id	sid	tid	token	lemma	pos
iajs-2287	1	1	109	109	NUM
iajs-2287	1	2	ibn	ibn	PROPN
iajs-2287	1	3	al	al	PROPN
iajs-2287	1	4	-	-	PUNCT
iajs-2287	1	5	haitham	haitham	PROPN
iajs-2287	1	6	jour	jour	X
iajs-2287	1	7	.	.	PROPN
iajs-2287	1	8	for	for	ADP
iajs-2287	1	9	pure	pure	ADJ
iajs-2287	1	10	&	&	CCONJ
iajs-2287	1	11	appl	appl	PROPN
iajs-2287	1	12	.	.	PUNCT
iajs-2287	2	1	sci	sci	PROPN
iajs-2287	2	2	.	.	PROPN
iajs-2287	2	3	32	32	NUM
iajs-2287	2	4	(	(	PUNCT
iajs-2287	2	5	3	3	NUM
iajs-2287	2	6	)	)	PUNCT
iajs-2287	2	7	2019	2019	NUM
iajs-2287	2	8	samah	samah	PROPN
iajs-2287	2	9	h.	h.	PROPN
iajs-2287	2	10	asaad	asaad	PROPN
iajs-2287	2	11	akram	akram	PROPN
iajs-2287	2	12	s.	s.	PROPN
iajs-2287	2	13	mohammed	mohammed	PROPN
iajs-2287	2	14	abstract	abstract	PROPN
iajs-2287	2	15	in	in	ADP
iajs-2287	2	16	this	this	DET
iajs-2287	2	17	article	article	NOUN
iajs-2287	2	18	,	,	PUNCT
iajs-2287	2	19	we	we	PRON
iajs-2287	2	20	study	study	VERB
iajs-2287	2	21	some	some	DET
iajs-2287	2	22	properties	property	NOUN
iajs-2287	2	23	of	of	ADP
iajs-2287	2	24	anti	anti	ADJ
iajs-2287	2	25	-	-	ADJ
iajs-2287	2	26	fuzzy	fuzzy	ADJ
iajs-2287	2	27	sub	sub	NOUN
iajs-2287	2	28	-	-	ADJ
iajs-2287	2	29	semigroup	semigroup	ADJ
iajs-2287	2	30	,	,	PUNCT
iajs-2287	2	31	anti	anti	X
iajs-2287	2	32	fuzzy	fuzzy	ADJ
iajs-2287	2	33	left	left	ADJ
iajs-2287	2	34	(	(	PUNCT
iajs-2287	2	35	right	right	INTJ
iajs-2287	2	36	,	,	PUNCT
iajs-2287	2	37	two	two	NUM
iajs-2287	2	38	sided	sided	ADJ
iajs-2287	2	39	)	)	PUNCT
iajs-2287	2	40	ideal	ideal	ADJ
iajs-2287	2	41	,	,	PUNCT
iajs-2287	2	42	anti	anti	X
iajs-2287	2	43	fuzzy	fuzzy	ADJ
iajs-2287	2	44	ideal	ideal	NOUN
iajs-2287	2	45	,	,	PUNCT
iajs-2287	2	46	anti	anti	X
iajs-2287	2	47	fuzzy	fuzzy	ADJ
iajs-2287	2	48	generalized	generalized	ADJ
iajs-2287	2	49	bi	bi	NOUN
iajs-2287	2	50	-	-	NOUN
iajs-2287	2	51	ideal	ideal	ADJ
iajs-2287	2	52	,	,	PUNCT
iajs-2287	2	53	anti	anti	X
iajs-2287	2	54	fuzzy	fuzzy	ADJ
iajs-2287	2	55	interior	interior	ADJ
iajs-2287	2	56	ideals	ideal	NOUN
iajs-2287	2	57	and	and	CCONJ
iajs-2287	2	58	anti	anti	ADJ
iajs-2287	2	59	fuzzy	fuzzy	ADJ
iajs-2287	2	60	two	two	NUM
iajs-2287	2	61	sided	sided	ADJ
iajs-2287	2	62	ideal	ideal	NOUN
iajs-2287	2	63	of	of	ADP
iajs-2287	2	64	regular	regular	ADJ
iajs-2287	2	65	semigroup	semigroup	NOUN
iajs-2287	2	66	.	.	PUNCT
iajs-2287	3	1	also	also	ADV
iajs-2287	3	2	,	,	PUNCT
iajs-2287	3	3	we	we	PRON
iajs-2287	3	4	characterized	characterize	VERB
iajs-2287	3	5	regular	regular	ADJ
iajs-2287	3	6	la	la	NOUN
iajs-2287	3	7	-	-	PUNCT
iajs-2287	3	8	semigroup	semigroup	NOUN
iajs-2287	3	9	in	in	ADP
iajs-2287	3	10	terms	term	NOUN
iajs-2287	3	11	of	of	ADP
iajs-2287	3	12	their	their	PRON
iajs-2287	3	13	anti	anti	ADJ
iajs-2287	3	14	fuzzy	fuzzy	ADJ
iajs-2287	3	15	ideal	ideal	NOUN
iajs-2287	3	16	.	.	PUNCT
iajs-2287	4	1	keywords	keyword	NOUN
iajs-2287	4	2	:	:	PUNCT
iajs-2287	4	3	fuzzy	fuzzy	ADJ
iajs-2287	4	4	ideal	ideal	NOUN
iajs-2287	4	5	,	,	PUNCT
iajs-2287	4	6	regular	regular	ADJ
iajs-2287	4	7	,	,	PUNCT
iajs-2287	4	8	anti	anti	X
iajs-2287	4	9	fuzzy	fuzzy	ADJ
iajs-2287	4	10	interior	interior	ADJ
iajs-2287	4	11	ideal	ideal	NOUN
iajs-2287	4	12	,	,	PUNCT
iajs-2287	4	13	anti	anti	X
iajs-2287	4	14	fuzzy	fuzzy	ADJ
iajs-2287	4	15	ideal	ideal	NOUN
iajs-2287	4	16	.	.	PUNCT
iajs-2287	5	1	1	1	X
iajs-2287	5	2	.	.	X
iajs-2287	5	3	introduction	introduction	NOUN
iajs-2287	5	4	and	and	CCONJ
iajs-2287	5	5	basic	basic	ADJ
iajs-2287	5	6	concept	concept	NOUN
iajs-2287	5	7	fuzzy	fuzzy	ADJ
iajs-2287	5	8	sub	sub	NOUN
iajs-2287	5	9	-	-	ADJ
iajs-2287	5	10	semigroup	semigroup	ADJ
iajs-2287	5	11	and	and	CCONJ
iajs-2287	5	12	fuzzy	fuzzy	ADJ
iajs-2287	5	13	interior	interior	ADJ
iajs-2287	5	14	ideal	ideal	NOUN
iajs-2287	5	15	in	in	ADP
iajs-2287	5	16	semigroup	semigroup	PROPN
iajs-2287	5	17	was	be	AUX
iajs-2287	5	18	introduced	introduce	VERB
iajs-2287	5	19	by	by	ADP
iajs-2287	5	20	hong	hong	PROPN
iajs-2287	5	21	,	,	PUNCT
iajs-2287	5	22	et	et	PROPN
iajs-2287	5	23	al	al	PROPN
iajs-2287	5	24	.	.	PROPN
iajs-2287	5	25	,	,	PUNCT
iajs-2287	5	26	in	in	ADP
iajs-2287	5	27	[	[	X
iajs-2287	5	28	1	1	NUM
iajs-2287	5	29	]	]	PUNCT
iajs-2287	5	30	.	.	PUNCT
iajs-2287	6	1	and	and	CCONJ
iajs-2287	6	2	the	the	DET
iajs-2287	6	3	concept	concept	NOUN
iajs-2287	6	4	of	of	ADP
iajs-2287	6	5	fuzzy	fuzzy	ADJ
iajs-2287	6	6	ideal	ideal	ADJ
iajs-2287	6	7	and	and	CCONJ
iajs-2287	6	8	fuzzy	fuzzy	ADJ
iajs-2287	6	9	bi	bi	NOUN
iajs-2287	6	10	-	-	NOUN
iajs-2287	6	11	ideals	ideal	NOUN
iajs-2287	6	12	in	in	ADP
iajs-2287	6	13	semigroups	semigroup	NOUN
iajs-2287	6	14	was	be	AUX
iajs-2287	6	15	studied	study	VERB
iajs-2287	6	16	by	by	ADP
iajs-2287	6	17	nobuaki	nobuaki	ADJ
iajs-2287	6	18	kuroki	kuroki	PROPN
iajs-2287	6	19	in	in	ADP
iajs-2287	6	20	(	(	PUNCT
iajs-2287	6	21	1981	1981	NUM
iajs-2287	6	22	)	)	PUNCT
iajs-2287	6	23	”	"	PUNCT
iajs-2287	6	24	,	,	PUNCT
iajs-2287	7	1	[	[	X
iajs-2287	7	2	2	2	NUM
iajs-2287	7	3	]	]	PUNCT
iajs-2287	7	4	.	.	PUNCT
iajs-2287	8	1	the	the	DET
iajs-2287	8	2	concept	concept	NOUN
iajs-2287	8	3	of	of	ADP
iajs-2287	8	4	the	the	DET
iajs-2287	8	5	product	product	NOUN
iajs-2287	8	6	of	of	ADP
iajs-2287	8	7	two	two	NUM
iajs-2287	8	8	fuzzy	fuzzy	ADJ
iajs-2287	8	9	subset	subset	NOUN
iajs-2287	8	10	and	and	CCONJ
iajs-2287	8	11	anti	anti	ADJ
iajs-2287	8	12	product	product	NOUN
iajs-2287	8	13	of	of	ADP
iajs-2287	8	14	two	two	NUM
iajs-2287	8	15	fuzzy	fuzzy	ADJ
iajs-2287	8	16	subset	subset	NOUN
iajs-2287	8	17	was	be	AUX
iajs-2287	8	18	introduced	introduce	VERB
iajs-2287	8	19	by	by	ADP
iajs-2287	8	20	shabir	shabir	NOUN
iajs-2287	8	21	and	and	CCONJ
iajs-2287	8	22	nawaz	nawaz	ADJ
iajs-2287	8	23	[	[	X
iajs-2287	8	24	3	3	NUM
iajs-2287	8	25	]	]	PUNCT
iajs-2287	8	26	.	.	PUNCT
iajs-2287	9	1	the	the	DET
iajs-2287	9	2	concept	concept	NOUN
iajs-2287	9	3	of	of	ADP
iajs-2287	9	4	characterizations	characterization	NOUN
iajs-2287	9	5	of	of	ADP
iajs-2287	9	6	semigroups	semigroup	NOUN
iajs-2287	9	7	by	by	ADP
iajs-2287	9	8	their	their	PRON
iajs-2287	9	9	anti	anti	ADJ
iajs-2287	9	10	fuzzy	fuzzy	ADJ
iajs-2287	9	11	ideals	ideal	NOUN
iajs-2287	9	12	was	be	AUX
iajs-2287	9	13	studied	study	VERB
iajs-2287	9	14	by	by	ADP
iajs-2287	9	15	khan	khan	PROPN
iajs-2287	9	16	and	and	CCONJ
iajs-2287	9	17	asif	asif	NOUN
iajs-2287	9	18	in	in	ADP
iajs-2287	9	19	[	[	X
iajs-2287	9	20	4	4	NUM
iajs-2287	9	21	]	]	PUNCT
iajs-2287	9	22	.	.	PUNCT
iajs-2287	10	1	the	the	DET
iajs-2287	10	2	concept	concept	NOUN
iajs-2287	10	3	of	of	ADP
iajs-2287	10	4	intra	intra	ADJ
iajs-2287	10	5	-	-	ADJ
iajs-2287	10	6	regular	regular	ADJ
iajs-2287	10	7	(	(	PUNCT
iajs-2287	10	8	left	leave	VERB
iajs-2287	10	9	almost	almost	ADV
iajs-2287	10	10	semigroup	semigroup	PROPN
iajs-2287	10	11	denoted	denote	VERB
iajs-2287	10	12	by	by	ADP
iajs-2287	10	13	la	la	NOUN
iajs-2287	10	14	-	-	PUNCT
iajs-2287	10	15	semigroups	semigroup	NOUN
iajs-2287	10	16	)	)	PUNCT
iajs-2287	10	17	characterized	characterize	VERB
iajs-2287	10	18	by	by	ADP
iajs-2287	10	19	their	their	PRON
iajs-2287	10	20	anti	anti	ADJ
iajs-2287	10	21	fuzzy	fuzzy	ADJ
iajs-2287	10	22	ideals	ideal	NOUN
iajs-2287	10	23	by	by	ADP
iajs-2287	10	24	khan	khan	PROPN
iajs-2287	10	25	and	and	CCONJ
iajs-2287	10	26	faisal	faisal	NOUN
iajs-2287	10	27	in	in	ADP
iajs-2287	10	28	[	[	X
iajs-2287	10	29	5	5	NUM
iajs-2287	10	30	]	]	PUNCT
iajs-2287	10	31	.	.	PUNCT
iajs-2287	11	1	many	many	ADJ
iajs-2287	11	2	other	other	ADJ
iajs-2287	11	3	authors	author	NOUN
iajs-2287	11	4	interested	interest	VERB
iajs-2287	11	5	studied	study	VERB
iajs-2287	11	6	of	of	ADP
iajs-2287	11	7	fuzzy	fuzzy	ADJ
iajs-2287	11	8	ideal	ideal	NOUN
iajs-2287	11	9	,	,	PUNCT
iajs-2287	11	10	for	for	ADP
iajs-2287	11	11	example	example	NOUN
iajs-2287	11	12	see	see	VERB
iajs-2287	11	13	[	[	X
iajs-2287	11	14	6	6	NUM
iajs-2287	11	15	-	-	SYM
iajs-2287	11	16	9	9	NUM
iajs-2287	11	17	]	]	PUNCT
iajs-2287	11	18	.	.	PUNCT
iajs-2287	12	1	through	through	ADP
iajs-2287	12	2	out	out	ADP
iajs-2287	12	3	of	of	ADP
iajs-2287	12	4	this	this	DET
iajs-2287	12	5	paper	paper	NOUN
iajs-2287	12	6	we	we	PRON
iajs-2287	12	7	are	be	AUX
iajs-2287	12	8	denoted	denote	VERB
iajs-2287	12	9	of	of	ADP
iajs-2287	12	10	a	a	DET
iajs-2287	12	11	regular	regular	ADJ
iajs-2287	12	12	semigroup	semigroup	ADJ
iajs-2287	12	13	byℵ𝑟.	byℵ𝑟.	NOUN
iajs-2287	12	14	definition	definition	NOUN
iajs-2287	12	15	1	1	NUM
iajs-2287	12	16	[	[	X
iajs-2287	12	17	1	1	NUM
iajs-2287	12	18	]	]	PUNCT
iajs-2287	12	19	.	.	PUNCT
iajs-2287	13	1	a	a	DET
iajs-2287	13	2	fuzzy	fuzzy	ADJ
iajs-2287	13	3	subset	subset	VERB
iajs-2287	13	4	ζ	ζ	NOUN
iajs-2287	13	5	in	in	ADP
iajs-2287	13	6	a	a	DET
iajs-2287	13	7	semigroup	semigroup	ADJ
iajs-2287	13	8	ℵ	ℵ	NOUN
iajs-2287	13	9	is	be	AUX
iajs-2287	13	10	said	say	VERB
iajs-2287	13	11	to	to	PART
iajs-2287	13	12	be	be	AUX
iajs-2287	13	13	a	a	DET
iajs-2287	13	14	fuzzy	fuzzy	ADJ
iajs-2287	13	15	sub	sub	NOUN
iajs-2287	13	16	-	-	ADJ
iajs-2287	13	17	semigroup	semigroup	ADJ
iajs-2287	13	18	of	of	ADP
iajs-2287	13	19	ℵ	ℵ	NOUN
iajs-2287	13	20	if	if	SCONJ
iajs-2287	13	21	ζ(wz)≥	ζ(wz)≥	PROPN
iajs-2287	13	22	min{ζ(w	min{ζ(w	PROPN
iajs-2287	13	23	)	)	PUNCT
iajs-2287	13	24	,	,	PUNCT
iajs-2287	13	25	ζ(z	ζ(z	PROPN
iajs-2287	13	26	)	)	PUNCT
iajs-2287	13	27	}	}	PUNCT
iajs-2287	13	28	,	,	PUNCT
iajs-2287	13	29	whenever	whenever	SCONJ
iajs-2287	13	30	w	w	NOUN
iajs-2287	13	31	,	,	PUNCT
iajs-2287	13	32	z	z	PROPN
iajs-2287	13	33	∈	∈	PROPN
iajs-2287	13	34	ℵ.	ℵ.	NOUN
iajs-2287	13	35	definition	definition	NOUN
iajs-2287	13	36	2	2	NUM
iajs-2287	14	1	[	[	X
iajs-2287	14	2	1	1	NUM
iajs-2287	14	3	]	]	PUNCT
iajs-2287	14	4	.	.	PUNCT
iajs-2287	15	1	a	a	DET
iajs-2287	15	2	fuzzy	fuzzy	ADJ
iajs-2287	15	3	sub	sub	ADJ
iajs-2287	15	4	-	-	ADJ
iajs-2287	15	5	semigroup	semigroup	ADJ
iajs-2287	15	6	ζ	ζ	NOUN
iajs-2287	15	7	of	of	ADP
iajs-2287	15	8	a	a	DET
iajs-2287	15	9	semigroup	semigroup	ADJ
iajs-2287	15	10	ℵ	ℵ	NOUN
iajs-2287	15	11	is	be	AUX
iajs-2287	15	12	said	say	VERB
iajs-2287	15	13	to	to	PART
iajs-2287	15	14	be	be	AUX
iajs-2287	15	15	a	a	DET
iajs-2287	15	16	fuzzy	fuzzy	ADJ
iajs-2287	15	17	interior	interior	ADJ
iajs-2287	15	18	ideal	ideal	NOUN
iajs-2287	15	19	of	of	ADP
iajs-2287	15	20	ℵ	ℵ	PRON
iajs-2287	15	21	if	if	SCONJ
iajs-2287	15	22	ζ(swr)≥	ζ(swr)≥	PROPN
iajs-2287	15	23	ζ(w	ζ(w	PROPN
iajs-2287	15	24	)	)	PUNCT
iajs-2287	15	25	,	,	PUNCT
iajs-2287	15	26	whenever	whenever	SCONJ
iajs-2287	15	27	s	s	VERB
iajs-2287	15	28	,	,	PUNCT
iajs-2287	15	29	w	w	PROPN
iajs-2287	15	30	,	,	PUNCT
iajs-2287	15	31	r	r	NOUN
iajs-2287	15	32	∈	∈	PROPN
iajs-2287	15	33	ℵ.	ℵ.	NOUN
iajs-2287	15	34	definition	definition	NOUN
iajs-2287	15	35	3	3	NUM
iajs-2287	16	1	[	[	X
iajs-2287	16	2	2	2	NUM
iajs-2287	16	3	]	]	PUNCT
iajs-2287	16	4	.	.	PUNCT
iajs-2287	17	1	a	a	DET
iajs-2287	17	2	fuzzy	fuzzy	ADJ
iajs-2287	17	3	function	function	NOUN
iajs-2287	17	4	ζ	ζ	NOUN
iajs-2287	17	5	of	of	ADP
iajs-2287	17	6	a	a	DET
iajs-2287	17	7	semigroup	semigroup	ADJ
iajs-2287	17	8	ℵ	ℵ	NOUN
iajs-2287	17	9	is	be	AUX
iajs-2287	17	10	said	say	VERB
iajs-2287	17	11	to	to	PART
iajs-2287	17	12	be	be	AUX
iajs-2287	17	13	a	a	DET
iajs-2287	17	14	fuzzy	fuzzy	ADJ
iajs-2287	17	15	ideal	ideal	NOUN
iajs-2287	17	16	if	if	SCONJ
iajs-2287	17	17	ζ(swr)≤max{ζ(s	ζ(swr)≤max{ζ(s	NOUN
iajs-2287	17	18	)	)	PUNCT
iajs-2287	17	19	,	,	PUNCT
iajs-2287	17	20	ζ(r)}={ζ(s)⋁	ζ(r)}={ζ(s)⋁	ADJ
iajs-2287	17	21	ζ(r	ζ(r	NOUN
iajs-2287	17	22	)	)	PUNCT
iajs-2287	17	23	}	}	PUNCT
iajs-2287	17	24	,	,	PUNCT
iajs-2287	17	25	whenever	whenever	SCONJ
iajs-2287	17	26	s	s	VERB
iajs-2287	17	27	,	,	PUNCT
iajs-2287	17	28	w	w	PROPN
iajs-2287	17	29	,	,	PUNCT
iajs-2287	17	30	r	r	NOUN
iajs-2287	17	31	∈	∈	PROPN
iajs-2287	17	32	ℵ.	ℵ.	PROPN
iajs-2287	18	1	ibn	ibn	PROPN
iajs-2287	18	2	al	al	PROPN
iajs-2287	18	3	haitham	haitham	PROPN
iajs-2287	18	4	journal	journal	PROPN
iajs-2287	18	5	for	for	ADP
iajs-2287	18	6	pure	pure	ADJ
iajs-2287	18	7	and	and	CCONJ
iajs-2287	18	8	applied	apply	VERB
iajs-2287	18	9	science	science	NOUN
iajs-2287	18	10	journal	journal	PROPN
iajs-2287	18	11	homepage	homepage	NOUN
iajs-2287	18	12	:	:	PUNCT
iajs-2287	18	13	http://jih.uobaghdad.edu.iq/index.php/j/index	http://jih.uobaghdad.edu.iq/index.php/j/index	PROPN
iajs-2287	18	14	doi:10.30526/32.3.2287	doi:10.30526/32.3.2287	PROPN
iajs-2287	18	15	new	new	ADJ
iajs-2287	18	16	properties	property	NOUN
iajs-2287	18	17	of	of	ADP
iajs-2287	18	18	anti	anti	X
iajs-2287	18	19	fuzzy	fuzzy	ADJ
iajs-2287	18	20	ideals	ideal	NOUN
iajs-2287	18	21	of	of	ADP
iajs-2287	18	22	regular	regular	ADJ
iajs-2287	18	23	semigroups	semigroup	NOUN
iajs-2287	18	24	department	department	PROPN
iajs-2287	18	25	of	of	ADP
iajs-2287	18	26	mathematics	mathematics	PROPN
iajs-2287	18	27	,	,	PUNCT
iajs-2287	18	28	college	college	NOUN
iajs-2287	18	29	of	of	ADP
iajs-2287	18	30	computer	computer	NOUN
iajs-2287	18	31	science	science	NOUN
iajs-2287	18	32	and	and	CCONJ
iajs-2287	18	33	mathematics	mathematic	NOUN
iajs-2287	18	34	,	,	PUNCT
iajs-2287	18	35	university	university	NOUN
iajs-2287	18	36	of	of	ADP
iajs-2287	18	37	tikrit	tikrit	NOUN
iajs-2287	18	38	,	,	PUNCT
iajs-2287	18	39	iraq	iraq	PROPN
iajs-2287	18	40	.	.	PUNCT
iajs-2287	19	1	ahmedibrahimsalh89@gmail.com	ahmedibrahimsalh89@gmail.com	X
iajs-2287	19	2	akr-tel@tu.edu.iq	akr-tel@tu.edu.iq	ADJ
iajs-2287	19	3	article	article	NOUN
iajs-2287	19	4	history	history	NOUN
iajs-2287	19	5	:	:	PUNCT
iajs-2287	19	6	received	receive	VERB
iajs-2287	19	7	25	25	NUM
iajs-2287	19	8	march	march	NOUN
iajs-2287	19	9	2019	2019	NUM
iajs-2287	19	10	,	,	PUNCT
iajs-2287	19	11	accepted	accept	VERB
iajs-2287	19	12	14	14	NUM
iajs-2287	19	13	april	april	PROPN
iajs-2287	19	14	2019	2019	NUM
iajs-2287	19	15	,	,	PUNCT
iajs-2287	19	16	publish	publish	VERB
iajs-2287	19	17	september	september	PROPN
iajs-2287	19	18	2019	2019	NUM
iajs-2287	19	19	.	.	PUNCT
iajs-2287	20	1	mailto:ahmedibrahimsalh89@gmail.com	mailto:ahmedibrahimsalh89@gmail.com	PROPN
iajs-2287	20	2	mailto:tel@tu.edu.iq	mailto:tel@tu.edu.iq	PROPN
iajs-2287	20	3	110	110	NUM
iajs-2287	20	4	ibn	ibn	PROPN
iajs-2287	20	5	al	al	PROPN
iajs-2287	20	6	-	-	PUNCT
iajs-2287	20	7	haitham	haitham	PROPN
iajs-2287	20	8	jour	jour	X
iajs-2287	20	9	.	.	PROPN
iajs-2287	21	1	for	for	ADP
iajs-2287	21	2	pure	pure	ADJ
iajs-2287	21	3	&	&	CCONJ
iajs-2287	21	4	appl	appl	PROPN
iajs-2287	21	5	.	.	PUNCT
iajs-2287	22	1	sci	sci	PROPN
iajs-2287	22	2	.	.	PROPN
iajs-2287	22	3	32	32	NUM
iajs-2287	22	4	(	(	PUNCT
iajs-2287	22	5	3	3	NUM
iajs-2287	22	6	)	)	SYM
iajs-2287	22	7	2019	2019	NUM
iajs-2287	22	8	definition	definition	NOUN
iajs-2287	22	9	4	4	NUM
iajs-2287	22	10	[	[	X
iajs-2287	22	11	2	2	NUM
iajs-2287	22	12	]	]	PUNCT
iajs-2287	22	13	.	.	PUNCT
iajs-2287	23	1	a	a	DET
iajs-2287	23	2	fuzzy	fuzzy	ADJ
iajs-2287	23	3	sub	sub	ADJ
iajs-2287	23	4	-	-	ADJ
iajs-2287	23	5	semigroup	semigroup	ADJ
iajs-2287	23	6	ζ	ζ	NOUN
iajs-2287	23	7	of	of	ADP
iajs-2287	23	8	a	a	DET
iajs-2287	23	9	semigroup	semigroup	ADJ
iajs-2287	23	10	ℵ	ℵ	NOUN
iajs-2287	23	11	is	be	AUX
iajs-2287	23	12	said	say	VERB
iajs-2287	23	13	to	to	PART
iajs-2287	23	14	be	be	AUX
iajs-2287	23	15	a	a	DET
iajs-2287	23	16	fuzzy	fuzzy	ADJ
iajs-2287	23	17	bi	bi	ADJ
iajs-2287	23	18	ideal	ideal	NOUN
iajs-2287	23	19	in	in	ADP
iajs-2287	23	20	ℵ	ℵ	ADJ
iajs-2287	23	21	if	if	SCONJ
iajs-2287	23	22	ζ(swr)≥min{ζ(s	ζ(swr)≥min{ζ(s	PROPN
iajs-2287	23	23	)	)	PUNCT
iajs-2287	23	24	,	,	PUNCT
iajs-2287	23	25	ζ(r	ζ(r	NOUN
iajs-2287	23	26	)	)	PUNCT
iajs-2287	23	27	}	}	PUNCT
iajs-2287	23	28	,	,	PUNCT
iajs-2287	23	29	whenever	whenever	SCONJ
iajs-2287	23	30	s	s	VERB
iajs-2287	23	31	,	,	PUNCT
iajs-2287	23	32	w	w	PROPN
iajs-2287	23	33	,	,	PUNCT
iajs-2287	23	34	r	r	NOUN
iajs-2287	23	35	∈	∈	PROPN
iajs-2287	23	36	ℵ.	ℵ.	NOUN
iajs-2287	23	37	definition	definition	NOUN
iajs-2287	23	38	5	5	NUM
iajs-2287	23	39	[	[	X
iajs-2287	23	40	3	3	NUM
iajs-2287	23	41	]	]	PUNCT
iajs-2287	23	42	.	.	PUNCT
iajs-2287	24	1	let	let	VERB
iajs-2287	24	2	ζ	ζ	NOUN
iajs-2287	24	3	and	and	CCONJ
iajs-2287	24	4	φ	φ	PROPN
iajs-2287	24	5	be	be	VERB
iajs-2287	24	6	any	any	DET
iajs-2287	24	7	fuzzy	fuzzy	ADJ
iajs-2287	24	8	subsets	subset	NOUN
iajs-2287	24	9	of	of	ADP
iajs-2287	24	10	a	a	DET
iajs-2287	24	11	semigroup	semigroup	NOUN
iajs-2287	24	12	ℵ	ℵ	NOUN
iajs-2287	24	13	then	then	ADV
iajs-2287	24	14	the	the	DET
iajs-2287	24	15	product	product	NOUN
iajs-2287	24	16	ζ	ζ	NOUN
iajs-2287	24	17	∘	∘	PROPN
iajs-2287	24	18	φ	φ	PROPN
iajs-2287	24	19	is	be	AUX
iajs-2287	24	20	defined	define	VERB
iajs-2287	24	21	by	by	ADP
iajs-2287	24	22	(	(	PUNCT
iajs-2287	24	23	ζ	ζ	NOUN
iajs-2287	24	24	∘	∘	PROPN
iajs-2287	24	25	φ)(w	φ)(w	NOUN
iajs-2287	24	26	)	)	PUNCT
iajs-2287	25	1	=	=	PRON
iajs-2287	25	2	{	{	PUNCT
iajs-2287	25	3	⋁	⋁	PROPN
iajs-2287	25	4	{	{	PUNCT
iajs-2287	25	5	ζ(s	ζ(s	PROPN
iajs-2287	25	6	)	)	PUNCT
iajs-2287	25	7	∧	∧	NOUN
iajs-2287	25	8	φ(r	φ(r	NOUN
iajs-2287	25	9	)	)	PUNCT
iajs-2287	25	10	}	}	PUNCT
iajs-2287	25	11	,	,	PUNCT
iajs-2287	25	12	∃	∃	PROPN
iajs-2287	25	13	s	s	PROPN
iajs-2287	25	14	,	,	PUNCT
iajs-2287	25	15	r	r	NOUN
iajs-2287	25	16	∈	∈	PROPN
iajs-2287	25	17	ℵ	ℵ	ADP
iajs-2287	25	18	s.	s.	PROPN
iajs-2287	25	19	t	t	PROPN
iajs-2287	25	20	w	w	PROPN
iajs-2287	25	21	=	=	PROPN
iajs-2287	25	22	srw	srw	PROPN
iajs-2287	25	23	=	=	PROPN
iajs-2287	25	24	sr	sr	PROPN
iajs-2287	25	25	0	0	NUM
iajs-2287	25	26	;	;	PUNCT
iajs-2287	25	27	other	other	ADJ
iajs-2287	25	28	wise	wise	ADJ
iajs-2287	25	29	definition	definition	NOUN
iajs-2287	25	30	6	6	NUM
iajs-2287	25	31	[	[	X
iajs-2287	25	32	3	3	NUM
iajs-2287	25	33	]	]	PUNCT
iajs-2287	25	34	.	.	PUNCT
iajs-2287	26	1	let	let	VERB
iajs-2287	26	2	ζ	ζ	NOUN
iajs-2287	26	3	and	and	CCONJ
iajs-2287	26	4	φ	φ	PROPN
iajs-2287	26	5	be	be	VERB
iajs-2287	26	6	any	any	DET
iajs-2287	26	7	fuzzy	fuzzy	ADJ
iajs-2287	26	8	subsets	subset	NOUN
iajs-2287	26	9	of	of	ADP
iajs-2287	26	10	a	a	DET
iajs-2287	26	11	semigroup	semigroup	NOUN
iajs-2287	26	12	ℵ	ℵ	NOUN
iajs-2287	26	13	then	then	ADV
iajs-2287	26	14	the	the	DET
iajs-2287	26	15	anti	anti	ADJ
iajs-2287	26	16	product	product	NOUN
iajs-2287	26	17	ζ	ζ	PROPN
iajs-2287	26	18	∗	∗	NOUN
iajs-2287	26	19	φ	φ	PROPN
iajs-2287	26	20	is	be	AUX
iajs-2287	26	21	defined	define	VERB
iajs-2287	26	22	by	by	ADP
iajs-2287	26	23	(	(	PUNCT
iajs-2287	26	24	ζ	ζ	NOUN
iajs-2287	26	25	∗	∗	NOUN
iajs-2287	26	26	φ)(w	φ)(w	NOUN
iajs-2287	26	27	)	)	PUNCT
iajs-2287	26	28	=	=	PRON
iajs-2287	26	29	{	{	PUNCT
iajs-2287	26	30	⋀	⋀	PROPN
iajs-2287	26	31	{	{	PUNCT
iajs-2287	26	32	ζ(s	ζ(s	PROPN
iajs-2287	26	33	)	)	PUNCT
iajs-2287	26	34	∨	∨	NOUN
iajs-2287	26	35	φ(r	φ(r	ADJ
iajs-2287	26	36	)	)	PUNCT
iajs-2287	26	37	}	}	PUNCT
iajs-2287	26	38	,	,	PUNCT
iajs-2287	26	39	∃	∃	PROPN
iajs-2287	26	40	s	s	PROPN
iajs-2287	26	41	,	,	PUNCT
iajs-2287	26	42	r	r	NOUN
iajs-2287	26	43	∈	∈	PROPN
iajs-2287	26	44	ℵ	ℵ	ADP
iajs-2287	26	45	s.	s.	PROPN
iajs-2287	26	46	t	t	PROPN
iajs-2287	26	47	w	w	PROPN
iajs-2287	26	48	=	=	PROPN
iajs-2287	26	49	s	s	PART
iajs-2287	26	50	rw	rw	NOUN
iajs-2287	26	51	=	=	NOUN
iajs-2287	26	52	s	s	NOUN
iajs-2287	26	53	r	r	NOUN
iajs-2287	26	54	1	1	NUM
iajs-2287	26	55	;	;	PUNCT
iajs-2287	26	56	other	other	ADJ
iajs-2287	26	57	wise	wise	ADJ
iajs-2287	26	58	definition	definition	NOUN
iajs-2287	26	59	7	7	NUM
iajs-2287	26	60	[	[	X
iajs-2287	26	61	4	4	NUM
iajs-2287	26	62	]	]	PUNCT
iajs-2287	26	63	.	.	PUNCT
iajs-2287	27	1	a	a	DET
iajs-2287	27	2	fuzzy	fuzzy	ADJ
iajs-2287	27	3	subset	subset	VERB
iajs-2287	27	4	ζ	ζ	NOUN
iajs-2287	27	5	of	of	ADP
iajs-2287	27	6	a	a	DET
iajs-2287	27	7	semigroup	semigroup	ADJ
iajs-2287	27	8	ℵ	ℵ	NOUN
iajs-2287	27	9	is	be	AUX
iajs-2287	27	10	said	say	VERB
iajs-2287	27	11	to	to	PART
iajs-2287	27	12	be	be	AUX
iajs-2287	27	13	anti	anti	X
iajs-2287	27	14	fuzzy	fuzzy	ADJ
iajs-2287	27	15	sub	sub	NOUN
iajs-2287	27	16	-	-	ADJ
iajs-2287	27	17	semigroup	semigroup	ADJ
iajs-2287	27	18	of	of	ADP
iajs-2287	27	19	ℵ	ℵ	NOUN
iajs-2287	27	20	if	if	SCONJ
iajs-2287	27	21	ζ(sr	ζ(sr	NUM
iajs-2287	27	22	)	)	PUNCT
iajs-2287	27	23	≤	≤	NUM
iajs-2287	27	24	ζ(s	ζ(s	NOUN
iajs-2287	27	25	)	)	PUNCT
iajs-2287	27	26	∨	∨	NUM
iajs-2287	27	27	ζ(r	ζ(r	NOUN
iajs-2287	27	28	)	)	PUNCT
iajs-2287	27	29	,	,	PUNCT
iajs-2287	27	30	whenever	whenever	SCONJ
iajs-2287	27	31	s	s	X
iajs-2287	27	32	,	,	PUNCT
iajs-2287	27	33	r	r	NOUN
iajs-2287	27	34	∈	∈	PROPN
iajs-2287	27	35	ℵ.	ℵ.	NOUN
iajs-2287	27	36	definition	definition	NOUN
iajs-2287	27	37	8	8	NUM
iajs-2287	28	1	[	[	X
iajs-2287	28	2	4	4	NUM
iajs-2287	28	3	]	]	PUNCT
iajs-2287	28	4	.	.	PUNCT
iajs-2287	29	1	a	a	DET
iajs-2287	29	2	fuzzy	fuzzy	ADJ
iajs-2287	29	3	subset	subset	VERB
iajs-2287	29	4	ζ	ζ	NOUN
iajs-2287	29	5	of	of	ADP
iajs-2287	29	6	a	a	DET
iajs-2287	29	7	semigroup	semigroup	ADJ
iajs-2287	29	8	ℵ	ℵ	NOUN
iajs-2287	29	9	is	be	AUX
iajs-2287	29	10	said	say	VERB
iajs-2287	29	11	to	to	PART
iajs-2287	29	12	be	be	AUX
iajs-2287	29	13	anti	anti	X
iajs-2287	29	14	fuzzy	fuzzy	ADJ
iajs-2287	29	15	left	left	ADJ
iajs-2287	29	16	(	(	PUNCT
iajs-2287	29	17	right	right	ADJ
iajs-2287	29	18	)	)	PUNCT
iajs-2287	29	19	ideal	ideal	NOUN
iajs-2287	29	20	of	of	ADP
iajs-2287	29	21	ℵ	ℵ	NOUN
iajs-2287	29	22	if	if	SCONJ
iajs-2287	29	23	ζ(sr	ζ(sr	NUM
iajs-2287	29	24	)	)	PUNCT
iajs-2287	29	25	≤	≤	NUM
iajs-2287	29	26	ζ(r	ζ(r	NOUN
iajs-2287	29	27	)	)	PUNCT
iajs-2287	29	28	,	,	PUNCT
iajs-2287	29	29	(	(	PUNCT
iajs-2287	29	30	ζ(sr	ζ(sr	NOUN
iajs-2287	29	31	)	)	PUNCT
iajs-2287	29	32	≤	≤	NUM
iajs-2287	29	33	ζ(s	ζ(s	PROPN
iajs-2287	29	34	)	)	PUNCT
iajs-2287	29	35	)	)	PUNCT
iajs-2287	30	1	,	,	PUNCT
iajs-2287	30	2	whenever	whenever	SCONJ
iajs-2287	30	3	s	s	X
iajs-2287	30	4	,	,	PUNCT
iajs-2287	30	5	r	r	NOUN
iajs-2287	30	6	∈	∈	PROPN
iajs-2287	30	7	ℵ.	ℵ.	NOUN
iajs-2287	30	8	definition	definition	NOUN
iajs-2287	30	9	9	9	NUM
iajs-2287	30	10	[	[	X
iajs-2287	30	11	4	4	NUM
iajs-2287	30	12	]	]	PUNCT
iajs-2287	30	13	.	.	PUNCT
iajs-2287	31	1	a	a	DET
iajs-2287	31	2	fuzzy	fuzzy	ADJ
iajs-2287	31	3	subset	subset	VERB
iajs-2287	31	4	ζ	ζ	NOUN
iajs-2287	31	5	of	of	ADP
iajs-2287	31	6	a	a	DET
iajs-2287	31	7	semigroup	semigroup	ADJ
iajs-2287	31	8	ℵ	ℵ	NOUN
iajs-2287	31	9	is	be	AUX
iajs-2287	31	10	said	say	VERB
iajs-2287	31	11	to	to	PART
iajs-2287	31	12	be	be	AUX
iajs-2287	31	13	anti	anti	X
iajs-2287	31	14	fuzzy	fuzzy	ADJ
iajs-2287	31	15	ideal	ideal	NOUN
iajs-2287	31	16	of	of	ADP
iajs-2287	31	17	ℵ	ℵ	NOUN
iajs-2287	31	18	if	if	SCONJ
iajs-2287	31	19	it	it	PRON
iajs-2287	31	20	is	be	AUX
iajs-2287	31	21	both	both	CCONJ
iajs-2287	31	22	anti	anti	X
iajs-2287	31	23	fuzzy	fuzzy	ADJ
iajs-2287	31	24	left	leave	VERB
iajs-2287	31	25	ideal	ideal	NOUN
iajs-2287	31	26	and	and	CCONJ
iajs-2287	31	27	anti	anti	ADJ
iajs-2287	31	28	fuzzy	fuzzy	ADJ
iajs-2287	31	29	right	right	ADJ
iajs-2287	31	30	ideal	ideal	NOUN
iajs-2287	31	31	.	.	PUNCT
iajs-2287	32	1	definition	definition	NOUN
iajs-2287	32	2	10	10	NUM
iajs-2287	33	1	[	[	X
iajs-2287	33	2	4	4	NUM
iajs-2287	33	3	]	]	PUNCT
iajs-2287	33	4	.	.	PUNCT
iajs-2287	34	1	a	a	DET
iajs-2287	34	2	fuzzy	fuzzy	ADJ
iajs-2287	34	3	subset	subset	VERB
iajs-2287	34	4	ζ	ζ	NOUN
iajs-2287	34	5	of	of	ADP
iajs-2287	34	6	a	a	DET
iajs-2287	34	7	semigroup	semigroup	ADJ
iajs-2287	34	8	ℵ	ℵ	NOUN
iajs-2287	34	9	is	be	AUX
iajs-2287	34	10	said	say	VERB
iajs-2287	34	11	to	to	PART
iajs-2287	34	12	be	be	AUX
iajs-2287	34	13	anti	anti	X
iajs-2287	34	14	fuzzy	fuzzy	ADJ
iajs-2287	34	15	interior	interior	ADJ
iajs-2287	34	16	ideal	ideal	NOUN
iajs-2287	34	17	of	of	ADP
iajs-2287	34	18	ℵ	ℵ	PRON
iajs-2287	34	19	if	if	SCONJ
iajs-2287	34	20	ζ(swr	ζ(swr	NOUN
iajs-2287	34	21	)	)	PUNCT
iajs-2287	34	22	≤	≤	NOUN
iajs-2287	34	23	ζ(w	ζ(w	PROPN
iajs-2287	34	24	)	)	PUNCT
iajs-2287	34	25	,	,	PUNCT
iajs-2287	34	26	whenever	whenever	SCONJ
iajs-2287	34	27	s	s	VERB
iajs-2287	34	28	,	,	PUNCT
iajs-2287	34	29	w	w	PROPN
iajs-2287	34	30	,	,	PUNCT
iajs-2287	34	31	r	r	NOUN
iajs-2287	34	32	∈	∈	PROPN
iajs-2287	34	33	ℵ.	ℵ.	NOUN
iajs-2287	34	34	definition	definition	NOUN
iajs-2287	34	35	11	11	NUM
iajs-2287	34	36	[	[	X
iajs-2287	34	37	4	4	NUM
iajs-2287	34	38	]	]	PUNCT
iajs-2287	34	39	.	.	PUNCT
iajs-2287	35	1	a	a	DET
iajs-2287	35	2	fuzzy	fuzzy	ADJ
iajs-2287	35	3	subset	subset	VERB
iajs-2287	35	4	ζ	ζ	NOUN
iajs-2287	35	5	of	of	ADP
iajs-2287	35	6	a	a	DET
iajs-2287	35	7	semigroup	semigroup	ADJ
iajs-2287	35	8	ℵ	ℵ	NOUN
iajs-2287	35	9	is	be	AUX
iajs-2287	35	10	said	say	VERB
iajs-2287	35	11	to	to	PART
iajs-2287	35	12	be	be	AUX
iajs-2287	35	13	anti	anti	X
iajs-2287	35	14	fuzzy	fuzzy	ADJ
iajs-2287	35	15	generalized	generalized	ADJ
iajs-2287	35	16	bi	bi	NOUN
iajs-2287	35	17	-	-	NOUN
iajs-2287	35	18	ideal	ideal	NOUN
iajs-2287	35	19	of	of	ADP
iajs-2287	35	20	ℵ	ℵ	NOUN
iajs-2287	35	21	if	if	SCONJ
iajs-2287	35	22	ζ(swr	ζ(swr	NOUN
iajs-2287	35	23	)	)	PUNCT
iajs-2287	35	24	≤	≤	NUM
iajs-2287	35	25	ζ(s	ζ(s	NOUN
iajs-2287	35	26	)	)	PUNCT
iajs-2287	35	27	∨	∨	NUM
iajs-2287	35	28	ζ(r	ζ(r	NOUN
iajs-2287	35	29	)	)	PUNCT
iajs-2287	35	30	,	,	PUNCT
iajs-2287	35	31	whenever	whenever	SCONJ
iajs-2287	35	32	s	s	VERB
iajs-2287	35	33	,	,	PUNCT
iajs-2287	35	34	w	w	PROPN
iajs-2287	35	35	,	,	PUNCT
iajs-2287	35	36	r	r	NOUN
iajs-2287	35	37	∈	∈	PROPN
iajs-2287	35	38	ℵ.	ℵ.	NOUN
iajs-2287	35	39	definition	definition	NOUN
iajs-2287	35	40	12	12	NUM
iajs-2287	36	1	[	[	X
iajs-2287	36	2	4	4	NUM
iajs-2287	36	3	]	]	PUNCT
iajs-2287	36	4	.	.	PUNCT
iajs-2287	37	1	a	a	DET
iajs-2287	37	2	fuzzy	fuzzy	ADJ
iajs-2287	37	3	sub	sub	ADJ
iajs-2287	37	4	-	-	ADJ
iajs-2287	37	5	semigroup	semigroup	ADJ
iajs-2287	37	6	ζ	ζ	NOUN
iajs-2287	37	7	is	be	AUX
iajs-2287	37	8	said	say	VERB
iajs-2287	37	9	to	to	PART
iajs-2287	37	10	be	be	AUX
iajs-2287	37	11	anti	anti	X
iajs-2287	37	12	fuzzy	fuzzy	ADJ
iajs-2287	37	13	bi	bi	NOUN
iajs-2287	37	14	-	-	NOUN
iajs-2287	37	15	ideal	ideal	NOUN
iajs-2287	37	16	of	of	ADP
iajs-2287	37	17	ℵ	ℵ	NOUN
iajs-2287	37	18	if	if	SCONJ
iajs-2287	37	19	ζ(swr	ζ(swr	NOUN
iajs-2287	37	20	)	)	PUNCT
iajs-2287	37	21	≤	≤	NUM
iajs-2287	37	22	ζ(s	ζ(s	NOUN
iajs-2287	37	23	)	)	PUNCT
iajs-2287	37	24	∨	∨	NUM
iajs-2287	37	25	ζ(r	ζ(r	NOUN
iajs-2287	37	26	)	)	PUNCT
iajs-2287	37	27	whenever	whenever	SCONJ
iajs-2287	37	28	s	s	X
iajs-2287	37	29	,	,	PUNCT
iajs-2287	37	30	w	w	PROPN
iajs-2287	37	31	,	,	PUNCT
iajs-2287	37	32	r	r	NOUN
iajs-2287	37	33	∈	∈	PROPN
iajs-2287	38	1	ℵ.	ℵ.	NOUN
iajs-2287	38	2	definition	definition	NOUN
iajs-2287	38	3	13	13	NUM
iajs-2287	39	1	[	[	X
iajs-2287	39	2	5	5	NUM
iajs-2287	39	3	]	]	PUNCT
iajs-2287	39	4	.	.	PUNCT
iajs-2287	40	1	a	a	DET
iajs-2287	40	2	fuzzy	fuzzy	ADJ
iajs-2287	40	3	subset	subset	VERB
iajs-2287	40	4	ζ	ζ	NOUN
iajs-2287	40	5	of	of	ADP
iajs-2287	40	6	a	a	DET
iajs-2287	40	7	la	la	ADJ
iajs-2287	40	8	-	-	PUNCT
iajs-2287	40	9	semigroup	semigroup	ADJ
iajs-2287	40	10	ℵ	ℵ	NOUN
iajs-2287	40	11	is	be	AUX
iajs-2287	40	12	said	say	VERB
iajs-2287	40	13	to	to	PART
iajs-2287	40	14	be	be	AUX
iajs-2287	40	15	a	a	DET
iajs-2287	40	16	fuzzy	fuzzy	ADJ
iajs-2287	40	17	la	la	ADJ
iajs-2287	40	18	-	-	PUNCT
iajs-2287	40	19	sub	sub	NOUN
iajs-2287	40	20	-	-	NOUN
iajs-2287	40	21	semigroup	semigroup	ADJ
iajs-2287	40	22	if	if	SCONJ
iajs-2287	40	23	ζ(sr	ζ(sr	NUM
iajs-2287	40	24	)	)	PUNCT
iajs-2287	40	25	≥	≥	NUM
iajs-2287	40	26	ζ(s	ζ(s	NOUN
iajs-2287	40	27	)	)	PUNCT
iajs-2287	40	28	∧	∧	NOUN
iajs-2287	40	29	ζ(r	ζ(r	NOUN
iajs-2287	40	30	)	)	PUNCT
iajs-2287	40	31	,	,	PUNCT
iajs-2287	40	32	whenever	whenever	SCONJ
iajs-2287	40	33	s	s	X
iajs-2287	40	34	,	,	PUNCT
iajs-2287	40	35	r	r	NOUN
iajs-2287	40	36	∈	∈	PROPN
iajs-2287	40	37	ℵ.	ℵ.	NOUN
iajs-2287	40	38	definition	definition	NOUN
iajs-2287	40	39	14	14	NUM
iajs-2287	41	1	[	[	X
iajs-2287	41	2	5	5	NUM
iajs-2287	41	3	]	]	PUNCT
iajs-2287	41	4	.	.	PUNCT
iajs-2287	42	1	a	a	DET
iajs-2287	42	2	fuzzy	fuzzy	ADJ
iajs-2287	42	3	subset	subset	VERB
iajs-2287	42	4	ζ	ζ	NOUN
iajs-2287	42	5	of	of	ADP
iajs-2287	42	6	a	a	DET
iajs-2287	42	7	la	la	ADJ
iajs-2287	42	8	-	-	PUNCT
iajs-2287	42	9	semigroup	semigroup	ADJ
iajs-2287	42	10	ℵ	ℵ	NOUN
iajs-2287	42	11	is	be	AUX
iajs-2287	42	12	said	say	VERB
iajs-2287	42	13	to	to	PART
iajs-2287	42	14	be	be	AUX
iajs-2287	42	15	a	a	DET
iajs-2287	42	16	fuzzy	fuzzy	ADJ
iajs-2287	42	17	left(right)ideal	left(right)ideal	NOUN
iajs-2287	42	18	of	of	ADP
iajs-2287	42	19	ℵ	ℵ	NOUN
iajs-2287	42	20	if	if	SCONJ
iajs-2287	42	21	ζ(sr	ζ(sr	NUM
iajs-2287	42	22	)	)	PUNCT
iajs-2287	42	23	≥	≥	NOUN
iajs-2287	42	24	ζ(r	ζ(r	NOUN
iajs-2287	42	25	)	)	PUNCT
iajs-2287	42	26	,	,	PUNCT
iajs-2287	42	27	(	(	PUNCT
iajs-2287	42	28	ζ(sr)≥	ζ(sr)≥	X
iajs-2287	42	29	ζ(s	ζ(s	PROPN
iajs-2287	42	30	)	)	PUNCT
iajs-2287	42	31	)	)	PUNCT
iajs-2287	43	1	,	,	PUNCT
iajs-2287	43	2	whenever	whenever	SCONJ
iajs-2287	43	3	s	s	X
iajs-2287	43	4	,	,	PUNCT
iajs-2287	43	5	r	r	NOUN
iajs-2287	43	6	∈	∈	PROPN
iajs-2287	43	7	ℵ.	ℵ.	NOUN
iajs-2287	43	8	definition	definition	NOUN
iajs-2287	43	9	15	15	NUM
iajs-2287	43	10	[	[	X
iajs-2287	43	11	5	5	NUM
iajs-2287	43	12	]	]	PUNCT
iajs-2287	43	13	.	.	PUNCT
iajs-2287	44	1	a	a	DET
iajs-2287	44	2	fuzzy	fuzzy	ADJ
iajs-2287	44	3	la	la	ADJ
iajs-2287	44	4	-	-	PUNCT
iajs-2287	44	5	sub	sub	ADJ
iajs-2287	44	6	-	-	ADJ
iajs-2287	44	7	semigroup	semigroup	ADJ
iajs-2287	44	8	ζ	ζ	NOUN
iajs-2287	44	9	of	of	ADP
iajs-2287	44	10	a	a	DET
iajs-2287	44	11	la	la	ADJ
iajs-2287	44	12	-	-	PUNCT
iajs-2287	44	13	semigroup	semigroup	ADJ
iajs-2287	44	14	ℵ	ℵ	NOUN
iajs-2287	44	15	is	be	AUX
iajs-2287	44	16	said	say	VERB
iajs-2287	44	17	to	to	PART
iajs-2287	44	18	be	be	AUX
iajs-2287	44	19	a	a	DET
iajs-2287	44	20	fuzzy	fuzzy	ADJ
iajs-2287	44	21	bi	bi	ADJ
iajs-2287	44	22	-	-	ADJ
iajs-2287	44	23	ideal	ideal	ADJ
iajs-2287	44	24	111	111	NUM
iajs-2287	44	25	ibn	ibn	PROPN
iajs-2287	44	26	al	al	PROPN
iajs-2287	44	27	-	-	PUNCT
iajs-2287	44	28	haitham	haitham	PROPN
iajs-2287	44	29	jour	jour	X
iajs-2287	44	30	.	.	PROPN
iajs-2287	45	1	for	for	ADP
iajs-2287	45	2	pure	pure	ADJ
iajs-2287	45	3	&	&	CCONJ
iajs-2287	45	4	appl	appl	PROPN
iajs-2287	45	5	.	.	PUNCT
iajs-2287	46	1	sci	sci	PROPN
iajs-2287	46	2	.	.	PROPN
iajs-2287	46	3	32	32	NUM
iajs-2287	46	4	(	(	PUNCT
iajs-2287	46	5	3	3	NUM
iajs-2287	46	6	)	)	PUNCT
iajs-2287	46	7	2019	2019	NUM
iajs-2287	46	8	if	if	SCONJ
iajs-2287	46	9	ζ((sr)t	ζ((sr)t	NOUN
iajs-2287	46	10	)	)	PUNCT
iajs-2287	46	11	≥	≥	NOUN
iajs-2287	46	12	ζ(s	ζ(s	NOUN
iajs-2287	46	13	)	)	PUNCT
iajs-2287	46	14	∧	∧	NOUN
iajs-2287	46	15	ζ(t	ζ(t	PROPN
iajs-2287	46	16	)	)	PUNCT
iajs-2287	46	17	,	,	PUNCT
iajs-2287	46	18	whenever	whenever	SCONJ
iajs-2287	46	19	s	s	X
iajs-2287	46	20	,	,	PUNCT
iajs-2287	46	21	r	r	NOUN
iajs-2287	46	22	,	,	PUNCT
iajs-2287	46	23	t	t	PROPN
iajs-2287	46	24	∈	∈	PROPN
iajs-2287	47	1	ℵ.	ℵ.	PROPN
iajs-2287	47	2	definition	definition	NOUN
iajs-2287	47	3	16	16	NUM
iajs-2287	48	1	[	[	X
iajs-2287	48	2	5	5	NUM
iajs-2287	48	3	]	]	PUNCT
iajs-2287	48	4	.	.	PUNCT
iajs-2287	49	1	a	a	DET
iajs-2287	49	2	fuzzy	fuzzy	ADJ
iajs-2287	49	3	la	la	ADJ
iajs-2287	49	4	-	-	PUNCT
iajs-2287	49	5	sub	sub	ADJ
iajs-2287	49	6	-	-	ADJ
iajs-2287	49	7	semigroup	semigroup	ADJ
iajs-2287	49	8	ζ	ζ	NOUN
iajs-2287	49	9	of	of	ADP
iajs-2287	49	10	a	a	DET
iajs-2287	49	11	la	la	ADJ
iajs-2287	49	12	-	-	PUNCT
iajs-2287	49	13	semigroup	semigroup	ADJ
iajs-2287	49	14	ℵ	ℵ	NOUN
iajs-2287	49	15	is	be	AUX
iajs-2287	49	16	said	say	VERB
iajs-2287	49	17	to	to	PART
iajs-2287	49	18	be	be	AUX
iajs-2287	49	19	fuzzy	fuzzy	ADJ
iajs-2287	49	20	interior	interior	ADJ
iajs-2287	49	21	ideal	ideal	NOUN
iajs-2287	49	22	if	if	SCONJ
iajs-2287	49	23	ζ((sr)t	ζ((sr)t	NOUN
iajs-2287	49	24	)	)	PUNCT
iajs-2287	49	25	≥	≥	NOUN
iajs-2287	49	26	ζ(r	ζ(r	NOUN
iajs-2287	49	27	)	)	PUNCT
iajs-2287	49	28	,	,	PUNCT
iajs-2287	49	29	whenever	whenever	SCONJ
iajs-2287	49	30	s	s	X
iajs-2287	49	31	,	,	PUNCT
iajs-2287	49	32	r	r	NOUN
iajs-2287	49	33	,	,	PUNCT
iajs-2287	49	34	t	t	PROPN
iajs-2287	49	35	∈	∈	PROPN
iajs-2287	49	36	ℵ.	ℵ.	NOUN
iajs-2287	49	37	2	2	X
iajs-2287	49	38	.	.	PUNCT
iajs-2287	49	39	new	new	ADJ
iajs-2287	49	40	properties	property	NOUN
iajs-2287	49	41	of	of	ADP
iajs-2287	49	42	anti	anti	X
iajs-2287	49	43	fuzzy	fuzzy	ADJ
iajs-2287	49	44	ideals	ideal	NOUN
iajs-2287	49	45	of	of	ADP
iajs-2287	49	46	a	a	DET
iajs-2287	49	47	regular	regular	ADJ
iajs-2287	49	48	semigroup	semigroup	NOUN
iajs-2287	49	49	in	in	ADP
iajs-2287	49	50	this	this	DET
iajs-2287	49	51	section	section	NOUN
iajs-2287	49	52	we	we	PRON
iajs-2287	49	53	introduce	introduce	VERB
iajs-2287	49	54	some	some	DET
iajs-2287	49	55	properties	property	NOUN
iajs-2287	49	56	anti	anti	X
iajs-2287	49	57	fuzzy	fuzzy	ADJ
iajs-2287	49	58	ideal	ideal	ADJ
iajs-2287	49	59	definition	definition	NOUN
iajs-2287	49	60	17	17	NUM
iajs-2287	49	61	ℵ	ℵ	NOUN
iajs-2287	49	62	is	be	AUX
iajs-2287	49	63	said	say	VERB
iajs-2287	49	64	to	to	PART
iajs-2287	49	65	be	be	AUX
iajs-2287	49	66	a	a	DET
iajs-2287	49	67	regular	regular	ADJ
iajs-2287	49	68	semigroup	semigroup	NOUN
iajs-2287	49	69	if	if	SCONJ
iajs-2287	49	70	w	w	NOUN
iajs-2287	49	71	=	=	NOUN
iajs-2287	49	72	wzw	wzw	NOUN
iajs-2287	49	73	,	,	PUNCT
iajs-2287	49	74	whenever	whenever	SCONJ
iajs-2287	49	75	w	w	PROPN
iajs-2287	49	76	,	,	PUNCT
iajs-2287	49	77	z	z	NOUN
iajs-2287	49	78	∈	∈	PROPN
iajs-2287	49	79	ℵ	ℵ	NOUN
iajs-2287	49	80	or	or	CCONJ
iajs-2287	49	81	equivalently	equivalently	ADV
iajs-2287	49	82	w	w	PROPN
iajs-2287	49	83	∈	∈	PROPN
iajs-2287	49	84	wℵw	wℵw	NOUN
iajs-2287	49	85	.	.	PUNCT
iajs-2287	50	1	theorem	theorem	VERB
iajs-2287	50	2	18	18	NUM
iajs-2287	50	3	every	every	DET
iajs-2287	50	4	fuzzy	fuzzy	ADJ
iajs-2287	50	5	interior	interior	ADJ
iajs-2287	50	6	ideal	ideal	NOUN
iajs-2287	50	7	in	in	ADP
iajs-2287	50	8	ℵ𝑟	ℵ𝑟	X
iajs-2287	50	9	is	be	AUX
iajs-2287	50	10	idempotent	idempotent	ADJ
iajs-2287	50	11	.	.	PUNCT
iajs-2287	51	1	proof	proof	NOUN
iajs-2287	51	2	suppose	suppose	VERB
iajs-2287	51	3	that	that	SCONJ
iajs-2287	51	4	ζ	ζ	NOUN
iajs-2287	51	5	is	be	AUX
iajs-2287	51	6	a	a	DET
iajs-2287	51	7	fuzzy	fuzzy	ADJ
iajs-2287	51	8	interior	interior	ADJ
iajs-2287	51	9	ideal	ideal	NOUN
iajs-2287	51	10	of	of	ADP
iajs-2287	51	11	a	a	DET
iajs-2287	51	12	semigroup	semigroup	ADJ
iajs-2287	51	13	ℵ	ℵ	NOUN
iajs-2287	51	14	,	,	PUNCT
iajs-2287	51	15	then	then	ADV
iajs-2287	51	16	clearly	clearly	ADV
iajs-2287	51	17	ζ	ζ	ADJ
iajs-2287	51	18	∘	∘	NOUN
iajs-2287	51	19	ζ	ζ	NOUN
iajs-2287	51	20	⊆	⊆	NUM
iajs-2287	51	21	ζ	ζ	NOUN
iajs-2287	51	22	,	,	PUNCT
iajs-2287	51	23	let	let	VERB
iajs-2287	51	24	w	w	NOUN
iajs-2287	51	25	∈	∈	PROPN
iajs-2287	51	26	ℵ	ℵ	NOUN
iajs-2287	51	27	then	then	ADV
iajs-2287	51	28	∃	∃	PROPN
iajs-2287	51	29	z	z	PROPN
iajs-2287	51	30	∈	∈	PROPN
iajs-2287	51	31	ℵ	ℵ	ADP
iajs-2287	51	32	s.	s.	PROPN
iajs-2287	51	33	t	t	PROPN
iajs-2287	51	34	w	w	PROPN
iajs-2287	51	35	=	=	PUNCT
iajs-2287	51	36	wzw	wzw	VERB
iajs-2287	51	37	⟹	⟹	PROPN
iajs-2287	51	38	w	w	NOUN
iajs-2287	51	39	=	=	PRON
iajs-2287	51	40	wzw	wzw	VERB
iajs-2287	51	41	=(	=(	NOUN
iajs-2287	51	42	wz)w(z)w=(wz)w(z)wzw=((wz)w(z))(wzwzw	wz)w(z)w=(wz)w(z)wzw=((wz)w(z))(wzwzw	NOUN
iajs-2287	51	43	)	)	PUNCT
iajs-2287	51	44	(	(	PUNCT
iajs-2287	51	45	ζ	ζ	NOUN
iajs-2287	51	46	∘	∘	NOUN
iajs-2287	51	47	ζ)(w)=	ζ)(w)=	PROPN
iajs-2287	51	48	⋁	⋁	PROPN
iajs-2287	51	49	{	{	PUNCT
iajs-2287	51	50	ζ(wz)w(z	ζ(wz)w(z	NOUN
iajs-2287	51	51	)	)	PUNCT
iajs-2287	51	52	∧	∧	PROPN
iajs-2287	51	53	ζ(wz)w(zw)}w=((wz)w(z))(wzwzw	ζ(wz)w(zw)}w=((wz)w(z))(wzwzw	PROPN
iajs-2287	51	54	)	)	PUNCT
iajs-2287	51	55	≥	≥	NOUN
iajs-2287	51	56	ζ(wz)w(z	ζ(wz)w(z	NOUN
iajs-2287	51	57	)	)	PUNCT
iajs-2287	51	58	∧	∧	PROPN
iajs-2287	51	59	ζ(wz)w(zw	ζ(wz)w(zw	PROPN
iajs-2287	51	60	)	)	PUNCT
iajs-2287	51	61	≥	≥	NOUN
iajs-2287	51	62	ζ(w	ζ(w	NOUN
iajs-2287	51	63	)	)	PUNCT
iajs-2287	51	64	∧	∧	PROPN
iajs-2287	51	65	ζ(w)=ζ(w	ζ(w)=ζ(w	PROPN
iajs-2287	51	66	)	)	PUNCT
iajs-2287	51	67	this	this	PRON
iajs-2287	51	68	is	be	AUX
iajs-2287	51	69	implies	imply	VERB
iajs-2287	51	70	that	that	SCONJ
iajs-2287	51	71	ζ	ζ	NOUN
iajs-2287	51	72	∘	∘	ADJ
iajs-2287	51	73	ζ	ζ	PROPN
iajs-2287	51	74	⊇	⊇	PROPN
iajs-2287	51	75	ζ	ζ	NOUN
iajs-2287	51	76	,	,	PUNCT
iajs-2287	51	77	hence	hence	ADV
iajs-2287	51	78	ζ	ζ	NOUN
iajs-2287	51	79	∘	∘	NUM
iajs-2287	51	80	ζ	ζ	NOUN
iajs-2287	51	81	=	=	SYM
iajs-2287	51	82	ζ	ζ	NOUN
iajs-2287	51	83	.	.	PUNCT
iajs-2287	52	1	then	then	ADV
iajs-2287	52	2	ζ	ζ	NOUN
iajs-2287	52	3	is	be	AUX
iajs-2287	52	4	idempotent	idempotent	ADJ
iajs-2287	52	5	.	.	PUNCT
iajs-2287	53	1	theorem	theorem	ADJ
iajs-2287	53	2	19	19	NUM
iajs-2287	53	3	let	let	VERB
iajs-2287	53	4	ζ	ζ	NOUN
iajs-2287	53	5	be	be	AUX
iajs-2287	53	6	a	a	DET
iajs-2287	53	7	fuzzy	fuzzy	ADJ
iajs-2287	53	8	subset	subset	NOUN
iajs-2287	53	9	in	in	ADP
iajs-2287	53	10	ℵ𝑟	ℵ𝑟	NOUN
iajs-2287	53	11	then	then	ADV
iajs-2287	53	12	it	it	PRON
iajs-2287	53	13	is	be	AUX
iajs-2287	53	14	an	an	DET
iajs-2287	53	15	anti	anti	ADJ
iajs-2287	53	16	fuzzy	fuzzy	ADJ
iajs-2287	53	17	two	two	NUM
iajs-2287	53	18	sided	sided	ADJ
iajs-2287	53	19	ideal	ideal	NOUN
iajs-2287	53	20	of	of	ADP
iajs-2287	53	21	ℵ	ℵ	PROPN
iajs-2287	53	22	iff	iff	PROPN
iajs-2287	53	23	it	it	PRON
iajs-2287	53	24	is	be	AUX
iajs-2287	53	25	an	an	DET
iajs-2287	53	26	anti	anti	ADJ
iajs-2287	53	27	fuzzy	fuzzy	ADJ
iajs-2287	53	28	interior	interior	ADJ
iajs-2287	53	29	ideal	ideal	NOUN
iajs-2287	53	30	of	of	ADP
iajs-2287	53	31	ℵ.	ℵ.	PROPN
iajs-2287	53	32	proof	proof	NOUN
iajs-2287	53	33	⟹since	⟹since	NOUN
iajs-2287	53	34	ζ	ζ	NOUN
iajs-2287	53	35	be	be	VERB
iajs-2287	53	36	anti	anti	X
iajs-2287	53	37	fuzzy	fuzzy	ADJ
iajs-2287	53	38	two	two	NUM
iajs-2287	53	39	sided	sided	ADJ
iajs-2287	53	40	ideal	ideal	NOUN
iajs-2287	53	41	of	of	ADP
iajs-2287	53	42	ℵ	ℵ	NOUN
iajs-2287	53	43	,	,	PUNCT
iajs-2287	53	44	then	then	ADV
iajs-2287	53	45	obviously	obviously	ADV
iajs-2287	53	46	,	,	PUNCT
iajs-2287	53	47	ζ	ζ	NOUN
iajs-2287	53	48	is	be	AUX
iajs-2287	53	49	an	an	DET
iajs-2287	53	50	anti	anti	ADJ
iajs-2287	53	51	fuzzy	fuzzy	ADJ
iajs-2287	53	52	interior	interior	ADJ
iajs-2287	53	53	ideal	ideal	NOUN
iajs-2287	53	54	of	of	ADP
iajs-2287	53	55	ℵ.	ℵ.	PROPN
iajs-2287	53	56	⟸	⟸	PROPN
iajs-2287	53	57	suppose	suppose	VERB
iajs-2287	53	58	that	that	SCONJ
iajs-2287	53	59	ζ	ζ	NOUN
iajs-2287	53	60	is	be	AUX
iajs-2287	53	61	an	an	DET
iajs-2287	53	62	anti	anti	ADJ
iajs-2287	53	63	fuzzy	fuzzy	ADJ
iajs-2287	53	64	interior	interior	ADJ
iajs-2287	53	65	ideal	ideal	NOUN
iajs-2287	53	66	of	of	ADP
iajs-2287	53	67	ℵ.	ℵ.	PROPN
iajs-2287	53	68	let	let	VERB
iajs-2287	53	69	w	w	NOUN
iajs-2287	53	70	,	,	PUNCT
iajs-2287	53	71	z	z	PROPN
iajs-2287	53	72	∈	∈	PROPN
iajs-2287	53	73	ℵ	ℵ	NOUN
iajs-2287	53	74	,	,	PUNCT
iajs-2287	53	75	by	by	ADP
iajs-2287	53	76	by	by	ADP
iajs-2287	53	77	hypotheses	hypothesis	NOUN
iajs-2287	54	1	so	so	SCONJ
iajs-2287	54	2	∃	∃	PROPN
iajs-2287	54	3	s	s	PROPN
iajs-2287	54	4	,	,	PUNCT
iajs-2287	54	5	r	r	NOUN
iajs-2287	54	6	∈	∈	PROPN
iajs-2287	54	7	ℵ	ℵ	NOUN
iajs-2287	54	8	,	,	PUNCT
iajs-2287	54	9	s.	s.	PROPN
iajs-2287	54	10	t	t	PROPN
iajs-2287	55	1	w	w	NOUN
iajs-2287	55	2	=	=	VERB
iajs-2287	55	3	wsw	wsw	ADJ
iajs-2287	55	4	and	and	CCONJ
iajs-2287	55	5	z	z	NOUN
iajs-2287	55	6	=	=	NOUN
iajs-2287	55	7	zrz	zrz	NOUN
iajs-2287	55	8	ζ(wz)=ζ((wsw)𝑧)=ζ((ws)wswz	ζ(wz)=ζ((wsw)𝑧)=ζ((ws)wswz	VERB
iajs-2287	55	9	)	)	PUNCT
iajs-2287	55	10	)	)	PUNCT
iajs-2287	56	1	=	=	SYM
iajs-2287	56	2	ζ((ws)w(swz))≤	ζ((ws)w(swz))≤	X
iajs-2287	56	3	ζ(w	ζ(w	PROPN
iajs-2287	56	4	)	)	PUNCT
iajs-2287	56	5	,	,	PUNCT
iajs-2287	56	6	and	and	CCONJ
iajs-2287	56	7	also	also	ADV
iajs-2287	56	8	ζ(wz)=	ζ(wz)=	ADV
iajs-2287	56	9	ζ(w(zrz	ζ(w(zrz	NOUN
iajs-2287	56	10	)	)	PUNCT
iajs-2287	56	11	)	)	PUNCT
iajs-2287	57	1	=	=	SYM
iajs-2287	57	2	ζ(wzrzrz	ζ(wzrzrz	ADJ
iajs-2287	57	3	)	)	PUNCT
iajs-2287	57	4	=	=	NOUN
iajs-2287	57	5	ζ((wzr)z(rz	ζ((wzr)z(rz	NOUN
iajs-2287	57	6	)	)	PUNCT
iajs-2287	57	7	)	)	PUNCT
iajs-2287	58	1	≤	≤	NUM
iajs-2287	58	2	ζ(z	ζ(z	NOUN
iajs-2287	58	3	)	)	PUNCT
iajs-2287	58	4	,	,	PUNCT
iajs-2287	58	5	hence	hence	ADV
iajs-2287	58	6	,	,	PUNCT
iajs-2287	58	7	ζ	ζ	PROPN
iajs-2287	58	8	is	be	AUX
iajs-2287	58	9	an	an	DET
iajs-2287	58	10	anti	anti	ADJ
iajs-2287	58	11	fuzzy	fuzzy	ADJ
iajs-2287	58	12	two	two	NUM
iajs-2287	58	13	sided	sided	ADJ
iajs-2287	58	14	ideal	ideal	NOUN
iajs-2287	58	15	of	of	ADP
iajs-2287	58	16	ℵ.	ℵ.	PROPN
iajs-2287	58	17	example	example	PROPN
iajs-2287	58	18	20	20	NUM
iajs-2287	58	19	let	let	VERB
iajs-2287	58	20	ℵ	ℵ	NOUN
iajs-2287	58	21	=	=	NOUN
iajs-2287	58	22	{	{	PUNCT
iajs-2287	58	23	s	s	PROPN
iajs-2287	58	24	,	,	PUNCT
iajs-2287	58	25	r	r	NOUN
iajs-2287	58	26	,	,	PUNCT
iajs-2287	58	27	t	t	PROPN
iajs-2287	58	28	,	,	PUNCT
iajs-2287	58	29	v	v	AUX
iajs-2287	58	30	}	}	PUNCT
iajs-2287	58	31	be	be	AUX
iajs-2287	58	32	a	a	DET
iajs-2287	58	33	set	set	NOUN
iajs-2287	58	34	with	with	ADP
iajs-2287	58	35	operation	operation	NOUN
iajs-2287	58	36	as	as	SCONJ
iajs-2287	58	37	follows	follow	VERB
iajs-2287	58	38	:	:	PUNCT
iajs-2287	58	39	.	.	PUNCT
iajs-2287	59	1	s	s	PART
iajs-2287	59	2	r	r	NOUN
iajs-2287	59	3	t	t	NOUN
iajs-2287	59	4	v	v	NOUN
iajs-2287	59	5	s	s	X
iajs-2287	59	6	s	s	NOUN
iajs-2287	59	7	s	s	X
iajs-2287	59	8	s	s	NOUN
iajs-2287	59	9	s	s	NOUN
iajs-2287	59	10	r	r	NOUN
iajs-2287	59	11	s	s	NOUN
iajs-2287	59	12	s	s	NOUN
iajs-2287	59	13	s	s	X
iajs-2287	59	14	s	s	X
iajs-2287	59	15	s	s	X
iajs-2287	59	16	s	s	NOUN
iajs-2287	59	17	s	s	NOUN
iajs-2287	59	18	r	r	NOUN
iajs-2287	59	19	s	s	NOUN
iajs-2287	59	20	v	v	NOUN
iajs-2287	59	21	s	s	NOUN
iajs-2287	59	22	s	s	NOUN
iajs-2287	59	23	r	r	NOUN
iajs-2287	59	24	r	r	NOUN
iajs-2287	59	25	112	112	NUM
iajs-2287	59	26	ibn	ibn	PROPN
iajs-2287	59	27	al	al	PROPN
iajs-2287	59	28	-	-	PUNCT
iajs-2287	59	29	haitham	haitham	PROPN
iajs-2287	59	30	jour	jour	X
iajs-2287	59	31	.	.	PROPN
iajs-2287	60	1	for	for	ADP
iajs-2287	60	2	pure	pure	ADJ
iajs-2287	60	3	&	&	CCONJ
iajs-2287	60	4	appl	appl	PROPN
iajs-2287	60	5	.	.	PUNCT
iajs-2287	61	1	sci	sci	PROPN
iajs-2287	61	2	.	.	PROPN
iajs-2287	61	3	32	32	NUM
iajs-2287	61	4	(	(	PUNCT
iajs-2287	61	5	3	3	NUM
iajs-2287	61	6	)	)	PUNCT
iajs-2287	61	7	2019	2019	NUM
iajs-2287	61	8	then	then	ADV
iajs-2287	61	9	we	we	PRON
iajs-2287	61	10	can	can	AUX
iajs-2287	61	11	easily	easily	ADV
iajs-2287	61	12	see	see	VERB
iajs-2287	61	13	that	that	PRON
iajs-2287	61	14	(	(	PUNCT
iajs-2287	61	15	ℵ	ℵ	NOUN
iajs-2287	61	16	,	,	PUNCT
iajs-2287	61	17	.	.	PUNCT
iajs-2287	61	18	)	)	PUNCT
iajs-2287	61	19	is	be	AUX
iajs-2287	61	20	not	not	PART
iajs-2287	61	21	a	a	DET
iajs-2287	61	22	regular	regular	ADJ
iajs-2287	61	23	semigroup	semigroup	NOUN
iajs-2287	61	24	.	.	PUNCT
iajs-2287	62	1	define	define	VERB
iajs-2287	62	2	the	the	DET
iajs-2287	62	3	fuzzy	fuzzy	ADJ
iajs-2287	62	4	subset	subset	VERB
iajs-2287	62	5	ζ	ζ	NOUN
iajs-2287	62	6	of	of	ADP
iajs-2287	62	7	ℵ	ℵ	NOUN
iajs-2287	62	8	as	as	ADP
iajs-2287	62	9	ζ(s	ζ(s	NOUN
iajs-2287	62	10	)	)	PUNCT
iajs-2287	62	11	=	=	SYM
iajs-2287	62	12	0.3	0.3	NUM
iajs-2287	62	13	,	,	PUNCT
iajs-2287	62	14	ζ(r	ζ(r	NOUN
iajs-2287	62	15	)	)	PUNCT
iajs-2287	62	16	=	=	SYM
iajs-2287	62	17	0.9	0.9	NUM
iajs-2287	62	18	,	,	PUNCT
iajs-2287	62	19	ζ(t	ζ(t	PROPN
iajs-2287	62	20	)	)	PUNCT
iajs-2287	62	21	=	=	SYM
iajs-2287	62	22	0.5	0.5	NUM
iajs-2287	62	23	,	,	PUNCT
iajs-2287	62	24	ζ(v	ζ(v	PROPN
iajs-2287	62	25	)	)	PUNCT
iajs-2287	62	26	=	=	PUNCT
iajs-2287	63	1	0.7	0.7	NUM
iajs-2287	63	2	.	.	PUNCT
iajs-2287	64	1	then	then	ADV
iajs-2287	64	2	clearly	clearly	ADV
iajs-2287	64	3	,	,	PUNCT
iajs-2287	64	4	ζ	ζ	PROPN
iajs-2287	64	5	is	be	AUX
iajs-2287	64	6	anti	anti	X
iajs-2287	64	7	fuzzy	fuzzy	ADJ
iajs-2287	64	8	interior	interior	ADJ
iajs-2287	64	9	ideal	ideal	NOUN
iajs-2287	64	10	of	of	ADP
iajs-2287	64	11	ℵ	ℵ	NOUN
iajs-2287	65	1	but	but	CCONJ
iajs-2287	65	2	it	it	PRON
iajs-2287	65	3	is	be	AUX
iajs-2287	65	4	not	not	PART
iajs-2287	65	5	an	an	DET
iajs-2287	65	6	anti	anti	ADJ
iajs-2287	65	7	fuzzy	fuzzy	ADJ
iajs-2287	65	8	two	two	NUM
iajs-2287	65	9	sided	sided	ADJ
iajs-2287	65	10	ideal	ideal	NOUN
iajs-2287	65	11	of	of	ADP
iajs-2287	65	12	ℵ	ℵ	NOUN
iajs-2287	65	13	,	,	PUNCT
iajs-2287	65	14	since	since	SCONJ
iajs-2287	65	15	{	{	PUNCT
iajs-2287	65	16	s	s	X
iajs-2287	65	17	,	,	PUNCT
iajs-2287	65	18	r	r	NOUN
iajs-2287	65	19	}	}	PUNCT
iajs-2287	65	20	is	be	AUX
iajs-2287	65	21	not	not	PART
iajs-2287	65	22	a	a	DET
iajs-2287	65	23	two	two	NUM
iajs-2287	65	24	sided	sided	ADJ
iajs-2287	65	25	ideal	ideal	NOUN
iajs-2287	65	26	of	of	ADP
iajs-2287	65	27	ℵ.	ℵ.	PROPN
iajs-2287	65	28	proposition	proposition	NOUN
iajs-2287	65	29	21	21	NUM
iajs-2287	65	30	in	in	ADP
iajs-2287	65	31	regular	regular	ADJ
iajs-2287	65	32	semigroup	semigroup	ADJ
iajs-2287	65	33	ℵ	ℵ	NOUN
iajs-2287	65	34	,	,	PUNCT
iajs-2287	65	35	then	then	ADV
iajs-2287	65	36	i	i	PRON
iajs-2287	65	37	every	every	DET
iajs-2287	65	38	anti	anti	X
iajs-2287	65	39	fuzzy	fuzzy	ADJ
iajs-2287	65	40	right	right	ADJ
iajs-2287	65	41	ideal	ideal	NOUN
iajs-2287	65	42	is	be	AUX
iajs-2287	65	43	idempotent	idempotent	ADJ
iajs-2287	65	44	.	.	PUNCT
iajs-2287	66	1	ii	ii	NOUN
iajs-2287	66	2	every	every	DET
iajs-2287	66	3	anti	anti	ADJ
iajs-2287	66	4	fuzzy	fuzzy	ADJ
iajs-2287	66	5	interior	interior	ADJ
iajs-2287	66	6	ideal	ideal	NOUN
iajs-2287	66	7	is	be	AUX
iajs-2287	66	8	idempotent	idempotent	ADJ
iajs-2287	66	9	.	.	PUNCT
iajs-2287	67	1	proof	proof	NOUN
iajs-2287	67	2	isuppose	isuppose	VERB
iajs-2287	67	3	that	that	SCONJ
iajs-2287	67	4	ζ	ζ	NOUN
iajs-2287	67	5	is	be	AUX
iajs-2287	67	6	an	an	DET
iajs-2287	67	7	anti	anti	ADJ
iajs-2287	67	8	fuzzy	fuzzy	ADJ
iajs-2287	67	9	right	right	ADJ
iajs-2287	67	10	ideal	ideal	NOUN
iajs-2287	67	11	of	of	ADP
iajs-2287	67	12	semigroup	semigroup	ADJ
iajs-2287	67	13	ℵ	ℵ	NOUN
iajs-2287	67	14	,	,	PUNCT
iajs-2287	67	15	then	then	ADV
iajs-2287	67	16	clearly	clearly	ADV
iajs-2287	67	17	ζ	ζ	ADJ
iajs-2287	67	18	⊆	⊆	NUM
iajs-2287	67	19	ζ	ζ	NOUN
iajs-2287	67	20	∗	∗	NOUN
iajs-2287	67	21	ζ	ζ	NOUN
iajs-2287	67	22	.	.	PUNCT
iajs-2287	68	1	since	since	SCONJ
iajs-2287	68	2	ℵ	ℵ	NOUN
iajs-2287	68	3	is	be	AUX
iajs-2287	68	4	a	a	DET
iajs-2287	68	5	regular	regular	ADJ
iajs-2287	68	6	so	so	ADV
iajs-2287	68	7	whenever	whenever	SCONJ
iajs-2287	68	8	w	w	PROPN
iajs-2287	68	9	∈	∈	PROPN
iajs-2287	68	10	ℵ	ℵ	NOUN
iajs-2287	68	11	,	,	PUNCT
iajs-2287	68	12	∃	∃	PROPN
iajs-2287	68	13	z	z	PROPN
iajs-2287	68	14	∈	∈	PROPN
iajs-2287	68	15	ℵ	ℵ	NOUN
iajs-2287	68	16	,	,	PUNCT
iajs-2287	68	17	s.t	s.t	PROPN
iajs-2287	68	18	w	w	PROPN
iajs-2287	68	19	=	=	PROPN
iajs-2287	68	20	wzw	wzw	NOUN
iajs-2287	68	21	,	,	PUNCT
iajs-2287	68	22	so	so	CCONJ
iajs-2287	68	23	(	(	PUNCT
iajs-2287	68	24	ζ	ζ	NOUN
iajs-2287	68	25	∗	∗	NOUN
iajs-2287	68	26	ζ)(w)=⋀	ζ)(w)=⋀	X
iajs-2287	68	27	{	{	PUNCT
iajs-2287	68	28	ζ(wz	ζ(wz	NOUN
iajs-2287	68	29	)	)	PUNCT
iajs-2287	68	30	∨	∨	NOUN
iajs-2287	68	31	ζ(wzw)}w	ζ(wzw)}w	NOUN
iajs-2287	68	32	=	=	SYM
iajs-2287	68	33	wzw	wzw	NOUN
iajs-2287	68	34	=	=	NOUN
iajs-2287	68	35	wzwzw	wzwzw	NOUN
iajs-2287	68	36	=	=	SYM
iajs-2287	68	37	⋀	⋀	PROPN
iajs-2287	68	38	{	{	PUNCT
iajs-2287	68	39	ζ(wz	ζ(wz	NOUN
iajs-2287	68	40	)	)	PUNCT
iajs-2287	68	41	∨	∨	NOUN
iajs-2287	68	42	ζ(wt)}w	ζ(wt)}w	NOUN
iajs-2287	68	43	=(	=(	NOUN
iajs-2287	68	44	wz)(wzw	wz)(wzw	NOUN
iajs-2287	68	45	)	)	PUNCT
iajs-2287	68	46	where	where	SCONJ
iajs-2287	68	47	t	t	PROPN
iajs-2287	68	48	=	=	SYM
iajs-2287	68	49	zw	zw	PROPN
iajs-2287	68	50	≤	≤	PROPN
iajs-2287	68	51	ζ(wz	ζ(wz	NOUN
iajs-2287	68	52	)	)	PUNCT
iajs-2287	68	53	∨	∨	NUM
iajs-2287	68	54	ζ(wt)≤	ζ(wt)≤	PROPN
iajs-2287	68	55	ζ(w	ζ(w	PROPN
iajs-2287	68	56	)	)	PUNCT
iajs-2287	68	57	∨	∨	PROPN
iajs-2287	68	58	ζ(w)=ζ(w	ζ(w)=ζ(w	PROPN
iajs-2287	68	59	)	)	PUNCT
iajs-2287	68	60	this	this	PRON
iajs-2287	68	61	implies	imply	VERB
iajs-2287	68	62	that	that	SCONJ
iajs-2287	68	63	ζ	ζ	NOUN
iajs-2287	68	64	∗	∗	NOUN
iajs-2287	68	65	ζ	ζ	NOUN
iajs-2287	68	66	⊆	⊆	NUM
iajs-2287	68	67	ζ	ζ	NOUN
iajs-2287	68	68	.	.	PUNCT
iajs-2287	69	1	hence	hence	ADV
iajs-2287	69	2	ζ	ζ	NOUN
iajs-2287	69	3	∗	∗	NOUN
iajs-2287	69	4	ζ	ζ	NOUN
iajs-2287	69	5	=	=	SYM
iajs-2287	69	6	ζ	ζ	NOUN
iajs-2287	69	7	.	.	PUNCT
iajs-2287	69	8	iisuppose	iisuppose	VERB
iajs-2287	69	9	that	that	SCONJ
iajs-2287	69	10	ζ	ζ	NOUN
iajs-2287	69	11	is	be	AUX
iajs-2287	69	12	an	an	DET
iajs-2287	69	13	anti	anti	ADJ
iajs-2287	69	14	fuzzy	fuzzy	ADJ
iajs-2287	69	15	interior	interior	ADJ
iajs-2287	69	16	ideal	ideal	NOUN
iajs-2287	69	17	of	of	ADP
iajs-2287	69	18	semigroup	semigroup	ADJ
iajs-2287	69	19	ℵ	ℵ	NOUN
iajs-2287	69	20	,	,	PUNCT
iajs-2287	69	21	then	then	ADV
iajs-2287	69	22	clearly	clearly	ADV
iajs-2287	69	23	ζ	ζ	ADJ
iajs-2287	69	24	⊆	⊆	NUM
iajs-2287	69	25	ζ	ζ	NOUN
iajs-2287	69	26	∗	∗	NOUN
iajs-2287	69	27	ζ	ζ	NOUN
iajs-2287	69	28	.	.	PUNCT
iajs-2287	70	1	since	since	SCONJ
iajs-2287	70	2	ℵ	ℵ	NOUN
iajs-2287	70	3	is	be	AUX
iajs-2287	70	4	a	a	DET
iajs-2287	70	5	regular	regular	ADJ
iajs-2287	70	6	so	so	ADV
iajs-2287	70	7	whenever	whenever	SCONJ
iajs-2287	70	8	w	w	PROPN
iajs-2287	70	9	∈	∈	PROPN
iajs-2287	70	10	ℵ	ℵ	NOUN
iajs-2287	70	11	,	,	PUNCT
iajs-2287	70	12	∃	∃	PROPN
iajs-2287	70	13	z∈	z∈	PROPN
iajs-2287	70	14	ℵ	ℵ	PROPN
iajs-2287	70	15	,	,	PUNCT
iajs-2287	70	16	s.t	s.t	PROPN
iajs-2287	70	17	w	w	PROPN
iajs-2287	70	18	=	=	PROPN
iajs-2287	70	19	wzw	wzw	NOUN
iajs-2287	70	20	,	,	PUNCT
iajs-2287	70	21	so	so	SCONJ
iajs-2287	70	22	w	w	NOUN
iajs-2287	70	23	=	=	VERB
iajs-2287	70	24	wzw	wzw	NOUN
iajs-2287	70	25	=	=	NOUN
iajs-2287	70	26	wzwzw=((wz)w(z	wzwzw=((wz)w(z	NOUN
iajs-2287	70	27	)	)	PUNCT
iajs-2287	70	28	)	)	PUNCT
iajs-2287	71	1	(	(	PUNCT
iajs-2287	71	2	(	(	PUNCT
iajs-2287	71	3	wz)w	wz)w	PROPN
iajs-2287	71	4	(	(	PUNCT
iajs-2287	71	5	z	z	NOUN
iajs-2287	71	6	w	w	PROPN
iajs-2287	71	7	)	)	PUNCT
iajs-2287	71	8	)	)	PUNCT
iajs-2287	71	9	(	(	PUNCT
iajs-2287	71	10	ζ	ζ	NOUN
iajs-2287	71	11	∗	∗	X
iajs-2287	71	12	ζ)(w	ζ)(w	NOUN
iajs-2287	71	13	)	)	PUNCT
iajs-2287	72	1	=	=	NOUN
iajs-2287	72	2	⋀	⋀	PROPN
iajs-2287	72	3	{	{	PUNCT
iajs-2287	72	4	ζ(wz)w(z	ζ(wz)w(z	NOUN
iajs-2287	72	5	)	)	PUNCT
iajs-2287	72	6	)	)	PUNCT
iajs-2287	72	7	∨	∨	NUM
iajs-2287	72	8	ζ((wz)w(zw))}w=((wz)w(z	ζ((wz)w(zw))}w=((wz)w(z	PROPN
iajs-2287	72	9	)	)	PUNCT
iajs-2287	72	10	)	)	PUNCT
iajs-2287	72	11	(	(	PUNCT
iajs-2287	72	12	(	(	PUNCT
iajs-2287	72	13	wz)w(zw	wz)w(zw	NUM
iajs-2287	72	14	)	)	PUNCT
iajs-2287	72	15	)	)	PUNCT
iajs-2287	72	16	≤	≤	NUM
iajs-2287	72	17	ζ(wz)w(z	ζ(wz)w(z	NOUN
iajs-2287	72	18	)	)	PUNCT
iajs-2287	72	19	)	)	PUNCT
iajs-2287	72	20	∨	∨	NUM
iajs-2287	72	21	ζ((wz)w(zw))≤	ζ((wz)w(zw))≤	X
iajs-2287	72	22	ζ(w	ζ(w	PROPN
iajs-2287	72	23	)	)	PUNCT
iajs-2287	72	24	∨	∨	PROPN
iajs-2287	72	25	ζ(w)=ζ(w	ζ(w)=ζ(w	PROPN
iajs-2287	72	26	)	)	PUNCT
iajs-2287	72	27	.	.	PUNCT
iajs-2287	73	1	this	this	PRON
iajs-2287	73	2	implies	imply	VERB
iajs-2287	73	3	that	that	SCONJ
iajs-2287	73	4	ζ	ζ	NOUN
iajs-2287	73	5	∗	∗	NOUN
iajs-2287	73	6	ζ	ζ	NOUN
iajs-2287	73	7	⊆	⊆	NUM
iajs-2287	73	8	ζ	ζ	NOUN
iajs-2287	73	9	.	.	PUNCT
iajs-2287	74	1	hence	hence	ADV
iajs-2287	74	2	ζ	ζ	NOUN
iajs-2287	74	3	∗	∗	NOUN
iajs-2287	74	4	ζ	ζ	NOUN
iajs-2287	74	5	=	=	SYM
iajs-2287	74	6	ζ	ζ	NOUN
iajs-2287	74	7	.	.	PUNCT
iajs-2287	74	8	proposition	proposition	NOUN
iajs-2287	74	9	22	22	NUM
iajs-2287	75	1	[	[	X
iajs-2287	75	2	3	3	NUM
iajs-2287	75	3	]	]	PUNCT
iajs-2287	75	4	.	.	PUNCT
iajs-2287	76	1	let	let	VERB
iajs-2287	76	2	ζ	ζ	NOUN
iajs-2287	76	3	be	be	AUX
iajs-2287	76	4	an	an	DET
iajs-2287	76	5	anti	anti	ADJ
iajs-2287	76	6	fuzzy	fuzzy	ADJ
iajs-2287	76	7	right	right	ADJ
iajs-2287	76	8	ideal	ideal	NOUN
iajs-2287	76	9	and	and	CCONJ
iajs-2287	76	10	μ	μ	NOUN
iajs-2287	76	11	an	an	DET
iajs-2287	76	12	anti	anti	ADJ
iajs-2287	76	13	fuzzy	fuzzy	ADJ
iajs-2287	76	14	left	leave	VERB
iajs-2287	76	15	ideal	ideal	NOUN
iajs-2287	76	16	of	of	ADP
iajs-2287	76	17	a	a	DET
iajs-2287	76	18	semigroup	semigroup	NOUN
iajs-2287	76	19	ℵ.	ℵ.	PROPN
iajs-2287	77	1	then	then	ADV
iajs-2287	77	2	ζ	ζ	NOUN
iajs-2287	77	3	∗	∗	PROPN
iajs-2287	77	4	μ	μ	PROPN
iajs-2287	77	5	⊇	⊇	PROPN
iajs-2287	77	6	ζ	ζ	PROPN
iajs-2287	77	7	∪	∪	ADP
iajs-2287	77	8	μ	μ	NOUN
iajs-2287	77	9	.	.	PUNCT
iajs-2287	78	1	it	it	PRON
iajs-2287	78	2	is	be	AUX
iajs-2287	78	3	clear	clear	ADJ
iajs-2287	78	4	that	that	SCONJ
iajs-2287	78	5	from	from	ADP
iajs-2287	78	6	proposition	proposition	NOUN
iajs-2287	78	7	22	22	NUM
iajs-2287	78	8	.	.	PUNCT
iajs-2287	79	1	ζ	ζ	NOUN
iajs-2287	79	2	∗	∗	PROPN
iajs-2287	79	3	μ	μ	PROPN
iajs-2287	79	4	⊇	⊇	PROPN
iajs-2287	79	5	ζ	ζ	PROPN
iajs-2287	79	6	∪	∪	ADP
iajs-2287	79	7	μ	μ	PROPN
iajs-2287	79	8	,	,	PUNCT
iajs-2287	79	9	but	but	CCONJ
iajs-2287	79	10	the	the	DET
iajs-2287	79	11	converse	converse	NOUN
iajs-2287	79	12	needs	need	VERB
iajs-2287	79	13	not	not	PART
iajs-2287	79	14	at	at	ADV
iajs-2287	79	15	all	all	ADV
iajs-2287	79	16	be	be	AUX
iajs-2287	79	17	true	true	ADJ
iajs-2287	79	18	.	.	PUNCT
iajs-2287	80	1	consider	consider	VERB
iajs-2287	80	2	the	the	DET
iajs-2287	80	3	following	follow	VERB
iajs-2287	80	4	example	example	NOUN
iajs-2287	80	5	,	,	PUNCT
iajs-2287	80	6	example	example	NOUN
iajs-2287	80	7	23	23	NUM
iajs-2287	80	8	consider	consider	VERB
iajs-2287	80	9	the	the	DET
iajs-2287	80	10	semigroup	semigroup	ADJ
iajs-2287	80	11	ℵ=	ℵ=	NOUN
iajs-2287	80	12	{	{	PUNCT
iajs-2287	80	13	s	s	NOUN
iajs-2287	80	14	,	,	PUNCT
iajs-2287	80	15	r	r	NOUN
iajs-2287	80	16	,	,	PUNCT
iajs-2287	80	17	t	t	PROPN
iajs-2287	80	18	,	,	PUNCT
iajs-2287	80	19	v	v	NOUN
iajs-2287	80	20	}	}	PUNCT
iajs-2287	80	21	with	with	ADP
iajs-2287	80	22	the	the	DET
iajs-2287	80	23	operation	operation	NOUN
iajs-2287	80	24	as	as	SCONJ
iajs-2287	80	25	follows	follow	VERB
iajs-2287	80	26	:	:	PUNCT
iajs-2287	80	27	.	.	PUNCT
iajs-2287	81	1	s	s	PART
iajs-2287	81	2	r	r	NOUN
iajs-2287	81	3	t	t	NOUN
iajs-2287	81	4	v	v	NOUN
iajs-2287	81	5	s	s	X
iajs-2287	81	6	s	s	NOUN
iajs-2287	81	7	s	s	X
iajs-2287	81	8	s	s	NOUN
iajs-2287	81	9	s	s	NOUN
iajs-2287	81	10	r	r	NOUN
iajs-2287	81	11	s	s	NOUN
iajs-2287	81	12	s	s	NOUN
iajs-2287	81	13	s	s	X
iajs-2287	81	14	s	s	X
iajs-2287	81	15	t	t	NOUN
iajs-2287	81	16	s	s	NOUN
iajs-2287	81	17	s	s	NOUN
iajs-2287	81	18	r	r	NOUN
iajs-2287	81	19	s	s	NOUN
iajs-2287	81	20	v	v	NOUN
iajs-2287	81	21	s	s	NOUN
iajs-2287	81	22	s	s	NOUN
iajs-2287	81	23	r	r	NOUN
iajs-2287	81	24	r	r	NOUN
iajs-2287	81	25	113	113	NUM
iajs-2287	81	26	ibn	ibn	PROPN
iajs-2287	81	27	al	al	PROPN
iajs-2287	81	28	-	-	PUNCT
iajs-2287	81	29	haitham	haitham	PROPN
iajs-2287	81	30	jour	jour	X
iajs-2287	81	31	.	.	PROPN
iajs-2287	82	1	for	for	ADP
iajs-2287	82	2	pure	pure	ADJ
iajs-2287	82	3	&	&	CCONJ
iajs-2287	82	4	appl	appl	PROPN
iajs-2287	82	5	.	.	PUNCT
iajs-2287	83	1	sci	sci	PROPN
iajs-2287	83	2	.	.	PROPN
iajs-2287	83	3	32	32	NUM
iajs-2287	83	4	(	(	PUNCT
iajs-2287	83	5	3	3	NUM
iajs-2287	83	6	)	)	PUNCT
iajs-2287	83	7	2019	2019	NUM
iajs-2287	83	8	the	the	DET
iajs-2287	83	9	ideals	ideal	NOUN
iajs-2287	83	10	of	of	ADP
iajs-2287	83	11	ℵ	ℵ	NOUN
iajs-2287	83	12	are	be	AUX
iajs-2287	83	13	{	{	PUNCT
iajs-2287	83	14	s	s	X
iajs-2287	83	15	}	}	PUNCT
iajs-2287	83	16	,	,	PUNCT
iajs-2287	83	17	{	{	PUNCT
iajs-2287	83	18	s	s	X
iajs-2287	83	19	,	,	PUNCT
iajs-2287	83	20	r	r	NOUN
iajs-2287	83	21	}	}	PUNCT
iajs-2287	83	22	,	,	PUNCT
iajs-2287	83	23	{	{	PUNCT
iajs-2287	83	24	s	s	X
iajs-2287	83	25	,	,	PUNCT
iajs-2287	83	26	r	r	NOUN
iajs-2287	83	27	,	,	PUNCT
iajs-2287	83	28	t	t	PROPN
iajs-2287	83	29	}	}	PUNCT
iajs-2287	83	30	and	and	CCONJ
iajs-2287	83	31	{	{	PUNCT
iajs-2287	83	32	s	s	X
iajs-2287	83	33	,	,	PUNCT
iajs-2287	83	34	r	r	NOUN
iajs-2287	83	35	,	,	PUNCT
iajs-2287	83	36	t	t	PROPN
iajs-2287	83	37	,	,	PUNCT
iajs-2287	83	38	v	v	NOUN
iajs-2287	83	39	}	}	PUNCT
iajs-2287	83	40	let	let	VERB
iajs-2287	83	41	us	we	PRON
iajs-2287	83	42	define	define	VERB
iajs-2287	83	43	two	two	NUM
iajs-2287	83	44	fuzzy	fuzzy	ADJ
iajs-2287	83	45	subsets	subset	NOUN
iajs-2287	83	46	ζ	ζ	NOUN
iajs-2287	83	47	and	and	CCONJ
iajs-2287	83	48	μ	μ	NOUN
iajs-2287	83	49	of	of	ADP
iajs-2287	83	50	ℵ	ℵ	PROPN
iajs-2287	83	51	as	as	SCONJ
iajs-2287	83	52	follows	follow	VERB
iajs-2287	83	53	ζ(s)=0.5	ζ(s)=0.5	NOUN
iajs-2287	83	54	,	,	PUNCT
iajs-2287	83	55	ζ(r)=0.6	ζ(r)=0.6	PROPN
iajs-2287	83	56	,	,	PUNCT
iajs-2287	83	57	ζ(t)=0.7	ζ(t)=0.7	PROPN
iajs-2287	83	58	,	,	PUNCT
iajs-2287	83	59	ζ(v)=0.8	ζ(v)=0.8	PROPN
iajs-2287	83	60	.	.	PUNCT
iajs-2287	84	1	μ(s)=0.6	μ(s)=0.6	ADP
iajs-2287	84	2	,	,	PUNCT
iajs-2287	84	3	μ(r)=0.7	μ(r)=0.7	PROPN
iajs-2287	84	4	,	,	PUNCT
iajs-2287	84	5	μ(t)=0.8	μ(t)=0.8	PROPN
iajs-2287	84	6	,	,	PUNCT
iajs-2287	84	7	μ(v)=0.9	μ(v)=0.9	PROPN
iajs-2287	84	8	.	.	PUNCT
iajs-2287	85	1	then	then	ADV
iajs-2287	85	2	ζ	ζ	PROPN
iajs-2287	85	3	and	and	CCONJ
iajs-2287	85	4	μ	μ	PROPN
iajs-2287	85	5	are	be	AUX
iajs-2287	85	6	an	an	DET
iajs-2287	85	7	anti	anti	ADJ
iajs-2287	85	8	fuzzy	fuzzy	ADJ
iajs-2287	85	9	ideal	ideal	NOUN
iajs-2287	85	10	of	of	ADP
iajs-2287	85	11	ℵ	ℵ	NOUN
iajs-2287	85	12	,	,	PUNCT
iajs-2287	85	13	and	and	CCONJ
iajs-2287	85	14	we	we	PRON
iajs-2287	85	15	note	note	VERB
iajs-2287	85	16	that	that	SCONJ
iajs-2287	85	17	:	:	PUNCT
iajs-2287	85	18	(	(	PUNCT
iajs-2287	85	19	ζ	ζ	NOUN
iajs-2287	85	20	∗	∗	NOUN
iajs-2287	85	21	μ)(r	μ)(r	NUM
iajs-2287	85	22	)	)	PUNCT
iajs-2287	86	1	=	=	SYM
iajs-2287	86	2	⋀	⋀	PROPN
iajs-2287	86	3	{	{	PUNCT
iajs-2287	86	4	ζ(x	ζ(x	NOUN
iajs-2287	86	5	)	)	PUNCT
iajs-2287	86	6	∨	∨	NUM
iajs-2287	86	7	μ(y)}r	μ(y)}r	NOUN
iajs-2287	86	8	=	=	SYM
iajs-2287	86	9	xy	xy	PROPN
iajs-2287	87	1	=	=	SYM
iajs-2287	87	2	⋀	⋀	PROPN
iajs-2287	87	3	{	{	PUNCT
iajs-2287	87	4	0.8	0.8	NUM
iajs-2287	87	5	,	,	PUNCT
iajs-2287	87	6	0.8	0.8	NUM
iajs-2287	87	7	,	,	PUNCT
iajs-2287	87	8	0.9	0.9	NUM
iajs-2287	87	9	}	}	PUNCT
iajs-2287	87	10	=	=	NUM
iajs-2287	87	11	0.8	0.8	NUM
iajs-2287	87	12	≥	≥	NUM
iajs-2287	87	13	(	(	PUNCT
iajs-2287	87	14	ζ	ζ	NOUN
iajs-2287	87	15	∪	∪	ADJ
iajs-2287	87	16	μ)(r	μ)(r	NUM
iajs-2287	87	17	)	)	PUNCT
iajs-2287	87	18	=	=	PUNCT
iajs-2287	87	19	0.7	0.7	NUM
iajs-2287	87	20	.	.	PUNCT
iajs-2287	87	21	to	to	PART
iajs-2287	87	22	consider	consider	VERB
iajs-2287	87	23	the	the	DET
iajs-2287	87	24	converse	converse	NOUN
iajs-2287	87	25	of	of	ADP
iajs-2287	87	26	proposition	proposition	NOUN
iajs-2287	87	27	22	22	NUM
iajs-2287	87	28	,	,	PUNCT
iajs-2287	87	29	we	we	PRON
iajs-2287	87	30	need	need	VERB
iajs-2287	87	31	to	to	PART
iajs-2287	87	32	strengthen	strengthen	VERB
iajs-2287	87	33	the	the	DET
iajs-2287	87	34	condition	condition	NOUN
iajs-2287	87	35	of	of	ADP
iajs-2287	87	36	semigroupℵ.	semigroupℵ.	NOUN
iajs-2287	87	37	theorem	theorem	VERB
iajs-2287	87	38	24	24	NUM
iajs-2287	87	39	if	if	SCONJ
iajs-2287	87	40	ζ	ζ	PROPN
iajs-2287	87	41	,	,	PUNCT
iajs-2287	87	42	μ	μ	PROPN
iajs-2287	87	43	are	be	AUX
iajs-2287	87	44	any	any	DET
iajs-2287	87	45	anti	anti	ADJ
iajs-2287	87	46	fuzzy	fuzzy	ADJ
iajs-2287	87	47	two	two	NUM
iajs-2287	87	48	sided	sided	ADJ
iajs-2287	87	49	ideals	ideal	NOUN
iajs-2287	87	50	of	of	ADP
iajs-2287	87	51	ℵ𝑟	ℵ𝑟	NOUN
iajs-2287	87	52	,	,	PUNCT
iajs-2287	87	53	then	then	ADV
iajs-2287	87	54	ζ	ζ	NOUN
iajs-2287	87	55	∗	∗	NOUN
iajs-2287	87	56	μ	μ	NOUN
iajs-2287	87	57	=	=	NOUN
iajs-2287	87	58	ζ	ζ	PROPN
iajs-2287	87	59	∪	∪	NOUN
iajs-2287	87	60	μ	μ	NUM
iajs-2287	87	61	.	.	PUNCT
iajs-2287	88	1	proof	proof	NOUN
iajs-2287	88	2	let	let	VERB
iajs-2287	88	3	ζ	ζ	NOUN
iajs-2287	88	4	and	and	CCONJ
iajs-2287	88	5	μ	μ	PROPN
iajs-2287	88	6	be	be	VERB
iajs-2287	88	7	any	any	DET
iajs-2287	88	8	anti	anti	ADJ
iajs-2287	88	9	fuzzy	fuzzy	ADJ
iajs-2287	88	10	two	two	NUM
iajs-2287	88	11	sided	sided	ADJ
iajs-2287	88	12	ideals	ideal	NOUN
iajs-2287	88	13	of	of	ADP
iajs-2287	88	14	ℵ	ℵ	NOUN
iajs-2287	88	15	,	,	PUNCT
iajs-2287	88	16	then	then	ADV
iajs-2287	88	17	obviously	obviously	ADV
iajs-2287	88	18	ζ	ζ	NOUN
iajs-2287	88	19	∗	∗	NOUN
iajs-2287	88	20	μ	μ	PROPN
iajs-2287	88	21	⊇	⊇	PROPN
iajs-2287	88	22	ζ	ζ	PROPN
iajs-2287	88	23	∪	∪	ADP
iajs-2287	88	24	μ	μ	PROPN
iajs-2287	88	25	.	.	PUNCT
iajs-2287	89	1	since	since	SCONJ
iajs-2287	89	2	ℵ	ℵ	NOUN
iajs-2287	89	3	is	be	AUX
iajs-2287	89	4	a	a	DET
iajs-2287	89	5	regular	regular	ADJ
iajs-2287	89	6	so	so	ADV
iajs-2287	89	7	whenever	whenever	SCONJ
iajs-2287	89	8	element	element	PROPN
iajs-2287	89	9	w	w	PROPN
iajs-2287	89	10	∈	∈	PROPN
iajs-2287	89	11	ℵ	ℵ	NOUN
iajs-2287	89	12	,	,	PUNCT
iajs-2287	89	13	∃	∃	PROPN
iajs-2287	89	14	z	z	PROPN
iajs-2287	89	15	∈	∈	PROPN
iajs-2287	89	16	ℵ	ℵ	NOUN
iajs-2287	89	17	,	,	PUNCT
iajs-2287	89	18	s.t	s.t	PROPN
iajs-2287	89	19	w	w	PROPN
iajs-2287	89	20	=	=	PROPN
iajs-2287	89	21	wzw	wzw	NOUN
iajs-2287	89	22	,	,	PUNCT
iajs-2287	89	23	so	so	CCONJ
iajs-2287	89	24	(	(	PUNCT
iajs-2287	89	25	ζ	ζ	NOUN
iajs-2287	89	26	∗	∗	NOUN
iajs-2287	89	27	μ)(w	μ)(w	NOUN
iajs-2287	89	28	)	)	PUNCT
iajs-2287	89	29	=	=	SYM
iajs-2287	89	30	⋀	⋀	PROPN
iajs-2287	89	31	{	{	PUNCT
iajs-2287	89	32	ζ(wz	ζ(wz	NOUN
iajs-2287	89	33	)	)	PUNCT
iajs-2287	89	34	∨	∨	NOUN
iajs-2287	89	35	μ(wzw)}w	μ(wzw)}w	NOUN
iajs-2287	89	36	=	=	SYM
iajs-2287	89	37	wzw	wzw	NOUN
iajs-2287	89	38	=	=	NOUN
iajs-2287	89	39	wzwzw	wzwzw	NOUN
iajs-2287	89	40	≤	≤	ADJ
iajs-2287	89	41	ζ(wz	ζ(wz	NOUN
iajs-2287	89	42	)	)	PUNCT
iajs-2287	89	43	∨	∨	NUM
iajs-2287	89	44	μ(wzw)≤	μ(wzw)≤	NOUN
iajs-2287	89	45	ζ(w	ζ(w	PROPN
iajs-2287	89	46	)	)	PUNCT
iajs-2287	89	47	∨	∨	NUM
iajs-2287	89	48	μ(w)=(ζ	μ(w)=(ζ	ADV
iajs-2287	89	49	∪	∪	ADJ
iajs-2287	89	50	μ)(w	μ)(w	NOUN
iajs-2287	89	51	)	)	PUNCT
iajs-2287	89	52	then	then	ADV
iajs-2287	89	53	(	(	PUNCT
iajs-2287	89	54	ζ	ζ	NOUN
iajs-2287	89	55	∗	∗	NUM
iajs-2287	89	56	μ	μ	NOUN
iajs-2287	89	57	)	)	PUNCT
iajs-2287	89	58	⊆	⊆	NUM
iajs-2287	89	59	ζ	ζ	NOUN
iajs-2287	89	60	∪	∪	NOUN
iajs-2287	89	61	μ	μ	NOUN
iajs-2287	89	62	.	.	PUNCT
iajs-2287	90	1	hence	hence	ADV
iajs-2287	90	2	,	,	PUNCT
iajs-2287	90	3	ζ	ζ	NOUN
iajs-2287	90	4	∗	∗	NOUN
iajs-2287	90	5	μ	μ	NOUN
iajs-2287	90	6	=	=	NOUN
iajs-2287	90	7	ζ	ζ	PROPN
iajs-2287	90	8	∪	∪	ADP
iajs-2287	90	9	μ	μ	PROPN
iajs-2287	90	10	.	.	PUNCT
iajs-2287	90	11	example	example	NOUN
iajs-2287	90	12	25	25	NUM
iajs-2287	90	13	let	let	VERB
iajs-2287	90	14	ℵ	ℵ	X
iajs-2287	90	15	=	=	NOUN
iajs-2287	90	16	{	{	PUNCT
iajs-2287	90	17	s	s	PROPN
iajs-2287	90	18	,	,	PUNCT
iajs-2287	90	19	r	r	NOUN
iajs-2287	90	20	,	,	PUNCT
iajs-2287	90	21	t	t	PROPN
iajs-2287	90	22	}	}	PUNCT
iajs-2287	90	23	be	be	AUX
iajs-2287	90	24	a	a	DET
iajs-2287	90	25	semigroup	semigroup	NOUN
iajs-2287	90	26	with	with	ADP
iajs-2287	90	27	the	the	DET
iajs-2287	90	28	following	follow	VERB
iajs-2287	90	29	table	table	NOUN
iajs-2287	90	30	:	:	PUNCT
iajs-2287	90	31	.	.	PUNCT
iajs-2287	91	1	s	s	AUX
iajs-2287	91	2	r	r	NOUN
iajs-2287	91	3	t	t	NOUN
iajs-2287	91	4	s	s	NOUN
iajs-2287	91	5	s	s	NOUN
iajs-2287	91	6	r	r	NOUN
iajs-2287	91	7	t	t	NOUN
iajs-2287	91	8	r	r	NOUN
iajs-2287	91	9	r	r	NOUN
iajs-2287	91	10	r	r	NOUN
iajs-2287	91	11	t	t	NOUN
iajs-2287	91	12	t	t	NOUN
iajs-2287	91	13	t	t	PROPN
iajs-2287	91	14	t	t	PROPN
iajs-2287	91	15	t	t	PROPN
iajs-2287	91	16	define	define	VERB
iajs-2287	91	17	a	a	DET
iajs-2287	91	18	fuzzy	fuzzy	ADJ
iajs-2287	91	19	subset	subset	VERB
iajs-2287	91	20	ζ	ζ	NOUN
iajs-2287	91	21	of	of	ADP
iajs-2287	91	22	ℵ	ℵ	NOUN
iajs-2287	91	23	by	by	ADP
iajs-2287	91	24	ζ(s)=0.6	ζ(s)=0.6	PROPN
iajs-2287	91	25	,	,	PUNCT
iajs-2287	91	26	ζ(r)=0.5	ζ(r)=0.5	PROPN
iajs-2287	91	27	,	,	PUNCT
iajs-2287	91	28	ζ(t)=0.4	ζ(t)=0.4	PROPN
iajs-2287	91	29	.	.	PUNCT
iajs-2287	92	1	by	by	ADP
iajs-2287	92	2	routine	routine	ADJ
iajs-2287	92	3	calculation	calculation	NOUN
iajs-2287	92	4	,	,	PUNCT
iajs-2287	92	5	we	we	PRON
iajs-2287	92	6	can	can	AUX
iajs-2287	92	7	check	check	VERB
iajs-2287	92	8	that	that	SCONJ
iajs-2287	92	9	ζ	ζ	NOUN
iajs-2287	92	10	is	be	AUX
iajs-2287	92	11	an	an	DET
iajs-2287	92	12	anti	anti	ADJ
iajs-2287	92	13	fuzzy	fuzzy	ADJ
iajs-2287	92	14	ideal	ideal	NOUN
iajs-2287	92	15	,	,	PUNCT
iajs-2287	92	16	anti	anti	X
iajs-2287	92	17	fuzzy	fuzzy	ADJ
iajs-2287	92	18	interior	interior	ADJ
iajs-2287	92	19	ideal	ideal	NOUN
iajs-2287	92	20	and	and	CCONJ
iajs-2287	92	21	anti	anti	ADJ
iajs-2287	92	22	fuzzy	fuzzy	ADJ
iajs-2287	92	23	bi	bi	NOUN
iajs-2287	92	24	-	-	NOUN
iajs-2287	92	25	ideal	ideal	NOUN
iajs-2287	92	26	of	of	ADP
iajs-2287	92	27	ℵ𝑟.	ℵ𝑟.	NOUN
iajs-2287	92	28	now	now	ADV
iajs-2287	92	29	,	,	PUNCT
iajs-2287	92	30	we	we	PRON
iajs-2287	92	31	give	give	VERB
iajs-2287	92	32	other	other	ADJ
iajs-2287	92	33	fuzzy	fuzzy	ADJ
iajs-2287	92	34	characterizations	characterization	NOUN
iajs-2287	92	35	of	of	ADP
iajs-2287	92	36	a	a	DET
iajs-2287	92	37	regular	regular	ADJ
iajs-2287	92	38	semigroup	semigroup	NOUN
iajs-2287	92	39	.	.	PUNCT
iajs-2287	93	1	proposition	proposition	NOUN
iajs-2287	93	2	26	26	NUM
iajs-2287	93	3	a	a	DET
iajs-2287	93	4	fuzzy	fuzzy	ADJ
iajs-2287	93	5	subset	subset	VERB
iajs-2287	93	6	ζ	ζ	NOUN
iajs-2287	93	7	of	of	ADP
iajs-2287	93	8	ℵ𝑟	ℵ𝑟	NOUN
iajs-2287	93	9	,	,	PUNCT
iajs-2287	93	10	then	then	ADV
iajs-2287	93	11	ζ	ζ	NOUN
iajs-2287	93	12	is	be	AUX
iajs-2287	93	13	anti	anti	X
iajs-2287	93	14	fuzzy	fuzzy	ADJ
iajs-2287	93	15	bi	bi	NOUN
iajs-2287	93	16	-	-	NOUN
iajs-2287	93	17	ideal	ideal	NOUN
iajs-2287	93	18	of	of	ADP
iajs-2287	93	19	ℵ	ℵ	PROPN
iajs-2287	93	20	iff	iff	PROPN
iajs-2287	93	21	it	it	PRON
iajs-2287	93	22	is	be	AUX
iajs-2287	93	23	an	an	DET
iajs-2287	93	24	anti	anti	ADJ
iajs-2287	93	25	fuzzy	fuzzy	ADJ
iajs-2287	93	26	generalized	generalized	ADJ
iajs-2287	93	27	bi	bi	NOUN
iajs-2287	93	28	-	-	NOUN
iajs-2287	93	29	ideal	ideal	NOUN
iajs-2287	93	30	of	of	ADP
iajs-2287	93	31	ℵ.	ℵ.	PROPN
iajs-2287	93	32	proof	proof	NOUN
iajs-2287	93	33	⟹	⟹	PUNCT
iajs-2287	93	34	suppose	suppose	VERB
iajs-2287	93	35	that	that	SCONJ
iajs-2287	93	36	ζ	ζ	NOUN
iajs-2287	93	37	be	be	AUX
iajs-2287	93	38	any	any	DET
iajs-2287	93	39	anti	anti	ADJ
iajs-2287	93	40	fuzzy	fuzzy	ADJ
iajs-2287	93	41	bi	bi	NOUN
iajs-2287	93	42	-	-	NOUN
iajs-2287	93	43	ideal	ideal	NOUN
iajs-2287	93	44	of	of	ADP
iajs-2287	93	45	ℵ	ℵ	NOUN
iajs-2287	93	46	,	,	PUNCT
iajs-2287	93	47	the	the	DET
iajs-2287	93	48	obviously	obviously	ADV
iajs-2287	93	49	,	,	PUNCT
iajs-2287	93	50	ζ	ζ	NOUN
iajs-2287	93	51	is	be	AUX
iajs-2287	93	52	an	an	DET
iajs-2287	93	53	anti	anti	ADJ
iajs-2287	93	54	fuzzy	fuzzy	ADJ
iajs-2287	93	55	generalized	generalized	ADJ
iajs-2287	93	56	bi	bi	NOUN
iajs-2287	93	57	-	-	NOUN
iajs-2287	93	58	ideal	ideal	NOUN
iajs-2287	93	59	of	of	ADP
iajs-2287	93	60	ℵ.	ℵ.	PROPN
iajs-2287	93	61	⟸	⟸	PROPN
iajs-2287	93	62	suppose	suppose	VERB
iajs-2287	93	63	that	that	SCONJ
iajs-2287	93	64	ζ	ζ	NOUN
iajs-2287	93	65	be	be	AUX
iajs-2287	93	66	any	any	DET
iajs-2287	93	67	anti	anti	ADJ
iajs-2287	93	68	fuzzy	fuzzy	ADJ
iajs-2287	93	69	generalized	generalized	ADJ
iajs-2287	93	70	bi	bi	NOUN
iajs-2287	93	71	-	-	NOUN
iajs-2287	93	72	ideal	ideal	NOUN
iajs-2287	93	73	of	of	ADP
iajs-2287	93	74	ℵ	ℵ	NOUN
iajs-2287	93	75	,	,	PUNCT
iajs-2287	93	76	since	since	SCONJ
iajs-2287	93	77	ℵ	ℵ	NOUN
iajs-2287	93	78	is	be	AUX
iajs-2287	93	79	a	a	DET
iajs-2287	93	80	regular	regular	NOUN
iajs-2287	93	81	of	of	ADP
iajs-2287	93	82	a	a	DET
iajs-2287	93	83	semigroup	semigroup	NOUN
iajs-2287	93	84	,	,	PUNCT
iajs-2287	93	85	so	so	CCONJ
iajs-2287	93	86	whenever	whenever	SCONJ
iajs-2287	93	87	w	w	PROPN
iajs-2287	93	88	∈	∈	PROPN
iajs-2287	93	89	ℵ	ℵ	NOUN
iajs-2287	93	90	,	,	PUNCT
iajs-2287	93	91	∃	∃	PROPN
iajs-2287	93	92	z	z	PROPN
iajs-2287	93	93	∈	∈	PROPN
iajs-2287	93	94	ℵ	ℵ	ADP
iajs-2287	93	95	s.t	s.t	PROPN
iajs-2287	93	96	w	w	PROPN
iajs-2287	93	97	=	=	PROPN
iajs-2287	93	98	w	w	PROPN
iajs-2287	93	99	z	z	PROPN
iajs-2287	93	100	w.	w.	NOUN
iajs-2287	93	101	we	we	PRON
iajs-2287	93	102	have	have	VERB
iajs-2287	93	103	ζ(wr)=ζ(wzwr)=ζ(w	ζ(wr)=ζ(wzwr)=ζ(w	NUM
iajs-2287	93	104	t	t	PROPN
iajs-2287	93	105	r	r	NOUN
iajs-2287	93	106	)	)	PUNCT
iajs-2287	93	107	≤	≤	NOUN
iajs-2287	93	108	ζ(w	ζ(w	PROPN
iajs-2287	93	109	)	)	PUNCT
iajs-2287	93	110	∨	∨	NUM
iajs-2287	93	111	ζ(r	ζ(r	NOUN
iajs-2287	93	112	)	)	PUNCT
iajs-2287	93	113	where	where	SCONJ
iajs-2287	93	114	𝑡=𝑧𝑤.	𝑡=𝑧𝑤.	NOUN
iajs-2287	93	115	therefore	therefore	ADV
iajs-2287	93	116	,	,	PUNCT
iajs-2287	93	117	ζ	ζ	NOUN
iajs-2287	93	118	is	be	AUX
iajs-2287	93	119	an	an	DET
iajs-2287	93	120	anti	anti	ADJ
iajs-2287	93	121	fuzzy	fuzzy	ADJ
iajs-2287	93	122	sub	sub	NOUN
iajs-2287	93	123	-	-	ADJ
iajs-2287	93	124	semigroup	semigroup	ADJ
iajs-2287	93	125	of	of	ADP
iajs-2287	93	126	ℵ.	ℵ.	PROPN
iajs-2287	93	127	hence	hence	ADV
iajs-2287	93	128	,	,	PUNCT
iajs-2287	93	129	ζ	ζ	PROPN
iajs-2287	93	130	is	be	AUX
iajs-2287	93	131	an	an	DET
iajs-2287	93	132	anti	anti	ADJ
iajs-2287	93	133	fuzzy	fuzzy	ADJ
iajs-2287	93	134	generalized	generalized	ADJ
iajs-2287	93	135	bi	bi	NOUN
iajs-2287	93	136	-	-	NOUN
iajs-2287	93	137	ideal	ideal	NOUN
iajs-2287	93	138	of	of	ADP
iajs-2287	93	139	ℵ.	ℵ.	PROPN
iajs-2287	93	140	114	114	NUM
iajs-2287	93	141	ibn	ibn	PROPN
iajs-2287	93	142	al	al	PROPN
iajs-2287	93	143	-	-	PUNCT
iajs-2287	93	144	haitham	haitham	PROPN
iajs-2287	93	145	jour	jour	X
iajs-2287	93	146	.	.	PROPN
iajs-2287	94	1	for	for	ADP
iajs-2287	94	2	pure	pure	ADJ
iajs-2287	94	3	&	&	CCONJ
iajs-2287	94	4	appl	appl	PROPN
iajs-2287	94	5	.	.	PUNCT
iajs-2287	95	1	sci	sci	PROPN
iajs-2287	95	2	.	.	PROPN
iajs-2287	95	3	32	32	NUM
iajs-2287	95	4	(	(	PUNCT
iajs-2287	95	5	3	3	NUM
iajs-2287	95	6	)	)	PUNCT
iajs-2287	95	7	2019	2019	NUM
iajs-2287	95	8	theorem	theorem	VERB
iajs-2287	95	9	27	27	NUM
iajs-2287	95	10	for	for	ADP
iajs-2287	95	11	anti	anti	X
iajs-2287	95	12	fuzzy	fuzzy	ADJ
iajs-2287	95	13	generalized	generalized	ADJ
iajs-2287	95	14	bi	bi	ADJ
iajs-2287	95	15	-	-	ADJ
iajs-2287	95	16	ideal	ideal	ADJ
iajs-2287	95	17	ζ	ζ	NOUN
iajs-2287	95	18	and	and	CCONJ
iajs-2287	95	19	anti	anti	ADJ
iajs-2287	95	20	fuzzy	fuzzy	ADJ
iajs-2287	95	21	right	right	ADJ
iajs-2287	95	22	ideal	ideal	PROPN
iajs-2287	95	23	μ	μ	PROPN
iajs-2287	95	24	of	of	ADP
iajs-2287	95	25	ℵ𝑟	ℵ𝑟	NOUN
iajs-2287	95	26	,	,	PUNCT
iajs-2287	95	27	then	then	ADV
iajs-2287	95	28	ζ	ζ	NOUN
iajs-2287	95	29	∗	∗	NOUN
iajs-2287	95	30	μ	μ	NUM
iajs-2287	95	31	⊆	⊆	NUM
iajs-2287	95	32	ζ	ζ	PROPN
iajs-2287	95	33	∪	∪	NOUN
iajs-2287	95	34	μ	μ	NUM
iajs-2287	95	35	.	.	PUNCT
iajs-2287	96	1	proof	proof	NOUN
iajs-2287	96	2	let	let	VERB
iajs-2287	96	3	ζ	ζ	NOUN
iajs-2287	96	4	and	and	CCONJ
iajs-2287	96	5	μ	μ	PROPN
iajs-2287	96	6	are	be	AUX
iajs-2287	96	7	any	any	DET
iajs-2287	96	8	anti	anti	ADJ
iajs-2287	96	9	fuzzy	fuzzy	ADJ
iajs-2287	96	10	generalized	generalized	ADJ
iajs-2287	96	11	bi	bi	NOUN
iajs-2287	96	12	-	-	ADJ
iajs-2287	96	13	ideal	ideal	ADJ
iajs-2287	96	14	and	and	CCONJ
iajs-2287	96	15	anti	anti	ADJ
iajs-2287	96	16	fuzzy	fuzzy	ADJ
iajs-2287	96	17	right	right	ADJ
iajs-2287	96	18	ideal	ideal	NOUN
iajs-2287	96	19	of	of	ADP
iajs-2287	96	20	ℵ	ℵ	NOUN
iajs-2287	96	21	,	,	PUNCT
iajs-2287	96	22	respectively	respectively	ADV
iajs-2287	96	23	,	,	PUNCT
iajs-2287	96	24	then	then	ADV
iajs-2287	96	25	whenever	whenever	SCONJ
iajs-2287	96	26	w	w	PROPN
iajs-2287	96	27	∈	∈	PROPN
iajs-2287	96	28	ℵ	ℵ	NOUN
iajs-2287	96	29	,	,	PUNCT
iajs-2287	96	30	∃	∃	PROPN
iajs-2287	96	31	z	z	PROPN
iajs-2287	96	32	∈	∈	PROPN
iajs-2287	96	33	ℵ	ℵ	ADP
iajs-2287	96	34	s.t	s.t	PROPN
iajs-2287	96	35	w	w	PROPN
iajs-2287	96	36	=	=	PROPN
iajs-2287	96	37	wzw	wzw	NOUN
iajs-2287	96	38	.	.	PUNCT
iajs-2287	97	1	then	then	ADV
iajs-2287	97	2	(	(	PUNCT
iajs-2287	97	3	ζ	ζ	NOUN
iajs-2287	97	4	∗	∗	NOUN
iajs-2287	97	5	μ)(w	μ)(w	NOUN
iajs-2287	97	6	)	)	PUNCT
iajs-2287	97	7	=	=	SYM
iajs-2287	97	8	⋀	⋀	PROPN
iajs-2287	97	9	{	{	PUNCT
iajs-2287	97	10	ζ(b	ζ(b	PROPN
iajs-2287	97	11	)	)	PUNCT
iajs-2287	97	12	∨	∨	NOUN
iajs-2287	97	13	μ(c)}w	μ(c)}w	NOUN
iajs-2287	97	14	=	=	SYM
iajs-2287	97	15	bc	bc	PROPN
iajs-2287	97	16	≤	≤	PROPN
iajs-2287	97	17	ζ(wzw	ζ(wzw	PROPN
iajs-2287	97	18	)	)	PUNCT
iajs-2287	97	19	∨	∨	NUM
iajs-2287	97	20	μ(zw	μ(zw	PROPN
iajs-2287	97	21	)	)	PUNCT
iajs-2287	97	22	≤	≤	NOUN
iajs-2287	97	23	ζ(w	ζ(w	PROPN
iajs-2287	97	24	)	)	PUNCT
iajs-2287	97	25	∨	∨	NUM
iajs-2287	97	26	μ(w)=(ζ	μ(w)=(ζ	PROPN
iajs-2287	97	27	∨	∨	NUM
iajs-2287	97	28	μ)(w	μ)(w	NOUN
iajs-2287	97	29	)	)	PUNCT
iajs-2287	97	30	and	and	CCONJ
iajs-2287	97	31	so	so	ADV
iajs-2287	97	32	we	we	PRON
iajs-2287	97	33	have	have	VERB
iajs-2287	97	34	ζ	ζ	NOUN
iajs-2287	97	35	∗	∗	NOUN
iajs-2287	97	36	μ	μ	NOUN
iajs-2287	97	37	⊆	⊆	NUM
iajs-2287	97	38	ζ	ζ	PROPN
iajs-2287	97	39	∪	∪	NOUN
iajs-2287	97	40	μ	μ	PROPN
iajs-2287	97	41	.	.	PUNCT
iajs-2287	98	1	theorem	theorem	PROPN
iajs-2287	98	2	28	28	NUM
iajs-2287	98	3	if	if	SCONJ
iajs-2287	98	4	ζ	ζ	PROPN
iajs-2287	98	5	and	and	CCONJ
iajs-2287	98	6	μ	μ	PROPN
iajs-2287	98	7	are	be	AUX
iajs-2287	98	8	any	any	DET
iajs-2287	98	9	anti	anti	ADJ
iajs-2287	98	10	fuzzy	fuzzy	ADJ
iajs-2287	98	11	interior	interior	ADJ
iajs-2287	98	12	ideals	ideal	NOUN
iajs-2287	98	13	of	of	ADP
iajs-2287	98	14	ℵ𝑟	ℵ𝑟	NOUN
iajs-2287	98	15	,	,	PUNCT
iajs-2287	98	16	then	then	ADV
iajs-2287	98	17	(	(	PUNCT
iajs-2287	98	18	ζ	ζ	NOUN
iajs-2287	98	19	∗	∗	NOUN
iajs-2287	98	20	μ	μ	NOUN
iajs-2287	98	21	)	)	PUNCT
iajs-2287	98	22	∪	∪	NOUN
iajs-2287	98	23	(	(	PUNCT
iajs-2287	98	24	μ	μ	PROPN
iajs-2287	98	25	∗	∗	NOUN
iajs-2287	98	26	ζ	ζ	NOUN
iajs-2287	98	27	)	)	PUNCT
iajs-2287	98	28	⊆	⊆	NUM
iajs-2287	98	29	ζ	ζ	PROPN
iajs-2287	98	30	∨	∨	NUM
iajs-2287	98	31	μ	μ	NUM
iajs-2287	98	32	.	.	PUNCT
iajs-2287	99	1	proof	proof	NOUN
iajs-2287	99	2	let	let	VERB
iajs-2287	99	3	ζ	ζ	NOUN
iajs-2287	99	4	,	,	PUNCT
iajs-2287	99	5	μ	μ	PROPN
iajs-2287	99	6	be	be	VERB
iajs-2287	99	7	any	any	DET
iajs-2287	99	8	anti	anti	ADJ
iajs-2287	99	9	fuzzy	fuzzy	ADJ
iajs-2287	99	10	interior	interior	ADJ
iajs-2287	99	11	ideals	ideal	NOUN
iajs-2287	99	12	of	of	ADP
iajs-2287	99	13	ℵ	ℵ	NOUN
iajs-2287	99	14	,	,	PUNCT
iajs-2287	99	15	and	and	CCONJ
iajs-2287	99	16	w	w	PROPN
iajs-2287	99	17	∈	∈	PROPN
iajs-2287	100	1	ℵ.	ℵ.	NOUN
iajs-2287	101	1	then	then	ADV
iajs-2287	101	2	since	since	SCONJ
iajs-2287	101	3	ℵ	ℵ	NOUN
iajs-2287	101	4	is	be	AUX
iajs-2287	101	5	regular	regular	ADJ
iajs-2287	101	6	semigroup	semigroup	NOUN
iajs-2287	101	7	then	then	ADV
iajs-2287	101	8	,	,	PUNCT
iajs-2287	101	9	∃	∃	PROPN
iajs-2287	101	10	z	z	PROPN
iajs-2287	101	11	∈	∈	PROPN
iajs-2287	101	12	ℵ	ℵ	PROPN
iajs-2287	101	13	s.t	s.t	PROPN
iajs-2287	101	14	𝑤=	𝑤=	PROPN
iajs-2287	101	15	wzw=((wz)w(z	wzw=((wz)w(z	PROPN
iajs-2287	101	16	)	)	PUNCT
iajs-2287	101	17	)	)	PUNCT
iajs-2287	101	18	(	(	PUNCT
iajs-2287	101	19	w(zw))=((wz)w(z	w(zw))=((wz)w(z	NUM
iajs-2287	101	20	)	)	PUNCT
iajs-2287	101	21	)	)	PUNCT
iajs-2287	102	1	(	(	PUNCT
iajs-2287	102	2	(	(	PUNCT
iajs-2287	102	3	wz)w(zw	wz)w(zw	NUM
iajs-2287	102	4	)	)	PUNCT
iajs-2287	102	5	)	)	PUNCT
iajs-2287	102	6	.	.	PUNCT
iajs-2287	103	1	hence	hence	ADV
iajs-2287	103	2	(	(	PUNCT
iajs-2287	103	3	ζ	ζ	NOUN
iajs-2287	103	4	∗	∗	NOUN
iajs-2287	103	5	μ)(w	μ)(w	NOUN
iajs-2287	103	6	)	)	PUNCT
iajs-2287	103	7	=	=	SYM
iajs-2287	103	8	⋀	⋀	PROPN
iajs-2287	103	9	{	{	PUNCT
iajs-2287	103	10	ζ(b	ζ(b	PROPN
iajs-2287	103	11	)	)	PUNCT
iajs-2287	103	12	∨	∨	NOUN
iajs-2287	103	13	μ(c)}w	μ(c)}w	NOUN
iajs-2287	103	14	=	=	SYM
iajs-2287	103	15	bc	bc	PROPN
iajs-2287	103	16	.	.	PUNCT
iajs-2287	103	17	≤	≤	NUM
iajs-2287	103	18	ζ((wz)w(z))∨	ζ((wz)w(z))∨	PROPN
iajs-2287	103	19	μ((w	μ((w	NOUN
iajs-2287	103	20	z)w(zw	z)w(zw	NUM
iajs-2287	103	21	)	)	PUNCT
iajs-2287	103	22	)	)	PUNCT
iajs-2287	104	1	≤	≤	NUM
iajs-2287	104	2	ζ(w	ζ(w	PROPN
iajs-2287	104	3	)	)	PUNCT
iajs-2287	104	4	∨	∨	NUM
iajs-2287	104	5	μ(w)=(ζ	μ(w)=(ζ	PROPN
iajs-2287	104	6	∨	∨	NUM
iajs-2287	104	7	μ)(w	μ)(w	NOUN
iajs-2287	104	8	)	)	PUNCT
iajs-2287	104	9	and	and	CCONJ
iajs-2287	104	10	so	so	ADV
iajs-2287	104	11	we	we	PRON
iajs-2287	104	12	have	have	VERB
iajs-2287	104	13	ζ	ζ	NOUN
iajs-2287	104	14	∗	∗	NOUN
iajs-2287	104	15	μ	μ	NOUN
iajs-2287	104	16	⊆	⊆	NUM
iajs-2287	104	17	ζ	ζ	PROPN
iajs-2287	104	18	∪	∪	NOUN
iajs-2287	104	19	μ	μ	NUM
iajs-2287	104	20	.	.	PUNCT
iajs-2287	105	1	similarly	similarly	ADV
iajs-2287	105	2	,	,	PUNCT
iajs-2287	105	3	we	we	PRON
iajs-2287	105	4	have	have	AUX
iajs-2287	105	5	(	(	PUNCT
iajs-2287	105	6	μ	μ	NOUN
iajs-2287	105	7	∗	∗	NOUN
iajs-2287	105	8	ζ	ζ	NOUN
iajs-2287	105	9	)	)	PUNCT
iajs-2287	105	10	⊆	⊆	NUM
iajs-2287	105	11	ζ	ζ	PROPN
iajs-2287	105	12	∪	∪	NOUN
iajs-2287	105	13	μ	μ	PROPN
iajs-2287	105	14	therefore	therefore	ADV
iajs-2287	105	15	(	(	PUNCT
iajs-2287	105	16	ζ	ζ	NOUN
iajs-2287	105	17	∗	∗	NOUN
iajs-2287	105	18	μ	μ	NOUN
iajs-2287	105	19	)	)	PUNCT
iajs-2287	105	20	∪	∪	NOUN
iajs-2287	105	21	(	(	PUNCT
iajs-2287	105	22	μ	μ	PROPN
iajs-2287	105	23	∗	∗	NOUN
iajs-2287	105	24	ζ	ζ	NOUN
iajs-2287	105	25	)	)	PUNCT
iajs-2287	105	26	⊆	⊆	NUM
iajs-2287	105	27	ζ	ζ	NOUN
iajs-2287	105	28	∪	∪	ADP
iajs-2287	105	29	μ	μ	PROPN
iajs-2287	105	30	.	.	PUNCT
iajs-2287	105	31	theorem	theorem	VERB
iajs-2287	105	32	29	29	NUM
iajs-2287	105	33	for	for	ADP
iajs-2287	105	34	every	every	DET
iajs-2287	105	35	anti	anti	ADJ
iajs-2287	105	36	fuzzy	fuzzy	NOUN
iajs-2287	105	37	left	leave	VERB
iajs-2287	105	38	ideal	ideal	PROPN
iajs-2287	105	39	α	α	NOUN
iajs-2287	105	40	,	,	PUNCT
iajs-2287	105	41	every	every	DET
iajs-2287	105	42	anti	anti	ADJ
iajs-2287	105	43	fuzzy	fuzzy	ADJ
iajs-2287	105	44	generalized	generalized	ADJ
iajs-2287	105	45	bi	bi	ADJ
iajs-2287	105	46	-	-	ADJ
iajs-2287	105	47	ideal	ideal	ADJ
iajs-2287	105	48	μ	μ	PROPN
iajs-2287	105	49	,	,	PUNCT
iajs-2287	105	50	and	and	CCONJ
iajs-2287	105	51	every	every	DET
iajs-2287	105	52	anti	anti	X
iajs-2287	105	53	fuzzy	fuzzy	ADJ
iajs-2287	105	54	interior	interior	ADJ
iajs-2287	105	55	ideal	ideal	ADJ
iajs-2287	105	56	ζ	ζ	NOUN
iajs-2287	105	57	of	of	ADP
iajs-2287	105	58	ℵ𝑟	ℵ𝑟	NOUN
iajs-2287	105	59	,	,	PUNCT
iajs-2287	105	60	then	then	ADV
iajs-2287	105	61	μ	μ	PROPN
iajs-2287	105	62	∗	∗	NOUN
iajs-2287	105	63	α	α	PROPN
iajs-2287	105	64	∗	∗	NOUN
iajs-2287	105	65	ζ	ζ	NOUN
iajs-2287	105	66	⊆	⊆	NUM
iajs-2287	105	67	μ	μ	NOUN
iajs-2287	105	68	∪	∪	ADP
iajs-2287	105	69	α	α	PROPN
iajs-2287	105	70	∪	∪	PROPN
iajs-2287	105	71	ζ	ζ	NOUN
iajs-2287	105	72	.	.	PUNCT
iajs-2287	106	1	proof	proof	NOUN
iajs-2287	106	2	let	let	VERB
iajs-2287	106	3	α	α	PRON
iajs-2287	106	4	,	,	PUNCT
iajs-2287	106	5	μ	μ	PROPN
iajs-2287	106	6	and	and	CCONJ
iajs-2287	106	7	ζ	ζ	NOUN
iajs-2287	106	8	be	be	AUX
iajs-2287	106	9	any	any	DET
iajs-2287	106	10	anti	anti	ADJ
iajs-2287	106	11	fuzzy	fuzzy	ADJ
iajs-2287	106	12	left	leave	VERB
iajs-2287	106	13	ideal	ideal	ADJ
iajs-2287	106	14	,	,	PUNCT
iajs-2287	106	15	any	any	DET
iajs-2287	106	16	anti	anti	ADJ
iajs-2287	106	17	fuzzy	fuzzy	ADJ
iajs-2287	106	18	generalized	generalized	ADJ
iajs-2287	106	19	bi	bi	NOUN
iajs-2287	106	20	-	-	ADJ
iajs-2287	106	21	ideal	ideal	ADJ
iajs-2287	106	22	and	and	CCONJ
iajs-2287	106	23	anti	anti	ADJ
iajs-2287	106	24	fuzzy	fuzzy	ADJ
iajs-2287	106	25	interior	interior	ADJ
iajs-2287	106	26	ideal	ideal	NOUN
iajs-2287	106	27	of	of	ADP
iajs-2287	106	28	ℵ𝑟	ℵ𝑟	NOUN
iajs-2287	106	29	,	,	PUNCT
iajs-2287	106	30	respectively	respectively	ADV
iajs-2287	106	31	,	,	PUNCT
iajs-2287	106	32	whenever	whenever	SCONJ
iajs-2287	106	33	w	w	PROPN
iajs-2287	106	34	∈	∈	PROPN
iajs-2287	106	35	ℵ	ℵ	NOUN
iajs-2287	106	36	,	,	PUNCT
iajs-2287	106	37	∃	∃	PROPN
iajs-2287	106	38	z	z	PROPN
iajs-2287	106	39	∈	∈	PROPN
iajs-2287	106	40	ℵ.	ℵ.	PROPN
iajs-2287	107	1	because	because	SCONJ
iajs-2287	107	2	ℵ	ℵ	NOUN
iajs-2287	107	3	is	be	AUX
iajs-2287	107	4	a	a	DET
iajs-2287	107	5	regular	regular	ADJ
iajs-2287	107	6	,	,	PUNCT
iajs-2287	107	7	s.t	s.t	PROPN
iajs-2287	107	8	w	w	PROPN
iajs-2287	107	9	=	=	PROPN
iajs-2287	107	10	wzw	wzw	NOUN
iajs-2287	107	11	=	=	NOUN
iajs-2287	107	12	wzwzw=(wzw	wzwzw=(wzw	X
iajs-2287	107	13	)	)	PUNCT
iajs-2287	107	14	(	(	PUNCT
iajs-2287	107	15	zw)zw=((wzw	zw)zw=((wzw	X
iajs-2287	107	16	)	)	PUNCT
iajs-2287	107	17	[	[	X
iajs-2287	107	18	(	(	PUNCT
iajs-2287	107	19	zw	zw	PROPN
iajs-2287	107	20	)	)	PUNCT
iajs-2287	107	21	(	(	PUNCT
iajs-2287	107	22	(	(	PUNCT
iajs-2287	107	23	z)w(zw	z)w(zw	NUM
iajs-2287	107	24	)	)	PUNCT
iajs-2287	107	25	]	]	PUNCT
iajs-2287	107	26	)	)	PUNCT
iajs-2287	107	27	.	.	PUNCT
iajs-2287	108	1	then	then	ADV
iajs-2287	108	2	we	we	PRON
iajs-2287	108	3	have	have	VERB
iajs-2287	108	4	:	:	PUNCT
iajs-2287	108	5	(	(	PUNCT
iajs-2287	108	6	μ	μ	NOUN
iajs-2287	108	7	∗	∗	NOUN
iajs-2287	108	8	α	α	PROPN
iajs-2287	108	9	∗	∗	NOUN
iajs-2287	108	10	ζ)(w)=⋀	ζ)(w)=⋀	X
iajs-2287	108	11	{	{	PUNCT
iajs-2287	108	12	μ((wzw	μ((wzw	NOUN
iajs-2287	108	13	)	)	PUNCT
iajs-2287	108	14	)	)	PUNCT
iajs-2287	109	1	∨	∨	NUM
iajs-2287	109	2	(	(	PUNCT
iajs-2287	109	3	α	α	NOUN
iajs-2287	109	4	∗	∗	NOUN
iajs-2287	109	5	ζ)((zw)((z)w(zw))}w=((wzw)[(zw))((z)w(zw	ζ)((zw)((z)w(zw))}w=((wzw)[(zw))((z)w(zw	NOUN
iajs-2287	109	6	)	)	PUNCT
iajs-2287	109	7	)	)	PUNCT
iajs-2287	109	8	≤	≤	NOUN
iajs-2287	110	1	μ(w	μ(w	NUM
iajs-2287	110	2	)	)	PUNCT
iajs-2287	110	3	∨{⋀	∨{⋀	PROPN
iajs-2287	110	4	{	{	PUNCT
iajs-2287	110	5	α(zw	α(zw	NOUN
iajs-2287	110	6	)	)	PUNCT
iajs-2287	110	7	∨	∨	NUM
iajs-2287	110	8	ζ((z)w(zw))}((zw)(z)w(zw	ζ((z)w(zw))}((zw)(z)w(zw	PROPN
iajs-2287	110	9	)	)	PUNCT
iajs-2287	110	10	)	)	PUNCT
iajs-2287	110	11	≤	≤	NOUN
iajs-2287	111	1	μ(w	μ(w	NUM
iajs-2287	111	2	)	)	PUNCT
iajs-2287	111	3	∨	∨	NUM
iajs-2287	111	4	α(w	α(w	NOUN
iajs-2287	111	5	)	)	PUNCT
iajs-2287	111	6	∨	∨	NUM
iajs-2287	111	7	ζ(w	ζ(w	PROPN
iajs-2287	111	8	)	)	PUNCT
iajs-2287	111	9	=	=	PUNCT
iajs-2287	112	1	(	(	PUNCT
iajs-2287	112	2	μ	μ	PROPN
iajs-2287	112	3	∪	∪	VERB
iajs-2287	112	4	α	α	PROPN
iajs-2287	112	5	∪	∪	ADJ
iajs-2287	112	6	ζ)(w	ζ)(w	NOUN
iajs-2287	112	7	)	)	PUNCT
iajs-2287	112	8	and	and	CCONJ
iajs-2287	112	9	so	so	ADV
iajs-2287	112	10	we	we	PRON
iajs-2287	112	11	have	have	VERB
iajs-2287	112	12	μ	μ	PROPN
iajs-2287	112	13	∗	∗	NOUN
iajs-2287	112	14	α	α	PROPN
iajs-2287	112	15	∗	∗	NOUN
iajs-2287	112	16	ζ	ζ	NOUN
iajs-2287	112	17	⊆	⊆	NUM
iajs-2287	112	18	μ	μ	NOUN
iajs-2287	112	19	∪	∪	ADP
iajs-2287	112	20	α	α	PROPN
iajs-2287	112	21	∪	∪	ADJ
iajs-2287	112	22	ζ	ζ	NOUN
iajs-2287	112	23	.	.	PUNCT
iajs-2287	113	1	now	now	ADV
iajs-2287	113	2	,	,	PUNCT
iajs-2287	113	3	we	we	PRON
iajs-2287	113	4	characterized	characterize	VERB
iajs-2287	113	5	regular	regular	ADV
iajs-2287	113	6	(	(	PUNCT
iajs-2287	113	7	left	leave	VERB
iajs-2287	113	8	almost	almost	ADV
iajs-2287	113	9	-	-	PUNCT
iajs-2287	113	10	semigroup	semigroup	NOUN
iajs-2287	113	11	for	for	ADP
iajs-2287	113	12	short	short	ADJ
iajs-2287	113	13	la	la	PROPN
iajs-2287	113	14	-	-	PUNCT
iajs-2287	113	15	semigroup	semigroup	NOUN
iajs-2287	113	16	)	)	PUNCT
iajs-2287	113	17	by	by	ADP
iajs-2287	113	18	the	the	DET
iajs-2287	113	19	properties	property	NOUN
iajs-2287	113	20	of	of	ADP
iajs-2287	113	21	their	their	PRON
iajs-2287	113	22	fuzzy	fuzzy	ADJ
iajs-2287	113	23	left	left	NOUN
iajs-2287	113	24	(	(	PUNCT
iajs-2287	113	25	right	right	INTJ
iajs-2287	113	26	,	,	PUNCT
iajs-2287	113	27	two	two	NUM
iajs-2287	113	28	sided	sided	ADJ
iajs-2287	113	29	)	)	PUNCT
iajs-2287	113	30	ideal	ideal	NOUN
iajs-2287	113	31	.	.	PUNCT
iajs-2287	114	1	let	let	VERB
iajs-2287	114	2	ℵ	ℵ	NOUN
iajs-2287	114	3	be	be	AUX
iajs-2287	114	4	a	a	DET
iajs-2287	114	5	gropoid	gropoid	NOUN
iajs-2287	114	6	.	.	PUNCT
iajs-2287	115	1	then	then	ADV
iajs-2287	115	2	1	1	X
iajs-2287	115	3	.	.	PUNCT
iajs-2287	115	4	ℵ	ℵ	PROPN
iajs-2287	115	5	is	be	AUX
iajs-2287	115	6	called	call	VERB
iajs-2287	115	7	la	la	ADJ
iajs-2287	115	8	-	-	PUNCT
iajs-2287	115	9	semigroup	semigroup	PROPN
iajs-2287	115	10	if	if	SCONJ
iajs-2287	115	11	(	(	PUNCT
iajs-2287	115	12	wr	wr	NOUN
iajs-2287	115	13	)	)	PUNCT
iajs-2287	115	14	j=(jr	j=(jr	NOUN
iajs-2287	115	15	)	)	PUNCT
iajs-2287	115	16	w	w	PROPN
iajs-2287	115	17	;	;	PUNCT
iajs-2287	115	18	whenever	whenever	SCONJ
iajs-2287	115	19	w	w	PROPN
iajs-2287	115	20	,	,	PUNCT
iajs-2287	115	21	r	r	NOUN
iajs-2287	115	22	,	,	PUNCT
iajs-2287	115	23	j	j	PROPN
iajs-2287	115	24	∈	∈	PROPN
iajs-2287	115	25	ℵ.	ℵ.	PROPN
iajs-2287	115	26	2	2	X
iajs-2287	115	27	.	.	PUNCT
iajs-2287	115	28	medial	medial	ADJ
iajs-2287	115	29	law	law	NOUN
iajs-2287	115	30	of	of	ADP
iajs-2287	115	31	a	a	DET
iajs-2287	115	32	la	la	ADJ
iajs-2287	115	33	-	-	PUNCT
iajs-2287	115	34	semigroup	semigroup	PROPN
iajs-2287	115	35	means	mean	NOUN
iajs-2287	115	36	(	(	PUNCT
iajs-2287	115	37	wr	wr	NOUN
iajs-2287	115	38	)	)	PUNCT
iajs-2287	115	39	(	(	PUNCT
iajs-2287	115	40	jv	jv	NOUN
iajs-2287	115	41	)	)	PUNCT
iajs-2287	115	42	=	=	SYM
iajs-2287	115	43	(	(	PUNCT
iajs-2287	115	44	wj	wj	PROPN
iajs-2287	115	45	)	)	PUNCT
iajs-2287	115	46	(	(	PUNCT
iajs-2287	115	47	rv	rv	NOUN
iajs-2287	115	48	)	)	PUNCT
iajs-2287	115	49	;	;	PUNCT
iajs-2287	115	50	whenever	whenever	SCONJ
iajs-2287	115	51	w	w	X
iajs-2287	115	52	,	,	PUNCT
iajs-2287	115	53	r	r	NOUN
iajs-2287	115	54	,	,	PUNCT
iajs-2287	115	55	j	j	PROPN
iajs-2287	115	56	,	,	PUNCT
iajs-2287	115	57	v	v	NOUN
iajs-2287	115	58	∈	∈	NOUN
iajs-2287	115	59	ℵ.	ℵ.	NOUN
iajs-2287	116	1	3	3	X
iajs-2287	116	2	.	.	X
iajs-2287	117	1	in	in	ADP
iajs-2287	117	2	additional	additional	ADJ
iajs-2287	117	3	if	if	SCONJ
iajs-2287	117	4	ℵ	ℵ	NOUN
iajs-2287	117	5	has	have	VERB
iajs-2287	117	6	a	a	DET
iajs-2287	117	7	left	left	ADJ
iajs-2287	117	8	identity(necessary	identity(necessary	ADJ
iajs-2287	117	9	unique	unique	ADJ
iajs-2287	117	10	)	)	PUNCT
iajs-2287	117	11	the	the	DET
iajs-2287	117	12	paramedical	paramedical	ADJ
iajs-2287	117	13	law	law	NOUN
iajs-2287	117	14	mean	mean	VERB
iajs-2287	117	15	4	4	NUM
iajs-2287	117	16	.	.	PUNCT
iajs-2287	117	17	(	(	PUNCT
iajs-2287	117	18	wr	wr	NOUN
iajs-2287	117	19	)	)	PUNCT
iajs-2287	117	20	(	(	PUNCT
iajs-2287	117	21	jv)=(vr	jv)=(vr	NOUN
iajs-2287	117	22	)	)	PUNCT
iajs-2287	117	23	(	(	PUNCT
iajs-2287	117	24	jw	jw	PROPN
iajs-2287	117	25	)	)	PUNCT
iajs-2287	117	26	;	;	PUNCT
iajs-2287	117	27	whenever	whenever	SCONJ
iajs-2287	117	28	w	w	X
iajs-2287	117	29	,	,	PUNCT
iajs-2287	117	30	r	r	NOUN
iajs-2287	117	31	,	,	PUNCT
iajs-2287	117	32	j	j	PROPN
iajs-2287	117	33	,	,	PUNCT
iajs-2287	117	34	v	v	NOUN
iajs-2287	117	35	∈	∈	NOUN
iajs-2287	117	36	ℵ.	ℵ.	NOUN
iajs-2287	117	37	5	5	X
iajs-2287	117	38	.	.	PUNCT
iajs-2287	118	1	an	an	DET
iajs-2287	118	2	la	la	NOUN
iajs-2287	118	3	-	-	PUNCT
iajs-2287	118	4	semigroup	semigroup	NOUN
iajs-2287	118	5	with	with	ADP
iajs-2287	118	6	right	right	ADJ
iajs-2287	118	7	identity	identity	NOUN
iajs-2287	118	8	becomes	become	VERB
iajs-2287	118	9	a	a	DET
iajs-2287	118	10	commutative	commutative	ADJ
iajs-2287	118	11	semigroup	semigroup	NOUN
iajs-2287	118	12	with	with	ADP
iajs-2287	118	13	identity	identity	NOUN
iajs-2287	118	14	.	.	PUNCT
iajs-2287	119	1	if	if	SCONJ
iajs-2287	119	2	an	an	DET
iajs-2287	119	3	la	la	ADJ
iajs-2287	119	4	-	-	PUNCT
iajs-2287	119	5	semigroup	semigroup	PROPN
iajs-2287	119	6	contains	contain	VERB
iajs-2287	119	7	left	leave	VERB
iajs-2287	119	8	identity	identity	NOUN
iajs-2287	119	9	,	,	PUNCT
iajs-2287	119	10	the	the	DET
iajs-2287	119	11	following	follow	VERB
iajs-2287	119	12	law	law	NOUN
iajs-2287	119	13	holds	hold	VERB
iajs-2287	119	14	w	w	PROPN
iajs-2287	119	15	(	(	PUNCT
iajs-2287	119	16	r	r	PROPN
iajs-2287	119	17	j	j	PROPN
iajs-2287	119	18	)	)	PUNCT
iajs-2287	120	1	=	=	SYM
iajs-2287	120	2	r	r	NOUN
iajs-2287	120	3	(	(	PUNCT
iajs-2287	120	4	w	w	PROPN
iajs-2287	120	5	j	j	PROPN
iajs-2287	120	6	)	)	PUNCT
iajs-2287	120	7	;	;	PUNCT
iajs-2287	120	8	whenever	whenever	SCONJ
iajs-2287	120	9	w	w	X
iajs-2287	120	10	,	,	PUNCT
iajs-2287	120	11	r	r	NOUN
iajs-2287	120	12	,	,	PUNCT
iajs-2287	120	13	j	j	PROPN
iajs-2287	120	14	∈	∈	PROPN
iajs-2287	120	15	ℵ.	ℵ.	PROPN
iajs-2287	120	16	115	115	NUM
iajs-2287	121	1	ibn	ibn	PROPN
iajs-2287	121	2	al	al	PROPN
iajs-2287	121	3	-	-	PUNCT
iajs-2287	121	4	haitham	haitham	PROPN
iajs-2287	121	5	jour	jour	X
iajs-2287	121	6	.	.	PROPN
iajs-2287	121	7	for	for	ADP
iajs-2287	121	8	pure	pure	ADJ
iajs-2287	121	9	&	&	CCONJ
iajs-2287	121	10	appl	appl	PROPN
iajs-2287	121	11	.	.	PUNCT
iajs-2287	122	1	sci	sci	PROPN
iajs-2287	122	2	.	.	PROPN
iajs-2287	122	3	32	32	NUM
iajs-2287	122	4	(	(	PUNCT
iajs-2287	122	5	3	3	NUM
iajs-2287	122	6	)	)	SYM
iajs-2287	122	7	2019	2019	NUM
iajs-2287	122	8	proposition	proposition	NOUN
iajs-2287	122	9	30	30	NUM
iajs-2287	122	10	a	a	DET
iajs-2287	122	11	fuzzy	fuzzy	ADJ
iajs-2287	122	12	subset	subset	VERB
iajs-2287	122	13	ζ	ζ	NOUN
iajs-2287	122	14	of	of	ADP
iajs-2287	122	15	ℵ𝑟	ℵ𝑟	NOUN
iajs-2287	122	16	is	be	AUX
iajs-2287	122	17	a	a	DET
iajs-2287	122	18	fuzzy	fuzzy	ADJ
iajs-2287	122	19	right	right	ADJ
iajs-2287	122	20	ideal	ideal	NOUN
iajs-2287	122	21	iff	iff	PROPN
iajs-2287	122	22	it	it	PRON
iajs-2287	122	23	is	be	AUX
iajs-2287	122	24	a	a	DET
iajs-2287	122	25	fuzzy	fuzzy	ADJ
iajs-2287	122	26	left	leave	VERB
iajs-2287	122	27	ideal	ideal	NOUN
iajs-2287	122	28	.	.	PUNCT
iajs-2287	123	1	proof	proof	NOUN
iajs-2287	123	2	⟹	⟹	ADV
iajs-2287	123	3	suppose	suppose	VERB
iajs-2287	123	4	that	that	SCONJ
iajs-2287	123	5	ζ	ζ	NOUN
iajs-2287	123	6	is	be	AUX
iajs-2287	123	7	a	a	DET
iajs-2287	123	8	fuzzy	fuzzy	ADJ
iajs-2287	123	9	right	right	ADJ
iajs-2287	123	10	ideal	ideal	NOUN
iajs-2287	123	11	of	of	ADP
iajs-2287	123	12	ℵ	ℵ	NOUN
iajs-2287	123	13	,	,	PUNCT
iajs-2287	123	14	since	since	SCONJ
iajs-2287	123	15	ℵ	ℵ	NOUN
iajs-2287	123	16	is	be	AUX
iajs-2287	123	17	a	a	DET
iajs-2287	123	18	regular	regular	ADJ
iajs-2287	123	19	so	so	ADV
iajs-2287	123	20	whenever	whenever	SCONJ
iajs-2287	123	21	w∈	w∈	PROPN
iajs-2287	123	22	ℵ	ℵ	NOUN
iajs-2287	123	23	,	,	PUNCT
iajs-2287	123	24	∃	∃	PROPN
iajs-2287	123	25	z	z	PROPN
iajs-2287	123	26	∈	∈	PROPN
iajs-2287	123	27	ℵ	ℵ	NOUN
iajs-2287	123	28	,	,	PUNCT
iajs-2287	123	29	s.t	s.t	PROPN
iajs-2287	123	30	w	w	PROPN
iajs-2287	123	31	=	=	PROPN
iajs-2287	123	32	wzw	wzw	NOUN
iajs-2287	123	33	,	,	PUNCT
iajs-2287	123	34	so	so	CCONJ
iajs-2287	123	35	by	by	ADP
iajs-2287	123	36	using	use	VERB
iajs-2287	123	37	(	(	PUNCT
iajs-2287	123	38	1	1	NUM
iajs-2287	123	39	)	)	PUNCT
iajs-2287	123	40	ζ(wb	ζ(wb	PROPN
iajs-2287	123	41	)	)	PUNCT
iajs-2287	123	42	=	=	SYM
iajs-2287	123	43	ζ((wzw	ζ((wzw	PROPN
iajs-2287	123	44	)	)	PUNCT
iajs-2287	123	45	b	b	NOUN
iajs-2287	123	46	)	)	PUNCT
iajs-2287	123	47	=	=	NOUN
iajs-2287	123	48	ζ((𝑤𝑧𝑤)(zw)b	ζ((𝑤𝑧𝑤)(zw)b	PROPN
iajs-2287	123	49	)	)	PUNCT
iajs-2287	123	50	)	)	PUNCT
iajs-2287	124	1	=	=	X
iajs-2287	124	2	ζ(b	ζ(b	NOUN
iajs-2287	124	3	(	(	PUNCT
iajs-2287	124	4	𝑧𝑤)(wzw	𝑧𝑤)(wzw	NOUN
iajs-2287	124	5	)	)	PUNCT
iajs-2287	124	6	)	)	PUNCT
iajs-2287	124	7	≥	≥	PROPN
iajs-2287	124	8	ζ(b(zw	ζ(b(zw	PROPN
iajs-2287	124	9	)	)	PUNCT
iajs-2287	124	10	)	)	PUNCT
iajs-2287	124	11	≥	≥	NOUN
iajs-2287	124	12	ζ(b	ζ(b	NOUN
iajs-2287	124	13	)	)	PUNCT
iajs-2287	124	14	⟸	⟸	NUM
iajs-2287	124	15	suppose	suppose	VERB
iajs-2287	124	16	that	that	SCONJ
iajs-2287	124	17	ζ	ζ	NOUN
iajs-2287	124	18	is	be	AUX
iajs-2287	124	19	a	a	DET
iajs-2287	124	20	fuzzy	fuzzy	ADJ
iajs-2287	124	21	left	leave	VERB
iajs-2287	124	22	ideal	ideal	NOUN
iajs-2287	124	23	of	of	ADP
iajs-2287	124	24	ℵ𝑟	ℵ𝑟	NOUN
iajs-2287	124	25	,	,	PUNCT
iajs-2287	124	26	then	then	ADV
iajs-2287	124	27	using	use	VERB
iajs-2287	124	28	(	(	PUNCT
iajs-2287	124	29	1	1	NUM
iajs-2287	124	30	)	)	PUNCT
iajs-2287	124	31	ζ(wr	ζ(wr	NOUN
iajs-2287	124	32	)	)	PUNCT
iajs-2287	124	33	=	=	SYM
iajs-2287	124	34	ζ((wzw)r)=ζ((𝑤𝑧𝑤)(zw)r	ζ((wzw)r)=ζ((𝑤𝑧𝑤)(zw)r	NOUN
iajs-2287	124	35	)	)	PUNCT
iajs-2287	125	1	=	=	SYM
iajs-2287	125	2	ζ(r(zw)(wzw))≥	ζ(r(zw)(wzw))≥	ADJ
iajs-2287	125	3	ζ(wzw	ζ(wzw	NOUN
iajs-2287	125	4	)	)	PUNCT
iajs-2287	125	5	=	=	PUNCT
iajs-2287	125	6	ζ((wz)w)≥	ζ((wz)w)≥	ADP
iajs-2287	125	7	ζ((w)w	ζ((w)w	PROPN
iajs-2287	125	8	)	)	PUNCT
iajs-2287	125	9	≥	≥	NOUN
iajs-2287	125	10	ζ(𝑤2	ζ(𝑤2	NOUN
iajs-2287	125	11	)	)	PUNCT
iajs-2287	125	12	≥	≥	NOUN
iajs-2287	125	13	ζ(w	ζ(w	PROPN
iajs-2287	125	14	)	)	PUNCT
iajs-2287	125	15	.	.	PUNCT
iajs-2287	126	1	theorem	theorem	VERB
iajs-2287	126	2	31	31	NUM
iajs-2287	126	3	every	every	DET
iajs-2287	126	4	fuzzy	fuzzy	ADJ
iajs-2287	126	5	two	two	NUM
iajs-2287	126	6	sided	sided	ADJ
iajs-2287	126	7	ideal	ideal	NOUN
iajs-2287	126	8	of	of	ADP
iajs-2287	126	9	a	a	DET
iajs-2287	126	10	regular	regular	ADJ
iajs-2287	126	11	la	la	ADJ
iajs-2287	126	12	-	-	PUNCT
iajs-2287	126	13	semigroup	semigroup	NOUN
iajs-2287	126	14	ℵ	ℵ	NOUN
iajs-2287	126	15	,	,	PUNCT
iajs-2287	126	16	with	with	ADP
iajs-2287	126	17	left	left	ADJ
iajs-2287	126	18	identity	identity	NOUN
iajs-2287	126	19	is	be	AUX
iajs-2287	126	20	idempotent	idempotent	ADJ
iajs-2287	126	21	.	.	PUNCT
iajs-2287	127	1	proof	proof	NOUN
iajs-2287	127	2	suppose	suppose	VERB
iajs-2287	127	3	that	that	SCONJ
iajs-2287	127	4	ζ	ζ	NOUN
iajs-2287	127	5	is	be	AUX
iajs-2287	127	6	a	a	DET
iajs-2287	127	7	fuzzy	fuzzy	ADJ
iajs-2287	127	8	two	two	NUM
iajs-2287	127	9	sided	sided	ADJ
iajs-2287	127	10	ideal	ideal	NOUN
iajs-2287	127	11	of	of	ADP
iajs-2287	127	12	ℵ	ℵ	NOUN
iajs-2287	127	13	,	,	PUNCT
iajs-2287	127	14	then	then	ADV
iajs-2287	127	15	clearly	clearly	ADV
iajs-2287	127	16	ζ	ζ	ADJ
iajs-2287	127	17	∘	∘	NOUN
iajs-2287	127	18	ζ	ζ	NOUN
iajs-2287	127	19	⊆	⊆	NUM
iajs-2287	127	20	ζ	ζ	NOUN
iajs-2287	127	21	∘	∘	NOUN
iajs-2287	127	22	ℵ	ℵ	ADP
iajs-2287	127	23	⊆	⊆	NUM
iajs-2287	127	24	ζ	ζ	NOUN
iajs-2287	127	25	.	.	PUNCT
iajs-2287	128	1	since	since	SCONJ
iajs-2287	128	2	ℵ	ℵ	NOUN
iajs-2287	128	3	is	be	AUX
iajs-2287	128	4	a	a	DET
iajs-2287	128	5	regular	regular	ADJ
iajs-2287	128	6	so	so	ADV
iajs-2287	128	7	whenever	whenever	SCONJ
iajs-2287	128	8	w	w	PROPN
iajs-2287	128	9	∈	∈	PROPN
iajs-2287	128	10	ℵ	ℵ	NOUN
iajs-2287	128	11	,	,	PUNCT
iajs-2287	128	12	∃	∃	PROPN
iajs-2287	128	13	z	z	PROPN
iajs-2287	128	14	∈	∈	PROPN
iajs-2287	128	15	ℵ	ℵ	NOUN
iajs-2287	128	16	,	,	PUNCT
iajs-2287	128	17	s.t	s.t	PROPN
iajs-2287	128	18	w	w	PROPN
iajs-2287	128	19	=	=	PROPN
iajs-2287	128	20	wzw	wzw	VERB
iajs-2287	128	21	so	so	ADV
iajs-2287	128	22	by	by	ADP
iajs-2287	128	23	using	use	VERB
iajs-2287	128	24	(	(	PUNCT
iajs-2287	128	25	1	1	NUM
iajs-2287	128	26	)	)	PUNCT
iajs-2287	128	27	w	w	NOUN
iajs-2287	128	28	=	=	NOUN
iajs-2287	128	29	wzw	wzw	NOUN
iajs-2287	128	30	=	=	NOUN
iajs-2287	128	31	w(zw)(zw)=(zwzw)w	w(zw)(zw)=(zwzw)w	X
iajs-2287	128	32	,	,	PUNCT
iajs-2287	128	33	(	(	PUNCT
iajs-2287	128	34	ζ	ζ	NOUN
iajs-2287	128	35	∘	∘	NOUN
iajs-2287	128	36	ζ)(w)=⋁	ζ)(w)=⋁	NUM
iajs-2287	128	37	ζ(zwzw	ζ(zwzw	NOUN
iajs-2287	128	38	)	)	PUNCT
iajs-2287	128	39	∧	∧	PROPN
iajs-2287	128	40	ζ(w)w=(zwzw)w	ζ(w)w=(zwzw)w	NOUN
iajs-2287	128	41	≥	≥	NUM
iajs-2287	128	42	ζ(zwzw	ζ(zwzw	NOUN
iajs-2287	128	43	)	)	PUNCT
iajs-2287	128	44	∧	∧	PROPN
iajs-2287	128	45	ζ(w	ζ(w	PROPN
iajs-2287	128	46	)	)	PUNCT
iajs-2287	128	47	≥	≥	NOUN
iajs-2287	128	48	ζ(w	ζ(w	PROPN
iajs-2287	128	49	)	)	PUNCT
iajs-2287	128	50	∧	∧	PROPN
iajs-2287	128	51	ζ(w)=ζ(w	ζ(w)=ζ(w	PROPN
iajs-2287	128	52	)	)	PUNCT
iajs-2287	128	53	.	.	PUNCT
iajs-2287	129	1	and	and	CCONJ
iajs-2287	129	2	this	this	PRON
iajs-2287	129	3	implies	imply	VERB
iajs-2287	129	4	that	that	SCONJ
iajs-2287	129	5	ζ	ζ	NOUN
iajs-2287	129	6	∘	∘	ADJ
iajs-2287	129	7	ζ	ζ	PROPN
iajs-2287	129	8	⊇	⊇	PROPN
iajs-2287	129	9	ζ	ζ	NOUN
iajs-2287	129	10	,	,	PUNCT
iajs-2287	129	11	hence	hence	ADV
iajs-2287	129	12	ζ	ζ	NOUN
iajs-2287	129	13	∘	∘	NUM
iajs-2287	129	14	ζ	ζ	NOUN
iajs-2287	129	15	=	=	SYM
iajs-2287	129	16	ζ	ζ	NOUN
iajs-2287	129	17	.	.	PUNCT
iajs-2287	129	18	theorem	theorem	VERB
iajs-2287	129	19	32	32	NUM
iajs-2287	129	20	for	for	ADP
iajs-2287	129	21	a	a	DET
iajs-2287	129	22	fuzzy	fuzzy	ADJ
iajs-2287	129	23	subset	subset	VERB
iajs-2287	129	24	ζ	ζ	NOUN
iajs-2287	129	25	of	of	ADP
iajs-2287	129	26	a	a	DET
iajs-2287	129	27	regular	regular	ADJ
iajs-2287	129	28	la	la	ADJ
iajs-2287	129	29	-	-	PUNCT
iajs-2287	129	30	semigroup	semigroup	NOUN
iajs-2287	129	31	ℵ	ℵ	NOUN
iajs-2287	129	32	,	,	PUNCT
iajs-2287	129	33	with	with	ADP
iajs-2287	129	34	left	left	ADJ
iajs-2287	129	35	identity	identity	NOUN
iajs-2287	129	36	then	then	ADV
iajs-2287	129	37	ζ	ζ	NOUN
iajs-2287	129	38	is	be	AUX
iajs-2287	129	39	a	a	DET
iajs-2287	129	40	fuzzy	fuzzy	ADJ
iajs-2287	129	41	two	two	NUM
iajs-2287	129	42	sided	sided	ADJ
iajs-2287	129	43	ideal	ideal	NOUN
iajs-2287	129	44	of	of	ADP
iajs-2287	129	45	ℵ	ℵ	PROPN
iajs-2287	129	46	iff	iff	PROPN
iajs-2287	129	47	it	it	PRON
iajs-2287	129	48	is	be	AUX
iajs-2287	129	49	a	a	DET
iajs-2287	129	50	fuzzy	fuzzy	ADJ
iajs-2287	129	51	interior	interior	ADJ
iajs-2287	129	52	ideal	ideal	NOUN
iajs-2287	129	53	of	of	ADP
iajs-2287	129	54	ℵ.	ℵ.	PROPN
iajs-2287	129	55	proof	proof	NOUN
iajs-2287	129	56	⟹	⟹	PUNCT
iajs-2287	129	57	suppose	suppose	VERB
iajs-2287	129	58	that	that	SCONJ
iajs-2287	129	59	ζ	ζ	NOUN
iajs-2287	129	60	be	be	AUX
iajs-2287	129	61	a	a	DET
iajs-2287	129	62	fuzzy	fuzzy	ADJ
iajs-2287	129	63	two	two	NUM
iajs-2287	129	64	sided	sided	ADJ
iajs-2287	129	65	ideal	ideal	NOUN
iajs-2287	129	66	of	of	ADP
iajs-2287	129	67	ℵ	ℵ	NOUN
iajs-2287	129	68	,	,	PUNCT
iajs-2287	129	69	then	then	ADV
iajs-2287	129	70	obviously	obviously	ADV
iajs-2287	129	71	,	,	PUNCT
iajs-2287	129	72	ζ	ζ	NOUN
iajs-2287	129	73	is	be	AUX
iajs-2287	129	74	a	a	DET
iajs-2287	129	75	fuzzy	fuzzy	ADJ
iajs-2287	129	76	interior	interior	ADJ
iajs-2287	129	77	ideal	ideal	NOUN
iajs-2287	129	78	of	of	ADP
iajs-2287	129	79	ℵ.	ℵ.	PROPN
iajs-2287	129	80	⟸	⟸	PROPN
iajs-2287	129	81	suppose	suppose	VERB
iajs-2287	129	82	that	that	SCONJ
iajs-2287	129	83	ζ	ζ	NOUN
iajs-2287	129	84	be	be	AUX
iajs-2287	129	85	a	a	DET
iajs-2287	129	86	fuzzy	fuzzy	ADJ
iajs-2287	129	87	interior	interior	ADJ
iajs-2287	129	88	ideal	ideal	NOUN
iajs-2287	129	89	of	of	ADP
iajs-2287	129	90	ℵ	ℵ	NOUN
iajs-2287	129	91	,	,	PUNCT
iajs-2287	129	92	and	and	CCONJ
iajs-2287	129	93	w	w	PROPN
iajs-2287	129	94	,	,	PUNCT
iajs-2287	129	95	r∈	r∈	PROPN
iajs-2287	129	96	ℵ	ℵ	NOUN
iajs-2287	129	97	,	,	PUNCT
iajs-2287	129	98	then	then	ADV
iajs-2287	129	99	since	since	SCONJ
iajs-2287	129	100	ℵ	ℵ	NOUN
iajs-2287	129	101	is	be	AUX
iajs-2287	129	102	a	a	DET
iajs-2287	129	103	regular	regular	NOUN
iajs-2287	129	104	of	of	ADP
iajs-2287	129	105	alsemigroup	alsemigroup	ADJ
iajs-2287	129	106	,	,	PUNCT
iajs-2287	129	107	so	so	ADV
iajs-2287	129	108	∃	∃	PROPN
iajs-2287	129	109	z	z	PROPN
iajs-2287	129	110	,	,	PUNCT
iajs-2287	129	111	y	y	PROPN
iajs-2287	129	112	∈	∈	PROPN
iajs-2287	129	113	ℵ	ℵ	ADP
iajs-2287	129	114	s.t	s.t	PROPN
iajs-2287	129	115	w	w	PROPN
iajs-2287	129	116	=	=	PROPN
iajs-2287	129	117	wzw	wzw	NOUN
iajs-2287	129	118	,	,	PUNCT
iajs-2287	129	119	r	r	NOUN
iajs-2287	129	120	=	=	SYM
iajs-2287	129	121	ryr	ryr	NOUN
iajs-2287	129	122	,	,	PUNCT
iajs-2287	129	123	then	then	ADV
iajs-2287	129	124	ζ(wr	ζ(wr	NOUN
iajs-2287	129	125	)	)	PUNCT
iajs-2287	129	126	=	=	SYM
iajs-2287	129	127	ζ((w	ζ((w	NOUN
iajs-2287	129	128	z	z	NOUN
iajs-2287	129	129	w)r	w)r	ADV
iajs-2287	129	130	)	)	PUNCT
iajs-2287	129	131	using	use	VERB
iajs-2287	129	132	(	(	PUNCT
iajs-2287	129	133	1	1	NUM
iajs-2287	129	134	)	)	PUNCT
iajs-2287	129	135	=	=	SYM
iajs-2287	130	1	ζ(r(z	ζ(r(z	NOUN
iajs-2287	130	2	w))(w	w))(w	NOUN
iajs-2287	130	3	z	z	PROPN
iajs-2287	130	4	w	w	NOUN
iajs-2287	130	5	)	)	PUNCT
iajs-2287	130	6	)	)	PUNCT
iajs-2287	131	1	using	use	VERB
iajs-2287	131	2	(	(	PUNCT
iajs-2287	131	3	2	2	NUM
iajs-2287	131	4	)	)	PUNCT
iajs-2287	131	5	=	=	SYM
iajs-2287	131	6	ζ(rw)((zw)(zw	ζ(rw)((zw)(zw	NOUN
iajs-2287	131	7	)	)	PUNCT
iajs-2287	131	8	)	)	PUNCT
iajs-2287	132	1	=	=	SYM
iajs-2287	132	2	ζ(𝑟𝑤)t	ζ(𝑟𝑤)t	NOUN
iajs-2287	132	3	)	)	PUNCT
iajs-2287	132	4	where	where	SCONJ
iajs-2287	132	5	t=	t=	PRON
iajs-2287	132	6	(	(	PUNCT
iajs-2287	132	7	(	(	PUNCT
iajs-2287	132	8	z	z	NOUN
iajs-2287	132	9	w)(z	w)(z	NOUN
iajs-2287	132	10	w	w	NOUN
iajs-2287	132	11	)	)	PUNCT
iajs-2287	132	12	)	)	PUNCT
iajs-2287	132	13	≥	≥	NOUN
iajs-2287	132	14	ζ(w	ζ(w	PROPN
iajs-2287	132	15	)	)	PUNCT
iajs-2287	132	16	,	,	PUNCT
iajs-2287	132	17	also	also	ADV
iajs-2287	132	18	ζ(wr	ζ(wr	NOUN
iajs-2287	132	19	)	)	PUNCT
iajs-2287	133	1	=	=	SYM
iajs-2287	133	2	ζ(w(ryr))=	ζ(w(ryr))=	ADJ
iajs-2287	133	3	ζ(w(ryry)r	ζ(w(ryry)r	NOUN
iajs-2287	133	4	)	)	PUNCT
iajs-2287	133	5	)	)	PUNCT
iajs-2287	133	6	using	use	VERB
iajs-2287	133	7	(	(	PUNCT
iajs-2287	133	8	4	4	NUM
iajs-2287	133	9	)	)	PUNCT
iajs-2287	133	10	=	=	NOUN
iajs-2287	133	11	ζ((ryry)(wr	ζ((ryry)(wr	NOUN
iajs-2287	133	12	)	)	PUNCT
iajs-2287	133	13	)	)	PUNCT
iajs-2287	134	1	=	=	SYM
iajs-2287	134	2	ζ((ry)r(ywr	ζ((ry)r(ywr	PROPN
iajs-2287	134	3	)	)	PUNCT
iajs-2287	134	4	)	)	PUNCT
iajs-2287	135	1	=	=	SYM
iajs-2287	135	2	ζ(jrt	ζ(jrt	PROPN
iajs-2287	135	3	)	)	PUNCT
iajs-2287	135	4	where	where	SCONJ
iajs-2287	135	5	j=	j=	PROPN
iajs-2287	135	6	ry	ry	PROPN
iajs-2287	135	7	and	and	CCONJ
iajs-2287	135	8	t=	t=	PRON
iajs-2287	135	9	y	y	PROPN
iajs-2287	135	10	w	w	NOUN
iajs-2287	135	11	r	r	NOUN
iajs-2287	135	12	and	and	CCONJ
iajs-2287	135	13	≥	≥	NOUN
iajs-2287	135	14	ζ(r	ζ(r	NOUN
iajs-2287	135	15	)	)	PUNCT
iajs-2287	135	16	,	,	PUNCT
iajs-2287	135	17	hence	hence	ADV
iajs-2287	135	18	,	,	PUNCT
iajs-2287	135	19	ζ	ζ	PROPN
iajs-2287	135	20	is	be	AUX
iajs-2287	135	21	a	a	DET
iajs-2287	135	22	fuzzy	fuzzy	ADJ
iajs-2287	135	23	two	two	NUM
iajs-2287	135	24	sided	sided	ADJ
iajs-2287	135	25	ideal	ideal	NOUN
iajs-2287	135	26	.	.	PUNCT
iajs-2287	136	1	116	116	NUM
iajs-2287	136	2	ibn	ibn	PROPN
iajs-2287	136	3	al	al	PROPN
iajs-2287	136	4	-	-	PUNCT
iajs-2287	136	5	haitham	haitham	PROPN
iajs-2287	136	6	jour	jour	X
iajs-2287	136	7	.	.	PROPN
iajs-2287	136	8	for	for	ADP
iajs-2287	136	9	pure	pure	ADJ
iajs-2287	136	10	&	&	CCONJ
iajs-2287	136	11	appl	appl	PROPN
iajs-2287	136	12	.	.	PUNCT
iajs-2287	137	1	sci	sci	PROPN
iajs-2287	137	2	.	.	PROPN
iajs-2287	137	3	32	32	NUM
iajs-2287	137	4	(	(	PUNCT
iajs-2287	137	5	3	3	NUM
iajs-2287	137	6	)	)	PUNCT
iajs-2287	137	7	2019	2019	NUM
iajs-2287	137	8	2	2	NUM
iajs-2287	137	9	.	.	PUNCT
iajs-2287	137	10	conclusion	conclusion	NOUN
iajs-2287	137	11	from	from	ADP
iajs-2287	137	12	the	the	DET
iajs-2287	137	13	research	research	NOUN
iajs-2287	137	14	/	/	PUNCT
iajs-2287	137	15	the	the	DET
iajs-2287	137	16	evidence	evidence	NOUN
iajs-2287	137	17	we	we	PRON
iajs-2287	137	18	conclude	conclude	VERB
iajs-2287	137	19	that	that	SCONJ
iajs-2287	137	20	1	1	X
iajs-2287	137	21	.	.	PUNCT
iajs-2287	138	1	let	let	VERB
iajs-2287	138	2	ζ	ζ	NOUN
iajs-2287	138	3	be	be	AUX
iajs-2287	138	4	a	a	DET
iajs-2287	138	5	fuzzy	fuzzy	ADJ
iajs-2287	138	6	subset	subset	NOUN
iajs-2287	138	7	in	in	ADP
iajs-2287	138	8	ℵ𝑟	ℵ𝑟	NOUN
iajs-2287	138	9	then	then	ADV
iajs-2287	138	10	it	it	PRON
iajs-2287	138	11	is	be	AUX
iajs-2287	138	12	an	an	DET
iajs-2287	138	13	anti	anti	ADJ
iajs-2287	138	14	fuzzy	fuzzy	ADJ
iajs-2287	138	15	two	two	NUM
iajs-2287	138	16	sided	sided	ADJ
iajs-2287	138	17	ideal	ideal	NOUN
iajs-2287	138	18	of	of	ADP
iajs-2287	138	19	ℵ	ℵ	PROPN
iajs-2287	138	20	iff	iff	PROPN
iajs-2287	138	21	is	be	AUX
iajs-2287	138	22	an	an	DET
iajs-2287	138	23	anti	anti	ADJ
iajs-2287	138	24	fuzzy	fuzzy	ADJ
iajs-2287	138	25	interior	interior	ADJ
iajs-2287	138	26	ideal	ideal	NOUN
iajs-2287	138	27	of	of	ADP
iajs-2287	138	28	ℵ.	ℵ.	PROPN
iajs-2287	138	29	2	2	X
iajs-2287	138	30	.	.	PUNCT
iajs-2287	139	1	in	in	ADP
iajs-2287	139	2	a	a	DET
iajs-2287	139	3	regular	regular	ADJ
iajs-2287	139	4	semigroup	semigroup	ADJ
iajs-2287	139	5	ℵ	ℵ	NOUN
iajs-2287	139	6	,	,	PUNCT
iajs-2287	139	7	then	then	ADV
iajs-2287	139	8	the	the	DET
iajs-2287	139	9	following	following	NOUN
iajs-2287	139	10	are	be	AUX
iajs-2287	139	11	satisfy	satisfy	NOUN
iajs-2287	139	12	the	the	DET
iajs-2287	139	13	following	follow	VERB
iajs-2287	139	14	i	i	NOUN
iajs-2287	139	15	)	)	PUNCT
iajs-2287	139	16	every	every	DET
iajs-2287	139	17	anti	anti	X
iajs-2287	139	18	fuzzy	fuzzy	ADJ
iajs-2287	139	19	right	right	ADJ
iajs-2287	139	20	ideal	ideal	NOUN
iajs-2287	139	21	is	be	AUX
iajs-2287	139	22	idempotent	idempotent	ADJ
iajs-2287	139	23	.	.	PUNCT
iajs-2287	140	1	ii	ii	X
iajs-2287	140	2	)	)	PUNCT
iajs-2287	140	3	every	every	DET
iajs-2287	140	4	anti	anti	X
iajs-2287	140	5	fuzzy	fuzzy	ADJ
iajs-2287	140	6	interior	interior	ADJ
iajs-2287	140	7	ideal	ideal	NOUN
iajs-2287	140	8	is	be	AUX
iajs-2287	140	9	idempotent	idempotent	ADJ
iajs-2287	140	10	.	.	PUNCT
iajs-2287	141	1	3	3	X
iajs-2287	141	2	.	.	X
iajs-2287	141	3	if	if	SCONJ
iajs-2287	141	4	ζ	ζ	PROPN
iajs-2287	141	5	,	,	PUNCT
iajs-2287	141	6	μ	μ	PROPN
iajs-2287	141	7	are	be	AUX
iajs-2287	141	8	an	an	DET
iajs-2287	141	9	anti	anti	ADJ
iajs-2287	141	10	fuzzy	fuzzy	ADJ
iajs-2287	141	11	two	two	NUM
iajs-2287	141	12	sided	sided	ADJ
iajs-2287	141	13	ideals	ideal	NOUN
iajs-2287	141	14	of	of	ADP
iajs-2287	141	15	ℵ𝑟	ℵ𝑟	NOUN
iajs-2287	141	16	,	,	PUNCT
iajs-2287	141	17	then	then	ADV
iajs-2287	141	18	ζ	ζ	NOUN
iajs-2287	141	19	∗	∗	NOUN
iajs-2287	141	20	μ	μ	NOUN
iajs-2287	141	21	=	=	NOUN
iajs-2287	141	22	ζ	ζ	PROPN
iajs-2287	141	23	∪	∪	VERB
iajs-2287	141	24	μ	μ	NUM
iajs-2287	141	25	.	.	PROPN
iajs-2287	141	26	4	4	NUM
iajs-2287	141	27	.	.	X
iajs-2287	142	1	for	for	ADP
iajs-2287	142	2	anti	anti	X
iajs-2287	142	3	fuzzy	fuzzy	ADJ
iajs-2287	142	4	generalized	generalized	ADJ
iajs-2287	142	5	bi	bi	ADJ
iajs-2287	142	6	-	-	ADJ
iajs-2287	142	7	ideal	ideal	ADJ
iajs-2287	142	8	ζ	ζ	NOUN
iajs-2287	142	9	and	and	CCONJ
iajs-2287	142	10	anti	anti	ADJ
iajs-2287	142	11	fuzzy	fuzzy	ADJ
iajs-2287	142	12	right	right	ADJ
iajs-2287	142	13	ideal	ideal	PROPN
iajs-2287	142	14	μ	μ	PROPN
iajs-2287	142	15	of	of	ADP
iajs-2287	142	16	ℵ𝑟	ℵ𝑟	NOUN
iajs-2287	142	17	,	,	PUNCT
iajs-2287	142	18	5	5	NUM
iajs-2287	142	19	.	.	X
iajs-2287	142	20	then	then	ADV
iajs-2287	142	21	ζ	ζ	NOUN
iajs-2287	142	22	∗	∗	NOUN
iajs-2287	142	23	μ	μ	NOUN
iajs-2287	142	24	≤	≤	NOUN
iajs-2287	142	25	ζ	ζ	PROPN
iajs-2287	142	26	∨	∨	NUM
iajs-2287	142	27	μ	μ	PROPN
iajs-2287	142	28	.	.	PROPN
iajs-2287	142	29	6	6	NUM
iajs-2287	142	30	.	.	X
iajs-2287	143	1	for	for	ADP
iajs-2287	143	2	every	every	DET
iajs-2287	143	3	anti	anti	ADJ
iajs-2287	143	4	fuzzy	fuzzy	NOUN
iajs-2287	143	5	left	leave	VERB
iajs-2287	143	6	ideal	ideal	PROPN
iajs-2287	143	7	α	α	NOUN
iajs-2287	143	8	,	,	PUNCT
iajs-2287	143	9	every	every	DET
iajs-2287	143	10	anti	anti	ADJ
iajs-2287	143	11	fuzzy	fuzzy	ADJ
iajs-2287	143	12	generalized	generalized	ADJ
iajs-2287	143	13	bi	bi	ADJ
iajs-2287	143	14	-	-	ADJ
iajs-2287	143	15	ideal	ideal	ADJ
iajs-2287	143	16	μ	μ	PROPN
iajs-2287	143	17	,	,	PUNCT
iajs-2287	143	18	and	and	CCONJ
iajs-2287	143	19	every	every	DET
iajs-2287	143	20	anti	anti	X
iajs-2287	143	21	fuzzy	fuzzy	ADJ
iajs-2287	143	22	interior	interior	ADJ
iajs-2287	143	23	ideal	ideal	ADJ
iajs-2287	143	24	ζ	ζ	NOUN
iajs-2287	143	25	of	of	ADP
iajs-2287	143	26	ℵ𝑟	ℵ𝑟	NOUN
iajs-2287	143	27	,	,	PUNCT
iajs-2287	143	28	then	then	ADV
iajs-2287	143	29	μ	μ	PROPN
iajs-2287	143	30	∗	∗	NOUN
iajs-2287	143	31	α	α	PROPN
iajs-2287	143	32	∗	∗	NOUN
iajs-2287	143	33	ζ	ζ	NOUN
iajs-2287	143	34	⊆	⊆	NUM
iajs-2287	143	35	μ	μ	NOUN
iajs-2287	143	36	∪	∪	ADP
iajs-2287	143	37	α	α	PROPN
iajs-2287	143	38	∪	∪	PROPN
iajs-2287	143	39	ζ	ζ	NOUN
iajs-2287	143	40	.	.	NOUN
iajs-2287	143	41	7	7	NUM
iajs-2287	143	42	.	.	X
iajs-2287	143	43	for	for	ADP
iajs-2287	143	44	a	a	DET
iajs-2287	143	45	fuzzy	fuzzy	ADJ
iajs-2287	143	46	subset	subset	VERB
iajs-2287	143	47	ζ	ζ	NOUN
iajs-2287	143	48	of	of	ADP
iajs-2287	143	49	a	a	DET
iajs-2287	143	50	regular	regular	ADJ
iajs-2287	143	51	la	la	ADJ
iajs-2287	143	52	-	-	PUNCT
iajs-2287	143	53	semigroup	semigroup	NOUN
iajs-2287	143	54	ℵ	ℵ	NOUN
iajs-2287	143	55	,	,	PUNCT
iajs-2287	143	56	with	with	ADP
iajs-2287	143	57	left	left	ADJ
iajs-2287	143	58	identity	identity	NOUN
iajs-2287	143	59	then	then	ADV
iajs-2287	143	60	ζ	ζ	NOUN
iajs-2287	143	61	is	be	AUX
iajs-2287	143	62	a	a	DET
iajs-2287	143	63	fuzzy	fuzzy	ADJ
iajs-2287	143	64	two	two	NUM
iajs-2287	143	65	sided	sided	ADJ
iajs-2287	143	66	ideal	ideal	NOUN
iajs-2287	143	67	of	of	ADP
iajs-2287	143	68	ℵ	ℵ	PROPN
iajs-2287	143	69	iff	iff	PROPN
iajs-2287	143	70	it	it	PRON
iajs-2287	143	71	is	be	AUX
iajs-2287	143	72	a	a	DET
iajs-2287	143	73	fuzzy	fuzzy	ADJ
iajs-2287	143	74	interior	interior	ADJ
iajs-2287	143	75	ideal	ideal	NOUN
iajs-2287	143	76	of	of	ADP
iajs-2287	143	77	ℵ.	ℵ.	PROPN
iajs-2287	143	78	references	reference	NOUN
iajs-2287	143	79	1	1	NUM
iajs-2287	143	80	.	.	PUNCT
iajs-2287	144	1	hong	hong	PROPN
iajs-2287	144	2	,	,	PUNCT
iajs-2287	144	3	s.m	s.m	PROPN
iajs-2287	144	4	.	.	PROPN
iajs-2287	144	5	;	;	PUNCT
iajs-2287	144	6	jun	jun	PROPN
iajs-2287	144	7	,	,	PUNCT
iajs-2287	144	8	y.b	y.b	PROPN
iajs-2287	144	9	.	.	PROPN
iajs-2287	144	10	;	;	PUNCT
iajs-2287	145	1	meng	meng	PROPN
iajs-2287	145	2	,	,	PUNCT
iajs-2287	145	3	j.	j.	PROPN
iajs-2287	145	4	in	in	ADP
iajs-2287	145	5	fuzzy	fuzzy	ADJ
iajs-2287	145	6	interior	interior	ADJ
iajs-2287	145	7	ideals	ideal	NOUN
iajs-2287	145	8	in	in	ADP
iajs-2287	145	9	semigroups	semigroup	NOUN
iajs-2287	145	10	.	.	PUNCT
iajs-2287	146	1	indain	indain	VERB
iajs-2287	146	2	j.	j.	PROPN
iajs-2287	146	3	pure	pure	PROPN
iajs-2287	146	4	appl	appl	PROPN
iajs-2287	146	5	.	.	PUNCT
iajs-2287	147	1	math.1995	math.1995	PROPN
iajs-2287	147	2	,	,	PUNCT
iajs-2287	147	3	26	26	NUM
iajs-2287	147	4	,	,	PUNCT
iajs-2287	147	5	9	9	NUM
iajs-2287	147	6	,	,	PUNCT
iajs-2287	147	7	859	859	NUM
iajs-2287	147	8	-	-	SYM
iajs-2287	147	9	863	863	NUM
iajs-2287	147	10	.	.	PUNCT
iajs-2287	148	1	2	2	X
iajs-2287	148	2	.	.	X
iajs-2287	148	3	nobuaki	nobuaki	PROPN
iajs-2287	148	4	,	,	PUNCT
iajs-2287	148	5	k.	k.	PROPN
iajs-2287	148	6	on	on	ADP
iajs-2287	148	7	fuzzy	fuzzy	ADJ
iajs-2287	148	8	ideal	ideal	ADJ
iajs-2287	148	9	and	and	CCONJ
iajs-2287	148	10	fuzzy	fuzzy	ADJ
iajs-2287	148	11	bi	bi	NOUN
iajs-2287	148	12	-	-	NOUN
iajs-2287	148	13	ideals	ideal	NOUN
iajs-2287	148	14	in	in	ADP
iajs-2287	148	15	semigroups	semigroup	NOUN
iajs-2287	148	16	.	.	PUNCT
iajs-2287	149	1	fuzzy	fuzzy	ADJ
iajs-2287	149	2	sets	set	NOUN
iajs-2287	149	3	and	and	CCONJ
iajs-2287	149	4	systems	system	NOUN
iajs-2287	149	5	.	.	PUNCT
iajs-2287	150	1	1981	1981	NUM
iajs-2287	150	2	,	,	PUNCT
iajs-2287	150	3	5	5	NUM
iajs-2287	150	4	,	,	PUNCT
iajs-2287	150	5	203	203	NUM
iajs-2287	150	6	-	-	SYM
iajs-2287	150	7	215	215	NUM
iajs-2287	150	8	.	.	PUNCT
iajs-2287	151	1	3	3	X
iajs-2287	151	2	.	.	X
iajs-2287	151	3	shabir	shabir	PROPN
iajs-2287	151	4	,	,	PUNCT
iajs-2287	151	5	m.	m.	NOUN
iajs-2287	151	6	;	;	PUNCT
iajs-2287	151	7	nawaz	nawaz	ADJ
iajs-2287	151	8	,	,	PUNCT
iajs-2287	151	9	y.	y.	PROPN
iajs-2287	151	10	semigroups	semigroup	NOUN
iajs-2287	151	11	characterized	characterize	VERB
iajs-2287	151	12	by	by	ADP
iajs-2287	151	13	the	the	DET
iajs-2287	151	14	properties	property	NOUN
iajs-2287	151	15	of	of	ADP
iajs-2287	151	16	their	their	PRON
iajs-2287	151	17	anti	anti	ADJ
iajs-2287	151	18	fuzzy	fuzzy	ADJ
iajs-2287	151	19	ideals	ideal	NOUN
iajs-2287	151	20	,	,	PUNCT
iajs-2287	151	21	journal	journal	NOUN
iajs-2287	151	22	of	of	ADP
iajs-2287	151	23	advanced	advanced	ADJ
iajs-2287	151	24	research	research	NOUN
iajs-2287	151	25	in	in	ADP
iajs-2287	151	26	pure	pure	ADJ
iajs-2287	151	27	mathematics.2009	mathematics.2009	PROPN
iajs-2287	151	28	,	,	PUNCT
iajs-2287	151	29	1	1	NUM
iajs-2287	151	30	,	,	PUNCT
iajs-2287	151	31	3	3	NUM
iajs-2287	151	32	,	,	PUNCT
iajs-2287	151	33	42	42	NUM
iajs-2287	151	34	-	-	SYM
iajs-2287	151	35	59	59	NUM
iajs-2287	151	36	.	.	PUNCT
iajs-2287	152	1	4	4	X
iajs-2287	152	2	.	.	X
iajs-2287	152	3	khan	khan	PROPN
iajs-2287	152	4	,	,	PUNCT
iajs-2287	152	5	m.	m.	NOUN
iajs-2287	152	6	;	;	PUNCT
iajs-2287	152	7	asif	asif	NOUN
iajs-2287	152	8	,	,	PUNCT
iajs-2287	152	9	t.	t.	NOUN
iajs-2287	152	10	characterizations	characterization	NOUN
iajs-2287	152	11	of	of	ADP
iajs-2287	152	12	semigroups	semigroup	NOUN
iajs-2287	152	13	by	by	ADP
iajs-2287	152	14	their	their	PRON
iajs-2287	152	15	anti	anti	ADJ
iajs-2287	152	16	fuzzy	fuzzy	ADJ
iajs-2287	152	17	ideals	ideal	NOUN
iajs-2287	152	18	.	.	PUNCT
iajs-2287	153	1	journal	journal	NOUN
iajs-2287	153	2	of	of	ADP
iajs-2287	153	3	mathematics	mathematics	PROPN
iajs-2287	153	4	research.2010	research.2010	PROPN
iajs-2287	153	5	,	,	PUNCT
iajs-2287	153	6	2	2	NUM
iajs-2287	153	7	,	,	PUNCT
iajs-2287	153	8	3	3	NUM
iajs-2287	153	9	,	,	PUNCT
iajs-2287	153	10	134	134	NUM
iajs-2287	153	11	-	-	SYM
iajs-2287	153	12	143	143	NUM
iajs-2287	153	13	.	.	PUNCT
iajs-2287	154	1	5	5	NUM
iajs-2287	154	2	.	.	X
iajs-2287	154	3	khan	khan	PROPN
iajs-2287	154	4	,	,	PUNCT
iajs-2287	154	5	m.	m.	NOUN
iajs-2287	154	6	;	;	PUNCT
iajs-2287	154	7	asif	asif	NOUN
iajs-2287	154	8	,	,	PUNCT
iajs-2287	154	9	t.	t.	PROPN
iajs-2287	154	10	faisal	faisal	PROPN
iajs-2287	154	11	.	.	PUNCT
iajs-2287	155	1	intra	intra	ADJ
iajs-2287	155	2	-	-	ADJ
iajs-2287	155	3	regular	regular	ADJ
iajs-2287	155	4	left	left	NOUN
iajs-2287	155	5	almost	almost	ADV
iajs-2287	155	6	semigroups	semigroup	NOUN
iajs-2287	155	7	characterized	characterize	VERB
iajs-2287	155	8	by	by	ADP
iajs-2287	155	9	their	their	PRON
iajs-2287	155	10	anti	anti	ADJ
iajs-2287	155	11	fuzzy	fuzzy	ADJ
iajs-2287	155	12	ideals	ideal	NOUN
iajs-2287	155	13	.	.	PUNCT
iajs-2287	156	1	journal	journal	NOUN
iajs-2287	156	2	of	of	ADP
iajs-2287	156	3	mathematics	mathematics	PROPN
iajs-2287	156	4	research.2010	research.2010	PROPN
iajs-2287	156	5	,	,	PUNCT
iajs-2287	156	6	2	2	NUM
iajs-2287	156	7	,	,	PUNCT
iajs-2287	156	8	4	4	NUM
iajs-2287	156	9	,	,	PUNCT
iajs-2287	156	10	100	100	NUM
iajs-2287	156	11	-	-	SYM
iajs-2287	156	12	110	110	NUM
iajs-2287	156	13	.	.	PUNCT
iajs-2287	157	1	6	6	NUM
iajs-2287	157	2	.	.	X
iajs-2287	157	3	wafaa	wafaa	PROPN
iajs-2287	157	4	,	,	PUNCT
iajs-2287	157	5	h.h	h.h	PROPN
iajs-2287	157	6	.	.	PROPN
iajs-2287	157	7	;	;	PUNCT
iajs-2287	157	8	hatem	hatem	PROPN
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