id	sid	tid	token	lemma	pos
ejpam-3343	1	1	protect	protect	VERB
ejpam-3343	1	2	elax	elax	NOUN
ejpam-3343	1	3	protect	protect	NOUN
ejpam-3343	1	4	�	�	PROPN
ejpam-3343	1	5	egingroup	egingroup	NOUN
ejpam-3343	1	6	immediate	immediate	ADJ
ejpam-3343	1	7	write	write	NOUN
ejpam-3343	1	8	@unused	@unuse	VERB
ejpam-3343	1	9	def	def	ADJ
ejpam-3343	1	10	messagebreak	messagebreak	NOUN
ejpam-3343	1	11	let	let	AUX
ejpam-3343	1	12	protect	protect	VERB
ejpam-3343	1	13	edef	edef	NOUN
ejpam-3343	1	14	you	you	PRON
ejpam-3343	1	15	're	be	AUX
ejpam-3343	1	16	in	in	ADP
ejpam-3343	1	17	trouble	trouble	NOUN
ejpam-3343	1	18	here	here	ADV
ejpam-3343	1	19	.	.	PUNCT
ejpam-3343	2	1	try	try	VERB
ejpam-3343	2	2	typing	type	VERB
ejpam-3343	2	3	<	<	X
ejpam-3343	2	4	return	return	NOUN
ejpam-3343	2	5	>	>	X
ejpam-3343	2	6	to	to	ADP
ejpam-3343	2	7	proceed.messagebreak	proceed.messagebreak	NOUN
ejpam-3343	2	8	if	if	SCONJ
ejpam-3343	2	9	that	that	PRON
ejpam-3343	2	10	does	do	AUX
ejpam-3343	2	11	n't	not	PART
ejpam-3343	2	12	work	work	VERB
ejpam-3343	2	13	,	,	PUNCT
ejpam-3343	2	14	type	type	NOUN
ejpam-3343	2	15	x	x	PART
ejpam-3343	2	16	<	<	X
ejpam-3343	2	17	return	return	NOUN
ejpam-3343	2	18	>	>	X
ejpam-3343	2	19	to	to	PART
ejpam-3343	2	20	quit	quit	VERB
ejpam-3343	2	21	.	.	PUNCT
ejpam-3343	3	1	errhelp	errhelp	VERB
ejpam-3343	3	2	let	let	VERB
ejpam-3343	3	3	def	def	ADJ
ejpam-3343	3	4	messagebreak	messagebreak	PROPN
ejpam-3343	3	5	def	def	PROPN
ejpam-3343	3	6	errmessage	errmessage	PROPN
ejpam-3343	3	7	latex	latex	NOUN
ejpam-3343	3	8	error	error	NOUN
ejpam-3343	3	9	:	:	PUNCT
ejpam-3343	3	10	mathcal	mathcal	ADJ
ejpam-3343	3	11	allowed	allow	VERB
ejpam-3343	3	12	only	only	ADV
ejpam-3343	3	13	in	in	ADP
ejpam-3343	3	14	math	math	NOUN
ejpam-3343	3	15	mode	mode	NOUN
ejpam-3343	3	16	.	.	PUNCT
ejpam-3343	4	1	see	see	VERB
ejpam-3343	4	2	the	the	DET
ejpam-3343	4	3	latex	latex	NOUN
ejpam-3343	4	4	manual	manual	NOUN
ejpam-3343	4	5	or	or	CCONJ
ejpam-3343	4	6	latex	latex	NOUN
ejpam-3343	4	7	companion	companion	NOUN
ejpam-3343	4	8	for	for	ADP
ejpam-3343	4	9	explanation	explanation	NOUN
ejpam-3343	4	10	.	.	PUNCT
ejpam-3343	5	1	type	type	NOUN
ejpam-3343	5	2	h	h	NOUN
ejpam-3343	5	3	<	<	X
ejpam-3343	5	4	return	return	VERB
ejpam-3343	5	5	>	>	X
ejpam-3343	5	6	for	for	ADP
ejpam-3343	5	7	immediate	immediate	ADJ
ejpam-3343	5	8	help	help	NOUN
ejpam-3343	5	9	endgroup	endgroup	PROPN
ejpam-3343	5	10	elax	elax	VERB
ejpam-3343	5	11	n}$-soft	n}$-soft	ADV
ejpam-3343	5	12	$	$	SYM
ejpam-3343	5	13	p$-ideals	p$-ideal	NOUN
ejpam-3343	5	14	of	of	ADP
ejpam-3343	5	15	$	$	SYM
ejpam-3343	5	16	bci$-algebras	bci$-algebras	PROPN
ejpam-3343	5	17	european	european	ADJ
ejpam-3343	5	18	journal	journal	NOUN
ejpam-3343	5	19	of	of	ADP
ejpam-3343	5	20	pure	pure	ADJ
ejpam-3343	5	21	and	and	CCONJ
ejpam-3343	5	22	applied	apply	VERB
ejpam-3343	5	23	mathematics	mathematic	NOUN
ejpam-3343	5	24	vol	vol	NOUN
ejpam-3343	5	25	.	.	PROPN
ejpam-3343	6	1	12	12	NUM
ejpam-3343	6	2	,	,	PUNCT
ejpam-3343	6	3	no	no	INTJ
ejpam-3343	6	4	.	.	NOUN
ejpam-3343	6	5	1	1	NUM
ejpam-3343	6	6	,	,	PUNCT
ejpam-3343	6	7	2019	2019	NUM
ejpam-3343	6	8	,	,	PUNCT
ejpam-3343	6	9	79	79	NUM
ejpam-3343	6	10	-	-	SYM
ejpam-3343	6	11	87	87	NUM
ejpam-3343	6	12	issn	issn	PROPN
ejpam-3343	6	13	1307	1307	NUM
ejpam-3343	6	14	-	-	SYM
ejpam-3343	6	15	5543	5543	NUM
ejpam-3343	6	16	–	–	PUNCT
ejpam-3343	6	17	www.ejpam.com	www.ejpam.com	X
ejpam-3343	6	18	published	publish	VERB
ejpam-3343	6	19	by	by	ADP
ejpam-3343	6	20	new	new	PROPN
ejpam-3343	6	21	york	york	PROPN
ejpam-3343	6	22	business	business	PROPN
ejpam-3343	6	23	global	global	ADJ
ejpam-3343	6	24	n	n	CCONJ
ejpam-3343	6	25	-soft	-soft	ADJ
ejpam-3343	6	26	p	p	NOUN
ejpam-3343	6	27	-	-	PUNCT
ejpam-3343	6	28	ideals	ideal	NOUN
ejpam-3343	6	29	of	of	ADP
ejpam-3343	6	30	bci	bci	NOUN
ejpam-3343	6	31	-	-	PUNCT
ejpam-3343	6	32	algebras	algebras	PROPN
ejpam-3343	6	33	g.	g.	PROPN
ejpam-3343	6	34	muhiuddin1,∗	muhiuddin1,∗	PROPN
ejpam-3343	6	35	,	,	PUNCT
ejpam-3343	6	36	shuaa	shuaa	ADV
ejpam-3343	6	37	aldhafeeri2	aldhafeeri2	PROPN
ejpam-3343	7	1	1	1	NUM
ejpam-3343	7	2	department	department	NOUN
ejpam-3343	7	3	of	of	ADP
ejpam-3343	7	4	mathematics	mathematic	NOUN
ejpam-3343	7	5	,	,	PUNCT
ejpam-3343	7	6	university	university	PROPN
ejpam-3343	7	7	of	of	ADP
ejpam-3343	7	8	tabuk	tabuk	PROPN
ejpam-3343	7	9	,	,	PUNCT
ejpam-3343	7	10	tabuk	tabuk	NOUN
ejpam-3343	7	11	71491	71491	NUM
ejpam-3343	7	12	,	,	PUNCT
ejpam-3343	7	13	saudi	saudi	PROPN
ejpam-3343	7	14	arabia	arabia	PROPN
ejpam-3343	7	15	2	2	NUM
ejpam-3343	7	16	department	department	NOUN
ejpam-3343	7	17	of	of	ADP
ejpam-3343	7	18	mathematics	mathematic	NOUN
ejpam-3343	7	19	,	,	PUNCT
ejpam-3343	7	20	college	college	NOUN
ejpam-3343	7	21	of	of	ADP
ejpam-3343	7	22	basic	basic	ADJ
ejpam-3343	7	23	education	education	NOUN
ejpam-3343	7	24	,	,	PUNCT
ejpam-3343	7	25	public	public	ADJ
ejpam-3343	7	26	authority	authority	NOUN
ejpam-3343	7	27	for	for	ADP
ejpam-3343	7	28	applied	apply	VERB
ejpam-3343	7	29	education	education	NOUN
ejpam-3343	7	30	and	and	CCONJ
ejpam-3343	7	31	training	training	NOUN
ejpam-3343	7	32	,	,	PUNCT
ejpam-3343	7	33	kuwait	kuwait	PROPN
ejpam-3343	7	34	abstract	abstract	NOUN
ejpam-3343	7	35	.	.	PUNCT
ejpam-3343	8	1	in	in	ADP
ejpam-3343	8	2	this	this	DET
ejpam-3343	8	3	paper	paper	NOUN
ejpam-3343	8	4	,	,	PUNCT
ejpam-3343	8	5	using	use	VERB
ejpam-3343	8	6	the	the	DET
ejpam-3343	8	7	notions	notion	NOUN
ejpam-3343	8	8	of	of	ADP
ejpam-3343	8	9	soft	soft	ADJ
ejpam-3343	8	10	sets	set	NOUN
ejpam-3343	8	11	and	and	CCONJ
ejpam-3343	8	12	n	n	DET
ejpam-3343	8	13	-structures	-structure	NOUN
ejpam-3343	8	14	,	,	PUNCT
ejpam-3343	8	15	the	the	DET
ejpam-3343	8	16	notion	notion	NOUN
ejpam-3343	8	17	of	of	ADP
ejpam-3343	8	18	n	n	CCONJ
ejpam-3343	8	19	-soft	-soft	ADJ
ejpam-3343	8	20	p	p	NOUN
ejpam-3343	8	21	-	-	PUNCT
ejpam-3343	8	22	ideals	ideal	NOUN
ejpam-3343	8	23	in	in	ADP
ejpam-3343	8	24	bci	bci	NOUN
ejpam-3343	8	25	-	-	PUNCT
ejpam-3343	8	26	algebras	algebras	PROPN
ejpam-3343	8	27	is	be	AUX
ejpam-3343	8	28	introduced	introduce	VERB
ejpam-3343	8	29	,	,	PUNCT
ejpam-3343	8	30	and	and	CCONJ
ejpam-3343	8	31	related	related	ADJ
ejpam-3343	8	32	properties	property	NOUN
ejpam-3343	8	33	are	be	AUX
ejpam-3343	8	34	investigated	investigate	VERB
ejpam-3343	8	35	.	.	PUNCT
ejpam-3343	9	1	furthermore	furthermore	ADV
ejpam-3343	9	2	,	,	PUNCT
ejpam-3343	9	3	relations	relation	NOUN
ejpam-3343	9	4	between	between	ADP
ejpam-3343	9	5	n	n	NUM
ejpam-3343	9	6	-soft	-soft	ADJ
ejpam-3343	9	7	ideals	ideal	NOUN
ejpam-3343	9	8	and	and	CCONJ
ejpam-3343	9	9	n	n	CCONJ
ejpam-3343	9	10	-soft	-soft	NOUN
ejpam-3343	9	11	p	p	NOUN
ejpam-3343	9	12	-	-	PUNCT
ejpam-3343	9	13	ideals	ideal	NOUN
ejpam-3343	9	14	are	be	AUX
ejpam-3343	9	15	discussed	discuss	VERB
ejpam-3343	9	16	.	.	PUNCT
ejpam-3343	10	1	finally	finally	ADV
ejpam-3343	10	2	,	,	PUNCT
ejpam-3343	10	3	conditions	condition	NOUN
ejpam-3343	10	4	for	for	ADP
ejpam-3343	10	5	an	an	DET
ejpam-3343	10	6	n	n	CCONJ
ejpam-3343	10	7	-soft	-soft	ADJ
ejpam-3343	10	8	ideal	ideal	NOUN
ejpam-3343	10	9	to	to	PART
ejpam-3343	10	10	be	be	AUX
ejpam-3343	10	11	an	an	DET
ejpam-3343	10	12	n	n	CCONJ
ejpam-3343	10	13	-soft	-soft	ADJ
ejpam-3343	10	14	p	p	NOUN
ejpam-3343	10	15	-	-	PUNCT
ejpam-3343	10	16	ideal	ideal	NOUN
ejpam-3343	10	17	are	be	AUX
ejpam-3343	10	18	established	establish	VERB
ejpam-3343	10	19	.	.	PUNCT
ejpam-3343	11	1	2010	2010	NUM
ejpam-3343	11	2	mathematics	mathematic	NOUN
ejpam-3343	11	3	subject	subject	NOUN
ejpam-3343	11	4	classifications	classification	NOUN
ejpam-3343	11	5	:	:	PUNCT
ejpam-3343	11	6	06d72	06d72	NOUN
ejpam-3343	11	7	,	,	PUNCT
ejpam-3343	11	8	06f35	06f35	NUM
ejpam-3343	11	9	,	,	PUNCT
ejpam-3343	11	10	03g25	03g25	NOUN
ejpam-3343	11	11	key	key	ADJ
ejpam-3343	11	12	words	word	NOUN
ejpam-3343	11	13	and	and	CCONJ
ejpam-3343	11	14	phrases	phrase	NOUN
ejpam-3343	11	15	:	:	PUNCT
ejpam-3343	11	16	p	p	X
ejpam-3343	11	17	-	-	PUNCT
ejpam-3343	11	18	ideal	ideal	ADJ
ejpam-3343	11	19	,	,	PUNCT
ejpam-3343	11	20	n	n	CCONJ
ejpam-3343	11	21	-ideal	-ideal	NOUN
ejpam-3343	11	22	,	,	PUNCT
ejpam-3343	11	23	pn	pn	NOUN
ejpam-3343	11	24	-ideal	-ideal	NOUN
ejpam-3343	11	25	,	,	PUNCT
ejpam-3343	11	26	n	n	CCONJ
ejpam-3343	11	27	-soft	-soft	ADJ
ejpam-3343	11	28	ideal	ideal	NOUN
ejpam-3343	11	29	,	,	PUNCT
ejpam-3343	11	30	n	n	CCONJ
ejpam-3343	11	31	-soft	-soft	VERB
ejpam-3343	11	32	p	p	NOUN
ejpam-3343	11	33	-	-	PUNCT
ejpam-3343	11	34	ideal	ideal	ADJ
ejpam-3343	11	35	1	1	NUM
ejpam-3343	11	36	.	.	PUNCT
ejpam-3343	12	1	introduction	introduction	NOUN
ejpam-3343	12	2	uncertainties	uncertainty	NOUN
ejpam-3343	12	3	ca	can	AUX
ejpam-3343	12	4	n’t	not	PART
ejpam-3343	12	5	be	be	AUX
ejpam-3343	12	6	handled	handle	VERB
ejpam-3343	12	7	using	use	VERB
ejpam-3343	12	8	traditional	traditional	ADJ
ejpam-3343	12	9	mathematical	mathematical	ADJ
ejpam-3343	12	10	tools	tool	NOUN
ejpam-3343	12	11	but	but	CCONJ
ejpam-3343	12	12	may	may	AUX
ejpam-3343	12	13	be	be	AUX
ejpam-3343	12	14	dealt	deal	VERB
ejpam-3343	12	15	with	with	ADP
ejpam-3343	12	16	using	use	VERB
ejpam-3343	12	17	a	a	DET
ejpam-3343	12	18	wide	wide	ADJ
ejpam-3343	12	19	range	range	NOUN
ejpam-3343	12	20	of	of	ADP
ejpam-3343	12	21	existing	exist	VERB
ejpam-3343	12	22	theories	theory	NOUN
ejpam-3343	12	23	such	such	ADJ
ejpam-3343	12	24	as	as	ADP
ejpam-3343	12	25	the	the	DET
ejpam-3343	12	26	probability	probability	NOUN
ejpam-3343	12	27	theory	theory	NOUN
ejpam-3343	12	28	,	,	PUNCT
ejpam-3343	12	29	the	the	DET
ejpam-3343	12	30	theory	theory	NOUN
ejpam-3343	12	31	of	of	ADP
ejpam-3343	12	32	(	(	PUNCT
ejpam-3343	12	33	intuitionistic	intuitionistic	ADJ
ejpam-3343	12	34	)	)	PUNCT
ejpam-3343	12	35	fuzzy	fuzzy	ADJ
ejpam-3343	12	36	sets	set	NOUN
ejpam-3343	12	37	,	,	PUNCT
ejpam-3343	12	38	the	the	DET
ejpam-3343	12	39	theory	theory	NOUN
ejpam-3343	12	40	of	of	ADP
ejpam-3343	12	41	vague	vague	ADJ
ejpam-3343	12	42	sets	set	NOUN
ejpam-3343	12	43	,	,	PUNCT
ejpam-3343	12	44	the	the	DET
ejpam-3343	12	45	theory	theory	NOUN
ejpam-3343	12	46	of	of	ADP
ejpam-3343	12	47	interval	interval	NOUN
ejpam-3343	12	48	mathematics	mathematic	NOUN
ejpam-3343	12	49	,	,	PUNCT
ejpam-3343	12	50	and	and	CCONJ
ejpam-3343	12	51	the	the	DET
ejpam-3343	12	52	theory	theory	NOUN
ejpam-3343	12	53	of	of	ADP
ejpam-3343	12	54	rough	rough	ADJ
ejpam-3343	12	55	sets	set	NOUN
ejpam-3343	12	56	.	.	PUNCT
ejpam-3343	13	1	however	however	ADV
ejpam-3343	13	2	,	,	PUNCT
ejpam-3343	13	3	all	all	PRON
ejpam-3343	13	4	of	of	ADP
ejpam-3343	13	5	these	these	DET
ejpam-3343	13	6	theories	theory	NOUN
ejpam-3343	13	7	have	have	VERB
ejpam-3343	13	8	their	their	PRON
ejpam-3343	13	9	own	own	ADJ
ejpam-3343	13	10	limitations	limitation	NOUN
ejpam-3343	13	11	which	which	PRON
ejpam-3343	13	12	are	be	AUX
ejpam-3343	13	13	pointed	point	VERB
ejpam-3343	13	14	out	out	ADP
ejpam-3343	13	15	in	in	ADP
ejpam-3343	13	16	[	[	X
ejpam-3343	13	17	15	15	NUM
ejpam-3343	13	18	]	]	PUNCT
ejpam-3343	13	19	.	.	PUNCT
ejpam-3343	14	1	maji	maji	PROPN
ejpam-3343	14	2	et	et	PROPN
ejpam-3343	14	3	al	al	PROPN
ejpam-3343	14	4	.	.	PUNCT
ejpam-3343	15	1	[	[	X
ejpam-3343	15	2	13	13	NUM
ejpam-3343	15	3	]	]	PUNCT
ejpam-3343	15	4	and	and	CCONJ
ejpam-3343	15	5	molodtsov	molodtsov	NOUN
ejpam-3343	16	1	[	[	X
ejpam-3343	16	2	15	15	NUM
ejpam-3343	16	3	]	]	PUNCT
ejpam-3343	16	4	suggested	suggest	VERB
ejpam-3343	16	5	that	that	SCONJ
ejpam-3343	16	6	one	one	NUM
ejpam-3343	16	7	reason	reason	NOUN
ejpam-3343	16	8	for	for	ADP
ejpam-3343	16	9	these	these	DET
ejpam-3343	16	10	difficulties	difficulty	NOUN
ejpam-3343	16	11	may	may	AUX
ejpam-3343	16	12	be	be	AUX
ejpam-3343	16	13	due	due	ADJ
ejpam-3343	16	14	to	to	ADP
ejpam-3343	16	15	the	the	DET
ejpam-3343	16	16	inadequacy	inadequacy	NOUN
ejpam-3343	16	17	of	of	ADP
ejpam-3343	16	18	the	the	DET
ejpam-3343	16	19	parametrization	parametrization	NOUN
ejpam-3343	16	20	tool	tool	NOUN
ejpam-3343	16	21	of	of	ADP
ejpam-3343	16	22	the	the	DET
ejpam-3343	16	23	theory	theory	NOUN
ejpam-3343	16	24	.	.	PUNCT
ejpam-3343	17	1	to	to	PART
ejpam-3343	17	2	overcome	overcome	VERB
ejpam-3343	17	3	these	these	DET
ejpam-3343	17	4	difficulties	difficulty	NOUN
ejpam-3343	17	5	,	,	PUNCT
ejpam-3343	17	6	molodtsov	molodtsov	NOUN
ejpam-3343	17	7	[	[	X
ejpam-3343	17	8	15	15	NUM
ejpam-3343	17	9	]	]	PUNCT
ejpam-3343	17	10	introduced	introduce	VERB
ejpam-3343	17	11	the	the	DET
ejpam-3343	17	12	concept	concept	NOUN
ejpam-3343	17	13	of	of	ADP
ejpam-3343	17	14	soft	soft	ADJ
ejpam-3343	17	15	set	set	NOUN
ejpam-3343	17	16	as	as	ADP
ejpam-3343	17	17	a	a	DET
ejpam-3343	17	18	new	new	ADJ
ejpam-3343	17	19	mathematical	mathematical	ADJ
ejpam-3343	17	20	tool	tool	NOUN
ejpam-3343	17	21	for	for	ADP
ejpam-3343	17	22	dealing	deal	VERB
ejpam-3343	17	23	with	with	ADP
ejpam-3343	17	24	uncertainties	uncertainty	NOUN
ejpam-3343	17	25	that	that	PRON
ejpam-3343	17	26	is	be	AUX
ejpam-3343	17	27	free	free	ADJ
ejpam-3343	17	28	from	from	ADP
ejpam-3343	17	29	the	the	DET
ejpam-3343	17	30	difficulties	difficulty	NOUN
ejpam-3343	17	31	that	that	PRON
ejpam-3343	17	32	have	have	AUX
ejpam-3343	17	33	troubled	trouble	VERB
ejpam-3343	17	34	the	the	DET
ejpam-3343	17	35	usual	usual	ADJ
ejpam-3343	17	36	theoretical	theoretical	ADJ
ejpam-3343	17	37	approaches	approach	NOUN
ejpam-3343	17	38	.	.	PUNCT
ejpam-3343	18	1	he	he	PRON
ejpam-3343	18	2	pointed	point	VERB
ejpam-3343	18	3	out	out	ADP
ejpam-3343	18	4	several	several	ADJ
ejpam-3343	18	5	directions	direction	NOUN
ejpam-3343	18	6	for	for	ADP
ejpam-3343	18	7	the	the	DET
ejpam-3343	18	8	applications	application	NOUN
ejpam-3343	18	9	of	of	ADP
ejpam-3343	18	10	soft	soft	ADJ
ejpam-3343	18	11	sets	set	NOUN
ejpam-3343	18	12	.	.	PUNCT
ejpam-3343	19	1	later	later	ADV
ejpam-3343	19	2	on	on	ADV
ejpam-3343	19	3	,	,	PUNCT
ejpam-3343	19	4	maji	maji	PROPN
ejpam-3343	19	5	et	et	PROPN
ejpam-3343	19	6	al	al	PROPN
ejpam-3343	19	7	.	.	PUNCT
ejpam-3343	20	1	[	[	X
ejpam-3343	20	2	13	13	NUM
ejpam-3343	20	3	]	]	PUNCT
ejpam-3343	20	4	described	describe	VERB
ejpam-3343	20	5	the	the	DET
ejpam-3343	20	6	application	application	NOUN
ejpam-3343	20	7	of	of	ADP
ejpam-3343	20	8	soft	soft	ADJ
ejpam-3343	20	9	set	set	NOUN
ejpam-3343	20	10	theory	theory	NOUN
ejpam-3343	20	11	to	to	ADP
ejpam-3343	20	12	a	a	DET
ejpam-3343	20	13	decision	decision	NOUN
ejpam-3343	20	14	making	make	VERB
ejpam-3343	20	15	problem	problem	NOUN
ejpam-3343	20	16	.	.	PUNCT
ejpam-3343	21	1	maji	maji	PROPN
ejpam-3343	21	2	et	et	PROPN
ejpam-3343	21	3	al	al	PROPN
ejpam-3343	21	4	.	.	PUNCT
ejpam-3343	22	1	[	[	X
ejpam-3343	22	2	12	12	NUM
ejpam-3343	22	3	]	]	PUNCT
ejpam-3343	22	4	also	also	ADV
ejpam-3343	22	5	studied	study	VERB
ejpam-3343	22	6	several	several	ADJ
ejpam-3343	22	7	operations	operation	NOUN
ejpam-3343	22	8	on	on	ADP
ejpam-3343	22	9	the	the	DET
ejpam-3343	22	10	theory	theory	NOUN
ejpam-3343	22	11	of	of	ADP
ejpam-3343	22	12	soft	soft	ADJ
ejpam-3343	22	13	sets	set	NOUN
ejpam-3343	22	14	.	.	PUNCT
ejpam-3343	23	1	chen	chen	PROPN
ejpam-3343	23	2	et	et	PROPN
ejpam-3343	23	3	al	al	PROPN
ejpam-3343	23	4	.	.	PUNCT
ejpam-3343	24	1	[	[	X
ejpam-3343	24	2	4	4	X
ejpam-3343	24	3	]	]	PUNCT
ejpam-3343	24	4	presented	present	VERB
ejpam-3343	24	5	a	a	DET
ejpam-3343	24	6	new	new	ADJ
ejpam-3343	24	7	definition	definition	NOUN
ejpam-3343	24	8	of	of	ADP
ejpam-3343	24	9	soft	soft	ADJ
ejpam-3343	24	10	set	set	NOUN
ejpam-3343	24	11	parametrization	parametrization	NOUN
ejpam-3343	24	12	reduction	reduction	NOUN
ejpam-3343	24	13	,	,	PUNCT
ejpam-3343	24	14	and	and	CCONJ
ejpam-3343	24	15	compared	compare	VERB
ejpam-3343	24	16	this	this	DET
ejpam-3343	24	17	definition	definition	NOUN
ejpam-3343	24	18	to	to	ADP
ejpam-3343	24	19	the	the	DET
ejpam-3343	24	20	related	relate	VERB
ejpam-3343	24	21	concept	concept	NOUN
ejpam-3343	24	22	of	of	ADP
ejpam-3343	24	23	attributes	attribute	NOUN
ejpam-3343	24	24	reduction	reduction	NOUN
ejpam-3343	24	25	in	in	ADP
ejpam-3343	24	26	rough	rough	ADJ
ejpam-3343	24	27	set	set	NOUN
ejpam-3343	24	28	theory	theory	NOUN
ejpam-3343	24	29	.	.	PUNCT
ejpam-3343	25	1	the	the	DET
ejpam-3343	25	2	algebraic	algebraic	ADJ
ejpam-3343	25	3	structure	structure	NOUN
ejpam-3343	25	4	of	of	ADP
ejpam-3343	25	5	set	set	NOUN
ejpam-3343	25	6	theories	theory	NOUN
ejpam-3343	25	7	dealing	deal	VERB
ejpam-3343	25	8	with	with	ADP
ejpam-3343	25	9	uncertainties	uncertainty	NOUN
ejpam-3343	25	10	has	have	AUX
ejpam-3343	25	11	been	be	AUX
ejpam-3343	25	12	studied	study	VERB
ejpam-3343	25	13	by	by	ADP
ejpam-3343	25	14	some	some	DET
ejpam-3343	25	15	authors	author	NOUN
ejpam-3343	25	16	.	.	PUNCT
ejpam-3343	26	1	the	the	DET
ejpam-3343	26	2	most	most	ADV
ejpam-3343	26	3	appropriate	appropriate	ADJ
ejpam-3343	26	4	theory	theory	NOUN
ejpam-3343	26	5	for	for	ADP
ejpam-3343	26	6	dealing	deal	VERB
ejpam-3343	26	7	with	with	ADP
ejpam-3343	26	8	uncertainties	uncertainty	NOUN
ejpam-3343	26	9	is	be	AUX
ejpam-3343	26	10	the	the	DET
ejpam-3343	26	11	theory	theory	NOUN
ejpam-3343	26	12	of	of	ADP
ejpam-3343	26	13	fuzzy	fuzzy	ADJ
ejpam-3343	26	14	sets	set	NOUN
ejpam-3343	26	15	developed	develop	VERB
ejpam-3343	26	16	by	by	ADP
ejpam-3343	26	17	zadeh	zadeh	PROPN
ejpam-3343	26	18	[	[	X
ejpam-3343	26	19	21	21	NUM
ejpam-3343	26	20	]	]	PUNCT
ejpam-3343	26	21	.	.	PUNCT
ejpam-3343	27	1	roy	roy	PROPN
ejpam-3343	27	2	et	et	PROPN
ejpam-3343	27	3	al	al	PROPN
ejpam-3343	27	4	.	.	PUNCT
ejpam-3343	28	1	[	[	X
ejpam-3343	28	2	20	20	NUM
ejpam-3343	28	3	]	]	PUNCT
ejpam-3343	28	4	presented	present	VERB
ejpam-3343	28	5	some	some	DET
ejpam-3343	28	6	results	result	NOUN
ejpam-3343	28	7	on	on	ADP
ejpam-3343	28	8	an	an	DET
ejpam-3343	28	9	application	application	NOUN
ejpam-3343	28	10	of	of	ADP
ejpam-3343	28	11	fuzzy	fuzzy	ADJ
ejpam-3343	28	12	soft	soft	ADJ
ejpam-3343	28	13	sets	set	NOUN
ejpam-3343	28	14	in	in	ADP
ejpam-3343	28	15	decision	decision	NOUN
ejpam-3343	28	16	making	making	NOUN
ejpam-3343	28	17	problem	problem	NOUN
ejpam-3343	28	18	.	.	PUNCT
ejpam-3343	29	1	∗corresponding	∗corresponde	VERB
ejpam-3343	29	2	author	author	NOUN
ejpam-3343	29	3	.	.	PUNCT
ejpam-3343	30	1	doi	doi	NOUN
ejpam-3343	30	2	:	:	PUNCT
ejpam-3343	30	3	https://doi.org/10.29020/nybg.ejpam.v12i1.3343	https://doi.org/10.29020/nybg.ejpam.v12i1.3343	PROPN
ejpam-3343	30	4	email	email	NOUN
ejpam-3343	30	5	addresses	address	NOUN
ejpam-3343	30	6	:	:	PUNCT
ejpam-3343	31	1	chishtygm@gmail.com	chishtygm@gmail.com	X
ejpam-3343	31	2	(	(	PUNCT
ejpam-3343	31	3	g.	g.	PROPN
ejpam-3343	31	4	muhiuddin	muhiuddin	PROPN
ejpam-3343	31	5	)	)	PUNCT
ejpam-3343	31	6	,	,	PUNCT
ejpam-3343	31	7	saldhafeeri@yahoo.com	saldhafeeri@yahoo.com	X
ejpam-3343	31	8	(	(	PUNCT
ejpam-3343	31	9	s.	s.	PROPN
ejpam-3343	31	10	aldhafeeri	aldhafeeri	PROPN
ejpam-3343	31	11	)	)	PUNCT
ejpam-3343	31	12	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3343	32	1	79	79	NUM
ejpam-3343	33	1	c	c	X
ejpam-3343	33	2	©	©	PROPN
ejpam-3343	33	3	2019	2019	NUM
ejpam-3343	33	4	ejpam	ejpam	NOUN
ejpam-3343	33	5	all	all	DET
ejpam-3343	33	6	rights	right	NOUN
ejpam-3343	33	7	reserved	reserve	VERB
ejpam-3343	33	8	.	.	PUNCT
ejpam-3343	34	1	g.	g.	PROPN
ejpam-3343	34	2	muhiuddin	muhiuddin	PROPN
ejpam-3343	34	3	,	,	PUNCT
ejpam-3343	34	4	s.	s.	PROPN
ejpam-3343	34	5	aldhafeeri	aldhafeeri	PROPN
ejpam-3343	34	6	/	/	SYM
ejpam-3343	34	7	eur	eur	PROPN
ejpam-3343	34	8	.	.	PUNCT
ejpam-3343	35	1	j.	j.	PROPN
ejpam-3343	35	2	pure	pure	PROPN
ejpam-3343	35	3	appl	appl	PROPN
ejpam-3343	35	4	.	.	PROPN
ejpam-3343	35	5	math	math	PROPN
ejpam-3343	35	6	,	,	PUNCT
ejpam-3343	35	7	12	12	NUM
ejpam-3343	35	8	(	(	PUNCT
ejpam-3343	35	9	1	1	NUM
ejpam-3343	35	10	)	)	PUNCT
ejpam-3343	35	11	(	(	PUNCT
ejpam-3343	35	12	2019	2019	NUM
ejpam-3343	35	13	)	)	PUNCT
ejpam-3343	35	14	,	,	PUNCT
ejpam-3343	35	15	79	79	NUM
ejpam-3343	35	16	-	-	SYM
ejpam-3343	35	17	87	87	NUM
ejpam-3343	35	18	80	80	NUM
ejpam-3343	35	19	aygünoǧlu	aygünoǧlu	NOUN
ejpam-3343	35	20	et	et	PROPN
ejpam-3343	35	21	al	al	PROPN
ejpam-3343	35	22	.	.	PUNCT
ejpam-3343	36	1	[	[	X
ejpam-3343	36	2	2	2	X
ejpam-3343	36	3	]	]	PUNCT
ejpam-3343	36	4	introduced	introduce	VERB
ejpam-3343	36	5	the	the	DET
ejpam-3343	36	6	notion	notion	NOUN
ejpam-3343	36	7	of	of	ADP
ejpam-3343	36	8	fuzzy	fuzzy	ADJ
ejpam-3343	36	9	soft	soft	ADJ
ejpam-3343	36	10	group	group	NOUN
ejpam-3343	36	11	and	and	CCONJ
ejpam-3343	36	12	studied	study	VERB
ejpam-3343	36	13	its	its	PRON
ejpam-3343	36	14	properties	property	NOUN
ejpam-3343	36	15	.	.	PUNCT
ejpam-3343	37	1	ali	ali	PROPN
ejpam-3343	37	2	et	et	PROPN
ejpam-3343	37	3	al	al	PROPN
ejpam-3343	37	4	.	.	PUNCT
ejpam-3343	38	1	[	[	X
ejpam-3343	38	2	3	3	X
ejpam-3343	38	3	]	]	PUNCT
ejpam-3343	38	4	discussed	discuss	VERB
ejpam-3343	38	5	new	new	ADJ
ejpam-3343	38	6	operations	operation	NOUN
ejpam-3343	38	7	in	in	ADP
ejpam-3343	38	8	soft	soft	ADJ
ejpam-3343	38	9	set	set	NOUN
ejpam-3343	38	10	theory	theory	NOUN
ejpam-3343	38	11	.	.	PUNCT
ejpam-3343	39	1	jun	jun	PROPN
ejpam-3343	40	1	[	[	X
ejpam-3343	40	2	6	6	NUM
ejpam-3343	40	3	]	]	PUNCT
ejpam-3343	40	4	applied	apply	VERB
ejpam-3343	40	5	the	the	DET
ejpam-3343	40	6	notion	notion	NOUN
ejpam-3343	40	7	of	of	ADP
ejpam-3343	40	8	soft	soft	ADJ
ejpam-3343	40	9	set	set	NOUN
ejpam-3343	40	10	to	to	PART
ejpam-3343	40	11	bck	bck	VERB
ejpam-3343	40	12	/	/	SYM
ejpam-3343	40	13	bci	bci	NOUN
ejpam-3343	40	14	-	-	PUNCT
ejpam-3343	40	15	algebras	algebra	NOUN
ejpam-3343	40	16	,	,	PUNCT
ejpam-3343	40	17	and	and	CCONJ
ejpam-3343	40	18	jun	jun	PROPN
ejpam-3343	40	19	et	et	PROPN
ejpam-3343	40	20	al	al	PROPN
ejpam-3343	40	21	.	.	PUNCT
ejpam-3343	41	1	[	[	X
ejpam-3343	41	2	8	8	NUM
ejpam-3343	41	3	]	]	PUNCT
ejpam-3343	41	4	considered	consider	VERB
ejpam-3343	41	5	applications	application	NOUN
ejpam-3343	41	6	of	of	ADP
ejpam-3343	41	7	soft	soft	ADJ
ejpam-3343	41	8	set	set	NOUN
ejpam-3343	41	9	theory	theory	NOUN
ejpam-3343	41	10	in	in	ADP
ejpam-3343	41	11	the	the	DET
ejpam-3343	41	12	ideals	ideal	NOUN
ejpam-3343	41	13	of	of	ADP
ejpam-3343	41	14	d	d	NOUN
ejpam-3343	41	15	-	-	PUNCT
ejpam-3343	41	16	algebras	algebras	X
ejpam-3343	41	17	.	.	PUNCT
ejpam-3343	42	1	also	also	ADV
ejpam-3343	42	2	,	,	PUNCT
ejpam-3343	42	3	muhiuddin	muhiuddin	VERB
ejpam-3343	42	4	et	et	PROPN
ejpam-3343	42	5	al	al	PROPN
ejpam-3343	42	6	.	.	PROPN
ejpam-3343	42	7	studied	study	VERB
ejpam-3343	42	8	the	the	DET
ejpam-3343	42	9	soft	soft	ADJ
ejpam-3343	42	10	set	set	NOUN
ejpam-3343	42	11	theory	theory	NOUN
ejpam-3343	42	12	on	on	ADP
ejpam-3343	42	13	various	various	ADJ
ejpam-3343	42	14	aspects	aspect	NOUN
ejpam-3343	42	15	(	(	PUNCT
ejpam-3343	42	16	see	see	VERB
ejpam-3343	42	17	for	for	ADP
ejpam-3343	42	18	e.g.	e.g.	ADV
ejpam-3343	42	19	,	,	PUNCT
ejpam-3343	42	20	[	[	X
ejpam-3343	42	21	1	1	NUM
ejpam-3343	42	22	]	]	PUNCT
ejpam-3343	42	23	,	,	PUNCT
ejpam-3343	43	1	[	[	X
ejpam-3343	43	2	16	16	NUM
ejpam-3343	43	3	]	]	PUNCT
ejpam-3343	43	4	,	,	PUNCT
ejpam-3343	43	5	[	[	X
ejpam-3343	43	6	17	17	NUM
ejpam-3343	43	7	]	]	NUM
ejpam-3343	43	8	)	)	PUNCT
ejpam-3343	43	9	,	,	PUNCT
ejpam-3343	43	10	[	[	X
ejpam-3343	43	11	18	18	NUM
ejpam-3343	43	12	]	]	PUNCT
ejpam-3343	43	13	,	,	PUNCT
ejpam-3343	43	14	[	[	X
ejpam-3343	43	15	19	19	NUM
ejpam-3343	43	16	]	]	NUM
ejpam-3343	43	17	)	)	PUNCT
ejpam-3343	43	18	.	.	PUNCT
ejpam-3343	44	1	a	a	PRON
ejpam-3343	44	2	(	(	PUNCT
ejpam-3343	44	3	crisp	crisp	ADJ
ejpam-3343	44	4	)	)	PUNCT
ejpam-3343	44	5	set	set	VERB
ejpam-3343	44	6	a	a	PRON
ejpam-3343	44	7	in	in	ADP
ejpam-3343	44	8	a	a	DET
ejpam-3343	44	9	universe	universe	NOUN
ejpam-3343	44	10	x	x	PRON
ejpam-3343	44	11	can	can	AUX
ejpam-3343	44	12	be	be	AUX
ejpam-3343	44	13	defined	define	VERB
ejpam-3343	44	14	in	in	ADP
ejpam-3343	44	15	the	the	DET
ejpam-3343	44	16	form	form	NOUN
ejpam-3343	44	17	of	of	ADP
ejpam-3343	44	18	its	its	PRON
ejpam-3343	44	19	characteristic	characteristic	ADJ
ejpam-3343	44	20	function	function	NOUN
ejpam-3343	44	21	µa	µa	NOUN
ejpam-3343	44	22	:	:	PUNCT
ejpam-3343	44	23	x	x	X
ejpam-3343	44	24	→	→	X
ejpam-3343	44	25	{	{	PUNCT
ejpam-3343	44	26	0	0	NUM
ejpam-3343	44	27	,	,	PUNCT
ejpam-3343	44	28	1	1	X
ejpam-3343	44	29	}	}	PUNCT
ejpam-3343	44	30	yielding	yield	VERB
ejpam-3343	44	31	the	the	DET
ejpam-3343	44	32	value	value	NOUN
ejpam-3343	44	33	1	1	NUM
ejpam-3343	44	34	for	for	ADP
ejpam-3343	44	35	elements	element	NOUN
ejpam-3343	44	36	belonging	belong	VERB
ejpam-3343	44	37	to	to	ADP
ejpam-3343	44	38	the	the	DET
ejpam-3343	44	39	set	set	NOUN
ejpam-3343	44	40	a	a	PRON
ejpam-3343	44	41	and	and	CCONJ
ejpam-3343	44	42	the	the	DET
ejpam-3343	44	43	value	value	NOUN
ejpam-3343	44	44	0	0	NUM
ejpam-3343	44	45	for	for	ADP
ejpam-3343	44	46	elements	element	NOUN
ejpam-3343	44	47	excluded	exclude	VERB
ejpam-3343	44	48	from	from	ADP
ejpam-3343	44	49	the	the	DET
ejpam-3343	44	50	set	set	NOUN
ejpam-3343	44	51	a.	a.	NOUN
ejpam-3343	44	52	so	so	ADV
ejpam-3343	44	53	far	far	ADV
ejpam-3343	44	54	most	most	ADJ
ejpam-3343	44	55	of	of	ADP
ejpam-3343	44	56	the	the	DET
ejpam-3343	44	57	generalization	generalization	NOUN
ejpam-3343	44	58	of	of	ADP
ejpam-3343	44	59	the	the	DET
ejpam-3343	44	60	crisp	crisp	ADJ
ejpam-3343	44	61	set	set	NOUN
ejpam-3343	44	62	have	have	AUX
ejpam-3343	44	63	been	be	AUX
ejpam-3343	44	64	conducted	conduct	VERB
ejpam-3343	44	65	on	on	ADP
ejpam-3343	44	66	the	the	DET
ejpam-3343	44	67	unit	unit	NOUN
ejpam-3343	44	68	interval	interval	NOUN
ejpam-3343	45	1	[	[	X
ejpam-3343	45	2	0	0	NUM
ejpam-3343	45	3	,	,	PUNCT
ejpam-3343	45	4	1	1	NUM
ejpam-3343	45	5	]	]	PUNCT
ejpam-3343	45	6	and	and	CCONJ
ejpam-3343	45	7	they	they	PRON
ejpam-3343	45	8	are	be	AUX
ejpam-3343	45	9	consistent	consistent	ADJ
ejpam-3343	45	10	with	with	ADP
ejpam-3343	45	11	the	the	DET
ejpam-3343	45	12	asymmetry	asymmetry	NOUN
ejpam-3343	45	13	observation	observation	NOUN
ejpam-3343	45	14	.	.	PUNCT
ejpam-3343	46	1	in	in	ADP
ejpam-3343	46	2	other	other	ADJ
ejpam-3343	46	3	words	word	NOUN
ejpam-3343	46	4	,	,	PUNCT
ejpam-3343	46	5	the	the	DET
ejpam-3343	46	6	generalization	generalization	NOUN
ejpam-3343	46	7	of	of	ADP
ejpam-3343	46	8	the	the	DET
ejpam-3343	46	9	crisp	crisp	ADJ
ejpam-3343	46	10	set	set	NOUN
ejpam-3343	46	11	to	to	ADP
ejpam-3343	46	12	fuzzy	fuzzy	ADJ
ejpam-3343	46	13	sets	set	NOUN
ejpam-3343	46	14	relied	rely	VERB
ejpam-3343	46	15	on	on	ADP
ejpam-3343	46	16	spreading	spread	VERB
ejpam-3343	46	17	positive	positive	ADJ
ejpam-3343	46	18	information	information	NOUN
ejpam-3343	46	19	that	that	PRON
ejpam-3343	46	20	fit	fit	VERB
ejpam-3343	46	21	the	the	DET
ejpam-3343	46	22	crisp	crisp	ADJ
ejpam-3343	46	23	point	point	NOUN
ejpam-3343	46	24	{	{	PUNCT
ejpam-3343	46	25	1	1	NUM
ejpam-3343	46	26	}	}	PUNCT
ejpam-3343	46	27	into	into	ADP
ejpam-3343	46	28	the	the	DET
ejpam-3343	46	29	interval	interval	NOUN
ejpam-3343	46	30	[	[	X
ejpam-3343	46	31	0	0	NUM
ejpam-3343	46	32	,	,	PUNCT
ejpam-3343	46	33	1	1	NUM
ejpam-3343	46	34	]	]	PUNCT
ejpam-3343	46	35	.	.	PUNCT
ejpam-3343	47	1	because	because	SCONJ
ejpam-3343	47	2	no	no	DET
ejpam-3343	47	3	negative	negative	ADJ
ejpam-3343	47	4	meaning	meaning	NOUN
ejpam-3343	47	5	of	of	ADP
ejpam-3343	47	6	information	information	NOUN
ejpam-3343	47	7	is	be	AUX
ejpam-3343	47	8	suggested	suggest	VERB
ejpam-3343	47	9	,	,	PUNCT
ejpam-3343	47	10	so	so	ADV
ejpam-3343	47	11	one	one	PRON
ejpam-3343	47	12	should	should	AUX
ejpam-3343	47	13	be	be	AUX
ejpam-3343	47	14	interested	interested	ADJ
ejpam-3343	47	15	to	to	PART
ejpam-3343	47	16	deal	deal	VERB
ejpam-3343	47	17	with	with	ADP
ejpam-3343	47	18	negative	negative	ADJ
ejpam-3343	47	19	information	information	NOUN
ejpam-3343	47	20	and	and	CCONJ
ejpam-3343	47	21	to	to	PART
ejpam-3343	47	22	supply	supply	VERB
ejpam-3343	47	23	a	a	DET
ejpam-3343	47	24	mathematical	mathematical	ADJ
ejpam-3343	47	25	tool	tool	NOUN
ejpam-3343	47	26	for	for	ADP
ejpam-3343	47	27	the	the	DET
ejpam-3343	47	28	same	same	ADJ
ejpam-3343	47	29	.	.	PUNCT
ejpam-3343	48	1	considering	consider	VERB
ejpam-3343	48	2	this	this	DET
ejpam-3343	48	3	fact	fact	NOUN
ejpam-3343	48	4	,	,	PUNCT
ejpam-3343	48	5	jun	jun	PROPN
ejpam-3343	48	6	et	et	PROPN
ejpam-3343	48	7	al	al	PROPN
ejpam-3343	48	8	.	.	PUNCT
ejpam-3343	49	1	[	[	X
ejpam-3343	49	2	9	9	NUM
ejpam-3343	49	3	]	]	PUNCT
ejpam-3343	49	4	introduced	introduce	VERB
ejpam-3343	49	5	a	a	DET
ejpam-3343	49	6	new	new	ADJ
ejpam-3343	49	7	function	function	NOUN
ejpam-3343	49	8	which	which	PRON
ejpam-3343	49	9	is	be	AUX
ejpam-3343	49	10	called	call	VERB
ejpam-3343	49	11	negative	negative	ADV
ejpam-3343	49	12	-	-	PUNCT
ejpam-3343	49	13	valued	value	VERB
ejpam-3343	49	14	function	function	NOUN
ejpam-3343	49	15	,	,	PUNCT
ejpam-3343	49	16	and	and	CCONJ
ejpam-3343	49	17	constructed	construct	VERB
ejpam-3343	49	18	n	n	PRON
ejpam-3343	49	19	-structures	-structure	NOUN
ejpam-3343	49	20	.	.	PUNCT
ejpam-3343	50	1	they	they	PRON
ejpam-3343	50	2	applied	apply	VERB
ejpam-3343	50	3	n	n	DET
ejpam-3343	50	4	-structures	-structure	NOUN
ejpam-3343	50	5	to	to	PART
ejpam-3343	50	6	bck	bck	VERB
ejpam-3343	50	7	/	/	SYM
ejpam-3343	50	8	bci	bci	NOUN
ejpam-3343	50	9	-	-	PUNCT
ejpam-3343	50	10	algebras	algebras	X
ejpam-3343	50	11	,	,	PUNCT
ejpam-3343	50	12	and	and	CCONJ
ejpam-3343	50	13	discussed	discuss	VERB
ejpam-3343	50	14	n	n	CCONJ
ejpam-3343	50	15	-subalgebras	-subalgebra	NOUN
ejpam-3343	50	16	and	and	CCONJ
ejpam-3343	50	17	n	n	NUM
ejpam-3343	50	18	-ideals	-ideal	NOUN
ejpam-3343	50	19	in	in	ADP
ejpam-3343	50	20	bck	bck	PROPN
ejpam-3343	50	21	/	/	SYM
ejpam-3343	50	22	bci	bci	NOUN
ejpam-3343	50	23	-	-	PUNCT
ejpam-3343	50	24	algebras	algebras	X
ejpam-3343	50	25	.	.	PUNCT
ejpam-3343	51	1	jun	jun	PROPN
ejpam-3343	51	2	et	et	PROPN
ejpam-3343	51	3	al	al	PROPN
ejpam-3343	51	4	.	.	PUNCT
ejpam-3343	52	1	[	[	X
ejpam-3343	52	2	10	10	NUM
ejpam-3343	52	3	]	]	PUNCT
ejpam-3343	52	4	considered	consider	VERB
ejpam-3343	52	5	closed	closed	ADJ
ejpam-3343	52	6	ideals	ideal	NOUN
ejpam-3343	52	7	in	in	ADP
ejpam-3343	52	8	bch	bch	PROPN
ejpam-3343	52	9	-	-	PUNCT
ejpam-3343	52	10	algebras	algebras	PROPN
ejpam-3343	52	11	based	base	VERB
ejpam-3343	52	12	on	on	ADP
ejpam-3343	52	13	n	n	DET
ejpam-3343	52	14	-structures	-structure	NOUN
ejpam-3343	52	15	.	.	PUNCT
ejpam-3343	53	1	jun	jun	PROPN
ejpam-3343	53	2	et	et	PROPN
ejpam-3343	53	3	al	al	PROPN
ejpam-3343	53	4	.	.	PUNCT
ejpam-3343	54	1	[	[	X
ejpam-3343	54	2	11	11	NUM
ejpam-3343	54	3	]	]	PUNCT
ejpam-3343	54	4	introduced	introduce	VERB
ejpam-3343	54	5	the	the	DET
ejpam-3343	54	6	notion	notion	NOUN
ejpam-3343	54	7	of	of	ADP
ejpam-3343	54	8	n	n	CCONJ
ejpam-3343	54	9	-soft	-soft	ADJ
ejpam-3343	54	10	sets	set	NOUN
ejpam-3343	54	11	which	which	PRON
ejpam-3343	54	12	are	be	AUX
ejpam-3343	54	13	a	a	DET
ejpam-3343	54	14	soft	soft	ADJ
ejpam-3343	54	15	set	set	NOUN
ejpam-3343	54	16	based	base	VERB
ejpam-3343	54	17	on	on	ADP
ejpam-3343	54	18	n	n	DET
ejpam-3343	54	19	-structures	-structure	NOUN
ejpam-3343	54	20	,	,	PUNCT
ejpam-3343	54	21	and	and	CCONJ
ejpam-3343	54	22	then	then	ADV
ejpam-3343	54	23	they	they	PRON
ejpam-3343	54	24	applied	apply	VERB
ejpam-3343	54	25	it	it	PRON
ejpam-3343	54	26	to	to	ADP
ejpam-3343	54	27	both	both	CCONJ
ejpam-3343	54	28	a	a	DET
ejpam-3343	54	29	decision	decision	NOUN
ejpam-3343	54	30	making	make	VERB
ejpam-3343	54	31	problem	problem	NOUN
ejpam-3343	54	32	and	and	CCONJ
ejpam-3343	54	33	a	a	DET
ejpam-3343	54	34	bck	bck	VERB
ejpam-3343	54	35	/	/	SYM
ejpam-3343	54	36	bci	bci	NOUN
ejpam-3343	54	37	-	-	NOUN
ejpam-3343	54	38	algebra	algebra	NOUN
ejpam-3343	54	39	.	.	PUNCT
ejpam-3343	55	1	jun	jun	PROPN
ejpam-3343	55	2	et	et	PROPN
ejpam-3343	55	3	al	al	PROPN
ejpam-3343	56	1	[	[	X
ejpam-3343	56	2	7	7	X
ejpam-3343	56	3	]	]	PUNCT
ejpam-3343	56	4	introduced	introduce	VERB
ejpam-3343	56	5	the	the	DET
ejpam-3343	56	6	notion	notion	NOUN
ejpam-3343	56	7	of	of	ADP
ejpam-3343	56	8	(	(	PUNCT
ejpam-3343	56	9	closed	closed	ADJ
ejpam-3343	56	10	)	)	PUNCT
ejpam-3343	56	11	n	n	X
ejpam-3343	57	1	-ideal	-ideal	ADJ
ejpam-3343	57	2	over	over	ADP
ejpam-3343	57	3	a	a	DET
ejpam-3343	57	4	bci	bci	NOUN
ejpam-3343	57	5	-	-	NOUN
ejpam-3343	57	6	algebra	algebra	NOUN
ejpam-3343	57	7	based	base	VERB
ejpam-3343	57	8	on	on	ADP
ejpam-3343	57	9	soft	soft	ADJ
ejpam-3343	57	10	sets	set	NOUN
ejpam-3343	57	11	and	and	CCONJ
ejpam-3343	57	12	n	n	DET
ejpam-3343	57	13	-structures	-structure	NOUN
ejpam-3343	57	14	,	,	PUNCT
ejpam-3343	57	15	and	and	CCONJ
ejpam-3343	57	16	investigated	investigate	VERB
ejpam-3343	57	17	related	related	ADJ
ejpam-3343	57	18	properties	property	NOUN
ejpam-3343	57	19	.	.	PUNCT
ejpam-3343	58	1	they	they	PRON
ejpam-3343	58	2	established	establish	VERB
ejpam-3343	58	3	relations	relation	NOUN
ejpam-3343	58	4	between	between	ADP
ejpam-3343	58	5	n	n	NOUN
ejpam-3343	58	6	-bci	-bci	ADV
ejpam-3343	58	7	-	-	PUNCT
ejpam-3343	58	8	algebras	algebra	NOUN
ejpam-3343	58	9	and	and	CCONJ
ejpam-3343	58	10	n	n	PRON
ejpam-3343	58	11	-ideals	-ideal	NOUN
ejpam-3343	58	12	.	.	PUNCT
ejpam-3343	59	1	they	they	PRON
ejpam-3343	59	2	also	also	ADV
ejpam-3343	59	3	provided	provide	VERB
ejpam-3343	59	4	characterizations	characterization	NOUN
ejpam-3343	59	5	of	of	ADP
ejpam-3343	59	6	a	a	DET
ejpam-3343	59	7	(	(	PUNCT
ejpam-3343	59	8	closed	closed	ADJ
ejpam-3343	59	9	)	)	PUNCT
ejpam-3343	59	10	n	n	X
ejpam-3343	59	11	-ideal	-ideal	ADJ
ejpam-3343	59	12	over	over	ADP
ejpam-3343	59	13	a	a	DET
ejpam-3343	59	14	bci	bci	NOUN
ejpam-3343	59	15	-	-	NOUN
ejpam-3343	59	16	algebra	algebra	NOUN
ejpam-3343	59	17	,	,	PUNCT
ejpam-3343	59	18	and	and	CCONJ
ejpam-3343	59	19	considered	consider	VERB
ejpam-3343	59	20	conditions	condition	NOUN
ejpam-3343	59	21	for	for	ADP
ejpam-3343	59	22	an	an	DET
ejpam-3343	59	23	n	n	ADV
ejpam-3343	59	24	-ideal	-ideal	NOUN
ejpam-3343	59	25	to	to	PART
ejpam-3343	59	26	be	be	AUX
ejpam-3343	59	27	an	an	DET
ejpam-3343	59	28	n	n	PRON
ejpam-3343	59	29	-bci	-bci	PRON
ejpam-3343	59	30	-	-	PUNCT
ejpam-3343	59	31	algebra	algebra	NOUN
ejpam-3343	59	32	.	.	PUNCT
ejpam-3343	60	1	in	in	ADP
ejpam-3343	60	2	this	this	DET
ejpam-3343	60	3	paper	paper	NOUN
ejpam-3343	60	4	,	,	PUNCT
ejpam-3343	60	5	we	we	PRON
ejpam-3343	60	6	apply	apply	VERB
ejpam-3343	60	7	the	the	DET
ejpam-3343	60	8	soft	soft	ADJ
ejpam-3343	60	9	sets	set	NOUN
ejpam-3343	60	10	and	and	CCONJ
ejpam-3343	60	11	n	n	DET
ejpam-3343	60	12	-structures	-structure	NOUN
ejpam-3343	60	13	to	to	ADP
ejpam-3343	60	14	p	p	NOUN
ejpam-3343	60	15	-	-	PUNCT
ejpam-3343	60	16	ideals	ideal	NOUN
ejpam-3343	60	17	in	in	ADP
ejpam-3343	60	18	bci	bci	NOUN
ejpam-3343	60	19	-	-	PUNCT
ejpam-3343	60	20	algebras	algebras	X
ejpam-3343	60	21	.	.	PUNCT
ejpam-3343	61	1	we	we	PRON
ejpam-3343	61	2	introduce	introduce	VERB
ejpam-3343	61	3	the	the	DET
ejpam-3343	61	4	notion	notion	NOUN
ejpam-3343	61	5	ofn	ofn	PROPN
ejpam-3343	61	6	-soft	-soft	PROPN
ejpam-3343	61	7	p	p	NOUN
ejpam-3343	61	8	-	-	PUNCT
ejpam-3343	61	9	ideals	ideal	NOUN
ejpam-3343	61	10	in	in	ADP
ejpam-3343	61	11	bci	bci	NOUN
ejpam-3343	61	12	-	-	PUNCT
ejpam-3343	61	13	algebras	algebras	X
ejpam-3343	61	14	,	,	PUNCT
ejpam-3343	61	15	and	and	CCONJ
ejpam-3343	61	16	investigate	investigate	VERB
ejpam-3343	61	17	related	related	ADJ
ejpam-3343	61	18	properties	property	NOUN
ejpam-3343	61	19	.	.	PUNCT
ejpam-3343	62	1	we	we	PRON
ejpam-3343	62	2	provide	provide	VERB
ejpam-3343	62	3	relations	relation	NOUN
ejpam-3343	62	4	between	between	ADP
ejpam-3343	62	5	n	n	NUM
ejpam-3343	62	6	-soft	-soft	ADJ
ejpam-3343	62	7	ideals	ideal	NOUN
ejpam-3343	62	8	and	and	CCONJ
ejpam-3343	62	9	n	n	CCONJ
ejpam-3343	62	10	-soft	-soft	ADJ
ejpam-3343	62	11	p	p	NOUN
ejpam-3343	62	12	-	-	PUNCT
ejpam-3343	62	13	ideals	ideal	NOUN
ejpam-3343	62	14	,	,	PUNCT
ejpam-3343	62	15	and	and	CCONJ
ejpam-3343	62	16	establish	establish	VERB
ejpam-3343	62	17	conditions	condition	NOUN
ejpam-3343	62	18	for	for	ADP
ejpam-3343	62	19	an	an	DET
ejpam-3343	62	20	n	n	CCONJ
ejpam-3343	62	21	-soft	-soft	ADJ
ejpam-3343	62	22	ideal	ideal	NOUN
ejpam-3343	62	23	to	to	PART
ejpam-3343	62	24	be	be	AUX
ejpam-3343	62	25	an	an	DET
ejpam-3343	62	26	n	n	CCONJ
ejpam-3343	62	27	-soft	-soft	ADJ
ejpam-3343	62	28	p	p	NOUN
ejpam-3343	62	29	-	-	PUNCT
ejpam-3343	62	30	ideal	ideal	NOUN
ejpam-3343	62	31	.	.	PUNCT
ejpam-3343	63	1	2	2	X
ejpam-3343	63	2	.	.	NUM
ejpam-3343	63	3	preliminaries	preliminary	NOUN
ejpam-3343	63	4	a	a	DET
ejpam-3343	63	5	bck	bck	PROPN
ejpam-3343	63	6	/	/	SYM
ejpam-3343	63	7	bci	bci	NOUN
ejpam-3343	63	8	-	-	NOUN
ejpam-3343	63	9	algebra	algebra	NOUN
ejpam-3343	63	10	is	be	AUX
ejpam-3343	63	11	an	an	DET
ejpam-3343	63	12	important	important	ADJ
ejpam-3343	63	13	class	class	NOUN
ejpam-3343	63	14	of	of	ADP
ejpam-3343	63	15	logical	logical	ADJ
ejpam-3343	63	16	algebras	algebra	NOUN
ejpam-3343	63	17	introduced	introduce	VERB
ejpam-3343	63	18	by	by	ADP
ejpam-3343	63	19	k.	k.	PROPN
ejpam-3343	63	20	iséki	iséki	PROPN
ejpam-3343	63	21	and	and	CCONJ
ejpam-3343	63	22	was	be	AUX
ejpam-3343	63	23	extensively	extensively	ADV
ejpam-3343	63	24	investigated	investigate	VERB
ejpam-3343	63	25	by	by	ADP
ejpam-3343	63	26	several	several	ADJ
ejpam-3343	63	27	researchers	researcher	NOUN
ejpam-3343	63	28	.	.	PUNCT
ejpam-3343	64	1	an	an	DET
ejpam-3343	64	2	algebra	algebra	NOUN
ejpam-3343	64	3	(	(	PUNCT
ejpam-3343	64	4	x	x	NOUN
ejpam-3343	64	5	;	;	PUNCT
ejpam-3343	64	6	∗	∗	NOUN
ejpam-3343	64	7	,	,	PUNCT
ejpam-3343	64	8	0	0	NUM
ejpam-3343	64	9	)	)	PUNCT
ejpam-3343	64	10	of	of	ADP
ejpam-3343	64	11	type	type	NOUN
ejpam-3343	64	12	(	(	PUNCT
ejpam-3343	64	13	2	2	NUM
ejpam-3343	64	14	,	,	PUNCT
ejpam-3343	64	15	0	0	NUM
ejpam-3343	64	16	)	)	PUNCT
ejpam-3343	64	17	is	be	AUX
ejpam-3343	64	18	called	call	VERB
ejpam-3343	64	19	a	a	DET
ejpam-3343	64	20	bci	bci	NOUN
ejpam-3343	64	21	-	-	NOUN
ejpam-3343	64	22	algebra	algebra	NOUN
ejpam-3343	64	23	if	if	SCONJ
ejpam-3343	64	24	it	it	PRON
ejpam-3343	64	25	satisfies	satisfy	VERB
ejpam-3343	64	26	the	the	DET
ejpam-3343	64	27	following	follow	VERB
ejpam-3343	64	28	conditions	condition	NOUN
ejpam-3343	64	29	:	:	PUNCT
ejpam-3343	64	30	(	(	PUNCT
ejpam-3343	64	31	i	i	NOUN
ejpam-3343	64	32	)	)	PUNCT
ejpam-3343	64	33	(	(	PUNCT
ejpam-3343	64	34	∀x	∀x	X
ejpam-3343	64	35	,	,	PUNCT
ejpam-3343	64	36	y	y	PROPN
ejpam-3343	64	37	,	,	PUNCT
ejpam-3343	64	38	z	z	NOUN
ejpam-3343	64	39	∈	∈	PROPN
ejpam-3343	64	40	x	x	X
ejpam-3343	64	41	)	)	PUNCT
ejpam-3343	64	42	(	(	PUNCT
ejpam-3343	64	43	(	(	PUNCT
ejpam-3343	64	44	(	(	PUNCT
ejpam-3343	64	45	x	x	SYM
ejpam-3343	64	46	∗	∗	PROPN
ejpam-3343	64	47	y	y	NOUN
ejpam-3343	64	48	)	)	PUNCT
ejpam-3343	64	49	∗	∗	NOUN
ejpam-3343	64	50	(	(	PUNCT
ejpam-3343	64	51	x	x	X
ejpam-3343	64	52	∗	∗	PROPN
ejpam-3343	64	53	z	z	NOUN
ejpam-3343	64	54	)	)	PUNCT
ejpam-3343	64	55	)	)	PUNCT
ejpam-3343	64	56	∗	∗	NOUN
ejpam-3343	64	57	(	(	PUNCT
ejpam-3343	64	58	z	z	NOUN
ejpam-3343	64	59	∗	∗	NOUN
ejpam-3343	64	60	y	y	NOUN
ejpam-3343	64	61	)	)	PUNCT
ejpam-3343	64	62	=	=	SYM
ejpam-3343	64	63	0	0	NUM
ejpam-3343	64	64	)	)	PUNCT
ejpam-3343	64	65	,	,	PUNCT
ejpam-3343	64	66	(	(	PUNCT
ejpam-3343	64	67	ii	ii	NOUN
ejpam-3343	64	68	)	)	PUNCT
ejpam-3343	64	69	(	(	PUNCT
ejpam-3343	64	70	∀x	∀x	X
ejpam-3343	64	71	,	,	PUNCT
ejpam-3343	64	72	y	y	PROPN
ejpam-3343	64	73	∈	∈	PROPN
ejpam-3343	64	74	x	x	X
ejpam-3343	64	75	)	)	PUNCT
ejpam-3343	64	76	(	(	PUNCT
ejpam-3343	64	77	(	(	PUNCT
ejpam-3343	64	78	x	x	SYM
ejpam-3343	64	79	∗	∗	NOUN
ejpam-3343	64	80	(	(	PUNCT
ejpam-3343	64	81	x	x	X
ejpam-3343	64	82	∗	∗	PROPN
ejpam-3343	64	83	y	y	NOUN
ejpam-3343	64	84	)	)	PUNCT
ejpam-3343	64	85	)	)	PUNCT
ejpam-3343	65	1	∗	∗	NOUN
ejpam-3343	65	2	y	y	NOUN
ejpam-3343	66	1	=	=	SYM
ejpam-3343	67	1	0	0	NUM
ejpam-3343	67	2	)	)	PUNCT
ejpam-3343	68	1	,	,	PUNCT
ejpam-3343	68	2	(	(	PUNCT
ejpam-3343	68	3	iii	iii	X
ejpam-3343	68	4	)	)	PUNCT
ejpam-3343	68	5	(	(	PUNCT
ejpam-3343	68	6	∀x	∀x	X
ejpam-3343	68	7	∈	∈	PROPN
ejpam-3343	68	8	x	x	NOUN
ejpam-3343	68	9	)	)	PUNCT
ejpam-3343	68	10	(	(	PUNCT
ejpam-3343	68	11	x	x	X
ejpam-3343	68	12	∗	∗	NOUN
ejpam-3343	68	13	x	x	SYM
ejpam-3343	68	14	=	=	NOUN
ejpam-3343	68	15	0	0	NUM
ejpam-3343	68	16	)	)	PUNCT
ejpam-3343	68	17	,	,	PUNCT
ejpam-3343	68	18	g.	g.	PROPN
ejpam-3343	68	19	muhiuddin	muhiuddin	PROPN
ejpam-3343	68	20	,	,	PUNCT
ejpam-3343	68	21	s.	s.	PROPN
ejpam-3343	68	22	aldhafeeri	aldhafeeri	PROPN
ejpam-3343	68	23	/	/	SYM
ejpam-3343	68	24	eur	eur	PROPN
ejpam-3343	68	25	.	.	PUNCT
ejpam-3343	69	1	j.	j.	PROPN
ejpam-3343	69	2	pure	pure	PROPN
ejpam-3343	69	3	appl	appl	PROPN
ejpam-3343	69	4	.	.	PROPN
ejpam-3343	69	5	math	math	PROPN
ejpam-3343	69	6	,	,	PUNCT
ejpam-3343	69	7	12	12	NUM
ejpam-3343	69	8	(	(	PUNCT
ejpam-3343	69	9	1	1	NUM
ejpam-3343	69	10	)	)	PUNCT
ejpam-3343	69	11	(	(	PUNCT
ejpam-3343	69	12	2019	2019	NUM
ejpam-3343	69	13	)	)	PUNCT
ejpam-3343	69	14	,	,	PUNCT
ejpam-3343	69	15	79	79	NUM
ejpam-3343	69	16	-	-	SYM
ejpam-3343	69	17	87	87	NUM
ejpam-3343	69	18	81	81	NUM
ejpam-3343	69	19	(	(	PUNCT
ejpam-3343	69	20	iv	iv	X
ejpam-3343	69	21	)	)	PUNCT
ejpam-3343	69	22	(	(	PUNCT
ejpam-3343	69	23	∀x	∀x	X
ejpam-3343	69	24	,	,	PUNCT
ejpam-3343	69	25	y	y	PROPN
ejpam-3343	69	26	∈	∈	PROPN
ejpam-3343	69	27	x	x	X
ejpam-3343	69	28	)	)	PUNCT
ejpam-3343	69	29	(	(	PUNCT
ejpam-3343	69	30	x	x	SYM
ejpam-3343	69	31	∗	∗	NOUN
ejpam-3343	69	32	y	y	NOUN
ejpam-3343	69	33	=	=	SYM
ejpam-3343	69	34	0	0	PROPN
ejpam-3343	69	35	,	,	PUNCT
ejpam-3343	69	36	y	y	PROPN
ejpam-3343	69	37	∗	∗	NOUN
ejpam-3343	69	38	x	x	PUNCT
ejpam-3343	69	39	=	=	SYM
ejpam-3343	69	40	0	0	NUM
ejpam-3343	69	41	⇒	⇒	NOUN
ejpam-3343	69	42	x	x	PUNCT
ejpam-3343	70	1	=	=	SYM
ejpam-3343	70	2	y	y	PROPN
ejpam-3343	70	3	)	)	PUNCT
ejpam-3343	70	4	.	.	PUNCT
ejpam-3343	71	1	define	define	VERB
ejpam-3343	71	2	a	a	DET
ejpam-3343	71	3	binary	binary	ADJ
ejpam-3343	71	4	relation	relation	NOUN
ejpam-3343	71	5	≤	≤	PUNCT
ejpam-3343	71	6	on	on	ADP
ejpam-3343	71	7	x	x	PUNCT
ejpam-3343	71	8	by	by	ADP
ejpam-3343	71	9	letting	let	VERB
ejpam-3343	71	10	x	x	PRON
ejpam-3343	71	11	∗	∗	NOUN
ejpam-3343	71	12	y	y	NOUN
ejpam-3343	71	13	=	=	SYM
ejpam-3343	71	14	0	0	PUNCT
ejpam-3343	72	1	if	if	SCONJ
ejpam-3343	72	2	and	and	CCONJ
ejpam-3343	72	3	only	only	ADV
ejpam-3343	72	4	if	if	SCONJ
ejpam-3343	72	5	x	x	SYM
ejpam-3343	72	6	≤	≤	X
ejpam-3343	72	7	y.	y.	NOUN
ejpam-3343	72	8	then	then	ADV
ejpam-3343	72	9	(	(	PUNCT
ejpam-3343	72	10	x,≤	x,≤	NOUN
ejpam-3343	72	11	)	)	PUNCT
ejpam-3343	72	12	is	be	AUX
ejpam-3343	72	13	a	a	DET
ejpam-3343	72	14	partially	partially	ADV
ejpam-3343	72	15	ordered	order	VERB
ejpam-3343	72	16	set	set	NOUN
ejpam-3343	72	17	.	.	PUNCT
ejpam-3343	73	1	a	a	DET
ejpam-3343	73	2	bci	bci	NOUN
ejpam-3343	73	3	-	-	NOUN
ejpam-3343	73	4	algebra	algebra	NOUN
ejpam-3343	73	5	x	x	PUNCT
ejpam-3343	73	6	satisfying	satisfy	VERB
ejpam-3343	73	7	0	0	NUM
ejpam-3343	73	8	≤	≤	NUM
ejpam-3343	73	9	x	x	PUNCT
ejpam-3343	73	10	for	for	ADP
ejpam-3343	73	11	all	all	DET
ejpam-3343	73	12	x	x	SYM
ejpam-3343	73	13	∈	∈	PROPN
ejpam-3343	73	14	x	x	X
ejpam-3343	73	15	,	,	PUNCT
ejpam-3343	73	16	is	be	AUX
ejpam-3343	73	17	called	call	VERB
ejpam-3343	73	18	bck	bck	NOUN
ejpam-3343	73	19	-	-	PUNCT
ejpam-3343	73	20	algebra	algebra	NOUN
ejpam-3343	73	21	.	.	PUNCT
ejpam-3343	74	1	theorem	theorem	NOUN
ejpam-3343	74	2	1	1	NUM
ejpam-3343	74	3	.	.	PUNCT
ejpam-3343	75	1	let	let	VERB
ejpam-3343	75	2	x	x	PRON
ejpam-3343	75	3	be	be	AUX
ejpam-3343	75	4	a	a	DET
ejpam-3343	75	5	bci	bci	NOUN
ejpam-3343	75	6	-	-	NOUN
ejpam-3343	75	7	algebra	algebra	NOUN
ejpam-3343	75	8	.	.	PUNCT
ejpam-3343	76	1	then	then	ADV
ejpam-3343	76	2	following	follow	VERB
ejpam-3343	76	3	hold	hold	NOUN
ejpam-3343	76	4	(	(	PUNCT
ejpam-3343	76	5	a1	a1	NOUN
ejpam-3343	76	6	)	)	PUNCT
ejpam-3343	76	7	(	(	PUNCT
ejpam-3343	76	8	∀x	∀x	X
ejpam-3343	76	9	∈	∈	PROPN
ejpam-3343	76	10	x	x	NOUN
ejpam-3343	76	11	)	)	PUNCT
ejpam-3343	76	12	(	(	PUNCT
ejpam-3343	76	13	(	(	PUNCT
ejpam-3343	76	14	x	x	X
ejpam-3343	76	15	∗	∗	NOUN
ejpam-3343	76	16	0	0	NUM
ejpam-3343	77	1	=	=	SYM
ejpam-3343	77	2	x	x	NOUN
ejpam-3343	77	3	)	)	PUNCT
ejpam-3343	77	4	)	)	PUNCT
ejpam-3343	77	5	,	,	PUNCT
ejpam-3343	77	6	(	(	PUNCT
ejpam-3343	77	7	a2	a2	PROPN
ejpam-3343	77	8	)	)	PUNCT
ejpam-3343	77	9	(	(	PUNCT
ejpam-3343	77	10	∀x	∀x	X
ejpam-3343	77	11	,	,	PUNCT
ejpam-3343	77	12	y	y	PROPN
ejpam-3343	77	13	,	,	PUNCT
ejpam-3343	77	14	z	z	NOUN
ejpam-3343	77	15	∈	∈	PROPN
ejpam-3343	77	16	x	x	X
ejpam-3343	77	17	)	)	PUNCT
ejpam-3343	77	18	(	(	PUNCT
ejpam-3343	77	19	(	(	PUNCT
ejpam-3343	77	20	x	x	SYM
ejpam-3343	77	21	∗	∗	PROPN
ejpam-3343	77	22	y	y	NOUN
ejpam-3343	77	23	)	)	PUNCT
ejpam-3343	77	24	∗	∗	NOUN
ejpam-3343	77	25	z	z	NOUN
ejpam-3343	77	26	=	=	SYM
ejpam-3343	78	1	(	(	PUNCT
ejpam-3343	78	2	x	x	X
ejpam-3343	78	3	∗	∗	PROPN
ejpam-3343	78	4	z	z	NOUN
ejpam-3343	78	5	)	)	PUNCT
ejpam-3343	78	6	∗	∗	PROPN
ejpam-3343	78	7	y	y	PROPN
ejpam-3343	78	8	)	)	PUNCT
ejpam-3343	78	9	,	,	PUNCT
ejpam-3343	78	10	(	(	PUNCT
ejpam-3343	78	11	a3	a3	NOUN
ejpam-3343	78	12	)	)	PUNCT
ejpam-3343	78	13	(	(	PUNCT
ejpam-3343	78	14	∀x	∀x	X
ejpam-3343	78	15	∈	∈	PROPN
ejpam-3343	78	16	x	x	X
ejpam-3343	78	17	)	)	PUNCT
ejpam-3343	78	18	(	(	PUNCT
ejpam-3343	78	19	0	0	NUM
ejpam-3343	78	20	∗	∗	NOUN
ejpam-3343	78	21	(	(	PUNCT
ejpam-3343	78	22	0	0	NUM
ejpam-3343	78	23	∗	∗	NOUN
ejpam-3343	78	24	(	(	PUNCT
ejpam-3343	78	25	0	0	NUM
ejpam-3343	78	26	∗	∗	NOUN
ejpam-3343	78	27	x	x	NOUN
ejpam-3343	78	28	)	)	PUNCT
ejpam-3343	78	29	)	)	PUNCT
ejpam-3343	79	1	=	=	SYM
ejpam-3343	79	2	0	0	NUM
ejpam-3343	79	3	∗	∗	NOUN
ejpam-3343	79	4	x	x	NOUN
ejpam-3343	79	5	)	)	PUNCT
ejpam-3343	79	6	,	,	PUNCT
ejpam-3343	79	7	(	(	PUNCT
ejpam-3343	79	8	a4	a4	NOUN
ejpam-3343	79	9	)	)	PUNCT
ejpam-3343	79	10	(	(	PUNCT
ejpam-3343	79	11	∀x	∀x	X
ejpam-3343	79	12	,	,	PUNCT
ejpam-3343	79	13	y	y	PROPN
ejpam-3343	79	14	,	,	PUNCT
ejpam-3343	79	15	z	z	NOUN
ejpam-3343	79	16	∈	∈	PROPN
ejpam-3343	79	17	x	x	X
ejpam-3343	79	18	)	)	PUNCT
ejpam-3343	79	19	(	(	PUNCT
ejpam-3343	79	20	0	0	NUM
ejpam-3343	79	21	∗	∗	NOUN
ejpam-3343	79	22	(	(	PUNCT
ejpam-3343	79	23	0	0	NUM
ejpam-3343	79	24	∗	∗	NOUN
ejpam-3343	79	25	(	(	PUNCT
ejpam-3343	79	26	(	(	PUNCT
ejpam-3343	79	27	x	x	SYM
ejpam-3343	79	28	∗	∗	PROPN
ejpam-3343	79	29	z	z	NOUN
ejpam-3343	79	30	)	)	PUNCT
ejpam-3343	79	31	∗	∗	NOUN
ejpam-3343	79	32	(	(	PUNCT
ejpam-3343	79	33	y	y	PROPN
ejpam-3343	79	34	∗	∗	PROPN
ejpam-3343	79	35	z	z	PROPN
ejpam-3343	79	36	)	)	PUNCT
ejpam-3343	79	37	)	)	PUNCT
ejpam-3343	79	38	)	)	PUNCT
ejpam-3343	80	1	=	=	PUNCT
ejpam-3343	80	2	(	(	PUNCT
ejpam-3343	80	3	0	0	NUM
ejpam-3343	80	4	∗	∗	PROPN
ejpam-3343	80	5	y	y	NOUN
ejpam-3343	80	6	)	)	PUNCT
ejpam-3343	80	7	∗	∗	NOUN
ejpam-3343	80	8	(	(	PUNCT
ejpam-3343	80	9	0	0	NUM
ejpam-3343	80	10	∗	∗	NOUN
ejpam-3343	80	11	x	x	NOUN
ejpam-3343	80	12	)	)	PUNCT
ejpam-3343	80	13	)	)	PUNCT
ejpam-3343	80	14	,	,	PUNCT
ejpam-3343	80	15	(	(	PUNCT
ejpam-3343	80	16	a5	a5	PROPN
ejpam-3343	80	17	)	)	PUNCT
ejpam-3343	80	18	(	(	PUNCT
ejpam-3343	80	19	∀x	∀x	X
ejpam-3343	80	20	,	,	PUNCT
ejpam-3343	80	21	y	y	PROPN
ejpam-3343	80	22	∈	∈	PROPN
ejpam-3343	80	23	x	x	X
ejpam-3343	80	24	)	)	PUNCT
ejpam-3343	80	25	(	(	PUNCT
ejpam-3343	80	26	0	0	NUM
ejpam-3343	80	27	∗	∗	NOUN
ejpam-3343	80	28	(	(	PUNCT
ejpam-3343	80	29	0	0	NUM
ejpam-3343	80	30	∗	∗	NOUN
ejpam-3343	80	31	(	(	PUNCT
ejpam-3343	80	32	x	x	X
ejpam-3343	80	33	∗	∗	PROPN
ejpam-3343	80	34	y	y	NOUN
ejpam-3343	80	35	)	)	PUNCT
ejpam-3343	80	36	)	)	PUNCT
ejpam-3343	81	1	=	=	PUNCT
ejpam-3343	81	2	(	(	PUNCT
ejpam-3343	81	3	0	0	NUM
ejpam-3343	81	4	∗	∗	PROPN
ejpam-3343	81	5	y	y	NOUN
ejpam-3343	81	6	)	)	PUNCT
ejpam-3343	81	7	∗	∗	NOUN
ejpam-3343	81	8	(	(	PUNCT
ejpam-3343	81	9	0	0	NUM
ejpam-3343	81	10	∗	∗	NOUN
ejpam-3343	81	11	x	x	NOUN
ejpam-3343	81	12	)	)	PUNCT
ejpam-3343	81	13	)	)	PUNCT
ejpam-3343	81	14	a	a	DET
ejpam-3343	81	15	non	non	ADJ
ejpam-3343	81	16	-	-	ADJ
ejpam-3343	81	17	empty	empty	ADJ
ejpam-3343	81	18	subset	subset	NOUN
ejpam-3343	81	19	s	s	NOUN
ejpam-3343	81	20	of	of	ADP
ejpam-3343	81	21	a	a	DET
ejpam-3343	81	22	bck	bck	PROPN
ejpam-3343	81	23	/	/	SYM
ejpam-3343	81	24	bci	bci	NOUN
ejpam-3343	81	25	-	-	NOUN
ejpam-3343	81	26	algebra	algebra	NOUN
ejpam-3343	81	27	x	x	PUNCT
ejpam-3343	81	28	is	be	AUX
ejpam-3343	81	29	called	call	VERB
ejpam-3343	81	30	a	a	DET
ejpam-3343	81	31	subalgebra	subalgebra	NOUN
ejpam-3343	81	32	of	of	ADP
ejpam-3343	81	33	x	x	PRON
ejpam-3343	81	34	if	if	SCONJ
ejpam-3343	81	35	x∗y	x∗y	X
ejpam-3343	81	36	∈	∈	PROPN
ejpam-3343	81	37	s	s	VERB
ejpam-3343	81	38	for	for	ADP
ejpam-3343	81	39	all	all	DET
ejpam-3343	81	40	x	x	NOUN
ejpam-3343	81	41	,	,	PUNCT
ejpam-3343	81	42	y	y	PROPN
ejpam-3343	81	43	∈	∈	PROPN
ejpam-3343	81	44	s.	s.	PROPN
ejpam-3343	81	45	a	a	PRON
ejpam-3343	81	46	subset	subset	VERB
ejpam-3343	81	47	a	a	PRON
ejpam-3343	81	48	of	of	ADP
ejpam-3343	81	49	a	a	DET
ejpam-3343	81	50	bck	bck	PROPN
ejpam-3343	81	51	/	/	SYM
ejpam-3343	81	52	bci	bci	NOUN
ejpam-3343	81	53	-	-	NOUN
ejpam-3343	81	54	algebra	algebra	NOUN
ejpam-3343	81	55	x	x	PUNCT
ejpam-3343	81	56	is	be	AUX
ejpam-3343	81	57	called	call	VERB
ejpam-3343	81	58	an	an	DET
ejpam-3343	81	59	ideal	ideal	NOUN
ejpam-3343	81	60	of	of	ADP
ejpam-3343	81	61	x	x	PRON
ejpam-3343	81	62	if	if	SCONJ
ejpam-3343	81	63	it	it	PRON
ejpam-3343	81	64	satisfies	satisfy	VERB
ejpam-3343	81	65	:	:	PUNCT
ejpam-3343	81	66	(	(	PUNCT
ejpam-3343	81	67	c1	c1	NOUN
ejpam-3343	81	68	)	)	PUNCT
ejpam-3343	81	69	0	0	PUNCT
ejpam-3343	82	1	∈	∈	PROPN
ejpam-3343	82	2	a	a	DET
ejpam-3343	82	3	,	,	PUNCT
ejpam-3343	82	4	(	(	PUNCT
ejpam-3343	82	5	c2	c2	PROPN
ejpam-3343	82	6	)	)	PUNCT
ejpam-3343	82	7	(	(	PUNCT
ejpam-3343	82	8	∀x	∀x	X
ejpam-3343	82	9	,	,	PUNCT
ejpam-3343	82	10	y	y	PROPN
ejpam-3343	82	11	∈	∈	PROPN
ejpam-3343	82	12	x	x	X
ejpam-3343	82	13	)	)	PUNCT
ejpam-3343	82	14	(	(	PUNCT
ejpam-3343	82	15	x	x	SYM
ejpam-3343	82	16	∗	∗	VERB
ejpam-3343	82	17	y	y	PROPN
ejpam-3343	82	18	∈	∈	PROPN
ejpam-3343	82	19	a	a	PRON
ejpam-3343	82	20	,	,	PUNCT
ejpam-3343	82	21	y	y	PROPN
ejpam-3343	82	22	∈	∈	PROPN
ejpam-3343	82	23	a	a	DET
ejpam-3343	82	24	⇒	⇒	NOUN
ejpam-3343	82	25	x	x	PUNCT
ejpam-3343	82	26	∈	∈	PROPN
ejpam-3343	82	27	a	a	PRON
ejpam-3343	82	28	)	)	PUNCT
ejpam-3343	82	29	.	.	PUNCT
ejpam-3343	83	1	we	we	PRON
ejpam-3343	83	2	refer	refer	VERB
ejpam-3343	83	3	the	the	DET
ejpam-3343	83	4	reader	reader	NOUN
ejpam-3343	83	5	to	to	ADP
ejpam-3343	83	6	the	the	DET
ejpam-3343	83	7	books	book	NOUN
ejpam-3343	83	8	[	[	X
ejpam-3343	83	9	5	5	NUM
ejpam-3343	83	10	,	,	PUNCT
ejpam-3343	83	11	14	14	NUM
ejpam-3343	83	12	]	]	PUNCT
ejpam-3343	83	13	for	for	ADP
ejpam-3343	83	14	further	further	ADJ
ejpam-3343	83	15	information	information	NOUN
ejpam-3343	83	16	regarding	regard	VERB
ejpam-3343	83	17	bck	bck	PROPN
ejpam-3343	83	18	/	/	SYM
ejpam-3343	83	19	bcialgebras	bcialgebras	NOUN
ejpam-3343	83	20	.	.	PUNCT
ejpam-3343	84	1	for	for	ADP
ejpam-3343	84	2	any	any	DET
ejpam-3343	84	3	family	family	NOUN
ejpam-3343	84	4	{	{	PUNCT
ejpam-3343	84	5	ai	ai	VERB
ejpam-3343	84	6	|	|	ADV
ejpam-3343	85	1	i	i	PRON
ejpam-3343	85	2	∈	∈	PROPN
ejpam-3343	85	3	λ	λ	NOUN
ejpam-3343	85	4	}	}	PUNCT
ejpam-3343	85	5	of	of	ADP
ejpam-3343	85	6	real	real	ADJ
ejpam-3343	85	7	numbers	number	NOUN
ejpam-3343	85	8	,	,	PUNCT
ejpam-3343	85	9	we	we	PRON
ejpam-3343	85	10	define∨	define∨	PROPN
ejpam-3343	85	11	{	{	PUNCT
ejpam-3343	85	12	ai	ai	VERB
ejpam-3343	85	13	|	|	ADV
ejpam-3343	86	1	i	i	PRON
ejpam-3343	86	2	∈	∈	PROPN
ejpam-3343	86	3	λ	λ	NOUN
ejpam-3343	86	4	}	}	PUNCT
ejpam-3343	86	5	:	:	PUNCT
ejpam-3343	86	6	=	=	SYM
ejpam-3343	86	7	{	{	PUNCT
ejpam-3343	86	8	max{ai	max{ai	NOUN
ejpam-3343	87	1	|	|	ADV
ejpam-3343	87	2	i	i	PRON
ejpam-3343	87	3	∈	∈	PROPN
ejpam-3343	87	4	λ	λ	NOUN
ejpam-3343	87	5	}	}	PUNCT
ejpam-3343	87	6	if	if	SCONJ
ejpam-3343	87	7	λ	λ	PROPN
ejpam-3343	87	8	is	be	AUX
ejpam-3343	87	9	finite	finite	ADJ
ejpam-3343	87	10	,	,	PUNCT
ejpam-3343	87	11	sup{ai	sup{ai	VERB
ejpam-3343	88	1	|	|	ADV
ejpam-3343	88	2	i	i	PRON
ejpam-3343	88	3	∈	∈	PROPN
ejpam-3343	88	4	λ	λ	NOUN
ejpam-3343	88	5	}	}	PUNCT
ejpam-3343	88	6	otherwise	otherwise	ADV
ejpam-3343	88	7	.	.	PUNCT
ejpam-3343	89	1	∧	∧	NOUN
ejpam-3343	89	2	{	{	PUNCT
ejpam-3343	89	3	ai	ai	VERB
ejpam-3343	89	4	|	|	ADV
ejpam-3343	90	1	i	i	PRON
ejpam-3343	90	2	∈	∈	PROPN
ejpam-3343	90	3	λ	λ	NOUN
ejpam-3343	90	4	}	}	PUNCT
ejpam-3343	90	5	:	:	PUNCT
ejpam-3343	90	6	=	=	SYM
ejpam-3343	90	7			PUNCT
ejpam-3343	90	8	min{ai	min{ai	X
ejpam-3343	91	1	|	|	ADV
ejpam-3343	91	2	i	i	PRON
ejpam-3343	91	3	∈	∈	PROPN
ejpam-3343	91	4	λ	λ	NOUN
ejpam-3343	91	5	}	}	PUNCT
ejpam-3343	91	6	if	if	SCONJ
ejpam-3343	91	7	λ	λ	PROPN
ejpam-3343	91	8	is	be	AUX
ejpam-3343	91	9	finite	finite	ADJ
ejpam-3343	91	10	,	,	PUNCT
ejpam-3343	91	11	inf{ai	inf{ai	PUNCT
ejpam-3343	92	1	|	|	ADV
ejpam-3343	92	2	i	i	PRON
ejpam-3343	92	3	∈	∈	PROPN
ejpam-3343	92	4	λ	λ	X
ejpam-3343	92	5	}	}	PUNCT
ejpam-3343	92	6	otherwise	otherwise	ADV
ejpam-3343	92	7	.	.	PUNCT
ejpam-3343	93	1	denote	denote	VERB
ejpam-3343	93	2	by	by	ADP
ejpam-3343	93	3	f	f	PROPN
ejpam-3343	93	4	(	(	PUNCT
ejpam-3343	93	5	x	x	X
ejpam-3343	93	6	,	,	PUNCT
ejpam-3343	93	7	[	[	X
ejpam-3343	93	8	−1	−1	NOUN
ejpam-3343	93	9	,	,	PUNCT
ejpam-3343	93	10	0	0	NUM
ejpam-3343	93	11	]	]	PUNCT
ejpam-3343	93	12	)	)	PUNCT
ejpam-3343	93	13	the	the	DET
ejpam-3343	93	14	collection	collection	NOUN
ejpam-3343	93	15	of	of	ADP
ejpam-3343	93	16	functions	function	NOUN
ejpam-3343	93	17	from	from	ADP
ejpam-3343	93	18	a	a	DET
ejpam-3343	93	19	set	set	NOUN
ejpam-3343	93	20	x	x	PUNCT
ejpam-3343	93	21	to	to	ADP
ejpam-3343	93	22	[	[	X
ejpam-3343	93	23	−1	−1	NOUN
ejpam-3343	93	24	,	,	PUNCT
ejpam-3343	93	25	0	0	NUM
ejpam-3343	93	26	]	]	PUNCT
ejpam-3343	93	27	.	.	PUNCT
ejpam-3343	94	1	we	we	PRON
ejpam-3343	94	2	say	say	VERB
ejpam-3343	94	3	that	that	SCONJ
ejpam-3343	94	4	an	an	DET
ejpam-3343	94	5	element	element	NOUN
ejpam-3343	94	6	of	of	ADP
ejpam-3343	94	7	f	f	PROPN
ejpam-3343	94	8	(	(	PUNCT
ejpam-3343	94	9	x	x	X
ejpam-3343	94	10	,	,	PUNCT
ejpam-3343	94	11	[	[	X
ejpam-3343	94	12	−1	−1	NOUN
ejpam-3343	94	13	,	,	PUNCT
ejpam-3343	94	14	0	0	NUM
ejpam-3343	94	15	]	]	PUNCT
ejpam-3343	94	16	)	)	PUNCT
ejpam-3343	94	17	is	be	AUX
ejpam-3343	94	18	a	a	DET
ejpam-3343	94	19	negative	negative	ADV
ejpam-3343	94	20	-	-	PUNCT
ejpam-3343	94	21	valued	value	VERB
ejpam-3343	94	22	function	function	NOUN
ejpam-3343	94	23	from	from	ADP
ejpam-3343	94	24	x	x	PRON
ejpam-3343	94	25	to	to	ADP
ejpam-3343	94	26	[	[	X
ejpam-3343	94	27	−1	−1	NOUN
ejpam-3343	94	28	,	,	PUNCT
ejpam-3343	94	29	0	0	NUM
ejpam-3343	94	30	]	]	PUNCT
ejpam-3343	94	31	(	(	PUNCT
ejpam-3343	94	32	briefly	briefly	ADV
ejpam-3343	94	33	,	,	PUNCT
ejpam-3343	94	34	n	n	X
ejpam-3343	94	35	-function	-function	NOUN
ejpam-3343	94	36	on	on	ADP
ejpam-3343	94	37	x	x	NOUN
ejpam-3343	94	38	)	)	PUNCT
ejpam-3343	94	39	.	.	PUNCT
ejpam-3343	95	1	by	by	ADP
ejpam-3343	95	2	an	an	DET
ejpam-3343	95	3	n	n	ADV
ejpam-3343	95	4	-structure	-structure	NOUN
ejpam-3343	95	5	we	we	PRON
ejpam-3343	95	6	mean	mean	VERB
ejpam-3343	95	7	an	an	DET
ejpam-3343	95	8	ordered	order	VERB
ejpam-3343	95	9	pair	pair	NOUN
ejpam-3343	95	10	(	(	PUNCT
ejpam-3343	95	11	x	x	NOUN
ejpam-3343	95	12	,	,	PUNCT
ejpam-3343	95	13	η	η	NOUN
ejpam-3343	95	14	)	)	PUNCT
ejpam-3343	95	15	of	of	ADP
ejpam-3343	95	16	x	x	X
ejpam-3343	95	17	and	and	CCONJ
ejpam-3343	95	18	an	an	DET
ejpam-3343	95	19	n	n	CCONJ
ejpam-3343	95	20	-function	-function	PROPN
ejpam-3343	95	21	η	η	NOUN
ejpam-3343	95	22	on	on	ADP
ejpam-3343	95	23	x.	x.	NOUN
ejpam-3343	95	24	definition	definition	NOUN
ejpam-3343	95	25	1	1	NUM
ejpam-3343	95	26	(	(	PUNCT
ejpam-3343	95	27	[	[	X
ejpam-3343	95	28	9	9	NUM
ejpam-3343	95	29	]	]	PUNCT
ejpam-3343	95	30	)	)	PUNCT
ejpam-3343	95	31	.	.	PUNCT
ejpam-3343	96	1	by	by	ADP
ejpam-3343	96	2	a	a	DET
ejpam-3343	96	3	subalgebra	subalgebra	NOUN
ejpam-3343	96	4	of	of	ADP
ejpam-3343	96	5	a	a	DET
ejpam-3343	96	6	bck	bck	VERB
ejpam-3343	96	7	/	/	SYM
ejpam-3343	96	8	bci	bci	NOUN
ejpam-3343	96	9	-	-	NOUN
ejpam-3343	96	10	algebra	algebra	NOUN
ejpam-3343	96	11	x	x	PUNCT
ejpam-3343	96	12	based	base	VERB
ejpam-3343	96	13	on	on	ADP
ejpam-3343	96	14	n	n	PRON
ejpam-3343	96	15	-function	-function	NOUN
ejpam-3343	96	16	η	η	NOUN
ejpam-3343	96	17	(	(	PUNCT
ejpam-3343	96	18	briefly	briefly	ADV
ejpam-3343	96	19	,	,	PUNCT
ejpam-3343	96	20	n	n	PRON
ejpam-3343	96	21	-subalgebra	-subalgebra	NOUN
ejpam-3343	96	22	of	of	ADP
ejpam-3343	96	23	x	x	NOUN
ejpam-3343	96	24	)	)	PUNCT
ejpam-3343	96	25	,	,	PUNCT
ejpam-3343	96	26	we	we	PRON
ejpam-3343	96	27	mean	mean	VERB
ejpam-3343	96	28	an	an	DET
ejpam-3343	96	29	n	n	ADV
ejpam-3343	96	30	-structure	-structure	NOUN
ejpam-3343	96	31	(	(	PUNCT
ejpam-3343	96	32	x	x	NOUN
ejpam-3343	96	33	,	,	PUNCT
ejpam-3343	96	34	η	η	NOUN
ejpam-3343	96	35	)	)	PUNCT
ejpam-3343	96	36	in	in	ADP
ejpam-3343	96	37	which	which	PRON
ejpam-3343	96	38	η	η	PROPN
ejpam-3343	96	39	satisfies	satisfy	VERB
ejpam-3343	96	40	the	the	DET
ejpam-3343	96	41	following	follow	VERB
ejpam-3343	96	42	assertion	assertion	NOUN
ejpam-3343	96	43	:	:	PUNCT
ejpam-3343	96	44	(	(	PUNCT
ejpam-3343	96	45	∀x	∀x	X
ejpam-3343	96	46	,	,	PUNCT
ejpam-3343	96	47	y	y	PROPN
ejpam-3343	96	48	∈	∈	PROPN
ejpam-3343	96	49	x	x	X
ejpam-3343	96	50	)	)	PUNCT
ejpam-3343	96	51	(	(	PUNCT
ejpam-3343	96	52	η(x	η(x	X
ejpam-3343	96	53	∗	∗	NOUN
ejpam-3343	96	54	y	y	NOUN
ejpam-3343	96	55	)	)	PUNCT
ejpam-3343	96	56	≤	≤	NOUN
ejpam-3343	96	57	∨	∨	NUM
ejpam-3343	96	58	{	{	PUNCT
ejpam-3343	96	59	η(x	η(x	NOUN
ejpam-3343	96	60	)	)	PUNCT
ejpam-3343	96	61	,	,	PUNCT
ejpam-3343	96	62	η(y	η(y	NOUN
ejpam-3343	96	63	)	)	PUNCT
ejpam-3343	96	64	}	}	PUNCT
ejpam-3343	96	65	)	)	PUNCT
ejpam-3343	96	66	.	.	PUNCT
ejpam-3343	97	1	(	(	PUNCT
ejpam-3343	97	2	1	1	X
ejpam-3343	97	3	)	)	PUNCT
ejpam-3343	97	4	g.	g.	PROPN
ejpam-3343	97	5	muhiuddin	muhiuddin	PROPN
ejpam-3343	97	6	,	,	PUNCT
ejpam-3343	97	7	s.	s.	PROPN
ejpam-3343	97	8	aldhafeeri	aldhafeeri	PROPN
ejpam-3343	97	9	/	/	SYM
ejpam-3343	97	10	eur	eur	PROPN
ejpam-3343	97	11	.	.	PUNCT
ejpam-3343	98	1	j.	j.	PROPN
ejpam-3343	98	2	pure	pure	PROPN
ejpam-3343	98	3	appl	appl	PROPN
ejpam-3343	98	4	.	.	PROPN
ejpam-3343	98	5	math	math	PROPN
ejpam-3343	98	6	,	,	PUNCT
ejpam-3343	98	7	12	12	NUM
ejpam-3343	98	8	(	(	PUNCT
ejpam-3343	98	9	1	1	NUM
ejpam-3343	98	10	)	)	PUNCT
ejpam-3343	98	11	(	(	PUNCT
ejpam-3343	98	12	2019	2019	NUM
ejpam-3343	98	13	)	)	PUNCT
ejpam-3343	98	14	,	,	PUNCT
ejpam-3343	98	15	79	79	NUM
ejpam-3343	98	16	-	-	SYM
ejpam-3343	98	17	87	87	NUM
ejpam-3343	98	18	82	82	NUM
ejpam-3343	98	19	definition	definition	NOUN
ejpam-3343	98	20	2	2	NUM
ejpam-3343	98	21	(	(	PUNCT
ejpam-3343	98	22	[	[	X
ejpam-3343	98	23	9	9	NUM
ejpam-3343	98	24	]	]	PUNCT
ejpam-3343	98	25	)	)	PUNCT
ejpam-3343	98	26	.	.	PUNCT
ejpam-3343	99	1	by	by	ADP
ejpam-3343	99	2	an	an	DET
ejpam-3343	99	3	ideal	ideal	NOUN
ejpam-3343	99	4	of	of	ADP
ejpam-3343	99	5	a	a	DET
ejpam-3343	99	6	bck	bck	PROPN
ejpam-3343	99	7	/	/	SYM
ejpam-3343	99	8	bci	bci	NOUN
ejpam-3343	99	9	-	-	NOUN
ejpam-3343	99	10	algebra	algebra	NOUN
ejpam-3343	99	11	x	x	PUNCT
ejpam-3343	99	12	based	base	VERB
ejpam-3343	99	13	on	on	ADP
ejpam-3343	99	14	n	n	PRON
ejpam-3343	99	15	-function	-function	NOUN
ejpam-3343	99	16	η	η	NOUN
ejpam-3343	99	17	(	(	PUNCT
ejpam-3343	99	18	briefly	briefly	ADV
ejpam-3343	99	19	,	,	PUNCT
ejpam-3343	99	20	n	n	DET
ejpam-3343	99	21	-ideal	-ideal	NOUN
ejpam-3343	99	22	of	of	ADP
ejpam-3343	99	23	x	x	NOUN
ejpam-3343	99	24	)	)	PUNCT
ejpam-3343	99	25	,	,	PUNCT
ejpam-3343	99	26	we	we	PRON
ejpam-3343	99	27	mean	mean	VERB
ejpam-3343	99	28	an	an	DET
ejpam-3343	99	29	n	n	ADV
ejpam-3343	99	30	-structure	-structure	NOUN
ejpam-3343	99	31	(	(	PUNCT
ejpam-3343	99	32	x	x	NOUN
ejpam-3343	99	33	,	,	PUNCT
ejpam-3343	99	34	η	η	NOUN
ejpam-3343	99	35	)	)	PUNCT
ejpam-3343	99	36	in	in	ADP
ejpam-3343	99	37	which	which	PRON
ejpam-3343	99	38	η	η	PROPN
ejpam-3343	99	39	satisfies	satisfy	VERB
ejpam-3343	99	40	the	the	DET
ejpam-3343	99	41	following	follow	VERB
ejpam-3343	99	42	assertion	assertion	NOUN
ejpam-3343	99	43	:	:	PUNCT
ejpam-3343	99	44	(	(	PUNCT
ejpam-3343	99	45	∀x	∀x	X
ejpam-3343	99	46	,	,	PUNCT
ejpam-3343	99	47	y	y	PROPN
ejpam-3343	99	48	∈	∈	PROPN
ejpam-3343	99	49	x	x	X
ejpam-3343	99	50	)	)	PUNCT
ejpam-3343	99	51	(	(	PUNCT
ejpam-3343	99	52	η(0	η(0	PROPN
ejpam-3343	99	53	)	)	PUNCT
ejpam-3343	99	54	≤	≤	NOUN
ejpam-3343	99	55	η(x	η(x	NOUN
ejpam-3343	99	56	)	)	PUNCT
ejpam-3343	99	57	≤	≤	NUM
ejpam-3343	99	58	∨	∨	NUM
ejpam-3343	99	59	{	{	PUNCT
ejpam-3343	99	60	η(x	η(x	X
ejpam-3343	99	61	∗	∗	NOUN
ejpam-3343	99	62	y	y	NOUN
ejpam-3343	99	63	)	)	PUNCT
ejpam-3343	99	64	,	,	PUNCT
ejpam-3343	99	65	η(y	η(y	PROPN
ejpam-3343	99	66	)	)	PUNCT
ejpam-3343	99	67	}	}	PUNCT
ejpam-3343	99	68	)	)	PUNCT
ejpam-3343	99	69	.	.	PUNCT
ejpam-3343	100	1	(	(	PUNCT
ejpam-3343	100	2	2	2	X
ejpam-3343	100	3	)	)	PUNCT
ejpam-3343	100	4	3	3	NUM
ejpam-3343	100	5	.	.	X
ejpam-3343	101	1	p	p	X
ejpam-3343	101	2	-	-	PUNCT
ejpam-3343	101	3	ideals	ideal	NOUN
ejpam-3343	101	4	based	base	VERB
ejpam-3343	101	5	on	on	ADP
ejpam-3343	101	6	n	n	CCONJ
ejpam-3343	101	7	-soft	-soft	ADJ
ejpam-3343	101	8	sets	set	NOUN
ejpam-3343	101	9	in	in	ADP
ejpam-3343	101	10	what	what	PRON
ejpam-3343	101	11	follows	follow	VERB
ejpam-3343	101	12	let	let	VERB
ejpam-3343	101	13	e	e	PRON
ejpam-3343	101	14	denote	denote	VERB
ejpam-3343	101	15	a	a	DET
ejpam-3343	101	16	set	set	NOUN
ejpam-3343	101	17	of	of	ADP
ejpam-3343	101	18	attributes	attribute	NOUN
ejpam-3343	101	19	unless	unless	SCONJ
ejpam-3343	101	20	otherwise	otherwise	ADV
ejpam-3343	101	21	specified	specify	VERB
ejpam-3343	101	22	.	.	PUNCT
ejpam-3343	102	1	we	we	PRON
ejpam-3343	102	2	will	will	AUX
ejpam-3343	102	3	use	use	VERB
ejpam-3343	102	4	the	the	DET
ejpam-3343	102	5	terminology	terminology	NOUN
ejpam-3343	102	6	“	"	PUNCT
ejpam-3343	102	7	soft	soft	ADJ
ejpam-3343	102	8	machine	machine	NOUN
ejpam-3343	102	9	”	"	PUNCT
ejpam-3343	102	10	which	which	PRON
ejpam-3343	102	11	means	mean	VERB
ejpam-3343	102	12	that	that	SCONJ
ejpam-3343	102	13	it	it	PRON
ejpam-3343	102	14	produces	produce	VERB
ejpam-3343	102	15	a	a	DET
ejpam-3343	102	16	bci	bci	NOUN
ejpam-3343	102	17	-	-	NOUN
ejpam-3343	102	18	algebra	algebra	NOUN
ejpam-3343	102	19	,	,	PUNCT
ejpam-3343	102	20	that	that	ADV
ejpam-3343	102	21	is	is	ADV
ejpam-3343	102	22	,	,	PUNCT
ejpam-3343	102	23	consider	consider	VERB
ejpam-3343	102	24	a	a	DET
ejpam-3343	102	25	soft	soft	ADJ
ejpam-3343	102	26	machine	machine	NOUN
ejpam-3343	102	27	“	"	PUNCT
ejpam-3343	102	28	]	]	X
ejpam-3343	102	29	(	(	PUNCT
ejpam-3343	102	30	−,−	−,−	NOUN
ejpam-3343	102	31	)	)	PUNCT
ejpam-3343	102	32	”	"	PUNCT
ejpam-3343	102	33	for	for	ADP
ejpam-3343	102	34	which	which	PRON
ejpam-3343	102	35	]	]	PUNCT
ejpam-3343	102	36	(	(	PUNCT
ejpam-3343	102	37	x	x	NOUN
ejpam-3343	102	38	,	,	PUNCT
ejpam-3343	102	39	y	y	NOUN
ejpam-3343	102	40	)	)	PUNCT
ejpam-3343	102	41	=	=	SYM
ejpam-3343	102	42	z	z	NOUN
ejpam-3343	102	43	means	mean	VERB
ejpam-3343	102	44	that	that	SCONJ
ejpam-3343	102	45	if	if	SCONJ
ejpam-3343	102	46	we	we	PRON
ejpam-3343	102	47	input	input	VERB
ejpam-3343	102	48	a	a	DET
ejpam-3343	102	49	couple	couple	NOUN
ejpam-3343	102	50	(	(	PUNCT
ejpam-3343	102	51	x	x	NOUN
ejpam-3343	102	52	,	,	PUNCT
ejpam-3343	102	53	y	y	NOUN
ejpam-3343	102	54	)	)	PUNCT
ejpam-3343	102	55	of	of	ADP
ejpam-3343	102	56	informations	information	NOUN
ejpam-3343	102	57	to	to	ADP
ejpam-3343	102	58	]	]	PUNCT
ejpam-3343	102	59	(	(	PUNCT
ejpam-3343	102	60	−,−	−,−	X
ejpam-3343	102	61	)	)	PUNCT
ejpam-3343	102	62	then	then	ADV
ejpam-3343	102	63	we	we	PRON
ejpam-3343	102	64	get	get	VERB
ejpam-3343	102	65	a	a	DET
ejpam-3343	102	66	new	new	ADJ
ejpam-3343	102	67	information	information	NOUN
ejpam-3343	102	68	z.	z.	PROPN
ejpam-3343	102	69	definition	definition	NOUN
ejpam-3343	102	70	3	3	NUM
ejpam-3343	102	71	(	(	PUNCT
ejpam-3343	102	72	[	[	X
ejpam-3343	102	73	11	11	NUM
ejpam-3343	102	74	]	]	NUM
ejpam-3343	102	75	)	)	PUNCT
ejpam-3343	102	76	.	.	PUNCT
ejpam-3343	103	1	let	let	VERB
ejpam-3343	103	2	x	x	PRON
ejpam-3343	103	3	be	be	AUX
ejpam-3343	103	4	an	an	DET
ejpam-3343	103	5	initial	initial	ADJ
ejpam-3343	103	6	universe	universe	NOUN
ejpam-3343	103	7	set	set	NOUN
ejpam-3343	103	8	.	.	PUNCT
ejpam-3343	104	1	by	by	ADP
ejpam-3343	104	2	an	an	DET
ejpam-3343	104	3	n	n	CCONJ
ejpam-3343	104	4	-soft	-soft	NOUN
ejpam-3343	104	5	set	set	VERB
ejpam-3343	104	6	over	over	ADP
ejpam-3343	104	7	x	x	PUNCT
ejpam-3343	104	8	we	we	PRON
ejpam-3343	104	9	mean	mean	VERB
ejpam-3343	104	10	a	a	DET
ejpam-3343	104	11	pair	pair	NOUN
ejpam-3343	104	12	(	(	PUNCT
ejpam-3343	104	13	η	η	PROPN
ejpam-3343	104	14	,	,	PUNCT
ejpam-3343	104	15	a	a	PRON
ejpam-3343	104	16	)	)	PUNCT
ejpam-3343	104	17	where	where	SCONJ
ejpam-3343	104	18	a	a	DET
ejpam-3343	104	19	⊂	⊂	PROPN
ejpam-3343	104	20	e	e	PROPN
ejpam-3343	104	21	and	and	CCONJ
ejpam-3343	104	22	η	η	PROPN
ejpam-3343	104	23	is	be	AUX
ejpam-3343	104	24	a	a	DET
ejpam-3343	104	25	mapping	mapping	NOUN
ejpam-3343	104	26	from	from	ADP
ejpam-3343	104	27	a	a	PRON
ejpam-3343	104	28	to	to	ADP
ejpam-3343	104	29	f	f	PROPN
ejpam-3343	104	30	(	(	PUNCT
ejpam-3343	104	31	x	x	X
ejpam-3343	104	32	,	,	PUNCT
ejpam-3343	104	33	[	[	X
ejpam-3343	104	34	−1	−1	NOUN
ejpam-3343	104	35	,	,	PUNCT
ejpam-3343	104	36	0	0	NUM
ejpam-3343	104	37	]	]	PUNCT
ejpam-3343	104	38	)	)	PUNCT
ejpam-3343	104	39	,	,	PUNCT
ejpam-3343	104	40	i.e.	i.e.	X
ejpam-3343	104	41	,	,	PUNCT
ejpam-3343	104	42	for	for	ADP
ejpam-3343	104	43	each	each	DET
ejpam-3343	104	44	a	a	DET
ejpam-3343	104	45	∈	∈	PROPN
ejpam-3343	104	46	a	a	PRON
ejpam-3343	104	47	,	,	PUNCT
ejpam-3343	104	48	η(a	η(a	ADJ
ejpam-3343	104	49	)	)	PUNCT
ejpam-3343	104	50	:	:	PUNCT
ejpam-3343	104	51	=	=	PUNCT
ejpam-3343	104	52	ηa	ηa	INTJ
ejpam-3343	104	53	is	be	AUX
ejpam-3343	104	54	an	an	DET
ejpam-3343	104	55	n	n	ADV
ejpam-3343	104	56	-function	-function	NOUN
ejpam-3343	104	57	on	on	ADP
ejpam-3343	104	58	x.	x.	NOUN
ejpam-3343	104	59	denote	denote	NOUN
ejpam-3343	104	60	by	by	ADP
ejpam-3343	104	61	n	n	PROPN
ejpam-3343	104	62	(	(	PUNCT
ejpam-3343	104	63	x	x	X
ejpam-3343	104	64	,	,	PUNCT
ejpam-3343	104	65	e	e	NOUN
ejpam-3343	104	66	)	)	PUNCT
ejpam-3343	104	67	the	the	DET
ejpam-3343	104	68	collection	collection	NOUN
ejpam-3343	104	69	of	of	ADP
ejpam-3343	104	70	all	all	DET
ejpam-3343	104	71	n	n	PRON
ejpam-3343	104	72	-soft	-soft	ADJ
ejpam-3343	104	73	sets	set	NOUN
ejpam-3343	104	74	over	over	ADP
ejpam-3343	104	75	x	x	PUNCT
ejpam-3343	104	76	with	with	ADP
ejpam-3343	104	77	attributes	attribute	NOUN
ejpam-3343	104	78	from	from	ADP
ejpam-3343	104	79	e	e	NOUN
ejpam-3343	105	1	and	and	CCONJ
ejpam-3343	105	2	we	we	PRON
ejpam-3343	105	3	call	call	VERB
ejpam-3343	105	4	it	it	PRON
ejpam-3343	105	5	an	an	DET
ejpam-3343	105	6	n	n	CCONJ
ejpam-3343	105	7	-soft	-soft	ADJ
ejpam-3343	105	8	class	class	NOUN
ejpam-3343	105	9	.	.	PUNCT
ejpam-3343	106	1	definition	definition	NOUN
ejpam-3343	106	2	4	4	NUM
ejpam-3343	106	3	(	(	PUNCT
ejpam-3343	106	4	[	[	X
ejpam-3343	106	5	11	11	NUM
ejpam-3343	106	6	]	]	NUM
ejpam-3343	106	7	)	)	PUNCT
ejpam-3343	106	8	.	.	PUNCT
ejpam-3343	107	1	let	let	AUX
ejpam-3343	107	2	(	(	PUNCT
ejpam-3343	107	3	η	η	PROPN
ejpam-3343	107	4	,	,	PUNCT
ejpam-3343	107	5	a	a	PRON
ejpam-3343	107	6	)	)	PUNCT
ejpam-3343	107	7	be	be	AUX
ejpam-3343	107	8	an	an	DET
ejpam-3343	107	9	n	n	ADV
ejpam-3343	107	10	-soft	-soft	NOUN
ejpam-3343	107	11	set	set	VERB
ejpam-3343	107	12	over	over	ADP
ejpam-3343	107	13	a	a	DET
ejpam-3343	107	14	bck	bck	NOUN
ejpam-3343	107	15	/	/	SYM
ejpam-3343	107	16	bci	bci	NOUN
ejpam-3343	107	17	-	-	NOUN
ejpam-3343	107	18	algebra	algebra	NOUN
ejpam-3343	107	19	x	x	PUNCT
ejpam-3343	107	20	where	where	SCONJ
ejpam-3343	107	21	a	a	PRON
ejpam-3343	107	22	is	be	AUX
ejpam-3343	107	23	a	a	DET
ejpam-3343	107	24	subset	subset	NOUN
ejpam-3343	107	25	of	of	ADP
ejpam-3343	107	26	e.	e.	PROPN
ejpam-3343	107	27	if	if	SCONJ
ejpam-3343	107	28	there	there	PRON
ejpam-3343	107	29	exists	exist	VERB
ejpam-3343	107	30	an	an	DET
ejpam-3343	107	31	attribute	attribute	NOUN
ejpam-3343	107	32	u	u	NOUN
ejpam-3343	107	33	∈	∈	PROPN
ejpam-3343	107	34	a	a	PRON
ejpam-3343	107	35	for	for	ADP
ejpam-3343	107	36	which	which	PRON
ejpam-3343	107	37	the	the	DET
ejpam-3343	107	38	n	n	ADV
ejpam-3343	107	39	-structure	-structure	NOUN
ejpam-3343	107	40	(	(	PUNCT
ejpam-3343	107	41	x	x	NOUN
ejpam-3343	107	42	,	,	PUNCT
ejpam-3343	107	43	ηu	ηu	NOUN
ejpam-3343	107	44	)	)	PUNCT
ejpam-3343	107	45	is	be	AUX
ejpam-3343	107	46	an	an	DET
ejpam-3343	107	47	n	n	ADV
ejpam-3343	107	48	-subalgebra	-subalgebra	NOUN
ejpam-3343	107	49	of	of	ADP
ejpam-3343	107	50	x	x	PRON
ejpam-3343	107	51	,	,	PUNCT
ejpam-3343	107	52	then	then	ADV
ejpam-3343	107	53	we	we	PRON
ejpam-3343	107	54	say	say	VERB
ejpam-3343	107	55	that	that	SCONJ
ejpam-3343	107	56	(	(	PUNCT
ejpam-3343	107	57	η	η	PROPN
ejpam-3343	107	58	,	,	PUNCT
ejpam-3343	107	59	a	a	PRON
ejpam-3343	107	60	)	)	PUNCT
ejpam-3343	107	61	is	be	AUX
ejpam-3343	107	62	an	an	DET
ejpam-3343	107	63	n	n	ADV
ejpam-3343	107	64	-soft	-soft	ADJ
ejpam-3343	107	65	bck	bck	NOUN
ejpam-3343	107	66	/	/	SYM
ejpam-3343	107	67	bci	bci	NOUN
ejpam-3343	107	68	-	-	ADJ
ejpam-3343	107	69	algebra	algebra	NOUN
ejpam-3343	107	70	related	relate	VERB
ejpam-3343	107	71	to	to	ADP
ejpam-3343	107	72	the	the	DET
ejpam-3343	107	73	attribute	attribute	NOUN
ejpam-3343	107	74	u	u	NOUN
ejpam-3343	107	75	(	(	PUNCT
ejpam-3343	107	76	briefly	briefly	ADV
ejpam-3343	107	77	,	,	PUNCT
ejpam-3343	107	78	nu	nu	ADJ
ejpam-3343	107	79	-	-	PUNCT
ejpam-3343	107	80	soft	soft	ADJ
ejpam-3343	107	81	bck	bck	NOUN
ejpam-3343	107	82	/	/	SYM
ejpam-3343	107	83	bci	bci	NOUN
ejpam-3343	107	84	-	-	NOUN
ejpam-3343	107	85	algebra	algebra	NOUN
ejpam-3343	107	86	)	)	PUNCT
ejpam-3343	107	87	.	.	PUNCT
ejpam-3343	108	1	if	if	SCONJ
ejpam-3343	108	2	(	(	PUNCT
ejpam-3343	108	3	η	η	PROPN
ejpam-3343	108	4	,	,	PUNCT
ejpam-3343	108	5	a	a	PRON
ejpam-3343	108	6	)	)	PUNCT
ejpam-3343	108	7	is	be	AUX
ejpam-3343	108	8	an	an	DET
ejpam-3343	108	9	nu	nu	ADJ
ejpam-3343	108	10	-	-	PUNCT
ejpam-3343	108	11	soft	soft	ADJ
ejpam-3343	108	12	bck	bck	NOUN
ejpam-3343	108	13	/	/	SYM
ejpam-3343	108	14	bcialgebra	bcialgebra	NOUN
ejpam-3343	108	15	for	for	ADP
ejpam-3343	108	16	all	all	PRON
ejpam-3343	108	17	u	u	PROPN
ejpam-3343	108	18	∈	∈	PROPN
ejpam-3343	108	19	a	a	PRON
ejpam-3343	108	20	,	,	PUNCT
ejpam-3343	108	21	we	we	PRON
ejpam-3343	108	22	say	say	VERB
ejpam-3343	108	23	that	that	SCONJ
ejpam-3343	108	24	(	(	PUNCT
ejpam-3343	108	25	η	η	PROPN
ejpam-3343	108	26	,	,	PUNCT
ejpam-3343	108	27	a	a	PRON
ejpam-3343	108	28	)	)	PUNCT
ejpam-3343	108	29	is	be	AUX
ejpam-3343	108	30	an	an	DET
ejpam-3343	108	31	n	n	ADV
ejpam-3343	108	32	-soft	-soft	ADJ
ejpam-3343	108	33	bck	bck	NOUN
ejpam-3343	108	34	/	/	SYM
ejpam-3343	108	35	bci	bci	NOUN
ejpam-3343	108	36	-	-	NOUN
ejpam-3343	108	37	algebra	algebra	NOUN
ejpam-3343	108	38	.	.	PUNCT
ejpam-3343	109	1	definition	definition	NOUN
ejpam-3343	109	2	5	5	NUM
ejpam-3343	109	3	(	(	PUNCT
ejpam-3343	109	4	[	[	X
ejpam-3343	109	5	7	7	NUM
ejpam-3343	109	6	]	]	NUM
ejpam-3343	109	7	)	)	PUNCT
ejpam-3343	109	8	.	.	PUNCT
ejpam-3343	110	1	let	let	AUX
ejpam-3343	110	2	(	(	PUNCT
ejpam-3343	110	3	η	η	PROPN
ejpam-3343	110	4	,	,	PUNCT
ejpam-3343	110	5	a	a	PRON
ejpam-3343	110	6	)	)	PUNCT
ejpam-3343	110	7	be	be	AUX
ejpam-3343	110	8	an	an	DET
ejpam-3343	110	9	n	n	ADV
ejpam-3343	110	10	-soft	-soft	NOUN
ejpam-3343	110	11	set	set	VERB
ejpam-3343	110	12	over	over	ADP
ejpam-3343	110	13	a	a	DET
ejpam-3343	110	14	bck	bck	NOUN
ejpam-3343	110	15	/	/	SYM
ejpam-3343	110	16	bci	bci	NOUN
ejpam-3343	110	17	-	-	NOUN
ejpam-3343	110	18	algebra	algebra	NOUN
ejpam-3343	110	19	x	x	PUNCT
ejpam-3343	110	20	where	where	SCONJ
ejpam-3343	110	21	a	a	PRON
ejpam-3343	110	22	is	be	AUX
ejpam-3343	110	23	a	a	DET
ejpam-3343	110	24	subset	subset	NOUN
ejpam-3343	110	25	of	of	ADP
ejpam-3343	110	26	e.	e.	PROPN
ejpam-3343	110	27	if	if	SCONJ
ejpam-3343	110	28	there	there	PRON
ejpam-3343	110	29	exists	exist	VERB
ejpam-3343	110	30	an	an	DET
ejpam-3343	110	31	attribute	attribute	NOUN
ejpam-3343	110	32	u	u	NOUN
ejpam-3343	110	33	∈	∈	PROPN
ejpam-3343	110	34	a	a	PRON
ejpam-3343	110	35	for	for	ADP
ejpam-3343	110	36	which	which	PRON
ejpam-3343	110	37	the	the	DET
ejpam-3343	110	38	n	n	ADV
ejpam-3343	110	39	-structure	-structure	NOUN
ejpam-3343	110	40	(	(	PUNCT
ejpam-3343	110	41	x	x	NOUN
ejpam-3343	110	42	,	,	PUNCT
ejpam-3343	110	43	ηu	ηu	NOUN
ejpam-3343	110	44	)	)	PUNCT
ejpam-3343	110	45	is	be	AUX
ejpam-3343	110	46	an	an	DET
ejpam-3343	110	47	n	n	ADV
ejpam-3343	110	48	-ideal	-ideal	NOUN
ejpam-3343	110	49	of	of	ADP
ejpam-3343	110	50	x	x	NOUN
ejpam-3343	110	51	,	,	PUNCT
ejpam-3343	110	52	then	then	ADV
ejpam-3343	110	53	we	we	PRON
ejpam-3343	110	54	say	say	VERB
ejpam-3343	110	55	that	that	SCONJ
ejpam-3343	110	56	(	(	PUNCT
ejpam-3343	110	57	η	η	PROPN
ejpam-3343	110	58	,	,	PUNCT
ejpam-3343	110	59	a	a	PRON
ejpam-3343	110	60	)	)	PUNCT
ejpam-3343	110	61	is	be	AUX
ejpam-3343	110	62	an	an	DET
ejpam-3343	110	63	n	n	CCONJ
ejpam-3343	110	64	-soft	-soft	ADJ
ejpam-3343	110	65	ideal	ideal	NOUN
ejpam-3343	110	66	of	of	ADP
ejpam-3343	110	67	x	x	SYM
ejpam-3343	110	68	related	relate	VERB
ejpam-3343	110	69	to	to	ADP
ejpam-3343	110	70	the	the	DET
ejpam-3343	110	71	attribute	attribute	NOUN
ejpam-3343	110	72	u	u	NOUN
ejpam-3343	110	73	(	(	PUNCT
ejpam-3343	110	74	briefly	briefly	ADV
ejpam-3343	110	75	,	,	PUNCT
ejpam-3343	110	76	nu	nu	ADJ
ejpam-3343	110	77	-	-	PUNCT
ejpam-3343	110	78	soft	soft	ADJ
ejpam-3343	110	79	ideal	ideal	NOUN
ejpam-3343	110	80	)	)	PUNCT
ejpam-3343	110	81	.	.	PUNCT
ejpam-3343	111	1	if	if	SCONJ
ejpam-3343	111	2	(	(	PUNCT
ejpam-3343	111	3	η	η	PROPN
ejpam-3343	111	4	,	,	PUNCT
ejpam-3343	111	5	a	a	PRON
ejpam-3343	111	6	)	)	PUNCT
ejpam-3343	111	7	is	be	AUX
ejpam-3343	111	8	an	an	DET
ejpam-3343	111	9	nu	nu	ADJ
ejpam-3343	111	10	-	-	PUNCT
ejpam-3343	111	11	soft	soft	ADJ
ejpam-3343	111	12	ideal	ideal	NOUN
ejpam-3343	111	13	of	of	ADP
ejpam-3343	111	14	x	x	PUNCT
ejpam-3343	111	15	for	for	ADP
ejpam-3343	111	16	all	all	PRON
ejpam-3343	111	17	u	u	NOUN
ejpam-3343	111	18	∈	∈	PROPN
ejpam-3343	111	19	a	a	PRON
ejpam-3343	111	20	,	,	PUNCT
ejpam-3343	111	21	we	we	PRON
ejpam-3343	111	22	say	say	VERB
ejpam-3343	111	23	that	that	SCONJ
ejpam-3343	111	24	(	(	PUNCT
ejpam-3343	111	25	η	η	PROPN
ejpam-3343	111	26	,	,	PUNCT
ejpam-3343	111	27	a	a	PRON
ejpam-3343	111	28	)	)	PUNCT
ejpam-3343	111	29	is	be	AUX
ejpam-3343	111	30	an	an	DET
ejpam-3343	111	31	n	n	CCONJ
ejpam-3343	111	32	-soft	-soft	ADJ
ejpam-3343	111	33	ideal	ideal	NOUN
ejpam-3343	111	34	over	over	ADP
ejpam-3343	111	35	x.	x.	NOUN
ejpam-3343	111	36	definition	definition	NOUN
ejpam-3343	111	37	6	6	NUM
ejpam-3343	111	38	.	.	PUNCT
ejpam-3343	112	1	by	by	ADP
ejpam-3343	112	2	a	a	DET
ejpam-3343	112	3	p	p	NOUN
ejpam-3343	112	4	-	-	PUNCT
ejpam-3343	112	5	ideal	ideal	NOUN
ejpam-3343	112	6	of	of	ADP
ejpam-3343	112	7	a	a	DET
ejpam-3343	112	8	bci	bci	NOUN
ejpam-3343	112	9	-	-	NOUN
ejpam-3343	112	10	algebra	algebra	NOUN
ejpam-3343	112	11	x	x	PUNCT
ejpam-3343	112	12	based	base	VERB
ejpam-3343	112	13	on	on	ADP
ejpam-3343	112	14	n	n	PRON
ejpam-3343	112	15	-function	-function	NOUN
ejpam-3343	112	16	ψ	ψ	X
ejpam-3343	112	17	(	(	PUNCT
ejpam-3343	112	18	briefly	briefly	ADV
ejpam-3343	112	19	,	,	PUNCT
ejpam-3343	112	20	pn	pn	PROPN
ejpam-3343	112	21	-ideal	-ideal	NOUN
ejpam-3343	112	22	of	of	ADP
ejpam-3343	112	23	x	x	NOUN
ejpam-3343	112	24	)	)	PUNCT
ejpam-3343	112	25	,	,	PUNCT
ejpam-3343	112	26	we	we	PRON
ejpam-3343	112	27	mean	mean	VERB
ejpam-3343	112	28	an	an	DET
ejpam-3343	112	29	n	n	ADV
ejpam-3343	112	30	-structure	-structure	NOUN
ejpam-3343	112	31	(	(	PUNCT
ejpam-3343	112	32	x	x	NOUN
ejpam-3343	112	33	,	,	PUNCT
ejpam-3343	112	34	ψ	ψ	NOUN
ejpam-3343	112	35	)	)	PUNCT
ejpam-3343	112	36	in	in	ADP
ejpam-3343	112	37	which	which	PRON
ejpam-3343	112	38	ψ	ψ	ADP
ejpam-3343	112	39	satisfies	satisfy	VERB
ejpam-3343	112	40	the	the	DET
ejpam-3343	112	41	following	follow	VERB
ejpam-3343	112	42	assertions	assertion	NOUN
ejpam-3343	112	43	:	:	PUNCT
ejpam-3343	112	44	(	(	PUNCT
ejpam-3343	112	45	i	i	NOUN
ejpam-3343	112	46	)	)	PUNCT
ejpam-3343	112	47	(	(	PUNCT
ejpam-3343	112	48	∀x	∀x	X
ejpam-3343	112	49	∈	∈	PROPN
ejpam-3343	112	50	x	x	NOUN
ejpam-3343	112	51	)	)	PUNCT
ejpam-3343	112	52	(	(	PUNCT
ejpam-3343	112	53	ψ(0	ψ(0	NOUN
ejpam-3343	112	54	)	)	PUNCT
ejpam-3343	112	55	≤	≤	NUM
ejpam-3343	112	56	ψ(x	ψ(x	NOUN
ejpam-3343	112	57	)	)	PUNCT
ejpam-3343	112	58	)	)	PUNCT
ejpam-3343	112	59	,	,	PUNCT
ejpam-3343	112	60	(	(	PUNCT
ejpam-3343	112	61	ii	ii	NOUN
ejpam-3343	112	62	)	)	PUNCT
ejpam-3343	112	63	(	(	PUNCT
ejpam-3343	112	64	∀x	∀x	X
ejpam-3343	112	65	,	,	PUNCT
ejpam-3343	112	66	y	y	PROPN
ejpam-3343	112	67	,	,	PUNCT
ejpam-3343	112	68	z	z	NOUN
ejpam-3343	112	69	∈	∈	PROPN
ejpam-3343	112	70	x	x	X
ejpam-3343	112	71	)	)	PUNCT
ejpam-3343	112	72	(	(	PUNCT
ejpam-3343	112	73	ψ(x	ψ(x	NOUN
ejpam-3343	112	74	)	)	PUNCT
ejpam-3343	112	75	≤	≤	NOUN
ejpam-3343	112	76	∨	∨	NUM
ejpam-3343	112	77	{	{	PUNCT
ejpam-3343	112	78	ψ	ψ	X
ejpam-3343	112	79	(	(	PUNCT
ejpam-3343	112	80	(	(	PUNCT
ejpam-3343	112	81	x	x	SYM
ejpam-3343	112	82	∗	∗	PROPN
ejpam-3343	112	83	z	z	NOUN
ejpam-3343	112	84	)	)	PUNCT
ejpam-3343	112	85	∗	∗	NOUN
ejpam-3343	112	86	(	(	PUNCT
ejpam-3343	112	87	y	y	PROPN
ejpam-3343	112	88	∗	∗	PROPN
ejpam-3343	112	89	z	z	PROPN
ejpam-3343	112	90	)	)	PUNCT
ejpam-3343	112	91	)	)	PUNCT
ejpam-3343	112	92	,	,	PUNCT
ejpam-3343	112	93	ψ(y	ψ(y	PROPN
ejpam-3343	112	94	)	)	PUNCT
ejpam-3343	112	95	}	}	PUNCT
ejpam-3343	112	96	)	)	PUNCT
ejpam-3343	112	97	.	.	PUNCT
ejpam-3343	113	1	definition	definition	NOUN
ejpam-3343	113	2	7	7	NUM
ejpam-3343	113	3	.	.	PUNCT
ejpam-3343	114	1	let	let	VERB
ejpam-3343	114	2	(	(	PUNCT
ejpam-3343	114	3	η	η	PROPN
ejpam-3343	114	4	,	,	PUNCT
ejpam-3343	114	5	a	a	PRON
ejpam-3343	114	6	)	)	PUNCT
ejpam-3343	114	7	be	be	AUX
ejpam-3343	114	8	an	an	DET
ejpam-3343	114	9	n	n	ADV
ejpam-3343	114	10	-soft	-soft	NOUN
ejpam-3343	114	11	set	set	VERB
ejpam-3343	114	12	over	over	ADP
ejpam-3343	114	13	a	a	DET
ejpam-3343	114	14	bci	bci	NOUN
ejpam-3343	114	15	-	-	NOUN
ejpam-3343	114	16	algebra	algebra	NOUN
ejpam-3343	114	17	x	x	PUNCT
ejpam-3343	114	18	where	where	SCONJ
ejpam-3343	114	19	a	a	PRON
ejpam-3343	114	20	is	be	AUX
ejpam-3343	114	21	a	a	DET
ejpam-3343	114	22	subset	subset	NOUN
ejpam-3343	114	23	of	of	ADP
ejpam-3343	114	24	e.	e.	PROPN
ejpam-3343	114	25	if	if	SCONJ
ejpam-3343	114	26	there	there	PRON
ejpam-3343	114	27	exists	exist	VERB
ejpam-3343	114	28	an	an	DET
ejpam-3343	114	29	attribute	attribute	NOUN
ejpam-3343	114	30	u	u	NOUN
ejpam-3343	114	31	∈	∈	PROPN
ejpam-3343	114	32	a	a	PRON
ejpam-3343	114	33	for	for	ADP
ejpam-3343	114	34	which	which	PRON
ejpam-3343	114	35	the	the	DET
ejpam-3343	114	36	n	n	ADV
ejpam-3343	114	37	-structure	-structure	NOUN
ejpam-3343	114	38	(	(	PUNCT
ejpam-3343	114	39	x	x	NOUN
ejpam-3343	114	40	,	,	PUNCT
ejpam-3343	114	41	ηu	ηu	NOUN
ejpam-3343	114	42	)	)	PUNCT
ejpam-3343	114	43	is	be	AUX
ejpam-3343	114	44	a	a	DET
ejpam-3343	114	45	pn	pn	NOUN
ejpam-3343	114	46	-ideal	-ideal	NOUN
ejpam-3343	114	47	of	of	ADP
ejpam-3343	114	48	x	x	NOUN
ejpam-3343	114	49	,	,	PUNCT
ejpam-3343	114	50	then	then	ADV
ejpam-3343	114	51	we	we	PRON
ejpam-3343	114	52	say	say	VERB
ejpam-3343	114	53	that	that	SCONJ
ejpam-3343	114	54	(	(	PUNCT
ejpam-3343	114	55	η	η	PROPN
ejpam-3343	114	56	,	,	PUNCT
ejpam-3343	114	57	a	a	PRON
ejpam-3343	114	58	)	)	PUNCT
ejpam-3343	114	59	is	be	AUX
ejpam-3343	114	60	an	an	DET
ejpam-3343	114	61	n	n	CCONJ
ejpam-3343	114	62	-soft	-soft	ADJ
ejpam-3343	114	63	p	p	NOUN
ejpam-3343	114	64	-	-	PUNCT
ejpam-3343	114	65	ideal	ideal	NOUN
ejpam-3343	114	66	of	of	ADP
ejpam-3343	114	67	x	x	SYM
ejpam-3343	114	68	related	relate	VERB
ejpam-3343	114	69	to	to	ADP
ejpam-3343	114	70	the	the	DET
ejpam-3343	114	71	attribute	attribute	NOUN
ejpam-3343	114	72	u	u	NOUN
ejpam-3343	114	73	(	(	PUNCT
ejpam-3343	114	74	briefly	briefly	ADV
ejpam-3343	114	75	,	,	PUNCT
ejpam-3343	114	76	nu	nu	ADJ
ejpam-3343	114	77	-	-	PUNCT
ejpam-3343	114	78	soft	soft	ADJ
ejpam-3343	114	79	p	p	NOUN
ejpam-3343	114	80	-	-	PUNCT
ejpam-3343	114	81	ideal	ideal	NOUN
ejpam-3343	114	82	)	)	PUNCT
ejpam-3343	114	83	.	.	PUNCT
ejpam-3343	115	1	if	if	SCONJ
ejpam-3343	115	2	(	(	PUNCT
ejpam-3343	115	3	η	η	PROPN
ejpam-3343	115	4	,	,	PUNCT
ejpam-3343	115	5	a	a	PRON
ejpam-3343	115	6	)	)	PUNCT
ejpam-3343	115	7	is	be	AUX
ejpam-3343	115	8	an	an	DET
ejpam-3343	115	9	nu	nu	NOUN
ejpam-3343	115	10	-	-	PUNCT
ejpam-3343	115	11	soft	soft	ADJ
ejpam-3343	115	12	p	p	NOUN
ejpam-3343	115	13	-	-	PUNCT
ejpam-3343	115	14	ideal	ideal	NOUN
ejpam-3343	115	15	of	of	ADP
ejpam-3343	115	16	x	x	PUNCT
ejpam-3343	115	17	for	for	ADP
ejpam-3343	115	18	all	all	PRON
ejpam-3343	115	19	u	u	NOUN
ejpam-3343	115	20	∈	∈	PROPN
ejpam-3343	115	21	a	a	PRON
ejpam-3343	115	22	,	,	PUNCT
ejpam-3343	115	23	we	we	PRON
ejpam-3343	115	24	say	say	VERB
ejpam-3343	115	25	that	that	SCONJ
ejpam-3343	115	26	(	(	PUNCT
ejpam-3343	115	27	η	η	PROPN
ejpam-3343	115	28	,	,	PUNCT
ejpam-3343	115	29	a	a	PRON
ejpam-3343	115	30	)	)	PUNCT
ejpam-3343	115	31	is	be	AUX
ejpam-3343	115	32	an	an	DET
ejpam-3343	115	33	n	n	CCONJ
ejpam-3343	115	34	-soft	-soft	ADJ
ejpam-3343	115	35	p	p	NOUN
ejpam-3343	115	36	-	-	PUNCT
ejpam-3343	115	37	ideal	ideal	NOUN
ejpam-3343	115	38	over	over	ADP
ejpam-3343	115	39	x.	x.	PROPN
ejpam-3343	115	40	example	example	NOUN
ejpam-3343	116	1	1	1	X
ejpam-3343	116	2	.	.	PUNCT
ejpam-3343	116	3	let	let	VERB
ejpam-3343	116	4	u	u	PRON
ejpam-3343	116	5	be	be	AUX
ejpam-3343	116	6	a	a	DET
ejpam-3343	116	7	initial	initial	ADJ
ejpam-3343	116	8	universe	universe	NOUN
ejpam-3343	116	9	set	set	NOUN
ejpam-3343	116	10	consists	consist	VERB
ejpam-3343	116	11	of	of	ADP
ejpam-3343	116	12	‘	'	PUNCT
ejpam-3343	116	13	white	white	ADJ
ejpam-3343	116	14	’	'	PUNCT
ejpam-3343	116	15	,	,	PUNCT
ejpam-3343	116	16	‘	'	PUNCT
ejpam-3343	116	17	reddish	reddish	ADJ
ejpam-3343	116	18	’	'	PUNCT
ejpam-3343	116	19	,	,	PUNCT
ejpam-3343	116	20	‘	'	PUNCT
ejpam-3343	116	21	green	green	ADJ
ejpam-3343	116	22	’	'	PUNCT
ejpam-3343	116	23	and	and	CCONJ
ejpam-3343	116	24	‘	'	PUNCT
ejpam-3343	116	25	yellow	yellow	ADJ
ejpam-3343	116	26	’	'	PUNCT
ejpam-3343	116	27	.	.	PUNCT
ejpam-3343	117	1	the	the	DET
ejpam-3343	117	2	soft	soft	ADJ
ejpam-3343	117	3	machine	machine	NOUN
ejpam-3343	117	4	“	"	PUNCT
ejpam-3343	117	5	]	]	X
ejpam-3343	117	6	(	(	PUNCT
ejpam-3343	117	7	−,−	−,−	NOUN
ejpam-3343	117	8	)	)	PUNCT
ejpam-3343	117	9	”	"	PUNCT
ejpam-3343	117	10	is	be	AUX
ejpam-3343	117	11	equipped	equip	VERB
ejpam-3343	117	12	as	as	SCONJ
ejpam-3343	117	13	follows	follow	VERB
ejpam-3343	117	14	:	:	PUNCT
ejpam-3343	117	15	g.	g.	PROPN
ejpam-3343	117	16	muhiuddin	muhiuddin	PROPN
ejpam-3343	117	17	,	,	PUNCT
ejpam-3343	117	18	s.	s.	PROPN
ejpam-3343	117	19	aldhafeeri	aldhafeeri	PROPN
ejpam-3343	117	20	/	/	SYM
ejpam-3343	117	21	eur	eur	PROPN
ejpam-3343	117	22	.	.	PUNCT
ejpam-3343	118	1	j.	j.	PROPN
ejpam-3343	118	2	pure	pure	PROPN
ejpam-3343	118	3	appl	appl	PROPN
ejpam-3343	118	4	.	.	PROPN
ejpam-3343	118	5	math	math	PROPN
ejpam-3343	118	6	,	,	PUNCT
ejpam-3343	118	7	12	12	NUM
ejpam-3343	118	8	(	(	PUNCT
ejpam-3343	118	9	1	1	NUM
ejpam-3343	118	10	)	)	PUNCT
ejpam-3343	118	11	(	(	PUNCT
ejpam-3343	118	12	2019	2019	NUM
ejpam-3343	118	13	)	)	PUNCT
ejpam-3343	118	14	,	,	PUNCT
ejpam-3343	118	15	79	79	NUM
ejpam-3343	118	16	-	-	SYM
ejpam-3343	118	17	87	87	NUM
ejpam-3343	118	18	83	83	NUM
ejpam-3343	118	19	table	table	NOUN
ejpam-3343	118	20	1	1	NUM
ejpam-3343	118	21	:	:	PUNCT
ejpam-3343	118	22	tabular	tabular	PROPN
ejpam-3343	118	23	representation	representation	NOUN
ejpam-3343	118	24	of	of	ADP
ejpam-3343	118	25	(	(	PUNCT
ejpam-3343	118	26	η	η	PROPN
ejpam-3343	118	27	,	,	PUNCT
ejpam-3343	118	28	a	a	PRON
ejpam-3343	118	29	)	)	PUNCT
ejpam-3343	118	30	(	(	PUNCT
ejpam-3343	118	31	η	η	PROPN
ejpam-3343	118	32	,	,	PUNCT
ejpam-3343	118	33	a	a	DET
ejpam-3343	118	34	)	)	PUNCT
ejpam-3343	118	35	white	white	ADJ
ejpam-3343	118	36	reddish	reddish	ADJ
ejpam-3343	118	37	green	green	ADJ
ejpam-3343	118	38	yellow	yellow	ADJ
ejpam-3343	118	39	beautiful	beautiful	ADJ
ejpam-3343	118	40	−0.8	−0.8	NOUN
ejpam-3343	118	41	−0.7	−0.7	NOUN
ejpam-3343	118	42	−0.3	−0.3	PROPN
ejpam-3343	119	1	−0.3	−0.3	PROPN
ejpam-3343	119	2	fine	fine	ADJ
ejpam-3343	119	3	−0.6	−0.6	PROPN
ejpam-3343	119	4	−0.5	−0.5	NUM
ejpam-3343	120	1	−0.4	−0.4	NUM
ejpam-3343	121	1	−0.4	−0.4	NUM
ejpam-3343	122	1	smart	smart	ADJ
ejpam-3343	123	1	−0.7	−0.7	PROPN
ejpam-3343	123	2	−0.5	−0.5	NUM
ejpam-3343	124	1	−0.1	−0.1	PROPN
ejpam-3343	124	2	−0.1	−0.1	X
ejpam-3343	124	3	]	]	X
ejpam-3343	124	4	(	(	PUNCT
ejpam-3343	124	5	x	x	NOUN
ejpam-3343	124	6	,	,	PUNCT
ejpam-3343	124	7	y	y	NOUN
ejpam-3343	124	8	)	)	PUNCT
ejpam-3343	125	1	=	=	PUNCT
ejpam-3343	125	2	y	y	PROPN
ejpam-3343	125	3	if	if	SCONJ
ejpam-3343	125	4	x	x	X
ejpam-3343	125	5	=	=	SYM
ejpam-3343	125	6	white	white	ADJ
ejpam-3343	125	7	and	and	CCONJ
ejpam-3343	125	8	y	y	PROPN
ejpam-3343	125	9	∈	∈	PROPN
ejpam-3343	125	10	u	u	PROPN
ejpam-3343	125	11	,	,	PUNCT
ejpam-3343	125	12	]	]	X
ejpam-3343	125	13	(	(	PUNCT
ejpam-3343	125	14	x	x	NOUN
ejpam-3343	125	15	,	,	PUNCT
ejpam-3343	125	16	y	y	NOUN
ejpam-3343	125	17	)	)	PUNCT
ejpam-3343	125	18	=	=	SYM
ejpam-3343	126	1			X
ejpam-3343	126	2	reddish	reddish	ADJ
ejpam-3343	126	3	if	if	SCONJ
ejpam-3343	126	4	(	(	PUNCT
ejpam-3343	126	5	x	x	NOUN
ejpam-3343	126	6	,	,	PUNCT
ejpam-3343	126	7	y	y	NOUN
ejpam-3343	126	8	)	)	PUNCT
ejpam-3343	126	9	=	=	SYM
ejpam-3343	126	10	(	(	PUNCT
ejpam-3343	126	11	reddish	reddish	ADJ
ejpam-3343	126	12	,	,	PUNCT
ejpam-3343	126	13	white	white	ADJ
ejpam-3343	126	14	)	)	PUNCT
ejpam-3343	126	15	,	,	PUNCT
ejpam-3343	126	16	white	white	ADJ
ejpam-3343	126	17	if	if	SCONJ
ejpam-3343	126	18	(	(	PUNCT
ejpam-3343	126	19	x	x	NOUN
ejpam-3343	126	20	,	,	PUNCT
ejpam-3343	126	21	y	y	NOUN
ejpam-3343	126	22	)	)	PUNCT
ejpam-3343	126	23	=	=	SYM
ejpam-3343	126	24	(	(	PUNCT
ejpam-3343	126	25	reddish	reddish	ADJ
ejpam-3343	126	26	,	,	PUNCT
ejpam-3343	126	27	reddish	reddish	ADJ
ejpam-3343	126	28	)	)	PUNCT
ejpam-3343	126	29	,	,	PUNCT
ejpam-3343	126	30	yellow	yellow	ADJ
ejpam-3343	126	31	if	if	SCONJ
ejpam-3343	126	32	(	(	PUNCT
ejpam-3343	126	33	x	x	NOUN
ejpam-3343	126	34	,	,	PUNCT
ejpam-3343	126	35	y	y	NOUN
ejpam-3343	126	36	)	)	PUNCT
ejpam-3343	126	37	=	=	SYM
ejpam-3343	126	38	(	(	PUNCT
ejpam-3343	126	39	reddish	reddish	ADJ
ejpam-3343	126	40	,	,	PUNCT
ejpam-3343	126	41	green	green	ADJ
ejpam-3343	126	42	)	)	PUNCT
ejpam-3343	126	43	,	,	PUNCT
ejpam-3343	126	44	green	green	ADJ
ejpam-3343	126	45	if	if	SCONJ
ejpam-3343	126	46	(	(	PUNCT
ejpam-3343	126	47	x	x	NOUN
ejpam-3343	126	48	,	,	PUNCT
ejpam-3343	126	49	y	y	NOUN
ejpam-3343	126	50	)	)	PUNCT
ejpam-3343	126	51	=	=	SYM
ejpam-3343	126	52	(	(	PUNCT
ejpam-3343	126	53	reddish	reddish	ADJ
ejpam-3343	126	54	,	,	PUNCT
ejpam-3343	126	55	yellow	yellow	ADJ
ejpam-3343	126	56	)	)	PUNCT
ejpam-3343	126	57	,	,	PUNCT
ejpam-3343	126	58	]	]	X
ejpam-3343	126	59	(	(	PUNCT
ejpam-3343	126	60	x	x	NOUN
ejpam-3343	126	61	,	,	PUNCT
ejpam-3343	126	62	y	y	PROPN
ejpam-3343	126	63	)	)	PUNCT
ejpam-3343	126	64	=	=	SYM
ejpam-3343	127	1			PUNCT
ejpam-3343	127	2	green	green	ADJ
ejpam-3343	128	1	if	if	SCONJ
ejpam-3343	128	2	(	(	PUNCT
ejpam-3343	128	3	x	x	NOUN
ejpam-3343	128	4	,	,	PUNCT
ejpam-3343	128	5	y	y	NOUN
ejpam-3343	128	6	)	)	PUNCT
ejpam-3343	128	7	=	=	SYM
ejpam-3343	128	8	(	(	PUNCT
ejpam-3343	128	9	green	green	ADJ
ejpam-3343	128	10	,	,	PUNCT
ejpam-3343	128	11	white	white	ADJ
ejpam-3343	128	12	)	)	PUNCT
ejpam-3343	128	13	,	,	PUNCT
ejpam-3343	128	14	yellow	yellow	VERB
ejpam-3343	128	15	if	if	SCONJ
ejpam-3343	128	16	(	(	PUNCT
ejpam-3343	128	17	x	x	NOUN
ejpam-3343	128	18	,	,	PUNCT
ejpam-3343	128	19	y	y	NOUN
ejpam-3343	128	20	)	)	PUNCT
ejpam-3343	128	21	=	=	SYM
ejpam-3343	128	22	(	(	PUNCT
ejpam-3343	128	23	green	green	ADJ
ejpam-3343	128	24	,	,	PUNCT
ejpam-3343	128	25	redish	redish	NOUN
ejpam-3343	128	26	)	)	PUNCT
ejpam-3343	128	27	,	,	PUNCT
ejpam-3343	128	28	white	white	ADJ
ejpam-3343	128	29	if	if	SCONJ
ejpam-3343	128	30	(	(	PUNCT
ejpam-3343	128	31	x	x	NOUN
ejpam-3343	128	32	,	,	PUNCT
ejpam-3343	128	33	y	y	NOUN
ejpam-3343	128	34	)	)	PUNCT
ejpam-3343	128	35	=	=	SYM
ejpam-3343	128	36	(	(	PUNCT
ejpam-3343	128	37	green	green	ADJ
ejpam-3343	128	38	,	,	PUNCT
ejpam-3343	128	39	green	green	ADJ
ejpam-3343	128	40	)	)	PUNCT
ejpam-3343	128	41	,	,	PUNCT
ejpam-3343	128	42	reddish	reddish	ADJ
ejpam-3343	128	43	if	if	SCONJ
ejpam-3343	128	44	(	(	PUNCT
ejpam-3343	128	45	x	x	NOUN
ejpam-3343	128	46	,	,	PUNCT
ejpam-3343	128	47	y	y	NOUN
ejpam-3343	128	48	)	)	PUNCT
ejpam-3343	128	49	=	=	SYM
ejpam-3343	128	50	(	(	PUNCT
ejpam-3343	128	51	green	green	ADJ
ejpam-3343	128	52	,	,	PUNCT
ejpam-3343	128	53	yellow	yellow	ADJ
ejpam-3343	128	54	)	)	PUNCT
ejpam-3343	128	55	,	,	PUNCT
ejpam-3343	128	56	]	]	X
ejpam-3343	128	57	(	(	PUNCT
ejpam-3343	128	58	x	x	NOUN
ejpam-3343	128	59	,	,	PUNCT
ejpam-3343	128	60	y	y	NOUN
ejpam-3343	128	61	)	)	PUNCT
ejpam-3343	128	62	=	=	SYM
ejpam-3343	128	63			VERB
ejpam-3343	128	64	yellow	yellow	ADJ
ejpam-3343	128	65	if	if	SCONJ
ejpam-3343	128	66	(	(	PUNCT
ejpam-3343	128	67	x	x	NOUN
ejpam-3343	128	68	,	,	PUNCT
ejpam-3343	128	69	y	y	NOUN
ejpam-3343	128	70	)	)	PUNCT
ejpam-3343	128	71	=	=	SYM
ejpam-3343	128	72	(	(	PUNCT
ejpam-3343	128	73	yellow	yellow	ADJ
ejpam-3343	128	74	,	,	PUNCT
ejpam-3343	128	75	white	white	ADJ
ejpam-3343	128	76	)	)	PUNCT
ejpam-3343	128	77	,	,	PUNCT
ejpam-3343	128	78	green	green	ADJ
ejpam-3343	128	79	if	if	SCONJ
ejpam-3343	128	80	(	(	PUNCT
ejpam-3343	128	81	x	x	NOUN
ejpam-3343	128	82	,	,	PUNCT
ejpam-3343	128	83	y	y	NOUN
ejpam-3343	128	84	)	)	PUNCT
ejpam-3343	128	85	=	=	SYM
ejpam-3343	128	86	(	(	PUNCT
ejpam-3343	128	87	yellow	yellow	ADJ
ejpam-3343	128	88	,	,	PUNCT
ejpam-3343	128	89	redish	redish	NOUN
ejpam-3343	128	90	)	)	PUNCT
ejpam-3343	128	91	,	,	PUNCT
ejpam-3343	128	92	reddish	reddish	ADJ
ejpam-3343	128	93	if	if	SCONJ
ejpam-3343	128	94	(	(	PUNCT
ejpam-3343	128	95	x	x	NOUN
ejpam-3343	128	96	,	,	PUNCT
ejpam-3343	128	97	y	y	NOUN
ejpam-3343	128	98	)	)	PUNCT
ejpam-3343	128	99	=	=	SYM
ejpam-3343	128	100	(	(	PUNCT
ejpam-3343	128	101	yellow	yellow	ADJ
ejpam-3343	128	102	,	,	PUNCT
ejpam-3343	128	103	green	green	ADJ
ejpam-3343	128	104	)	)	PUNCT
ejpam-3343	128	105	,	,	PUNCT
ejpam-3343	128	106	white	white	ADJ
ejpam-3343	128	107	if	if	SCONJ
ejpam-3343	128	108	(	(	PUNCT
ejpam-3343	128	109	x	x	NOUN
ejpam-3343	128	110	,	,	PUNCT
ejpam-3343	128	111	y	y	NOUN
ejpam-3343	128	112	)	)	PUNCT
ejpam-3343	128	113	=	=	SYM
ejpam-3343	128	114	(	(	PUNCT
ejpam-3343	128	115	yellow	yellow	ADJ
ejpam-3343	128	116	,	,	PUNCT
ejpam-3343	128	117	yellow	yellow	ADJ
ejpam-3343	128	118	)	)	PUNCT
ejpam-3343	128	119	.	.	PUNCT
ejpam-3343	129	1	then	then	ADV
ejpam-3343	129	2	the	the	DET
ejpam-3343	129	3	soft	soft	ADJ
ejpam-3343	129	4	machine	machine	NOUN
ejpam-3343	129	5	“	"	PUNCT
ejpam-3343	129	6	]	]	X
ejpam-3343	129	7	(	(	PUNCT
ejpam-3343	129	8	−,−	−,−	NOUN
ejpam-3343	129	9	)	)	PUNCT
ejpam-3343	129	10	”	"	PUNCT
ejpam-3343	129	11	makes	make	VERB
ejpam-3343	129	12	u	u	NOUN
ejpam-3343	129	13	into	into	ADP
ejpam-3343	129	14	a	a	DET
ejpam-3343	129	15	bci	bci	NOUN
ejpam-3343	129	16	-	-	NOUN
ejpam-3343	129	17	algebra	algebra	NOUN
ejpam-3343	129	18	.	.	PUNCT
ejpam-3343	130	1	consider	consider	VERB
ejpam-3343	130	2	a	a	DET
ejpam-3343	130	3	set	set	NOUN
ejpam-3343	130	4	of	of	ADP
ejpam-3343	130	5	attributes	attribute	NOUN
ejpam-3343	130	6	:	:	PUNCT
ejpam-3343	130	7	a	a	DET
ejpam-3343	130	8	:	:	PUNCT
ejpam-3343	130	9	=	=	X
ejpam-3343	130	10	{	{	PUNCT
ejpam-3343	130	11	beautiful	beautiful	ADJ
ejpam-3343	130	12	,	,	PUNCT
ejpam-3343	130	13	fine	fine	ADJ
ejpam-3343	130	14	,	,	PUNCT
ejpam-3343	130	15	smart	smart	ADJ
ejpam-3343	130	16	}	}	PUNCT
ejpam-3343	130	17	,	,	PUNCT
ejpam-3343	130	18	and	and	CCONJ
ejpam-3343	130	19	let	let	VERB
ejpam-3343	130	20	(	(	PUNCT
ejpam-3343	130	21	η	η	NOUN
ejpam-3343	130	22	,	,	PUNCT
ejpam-3343	130	23	a	a	PRON
ejpam-3343	130	24	)	)	PUNCT
ejpam-3343	130	25	be	be	AUX
ejpam-3343	130	26	an	an	DET
ejpam-3343	130	27	n	n	CCONJ
ejpam-3343	130	28	-soft	-soft	ADJ
ejpam-3343	130	29	sets	set	NOUN
ejpam-3343	130	30	over	over	ADP
ejpam-3343	130	31	u	u	NOUN
ejpam-3343	130	32	with	with	ADP
ejpam-3343	130	33	the	the	DET
ejpam-3343	130	34	tabular	tabular	ADJ
ejpam-3343	130	35	representations	representation	NOUN
ejpam-3343	130	36	which	which	PRON
ejpam-3343	130	37	is	be	AUX
ejpam-3343	130	38	given	give	VERB
ejpam-3343	130	39	by	by	ADP
ejpam-3343	130	40	table	table	NOUN
ejpam-3343	130	41	1	1	NUM
ejpam-3343	130	42	.	.	PUNCT
ejpam-3343	131	1	then	then	ADV
ejpam-3343	131	2	the	the	DET
ejpam-3343	131	3	n	n	PRON
ejpam-3343	131	4	-structures	-structures	PROPN
ejpam-3343	131	5	(	(	PUNCT
ejpam-3343	131	6	u	u	NOUN
ejpam-3343	131	7	,	,	PUNCT
ejpam-3343	131	8	ηbeautiful	ηbeautiful	ADJ
ejpam-3343	131	9	)	)	PUNCT
ejpam-3343	131	10	,	,	PUNCT
ejpam-3343	131	11	(	(	PUNCT
ejpam-3343	131	12	u	u	NOUN
ejpam-3343	131	13	,	,	PUNCT
ejpam-3343	131	14	ηfine	ηfine	NOUN
ejpam-3343	131	15	)	)	PUNCT
ejpam-3343	131	16	and	and	CCONJ
ejpam-3343	131	17	(	(	PUNCT
ejpam-3343	131	18	u	u	NOUN
ejpam-3343	131	19	,	,	PUNCT
ejpam-3343	131	20	ηsmart	ηsmart	ADJ
ejpam-3343	131	21	)	)	PUNCT
ejpam-3343	131	22	are	be	AUX
ejpam-3343	131	23	pn	pn	PROPN
ejpam-3343	131	24	-ideals	-ideal	NOUN
ejpam-3343	131	25	of	of	ADP
ejpam-3343	131	26	u.	u.	NOUN
ejpam-3343	131	27	hence	hence	ADV
ejpam-3343	131	28	(	(	PUNCT
ejpam-3343	131	29	η	η	PROPN
ejpam-3343	131	30	,	,	PUNCT
ejpam-3343	131	31	a	a	PRON
ejpam-3343	131	32	)	)	PUNCT
ejpam-3343	131	33	is	be	AUX
ejpam-3343	131	34	an	an	DET
ejpam-3343	131	35	n	n	CCONJ
ejpam-3343	131	36	-soft	-soft	ADJ
ejpam-3343	131	37	p	p	NOUN
ejpam-3343	131	38	-	-	PUNCT
ejpam-3343	131	39	ideal	ideal	NOUN
ejpam-3343	131	40	over	over	ADP
ejpam-3343	131	41	u.	u.	NOUN
ejpam-3343	131	42	proposition	proposition	NOUN
ejpam-3343	131	43	1	1	NUM
ejpam-3343	131	44	.	.	X
ejpam-3343	132	1	for	for	ADP
ejpam-3343	132	2	any	any	DET
ejpam-3343	132	3	attribute	attribute	NOUN
ejpam-3343	132	4	u	u	NOUN
ejpam-3343	132	5	∈	∈	PROPN
ejpam-3343	132	6	a	a	PRON
ejpam-3343	132	7	,	,	PUNCT
ejpam-3343	132	8	every	every	DET
ejpam-3343	132	9	nu	nu	ADJ
ejpam-3343	132	10	-	-	PUNCT
ejpam-3343	132	11	soft	soft	ADJ
ejpam-3343	132	12	p	p	NOUN
ejpam-3343	132	13	-	-	PUNCT
ejpam-3343	132	14	ideal	ideal	NOUN
ejpam-3343	132	15	(	(	PUNCT
ejpam-3343	132	16	η	η	PROPN
ejpam-3343	132	17	,	,	PUNCT
ejpam-3343	132	18	a	a	PRON
ejpam-3343	132	19	)	)	PUNCT
ejpam-3343	132	20	over	over	ADP
ejpam-3343	132	21	a	a	DET
ejpam-3343	132	22	bci	bci	NOUN
ejpam-3343	132	23	-	-	NOUN
ejpam-3343	132	24	algebra	algebra	NOUN
ejpam-3343	132	25	x	x	PRON
ejpam-3343	132	26	satisfies	satisfy	VERB
ejpam-3343	132	27	the	the	DET
ejpam-3343	132	28	following	follow	VERB
ejpam-3343	132	29	inequality	inequality	NOUN
ejpam-3343	132	30	:	:	PUNCT
ejpam-3343	132	31	(	(	PUNCT
ejpam-3343	132	32	∀x	∀x	X
ejpam-3343	132	33	∈	∈	PROPN
ejpam-3343	132	34	x	x	NOUN
ejpam-3343	132	35	)	)	PUNCT
ejpam-3343	132	36	(	(	PUNCT
ejpam-3343	132	37	ηu(x	ηu(x	NOUN
ejpam-3343	132	38	)	)	PUNCT
ejpam-3343	132	39	≤	≤	NOUN
ejpam-3343	132	40	ηu	ηu	X
ejpam-3343	132	41	(	(	PUNCT
ejpam-3343	132	42	0	0	NUM
ejpam-3343	132	43	∗	∗	NOUN
ejpam-3343	132	44	(	(	PUNCT
ejpam-3343	132	45	0	0	NUM
ejpam-3343	132	46	∗	∗	NOUN
ejpam-3343	132	47	x	x	NOUN
ejpam-3343	132	48	)	)	PUNCT
ejpam-3343	132	49	)	)	PUNCT
ejpam-3343	132	50	)	)	PUNCT
ejpam-3343	132	51	.	.	PUNCT
ejpam-3343	133	1	(	(	PUNCT
ejpam-3343	133	2	3	3	X
ejpam-3343	133	3	)	)	PUNCT
ejpam-3343	133	4	proof	proof	NOUN
ejpam-3343	133	5	.	.	PUNCT
ejpam-3343	134	1	using	use	VERB
ejpam-3343	134	2	definition	definition	NOUN
ejpam-3343	134	3	6(ii	6(ii	PROPN
ejpam-3343	134	4	)	)	PUNCT
ejpam-3343	134	5	,	,	PUNCT
ejpam-3343	134	6	we	we	PRON
ejpam-3343	134	7	have	have	VERB
ejpam-3343	134	8	ηu(x	ηu(x	NOUN
ejpam-3343	134	9	)	)	PUNCT
ejpam-3343	134	10	≤	≤	NUM
ejpam-3343	134	11	∨	∨	NUM
ejpam-3343	134	12	{	{	PUNCT
ejpam-3343	134	13	ηu((x	ηu((x	PROPN
ejpam-3343	134	14	∗	∗	PROPN
ejpam-3343	134	15	z	z	NOUN
ejpam-3343	134	16	)	)	PUNCT
ejpam-3343	134	17	∗	∗	NOUN
ejpam-3343	134	18	(	(	PUNCT
ejpam-3343	134	19	y	y	PROPN
ejpam-3343	134	20	∗	∗	PROPN
ejpam-3343	134	21	z	z	PROPN
ejpam-3343	134	22	)	)	PUNCT
ejpam-3343	134	23	)	)	PUNCT
ejpam-3343	134	24	,	,	PUNCT
ejpam-3343	134	25	ηu(y	ηu(y	NOUN
ejpam-3343	134	26	)	)	PUNCT
ejpam-3343	134	27	}	}	PUNCT
ejpam-3343	134	28	(	(	PUNCT
ejpam-3343	134	29	4	4	X
ejpam-3343	134	30	)	)	PUNCT
ejpam-3343	134	31	for	for	ADP
ejpam-3343	134	32	all	all	DET
ejpam-3343	134	33	x	x	NOUN
ejpam-3343	134	34	,	,	PUNCT
ejpam-3343	134	35	y	y	PROPN
ejpam-3343	134	36	,	,	PUNCT
ejpam-3343	134	37	z	z	NOUN
ejpam-3343	134	38	∈	∈	PROPN
ejpam-3343	134	39	x.	x.	NOUN
ejpam-3343	135	1	if	if	SCONJ
ejpam-3343	135	2	we	we	PRON
ejpam-3343	135	3	substitute	substitute	VERB
ejpam-3343	135	4	x	x	PUNCT
ejpam-3343	135	5	for	for	ADP
ejpam-3343	135	6	z	z	PROPN
ejpam-3343	135	7	,	,	PUNCT
ejpam-3343	135	8	and	and	CCONJ
ejpam-3343	135	9	0	0	NUM
ejpam-3343	135	10	for	for	SCONJ
ejpam-3343	135	11	y	y	PROPN
ejpam-3343	135	12	in	in	ADP
ejpam-3343	135	13	(	(	PUNCT
ejpam-3343	135	14	4	4	NUM
ejpam-3343	135	15	)	)	PUNCT
ejpam-3343	135	16	,	,	PUNCT
ejpam-3343	135	17	then	then	ADV
ejpam-3343	135	18	ηu(x	ηu(x	PUNCT
ejpam-3343	135	19	)	)	PUNCT
ejpam-3343	135	20	≤	≤	NUM
ejpam-3343	135	21	∨	∨	NUM
ejpam-3343	135	22	{	{	PUNCT
ejpam-3343	135	23	ηu((x	ηu((x	PROPN
ejpam-3343	135	24	∗	∗	PROPN
ejpam-3343	135	25	x	x	NOUN
ejpam-3343	135	26	)	)	PUNCT
ejpam-3343	135	27	∗	∗	NOUN
ejpam-3343	135	28	(	(	PUNCT
ejpam-3343	135	29	0	0	NUM
ejpam-3343	135	30	∗	∗	NOUN
ejpam-3343	135	31	x	x	NOUN
ejpam-3343	135	32	)	)	PUNCT
ejpam-3343	135	33	)	)	PUNCT
ejpam-3343	135	34	,	,	PUNCT
ejpam-3343	135	35	ηu(0	ηu(0	NOUN
ejpam-3343	135	36	)	)	PUNCT
ejpam-3343	135	37	}	}	PUNCT
ejpam-3343	136	1	=	=	SYM
ejpam-3343	136	2	∨	∨	X
ejpam-3343	136	3	{	{	PUNCT
ejpam-3343	136	4	ηu(0	ηu(0	NOUN
ejpam-3343	136	5	∗	∗	NOUN
ejpam-3343	136	6	(	(	PUNCT
ejpam-3343	136	7	0	0	NUM
ejpam-3343	136	8	∗	∗	NOUN
ejpam-3343	136	9	x	x	NOUN
ejpam-3343	136	10	)	)	PUNCT
ejpam-3343	136	11	)	)	PUNCT
ejpam-3343	136	12	,	,	PUNCT
ejpam-3343	136	13	ηu(0	ηu(0	NOUN
ejpam-3343	136	14	)	)	PUNCT
ejpam-3343	136	15	}	}	PUNCT
ejpam-3343	136	16	=	=	SYM
ejpam-3343	136	17	ηu(0	ηu(0	ADJ
ejpam-3343	136	18	∗	∗	NOUN
ejpam-3343	136	19	(	(	PUNCT
ejpam-3343	136	20	0	0	NUM
ejpam-3343	136	21	∗	∗	NOUN
ejpam-3343	136	22	x	x	NOUN
ejpam-3343	136	23	)	)	PUNCT
ejpam-3343	136	24	)	)	PUNCT
ejpam-3343	137	1	g.	g.	PROPN
ejpam-3343	137	2	muhiuddin	muhiuddin	PROPN
ejpam-3343	137	3	,	,	PUNCT
ejpam-3343	137	4	s.	s.	PROPN
ejpam-3343	137	5	aldhafeeri	aldhafeeri	PROPN
ejpam-3343	137	6	/	/	SYM
ejpam-3343	137	7	eur	eur	PROPN
ejpam-3343	137	8	.	.	PUNCT
ejpam-3343	138	1	j.	j.	PROPN
ejpam-3343	138	2	pure	pure	PROPN
ejpam-3343	138	3	appl	appl	PROPN
ejpam-3343	138	4	.	.	PROPN
ejpam-3343	138	5	math	math	PROPN
ejpam-3343	138	6	,	,	PUNCT
ejpam-3343	138	7	12	12	NUM
ejpam-3343	138	8	(	(	PUNCT
ejpam-3343	138	9	1	1	NUM
ejpam-3343	138	10	)	)	PUNCT
ejpam-3343	138	11	(	(	PUNCT
ejpam-3343	138	12	2019	2019	NUM
ejpam-3343	138	13	)	)	PUNCT
ejpam-3343	138	14	,	,	PUNCT
ejpam-3343	138	15	79	79	NUM
ejpam-3343	138	16	-	-	SYM
ejpam-3343	138	17	87	87	NUM
ejpam-3343	138	18	84	84	NUM
ejpam-3343	138	19	by	by	ADP
ejpam-3343	138	20	using	use	VERB
ejpam-3343	138	21	(	(	PUNCT
ejpam-3343	138	22	iii	iii	NOUN
ejpam-3343	138	23	)	)	PUNCT
ejpam-3343	138	24	and	and	CCONJ
ejpam-3343	138	25	definition	definition	NOUN
ejpam-3343	138	26	6(i	6(i	NUM
ejpam-3343	138	27	)	)	PUNCT
ejpam-3343	138	28	.	.	PUNCT
ejpam-3343	139	1	this	this	PRON
ejpam-3343	139	2	completes	complete	VERB
ejpam-3343	139	3	the	the	DET
ejpam-3343	139	4	proof	proof	NOUN
ejpam-3343	139	5	.	.	PUNCT
ejpam-3343	140	1	corollary	corollary	ADJ
ejpam-3343	140	2	1	1	NUM
ejpam-3343	140	3	.	.	PUNCT
ejpam-3343	141	1	every	every	DET
ejpam-3343	141	2	n	n	CCONJ
ejpam-3343	141	3	-soft	-soft	ADJ
ejpam-3343	141	4	p	p	NOUN
ejpam-3343	141	5	-	-	PUNCT
ejpam-3343	141	6	ideal	ideal	NOUN
ejpam-3343	141	7	(	(	PUNCT
ejpam-3343	141	8	η	η	PROPN
ejpam-3343	141	9	,	,	PUNCT
ejpam-3343	141	10	a	a	PRON
ejpam-3343	141	11	)	)	PUNCT
ejpam-3343	141	12	over	over	ADP
ejpam-3343	141	13	a	a	DET
ejpam-3343	141	14	bci	bci	NOUN
ejpam-3343	141	15	-	-	NOUN
ejpam-3343	141	16	algebra	algebra	NOUN
ejpam-3343	141	17	x	x	PRON
ejpam-3343	141	18	satisfies	satisfy	VERB
ejpam-3343	141	19	the	the	DET
ejpam-3343	141	20	following	follow	VERB
ejpam-3343	141	21	inequality	inequality	NOUN
ejpam-3343	141	22	:	:	PUNCT
ejpam-3343	141	23	(	(	PUNCT
ejpam-3343	141	24	∀x	∀x	X
ejpam-3343	141	25	∈	∈	PROPN
ejpam-3343	141	26	x	x	NOUN
ejpam-3343	141	27	)	)	PUNCT
ejpam-3343	141	28	(	(	PUNCT
ejpam-3343	141	29	η(x	η(x	X
ejpam-3343	141	30	)	)	PUNCT
ejpam-3343	141	31	≤	≤	NUM
ejpam-3343	141	32	η(0	η(0	PROPN
ejpam-3343	141	33	∗	∗	NOUN
ejpam-3343	141	34	(	(	PUNCT
ejpam-3343	141	35	0	0	NUM
ejpam-3343	141	36	∗	∗	NOUN
ejpam-3343	141	37	x	x	NOUN
ejpam-3343	141	38	)	)	PUNCT
ejpam-3343	141	39	)	)	PUNCT
ejpam-3343	141	40	)	)	PUNCT
ejpam-3343	141	41	.	.	PUNCT
ejpam-3343	142	1	theorem	theorem	NOUN
ejpam-3343	142	2	2	2	NUM
ejpam-3343	142	3	.	.	X
ejpam-3343	142	4	for	for	ADP
ejpam-3343	142	5	any	any	DET
ejpam-3343	142	6	attribute	attribute	NOUN
ejpam-3343	142	7	u	u	NOUN
ejpam-3343	142	8	∈	∈	PROPN
ejpam-3343	142	9	a	a	PRON
ejpam-3343	142	10	,	,	PUNCT
ejpam-3343	142	11	every	every	DET
ejpam-3343	142	12	nu	nu	ADJ
ejpam-3343	142	13	-	-	PUNCT
ejpam-3343	142	14	soft	soft	ADJ
ejpam-3343	142	15	p	p	NOUN
ejpam-3343	142	16	-	-	PUNCT
ejpam-3343	142	17	ideal	ideal	NOUN
ejpam-3343	142	18	over	over	ADP
ejpam-3343	142	19	a	a	DET
ejpam-3343	142	20	bci	bci	NOUN
ejpam-3343	142	21	-	-	NOUN
ejpam-3343	142	22	algebra	algebra	NOUN
ejpam-3343	142	23	x	x	PUNCT
ejpam-3343	142	24	is	be	AUX
ejpam-3343	142	25	an	an	DET
ejpam-3343	142	26	nu	nu	ADJ
ejpam-3343	142	27	-	-	PUNCT
ejpam-3343	142	28	soft	soft	ADJ
ejpam-3343	142	29	ideal	ideal	NOUN
ejpam-3343	142	30	over	over	ADP
ejpam-3343	142	31	x.	x.	NOUN
ejpam-3343	142	32	proof	proof	NOUN
ejpam-3343	142	33	.	.	PUNCT
ejpam-3343	143	1	let	let	AUX
ejpam-3343	143	2	(	(	PUNCT
ejpam-3343	143	3	η	η	PROPN
ejpam-3343	143	4	,	,	PUNCT
ejpam-3343	143	5	a	a	PRON
ejpam-3343	143	6	)	)	PUNCT
ejpam-3343	143	7	be	be	AUX
ejpam-3343	143	8	an	an	DET
ejpam-3343	143	9	nu	nu	NOUN
ejpam-3343	143	10	-	-	PUNCT
ejpam-3343	143	11	soft	soft	ADJ
ejpam-3343	143	12	p	p	NOUN
ejpam-3343	143	13	-	-	PUNCT
ejpam-3343	143	14	ideal	ideal	NOUN
ejpam-3343	143	15	over	over	ADP
ejpam-3343	143	16	a	a	DET
ejpam-3343	143	17	bci	bci	NOUN
ejpam-3343	143	18	-	-	NOUN
ejpam-3343	143	19	algebra	algebra	NOUN
ejpam-3343	143	20	x.	x.	NOUN
ejpam-3343	143	21	since	since	SCONJ
ejpam-3343	143	22	x	x	PROPN
ejpam-3343	143	23	∗	∗	NOUN
ejpam-3343	143	24	0	0	NUM
ejpam-3343	144	1	=	=	NOUN
ejpam-3343	144	2	x	x	PROPN
ejpam-3343	144	3	for	for	ADP
ejpam-3343	144	4	all	all	DET
ejpam-3343	144	5	x	x	SYM
ejpam-3343	144	6	∈	∈	NOUN
ejpam-3343	144	7	x	x	X
ejpam-3343	144	8	,	,	PUNCT
ejpam-3343	144	9	it	it	PRON
ejpam-3343	144	10	follows	follow	VERB
ejpam-3343	144	11	from	from	ADP
ejpam-3343	144	12	definition	definition	NOUN
ejpam-3343	144	13	6(ii	6(ii	NOUN
ejpam-3343	144	14	)	)	PUNCT
ejpam-3343	144	15	and	and	CCONJ
ejpam-3343	144	16	(	(	PUNCT
ejpam-3343	144	17	a1	a1	NOUN
ejpam-3343	144	18	)	)	PUNCT
ejpam-3343	144	19	that	that	PRON
ejpam-3343	144	20	ηu(x	ηu(x	VERB
ejpam-3343	144	21	)	)	PUNCT
ejpam-3343	144	22	≤	≤	NUM
ejpam-3343	144	23	∨	∨	NUM
ejpam-3343	144	24	{	{	PUNCT
ejpam-3343	144	25	ηu((x	ηu((x	PROPN
ejpam-3343	144	26	∗	∗	PROPN
ejpam-3343	144	27	0	0	NUM
ejpam-3343	144	28	)	)	PUNCT
ejpam-3343	144	29	∗	∗	NOUN
ejpam-3343	144	30	(	(	PUNCT
ejpam-3343	144	31	y	y	PROPN
ejpam-3343	144	32	∗	∗	NOUN
ejpam-3343	144	33	0	0	NUM
ejpam-3343	144	34	)	)	PUNCT
ejpam-3343	144	35	)	)	PUNCT
ejpam-3343	144	36	,	,	PUNCT
ejpam-3343	144	37	ηu(y	ηu(y	NOUN
ejpam-3343	144	38	)	)	PUNCT
ejpam-3343	144	39	}	}	PUNCT
ejpam-3343	145	1	=	=	SYM
ejpam-3343	145	2	∨	∨	X
ejpam-3343	145	3	{	{	PUNCT
ejpam-3343	145	4	ηu(x	ηu(x	ADP
ejpam-3343	145	5	∗	∗	NOUN
ejpam-3343	145	6	y	y	NOUN
ejpam-3343	145	7	)	)	PUNCT
ejpam-3343	145	8	,	,	PUNCT
ejpam-3343	145	9	ηu(y	ηu(y	NOUN
ejpam-3343	145	10	)	)	PUNCT
ejpam-3343	145	11	}	}	PUNCT
ejpam-3343	145	12	for	for	ADP
ejpam-3343	145	13	all	all	DET
ejpam-3343	145	14	x	x	NOUN
ejpam-3343	145	15	,	,	PUNCT
ejpam-3343	145	16	y	y	PROPN
ejpam-3343	145	17	∈	∈	PROPN
ejpam-3343	145	18	x.	x.	NOUN
ejpam-3343	145	19	therefore	therefore	ADV
ejpam-3343	145	20	(	(	PUNCT
ejpam-3343	145	21	η	η	PROPN
ejpam-3343	145	22	,	,	PUNCT
ejpam-3343	145	23	a	a	PRON
ejpam-3343	145	24	)	)	PUNCT
ejpam-3343	145	25	is	be	AUX
ejpam-3343	145	26	an	an	DET
ejpam-3343	145	27	nu	nu	ADJ
ejpam-3343	145	28	-	-	PUNCT
ejpam-3343	145	29	soft	soft	ADJ
ejpam-3343	145	30	ideal	ideal	NOUN
ejpam-3343	145	31	over	over	ADP
ejpam-3343	145	32	x.	x.	NOUN
ejpam-3343	145	33	corollary	corollary	NOUN
ejpam-3343	145	34	2	2	NUM
ejpam-3343	145	35	.	.	PUNCT
ejpam-3343	146	1	every	every	DET
ejpam-3343	146	2	n	n	CCONJ
ejpam-3343	146	3	-soft	-soft	ADJ
ejpam-3343	146	4	p	p	NOUN
ejpam-3343	146	5	-	-	PUNCT
ejpam-3343	146	6	ideal	ideal	NOUN
ejpam-3343	146	7	over	over	ADP
ejpam-3343	146	8	a	a	DET
ejpam-3343	146	9	bci	bci	NOUN
ejpam-3343	146	10	-	-	NOUN
ejpam-3343	146	11	algebra	algebra	NOUN
ejpam-3343	146	12	x	x	PUNCT
ejpam-3343	146	13	is	be	AUX
ejpam-3343	146	14	an	an	DET
ejpam-3343	146	15	n	n	CCONJ
ejpam-3343	146	16	-soft	-soft	ADJ
ejpam-3343	146	17	ideal	ideal	NOUN
ejpam-3343	146	18	over	over	ADP
ejpam-3343	146	19	x.	x.	NOUN
ejpam-3343	146	20	the	the	DET
ejpam-3343	146	21	converse	converse	NOUN
ejpam-3343	146	22	of	of	ADP
ejpam-3343	146	23	theorem	theorem	ADJ
ejpam-3343	146	24	2	2	NUM
ejpam-3343	146	25	is	be	AUX
ejpam-3343	146	26	not	not	PART
ejpam-3343	146	27	true	true	ADJ
ejpam-3343	146	28	as	as	SCONJ
ejpam-3343	146	29	seen	see	VERB
ejpam-3343	146	30	in	in	ADP
ejpam-3343	146	31	the	the	DET
ejpam-3343	146	32	following	follow	VERB
ejpam-3343	146	33	example	example	NOUN
ejpam-3343	146	34	.	.	PUNCT
ejpam-3343	147	1	example	example	NOUN
ejpam-3343	148	1	2	2	NUM
ejpam-3343	148	2	.	.	PUNCT
ejpam-3343	148	3	let	let	VERB
ejpam-3343	148	4	u	u	PRON
ejpam-3343	148	5	be	be	AUX
ejpam-3343	148	6	an	an	DET
ejpam-3343	148	7	initial	initial	ADJ
ejpam-3343	148	8	universe	universe	NOUN
ejpam-3343	148	9	set	set	NOUN
ejpam-3343	148	10	consists	consist	VERB
ejpam-3343	148	11	of	of	ADP
ejpam-3343	148	12	‘	'	PUNCT
ejpam-3343	148	13	white	white	ADJ
ejpam-3343	148	14	’	'	PUNCT
ejpam-3343	148	15	,	,	PUNCT
ejpam-3343	148	16	‘	'	PUNCT
ejpam-3343	148	17	blackish	blackish	ADJ
ejpam-3343	148	18	’	'	PUNCT
ejpam-3343	148	19	,	,	PUNCT
ejpam-3343	148	20	‘	'	PUNCT
ejpam-3343	148	21	reddish	reddish	ADJ
ejpam-3343	148	22	’	'	PUNCT
ejpam-3343	148	23	,	,	PUNCT
ejpam-3343	148	24	‘	'	PUNCT
ejpam-3343	148	25	green	green	ADJ
ejpam-3343	148	26	’	'	PUNCT
ejpam-3343	148	27	and	and	CCONJ
ejpam-3343	148	28	‘	'	PUNCT
ejpam-3343	148	29	yellow	yellow	ADJ
ejpam-3343	148	30	’	'	PUNCT
ejpam-3343	148	31	.	.	PUNCT
ejpam-3343	149	1	the	the	DET
ejpam-3343	149	2	soft	soft	ADJ
ejpam-3343	149	3	machine	machine	NOUN
ejpam-3343	149	4	“	"	PUNCT
ejpam-3343	149	5	]	]	X
ejpam-3343	149	6	(	(	PUNCT
ejpam-3343	149	7	−,−	−,−	NOUN
ejpam-3343	149	8	)	)	PUNCT
ejpam-3343	149	9	”	"	PUNCT
ejpam-3343	149	10	is	be	AUX
ejpam-3343	149	11	equipped	equip	VERB
ejpam-3343	149	12	as	as	SCONJ
ejpam-3343	149	13	follows	follow	VERB
ejpam-3343	149	14	:	:	PUNCT
ejpam-3343	149	15	]	]	PUNCT
ejpam-3343	149	16	(	(	PUNCT
ejpam-3343	149	17	x	x	NOUN
ejpam-3343	149	18	,	,	PUNCT
ejpam-3343	149	19	y	y	NOUN
ejpam-3343	149	20	)	)	PUNCT
ejpam-3343	149	21	=	=	PUNCT
ejpam-3343	150	1	x	x	X
ejpam-3343	150	2	if	if	SCONJ
ejpam-3343	150	3	x	x	SYM
ejpam-3343	150	4	∈	∈	NOUN
ejpam-3343	150	5	u	u	NOUN
ejpam-3343	150	6	and	and	CCONJ
ejpam-3343	150	7	y	y	NOUN
ejpam-3343	150	8	=	=	PUNCT
ejpam-3343	150	9	blackish	blackish	PROPN
ejpam-3343	150	10	,	,	PUNCT
ejpam-3343	150	11	]	]	PUNCT
ejpam-3343	150	12	(	(	PUNCT
ejpam-3343	150	13	x	x	NOUN
ejpam-3343	150	14	,	,	PUNCT
ejpam-3343	150	15	y	y	PROPN
ejpam-3343	150	16	)	)	PUNCT
ejpam-3343	150	17	=	=	PRON
ejpam-3343	150	18	{	{	PUNCT
ejpam-3343	150	19	blackish	blackish	ADJ
ejpam-3343	150	20	if	if	SCONJ
ejpam-3343	150	21	(	(	PUNCT
ejpam-3343	150	22	x	x	NOUN
ejpam-3343	150	23	,	,	PUNCT
ejpam-3343	150	24	y	y	NOUN
ejpam-3343	150	25	)	)	PUNCT
ejpam-3343	150	26	∈	∈	PROPN
ejpam-3343	150	27	{	{	PUNCT
ejpam-3343	150	28	(	(	PUNCT
ejpam-3343	150	29	blackish	blackish	ADJ
ejpam-3343	150	30	,	,	PUNCT
ejpam-3343	150	31	reddish	reddish	ADJ
ejpam-3343	150	32	)	)	PUNCT
ejpam-3343	150	33	,	,	PUNCT
ejpam-3343	150	34	(	(	PUNCT
ejpam-3343	150	35	reddish	reddish	ADJ
ejpam-3343	150	36	,	,	PUNCT
ejpam-3343	150	37	reddish	reddish	ADJ
ejpam-3343	150	38	)	)	PUNCT
ejpam-3343	150	39	}	}	PUNCT
ejpam-3343	150	40	,	,	PUNCT
ejpam-3343	150	41	x	x	SYM
ejpam-3343	150	42	if	if	SCONJ
ejpam-3343	150	43	(	(	PUNCT
ejpam-3343	150	44	x	x	NOUN
ejpam-3343	150	45	,	,	PUNCT
ejpam-3343	150	46	y	y	NOUN
ejpam-3343	150	47	)	)	PUNCT
ejpam-3343	150	48	∈	∈	NOUN
ejpam-3343	150	49	{	{	PUNCT
ejpam-3343	150	50	(	(	PUNCT
ejpam-3343	150	51	green	green	ADJ
ejpam-3343	150	52	,	,	PUNCT
ejpam-3343	150	53	reddish	reddish	ADJ
ejpam-3343	150	54	)	)	PUNCT
ejpam-3343	150	55	,	,	PUNCT
ejpam-3343	150	56	(	(	PUNCT
ejpam-3343	150	57	yellow	yellow	ADJ
ejpam-3343	150	58	,	,	PUNCT
ejpam-3343	150	59	reddish	reddish	ADJ
ejpam-3343	150	60	)	)	PUNCT
ejpam-3343	150	61	,	,	PUNCT
ejpam-3343	150	62	(	(	PUNCT
ejpam-3343	150	63	white	white	ADJ
ejpam-3343	150	64	,	,	PUNCT
ejpam-3343	150	65	reddish	reddish	ADJ
ejpam-3343	150	66	)	)	PUNCT
ejpam-3343	150	67	}	}	PUNCT
ejpam-3343	150	68	,	,	PUNCT
ejpam-3343	150	69	]	]	X
ejpam-3343	150	70	(	(	PUNCT
ejpam-3343	150	71	x	x	NOUN
ejpam-3343	150	72	,	,	PUNCT
ejpam-3343	150	73	y	y	NOUN
ejpam-3343	150	74	)	)	PUNCT
ejpam-3343	150	75	=	=	SYM
ejpam-3343	151	1			X
ejpam-3343	151	2	white	white	ADJ
ejpam-3343	152	1	if	if	SCONJ
ejpam-3343	152	2	(	(	PUNCT
ejpam-3343	152	3	x	x	NOUN
ejpam-3343	152	4	,	,	PUNCT
ejpam-3343	152	5	y	y	NOUN
ejpam-3343	152	6	)	)	PUNCT
ejpam-3343	152	7	∈	∈	PROPN
ejpam-3343	152	8	{	{	PUNCT
ejpam-3343	152	9	(	(	PUNCT
ejpam-3343	152	10	blackish	blackish	ADJ
ejpam-3343	152	11	,	,	PUNCT
ejpam-3343	152	12	green	green	ADJ
ejpam-3343	152	13	)	)	PUNCT
ejpam-3343	152	14	,	,	PUNCT
ejpam-3343	152	15	(	(	PUNCT
ejpam-3343	152	16	reddish	reddish	ADJ
ejpam-3343	152	17	,	,	PUNCT
ejpam-3343	152	18	green	green	ADJ
ejpam-3343	152	19	)	)	PUNCT
ejpam-3343	152	20	}	}	PUNCT
ejpam-3343	152	21	,	,	PUNCT
ejpam-3343	152	22	blackish	blackish	ADJ
ejpam-3343	152	23	if	if	SCONJ
ejpam-3343	152	24	(	(	PUNCT
ejpam-3343	152	25	x	x	NOUN
ejpam-3343	152	26	,	,	PUNCT
ejpam-3343	152	27	y	y	NOUN
ejpam-3343	152	28	)	)	PUNCT
ejpam-3343	152	29	=	=	SYM
ejpam-3343	152	30	(	(	PUNCT
ejpam-3343	152	31	green	green	ADJ
ejpam-3343	152	32	,	,	PUNCT
ejpam-3343	152	33	green	green	ADJ
ejpam-3343	152	34	)	)	PUNCT
ejpam-3343	152	35	,	,	PUNCT
ejpam-3343	152	36	green	green	ADJ
ejpam-3343	152	37	if	if	SCONJ
ejpam-3343	152	38	(	(	PUNCT
ejpam-3343	152	39	x	x	NOUN
ejpam-3343	152	40	,	,	PUNCT
ejpam-3343	152	41	y	y	NOUN
ejpam-3343	152	42	)	)	PUNCT
ejpam-3343	152	43	=	=	SYM
ejpam-3343	152	44	(	(	PUNCT
ejpam-3343	152	45	yellow	yellow	ADJ
ejpam-3343	152	46	,	,	PUNCT
ejpam-3343	152	47	green	green	ADJ
ejpam-3343	152	48	)	)	PUNCT
ejpam-3343	152	49	,	,	PUNCT
ejpam-3343	152	50	yellow	yellow	ADJ
ejpam-3343	152	51	if	if	SCONJ
ejpam-3343	152	52	(	(	PUNCT
ejpam-3343	152	53	x	x	NOUN
ejpam-3343	152	54	,	,	PUNCT
ejpam-3343	152	55	y	y	NOUN
ejpam-3343	152	56	)	)	PUNCT
ejpam-3343	152	57	=	=	SYM
ejpam-3343	152	58	(	(	PUNCT
ejpam-3343	152	59	white	white	ADJ
ejpam-3343	152	60	,	,	PUNCT
ejpam-3343	152	61	green	green	ADJ
ejpam-3343	152	62	)	)	PUNCT
ejpam-3343	152	63	,	,	PUNCT
ejpam-3343	152	64	]	]	X
ejpam-3343	152	65	(	(	PUNCT
ejpam-3343	152	66	x	x	NOUN
ejpam-3343	152	67	,	,	PUNCT
ejpam-3343	152	68	y	y	NOUN
ejpam-3343	152	69	)	)	PUNCT
ejpam-3343	152	70	=	=	SYM
ejpam-3343	153	1			VERB
ejpam-3343	153	2	yellow	yellow	ADJ
ejpam-3343	153	3	if	if	SCONJ
ejpam-3343	153	4	(	(	PUNCT
ejpam-3343	153	5	x	x	NOUN
ejpam-3343	153	6	,	,	PUNCT
ejpam-3343	153	7	y	y	NOUN
ejpam-3343	153	8	)	)	PUNCT
ejpam-3343	153	9	∈	∈	PROPN
ejpam-3343	153	10	{	{	PUNCT
ejpam-3343	153	11	(	(	PUNCT
ejpam-3343	153	12	blackish	blackish	ADJ
ejpam-3343	153	13	,	,	PUNCT
ejpam-3343	153	14	yellow	yellow	ADJ
ejpam-3343	153	15	)	)	PUNCT
ejpam-3343	153	16	,	,	PUNCT
ejpam-3343	153	17	(	(	PUNCT
ejpam-3343	153	18	reddish	reddish	ADJ
ejpam-3343	153	19	,	,	PUNCT
ejpam-3343	153	20	yellow	yellow	ADJ
ejpam-3343	153	21	)	)	PUNCT
ejpam-3343	153	22	}	}	PUNCT
ejpam-3343	153	23	,	,	PUNCT
ejpam-3343	153	24	white	white	ADJ
ejpam-3343	153	25	if	if	SCONJ
ejpam-3343	153	26	(	(	PUNCT
ejpam-3343	153	27	x	x	NOUN
ejpam-3343	153	28	,	,	PUNCT
ejpam-3343	153	29	y	y	NOUN
ejpam-3343	153	30	)	)	PUNCT
ejpam-3343	153	31	=	=	SYM
ejpam-3343	153	32	(	(	PUNCT
ejpam-3343	153	33	green	green	ADJ
ejpam-3343	153	34	,	,	PUNCT
ejpam-3343	153	35	yellow	yellow	ADJ
ejpam-3343	153	36	)	)	PUNCT
ejpam-3343	153	37	,	,	PUNCT
ejpam-3343	153	38	blackish	blackish	ADJ
ejpam-3343	153	39	if	if	SCONJ
ejpam-3343	153	40	(	(	PUNCT
ejpam-3343	153	41	x	x	NOUN
ejpam-3343	153	42	,	,	PUNCT
ejpam-3343	153	43	y	y	NOUN
ejpam-3343	153	44	)	)	PUNCT
ejpam-3343	153	45	=	=	SYM
ejpam-3343	153	46	(	(	PUNCT
ejpam-3343	153	47	yellow	yellow	ADJ
ejpam-3343	153	48	,	,	PUNCT
ejpam-3343	153	49	yellow	yellow	ADJ
ejpam-3343	153	50	)	)	PUNCT
ejpam-3343	153	51	,	,	PUNCT
ejpam-3343	153	52	green	green	ADJ
ejpam-3343	153	53	if	if	SCONJ
ejpam-3343	153	54	(	(	PUNCT
ejpam-3343	153	55	x	x	NOUN
ejpam-3343	153	56	,	,	PUNCT
ejpam-3343	153	57	y	y	NOUN
ejpam-3343	153	58	)	)	PUNCT
ejpam-3343	153	59	=	=	SYM
ejpam-3343	153	60	(	(	PUNCT
ejpam-3343	153	61	white	white	ADJ
ejpam-3343	153	62	,	,	PUNCT
ejpam-3343	153	63	yellow	yellow	ADJ
ejpam-3343	153	64	)	)	PUNCT
ejpam-3343	153	65	,	,	PUNCT
ejpam-3343	153	66	]	]	X
ejpam-3343	153	67	(	(	PUNCT
ejpam-3343	153	68	x	x	NOUN
ejpam-3343	153	69	,	,	PUNCT
ejpam-3343	153	70	y	y	PROPN
ejpam-3343	153	71	)	)	PUNCT
ejpam-3343	153	72	=	=	SYM
ejpam-3343	154	1			PUNCT
ejpam-3343	154	2	green	green	ADJ
ejpam-3343	155	1	if	if	SCONJ
ejpam-3343	155	2	(	(	PUNCT
ejpam-3343	155	3	x	x	NOUN
ejpam-3343	155	4	,	,	PUNCT
ejpam-3343	155	5	y	y	NOUN
ejpam-3343	155	6	)	)	PUNCT
ejpam-3343	155	7	∈	∈	PROPN
ejpam-3343	155	8	{	{	PUNCT
ejpam-3343	155	9	(	(	PUNCT
ejpam-3343	155	10	blackish	blackish	ADJ
ejpam-3343	155	11	,	,	PUNCT
ejpam-3343	155	12	white	white	ADJ
ejpam-3343	155	13	)	)	PUNCT
ejpam-3343	155	14	,	,	PUNCT
ejpam-3343	155	15	(	(	PUNCT
ejpam-3343	155	16	reddish	reddish	ADJ
ejpam-3343	155	17	,	,	PUNCT
ejpam-3343	155	18	white	white	ADJ
ejpam-3343	155	19	)	)	PUNCT
ejpam-3343	155	20	}	}	PUNCT
ejpam-3343	155	21	,	,	PUNCT
ejpam-3343	155	22	yellow	yellow	ADJ
ejpam-3343	155	23	if	if	SCONJ
ejpam-3343	155	24	(	(	PUNCT
ejpam-3343	155	25	x	x	NOUN
ejpam-3343	155	26	,	,	PUNCT
ejpam-3343	155	27	y	y	NOUN
ejpam-3343	155	28	)	)	PUNCT
ejpam-3343	155	29	=	=	SYM
ejpam-3343	155	30	(	(	PUNCT
ejpam-3343	155	31	green	green	ADJ
ejpam-3343	155	32	,	,	PUNCT
ejpam-3343	155	33	white	white	ADJ
ejpam-3343	155	34	)	)	PUNCT
ejpam-3343	155	35	,	,	PUNCT
ejpam-3343	155	36	white	white	ADJ
ejpam-3343	155	37	if	if	SCONJ
ejpam-3343	155	38	(	(	PUNCT
ejpam-3343	155	39	x	x	NOUN
ejpam-3343	155	40	,	,	PUNCT
ejpam-3343	155	41	y	y	NOUN
ejpam-3343	155	42	)	)	PUNCT
ejpam-3343	155	43	=	=	SYM
ejpam-3343	155	44	(	(	PUNCT
ejpam-3343	155	45	yellow	yellow	ADJ
ejpam-3343	155	46	,	,	PUNCT
ejpam-3343	155	47	white	white	ADJ
ejpam-3343	155	48	)	)	PUNCT
ejpam-3343	155	49	,	,	PUNCT
ejpam-3343	155	50	blackish	blackish	ADJ
ejpam-3343	155	51	if	if	SCONJ
ejpam-3343	155	52	(	(	PUNCT
ejpam-3343	155	53	x	x	NOUN
ejpam-3343	155	54	,	,	PUNCT
ejpam-3343	155	55	y	y	NOUN
ejpam-3343	155	56	)	)	PUNCT
ejpam-3343	155	57	=	=	SYM
ejpam-3343	155	58	(	(	PUNCT
ejpam-3343	155	59	white	white	ADJ
ejpam-3343	155	60	,	,	PUNCT
ejpam-3343	155	61	white	white	ADJ
ejpam-3343	155	62	)	)	PUNCT
ejpam-3343	155	63	.	.	PUNCT
ejpam-3343	156	1	then	then	ADV
ejpam-3343	156	2	the	the	DET
ejpam-3343	156	3	soft	soft	ADJ
ejpam-3343	156	4	machine	machine	NOUN
ejpam-3343	156	5	“	"	PUNCT
ejpam-3343	156	6	]	]	X
ejpam-3343	156	7	(	(	PUNCT
ejpam-3343	156	8	−,−	−,−	NOUN
ejpam-3343	156	9	)	)	PUNCT
ejpam-3343	156	10	”	"	PUNCT
ejpam-3343	156	11	makes	make	VERB
ejpam-3343	156	12	u	u	NOUN
ejpam-3343	156	13	into	into	ADP
ejpam-3343	156	14	a	a	DET
ejpam-3343	156	15	bci	bci	NOUN
ejpam-3343	156	16	-	-	NOUN
ejpam-3343	156	17	algebra	algebra	NOUN
ejpam-3343	156	18	.	.	PUNCT
ejpam-3343	157	1	consider	consider	VERB
ejpam-3343	157	2	a	a	DET
ejpam-3343	157	3	set	set	NOUN
ejpam-3343	157	4	of	of	ADP
ejpam-3343	157	5	attributes	attribute	NOUN
ejpam-3343	157	6	:	:	PUNCT
ejpam-3343	157	7	a	a	DET
ejpam-3343	157	8	:	:	PUNCT
ejpam-3343	157	9	=	=	X
ejpam-3343	157	10	{	{	PUNCT
ejpam-3343	157	11	beautiful	beautiful	ADJ
ejpam-3343	157	12	,	,	PUNCT
ejpam-3343	157	13	fine	fine	ADJ
ejpam-3343	157	14	,	,	PUNCT
ejpam-3343	157	15	moderate	moderate	ADJ
ejpam-3343	157	16	}	}	PUNCT
ejpam-3343	157	17	,	,	PUNCT
ejpam-3343	157	18	and	and	CCONJ
ejpam-3343	157	19	let	let	VERB
ejpam-3343	157	20	(	(	PUNCT
ejpam-3343	157	21	η	η	NOUN
ejpam-3343	157	22	,	,	PUNCT
ejpam-3343	157	23	a	a	PRON
ejpam-3343	157	24	)	)	PUNCT
ejpam-3343	157	25	be	be	AUX
ejpam-3343	157	26	an	an	DET
ejpam-3343	157	27	n	n	CCONJ
ejpam-3343	157	28	-soft	-soft	ADJ
ejpam-3343	157	29	sets	set	NOUN
ejpam-3343	157	30	over	over	ADP
ejpam-3343	157	31	u	u	NOUN
ejpam-3343	157	32	with	with	ADP
ejpam-3343	157	33	the	the	DET
ejpam-3343	157	34	tabular	tabular	PROPN
ejpam-3343	157	35	representation	representation	NOUN
ejpam-3343	157	36	which	which	PRON
ejpam-3343	157	37	is	be	AUX
ejpam-3343	157	38	given	give	VERB
ejpam-3343	157	39	by	by	ADP
ejpam-3343	157	40	table	table	NOUN
ejpam-3343	157	41	2	2	NUM
ejpam-3343	157	42	.	.	PUNCT
ejpam-3343	158	1	then	then	ADV
ejpam-3343	158	2	(	(	PUNCT
ejpam-3343	158	3	η	η	PROPN
ejpam-3343	158	4	,	,	PUNCT
ejpam-3343	158	5	a	a	PRON
ejpam-3343	158	6	)	)	PUNCT
ejpam-3343	158	7	is	be	AUX
ejpam-3343	158	8	an	an	DET
ejpam-3343	158	9	nfine	nfine	ADJ
ejpam-3343	158	10	-	-	PUNCT
ejpam-3343	158	11	soft	soft	ADJ
ejpam-3343	158	12	ideal	ideal	NOUN
ejpam-3343	158	13	over	over	ADP
ejpam-3343	158	14	u	u	NOUN
ejpam-3343	158	15	,	,	PUNCT
ejpam-3343	158	16	but	but	CCONJ
ejpam-3343	158	17	it	it	PRON
ejpam-3343	158	18	is	be	AUX
ejpam-3343	158	19	not	not	PART
ejpam-3343	158	20	an	an	DET
ejpam-3343	158	21	nfine	nfine	ADJ
ejpam-3343	158	22	-	-	PUNCT
ejpam-3343	158	23	soft	soft	ADJ
ejpam-3343	158	24	p	p	NOUN
ejpam-3343	158	25	-	-	PUNCT
ejpam-3343	158	26	ideal	ideal	NOUN
ejpam-3343	158	27	over	over	ADP
ejpam-3343	158	28	u	u	NOUN
ejpam-3343	158	29	since	since	SCONJ
ejpam-3343	158	30	ηfine(reddish	ηfine(reddish	PROPN
ejpam-3343	158	31	)	)	PUNCT
ejpam-3343	158	32	=	=	PUNCT
ejpam-3343	159	1	−0.5	−0.5	PUNCT
ejpam-3343	159	2	>	>	PUNCT
ejpam-3343	160	1	−0.7	−0.7	PROPN
ejpam-3343	160	2	=	=	PUNCT
ejpam-3343	160	3	ηfine(blackish	ηfine(blackish	PROPN
ejpam-3343	160	4	)	)	PUNCT
ejpam-3343	160	5	=	=	PUNCT
ejpam-3343	160	6	∨	∨	X
ejpam-3343	160	7	{	{	PUNCT
ejpam-3343	160	8	ηfine(](](reddish	ηfine(](](reddish	PROPN
ejpam-3343	160	9	,	,	PUNCT
ejpam-3343	160	10	green),](blackish	green),](blackish	ADJ
ejpam-3343	160	11	,	,	PUNCT
ejpam-3343	160	12	green	green	ADJ
ejpam-3343	160	13	)	)	PUNCT
ejpam-3343	160	14	)	)	PUNCT
ejpam-3343	160	15	)	)	PUNCT
ejpam-3343	160	16	,	,	PUNCT
ejpam-3343	160	17	ηfine(blackish	ηfine(blackish	PROPN
ejpam-3343	160	18	)	)	PUNCT
ejpam-3343	160	19	}	}	PUNCT
ejpam-3343	160	20	.	.	PUNCT
ejpam-3343	161	1	g.	g.	PROPN
ejpam-3343	161	2	muhiuddin	muhiuddin	PROPN
ejpam-3343	161	3	,	,	PUNCT
ejpam-3343	161	4	s.	s.	PROPN
ejpam-3343	161	5	aldhafeeri	aldhafeeri	PROPN
ejpam-3343	161	6	/	/	SYM
ejpam-3343	161	7	eur	eur	PROPN
ejpam-3343	161	8	.	.	PUNCT
ejpam-3343	162	1	j.	j.	PROPN
ejpam-3343	162	2	pure	pure	PROPN
ejpam-3343	162	3	appl	appl	PROPN
ejpam-3343	162	4	.	.	PROPN
ejpam-3343	162	5	math	math	PROPN
ejpam-3343	162	6	,	,	PUNCT
ejpam-3343	162	7	12	12	NUM
ejpam-3343	162	8	(	(	PUNCT
ejpam-3343	162	9	1	1	NUM
ejpam-3343	162	10	)	)	PUNCT
ejpam-3343	162	11	(	(	PUNCT
ejpam-3343	162	12	2019	2019	NUM
ejpam-3343	162	13	)	)	PUNCT
ejpam-3343	162	14	,	,	PUNCT
ejpam-3343	162	15	79	79	NUM
ejpam-3343	162	16	-	-	SYM
ejpam-3343	162	17	87	87	NUM
ejpam-3343	162	18	85	85	NUM
ejpam-3343	162	19	table	table	NOUN
ejpam-3343	162	20	2	2	NUM
ejpam-3343	162	21	:	:	PUNCT
ejpam-3343	162	22	tabular	tabular	PROPN
ejpam-3343	162	23	representation	representation	NOUN
ejpam-3343	162	24	of	of	ADP
ejpam-3343	162	25	(	(	PUNCT
ejpam-3343	162	26	η	η	PROPN
ejpam-3343	162	27	,	,	PUNCT
ejpam-3343	162	28	a	a	PRON
ejpam-3343	162	29	)	)	PUNCT
ejpam-3343	162	30	(	(	PUNCT
ejpam-3343	162	31	η	η	PROPN
ejpam-3343	162	32	,	,	PUNCT
ejpam-3343	162	33	a	a	PRON
ejpam-3343	162	34	)	)	PUNCT
ejpam-3343	162	35	blackish	blackish	ADJ
ejpam-3343	162	36	reddish	reddish	ADJ
ejpam-3343	162	37	green	green	ADJ
ejpam-3343	162	38	yellow	yellow	ADJ
ejpam-3343	162	39	white	white	ADJ
ejpam-3343	162	40	beautiful	beautiful	ADJ
ejpam-3343	162	41	−0.9	−0.9	PROPN
ejpam-3343	162	42	−0.2	−0.2	PROPN
ejpam-3343	163	1	−0.4	−0.4	PROPN
ejpam-3343	164	1	−0.6	−0.6	PROPN
ejpam-3343	164	2	−0.1	−0.1	PROPN
ejpam-3343	164	3	fine	fine	NOUN
ejpam-3343	165	1	−0.7	−0.7	PROPN
ejpam-3343	166	1	−0.5	−0.5	NUM
ejpam-3343	166	2	−0.2	−0.2	PROPN
ejpam-3343	167	1	−0.3	−0.3	PROPN
ejpam-3343	167	2	−0.4	−0.4	NUM
ejpam-3343	167	3	moderate	moderate	ADJ
ejpam-3343	167	4	−0.8	−0.8	PROPN
ejpam-3343	167	5	−0.4	−0.4	NUM
ejpam-3343	168	1	−0.3	−0.3	PROPN
ejpam-3343	168	2	−0.2	−0.2	INTJ
ejpam-3343	169	1	−0.5	−0.5	DET
ejpam-3343	169	2	proposition	proposition	NOUN
ejpam-3343	169	3	2	2	NUM
ejpam-3343	169	4	.	.	X
ejpam-3343	169	5	for	for	ADP
ejpam-3343	169	6	any	any	DET
ejpam-3343	169	7	attribute	attribute	NOUN
ejpam-3343	169	8	u	u	NOUN
ejpam-3343	169	9	∈	∈	PROPN
ejpam-3343	169	10	a	a	PRON
ejpam-3343	169	11	,	,	PUNCT
ejpam-3343	169	12	every	every	DET
ejpam-3343	169	13	nu	nu	ADJ
ejpam-3343	169	14	-	-	PUNCT
ejpam-3343	169	15	soft	soft	ADJ
ejpam-3343	169	16	p	p	NOUN
ejpam-3343	169	17	-	-	PUNCT
ejpam-3343	169	18	ideal	ideal	NOUN
ejpam-3343	169	19	(	(	PUNCT
ejpam-3343	169	20	η	η	PROPN
ejpam-3343	169	21	,	,	PUNCT
ejpam-3343	169	22	a	a	PRON
ejpam-3343	169	23	)	)	PUNCT
ejpam-3343	169	24	over	over	ADP
ejpam-3343	169	25	a	a	DET
ejpam-3343	169	26	bci	bci	NOUN
ejpam-3343	169	27	-	-	NOUN
ejpam-3343	169	28	algebra	algebra	NOUN
ejpam-3343	169	29	x	x	PRON
ejpam-3343	169	30	satisfies	satisfy	VERB
ejpam-3343	169	31	the	the	DET
ejpam-3343	169	32	following	follow	VERB
ejpam-3343	169	33	inequality	inequality	NOUN
ejpam-3343	169	34	:	:	PUNCT
ejpam-3343	169	35	(	(	PUNCT
ejpam-3343	169	36	∀x	∀x	X
ejpam-3343	169	37	,	,	PUNCT
ejpam-3343	169	38	y	y	PROPN
ejpam-3343	169	39	,	,	PUNCT
ejpam-3343	169	40	z	z	NOUN
ejpam-3343	169	41	∈	∈	PROPN
ejpam-3343	169	42	x	x	X
ejpam-3343	169	43	)	)	PUNCT
ejpam-3343	169	44	(	(	PUNCT
ejpam-3343	169	45	ηu(x	ηu(x	ADP
ejpam-3343	169	46	∗	∗	PROPN
ejpam-3343	169	47	y	y	PROPN
ejpam-3343	169	48	)	)	PUNCT
ejpam-3343	169	49	≥	≥	NOUN
ejpam-3343	169	50	ηu	ηu	X
ejpam-3343	169	51	(	(	PUNCT
ejpam-3343	169	52	(	(	PUNCT
ejpam-3343	169	53	x	x	NOUN
ejpam-3343	169	54	∗	∗	PROPN
ejpam-3343	169	55	z	z	NOUN
ejpam-3343	169	56	)	)	PUNCT
ejpam-3343	169	57	∗	∗	NOUN
ejpam-3343	169	58	(	(	PUNCT
ejpam-3343	169	59	y	y	PROPN
ejpam-3343	169	60	∗	∗	PROPN
ejpam-3343	169	61	z	z	PROPN
ejpam-3343	169	62	)	)	PUNCT
ejpam-3343	169	63	)	)	PUNCT
ejpam-3343	169	64	)	)	PUNCT
ejpam-3343	169	65	.	.	PUNCT
ejpam-3343	170	1	(	(	PUNCT
ejpam-3343	170	2	5	5	X
ejpam-3343	170	3	)	)	PUNCT
ejpam-3343	170	4	proof	proof	NOUN
ejpam-3343	170	5	.	.	PUNCT
ejpam-3343	171	1	let	let	VERB
ejpam-3343	171	2	u	u	PRON
ejpam-3343	171	3	∈	∈	PROPN
ejpam-3343	171	4	a.	a.	NOUN
ejpam-3343	171	5	if	if	SCONJ
ejpam-3343	171	6	(	(	PUNCT
ejpam-3343	171	7	η	η	PROPN
ejpam-3343	171	8	,	,	PUNCT
ejpam-3343	171	9	a	a	PRON
ejpam-3343	171	10	)	)	PUNCT
ejpam-3343	171	11	is	be	AUX
ejpam-3343	171	12	an	an	DET
ejpam-3343	171	13	nu	nu	NOUN
ejpam-3343	171	14	-	-	PUNCT
ejpam-3343	171	15	soft	soft	ADJ
ejpam-3343	171	16	p	p	NOUN
ejpam-3343	171	17	-	-	PUNCT
ejpam-3343	171	18	ideal	ideal	NOUN
ejpam-3343	171	19	over	over	ADP
ejpam-3343	171	20	a	a	DET
ejpam-3343	171	21	bci	bci	NOUN
ejpam-3343	171	22	-	-	NOUN
ejpam-3343	171	23	algebra	algebra	NOUN
ejpam-3343	171	24	x	x	NOUN
ejpam-3343	171	25	,	,	PUNCT
ejpam-3343	171	26	then	then	ADV
ejpam-3343	171	27	it	it	PRON
ejpam-3343	171	28	is	be	AUX
ejpam-3343	171	29	an	an	DET
ejpam-3343	171	30	nu	nu	ADJ
ejpam-3343	171	31	-	-	PUNCT
ejpam-3343	171	32	soft	soft	ADJ
ejpam-3343	171	33	ideal	ideal	NOUN
ejpam-3343	171	34	over	over	ADP
ejpam-3343	171	35	x	x	PUNCT
ejpam-3343	171	36	by	by	ADP
ejpam-3343	171	37	theorem	theorem	NOUN
ejpam-3343	171	38	2	2	NUM
ejpam-3343	171	39	.	.	X
ejpam-3343	172	1	note	note	VERB
ejpam-3343	172	2	that	that	SCONJ
ejpam-3343	172	3	(	(	PUNCT
ejpam-3343	172	4	(	(	PUNCT
ejpam-3343	172	5	x	x	SYM
ejpam-3343	172	6	∗	∗	PROPN
ejpam-3343	172	7	z	z	NOUN
ejpam-3343	172	8	)	)	PUNCT
ejpam-3343	172	9	∗	∗	NOUN
ejpam-3343	172	10	(	(	PUNCT
ejpam-3343	172	11	y	y	PROPN
ejpam-3343	172	12	∗	∗	PROPN
ejpam-3343	172	13	z	z	NOUN
ejpam-3343	172	14	)	)	PUNCT
ejpam-3343	172	15	)	)	PUNCT
ejpam-3343	172	16	∗	∗	NOUN
ejpam-3343	172	17	(	(	PUNCT
ejpam-3343	172	18	x	x	X
ejpam-3343	172	19	∗	∗	NOUN
ejpam-3343	172	20	y	y	NOUN
ejpam-3343	172	21	)	)	PUNCT
ejpam-3343	172	22	=	=	SYM
ejpam-3343	172	23	0	0	NUM
ejpam-3343	172	24	for	for	ADP
ejpam-3343	172	25	all	all	DET
ejpam-3343	172	26	x	x	NOUN
ejpam-3343	172	27	,	,	PUNCT
ejpam-3343	172	28	y	y	PROPN
ejpam-3343	172	29	,	,	PUNCT
ejpam-3343	172	30	z	z	PROPN
ejpam-3343	172	31	∈	∈	NOUN
ejpam-3343	172	32	x.	x.	NOUN
ejpam-3343	173	1	thus	thus	ADV
ejpam-3343	173	2	we	we	PRON
ejpam-3343	173	3	have	have	VERB
ejpam-3343	173	4	ηu	ηu	X
ejpam-3343	173	5	(	(	PUNCT
ejpam-3343	173	6	(	(	PUNCT
ejpam-3343	173	7	x	x	NOUN
ejpam-3343	173	8	∗	∗	PROPN
ejpam-3343	173	9	z	z	NOUN
ejpam-3343	173	10	)	)	PUNCT
ejpam-3343	173	11	∗	∗	NOUN
ejpam-3343	173	12	(	(	PUNCT
ejpam-3343	173	13	y	y	PROPN
ejpam-3343	173	14	∗	∗	PROPN
ejpam-3343	173	15	z	z	NOUN
ejpam-3343	173	16	)	)	PUNCT
ejpam-3343	173	17	)	)	PUNCT
ejpam-3343	173	18	≤	≤	NUM
ejpam-3343	173	19	∨	∨	NUM
ejpam-3343	173	20	{	{	PUNCT
ejpam-3343	173	21	ηu	ηu	X
ejpam-3343	173	22	(	(	PUNCT
ejpam-3343	173	23	(	(	PUNCT
ejpam-3343	173	24	(	(	PUNCT
ejpam-3343	173	25	x	x	SYM
ejpam-3343	173	26	∗	∗	PROPN
ejpam-3343	173	27	z	z	NOUN
ejpam-3343	173	28	)	)	PUNCT
ejpam-3343	173	29	∗	∗	NOUN
ejpam-3343	173	30	(	(	PUNCT
ejpam-3343	173	31	y	y	PROPN
ejpam-3343	173	32	∗	∗	PROPN
ejpam-3343	173	33	z	z	NOUN
ejpam-3343	173	34	)	)	PUNCT
ejpam-3343	173	35	)	)	PUNCT
ejpam-3343	174	1	∗	∗	NOUN
ejpam-3343	174	2	(	(	PUNCT
ejpam-3343	174	3	x	x	X
ejpam-3343	174	4	∗	∗	PROPN
ejpam-3343	174	5	y	y	PROPN
ejpam-3343	174	6	)	)	PUNCT
ejpam-3343	174	7	)	)	PUNCT
ejpam-3343	174	8	,	,	PUNCT
ejpam-3343	174	9	ηu(x	ηu(x	PUNCT
ejpam-3343	174	10	∗	∗	PROPN
ejpam-3343	174	11	y	y	NOUN
ejpam-3343	174	12	)	)	PUNCT
ejpam-3343	174	13	}	}	PUNCT
ejpam-3343	174	14	=	=	SYM
ejpam-3343	174	15	∨	∨	X
ejpam-3343	174	16	{	{	PUNCT
ejpam-3343	174	17	ηu(0	ηu(0	NOUN
ejpam-3343	174	18	)	)	PUNCT
ejpam-3343	174	19	,	,	PUNCT
ejpam-3343	174	20	ηu(x	ηu(x	PUNCT
ejpam-3343	174	21	∗	∗	PROPN
ejpam-3343	174	22	y	y	PROPN
ejpam-3343	174	23	)	)	PUNCT
ejpam-3343	174	24	}	}	PUNCT
ejpam-3343	174	25	=	=	SYM
ejpam-3343	174	26	ηu(x	ηu(x	NOUN
ejpam-3343	174	27	∗	∗	PROPN
ejpam-3343	174	28	y	y	PROPN
ejpam-3343	174	29	)	)	PUNCT
ejpam-3343	174	30	for	for	ADP
ejpam-3343	174	31	all	all	DET
ejpam-3343	174	32	x	x	NOUN
ejpam-3343	174	33	,	,	PUNCT
ejpam-3343	174	34	y	y	PROPN
ejpam-3343	174	35	,	,	PUNCT
ejpam-3343	174	36	z	z	NOUN
ejpam-3343	174	37	∈	∈	PROPN
ejpam-3343	174	38	x.	x.	NOUN
ejpam-3343	175	1	we	we	PRON
ejpam-3343	175	2	provide	provide	VERB
ejpam-3343	175	3	conditions	condition	NOUN
ejpam-3343	175	4	for	for	ADP
ejpam-3343	175	5	an	an	DET
ejpam-3343	175	6	n	n	CCONJ
ejpam-3343	175	7	-soft	-soft	ADJ
ejpam-3343	175	8	ideal	ideal	NOUN
ejpam-3343	175	9	to	to	PART
ejpam-3343	175	10	be	be	AUX
ejpam-3343	175	11	an	an	DET
ejpam-3343	175	12	n	n	CCONJ
ejpam-3343	175	13	-soft	-soft	ADJ
ejpam-3343	175	14	p	p	NOUN
ejpam-3343	175	15	-	-	PUNCT
ejpam-3343	175	16	ideal	ideal	NOUN
ejpam-3343	175	17	.	.	PUNCT
ejpam-3343	176	1	theorem	theorem	NOUN
ejpam-3343	176	2	3	3	NUM
ejpam-3343	176	3	.	.	X
ejpam-3343	176	4	for	for	ADP
ejpam-3343	176	5	any	any	DET
ejpam-3343	176	6	attribute	attribute	NOUN
ejpam-3343	176	7	u	u	NOUN
ejpam-3343	176	8	∈	∈	PROPN
ejpam-3343	176	9	a	a	PRON
ejpam-3343	176	10	,	,	PUNCT
ejpam-3343	176	11	let	let	VERB
ejpam-3343	176	12	(	(	PUNCT
ejpam-3343	176	13	η	η	NOUN
ejpam-3343	176	14	,	,	PUNCT
ejpam-3343	176	15	a	a	PRON
ejpam-3343	176	16	)	)	PUNCT
ejpam-3343	176	17	be	be	AUX
ejpam-3343	176	18	an	an	DET
ejpam-3343	176	19	nu	nu	ADJ
ejpam-3343	176	20	-	-	PUNCT
ejpam-3343	176	21	soft	soft	ADJ
ejpam-3343	176	22	ideal	ideal	NOUN
ejpam-3343	176	23	over	over	ADP
ejpam-3343	176	24	a	a	DET
ejpam-3343	176	25	bci	bci	NOUN
ejpam-3343	176	26	-	-	NOUN
ejpam-3343	176	27	algebra	algebra	NOUN
ejpam-3343	176	28	x	x	PUNCT
ejpam-3343	176	29	that	that	PRON
ejpam-3343	176	30	satisfies	satisfy	VERB
ejpam-3343	176	31	:	:	PUNCT
ejpam-3343	176	32	(	(	PUNCT
ejpam-3343	176	33	∀x	∀x	X
ejpam-3343	176	34	,	,	PUNCT
ejpam-3343	176	35	y	y	PROPN
ejpam-3343	176	36	,	,	PUNCT
ejpam-3343	176	37	z	z	NOUN
ejpam-3343	176	38	∈	∈	PROPN
ejpam-3343	176	39	x	x	X
ejpam-3343	176	40	)	)	PUNCT
ejpam-3343	176	41	(	(	PUNCT
ejpam-3343	176	42	ηu	ηu	X
ejpam-3343	176	43	(	(	PUNCT
ejpam-3343	176	44	x	x	NOUN
ejpam-3343	176	45	∗	∗	PROPN
ejpam-3343	176	46	y	y	NOUN
ejpam-3343	176	47	)	)	PUNCT
ejpam-3343	176	48	≤	≤	NOUN
ejpam-3343	176	49	ηu	ηu	X
ejpam-3343	176	50	(	(	PUNCT
ejpam-3343	176	51	(	(	PUNCT
ejpam-3343	176	52	x	x	NOUN
ejpam-3343	176	53	∗	∗	PROPN
ejpam-3343	176	54	z	z	NOUN
ejpam-3343	176	55	)	)	PUNCT
ejpam-3343	176	56	∗	∗	NOUN
ejpam-3343	176	57	(	(	PUNCT
ejpam-3343	176	58	y	y	PROPN
ejpam-3343	176	59	∗	∗	PROPN
ejpam-3343	176	60	z	z	PROPN
ejpam-3343	176	61	)	)	PUNCT
ejpam-3343	176	62	)	)	PUNCT
ejpam-3343	176	63	)	)	PUNCT
ejpam-3343	176	64	.	.	PUNCT
ejpam-3343	177	1	(	(	PUNCT
ejpam-3343	177	2	6	6	NUM
ejpam-3343	177	3	)	)	PUNCT
ejpam-3343	177	4	then	then	ADV
ejpam-3343	177	5	(	(	PUNCT
ejpam-3343	177	6	η	η	PROPN
ejpam-3343	177	7	,	,	PUNCT
ejpam-3343	177	8	a	a	PRON
ejpam-3343	177	9	)	)	PUNCT
ejpam-3343	177	10	is	be	AUX
ejpam-3343	177	11	an	an	DET
ejpam-3343	177	12	nu	nu	NOUN
ejpam-3343	177	13	-	-	PUNCT
ejpam-3343	177	14	soft	soft	ADJ
ejpam-3343	177	15	p	p	NOUN
ejpam-3343	177	16	-	-	PUNCT
ejpam-3343	177	17	ideal	ideal	NOUN
ejpam-3343	177	18	over	over	ADP
ejpam-3343	177	19	x.	x.	NOUN
ejpam-3343	177	20	proof	proof	NOUN
ejpam-3343	177	21	.	.	PUNCT
ejpam-3343	178	1	if	if	SCONJ
ejpam-3343	178	2	an	an	DET
ejpam-3343	178	3	nu	nu	ADJ
ejpam-3343	178	4	-	-	PUNCT
ejpam-3343	178	5	soft	soft	ADJ
ejpam-3343	178	6	ideal	ideal	NOUN
ejpam-3343	178	7	(	(	PUNCT
ejpam-3343	178	8	η	η	PROPN
ejpam-3343	178	9	,	,	PUNCT
ejpam-3343	178	10	a	a	PRON
ejpam-3343	178	11	)	)	PUNCT
ejpam-3343	178	12	over	over	ADP
ejpam-3343	178	13	a	a	DET
ejpam-3343	178	14	bci	bci	NOUN
ejpam-3343	178	15	-	-	NOUN
ejpam-3343	178	16	algebra	algebra	NOUN
ejpam-3343	178	17	x	x	NUM
ejpam-3343	178	18	satisfies	satisfie	NOUN
ejpam-3343	178	19	(	(	PUNCT
ejpam-3343	178	20	6	6	NUM
ejpam-3343	178	21	)	)	PUNCT
ejpam-3343	178	22	,	,	PUNCT
ejpam-3343	178	23	then	then	ADV
ejpam-3343	178	24	ηu(x	ηu(x	PUNCT
ejpam-3343	178	25	)	)	PUNCT
ejpam-3343	178	26	≤	≤	NUM
ejpam-3343	178	27	∨	∨	NUM
ejpam-3343	178	28	{	{	PUNCT
ejpam-3343	178	29	ηu(x	ηu(x	ADP
ejpam-3343	178	30	∗	∗	NOUN
ejpam-3343	178	31	y	y	NOUN
ejpam-3343	178	32	)	)	PUNCT
ejpam-3343	178	33	,	,	PUNCT
ejpam-3343	178	34	ηu(y	ηu(y	NOUN
ejpam-3343	178	35	)	)	PUNCT
ejpam-3343	178	36	}	}	PUNCT
ejpam-3343	178	37	≤	≤	NUM
ejpam-3343	178	38	∨	∨	NUM
ejpam-3343	178	39	{	{	PUNCT
ejpam-3343	178	40	ηu	ηu	X
ejpam-3343	178	41	(	(	PUNCT
ejpam-3343	178	42	(	(	PUNCT
ejpam-3343	178	43	x	x	NOUN
ejpam-3343	178	44	∗	∗	PROPN
ejpam-3343	178	45	z	z	NOUN
ejpam-3343	178	46	)	)	PUNCT
ejpam-3343	178	47	∗	∗	NOUN
ejpam-3343	178	48	(	(	PUNCT
ejpam-3343	178	49	y	y	PROPN
ejpam-3343	178	50	∗	∗	PROPN
ejpam-3343	178	51	z	z	PROPN
ejpam-3343	178	52	)	)	PUNCT
ejpam-3343	178	53	)	)	PUNCT
ejpam-3343	178	54	,	,	PUNCT
ejpam-3343	178	55	ηu(y	ηu(y	NOUN
ejpam-3343	178	56	)	)	PUNCT
ejpam-3343	178	57	}	}	PUNCT
ejpam-3343	178	58	for	for	ADP
ejpam-3343	178	59	all	all	DET
ejpam-3343	178	60	x	x	NOUN
ejpam-3343	178	61	,	,	PUNCT
ejpam-3343	178	62	y	y	PROPN
ejpam-3343	178	63	,	,	PUNCT
ejpam-3343	178	64	z	z	PROPN
ejpam-3343	178	65	∈	∈	PROPN
ejpam-3343	178	66	x.	x.	NOUN
ejpam-3343	178	67	therefore	therefore	ADV
ejpam-3343	178	68	(	(	PUNCT
ejpam-3343	178	69	η	η	PROPN
ejpam-3343	178	70	,	,	PUNCT
ejpam-3343	178	71	a	a	PRON
ejpam-3343	178	72	)	)	PUNCT
ejpam-3343	178	73	is	be	AUX
ejpam-3343	178	74	an	an	DET
ejpam-3343	178	75	nu	nu	NOUN
ejpam-3343	178	76	-	-	PUNCT
ejpam-3343	178	77	soft	soft	ADJ
ejpam-3343	178	78	p	p	NOUN
ejpam-3343	178	79	-	-	PUNCT
ejpam-3343	178	80	ideal	ideal	NOUN
ejpam-3343	178	81	over	over	ADP
ejpam-3343	178	82	x.	x.	PROPN
ejpam-3343	178	83	lemma	lemma	PROPN
ejpam-3343	178	84	1	1	NUM
ejpam-3343	178	85	(	(	PUNCT
ejpam-3343	178	86	[	[	X
ejpam-3343	178	87	7	7	NUM
ejpam-3343	178	88	]	]	NUM
ejpam-3343	178	89	)	)	PUNCT
ejpam-3343	178	90	.	.	PUNCT
ejpam-3343	179	1	for	for	ADP
ejpam-3343	179	2	any	any	DET
ejpam-3343	179	3	attribute	attribute	NOUN
ejpam-3343	179	4	u	u	NOUN
ejpam-3343	179	5	∈	∈	PROPN
ejpam-3343	179	6	a	a	PRON
ejpam-3343	179	7	,	,	PUNCT
ejpam-3343	179	8	every	every	DET
ejpam-3343	179	9	nu	nu	ADJ
ejpam-3343	179	10	-	-	PUNCT
ejpam-3343	179	11	soft	soft	ADJ
ejpam-3343	179	12	ideal	ideal	NOUN
ejpam-3343	179	13	(	(	PUNCT
ejpam-3343	179	14	η	η	PROPN
ejpam-3343	179	15	,	,	PUNCT
ejpam-3343	179	16	a	a	PRON
ejpam-3343	179	17	)	)	PUNCT
ejpam-3343	179	18	over	over	ADP
ejpam-3343	179	19	a	a	DET
ejpam-3343	179	20	bci	bci	NOUN
ejpam-3343	179	21	-	-	NOUN
ejpam-3343	179	22	algebra	algebra	NOUN
ejpam-3343	179	23	x	x	PRON
ejpam-3343	179	24	satisfies	satisfy	VERB
ejpam-3343	179	25	the	the	DET
ejpam-3343	179	26	following	follow	VERB
ejpam-3343	179	27	inequality	inequality	NOUN
ejpam-3343	179	28	:	:	PUNCT
ejpam-3343	179	29	(	(	PUNCT
ejpam-3343	179	30	∀x	∀x	X
ejpam-3343	179	31	∈	∈	PROPN
ejpam-3343	179	32	x	x	X
ejpam-3343	179	33	)	)	PUNCT
ejpam-3343	179	34	(	(	PUNCT
ejpam-3343	179	35	ηu(0	ηu(0	NOUN
ejpam-3343	179	36	∗	∗	NOUN
ejpam-3343	179	37	(	(	PUNCT
ejpam-3343	179	38	0	0	NUM
ejpam-3343	179	39	∗	∗	NOUN
ejpam-3343	179	40	x	x	NOUN
ejpam-3343	179	41	)	)	PUNCT
ejpam-3343	179	42	)	)	PUNCT
ejpam-3343	179	43	≤	≤	NOUN
ejpam-3343	179	44	ηu(x	ηu(x	NOUN
ejpam-3343	179	45	)	)	PUNCT
ejpam-3343	179	46	)	)	PUNCT
ejpam-3343	179	47	.	.	PUNCT
ejpam-3343	180	1	(	(	PUNCT
ejpam-3343	180	2	7	7	X
ejpam-3343	180	3	)	)	PUNCT
ejpam-3343	180	4	theorem	theorem	NOUN
ejpam-3343	180	5	4	4	NUM
ejpam-3343	180	6	.	.	X
ejpam-3343	181	1	for	for	ADP
ejpam-3343	181	2	any	any	DET
ejpam-3343	181	3	attribute	attribute	NOUN
ejpam-3343	181	4	u	u	NOUN
ejpam-3343	181	5	∈	∈	PROPN
ejpam-3343	181	6	a	a	PRON
ejpam-3343	181	7	,	,	PUNCT
ejpam-3343	181	8	let	let	VERB
ejpam-3343	181	9	(	(	PUNCT
ejpam-3343	181	10	η	η	NOUN
ejpam-3343	181	11	,	,	PUNCT
ejpam-3343	181	12	a	a	PRON
ejpam-3343	181	13	)	)	PUNCT
ejpam-3343	181	14	be	be	AUX
ejpam-3343	181	15	an	an	DET
ejpam-3343	181	16	nu	nu	ADJ
ejpam-3343	181	17	-	-	PUNCT
ejpam-3343	181	18	soft	soft	ADJ
ejpam-3343	181	19	ideal	ideal	NOUN
ejpam-3343	181	20	over	over	ADP
ejpam-3343	181	21	a	a	DET
ejpam-3343	181	22	bci	bci	NOUN
ejpam-3343	181	23	-	-	NOUN
ejpam-3343	181	24	algebra	algebra	NOUN
ejpam-3343	181	25	x	x	PUNCT
ejpam-3343	181	26	that	that	PRON
ejpam-3343	181	27	satisfies	satisfy	VERB
ejpam-3343	181	28	:	:	PUNCT
ejpam-3343	181	29	(	(	PUNCT
ejpam-3343	181	30	∀x	∀x	X
ejpam-3343	181	31	∈	∈	PROPN
ejpam-3343	181	32	x	x	NOUN
ejpam-3343	181	33	)	)	PUNCT
ejpam-3343	181	34	(	(	PUNCT
ejpam-3343	181	35	ηu(x	ηu(x	NOUN
ejpam-3343	181	36	)	)	PUNCT
ejpam-3343	181	37	≤	≤	NOUN
ejpam-3343	181	38	ηu	ηu	X
ejpam-3343	181	39	(	(	PUNCT
ejpam-3343	181	40	0	0	NUM
ejpam-3343	181	41	∗	∗	NOUN
ejpam-3343	181	42	(	(	PUNCT
ejpam-3343	181	43	0	0	NUM
ejpam-3343	181	44	∗	∗	NOUN
ejpam-3343	181	45	x	x	NOUN
ejpam-3343	181	46	)	)	PUNCT
ejpam-3343	181	47	)	)	PUNCT
ejpam-3343	181	48	)	)	PUNCT
ejpam-3343	181	49	.	.	PUNCT
ejpam-3343	182	1	(	(	PUNCT
ejpam-3343	182	2	8)	8)	NUM
ejpam-3343	182	3	then	then	ADV
ejpam-3343	182	4	(	(	PUNCT
ejpam-3343	182	5	η	η	PROPN
ejpam-3343	182	6	,	,	PUNCT
ejpam-3343	182	7	a	a	PRON
ejpam-3343	182	8	)	)	PUNCT
ejpam-3343	182	9	is	be	AUX
ejpam-3343	182	10	an	an	DET
ejpam-3343	182	11	nu	nu	NOUN
ejpam-3343	182	12	-	-	PUNCT
ejpam-3343	182	13	soft	soft	ADJ
ejpam-3343	182	14	p	p	NOUN
ejpam-3343	182	15	-	-	PUNCT
ejpam-3343	182	16	ideal	ideal	NOUN
ejpam-3343	182	17	over	over	ADP
ejpam-3343	182	18	x.	x.	NOUN
ejpam-3343	182	19	references	reference	NOUN
ejpam-3343	182	20	86	86	NUM
ejpam-3343	182	21	proof	proof	NOUN
ejpam-3343	182	22	.	.	PUNCT
ejpam-3343	183	1	by	by	ADP
ejpam-3343	183	2	using	use	VERB
ejpam-3343	183	3	lemma	lemma	PROPN
ejpam-3343	183	4	1	1	NUM
ejpam-3343	183	5	,	,	PUNCT
ejpam-3343	183	6	(	(	PUNCT
ejpam-3343	183	7	a4	a4	NOUN
ejpam-3343	183	8	)	)	PUNCT
ejpam-3343	183	9	,	,	PUNCT
ejpam-3343	183	10	(	(	PUNCT
ejpam-3343	183	11	a5	a5	PROPN
ejpam-3343	183	12	)	)	PUNCT
ejpam-3343	183	13	and	and	CCONJ
ejpam-3343	183	14	(	(	PUNCT
ejpam-3343	183	15	8)	8)	NUM
ejpam-3343	183	16	,	,	PUNCT
ejpam-3343	183	17	we	we	PRON
ejpam-3343	183	18	have	have	VERB
ejpam-3343	183	19	ηu	ηu	X
ejpam-3343	183	20	(	(	PUNCT
ejpam-3343	183	21	(	(	PUNCT
ejpam-3343	183	22	x	x	NOUN
ejpam-3343	183	23	∗	∗	PROPN
ejpam-3343	183	24	z	z	NOUN
ejpam-3343	183	25	)	)	PUNCT
ejpam-3343	183	26	∗	∗	NOUN
ejpam-3343	183	27	(	(	PUNCT
ejpam-3343	183	28	y	y	PROPN
ejpam-3343	183	29	∗	∗	PROPN
ejpam-3343	183	30	z	z	NOUN
ejpam-3343	183	31	)	)	PUNCT
ejpam-3343	183	32	)	)	PUNCT
ejpam-3343	183	33	≥	≥	NOUN
ejpam-3343	183	34	ηu	ηu	X
ejpam-3343	183	35	(	(	PUNCT
ejpam-3343	183	36	0	0	NUM
ejpam-3343	183	37	∗	∗	NOUN
ejpam-3343	183	38	(	(	PUNCT
ejpam-3343	183	39	0	0	NUM
ejpam-3343	183	40	∗	∗	NOUN
ejpam-3343	183	41	(	(	PUNCT
ejpam-3343	183	42	(	(	PUNCT
ejpam-3343	183	43	x	x	SYM
ejpam-3343	183	44	∗	∗	PROPN
ejpam-3343	183	45	z	z	NOUN
ejpam-3343	183	46	)	)	PUNCT
ejpam-3343	183	47	∗	∗	NOUN
ejpam-3343	183	48	(	(	PUNCT
ejpam-3343	183	49	y	y	PROPN
ejpam-3343	183	50	∗	∗	PROPN
ejpam-3343	183	51	z	z	PROPN
ejpam-3343	183	52	)	)	PUNCT
ejpam-3343	183	53	)	)	PUNCT
ejpam-3343	183	54	)	)	PUNCT
ejpam-3343	183	55	)	)	PUNCT
ejpam-3343	184	1	=	=	PRON
ejpam-3343	184	2	ηu	ηu	X
ejpam-3343	184	3	(	(	PUNCT
ejpam-3343	184	4	(	(	PUNCT
ejpam-3343	184	5	0	0	NUM
ejpam-3343	184	6	∗	∗	PROPN
ejpam-3343	184	7	y	y	NOUN
ejpam-3343	184	8	)	)	PUNCT
ejpam-3343	184	9	∗	∗	NOUN
ejpam-3343	184	10	(	(	PUNCT
ejpam-3343	184	11	0	0	NUM
ejpam-3343	184	12	∗	∗	NOUN
ejpam-3343	184	13	x	x	NOUN
ejpam-3343	184	14	)	)	PUNCT
ejpam-3343	184	15	)	)	PUNCT
ejpam-3343	185	1	=	=	SYM
ejpam-3343	185	2	ηu	ηu	X
ejpam-3343	185	3	(	(	PUNCT
ejpam-3343	185	4	0	0	NUM
ejpam-3343	185	5	∗	∗	NOUN
ejpam-3343	185	6	(	(	PUNCT
ejpam-3343	185	7	0	0	NUM
ejpam-3343	185	8	∗	∗	NOUN
ejpam-3343	185	9	(	(	PUNCT
ejpam-3343	185	10	x	x	X
ejpam-3343	185	11	∗	∗	PROPN
ejpam-3343	185	12	y	y	PROPN
ejpam-3343	185	13	)	)	PUNCT
ejpam-3343	185	14	)	)	PUNCT
ejpam-3343	185	15	)	)	PUNCT
ejpam-3343	185	16	)	)	PUNCT
ejpam-3343	185	17	≥	≥	NOUN
ejpam-3343	185	18	ηu(x	ηu(x	ADP
ejpam-3343	185	19	∗	∗	PROPN
ejpam-3343	185	20	y	y	PROPN
ejpam-3343	185	21	)	)	PUNCT
ejpam-3343	185	22	for	for	ADP
ejpam-3343	185	23	all	all	DET
ejpam-3343	185	24	x	x	NOUN
ejpam-3343	185	25	,	,	PUNCT
ejpam-3343	185	26	y	y	PROPN
ejpam-3343	185	27	,	,	PUNCT
ejpam-3343	185	28	z	z	NOUN
ejpam-3343	185	29	∈	∈	PROPN
ejpam-3343	185	30	x.	x.	NOUN
ejpam-3343	185	31	it	it	PRON
ejpam-3343	185	32	follows	follow	VERB
ejpam-3343	185	33	from	from	ADP
ejpam-3343	185	34	theorem	theorem	ADJ
ejpam-3343	185	35	3	3	NUM
ejpam-3343	185	36	that	that	SCONJ
ejpam-3343	185	37	(	(	PUNCT
ejpam-3343	185	38	η	η	PROPN
ejpam-3343	185	39	,	,	PUNCT
ejpam-3343	185	40	a	a	PRON
ejpam-3343	185	41	)	)	PUNCT
ejpam-3343	185	42	is	be	AUX
ejpam-3343	185	43	an	an	DET
ejpam-3343	185	44	nu	nu	NOUN
ejpam-3343	185	45	-	-	PUNCT
ejpam-3343	185	46	soft	soft	ADJ
ejpam-3343	185	47	p	p	NOUN
ejpam-3343	185	48	-	-	PUNCT
ejpam-3343	185	49	ideal	ideal	NOUN
ejpam-3343	185	50	over	over	ADP
ejpam-3343	185	51	x.	x.	NOUN
ejpam-3343	185	52	acknowledgements	acknowledgement	NOUN
ejpam-3343	185	53	the	the	DET
ejpam-3343	185	54	authors	author	NOUN
ejpam-3343	185	55	would	would	AUX
ejpam-3343	185	56	like	like	VERB
ejpam-3343	185	57	to	to	PART
ejpam-3343	185	58	express	express	VERB
ejpam-3343	185	59	their	their	PRON
ejpam-3343	185	60	sincere	sincere	ADJ
ejpam-3343	185	61	thanks	thank	NOUN
ejpam-3343	185	62	to	to	ADP
ejpam-3343	185	63	the	the	DET
ejpam-3343	185	64	learned	learn	VERB
ejpam-3343	185	65	referee(s	referee(s	PROPN
ejpam-3343	185	66	)	)	PUNCT
ejpam-3343	185	67	for	for	ADP
ejpam-3343	185	68	valuable	valuable	ADJ
ejpam-3343	185	69	comments	comment	NOUN
ejpam-3343	185	70	and	and	CCONJ
ejpam-3343	185	71	several	several	ADJ
ejpam-3343	185	72	useful	useful	ADJ
ejpam-3343	185	73	suggestions	suggestion	NOUN
ejpam-3343	185	74	that	that	PRON
ejpam-3343	185	75	improved	improve	VERB
ejpam-3343	185	76	the	the	DET
ejpam-3343	185	77	overall	overall	ADJ
ejpam-3343	185	78	presentation	presentation	NOUN
ejpam-3343	185	79	of	of	ADP
ejpam-3343	185	80	this	this	DET
ejpam-3343	185	81	paper	paper	NOUN
ejpam-3343	185	82	.	.	PUNCT
ejpam-3343	186	1	the	the	DET
ejpam-3343	186	2	first	first	ADJ
ejpam-3343	186	3	author	author	NOUN
ejpam-3343	186	4	was	be	AUX
ejpam-3343	186	5	partially	partially	ADV
ejpam-3343	186	6	supported	support	VERB
ejpam-3343	186	7	by	by	ADP
ejpam-3343	186	8	the	the	DET
ejpam-3343	186	9	research	research	NOUN
ejpam-3343	186	10	grant	grant	NOUN
ejpam-3343	186	11	s-0064	s-0064	PROPN
ejpam-3343	186	12	-	-	PUNCT
ejpam-3343	186	13	1439	1439	NUM
ejpam-3343	186	14	,	,	PUNCT
ejpam-3343	186	15	deanship	deanship	NOUN
ejpam-3343	186	16	of	of	ADP
ejpam-3343	186	17	scientific	scientific	ADJ
ejpam-3343	186	18	research	research	NOUN
ejpam-3343	186	19	(	(	PUNCT
ejpam-3343	186	20	drs	drs	PROPN
ejpam-3343	186	21	)	)	PUNCT
ejpam-3343	186	22	,	,	PUNCT
ejpam-3343	186	23	university	university	NOUN
ejpam-3343	186	24	of	of	ADP
ejpam-3343	186	25	tabuk	tabuk	PROPN
ejpam-3343	186	26	,	,	PUNCT
ejpam-3343	186	27	tabuk-71491	tabuk-71491	NOUN
ejpam-3343	186	28	,	,	PUNCT
ejpam-3343	186	29	saudi	saudi	PROPN
ejpam-3343	186	30	arabia	arabia	PROPN
ejpam-3343	186	31	.	.	PUNCT
ejpam-3343	187	1	references	reference	NOUN
ejpam-3343	187	2	[	[	X
ejpam-3343	187	3	1	1	NUM
ejpam-3343	187	4	]	]	PUNCT
ejpam-3343	187	5	a.	a.	PROPN
ejpam-3343	187	6	al	al	PROPN
ejpam-3343	187	7	-	-	PUNCT
ejpam-3343	187	8	roqi	roqi	ADV
ejpam-3343	187	9	,	,	PUNCT
ejpam-3343	187	10	g.	g.	PROPN
ejpam-3343	187	11	muhiuddin	muhiuddin	PROPN
ejpam-3343	187	12	and	and	CCONJ
ejpam-3343	187	13	s.	s.	PROPN
ejpam-3343	187	14	aldhafeeri	aldhafeeri	PROPN
ejpam-3343	187	15	,	,	PUNCT
ejpam-3343	187	16	normal	normal	ADJ
ejpam-3343	187	17	unisoft	unisoft	ADJ
ejpam-3343	187	18	filters	filter	NOUN
ejpam-3343	187	19	in	in	ADP
ejpam-3343	187	20	r0	r0	NOUN
ejpam-3343	187	21	-	-	PUNCT
ejpam-3343	187	22	algebras	algebras	PROPN
ejpam-3343	187	23	,	,	PUNCT
ejpam-3343	187	24	cogent	cogent	NOUN
ejpam-3343	187	25	mathematics	mathematic	NOUN
ejpam-3343	187	26	,	,	PUNCT
ejpam-3343	187	27	vol	vol	NOUN
ejpam-3343	187	28	.	.	PROPN
ejpam-3343	187	29	1	1	NUM
ejpam-3343	187	30	,	,	PUNCT
ejpam-3343	187	31	no.4	no.4	PROPN
ejpam-3343	187	32	,	,	PUNCT
ejpam-3343	187	33	1	1	NUM
ejpam-3343	187	34	-	-	SYM
ejpam-3343	187	35	9	9	NUM
ejpam-3343	187	36	(	(	PUNCT
ejpam-3343	187	37	2017	2017	NUM
ejpam-3343	187	38	)	)	PUNCT
ejpam-3343	187	39	.	.	PUNCT
ejpam-3343	188	1	[	[	X
ejpam-3343	188	2	2	2	NUM
ejpam-3343	188	3	]	]	PUNCT
ejpam-3343	188	4	a.	a.	NOUN
ejpam-3343	188	5	aygünoǧlu	aygünoǧlu	PROPN
ejpam-3343	188	6	and	and	CCONJ
ejpam-3343	188	7	h.	h.	PROPN
ejpam-3343	188	8	aygün	aygün	PROPN
ejpam-3343	188	9	,	,	PUNCT
ejpam-3343	188	10	introduction	introduction	NOUN
ejpam-3343	188	11	to	to	ADP
ejpam-3343	188	12	fuzzy	fuzzy	ADJ
ejpam-3343	188	13	soft	soft	ADJ
ejpam-3343	188	14	groups	group	NOUN
ejpam-3343	188	15	,	,	PUNCT
ejpam-3343	188	16	comput	comput	NOUN
ejpam-3343	188	17	.	.	PUNCT
ejpam-3343	189	1	math	math	NOUN
ejpam-3343	189	2	.	.	PUNCT
ejpam-3343	190	1	appl	appl	PROPN
ejpam-3343	190	2	.	.	PUNCT
ejpam-3343	191	1	58	58	NUM
ejpam-3343	191	2	(	(	PUNCT
ejpam-3343	191	3	2009	2009	NUM
ejpam-3343	191	4	)	)	PUNCT
ejpam-3343	191	5	1279–1286	1279–1286	NOUN
ejpam-3343	191	6	.	.	PUNCT
ejpam-3343	192	1	[	[	X
ejpam-3343	192	2	3	3	X
ejpam-3343	192	3	]	]	X
ejpam-3343	192	4	m.	m.	PROPN
ejpam-3343	192	5	i.	i.	PROPN
ejpam-3343	192	6	ali	ali	PROPN
ejpam-3343	192	7	,	,	PUNCT
ejpam-3343	192	8	f.	f.	PROPN
ejpam-3343	192	9	feng	feng	PROPN
ejpam-3343	192	10	,	,	PUNCT
ejpam-3343	192	11	x	x	PROPN
ejpam-3343	192	12	,	,	PUNCT
ejpam-3343	192	13	liu	liu	PROPN
ejpam-3343	192	14	,	,	PUNCT
ejpam-3343	192	15	w.	w.	PROPN
ejpam-3343	192	16	k.	k.	PROPN
ejpam-3343	192	17	min	min	PROPN
ejpam-3343	192	18	and	and	CCONJ
ejpam-3343	192	19	m.	m.	NOUN
ejpam-3343	192	20	shabir	shabir	PROPN
ejpam-3343	192	21	,	,	PUNCT
ejpam-3343	192	22	on	on	ADP
ejpam-3343	192	23	some	some	DET
ejpam-3343	192	24	new	new	ADJ
ejpam-3343	192	25	operations	operation	NOUN
ejpam-3343	192	26	in	in	ADP
ejpam-3343	192	27	soft	soft	ADJ
ejpam-3343	192	28	set	set	NOUN
ejpam-3343	192	29	theory	theory	NOUN
ejpam-3343	192	30	,	,	PUNCT
ejpam-3343	192	31	comput	comput	NOUN
ejpam-3343	192	32	.	.	PUNCT
ejpam-3343	193	1	math	math	NOUN
ejpam-3343	193	2	.	.	PUNCT
ejpam-3343	194	1	appl	appl	PROPN
ejpam-3343	194	2	.	.	PUNCT
ejpam-3343	195	1	57	57	NUM
ejpam-3343	195	2	(	(	PUNCT
ejpam-3343	195	3	2009	2009	NUM
ejpam-3343	195	4	)	)	PUNCT
ejpam-3343	195	5	1547–1553	1547–1553	NUM
ejpam-3343	195	6	.	.	PUNCT
ejpam-3343	196	1	[	[	X
ejpam-3343	196	2	4	4	X
ejpam-3343	196	3	]	]	X
ejpam-3343	196	4	d.	d.	PROPN
ejpam-3343	196	5	chen	chen	PROPN
ejpam-3343	196	6	,	,	PUNCT
ejpam-3343	196	7	e.	e.	PROPN
ejpam-3343	196	8	c.	c.	PROPN
ejpam-3343	196	9	c.	c.	PROPN
ejpam-3343	196	10	tsang	tsang	PROPN
ejpam-3343	196	11	,	,	PUNCT
ejpam-3343	196	12	d.	d.	PROPN
ejpam-3343	196	13	s.	s.	PROPN
ejpam-3343	196	14	yeung	yeung	PROPN
ejpam-3343	196	15	and	and	CCONJ
ejpam-3343	196	16	x.	x.	PROPN
ejpam-3343	196	17	wang	wang	PROPN
ejpam-3343	196	18	,	,	PUNCT
ejpam-3343	196	19	the	the	DET
ejpam-3343	196	20	parametrization	parametrization	NOUN
ejpam-3343	196	21	reduction	reduction	NOUN
ejpam-3343	196	22	of	of	ADP
ejpam-3343	196	23	soft	soft	ADJ
ejpam-3343	196	24	sets	set	NOUN
ejpam-3343	196	25	and	and	CCONJ
ejpam-3343	196	26	its	its	PRON
ejpam-3343	196	27	applications	application	NOUN
ejpam-3343	196	28	,	,	PUNCT
ejpam-3343	196	29	comput	comput	NOUN
ejpam-3343	196	30	.	.	PUNCT
ejpam-3343	197	1	math	math	NOUN
ejpam-3343	197	2	.	.	PUNCT
ejpam-3343	198	1	appl	appl	PROPN
ejpam-3343	198	2	.	.	PROPN
ejpam-3343	199	1	49	49	NUM
ejpam-3343	199	2	(	(	PUNCT
ejpam-3343	199	3	2005	2005	NUM
ejpam-3343	199	4	)	)	PUNCT
ejpam-3343	200	1	757–763	757–763	NUM
ejpam-3343	200	2	.	.	PUNCT
ejpam-3343	201	1	[	[	X
ejpam-3343	201	2	5	5	X
ejpam-3343	201	3	]	]	X
ejpam-3343	201	4	y.	y.	PROPN
ejpam-3343	201	5	s.	s.	PROPN
ejpam-3343	201	6	huang	huang	PROPN
ejpam-3343	201	7	,	,	PUNCT
ejpam-3343	201	8	bci	bci	PROPN
ejpam-3343	201	9	-	-	NOUN
ejpam-3343	201	10	algebra	algebra	NOUN
ejpam-3343	201	11	,	,	PUNCT
ejpam-3343	201	12	science	science	NOUN
ejpam-3343	201	13	press	press	NOUN
ejpam-3343	201	14	,	,	PUNCT
ejpam-3343	201	15	beijing	beijing	PROPN
ejpam-3343	201	16	,	,	PUNCT
ejpam-3343	201	17	2006	2006	NUM
ejpam-3343	201	18	.	.	PUNCT
ejpam-3343	202	1	[	[	X
ejpam-3343	202	2	6	6	NUM
ejpam-3343	202	3	]	]	X
ejpam-3343	202	4	y.	y.	PROPN
ejpam-3343	202	5	b.	b.	PROPN
ejpam-3343	202	6	jun	jun	PROPN
ejpam-3343	202	7	,	,	PUNCT
ejpam-3343	202	8	soft	soft	ADJ
ejpam-3343	202	9	bck	bck	NOUN
ejpam-3343	202	10	/	/	SYM
ejpam-3343	202	11	bci	bci	NOUN
ejpam-3343	202	12	-	-	PUNCT
ejpam-3343	202	13	algerbas	algerbas	ADJ
ejpam-3343	202	14	,	,	PUNCT
ejpam-3343	202	15	comput	comput	NOUN
ejpam-3343	202	16	.	.	PUNCT
ejpam-3343	202	17	math	math	NOUN
ejpam-3343	202	18	.	.	PUNCT
ejpam-3343	203	1	appl	appl	PROPN
ejpam-3343	203	2	.	.	PUNCT
ejpam-3343	204	1	56	56	NUM
ejpam-3343	204	2	(	(	PUNCT
ejpam-3343	204	3	2008	2008	NUM
ejpam-3343	204	4	)	)	PUNCT
ejpam-3343	204	5	1408–1413	1408–1413	NUM
ejpam-3343	204	6	.	.	PUNCT
ejpam-3343	205	1	[	[	X
ejpam-3343	205	2	7	7	X
ejpam-3343	205	3	]	]	X
ejpam-3343	205	4	y.	y.	PROPN
ejpam-3343	205	5	b.	b.	PROPN
ejpam-3343	205	6	jun	jun	PROPN
ejpam-3343	205	7	,	,	PUNCT
ejpam-3343	205	8	k.	k.	PROPN
ejpam-3343	205	9	j.	j.	PROPN
ejpam-3343	205	10	lee	lee	PROPN
ejpam-3343	205	11	and	and	CCONJ
ejpam-3343	205	12	m.	m.	PROPN
ejpam-3343	205	13	s.	s.	PROPN
ejpam-3343	205	14	kang	kang	PROPN
ejpam-3343	205	15	,	,	PUNCT
ejpam-3343	205	16	ideal	ideal	ADJ
ejpam-3343	205	17	theory	theory	NOUN
ejpam-3343	205	18	in	in	ADP
ejpam-3343	205	19	bck	bck	PROPN
ejpam-3343	205	20	/	/	SYM
ejpam-3343	205	21	bci	bci	PROPN
ejpam-3343	205	22	-	-	PUNCT
ejpam-3343	205	23	algebras	algebra	NOUN
ejpam-3343	205	24	based	base	VERB
ejpam-3343	205	25	on	on	ADP
ejpam-3343	205	26	soft	soft	ADJ
ejpam-3343	205	27	sets	set	NOUN
ejpam-3343	205	28	and	and	CCONJ
ejpam-3343	205	29	n	n	PRON
ejpam-3343	205	30	-structures	-structure	NOUN
ejpam-3343	205	31	,	,	PUNCT
ejpam-3343	205	32	discrete	discrete	ADJ
ejpam-3343	205	33	dyn	dyn	NOUN
ejpam-3343	205	34	.	.	PUNCT
ejpam-3343	206	1	nat	nat	PROPN
ejpam-3343	206	2	.	.	PUNCT
ejpam-3343	207	1	soc	soc	PROPN
ejpam-3343	207	2	.	.	PUNCT
ejpam-3343	208	1	volume	volume	NOUN
ejpam-3343	208	2	2012	2012	NUM
ejpam-3343	208	3	,	,	PUNCT
ejpam-3343	208	4	article	article	NOUN
ejpam-3343	208	5	i	i	PROPN
ejpam-3343	208	6	d	d	PROPN
ejpam-3343	208	7	910450	910450	NUM
ejpam-3343	208	8	,	,	PUNCT
ejpam-3343	208	9	13	13	NUM
ejpam-3343	208	10	pages	page	NOUN
ejpam-3343	208	11	[	[	X
ejpam-3343	208	12	8	8	NUM
ejpam-3343	208	13	]	]	X
ejpam-3343	208	14	y.	y.	PROPN
ejpam-3343	208	15	b.	b.	PROPN
ejpam-3343	208	16	jun	jun	PROPN
ejpam-3343	208	17	,	,	PUNCT
ejpam-3343	208	18	k.	k.	PROPN
ejpam-3343	208	19	j.	j.	PROPN
ejpam-3343	208	20	lee	lee	PROPN
ejpam-3343	208	21	and	and	CCONJ
ejpam-3343	208	22	c.	c.	PROPN
ejpam-3343	208	23	h.	h.	PROPN
ejpam-3343	208	24	park	park	PROPN
ejpam-3343	208	25	,	,	PUNCT
ejpam-3343	208	26	soft	soft	ADJ
ejpam-3343	208	27	set	set	NOUN
ejpam-3343	208	28	theory	theory	NOUN
ejpam-3343	208	29	applied	apply	VERB
ejpam-3343	208	30	to	to	ADP
ejpam-3343	208	31	ideals	ideal	NOUN
ejpam-3343	208	32	in	in	ADP
ejpam-3343	208	33	d	d	NOUN
ejpam-3343	208	34	-	-	PUNCT
ejpam-3343	208	35	algebras	algebra	NOUN
ejpam-3343	208	36	,	,	PUNCT
ejpam-3343	208	37	comput	comput	NOUN
ejpam-3343	208	38	.	.	PUNCT
ejpam-3343	209	1	math	math	NOUN
ejpam-3343	209	2	.	.	PUNCT
ejpam-3343	210	1	appl	appl	PROPN
ejpam-3343	210	2	.	.	PUNCT
ejpam-3343	211	1	57	57	NUM
ejpam-3343	211	2	(	(	PUNCT
ejpam-3343	211	3	2009	2009	NUM
ejpam-3343	211	4	)	)	PUNCT
ejpam-3343	212	1	367–378	367–378	NUM
ejpam-3343	212	2	.	.	PUNCT
ejpam-3343	213	1	[	[	X
ejpam-3343	213	2	9	9	NUM
ejpam-3343	213	3	]	]	X
ejpam-3343	213	4	y.	y.	PROPN
ejpam-3343	213	5	b.	b.	PROPN
ejpam-3343	213	6	jun	jun	PROPN
ejpam-3343	213	7	,	,	PUNCT
ejpam-3343	213	8	k.	k.	PROPN
ejpam-3343	213	9	j.	j.	PROPN
ejpam-3343	213	10	lee	lee	PROPN
ejpam-3343	213	11	and	and	CCONJ
ejpam-3343	213	12	s.	s.	PROPN
ejpam-3343	213	13	z.	z.	PROPN
ejpam-3343	213	14	song	song	PROPN
ejpam-3343	213	15	,	,	PUNCT
ejpam-3343	213	16	n	n	PRON
ejpam-3343	213	17	-ideals	-ideal	NOUN
ejpam-3343	213	18	of	of	ADP
ejpam-3343	213	19	bck	bck	PROPN
ejpam-3343	213	20	/	/	SYM
ejpam-3343	213	21	bci	bci	NOUN
ejpam-3343	213	22	-	-	PUNCT
ejpam-3343	213	23	algebras	algebra	NOUN
ejpam-3343	213	24	,	,	PUNCT
ejpam-3343	213	25	j.	j.	PROPN
ejpam-3343	213	26	chungcheong	chungcheong	PROPN
ejpam-3343	213	27	math	math	PROPN
ejpam-3343	213	28	.	.	PUNCT
ejpam-3343	214	1	soc	soc	PROPN
ejpam-3343	214	2	.	.	PUNCT
ejpam-3343	215	1	22	22	NUM
ejpam-3343	215	2	(	(	PUNCT
ejpam-3343	215	3	2009	2009	NUM
ejpam-3343	215	4	)	)	PUNCT
ejpam-3343	216	1	417–437	417–437	NUM
ejpam-3343	216	2	.	.	PUNCT
ejpam-3343	217	1	[	[	X
ejpam-3343	217	2	10	10	NUM
ejpam-3343	217	3	]	]	X
ejpam-3343	217	4	y.	y.	PROPN
ejpam-3343	217	5	b.	b.	PROPN
ejpam-3343	217	6	jun	jun	PROPN
ejpam-3343	217	7	,	,	PUNCT
ejpam-3343	217	8	m.	m.	NOUN
ejpam-3343	217	9	a.	a.	PROPN
ejpam-3343	217	10	öztürk	öztürk	PROPN
ejpam-3343	217	11	and	and	CCONJ
ejpam-3343	217	12	e.	e.	PROPN
ejpam-3343	217	13	h.	h.	PROPN
ejpam-3343	217	14	roh	roh	PROPN
ejpam-3343	217	15	,	,	PUNCT
ejpam-3343	217	16	n	n	DET
ejpam-3343	217	17	-structures	-structure	NOUN
ejpam-3343	217	18	applied	apply	VERB
ejpam-3343	217	19	to	to	ADP
ejpam-3343	217	20	closed	closed	ADJ
ejpam-3343	217	21	ideals	ideal	NOUN
ejpam-3343	217	22	in	in	ADP
ejpam-3343	217	23	bch	bch	PROPN
ejpam-3343	217	24	-	-	PUNCT
ejpam-3343	217	25	algebras	algebras	PROPN
ejpam-3343	217	26	,	,	PUNCT
ejpam-3343	217	27	int	int	PROPN
ejpam-3343	217	28	.	.	PUNCT
ejpam-3343	218	1	j.	j.	PROPN
ejpam-3343	218	2	math	math	PROPN
ejpam-3343	218	3	.	.	PUNCT
ejpam-3343	219	1	math	math	NOUN
ejpam-3343	219	2	.	.	PUNCT
ejpam-3343	220	1	sci	sci	PROPN
ejpam-3343	220	2	.	.	PROPN
ejpam-3343	220	3	volume	volume	NOUN
ejpam-3343	220	4	2010	2010	NUM
ejpam-3343	220	5	,	,	PUNCT
ejpam-3343	220	6	article	article	NOUN
ejpam-3343	220	7	i	i	PROPN
ejpam-3343	220	8	d	d	PROPN
ejpam-3343	220	9	943565	943565	NUM
ejpam-3343	220	10	,	,	PUNCT
ejpam-3343	220	11	9	9	NUM
ejpam-3343	220	12	pages	page	NOUN
ejpam-3343	220	13	.	.	PUNCT
ejpam-3343	221	1	references	reference	NOUN
ejpam-3343	221	2	87	87	NUM
ejpam-3343	222	1	[	[	X
ejpam-3343	222	2	11	11	NUM
ejpam-3343	222	3	]	]	X
ejpam-3343	222	4	y.	y.	PROPN
ejpam-3343	222	5	b.	b.	PROPN
ejpam-3343	222	6	jun	jun	PROPN
ejpam-3343	222	7	,	,	PUNCT
ejpam-3343	222	8	s.	s.	PROPN
ejpam-3343	222	9	z.	z.	PROPN
ejpam-3343	222	10	song	song	PROPN
ejpam-3343	222	11	and	and	CCONJ
ejpam-3343	222	12	k.	k.	PROPN
ejpam-3343	222	13	j.	j.	PROPN
ejpam-3343	222	14	lee	lee	PROPN
ejpam-3343	222	15	,	,	PUNCT
ejpam-3343	222	16	the	the	DET
ejpam-3343	222	17	combination	combination	NOUN
ejpam-3343	222	18	of	of	ADP
ejpam-3343	222	19	soft	soft	ADJ
ejpam-3343	222	20	sets	set	NOUN
ejpam-3343	222	21	and	and	CCONJ
ejpam-3343	222	22	n	n	PRON
ejpam-3343	222	23	-structures	-structure	NOUN
ejpam-3343	222	24	with	with	ADP
ejpam-3343	222	25	applications	application	NOUN
ejpam-3343	222	26	,	,	PUNCT
ejpam-3343	222	27	journal	journal	NOUN
ejpam-3343	222	28	of	of	ADP
ejpam-3343	222	29	applied	apply	VERB
ejpam-3343	222	30	mathematics	mathematic	NOUN
ejpam-3343	222	31	volume	volume	NOUN
ejpam-3343	222	32	2013	2013	NUM
ejpam-3343	222	33	,	,	PUNCT
ejpam-3343	222	34	article	article	NOUN
ejpam-3343	222	35	i	i	PROPN
ejpam-3343	222	36	d	d	PROPN
ejpam-3343	222	37	420312	420312	NUM
ejpam-3343	222	38	,	,	PUNCT
ejpam-3343	222	39	10	10	NUM
ejpam-3343	222	40	pages	page	NOUN
ejpam-3343	222	41	.	.	PUNCT
ejpam-3343	223	1	[	[	X
ejpam-3343	223	2	12	12	NUM
ejpam-3343	223	3	]	]	PUNCT
ejpam-3343	223	4	p.	p.	PROPN
ejpam-3343	223	5	k.	k.	PROPN
ejpam-3343	224	1	maji	maji	PROPN
ejpam-3343	224	2	,	,	PUNCT
ejpam-3343	224	3	r.	r.	PROPN
ejpam-3343	224	4	biswas	biswas	PROPN
ejpam-3343	224	5	and	and	CCONJ
ejpam-3343	224	6	a.	a.	PROPN
ejpam-3343	224	7	r.	r.	PROPN
ejpam-3343	224	8	roy	roy	PROPN
ejpam-3343	224	9	,	,	PUNCT
ejpam-3343	224	10	soft	soft	ADJ
ejpam-3343	224	11	set	set	NOUN
ejpam-3343	224	12	theory	theory	NOUN
ejpam-3343	224	13	,	,	PUNCT
ejpam-3343	224	14	comput	comput	NOUN
ejpam-3343	224	15	.	.	PUNCT
ejpam-3343	225	1	math	math	NOUN
ejpam-3343	225	2	.	.	PUNCT
ejpam-3343	226	1	appl	appl	PROPN
ejpam-3343	226	2	.	.	PROPN
ejpam-3343	227	1	45	45	NUM
ejpam-3343	227	2	(	(	PUNCT
ejpam-3343	227	3	2003	2003	NUM
ejpam-3343	227	4	)	)	PUNCT
ejpam-3343	228	1	555–562	555–562	NUM
ejpam-3343	228	2	.	.	PUNCT
ejpam-3343	229	1	[	[	X
ejpam-3343	229	2	13	13	NUM
ejpam-3343	229	3	]	]	PUNCT
ejpam-3343	229	4	p.	p.	PROPN
ejpam-3343	229	5	k.	k.	PROPN
ejpam-3343	230	1	maji	maji	PROPN
ejpam-3343	230	2	,	,	PUNCT
ejpam-3343	230	3	a.	a.	PROPN
ejpam-3343	230	4	r.	r.	PROPN
ejpam-3343	230	5	roy	roy	PROPN
ejpam-3343	230	6	and	and	CCONJ
ejpam-3343	230	7	r.	r.	PROPN
ejpam-3343	230	8	biswas	biswas	PROPN
ejpam-3343	230	9	,	,	PUNCT
ejpam-3343	230	10	an	an	DET
ejpam-3343	230	11	application	application	NOUN
ejpam-3343	230	12	of	of	ADP
ejpam-3343	230	13	soft	soft	ADJ
ejpam-3343	230	14	sets	set	NOUN
ejpam-3343	230	15	in	in	ADP
ejpam-3343	230	16	a	a	DET
ejpam-3343	230	17	decision	decision	NOUN
ejpam-3343	230	18	making	making	NOUN
ejpam-3343	230	19	problem	problem	NOUN
ejpam-3343	230	20	,	,	PUNCT
ejpam-3343	230	21	comput	comput	NOUN
ejpam-3343	230	22	.	.	PUNCT
ejpam-3343	231	1	math	math	NOUN
ejpam-3343	231	2	.	.	PUNCT
ejpam-3343	232	1	appl	appl	PROPN
ejpam-3343	232	2	.	.	PROPN
ejpam-3343	233	1	44	44	NUM
ejpam-3343	233	2	(	(	PUNCT
ejpam-3343	233	3	2002	2002	NUM
ejpam-3343	233	4	)	)	PUNCT
ejpam-3343	233	5	1077–1083	1077–1083	NUM
ejpam-3343	233	6	.	.	PUNCT
ejpam-3343	234	1	[	[	X
ejpam-3343	234	2	14	14	NUM
ejpam-3343	234	3	]	]	PUNCT
ejpam-3343	234	4	j.	j.	PROPN
ejpam-3343	234	5	meng	meng	PROPN
ejpam-3343	234	6	and	and	CCONJ
ejpam-3343	234	7	y.	y.	PROPN
ejpam-3343	234	8	b.	b.	PROPN
ejpam-3343	234	9	jun	jun	PROPN
ejpam-3343	234	10	,	,	PUNCT
ejpam-3343	234	11	bck	bck	PROPN
ejpam-3343	234	12	-	-	PUNCT
ejpam-3343	234	13	algebras	algebras	PROPN
ejpam-3343	234	14	,	,	PUNCT
ejpam-3343	234	15	kyungmoon	kyungmoon	PROPN
ejpam-3343	234	16	sa	sa	PROPN
ejpam-3343	234	17	co.	co.	PROPN
ejpam-3343	234	18	seoul	seoul	PROPN
ejpam-3343	234	19	,	,	PUNCT
ejpam-3343	234	20	1994	1994	NUM
ejpam-3343	234	21	.	.	PUNCT
ejpam-3343	235	1	[	[	X
ejpam-3343	235	2	15	15	NUM
ejpam-3343	235	3	]	]	X
ejpam-3343	235	4	d.	d.	PROPN
ejpam-3343	235	5	molodtsov	molodtsov	PROPN
ejpam-3343	235	6	,	,	PUNCT
ejpam-3343	235	7	soft	soft	ADJ
ejpam-3343	235	8	set	set	NOUN
ejpam-3343	235	9	theory	theory	NOUN
ejpam-3343	235	10	first	first	ADJ
ejpam-3343	235	11	results	result	NOUN
ejpam-3343	235	12	,	,	PUNCT
ejpam-3343	235	13	comput	comput	NOUN
ejpam-3343	235	14	.	.	PUNCT
ejpam-3343	236	1	math	math	NOUN
ejpam-3343	236	2	.	.	PUNCT
ejpam-3343	237	1	appl	appl	PROPN
ejpam-3343	237	2	.	.	PUNCT
ejpam-3343	238	1	37	37	NUM
ejpam-3343	238	2	(	(	PUNCT
ejpam-3343	238	3	1999	1999	NUM
ejpam-3343	238	4	)	)	PUNCT
ejpam-3343	238	5	19–31	19–31	NUM
ejpam-3343	238	6	.	.	PUNCT
ejpam-3343	239	1	[	[	X
ejpam-3343	239	2	16	16	NUM
ejpam-3343	239	3	]	]	X
ejpam-3343	239	4	g.	g.	PROPN
ejpam-3343	239	5	muhiuddin	muhiuddin	PROPN
ejpam-3343	239	6	,	,	PUNCT
ejpam-3343	239	7	abdullah	abdullah	PROPN
ejpam-3343	239	8	m.	m.	PROPN
ejpam-3343	239	9	al	al	PROPN
ejpam-3343	239	10	-	-	PUNCT
ejpam-3343	239	11	roqi	roqi	PROPN
ejpam-3343	239	12	and	and	CCONJ
ejpam-3343	239	13	shuaa	shuaa	ADV
ejpam-3343	239	14	aldhafeeri	aldhafeeri	PROPN
ejpam-3343	239	15	,	,	PUNCT
ejpam-3343	239	16	filter	filter	NOUN
ejpam-3343	239	17	theory	theory	NOUN
ejpam-3343	239	18	in	in	ADP
ejpam-3343	239	19	mtlalgebras	mtlalgebras	PROPN
ejpam-3343	239	20	based	base	VERB
ejpam-3343	239	21	on	on	ADP
ejpam-3343	239	22	uni	uni	ADJ
ejpam-3343	239	23	-	-	ADJ
ejpam-3343	239	24	soft	soft	ADJ
ejpam-3343	239	25	property	property	NOUN
ejpam-3343	239	26	,	,	PUNCT
ejpam-3343	239	27	bulletin	bulletin	NOUN
ejpam-3343	239	28	of	of	ADP
ejpam-3343	239	29	the	the	DET
ejpam-3343	239	30	iranian	iranian	PROPN
ejpam-3343	239	31	mathematical	mathematical	ADJ
ejpam-3343	239	32	society	society	NOUN
ejpam-3343	239	33	,	,	PUNCT
ejpam-3343	239	34	vol	vol	NOUN
ejpam-3343	239	35	.	.	PROPN
ejpam-3343	239	36	43	43	NUM
ejpam-3343	239	37	,	,	PUNCT
ejpam-3343	239	38	no.7	no.7	PROPN
ejpam-3343	239	39	(	(	PUNCT
ejpam-3343	239	40	2017	2017	NUM
ejpam-3343	239	41	)	)	PUNCT
ejpam-3343	239	42	2293–2306	2293–2306	NUM
ejpam-3343	239	43	.	.	PUNCT
ejpam-3343	240	1	[	[	X
ejpam-3343	240	2	17	17	NUM
ejpam-3343	240	3	]	]	X
ejpam-3343	240	4	g.	g.	PROPN
ejpam-3343	240	5	muhiuddin	muhiuddin	PROPN
ejpam-3343	240	6	and	and	CCONJ
ejpam-3343	240	7	abdullah	abdullah	PROPN
ejpam-3343	240	8	m.	m.	PROPN
ejpam-3343	240	9	al	al	PROPN
ejpam-3343	240	10	-	-	PUNCT
ejpam-3343	240	11	roqi	roqi	PROPN
ejpam-3343	240	12	,	,	PUNCT
ejpam-3343	240	13	unisoft	unisoft	ADJ
ejpam-3343	240	14	filters	filter	NOUN
ejpam-3343	240	15	in	in	ADP
ejpam-3343	240	16	r0	r0	NOUN
ejpam-3343	240	17	-	-	PUNCT
ejpam-3343	240	18	algebras	algebras	PROPN
ejpam-3343	240	19	,	,	PUNCT
ejpam-3343	240	20	journal	journal	NOUN
ejpam-3343	240	21	of	of	ADP
ejpam-3343	240	22	computational	computational	ADJ
ejpam-3343	240	23	analysis	analysis	NOUN
ejpam-3343	240	24	and	and	CCONJ
ejpam-3343	240	25	applications	application	NOUN
ejpam-3343	240	26	,	,	PUNCT
ejpam-3343	240	27	19	19	NUM
ejpam-3343	240	28	,	,	PUNCT
ejpam-3343	240	29	no	no	INTJ
ejpam-3343	240	30	.	.	NOUN
ejpam-3343	240	31	1	1	NUM
ejpam-3343	240	32	,	,	PUNCT
ejpam-3343	240	33	(	(	PUNCT
ejpam-3343	240	34	2015	2015	NUM
ejpam-3343	240	35	)	)	PUNCT
ejpam-3343	240	36	133–143	133–143	NUM
ejpam-3343	240	37	.	.	PUNCT
ejpam-3343	241	1	[	[	X
ejpam-3343	241	2	18	18	NUM
ejpam-3343	241	3	]	]	X
ejpam-3343	241	4	g.	g.	PROPN
ejpam-3343	241	5	muhiuddin	muhiuddin	PROPN
ejpam-3343	241	6	,	,	PUNCT
ejpam-3343	241	7	feng	feng	PROPN
ejpam-3343	241	8	feng	feng	PROPN
ejpam-3343	241	9	and	and	CCONJ
ejpam-3343	241	10	young	young	PROPN
ejpam-3343	241	11	bae	bae	PROPN
ejpam-3343	241	12	jun	jun	PROPN
ejpam-3343	241	13	,	,	PUNCT
ejpam-3343	241	14	subalgebras	subalgebras	PROPN
ejpam-3343	241	15	of	of	ADP
ejpam-3343	241	16	bck	bck	PROPN
ejpam-3343	241	17	/	/	SYM
ejpam-3343	241	18	bci	bci	NOUN
ejpam-3343	241	19	-	-	PUNCT
ejpam-3343	241	20	algebras	algebras	PROPN
ejpam-3343	241	21	based	base	VERB
ejpam-3343	241	22	on	on	ADP
ejpam-3343	241	23	cubic	cubic	ADJ
ejpam-3343	241	24	soft	soft	ADJ
ejpam-3343	241	25	sets	set	NOUN
ejpam-3343	241	26	,	,	PUNCT
ejpam-3343	241	27	the	the	DET
ejpam-3343	241	28	scientific	scientific	ADJ
ejpam-3343	241	29	world	world	NOUN
ejpam-3343	241	30	journal	journal	NOUN
ejpam-3343	241	31	,	,	PUNCT
ejpam-3343	241	32	volume	volume	NOUN
ejpam-3343	241	33	2014	2014	NUM
ejpam-3343	241	34	,	,	PUNCT
ejpam-3343	241	35	article	article	NOUN
ejpam-3343	241	36	i	i	PROPN
ejpam-3343	241	37	d	d	PROPN
ejpam-3343	241	38	458638	458638	NUM
ejpam-3343	241	39	,	,	PUNCT
ejpam-3343	241	40	(	(	PUNCT
ejpam-3343	241	41	2014	2014	NUM
ejpam-3343	241	42	)	)	PUNCT
ejpam-3343	241	43	9	9	NUM
ejpam-3343	241	44	pages	page	NOUN
ejpam-3343	241	45	.	.	PUNCT
ejpam-3343	242	1	[	[	X
ejpam-3343	242	2	19	19	NUM
ejpam-3343	242	3	]	]	X
ejpam-3343	242	4	g.	g.	PROPN
ejpam-3343	242	5	muhiuddin	muhiuddin	PROPN
ejpam-3343	242	6	and	and	CCONJ
ejpam-3343	242	7	abdullah	abdullah	PROPN
ejpam-3343	242	8	m.	m.	PROPN
ejpam-3343	242	9	al	al	PROPN
ejpam-3343	242	10	-	-	PUNCT
ejpam-3343	242	11	roqi	roqi	ADJ
ejpam-3343	242	12	,	,	PUNCT
ejpam-3343	242	13	cubic	cubic	ADJ
ejpam-3343	242	14	soft	soft	ADJ
ejpam-3343	242	15	sets	set	NOUN
ejpam-3343	242	16	with	with	ADP
ejpam-3343	242	17	applications	application	NOUN
ejpam-3343	242	18	in	in	ADP
ejpam-3343	242	19	bck	bck	PROPN
ejpam-3343	242	20	/	/	SYM
ejpam-3343	242	21	bci	bci	PROPN
ejpam-3343	242	22	-	-	PUNCT
ejpam-3343	242	23	algebras	algebra	NOUN
ejpam-3343	242	24	,	,	PUNCT
ejpam-3343	242	25	annals	annal	NOUN
ejpam-3343	242	26	of	of	ADP
ejpam-3343	242	27	fuzzy	fuzzy	ADJ
ejpam-3343	242	28	mathematics	mathematic	NOUN
ejpam-3343	242	29	and	and	CCONJ
ejpam-3343	242	30	informatics	informatic	NOUN
ejpam-3343	242	31	,	,	PUNCT
ejpam-3343	242	32	volume	volume	NOUN
ejpam-3343	242	33	8	8	NUM
ejpam-3343	242	34	,	,	PUNCT
ejpam-3343	242	35	no	no	INTJ
ejpam-3343	242	36	.	.	NOUN
ejpam-3343	242	37	2	2	NUM
ejpam-3343	242	38	,	,	PUNCT
ejpam-3343	242	39	(	(	PUNCT
ejpam-3343	242	40	2014	2014	NUM
ejpam-3343	242	41	)	)	PUNCT
ejpam-3343	242	42	291–304	291–304	NUM
ejpam-3343	242	43	.	.	PUNCT
ejpam-3343	243	1	[	[	X
ejpam-3343	243	2	20	20	NUM
ejpam-3343	243	3	]	]	PUNCT
ejpam-3343	243	4	a.	a.	PROPN
ejpam-3343	243	5	r.	r.	PROPN
ejpam-3343	243	6	roy	roy	PROPN
ejpam-3343	243	7	and	and	CCONJ
ejpam-3343	243	8	p.	p.	PROPN
ejpam-3343	243	9	k.	k.	PROPN
ejpam-3343	244	1	maji	maji	PROPN
ejpam-3343	244	2	,	,	PUNCT
ejpam-3343	244	3	a	a	DET
ejpam-3343	244	4	fuzzy	fuzzy	ADJ
ejpam-3343	244	5	soft	soft	ADJ
ejpam-3343	244	6	set	set	ADJ
ejpam-3343	244	7	theoretic	theoretic	ADJ
ejpam-3343	244	8	approach	approach	NOUN
ejpam-3343	244	9	to	to	ADP
ejpam-3343	244	10	decision	decision	NOUN
ejpam-3343	244	11	making	making	NOUN
ejpam-3343	244	12	problems	problem	NOUN
ejpam-3343	244	13	,	,	PUNCT
ejpam-3343	244	14	j.	j.	PROPN
ejpam-3343	244	15	comput	comput	PROPN
ejpam-3343	244	16	.	.	PUNCT
ejpam-3343	245	1	appl	appl	PROPN
ejpam-3343	245	2	.	.	PROPN
ejpam-3343	245	3	math	math	NOUN
ejpam-3343	245	4	.	.	PUNCT
ejpam-3343	246	1	203	203	NUM
ejpam-3343	246	2	(	(	PUNCT
ejpam-3343	246	3	2007	2007	NUM
ejpam-3343	246	4	)	)	PUNCT
ejpam-3343	247	1	412–418	412–418	NUM
ejpam-3343	247	2	.	.	PUNCT
ejpam-3343	248	1	[	[	X
ejpam-3343	248	2	21	21	NUM
ejpam-3343	248	3	]	]	X
ejpam-3343	248	4	l.	l.	PROPN
ejpam-3343	248	5	a.	a.	PROPN
ejpam-3343	248	6	zadeh	zadeh	PROPN
ejpam-3343	248	7	,	,	PUNCT
ejpam-3343	248	8	fuzzy	fuzzy	ADJ
ejpam-3343	248	9	sets	set	NOUN
ejpam-3343	248	10	,	,	PUNCT
ejpam-3343	248	11	inform	inform	NOUN
ejpam-3343	248	12	.	.	PUNCT
ejpam-3343	249	1	control	control	NOUN
ejpam-3343	249	2	8	8	NUM
ejpam-3343	249	3	(	(	PUNCT
ejpam-3343	249	4	1965	1965	NUM
ejpam-3343	249	5	)	)	PUNCT
ejpam-3343	249	6	338–353	338–353	NUM
ejpam-3343	249	7	.	.	PUNCT