ejpam-5385	86	4	fuzzy	fuzzy	ADJ
ejpam-5385	86	5	subset	subset	NOUN
ejpam-5385	86	6	f(e	f(e	NOUN
ejpam-5385	86	7	)	)	PUNCT
ejpam-5385	86	8	of	of	ADP
ejpam-5385	86	9	f(m1	f(m1	NOUN
ejpam-5385	86	10	)	)	PUNCT
ejpam-5385	86	11	is	be	AUX
ejpam-5385	86	12	defined	define	VERB
ejpam-5385	86	13	as	as	ADP
ejpam-5385	86	14	f(e	f(e	NOUN
ejpam-5385	86	15	)	)	PUNCT
ejpam-5385	86	16	=	=	SYM
ejpam-5385	86	17	(	(	PUNCT
ejpam-5385	86	18	ϕf(e	ϕf(e	NOUN
ejpam-5385	86	19	)	)	PUNCT
ejpam-5385	86	20	,	,	PUNCT
ejpam-5385	86	21	ψf(e	ψf(e	ADJ
ejpam-5385	86	22	)	)	PUNCT
ejpam-5385	86	23	)	)	PUNCT
ejpam-5385	86	24	.	.	PUNCT
ejpam-5385	87	1	here	here	ADV
ejpam-5385	87	2	(	(	PUNCT
ejpam-5385	87	3	m2	m2	PROPN
ejpam-5385	87	4	∈	∈	PROPN
ejpam-5385	87	5	f(m1	f(m1	NOUN
ejpam-5385	87	6	)	)	PUNCT
ejpam-5385	87	7	)	)	PUNCT
ejpam-5385	87	8	,	,	PUNCT
ejpam-5385	87	9	ϕf(e)(m2	ϕf(e)(m2	NUM
ejpam-5385	87	10	)	)	PUNCT
ejpam-5385	87	11	=	=	SYM
ejpam-5385	87	12	supm1∈f−1({m2}){ϕe(m1	supm1∈f−1({m2}){ϕe(m1	NOUN
ejpam-5385	87	13	)	)	PUNCT
ejpam-5385	87	14	}	}	PUNCT
ejpam-5385	87	15	,	,	PUNCT
ejpam-5385	87	16	and	and	CCONJ
ejpam-5385	87	17	ψf(e)(m2	ψf(e)(m2	ADJ
ejpam-5385	87	18	)	)	PUNCT
ejpam-5385	87	19	=	=	SYM
ejpam-5385	87	20	infm1∈f−1({m2}){ψe(m1	infm1∈f−1({m2}){ψe(m1	NOUN
ejpam-5385	87	21	)	)	PUNCT
ejpam-5385	87	22	}	}	PUNCT
ejpam-5385	87	23	.	.	PUNCT
ejpam-5385	88	1	this	this	DET
ejpam-5385	88	2	subset	subset	NOUN
ejpam-5385	88	3	is	be	AUX
ejpam-5385	88	4	termed	term	VERB
ejpam-5385	88	5	as	as	ADP
ejpam-5385	88	6	the	the	DET
ejpam-5385	88	7	mapping	mapping	NOUN
ejpam-5385	88	8	of	of	ADP
ejpam-5385	88	9	e	e	PROPN
ejpam-5385	88	10	through	through	ADP
ejpam-5385	88	11	f	f	PROPN
ejpam-5385	88	12	.	.	PUNCT
ejpam-5385	89	1	in	in	ADP
ejpam-5385	89	2	a	a	DET
ejpam-5385	89	3	similar	similar	ADJ
ejpam-5385	89	4	manner	manner	NOUN
ejpam-5385	89	5	,	,	PUNCT
ejpam-5385	89	6	for	for	ADP
ejpam-5385	89	7	a	a	DET
ejpam-5385	89	8	complex	complex	ADJ
ejpam-5385	89	9	intuitionistic	intuitionistic	ADJ
ejpam-5385	89	10	fuzzy	fuzzy	ADJ
ejpam-5385	89	11	subset	subset	NOUN
ejpam-5385	89	12	p	p	X
ejpam-5385	89	13	=	=	X
ejpam-5385	89	14	(	(	PUNCT
ejpam-5385	89	15	ϕp	ϕp	INTJ
ejpam-5385	89	16	,	,	PUNCT
ejpam-5385	89	17	ψp	ψp	NOUN
ejpam-5385	89	18	)	)	PUNCT
ejpam-5385	89	19	of	of	ADP
ejpam-5385	89	20	m2	m2	PROPN
ejpam-5385	89	21	,	,	PUNCT
ejpam-5385	89	22	the	the	DET
ejpam-5385	89	23	inverse	inverse	NOUN
ejpam-5385	89	24	mapping	mapping	NOUN
ejpam-5385	89	25	of	of	ADP
ejpam-5385	89	26	p	p	PROPN
ejpam-5385	89	27	under	under	ADP
ejpam-5385	89	28	f	f	PROPN
ejpam-5385	89	29	,	,	PUNCT
ejpam-5385	89	30	f−1(p	f−1(p	PROPN
ejpam-5385	89	31	)	)	PUNCT
ejpam-5385	89	32	,	,	PUNCT
ejpam-5385	89	33	is	be	AUX
ejpam-5385	89	34	defined	define	VERB
ejpam-5385	89	35	as	as	ADP
ejpam-5385	89	36	(	(	PUNCT
ejpam-5385	89	37	ϕf−1(p	ϕf−1(p	PROPN
ejpam-5385	89	38	)	)	PUNCT
ejpam-5385	89	39	,	,	PUNCT
ejpam-5385	89	40	ψf−1(p	ψf−1(p	NOUN
ejpam-5385	89	41	)	)	PUNCT
ejpam-5385	89	42	)	)	PUNCT
ejpam-5385	89	43	,	,	PUNCT
ejpam-5385	89	44	where	where	SCONJ
ejpam-5385	89	45	(	(	PUNCT
ejpam-5385	89	46	m1	m1	PROPN
ejpam-5385	89	47	∈	∈	PROPN
ejpam-5385	89	48	m1	m1	NOUN
ejpam-5385	89	49	)	)	PUNCT
ejpam-5385	89	50	ϕf−1(p)(m1	ϕf−1(p)(m1	NOUN
ejpam-5385	89	51	)	)	PUNCT
ejpam-5385	90	1	=	=	SYM
ejpam-5385	90	2	ϕp(f(m1	ϕp(f(m1	NOUN
ejpam-5385	90	3	)	)	PUNCT
ejpam-5385	90	4	)	)	PUNCT
ejpam-5385	90	5	and	and	CCONJ
ejpam-5385	90	6	ψf−1(p)(m1	ψf−1(p)(m1	NOUN
ejpam-5385	90	7	)	)	PUNCT
ejpam-5385	91	1	=	=	SYM
ejpam-5385	91	2	ψp(f(m1	ψp(f(m1	NOUN
ejpam-5385	91	3	)	)	PUNCT
ejpam-5385	91	4	)	)	PUNCT
ejpam-5385	91	5	.	.	PUNCT
ejpam-5385	92	1	theorem	theorem	NOUN
ejpam-5385	92	2	1	1	NUM
ejpam-5385	92	3	.	.	PUNCT
ejpam-5385	93	1	assume	assume	VERB
ejpam-5385	93	2	f	f	X
ejpam-5385	93	3	:	:	PUNCT
ejpam-5385	93	4	m1	m1	PROPN
ejpam-5385	93	5	→	→	SYM
ejpam-5385	93	6	m2	m2	PROPN
ejpam-5385	93	7	is	be	AUX
ejpam-5385	93	8	a	a	DET
ejpam-5385	93	9	homomorphism	homomorphism	NOUN
ejpam-5385	93	10	between	between	ADP
ejpam-5385	93	11	lie	lie	NOUN
ejpam-5385	93	12	algebras	algebra	NOUN
ejpam-5385	93	13	.	.	PUNCT
ejpam-5385	94	1	if	if	SCONJ
ejpam-5385	94	2	p	p	NOUN
ejpam-5385	94	3	=	=	X
ejpam-5385	94	4	(	(	PUNCT
ejpam-5385	94	5	ϕp	ϕp	INTJ
ejpam-5385	94	6	,	,	PUNCT
ejpam-5385	94	7	ψp	ψp	PROPN
ejpam-5385	94	8	)	)	PUNCT
ejpam-5385	94	9	is	be	AUX
ejpam-5385	94	10	a	a	DET
ejpam-5385	94	11	complex	complex	ADJ
ejpam-5385	94	12	intuitionistic	intuitionistic	ADJ
ejpam-5385	94	13	fuzzy	fuzzy	ADJ
ejpam-5385	94	14	lie	lie	NOUN
ejpam-5385	94	15	subalgebra	subalgebra	NOUN
ejpam-5385	94	16	of	of	ADP
ejpam-5385	94	17	m2	m2	PROPN
ejpam-5385	94	18	,	,	PUNCT
ejpam-5385	94	19	then	then	ADV
ejpam-5385	94	20	the	the	DET
ejpam-5385	94	21	complex	complex	ADJ
ejpam-5385	94	22	intuitionistic	intuitionistic	ADJ
ejpam-5385	94	23	fuzzy	fuzzy	ADJ
ejpam-5385	94	24	set	set	VERB
ejpam-5385	94	25	f−1(p	f−1(p	PROPN
ejpam-5385	94	26	)	)	PUNCT
ejpam-5385	94	27	is	be	AUX
ejpam-5385	94	28	a	a	DET
ejpam-5385	94	29	complex	complex	ADJ
ejpam-5385	94	30	intuitionistic	intuitionistic	ADJ
ejpam-5385	94	31	fuzzy	fuzzy	ADJ
ejpam-5385	94	32	lie	lie	NOUN
ejpam-5385	94	33	subalgebra	subalgebra	NOUN
ejpam-5385	94	34	of	of	ADP
ejpam-5385	94	35	m1	m1	PROPN
ejpam-5385	94	36	.	.	PUNCT
ejpam-5385	95	1	s.	s.	PROPN
ejpam-5385	95	2	shaqaqha	shaqaqha	PROPN
ejpam-5385	95	3	,	,	PUNCT
ejpam-5385	95	4	m.	m.	PROPN
ejpam-5385	95	5	y.	y.	PROPN
ejpam-5385	95	6	al	al	PROPN
ejpam-5385	95	7	-	-	PUNCT
ejpam-5385	95	8	deiakeh	deiakeh	PROPN
ejpam-5385	95	9	/	/	SYM
ejpam-5385	95	10	eur	eur	NOUN
ejpam-5385	95	11	.	.	PUNCT
ejpam-5385	96	1	j.	j.	PROPN
ejpam-5385	96	2	pure	pure	PROPN
ejpam-5385	96	3	appl	appl	PROPN
ejpam-5385	96	4	.	.	PROPN
ejpam-5385	96	5	math	math	PROPN
ejpam-5385	96	6	,	,	PUNCT
ejpam-5385	96	7	17	17	NUM
ejpam-5385	96	8	(	(	PUNCT
ejpam-5385	96	9	4	4	NUM
ejpam-5385	96	10	)	)	PUNCT
ejpam-5385	96	11	(	(	PUNCT
ejpam-5385	96	12	2024	2024	NUM
ejpam-5385	96	13	)	)	PUNCT
ejpam-5385	96	14	,	,	PUNCT
ejpam-5385	96	15	3291	3291	NUM
ejpam-5385	96	16	-	-	SYM
ejpam-5385	96	17	3303	3303	NUM
ejpam-5385	96	18	3295	3295	NUM
ejpam-5385	96	19	proof	proof	NOUN
ejpam-5385	96	20	.	.	PUNCT
ejpam-5385	97	1	to	to	PART
ejpam-5385	97	2	show	show	VERB
ejpam-5385	97	3	that	that	SCONJ
ejpam-5385	97	4	f−1(p	f−1(p	PROPN
ejpam-5385	97	5	)	)	PUNCT
ejpam-5385	97	6	is	be	AUX
ejpam-5385	97	7	a	a	DET
ejpam-5385	97	8	complex	complex	ADJ
ejpam-5385	97	9	intuitionistic	intuitionistic	ADJ
ejpam-5385	97	10	fuzzy	fuzzy	ADJ
ejpam-5385	97	11	lie	lie	NOUN
ejpam-5385	97	12	subalgebra	subalgebra	NOUN
ejpam-5385	97	13	in	in	ADP
ejpam-5385	97	14	m1	m1	PROPN
ejpam-5385	97	15	,	,	PUNCT
ejpam-5385	97	16	we	we	PRON
ejpam-5385	97	17	need	need	VERB
ejpam-5385	97	18	to	to	PART
ejpam-5385	97	19	verify	verify	VERB
ejpam-5385	97	20	that	that	SCONJ
ejpam-5385	97	21	it	it	PRON
ejpam-5385	97	22	satisfies	satisfy	VERB
ejpam-5385	97	23	the	the	DET
ejpam-5385	97	24	properties	property	NOUN
ejpam-5385	97	25	of	of	ADP
ejpam-5385	97	26	a	a	DET
ejpam-5385	97	27	complex	complex	ADJ
ejpam-5385	97	28	intuitionistic	intuitionistic	ADJ
ejpam-5385	97	29	fuzzy	fuzzy	ADJ
ejpam-5385	97	30	set	set	NOUN
ejpam-5385	97	31	and	and	CCONJ
ejpam-5385	97	32	maintains	maintain	VERB
ejpam-5385	97	33	the	the	DET
ejpam-5385	97	34	closure	closure	NOUN
ejpam-5385	97	35	properties	property	NOUN
ejpam-5385	97	36	under	under	ADP
ejpam-5385	97	37	lie	lie	NOUN
ejpam-5385	97	38	operations	operation	NOUN
ejpam-5385	97	39	within	within	ADP
ejpam-5385	97	40	m1	m1	PROPN
ejpam-5385	97	41	.	.	PUNCT
ejpam-5385	98	1	we	we	PRON
ejpam-5385	98	2	start	start	VERB
ejpam-5385	98	3	by	by	ADP
ejpam-5385	98	4	checking	check	VERB
ejpam-5385	98	5	the	the	DET
ejpam-5385	98	6	homogeneity	homogeneity	NOUN
ejpam-5385	98	7	property	property	NOUN
ejpam-5385	98	8	.	.	PUNCT
ejpam-5385	99	1	for	for	ADP
ejpam-5385	99	2	any	any	DET
ejpam-5385	99	3	m1	m1	PROPN
ejpam-5385	99	4	∈	∈	PROPN
ejpam-5385	99	5	m1	m1	NOUN
ejpam-5385	99	6	,	,	PUNCT
ejpam-5385	99	7	by	by	ADP
ejpam-5385	99	8	definition	definition	NOUN
ejpam-5385	99	9	of	of	ADP
ejpam-5385	99	10	the	the	DET
ejpam-5385	99	11	inverse	inverse	NOUN
ejpam-5385	99	12	image	image	NOUN
ejpam-5385	99	13	under	under	ADP
ejpam-5385	99	14	the	the	DET
ejpam-5385	99	15	homomorphism	homomorphism	PROPN
ejpam-5385	99	16	f	f	X
ejpam-5385	99	17	,	,	PUNCT
ejpam-5385	99	18	we	we	PRON
ejpam-5385	99	19	have	have	VERB
ejpam-5385	99	20	:	:	PUNCT
ejpam-5385	99	21	ϕf−1(p)(m1	ϕf−1(p)(m1	NOUN
ejpam-5385	99	22	)	)	PUNCT
ejpam-5385	100	1	=	=	SYM
ejpam-5385	100	2	ϕp(f(m1	ϕp(f(m1	NOUN
ejpam-5385	100	3	)	)	PUNCT
ejpam-5385	100	4	)	)	PUNCT
ejpam-5385	101	1	=	=	SYM
ejpam-5385	102	1	ρp(f(m1))e	ρp(f(m1))e	PRON
ejpam-5385	102	2	iζp	iζp	NOUN
ejpam-5385	102	3	(	(	PUNCT
ejpam-5385	102	4	f(m1	f(m1	NOUN
ejpam-5385	102	5	)	)	PUNCT
ejpam-5385	102	6	)	)	PUNCT
ejpam-5385	102	7	,	,	PUNCT
ejpam-5385	102	8	and	and	CCONJ
ejpam-5385	102	9	similarly	similarly	ADV
ejpam-5385	102	10	,	,	PUNCT
ejpam-5385	102	11	ψf−1(p)(m1	ψf−1(p)(m1	NOUN
ejpam-5385	102	12	)	)	PUNCT
ejpam-5385	102	13	=	=	SYM
ejpam-5385	102	14	ψp(f(m1	ψp(f(m1	NOUN
ejpam-5385	102	15	)	)	PUNCT
ejpam-5385	102	16	)	)	PUNCT
ejpam-5385	103	1	=	=	SYM
ejpam-5385	103	2	ρ̂p(f(m1))e	ρ̂p(f(m1))e	PROPN
ejpam-5385	103	3	iζ̂p	iζ̂p	PROPN
ejpam-5385	103	4	(	(	PUNCT
ejpam-5385	103	5	f(m1	f(m1	NOUN
ejpam-5385	103	6	)	)	PUNCT
ejpam-5385	103	7	)	)	PUNCT
ejpam-5385	103	8	.	.	PUNCT
ejpam-5385	104	1	now	now	ADV
ejpam-5385	104	2	,	,	PUNCT
ejpam-5385	104	3	consider	consider	VERB
ejpam-5385	104	4	two	two	NUM
ejpam-5385	104	5	elements	element	NOUN
ejpam-5385	104	6	m1,m2	m1,m2	PROPN
ejpam-5385	104	7	∈	∈	PROPN
ejpam-5385	104	8	m1	m1	NOUN
ejpam-5385	104	9	.	.	PUNCT
ejpam-5385	105	1	if	if	SCONJ
ejpam-5385	105	2	ρp(f(m1	ρp(f(m1	NOUN
ejpam-5385	105	3	)	)	PUNCT
ejpam-5385	105	4	)	)	PUNCT
ejpam-5385	106	1	≤	≤	PUNCT
ejpam-5385	106	2	ρp(f(m2	ρp(f(m2	PROPN
ejpam-5385	106	3	)	)	PUNCT
ejpam-5385	106	4	)	)	PUNCT
ejpam-5385	106	5	,	,	PUNCT
ejpam-5385	106	6	then	then	ADV
ejpam-5385	106	7	by	by	ADP
ejpam-5385	106	8	the	the	DET
ejpam-5385	106	9	homogeneity	homogeneity	NOUN
ejpam-5385	106	10	property	property	NOUN
ejpam-5385	106	11	of	of	ADP
ejpam-5385	106	12	p	p	X
ejpam-5385	106	13	,	,	PUNCT
ejpam-5385	106	14	we	we	PRON
ejpam-5385	106	15	know	know	VERB
ejpam-5385	106	16	that	that	SCONJ
ejpam-5385	106	17	ζp(f(m1	ζp(f(m1	VERB
ejpam-5385	106	18	)	)	PUNCT
ejpam-5385	106	19	)	)	PUNCT
ejpam-5385	106	20	≤	≤	NUM
ejpam-5385	106	21	ζp(f(m2	ζp(f(m2	NOUN
ejpam-5385	106	22	)	)	PUNCT
ejpam-5385	106	23	)	)	PUNCT
ejpam-5385	106	24	.	.	PUNCT
ejpam-5385	107	1	similarly	similarly	ADV
ejpam-5385	107	2	,	,	PUNCT
ejpam-5385	107	3	if	if	SCONJ
ejpam-5385	107	4	ρ̂p(f(m1	ρ̂p(f(m1	NOUN
ejpam-5385	107	5	)	)	PUNCT
ejpam-5385	107	6	)	)	PUNCT
ejpam-5385	107	7	≤	≤	NUM
ejpam-5385	107	8	ρ̂p(f(m2	ρ̂p(f(m2	PROPN
ejpam-5385	107	9	)	)	PUNCT
ejpam-5385	107	10	)	)	PUNCT
ejpam-5385	107	11	,	,	PUNCT
ejpam-5385	107	12	then	then	ADV
ejpam-5385	107	13	ζ̂p(f(m1	ζ̂p(f(m1	NOUN
ejpam-5385	107	14	)	)	PUNCT
ejpam-5385	107	15	)	)	PUNCT
ejpam-5385	107	16	≤	≤	NUM
ejpam-5385	107	17	ζ̂p(f(m2	ζ̂p(f(m2	NOUN
ejpam-5385	107	18	)	)	PUNCT
ejpam-5385	107	19	)	)	PUNCT
ejpam-5385	107	20	.	.	PUNCT
ejpam-5385	108	1	therefore	therefore	ADV
ejpam-5385	108	2	,	,	PUNCT
ejpam-5385	108	3	the	the	DET
ejpam-5385	108	4	homogeneity	homogeneity	NOUN
ejpam-5385	108	5	property	property	NOUN
ejpam-5385	108	6	holds	hold	VERB
ejpam-5385	108	7	for	for	ADP
ejpam-5385	108	8	f−1(p	f−1(p	PROPN
ejpam-5385	108	9	)	)	PUNCT
ejpam-5385	108	10	in	in	ADP
ejpam-5385	108	11	m1	m1	PROPN
ejpam-5385	108	12	.	.	PUNCT
ejpam-5385	109	1	next	next	ADV
ejpam-5385	109	2	,	,	PUNCT
ejpam-5385	109	3	we	we	PRON
ejpam-5385	109	4	verify	verify	VERB
ejpam-5385	109	5	the	the	DET
ejpam-5385	109	6	algebraic	algebraic	ADJ
ejpam-5385	109	7	properties	property	NOUN
ejpam-5385	109	8	under	under	ADP
ejpam-5385	109	9	addition	addition	NOUN
ejpam-5385	109	10	,	,	PUNCT
ejpam-5385	109	11	scalar	scalar	ADJ
ejpam-5385	109	12	multiplication	multiplication	NOUN
ejpam-5385	109	13	,	,	PUNCT
ejpam-5385	109	14	and	and	CCONJ
ejpam-5385	109	15	the	the	DET
ejpam-5385	109	16	lie	lie	NOUN
ejpam-5385	109	17	bracket	bracket	NOUN
ejpam-5385	109	18	.	.	PUNCT
ejpam-5385	110	1	for	for	ADP
ejpam-5385	110	2	m1,m2	m1,m2	PROPN
ejpam-5385	110	3	∈	∈	PROPN
ejpam-5385	110	4	m1	m1	PROPN
ejpam-5385	110	5	and	and	CCONJ
ejpam-5385	111	1	k	k	PROPN
ejpam-5385	111	2	∈	∈	PROPN
ejpam-5385	111	3	k	k	NOUN
ejpam-5385	111	4	,	,	PUNCT
ejpam-5385	111	5	we	we	PRON
ejpam-5385	111	6	need	need	VERB
ejpam-5385	111	7	to	to	PART
ejpam-5385	111	8	show	show	VERB
ejpam-5385	111	9	the	the	DET
ejpam-5385	111	10	following	following	NOUN
ejpam-5385	111	11	:	:	PUNCT
ejpam-5385	112	1	1	1	X
ejpam-5385	112	2	.	.	X
ejpam-5385	113	1	*	*	PUNCT
ejpam-5385	113	2	*	*	PUNCT
ejpam-5385	113	3	addition	addition	NOUN
ejpam-5385	113	4	*	*	PUNCT
ejpam-5385	113	5	*	*	NOUN
ejpam-5385	113	6	:	:	PUNCT
ejpam-5385	113	7	ϕf−1(p)(m1	ϕf−1(p)(m1	NOUN
ejpam-5385	114	1	+	+	ADJ
ejpam-5385	114	2	m2	m2	NOUN
ejpam-5385	114	3	)	)	PUNCT
ejpam-5385	115	1	=	=	PUNCT
ejpam-5385	115	2	ϕp(f(m1	ϕp(f(m1	NOUN
ejpam-5385	115	3	+	+	NOUN
ejpam-5385	115	4	m2	m2	NOUN
ejpam-5385	115	5	)	)	PUNCT
ejpam-5385	115	6	)	)	PUNCT
ejpam-5385	116	1	=	=	SYM
ejpam-5385	116	2	ϕp(f(m1	ϕp(f(m1	NOUN
ejpam-5385	116	3	)	)	PUNCT
ejpam-5385	116	4	+	+	NUM
ejpam-5385	116	5	f(m2	f(m2	NOUN
ejpam-5385	116	6	)	)	PUNCT
ejpam-5385	116	7	)	)	PUNCT
ejpam-5385	116	8	,	,	PUNCT
ejpam-5385	116	9	since	since	SCONJ
ejpam-5385	116	10	f	f	PROPN
ejpam-5385	116	11	is	be	AUX
ejpam-5385	116	12	linear	linear	ADJ
ejpam-5385	116	13	.	.	PUNCT
ejpam-5385	117	1	by	by	ADP
ejpam-5385	117	2	definition	definition	NOUN
ejpam-5385	117	3	1	1	NUM
ejpam-5385	117	4	(	(	PUNCT
ejpam-5385	117	5	the	the	DET
ejpam-5385	117	6	property	property	NOUN
ejpam-5385	117	7	of	of	ADP
ejpam-5385	117	8	complex	complex	ADJ
ejpam-5385	117	9	intuitionistic	intuitionistic	ADJ
ejpam-5385	117	10	fuzzy	fuzzy	ADJ
ejpam-5385	117	11	lie	lie	NOUN
ejpam-5385	117	12	subalgebras	subalgebras	PROPN
ejpam-5385	117	13	)	)	PUNCT
ejpam-5385	117	14	,	,	PUNCT
ejpam-5385	117	15	we	we	PRON
ejpam-5385	117	16	have	have	VERB
ejpam-5385	117	17	:	:	PUNCT
ejpam-5385	117	18	ϕp(f(m1	ϕp(f(m1	NOUN
ejpam-5385	117	19	)	)	PUNCT
ejpam-5385	117	20	+	+	NUM
ejpam-5385	118	1	f(m2	f(m2	NOUN
ejpam-5385	118	2	)	)	PUNCT
ejpam-5385	118	3	)	)	PUNCT
ejpam-5385	118	4	≥	≥	NOUN
ejpam-5385	118	5	ϕp(f(m1	ϕp(f(m1	NOUN
ejpam-5385	118	6	)	)	PUNCT
ejpam-5385	118	7	)	)	PUNCT
ejpam-5385	119	1	∧	∧	NOUN
ejpam-5385	119	2	ϕp(f(m2	ϕp(f(m2	PROPN
ejpam-5385	119	3	)	)	PUNCT
ejpam-5385	119	4	)	)	PUNCT
ejpam-5385	119	5	.	.	PUNCT
ejpam-5385	120	1	thus	thus	ADV
ejpam-5385	120	2	,	,	PUNCT
ejpam-5385	120	3	ϕf−1(p)(m1	ϕf−1(p)(m1	VERB
ejpam-5385	120	4	+	+	ADJ
ejpam-5385	120	5	m2	m2	PROPN
ejpam-5385	120	6	)	)	PUNCT
ejpam-5385	120	7	≥	≥	NOUN
ejpam-5385	120	8	ϕf−1(p)(m1	ϕf−1(p)(m1	NOUN
ejpam-5385	120	9	)	)	PUNCT
ejpam-5385	120	10	∧	∧	PROPN
ejpam-5385	120	11	ϕf−1(p)(m2	ϕf−1(p)(m2	NOUN
ejpam-5385	120	12	)	)	PUNCT
ejpam-5385	120	13	.	.	PUNCT
ejpam-5385	121	1	for	for	ADP
ejpam-5385	121	2	ψ	ψ	SYM
ejpam-5385	121	3	,	,	PUNCT
ejpam-5385	121	4	we	we	PRON
ejpam-5385	121	5	proceed	proceed	VERB
ejpam-5385	121	6	similarly	similarly	ADV
ejpam-5385	121	7	:	:	PUNCT
ejpam-5385	121	8	ψf−1(p)(m1	ψf−1(p)(m1	VERB
ejpam-5385	122	1	+	+	NOUN
ejpam-5385	122	2	m2	m2	NOUN
ejpam-5385	122	3	)	)	PUNCT
ejpam-5385	122	4	=	=	PUNCT
ejpam-5385	122	5	ψp(f(m1	ψp(f(m1	VERB
ejpam-5385	122	6	+	+	NOUN
ejpam-5385	122	7	m2	m2	NOUN
ejpam-5385	122	8	)	)	PUNCT
ejpam-5385	122	9	)	)	PUNCT
ejpam-5385	123	1	=	=	PUNCT
ejpam-5385	123	2	ψp(f(m1	ψp(f(m1	NOUN
ejpam-5385	123	3	)	)	PUNCT
ejpam-5385	123	4	+	+	NUM
ejpam-5385	123	5	f(m2	f(m2	NOUN
ejpam-5385	123	6	)	)	PUNCT
ejpam-5385	123	7	)	)	PUNCT
ejpam-5385	123	8	,	,	PUNCT
ejpam-5385	123	9	and	and	CCONJ
ejpam-5385	123	10	by	by	ADP
ejpam-5385	123	11	definition	definition	NOUN
ejpam-5385	123	12	1	1	NUM
ejpam-5385	123	13	:	:	PUNCT
ejpam-5385	123	14	ψp(f(m1	ψp(f(m1	NOUN
ejpam-5385	123	15	)	)	PUNCT
ejpam-5385	123	16	+	+	NUM
ejpam-5385	123	17	f(m2	f(m2	NOUN
ejpam-5385	123	18	)	)	PUNCT
ejpam-5385	123	19	)	)	PUNCT
ejpam-5385	124	1	≤	≤	NUM
ejpam-5385	124	2	ψp(f(m1	ψp(f(m1	NOUN
ejpam-5385	124	3	)	)	PUNCT
ejpam-5385	124	4	)	)	PUNCT
ejpam-5385	124	5	∨	∨	PROPN
ejpam-5385	124	6	ψp(f(m2	ψp(f(m2	X
ejpam-5385	124	7	)	)	PUNCT
ejpam-5385	124	8	)	)	PUNCT
ejpam-5385	124	9	.	.	PUNCT
ejpam-5385	125	1	hence	hence	ADV
ejpam-5385	125	2	,	,	PUNCT
ejpam-5385	125	3	ψf−1(p)(m1	ψf−1(p)(m1	VERB
ejpam-5385	126	1	+	+	ADJ
ejpam-5385	126	2	m2	m2	PROPN
ejpam-5385	126	3	)	)	PUNCT
ejpam-5385	126	4	≤	≤	NOUN
ejpam-5385	126	5	ψf−1(p)(m1	ψf−1(p)(m1	NOUN
ejpam-5385	126	6	)	)	PUNCT
ejpam-5385	126	7	∨	∨	NUM
ejpam-5385	126	8	ψf−1(p)(m2	ψf−1(p)(m2	NOUN
ejpam-5385	126	9	)	)	PUNCT
ejpam-5385	126	10	.	.	PUNCT
ejpam-5385	127	1	2	2	X
ejpam-5385	127	2	.	.	X
ejpam-5385	127	3	*	*	PUNCT
ejpam-5385	127	4	*	*	PUNCT
ejpam-5385	127	5	scalar	scalar	ADJ
ejpam-5385	127	6	multiplication	multiplication	NOUN
ejpam-5385	127	7	*	*	NOUN
ejpam-5385	127	8	*	*	NOUN
ejpam-5385	127	9	:	:	PUNCT
ejpam-5385	127	10	for	for	ADP
ejpam-5385	127	11	any	any	DET
ejpam-5385	127	12	k	k	PROPN
ejpam-5385	127	13	∈	∈	PROPN
ejpam-5385	127	14	k	k	NOUN
ejpam-5385	127	15	,	,	PUNCT
ejpam-5385	127	16	we	we	PRON
ejpam-5385	127	17	have	have	VERB
ejpam-5385	127	18	:	:	PUNCT
ejpam-5385	127	19	ϕf−1(p)(km1	ϕf−1(p)(km1	X
ejpam-5385	127	20	)	)	PUNCT
ejpam-5385	127	21	=	=	SYM
ejpam-5385	127	22	ϕp(f(km1	ϕp(f(km1	NOUN
ejpam-5385	127	23	)	)	PUNCT
ejpam-5385	127	24	)	)	PUNCT
ejpam-5385	128	1	=	=	SYM
ejpam-5385	128	2	ϕp(kf(m1	ϕp(kf(m1	NOUN
ejpam-5385	128	3	)	)	PUNCT
ejpam-5385	128	4	)	)	PUNCT
ejpam-5385	128	5	,	,	PUNCT
ejpam-5385	128	6	and	and	CCONJ
ejpam-5385	128	7	by	by	ADP
ejpam-5385	128	8	definition	definition	NOUN
ejpam-5385	128	9	1	1	NUM
ejpam-5385	128	10	:	:	PUNCT
ejpam-5385	128	11	ϕp(kf(m1	ϕp(kf(m1	NOUN
ejpam-5385	128	12	)	)	PUNCT
ejpam-5385	128	13	)	)	PUNCT
ejpam-5385	128	14	≥	≥	NOUN
ejpam-5385	128	15	ϕp(f(m1	ϕp(f(m1	NOUN
ejpam-5385	128	16	)	)	PUNCT
ejpam-5385	128	17	)	)	PUNCT
ejpam-5385	128	18	.	.	PUNCT
ejpam-5385	129	1	thus	thus	ADV
ejpam-5385	129	2	,	,	PUNCT
ejpam-5385	129	3	ϕf−1(p)(km1	ϕf−1(p)(km1	X
ejpam-5385	129	4	)	)	PUNCT
ejpam-5385	129	5	≥	≥	NOUN
ejpam-5385	129	6	ϕf−1(p)(m1	ϕf−1(p)(m1	NOUN
ejpam-5385	129	7	)	)	PUNCT
ejpam-5385	129	8	.	.	PUNCT
ejpam-5385	130	1	s.	s.	PROPN
ejpam-5385	130	2	shaqaqha	shaqaqha	PROPN
ejpam-5385	130	3	,	,	PUNCT
ejpam-5385	130	4	m.	m.	PROPN
ejpam-5385	130	5	y.	y.	PROPN
ejpam-5385	130	6	al	al	PROPN
ejpam-5385	130	7	-	-	PUNCT
ejpam-5385	130	8	deiakeh	deiakeh	PROPN
ejpam-5385	130	9	/	/	SYM
ejpam-5385	130	10	eur	eur	NOUN
ejpam-5385	130	11	.	.	PUNCT
ejpam-5385	131	1	j.	j.	PROPN
ejpam-5385	131	2	pure	pure	PROPN
ejpam-5385	131	3	appl	appl	PROPN
ejpam-5385	131	4	.	.	PROPN
ejpam-5385	131	5	math	math	PROPN
ejpam-5385	131	6	,	,	PUNCT
ejpam-5385	131	7	17	17	NUM
ejpam-5385	131	8	(	(	PUNCT
ejpam-5385	131	9	4	4	NUM
ejpam-5385	131	10	)	)	PUNCT
ejpam-5385	131	11	(	(	PUNCT
ejpam-5385	131	12	2024	2024	NUM
ejpam-5385	131	13	)	)	PUNCT
ejpam-5385	131	14	,	,	PUNCT
ejpam-5385	131	15	3291	3291	NUM
ejpam-5385	131	16	-	-	SYM
ejpam-5385	131	17	3303	3303	NUM
ejpam-5385	131	18	3296	3296	NUM
ejpam-5385	131	19	similarly	similarly	ADV
ejpam-5385	131	20	,	,	PUNCT
ejpam-5385	131	21	for	for	ADP
ejpam-5385	131	22	ψ	ψ	X
ejpam-5385	131	23	:	:	PUNCT
ejpam-5385	131	24	ψf−1(p)(km1	ψf−1(p)(km1	NUM
ejpam-5385	131	25	)	)	PUNCT
ejpam-5385	131	26	=	=	SYM
ejpam-5385	131	27	ψp(f(km1	ψp(f(km1	PROPN
ejpam-5385	131	28	)	)	PUNCT
ejpam-5385	131	29	)	)	PUNCT
ejpam-5385	132	1	=	=	SYM
ejpam-5385	132	2	ψp(kf(m1	ψp(kf(m1	NOUN
ejpam-5385	132	3	)	)	PUNCT
ejpam-5385	132	4	)	)	PUNCT
ejpam-5385	132	5	,	,	PUNCT
ejpam-5385	132	6	and	and	CCONJ
ejpam-5385	132	7	by	by	ADP
ejpam-5385	132	8	definition	definition	NOUN
ejpam-5385	132	9	1	1	NUM
ejpam-5385	132	10	:	:	PUNCT
ejpam-5385	132	11	ψp(kf(m1	ψp(kf(m1	NOUN
ejpam-5385	132	12	)	)	PUNCT
ejpam-5385	132	13	)	)	PUNCT
ejpam-5385	132	14	≤	≤	NUM
ejpam-5385	132	15	ψp(f(m1	ψp(f(m1	NOUN
ejpam-5385	132	16	)	)	PUNCT
ejpam-5385	132	17	)	)	PUNCT
ejpam-5385	132	18	,	,	PUNCT
ejpam-5385	132	19	so	so	ADV
ejpam-5385	132	20	ψf−1(p)(km1	ψf−1(p)(km1	NUM
ejpam-5385	132	21	)	)	PUNCT
ejpam-5385	132	22	≤	≤	NOUN
ejpam-5385	132	23	ψf−1(p)(m1	ψf−1(p)(m1	NOUN
ejpam-5385	132	24	)	)	PUNCT
ejpam-5385	132	25	.	.	PUNCT
ejpam-5385	133	1	3	3	X
ejpam-5385	133	2	.	.	X
ejpam-5385	133	3	*	*	PUNCT
ejpam-5385	133	4	*	*	PUNCT
ejpam-5385	133	5	lie	lie	NOUN
ejpam-5385	133	6	bracket	bracket	NOUN
ejpam-5385	133	7	*	*	PROPN
ejpam-5385	133	8	*	*	PUNCT
ejpam-5385	133	9	:	:	PUNCT
ejpam-5385	133	10	finally	finally	ADV
ejpam-5385	133	11	,	,	PUNCT
ejpam-5385	133	12	for	for	ADP
ejpam-5385	133	13	the	the	DET
ejpam-5385	133	14	lie	lie	NOUN
ejpam-5385	133	15	bracket	bracket	NOUN
ejpam-5385	133	16	,	,	PUNCT
ejpam-5385	133	17	we	we	PRON
ejpam-5385	133	18	have	have	VERB
ejpam-5385	133	19	:	:	PUNCT
ejpam-5385	133	20	ϕf−1(p)([m1,m2	ϕf−1(p)([m1,m2	NOUN
ejpam-5385	133	21	]	]	PUNCT
ejpam-5385	133	22	)	)	PUNCT
ejpam-5385	133	23	=	=	SYM
ejpam-5385	133	24	ϕp(f([m1,m2	ϕp(f([m1,m2	NOUN
ejpam-5385	133	25	]	]	PUNCT
ejpam-5385	133	26	)	)	PUNCT
ejpam-5385	133	27	)	)	PUNCT
ejpam-5385	134	1	=	=	PUNCT
ejpam-5385	134	2	ϕp([f(m1	ϕp([f(m1	PROPN
ejpam-5385	134	3	)	)	PUNCT
ejpam-5385	134	4	,	,	PUNCT
ejpam-5385	134	5	f(m2	f(m2	NOUN
ejpam-5385	134	6	)	)	PUNCT
ejpam-5385	134	7	]	]	PUNCT
ejpam-5385	134	8	)	)	PUNCT
ejpam-5385	134	9	,	,	PUNCT
ejpam-5385	134	10	and	and	CCONJ
ejpam-5385	134	11	by	by	ADP
ejpam-5385	134	12	definition	definition	NOUN
ejpam-5385	134	13	1	1	NUM
ejpam-5385	134	14	:	:	PUNCT
ejpam-5385	134	15	ϕp([f(m1	ϕp([f(m1	NUM
ejpam-5385	134	16	)	)	PUNCT
ejpam-5385	134	17	,	,	PUNCT
ejpam-5385	134	18	f(m2	f(m2	NOUN
ejpam-5385	134	19	)	)	PUNCT
ejpam-5385	134	20	]	]	PUNCT
ejpam-5385	134	21	)	)	PUNCT
ejpam-5385	134	22	≥	≥	NOUN
ejpam-5385	134	23	ϕp(f(m1	ϕp(f(m1	NOUN
ejpam-5385	134	24	)	)	PUNCT
ejpam-5385	134	25	)	)	PUNCT
ejpam-5385	134	26	∧	∧	PROPN
ejpam-5385	134	27	ϕp(f(m2	ϕp(f(m2	PROPN
ejpam-5385	134	28	)	)	PUNCT
ejpam-5385	134	29	)	)	PUNCT
ejpam-5385	134	30	,	,	PUNCT
ejpam-5385	134	31	so	so	SCONJ
ejpam-5385	134	32	ϕf−1(p)([m1,m2	ϕf−1(p)([m1,m2	NOUN
ejpam-5385	134	33	]	]	PUNCT
ejpam-5385	134	34	)	)	PUNCT
ejpam-5385	134	35	≥	≥	NOUN
ejpam-5385	134	36	ϕf−1(p)(m1	ϕf−1(p)(m1	NOUN
ejpam-5385	134	37	)	)	PUNCT
ejpam-5385	134	38	∧	∧	PROPN
ejpam-5385	134	39	ϕf−1(p)(m2	ϕf−1(p)(m2	NOUN
ejpam-5385	134	40	)	)	PUNCT
ejpam-5385	134	41	.	.	PUNCT
ejpam-5385	135	1	similarly	similarly	ADV
ejpam-5385	135	2	,	,	PUNCT
ejpam-5385	135	3	for	for	ADP
ejpam-5385	135	4	ψ	ψ	X
ejpam-5385	135	5	:	:	PUNCT
ejpam-5385	135	6	ψf−1(p)([m1,m2	ψf−1(p)([m1,m2	NOUN
ejpam-5385	135	7	]	]	PUNCT
ejpam-5385	135	8	)	)	PUNCT
ejpam-5385	135	9	=	=	SYM
ejpam-5385	135	10	ψp(f([m1,m2	ψp(f([m1,m2	NOUN
ejpam-5385	135	11	]	]	PUNCT
ejpam-5385	135	12	)	)	PUNCT
ejpam-5385	135	13	)	)	PUNCT
ejpam-5385	135	14	=	=	SYM
ejpam-5385	135	15	ψp([f(m1	ψp([f(m1	NOUN
ejpam-5385	135	16	)	)	PUNCT
ejpam-5385	135	17	,	,	PUNCT
ejpam-5385	135	18	f(m2	f(m2	NOUN
ejpam-5385	135	19	)	)	PUNCT
ejpam-5385	135	20	]	]	PUNCT
ejpam-5385	135	21	)	)	PUNCT
ejpam-5385	135	22	,	,	PUNCT
ejpam-5385	135	23	and	and	CCONJ
ejpam-5385	135	24	by	by	ADP
ejpam-5385	135	25	definition	definition	NOUN
ejpam-5385	135	26	1	1	NUM
ejpam-5385	135	27	:	:	PUNCT
ejpam-5385	135	28	ψp([f(m1	ψp([f(m1	NUM
ejpam-5385	135	29	)	)	PUNCT
ejpam-5385	135	30	,	,	PUNCT
ejpam-5385	135	31	f(m2	f(m2	NOUN
ejpam-5385	135	32	)	)	PUNCT
ejpam-5385	135	33	]	]	PUNCT
ejpam-5385	135	34	)	)	PUNCT
ejpam-5385	135	35	≤	≤	NUM
ejpam-5385	135	36	ψp(f(m1	ψp(f(m1	NOUN
ejpam-5385	135	37	)	)	PUNCT
ejpam-5385	135	38	)	)	PUNCT
ejpam-5385	135	39	∨	∨	PROPN
ejpam-5385	135	40	ψp(f(m2	ψp(f(m2	X
ejpam-5385	135	41	)	)	PUNCT
ejpam-5385	135	42	)	)	PUNCT
ejpam-5385	135	43	,	,	PUNCT
ejpam-5385	135	44	so	so	ADV
ejpam-5385	135	45	ψf−1(p)([m1,m2	ψf−1(p)([m1,m2	NOUN
ejpam-5385	135	46	]	]	PUNCT
ejpam-5385	135	47	)	)	PUNCT
ejpam-5385	135	48	≤	≤	NUM
ejpam-5385	135	49	ψf−1(p)(m1	ψf−1(p)(m1	NOUN
ejpam-5385	135	50	)	)	PUNCT
ejpam-5385	135	51	∨	∨	NUM
ejpam-5385	135	52	ψf−1(p)(m2	ψf−1(p)(m2	NOUN
ejpam-5385	135	53	)	)	PUNCT
ejpam-5385	135	54	.	.	PUNCT
ejpam-5385	136	1	thus	thus	ADV
ejpam-5385	136	2	,	,	PUNCT
ejpam-5385	136	3	f−1(p	f−1(p	PROPN
ejpam-5385	136	4	)	)	PUNCT
ejpam-5385	136	5	satisfies	satisfy	VERB
ejpam-5385	136	6	the	the	DET
ejpam-5385	136	7	necessary	necessary	ADJ
ejpam-5385	136	8	properties	property	NOUN
ejpam-5385	136	9	and	and	CCONJ
ejpam-5385	136	10	constitutes	constitute	VERB
ejpam-5385	136	11	a	a	DET
ejpam-5385	136	12	complex	complex	ADJ
ejpam-5385	136	13	intuitionistic	intuitionistic	ADJ
ejpam-5385	136	14	fuzzy	fuzzy	ADJ
ejpam-5385	136	15	lie	lie	NOUN
ejpam-5385	136	16	subalgebra	subalgebra	NOUN
ejpam-5385	136	17	within	within	ADP
ejpam-5385	136	18	m1	m1	PROPN
ejpam-5385	136	19	.	.	PUNCT
ejpam-5385	137	1	corollary	corollary	ADJ
ejpam-5385	137	2	1	1	NUM
ejpam-5385	137	3	.	.	PUNCT
ejpam-5385	138	1	assume	assume	VERB
ejpam-5385	138	2	f	f	X
ejpam-5385	138	3	:	:	PUNCT
ejpam-5385	138	4	m1	m1	PROPN
ejpam-5385	138	5	→	→	SYM
ejpam-5385	138	6	m2	m2	PROPN
ejpam-5385	138	7	is	be	AUX
ejpam-5385	138	8	a	a	DET
ejpam-5385	138	9	homomorphism	homomorphism	NOUN
ejpam-5385	138	10	between	between	ADP
ejpam-5385	138	11	lie	lie	NOUN
ejpam-5385	138	12	algebras	algebra	NOUN
ejpam-5385	138	13	.	.	PUNCT
ejpam-5385	139	1	if	if	SCONJ
ejpam-5385	139	2	p	p	NOUN
ejpam-5385	139	3	=	=	X
ejpam-5385	139	4	(	(	PUNCT
ejpam-5385	139	5	ϕp	ϕp	INTJ
ejpam-5385	139	6	,	,	PUNCT
ejpam-5385	139	7	ψp	ψp	PROPN
ejpam-5385	139	8	)	)	PUNCT
ejpam-5385	139	9	is	be	AUX
ejpam-5385	139	10	a	a	DET
ejpam-5385	139	11	complex	complex	ADJ
ejpam-5385	139	12	intuitionistic	intuitionistic	ADJ
ejpam-5385	139	13	fuzzy	fuzzy	ADJ
ejpam-5385	139	14	lie	lie	NOUN
ejpam-5385	139	15	ideal	ideal	NOUN
ejpam-5385	139	16	within	within	ADP
ejpam-5385	139	17	m2	m2	PROPN
ejpam-5385	139	18	,	,	PUNCT
ejpam-5385	139	19	then	then	ADV
ejpam-5385	139	20	the	the	DET
ejpam-5385	139	21	complex	complex	ADJ
ejpam-5385	139	22	intuitionistic	intuitionistic	ADJ
ejpam-5385	139	23	fuzzy	fuzzy	ADJ
ejpam-5385	139	24	set	set	VERB
ejpam-5385	139	25	f−1(p	f−1(p	PROPN
ejpam-5385	139	26	)	)	PUNCT
ejpam-5385	139	27	is	be	AUX
ejpam-5385	139	28	also	also	ADV
ejpam-5385	139	29	a	a	DET
ejpam-5385	139	30	complex	complex	ADJ
ejpam-5385	139	31	intuitionistic	intuitionistic	ADJ
ejpam-5385	139	32	fuzzy	fuzzy	ADJ
ejpam-5385	139	33	lie	lie	NOUN
ejpam-5385	139	34	ideal	ideal	NOUN
ejpam-5385	139	35	in	in	ADP
ejpam-5385	139	36	m1	m1	NOUN
ejpam-5385	139	37	.	.	PUNCT
ejpam-5385	140	1	proof	proof	NOUN
ejpam-5385	140	2	.	.	PUNCT
ejpam-5385	141	1	we	we	PRON
ejpam-5385	141	2	will	will	AUX
ejpam-5385	141	3	follow	follow	VERB
ejpam-5385	141	4	the	the	DET
ejpam-5385	141	5	same	same	ADJ
ejpam-5385	141	6	general	general	ADJ
ejpam-5385	141	7	approach	approach	NOUN
ejpam-5385	141	8	used	use	VERB
ejpam-5385	141	9	in	in	ADP
ejpam-5385	141	10	the	the	DET
ejpam-5385	141	11	proof	proof	NOUN
ejpam-5385	141	12	of	of	ADP
ejpam-5385	141	13	theorem	theorem	NOUN
ejpam-5385	141	14	1	1	NUM
ejpam-5385	141	15	.	.	PUNCT
ejpam-5385	142	1	the	the	DET
ejpam-5385	142	2	only	only	ADJ
ejpam-5385	142	3	key	key	ADJ
ejpam-5385	142	4	difference	difference	NOUN
ejpam-5385	142	5	lies	lie	VERB
ejpam-5385	142	6	in	in	ADP
ejpam-5385	142	7	the	the	DET
ejpam-5385	142	8	third	third	ADJ
ejpam-5385	142	9	requirement	requirement	NOUN
ejpam-5385	142	10	of	of	ADP
ejpam-5385	142	11	definition	definition	NOUN
ejpam-5385	142	12	1	1	NUM
ejpam-5385	142	13	,	,	PUNCT
ejpam-5385	142	14	which	which	PRON
ejpam-5385	142	15	pertains	pertain	VERB
ejpam-5385	142	16	to	to	ADP
ejpam-5385	142	17	the	the	DET
ejpam-5385	142	18	behavior	behavior	NOUN
ejpam-5385	142	19	under	under	ADP
ejpam-5385	142	20	the	the	DET
ejpam-5385	142	21	lie	lie	NOUN
ejpam-5385	142	22	bracket	bracket	NOUN
ejpam-5385	142	23	,	,	PUNCT
ejpam-5385	142	24	as	as	SCONJ
ejpam-5385	142	25	the	the	DET
ejpam-5385	142	26	structure	structure	NOUN
ejpam-5385	142	27	involved	involve	VERB
ejpam-5385	142	28	is	be	AUX
ejpam-5385	142	29	now	now	ADV
ejpam-5385	142	30	a	a	DET
ejpam-5385	142	31	fuzzy	fuzzy	ADJ
ejpam-5385	142	32	lie	lie	NOUN
ejpam-5385	142	33	ideal	ideal	NOUN
ejpam-5385	142	34	rather	rather	ADV
ejpam-5385	142	35	than	than	ADP
ejpam-5385	142	36	a	a	DET
ejpam-5385	142	37	fuzzy	fuzzy	ADJ
ejpam-5385	142	38	subalgebra	subalgebra	NOUN
ejpam-5385	142	39	.	.	PUNCT
ejpam-5385	143	1	we	we	PRON
ejpam-5385	143	2	begin	begin	VERB
ejpam-5385	143	3	by	by	ADP
ejpam-5385	143	4	considering	consider	VERB
ejpam-5385	143	5	two	two	NUM
ejpam-5385	143	6	elements	element	NOUN
ejpam-5385	143	7	m1,m2	m1,m2	PROPN
ejpam-5385	143	8	∈	∈	PROPN
ejpam-5385	143	9	m1	m1	NOUN
ejpam-5385	143	10	.	.	PUNCT
ejpam-5385	144	1	our	our	PRON
ejpam-5385	144	2	goal	goal	NOUN
ejpam-5385	144	3	is	be	AUX
ejpam-5385	144	4	to	to	PART
ejpam-5385	144	5	show	show	VERB
ejpam-5385	144	6	that	that	SCONJ
ejpam-5385	144	7	the	the	DET
ejpam-5385	144	8	inverse	inverse	NOUN
ejpam-5385	144	9	image	image	NOUN
ejpam-5385	144	10	f−1(p	f−1(p	PROPN
ejpam-5385	144	11	)	)	PUNCT
ejpam-5385	144	12	satisfies	satisfy	VERB
ejpam-5385	144	13	the	the	DET
ejpam-5385	144	14	condition	condition	NOUN
ejpam-5385	144	15	for	for	ADP
ejpam-5385	144	16	being	be	AUX
ejpam-5385	144	17	a	a	DET
ejpam-5385	144	18	complex	complex	ADJ
ejpam-5385	144	19	intuitionistic	intuitionistic	ADJ
ejpam-5385	144	20	fuzzy	fuzzy	ADJ
ejpam-5385	144	21	lie	lie	NOUN
ejpam-5385	144	22	ideal	ideal	ADJ
ejpam-5385	144	23	.	.	PUNCT
ejpam-5385	145	1	for	for	ADP
ejpam-5385	145	2	the	the	DET
ejpam-5385	145	3	membership	membership	NOUN
ejpam-5385	145	4	function	function	NOUN
ejpam-5385	145	5	ϕf−1(p	ϕf−1(p	PROPN
ejpam-5385	145	6	)	)	PUNCT
ejpam-5385	145	7	under	under	ADP
ejpam-5385	145	8	the	the	DET
ejpam-5385	145	9	lie	lie	NOUN
ejpam-5385	145	10	bracket	bracket	NOUN
ejpam-5385	145	11	,	,	PUNCT
ejpam-5385	145	12	we	we	PRON
ejpam-5385	145	13	have	have	VERB
ejpam-5385	145	14	:	:	PUNCT
ejpam-5385	145	15	ϕf−1(p)([m1,m2	ϕf−1(p)([m1,m2	NOUN
ejpam-5385	145	16	]	]	PUNCT
ejpam-5385	145	17	)	)	PUNCT
ejpam-5385	145	18	=	=	SYM
ejpam-5385	145	19	ϕp(f([m1,m2	ϕp(f([m1,m2	NOUN
ejpam-5385	145	20	]	]	PUNCT
ejpam-5385	145	21	)	)	PUNCT
ejpam-5385	145	22	)	)	PUNCT
ejpam-5385	146	1	=	=	PUNCT
ejpam-5385	146	2	ϕp([f(m1	ϕp([f(m1	PROPN
ejpam-5385	146	3	)	)	PUNCT
ejpam-5385	146	4	,	,	PUNCT
ejpam-5385	146	5	f(m2	f(m2	NOUN
ejpam-5385	146	6	)	)	PUNCT
ejpam-5385	146	7	]	]	PUNCT
ejpam-5385	146	8	)	)	PUNCT
ejpam-5385	146	9	,	,	PUNCT
ejpam-5385	146	10	s.	s.	PROPN
ejpam-5385	146	11	shaqaqha	shaqaqha	PROPN
ejpam-5385	146	12	,	,	PUNCT
ejpam-5385	146	13	m.	m.	PROPN
ejpam-5385	146	14	y.	y.	PROPN
ejpam-5385	146	15	al	al	PROPN
ejpam-5385	146	16	-	-	PUNCT
ejpam-5385	146	17	deiakeh	deiakeh	PROPN
ejpam-5385	146	18	/	/	SYM
ejpam-5385	146	19	eur	eur	NOUN
ejpam-5385	146	20	.	.	PUNCT
ejpam-5385	147	1	j.	j.	PROPN
ejpam-5385	147	2	pure	pure	PROPN
ejpam-5385	147	3	appl	appl	PROPN
ejpam-5385	147	4	.	.	PROPN
ejpam-5385	147	5	math	math	PROPN
ejpam-5385	147	6	,	,	PUNCT
ejpam-5385	147	7	17	17	NUM
ejpam-5385	147	8	(	(	PUNCT
ejpam-5385	147	9	4	4	NUM
ejpam-5385	147	10	)	)	PUNCT
ejpam-5385	147	11	(	(	PUNCT
ejpam-5385	147	12	2024	2024	NUM
ejpam-5385	147	13	)	)	PUNCT
ejpam-5385	147	14	,	,	PUNCT
ejpam-5385	147	15	3291	3291	NUM
ejpam-5385	147	16	-	-	SYM
ejpam-5385	147	17	3303	3303	NUM
ejpam-5385	147	18	3297	3297	NUM
ejpam-5385	147	19	where	where	SCONJ
ejpam-5385	147	20	the	the	DET
ejpam-5385	147	21	second	second	ADJ
ejpam-5385	147	22	equality	equality	NOUN
ejpam-5385	147	23	follows	follow	VERB
ejpam-5385	147	24	from	from	ADP
ejpam-5385	147	25	the	the	DET
ejpam-5385	147	26	fact	fact	NOUN
ejpam-5385	147	27	that	that	SCONJ
ejpam-5385	147	28	f	f	PROPN
ejpam-5385	147	29	is	be	AUX
ejpam-5385	147	30	a	a	DET
ejpam-5385	147	31	homomorphism	homomorphism	NOUN
ejpam-5385	147	32	.	.	PUNCT
ejpam-5385	148	1	since	since	SCONJ
ejpam-5385	148	2	p	p	NOUN
ejpam-5385	148	3	is	be	AUX
ejpam-5385	148	4	a	a	DET
ejpam-5385	148	5	fuzzy	fuzzy	ADJ
ejpam-5385	148	6	lie	lie	NOUN
ejpam-5385	148	7	ideal	ideal	NOUN
ejpam-5385	148	8	in	in	ADP
ejpam-5385	148	9	m2	m2	PROPN
ejpam-5385	148	10	,	,	PUNCT
ejpam-5385	148	11	by	by	ADP
ejpam-5385	148	12	definition	definition	NOUN
ejpam-5385	148	13	1	1	NUM
ejpam-5385	148	14	,	,	PUNCT
ejpam-5385	148	15	we	we	PRON
ejpam-5385	148	16	know	know	VERB
ejpam-5385	148	17	:	:	PUNCT
ejpam-5385	148	18	ϕp([f(m1	ϕp([f(m1	NUM
ejpam-5385	148	19	)	)	PUNCT
ejpam-5385	148	20	,	,	PUNCT
ejpam-5385	148	21	f(m2	f(m2	NOUN
ejpam-5385	148	22	)	)	PUNCT
ejpam-5385	148	23	]	]	PUNCT
ejpam-5385	148	24	)	)	PUNCT
ejpam-5385	148	25	≥	≥	NOUN
ejpam-5385	148	26	ϕp(f(m1	ϕp(f(m1	NOUN
ejpam-5385	148	27	)	)	PUNCT
ejpam-5385	148	28	)	)	PUNCT
ejpam-5385	149	1	∨	∨	NUM
ejpam-5385	149	2	ϕp(f(m2	ϕp(f(m2	PROPN
ejpam-5385	149	3	)	)	PUNCT
ejpam-5385	149	4	)	)	PUNCT
ejpam-5385	149	5	.	.	PUNCT
ejpam-5385	150	1	thus	thus	ADV
ejpam-5385	150	2	,	,	PUNCT
ejpam-5385	150	3	we	we	PRON
ejpam-5385	150	4	obtain	obtain	VERB
ejpam-5385	150	5	:	:	PUNCT
ejpam-5385	150	6	ϕf−1(p)([m1,m2	ϕf−1(p)([m1,m2	NOUN
ejpam-5385	150	7	]	]	PUNCT
ejpam-5385	150	8	)	)	PUNCT
ejpam-5385	150	9	≥	≥	NOUN
ejpam-5385	150	10	ϕf−1(p)(m1	ϕf−1(p)(m1	NOUN
ejpam-5385	150	11	)	)	PUNCT
ejpam-5385	150	12	∨	∨	NUM
ejpam-5385	150	13	ϕf−1(p)(m2	ϕf−1(p)(m2	X
ejpam-5385	150	14	)	)	PUNCT
ejpam-5385	150	15	.	.	PUNCT
ejpam-5385	151	1	this	this	PRON
ejpam-5385	151	2	demonstrates	demonstrate	VERB
ejpam-5385	151	3	that	that	SCONJ
ejpam-5385	151	4	ϕf−1(p	ϕf−1(p	PROPN
ejpam-5385	151	5	)	)	PUNCT
ejpam-5385	151	6	satisfies	satisfy	VERB
ejpam-5385	151	7	the	the	DET
ejpam-5385	151	8	required	require	VERB
ejpam-5385	151	9	condition	condition	NOUN
ejpam-5385	151	10	under	under	ADP
ejpam-5385	151	11	the	the	DET
ejpam-5385	151	12	lie	lie	NOUN
ejpam-5385	151	13	bracket	bracket	NOUN
ejpam-5385	151	14	.	.	PUNCT
ejpam-5385	152	1	for	for	ADP
ejpam-5385	152	2	the	the	DET
ejpam-5385	152	3	non	non	ADJ
ejpam-5385	152	4	-	-	ADJ
ejpam-5385	152	5	membership	membership	ADJ
ejpam-5385	152	6	function	function	NOUN
ejpam-5385	152	7	ψf−1(p	ψf−1(p	NOUN
ejpam-5385	152	8	)	)	PUNCT
ejpam-5385	152	9	,	,	PUNCT
ejpam-5385	152	10	we	we	PRON
ejpam-5385	152	11	similarly	similarly	ADV
ejpam-5385	152	12	have	have	VERB
ejpam-5385	152	13	:	:	PUNCT
ejpam-5385	152	14	ψf−1(p)([m1,m2	ψf−1(p)([m1,m2	NOUN
ejpam-5385	152	15	]	]	PUNCT
ejpam-5385	152	16	)	)	PUNCT
ejpam-5385	152	17	=	=	SYM
ejpam-5385	152	18	ψp(f([m1,m2	ψp(f([m1,m2	NOUN
ejpam-5385	152	19	]	]	PUNCT
ejpam-5385	152	20	)	)	PUNCT
ejpam-5385	152	21	)	)	PUNCT
ejpam-5385	153	1	=	=	SYM
ejpam-5385	153	2	ψp([f(m1	ψp([f(m1	NOUN
ejpam-5385	153	3	)	)	PUNCT
ejpam-5385	153	4	,	,	PUNCT
ejpam-5385	153	5	f(m2	f(m2	NOUN
ejpam-5385	153	6	)	)	PUNCT
ejpam-5385	153	7	]	]	PUNCT
ejpam-5385	153	8	)	)	PUNCT
ejpam-5385	153	9	.	.	PUNCT
ejpam-5385	154	1	since	since	SCONJ
ejpam-5385	154	2	p	p	NOUN
ejpam-5385	154	3	is	be	AUX
ejpam-5385	154	4	a	a	DET
ejpam-5385	154	5	fuzzy	fuzzy	ADJ
ejpam-5385	154	6	lie	lie	NOUN
ejpam-5385	154	7	ideal	ideal	ADJ
ejpam-5385	154	8	,	,	PUNCT
ejpam-5385	154	9	it	it	PRON
ejpam-5385	154	10	follows	follow	VERB
ejpam-5385	154	11	that	that	SCONJ
ejpam-5385	154	12	:	:	PUNCT
ejpam-5385	154	13	ψp([f(m1	ψp([f(m1	NUM
ejpam-5385	154	14	)	)	PUNCT
ejpam-5385	154	15	,	,	PUNCT
ejpam-5385	154	16	f(m2	f(m2	NOUN
ejpam-5385	154	17	)	)	PUNCT
ejpam-5385	154	18	]	]	PUNCT
ejpam-5385	154	19	)	)	PUNCT
ejpam-5385	154	20	≤	≤	NUM
ejpam-5385	154	21	ψp(f(m1	ψp(f(m1	NOUN
ejpam-5385	154	22	)	)	PUNCT
ejpam-5385	154	23	)	)	PUNCT
ejpam-5385	155	1	∧	∧	NOUN
ejpam-5385	155	2	ψp(f(m2	ψp(f(m2	NOUN
ejpam-5385	155	3	)	)	PUNCT
ejpam-5385	155	4	)	)	PUNCT
ejpam-5385	155	5	.	.	PUNCT
ejpam-5385	156	1	therefore	therefore	ADV
ejpam-5385	156	2	,	,	PUNCT
ejpam-5385	156	3	we	we	PRON
ejpam-5385	156	4	have	have	VERB
ejpam-5385	156	5	:	:	PUNCT
ejpam-5385	156	6	ψf−1(p)([m1,m2	ψf−1(p)([m1,m2	NOUN
ejpam-5385	156	7	]	]	PUNCT
ejpam-5385	156	8	)	)	PUNCT
ejpam-5385	156	9	≤	≤	NUM
ejpam-5385	156	10	ψf−1(p)(m1	ψf−1(p)(m1	NOUN
ejpam-5385	156	11	)	)	PUNCT
ejpam-5385	156	12	∧	∧	PROPN
ejpam-5385	156	13	ψf−1(p)(m2	ψf−1(p)(m2	NOUN
ejpam-5385	156	14	)	)	PUNCT
ejpam-5385	156	15	.	.	PUNCT
ejpam-5385	157	1	thus	thus	ADV
ejpam-5385	157	2	,	,	PUNCT
ejpam-5385	157	3	the	the	DET
ejpam-5385	157	4	set	set	NOUN
ejpam-5385	157	5	f−1(p	f−1(p	PROPN
ejpam-5385	157	6	)	)	PUNCT
ejpam-5385	157	7	satisfies	satisfy	VERB
ejpam-5385	157	8	the	the	DET
ejpam-5385	157	9	conditions	condition	NOUN
ejpam-5385	157	10	for	for	ADP
ejpam-5385	157	11	being	be	AUX
ejpam-5385	157	12	a	a	DET
ejpam-5385	157	13	complex	complex	ADJ
ejpam-5385	157	14	intuitionistic	intuitionistic	ADJ
ejpam-5385	157	15	fuzzy	fuzzy	ADJ
ejpam-5385	157	16	lie	lie	NOUN
ejpam-5385	157	17	ideal	ideal	NOUN
ejpam-5385	157	18	in	in	ADP
ejpam-5385	157	19	m1	m1	PROPN
ejpam-5385	157	20	,	,	PUNCT
ejpam-5385	157	21	completing	complete	VERB
ejpam-5385	157	22	the	the	DET
ejpam-5385	157	23	proof	proof	NOUN
ejpam-5385	157	24	.	.	PUNCT
ejpam-5385	158	1	lemma	lemma	PROPN
ejpam-5385	158	2	1	1	NUM
ejpam-5385	158	3	.	.	PUNCT
ejpam-5385	159	1	(	(	PUNCT
ejpam-5385	159	2	[	[	X
ejpam-5385	159	3	1	1	NUM
ejpam-5385	159	4	]	]	PUNCT
ejpam-5385	159	5	)	)	PUNCT
ejpam-5385	159	6	if	if	SCONJ
ejpam-5385	159	7	f	f	PROPN
ejpam-5385	159	8	:	:	PUNCT
ejpam-5385	159	9	m1	m1	PROPN
ejpam-5385	160	1	→	→	SYM
ejpam-5385	160	2	m2	m2	PROPN
ejpam-5385	160	3	represents	represent	VERB
ejpam-5385	160	4	a	a	DET
ejpam-5385	160	5	lie	lie	NOUN
ejpam-5385	160	6	algebra	algebra	NOUN
ejpam-5385	160	7	homomorphism	homomorphism	NOUN
ejpam-5385	160	8	,	,	PUNCT
ejpam-5385	160	9	and	and	CCONJ
ejpam-5385	160	10	e	e	X
ejpam-5385	160	11	=	=	SYM
ejpam-5385	160	12	(	(	PUNCT
ejpam-5385	160	13	ϕe	ϕe	INTJ
ejpam-5385	160	14	,	,	PUNCT
ejpam-5385	160	15	ψe	ψe	NOUN
ejpam-5385	160	16	)	)	PUNCT
ejpam-5385	160	17	constitutes	constitute	VERB
ejpam-5385	160	18	an	an	DET
ejpam-5385	160	19	intuitionistic	intuitionistic	ADJ
ejpam-5385	160	20	fuzzy	fuzzy	ADJ
ejpam-5385	160	21	lie	lie	NOUN
ejpam-5385	160	22	subalgebra	subalgebra	NOUN
ejpam-5385	160	23	within	within	ADP
ejpam-5385	160	24	m1	m1	NOUN
ejpam-5385	160	25	,	,	PUNCT
ejpam-5385	160	26	then	then	ADV
ejpam-5385	160	27	the	the	DET
ejpam-5385	160	28	intuitionistic	intuitionistic	ADJ
ejpam-5385	160	29	fuzzy	fuzzy	ADJ
ejpam-5385	160	30	set	set	VERB
ejpam-5385	160	31	f(e	f(e	NOUN
ejpam-5385	160	32	)	)	PUNCT
ejpam-5385	160	33	transforms	transform	VERB
ejpam-5385	160	34	into	into	ADP
ejpam-5385	160	35	an	an	DET
ejpam-5385	160	36	intuitionistic	intuitionistic	ADJ
ejpam-5385	160	37	fuzzy	fuzzy	ADJ
ejpam-5385	160	38	lie	lie	NOUN
ejpam-5385	160	39	subalgebra	subalgebra	NOUN
ejpam-5385	160	40	over	over	ADP
ejpam-5385	160	41	the	the	DET
ejpam-5385	160	42	domain	domain	NOUN
ejpam-5385	160	43	im(f	im(f	NOUN
ejpam-5385	160	44	)	)	PUNCT
ejpam-5385	160	45	.	.	PUNCT
ejpam-5385	161	1	lemma	lemma	PROPN
ejpam-5385	161	2	2	2	NUM
ejpam-5385	161	3	.	.	PUNCT
ejpam-5385	162	1	(	(	PUNCT
ejpam-5385	162	2	[	[	X
ejpam-5385	162	3	14	14	NUM
ejpam-5385	162	4	]	]	SYM
ejpam-5385	162	5	)	)	PUNCT
ejpam-5385	162	6	if	if	SCONJ
ejpam-5385	162	7	e	e	X
ejpam-5385	162	8	=	=	SYM
ejpam-5385	162	9	(	(	PUNCT
ejpam-5385	162	10	ϕe	ϕe	INTJ
ejpam-5385	162	11	,	,	PUNCT
ejpam-5385	162	12	ψe	ψe	NOUN
ejpam-5385	162	13	)	)	PUNCT
ejpam-5385	162	14	represents	represent	VERB
ejpam-5385	162	15	a	a	DET
ejpam-5385	162	16	complex	complex	ADJ
ejpam-5385	162	17	intuitionistic	intuitionistic	ADJ
ejpam-5385	162	18	fuzzy	fuzzy	ADJ
ejpam-5385	162	19	set	set	NOUN
ejpam-5385	162	20	of	of	ADP
ejpam-5385	162	21	a	a	DET
ejpam-5385	162	22	lie	lie	NOUN
ejpam-5385	162	23	algebra	algebra	NOUN
ejpam-5385	162	24	m	m	PRON
ejpam-5385	162	25	,	,	PUNCT
ejpam-5385	162	26	then	then	ADV
ejpam-5385	162	27	e	e	NOUN
ejpam-5385	162	28	qualifies	qualify	VERB
ejpam-5385	162	29	as	as	ADP
ejpam-5385	162	30	a	a	DET
ejpam-5385	162	31	complex	complex	ADJ
ejpam-5385	162	32	intuitionistic	intuitionistic	ADJ
ejpam-5385	162	33	fuzzy	fuzzy	ADJ
ejpam-5385	162	34	lie	lie	NOUN
ejpam-5385	162	35	ideal	ideal	NOUN
ejpam-5385	162	36	(	(	PUNCT
ejpam-5385	162	37	or	or	CCONJ
ejpam-5385	162	38	subalgebra	subalgebra	NOUN
ejpam-5385	162	39	)	)	PUNCT
ejpam-5385	162	40	of	of	ADP
ejpam-5385	162	41	m	m	PRON
ejpam-5385	162	42	if	if	SCONJ
ejpam-5385	163	1	and	and	CCONJ
ejpam-5385	163	2	only	only	ADV
ejpam-5385	163	3	if	if	SCONJ
ejpam-5385	163	4	the	the	DET
ejpam-5385	163	5	associated	associated	ADJ
ejpam-5385	163	6	intuitionistic	intuitionistic	ADJ
ejpam-5385	163	7	fuzzy	fuzzy	ADJ
ejpam-5385	163	8	subset	subset	NOUN
ejpam-5385	163	9	e	e	NOUN
ejpam-5385	163	10	=	=	SYM
ejpam-5385	163	11	{	{	PUNCT
ejpam-5385	163	12	(	(	PUNCT
ejpam-5385	163	13	m	m	NOUN
ejpam-5385	163	14	,	,	PUNCT
ejpam-5385	163	15	ρe(m	ρe(m	NUM
ejpam-5385	163	16	)	)	PUNCT
ejpam-5385	163	17	,	,	PUNCT
ejpam-5385	163	18	ρ̂e(m	ρ̂e(m	NUM
ejpam-5385	163	19	)	)	PUNCT
ejpam-5385	163	20	)	)	PUNCT
ejpam-5385	163	21	:	:	PUNCT
ejpam-5385	164	1	m	m	VERB
ejpam-5385	164	2	∈	∈	PROPN
ejpam-5385	164	3	m	m	PRON
ejpam-5385	164	4	}	}	PUNCT
ejpam-5385	164	5	emerges	emerge	NOUN
ejpam-5385	164	6	as	as	ADP
ejpam-5385	164	7	an	an	DET
ejpam-5385	164	8	intuitionistic	intuitionistic	ADJ
ejpam-5385	164	9	fuzzy	fuzzy	ADJ
ejpam-5385	164	10	lie	lie	NOUN
ejpam-5385	164	11	ideal	ideal	NOUN
ejpam-5385	164	12	(	(	PUNCT
ejpam-5385	164	13	or	or	CCONJ
ejpam-5385	164	14	subalgebra	subalgebra	NOUN
ejpam-5385	164	15	)	)	PUNCT
ejpam-5385	164	16	of	of	ADP
ejpam-5385	164	17	m.	m.	NOUN
ejpam-5385	164	18	theorem	theorem	NOUN
ejpam-5385	164	19	2	2	X
ejpam-5385	164	20	.	.	X
ejpam-5385	164	21	assume	assume	VERB
ejpam-5385	164	22	f	f	X
ejpam-5385	164	23	:	:	PUNCT
ejpam-5385	164	24	m1	m1	PROPN
ejpam-5385	164	25	→	→	SYM
ejpam-5385	164	26	m2	m2	PROPN
ejpam-5385	164	27	is	be	AUX
ejpam-5385	164	28	a	a	DET
ejpam-5385	164	29	homomorphism	homomorphism	NOUN
ejpam-5385	164	30	between	between	ADP
ejpam-5385	164	31	lie	lie	NOUN
ejpam-5385	164	32	algebras	algebra	NOUN
ejpam-5385	164	33	.	.	PUNCT
ejpam-5385	165	1	if	if	SCONJ
ejpam-5385	165	2	e	e	X
ejpam-5385	165	3	=	=	SYM
ejpam-5385	165	4	(	(	PUNCT
ejpam-5385	165	5	ϕe	ϕe	INTJ
ejpam-5385	165	6	,	,	PUNCT
ejpam-5385	165	7	ψe	ψe	NOUN
ejpam-5385	165	8	)	)	PUNCT
ejpam-5385	165	9	constitutes	constitute	VERB
ejpam-5385	165	10	a	a	DET
ejpam-5385	165	11	complex	complex	ADJ
ejpam-5385	165	12	intuitionistic	intuitionistic	ADJ
ejpam-5385	165	13	fuzzy	fuzzy	ADJ
ejpam-5385	165	14	lie	lie	NOUN
ejpam-5385	165	15	subalgebra	subalgebra	NOUN
ejpam-5385	165	16	within	within	ADP
ejpam-5385	165	17	m1	m1	NOUN
ejpam-5385	165	18	,	,	PUNCT
ejpam-5385	165	19	then	then	ADV
ejpam-5385	165	20	the	the	DET
ejpam-5385	165	21	complex	complex	ADJ
ejpam-5385	165	22	intuitionistic	intuitionistic	ADJ
ejpam-5385	165	23	fuzzy	fuzzy	ADJ
ejpam-5385	165	24	set	set	VERB
ejpam-5385	165	25	f(e	f(e	NOUN
ejpam-5385	165	26	)	)	PUNCT
ejpam-5385	165	27	forms	form	VERB
ejpam-5385	165	28	a	a	DET
ejpam-5385	165	29	complex	complex	ADJ
ejpam-5385	165	30	intuitionistic	intuitionistic	ADJ
ejpam-5385	165	31	fuzzy	fuzzy	ADJ
ejpam-5385	165	32	lie	lie	NOUN
ejpam-5385	165	33	subalgebra	subalgebra	NOUN
ejpam-5385	165	34	in	in	ADP
ejpam-5385	165	35	the	the	DET
ejpam-5385	165	36	context	context	NOUN
ejpam-5385	165	37	of	of	ADP
ejpam-5385	165	38	the	the	DET
ejpam-5385	165	39	image	image	NOUN
ejpam-5385	165	40	of	of	ADP
ejpam-5385	165	41	f	f	PROPN
ejpam-5385	165	42	.	.	PUNCT
ejpam-5385	166	1	proof	proof	NOUN
ejpam-5385	166	2	.	.	PUNCT
ejpam-5385	167	1	initially	initially	ADV
ejpam-5385	167	2	,	,	PUNCT
ejpam-5385	167	3	we	we	PRON
ejpam-5385	167	4	demonstrate	demonstrate	VERB
ejpam-5385	167	5	the	the	DET
ejpam-5385	167	6	homogeneity	homogeneity	NOUN
ejpam-5385	167	7	of	of	ADP
ejpam-5385	167	8	f(e	f(e	NOUN
ejpam-5385	167	9	)	)	PUNCT
ejpam-5385	167	10	as	as	SCONJ
ejpam-5385	167	11	follows	follow	VERB
ejpam-5385	167	12	:	:	PUNCT
ejpam-5385	167	13	ϕf(e)(n	ϕf(e)(n	NUM
ejpam-5385	167	14	)	)	PUNCT
ejpam-5385	168	1	=	=	SYM
ejpam-5385	168	2	sup	sup	NOUN
ejpam-5385	168	3	n	n	CCONJ
ejpam-5385	168	4	=	=	SYM
ejpam-5385	168	5	f(m	f(m	PROPN
ejpam-5385	168	6	)	)	PUNCT
ejpam-5385	168	7	{	{	PUNCT
ejpam-5385	168	8	ϕe(m	ϕe(m	ADJ
ejpam-5385	168	9	)	)	PUNCT
ejpam-5385	168	10	}	}	PUNCT
ejpam-5385	168	11	=	=	SYM
ejpam-5385	168	12	sup	sup	NOUN
ejpam-5385	168	13	n	n	CCONJ
ejpam-5385	168	14	=	=	SYM
ejpam-5385	168	15	f(m	f(m	PROPN
ejpam-5385	168	16	)	)	PUNCT
ejpam-5385	168	17	{	{	PUNCT
ejpam-5385	168	18	ρe(m)eiζe(m	ρe(m)eiζe(m	PROPN
ejpam-5385	168	19	)	)	PUNCT
ejpam-5385	168	20	}	}	PUNCT
ejpam-5385	168	21	s.	s.	PROPN
ejpam-5385	168	22	shaqaqha	shaqaqha	PROPN
ejpam-5385	168	23	,	,	PUNCT
ejpam-5385	168	24	m.	m.	PROPN
ejpam-5385	168	25	y.	y.	PROPN
ejpam-5385	168	26	al	al	PROPN
ejpam-5385	168	27	-	-	PUNCT
ejpam-5385	168	28	deiakeh	deiakeh	PROPN
ejpam-5385	168	29	/	/	SYM
ejpam-5385	168	30	eur	eur	NOUN
ejpam-5385	168	31	.	.	PUNCT
ejpam-5385	169	1	j.	j.	PROPN
ejpam-5385	169	2	pure	pure	PROPN
ejpam-5385	169	3	appl	appl	PROPN
ejpam-5385	169	4	.	.	PROPN
ejpam-5385	169	5	math	math	PROPN
ejpam-5385	169	6	,	,	PUNCT
ejpam-5385	169	7	17	17	NUM
ejpam-5385	169	8	(	(	PUNCT
ejpam-5385	169	9	4	4	NUM
ejpam-5385	169	10	)	)	PUNCT
ejpam-5385	169	11	(	(	PUNCT
ejpam-5385	169	12	2024	2024	NUM
ejpam-5385	169	13	)	)	PUNCT
ejpam-5385	169	14	,	,	PUNCT
ejpam-5385	169	15	3291	3291	NUM
ejpam-5385	169	16	-	-	SYM
ejpam-5385	169	17	3303	3303	NUM
ejpam-5385	169	18	3298	3298	NUM
ejpam-5385	169	19	=	=	SYM
ejpam-5385	169	20	sup	sup	NOUN
ejpam-5385	169	21	n	n	CCONJ
ejpam-5385	169	22	=	=	SYM
ejpam-5385	169	23	f(m	f(m	PROPN
ejpam-5385	169	24	)	)	PUNCT
ejpam-5385	169	25	{	{	PUNCT
ejpam-5385	169	26	ρe(m)}ei(supn	ρe(m)}ei(supn	NOUN
ejpam-5385	169	27	=	=	NOUN
ejpam-5385	169	28	f(m){ζe(m	f(m){ζe(m	NOUN
ejpam-5385	169	29	)	)	PUNCT
ejpam-5385	169	30	}	}	PUNCT
ejpam-5385	169	31	)	)	PUNCT
ejpam-5385	170	1	(	(	PUNCT
ejpam-5385	170	2	since	since	SCONJ
ejpam-5385	170	3	e	e	NOUN
ejpam-5385	170	4	is	be	AUX
ejpam-5385	170	5	homogeneous	homogeneous	ADJ
ejpam-5385	170	6	)	)	PUNCT
ejpam-5385	170	7	.	.	PUNCT
ejpam-5385	171	1	in	in	ADP
ejpam-5385	171	2	a	a	DET
ejpam-5385	171	3	similar	similar	ADJ
ejpam-5385	171	4	manner	manner	NOUN
ejpam-5385	171	5	,	,	PUNCT
ejpam-5385	171	6	we	we	PRON
ejpam-5385	171	7	can	can	AUX
ejpam-5385	171	8	derive	derive	VERB
ejpam-5385	171	9	ψf(e)(n	ψf(e)(n	NOUN
ejpam-5385	171	10	)	)	PUNCT
ejpam-5385	171	11	=	=	SYM
ejpam-5385	171	12	inf	inf	PROPN
ejpam-5385	171	13	n	n	CCONJ
ejpam-5385	171	14	=	=	SYM
ejpam-5385	171	15	f(m	f(m	PROPN
ejpam-5385	171	16	)	)	PUNCT
ejpam-5385	171	17	{	{	PUNCT
ejpam-5385	171	18	ρ̂e(m)}ei(infn	ρ̂e(m)}ei(infn	X
ejpam-5385	171	19	=	=	SYM
ejpam-5385	171	20	f(m){ζ̂e(m	f(m){ζ̂e(m	VERB
ejpam-5385	171	21	)	)	PUNCT
ejpam-5385	171	22	}	}	PUNCT
ejpam-5385	171	23	)	)	PUNCT
ejpam-5385	171	24	.	.	PUNCT
ejpam-5385	172	1	next	next	ADV
ejpam-5385	172	2	,	,	PUNCT
ejpam-5385	172	3	we	we	PRON
ejpam-5385	172	4	analyze	analyze	VERB
ejpam-5385	172	5	the	the	DET
ejpam-5385	172	6	case	case	NOUN
ejpam-5385	172	7	where	where	SCONJ
ejpam-5385	172	8	n1	n1	PROPN
ejpam-5385	172	9	and	and	CCONJ
ejpam-5385	172	10	n2	n2	PROPN
ejpam-5385	172	11	belong	belong	VERB
ejpam-5385	172	12	to	to	ADP
ejpam-5385	172	13	the	the	DET
ejpam-5385	172	14	image	image	NOUN
ejpam-5385	172	15	of	of	ADP
ejpam-5385	172	16	f	f	PROPN
ejpam-5385	172	17	,	,	PUNCT
ejpam-5385	172	18	denoted	denote	VERB
ejpam-5385	172	19	as	as	ADP
ejpam-5385	172	20	im(f	im(f	NOUN
ejpam-5385	172	21	)	)	PUNCT
ejpam-5385	172	22	,	,	PUNCT
ejpam-5385	172	23	and	and	CCONJ
ejpam-5385	172	24	where	where	SCONJ
ejpam-5385	172	25	supn1	supn1	ADP
ejpam-5385	172	26	=	=	NOUN
ejpam-5385	172	27	f(m){ρe(m	f(m){ρe(m	ADJ
ejpam-5385	172	28	)	)	PUNCT
ejpam-5385	172	29	}	}	PUNCT
ejpam-5385	172	30	≤	≤	NUM
ejpam-5385	172	31	supn2	supn2	NOUN
ejpam-5385	172	32	=	=	NOUN
ejpam-5385	172	33	f(m){ρe(m	f(m){ρe(m	NOUN
ejpam-5385	172	34	)	)	PUNCT
ejpam-5385	172	35	}	}	PUNCT
ejpam-5385	172	36	.	.	PUNCT
ejpam-5385	173	1	suppose	suppose	VERB
ejpam-5385	173	2	,	,	PUNCT
ejpam-5385	173	3	for	for	ADP
ejpam-5385	173	4	the	the	DET
ejpam-5385	173	5	sake	sake	NOUN
ejpam-5385	173	6	of	of	ADP
ejpam-5385	173	7	contradiction	contradiction	NOUN
ejpam-5385	173	8	,	,	PUNCT
ejpam-5385	173	9	that	that	DET
ejpam-5385	173	10	supn2	supn2	NOUN
ejpam-5385	173	11	=	=	NOUN
ejpam-5385	173	12	f(m){ζe(m	f(m){ζe(m	NOUN
ejpam-5385	173	13	)	)	PUNCT
ejpam-5385	173	14	}	}	PUNCT
ejpam-5385	173	15	<	<	X
ejpam-5385	173	16	supn1	supn1	PROPN
ejpam-5385	173	17	=	=	SYM
ejpam-5385	173	18	f(m){ζe(m	f(m){ζe(m	NOUN
ejpam-5385	173	19	)	)	PUNCT
ejpam-5385	173	20	}	}	PUNCT
ejpam-5385	173	21	.	.	PUNCT
ejpam-5385	174	1	this	this	PRON
ejpam-5385	174	2	implies	imply	VERB
ejpam-5385	174	3	the	the	DET
ejpam-5385	174	4	existence	existence	NOUN
ejpam-5385	174	5	of	of	ADP
ejpam-5385	174	6	m1	m1	PROPN
ejpam-5385	174	7	∈	∈	PROPN
ejpam-5385	174	8	m1	m1	PROPN
ejpam-5385	174	9	such	such	ADJ
ejpam-5385	174	10	that	that	DET
ejpam-5385	174	11	f(m1	f(m1	NOUN
ejpam-5385	174	12	)	)	PUNCT
ejpam-5385	174	13	=	=	SYM
ejpam-5385	174	14	n1	n1	NOUN
ejpam-5385	174	15	and	and	CCONJ
ejpam-5385	174	16	supn2	supn2	ADJ
ejpam-5385	174	17	=	=	ADJ
ejpam-5385	174	18	φ(m){ζe(m	φ(m){ζe(m	PRON
ejpam-5385	174	19	)	)	PUNCT
ejpam-5385	174	20	}	}	PUNCT
ejpam-5385	174	21	<	<	X
ejpam-5385	174	22	ζe(m1	ζe(m1	NOUN
ejpam-5385	174	23	)	)	PUNCT
ejpam-5385	174	24	.	.	PUNCT
ejpam-5385	175	1	consider	consider	VERB
ejpam-5385	175	2	the	the	DET
ejpam-5385	175	3	case	case	NOUN
ejpam-5385	175	4	where	where	SCONJ
ejpam-5385	175	5	f(m	f(m	PROPN
ejpam-5385	175	6	)	)	PUNCT
ejpam-5385	175	7	=	=	SYM
ejpam-5385	175	8	n2	n2	NOUN
ejpam-5385	175	9	.	.	PUNCT
ejpam-5385	176	1	this	this	PRON
ejpam-5385	176	2	leads	lead	VERB
ejpam-5385	176	3	to	to	ADP
ejpam-5385	176	4	ζe(m	ζe(m	NUM
ejpam-5385	176	5	)	)	PUNCT
ejpam-5385	176	6	<	<	X
ejpam-5385	176	7	ζe(m1	ζe(m1	NOUN
ejpam-5385	176	8	)	)	PUNCT
ejpam-5385	176	9	,	,	PUNCT
ejpam-5385	176	10	and	and	CCONJ
ejpam-5385	176	11	due	due	ADP
ejpam-5385	176	12	to	to	ADP
ejpam-5385	176	13	the	the	DET
ejpam-5385	176	14	homogeneity	homogeneity	NOUN
ejpam-5385	176	15	of	of	ADP
ejpam-5385	176	16	e	e	NOUN
ejpam-5385	176	17	,	,	PUNCT
ejpam-5385	176	18	we	we	PRON
ejpam-5385	176	19	deduce	deduce	VERB
ejpam-5385	176	20	that	that	PRON
ejpam-5385	176	21	ρe(m	ρe(m	NUM
ejpam-5385	176	22	)	)	PUNCT
ejpam-5385	176	23	<	<	X
ejpam-5385	176	24	ρe(m1	ρe(m1	NOUN
ejpam-5385	176	25	)	)	PUNCT
ejpam-5385	176	26	.	.	PUNCT
ejpam-5385	177	1	consequently	consequently	ADV
ejpam-5385	177	2	,	,	PUNCT
ejpam-5385	177	3	we	we	PRON
ejpam-5385	177	4	find	find	VERB
ejpam-5385	177	5	supn2	supn2	ADJ
ejpam-5385	177	6	=	=	ADJ
ejpam-5385	177	7	f(m){ρe(m	f(m){ρe(m	ADJ
ejpam-5385	177	8	)	)	PUNCT
ejpam-5385	177	9	}	}	PUNCT
ejpam-5385	178	1	<	<	X
ejpam-5385	178	2	ρe(m1	ρe(m1	NOUN
ejpam-5385	178	3	)	)	PUNCT
ejpam-5385	178	4	.	.	PUNCT
ejpam-5385	179	1	this	this	PRON
ejpam-5385	179	2	directly	directly	ADV
ejpam-5385	179	3	contradicts	contradict	VERB
ejpam-5385	179	4	our	our	PRON
ejpam-5385	179	5	assumption	assumption	NOUN
ejpam-5385	179	6	supn1	supn1	NOUN
ejpam-5385	179	7	=	=	NOUN
ejpam-5385	179	8	f(m){ρe(m	f(m){ρe(m	ADJ
ejpam-5385	179	9	)	)	PUNCT
ejpam-5385	179	10	}	}	PUNCT
ejpam-5385	179	11	≤	≤	NUM
ejpam-5385	179	12	supn2	supn2	NOUN
ejpam-5385	179	13	=	=	NOUN
ejpam-5385	179	14	f(m){ρe(m	f(m){ρe(m	NOUN
ejpam-5385	179	15	)	)	PUNCT
ejpam-5385	179	16	}	}	PUNCT
ejpam-5385	179	17	.	.	PUNCT
ejpam-5385	180	1	by	by	ADP
ejpam-5385	180	2	employing	employ	VERB
ejpam-5385	180	3	a	a	DET
ejpam-5385	180	4	similar	similar	ADJ
ejpam-5385	180	5	reasoning	reasoning	NOUN
ejpam-5385	180	6	,	,	PUNCT
ejpam-5385	180	7	we	we	PRON
ejpam-5385	180	8	can	can	AUX
ejpam-5385	180	9	establish	establish	VERB
ejpam-5385	180	10	that	that	SCONJ
ejpam-5385	180	11	if	if	SCONJ
ejpam-5385	180	12	infn1	infn1	NOUN
ejpam-5385	180	13	=	=	SYM
ejpam-5385	180	14	f(m){ρ̂e(m	f(m){ρ̂e(m	ADJ
ejpam-5385	180	15	)	)	PUNCT
ejpam-5385	180	16	}	}	PUNCT
ejpam-5385	180	17	≤	≤	ADV
ejpam-5385	180	18	infn2	infn2	NOUN
ejpam-5385	180	19	=	=	SYM
ejpam-5385	180	20	f(m){ρ̂e(m	f(m){ρ̂e(m	ADJ
ejpam-5385	180	21	)	)	PUNCT
ejpam-5385	180	22	}	}	PUNCT
ejpam-5385	180	23	,	,	PUNCT
ejpam-5385	180	24	then	then	ADV
ejpam-5385	180	25	infn1	infn1	NOUN
ejpam-5385	180	26	=	=	SYM
ejpam-5385	180	27	f(m){ζ̂e(m	f(m){ζ̂e(m	X
ejpam-5385	180	28	)	)	PUNCT
ejpam-5385	180	29	}	}	PUNCT
ejpam-5385	180	30	≤	≤	ADV
ejpam-5385	180	31	infn2	infn2	NOUN
ejpam-5385	180	32	=	=	SYM
ejpam-5385	180	33	f(m){ζ̂e(m	f(m){ζ̂e(m	VERB
ejpam-5385	180	34	)	)	PUNCT
ejpam-5385	180	35	}	}	PUNCT
ejpam-5385	180	36	.	.	PUNCT
ejpam-5385	181	1	as	as	ADP
ejpam-5385	181	2	a	a	DET
ejpam-5385	181	3	result	result	NOUN
ejpam-5385	181	4	of	of	ADP
ejpam-5385	181	5	the	the	DET
ejpam-5385	181	6	above	above	ADJ
ejpam-5385	181	7	analysis	analysis	NOUN
ejpam-5385	181	8	,	,	PUNCT
ejpam-5385	181	9	we	we	PRON
ejpam-5385	181	10	conclude	conclude	VERB
ejpam-5385	181	11	that	that	SCONJ
ejpam-5385	181	12	f(e	f(e	NOUN
ejpam-5385	181	13	)	)	PUNCT
ejpam-5385	181	14	exhibits	exhibit	VERB
ejpam-5385	181	15	homogeneity	homogeneity	NOUN
ejpam-5385	181	16	within	within	ADP
ejpam-5385	181	17	im(f	im(f	NOUN
ejpam-5385	181	18	)	)	PUNCT
ejpam-5385	181	19	.	.	PUNCT
ejpam-5385	182	1	given	give	VERB
ejpam-5385	182	2	that	that	SCONJ
ejpam-5385	182	3	e	e	NOUN
ejpam-5385	182	4	is	be	AUX
ejpam-5385	182	5	a	a	DET
ejpam-5385	182	6	complex	complex	ADJ
ejpam-5385	182	7	intuitionistic	intuitionistic	ADJ
ejpam-5385	182	8	fuzzy	fuzzy	ADJ
ejpam-5385	182	9	lie	lie	NOUN
ejpam-5385	182	10	subalgebra	subalgebra	NOUN
ejpam-5385	182	11	,	,	PUNCT
ejpam-5385	182	12	we	we	PRON
ejpam-5385	182	13	can	can	AUX
ejpam-5385	182	14	deduce	deduce	VERB
ejpam-5385	182	15	from	from	ADP
ejpam-5385	182	16	lemma	lemma	PROPN
ejpam-5385	182	17	2	2	NUM
ejpam-5385	182	18	that	that	PRON
ejpam-5385	182	19	e	e	AUX
ejpam-5385	182	20	=	=	PRON
ejpam-5385	182	21	{	{	PUNCT
ejpam-5385	182	22	(	(	PUNCT
ejpam-5385	182	23	m	m	NOUN
ejpam-5385	182	24	,	,	PUNCT
ejpam-5385	182	25	ρe(m	ρe(m	NUM
ejpam-5385	182	26	)	)	PUNCT
ejpam-5385	182	27	,	,	PUNCT
ejpam-5385	182	28	ρ̂e(m	ρ̂e(m	NUM
ejpam-5385	182	29	)	)	PUNCT
ejpam-5385	182	30	)	)	PUNCT
ejpam-5385	182	31	:	:	PUNCT
ejpam-5385	182	32	m	m	PROPN
ejpam-5385	182	33	∈	∈	PROPN
ejpam-5385	182	34	m1	m1	NOUN
ejpam-5385	182	35	}	}	PUNCT
ejpam-5385	182	36	constitutes	constitute	VERB
ejpam-5385	182	37	an	an	DET
ejpam-5385	182	38	intuitionistic	intuitionistic	ADJ
ejpam-5385	182	39	fuzzy	fuzzy	ADJ
ejpam-5385	182	40	lie	lie	NOUN
ejpam-5385	182	41	subalgebra	subalgebra	NOUN
ejpam-5385	182	42	.	.	PUNCT
ejpam-5385	183	1	according	accord	VERB
ejpam-5385	183	2	to	to	ADP
ejpam-5385	183	3	lemma	lemma	PROPN
ejpam-5385	183	4	1	1	NUM
ejpam-5385	183	5	,	,	PUNCT
ejpam-5385	183	6	when	when	SCONJ
ejpam-5385	183	7	considering	consider	VERB
ejpam-5385	183	8	the	the	DET
ejpam-5385	183	9	transformation	transformation	NOUN
ejpam-5385	183	10	of	of	ADP
ejpam-5385	183	11	an	an	DET
ejpam-5385	183	12	intuitionistic	intuitionistic	ADJ
ejpam-5385	183	13	fuzzy	fuzzy	ADJ
ejpam-5385	183	14	lie	lie	NOUN
ejpam-5385	183	15	subalgebra	subalgebra	NOUN
ejpam-5385	183	16	,	,	PUNCT
ejpam-5385	183	17	it	it	PRON
ejpam-5385	183	18	maintains	maintain	VERB
ejpam-5385	183	19	its	its	PRON
ejpam-5385	183	20	nature	nature	NOUN
ejpam-5385	183	21	as	as	ADP
ejpam-5385	183	22	an	an	DET
ejpam-5385	183	23	intuitionistic	intuitionistic	ADJ
ejpam-5385	183	24	fuzzy	fuzzy	ADJ
ejpam-5385	183	25	lie	lie	NOUN
ejpam-5385	183	26	subalgebra	subalgebra	NOUN
ejpam-5385	183	27	.	.	PUNCT
ejpam-5385	184	1	consequently	consequently	ADV
ejpam-5385	184	2	,	,	PUNCT
ejpam-5385	184	3	the	the	DET
ejpam-5385	184	4	transformed	transform	VERB
ejpam-5385	184	5	set	set	VERB
ejpam-5385	184	6	f(e	f(e	NOUN
ejpam-5385	184	7	)	)	PUNCT
ejpam-5385	184	8	=	=	PRON
ejpam-5385	184	9	{	{	PUNCT
ejpam-5385	184	10	(	(	PUNCT
ejpam-5385	184	11	n	n	CCONJ
ejpam-5385	184	12	,	,	PUNCT
ejpam-5385	184	13	ρef(e	ρef(e	NOUN
ejpam-5385	184	14	)	)	PUNCT
ejpam-5385	184	15	(	(	PUNCT
ejpam-5385	184	16	n	n	CCONJ
ejpam-5385	184	17	)	)	PUNCT
ejpam-5385	184	18	,	,	PUNCT
ejpam-5385	184	19	ρ̂ef(e	ρ̂ef(e	NUM
ejpam-5385	184	20	)	)	PUNCT
ejpam-5385	184	21	(	(	PUNCT
ejpam-5385	184	22	n	n	CCONJ
ejpam-5385	184	23	)	)	PUNCT
ejpam-5385	184	24	)	)	PUNCT
ejpam-5385	184	25	:	:	PUNCT
ejpam-5385	184	26	n	n	X
ejpam-5385	184	27	∈	∈	PROPN
ejpam-5385	184	28	im(f	im(f	NOUN
ejpam-5385	184	29	)	)	PUNCT
ejpam-5385	184	30	}	}	PUNCT
ejpam-5385	184	31	represents	represent	VERB
ejpam-5385	184	32	an	an	DET
ejpam-5385	184	33	intuitionistic	intuitionistic	ADJ
ejpam-5385	184	34	fuzzy	fuzzy	ADJ
ejpam-5385	184	35	lie	lie	NOUN
ejpam-5385	184	36	subalgebra	subalgebra	NOUN
ejpam-5385	184	37	within	within	ADP
ejpam-5385	184	38	the	the	DET
ejpam-5385	184	39	domain	domain	NOUN
ejpam-5385	184	40	of	of	ADP
ejpam-5385	184	41	im(f	im(f	NOUN
ejpam-5385	184	42	)	)	PUNCT
ejpam-5385	184	43	.	.	PUNCT
ejpam-5385	185	1	for	for	ADP
ejpam-5385	185	2	any	any	DET
ejpam-5385	185	3	elements	element	NOUN
ejpam-5385	185	4	n1	n1	NOUN
ejpam-5385	185	5	and	and	CCONJ
ejpam-5385	185	6	n2	n2	NOUN
ejpam-5385	185	7	belonging	belong	VERB
ejpam-5385	185	8	to	to	ADP
ejpam-5385	185	9	im(f	im(f	NOUN
ejpam-5385	185	10	)	)	PUNCT
ejpam-5385	185	11	,	,	PUNCT
ejpam-5385	185	12	as	as	ADV
ejpam-5385	185	13	well	well	ADV
ejpam-5385	185	14	as	as	ADP
ejpam-5385	185	15	for	for	ADP
ejpam-5385	185	16	scalar	scalar	ADJ
ejpam-5385	185	17	k	k	PROPN
ejpam-5385	185	18	∈	∈	PROPN
ejpam-5385	185	19	k	k	NOUN
ejpam-5385	185	20	,	,	PUNCT
ejpam-5385	185	21	we	we	PRON
ejpam-5385	185	22	can	can	AUX
ejpam-5385	185	23	ascertain	ascertain	VERB
ejpam-5385	185	24	the	the	DET
ejpam-5385	185	25	following	follow	VERB
ejpam-5385	185	26	assertions	assertion	NOUN
ejpam-5385	185	27	concerning	concern	VERB
ejpam-5385	185	28	ef(e	ef(e	VERB
ejpam-5385	185	29	):	):	PUNCT
ejpam-5385	185	30	(	(	PUNCT
ejpam-5385	185	31	i	i	NOUN
ejpam-5385	185	32	)	)	PUNCT
ejpam-5385	185	33	ρef(e	ρef(e	PROPN
ejpam-5385	185	34	)	)	PUNCT
ejpam-5385	185	35	(	(	PUNCT
ejpam-5385	185	36	n1	n1	PROPN
ejpam-5385	185	37	+	+	NOUN
ejpam-5385	185	38	n2	n2	ADJ
ejpam-5385	185	39	)	)	PUNCT
ejpam-5385	185	40	≥	≥	NOUN
ejpam-5385	185	41	ρef(e	ρef(e	NOUN
ejpam-5385	185	42	)	)	PUNCT
ejpam-5385	185	43	(	(	PUNCT
ejpam-5385	185	44	n1)∧	n1)∧	INTJ
ejpam-5385	185	45	ρef(e	ρef(e	NOUN
ejpam-5385	185	46	)	)	PUNCT
ejpam-5385	185	47	(	(	PUNCT
ejpam-5385	185	48	n2	n2	NOUN
ejpam-5385	185	49	)	)	PUNCT
ejpam-5385	185	50	and	and	CCONJ
ejpam-5385	185	51	ρ̂ef(e	ρ̂ef(e	NUM
ejpam-5385	185	52	)	)	PUNCT
ejpam-5385	185	53	(	(	PUNCT
ejpam-5385	185	54	n1	n1	PROPN
ejpam-5385	185	55	+	+	NOUN
ejpam-5385	185	56	n2	n2	ADJ
ejpam-5385	185	57	)	)	PUNCT
ejpam-5385	185	58	≤	≤	NOUN
ejpam-5385	185	59	ρ̂ef(e	ρ̂ef(e	NUM
ejpam-5385	185	60	)	)	PUNCT
ejpam-5385	185	61	(	(	PUNCT
ejpam-5385	185	62	n1)∨	n1)∨	PROPN
ejpam-5385	185	63	ρ̂ef(e	ρ̂ef(e	NUM
ejpam-5385	185	64	)	)	PUNCT
ejpam-5385	185	65	(	(	PUNCT
ejpam-5385	185	66	n2	n2	NOUN
ejpam-5385	185	67	)	)	PUNCT
ejpam-5385	185	68	,	,	PUNCT
ejpam-5385	185	69	(	(	PUNCT
ejpam-5385	185	70	ii	ii	NOUN
ejpam-5385	185	71	)	)	PUNCT
ejpam-5385	185	72	ρef(e	ρef(e	PROPN
ejpam-5385	185	73	)	)	PUNCT
ejpam-5385	185	74	(	(	PUNCT
ejpam-5385	185	75	kn1	kn1	NOUN
ejpam-5385	185	76	)	)	PUNCT
ejpam-5385	185	77	≥	≥	NOUN
ejpam-5385	185	78	ρef(e	ρef(e	NOUN
ejpam-5385	185	79	)	)	PUNCT
ejpam-5385	185	80	(	(	PUNCT
ejpam-5385	185	81	n1	n1	NOUN
ejpam-5385	185	82	)	)	PUNCT
ejpam-5385	185	83	and	and	CCONJ
ejpam-5385	185	84	ρ̂ef(e	ρ̂ef(e	NUM
ejpam-5385	185	85	)	)	PUNCT
ejpam-5385	185	86	(	(	PUNCT
ejpam-5385	185	87	kn1	kn1	NOUN
ejpam-5385	185	88	)	)	PUNCT
ejpam-5385	185	89	≤	≤	NOUN
ejpam-5385	185	90	ρ̂ef(e	ρ̂ef(e	NUM
ejpam-5385	185	91	)	)	PUNCT
ejpam-5385	185	92	(	(	PUNCT
ejpam-5385	185	93	n1	n1	NOUN
ejpam-5385	185	94	)	)	PUNCT
ejpam-5385	185	95	,	,	PUNCT
ejpam-5385	185	96	(	(	PUNCT
ejpam-5385	185	97	iii	iii	X
ejpam-5385	185	98	)	)	PUNCT
ejpam-5385	185	99	ρef(e	ρef(e	NOUN
ejpam-5385	185	100	)	)	PUNCT
ejpam-5385	185	101	(	(	PUNCT
ejpam-5385	185	102	[	[	X
ejpam-5385	185	103	n1	n1	NOUN
ejpam-5385	185	104	,	,	PUNCT
ejpam-5385	185	105	n2	n2	NOUN
ejpam-5385	185	106	]	]	PUNCT
ejpam-5385	185	107	)	)	PUNCT
ejpam-5385	185	108	≥	≥	PROPN
ejpam-5385	185	109	ρef(e	ρef(e	NOUN
ejpam-5385	185	110	)	)	PUNCT
ejpam-5385	185	111	(	(	PUNCT
ejpam-5385	185	112	n1)∧ρef(e	n1)∧ρef(e	ADJ
ejpam-5385	185	113	)	)	PUNCT
ejpam-5385	185	114	(	(	PUNCT
ejpam-5385	185	115	n2	n2	NOUN
ejpam-5385	185	116	)	)	PUNCT
ejpam-5385	185	117	and	and	CCONJ
ejpam-5385	185	118	ρ̂ef(e	ρ̂ef(e	NUM
ejpam-5385	185	119	)	)	PUNCT
ejpam-5385	185	120	(	(	PUNCT
ejpam-5385	185	121	[	[	X
ejpam-5385	185	122	n1	n1	NOUN
ejpam-5385	185	123	,	,	PUNCT
ejpam-5385	185	124	n2	n2	NOUN
ejpam-5385	185	125	]	]	PUNCT
ejpam-5385	185	126	)	)	PUNCT
ejpam-5385	185	127	≤	≤	NOUN
ejpam-5385	185	128	ρ̂ef(e	ρ̂ef(e	NUM
ejpam-5385	185	129	)	)	PUNCT
ejpam-5385	185	130	(	(	PUNCT
ejpam-5385	185	131	n1)∨	n1)∨	PROPN
ejpam-5385	185	132	ρ̂ef(e	ρ̂ef(e	NUM
ejpam-5385	185	133	)	)	PUNCT
ejpam-5385	185	134	(	(	PUNCT
ejpam-5385	185	135	n2	n2	ADJ
ejpam-5385	185	136	)	)	PUNCT
ejpam-5385	185	137	.	.	PUNCT
ejpam-5385	186	1	given	give	VERB
ejpam-5385	186	2	that	that	DET
ejpam-5385	186	3	f(e	f(e	NOUN
ejpam-5385	186	4	)	)	PUNCT
ejpam-5385	186	5	is	be	AUX
ejpam-5385	186	6	endowed	endow	VERB
ejpam-5385	186	7	with	with	ADP
ejpam-5385	186	8	homogeneity	homogeneity	NOUN
ejpam-5385	186	9	,	,	PUNCT
ejpam-5385	186	10	we	we	PRON
ejpam-5385	186	11	can	can	AUX
ejpam-5385	186	12	thereby	thereby	ADV
ejpam-5385	186	13	conclude	conclude	VERB
ejpam-5385	186	14	that	that	DET
ejpam-5385	186	15	f(e	f(e	NOUN
ejpam-5385	186	16	)	)	PUNCT
ejpam-5385	186	17	qualifies	qualify	VERB
ejpam-5385	186	18	as	as	ADP
ejpam-5385	186	19	a	a	DET
ejpam-5385	186	20	complex	complex	ADJ
ejpam-5385	186	21	intuitionistic	intuitionistic	ADJ
ejpam-5385	186	22	fuzzy	fuzzy	ADJ
ejpam-5385	186	23	lie	lie	NOUN
ejpam-5385	186	24	subalgebra	subalgebra	NOUN
ejpam-5385	186	25	situated	situate	VERB
ejpam-5385	186	26	within	within	ADP
ejpam-5385	186	27	the	the	DET
ejpam-5385	186	28	realm	realm	NOUN
ejpam-5385	186	29	of	of	ADP
ejpam-5385	186	30	im(f	im(f	NOUN
ejpam-5385	186	31	)	)	PUNCT
ejpam-5385	186	32	.	.	PUNCT
ejpam-5385	187	1	here	here	ADV
ejpam-5385	187	2	,	,	PUNCT
ejpam-5385	187	3	we	we	PRON
ejpam-5385	187	4	present	present	VERB
ejpam-5385	187	5	the	the	DET
ejpam-5385	187	6	proof	proof	NOUN
ejpam-5385	187	7	of	of	ADP
ejpam-5385	187	8	the	the	DET
ejpam-5385	187	9	subsequent	subsequent	ADJ
ejpam-5385	187	10	outcome	outcome	NOUN
ejpam-5385	187	11	,	,	PUNCT
ejpam-5385	187	12	originally	originally	ADV
ejpam-5385	187	13	established	establish	VERB
ejpam-5385	187	14	in	in	ADP
ejpam-5385	187	15	[	[	X
ejpam-5385	187	16	8	8	NUM
ejpam-5385	187	17	]	]	PUNCT
ejpam-5385	187	18	for	for	ADP
ejpam-5385	187	19	lie	lie	NOUN
ejpam-5385	187	20	superalgebras	superalgebra	NOUN
ejpam-5385	187	21	,	,	PUNCT
ejpam-5385	187	22	adapted	adapt	VERB
ejpam-5385	187	23	to	to	ADP
ejpam-5385	187	24	the	the	DET
ejpam-5385	187	25	context	context	NOUN
ejpam-5385	187	26	of	of	ADP
ejpam-5385	187	27	lie	lie	NOUN
ejpam-5385	187	28	algebra	algebra	NOUN
ejpam-5385	187	29	homomorphisms	homomorphism	NOUN
ejpam-5385	187	30	.	.	PUNCT
ejpam-5385	188	1	this	this	DET
ejpam-5385	188	2	outcome	outcome	NOUN
ejpam-5385	188	3	demonstrates	demonstrate	VERB
ejpam-5385	188	4	that	that	SCONJ
ejpam-5385	188	5	the	the	DET
ejpam-5385	188	6	transformation	transformation	NOUN
ejpam-5385	188	7	of	of	ADP
ejpam-5385	188	8	an	an	DET
ejpam-5385	188	9	intuitionistic	intuitionistic	ADJ
ejpam-5385	188	10	fuzzy	fuzzy	ADJ
ejpam-5385	188	11	lie	lie	NOUN
ejpam-5385	188	12	ideal	ideal	ADJ
ejpam-5385	188	13	through	through	ADP
ejpam-5385	188	14	a	a	DET
ejpam-5385	188	15	lie	lie	NOUN
ejpam-5385	188	16	algebra	algebra	NOUN
ejpam-5385	188	17	homomorphism	homomorphism	NOUN
ejpam-5385	188	18	maintains	maintain	VERB
ejpam-5385	188	19	its	its	PRON
ejpam-5385	188	20	nature	nature	NOUN
ejpam-5385	188	21	as	as	ADP
ejpam-5385	188	22	an	an	DET
ejpam-5385	188	23	intuitionistic	intuitionistic	ADJ
ejpam-5385	188	24	fuzzy	fuzzy	ADJ
ejpam-5385	188	25	lie	lie	NOUN
ejpam-5385	188	26	ideal	ideal	NOUN
ejpam-5385	188	27	as	as	ADV
ejpam-5385	188	28	well	well	ADV
ejpam-5385	188	29	.	.	PUNCT
ejpam-5385	189	1	corollary	corollary	ADJ
ejpam-5385	189	2	2	2	NUM
ejpam-5385	189	3	.	.	PUNCT
ejpam-5385	189	4	consider	consider	VERB
ejpam-5385	189	5	a	a	DET
ejpam-5385	189	6	lie	lie	NOUN
ejpam-5385	189	7	algebra	algebra	NOUN
ejpam-5385	189	8	homomorphism	homomorphism	PROPN
ejpam-5385	189	9	f	f	X
ejpam-5385	189	10	:	:	PUNCT
ejpam-5385	189	11	m1	m1	PROPN
ejpam-5385	189	12	→	→	SYM
ejpam-5385	189	13	m2	m2	PROPN
ejpam-5385	189	14	.	.	PUNCT
ejpam-5385	190	1	if	if	SCONJ
ejpam-5385	190	2	e	e	X
ejpam-5385	190	3	=	=	SYM
ejpam-5385	190	4	(	(	PUNCT
ejpam-5385	190	5	ϕe	ϕe	INTJ
ejpam-5385	190	6	,	,	PUNCT
ejpam-5385	190	7	ψe	ψe	NOUN
ejpam-5385	190	8	)	)	PUNCT
ejpam-5385	190	9	constitutes	constitute	VERB
ejpam-5385	190	10	an	an	DET
ejpam-5385	190	11	intuitionistic	intuitionistic	ADJ
ejpam-5385	190	12	fuzzy	fuzzy	ADJ
ejpam-5385	190	13	lie	lie	NOUN
ejpam-5385	190	14	ideal	ideal	NOUN
ejpam-5385	190	15	within	within	ADP
ejpam-5385	190	16	m1	m1	PROPN
ejpam-5385	190	17	,	,	PUNCT
ejpam-5385	190	18	then	then	ADV
ejpam-5385	190	19	the	the	DET
ejpam-5385	190	20	intuitionistic	intuitionistic	ADJ
ejpam-5385	190	21	fuzzy	fuzzy	ADJ
ejpam-5385	190	22	set	set	VERB
ejpam-5385	190	23	f(e	f(e	NOUN
ejpam-5385	190	24	)	)	PUNCT
ejpam-5385	190	25	preserves	preserve	VERB
ejpam-5385	190	26	its	its	PRON
ejpam-5385	190	27	character	character	NOUN
ejpam-5385	190	28	as	as	ADP
ejpam-5385	190	29	an	an	DET
ejpam-5385	190	30	intuitionistic	intuitionistic	ADJ
ejpam-5385	190	31	fuzzy	fuzzy	ADJ
ejpam-5385	190	32	lie	lie	NOUN
ejpam-5385	190	33	ideal	ideal	NOUN
ejpam-5385	190	34	even	even	ADV
ejpam-5385	190	35	within	within	ADP
ejpam-5385	190	36	the	the	DET
ejpam-5385	190	37	domain	domain	NOUN
ejpam-5385	190	38	im(f	im(f	NOUN
ejpam-5385	190	39	)	)	PUNCT
ejpam-5385	190	40	.	.	PUNCT
ejpam-5385	191	1	s.	s.	PROPN
ejpam-5385	191	2	shaqaqha	shaqaqha	PROPN
ejpam-5385	191	3	,	,	PUNCT
ejpam-5385	191	4	m.	m.	PROPN
ejpam-5385	191	5	y.	y.	PROPN
ejpam-5385	191	6	al	al	PROPN
ejpam-5385	191	7	-	-	PUNCT
ejpam-5385	191	8	deiakeh	deiakeh	PROPN
ejpam-5385	191	9	/	/	SYM
ejpam-5385	191	10	eur	eur	NOUN
ejpam-5385	191	11	.	.	PUNCT
ejpam-5385	192	1	j.	j.	PROPN
ejpam-5385	192	2	pure	pure	PROPN
ejpam-5385	192	3	appl	appl	PROPN
ejpam-5385	192	4	.	.	PROPN
ejpam-5385	192	5	math	math	PROPN
ejpam-5385	192	6	,	,	PUNCT
ejpam-5385	192	7	17	17	NUM
ejpam-5385	192	8	(	(	PUNCT
ejpam-5385	192	9	4	4	NUM
ejpam-5385	192	10	)	)	PUNCT
ejpam-5385	192	11	(	(	PUNCT
ejpam-5385	192	12	2024	2024	NUM
ejpam-5385	192	13	)	)	PUNCT
ejpam-5385	192	14	,	,	PUNCT
ejpam-5385	192	15	3291	3291	NUM
ejpam-5385	192	16	-	-	SYM
ejpam-5385	192	17	3303	3303	NUM
ejpam-5385	192	18	3299	3299	NUM
ejpam-5385	192	19	proof	proof	NOUN
ejpam-5385	192	20	.	.	PUNCT
ejpam-5385	193	1	it	it	PRON
ejpam-5385	193	2	suffices	suffice	VERB
ejpam-5385	193	3	to	to	PART
ejpam-5385	193	4	demonstrate	demonstrate	VERB
ejpam-5385	193	5	that	that	SCONJ
ejpam-5385	193	6	for	for	ADP
ejpam-5385	193	7	any	any	DET
ejpam-5385	193	8	n1	n1	NOUN
ejpam-5385	193	9	and	and	CCONJ
ejpam-5385	193	10	n2	n2	ADJ
ejpam-5385	193	11	in	in	ADP
ejpam-5385	193	12	im(f	im(f	PROPN
ejpam-5385	193	13	)	)	PUNCT
ejpam-5385	193	14	,	,	PUNCT
ejpam-5385	193	15	the	the	DET
ejpam-5385	193	16	conditions	condition	NOUN
ejpam-5385	193	17	ϕf(e)([n1	ϕf(e)([n1	PROPN
ejpam-5385	193	18	,	,	PUNCT
ejpam-5385	193	19	n2	n2	NOUN
ejpam-5385	193	20	]	]	PUNCT
ejpam-5385	193	21	)	)	PUNCT
ejpam-5385	193	22	≥	≥	NOUN
ejpam-5385	193	23	ϕf(e)(n1	ϕf(e)(n1	NUM
ejpam-5385	193	24	)	)	PUNCT
ejpam-5385	193	25	∨	∨	NUM
ejpam-5385	193	26	ϕf(e)(n2	ϕf(e)(n2	NUM
ejpam-5385	193	27	)	)	PUNCT
ejpam-5385	193	28	and	and	CCONJ
ejpam-5385	193	29	ψf(e)([n1	ψf(e)([n1	NOUN
ejpam-5385	193	30	,	,	PUNCT
ejpam-5385	193	31	n2	n2	ADJ
ejpam-5385	193	32	]	]	PUNCT
ejpam-5385	193	33	)	)	PUNCT
ejpam-5385	193	34	≤	≤	NOUN
ejpam-5385	193	35	ψf(e)(n1	ψf(e)(n1	NOUN
ejpam-5385	193	36	)	)	PUNCT
ejpam-5385	193	37	∧	∧	NOUN
ejpam-5385	193	38	ψf(e)(n2	ψf(e)(n2	NOUN
ejpam-5385	193	39	)	)	PUNCT
ejpam-5385	193	40	hold	hold	NOUN
ejpam-5385	193	41	.	.	PUNCT
ejpam-5385	194	1	let	let	VERB
ejpam-5385	194	2	n1	n1	NOUN
ejpam-5385	194	3	and	and	CCONJ
ejpam-5385	194	4	n2	n2	ADJ
ejpam-5385	194	5	be	be	AUX
ejpam-5385	194	6	elements	element	NOUN
ejpam-5385	194	7	of	of	ADP
ejpam-5385	194	8	im(f	im(f	NOUN
ejpam-5385	194	9	)	)	PUNCT
ejpam-5385	194	10	.	.	PUNCT
ejpam-5385	195	1	suppose	suppose	VERB
ejpam-5385	195	2	,	,	PUNCT
ejpam-5385	195	3	for	for	ADP
ejpam-5385	195	4	the	the	DET
ejpam-5385	195	5	sake	sake	NOUN
ejpam-5385	195	6	of	of	ADP
ejpam-5385	195	7	contradiction	contradiction	NOUN
ejpam-5385	195	8	,	,	PUNCT
ejpam-5385	195	9	that	that	SCONJ
ejpam-5385	195	10	ϕψ(e)([n1	ϕψ(e)([n1	NOUN
ejpam-5385	195	11	,	,	PUNCT
ejpam-5385	195	12	n2	n2	NOUN
ejpam-5385	195	13	]	]	PUNCT
ejpam-5385	195	14	)	)	PUNCT
ejpam-5385	195	15	<	<	X
ejpam-5385	195	16	ϕf(e)(n1)∨ϕf(e)(n2	ϕf(e)(n1)∨ϕf(e)(n2	NOUN
ejpam-5385	195	17	)	)	PUNCT
ejpam-5385	195	18	.	.	PUNCT
ejpam-5385	196	1	let	let	VERB
ejpam-5385	196	2	t	t	PROPN
ejpam-5385	196	3	be	be	AUX
ejpam-5385	196	4	chosen	choose	VERB
ejpam-5385	196	5	from	from	ADP
ejpam-5385	196	6	the	the	DET
ejpam-5385	196	7	interval	interval	NOUN
ejpam-5385	196	8	[	[	X
ejpam-5385	196	9	0	0	NUM
ejpam-5385	196	10	,	,	PUNCT
ejpam-5385	196	11	1	1	NUM
ejpam-5385	196	12	]	]	PUNCT
ejpam-5385	196	13	such	such	ADJ
ejpam-5385	196	14	that	that	DET
ejpam-5385	196	15	ϕf(e)([n1	ϕf(e)([n1	PROPN
ejpam-5385	196	16	,	,	PUNCT
ejpam-5385	196	17	n2	n2	NOUN
ejpam-5385	196	18	]	]	PUNCT
ejpam-5385	196	19	)	)	PUNCT
ejpam-5385	196	20	<	<	X
ejpam-5385	196	21	t	t	X
ejpam-5385	196	22	<	<	X
ejpam-5385	196	23	ϕf(e)(n1	ϕf(e)(n1	NUM
ejpam-5385	196	24	)	)	PUNCT
ejpam-5385	196	25	∨	∨	NOUN
ejpam-5385	196	26	ϕf(e)(n2	ϕf(e)(n2	NUM
ejpam-5385	196	27	)	)	PUNCT
ejpam-5385	196	28	.	.	PUNCT
ejpam-5385	197	1	without	without	ADP
ejpam-5385	197	2	any	any	DET
ejpam-5385	197	3	loss	loss	NOUN
ejpam-5385	197	4	of	of	ADP
ejpam-5385	197	5	generality	generality	NOUN
ejpam-5385	197	6	,	,	PUNCT
ejpam-5385	197	7	we	we	PRON
ejpam-5385	197	8	can	can	AUX
ejpam-5385	197	9	assume	assume	VERB
ejpam-5385	197	10	ϕf(e)(n1	ϕf(e)(n1	NUM
ejpam-5385	197	11	)	)	PUNCT
ejpam-5385	197	12	≥	≥	NOUN
ejpam-5385	197	13	ϕf(e)(n2	ϕf(e)(n2	NUM
ejpam-5385	197	14	)	)	PUNCT
ejpam-5385	197	15	.	.	PUNCT
ejpam-5385	198	1	consequently	consequently	ADV
ejpam-5385	198	2	,	,	PUNCT
ejpam-5385	198	3	it	it	PRON
ejpam-5385	198	4	follows	follow	VERB
ejpam-5385	198	5	that	that	SCONJ
ejpam-5385	198	6	ϕf(e)([n1	ϕf(e)([n1	PROPN
ejpam-5385	198	7	,	,	PUNCT
ejpam-5385	198	8	n2	n2	NOUN
ejpam-5385	198	9	]	]	PUNCT
ejpam-5385	198	10	)	)	PUNCT
ejpam-5385	198	11	<	<	X
ejpam-5385	198	12	t	t	X
ejpam-5385	198	13	<	<	X
ejpam-5385	198	14	supn1	supn1	X
ejpam-5385	198	15	=	=	NOUN
ejpam-5385	198	16	f(m){ϕe(m	f(m){ϕe(m	NOUN
ejpam-5385	198	17	)	)	PUNCT
ejpam-5385	198	18	}	}	PUNCT
ejpam-5385	198	19	.	.	PUNCT
ejpam-5385	199	1	hence	hence	ADV
ejpam-5385	199	2	,	,	PUNCT
ejpam-5385	199	3	there	there	PRON
ejpam-5385	199	4	exists	exist	VERB
ejpam-5385	199	5	an	an	DET
ejpam-5385	199	6	q	q	NOUN
ejpam-5385	199	7	within	within	ADP
ejpam-5385	199	8	m1	m1	PROPN
ejpam-5385	199	9	such	such	ADJ
ejpam-5385	199	10	that	that	DET
ejpam-5385	199	11	f(q	f(q	NOUN
ejpam-5385	199	12	)	)	PUNCT
ejpam-5385	200	1	=	=	SYM
ejpam-5385	200	2	n1	n1	PROPN
ejpam-5385	200	3	and	and	CCONJ
ejpam-5385	200	4	ϕf(e)([n1	ϕf(e)([n1	PROPN
ejpam-5385	200	5	,	,	PUNCT
ejpam-5385	200	6	n2	n2	NOUN
ejpam-5385	200	7	]	]	PUNCT
ejpam-5385	200	8	)	)	PUNCT
ejpam-5385	200	9	<	<	X
ejpam-5385	200	10	t	t	X
ejpam-5385	200	11	<	<	X
ejpam-5385	200	12	ϕe(q	ϕe(q	NUM
ejpam-5385	200	13	)	)	PUNCT
ejpam-5385	200	14	.	.	PUNCT
ejpam-5385	201	1	for	for	ADP
ejpam-5385	201	2	any	any	DET
ejpam-5385	201	3	s	s	NOUN
ejpam-5385	201	4	in	in	ADP
ejpam-5385	201	5	m1	m1	NOUN
ejpam-5385	201	6	with	with	ADP
ejpam-5385	201	7	f(s	f(	NOUN
ejpam-5385	201	8	)	)	PUNCT
ejpam-5385	201	9	=	=	SYM
ejpam-5385	201	10	n2	n2	NOUN
ejpam-5385	201	11	,	,	PUNCT
ejpam-5385	201	12	it	it	PRON
ejpam-5385	201	13	holds	hold	VERB
ejpam-5385	201	14	that	that	DET
ejpam-5385	201	15	f([q	f([q	NOUN
ejpam-5385	201	16	,	,	PUNCT
ejpam-5385	201	17	s	s	NOUN
ejpam-5385	201	18	]	]	X
ejpam-5385	201	19	)	)	PUNCT
ejpam-5385	201	20	=	=	PUNCT
ejpam-5385	202	1	[	[	X
ejpam-5385	202	2	f(q	f(q	NOUN
ejpam-5385	202	3	)	)	PUNCT
ejpam-5385	202	4	,	,	PUNCT
ejpam-5385	202	5	f(s	f(s	ADV
ejpam-5385	202	6	)	)	PUNCT
ejpam-5385	202	7	]	]	PUNCT
ejpam-5385	203	1	=	=	PUNCT
ejpam-5385	204	1	[	[	X
ejpam-5385	204	2	n1	n1	NOUN
ejpam-5385	204	3	,	,	PUNCT
ejpam-5385	204	4	n2	n2	NOUN
ejpam-5385	204	5	]	]	PUNCT
ejpam-5385	204	6	.	.	PUNCT
ejpam-5385	205	1	as	as	ADP
ejpam-5385	205	2	a	a	DET
ejpam-5385	205	3	result	result	NOUN
ejpam-5385	205	4	,	,	PUNCT
ejpam-5385	205	5	we	we	PRON
ejpam-5385	205	6	find	find	VERB
ejpam-5385	205	7	that	that	SCONJ
ejpam-5385	205	8	ϕf(e)([n1	ϕf(e)([n1	PROPN
ejpam-5385	205	9	,	,	PUNCT
ejpam-5385	205	10	n2	n2	NOUN
ejpam-5385	205	11	]	]	X
ejpam-5385	205	12	)	)	PUNCT
ejpam-5385	205	13	=	=	SYM
ejpam-5385	206	1	sup	sup	NUM
ejpam-5385	207	1	[	[	X
ejpam-5385	207	2	n1	n1	NOUN
ejpam-5385	207	3	,	,	PUNCT
ejpam-5385	207	4	n2]=f([m1	n2]=f([m1	PROPN
ejpam-5385	207	5	,	,	PUNCT
ejpam-5385	207	6	m2	m2	PROPN
ejpam-5385	207	7	]	]	SYM
ejpam-5385	207	8	)	)	PUNCT
ejpam-5385	208	1	ϕe([m1	ϕe([m1	NOUN
ejpam-5385	208	2	,	,	PUNCT
ejpam-5385	208	3	m2	m2	PROPN
ejpam-5385	208	4	]	]	X
ejpam-5385	208	5	)	)	PUNCT
ejpam-5385	208	6	≥	≥	NOUN
ejpam-5385	209	1	ϕe([q	ϕe([q	PROPN
ejpam-5385	209	2	,	,	PUNCT
ejpam-5385	209	3	s	s	PROPN
ejpam-5385	209	4	]	]	X
ejpam-5385	209	5	)	)	PUNCT
ejpam-5385	209	6	≥	≥	NOUN
ejpam-5385	209	7	ϕe(q	ϕe(q	NUM
ejpam-5385	209	8	)	)	PUNCT
ejpam-5385	209	9	∨	∨	NUM
ejpam-5385	209	10	ϕe(s	ϕe(s	NUM
ejpam-5385	209	11	)	)	PUNCT
ejpam-5385	210	1	>	>	X
ejpam-5385	210	2	t	t	X
ejpam-5385	210	3	>	>	X
ejpam-5385	210	4	ϕf(e)([n1	ϕf(e)([n1	PROPN
ejpam-5385	210	5	,	,	PUNCT
ejpam-5385	210	6	n2	n2	NOUN
ejpam-5385	210	7	]	]	X
ejpam-5385	210	8	)	)	PUNCT
ejpam-5385	210	9	,	,	PUNCT
ejpam-5385	210	10	leading	lead	VERB
ejpam-5385	210	11	to	to	ADP
ejpam-5385	210	12	a	a	DET
ejpam-5385	210	13	contradiction	contradiction	NOUN
ejpam-5385	210	14	.	.	PUNCT
ejpam-5385	211	1	additionally	additionally	ADV
ejpam-5385	211	2	,	,	PUNCT
ejpam-5385	211	3	if	if	SCONJ
ejpam-5385	211	4	ψf(e)([n1	ψf(e)([n1	NOUN
ejpam-5385	211	5	,	,	PUNCT
ejpam-5385	211	6	n2	n2	ADJ
ejpam-5385	211	7	]	]	X
ejpam-5385	211	8	)	)	PUNCT
ejpam-5385	211	9	>	>	X
ejpam-5385	211	10	ψf(e)(n1)∧ψf(e)(n2	ψf(e)(n1)∧ψf(e)(n2	NOUN
ejpam-5385	211	11	)	)	PUNCT
ejpam-5385	211	12	,	,	PUNCT
ejpam-5385	211	13	then	then	ADV
ejpam-5385	211	14	a	a	DET
ejpam-5385	211	15	value	value	NOUN
ejpam-5385	211	16	r	r	NOUN
ejpam-5385	211	17	within	within	ADP
ejpam-5385	211	18	the	the	DET
ejpam-5385	211	19	interval	interval	NOUN
ejpam-5385	212	1	[	[	X
ejpam-5385	212	2	0	0	NUM
ejpam-5385	212	3	,	,	PUNCT
ejpam-5385	212	4	1	1	NUM
ejpam-5385	212	5	]	]	PUNCT
ejpam-5385	212	6	can	can	AUX
ejpam-5385	212	7	be	be	AUX
ejpam-5385	212	8	selected	select	VERB
ejpam-5385	212	9	such	such	ADJ
ejpam-5385	212	10	that	that	DET
ejpam-5385	212	11	ψf(e)([n1	ψf(e)([n1	NOUN
ejpam-5385	212	12	,	,	PUNCT
ejpam-5385	212	13	n2	n2	NOUN
ejpam-5385	212	14	]	]	PUNCT
ejpam-5385	212	15	)	)	PUNCT
ejpam-5385	212	16	>	>	PUNCT
ejpam-5385	213	1	r	r	X
ejpam-5385	213	2	>	>	SYM
ejpam-5385	213	3	ψf(e)(n1	ψf(e)(n1	PROPN
ejpam-5385	213	4	)	)	PUNCT
ejpam-5385	213	5	∧	∧	NOUN
ejpam-5385	213	6	ψf(e)(n2	ψf(e)(n2	NOUN
ejpam-5385	213	7	)	)	PUNCT
ejpam-5385	213	8	.	.	PUNCT
ejpam-5385	214	1	without	without	ADP
ejpam-5385	214	2	loss	loss	NOUN
ejpam-5385	214	3	of	of	ADP
ejpam-5385	214	4	generality	generality	NOUN
ejpam-5385	214	5	,	,	PUNCT
ejpam-5385	214	6	let	let	VERB
ejpam-5385	214	7	’s	’s	PRON
ejpam-5385	214	8	assume	assume	VERB
ejpam-5385	214	9	ψf(e)(n1	ψf(e)(n1	NOUN
ejpam-5385	214	10	)	)	PUNCT
ejpam-5385	214	11	≤	≤	NOUN
ejpam-5385	214	12	ψf(e)(n2	ψf(e)(n2	PUNCT
ejpam-5385	214	13	)	)	PUNCT
ejpam-5385	214	14	.	.	PUNCT
ejpam-5385	215	1	this	this	PRON
ejpam-5385	215	2	leads	lead	VERB
ejpam-5385	215	3	to	to	ADP
ejpam-5385	215	4	ψf(e)([n1	ψf(e)([n1	NOUN
ejpam-5385	215	5	,	,	PUNCT
ejpam-5385	215	6	n2	n2	ADJ
ejpam-5385	215	7	]	]	PUNCT
ejpam-5385	215	8	)	)	PUNCT
ejpam-5385	215	9	>	>	PUNCT
ejpam-5385	216	1	r	r	X
ejpam-5385	216	2	>	>	X
ejpam-5385	216	3	infn1	infn1	PROPN
ejpam-5385	216	4	=	=	SYM
ejpam-5385	216	5	f(m	f(m	PROPN
ejpam-5385	216	6	)	)	PUNCT
ejpam-5385	216	7	ψe(m	ψe(m	NUM
ejpam-5385	216	8	)	)	PUNCT
ejpam-5385	216	9	,	,	PUNCT
ejpam-5385	216	10	which	which	PRON
ejpam-5385	216	11	enables	enable	VERB
ejpam-5385	216	12	the	the	DET
ejpam-5385	216	13	identification	identification	NOUN
ejpam-5385	216	14	of	of	ADP
ejpam-5385	216	15	an	an	DET
ejpam-5385	216	16	q	q	NOUN
ejpam-5385	216	17	in	in	ADP
ejpam-5385	216	18	m1	m1	PROPN
ejpam-5385	216	19	such	such	ADJ
ejpam-5385	216	20	that	that	DET
ejpam-5385	216	21	f(q	f(q	NOUN
ejpam-5385	216	22	)	)	PUNCT
ejpam-5385	217	1	=	=	SYM
ejpam-5385	217	2	n1	n1	NOUN
ejpam-5385	217	3	and	and	CCONJ
ejpam-5385	217	4	ψf(e)([n1	ψf(e)([n1	NOUN
ejpam-5385	217	5	,	,	PUNCT
ejpam-5385	217	6	n2	n2	NOUN
ejpam-5385	217	7	]	]	PUNCT
ejpam-5385	217	8	)	)	PUNCT
ejpam-5385	217	9	>	>	PUNCT
ejpam-5385	218	1	r	r	X
ejpam-5385	218	2	>	>	X
ejpam-5385	218	3	ψe(q	ψe(q	NUM
ejpam-5385	218	4	)	)	PUNCT
ejpam-5385	218	5	.	.	PUNCT
ejpam-5385	219	1	by	by	ADP
ejpam-5385	219	2	choosing	choose	VERB
ejpam-5385	219	3	s	s	PROPN
ejpam-5385	219	4	∈	∈	PROPN
ejpam-5385	219	5	m1	m1	NOUN
ejpam-5385	219	6	with	with	ADP
ejpam-5385	219	7	f(s	f(	NOUN
ejpam-5385	219	8	)	)	PUNCT
ejpam-5385	219	9	=	=	SYM
ejpam-5385	219	10	n2	n2	NOUN
ejpam-5385	219	11	,	,	PUNCT
ejpam-5385	219	12	it	it	PRON
ejpam-5385	219	13	becomes	become	VERB
ejpam-5385	219	14	evident	evident	ADJ
ejpam-5385	219	15	that	that	SCONJ
ejpam-5385	219	16	f([q	f([q	NOUN
ejpam-5385	219	17	,	,	PUNCT
ejpam-5385	219	18	s	s	NOUN
ejpam-5385	219	19	]	]	X
ejpam-5385	219	20	)	)	PUNCT
ejpam-5385	219	21	=	=	PUNCT
ejpam-5385	220	1	[	[	X
ejpam-5385	220	2	f(q	f(q	NOUN
ejpam-5385	220	3	)	)	PUNCT
ejpam-5385	220	4	,	,	PUNCT
ejpam-5385	220	5	f(s	f(s	ADV
ejpam-5385	220	6	)	)	PUNCT
ejpam-5385	220	7	]	]	PUNCT
ejpam-5385	221	1	=	=	PUNCT
ejpam-5385	222	1	[	[	X
ejpam-5385	222	2	n1	n1	NOUN
ejpam-5385	222	3	,	,	PUNCT
ejpam-5385	222	4	n2	n2	NOUN
ejpam-5385	222	5	]	]	PUNCT
ejpam-5385	222	6	.	.	PUNCT
ejpam-5385	223	1	consequently	consequently	ADV
ejpam-5385	223	2	,	,	PUNCT
ejpam-5385	223	3	ψf(e)([n1	ψf(e)([n1	NOUN
ejpam-5385	223	4	,	,	PUNCT
ejpam-5385	223	5	n2	n2	ADJ
ejpam-5385	223	6	]	]	X
ejpam-5385	223	7	)	)	PUNCT
ejpam-5385	223	8	=	=	SYM
ejpam-5385	223	9	inf	inf	PROPN
ejpam-5385	224	1	[	[	X
ejpam-5385	224	2	n1	n1	NOUN
ejpam-5385	224	3	,	,	PUNCT
ejpam-5385	224	4	n2]=f([m1	n2]=f([m1	PROPN
ejpam-5385	224	5	,	,	PUNCT
ejpam-5385	224	6	m2])ψe([m1	m2])ψe([m1	PROPN
ejpam-5385	224	7	,	,	PUNCT
ejpam-5385	224	8	m2	m2	PROPN
ejpam-5385	224	9	]	]	X
ejpam-5385	224	10	)	)	PUNCT
ejpam-5385	224	11	≤	≤	PUNCT
ejpam-5385	224	12	ψe([q	ψe([q	PROPN
ejpam-5385	224	13	,	,	PUNCT
ejpam-5385	224	14	s	s	NOUN
ejpam-5385	224	15	]	]	X
ejpam-5385	224	16	)	)	PUNCT
ejpam-5385	224	17	≤	≤	NUM
ejpam-5385	224	18	ψe(q	ψe(q	X
ejpam-5385	224	19	)	)	PUNCT
ejpam-5385	224	20	∧	∧	NOUN
ejpam-5385	224	21	ψe(s	ψe(s	PUNCT
ejpam-5385	224	22	)	)	PUNCT
ejpam-5385	224	23	<	<	X
ejpam-5385	224	24	r	r	X
ejpam-5385	224	25	<	<	X
ejpam-5385	224	26	ψf(e)([n1	ψf(e)([n1	NOUN
ejpam-5385	224	27	,	,	PUNCT
ejpam-5385	224	28	n2	n2	ADJ
ejpam-5385	224	29	]	]	X
ejpam-5385	224	30	)	)	PUNCT
ejpam-5385	224	31	,	,	PUNCT
ejpam-5385	224	32	leading	lead	VERB
ejpam-5385	224	33	to	to	ADP
ejpam-5385	224	34	a	a	DET
ejpam-5385	224	35	contradiction	contradiction	NOUN
ejpam-5385	224	36	.	.	PUNCT
ejpam-5385	225	1	therefore	therefore	ADV
ejpam-5385	225	2	,	,	PUNCT
ejpam-5385	225	3	it	it	PRON
ejpam-5385	225	4	can	can	AUX
ejpam-5385	225	5	be	be	AUX
ejpam-5385	225	6	concluded	conclude	VERB
ejpam-5385	225	7	that	that	SCONJ
ejpam-5385	225	8	f(e	f(e	NOUN
ejpam-5385	225	9	)	)	PUNCT
ejpam-5385	225	10	indeed	indeed	ADV
ejpam-5385	225	11	constitutes	constitute	VERB
ejpam-5385	225	12	an	an	DET
ejpam-5385	225	13	intuitionistic	intuitionistic	ADJ
ejpam-5385	225	14	fuzzy	fuzzy	ADJ
ejpam-5385	225	15	lie	lie	NOUN
ejpam-5385	225	16	ideal	ideal	NOUN
ejpam-5385	225	17	within	within	ADP
ejpam-5385	225	18	im(f	im(f	NOUN
ejpam-5385	225	19	)	)	PUNCT
ejpam-5385	225	20	.	.	PUNCT
ejpam-5385	226	1	in	in	ADP
ejpam-5385	226	2	corollary	corollary	ADJ
ejpam-5385	226	3	2	2	NUM
ejpam-5385	226	4	,	,	PUNCT
ejpam-5385	226	5	we	we	PRON
ejpam-5385	226	6	establish	establish	VERB
ejpam-5385	226	7	that	that	SCONJ
ejpam-5385	226	8	if	if	SCONJ
ejpam-5385	226	9	f	f	PROPN
ejpam-5385	226	10	:	:	PUNCT
ejpam-5385	226	11	m1	m1	PROPN
ejpam-5385	226	12	→	→	SYM
ejpam-5385	226	13	m2	m2	PROPN
ejpam-5385	226	14	serves	serve	VERB
ejpam-5385	226	15	as	as	ADP
ejpam-5385	226	16	a	a	DET
ejpam-5385	226	17	lie	lie	NOUN
ejpam-5385	226	18	algebra	algebra	NOUN
ejpam-5385	226	19	homomorphism	homomorphism	NOUN
ejpam-5385	226	20	,	,	PUNCT
ejpam-5385	226	21	and	and	CCONJ
ejpam-5385	226	22	e	e	X
ejpam-5385	226	23	=	=	SYM
ejpam-5385	226	24	(	(	PUNCT
ejpam-5385	226	25	ϕe	ϕe	INTJ
ejpam-5385	226	26	,	,	PUNCT
ejpam-5385	226	27	ψe	ψe	NOUN
ejpam-5385	226	28	)	)	PUNCT
ejpam-5385	226	29	constitutes	constitute	VERB
ejpam-5385	226	30	an	an	DET
ejpam-5385	226	31	intuitionistic	intuitionistic	ADJ
ejpam-5385	226	32	fuzzy	fuzzy	ADJ
ejpam-5385	226	33	lie	lie	NOUN
ejpam-5385	226	34	ideal	ideal	NOUN
ejpam-5385	226	35	within	within	ADP
ejpam-5385	226	36	m1	m1	PROPN
ejpam-5385	226	37	,	,	PUNCT
ejpam-5385	226	38	then	then	ADV
ejpam-5385	226	39	the	the	DET
ejpam-5385	226	40	intuitionistic	intuitionistic	ADJ
ejpam-5385	226	41	fuzzy	fuzzy	ADJ
ejpam-5385	226	42	set	set	VERB
ejpam-5385	226	43	f(e	f(e	NOUN
ejpam-5385	226	44	)	)	PUNCT
ejpam-5385	226	45	transforms	transform	VERB
ejpam-5385	226	46	into	into	ADP
ejpam-5385	226	47	an	an	DET
ejpam-5385	226	48	intuitionistic	intuitionistic	ADJ
ejpam-5385	226	49	fuzzy	fuzzy	ADJ
ejpam-5385	226	50	lie	lie	NOUN
ejpam-5385	226	51	ideal	ideal	NOUN
ejpam-5385	226	52	within	within	ADP
ejpam-5385	226	53	im(f	im(f	NOUN
ejpam-5385	226	54	)	)	PUNCT
ejpam-5385	226	55	.	.	PUNCT
ejpam-5385	227	1	this	this	DET
ejpam-5385	227	2	result	result	NOUN
ejpam-5385	227	3	,	,	PUNCT
ejpam-5385	227	4	combined	combine	VERB
ejpam-5385	227	5	with	with	ADP
ejpam-5385	227	6	the	the	DET
ejpam-5385	227	7	insights	insight	NOUN
ejpam-5385	227	8	from	from	ADP
ejpam-5385	227	9	theorem	theorem	ADJ
ejpam-5385	227	10	2	2	NUM
ejpam-5385	227	11	,	,	PUNCT
ejpam-5385	227	12	allows	allow	VERB
ejpam-5385	227	13	us	we	PRON
ejpam-5385	227	14	to	to	PART
ejpam-5385	227	15	expand	expand	VERB
ejpam-5385	227	16	this	this	DET
ejpam-5385	227	17	understanding	understanding	NOUN
ejpam-5385	227	18	into	into	ADP
ejpam-5385	227	19	the	the	DET
ejpam-5385	227	20	realm	realm	NOUN
ejpam-5385	227	21	of	of	ADP
ejpam-5385	227	22	complex	complex	ADJ
ejpam-5385	227	23	intuitionistic	intuitionistic	ADJ
ejpam-5385	227	24	fuzzy	fuzzy	ADJ
ejpam-5385	227	25	lie	lie	NOUN
ejpam-5385	227	26	algebras	algebra	NOUN
ejpam-5385	227	27	.	.	PUNCT
ejpam-5385	228	1	corollary	corollary	ADJ
ejpam-5385	228	2	3	3	X
ejpam-5385	228	3	.	.	PUNCT
ejpam-5385	229	1	let	let	VERB
ejpam-5385	229	2	f	f	NOUN
ejpam-5385	229	3	:	:	PUNCT
ejpam-5385	229	4	m1	m1	PROPN
ejpam-5385	229	5	→	→	SYM
ejpam-5385	229	6	m2	m2	PROPN
ejpam-5385	229	7	represent	represent	VERB
ejpam-5385	229	8	a	a	DET
ejpam-5385	229	9	lie	lie	NOUN
ejpam-5385	229	10	algebra	algebra	NOUN
ejpam-5385	229	11	homomorphism	homomorphism	NOUN
ejpam-5385	229	12	.	.	PUNCT
ejpam-5385	230	1	if	if	SCONJ
ejpam-5385	230	2	e	e	X
ejpam-5385	230	3	=	=	SYM
ejpam-5385	230	4	(	(	PUNCT
ejpam-5385	230	5	ϕe	ϕe	INTJ
ejpam-5385	230	6	,	,	PUNCT
ejpam-5385	230	7	ψe	ψe	NOUN
ejpam-5385	230	8	)	)	PUNCT
ejpam-5385	230	9	denotes	denote	VERB
ejpam-5385	230	10	a	a	DET
ejpam-5385	230	11	complex	complex	ADJ
ejpam-5385	230	12	intuitionistic	intuitionistic	ADJ
ejpam-5385	230	13	fuzzy	fuzzy	ADJ
ejpam-5385	230	14	lie	lie	NOUN
ejpam-5385	230	15	ideal	ideal	NOUN
ejpam-5385	230	16	of	of	ADP
ejpam-5385	230	17	m1	m1	NOUN
ejpam-5385	230	18	,	,	PUNCT
ejpam-5385	230	19	then	then	ADV
ejpam-5385	230	20	the	the	DET
ejpam-5385	230	21	complex	complex	ADJ
ejpam-5385	230	22	intuitionistic	intuitionistic	ADJ
ejpam-5385	230	23	fuzzy	fuzzy	ADJ
ejpam-5385	230	24	set	set	VERB
ejpam-5385	230	25	f(e	f(e	NOUN
ejpam-5385	230	26	)	)	PUNCT
ejpam-5385	230	27	evolves	evolve	NOUN
ejpam-5385	230	28	into	into	ADP
ejpam-5385	230	29	a	a	DET
ejpam-5385	230	30	complex	complex	ADJ
ejpam-5385	230	31	intuitionistic	intuitionistic	ADJ
ejpam-5385	230	32	fuzzy	fuzzy	ADJ
ejpam-5385	230	33	lie	lie	NOUN
ejpam-5385	230	34	ideal	ideal	NOUN
ejpam-5385	230	35	within	within	ADP
ejpam-5385	230	36	the	the	DET
ejpam-5385	230	37	domain	domain	NOUN
ejpam-5385	230	38	im(f	im(f	NOUN
ejpam-5385	230	39	)	)	PUNCT
ejpam-5385	230	40	.	.	PUNCT
ejpam-5385	231	1	s.	s.	PROPN
ejpam-5385	231	2	shaqaqha	shaqaqha	PROPN
ejpam-5385	231	3	,	,	PUNCT
ejpam-5385	231	4	m.	m.	PROPN
ejpam-5385	231	5	y.	y.	PROPN
ejpam-5385	231	6	al	al	PROPN
ejpam-5385	231	7	-	-	PUNCT
ejpam-5385	231	8	deiakeh	deiakeh	PROPN
ejpam-5385	231	9	/	/	SYM
ejpam-5385	231	10	eur	eur	NOUN
ejpam-5385	231	11	.	.	PUNCT
ejpam-5385	232	1	j.	j.	PROPN
ejpam-5385	232	2	pure	pure	PROPN
ejpam-5385	232	3	appl	appl	PROPN
ejpam-5385	232	4	.	.	PROPN
ejpam-5385	232	5	math	math	PROPN
ejpam-5385	232	6	,	,	PUNCT
ejpam-5385	232	7	17	17	NUM
ejpam-5385	232	8	(	(	PUNCT
ejpam-5385	232	9	4	4	NUM
ejpam-5385	232	10	)	)	PUNCT
ejpam-5385	232	11	(	(	PUNCT
ejpam-5385	232	12	2024	2024	NUM
ejpam-5385	232	13	)	)	PUNCT
ejpam-5385	232	14	,	,	PUNCT
ejpam-5385	232	15	3291	3291	NUM
ejpam-5385	232	16	-	-	SYM
ejpam-5385	232	17	3303	3303	NUM
ejpam-5385	232	18	3300	3300	NUM
ejpam-5385	232	19	4	4	NUM
ejpam-5385	232	20	.	.	PUNCT
ejpam-5385	233	1	more	more	ADJ
ejpam-5385	233	2	homomorphism	homomorphism	NOUN
ejpam-5385	233	3	properties	property	NOUN
ejpam-5385	233	4	of	of	ADP
ejpam-5385	233	5	complex	complex	ADJ
ejpam-5385	233	6	intuitionistic	intuitionistic	ADJ
ejpam-5385	233	7	fuzzy	fuzzy	ADJ
ejpam-5385	233	8	lie	lie	NOUN
ejpam-5385	233	9	algebras	algebra	NOUN
ejpam-5385	233	10	let	let	VERB
ejpam-5385	233	11	e	e	X
ejpam-5385	233	12	=	=	SYM
ejpam-5385	233	13	(	(	PUNCT
ejpam-5385	233	14	ϕe	ϕe	INTJ
ejpam-5385	233	15	,	,	PUNCT
ejpam-5385	233	16	ψe	ψe	NOUN
ejpam-5385	233	17	)	)	PUNCT
ejpam-5385	233	18	and	and	CCONJ
ejpam-5385	233	19	p	p	NOUN
ejpam-5385	233	20	=	=	PUNCT
ejpam-5385	233	21	(	(	PUNCT
ejpam-5385	233	22	ϕp	ϕp	INTJ
ejpam-5385	233	23	,	,	PUNCT
ejpam-5385	233	24	ψp	ψp	AUX
ejpam-5385	233	25	)	)	PUNCT
ejpam-5385	233	26	be	be	VERB
ejpam-5385	233	27	two	two	NUM
ejpam-5385	233	28	complex	complex	ADJ
ejpam-5385	233	29	intuitionistic	intuitionistic	ADJ
ejpam-5385	233	30	fuzzy	fuzzy	ADJ
ejpam-5385	233	31	sets	set	NOUN
ejpam-5385	233	32	on	on	ADP
ejpam-5385	233	33	a	a	DET
ejpam-5385	233	34	lie	lie	NOUN
ejpam-5385	233	35	algebra	algebra	NOUN
ejpam-5385	233	36	m	m	VERB
ejpam-5385	233	37	over	over	ADP
ejpam-5385	233	38	a	a	DET
ejpam-5385	233	39	field	field	NOUN
ejpam-5385	233	40	k.	k.	ADV
ejpam-5385	234	1	the	the	DET
ejpam-5385	234	2	sum	sum	NOUN
ejpam-5385	234	3	of	of	ADP
ejpam-5385	234	4	e	e	PROPN
ejpam-5385	234	5	and	and	CCONJ
ejpam-5385	234	6	p	p	X
ejpam-5385	234	7	,	,	PUNCT
ejpam-5385	234	8	which	which	PRON
ejpam-5385	234	9	was	be	AUX
ejpam-5385	234	10	defined	define	VERB
ejpam-5385	234	11	by	by	ADP
ejpam-5385	234	12	chen	chen	PROPN
ejpam-5385	234	13	and	and	CCONJ
ejpam-5385	234	14	zhang	zhang	PROPN
ejpam-5385	235	1	[	[	X
ejpam-5385	235	2	8	8	NUM
ejpam-5385	235	3	]	]	PUNCT
ejpam-5385	235	4	in	in	ADP
ejpam-5385	235	5	the	the	DET
ejpam-5385	235	6	case	case	NOUN
ejpam-5385	235	7	of	of	ADP
ejpam-5385	235	8	intuitionistic	intuitionistic	ADJ
ejpam-5385	235	9	fuzzy	fuzzy	ADJ
ejpam-5385	235	10	lie	lie	NOUN
ejpam-5385	235	11	superalgebras	superalgebra	NOUN
ejpam-5385	235	12	,	,	PUNCT
ejpam-5385	235	13	is	be	AUX
ejpam-5385	235	14	defined	define	VERB
ejpam-5385	235	15	as	as	SCONJ
ejpam-5385	235	16	follows	follow	VERB
ejpam-5385	235	17	:	:	PUNCT
ejpam-5385	236	1	e	e	X
ejpam-5385	236	2	+	+	CCONJ
ejpam-5385	236	3	p	p	X
ejpam-5385	236	4	=	=	SYM
ejpam-5385	236	5	(	(	PUNCT
ejpam-5385	236	6	ϕe+p	ϕe+p	PROPN
ejpam-5385	236	7	,	,	PUNCT
ejpam-5385	236	8	ψe+p	ψe+p	PROPN
ejpam-5385	236	9	)	)	PUNCT
ejpam-5385	236	10	,	,	PUNCT
ejpam-5385	236	11	where	where	SCONJ
ejpam-5385	236	12	ϕe+p(m	ϕe+p(m	X
ejpam-5385	236	13	)	)	PUNCT
ejpam-5385	236	14	=	=	SYM
ejpam-5385	237	1	sup	sup	NOUN
ejpam-5385	237	2	m1+m2	m1+m2	NOUN
ejpam-5385	237	3	{	{	PUNCT
ejpam-5385	237	4	ϕe(m1	ϕe(m1	NOUN
ejpam-5385	237	5	)	)	PUNCT
ejpam-5385	237	6	∧	∧	PROPN
ejpam-5385	237	7	ϕp(m2	ϕp(m2	NOUN
ejpam-5385	237	8	)	)	PUNCT
ejpam-5385	237	9	}	}	PUNCT
ejpam-5385	237	10	,	,	PUNCT
ejpam-5385	237	11	and	and	CCONJ
ejpam-5385	237	12	ψe+p(m	ψe+p(m	X
ejpam-5385	237	13	)	)	PUNCT
ejpam-5385	237	14	=	=	NOUN
ejpam-5385	237	15	inf	inf	NOUN
ejpam-5385	237	16	m	m	NOUN
ejpam-5385	237	17	=	=	NOUN
ejpam-5385	237	18	m1+m2	m1+m2	NOUN
ejpam-5385	237	19	{	{	PUNCT
ejpam-5385	237	20	ψe(m1	ψe(m1	NOUN
ejpam-5385	237	21	)	)	PUNCT
ejpam-5385	237	22	∨	∨	NUM
ejpam-5385	237	23	ψp(m2	ψp(m2	NUM
ejpam-5385	237	24	)	)	PUNCT
ejpam-5385	237	25	}	}	PUNCT
ejpam-5385	237	26	.	.	PUNCT
ejpam-5385	238	1	let	let	VERB
ejpam-5385	239	1	e	e	NOUN
ejpam-5385	239	2	=	=	SYM
ejpam-5385	239	3	(	(	PUNCT
ejpam-5385	239	4	ϕe	ϕe	INTJ
ejpam-5385	239	5	,	,	PUNCT
ejpam-5385	239	6	ψe	ψe	NOUN
ejpam-5385	239	7	)	)	PUNCT
ejpam-5385	239	8	and	and	CCONJ
ejpam-5385	239	9	q	q	NOUN
ejpam-5385	239	10	=	=	SYM
ejpam-5385	239	11	(	(	PUNCT
ejpam-5385	239	12	ϕq	ϕq	PROPN
ejpam-5385	239	13	,	,	PUNCT
ejpam-5385	239	14	ψq	ψq	PRON
ejpam-5385	239	15	)	)	PUNCT
ejpam-5385	239	16	be	be	VERB
ejpam-5385	239	17	two	two	NUM
ejpam-5385	239	18	complex	complex	ADJ
ejpam-5385	239	19	intuitionistic	intuitionistic	ADJ
ejpam-5385	239	20	fuzzy	fuzzy	ADJ
ejpam-5385	239	21	sets	set	NOUN
ejpam-5385	239	22	on	on	ADP
ejpam-5385	239	23	the	the	DET
ejpam-5385	239	24	same	same	ADJ
ejpam-5385	239	25	setm	setm	NOUN
ejpam-5385	239	26	,	,	PUNCT
ejpam-5385	239	27	where	where	SCONJ
ejpam-5385	239	28	ϕe	ϕe	NOUN
ejpam-5385	239	29	=	=	NOUN
ejpam-5385	239	30	ρee	ρee	NOUN
ejpam-5385	239	31	iζe	iζe	ADJ
ejpam-5385	239	32	,	,	PUNCT
ejpam-5385	239	33	ψe	ψe	PROPN
ejpam-5385	239	34	=	=	PUNCT
ejpam-5385	239	35	ρ̂ee	ρ̂ee	PROPN
ejpam-5385	239	36	iζ̂e	iζ̂e	PROPN
ejpam-5385	239	37	,	,	PUNCT
ejpam-5385	239	38	ϕq	ϕq	PRON
ejpam-5385	239	39	=	=	PUNCT
ejpam-5385	239	40	ρqe	ρqe	ADJ
ejpam-5385	239	41	iζq	iζq	NOUN
ejpam-5385	239	42	,	,	PUNCT
ejpam-5385	239	43	and	and	CCONJ
ejpam-5385	239	44	ψq	ψq	X
ejpam-5385	239	45	=	=	NUM
ejpam-5385	239	46	ρ̂qe	ρ̂qe	PROPN
ejpam-5385	239	47	iζ̂q	iζ̂q	PROPN
ejpam-5385	239	48	.	.	PUNCT
ejpam-5385	240	1	we	we	PRON
ejpam-5385	240	2	say	say	VERB
ejpam-5385	240	3	that	that	SCONJ
ejpam-5385	240	4	e	e	PRON
ejpam-5385	240	5	is	be	AUX
ejpam-5385	240	6	homogeneous	homogeneous	ADJ
ejpam-5385	240	7	with	with	ADP
ejpam-5385	240	8	q	q	PROPN
ejpam-5385	240	9	if	if	SCONJ
ejpam-5385	240	10	the	the	DET
ejpam-5385	240	11	following	follow	VERB
ejpam-5385	240	12	hold	hold	NOUN
ejpam-5385	240	13	for	for	ADP
ejpam-5385	240	14	all	all	DET
ejpam-5385	240	15	m	m	NOUN
ejpam-5385	240	16	,	,	PUNCT
ejpam-5385	240	17	n	n	CCONJ
ejpam-5385	240	18	∈m	∈m	NOUN
ejpam-5385	240	19	:	:	PUNCT
ejpam-5385	240	20	(	(	PUNCT
ejpam-5385	240	21	i	i	NOUN
ejpam-5385	240	22	)	)	PUNCT
ejpam-5385	240	23	ρe(m	ρe(m	NUM
ejpam-5385	240	24	)	)	PUNCT
ejpam-5385	240	25	≤	≤	NUM
ejpam-5385	240	26	ρq(n	ρq(n	NOUN
ejpam-5385	240	27	)	)	PUNCT
ejpam-5385	240	28	if	if	SCONJ
ejpam-5385	240	29	and	and	CCONJ
ejpam-5385	240	30	only	only	ADV
ejpam-5385	240	31	if	if	SCONJ
ejpam-5385	240	32	ζe(m	ζe(m	NUM
ejpam-5385	240	33	)	)	PUNCT
ejpam-5385	240	34	≤	≤	NOUN
ejpam-5385	240	35	ζq(n	ζq(n	NOUN
ejpam-5385	240	36	)	)	PUNCT
ejpam-5385	240	37	(	(	PUNCT
ejpam-5385	240	38	in	in	ADP
ejpam-5385	240	39	this	this	DET
ejpam-5385	240	40	case	case	NOUN
ejpam-5385	240	41	ϕe(m	ϕe(m	ADP
ejpam-5385	240	42	)	)	PUNCT
ejpam-5385	240	43	≤	≤	NOUN
ejpam-5385	240	44	ϕq(n	ϕq(n	PRON
ejpam-5385	240	45	)	)	PUNCT
ejpam-5385	240	46	)	)	PUNCT
ejpam-5385	240	47	,	,	PUNCT
ejpam-5385	240	48	(	(	PUNCT
ejpam-5385	240	49	ii	ii	NOUN
ejpam-5385	240	50	)	)	PUNCT
ejpam-5385	240	51	ρ̂e(m	ρ̂e(m	NUM
ejpam-5385	240	52	)	)	PUNCT
ejpam-5385	240	53	≤	≤	PUNCT
ejpam-5385	241	1	ρ̂q(n	ρ̂q(n	PROPN
ejpam-5385	241	2	)	)	PUNCT
ejpam-5385	241	3	if	if	SCONJ
ejpam-5385	241	4	and	and	CCONJ
ejpam-5385	241	5	only	only	ADV
ejpam-5385	241	6	if	if	SCONJ
ejpam-5385	241	7	ζ̂e(m	ζ̂e(m	NUM
ejpam-5385	241	8	)	)	PUNCT
ejpam-5385	241	9	≤	≤	NOUN
ejpam-5385	241	10	ζ̂q(n	ζ̂q(n	PROPN
ejpam-5385	241	11	)	)	PUNCT
ejpam-5385	241	12	(	(	PUNCT
ejpam-5385	241	13	in	in	ADP
ejpam-5385	241	14	this	this	DET
ejpam-5385	241	15	case	case	NOUN
ejpam-5385	241	16	ψe(m	ψe(m	NUM
ejpam-5385	241	17	)	)	PUNCT
ejpam-5385	241	18	≤	≤	NOUN
ejpam-5385	241	19	ψq(n	ψq(n	NUM
ejpam-5385	241	20	)	)	PUNCT
ejpam-5385	241	21	)	)	PUNCT
ejpam-5385	241	22	.	.	PUNCT
ejpam-5385	242	1	theorem	theorem	NOUN
ejpam-5385	242	2	3	3	NUM
ejpam-5385	242	3	.	.	PUNCT
ejpam-5385	243	1	(	(	PUNCT
ejpam-5385	243	2	[	[	X
ejpam-5385	243	3	14	14	NUM
ejpam-5385	243	4	]	]	PUNCT
ejpam-5385	243	5	)	)	PUNCT
ejpam-5385	243	6	let	let	VERB
ejpam-5385	243	7	e	e	NOUN
ejpam-5385	243	8	=	=	SYM
ejpam-5385	243	9	(	(	PUNCT
ejpam-5385	243	10	ϕe	ϕe	INTJ
ejpam-5385	243	11	,	,	PUNCT
ejpam-5385	243	12	ψe	ψe	NOUN
ejpam-5385	243	13	)	)	PUNCT
ejpam-5385	243	14	and	and	CCONJ
ejpam-5385	243	15	p	p	NOUN
ejpam-5385	243	16	=	=	PUNCT
ejpam-5385	243	17	(	(	PUNCT
ejpam-5385	243	18	ϕp	ϕp	INTJ
ejpam-5385	243	19	,	,	PUNCT
ejpam-5385	243	20	ψp	ψp	AUX
ejpam-5385	243	21	)	)	PUNCT
ejpam-5385	243	22	be	be	VERB
ejpam-5385	243	23	two	two	NUM
ejpam-5385	243	24	complex	complex	ADJ
ejpam-5385	243	25	intuitionistic	intuitionistic	ADJ
ejpam-5385	243	26	fuzzy	fuzzy	ADJ
ejpam-5385	243	27	lie	lie	NOUN
ejpam-5385	243	28	ideals	ideal	NOUN
ejpam-5385	243	29	on	on	ADP
ejpam-5385	243	30	m	m	PRON
ejpam-5385	243	31	such	such	ADJ
ejpam-5385	243	32	that	that	SCONJ
ejpam-5385	243	33	e	e	NOUN
ejpam-5385	243	34	is	be	AUX
ejpam-5385	243	35	homogeneous	homogeneous	ADJ
ejpam-5385	243	36	with	with	ADP
ejpam-5385	243	37	p	p	PROPN
ejpam-5385	243	38	and	and	CCONJ
ejpam-5385	243	39	e	e	PROPN
ejpam-5385	244	1	+	+	CCONJ
ejpam-5385	244	2	p	p	NOUN
ejpam-5385	244	3	is	be	AUX
ejpam-5385	244	4	homogeneous	homogeneous	ADJ
ejpam-5385	244	5	.	.	PUNCT
ejpam-5385	245	1	then	then	ADV
ejpam-5385	245	2	e	e	X
ejpam-5385	245	3	+	+	CCONJ
ejpam-5385	245	4	p	p	NOUN
ejpam-5385	245	5	is	be	AUX
ejpam-5385	245	6	a	a	DET
ejpam-5385	245	7	complex	complex	ADJ
ejpam-5385	245	8	intuitionistic	intuitionistic	ADJ
ejpam-5385	245	9	fuzzy	fuzzy	ADJ
ejpam-5385	245	10	lie	lie	NOUN
ejpam-5385	245	11	ideal	ideal	NOUN
ejpam-5385	245	12	of	of	ADP
ejpam-5385	245	13	m.	m.	NOUN
ejpam-5385	245	14	consider	consider	VERB
ejpam-5385	245	15	a	a	DET
ejpam-5385	245	16	surjective	surjective	ADJ
ejpam-5385	245	17	lie	lie	NOUN
ejpam-5385	245	18	algebra	algebra	NOUN
ejpam-5385	245	19	homomorphism	homomorphism	PROPN
ejpam-5385	245	20	f	f	X
ejpam-5385	245	21	:	:	PUNCT
ejpam-5385	245	22	m1	m1	PROPN
ejpam-5385	245	23	→	→	SYM
ejpam-5385	245	24	m2	m2	PROPN
ejpam-5385	245	25	.	.	PROPN
ejpam-5385	245	26	suppose	suppose	VERB
ejpam-5385	245	27	we	we	PRON
ejpam-5385	245	28	have	have	VERB
ejpam-5385	245	29	two	two	NUM
ejpam-5385	245	30	complex	complex	ADJ
ejpam-5385	245	31	intuitionistic	intuitionistic	ADJ
ejpam-5385	245	32	fuzzy	fuzzy	ADJ
ejpam-5385	245	33	lie	lie	NOUN
ejpam-5385	245	34	ideals	ideal	NOUN
ejpam-5385	245	35	,	,	PUNCT
ejpam-5385	245	36	denoted	denote	VERB
ejpam-5385	245	37	as	as	ADP
ejpam-5385	245	38	e	e	PROPN
ejpam-5385	245	39	and	and	CCONJ
ejpam-5385	245	40	p	p	X
ejpam-5385	245	41	,	,	PUNCT
ejpam-5385	245	42	on	on	ADP
ejpam-5385	245	43	m1	m1	PROPN
ejpam-5385	245	44	.	.	PUNCT
ejpam-5385	246	1	assume	assume	VERB
ejpam-5385	246	2	that	that	SCONJ
ejpam-5385	246	3	e	e	PRON
ejpam-5385	246	4	is	be	AUX
ejpam-5385	246	5	homogeneous	homogeneous	ADJ
ejpam-5385	246	6	with	with	ADP
ejpam-5385	246	7	respect	respect	NOUN
ejpam-5385	246	8	to	to	ADP
ejpam-5385	246	9	p	p	NOUN
ejpam-5385	246	10	,	,	PUNCT
ejpam-5385	246	11	and	and	CCONJ
ejpam-5385	246	12	the	the	DET
ejpam-5385	246	13	sum	sum	NOUN
ejpam-5385	246	14	e	e	NOUN
ejpam-5385	247	1	+	+	CCONJ
ejpam-5385	247	2	p	p	NOUN
ejpam-5385	247	3	is	be	AUX
ejpam-5385	247	4	also	also	ADV
ejpam-5385	247	5	homogeneous	homogeneous	ADJ
ejpam-5385	247	6	.	.	PUNCT
ejpam-5385	248	1	in	in	ADP
ejpam-5385	248	2	accordance	accordance	NOUN
ejpam-5385	248	3	with	with	ADP
ejpam-5385	248	4	corollary	corollary	ADJ
ejpam-5385	248	5	3	3	NUM
ejpam-5385	248	6	,	,	PUNCT
ejpam-5385	248	7	we	we	PRON
ejpam-5385	248	8	can	can	AUX
ejpam-5385	248	9	conclude	conclude	VERB
ejpam-5385	248	10	that	that	PRON
ejpam-5385	248	11	f(e+p	f(e+p	PRON
ejpam-5385	248	12	)	)	PUNCT
ejpam-5385	248	13	constitutes	constitute	VERB
ejpam-5385	248	14	a	a	DET
ejpam-5385	248	15	complex	complex	ADJ
ejpam-5385	248	16	intuitionistic	intuitionistic	ADJ
ejpam-5385	248	17	fuzzy	fuzzy	ADJ
ejpam-5385	248	18	lie	lie	NOUN
ejpam-5385	248	19	ideal	ideal	NOUN
ejpam-5385	248	20	of	of	ADP
ejpam-5385	248	21	the	the	DET
ejpam-5385	248	22	image	image	NOUN
ejpam-5385	248	23	of	of	ADP
ejpam-5385	248	24	f	f	PROPN
ejpam-5385	248	25	,	,	PUNCT
ejpam-5385	248	26	denoted	denote	VERB
ejpam-5385	248	27	as	as	ADP
ejpam-5385	248	28	im(f	im(f	NOUN
ejpam-5385	248	29	)	)	PUNCT
ejpam-5385	248	30	.	.	PUNCT
ejpam-5385	249	1	the	the	DET
ejpam-5385	249	2	subsequent	subsequent	ADJ
ejpam-5385	249	3	theorem	theorem	NOUN
ejpam-5385	249	4	establishes	establish	VERB
ejpam-5385	249	5	the	the	DET
ejpam-5385	249	6	relationship	relationship	NOUN
ejpam-5385	249	7	between	between	ADP
ejpam-5385	249	8	the	the	DET
ejpam-5385	249	9	sets	set	NOUN
ejpam-5385	249	10	f(e	f(e	VERB
ejpam-5385	249	11	+	+	CCONJ
ejpam-5385	249	12	p	p	X
ejpam-5385	249	13	)	)	PUNCT
ejpam-5385	249	14	,	,	PUNCT
ejpam-5385	249	15	f(e	f(e	NOUN
ejpam-5385	249	16	)	)	PUNCT
ejpam-5385	249	17	,	,	PUNCT
ejpam-5385	249	18	and	and	CCONJ
ejpam-5385	249	19	f(p	f(p	NOUN
ejpam-5385	249	20	)	)	PUNCT
ejpam-5385	249	21	.	.	PUNCT
ejpam-5385	250	1	theorem	theorem	ADJ
ejpam-5385	250	2	4	4	NUM
ejpam-5385	250	3	.	.	PUNCT
ejpam-5385	250	4	consider	consider	VERB
ejpam-5385	250	5	a	a	DET
ejpam-5385	250	6	surjective	surjective	ADJ
ejpam-5385	250	7	lie	lie	NOUN
ejpam-5385	250	8	algebra	algebra	NOUN
ejpam-5385	250	9	homomorphism	homomorphism	PROPN
ejpam-5385	250	10	f	f	X
ejpam-5385	250	11	:	:	PUNCT
ejpam-5385	250	12	m1	m1	PROPN
ejpam-5385	250	13	→	→	SYM
ejpam-5385	250	14	m2	m2	PROPN
ejpam-5385	250	15	.	.	PUNCT
ejpam-5385	251	1	let	let	VERB
ejpam-5385	251	2	e	e	NOUN
ejpam-5385	251	3	=	=	SYM
ejpam-5385	251	4	(	(	PUNCT
ejpam-5385	251	5	ϕe	ϕe	INTJ
ejpam-5385	251	6	,	,	PUNCT
ejpam-5385	251	7	ψe	ψe	NOUN
ejpam-5385	251	8	)	)	PUNCT
ejpam-5385	251	9	and	and	CCONJ
ejpam-5385	251	10	p	p	NOUN
ejpam-5385	251	11	=	=	PUNCT
ejpam-5385	251	12	(	(	PUNCT
ejpam-5385	251	13	ϕp	ϕp	INTJ
ejpam-5385	251	14	,	,	PUNCT
ejpam-5385	251	15	ψp	ψp	AUX
ejpam-5385	251	16	)	)	PUNCT
ejpam-5385	251	17	be	be	AUX
ejpam-5385	251	18	complex	complex	ADJ
ejpam-5385	251	19	intuitionistic	intuitionistic	ADJ
ejpam-5385	251	20	fuzzy	fuzzy	ADJ
ejpam-5385	251	21	lie	lie	NOUN
ejpam-5385	251	22	ideals	ideal	NOUN
ejpam-5385	251	23	on	on	ADP
ejpam-5385	251	24	m1	m1	PROPN
ejpam-5385	251	25	such	such	ADJ
ejpam-5385	251	26	that	that	SCONJ
ejpam-5385	251	27	e	e	NOUN
ejpam-5385	251	28	is	be	AUX
ejpam-5385	251	29	homogeneous	homogeneous	ADJ
ejpam-5385	251	30	with	with	ADP
ejpam-5385	251	31	respect	respect	NOUN
ejpam-5385	251	32	to	to	ADP
ejpam-5385	251	33	p.	p.	NOUN
ejpam-5385	251	34	then	then	ADV
ejpam-5385	251	35	,	,	PUNCT
ejpam-5385	252	1	f(e	f(e	PROPN
ejpam-5385	252	2	+	+	CCONJ
ejpam-5385	252	3	p	p	X
ejpam-5385	252	4	)	)	PUNCT
ejpam-5385	252	5	=	=	SYM
ejpam-5385	252	6	f(e	f(e	NOUN
ejpam-5385	252	7	)	)	PUNCT
ejpam-5385	252	8	+	+	NUM
ejpam-5385	252	9	f(p	f(p	NOUN
ejpam-5385	252	10	)	)	PUNCT
ejpam-5385	252	11	.	.	PUNCT
ejpam-5385	253	1	proof	proof	NOUN
ejpam-5385	253	2	.	.	PUNCT
ejpam-5385	254	1	let	let	VERB
ejpam-5385	254	2	n	n	PRON
ejpam-5385	254	3	∈	∈	PROPN
ejpam-5385	254	4	m2	m2	PROPN
ejpam-5385	254	5	.	.	PUNCT
ejpam-5385	255	1	then	then	ADV
ejpam-5385	255	2	ϕf(e+p)(n	ϕf(e+p)(n	PROPN
ejpam-5385	255	3	)	)	PUNCT
ejpam-5385	255	4	=	=	SYM
ejpam-5385	255	5	sup	sup	NOUN
ejpam-5385	255	6	n	n	CCONJ
ejpam-5385	255	7	=	=	SYM
ejpam-5385	255	8	f(m	f(m	PROPN
ejpam-5385	255	9	)	)	PUNCT
ejpam-5385	255	10	{	{	PUNCT
ejpam-5385	255	11	ϕe+p(m	ϕe+p(m	NOUN
ejpam-5385	255	12	)	)	PUNCT
ejpam-5385	255	13	}	}	PUNCT
ejpam-5385	255	14	=	=	SYM
ejpam-5385	255	15	sup	sup	NOUN
ejpam-5385	255	16	n	n	CCONJ
ejpam-5385	255	17	=	=	SYM
ejpam-5385	255	18	f(m	f(m	PROPN
ejpam-5385	255	19	)	)	PUNCT
ejpam-5385	255	20	{	{	PUNCT
ejpam-5385	256	1	sup	sup	NOUN
ejpam-5385	256	2	m	m	NOUN
ejpam-5385	256	3	=	=	NOUN
ejpam-5385	256	4	m1+m2	m1+m2	NOUN
ejpam-5385	256	5	{	{	PUNCT
ejpam-5385	256	6	ϕe(m1	ϕe(m1	NOUN
ejpam-5385	256	7	)	)	PUNCT
ejpam-5385	256	8	∧	∧	PROPN
ejpam-5385	256	9	ϕp(m2	ϕp(m2	PRON
ejpam-5385	256	10	)	)	PUNCT
ejpam-5385	256	11	}	}	PUNCT
ejpam-5385	256	12	}	}	PUNCT
ejpam-5385	256	13	=	=	SYM
ejpam-5385	256	14	sup	sup	NOUN
ejpam-5385	256	15	n	n	CCONJ
ejpam-5385	256	16	=	=	NOUN
ejpam-5385	256	17	q+s	q+s	X
ejpam-5385	256	18	{	{	PUNCT
ejpam-5385	256	19	sup	sup	NOUN
ejpam-5385	256	20	q	q	NOUN
ejpam-5385	256	21	=	=	NOUN
ejpam-5385	256	22	f(m1	f(m1	NOUN
ejpam-5385	256	23	)	)	PUNCT
ejpam-5385	256	24	{	{	PUNCT
ejpam-5385	256	25	ϕe(m1	ϕe(m1	NOUN
ejpam-5385	256	26	)	)	PUNCT
ejpam-5385	256	27	}	}	PUNCT
ejpam-5385	256	28	∧	∧	PROPN
ejpam-5385	256	29	sup	sup	NOUN
ejpam-5385	256	30	s	s	NOUN
ejpam-5385	256	31	=	=	NOUN
ejpam-5385	256	32	f(m2	f(m2	NOUN
ejpam-5385	256	33	)	)	PUNCT
ejpam-5385	256	34	{	{	PUNCT
ejpam-5385	256	35	ϕp(m2	ϕp(m2	X
ejpam-5385	256	36	)	)	PUNCT
ejpam-5385	256	37	}	}	PUNCT
ejpam-5385	256	38	}	}	PUNCT
ejpam-5385	257	1	=	=	X
ejpam-5385	257	2	ϕf(e)+f(p)(n	ϕf(e)+f(p)(n	NUM
ejpam-5385	257	3	)	)	PUNCT
ejpam-5385	257	4	.	.	PUNCT
ejpam-5385	258	1	s.	s.	PROPN
ejpam-5385	258	2	shaqaqha	shaqaqha	PROPN
ejpam-5385	258	3	,	,	PUNCT
ejpam-5385	258	4	m.	m.	PROPN
ejpam-5385	258	5	y.	y.	PROPN
ejpam-5385	258	6	al	al	PROPN
ejpam-5385	258	7	-	-	PUNCT
ejpam-5385	258	8	deiakeh	deiakeh	PROPN
ejpam-5385	258	9	/	/	SYM
ejpam-5385	258	10	eur	eur	NOUN
ejpam-5385	258	11	.	.	PUNCT
ejpam-5385	259	1	j.	j.	PROPN
ejpam-5385	259	2	pure	pure	PROPN
ejpam-5385	259	3	appl	appl	PROPN
ejpam-5385	259	4	.	.	PROPN
ejpam-5385	259	5	math	math	PROPN
ejpam-5385	259	6	,	,	PUNCT
ejpam-5385	259	7	17	17	NUM
ejpam-5385	259	8	(	(	PUNCT
ejpam-5385	259	9	4	4	NUM
ejpam-5385	259	10	)	)	PUNCT
ejpam-5385	259	11	(	(	PUNCT
ejpam-5385	259	12	2024	2024	NUM
ejpam-5385	259	13	)	)	PUNCT
ejpam-5385	259	14	,	,	PUNCT
ejpam-5385	259	15	3291	3291	NUM
ejpam-5385	259	16	-	-	SYM
ejpam-5385	259	17	3303	3303	NUM
ejpam-5385	259	18	3301	3301	NUM
ejpam-5385	259	19	in	in	ADP
ejpam-5385	259	20	addition	addition	NOUN
ejpam-5385	259	21	,	,	PUNCT
ejpam-5385	259	22	ψf(e+p)(n	ψf(e+p)(n	PROPN
ejpam-5385	259	23	)	)	PUNCT
ejpam-5385	259	24	=	=	SYM
ejpam-5385	259	25	inf	inf	PROPN
ejpam-5385	259	26	n	n	CCONJ
ejpam-5385	259	27	=	=	SYM
ejpam-5385	259	28	f(m	f(m	PROPN
ejpam-5385	259	29	)	)	PUNCT
ejpam-5385	259	30	{	{	PUNCT
ejpam-5385	259	31	ψe+p(m	ψe+p(m	NOUN
ejpam-5385	259	32	)	)	PUNCT
ejpam-5385	259	33	}	}	PUNCT
ejpam-5385	259	34	=	=	SYM
ejpam-5385	259	35	inf	inf	PROPN
ejpam-5385	259	36	n	n	CCONJ
ejpam-5385	259	37	=	=	SYM
ejpam-5385	259	38	f(m	f(m	PROPN
ejpam-5385	259	39	)	)	PUNCT
ejpam-5385	259	40	{	{	PUNCT
ejpam-5385	259	41	inf	inf	NOUN
ejpam-5385	259	42	m	m	NOUN
ejpam-5385	259	43	=	=	NOUN
ejpam-5385	259	44	m1+m2	m1+m2	NOUN
ejpam-5385	259	45	{	{	PUNCT
ejpam-5385	259	46	ψe(m1	ψe(m1	NOUN
ejpam-5385	259	47	)	)	PUNCT
ejpam-5385	259	48	∨	∨	NUM
ejpam-5385	259	49	ψp(m2	ψp(m2	PART
ejpam-5385	259	50	)	)	PUNCT
ejpam-5385	259	51	}	}	PUNCT
ejpam-5385	259	52	}	}	PUNCT
ejpam-5385	259	53	=	=	SYM
ejpam-5385	259	54	inf	inf	ADJ
ejpam-5385	259	55	n	n	CCONJ
ejpam-5385	259	56	=	=	NOUN
ejpam-5385	259	57	q+s	q+s	X
ejpam-5385	259	58	{	{	PUNCT
ejpam-5385	259	59	inf	inf	NOUN
ejpam-5385	259	60	q	q	NOUN
ejpam-5385	259	61	=	=	NOUN
ejpam-5385	259	62	f(m1	f(m1	NOUN
ejpam-5385	259	63	)	)	PUNCT
ejpam-5385	259	64	{	{	PUNCT
ejpam-5385	259	65	ψe(m1	ψe(m1	NOUN
ejpam-5385	259	66	)	)	PUNCT
ejpam-5385	259	67	}	}	PUNCT
ejpam-5385	259	68	∨	∨	NUM
ejpam-5385	259	69	inf	inf	PROPN
ejpam-5385	259	70	s	s	PART
ejpam-5385	259	71	=	=	NOUN
ejpam-5385	259	72	f(m2	f(m2	NOUN
ejpam-5385	259	73	)	)	PUNCT
ejpam-5385	259	74	{	{	PUNCT
ejpam-5385	259	75	ψp(m2	ψp(m2	NOUN
ejpam-5385	259	76	)	)	PUNCT
ejpam-5385	259	77	}	}	PUNCT
ejpam-5385	259	78	}	}	PUNCT
ejpam-5385	259	79	=	=	SYM
ejpam-5385	259	80	ψf(e)+f(p)(n	ψf(e)+f(p)(n	NOUN
ejpam-5385	259	81	)	)	PUNCT
ejpam-5385	259	82	.	.	PUNCT
ejpam-5385	260	1	therefore	therefore	ADV
ejpam-5385	260	2	,	,	PUNCT
ejpam-5385	260	3	f(e	f(e	PROPN
ejpam-5385	260	4	+	+	CCONJ
ejpam-5385	260	5	p	p	X
ejpam-5385	260	6	)	)	PUNCT
ejpam-5385	260	7	=	=	SYM
ejpam-5385	260	8	f(e	f(e	NOUN
ejpam-5385	260	9	)	)	PUNCT
ejpam-5385	260	10	+	+	NUM
ejpam-5385	260	11	f(p	f(p	NOUN
ejpam-5385	260	12	)	)	PUNCT
ejpam-5385	260	13	.	.	PUNCT
ejpam-5385	261	1	let	let	VERB
ejpam-5385	261	2	x	x	PRON
ejpam-5385	261	3	be	be	AUX
ejpam-5385	261	4	a	a	DET
ejpam-5385	261	5	nonempty	nonempty	ADJ
ejpam-5385	261	6	set	set	VERB
ejpam-5385	261	7	.	.	PUNCT
ejpam-5385	262	1	let	let	VERB
ejpam-5385	262	2	ϕe(x	ϕe(x	PUNCT
ejpam-5385	262	3	)	)	PUNCT
ejpam-5385	263	1	=	=	SYM
ejpam-5385	264	1	ρe(x)e	ρe(x)e	PROPN
ejpam-5385	264	2	iζe(x	iζe(x	PROPN
ejpam-5385	264	3	)	)	PUNCT
ejpam-5385	264	4	,	,	PUNCT
ejpam-5385	264	5	ψe(x	ψe(x	X
ejpam-5385	264	6	)	)	PUNCT
ejpam-5385	264	7	=	=	SYM
ejpam-5385	265	1	ρ̂e(x)e	ρ̂e(x)e	NUM
ejpam-5385	265	2	iζ̂e(x	iζ̂e(x	ADJ
ejpam-5385	265	3	)	)	PUNCT
ejpam-5385	265	4	,	,	PUNCT
ejpam-5385	265	5	and	and	CCONJ
ejpam-5385	265	6	e	e	X
ejpam-5385	265	7	=	=	PRON
ejpam-5385	265	8	{	{	PUNCT
ejpam-5385	265	9	(	(	PUNCT
ejpam-5385	265	10	x	x	NOUN
ejpam-5385	265	11	,	,	PUNCT
ejpam-5385	265	12	ϕe(x	ϕe(x	NUM
ejpam-5385	265	13	)	)	PUNCT
ejpam-5385	265	14	,	,	PUNCT
ejpam-5385	265	15	ψe(x	ψe(x	PROPN
ejpam-5385	265	16	)	)	PUNCT
ejpam-5385	265	17	)	)	PUNCT
ejpam-5385	265	18	:	:	PUNCT
ejpam-5385	266	1	x	x	X
ejpam-5385	266	2	∈	∈	NOUN
ejpam-5385	266	3	x	x	PRON
ejpam-5385	266	4	}	}	PUNCT
ejpam-5385	266	5	be	be	AUX
ejpam-5385	266	6	a	a	DET
ejpam-5385	266	7	complex	complex	ADJ
ejpam-5385	266	8	intuitionistic	intuitionistic	ADJ
ejpam-5385	266	9	fuzzy	fuzzy	ADJ
ejpam-5385	266	10	set	set	NOUN
ejpam-5385	266	11	within	within	ADP
ejpam-5385	266	12	x.	x.	NOUN
ejpam-5385	266	13	for	for	ADP
ejpam-5385	266	14	α	α	NOUN
ejpam-5385	266	15	,	,	PUNCT
ejpam-5385	266	16	α̂	α̂	NUM
ejpam-5385	266	17	∈	∈	PROPN
ejpam-5385	267	1	[	[	X
ejpam-5385	267	2	0	0	NUM
ejpam-5385	267	3	,	,	PUNCT
ejpam-5385	267	4	1	1	NUM
ejpam-5385	267	5	]	]	PUNCT
ejpam-5385	267	6	and	and	CCONJ
ejpam-5385	267	7	β	β	X
ejpam-5385	267	8	,	,	PUNCT
ejpam-5385	267	9	β̂	β̂	ADP
ejpam-5385	267	10	∈	∈	PROPN
ejpam-5385	268	1	[	[	X
ejpam-5385	268	2	0	0	NUM
ejpam-5385	268	3	,	,	PUNCT
ejpam-5385	268	4	2π	2π	NOUN
ejpam-5385	268	5	]	]	PUNCT
ejpam-5385	268	6	,	,	PUNCT
ejpam-5385	268	7	the	the	DET
ejpam-5385	268	8	set	set	NOUN
ejpam-5385	268	9	e(α̂,β̂	e(α̂,β̂	NOUN
ejpam-5385	268	10	)	)	PUNCT
ejpam-5385	268	11	(	(	PUNCT
ejpam-5385	268	12	α	α	X
ejpam-5385	268	13	,	,	PUNCT
ejpam-5385	268	14	β	β	NOUN
ejpam-5385	268	15	)	)	PUNCT
ejpam-5385	268	16	=	=	SYM
ejpam-5385	268	17	{	{	PUNCT
ejpam-5385	268	18	x	x	X
ejpam-5385	268	19	:	:	PUNCT
ejpam-5385	268	20	ρe(x	ρe(x	NUM
ejpam-5385	268	21	)	)	PUNCT
ejpam-5385	268	22	≥	≥	NUM
ejpam-5385	268	23	α	α	NOUN
ejpam-5385	268	24	,	,	PUNCT
ejpam-5385	268	25	ζe(x	ζe(x	NUM
ejpam-5385	268	26	)	)	PUNCT
ejpam-5385	268	27	≥	≥	NOUN
ejpam-5385	268	28	β	β	X
ejpam-5385	268	29	,	,	PUNCT
ejpam-5385	268	30	ρ̂e(x	ρ̂e(x	PROPN
ejpam-5385	268	31	)	)	PUNCT
ejpam-5385	268	32	≤	≤	NOUN
ejpam-5385	268	33	α̂	α̂	NOUN
ejpam-5385	268	34	,	,	PUNCT
ejpam-5385	268	35	ζ̂e(x	ζ̂e(x	PROPN
ejpam-5385	268	36	)	)	PUNCT
ejpam-5385	268	37	≤	≤	NOUN
ejpam-5385	268	38	β̂	β̂	ADP
ejpam-5385	268	39	}	}	PUNCT
ejpam-5385	268	40	is	be	AUX
ejpam-5385	268	41	called	call	VERB
ejpam-5385	268	42	the	the	DET
ejpam-5385	268	43	upper	upper	ADJ
ejpam-5385	268	44	level	level	NOUN
ejpam-5385	268	45	subset	subset	NOUN
ejpam-5385	268	46	of	of	ADP
ejpam-5385	268	47	the	the	DET
ejpam-5385	268	48	complex	complex	ADJ
ejpam-5385	268	49	intuitionistic	intuitionistic	ADJ
ejpam-5385	268	50	fuzzy	fuzzy	ADJ
ejpam-5385	268	51	subset	subset	NOUN
ejpam-5385	268	52	e	e	NOUN
ejpam-5385	268	53	.	.	PUNCT
ejpam-5385	269	1	the	the	DET
ejpam-5385	269	2	subsets	subset	NOUN
ejpam-5385	269	3	e(α̂<,β̂	e(α̂<,β̂	NUM
ejpam-5385	269	4	)	)	PUNCT
ejpam-5385	269	5	(	(	PUNCT
ejpam-5385	269	6	α>,β	α>,β	NOUN
ejpam-5385	269	7	)	)	PUNCT
ejpam-5385	269	8	=	=	PRON
ejpam-5385	269	9	{	{	PUNCT
ejpam-5385	269	10	x	x	X
ejpam-5385	269	11	:	:	PUNCT
ejpam-5385	269	12	ρe(x	ρe(x	NUM
ejpam-5385	269	13	)	)	PUNCT
ejpam-5385	269	14	>	>	X
ejpam-5385	270	1	α	α	X
ejpam-5385	270	2	,	,	PUNCT
ejpam-5385	270	3	ζe(x	ζe(x	NUM
ejpam-5385	270	4	)	)	PUNCT
ejpam-5385	270	5	≥	≥	NOUN
ejpam-5385	270	6	β	β	X
ejpam-5385	270	7	,	,	PUNCT
ejpam-5385	270	8	ρ̂e(x	ρ̂e(x	PROPN
ejpam-5385	270	9	)	)	PUNCT
ejpam-5385	270	10	<	<	X
ejpam-5385	270	11	α̂	α̂	NOUN
ejpam-5385	270	12	,	,	PUNCT
ejpam-5385	270	13	ζ̂e(x	ζ̂e(x	PROPN
ejpam-5385	270	14	)	)	PUNCT
ejpam-5385	270	15	≤	≤	NOUN
ejpam-5385	270	16	β̂	β̂	ADP
ejpam-5385	270	17	}	}	PUNCT
ejpam-5385	270	18	,	,	PUNCT
ejpam-5385	270	19	e(α̂,β̂	e(α̂,β̂	NOUN
ejpam-5385	270	20	<	<	X
ejpam-5385	270	21	)	)	PUNCT
ejpam-5385	270	22	(	(	PUNCT
ejpam-5385	270	23	α	α	X
ejpam-5385	270	24	,	,	PUNCT
ejpam-5385	270	25	β	β	NOUN
ejpam-5385	270	26	>	>	X
ejpam-5385	270	27	)	)	PUNCT
ejpam-5385	270	28	=	=	PRON
ejpam-5385	270	29	{	{	PUNCT
ejpam-5385	270	30	x	x	X
ejpam-5385	270	31	:	:	PUNCT
ejpam-5385	270	32	ρe(x	ρe(x	NUM
ejpam-5385	270	33	)	)	PUNCT
ejpam-5385	270	34	≥	≥	NUM
ejpam-5385	270	35	α	α	NOUN
ejpam-5385	270	36	,	,	PUNCT
ejpam-5385	270	37	ζe(x	ζe(x	NUM
ejpam-5385	270	38	)	)	PUNCT
ejpam-5385	270	39	>	>	X
ejpam-5385	271	1	β	β	X
ejpam-5385	271	2	,	,	PUNCT
ejpam-5385	271	3	ρ̂e(x	ρ̂e(x	PROPN
ejpam-5385	271	4	)	)	PUNCT
ejpam-5385	271	5	≤	≤	NOUN
ejpam-5385	271	6	α̂	α̂	NOUN
ejpam-5385	271	7	,	,	PUNCT
ejpam-5385	271	8	ζ̂e(x	ζ̂e(x	PROPN
ejpam-5385	271	9	)	)	PUNCT
ejpam-5385	271	10	<	<	X
ejpam-5385	271	11	β̂	β̂	ADP
ejpam-5385	271	12	}	}	PUNCT
ejpam-5385	271	13	,	,	PUNCT
ejpam-5385	271	14	and	and	CCONJ
ejpam-5385	271	15	e(α̂<,β̂	e(α̂<,β̂	NOUN
ejpam-5385	271	16	<	<	X
ejpam-5385	271	17	)	)	PUNCT
ejpam-5385	271	18	(	(	PUNCT
ejpam-5385	271	19	α>,β	α>,β	NOUN
ejpam-5385	271	20	>	>	X
ejpam-5385	271	21	)	)	PUNCT
ejpam-5385	271	22	=	=	PRON
ejpam-5385	271	23	{	{	PUNCT
ejpam-5385	271	24	x	x	X
ejpam-5385	271	25	:	:	PUNCT
ejpam-5385	271	26	ρe(x	ρe(x	NUM
ejpam-5385	271	27	)	)	PUNCT
ejpam-5385	271	28	>	>	X
ejpam-5385	272	1	α	α	X
ejpam-5385	272	2	,	,	PUNCT
ejpam-5385	272	3	ζe(x	ζe(x	NUM
ejpam-5385	272	4	)	)	PUNCT
ejpam-5385	272	5	>	>	X
ejpam-5385	272	6	β	β	X
ejpam-5385	272	7	,	,	PUNCT
ejpam-5385	272	8	ρ̂e(x	ρ̂e(x	PROPN
ejpam-5385	272	9	)	)	PUNCT
ejpam-5385	272	10	<	<	X
ejpam-5385	272	11	α̂	α̂	NOUN
ejpam-5385	272	12	,	,	PUNCT
ejpam-5385	272	13	ζ̂e(x	ζ̂e(x	PROPN
ejpam-5385	272	14	)	)	PUNCT
ejpam-5385	272	15	<	<	X
ejpam-5385	272	16	β̂	β̂	X
ejpam-5385	272	17	}	}	PUNCT
ejpam-5385	272	18	are	be	AUX
ejpam-5385	272	19	called	call	VERB
ejpam-5385	272	20	strong	strong	ADJ
ejpam-5385	272	21	upper	upper	ADJ
ejpam-5385	272	22	level	level	NOUN
ejpam-5385	272	23	subsets	subset	NOUN
ejpam-5385	272	24	of	of	ADP
ejpam-5385	272	25	the	the	DET
ejpam-5385	272	26	complex	complex	ADJ
ejpam-5385	272	27	intuitionistic	intuitionistic	ADJ
ejpam-5385	272	28	fuzzy	fuzzy	ADJ
ejpam-5385	272	29	subset	subset	NOUN
ejpam-5385	272	30	a.	a.	NOUN
ejpam-5385	272	31	the	the	DET
ejpam-5385	272	32	following	follow	VERB
ejpam-5385	272	33	theorem	theorem	NOUN
ejpam-5385	272	34	was	be	AUX
ejpam-5385	272	35	obtained	obtain	VERB
ejpam-5385	272	36	by	by	ADP
ejpam-5385	272	37	s.	s.	PROPN
ejpam-5385	272	38	shaqaqha	shaqaqha	PROPN
ejpam-5385	272	39	in	in	ADP
ejpam-5385	272	40	the	the	DET
ejpam-5385	272	41	setting	setting	NOUN
ejpam-5385	272	42	of	of	ADP
ejpam-5385	272	43	complex	complex	ADJ
ejpam-5385	272	44	fuzzy	fuzzy	ADJ
ejpam-5385	272	45	lie	lie	NOUN
ejpam-5385	272	46	subalgebras	subalgebras	PROPN
ejpam-5385	273	1	[	[	X
ejpam-5385	273	2	13	13	NUM
ejpam-5385	273	3	]	]	PUNCT
ejpam-5385	273	4	.	.	PUNCT
ejpam-5385	274	1	we	we	PRON
ejpam-5385	274	2	extend	extend	VERB
ejpam-5385	274	3	it	it	PRON
ejpam-5385	274	4	to	to	ADP
ejpam-5385	274	5	the	the	DET
ejpam-5385	274	6	case	case	NOUN
ejpam-5385	274	7	of	of	ADP
ejpam-5385	274	8	complex	complex	ADJ
ejpam-5385	274	9	intuitionistic	intuitionistic	ADJ
ejpam-5385	274	10	fuzzy	fuzzy	ADJ
ejpam-5385	274	11	lie	lie	NOUN
ejpam-5385	274	12	subalgebras	subalgebras	PROPN
ejpam-5385	274	13	.	.	PUNCT
ejpam-5385	275	1	theorem	theorem	ADJ
ejpam-5385	275	2	5	5	NUM
ejpam-5385	275	3	.	.	PUNCT
ejpam-5385	276	1	let	let	VERB
ejpam-5385	276	2	f	f	NOUN
ejpam-5385	276	3	:	:	PUNCT
ejpam-5385	276	4	m1	m1	PROPN
ejpam-5385	276	5	→	→	SYM
ejpam-5385	276	6	m2	m2	PROPN
ejpam-5385	276	7	be	be	AUX
ejpam-5385	276	8	a	a	DET
ejpam-5385	276	9	lie	lie	NOUN
ejpam-5385	276	10	algebra	algebra	NOUN
ejpam-5385	276	11	homomorphism	homomorphism	NOUN
ejpam-5385	276	12	.	.	PUNCT
ejpam-5385	277	1	if	if	SCONJ
ejpam-5385	277	2	p	p	NOUN
ejpam-5385	277	3	=	=	X
ejpam-5385	277	4	(	(	PUNCT
ejpam-5385	277	5	ϕp	ϕp	INTJ
ejpam-5385	277	6	,	,	PUNCT
ejpam-5385	277	7	ψp	ψp	PROPN
ejpam-5385	277	8	)	)	PUNCT
ejpam-5385	277	9	is	be	AUX
ejpam-5385	277	10	a	a	DET
ejpam-5385	277	11	complex	complex	ADJ
ejpam-5385	277	12	intuitionistic	intuitionistic	ADJ
ejpam-5385	277	13	fuzzy	fuzzy	ADJ
ejpam-5385	277	14	set	set	NOUN
ejpam-5385	277	15	of	of	ADP
ejpam-5385	277	16	m2	m2	PROPN
ejpam-5385	277	17	.	.	PROPN
ejpam-5385	278	1	for	for	ADP
ejpam-5385	278	2	α	α	NUM
ejpam-5385	278	3	,	,	PUNCT
ejpam-5385	278	4	α̂	α̂	NUM
ejpam-5385	278	5	∈	∈	PROPN
ejpam-5385	279	1	[	[	X
ejpam-5385	279	2	0	0	NUM
ejpam-5385	279	3	,	,	PUNCT
ejpam-5385	279	4	1	1	NUM
ejpam-5385	279	5	]	]	PUNCT
ejpam-5385	279	6	and	and	CCONJ
ejpam-5385	279	7	β	β	X
ejpam-5385	279	8	,	,	PUNCT
ejpam-5385	279	9	β̂	β̂	ADP
ejpam-5385	279	10	∈	∈	PROPN
ejpam-5385	280	1	[	[	X
ejpam-5385	280	2	0	0	NUM
ejpam-5385	280	3	,	,	PUNCT
ejpam-5385	280	4	2π	2π	NOUN
ejpam-5385	280	5	]	]	PUNCT
ejpam-5385	280	6	,	,	PUNCT
ejpam-5385	280	7	we	we	PRON
ejpam-5385	280	8	have	have	VERB
ejpam-5385	280	9	(	(	PUNCT
ejpam-5385	280	10	i	i	NOUN
ejpam-5385	280	11	)	)	PUNCT
ejpam-5385	280	12	f−1	f−1	PROPN
ejpam-5385	280	13	(	(	PUNCT
ejpam-5385	280	14	p(α̂,β̂	p(α̂,β̂	PROPN
ejpam-5385	280	15	)	)	PUNCT
ejpam-5385	280	16	(	(	PUNCT
ejpam-5385	280	17	α	α	X
ejpam-5385	280	18	,	,	PUNCT
ejpam-5385	280	19	β	β	NOUN
ejpam-5385	280	20	)	)	PUNCT
ejpam-5385	280	21	)	)	PUNCT
ejpam-5385	281	1	=	=	PRON
ejpam-5385	281	2	(	(	PUNCT
ejpam-5385	281	3	f−1(p	f−1(p	PROPN
ejpam-5385	281	4	)	)	PUNCT
ejpam-5385	281	5	)	)	PUNCT
ejpam-5385	281	6	(	(	PUNCT
ejpam-5385	281	7	α̂,β̂	α̂,β̂	NOUN
ejpam-5385	281	8	)	)	PUNCT
ejpam-5385	281	9	(	(	PUNCT
ejpam-5385	281	10	α	α	X
ejpam-5385	281	11	,	,	PUNCT
ejpam-5385	281	12	β	β	NOUN
ejpam-5385	281	13	)	)	PUNCT
ejpam-5385	281	14	,	,	PUNCT
ejpam-5385	281	15	(	(	PUNCT
ejpam-5385	281	16	ii	ii	NOUN
ejpam-5385	281	17	)	)	PUNCT
ejpam-5385	281	18	f−1	f−1	PROPN
ejpam-5385	281	19	(	(	PUNCT
ejpam-5385	281	20	p(α̂<,β̂	p(α̂<,β̂	NUM
ejpam-5385	281	21	)	)	PUNCT
ejpam-5385	281	22	(	(	PUNCT
ejpam-5385	281	23	α>,β	α>,β	NOUN
ejpam-5385	281	24	)	)	PUNCT
ejpam-5385	281	25	)	)	PUNCT
ejpam-5385	281	26	=	=	SYM
ejpam-5385	281	27	(	(	PUNCT
ejpam-5385	281	28	f−1(p	f−1(p	PROPN
ejpam-5385	281	29	)	)	PUNCT
ejpam-5385	281	30	)	)	PUNCT
ejpam-5385	281	31	(	(	PUNCT
ejpam-5385	281	32	α̂<,β̂	α̂<,β̂	PROPN
ejpam-5385	281	33	)	)	PUNCT
ejpam-5385	281	34	(	(	PUNCT
ejpam-5385	281	35	α>,β	α>,β	NOUN
ejpam-5385	281	36	)	)	PUNCT
ejpam-5385	281	37	,	,	PUNCT
ejpam-5385	281	38	(	(	PUNCT
ejpam-5385	281	39	iii	iii	X
ejpam-5385	281	40	)	)	PUNCT
ejpam-5385	281	41	f−1	f−1	PROPN
ejpam-5385	281	42	(	(	PUNCT
ejpam-5385	281	43	p(α̂,β̂	p(α̂,β̂	PROPN
ejpam-5385	281	44	<	<	X
ejpam-5385	281	45	)	)	PUNCT
ejpam-5385	281	46	(	(	PUNCT
ejpam-5385	281	47	α	α	X
ejpam-5385	281	48	,	,	PUNCT
ejpam-5385	281	49	β	β	NOUN
ejpam-5385	281	50	>	>	NOUN
ejpam-5385	281	51	)	)	PUNCT
ejpam-5385	281	52	)	)	PUNCT
ejpam-5385	282	1	=	=	PRON
ejpam-5385	282	2	(	(	PUNCT
ejpam-5385	282	3	f−1(p	f−1(p	PROPN
ejpam-5385	282	4	)	)	PUNCT
ejpam-5385	282	5	)	)	PUNCT
ejpam-5385	282	6	(	(	PUNCT
ejpam-5385	282	7	α̂,β̂	α̂,β̂	NOUN
ejpam-5385	282	8	<	<	X
ejpam-5385	282	9	)	)	PUNCT
ejpam-5385	282	10	(	(	PUNCT
ejpam-5385	282	11	α	α	X
ejpam-5385	282	12	,	,	PUNCT
ejpam-5385	282	13	β	β	NOUN
ejpam-5385	282	14	>	>	NOUN
ejpam-5385	282	15	)	)	PUNCT
ejpam-5385	282	16	,	,	PUNCT
ejpam-5385	282	17	(	(	PUNCT
ejpam-5385	282	18	iv	iv	X
ejpam-5385	282	19	)	)	PUNCT
ejpam-5385	282	20	f−1	f−1	PROPN
ejpam-5385	282	21	(	(	PUNCT
ejpam-5385	282	22	p(α̂<,β̂	p(α̂<,β̂	X
ejpam-5385	282	23	<	<	X
ejpam-5385	282	24	)	)	PUNCT
ejpam-5385	282	25	(	(	PUNCT
ejpam-5385	282	26	α>,β	α>,β	NOUN
ejpam-5385	282	27	>	>	X
ejpam-5385	282	28	)	)	PUNCT
ejpam-5385	282	29	)	)	PUNCT
ejpam-5385	283	1	=	=	PRON
ejpam-5385	284	1	(	(	PUNCT
ejpam-5385	284	2	f−1(p	f−1(p	PROPN
ejpam-5385	284	3	)	)	PUNCT
ejpam-5385	284	4	)	)	PUNCT
ejpam-5385	285	1	(	(	PUNCT
ejpam-5385	285	2	α̂<,β̂	α̂<,β̂	PROPN
ejpam-5385	285	3	<	<	X
ejpam-5385	285	4	)	)	PUNCT
ejpam-5385	285	5	(	(	PUNCT
ejpam-5385	285	6	α>,β	α>,β	NOUN
ejpam-5385	285	7	>	>	X
ejpam-5385	285	8	)	)	PUNCT
ejpam-5385	285	9	.	.	PUNCT
ejpam-5385	286	1	proof	proof	NOUN
ejpam-5385	286	2	.	.	PUNCT
ejpam-5385	287	1	(	(	PUNCT
ejpam-5385	287	2	i	i	NOUN
ejpam-5385	287	3	)	)	PUNCT
ejpam-5385	287	4	m	m	VERB
ejpam-5385	287	5	∈	∈	PROPN
ejpam-5385	287	6	f−1	f−1	PROPN
ejpam-5385	287	7	(	(	PUNCT
ejpam-5385	287	8	p(α̂,β̂	p(α̂,β̂	PROPN
ejpam-5385	287	9	)	)	PUNCT
ejpam-5385	287	10	(	(	PUNCT
ejpam-5385	287	11	α	α	X
ejpam-5385	287	12	,	,	PUNCT
ejpam-5385	287	13	β	β	NOUN
ejpam-5385	287	14	)	)	PUNCT
ejpam-5385	287	15	)	)	PUNCT
ejpam-5385	288	1	if	if	SCONJ
ejpam-5385	288	2	and	and	CCONJ
ejpam-5385	288	3	only	only	ADV
ejpam-5385	288	4	if	if	SCONJ
ejpam-5385	288	5	f(m	f(m	PROPN
ejpam-5385	288	6	)	)	PUNCT
ejpam-5385	288	7	∈	∈	PROPN
ejpam-5385	288	8	p(α̂,β̂	p(α̂,β̂	PROPN
ejpam-5385	288	9	)	)	PUNCT
ejpam-5385	288	10	(	(	PUNCT
ejpam-5385	288	11	α	α	X
ejpam-5385	288	12	,	,	PUNCT
ejpam-5385	288	13	β	β	NOUN
ejpam-5385	288	14	)	)	PUNCT
ejpam-5385	288	15	if	if	SCONJ
ejpam-5385	288	16	and	and	CCONJ
ejpam-5385	288	17	only	only	ADV
ejpam-5385	288	18	if	if	SCONJ
ejpam-5385	288	19	ϕp(f(m	ϕp(f(m	NOUN
ejpam-5385	288	20	)	)	PUNCT
ejpam-5385	288	21	)	)	PUNCT
ejpam-5385	289	1	=	=	SYM
ejpam-5385	289	2	ϕf−1(p)(m	ϕf−1(p)(m	X
ejpam-5385	289	3	)	)	PUNCT
ejpam-5385	289	4	≥	≥	NOUN
ejpam-5385	289	5	αeiβ	αeiβ	NOUN
ejpam-5385	289	6	and	and	CCONJ
ejpam-5385	289	7	ψp(f(m	ψp(f(m	NOUN
ejpam-5385	289	8	)	)	PUNCT
ejpam-5385	289	9	)	)	PUNCT
ejpam-5385	290	1	=	=	SYM
ejpam-5385	290	2	ψf−1(p)(m	ψf−1(p)(m	X
ejpam-5385	290	3	)	)	PUNCT
ejpam-5385	290	4	≤	≤	NOUN
ejpam-5385	290	5	α̂eiβ̂	α̂eiβ̂	NOUN
ejpam-5385	290	6	if	if	SCONJ
ejpam-5385	291	1	and	and	CCONJ
ejpam-5385	291	2	only	only	ADV
ejpam-5385	291	3	if	if	SCONJ
ejpam-5385	291	4	m	m	VERB
ejpam-5385	291	5	∈	∈	NOUN
ejpam-5385	291	6	(	(	PUNCT
ejpam-5385	291	7	f−1(p	f−1(p	PROPN
ejpam-5385	291	8	)	)	PUNCT
ejpam-5385	291	9	)	)	PUNCT
ejpam-5385	291	10	(	(	PUNCT
ejpam-5385	291	11	α̂,β̂	α̂,β̂	NOUN
ejpam-5385	291	12	)	)	PUNCT
ejpam-5385	291	13	(	(	PUNCT
ejpam-5385	291	14	α	α	X
ejpam-5385	291	15	,	,	PUNCT
ejpam-5385	291	16	β	β	NOUN
ejpam-5385	291	17	)	)	PUNCT
ejpam-5385	291	18	.	.	PUNCT
ejpam-5385	292	1	the	the	DET
ejpam-5385	292	2	proofs	proof	NOUN
ejpam-5385	292	3	of	of	ADP
ejpam-5385	292	4	(	(	PUNCT
ejpam-5385	292	5	ii	ii	NOUN
ejpam-5385	292	6	)	)	PUNCT
ejpam-5385	292	7	,	,	PUNCT
ejpam-5385	292	8	(	(	PUNCT
ejpam-5385	292	9	iii	iii	NOUN
ejpam-5385	292	10	)	)	PUNCT
ejpam-5385	292	11	and	and	CCONJ
ejpam-5385	292	12	(	(	PUNCT
ejpam-5385	292	13	iv	iv	X
ejpam-5385	292	14	)	)	PUNCT
ejpam-5385	292	15	are	be	AUX
ejpam-5385	292	16	same	same	ADJ
ejpam-5385	292	17	.	.	PUNCT
ejpam-5385	293	1	references	reference	NOUN
ejpam-5385	293	2	3302	3302	NUM
ejpam-5385	293	3	5	5	NUM
ejpam-5385	293	4	.	.	PUNCT
ejpam-5385	293	5	conclusions	conclusion	NOUN
ejpam-5385	293	6	in	in	ADP
ejpam-5385	293	7	this	this	DET
ejpam-5385	293	8	paper	paper	NOUN
ejpam-5385	293	9	,	,	PUNCT
ejpam-5385	293	10	we	we	PRON
ejpam-5385	293	11	explored	explore	VERB
ejpam-5385	293	12	the	the	DET
ejpam-5385	293	13	interaction	interaction	NOUN
ejpam-5385	293	14	between	between	ADP
ejpam-5385	293	15	complex	complex	ADJ
ejpam-5385	293	16	intuitionistic	intuitionistic	ADJ
ejpam-5385	293	17	fuzzy	fuzzy	ADJ
ejpam-5385	293	18	sets	set	NOUN
ejpam-5385	293	19	and	and	CCONJ
ejpam-5385	293	20	lie	lie	VERB
ejpam-5385	293	21	algebra	algebra	NOUN
ejpam-5385	293	22	homomorphisms	homomorphism	NOUN
ejpam-5385	293	23	,	,	PUNCT
ejpam-5385	293	24	deriving	derive	VERB
ejpam-5385	293	25	several	several	ADJ
ejpam-5385	293	26	significant	significant	ADJ
ejpam-5385	293	27	results	result	NOUN
ejpam-5385	293	28	.	.	PUNCT
ejpam-5385	294	1	we	we	PRON
ejpam-5385	294	2	showed	show	VERB
ejpam-5385	294	3	that	that	SCONJ
ejpam-5385	294	4	the	the	DET
ejpam-5385	294	5	images	image	NOUN
ejpam-5385	294	6	and	and	CCONJ
ejpam-5385	294	7	preimages	preimage	NOUN
ejpam-5385	294	8	of	of	ADP
ejpam-5385	294	9	complex	complex	ADJ
ejpam-5385	294	10	intuitionistic	intuitionistic	ADJ
ejpam-5385	294	11	fuzzy	fuzzy	ADJ
ejpam-5385	294	12	lie	lie	NOUN
ejpam-5385	294	13	subalgebras	subalgebra	NOUN
ejpam-5385	294	14	and	and	CCONJ
ejpam-5385	294	15	ideals	ideal	NOUN
ejpam-5385	294	16	under	under	ADP
ejpam-5385	294	17	homomorphisms	homomorphism	NOUN
ejpam-5385	294	18	maintain	maintain	VERB
ejpam-5385	294	19	their	their	PRON
ejpam-5385	294	20	structural	structural	ADJ
ejpam-5385	294	21	properties	property	NOUN
ejpam-5385	294	22	,	,	PUNCT
ejpam-5385	294	23	extending	extend	VERB
ejpam-5385	294	24	known	know	VERB
ejpam-5385	294	25	results	result	NOUN
ejpam-5385	294	26	in	in	ADP
ejpam-5385	294	27	fuzzy	fuzzy	ADJ
ejpam-5385	294	28	and	and	CCONJ
ejpam-5385	294	29	intuitionistic	intuitionistic	ADJ
ejpam-5385	294	30	fuzzy	fuzzy	ADJ
ejpam-5385	294	31	algebra	algebra	NOUN
ejpam-5385	294	32	to	to	ADP
ejpam-5385	294	33	the	the	DET
ejpam-5385	294	34	complex	complex	ADJ
ejpam-5385	294	35	intuitionistic	intuitionistic	ADJ
ejpam-5385	294	36	fuzzy	fuzzy	ADJ
ejpam-5385	294	37	setting	setting	NOUN
ejpam-5385	294	38	.	.	PUNCT
ejpam-5385	295	1	the	the	DET
ejpam-5385	295	2	method	method	NOUN
ejpam-5385	295	3	used	use	VERB
ejpam-5385	295	4	focused	focus	VERB
ejpam-5385	295	5	on	on	ADP
ejpam-5385	295	6	analyzing	analyze	VERB
ejpam-5385	295	7	the	the	DET
ejpam-5385	295	8	effects	effect	NOUN
ejpam-5385	295	9	of	of	ADP
ejpam-5385	295	10	homomorphisms	homomorphism	NOUN
ejpam-5385	295	11	on	on	ADP
ejpam-5385	295	12	membership	membership	NOUN
ejpam-5385	295	13	and	and	CCONJ
ejpam-5385	295	14	non	non	ADJ
ejpam-5385	295	15	-	-	ADJ
ejpam-5385	295	16	membership	membership	ADJ
ejpam-5385	295	17	functions	function	NOUN
ejpam-5385	295	18	,	,	PUNCT
ejpam-5385	295	19	providing	provide	VERB
ejpam-5385	295	20	a	a	DET
ejpam-5385	295	21	deeper	deep	ADJ
ejpam-5385	295	22	understanding	understanding	NOUN
ejpam-5385	295	23	of	of	ADP
ejpam-5385	295	24	the	the	DET
ejpam-5385	295	25	preservation	preservation	NOUN
ejpam-5385	295	26	of	of	ADP
ejpam-5385	295	27	these	these	DET
ejpam-5385	295	28	fuzzy	fuzzy	ADJ
ejpam-5385	295	29	structures	structure	NOUN
ejpam-5385	295	30	.	.	PUNCT
ejpam-5385	296	1	our	our	PRON
ejpam-5385	296	2	results	result	NOUN
ejpam-5385	296	3	generalize	generalize	VERB
ejpam-5385	296	4	existing	exist	VERB
ejpam-5385	296	5	findings	finding	NOUN
ejpam-5385	296	6	on	on	ADP
ejpam-5385	296	7	fuzzy	fuzzy	ADJ
ejpam-5385	296	8	lie	lie	NOUN
ejpam-5385	296	9	algebras	algebra	NOUN
ejpam-5385	296	10	[	[	X
ejpam-5385	296	11	21	21	NUM
ejpam-5385	296	12	]	]	PUNCT
ejpam-5385	296	13	,	,	PUNCT
ejpam-5385	296	14	intuitionistic	intuitionistic	ADJ
ejpam-5385	296	15	fuzzy	fuzzy	ADJ
ejpam-5385	296	16	lie	lie	NOUN
ejpam-5385	296	17	algebras	algebra	NOUN
ejpam-5385	297	1	[	[	X
ejpam-5385	297	2	1	1	NUM
ejpam-5385	297	3	]	]	PUNCT
ejpam-5385	297	4	,	,	PUNCT
ejpam-5385	297	5	and	and	CCONJ
ejpam-5385	297	6	complex	complex	ADJ
ejpam-5385	297	7	fuzzy	fuzzy	ADJ
ejpam-5385	297	8	lie	lie	NOUN
ejpam-5385	297	9	algebras	algebra	NOUN
ejpam-5385	298	1	[	[	X
ejpam-5385	298	2	13	13	NUM
ejpam-5385	298	3	]	]	PUNCT
ejpam-5385	298	4	,	,	PUNCT
ejpam-5385	298	5	offering	offer	VERB
ejpam-5385	298	6	new	new	ADJ
ejpam-5385	298	7	insights	insight	NOUN
ejpam-5385	298	8	into	into	ADP
ejpam-5385	298	9	their	their	PRON
ejpam-5385	298	10	behavior	behavior	NOUN
ejpam-5385	298	11	in	in	ADP
ejpam-5385	298	12	more	more	ADV
ejpam-5385	298	13	expressive	expressive	ADJ
ejpam-5385	298	14	contexts	contexts	NOUN
ejpam-5385	298	15	.	.	PUNCT
ejpam-5385	299	1	these	these	DET
ejpam-5385	299	2	findings	finding	NOUN
ejpam-5385	299	3	pave	pave	VERB
ejpam-5385	299	4	the	the	DET
ejpam-5385	299	5	way	way	NOUN
ejpam-5385	299	6	for	for	ADP
ejpam-5385	299	7	further	further	ADJ
ejpam-5385	299	8	research	research	NOUN
ejpam-5385	299	9	,	,	PUNCT
ejpam-5385	299	10	including	include	VERB
ejpam-5385	299	11	extensions	extension	NOUN
ejpam-5385	299	12	to	to	ADP
ejpam-5385	299	13	gamma	gamma	PROPN
ejpam-5385	299	14	rings	ring	NOUN
ejpam-5385	299	15	[	[	X
ejpam-5385	299	16	14	14	NUM
ejpam-5385	299	17	,	,	PUNCT
ejpam-5385	299	18	15	15	NUM
ejpam-5385	299	19	]	]	PUNCT
ejpam-5385	299	20	,	,	PUNCT
ejpam-5385	299	21	n	n	CCONJ
ejpam-5385	299	22	-	-	PUNCT
ejpam-5385	299	23	lie	lie	NOUN
ejpam-5385	299	24	algebras	algebra	NOUN
ejpam-5385	300	1	[	[	X
ejpam-5385	300	2	16	16	NUM
ejpam-5385	300	3	]	]	PUNCT
ejpam-5385	300	4	,	,	PUNCT
ejpam-5385	300	5	and	and	CCONJ
ejpam-5385	300	6	hom	hom	X
ejpam-5385	300	7	-	-	PUNCT
ejpam-5385	300	8	lie	lie	NOUN
ejpam-5385	300	9	algebras	algebra	NOUN
ejpam-5385	300	10	[	[	X
ejpam-5385	300	11	17	17	NUM
ejpam-5385	300	12	]	]	PUNCT
ejpam-5385	300	13	.	.	PUNCT
ejpam-5385	301	1	additionally	additionally	ADV
ejpam-5385	301	2	,	,	PUNCT
ejpam-5385	301	3	investigating	investigate	VERB
ejpam-5385	301	4	the	the	DET
ejpam-5385	301	5	application	application	NOUN
ejpam-5385	301	6	of	of	ADP
ejpam-5385	301	7	these	these	DET
ejpam-5385	301	8	methods	method	NOUN
ejpam-5385	301	9	to	to	PART
ejpam-5385	301	10	complex	complex	ADJ
ejpam-5385	301	11	pythagorean	pythagorean	PROPN
ejpam-5385	301	12	lie	lie	NOUN
ejpam-5385	301	13	algebras	algebra	NOUN
ejpam-5385	302	1	[	[	X
ejpam-5385	302	2	19	19	NUM
ejpam-5385	302	3	,	,	PUNCT
ejpam-5385	302	4	20	20	NUM
ejpam-5385	302	5	]	]	PUNCT
ejpam-5385	302	6	could	could	AUX
ejpam-5385	302	7	reveal	reveal	VERB
ejpam-5385	302	8	new	new	ADJ
ejpam-5385	302	9	structural	structural	ADJ
ejpam-5385	302	10	insights	insight	NOUN
ejpam-5385	302	11	.	.	PUNCT
ejpam-5385	303	1	acknowledgements	acknowledgement	NOUN
ejpam-5385	303	2	this	this	DET
ejpam-5385	303	3	manuscript	manuscript	NOUN
ejpam-5385	303	4	builds	build	VERB
ejpam-5385	303	5	upon	upon	SCONJ
ejpam-5385	303	6	the	the	DET
ejpam-5385	303	7	thesis	thesis	NOUN
ejpam-5385	303	8	work	work	NOUN
ejpam-5385	303	9	of	of	ADP
ejpam-5385	303	10	mounther	mounth	ADJ
ejpam-5385	303	11	al	al	PROPN
ejpam-5385	303	12	-	-	PUNCT
ejpam-5385	303	13	deiakeh	deiakeh	NOUN
ejpam-5385	304	1	[	[	X
ejpam-5385	304	2	4	4	NUM
ejpam-5385	304	3	]	]	PUNCT
ejpam-5385	304	4	,	,	PUNCT
ejpam-5385	304	5	whose	whose	DET
ejpam-5385	304	6	research	research	NOUN
ejpam-5385	304	7	significantly	significantly	ADV
ejpam-5385	304	8	contributed	contribute	VERB
ejpam-5385	304	9	to	to	ADP
ejpam-5385	304	10	the	the	DET
ejpam-5385	304	11	development	development	NOUN
ejpam-5385	304	12	of	of	ADP
ejpam-5385	304	13	the	the	DET
ejpam-5385	304	14	techniques	technique	NOUN
ejpam-5385	304	15	and	and	CCONJ
ejpam-5385	304	16	results	result	NOUN
ejpam-5385	304	17	presented	present	VERB
ejpam-5385	304	18	here	here	ADV
ejpam-5385	304	19	.	.	PUNCT
ejpam-5385	305	1	his	his	PRON
ejpam-5385	305	2	foundational	foundational	ADJ
ejpam-5385	305	3	work	work	NOUN
ejpam-5385	305	4	laid	lay	VERB
ejpam-5385	305	5	the	the	DET
ejpam-5385	305	6	groundwork	groundwork	NOUN
ejpam-5385	305	7	for	for	ADP
ejpam-5385	305	8	the	the	DET
ejpam-5385	305	9	ideas	idea	NOUN
ejpam-5385	305	10	and	and	CCONJ
ejpam-5385	305	11	methodologies	methodology	NOUN
ejpam-5385	305	12	explored	explore	VERB
ejpam-5385	305	13	in	in	ADP
ejpam-5385	305	14	this	this	DET
ejpam-5385	305	15	paper	paper	NOUN
ejpam-5385	305	16	,	,	PUNCT
ejpam-5385	305	17	and	and	CCONJ
ejpam-5385	305	18	his	his	PRON
ejpam-5385	305	19	contributions	contribution	NOUN
ejpam-5385	305	20	are	be	AUX
ejpam-5385	305	21	gratefully	gratefully	ADV
ejpam-5385	305	22	acknowledged	acknowledge	VERB
ejpam-5385	305	23	.	.	PUNCT
ejpam-5385	306	1	the	the	DET
ejpam-5385	306	2	authors	author	NOUN
ejpam-5385	306	3	would	would	AUX
ejpam-5385	306	4	also	also	ADV
ejpam-5385	306	5	like	like	VERB
ejpam-5385	306	6	to	to	PART
ejpam-5385	306	7	express	express	VERB
ejpam-5385	306	8	gratitude	gratitude	NOUN
ejpam-5385	306	9	to	to	ADP
ejpam-5385	306	10	the	the	DET
ejpam-5385	306	11	anonymous	anonymous	ADJ
ejpam-5385	306	12	reviewers	reviewer	NOUN
ejpam-5385	306	13	for	for	ADP
ejpam-5385	306	14	their	their	PRON
ejpam-5385	306	15	valuable	valuable	ADJ
ejpam-5385	306	16	comments	comment	NOUN
ejpam-5385	306	17	and	and	CCONJ
ejpam-5385	306	18	suggestions	suggestion	NOUN
ejpam-5385	306	19	,	,	PUNCT
ejpam-5385	306	20	which	which	PRON
ejpam-5385	306	21	have	have	AUX
ejpam-5385	306	22	greatly	greatly	ADV
ejpam-5385	306	23	improved	improve	VERB
ejpam-5385	306	24	the	the	DET
ejpam-5385	306	25	quality	quality	NOUN
ejpam-5385	306	26	and	and	CCONJ
ejpam-5385	306	27	clarity	clarity	NOUN
ejpam-5385	306	28	of	of	ADP
ejpam-5385	306	29	this	this	DET
ejpam-5385	306	30	manuscript	manuscript	NOUN
ejpam-5385	306	31	.	.	PUNCT
ejpam-5385	307	1	references	reference	NOUN
ejpam-5385	307	2	[	[	X
ejpam-5385	307	3	1	1	NUM
ejpam-5385	307	4	]	]	PUNCT
ejpam-5385	307	5	m.	m.	NOUN
ejpam-5385	307	6	akram	akram	PROPN
ejpam-5385	307	7	.	.	PUNCT
ejpam-5385	308	1	intuitionistic	intuitionistic	ADJ
ejpam-5385	308	2	fuzzy	fuzzy	ADJ
ejpam-5385	308	3	lie	lie	NOUN
ejpam-5385	308	4	subalgebras	subalgebras	PROPN
ejpam-5385	308	5	.	.	PUNCT
ejpam-5385	309	1	southeast	southeast	ADJ
ejpam-5385	309	2	asian	asian	ADJ
ejpam-5385	309	3	bulletin	bulletin	NOUN
ejpam-5385	309	4	of	of	ADP
ejpam-5385	309	5	mathematics	mathematic	NOUN
ejpam-5385	309	6	,	,	PUNCT
ejpam-5385	309	7	31:843–855	31:843–855	NUM
ejpam-5385	309	8	,	,	PUNCT
ejpam-5385	309	9	2007	2007	NUM
ejpam-5385	309	10	.	.	PUNCT
ejpam-5385	310	1	[	[	X
ejpam-5385	310	2	2	2	NUM
ejpam-5385	310	3	]	]	PUNCT
ejpam-5385	310	4	m.	m.	NOUN
ejpam-5385	310	5	akram	akram	PROPN
ejpam-5385	310	6	.	.	PUNCT
ejpam-5385	311	1	bipolar	bipolar	ADJ
ejpam-5385	311	2	fuzzy	fuzzy	ADJ
ejpam-5385	311	3	soft	soft	ADJ
ejpam-5385	311	4	lie	lie	NOUN
ejpam-5385	311	5	algebras	algebra	NOUN
ejpam-5385	311	6	.	.	PUNCT
ejpam-5385	312	1	quasigroups	quasigroups	PROPN
ejpam-5385	312	2	and	and	CCONJ
ejpam-5385	312	3	related	related	ADJ
ejpam-5385	312	4	systems	system	NOUN
ejpam-5385	312	5	,	,	PUNCT
ejpam-5385	312	6	21:1–10	21:1–10	NUM
ejpam-5385	312	7	,	,	PUNCT
ejpam-5385	312	8	2013	2013	NUM
ejpam-5385	312	9	.	.	PUNCT
ejpam-5385	313	1	[	[	X
ejpam-5385	313	2	3	3	X
ejpam-5385	313	3	]	]	X
ejpam-5385	313	4	m.	m.	NOUN
ejpam-5385	313	5	akram	akram	PROPN
ejpam-5385	313	6	.	.	PUNCT
ejpam-5385	314	1	fuzzy	fuzzy	ADJ
ejpam-5385	314	2	lie	lie	NOUN
ejpam-5385	314	3	algebras	algebras	PROPN
ejpam-5385	314	4	.	.	PUNCT
ejpam-5385	315	1	infosys	infosys	PROPN
ejpam-5385	315	2	science	science	PROPN
ejpam-5385	315	3	foundation	foundation	PROPN
ejpam-5385	315	4	series	series	PROPN
ejpam-5385	315	5	in	in	ADP
ejpam-5385	315	6	mathematical	mathematical	ADJ
ejpam-5385	315	7	sciences	sciences	PROPN
ejpam-5385	315	8	.	.	PUNCT
ejpam-5385	316	1	springer	springer	NOUN
ejpam-5385	316	2	,	,	PUNCT
ejpam-5385	316	3	2018	2018	NUM
ejpam-5385	316	4	.	.	PUNCT
ejpam-5385	317	1	[	[	X
ejpam-5385	317	2	4	4	X
ejpam-5385	317	3	]	]	PUNCT
ejpam-5385	317	4	m.	m.	NOUN
ejpam-5385	317	5	al	al	PROPN
ejpam-5385	317	6	-	-	PUNCT
ejpam-5385	317	7	deiakeh	deiakeh	NOUN
ejpam-5385	317	8	.	.	PUNCT
ejpam-5385	318	1	on	on	ADP
ejpam-5385	318	2	intuitionistic	intuitionistic	ADJ
ejpam-5385	318	3	fuzzy	fuzzy	ADJ
ejpam-5385	318	4	lie	lie	NOUN
ejpam-5385	318	5	algebras	algebra	NOUN
ejpam-5385	318	6	.	.	PUNCT
ejpam-5385	319	1	master	master	PROPN
ejpam-5385	319	2	thesis	thesis	NOUN
ejpam-5385	319	3	,	,	PUNCT
ejpam-5385	319	4	yarmouk	yarmouk	CCONJ
ejpam-5385	319	5	university	university	NOUN
ejpam-5385	319	6	,	,	PUNCT
ejpam-5385	319	7	jordan	jordan	PROPN
ejpam-5385	319	8	,	,	PUNCT
ejpam-5385	319	9	2019	2019	NUM
ejpam-5385	319	10	.	.	PUNCT
ejpam-5385	320	1	[	[	X
ejpam-5385	320	2	5	5	NUM
ejpam-5385	320	3	]	]	PUNCT
ejpam-5385	320	4	a.	a.	PROPN
ejpam-5385	320	5	s.	s.	PROPN
ejpam-5385	320	6	alkouri	alkouri	PROPN
ejpam-5385	320	7	and	and	CCONJ
ejpam-5385	320	8	a.	a.	PROPN
ejpam-5385	320	9	salleh	salleh	PROPN
ejpam-5385	320	10	.	.	PUNCT
ejpam-5385	321	1	complex	complex	ADJ
ejpam-5385	321	2	intuitionistic	intuitionistic	ADJ
ejpam-5385	321	3	fuzzy	fuzzy	ADJ
ejpam-5385	321	4	sets	set	NOUN
ejpam-5385	321	5	.	.	PUNCT
ejpam-5385	322	1	proceedings	proceeding	NOUN
ejpam-5385	322	2	of	of	ADP
ejpam-5385	322	3	the	the	DET
ejpam-5385	322	4	international	international	ADJ
ejpam-5385	322	5	conference	conference	NOUN
ejpam-5385	322	6	on	on	ADP
ejpam-5385	322	7	fundamental	fundamental	ADJ
ejpam-5385	322	8	and	and	CCONJ
ejpam-5385	322	9	applied	applied	ADJ
ejpam-5385	322	10	sciences	science	NOUN
ejpam-5385	322	11	(	(	PUNCT
ejpam-5385	322	12	icfas	icfas	NOUN
ejpam-5385	322	13	’	'	PUNCT
ejpam-5385	322	14	12	12	NUM
ejpam-5385	322	15	)	)	PUNCT
ejpam-5385	322	16	,	,	PUNCT
ejpam-5385	322	17	1482:464	1482:464	NUM
ejpam-5385	322	18	–	–	PUNCT
ejpam-5385	322	19	470	470	NUM
ejpam-5385	322	20	,	,	PUNCT
ejpam-5385	322	21	2012	2012	NUM
ejpam-5385	322	22	.	.	PUNCT
ejpam-5385	323	1	references	reference	NOUN
ejpam-5385	323	2	3303	3303	NUM
ejpam-5385	323	3	[	[	X
ejpam-5385	323	4	6	6	NUM
ejpam-5385	323	5	]	]	PUNCT
ejpam-5385	323	6	k.	k.	PROPN
ejpam-5385	323	7	t.	t.	PROPN
ejpam-5385	323	8	atanassov	atanassov	PROPN
ejpam-5385	323	9	.	.	PUNCT
ejpam-5385	324	1	intuitionistic	intuitionistic	ADJ
ejpam-5385	324	2	fuzzy	fuzzy	ADJ
ejpam-5385	324	3	sets	set	NOUN
ejpam-5385	324	4	.	.	PUNCT
ejpam-5385	325	1	fuzzy	fuzzy	ADJ
ejpam-5385	325	2	sets	set	NOUN
ejpam-5385	325	3	and	and	CCONJ
ejpam-5385	325	4	systems	system	NOUN
ejpam-5385	325	5	,	,	PUNCT
ejpam-5385	325	6	20:87–96	20:87–96	NUM
ejpam-5385	325	7	,	,	PUNCT
ejpam-5385	325	8	1986	1986	NUM
ejpam-5385	325	9	.	.	PUNCT
ejpam-5385	326	1	[	[	X
ejpam-5385	326	2	7	7	X
ejpam-5385	326	3	]	]	X
ejpam-5385	326	4	y.	y.	NOUN
ejpam-5385	326	5	bahturin	bahturin	PROPN
ejpam-5385	326	6	.	.	PUNCT
ejpam-5385	327	1	identical	identical	ADJ
ejpam-5385	327	2	relations	relation	NOUN
ejpam-5385	327	3	in	in	ADP
ejpam-5385	327	4	lie	lie	NOUN
ejpam-5385	327	5	algebras	algebras	PROPN
ejpam-5385	327	6	.	.	PUNCT
ejpam-5385	328	1	vnu	vnu	PROPN
ejpam-5385	328	2	science	science	PROPN
ejpam-5385	328	3	press	press	PROPN
ejpam-5385	328	4	,	,	PUNCT
ejpam-5385	328	5	utrecht	utrecht	PROPN
ejpam-5385	328	6	,	,	PUNCT
ejpam-5385	328	7	1987	1987	NUM
ejpam-5385	328	8	.	.	PUNCT
ejpam-5385	329	1	[	[	X
ejpam-5385	329	2	8	8	NUM
ejpam-5385	329	3	]	]	X
ejpam-5385	329	4	w.	w.	PROPN
ejpam-5385	329	5	chen	chen	PROPN
ejpam-5385	329	6	and	and	CCONJ
ejpam-5385	329	7	s.	s.	PROPN
ejpam-5385	329	8	zhang	zhang	PROPN
ejpam-5385	329	9	.	.	PUNCT
ejpam-5385	330	1	intuitionistic	intuitionistic	ADJ
ejpam-5385	330	2	fuzzy	fuzzy	ADJ
ejpam-5385	330	3	lie	lie	NOUN
ejpam-5385	330	4	sub	sub	NOUN
ejpam-5385	330	5	-	-	NOUN
ejpam-5385	330	6	superalgebras	superalgebra	NOUN
ejpam-5385	330	7	and	and	CCONJ
ejpam-5385	330	8	intuitionistic	intuitionistic	ADJ
ejpam-5385	330	9	fuzzy	fuzzy	ADJ
ejpam-5385	330	10	ideals	ideal	NOUN
ejpam-5385	330	11	.	.	PUNCT
ejpam-5385	331	1	computers	computer	NOUN
ejpam-5385	331	2	and	and	CCONJ
ejpam-5385	331	3	mathematics	mathematic	NOUN
ejpam-5385	331	4	with	with	ADP
ejpam-5385	331	5	applications	application	NOUN
ejpam-5385	331	6	,	,	PUNCT
ejpam-5385	331	7	58:1645–1661	58:1645–1661	NUM
ejpam-5385	331	8	,	,	PUNCT
ejpam-5385	331	9	2009	2009	NUM
ejpam-5385	331	10	.	.	PUNCT
ejpam-5385	332	1	[	[	X
ejpam-5385	332	2	9	9	NUM
ejpam-5385	332	3	]	]	X
ejpam-5385	332	4	n.	n.	PROPN
ejpam-5385	332	5	jacobson	jacobson	PROPN
ejpam-5385	332	6	.	.	PROPN
ejpam-5385	333	1	lie	lie	PROPN
ejpam-5385	333	2	algebras	algebras	PROPN
ejpam-5385	333	3	.	.	PUNCT
ejpam-5385	334	1	wiley	wiley	PROPN
ejpam-5385	334	2	,	,	PUNCT
ejpam-5385	334	3	new	new	PROPN
ejpam-5385	334	4	york	york	PROPN
ejpam-5385	334	5	,	,	PUNCT
ejpam-5385	334	6	1962	1962	NUM
ejpam-5385	334	7	.	.	PUNCT
ejpam-5385	335	1	[	[	X
ejpam-5385	335	2	10	10	NUM
ejpam-5385	335	3	]	]	X
ejpam-5385	335	4	l.	l.	PROPN
ejpam-5385	335	5	platil	platil	PROPN
ejpam-5385	335	6	and	and	CCONJ
ejpam-5385	335	7	t.	t.	PROPN
ejpam-5385	335	8	tanaka	tanaka	PROPN
ejpam-5385	335	9	.	.	PUNCT
ejpam-5385	336	1	multi	multi	ADJ
ejpam-5385	336	2	-	-	ADJ
ejpam-5385	336	3	criteria	criteria	ADJ
ejpam-5385	336	4	evaluation	evaluation	NOUN
ejpam-5385	336	5	for	for	ADP
ejpam-5385	336	6	intuitionistic	intuitionistic	ADJ
ejpam-5385	336	7	fuzzy	fuzzy	ADJ
ejpam-5385	336	8	sets	set	NOUN
ejpam-5385	336	9	based	base	VERB
ejpam-5385	336	10	on	on	ADP
ejpam-5385	336	11	set	set	NOUN
ejpam-5385	336	12	-	-	PUNCT
ejpam-5385	336	13	relations	relation	NOUN
ejpam-5385	336	14	.	.	PUNCT
ejpam-5385	337	1	nihonkai	nihonkai	PROPN
ejpam-5385	337	2	mathematical	mathematical	PROPN
ejpam-5385	337	3	journal	journal	PROPN
ejpam-5385	337	4	,	,	PUNCT
ejpam-5385	337	5	34:1–18	34:1–18	NUM
ejpam-5385	337	6	,	,	PUNCT
ejpam-5385	337	7	2023	2023	NUM
ejpam-5385	337	8	.	.	PUNCT
ejpam-5385	338	1	[	[	X
ejpam-5385	338	2	11	11	NUM
ejpam-5385	338	3	]	]	X
ejpam-5385	338	4	l.	l.	PROPN
ejpam-5385	338	5	c.	c.	PROPN
ejpam-5385	338	6	platil	platil	PROPN
ejpam-5385	338	7	and	and	CCONJ
ejpam-5385	338	8	g.	g.	PROPN
ejpam-5385	338	9	c.	c.	PROPN
ejpam-5385	338	10	petalcorin	petalcorin	PROPN
ejpam-5385	338	11	.	.	PUNCT
ejpam-5385	339	1	fuzzy	fuzzy	ADJ
ejpam-5385	339	2	γ	γ	NOUN
ejpam-5385	339	3	-	-	NOUN
ejpam-5385	339	4	semimodules	semimodule	NOUN
ejpam-5385	339	5	over	over	ADP
ejpam-5385	339	6	γ	γ	NOUN
ejpam-5385	339	7	-	-	PUNCT
ejpam-5385	339	8	semirings	semiring	NOUN
ejpam-5385	339	9	.	.	PUNCT
ejpam-5385	340	1	journal	journal	PROPN
ejpam-5385	340	2	of	of	ADP
ejpam-5385	340	3	analysis	analysis	NOUN
ejpam-5385	340	4	&	&	CCONJ
ejpam-5385	340	5	applications	application	NOUN
ejpam-5385	340	6	,	,	PUNCT
ejpam-5385	340	7	15:71–83	15:71–83	NUM
ejpam-5385	340	8	,	,	PUNCT
ejpam-5385	340	9	2017	2017	NUM
ejpam-5385	340	10	.	.	PUNCT
ejpam-5385	341	1	[	[	X
ejpam-5385	341	2	12	12	NUM
ejpam-5385	341	3	]	]	PUNCT
ejpam-5385	341	4	e.	e.	PROPN
ejpam-5385	341	5	h.	h.	PROPN
ejpam-5385	341	6	roh	roh	PROPN
ejpam-5385	341	7	,	,	PUNCT
ejpam-5385	341	8	e.	e.	PROPN
ejpam-5385	341	9	yang	yang	PROPN
ejpam-5385	341	10	,	,	PUNCT
ejpam-5385	341	11	and	and	CCONJ
ejpam-5385	341	12	y.	y.	PROPN
ejpam-5385	341	13	b.	b.	PROPN
ejpam-5385	341	14	jun	jun	PROPN
ejpam-5385	341	15	.	.	PROPN
ejpam-5385	342	1	intuitionistic	intuitionistic	ADJ
ejpam-5385	342	2	fuzzy	fuzzy	ADJ
ejpam-5385	342	3	ordered	order	VERB
ejpam-5385	342	4	subalgebras	subalgebras	PROPN
ejpam-5385	342	5	in	in	ADP
ejpam-5385	342	6	ordered	order	VERB
ejpam-5385	342	7	bci	bci	NOUN
ejpam-5385	342	8	-	-	PUNCT
ejpam-5385	342	9	algebras	algebra	NOUN
ejpam-5385	342	10	.	.	PUNCT
ejpam-5385	343	1	european	european	PROPN
ejpam-5385	343	2	journal	journal	PROPN
ejpam-5385	343	3	of	of	ADP
ejpam-5385	343	4	pure	pure	ADJ
ejpam-5385	343	5	and	and	CCONJ
ejpam-5385	343	6	applied	applied	ADJ
ejpam-5385	343	7	mathematics	mathematic	NOUN
ejpam-5385	343	8	,	,	PUNCT
ejpam-5385	343	9	16(3):1342–1358	16(3):1342–1358	NUM
ejpam-5385	343	10	,	,	PUNCT
ejpam-5385	343	11	2023	2023	NUM
ejpam-5385	343	12	.	.	PUNCT
ejpam-5385	344	1	[	[	X
ejpam-5385	344	2	13	13	NUM
ejpam-5385	344	3	]	]	PUNCT
ejpam-5385	344	4	s.	s.	PROPN
ejpam-5385	344	5	shaqaqha	shaqaqha	PROPN
ejpam-5385	344	6	.	.	PUNCT
ejpam-5385	345	1	complex	complex	ADJ
ejpam-5385	345	2	fuzzy	fuzzy	ADJ
ejpam-5385	345	3	lie	lie	NOUN
ejpam-5385	345	4	algebras	algebra	NOUN
ejpam-5385	345	5	.	.	PUNCT
ejpam-5385	346	1	jordan	jordan	PROPN
ejpam-5385	346	2	j.	j.	PROPN
ejpam-5385	346	3	math	math	PROPN
ejpam-5385	346	4	.	.	PUNCT
ejpam-5385	347	1	stat	stat	PROPN
ejpam-5385	347	2	.	.	PUNCT
ejpam-5385	347	3	,	,	PUNCT
ejpam-5385	347	4	13(2):231–247	13(2):231–247	PROPN
ejpam-5385	347	5	,	,	PUNCT
ejpam-5385	347	6	2020	2020	NUM
ejpam-5385	347	7	.	.	PUNCT
ejpam-5385	348	1	[	[	X
ejpam-5385	348	2	14	14	NUM
ejpam-5385	348	3	]	]	X
ejpam-5385	348	4	s.	s.	PROPN
ejpam-5385	348	5	shaqaqha	shaqaqha	PROPN
ejpam-5385	348	6	.	.	PUNCT
ejpam-5385	349	1	characterizations	characterization	NOUN
ejpam-5385	349	2	of	of	ADP
ejpam-5385	349	3	artinian	artinian	ADJ
ejpam-5385	349	4	and	and	CCONJ
ejpam-5385	349	5	noetherian	noetherian	ADJ
ejpam-5385	349	6	gamma	gamma	NOUN
ejpam-5385	349	7	rings	ring	NOUN
ejpam-5385	349	8	in	in	ADP
ejpam-5385	349	9	terms	term	NOUN
ejpam-5385	349	10	of	of	ADP
ejpam-5385	349	11	homogeneous	homogeneous	ADJ
ejpam-5385	349	12	complex	complex	ADJ
ejpam-5385	349	13	fuzzy	fuzzy	ADJ
ejpam-5385	349	14	ideals	ideal	NOUN
ejpam-5385	349	15	.	.	PUNCT
ejpam-5385	350	1	palestine	palestine	PROPN
ejpam-5385	350	2	journal	journal	PROPN
ejpam-5385	350	3	of	of	ADP
ejpam-5385	350	4	mathematics	mathematics	PROPN
ejpam-5385	350	5	,	,	PUNCT
ejpam-5385	350	6	11(4):167–171	11(4):167–171	PROPN
ejpam-5385	350	7	,	,	PUNCT
ejpam-5385	350	8	2022	2022	NUM
ejpam-5385	350	9	.	.	PUNCT
ejpam-5385	351	1	[	[	X
ejpam-5385	351	2	15	15	NUM
ejpam-5385	351	3	]	]	X
ejpam-5385	351	4	s.	s.	PROPN
ejpam-5385	351	5	shaqaqha	shaqaqha	PROPN
ejpam-5385	351	6	.	.	PUNCT
ejpam-5385	352	1	isomorphism	isomorphism	NOUN
ejpam-5385	352	2	theorems	theorem	NOUN
ejpam-5385	352	3	for	for	ADP
ejpam-5385	352	4	complex	complex	ADJ
ejpam-5385	352	5	fuzzy	fuzzy	ADJ
ejpam-5385	352	6	gamma	gamma	NOUN
ejpam-5385	352	7	rings	ring	NOUN
ejpam-5385	352	8	.	.	PUNCT
ejpam-5385	353	1	missouri	missouri	PROPN
ejpam-5385	353	2	journal	journal	PROPN
ejpam-5385	353	3	of	of	ADP
ejpam-5385	353	4	mathematical	mathematical	ADJ
ejpam-5385	353	5	sciences	sciences	PROPN
ejpam-5385	353	6	,	,	PUNCT
ejpam-5385	353	7	34(2):196–207	34(2):196–207	NOUN
ejpam-5385	353	8	,	,	PUNCT
ejpam-5385	353	9	2022	2022	NUM
ejpam-5385	353	10	.	.	PUNCT
ejpam-5385	354	1	[	[	X
ejpam-5385	354	2	16	16	NUM
ejpam-5385	354	3	]	]	X
ejpam-5385	354	4	s.	s.	PROPN
ejpam-5385	354	5	shaqaqha	shaqaqha	PROPN
ejpam-5385	354	6	.	.	PUNCT
ejpam-5385	355	1	on	on	ADP
ejpam-5385	355	2	fuzzification	fuzzification	NOUN
ejpam-5385	355	3	of	of	ADP
ejpam-5385	355	4	n	n	CCONJ
ejpam-5385	355	5	-	-	PUNCT
ejpam-5385	355	6	lie	lie	NOUN
ejpam-5385	355	7	algebra	algebra	NOUN
ejpam-5385	355	8	.	.	PUNCT
ejpam-5385	356	1	jordan	jordan	PROPN
ejpam-5385	356	2	j.	j.	PROPN
ejpam-5385	356	3	math	math	PROPN
ejpam-5385	356	4	.	.	PUNCT
ejpam-5385	357	1	stat	stat	PROPN
ejpam-5385	357	2	.	.	PUNCT
ejpam-5385	357	3	,	,	PUNCT
ejpam-5385	357	4	15(3a):523	15(3a):523	NUM
ejpam-5385	357	5	–	–	PUNCT
ejpam-5385	357	6	540	540	NUM
ejpam-5385	357	7	,	,	PUNCT
ejpam-5385	357	8	2022	2022	NUM
ejpam-5385	357	9	.	.	PUNCT
ejpam-5385	358	1	[	[	X
ejpam-5385	358	2	17	17	NUM
ejpam-5385	358	3	]	]	PUNCT
ejpam-5385	358	4	s.	s.	PROPN
ejpam-5385	358	5	shaqaqha	shaqaqha	PROPN
ejpam-5385	358	6	.	.	PUNCT
ejpam-5385	359	1	fuzzy	fuzzy	PROPN
ejpam-5385	359	2	hom	hom	NOUN
ejpam-5385	359	3	–	–	PUNCT
ejpam-5385	359	4	lie	lie	NOUN
ejpam-5385	359	5	ideals	ideal	NOUN
ejpam-5385	359	6	of	of	ADP
ejpam-5385	359	7	hom	hom	NOUN
ejpam-5385	359	8	–	–	PUNCT
ejpam-5385	359	9	lie	lie	NOUN
ejpam-5385	359	10	algebras	algebra	NOUN
ejpam-5385	359	11	.	.	PUNCT
ejpam-5385	360	1	axioms	axiom	NOUN
ejpam-5385	360	2	,	,	PUNCT
ejpam-5385	360	3	12(7):630	12(7):630	NUM
ejpam-5385	360	4	,	,	PUNCT
ejpam-5385	360	5	2023	2023	NUM
ejpam-5385	360	6	.	.	PUNCT
ejpam-5385	361	1	[	[	X
ejpam-5385	361	2	18	18	NUM
ejpam-5385	361	3	]	]	X
ejpam-5385	361	4	s.	s.	PROPN
ejpam-5385	361	5	shaqaqha	shaqaqha	PROPN
ejpam-5385	361	6	and	and	CCONJ
ejpam-5385	361	7	m.	m.	PROPN
ejpam-5385	361	8	al	al	PROPN
ejpam-5385	361	9	-	-	PUNCT
ejpam-5385	361	10	deiakeh	deiakeh	NOUN
ejpam-5385	361	11	.	.	PUNCT
ejpam-5385	362	1	towards	towards	ADP
ejpam-5385	362	2	studying	study	VERB
ejpam-5385	362	3	complex	complex	ADJ
ejpam-5385	362	4	intuitionistic	intuitionistic	ADJ
ejpam-5385	362	5	fuzzy	fuzzy	ADJ
ejpam-5385	362	6	lie	lie	NOUN
ejpam-5385	362	7	algebras	algebra	NOUN
ejpam-5385	362	8	.	.	PUNCT
ejpam-5385	363	1	submitted	submit	VERB
ejpam-5385	363	2	manuscript	manuscript	NOUN
ejpam-5385	363	3	,	,	PUNCT
ejpam-5385	363	4	2023	2023	NUM
ejpam-5385	363	5	.	.	PUNCT
ejpam-5385	364	1	[	[	X
ejpam-5385	364	2	19	19	NUM
ejpam-5385	364	3	]	]	X
ejpam-5385	364	4	r.	r.	PROPN
ejpam-5385	364	5	r.	r.	PROPN
ejpam-5385	364	6	yager	yager	PROPN
ejpam-5385	364	7	.	.	PUNCT
ejpam-5385	365	1	pythagorean	pythagorean	PROPN
ejpam-5385	365	2	fuzzy	fuzzy	ADJ
ejpam-5385	365	3	subsets	subset	NOUN
ejpam-5385	365	4	.	.	PUNCT
ejpam-5385	366	1	in	in	ADP
ejpam-5385	366	2	proc	proc	NOUN
ejpam-5385	366	3	.	.	PUNCT
ejpam-5385	367	1	joint	joint	ADJ
ejpam-5385	367	2	ifsa	ifsa	PROPN
ejpam-5385	367	3	world	world	PROPN
ejpam-5385	367	4	congr	congr	PROPN
ejpam-5385	367	5	.	.	PUNCT
ejpam-5385	368	1	nafips	nafip	NOUN
ejpam-5385	368	2	annu	annu	NOUN
ejpam-5385	368	3	.	.	PUNCT
ejpam-5385	369	1	meeting	meeting	NOUN
ejpam-5385	369	2	(	(	PUNCT
ejpam-5385	369	3	ifsa	ifsa	PROPN
ejpam-5385	369	4	/	/	SYM
ejpam-5385	369	5	nafips	nafip	NOUN
ejpam-5385	369	6	)	)	PUNCT
ejpam-5385	369	7	,	,	PUNCT
ejpam-5385	369	8	pages	page	NOUN
ejpam-5385	369	9	57–61	57–61	NUM
ejpam-5385	369	10	,	,	PUNCT
ejpam-5385	369	11	edmonton	edmonton	PROPN
ejpam-5385	369	12	,	,	PUNCT
ejpam-5385	369	13	ab	ab	PROPN
ejpam-5385	369	14	,	,	PUNCT
ejpam-5385	369	15	canada	canada	PROPN
ejpam-5385	369	16	,	,	PUNCT
ejpam-5385	369	17	2013	2013	NUM
ejpam-5385	369	18	.	.	PUNCT
ejpam-5385	370	1	[	[	X
ejpam-5385	370	2	20	20	NUM
ejpam-5385	370	3	]	]	PUNCT
ejpam-5385	370	4	r.	r.	PROPN
ejpam-5385	370	5	r.	r.	PROPN
ejpam-5385	370	6	yager	yager	PROPN
ejpam-5385	370	7	.	.	PUNCT
ejpam-5385	371	1	pythagorean	pythagorean	PROPN
ejpam-5385	371	2	membership	membership	NOUN
ejpam-5385	371	3	grades	grade	NOUN
ejpam-5385	371	4	in	in	ADP
ejpam-5385	371	5	multicriteria	multicriteria	PROPN
ejpam-5385	371	6	decision	decision	NOUN
ejpam-5385	371	7	making	making	NOUN
ejpam-5385	371	8	.	.	PUNCT
ejpam-5385	372	1	ieee	ieee	PROPN
ejpam-5385	372	2	trans	trans	PROPN
ejpam-5385	372	3	.	.	PUNCT
ejpam-5385	372	4	fuzzy	fuzzy	ADJ
ejpam-5385	372	5	syst	syst	PROPN
ejpam-5385	372	6	.	.	PROPN
ejpam-5385	372	7	,	,	PUNCT
ejpam-5385	372	8	22(4):958–965	22(4):958–965	PROPN
ejpam-5385	372	9	,	,	PUNCT
ejpam-5385	372	10	2014	2014	NUM
ejpam-5385	372	11	.	.	PUNCT
ejpam-5385	373	1	[	[	X
ejpam-5385	373	2	21	21	NUM
ejpam-5385	373	3	]	]	PUNCT
ejpam-5385	373	4	s.	s.	PROPN
ejpam-5385	373	5	e.	e.	PROPN
ejpam-5385	373	6	yehia	yehia	PROPN
ejpam-5385	373	7	.	.	PUNCT
ejpam-5385	373	8	fuzzy	fuzzy	ADJ
ejpam-5385	373	9	ideals	ideal	NOUN
ejpam-5385	373	10	and	and	CCONJ
ejpam-5385	373	11	fuzzy	fuzzy	ADJ
ejpam-5385	373	12	subalgebras	subalgebra	NOUN
ejpam-5385	373	13	of	of	ADP
ejpam-5385	373	14	lie	lie	NOUN
ejpam-5385	373	15	algebra	algebra	NOUN
ejpam-5385	373	16	.	.	PUNCT
ejpam-5385	374	1	fuzzy	fuzzy	ADJ
ejpam-5385	374	2	sets	set	NOUN
ejpam-5385	374	3	and	and	CCONJ
ejpam-5385	374	4	systems	system	NOUN
ejpam-5385	374	5	,	,	PUNCT
ejpam-5385	374	6	80:237–244	80:237–244	NUM
ejpam-5385	374	7	,	,	PUNCT
ejpam-5385	374	8	1996	1996	NUM
ejpam-5385	374	9	.	.	PUNCT
ejpam-5385	375	1	[	[	X
ejpam-5385	375	2	22	22	NUM
ejpam-5385	375	3	]	]	PUNCT
ejpam-5385	375	4	l.	l.	PROPN
ejpam-5385	375	5	zadeh	zadeh	PROPN
ejpam-5385	375	6	.	.	PUNCT
ejpam-5385	375	7	fuzzy	fuzzy	ADJ
ejpam-5385	375	8	sets	set	NOUN
ejpam-5385	375	9	.	.	PUNCT
ejpam-5385	376	1	inform	inform	NOUN
ejpam-5385	376	2	.	.	PUNCT
ejpam-5385	377	1	control	control	NOUN
ejpam-5385	377	2	,	,	PUNCT
ejpam-5385	377	3	8:338–358	8:338–358	NOUN
ejpam-5385	377	4	,	,	PUNCT
ejpam-5385	377	5	1965	1965	NUM
ejpam-5385	377	6	.	.	PUNCT